LMFDB - Embedded newform 350.2.h.b.141.3

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			141.3
Root			$1.03979 - 1.59275i$ of defining polynomial
Character	$\chi$	$=$	350.141
Dual form			350.2.h.b.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.764888 + 2.35408i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23328 + 0.111663i) q^{5} +(-0.764888 + 2.35408i) q^{6} -1.00000 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.52960 + 1.83786i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.764888 + 2.35408i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23328 + 0.111663i) q^{5} +(-0.764888 + 2.35408i) q^{6} -1.00000 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.52960 + 1.83786i) q^{9} +(-1.87239 - 1.22235i) q^{10} +(1.95164 + 1.41795i) q^{11} +(-2.00250 + 1.45490i) q^{12} +(-0.582288 + 0.423057i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.97107 - 5.17191i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.414022 - 1.27423i) q^{17} -3.12675 q^{18} +(-1.31637 + 4.05137i) q^{19} +(-0.796319 - 2.08947i) q^{20} +(-0.764888 - 2.35408i) q^{21} +(0.745462 + 2.29430i) q^{22} +(4.65736 + 3.38377i) q^{23} -2.47523 q^{24} +(4.97506 - 0.498749i) q^{25} -0.719747 q^{26} +(-0.253824 - 0.184414i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-1.86600 - 5.74295i) q^{29} +(1.44534 - 5.34273i) q^{30} +(2.60388 - 8.01393i) q^{31} -1.00000 q^{32} +(-1.84519 + 5.67891i) q^{33} +(1.08392 - 0.787516i) q^{34} +(2.23328 - 0.111663i) q^{35} +(-2.52960 - 1.83786i) q^{36} +(3.93630 - 2.85989i) q^{37} +(-3.44630 + 2.50388i) q^{38} +(-1.44130 - 1.04716i) q^{39} +(0.583923 - 2.15848i) q^{40} +(-7.85364 + 5.70600i) q^{41} +(0.764888 - 2.35408i) q^{42} +7.94381 q^{43} +(-0.745462 + 2.29430i) q^{44} +(5.44407 - 4.38691i) q^{45} +(1.77895 + 5.47506i) q^{46} +(1.06751 + 3.28545i) q^{47} +(-2.00250 - 1.45490i) q^{48} +1.00000 q^{49} +(4.31807 + 2.52077i) q^{50} +3.31632 q^{51} +(-0.582288 - 0.423057i) q^{52} +(3.94101 + 12.1292i) q^{53} +(-0.0969523 - 0.298389i) q^{54} +(-4.51690 - 2.94876i) q^{55} +(0.309017 - 0.951057i) q^{56} -10.5441 q^{57} +(1.86600 - 5.74295i) q^{58} +(1.85886 - 1.35054i) q^{59} +(4.30968 - 3.47281i) q^{60} +(0.115532 + 0.0839393i) q^{61} +(6.81706 - 4.95288i) q^{62} +(2.52960 - 1.83786i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.25317 - 1.00982i) q^{65} +(-4.83077 + 3.50976i) q^{66} +(0.485370 - 1.49381i) q^{67} +1.33980 q^{68} +(-4.40332 + 13.5520i) q^{69} +(1.87239 + 1.22235i) q^{70} +(-1.12360 - 3.45809i) q^{71} +(-0.966220 - 2.97372i) q^{72} +(9.50503 + 6.90581i) q^{73} +4.86554 q^{74} +(4.97946 + 11.3302i) q^{75} -4.25986 q^{76} +(-1.95164 - 1.41795i) q^{77} +(-0.550526 - 1.69434i) q^{78} +(-4.93270 - 15.1813i) q^{79} +(1.74113 - 1.40303i) q^{80} +(-2.65868 + 8.18258i) q^{81} -9.70763 q^{82} +(0.226661 - 0.697591i) q^{83} +(2.00250 - 1.45490i) q^{84} +(-0.782342 + 2.89194i) q^{85} +(6.42667 + 4.66925i) q^{86} +(12.0921 - 8.78542i) q^{87} +(-1.95164 + 1.41795i) q^{88} +(-8.26235 - 6.00295i) q^{89} +(6.98291 - 0.349143i) q^{90} +(0.582288 - 0.423057i) q^{91} +(-1.77895 + 5.47506i) q^{92} +20.8571 q^{93} +(-1.06751 + 3.28545i) q^{94} +(2.48743 - 9.19482i) q^{95} +(-0.764888 - 2.35408i) q^{96} +(-4.14808 - 12.7665i) q^{97} +(0.809017 + 0.587785i) q^{98} -7.54287 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.764888	+	2.35408i	0.441608	+	1.35913i	0.886161	+	0.463377i	$0.153362\pi$
$3$	0.764888	+	2.35408i	0.441608	+	1.35913i	−0.444553	+	0.895752i	$0.646638\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.23328	+	0.111663i	−0.998752	+	0.0499372i
$5$	−2.23328	+	0.111663i	−0.998752	+	0.0499372i
$6$	−0.764888	+	2.35408i	−0.312264	+	0.961050i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.52960	+	1.83786i	−0.843199	+	0.612620i
$10$	−1.87239	−	1.22235i	−0.592103	−	0.386541i
$11$	1.95164	+	1.41795i	0.588443	+	0.427529i	0.841758	−	0.539855i	$-0.181521\pi$
$11$	1.95164	+	1.41795i	0.588443	+	0.427529i	−0.253315	+	0.967384i	$0.581521\pi$
$12$	−2.00250	+	1.45490i	−0.578072	+	0.419994i
$13$	−0.582288	+	0.423057i	−0.161498	+	0.117335i	−0.665599	−	0.746310i	$-0.731824\pi$
$13$	−0.582288	+	0.423057i	−0.161498	+	0.117335i	0.504101	+	0.863645i	$0.331824\pi$
$14$	−0.809017	−	0.587785i	−0.216219	−	0.157092i
$15$	−1.97107	−	5.17191i	−0.508928	−	1.33538i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.414022	−	1.27423i	0.100415	−	0.309046i	−0.888212	−	0.459434i	$-0.848052\pi$
$17$	0.414022	−	1.27423i	0.100415	−	0.309046i	0.988627	+	0.150388i	$0.0480523\pi$
$18$	−3.12675			−0.736983
$19$	−1.31637	+	4.05137i	−0.301996	+	0.929447i	0.678786	+	0.734337i	$0.262507\pi$
$19$	−1.31637	+	4.05137i	−0.301996	+	0.929447i	−0.980781	+	0.195111i	$0.937493\pi$
$20$	−0.796319	−	2.08947i	−0.178062	−	0.467219i
$21$	−0.764888	−	2.35408i	−0.166912	−	0.513703i
$22$	0.745462	+	2.29430i	0.158933	+	0.489146i
$23$	4.65736	+	3.38377i	0.971127	+	0.705565i	0.955708	−	0.294316i	$-0.0950918\pi$
$23$	4.65736	+	3.38377i	0.971127	+	0.705565i	0.0154188	+	0.999881i	$0.495092\pi$
$24$	−2.47523			−0.505254
