LMFDB - Embedded newform 357.2.u.a.274.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(43,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.u (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			274.1
Character	$\chi$	$=$	357.274
Dual form			357.2.u.a.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.83460 - 1.83460i) q^{2} +(-0.923880 + 0.382683i) q^{3} +4.73152i q^{4} +(-0.623364 - 1.50493i) q^{5} +(2.39702 + 0.992879i) q^{6} +(-0.382683 + 0.923880i) q^{7} +(5.01125 - 5.01125i) q^{8} +(0.707107 - 0.707107i) q^{9} +(-1.61733 + 3.90458i) q^{10} +(3.88638 + 1.60979i) q^{11} +(-1.81067 - 4.37136i) q^{12} -0.414752i q^{13} +(2.39702 - 0.992879i) q^{14} +(1.15183 + 1.15183i) q^{15} -8.92425 q^{16} +(0.842005 - 4.03621i) q^{17} -2.59452 q^{18} +(-1.63232 - 1.63232i) q^{19} +(7.12062 - 2.94946i) q^{20} -1.00000i q^{21} +(-4.17663 - 10.0833i) q^{22} +(-4.67383 - 1.93596i) q^{23} +(-2.71207 + 6.54752i) q^{24} +(1.65929 - 1.65929i) q^{25} +(-0.760904 + 0.760904i) q^{26} +(-0.382683 + 0.923880i) q^{27} +(-4.37136 - 1.81067i) q^{28} +(-2.55775 - 6.17496i) q^{29} -4.22628i q^{30} +(-4.47086 + 1.85189i) q^{31} +(6.34993 + 6.34993i) q^{32} -4.20659 q^{33} +(-8.94959 + 5.86010i) q^{34} +1.62893 q^{35} +(3.34569 + 3.34569i) q^{36} +(8.78668 - 3.63956i) q^{37} +5.98931i q^{38} +(0.158719 + 0.383181i) q^{39} +(-10.6654 - 4.41777i) q^{40} +(-3.08161 + 7.43967i) q^{41} +(-1.83460 + 1.83460i) q^{42} +(-0.598929 + 0.598929i) q^{43} +(-7.61676 + 18.3885i) q^{44} +(-1.50493 - 0.623364i) q^{45} +(5.02289 + 12.1263i) q^{46} -9.46139i q^{47} +(8.24493 - 3.41516i) q^{48} +(-0.707107 - 0.707107i) q^{49} -6.08828 q^{50} +(0.766681 + 4.05120i) q^{51} +1.96241 q^{52} +(-5.35782 - 5.35782i) q^{53} +(2.39702 - 0.992879i) q^{54} -6.85223i q^{55} +(2.71207 + 6.54752i) q^{56} +(2.13273 + 0.883405i) q^{57} +(-6.63613 + 16.0210i) q^{58} +(2.19591 - 2.19591i) q^{59} +(-5.44989 + 5.44989i) q^{60} +(3.69557 - 8.92189i) q^{61} +(11.5997 + 4.80476i) q^{62} +(0.382683 + 0.923880i) q^{63} -5.45069i q^{64} +(-0.624174 + 0.258541i) q^{65} +(7.71741 + 7.71741i) q^{66} +1.49458 q^{67} +(19.0974 + 3.98397i) q^{68} +5.05892 q^{69} +(-2.98843 - 2.98843i) q^{70} +(11.6971 - 4.84511i) q^{71} -7.08698i q^{72} +(-3.95924 - 9.55846i) q^{73} +(-22.7972 - 9.44291i) q^{74} +(-0.898002 + 2.16797i) q^{75} +(7.72335 - 7.72335i) q^{76} +(-2.97451 + 2.97451i) q^{77} +(0.411798 - 0.994169i) q^{78} +(8.89036 + 3.68251i) q^{79} +(5.56305 + 13.4304i) q^{80} -1.00000i q^{81} +(19.3024 - 7.99530i) q^{82} +(-8.79272 - 8.79272i) q^{83} +4.73152 q^{84} +(-6.59911 + 1.24887i) q^{85} +2.19759 q^{86} +(4.72611 + 4.72611i) q^{87} +(27.5427 - 11.4086i) q^{88} +0.0665286i q^{89} +(1.61733 + 3.90458i) q^{90} +(0.383181 + 0.158719i) q^{91} +(9.16005 - 22.1143i) q^{92} +(3.42185 - 3.42185i) q^{93} +(-17.3579 + 17.3579i) q^{94} +(-1.43900 + 3.47406i) q^{95} +(-8.29659 - 3.43656i) q^{96} +(-4.57672 - 11.0492i) q^{97} +2.59452i q^{98} +(3.88638 - 1.60979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−1.83460	−	1.83460i	−1.29726	−	1.29726i	−0.930196	−	0.367062i	$-0.880364\pi$
$2$	−1.83460	−	1.83460i	−1.29726	−	1.29726i	−0.367062	−	0.930196i	$-0.619636\pi$
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$3$	−0.923880	+	0.382683i	−0.533402	+	0.220942i
$4$			4.73152i			2.36576i
$5$	−0.623364	−	1.50493i	−0.278777	−	0.673027i	0.721026	−	0.692908i	$-0.243671\pi$
$5$	−0.623364	−	1.50493i	−0.278777	−	0.673027i	−0.999802	+	0.0198818i	$0.993671\pi$
$6$	2.39702	+	0.992879i	0.978580	+	0.405341i
$7$	−0.382683	+	0.923880i	−0.144641	+	0.349194i
$7$	−0.382683	+	0.923880i	−0.144641	+	0.349194i
$8$	5.01125	−	5.01125i	1.77174	−	1.77174i
$9$	0.707107	−	0.707107i	0.235702	−	0.235702i
$10$	−1.61733	+	3.90458i	−0.511444	+	1.23474i
$11$	3.88638	+	1.60979i	1.17179	+	0.485370i	0.881783	−	0.471655i	$-0.156343\pi$
$11$	3.88638	+	1.60979i	1.17179	+	0.485370i	0.290005	+	0.957025i	$0.406343\pi$
$12$	−1.81067	−	4.37136i	−0.522697	−	1.26190i
$13$		−	0.414752i		−	0.115031i	−0.998345	−	0.0575157i	$-0.981682\pi$
$13$		−	0.414752i		−	0.115031i	0.998345	−	0.0575157i	$-0.0183179\pi$
$14$	2.39702	−	0.992879i	0.640631	−	0.265358i
$15$	1.15183	+	1.15183i	0.297400	+	0.297400i
$16$	−8.92425			−2.23106
$17$	0.842005	−	4.03621i	0.204216	−	0.978926i
$17$	0.842005	−	4.03621i	0.204216	−	0.978926i
$18$	−2.59452			−0.611534
$19$	−1.63232	−	1.63232i	−0.374480	−	0.374480i	0.494626	−	0.869106i	$-0.335305\pi$
$19$	−1.63232	−	1.63232i	−0.374480	−	0.374480i	−0.869106	+	0.494626i	$0.835305\pi$
$20$	7.12062	−	2.94946i	1.59222	−	0.659519i
$21$		−	1.00000i		−	0.218218i
$22$	−4.17663	−	10.0833i	−0.890461	−	2.14976i
$23$	−4.67383	−	1.93596i	−0.974561	−	0.403676i	−0.162153	−	0.986766i	$-0.551844\pi$
$23$	−4.67383	−	1.93596i	−0.974561	−	0.403676i	−0.812408	+	0.583089i	$0.801844\pi$
$24$	−2.71207	+	6.54752i	−0.553599	+	1.33651i
$25$	1.65929	−	1.65929i	0.331858	−	0.331858i
$26$	−0.760904	+	0.760904i	−0.149226	+	0.149226i
$27$	−0.382683	+	0.923880i	−0.0736475	+	0.177801i
$28$	−4.37136	−	1.81067i	−0.826109	−	0.342185i
$29$	−2.55775	−	6.17496i	−0.474963	−	1.14666i	−0.961943	−	0.273249i	$-0.911902\pi$
$29$	−2.55775	−	6.17496i	−0.474963	−	1.14666i	0.486981	−	0.873413i	$-0.338098\pi$
$30$		−	4.22628i		−	0.771610i
$31$	−4.47086	+	1.85189i	−0.802990	+	0.332609i	−0.746153	−	0.665774i	$-0.768101\pi$
$31$	−4.47086	+	1.85189i	−0.802990	+	0.332609i	−0.0568367	+	0.998383i	$0.518101\pi$
$32$	6.34993	+	6.34993i	1.12252	+	1.12252i
$33$	−4.20659			−0.732273
$34$	−8.94959	+	5.86010i	−1.53484	+	1.00500i
$35$	1.62893			0.275339
$36$	3.34569	+	3.34569i	0.557615	+	0.557615i
$37$	8.78668	−	3.63956i	1.44452	−	0.598341i	0.483632	−	0.875271i	$-0.339317\pi$
$37$	8.78668	−	3.63956i	1.44452	−	0.598341i	0.960890	+	0.276931i	$0.0893172\pi$
$38$			5.98931i			0.971594i
$39$	0.158719	+	0.383181i	0.0254153	+	0.0613580i
$40$	−10.6654	−	4.41777i	−1.68635	−	0.698510i
$41$	−3.08161	+	7.43967i	−0.481267	+	1.16188i	0.477740	+	0.878501i	$0.341456\pi$
$41$	−3.08161	+	7.43967i	−0.481267	+	1.16188i	−0.959008	+	0.283381i	$0.908544\pi$
$42$	−1.83460	+	1.83460i	−0.283085	+	0.283085i
$43$	−0.598929	+	0.598929i	−0.0913358	+	0.0913358i	−0.751298	−	0.659963i	$-0.770572\pi$
$43$	−0.598929	+	0.598929i	−0.0913358	+	0.0913358i	0.659963	+	0.751298i	$0.270572\pi$
$44$	−7.61676	+	18.3885i	−1.14827	+	2.77217i
$45$	−1.50493	−	0.623364i	−0.224342	−	0.0929256i
$46$	5.02289	+	12.1263i	0.740585	+	1.78793i
$47$		−	9.46139i		−	1.38009i	−0.723769	−	0.690043i	$-0.757592\pi$
$47$		−	9.46139i		−	1.38009i	0.723769	−	0.690043i	$-0.242408\pi$
$48$	8.24493	−	3.41516i	1.19005	−	0.492936i
$49$	−0.707107	−	0.707107i	−0.101015	−	0.101015i
$50$	−6.08828			−0.861012
$51$	0.766681	+	4.05120i	0.107357	+	0.567281i
$52$	1.96241			0.272137
$53$	−5.35782	−	5.35782i	−0.735953	−	0.735953i	0.235839	−	0.971792i	$-0.424216\pi$
$53$	−5.35782	−	5.35782i	−0.735953	−	0.735953i	−0.971792	+	0.235839i	$0.924216\pi$
$54$	2.39702	−	0.992879i	0.326193	−	0.135114i
$55$		−	6.85223i		−	0.923954i
$56$	2.71207	+	6.54752i	0.362416	+	0.874949i
$57$	2.13273	+	0.883405i	0.282487	+	0.117010i
$58$	−6.63613	+	16.0210i	−0.871367	+	2.10367i
$59$	2.19591	−	2.19591i	0.285884	−	0.285884i	−0.549566	−	0.835450i	$-0.685207\pi$
$59$	2.19591	−	2.19591i	0.285884	−	0.285884i	0.835450	+	0.549566i	$0.185207\pi$
$60$	−5.44989	+	5.44989i	−0.703578	+	0.703578i
$61$	3.69557	−	8.92189i	0.473169	−	1.14233i	−0.489586	−	0.871955i	$-0.662852\pi$
$61$	3.69557	−	8.92189i	0.473169	−	1.14233i	0.962755	−	0.270376i	$-0.0871480\pi$
$62$	11.5997	+	4.80476i	1.47317	+	0.610205i
$63$	0.382683	+	0.923880i	0.0482136	+	0.116398i
$64$		−	5.45069i		−	0.681337i
$65$	−0.624174	+	0.258541i	−0.0774193	+	0.0320681i
$66$	7.71741	+	7.71741i	0.949947	+	0.949947i
$67$	1.49458			0.182592			0.0912958	−	0.995824i	$-0.470899\pi$
$67$	1.49458			0.182592			0.0912958	+	0.995824i	$0.470899\pi$
$68$	19.0974	+	3.98397i	2.31590	+	0.483127i
$69$	5.05892			0.609022
$70$	−2.98843	−	2.98843i	−0.357186	−	0.357186i
$71$	11.6971	−	4.84511i	1.38819	−	0.575008i	0.441534	−	0.897245i	$-0.354435\pi$
$71$	11.6971	−	4.84511i	1.38819	−	0.575008i	0.946659	+	0.322236i	$0.104435\pi$
$72$		−	7.08698i		−	0.835209i
$73$	−3.95924	−	9.55846i	−0.463394	−	1.11873i	−0.966995	−	0.254796i	$-0.917992\pi$
$73$	−3.95924	−	9.55846i	−0.463394	−	1.11873i	0.503600	−	0.863937i	$-0.332008\pi$
$74$	−22.7972	−	9.44291i	−2.65012	−	1.09772i
$75$	−0.898002	+	2.16797i	−0.103692	+	0.250336i
$76$	7.72335	−	7.72335i	0.885929	−	0.885929i
$77$	−2.97451	+	2.97451i	−0.338977	+	0.338977i
$78$	0.411798	−	0.994169i	0.0466270	−	0.112568i
