LMFDB - Embedded newform 350.2.h.b.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 6 x^{10} + x^{9} - 14 x^{8} + 10 x^{7} + 35 x^{6} - 110 x^{5} + 230 x^{4} + \cdots + 125 $ x^12 - 4x^11 + 6x^10 + x^9 - 14x^8 + 10x^7 + 35x^6 - 110x^5 + 230x^4 - 325x^3 + 300x^2 - 250x + 125
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.3
Root			$1.17529 + 0.0257946i$ of defining polynomial
Character	$\chi$	$=$	350.71
Dual form			350.2.h.b.281.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(1.71998 + 1.24964i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.14128 + 0.644154i) q^{5} +(-1.71998 + 1.24964i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.469677 + 1.44552i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(1.71998 + 1.24964i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.14128 + 0.644154i) q^{5} +(-1.71998 + 1.24964i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.469677 + 1.44552i) q^{9} +(0.0490643 - 2.23553i) q^{10} +(-1.71067 + 5.26491i) q^{11} +(-0.656972 - 2.02195i) q^{12} +(0.963285 + 2.96469i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-4.48790 - 1.56789i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.23503 + 1.62384i) q^{17} -1.51991 q^{18} +(-3.56549 + 2.59048i) q^{19} +(2.11095 + 0.737480i) q^{20} +(-1.71998 - 1.24964i) q^{21} +(-4.47860 - 3.25389i) q^{22} +(0.681942 - 2.09880i) q^{23} +2.12601 q^{24} +(4.17013 - 2.75862i) q^{25} -3.11725 q^{26} +(0.972381 - 2.99268i) q^{27} +(0.809017 + 0.587785i) q^{28} +(6.93966 + 5.04196i) q^{29} +(2.87799 - 3.78374i) q^{30} +(8.38622 - 6.09294i) q^{31} -1.00000 q^{32} +(-9.52153 + 6.91780i) q^{33} +(-0.853705 - 2.62743i) q^{34} +(2.14128 - 0.644154i) q^{35} +(0.469677 - 1.44552i) q^{36} +(-1.75390 - 5.39795i) q^{37} +(-1.36189 - 4.19148i) q^{38} +(-2.04795 + 6.30294i) q^{39} +(-1.35371 + 1.77974i) q^{40} +(0.729413 + 2.24490i) q^{41} +(1.71998 - 1.24964i) q^{42} +4.41997 q^{43} +(4.47860 - 3.25389i) q^{44} +(-1.93684 - 2.79271i) q^{45} +(1.78535 + 1.29713i) q^{46} +(-5.97964 - 4.34446i) q^{47} +(-0.656972 + 2.02195i) q^{48} +1.00000 q^{49} +(1.33496 + 4.81849i) q^{50} -5.87341 q^{51} +(0.963285 - 2.96469i) q^{52} +(7.58227 + 5.50884i) q^{53} +(2.54573 + 1.84958i) q^{54} +(0.271613 - 12.3756i) q^{55} +(-0.809017 + 0.587785i) q^{56} -9.36970 q^{57} +(-6.93966 + 5.04196i) q^{58} +(2.42691 + 7.46927i) q^{59} +(2.70921 + 3.90637i) q^{60} +(-0.775006 + 2.38522i) q^{61} +(3.20325 + 9.85859i) q^{62} +(-0.469677 - 1.44552i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.97237 - 5.72771i) q^{65} +(-3.63690 - 11.1932i) q^{66} +(-5.12885 + 3.72633i) q^{67} +2.76265 q^{68} +(3.79566 - 2.75771i) q^{69} +(-0.0490643 + 2.23553i) q^{70} +(-2.75939 - 2.00481i) q^{71} +(1.22963 + 0.893378i) q^{72} +(-0.452770 + 1.39348i) q^{73} +5.67574 q^{74} +(10.6198 + 0.466381i) q^{75} +4.40718 q^{76} +(1.71067 - 5.26491i) q^{77} +(-5.36160 - 3.89543i) q^{78} +(7.51570 + 5.46048i) q^{79} +(-1.27432 - 1.83742i) q^{80} +(9.10112 - 6.61235i) q^{81} -2.36043 q^{82} +(-12.1993 + 8.86331i) q^{83} +(0.656972 + 2.02195i) q^{84} +(3.73981 - 4.91680i) q^{85} +(-1.36585 + 4.20365i) q^{86} +(5.63544 + 17.3441i) q^{87} +(1.71067 + 5.26491i) q^{88} +(0.851517 - 2.62070i) q^{89} +(3.25454 - 0.979053i) q^{90} +(-0.963285 - 2.96469i) q^{91} +(-1.78535 + 1.29713i) q^{92} +22.0381 q^{93} +(5.97964 - 4.34446i) q^{94} +(5.96603 - 7.84365i) q^{95} +(-1.71998 - 1.24964i) q^{96} +(7.01947 + 5.09995i) q^{97} +(-0.309017 + 0.951057i) q^{98} -8.41397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9} + 7 q^{11} - 4 q^{12} + 3 q^{13} - 3 q^{14} - 10 q^{15} - 3 q^{16} + 4 q^{17} - 6 q^{18} + 4 q^{19} + 5 q^{20} - q^{21} - 2 q^{22} - q^{23} - 6 q^{24} - 5 q^{25} + 12 q^{26} + 10 q^{27} + 3 q^{28} + 22 q^{29} + 15 q^{30} + 31 q^{31} - 12 q^{32} - 21 q^{33} + 6 q^{34} + 5 q^{35} + 6 q^{36} + 9 q^{37} - 4 q^{38} - 20 q^{39} - 19 q^{41} + q^{42} + 50 q^{43} + 2 q^{44} - 25 q^{45} + 16 q^{46} - 24 q^{47} - 4 q^{48} + 12 q^{49} - 58 q^{51} + 3 q^{52} + 35 q^{53} + 25 q^{54} - 10 q^{55} - 3 q^{56} - 44 q^{57} - 22 q^{58} + q^{59} - 5 q^{60} + 8 q^{61} + 19 q^{62} - 6 q^{63} - 3 q^{64} - 25 q^{65} - 14 q^{66} - 36 q^{67} + 4 q^{68} - 31 q^{69} + q^{71} + 9 q^{72} - 31 q^{73} - 14 q^{74} + 55 q^{75} - 16 q^{76} - 7 q^{77} - 30 q^{78} + 2 q^{79} - 8 q^{81} - 6 q^{82} - 19 q^{83} + 4 q^{84} + 20 q^{85} + 10 q^{86} + 28 q^{87} - 7 q^{88} + 40 q^{89} + 20 q^{90} - 3 q^{91} - 16 q^{92} + 50 q^{93} + 24 q^{94} - q^{96} + 28 q^{97} + 3 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9 + 7 * q^11 - 4 * q^12 + 3 * q^13 - 3 * q^14 - 10 * q^15 - 3 * q^16 + 4 * q^17 - 6 * q^18 + 4 * q^19 + 5 * q^20 - q^21 - 2 * q^22 - q^23 - 6 * q^24 - 5 * q^25 + 12 * q^26 + 10 * q^27 + 3 * q^28 + 22 * q^29 + 15 * q^30 + 31 * q^31 - 12 * q^32 - 21 * q^33 + 6 * q^34 + 5 * q^35 + 6 * q^36 + 9 * q^37 - 4 * q^38 - 20 * q^39 - 19 * q^41 + q^42 + 50 * q^43 + 2 * q^44 - 25 * q^45 + 16 * q^46 - 24 * q^47 - 4 * q^48 + 12 * q^49 - 58 * q^51 + 3 * q^52 + 35 * q^53 + 25 * q^54 - 10 * q^55 - 3 * q^56 - 44 * q^57 - 22 * q^58 + q^59 - 5 * q^60 + 8 * q^61 + 19 * q^62 - 6 * q^63 - 3 * q^64 - 25 * q^65 - 14 * q^66 - 36 * q^67 + 4 * q^68 - 31 * q^69 + q^71 + 9 * q^72 - 31 * q^73 - 14 * q^74 + 55 * q^75 - 16 * q^76 - 7 * q^77 - 30 * q^78 + 2 * q^79 - 8 * q^81 - 6 * q^82 - 19 * q^83 + 4 * q^84 + 20 * q^85 + 10 * q^86 + 28 * q^87 - 7 * q^88 + 40 * q^89 + 20 * q^90 - 3 * q^91 - 16 * q^92 + 50 * q^93 + 24 * q^94 - q^96 + 28 * q^97 + 3 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	1.71998	+	1.24964i	0.993028	+	0.721477i	0.960582	−	0.277996i	$-0.0896702\pi$
$3$	1.71998	+	1.24964i	0.993028	+	0.721477i	0.0324462	+	0.999473i	$0.489670\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−2.14128	+	0.644154i	−0.957608	+	0.288074i
$5$	−2.14128	+	0.644154i	−0.957608	+	0.288074i
$6$	−1.71998	+	1.24964i	−0.702177	+	0.510162i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.469677	+	1.44552i	0.156559	+	0.481839i
$10$	0.0490643	−	2.23553i	0.0155155	−	0.706937i
$11$	−1.71067	+	5.26491i	−0.515787	+	1.58743i	0.266058	+	0.963957i	$0.414279\pi$
$11$	−1.71067	+	5.26491i	−0.515787	+	1.58743i	−0.781845	+	0.623472i	$0.785721\pi$
$12$	−0.656972	−	2.02195i	−0.189652	−	0.583687i
$13$	0.963285	+	2.96469i	0.267167	+	0.822256i	0.991186	+	0.132476i	$0.0422927\pi$
$13$	0.963285	+	2.96469i	0.267167	+	0.822256i	−0.724019	+	0.689780i	$0.757707\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	−4.48790	−	1.56789i	−1.15877	−	0.404827i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.23503	+	1.62384i	−0.542074	+	0.393840i	−0.824855	−	0.565345i	$-0.808743\pi$
$17$	−2.23503	+	1.62384i	−0.542074	+	0.393840i	0.282781	+	0.959185i	$0.408743\pi$
$18$	−1.51991			−0.358245
$19$	−3.56549	+	2.59048i	−0.817979	+	0.594296i	−0.916133	−	0.400875i	$-0.868706\pi$
$19$	−3.56549	+	2.59048i	−0.817979	+	0.594296i	0.0981542	+	0.995171i	$0.468706\pi$
$20$	2.11095	+	0.737480i	0.472024	+	0.164905i
$21$	−1.71998	−	1.24964i	−0.375329	−	0.272693i
$22$	−4.47860	−	3.25389i	−0.954840	−	0.693732i
$23$	0.681942	−	2.09880i	0.142195	−	0.437631i	−0.854445	−	0.519542i	$-0.826102\pi$
$23$	0.681942	−	2.09880i	0.142195	−	0.437631i	0.996640	+	0.0819115i	$0.0261025\pi$
$24$	2.12601			0.433969
$25$	4.17013	−	2.75862i	0.834026	−	0.551725i
$26$	−3.11725			−0.611344
$27$	0.972381	−	2.99268i	0.187135	−	0.575942i
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	6.93966	+	5.04196i	1.28866	+	0.936268i	0.999777	−	0.0210958i	$-0.00671550\pi$
$29$	6.93966	+	5.04196i	1.28866	+	0.936268i	0.288885	+	0.957364i	$0.406715\pi$
$30$	2.87799	−	3.78374i	0.525446	−	0.690814i
$31$	8.38622	−	6.09294i	1.50621	−	1.09433i	0.538385	−	0.842699i	$-0.319035\pi$
$31$	8.38622	−	6.09294i	1.50621	−	1.09433i	0.967825	−	0.251626i	$-0.0809653\pi$
$32$	−1.00000			−0.176777
$33$	−9.52153	+	6.91780i	−1.65749	+	1.20423i
$34$	−0.853705	−	2.62743i	−0.146409	−	0.450601i
$35$	2.14128	−	0.644154i	0.361942	−	0.108882i
$36$	0.469677	−	1.44552i	0.0782794	−	0.240919i
$37$	−1.75390	−	5.39795i	−0.288340	−	0.887418i	−0.985378	−	0.170384i	$-0.945499\pi$
$37$	−1.75390	−	5.39795i	−0.288340	−	0.887418i	0.697038	−	0.717034i	$-0.254501\pi$
$38$	−1.36189	−	4.19148i	−0.220928	−	0.679948i
$39$	−2.04795	+	6.30294i	−0.327934	+	1.00928i
$40$	−1.35371	+	1.77974i	−0.214040	+	0.281402i
$41$	0.729413	+	2.24490i	0.113915	+	0.350595i	0.991719	−	0.128425i	$-0.0409922\pi$
$41$	0.729413	+	2.24490i	0.113915	+	0.350595i	−0.877804	+	0.479020i	$0.840992\pi$
$42$	1.71998	−	1.24964i	0.265398	−	0.192823i
$43$	4.41997			0.674040			0.337020	−	0.941498i	$-0.390581\pi$
$43$	4.41997			0.674040			0.337020	+	0.941498i	$0.390581\pi$
$44$	4.47860	−	3.25389i	0.675174	−	0.490543i
$45$	−1.93684	−	2.79271i	−0.288727	−	0.416312i
$46$	1.78535	+	1.29713i	0.263235	+	0.191252i
$47$	−5.97964	−	4.34446i	−0.872220	−	0.633705i	0.0589620	−	0.998260i	$-0.481221\pi$
$47$	−5.97964	−	4.34446i	−0.872220	−	0.633705i	−0.931182	+	0.364556i	$0.881221\pi$
$48$	−0.656972	+	2.02195i	−0.0948258	+	0.291844i
$49$	1.00000			0.142857
$50$	1.33496	+	4.81849i	0.188792	+	0.681438i
$51$	−5.87341			−0.822442
$52$	0.963285	−	2.96469i	0.133584	−	0.411128i
$53$	7.58227	+	5.50884i	1.04150	+	0.756697i	0.970579	−	0.240784i	$-0.0774046\pi$
$53$	7.58227	+	5.50884i	1.04150	+	0.756697i	0.0709258	+	0.997482i	$0.477405\pi$
$54$	2.54573	+	1.84958i	0.346430	+	0.251696i
