LMFDB - Embedded newform 465.2.n.e.376.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(16,465)] 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("465.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 14 x^{18} - 34 x^{17} + 102 x^{16} - 176 x^{15} + 468 x^{14} - 806 x^{13} + 2268 x^{12} + \cdots + 1 $ x^20 - 4x^19 + 14x^18 - 34x^17 + 102x^16 - 176x^15 + 468x^14 - 806x^13 + 2268x^12 - 4350x^11 + 8118x^10 - 9948x^9 + 13072x^8 - 10268x^7 + 9466x^6 - 3112x^5 + 92x^4 + 288x^3 + 94x^2 + 10*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			376.1
Root			$2.26261 + 1.64389i$ of defining polynomial
Character	$\chi$	$=$	465.376
Dual form			465.2.n.e.256.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.864242 - 2.65986i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-4.70992 + 3.42196i) q^{4} -1.00000 q^{5} +2.79674 q^{6} +(3.88423 - 2.82206i) q^{7} +(8.64721 + 6.28257i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.864242 + 2.65986i) q^{10} +(-2.44380 + 1.77553i) q^{11} +(-1.79903 - 5.53684i) q^{12} +(1.17463 - 3.61513i) q^{13} +(-10.8632 - 7.89258i) q^{14} +(0.309017 - 0.951057i) q^{15} +(5.63942 - 17.3564i) q^{16} +(-1.54523 - 1.12267i) q^{17} +(-0.864242 + 2.65986i) q^{18} +(-0.532434 - 1.63866i) q^{19} +(4.70992 - 3.42196i) q^{20} +(1.48364 + 4.56619i) q^{21} +(6.83469 + 4.96570i) q^{22} +(-3.47275 - 2.52310i) q^{23} +(-8.64721 + 6.28257i) q^{24} +1.00000 q^{25} -10.6309 q^{26} +(0.809017 - 0.587785i) q^{27} +(-8.63745 + 26.5834i) q^{28} +(0.272714 + 0.839327i) q^{29} -2.79674 q^{30} +(0.554757 - 5.54006i) q^{31} -29.6623 q^{32} +(-0.933450 - 2.87286i) q^{33} +(-1.65071 + 5.08035i) q^{34} +(-3.88423 + 2.82206i) q^{35} +5.82178 q^{36} -5.01663 q^{37} +(-3.89847 + 2.83240i) q^{38} +(3.07522 + 2.23428i) q^{39} +(-8.64721 - 6.28257i) q^{40} +(-0.413364 - 1.27220i) q^{41} +(10.8632 - 7.89258i) q^{42} +(0.382651 + 1.17768i) q^{43} +(5.43434 - 16.7252i) q^{44} +(0.809017 + 0.587785i) q^{45} +(-3.70980 + 11.4176i) q^{46} +(0.794202 - 2.44430i) q^{47} +(14.7642 + 10.7268i) q^{48} +(4.96012 - 15.2657i) q^{49} +(-0.864242 - 2.65986i) q^{50} +(1.54523 - 1.12267i) q^{51} +(6.83843 + 21.0465i) q^{52} +(1.49628 + 1.08711i) q^{53} +(-2.26261 - 1.64389i) q^{54} +(2.44380 - 1.77553i) q^{55} +51.3176 q^{56} +1.72299 q^{57} +(1.99680 - 1.45076i) q^{58} +(3.71658 - 11.4384i) q^{59} +(1.79903 + 5.53684i) q^{60} -11.3292 q^{61} +(-15.2152 + 3.31237i) q^{62} -4.80118 q^{63} +(14.3565 + 44.1848i) q^{64} +(-1.17463 + 3.61513i) q^{65} +(-6.83469 + 4.96570i) q^{66} -4.69083 q^{67} +11.1196 q^{68} +(3.47275 - 2.52310i) q^{69} +(10.8632 + 7.89258i) q^{70} +(-1.61662 - 1.17454i) q^{71} +(-3.30294 - 10.1654i) q^{72} +(12.3093 - 8.94321i) q^{73} +(4.33558 + 13.3436i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(8.11516 + 5.89601i) q^{76} +(-4.48166 + 13.7931i) q^{77} +(3.28513 - 10.1106i) q^{78} +(-3.61852 - 2.62901i) q^{79} +(-5.63942 + 17.3564i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-3.02664 + 2.19898i) q^{82} +(-2.28301 - 7.02638i) q^{83} +(-22.6131 - 16.4294i) q^{84} +(1.54523 + 1.12267i) q^{85} +(2.80176 - 2.03560i) q^{86} -0.882521 q^{87} -32.2870 q^{88} +(4.97349 - 3.61345i) q^{89} +(0.864242 - 2.65986i) q^{90} +(-5.63960 - 17.3569i) q^{91} +24.9903 q^{92} +(5.09748 + 2.23958i) q^{93} -7.18789 q^{94} +(0.532434 + 1.63866i) q^{95} +(9.16615 - 28.2105i) q^{96} +(4.30594 - 3.12845i) q^{97} -44.8914 q^{98} +3.02071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + 5 q^{3} - 7 q^{4} - 20 q^{5} + 6 q^{6} + 3 q^{7} + 7 q^{8} - 5 q^{9} + q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{13} - 21 q^{14} - 5 q^{15} + 15 q^{16} - 8 q^{17} - q^{18} - 15 q^{19} + 7 q^{20}+ \cdots + 14 q^{99}+O(q^{100}) $ 20 * q - q^2 + 5 * q^3 - 7 * q^4 - 20 * q^5 + 6 * q^6 + 3 * q^7 + 7 * q^8 - 5 * q^9 + q^10 - 6 * q^11 + 2 * q^12 + 2 * q^13 - 21 * q^14 - 5 * q^15 + 15 * q^16 - 8 * q^17 - q^18 - 15 * q^19 + 7 * q^20 - 3 * q^21 - 15 * q^22 + 12 * q^23 - 7 * q^24 + 20 * q^25 - 28 * q^26 + 5 * q^27 - 29 * q^28 - 11 * q^29 - 6 * q^30 - 6 * q^31 - 92 * q^32 + q^33 + 9 * q^34 - 3 * q^35 + 18 * q^36 + 10 * q^37 + q^38 - 2 * q^39 - 7 * q^40 + 18 * q^41 + 21 * q^42 + 3 * q^43 - 29 * q^44 + 5 * q^45 - 16 * q^46 + 2 * q^47 + 30 * q^48 + 4 * q^49 - q^50 + 8 * q^51 + 31 * q^52 - 14 * q^53 - 4 * q^54 + 6 * q^55 + 110 * q^56 + 10 * q^57 - 45 * q^58 + 12 * q^59 - 2 * q^60 - 4 * q^61 - 16 * q^62 - 12 * q^63 + 33 * q^64 - 2 * q^65 + 15 * q^66 - 8 * q^67 + 28 * q^68 - 12 * q^69 + 21 * q^70 - 12 * q^71 + 2 * q^72 + 28 * q^73 - 23 * q^74 + 5 * q^75 + 45 * q^76 + 26 * q^77 + 3 * q^78 - 15 * q^80 - 5 * q^81 - 53 * q^82 + 4 * q^83 - 46 * q^84 + 8 * q^85 + 38 * q^86 - 4 * q^87 - 62 * q^88 + 4 * q^89 + q^90 + 28 * q^91 + 66 * q^92 + 31 * q^93 + 12 * q^94 + 15 * q^95 + 7 * q^96 + 66 * q^97 - 104 * q^98 + 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.864242	−	2.65986i	−0.611111	−	1.88081i	−0.447507	−	0.894280i	$-0.647688\pi$
$2$	−0.864242	−	2.65986i	−0.611111	−	1.88081i	−0.163604	−	0.986526i	$-0.552312\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−4.70992	+	3.42196i	−2.35496	+	1.71098i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	2.79674			1.14177
$7$	3.88423	−	2.82206i	1.46810	−	1.06664i	0.486944	−	0.873433i	$-0.338112\pi$
$7$	3.88423	−	2.82206i	1.46810	−	1.06664i	0.981158	−	0.193205i	$-0.0618883\pi$
$8$	8.64721	+	6.28257i	3.05725	+	2.22122i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.864242	+	2.65986i	0.273297	+	0.841122i
$11$	−2.44380	+	1.77553i	−0.736834	+	0.535342i	−0.891718	−	0.452591i	$-0.850500\pi$
$11$	−2.44380	+	1.77553i	−0.736834	+	0.535342i	0.154884	+	0.987933i	$0.450500\pi$
$12$	−1.79903	−	5.53684i	−0.519335	−	1.59835i
$13$	1.17463	−	3.61513i	0.325783	−	1.00266i	−0.645303	−	0.763927i	$-0.723269\pi$
$13$	1.17463	−	3.61513i	0.325783	−	1.00266i	0.971086	−	0.238731i	$-0.0767313\pi$
$14$	−10.8632	−	7.89258i	−2.90331	−	2.10938i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	5.63942	−	17.3564i	1.40986	−	4.33909i
$17$	−1.54523	−	1.12267i	−0.374773	−	0.272288i	0.384415	−	0.923161i	$-0.374403\pi$
$17$	−1.54523	−	1.12267i	−0.374773	−	0.272288i	−0.759187	+	0.650872i	$0.774403\pi$
$18$	−0.864242	+	2.65986i	−0.203704	+	0.626936i
$19$	−0.532434	−	1.63866i	−0.122149	−	0.375935i	0.871222	−	0.490889i	$-0.163328\pi$
$19$	−0.532434	−	1.63866i	−0.122149	−	0.375935i	−0.993371	+	0.114954i	$0.963328\pi$
$20$	4.70992	−	3.42196i	1.05317	−	0.765173i
$21$	1.48364	+	4.56619i	0.323758	+	0.996424i
$22$	6.83469	+	4.96570i	1.45716	+	1.05869i
$23$	−3.47275	−	2.52310i	−0.724118	−	0.526103i	0.163579	−	0.986530i	$-0.447696\pi$
$23$	−3.47275	−	2.52310i	−0.724118	−	0.526103i	−0.887697	+	0.460428i	$0.847696\pi$
$24$	−8.64721	+	6.28257i	−1.76510	+	1.28242i
$25$	1.00000			0.200000
$26$	−10.6309			−2.08489
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−8.63745	+	26.5834i	−1.63233	+	5.02378i
$29$	0.272714	+	0.839327i	0.0506417	+	0.155859i	0.973179	−	0.230048i	$-0.0738884\pi$
$29$	0.272714	+	0.839327i	0.0506417	+	0.155859i	−0.922538	+	0.385907i	$0.873888\pi$
$30$	−2.79674			−0.510613
$31$	0.554757	−	5.54006i	0.0996373	−	0.995024i
$31$	0.554757	−	5.54006i	0.0996373	−	0.995024i
$32$	−29.6623			−5.24360
$33$	−0.933450	−	2.87286i	−0.162493	−	0.500101i
$34$	−1.65071	+	5.08035i	−0.283094	+	0.871273i
$35$	−3.88423	+	2.82206i	−0.656555	+	0.477015i
$36$	5.82178			0.970297
$37$	−5.01663			−0.824730			−0.412365	−	0.911019i	$-0.635297\pi$
$37$	−5.01663			−0.824730			−0.412365	+	0.911019i	$0.635297\pi$
$38$	−3.89847	+	2.83240i	−0.632415	+	0.459476i
$39$	3.07522	+	2.23428i	0.492429	+	0.357770i
$40$	−8.64721	−	6.28257i	−1.36724	−	0.993361i
$41$	−0.413364	−	1.27220i	−0.0645565	−	0.198685i	0.913576	−	0.406669i	$-0.133310\pi$
$41$	−0.413364	−	1.27220i	−0.0645565	−	0.198685i	−0.978132	+	0.207984i	$0.933310\pi$
$42$	10.8632	−	7.89258i	1.67623	−	1.21785i
$43$	0.382651	+	1.17768i	0.0583537	+	0.179594i	0.975985	−	0.217839i	$-0.0699009\pi$
$43$	0.382651	+	1.17768i	0.0583537	+	0.179594i	−0.917631	+	0.397434i	$0.869901\pi$
$44$	5.43434	−	16.7252i	0.819257	−	2.52142i
$45$	0.809017	+	0.587785i	0.120601	+	0.0876219i
$46$	−3.70980	+	11.4176i	−0.546981	+	1.68343i
$47$	0.794202	−	2.44430i	0.115846	−	0.356538i	−0.876276	−	0.481809i	$-0.839980\pi$
$47$	0.794202	−	2.44430i	0.115846	−	0.356538i	0.992123	+	0.125271i	$0.0399800\pi$
$48$	14.7642	+	10.7268i	2.13103	+	1.54828i
$49$	4.96012	−	15.2657i	0.708589	−	2.18081i
$50$	−0.864242	−	2.65986i	−0.122222	−	0.376161i
$51$	1.54523	−	1.12267i	0.216375	−	0.157206i
$52$	6.83843	+	21.0465i	0.948319	+	2.91863i
$53$	1.49628	+	1.08711i	0.205530	+	0.149326i	0.685789	−	0.727800i	$-0.259457\pi$
$53$	1.49628	+	1.08711i	0.205530	+	0.149326i	−0.480259	+	0.877127i	$0.659457\pi$
$54$	−2.26261	−	1.64389i	−0.307903	−	0.223704i
$55$	2.44380	−	1.77553i	0.329522	−	0.239412i
$56$	51.3176			6.85760
$57$	1.72299			0.228216
$58$	1.99680	−	1.45076i	0.262193	−	0.190494i
$59$	3.71658	−	11.4384i	0.483857	−	1.48916i	−0.349772	−	0.936835i	$-0.613741\pi$
