LMFDB - Embedded newform 731.2.m.c.689.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.4
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56129 + 1.56129i) q^{2} +(-2.36310 - 0.978828i) q^{3} -2.87526i q^{4} +(1.21177 - 2.92548i) q^{5} +(5.21772 - 2.16125i) q^{6} +(1.72340 + 4.16065i) q^{7} +(1.36654 + 1.36654i) q^{8} +(2.50481 + 2.50481i) q^{9} +O(q^{10})$	\(q+(-1.56129 + 1.56129i) q^{2} +(-2.36310 - 0.978828i) q^{3} -2.87526i q^{4} +(1.21177 - 2.92548i) q^{5} +(5.21772 - 2.16125i) q^{6} +(1.72340 + 4.16065i) q^{7} +(1.36654 + 1.36654i) q^{8} +(2.50481 + 2.50481i) q^{9} +(2.67560 + 6.45946i) q^{10} +(2.87243 - 1.18980i) q^{11} +(-2.81439 + 6.79453i) q^{12} -1.03249i q^{13} +(-9.18672 - 3.80527i) q^{14} +(-5.72708 + 5.72708i) q^{15} +1.48338 q^{16} +(-4.07859 + 0.604236i) q^{17} -7.82149 q^{18} +(-0.211276 + 0.211276i) q^{19} +(-8.41153 - 3.48417i) q^{20} -11.5189i q^{21} +(-2.62708 + 6.34234i) q^{22} +(-3.32590 + 1.37763i) q^{23} +(-1.89167 - 4.56689i) q^{24} +(-3.55451 - 3.55451i) q^{25} +(1.61202 + 1.61202i) q^{26} +(-0.530857 - 1.28160i) q^{27} +(11.9630 - 4.95523i) q^{28} +(1.75074 - 4.22665i) q^{29} -17.8833i q^{30} +(4.62662 + 1.91641i) q^{31} +(-5.04908 + 5.04908i) q^{32} -7.95246 q^{33} +(5.42448 - 7.31126i) q^{34} +14.2603 q^{35} +(7.20200 - 7.20200i) q^{36} +(6.56065 + 2.71751i) q^{37} -0.659726i q^{38} +(-1.01063 + 2.43987i) q^{39} +(5.65374 - 2.34185i) q^{40} +(0.389323 + 0.939910i) q^{41} +(17.9844 + 17.9844i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-3.42099 - 8.25901i) q^{44} +(10.3630 - 4.29251i) q^{45} +(3.04181 - 7.34358i) q^{46} -3.37242i q^{47} +(-3.50538 - 1.45198i) q^{48} +(-9.39119 + 9.39119i) q^{49} +11.0993 q^{50} +(10.2296 + 2.56437i) q^{51} -2.96868 q^{52} +(9.44775 - 9.44775i) q^{53} +(2.82978 + 1.17213i) q^{54} -9.84502i q^{55} +(-3.33061 + 8.04081i) q^{56} +(0.706068 - 0.292463i) q^{57} +(3.86563 + 9.33245i) q^{58} +(5.23580 + 5.23580i) q^{59} +(16.4669 + 16.4669i) q^{60} +(-2.69928 - 6.51664i) q^{61} +(-10.2156 + 4.23143i) q^{62} +(-6.10487 + 14.7384i) q^{63} -12.7994i q^{64} +(-3.02053 - 1.25114i) q^{65} +(12.4161 - 12.4161i) q^{66} -7.74847 q^{67} +(1.73734 + 11.7270i) q^{68} +9.20788 q^{69} +(-22.2645 + 22.2645i) q^{70} +(8.36432 + 3.46461i) q^{71} +6.84587i q^{72} +(-4.57810 + 11.0525i) q^{73} +(-14.4859 + 6.00026i) q^{74} +(4.92040 + 11.8789i) q^{75} +(0.607474 + 0.607474i) q^{76} +(9.90070 + 9.90070i) q^{77} +(-2.23147 - 5.38724i) q^{78} +(13.6896 - 5.67041i) q^{79} +(1.79753 - 4.33961i) q^{80} -7.07885i q^{81} +(-2.07532 - 0.859626i) q^{82} +(9.21094 - 9.21094i) q^{83} -33.1200 q^{84} +(-3.17465 + 12.6640i) q^{85} +2.20800 q^{86} +(-8.27433 + 8.27433i) q^{87} +(5.55122 + 2.29939i) q^{88} -0.648155i q^{89} +(-9.47787 + 22.8816i) q^{90} +(4.29583 - 1.77939i) q^{91} +(3.96105 + 9.56283i) q^{92} +(-9.05732 - 9.05732i) q^{93} +(5.26533 + 5.26533i) q^{94} +(0.362065 + 0.874102i) q^{95} +(16.8737 - 6.98930i) q^{96} +(3.19206 - 7.70631i) q^{97} -29.3248i q^{98} +(10.1751 + 4.21468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	−1.56129	+	1.56129i	−1.10400	+	1.10400i	−0.110077	+	0.993923i	$0.535110\pi$
$2$	−1.56129	+	1.56129i	−1.10400	+	1.10400i	−0.993923	+	0.110077i	$0.964890\pi$
$3$	−2.36310	−	0.978828i	−1.36434	−	0.565126i	−0.424089	−	0.905620i	$-0.639406\pi$
$3$	−2.36310	−	0.978828i	−1.36434	−	0.565126i	−0.940247	+	0.340494i	$0.889406\pi$
$4$		−	2.87526i		−	1.43763i
$5$	1.21177	−	2.92548i	0.541922	−	1.30831i	−0.381444	−	0.924392i	$-0.624573\pi$
$5$	1.21177	−	2.92548i	0.541922	−	1.30831i	0.923365	−	0.383923i	$-0.125427\pi$
$6$	5.21772	−	2.16125i	2.13013	−	0.882327i
$7$	1.72340	+	4.16065i	0.651384	+	1.57258i	0.810771	+	0.585363i	$0.199048\pi$
$7$	1.72340	+	4.16065i	0.651384	+	1.57258i	−0.159388	+	0.987216i	$0.550952\pi$
$8$	1.36654	+	1.36654i	0.483146	+	0.483146i
$9$	2.50481	+	2.50481i	0.834937	+	0.834937i
$10$	2.67560	+	6.45946i	0.846098	+	2.04266i
$11$	2.87243	−	1.18980i	0.866072	−	0.358739i	0.0949925	−	0.995478i	$-0.469717\pi$
$11$	2.87243	−	1.18980i	0.866072	−	0.358739i	0.771079	+	0.636739i	$0.219717\pi$
$12$	−2.81439	+	6.79453i	−0.812444	+	1.96141i
$13$		−	1.03249i		−	0.286361i	−0.989697	−	0.143180i	$-0.954267\pi$
$13$		−	1.03249i		−	0.286361i	0.989697	−	0.143180i	$-0.0457329\pi$
$14$	−9.18672	−	3.80527i	−2.45526	−	1.01700i
$15$	−5.72708	+	5.72708i	−1.47873	+	1.47873i
$16$	1.48338			0.370846
$17$	−4.07859	+	0.604236i	−0.989203	+	0.146549i
$17$	−4.07859	+	0.604236i	−0.989203	+	0.146549i
$18$	−7.82149			−1.84354
$19$	−0.211276	+	0.211276i	−0.0484700	+	0.0484700i	−0.730926	−	0.682456i	$-0.760912\pi$
$19$	−0.211276	+	0.211276i	−0.0484700	+	0.0484700i	0.682456	+	0.730926i	$0.260912\pi$
$20$	−8.41153	−	3.48417i	−1.88088	−	0.779084i
$21$		−	11.5189i		−	2.51364i
$22$	−2.62708	+	6.34234i	−0.560096	+	1.35219i
$23$	−3.32590	+	1.37763i	−0.693497	+	0.287256i	−0.701456	−	0.712712i	$-0.747466\pi$
$23$	−3.32590	+	1.37763i	−0.693497	+	0.287256i	0.00795922	+	0.999968i	$0.497466\pi$
$24$	−1.89167	−	4.56689i	−0.386135	−	0.932212i
$25$	−3.55451	−	3.55451i	−0.710902	−	0.710902i
$26$	1.61202	+	1.61202i	0.316142	+	0.316142i
$27$	−0.530857	−	1.28160i	−0.102163	−	0.246645i
$28$	11.9630	−	4.95523i	2.26079	−	0.936450i
$29$	1.75074	−	4.22665i	0.325104	−	0.784870i	−0.673838	−	0.738879i	$-0.735355\pi$
$29$	1.75074	−	4.22665i	0.325104	−	0.784870i	0.998942	−	0.0459908i	$-0.0146445\pi$
$30$		−	17.8833i		−	3.26503i
$31$	4.62662	+	1.91641i	0.830965	+	0.344197i	0.757285	−	0.653085i	$-0.226526\pi$
$31$	4.62662	+	1.91641i	0.830965	+	0.344197i	0.0736805	+	0.997282i	$0.476526\pi$
$32$	−5.04908	+	5.04908i	−0.892560	+	0.892560i
$33$	−7.95246			−1.38435
$34$	5.42448	−	7.31126i	0.930291	−	1.25387i
$35$	14.2603			2.41043
$36$	7.20200	−	7.20200i	1.20033	−	1.20033i
$37$	6.56065	+	2.71751i	1.07856	+	0.446756i	0.850005	−	0.526774i	$-0.176599\pi$
$37$	6.56065	+	2.71751i	1.07856	+	0.446756i	0.228559	+	0.973530i	$0.426599\pi$
$38$		−	0.659726i		−	0.107022i
$39$	−1.01063	+	2.43987i	−0.161830	+	0.390692i
$40$	5.65374	−	2.34185i	0.893934	−	0.370280i
$41$	0.389323	+	0.939910i	0.0608021	+	0.146789i	0.951361	−	0.308079i	$-0.0996862\pi$
$41$	0.389323	+	0.939910i	0.0608021	+	0.146789i	−0.890559	+	0.454869i	$0.849686\pi$
$42$	17.9844	+	17.9844i	2.77506	+	2.77506i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	−3.42099	−	8.25901i	−0.515734	−	1.24509i
$45$	10.3630	−	4.29251i	1.54483	−	0.639890i
$46$	3.04181	−	7.34358i	0.448490	−	1.08275i
$47$		−	3.37242i		−	0.491918i	−0.969280	−	0.245959i	$-0.920897\pi$
$47$		−	3.37242i		−	0.491918i	0.969280	−	0.245959i	$-0.0791028\pi$
$48$	−3.50538	−	1.45198i	−0.505958	−	0.209575i
$49$	−9.39119	+	9.39119i	−1.34160	+	1.34160i
$50$	11.0993			1.56967
$51$	10.2296	+	2.56437i	1.43242	+	0.359083i
$52$	−2.96868			−0.411681
$53$	9.44775	−	9.44775i	1.29775	−	1.29775i	0.367871	−	0.929877i	$-0.380087\pi$
$53$	9.44775	−	9.44775i	1.29775	−	1.29775i	0.929877	−	0.367871i	$-0.119913\pi$
$54$	2.82978	+	1.17213i	0.385084	+	0.159507i
$55$		−	9.84502i		−	1.32750i
$56$	−3.33061	+	8.04081i	−0.445072	+	1.07450i
$57$	0.706068	−	0.292463i	0.0935210	−	0.0387377i
$58$	3.86563	+	9.33245i	0.507582	+	1.22541i
$59$	5.23580	+	5.23580i	0.681643	+	0.681643i	0.960370	−	0.278727i	$-0.0899126\pi$
$59$	5.23580	+	5.23580i	0.681643	+	0.681643i	−0.278727	+	0.960370i	$0.589913\pi$
$60$	16.4669	+	16.4669i	2.12586	+	2.12586i
$61$	−2.69928	−	6.51664i	−0.345607	−	0.834370i	−0.997128	−	0.0757389i	$-0.975868\pi$
$61$	−2.69928	−	6.51664i	−0.345607	−	0.834370i	0.651520	−	0.758631i	$-0.274132\pi$
$62$	−10.2156	+	4.23143i	−1.29738	+	0.537392i
$63$	−6.10487	+	14.7384i	−0.769141	+	1.85687i
$64$		−	12.7994i		−	1.59993i
$65$	−3.02053	−	1.25114i	−0.374650	−	0.155185i
$66$	12.4161	−	12.4161i	1.52832	−	1.52832i
$67$	−7.74847			−0.946627			−0.473313	−	0.880894i	$-0.656942\pi$
$67$	−7.74847			−0.946627			−0.473313	+	0.880894i	$0.656942\pi$
$68$	1.73734	+	11.7270i	0.210683	+	1.42211i
$69$	9.20788			1.10850
$70$	−22.2645	+	22.2645i	−2.66111	+	2.66111i
$71$	8.36432	+	3.46461i	0.992662	+	0.411174i	0.819101	−	0.573649i	$-0.194473\pi$
$71$	8.36432	+	3.46461i	0.992662	+	0.411174i	0.173561	+	0.984823i	$0.444473\pi$
$72$			6.84587i			0.806793i
$73$	−4.57810	+	11.0525i	−0.535826	+	1.29360i	0.391787	+	0.920056i	$0.371857\pi$
$73$	−4.57810	+	11.0525i	−0.535826	+	1.29360i	−0.927613	+	0.373542i	$0.878143\pi$
$74$	−14.4859	+	6.00026i	−1.68395	+	0.697517i
$75$	4.92040	+	11.8789i	0.568159	+	1.37166i
$76$	0.607474	+	0.607474i	0.0696820	+	0.0696820i
$77$	9.90070	+	9.90070i	1.12829	+	1.12829i
$78$	−2.23147	−	5.38724i	−0.252664	−	0.609985i