$55$	0.271613	−	12.3756i	0.0366243	−	1.66872i
$56$	−0.809017	+	0.587785i	−0.108109	+	0.0785461i
$57$	−9.36970			−1.24105
$58$	−6.93966	+	5.04196i	−0.911222	+	0.662041i
$59$	2.42691	+	7.46927i	0.315957	+	0.972416i	0.975359	+	0.220625i	$0.0708098\pi$
$59$	2.42691	+	7.46927i	0.315957	+	0.972416i	−0.659401	+	0.751791i	$0.729190\pi$
$60$	2.70921	+	3.90637i	0.349757	+	0.504310i
$61$	−0.775006	+	2.38522i	−0.0992294	+	0.305397i	−0.988333	−	0.152310i	$-0.951329\pi$
$61$	−0.775006	+	2.38522i	−0.0992294	+	0.305397i	0.889103	+	0.457706i	$0.151329\pi$
$62$	3.20325	+	9.85859i	0.406813	+	1.25204i
$63$	−0.469677	−	1.44552i	−0.0591737	−	0.182118i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−3.97237	−	5.72771i	−0.492712	−	0.710435i
$66$	−3.63690	−	11.1932i	−0.447672	−	1.37779i
$67$	−5.12885	+	3.72633i	−0.626589	+	0.455243i	−0.855217	−	0.518271i	$-0.826576\pi$
$67$	−5.12885	+	3.72633i	−0.626589	+	0.455243i	0.228628	+	0.973514i	$0.426576\pi$
$68$	2.76265			0.335020
$69$	3.79566	−	2.75771i	0.456944	−	0.331989i
$70$	−0.0490643	+	2.23553i	−0.00586431	+	0.267197i
$71$	−2.75939	−	2.00481i	−0.327479	−	0.237927i	0.411881	−	0.911238i	$-0.364872\pi$
$71$	−2.75939	−	2.00481i	−0.327479	−	0.237927i	−0.739360	+	0.673310i	$0.764872\pi$
$72$	1.22963	+	0.893378i	0.144913	+	0.105286i
$73$	−0.452770	+	1.39348i	−0.0529927	+	0.163095i	−0.974050	−	0.226332i	$-0.927327\pi$
$73$	−0.452770	+	1.39348i	−0.0529927	+	0.163095i	0.921058	+	0.389426i	$0.127327\pi$
$74$	5.67574			0.659792
$75$	10.6198	+	0.466381i	1.22627	+	0.0538531i
$76$	4.40718			0.505539
$77$	1.71067	−	5.26491i	0.194949	−	0.599992i
$78$	−5.36160	−	3.89543i	−0.607082	−	0.441071i
$79$	7.51570	+	5.46048i	0.845582	+	0.614352i	0.923924	−	0.382575i	$-0.124963\pi$
$79$	7.51570	+	5.46048i	0.845582	+	0.614352i	−0.0783421	+	0.996927i	$0.524963\pi$
$80$	−1.27432	−	1.83742i	−0.142473	−	0.205430i
$81$	9.10112	−	6.61235i	1.01124	−	0.734706i
$82$	−2.36043			−0.260666
$83$	−12.1993	+	8.86331i	−1.33905	+	0.972875i	−0.339569	+	0.940581i	$0.610281\pi$
$83$	−12.1993	+	8.86331i	−1.33905	+	0.972875i	−0.999478	+	0.0322941i	$0.989719\pi$
$84$	0.656972	+	2.02195i	0.0716816	+	0.220613i
$85$	3.73981	−	4.91680i	0.405639	−	0.533302i
$86$	−1.36585	+	4.20365i	−0.147283	+	0.453291i
$87$	5.63544	+	17.3441i	0.604182	+	1.85948i
$88$	1.71067	+	5.26491i	0.182358	+	0.561241i
$89$	0.851517	−	2.62070i	0.0902606	−	0.277794i	−0.895729	−	0.444601i	$-0.853346\pi$
$89$	0.851517	−	2.62070i	0.0902606	−	0.277794i	0.985990	+	0.166807i	$0.0533457\pi$
$90$	3.25454	−	0.979053i	0.343058	−	0.103201i
$91$	−0.963285	−	2.96469i	−0.100980	−	0.310783i
$92$	−1.78535	+	1.29713i	−0.186135	+	0.135235i
$93$	22.0381			2.28524
$94$	5.97964	−	4.34446i	0.616752	−	0.448097i
$95$	5.96603	−	7.84365i	0.612101	−	0.804741i
$96$	−1.71998	−	1.24964i	−0.175544	−	0.127540i
$97$	7.01947	+	5.09995i	0.712719	+	0.517821i	0.884050	−	0.467393i	$-0.154807\pi$
$97$	7.01947	+	5.09995i	0.712719	+	0.517821i	−0.171330	+	0.985214i	$0.554807\pi$
$98$	−0.309017	+	0.951057i	−0.0312154	+	0.0960712i
$99$	−8.41397			−0.845636
$100$	−4.99519	−	0.219370i	−0.499519	−	0.0219370i
$101$	17.0210			1.69365			0.846826	−	0.531870i	$-0.178510\pi$
$101$	17.0210			1.69365			0.846826	+	0.531870i	$0.178510\pi$
$102$	1.81498	−	5.58594i	0.179710	−	0.553091i
$103$	−4.06269	−	2.95172i	−0.400309	−	0.290841i	0.369358	−	0.929287i	$-0.379578\pi$
$103$	−4.06269	−	2.95172i	−0.400309	−	0.290841i	−0.769667	+	0.638446i	$0.779578\pi$
$104$	2.52191	+	1.83228i	0.247294	+	0.179669i
$105$	4.48790	+	1.56789i	0.437974	+	0.153010i
$106$	−7.58227	+	5.50884i	−0.736455	+	0.535066i
$107$	7.58896			0.733652			0.366826	−	0.930290i	$-0.380444\pi$
$107$	7.58896			0.733652			0.366826	+	0.930290i	$0.380444\pi$
$108$	−2.54573	+	1.84958i	−0.244963	+	0.177976i
$109$	−6.12099	−	18.8385i	−0.586285	−	1.80440i	−0.594049	−	0.804429i	$-0.702472\pi$
$109$	−6.12099	−	18.8385i	−0.586285	−	1.80440i	0.00776483	−	0.999970i	$-0.497528\pi$
$110$	11.6859	+	4.08258i	1.11421	+	0.389258i
$111$	3.72881	−	11.4761i	0.353923	−	1.08926i
$112$	−0.309017	−	0.951057i	−0.0291994	−	0.0898664i
$113$	0.782425	+	2.40806i	0.0736044	+	0.226531i	0.981090	−	0.193552i	$-0.0620009\pi$
$113$	0.782425	+	2.40806i	0.0736044	+	0.226531i	−0.907486	+	0.420083i	$0.862001\pi$
$114$	2.89540	−	8.91112i	0.271179	−	0.834602i
$115$	−0.108276	+	4.93339i	−0.0100968	+	0.460041i
$116$	−2.65071	−	8.15806i	−0.246113	−	0.757457i
$117$	−3.83307	+	2.78489i	−0.354367	+	0.257463i
$118$	−7.85366			−0.722988
$119$	2.23503	−	1.62384i	0.204885	−	0.148858i
$120$	−4.55237	+	1.36948i	−0.415573	+	0.125015i
$121$	−15.8937	−	11.5474i	−1.44488	−	1.04977i
$122$	−2.02899	−	1.47415i	−0.183696	−	0.133463i
$123$	−1.55074	+	4.77268i	−0.139825	+	0.430338i
$124$	−10.3659			−0.930889
$125$	−7.15243	+	8.59318i	−0.639733	+	0.768597i
$126$	1.51991			0.135404
$127$	1.83115	−	5.63569i	0.162488	−	0.500087i	−0.836354	−	0.548189i	$-0.815317\pi$
$127$	1.83115	−	5.63569i	0.162488	−	0.500087i	0.998842	+	0.0481024i	$0.0153174\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	7.60225	+	5.52336i	0.669341	+	0.486304i
$130$	6.67490	−	2.00799i	0.585428	−	0.176112i
$131$	−11.8925	+	8.64041i	−1.03905	+	0.754916i	−0.970100	−	0.242704i	$-0.921966\pi$
$131$	−11.8925	+	8.64041i	−1.03905	+	0.754916i	−0.0689523	+	0.997620i	$0.521966\pi$
$132$	11.7693			1.02438
$133$	3.56549	−	2.59048i	0.309167	−	0.224623i
$134$	−1.95905	−	6.02932i	−0.169236	−	0.520854i
$135$	−0.154390	+	7.03452i	−0.0132878	+	0.605435i
$136$	−0.853705	+	2.62743i	−0.0732046	+	0.225301i
$137$	−3.07635	−	9.46804i	−0.262831	−	0.808909i	−0.992185	−	0.124774i	$-0.960180\pi$
$137$	−3.07635	−	9.46804i	−0.262831	−	0.808909i	0.729355	−	0.684136i	$-0.239820\pi$
$138$	1.44981	+	4.46207i	0.123416	+	0.379837i
$139$	−2.41226	+	7.42417i	−0.204605	+	0.629710i	0.795124	+	0.606447i	$0.207406\pi$
$139$	−2.41226	+	7.42417i	−0.204605	+	0.629710i	−0.999729	+	0.0232633i	$0.992594\pi$
$140$	−2.11095	−	0.737480i	−0.178408	−	0.0623284i
$141$	−4.85584	−	14.9447i	−0.408935	−	1.25857i
$142$	2.75939	−	2.00481i	0.231563	−	0.168240i
$143$	−17.2567			−1.44307
$144$	−1.22963	+	0.893378i	−0.102469	+	0.0744482i
$145$	−18.1075	−	6.32602i	−1.50375	−	0.525347i
$146$	−1.18537	−	0.861219i	−0.0981016	−	0.0712750i
$147$	1.71998	+	1.24964i	0.141861	+	0.103068i
$148$	−1.75390	+	5.39795i	−0.144170	+	0.443709i
$149$	9.20036			0.753723			0.376862	−	0.926270i	$-0.377003\pi$
$149$	9.20036			0.753723			0.376862	+	0.926270i	$0.377003\pi$
$150$	−3.72525	+	9.95591i	−0.304166	+	0.812897i
$151$	14.0420			1.14273			0.571363	−	0.820698i	$-0.306415\pi$
$151$	14.0420			1.14273			0.571363	+	0.820698i	$0.306415\pi$
$152$	−1.36189	+	4.19148i	−0.110464	+	0.339974i
$153$	−3.39703	−	2.46809i	−0.274634	−	0.199533i
$154$	4.47860	+	3.25389i	0.360896	+	0.262206i
$155$	−14.0324	+	18.4487i	−1.12711	+	1.48183i
$156$	5.36160	−	3.89543i	0.429272	−	0.311884i
$157$	−15.4929			−1.23647			−0.618235	−	0.785993i	$-0.712152\pi$
$157$	−15.4929			−1.23647			−0.618235	+	0.785993i	$0.712152\pi$
$158$	−7.51570	+	5.46048i	−0.597917	+	0.434412i
$159$	6.15727	+	18.9501i	0.488304	+	1.50284i
$160$	2.14128	−	0.644154i	0.169283	−	0.0509248i
$161$	−0.681942	+	2.09880i	−0.0537446	+	0.165409i
$162$	3.47632	+	10.6990i	0.273125	+	0.840594i
$163$	−4.64685	−	14.3015i	−0.363969	−	1.12018i	−0.950624	−	0.310345i	$-0.899556\pi$
$163$	−4.64685	−	14.3015i	−0.363969	−	1.12018i	0.586655	−	0.809837i	$-0.300444\pi$
$164$	0.729413	−	2.24490i	0.0569576	−	0.175297i
$165$	15.9321	−	20.9462i	1.24031	−	1.63066i
$166$	−4.65972	−	14.3411i	−0.361664	−	1.11309i
$167$	−15.0185	+	10.9116i	−1.16217	+	0.844364i	−0.990050	−	0.140713i	$-0.955061\pi$
$167$	−15.0185	+	10.9116i	−1.16217	+	0.844364i	−0.172117	+	0.985077i	$0.555061\pi$
$168$	−2.12601			−0.164025
$169$	2.65578	−	1.92954i	0.204291	−	0.148426i
$170$	3.52049	+	5.07615i	0.270009	+	0.389323i
$171$	−5.41920	−	3.93728i	−0.414417	−	0.301091i
$172$	−3.57583	−	2.59800i	−0.272655	−	0.198095i
$173$	5.16169	−	15.8860i	0.392436	−	1.20779i	−0.538504	−	0.842623i	$-0.681011\pi$
$173$	5.16169	−	15.8860i	0.392436	−	1.20779i	0.930940	−	0.365171i	$-0.118989\pi$
$174$	−18.2367			−1.38252
$175$	−4.17013	+	2.75862i	−0.315232	+	0.208532i
$176$	−5.53585			−0.417280
$177$	−5.15964	+	15.8797i	−0.387822	+	1.19359i
$178$	2.22930	+	1.61968i	0.167093	+	0.121400i
$179$	−4.56517	−	3.31679i	−0.341217	−	0.247909i	0.403958	−	0.914777i	$-0.367634\pi$
$179$	−4.56517	−	3.31679i	−0.341217	−	0.247909i	−0.745175	+	0.666869i	$0.767634\pi$
$180$	−0.0745731	+	3.39779i	−0.00555835	+	0.253257i
$181$	−3.74391	+	2.72011i	−0.278282	+	0.202184i	−0.718168	−	0.695870i	$-0.755019\pi$
$181$	−3.74391	+	2.72011i	−0.278282	+	0.202184i	0.439885	+	0.898054i	$0.355019\pi$
$182$	3.11725			0.231066
$183$	−4.31365	+	3.13405i	−0.318874	+	0.231676i
$184$	−0.681942	−	2.09880i	−0.0502735	−	0.154726i
$185$	7.23270	+	10.4287i	0.531759	+	0.766736i
$186$	−6.81013	+	20.9594i	−0.499343	+	1.53682i
$187$	−4.72599	−	14.5451i	−0.345598	−	1.06364i
$188$	2.28402	+	7.02948i	0.166579	+	0.512678i
$189$	−0.972381	+	2.99268i	−0.0707303	+	0.217686i
$190$	5.61615	+	8.09785i	0.407438	+	0.587480i
$191$	7.54112	+	23.2092i	0.545657	+	1.67936i	0.719424	+	0.694571i	$0.244406\pi$
$191$	7.54112	+	23.2092i	0.545657	+	1.67936i	−0.173767	+	0.984787i	$0.555594\pi$
$192$	1.71998	−	1.24964i	0.124129	−	0.0901847i
$193$	11.3722			0.818589			0.409294	−	0.912402i	$-0.365775\pi$
