LMFDB - Embedded newform 399.2.j.d.58.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.1
Root			$0.882007 - 1.52768i$ of defining polynomial
Character	$\chi$	$=$	399.58
Dual form			399.2.j.d.172.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.882007 + 1.52768i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.555874 - 0.962803i) q^{4} +(-1.05587 + 1.82883i) q^{5} -1.76401 q^{6} +(-0.893022 + 2.49048i) q^{7} -1.56689 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.882007 + 1.52768i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.555874 - 0.962803i) q^{4} +(-1.05587 + 1.82883i) q^{5} -1.76401 q^{6} +(-0.893022 + 2.49048i) q^{7} -1.56689 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.86258 - 3.22608i) q^{10} +(-0.926867 - 1.60538i) q^{11} +(0.555874 - 0.962803i) q^{12} +3.85373 q^{13} +(-3.01702 - 3.56088i) q^{14} -2.11175 q^{15} +(2.49376 - 4.31931i) q^{16} +(-0.697126 - 1.20746i) q^{17} +(-0.882007 - 1.52768i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.34773 q^{20} +(-2.60333 + 0.471863i) q^{21} +3.27002 q^{22} +(-1.65444 + 2.86557i) q^{23} +(-0.783444 - 1.35697i) q^{24} +(0.270259 + 0.468102i) q^{25} +(-3.39902 + 5.88728i) q^{26} -1.00000 q^{27} +(2.89425 - 0.524593i) q^{28} -4.13624 q^{29} +(1.86258 - 3.22608i) q^{30} +(-2.14219 - 3.71039i) q^{31} +(2.83213 + 4.90540i) q^{32} +(0.926867 - 1.60538i) q^{33} +2.45948 q^{34} +(-3.61175 - 4.26282i) q^{35} +1.11175 q^{36} +(-0.328304 + 0.568640i) q^{37} +(-0.882007 - 1.52768i) q^{38} +(1.92687 + 3.33743i) q^{39} +(1.65444 - 2.86557i) q^{40} +6.74718 q^{41} +(1.57530 - 4.39325i) q^{42} +1.83690 q^{43} +(-1.03044 + 1.78478i) q^{44} +(-1.05587 - 1.82883i) q^{45} +(-2.91845 - 5.05491i) q^{46} +(-2.98151 + 5.16413i) q^{47} +4.98751 q^{48} +(-5.40502 - 4.44811i) q^{49} -0.953481 q^{50} +(0.697126 - 1.20746i) q^{51} +(-2.14219 - 3.71039i) q^{52} +(3.91004 + 6.77238i) q^{53} +(0.882007 - 1.52768i) q^{54} +3.91462 q^{55} +(1.39927 - 3.90231i) q^{56} -1.00000 q^{57} +(3.64819 - 6.31886i) q^{58} +(-2.40267 - 4.16154i) q^{59} +(1.17387 + 2.03320i) q^{60} +(-2.05970 + 3.56751i) q^{61} +7.55772 q^{62} +(-1.71031 - 2.01862i) q^{63} -0.0168302 q^{64} +(-4.06906 + 7.04782i) q^{65} +(1.63501 + 2.83192i) q^{66} +(3.05847 + 5.29743i) q^{67} +(-0.775029 + 1.34239i) q^{68} -3.30887 q^{69} +(9.69782 - 1.75776i) q^{70} +1.36976 q^{71} +(0.783444 - 1.35697i) q^{72} +(-2.37984 - 4.12200i) q^{73} +(-0.579134 - 1.00309i) q^{74} +(-0.270259 + 0.468102i) q^{75} +1.11175 q^{76} +(4.82589 - 0.874708i) q^{77} -6.79805 q^{78} +(-7.99257 + 13.8435i) q^{79} +(5.26619 + 9.12130i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.95107 + 10.3076i) q^{82} +3.27050 q^{83} +(1.90144 + 2.24420i) q^{84} +2.94431 q^{85} +(-1.62016 + 2.80621i) q^{86} +(-2.06812 - 3.58209i) q^{87} +(1.45230 + 2.51545i) q^{88} +(-6.99257 + 12.1115i) q^{89} +3.72516 q^{90} +(-3.44147 + 9.59767i) q^{91} +3.67864 q^{92} +(2.14219 - 3.71039i) q^{93} +(-5.25943 - 9.10960i) q^{94} +(-1.05587 - 1.82883i) q^{95} +(-2.83213 + 4.90540i) q^{96} -5.97314 q^{97} +(11.5626 - 4.33389i) q^{98} +1.85373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{5} + 2 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 - 6 * q^8 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{5} + 2 q^{7} - 6 q^{8} - 4 q^{9} + 3 q^{10} + 2 q^{11} + 12 q^{13} + 2 q^{14} - 8 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{19} + 24 q^{20} + q^{21} - 12 q^{22} - 5 q^{23} - 3 q^{24} + 4 q^{25} + 6 q^{26} - 8 q^{27} + 8 q^{28} - 8 q^{29} - 3 q^{30} - 17 q^{31} - 4 q^{32} - 2 q^{33} + 16 q^{34} - 20 q^{35} + 3 q^{37} + 6 q^{39} + 5 q^{40} + 14 q^{41} + 19 q^{42} - 30 q^{43} - 17 q^{44} - 4 q^{45} - q^{46} - 16 q^{47} + 8 q^{48} + 14 q^{49} - 28 q^{50} - 2 q^{51} - 17 q^{52} - 4 q^{53} + 30 q^{55} + 18 q^{56} - 8 q^{57} + 5 q^{58} - 17 q^{59} + 12 q^{60} + 9 q^{61} - 14 q^{62} - q^{63} - 26 q^{64} - 23 q^{65} - 6 q^{66} + 5 q^{67} + 10 q^{68} - 10 q^{69} + 33 q^{70} + 12 q^{71} + 3 q^{72} - 15 q^{73} + 10 q^{74} - 4 q^{75} - 4 q^{77} + 12 q^{78} - 5 q^{79} + 25 q^{80} - 4 q^{81} - 31 q^{82} + 68 q^{83} + 19 q^{84} - 24 q^{85} - 17 q^{86} - 4 q^{87} - 11 q^{88} + 3 q^{89} - 6 q^{90} + 45 q^{91} + 14 q^{92} + 17 q^{93} + 6 q^{94} - 4 q^{95} + 4 q^{96} + 22 q^{97} + 27 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 - 6 * q^8 - 4 * q^9 + 3 * q^10 + 2 * q^11 + 12 * q^13 + 2 * q^14 - 8 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^19 + 24 * q^20 + q^21 - 12 * q^22 - 5 * q^23 - 3 * q^24 + 4 * q^25 + 6 * q^26 - 8 * q^27 + 8 * q^28 - 8 * q^29 - 3 * q^30 - 17 * q^31 - 4 * q^32 - 2 * q^33 + 16 * q^34 - 20 * q^35 + 3 * q^37 + 6 * q^39 + 5 * q^40 + 14 * q^41 + 19 * q^42 - 30 * q^43 - 17 * q^44 - 4 * q^45 - q^46 - 16 * q^47 + 8 * q^48 + 14 * q^49 - 28 * q^50 - 2 * q^51 - 17 * q^52 - 4 * q^53 + 30 * q^55 + 18 * q^56 - 8 * q^57 + 5 * q^58 - 17 * q^59 + 12 * q^60 + 9 * q^61 - 14 * q^62 - q^63 - 26 * q^64 - 23 * q^65 - 6 * q^66 + 5 * q^67 + 10 * q^68 - 10 * q^69 + 33 * q^70 + 12 * q^71 + 3 * q^72 - 15 * q^73 + 10 * q^74 - 4 * q^75 - 4 * q^77 + 12 * q^78 - 5 * q^79 + 25 * q^80 - 4 * q^81 - 31 * q^82 + 68 * q^83 + 19 * q^84 - 24 * q^85 - 17 * q^86 - 4 * q^87 - 11 * q^88 + 3 * q^89 - 6 * q^90 + 45 * q^91 + 14 * q^92 + 17 * q^93 + 6 * q^94 - 4 * q^95 + 4 * q^96 + 22 * q^97 + 27 * q^98 - 4 * 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 $

$2$	−0.882007	+	1.52768i	−0.623673	+	1.08023i	0.365122	+	0.930960i	$0.381027\pi$
$2$	−0.882007	+	1.52768i	−0.623673	+	1.08023i	−0.988796	+	0.149275i	$0.952306\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.555874	−	0.962803i	−0.277937	−	0.481401i
$5$	−1.05587	+	1.82883i	−0.472201	+	0.817877i	−0.999494	−	0.0318070i	$-0.989874\pi$
$5$	−1.05587	+	1.82883i	−0.472201	+	0.817877i	0.527293	+	0.849684i	$0.323207\pi$
$6$	−1.76401			−0.720156
$7$	−0.893022	+	2.49048i	−0.337530	+	0.941315i
$7$	−0.893022	+	2.49048i	−0.337530	+	0.941315i
$8$	−1.56689			−0.553979
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.86258	−	3.22608i	−0.588999	−	1.02018i
$11$	−0.926867	−	1.60538i	−0.279461	−	0.484041i	0.691790	−	0.722099i	$-0.256822\pi$
$11$	−0.926867	−	1.60538i	−0.279461	−	0.484041i	−0.971251	+	0.238058i	$0.923489\pi$
$12$	0.555874	−	0.962803i	0.160467	−	0.277937i
$13$	3.85373			1.06883			0.534417	−	0.845221i	$-0.320531\pi$
$13$	3.85373			1.06883			0.534417	+	0.845221i	$0.320531\pi$
$14$	−3.01702	−	3.56088i	−0.806331	−	0.951685i
$15$	−2.11175			−0.545251
$16$	2.49376	−	4.31931i	0.623439	−	1.07983i
$17$	−0.697126	−	1.20746i	−0.169078	−	0.292852i	0.769018	−	0.639227i	$-0.220746\pi$
$17$	−0.697126	−	1.20746i	−0.169078	−	0.292852i	−0.938096	+	0.346376i	$0.887412\pi$
$18$	−0.882007	−	1.52768i	−0.207891	−	0.360078i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	2.34773			0.524969
$21$	−2.60333	+	0.471863i	−0.568094	+	0.102969i
$22$	3.27002			0.697170
$23$	−1.65444	+	2.86557i	−0.344974	+	0.597513i	−0.985349	−	0.170550i	$-0.945446\pi$
$23$	−1.65444	+	2.86557i	−0.344974	+	0.597513i	0.640375	+	0.768062i	$0.278779\pi$
$24$	−0.783444	−	1.35697i	−0.159920	−	0.276989i
$25$	0.270259	+	0.468102i	0.0540518	+	0.0936204i
$26$	−3.39902	+	5.88728i	−0.666603	+	1.15459i
$27$	−1.00000			−0.192450
$28$	2.89425	−	0.524593i	0.546962	−	0.0991387i
$29$	−4.13624			−0.768080			−0.384040	−	0.923316i	$-0.625468\pi$
$29$	−4.13624			−0.768080			−0.384040	+	0.923316i	$0.625468\pi$
$30$	1.86258	−	3.22608i	0.340059	−	0.588999i
$31$	−2.14219	−	3.71039i	−0.384749	−	0.666405i	0.606985	−	0.794713i	$-0.292379\pi$
$31$	−2.14219	−	3.71039i	−0.384749	−	0.666405i	−0.991734	+	0.128308i	$0.959045\pi$
$32$	2.83213	+	4.90540i	0.500655	+	0.867161i
$33$	0.926867	−	1.60538i	0.161347	−	0.279461i
$34$	2.45948			0.421798
$35$	−3.61175	−	4.26282i	−0.610497	−	0.720548i
$36$	1.11175			0.185291
$37$	−0.328304	+	0.568640i	−0.0539729	+	0.0934838i	−0.891750	−	0.452529i	$-0.850522\pi$
$37$	−0.328304	+	0.568640i	−0.0539729	+	0.0934838i	0.837777	+	0.546013i	$0.183855\pi$
$38$	−0.882007	−	1.52768i	−0.143081	−	0.247823i
$39$	1.92687	+	3.33743i	0.308546	+	0.534417i
$40$	1.65444	−	2.86557i	0.261590	−	0.453086i
$41$	6.74718			1.05373			0.526867	−	0.849948i	$-0.323367\pi$
$41$	6.74718			1.05373			0.526867	+	0.849948i	$0.323367\pi$
$42$	1.57530	−	4.39325i	0.243075	−	0.677893i
$43$	1.83690			0.280125			0.140063	−	0.990143i	$-0.455270\pi$
$43$	1.83690			0.280125			0.140063	+	0.990143i	$0.455270\pi$
$44$	−1.03044	+	1.78478i	−0.155345	+	0.269066i
$45$	−1.05587	−	1.82883i	−0.157400	−	0.272626i
$46$	−2.91845	−	5.05491i	−0.430302	−	0.745306i
$47$	−2.98151	+	5.16413i	−0.434898	+	0.753266i	−0.997287	−	0.0736071i	$-0.976549\pi$
$47$	−2.98151	+	5.16413i	−0.434898	+	0.753266i	0.562389	+	0.826873i	$0.309882\pi$
$48$	4.98751			0.719885
$49$	−5.40502	−	4.44811i	−0.772146	−	0.635445i
$50$	−0.953481			−0.134843
$51$	0.697126	−	1.20746i	0.0976172	−	0.169078i
$52$	−2.14219	−	3.71039i	−0.297069	−	0.514538i
$53$	3.91004	+	6.77238i	0.537085	+	0.930258i	0.999059	+	0.0433651i	$0.0138079\pi$
