LMFDB - Embedded newform 304.2.k.b.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			229.3
Character	$\chi$	$=$	304.229
Dual form			304.2.k.b.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36784 + 0.359174i) q^{2} +(-1.75469 + 1.75469i) q^{3} +(1.74199 - 0.982587i) q^{4} +(0.519383 + 0.519383i) q^{5} +(1.76991 - 3.03039i) q^{6} +1.79541i q^{7} +(-2.02985 + 1.96970i) q^{8} -3.15791i q^{9} +O(q^{10})$	\(q+(-1.36784 + 0.359174i) q^{2} +(-1.75469 + 1.75469i) q^{3} +(1.74199 - 0.982587i) q^{4} +(0.519383 + 0.519383i) q^{5} +(1.76991 - 3.03039i) q^{6} +1.79541i q^{7} +(-2.02985 + 1.96970i) q^{8} -3.15791i q^{9} +(-0.896983 - 0.523885i) q^{10} +(3.97560 + 3.97560i) q^{11} +(-1.33252 + 4.78080i) q^{12} +(0.114860 - 0.114860i) q^{13} +(-0.644863 - 2.45583i) q^{14} -1.82272 q^{15} +(2.06904 - 3.42331i) q^{16} -5.90956 q^{17} +(1.13424 + 4.31952i) q^{18} +(-0.707107 + 0.707107i) q^{19} +(1.41510 + 0.394420i) q^{20} +(-3.15039 - 3.15039i) q^{21} +(-6.86592 - 4.01006i) q^{22} +2.02675i q^{23} +(0.105535 - 7.01798i) q^{24} -4.46048i q^{25} +(-0.115856 + 0.198366i) q^{26} +(0.277075 + 0.277075i) q^{27} +(1.76414 + 3.12757i) q^{28} +(-2.66440 + 2.66440i) q^{29} +(2.49319 - 0.654672i) q^{30} -7.42624 q^{31} +(-1.60056 + 5.42570i) q^{32} -13.9519 q^{33} +(8.08335 - 2.12256i) q^{34} +(-0.932503 + 0.932503i) q^{35} +(-3.10292 - 5.50103i) q^{36} +(-3.31665 - 3.31665i) q^{37} +(0.713237 - 1.22119i) q^{38} +0.403090i q^{39} +(-2.07730 - 0.0312380i) q^{40} +1.52590i q^{41} +(5.44077 + 3.17770i) q^{42} +(4.08964 + 4.08964i) q^{43} +(10.8318 + 3.01907i) q^{44} +(1.64016 - 1.64016i) q^{45} +(-0.727956 - 2.77228i) q^{46} -7.56238 q^{47} +(2.37632 + 9.63740i) q^{48} +3.77652 q^{49} +(1.60209 + 6.10124i) q^{50} +(10.3695 - 10.3695i) q^{51} +(0.0872252 - 0.312946i) q^{52} +(8.64094 + 8.64094i) q^{53} +(-0.478513 - 0.279477i) q^{54} +4.12971i q^{55} +(-3.53641 - 3.64440i) q^{56} -2.48151i q^{57} +(2.68750 - 4.60147i) q^{58} +(3.11287 + 3.11287i) q^{59} +(-3.17515 + 1.79098i) q^{60} +(9.26240 - 9.26240i) q^{61} +(10.1579 - 2.66731i) q^{62} +5.66972 q^{63} +(0.240551 - 7.99638i) q^{64} +0.119313 q^{65} +(19.0840 - 5.01117i) q^{66} +(-1.50340 + 1.50340i) q^{67} +(-10.2944 + 5.80666i) q^{68} +(-3.55633 - 3.55633i) q^{69} +(0.940586 - 1.61045i) q^{70} +2.02030i q^{71} +(6.22013 + 6.41006i) q^{72} +9.15775i q^{73} +(5.72792 + 3.34541i) q^{74} +(7.82678 + 7.82678i) q^{75} +(-0.536978 + 1.92657i) q^{76} +(-7.13781 + 7.13781i) q^{77} +(-0.144779 - 0.551364i) q^{78} -7.21117 q^{79} +(2.85263 - 0.703382i) q^{80} +8.50135 q^{81} +(-0.548064 - 2.08719i) q^{82} +(-0.619740 + 0.619740i) q^{83} +(-8.58347 - 2.39241i) q^{84} +(-3.06932 - 3.06932i) q^{85} +(-7.06287 - 4.12509i) q^{86} -9.35043i q^{87} +(-15.9006 - 0.239110i) q^{88} -1.20409i q^{89} +(-1.65438 + 2.83259i) q^{90} +(0.206221 + 0.206221i) q^{91} +(1.99146 + 3.53058i) q^{92} +(13.0308 - 13.0308i) q^{93} +(10.3441 - 2.71621i) q^{94} -0.734518 q^{95} +(-6.71194 - 12.3289i) q^{96} +7.23953 q^{97} +(-5.16568 + 1.35643i) q^{98} +(12.5546 - 12.5546i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.36784	+	0.359174i	−0.967211	+	0.253974i
$2$	−1.36784	+	0.359174i	−0.967211	+	0.253974i
$3$	−1.75469	+	1.75469i	−1.01307	+	1.01307i	−0.0131599	+	0.999913i	$0.504189\pi$
$3$	−1.75469	+	1.75469i	−1.01307	+	1.01307i	−0.999913	+	0.0131599i	$0.995811\pi$
$4$	1.74199	−	0.982587i	0.870994	−	0.491294i
$5$	0.519383	+	0.519383i	0.232275	+	0.232275i	0.813642	−	0.581367i	$-0.197482\pi$
$5$	0.519383	+	0.519383i	0.232275	+	0.232275i	−0.581367	+	0.813642i	$0.697482\pi$
$6$	1.76991	−	3.03039i	0.722561	−	1.23715i
$7$			1.79541i			0.678599i	0.940678	+	0.339300i	$0.110190\pi$
$7$			1.79541i			0.678599i	−0.940678	+	0.339300i	$0.889810\pi$
$8$	−2.02985	+	1.96970i	−0.717659	+	0.696395i
$9$		−	3.15791i		−	1.05264i
$10$	−0.896983	−	0.523885i	−0.283651	−	0.165667i
$11$	3.97560	+	3.97560i	1.19869	+	1.19869i	0.974560	+	0.224128i	$0.0719533\pi$
$11$	3.97560	+	3.97560i	1.19869	+	1.19869i	0.224128	+	0.974560i	$0.428047\pi$
$12$	−1.33252	+	4.78080i	−0.384664	+	1.38010i
$13$	0.114860	−	0.114860i	0.0318566	−	0.0318566i	−0.690999	−	0.722856i	$-0.742829\pi$
$13$	0.114860	−	0.114860i	0.0318566	−	0.0318566i	0.722856	+	0.690999i	$0.242829\pi$
$14$	−0.644863	−	2.45583i	−0.172347	−	0.656349i
$15$	−1.82272			−0.470623
$16$	2.06904	−	3.42331i	0.517261	−	0.855828i
$17$	−5.90956			−1.43328			−0.716639	−	0.697444i	$-0.754321\pi$
$17$	−5.90956			−1.43328			−0.716639	+	0.697444i	$0.754321\pi$
$18$	1.13424	+	4.31952i	0.267342	+	1.01812i
$19$	−0.707107	+	0.707107i	−0.162221	+	0.162221i
$19$	−0.707107	+	0.707107i	−0.162221	+	0.162221i
$20$	1.41510	+	0.394420i	0.316425	+	0.0881949i
$21$	−3.15039	−	3.15039i	−0.687471	−	0.687471i
$22$	−6.86592	−	4.01006i	−1.46382	−	0.854948i
$23$			2.02675i			0.422607i	0.977421	+	0.211303i	$0.0677708\pi$
$23$			2.02675i			0.422607i	−0.977421	+	0.211303i	$0.932229\pi$
$24$	0.105535	−	7.01798i	0.0215423	−	1.43254i
$25$		−	4.46048i		−	0.892097i
$26$	−0.115856	+	0.198366i	−0.0227213	+	0.0389028i
$27$	0.277075	+	0.277075i	0.0533231	+	0.0533231i
$28$	1.76414	+	3.12757i	0.333392	+	0.591056i
$29$	−2.66440	+	2.66440i	−0.494767	+	0.494767i	−0.909804	−	0.415037i	$-0.863769\pi$
$29$	−2.66440	+	2.66440i	−0.494767	+	0.494767i	0.415037	+	0.909804i	$0.363769\pi$
$30$	2.49319	−	0.654672i	0.455192	−	0.119526i
$31$	−7.42624			−1.33379			−0.666896	−	0.745151i	$-0.732377\pi$
$31$	−7.42624			−1.33379			−0.666896	+	0.745151i	$0.732377\pi$
$32$	−1.60056	+	5.42570i	−0.282942	+	0.959137i
$33$	−13.9519			−2.42872
$34$	8.08335	−	2.12256i	1.38628	−	0.364016i
$35$	−0.932503	+	0.932503i	−0.157622	+	0.157622i
$36$	−3.10292	−	5.50103i	−0.517153	−	0.916839i
$37$	−3.31665	−	3.31665i	−0.545255	−	0.545255i	0.379810	−	0.925065i	$-0.375989\pi$
$37$	−3.31665	−	3.31665i	−0.545255	−	0.545255i	−0.925065	+	0.379810i	$0.875989\pi$
$38$	0.713237	−	1.22119i	0.115702	−	0.198102i
$39$			0.403090i			0.0645461i
$40$	−2.07730	−	0.0312380i	−0.328449	−	0.00493916i
$41$			1.52590i			0.238306i	0.992876	+	0.119153i	$0.0380179\pi$
$41$			1.52590i			0.238306i	−0.992876	+	0.119153i	$0.961982\pi$
$42$	5.44077	+	3.17770i	0.839530	+	0.490329i
$43$	4.08964	+	4.08964i	0.623664	+	0.623664i	0.946466	−	0.322803i	$-0.104625\pi$
$43$	4.08964	+	4.08964i	0.623664	+	0.623664i	−0.322803	+	0.946466i	$0.604625\pi$
$44$	10.8318	+	3.01907i	1.63296	+	0.455142i
$45$	1.64016	−	1.64016i	0.244501	−	0.244501i
$46$	−0.727956	−	2.77228i	−0.107331	−	0.408750i
$47$	−7.56238			−1.10309			−0.551543	−	0.834146i	$-0.685961\pi$
$47$	−7.56238			−1.10309			−0.551543	+	0.834146i	$0.685961\pi$
$48$	2.37632	+	9.63740i	0.342993	+	1.39104i
$49$	3.77652			0.539503
$50$	1.60209	+	6.10124i	0.226570	+	0.862846i
$51$	10.3695	−	10.3695i	1.45202	−	1.45202i
$52$	0.0872252	−	0.312946i	0.0120960	−	0.0433978i
$53$	8.64094	+	8.64094i	1.18692	+	1.18692i	0.977913	+	0.209011i	$0.0670244\pi$
$53$	8.64094	+	8.64094i	1.18692	+	1.18692i	0.209011	+	0.977913i	$0.432976\pi$
$54$	−0.478513	−	0.279477i	−0.0651174	−	0.0380320i
$55$			4.12971i			0.556850i
$56$	−3.53641	−	3.64440i	−0.472573	−	0.487003i
$57$		−	2.48151i		−	0.328684i
$58$	2.68750	−	4.60147i	0.352886	−	0.604202i
$59$	3.11287	+	3.11287i	0.405262	+	0.405262i	0.880082	−	0.474821i	$-0.157487\pi$
$59$	3.11287	+	3.11287i	0.405262	+	0.405262i	−0.474821	+	0.880082i	$0.657487\pi$
$60$	−3.17515	+	1.79098i	−0.409910	+	0.231214i
$61$	9.26240	−	9.26240i	1.18593	−	1.18593i	0.207746	−	0.978183i	$-0.433387\pi$
$61$	9.26240	−	9.26240i	1.18593	−	1.18593i	0.978183	−	0.207746i	$-0.0666126\pi$
$62$	10.1579	−	2.66731i	1.29006	−	0.338749i
$63$	5.66972			0.714318
$64$	0.240551	−	7.99638i	0.0300688	−	0.999548i
$65$	0.119313			0.0147990
$66$	19.0840	−	5.01117i	2.34908	−	0.616832i
$67$	−1.50340	+	1.50340i	−0.183670	+	0.183670i	−0.792953	−	0.609283i	$-0.791457\pi$
$67$	−1.50340	+	1.50340i	−0.183670	+	0.183670i	0.609283	+	0.792953i	$0.291457\pi$
$68$	−10.2944	+	5.80666i	−1.24838	+	0.704161i
$69$	−3.55633	−	3.55633i	−0.428132	−	0.428132i
$70$	0.940586	−	1.61045i	0.112422	−	0.192485i
$71$			2.02030i			0.239765i	0.992788	+	0.119883i	$0.0382518\pi$
$71$			2.02030i			0.239765i	−0.992788	+	0.119883i	$0.961748\pi$
$72$	6.22013	+	6.41006i	0.733049	+	0.755433i
$73$			9.15775i			1.07183i	0.844271	+	0.535917i	$0.180034\pi$
$73$			9.15775i			1.07183i	−0.844271	+	0.535917i	$0.819966\pi$
$74$	5.72792	+	3.34541i	0.665857	+	0.388896i
$75$	7.82678	+	7.82678i	0.903759	+	0.903759i
$76$	−0.536978	+	1.92657i	−0.0615955	+	0.220992i
$77$	−7.13781	+	7.13781i	−0.813429	+	0.813429i