$79$	13.6896	−	5.67041i	1.54020	−	0.637971i	0.558688	−	0.829378i	$-0.311305\pi$
$79$	13.6896	−	5.67041i	1.54020	−	0.637971i	0.981511	+	0.191407i	$0.0613050\pi$
$80$	1.79753	−	4.33961i	0.200969	−	0.485183i
$81$		−	7.07885i		−	0.786539i
$82$	−2.07532	−	0.859626i	−0.229181	−	0.0949298i
$83$	9.21094	−	9.21094i	1.01103	−	1.01103i	0.0110933	−	0.999938i	$-0.496469\pi$
$83$	9.21094	−	9.21094i	1.01103	−	1.01103i	0.999938	−	0.0110933i	$-0.00353117\pi$
$84$	−33.1200			−3.61369
$85$	−3.17465	+	12.6640i	−0.344339	+	1.37361i
$86$	2.20800			0.238095
$87$	−8.27433	+	8.27433i	−0.887101	+	0.887101i
$88$	5.55122	+	2.29939i	0.591762	+	0.245116i
$89$		−	0.648155i		−	0.0687043i	−0.999410	−	0.0343521i	$-0.989063\pi$
$89$		−	0.648155i		−	0.0687043i	0.999410	−	0.0343521i	$-0.0109368\pi$
$90$	−9.47787	+	22.8816i	−0.999056	+	2.41193i
$91$	4.29583	−	1.77939i	0.450325	−	0.186531i
$92$	3.96105	+	9.56283i	0.412968	+	0.996994i
$93$	−9.05732	−	9.05732i	−0.939201	−	0.939201i
$94$	5.26533	+	5.26533i	0.543077	+	0.543077i
$95$	0.362065	+	0.874102i	0.0371471	+	0.0896810i
$96$	16.8737	−	6.98930i	1.72216	−	0.713342i
$97$	3.19206	−	7.70631i	0.324105	−	0.782458i	−0.674903	−	0.737907i	$-0.735814\pi$
$97$	3.19206	−	7.70631i	0.324105	−	0.782458i	0.999007	−	0.0445508i	$-0.0141857\pi$
$98$		−	29.3248i		−	2.96225i
$99$	10.1751	+	4.21468i	1.02264	+	0.423591i
$100$	−10.2202	+	10.2202i	−1.02202	+	1.02202i
$101$	−2.47902			−0.246672			−0.123336	−	0.992365i	$-0.539359\pi$
$101$	−2.47902			−0.246672			−0.123336	+	0.992365i	$0.539359\pi$
$102$	−19.9750	+	11.9676i	−1.97782	+	1.18497i
$103$	19.3793			1.90950			0.954749	−	0.297411i	$-0.0961233\pi$
$103$	19.3793			1.90950			0.954749	+	0.297411i	$0.0961233\pi$
$104$	1.41094	−	1.41094i	0.138354	−	0.138354i
$105$	−33.6985	−	13.9584i	−3.28863	−	1.36220i
$106$			29.5014i			2.86543i
$107$	5.91420	−	14.2781i	0.571747	−	1.38032i	−0.328319	−	0.944567i	$-0.606482\pi$
$107$	5.91420	−	14.2781i	0.571747	−	1.38032i	0.900066	−	0.435753i	$-0.143518\pi$
$108$	−3.68495	+	1.52635i	−0.354584	+	0.146874i
$109$	−3.12465	−	7.54356i	−0.299287	−	0.722542i	−0.999959	−	0.00905877i	$-0.997116\pi$
$109$	−3.12465	−	7.54356i	−0.299287	−	0.722542i	0.700672	−	0.713483i	$-0.252884\pi$
$110$	15.3710	+	15.3710i	1.46556	+	1.46556i
$111$	−12.8435	−	12.8435i	−1.21905	−	1.21905i
$112$	2.55646	+	6.17185i	0.241563	+	0.583185i
$113$	−8.89575	+	3.68474i	−0.836842	+	0.346631i	−0.759607	−	0.650382i	$-0.774609\pi$
$113$	−8.89575	+	3.68474i	−0.836842	+	0.346631i	−0.0772342	+	0.997013i	$0.524609\pi$
$114$	−0.645759	+	1.55900i	−0.0604808	+	0.146014i
$115$			11.3992i			1.06298i
$116$	−12.1527	−	5.03383i	−1.12835	−	0.467380i
$117$	2.58619	−	2.58619i	0.239093	−	0.239093i
$118$	−16.3492			−1.50507
$119$	−9.54305	−	15.9283i	−0.874810	−	1.46014i
$120$	−15.6526			−1.42888
$121$	−0.942922	+	0.942922i	−0.0857202	+	0.0857202i
$122$	14.3887	+	5.96001i	1.30270	+	0.539594i
$123$		−	2.60218i		−	0.234631i
$124$	5.51018	−	13.3028i	0.494829	−	1.19462i
$125$	−0.0785031	+	0.0325171i	−0.00702153	+	0.00290841i
$126$	−13.4795	−	32.5425i	−1.20085	−	2.89912i
$127$	3.04865	+	3.04865i	0.270524	+	0.270524i	0.829311	−	0.558787i	$-0.188733\pi$
$127$	3.04865	+	3.04865i	0.270524	+	0.270524i	−0.558787	+	0.829311i	$0.688733\pi$
$128$	9.88545	+	9.88545i	0.873759	+	0.873759i
$129$	0.978828	+	2.36310i	0.0861810	+	0.208059i
$130$	6.66932	−	2.76252i	0.584938	−	0.242289i
$131$	4.22983	−	10.2117i	0.369562	−	0.892202i	−0.624260	−	0.781217i	$-0.714599\pi$
$131$	4.22983	−	10.2117i	0.369562	−	0.892202i	0.993822	−	0.110985i	$-0.0354007\pi$
$132$			22.8654i			1.99018i
$133$	−1.24316	−	0.514933i	−0.107795	−	0.0446504i
$134$	12.0976	−	12.0976i	1.04508	−	1.04508i
$135$	−4.39258			−0.378053
$136$	−6.39928	−	4.74786i	−0.548734	−	0.407125i
$137$	16.2543			1.38870			0.694348	−	0.719639i	$-0.255693\pi$
$137$	16.2543			1.38870			0.694348	+	0.719639i	$0.255693\pi$
$138$	−14.3762	+	14.3762i	−1.22378	+	1.22378i
$139$	−13.3405	−	5.52581i	−1.13153	−	0.468693i	−0.263226	−	0.964734i	$-0.584787\pi$
$139$	−13.3405	−	5.52581i	−1.13153	−	0.468693i	−0.868299	+	0.496041i	$0.834787\pi$
$140$		−	41.0021i		−	3.46531i
$141$	−3.30102	+	7.96936i	−0.277996	+	0.671141i
$142$	−18.4684	+	7.64987i	−1.54983	+	0.641963i
$143$	−1.22846	−	2.96576i	−0.102729	−	0.248009i
$144$	3.71560	+	3.71560i	0.309633	+	0.309633i
$145$	−10.2435	−	10.2435i	−0.850676	−	0.850676i
$146$	−10.1084	−	24.4039i	−0.836580	−	2.01968i
$147$	31.3847	−	12.9999i	2.58856	−	1.07222i
$148$	7.81356	−	18.8636i	0.642271	−	1.55058i
$149$		−	4.48722i		−	0.367607i	−0.982963	−	0.183804i	$-0.941159\pi$
$149$		−	4.48722i		−	0.367607i	0.982963	−	0.183804i	$-0.0588411\pi$
$150$	−26.2286	−	10.8643i	−2.14156	−	0.887063i
$151$	5.35678	−	5.35678i	0.435929	−	0.435929i	−0.454710	−	0.890639i	$-0.650257\pi$
$151$	5.35678	−	5.35678i	0.435929	−	0.435929i	0.890639	+	0.454710i	$0.150257\pi$
$152$	−0.577435			−0.0468362
$153$	−11.7296	−	8.70261i	−0.948282	−	0.703564i
$154$	−30.9158			−2.49126
$155$	11.2128	−	11.2128i	0.900636	−	0.900636i
$156$	7.01528	+	2.90582i	0.561672	+	0.232652i
$157$			14.8088i			1.18187i	0.806719	+	0.590936i	$0.201241\pi$
$157$			14.8088i			1.18187i	−0.806719	+	0.590936i	$0.798759\pi$
$158$	−12.5203	+	30.2266i	−0.996059	+	2.40470i
$159$	−31.5737	+	13.0782i	−2.50396	+	1.03717i
$160$	8.65265	+	20.8893i	0.684052	+	1.65145i
$161$	−11.4637	−	11.4637i	−0.903465	−	0.903465i
$162$	11.0521	+	11.0521i	0.868339	+	0.868339i
$163$	−2.81500	−	6.79601i	−0.220488	−	0.532304i	0.774469	−	0.632612i	$-0.218017\pi$
$163$	−2.81500	−	6.79601i	−0.220488	−	0.532304i	−0.994956	+	0.100308i	$0.968017\pi$
$164$	2.70249	−	1.11941i	0.211029	−	0.0874111i
$165$	−9.63658	+	23.2648i	−0.750207	+	1.81116i
$166$			28.7619i			2.23236i
$167$	−18.0110	−	7.46040i	−1.39373	−	0.577303i	−0.445616	−	0.895224i	$-0.647015\pi$
$167$	−18.0110	−	7.46040i	−1.39373	−	0.577303i	−0.948117	+	0.317921i	$0.897015\pi$
$168$	15.7411	−	15.7411i	1.21445	−	1.21445i
$169$	11.9340			0.917997
$170$	−14.8157	−	24.7288i	−1.13631	−	1.89661i
$171$	−1.05841			−0.0809388
$172$	−2.03312	+	2.03312i	−0.155024	+	0.155024i
$173$	9.80522	+	4.06146i	0.745477	+	0.308787i	0.722895	−	0.690958i	$-0.242811\pi$
$173$	9.80522	+	4.06146i	0.745477	+	0.308787i	0.0225826	+	0.999745i	$0.492811\pi$
$174$		−	25.8373i		−	1.95872i
$175$	8.66324	−	20.9149i	0.654880	−	1.58102i
$176$	4.26092	−	1.76493i	0.321179	−	0.133037i
$177$	−7.24777	−	17.4977i	−0.544775	−	1.31520i
$178$	1.01196	+	1.01196i	0.0758495	+	0.0758495i
$179$	11.2228	+	11.2228i	0.838829	+	0.838829i	0.988705	−	0.149876i	$-0.0478874\pi$
$179$	11.2228	+	11.2228i	0.838829	+	0.838829i	−0.149876	+	0.988705i	$0.547887\pi$
$180$	−12.3421	−	29.7965i	−0.919927	−	2.22090i
$181$	4.43323	−	1.83630i	0.329519	−	0.136491i	−0.211789	−	0.977315i	$-0.567929\pi$
$181$	4.43323	−	1.83630i	0.329519	−	0.136491i	0.541309	+	0.840824i	$0.317929\pi$
$182$	−3.92889	+	9.48519i	−0.291229	+	0.703089i
$183$			18.0416i			1.33367i
$184$	−6.42757	−	2.66239i	−0.473847	−	0.196274i
$185$	15.9001	−	15.9001i	1.16900	−	1.16900i
$186$	28.2823			2.07376
$187$	−10.9966	+	6.58834i	−0.804148	+	0.481787i
$188$	−9.69660			−0.707197
$189$	4.41742	−	4.41742i	0.321320	−	0.321320i
$190$	−1.93002	−	0.799439i	−0.140018	−	0.0579974i
$191$			7.78341i			0.563188i	0.959534	+	0.281594i	$0.0908631\pi$
$191$			7.78341i			0.563188i	−0.959534	+	0.281594i	$0.909137\pi$
$192$	−12.5284	+	30.2463i	−0.904161	+	2.18284i
$193$	1.75426	−	0.726638i	0.126274	−	0.0523046i	−0.318652	−	0.947872i	$-0.603230\pi$
$193$	1.75426	−	0.726638i	0.126274	−	0.0523046i	0.444926	+	0.895567i	$0.353230\pi$
$194$	7.04807	+	17.0155i	0.506022	+	1.22164i
$195$	5.91315	+	5.91315i	0.423449	+	0.423449i
$196$	27.0021	+	27.0021i	1.92872	+	1.92872i
$197$	−8.02546	−	19.3752i	−0.571791	−	1.38042i	−0.900029	−	0.435830i	$-0.856455\pi$
$197$	−8.02546	−	19.3752i	−0.571791	−	1.38042i	0.328238	−	0.944595i	$-0.393545\pi$
$198$	−22.4667	+	9.30601i	−1.59664	+	0.661350i
$199$	0.0611925	−	0.147732i	0.00433782	−	0.0104724i	−0.921696	−	0.387914i	$-0.873196\pi$
$199$	0.0611925	−	0.147732i	0.00433782	−	0.0104724i	0.926034	+	0.377441i	$0.123196\pi$
$200$		−	9.71478i		−	0.686939i
$201$	18.3104	+	7.58442i	1.29152	+	0.534964i
$202$	3.87048	−	3.87048i	0.272326	−	0.272326i
$203$	20.6029			1.44604
$204$	7.37324	−	29.4127i	0.516230	−	2.05930i
$205$	3.22146			0.224997
$206$	−30.2567	+	30.2567i	−2.10809	+	2.10809i
$207$	−11.7815	−	4.88004i	−0.818868	−	0.339186i
$208$		−	1.53158i		−	0.106196i
$209$	−0.355500	+	0.858252i	−0.0245904	+	0.0593666i
$210$	74.4062	−	30.8201i	5.13452	−	2.12679i