$53$	3.91004	+	6.77238i	0.537085	+	0.930258i	−0.461974	+	0.886893i	$0.652859\pi$
$54$	0.882007	−	1.52768i	0.120026	−	0.207891i
$55$	3.91462			0.527848
$56$	1.39927	−	3.90231i	0.186985	−	0.521468i
$57$	−1.00000			−0.132453
$58$	3.64819	−	6.31886i	0.479031	−	0.829707i
$59$	−2.40267	−	4.16154i	−0.312801	−	0.541787i	0.666167	−	0.745803i	$-0.267934\pi$
$59$	−2.40267	−	4.16154i	−0.312801	−	0.541787i	−0.978968	+	0.204016i	$0.934601\pi$
$60$	1.17387	+	2.03320i	0.151546	+	0.262485i
$61$	−2.05970	+	3.56751i	−0.263718	+	0.456773i	−0.967227	−	0.253913i	$-0.918282\pi$
$61$	−2.05970	+	3.56751i	−0.263718	+	0.456773i	0.703509	+	0.710686i	$0.251616\pi$
$62$	7.55772			0.959831
$63$	−1.71031	−	2.01862i	−0.215479	−	0.254322i
$64$	−0.0168302			−0.00210377
$65$	−4.06906	+	7.04782i	−0.504705	+	0.874174i
$66$	1.63501	+	2.83192i	0.201256	+	0.348585i
$67$	3.05847	+	5.29743i	0.373652	+	0.647184i	0.990124	−	0.140192i	$-0.0447721\pi$
$67$	3.05847	+	5.29743i	0.373652	+	0.647184i	−0.616472	+	0.787377i	$0.711439\pi$
$68$	−0.775029	+	1.34239i	−0.0939861	+	0.162789i
$69$	−3.30887			−0.398342
$70$	9.69782	−	1.75776i	1.15911	−	0.210093i
$71$	1.36976			0.162561			0.0812804	−	0.996691i	$-0.474099\pi$
$71$	1.36976			0.162561			0.0812804	+	0.996691i	$0.474099\pi$
$72$	0.783444	−	1.35697i	0.0923298	−	0.159920i
$73$	−2.37984	−	4.12200i	−0.278539	−	0.482443i	0.692483	−	0.721434i	$-0.256517\pi$
$73$	−2.37984	−	4.12200i	−0.278539	−	0.482443i	−0.971022	+	0.238991i	$0.923183\pi$
$74$	−0.579134	−	1.00309i	−0.0673229	−	0.116607i
$75$	−0.270259	+	0.468102i	−0.0312068	+	0.0540518i
$76$	1.11175			0.127526
$77$	4.82589	−	0.874708i	0.549961	−	0.0996823i
$78$	−6.79805			−0.769727
$79$	−7.99257	+	13.8435i	−0.899235	+	1.55752i	−0.0707603	+	0.997493i	$0.522543\pi$
$79$	−7.99257	+	13.8435i	−0.899235	+	1.55752i	−0.828474	+	0.560027i	$0.810791\pi$
$80$	5.26619	+	9.12130i	0.588778	+	1.01979i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.95107	+	10.3076i	−0.657185	+	1.13828i
$83$	3.27050			0.358984			0.179492	−	0.983759i	$-0.442555\pi$
$83$	3.27050			0.358984			0.179492	+	0.983759i	$0.442555\pi$
$84$	1.90144	+	2.24420i	0.207464	+	0.244862i
$85$	2.94431			0.319355
$86$	−1.62016	+	2.80621i	−0.174707	+	0.302601i
$87$	−2.06812	−	3.58209i	−0.221726	−	0.384040i
$88$	1.45230	+	2.51545i	0.154816	+	0.268148i
$89$	−6.99257	+	12.1115i	−0.741211	+	1.28382i	0.210733	+	0.977544i	$0.432415\pi$
$89$	−6.99257	+	12.1115i	−0.741211	+	1.28382i	−0.951944	+	0.306272i	$0.900918\pi$
$90$	3.72516			0.392666
$91$	−3.44147	+	9.59767i	−0.360764	+	1.00611i
$92$	3.67864			0.383524
$93$	2.14219	−	3.71039i	0.222135	−	0.384749i
$94$	−5.25943	−	9.10960i	−0.542469	−	0.939583i
$95$	−1.05587	−	1.82883i	−0.108330	−	0.187634i
$96$	−2.83213	+	4.90540i	−0.289054	+	0.500655i
$97$	−5.97314			−0.606481			−0.303240	−	0.952914i	$-0.598069\pi$
$97$	−5.97314			−0.606481			−0.303240	+	0.952914i	$0.598069\pi$
$98$	11.5626	−	4.33389i	1.16800	−	0.437789i
$99$	1.85373			0.186307
$100$	0.300460	−	0.520412i	0.0300460	−	0.0520412i
$101$	4.87335	+	8.44089i	0.484916	+	0.839900i	0.999850	−	0.0173303i	$-0.00551668\pi$
$101$	4.87335	+	8.44089i	0.484916	+	0.839900i	−0.514933	+	0.857230i	$0.672183\pi$
$102$	1.22974	+	2.12997i	0.121763	+	0.210899i
$103$	−0.974569	+	1.68800i	−0.0960272	+	0.166324i	−0.910037	−	0.414527i	$-0.863947\pi$
$103$	−0.974569	+	1.68800i	−0.0960272	+	0.166324i	0.814010	+	0.580851i	$0.197280\pi$
$104$	−6.03837			−0.592111
$105$	1.88584	−	5.25928i	0.184039	−	0.513253i
$106$	−13.7947			−1.33986
$107$	−2.49783	+	4.32637i	−0.241474	+	0.418246i	−0.961134	−	0.276081i	$-0.910964\pi$
$107$	−2.49783	+	4.32637i	−0.241474	+	0.418246i	0.719660	+	0.694326i	$0.244298\pi$
$108$	0.555874	+	0.962803i	0.0534890	+	0.0926457i
$109$	7.23451	+	12.5305i	0.692941	+	1.20021i	0.970870	+	0.239607i	$0.0770185\pi$
$109$	7.23451	+	12.5305i	0.692941	+	1.20021i	−0.277929	+	0.960601i	$0.589648\pi$
$110$	−3.45273	+	5.98030i	−0.329205	+	0.570199i
$111$	−0.656609			−0.0623225
$112$	8.53020	+	10.0679i	0.806028	+	0.951327i
$113$	18.3663			1.72776			0.863880	−	0.503699i	$-0.168028\pi$
$113$	18.3663			1.72776			0.863880	+	0.503699i	$0.168028\pi$
$114$	0.882007	−	1.52768i	0.0826076	−	0.143081i
$115$	−3.49376	−	6.05136i	−0.325794	−	0.564293i
$116$	2.29923	+	3.98238i	0.213478	+	0.369755i
$117$	−1.92687	+	3.33743i	−0.178139	+	0.308546i
$118$	8.47668			0.780342
$119$	3.62970	−	0.657896i	0.332734	−	0.0603092i
$120$	3.30887			0.302058
$121$	3.78183	−	6.55033i	0.343803	−	0.595484i
$122$	−3.63335	−	6.29315i	−0.328948	−	0.569755i
$123$	3.37359	+	5.84323i	0.304187	+	0.526867i
$124$	−2.38158	+	4.12502i	−0.213872	+	0.370437i
$125$	−11.7002			−1.04650
$126$	4.59232	−	0.832373i	0.409116	−	0.0741537i
$127$	19.3701			1.71882			0.859411	−	0.511286i	$-0.170831\pi$
$127$	19.3701			1.71882			0.859411	+	0.511286i	$0.170831\pi$
$128$	−5.64942	+	9.78509i	−0.499343	+	0.864888i
$129$	0.918452	+	1.59081i	0.0808652	+	0.140063i
$130$	−7.17788	−	12.4325i	−0.629542	−	1.09040i
$131$	9.49040	−	16.4379i	0.829180	−	1.43618i	−0.0695019	−	0.997582i	$-0.522141\pi$
$131$	9.49040	−	16.4379i	0.829180	−	1.43618i	0.898682	−	0.438601i	$-0.144526\pi$
$132$	−2.06089			−0.179377
$133$	−1.71031	−	2.01862i	−0.148303	−	0.175037i
$134$	−10.7904			−0.932147
$135$	1.05587	−	1.82883i	0.0908752	−	0.157400i
$136$	1.09232	+	1.89195i	0.0936656	+	0.162234i
$137$	5.96548	+	10.3325i	0.509666	+	0.882767i	0.999937	+	0.0111971i	$0.00356423\pi$
$137$	5.96548	+	10.3325i	0.509666	+	0.882767i	−0.490272	+	0.871570i	$0.663102\pi$
$138$	2.91845	−	5.05491i	0.248435	−	0.430302i
$139$	−13.3932			−1.13600			−0.567998	−	0.823030i	$-0.692282\pi$
$139$	−13.3932			−1.13600			−0.567998	+	0.823030i	$0.692282\pi$
$140$	−2.09658	+	5.84699i	−0.177193	+	0.494161i
$141$	−5.96302			−0.502177
$142$	−1.20814	+	2.09256i	−0.101385	+	0.175604i
$143$	−3.57190	−	6.18672i	−0.298697	−	0.517359i
$144$	2.49376	+	4.31931i	0.207813	+	0.359943i
$145$	4.36735	−	7.56447i	0.362689	−	0.628195i
$146$	8.39613			0.694869
$147$	1.14967	−	6.90495i	0.0948229	−	0.569510i
$148$	0.729984			0.0600043
$149$	−0.321363	+	0.556617i	−0.0263271	+	0.0455998i	−0.878889	−	0.477027i	$-0.841714\pi$
$149$	−0.321363	+	0.556617i	−0.0263271	+	0.0455998i	0.852562	+	0.522627i	$0.175048\pi$
$150$	−0.476741	−	0.825739i	−0.0389257	−	0.0674213i
$151$	4.12182	+	7.13921i	0.335429	+	0.580980i	0.983567	−	0.180543i	$-0.0577853\pi$
$151$	4.12182	+	7.13921i	0.335429	+	0.580980i	−0.648138	+	0.761523i	$0.724452\pi$
$152$	0.783444	−	1.35697i	0.0635457	−	0.110064i
$153$	1.39425			0.112719
$154$	−2.92020	+	8.14392i	−0.235316	+	0.656256i
$155$	9.04754			0.726716
$156$	2.14219	−	3.71039i	0.171513	−	0.297069i
$157$	−10.2676	−	17.7840i	−0.819444	−	1.41932i	−0.906093	−	0.423079i	$-0.860949\pi$
$157$	−10.2676	−	17.7840i	−0.819444	−	1.41932i	0.0866487	−	0.996239i	$-0.472384\pi$
$158$	−14.0990	−	24.4202i	−1.12166	−	1.94277i
$159$	−3.91004	+	6.77238i	−0.310086	+	0.537085i
$160$	−11.9615			−0.945641
$161$	−5.65921	−	6.67937i	−0.446008	−	0.526408i
$162$	1.76401			0.138594
$163$	−7.38530	+	12.7917i	−0.578462	+	1.00193i	0.417194	+	0.908817i	$0.363013\pi$
$163$	−7.38530	+	12.7917i	−0.578462	+	1.00193i	−0.995656	+	0.0931077i	$0.970320\pi$
$164$	−3.75059	−	6.49621i	−0.292872	−	0.507269i
$165$	1.95731	+	3.39016i	0.152376	+	0.263924i
$166$	−2.88461	+	4.99629i	−0.223889	+	0.387787i
$167$	4.66722			0.361160			0.180580	−	0.983560i	$-0.442203\pi$
$167$	4.66722			0.361160			0.180580	+	0.983560i	$0.442203\pi$
$168$	4.07913	−	0.739356i	0.314712	−	0.0570426i
$169$	1.85127			0.142406
$170$	−2.59690	+	4.49797i	−0.199173	+	0.344979i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−1.02109	−	1.76858i	−0.0778572	−	0.134853i
$173$	9.98553	−	17.2954i	0.759186	−	1.31495i	−0.184081	−	0.982911i	$-0.558931\pi$
$173$	9.98553	−	17.2954i	0.759186	−	1.31495i	0.943266	−	0.332037i	$-0.107736\pi$
$174$	7.29639			0.553138
$175$	−1.40715	+	0.255050i	−0.106370	+	0.0192800i
$176$	−9.24553			−0.696908
$177$	2.40267	−	4.16154i	0.180596	−	0.312801i
$178$	−12.3350	−	21.3649i	−0.924548	−	1.60136i
$179$	−10.4204	−	18.0486i	−0.778856	−	1.34902i	−0.932602	−	0.360907i	$-0.882467\pi$
$179$	−10.4204	−	18.0486i	−0.778856	−	1.34902i	0.153746	−	0.988110i	$-0.450866\pi$
$180$	−1.17387	+	2.03320i	−0.0874949	+	0.151546i
$181$	23.0771			1.71531			0.857654	−	0.514227i	$-0.171921\pi$
$181$	23.0771			1.71531			0.857654	+	0.514227i	$0.171921\pi$
$182$	−11.6268	−	13.7227i	−0.861834	−	1.01719i
$183$	−4.11941			−0.304515
$184$	2.59232	−	4.49003i	0.191108	−	0.331009i
$185$	−0.693296	−	1.20082i	−0.0509722	−	0.0882864i
$186$	3.77886	+	6.54518i	0.277079	+	0.479916i
$187$	−1.29229	+	2.23831i	−0.0945014	+	0.163681i
$188$	6.62938			0.483497
$189$	0.893022	−	2.49048i	0.0649578	−	0.181156i
$190$	3.72516			0.270251
$191$	6.08417	−	10.5381i	0.440235	−	0.762510i	−0.557471	−	0.830196i	$-0.688228\pi$
$191$	6.08417	−	10.5381i	0.440235	−	0.762510i	0.997707	+	0.0676862i	$0.0215617\pi$
$192$	−0.00841509	−	0.0145754i	−0.000607307	−	0.00105189i
