LMFDB - Embedded newform 1155.2.q.j.331.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (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:	$9.22272143346$
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} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.2
Root			$-1.13705 - 1.96943i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.j.991.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13705 + 1.96943i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.58577 - 2.74664i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.27410 q^{6} +(1.22797 + 2.34352i) q^{7} +2.66421 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.13705 + 1.96943i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.58577 - 2.74664i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.27410 q^{6} +(1.22797 + 2.34352i) q^{7} +2.66421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.13705 + 1.96943i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.58577 + 2.74664i) q^{12} -0.463858 q^{13} +(-6.01167 - 0.246298i) q^{14} -1.00000 q^{15} +(0.142200 - 0.246298i) q^{16} +(-2.17154 - 3.76122i) q^{17} +(-1.13705 - 1.96943i) q^{18} +(-3.28394 + 5.68794i) q^{19} -3.17154 q^{20} +(1.41556 - 2.23521i) q^{21} -2.27410 q^{22} +(1.66533 - 2.88443i) q^{23} +(-1.33210 - 2.30727i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.527431 - 0.913536i) q^{26} +1.00000 q^{27} +(4.48952 - 7.08908i) q^{28} +9.40734 q^{29} +(1.13705 - 1.96943i) q^{30} +(2.24767 + 3.89307i) q^{31} +(2.98759 + 5.17465i) q^{32} +(0.500000 - 0.866025i) q^{33} +9.87662 q^{34} +(2.64353 + 0.108305i) q^{35} +3.17154 q^{36} +(-4.15801 + 7.20188i) q^{37} +(-7.46801 - 12.9350i) q^{38} +(0.231929 + 0.401713i) q^{39} +(1.33210 - 2.30727i) q^{40} +11.4417 q^{41} +(2.79253 + 5.32941i) q^{42} -11.0887 q^{43} +(1.58577 - 2.74664i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.78713 + 6.55950i) q^{46} +(-3.65306 + 6.32728i) q^{47} -0.284400 q^{48} +(-3.98417 + 5.75555i) q^{49} +2.27410 q^{50} +(-2.17154 + 3.76122i) q^{51} +(0.735573 + 1.27405i) q^{52} +(0.362436 + 0.627758i) q^{53} +(-1.13705 + 1.96943i) q^{54} +1.00000 q^{55} +(3.27157 + 6.24363i) q^{56} +6.56787 q^{57} +(-10.6966 + 18.5271i) q^{58} +(-1.49762 - 2.59395i) q^{59} +(1.58577 + 2.74664i) q^{60} +(-0.625867 + 1.08403i) q^{61} -10.2229 q^{62} +(-2.64353 - 0.108305i) q^{63} -13.0194 q^{64} +(-0.231929 + 0.401713i) q^{65} +(1.13705 + 1.96943i) q^{66} +(0.404064 + 0.699859i) q^{67} +(-6.88714 + 11.9289i) q^{68} -3.33066 q^{69} +(-3.21913 + 5.08311i) q^{70} -7.63435 q^{71} +(-1.33210 + 2.30727i) q^{72} +(5.91223 + 10.2403i) q^{73} +(-9.45573 - 16.3778i) q^{74} +(-0.500000 + 0.866025i) q^{75} +20.8303 q^{76} +(-1.41556 + 2.23521i) q^{77} -1.05486 q^{78} +(1.42653 - 2.47083i) q^{79} +(-0.142200 - 0.246298i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.0098 + 22.5337i) q^{82} +8.53447 q^{83} +(-8.38408 - 0.343495i) q^{84} -4.34309 q^{85} +(12.6085 - 21.8385i) q^{86} +(-4.70367 - 8.14700i) q^{87} +(1.33210 + 2.30727i) q^{88} +(-7.41507 + 12.8433i) q^{89} -2.27410 q^{90} +(-0.569605 - 1.08706i) q^{91} -10.5633 q^{92} +(2.24767 - 3.89307i) q^{93} +(-8.30743 - 14.3889i) q^{94} +(3.28394 + 5.68794i) q^{95} +(2.98759 - 5.17465i) q^{96} +10.1835 q^{97} +(-6.80495 - 14.3909i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.13705	+	1.96943i	−0.804017	+	1.39260i	0.112936	+	0.993602i	$0.463974\pi$
$2$	−1.13705	+	1.96943i	−0.804017	+	1.39260i	−0.916953	+	0.398996i	$0.869359\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.58577	−	2.74664i	−0.792886	−	1.37332i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.27410			0.928399
$7$	1.22797	+	2.34352i	0.464130	+	0.885767i
$7$	1.22797	+	2.34352i	0.464130	+	0.885767i
$8$	2.66421			0.941940
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.13705	+	1.96943i	0.359567	+	0.622789i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.58577	+	2.74664i	−0.457773	+	0.792886i
$13$	−0.463858			−0.128651			−0.0643256	−	0.997929i	$-0.520490\pi$
$13$	−0.463858			−0.128651			−0.0643256	+	0.997929i	$0.520490\pi$
$14$	−6.01167	−	0.246298i	−1.60669	−	0.0658258i
$15$	−1.00000			−0.258199
$16$	0.142200	−	0.246298i	0.0355500	−	0.0615744i
$17$	−2.17154	−	3.76122i	−0.526677	−	0.912231i	−0.999517	−	0.0310824i	$-0.990105\pi$
$17$	−2.17154	−	3.76122i	−0.526677	−	0.912231i	0.472840	−	0.881148i	$-0.343229\pi$
$18$	−1.13705	−	1.96943i	−0.268006	−	0.464199i
$19$	−3.28394	+	5.68794i	−0.753386	+	1.30490i	0.192786	+	0.981241i	$0.438248\pi$
$19$	−3.28394	+	5.68794i	−0.753386	+	1.30490i	−0.946172	+	0.323663i	$0.895086\pi$
$20$	−3.17154			−0.709179
$21$	1.41556	−	2.23521i	0.308901	−	0.487764i
$22$	−2.27410			−0.484840
$23$	1.66533	−	2.88443i	0.347245	−	0.601446i	−0.638514	−	0.769610i	$-0.720451\pi$
$23$	1.66533	−	2.88443i	0.347245	−	0.601446i	0.985759	+	0.168164i	$0.0537839\pi$
$24$	−1.33210	−	2.30727i	−0.271915	−	0.470970i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.527431	−	0.913536i	0.103438	−	0.179159i
$27$	1.00000			0.192450
$28$	4.48952	−	7.08908i	0.848439	−	1.33971i
$29$	9.40734			1.74690			0.873450	−	0.486914i	$-0.161877\pi$
$29$	9.40734			1.74690			0.873450	+	0.486914i	$0.161877\pi$
$30$	1.13705	−	1.96943i	0.207596	−	0.359567i
$31$	2.24767	+	3.89307i	0.403693	+	0.699217i	0.994168	−	0.107839i	$-0.0343931\pi$
$31$	2.24767	+	3.89307i	0.403693	+	0.699217i	−0.590475	+	0.807056i	$0.701060\pi$
$32$	2.98759	+	5.17465i	0.528136	+	0.914758i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	9.87662			1.69383
$35$	2.64353	+	0.108305i	0.446839	+	0.0183070i
$36$	3.17154			0.528591
$37$	−4.15801	+	7.20188i	−0.683572	+	1.18398i	0.290311	+	0.956932i	$0.406241\pi$
$37$	−4.15801	+	7.20188i	−0.683572	+	1.18398i	−0.973883	+	0.227049i	$0.927092\pi$
$38$	−7.46801	−	12.9350i	−1.21147	−	2.09833i
$39$	0.231929	+	0.401713i	0.0371384	+	0.0643256i
$40$	1.33210	−	2.30727i	0.210624	−	0.364812i
$41$	11.4417			1.78690			0.893449	−	0.449164i	$-0.148278\pi$
$41$	11.4417			1.78690			0.893449	+	0.449164i	$0.148278\pi$
$42$	2.79253	+	5.32941i	0.430897	+	0.822345i
$43$	−11.0887			−1.69102			−0.845509	−	0.533961i	$-0.820703\pi$
$43$	−11.0887			−1.69102			−0.845509	+	0.533961i	$0.820703\pi$
$44$	1.58577	−	2.74664i	0.239064	−	0.414071i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	3.78713	+	6.55950i	0.558382	+	0.967146i
$47$	−3.65306	+	6.32728i	−0.532853	+	0.922929i	0.466411	+	0.884568i	$0.345547\pi$
$47$	−3.65306	+	6.32728i	−0.532853	+	0.922929i	−0.999264	+	0.0383605i	$0.987786\pi$
$48$	−0.284400			−0.0410496
$49$	−3.98417	+	5.75555i	−0.569167	+	0.822222i
$50$	2.27410			0.321607
$51$	−2.17154	+	3.76122i	−0.304077	+	0.526677i
$52$	0.735573	+	1.27405i	0.102006	+	0.176679i
$53$	0.362436	+	0.627758i	0.0497845	+	0.0862292i	0.889844	−	0.456265i	$-0.150813\pi$
$53$	0.362436	+	0.627758i	0.0497845	+	0.0862292i	−0.840059	+	0.542495i	$0.817480\pi$
$54$	−1.13705	+	1.96943i	−0.154733	+	0.268006i
$55$	1.00000			0.134840
$56$	3.27157	+	6.24363i	0.437182	+	0.834340i
$57$	6.56787			0.869936
$58$	−10.6966	+	18.5271i	−1.40454	+	2.43273i
$59$	−1.49762	−	2.59395i	−0.194973	−	0.337703i	0.751919	−	0.659256i	$-0.229129\pi$
$59$	−1.49762	−	2.59395i	−0.194973	−	0.337703i	−0.946892	+	0.321553i	$0.895795\pi$
$60$	1.58577	+	2.74664i	0.204722	+	0.354589i
$61$	−0.625867	+	1.08403i	−0.0801340	+	0.138796i	−0.903307	−	0.428994i	$-0.858868\pi$
$61$	−0.625867	+	1.08403i	−0.0801340	+	0.138796i	0.823173	+	0.567790i	$0.192201\pi$
$62$	−10.2229			−1.29830
$63$	−2.64353	−	0.108305i	−0.333054	−	0.0136452i
$64$	−13.0194			−1.62742
$65$	−0.231929	+	0.401713i	−0.0287673	+	0.0498264i
$66$	1.13705	+	1.96943i	0.139961	+	0.242420i
$67$	0.404064	+	0.699859i	0.0493643	+	0.0855014i	0.889652	−	0.456640i	$-0.150947\pi$
$67$	0.404064	+	0.699859i	0.0493643	+	0.0855014i	−0.840287	+	0.542141i	$0.817614\pi$
$68$	−6.88714	+	11.9289i	−0.835189	+	1.44659i
$69$	−3.33066			−0.400964
$70$	−3.21913	+	5.08311i	−0.384760	+	0.607548i
$71$	−7.63435			−0.906031			−0.453016	−	0.891503i	$-0.649652\pi$
$71$	−7.63435			−0.906031			−0.453016	+	0.891503i	$0.649652\pi$
$72$	−1.33210	+	2.30727i	−0.156990	+	0.271915i
$73$	5.91223	+	10.2403i	0.691974	+	1.19853i	0.971190	+	0.238306i	$0.0765922\pi$
$73$	5.91223	+	10.2403i	0.691974	+	1.19853i	−0.279216	+	0.960228i	$0.590074\pi$
$74$	−9.45573	−	16.3778i	−1.09921	−	1.90388i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	20.8303			2.38940