$59$	3.71658	−	11.4384i	0.483857	−	1.48916i	0.833629	−	0.552324i	$-0.186259\pi$
$60$	1.79903	+	5.53684i	0.232254	+	0.714803i
$61$	−11.3292			−1.45056			−0.725280	−	0.688454i	$-0.758290\pi$
$61$	−11.3292			−1.45056			−0.725280	+	0.688454i	$0.758290\pi$
$62$	−15.2152	+	3.31237i	−1.93234	+	0.420672i
$63$	−4.80118			−0.604891
$64$	14.3565	+	44.1848i	1.79457	+	5.52310i
$65$	−1.17463	+	3.61513i	−0.145695	+	0.448402i
$66$	−6.83469	+	4.96570i	−0.841293	+	0.611235i
$67$	−4.69083			−0.573076			−0.286538	−	0.958069i	$-0.592505\pi$
$67$	−4.69083			−0.573076			−0.286538	+	0.958069i	$0.592505\pi$
$68$	11.1196			1.34845
$69$	3.47275	−	2.52310i	0.418070	−	0.303745i
$70$	10.8632	+	7.89258i	1.29840	+	0.943344i
$71$	−1.61662	−	1.17454i	−0.191857	−	0.139393i	0.487710	−	0.873006i	$-0.337832\pi$
$71$	−1.61662	−	1.17454i	−0.191857	−	0.139393i	−0.679567	+	0.733613i	$0.737832\pi$
$72$	−3.30294	−	10.1654i	−0.389255	−	1.19800i
$73$	12.3093	−	8.94321i	1.44069	−	1.04672i	0.452794	−	0.891615i	$-0.350427\pi$
$73$	12.3093	−	8.94321i	1.44069	−	1.04672i	0.987897	−	0.155108i	$-0.0495727\pi$
$74$	4.33558	+	13.3436i	0.504001	+	1.55116i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	8.11516	+	5.89601i	0.930872	+	0.676318i
$77$	−4.48166	+	13.7931i	−0.510732	+	1.57187i
$78$	3.28513	−	10.1106i	0.371968	−	1.14480i
$79$	−3.61852	−	2.62901i	−0.407115	−	0.295787i	0.365318	−	0.930883i	$-0.380960\pi$
$79$	−3.61852	−	2.62901i	−0.407115	−	0.295787i	−0.772433	+	0.635096i	$0.780960\pi$
$80$	−5.63942	+	17.3564i	−0.630507	+	1.94050i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−3.02664	+	2.19898i	−0.334236	+	0.242837i
$83$	−2.28301	−	7.02638i	−0.250593	−	0.771246i	−0.994666	−	0.103148i	$-0.967109\pi$
$83$	−2.28301	−	7.02638i	−0.250593	−	0.771246i	0.744073	−	0.668098i	$-0.232891\pi$
$84$	−22.6131	−	16.4294i	−2.46730	−	1.79260i
$85$	1.54523	+	1.12267i	0.167603	+	0.121771i
$86$	2.80176	−	2.03560i	0.302121	−	0.219504i
$87$	−0.882521			−0.0946162
$88$	−32.2870			−3.44180
$89$	4.97349	−	3.61345i	0.527189	−	0.383025i	−0.292116	−	0.956383i	$-0.594359\pi$
$89$	4.97349	−	3.61345i	0.527189	−	0.383025i	0.819305	+	0.573358i	$0.194359\pi$
$90$	0.864242	−	2.65986i	0.0910991	−	0.280374i
$91$	−5.63960	−	17.3569i	−0.591190	−	1.81950i
$92$	24.9903			2.60542
$93$	5.09748	+	2.23958i	0.528584	+	0.232233i
$94$	−7.18789			−0.741374
$95$	0.532434	+	1.63866i	0.0546266	+	0.168123i
$96$	9.16615	−	28.2105i	0.935516	−	2.87922i
$97$	4.30594	−	3.12845i	0.437202	−	0.317646i	−0.347320	−	0.937747i	$-0.612908\pi$
$97$	4.30594	−	3.12845i	0.437202	−	0.317646i	0.784522	+	0.620101i	$0.212908\pi$
$98$	−44.8914			−4.53471
$99$	3.02071			0.303592
$100$	−4.70992	+	3.42196i	−0.470992	+	0.342196i
$101$	3.57420	+	2.59681i	0.355646	+	0.258392i	0.751234	−	0.660036i	$-0.229459\pi$
$101$	3.57420	+	2.59681i	0.355646	+	0.258392i	−0.395588	+	0.918428i	$0.629459\pi$
$102$	−4.32161	−	3.13983i	−0.427903	−	0.310890i
$103$	5.18550	+	15.9593i	0.510943	+	1.57252i	0.790545	+	0.612404i	$0.209797\pi$
$103$	5.18550	+	15.9593i	0.510943	+	1.57252i	−0.279602	+	0.960116i	$0.590203\pi$
$104$	32.8696	−	23.8811i	3.22313	−	2.34174i
$105$	−1.48364	−	4.56619i	−0.144789	−	0.445614i
$106$	1.59842	−	4.91943i	0.155252	−	0.477818i
$107$	12.7329	+	9.25100i	1.23094	+	0.894328i	0.996960	−	0.0779147i	$-0.0248262\pi$
$107$	12.7329	+	9.25100i	1.23094	+	0.894328i	0.233976	+	0.972242i	$0.424826\pi$
$108$	−1.79903	+	5.53684i	−0.173112	+	0.532783i
$109$	−1.11397	+	3.42845i	−0.106699	+	0.328386i	−0.990125	−	0.140184i	$-0.955231\pi$
$109$	−1.11397	+	3.42845i	−0.106699	+	0.328386i	0.883426	+	0.468570i	$0.155231\pi$
$110$	−6.83469	−	4.96570i	−0.651662	−	0.473460i
$111$	1.55023	−	4.77110i	0.147141	−	0.452853i
$112$	−27.0759	−	83.3310i	−2.55843	−	7.87404i
$113$	−3.24130	+	2.35494i	−0.304916	+	0.221534i	−0.729712	−	0.683755i	$-0.760346\pi$
$113$	−3.24130	+	2.35494i	−0.304916	+	0.221534i	0.424796	+	0.905289i	$0.360346\pi$
$114$	−1.48908	−	4.58292i	−0.139465	−	0.429230i
$115$	3.47275	+	2.52310i	0.323835	+	0.235280i
$116$	−4.15660	−	3.01995i	−0.385931	−	0.280395i
$117$	−3.07522	+	2.23428i	−0.284304	+	0.206559i
$118$	−33.6367			−3.09651
$119$	−9.17028			−0.840638
$120$	8.64721	−	6.28257i	0.789379	−	0.573517i
$121$	−0.579509	+	1.78354i	−0.0526826	+	0.162140i
$122$	9.79119	+	30.1342i	0.886453	+	2.72822i
$123$	1.33767			0.120614
$124$	16.3450	+	27.9916i	1.46782	+	2.51372i
$125$	−1.00000			−0.0894427
$126$	4.14938	+	12.7705i	0.369656	+	1.13768i
$127$	−3.93970	+	12.1252i	−0.349592	+	1.07593i	0.609487	+	0.792796i	$0.291375\pi$
$127$	−3.93970	+	12.1252i	−0.349592	+	1.07593i	−0.959079	+	0.283138i	$0.908625\pi$
$128$	57.1235	−	41.5026i	5.04905	−	3.66835i
$129$	−1.23828			−0.109025
$130$	10.6309			0.932393
$131$	−0.182087	+	0.132294i	−0.0159090	+	0.0115585i	−0.595711	−	0.803199i	$-0.703130\pi$
$131$	−0.182087	+	0.132294i	−0.0159090	+	0.0115585i	0.579802	+	0.814757i	$0.303130\pi$
$132$	14.2273	+	10.3367i	1.23833	+	0.899697i
$133$	−6.69251	−	4.86239i	−0.580314	−	0.421623i
$134$	4.05401	+	12.4770i	0.350213	+	1.07785i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	−6.30864	−	19.4160i	−0.540961	−	1.66491i
$137$	6.23939	−	19.2029i	0.533067	−	1.64061i	−0.214722	−	0.976675i	$-0.568885\pi$
$137$	6.23939	−	19.2029i	0.533067	−	1.64061i	0.747789	−	0.663936i	$-0.231115\pi$
$138$	−9.71239	−	7.05646i	−0.826773	−	0.600686i
$139$	−4.14441	+	12.7552i	−0.351524	+	1.08188i	0.606473	+	0.795104i	$0.292584\pi$
$139$	−4.14441	+	12.7552i	−0.351524	+	1.08188i	−0.957997	+	0.286777i	$0.907416\pi$
$140$	8.63745	−	26.5834i	0.729998	−	2.24670i
$141$	2.07925	+	1.51066i	0.175104	+	0.127221i
$142$	−1.72697	+	5.31507i	−0.144924	+	0.446031i
$143$	3.54821	+	10.9203i	0.296716	+	0.913198i
$144$	−14.7642	+	10.7268i	−1.23035	+	0.893902i
$145$	−0.272714	−	0.839327i	−0.0226477	−	0.0697023i
$146$	−34.4259	−	25.0119i	−2.84911	−	2.07000i
$147$	12.9858	+	9.43471i	1.07105	+	0.778162i
$148$	23.6279	−	17.1667i	1.94220	−	1.41109i
$149$	−6.35138			−0.520325			−0.260163	−	0.965565i	$-0.583776\pi$
$149$	−6.35138			−0.520325			−0.260163	+	0.965565i	$0.583776\pi$
$150$	2.79674			0.228353
$151$	9.75481	−	7.08729i	0.793835	−	0.576755i	−0.115264	−	0.993335i	$-0.536771\pi$
$151$	9.75481	−	7.08729i	0.793835	−	0.576755i	0.909099	+	0.416580i	$0.136771\pi$
$152$	5.69094	−	17.5149i	0.461597	−	1.42065i
$153$	0.590224	+	1.81652i	0.0477168	+	0.146857i
$154$	40.5610			3.26850
$155$	−0.554757	+	5.54006i	−0.0445591	+	0.444988i
$156$	−22.1296			−1.77179
$157$	3.94552	+	12.1431i	0.314887	+	0.969122i	0.975801	+	0.218661i	$0.0701688\pi$
$157$	3.94552	+	12.1431i	0.314887	+	0.969122i	−0.660914	+	0.750462i	$0.729831\pi$
$158$	−3.86553	+	11.8969i	−0.307525	+	0.946464i
$159$	−1.49628	+	1.08711i	−0.118663	+	0.0862137i
$160$	29.6623			2.34501
$161$	−20.6093			−1.62424
$162$	2.26261	−	1.64389i	0.177768	−	0.129156i
$163$	5.16457	+	3.75228i	0.404520	+	0.293901i	0.771380	−	0.636375i	$-0.219567\pi$
$163$	5.16457	+	3.75228i	0.404520	+	0.293901i	−0.366859	+	0.930276i	$0.619567\pi$
$164$	6.30033	+	4.57746i	0.491973	+	0.357439i
$165$	0.933450	+	2.87286i	0.0726690	+	0.223652i
$166$	−16.7161	+	12.1450i	−1.29742	+	0.942634i
$167$	4.82458	+	14.8485i	0.373337	+	1.14901i	0.944594	+	0.328242i	$0.106456\pi$
$167$	4.82458	+	14.8485i	0.373337	+	1.14901i	−0.571256	+	0.820772i	$0.693544\pi$
$168$	−15.8580	+	48.8059i	−1.22347	+	3.76546i
$169$	−1.17221	−	0.851664i	−0.0901704	−	0.0655126i
$170$	1.65071	−	5.08035i	0.126603	−	0.389645i
$171$	−0.532434	+	1.63866i	−0.0407163	+	0.125312i
$172$	−5.83222	−	4.23736i	−0.444703	−	0.323095i
$173$	6.68218	−	20.5656i	0.508037	−	1.56358i	−0.287567	−	0.957760i	$-0.592846\pi$
$173$	6.68218	−	20.5656i	0.508037	−	1.56358i	0.795604	−	0.605817i	$-0.207154\pi$
$174$	0.762711	+	2.34738i	0.0578210	+	0.177955i
$175$	3.88423	−	2.82206i	0.293620	−	0.213328i
$176$	17.0350	+	52.4285i	1.28407	+	3.95195i
$177$	9.73013	+	7.06935i	0.731361	+	0.531365i
$178$	−13.9096	−	10.1059i	−1.04257	−	0.757470i
$179$	−12.3162	+	8.94821i	−0.920553	+	0.668821i	−0.943662	−	0.330912i	$-0.892644\pi$
$179$	−12.3162	+	8.94821i	−0.920553	+	0.668821i	0.0231088	+	0.999733i	$0.492644\pi$
$180$	−5.82178			−0.433930
$181$	20.1397			1.49697			0.748486	−	0.663150i	$-0.230781\pi$
$181$	20.1397			1.49697			0.748486	+	0.663150i	$0.230781\pi$
$182$	−41.2930	+	30.0011i	−3.06084	+	2.22383i
$183$	3.50092	−	10.7747i	0.258796	−	0.796492i
$184$	−14.1780	−	43.6355i	−1.04522	−	3.21686i
$185$	5.01663			0.368830
$186$	1.55151	−	15.4941i	0.113762	−	1.13608i
$187$	5.76957			0.421913
$188$	4.62367	+	14.2302i	0.337216	+	1.03784i
$189$	1.48364	−	4.56619i	0.107919	−	0.332141i
$190$	3.89847	−	2.83240i	0.282825	−	0.205484i
$191$	3.64160			0.263497			0.131749	−	0.991283i	$-0.457941\pi$
$191$	3.64160			0.263497			0.131749	+	0.991283i	$0.457941\pi$
$192$	−46.4587			−3.35287
$193$	14.6106	−	10.6152i	1.05169	−	0.764100i	0.0791595	−	0.996862i	$-0.474776\pi$
$193$	14.6106	−	10.6152i	1.05169	−	0.764100i	0.972534	+	0.232762i	$0.0747763\pi$