$79$	8.89036	+	3.68251i	1.00024	+	0.414315i	0.821887	−	0.569651i	$-0.192922\pi$
$79$	8.89036	+	3.68251i	1.00024	+	0.414315i	0.178357	+	0.983966i	$0.442922\pi$
$80$	5.56305	+	13.4304i	0.621968	+	1.50156i
$81$		−	1.00000i		−	0.111111i
$82$	19.3024	−	7.99530i	2.13159	−	0.882933i
$83$	−8.79272	−	8.79272i	−0.965126	−	0.965126i	0.0342860	−	0.999412i	$-0.489084\pi$
$83$	−8.79272	−	8.79272i	−0.965126	−	0.965126i	−0.999412	+	0.0342860i	$0.989084\pi$
$84$	4.73152			0.516251
$85$	−6.59911	+	1.24887i	−0.715774	+	0.135459i
$86$	2.19759			0.236972
$87$	4.72611	+	4.72611i	0.506692	+	0.506692i
$88$	27.5427	−	11.4086i	2.93606	−	1.21616i
$89$			0.0665286i			0.00705202i	0.999994	+	0.00352601i	$0.00112237\pi$
$89$			0.0665286i			0.00705202i	−0.999994	+	0.00352601i	$0.998878\pi$
$90$	1.61733	+	3.90458i	0.170481	+	0.411578i
$91$	0.383181	+	0.158719i	0.0401683	+	0.0166382i
$92$	9.16005	−	22.1143i	0.955002	−	2.30558i
$93$	3.42185	−	3.42185i	0.354829	−	0.354829i
$94$	−17.3579	+	17.3579i	−1.79033	+	1.79033i
$95$	−1.43900	+	3.47406i	−0.147639	+	0.356431i
$96$	−8.29659	−	3.43656i	−0.846767	−	0.350742i
$97$	−4.57672	−	11.0492i	−0.464695	−	1.12187i	−0.966448	−	0.256862i	$-0.917311\pi$
$97$	−4.57672	−	11.0492i	−0.464695	−	1.12187i	0.501753	−	0.865011i	$-0.332689\pi$
$98$			2.59452i			0.262086i
$99$	3.88638	−	1.60979i	0.390596	−	0.161790i
$100$	7.85098	+	7.85098i	0.785098	+	0.785098i
$101$	5.80507			0.577626			0.288813	−	0.957385i	$-0.406739\pi$
$101$	5.80507			0.577626			0.288813	+	0.957385i	$0.406739\pi$
$102$	6.02578	−	8.83888i	0.596641	−	0.875180i
$103$	13.5671			1.33680			0.668401	−	0.743801i	$-0.266979\pi$
$103$	13.5671			1.33680			0.668401	+	0.743801i	$0.266979\pi$
$104$	−2.07843	−	2.07843i	−0.203806	−	0.203806i
$105$	−1.50493	+	0.623364i	−0.146866	+	0.0608341i
$106$			19.6589i			1.90944i
$107$	6.99934	+	16.8979i	0.676652	+	1.63358i	0.770074	+	0.637955i	$0.220219\pi$
$107$	6.99934	+	16.8979i	0.676652	+	1.63358i	−0.0934221	+	0.995627i	$0.529781\pi$
$108$	−4.37136	−	1.81067i	−0.420634	−	0.174232i
$109$	−4.47999	+	10.8156i	−0.429105	+	1.03595i	0.550467	+	0.834857i	$0.314450\pi$
$109$	−4.47999	+	10.8156i	−0.429105	+	1.03595i	−0.979572	+	0.201094i	$0.935550\pi$
$110$	−12.5711	+	12.5711i	−1.19861	+	1.19861i
$111$	−6.72504	+	6.72504i	−0.638312	+	0.638312i
$112$	3.41516	−	8.24493i	0.322703	−	0.779073i
$113$	0.766264	+	0.317397i	0.0720840	+	0.0298582i	0.418434	−	0.908247i	$-0.362579\pi$
$113$	0.766264	+	0.317397i	0.0720840	+	0.0298582i	−0.346350	+	0.938105i	$0.612579\pi$
$114$	−2.29201	−	5.53340i	−0.214666	−	0.518250i
$115$			8.24061i			0.768441i
$116$	29.2170	−	12.1021i	2.71273	−	1.12365i
$117$	−0.293274	−	0.293274i	−0.0271132	−	0.0271132i
$118$	−8.05725			−0.741730
$119$	3.40675	+	2.32250i	0.312297	+	0.212904i
$120$	11.5442			1.05383
$121$	4.73435	+	4.73435i	0.430395	+	0.430395i
$122$	−23.1480	+	9.58822i	−2.09572	+	0.868076i
$123$		−	8.05264i		−	0.726082i
$124$	−8.76226	−	21.1540i	−0.786874	−	1.89968i
$125$	−11.0561	−	4.57960i	−0.988891	−	0.409612i
$126$	0.992879	−	2.39702i	0.0884527	−	0.213544i
$127$	5.40662	−	5.40662i	0.479760	−	0.479760i	−0.425295	−	0.905055i	$-0.639830\pi$
$127$	5.40662	−	5.40662i	0.479760	−	0.479760i	0.905055	+	0.425295i	$0.139830\pi$
$128$	2.70002	−	2.70002i	0.238651	−	0.238651i
$129$	0.324138	−	0.782538i	0.0285388	−	0.0688987i
$130$	1.61943	+	0.670790i	0.142033	+	0.0588322i
$131$	4.77531	+	11.5286i	0.417221	+	1.00726i	0.983149	+	0.182805i	$0.0585178\pi$
$131$	4.77531	+	11.5286i	0.417221	+	1.00726i	−0.565929	+	0.824454i	$0.691482\pi$
$132$		−	19.9036i		−	1.73238i
$133$	2.13273	−	0.883405i	0.184931	−	0.0766009i
$134$	−2.74195	−	2.74195i	−0.236869	−	0.236869i
$135$	1.62893			0.140196
$136$	−16.0070	−	24.4460i	−1.37259	−	2.09623i
$137$	−18.9471			−1.61876			−0.809379	−	0.587287i	$-0.800196\pi$
$137$	−18.9471			−1.61876			−0.809379	+	0.587287i	$0.800196\pi$
$138$	−9.28110	−	9.28110i	−0.790059	−	0.790059i
$139$	−11.0849	+	4.59150i	−0.940206	+	0.389446i	−0.799541	−	0.600611i	$-0.794924\pi$
$139$	−11.0849	+	4.59150i	−0.940206	+	0.389446i	−0.140665	+	0.990057i	$0.544924\pi$
$140$			7.70731i			0.651386i
$141$	3.62072	+	8.74118i	0.304919	+	0.736140i
$142$	−30.3484	−	12.5707i	−2.54678	−	1.05491i
$143$	0.667664	−	1.61188i	0.0558329	−	0.134792i
$144$	−6.31040	+	6.31040i	−0.525866	+	0.525866i
$145$	−7.69849	+	7.69849i	−0.639325	+	0.639325i
$146$	−10.2723	+	24.7996i	−0.850144	+	2.05243i
$147$	0.923880	+	0.382683i	0.0762003	+	0.0315632i
$148$	17.2207	+	41.5744i	1.41553	+	3.41739i
$149$		−	0.120835i		−	0.00989916i	−0.999988	−	0.00494958i	$-0.998424\pi$
$149$		−	0.120835i		−	0.00989916i	0.999988	−	0.00494958i	$-0.00157551\pi$
$150$	5.62483	−	2.32988i	0.459266	−	0.190234i
$151$	6.96222	+	6.96222i	0.566578	+	0.566578i	0.931168	−	0.364590i	$-0.118791\pi$
$151$	6.96222	+	6.96222i	0.566578	+	0.566578i	−0.364590	+	0.931168i	$0.618791\pi$
$152$	−16.3599			−1.32696
$153$	−2.25865	−	3.44942i	−0.182601	−	0.278869i
$154$	10.9141			0.879480
$155$	5.57394	+	5.57394i	0.447710	+	0.447710i
$156$	−1.81303	+	0.750981i	−0.145158	+	0.0601266i
$157$			6.65946i			0.531483i	0.964044	+	0.265741i	$0.0856168\pi$
$157$			6.65946i			0.531483i	−0.964044	+	0.265741i	$0.914383\pi$
$158$	−9.55433	−	23.0662i	−0.760102	−	1.83505i
$159$	7.00033	+	2.89963i	0.555162	+	0.229956i
$160$	5.59791	−	13.5145i	0.442554	−	1.06842i
$161$	3.57720	−	3.57720i	0.281922	−	0.281922i
$162$	−1.83460	+	1.83460i	−0.144140	+	0.144140i
$163$	−4.94790	+	11.9453i	−0.387550	+	0.935628i	0.602908	+	0.797811i	$0.294009\pi$
$163$	−4.94790	+	11.9453i	−0.387550	+	0.935628i	−0.990458	+	0.137817i	$0.955991\pi$
$164$	−35.2010	−	14.5807i	−2.74873	−	1.13856i
$165$	2.62223	+	6.33063i	0.204141	+	0.492839i
$166$			32.2623i			2.50404i
$167$	8.73215	−	3.61697i	0.675714	−	0.279890i	−0.0183201	−	0.999832i	$-0.505832\pi$
$167$	8.73215	−	3.61697i	0.675714	−	0.279890i	0.694034	+	0.719942i	$0.255832\pi$
$168$	−5.01125	−	5.01125i	−0.386626	−	0.386626i
$169$	12.8280			0.986768
$170$	14.3979	+	9.81556i	1.10427	+	0.752819i
$171$	−2.30845			−0.176531
$172$	−2.83385	−	2.83385i	−0.216079	−	0.216079i
$173$	−21.0025	+	8.69953i	−1.59679	+	0.661413i	−0.990957	−	0.134178i	$-0.957161\pi$
$173$	−21.0025	+	8.69953i	−1.59679	+	0.661413i	−0.605834	+	0.795591i	$0.707161\pi$
$174$		−	17.3411i		−	1.31462i
$175$	0.898002	+	2.16797i	0.0678826	+	0.163883i
$176$	−34.6830	−	14.3662i	−2.61433	−	1.08289i
$177$	−1.18842	+	2.86910i	−0.0893271	+	0.215655i
$178$	0.122053	−	0.122053i	0.00914829	−	0.00914829i
$179$	−9.65024	+	9.65024i	−0.721293	+	0.721293i	−0.968869	−	0.247576i	$-0.920366\pi$
$179$	−9.65024	+	9.65024i	−0.721293	+	0.721293i	0.247576	+	0.968869i	$0.420366\pi$
$180$	2.94946	−	7.12062i	0.219840	−	0.530740i
$181$	−9.11141	−	3.77407i	−0.677246	−	0.280525i	0.0174291	−	0.999848i	$-0.494452\pi$
$181$	−9.11141	−	3.77407i	−0.677246	−	0.280525i	−0.694675	+	0.719324i	$0.744452\pi$
$182$	−0.411798	−	0.994169i	−0.0305245	−	0.0736927i
$183$			9.65699i			0.713865i
$184$	−33.1233	+	13.7201i	−2.44189	+	1.01146i
$185$	−10.9546	−	10.9546i	−0.805398	−	0.805398i
$186$	−12.5554			−0.920610
$187$	9.76982	−	14.3308i	0.714440	−	1.04797i
$188$	44.7667			3.26495
$189$	−0.707107	−	0.707107i	−0.0514344	−	0.0514344i
$190$	9.01351	−	3.73352i	0.653909	−	0.270858i
$191$		−	24.7714i		−	1.79239i	−0.443658	−	0.896196i	$-0.646319\pi$
$191$		−	24.7714i		−	1.79239i	0.443658	−	0.896196i	$-0.353681\pi$
$192$	2.08589	+	5.03578i	0.150536	+	0.363426i
$193$	19.5994	+	8.11833i	1.41079	+	0.584370i	0.952530	−	0.304446i	$-0.0984714\pi$
$193$	19.5994	+	8.11833i	1.41079	+	0.584370i	0.458264	+	0.888816i	$0.348471\pi$
$194$	−11.8744	+	28.6673i	−0.852530	+	2.05819i
$195$	0.477722	−	0.477722i	0.0342104	−	0.0342104i
$196$	3.34569	−	3.34569i	0.238978	−	0.238978i
$197$	−1.27552	+	3.07938i	−0.0908770	+	0.219397i	−0.962782	−	0.270278i	$-0.912884\pi$
$197$	−1.27552	+	3.07938i	−0.0908770	+	0.219397i	0.871905	+	0.489675i	$0.162884\pi$
$198$	−10.0833	−	4.17663i	−0.716588	−	0.296820i
$199$	−4.28833	−	10.3530i	−0.303992	−	0.733901i	−0.999876	−	0.0157472i	$-0.994987\pi$
$199$	−4.28833	−	10.3530i	−0.303992	−	0.733901i	0.695884	−	0.718154i	$-0.255013\pi$
$200$		−	16.6303i		−	1.17594i
$201$	−1.38081	+	0.571950i	−0.0973948	+	0.0403422i
$202$	−10.6500	−	10.6500i	−0.749331	−	0.749331i
$203$	6.68373			0.469106
$204$	−19.1683	+	3.62757i	−1.34205	+	0.253980i
$205$	13.1172			0.916143
$206$	−24.8901	−	24.8901i	−1.73418	−	1.73418i
$207$	−4.67383	+	1.93596i	−0.324854	+	0.134559i
$208$			3.70135i			0.256642i
$209$	−3.71612	−	8.97151i	−0.257049	−	0.620572i
$210$	3.90458	+	1.61733i	0.269441	+	0.111606i