$193$	10.9300	+	18.9314i	0.786761	+	1.36271i	0.927942	+	0.372725i	$0.121577\pi$
$193$	10.9300	+	18.9314i	0.786761	+	1.36271i	−0.141181	+	0.989984i	$0.545090\pi$
$194$	5.26836	−	9.12506i	0.378246	−	0.655141i
$195$	−8.13812			−0.582783
$196$	−1.27814	+	7.67656i	−0.0912958	+	0.548326i
$197$	1.33905			0.0954033			0.0477016	−	0.998862i	$-0.484810\pi$
$197$	1.33905			0.0954033			0.0477016	+	0.998862i	$0.484810\pi$
$198$	−1.63501	+	2.83192i	−0.116195	+	0.201256i
$199$	−4.35904	−	7.55008i	−0.309004	−	0.535211i	0.669141	−	0.743136i	$-0.266662\pi$
$199$	−4.35904	−	7.55008i	−0.309004	−	0.535211i	−0.978145	+	0.207925i	$0.933329\pi$
$200$	−0.423465	−	0.733464i	−0.0299435	−	0.0518637i
$201$	−3.05847	+	5.29743i	−0.215728	+	0.373652i
$202$	−17.1933			−1.20972
$203$	3.69375	−	10.3012i	0.259251	−	0.723005i
$204$	−1.55006			−0.108526
$205$	−7.12418	+	12.3394i	−0.497574	+	0.861824i
$206$	−1.71915	−	2.97766i	−0.119779	−	0.207464i
$207$	−1.65444	−	2.86557i	−0.114991	−	0.199171i
$208$	9.61028	−	16.6455i	0.666353	−	1.15416i
$209$	1.85373			0.128226
$210$	6.37118	+	7.51968i	0.439653	+	0.518907i
$211$	−13.0243			−0.896628			−0.448314	−	0.893876i	$-0.647975\pi$
$211$	−13.0243			−0.896628			−0.448314	+	0.893876i	$0.647975\pi$
$212$	4.34698	−	7.52919i	0.298552	−	0.517107i
$213$	0.684881	+	1.18625i	0.0469273	+	0.0812804i
$214$	−4.40621	−	7.63177i	−0.301202	−	0.521697i
$215$	−1.93954	+	3.35938i	−0.132276	+	0.229108i
$216$	1.56689			0.106613
$217$	11.1537	−	2.02164i	0.757161	−	0.137238i
$218$	−25.5236			−1.72867
$219$	2.37984	−	4.12200i	0.160814	−	0.278539i
$220$	−2.17604	−	3.76901i	−0.146708	−	0.254107i
$221$	−2.68654	−	4.65322i	−0.180716	−	0.313010i
$222$	0.579134	−	1.00309i	0.0388689	−	0.0673229i
$223$	−14.0828			−0.943054			−0.471527	−	0.881852i	$-0.656297\pi$
$223$	−14.0828			−0.943054			−0.471527	+	0.881852i	$0.656297\pi$
$224$	−14.7460	+	2.67276i	−0.985257	+	0.178581i
$225$	−0.540518			−0.0360345
$226$	−16.1992	+	28.0579i	−1.07756	+	1.86638i
$227$	9.36617	+	16.2227i	0.621654	+	1.07674i	0.989178	+	0.146722i	$0.0468724\pi$
$227$	9.36617	+	16.2227i	0.621654	+	1.07674i	−0.367523	+	0.930014i	$0.619794\pi$
$228$	0.555874	+	0.962803i	0.0368137	+	0.0637632i
$229$	7.34551	−	12.7228i	0.485405	−	0.840746i	−0.514455	−	0.857518i	$-0.672006\pi$
$229$	7.34551	−	12.7228i	0.485405	−	0.840746i	0.999859	+	0.0167720i	$0.00533896\pi$
$230$	12.3261			0.812757
$231$	3.17046	+	3.74199i	0.208601	+	0.246205i
$232$	6.48103			0.425500
$233$	8.71404	−	15.0932i	0.570876	−	0.988785i	−0.425601	−	0.904911i	$-0.639937\pi$
$233$	8.71404	−	15.0932i	0.570876	−	0.988785i	0.996476	−	0.0838744i	$-0.0267295\pi$
$234$	−3.39902	−	5.88728i	−0.222201	−	0.384864i
$235$	−6.29620	−	10.9053i	−0.410719	−	0.711386i
$236$	−2.67116	+	4.62659i	−0.173878	+	0.301165i
$237$	−15.9851			−1.03835
$238$	−2.19637	+	6.12530i	−0.142370	+	0.397044i
$239$	−21.4468			−1.38728			−0.693639	−	0.720323i	$-0.743993\pi$
$239$	−21.4468			−1.38728			−0.693639	+	0.720323i	$0.743993\pi$
$240$	−5.26619	+	9.12130i	−0.339931	+	0.588778i
$241$	−8.16545	−	14.1430i	−0.525983	−	0.911029i	−0.999542	−	0.0302671i	$-0.990364\pi$
$241$	−8.16545	−	14.1430i	−0.525983	−	0.911029i	0.473559	−	0.880762i	$-0.342969\pi$
$242$	6.67121	+	11.5549i	0.428842	+	0.742776i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.57975			0.293188
$245$	13.8419	−	5.18821i	0.884324	−	0.331463i
$246$	−11.9021			−0.758852
$247$	−1.92687	+	3.33743i	−0.122604	+	0.212356i
$248$	3.35658	+	5.81376i	0.213143	+	0.369174i
$249$	1.63525	+	2.83234i	0.103630	+	0.179492i
$250$	10.3196	−	17.8742i	0.652672	−	1.13046i
$251$	0.829730			0.0523721			0.0261860	−	0.999657i	$-0.491664\pi$
$251$	0.829730			0.0523721			0.0261860	+	0.999657i	$0.491664\pi$
$252$	−0.992816	+	2.76879i	−0.0625415	+	0.174418i
$253$	6.13378			0.385627
$254$	−17.0846	+	29.5914i	−1.07198	+	1.85673i
$255$	1.47216	+	2.54985i	0.0921900	+	0.159678i
$256$	−9.98250	−	17.2902i	−0.623906	−	1.08064i
$257$	13.6733	−	23.6828i	0.852916	−	1.47729i	−0.0256498	−	0.999671i	$-0.508165\pi$
$257$	13.6733	−	23.6828i	0.852916	−	1.47729i	0.878565	−	0.477622i	$-0.158501\pi$
$258$	−3.24033			−0.201734
$259$	−1.12301	−	1.32544i	−0.0697802	−	0.0823591i
$260$	9.04754			0.561105
$261$	2.06812	−	3.58209i	0.128013	−	0.221726i
$262$	16.7412	+	28.9966i	1.03428	+	1.79142i
$263$	−7.63107	−	13.2174i	−0.470552	−	0.815020i	0.528881	−	0.848696i	$-0.322612\pi$
$263$	−7.63107	−	13.2174i	−0.470552	−	0.815020i	−0.999433	+	0.0336760i	$0.989279\pi$
$264$	−1.45230	+	2.51545i	−0.0893828	+	0.154816i
$265$	−16.5140			−1.01445
$266$	4.59232	−	0.832373i	0.281573	−	0.0510360i
$267$	−13.9851			−0.855877
$268$	3.40025	−	5.88941i	0.207704	−	0.359753i
$269$	13.9010	+	24.0772i	0.847556	+	1.46801i	0.883383	+	0.468652i	$0.155260\pi$
$269$	13.9010	+	24.0772i	0.847556	+	1.46801i	−0.0358269	+	0.999358i	$0.511406\pi$
$270$	1.86258	+	3.22608i	0.113353	+	0.196333i
$271$	−4.82329	+	8.35419i	−0.292994	+	0.507481i	−0.974516	−	0.224317i	$-0.927985\pi$
$271$	−4.82329	+	8.35419i	−0.292994	+	0.507481i	0.681522	+	0.731797i	$0.261318\pi$
$272$	−6.95385			−0.421639
$273$	−10.0326	+	1.81843i	−0.607198	+	0.110057i
$274$	−21.0464			−1.27146
$275$	0.500988	−	0.867737i	0.0302107	−	0.0523265i
$276$	1.83932	+	3.18579i	0.110714	+	0.191762i
$277$	13.8357	+	23.9641i	0.831305	+	1.43986i	0.897004	+	0.442023i	$0.145739\pi$
$277$	13.8357	+	23.9641i	0.831305	+	1.43986i	−0.0656986	+	0.997840i	$0.520928\pi$
$278$	11.8129	−	20.4605i	0.708490	−	1.22714i
$279$	4.28438			0.256499
$280$	5.65921	+	6.67937i	0.338202	+	0.399169i
$281$	11.8994			0.709859			0.354929	−	0.934893i	$-0.384505\pi$
$281$	11.8994			0.709859			0.354929	+	0.934893i	$0.384505\pi$
$282$	5.25943	−	9.10960i	0.313194	−	0.542469i
$283$	6.36263	+	11.0204i	0.378219	+	0.655094i	0.990803	−	0.135311i	$-0.0432033\pi$
$283$	6.36263	+	11.0204i	0.378219	+	0.655094i	−0.612584	+	0.790405i	$0.709870\pi$
$284$	−0.761416	−	1.31881i	−0.0451817	−	0.0782570i
$285$	1.05587	−	1.82883i	0.0625446	−	0.108330i
$286$	12.6018			0.745159
$287$	−6.02538	+	16.8038i	−0.355667	+	0.991894i
$288$	−5.66427			−0.333770
$289$	7.52803	−	13.0389i	0.442825	−	0.766996i
$290$	7.70407	+	13.3438i	0.452398	+	0.783577i
$291$	−2.98657	−	5.17289i	−0.175076	−	0.303240i
$292$	−2.64578	+	4.58262i	−0.154833	+	0.268178i
$293$	23.9055			1.39657			0.698287	−	0.715818i	$-0.253946\pi$
$293$	23.9055			1.39657			0.698287	+	0.715818i	$0.253946\pi$
$294$	9.53454	+	7.84654i	0.556066	+	0.457619i
$295$	10.1477			0.590820
$296$	0.514416	−	0.890995i	0.0298998	−	0.0517880i
$297$	0.926867	+	1.60538i	0.0537823	+	0.0931537i
$298$	−0.566889	−	0.981880i	−0.0328390	−	0.0568788i
$299$	−6.37576	+	11.0431i	−0.368720	+	0.638642i
$300$	0.600920			0.0346941
$301$	−1.64040	+	4.57478i	−0.0945509	+	0.263686i
$302$	−14.5419			−0.836793
$303$	−4.87335	+	8.44089i	−0.279967	+	0.484916i
$304$	2.49376	+	4.31931i	0.143027	+	0.247730i
$305$	−4.34958	−	7.53369i	−0.249056	−	0.431378i
$306$	−1.22974	+	2.12997i	−0.0702996	+	0.121763i
$307$	14.3010			0.816201			0.408101	−	0.912937i	$-0.366191\pi$
$307$	14.3010			0.816201			0.408101	+	0.912937i	$0.366191\pi$
$308$	−3.52476	−	4.16015i	−0.200842	−	0.237047i
$309$	−1.94914			−0.110883
$310$	−7.98000	+	13.8218i	−0.453234	+	0.785024i
$311$	−1.68994	−	2.92707i	−0.0958278	−	0.165979i	0.814126	−	0.580688i	$-0.197216\pi$
$311$	−1.68994	−	2.92707i	−0.0958278	−	0.165979i	−0.909954	+	0.414710i	$0.863883\pi$
$312$	−3.01919	−	5.22938i	−0.170928	−	0.296056i
$313$	16.9577	−	29.3716i	0.958505	−	1.66018i	0.232369	−	0.972628i	$-0.425352\pi$
$313$	16.9577	−	29.3716i	0.958505	−	1.66018i	0.726136	−	0.687551i	$-0.241314\pi$
$314$	36.2244			2.04426
$315$	5.49759	−	0.996455i	0.309754	−	0.0561439i
$316$	17.7715			0.999723
$317$	−5.78591	+	10.0215i	−0.324969	+	0.562863i	−0.981506	−	0.191431i	$-0.938687\pi$
$317$	−5.78591	+	10.0215i	−0.324969	+	0.562863i	0.656537	+	0.754294i	$0.272020\pi$
$318$	−6.89736	−	11.9466i	−0.386785	−	0.669931i
$319$	3.83375	+	6.64024i	0.214649	+	0.371782i
$320$	0.0177706	−	0.0307795i	0.000993404	−	0.00172063i
$321$	−4.99566			−0.278830
$322$	15.1954	−	2.75422i	0.846807	−	0.153487i
$323$	1.39425			0.0775783
$324$	−0.555874	+	0.962803i	−0.0308819	+	0.0534890i
$325$	1.04151	+	1.80394i	0.0577723	+	0.100065i
$326$	−13.0278	−	22.5648i	−0.721542	−	1.24975i
$327$	−7.23451	+	12.5305i	−0.400069	+	0.692941i
$328$	−10.5721			−0.583746
$329$	−10.1986	−	12.0371i	−0.562269	−	0.663626i
$330$	−6.90545			−0.380133
$331$	−15.1045	+	26.1617i	−0.830218	+	1.43798i	0.0676478	+	0.997709i	$0.478451\pi$
$331$	−15.1045	+	26.1617i	−0.830218	+	1.43798i	−0.897865	+	0.440270i	$0.854883\pi$
$332$	−1.81799	−	3.14885i	−0.0997750	−	0.172815i
$333$	−0.328304	−	0.568640i	−0.0179910	−	0.0311613i
$334$	−4.11652	+	7.13002i	−0.225246	+	0.390137i
$335$	−12.9175			−0.705756
$336$	−4.45396	+	12.4213i	−0.242983	+	0.677639i
$337$	−6.68523			−0.364168			−0.182084	−	0.983283i	$-0.558284\pi$
$337$	−6.68523			−0.364168			−0.182084	+	0.983283i	$0.558284\pi$
$338$	−1.63284	+	2.82816i	−0.0888146	+	0.153831i