$194$	−12.0426	−	8.74947i	−0.864609	−	0.628175i
$195$	−3.07522	−	2.23428i	−0.220221	−	0.160000i
$196$	28.8767	+	88.8734i	2.06262	+	6.34810i
$197$	−4.38775	+	3.18788i	−0.312614	+	0.227127i	−0.733017	−	0.680210i	$-0.761889\pi$
$197$	−4.38775	+	3.18788i	−0.312614	+	0.227127i	0.420403	+	0.907337i	$0.361889\pi$
$198$	−2.61062	−	8.03466i	−0.185529	−	0.570999i
$199$	−4.07777	+	12.5501i	−0.289066	+	0.889653i	0.696085	+	0.717960i	$0.254924\pi$
$199$	−4.07777	+	12.5501i	−0.289066	+	0.889653i	−0.985150	+	0.171693i	$0.945076\pi$
$200$	8.64721	+	6.28257i	0.611450	+	0.444245i
$201$	1.44955	−	4.46125i	0.102243	−	0.314672i
$202$	3.81818	−	11.7511i	0.268646	−	0.826807i
$203$	3.42792	+	2.49053i	0.240593	+	0.174801i
$204$	−3.43616	+	10.5754i	−0.240579	+	0.740426i
$205$	0.413364	+	1.27220i	0.0288706	+	0.0888544i
$206$	37.9681	−	27.5854i	2.64536	−	1.92197i
$207$	1.32647	+	4.08246i	0.0921962	+	0.283751i
$208$	−56.1213	−	40.7745i	−3.89131	−	2.82721i
$209$	4.21066	+	3.05922i	0.291257	+	0.211611i
$210$	−10.8632	+	7.89258i	−0.749632	+	0.544640i
$211$	14.4274			0.993225			0.496613	−	0.867972i	$-0.334577\pi$
$211$	14.4274			0.993225			0.496613	+	0.867972i	$0.334577\pi$
$212$	−10.7674			−0.739510
$213$	1.61662	−	1.17454i	0.110769	−	0.0804784i
$214$	13.6021	−	41.8629i	0.929818	−	2.86169i
$215$	−0.382651	−	1.17768i	−0.0260966	−	0.0803170i
$216$	10.6885			0.727263
$217$	−13.4796	−	23.0844i	−0.915053	−	1.56707i
$218$	10.0819			0.682835
$219$	4.70172	+	14.4704i	0.317713	+	0.977820i
$220$	−5.43434	+	16.7252i	−0.366383	+	1.12761i
$221$	−5.87368	+	4.26748i	−0.395107	+	0.287062i
$222$	−14.0302			−0.941648
$223$	−20.8120			−1.39368			−0.696839	−	0.717228i	$-0.745411\pi$
$223$	−20.8120			−1.39368			−0.696839	+	0.717228i	$0.745411\pi$
$224$	−115.215	+	83.7087i	−7.69814	+	5.59302i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	9.06509	+	6.58618i	0.603001	+	0.438106i
$227$	1.13271	+	3.48612i	0.0751806	+	0.231382i	0.981584	−	0.191031i	$-0.0611831\pi$
$227$	1.13271	+	3.48612i	0.0751806	+	0.231382i	−0.906403	+	0.422413i	$0.861183\pi$
$228$	−8.11516	+	5.89601i	−0.537439	+	0.390473i
$229$	−1.12982	−	3.47724i	−0.0746609	−	0.229783i	0.906761	−	0.421645i	$-0.138547\pi$
$229$	−1.12982	−	3.47724i	−0.0746609	−	0.229783i	−0.981422	+	0.191863i	$0.938547\pi$
$230$	3.70980	−	11.4176i	0.244617	−	0.752854i
$231$	−11.7331	−	8.52462i	−0.771983	−	0.560879i
$232$	−2.91491	+	8.97118i	−0.191373	+	0.588987i
$233$	4.74628	−	14.6076i	0.310939	−	0.956973i	−0.666454	−	0.745546i	$-0.732189\pi$
$233$	4.74628	−	14.6076i	0.310939	−	0.956973i	0.977394	−	0.211427i	$-0.0678111\pi$
$234$	8.60059	+	6.24870i	0.562238	+	0.408490i
$235$	−0.794202	+	2.44430i	−0.0518080	+	0.159449i
$236$	21.6371	+	66.5921i	1.40845	+	4.33478i
$237$	3.61852	−	2.62901i	0.235048	−	0.170773i
$238$	7.92533	+	24.3917i	0.513723	+	1.58108i
$239$	−20.8449	−	15.1447i	−1.34834	−	0.979628i	−0.999092	−	0.0425984i	$-0.986436\pi$
$239$	−20.8449	−	15.1447i	−1.34834	−	0.979628i	−0.349250	−	0.937030i	$-0.613564\pi$
$240$	−14.7642	−	10.7268i	−0.953025	−	0.692413i
$241$	−12.0424	+	8.74931i	−0.775719	+	0.563593i	−0.903691	−	0.428185i	$-0.859153\pi$
$241$	−12.0424	+	8.74931i	−0.775719	+	0.563593i	0.127972	+	0.991778i	$0.459153\pi$
$242$	5.24482			0.337150
$243$	−1.00000			−0.0641500
$244$	53.3598	−	38.7681i	3.41601	−	2.48188i
$245$	−4.96012	+	15.2657i	−0.316891	+	0.975289i
$246$	−1.15607	−	3.55802i	−0.0737085	−	0.226851i
$247$	−6.54940			−0.416728
$248$	39.6029	−	44.4208i	2.51479	−	2.82072i
$249$	7.38798			0.468194
$250$	0.864242	+	2.65986i	0.0546594	+	0.168224i
$251$	−5.42906	+	16.7089i	−0.342679	+	1.05466i	0.620135	+	0.784495i	$0.287078\pi$
$251$	−5.42906	+	16.7089i	−0.342679	+	1.05466i	−0.962815	+	0.270163i	$0.912922\pi$
$252$	22.6131	−	16.4294i	1.42449	−	1.03496i
$253$	12.9665			0.815200
$254$	35.6561			2.23726
$255$	−1.54523	+	1.12267i	−0.0967659	+	0.0703045i
$256$	−84.5881	−	61.4568i	−5.28676	−	3.84105i
$257$	9.80929	+	7.12687i	0.611887	+	0.444562i	0.850078	−	0.526657i	$-0.176555\pi$
$257$	9.80929	+	7.12687i	0.611887	+	0.444562i	−0.238192	+	0.971218i	$0.576555\pi$
$258$	1.07018	+	3.29367i	0.0666263	+	0.205055i
$259$	−19.4858	+	14.1572i	−1.21079	+	0.879688i
$260$	−6.83843	−	21.0465i	−0.424101	−	1.30525i
$261$	0.272714	−	0.839327i	0.0168806	−	0.0519530i
$262$	0.509250	+	0.369991i	0.0314615	+	0.0228581i
$263$	−7.11778	+	21.9063i	−0.438901	+	1.35080i	0.450134	+	0.892961i	$0.351376\pi$
$263$	−7.11778	+	21.9063i	−0.438901	+	1.35080i	−0.889036	+	0.457838i	$0.848624\pi$
$264$	9.97722	−	30.7067i	0.614055	−	1.88987i
$265$	−1.49628	−	1.08711i	−0.0919159	−	0.0667808i
$266$	−7.14935	+	22.0034i	−0.438355	+	1.34912i
$267$	1.89970	+	5.84669i	0.116260	+	0.357812i
$268$	22.0934	−	16.0518i	1.34957	−	0.980521i
$269$	0.0786964	+	0.242203i	0.00479820	+	0.0147674i	0.953427	−	0.301624i	$-0.0975287\pi$
$269$	0.0786964	+	0.242203i	0.00479820	+	0.0147674i	−0.948629	+	0.316391i	$0.897529\pi$
$270$	2.26261	+	1.64389i	0.137698	+	0.100044i
$271$	10.6034	+	7.70382i	0.644110	+	0.467973i	0.861260	−	0.508165i	$-0.169676\pi$
$271$	10.6034	+	7.70382i	0.644110	+	0.467973i	−0.217150	+	0.976138i	$0.569676\pi$
$272$	−28.1997	+	20.4883i	−1.70986	+	1.24229i
$273$	18.2501			1.10455
$274$	−56.4693			−3.41144
$275$	−2.44380	+	1.77553i	−0.147367	+	0.107068i
$276$	−7.72243	+	23.7672i	−0.464835	+	1.43062i
$277$	6.59446	+	20.2957i	0.396223	+	1.21945i	0.928005	+	0.372567i	$0.121522\pi$
$277$	6.59446	+	20.2957i	0.396223	+	1.21945i	−0.531783	+	0.846881i	$0.678478\pi$
$278$	37.5088			2.24963
$279$	−3.70517	+	4.15592i	−0.221823	+	0.248809i
$280$	−51.3176			−3.06681
$281$	−6.18933	−	19.0488i	−0.369225	−	1.13636i	−0.947293	−	0.320368i	$-0.896193\pi$
$281$	−6.18933	−	19.0488i	−0.369225	−	1.13636i	0.578069	−	0.815988i	$-0.303807\pi$
$282$	2.22118	−	6.83609i	0.132269	−	0.407083i
$283$	−10.0515	+	7.30286i	−0.597501	+	0.434110i	−0.844991	−	0.534781i	$-0.820394\pi$
$283$	−10.0515	+	7.30286i	−0.597501	+	0.434110i	0.247490	+	0.968890i	$0.420394\pi$
$284$	11.6334			0.690314
$285$	−1.72299			−0.102061
$286$	25.9799	−	18.8755i	1.53622	−	1.11613i
$287$	−5.19583	−	3.77499i	−0.306700	−	0.222831i
$288$	23.9973	+	17.4350i	1.41405	+	1.02737i
$289$	−4.12596	−	12.6984i	−0.242703	−	0.746964i
$290$	−1.99680	+	1.45076i	−0.117256	+	0.0851917i
$291$	1.64472	+	5.06194i	0.0964154	+	0.296736i
$292$	−27.3724	+	84.2436i	−1.60185	+	4.92998i
$293$	−1.06782	−	0.775815i	−0.0623826	−	0.0453236i	0.556157	−	0.831077i	$-0.312275\pi$
$293$	−1.06782	−	0.775815i	−0.0623826	−	0.0453236i	−0.618540	+	0.785754i	$0.712275\pi$
$294$	13.8722	−	42.6942i	0.809043	−	2.48998i
$295$	−3.71658	+	11.4384i	−0.216388	+	0.665972i
$296$	−43.3799	−	31.5173i	−2.52141	−	1.83191i
$297$	−0.933450	+	2.87286i	−0.0541642	+	0.166700i
$298$	5.48912	+	16.8938i	0.317976	+	0.978631i
$299$	−13.2005	+	9.59074i	−0.763406	+	0.554647i
$300$	−1.79903	−	5.53684i	−0.103867	−	0.319670i
$301$	4.80978	+	3.49451i	0.277231	+	0.201420i
$302$	−27.2817	−	19.8213i	−1.56989	−	1.14059i
$303$	−3.57420	+	2.59681i	−0.205332	+	0.149183i
$304$	−31.4439			−1.80343
$305$	11.3292			0.648710
$306$	4.32161	−	3.13983i	0.247050	−	0.179492i
$307$	−1.12231	+	3.45411i	−0.0640535	+	0.197136i	−0.977962	−	0.208785i	$-0.933049\pi$
$307$	−1.12231	+	3.45411i	−0.0640535	+	0.197136i	0.913908	+	0.405921i	$0.133049\pi$
$308$	−26.0912	−	80.3005i	−1.48669	−	4.57555i
$309$	−16.7806			−0.954617
$310$	15.2152	−	3.31237i	0.864167	−	0.188130i
$311$	4.24963			0.240974			0.120487	−	0.992715i	$-0.461554\pi$
$311$	4.24963			0.240974			0.120487	+	0.992715i	$0.461554\pi$
$312$	12.5551	+	38.6405i	0.710790	+	2.18759i
$313$	5.60881	−	17.2621i	0.317029	−	0.975714i	−0.657883	−	0.753120i	$-0.728548\pi$
$313$	5.60881	−	17.2621i	0.317029	−	0.975714i	0.974911	−	0.222594i	$-0.0714523\pi$
$314$	28.8890	−	20.9891i	1.63030	−	1.18448i
$315$	4.80118			0.270516
$316$	26.0393			1.46482
$317$	13.8681	−	10.0758i	0.778910	−	0.565911i	−0.125742	−	0.992063i	$-0.540131\pi$
$317$	13.8681	−	10.0758i	0.778910	−	0.565911i	0.904652	+	0.426152i	$0.140131\pi$
$318$	4.18472	+	3.04038i	0.234667	+	0.170496i
$319$	−2.15671	−	1.56694i	−0.120752	−	0.0877318i
$320$	−14.3565	−	44.1848i	−0.802554	−	2.47001i
$321$	−12.7329	+	9.25100i	−0.710681	+	0.516340i
$322$	17.8114	+	54.8179i	0.992591	+	3.05488i
$323$	−1.01695	+	3.12986i	−0.0565848	+	0.174150i
$324$	−4.70992	−	3.42196i	−0.261662	−	0.190109i
$325$	1.17463	−	3.61513i	0.0651566	−	0.200531i
$326$	5.51711	−	16.9799i	0.305564	−	0.940430i
$327$	−2.91641	−	2.11890i	−0.161278	−	0.117175i
$328$	4.41825	−	13.5980i	0.243957	−	0.750823i
$329$	−3.81310	−	11.7355i	−0.210223	−	0.647000i
$330$	6.83469	−	4.96570i	0.376237	−	0.273353i
$331$	0.824128	+	2.53640i	0.0452982	+	0.139413i	0.971148	−	0.238479i	$-0.0766489\pi$
$331$	0.824128	+	2.53640i	0.0452982	+	0.139413i	−0.925849	+	0.377893i	$0.876649\pi$
$332$	34.7968	+	25.2813i	1.90972	+	1.38749i
$333$	4.05854	+	2.94870i	0.222407	+	0.161588i
$334$	35.3255	−	25.6654i	1.93292	−	1.40435i
$335$	4.69083			0.256288
$336$	87.6194			4.78003