$211$	8.42619	+	20.3426i	0.580083	+	1.40044i	0.892738	+	0.450577i	$0.148782\pi$
$211$	8.42619	+	20.3426i	0.580083	+	1.40044i	−0.312655	+	0.949867i	$0.601218\pi$
$212$	−27.1648	−	27.1648i	−1.86568	−	1.86568i
$213$	−16.3744	−	16.3744i	−1.12196	−	1.12196i
$214$	13.0585	+	31.5261i	0.892664	+	2.15508i
$215$	−2.92548	+	1.21177i	−0.199516	+	0.0826423i
$216$	1.02593	−	2.47680i	0.0698054	−	0.168525i
$217$			22.5525i			1.53096i
$218$	16.6562	+	6.89922i	1.12810	+	0.467274i
$219$	21.6370	−	21.6370i	1.46209	−	1.46209i
$220$	−28.3070			−1.90846
$221$	0.623866	+	4.21110i	0.0419658	+	0.283269i
$222$	40.1049			2.69166
$223$	1.50932	−	1.50932i	0.101071	−	0.101071i	−0.654763	−	0.755834i	$-0.727232\pi$
$223$	1.50932	−	1.50932i	0.101071	−	0.101071i	0.755834	+	0.654763i	$0.227232\pi$
$224$	−29.7091	−	12.3059i	−1.98502	−	0.822222i
$225$		−	17.8068i		−	1.18712i
$226$	8.13591	−	19.6418i	0.541192	−	1.30655i
$227$	−8.40737	+	3.48245i	−0.558017	+	0.231138i	−0.643824	−	0.765174i	$-0.722653\pi$
$227$	−8.40737	+	3.48245i	−0.558017	+	0.231138i	0.0858073	+	0.996312i	$0.472653\pi$
$228$	−0.840909	−	2.03013i	−0.0556905	−	0.134449i
$229$	−6.38078	−	6.38078i	−0.421654	−	0.421654i	0.464119	−	0.885773i	$-0.346371\pi$
$229$	−6.38078	−	6.38078i	−0.421654	−	0.421654i	−0.885773	+	0.464119i	$0.846371\pi$
$230$	−17.7975	−	17.7975i	−1.17353	−	1.17353i
$231$	−13.7053	−	33.0874i	−0.901740	−	2.17699i
$232$	8.16836	−	3.38345i	0.536279	−	0.222134i
$233$	−11.5654	+	27.9213i	−0.757673	+	1.82919i	−0.248169	+	0.968717i	$0.579829\pi$
$233$	−11.5654	+	27.9213i	−0.757673	+	1.82919i	−0.509504	+	0.860468i	$0.670171\pi$
$234$			8.07559i			0.527918i
$235$	−9.86595	−	4.08661i	−0.643583	−	0.266581i
$236$	15.0543	−	15.0543i	0.979952	−	0.979952i
$237$	−37.9002			−2.46188
$238$	39.7682	+	9.96917i	2.57779	+	0.646206i
$239$	−3.13654			−0.202886			−0.101443	−	0.994841i	$-0.532346\pi$
$239$	−3.13654			−0.202886			−0.101443	+	0.994841i	$0.532346\pi$
$240$	−8.49546	+	8.49546i	−0.548380	+	0.548380i
$241$	−15.7579	−	6.52712i	−1.01505	−	0.420449i	−0.187757	−	0.982215i	$-0.560122\pi$
$241$	−15.7579	−	6.52712i	−1.01505	−	0.420449i	−0.827296	+	0.561767i	$0.810122\pi$
$242$		−	2.94435i		−	0.189270i
$243$	−8.52154	+	20.5728i	−0.546657	+	1.31975i
$244$	−18.7371	+	7.76114i	−1.19952	+	0.496856i
$245$	16.0937	+	38.8537i	1.02819	+	2.48227i
$246$	4.06276	+	4.06276i	0.259032	+	0.259032i
$247$	0.218140	+	0.218140i	0.0138799	+	0.0138799i
$248$	3.70362	+	8.94133i	0.235180	+	0.567775i
$249$	−30.7823	+	12.7504i	−1.95075	+	0.808026i
$250$	0.0717977	−	0.173335i	0.00454088	−	0.0109627i
$251$			11.6656i			0.736326i	0.929761	+	0.368163i	$0.120013\pi$
$251$			11.6656i			0.736326i	−0.929761	+	0.368163i	$0.879987\pi$
$252$	42.3769	+	17.5531i	2.66950	+	1.10574i
$253$	−7.91431	+	7.91431i	−0.497568	+	0.497568i
$254$	−9.51967			−0.597317
$255$	19.8979	−	26.8189i	1.24606	−	1.67947i
$256$	−5.26933			−0.329333
$257$	18.2096	−	18.2096i	1.13588	−	1.13588i	0.146704	−	0.989180i	$-0.453133\pi$
$257$	18.2096	−	18.2096i	1.13588	−	1.13588i	0.989180	−	0.146704i	$-0.0468666\pi$
$258$	−5.21772	−	2.16125i	−0.324841	−	0.134554i
$259$			31.9800i			1.98714i
$260$	−3.59737	+	8.68481i	−0.223099	+	0.538609i
$261$	14.9722	−	6.20171i	0.926759	−	0.383876i
$262$	9.33947	+	22.5475i	0.576994	+	1.39299i
$263$	0.908644	+	0.908644i	0.0560294	+	0.0560294i	0.734566	−	0.678537i	$-0.237386\pi$
$263$	0.908644	+	0.908644i	0.0560294	+	0.0560294i	−0.678537	+	0.734566i	$0.737386\pi$
$264$	−10.8674	−	10.8674i	−0.668841	−	0.668841i
$265$	−16.1907	−	39.0877i	−0.994585	−	2.40114i
$266$	2.74489	−	1.13697i	0.168300	−	0.0697122i
$267$	−0.634432	+	1.53165i	−0.0388266	+	0.0937357i
$268$			22.2789i			1.36090i
$269$	−22.5557	−	9.34288i	−1.37525	−	0.569646i	−0.432040	−	0.901854i	$-0.642206\pi$
$269$	−22.5557	−	9.34288i	−1.37525	−	0.569646i	−0.943206	+	0.332209i	$0.892206\pi$
$270$	6.85810	−	6.85810i	0.417371	−	0.417371i
$271$	3.42702			0.208177			0.104088	−	0.994568i	$-0.466808\pi$
$271$	3.42702			0.208177			0.104088	+	0.994568i	$0.466808\pi$
$272$	−6.05011	+	0.896313i	−0.366842	+	0.0543470i
$273$	−11.8932			−0.719808
$274$	−25.3777	+	25.3777i	−1.53312	+	1.53312i
$275$	−14.4393	−	5.98093i	−0.870720	−	0.360664i
$276$		−	26.4751i		−	1.59361i
$277$	−0.933522	+	2.25372i	−0.0560899	+	0.135413i	−0.949440	−	0.313948i	$-0.898348\pi$
$277$	−0.933522	+	2.25372i	−0.0560899	+	0.135413i	0.893350	+	0.449361i	$0.148348\pi$
$278$	29.4558	−	12.2010i	1.76664	−	0.731767i
$279$	6.78857	+	16.3891i	0.406421	+	0.981187i
$280$	19.4873	+	19.4873i	1.16459	+	1.16459i
$281$	−19.4656	−	19.4656i	−1.16122	−	1.16122i	−0.984209	−	0.177009i	$-0.943358\pi$
$281$	−19.4656	−	19.4656i	−1.16122	−	1.16122i	−0.177009	−	0.984209i	$-0.556642\pi$
$282$	−7.28865	−	17.5963i	−0.434032	−	1.04785i
$283$	−23.6803	+	9.80869i	−1.40765	+	0.583066i	−0.951724	−	0.306954i	$-0.900690\pi$
$283$	−23.6803	+	9.80869i	−1.40765	+	0.583066i	−0.455921	+	0.890020i	$0.650690\pi$
$284$	9.96168	−	24.0496i	0.591117	−	1.42708i
$285$		−	2.41999i		−	0.143348i
$286$	6.54839	+	2.71243i	0.387214	+	0.160389i
$287$	−3.23968	+	3.23968i	−0.191232	+	0.191232i
$288$	−25.2940			−1.49046
$289$	16.2698	−	4.92886i	0.957047	−	0.289933i
$290$	31.9862			1.87829
$291$	−15.0863	+	15.0863i	−0.884375	+	0.884375i
$292$	31.7789	+	13.1632i	1.85972	+	0.770320i
$293$			32.4619i			1.89645i	0.317607	+	0.948223i	$0.397121\pi$
$293$			32.4619i			1.89645i	−0.317607	+	0.948223i	$0.602879\pi$
$294$	−28.7039	+	69.2973i	−1.67404	+	4.04150i
$295$	21.6618	−	8.97263i	1.26120	−	0.522406i
$296$	5.25182	+	12.6790i	0.305256	+	0.736952i
$297$	−3.04970	−	3.04970i	−0.176962	−	0.176962i
$298$	7.00586	+	7.00586i	0.405838	+	0.405838i
$299$	1.42239	+	3.43395i	0.0822588	+	0.198590i
$300$	34.1550	−	14.1475i	1.97194	−	0.816804i
$301$	1.72340	−	4.16065i	0.0993351	−	0.239816i
$302$			16.7270i			0.962531i
$303$	5.85818	+	2.42654i	0.336544	+	0.139401i
$304$	−0.313403	+	0.313403i	−0.0179749	+	0.0179749i
$305$	−22.3352			−1.27891
$306$	31.9006	−	4.72602i	1.82364	−	0.270169i
$307$	−10.6281			−0.606575			−0.303288	−	0.952899i	$-0.598084\pi$
$307$	−10.6281			−0.606575			−0.303288	+	0.952899i	$0.598084\pi$
$308$	28.4671	−	28.4671i	1.62207	−	1.62207i
$309$	−45.7952	−	18.9690i	−2.60520	−	1.07911i
$310$			35.0130i			1.98860i
$311$	3.61462	−	8.72647i	0.204966	−	0.494833i	−0.787651	−	0.616122i	$-0.788703\pi$
$311$	3.61462	−	8.72647i	0.204966	−	0.494833i	0.992617	+	0.121289i	$0.0387029\pi$
$312$	−4.71526	+	1.95312i	−0.266949	+	0.110574i
$313$	−10.6299	−	25.6630i	−0.600840	−	1.45056i	−0.872718	−	0.488224i	$-0.837645\pi$
$313$	−10.6299	−	25.6630i	−0.600840	−	1.45056i	0.271878	−	0.962332i	$-0.412355\pi$
$314$	−23.1209	−	23.1209i	−1.30479	−	1.30479i
$315$	35.7193	+	35.7193i	2.01256	+	2.01256i
$316$	−16.3039	−	39.3612i	−0.917168	−	2.21424i
$317$	29.0241	−	12.0222i	1.63016	−	0.675233i	0.634907	−	0.772588i	$-0.281038\pi$
$317$	29.0241	−	12.0222i	1.63016	−	0.675233i	0.995250	+	0.0973552i	$0.0310383\pi$
$318$	28.8768	−	69.7147i	1.61933	−	3.90941i
$319$		−	14.2238i		−	0.796381i
$320$	−37.4444	−	15.5100i	−2.09321	−	0.867035i
$321$	−27.9517	+	27.9517i	−1.56011	+	1.56011i
$322$	35.7963			1.99485
$323$	0.734047	−	0.989368i	0.0408435	−	0.0550499i
$324$	−20.3536			−1.13075
$325$	−3.66999	+	3.66999i	−0.203574	+	0.203574i
$326$	15.0056	+	6.21552i	0.831082	+	0.344246i
$327$			20.8847i			1.15492i
$328$	−0.752400	+	1.81645i	−0.0415443	+	0.100297i
$329$	14.0315	−	5.81202i	0.773580	−	0.320427i
$330$	−21.2776	−	51.3686i	−1.17129	−	2.82775i
$331$	8.67152	+	8.67152i	0.476630	+	0.476630i	0.904052	−	0.427422i	$-0.140578\pi$
$331$	8.67152	+	8.67152i	0.476630	+	0.476630i	−0.427422	+	0.904052i	$0.640578\pi$
$332$	−26.4839	−	26.4839i	−1.45349	−	1.45349i
$333$	9.62635	+	23.2401i	0.527521	+	1.27355i
$334$	39.7683	−	16.4726i	2.17602	−	0.901338i
$335$	−9.38940	+	22.6680i	−0.512998	+	1.23849i
$336$		−	17.0870i		−	0.932173i
$337$	15.4110	+	6.38343i	0.839488	+	0.347727i	0.760652	−	0.649160i	$-0.224879\pi$
$337$	15.4110	+	6.38343i	0.839488	+	0.347727i	0.0788366	+	0.996888i	$0.474879\pi$
$338$	−18.6324	+	18.6324i	−1.01347	+	1.01347i
$339$	24.6283			1.33762
$340$	36.4124	+	9.12796i	1.97474	+	0.495033i
$341$	15.5698			0.843152
$342$	1.65249	−	1.65249i	0.0893565	−	0.0893565i
$343$	−26.1337	−	10.8249i	−1.41108	−	0.584490i
$344$		−	1.93258i		−	0.104198i
$345$	11.1579	−	26.9375i	0.600720	−	1.45027i
$346$	−21.6499	+	8.96770i	−1.16391	+	0.482106i
$347$	6.88925	+	16.6321i	0.369834	+	0.892859i	0.993777	+	0.111389i	$0.0355298\pi$
$347$	6.88925	+	16.6321i	0.369834	+	0.892859i	−0.623943	+	0.781470i	$0.714470\pi$