$339$	9.18317	+	15.9057i	0.498761	+	0.863880i
$340$	−1.63667	−	2.83479i	−0.0887607	−	0.153738i
$341$	−3.97106	+	6.87807i	−0.215045	+	0.372468i
$342$	1.76401			0.0953870
$343$	15.9048	−	9.48887i	0.858776	−	0.512351i
$344$	−2.87823			−0.155184
$345$	3.49376	−	6.05136i	0.188098	−	0.325794i
$346$	17.6146	+	30.5094i	0.946968	+	1.64020i
$347$	−4.25830	−	7.37560i	−0.228598	−	0.395943i	0.728795	−	0.684732i	$-0.240081\pi$
$347$	−4.25830	−	7.37560i	−0.228598	−	0.395943i	−0.957393	+	0.288789i	$0.906747\pi$
$348$	−2.29923	+	3.98238i	−0.123252	+	0.213478i
$349$	−9.37979			−0.502089			−0.251044	−	0.967976i	$-0.580774\pi$
$349$	−9.37979			−0.502089			−0.251044	+	0.967976i	$0.580774\pi$
$350$	0.851479	−	2.37463i	0.0455135	−	0.126929i
$351$	−3.85373			−0.205697
$352$	5.25003	−	9.09331i	0.279827	−	0.484675i
$353$	−10.6973	−	18.5283i	−0.569362	−	0.986164i	−0.996629	−	0.0820384i	$-0.973857\pi$
$353$	−10.6973	−	18.5283i	−0.569362	−	0.986164i	0.427267	−	0.904125i	$-0.359476\pi$
$354$	4.23834	+	7.34102i	0.225265	+	0.390171i
$355$	−1.44630	+	2.50506i	−0.0767615	+	0.132955i
$356$	15.5480			0.824041
$357$	2.38461	+	2.81447i	0.126207	+	0.148957i
$358$	36.7634			1.94301
$359$	2.23167	−	3.86537i	0.117783	−	0.204006i	−0.801106	−	0.598523i	$-0.795755\pi$
$359$	2.23167	−	3.86537i	0.117783	−	0.204006i	0.918889	+	0.394517i	$0.129088\pi$
$360$	1.65444	+	2.86557i	0.0871965	+	0.151029i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−20.3542	+	35.2545i	−1.06979	+	1.85293i
$363$	7.56367			0.396990
$364$	11.1537	−	2.02164i	0.584612	−	0.105963i
$365$	10.0512			0.526106
$366$	3.63335	−	6.29315i	0.189918	−	0.328948i
$367$	−1.16914	−	2.02502i	−0.0610288	−	0.105705i	0.833897	−	0.551921i	$-0.186105\pi$
$367$	−1.16914	−	2.02502i	−0.0610288	−	0.105705i	−0.894926	+	0.446215i	$0.852771\pi$
$368$	8.25153	+	14.2921i	0.430141	+	0.745025i
$369$	−3.37359	+	5.84323i	−0.175622	+	0.304187i
$370$	2.44597			0.127160
$371$	−20.3583	+	3.69000i	−1.05695	+	0.191575i
$372$	−4.76316			−0.246958
$373$	17.1110	−	29.6372i	0.885975	−	1.53455i	0.0413831	−	0.999143i	$-0.486824\pi$
$373$	17.1110	−	29.6372i	0.885975	−	1.53455i	0.844592	−	0.535410i	$-0.179843\pi$
$374$	−2.27961	−	3.94841i	−0.117876	−	0.204167i
$375$	−5.85009	−	10.1327i	−0.302097	−	0.523248i
$376$	4.67170	−	8.09161i	0.240924	−	0.417293i
$377$	−15.9400			−0.820950
$378$	3.01702	+	3.56088i	0.155179	+	0.183152i
$379$	2.11646			0.108715			0.0543577	−	0.998522i	$-0.482689\pi$
$379$	2.11646			0.108715			0.0543577	+	0.998522i	$0.482689\pi$
$380$	−1.17387	+	2.03320i	−0.0602181	+	0.104301i
$381$	9.68507	+	16.7750i	0.496181	+	0.859411i
$382$	10.7326	+	18.5894i	0.549126	+	0.951115i
$383$	7.37566	−	12.7750i	0.376879	−	0.652773i	−0.613728	−	0.789518i	$-0.710331\pi$
$383$	7.37566	−	12.7750i	0.376879	−	0.652773i	0.990606	+	0.136745i	$0.0436641\pi$
$384$	−11.2988			−0.576592
$385$	−3.49584	+	9.74931i	−0.178165	+	0.496871i
$386$	−38.5615			−1.96273
$387$	−0.918452	+	1.59081i	−0.0466876	+	0.0808652i
$388$	3.32032	+	5.75096i	0.168564	+	0.291961i
$389$	17.6664	+	30.5991i	0.895721	+	1.55143i	0.832910	+	0.553409i	$0.186673\pi$
$389$	17.6664	+	30.5991i	0.895721	+	1.55143i	0.0628116	+	0.998025i	$0.479993\pi$
$390$	7.17788	−	12.4325i	0.363466	−	0.629542i
$391$	4.61341			0.233310
$392$	8.46907	+	6.96970i	0.427753	+	0.352023i
$393$	18.9808			0.957455
$394$	−1.18105	+	2.04564i	−0.0595005	+	0.103058i
$395$	−16.8783	−	29.2341i	−0.849240	−	1.47093i
$396$	−1.03044	−	1.78478i	−0.0517817	−	0.0896886i
$397$	−13.0360	+	22.5789i	−0.654256	+	1.13320i	0.327824	+	0.944739i	$0.393685\pi$
$397$	−13.0360	+	22.5789i	−0.654256	+	1.13320i	−0.982080	+	0.188466i	$0.939649\pi$
$398$	15.3788			0.770870
$399$	0.893022	−	2.49048i	0.0447070	−	0.124680i
$400$	2.69584			0.134792
$401$	−13.5755	+	23.5135i	−0.677930	+	1.17421i	0.297673	+	0.954668i	$0.403789\pi$
$401$	−13.5755	+	23.5135i	−0.677930	+	1.17421i	−0.975603	+	0.219541i	$0.929544\pi$
$402$	−5.39519	−	9.34475i	−0.269088	−	0.466074i
$403$	−8.25544	−	14.2988i	−0.411233	−	0.712276i
$404$	5.41794	−	9.38415i	0.269553	−	0.466879i
$405$	2.11175			0.104934
$406$	12.4791	+	14.7286i	0.619327	+	0.730970i
$407$	1.21718			0.0603333
$408$	−1.09232	+	1.89195i	−0.0540779	+	0.0936656i
$409$	1.96776	+	3.40826i	0.0972995	+	0.168528i	0.910566	−	0.413364i	$-0.135646\pi$
$409$	1.96776	+	3.40826i	0.0972995	+	0.168528i	−0.813267	+	0.581891i	$0.802313\pi$
$410$	−12.5672	−	21.7670i	−0.620648	−	1.07499i
$411$	−5.96548	+	10.3325i	−0.294256	+	0.509666i
$412$	2.16695			0.106758
$413$	12.5099	−	2.26746i	0.615571	−	0.111574i
$414$	5.83690			0.286868
$415$	−3.45324	+	5.98118i	−0.169513	+	0.293605i
$416$	10.9143	+	18.9041i	0.535117	+	0.926850i
$417$	−6.69659	−	11.5988i	−0.327934	−	0.567998i
$418$	−1.63501	+	2.83192i	−0.0799709	+	0.138514i
$419$	−10.7269			−0.524044			−0.262022	−	0.965062i	$-0.584389\pi$
$419$	−10.7269			−0.524044			−0.262022	+	0.965062i	$0.584389\pi$
$420$	−6.11193	+	1.10781i	−0.298232	+	0.0540555i
$421$	−9.98526			−0.486652			−0.243326	−	0.969945i	$-0.578238\pi$
$421$	−9.98526			−0.486652			−0.243326	+	0.969945i	$0.578238\pi$
$422$	11.4875	−	19.8970i	0.559203	−	0.968569i
$423$	−2.98151	−	5.16413i	−0.144966	−	0.251089i
$424$	−6.12659	−	10.6116i	−0.297534	−	0.515343i
$425$	0.376809	−	0.652652i	0.0182779	−	0.0316583i
$426$	−2.41628			−0.117069
$427$	−7.04547	−	8.31553i	−0.340954	−	0.402417i
$428$	5.55392			0.268459
$429$	3.57190	−	6.18672i	0.172453	−	0.298697i
$430$	−3.42138	−	5.92600i	−0.164994	−	0.285777i
$431$	4.73261	+	8.19712i	0.227962	+	0.394841i	0.957204	−	0.289414i	$-0.0934605\pi$
$431$	4.73261	+	8.19712i	0.227962	+	0.394841i	−0.729242	+	0.684256i	$0.760127\pi$
$432$	−2.49376	+	4.31931i	−0.119981	+	0.207813i
$433$	−23.5884			−1.13359			−0.566794	−	0.823860i	$-0.691816\pi$
$433$	−23.5884			−1.13359			−0.566794	+	0.823860i	$0.691816\pi$
$434$	−6.74921	+	18.8224i	−0.323972	+	0.903503i
$435$	8.73470			0.418797
$436$	8.04296	−	13.9308i	0.385188	−	0.667165i
$437$	−1.65444	−	2.86557i	−0.0791425	−	0.137079i
$438$	4.19807	+	7.27126i	0.200591	+	0.347434i
$439$	16.9194	−	29.3052i	0.807518	−	1.39866i	−0.107060	−	0.994253i	$-0.534144\pi$
$439$	16.9194	−	29.3052i	0.807518	−	1.39866i	0.914578	−	0.404410i	$-0.132523\pi$
$440$	−6.13378			−0.292416
$441$	6.55469	−	2.45683i	0.312128	−	0.116992i
$442$	9.47819			0.450832
$443$	−2.67282	+	4.62946i	−0.126990	+	0.219952i	−0.922509	−	0.385976i	$-0.873865\pi$
$443$	−2.67282	+	4.62946i	−0.126990	+	0.219952i	0.795519	+	0.605928i	$0.207198\pi$
$444$	0.364992	+	0.632185i	0.0173217	+	0.0300022i
$445$	−14.7666	−	25.5764i	−0.700002	−	1.21244i
$446$	12.4211	−	21.5140i	0.588158	−	1.01872i
$447$	−0.642725			−0.0303999
$448$	0.0150297	−	0.0419153i	0.000710087	−	0.00198031i
$449$	10.1900			0.480894			0.240447	−	0.970662i	$-0.422706\pi$
$449$	10.1900			0.480894			0.240447	+	0.970662i	$0.422706\pi$
$450$	0.476741	−	0.825739i	0.0224738	−	0.0389257i
$451$	−6.25375	−	10.8318i	−0.294477	−	0.510050i
$452$	−10.2094	−	17.6832i	−0.480208	−	0.831745i
$453$	−4.12182	+	7.13921i	−0.193660	+	0.335429i
$454$	−33.0441			−1.55084
$455$	−13.9187	−	16.4278i	−0.652520	−	0.770146i
$456$	1.56689			0.0733763
$457$	14.9489	−	25.8922i	0.699280	−	1.21119i	−0.269437	−	0.963018i	$-0.586837\pi$
$457$	14.9489	−	25.8922i	0.699280	−	1.21119i	0.968716	−	0.248170i	$-0.0798292\pi$
$458$	12.9576	+	22.4432i	0.605468	+	1.04870i
$459$	0.697126	+	1.20746i	0.0325391	+	0.0563593i
$460$	−3.88418	+	6.72759i	−0.181101	+	0.313676i
$461$	35.2500			1.64176			0.820879	−	0.571102i	$-0.193484\pi$
$461$	35.2500			1.64176			0.820879	+	0.571102i	$0.193484\pi$
$462$	−8.51294	+	1.54300i	−0.396058	+	0.0717868i
$463$	−28.0784			−1.30491			−0.652457	−	0.757825i	$-0.726262\pi$
$463$	−28.0784			−1.30491			−0.652457	+	0.757825i	$0.726262\pi$
$464$	−10.3148	+	17.8657i	−0.478851	+	0.829395i
$465$	4.52377	+	7.83540i	0.209785	+	0.363358i
$466$	15.3717	+	26.6245i	0.712080	+	1.23336i
$467$	−15.6692	+	27.1398i	−0.725083	+	1.25588i	0.233857	+	0.972271i	$0.424865\pi$
$467$	−15.6692	+	27.1398i	−0.725083	+	1.25588i	−0.958940	+	0.283610i	$0.908468\pi$
$468$	4.28438			0.198046
$469$	−15.9245	+	2.88636i	−0.735323	+	0.133280i
$470$	22.2132			1.02462
$471$	10.2676	−	17.7840i	0.473106	−	0.819444i
$472$	3.76471	+	6.52067i	0.173285	+	0.300138i
$473$	−1.70257	−	2.94893i	−0.0782841	−	0.135592i
$474$	14.0990	−	24.4202i	0.647589	−	1.12166i
$475$	−0.540518			−0.0248006
$476$	−2.65108	−	3.12898i	−0.121512	−	0.143417i
$477$	−7.82007			−0.358057
$478$	18.9162	−	32.7639i	0.865208	−	1.49858i
$479$	9.83661	+	17.0375i	0.449446	+	0.778464i	0.998350	−	0.0574217i	$-0.0182879\pi$
$479$	9.83661	+	17.0375i	0.449446	+	0.778464i	−0.548904	+	0.835886i	$0.684955\pi$
$480$	−5.98076	−	10.3590i	−0.272983	−	0.472820i
$481$	−1.26520	+	2.19139i	−0.0576881	+	0.0999187i
$482$	28.8080			1.31217
$483$	2.95490	−	8.24070i	0.134452	−	0.374965i
$484$	−8.40890			−0.382223
$485$	6.30689	−	10.9239i	0.286381	−	0.496027i
$486$	0.882007	+	1.52768i	0.0400087	+	0.0692971i
$487$	2.96259	+	5.13136i	0.134248	+	0.232524i	0.925310	−	0.379212i	$-0.123805\pi$