$337$	16.7783	−	12.1902i	0.913974	−	0.664041i	−0.0280432	−	0.999607i	$-0.508928\pi$
$337$	16.7783	−	12.1902i	0.913974	−	0.664041i	0.942017	+	0.335566i	$0.108928\pi$
$338$	−1.25223	+	3.85397i	−0.0681124	+	0.209629i
$339$	−1.23807	−	3.81038i	−0.0672426	−	0.206951i
$340$	−11.1196			−0.603047
$341$	8.48081	+	14.5238i	0.459261	+	0.786508i
$342$	4.81877			0.260569
$343$	−13.4289	−	41.3299i	−0.725092	−	2.23160i
$344$	−4.08998	+	12.5877i	−0.220517	+	0.678681i
$345$	−3.47275	+	2.52310i	−0.186966	+	0.135839i
$346$	−60.4768			−3.25125
$347$	27.9485			1.50035			0.750177	−	0.661237i	$-0.229968\pi$
$347$	27.9485			1.50035			0.750177	+	0.661237i	$0.229968\pi$
$348$	4.15660	−	3.01995i	0.222817	−	0.161886i
$349$	−6.58087	−	4.78128i	−0.352266	−	0.255936i	0.397553	−	0.917579i	$-0.369859\pi$
$349$	−6.58087	−	4.78128i	−0.352266	−	0.255936i	−0.749819	+	0.661643i	$0.769859\pi$
$350$	−10.8632	−	7.89258i	−0.580663	−	0.421876i
$351$	−1.17463	−	3.61513i	−0.0626970	−	0.192962i
$352$	72.4888	−	52.6662i	3.86366	−	2.80712i
$353$	7.93734	+	24.4286i	0.422462	+	1.30020i	0.905404	+	0.424552i	$0.139568\pi$
$353$	7.93734	+	24.4286i	0.422462	+	1.30020i	−0.482941	+	0.875653i	$0.660432\pi$
$354$	10.3943	−	31.9904i	0.552452	−	1.70027i
$355$	1.61662	+	1.17454i	0.0858013	+	0.0623383i
$356$	−11.0597	+	34.0381i	−0.586161	+	1.80402i
$357$	2.83377	−	8.72145i	0.149979	−	0.461588i
$358$	34.4451	+	25.0259i	1.82048	+	1.32266i
$359$	6.04084	−	18.5918i	0.318823	−	0.981237i	−0.655329	−	0.755344i	$-0.727470\pi$
$359$	6.04084	−	18.5918i	0.318823	−	0.981237i	0.974152	−	0.225893i	$-0.0725301\pi$
$360$	3.30294	+	10.1654i	0.174080	+	0.535764i
$361$	12.9696	−	9.42296i	0.682610	−	0.495945i
$362$	−17.4056	−	53.5688i	−0.914816	−	2.81552i
$363$	−1.51717	−	1.10229i	−0.0796310	−	0.0578553i
$364$	85.9566	+	62.4511i	4.50535	+	3.27333i
$365$	−12.3093	+	8.94321i	−0.644297	+	0.468109i
$366$	−31.6850			−1.65620
$367$	0.474245			0.0247554			0.0123777	−	0.999923i	$-0.496060\pi$
$367$	0.474245			0.0247554			0.0123777	+	0.999923i	$0.496060\pi$
$368$	−63.3761	+	46.0455i	−3.30371	+	2.40029i
$369$	−0.413364	+	1.27220i	−0.0215188	+	0.0662282i
$370$	−4.33558	−	13.3436i	−0.225396	−	0.693698i
$371$	8.87981			0.461017
$372$	−31.6724	+	6.89512i	−1.64214	+	0.357496i
$373$	−3.59280			−0.186028			−0.0930142	−	0.995665i	$-0.529650\pi$
$373$	−3.59280			−0.186028			−0.0930142	+	0.995665i	$0.529650\pi$
$374$	−4.98630	−	15.3463i	−0.257836	−	0.793536i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	22.2241	−	16.1468i	1.14612	−	0.832706i
$377$	3.35462			0.172772
$378$	−13.4277			−0.690644
$379$	−15.6632	+	11.3800i	−0.804566	+	0.584552i	−0.912250	−	0.409633i	$-0.865657\pi$
$379$	−15.6632	+	11.3800i	−0.804566	+	0.584552i	0.107684	+	0.994185i	$0.465657\pi$
$380$	−8.11516	−	5.89601i	−0.416299	−	0.302459i
$381$	−10.3143	−	7.49376i	−0.528416	−	0.383917i
$382$	−3.14722	−	9.68616i	−0.161026	−	0.495587i
$383$	−11.1973	+	8.13531i	−0.572155	+	0.415695i	−0.835887	−	0.548901i	$-0.815046\pi$
$383$	−11.1973	+	8.13531i	−0.572155	+	0.415695i	0.263733	+	0.964596i	$0.415046\pi$
$384$	21.8192	+	67.1527i	1.11346	+	3.42687i
$385$	4.48166	−	13.7931i	0.228406	−	0.702962i
$386$	−40.8621	−	29.6880i	−2.07983	−	1.51108i
$387$	0.382651	−	1.17768i	0.0194512	−	0.0598648i
$388$	−9.57521	+	29.4695i	−0.486108	+	1.49609i
$389$	−8.03961	−	5.84112i	−0.407624	−	0.296156i	0.365015	−	0.931002i	$-0.381064\pi$
$389$	−8.03961	−	5.84112i	−0.407624	−	0.296156i	−0.772639	+	0.634845i	$0.781064\pi$
$390$	−3.28513	+	10.1106i	−0.166349	+	0.511970i
$391$	2.53357	+	7.79753i	0.128128	+	0.394338i
$392$	138.799	−	100.843i	7.01040	−	5.09336i
$393$	−0.0695509	−	0.214056i	−0.00350838	−	0.0107977i
$394$	12.2714	+	8.91570i	0.618225	+	0.449166i
$395$	3.61852	+	2.62901i	0.182068	+	0.132280i
$396$	−14.2273	+	10.3367i	−0.714948	+	0.519440i
$397$	−5.45057			−0.273556			−0.136778	−	0.990602i	$-0.543675\pi$
$397$	−5.45057			−0.273556			−0.136778	+	0.990602i	$0.543675\pi$
$398$	36.9057			1.84992
$399$	6.69251	−	4.86239i	0.335044	−	0.243424i
$400$	5.63942	−	17.3564i	0.281971	−	0.867818i
$401$	−2.13023	−	6.55618i	−0.106379	−	0.327400i	0.883673	−	0.468105i	$-0.155063\pi$
$401$	−2.13023	−	6.55618i	−0.106379	−	0.327400i	−0.990052	+	0.140705i	$0.955063\pi$
$402$	−13.1191			−0.654319
$403$	−19.3764	−	8.51303i	−0.965208	−	0.424064i
$404$	−25.7203			−1.27963
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	3.66191	−	11.2702i	0.181738	−	0.559331i
$407$	12.2597	−	8.90717i	0.607689	−	0.441512i
$408$	20.4152			1.01070
$409$	3.51634			0.173872			0.0869359	−	0.996214i	$-0.472292\pi$
$409$	3.51634			0.173872			0.0869359	+	0.996214i	$0.472292\pi$
$410$	3.02664	−	2.19898i	0.149475	−	0.108600i
$411$	16.3349	+	11.8680i	0.805743	+	0.585406i
$412$	−79.0354	−	57.4226i	−3.89380	−	2.82901i
$413$	−17.8439	−	54.9180i	−0.878043	−	2.70234i
$414$	9.71239	−	7.05646i	0.477338	−	0.346806i
$415$	2.28301	+	7.02638i	0.112069	+	0.344912i
$416$	−34.8421	+	107.233i	−1.70828	+	5.25753i
$417$	−10.8502	−	7.88314i	−0.531337	−	0.386039i
$418$	4.49808	−	13.8437i	0.220008	−	0.677116i
$419$	4.30897	−	13.2616i	0.210507	−	0.647874i	−0.788935	−	0.614476i	$-0.789367\pi$
$419$	4.30897	−	13.2616i	0.210507	−	0.647874i	0.999442	−	0.0333974i	$-0.0106327\pi$
$420$	22.6131	+	16.4294i	1.10341	+	0.801673i
$421$	2.07754	−	6.39400i	0.101253	−	0.311625i	−0.887580	−	0.460654i	$-0.847615\pi$
$421$	2.07754	−	6.39400i	0.101253	−	0.311625i	0.988833	+	0.149029i	$0.0476149\pi$
$422$	−12.4688	−	38.3750i	−0.606971	−	1.86806i
$423$	−2.07925	+	1.51066i	−0.101096	+	0.0734509i
$424$	6.10881	+	18.8010i	0.296670	+	0.913057i
$425$	−1.54523	−	1.12267i	−0.0749545	−	0.0544577i
$426$	−4.52127	−	3.28490i	−0.219056	−	0.159154i
$427$	−44.0054	+	31.9718i	−2.12957	+	1.54722i
$428$	−91.6275			−4.42898
$429$	−11.4822			−0.554368
$430$	−2.80176	+	2.03560i	−0.135113	+	0.0981652i
$431$	1.20685	−	3.71430i	0.0581320	−	0.178912i	−0.917774	−	0.397103i	$-0.870016\pi$
$431$	1.20685	−	3.71430i	0.0581320	−	0.178912i	0.975906	+	0.218191i	$0.0700156\pi$
$432$	−5.63942	−	17.3564i	−0.271327	−	0.835058i
$433$	−11.0000			−0.528625			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528625			−0.264313	+	0.964437i	$0.585145\pi$
$434$	−49.7518	+	55.8043i	−2.38816	+	2.67869i
$435$	0.882521			0.0423136
$436$	−6.48529	−	19.9597i	−0.310589	−	0.955895i
$437$	−2.28550	+	7.03405i	−0.109330	+	0.336484i
$438$	34.4259	−	25.0119i	1.64493	−	1.19511i
$439$	−24.4860			−1.16865			−0.584327	−	0.811519i	$-0.698641\pi$
$439$	−24.4860			−1.16865			−0.584327	+	0.811519i	$0.698641\pi$
$440$	32.2870			1.53922
$441$	−12.9858	+	9.43471i	−0.618370	+	0.449272i
$442$	16.4272	+	11.9351i	0.781362	+	0.567692i
$443$	32.4577	+	23.5819i	1.54211	+	1.12041i	0.948993	+	0.315297i	$0.102104\pi$
$443$	32.4577	+	23.5819i	1.54211	+	1.12041i	0.593120	+	0.805114i	$0.297896\pi$
$444$	9.02507	+	27.7763i	0.428311	+	1.31821i
$445$	−4.97349	+	3.61345i	−0.235766	+	0.171294i
$446$	17.9866	+	55.3572i	0.851692	+	2.62124i
$447$	1.96268	−	6.04052i	0.0928317	−	0.285707i
$448$	180.456	+	131.109i	8.52576	+	6.19433i
$449$	0.236628	−	0.728266i	0.0111672	−	0.0343690i	−0.945318	−	0.326151i	$-0.894248\pi$
$449$	0.236628	−	0.728266i	0.0111672	−	0.0343690i	0.956485	+	0.291782i	$0.0942482\pi$
$450$	−0.864242	+	2.65986i	−0.0407407	+	0.125387i
$451$	3.26901	+	2.37507i	0.153932	+	0.111838i
$452$	7.20776	−	22.1832i	0.339024	−	1.04341i
$453$	3.72601	+	11.4675i	0.175063	+	0.538789i
$454$	8.29367	−	6.02570i	0.389241	−	0.282800i
$455$	5.63960	+	17.3569i	0.264388	+	0.813704i
$456$	14.8991	+	10.8248i	0.697714	+	0.506919i
$457$	−28.1997	−	20.4883i	−1.31913	−	0.958403i	−0.999943	−	0.0107109i	$-0.996591\pi$
$457$	−28.1997	−	20.4883i	−1.31913	−	0.958403i	−0.319186	−	0.947692i	$-0.603409\pi$
$458$	−8.27254	+	6.01035i	−0.386550	+	0.280845i
$459$	−1.91001			−0.0891515
$460$	−24.9903			−1.16518
$461$	5.71993	−	4.15577i	0.266404	−	0.193554i	−0.446562	−	0.894753i	$-0.647352\pi$
$461$	5.71993	−	4.15577i	0.266404	−	0.193554i	0.712965	+	0.701199i	$0.247352\pi$
$462$	−12.5340	+	38.5758i	−0.583137	+	1.79471i
$463$	−4.59859	−	14.1530i	−0.213715	−	0.657746i	−0.999242	−	0.0389195i	$-0.987608\pi$
$463$	−4.59859	−	14.1530i	−0.213715	−	0.657746i	0.785528	−	0.618826i	$-0.212392\pi$
$464$	16.1056			0.747684
$465$	−5.09748	−	2.23958i	−0.236390	−	0.103858i
$466$	−42.9560			−1.98990
$467$	2.14755	+	6.60949i	0.0993769	+	0.305851i	0.988370	−	0.152071i	$-0.0485942\pi$
$467$	2.14755	+	6.60949i	0.0993769	+	0.305851i	−0.888993	+	0.457921i	$0.848594\pi$
$468$	6.83843	−	21.0465i	0.316106	−	0.972875i
$469$	−18.2203	+	13.2378i	−0.841335	+	0.611265i
$470$	7.18789			0.331552
$471$	−12.7680			−0.588317
$472$	104.001	−	75.5610i	4.78703	−	3.47798i
$473$	−3.02612	−	2.19861i	−0.139141	−	0.101092i
$474$	−10.1201	−	7.35267i	−0.464831	−	0.337719i
$475$	−0.532434	−	1.63866i	−0.0244298	−	0.0751871i
$476$	43.1913	−	31.3803i	1.97967	−	1.43831i
$477$	−0.571529	−	1.75899i	−0.0261685	−	0.0805384i
$478$	−22.2678	+	68.5331i	−1.01850	+	3.13463i
$479$	12.7509	+	9.26409i	0.582605	+	0.423287i	0.839662	−	0.543109i	$-0.182753\pi$