$193$	11.3722			0.818589			0.409294	+	0.912402i	$0.365775\pi$
$194$	−7.01947	+	5.09995i	−0.503969	+	0.366155i
$195$	0.325164	−	14.8155i	0.0232855	−	1.06096i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	2.00188	+	1.45445i	0.142628	+	0.103625i	0.656811	−	0.754055i	$-0.271905\pi$
$197$	2.00188	+	1.45445i	0.142628	+	0.103625i	−0.514183	+	0.857680i	$0.671905\pi$
$198$	2.60006	−	8.00216i	0.184778	−	0.568689i
$199$	−13.3344			−0.945254			−0.472627	−	0.881263i	$-0.656694\pi$
$199$	−13.3344			−0.945254			−0.472627	+	0.881263i	$0.656694\pi$
$200$	1.75223	−	4.68291i	0.123901	−	0.331132i
$201$	−13.4780			−0.950668
$202$	−5.25978	+	16.1879i	−0.370077	+	1.13898i
$203$	−6.93966	−	5.04196i	−0.487069	−	0.353876i
$204$	4.75169	+	3.45230i	0.332685	+	0.241710i
$205$	−3.00794	−	4.33710i	−0.210083	−	0.302916i
$206$	4.06269	−	2.95172i	0.283061	−	0.205656i
$207$	3.35415			0.233129
$208$	−2.52191	+	1.83228i	−0.174863	+	0.127046i
$209$	−7.53924	−	23.2034i	−0.521500	−	1.60501i
$210$	−2.87799	+	3.78374i	−0.198600	+	0.261103i
$211$	−4.09236	+	12.5950i	−0.281730	+	0.867074i	0.705630	+	0.708580i	$0.250664\pi$
$211$	−4.09236	+	12.5950i	−0.281730	+	0.867074i	−0.987360	+	0.158494i	$0.949336\pi$
$212$	−2.89617	−	8.91349i	−0.198910	−	0.612181i
$213$	−2.24079	−	6.89645i	−0.153537	−	0.472537i
$214$	−2.34512	+	7.21753i	−0.160309	+	0.493380i
$215$	−9.46439	+	2.84714i	−0.645466	+	0.194174i
$216$	−0.972381	−	2.99268i	−0.0661622	−	0.203626i
$217$	−8.38622	+	6.09294i	−0.569294	+	0.413616i
$218$	19.8079			1.34156
$219$	−2.52010	+	1.83096i	−0.170292	+	0.123725i
$220$	−7.49391	+	9.85239i	−0.505239	+	0.664248i
$221$	−6.96716	−	5.06193i	−0.468662	−	0.340503i
$222$	9.76214	+	7.09261i	0.655192	+	0.476025i
$223$	3.36353	−	10.3519i	0.225238	−	0.693212i	−0.773029	−	0.634371i	$-0.781259\pi$
$223$	3.36353	−	10.3519i	0.225238	−	0.693212i	0.998267	−	0.0588417i	$-0.0187407\pi$
$224$	1.00000			0.0668153
$225$	5.94625	+	4.73233i	0.396416	+	0.315489i
$226$	−2.53198			−0.168425
$227$	0.906960	−	2.79133i	0.0601970	−	0.185267i	−0.916436	−	0.400181i	$-0.868947\pi$
$227$	0.906960	−	2.79133i	0.0601970	−	0.185267i	0.976633	+	0.214914i	$0.0689471\pi$
$228$	7.58025	+	5.50737i	0.502014	+	0.364735i
$229$	8.76378	+	6.36726i	0.579127	+	0.420760i	0.838409	−	0.545041i	$-0.183486\pi$
$229$	8.76378	+	6.36726i	0.579127	+	0.420760i	−0.259282	+	0.965802i	$0.583486\pi$
$230$	−4.65848	−	1.62748i	−0.307171	−	0.107313i
$231$	9.52153	−	6.91780i	0.626471	−	0.455158i
$232$	8.57789			0.563166
$233$	19.5564	−	14.2086i	1.28118	−	0.930835i	0.281596	−	0.959533i	$-0.409136\pi$
$233$	19.5564	−	14.2086i	1.28118	−	0.930835i	0.999588	+	0.0286983i	$0.00913619\pi$
$234$	−1.46410	−	4.50604i	−0.0957113	−	0.294569i
$235$	15.6026	+	5.45089i	1.01780	+	0.355577i
$236$	2.42691	−	7.46927i	0.157979	−	0.486208i
$237$	6.10322	+	18.7838i	0.396447	+	1.22014i
$238$	0.853705	+	2.62743i	0.0553375	+	0.170311i
$239$	3.61464	−	11.1247i	0.233812	−	0.719598i	−0.763465	−	0.645849i	$-0.776504\pi$
$239$	3.61464	−	11.1247i	0.233812	−	0.719598i	0.997277	−	0.0737493i	$-0.0234965\pi$
$240$	0.104311	−	4.75275i	0.00673325	−	0.306789i
$241$	−3.23808	−	9.96577i	−0.208583	−	0.641952i	−0.999547	−	0.0300897i	$-0.990421\pi$
$241$	−3.23808	−	9.96577i	−0.208583	−	0.641952i	0.790964	−	0.611862i	$-0.209579\pi$
$242$	15.8937	−	11.5474i	1.02168	−	0.742296i
$243$	14.4767			0.928678
$244$	2.02899	−	1.47415i	0.129893	−	0.0943728i
$245$	−2.14128	+	0.644154i	−0.136801	+	0.0411535i
$246$	−4.05988	−	2.94968i	−0.258849	−	0.188065i
$247$	−11.1145	−	8.07518i	−0.707200	−	0.513811i
$248$	3.20325	−	9.85859i	0.203407	−	0.626021i
$249$	−32.0584			−2.03162
$250$	−5.96238	−	9.45780i	−0.377094	−	0.598164i
$251$	11.9118			0.751864			0.375932	−	0.926647i	$-0.377323\pi$
$251$	11.9118			0.751864			0.375932	+	0.926647i	$0.377323\pi$
$252$	−0.469677	+	1.44552i	−0.0295868	+	0.0910589i
$253$	9.88342	+	7.18073i	0.621366	+	0.451448i
$254$	4.79401	+	3.48305i	0.300803	+	0.218546i
$255$	12.5766	−	3.78338i	0.787577	−	0.236924i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.1930			−1.32198			−0.660992	−	0.750393i	$-0.729864\pi$
$257$	−21.1930			−1.32198			−0.660992	+	0.750393i	$0.729864\pi$
$258$	−7.60225	+	5.52336i	−0.473295	+	0.343869i
$259$	1.75390	+	5.39795i	0.108982	+	0.335413i
$260$	−0.152946	+	6.96872i	−0.00948531	+	0.432181i
$261$	−4.02883	+	12.3995i	−0.249379	+	0.767508i
$262$	−4.54253	−	13.9805i	−0.280639	−	0.863717i
$263$	−5.80537	−	17.8671i	−0.357975	−	1.10173i	−0.954265	−	0.298964i	$-0.903359\pi$
$263$	−5.80537	−	17.8671i	−0.357975	−	1.10173i	0.596290	−	0.802769i	$-0.296641\pi$
$264$	−3.63690	+	11.1932i	−0.223836	+	0.688896i
$265$	−19.7843	−	6.91180i	−1.21534	−	0.424589i
$266$	1.36189	+	4.19148i	0.0835031	+	0.256996i
$267$	4.73951	−	3.44345i	0.290053	−	0.210736i
$268$	6.33961			0.387253
$269$	4.45473	−	3.23655i	0.271610	−	0.197336i	−0.443640	−	0.896205i	$-0.646313\pi$
$269$	4.45473	−	3.23655i	0.271610	−	0.197336i	0.715250	+	0.698869i	$0.246313\pi$
$270$	−6.64252	−	2.32062i	−0.404251	−	0.141228i
$271$	24.6769	+	17.9288i	1.49901	+	1.08910i	0.970772	+	0.240003i	$0.0771484\pi$
$271$	24.6769	+	17.9288i	1.49901	+	1.08910i	0.528241	+	0.849094i	$0.322852\pi$
$272$	−2.23503	−	1.62384i	−0.135519	−	0.0984600i
$273$	2.04795	−	6.30294i	0.123948	−	0.381471i
$274$	9.95529			0.601421
$275$	7.39016	+	26.6745i	0.445644	+	1.60853i
$276$	−4.69170			−0.282407
$277$	8.47838	−	26.0938i	0.509416	−	1.56782i	−0.283801	−	0.958883i	$-0.591595\pi$
$277$	8.47838	−	26.0938i	0.509416	−	1.56782i	0.793217	−	0.608939i	$-0.208405\pi$
$278$	−6.31538	−	4.58839i	−0.378771	−	0.275193i
$279$	12.7463	+	9.26070i	0.763099	+	0.554424i
$280$	1.35371	−	1.77974i	0.0808994	−	0.106360i
$281$	6.69616	−	4.86505i	0.399460	−	0.290224i	−0.369861	−	0.929087i	$-0.620595\pi$
$281$	6.69616	−	4.86505i	0.399460	−	0.290224i	0.769321	+	0.638863i	$0.220595\pi$
$282$	15.7138			0.935744
$283$	−9.83104	+	7.14267i	−0.584395	+	0.424588i	−0.840306	−	0.542113i	$-0.817625\pi$
$283$	−9.83104	+	7.14267i	−0.584395	+	0.424588i	0.255911	+	0.966700i	$0.417625\pi$
$284$	1.05399	+	3.24385i	0.0625429	+	0.192487i
$285$	20.0631	−	6.03553i	1.18844	−	0.357514i
$286$	5.33260	−	16.4121i	0.315323	−	0.970465i
$287$	−0.729413	−	2.24490i	−0.0430559	−	0.132512i
$288$	−0.469677	−	1.44552i	−0.0276760	−	0.0851778i
$289$	−2.89480	+	8.90928i	−0.170282	+	0.524076i
$290$	11.6119	−	15.2664i	0.681876	−	0.896476i
$291$	5.70025	+	17.5436i	0.334155	+	1.02842i
$292$	1.18537	−	0.861219i	0.0693683	−	0.0503990i
$293$	−12.2645			−0.716501			−0.358250	−	0.933626i	$-0.616627\pi$
$293$	−12.2645			−0.716501			−0.358250	+	0.933626i	$0.616627\pi$
$294$	−1.71998	+	1.24964i	−0.100311	+	0.0728802i
$295$	−10.0081	−	14.4305i	−0.582691	−	0.840175i
$296$	−4.59177	−	3.33612i	−0.266891	−	0.193908i
$297$	14.0928	+	10.2390i	0.817745	+	0.594127i
$298$	−2.84307	+	8.75007i	−0.164695	+	0.506878i
$299$	6.87920			0.397834
$300$	−8.31747	−	6.61947i	−0.480209	−	0.382175i
$301$	−4.41997			−0.254763
$302$	−4.33923	+	13.3548i	−0.249695	+	0.768481i
$303$	29.2757	+	21.2700i	1.68185	+	1.22193i
$304$	−3.56549	−	2.59048i	−0.204495	−	0.148574i
$305$	0.123052	−	5.60665i	0.00704594	−	0.321036i
$306$	3.39703	−	2.46809i	0.194195	−	0.141091i
$307$	9.09326			0.518980			0.259490	−	0.965746i	$-0.416446\pi$
$307$	9.09326			0.518980			0.259490	+	0.965746i	$0.416446\pi$
$308$	−4.47860	+	3.25389i	−0.255192	+	0.185408i
$309$	−3.29916	−	10.1538i	−0.187683	−	0.577628i
$310$	−13.2095	−	19.0466i	−0.750249	−	1.08177i
$311$	−1.07998	+	3.32385i	−0.0612403	+	0.188478i	−0.976996	−	0.213257i	$-0.931593\pi$
$311$	−1.07998	+	3.32385i	−0.0612403	+	0.188478i	0.915756	+	0.401735i	$0.131593\pi$
$312$	2.04795	+	6.30294i	0.115942	+	0.356834i
$313$	3.47417	+	10.6924i	0.196372	+	0.604370i	0.999958	+	0.00918140i	$0.00292257\pi$
$313$	3.47417	+	10.6924i	0.196372	+	0.604370i	−0.803586	+	0.595188i	$0.797077\pi$
$314$	4.78758	−	14.7347i	0.270179	−	0.831525i
$315$	1.93684	+	2.79271i	0.109129	+	0.157351i
$316$	−2.87074	−	8.83524i	−0.161492	−	0.497021i
$317$	−10.1419	+	7.36850i	−0.569624	+	0.413856i	−0.834969	−	0.550298i	$-0.814514\pi$
$317$	−10.1419	+	7.36850i	−0.569624	+	0.413856i	0.265345	+	0.964154i	$0.414514\pi$
$318$	−19.9254			−1.11736
$319$	−38.4169	+	27.9115i	−2.15093	+	1.56275i
$320$	−0.0490643	+	2.23553i	−0.00274278	+	0.124970i
$321$	13.0528	+	9.48343i	0.728538	+	0.529314i
$322$	−1.78535	−	1.29713i	−0.0994936	−	0.0722863i
$323$	3.76243	−	11.5796i	0.209347	−	0.644305i
$324$	−11.2496			−0.624978
$325$	12.1955	+	9.70579i	0.676483	+	0.538380i
$326$	15.0375			0.832850
$327$	13.0133	−	40.0507i	0.719635	−	2.21481i
$328$	1.90963	+	1.38743i	0.105442	+	0.0766078i
$329$	5.97964	+	4.34446i	0.329668	+	0.239518i
$330$	14.9978	+	21.6251i	0.825600	+	1.19042i
$331$	−21.1242	+	15.3476i	−1.16109	+	0.843580i	−0.989915	−	0.141661i	$-0.954756\pi$
$331$	−21.1242	+	15.3476i	−1.16109	+	0.843580i	−0.171173	+	0.985241i	$0.554756\pi$
$332$	15.0792			0.827577
$333$	6.97906	−	5.07058i	0.382450	−	0.277866i
$334$	−5.73656	−	17.6553i	−0.313891	−	0.966056i
$335$	8.58196	−	11.2829i	0.468882	−	0.616449i
$336$	0.656972	−	2.02195i	0.0358408	−	0.110307i
$337$	−1.16577	−	3.58788i	−0.0635036	−	0.195444i	0.914271	−	0.405103i	$-0.132764\pi$
$337$	−1.16577	−	3.58788i	−0.0635036	−	0.195444i	−0.977774	+	0.209659i	$0.932764\pi$
$338$	1.01442	+	3.12206i	0.0551770	+	0.169817i
$339$	−1.66344	+	5.11955i	−0.0903458	+	0.278056i