$348$	23.7909	+	23.7909i	1.27533	+	1.27533i
$349$	3.14299	+	3.14299i	0.168241	+	0.168241i	0.786206	−	0.617965i	$-0.212043\pi$
$349$	3.14299	+	3.14299i	0.168241	+	0.168241i	−0.617965	+	0.786206i	$0.712043\pi$
$350$	19.1284	+	46.1801i	1.02246	+	2.46843i
$351$	−1.32324	+	0.548104i	−0.0706293	+	0.0292556i
$352$	−8.49575	+	20.5106i	−0.452825	+	1.09322i
$353$			25.9443i			1.38088i	0.723392	+	0.690438i	$0.242582\pi$
$353$			25.9443i			1.38088i	−0.723392	+	0.690438i	$0.757418\pi$
$354$	38.6348	+	16.0031i	2.05342	+	0.850554i
$355$	20.2713	−	20.2713i	1.07589	−	1.07589i
$356$	−1.86362			−0.0987715
$357$	6.96016	+	46.9811i	0.368371	+	2.48650i
$358$	−35.0440			−1.85213
$359$	9.05355	−	9.05355i	0.477828	−	0.477828i	−0.426609	−	0.904436i	$-0.640292\pi$
$359$	9.05355	−	9.05355i	0.477828	−	0.477828i	0.904436	+	0.426609i	$0.140292\pi$
$360$	20.0275	+	8.29564i	1.05554	+	0.437219i
$361$			18.9107i			0.995301i
$362$	−4.05456	+	9.78857i	−0.213103	+	0.514476i
$363$	3.15118	−	1.30526i	0.165394	−	0.0685084i
$364$	−5.11622	−	12.3516i	−0.268163	−	0.647402i
$365$	26.7863	+	26.7863i	1.40206	+	1.40206i
$366$	−28.1682	−	28.1682i	−1.47237	−	1.47237i
$367$	−2.15269	−	5.19704i	−0.112369	−	0.271283i	0.857683	−	0.514178i	$-0.171903\pi$
$367$	−2.15269	−	5.19704i	−0.112369	−	0.271283i	−0.970053	+	0.242895i	$0.921903\pi$
$368$	−4.93358	+	2.04356i	−0.257181	+	0.106528i
$369$	−1.37912	+	3.32948i	−0.0717939	+	0.173326i
$370$			49.6492i			2.58114i
$371$	55.5910	+	23.0266i	2.88614	+	1.19548i
$372$	−26.0422	+	26.0422i	−1.35023	+	1.35023i
$373$	14.5728			0.754550			0.377275	−	0.926101i	$-0.376861\pi$
$373$	14.5728			0.754550			0.377275	+	0.926101i	$0.376861\pi$
$374$	6.88252	−	27.4552i	0.355887	−	1.41967i
$375$	0.217339			0.0112234
$376$	4.60856	−	4.60856i	0.237668	−	0.237668i
$377$	−4.36397	−	1.80762i	−0.224756	−	0.0930970i
$378$			13.7938i			0.709475i
$379$	0.496843	−	1.19948i	0.0255211	−	0.0616134i	−0.910605	−	0.413277i	$-0.864384\pi$
$379$	0.496843	−	1.19948i	0.0255211	−	0.0616134i	0.936126	+	0.351664i	$0.114384\pi$
$380$	2.51327	−	1.04103i	0.128928	−	0.0534038i
$381$	−4.22016	−	10.1884i	−0.216205	−	0.521966i
$382$	−12.1522	−	12.1522i	−0.621760	−	0.621760i
$383$	10.2049	+	10.2049i	0.521445	+	0.521445i	0.918008	−	0.396563i	$-0.129797\pi$
$383$	10.2049	+	10.2049i	0.521445	+	0.521445i	−0.396563	+	0.918008i	$0.629797\pi$
$384$	−13.6841	−	33.0365i	−0.698316	−	1.68588i
$385$	40.9617	−	16.9669i	2.08760	−	0.864713i
$386$	−1.60442	+	3.87341i	−0.0816627	+	0.197151i
$387$		−	3.54234i		−	0.180067i
$388$	−22.1577	−	9.17802i	−1.12489	−	0.465943i
$389$	−19.8049	+	19.8049i	−1.00415	+	1.00415i	−0.00415819	+	0.999991i	$0.501324\pi$
$389$	−19.8049	+	19.8049i	−1.00415	+	1.00415i	−0.999991	+	0.00415819i	$0.998676\pi$
$390$	−18.4643			−0.934976
$391$	12.7326	−	7.62842i	0.643913	−	0.385786i
$392$	−25.6669			−1.29638
$393$	−19.9910	+	19.9910i	−1.00841	+	1.00841i
$394$	42.7804	+	17.7202i	2.15525	+	0.892732i
$395$		−	46.9199i		−	2.36080i
$396$	12.1183	−	29.2562i	0.608969	−	1.47018i
$397$	20.9853	−	8.69241i	1.05322	−	0.436259i	0.212182	−	0.977230i	$-0.431943\pi$
$397$	20.9853	−	8.69241i	1.05322	−	0.436259i	0.841041	+	0.540971i	$0.181943\pi$
$398$	0.135113	+	0.326192i	0.00677261	+	0.0163505i
$399$	2.43368	+	2.43368i	0.121836	+	0.121836i
$400$	−5.27270	−	5.27270i	−0.263635	−	0.263635i
$401$	−4.86218	−	11.7383i	−0.242806	−	0.586184i	0.754754	−	0.656008i	$-0.227756\pi$
$401$	−4.86218	−	11.7383i	−0.242806	−	0.586184i	−0.997559	+	0.0698237i	$0.977756\pi$
$402$	−40.4294	+	16.7464i	−2.01643	+	0.835235i
$403$	1.97867	−	4.77693i	0.0985645	−	0.237956i
$404$			7.12785i			0.354624i
$405$	−20.7090	−	8.57796i	−1.02904	−	0.426242i
$406$	−32.1671	+	32.1671i	−1.59643	+	1.59643i
$407$	22.0783			1.09438
$408$	10.4748	+	17.4834i	0.518580	+	0.865560i
$409$	−7.15006			−0.353548			−0.176774	−	0.984252i	$-0.556566\pi$
$409$	−7.15006			−0.353548			−0.176774	+	0.984252i	$0.556566\pi$
$410$	−5.02964	+	5.02964i	−0.248396	+	0.248396i
$411$	−38.4105	−	15.9101i	−1.89465	−	0.784789i
$412$		−	55.7206i		−	2.74516i
$413$	−12.7610	+	30.8077i	−0.627927	+	1.51595i
$414$	26.0134	−	10.7751i	1.27849	−	0.529568i
$415$	−15.7848	−	38.1080i	−0.774848	−	1.87065i
$416$	5.21312	+	5.21312i	0.255594	+	0.255594i
$417$	26.1161	+	26.1161i	1.27891	+	1.27891i
$418$	−0.784943	−	1.89502i	−0.0383928	−	0.0926885i
$419$	−3.62351	+	1.50091i	−0.177020	+	0.0733241i	−0.469433	−	0.882968i	$-0.655542\pi$
$419$	−3.62351	+	1.50091i	−0.177020	+	0.0733241i	0.292413	+	0.956292i	$0.405542\pi$
$420$	−40.1340	+	96.8920i	−1.95834	+	4.72784i
$421$		−	32.2725i		−	1.57287i	−0.617676	−	0.786433i	$-0.711926\pi$
$421$		−	32.2725i		−	1.57287i	0.617676	−	0.786433i	$-0.288074\pi$
$422$	−44.9165	−	18.6050i	−2.18650	−	0.905678i
$423$	8.44728	−	8.44728i	0.410721	−	0.410721i
$424$	25.8215			1.25400
$425$	16.6451	+	12.3496i	0.807408	+	0.599045i
$426$	51.1306			2.47728
$427$	22.4615	−	22.4615i	1.08699	−	1.08699i
$428$	−41.0534	−	17.0049i	−1.98439	−	0.821962i
$429$			8.21082i			0.396422i
$430$	2.67560	−	6.45946i	0.129029	−	0.311503i
$431$	4.98703	−	2.06569i	0.240217	−	0.0995010i	−0.259327	−	0.965789i	$-0.583501\pi$
$431$	4.98703	−	2.06569i	0.240217	−	0.0995010i	0.499544	+	0.866288i	$0.333501\pi$
$432$	−0.787465	−	1.90111i	−0.0378869	−	0.0914671i
$433$	−2.89931	−	2.89931i	−0.139332	−	0.139332i	0.634000	−	0.773333i	$-0.281412\pi$
$433$	−2.89931	−	2.89931i	−0.139332	−	0.139332i	−0.773333	+	0.634000i	$0.781412\pi$
$434$	−35.2110	−	35.2110i	−1.69018	−	1.69018i
$435$	14.1798	+	34.2330i	0.679868	+	1.64135i
$436$	−21.6897	+	8.98418i	−1.03875	+	0.430264i
$437$	0.411621	−	0.993742i	0.0196905	−	0.0475371i
$438$			67.5633i			3.22830i
$439$	20.9200	+	8.66533i	0.998455	+	0.413574i	0.821230	−	0.570597i	$-0.193288\pi$
$439$	20.9200	+	8.66533i	0.998455	+	0.413574i	0.177225	+	0.984170i	$0.443288\pi$
$440$	13.4536	−	13.4536i	0.641377	−	0.641377i
$441$	−47.0463			−2.24030
$442$	−7.54879	−	5.60072i	−0.359059	−	0.266399i
$443$	−4.94708			−0.235043			−0.117521	−	0.993070i	$-0.537495\pi$
$443$	−4.94708			−0.235043			−0.117521	+	0.993070i	$0.537495\pi$
$444$	−36.9284	+	36.9284i	−1.75255	+	1.75255i
$445$	−1.89616	−	0.785417i	−0.0898868	−	0.0372323i
$446$			4.71297i			0.223166i
$447$	−4.39221	+	10.6037i	−0.207745	+	0.501540i
$448$	53.2539	−	22.0585i	2.51601	−	1.04217i
$449$	1.68781	+	4.07473i	0.0796526	+	0.192298i	0.958689	−	0.284456i	$-0.0918131\pi$
$449$	1.68781	+	4.07473i	0.0796526	+	0.192298i	−0.879036	+	0.476755i	$0.841813\pi$
$450$	27.8015	+	27.8015i	1.31058	+	1.31058i
$451$	2.23661	+	2.23661i	0.105318	+	0.105318i
$452$	10.5946	+	25.5776i	0.498328	+	1.20307i
$453$	−17.9020	+	7.41524i	−0.841108	+	0.348398i
$454$	7.68924	−	18.5635i	0.360874	−	0.871227i
$455$		−	14.7236i		−	0.690252i
$456$	1.36454	+	0.565209i	0.0639003	+	0.0264684i
$457$	23.9409	−	23.9409i	1.11991	−	1.11991i	0.128154	−	0.991754i	$-0.459095\pi$
$457$	23.9409	−	23.9409i	1.11991	−	1.11991i	0.991754	−	0.128154i	$-0.0409052\pi$
$458$	19.9245			0.931011
$459$	2.93954	+	4.90637i	0.137206	+	0.229010i
$460$	32.7758			1.52818
$461$	−9.82111	+	9.82111i	−0.457415	+	0.457415i	−0.897806	−	0.440391i	$-0.854840\pi$
$461$	−9.82111	+	9.82111i	−0.457415	+	0.457415i	0.440391	+	0.897806i	$0.354840\pi$
$462$	73.0570	+	30.2612i	3.39892	+	1.40788i
$463$			34.8610i			1.62013i	0.586342	+	0.810064i	$0.300568\pi$
$463$			34.8610i			1.62013i	−0.586342	+	0.810064i	$0.699432\pi$
$464$	2.59701	−	6.26975i	0.120563	−	0.291066i
$465$	−37.4725	+	15.5216i	−1.73774	+	0.719797i
$466$	−25.5364	−	61.6502i	−1.18295	−	2.85589i
$467$	−7.99744	−	7.99744i	−0.370077	−	0.370077i	0.497428	−	0.867505i	$-0.334278\pi$
$467$	−7.99744	−	7.99744i	−0.370077	−	0.370077i	−0.867505	+	0.497428i	$0.834278\pi$
$468$	−7.43598	−	7.43598i	−0.343728	−	0.343728i
$469$	−13.3537	−	32.2387i	−0.616617	−	1.48865i
$470$	21.7840	−	9.02323i	1.00482	−	0.416211i
$471$	14.4953	−	34.9947i	0.667907	−	1.61247i
$472$			14.3099i			0.658666i
$473$	−2.87243	−	1.18980i	−0.132075	−	0.0547071i
$474$	59.1733	−	59.1733i	2.71792	−	2.71792i
$475$	1.50196			0.0689148
$476$	−45.7980	+	27.4388i	−2.09915	+	1.25766i
$477$	47.3297			2.16708
$478$	4.89705	−	4.89705i	0.223986	−	0.223986i
$479$	9.27306	+	3.84103i	0.423697	+	0.175501i	0.584335	−	0.811512i	$-0.301355\pi$
$479$	9.27306	+	3.84103i	0.423697	+	0.175501i	−0.160638	+	0.987013i	$0.551355\pi$
$480$		−	57.8330i		−	2.63970i
$481$	2.80580	−	6.77380i	0.127933	−	0.308859i
$482$	34.7933	−	14.4119i	1.58479	−	0.656443i
$483$	15.8689	+	38.3108i	0.722058	+	1.74320i
$484$	2.71115	+	2.71115i	0.123234	+	0.123234i
$485$	−18.6766	−	18.6766i	−0.848062	−	0.848062i