$77$	−1.41556	+	2.23521i	−0.161318	+	0.254726i
$78$	−1.05486			−0.119439
$79$	1.42653	−	2.47083i	0.160497	−	0.277990i	−0.774550	−	0.632513i	$-0.782024\pi$
$79$	1.42653	−	2.47083i	0.160497	−	0.277990i	0.935047	+	0.354523i	$0.115357\pi$
$80$	−0.142200	−	0.246298i	−0.0158984	−	0.0275369i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−13.0098	+	22.5337i	−1.43670	+	2.48843i
$83$	8.53447			0.936780			0.468390	−	0.883522i	$-0.344834\pi$
$83$	8.53447			0.936780			0.468390	+	0.883522i	$0.344834\pi$
$84$	−8.38408	−	0.343495i	−0.914778	−	0.0374784i
$85$	−4.34309			−0.471074
$86$	12.6085	−	21.8385i	1.35961	−	2.35491i
$87$	−4.70367	−	8.14700i	−0.504287	−	0.873450i
$88$	1.33210	+	2.30727i	0.142003	+	0.245956i
$89$	−7.41507	+	12.8433i	−0.785996	+	1.36138i	0.142406	+	0.989808i	$0.454516\pi$
$89$	−7.41507	+	12.8433i	−0.785996	+	1.36138i	−0.928402	+	0.371577i	$0.878817\pi$
$90$	−2.27410			−0.239711
$91$	−0.569605	−	1.08706i	−0.0597108	−	0.113955i
$92$	−10.5633			−1.10130
$93$	2.24767	−	3.89307i	0.233072	−	0.403693i
$94$	−8.30743	−	14.3889i	−0.856846	−	1.48410i
$95$	3.28394	+	5.68794i	0.336925	+	0.583571i
$96$	2.98759	−	5.17465i	0.304919	−	0.528136i
$97$	10.1835			1.03397			0.516987	−	0.855993i	$-0.327053\pi$
$97$	10.1835			1.03397			0.516987	+	0.855993i	$0.327053\pi$
$98$	−6.80495	−	14.3909i	−0.687404	−	1.45370i
$99$	−1.00000			−0.100504
$100$	−1.58577	+	2.74664i	−0.158577	+	0.274664i
$101$	5.75533	+	9.96853i	0.572677	+	0.991906i	0.996290	+	0.0860625i	$0.0274285\pi$
$101$	5.75533	+	9.96853i	0.572677	+	0.991906i	−0.423613	+	0.905843i	$0.639238\pi$
$102$	−4.93831	−	8.55341i	−0.488966	−	0.846914i
$103$	−7.24406	+	12.5471i	−0.713779	+	1.23630i	0.249650	+	0.968336i	$0.419685\pi$
$103$	−7.24406	+	12.5471i	−0.713779	+	1.23630i	−0.963429	+	0.267965i	$0.913649\pi$
$104$	−1.23582			−0.121182
$105$	−1.22797	−	2.34352i	−0.119838	−	0.228704i
$106$	−1.64843			−0.160110
$107$	−9.63955	+	16.6962i	−0.931890	+	1.61408i	−0.151803	+	0.988411i	$0.548508\pi$
$107$	−9.63955	+	16.6962i	−0.931890	+	1.61408i	−0.780087	+	0.625671i	$0.784825\pi$
$108$	−1.58577	−	2.74664i	−0.152591	−	0.264295i
$109$	1.26105	+	2.18420i	0.120786	+	0.209208i	0.920078	−	0.391735i	$-0.128125\pi$
$109$	1.26105	+	2.18420i	0.120786	+	0.209208i	−0.799292	+	0.600943i	$0.794792\pi$
$110$	−1.13705	+	1.96943i	−0.108414	+	0.187778i
$111$	8.31601			0.789321
$112$	0.751821	+	0.0308020i	0.0710404	+	0.00291052i
$113$	−16.0059			−1.50571			−0.752853	−	0.658188i	$-0.771323\pi$
$113$	−16.0059			−1.50571			−0.752853	+	0.658188i	$0.771323\pi$
$114$	−7.46801	+	12.9350i	−0.699443	+	1.21147i
$115$	−1.66533	−	2.88443i	−0.155293	−	0.268975i
$116$	−14.9179	−	25.8386i	−1.38509	−	2.39905i
$117$	0.231929	−	0.401713i	0.0214419	−	0.0371384i
$118$	6.81147			0.627046
$119$	6.14791	−	9.70773i	0.563578	−	0.889906i
$120$	−2.66421			−0.243208
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.42329	−	2.46520i	−0.128858	−	0.223189i
$123$	−5.72087	−	9.90883i	−0.515833	−	0.893449i
$124$	7.12857	−	12.3471i	0.640165	−	1.10880i
$125$	−1.00000			−0.0894427
$126$	3.21913	−	5.08311i	0.286783	−	0.452839i
$127$	12.8041			1.13618			0.568088	−	0.822968i	$-0.307683\pi$
$127$	12.8041			1.13618			0.568088	+	0.822968i	$0.307683\pi$
$128$	8.82851	−	15.2914i	0.780337	−	1.35158i
$129$	5.54437	+	9.60314i	0.488155	+	0.845509i
$130$	−0.527431	−	0.913536i	−0.0462587	−	0.0801225i
$131$	−2.51534	+	4.35669i	−0.219766	+	0.380646i	−0.954736	−	0.297453i	$-0.903863\pi$
$131$	−2.51534	+	4.35669i	−0.219766	+	0.380646i	0.734970	+	0.678099i	$0.237196\pi$
$132$	−3.17154			−0.276047
$133$	−17.3624	−	0.711336i	−1.50551	−	0.0616806i
$134$	−1.83777			−0.158759
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−5.78545	−	10.0207i	−0.496098	−	0.859267i
$137$	−11.0712	−	19.1759i	−0.945877	−	1.63831i	−0.753985	−	0.656892i	$-0.771871\pi$
$137$	−11.0712	−	19.1759i	−0.945877	−	1.63831i	−0.191892	−	0.981416i	$-0.561462\pi$
$138$	3.78713	−	6.55950i	0.322382	−	0.558382i
$139$	13.7069			1.16260			0.581300	−	0.813689i	$-0.302544\pi$
$139$	13.7069			1.16260			0.581300	+	0.813689i	$0.302544\pi$
$140$	−3.89457	−	7.43257i	−0.329151	−	0.628167i
$141$	7.30611			0.615286
$142$	8.68065	−	15.0353i	0.728464	−	1.26174i
$143$	−0.231929	−	0.401713i	−0.0193949	−	0.0335929i
$144$	0.142200	+	0.246298i	0.0118500	+	0.0205248i
$145$	4.70367	−	8.14700i	0.390619	−	0.676571i
$146$	−26.8900			−2.22544
$147$	6.97654	+	0.572618i	0.575415	+	0.0472287i
$148$	26.3746			2.16798
$149$	6.04902	−	10.4772i	0.495555	−	0.858326i	−0.504432	−	0.863451i	$-0.668298\pi$
$149$	6.04902	−	10.4772i	0.495555	−	0.858326i	0.999987	+	0.00512547i	$0.00163149\pi$
$150$	−1.13705	−	1.96943i	−0.0928399	−	0.160803i
$151$	−0.727907	−	1.26077i	−0.0592362	−	0.102600i	0.834887	−	0.550422i	$-0.185533\pi$
$151$	−0.727907	−	1.26077i	−0.0592362	−	0.102600i	−0.894123	+	0.447822i	$0.852200\pi$
$152$	−8.74909	+	15.1539i	−0.709645	+	1.22914i
$153$	4.34309			0.351118
$154$	−2.79253	−	5.32941i	−0.225029	−	0.429456i
$155$	4.49533			0.361074
$156$	0.735573	−	1.27405i	0.0588930	−	0.102006i
$157$	2.51079	+	4.34881i	0.200383	+	0.347073i	0.948652	−	0.316322i	$-0.102448\pi$
$157$	2.51079	+	4.34881i	0.200383	+	0.347073i	−0.748269	+	0.663395i	$0.769115\pi$
$158$	3.24408	+	5.61891i	0.258085	+	0.447017i
$159$	0.362436	−	0.627758i	0.0287431	−	0.0497845i
$160$	5.97517			0.472379
$161$	8.80471	+	0.360728i	0.693908	+	0.0284294i
$162$	2.27410			0.178670
$163$	−11.3582	+	19.6729i	−0.889641	+	1.54090i	−0.0493408	+	0.998782i	$0.515712\pi$
$163$	−11.3582	+	19.6729i	−0.889641	+	1.54090i	−0.840300	+	0.542121i	$0.817621\pi$
$164$	−18.1440	−	31.4263i	−1.41681	−	2.45398i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	−9.70413	+	16.8080i	−0.753187	+	1.30456i
$167$	−7.64931			−0.591921			−0.295961	−	0.955200i	$-0.595640\pi$
$167$	−7.64931			−0.591921			−0.295961	+	0.955200i	$0.595640\pi$
$168$	3.77135	−	5.95508i	0.290966	−	0.459444i
$169$	−12.7848			−0.983449
$170$	4.93831	−	8.55341i	0.378751	−	0.656016i
$171$	−3.28394	−	5.68794i	−0.251129	−	0.434968i
$172$	17.5842	+	30.4568i	1.34078	+	2.32231i
$173$	8.28338	−	14.3472i	0.629774	−	1.09080i	−0.357823	−	0.933789i	$-0.616481\pi$
$173$	8.28338	−	14.3472i	0.629774	−	1.09080i	0.987597	−	0.157011i	$-0.0501858\pi$
$174$	21.3933			1.62182
$175$	1.41556	−	2.23521i	0.107006	−	0.168966i
$176$	0.284400			0.0214375
$177$	−1.49762	+	2.59395i	−0.112568	+	0.194973i
$178$	−16.8626	−	29.2069i	−1.26391	−	2.18915i
$179$	3.75676	+	6.50690i	0.280794	+	0.486349i	0.971580	−	0.236710i	$-0.0760690\pi$
$179$	3.75676	+	6.50690i	0.280794	+	0.486349i	−0.690787	+	0.723058i	$0.742736\pi$
$180$	1.58577	−	2.74664i	0.118196	−	0.204722i
$181$	5.79006			0.430372			0.215186	−	0.976573i	$-0.430964\pi$
$181$	5.79006			0.430372			0.215186	+	0.976573i	$0.430964\pi$
$182$	2.78856	+	0.114247i	0.206702	+	0.00846856i
$183$	1.25173			0.0925308
$184$	4.43679	−	7.68474i	0.327084	−	0.566526i
$185$	4.15801	+	7.20188i	0.305703	+	0.529493i
$186$	5.11143	+	8.85325i	0.374788	+	0.649152i
$187$	2.17154	−	3.76122i	0.158799	−	0.275048i
$188$	23.1717			1.68997
$189$	1.22797	+	2.34352i	0.0893218	+	0.170466i
$190$	−14.9360			−1.08357
$191$	3.70142	−	6.41105i	0.267825	−	0.463887i	−0.700475	−	0.713677i	$-0.747028\pi$
$191$	3.70142	−	6.41105i	0.267825	−	0.463887i	0.968300	+	0.249790i	$0.0803616\pi$
$192$	6.50968	+	11.2751i	0.469796	+	0.813710i
$193$	−3.40056	−	5.88995i	−0.244778	−	0.423968i	0.717291	−	0.696773i	$-0.245382\pi$
$193$	−3.40056	−	5.88995i	−0.244778	−	0.423968i	−0.962069	+	0.272806i	$0.912048\pi$
$194$	−11.5791	+	20.0556i	−0.831333	+	1.43991i
$195$	0.463858			0.0332176
$196$	22.1264	+	1.81608i	1.58046	+	0.129720i
$197$	−13.0948			−0.932968			−0.466484	−	0.884530i	$-0.654479\pi$
$197$	−13.0948			−0.932968			−0.466484	+	0.884530i	$0.654479\pi$
$198$	1.13705	−	1.96943i	0.0808067	−	0.139961i
$199$	3.01934	+	5.22965i	0.214035	+	0.370720i	0.952974	−	0.303053i	$-0.0980059\pi$
$199$	3.01934	+	5.22965i	0.214035	+	0.370720i	−0.738938	+	0.673773i	$0.764673\pi$
$200$	−1.33210	−	2.30727i	−0.0941940	−	0.163149i
$201$	0.404064	−	0.699859i	0.0285005	−	0.0493643i
$202$	−26.1764			−1.84177
$203$	11.5520	+	22.0463i	0.810788	+	1.54735i
$204$	13.7743			0.964393
$205$	5.72087	−	9.90883i	0.399563	−	0.692063i
$206$	−16.4737	−	28.5334i	−1.14778	−	1.98801i
$207$	1.66533	+	2.88443i	0.115748	+	0.200482i
$208$	−0.0659606	+	0.114247i	−0.00457355	+	0.00792161i
$209$	−6.56787			−0.454309