$340$	−5.91559	+	1.77957i	−0.320818	+	0.0965107i
$341$	17.7327	+	54.5757i	0.960281	+	2.95544i
$342$	5.41920	−	3.93728i	0.293037	−	0.212904i
$343$	−1.00000			−0.0539949
$344$	3.57583	−	2.59800i	0.192796	−	0.140075i
$345$	−6.35118	+	8.35001i	−0.341936	+	0.449550i
$346$	13.5135	+	9.81812i	0.726489	+	0.527825i
$347$	−8.63720	−	6.27529i	−0.463669	−	0.336875i	0.331300	−	0.943526i	$-0.392513\pi$
$347$	−8.63720	−	6.27529i	−0.463669	−	0.336875i	−0.794969	+	0.606650i	$0.792513\pi$
$348$	5.63544	−	17.3441i	0.302091	−	0.929741i
$349$	−3.36860			−0.180317			−0.0901585	−	0.995927i	$-0.528737\pi$
$349$	−3.36860			−0.180317			−0.0901585	+	0.995927i	$0.528737\pi$
$350$	−1.33496	−	4.81849i	−0.0713568	−	0.257559i
$351$	9.80904			0.523568
$352$	1.71067	−	5.26491i	0.0911791	−	0.280621i
$353$	17.6543	+	12.8266i	0.939646	+	0.682693i	0.948335	−	0.317270i	$-0.102766\pi$
$353$	17.6543	+	12.8266i	0.939646	+	0.682693i	−0.00868950	+	0.999962i	$0.502766\pi$
$354$	−13.5081	−	9.81421i	−0.717947	−	0.521619i
$355$	7.20002	+	2.51539i	0.382137	+	0.133503i
$356$	−2.22930	+	1.61968i	−0.118153	+	0.0858429i
$357$	5.87341			0.310854
$358$	4.56517	−	3.31679i	0.241277	−	0.175298i
$359$	−6.76874	−	20.8320i	−0.357240	−	1.09947i	−0.954699	−	0.297573i	$-0.903823\pi$
$359$	−6.76874	−	20.8320i	−0.357240	−	1.09947i	0.597459	−	0.801900i	$-0.296177\pi$
$360$	−3.20845	−	1.12090i	−0.169100	−	0.0590766i
$361$	0.130795	−	0.402544i	0.00688392	−	0.0211865i
$362$	−1.43005	−	4.40123i	−0.0751615	−	0.231323i
$363$	−12.9066	−	39.7226i	−0.677423	−	2.08489i
$364$	−0.963285	+	2.96469i	−0.0504898	+	0.155392i
$365$	0.0718888	−	3.27548i	0.00376283	−	0.171447i
$366$	−1.64767	−	5.07100i	−0.0861250	−	0.265066i
$367$	10.0078	−	7.27110i	0.522403	−	0.379548i	−0.295105	−	0.955465i	$-0.595355\pi$
$367$	10.0078	−	7.27110i	0.522403	−	0.379548i	0.817508	+	0.575917i	$0.195355\pi$
$368$	2.20681			0.115038
$369$	−2.90245	+	2.10876i	−0.151096	+	0.109777i
$370$	−12.1533	+	3.65605i	−0.631822	+	0.190069i
$371$	−7.58227	−	5.50884i	−0.393652	−	0.286005i
$372$	−17.8292	−	12.9536i	−0.924399	−	0.671615i
$373$	3.85677	−	11.8699i	0.199696	−	0.614601i	−0.800194	−	0.599742i	$-0.795270\pi$
$373$	3.85677	−	11.8699i	0.199696	−	0.614601i	0.999890	−	0.0148593i	$-0.00473005\pi$
$374$	15.2936			0.790814
$375$	−23.0403	+	5.84213i	−1.18980	+	0.301686i
$376$	−7.39124			−0.381174
$377$	−8.26295	+	25.4307i	−0.425564	+	1.30975i
$378$	−2.54573	−	1.84958i	−0.130938	−	0.0951321i
$379$	7.49440	+	5.44500i	0.384961	+	0.279691i	0.763388	−	0.645941i	$-0.223535\pi$
$379$	7.49440	+	5.44500i	0.384961	+	0.279691i	−0.378426	+	0.925631i	$0.623535\pi$
$380$	−9.43700	+	2.83890i	−0.484108	+	0.145633i
$381$	10.1921	−	7.40499i	0.522157	−	0.379369i
$382$	−24.4036			−1.24860
$383$	−22.2151	+	16.1402i	−1.13514	+	0.824725i	−0.986434	−	0.164156i	$-0.947510\pi$
$383$	−22.2151	+	16.1402i	−1.13514	+	0.824725i	−0.148703	+	0.988882i	$0.547510\pi$
$384$	0.656972	+	2.02195i	0.0335260	+	0.103182i
$385$	−0.271613	+	12.3756i	−0.0138427	+	0.630717i
$386$	−3.51420	+	10.8156i	−0.178868	+	0.550500i
$387$	2.07596	+	6.38914i	0.105527	+	0.324778i
$388$	−2.68120	−	8.25189i	−0.136117	−	0.418926i
$389$	1.50534	−	4.63296i	0.0763238	−	0.234900i	−0.905615	−	0.424102i	$-0.860590\pi$
$389$	1.50534	−	4.63296i	0.0763238	−	0.234900i	0.981938	+	0.189201i	$0.0605899\pi$
$390$	13.9899	+	4.88750i	0.708408	+	0.247488i
$391$	1.88397	+	5.79825i	0.0952763	+	0.293230i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−31.2522			−1.57646
$394$	−2.00188	+	1.45445i	−0.100853	+	0.0732741i
$395$	−19.6106	−	6.85112i	−0.986715	−	0.344717i
$396$	6.80704	+	4.94561i	0.342067	+	0.248526i
$397$	−1.38100	−	1.00336i	−0.0693104	−	0.0503570i	0.552591	−	0.833453i	$-0.313639\pi$
$397$	−1.38100	−	1.00336i	−0.0693104	−	0.0503570i	−0.621901	+	0.783096i	$0.713639\pi$
$398$	4.12057	−	12.6818i	0.206546	−	0.635682i
$399$	9.36970			0.469072
$400$	3.91225	+	3.11357i	0.195612	+	0.155679i
$401$	21.6246			1.07988			0.539940	−	0.841704i	$-0.318447\pi$
$401$	21.6246			1.07988			0.539940	+	0.841704i	$0.318447\pi$
$402$	4.16495	−	12.8184i	0.207729	−	0.639323i
$403$	26.1420	+	18.9933i	1.30222	+	0.946122i
$404$	−13.7703	−	10.0047i	−0.685097	−	0.497752i
$405$	−15.2286	+	20.0214i	−0.756718	+	0.994871i
$406$	6.93966	−	5.04196i	0.344410	−	0.250228i
$407$	31.4201			1.55744
$408$	−4.75169	+	3.45230i	−0.235244	+	0.170914i
$409$	0.993930	+	3.05900i	0.0491467	+	0.151258i	0.972618	−	0.232409i	$-0.0746609\pi$
$409$	0.993930	+	3.05900i	0.0491467	+	0.151258i	−0.923471	+	0.383667i	$0.874661\pi$
$410$	5.05433	−	1.52048i	0.249616	−	0.0750911i
$411$	6.54035	−	20.1291i	0.322612	−	0.992896i
$412$	1.55181	+	4.77598i	0.0764522	+	0.235296i
$413$	−2.42691	−	7.46927i	−0.119421	−	0.367539i
$414$	−1.03649	+	3.18998i	−0.0509406	+	0.156779i
$415$	20.4128	−	26.8370i	1.00202	−	1.31738i
$416$	−0.963285	−	2.96469i	−0.0472289	−	0.145356i
$417$	−13.4265	+	9.75495i	−0.657500	+	0.477702i
$418$	24.3975			1.19332
$419$	19.4859	−	14.1573i	0.951946	−	0.691629i	0.000679828	−	1.00000i	$-0.499784\pi$
$419$	19.4859	−	14.1573i	0.951946	−	0.691629i	0.951266	+	0.308370i	$0.0997836\pi$
$420$	−2.70921	−	3.90637i	−0.132196	−	0.190611i
$421$	15.7590	+	11.4496i	0.768047	+	0.558019i	0.901368	−	0.433054i	$-0.142564\pi$
$421$	15.7590	+	11.4496i	0.768047	+	0.558019i	−0.133321	+	0.991073i	$0.542564\pi$
$422$	−10.7139	−	7.78413i	−0.521546	−	0.378925i
$423$	3.47149	−	10.6842i	0.168790	−	0.519481i
$424$	9.37220			0.455154
$425$	−4.84080	+	12.9372i	−0.234813	+	0.627549i
$426$	7.25136			0.351330
$427$	0.775006	−	2.38522i	0.0375052	−	0.115429i
$428$	−6.13960	−	4.46068i	−0.296769	−	0.215615i
$429$	−29.6810	−	21.5645i	−1.43301	−	1.04115i
$430$	0.216863	−	9.88098i	0.0104581	−	0.476503i
$431$	−27.1035	+	19.6919i	−1.30553	+	0.948524i	−0.999993	−	0.00365629i	$-0.998836\pi$
$431$	−27.1035	+	19.6919i	−1.30553	+	0.948524i	−0.305538	+	0.952180i	$0.598836\pi$
$432$	3.14669			0.151395
$433$	16.0957	−	11.6942i	0.773512	−	0.561989i	−0.129513	−	0.991578i	$-0.541341\pi$
$433$	16.0957	−	11.6942i	0.773512	−	0.561989i	0.903025	+	0.429588i	$0.141341\pi$
$434$	−3.20325	−	9.85859i	−0.153761	−	0.473228i
$435$	−23.2393	−	33.5084i	−1.11424	−	1.60661i
$436$	−6.12099	+	18.8385i	−0.293142	+	0.902199i
$437$	3.00545	+	9.24981i	0.143770	+	0.442478i
$438$	−0.962592	−	2.96255i	−0.0459944	−	0.141556i
$439$	3.77605	−	11.6215i	0.180221	−	0.554664i	−0.819612	−	0.572919i	$-0.805811\pi$
$439$	3.77605	−	11.6215i	0.180221	−	0.554664i	0.999833	+	0.0182549i	$0.00581103\pi$
$440$	−7.05443	−	10.1717i	−0.336307	−	0.484916i
$441$	0.469677	+	1.44552i	0.0223656	+	0.0688341i
$442$	6.96716	−	5.06193i	0.331394	−	0.240772i
$443$	−20.9633			−0.995996			−0.497998	−	0.867178i	$-0.665931\pi$
$443$	−20.9633			−0.995996			−0.497998	+	0.867178i	$0.665931\pi$
$444$	−9.76214	+	7.09261i	−0.463291	+	0.336600i
$445$	−0.135200	+	6.16015i	−0.00640910	+	0.292019i
$446$	8.80583	+	6.39781i	0.416968	+	0.302945i
$447$	15.8244	+	11.4971i	0.748468	+	0.543794i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	−1.18423			−0.0558871			−0.0279436	−	0.999610i	$-0.508896\pi$
$449$	−1.18423			−0.0558871			−0.0279436	+	0.999610i	$0.508896\pi$
$450$	−6.33821	+	4.19285i	−0.298786	+	0.197653i
$451$	−13.0670			−0.615300
$452$	0.782425	−	2.40806i	0.0368022	−	0.113266i
$453$	24.1520	+	17.5474i	1.13476	+	0.824451i
$454$	2.37445	+	1.72514i	0.111439	+	0.0809648i
$455$	3.97237	+	5.72771i	0.186228	+	0.268519i
$456$	−7.58025	+	5.50737i	−0.354978	+	0.257906i
$457$	27.9920			1.30941			0.654704	−	0.755885i	$-0.272793\pi$
$457$	27.9920			1.30941			0.654704	+	0.755885i	$0.272793\pi$
$458$	−8.76378	+	6.36726i	−0.409505	+	0.297523i
$459$	2.68635	+	8.26773i	0.125388	+	0.385904i
$460$	2.98737	−	3.92756i	0.139287	−	0.183123i
$461$	7.02079	−	21.6078i	0.326991	−	1.00637i	−0.643543	−	0.765410i	$-0.722536\pi$
$461$	7.02079	−	21.6078i	0.326991	−	1.00637i	0.970534	−	0.240965i	$-0.0774638\pi$
$462$	3.63690	+	11.1932i	0.169204	+	0.520756i
$463$	−8.88395	−	27.3420i	−0.412872	−	1.27069i	−0.914140	−	0.405398i	$-0.867133\pi$
$463$	−8.88395	−	27.3420i	−0.412872	−	1.27069i	0.501268	−	0.865292i	$-0.332867\pi$
$464$	−2.65071	+	8.15806i	−0.123056	+	0.378728i
$465$	−47.1896	+	14.1959i	−2.18836	+	0.658319i
$466$	7.46989	+	22.9900i	0.346036	+	1.06499i
$467$	28.9566	−	21.0382i	1.33995	−	0.973533i	0.340507	−	0.940242i	$-0.389401\pi$
$467$	28.9566	−	21.0382i	1.33995	−	0.973533i	0.999446	−	0.0332907i	$-0.0105987\pi$
$468$	4.73793			0.219011
$469$	5.12885	−	3.72633i	0.236828	−	0.172066i
$470$	−10.0056	+	13.1545i	−0.461522	+	0.606772i
$471$	−26.6475	−	19.3605i	−1.22785	−	0.892086i
$472$	6.35374	+	4.61626i	0.292455	+	0.212481i
$473$	−7.56113	+	23.2708i	−0.347661	+	1.06999i
$474$	−19.7504			−0.907167
$475$	−7.72240	+	20.6385i	−0.354328	+	0.946958i
$476$	−2.76265			−0.126626
$477$	−4.40190	+	13.5477i	−0.201549	+	0.620305i
$478$	9.46325	+	6.87546i	0.432839	+	0.314476i
$479$	−16.1793	−	11.7550i	−0.739253	−	0.537099i	0.153224	−	0.988191i	$-0.451034\pi$
$479$	−16.1793	−	11.7550i	−0.739253	−	0.537099i	−0.892477	+	0.451093i	$0.851034\pi$
$480$	4.48790	+	1.56789i	0.204844	+	0.0715639i
$481$	14.3137	−	10.3995i	0.652650	−	0.474178i
$482$	10.4786			0.477289
$483$	−3.79566	+	2.75771i	−0.172709	+	0.125480i
$484$	6.07084	+	18.6841i	0.275947	+	0.849278i
$485$	−18.3158	−	6.39878i	−0.831677	−	0.290553i
$486$	−4.47353	+	13.7681i	−0.202924	+	0.624535i