$78$	−0.144779	−	0.551364i	−0.0163930	−	0.0624297i
$79$	−7.21117			−0.811320			−0.405660	−	0.914024i	$-0.632958\pi$
$79$	−7.21117			−0.811320			−0.405660	+	0.914024i	$0.632958\pi$
$80$	2.85263	−	0.703382i	0.318934	−	0.0786405i
$81$	8.50135			0.944595
$82$	−0.548064	−	2.08719i	−0.0605235	−	0.230492i
$83$	−0.619740	+	0.619740i	−0.0680253	+	0.0680253i	−0.740301	−	0.672276i	$-0.765317\pi$
$83$	−0.619740	+	0.619740i	−0.0680253	+	0.0680253i	0.672276	+	0.740301i	$0.265317\pi$
$84$	−8.58347	−	2.39241i	−0.936533	−	0.261033i
$85$	−3.06932	−	3.06932i	−0.332915	−	0.332915i
$86$	−7.06287	−	4.12509i	−0.761609	−	0.444820i
$87$		−	9.35043i		−	1.00247i
$88$	−15.9006	−	0.239110i	−1.69501	−	0.0254892i
$89$		−	1.20409i		−	0.127634i	−0.997962	−	0.0638169i	$-0.979673\pi$
$89$		−	1.20409i		−	0.127634i	0.997962	−	0.0638169i	$-0.0203274\pi$
$90$	−1.65438	+	2.83259i	−0.174387	+	0.298581i
$91$	0.206221	+	0.206221i	0.0216178	+	0.0216178i
$92$	1.99146	+	3.53058i	0.207624	+	0.368088i
$93$	13.0308	−	13.0308i	1.35123	−	1.35123i
$94$	10.3441	−	2.71621i	1.06692	−	0.280156i
$95$	−0.734518			−0.0753600
$96$	−6.71194	−	12.3289i	−0.685035	−	1.25832i
$97$	7.23953			0.735063			0.367532	−	0.930011i	$-0.380203\pi$
$97$	7.23953			0.735063			0.367532	+	0.930011i	$0.380203\pi$
$98$	−5.16568	+	1.35643i	−0.521813	+	0.137020i
$99$	12.5546	−	12.5546i	1.26178	−	1.26178i
$100$	−4.38281	−	7.77011i	−0.438281	−	0.777011i
$101$	−1.07929	−	1.07929i	−0.107394	−	0.107394i	0.651368	−	0.758762i	$-0.274195\pi$
$101$	−1.07929	−	1.07929i	−0.107394	−	0.107394i	−0.758762	+	0.651368i	$0.774195\pi$
$102$	−10.4594	+	17.9083i	−1.03563	+	1.77318i
$103$		−	14.2306i		−	1.40218i	−0.713073	−	0.701090i	$-0.752697\pi$
$103$		−	14.2306i		−	1.40218i	0.713073	−	0.701090i	$-0.247303\pi$
$104$	−0.00690822	+	0.459390i	−0.000677407	+	0.0450469i
$105$		−	3.27251i		−	0.319365i
$106$	−14.9230	−	8.71584i	−1.44945	−	0.846558i
$107$	9.37925	+	9.37925i	0.906726	+	0.906726i	0.996007	−	0.0892805i	$-0.0284568\pi$
$107$	9.37925	+	9.37925i	0.906726	+	0.906726i	−0.0892805	+	0.996007i	$0.528457\pi$
$108$	0.754912	+	0.210411i	0.0726414	+	0.0202468i
$109$	−12.7353	+	12.7353i	−1.21982	+	1.21982i	−0.252129	+	0.967694i	$0.581131\pi$
$109$	−12.7353	+	12.7353i	−1.21982	+	1.21982i	−0.967694	+	0.252129i	$0.918869\pi$
$110$	−1.48329	−	5.64880i	−0.141426	−	0.538592i
$111$	11.6394			1.10477
$112$	6.14623	+	3.71477i	0.580764	+	0.351013i
$113$	−4.00631			−0.376882			−0.188441	−	0.982084i	$-0.560343\pi$
$113$	−4.00631			−0.376882			−0.188441	+	0.982084i	$0.560343\pi$
$114$	0.891295	+	3.39432i	0.0834774	+	0.317907i
$115$	−1.05266	+	1.05266i	−0.0981610	+	0.0981610i
$116$	−2.02335	+	7.25937i	−0.187863	+	0.674015i
$117$	−0.362719	−	0.362719i	−0.0335333	−	0.0335333i
$118$	−5.37598	−	3.13986i	−0.494900	−	0.289047i
$119$		−	10.6101i		−	0.972622i
$120$	3.69983	−	3.59021i	0.337747	−	0.327740i
$121$			20.6107i			1.87370i
$122$	−9.34269	+	15.9963i	−0.845848	+	1.44824i
$123$	−2.67749	−	2.67749i	−0.241421	−	0.241421i
$124$	−12.9364	+	7.29693i	−1.16172	+	0.655283i
$125$	4.91361	−	4.91361i	0.439487	−	0.439487i
$126$	−7.75529	+	2.03642i	−0.690896	+	0.181418i
$127$	18.8692			1.67437			0.837185	−	0.546920i	$-0.184200\pi$
$127$	18.8692			1.67437			0.837185	+	0.546920i	$0.184200\pi$
$128$	2.54306	+	11.0242i	0.224777	+	0.974410i
$129$	−14.3521			−1.26363
$130$	−0.163202	+	0.0428542i	−0.0143137	+	0.00375856i
$131$	−10.8353	+	10.8353i	−0.946682	+	0.946682i	−0.998649	−	0.0519671i	$-0.983451\pi$
$131$	−10.8353	+	10.8353i	−0.946682	+	0.946682i	0.0519671	+	0.998649i	$0.483451\pi$
$132$	−24.3041	+	13.7090i	−2.11540	+	1.19321i
$133$	−1.26954	−	1.26954i	−0.110083	−	0.110083i
$134$	1.51643	−	2.59640i	0.131000	−	0.224295i
$135$			0.287816i			0.0247713i
$136$	11.9955	−	11.6401i	1.02861	−	0.998128i
$137$		−	3.51487i		−	0.300295i	−0.988664	−	0.150148i	$-0.952025\pi$
$137$		−	3.51487i		−	0.300295i	0.988664	−	0.150148i	$-0.0479749\pi$
$138$	6.14184	+	3.58716i	0.522828	+	0.305359i
$139$	8.24372	+	8.24372i	0.699223	+	0.699223i	0.964243	−	0.265020i	$-0.0853784\pi$
$139$	8.24372	+	8.24372i	0.699223	+	0.699223i	−0.265020	+	0.964243i	$0.585378\pi$
$140$	−0.708143	+	2.54067i	−0.0598490	+	0.214726i
$141$	13.2697	−	13.2697i	1.11751	−	1.11751i
$142$	−0.725638	−	2.76345i	−0.0608942	−	0.231903i
$143$	0.913278			0.0763721
$144$	−10.8105	−	6.53385i	−0.900874	−	0.544487i
$145$	−2.76769			−0.229844
$146$	−3.28923	−	12.5264i	−0.272218	−	1.03669i
$147$	−6.62664	+	6.62664i	−0.546556	+	0.546556i
$148$	−9.03648	−	2.51867i	−0.742794	−	0.207033i
$149$	0.290993	+	0.290993i	0.0238391	+	0.0238391i	0.718926	−	0.695087i	$-0.244634\pi$
$149$	0.290993	+	0.290993i	0.0238391	+	0.0238391i	−0.695087	+	0.718926i	$0.744634\pi$
$150$	−13.5170	−	7.89463i	−1.10366	−	0.644594i
$151$		−	3.02281i		−	0.245993i	−0.992407	−	0.122996i	$-0.960750\pi$
$151$		−	3.02281i		−	0.245993i	0.992407	−	0.122996i	$-0.0392503\pi$
$152$	0.0425286	−	2.82811i	0.00344952	−	0.229390i
$153$			18.6618i			1.50872i
$154$	7.19968	−	12.3271i	0.580167	−	0.993347i
$155$	−3.85706	−	3.85706i	−0.309807	−	0.309807i
$156$	0.396071	+	0.702178i	0.0317111	+	0.0562192i
$157$	10.7428	−	10.7428i	0.857370	−	0.857370i	−0.133658	−	0.991028i	$-0.542672\pi$
$157$	10.7428	−	10.7428i	0.857370	−	0.857370i	0.991028	+	0.133658i	$0.0426722\pi$
$158$	9.86374	−	2.59006i	0.784717	−	0.206054i
$159$	−30.3244			−2.40488
$160$	−3.64932	+	1.98671i	−0.288504	+	0.157063i
$161$	−3.63884			−0.286781
$162$	−11.6285	+	3.05346i	−0.913622	+	0.239903i
$163$	−11.7852	+	11.7852i	−0.923085	+	0.923085i	−0.997246	−	0.0741615i	$-0.976372\pi$
$163$	−11.7852	+	11.7852i	−0.923085	+	0.923085i	0.0741615	+	0.997246i	$0.476372\pi$
$164$	1.49933	+	2.65810i	0.117078	+	0.207563i
$165$	−7.24638	−	7.24638i	−0.564130	−	0.564130i
$166$	0.625112	−	1.07030i	0.0485181	−	0.0830714i
$167$		−	19.6990i		−	1.52436i	−0.647366	−	0.762179i	$-0.724130\pi$
$167$		−	19.6990i		−	1.52436i	0.647366	−	0.762179i	$-0.275870\pi$
$168$	12.6001	+	0.189478i	0.972121	+	0.0146186i
$169$			12.9736i			0.997970i
$170$	5.30077	+	3.09593i	0.406551	+	0.237447i
$171$	2.23298	+	2.23298i	0.170760	+	0.170760i
$172$	11.1425	+	3.10567i	0.849609	+	0.236805i
$173$	8.26934	−	8.26934i	0.628706	−	0.628706i	−0.319036	−	0.947742i	$-0.603359\pi$
$173$	8.26934	−	8.26934i	0.628706	−	0.628706i	0.947742	+	0.319036i	$0.103359\pi$
$174$	3.35843	+	12.7899i	0.254602	+	0.969601i
$175$	8.00838			0.605376
$176$	21.8354	−	5.38401i	1.64590	−	0.405835i
$177$	−10.9243			−0.821119
$178$	0.432479	+	1.64701i	0.0324157	+	0.123449i
$179$	15.4524	−	15.4524i	1.15496	−	1.15496i	0.169419	−	0.985544i	$-0.445811\pi$
$179$	15.4524	−	15.4524i	1.15496	−	1.15496i	0.985544	−	0.169419i	$-0.0541891\pi$
$180$	1.24554	−	4.46874i	0.0928371	−	0.333080i
$181$	8.25810	+	8.25810i	0.613820	+	0.613820i	0.943939	−	0.330119i	$-0.107089\pi$
$181$	8.25810	+	8.25810i	0.613820	+	0.613820i	−0.330119	+	0.943939i	$0.607089\pi$
$182$	−0.356147	−	0.208009i	−0.0263994	−	0.0154186i
$183$			32.5054i			2.40287i
$184$	−3.99209	−	4.11399i	−0.294301	−	0.303288i
$185$		−	3.44523i		−	0.253298i
$186$	−13.1437	+	22.5044i	−0.963746	+	1.65010i
$187$	−23.4940	−	23.4940i	−1.71805	−	1.71805i
$188$	−13.1736	+	7.43069i	−0.960781	+	0.541939i
$189$	−0.497462	+	0.497462i	−0.0361850	+	0.0361850i
$190$	1.00471	−	0.263820i	0.0728890	−	0.0191395i
$191$	−10.2620			−0.742534			−0.371267	−	0.928526i	$-0.621076\pi$
$191$	−10.2620			−0.742534			−0.371267	+	0.928526i	$0.621076\pi$
$192$	13.6091	+	14.4533i	0.982153	+	1.04308i
$193$	22.9612			1.65278			0.826392	−	0.563096i	$-0.190390\pi$
$193$	22.9612			1.65278			0.826392	+	0.563096i	$0.190390\pi$
$194$	−9.90255	+	2.60025i	−0.710961	+	0.186687i
$195$	−0.209358	+	0.209358i	−0.0149924	+	0.0149924i
$196$	6.57865	−	3.71076i	0.469904	−	0.265054i
$197$	−4.79894	−	4.79894i	−0.341910	−	0.341910i	0.515175	−	0.857085i	$-0.327727\pi$
$197$	−4.79894	−	4.79894i	−0.341910	−	0.341910i	−0.857085	+	0.515175i	$0.827727\pi$
$198$	−12.6634	+	21.6819i	−0.899948	+	1.54087i
$199$			13.7926i			0.977733i	0.872359	+	0.488867i	$0.162590\pi$
$199$			13.7926i			0.977733i	−0.872359	+	0.488867i	$0.837410\pi$
$200$	8.78582	+	9.05409i	0.621251	+	0.640221i
$201$		−	5.27602i		−	0.372142i
$202$	1.86396	+	1.08865i	0.131148	+	0.0765972i
$203$	−4.78368	−	4.78368i	−0.335749	−	0.335749i
$204$	7.87459	−	28.2524i	0.551331	−	1.97806i
$205$	−0.792527	+	0.792527i	−0.0553525	+	0.0553525i
$206$	5.11125	+	19.4652i	0.356118	+	1.35620i
$207$	6.40029			0.444851
$208$	−0.155552	−	0.630855i	−0.0107856	−	0.0437419i
$209$	−5.62234			−0.388906