$210$	6.01167	+	0.246298i	0.414844	+	0.0169961i
$211$	−14.0025			−0.963970			−0.481985	−	0.876179i	$-0.660084\pi$
$211$	−14.0025			−0.963970			−0.481985	+	0.876179i	$0.660084\pi$
$212$	1.14948	−	1.99096i	0.0789468	−	0.136740i
$213$	3.81718	+	6.61154i	0.261549	+	0.453016i
$214$	−21.9213	−	37.9689i	−1.49851	−	2.59550i
$215$	−5.54437	+	9.60314i	−0.378123	+	0.654929i
$216$	2.66421			0.181277
$217$	−6.36342	+	10.0480i	−0.431977	+	0.682105i
$218$	−5.73550			−0.388457
$219$	5.91223	−	10.2403i	0.399512	−	0.691974i
$220$	−1.58577	−	2.74664i	−0.106913	−	0.185178i
$221$	1.00729	+	1.74467i	0.0677575	+	0.117359i
$222$	−9.45573	+	16.3778i	−0.634627	+	1.09921i
$223$	22.8887			1.53274			0.766371	−	0.642399i	$-0.222061\pi$
$223$	22.8887			1.53274			0.766371	+	0.642399i	$0.222061\pi$
$224$	−8.45823	+	13.3558i	−0.565139	+	0.892372i
$225$	1.00000			0.0666667
$226$	18.1995	−	31.5225i	1.21061	−	2.09684i
$227$	1.79083	+	3.10181i	0.118862	+	0.205875i	0.919317	−	0.393518i	$-0.128742\pi$
$227$	1.79083	+	3.10181i	0.118862	+	0.205875i	−0.800455	+	0.599393i	$0.795409\pi$
$228$	−10.4151	−	18.0396i	−0.689760	−	1.19470i
$229$	12.6447	−	21.9013i	0.835588	−	1.44728i	−0.0579626	−	0.998319i	$-0.518460\pi$
$229$	12.6447	−	21.9013i	0.835588	−	1.44728i	0.893551	−	0.448962i	$-0.148206\pi$
$230$	7.57426			0.499432
$231$	2.64353	+	0.108305i	0.173932	+	0.00712597i
$232$	25.0631			1.64548
$233$	3.23286	−	5.59948i	0.211792	−	0.366834i	−0.740484	−	0.672074i	$-0.765404\pi$
$233$	3.23286	−	5.59948i	0.211792	−	0.366834i	0.952275	+	0.305240i	$0.0987368\pi$
$234$	0.527431	+	0.913536i	0.0344792	+	0.0597197i
$235$	3.65306	+	6.32728i	0.238299	+	0.412746i
$236$	−4.74975	+	8.22682i	−0.309183	+	0.535520i
$237$	−2.85306			−0.185326
$238$	12.1282	+	23.1461i	0.786155	+	1.50034i
$239$	18.2972			1.18355			0.591775	−	0.806103i	$-0.298427\pi$
$239$	18.2972			1.18355			0.591775	+	0.806103i	$0.298427\pi$
$240$	−0.142200	+	0.246298i	−0.00917897	+	0.0158984i
$241$	12.2111	+	21.1503i	0.786588	+	1.36241i	0.928046	+	0.372466i	$0.121488\pi$
$241$	12.2111	+	21.1503i	0.786588	+	1.36241i	−0.141458	+	0.989944i	$0.545179\pi$
$242$	−1.13705	−	1.96943i	−0.0730924	−	0.126600i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.96993			0.254149
$245$	2.99237	+	6.32817i	0.191175	+	0.404292i
$246$	26.0197			1.65895
$247$	1.52328	−	2.63840i	0.0969240	−	0.167877i
$248$	5.98826	+	10.3720i	0.380255	+	0.658620i
$249$	−4.26723	−	7.39107i	−0.270425	−	0.468390i
$250$	1.13705	−	1.96943i	0.0719134	−	0.124558i
$251$	2.85417			0.180154			0.0900769	−	0.995935i	$-0.471289\pi$
$251$	2.85417			0.180154			0.0900769	+	0.995935i	$0.471289\pi$
$252$	3.89457	+	7.43257i	0.245335	+	0.468208i
$253$	3.33066			0.209397
$254$	−14.5589	+	25.2167i	−0.913504	+	1.58224i
$255$	2.17154	+	3.76122i	0.135987	+	0.235537i
$256$	7.05757	+	12.2241i	0.441098	+	0.764005i
$257$	−0.0183153	+	0.0317230i	−0.00114248	+	0.00197883i	−0.866596	−	0.499010i	$-0.833697\pi$
$257$	−0.0183153	+	0.0317230i	−0.00114248	+	0.00197883i	0.865454	+	0.500989i	$0.167030\pi$
$258$	−25.2170			−1.56994
$259$	−21.9837	−	0.900669i	−1.36600	−	0.0559649i
$260$	1.47115			0.0912366
$261$	−4.70367	+	8.14700i	−0.291150	+	0.504287i
$262$	−5.72014	−	9.90757i	−0.353391	−	0.612092i
$263$	12.0656	+	20.8982i	0.743996	+	1.28864i	0.950662	+	0.310227i	$0.100405\pi$
$263$	12.0656	+	20.8982i	0.743996	+	1.28864i	−0.206666	+	0.978411i	$0.566261\pi$
$264$	1.33210	−	2.30727i	0.0819854	−	0.142003i
$265$	0.724873			0.0445286
$266$	21.1429	−	33.3852i	1.29635	−	2.04698i
$267$	14.8301			0.907590
$268$	1.28151	−	2.21963i	0.0782804	−	0.135586i
$269$	7.75491	+	13.4319i	0.472825	+	0.818957i	0.999516	−	0.0310995i	$-0.00990088\pi$
$269$	7.75491	+	13.4319i	0.472825	+	0.818957i	−0.526691	+	0.850057i	$0.676568\pi$
$270$	1.13705	+	1.96943i	0.0691987	+	0.119856i
$271$	−9.58797	+	16.6068i	−0.582428	+	1.00879i	0.412763	+	0.910838i	$0.364564\pi$
$271$	−9.58797	+	16.6068i	−0.582428	+	1.00879i	−0.995191	+	0.0979558i	$0.968770\pi$
$272$	−1.23517			−0.0748934
$273$	−0.656620	+	1.03682i	−0.0397404	+	0.0627514i
$274$	50.3541			3.04200
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	5.28166	+	9.14811i	0.317919	+	0.550651i
$277$	−3.83072	−	6.63501i	−0.230166	−	0.398659i	0.727691	−	0.685905i	$-0.240594\pi$
$277$	−3.83072	−	6.63501i	−0.230166	−	0.398659i	−0.957857	+	0.287246i	$0.907260\pi$
$278$	−15.5854	+	26.9947i	−0.934750	+	1.61904i
$279$	−4.49533			−0.269129
$280$	7.04293	+	0.288548i	0.420895	+	0.0172441i
$281$	−15.6678			−0.934660			−0.467330	−	0.884083i	$-0.654784\pi$
$281$	−15.6678			−0.934660			−0.467330	+	0.884083i	$0.654784\pi$
$282$	−8.30743	+	14.3889i	−0.494700	+	0.856846i
$283$	−4.81572	−	8.34107i	−0.286265	−	0.495825i	0.686650	−	0.726988i	$-0.259080\pi$
$283$	−4.81572	−	8.34107i	−0.286265	−	0.495825i	−0.972915	+	0.231163i	$0.925747\pi$
$284$	12.1063	+	20.9688i	0.718379	+	1.24427i
$285$	3.28394	−	5.68794i	0.194524	−	0.336925i
$286$	1.05486			0.0623752
$287$	14.0501	+	26.8139i	0.829353	+	1.58278i
$288$	−5.97517			−0.352091
$289$	−0.931200	+	1.61289i	−0.0547765	+	0.0948756i
$290$	10.6966	+	18.5271i	0.628128	+	1.08795i
$291$	−5.09173	−	8.81914i	−0.298483	−	0.516987i
$292$	18.7509	−	32.4775i	1.09731	−	1.90060i
$293$	−4.72029			−0.275762			−0.137881	−	0.990449i	$-0.544029\pi$
$293$	−4.72029			−0.275762			−0.137881	+	0.990449i	$0.544029\pi$
$294$	−9.06042	+	13.0887i	−0.528414	+	0.763349i
$295$	−2.99523			−0.174389
$296$	−11.0778	+	19.1873i	−0.643884	+	1.11524i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	13.7561	+	23.8262i	0.796868	+	1.38022i
$299$	−0.772476	+	1.33797i	−0.0446735	+	0.0773767i
$300$	3.17154			0.183109
$301$	−13.6167	−	25.9867i	−0.784852	−	1.49785i
$302$	3.31067			0.190508
$303$	5.75533	−	9.96853i	0.330635	−	0.572677i
$304$	0.933951	+	1.61765i	0.0535658	+	0.0927786i
$305$	0.625867	+	1.08403i	0.0358370	+	0.0620715i
$306$	−4.93831	+	8.55341i	−0.282305	+	0.488966i
$307$	0.747214			0.0426458			0.0213229	−	0.999773i	$-0.493212\pi$
$307$	0.747214			0.0426458			0.0213229	+	0.999773i	$0.493212\pi$
$308$	8.38408	+	0.343495i	0.477727	+	0.0195725i
$309$	14.4881			0.824201
$310$	−5.11143	+	8.85325i	−0.290309	+	0.502831i
$311$	−2.38343	−	4.12822i	−0.135152	−	0.234090i	0.790504	−	0.612457i	$-0.209819\pi$
$311$	−2.38343	−	4.12822i	−0.135152	−	0.234090i	−0.925655	+	0.378368i	$0.876486\pi$
$312$	0.617908	+	1.07025i	0.0349821	+	0.0605908i
$313$	15.0070	−	25.9930i	0.848248	−	1.46921i	−0.0345217	−	0.999404i	$-0.510991\pi$
$313$	15.0070	−	25.9930i	0.848248	−	1.46921i	0.882770	−	0.469805i	$-0.155676\pi$
$314$	−11.4196			−0.644444
$315$	−1.41556	+	2.23521i	−0.0797579	+	0.125940i
$316$	−9.04862			−0.509024
$317$	5.54842	−	9.61015i	0.311631	−	0.539760i	−0.667085	−	0.744982i	$-0.732458\pi$
$317$	5.54842	−	9.61015i	0.311631	−	0.539760i	0.978716	+	0.205222i	$0.0657915\pi$
$318$	0.824217	+	1.42759i	0.0462198	+	0.0800551i
$319$	4.70367	+	8.14700i	0.263355	+	0.456144i
$320$	−6.50968	+	11.2751i	−0.363902	+	0.630297i
$321$	19.2791			1.07605
$322$	−10.7218	+	16.9301i	−0.597504	+	0.943477i
$323$	28.5248			1.58716
$324$	−1.58577	+	2.74664i	−0.0880984	+	0.152591i
$325$	0.231929	+	0.401713i	0.0128651	+	0.0222830i
$326$	−25.8297	−	44.7383i	−1.43057	−	2.47782i
$327$	1.26105	−	2.18420i	0.0697360	−	0.120786i
$328$	30.4832			1.68315
$329$	−19.3140	−	0.791292i	−1.06481	−	0.0436253i
$330$	2.27410			0.125185
$331$	−0.524756	+	0.908904i	−0.0288432	+	0.0499579i	−0.880087	−	0.474813i	$-0.842516\pi$
$331$	−0.524756	+	0.908904i	−0.0288432	+	0.0499579i	0.851243	+	0.524771i	$0.175849\pi$
$332$	−13.5337	−	23.4411i	−0.742759	−	1.28650i
$333$	−4.15801	−	7.20188i	−0.227857	−	0.394661i
$334$	8.69766	−	15.0648i	0.475915	−	0.824309i
$335$	0.808128			0.0441527
$336$	−0.349235	−	0.666497i	−0.0190523	−	0.0363604i
$337$	−3.52737			−0.192148			−0.0960740	−	0.995374i	$-0.530629\pi$
$337$	−3.52737			−0.192148			−0.0960740	+	0.995374i	$0.530629\pi$
$338$	14.5370	−	25.1788i	0.790709	−	1.36955i
$339$	8.00294	+	13.8615i	0.434660	+	0.752853i
$340$	6.88714	+	11.9289i	0.373508	+	0.646934i
$341$	−2.24767	+	3.89307i	−0.121718	+	0.210822i
$342$	14.9360			0.807647
$343$	−18.3807	−	2.26933i	−0.992465	−	0.122532i
$344$	−29.5428			−1.59284
$345$	−1.66533	+	2.88443i	−0.0896583	+	0.155293i
$346$	18.8373	+	32.6271i	1.01270	+	1.75404i
$347$	5.43046	+	9.40584i	0.291523	+	0.504932i	0.974170	−	0.225816i	$-0.0725048\pi$
$347$	5.43046	+	9.40584i	0.291523	+	0.504932i	−0.682647	+	0.730748i	$0.739171\pi$