$211$	6.38658	−	15.4186i	0.439670	−	1.06146i	−0.536393	−	0.843969i	$-0.680213\pi$
$211$	6.38658	−	15.4186i	0.439670	−	1.06146i	0.976063	−	0.217489i	$-0.0697867\pi$
$212$	25.3506	−	25.3506i	1.74109	−	1.74109i
$213$	−8.95259	+	8.95259i	−0.613421	+	0.613421i
$214$	18.1599	−	43.8419i	1.24139	−	2.99697i
$215$	1.27470	+	0.527998i	0.0869337	+	0.0360091i
$216$	2.71207	+	6.54752i	0.184533	+	0.445502i
$217$		−	4.83922i		−	0.328508i
$218$	28.0614	−	11.6234i	1.90056	−	0.787236i
$219$	7.31573	+	7.31573i	0.494351	+	0.494351i
$220$	32.4215			2.18585
$221$	−1.67403	−	0.349223i	−0.112607	−	0.0234913i
$222$	24.6755			1.65611
$223$	2.89912	+	2.89912i	0.194140	+	0.194140i	0.797482	−	0.603342i	$-0.206165\pi$
$223$	2.89912	+	2.89912i	0.194140	+	0.194140i	−0.603342	+	0.797482i	$0.706165\pi$
$224$	−8.29659	+	3.43656i	−0.554339	+	0.229615i
$225$		−	2.34659i		−	0.156440i
$226$	−0.823491	−	1.98808i	−0.0547778	−	0.132245i
$227$	21.0245	+	8.70864i	1.39545	+	0.578013i	0.948565	−	0.316581i	$-0.102535\pi$
$227$	21.0245	+	8.70864i	1.39545	+	0.578013i	0.446880	+	0.894594i	$0.352535\pi$
$228$	−4.17985	+	10.0910i	−0.276817	+	0.668296i
$229$	3.53828	−	3.53828i	0.233816	−	0.233816i	−0.580467	−	0.814284i	$-0.697130\pi$
$229$	3.53828	−	3.53828i	0.233816	−	0.233816i	0.814284	+	0.580467i	$0.197130\pi$
$230$	15.1182	−	15.1182i	0.996867	−	0.996867i
$231$	1.60979	−	3.88638i	0.105917	−	0.255705i
$232$	−43.7618	−	18.1267i	−2.87310	−	1.19008i
$233$	9.16463	+	22.1254i	0.600395	+	1.44948i	0.873176	+	0.487405i	$0.162056\pi$
$233$	9.16463	+	22.1254i	0.600395	+	1.44948i	−0.272781	+	0.962076i	$0.587944\pi$
$234$			1.07608i			0.0703456i
$235$	−14.2388	+	5.89789i	−0.928834	+	0.384736i
$236$	10.3900	+	10.3900i	0.676332	+	0.676332i
$237$	−9.62286			−0.625072
$238$	−1.98917	−	10.5109i	−0.128939	−	0.681321i
$239$	−22.4124			−1.44974			−0.724869	−	0.688887i	$-0.758100\pi$
$239$	−22.4124			−1.44974			−0.724869	+	0.688887i	$0.758100\pi$
$240$	−10.2792	−	10.2792i	−0.663518	−	0.663518i
$241$	4.40756	−	1.82567i	0.283916	−	0.117602i	−0.236181	−	0.971709i	$-0.575896\pi$
$241$	4.40756	−	1.82567i	0.283916	−	0.117602i	0.520097	+	0.854107i	$0.325896\pi$
$242$		−	17.3713i		−	1.11667i
$243$	0.382683	+	0.923880i	0.0245492	+	0.0592669i
$244$	42.2141	+	17.4857i	2.70248	+	1.11940i
$245$	−0.623364	+	1.50493i	−0.0398253	+	0.0961467i
$246$	−14.7734	+	14.7734i	−0.941917	+	0.941917i
$247$	−0.677007	+	0.677007i	−0.0430770	+	0.0430770i
$248$	−13.1243	+	31.6849i	−0.833394	+	2.01199i
$249$	11.4882	+	4.75858i	0.728038	+	0.301563i
$250$	11.8819	+	28.6853i	0.751474	+	1.81422i
$251$			19.0410i			1.20186i	0.799303	+	0.600928i	$0.205202\pi$
$251$			19.0410i			1.20186i	−0.799303	+	0.600928i	$0.794798\pi$
$252$	−4.37136	+	1.81067i	−0.275370	+	0.114062i
$253$	−15.0478	−	15.0478i	−0.946046	−	0.946046i
$254$	−19.8380			−1.24475
$255$	5.61886	−	3.67917i	0.351867	−	0.230399i
$256$	−20.8083			−1.30052
$257$	4.22222	+	4.22222i	0.263375	+	0.263375i	0.826424	−	0.563049i	$-0.190372\pi$
$257$	4.22222	+	4.22222i	0.263375	+	0.263375i	−0.563049	+	0.826424i	$0.690372\pi$
$258$	−2.03031	+	0.840982i	−0.126402	+	0.0523572i
$259$			9.51064i			0.590962i
$260$	−1.22329	−	2.95329i	−0.0758655	−	0.183155i
$261$	−6.17496	−	2.55775i	−0.382220	−	0.158321i
$262$	12.3896	−	29.9112i	0.765433	−	1.84792i
$263$	−2.37366	+	2.37366i	−0.146366	+	0.146366i	−0.776493	−	0.630126i	$-0.783003\pi$
$263$	−2.37366	+	2.37366i	−0.146366	+	0.146366i	0.630126	+	0.776493i	$0.283003\pi$
$264$	−21.0803	+	21.0803i	−1.29740	+	1.29740i
$265$	−4.72329	+	11.4030i	−0.290150	+	0.700483i
$266$	−5.53340	−	2.29201i	−0.339274	−	0.140532i
$267$	−0.0254594	−	0.0614644i	−0.00155809	−	0.00376156i
$268$			7.07162i			0.431968i
$269$	9.90321	−	4.10205i	0.603810	−	0.250106i	−0.0597696	−	0.998212i	$-0.519037\pi$
$269$	9.90321	−	4.10205i	0.603810	−	0.250106i	0.663579	+	0.748106i	$0.269037\pi$
$270$	−2.98843	−	2.98843i	−0.181870	−	0.181870i
$271$	−27.2469			−1.65513			−0.827567	−	0.561367i	$-0.810276\pi$
$271$	−27.2469			−1.65513			−0.827567	+	0.561367i	$0.810276\pi$
$272$	−7.51427	+	36.0202i	−0.455619	+	2.18404i
$273$	−0.414752			−0.0251019
$274$	34.7603	+	34.7603i	2.09995	+	2.09995i
$275$	9.11975	−	3.77753i	0.549942	−	0.227793i
$276$			23.9364i			1.44080i
$277$	−2.74544	−	6.62809i	−0.164958	−	0.398243i	0.819687	−	0.572811i	$-0.194147\pi$
$277$	−2.74544	−	6.62809i	−0.164958	−	0.398243i	−0.984645	+	0.174568i	$0.944147\pi$
$278$	28.7599	+	11.9127i	1.72490	+	0.714478i
$279$	−1.85189	+	4.47086i	−0.110870	+	0.267663i
$280$	8.16297	−	8.16297i	0.487831	−	0.487831i
$281$	9.52769	−	9.52769i	0.568374	−	0.568374i	−0.363299	−	0.931673i	$-0.618350\pi$
$281$	9.52769	−	9.52769i	0.568374	−	0.568374i	0.931673	+	0.363299i	$0.118350\pi$
$282$	9.39401	−	22.6791i	0.559405	−	1.35052i
$283$	6.49189	+	2.68903i	0.385903	+	0.159846i	0.567196	−	0.823583i	$-0.308028\pi$
$283$	6.49189	+	2.68903i	0.385903	+	0.159846i	−0.181293	+	0.983429i	$0.558028\pi$
$284$	22.9247	+	55.3452i	1.36033	+	3.28413i
$285$		−	3.76030i		−	0.222741i
$286$	−4.18206	+	1.73227i	−0.247290	+	0.102431i
$287$	−5.69408	−	5.69408i	−0.336111	−	0.336111i
$288$	8.98016			0.529161
$289$	−15.5821	−	6.79703i	−0.916591	−	0.399825i
$290$	28.2473			1.65874
$291$	8.45667	+	8.45667i	0.495739	+	0.495739i
$292$	45.2260	−	18.7332i	2.64665	−	1.09628i
$293$		−	1.63134i		−	0.0953039i	−0.998864	−	0.0476520i	$-0.984826\pi$
$293$		−	1.63134i		−	0.0953039i	0.998864	−	0.0476520i	$-0.0151738\pi$
$294$	−0.992879	−	2.39702i	−0.0579059	−	0.139797i
$295$	−4.67356	−	1.93585i	−0.272105	−	0.112710i
$296$	25.7935	−	62.2711i	1.49922	−	3.61943i
$297$	−2.97451	+	2.97451i	−0.172598	+	0.172598i
$298$	−0.221683	+	0.221683i	−0.0128418	+	0.0128418i
$299$	−0.802945	+	1.93848i	−0.0464355	+	0.112105i
$300$	−10.2578	−	4.24892i	−0.592234	−	0.245311i
$301$	−0.324138	−	0.782538i	−0.0186830	−	0.0451048i
$302$		−	25.5458i		−	1.47000i
$303$	−5.36319	+	2.22151i	−0.308107	+	0.127622i
$304$	14.5672	+	14.5672i	0.835488	+	0.835488i
$305$	−15.7305			−0.900728
$306$	−2.18460	+	10.4720i	−0.124885	+	0.598646i
$307$	−20.5937			−1.17534			−0.587671	−	0.809100i	$-0.699955\pi$
$307$	−20.5937			−1.17534			−0.587671	+	0.809100i	$0.699955\pi$
$308$	−14.0739	−	14.0739i	−0.801937	−	0.801937i
$309$	−12.5343	+	5.19189i	−0.713053	+	0.295356i
$310$		−	20.4519i		−	1.16159i
$311$	6.64331	+	16.0384i	0.376707	+	0.909452i	0.992579	+	0.121605i	$0.0388042\pi$
$311$	6.64331	+	16.0384i	0.376707	+	0.909452i	−0.615871	+	0.787847i	$0.711196\pi$
$312$	2.71559	+	1.12484i	0.153740	+	0.0636813i
$313$	−5.43780	+	13.1280i	−0.307363	+	0.742039i	0.692426	+	0.721489i	$0.256542\pi$
$313$	−5.43780	+	13.1280i	−0.307363	+	0.742039i	−0.999789	+	0.0205503i	$0.993458\pi$
$314$	12.2175	−	12.2175i	0.689471	−	0.689471i
$315$	1.15183	−	1.15183i	0.0648980	−	0.0648980i
$316$	−17.4239	+	42.0649i	−0.980169	+	2.36634i
$317$	10.0420	+	4.15951i	0.564013	+	0.233622i	0.646426	−	0.762977i	$-0.276263\pi$
$317$	10.0420	+	4.15951i	0.564013	+	0.233622i	−0.0824136	+	0.996598i	$0.526263\pi$
$318$	−7.52315	−	18.1625i	−0.421877	−	1.01850i
$319$		−	28.1157i		−	1.57418i
$320$	−8.20293	+	3.39776i	−0.458558	+	0.189941i
$321$	−12.9331	−	12.9331i	−0.721855	−	0.721855i
$322$	−13.1255			−0.731453
$323$	−7.96281	+	5.21397i	−0.443063	+	0.290113i
$324$	4.73152			0.262862
$325$	−0.688195	−	0.688195i	−0.0381742	−	0.0381742i
$326$	30.9923	−	12.8374i	1.71650	−	0.710999i
$327$		−	11.7068i		−	0.647386i
$328$	21.8393	+	52.7248i	1.20588	+	2.91124i
$329$	8.74118	+	3.62072i	0.481917	+	0.199617i
$330$	6.80343	−	16.4249i	0.374517	−	0.904163i
$331$	23.6137	−	23.6137i	1.29793	−	1.29793i	0.368165	−	0.929760i	$-0.379986\pi$
$331$	23.6137	−	23.6137i	1.29793	−	1.29793i	0.929760	−	0.368165i	$-0.120014\pi$
$332$	41.6029	−	41.6029i	2.28326	−	2.28326i
$333$	3.63956	−	8.78668i	0.199447	−	0.481507i
$334$	−22.6557	−	9.38430i	−1.23967	−	0.513486i
$335$	−0.931665	−	2.24924i	−0.0509023	−	0.122889i
$336$			8.92425i			0.486858i
$337$	−9.72640	+	4.02881i	−0.529831	+	0.219463i	−0.631529	−	0.775352i	$-0.717572\pi$
$337$	−9.72640	+	4.02881i	−0.529831	+	0.219463i	0.101698	+	0.994815i	$0.467572\pi$
$338$	−23.5342	−	23.5342i	−1.28009	−	1.28009i
$339$	−0.829398			−0.0450467
$340$	−5.90904	−	31.2238i	−0.320463	−	1.69335i
$341$	−20.3566			−1.10237
$342$	4.23508	+	4.23508i	0.229007	+	0.229007i
$343$	0.923880	−	0.382683i	0.0498848	−	0.0206630i
$344$			6.00277i			0.323648i
$345$	−3.15355	−	7.61333i	−0.169781	−	0.409888i
$346$	54.4914	+	22.5711i	2.92948	+	1.21343i
$347$	−9.71054	+	23.4433i	−0.521289	+	1.25850i	0.415813	+	0.909450i	$0.363497\pi$
$347$	−9.71054	+	23.4433i	−0.521289	+	1.25850i	−0.937103	+	0.349054i	$0.886503\pi$