$486$	−18.8156	−	45.4248i	−0.853492	−	2.06051i
$487$	19.9107	−	8.24729i	0.902240	−	0.373720i	0.117159	−	0.993113i	$-0.462621\pi$
$487$	19.9107	−	8.24729i	0.902240	−	0.373720i	0.785081	+	0.619393i	$0.212621\pi$
$488$	5.21658	−	12.5939i	0.236144	−	0.570101i
$489$			18.8150i			0.850845i
$490$	−85.7890	−	35.5350i	−3.87555	−	1.60531i
$491$	−15.8274	+	15.8274i	−0.714279	+	0.714279i	−0.967427	−	0.253149i	$-0.918534\pi$
$491$	−15.8274	+	15.8274i	−0.714279	+	0.714279i	0.253149	+	0.967427i	$0.418534\pi$
$492$	−7.48196			−0.337313
$493$	−4.58665	+	18.2966i	−0.206572	+	0.824039i
$494$	−0.681160			−0.0306468
$495$	24.6599	−	24.6599i	1.10838	−	1.10838i
$496$	6.86305	+	2.84277i	0.308160	+	0.127644i
$497$			40.7719i			1.82887i
$498$	28.1530	−	67.9673i	1.26156	−	3.04569i
$499$	−13.3268	+	5.52013i	−0.596589	+	0.247115i	−0.660482	−	0.750842i	$-0.729648\pi$
$499$	−13.3268	+	5.52013i	−0.596589	+	0.247115i	0.0638936	+	0.997957i	$0.479648\pi$
$500$	0.0934952	+	0.225717i	0.00418123	+	0.0100944i
$501$	35.2593	+	35.2593i	1.57527	+	1.57527i
$502$	−18.2134	−	18.2134i	−0.812903	−	0.812903i
$503$	−2.35434	−	5.68389i	−0.104975	−	0.253432i	0.862661	−	0.505783i	$-0.168796\pi$
$503$	−2.35434	−	5.68389i	−0.104975	−	0.253432i	−0.967636	+	0.252351i	$0.918796\pi$
$504$	−28.4833	+	11.7982i	−1.26875	+	0.525532i
$505$	−3.00402	+	7.25234i	−0.133677	+	0.322725i
$506$		−	24.7131i		−	1.09863i
$507$	−28.2011	−	11.6813i	−1.25246	−	0.518785i
$508$	8.76568	−	8.76568i	0.388914	−	0.388914i
$509$	−28.7701			−1.27521			−0.637605	−	0.770363i	$-0.720075\pi$
$509$	−28.7701			−1.27521			−0.637605	+	0.770363i	$0.720075\pi$
$510$	10.8057	+	72.9386i	0.478485	+	3.22978i
$511$	−53.8755			−2.38331
$512$	−11.5439	+	11.5439i	−0.510175	+	0.510175i
$513$	0.382929	+	0.158614i	0.0169067	+	0.00700299i
$514$			56.8611i			2.50803i
$515$	23.4833	−	56.6938i	1.03480	−	2.49823i
$516$	6.79453	−	2.81439i	0.299113	−	0.123897i
$517$	−4.01251	−	9.68705i	−0.176470	−	0.426036i
$518$	−49.9300	−	49.9300i	−2.19380	−	2.19380i
$519$	−19.1952	−	19.1952i	−0.842578	−	0.842578i
$520$	−2.41794	−	5.83742i	−0.106034	−	0.255988i
$521$	−9.07837	+	3.76039i	−0.397731	+	0.164745i	−0.572578	−	0.819850i	$-0.694057\pi$
$521$	−9.07837	+	3.76039i	−0.397731	+	0.164745i	0.174848	+	0.984596i	$0.444057\pi$
$522$	−13.6934	+	33.0587i	−0.599342	+	1.44694i
$523$		−	11.5287i		−	0.504115i	−0.967712	−	0.252058i	$-0.918893\pi$
$523$		−	11.5287i		−	0.504115i	0.967712	−	0.252058i	$-0.0811073\pi$
$524$	−29.3614	−	12.1619i	−1.28266	−	0.531295i
$525$	−40.9442	+	40.9442i	−1.78695	+	1.78695i
$526$	−2.83732			−0.123713
$527$	−20.0280	−	5.02068i	−0.872435	−	0.218704i
$528$	−11.7965			−0.513379
$529$	−7.09974	+	7.09974i	−0.308684	+	0.308684i
$530$	86.3057	+	35.7490i	3.74888	+	1.55284i
$531$			26.2294i			1.13826i
$532$	−1.48057	+	3.57441i	−0.0641908	+	0.154970i
$533$	0.970446	−	0.401972i	0.0420347	−	0.0174113i
$534$	−1.40083	−	3.38189i	−0.0606196	−	0.146349i
$535$	−34.6037	−	34.6037i	−1.49605	−	1.49605i
$536$	−10.5886	−	10.5886i	−0.457359	−	0.457359i
$537$	−15.5354	−	37.5057i	−0.670400	−	1.61849i
$538$	49.8030	−	20.6291i	2.14716	−	0.889383i
$539$	−15.8019	+	38.1492i	−0.680637	+	1.64320i
$540$			12.6298i			0.543502i
$541$	25.5810	+	10.5960i	1.09981	+	0.455558i	0.857419	−	0.514619i	$-0.172067\pi$
$541$	25.5810	+	10.5960i	1.09981	+	0.455558i	0.242396	+	0.970177i	$0.422067\pi$
$542$	−5.35058	+	5.35058i	−0.229827	+	0.229827i
$543$	−12.2736			−0.526710
$544$	17.5423	−	23.6440i	0.752120	−	1.01373i
$545$	−25.8549			−1.10750
$546$	18.5687	−	18.5687i	0.794668	−	0.794668i
$547$	7.46051	+	3.09024i	0.318988	+	0.132129i	0.536432	−	0.843944i	$-0.319772\pi$
$547$	7.46051	+	3.09024i	0.318988	+	0.132129i	−0.217444	+	0.976073i	$0.569772\pi$
$548$		−	46.7353i		−	1.99644i
$549$	9.56177	−	23.0841i	0.408086	−	0.985207i
$550$	31.8819	−	13.2059i	1.35945	−	0.563102i
$551$	0.523101	+	1.26288i	0.0222849	+	0.0538004i
$552$	12.5830	+	12.5830i	0.535567	+	0.535567i
$553$	47.1852	+	47.1852i	2.00652	+	2.00652i
$554$	−2.06122	−	4.97622i	−0.0875727	−	0.211419i
$555$	−53.1368	+	22.0100i	−2.25553	+	0.934272i
$556$	−15.8882	+	38.3574i	−0.673808	+	1.62672i
$557$		−	46.6793i		−	1.97787i	−0.148362	−	0.988933i	$-0.547400\pi$
$557$		−	46.6793i		−	1.97787i	0.148362	−	0.988933i	$-0.452600\pi$
$558$	−36.1870	−	14.9892i	−1.53192	−	0.634542i
$559$	−0.730080	+	0.730080i	−0.0308791	+	0.0308791i
$560$	21.1535			0.893897
$561$	32.4348	−	4.80516i	1.36940	−	0.202874i
$562$	60.7829			2.56397
$563$	−6.15039	+	6.15039i	−0.259208	+	0.259208i	−0.824732	−	0.565524i	$-0.808674\pi$
$563$	−6.15039	+	6.15039i	−0.259208	+	0.259208i	0.565524	+	0.824732i	$0.308674\pi$
$564$	22.9140	+	9.49130i	0.964854	+	0.399656i
$565$			30.4894i			1.28270i
$566$	21.6576	−	52.2860i	0.910336	−	2.19775i
$567$	29.4526	−	12.1997i	1.23689	−	0.512338i
$568$	6.69566	+	16.1647i	0.280943	+	0.678257i
$569$	11.4552	+	11.4552i	0.480229	+	0.480229i	0.905205	−	0.424976i	$-0.139717\pi$
$569$	11.4552	+	11.4552i	0.480229	+	0.480229i	−0.424976	+	0.905205i	$0.639717\pi$
$570$	3.77831	+	3.77831i	0.158256	+	0.158256i
$571$	12.2475	+	29.5680i	0.512541	+	1.23738i	0.942400	+	0.334487i	$0.108563\pi$
$571$	12.2475	+	29.5680i	0.512541	+	1.23738i	−0.429860	+	0.902896i	$0.641437\pi$
$572$	−8.52733	+	3.53214i	−0.356546	+	0.147686i
$573$	7.61862	−	18.3930i	0.318272	−	0.768378i
$574$		−	10.1162i		−	0.422241i
$575$	16.7187	+	6.92512i	0.697219	+	0.288798i
$576$	32.0601	−	32.0601i	1.33584	−	1.33584i
$577$	−25.8407			−1.07576			−0.537881	−	0.843021i	$-0.680775\pi$
$577$	−25.8407			−1.07576			−0.537881	+	0.843021i	$0.680775\pi$
$578$	−17.7065	+	33.0973i	−0.736494	+	1.37667i
$579$	−4.85674			−0.201839
$580$	−29.4528	+	29.4528i	−1.22296	+	1.22296i
$581$	54.1976	+	22.4494i	2.24850	+	0.931358i
$582$		−	47.1083i		−	1.95270i
$583$	15.8971	−	38.3790i	0.658390	−	1.58949i
$584$	−21.3599	+	8.84756i	−0.883879	+	0.366115i
$585$	−4.43197	−	10.6997i	−0.183239	−	0.442379i
$586$	−50.6825	−	50.6825i	−2.09368	−	2.09368i
$587$	6.44529	+	6.44529i	0.266026	+	0.266026i	0.827496	−	0.561471i	$-0.189764\pi$
$587$	6.44529	+	6.44529i	0.266026	+	0.266026i	−0.561471	+	0.827496i	$0.689764\pi$
$588$	−37.3783	−	90.2392i	−1.54145	−	3.72140i
$589$	−1.38238	+	0.572602i	−0.0569601	+	0.0235937i
$590$	−19.8116	+	47.8293i	−0.815629	+	1.96910i
$591$			53.6410i			2.20650i
$592$	9.73196	+	4.03111i	0.399981	+	0.165678i
$593$	14.9549	−	14.9549i	0.614123	−	0.614123i	−0.329895	−	0.944018i	$-0.607013\pi$
$593$	14.9549	−	14.9549i	0.614123	−	0.614123i	0.944018	+	0.329895i	$0.107013\pi$
$594$	9.52296			0.390732
$595$	−58.1618	+	8.61657i	−2.38440	+	0.353245i
$596$	−12.9019			−0.528484
$597$	−0.289208	+	0.289208i	−0.0118365	+	0.0118365i
$598$	−7.58216	−	3.14063i	−0.310058	−	0.128430i
$599$		−	13.0569i		−	0.533490i	−0.963767	−	0.266745i	$-0.914052\pi$
$599$		−	13.0569i		−	0.533490i	0.963767	−	0.266745i	$-0.0859481\pi$
$600$	−9.50909	+	22.9570i	−0.388207	+	0.937215i
$601$	−3.71887	+	1.54041i	−0.151696	+	0.0628345i	−0.457240	−	0.889344i	$-0.651162\pi$
$601$	−3.71887	+	1.54041i	−0.151696	+	0.0628345i	0.305544	+	0.952178i	$0.401162\pi$
$602$	3.80527	+	9.18672i	0.155091	+	0.374423i
$603$	−19.4085	−	19.4085i	−0.790374	−	0.790374i
$604$	−15.4022	−	15.4022i	−0.626705	−	0.626705i
$605$	1.61589	+	3.90111i	0.0656954	+	0.158603i
$606$	−12.9349	+	5.35780i	−0.525443	+	0.217646i
$607$	−10.6487	+	25.7083i	−0.432219	+	1.04347i	0.546352	+	0.837556i	$0.316016\pi$
$607$	−10.6487	+	25.7083i	−0.432219	+	1.04347i	−0.978570	+	0.205912i	$0.933984\pi$
$608$		−	2.13350i		−	0.0865248i
$609$	−48.6866	−	20.1666i	−1.97288	−	0.817194i
$610$	34.8718	−	34.8718i	1.41192	−	1.41192i
$611$	−3.48198			−0.140866
$612$	−25.0223	+	33.7257i	−1.01147	+	1.36328i
$613$	0.584613			0.0236123			0.0118061	−	0.999930i	$-0.496242\pi$
$613$	0.584613			0.0236123			0.0118061	+	0.999930i	$0.496242\pi$
$614$	16.5935	−	16.5935i	0.669659	−	0.669659i
$615$	−7.61263	−	3.15325i	−0.306971	−	0.127151i
$616$			27.0595i			1.09026i
$617$	−16.8921	+	40.7812i	−0.680051	+	1.64179i	0.0838674	+	0.996477i	$0.473273\pi$
$617$	−16.8921	+	40.7812i	−0.680051	+	1.64179i	−0.763919	+	0.645312i	$0.776727\pi$
$618$	101.116	−	41.8835i	4.06747	−	1.68480i
$619$	−2.52394	−	6.09332i	−0.101446	−	0.244911i	0.865005	−	0.501763i	$-0.167315\pi$
$619$	−2.52394	−	6.09332i	−0.101446	−	0.244911i	−0.966451	+	0.256851i	$0.917315\pi$
$620$	−32.2399	−	32.2399i	−1.29478	−	1.29478i
$621$	3.53115	+	3.53115i	0.141700	+	0.141700i
$622$	7.98108	+	19.2680i	0.320012	+	0.772578i
$623$	2.69675	−	1.11703i	0.108043	−	0.0447528i
$624$	−1.49915	+	3.61927i	−0.0600140	+	0.144887i