$348$	−14.9179	+	25.8386i	−0.799683	+	1.38509i
$349$	15.8916			0.850660			0.425330	−	0.905038i	$-0.360158\pi$
$349$	15.8916			0.850660			0.425330	+	0.905038i	$0.360158\pi$
$350$	2.79253	+	5.32941i	0.149267	+	0.284869i
$351$	−0.463858			−0.0247589
$352$	−2.98759	+	5.17465i	−0.159239	+	0.275810i
$353$	2.18415	+	3.78306i	0.116251	+	0.201352i	0.918279	−	0.395934i	$-0.129579\pi$
$353$	2.18415	+	3.78306i	0.116251	+	0.201352i	−0.802028	+	0.597286i	$0.796246\pi$
$354$	−3.40573	−	5.89890i	−0.181013	−	0.313523i
$355$	−3.81718	+	6.61154i	−0.202595	+	0.350904i
$356$	47.0344			2.49282
$357$	−11.4811	−	0.470380i	−0.607644	−	0.0248951i
$358$	−17.0865			−0.903051
$359$	14.3265	−	24.8143i	0.756126	−	1.30965i	−0.188686	−	0.982037i	$-0.560423\pi$
$359$	14.3265	−	24.8143i	0.756126	−	1.30965i	0.944812	−	0.327612i	$-0.106244\pi$
$360$	1.33210	+	2.30727i	0.0702081	+	0.121604i
$361$	−12.0685	−	20.9032i	−0.635182	−	1.10017i
$362$	−6.58360	+	11.4031i	−0.346026	+	0.599335i
$363$	1.00000			0.0524864
$364$	−2.08250	+	3.28833i	−0.109153	+	0.172355i
$365$	11.8245			0.618921
$366$	−1.42329	+	2.46520i	−0.0743963	+	0.128858i
$367$	−12.7303	−	22.0495i	−0.664516	−	1.15098i	−0.979416	−	0.201851i	$-0.935304\pi$
$367$	−12.7303	−	22.0495i	−0.664516	−	1.15098i	0.314900	−	0.949125i	$-0.398029\pi$
$368$	−0.473619	−	0.820333i	−0.0246891	−	0.0427628i
$369$	−5.72087	+	9.90883i	−0.297816	+	0.515833i
$370$	−18.9115			−0.983161
$371$	−1.02610	+	1.62025i	−0.0532726	+	0.0841190i
$372$	−14.2571			−0.739199
$373$	9.14781	−	15.8445i	0.473656	−	0.820396i	−0.525889	−	0.850553i	$-0.676267\pi$
$373$	9.14781	−	15.8445i	0.473656	−	0.820396i	0.999545	+	0.0301572i	$0.00960079\pi$
$374$	4.93831	+	8.55341i	0.255354	+	0.442286i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−9.73251	+	16.8572i	−0.501916	+	0.869344i
$377$	−4.36367			−0.224741
$378$	−6.01167	−	0.246298i	−0.309207	−	0.0126682i
$379$	28.8124			1.47999			0.739996	−	0.672612i	$-0.234828\pi$
$379$	28.8124			1.47999			0.739996	+	0.672612i	$0.234828\pi$
$380$	10.4151	−	18.0396i	0.534286	−	0.925410i
$381$	−6.40203	−	11.0886i	−0.327986	−	0.568088i
$382$	8.41741	+	14.5794i	0.430672	+	0.745946i
$383$	8.39980	−	14.5489i	0.429210	−	0.743413i	−0.567594	−	0.823309i	$-0.692125\pi$
$383$	8.39980	−	14.5489i	0.429210	−	0.743413i	0.996803	+	0.0798960i	$0.0254588\pi$
$384$	−17.6570			−0.901056
$385$	1.22797	+	2.34352i	0.0625832	+	0.119437i
$386$	15.4665			0.787222
$387$	5.54437	−	9.60314i	0.281836	−	0.488155i
$388$	−16.1487	−	27.9703i	−0.819824	−	1.41998i
$389$	3.32662	+	5.76187i	0.168666	+	0.292138i	0.937951	−	0.346767i	$-0.112721\pi$
$389$	3.32662	+	5.76187i	0.168666	+	0.292138i	−0.769285	+	0.638906i	$0.779387\pi$
$390$	−0.527431	+	0.913536i	−0.0267075	+	0.0462587i
$391$	−14.4653			−0.731543
$392$	−10.6147	+	15.3340i	−0.536122	+	0.774484i
$393$	5.03068			0.253764
$394$	14.8895	−	25.7893i	0.750122	−	1.29925i
$395$	−1.42653	−	2.47083i	−0.0717766	−	0.124321i
$396$	1.58577	+	2.74664i	0.0796880	+	0.138024i
$397$	−11.9270	+	20.6582i	−0.598601	+	1.03681i	0.394427	+	0.918927i	$0.370943\pi$
$397$	−11.9270	+	20.6582i	−0.598601	+	1.03681i	−0.993028	+	0.117880i	$0.962390\pi$
$398$	−13.7326			−0.688352
$399$	8.06516	+	15.3919i	0.403763	+	0.770561i
$400$	−0.284400			−0.0142200
$401$	19.5729	−	33.9013i	0.977425	−	1.69295i	0.305737	−	0.952116i	$-0.401097\pi$
$401$	19.5729	−	33.9013i	0.977425	−	1.69295i	0.671689	−	0.740834i	$-0.265569\pi$
$402$	0.918883	+	1.59155i	0.0458297	+	0.0793794i
$403$	−1.04260	−	1.80583i	−0.0519355	−	0.0899550i
$404$	18.2533	−	31.6156i	0.908135	−	1.57294i
$405$	−1.00000			−0.0496904
$406$	−56.5538	−	2.31701i	−2.80672	−	0.114991i
$407$	−8.31601			−0.412210
$408$	−5.78545	+	10.0207i	−0.286422	+	0.496098i
$409$	−5.32055	−	9.21547i	−0.263084	−	0.455675i	0.703976	−	0.710224i	$-0.251406\pi$
$409$	−5.32055	−	9.21547i	−0.263084	−	0.455675i	−0.967060	+	0.254549i	$0.918073\pi$
$410$	13.0098	+	22.5337i	0.642510	+	1.11286i
$411$	−11.0712	+	19.1759i	−0.546103	+	0.945877i
$412$	45.9497			2.26378
$413$	4.23994	−	6.69499i	0.208634	−	0.329439i
$414$	−7.57426			−0.372254
$415$	4.26723	−	7.39107i	0.209470	−	0.362813i
$416$	−1.38582	−	2.40030i	−0.0679452	−	0.117685i
$417$	−6.85343	−	11.8705i	−0.335614	−	0.581300i
$418$	7.46801	−	12.9350i	0.365272	−	0.632670i
$419$	−14.4810			−0.707443			−0.353722	−	0.935351i	$-0.615084\pi$
$419$	−14.4810			−0.707443			−0.353722	+	0.935351i	$0.615084\pi$
$420$	−4.48952	+	7.08908i	−0.219066	+	0.345912i
$421$	−5.39833			−0.263098			−0.131549	−	0.991310i	$-0.541995\pi$
$421$	−5.39833			−0.263098			−0.131549	+	0.991310i	$0.541995\pi$
$422$	15.9215	−	27.5769i	0.775048	−	1.34242i
$423$	−3.65306	−	6.32728i	−0.177618	−	0.307643i
$424$	0.965606	+	1.67248i	0.0468940	+	0.0812228i
$425$	−2.17154	+	3.76122i	−0.105335	+	0.182446i
$426$	−17.3613			−0.841158
$427$	−3.30900	−	0.135569i	−0.160134	−	0.00656067i
$428$	61.1445			2.95553
$429$	−0.231929	+	0.401713i	−0.0111976	+	0.0193949i
$430$	−12.6085	−	21.8385i	−0.608035	−	1.05315i
$431$	−3.52647	−	6.10803i	−0.169864	−	0.294213i	0.768508	−	0.639840i	$-0.221000\pi$
$431$	−3.52647	−	6.10803i	−0.169864	−	0.294213i	−0.938372	+	0.345627i	$0.887666\pi$
$432$	0.142200	−	0.246298i	0.00684160	−	0.0118500i
$433$	−18.6652			−0.896992			−0.448496	−	0.893785i	$-0.648040\pi$
$433$	−18.6652			−0.896992			−0.448496	+	0.893785i	$0.648040\pi$
$434$	−12.5534	−	23.9575i	−0.602581	−	1.14999i
$435$	−9.40734			−0.451048
$436$	3.99946	−	6.92728i	0.191540	−	0.331756i
$437$	10.9377	+	18.9446i	0.523220	+	0.906243i
$438$	13.4450	+	23.2875i	0.642428	+	1.11272i
$439$	16.1328	−	27.9428i	0.769976	−	1.33364i	−0.167600	−	0.985855i	$-0.553602\pi$
$439$	16.1328	−	27.9428i	0.769976	−	1.33364i	0.937575	−	0.347782i	$-0.113065\pi$
$440$	2.66421			0.127011
$441$	−2.99237	−	6.32817i	−0.142494	−	0.301341i
$442$	−4.58135			−0.217913
$443$	1.89384	−	3.28023i	0.0899793	−	0.155849i	−0.817523	−	0.575896i	$-0.804653\pi$
$443$	1.89384	−	3.28023i	0.0899793	−	0.155849i	0.907502	+	0.420047i	$0.137987\pi$
$444$	−13.1873	−	22.8411i	−0.625842	−	1.08399i
$445$	7.41507	+	12.8433i	0.351508	+	0.608830i
$446$	−26.0256	+	45.0777i	−1.23235	+	2.13449i
$447$	−12.0980			−0.572217
$448$	−15.9874	−	30.5111i	−0.755334	−	1.44152i
$449$	7.69760			0.363272			0.181636	−	0.983366i	$-0.441861\pi$
$449$	7.69760			0.363272			0.181636	+	0.983366i	$0.441861\pi$
$450$	−1.13705	+	1.96943i	−0.0536011	+	0.0928399i
$451$	5.72087	+	9.90883i	0.269385	+	0.466589i
$452$	25.3817	+	43.9623i	1.19385	+	2.06781i
$453$	−0.727907	+	1.26077i	−0.0342000	+	0.0592362i
$454$	−8.14508			−0.382267
$455$	−1.22622	−	0.0502383i	−0.0574863	−	0.00235521i
$456$	17.4982			0.819428
$457$	16.1093	−	27.9021i	0.753561	−	1.30521i	−0.192525	−	0.981292i	$-0.561668\pi$
$457$	16.1093	−	27.9021i	0.753561	−	1.30521i	0.946086	−	0.323914i	$-0.104999\pi$
$458$	28.7554	+	49.8059i	1.34365	+	2.32728i
$459$	−2.17154	−	3.76122i	−0.101359	−	0.175559i
$460$	−5.28166	+	9.14811i	−0.246259	+	0.426533i
$461$	−12.6816			−0.590642			−0.295321	−	0.955398i	$-0.595427\pi$
$461$	−12.6816			−0.590642			−0.295321	+	0.955398i	$0.595427\pi$
$462$	−3.21913	+	5.08311i	−0.149768	+	0.236488i
$463$	4.24429			0.197249			0.0986244	−	0.995125i	$-0.468556\pi$
$463$	4.24429			0.197249			0.0986244	+	0.995125i	$0.468556\pi$
$464$	1.33772	−	2.31701i	0.0621023	−	0.107564i
$465$	−2.24767	−	3.89307i	−0.104233	−	0.180537i
$466$	7.35185	+	12.7338i	0.340568	+	0.589881i
$467$	11.2190	−	19.4319i	0.519153	−	0.899199i	−0.480599	−	0.876940i	$-0.659581\pi$
$467$	11.2190	−	19.4319i	0.519153	−	0.899199i	0.999752	−	0.0222591i	$-0.00708588\pi$
$468$	−1.47115			−0.0680038
$469$	−1.14395	+	1.80634i	−0.0528229	+	0.0834090i
$470$	−16.6149			−0.766386
$471$	2.51079	−	4.34881i	0.115691	−	0.200383i
$472$	−3.98996	−	6.91082i	−0.183653	−	0.318096i
$473$	−5.54437	−	9.60314i	−0.254931	−	0.441553i
$474$	3.24408	−	5.61891i	0.149006	−	0.258085i
$475$	6.56787			0.301355
$476$	−36.4128	−	1.49183i	−1.66898	−	0.0683779i
$477$	−0.724873			−0.0331896
$478$	−20.8049	+	36.0351i	−0.951594	+	1.64821i
$479$	4.00758	+	6.94133i	0.183111	+	0.317157i	0.942938	−	0.332967i	$-0.108050\pi$
$479$	4.00758	+	6.94133i	0.183111	+	0.317157i	−0.759827	+	0.650125i	$0.774717\pi$
$480$	−2.98759	−	5.17465i	−0.136364	−	0.236189i
$481$	1.92873	−	3.34065i	0.0879423	−	0.152321i
$482$	−55.5387			−2.52972
$483$	−4.08995	−	7.80546i	−0.186099	−	0.355161i
$484$	3.17154			0.144161
$485$	5.09173	−	8.81914i	0.231204	−	0.400457i