$479$	12.7509	+	9.26409i	0.582605	+	0.423287i	−0.257057	+	0.966396i	$0.582753\pi$
$480$	−9.16615	+	28.2105i	−0.418375	+	1.28763i
$481$	−5.89268	+	18.1358i	−0.268683	+	0.826921i
$482$	33.6795	+	24.4696i	1.53406	+	1.11456i
$483$	6.36862	−	19.6006i	0.289782	−	0.891859i
$484$	−3.37377	−	10.3834i	−0.153353	−	0.471973i
$485$	−4.30594	+	3.12845i	−0.195523	+	0.142056i
$486$	0.864242	+	2.65986i	0.0392028	+	0.120654i
$487$	8.23307	+	5.98168i	0.373076	+	0.271056i	0.758485	−	0.651690i	$-0.225940\pi$
$487$	8.23307	+	5.98168i	0.373076	+	0.271056i	−0.385409	+	0.922746i	$0.625940\pi$
$488$	−97.9662	−	71.1766i	−4.43472	−	3.22202i
$489$	−5.16457	+	3.75228i	−0.233550	+	0.169684i
$490$	44.8914			2.02798
$491$	−20.2157			−0.912324			−0.456162	−	0.889897i	$-0.650776\pi$
$491$	−20.2157			−0.912324			−0.456162	+	0.889897i	$0.650776\pi$
$492$	−6.30033	+	4.57746i	−0.284041	+	0.206368i
$493$	0.520885	−	1.60312i	0.0234595	−	0.0722009i
$494$	5.66026	+	17.4205i	0.254667	+	0.783785i
$495$	−3.02071			−0.135771
$496$	−93.0268	−	40.8713i	−4.17702	−	1.83518i
$497$	−9.59396			−0.430348
$498$	−6.38500	−	19.6510i	−0.286119	−	0.880582i
$499$	4.78310	−	14.7209i	0.214121	−	0.658996i	−0.785094	−	0.619377i	$-0.787385\pi$
$499$	4.78310	−	14.7209i	0.214121	−	0.658996i	0.999215	−	0.0396195i	$-0.0126146\pi$
$500$	4.70992	−	3.42196i	0.210634	−	0.153035i
$501$	−15.6127			−0.697523
$502$	49.1355			2.19302
$503$	−14.0578	+	10.2136i	−0.626808	+	0.455402i	−0.855293	−	0.518145i	$-0.826623\pi$
$503$	−14.0578	+	10.2136i	−0.626808	+	0.455402i	0.228485	+	0.973547i	$0.426623\pi$
$504$	−41.5168	−	30.1637i	−1.84930	−	1.34360i
$505$	−3.57420	−	2.59681i	−0.159050	−	0.115556i
$506$	−11.2062	−	34.4892i	−0.498178	−	1.53323i
$507$	1.17221	−	0.851664i	0.0520599	−	0.0378237i
$508$	−22.9361	−	70.5900i	−1.01762	−	3.13193i
$509$	−0.274848	+	0.845894i	−0.0121824	+	0.0374936i	−0.956963	−	0.290210i	$-0.906275\pi$
$509$	−0.274848	+	0.845894i	−0.0121824	+	0.0374936i	0.944781	+	0.327704i	$0.106275\pi$
$510$	4.32161	+	3.13983i	0.191364	+	0.139034i
$511$	22.5738	−	69.4750i	0.998606	−	3.07339i
$512$	−46.7237	+	143.801i	−2.06492	+	6.35516i
$513$	−1.39393	−	1.01275i	−0.0615435	−	0.0447140i
$514$	10.4789	−	32.2507i	0.462204	−	1.42252i
$515$	−5.18550	−	15.9593i	−0.228501	−	0.703252i
$516$	5.83222	−	4.23736i	0.256749	−	0.186539i
$517$	2.39905	+	7.38352i	0.105510	+	0.324727i
$518$	54.4967	+	39.5942i	2.39445	+	1.73967i
$519$	17.4942	+	12.7103i	0.767909	+	0.557919i
$520$	−32.8696	+	23.8811i	−1.44143	+	1.04726i
$521$	19.8625			0.870193			0.435097	−	0.900384i	$-0.356714\pi$
$521$	19.8625			0.870193			0.435097	+	0.900384i	$0.356714\pi$
$522$	−2.46819			−0.108030
$523$	8.02031	−	5.82710i	0.350704	−	0.254801i	−0.398460	−	0.917186i	$-0.630455\pi$
$523$	8.02031	−	5.82710i	0.350704	−	0.254801i	0.749164	+	0.662384i	$0.230455\pi$
$524$	0.404910	−	1.24618i	0.0176886	−	0.0544398i
$525$	1.48364	+	4.56619i	0.0647516	+	0.199285i
$526$	64.4192			2.80881
$527$	−7.07690	+	7.93784i	−0.308275	+	0.345778i
$528$	−55.1266			−2.39908
$529$	−1.41344	−	4.35012i	−0.0614540	−	0.189136i
$530$	−1.59842	+	4.91943i	−0.0694310	+	0.213687i
$531$	−9.73013	+	7.06935i	−0.422252	+	0.306784i
$532$	48.1600			2.08800
$533$	−5.08473			−0.220244
$534$	13.9096	−	10.1059i	0.601927	−	0.437325i
$535$	−12.7329	−	9.25100i	−0.550491	−	0.399955i
$536$	−40.5626	−	29.4705i	−1.75204	−	1.27293i
$537$	−4.70435	−	14.4785i	−0.203008	−	0.624794i
$538$	0.576213	−	0.418643i	0.0248423	−	0.0180490i
$539$	14.9831	+	46.1132i	0.645367	+	1.98623i
$540$	1.79903	−	5.53684i	0.0774179	−	0.238268i
$541$	34.7228	+	25.2276i	1.49285	+	1.08462i	0.973123	+	0.230288i	$0.0739668\pi$
$541$	34.7228	+	25.2276i	1.49285	+	1.08462i	0.519728	+	0.854332i	$0.326033\pi$
$542$	11.3272	−	34.8615i	0.486545	−	1.49743i
$543$	−6.22351	+	19.1540i	−0.267076	+	0.821977i
$544$	45.8350	+	33.3011i	1.96516	+	1.42777i
$545$	1.11397	−	3.42845i	0.0477172	−	0.146859i
$546$	−15.7725	−	48.5428i	−0.675001	−	2.07744i
$547$	−20.0987	+	14.6025i	−0.859357	+	0.624359i	−0.927710	−	0.373302i	$-0.878226\pi$
$547$	−20.0987	+	14.6025i	−0.859357	+	0.624359i	0.0683530	+	0.997661i	$0.478226\pi$
$548$	36.3243	+	111.795i	1.55170	+	4.77564i
$549$	9.16554	+	6.65915i	0.391176	+	0.284206i
$550$	6.83469	+	4.96570i	0.291432	+	0.211738i
$551$	1.23017	−	0.893773i	0.0524071	−	0.0380760i
$552$	45.8811			1.95283
$553$	−21.4744			−0.913184
$554$	48.2844	−	35.0807i	2.05141	−	1.49044i
$555$	−1.55023	+	4.77110i	−0.0658034	+	0.202522i
$556$	−24.1279	−	74.2579i	−1.02325	−	3.14924i
$557$	−26.2484			−1.11218			−0.556090	−	0.831122i	$-0.687699\pi$
$557$	−26.2484			−1.11218			−0.556090	+	0.831122i	$0.687699\pi$
$558$	14.2563	+	6.26353i	0.603519	+	0.265156i
$559$	4.70694			0.199082
$560$	27.0759	+	83.3310i	1.14416	+	3.52138i
$561$	−1.78289	+	5.48719i	−0.0752739	+	0.231669i
$562$	−45.3181	+	32.9255i	−1.91163	+	1.38888i
$563$	27.8704			1.17460			0.587299	−	0.809370i	$-0.300191\pi$
$563$	27.8704			1.17460			0.587299	+	0.809370i	$0.300191\pi$
$564$	−14.9625			−0.630035
$565$	3.24130	−	2.35494i	0.136363	−	0.0990732i
$566$	28.1115	+	20.4242i	1.18162	+	0.858494i
$567$	3.88423	+	2.82206i	0.163122	+	0.118515i
$568$	−6.60011	−	20.3130i	−0.276934	−	0.852316i
$569$	−34.0006	+	24.7029i	−1.42538	+	1.03560i	−0.434525	+	0.900660i	$0.643084\pi$
$569$	−34.0006	+	24.7029i	−1.42538	+	1.03560i	−0.990854	+	0.134939i	$0.956916\pi$
$570$	1.48908	+	4.58292i	0.0623708	+	0.191958i
$571$	9.88965	−	30.4372i	0.413869	−	1.27376i	−0.499390	−	0.866377i	$-0.666442\pi$
$571$	9.88965	−	30.4372i	0.413869	−	1.27376i	0.913259	−	0.407380i	$-0.133558\pi$
$572$	−54.0804	−	39.2917i	−2.26122	−	1.64287i
$573$	−1.12532	+	3.46337i	−0.0470108	+	0.144684i
$574$	−5.55051	+	17.0827i	−0.231674	+	0.713018i
$575$	−3.47275	−	2.52310i	−0.144824	−	0.105221i
$576$	14.3565	−	44.1848i	0.598188	−	1.84103i
$577$	10.4831	+	32.2637i	0.436418	+	1.34316i	0.891627	+	0.452771i	$0.149565\pi$
$577$	10.4831	+	32.2637i	0.436418	+	1.34316i	−0.455209	+	0.890385i	$0.650435\pi$
$578$	−30.2101	+	21.9490i	−1.25658	+	0.912956i
$579$	5.58075	+	17.1758i	0.231928	+	0.713801i
$580$	4.15660	+	3.01995i	0.172593	+	0.125396i
$581$	−28.6966	−	20.8493i	−1.19054	−	0.864976i
$582$	12.0426	−	8.74947i	0.499182	−	0.362677i
$583$	−5.58682			−0.231382
$584$	162.627			6.72956
$585$	3.07522	−	2.23428i	0.127145	−	0.0923759i
$586$	−1.14071	+	3.51074i	−0.0471222	+	0.145027i
$587$	5.24570	+	16.1446i	0.216513	+	0.666359i	0.999043	+	0.0437454i	$0.0139291\pi$
$587$	5.24570	+	16.1446i	0.216513	+	0.666359i	−0.782530	+	0.622613i	$0.786071\pi$
$588$	−93.4471			−3.85369
$589$	−9.37366	+	2.04066i	−0.386235	+	0.0840838i
$590$	33.6367			1.38480
$591$	−1.67597	−	5.15811i	−0.0689402	−	0.212176i
$592$	−28.2909	+	87.0705i	−1.16275	+	3.57858i
$593$	23.9802	−	17.4226i	0.984748	−	0.715461i	0.0259830	−	0.999662i	$-0.491728\pi$
$593$	23.9802	−	17.4226i	0.984748	−	0.715461i	0.958765	+	0.284201i	$0.0917284\pi$
$594$	8.44815			0.346632
$595$	9.17028			0.375945
$596$	29.9145	−	21.7341i	1.22534	−	0.890265i
$597$	−10.6757	−	7.75639i	−0.436929	−	0.317448i
$598$	36.9185	+	26.8229i	1.50971	+	1.09687i
$599$	−3.81405	−	11.7384i	−0.155838	−	0.479619i	0.842407	−	0.538842i	$-0.181138\pi$
$599$	−3.81405	−	11.7384i	−0.155838	−	0.479619i	−0.998245	+	0.0592223i	$0.981138\pi$
$600$	−8.64721	+	6.28257i	−0.353021	+	0.256485i
$601$	5.32731	+	16.3958i	0.217305	+	0.668797i	0.998982	+	0.0451132i	$0.0143649\pi$
$601$	5.32731	+	16.3958i	0.217305	+	0.668797i	−0.781676	+	0.623684i	$0.785635\pi$
$602$	5.13811	−	15.8135i	0.209414	−	0.644509i
$603$	3.79496	+	2.75720i	0.154543	+	0.112282i
$604$	−21.6920	+	66.7611i	−0.882635	+	2.71647i
$605$	0.579509	−	1.78354i	0.0235604	−	0.0725114i
$606$	9.99611	+	7.26260i	0.406064	+	0.295023i
$607$	3.65193	−	11.2395i	0.148227	−	0.456197i	−0.849184	−	0.528096i	$-0.822906\pi$
$607$	3.65193	−	11.2395i	0.148227	−	0.456197i	0.997412	+	0.0718992i	$0.0229060\pi$
$608$	15.7932	+	48.6065i	0.640499	+	1.97125i
$609$	−3.42792	+	2.49053i	−0.138906	+	0.100921i
$610$	−9.79119	−	30.1342i	−0.396434	−	1.22010i
$611$	−7.90358	−	5.74229i	−0.319745	−	0.232308i
$612$	−8.99597	−	6.53596i	−0.363641	−	0.264200i
$613$	−13.5078	+	9.81396i	−0.545573	+	0.396382i	−0.826151	−	0.563449i	$-0.809474\pi$
$613$	−13.5078	+	9.81396i	−0.545573	+	0.396382i	0.280577	+	0.959831i	$0.409474\pi$
$614$	10.1574			0.409919
$615$	−1.33767			−0.0539402
$616$	−125.410	+	91.1157i	−5.05291	+	3.67116i
$617$	−4.68378	+	14.4152i	−0.188562	+	0.580334i	−0.999992	−	0.00411597i	$-0.998690\pi$
$617$	−4.68378	+	14.4152i	−0.188562	+	0.580334i	0.811429	+	0.584450i	$0.198690\pi$
$618$	14.5025	+	44.6342i	0.583377	+	1.79545i
$619$	−1.52053			−0.0611153			−0.0305577	−	0.999533i	$-0.509728\pi$
$619$	−1.52053			−0.0611153			−0.0305577	+	0.999533i	$0.509728\pi$
$620$	−16.3450	−	27.9916i	−0.656430	−	1.12417i
$621$	−4.29255			−0.172254
$622$	−3.67271	−	11.3034i	−0.147262	−	0.453226i
$623$	9.12082	−	28.0710i	0.365418	−	1.12464i
$624$	56.1213	−	40.7745i	2.24665	−	1.63229i
$625$	1.00000			0.0400000