$487$	2.96259	+	5.13136i	0.134248	+	0.232524i	−0.791062	+	0.611736i	$0.790471\pi$
$488$	3.22733	−	5.58989i	0.146094	−	0.253043i
$489$	−14.7706			−0.667950
$490$	−4.28269	+	25.7220i	−0.193472	+	1.16200i
$491$	21.3951			0.965548			0.482774	−	0.875745i	$-0.339629\pi$
$491$	21.3951			0.965548			0.482774	+	0.875745i	$0.339629\pi$
$492$	3.75059	−	6.49621i	0.169090	−	0.292872i
$493$	2.88348	+	4.99434i	0.129865	+	0.224934i
$494$	−3.39902	−	5.88728i	−0.152929	−	0.264881i
$495$	−1.95731	+	3.39016i	−0.0879746	+	0.152376i
$496$	−21.3684			−0.959470
$497$	−1.22323	+	3.41137i	−0.0548693	+	0.153021i
$498$	−5.76921			−0.258525
$499$	14.4680	−	25.0593i	0.647676	−	1.12181i	−0.336001	−	0.941862i	$-0.609075\pi$
$499$	14.4680	−	25.0593i	0.647676	−	1.12181i	0.983677	−	0.179945i	$-0.0575921\pi$
$500$	6.50383	+	11.2650i	0.290860	+	0.503785i
$501$	2.33361	+	4.04193i	0.104258	+	0.180580i
$502$	−0.731828	+	1.26756i	−0.0326631	+	0.0565741i
$503$	13.3877			0.596929			0.298464	−	0.954421i	$-0.403526\pi$
$503$	13.3877			0.596929			0.298464	+	0.954421i	$0.403526\pi$
$504$	2.67987	+	3.16296i	0.119371	+	0.140889i
$505$	−20.5826			−0.915913
$506$	−5.41004	+	9.37046i	−0.240505	+	0.416568i
$507$	0.925637	+	1.60325i	0.0411090	+	0.0712028i
$508$	−10.7674	−	18.6496i	−0.477724	−	0.827443i
$509$	16.4703	−	28.5274i	0.730033	−	1.26445i	−0.226835	−	0.973933i	$-0.572838\pi$
$509$	16.4703	−	28.5274i	0.730033	−	1.26445i	0.956868	−	0.290522i	$-0.0938288\pi$
$510$	−5.19381			−0.229986
$511$	12.3910	−	2.24591i	0.548146	−	0.0993533i
$512$	12.6209			0.557768
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	24.1199	+	41.7768i	1.06388	+	1.84270i
$515$	−2.05805	−	3.56464i	−0.0906883	−	0.157077i
$516$	1.02109	−	1.76858i	0.0449509	−	0.0778572i
$517$	11.0539			0.486148
$518$	3.01536	−	0.546543i	0.132487	−	0.0240137i
$519$	19.9711			0.876632
$520$	6.37576	−	11.0431i	0.279596	−	0.484274i
$521$	−4.45230	−	7.71161i	−0.195059	−	0.337852i	0.751861	−	0.659322i	$-0.229156\pi$
$521$	−4.45230	−	7.71161i	−0.195059	−	0.337852i	−0.946920	+	0.321470i	$0.895823\pi$
$522$	3.64819	+	6.31886i	0.159677	+	0.276569i
$523$	−6.75788	+	11.7050i	−0.295501	+	0.511823i	−0.975101	−	0.221760i	$-0.928820\pi$
$523$	−6.75788	+	11.7050i	−0.295501	+	0.511823i	0.679600	+	0.733583i	$0.262153\pi$
$524$	−21.1019			−0.921840
$525$	−0.924454	−	1.09110i	−0.0403465	−	0.0476195i
$526$	26.9227			1.17388
$527$	−2.98676	+	5.17322i	−0.130105	+	0.225349i
$528$	−4.62276	−	8.00686i	−0.201180	−	0.348454i
$529$	6.02567	+	10.4368i	0.261986	+	0.453773i
$530$	14.5655	−	25.2282i	0.632685	−	1.09584i
$531$	4.80534			0.208534
$532$	−0.992816	+	2.76879i	−0.0430440	+	0.120042i
$533$	26.0019			1.12627
$534$	12.3350	−	21.3649i	0.533788	−	0.924548i
$535$	−5.27479	−	9.13620i	−0.228049	−	0.394992i
$536$	−4.79229	−	8.30049i	−0.206995	−	0.358526i
$537$	10.4204	−	18.0486i	0.449673	−	0.778856i
$538$	−49.0430			−2.11439
$539$	−2.13118	+	12.7999i	−0.0917963	+	0.551332i
$540$	−2.34773			−0.101030
$541$	−4.22449	+	7.31702i	−0.181625	+	0.314583i	−0.942434	−	0.334392i	$-0.891469\pi$
$541$	−4.22449	+	7.31702i	−0.181625	+	0.314583i	0.760809	+	0.648976i	$0.224802\pi$
$542$	−8.50836	−	14.7369i	−0.365465	−	0.633004i
$543$	11.5386	+	19.9854i	0.495167	+	0.857654i
$544$	3.94871	−	6.83937i	0.169300	−	0.293235i
$545$	−30.5549			−1.30883
$546$	6.07080	−	16.9304i	0.259806	−	0.724555i
$547$	−33.0166			−1.41169			−0.705844	−	0.708367i	$-0.749432\pi$
$547$	−33.0166			−1.41169			−0.705844	+	0.708367i	$0.749432\pi$
$548$	6.63212	−	11.4872i	0.283310	−	0.490707i
$549$	−2.05970	−	3.56751i	−0.0879060	−	0.152258i
$550$	0.883751	+	1.53070i	0.0376833	+	0.0652693i
$551$	2.06812	−	3.58209i	0.0881049	−	0.152602i
$552$	5.18464			0.220673
$553$	−27.3396	−	32.2680i	−1.16260	−	1.37217i
$554$	−48.8127			−2.07385
$555$	0.693296	−	1.20082i	0.0294288	−	0.0509722i
$556$	7.44493	+	12.8950i	0.315735	+	0.546870i
$557$	13.1049	+	22.6983i	0.555272	+	0.961759i	0.997882	+	0.0650451i	$0.0207191\pi$
$557$	13.1049	+	22.6983i	0.555272	+	0.961759i	−0.442610	+	0.896714i	$0.645948\pi$
$558$	−3.77886	+	6.54518i	−0.159972	+	0.277079i
$559$	7.07894			0.299407
$560$	−27.4193	+	4.96983i	−1.15868	+	0.210014i
$561$	−2.58457			−0.109121
$562$	−10.4954	+	18.1785i	−0.442720	+	0.766813i
$563$	11.3938	+	19.7347i	0.480192	+	0.831718i	0.999742	−	0.0227227i	$-0.00723349\pi$
$563$	11.3938	+	19.7347i	0.480192	+	0.831718i	−0.519549	+	0.854440i	$0.673900\pi$
$564$	3.31469	+	5.74121i	0.139574	+	0.241749i
$565$	−19.3925	+	33.5889i	−0.815850	+	1.41309i
$566$	−22.4475			−0.943540
$567$	2.60333	−	0.471863i	0.109330	−	0.0198164i
$568$	−2.14627			−0.0900553
$569$	1.57096	−	2.72098i	0.0658581	−	0.114070i	−0.831216	−	0.555949i	$-0.812355\pi$
$569$	1.57096	−	2.72098i	0.0658581	−	0.114070i	0.897074	+	0.441880i	$0.145688\pi$
$570$	1.86258	+	3.22608i	0.0780148	+	0.135126i
$571$	−18.1589	−	31.4522i	−0.759927	−	1.31623i	−0.942887	−	0.333112i	$-0.891901\pi$
$571$	−18.1589	−	31.4522i	−0.759927	−	1.31623i	0.182960	−	0.983120i	$-0.441432\pi$
$572$	−3.97106	+	6.87807i	−0.166038	+	0.287587i
$573$	12.1683			0.508340
$574$	−20.3564	−	24.0259i	−0.849658	−	1.00282i
$575$	−1.78851			−0.0745858
$576$	0.00841509	−	0.0145754i	0.000350629	−	0.000607307i
$577$	−7.02731	−	12.1717i	−0.292551	−	0.506713i	0.681861	−	0.731481i	$-0.261171\pi$
$577$	−7.02731	−	12.1717i	−0.292551	−	0.506713i	−0.974412	+	0.224769i	$0.927837\pi$
$578$	13.2796	+	23.0009i	0.552357	+	0.956710i
$579$	−10.9300	+	18.9314i	−0.454236	+	0.786761i
$580$	−9.71079			−0.403219
$581$	−2.92063	+	8.14513i	−0.121168	+	0.337917i
$582$	10.5367			0.436761
$583$	7.24817	−	12.5542i	0.300189	−	0.519942i
$584$	3.72894	+	6.45871i	0.154305	+	0.267263i
$585$	−4.06906	−	7.04782i	−0.168235	−	0.291391i
$586$	−21.0848	+	36.5200i	−0.871007	+	1.50863i
$587$	−16.1927			−0.668346			−0.334173	−	0.942512i	$-0.608457\pi$
$587$	−16.1927			−0.668346			−0.334173	+	0.942512i	$0.608457\pi$
$588$	−7.28717	+	2.73138i	−0.300518	+	0.112640i
$589$	4.28438			0.176535
$590$	−8.95031	+	15.5024i	−0.368479	+	0.638224i
$591$	0.669524	+	1.15965i	0.0275406	+	0.0477016i
$592$	1.63742	+	2.83610i	0.0672976	+	0.116563i
$593$	1.59666	−	2.76550i	0.0655670	−	0.113565i	−0.831378	−	0.555707i	$-0.812448\pi$
$593$	1.59666	−	2.76550i	0.0655670	−	0.113565i	0.896945	+	0.442141i	$0.145781\pi$
$594$	−3.27002			−0.134170
$595$	−2.62933	+	7.33276i	−0.107792	+	0.300614i
$596$	0.714549			0.0292691
$597$	4.35904	−	7.55008i	0.178404	−	0.309004i
$598$	−11.2469	−	19.4803i	−0.459922	−	0.796608i
$599$	5.79016	+	10.0289i	0.236580	+	0.409768i	0.959731	−	0.280922i	$-0.0906402\pi$
$599$	5.79016	+	10.0289i	0.236580	+	0.409768i	−0.723151	+	0.690690i	$0.757307\pi$
$600$	0.423465	−	0.733464i	0.0172879	−	0.0299435i
$601$	−17.2632			−0.704179			−0.352090	−	0.935966i	$-0.614529\pi$
$601$	−17.2632			−0.704179			−0.352090	+	0.935966i	$0.614529\pi$
$602$	−5.54197	−	6.54100i	−0.225874	−	0.266591i
$603$	−6.11695			−0.249101
$604$	4.58243	−	7.93700i	0.186456	−	0.322952i
$605$	7.98628	+	13.8326i	0.324689	+	0.562377i
$606$	−8.59666	−	14.8899i	−0.349216	−	0.604859i
$607$	−16.1522	+	27.9764i	−0.655596	+	1.13553i	0.326148	+	0.945319i	$0.394249\pi$
$607$	−16.1522	+	27.9764i	−0.655596	+	1.13553i	−0.981744	+	0.190207i	$0.939084\pi$
$608$	−5.66427			−0.229716
$609$	10.7680	−	1.95174i	0.436342	−	0.0790884i
$610$	15.3454			0.621319
$611$	−11.4900	+	19.9012i	−0.464834	+	0.805116i
$612$	−0.775029	−	1.34239i	−0.0313287	−	0.0542629i
$613$	23.9323	+	41.4519i	0.966616	+	1.67423i	0.705210	+	0.708998i	$0.250853\pi$
$613$	23.9323	+	41.4519i	0.966616	+	1.67423i	0.261405	+	0.965229i	$0.415814\pi$
$614$	−12.6136	+	21.8474i	−0.509043	+	0.881689i
$615$	−14.2484			−0.574549
$616$	−7.56163	+	1.37057i	−0.304667	+	0.0552219i
$617$	−11.2397			−0.452494			−0.226247	−	0.974070i	$-0.572646\pi$
$617$	−11.2397			−0.452494			−0.226247	+	0.974070i	$0.572646\pi$
$618$	1.71915	−	2.97766i	0.0691546	−	0.119779i
$619$	7.51267	+	13.0123i	0.301960	+	0.523010i	0.976580	−	0.215155i	$-0.0690258\pi$
$619$	7.51267	+	13.0123i	0.301960	+	0.523010i	−0.674620	+	0.738165i	$0.735692\pi$
$620$	−5.02930	−	8.71100i	−0.201981	−	0.349842i
$621$	1.65444	−	2.86557i	0.0663903	−	0.114991i
$622$	5.96217			0.239061
$623$	−23.9190	−	28.2307i	−0.958293	−	1.13104i
$624$	19.2206			0.769438
$625$	11.0026	−	19.0571i	0.440105	−	0.762284i
$626$	29.9136	+	51.8119i	1.19559	+	2.07082i
$627$	0.926867	+	1.60538i	0.0370155	+	0.0641128i
$628$	−11.4150	+	19.7713i	−0.455508	+	0.788963i
$629$	0.915478			0.0365025
$630$	−3.32665	+	9.27744i	−0.132537	+	0.369622i
$631$	−34.5520			−1.37549			−0.687747	−	0.725950i	$-0.741400\pi$
$631$	−34.5520			−1.37549			−0.687747	+	0.725950i	$0.741400\pi$
$632$	12.5235	−	21.6913i	0.498157	−	0.862833i
$633$	−6.51214	−	11.2794i	−0.258834	−	0.448314i
$634$	−10.2064	−	17.6780i	−0.405349	−	0.702085i
$635$	−20.4524	+	35.4246i	−0.811630	+	1.40578i
$636$	8.69396			0.344738
$637$	−20.8295	−	17.1419i	−0.825296	−	0.679185i
$638$	−13.5256			−0.535482
$639$	−0.684881	+	1.18625i	−0.0270935	+	0.0469273i