$486$	−1.13705	−	1.96943i	−0.0515777	−	0.0893352i
$487$	−1.93043	−	3.34360i	−0.0874761	−	0.151513i	0.818968	−	0.573840i	$-0.194547\pi$
$487$	−1.93043	−	3.34360i	−0.0874761	−	0.151513i	−0.906444	+	0.422327i	$0.861213\pi$
$488$	−1.66744	+	2.88809i	−0.0754815	+	0.130738i
$489$	22.7164			1.02727
$490$	−15.8654	−	1.30219i	−0.716724	−	0.0588270i
$491$	−22.6560			−1.02245			−0.511226	−	0.859446i	$-0.670808\pi$
$491$	−22.6560			−1.02245			−0.511226	+	0.859446i	$0.670808\pi$
$492$	−18.1440	+	31.4263i	−0.817994	+	1.41681i
$493$	−20.4285	−	35.3831i	−0.920051	−	1.59358i
$494$	3.46410	+	5.99999i	0.155857	+	0.269952i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	1.27847			0.0574051
$497$	−9.37477	−	17.8913i	−0.420516	−	0.802533i
$498$	19.4083			0.869705
$499$	−12.2964	+	21.2980i	−0.550464	+	0.953432i	0.447777	+	0.894145i	$0.352216\pi$
$499$	−12.2964	+	21.2980i	−0.550464	+	0.953432i	−0.998241	+	0.0592864i	$0.981117\pi$
$500$	1.58577	+	2.74664i	0.0709179	+	0.122833i
$501$	3.82466	+	6.62450i	0.170873	+	0.295961i
$502$	−3.24534	+	5.62110i	−0.144847	+	0.250882i
$503$	−13.2299			−0.589892			−0.294946	−	0.955514i	$-0.595302\pi$
$503$	−13.2299			−0.589892			−0.294946	+	0.955514i	$0.595302\pi$
$504$	−7.04293	−	0.288548i	−0.313717	−	0.0128530i
$505$	11.5107			0.512218
$506$	−3.78713	+	6.55950i	−0.168358	+	0.291605i
$507$	6.39242	+	11.0720i	0.283897	+	0.491724i
$508$	−20.3043	−	35.1681i	−0.900858	−	1.56033i
$509$	10.3783	−	17.9758i	0.460012	−	0.796765i	−0.538949	−	0.842339i	$-0.681178\pi$
$509$	10.3783	−	17.9758i	0.460012	−	0.796765i	0.998961	+	0.0455740i	$0.0145117\pi$
$510$	−9.87662			−0.437344
$511$	−16.7383	+	26.4302i	−0.740457	+	1.16920i
$512$	3.21474			0.142073
$513$	−3.28394	+	5.68794i	−0.144989	+	0.251129i
$514$	−0.0416508	−	0.0721413i	−0.00183714	−	0.00318202i
$515$	7.24406	+	12.5471i	0.319212	+	0.552891i
$516$	17.5842	−	30.4568i	0.774102	−	1.34078i
$517$	−7.30611			−0.321323
$518$	26.7704	−	42.2712i	1.17622	−	1.85729i
$519$	−16.5668			−0.727200
$520$	−0.617908	+	1.07025i	−0.0270970	+	0.0469335i
$521$	−14.6786	−	25.4242i	−0.643083	−	1.11385i	−0.984741	−	0.174028i	$-0.944322\pi$
$521$	−14.6786	−	25.4242i	−0.643083	−	1.11385i	0.341657	−	0.939825i	$-0.389012\pi$
$522$	−10.6966	−	18.5271i	−0.468179	−	0.810910i
$523$	−7.11710	+	12.3272i	−0.311209	+	0.539030i	−0.978624	−	0.205656i	$-0.934067\pi$
$523$	−7.11710	+	12.3272i	−0.311209	+	0.539030i	0.667415	+	0.744686i	$0.267401\pi$
$524$	15.9550			0.696998
$525$	−2.64353	−	0.108305i	−0.115373	−	0.00472683i
$526$	−54.8768			−2.39274
$527$	9.76181	−	16.9080i	0.425231	−	0.736522i
$528$	−0.142200	−	0.246298i	−0.00618846	−	0.0107187i
$529$	5.95336	+	10.3115i	0.258842	+	0.448327i
$530$	−0.824217	+	1.42759i	−0.0358017	+	0.0620104i
$531$	2.99523			0.129982
$532$	25.5790	+	48.8162i	1.10899	+	2.11645i
$533$	−5.30734			−0.229887
$534$	−16.8626	+	29.2069i	−0.729717	+	1.26391i
$535$	9.63955	+	16.6962i	0.416754	+	0.721839i
$536$	1.07651	+	1.86457i	0.0464982	+	0.0805372i
$537$	3.75676	−	6.50690i	0.162116	−	0.280794i
$538$	−35.2709			−1.52064
$539$	−6.97654	−	0.572618i	−0.300501	−	0.0246644i
$540$	−3.17154			−0.136481
$541$	−1.90722	+	3.30341i	−0.0819979	+	0.142024i	−0.904108	−	0.427304i	$-0.859463\pi$
$541$	−1.90722	+	3.30341i	−0.0819979	+	0.142024i	0.822110	+	0.569328i	$0.192797\pi$
$542$	−21.8040	−	37.7657i	−0.936563	−	1.62217i
$543$	−2.89503	−	5.01434i	−0.124238	−	0.215186i
$544$	12.9753	−	22.4740i	0.556313	−	0.963563i
$545$	2.52209			0.108035
$546$	−1.29534	−	2.47209i	−0.0554354	−	0.105796i
$547$	−1.73293			−0.0740948			−0.0370474	−	0.999314i	$-0.511795\pi$
$547$	−1.73293			−0.0740948			−0.0370474	+	0.999314i	$0.511795\pi$
$548$	−35.1128	+	60.8172i	−1.49995	+	2.59798i
$549$	−0.625867	−	1.08403i	−0.0267113	−	0.0462654i
$550$	1.13705	+	1.96943i	0.0484840	+	0.0839768i
$551$	−30.8931	+	53.5084i	−1.31609	+	2.27954i
$552$	−8.87357			−0.377684
$553$	7.54217	+	0.309002i	0.320726	+	0.0131401i
$554$	17.4229			0.740229
$555$	4.15801	−	7.20188i	0.176498	−	0.305703i
$556$	−21.7359	−	37.6478i	−0.921810	−	1.59662i
$557$	12.8600	+	22.2741i	0.544894	+	0.943785i	0.998614	+	0.0526401i	$0.0167636\pi$
$557$	12.8600	+	22.2741i	0.544894	+	0.943785i	−0.453719	+	0.891145i	$0.649903\pi$
$558$	5.11143	−	8.85325i	0.216384	−	0.374788i
$559$	5.14361			0.217551
$560$	0.402586	−	0.635695i	0.0170124	−	0.0268630i
$561$	−4.34309			−0.183365
$562$	17.8151	−	30.8566i	0.751483	−	1.30161i
$563$	10.8215	+	18.7435i	0.456074	+	0.789943i	0.998749	−	0.0499996i	$-0.0159220\pi$
$563$	10.8215	+	18.7435i	0.456074	+	0.789943i	−0.542676	+	0.839942i	$0.682589\pi$
$564$	−11.5858	−	20.0672i	−0.487851	−	0.844983i
$565$	−8.00294	+	13.8615i	−0.336686	+	0.583158i
$566$	21.9029			0.920647
$567$	1.41556	−	2.23521i	0.0594480	−	0.0938702i
$568$	−20.3395			−0.853427
$569$	−1.91234	+	3.31228i	−0.0801696	+	0.138858i	−0.903323	−	0.428962i	$-0.858880\pi$
$569$	−1.91234	+	3.31228i	−0.0801696	+	0.138858i	0.823153	+	0.567820i	$0.192213\pi$
$570$	7.46801	+	12.9350i	0.312800	+	0.541786i
$571$	10.4518	+	18.1031i	0.437396	+	0.757592i	0.997488	−	0.0708388i	$-0.0225676\pi$
$571$	10.4518	+	18.1031i	0.437396	+	0.757592i	−0.560092	+	0.828430i	$0.689234\pi$
$572$	−0.735573	+	1.27405i	−0.0307559	+	0.0532707i
$573$	−7.40284			−0.309258
$574$	−68.7839	−	2.81807i	−2.87098	−	0.117624i
$575$	−3.33066			−0.138898
$576$	6.50968	−	11.2751i	0.271237	−	0.469796i
$577$	−12.0499	−	20.8710i	−0.501644	−	0.868873i	−0.999998	−	0.00189953i	$-0.999395\pi$
$577$	−12.0499	−	20.8710i	−0.501644	−	0.868873i	0.498354	−	0.866974i	$-0.333938\pi$
$578$	−2.11764	−	3.66787i	−0.0880824	−	0.152563i
$579$	−3.40056	+	5.88995i	−0.141323	+	0.244778i
$580$	−29.8358			−1.23886
$581$	10.4801	+	20.0007i	0.434787	+	0.829769i
$582$	23.1583			0.959940
$583$	−0.362436	+	0.627758i	−0.0150106	+	0.0259991i
$584$	15.7514	+	27.2823i	0.651799	+	1.12895i
$585$	−0.231929	−	0.401713i	−0.00958909	−	0.0166088i
$586$	5.36721	−	9.29628i	0.221717	−	0.384026i
$587$	−1.71054			−0.0706014			−0.0353007	−	0.999377i	$-0.511239\pi$
$587$	−1.71054			−0.0706014			−0.0353007	+	0.999377i	$0.511239\pi$
$588$	−9.49043	−	20.0701i	−0.391379	−	0.827675i
$589$	−29.5248			−1.21655
$590$	3.40573	−	5.89890i	0.140212	−	0.242854i
$591$	6.54741	+	11.3405i	0.269325	+	0.466484i
$592$	1.18254	+	2.04821i	0.0486020	+	0.0841811i
$593$	10.3032	−	17.8457i	0.423103	−	0.732836i	−0.573138	−	0.819459i	$-0.694274\pi$
$593$	10.3032	−	17.8457i	0.423103	−	0.732836i	0.996241	+	0.0866229i	$0.0276075\pi$
$594$	−2.27410			−0.0933076
$595$	−5.33319	−	10.1781i	−0.218639	−	0.417262i
$596$	−38.3694			−1.57167
$597$	3.01934	−	5.22965i	0.123573	−	0.214035i
$598$	−1.75669	−	3.04268i	−0.0718364	−	0.124424i
$599$	−7.04256	−	12.1981i	−0.287751	−	0.498399i	0.685522	−	0.728052i	$-0.259574\pi$
$599$	−7.04256	−	12.1981i	−0.287751	−	0.498399i	−0.973273	+	0.229653i	$0.926241\pi$
$600$	−1.33210	+	2.30727i	−0.0543830	+	0.0941940i
$601$	−23.5306			−0.959835			−0.479917	−	0.877314i	$-0.659333\pi$
$601$	−23.5306			−0.959835			−0.479917	+	0.877314i	$0.659333\pi$
$602$	66.6619	+	2.73113i	2.71694	+	0.111313i
$603$	−0.808128			−0.0329095
$604$	−2.30859	+	3.99859i	−0.0939351	+	0.162700i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	13.0882	+	22.6695i	0.531673	+	0.920884i
$607$	−7.66829	+	13.2819i	−0.311246	+	0.539095i	−0.978632	−	0.205617i	$-0.934080\pi$
$607$	−7.66829	+	13.2819i	−0.311246	+	0.539095i	0.667386	+	0.744712i	$0.267413\pi$
$608$	−39.2442			−1.59156
$609$	13.3167	−	21.0274i	0.539619	−	0.852075i
$610$	−2.84657			−0.115254
$611$	1.69450	−	2.93496i	0.0685521	−	0.118736i
$612$	−6.88714	−	11.9289i	−0.278396	−	0.482196i
$613$	−13.3258	−	23.0809i	−0.538223	−	0.932230i	−0.999000	−	0.0447136i	$-0.985762\pi$
$613$	−13.3258	−	23.0809i	−0.538223	−	0.932230i	0.460777	−	0.887516i	$-0.347571\pi$
$614$	−0.849621	+	1.47159i	−0.0342879	+	0.0593884i
$615$	−11.4417			−0.461375
$616$	−3.77135	+	5.95508i	−0.151952	+	0.239937i
$617$	11.3333			0.456261			0.228130	−	0.973631i	$-0.426739\pi$
$617$	11.3333			0.456261			0.228130	+	0.973631i	$0.426739\pi$
$618$	−16.4737	+	28.5334i	−0.662671	+	1.14778i
$619$	7.30754	+	12.6570i	0.293715	+	0.508729i	0.974685	−	0.223582i	$-0.0717751\pi$
$619$	7.30754	+	12.6570i	0.293715	+	0.508729i	−0.680970	+	0.732311i	$0.738442\pi$
$620$	−7.12857	−	12.3471i	−0.286290	−	0.495869i
$621$	1.66533	−	2.88443i	0.0668273	−	0.115748i
$622$	10.8403			0.434657
$623$	−39.2040	−	1.60618i	−1.57067	−	0.0643504i