$487$	6.21871	+	19.1392i	0.281796	+	0.867280i	0.987341	+	0.158614i	$0.0507027\pi$
$487$	6.21871	+	19.1392i	0.281796	+	0.867280i	−0.705544	+	0.708666i	$0.749297\pi$
$488$	0.775006	+	2.38522i	0.0350829	+	0.107974i
$489$	9.87922	−	30.4051i	0.446754	−	1.37497i
$490$	0.0490643	−	2.23553i	0.00221650	−	0.100991i
$491$	−1.65908	−	5.10613i	−0.0748733	−	0.230436i	0.906615	−	0.421959i	$-0.138657\pi$
$491$	−1.65908	−	5.10613i	−0.0748733	−	0.230436i	−0.981488	+	0.191523i	$0.938657\pi$
$492$	4.05988	−	2.94968i	0.183034	−	0.132982i
$493$	−23.6977			−1.06729
$494$	11.1145	−	8.07518i	0.500066	−	0.363319i
$495$	18.0166	−	5.41989i	0.809788	−	0.243606i
$496$	8.38622	+	6.09294i	0.376552	+	0.273581i
$497$	2.75939	+	2.00481i	0.123775	+	0.0899281i
$498$	9.90660	−	30.4894i	0.443925	−	1.36626i
$499$	−8.81352			−0.394547			−0.197274	−	0.980348i	$-0.563209\pi$
$499$	−8.81352			−0.394547			−0.197274	+	0.980348i	$0.563209\pi$
$500$	10.8374	−	2.74794i	0.484662	−	0.122891i
$501$	−39.4670			−1.76325
$502$	−3.68094	+	11.3288i	−0.164288	+	0.505627i
$503$	−10.5588	−	7.67145i	−0.470795	−	0.342053i	0.326956	−	0.945040i	$-0.393977\pi$
$503$	−10.5588	−	7.67145i	−0.470795	−	0.342053i	−0.797751	+	0.602987i	$0.793977\pi$
$504$	−1.22963	−	0.893378i	−0.0547720	−	0.0397942i
$505$	−36.4467	+	10.9641i	−1.62186	+	0.487898i
$506$	−9.88342	+	7.18073i	−0.439372	+	0.319222i
$507$	6.97909			0.309952
$508$	−4.79401	+	3.48305i	−0.212700	+	0.154535i
$509$	−2.23676	−	6.88405i	−0.0991428	−	0.305130i	0.889168	−	0.457580i	$-0.151284\pi$
$509$	−2.23676	−	6.88405i	−0.0991428	−	0.305130i	−0.988311	+	0.152450i	$0.951284\pi$
$510$	−0.288175	+	13.1302i	−0.0127606	+	0.581414i
$511$	0.452770	−	1.39348i	0.0200294	−	0.0616440i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	4.28546	+	13.1893i	0.189208	+	0.582322i
$514$	6.54900	−	20.1557i	0.288864	−	0.889032i
$515$	10.6007	+	3.70345i	0.467123	+	0.163193i
$516$	−2.90380	−	8.93698i	−0.127833	−	0.393429i
$517$	33.1024	−	24.0503i	1.45584	−	1.05773i
$518$	−5.67574			−0.249378
$519$	28.7297	−	20.8734i	1.26110	−	0.916240i
$520$	−6.58038	−	2.29891i	−0.288569	−	0.100814i
$521$	−4.99616	−	3.62992i	−0.218886	−	0.159030i	0.472939	−	0.881095i	$-0.343193\pi$
$521$	−4.99616	−	3.62992i	−0.218886	−	0.159030i	−0.691825	+	0.722065i	$0.743193\pi$
$522$	−10.5476	−	7.66330i	−0.461657	−	0.335413i
$523$	0.0319677	−	0.0983865i	0.00139785	−	0.00430214i	−0.950355	−	0.311167i	$-0.899280\pi$
$523$	0.0319677	−	0.0983865i	0.00139785	−	0.00430214i	0.951753	+	0.306865i	$0.0992801\pi$
$524$	14.6999			0.642170
$525$	−10.6198	−	0.466381i	−0.463486	−	0.0203545i
$526$	18.7866			0.819134
$527$	−8.84945	+	27.2358i	−0.385488	+	1.18641i
$528$	−9.52153	−	6.91780i	−0.414371	−	0.301058i
$529$	14.6675	+	10.6565i	0.637716	+	0.463328i
$530$	12.6872	−	16.6801i	0.551096	−	0.724537i
$531$	−9.65709	+	7.01628i	−0.419082	+	0.304481i
$532$	−4.40718			−0.191076
$533$	−5.95280	+	4.32496i	−0.257844	+	0.187335i
$534$	1.81033	+	5.57163i	0.0783407	+	0.241108i
$535$	−16.2501	+	4.88846i	−0.702551	+	0.211346i
$536$	−1.95905	+	6.02932i	−0.0846179	+	0.260427i
$537$	−3.70721	−	11.4096i	−0.159978	−	0.492361i
$538$	1.70156	+	5.23685i	0.0733593	+	0.225777i
$539$	−1.71067	+	5.26491i	−0.0736839	+	0.226776i
$540$	4.25969	−	5.60030i	0.183308	−	0.240999i
$541$	11.5721	+	35.6151i	0.497521	+	1.53121i	0.812990	+	0.582277i	$0.197838\pi$
$541$	11.5721	+	35.6151i	0.497521	+	1.53121i	−0.315469	+	0.948936i	$0.602162\pi$
$542$	−24.6769	+	17.9288i	−1.05996	+	0.770108i
$543$	−9.83857			−0.422214
$544$	2.23503	−	1.62384i	0.0958261	−	0.0696217i
$545$	25.2416	+	36.3955i	1.08123	+	1.55901i
$546$	5.36160	+	3.89543i	0.229455	+	0.166709i
$547$	30.7038	+	22.3076i	1.31280	+	0.953806i	0.999992	+	0.00399030i	$0.00127015\pi$
$547$	30.7038	+	22.3076i	1.31280	+	0.953806i	0.312810	+	0.949816i	$0.398730\pi$
$548$	−3.07635	+	9.46804i	−0.131415	+	0.404455i
$549$	−3.81188			−0.162687
$550$	−27.6526	−	1.21440i	−1.17911	−	0.0517821i
$551$	−37.8043			−1.61052
$552$	1.44981	−	4.46207i	0.0617082	−	0.189918i
$553$	−7.51570	−	5.46048i	−0.319600	−	0.232203i
$554$	22.1967	+	16.1268i	0.943047	+	0.685163i
$555$	−0.592043	+	26.9754i	−0.0251308	+	1.14504i
$556$	6.31538	−	4.58839i	0.267832	−	0.194591i
$557$	−29.0293			−1.23001			−0.615006	−	0.788523i	$-0.710846\pi$
$557$	−29.0293			−1.23001			−0.615006	+	0.788523i	$0.710846\pi$
$558$	−12.7463	+	9.26070i	−0.539592	+	0.392037i
$559$	4.25769	+	13.1038i	0.180081	+	0.554233i
$560$	1.27432	+	1.83742i	0.0538497	+	0.0776452i
$561$	10.0475	−	30.9230i	0.424205	−	1.30557i
$562$	2.55771	+	7.87181i	0.107890	+	0.332052i
$563$	−4.89318	−	15.0597i	−0.206223	−	0.634689i	−0.999661	−	0.0260377i	$-0.991711\pi$
$563$	−4.89318	−	15.0597i	−0.206223	−	0.634689i	0.793438	−	0.608651i	$-0.208289\pi$
$564$	−4.85584	+	14.9447i	−0.204468	+	0.629287i
$565$	−3.22655	−	4.65232i	−0.135742	−	0.195724i
$566$	−3.75512	−	11.5571i	−0.157840	−	0.485781i
$567$	−9.10112	+	6.61235i	−0.382211	+	0.277693i
$568$	−3.41079			−0.143114
$569$	13.3613	−	9.70758i	0.560136	−	0.406963i	−0.271372	−	0.962474i	$-0.587478\pi$
$569$	13.3613	−	9.70758i	0.560136	−	0.406963i	0.831509	+	0.555512i	$0.187478\pi$
$570$	−0.459718	+	20.9462i	−0.0192555	+	0.877342i
$571$	29.4451	+	21.3932i	1.23224	+	0.895276i	0.997056	−	0.0766750i	$-0.0244304\pi$
$571$	29.4451	+	21.3932i	1.23224	+	0.895276i	0.235185	+	0.971951i	$0.424430\pi$
$572$	13.9609	+	10.1432i	0.583736	+	0.424109i
$573$	−16.0325	+	49.3429i	−0.669766	+	2.06133i
$574$	2.36043			0.0985224
$575$	−2.94602	−	10.6335i	−0.122857	−	0.443448i
$576$	1.51991			0.0633294
$577$	−2.30879	+	7.10572i	−0.0961161	+	0.295815i	−0.987543	−	0.157350i	$-0.949705\pi$
$577$	−2.30879	+	7.10572i	−0.0961161	+	0.295815i	0.891427	+	0.453165i	$0.149705\pi$
$578$	−7.57869	−	5.50624i	−0.315232	−	0.229029i
$579$	19.5599	+	14.2111i	0.812882	+	0.590593i
$580$	10.9310	+	15.7612i	0.453883	+	0.654448i
$581$	12.1993	−	8.86331i	0.506112	−	0.367712i
$582$	−18.4464			−0.764628
$583$	−41.9743	+	30.4961i	−1.73840	+	1.26302i
$584$	0.452770	+	1.39348i	0.0187357	+	0.0576627i
$585$	6.41376	−	8.43230i	0.265176	−	0.348633i
$586$	3.78994	−	11.6642i	0.156561	−	0.481846i
$587$	−13.9826	−	43.0340i	−0.577124	−	1.77621i	−0.628830	−	0.777543i	$-0.716466\pi$
$587$	−13.9826	−	43.0340i	−0.577124	−	1.77621i	0.0517059	−	0.998662i	$-0.483534\pi$
$588$	−0.656972	−	2.02195i	−0.0270931	−	0.0833839i
$589$	−14.1173	+	43.4486i	−0.581694	+	1.79027i
$590$	16.8169	−	5.05896i	0.692339	−	0.208274i
$591$	1.62565	+	5.00324i	0.0668703	+	0.205806i
$592$	4.59177	−	3.33612i	0.188721	−	0.137114i
$593$	0.517361			0.0212455			0.0106227	−	0.999944i	$-0.496619\pi$
$593$	0.517361			0.0212455			0.0106227	+	0.999944i	$0.496619\pi$
$594$	−14.0928	+	10.2390i	−0.578233	+	0.420111i
$595$	−3.73981	+	4.91680i	−0.153317	+	0.201569i
$596$	−7.44325	−	5.40784i	−0.304887	−	0.221514i
$597$	−22.9349	−	16.6632i	−0.938664	−	0.681979i
$598$	−2.12579	+	6.54250i	−0.0869300	+	0.267543i
$599$	−38.7092			−1.58161			−0.790807	−	0.612066i	$-0.790339\pi$
$599$	−38.7092			−1.58161			−0.790807	+	0.612066i	$0.790339\pi$
$600$	8.86573	−	5.86485i	0.361942	−	0.239432i
$601$	−27.4339			−1.11905			−0.559525	−	0.828813i	$-0.689016\pi$
$601$	−27.4339			−1.11905			−0.559525	+	0.828813i	$0.689016\pi$
$602$	1.36585	−	4.20365i	0.0556678	−	0.171328i
$603$	−7.79536	−	5.66366i	−0.317452	−	0.230642i
$604$	−11.3603	−	8.25371i	−0.462242	−	0.335839i
$605$	41.4710	+	14.4883i	1.68604	+	0.589032i
$606$	−29.2757	+	21.2700i	−1.18924	+	0.864036i
$607$	11.8840			0.482357			0.241179	−	0.970481i	$-0.422466\pi$
$607$	11.8840			0.482357			0.241179	+	0.970481i	$0.422466\pi$
$608$	3.56549	−	2.59048i	0.144600	−	0.105058i
$609$	−5.63544	−	17.3441i	−0.228359	−	0.702818i
$610$	5.29421	+	1.84958i	0.214356	+	0.0748873i
$611$	7.11987	−	21.9127i	0.288039	−	0.886493i
$612$	1.29755	+	3.99345i	0.0524504	+	0.161426i
$613$	1.60186	+	4.93003i	0.0646987	+	0.199122i	0.978180	−	0.207758i	$-0.0666167\pi$
$613$	1.60186	+	4.93003i	0.0646987	+	0.199122i	−0.913482	+	0.406880i	$0.866617\pi$
$614$	−2.80997	+	8.64821i	−0.113401	+	0.349013i
$615$	0.246219	−	11.2185i	0.00992851	−	0.452375i
$616$	−1.71067	−	5.26491i	−0.0689249	−	0.212129i
$617$	−10.1187	+	7.35163i	−0.407362	+	0.295966i	−0.772533	−	0.634975i	$-0.781010\pi$
$617$	−10.1187	+	7.35163i	−0.407362	+	0.295966i	0.365171	+	0.930940i	$0.381010\pi$
$618$	10.6763			0.429464
$619$	2.96215	−	2.15213i	0.119059	−	0.0865014i	−0.526662	−	0.850075i	$-0.676557\pi$
$619$	2.96215	−	2.15213i	0.119059	−	0.0865014i	0.645721	+	0.763573i	$0.276557\pi$
$620$	22.1963	−	6.67726i	0.891426	−	0.268165i
$621$	−5.61794	−	4.08167i	−0.225440	−	0.163792i
$622$	−2.82744	−	2.05425i	−0.113370	−	0.0823680i
$623$	−0.851517	+	2.62070i	−0.0341153	+	0.104996i
$624$	−6.62730			−0.265305
$625$	9.78000	−	23.0076i	0.391200	−	0.920306i
$626$	−11.2426			−0.449347
$627$	16.0285	−	49.3306i	0.640116	−	1.97007i
$628$	12.5340	+	9.10652i	0.500163	+	0.363390i
$629$	12.6855	+	9.21652i	0.505802	+	0.367487i
$630$	−3.25454	+	0.979053i	−0.129664	+	0.0390064i
$631$	35.3715	−	25.6989i	1.40812	−	1.02306i	0.414523	−	0.910039i	$-0.363948\pi$
$631$	35.3715	−	25.6989i	1.40812	−	1.02306i	0.993593	−	0.113017i	$-0.0360515\pi$
$632$	9.28992			0.369533
$633$	−22.7779	+	16.5491i	−0.905340	+	0.657768i
$634$	−3.87385	−	11.9225i	−0.153850	−	0.473502i
$635$	−0.290741	+	13.2471i	−0.0115377	+	0.525696i
$636$	6.15727	−	18.9501i	0.244152	−	0.751422i