$348$	−22.3617	+	22.3617i	−1.19871	+	1.19871i
$349$	4.65324	−	4.65324i	0.249082	−	0.249082i	−0.571512	−	0.820594i	$-0.693643\pi$
$349$	4.65324	−	4.65324i	0.249082	−	0.249082i	0.820594	+	0.571512i	$0.193643\pi$
$350$	2.32988	−	5.62483i	0.124537	−	0.300660i
$351$	0.383181	+	0.158719i	0.0204527	+	0.00847178i
$352$	14.4562	+	34.9003i	0.770518	+	1.86019i
$353$		−	7.52053i		−	0.400278i	−0.979768	−	0.200139i	$-0.935861\pi$
$353$		−	7.52053i		−	0.400278i	0.979768	−	0.200139i	$-0.0641393\pi$
$354$	7.44393	−	3.08338i	0.395640	−	0.163880i
$355$	−14.5831	−	14.5831i	−0.773992	−	0.773992i
$356$	−0.314782			−0.0166834
$357$	−4.03621	−	0.842005i	−0.213619	−	0.0445637i
$358$	35.4087			1.87141
$359$	−6.95353	−	6.95353i	−0.366993	−	0.366993i	0.499386	−	0.866379i	$-0.333559\pi$
$359$	−6.95353	−	6.95353i	−0.366993	−	0.366993i	−0.866379	+	0.499386i	$0.833559\pi$
$360$	−10.6654	+	4.41777i	−0.562118	+	0.232837i
$361$		−	13.6711i		−	0.719530i
$362$	9.79189	+	23.6397i	0.514651	+	1.24248i
$363$	−6.18573	−	2.56221i	−0.324666	−	0.134481i
$364$	−0.750981	+	1.81303i	−0.0393621	+	0.0950285i
$365$	−11.9168	+	11.9168i	−0.623753	+	0.623753i
$366$	17.7167	−	17.7167i	0.926067	−	0.926067i
$367$	−3.55862	+	8.59127i	−0.185758	+	0.448460i	−0.989135	−	0.147011i	$-0.953035\pi$
$367$	−3.55862	+	8.59127i	−0.185758	+	0.448460i	0.803376	+	0.595471i	$0.203035\pi$
$368$	41.7104	+	17.2770i	2.17431	+	0.900627i
$369$	3.08161	+	7.43967i	0.160422	+	0.387294i
$370$			40.1946i			2.08962i
$371$	7.00033	−	2.89963i	0.363439	−	0.150541i
$372$	16.1905	+	16.1905i	0.839441	+	0.839441i
$373$	−12.5527			−0.649953			−0.324976	−	0.945722i	$-0.605356\pi$
$373$	−12.5527			−0.649953			−0.324976	+	0.945722i	$0.605356\pi$
$374$	−44.2150	+	8.36760i	−2.28631	+	0.432679i
$375$	11.9671			0.617977
$376$	−47.4134	−	47.4134i	−2.44516	−	2.44516i
$377$	−2.56108	+	1.06083i	−0.131902	+	0.0546357i
$378$			2.59452i			0.133448i
$379$	6.08538	+	14.6914i	0.312585	+	0.754646i	0.999608	+	0.0280106i	$0.00891723\pi$
$379$	6.08538	+	14.6914i	0.312585	+	0.754646i	−0.687023	+	0.726636i	$0.741083\pi$
$380$	−16.4376	−	6.80867i	−0.843230	−	0.349277i
$381$	−2.92604	+	7.06409i	−0.149906	+	0.361904i
$382$	−45.4456	+	45.4456i	−2.32520	+	2.32520i
$383$	25.1870	−	25.1870i	1.28700	−	1.28700i	0.350392	−	0.936603i	$-0.386048\pi$
$383$	25.1870	−	25.1870i	1.28700	−	1.28700i	0.936603	−	0.350392i	$-0.113952\pi$
$384$	−1.46124	+	3.52775i	−0.0745687	+	0.180025i
$385$	6.33063	+	2.62223i	0.322639	+	0.133641i
$386$	−21.0631	−	50.8509i	−1.07209	−	2.58824i
$387$			0.847014i			0.0430561i
$388$	52.2794	−	21.6548i	2.65408	−	1.09936i
$389$	19.5768	+	19.5768i	0.992584	+	0.992584i	0.999973	−	0.00738823i	$-0.00235177\pi$
$389$	19.5768	+	19.5768i	0.992584	+	0.992584i	−0.00738823	+	0.999973i	$0.502352\pi$
$390$	−1.75286			−0.0887595
$391$	−11.7494	+	17.2345i	−0.594191	+	0.871586i
$392$	−7.08698			−0.357947
$393$	−8.82362	−	8.82362i	−0.445093	−	0.445093i
$394$	7.98950	−	3.30936i	0.402505	−	0.166723i
$395$		−	15.6749i		−	0.788692i
$396$	7.61676	+	18.3885i	0.382757	+	0.924056i
$397$	18.5827	+	7.69721i	0.932639	+	0.386312i	0.796679	−	0.604402i	$-0.206588\pi$
$397$	18.5827	+	7.69721i	0.932639	+	0.386312i	0.135960	+	0.990714i	$0.456588\pi$
$398$	−11.1262	+	26.8609i	−0.557704	+	1.34642i
$399$	−1.63232	+	1.63232i	−0.0817182	+	0.0817182i
$400$	−14.8079	+	14.8079i	−0.740397	+	0.740397i
$401$	0.278533	−	0.672437i	0.0139093	−	0.0335799i	−0.916772	−	0.399410i	$-0.869215\pi$
$401$	0.278533	−	0.672437i	0.0139093	−	0.0335799i	0.930682	+	0.365830i	$0.119215\pi$
$402$	3.58253	+	1.48393i	0.178681	+	0.0740119i
$403$	0.768075	+	1.85430i	0.0382605	+	0.0923691i
$404$			27.4668i			1.36653i
$405$	−1.50493	+	0.623364i	−0.0747807	+	0.0309752i
$406$	−12.2620	−	12.2620i	−0.608552	−	0.608552i
$407$	40.0073			1.98309
$408$	24.1436	+	16.4595i	1.19529	+	0.814869i
$409$	−27.7215			−1.37074			−0.685370	−	0.728195i	$-0.740360\pi$
$409$	−27.7215			−1.37074			−0.685370	+	0.728195i	$0.740360\pi$
$410$	−24.0648	−	24.0648i	−1.18848	−	1.18848i
$411$	17.5048	−	7.25073i	0.863449	−	0.357652i
$412$			64.1928i			3.16255i
$413$	1.18842	+	2.86910i	0.0584783	+	0.141179i
$414$	12.1263	+	5.02289i	0.595977	+	0.246862i
$415$	−7.75139	+	18.7135i	−0.380501	+	0.918610i
$416$	2.63365	−	2.63365i	0.129125	−	0.129125i
$417$	8.48399	−	8.48399i	0.415463	−	0.415463i
$418$	−9.64154	+	23.2767i	−0.471583	+	1.13850i
$419$	10.8456	+	4.49239i	0.529842	+	0.219468i	0.631534	−	0.775348i	$-0.282426\pi$
$419$	10.8456	+	4.49239i	0.529842	+	0.219468i	−0.101692	+	0.994816i	$0.532426\pi$
$420$	−2.94946	−	7.12062i	−0.143919	−	0.347451i
$421$			2.15106i			0.104836i	0.998625	+	0.0524182i	$0.0166929\pi$
$421$			2.15106i			0.104836i	−0.998625	+	0.0524182i	$0.983307\pi$
$422$	−40.0037	+	16.5701i	−1.94735	+	0.806619i
$423$	−6.69021	−	6.69021i	−0.325289	−	0.325289i
$424$	−53.6988			−2.60784
$425$	−5.30013	−	8.09439i	−0.257094	−	0.392636i
$426$	32.8489			1.59153
$427$	6.82852	+	6.82852i	0.330455	+	0.330455i
$428$	−79.9528	+	33.1175i	−3.86466	+	1.60080i
$429$			1.74469i			0.0842345i
$430$	−1.36990	−	3.30723i	−0.0660624	−	0.159489i
$431$	2.69648	+	1.11692i	0.129885	+	0.0538000i	0.446679	−	0.894694i	$-0.352607\pi$
$431$	2.69648	+	1.11692i	0.129885	+	0.0538000i	−0.316794	+	0.948494i	$0.602607\pi$
$432$	3.41516	−	8.24493i	0.164312	−	0.396684i
$433$	23.9479	−	23.9479i	1.15086	−	1.15086i	0.164482	−	0.986380i	$-0.447405\pi$
$433$	23.9479	−	23.9479i	1.15086	−	1.15086i	0.986380	−	0.164482i	$-0.0525952\pi$
$434$	−8.87804	+	8.87804i	−0.426160	+	0.426160i
$435$	4.16640	−	10.0586i	0.199763	−	0.482271i
$436$	−51.1744	−	21.1971i	−2.45081	−	1.01516i
$437$	4.46907	+	10.7893i	0.213785	+	0.516122i
$438$		−	26.8429i		−	1.28260i
$439$	25.3636	−	10.5059i	1.21054	−	0.501421i	0.316148	−	0.948710i	$-0.397610\pi$
$439$	25.3636	−	10.5059i	1.21054	−	0.501421i	0.894390	+	0.447289i	$0.147610\pi$
$440$	−34.3382	−	34.3382i	−1.63701	−	1.63701i
$441$	−1.00000			−0.0476190
$442$	2.43049	+	3.71186i	0.115606	+	0.176555i
$443$	−10.3202			−0.490328			−0.245164	−	0.969482i	$-0.578842\pi$
$443$	−10.3202			−0.490328			−0.245164	+	0.969482i	$0.578842\pi$
$444$	−31.8197	−	31.8197i	−1.51009	−	1.51009i
$445$	0.100121	−	0.0414715i	0.00474620	−	0.00196594i
$446$		−	10.6375i		−	0.503699i
$447$	0.0462414	+	0.111637i	0.00218714	+	0.00528023i
$448$	5.03578	+	2.08589i	0.237918	+	0.0985490i
$449$	5.94113	−	14.3431i	0.280379	−	0.676895i	−0.719465	−	0.694528i	$-0.755613\pi$
$449$	5.94113	−	14.3431i	0.280379	−	0.676895i	0.999845	+	0.0176333i	$0.00561316\pi$
$450$	−4.30506	+	4.30506i	−0.202943	+	0.202943i
$451$	−23.9526	+	23.9526i	−1.12789	+	1.12789i
$452$	−1.50177	+	3.62559i	−0.0706373	+	0.170534i
$453$	−9.09658	−	3.76793i	−0.427395	−	0.177033i
$454$	−22.5947	−	54.5485i	−1.06042	−	2.56009i
$455$		−	0.675601i		−	0.0316727i
$456$	15.1146	−	6.26067i	0.707806	−	0.293183i
$457$	−2.46562	−	2.46562i	−0.115337	−	0.115337i	0.647083	−	0.762420i	$-0.275989\pi$
$457$	−2.46562	−	2.46562i	−0.115337	−	0.115337i	−0.762420	+	0.647083i	$0.775989\pi$
$458$	−12.9827			−0.606641
$459$	3.40675	+	2.32250i	0.159014	+	0.108405i
$460$	−38.9906			−1.81795
$461$	−7.58859	−	7.58859i	−0.353436	−	0.353436i	0.507951	−	0.861386i	$-0.330403\pi$
$461$	−7.58859	−	7.58859i	−0.353436	−	0.353436i	−0.861386	+	0.507951i	$0.830403\pi$
$462$	−10.0833	+	4.17663i	−0.469117	+	0.194315i
$463$		−	18.8429i		−	0.875703i	−0.899047	−	0.437852i	$-0.855739\pi$
$463$		−	18.8429i		−	0.875703i	0.899047	−	0.437852i	$-0.144261\pi$
$464$	22.8260	+	55.1069i	1.05967	+	2.55827i
$465$	−7.28271	−	3.01660i	−0.337727	−	0.139891i
$466$	23.7778	−	57.4047i	1.10148	−	2.65922i
$467$	−6.97392	+	6.97392i	−0.322714	+	0.322714i	−0.849808	−	0.527093i	$-0.823282\pi$
$467$	−6.97392	+	6.97392i	−0.322714	+	0.322714i	0.527093	+	0.849808i	$0.323282\pi$
$468$	1.38763	−	1.38763i	0.0641433	−	0.0641433i
$469$	−0.571950	+	1.38081i	−0.0264102	+	0.0637598i
$470$	36.9427	+	15.3022i	1.70404	+	0.705836i
$471$	−2.54847	−	6.15254i	−0.117427	−	0.283494i
$472$		−	22.0085i		−	1.01303i
$473$	−3.29182	+	1.36352i	−0.151358	+	0.0626945i
$474$	17.6541	+	17.6541i	0.810880	+	0.810880i
$475$	−5.41699			−0.248548
$476$	−10.9890	+	16.1191i	−0.503679	+	0.738819i
$477$	−7.57710			−0.346932
$478$	41.1178	+	41.1178i	1.88068	+	1.88068i
$479$	−24.2126	+	10.0292i	−1.10630	+	0.458246i	−0.859663	−	0.510861i	$-0.829327\pi$
$479$	−24.2126	+	10.0292i	−1.10630	+	0.458246i	−0.246641	+	0.969107i	$0.579327\pi$
$480$			14.6280i			0.667676i
$481$	−1.50952	−	3.64429i	−0.0688280	−	0.166166i
$482$	−11.4355	−	4.73674i	−0.520872	−	0.215752i
$483$	−1.93596	+	4.67383i	−0.0880894	+	0.212667i