$626$	−50.7623			−2.02887
$627$	−4.21066	+	3.05922i	−0.168157	+	0.122174i
$628$	−60.1361	−	43.6915i	−2.39969	−	1.74348i
$629$	7.75184	+	5.63204i	0.309086	+	0.224564i
$630$	−4.14938	−	12.7705i	−0.165315	−	0.508788i
$631$	14.7508	−	10.7171i	0.587221	−	0.426641i	−0.254099	−	0.967178i	$-0.581779\pi$
$631$	14.7508	−	10.7171i	0.587221	−	0.426641i	0.841320	+	0.540537i	$0.181779\pi$
$632$	−14.7732	−	45.4672i	−0.587646	−	1.80859i
$633$	−4.45832	+	13.7213i	−0.177202	+	0.545373i
$634$	−38.7855	−	28.1793i	−1.54037	−	1.11914i
$635$	3.93970	−	12.1252i	0.156342	−	0.481172i
$636$	3.32732	−	10.2404i	0.131937	−	0.406059i
$637$	−49.3612	−	35.8630i	−1.95576	−	1.42094i
$638$	−2.30393	+	7.09076i	−0.0912133	+	0.280726i
$639$	0.617494	+	1.90045i	0.0244277	+	0.0751807i
$640$	−57.1235	+	41.5026i	−2.25800	+	1.64054i
$641$	−7.62384	−	23.4638i	−0.301124	−	0.926763i	−0.981095	−	0.193525i	$-0.938008\pi$
$641$	−7.62384	−	23.4638i	−0.301124	−	0.926763i	0.679972	−	0.733238i	$-0.261992\pi$
$642$	35.6107	+	25.8727i	1.40544	+	1.02111i
$643$	−4.67241	−	3.39470i	−0.184262	−	0.133874i	0.491831	−	0.870691i	$-0.336328\pi$
$643$	−4.67241	−	3.39470i	−0.184262	−	0.133874i	−0.676092	+	0.736817i	$0.736328\pi$
$644$	97.0681	−	70.5241i	3.82502	−	2.77904i
$645$	1.23828			0.0487574
$646$	9.20388			0.362122
$647$	28.6896	−	20.8442i	1.12790	−	0.819469i	0.142515	−	0.989793i	$-0.454481\pi$
$647$	28.6896	−	20.8442i	1.12790	−	0.819469i	0.985388	+	0.170323i	$0.0544812\pi$
$648$	−3.30294	+	10.1654i	−0.129752	+	0.399335i
$649$	11.2267	+	34.5522i	0.440686	+	1.35629i
$650$	−10.6309			−0.416979
$651$	26.1200	−	5.68635i	1.02372	−	0.222866i
$652$	−37.1648			−1.45549
$653$	−0.982837	−	3.02486i	−0.0384614	−	0.118372i	0.929982	−	0.367604i	$-0.119822\pi$
$653$	−0.982837	−	3.02486i	−0.0384614	−	0.118372i	−0.968444	+	0.249232i	$0.919822\pi$
$654$	−3.11549	+	9.58849i	−0.121825	+	0.374940i
$655$	0.182087	−	0.132294i	0.00711471	−	0.00516914i
$656$	−24.4119			−0.953126
$657$	−15.2151			−0.593598
$658$	−27.9194	+	20.2847i	−1.08841	+	0.790778i
$659$	10.5315	+	7.65155i	0.410247	+	0.298062i	0.773702	−	0.633550i	$-0.218403\pi$
$659$	10.5315	+	7.65155i	0.410247	+	0.298062i	−0.363455	+	0.931612i	$0.618403\pi$
$660$	−14.2273	−	10.3367i	−0.553796	−	0.402357i
$661$	−1.19913	−	3.69053i	−0.0466406	−	0.143545i	0.925024	−	0.379908i	$-0.124044\pi$
$661$	−1.19913	−	3.69053i	−0.0466406	−	0.143545i	−0.971665	+	0.236363i	$0.924044\pi$
$662$	6.03424	−	4.38413i	0.234527	−	0.170394i
$663$	−2.24355	−	6.90493i	−0.0871321	−	0.268165i
$664$	24.4021	−	75.1018i	0.946983	−	2.91452i
$665$	6.69251	+	4.86239i	0.259524	+	0.188555i
$666$	4.33558	−	13.3436i	0.168000	−	0.517052i
$667$	1.17064	−	3.60286i	0.0453273	−	0.139503i
$668$	−73.5344	−	53.4259i	−2.84513	−	2.06711i
$669$	6.43127	−	19.7934i	0.248647	−	0.765258i
$670$	−4.05401	−	12.4770i	−0.156620	−	0.482027i
$671$	27.6864	−	20.1154i	1.06882	−	0.776545i
$672$	−44.0083	−	135.444i	−1.69766	−	5.22485i
$673$	31.3883	+	22.8050i	1.20993	+	0.879067i	0.995225	−	0.0976114i	$-0.0311202\pi$
$673$	31.3883	+	22.8050i	1.20993	+	0.879067i	0.214707	+	0.976678i	$0.431120\pi$
$674$	−46.9247	−	34.0928i	−1.80747	−	1.31320i
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	8.43539			0.324438
$677$	−8.63056			−0.331699			−0.165850	−	0.986151i	$-0.553037\pi$
$677$	−8.63056			−0.331699			−0.165850	+	0.986151i	$0.553037\pi$
$678$	−9.06509	+	6.58618i	−0.348143	+	0.252941i
$679$	7.89660	−	24.3032i	0.303044	−	0.932673i
$680$	6.30864	+	19.4160i	0.241925	+	0.744569i
$681$	−3.66552			−0.140463
$682$	31.3018	−	35.1098i	1.19861	−	1.34443i
$683$	21.7908			0.833801			0.416901	−	0.908952i	$-0.363116\pi$
$683$	21.7908			0.833801			0.416901	+	0.908952i	$0.363116\pi$
$684$	−3.09971	−	9.53994i	−0.118521	−	0.364769i
$685$	−6.23939	+	19.2029i	−0.238395	+	0.733704i
$686$	−98.3260	+	71.4380i	−3.75410	+	2.72752i
$687$	3.65619			0.139492
$688$	22.5981			0.861546
$689$	5.68763	−	4.13231i	0.216682	−	0.157428i
$690$	9.71239	+	7.05646i	0.369744	+	0.268635i
$691$	6.96242	+	5.05849i	0.264863	+	0.192434i	0.712288	−	0.701887i	$-0.247659\pi$
$691$	6.96242	+	5.05849i	0.264863	+	0.192434i	−0.447425	+	0.894321i	$0.647659\pi$
$692$	38.9022	+	119.729i	1.47884	+	4.55140i
$693$	11.7331	−	8.52462i	0.445705	−	0.323823i
$694$	−24.1543	−	74.3392i	−0.916883	−	2.82188i
$695$	4.14441	−	12.7552i	0.157206	−	0.483832i
$696$	−7.63134	−	5.54450i	−0.289265	−	0.210164i
$697$	−0.789527	+	2.42991i	−0.0299055	+	0.0920396i
$698$	−7.03009	+	21.6364i	−0.266093	+	0.818949i
$699$	12.4259	+	9.02797i	0.469992	+	0.341469i
$700$	−8.63745	+	26.5834i	−0.326465	+	1.00476i
$701$	−14.9880	−	46.1284i	−0.566090	−	1.74225i	−0.664689	−	0.747120i	$-0.731436\pi$
$701$	−14.9880	−	46.1284i	−0.566090	−	1.74225i	0.0985986	−	0.995127i	$-0.468564\pi$
$702$	−8.60059	+	6.24870i	−0.324608	+	0.235842i
$703$	2.67103	+	8.22058i	0.100740	+	0.310045i
$704$	−113.536	−	82.4886i	−4.27904	−	3.10891i
$705$	−2.07925	−	1.51066i	−0.0783090	−	0.0568948i
$706$	58.1170	−	42.2245i	2.18726	−	1.58914i
$707$	21.2114			0.797735
$708$	−70.0191			−2.63148
$709$	13.9133	−	10.1086i	0.522526	−	0.379638i	−0.295028	−	0.955488i	$-0.595329\pi$
$709$	13.9133	−	10.1086i	0.522526	−	0.379638i	0.817555	+	0.575851i	$0.195329\pi$
$710$	1.72697	−	5.31507i	0.0648121	−	0.199471i
$711$	1.38215	+	4.25383i	0.0518348	+	0.159531i
$712$	65.7086			2.46253
$713$	−15.9046	+	17.8395i	−0.595634	+	0.668095i
$714$	−25.6469			−0.959812
$715$	−3.54821	−	10.9203i	−0.132695	−	0.408394i
$716$	27.3877	−	84.2907i	1.02353	−	3.15009i
$717$	20.8449	−	15.1447i	0.778466	−	0.565588i
$718$	−54.6723			−2.04035
$719$	11.6841			0.435744			0.217872	−	0.975977i	$-0.430088\pi$
$719$	11.6841			0.435744			0.217872	+	0.975977i	$0.430088\pi$
$720$	14.7642	−	10.7268i	0.550229	−	0.399765i
$721$	65.1799	+	47.3560i	2.42743	+	1.76363i
$722$	−36.2726	−	26.3536i	−1.34993	−	0.980780i
$723$	−4.59979	−	14.1567i	−0.171068	−	0.526493i
$724$	−94.8564	+	68.9172i	−3.52531	+	2.56129i
$725$	0.272714	+	0.839327i	0.0101283	+	0.0311718i
$726$	−1.62074	+	4.98812i	−0.0601512	+	0.185126i
$727$	−16.1259	−	11.7162i	−0.598077	−	0.434528i	0.247119	−	0.968985i	$-0.420516\pi$
$727$	−16.1259	−	11.7162i	−0.598077	−	0.434528i	−0.845196	+	0.534457i	$0.820516\pi$
$728$	60.2790	−	185.520i	2.23409	−	6.87582i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	34.4259	+	25.0119i	1.27416	+	0.925731i
$731$	0.730866	−	2.24937i	0.0270320	−	0.0831961i
$732$	20.3816	+	62.7281i	0.753326	+	2.31850i
$733$	18.5467	−	13.4749i	0.685037	−	0.497709i	−0.189988	−	0.981786i	$-0.560845\pi$
$733$	18.5467	−	13.4749i	0.685037	−	0.497709i	0.875025	+	0.484078i	$0.160845\pi$
$734$	−0.409862	−	1.26143i	−0.0151283	−	0.0465601i
$735$	−12.9858	−	9.43471i	−0.478987	−	0.348005i
$736$	103.010	+	74.8409i	3.79698	+	2.75867i
$737$	11.4635	−	8.32870i	0.422262	−	0.306792i
$738$	3.74113			0.137713
$739$	−6.42919			−0.236502			−0.118251	−	0.992984i	$-0.537729\pi$
$739$	−6.42919			−0.236502			−0.118251	+	0.992984i	$0.537729\pi$
$740$	−23.6279	+	17.1667i	−0.868580	+	0.631061i
$741$	2.02388	−	6.22885i	0.0743489	−	0.228822i
$742$	−7.67430	−	23.6191i	−0.281732	−	0.867083i
$743$	14.0823			0.516630			0.258315	−	0.966061i	$-0.416833\pi$
$743$	14.0823			0.516630			0.258315	+	0.966061i	$0.416833\pi$
$744$	30.0087	+	51.3914i	1.10017	+	1.88410i
$745$	6.35138			0.232696
$746$	3.10505	+	9.55636i	0.113684	+	0.349883i
$747$	−2.28301	+	7.02638i	−0.0835310	+	0.257082i
$748$	−27.1742	+	19.7432i	−0.993587	+	0.721883i
$749$	75.5644			2.76106
$750$	−2.79674			−0.102123
$751$	−40.7771	+	29.6263i	−1.48798	+	1.08108i	−0.513101	+	0.858328i	$0.671503\pi$
$751$	−40.7771	+	29.6263i	−1.48798	+	1.08108i	−0.974876	+	0.222750i	$0.928497\pi$
$752$	−37.9453	−	27.5689i	−1.38372	−	1.00533i
$753$	−14.2135	−	10.3267i	−0.517967	−	0.376325i
$754$	−2.89920	−	8.92282i	−0.105583	−	0.324950i
$755$	−9.75481	+	7.08729i	−0.355014	+	0.257933i
$756$	8.63745	+	26.5834i	0.314141	+	0.966827i
$757$	−1.38154	+	4.25195i	−0.0502130	+	0.154540i	−0.973019	−	0.230726i	$-0.925890\pi$
$757$	−1.38154	+	4.25195i	−0.0502130	+	0.154540i	0.922806	+	0.385265i	$0.125890\pi$
$758$	43.8061	+	31.8270i	1.59111	+	1.15601i
$759$	−4.00688	+	12.3319i	−0.145441	+	0.447620i
$760$	−5.69094	+	17.5149i	−0.206432	+	0.635333i
$761$	25.1191	+	18.2501i	0.910566	+	0.661565i	0.941158	−	0.337967i	$-0.109739\pi$
$761$	25.1191	+	18.2501i	0.910566	+	0.661565i	−0.0305921	+	0.999532i	$0.509739\pi$
$762$	−11.0183	+	33.9110i	−0.399152	+	1.22846i
$763$	5.34837	+	16.4606i	0.193624	+	0.595913i
$764$	−17.1516	+	12.4614i	−0.620525	+	0.450838i
$765$	−0.590224	−	1.81652i	−0.0213396	−	0.0656766i
$766$	31.3160	+	22.7524i	1.13149	+	0.822077i
$767$	−36.9859	−	26.8718i	−1.33548	−	0.970286i
$768$	84.5881	−	61.4568i	3.05231	−	2.21763i
$769$	−5.00586			−0.180516			−0.0902580	−	0.995918i	$-0.528769\pi$
$769$	−5.00586			−0.180516			−0.0902580	+	0.995918i	$0.528769\pi$
$770$	−40.5610			−1.46172
$771$	−9.80929	+	7.12687i	−0.353273	+	0.256668i
$772$	−32.4899	+	99.9936i	−1.16934	+	3.59885i