$637$	0.963285	+	2.96469i	0.0381667	+	0.117465i
$638$	−14.6740	−	45.1618i	−0.580948	−	1.78797i
$639$	1.60197	−	4.93035i	0.0633729	−	0.195042i
$640$	−2.11095	−	0.737480i	−0.0834428	−	0.0291514i
$641$	−8.95074	−	27.5475i	−0.353533	−	1.08806i	−0.956855	−	0.290565i	$-0.906157\pi$
$641$	−8.95074	−	27.5475i	−0.353533	−	1.08806i	0.603322	−	0.797497i	$-0.293843\pi$
$642$	−13.0528	+	9.48343i	−0.515154	+	0.374281i
$643$	29.5425			1.16504			0.582521	−	0.812815i	$-0.302066\pi$
$643$	29.5425			1.16504			0.582521	+	0.812815i	$0.302066\pi$
$644$	1.78535	−	1.29713i	0.0703526	−	0.0511141i
$645$	−19.8364	−	6.93002i	−0.781058	−	0.272869i
$646$	9.85018	+	7.15658i	0.387550	+	0.281572i
$647$	15.3064	+	11.1208i	0.601758	+	0.437203i	0.846502	−	0.532385i	$-0.178704\pi$
$647$	15.3064	+	11.1208i	0.601758	+	0.437203i	−0.244744	+	0.969588i	$0.578704\pi$
$648$	3.47632	−	10.6990i	0.136563	−	0.420297i
$649$	−43.4767			−1.70661
$650$	−12.9994	+	8.59933i	−0.509877	+	0.337293i
$651$	−22.0381			−0.863739
$652$	−4.64685	+	14.3015i	−0.181984	+	0.560091i
$653$	−0.554071	−	0.402556i	−0.0216825	−	0.0157532i	0.576891	−	0.816821i	$-0.304266\pi$
$653$	−0.554071	−	0.402556i	−0.0216825	−	0.0157532i	−0.598574	+	0.801068i	$0.704266\pi$
$654$	34.0692	+	24.7527i	1.33221	+	0.967907i
$655$	19.8994	−	26.1621i	0.777533	−	1.02224i
$656$	−1.90963	+	1.38743i	−0.0745584	+	0.0541699i
$657$	−2.22696			−0.0868818
$658$	−5.97964	+	4.34446i	−0.233110	+	0.169365i
$659$	−7.80067	−	24.0080i	−0.303871	−	0.935219i	−0.980096	−	0.198524i	$-0.936385\pi$
$659$	−7.80067	−	24.0080i	−0.303871	−	0.935219i	0.676225	−	0.736695i	$-0.263615\pi$
$660$	−25.2012	+	7.58121i	−0.980957	+	0.295098i
$661$	14.6761	−	45.1685i	0.570835	−	1.75685i	−0.0791079	−	0.996866i	$-0.525207\pi$
$661$	14.6761	−	45.1685i	0.570835	−	1.75685i	0.649943	−	0.759983i	$-0.274793\pi$
$662$	−8.06871	−	24.8329i	−0.313599	−	0.965159i
$663$	−5.65776	−	17.4128i	−0.219729	−	0.676257i
$664$	−4.65972	+	14.3411i	−0.180832	+	0.556544i
$665$	−5.96603	+	7.84365i	−0.231353	+	0.304164i
$666$	2.66576	+	8.20438i	0.103296	+	0.317913i
$667$	15.3145	−	11.1267i	0.592981	−	0.430826i
$668$	18.5639			0.718259
$669$	18.7212	−	13.6018i	0.723805	−	0.525875i
$670$	8.07867	+	11.6485i	0.312106	+	0.450022i
$671$	−11.2322	−	8.16067i	−0.433614	−	0.315039i
$672$	1.71998	+	1.24964i	0.0663495	+	0.0482057i
$673$	−8.68399	+	26.7266i	−0.334743	+	1.03023i	0.632105	+	0.774883i	$0.282191\pi$
$673$	−8.68399	+	26.7266i	−0.334743	+	1.03023i	−0.966848	+	0.255351i	$0.917809\pi$
$674$	3.77252			0.145312
$675$	−4.20072	−	15.1623i	−0.161686	−	0.583598i
$676$	−3.28272			−0.126259
$677$	8.62488	−	26.5446i	0.331481	−	1.02019i	−0.636949	−	0.770906i	$-0.719804\pi$
$677$	8.62488	−	26.5446i	0.331481	−	1.02019i	0.968430	−	0.249287i	$-0.0801963\pi$
$678$	−4.35495	−	3.16405i	−0.167251	−	0.121515i
$679$	−7.01947	−	5.09995i	−0.269383	−	0.195718i
$680$	0.135548	−	6.17598i	0.00519801	−	0.236838i
$681$	5.04810	−	3.66766i	0.193444	−	0.140545i
$682$	−57.3843			−2.19736
$683$	34.5456	−	25.0988i	1.32185	−	0.960380i	0.321942	−	0.946759i	$-0.395664\pi$
$683$	34.5456	−	25.0988i	1.32185	−	0.960380i	0.999907	−	0.0136202i	$-0.00433559\pi$
$684$	2.06995	+	6.37065i	0.0791465	+	0.243588i
$685$	12.6862	+	18.2921i	0.484715	+	0.698903i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	7.11674	+	21.9031i	0.271521	+	0.835654i
$688$	1.36585	+	4.20365i	0.0520724	+	0.160262i
$689$	−9.02809	+	27.7856i	−0.343943	+	1.05855i
$690$	−5.97871	−	8.62062i	−0.227606	−	0.328182i
$691$	−8.61131	−	26.5029i	−0.327590	−	1.00822i	−0.970258	−	0.242073i	$-0.922173\pi$
$691$	−8.61131	−	26.5029i	−0.327590	−	1.00822i	0.642668	−	0.766145i	$-0.277827\pi$
$692$	−13.5135	+	9.81812i	−0.513705	+	0.373229i
$693$	8.41397			0.319620
$694$	8.63720	−	6.27529i	0.327864	−	0.238207i
$695$	0.383008	−	17.4511i	0.0145283	−	0.661957i
$696$	14.7538	+	10.7192i	0.559240	+	0.406312i
$697$	−5.27563	−	3.83297i	−0.199829	−	0.145184i
$698$	1.04095	−	3.20373i	0.0394007	−	0.121263i
$699$	51.3921			1.94383
$700$	4.99519	+	0.219370i	0.188800	+	0.00829139i
$701$	21.5931			0.815562			0.407781	−	0.913080i	$-0.366303\pi$
$701$	21.5931			0.815562			0.407781	+	0.913080i	$0.366303\pi$
$702$	−3.03116	+	9.32895i	−0.114404	+	0.352099i
$703$	20.2368	+	14.7029i	0.763245	+	0.554530i
$704$	4.47860	+	3.25389i	0.168793	+	0.122636i
$705$	20.0244	+	28.8729i	0.754162	+	1.08742i
$706$	−17.6543	+	12.8266i	−0.664430	+	0.482737i
$707$	−17.0210			−0.640140
$708$	13.5081	−	9.81421i	0.507665	−	0.368841i
$709$	−2.46291	−	7.58005i	−0.0924964	−	0.284675i	0.894097	−	0.447874i	$-0.147819\pi$
$709$	−2.46291	−	7.58005i	−0.0924964	−	0.284675i	−0.986593	+	0.163199i	$0.947819\pi$
$710$	−4.61720	+	6.07033i	−0.173281	+	0.227815i
$711$	−4.36326	+	13.4287i	−0.163635	+	0.503616i
$712$	−0.851517	−	2.62070i	−0.0319119	−	0.0982149i
$713$	−7.06897	−	21.7561i	−0.264735	−	0.814771i
$714$	−1.81498	+	5.58594i	−0.0679240	+	0.209049i
$715$	36.9513	−	11.1159i	1.38190	−	0.415713i
$716$	1.74374	+	5.36668i	0.0651667	+	0.200562i
$717$	20.1189	−	14.6173i	0.751356	−	0.545892i
$718$	21.9041			0.817454
$719$	26.5810	−	19.3122i	0.991304	−	0.720225i	0.0310981	−	0.999516i	$-0.490100\pi$
$719$	26.5810	−	19.3122i	0.991304	−	0.720225i	0.960206	+	0.279292i	$0.0900996\pi$
$720$	2.05750	−	2.70504i	0.0766786	−	0.100811i
$721$	4.06269	+	2.95172i	0.151303	+	0.109928i
$722$	0.342425	+	0.248786i	0.0127437	+	0.00925886i
$723$	6.88417	−	21.1873i	0.256025	−	0.787964i
$724$	4.62772			0.171988
$725$	42.8482	+	1.88173i	1.59134	+	0.0698856i
$726$	41.7668			1.55011
$727$	−12.0516	+	37.0910i	−0.446968	+	1.37563i	0.433342	+	0.901230i	$0.357334\pi$
$727$	−12.0516	+	37.0910i	−0.446968	+	1.37563i	−0.880310	+	0.474398i	$0.842666\pi$
$728$	−2.52191	−	1.83228i	−0.0934683	−	0.0679087i
$729$	−2.40386	−	1.74650i	−0.0890318	−	0.0646854i
$730$	3.09296	+	1.08055i	0.114475	+	0.0399930i
$731$	−9.87877	+	7.17735i	−0.365380	+	0.265464i
$732$	5.33197			0.197075
$733$	27.2132	−	19.7715i	1.00514	−	0.730278i	0.0419564	−	0.999119i	$-0.486641\pi$
$733$	27.2132	−	19.7715i	1.00514	−	0.730278i	0.963184	+	0.268842i	$0.0866409\pi$
$734$	3.82264	+	11.7649i	0.141096	+	0.434250i
$735$	−4.48790	−	1.56789i	−0.165539	−	0.0578324i
$736$	−0.681942	+	2.09880i	−0.0251367	+	0.0773629i
$737$	−10.8450	−	33.3774i	−0.399480	−	1.22947i
$738$	−1.10864	−	3.41204i	−0.0408096	−	0.125599i
$739$	−13.8305	+	42.5658i	−0.508762	+	1.56581i	0.285592	+	0.958351i	$0.407810\pi$
$739$	−13.8305	+	42.5658i	−0.508762	+	1.56581i	−0.794354	+	0.607456i	$0.792190\pi$
$740$	0.278477	−	12.6883i	0.0102370	−	0.466431i
$741$	−9.02569	−	27.7782i	−0.331567	−	1.02046i
$742$	7.58227	−	5.50884i	0.278354	−	0.202236i
$743$	−5.02311			−0.184280			−0.0921400	−	0.995746i	$-0.529371\pi$
$743$	−5.02311			−0.184280			−0.0921400	+	0.995746i	$0.529371\pi$
$744$	17.8292	−	12.9536i	0.653649	−	0.474904i
$745$	−19.7005	+	5.92645i	−0.721771	+	0.217128i
$746$	10.0972	+	7.33601i	0.369683	+	0.268591i
$747$	−18.5418	−	13.4714i	−0.678409	−	0.492893i
$748$	−4.72599	+	14.5451i	−0.172799	+	0.531821i
$749$	−7.58896			−0.277294
$750$	1.56366	−	23.7180i	0.0570969	−	0.866059i
$751$	−37.9288			−1.38404			−0.692021	−	0.721877i	$-0.743280\pi$
$751$	−37.9288			−1.38404			−0.692021	+	0.721877i	$0.743280\pi$
$752$	2.28402	−	7.02948i	0.0832896	−	0.256339i
$753$	20.4879	+	14.8854i	0.746622	+	0.542453i
$754$	−21.6327	−	15.7171i	−0.787816	−	0.572382i
$755$	−30.0679	+	9.04524i	−1.09428	+	0.329190i
$756$	2.54573	−	1.84958i	0.0925872	−	0.0672685i
$757$	36.5174			1.32725			0.663623	−	0.748067i	$-0.269018\pi$
$757$	36.5174			1.32725			0.663623	+	0.748067i	$0.269018\pi$
$758$	−7.49440	+	5.44500i	−0.272209	+	0.197771i
$759$	8.02596	+	24.7014i	0.291324	+	0.896602i
$760$	0.216236	−	9.85239i	0.00784369	−	0.357384i
$761$	−16.7298	+	51.4891i	−0.606456	+	1.86648i	−0.120003	+	0.992774i	$0.538290\pi$
$761$	−16.7298	+	51.4891i	−0.606456	+	1.86648i	−0.486453	+	0.873707i	$0.661710\pi$
$762$	3.89303	+	11.9815i	0.141030	+	0.434045i
$763$	6.12099	+	18.8385i	0.221595	+	0.681998i
$764$	7.54112	−	23.2092i	0.272828	−	0.839679i
$765$	8.86382	+	3.09665i	0.320472	+	0.111960i
$766$	−8.48540	−	26.1154i	−0.306590	−	0.943587i
$767$	−19.8062	+	14.3901i	−0.715162	+	0.519595i
$768$	−2.12601			−0.0767157
$769$	29.0882	−	21.1338i	1.04895	−	0.762106i	0.0769361	−	0.997036i	$-0.475486\pi$
$769$	29.0882	−	21.1338i	1.04895	−	0.762106i	0.972012	+	0.234930i	$0.0754862\pi$
$770$	−11.6859	−	4.08258i	−0.421131	−	0.147126i
$771$	−36.4514	−	26.4835i	−1.31277	−	0.953781i
$772$	−9.20030	−	6.68441i	−0.331126	−	0.240577i
$773$	0.303986	−	0.935573i	0.0109336	−	0.0336502i	−0.945441	−	0.325794i	$-0.894368\pi$
$773$	0.303986	−	0.935573i	0.0109336	−	0.0336502i	0.956374	+	0.292144i	$0.0943685\pi$
$774$	−6.71794			−0.241471
$775$	18.1635	−	48.5428i	0.652452	−	1.74371i
$776$	8.67655			0.311470
$777$	−3.72881	+	11.4761i	−0.133770	+	0.411702i
$778$	3.94103	+	2.86333i	0.141293	+	0.102655i
$779$	−8.41608	−	6.11464i	−0.301537	−	0.219080i
$780$	−8.97142	+	11.7949i	−0.321228	+	0.422325i
$781$	15.2756	−	11.0983i	0.546602	−	0.397130i
$782$	−6.09665			−0.218016
$783$	21.8370	−	15.8655i	0.780390	−	0.566986i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	33.1747	−	9.97983i	1.18405	−	0.356195i
$786$	9.65745	−	29.7226i	0.344470	−	1.06017i
$787$	4.45819	+	13.7209i	0.158917	+	0.489097i	0.998537	−	0.0540782i	$-0.0172220\pi$