$625$		−	24.8651i		−	0.994604i
$626$	56.6638	+	23.4709i	2.26474	+	0.938086i
$627$	1.68016	−	1.68016i	0.0670992	−	0.0670992i
$628$	42.5792			1.69910
$629$	−28.4002	−	7.11943i	−1.13239	−	0.283870i
$630$	−111.537			−4.44372
$631$	−8.11252	+	8.11252i	−0.322954	+	0.322954i	−0.849899	−	0.526945i	$-0.823337\pi$
$631$	−8.11252	+	8.11252i	−0.322954	+	0.322954i	0.526945	+	0.849899i	$0.323337\pi$
$632$	26.4563	+	10.9585i	1.05237	+	0.435908i
$633$		−	56.3194i		−	2.23850i
$634$	−26.5450	+	64.0853i	−1.05424	+	2.54515i
$635$	12.6130	−	5.22449i	0.500533	−	0.207328i
$636$	37.6034	+	90.7827i	1.49107	+	3.59977i
$637$	9.69629	+	9.69629i	0.384181	+	0.384181i
$638$	22.2075	+	22.2075i	0.879204	+	0.879204i
$639$	12.2728	+	29.6293i	0.485506	+	1.17212i
$640$	40.8986	−	16.9408i	1.61666	−	0.669643i
$641$	−4.86844	+	11.7534i	−0.192292	+	0.464233i	−0.990392	−	0.138292i	$-0.955839\pi$
$641$	−4.86844	+	11.7534i	−0.192292	+	0.464233i	0.798100	+	0.602525i	$0.205839\pi$
$642$		−	87.2814i		−	3.44472i
$643$	−32.7679	−	13.5729i	−1.29224	−	0.535263i	−0.372587	−	0.927997i	$-0.621529\pi$
$643$	−32.7679	−	13.5729i	−1.29224	−	0.535263i	−0.919652	+	0.392734i	$0.871529\pi$
$644$	−32.9611	+	32.9611i	−1.29885	+	1.29885i
$645$	8.09932			0.318910
$646$	0.398630	+	2.69075i	0.0156839	+	0.105866i
$647$	−0.956215			−0.0375927			−0.0187963	−	0.999823i	$-0.505983\pi$
$647$	−0.956215			−0.0375927			−0.0187963	+	0.999823i	$0.505983\pi$
$648$	9.67355	−	9.67355i	0.380013	−	0.380013i
$649$	21.2691	+	8.80993i	0.834883	+	0.345820i
$650$		−	11.4598i		−	0.449492i
$651$	22.0750	−	53.2938i	0.865188	−	2.08875i
$652$	−19.5403	+	8.09386i	−0.765258	+	0.316980i
$653$	0.112945	+	0.272673i	0.00441988	+	0.0106705i	0.926074	−	0.377342i	$-0.123162\pi$
$653$	0.112945	+	0.272673i	0.00441988	+	0.0106705i	−0.921654	+	0.388012i	$0.873162\pi$
$654$	−32.6071	−	32.6071i	−1.27504	−	1.27504i
$655$	−24.7486	−	24.7486i	−0.967007	−	0.967007i
$656$	0.577516	+	1.39425i	0.0225482	+	0.0544362i
$657$	−39.1517	+	16.2172i	−1.52745	+	0.632692i
$658$	−12.8329	+	30.9815i	−0.500280	+	1.20778i
$659$			41.0073i			1.59742i	0.601719	+	0.798708i	$0.294483\pi$
$659$			41.0073i			1.59742i	−0.601719	+	0.798708i	$0.705517\pi$
$660$	66.8923	+	27.7077i	2.60378	+	1.07852i
$661$	4.32848	−	4.32848i	0.168358	−	0.168358i	−0.617899	−	0.786257i	$-0.712016\pi$
$661$	4.32848	−	4.32848i	0.168358	−	0.168358i	0.786257	+	0.617899i	$0.212016\pi$
$662$	−27.0775			−1.05240
$663$	2.64768	−	10.5619i	0.102827	−	0.410190i
$664$	25.1743			0.976952
$665$	−3.01285	+	3.01285i	−0.116833	+	0.116833i
$666$	−51.3140	−	21.2550i	−1.98838	−	0.823614i
$667$			16.4693i			0.637693i
$668$	−21.4506	+	51.7864i	−0.829949	+	2.00367i
$669$	−5.04403	+	2.08931i	−0.195013	+	0.0807772i
$670$	−20.7318	−	50.0510i	−0.800939	−	1.93364i
$671$	−15.5070	−	15.5070i	−0.598641	−	0.598641i
$672$	58.1601	+	58.1601i	2.24357	+	2.24357i
$673$	−7.70629	−	18.6046i	−0.297055	−	0.717155i	−0.999983	−	0.00589354i	$-0.998124\pi$
$673$	−7.70629	−	18.6046i	−0.297055	−	0.717155i	0.702927	−	0.711262i	$-0.251876\pi$
$674$	−34.0274	+	14.0946i	−1.31069	+	0.542904i
$675$	−2.66853	+	6.44240i	−0.102712	+	0.247968i
$676$		−	34.3133i		−	1.31974i
$677$	−32.5693	−	13.4906i	−1.25174	−	0.518487i	−0.344374	−	0.938832i	$-0.611909\pi$
$677$	−32.5693	−	13.4906i	−1.25174	−	0.518487i	−0.907364	+	0.420345i	$0.861909\pi$
$678$	−38.4519	+	38.4519i	−1.47674	+	1.47674i
$679$	37.5645			1.44159
$680$	−21.6442	+	12.9677i	−0.830019	+	0.497287i
$681$	23.2762			0.891944
$682$	−24.3090	+	24.3090i	−0.930840	+	0.930840i
$683$	−26.6272	−	11.0293i	−1.01886	−	0.422026i	−0.190181	−	0.981749i	$-0.560908\pi$
$683$	−26.6272	−	11.0293i	−1.01886	−	0.422026i	−0.828680	+	0.559723i	$0.810908\pi$
$684$			3.04322i			0.116360i
$685$	19.6965	−	47.5516i	0.752565	−	1.81685i
$686$	57.7031	−	23.9014i	2.20311	−	0.912560i
$687$	8.83273	+	21.3241i	0.336990	+	0.813565i
$688$	−1.04891	−	1.04891i	−0.0399893	−	0.0399893i
$689$	−9.75469	−	9.75469i	−0.371624	−	0.371624i
$690$	24.6366	+	59.4780i	0.937899	+	2.26429i
$691$	10.6352	−	4.40526i	0.404584	−	0.167584i	−0.171105	−	0.985253i	$-0.554734\pi$
$691$	10.6352	−	4.40526i	0.404584	−	0.167584i	0.575689	+	0.817669i	$0.304734\pi$
$692$	11.6778	−	28.1926i	0.443922	−	1.07172i
$693$			49.5988i			1.88410i
$694$	−36.7237	−	15.2115i	−1.39401	−	0.577419i
$695$	−32.3313	+	32.3313i	−1.22640	+	1.22640i
$696$	−22.6145			−0.857199
$697$	−2.15582	−	3.59826i	−0.0816574	−	0.136294i
$698$	−9.81426			−0.371475
$699$	54.6603	−	54.6603i	2.06744	−	2.06744i
$700$	−60.1359	−	24.9091i	−2.27292	−	0.941476i
$701$			39.1601i			1.47905i	0.673126	+	0.739527i	$0.264951\pi$
$701$			39.1601i			1.47905i	−0.673126	+	0.739527i	$0.735049\pi$
$702$	1.21021	−	2.92171i	0.0456766	−	0.110273i
$703$	−1.96025	+	0.811963i	−0.0739323	+	0.0306238i
$704$	−15.2288	−	36.7655i	−0.573955	−	1.38565i
$705$	19.3141	+	19.3141i	0.727412	+	0.727412i
$706$	−40.5066	−	40.5066i	−1.52449	−	1.52449i
$707$	−4.27235	−	10.3144i	−0.160678	−	0.387912i
$708$	−50.3104	+	20.8392i	−1.89078	+	0.783187i
$709$	2.57992	−	6.22847i	0.0968908	−	0.233915i	−0.868001	−	0.496562i	$-0.834595\pi$
$709$	2.57992	−	6.22847i	0.0968908	−	0.233915i	0.964892	+	0.262647i	$0.0845955\pi$
$710$			63.2989i			2.37557i
$711$	48.4932	+	20.0865i	1.81864	+	0.753304i
$712$	0.885731	−	0.885731i	0.0331942	−	0.0331942i
$713$	−18.0278			−0.675145
$714$	−84.2180	−	62.4843i	−3.15178	−	2.33842i
$715$	−10.1649			−0.380145
$716$	32.2684	−	32.2684i	1.20593	−	1.20593i
$717$	7.41195	+	3.07013i	0.276804	+	0.114656i
$718$			28.2705i			1.05504i
$719$	1.07944	−	2.60601i	0.0402565	−	0.0971877i	−0.902472	−	0.430748i	$-0.858250\pi$
$719$	1.07944	−	2.60601i	0.0402565	−	0.0971877i	0.942729	+	0.333560i	$0.108250\pi$
$720$	15.3724	−	6.36745i	0.572895	−	0.237301i
$721$	33.3983	+	80.6305i	1.24382	+	3.00284i
$722$	−29.5252	−	29.5252i	−1.09881	−	1.09881i
$723$	30.8484	+	30.8484i	1.14727	+	1.14727i
$724$	−5.27986	−	12.7467i	−0.196224	−	0.473728i
$725$	−21.2467	+	8.80067i	−0.789082	+	0.326849i
$726$	−2.88201	+	6.95780i	−0.106962	+	0.258228i
$727$			19.7635i			0.732988i	0.930420	+	0.366494i	$0.119442\pi$
$727$			19.7635i			0.732988i	−0.930420	+	0.366494i	$0.880558\pi$
$728$	8.30205	+	3.43882i	0.307694	+	0.127451i
$729$	25.2580	−	25.2580i	0.935481	−	0.935481i
$730$	−83.6424			−3.09574
$731$	3.31126	+	2.45674i	0.122471	+	0.0908658i
$732$	51.8743			1.91733
$733$	−20.0771	+	20.0771i	−0.741566	+	0.741566i	−0.972879	−	0.231313i	$-0.925698\pi$
$733$	−20.0771	+	20.0771i	−0.741566	+	0.741566i	0.231313	+	0.972879i	$0.425698\pi$
$734$	11.4751	+	4.75313i	0.423553	+	0.175441i
$735$		−	107.568i		−	3.96771i
$736$	9.83694	−	23.7485i	0.362595	−	0.875381i
$737$	−22.2570	+	9.21915i	−0.819847	+	0.339592i
$738$	−3.04509	−	7.35149i	−0.112091	−	0.270612i
$739$	21.3421	+	21.3421i	0.785080	+	0.785080i	0.980683	−	0.195603i	$-0.0626664\pi$
$739$	21.3421	+	21.3421i	0.785080	+	0.785080i	−0.195603	+	0.980683i	$0.562666\pi$
$740$	−45.7169	−	45.7169i	−1.68058	−	1.68058i
$741$	−0.301965	−	0.729007i	−0.0110930	−	0.0267808i
$742$	−122.745	+	50.8427i	−4.50611	+	1.86649i
$743$	8.65078	−	20.8848i	0.317366	−	0.766190i	−0.682026	−	0.731328i	$-0.738901\pi$
$743$	8.65078	−	20.8848i	0.317366	−	0.766190i	0.999392	−	0.0348620i	$-0.0110992\pi$
$744$		−	24.7544i		−	0.907542i
$745$	−13.1273	−	5.43749i	−0.480946	−	0.199214i
$746$	−22.7523	+	22.7523i	−0.833023	+	0.833023i
$747$	46.1433			1.68830
$748$	18.9432	+	31.6180i	0.692633	+	1.15607i
$749$	69.5989			2.54309
$750$	−0.339330	+	0.339330i	−0.0123906	+	0.0123906i
$751$	9.28064	+	3.84417i	0.338656	+	0.140276i	0.545529	−	0.838092i	$-0.316329\pi$
$751$	9.28064	+	3.84417i	0.338656	+	0.140276i	−0.206873	+	0.978368i	$0.566329\pi$
$752$		−	5.00259i		−	0.182426i
$753$	11.4186	−	27.5669i	0.416117	−	1.00460i
$754$	9.63565	−	3.99122i	0.350910	−	0.145352i
$755$	−9.17996	−	22.1624i	−0.334093	−	0.806572i
$756$	−12.7013	−	12.7013i	−0.461941	−	0.461941i
$757$	−26.6178	−	26.6178i	−0.967441	−	0.967441i	0.0320455	−	0.999486i	$-0.489798\pi$
$757$	−26.6178	−	26.6178i	−0.967441	−	0.967441i	−0.999486	+	0.0320455i	$0.989798\pi$
$758$	1.09703	+	2.64846i	0.0398459	+	0.0961964i
$759$	26.4490	−	10.9556i	0.960039	−	0.397661i
$760$	−0.699721	+	1.68928i	−0.0253815	+	0.0612765i
$761$		−	15.6442i		−	0.567104i	−0.958957	−	0.283552i	$-0.908487\pi$
$761$		−	15.6442i		−	0.567104i	0.958957	−	0.283552i	$-0.0915128\pi$
$762$	22.4959	+	9.31811i	0.814941	+	0.337560i
$763$	26.0011	−	26.0011i	0.941304	−	0.941304i
$764$	22.3794			0.809657
$765$	−39.6729	+	23.7691i	−1.43438	+	0.859375i
$766$	−31.8656			−1.15135
$767$	5.40590	−	5.40590i	0.195196	−	0.195196i