$210$	1.17540	+	4.47629i	0.0811105	+	0.308893i
$211$	−5.14269	+	5.14269i	−0.354037	+	0.354037i	−0.861609	−	0.507572i	$-0.830543\pi$
$211$	−5.14269	+	5.14269i	−0.354037	+	0.354037i	0.507572	+	0.861609i	$0.330543\pi$
$212$	23.5429	+	6.56194i	1.61693	+	0.450676i
$213$	−3.54500	−	3.54500i	−0.242900	−	0.242900i
$214$	−16.1981	−	9.46055i	−1.10728	−	0.646710i
$215$			4.24817i			0.289723i
$216$	−1.10817	−	0.0166645i	−0.0754018	−	0.00113388i
$217$		−	13.3331i		−	0.905111i
$218$	12.8457	−	21.9941i	0.870022	−	1.48963i
$219$	−16.0691	−	16.0691i	−1.08585	−	1.08585i
$220$	4.05780	+	7.19391i	0.273577	+	0.485013i
$221$	−0.678775	+	0.678775i	−0.0456593	+	0.0456593i
$222$	−15.9209	+	4.18058i	−1.06854	+	0.280582i
$223$	−2.11217			−0.141442			−0.0707208	−	0.997496i	$-0.522530\pi$
$223$	−2.11217			−0.141442			−0.0707208	+	0.997496i	$0.522530\pi$
$224$	−9.74133	−	2.87366i	−0.650870	−	0.192005i
$225$	−14.0858			−0.939052
$226$	5.48001	−	1.43896i	0.364525	−	0.0957185i
$227$	−8.77347	+	8.77347i	−0.582316	+	0.582316i	−0.935539	−	0.353223i	$-0.885086\pi$
$227$	−8.77347	+	8.77347i	−0.582316	+	0.582316i	0.353223	+	0.935539i	$0.385086\pi$
$228$	−2.43830	−	4.32277i	−0.161481	−	0.286282i
$229$	−9.68181	−	9.68181i	−0.639792	−	0.639792i	0.310712	−	0.950504i	$-0.399433\pi$
$229$	−9.68181	−	9.68181i	−0.639792	−	0.639792i	−0.950504	+	0.310712i	$0.899433\pi$
$230$	1.06178	−	1.81796i	0.0700120	−	0.119873i
$231$		−	25.0493i		−	1.64813i
$232$	0.160249	−	10.6564i	0.0105209	−	0.699627i
$233$			9.79821i			0.641902i	0.947096	+	0.320951i	$0.104003\pi$
$233$			9.79821i			0.641902i	−0.947096	+	0.320951i	$0.895997\pi$
$234$	0.626421	+	0.365863i	0.0409504	+	0.0239172i
$235$	−3.92777	−	3.92777i	−0.256219	−	0.256219i
$236$	8.48126	+	2.36392i	0.552083	+	0.153878i
$237$	12.6534	−	12.6534i	0.821926	−	0.821926i
$238$	3.81086	+	14.5129i	0.247021	+	0.940731i
$239$	24.9486			1.61379			0.806896	−	0.590693i	$-0.201146\pi$
$239$	24.9486			1.61379			0.806896	+	0.590693i	$0.201146\pi$
$240$	−3.77128	+	6.23972i	−0.243435	+	0.402772i
$241$	13.4822			0.868467			0.434234	−	0.900800i	$-0.357019\pi$
$241$	13.4822			0.868467			0.434234	+	0.900800i	$0.357019\pi$
$242$	−7.40284	−	28.1923i	−0.475873	−	1.81227i
$243$	−15.7485	+	15.7485i	−1.01027	+	1.01027i
$244$	7.03387	−	25.2361i	0.450298	−	1.61558i
$245$	1.96146	+	1.96146i	0.125313	+	0.125313i
$246$	4.62407	+	2.70070i	0.294820	+	0.172190i
$247$			0.162437i			0.0103356i
$248$	15.0741	−	14.6275i	0.957208	−	0.928846i
$249$		−	2.17491i		−	0.137829i
$250$	−4.95621	+	8.48589i	−0.313458	+	0.536695i
$251$	7.51924	+	7.51924i	0.474610	+	0.474610i	0.903403	−	0.428793i	$-0.141061\pi$
$251$	7.51924	+	7.51924i	0.474610	+	0.474610i	−0.428793	+	0.903403i	$0.641061\pi$
$252$	9.87658	−	5.57099i	0.622166	−	0.350940i
$253$	−8.05755	+	8.05755i	−0.506574	+	0.506574i
$254$	−25.8101	+	6.77732i	−1.61947	+	0.425247i
$255$	10.7714			0.674534
$256$	−7.43811	−	14.1660i	−0.464882	−	0.885373i
$257$	19.8302			1.23698			0.618488	−	0.785794i	$-0.287746\pi$
$257$	19.8302			1.23698			0.618488	+	0.785794i	$0.287746\pi$
$258$	19.6314	−	5.15491i	1.22220	−	0.320931i
$259$	5.95474	−	5.95474i	0.370010	−	0.370010i
$260$	0.207842	−	0.117236i	0.0128898	−	0.00727064i
$261$	8.41393	+	8.41393i	0.520809	+	0.520809i
$262$	10.9292	−	18.7127i	0.675208	−	1.15607i
$263$			2.48614i			0.153302i	0.997058	+	0.0766508i	$0.0244227\pi$
$263$			2.48614i			0.153302i	−0.997058	+	0.0766508i	$0.975577\pi$
$264$	28.3202	−	27.4811i	1.74299	−	1.69135i
$265$			8.97591i			0.551386i
$266$	2.19252	+	1.28055i	0.134432	+	0.0785155i
$267$	2.11282	+	2.11282i	0.129302	+	0.129302i
$268$	−1.14168	+	4.09613i	−0.0697395	+	0.250211i
$269$	−5.67662	+	5.67662i	−0.346109	+	0.346109i	−0.858658	−	0.512549i	$-0.828701\pi$
$269$	−5.67662	+	5.67662i	−0.346109	+	0.346109i	0.512549	+	0.858658i	$0.328701\pi$
$270$	−0.103376	−	0.393687i	−0.00629127	−	0.0239590i
$271$	−30.1161			−1.82942			−0.914712	−	0.404107i	$-0.867582\pi$
$271$	−30.1161			−1.82942			−0.914712	+	0.404107i	$0.867582\pi$
$272$	−12.2271	+	20.2303i	−0.741379	+	1.22664i
$273$	−0.723710			−0.0438009
$274$	1.26245	+	4.80779i	0.0762673	+	0.290449i
$275$	17.7331	−	17.7331i	1.06935	−	1.06935i
$276$	−9.68949	−	2.70068i	−0.583238	−	0.162562i
$277$	−2.05175	−	2.05175i	−0.123278	−	0.123278i	0.642776	−	0.766054i	$-0.277782\pi$
$277$	−2.05175	−	2.05175i	−0.123278	−	0.123278i	−0.766054	+	0.642776i	$0.777782\pi$
$278$	−14.2370	−	8.31519i	−0.853881	−	0.498712i
$279$			23.4514i			1.40400i
$280$	0.0560849	−	3.72959i	0.00335171	−	0.222886i
$281$			12.2698i			0.731955i	0.930624	+	0.365977i	$0.119265\pi$
$281$			12.2698i			0.731955i	−0.930624	+	0.365977i	$0.880735\pi$
$282$	−13.3847	+	22.9169i	−0.797047	+	1.36468i
$283$	22.0540	+	22.0540i	1.31097	+	1.31097i	0.920697	+	0.390277i	$0.127621\pi$
$283$	22.0540	+	22.0540i	1.31097	+	1.31097i	0.390277	+	0.920697i	$0.372379\pi$
$284$	1.98512	+	3.51933i	0.117795	+	0.208834i
$285$	1.28885	−	1.28885i	0.0763452	−	0.0763452i
$286$	−1.24922	+	0.328026i	−0.0738680	+	0.0193966i
$287$	−2.73961			−0.161714
$288$	17.1338	+	5.05443i	1.00962	+	0.297835i
$289$	17.9229			1.05429
$290$	3.78576	−	0.994082i	0.222308	−	0.0583745i
$291$	−12.7032	+	12.7032i	−0.744673	+	0.744673i
$292$	8.99829	+	15.9527i	0.526585	+	0.933561i
$293$	20.0399	+	20.0399i	1.17074	+	1.17074i	0.982033	+	0.188708i	$0.0604300\pi$
$293$	20.0399	+	20.0399i	1.17074	+	1.17074i	0.188708	+	0.982033i	$0.439570\pi$
$294$	6.68408	−	11.4443i	0.389824	−	0.667446i
$295$			3.23355i			0.188264i
$296$	13.2651	+	0.199478i	0.771019	+	0.0115944i
$297$			2.20308i			0.127836i
$298$	−0.502550	−	0.293516i	−0.0291119	−	0.0170029i
$299$	0.232794	+	0.232794i	0.0134628	+	0.0134628i
$300$	21.3247	+	5.94367i	1.23118	+	0.343158i
$301$	−7.34255	+	7.34255i	−0.423218	+	0.423218i
$302$	1.08571	+	4.13473i	0.0624758	+	0.237927i
$303$	3.78766			0.217596
$304$	0.957610	+	3.88368i	0.0549227	+	0.222744i
$305$	9.62146			0.550923
$306$	−6.70284	−	25.5264i	−0.383176	−	1.45925i
$307$	13.1915	−	13.1915i	0.752878	−	0.752878i	−0.222138	−	0.975015i	$-0.571303\pi$
$307$	13.1915	−	13.1915i	0.752878	−	0.752878i	0.975015	+	0.222138i	$0.0713035\pi$
$308$	−5.42046	+	19.4475i	−0.308859	+	1.10812i
$309$	24.9703	+	24.9703i	1.42051	+	1.42051i
$310$	6.66121	+	3.89050i	0.378331	+	0.220965i
$311$		−	25.8163i		−	1.46391i	−0.681353	−	0.731955i	$-0.738608\pi$
$311$		−	25.8163i		−	1.46391i	0.681353	−	0.731955i	$-0.261392\pi$
$312$	−0.793967	−	0.818211i	−0.0449495	−	0.0463221i
$313$			9.16966i			0.518300i	0.965837	+	0.259150i	$0.0834424\pi$
$313$			9.16966i			0.518300i	−0.965837	+	0.259150i	$0.916558\pi$
$314$	−10.8359	+	18.5530i	−0.611508	+	1.04701i
$315$	2.94475	+	2.94475i	0.165918	+	0.165918i
$316$	−12.5618	+	7.08560i	−0.706655	+	0.398596i
$317$	−13.4010	+	13.4010i	−0.752674	+	0.752674i	−0.974977	−	0.222304i	$-0.928642\pi$
$317$	−13.4010	+	13.4010i	−0.752674	+	0.752674i	0.222304	+	0.974977i	$0.428642\pi$
$318$	41.4790	−	10.8917i	2.32603	−	0.610778i
$319$	−21.1852			−1.18614
$320$	4.27812	−	4.02825i	0.239154	−	0.225186i
$321$	−32.9154			−1.83716
$322$	4.97736	−	1.30698i	0.277377	−	0.0728350i
$323$	4.17869	−	4.17869i	0.232509	−	0.232509i
$324$	14.8093	−	8.35332i	0.822736	−	0.464073i
$325$	−0.512333	−	0.512333i	−0.0284191	−	0.0284191i
$326$	11.8873	−	20.3532i	0.658378	−	1.12726i
$327$		−	44.6932i		−	2.47154i
$328$	−3.00557	−	3.09734i	−0.165955	−	0.171022i
$329$		−	13.5775i		−	0.748554i
$330$	12.5146	+	7.30920i	0.688908	+	0.402358i
$331$	1.98629	+	1.98629i	0.109176	+	0.109176i	0.759585	−	0.650408i	$-0.225402\pi$
$331$	1.98629	+	1.98629i	0.109176	+	0.109176i	−0.650408	+	0.759585i	$0.725402\pi$
$332$	−0.470631	+	1.68853i	−0.0258292	+	0.0926700i
$333$	−10.4737	+	10.4737i	−0.573954	+	0.573954i
$334$	7.07538	+	26.9452i	0.387148	+	1.47438i
$335$	−1.56168			−0.0853238
$336$	−17.3030	+	4.26646i	−0.943959	+	0.232755i
$337$	28.9054			1.57458			0.787290	−	0.616583i	$-0.211484\pi$
$337$	28.9054			1.57458			0.787290	+	0.616583i	$0.211484\pi$
$338$	−4.65978	−	17.7459i	−0.253459	−	0.965248i
$339$	7.02986	−	7.02986i	0.381809	−	0.381809i
$340$	−8.36260	−	2.33085i	−0.453526	−	0.126408i
$341$	−29.5237	−	29.5237i	−1.59880	−	1.59880i
$342$	−3.85639	−	2.25233i	−0.208530	−	0.121792i
$343$			19.3482i			1.04471i
$344$	−16.3567	−	0.245969i	−0.881894	−	0.0132618i
$345$		−	3.69419i		−	0.198889i
$346$	−8.34102	+	14.2813i	−0.448416	+	0.767766i
$347$	−21.5539	−	21.5539i	−1.15707	−	1.15707i	−0.985102	−	0.171970i	$-0.944987\pi$
$347$	−21.5539	−	21.5539i	−1.15707	−	1.15707i	−0.171970	−	0.985102i	$-0.555013\pi$
$348$	−9.18761	−	16.2883i	−0.492508	−	0.873146i