$484$	−22.4007	+	22.4007i	−1.01821	+	1.01821i
$485$	−13.7753	+	13.7753i	−0.625504	+	0.625504i
$486$	0.992879	−	2.39702i	0.0450379	−	0.108731i
$487$	0.667057	+	0.276304i	0.0302273	+	0.0125205i	0.397746	−	0.917496i	$-0.369793\pi$
$487$	0.667057	+	0.276304i	0.0302273	+	0.0125205i	−0.367519	+	0.930016i	$0.619793\pi$
$488$	−26.1904	−	63.2293i	−1.18558	−	2.86225i
$489$		−	12.9295i		−	0.584692i
$490$	3.90458	−	1.61733i	0.176391	−	0.0730634i
$491$	21.4375	+	21.4375i	0.967463	+	0.967463i	0.999487	−	0.0320242i	$-0.0101954\pi$
$491$	21.4375	+	21.4375i	0.967463	+	0.967463i	−0.0320242	+	0.999487i	$0.510195\pi$
$492$	38.1013			1.71774
$493$	−27.0771	+	5.12429i	−1.21949	+	0.230786i
$494$	2.48408			0.111764
$495$	−4.84526	−	4.84526i	−0.217778	−	0.217778i
$496$	39.8991	−	16.5267i	1.79152	−	0.742072i
$497$			12.6609i			0.567918i
$498$	−12.3462	−	29.8064i	−0.553248	−	1.33566i
$499$	11.7606	+	4.87140i	0.526477	+	0.218074i	0.630059	−	0.776547i	$-0.283031\pi$
$499$	11.7606	+	4.87140i	0.526477	+	0.218074i	−0.103582	+	0.994621i	$0.533031\pi$
$500$	21.6685	−	52.3123i	0.969044	−	2.33948i
$501$	−6.68330	+	6.68330i	−0.298588	+	0.298588i
$502$	34.9326	−	34.9326i	1.55912	−	1.55912i
$503$	−3.49883	+	8.44693i	−0.156005	+	0.376630i	−0.982486	−	0.186334i	$-0.940339\pi$
$503$	−3.49883	+	8.44693i	−0.156005	+	0.376630i	0.826481	+	0.562964i	$0.190339\pi$
$504$	6.54752	+	2.71207i	0.291650	+	0.120805i
$505$	−3.61867	−	8.73625i	−0.161029	−	0.388758i
$506$			55.2134i			2.45453i
$507$	−11.8515	+	4.90906i	−0.526344	+	0.218019i
$508$	25.5815	+	25.5815i	1.13500	+	1.13500i
$509$	21.9242			0.971773			0.485887	−	0.874022i	$-0.338497\pi$
$509$	21.9242			0.971773			0.485887	+	0.874022i	$0.338497\pi$
$510$	−17.0582	−	3.55855i	−0.755349	−	0.157575i
$511$	10.3460			0.457680
$512$	32.7749	+	32.7749i	1.44846	+	1.44846i
$513$	2.13273	−	0.883405i	0.0941622	−	0.0390033i
$514$		−	15.4922i		−	0.683331i
$515$	−8.45721	−	20.4175i	−0.372669	−	0.899703i
$516$	3.70260	+	1.53367i	0.162998	+	0.0675159i
$517$	15.2309	−	36.7705i	0.669852	−	1.61717i
$518$	17.4482	−	17.4482i	0.766631	−	0.766631i
$519$	16.0746	−	16.0746i	0.705598	−	0.705598i
$520$	−1.83228	+	4.42351i	−0.0803507	+	0.193984i
$521$	31.7733	+	13.1609i	1.39201	+	0.576591i	0.947666	−	0.319263i	$-0.103435\pi$
$521$	31.7733	+	13.1609i	1.39201	+	0.576591i	0.444348	+	0.895854i	$0.353435\pi$
$522$	6.63613	+	16.0210i	0.290456	+	0.701222i
$523$		−	4.17422i		−	0.182526i	−0.995827	−	0.0912629i	$-0.970910\pi$
$523$		−	4.17422i		−	0.182526i	0.995827	−	0.0912629i	$-0.0290904\pi$
$524$	−54.5479	+	22.5945i	−2.38293	+	0.987044i
$525$	−1.65929	−	1.65929i	−0.0724174	−	0.0724174i
$526$	8.70943			0.379749
$527$	3.71014	+	19.6046i	0.161616	+	0.853992i
$528$	37.5406			1.63375
$529$	1.83328	+	1.83328i	0.0797078	+	0.0797078i
$530$	29.5854	−	12.2547i	1.28511	−	0.532309i
$531$		−	3.10549i		−	0.134767i
$532$	4.17985	+	10.0910i	0.181219	+	0.437502i
$533$	3.08562	+	1.27811i	0.133653	+	0.0553609i
$534$	−0.0660549	+	0.159471i	−0.00285847	+	0.00690097i
$535$	21.0671	−	21.0671i	0.910809	−	0.910809i
$536$	7.48970	−	7.48970i	0.323506	−	0.323506i
$537$	5.22267	−	12.6087i	0.225375	−	0.544103i
$538$	−25.6941	−	10.6428i	−1.10775	−	0.458845i
$539$	−1.60979	−	3.88638i	−0.0693386	−	0.167398i
$540$			7.70731i			0.331670i
$541$	34.6687	−	14.3602i	1.49052	−	0.617395i	0.519092	−	0.854718i	$-0.326270\pi$
$541$	34.6687	−	14.3602i	1.49052	−	0.617395i	0.971431	+	0.237324i	$0.0762703\pi$
$542$	49.9873	+	49.9873i	2.14714	+	2.14714i
$543$	9.86212			0.423224
$544$	30.9764	−	20.2830i	1.32810	−	0.869627i
$545$	19.0695			0.816847
$546$	0.760904	+	0.760904i	0.0325637	+	0.0325637i
$547$	−35.0735	+	14.5279i	−1.49964	+	0.621169i	−0.973388	−	0.229162i	$-0.926401\pi$
$547$	−35.0735	+	14.5279i	−1.49964	+	0.621169i	−0.526247	+	0.850332i	$0.676401\pi$
$548$		−	89.6485i		−	3.82959i
$549$	−3.69557	−	8.92189i	−0.157723	−	0.380777i
$550$	−23.6614	−	9.80086i	−1.00892	−	0.417910i
$551$	−5.90444	+	14.2546i	−0.251538	+	0.607265i
$552$	25.3515	−	25.3515i	1.07903	−	1.07903i
$553$	−6.80439	+	6.80439i	−0.289352	+	0.289352i
$554$	−7.12310	+	17.1967i	−0.302632	+	0.730617i
$555$	14.3129	+	5.92859i	0.607548	+	0.251655i
$556$	−21.7248	−	52.4483i	−0.921336	−	2.22430i
$557$			6.35890i			0.269435i	0.990884	+	0.134718i	$0.0430127\pi$
$557$			6.35890i			0.269435i	−0.990884	+	0.134718i	$0.956987\pi$
$558$	11.5997	−	4.80476i	0.491055	−	0.203402i
$559$	0.248407	+	0.248407i	0.0105065	+	0.0105065i
$560$	−14.5370			−0.614299
$561$	−3.54197	+	16.9787i	−0.149542	+	0.716841i
$562$	−34.9590			−1.47466
$563$	−1.33878	−	1.33878i	−0.0564229	−	0.0564229i	0.678332	−	0.734755i	$-0.262703\pi$
$563$	−1.33878	−	1.33878i	−0.0564229	−	0.0564229i	−0.734755	+	0.678332i	$0.762703\pi$
$564$	−41.3591	+	17.1315i	−1.74153	+	0.721366i
$565$		−	1.35103i		−	0.0568382i
$566$	−6.97674	−	16.8433i	−0.293254	−	0.707978i
$567$	0.923880	+	0.382683i	0.0387993	+	0.0160712i
$568$	34.3372	−	82.8973i	1.44076	−	3.47829i
$569$	−3.40057	+	3.40057i	−0.142559	+	0.142559i	−0.774785	−	0.632225i	$-0.782142\pi$
$569$	−3.40057	+	3.40057i	−0.142559	+	0.142559i	0.632225	+	0.774785i	$0.282142\pi$
$570$	−6.89864	+	6.89864i	−0.288952	+	0.288952i
$571$	2.34339	−	5.65744i	0.0980678	−	0.236757i	−0.867230	−	0.497907i	$-0.834102\pi$
$571$	2.34339	−	5.65744i	0.0980678	−	0.236757i	0.965298	+	0.261151i	$0.0841020\pi$
$572$	7.62666	+	3.15907i	0.318887	+	0.132087i
$573$	9.47959	+	22.8858i	0.396016	+	0.956066i
$574$			20.8927i			0.872045i
$575$	−10.9676	+	4.54292i	−0.457380	+	0.189453i
$576$	−3.85422	−	3.85422i	−0.160593	−	0.160593i
$577$	42.1179			1.75339			0.876695	−	0.481046i	$-0.159743\pi$
$577$	42.1179			1.75339			0.876695	+	0.481046i	$0.159743\pi$
$578$	16.1170	+	41.0567i	0.670379	+	1.70773i
$579$	−21.2142			−0.881632
$580$	−36.4256	−	36.4256i	−1.51249	−	1.51249i
$581$	11.4882	−	4.75858i	0.476612	−	0.197419i
$582$		−	31.0292i		−	1.28620i
$583$	−12.1976	−	29.4475i	−0.505171	−	1.21959i
$584$	−67.7406	−	28.0591i	−2.80313	−	1.16109i
$585$	−0.258541	+	0.624174i	−0.0106894	+	0.0258064i
$586$	−2.99286	+	2.99286i	−0.123634	+	0.123634i
$587$	−19.0338	+	19.0338i	−0.785608	+	0.785608i	−0.980771	−	0.195162i	$-0.937477\pi$
$587$	−19.0338	+	19.0338i	−0.785608	+	0.785608i	0.195162	+	0.980771i	$0.437477\pi$
$588$	−1.81067	+	4.37136i	−0.0746710	+	0.180272i
$589$	10.3207	+	4.27499i	0.425259	+	0.176148i
$590$	5.02260	+	12.1256i	0.206777	+	0.499204i
$591$		−	3.33309i		−	0.137105i
$592$	−78.4146	+	32.4804i	−3.22282	+	1.33494i
$593$	−28.9624	−	28.9624i	−1.18935	−	1.18935i	−0.977249	−	0.212096i	$-0.931971\pi$
$593$	−28.9624	−	28.9624i	−1.18935	−	1.18935i	−0.212096	−	0.977249i	$-0.568029\pi$
$594$	10.9141			0.447810
$595$	1.37157	−	6.57470i	0.0562287	−	0.269537i
$596$	0.571732			0.0234190
$597$	7.92381	+	7.92381i	0.324300	+	0.324300i
$598$	5.02942	−	2.08325i	0.205668	−	0.0851906i
$599$		−	7.28744i		−	0.297757i	−0.988856	−	0.148878i	$-0.952434\pi$
$599$		−	7.28744i		−	0.297757i	0.988856	−	0.148878i	$-0.0475663\pi$
$600$	6.36412	+	15.3644i	0.259814	+	0.627247i
$601$	34.4837	+	14.2836i	1.40662	+	0.582640i	0.951461	−	0.307770i	$-0.0995828\pi$
$601$	34.4837	+	14.2836i	1.40662	+	0.582640i	0.455158	+	0.890411i	$0.349583\pi$
$602$	−0.840982	+	2.03031i	−0.0342759	+	0.0827492i
$603$	1.05683	−	1.05683i	0.0430373	−	0.0430373i
$604$	−32.9419	+	32.9419i	−1.34039	+	1.34039i
$605$	4.17366	−	10.0761i	0.169683	−	0.409652i
$606$	13.9149	+	5.76373i	0.565254	+	0.234136i
$607$	2.89202	+	6.98196i	0.117383	+	0.283389i	0.971641	−	0.236461i	$-0.0759877\pi$
$607$	2.89202	+	6.98196i	0.117383	+	0.283389i	−0.854257	+	0.519850i	$0.825988\pi$
$608$		−	20.7302i		−	0.840722i
$609$	−6.17496	+	2.55775i	−0.250222	+	0.103645i
$610$	28.8593	+	28.8593i	1.16848	+	1.16848i
$611$	−3.92413			−0.158753
$612$	16.3210	−	10.6868i	0.659738	−	0.431990i
$613$	−44.6327			−1.80270			−0.901349	−	0.433094i	$-0.857422\pi$
$613$	−44.6327			−1.80270			−0.901349	+	0.433094i	$0.857422\pi$
$614$	37.7812	+	37.7812i	1.52472	+	1.52472i
$615$	−12.1187	+	5.01973i	−0.488673	+	0.202415i
$616$			29.8120i			1.20116i
$617$	−6.60123	−	15.9368i	−0.265755	−	0.641590i	0.733519	−	0.679668i	$-0.237876\pi$
$617$	−6.60123	−	15.9368i	−0.265755	−	0.641590i	−0.999275	+	0.0380784i	$0.987876\pi$
$618$	32.5205	+	13.4704i	1.30817	+	0.541860i
$619$	−4.77838	+	11.5360i	−0.192059	+	0.463672i	−0.990348	−	0.138603i	$-0.955739\pi$
$619$	−4.77838	+	11.5360i	−0.192059	+	0.463672i	0.798289	+	0.602275i	$0.205739\pi$
$620$	−26.3732	+	26.3732i	−1.05917	+	1.05917i
$621$	3.57720	−	3.57720i	0.143548	−	0.143548i
$622$	17.2362	−	41.6118i	0.691108	−	1.66848i
$623$	−0.0614644	−	0.0254594i	−0.00246252	−	0.00102001i