$25$	4.97506	−	0.498749i	0.995013	−	0.0997498i
$26$	−0.719747			−0.141154
$27$	−0.253824	−	0.184414i	−0.0488485	−	0.0354905i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	−1.86600	−	5.74295i	−0.346507	−	1.06644i	−0.960772	−	0.277339i	$-0.910547\pi$
$29$	−1.86600	−	5.74295i	−0.346507	−	1.06644i	0.614265	−	0.789100i	$-0.289453\pi$
$30$	1.44534	−	5.34273i	0.263882	−	0.975444i
$31$	2.60388	−	8.01393i	0.467671	−	1.43934i	−0.387920	−	0.921693i	$-0.626806\pi$
$31$	2.60388	−	8.01393i	0.467671	−	1.43934i	0.855592	−	0.517652i	$-0.173194\pi$
$32$	−1.00000			−0.176777
$33$	−1.84519	+	5.67891i	−0.321206	+	0.988571i
$34$	1.08392	−	0.787516i	0.185891	−	0.135058i
$35$	2.23328	−	0.111663i	0.377493	−	0.0188745i
$36$	−2.52960	−	1.83786i	−0.421599	−	0.306310i
$37$	3.93630	−	2.85989i	0.647124	−	0.470163i	−0.215166	−	0.976577i	$-0.569029\pi$
$37$	3.93630	−	2.85989i	0.647124	−	0.470163i	0.862290	+	0.506414i	$0.169029\pi$
$38$	−3.44630	+	2.50388i	−0.559063	+	0.406183i
$39$	−1.44130	−	1.04716i	−0.230792	−	0.167680i
$40$	0.583923	−	2.15848i	0.0923264	−	0.341286i
$41$	−7.85364	+	5.70600i	−1.22653	+	0.891128i	−0.996625	−	0.0820852i	$-0.973842\pi$
$41$	−7.85364	+	5.70600i	−1.22653	+	0.891128i	−0.229906	+	0.973213i	$0.573842\pi$
$42$	0.764888	−	2.35408i	0.118025	−	0.363243i
$43$	7.94381			1.21142			0.605709	−	0.795686i	$-0.292889\pi$
$43$	7.94381			1.21142			0.605709	+	0.795686i	$0.292889\pi$
$44$	−0.745462	+	2.29430i	−0.112383	+	0.345878i
$45$	5.44407	−	4.38691i	0.811554	−	0.653963i
$46$	1.77895	+	5.47506i	0.262292	+	0.807253i
$47$	1.06751	+	3.28545i	0.155712	+	0.479232i	0.998232	−	0.0594322i	$-0.0189290\pi$
$47$	1.06751	+	3.28545i	0.155712	+	0.479232i	−0.842520	+	0.538665i	$0.818929\pi$
$48$	−2.00250	−	1.45490i	−0.289036	−	0.209997i
$49$	1.00000			0.142857
$50$	4.31807	+	2.52077i	0.610667	+	0.356491i
$51$	3.31632			0.464377
$52$	−0.582288	−	0.423057i	−0.0807488	−	0.0586674i
$53$	3.94101	+	12.1292i	0.541339	+	1.66607i	0.729539	+	0.683939i	$0.239735\pi$
$53$	3.94101	+	12.1292i	0.541339	+	1.66607i	−0.188200	+	0.982131i	$0.560265\pi$
$54$	−0.0969523	−	0.298389i	−0.0131935	−	0.0406055i
$55$	−4.51690	−	2.94876i	−0.609058	−	0.397610i
$56$	0.309017	−	0.951057i	0.0412941	−	0.127090i
$57$	−10.5441			−1.39660
$58$	1.86600	−	5.74295i	0.245017	−	0.754086i
$59$	1.85886	−	1.35054i	0.242003	−	0.175826i	−0.460172	−	0.887830i	$-0.652212\pi$
$59$	1.85886	−	1.35054i	0.242003	−	0.175826i	0.702175	+	0.712004i	$0.252212\pi$
$60$	4.30968	−	3.47281i	0.556378	−	0.448337i