$624$	0.131921			0.00528108
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	34.1276	+	59.1107i	1.36401	+	2.36254i
$627$	3.28394	+	5.68794i	0.131148	+	0.227155i
$628$	7.96307	−	13.7924i	0.317761	−	0.550379i
$629$	36.1172			1.44009
$630$	−2.79253	−	5.32941i	−0.111257	−	0.212329i
$631$	−3.66680			−0.145973			−0.0729866	−	0.997333i	$-0.523253\pi$
$631$	−3.66680			−0.145973			−0.0729866	+	0.997333i	$0.523253\pi$
$632$	3.80058	−	6.58280i	0.151179	−	0.261850i
$633$	7.00124	+	12.1265i	0.278274	+	0.481985i
$634$	12.6177	+	21.8545i	0.501112	+	0.867952i
$635$	6.40203	−	11.0886i	0.254057	−	0.440039i
$636$	−2.29896			−0.0911599
$637$	1.84809	−	2.66976i	0.0732240	−	0.105780i
$638$	−21.3933			−0.846968
$639$	3.81718	−	6.61154i	0.151005	−	0.261549i
$640$	−8.82851	−	15.2914i	−0.348977	−	0.604447i
$641$	−18.5835	−	32.1875i	−0.734002	−	1.27133i	−0.955160	−	0.296091i	$-0.904317\pi$
$641$	−18.5835	−	32.1875i	−0.734002	−	1.27133i	0.221157	−	0.975238i	$-0.429017\pi$
$642$	−21.9213	+	37.9689i	−0.865166	+	1.49851i
$643$	3.66443			0.144511			0.0722555	−	0.997386i	$-0.476980\pi$
$643$	3.66443			0.144511			0.0722555	+	0.997386i	$0.476980\pi$
$644$	−12.9715	−	24.7554i	−0.511147	−	0.975498i
$645$	11.0887			0.436619
$646$	−32.4342	+	56.1777i	−1.27611	+	2.21028i
$647$	5.46142	+	9.45946i	0.214711	+	0.371890i	0.953183	−	0.302394i	$-0.0977858\pi$
$647$	5.46142	+	9.45946i	0.214711	+	0.371890i	−0.738472	+	0.674284i	$0.764452\pi$
$648$	−1.33210	−	2.30727i	−0.0523300	−	0.0906383i
$649$	1.49762	−	2.59395i	0.0587866	−	0.101821i
$650$	−1.05486			−0.0413751
$651$	11.8836	+	0.486869i	0.465754	+	0.0190819i
$652$	72.0459			2.82153
$653$	−6.62735	+	11.4789i	−0.259348	+	0.449204i	−0.966067	−	0.258290i	$-0.916841\pi$
$653$	−6.62735	+	11.4789i	−0.259348	+	0.449204i	0.706719	+	0.707494i	$0.250174\pi$
$654$	2.86775	+	4.96709i	0.112138	+	0.194229i
$655$	2.51534	+	4.35669i	0.0982824	+	0.170230i
$656$	1.62701	−	2.81807i	0.0635242	−	0.110027i
$657$	−11.8245			−0.461316
$658$	23.5194	−	37.1378i	0.916880	−	1.44778i
$659$	7.24531			0.282237			0.141119	−	0.989993i	$-0.454930\pi$
$659$	7.24531			0.282237			0.141119	+	0.989993i	$0.454930\pi$
$660$	−1.58577	+	2.74664i	−0.0617261	+	0.106913i
$661$	11.1708	+	19.3484i	0.434493	+	0.752564i	0.997254	−	0.0740555i	$-0.0235942\pi$
$661$	11.1708	+	19.3484i	0.434493	+	0.752564i	−0.562761	+	0.826620i	$0.690261\pi$
$662$	−1.19335	−	2.06694i	−0.0463808	−	0.0803340i
$663$	1.00729	−	1.74467i	0.0391198	−	0.0677575i
$664$	22.7376			0.882391
$665$	−9.29723	+	14.6806i	−0.360531	+	0.569289i
$666$	18.9115			0.732805
$667$	15.6663	−	27.1349i	0.606602	−	1.05067i
$668$	12.1301	+	21.0099i	0.469326	+	0.812897i
$669$	−11.4444	−	19.8222i	−0.442464	−	0.766371i
$670$	−0.918883	+	1.59155i	−0.0354995	+	0.0614870i
$671$	−1.25173			−0.0483226
$672$	15.7956	+	0.647144i	0.609327	+	0.0249641i
$673$	46.4531			1.79064			0.895319	−	0.445426i	$-0.146948\pi$
$673$	46.4531			1.79064			0.895319	+	0.445426i	$0.146948\pi$
$674$	4.01080	−	6.94691i	0.154490	−	0.267585i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	20.2738	+	35.1153i	0.779763	+	1.35059i
$677$	−19.6790	+	34.0850i	−0.756325	+	1.30999i	0.188387	+	0.982095i	$0.439674\pi$
$677$	−19.6790	+	34.0850i	−0.756325	+	1.30999i	−0.944713	+	0.327899i	$0.893659\pi$
$678$	−36.3990			−1.39790
$679$	12.5050	+	23.8652i	0.479898	+	0.915861i
$680$	−11.5709			−0.443723
$681$	1.79083	−	3.10181i	0.0686249	−	0.118862i
$682$	−5.11143	−	8.85325i	−0.195727	−	0.339008i
$683$	−18.6089	−	32.2316i	−0.712051	−	1.23331i	−0.964086	−	0.265590i	$-0.914433\pi$
$683$	−18.6089	−	32.2316i	−0.712051	−	1.23331i	0.252035	−	0.967718i	$-0.418900\pi$
$684$	−10.4151	+	18.0396i	−0.398233	+	0.689760i
$685$	−22.1424			−0.846018
$686$	25.3691	−	33.6192i	0.968596	−	1.28359i
$687$	−25.2895			−0.964854
$688$	−1.57682	+	2.73113i	−0.0601157	+	0.104123i
$689$	−0.168119	−	0.291191i	−0.00640482	−	0.0110935i
$690$	−3.78713	−	6.55950i	−0.144174	−	0.249716i
$691$	8.62984	−	14.9473i	0.328295	−	0.568623i	−0.653879	−	0.756599i	$-0.726859\pi$
$691$	8.62984	−	14.9473i	0.328295	−	0.568623i	0.982174	+	0.187976i	$0.0601928\pi$
$692$	−52.5422			−1.99736
$693$	−1.22797	−	2.34352i	−0.0466468	−	0.0890230i
$694$	−24.6989			−0.937556
$695$	6.85343	−	11.8705i	0.259965	−	0.450273i
$696$	−12.5316	−	21.7053i	−0.475008	−	0.822738i
$697$	−24.8462	−	43.0349i	−0.941118	−	1.63006i
$698$	−18.0696	+	31.2975i	−0.683945	+	1.18463i
$699$	−6.46572			−0.244556
$700$	−8.38408	−	0.343495i	−0.316888	−	0.0129829i
$701$	−41.3462			−1.56162			−0.780812	−	0.624766i	$-0.785194\pi$
$701$	−41.3462			−1.56162			−0.780812	+	0.624766i	$0.785194\pi$
$702$	0.527431	−	0.913536i	0.0199066	−	0.0344792i
$703$	−27.3093	−	47.3010i	−1.02999	−	1.78399i
$704$	−6.50968	−	11.2751i	−0.245343	−	0.424946i
$705$	3.65306	−	6.32728i	0.137582	−	0.238299i
$706$	−9.93397			−0.373870
$707$	−16.2941	+	25.7288i	−0.612801	+	0.967632i
$708$	9.49951			0.357013
$709$	−22.3421	+	38.6977i	−0.839076	+	1.45332i	0.0515914	+	0.998668i	$0.483571\pi$
$709$	−22.3421	+	38.6977i	−0.839076	+	1.45332i	−0.890668	+	0.454655i	$0.849763\pi$
$710$	−8.68065	−	15.0353i	−0.325779	−	0.564266i
$711$	1.42653	+	2.47083i	0.0534991	+	0.0926632i
$712$	−19.7553	+	34.2172i	−0.740361	+	1.28234i
$713$	14.9724			0.560721
$714$	13.9810	−	22.0764i	0.523225	−	0.826188i
$715$	−0.463858			−0.0173473
$716$	11.9147	−	20.6369i	0.445274	−	0.771238i
$717$	−9.14862	−	15.8459i	−0.341661	−	0.591775i
$718$	32.5800	+	56.4303i	1.21588	+	2.10596i
$719$	18.0009	−	31.1785i	0.671321	−	1.16276i	−0.306209	−	0.951964i	$-0.599061\pi$
$719$	18.0009	−	31.1785i	0.671321	−	1.16276i	0.977530	−	0.210797i	$-0.0676061\pi$
$720$	0.284400			0.0105990
$721$	−38.2999	−	1.56914i	−1.42636	−	0.0584379i
$722$	54.8899			2.04279
$723$	12.2111	−	21.1503i	0.454137	−	0.786588i
$724$	−9.18172	−	15.9032i	−0.341236	−	0.591038i
$725$	−4.70367	−	8.14700i	−0.174690	−	0.302572i
$726$	−1.13705	+	1.96943i	−0.0421999	+	0.0730924i
$727$	24.5355			0.909971			0.454986	−	0.890499i	$-0.349644\pi$
$727$	24.5355			0.909971			0.454986	+	0.890499i	$0.349644\pi$
$728$	−1.51755	−	2.89616i	−0.0562440	−	0.107339i
$729$	1.00000			0.0370370
$730$	−13.4450	+	23.2875i	−0.497623	+	0.861908i
$731$	24.0797	+	41.7073i	0.890620	+	1.54260i
$732$	−1.98496	−	3.43806i	−0.0733664	−	0.127074i
$733$	−9.69149	+	16.7861i	−0.357963	+	0.620011i	−0.987620	−	0.156863i	$-0.949862\pi$
$733$	−9.69149	+	16.7861i	−0.357963	+	0.620011i	0.629657	+	0.776873i	$0.283195\pi$
$734$	57.9000			2.13713
$735$	3.98417	−	5.75555i	0.146958	−	0.212297i
$736$	19.9013			0.733570
$737$	−0.404064	+	0.699859i	−0.0148839	+	0.0257796i
$738$	−13.0098	−	22.5337i	−0.478899	−	0.829477i
$739$	5.23942	+	9.07494i	0.192735	+	0.333827i	0.946156	−	0.323712i	$-0.104931\pi$
$739$	5.23942	+	9.07494i	0.192735	+	0.333827i	−0.753421	+	0.657539i	$0.771598\pi$
$740$	13.1873	−	22.8411i	0.484775	−	0.839654i
$741$	−3.04656			−0.111918
$742$	−2.02423	−	3.86314i	−0.0743119	−	0.141820i
$743$	−12.4361			−0.456236			−0.228118	−	0.973633i	$-0.573257\pi$
$743$	−12.4361			−0.456236			−0.228118	+	0.973633i	$0.573257\pi$
$744$	5.98826	−	10.3720i	0.219540	−	0.380255i
$745$	−6.04902	−	10.4772i	−0.221619	−	0.383855i
$746$	20.8031	+	36.0320i	0.761654	+	1.31922i
$747$	−4.26723	+	7.39107i	−0.156130	+	0.270425i
$748$	−13.7743			−0.503638
$749$	−50.9649	−	2.08803i	−1.86222	−	0.0762950i
$750$	−2.27410			−0.0830385
$751$	1.80576	−	3.12767i	0.0658932	−	0.114130i	−0.831197	−	0.555979i	$-0.812344\pi$
$751$	1.80576	−	3.12767i	0.0658932	−	0.114130i	0.897090	+	0.441848i	$0.145677\pi$
$752$	1.03893	+	1.79948i	0.0378859	+	0.0656202i
$753$	−1.42709	−	2.47179i	−0.0520059	−	0.0900769i
$754$	4.96172	−	8.59395i	0.180695	−	0.312973i
$755$	−1.45581			−0.0529825
$756$	4.48952	−	7.08908i	0.163282	−	0.257827i
$757$	−10.5653			−0.384002			−0.192001	−	0.981395i	$-0.561498\pi$
$757$	−10.5653			−0.384002			−0.192001	+	0.981395i	$0.561498\pi$
$758$	−32.7611	+	56.7439i	−1.18994	+	2.06103i
$759$	−1.66533	−	2.88443i	−0.0604476	−	0.104698i
$760$	8.74909	+	15.1539i	0.317363	+	0.549689i
$761$	−22.1010	+	38.2800i	−0.801160	+	1.38765i	0.117693	+	0.993050i	$0.462450\pi$
$761$	−22.1010	+	38.2800i	−0.801160	+	1.38765i	−0.918853	+	0.394600i	$0.870883\pi$
$762$	29.1177			1.05482
$763$	−3.57018	+	5.63742i	−0.129249	+	0.204088i
$764$	−23.4784			−0.849420
$765$	2.17154	−	3.76122i	0.0785123	−	0.135987i
$766$	19.1020	+	33.0856i	0.690183	+	1.19543i