$349$	−0.715232	+	0.715232i	−0.0382855	+	0.0382855i	−0.725990	−	0.687705i	$-0.758618\pi$
$349$	−0.715232	+	0.715232i	−0.0382855	+	0.0382855i	0.687705	+	0.725990i	$0.258618\pi$
$350$	−10.9542	+	2.87640i	−0.585527	+	0.153750i
$351$	0.0636500			0.00339738
$352$	−27.9336	+	15.2072i	−1.48887	+	0.810546i
$353$	−2.39173			−0.127299			−0.0636495	−	0.997972i	$-0.520274\pi$
$353$	−2.39173			−0.127299			−0.0636495	+	0.997972i	$0.520274\pi$
$354$	14.9427	−	3.92372i	0.794196	−	0.208543i
$355$	−1.04931	+	1.04931i	−0.0556914	+	0.0556914i
$356$	−1.18313	−	2.09752i	−0.0627056	−	0.111168i
$357$	18.6174	+	18.6174i	0.985338	+	0.985338i
$358$	−15.5863	+	26.6865i	−0.823762	+	1.41042i
$359$		−	6.10038i		−	0.321966i	−0.986957	−	0.160983i	$-0.948534\pi$
$359$		−	6.10038i		−	0.321966i	0.986957	−	0.160983i	$-0.0514664\pi$
$360$	−0.0986466	+	6.55990i	−0.00519913	+	0.345737i
$361$		−	1.00000i		−	0.0526316i
$362$	−14.2619	−	8.32969i	−0.749588	−	0.437799i
$363$	−36.1656	−	36.1656i	−1.89820	−	1.89820i
$364$	0.561865	+	0.156605i	0.0294497	+	0.00820831i
$365$	−4.75638	+	4.75638i	−0.248960	+	0.248960i
$366$	−11.6751	−	44.4622i	−0.610266	−	2.32408i
$367$	−10.9050			−0.569235			−0.284618	−	0.958641i	$-0.591867\pi$
$367$	−10.9050			−0.569235			−0.284618	+	0.958641i	$0.591867\pi$
$368$	6.93820	+	4.19344i	0.361679	+	0.218598i
$369$	4.81865			0.250849
$370$	1.23744	+	4.71253i	0.0643312	+	0.244993i
$371$	−15.5140	+	15.5140i	−0.805446	+	0.805446i
$372$	9.89559	−	35.5033i	0.513062	−	1.84076i
$373$	10.7984	+	10.7984i	0.559119	+	0.559119i	0.929057	−	0.369937i	$-0.120621\pi$
$373$	10.7984	+	10.7984i	0.559119	+	0.559119i	−0.369937	+	0.929057i	$0.620621\pi$
$374$	40.5746	+	23.6977i	2.09806	+	1.22538i
$375$			17.2438i			0.890465i
$376$	15.3505	−	14.8956i	0.791640	−	0.768183i
$377$			0.612069i			0.0315232i
$378$	0.501774	−	0.859125i	0.0258085	−	0.0441886i
$379$	16.8840	+	16.8840i	0.867274	+	0.867274i	0.992170	−	0.124896i	$-0.0398598\pi$
$379$	16.8840	+	16.8840i	0.867274	+	0.867274i	−0.124896	+	0.992170i	$0.539860\pi$
$380$	−1.27952	+	0.721728i	−0.0656381	+	0.0370239i
$381$	−33.1096	+	33.1096i	−1.69626	+	1.69626i
$382$	14.0368	−	3.68585i	0.718187	−	0.188585i
$383$	−24.3464			−1.24404			−0.622021	−	0.783001i	$-0.713688\pi$
$383$	−24.3464			−1.24404			−0.622021	+	0.783001i	$0.713688\pi$
$384$	−23.8064	−	14.8818i	−1.21486	−	0.759434i
$385$	−7.41451			−0.377878
$386$	−31.4073	+	8.24707i	−1.59859	+	0.419765i
$387$	12.9147	−	12.9147i	0.656490	−	0.656490i
$388$	12.6112	−	7.11347i	0.640236	−	0.361132i
$389$	−13.9421	−	13.9421i	−0.706892	−	0.706892i	0.258988	−	0.965880i	$-0.416611\pi$
$389$	−13.9421	−	13.9421i	−0.706892	−	0.706892i	−0.965880	+	0.258988i	$0.916611\pi$
$390$	0.211173	−	0.361565i	0.0106932	−	0.0183085i
$391$		−	11.9772i		−	0.605713i
$392$	−7.66575	+	7.43862i	−0.387179	+	0.375707i
$393$		−	38.0252i		−	1.91812i
$394$	8.28785	+	4.84054i	0.417536	+	0.243863i
$395$	−3.74536	−	3.74536i	−0.188449	−	0.188449i
$396$	9.53394	−	34.2058i	0.479099	−	1.71891i
$397$	−22.0960	+	22.0960i	−1.10897	+	1.10897i	−0.115683	+	0.993286i	$0.536906\pi$
$397$	−22.0960	+	22.0960i	−1.10897	+	1.10897i	−0.993286	+	0.115683i	$0.963094\pi$
$398$	−4.95395	−	18.8661i	−0.248319	−	0.945674i
$399$	4.45532			0.223045
$400$	−15.2696	−	9.22894i	−0.763481	−	0.461447i
$401$	−4.23713			−0.211592			−0.105796	−	0.994388i	$-0.533739\pi$
$401$	−4.23713			−0.211592			−0.105796	+	0.994388i	$0.533739\pi$
$402$	1.89501	+	7.21677i	0.0945145	+	0.359940i
$403$	−0.852981	+	0.852981i	−0.0424900	+	0.0424900i
$404$	−2.94062	−	0.819617i	−0.146301	−	0.0407775i
$405$	4.41546	+	4.41546i	0.219406	+	0.219406i
$406$	8.26150	+	4.82515i	0.410011	+	0.239468i
$407$		−	26.3714i		−	1.30718i
$408$	−0.623666	+	41.4732i	−0.0308761	+	2.05323i
$409$		−	22.5380i		−	1.11443i	−0.830367	−	0.557217i	$-0.811869\pi$
$409$		−	22.5380i		−	1.11443i	0.830367	−	0.557217i	$-0.188131\pi$
$410$	0.799397	−	1.36871i	0.0394794	−	0.0675956i
$411$	6.16752	+	6.16752i	0.304221	+	0.304221i
$412$	−13.9828	−	24.7895i	−0.688882	−	1.22129i
$413$	−5.58887	+	5.58887i	−0.275010	+	0.275010i
$414$	−8.75459	+	2.29882i	−0.430264	+	0.112981i
$415$	−0.643764			−0.0316011
$416$	0.439357	+	0.807040i	0.0215412	+	0.0395684i
$417$	−28.9304			−1.41673
$418$	7.69048	−	2.01940i	0.376154	−	0.0987721i
$419$	−1.04797	+	1.04797i	−0.0511966	+	0.0511966i	−0.732242	−	0.681045i	$-0.761526\pi$
$419$	−1.04797	+	1.04797i	−0.0511966	+	0.0511966i	0.681045	+	0.732242i	$0.261526\pi$
$420$	−3.21553	−	5.70068i	−0.156902	−	0.278165i
$421$	12.1276	+	12.1276i	0.591065	+	0.591065i	0.937919	−	0.346854i	$-0.112750\pi$
$421$	12.1276	+	12.1276i	0.591065	+	0.591065i	−0.346854	+	0.937919i	$0.612750\pi$
$422$	5.18727	−	8.88151i	0.252512	−	0.432345i
$423$			23.8813i			1.16115i
$424$	−34.5598	−	0.519705i	−1.67837	−	0.0252391i
$425$			26.3595i			1.27862i
$426$	6.12228	+	3.57573i	0.296625	+	0.173245i
$427$	16.6298	+	16.6298i	0.804770	+	0.804770i
$428$	25.5545	+	7.12261i	1.23522	+	0.344284i
$429$	−1.60252	+	1.60252i	−0.0773706	+	0.0773706i
$430$	−1.52583	−	5.81083i	−0.0735822	−	0.280223i
$431$	32.0114			1.54194			0.770969	−	0.636873i	$-0.219773\pi$
$431$	32.0114			1.54194			0.770969	+	0.636873i	$0.219773\pi$
$432$	1.52179	−	0.375233i	0.0732174	−	0.0180534i
$433$	4.13412			0.198673			0.0993365	−	0.995054i	$-0.468328\pi$
$433$	4.13412			0.198673			0.0993365	+	0.995054i	$0.468328\pi$
$434$	4.78891	+	18.2376i	0.229875	+	0.875433i
$435$	4.85645	−	4.85645i	0.232849	−	0.232849i
$436$	−9.67121	+	34.6983i	−0.463167	+	1.66175i
$437$	−1.43313	−	1.43313i	−0.0685559	−	0.0685559i
$438$	27.7515	+	16.2084i	1.32602	+	0.774465i
$439$			28.1909i			1.34548i	0.739881	+	0.672738i	$0.234882\pi$
$439$			28.1909i			1.34548i	−0.739881	+	0.672738i	$0.765118\pi$
$440$	−8.13430	−	8.38268i	−0.387788	−	0.399629i
$441$		−	11.9259i		−	0.567899i
$442$	0.684659	−	1.17226i	0.0325659	−	0.0557585i
$443$	−21.6305	−	21.6305i	−1.02770	−	1.02770i	−0.999605	−	0.0280917i	$-0.991057\pi$
$443$	−21.6305	−	21.6305i	−1.02770	−	1.02770i	−0.0280917	−	0.999605i	$-0.508943\pi$
$444$	20.2758	−	11.4368i	0.962245	−	0.542764i
$445$	0.625386	−	0.625386i	0.0296461	−	0.0296461i
$446$	2.88912	−	0.758637i	0.136804	−	0.0359225i
$447$	−1.02121			−0.0483015
$448$	14.3567	+	0.431886i	0.678293	+	0.0204047i
$449$	−25.7875			−1.21699			−0.608494	−	0.793558i	$-0.708226\pi$
$449$	−25.7875			−1.21699			−0.608494	+	0.793558i	$0.708226\pi$
$450$	19.2671	−	5.05925i	0.908262	−	0.238495i
$451$	−6.06637	+	6.06637i	−0.285654	+	0.285654i
$452$	−6.97895	+	3.93655i	−0.328262	+	0.185160i
$453$	5.30410	+	5.30410i	0.249209	+	0.249209i
$454$	8.84953	−	15.1519i	0.415329	−	0.711116i
$455$			0.214215i			0.0100426i
$456$	4.88784	+	5.03709i	0.228894	+	0.235883i
$457$		−	38.7405i		−	1.81220i	−0.423061	−	0.906101i	$-0.639044\pi$
$457$		−	38.7405i		−	1.81220i	0.423061	−	0.906101i	$-0.360956\pi$
$458$	16.7207	+	9.76574i	0.781305	+	0.456323i
$459$	−1.63739	−	1.63739i	−0.0764269	−	0.0764269i
$460$	−0.799391	+	2.86805i	−0.0372718	+	0.133724i
$461$	−15.6730	+	15.6730i	−0.729966	+	0.729966i	−0.970613	−	0.240647i	$-0.922640\pi$
$461$	−15.6730	+	15.6730i	−0.729966	+	0.729966i	0.240647	+	0.970613i	$0.422640\pi$
$462$	8.99707	+	34.2636i	0.418582	+	1.59409i
$463$	10.4203			0.484272			0.242136	−	0.970242i	$-0.422152\pi$
$463$	10.4203			0.484272			0.242136	+	0.970242i	$0.422152\pi$
$464$	3.60831	+	14.6338i	0.167512	+	0.679359i
$465$	13.5359			0.627714
$466$	−3.51926	−	13.4024i	−0.163027	−	0.620855i
$467$	8.13376	−	8.13376i	0.376386	−	0.376386i	−0.493411	−	0.869796i	$-0.664250\pi$
$467$	8.13376	−	8.13376i	0.376386	−	0.376386i	0.869796	+	0.493411i	$0.164250\pi$
$468$	−0.988254	−	0.275449i	−0.0456821	−	0.0127326i
$469$	−2.69921	−	2.69921i	−0.124638	−	0.124638i
$470$	6.78332	+	3.96182i	0.312891	+	0.182745i
$471$			37.7007i			1.73716i
$472$	−12.4501	−	0.187222i	−0.573062	−	0.00861760i
$473$			32.5175i			1.49516i
$474$	−12.7631	+	21.8526i	−0.586228	+	1.00372i
$475$	3.15404	+	3.15404i	0.144717	+	0.144717i
$476$	−10.4253	−	18.4826i	−0.477843	−	0.847148i
$477$	27.2873	−	27.2873i	1.24940	−	1.24940i
$478$	−34.1258	+	8.96090i	−1.56088	+	0.409862i
$479$	−0.270353			−0.0123527			−0.00617637	−	0.999981i	$-0.501966\pi$
$479$	−0.270353			−0.0123527			−0.00617637	+	0.999981i	$0.501966\pi$
$480$	2.91737	−	9.88951i	0.133159	−	0.451392i
$481$	−0.761905			−0.0347399
$482$	−18.4416	+	4.84247i	−0.839991	+	0.220568i
$483$	6.38505	−	6.38505i	0.290530	−	0.290530i
$484$	20.2518	+	35.9037i	0.920539	+	1.63198i
$485$	3.76009	+	3.76009i	0.170737	+	0.170737i