$61$	0.115532	+	0.0839393i	0.0147924	+	0.0107473i	0.595157	−	0.803610i	$-0.297090\pi$
$61$	0.115532	+	0.0839393i	0.0147924	+	0.0107473i	−0.580364	+	0.814357i	$0.697090\pi$
$62$	6.81706	−	4.95288i	0.865767	−	0.629017i
$63$	2.52960	−	1.83786i	0.318699	−	0.231549i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.25317	−	1.00982i	0.155437	−	0.125253i
$66$	−4.83077	+	3.50976i	−0.594626	+	0.432021i
$67$	0.485370	−	1.49381i	0.0592973	−	0.182498i	−0.917020	−	0.398841i	$-0.869413\pi$
$67$	0.485370	−	1.49381i	0.0592973	−	0.182498i	0.976318	+	0.216342i	$0.0694127\pi$
$68$	1.33980			0.162475
$69$	−4.40332	+	13.5520i	−0.530097	+	1.63147i
$70$	1.87239	+	1.22235i	0.223794	+	0.146099i
$71$	−1.12360	−	3.45809i	−0.133347	−	0.410400i	0.861982	−	0.506938i	$-0.169223\pi$
$71$	−1.12360	−	3.45809i	−0.133347	−	0.410400i	−0.995329	+	0.0965387i	$0.969223\pi$
$72$	−0.966220	−	2.97372i	−0.113870	−	0.350456i
$73$	9.50503	+	6.90581i	1.11248	+	0.808263i	0.983052	−	0.183326i	$-0.0586863\pi$
$73$	9.50503	+	6.90581i	1.11248	+	0.808263i	0.129427	+	0.991589i	$0.458686\pi$
$74$	4.86554			0.565607
$75$	4.97946	+	11.3302i	0.574978	+	1.30830i
$76$	−4.25986			−0.488639
$77$	−1.95164	−	1.41795i	−0.222411	−	0.161591i
$78$	−0.550526	−	1.69434i	−0.0623348	−	0.191847i
$79$	−4.93270	−	15.1813i	−0.554972	−	1.70803i	−0.696017	−	0.718025i	$-0.745046\pi$
$79$	−4.93270	−	15.1813i	−0.554972	−	1.70803i	0.141045	−	0.990003i	$-0.454954\pi$
$80$	1.74113	−	1.40303i	0.194664	−	0.156863i
$81$	−2.65868	+	8.18258i	−0.295409	+	0.909175i
$82$	−9.70763			−1.07203
$83$	0.226661	−	0.697591i	0.0248793	−	0.0765706i	−0.937846	−	0.347052i	$-0.887183\pi$
$83$	0.226661	−	0.697591i	0.0248793	−	0.0765706i	0.962725	+	0.270481i	$0.0871828\pi$
$84$	2.00250	−	1.45490i	0.218491	−	0.158743i
$85$	−0.782342	+	2.89194i	−0.0848569	+	0.313675i
$86$	6.42667	+	4.66925i	0.693006	+	0.503498i
$87$	12.0921	−	8.78542i	1.29641	−	0.941896i
$88$	−1.95164	+	1.41795i	−0.208046	+	0.151154i
$89$	−8.26235	−	6.00295i	−0.875808	−	0.636312i	0.0563313	−	0.998412i	$-0.482060\pi$
$89$	−8.26235	−	6.00295i	−0.875808	−	0.636312i	−0.932139	+	0.362101i	$0.882060\pi$
$90$	6.98291	−	0.349143i	0.736063	−	0.0368029i
$91$	0.582288	−	0.423057i	0.0610404	−	0.0443484i
$92$	−1.77895	+	5.47506i	−0.185469	+	0.570814i
$93$	20.8571			2.16278
$94$	−1.06751	+	3.28545i	−0.110105	+	0.338869i
$95$	2.48743	−	9.19482i	0.255205	−	0.943368i
$96$	−0.764888	−	2.35408i	−0.0780660	−	0.240262i
$97$	−4.14808	−	12.7665i	−0.421173	−	1.29624i	−0.906611	−	0.421967i	$-0.861340\pi$
$97$	−4.14808	−	12.7665i	−0.421173	−	1.29624i	0.485438	−	0.874271i	$-0.338660\pi$