$624$	−1.41645	−	3.41960i	−0.0567032	−	0.136894i
$625$			7.76053i			0.310421i
$626$	34.0609	−	14.1085i	1.36135	−	0.563888i
$627$	6.86649	+	6.86649i	0.274221	+	0.274221i
$628$	−31.5094			−1.25736
$629$	−7.29162	−	38.5295i	−0.290736	−	1.53627i
$630$	−4.22628			−0.168379
$631$	−19.0864	−	19.0864i	−0.759818	−	0.759818i	0.216471	−	0.976289i	$-0.430545\pi$
$631$	−19.0864	−	19.0864i	−0.759818	−	0.759818i	−0.976289	+	0.216471i	$0.930545\pi$
$632$	63.0058	−	26.0979i	2.50624	−	1.03812i
$633$			16.6889i			0.663326i
$634$	−10.7919	−	26.0540i	−0.428602	−	1.03474i
$635$	−11.5069	−	4.76631i	−0.456637	−	0.189145i
$636$	−13.7197	+	33.1222i	−0.544020	+	1.31338i
$637$	−0.293274	+	0.293274i	−0.0116199	+	0.0116199i
$638$	−51.5811	+	51.5811i	−2.04211	+	2.04211i
$639$	4.84511	−	11.6971i	0.191669	−	0.462731i
$640$	−5.74645	−	2.38026i	−0.227148	−	0.0940880i
$641$	13.1282	+	31.6944i	0.518534	+	1.25185i	0.938804	+	0.344453i	$0.111936\pi$
$641$	13.1282	+	31.6944i	0.518534	+	1.25185i	−0.420269	+	0.907399i	$0.638064\pi$
$642$			47.4541i			1.87286i
$643$	−40.8682	+	16.9282i	−1.61168	+	0.667581i	−0.993006	−	0.118063i	$-0.962331\pi$
$643$	−40.8682	+	16.9282i	−1.61168	+	0.667581i	−0.618678	+	0.785645i	$0.712331\pi$
$644$	16.9256	+	16.9256i	0.666961	+	0.666961i
$645$	−1.37972			−0.0543266
$646$	24.1741	+	5.04303i	0.951118	+	0.198415i
$647$	39.1592			1.53951			0.769753	−	0.638341i	$-0.220379\pi$
$647$	39.1592			1.53951			0.769753	+	0.638341i	$0.220379\pi$
$648$	−5.01125	−	5.01125i	−0.196861	−	0.196861i
$649$	12.0691	−	4.99919i	0.473754	−	0.196235i
$650$			2.52512i			0.0990435i
$651$	1.85189	+	4.47086i	0.0725813	+	0.175227i
$652$	−56.5194	−	23.4111i	−2.21347	−	0.916850i
$653$	−4.52665	+	10.9283i	−0.177141	+	0.427657i	−0.987365	−	0.158464i	$-0.949346\pi$
$653$	−4.52665	+	10.9283i	−0.177141	+	0.427657i	0.810223	+	0.586121i	$0.199346\pi$
$654$	−21.4772	+	21.4772i	−0.839827	+	0.839827i
$655$	14.3730	−	14.3730i	0.561601	−	0.561601i
$656$	27.5011	−	66.3935i	1.07374	−	2.59223i
$657$	−9.55846	−	3.95924i	−0.372911	−	0.154465i
$658$	−9.39401	−	22.6791i	−0.366217	−	0.884125i
$659$			17.7427i			0.691158i	0.938390	+	0.345579i	$0.112317\pi$
$659$			17.7427i			0.691158i	−0.938390	+	0.345579i	$0.887683\pi$
$660$	−29.9535	+	12.4072i	−1.16594	+	0.482948i
$661$	1.22011	+	1.22011i	0.0474568	+	0.0474568i	0.730437	−	0.682980i	$-0.239316\pi$
$661$	1.22011	+	1.22011i	0.0474568	+	0.0474568i	−0.682980	+	0.730437i	$0.739316\pi$
$662$	−86.6434			−3.36749
$663$	1.68024	−	0.317982i	0.0652552	−	0.0123494i
$664$	−88.1250			−3.41991
$665$	−2.65893	−	2.65893i	−0.103109	−	0.103109i
$666$	−22.7972	+	9.44291i	−0.883374	+	0.365905i
$667$			33.8124i			1.30922i
$668$	17.1138	+	41.3163i	0.662152	+	1.59858i
$669$	−3.78789	−	1.56899i	−0.146448	−	0.0606608i
$670$	−2.41722	+	5.83569i	−0.0933854	+	0.225452i
$671$	28.7248	−	28.7248i	1.10891	−	1.10891i
$672$	6.34993	−	6.34993i	0.244954	−	0.244954i
$673$	−2.30063	+	5.55421i	−0.0886827	+	0.214099i	−0.961998	−	0.273056i	$-0.911965\pi$
$673$	−2.30063	+	5.55421i	−0.0886827	+	0.214099i	0.873315	+	0.487155i	$0.161965\pi$
$674$	25.2353	+	10.4528i	0.972028	+	0.402627i
$675$	0.898002	+	2.16797i	0.0345641	+	0.0834452i
$676$			60.6959i			2.33446i
$677$	−46.4294	+	19.2317i	−1.78443	+	0.739133i	−0.792879	+	0.609379i	$0.791419\pi$
$677$	−46.4294	+	19.2317i	−1.78443	+	0.739133i	−0.991546	+	0.129754i	$0.958581\pi$
$678$	1.52161	+	1.52161i	0.0584372	+	0.0584372i
$679$	11.9595			0.458965
$680$	−26.8114	+	39.3282i	−1.02817	+	1.50817i
$681$	−22.7568			−0.872041
$682$	37.3463	+	37.3463i	1.43006	+	1.43006i
$683$	−1.35351	+	0.560640i	−0.0517905	+	0.0214523i	−0.408428	−	0.912790i	$-0.633923\pi$
$683$	−1.35351	+	0.560640i	−0.0517905	+	0.0214523i	0.356638	+	0.934243i	$0.383923\pi$
$684$		−	10.9225i		−	0.417631i
$685$	11.8109	+	28.5141i	0.451272	+	1.08947i
$686$	−2.39702	−	0.992879i	−0.0915187	−	0.0379083i
$687$	−1.91491	+	4.62299i	−0.0730582	+	0.176378i
$688$	5.34499	−	5.34499i	0.203776	−	0.203776i
$689$	−2.22217	+	2.22217i	−0.0846578	+	0.0846578i
$690$	−8.18193	+	19.7529i	−0.311481	+	0.751981i
$691$	3.34103	+	1.38390i	0.127099	+	0.0526460i	0.445326	−	0.895368i	$-0.353088\pi$
$691$	3.34103	+	1.38390i	0.127099	+	0.0526460i	−0.318228	+	0.948014i	$0.603088\pi$
$692$	−41.1620	−	99.3738i	−1.56474	−	3.77763i
$693$			4.20659i			0.159795i
$694$	60.8241	−	25.1942i	2.30885	−	0.956358i
$695$	13.8198	+	13.8198i	0.524215	+	0.524215i
$696$	47.3675			1.79546
$697$	27.4334	+	18.7023i	1.03911	+	0.708400i
$698$	−17.0737			−0.646248
$699$	−16.9340	−	16.9340i	−0.640504	−	0.640504i
$700$	−10.2578	+	4.24892i	−0.387708	+	0.160594i
$701$		−	25.1415i		−	0.949581i	−0.880099	−	0.474791i	$-0.842524\pi$
$701$		−	25.1415i		−	0.949581i	0.880099	−	0.474791i	$-0.157476\pi$
$702$	−0.411798	−	0.994169i	−0.0155423	−	0.0375225i
$703$	−20.2836	−	8.40174i	−0.765011	−	0.316878i
$704$	8.77448	−	21.1835i	0.330701	−	0.798382i
$705$	10.8979	−	10.8979i	0.410438	−	0.410438i
$706$	−13.7972	+	13.7972i	−0.519264	+	0.519264i
$707$	−2.22151	+	5.36319i	−0.0835483	+	0.201703i
$708$	−13.5752	−	5.62303i	−0.510187	−	0.211327i
$709$	13.8529	+	33.4440i	0.520258	+	1.25601i	0.937743	+	0.347331i	$0.112912\pi$
$709$	13.8529	+	33.4440i	0.520258	+	1.25601i	−0.417484	+	0.908684i	$0.637088\pi$
$710$			53.5084i			2.00814i
$711$	8.89036	−	3.68251i	0.333415	−	0.138105i
$712$	0.333392	+	0.333392i	0.0124944	+	0.0124944i
$713$	24.4812			0.916829
$714$	5.86010	+	8.94959i	0.219309	+	0.334930i
$715$	−2.84198			−0.106284
$716$	−45.6603	−	45.6603i	−1.70641	−	1.70641i
$717$	20.7064	−	8.57685i	0.773293	−	0.320308i
$718$			25.5139i			0.952170i
$719$	−6.27839	−	15.1574i	−0.234145	−	0.565275i	0.762512	−	0.646973i	$-0.223966\pi$
$719$	−6.27839	−	15.1574i	−0.234145	−	0.565275i	−0.996657	+	0.0816984i	$0.973966\pi$
$720$	13.4304	+	5.56305i	0.500522	+	0.207323i
$721$	−5.19189	+	12.5343i	−0.193356	+	0.466803i
$722$	−25.0810	+	25.0810i	−0.933417	+	0.933417i
$723$	−3.37340	+	3.37340i	−0.125458	+	0.125458i
$724$	17.8571	−	43.1109i	0.663654	−	1.60220i
$725$	−14.4901	−	6.00200i	−0.538150	−	0.222909i
$726$	6.64770	+	16.0490i	0.246719	+	0.595633i
$727$			46.3095i			1.71753i	0.512374	+	0.858763i	$0.328766\pi$
$727$			46.3095i			1.71753i	−0.512374	+	0.858763i	$0.671234\pi$
$728$	2.71559	−	1.12484i	0.100647	−	0.0416892i
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$	43.7251			1.61834
$731$	1.91310	+	2.92171i	0.0707587	+	0.108063i
$732$	−45.6922			−1.68883
$733$	13.0076	+	13.0076i	0.480446	+	0.480446i	0.905274	−	0.424828i	$-0.139666\pi$
$733$	13.0076	+	13.0076i	0.480446	+	0.480446i	−0.424828	+	0.905274i	$0.639666\pi$
$734$	22.2902	−	9.23290i	0.822746	−	0.340793i
$735$		−	1.62893i		−	0.0600839i
$736$	−17.3853	−	41.9718i	−0.640830	−	1.54710i
$737$	5.80849	+	2.40596i	0.213959	+	0.0886246i
$738$	7.99530	−	19.3024i	0.294311	−	0.710530i
$739$	16.5831	−	16.5831i	0.610021	−	0.610021i	−0.332930	−	0.942951i	$-0.608037\pi$
$739$	16.5831	−	16.5831i	0.610021	−	0.610021i	0.942951	+	0.332930i	$0.108037\pi$
$740$	51.8319	−	51.8319i	1.90538	−	1.90538i
$741$	0.366394	−	0.884553i	0.0134598	−	0.0324949i
$742$	−18.1625	−	7.52315i	−0.666766	−	0.276183i
$743$	2.01538	+	4.86555i	0.0739370	+	0.178500i	0.956527	−	0.291644i	$-0.0942022\pi$
$743$	2.01538	+	4.86555i	0.0739370	+	0.178500i	−0.882590	+	0.470143i	$0.844202\pi$
$744$		−	34.2955i		−	1.25733i
$745$	−0.181848	+	0.0753240i	−0.00666240	+	0.00275966i
$746$	23.0291	+	23.0291i	0.843157	+	0.843157i
$747$	−12.4348			−0.454965
$748$	67.8065	+	46.2261i	2.47925	+	1.69019i
$749$	−18.2902			−0.668308
$750$	−21.9548	−	21.9548i	−0.801676	−	0.801676i
$751$	−7.60999	+	3.15216i	−0.277693	+	0.115024i	−0.517183	−	0.855875i	$-0.673019\pi$
$751$	−7.60999	+	3.15216i	−0.277693	+	0.115024i	0.239491	+	0.970899i	$0.423019\pi$
$752$			84.4358i			3.07906i
$753$	−7.28667	−	17.5916i	−0.265541	−	0.641073i
$754$	6.64476	+	2.75235i	0.241988	+	0.100235i
$755$	6.13768	−	14.8177i	0.223373	−	0.539270i
$756$	3.34569	−	3.34569i	0.121682	−	0.121682i
$757$	−17.2455	+	17.2455i	−0.626797	+	0.626797i	−0.947261	−	0.320464i	$-0.896161\pi$
$757$	−17.2455	+	17.2455i	−0.626797	+	0.626797i	0.320464	+	0.947261i	$0.396161\pi$
$758$	15.7886	−	38.1171i	0.573468	−	1.38448i
$759$	19.6609	+	8.14380i	0.713645	+	0.295601i
$760$	10.1982	+	24.6206i	0.369927	+	0.893083i
$761$		−	23.4771i		−	0.851043i	−0.904948	−	0.425522i	$-0.860091\pi$
$761$		−	23.4771i		−	0.851043i	0.904948	−	0.425522i	$-0.139909\pi$
$762$	18.3279	−	7.59166i	0.663950	−	0.275017i
$763$	−8.27793	−	8.27793i	−0.299681	−	0.299681i
$764$	117.206			4.24037
$765$	−3.78319	+	5.54936i	−0.136782	+	0.200637i