$486$	15.8850	−	27.1979i	0.720559	−	1.23372i
$487$		−	6.27380i		−	0.284293i	−0.989846	−	0.142147i	$-0.954600\pi$
$487$		−	6.27380i		−	0.284293i	0.989846	−	0.142147i	$-0.0454004\pi$
$488$	−0.557082	+	37.0454i	−0.0252179	+	1.67697i
$489$		−	41.3587i		−	1.87031i
$490$	−3.38747	−	1.97846i	−0.153030	−	0.0893778i
$491$	2.16934	+	2.16934i	0.0979008	+	0.0979008i	0.754361	−	0.656460i	$-0.227947\pi$
$491$	2.16934	+	2.16934i	0.0979008	+	0.0979008i	−0.656460	+	0.754361i	$0.727947\pi$
$492$	−7.29502	−	2.03329i	−0.328885	−	0.0916677i
$493$	15.7454	−	15.7454i	0.709139	−	0.709139i
$494$	−0.0583432	−	0.222189i	−0.00262499	−	0.00999674i
$495$	13.0412			0.586160
$496$	−15.3652	+	25.4223i	−0.689919	+	1.14150i
$497$	−3.62725			−0.162704
$498$	0.781170	+	2.97493i	0.0350051	+	0.133310i
$499$	−0.0872085	+	0.0872085i	−0.00390399	+	0.00390399i	−0.709056	−	0.705152i	$-0.750879\pi$
$499$	−0.0872085	+	0.0872085i	−0.00390399	+	0.00390399i	0.705152	+	0.709056i	$0.250879\pi$
$500$	3.73140	−	13.3875i	0.166873	−	0.598707i
$501$	34.5658	+	34.5658i	1.54429	+	1.54429i
$502$	−12.9859	−	7.58442i	−0.579587	−	0.338509i
$503$		−	21.2559i		−	0.947755i	−0.880591	−	0.473878i	$-0.842854\pi$
$503$		−	21.2559i		−	0.947755i	0.880591	−	0.473878i	$-0.157146\pi$
$504$	−11.5087	+	11.1677i	−0.512636	+	0.497447i
$505$		−	1.12113i		−	0.0498898i
$506$	8.12739	−	13.9155i	0.361307	−	0.618620i
$507$	−22.7647	−	22.7647i	−1.01102	−	1.01102i
$508$	32.8699	−	18.5406i	1.45837	−	0.822607i
$509$	19.8075	−	19.8075i	0.877952	−	0.877952i	−0.115370	−	0.993323i	$-0.536805\pi$
$509$	19.8075	−	19.8075i	0.877952	−	0.877952i	0.993323	+	0.115370i	$0.0368055\pi$
$510$	−14.7336	+	3.86882i	−0.652417	+	0.171314i
$511$	−16.4419			−0.727346
$512$	15.2622	+	16.7052i	0.674501	+	0.738274i
$513$	−0.391843			−0.0173003
$514$	−27.1246	+	7.12250i	−1.19642	+	0.314160i
$515$	7.39112	−	7.39112i	0.325692	−	0.325692i
$516$	−25.0012	+	14.1022i	−1.10062	+	0.620815i
$517$	−30.0650	−	30.0650i	−1.32226	−	1.32226i
$518$	−6.00636	+	10.2839i	−0.263904	+	0.451850i
$519$			29.0203i			1.27385i
$520$	−0.242187	+	0.235011i	−0.0106206	+	0.0103059i
$521$		−	35.8522i		−	1.57071i	−0.619043	−	0.785357i	$-0.712479\pi$
$521$		−	35.8522i		−	1.57071i	0.619043	−	0.785357i	$-0.287521\pi$
$522$	−14.5310	−	8.48687i	−0.636005	−	0.371460i
$523$	−29.7189	−	29.7189i	−1.29952	−	1.29952i	−0.928709	−	0.370808i	$-0.879081\pi$
$523$	−29.7189	−	29.7189i	−1.29952	−	1.29952i	−0.370808	−	0.928709i	$-0.620919\pi$
$524$	−8.22831	+	29.5215i	−0.359455	+	1.28965i
$525$	−14.0523	+	14.0523i	−0.613291	+	0.613291i
$526$	−0.892955	−	3.40064i	−0.0389347	−	0.148275i
$527$	43.8858			1.91170
$528$	−28.8671	+	47.7617i	−1.25628	+	2.07856i
$529$	18.8923			0.821403
$530$	−3.22391	−	12.2776i	−0.140038	−	0.533306i
$531$	9.83016	−	9.83016i	0.426593	−	0.426593i
$532$	−3.45897	−	0.964092i	−0.149965	−	0.0417987i
$533$	0.175266	+	0.175266i	0.00759160	+	0.00759160i
$534$	−3.64887	−	2.13113i	−0.157902	−	0.0922231i
$535$			9.74284i			0.421220i
$536$	0.0904213	−	6.01292i	0.00390560	−	0.259719i
$537$			54.2283i			2.34012i
$538$	5.72583	−	9.80361i	0.246858	−	0.422664i
$539$	15.0139	+	15.0139i	0.646695	+	0.646695i
$540$	0.282804	+	0.501372i	0.0121700	+	0.0215756i
$541$	13.7203	−	13.7203i	0.589881	−	0.589881i	−0.347718	−	0.937599i	$-0.613043\pi$
$541$	13.7203	−	13.7203i	0.589881	−	0.589881i	0.937599	+	0.347718i	$0.113043\pi$
$542$	41.1941	−	10.8169i	1.76944	−	0.464627i
$543$	−28.9809			−1.24369
$544$	9.45863	−	32.0635i	0.405535	−	1.37471i
$545$	−13.2290			−0.566669
$546$	0.989922	−	0.259938i	0.0423647	−	0.0111243i
$547$	10.4847	−	10.4847i	0.448295	−	0.448295i	−0.446492	−	0.894787i	$-0.647327\pi$
$547$	10.4847	−	10.4847i	0.448295	−	0.448295i	0.894787	+	0.446492i	$0.147327\pi$
$548$	−3.45366	−	6.12286i	−0.147533	−	0.261556i
$549$	−29.2498	−	29.2498i	−1.24835	−	1.24835i
$550$	−17.8868	+	30.6253i	−0.762696	+	1.30587i
$551$		−	3.76803i		−	0.160524i
$552$	14.2237	+	0.213893i	0.605401	+	0.00910391i
$553$		−	12.9470i		−	0.550561i
$554$	3.54340	+	2.06953i	0.150545	+	0.0879261i
$555$	6.04532	+	6.04532i	0.256610	+	0.256610i
$556$	22.4606	+	6.26029i	0.952543	+	0.265495i
$557$	−28.1531	+	28.1531i	−1.19288	+	1.19288i	−0.216631	+	0.976254i	$0.569507\pi$
$557$	−28.1531	+	28.1531i	−1.19288	+	1.19288i	−0.976254	+	0.216631i	$0.930493\pi$
$558$	−8.42312	−	32.0778i	−0.356579	−	1.35796i
$559$	0.939475			0.0397356
$560$	1.26286	+	5.12164i	0.0533654	+	0.216429i
$561$	82.4497			3.48103
$562$	−4.40699	−	16.7832i	−0.185898	−	0.707955i
$563$	−4.11408	+	4.11408i	−0.173388	+	0.173388i	−0.788466	−	0.615078i	$-0.789124\pi$
$563$	−4.11408	+	4.11408i	−0.173388	+	0.173388i	0.615078	+	0.788466i	$0.289124\pi$
$564$	10.0770	−	36.1542i	0.424318	−	1.52237i
$565$	−2.08081	−	2.08081i	−0.0875404	−	0.0875404i
$566$	−38.0876	−	22.2452i	−1.60094	−	0.935035i
$567$			15.2634i			0.641001i
$568$	−3.97938	−	4.10089i	−0.166971	−	0.172070i
$569$		−	28.8203i		−	1.20821i	−0.796905	−	0.604105i	$-0.793531\pi$
$569$		−	28.8203i		−	1.20821i	0.796905	−	0.604105i	$-0.206469\pi$
$570$	−1.30003	+	2.22587i	−0.0544522	+	0.0932316i
$571$	21.4811	+	21.4811i	0.898956	+	0.898956i	0.995344	−	0.0963875i	$-0.0307288\pi$
$571$	21.4811	+	21.4811i	0.898956	+	0.898956i	−0.0963875	+	0.995344i	$0.530729\pi$
$572$	1.59092	−	0.897375i	0.0665197	−	0.0375211i
$573$	18.0067	−	18.0067i	0.752241	−	0.752241i
$574$	3.74736	−	0.983997i	0.156412	−	0.0410712i
$575$	9.04029			0.377006
$576$	−25.2518	−	0.759636i	−1.05216	−	0.0316515i
$577$	−3.64924			−0.151920			−0.0759600	−	0.997111i	$-0.524202\pi$
$577$	−3.64924			−0.151920			−0.0759600	+	0.997111i	$0.524202\pi$
$578$	−24.5157	+	6.43744i	−1.01972	+	0.267762i
$579$	−40.2899	+	40.2899i	−1.67439	+	1.67439i
$580$	−4.82128	+	2.71950i	−0.200193	+	0.112921i
$581$	−1.11268	−	1.11268i	−0.0461619	−	0.0461619i
$582$	12.8133	−	21.9386i	0.531128	−	0.909384i
$583$			68.7058i			2.84550i
$584$	−18.0380	−	18.5888i	−0.746419	−	0.769211i
$585$		−	0.376779i		−	0.0155779i
$586$	−34.6092	−	20.2136i	−1.42969	−	0.835016i
$587$	13.8244	+	13.8244i	0.570595	+	0.570595i	0.932295	−	0.361700i	$-0.117803\pi$
$587$	13.8244	+	13.8244i	0.570595	+	0.570595i	−0.361700	+	0.932295i	$0.617803\pi$
$588$	−5.03227	+	18.0548i	−0.207527	+	0.744566i
$589$	5.25114	−	5.25114i	0.216370	−	0.216370i
$590$	−1.16141	−	4.42298i	−0.0478143	−	0.182091i
$591$	16.8413			0.692760
$592$	−18.2162	+	4.49163i	−0.748683	+	0.184605i
$593$	−12.1807			−0.500201			−0.250100	−	0.968220i	$-0.580464\pi$
$593$	−12.1807			−0.500201			−0.250100	+	0.968220i	$0.580464\pi$
$594$	−0.791288	−	3.01346i	−0.0324669	−	0.123644i
$595$	5.51068	−	5.51068i	0.225916	−	0.225916i
$596$	0.792833	+	0.220980i	0.0324757	+	0.00905171i
$597$	−24.2018	−	24.2018i	−0.990516	−	0.990516i
$598$	−0.402038	−	0.234812i	−0.0164406	−	0.00960216i
$599$		−	10.9910i		−	0.449079i	−0.974465	−	0.224539i	$-0.927912\pi$
$599$		−	10.9910i		−	0.449079i	0.974465	−	0.224539i	$-0.0720877\pi$
$600$	−31.3036	−	0.470738i	−1.27796	−	0.0192178i
$601$			22.8580i			0.932396i	0.884680	+	0.466198i	$0.154377\pi$
$601$			22.8580i			0.932396i	−0.884680	+	0.466198i	$0.845623\pi$
$602$	7.40621	−	12.6807i	0.301854	−	0.516827i
$603$	4.74760	+	4.74760i	0.193337	+	0.193337i
$604$	−2.97017	−	5.26570i	−0.120855	−	0.214258i
$605$	−10.7049	+	10.7049i	−0.435215	+	0.435215i
$606$	−5.18093	+	1.36043i	−0.210461	+	0.0552637i
$607$	23.1676			0.940344			0.470172	−	0.882575i	$-0.344192\pi$
$607$	23.1676			0.940344			0.470172	+	0.882575i	$0.344192\pi$
$608$	−2.70478	−	4.96832i	−0.109693	−	0.201492i
$609$	16.7878			0.680276
$610$	−13.1606	+	3.45578i	−0.532859	+	0.139920i
$611$	−0.868618	+	0.868618i	−0.0351405	+	0.0351405i
$612$	18.3369	+	32.5087i	0.741224	+	1.31409i
$613$	−1.17929	−	1.17929i	−0.0476312	−	0.0476312i	0.682890	−	0.730521i	$-0.260723\pi$
$613$	−1.17929	−	1.17929i	−0.0476312	−	0.0476312i	−0.730521	+	0.682890i	$0.760723\pi$
$614$	−13.3058	+	22.7819i	−0.536980	+	0.919403i
$615$		−	2.78128i		−	0.112152i
$616$	0.429300	−	28.5480i	0.0172970	−	1.15023i
$617$		−	45.4159i		−	1.82838i	−0.405291	−	0.914188i	$-0.632830\pi$
$617$		−	45.4159i		−	1.82838i	0.405291	−	0.914188i	$-0.367170\pi$
$618$	−43.1242	−	25.1868i	−1.73471	−	1.01316i
$619$	−1.25969	−	1.25969i	−0.0506312	−	0.0506312i	0.681338	−	0.731969i	$-0.261398\pi$
$619$	−1.25969	−	1.25969i	−0.0506312	−	0.0506312i	−0.731969	+	0.681338i	$0.761398\pi$
$620$	−10.5089	−	2.92906i	−0.422046	−	0.117634i
$621$	−0.561562	+	0.561562i	−0.0225347	+	0.0225347i
$622$	9.27256	+	35.3127i	0.371796	+	1.41591i
$623$	2.16184			0.0866122
$624$	1.37990	+	0.834012i	0.0552403	+	0.0333872i