$98$	0.809017	+	0.587785i	0.0817231	+	0.0593753i
$99$	−7.54287			−0.758087
$100$	2.01172	+	4.57744i	0.201172	+	0.457744i
$101$	−4.34978			−0.432820			−0.216410	−	0.976303i	$-0.569435\pi$
$101$	−4.34978			−0.432820			−0.216410	+	0.976303i	$0.569435\pi$
$102$	2.68296	+	1.94928i	0.265652	+	0.193008i
$103$	−2.00397	−	6.16759i	−0.197457	−	0.607711i	−0.999939	−	0.0110343i	$-0.996488\pi$
$103$	−2.00397	−	6.16759i	−0.197457	−	0.607711i	0.802482	−	0.596676i	$-0.203512\pi$
$104$	−0.222414	−	0.684520i	−0.0218095	−	0.0671228i
$105$	1.97107	+	5.17191i	0.192357	+	0.504727i
$106$	−3.94101	+	12.1292i	−0.382784	+	1.17809i
$107$	−16.5272			−1.59775			−0.798873	−	0.601499i	$-0.794570\pi$
$107$	−16.5272			−1.59775			−0.798873	+	0.601499i	$0.794570\pi$
$108$	0.0969523	−	0.298389i	0.00932924	−	0.0287124i
$109$	14.3461	−	10.4230i	1.37411	−	0.998347i	0.376703	−	0.926334i	$-0.377058\pi$
$109$	14.3461	−	10.4230i	1.37411	−	0.998347i	0.997404	−	0.0720126i	$-0.0229422\pi$
$110$	−1.92101	−	5.04056i	−0.183161	−	0.480599i
$111$	9.74324	+	7.07888i	0.924788	+	0.671897i
$112$	0.809017	−	0.587785i	0.0764449	−	0.0555405i
$113$	4.83053	−	3.50959i	0.454418	−	0.330154i	−0.336919	−	0.941533i	$-0.609385\pi$
$113$	4.83053	−	3.50959i	0.454418	−	0.330154i	0.791338	+	0.611379i	$0.209385\pi$
$114$	−8.53037	−	6.19768i	−0.798943	−	0.580466i
$115$	−10.7790	−	7.03685i	−1.00515	−	0.656189i
$116$	4.88524	−	3.54934i	0.453584	−	0.329548i
$117$	0.695434	−	2.14033i	0.0642929	−	0.197873i
$118$	2.29768			0.211519
$119$	−0.414022	+	1.27423i	−0.0379533	+	0.116808i
$120$	5.52787	−	0.276391i	0.504623	−	0.0252310i
$121$	−1.60086	−	4.92694i	−0.145533	−	0.447904i
$122$	0.0441295	+	0.135817i	0.00399529	+	0.0122963i
$123$	−19.4395	−	14.1237i	−1.75280	−	1.27349i
$124$	8.42635			0.756708
$125$	−11.0550	+	1.66938i	−0.988790	+	0.149313i
$126$	3.12675			0.278553
$127$	−7.85878	−	5.70974i	−0.697354	−	0.506657i	0.181715	−	0.983351i	$-0.441835\pi$
$127$	−7.85878	−	5.70974i	−0.697354	−	0.506657i	−0.879069	+	0.476694i	$0.841835\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	6.07612	+	18.7004i	0.534972	+	1.64648i
$130$	1.60740	−	0.0803691i	0.140978	−	0.00704884i
$131$	0.262912	−	0.809159i	0.0229707	−	0.0706966i	−0.938914	−	0.344152i	$-0.888167\pi$
$131$	0.262912	−	0.809159i	0.0229707	−	0.0706966i	0.961885	+	0.273455i	$0.0881665\pi$
$132$	−5.97116			−0.519722
$133$	1.31637	−	4.05137i	0.114144	−	0.351298i
$134$	1.27071	−	0.923228i	0.109773	−	0.0797547i
$135$	0.587453	+	0.383506i	0.0505599	+	0.0330069i