$787$	4.45819	+	13.7209i	0.158917	+	0.489097i	−0.839620	+	0.543175i	$0.817222\pi$
$788$	−0.764650	−	2.35335i	−0.0272395	−	0.0838346i
$789$	12.3423	−	37.9856i	0.439396	−	1.35232i
$790$	12.5758	−	16.5337i	0.447427	−	0.588241i
$791$	−0.782425	−	2.40806i	−0.0278198	−	0.0856207i
$792$	−6.80704	+	4.94561i	−0.241878	+	0.175734i
$793$	−7.81799			−0.277625
$794$	1.38100	−	1.00336i	0.0490099	−	0.0356078i
$795$	−25.3912	−	36.6113i	−0.900534	−	1.29847i
$796$	10.7878	+	7.83779i	0.382363	+	0.277803i
$797$	−18.6316	−	13.5366i	−0.659964	−	0.479492i	0.206687	−	0.978407i	$-0.433732\pi$
$797$	−18.6316	−	13.5366i	−0.659964	−	0.479492i	−0.866651	+	0.498916i	$0.833732\pi$
$798$	−2.89540	+	8.91112i	−0.102496	+	0.315450i
$799$	20.4194			0.722386
$800$	−4.17013	+	2.75862i	−0.147436	+	0.0975320i
$801$	4.18820			0.147983
$802$	−6.68236	+	20.5662i	−0.235962	+	0.726217i
$803$	−6.56201	−	4.76758i	−0.231568	−	0.168244i
$804$	10.9040	+	7.92220i	0.384553	+	0.279394i
$805$	0.108276	−	4.93339i	0.00381622	−	0.173879i
$806$	−26.1420	+	18.9933i	−0.920812	+	0.669009i
$807$	11.7065			0.412090
$808$	13.7703	−	10.0047i	0.484437	−	0.351964i
$809$	−5.17811	−	15.9366i	−0.182053	−	0.560301i	0.817832	−	0.575456i	$-0.195176\pi$
$809$	−5.17811	−	15.9366i	−0.182053	−	0.560301i	−0.999885	+	0.0151558i	$0.995176\pi$
$810$	−14.3356	−	20.6703i	−0.503700	−	0.726279i
$811$	4.07294	−	12.5352i	0.143020	−	0.440171i	−0.853731	−	0.520714i	$-0.825666\pi$
$811$	4.07294	−	12.5352i	0.143020	−	0.440171i	0.996751	+	0.0805436i	$0.0256656\pi$
$812$	2.65071	+	8.15806i	0.0930218	+	0.286292i
$813$	20.0392	+	61.6742i	0.702804	+	2.16301i
$814$	−9.70934	+	29.8823i	−0.340312	+	1.04737i
$815$	19.1626	+	27.6302i	0.671235	+	0.967845i
$816$	−1.81498	−	5.58594i	−0.0635371	−	0.195547i
$817$	−15.7594	+	11.4498i	−0.551350	+	0.400579i
$818$	−3.21643			−0.112460
$819$	3.83307	−	2.78489i	0.133938	−	0.0973118i
$820$	−0.115813	+	5.27681i	−0.00404436	+	0.184274i
$821$	−10.9225	−	7.93567i	−0.381199	−	0.276957i	0.380641	−	0.924723i	$-0.375703\pi$
$821$	−10.9225	−	7.93567i	−0.381199	−	0.276957i	−0.761839	+	0.647766i	$0.775703\pi$
$822$	17.1229	+	12.4405i	0.597228	+	0.433912i
$823$	−11.8343	+	36.4221i	−0.412516	+	1.26959i	0.501937	+	0.864904i	$0.332621\pi$
$823$	−11.8343	+	36.4221i	−0.412516	+	1.26959i	−0.914454	+	0.404691i	$0.867379\pi$
$824$	−5.02176			−0.174941
$825$	−20.6224	+	55.1144i	−0.717981	+	1.91884i
$826$	7.85366			0.273264
$827$	−9.21584	+	28.3634i	−0.320466	+	0.986294i	0.652979	+	0.757376i	$0.273519\pi$
$827$	−9.21584	+	28.3634i	−0.320466	+	0.986294i	−0.973446	+	0.228918i	$0.926481\pi$
$828$	−2.71356	−	1.97152i	−0.0943028	−	0.0685150i
$829$	−24.1613	−	17.5542i	−0.839156	−	0.609683i	0.0829787	−	0.996551i	$-0.473557\pi$
$829$	−24.1613	−	17.5542i	−0.839156	−	0.609683i	−0.922135	+	0.386869i	$0.873557\pi$
$830$	19.2157	+	27.7068i	0.666985	+	0.961716i
$831$	47.1903	−	34.2858i	1.63701	−	1.18936i
$832$	3.11725			0.108071
$833$	−2.23503	+	1.62384i	−0.0774392	+	0.0562629i
$834$	−5.12848	−	15.7838i	−0.177585	−	0.546550i
$835$	25.1300	−	33.0390i	0.869661	−	1.14336i
$836$	−7.53924	+	23.2034i	−0.260750	+	0.802507i
$837$	−10.0796	−	31.0219i	−0.348403	−	1.07228i
$838$	7.44293	+	22.9070i	0.257112	+	0.791309i
$839$	−15.6552	+	48.1819i	−0.540479	+	1.66342i	0.191025	+	0.981585i	$0.438819\pi$
$839$	−15.6552	+	48.1819i	−0.540479	+	1.66342i	−0.731503	+	0.681838i	$0.761181\pi$
$840$	4.55237	−	1.36948i	0.157072	−	0.0472514i
$841$	13.7760	+	42.3983i	0.475036	+	1.46201i
$842$	−15.7590	+	11.4496i	−0.543091	+	0.394579i
$843$	17.5968			0.606065
$844$	10.7139	−	7.78413i	0.368789	−	0.267941i
$845$	−4.44384	+	5.84240i	−0.152873	+	0.200985i
$846$	9.08848	+	6.60317i	0.312468	+	0.227022i
$847$	15.8937	+	11.5474i	0.546113	+	0.396774i
$848$	−2.89617	+	8.91349i	−0.0994548	+	0.306090i
$849$	−25.8349			−0.886651
$850$	−10.8082	−	8.60170i	−0.370717	−	0.295036i
$851$	−12.5253			−0.429362
$852$	−2.24079	+	6.89645i	−0.0767683	+	0.236269i
$853$	9.43663	+	6.85611i	0.323104	+	0.234749i	0.737499	−	0.675348i	$-0.236007\pi$
$853$	9.43663	+	6.85611i	0.323104	+	0.234749i	−0.414395	+	0.910097i	$0.636007\pi$
$854$	2.02899	+	1.47415i	0.0694307	+	0.0504444i
$855$	14.1402	+	4.94001i	0.483585	+	0.168945i
$856$	6.13960	−	4.46068i	0.209847	−	0.152463i
$857$	−18.8423			−0.643642			−0.321821	−	0.946800i	$-0.604295\pi$
$857$	−18.8423			−0.643642			−0.321821	+	0.946800i	$0.604295\pi$
$858$	29.6810	−	21.5645i	1.01329	−	0.736201i
$859$	−11.7513	−	36.1669i	−0.400951	−	1.23400i	−0.924229	−	0.381838i	$-0.875291\pi$
$859$	−11.7513	−	36.1669i	−0.400951	−	1.23400i	0.523279	−	0.852162i	$-0.324709\pi$
$860$	9.33036	+	3.25964i	0.318163	+	0.111153i
$861$	1.55074	−	4.77268i	0.0528490	−	0.162652i
$862$	−10.3526	−	31.8621i	−0.352612	−	1.08523i
$863$	1.80062	+	5.54174i	0.0612938	+	0.188643i	0.977015	−	0.213172i	$-0.0683795\pi$
$863$	1.80062	+	5.54174i	0.0612938	+	0.188643i	−0.915721	+	0.401815i	$0.868379\pi$
$864$	−0.972381	+	2.99268i	−0.0330811	+	0.101813i
$865$	−0.819550	+	37.3413i	−0.0278655	+	1.26964i
$866$	6.14803	+	18.9217i	0.208918	+	0.642985i
$867$	−16.1123	+	11.7063i	−0.547204	+	0.397567i
$868$	10.3659			0.351843
$869$	−41.6058	+	30.2284i	−1.41138	+	1.02543i
$870$	39.0497	−	11.7472i	1.32391	−	0.398268i
$871$	−15.9879	−	11.6159i	−0.541730	−	0.393590i
$872$	−16.0250	−	11.6428i	−0.542674	−	0.394276i
$873$	−4.07517	+	12.5421i	−0.137924	+	0.424485i
$874$	−9.72582			−0.328981
$875$	7.15243	−	8.59318i	0.241796	−	0.290503i
$876$	3.11501			0.105247
$877$	−13.3007	+	40.9354i	−0.449133	+	1.38229i	0.428754	+	0.903421i	$0.358953\pi$
$877$	−13.3007	+	40.9354i	−0.449133	+	1.38229i	−0.877887	+	0.478867i	$0.841047\pi$
$878$	9.88584	+	7.18248i	0.333631	+	0.242397i
$879$	−21.0947	−	15.3262i	−0.711506	−	0.516939i
$880$	11.8538	−	3.56594i	0.399591	−	0.120208i
$881$	−29.7248	+	21.5963i	−1.00145	+	0.727599i	−0.962399	−	0.271638i	$-0.912435\pi$
$881$	−29.7248	+	21.5963i	−1.00145	+	0.727599i	−0.0390542	+	0.999237i	$0.512435\pi$
$882$	−1.51991			−0.0511779
$883$	−18.1969	+	13.2208i	−0.612374	+	0.444916i	−0.850250	−	0.526380i	$-0.823549\pi$
$883$	−18.1969	+	13.2208i	−0.612374	+	0.444916i	0.237875	+	0.971296i	$0.423549\pi$
$884$	2.66122	+	8.19038i	0.0895064	+	0.275472i
$885$	0.819224	−	37.3265i	0.0275379	−	1.25472i
$886$	6.47801	−	19.9373i	0.217633	−	0.669806i
$887$	11.7919	+	36.2916i	0.395932	+	1.21855i	0.928234	+	0.371998i	$0.121327\pi$
$887$	11.7919	+	36.2916i	0.395932	+	1.21855i	−0.532302	+	0.846555i	$0.678673\pi$
$888$	−3.72881	−	11.4761i	−0.125131	−	0.385112i
$889$	−1.83115	+	5.63569i	−0.0614147	+	0.189015i
$890$	−5.81687	−	2.03217i	−0.194982	−	0.0681186i
$891$	19.2444	+	59.2281i	0.644711	+	1.98422i
$892$	−8.80583	+	6.39781i	−0.294841	+	0.214214i
$893$	32.5745			1.09007
$894$	−15.8244	+	11.4971i	−0.529247	+	0.384521i
$895$	11.9118	+	4.16150i	0.398168	+	0.139104i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	11.8320	+	8.59649i	0.395061	+	0.287028i
$898$	0.365946	−	1.12627i	0.0122118	−	0.0375840i
$899$	88.9179			2.96558
$900$	−2.02902	−	7.32365i	−0.0676340	−	0.244122i
$901$	−25.8921			−0.862590
$902$	4.03792	−	12.4274i	0.134448	−	0.413789i
$903$	−7.60225	−	5.52336i	−0.252987	−	0.183806i
$904$	2.04842	+	1.48826i	0.0681293	+	0.0494988i
$905$	6.26457	−	8.23616i	0.208241	−	0.273779i
$906$	−24.1520	+	17.5474i	−0.802396	+	0.582975i
$907$	34.9575			1.16075			0.580373	−	0.814351i	$-0.302907\pi$
$907$	34.9575			1.16075			0.580373	+	0.814351i	$0.302907\pi$
$908$	−2.37445	+	1.72514i	−0.0787989	+	0.0572508i
$909$	7.99436	+	24.6041i	0.265156	+	0.816067i
$910$	−6.67490	+	2.00799i	−0.221271	+	0.0665643i
$911$	−2.12857	+	6.55107i	−0.0705227	+	0.217047i	−0.980106	−	0.198475i	$-0.936401\pi$
$911$	−2.12857	+	6.55107i	−0.0705227	+	0.217047i	0.909583	+	0.415522i	$0.136401\pi$
$912$	−2.89540	−	8.91112i	−0.0958762	−	0.295077i
$913$	−25.7955	−	79.3904i	−0.853707	−	2.62744i
$914$	−8.64999	+	26.6219i	−0.286116	+	0.880575i
$915$	7.21791	−	9.48953i	0.238617	−	0.313714i
$916$	−3.34747	−	10.3024i	−0.110603	−	0.340402i
$917$	11.8925	−	8.64041i	0.392725	−	0.285331i
$918$	−8.69320			−0.286918
$919$	−30.7087	+	22.3112i	−1.01299	+	0.735979i	−0.964834	−	0.262861i	$-0.915334\pi$
$919$	−30.7087	+	22.3112i	−1.01299	+	0.735979i	−0.0481539	+	0.998840i	$0.515334\pi$
$920$	2.81218	+	4.05484i	0.0927148	+	0.133684i
$921$	15.6402	+	11.3633i	0.515362	+	0.374432i
$922$	18.3807	+	13.3543i	0.605335	+	0.439802i
$923$	3.28556	−	10.1119i	0.108146	−	0.332838i
$924$	−11.7693			−0.387180
$925$	−22.2049	−	17.6718i	−0.730093	−	0.581046i
$926$	28.7491			0.944753
$927$	2.35860	−	7.25904i	0.0774667	−	0.238418i
$928$	−6.93966	−	5.04196i	−0.227805	−	0.165510i
$929$	23.8487	+	17.3271i	0.782452	+	0.568484i	0.905714	−	0.423890i	$-0.139336\pi$
$929$	23.8487	+	17.3271i	0.782452	+	0.568484i	−0.123262	+	0.992374i	$0.539336\pi$
$930$	1.08128	−	49.2667i	0.0354566	−	1.61552i
$931$	−3.56549	+	2.59048i	−0.116854	+	0.0848995i
$932$	−24.1731			−0.791815
$933$	−6.01115	+	4.36736i	−0.196796	+	0.142981i
$934$	11.0604	+	34.0406i	0.361909	+	1.11384i
$935$	19.4889	+	28.1008i	0.637356	+	0.918994i
$936$	−1.46410	+	4.50604i	−0.0478557	+	0.147285i
$937$	−1.79449	−	5.52286i	−0.0586233	−	0.180424i	0.917457	−	0.397836i	$-0.130239\pi$
$937$	−1.79449	−	5.52286i	−0.0586233	−	0.180424i	−0.976080	+	0.217412i	$0.930239\pi$
$938$	1.95905	+	6.02932i	0.0639651	+	0.196864i
$939$	−7.38611	+	22.7321i	−0.241037	+	0.741834i
$940$	−9.41878	−	13.5808i	−0.307207	−	0.442957i