$625$	−17.1983			−0.687933
$626$	−3.29350	−	12.5427i	−0.131635	−	0.501305i
$627$	9.86549	−	9.86549i	0.393990	−	0.393990i
$628$	8.15810	−	29.2696i	0.325544	−	1.16798i
$629$	19.6000	+	19.6000i	0.781502	+	0.781502i
$630$	−5.08564	−	2.97028i	−0.202617	−	0.118339i
$631$			0.289816i			0.0115374i	0.999983	+	0.00576869i	$0.00183624\pi$
$631$			0.289816i			0.0115374i	−0.999983	+	0.00576869i	$0.998164\pi$
$632$	14.6376	−	14.2038i	0.582251	−	0.564999i
$633$		−	18.0477i		−	0.717331i
$634$	13.5171	−	23.1437i	0.536835	−	0.919154i
$635$	9.80033	+	9.80033i	0.388914	+	0.388914i
$636$	−52.8248	+	29.7964i	−2.09464	+	1.18150i
$637$	0.433773	−	0.433773i	0.0171867	−	0.0171867i
$638$	28.9780	−	7.60917i	1.14725	−	0.301250i
$639$	6.37990			0.252385
$640$	−4.40496	+	7.04660i	−0.174121	+	0.278541i
$641$	13.0742			0.516401			0.258201	−	0.966091i	$-0.416870\pi$
$641$	13.0742			0.516401			0.258201	+	0.966091i	$0.416870\pi$
$642$	45.0231	−	11.8224i	1.77692	−	0.466592i
$643$	14.8365	−	14.8365i	0.585096	−	0.585096i	−0.351203	−	0.936299i	$-0.614227\pi$
$643$	14.8365	−	14.8365i	0.585096	−	0.585096i	0.936299	+	0.351203i	$0.114227\pi$
$644$	−6.33882	+	3.57548i	−0.249784	+	0.140894i
$645$	−7.45425	−	7.45425i	−0.293511	−	0.293511i
$646$	−4.21491	+	7.21667i	−0.165834	+	0.283936i
$647$		−	21.7068i		−	0.853383i	−0.904397	−	0.426691i	$-0.859679\pi$
$647$		−	21.7068i		−	0.853383i	0.904397	−	0.426691i	$-0.140321\pi$
$648$	−17.2564	+	16.7451i	−0.677897	+	0.657811i
$649$			24.7511i			0.971564i
$650$	0.884808	+	0.516775i	0.0347050	+	0.0202696i
$651$	23.3955	+	23.3955i	0.916943	+	0.916943i
$652$	−8.94966	+	32.1095i	−0.350496	+	1.25751i
$653$	25.9365	−	25.9365i	1.01497	−	1.01497i	0.0150866	−	0.999886i	$-0.495198\pi$
$653$	25.9365	−	25.9365i	1.01497	−	1.01497i	0.999886	−	0.0150866i	$-0.00480240\pi$
$654$	16.0526	+	61.1333i	0.627708	+	2.39050i
$655$	−11.2553			−0.439781
$656$	5.22363	+	3.15716i	0.203949	+	0.123266i
$657$	28.9193			1.12825
$658$	4.87670	+	18.5719i	0.190113	+	0.724009i
$659$	−19.0656	+	19.0656i	−0.742691	+	0.742691i	−0.973095	−	0.230404i	$-0.925995\pi$
$659$	−19.0656	+	19.0656i	−0.742691	+	0.742691i	0.230404	+	0.973095i	$0.425995\pi$
$660$	−19.7433	−	5.50291i	−0.768508	−	0.214201i
$661$	−15.7242	−	15.7242i	−0.611601	−	0.611601i	0.331762	−	0.943363i	$-0.392357\pi$
$661$	−15.7242	−	15.7242i	−0.611601	−	0.611601i	−0.943363	+	0.331762i	$0.892357\pi$
$662$	−3.43035	−	2.00351i	−0.133324	−	0.0778685i
$663$		−	2.38208i		−	0.0925125i
$664$	0.0372739	−	2.47868i	0.00144651	−	0.0961914i
$665$		−	1.31876i		−	0.0511392i
$666$	10.5645	−	18.0882i	0.409365	−	0.700904i
$667$	−5.40008	−	5.40008i	−0.209092	−	0.209092i
$668$	−19.3560	−	34.3155i	−0.748907	−	1.32771i
$669$	3.70622	−	3.70622i	0.143291	−	0.143291i
$670$	2.13613	−	0.560915i	0.0825261	−	0.0216701i
$671$	73.6471			2.84312
$672$	22.1355	−	12.0507i	0.853894	−	0.464864i
$673$	−27.1994			−1.04846			−0.524230	−	0.851577i	$-0.675647\pi$
$673$	−27.1994			−1.04846			−0.524230	+	0.851577i	$0.675647\pi$
$674$	−39.5381	+	10.3821i	−1.52295	+	0.399903i
$675$	1.23589	−	1.23589i	0.0475694	−	0.0475694i
$676$	12.7477	+	22.5999i	0.490296	+	0.869226i
$677$	−29.1773	−	29.1773i	−1.12138	−	1.12138i	−0.991535	−	0.129840i	$-0.958554\pi$
$677$	−29.1773	−	29.1773i	−1.12138	−	1.12138i	−0.129840	−	0.991535i	$-0.541446\pi$
$678$	−7.09080	+	12.1407i	−0.272320	+	0.466260i
$679$			12.9979i			0.498814i
$680$	12.2759	+	0.184603i	0.470759	+	0.00707919i
$681$		−	30.7895i		−	1.17986i
$682$	50.9880	+	29.7797i	1.95243	+	1.14032i
$683$	24.8661	+	24.8661i	0.951473	+	0.951473i	0.998876	−	0.0474029i	$-0.0150945\pi$
$683$	24.8661	+	24.8661i	0.951473	+	0.951473i	−0.0474029	+	0.998876i	$0.515094\pi$
$684$	6.08391	+	1.69572i	0.232624	+	0.0648376i
$685$	1.82556	−	1.82556i	0.0697511	−	0.0697511i
$686$	−6.94938	−	26.4653i	−0.265328	−	1.01045i
$687$	33.9772			1.29631
$688$	22.4617	−	5.53845i	0.856346	−	0.211152i
$689$	1.98500			0.0756227
$690$	1.32686	+	5.05307i	0.0505126	+	0.192367i
$691$	−6.54782	+	6.54782i	−0.249091	+	0.249091i	−0.820597	−	0.571507i	$-0.806359\pi$
$691$	−6.54782	+	6.54782i	−0.249091	+	0.249091i	0.571507	+	0.820597i	$0.306359\pi$
$692$	6.27974	−	22.5304i	0.238720	−	0.856478i
$693$	22.5405	+	22.5405i	0.856244	+	0.856244i
$694$	37.2239	+	21.7407i	1.41300	+	0.825266i
$695$			8.56330i			0.324824i
$696$	18.4175	+	18.9799i	0.698115	+	0.719432i
$697$		−	9.01740i		−	0.341559i
$698$	0.721432	−	1.23522i	0.0273066	−	0.0467537i
$699$	−17.1929	−	17.1929i	−0.650294	−	0.650294i
$700$	13.9505	−	7.86893i	0.527279	−	0.297417i
$701$	20.4784	−	20.4784i	0.773460	−	0.773460i	−0.205250	−	0.978710i	$-0.565801\pi$
$701$	20.4784	−	20.4784i	0.773460	−	0.773460i	0.978710	+	0.205250i	$0.0658006\pi$
$702$	−0.0870631	+	0.0228614i	−0.00328599	+	0.000862848i
$703$	4.69046			0.176904
$704$	32.7467	−	30.8341i	1.23419	−	1.16210i
$705$	13.7841			0.519138
$706$	3.27151	−	0.859048i	0.123125	−	0.0323307i
$707$	1.93777	−	1.93777i	0.0728774	−	0.0728774i
$708$	−19.0300	+	10.7341i	−0.715190	+	0.403411i
$709$	−24.2106	−	24.2106i	−0.909247	−	0.909247i	0.0869648	−	0.996211i	$-0.472283\pi$
$709$	−24.2106	−	24.2106i	−0.909247	−	0.909247i	−0.996211	+	0.0869648i	$0.972283\pi$
$710$	1.05840	−	1.81217i	0.0397212	−	0.0680096i
$711$			22.7722i			0.854023i
$712$	2.37171	+	2.44413i	0.0888834	+	0.0915975i
$713$		−	15.0511i		−	0.563670i
$714$	−32.1526	−	18.7788i	−1.20328	−	0.702779i
$715$	0.474341	+	0.474341i	0.0177393	+	0.0177393i
$716$	11.7345	−	42.1011i	0.438540	−	1.57339i
$717$	−43.7772	+	43.7772i	−1.63489	+	1.63489i
$718$	2.19110	+	8.34436i	0.0817710	+	0.311409i
$719$	38.4674			1.43459			0.717296	−	0.696768i	$-0.245379\pi$
$719$	38.4674			1.43459			0.717296	+	0.696768i	$0.245379\pi$
$720$	−2.22121	−	9.00835i	−0.0827798	−	0.335721i
$721$	25.5497			0.951519
$722$	0.359174	+	1.36784i	0.0133671	+	0.0509058i
$723$	−23.6572	+	23.6572i	−0.879821	+	0.879821i
$724$	22.4998	+	6.27121i	0.836199	+	0.233068i
$725$	11.8845	+	11.8845i	0.441380	+	0.441380i
$726$	62.4585	+	36.4791i	2.31805	+	1.35387i
$727$		−	28.8436i		−	1.06975i	−0.844932	−	0.534874i	$-0.820359\pi$
$727$		−	28.8436i		−	1.06975i	0.844932	−	0.534874i	$-0.179641\pi$
$728$	−0.824791	−	0.0124031i	−0.0305688	−	0.000459688i
$729$		−	29.7636i		−	1.10235i
$730$	4.79761	−	8.21435i	0.177568	−	0.304027i
$731$	−24.1679	−	24.1679i	−0.893884	−	0.893884i
$732$	31.9393	+	56.6239i	1.18051	+	2.09288i
$733$	−16.2497	+	16.2497i	−0.600198	+	0.600198i	−0.940365	−	0.340167i	$-0.889516\pi$
$733$	−16.2497	+	16.2497i	−0.600198	+	0.600198i	0.340167	+	0.940365i	$0.389516\pi$
$734$	14.9163	−	3.91679i	0.550571	−	0.144571i
$735$	−6.88352			−0.253903
$736$	−10.9965	−	3.24395i	−0.405338	−	0.119573i
$737$	−11.9538			−0.440325
$738$	−6.59116	+	1.73073i	−0.242624	+	0.0637092i
$739$	19.4393	−	19.4393i	0.715084	−	0.715084i	−0.252510	−	0.967594i	$-0.581256\pi$
$739$	19.4393	−	19.4393i	0.715084	−	0.715084i	0.967594	+	0.252510i	$0.0812560\pi$
$740$	−3.38524	−	6.00154i	−0.124444	−	0.220621i
$741$	−0.285028	−	0.285028i	−0.0104708	−	0.0104708i
$742$	15.6485	−	26.7929i	0.574474	−	0.983599i
$743$		−	11.4606i		−	0.420447i	−0.977653	−	0.210224i	$-0.932581\pi$
$743$		−	11.4606i		−	0.420447i	0.977653	−	0.210224i	$-0.0674192\pi$
$744$	−0.783729	+	52.1172i	−0.0287329	+	1.91071i
$745$			0.302274i			0.0110745i
$746$	−18.6490	−	10.8920i	−0.682789	−	0.398784i
$747$	1.95708	+	1.95708i	0.0716058	+	0.0716058i
$748$	−64.0112	−	17.8414i	−2.34048	−	0.652346i
$749$	−16.8396	+	16.8396i	−0.615304	+	0.615304i
$750$	−6.19352	−	23.5868i	−0.226155	−	0.861267i
$751$	−21.2506			−0.775444			−0.387722	−	0.921776i	$-0.626738\pi$
$751$	−21.2506			−0.775444			−0.387722	+	0.921776i	$0.626738\pi$
$752$	−15.6469	+	25.8884i	−0.570584	+	0.944051i
$753$	−26.3879			−0.961630
$754$	−0.219839	−	0.837215i	−0.00800608	−	0.0304896i
$755$	1.56999	−	1.56999i	0.0571379	−	0.0571379i
$756$	−0.377773	+	1.35537i	−0.0137395	+	0.0492944i
$757$	−8.02688	−	8.02688i	−0.291742	−	0.291742i	0.546026	−	0.837768i	$-0.316140\pi$
$757$	−8.02688	−	8.02688i	−0.291742	−	0.291742i	−0.837768	+	0.546026i	$0.816140\pi$
$758$	−29.1590	−	17.0304i	−1.05910	−	0.618571i
$759$		−	28.2771i		−	1.02639i
$760$	1.49096	−	1.44678i	0.0540828	−	0.0524803i
$761$			23.7088i			0.859443i	0.902962	+	0.429721i	$0.141388\pi$
$761$			23.7088i			0.859443i	−0.902962	+	0.429721i	$0.858612\pi$
$762$	33.3967	−	57.1809i	1.20983	−	2.07145i
$763$	−22.8651	−	22.8651i	−0.827771	−	0.827771i
$764$	−17.8763	+	10.0833i	−0.646742	+	0.364802i
$765$	−9.69263	+	9.69263i	−0.350438	+	0.350438i
$766$	33.3020	−	8.74458i	1.20325	−	0.315955i