$773$	−4.82810	−	14.8594i	−0.173655	−	0.534454i	0.825915	−	0.563795i	$-0.190659\pi$
$773$	−4.82810	−	14.8594i	−0.173655	−	0.534454i	−0.999569	+	0.0293408i	$0.990659\pi$
$774$	−3.46317			−0.124481
$775$	0.554757	−	5.54006i	0.0199275	−	0.199005i
$776$	56.8891			2.04220
$777$	−7.44290	−	22.9069i	−0.267013	−	0.821780i
$778$	−8.58840	+	26.4324i	−0.307909	+	0.947647i
$779$	−1.86462	+	1.35473i	−0.0668070	+	0.0485382i
$780$	22.1296			0.792367
$781$	6.03613			0.215990
$782$	18.5507	−	13.4779i	0.663373	−	0.481968i
$783$	0.713974	+	0.518733i	0.0255154	+	0.0185380i
$784$	−236.985	−	172.179i	−8.46373	−	6.14926i
$785$	−3.94552	−	12.1431i	−0.140822	−	0.433405i
$786$	−0.509250	+	0.369991i	−0.0181643	+	0.0131972i
$787$	−15.0236	−	46.2379i	−0.535534	−	1.64820i	−0.742493	−	0.669854i	$-0.766357\pi$
$787$	−15.0236	−	46.2379i	−0.535534	−	1.64820i	0.206959	−	0.978350i	$-0.433643\pi$
$788$	9.75713	−	30.0294i	0.347583	−	1.06975i
$789$	−18.6346	−	13.5388i	−0.663409	−	0.481995i
$790$	3.86553	−	11.8969i	0.137529	−	0.423271i
$791$	−5.94418	+	18.2943i	−0.211351	+	0.650470i
$792$	26.1207	+	18.9778i	0.928158	+	0.674347i
$793$	−13.3076	+	40.9567i	−0.472568	+	1.45441i
$794$	4.71061	+	14.4978i	0.167173	+	0.514507i
$795$	1.49628	−	1.08711i	0.0530677	−	0.0385559i
$796$	−23.7399	−	73.0639i	−0.841438	−	2.58968i
$797$	42.7241	+	31.0409i	1.51336	+	1.09952i	0.964657	+	0.263509i	$0.0848800\pi$
$797$	42.7241	+	31.0409i	1.51336	+	1.09952i	0.548708	+	0.836014i	$0.315120\pi$
$798$	−18.7172	−	13.5989i	−0.662583	−	0.481395i
$799$	−3.97138	+	2.88537i	−0.140497	+	0.102077i
$800$	−29.6623			−1.04872
$801$	−6.14757			−0.217214
$802$	−15.5975	+	11.3323i	−0.550767	+	0.400156i
$803$	−14.2025	+	43.7109i	−0.501196	+	1.54252i
$804$	8.43894	+	25.9724i	0.297619	+	0.915976i
$805$	20.6093			0.726382
$806$	−5.89757	+	58.8959i	−0.207733	+	2.07452i
$807$	−0.254667			−0.00896470
$808$	14.5922	+	44.9103i	0.513353	+	1.57994i
$809$	0.742978	−	2.28665i	0.0261217	−	0.0803944i	−0.937146	−	0.348938i	$-0.886542\pi$
$809$	0.742978	−	2.28665i	0.0261217	−	0.0803944i	0.963268	+	0.268544i	$0.0865424\pi$
$810$	−2.26261	+	1.64389i	−0.0795001	+	0.0577602i
$811$	−14.8582			−0.521742			−0.260871	−	0.965374i	$-0.584010\pi$
$811$	−14.8582			−0.521742			−0.260871	+	0.965374i	$0.584010\pi$
$812$	−24.6677			−0.865666
$813$	−10.6034	+	7.70382i	−0.371877	+	0.270185i
$814$	−34.2872	−	24.9111i	−1.20176	−	0.873133i
$815$	−5.16457	−	3.75228i	−0.180907	−	0.131437i
$816$	−10.7713	−	33.1508i	−0.377072	−	1.16051i
$817$	1.72608	−	1.25407i	0.0603880	−	0.0438744i
$818$	−3.03897	−	9.35298i	−0.106255	−	0.327019i
$819$	−5.63960	+	17.3569i	−0.197063	+	0.606499i
$820$	−6.30033	−	4.57746i	−0.220017	−	0.159852i
$821$	−6.42044	+	19.7601i	−0.224075	+	0.689632i	0.774309	+	0.632808i	$0.218098\pi$
$821$	−6.42044	+	19.7601i	−0.224075	+	0.689632i	−0.998384	+	0.0568246i	$0.981902\pi$
$822$	17.4500	−	53.7055i	0.608638	−	1.87319i
$823$	32.1709	+	23.3735i	1.12141	+	0.814751i	0.984422	−	0.175822i	$-0.0562584\pi$
$823$	32.1709	+	23.3735i	1.12141	+	0.814751i	0.136986	+	0.990573i	$0.456258\pi$
$824$	−55.4255	+	170.582i	−1.93084	+	5.94251i
$825$	−0.933450	−	2.87286i	−0.0324985	−	0.100020i
$826$	−130.653	+	94.9248i	−4.54599	+	3.30286i
$827$	16.7525	+	51.5590i	0.582543	+	1.79288i	0.608921	+	0.793231i	$0.291603\pi$
$827$	16.7525	+	51.5590i	0.582543	+	1.79288i	−0.0263777	+	0.999652i	$0.508397\pi$
$828$	−20.2176	−	14.6889i	−0.702609	−	0.510476i
$829$	16.7688	+	12.1833i	0.582406	+	0.423143i	0.839591	−	0.543220i	$-0.182795\pi$
$829$	16.7688	+	12.1833i	0.582406	+	0.423143i	−0.257185	+	0.966362i	$0.582795\pi$
$830$	16.7161	−	12.1450i	0.580226	−	0.421559i
$831$	−21.3401			−0.740280
$832$	176.598			6.12242
$833$	−24.8029	+	18.0204i	−0.859369	+	0.624368i
$834$	−11.5909	+	35.6730i	−0.401359	+	1.23526i
$835$	−4.82458	−	14.8485i	−0.166962	−	0.513855i
$836$	−30.3004			−1.04796
$837$	−2.80756	−	4.80808i	−0.0970434	−	0.166192i
$838$	−38.9981			−1.34717
$839$	0.721361	+	2.22012i	0.0249041	+	0.0766470i	0.962736	−	0.270442i	$-0.0871700\pi$
$839$	0.721361	+	2.22012i	0.0249041	+	0.0766470i	−0.937832	+	0.347090i	$0.887170\pi$
$840$	15.8580	−	48.8059i	0.547153	−	1.68396i
$841$	22.8314	−	16.5880i	0.787290	−	0.571999i
$842$	−18.8027			−0.647982
$843$	20.0291			0.689839
$844$	−67.9520	+	49.3700i	−2.33900	+	1.69939i
$845$	1.17221	+	0.851664i	0.0403254	+	0.0292981i
$846$	5.81512	+	4.22493i	0.199928	+	0.145256i
$847$	2.78232	+	8.56311i	0.0956018	+	0.294232i
$848$	27.3065	−	19.8393i	0.937709	−	0.681286i
$849$	−3.83934	−	11.8163i	−0.131766	−	0.405533i
$850$	−1.65071	+	5.08035i	−0.0566188	+	0.174255i
$851$	17.4215	+	12.6575i	0.597202	+	0.433892i
$852$	−3.59491	+	11.0640i	−0.123160	+	0.379047i
$853$	6.79615	−	20.9164i	0.232696	−	0.716164i	−0.764723	−	0.644359i	$-0.777124\pi$
$853$	6.79615	−	20.9164i	0.232696	−	0.716164i	0.997419	−	0.0718045i	$-0.0228758\pi$
$854$	123.072	+	89.4169i	4.21143	+	3.05978i
$855$	0.532434	−	1.63866i	0.0182089	−	0.0560411i
$856$	51.9841	+	159.991i	1.77678	+	5.46837i
$857$	6.74100	−	4.89762i	0.230268	−	0.167300i	−0.466668	−	0.884432i	$-0.654546\pi$
$857$	6.74100	−	4.89762i	0.230268	−	0.167300i	0.696937	+	0.717133i	$0.254546\pi$
$858$	9.92343	+	30.5412i	0.338780	+	1.04266i
$859$	27.1140	+	19.6995i	0.925119	+	0.672138i	0.944793	−	0.327668i	$-0.106263\pi$
$859$	27.1140	+	19.6995i	0.925119	+	0.672138i	−0.0196741	+	0.999806i	$0.506263\pi$
$860$	5.83222	+	4.23736i	0.198877	+	0.144493i
$861$	5.19583	−	3.77499i	0.177073	−	0.128651i
$862$	−10.9225			−0.372023
$863$	34.1851			1.16367			0.581837	−	0.813305i	$-0.302334\pi$
$863$	34.1851			1.16367			0.581837	+	0.813305i	$0.302334\pi$
$864$	−23.9973	+	17.4350i	−0.816404	+	0.593152i
$865$	−6.68218	+	20.5656i	−0.227201	+	0.699253i
$866$	9.50664	+	29.2584i	0.323049	+	0.994242i
$867$	13.3519			0.453453
$868$	142.482	+	62.5993i	4.83614	+	2.12476i
$869$	13.5108			0.458324
$870$	−0.762711	−	2.34738i	−0.0258583	−	0.0795838i
$871$	−5.50998	+	16.9580i	−0.186699	+	0.574599i
$872$	−31.1722	+	22.6479i	−1.05562	+	0.766955i
$873$	−5.32244			−0.180137
$874$	20.6848			0.699675
$875$	−3.88423	+	2.82206i	−0.131311	+	0.0954031i
$876$	−71.6619	−	52.0654i	−2.42123	−	1.75913i
$877$	−19.4286	−	14.1157i	−0.656056	−	0.476652i	0.209273	−	0.977857i	$-0.432890\pi$
$877$	−19.4286	−	14.1157i	−0.656056	−	0.476652i	−0.865329	+	0.501205i	$0.832890\pi$
$878$	21.1618	+	65.1294i	0.714177	+	2.19801i
$879$	1.06782	−	0.775815i	0.0360166	−	0.0261676i
$880$	−17.0350	−	52.4285i	−0.574251	−	1.76736i
$881$	−9.06863	+	27.9104i	−0.305530	+	0.940325i	0.673949	+	0.738778i	$0.264597\pi$
$881$	−9.06863	+	27.9104i	−0.305530	+	0.940325i	−0.979479	+	0.201547i	$0.935403\pi$
$882$	36.3179	+	26.3865i	1.22289	+	0.888479i
$883$	13.8472	−	42.6172i	0.465994	−	1.43418i	−0.391734	−	0.920079i	$-0.628124\pi$
$883$	13.8472	−	42.6172i	0.465994	−	1.43418i	0.857728	−	0.514104i	$-0.171876\pi$
$884$	13.0614	−	40.1990i	0.439304	−	1.35204i
$885$	−9.73013	−	7.06935i	−0.327075	−	0.237634i
$886$	34.6733	−	106.714i	1.16487	−	3.58511i
$887$	14.1442	+	43.5315i	0.474917	+	1.46164i	0.846070	+	0.533072i	$0.178962\pi$
$887$	14.1442	+	43.5315i	0.474917	+	1.46164i	−0.371153	+	0.928572i	$0.621038\pi$
$888$	43.3799	−	31.5173i	1.45573	−	1.05765i
$889$	18.9152	+	58.2150i	0.634396	+	1.95247i
$890$	13.9096	+	10.1059i	0.466250	+	0.338751i
$891$	−2.44380	−	1.77553i	−0.0818705	−	0.0594824i
$892$	98.0230	−	71.2179i	3.28205	−	2.38455i
$893$	−4.42825			−0.148186
$894$	−17.7632			−0.594090
$895$	12.3162	−	8.94821i	0.411684	−	0.299106i
$896$	104.758	−	322.412i	3.49972	−	10.7710i
$897$	−5.04215	−	15.5181i	−0.168353	−	0.518136i
$898$	−2.14159			−0.0714658
$899$	4.80121	−	1.04523i	0.160129	−	0.0348603i
$900$	5.82178			0.194059
$901$	−1.09162	−	3.35967i	−0.0363673	−	0.111927i
$902$	3.49216	−	10.7477i	0.116276	−	0.357861i
$903$	−4.80978	+	3.49451i	−0.160060	+	0.116290i
$904$	−42.8233			−1.42428
$905$	−20.1397			−0.669466
$906$	27.2817	−	19.8213i	0.906374	−	0.658519i
$907$	−48.6875	−	35.3735i	−1.61664	−	1.17456i	−0.832711	−	0.553708i	$-0.813212\pi$
$907$	−48.6875	−	35.3735i	−1.61664	−	1.17456i	−0.783930	−	0.620850i	$-0.786788\pi$
$908$	−17.2643	−	12.5433i	−0.572937	−	0.416263i
$909$	−1.36522	−	4.20172i	−0.0452815	−	0.139362i
$910$	41.2930	−	30.0011i	1.36885	−	0.994526i
$911$	0.467564	+	1.43901i	0.0154911	+	0.0476767i	0.958503	−	0.285082i	$-0.0920207\pi$
$911$	0.467564	+	1.43901i	0.0154911	+	0.0476767i	−0.943012	+	0.332758i	$0.892021\pi$
$912$	9.71669	−	29.9049i	0.321752	−	0.990250i
$913$	18.0548	+	13.1176i	0.597525	+	0.434128i
$914$	−30.1247	+	92.7143i	−0.996437	+	3.06672i
$915$	−3.50092	+	10.7747i	−0.115737	+	0.356202i
$916$	17.2203	+	12.5113i	0.568976	+	0.413385i
$917$	−0.333926	+	1.02772i	−0.0110272	+	0.0339383i
$918$	1.65071	+	5.08035i	0.0544814	+	0.167677i
$919$	−46.8128	+	34.0115i	−1.54421	+	1.12193i	−0.596586	+	0.802549i	$0.703477\pi$
$919$	−46.8128	+	34.0115i	−1.54421	+	1.12193i	−0.947625	+	0.319386i	$0.896523\pi$
$920$	14.1780	+	43.6355i	0.467436	+	1.43862i
$921$	−2.93824	−	2.13476i	−0.0968183	−	0.0703426i