$767$	0.694682	+	1.20322i	0.0250835	+	0.0434459i
$768$	7.05757	−	12.2241i	0.254668	−	0.441098i
$769$	23.8628			0.860516			0.430258	−	0.902706i	$-0.358423\pi$
$769$	23.8628			0.860516			0.430258	+	0.902706i	$0.358423\pi$
$770$	−6.01167	−	0.246298i	−0.216645	−	0.00887595i
$771$	0.0366305			0.00131922
$772$	−10.7850	+	18.6802i	−0.388162	+	0.672316i
$773$	1.15217	+	1.99562i	0.0414408	+	0.0717776i	0.886002	−	0.463682i	$-0.153472\pi$
$773$	1.15217	+	1.99562i	0.0414408	+	0.0717776i	−0.844561	+	0.535459i	$0.820139\pi$
$774$	12.6085	+	21.8385i	0.453202	+	0.784970i
$775$	2.24767	−	3.89307i	0.0807386	−	0.139843i
$776$	27.1309			0.973942
$777$	10.2118	+	19.4887i	0.366347	+	0.699155i
$778$	−15.1301			−0.542442
$779$	−37.5739	+	65.0799i	−1.34623	+	2.33173i
$780$	−0.735573	−	1.27405i	−0.0263377	−	0.0456183i
$781$	−3.81718	−	6.61154i	−0.136589	−	0.236580i
$782$	16.4478	−	28.4885i	0.588173	−	1.01875i
$783$	9.40734			0.336191
$784$	0.851029	+	1.79973i	0.0303939	+	0.0642761i
$785$	5.02158			0.179228
$786$	−5.72014	+	9.90757i	−0.204031	+	0.353391i
$787$	22.9984	+	39.8344i	0.819804	+	1.41994i	0.905826	+	0.423649i	$0.139251\pi$
$787$	22.9984	+	39.8344i	0.819804	+	1.41994i	−0.0860221	+	0.996293i	$0.527416\pi$
$788$	20.7654	+	35.9667i	0.739737	+	1.28126i
$789$	12.0656	−	20.8982i	0.429546	−	0.743996i
$790$	6.48816			0.230838
$791$	−19.6548	−	37.5101i	−0.698843	−	1.33371i
$792$	−2.66421			−0.0946686
$793$	0.290313	−	0.502838i	0.0103093	−	0.0178563i
$794$	−27.1233	−	46.9790i	−0.962570	−	1.66722i
$795$	−0.362436	−	0.627758i	−0.0128543	−	0.0222643i
$796$	9.57597	−	16.5861i	0.339411	−	0.587877i
$797$	−35.6646			−1.26331			−0.631653	−	0.775251i	$-0.717623\pi$
$797$	−35.6646			−1.26331			−0.631653	+	0.775251i	$0.717623\pi$
$798$	−39.4839	−	1.61765i	−1.39771	−	0.0572642i
$799$	31.7311			1.12257
$800$	2.98759	−	5.17465i	0.105627	−	0.182952i
$801$	−7.41507	−	12.8433i	−0.261999	−	0.453795i
$802$	44.5108	+	77.0950i	1.57173	+	2.72232i
$803$	−5.91223	+	10.2403i	−0.208638	+	0.361372i
$804$	−2.56301			−0.0903905
$805$	4.71475	−	7.44474i	0.166173	−	0.262392i
$806$	4.74195			0.167028
$807$	7.75491	−	13.4319i	0.272986	−	0.472825i
$808$	15.3334	+	26.5583i	0.539428	+	0.934316i
$809$	5.49620	+	9.51970i	0.193236	+	0.334695i	0.946321	−	0.323229i	$-0.104768\pi$
$809$	5.49620	+	9.51970i	0.193236	+	0.334695i	−0.753085	+	0.657923i	$0.771435\pi$
$810$	1.13705	−	1.96943i	0.0399519	−	0.0691987i
$811$	−13.7401			−0.482479			−0.241239	−	0.970466i	$-0.577554\pi$
$811$	−13.7401			−0.482479			−0.241239	+	0.970466i	$0.577554\pi$
$812$	42.2344	−	66.6894i	1.48214	−	2.34034i
$813$	19.1759			0.672529
$814$	9.45573	−	16.3778i	0.331423	−	0.574042i
$815$	11.3582	+	19.6729i	0.397860	+	0.689113i
$816$	0.617587	+	1.06969i	0.0216199	+	0.0374467i
$817$	36.4147	−	63.0722i	1.27399	−	2.20662i
$818$	24.1990			0.846097
$819$	1.22622	+	0.0502383i	0.0428478	+	0.00175547i
$820$	−36.2880			−1.26723
$821$	12.4062	−	21.4881i	0.432978	−	0.749940i	−0.564150	−	0.825672i	$-0.690796\pi$
$821$	12.4062	−	21.4881i	0.432978	−	0.749940i	0.997128	+	0.0757323i	$0.0241294\pi$
$822$	−25.1771	−	43.6080i	−0.878151	−	1.52100i
$823$	−18.8787	−	32.6989i	−0.658071	−	1.13981i	−0.981114	−	0.193429i	$-0.938039\pi$
$823$	−18.8787	−	32.6989i	−0.658071	−	1.13981i	0.323043	−	0.946384i	$-0.395294\pi$
$824$	−19.2997	+	33.4281i	−0.672337	+	1.16452i
$825$	−1.00000			−0.0348155
$826$	8.36429	+	15.9628i	0.291031	+	0.555417i
$827$	31.3117			1.08881			0.544407	−	0.838821i	$-0.316755\pi$
$827$	31.3117			1.08881			0.544407	+	0.838821i	$0.316755\pi$
$828$	5.28166	−	9.14811i	0.183550	−	0.317919i
$829$	19.8794	+	34.4321i	0.690439	+	1.19588i	0.971694	+	0.236243i	$0.0759160\pi$
$829$	19.8794	+	34.4321i	0.690439	+	1.19588i	−0.281255	+	0.959633i	$0.590751\pi$
$830$	9.70413	+	16.8080i	0.336835	+	0.583416i
$831$	−3.83072	+	6.63501i	−0.132886	+	0.230166i
$832$	6.03914			0.209369
$833$	30.2997	+	2.48693i	1.04982	+	0.0861670i
$834$	31.1708			1.07936
$835$	−3.82466	+	6.62450i	−0.132358	+	0.229250i
$836$	10.4151	+	18.0396i	0.360215	+	0.623911i
$837$	2.24767	+	3.89307i	0.0776907	+	0.134564i
$838$	16.4656	−	28.5193i	0.568796	−	0.985184i
$839$	30.5519			1.05477			0.527384	−	0.849627i	$-0.323173\pi$
$839$	30.5519			1.05477			0.527384	+	0.849627i	$0.323173\pi$
$840$	−3.27157	−	6.24363i	−0.112880	−	0.215426i
$841$	59.4981			2.05166
$842$	6.13818	−	10.6316i	0.211535	−	0.366390i
$843$	7.83388	+	13.5687i	0.269813	+	0.467330i
$844$	22.2047	+	38.4597i	0.764318	+	1.32384i
$845$	−6.39242	+	11.0720i	−0.219906	+	0.380888i
$846$	16.6149			0.571230
$847$	−2.64353	−	0.108305i	−0.0908329	−	0.00372142i
$848$	0.206154			0.00707935
$849$	−4.81572	+	8.34107i	−0.165275	+	0.286265i
$850$	−4.93831	−	8.55341i	−0.169383	−	0.293379i
$851$	13.8489	+	23.9870i	0.474734	+	0.822264i
$852$	12.1063	−	20.9688i	0.414756	−	0.718379i
$853$	0.873513			0.0299085			0.0149543	−	0.999888i	$-0.495240\pi$
$853$	0.873513			0.0299085			0.0149543	+	0.999888i	$0.495240\pi$
$854$	4.02950	−	6.36270i	0.137887	−	0.217727i
$855$	−6.56787			−0.224616
$856$	−25.6818	+	44.4822i	−0.877785	+	1.52037i
$857$	3.63281	+	6.29221i	0.124094	+	0.214938i	0.921379	−	0.388666i	$-0.127064\pi$
$857$	3.63281	+	6.29221i	0.124094	+	0.214938i	−0.797284	+	0.603604i	$0.793731\pi$
$858$	−0.527431	−	0.913536i	−0.0180062	−	0.0311876i
$859$	−0.446460	+	0.773291i	−0.0152330	+	0.0263844i	−0.873541	−	0.486750i	$-0.838182\pi$
$859$	−0.446460	+	0.773291i	−0.0152330	+	0.0263844i	0.858308	+	0.513134i	$0.171516\pi$
$860$	35.1684			1.19923
$861$	16.1965	−	25.5747i	0.551975	−	0.871585i
$862$	16.0391			0.546294
$863$	19.7575	−	34.2209i	0.672552	−	1.16489i	−0.304626	−	0.952472i	$-0.598532\pi$
$863$	19.7575	−	34.2209i	0.672552	−	1.16489i	0.977178	−	0.212422i	$-0.0681350\pi$
$864$	2.98759	+	5.17465i	0.101640	+	0.176045i
$865$	−8.28338	−	14.3472i	−0.281643	−	0.487821i
$866$	21.2233	−	36.7598i	0.721197	−	1.24915i
$867$	1.86240			0.0632504
$868$	37.6892	+	1.54413i	1.27926	+	0.0524110i
$869$	2.85306			0.0967836
$870$	10.6966	−	18.5271i	0.362650	−	0.628128i
$871$	−0.187428	−	0.324635i	−0.00635077	−	0.0109999i
$872$	3.35969	+	5.81916i	0.113774	+	0.197062i
$873$	−5.09173	+	8.81914i	−0.172329	+	0.298483i
$874$	−49.7468			−1.68271
$875$	−1.22797	−	2.34352i	−0.0415130	−	0.0792254i
$876$	−37.5018			−1.26707
$877$	4.12046	−	7.13685i	0.139138	−	0.240994i	−0.788032	−	0.615634i	$-0.788900\pi$
$877$	4.12046	−	7.13685i	0.139138	−	0.240994i	0.927171	+	0.374639i	$0.122233\pi$
$878$	36.6876	+	63.5448i	1.23815	+	2.14453i
$879$	2.36014	+	4.08789i	0.0796057	+	0.137881i
$880$	0.142200	−	0.246298i	0.00479356	−	0.00830269i
$881$	−39.6155			−1.33468			−0.667340	−	0.744753i	$-0.732567\pi$
$881$	−39.6155			−1.33468			−0.667340	+	0.744753i	$0.732567\pi$
$882$	15.8654	+	1.30219i	0.534215	+	0.0438471i
$883$	−6.75074			−0.227181			−0.113590	−	0.993528i	$-0.536235\pi$
$883$	−6.75074			−0.227181			−0.113590	+	0.993528i	$0.536235\pi$
$884$	3.19466	−	5.53331i	0.107448	−	0.186105i
$885$	1.49762	+	2.59395i	0.0503418	+	0.0871946i
$886$	4.30680	+	7.45959i	0.144690	+	0.250610i
$887$	19.5808	−	33.9149i	0.657459	−	1.13875i	−0.323812	−	0.946121i	$-0.604965\pi$
$887$	19.5808	−	33.9149i	0.657459	−	1.13875i	0.981271	−	0.192631i	$-0.0617021\pi$
$888$	22.1556			0.743493
$889$	15.7230	+	30.0065i	0.527333	+	1.00639i
$890$	−33.7253			−1.13047
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−36.2963	−	62.8670i	−1.21529	−	2.10494i
$893$	−23.9928	−	41.5568i	−0.802889	−	1.39064i
$894$	13.7561	−	23.8262i	0.460072	−	0.796868i
$895$	7.51352			0.251149
$896$	46.6769	+	1.91235i	1.55937	+	0.0638871i
$897$	1.54495			0.0515845
$898$	−8.75256	+	15.1599i	−0.292077	+	0.505892i
$899$	21.1446	+	36.6235i	0.705211	+	1.22146i
$900$	−1.58577	−	2.74664i	−0.0528591	−	0.0915546i
$901$	1.57409	−	2.72641i	0.0524406	−	0.0908298i
$902$	−26.0197			−0.866361
$903$	−15.6968	+	24.7857i	−0.522357	+	0.824818i
$904$	−42.6430			−1.41829
$905$	2.89503	−	5.01434i	0.0962341	−	0.166682i
$906$	−1.65533	−	2.86712i	−0.0549948	−	0.0952538i
$907$	−0.535515	−	0.927538i	−0.0177815	−	0.0307984i	0.856998	−	0.515320i	$-0.172327\pi$
$907$	−0.535515	−	0.927538i	−0.0177815	−	0.0307984i	−0.874779	+	0.484522i	$0.838994\pi$
$908$	5.67970	−	9.83754i	0.188488	−	0.326470i
$909$	−11.5107			−0.381785
$910$	1.49322	−	2.35784i	0.0494998	−	0.0781617i
$911$	−49.6173			−1.64389			−0.821947	−	0.569565i	$-0.807112\pi$
$911$	−49.6173			−1.64389			−0.821947	+	0.569565i	$0.807112\pi$