$640$	−11.9302	−	20.6637i	−0.471581	−	0.816803i
$641$	5.05221	+	8.75068i	0.199550	+	0.345631i	0.948383	−	0.317128i	$-0.102719\pi$
$641$	5.05221	+	8.75068i	0.199550	+	0.345631i	−0.748832	+	0.662759i	$0.769385\pi$
$642$	4.40621	−	7.63177i	0.173899	−	0.301202i
$643$	−10.3803			−0.409357			−0.204679	−	0.978829i	$-0.565615\pi$
$643$	−10.3803			−0.409357			−0.204679	+	0.978829i	$0.565615\pi$
$644$	−3.28510	+	9.16159i	−0.129451	+	0.361017i
$645$	−3.87908			−0.152739
$646$	−1.22974	+	2.12997i	−0.0483835	+	0.0838027i
$647$	−14.1766	−	24.5546i	−0.557341	−	0.965343i	−0.997717	−	0.0675295i	$-0.978488\pi$
$647$	−14.1766	−	24.5546i	−0.557341	−	0.965343i	0.440376	−	0.897813i	$-0.354845\pi$
$648$	0.783444	+	1.35697i	0.0307766	+	0.0533066i
$649$	−4.45391	+	7.71440i	−0.174831	+	0.302817i
$650$	−3.67446			−0.144124
$651$	7.32763	+	8.64855i	0.287193	+	0.338963i
$652$	16.4212			0.643104
$653$	−9.54243	+	16.5280i	−0.373424	+	0.646789i	−0.990090	−	0.140436i	$-0.955150\pi$
$653$	−9.54243	+	16.5280i	−0.373424	+	0.646789i	0.616666	+	0.787225i	$0.288483\pi$
$654$	−12.7618	−	22.1041i	−0.499025	−	0.864337i
$655$	20.0413	+	34.7126i	0.783080	+	1.35633i
$656$	16.8258	−	29.1432i	0.656938	−	1.13785i
$657$	4.75967			0.185693
$658$	27.3841	−	4.96346i	1.06754	−	0.193496i
$659$	38.9663			1.51791			0.758957	−	0.651141i	$-0.225709\pi$
$659$	38.9663			1.51791			0.758957	+	0.651141i	$0.225709\pi$
$660$	2.17604	−	3.76901i	0.0847022	−	0.146708i
$661$	−5.17486	−	8.96311i	−0.201279	−	0.348625i	0.747662	−	0.664079i	$-0.231176\pi$
$661$	−5.17486	−	8.96311i	−0.201279	−	0.348625i	−0.948941	+	0.315455i	$0.897843\pi$
$662$	−26.6445	−	46.1497i	−1.03557	−	1.79366i
$663$	2.68654	−	4.65322i	0.104337	−	0.180716i
$664$	−5.12451			−0.198870
$665$	5.49759	−	0.996455i	0.213187	−	0.0386409i
$666$	1.15827			0.0448820
$667$	6.84315	−	11.8527i	0.264968	−	0.458938i
$668$	−2.59439	−	4.49361i	−0.100380	−	0.173863i
$669$	−7.04140	−	12.1961i	−0.272236	−	0.471527i
$670$	11.3933	−	19.7338i	0.440161	−	0.762382i
$671$	7.63629			0.294796
$672$	−9.68767	−	11.4340i	−0.373710	−	0.441077i
$673$	8.42309			0.324686			0.162343	−	0.986734i	$-0.448095\pi$
$673$	8.42309			0.324686			0.162343	+	0.986734i	$0.448095\pi$
$674$	5.89642	−	10.2129i	0.227122	−	0.393386i
$675$	−0.270259	−	0.468102i	−0.0104023	−	0.0180173i
$676$	−1.02908	−	1.78241i	−0.0395798	−	0.0685543i
$677$	−13.5472	+	23.4644i	−0.520660	+	0.901809i	0.479052	+	0.877787i	$0.340981\pi$
$677$	−13.5472	+	23.4644i	−0.520660	+	0.901809i	−0.999711	+	0.0240223i	$0.992353\pi$
$678$	−32.3985			−1.24426
$679$	5.33415	−	14.8760i	0.204706	−	0.570889i
$680$	−4.61341			−0.176916
$681$	−9.36617	+	16.2227i	−0.358912	+	0.621654i
$682$	−7.00500	−	12.1330i	−0.268235	−	0.464597i
$683$	2.21744	+	3.84072i	0.0848479	+	0.146961i	0.905326	−	0.424716i	$-0.139626\pi$
$683$	2.21744	+	3.84072i	0.0848479	+	0.146961i	−0.820478	+	0.571677i	$0.806293\pi$
$684$	−0.555874	+	0.962803i	−0.0212544	+	0.0368137i
$685$	−25.1952			−0.962659
$686$	0.467850	+	32.6667i	0.0178626	+	1.24722i
$687$	14.6910			0.560497
$688$	4.58079	−	7.93417i	0.174641	−	0.302487i
$689$	15.0682	+	26.0990i	0.574055	+	0.994292i
$690$	6.16304	+	10.6747i	0.234623	+	0.406379i
$691$	13.0331	−	22.5740i	0.495802	−	0.858754i	−0.504186	−	0.863595i	$-0.668207\pi$
$691$	13.0331	−	22.5740i	0.495802	−	0.858754i	0.999988	+	0.00484051i	$0.00154079\pi$
$692$	−22.2028			−0.844023
$693$	−1.65543	+	4.61670i	−0.0628844	+	0.175374i
$694$	15.0234			0.570281
$695$	14.1415	−	24.4938i	0.536418	−	0.929104i
$696$	3.24051	+	5.61273i	0.122831	+	0.212750i
$697$	−4.70364	−	8.14694i	−0.178163	−	0.308587i
$698$	8.27304	−	14.3293i	0.313139	−	0.542373i
$699$	17.4281			0.659190
$700$	1.02776	+	1.21303i	0.0388457	+	0.0458482i
$701$	−1.46977			−0.0555126			−0.0277563	−	0.999615i	$-0.508836\pi$
$701$	−1.46977			−0.0555126			−0.0277563	+	0.999615i	$0.508836\pi$
$702$	3.39902	−	5.88728i	0.128288	−	0.222201i
$703$	−0.328304	−	0.568640i	−0.0123822	−	0.0214467i
$704$	0.0155993	+	0.0270189i	0.000587922	+	0.00101831i
$705$	6.29620	−	10.9053i	0.237129	−	0.410719i
$706$	37.7405			1.42038
$707$	−25.3739	+	4.59910i	−0.954284	+	0.172967i
$708$	−5.34233			−0.200777
$709$	13.7704	−	23.8511i	0.517160	−	0.895747i	−0.482642	−	0.875818i	$-0.660323\pi$
$709$	13.7704	−	23.8511i	0.517160	−	0.895747i	0.999801	−	0.0199292i	$-0.00634408\pi$
$710$	−2.55129	−	4.41896i	−0.0957482	−	0.165841i
$711$	−7.99257	−	13.8435i	−0.299745	−	0.519173i
$712$	10.9566	−	18.9774i	0.410615	−	0.711207i
$713$	14.1765			0.530914
$714$	−6.40285	+	1.16054i	−0.239621	+	0.0434320i
$715$	15.0859			0.564181
$716$	−11.5848	+	20.0655i	−0.432946	+	0.749884i
$717$	−10.7234	−	18.5735i	−0.400472	−	0.693639i
$718$	3.93670	+	6.81856i	0.146916	+	0.254466i
$719$	−11.3758	+	19.7035i	−0.424247	+	0.734818i	−0.996350	−	0.0853641i	$-0.972795\pi$
$719$	−11.3758	+	19.7035i	−0.424247	+	0.734818i	0.572102	+	0.820182i	$0.306128\pi$
$720$	−10.5324			−0.392518
$721$	−3.33363	−	3.93457i	−0.124151	−	0.146531i
$722$	1.76401			0.0656498
$723$	8.16545	−	14.1430i	0.303676	−	0.525983i
$724$	−12.8280	−	22.2187i	−0.476748	−	0.825752i
$725$	−1.11785	−	1.93618i	−0.0415161	−	0.0719080i
$726$	−6.67121	+	11.5549i	−0.247592	+	0.428842i
$727$	39.3667			1.46003			0.730016	−	0.683430i	$-0.239513\pi$
$727$	39.3667			1.46003			0.730016	+	0.683430i	$0.239513\pi$
$728$	5.39240	−	15.0385i	0.199856	−	0.557363i
$729$	1.00000			0.0370370
$730$	−8.86526	+	15.3551i	−0.328118	+	0.568317i
$731$	−1.28055	−	2.21799i	−0.0473630	−	0.0820352i
$732$	2.28987	+	3.96618i	0.0846362	+	0.146594i
$733$	0.985769	−	1.70740i	0.0364102	−	0.0630643i	−0.847246	−	0.531201i	$-0.821741\pi$
$733$	0.985769	−	1.70740i	0.0364102	−	0.0630643i	0.883656	+	0.468136i	$0.155074\pi$
$734$	4.12478			0.152248
$735$	11.4141	+	9.39330i	0.421014	+	0.346477i
$736$	−18.7424			−0.690852
$737$	5.66960	−	9.82003i	0.208842	−	0.361726i
$738$	−5.95107	−	10.3076i	−0.219062	−	0.379426i
$739$	5.85636	+	10.1435i	0.215430	+	0.373135i	0.953405	−	0.301692i	$-0.0975514\pi$
$739$	5.85636	+	10.1435i	0.215430	+	0.373135i	−0.737976	+	0.674827i	$0.764218\pi$
$740$	−0.770771	+	1.33501i	−0.0283341	+	0.0490761i
$741$	−3.85373			−0.141570
$742$	12.3190	−	34.3556i	0.452244	−	1.26123i
$743$	50.4205			1.84975			0.924875	−	0.380272i	$-0.124170\pi$
$743$	50.4205			1.84975			0.924875	+	0.380272i	$0.124170\pi$
$744$	−3.35658	+	5.81376i	−0.123058	+	0.213143i
$745$	−0.678637	−	1.17543i	−0.0248633	−	0.0430646i
$746$	30.1841	+	52.2804i	1.10512	+	1.91412i
$747$	−1.63525	+	2.83234i	−0.0598307	+	0.103630i
$748$	2.87340			0.105062
$749$	−8.54413	−	10.0843i	−0.312196	−	0.368474i
$750$	20.6393			0.753640
$751$	15.3504	−	26.5876i	0.560143	−	0.970197i	−0.437340	−	0.899296i	$-0.644079\pi$
$751$	15.3504	−	26.5876i	0.560143	−	0.970197i	0.997483	−	0.0709005i	$-0.0225873\pi$
$752$	14.8703	+	25.7562i	0.542265	+	0.939230i
$753$	0.414865	+	0.718567i	0.0151185	+	0.0261860i
$754$	14.0592	−	24.3512i	0.512005	−	0.886818i
$755$	−17.4085			−0.633560
$756$	−2.89425	+	0.524593i	−0.105263	+	0.0190792i
$757$	31.5476			1.14662			0.573308	−	0.819340i	$-0.305660\pi$
$757$	31.5476			1.14662			0.573308	+	0.819340i	$0.305660\pi$
$758$	−1.86674	+	3.23328i	−0.0678029	+	0.117438i
$759$	3.06689	+	5.31201i	0.111321	+	0.192814i
$760$	1.65444	+	2.86557i	0.0600128	+	0.103945i
$761$	−1.13705	+	1.96942i	−0.0412179	+	0.0713915i	−0.885898	−	0.463879i	$-0.846457\pi$
$761$	−1.13705	+	1.96942i	−0.0412179	+	0.0713915i	0.844680	+	0.535271i	$0.179790\pi$
$762$	−34.1692			−1.23782
$763$	−37.6677	+	6.82739i	−1.36366	+	0.247168i
$764$	−13.5281			−0.489431
$765$	−1.47216	+	2.54985i	−0.0532259	+	0.0921900i
$766$	13.0108	+	22.5353i	0.470098	+	0.814234i
$767$	−9.25924	−	16.0375i	−0.334332	−	0.579080i
$768$	9.98250	−	17.2902i	0.360212	−	0.623906i
$769$	37.9412			1.36819			0.684097	−	0.729391i	$-0.260196\pi$
$769$	37.9412			1.36819			0.684097	+	0.729391i	$0.260196\pi$
$770$	−11.8105	−	13.9395i	−0.425620	−	0.502345i
$771$	27.3466			0.984862
$772$	12.1514	−	21.0469i	0.437340	−	0.757495i
$773$	−6.08642	−	10.5420i	−0.218913	−	0.379169i	0.735563	−	0.677457i	$-0.236918\pi$
$773$	−6.08642	−	10.5420i	−0.218913	−	0.379169i	−0.954476	+	0.298288i	$0.903585\pi$
$774$	−1.62016	−	2.80621i	−0.0582356	−	0.100867i
$775$	1.15789	−	2.00553i	0.0415927	−	0.0720407i
$776$	9.35925			0.335978
$777$	0.586366	−	1.63527i	0.0210358	−	0.0586651i
$778$	−62.3275			−2.23455
$779$	−3.37359	+	5.84323i	−0.120871	+	0.209356i
$780$	4.52377	+	7.83540i	0.161977	+	0.280552i
$781$	−1.26959	−	2.19899i	−0.0454294	−	0.0786861i
$782$	−4.06906	+	7.04782i	−0.145509	+	0.252029i
$783$	4.13624			0.147817
$784$	−32.6916	+	12.2535i	−1.16756	+	0.437624i
$785$	43.3652			1.54777
$786$	−16.7412	+	28.9966i	−0.597139	+	1.03428i
$787$	26.0572	+	45.1324i	0.928839	+	1.60880i	0.785267	+	0.619157i	$0.212526\pi$
$787$	26.0572	+	45.1324i	0.928839	+	1.60880i	0.143572	+	0.989640i	$0.454141\pi$
$788$	−0.744343	−	1.28924i	−0.0265161	−	0.0459273i
$789$	7.63107	−	13.2174i	0.271673	−	0.470552i
$790$	59.5472			2.11859
$791$	−16.4015	+	45.7411i	−0.583171	+	1.62636i