$922$	−15.9972	−	11.6226i	−0.526839	−	0.382771i
$923$	−6.14506	+	4.46464i	−0.202267	+	0.146956i
$924$	84.4330			2.77764
$925$	−5.01663			−0.164946
$926$	−33.6708	+	24.4632i	−1.10649	+	0.803912i
$927$	5.18550	−	15.9593i	0.170314	−	0.524173i
$928$	−8.08932	−	24.8964i	−0.265545	−	0.817263i
$929$	11.3872			0.373600			0.186800	−	0.982398i	$-0.440188\pi$
$929$	11.3872			0.373600			0.186800	+	0.982398i	$0.440188\pi$
$930$	−1.55151	+	15.4941i	−0.0508761	+	0.508072i
$931$	−27.6563			−0.906397
$932$	27.6318	+	85.0420i	0.905110	+	2.78564i
$933$	−1.31321	+	4.04164i	−0.0429925	+	0.132317i
$934$	15.7243	−	11.4244i	0.514515	−	0.373817i
$935$	−5.76957			−0.188685
$936$	−40.6290			−1.32800
$937$	23.0799	−	16.7685i	0.753987	−	0.547804i	−0.143073	−	0.989712i	$-0.545698\pi$
$937$	23.0799	−	16.7685i	0.753987	−	0.547804i	0.897060	+	0.441908i	$0.145698\pi$
$938$	50.9575	+	37.0228i	1.66382	+	1.20884i
$939$	14.6841	+	10.6686i	0.479196	+	0.348156i
$940$	−4.62367	−	14.2302i	−0.150807	−	0.464137i
$941$	26.0092	−	18.8968i	0.847877	−	0.616019i	−0.0766829	−	0.997056i	$-0.524433\pi$
$941$	26.0092	−	18.8968i	0.847877	−	0.616019i	0.924560	+	0.381037i	$0.124433\pi$
$942$	11.0346	+	33.9611i	0.359527	+	1.10651i
$943$	−1.77438	+	5.46099i	−0.0577819	+	0.177834i
$944$	−177.571	−	129.013i	−5.77943	−	4.19900i
$945$	−1.48364	+	4.56619i	−0.0482630	+	0.148538i
$946$	−3.23269	+	9.94920i	−0.105104	+	0.323476i
$947$	−24.9904	−	18.1566i	−0.812079	−	0.590010i	0.102354	−	0.994748i	$-0.467363\pi$
$947$	−24.9904	−	18.1566i	−0.812079	−	0.590010i	−0.914433	+	0.404738i	$0.867363\pi$
$948$	−8.04658	+	24.7648i	−0.261341	+	0.804325i
$949$	−17.8721	−	55.0046i	−0.580152	−	1.78552i
$950$	−3.89847	+	2.83240i	−0.126483	+	0.0918953i
$951$	5.29714	+	16.3029i	0.171772	+	0.528659i
$952$	−79.2973	−	57.6129i	−2.57004	−	1.86724i
$953$	−9.19299	−	6.67910i	−0.297790	−	0.216357i	0.428850	−	0.903376i	$-0.358919\pi$
$953$	−9.19299	−	6.67910i	−0.297790	−	0.216357i	−0.726640	+	0.687019i	$0.758919\pi$
$954$	−4.18472	+	3.04038i	−0.135485	+	0.0984359i
$955$	−3.64160			−0.117839
$956$	150.002			4.85141
$957$	2.15671	−	1.56694i	0.0697164	−	0.0506520i
$958$	13.6213	−	41.9221i	0.440085	−	1.35444i
$959$	−29.9564	−	92.1963i	−0.967343	−	2.97717i
$960$	46.4587			1.49945
$961$	−30.3845	−	6.14677i	−0.980145	−	0.198283i
$962$	53.3314			1.71947
$963$	−4.86354	−	14.9684i	−0.156725	−	0.482351i
$964$	26.7789	−	82.4171i	0.862492	−	2.65448i
$965$	−14.6106	+	10.6152i	−0.470332	+	0.341716i
$966$	−57.6389			−1.85450
$967$	32.5403			1.04642			0.523212	−	0.852202i	$-0.324734\pi$
$967$	32.5403			1.04642			0.523212	+	0.852202i	$0.324734\pi$
$968$	−16.2164	+	11.7819i	−0.521214	+	0.378684i
$969$	−2.66242	−	1.93436i	−0.0855291	−	0.0621406i
$970$	12.0426	+	8.74947i	0.386665	+	0.280929i
$971$	−5.70274	−	17.5512i	−0.183010	−	0.563246i	0.816899	−	0.576781i	$-0.195692\pi$
$971$	−5.70274	−	17.5512i	−0.183010	−	0.563246i	−0.999908	+	0.0135351i	$0.995692\pi$
$972$	4.70992	−	3.42196i	0.151071	−	0.109759i
$973$	19.8980	+	61.2399i	0.637902	+	1.96326i
$974$	8.79507	−	27.0684i	0.281812	−	0.867329i
$975$	3.07522	+	2.23428i	0.0984857	+	0.0715541i
$976$	−63.8903	+	196.634i	−2.04508	+	6.29411i
$977$	11.9584	−	36.8041i	0.382582	−	1.17747i	−0.555637	−	0.831425i	$-0.687525\pi$
$977$	11.9584	−	36.8041i	0.382582	−	1.17747i	0.938219	−	0.346042i	$-0.112475\pi$
$978$	14.4440	+	10.4942i	0.461867	+	0.335566i
$979$	−5.73845	+	17.6611i	−0.183402	+	0.564452i
$980$	−28.8767	−	88.8734i	−0.922433	−	2.83896i
$981$	2.91641	−	2.11890i	0.0931139	−	0.0676512i
$982$	17.4713	+	53.7711i	0.557531	+	1.71590i
$983$	−7.15532	−	5.19865i	−0.228219	−	0.165811i	0.467799	−	0.883835i	$-0.345047\pi$
$983$	−7.15532	−	5.19865i	−0.228219	−	0.165811i	−0.696019	+	0.718024i	$0.745047\pi$
$984$	11.5671	+	8.40402i	0.368747	+	0.267910i
$985$	4.38775	−	3.18788i	0.139805	−	0.101574i
$986$	−4.71425			−0.150132
$987$	12.3395			0.392769
$988$	30.8471	−	22.4118i	0.981378	−	0.713013i
$989$	1.64255	−	5.05525i	0.0522300	−	0.160747i
$990$	2.61062	+	8.03466i	0.0829710	+	0.255358i
$991$	20.1456			0.639947			0.319974	−	0.947426i	$-0.396326\pi$
$991$	20.1456			0.639947			0.319974	+	0.947426i	$0.396326\pi$
$992$	−16.4554	+	164.331i	−0.522458	+	5.21751i
$993$	−2.66693			−0.0846326
$994$	8.29150	+	25.5186i	0.262990	+	0.809401i
$995$	4.07777	−	12.5501i	0.129274	−	0.397865i
$996$	−34.7968	+	25.2813i	−1.10258	+	0.801070i
$997$	4.65564			0.147445			0.0737227	−	0.997279i	$-0.476512\pi$
$997$	4.65564			0.147445			0.0737227	+	0.997279i	$0.476512\pi$
$998$	−43.2892			−1.37030
$999$	−4.05854	+	2.94870i	−0.128407	+	0.0932928i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.n.e.376.1	yes	20
31.8	even	5	inner	465.2.n.e.256.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.n.e.256.1	✓	20	31.8	even	5	inner
465.2.n.e.376.1	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.864242 - 2.65986i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-4.70992 + 3.42196i) q^{4} -1.00000 q^{5} +2.79674 q^{6} +(3.88423 - 2.82206i) q^{7} +(8.64721 + 6.28257i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.864242 + 2.65986i) q^{10} +(-2.44380 + 1.77553i) q^{11} +(-1.79903 - 5.53684i) q^{12} +(1.17463 - 3.61513i) q^{13} +(-10.8632 - 7.89258i) q^{14} +(0.309017 - 0.951057i) q^{15} +(5.63942 - 17.3564i) q^{16} +(-1.54523 - 1.12267i) q^{17} +(-0.864242 + 2.65986i) q^{18} +(-0.532434 - 1.63866i) q^{19} +(4.70992 - 3.42196i) q^{20} +(1.48364 + 4.56619i) q^{21} +(6.83469 + 4.96570i) q^{22} +(-3.47275 - 2.52310i) q^{23} +(-8.64721 + 6.28257i) q^{24} +1.00000 q^{25} -10.6309 q^{26} +(0.809017 - 0.587785i) q^{27} +(-8.63745 + 26.5834i) q^{28} +(0.272714 + 0.839327i) q^{29} -2.79674 q^{30} +(0.554757 - 5.54006i) q^{31} -29.6623 q^{32} +(-0.933450 - 2.87286i) q^{33} +(-1.65071 + 5.08035i) q^{34} +(-3.88423 + 2.82206i) q^{35} +5.82178 q^{36} -5.01663 q^{37} +(-3.89847 + 2.83240i) q^{38} +(3.07522 + 2.23428i) q^{39} +(-8.64721 - 6.28257i) q^{40} +(-0.413364 - 1.27220i) q^{41} +(10.8632 - 7.89258i) q^{42} +(0.382651 + 1.17768i) q^{43} +(5.43434 - 16.7252i) q^{44} +(0.809017 + 0.587785i) q^{45} +(-3.70980 + 11.4176i) q^{46} +(0.794202 - 2.44430i) q^{47} +(14.7642 + 10.7268i) q^{48} +(4.96012 - 15.2657i) q^{49} +(-0.864242 - 2.65986i) q^{50} +(1.54523 - 1.12267i) q^{51} +(6.83843 + 21.0465i) q^{52} +(1.49628 + 1.08711i) q^{53} +(-2.26261 - 1.64389i) q^{54} +(2.44380 - 1.77553i) q^{55} +51.3176 q^{56} +1.72299 q^{57} +(1.99680 - 1.45076i) q^{58} +(3.71658 - 11.4384i) q^{59} +(1.79903 + 5.53684i) q^{60} -11.3292 q^{61} +(-15.2152 + 3.31237i) q^{62} -4.80118 q^{63} +(14.3565 + 44.1848i) q^{64} +(-1.17463 + 3.61513i) q^{65} +(-6.83469 + 4.96570i) q^{66} -4.69083 q^{67} +11.1196 q^{68} +(3.47275 - 2.52310i) q^{69} +(10.8632 + 7.89258i) q^{70} +(-1.61662 - 1.17454i) q^{71} +(-3.30294 - 10.1654i) q^{72} +(12.3093 - 8.94321i) q^{73} +(4.33558 + 13.3436i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(8.11516 + 5.89601i) q^{76} +(-4.48166 + 13.7931i) q^{77} +(3.28513 - 10.1106i) q^{78} +(-3.61852 - 2.62901i) q^{79} +(-5.63942 + 17.3564i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-3.02664 + 2.19898i) q^{82} +(-2.28301 - 7.02638i) q^{83} +(-22.6131 - 16.4294i) q^{84} +(1.54523 + 1.12267i) q^{85} +(2.80176 - 2.03560i) q^{86} -0.882521 q^{87} -32.2870 q^{88} +(4.97349 - 3.61345i) q^{89} +(0.864242 - 2.65986i) q^{90} +(-5.63960 - 17.3569i) q^{91} +24.9903 q^{92} +(5.09748 + 2.23958i) q^{93} -7.18789 q^{94} +(0.532434 + 1.63866i) q^{95} +(9.16615 - 28.2105i) q^{96} +(4.30594 - 3.12845i) q^{97} -44.8914 q^{98} +3.02071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + 5 q^{3} - 7 q^{4} - 20 q^{5} + 6 q^{6} + 3 q^{7} + 7 q^{8} - 5 q^{9} + q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{13} - 21 q^{14} - 5 q^{15} + 15 q^{16} - 8 q^{17} - q^{18} - 15 q^{19} + 7 q^{20}+ \cdots + 14 q^{99}+O(q^{100}) \) 20 * q - q^2 + 5 * q^3 - 7 * q^4 - 20 * q^5 + 6 * q^6 + 3 * q^7 + 7 * q^8 - 5 * q^9 + q^10 - 6 * q^11 + 2 * q^12 + 2 * q^13 - 21 * q^14 - 5 * q^15 + 15 * q^16 - 8 * q^17 - q^18 - 15 * q^19 + 7 * q^20 - 3 * q^21 - 15 * q^22 + 12 * q^23 - 7 * q^24 + 20 * q^25 - 28 * q^26 + 5 * q^27 - 29 * q^28 - 11 * q^29 - 6 * q^30 - 6 * q^31 - 92 * q^32 + q^33 + 9 * q^34 - 3 * q^35 + 18 * q^36 + 10 * q^37 + q^38 - 2 * q^39 - 7 * q^40 + 18 * q^41 + 21 * q^42 + 3 * q^43 - 29 * q^44 + 5 * q^45 - 16 * q^46 + 2 * q^47 + 30 * q^48 + 4 * q^49 - q^50 + 8 * q^51 + 31 * q^52 - 14 * q^53 - 4 * q^54 + 6 * q^55 + 110 * q^56 + 10 * q^57 - 45 * q^58 + 12 * q^59 - 2 * q^60 - 4 * q^61 - 16 * q^62 - 12 * q^63 + 33 * q^64 - 2 * q^65 + 15 * q^66 - 8 * q^67 + 28 * q^68 - 12 * q^69 + 21 * q^70 - 12 * q^71 + 2 * q^72 + 28 * q^73 - 23 * q^74 + 5 * q^75 + 45 * q^76 + 26 * q^77 + 3 * q^78 - 15 * q^80 - 5 * q^81 - 53 * q^82 + 4 * q^83 - 46 * q^84 + 8 * q^85 + 38 * q^86 - 4 * q^87 - 62 * q^88 + 4 * q^89 + q^90 + 28 * q^91 + 66 * q^92 + 31 * q^93 + 12 * q^94 + 15 * q^95 + 7 * q^96 + 66 * q^97 - 104 * q^98 + 14 * q^99

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