$767$	0.715092			0.0258205
$768$	37.9085	+	11.8053i	1.36791	+	0.425988i
$769$	7.97833			0.287706			0.143853	−	0.989599i	$-0.454051\pi$
$769$	7.97833			0.287706			0.143853	+	0.989599i	$0.454051\pi$
$770$	10.1419	−	2.66310i	0.365488	−	0.0959714i
$771$	−34.7960	+	34.7960i	−1.25315	+	1.25315i
$772$	39.9981	−	22.5614i	1.43956	−	0.812002i
$773$	24.5175	+	24.5175i	0.881835	+	0.881835i	0.993721	−	0.111886i	$-0.0356893\pi$
$773$	24.5175	+	24.5175i	0.881835	+	0.881835i	−0.111886	+	0.993721i	$0.535689\pi$
$774$	−13.0266	+	22.3039i	−0.468233	+	0.801696i
$775$			33.1246i			1.18987i
$776$	−14.6951	+	14.2597i	−0.527525	+	0.511894i
$777$			20.8975i			0.749694i
$778$	24.0782	+	14.0630i	0.863246	+	0.504181i
$779$	−1.07898	−	1.07898i	−0.0386583	−	0.0386583i
$780$	−0.158987	+	0.570412i	−0.00569264	+	0.0204240i
$781$	−8.03188	+	8.03188i	−0.287403	+	0.287403i
$782$	4.30190	+	16.3829i	0.153836	+	0.585853i
$783$	−1.47648			−0.0527651
$784$	7.81379	−	12.9282i	0.279064	−	0.461721i
$785$	11.1593			0.398291
$786$	13.6577	+	52.0125i	0.487152	+	1.85522i
$787$	1.63463	−	1.63463i	0.0582682	−	0.0582682i	−0.677372	−	0.735640i	$-0.736881\pi$
$787$	1.63463	−	1.63463i	0.0582682	−	0.0582682i	0.735640	+	0.677372i	$0.236881\pi$
$788$	−13.0751	−	3.64432i	−0.465780	−	0.129823i
$789$	−4.36241	−	4.36241i	−0.155306	−	0.155306i
$790$	6.46829	+	3.77782i	0.230132	+	0.134409i
$791$		−	7.19296i		−	0.255752i
$792$	−0.755087	+	50.2126i	−0.0268309	+	1.78423i
$793$		−	2.12777i		−	0.0755592i
$794$	22.2876	−	38.1602i	0.790957	−	1.35426i
$795$	−15.7500	−	15.7500i	−0.558594	−	0.558594i
$796$	13.5525	+	24.0266i	0.480354	+	0.851600i
$797$	−15.1868	+	15.1868i	−0.537945	+	0.537945i	−0.922925	−	0.384980i	$-0.874208\pi$
$797$	−15.1868	+	15.1868i	−0.537945	+	0.537945i	0.384980	+	0.922925i	$0.374208\pi$
$798$	−6.09418	+	1.60024i	−0.215732	+	0.0566477i
$799$	44.6903			1.58103
$800$	24.2012	+	7.13929i	0.855643	+	0.252412i
$801$	−3.80241			−0.134352
$802$	5.79573	−	1.52187i	0.204654	−	0.0537390i
$803$	−36.4075	+	36.4075i	−1.28479	+	1.28479i
$804$	−5.18415	−	9.19076i	−0.182831	−	0.324133i
$805$	−1.88995	−	1.88995i	−0.0666120	−	0.0666120i
$806$	0.860376	−	1.47311i	0.0303054	−	0.0518882i
$807$		−	19.9215i		−	0.701268i
$808$	4.31669	+	0.0649136i	0.151861	+	0.00228365i
$809$			37.3054i			1.31159i	0.754940	+	0.655794i	$0.227666\pi$
$809$			37.3054i			1.31159i	−0.754940	+	0.655794i	$0.772334\pi$
$810$	−7.62557	−	4.45373i	−0.267935	−	0.156488i
$811$	−23.2215	−	23.2215i	−0.815419	−	0.815419i	0.170022	−	0.985440i	$-0.445616\pi$
$811$	−23.2215	−	23.2215i	−0.815419	−	0.815419i	−0.985440	+	0.170022i	$0.945616\pi$
$812$	−13.0335	−	3.63273i	−0.457386	−	0.127484i
$813$	52.8446	−	52.8446i	1.85334	−	1.85334i
$814$	9.47191	+	36.0719i	0.331990	+	1.26432i
$815$	−12.2420			−0.428819
$816$	−14.0430	−	56.9528i	−0.491604	−	1.99375i
$817$	−5.78362			−0.202343
$818$	8.09508	+	30.8285i	0.283038	+	1.07789i
$819$	0.651227	−	0.651227i	0.0227557	−	0.0227557i
$820$	−0.601846	+	2.15930i	−0.0210174	+	0.0754060i
$821$	6.06148	+	6.06148i	0.211547	+	0.211547i	0.804924	−	0.593377i	$-0.202206\pi$
$821$	6.06148	+	6.06148i	0.211547	+	0.211547i	−0.593377	+	0.804924i	$0.702206\pi$
$822$	−10.6514	−	6.22098i	−0.371511	−	0.216982i
$823$		−	33.3591i		−	1.16283i	−0.813608	−	0.581413i	$-0.802500\pi$
$823$		−	33.3591i		−	1.16283i	0.813608	−	0.581413i	$-0.197500\pi$
$824$	28.0300	+	28.8859i	0.976471	+	1.00629i
$825$			62.2323i			2.16665i
$826$	5.63732	−	9.65207i	0.196147	−	0.335839i
$827$	−1.24138	−	1.24138i	−0.0431669	−	0.0431669i	0.685194	−	0.728361i	$-0.259717\pi$
$827$	−1.24138	−	1.24138i	−0.0431669	−	0.0431669i	−0.728361	+	0.685194i	$0.759717\pi$
$828$	11.1492	−	6.28884i	0.387462	−	0.218552i
$829$	11.5162	−	11.5162i	0.399975	−	0.399975i	−0.478249	−	0.878224i	$-0.658728\pi$
$829$	11.5162	−	11.5162i	0.399975	−	0.399975i	0.878224	+	0.478249i	$0.158728\pi$
$830$	0.880568	−	0.231223i	0.0305650	−	0.00802588i
$831$	7.20038			0.249778
$832$	−0.890839	−	0.946098i	−0.0308843	−	0.0328001i
$833$	−22.3176			−0.773258
$834$	39.5723	−	10.3911i	1.37028	−	0.359813i
$835$	10.2313	−	10.2313i	0.354070	−	0.354070i
$836$	−9.79405	+	5.52444i	−0.338734	+	0.191067i
$837$	−2.05763	−	2.05763i	−0.0711219	−	0.0711219i
$838$	1.05705	−	1.80986i	0.0365153	−	0.0625206i
$839$			7.69921i			0.265806i	0.991129	+	0.132903i	$0.0424299\pi$
$839$			7.69921i			0.265806i	−0.991129	+	0.132903i	$0.957570\pi$
$840$	6.44588	+	6.64270i	0.222404	+	0.229195i
$841$			14.8019i			0.510411i
$842$	−20.9447	−	12.2328i	−0.721800	−	0.421570i
$843$	−21.5297	−	21.5297i	−0.741524	−	0.741524i
$844$	−3.90536	+	14.0116i	−0.134428	+	0.482300i
$845$	−6.73827	+	6.73827i	−0.231804	+	0.231804i
$846$	−8.57753	−	32.6658i	−0.294902	−	1.12307i
$847$	−37.0046			−1.27149
$848$	47.4591	−	11.7021i	1.62975	−	0.401853i
$849$	−77.3961			−2.65623
$850$	−9.46764	−	36.0556i	−0.324737	−	1.23670i
$851$	6.72203	−	6.72203i	0.230428	−	0.230428i
$852$	−9.65863	−	2.69208i	−0.330899	−	0.0922291i
$853$	17.2622	+	17.2622i	0.591046	+	0.591046i	0.937914	−	0.346868i	$-0.112755\pi$
$853$	17.2622	+	17.2622i	0.591046	+	0.591046i	−0.346868	+	0.937914i	$0.612755\pi$
$854$	−28.7199	−	16.7739i	−0.982774	−	0.573992i
$855$			2.31954i			0.0793265i
$856$	−37.5127	−	0.564110i	−1.28216	−	0.0192809i
$857$		−	7.03579i		−	0.240338i	−0.992753	−	0.120169i	$-0.961656\pi$
$857$		−	7.03579i		−	0.240338i	0.992753	−	0.120169i	$-0.0383436\pi$
$858$	1.61642	−	2.76759i	0.0551835	−	0.0944838i
$859$	19.7672	+	19.7672i	0.674448	+	0.674448i	0.958738	−	0.284290i	$-0.0917579\pi$
$859$	19.7672	+	19.7672i	0.674448	+	0.674448i	−0.284290	+	0.958738i	$0.591758\pi$
$860$	4.17420	+	7.40027i	0.142339	+	0.252347i
$861$	4.80718	−	4.80718i	0.163828	−	0.163828i
$862$	−43.7866	+	11.4977i	−1.49138	+	0.391613i
$863$	−15.5745			−0.530164			−0.265082	−	0.964226i	$-0.585399\pi$
$863$	−15.5745			−0.530164			−0.265082	+	0.964226i	$0.585399\pi$
$864$	−1.94680	+	1.05985i	−0.0662315	+	0.0360568i
$865$	8.58990			0.292065
$866$	−5.65482	+	1.48487i	−0.192159	+	0.0504579i
$867$	−31.4492	+	31.4492i	−1.06807	+	1.06807i
$868$	−13.1009	−	23.2261i	−0.444675	−	0.788346i
$869$	−28.6687	−	28.6687i	−0.972519	−	0.972519i
$870$	−4.89855	+	8.38717i	−0.166076	+	0.284352i
$871$			0.345363i			0.0117022i
$872$	0.765959	−	50.9355i	0.0259386	−	1.72489i
$873$		−	22.8618i		−	0.773753i
$874$	2.47504	+	1.44555i	0.0837194	+	0.0488966i
$875$	8.82193	+	8.82193i	0.298236	+	0.298236i
$876$	−43.7814	−	12.2029i	−1.47924	−	0.412296i
$877$	8.06498	−	8.06498i	0.272335	−	0.272335i	−0.557705	−	0.830040i	$-0.688318\pi$
$877$	8.06498	−	8.06498i	0.272335	−	0.272335i	0.830040	+	0.557705i	$0.188318\pi$
$878$	−10.1254	−	38.5607i	−0.341716	−	1.30136i
$879$	−70.3277			−2.37209
$880$	14.1373	+	8.54456i	0.476568	+	0.288037i
$881$	−44.7768			−1.50857			−0.754284	−	0.656549i	$-0.772016\pi$
$881$	−44.7768			−1.50857			−0.754284	+	0.656549i	$0.772016\pi$
$882$	4.28347	+	16.3127i	0.144232	+	0.549279i
$883$	11.9531	−	11.9531i	0.402253	−	0.402253i	−0.476773	−	0.879026i	$-0.658194\pi$
$883$	11.9531	−	11.9531i	0.402253	−	0.402253i	0.879026	+	0.476773i	$0.158194\pi$
$884$	−0.515462	+	1.84937i	−0.0173369	+	0.0622012i
$885$	−5.67388	−	5.67388i	−0.190726	−	0.190726i
$886$	37.3563	+	21.8180i	1.25501	+	0.732991i
$887$			50.2212i			1.68626i	0.537707	+	0.843132i	$0.319291\pi$
$887$			50.2212i			1.68626i	−0.537707	+	0.843132i	$0.680709\pi$
$888$	−23.6263	+	22.9262i	−0.792845	+	0.769353i
$889$			33.8778i			1.13623i
$890$	−0.630807	+	1.08005i	−0.0211447	+	0.0362034i
$891$	33.7979	+	33.7979i	1.13227	+	1.13227i
$892$	−3.67938	+	2.07539i	−0.123195	+	0.0694893i
$893$	5.34741	−	5.34741i	0.178944	−	0.178944i
$894$	1.39685	−	0.366791i	0.0467177	−	0.0122673i
$895$	16.0514			0.536538
$896$	−19.7929	+	4.56582i	−0.661234	+	0.152533i
$897$	−0.816963			−0.0272776
$898$	35.2733	−	9.26221i	1.17708	−	0.309084i
$899$	19.7865	−	19.7865i	0.659917	−	0.659917i
$900$	−24.5373	+	13.8405i	−0.817909	+	0.461350i
$901$	−51.0641	−	51.0641i	−1.70119	−	1.70119i
$902$	6.11896	−	10.4767i	0.203739	−	0.348837i
$903$		−	25.7679i		−	0.857501i
$904$	8.13220	−	7.89124i	0.270473	−	0.262459i
$905$			8.57823i			0.285150i
$906$	−9.16028	−	5.35008i	−0.304330	−	0.177745i
$907$	−36.6618	−	36.6618i	−1.21733	−	1.21733i	−0.968562	−	0.248773i	$-0.919973\pi$
$907$	−36.6618	−	36.6618i	−1.21733	−	1.21733i	−0.248773	−	0.968562i	$-0.580027\pi$
$908$	−6.66258	+	23.9040i	−0.221106	+	0.793282i
$909$	−3.40831	+	3.40831i	−0.113046	+	0.113046i
$910$	−0.0769406	−	0.293013i	−0.00255056	−	0.00971329i
$911$	−37.6456			−1.24726			−0.623628	−	0.781721i	$-0.714342\pi$