$792$	−2.90460			−0.103210
$793$	−7.93755	+	13.7482i	−0.281871	+	0.488215i
$794$	−22.9956	−	39.8296i	−0.816084	−	1.41350i
$795$	−8.25702	−	14.3016i	−0.292846	−	0.507224i
$796$	−4.84616	+	8.39379i	−0.171767	+	0.297510i
$797$	23.5613			0.834583			0.417291	−	0.908773i	$-0.362979\pi$
$797$	23.5613			0.834583			0.417291	+	0.908773i	$0.362979\pi$
$798$	3.01702	+	3.56088i	0.106801	+	0.126054i
$799$	8.31396			0.294127
$800$	−1.53082	+	2.65146i	−0.0541226	+	0.0937431i
$801$	−6.99257	−	12.1115i	−0.247070	−	0.427939i
$802$	−23.9474	−	41.4782i	−0.845614	−	1.46465i
$803$	−4.41159	+	7.64109i	−0.155681	+	0.269648i
$804$	6.80051			0.239835
$805$	18.1908	−	3.29715i	0.641142	−	0.116209i
$806$	29.1254			1.02590
$807$	−13.9010	+	24.0772i	−0.489337	+	0.847556i
$808$	−7.63600	−	13.2259i	−0.268633	−	0.465287i
$809$	−7.10719	−	12.3100i	−0.249876	−	0.432797i	0.713616	−	0.700538i	$-0.247056\pi$
$809$	−7.10719	−	12.3100i	−0.249876	−	0.432797i	−0.963491	+	0.267740i	$0.913723\pi$
$810$	−1.86258	+	3.22608i	−0.0654443	+	0.113353i
$811$	13.5557			0.476004			0.238002	−	0.971265i	$-0.423507\pi$
$811$	13.5557			0.476004			0.238002	+	0.971265i	$0.423507\pi$
$812$	−11.9713	+	2.16984i	−0.420111	+	0.0761465i
$813$	−9.64658			−0.338320
$814$	−1.07356	+	1.85946i	−0.0376283	+	0.0651741i
$815$	−15.5959	−	27.0129i	−0.546301	−	0.946221i
$816$	−3.47693	−	6.02221i	−0.121717	−	0.210820i
$817$	−0.918452	+	1.59081i	−0.0321326	+	0.0556553i
$818$	−6.94232			−0.242732
$819$	−6.59109	−	7.77923i	−0.230311	−	0.271828i
$820$	15.8406			0.553178
$821$	−3.75204	+	6.49872i	−0.130947	+	0.226807i	−0.924042	−	0.382291i	$-0.875135\pi$
$821$	−3.75204	+	6.49872i	−0.130947	+	0.226807i	0.793095	+	0.609098i	$0.208468\pi$
$822$	−10.5232	−	18.2267i	−0.367039	−	0.635730i
$823$	10.9842	+	19.0253i	0.382887	+	0.663179i	0.991474	−	0.130308i	$-0.0415967\pi$
$823$	10.9842	+	19.0253i	0.382887	+	0.663179i	−0.608587	+	0.793487i	$0.708263\pi$
$824$	1.52704	−	2.64491i	0.0531970	−	0.0921399i
$825$	1.00198			0.0348843
$826$	−7.56986	+	21.1110i	−0.263389	+	0.734547i
$827$	−40.3377			−1.40268			−0.701339	−	0.712828i	$-0.747414\pi$
$827$	−40.3377			−1.40268			−0.701339	+	0.712828i	$0.747414\pi$
$828$	−1.83932	+	3.18579i	−0.0639207	+	0.110714i
$829$	6.47596	+	11.2167i	0.224920	+	0.389572i	0.956295	−	0.292403i	$-0.0944547\pi$
$829$	6.47596	+	11.2167i	0.224920	+	0.389572i	−0.731376	+	0.681975i	$0.761121\pi$
$830$	−6.09156	−	10.5509i	−0.211441	−	0.366227i
$831$	−13.8357	+	23.9641i	−0.479954	+	0.831305i
$832$	−0.0648590			−0.00224858
$833$	−1.60293	+	9.62724i	−0.0555381	+	0.333564i
$834$	23.6258			0.818094
$835$	−4.92799	+	8.53553i	−0.170540	+	0.295384i
$836$	−1.03044	−	1.78478i	−0.0356386	−	0.0617279i
$837$	2.14219	+	3.71039i	0.0740450	+	0.128250i
$838$	9.46123	−	16.3873i	0.326833	−	0.566091i
$839$	−3.47905			−0.120110			−0.0600551	−	0.998195i	$-0.519128\pi$
$839$	−3.47905			−0.120110			−0.0600551	+	0.998195i	$0.519128\pi$
$840$	−2.95490	+	8.24070i	−0.101954	+	0.284331i
$841$	−11.8915			−0.410053
$842$	8.80707	−	15.2543i	0.303512	−	0.525698i
$843$	5.94970	+	10.3052i	0.204919	+	0.354929i
$844$	7.23986	+	12.5398i	0.249206	+	0.431638i
$845$	−1.95471	+	3.38566i	−0.0672441	+	0.116470i
$846$	10.5189			0.361646
$847$	12.9362	+	15.2682i	0.444494	+	0.524621i
$848$	39.0027			1.33936
$849$	−6.36263	+	11.0204i	−0.218365	+	0.378219i
$850$	0.664697	+	1.15129i	0.0227989	+	0.0394889i
$851$	−1.08632	−	1.88156i	−0.0372385	−	0.0644990i
$852$	0.761416	−	1.31881i	0.0260857	−	0.0451817i
$853$	−9.59308			−0.328461			−0.164230	−	0.986422i	$-0.552514\pi$
$853$	−9.59308			−0.328461			−0.164230	+	0.986422i	$0.552514\pi$
$854$	18.9176	−	3.42888i	0.647348	−	0.117334i
$855$	2.11175			0.0722203
$856$	3.91382	−	6.77893i	0.133772	−	0.231699i
$857$	−26.3851	−	45.7003i	−0.901297	−	1.56109i	−0.825812	−	0.563946i	$-0.809283\pi$
$857$	−26.3851	−	45.7003i	−0.901297	−	1.56109i	−0.0754854	−	0.997147i	$-0.524051\pi$
$858$	6.30089	+	10.9135i	0.215109	+	0.372579i
$859$	−3.18536	+	5.51720i	−0.108683	+	0.188244i	−0.915237	−	0.402916i	$-0.867997\pi$
$859$	−3.18536	+	5.51720i	−0.108683	+	0.188244i	0.806554	+	0.591160i	$0.201330\pi$
$860$	4.31256			0.147057
$861$	−17.5652	+	3.18374i	−0.598619	+	0.108502i
$862$	−16.6968			−0.568695
$863$	−4.08401	+	7.07371i	−0.139021	+	0.240792i	−0.927126	−	0.374749i	$-0.877729\pi$
$863$	−4.08401	+	7.07371i	−0.139021	+	0.240792i	0.788105	+	0.615541i	$0.211062\pi$
$864$	−2.83213	−	4.90540i	−0.0963512	−	0.166885i
$865$	21.0869	+	36.5236i	0.716977	+	1.24184i
$866$	20.8052	−	36.0356i	0.706989	−	1.22454i
$867$	15.0561			0.511331
$868$	−8.14649	−	9.61502i	−0.276510	−	0.326355i
$869$	29.6322			1.00520
$870$	−7.70407	+	13.3438i	−0.261192	+	0.452398i
$871$	11.7865	+	20.4149i	0.399372	+	0.691732i
$872$	−11.3357	−	19.6340i	−0.383874	−	0.664890i
$873$	2.98657	−	5.17289i	0.101080	−	0.175076i
$874$	5.83690			0.197436
$875$	10.4485	−	29.1391i	0.353224	−	0.985082i
$876$	−5.29156			−0.178785
$877$	−8.27393	+	14.3309i	−0.279391	+	0.483919i	−0.971233	−	0.238129i	$-0.923466\pi$
$877$	−8.27393	+	14.3309i	−0.279391	+	0.483919i	0.691843	+	0.722048i	$0.256799\pi$
$878$	29.8460	+	51.6949i	1.00726	+	1.74462i
$879$	11.9528	+	20.7028i	0.403156	+	0.698287i
$880$	9.76211	−	16.9085i	0.329081	−	0.569985i
$881$	−46.4499			−1.56494			−0.782469	−	0.622690i	$-0.786040\pi$
$881$	−46.4499			−1.56494			−0.782469	+	0.622690i	$0.786040\pi$
$882$	−2.02803	+	12.1804i	−0.0682873	+	0.410136i
$883$	34.9542			1.17630			0.588152	−	0.808751i	$-0.299856\pi$
$883$	34.9542			1.17630			0.588152	+	0.808751i	$0.299856\pi$
$884$	−2.98676	+	5.17322i	−0.100456	+	0.173994i
$885$	5.07383	+	8.78813i	0.170555	+	0.295410i
$886$	−4.71490	−	8.16644i	−0.158400	−	0.274357i
$887$	2.09931	−	3.63611i	0.0704879	−	0.122089i	−0.828627	−	0.559801i	$-0.810878\pi$
$887$	2.09931	−	3.63611i	0.0704879	−	0.122089i	0.899115	+	0.437712i	$0.144211\pi$
$888$	1.02883			0.0345254
$889$	−17.2980	+	48.2410i	−0.580155	+	1.61795i
$890$	52.0969			1.74629
$891$	−0.926867	+	1.60538i	−0.0310512	+	0.0537823i
$892$	7.82827	+	13.5590i	0.262110	+	0.453987i
$893$	−2.98151	−	5.16413i	−0.0997725	−	0.172811i
$894$	0.566889	−	0.981880i	0.0189596	−	0.0328390i
$895$	44.0105			1.47111
$896$	−19.3246	−	22.8081i	−0.645588	−	0.761965i
$897$	−12.7515			−0.425761
$898$	−8.98761	+	15.5670i	−0.299921	+	0.519478i
$899$	8.86062	+	15.3470i	0.295518	+	0.511853i
$900$	0.300460	+	0.520412i	0.0100153	+	0.0173471i
$901$	5.45158	−	9.44241i	0.181618	−	0.314572i
$902$	22.0634			0.734631
$903$	−4.78208	+	0.866767i	−0.159138	+	0.0288442i
$904$	−28.7780			−0.957142
$905$	−24.3665	+	42.2041i	−0.809971	+	1.40291i
$906$	−7.27096	−	12.5937i	−0.241561	−	0.418397i
$907$	−3.90780	−	6.76850i	−0.129756	−	0.224744i	0.793826	−	0.608145i	$-0.208086\pi$
$907$	−3.90780	−	6.76850i	−0.129756	−	0.224744i	−0.923582	+	0.383401i	$0.874753\pi$
$908$	10.4128	−	18.0355i	0.345562	−	0.598530i
$909$	−9.74670			−0.323278
$910$	37.3728	−	6.77395i	1.23890	−	0.224554i
$911$	3.36489			0.111484			0.0557419	−	0.998445i	$-0.482248\pi$
$911$	3.36489			0.111484			0.0557419	+	0.998445i	$0.482248\pi$
$912$	−2.49376	+	4.31931i	−0.0825765	+	0.143027i
$913$	−3.03132	−	5.25040i	−0.100322	−	0.173763i
$914$	26.3701	+	45.6743i	0.872245	+	1.51077i
$915$	4.34958	−	7.53369i	0.143793	−	0.249056i
$916$	−16.3327			−0.539648
$917$	32.4631	+	38.3151i	1.07203	+	1.26527i
$918$	−2.45948			−0.0811750
$919$	20.4932	−	35.4952i	0.676007	−	1.17088i	−0.300166	−	0.953887i	$-0.597042\pi$
$919$	20.4932	−	35.4952i	0.676007	−	1.17088i	0.976173	−	0.216992i	$-0.0696245\pi$
$920$	5.47433	+	9.48181i	0.180483	+	0.312606i
$921$	7.15050	+	12.3850i	0.235617	+	0.408101i
$922$	−31.0908	+	53.8508i	−1.02392	+	1.77348i
$923$	5.27870			0.173751
$924$	1.84042	−	5.13261i	0.0605453	−	0.168850i
$925$	−0.354909			−0.0116693
$926$	24.7654	−	42.8949i	0.813841	−	1.40961i
$927$	−0.974569	−	1.68800i	−0.0320091	−	0.0554413i
$928$	−11.7144	−	20.2899i	−0.384544	−	0.666049i
$929$	−22.0702	+	38.2267i	−0.724099	+	1.25418i	0.235245	+	0.971936i	$0.424411\pi$
$929$	−22.0702	+	38.2267i	−0.724099	+	1.25418i	−0.959344	+	0.282240i	$0.908923\pi$
$930$	−15.9600			−0.523349
$931$	6.55469	−	2.45683i	0.214821	−	0.0805194i
$932$	−19.3756			−0.634670
$933$	1.68994	−	2.92707i	0.0553262	−	0.0958278i
$934$	−27.6407	−	47.8750i	−0.904430	−	1.56652i
$935$	−2.72899	−	4.72674i	−0.0892474	−	0.154581i
$936$	3.01919	−	5.22938i	0.0986852	−	0.170928i
$937$	19.6219			0.641019			0.320509	−	0.947245i	$-0.396146\pi$
$937$	19.6219			0.641019			0.320509	+	0.947245i	$0.396146\pi$
$938$	9.63605	−	26.8733i	0.314628	−	0.877444i
$939$	33.9154			1.10679
$940$	−6.99979	+	12.1240i	−0.228308	+	0.395441i
$941$	−5.60981	−	9.71648i	−0.182875	−	0.316748i	0.759984	−	0.649942i	$-0.225207\pi$
$941$	−5.60981	−	9.71648i	−0.182875	−	0.316748i	−0.942858	+	0.333194i	$0.891874\pi$
$942$	18.1122	+	31.3713i	0.590127	+	1.02213i
$943$	−11.1628	+	19.3345i	−0.363511	+	0.629619i
$944$	−23.9667			−0.780049
$945$	3.61175	+	4.26282i	0.117490	+	0.138670i
$946$	6.00671			0.195295