$912$	0.933951	−	1.61765i	0.0309262	−	0.0535658i
$913$	4.26723	+	7.39107i	0.141225	+	0.244609i
$914$	36.6342	+	63.4523i	1.21175	+	2.09882i
$915$	0.625867	−	1.08403i	0.0206905	−	0.0358370i
$916$	−80.2067			−2.65010
$917$	−13.2988	−	0.544849i	−0.439164	−	0.0179925i
$918$	9.87662			0.325977
$919$	−16.0962	+	27.8794i	−0.530963	+	0.919655i	0.468384	+	0.883525i	$0.344836\pi$
$919$	−16.0962	+	27.8794i	−0.530963	+	0.919655i	−0.999347	+	0.0361300i	$0.988497\pi$
$920$	−4.43679	−	7.68474i	−0.146276	−	0.253358i
$921$	−0.373607	−	0.647106i	−0.0123108	−	0.0213229i
$922$	14.4197	−	24.9756i	0.474886	−	0.822527i
$923$	3.54126			0.116562
$924$	−3.89457	−	7.43257i	−0.128122	−	0.244514i
$925$	8.31601			0.273429
$926$	−4.82598	+	8.35884i	−0.158591	+	0.274688i
$927$	−7.24406	−	12.5471i	−0.237926	−	0.412100i
$928$	28.1053	+	48.6797i	0.922600	+	1.59799i
$929$	1.83314	−	3.17510i	0.0601435	−	0.104172i	−0.834386	−	0.551181i	$-0.814177\pi$
$929$	1.83314	−	3.17510i	0.0601435	−	0.104172i	0.894529	+	0.447009i	$0.147511\pi$
$930$	10.2229			0.335220
$931$	−19.6535	−	41.5626i	−0.644117	−	1.36216i
$932$	−20.5063			−0.671706
$933$	−2.38343	+	4.12822i	−0.0780299	+	0.135152i
$934$	25.5131	+	44.1901i	0.834816	+	1.44594i
$935$	−2.17154	−	3.76122i	−0.0710171	−	0.123005i
$936$	0.617908	−	1.07025i	0.0201969	−	0.0349821i
$937$	−37.0833			−1.21146			−0.605730	−	0.795670i	$-0.707119\pi$
$937$	−37.0833			−1.21146			−0.605730	+	0.795670i	$0.707119\pi$
$938$	−2.25672	−	4.30684i	−0.0736846	−	0.140623i
$939$	−30.0141			−0.979473
$940$	11.5858	−	20.0672i	0.377888	−	0.654521i
$941$	−14.1917	−	24.5807i	−0.462635	−	0.801307i	0.536456	−	0.843928i	$-0.319763\pi$
$941$	−14.1917	−	24.5807i	−0.462635	−	0.801307i	−0.999091	+	0.0426207i	$0.986429\pi$
$942$	5.70979	+	9.88965i	0.186035	+	0.322222i
$943$	19.0543	−	33.0029i	0.620492	−	1.07472i
$944$	−0.851844			−0.0277252
$945$	2.64353	+	0.108305i	0.0859942	+	0.00352317i
$946$	25.2170			0.819874
$947$	−21.6641	+	37.5233i	−0.703988	+	1.21934i	0.263068	+	0.964777i	$0.415266\pi$
$947$	−21.6641	+	37.5233i	−0.703988	+	1.21934i	−0.967056	+	0.254565i	$0.918068\pi$
$948$	4.52431	+	7.83633i	0.146943	+	0.254512i
$949$	−2.74244	−	4.75004i	−0.0890233	−	0.154193i
$950$	−7.46801	+	12.9350i	−0.242294	+	0.419666i
$951$	−11.0968			−0.359840
$952$	16.3793	−	25.8634i	0.530857	−	0.838239i
$953$	56.6159			1.83397			0.916985	−	0.398922i	$-0.130615\pi$
$953$	56.6159			1.83397			0.916985	+	0.398922i	$0.130615\pi$
$954$	0.824217	−	1.42759i	0.0266850	−	0.0462198i
$955$	−3.70142	−	6.41105i	−0.119775	−	0.207457i
$956$	−29.0152	−	50.2559i	−0.938420	−	1.62539i
$957$	4.70367	−	8.14700i	0.152048	−	0.263355i
$958$	−18.2273			−0.588897
$959$	31.3440	−	49.4931i	1.01215	−	1.59821i
$960$	13.0194			0.420198
$961$	5.39599	−	9.34612i	0.174064	−	0.301488i
$962$	4.38612	+	7.59698i	0.141414	+	0.244937i
$963$	−9.63955	−	16.6962i	−0.310630	−	0.538027i
$964$	38.7281	−	67.0791i	1.24735	−	2.16047i
$965$	−6.80112			−0.218936
$966$	20.0228	+	0.820333i	0.644223	+	0.0263938i
$967$	45.3223			1.45747			0.728733	−	0.684797i	$-0.240109\pi$
$967$	45.3223			1.45747			0.728733	+	0.684797i	$0.240109\pi$
$968$	−1.33210	+	2.30727i	−0.0428155	+	0.0741586i
$969$	−14.2624	−	24.7032i	−0.458175	−	0.793582i
$970$	11.5791	+	20.0556i	0.371783	+	0.643948i
$971$	−13.6322	+	23.6117i	−0.437480	+	0.757737i	−0.997494	−	0.0707457i	$-0.977462\pi$
$971$	−13.6322	+	23.6117i	−0.437480	+	0.757737i	0.560015	+	0.828483i	$0.310795\pi$
$972$	3.17154			0.101727
$973$	16.8316	+	32.1223i	0.539597	+	1.02979i
$974$	8.77999			0.281329
$975$	0.231929	−	0.401713i	0.00742767	−	0.0128651i
$976$	0.177996	+	0.308299i	0.00569753	+	0.00986841i
$977$	23.1865	+	40.1602i	0.741801	+	1.28484i	0.951674	+	0.307109i	$0.0993615\pi$
$977$	23.1865	+	40.1602i	0.741801	+	1.28484i	−0.209873	+	0.977729i	$0.567305\pi$
$978$	−25.8297	+	44.7383i	−0.825941	+	1.43057i
$979$	−14.8301			−0.473973
$980$	12.6360	−	18.2540i	0.403641	−	0.583102i
$981$	−2.52209			−0.0805242
$982$	25.7611	−	44.6195i	0.822068	−	1.42386i
$983$	−5.08563	−	8.80857i	−0.162206	−	0.280950i	0.773453	−	0.633853i	$-0.218528\pi$
$983$	−5.08563	−	8.80857i	−0.162206	−	0.280950i	−0.935660	+	0.352904i	$0.885194\pi$
$984$	−15.2416	−	26.3992i	−0.485884	−	0.841576i
$985$	−6.54741	+	11.3405i	−0.208618	+	0.361337i
$986$	92.9128			2.95895
$987$	8.97170	+	17.1220i	0.285572	+	0.545000i
$988$	−9.66230			−0.307399
$989$	−18.4664	+	31.9848i	−0.587198	+	1.01706i
$990$	−1.13705	−	1.96943i	−0.0361379	−	0.0625926i
$991$	5.15913	+	8.93588i	0.163885	+	0.283858i	0.936259	−	0.351311i	$-0.114264\pi$
$991$	5.15913	+	8.93588i	0.163885	+	0.283858i	−0.772374	+	0.635169i	$0.780931\pi$
$992$	−13.4302	+	23.2618i	−0.426409	+	0.738563i
$993$	1.04951			0.0333053
$994$	45.8952	+	1.88032i	1.45571	+	0.0596402i
$995$	6.03868			0.191439
$996$	−13.5337	+	23.4411i	−0.428832	+	0.742759i
$997$	10.6668	+	18.4755i	0.337822	+	0.585124i	0.984023	−	0.178043i	$-0.0569766\pi$
$997$	10.6668	+	18.4755i	0.337822	+	0.585124i	−0.646201	+	0.763167i	$0.723643\pi$
$998$	−27.9634	−	48.4340i	−0.885165	−	1.53315i
$999$	−4.15801	+	7.20188i	−0.131554	+	0.227857i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.331.2	✓	16
7.2	even	3		8085.2.a.cf.1.7		8
7.4	even	3	inner	1155.2.q.j.991.2	yes	16
7.5	odd	6		8085.2.a.ce.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.2	✓	16	1.1	even	1	trivial
1155.2.q.j.991.2	yes	16	7.4	even	3	inner
8085.2.a.ce.1.7		8	7.5	odd	6
8085.2.a.cf.1.7		8	7.2	even	3

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13705 + 1.96943i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.58577 - 2.74664i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.27410 q^{6} +(1.22797 + 2.34352i) q^{7} +2.66421 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.13705 + 1.96943i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.58577 - 2.74664i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.27410 q^{6} +(1.22797 + 2.34352i) q^{7} +2.66421 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.13705 + 1.96943i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.58577 + 2.74664i) q^{12} -0.463858 q^{13} +(-6.01167 - 0.246298i) q^{14} -1.00000 q^{15} +(0.142200 - 0.246298i) q^{16} +(-2.17154 - 3.76122i) q^{17} +(-1.13705 - 1.96943i) q^{18} +(-3.28394 + 5.68794i) q^{19} -3.17154 q^{20} +(1.41556 - 2.23521i) q^{21} -2.27410 q^{22} +(1.66533 - 2.88443i) q^{23} +(-1.33210 - 2.30727i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.527431 - 0.913536i) q^{26} +1.00000 q^{27} +(4.48952 - 7.08908i) q^{28} +9.40734 q^{29} +(1.13705 - 1.96943i) q^{30} +(2.24767 + 3.89307i) q^{31} +(2.98759 + 5.17465i) q^{32} +(0.500000 - 0.866025i) q^{33} +9.87662 q^{34} +(2.64353 + 0.108305i) q^{35} +3.17154 q^{36} +(-4.15801 + 7.20188i) q^{37} +(-7.46801 - 12.9350i) q^{38} +(0.231929 + 0.401713i) q^{39} +(1.33210 - 2.30727i) q^{40} +11.4417 q^{41} +(2.79253 + 5.32941i) q^{42} -11.0887 q^{43} +(1.58577 - 2.74664i) q^{44} +(0.500000 + 0.866025i) q^{45} +(3.78713 + 6.55950i) q^{46} +(-3.65306 + 6.32728i) q^{47} -0.284400 q^{48} +(-3.98417 + 5.75555i) q^{49} +2.27410 q^{50} +(-2.17154 + 3.76122i) q^{51} +(0.735573 + 1.27405i) q^{52} +(0.362436 + 0.627758i) q^{53} +(-1.13705 + 1.96943i) q^{54} +1.00000 q^{55} +(3.27157 + 6.24363i) q^{56} +6.56787 q^{57} +(-10.6966 + 18.5271i) q^{58} +(-1.49762 - 2.59395i) q^{59} +(1.58577 + 2.74664i) q^{60} +(-0.625867 + 1.08403i) q^{61} -10.2229 q^{62} +(-2.64353 - 0.108305i) q^{63} -13.0194 q^{64} +(-0.231929 + 0.401713i) q^{65} +(1.13705 + 1.96943i) q^{66} +(0.404064 + 0.699859i) q^{67} +(-6.88714 + 11.9289i) q^{68} -3.33066 q^{69} +(-3.21913 + 5.08311i) q^{70} -7.63435 q^{71} +(-1.33210 + 2.30727i) q^{72} +(5.91223 + 10.2403i) q^{73} +(-9.45573 - 16.3778i) q^{74} +(-0.500000 + 0.866025i) q^{75} +20.8303 q^{76} +(-1.41556 + 2.23521i) q^{77} -1.05486 q^{78} +(1.42653 - 2.47083i) q^{79} +(-0.142200 - 0.246298i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-13.0098 + 22.5337i) q^{82} +8.53447 q^{83} +(-8.38408 - 0.343495i) q^{84} -4.34309 q^{85} +(12.6085 - 21.8385i) q^{86} +(-4.70367 - 8.14700i) q^{87} +(1.33210 + 2.30727i) q^{88} +(-7.41507 + 12.8433i) q^{89} -2.27410 q^{90} +(-0.569605 - 1.08706i) q^{91} -10.5633 q^{92} +(2.24767 - 3.89307i) q^{93} +(-8.30743 - 14.3889i) q^{94} +(3.28394 + 5.68794i) q^{95} +(2.98759 - 5.17465i) q^{96} +10.1835 q^{97} +(-6.80495 - 14.3909i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more