$768$	12.4520	+	5.15777i	0.449321	+	0.186115i
$769$			39.9706i			1.44138i	0.693260	+	0.720688i	$0.256174\pi$
$769$			39.9706i			1.44138i	−0.693260	+	0.720688i	$0.743826\pi$
$770$	−37.4629	+	90.4435i	−1.35007	+	3.25936i
$771$	−60.8552	+	25.2070i	−2.19165	+	0.907810i
$772$	−2.08928	−	5.04396i	−0.0751947	−	0.181536i
$773$	−31.8261	−	31.8261i	−1.14471	−	1.14471i	−0.987578	−	0.157129i	$-0.949776\pi$
$773$	−31.8261	−	31.8261i	−1.14471	−	1.14471i	−0.157129	−	0.987578i	$-0.550224\pi$
$774$	5.53063	+	5.53063i	0.198794	+	0.198794i
$775$	−9.63347	−	23.2572i	−0.346044	−	0.835425i
$776$	14.8931	−	6.16892i	0.534631	−	0.221451i
$777$	31.3029	−	75.5718i	1.12298	−	2.71112i
$778$		−	61.8425i		−	2.21716i
$779$	−0.280835	−	0.116326i	−0.0100620	−	0.00416780i
$780$	17.0019	−	17.0019i	0.608764	−	0.608764i
$781$	28.1482			1.00722
$782$	−7.96904	+	31.7894i	−0.284972	+	1.13679i
$783$	−6.34628			−0.226798
$784$	−13.9307	+	13.9307i	−0.497526	+	0.497526i
$785$	43.3229	+	17.9449i	1.54626	+	0.640482i
$786$		−	62.4237i		−	2.22658i
$787$	−8.83922	+	21.3398i	−0.315084	+	0.760681i	0.684417	+	0.729091i	$0.260057\pi$
$787$	−8.83922	+	21.3398i	−0.315084	+	0.760681i	−0.999501	+	0.0315895i	$0.989943\pi$
$788$	−55.7088	+	23.0753i	−1.98454	+	0.822025i
$789$	−1.25781	−	3.03662i	−0.0447792	−	0.108107i
$790$	73.2556	+	73.2556i	2.60632	+	2.60632i
$791$	−30.6619	−	30.6619i	−1.09021	−	1.09021i
$792$	8.14522	+	19.6643i	0.289428	+	0.698741i
$793$	−6.72835	+	2.78698i	−0.238931	+	0.0989684i
$794$	−19.1928	+	46.3356i	−0.681128	+	1.64439i
$795$			108.216i			3.83803i
$796$	−0.424768	−	0.175945i	−0.0150555	−	0.00623619i
$797$	31.4431	−	31.4431i	1.11377	−	1.11377i	0.121134	−	0.992636i	$-0.461347\pi$
$797$	31.4431	−	31.4431i	1.11377	−	1.11377i	0.992636	−	0.121134i	$-0.0386532\pi$
$798$	−7.59935			−0.269014
$799$	2.03774	+	13.7547i	0.0720899	+	0.486607i
$800$	35.8940			1.26904
$801$	1.62351	−	1.62351i	0.0573638	−	0.0573638i
$802$	25.9182	+	10.7357i	0.915205	+	0.379090i
$803$			37.1946i			1.31257i
$804$	21.8072	−	52.6473i	0.769081	−	1.85673i
$805$	−47.4282	+	19.6454i	−1.67162	+	0.692410i
$806$	4.36890	+	10.5475i	0.153888	+	0.371519i
$807$	44.1563	+	44.1563i	1.55438	+	1.55438i
$808$	−3.38769	−	3.38769i	−0.119179	−	0.119179i
$809$	7.38441	+	17.8275i	0.259622	+	0.626783i	0.998914	−	0.0466026i	$-0.0148394\pi$
$809$	7.38441	+	17.8275i	0.259622	+	0.626783i	−0.739292	+	0.673386i	$0.764839\pi$
$810$	45.7256	−	18.9401i	1.60663	−	0.665489i
$811$	12.6548	−	30.5514i	0.444370	−	1.07280i	−0.530030	−	0.847979i	$-0.677819\pi$
$811$	12.6548	−	30.5514i	0.444370	−	1.07280i	0.974399	−	0.224824i	$-0.0721808\pi$
$812$		−	59.2387i		−	2.07887i
$813$	−8.09839	−	3.35446i	−0.284023	−	0.117646i
$814$	−34.4707	+	34.4707i	−1.20820	+	1.20820i
$815$	−23.2927			−0.815909
$816$	15.1744	+	3.80394i	0.531209	+	0.133165i
$817$	0.298789			0.0104533
$818$	11.1633	−	11.1633i	0.390316	−	0.390316i
$819$	15.2173	+	6.30320i	0.531735	+	0.220252i
$820$		−	9.26255i		−	0.323462i
$821$	−13.6751	+	33.0146i	−0.477264	+	1.15222i	0.483624	+	0.875276i	$0.339320\pi$
$821$	−13.6751	+	33.0146i	−0.477264	+	1.15222i	−0.960887	+	0.276940i	$0.910680\pi$
$822$	84.8103	−	35.1296i	2.95810	−	1.22528i
$823$	−11.5066	−	27.7795i	−0.401097	−	0.968333i	−0.987400	−	0.158242i	$-0.949418\pi$
$823$	−11.5066	−	27.7795i	−0.401097	−	0.968333i	0.586304	−	0.810091i	$-0.300582\pi$
$824$	26.4826	+	26.4826i	0.922567	+	0.922567i
$825$	28.2671	+	28.2671i	0.984133	+	0.984133i
$826$	−28.1762	−	68.0234i	−0.980377	−	2.36684i
$827$	−28.2982	+	11.7215i	−0.984024	+	0.407596i	−0.815915	−	0.578172i	$-0.803766\pi$
$827$	−28.2982	+	11.7215i	−0.984024	+	0.407596i	−0.168109	+	0.985768i	$0.553766\pi$
$828$	−14.0314	+	33.8748i	−0.487625	+	1.17723i
$829$		−	19.5972i		−	0.680638i	−0.940310	−	0.340319i	$-0.889465\pi$
$829$		−	19.5972i		−	0.680638i	0.940310	−	0.340319i	$-0.110535\pi$
$830$	84.1425	+	34.8529i	2.92063	+	1.20976i
$831$	4.41201	−	4.41201i	0.153051	−	0.153051i
$832$	−13.2152			−0.458156
$833$	32.6283	−	43.9773i	1.13050	−	1.52372i
$834$	−81.5496			−2.82383
$835$	−43.6505	+	43.6505i	−1.51059	+	1.51059i
$836$	2.46770	+	1.02216i	0.0853473	+	0.0353520i
$837$		−	6.94682i		−	0.240117i
$838$	3.31400	−	8.00071i	0.114480	−	0.276380i
$839$	−40.8312	+	16.9128i	−1.40965	+	0.583896i	−0.952237	−	0.305359i	$-0.901223\pi$
$839$	−40.8312	+	16.9128i	−1.40965	+	0.583896i	−0.457412	+	0.889255i	$0.651223\pi$
$840$	−26.9757	−	65.1251i	−0.930750	−	2.24703i
$841$	5.70658	+	5.70658i	0.196779	+	0.196779i
$842$	50.3868	+	50.3868i	1.73644	+	1.73644i
$843$	26.9456	+	65.0525i	0.928057	+	2.24053i
$844$	58.4904	−	24.2275i	2.01332	−	0.833946i
$845$	14.4613	−	34.9126i	0.497483	−	1.20103i
$846$			26.3773i			0.906871i
$847$	−5.54820	−	2.29814i	−0.190638	−	0.0789650i
$848$	14.0146	−	14.0146i	0.481265	−	0.481265i
$849$	65.5598			2.25001
$850$	−45.2693	+	6.70656i	−1.55272	+	0.230033i
$851$	−25.5638			−0.876315
$852$	−47.0809	+	47.0809i	−1.61296	+	1.61296i
$853$	−33.9370	−	14.0572i	−1.16198	−	0.481309i	−0.283448	−	0.958988i	$-0.591478\pi$
$853$	−33.9370	−	14.0572i	−1.16198	−	0.481309i	−0.878535	+	0.477679i	$0.841478\pi$
$854$			70.1380i			2.40007i
$855$	−1.28256	+	3.09637i	−0.0438625	+	0.105893i
$856$	27.5937	−	11.4297i	0.943133	−	0.390659i
$857$	0.0655035	+	0.158139i	0.00223756	+	0.00540194i	0.924994	−	0.379981i	$-0.124069\pi$
$857$	0.0655035	+	0.158139i	0.00223756	+	0.00540194i	−0.922757	+	0.385383i	$0.874069\pi$
$858$	−12.8195	−	12.8195i	−0.437650	−	0.437650i
$859$	29.9857	+	29.9857i	1.02310	+	1.02310i	0.999727	+	0.0233722i	$0.00744028\pi$
$859$	29.9857	+	29.9857i	1.02310	+	1.02310i	0.0233722	+	0.999727i	$0.492560\pi$
$860$	3.48417	+	8.41153i	0.118809	+	0.286831i
$861$	10.8268	−	4.48460i	0.368975	−	0.152835i
$862$	−4.56105	+	11.0114i	−0.155350	+	0.375048i
$863$			29.3577i			0.999349i	0.866213	+	0.499675i	$0.166547\pi$
$863$			29.3577i			0.999349i	−0.866213	+	0.499675i	$0.833453\pi$
$864$	9.15125	+	3.79057i	0.311332	+	0.128958i
$865$	23.7634	−	23.7634i	0.807981	−	0.807981i
$866$	9.05335			0.307645
$867$	−43.2716	−	4.27795i	−1.46958	−	0.145287i
$868$	64.8444			2.20096
$869$	32.5758	−	32.5758i	1.10506	−	1.10506i
$870$	−75.5865	−	31.3089i	−2.56262	−	1.06147i
$871$			8.00021i			0.271077i
$872$	6.03864	−	14.5786i	0.204494	−	0.493692i
$873$	27.2984	−	11.3074i	0.923910	−	0.382696i
$874$	0.908860	+	2.19418i	0.0307426	+	0.0742193i
$875$	−0.270584	−	0.270584i	−0.00914742	−	0.00914742i
$876$	−62.2121	−	62.2121i	−2.10195	−	2.10195i
$877$	7.12616	+	17.2041i	0.240633	+	0.580940i	0.997346	−	0.0728075i	$-0.0231959\pi$
$877$	7.12616	+	17.2041i	0.240633	+	0.580940i	−0.756713	+	0.653747i	$0.773196\pi$
$878$	−46.1913	+	19.1331i	−1.55888	+	0.645709i
$879$	31.7746	−	76.7107i	1.07173	−	2.58739i
$880$		−	14.6039i		−	0.492299i
$881$	−16.9927	−	7.03859i	−0.572498	−	0.237136i	0.0776031	−	0.996984i	$-0.475273\pi$
$881$	−16.9927	−	7.03859i	−0.572498	−	0.237136i	−0.650101	+	0.759848i	$0.725273\pi$
$882$	73.4530	−	73.4530i	2.47329	−	2.47329i
$883$	48.3308			1.62646			0.813230	−	0.581942i	$-0.197707\pi$
$883$	48.3308			1.62646			0.813230	+	0.581942i	$0.197707\pi$
$884$	12.1080	−	1.79378i	0.407237	−	0.0603314i
$885$	−59.9717			−2.01593
$886$	7.72384	−	7.72384i	0.259487	−	0.259487i
$887$	−16.8561	−	6.98201i	−0.565971	−	0.234433i	0.0813039	−	0.996689i	$-0.474092\pi$
$887$	−16.8561	−	6.98201i	−0.565971	−	0.234433i	−0.647275	+	0.762256i	$0.724092\pi$
$888$		−	35.1024i		−	1.17796i
$889$	−7.43034	+	17.9384i	−0.249205	+	0.601635i
$890$	4.18673	−	1.73420i	0.140340	−	0.0581305i
$891$	−8.42242	−	20.3335i	−0.282162	−	0.681199i
$892$	−4.33969	−	4.33969i	−0.145304	−	0.145304i
$893$	0.712511	+	0.712511i	0.0238433	+	0.0238433i
$894$	−9.69801	−	23.4131i	−0.324350	−	0.783050i
$895$	46.4314	−	19.2325i	1.55203	−	0.642873i
$896$	−24.0934	+	58.1665i	−0.804903	+	1.94321i
$897$		−	9.50703i		−	0.317431i
$898$	−8.99700	−	3.72668i	−0.300234	−	0.124361i
$899$	16.2000	−	16.2000i	0.540300	−	0.540300i
$900$	−51.1991			−1.70664
$901$	−32.8248	+	44.2422i	−1.09355	+	1.47392i
$902$	−6.98401			−0.232542
$903$	−8.14512	+	8.14512i	−0.271053	+	0.271053i
$904$	−17.1918	−	7.12107i	−0.571790	−	0.236843i
$905$		−	15.1945i		−	0.505083i
$906$	16.3729	−	39.5276i	0.543952	−	1.31322i
$907$	−1.88069	+	0.779008i	−0.0624473	+	0.0258665i	−0.413688	−	0.910419i	$-0.635760\pi$
$907$	−1.88069	+	0.779008i	−0.0624473	+	0.0258665i	0.351241	+	0.936285i	$0.385760\pi$
$908$	10.0130	+	24.1734i	0.332291	+	0.802223i
$909$	−6.20949	−	6.20949i	−0.205956	−	0.205956i
$910$	22.9878	+	22.9878i	0.762038	+	0.762038i
$911$	11.0385	+	26.6492i	0.365721	+	0.882928i	0.994441	+	0.105296i	$0.0335791\pi$