$911$	−37.6456			−1.24726			−0.623628	+	0.781721i	$0.714342\pi$
$912$	−8.49499	−	5.13436i	−0.281297	−	0.170016i
$913$	−4.92767			−0.163082
$914$	13.9146	+	52.9909i	0.460253	+	1.75278i
$915$	−16.8827	+	16.8827i	−0.558126	+	0.558126i
$916$	−26.3788	−	7.35238i	−0.871581	−	0.242929i
$917$	−19.4537	−	19.4537i	−0.642418	−	0.642418i
$918$	2.82780	+	1.65159i	0.0933314	+	0.0545105i
$919$		−	27.3362i		−	0.901739i	−0.892590	−	0.450869i	$-0.851114\pi$
$919$		−	27.3362i		−	0.901739i	0.892590	−	0.450869i	$-0.148886\pi$
$920$	0.0633116	−	4.21016i	0.00208732	−	0.138805i
$921$			46.2940i			1.52544i
$922$	15.8089	−	27.0676i	0.520638	−	0.891424i
$923$	0.232052	+	0.232052i	0.00763809	+	0.00763809i
$924$	−24.6132	−	43.6357i	−0.809714	−	1.43551i
$925$	−14.7939	+	14.7939i	−0.486420	+	0.486420i
$926$	−14.2533	+	3.74270i	−0.468393	+	0.122993i
$927$	−44.9388			−1.47598
$928$	−10.1917	−	18.7208i	−0.334559	−	0.614540i
$929$	−21.6573			−0.710552			−0.355276	−	0.934761i	$-0.615613\pi$
$929$	−21.6573			−0.710552			−0.355276	+	0.934761i	$0.615613\pi$
$930$	−18.5150	+	4.86175i	−0.607131	+	0.159423i
$931$	−2.67040	+	2.67040i	−0.0875189	+	0.0875189i
$932$	9.62760	+	17.0684i	0.315362	+	0.559093i
$933$	45.2998	+	45.2998i	1.48305	+	1.48305i
$934$	−8.20427	+	14.0471i	−0.268452	+	0.459637i
$935$		−	24.4048i		−	0.798122i
$936$	1.45071	+	0.0218155i	0.0474179	+	0.000713062i
$937$			30.1453i			0.984804i	0.870368	+	0.492402i	$0.163881\pi$
$937$			30.1453i			0.984804i	−0.870368	+	0.492402i	$0.836119\pi$
$938$	4.66159	+	2.72261i	0.152206	+	0.0888965i
$939$	−16.0900	−	16.0900i	−0.525076	−	0.525076i
$940$	−10.7015	−	2.98275i	−0.349044	−	0.0972866i
$941$	−15.1241	+	15.1241i	−0.493032	+	0.493032i	−0.909260	−	0.416228i	$-0.863352\pi$
$941$	−15.1241	+	15.1241i	−0.493032	+	0.493032i	0.416228	+	0.909260i	$0.363352\pi$
$942$	−13.5411	−	51.5687i	−0.441193	−	1.68020i
$943$	−3.09262			−0.100710
$944$	17.0970	−	4.21566i	0.556460	−	0.137208i
$945$	−0.516746			−0.0168098
$946$	−11.6794	−	44.4788i	−0.379731	−	1.44613i
$947$	37.6952	−	37.6952i	1.22493	−	1.22493i	0.259072	−	0.965858i	$-0.416583\pi$
$947$	37.6952	−	37.6952i	1.22493	−	1.22493i	0.965858	−	0.259072i	$-0.0834169\pi$
$948$	9.60900	−	34.4751i	0.312086	−	1.11970i
$949$	1.05186	+	1.05186i	0.0341449	+	0.0341449i
$950$	−5.44708	−	3.18138i	−0.176726	−	0.103218i
$951$		−	47.0292i		−	1.52503i
$952$	20.8986	+	21.5368i	0.677329	+	0.698011i
$953$		−	25.2610i		−	0.818283i	−0.912471	−	0.409142i	$-0.865828\pi$
$953$		−	25.2610i		−	0.818283i	0.912471	−	0.409142i	$-0.134172\pi$
$954$	−27.5238	+	47.1256i	−0.891116	+	1.52575i
$955$	−5.32992	−	5.32992i	−0.172472	−	0.172472i
$956$	43.4602	−	24.5142i	1.40560	−	0.792846i
$957$	37.1735	−	37.1735i	1.20165	−	1.20165i
$958$	0.369800	−	0.0971037i	0.0119477	−	0.00313728i
$959$	6.31061			0.203780
$960$	−0.438456	+	14.5751i	−0.0141511	+	0.470410i
$961$	24.1490			0.779001
$962$	1.04217	−	0.273657i	0.0336008	−	0.00882304i
$963$	29.6188	−	29.6188i	0.954452	−	0.954452i
$964$	23.4859	−	13.2475i	0.756430	−	0.426672i
$965$	11.9257	+	11.9257i	0.383900	+	0.383900i
$966$	−6.44040	+	11.0271i	−0.207217	+	0.354791i
$967$			46.6651i			1.50065i	0.661070	+	0.750324i	$0.270103\pi$
$967$			46.6651i			1.50065i	−0.661070	+	0.750324i	$0.729897\pi$
$968$	−40.5970	−	41.8366i	−1.30484	−	1.34468i
$969$			14.6646i			0.471096i
$970$	−6.49374	−	3.79268i	−0.208501	−	0.121776i
$971$	4.16127	+	4.16127i	0.133542	+	0.133542i	0.770718	−	0.637176i	$-0.219898\pi$
$971$	4.16127	+	4.16127i	0.133542	+	0.133542i	−0.637176	+	0.770718i	$0.719898\pi$
$972$	−11.9594	+	42.9080i	−0.383599	+	1.37627i
$973$	−14.8008	+	14.8008i	−0.474493	+	0.474493i
$974$	2.25339	+	8.58157i	0.0722031	+	0.274971i
$975$	1.79798			0.0575813
$976$	−12.5437	−	50.8724i	−0.401516	−	1.62839i
$977$	−11.2429			−0.359693			−0.179846	−	0.983695i	$-0.557560\pi$
$977$	−11.2429			−0.359693			−0.179846	+	0.983695i	$0.557560\pi$
$978$	14.8550	+	56.5722i	0.475010	+	1.80898i
$979$	4.78699	−	4.78699i	0.152993	−	0.152993i
$980$	5.34414	+	1.48953i	0.170712	+	0.0475814i
$981$	40.2169	+	40.2169i	1.28403	+	1.28403i
$982$	−3.74648	−	2.18814i	−0.119555	−	0.0698265i
$983$			27.0230i			0.861899i	0.902376	+	0.430949i	$0.141821\pi$
$983$			27.0230i			0.861899i	−0.902376	+	0.430949i	$0.858179\pi$
$984$	10.7088	+	0.161036i	0.341382	+	0.00513365i
$985$		−	4.98497i		−	0.158834i
$986$	−15.8819	+	27.1927i	−0.505784	+	0.865990i
$987$	23.8244	+	23.8244i	0.758340	+	0.758340i
$988$	0.159609	+	0.282964i	0.00507783	+	0.00900228i
$989$	−8.28867	+	8.28867i	−0.263565	+	0.263565i
$990$	−17.8384	+	4.68407i	−0.566941	+	0.148870i
$991$	−38.4609			−1.22175			−0.610876	−	0.791726i	$-0.709183\pi$
$991$	−38.4609			−1.22175			−0.610876	+	0.791726i	$0.709183\pi$
$992$	11.8862	−	40.2925i	0.377386	−	1.27929i
$993$	−6.97066			−0.221207
$994$	4.96151	−	1.30281i	0.157370	−	0.0413228i
$995$	−7.16365	+	7.16365i	−0.227103	+	0.227103i
$996$	−2.13704	−	3.78866i	−0.0677146	−	0.120048i
$997$	40.0963	+	40.0963i	1.26986	+	1.26986i	0.946159	+	0.323703i	$0.104928\pi$
$997$	40.0963	+	40.0963i	1.26986	+	1.26986i	0.323703	+	0.946159i	$0.395072\pi$
$998$	0.0879645	−	0.150611i	0.00278447	−	0.00476750i
$999$		−	1.83792i		−	0.0581494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.229.3	yes	68
4.3	odd	2		1216.2.k.b.305.29		68
16.3	odd	4		1216.2.k.b.913.29		68
16.13	even	4	inner	304.2.k.b.77.3	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.3	✓	68	16.13	even	4	inner
304.2.k.b.229.3	yes	68	1.1	even	1	trivial
1216.2.k.b.305.29		68	4.3	odd	2
1216.2.k.b.913.29		68	16.3	odd	4

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36784 + 0.359174i) q^{2} +(-1.75469 + 1.75469i) q^{3} +(1.74199 - 0.982587i) q^{4} +(0.519383 + 0.519383i) q^{5} +(1.76991 - 3.03039i) q^{6} +1.79541i q^{7} +(-2.02985 + 1.96970i) q^{8} -3.15791i q^{9} +O(q^{10})\)	\(q+(-1.36784 + 0.359174i) q^{2} +(-1.75469 + 1.75469i) q^{3} +(1.74199 - 0.982587i) q^{4} +(0.519383 + 0.519383i) q^{5} +(1.76991 - 3.03039i) q^{6} +1.79541i q^{7} +(-2.02985 + 1.96970i) q^{8} -3.15791i q^{9} +(-0.896983 - 0.523885i) q^{10} +(3.97560 + 3.97560i) q^{11} +(-1.33252 + 4.78080i) q^{12} +(0.114860 - 0.114860i) q^{13} +(-0.644863 - 2.45583i) q^{14} -1.82272 q^{15} +(2.06904 - 3.42331i) q^{16} -5.90956 q^{17} +(1.13424 + 4.31952i) q^{18} +(-0.707107 + 0.707107i) q^{19} +(1.41510 + 0.394420i) q^{20} +(-3.15039 - 3.15039i) q^{21} +(-6.86592 - 4.01006i) q^{22} +2.02675i q^{23} +(0.105535 - 7.01798i) q^{24} -4.46048i q^{25} +(-0.115856 + 0.198366i) q^{26} +(0.277075 + 0.277075i) q^{27} +(1.76414 + 3.12757i) q^{28} +(-2.66440 + 2.66440i) q^{29} +(2.49319 - 0.654672i) q^{30} -7.42624 q^{31} +(-1.60056 + 5.42570i) q^{32} -13.9519 q^{33} +(8.08335 - 2.12256i) q^{34} +(-0.932503 + 0.932503i) q^{35} +(-3.10292 - 5.50103i) q^{36} +(-3.31665 - 3.31665i) q^{37} +(0.713237 - 1.22119i) q^{38} +0.403090i q^{39} +(-2.07730 - 0.0312380i) q^{40} +1.52590i q^{41} +(5.44077 + 3.17770i) q^{42} +(4.08964 + 4.08964i) q^{43} +(10.8318 + 3.01907i) q^{44} +(1.64016 - 1.64016i) q^{45} +(-0.727956 - 2.77228i) q^{46} -7.56238 q^{47} +(2.37632 + 9.63740i) q^{48} +3.77652 q^{49} +(1.60209 + 6.10124i) q^{50} +(10.3695 - 10.3695i) q^{51} +(0.0872252 - 0.312946i) q^{52} +(8.64094 + 8.64094i) q^{53} +(-0.478513 - 0.279477i) q^{54} +4.12971i q^{55} +(-3.53641 - 3.64440i) q^{56} -2.48151i q^{57} +(2.68750 - 4.60147i) q^{58} +(3.11287 + 3.11287i) q^{59} +(-3.17515 + 1.79098i) q^{60} +(9.26240 - 9.26240i) q^{61} +(10.1579 - 2.66731i) q^{62} +5.66972 q^{63} +(0.240551 - 7.99638i) q^{64} +0.119313 q^{65} +(19.0840 - 5.01117i) q^{66} +(-1.50340 + 1.50340i) q^{67} +(-10.2944 + 5.80666i) q^{68} +(-3.55633 - 3.55633i) q^{69} +(0.940586 - 1.61045i) q^{70} +2.02030i q^{71} +(6.22013 + 6.41006i) q^{72} +9.15775i q^{73} +(5.72792 + 3.34541i) q^{74} +(7.82678 + 7.82678i) q^{75} +(-0.536978 + 1.92657i) q^{76} +(-7.13781 + 7.13781i) q^{77} +(-0.144779 - 0.551364i) q^{78} -7.21117 q^{79} +(2.85263 - 0.703382i) q^{80} +8.50135 q^{81} +(-0.548064 - 2.08719i) q^{82} +(-0.619740 + 0.619740i) q^{83} +(-8.58347 - 2.39241i) q^{84} +(-3.06932 - 3.06932i) q^{85} +(-7.06287 - 4.12509i) q^{86} -9.35043i q^{87} +(-15.9006 - 0.239110i) q^{88} -1.20409i q^{89} +(-1.65438 + 2.83259i) q^{90} +(0.206221 + 0.206221i) q^{91} +(1.99146 + 3.53058i) q^{92} +(13.0308 - 13.0308i) q^{93} +(10.3441 - 2.71621i) q^{94} -0.734518 q^{95} +(-6.71194 - 12.3289i) q^{96} +7.23953 q^{97} +(-5.16568 + 1.35643i) q^{98} +(12.5546 - 12.5546i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more