$766$	−92.4162			−3.33913
$767$	−0.910759	−	0.910759i	−0.0328856	−	0.0328856i
$768$	19.2244	−	7.96300i	0.693700	−	0.287340i
$769$			5.08040i			0.183204i	0.995796	+	0.0916019i	$0.0291987\pi$
$769$			5.08040i			0.183204i	−0.995796	+	0.0916019i	$0.970801\pi$
$770$	−6.80343	−	16.4249i	−0.245179	−	0.591914i
$771$	−5.51660	−	2.28505i	−0.198676	−	0.0822941i
$772$	−38.4120	+	92.7348i	−1.38248	+	3.33760i
$773$	−24.6299	+	24.6299i	−0.885875	+	0.885875i	−0.994124	−	0.108249i	$-0.965476\pi$
$773$	−24.6299	+	24.6299i	−0.885875	+	0.885875i	0.108249	+	0.994124i	$0.465476\pi$
$774$	1.55393	−	1.55393i	0.0558549	−	0.0558549i
$775$	−4.34563	+	10.4913i	−0.156100	+	0.376858i
$776$	−78.3052	−	32.4351i	−2.81099	−	1.16435i
$777$	−3.63956	−	8.78668i	−0.130569	−	0.315221i
$778$		−	71.8313i		−	2.57528i
$779$	17.1741	−	7.11374i	0.615326	−	0.254876i
$780$	2.26035	+	2.26035i	0.0809336	+	0.0809336i
$781$	53.2591			1.90576
$782$	53.1738	−	10.0630i	1.90149	−	0.359853i
$783$	6.68373			0.238857
$784$	6.31040	+	6.31040i	0.225371	+	0.225371i
$785$	10.0220	−	4.15127i	0.357702	−	0.148165i
$786$			32.3756i			1.15480i
$787$	0.961973	+	2.32241i	0.0342906	+	0.0827849i	0.940097	−	0.340907i	$-0.110734\pi$
$787$	0.961973	+	2.32241i	0.0342906	+	0.0827849i	−0.905806	+	0.423692i	$0.860734\pi$
$788$	−14.5701	−	6.03515i	−0.519040	−	0.214993i
$789$	1.28462	−	3.10134i	0.0457335	−	0.110410i
$790$	−28.7573	+	28.7573i	−1.02314	+	1.02314i
$791$	−0.586473	+	0.586473i	−0.0208526	+	0.0208526i
$792$	11.4086	−	27.5427i	0.405385	−	0.978687i
$793$	−3.70037	−	1.53274i	−0.131404	−	0.0544293i
$794$	−19.9705	−	48.2132i	−0.708728	−	1.71102i
$795$		−	12.3426i		−	0.437745i
$796$	48.9852	−	20.2903i	1.73623	−	0.719172i
$797$	17.5098	+	17.5098i	0.620229	+	0.620229i	0.945590	−	0.325361i	$-0.105486\pi$
$797$	17.5098	+	17.5098i	0.620229	+	0.620229i	−0.325361	+	0.945590i	$0.605486\pi$
$798$	5.98931			0.212019
$799$	−38.1882	−	7.96654i	−1.35100	−	0.281836i
$800$	21.0728			0.745036
$801$	0.0470428	+	0.0470428i	0.00166218	+	0.00166218i
$802$	−1.74465	+	0.722658i	−0.0616057	+	0.0255179i
$803$		−	43.5214i		−	1.53584i
$804$	−2.70619	−	6.53333i	−0.0954401	−	0.230413i
$805$	−7.61333	−	3.15355i	−0.268335	−	0.111148i
$806$	1.99278	−	4.81101i	0.0701928	−	0.169461i
$807$	−7.57959	+	7.57959i	−0.266814	+	0.266814i
$808$	29.0907	−	29.0907i	1.02341	−	1.02341i
$809$	4.40431	−	10.6329i	0.154847	−	0.373834i	−0.827350	−	0.561687i	$-0.810153\pi$
$809$	4.40431	−	10.6329i	0.154847	−	0.373834i	0.982197	+	0.187852i	$0.0601527\pi$
$810$	3.90458	+	1.61733i	0.137193	+	0.0568271i
$811$	−5.24984	−	12.6742i	−0.184347	−	0.445052i	0.804507	−	0.593943i	$-0.202430\pi$
$811$	−5.24984	−	12.6742i	−0.184347	−	0.445052i	−0.988854	+	0.148891i	$0.952430\pi$
$812$			31.6242i			1.10979i
$813$	25.1729	−	10.4270i	0.882852	−	0.365689i
$814$	−73.3975	−	73.3975i	−2.57258	−	2.57258i
$815$	21.0612			0.737742
$816$	−6.84205	−	36.1539i	−0.239520	−	1.26564i
$817$	1.95529			0.0684068
$818$	50.8579	+	50.8579i	1.77821	+	1.77821i
$819$	0.383181	−	0.158719i	0.0133894	−	0.00554608i
$820$			62.0642i			2.16738i
$821$	−2.91383	−	7.03461i	−0.101693	−	0.245509i	0.864841	−	0.502045i	$-0.167419\pi$
$821$	−2.91383	−	7.03461i	−0.101693	−	0.245509i	−0.966535	+	0.256536i	$0.917419\pi$
$822$	−45.4165	−	18.8121i	−1.58408	−	0.656149i
$823$	−0.148099	+	0.357542i	−0.00516239	+	0.0124631i	−0.926440	−	0.376443i	$-0.877147\pi$
$823$	−0.148099	+	0.357542i	−0.00516239	+	0.0124631i	0.921277	+	0.388906i	$0.127147\pi$
$824$	67.9879	−	67.9879i	2.36847	−	2.36847i
$825$	−6.97996	+	6.97996i	−0.243011	+	0.243011i
$826$	3.08338	−	7.44393i	0.107284	−	0.259007i
$827$	30.2775	+	12.5414i	1.05285	+	0.436106i	0.840909	−	0.541176i	$-0.182021\pi$
$827$	30.2775	+	12.5414i	1.05285	+	0.436106i	0.211943	+	0.977282i	$0.432021\pi$
$828$	−9.16005	−	22.1143i	−0.318334	−	0.768526i
$829$			2.98545i			0.103689i	0.998655	+	0.0518444i	$0.0165100\pi$
$829$			2.98545i			0.103689i	−0.998655	+	0.0518444i	$0.983490\pi$
$830$	48.5525	−	20.1111i	1.68528	−	0.698067i
$831$	5.07292	+	5.07292i	0.175978	+	0.175978i
$832$	−2.26069			−0.0783752
$833$	−3.44942	+	2.25865i	−0.119515	+	0.0782575i
$834$	−31.1295			−1.07793
$835$	−10.8866	−	10.8866i	−0.376747	−	0.376747i
$836$	42.4489	−	17.5829i	1.46812	−	0.608117i
$837$		−	4.83922i		−	0.167268i
$838$	−11.6556	−	28.1391i	−0.402636	−	0.972048i
$839$	30.7254	+	12.7269i	1.06076	+	0.439380i	0.843720	−	0.536783i	$-0.180361\pi$
$839$	30.7254	+	12.7269i	1.06076	+	0.439380i	0.217037	+	0.976163i	$0.430361\pi$
$840$	−4.41777	+	10.6654i	−0.152427	+	0.367992i
$841$	−11.0819	+	11.0819i	−0.382136	+	0.382136i
$842$	3.94634	−	3.94634i	0.136000	−	0.136000i
$843$	−5.15635	+	12.4485i	−0.177594	+	0.428750i
$844$	72.9533	+	30.2182i	2.51115	+	1.04015i
$845$	−7.99650	−	19.3053i	−0.275088	−	0.664121i
$846$			24.5477i			0.843968i
$847$	−6.18573	+	2.56221i	−0.212544	+	0.0880386i
$848$	47.8145	+	47.8145i	1.64196	+	1.64196i
$849$	−7.02678			−0.241158
$850$	−5.12636	+	24.5736i	−0.175833	+	0.842867i
$851$	−48.1135			−1.64931
$852$	−42.3594	−	42.3594i	−1.45121	−	1.45121i
$853$	23.0625	−	9.55280i	0.789645	−	0.327081i	0.0488439	−	0.998806i	$-0.484446\pi$
$853$	23.0625	−	9.55280i	0.789645	−	0.327081i	0.740801	+	0.671725i	$0.234446\pi$
$854$		−	25.0552i		−	0.857372i
$855$	1.43900	+	3.47406i	0.0492129	+	0.118810i
$856$	119.755	+	49.6042i	4.09314	+	1.69544i
$857$	2.47918	−	5.98527i	0.0846871	−	0.204453i	−0.875863	−	0.482560i	$-0.839707\pi$
$857$	2.47918	−	5.98527i	0.0846871	−	0.204453i	0.960550	+	0.278107i	$0.0897070\pi$
$858$	3.20081	−	3.20081i	0.109274	−	0.109274i
$859$	−15.6588	+	15.6588i	−0.534272	+	0.534272i	−0.921841	−	0.387569i	$-0.873315\pi$
$859$	−15.6588	+	15.6588i	−0.534272	+	0.534272i	0.387569	+	0.921841i	$0.373315\pi$
$860$	−2.49823	+	6.03126i	−0.0851890	+	0.205664i
$861$	7.43967	+	3.08161i	0.253543	+	0.105021i
$862$	−2.89786	−	6.99606i	−0.0987016	−	0.238287i
$863$		−	30.7167i		−	1.04561i	−0.852452	−	0.522805i	$-0.824886\pi$
$863$		−	30.7167i		−	1.04561i	0.852452	−	0.522805i	$-0.175114\pi$
$864$	−8.29659	+	3.43656i	−0.282256	+	0.116914i
$865$	26.1844	+	26.1844i	0.890297	+	0.890297i
$866$	−87.8696			−2.98593
$867$	16.9971	+	0.316642i	0.577250	+	0.0107537i
$868$	22.8969			0.777171
$869$	28.6233	+	28.6233i	0.970977	+	0.970977i
$870$	−26.0971	+	10.8098i	−0.884776	+	0.366486i
$871$		−	0.619879i		−	0.0210038i
$872$	31.7496	+	76.6502i	1.07518	+	2.59570i
$873$	−11.0492	−	4.57672i	−0.373958	−	0.154898i
$874$	11.5951	−	27.9930i	0.392210	−	0.946878i
$875$	8.46200	−	8.46200i	0.286068	−	0.286068i
$876$	−34.6145	+	34.6145i	−1.16952	+	1.16952i
$877$	8.77348	−	21.1811i	0.296259	−	0.715233i	−0.703729	−	0.710468i	$-0.748483\pi$
$877$	8.77348	−	21.1811i	0.296259	−	0.715233i	0.999989	−	0.00476512i	$-0.00151679\pi$
$878$	−65.8062	−	27.2578i	−2.22085	−	0.919908i
$879$	0.624287	+	1.50716i	0.0210567	+	0.0508353i
$880$			61.1510i			2.06140i
$881$	31.4603	−	13.0313i	1.05993	−	0.439035i	0.216500	−	0.976283i	$-0.430536\pi$
$881$	31.4603	−	13.0313i	1.05993	−	0.439035i	0.843425	+	0.537247i	$0.180536\pi$
$882$	1.83460	+	1.83460i	0.0617742	+	0.0617742i
$883$	−17.5568			−0.590835			−0.295417	−	0.955368i	$-0.595459\pi$
$883$	−17.5568			−0.590835			−0.295417	+	0.955368i	$0.595459\pi$
$884$	1.65236	−	7.92070i	0.0555748	−	0.266402i
$885$	5.05862			0.170044
$886$	18.9335	+	18.9335i	0.636082	+	0.636082i
$887$	−47.5772	+	19.7071i	−1.59749	+	0.661701i	−0.991057	−	0.133436i	$-0.957399\pi$
$887$	−47.5772	+	19.7071i	−1.59749	+	0.661701i	−0.606430	+	0.795137i	$0.707399\pi$
$888$			67.4017i			2.26185i
$889$	2.92604	+	7.06409i	0.0981363	+	0.236922i
$890$	−0.259766	−	0.107599i	−0.00870738	−	0.00360671i
$891$	1.60979	−	3.88638i	0.0539300	−	0.130199i
$892$	−13.7173	+	13.7173i	−0.459288	+	0.459288i
$893$	−15.4440	+	15.4440i	−0.516814	+	0.516814i
$894$	0.119974	−	0.289643i	0.00401254	−	0.00968712i
$895$	20.5386	+	8.50736i	0.686529	+	0.284370i
$896$	1.46124	+	3.52775i	0.0488167	+	0.117854i
$897$		−	2.09820i		−	0.0700567i
$898$	−37.2135	+	15.4144i	−1.24183	+	0.514384i
$899$	22.8707	+	22.8707i	0.762781	+	0.762781i
$900$	11.1030			0.370099
$901$	−26.1366	+	17.1140i	−0.870737	+	0.570150i
$902$	87.8871			2.92632
$903$	0.598929	+	0.598929i	0.0199311	+	0.0199311i
$904$	5.43049	−	2.24938i	0.180616	−	0.0748134i
$905$			16.0647i			0.534008i
$906$	9.77595	+	23.6012i	0.324784	+	0.784099i
$907$	6.39312	+	2.64812i	0.212280	+	0.0879293i	0.486290	−	0.873798i	$-0.338350\pi$
$907$	6.39312	+	2.64812i	0.212280	+	0.0879293i	−0.274010	+	0.961727i	$0.588350\pi$
$908$	−41.2051	+	99.4779i	−1.36744	+	3.30129i
$909$	4.10481	−	4.10481i	0.136148	−	0.136148i