$947$	−1.96629	+	3.40572i	−0.0638959	+	0.110671i	−0.896204	−	0.443643i	$-0.853686\pi$
$947$	−1.96629	+	3.40572i	−0.0638959	+	0.110671i	0.832308	+	0.554314i	$0.187019\pi$
$948$	8.88573	+	15.3905i	0.288595	+	0.499862i
$949$	−9.17126	−	15.8851i	−0.297712	−	0.515652i
$950$	0.476741	−	0.825739i	0.0154675	−	0.0267905i
$951$	−11.5718			−0.375242
$952$	−5.68734	+	1.03085i	−0.184328	+	0.0334100i
$953$	−1.45702			−0.0471975			−0.0235988	−	0.999722i	$-0.507512\pi$
$953$	−1.45702			−0.0471975			−0.0235988	+	0.999722i	$0.507512\pi$
$954$	6.89736	−	11.9466i	0.223310	−	0.386785i
$955$	12.8482	+	22.2538i	0.415759	+	0.720117i
$956$	11.9217	+	20.6490i	0.385576	+	0.667837i
$957$	−3.83375	+	6.64024i	−0.123927	+	0.214649i
$958$	−34.7039			−1.12123
$959$	−31.0603	+	5.62978i	−1.00299	+	0.181795i
$960$	0.0355411			0.00114708
$961$	6.32202	−	10.9501i	0.203936	−	0.353228i
$962$	−2.23183	−	3.86564i	−0.0719570	−	0.124633i
$963$	−2.49783	−	4.32637i	−0.0804914	−	0.139415i
$964$	−9.07793	+	15.7234i	−0.292380	+	0.506418i
$965$	−46.1629			−1.48604
$966$	9.98293	+	11.7825i	0.321195	+	0.379096i
$967$	34.2169			1.10034			0.550170	−	0.835052i	$-0.314563\pi$
$967$	34.2169			1.10034			0.550170	+	0.835052i	$0.314563\pi$
$968$	−5.92571	+	10.2636i	−0.190460	+	0.329886i
$969$	0.697126	+	1.20746i	0.0223949	+	0.0387891i
$970$	11.1254	+	19.2698i	0.357217	+	0.618717i
$971$	−10.4370	+	18.0774i	−0.334938	+	0.580130i	−0.983473	−	0.181055i	$-0.942049\pi$
$971$	−10.4370	+	18.0774i	−0.334938	+	0.580130i	0.648535	+	0.761185i	$0.275382\pi$
$972$	−1.11175			−0.0356594
$973$	11.9604	−	33.3555i	0.383433	−	1.06933i
$974$	−10.4521			−0.334908
$975$	−1.04151	+	1.80394i	−0.0333549	+	0.0577723i
$976$	10.2728	+	17.7930i	0.328824	+	0.569540i
$977$	−16.6022	−	28.7558i	−0.531151	−	0.919980i	−0.999339	−	0.0363515i	$-0.988426\pi$
$977$	−16.6022	−	28.7558i	−0.531151	−	0.919980i	0.468188	−	0.883629i	$-0.344907\pi$
$978$	13.0278	−	22.5648i	0.416583	−	0.721542i
$979$	25.9248			0.828559
$980$	−12.6896	−	10.4430i	−0.405353	−	0.333589i
$981$	−14.4690			−0.461960
$982$	−18.8706	+	32.6849i	−0.602186	+	1.04302i
$983$	−9.23588	−	15.9970i	−0.294579	−	0.510225i	0.680308	−	0.732926i	$-0.261846\pi$
$983$	−9.23588	−	15.9970i	−0.294579	−	0.510225i	−0.974887	+	0.222701i	$0.928513\pi$
$984$	−5.28604	−	9.15570i	−0.168513	−	0.291873i
$985$	−1.41387	+	2.44889i	−0.0450496	+	0.0780281i
$986$	−10.1730			−0.323975
$987$	5.32511	−	14.8508i	0.169500	−	0.472707i
$988$	4.28438			0.136304
$989$	−3.03904	+	5.26378i	−0.0966360	+	0.167378i
$990$	−3.45273	−	5.98030i	−0.109735	−	0.190066i
$991$	−17.6821	−	30.6263i	−0.561690	−	0.972876i	−0.997349	−	0.0727639i	$-0.976818\pi$
$991$	−17.6821	−	30.6263i	−0.561690	−	0.972876i	0.435659	−	0.900112i	$-0.356515\pi$
$992$	12.1340	−	21.0166i	0.385253	−	0.667278i
$993$	−30.2090			−0.958653
$994$	−4.13259	−	4.87756i	−0.131078	−	0.154707i
$995$	18.4104			0.583649
$996$	1.81799	−	3.14885i	0.0576051	−	0.0997750i
$997$	18.2688	+	31.6424i	0.578578	+	1.00213i	0.995643	+	0.0932496i	$0.0297255\pi$
$997$	18.2688	+	31.6424i	0.578578	+	1.00213i	−0.417065	+	0.908877i	$0.636941\pi$
$998$	25.5217	+	44.2049i	0.807876	+	1.39928i
$999$	0.328304	−	0.568640i	0.0103871	−	0.0179910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.d.58.1	✓	8
3.2	odd	2		1197.2.j.k.856.4		8
7.2	even	3		2793.2.a.bc.1.4		4
7.4	even	3	inner	399.2.j.d.172.1	yes	8
7.5	odd	6		2793.2.a.bd.1.4		4
21.2	odd	6		8379.2.a.br.1.1		4
21.5	even	6		8379.2.a.bt.1.1		4
21.11	odd	6		1197.2.j.k.172.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.d.58.1	✓	8	1.1	even	1	trivial
399.2.j.d.172.1	yes	8	7.4	even	3	inner
1197.2.j.k.172.4		8	21.11	odd	6
1197.2.j.k.856.4		8	3.2	odd	2
2793.2.a.bc.1.4		4	7.2	even	3
2793.2.a.bd.1.4		4	7.5	odd	6
8379.2.a.br.1.1		4	21.2	odd	6
8379.2.a.bt.1.1		4	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.882007 + 1.52768i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.555874 - 0.962803i) q^{4} +(-1.05587 + 1.82883i) q^{5} -1.76401 q^{6} +(-0.893022 + 2.49048i) q^{7} -1.56689 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.882007 + 1.52768i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.555874 - 0.962803i) q^{4} +(-1.05587 + 1.82883i) q^{5} -1.76401 q^{6} +(-0.893022 + 2.49048i) q^{7} -1.56689 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.86258 - 3.22608i) q^{10} +(-0.926867 - 1.60538i) q^{11} +(0.555874 - 0.962803i) q^{12} +3.85373 q^{13} +(-3.01702 - 3.56088i) q^{14} -2.11175 q^{15} +(2.49376 - 4.31931i) q^{16} +(-0.697126 - 1.20746i) q^{17} +(-0.882007 - 1.52768i) q^{18} +(-0.500000 + 0.866025i) q^{19} +2.34773 q^{20} +(-2.60333 + 0.471863i) q^{21} +3.27002 q^{22} +(-1.65444 + 2.86557i) q^{23} +(-0.783444 - 1.35697i) q^{24} +(0.270259 + 0.468102i) q^{25} +(-3.39902 + 5.88728i) q^{26} -1.00000 q^{27} +(2.89425 - 0.524593i) q^{28} -4.13624 q^{29} +(1.86258 - 3.22608i) q^{30} +(-2.14219 - 3.71039i) q^{31} +(2.83213 + 4.90540i) q^{32} +(0.926867 - 1.60538i) q^{33} +2.45948 q^{34} +(-3.61175 - 4.26282i) q^{35} +1.11175 q^{36} +(-0.328304 + 0.568640i) q^{37} +(-0.882007 - 1.52768i) q^{38} +(1.92687 + 3.33743i) q^{39} +(1.65444 - 2.86557i) q^{40} +6.74718 q^{41} +(1.57530 - 4.39325i) q^{42} +1.83690 q^{43} +(-1.03044 + 1.78478i) q^{44} +(-1.05587 - 1.82883i) q^{45} +(-2.91845 - 5.05491i) q^{46} +(-2.98151 + 5.16413i) q^{47} +4.98751 q^{48} +(-5.40502 - 4.44811i) q^{49} -0.953481 q^{50} +(0.697126 - 1.20746i) q^{51} +(-2.14219 - 3.71039i) q^{52} +(3.91004 + 6.77238i) q^{53} +(0.882007 - 1.52768i) q^{54} +3.91462 q^{55} +(1.39927 - 3.90231i) q^{56} -1.00000 q^{57} +(3.64819 - 6.31886i) q^{58} +(-2.40267 - 4.16154i) q^{59} +(1.17387 + 2.03320i) q^{60} +(-2.05970 + 3.56751i) q^{61} +7.55772 q^{62} +(-1.71031 - 2.01862i) q^{63} -0.0168302 q^{64} +(-4.06906 + 7.04782i) q^{65} +(1.63501 + 2.83192i) q^{66} +(3.05847 + 5.29743i) q^{67} +(-0.775029 + 1.34239i) q^{68} -3.30887 q^{69} +(9.69782 - 1.75776i) q^{70} +1.36976 q^{71} +(0.783444 - 1.35697i) q^{72} +(-2.37984 - 4.12200i) q^{73} +(-0.579134 - 1.00309i) q^{74} +(-0.270259 + 0.468102i) q^{75} +1.11175 q^{76} +(4.82589 - 0.874708i) q^{77} -6.79805 q^{78} +(-7.99257 + 13.8435i) q^{79} +(5.26619 + 9.12130i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.95107 + 10.3076i) q^{82} +3.27050 q^{83} +(1.90144 + 2.24420i) q^{84} +2.94431 q^{85} +(-1.62016 + 2.80621i) q^{86} +(-2.06812 - 3.58209i) q^{87} +(1.45230 + 2.51545i) q^{88} +(-6.99257 + 12.1115i) q^{89} +3.72516 q^{90} +(-3.44147 + 9.59767i) q^{91} +3.67864 q^{92} +(2.14219 - 3.71039i) q^{93} +(-5.25943 - 9.10960i) q^{94} +(-1.05587 - 1.82883i) q^{95} +(-2.83213 + 4.90540i) q^{96} -5.97314 q^{97} +(11.5626 - 4.33389i) q^{98} +1.85373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{5} + 2 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 - 6 * q^8 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{5} + 2 q^{7} - 6 q^{8} - 4 q^{9} + 3 q^{10} + 2 q^{11} + 12 q^{13} + 2 q^{14} - 8 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{19} + 24 q^{20} + q^{21} - 12 q^{22} - 5 q^{23} - 3 q^{24} + 4 q^{25} + 6 q^{26} - 8 q^{27} + 8 q^{28} - 8 q^{29} - 3 q^{30} - 17 q^{31} - 4 q^{32} - 2 q^{33} + 16 q^{34} - 20 q^{35} + 3 q^{37} + 6 q^{39} + 5 q^{40} + 14 q^{41} + 19 q^{42} - 30 q^{43} - 17 q^{44} - 4 q^{45} - q^{46} - 16 q^{47} + 8 q^{48} + 14 q^{49} - 28 q^{50} - 2 q^{51} - 17 q^{52} - 4 q^{53} + 30 q^{55} + 18 q^{56} - 8 q^{57} + 5 q^{58} - 17 q^{59} + 12 q^{60} + 9 q^{61} - 14 q^{62} - q^{63} - 26 q^{64} - 23 q^{65} - 6 q^{66} + 5 q^{67} + 10 q^{68} - 10 q^{69} + 33 q^{70} + 12 q^{71} + 3 q^{72} - 15 q^{73} + 10 q^{74} - 4 q^{75} - 4 q^{77} + 12 q^{78} - 5 q^{79} + 25 q^{80} - 4 q^{81} - 31 q^{82} + 68 q^{83} + 19 q^{84} - 24 q^{85} - 17 q^{86} - 4 q^{87} - 11 q^{88} + 3 q^{89} - 6 q^{90} + 45 q^{91} + 14 q^{92} + 17 q^{93} + 6 q^{94} - 4 q^{95} + 4 q^{96} + 22 q^{97} + 27 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^5 + 2 * q^7 - 6 * q^8 - 4 * q^9 + 3 * q^10 + 2 * q^11 + 12 * q^13 + 2 * q^14 - 8 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^19 + 24 * q^20 + q^21 - 12 * q^22 - 5 * q^23 - 3 * q^24 + 4 * q^25 + 6 * q^26 - 8 * q^27 + 8 * q^28 - 8 * q^29 - 3 * q^30 - 17 * q^31 - 4 * q^32 - 2 * q^33 + 16 * q^34 - 20 * q^35 + 3 * q^37 + 6 * q^39 + 5 * q^40 + 14 * q^41 + 19 * q^42 - 30 * q^43 - 17 * q^44 - 4 * q^45 - q^46 - 16 * q^47 + 8 * q^48 + 14 * q^49 - 28 * q^50 - 2 * q^51 - 17 * q^52 - 4 * q^53 + 30 * q^55 + 18 * q^56 - 8 * q^57 + 5 * q^58 - 17 * q^59 + 12 * q^60 + 9 * q^61 - 14 * q^62 - q^63 - 26 * q^64 - 23 * q^65 - 6 * q^66 + 5 * q^67 + 10 * q^68 - 10 * q^69 + 33 * q^70 + 12 * q^71 + 3 * q^72 - 15 * q^73 + 10 * q^74 - 4 * q^75 - 4 * q^77 + 12 * q^78 - 5 * q^79 + 25 * q^80 - 4 * q^81 - 31 * q^82 + 68 * q^83 + 19 * q^84 - 24 * q^85 - 17 * q^86 - 4 * q^87 - 11 * q^88 + 3 * q^89 - 6 * q^90 + 45 * q^91 + 14 * q^92 + 17 * q^93 + 6 * q^94 - 4 * q^95 + 4 * q^96 + 22 * q^97 + 27 * q^98 - 4 * q^99

Introduction

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