$911$	11.0385	+	26.6492i	0.365721	+	0.882928i	−0.628720	+	0.777632i	$0.716421\pi$
$912$	1.04737	−	0.433835i	0.0346819	−	0.0143657i
$913$	15.4986	−	37.4170i	0.512930	−	1.23832i
$914$			74.7575i			2.47276i
$915$	52.7803	+	21.8623i	1.74486	+	0.722746i
$916$	−18.3464	+	18.3464i	−0.606183	+	0.606183i
$917$	49.7771			1.64379
$918$	−12.2498	−	3.07080i	−0.404302	−	0.101351i
$919$	8.17432			0.269646			0.134823	−	0.990870i	$-0.456953\pi$
$919$	8.17432			0.269646			0.134823	+	0.990870i	$0.456953\pi$
$920$	−15.5775	+	15.5775i	−0.513576	+	0.513576i
$921$	25.1151	+	10.4030i	0.827572	+	0.342792i
$922$		−	30.6672i		−	1.00997i
$923$	3.57717	−	8.63606i	0.117744	−	0.284259i
$924$	−95.1351	+	39.4062i	−3.12971	+	1.29637i
$925$	−13.6605	−	32.9793i	−0.449154	−	1.08435i
$926$	−54.4282	−	54.4282i	−1.78862	−	1.78862i
$927$	48.5415	+	48.5415i	1.59431	+	1.59431i
$928$	12.5011	+	30.1803i	0.410369	+	0.990718i
$929$	6.56473	−	2.71920i	0.215382	−	0.0892141i	−0.272384	−	0.962189i	$-0.587812\pi$
$929$	6.56473	−	2.71920i	0.215382	−	0.0892141i	0.487766	+	0.872975i	$0.337812\pi$
$930$	34.2717	−	82.7392i	1.12381	−	2.71312i
$931$		−	3.96826i		−	0.130055i
$932$	80.2811	+	33.2535i	2.62970	+	1.08926i
$933$	−17.0834	+	17.0834i	−0.559286	+	0.559286i
$934$	24.9727			0.817131
$935$	5.94871	+	40.1538i	0.194544	+	1.31317i
$936$	7.06828			0.231034
$937$	−17.4927	+	17.4927i	−0.571463	+	0.571463i	−0.932537	−	0.361074i	$-0.882410\pi$
$937$	−17.4927	+	17.4927i	−0.571463	+	0.571463i	0.361074	+	0.932537i	$0.382410\pi$
$938$	71.1831	+	29.4850i	2.32421	+	0.962719i
$939$			71.0490i			2.31860i
$940$	−11.7501	+	28.3672i	−0.383245	+	0.925236i
$941$	−4.46520	+	1.84955i	−0.145561	+	0.0602935i	−0.454275	−	0.890862i	$-0.650102\pi$
$941$	−4.46520	+	1.84955i	−0.145561	+	0.0602935i	0.308713	+	0.951155i	$0.400102\pi$
$942$	32.0056	+	77.2682i	1.04280	+	2.51754i
$943$	−2.58970	−	2.58970i	−0.0843322	−	0.0843322i
$944$	7.76670	+	7.76670i	0.252785	+	0.252785i
$945$	−7.57017	−	18.2760i	−0.246258	−	0.594519i
$946$	6.34234	−	2.62708i	0.206207	−	0.0854138i
$947$	−3.81544	+	9.21130i	−0.123985	+	0.299327i	−0.973669	−	0.227965i	$-0.926793\pi$
$947$	−3.81544	+	9.21130i	−0.123985	+	0.299327i	0.849684	+	0.527292i	$0.176793\pi$
$948$			108.973i			3.53928i
$949$	11.4116	+	4.72683i	0.370436	+	0.153440i
$950$	−2.34500	+	2.34500i	−0.0760820	+	0.0760820i
$951$	−80.3545			−2.60567
$952$	8.72566	−	34.8076i	0.282800	−	1.12812i
$953$	59.3939			1.92396			0.961978	−	0.273126i	$-0.0880576\pi$
$953$	59.3939			1.92396			0.961978	+	0.273126i	$0.0880576\pi$
$954$	−73.8954	+	73.8954i	−2.39245	+	2.39245i
$955$	22.7702	+	9.43174i	0.736827	+	0.305204i
$956$			9.01837i			0.291675i
$957$	−13.9227	+	33.6123i	−0.450056	+	1.08653i
$958$	−20.4749	+	8.48099i	−0.661515	+	0.274008i
$959$	28.0126	+	67.6284i	0.904574	+	2.18384i
$960$	73.3033	+	73.3033i	2.36585	+	2.36585i
$961$	−4.18733	−	4.18733i	−0.135075	−	0.135075i
$962$	6.19520	+	14.9565i	0.199741	+	0.482218i
$963$	50.5780	−	20.9501i	1.62985	−	0.675107i
$964$	−18.7672	+	45.3080i	−0.604450	+	1.45927i
$965$		−	6.01258i		−	0.193552i
$966$	−84.5903	−	35.0384i	−2.72165	−	1.12734i
$967$	−0.102275	+	0.102275i	−0.00328894	+	0.00328894i	−0.708749	−	0.705460i	$-0.750740\pi$
$967$	−0.102275	+	0.102275i	−0.00328894	+	0.00328894i	0.705460	+	0.708749i	$0.250740\pi$
$968$	−2.57709			−0.0828307
$969$	−2.70305	+	1.61947i	−0.0868344	+	0.0520248i
$970$	58.3193			1.87252
$971$	−11.3247	+	11.3247i	−0.363427	+	0.363427i	−0.865073	−	0.501646i	$-0.832728\pi$
$971$	−11.3247	+	11.3247i	−0.363427	+	0.363427i	0.501646	+	0.865073i	$0.332728\pi$
$972$	59.1523	+	24.5017i	1.89731	+	0.785892i
$973$		−	65.0283i		−	2.08471i
$974$	−18.2100	+	43.9628i	−0.583486	+	1.40866i
$975$	12.2648	−	5.08026i	0.392789	−	0.162699i
$976$	−4.00407	−	9.66668i	−0.128167	−	0.309423i
$977$	21.9982	+	21.9982i	0.703784	+	0.703784i	0.965221	−	0.261437i	$-0.0841963\pi$
$977$	21.9982	+	21.9982i	0.703784	+	0.703784i	−0.261437	+	0.965221i	$0.584196\pi$
$978$	−29.3758	−	29.3758i	−0.939333	−	0.939333i
$979$	−0.771175	−	1.86178i	−0.0246469	−	0.0595028i
$980$	111.715	−	46.2738i	3.56860	−	1.47816i
$981$	11.0686	−	26.7219i	0.353392	−	0.853163i
$982$		−	49.4223i		−	1.57713i
$983$	−34.8952	−	14.4541i	−1.11298	−	0.461013i	−0.251020	−	0.967982i	$-0.580766\pi$
$983$	−34.8952	−	14.4541i	−1.11298	−	0.461013i	−0.861965	+	0.506969i	$0.830766\pi$
$984$	3.55599	−	3.55599i	0.113361	−	0.113361i
$985$	−66.4068			−2.11590
$986$	−21.4053	−	35.7275i	−0.681684	−	1.13780i
$987$	−38.8467			−1.23650
$988$	0.627210	−	0.627210i	0.0199542	−	0.0199542i
$989$	3.32590	+	1.37763i	0.105757	+	0.0438061i
$990$			77.0027i			2.44731i
$991$	0.350156	−	0.845351i	0.0111231	−	0.0268535i	−0.918220	−	0.396070i	$-0.870374\pi$
$991$	0.350156	−	0.845351i	0.0111231	−	0.0268535i	0.929343	+	0.369216i	$0.120374\pi$
$992$	−33.0363	+	13.6841i	−1.04890	+	0.434470i
$993$	−12.0037	−	28.9796i	−0.380927	−	0.919639i
$994$	−63.6569	−	63.6569i	−2.01907	−	2.01907i
$995$	−0.358035	−	0.358035i	−0.0113505	−	0.0113505i
$996$	36.6609	+	88.5072i	1.16164	+	2.80446i
$997$	−26.2334	+	10.8662i	−0.830821	+	0.344137i	−0.757228	−	0.653151i	$-0.773447\pi$
$997$	−26.2334	+	10.8662i	−0.830821	+	0.344137i	−0.0735931	+	0.997288i	$0.523447\pi$
$998$	12.1885	−	29.4255i	0.385819	−	0.931449i
$999$		−	9.85076i		−	0.311664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.4	yes	128
17.2	even	8	inner	731.2.m.c.87.4	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.4	✓	128	17.2	even	8	inner
731.2.m.c.689.4	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56129 + 1.56129i) q^{2} +(-2.36310 - 0.978828i) q^{3} -2.87526i q^{4} +(1.21177 - 2.92548i) q^{5} +(5.21772 - 2.16125i) q^{6} +(1.72340 + 4.16065i) q^{7} +(1.36654 + 1.36654i) q^{8} +(2.50481 + 2.50481i) q^{9} +O(q^{10})\)	\(q+(-1.56129 + 1.56129i) q^{2} +(-2.36310 - 0.978828i) q^{3} -2.87526i q^{4} +(1.21177 - 2.92548i) q^{5} +(5.21772 - 2.16125i) q^{6} +(1.72340 + 4.16065i) q^{7} +(1.36654 + 1.36654i) q^{8} +(2.50481 + 2.50481i) q^{9} +(2.67560 + 6.45946i) q^{10} +(2.87243 - 1.18980i) q^{11} +(-2.81439 + 6.79453i) q^{12} -1.03249i q^{13} +(-9.18672 - 3.80527i) q^{14} +(-5.72708 + 5.72708i) q^{15} +1.48338 q^{16} +(-4.07859 + 0.604236i) q^{17} -7.82149 q^{18} +(-0.211276 + 0.211276i) q^{19} +(-8.41153 - 3.48417i) q^{20} -11.5189i q^{21} +(-2.62708 + 6.34234i) q^{22} +(-3.32590 + 1.37763i) q^{23} +(-1.89167 - 4.56689i) q^{24} +(-3.55451 - 3.55451i) q^{25} +(1.61202 + 1.61202i) q^{26} +(-0.530857 - 1.28160i) q^{27} +(11.9630 - 4.95523i) q^{28} +(1.75074 - 4.22665i) q^{29} -17.8833i q^{30} +(4.62662 + 1.91641i) q^{31} +(-5.04908 + 5.04908i) q^{32} -7.95246 q^{33} +(5.42448 - 7.31126i) q^{34} +14.2603 q^{35} +(7.20200 - 7.20200i) q^{36} +(6.56065 + 2.71751i) q^{37} -0.659726i q^{38} +(-1.01063 + 2.43987i) q^{39} +(5.65374 - 2.34185i) q^{40} +(0.389323 + 0.939910i) q^{41} +(17.9844 + 17.9844i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-3.42099 - 8.25901i) q^{44} +(10.3630 - 4.29251i) q^{45} +(3.04181 - 7.34358i) q^{46} -3.37242i q^{47} +(-3.50538 - 1.45198i) q^{48} +(-9.39119 + 9.39119i) q^{49} +11.0993 q^{50} +(10.2296 + 2.56437i) q^{51} -2.96868 q^{52} +(9.44775 - 9.44775i) q^{53} +(2.82978 + 1.17213i) q^{54} -9.84502i q^{55} +(-3.33061 + 8.04081i) q^{56} +(0.706068 - 0.292463i) q^{57} +(3.86563 + 9.33245i) q^{58} +(5.23580 + 5.23580i) q^{59} +(16.4669 + 16.4669i) q^{60} +(-2.69928 - 6.51664i) q^{61} +(-10.2156 + 4.23143i) q^{62} +(-6.10487 + 14.7384i) q^{63} -12.7994i q^{64} +(-3.02053 - 1.25114i) q^{65} +(12.4161 - 12.4161i) q^{66} -7.74847 q^{67} +(1.73734 + 11.7270i) q^{68} +9.20788 q^{69} +(-22.2645 + 22.2645i) q^{70} +(8.36432 + 3.46461i) q^{71} +6.84587i q^{72} +(-4.57810 + 11.0525i) q^{73} +(-14.4859 + 6.00026i) q^{74} +(4.92040 + 11.8789i) q^{75} +(0.607474 + 0.607474i) q^{76} +(9.90070 + 9.90070i) q^{77} +(-2.23147 - 5.38724i) q^{78} +(13.6896 - 5.67041i) q^{79} +(1.79753 - 4.33961i) q^{80} -7.07885i q^{81} +(-2.07532 - 0.859626i) q^{82} +(9.21094 - 9.21094i) q^{83} -33.1200 q^{84} +(-3.17465 + 12.6640i) q^{85} +2.20800 q^{86} +(-8.27433 + 8.27433i) q^{87} +(5.55122 + 2.29939i) q^{88} -0.648155i q^{89} +(-9.47787 + 22.8816i) q^{90} +(4.29583 - 1.77939i) q^{91} +(3.96105 + 9.56283i) q^{92} +(-9.05732 - 9.05732i) q^{93} +(5.26533 + 5.26533i) q^{94} +(0.362065 + 0.874102i) q^{95} +(16.8737 - 6.98930i) q^{96} +(3.19206 - 7.70631i) q^{97} -29.3248i q^{98} +(10.1751 + 4.21468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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