$910$	−1.23946	+	1.23946i	−0.0410876	+	0.0410876i
$911$	22.7850	−	55.0079i	0.754901	−	1.82249i	0.225192	−	0.974315i	$-0.427699\pi$
$911$	22.7850	−	55.0079i	0.754901	−	1.82249i	0.529710	−	0.848179i	$-0.322301\pi$
$912$	−19.0330	−	7.88372i	−0.630245	−	0.261056i
$913$	−20.0174	−	48.3263i	−0.662479	−	1.59937i
$914$			9.04687i			0.299244i
$915$	14.5331	−	6.01981i	0.480450	−	0.199009i
$916$	16.7415	+	16.7415i	0.553154	+	0.553154i
$917$	−12.4785			−0.412076
$918$	−1.98917	−	10.5109i	−0.0656523	−	0.346911i
$919$	2.36415			0.0779860			0.0389930	−	0.999239i	$-0.487585\pi$
$919$	2.36415			0.0779860			0.0389930	+	0.999239i	$0.487585\pi$
$920$	41.2958	+	41.2958i	1.36148	+	1.36148i
$921$	19.0261	−	7.88086i	0.626930	−	0.259683i
$922$			27.8441i			0.916995i
$923$	−2.00952	−	4.85140i	−0.0661441	−	0.159686i
$924$	18.3885	+	7.61676i	0.604937	+	0.250573i
$925$	8.54058	−	20.6188i	0.280812	−	0.677941i
$926$	−34.5692	+	34.5692i	−1.13601	+	1.13601i
$927$	9.59335	−	9.59335i	0.315087	−	0.315087i
$928$	22.9690	−	55.4522i	0.753996	−	1.82031i
$929$	−17.9180	−	7.42189i	−0.587871	−	0.243504i	0.0688631	−	0.997626i	$-0.478063\pi$
$929$	−17.9180	−	7.42189i	−0.587871	−	0.243504i	−0.656735	+	0.754122i	$0.728063\pi$
$930$	7.82661	+	18.8951i	0.256645	+	0.619595i
$931$			2.30845i			0.0756563i
$932$	−104.687	+	43.3626i	−3.42913	+	1.42039i
$933$	−12.2752	−	12.2752i	−0.401873	−	0.401873i
$934$	25.5887			0.837288
$935$	−27.6571	−	5.76961i	−0.904483	−	0.188687i
$936$	−2.93934			−0.0960753
$937$	−15.3047	−	15.3047i	−0.499982	−	0.499982i	0.411450	−	0.911432i	$-0.365022\pi$
$937$	−15.3047	−	15.3047i	−0.499982	−	0.499982i	−0.911432	+	0.411450i	$0.865022\pi$
$938$	3.58253	−	1.48393i	0.116974	−	0.0484522i
$939$		−	14.2097i		−	0.463715i
$940$	−27.9060	−	67.3710i	−0.910192	−	2.19740i
$941$	−46.6597	−	19.3271i	−1.52106	−	0.630045i	−0.543259	−	0.839565i	$-0.682810\pi$
$941$	−46.6597	−	19.3271i	−1.52106	−	0.630045i	−0.977804	+	0.209520i	$0.932810\pi$
$942$	−6.61204	+	15.9629i	−0.215432	+	0.520099i
$943$	28.8059	−	28.8059i	0.938048	−	0.938048i
$944$	−19.5969	+	19.5969i	−0.637824	+	0.637824i
$945$	−0.623364	+	1.50493i	−0.0202780	+	0.0489555i
$946$	8.54068	+	3.53766i	0.277681	+	0.115019i
$947$	−14.2776	−	34.4692i	−0.463961	−	1.12010i	−0.966757	−	0.255695i	$-0.917696\pi$
$947$	−14.2776	−	34.4692i	−0.463961	−	1.12010i	0.502797	−	0.864405i	$-0.332304\pi$
$948$		−	45.5308i		−	1.47877i
$949$	−3.96439	+	1.64210i	−0.128690	+	0.0533049i
$950$	9.93801	+	9.93801i	0.322432	+	0.322432i
$951$	−10.8693			−0.352462
$952$	28.7108	−	5.43345i	0.930521	−	0.176099i
$953$	4.16774			0.135006			0.0675032	−	0.997719i	$-0.478497\pi$
$953$	4.16774			0.135006			0.0675032	+	0.997719i	$0.478497\pi$
$954$	13.9010	+	13.9010i	0.450060	+	0.450060i
$955$	−37.2792	+	15.4416i	−1.20633	+	0.499677i
$956$		−	106.045i		−	3.42973i
$957$	10.7594	+	25.9755i	0.347802	+	0.839669i
$958$	62.8201	+	26.0209i	2.02963	+	0.840699i
$959$	7.25073	−	17.5048i	0.234138	−	0.565260i
$960$	6.27825	−	6.27825i	0.202630	−	0.202630i
$961$	−5.36123	+	5.36123i	−0.172943	+	0.172943i
$962$	−3.91647	+	9.45519i	−0.126272	+	0.304847i
$963$	16.8979	+	6.99934i	0.544527	+	0.225551i
$964$	8.63820	+	20.8545i	0.278218	+	0.671677i
$965$		−	34.5564i		−	1.11241i
$966$	12.1263	−	5.02289i	0.390158	−	0.161609i
$967$	−25.2418	−	25.2418i	−0.811723	−	0.811723i	0.173169	−	0.984892i	$-0.444599\pi$
$967$	−25.2418	−	25.2418i	−0.811723	−	0.811723i	−0.984892	+	0.173169i	$0.944599\pi$
$968$	47.4500			1.52510
$969$	5.36138	−	7.86431i	0.172232	−	0.252638i
$970$	50.5444			1.62288
$971$	16.7560	+	16.7560i	0.537725	+	0.537725i	0.922860	−	0.385135i	$-0.125845\pi$
$971$	16.7560	+	16.7560i	0.537725	+	0.537725i	−0.385135	+	0.922860i	$0.625845\pi$
$972$	−4.37136	+	1.81067i	−0.140211	+	0.0580774i
$973$		−	11.9982i		−	0.384644i
$974$	−0.716876	−	1.73069i	−0.0229702	−	0.0554549i
$975$	0.899170	+	0.372448i	0.0287965	+	0.0119279i
$976$	−32.9802	+	79.6212i	−1.05567	+	2.54861i
$977$	20.3593	−	20.3593i	0.651353	−	0.651353i	−0.301966	−	0.953319i	$-0.597643\pi$
$977$	20.3593	−	20.3593i	0.651353	−	0.651353i	0.953319	+	0.301966i	$0.0976428\pi$
$978$	−23.7205	+	23.7205i	−0.758497	+	0.758497i
$979$	−0.107097	+	0.258556i	−0.00342284	+	0.00826347i
$980$	−7.12062	−	2.94946i	−0.227460	−	0.0942170i
$981$	4.47999	+	10.8156i	0.143035	+	0.345317i
$982$		−	78.6587i		−	2.51010i
$983$	4.31729	−	1.78828i	0.137700	−	0.0570372i	−0.312769	−	0.949829i	$-0.601257\pi$
$983$	4.31729	−	1.78828i	0.137700	−	0.0570372i	0.450469	+	0.892792i	$0.351257\pi$
$984$	−40.3538	−	40.3538i	−1.28643	−	1.28643i
$985$	5.42937			0.172994
$986$	59.0767	+	40.2747i	1.88139	+	1.28261i
$987$	−9.46139			−0.301159
$988$	−3.20328	−	3.20328i	−0.101910	−	0.101910i
$989$	3.95880	−	1.63979i	0.125882	−	0.0521422i
$990$			17.7782i			0.565029i
$991$	4.30379	+	10.3903i	0.136714	+	0.330057i	0.977378	−	0.211500i	$-0.0678348\pi$
$991$	4.30379	+	10.3903i	0.136714	+	0.330057i	−0.840664	+	0.541557i	$0.817835\pi$
$992$	−40.1490	−	16.6303i	−1.27473	−	0.528012i
$993$	−12.7796	+	30.8528i	−0.405549	+	0.979083i
$994$	23.2276	−	23.2276i	0.736736	−	0.736736i
$995$	−12.9073	+	12.9073i	−0.409189	+	0.409189i
$996$	−22.5153	+	54.3568i	−0.713426	+	1.72236i
$997$	47.9461	+	19.8599i	1.51847	+	0.628971i	0.977284	−	0.211933i	$-0.0679758\pi$
$997$	47.9461	+	19.8599i	1.51847	+	0.628971i	0.541185	+	0.840903i	$0.317976\pi$
$998$	−12.6389	−	30.5131i	−0.400079	−	0.965875i
$999$			9.51064i			0.300903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.u.a.274.1	yes	32
17.3	odd	16		6069.2.a.bj.1.2		16
17.9	even	8	inner	357.2.u.a.43.1	✓	32
17.14	odd	16		6069.2.a.bk.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.u.a.43.1	✓	32	17.9	even	8	inner
357.2.u.a.274.1	yes	32	1.1	even	1	trivial
6069.2.a.bj.1.2		16	17.3	odd	16
6069.2.a.bk.1.2		16	17.14	odd	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.83460 - 1.83460i) q^{2} +(-0.923880 + 0.382683i) q^{3} +4.73152i q^{4} +(-0.623364 - 1.50493i) q^{5} +(2.39702 + 0.992879i) q^{6} +(-0.382683 + 0.923880i) q^{7} +(5.01125 - 5.01125i) q^{8} +(0.707107 - 0.707107i) q^{9} +(-1.61733 + 3.90458i) q^{10} +(3.88638 + 1.60979i) q^{11} +(-1.81067 - 4.37136i) q^{12} -0.414752i q^{13} +(2.39702 - 0.992879i) q^{14} +(1.15183 + 1.15183i) q^{15} -8.92425 q^{16} +(0.842005 - 4.03621i) q^{17} -2.59452 q^{18} +(-1.63232 - 1.63232i) q^{19} +(7.12062 - 2.94946i) q^{20} -1.00000i q^{21} +(-4.17663 - 10.0833i) q^{22} +(-4.67383 - 1.93596i) q^{23} +(-2.71207 + 6.54752i) q^{24} +(1.65929 - 1.65929i) q^{25} +(-0.760904 + 0.760904i) q^{26} +(-0.382683 + 0.923880i) q^{27} +(-4.37136 - 1.81067i) q^{28} +(-2.55775 - 6.17496i) q^{29} -4.22628i q^{30} +(-4.47086 + 1.85189i) q^{31} +(6.34993 + 6.34993i) q^{32} -4.20659 q^{33} +(-8.94959 + 5.86010i) q^{34} +1.62893 q^{35} +(3.34569 + 3.34569i) q^{36} +(8.78668 - 3.63956i) q^{37} +5.98931i q^{38} +(0.158719 + 0.383181i) q^{39} +(-10.6654 - 4.41777i) q^{40} +(-3.08161 + 7.43967i) q^{41} +(-1.83460 + 1.83460i) q^{42} +(-0.598929 + 0.598929i) q^{43} +(-7.61676 + 18.3885i) q^{44} +(-1.50493 - 0.623364i) q^{45} +(5.02289 + 12.1263i) q^{46} -9.46139i q^{47} +(8.24493 - 3.41516i) q^{48} +(-0.707107 - 0.707107i) q^{49} -6.08828 q^{50} +(0.766681 + 4.05120i) q^{51} +1.96241 q^{52} +(-5.35782 - 5.35782i) q^{53} +(2.39702 - 0.992879i) q^{54} -6.85223i q^{55} +(2.71207 + 6.54752i) q^{56} +(2.13273 + 0.883405i) q^{57} +(-6.63613 + 16.0210i) q^{58} +(2.19591 - 2.19591i) q^{59} +(-5.44989 + 5.44989i) q^{60} +(3.69557 - 8.92189i) q^{61} +(11.5997 + 4.80476i) q^{62} +(0.382683 + 0.923880i) q^{63} -5.45069i q^{64} +(-0.624174 + 0.258541i) q^{65} +(7.71741 + 7.71741i) q^{66} +1.49458 q^{67} +(19.0974 + 3.98397i) q^{68} +5.05892 q^{69} +(-2.98843 - 2.98843i) q^{70} +(11.6971 - 4.84511i) q^{71} -7.08698i q^{72} +(-3.95924 - 9.55846i) q^{73} +(-22.7972 - 9.44291i) q^{74} +(-0.898002 + 2.16797i) q^{75} +(7.72335 - 7.72335i) q^{76} +(-2.97451 + 2.97451i) q^{77} +(0.411798 - 0.994169i) q^{78} +(8.89036 + 3.68251i) q^{79} +(5.56305 + 13.4304i) q^{80} -1.00000i q^{81} +(19.3024 - 7.99530i) q^{82} +(-8.79272 - 8.79272i) q^{83} +4.73152 q^{84} +(-6.59911 + 1.24887i) q^{85} +2.19759 q^{86} +(4.72611 + 4.72611i) q^{87} +(27.5427 - 11.4086i) q^{88} +0.0665286i q^{89} +(1.61733 + 3.90458i) q^{90} +(0.383181 + 0.158719i) q^{91} +(9.16005 - 22.1143i) q^{92} +(3.42185 - 3.42185i) q^{93} +(-17.3579 + 17.3579i) q^{94} +(-1.43900 + 3.47406i) q^{95} +(-8.29659 - 3.43656i) q^{96} +(-4.57672 - 11.0492i) q^{97} +2.59452i q^{98} +(3.88638 - 1.60979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

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