$941$	−12.9840	−	39.9608i	−0.423268	−	1.30268i	−0.904643	−	0.426170i	$-0.859863\pi$
$941$	−12.9840	−	39.9608i	−0.423268	−	1.30268i	0.481375	−	0.876515i	$-0.340137\pi$
$942$	26.6475	−	19.3605i	0.868222	−	0.630800i
$943$	5.20903			0.169629
$944$	−6.35374	+	4.61626i	−0.206797	+	0.150247i
$945$	0.154390	−	7.03452i	0.00502232	−	0.228833i
$946$	−19.7953	−	14.3821i	−0.643600	−	0.467603i
$947$	−23.1921	−	16.8501i	−0.753643	−	0.547554i	0.143311	−	0.989678i	$-0.454225\pi$
$947$	−23.1921	−	16.8501i	−0.753643	−	0.547554i	−0.896954	+	0.442124i	$0.854225\pi$
$948$	6.10322	−	18.7838i	0.198223	−	0.610069i
$949$	−4.56738			−0.148264
$950$	−17.2420	−	13.7221i	−0.559404	−	0.445203i
$951$	−26.6517			−0.864241
$952$	0.853705	−	2.62743i	0.0276687	−	0.0851556i
$953$	−23.4433	−	17.0326i	−0.759404	−	0.551739i	0.139324	−	0.990247i	$-0.455507\pi$
$953$	−23.4433	−	17.0326i	−0.759404	−	0.551739i	−0.898727	+	0.438508i	$0.855507\pi$
$954$	−11.5243	−	8.37291i	−0.373114	−	0.271083i
$955$	−31.0979	−	44.8397i	−1.00630	−	1.45098i
$956$	−9.46325	+	6.87546i	−0.306063	+	0.222368i
$957$	−100.955			−3.26342
$958$	16.1793	−	11.7550i	0.522731	−	0.379786i
$959$	3.07635	+	9.46804i	0.0993406	+	0.305739i
$960$	−2.87799	+	3.78374i	−0.0928866	+	0.122120i
$961$	23.6252	−	72.7108i	0.762102	−	2.34551i
$962$	5.46736	+	16.8268i	0.176275	+	0.542518i
$963$	3.56436	+	10.9700i	0.114860	+	0.353502i
$964$	−3.23808	+	9.96577i	−0.104291	+	0.320976i
$965$	−24.3510	+	7.32544i	−0.783887	+	0.235814i
$966$	−1.44981	−	4.46207i	−0.0466470	−	0.143565i
$967$	26.7552	−	19.4388i	0.860389	−	0.625109i	−0.0676017	−	0.997712i	$-0.521535\pi$
$967$	26.7552	−	19.4388i	0.860389	−	0.625109i	0.927991	+	0.372603i	$0.121535\pi$
$968$	−19.6456			−0.631435
$969$	20.9416	−	15.2149i	0.672740	−	0.488774i
$970$	11.7455	−	15.4420i	0.377125	−	0.495813i
$971$	−0.775728	−	0.563599i	−0.0248943	−	0.0180868i	0.575269	−	0.817965i	$-0.304898\pi$
$971$	−0.775728	−	0.563599i	−0.0248943	−	0.0180868i	−0.600163	+	0.799878i	$0.704898\pi$
$972$	−11.7119	−	8.50917i	−0.375658	−	0.272932i
$973$	2.41226	−	7.42417i	0.0773335	−	0.238008i
$974$	−20.1242			−0.644820
$975$	8.84722	+	31.9336i	0.283338	+	1.02269i
$976$	−2.50797			−0.0802783
$977$	−0.0462000	+	0.142189i	−0.00147807	+	0.00454903i	−0.951793	−	0.306742i	$-0.900761\pi$
$977$	−0.0462000	+	0.142189i	−0.00147807	+	0.00454903i	0.950315	+	0.311291i	$0.100761\pi$
$978$	25.8641	+	18.7914i	0.827044	+	0.600883i
$979$	12.3411	+	8.96631i	0.394422	+	0.286565i
$980$	2.11095	+	0.737480i	0.0674319	+	0.0235579i
$981$	24.3564	−	17.6960i	0.777641	−	0.564989i
$982$	5.36890			0.171329
$983$	−24.3601	+	17.6986i	−0.776966	+	0.564499i	−0.904067	−	0.427391i	$-0.859433\pi$
$983$	−24.3601	+	17.6986i	−0.776966	+	0.564499i	0.127101	+	0.991890i	$0.459433\pi$
$984$	1.55074	+	4.77268i	0.0494357	+	0.152147i
$985$	−5.22347	−	1.82486i	−0.166433	−	0.0581450i
$986$	7.32299	−	22.5378i	0.233212	−	0.717751i
$987$	4.85584	+	14.9447i	0.154563	+	0.475696i
$988$	4.24537	+	13.0659i	0.135063	+	0.415682i
$989$	3.01417	−	9.27666i	0.0958450	−	0.294980i
$990$	−0.412826	+	18.8097i	−0.0131205	+	0.597811i
$991$	0.0363103	+	0.111751i	0.00115343	+	0.00354990i	0.951632	−	0.307242i	$-0.0994059\pi$
$991$	0.0363103	+	0.111751i	0.00115343	+	0.00354990i	−0.950478	+	0.310791i	$0.899406\pi$
$992$	−8.38622	+	6.09294i	−0.266263	+	0.193451i
$993$	−55.5119			−1.76162
$994$	−2.75939	+	2.00481i	−0.0875224	+	0.0635888i
$995$	28.5527	−	8.58943i	0.905183	−	0.272303i
$996$	25.9358	+	18.8435i	0.821807	+	0.597078i
$997$	7.29368	+	5.29917i	0.230993	+	0.167826i	0.697261	−	0.716817i	$-0.254402\pi$
$997$	7.29368	+	5.29917i	0.230993	+	0.167826i	−0.466268	+	0.884644i	$0.654402\pi$
$998$	2.72353	−	8.38216i	0.0862118	−	0.265333i
$999$	−17.8598			−0.565060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.b.71.3	✓	12
25.6	even	5	inner	350.2.h.b.281.3	yes	12
25.9	even	10		8750.2.a.q.1.6		6
25.16	even	5		8750.2.a.p.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.b.71.3	✓	12	1.1	even	1	trivial
350.2.h.b.281.3	yes	12	25.6	even	5	inner
8750.2.a.p.1.1		6	25.16	even	5
8750.2.a.q.1.6		6	25.9	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.71998 + 1.24964i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.14128 + 0.644154i) q^{5} +(-1.71998 + 1.24964i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.469677 + 1.44552i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(1.71998 + 1.24964i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.14128 + 0.644154i) q^{5} +(-1.71998 + 1.24964i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.469677 + 1.44552i) q^{9} +(0.0490643 - 2.23553i) q^{10} +(-1.71067 + 5.26491i) q^{11} +(-0.656972 - 2.02195i) q^{12} +(0.963285 + 2.96469i) q^{13} +(0.309017 - 0.951057i) q^{14} +(-4.48790 - 1.56789i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.23503 + 1.62384i) q^{17} -1.51991 q^{18} +(-3.56549 + 2.59048i) q^{19} +(2.11095 + 0.737480i) q^{20} +(-1.71998 - 1.24964i) q^{21} +(-4.47860 - 3.25389i) q^{22} +(0.681942 - 2.09880i) q^{23} +2.12601 q^{24} +(4.17013 - 2.75862i) q^{25} -3.11725 q^{26} +(0.972381 - 2.99268i) q^{27} +(0.809017 + 0.587785i) q^{28} +(6.93966 + 5.04196i) q^{29} +(2.87799 - 3.78374i) q^{30} +(8.38622 - 6.09294i) q^{31} -1.00000 q^{32} +(-9.52153 + 6.91780i) q^{33} +(-0.853705 - 2.62743i) q^{34} +(2.14128 - 0.644154i) q^{35} +(0.469677 - 1.44552i) q^{36} +(-1.75390 - 5.39795i) q^{37} +(-1.36189 - 4.19148i) q^{38} +(-2.04795 + 6.30294i) q^{39} +(-1.35371 + 1.77974i) q^{40} +(0.729413 + 2.24490i) q^{41} +(1.71998 - 1.24964i) q^{42} +4.41997 q^{43} +(4.47860 - 3.25389i) q^{44} +(-1.93684 - 2.79271i) q^{45} +(1.78535 + 1.29713i) q^{46} +(-5.97964 - 4.34446i) q^{47} +(-0.656972 + 2.02195i) q^{48} +1.00000 q^{49} +(1.33496 + 4.81849i) q^{50} -5.87341 q^{51} +(0.963285 - 2.96469i) q^{52} +(7.58227 + 5.50884i) q^{53} +(2.54573 + 1.84958i) q^{54} +(0.271613 - 12.3756i) q^{55} +(-0.809017 + 0.587785i) q^{56} -9.36970 q^{57} +(-6.93966 + 5.04196i) q^{58} +(2.42691 + 7.46927i) q^{59} +(2.70921 + 3.90637i) q^{60} +(-0.775006 + 2.38522i) q^{61} +(3.20325 + 9.85859i) q^{62} +(-0.469677 - 1.44552i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.97237 - 5.72771i) q^{65} +(-3.63690 - 11.1932i) q^{66} +(-5.12885 + 3.72633i) q^{67} +2.76265 q^{68} +(3.79566 - 2.75771i) q^{69} +(-0.0490643 + 2.23553i) q^{70} +(-2.75939 - 2.00481i) q^{71} +(1.22963 + 0.893378i) q^{72} +(-0.452770 + 1.39348i) q^{73} +5.67574 q^{74} +(10.6198 + 0.466381i) q^{75} +4.40718 q^{76} +(1.71067 - 5.26491i) q^{77} +(-5.36160 - 3.89543i) q^{78} +(7.51570 + 5.46048i) q^{79} +(-1.27432 - 1.83742i) q^{80} +(9.10112 - 6.61235i) q^{81} -2.36043 q^{82} +(-12.1993 + 8.86331i) q^{83} +(0.656972 + 2.02195i) q^{84} +(3.73981 - 4.91680i) q^{85} +(-1.36585 + 4.20365i) q^{86} +(5.63544 + 17.3441i) q^{87} +(1.71067 + 5.26491i) q^{88} +(0.851517 - 2.62070i) q^{89} +(3.25454 - 0.979053i) q^{90} +(-0.963285 - 2.96469i) q^{91} +(-1.78535 + 1.29713i) q^{92} +22.0381 q^{93} +(5.97964 - 4.34446i) q^{94} +(5.96603 - 7.84365i) q^{95} +(-1.71998 - 1.24964i) q^{96} +(7.01947 + 5.09995i) q^{97} +(-0.309017 + 0.951057i) q^{98} -8.41397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9	\( 12 q + 3 q^{2} + q^{3} - 3 q^{4} - 5 q^{5} - q^{6} - 12 q^{7} + 3 q^{8} + 6 q^{9} + 7 q^{11} - 4 q^{12} + 3 q^{13} - 3 q^{14} - 10 q^{15} - 3 q^{16} + 4 q^{17} - 6 q^{18} + 4 q^{19} + 5 q^{20} - q^{21} - 2 q^{22} - q^{23} - 6 q^{24} - 5 q^{25} + 12 q^{26} + 10 q^{27} + 3 q^{28} + 22 q^{29} + 15 q^{30} + 31 q^{31} - 12 q^{32} - 21 q^{33} + 6 q^{34} + 5 q^{35} + 6 q^{36} + 9 q^{37} - 4 q^{38} - 20 q^{39} - 19 q^{41} + q^{42} + 50 q^{43} + 2 q^{44} - 25 q^{45} + 16 q^{46} - 24 q^{47} - 4 q^{48} + 12 q^{49} - 58 q^{51} + 3 q^{52} + 35 q^{53} + 25 q^{54} - 10 q^{55} - 3 q^{56} - 44 q^{57} - 22 q^{58} + q^{59} - 5 q^{60} + 8 q^{61} + 19 q^{62} - 6 q^{63} - 3 q^{64} - 25 q^{65} - 14 q^{66} - 36 q^{67} + 4 q^{68} - 31 q^{69} + q^{71} + 9 q^{72} - 31 q^{73} - 14 q^{74} + 55 q^{75} - 16 q^{76} - 7 q^{77} - 30 q^{78} + 2 q^{79} - 8 q^{81} - 6 q^{82} - 19 q^{83} + 4 q^{84} + 20 q^{85} + 10 q^{86} + 28 q^{87} - 7 q^{88} + 40 q^{89} + 20 q^{90} - 3 q^{91} - 16 q^{92} + 50 q^{93} + 24 q^{94} - q^{96} + 28 q^{97} + 3 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + q^3 - 3 * q^4 - 5 * q^5 - q^6 - 12 * q^7 + 3 * q^8 + 6 * q^9 + 7 * q^11 - 4 * q^12 + 3 * q^13 - 3 * q^14 - 10 * q^15 - 3 * q^16 + 4 * q^17 - 6 * q^18 + 4 * q^19 + 5 * q^20 - q^21 - 2 * q^22 - q^23 - 6 * q^24 - 5 * q^25 + 12 * q^26 + 10 * q^27 + 3 * q^28 + 22 * q^29 + 15 * q^30 + 31 * q^31 - 12 * q^32 - 21 * q^33 + 6 * q^34 + 5 * q^35 + 6 * q^36 + 9 * q^37 - 4 * q^38 - 20 * q^39 - 19 * q^41 + q^42 + 50 * q^43 + 2 * q^44 - 25 * q^45 + 16 * q^46 - 24 * q^47 - 4 * q^48 + 12 * q^49 - 58 * q^51 + 3 * q^52 + 35 * q^53 + 25 * q^54 - 10 * q^55 - 3 * q^56 - 44 * q^57 - 22 * q^58 + q^59 - 5 * q^60 + 8 * q^61 + 19 * q^62 - 6 * q^63 - 3 * q^64 - 25 * q^65 - 14 * q^66 - 36 * q^67 + 4 * q^68 - 31 * q^69 + q^71 + 9 * q^72 - 31 * q^73 - 14 * q^74 + 55 * q^75 - 16 * q^76 - 7 * q^77 - 30 * q^78 + 2 * q^79 - 8 * q^81 - 6 * q^82 - 19 * q^83 + 4 * q^84 + 20 * q^85 + 10 * q^86 + 28 * q^87 - 7 * q^88 + 40 * q^89 + 20 * q^90 - 3 * q^91 - 16 * q^92 + 50 * q^93 + 24 * q^94 - q^96 + 28 * q^97 + 3 * q^98 - 24 * q^99

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