$136$	1.08392	+	0.787516i	0.0929456	+	0.0675290i
$137$	6.92330	−	5.03007i	0.591497	−	0.429748i	−0.251353	−	0.967895i	$-0.580876\pi$
$137$	6.92330	−	5.03007i	0.591497	−	0.429748i	0.842851	+	0.538147i	$0.180876\pi$
$138$	−11.5280	+	8.37560i	−0.981331	+	0.712979i
$139$	13.4472	+	9.76994i	1.14057	+	0.828676i	0.987199	−	0.159492i	$-0.0509857\pi$
$139$	13.4472	+	9.76994i	1.14057	+	0.828676i	0.153375	+	0.988168i	$0.450986\pi$
$140$	0.796319	+	2.08947i	0.0673012	+	0.176592i
$141$	−6.91770	+	5.02600i	−0.582575	+	0.423266i
$142$	1.12360	−	3.45809i	0.0942905	−	0.290196i
$143$	−1.73629			−0.145196
$144$	0.966220	−	2.97372i	0.0805183	−	0.247810i
$145$	4.80857	+	12.6172i	0.399330	+	1.04780i
$146$	3.63060	+	11.1738i	0.300470	+	0.924753i
$147$	0.764888	+	2.35408i	0.0630869	+	0.194161i
$148$	3.93630	+	2.85989i	0.323562	+	0.235081i
$149$	−6.60133			−0.540802			−0.270401	−	0.962748i	$-0.587156\pi$
$149$	−6.60133			−0.540802			−0.270401	+	0.962748i	$0.587156\pi$
$150$	−2.63127	+	12.0932i	−0.214842	+	0.987405i
$151$	−12.7777			−1.03984			−0.519918	−	0.854216i	$-0.674037\pi$
$151$	−12.7777			−1.03984			−0.519918	+	0.854216i	$0.674037\pi$
$152$	−3.44630	−	2.50388i	−0.279532	−	0.203092i
$153$	1.29454	+	3.98420i	0.104658	+	0.322103i
$154$	−0.745462	−	2.29430i	−0.0600710	−	0.184880i
$155$	−4.92034	+	18.1881i	−0.395211	+	1.46090i
$156$	0.550526	−	1.69434i	0.0440773	−	0.135656i
$157$	4.43217			0.353726			0.176863	−	0.984235i	$-0.443405\pi$
$157$	4.43217			0.353726			0.176863	+	0.984235i	$0.443405\pi$
$158$	4.93270	−	15.1813i	0.392425	−	1.20776i
$159$	−25.5386	+	18.5549i	−2.02535	+	1.47150i
$160$	2.23328	−	0.111663i	0.176556	−	0.00882773i
$161$	−4.65736	−	3.38377i	−0.367051	−	0.266679i
$162$	−6.96052	+	5.05711i	−0.546870	+	0.397324i
$163$	11.1898	−	8.12984i	0.876450	−	0.636778i	−0.0558601	−	0.998439i	$-0.517790\pi$
$163$	11.1898	−	8.12984i	0.876450	−	0.636778i	0.932310	+	0.361661i	$0.117790\pi$
$164$	−7.85364	−	5.70600i	−0.613266	−	0.445564i
$165$	3.48670	−	12.8886i	0.271439	−	1.00338i
$166$	0.593406	−	0.431135i	0.0460573	−	0.0334626i
$167$	1.73814	−	5.34944i	0.134501	−	0.413952i	−0.861011	−	0.508587i	$-0.830168\pi$
$167$	1.73814	−	5.34944i	0.134501	−	0.413952i	0.995512	+	0.0946342i	$0.0301682\pi$
$168$	2.47523			0.190968
$169$	−3.85714	+	11.8711i	−0.296703	+	0.913158i
$170$	−2.33277	+	1.87978i	−0.178915	+	0.144172i
$171$	−4.11596	−	12.6676i	−0.314755	−	0.968718i
$172$	2.45477	+	7.55501i	0.187175	+	0.576064i
$173$	−2.54197	−	1.84685i	−0.193263	−	0.140414i	0.486946	−	0.873432i	$-0.338111\pi$
$173$	−2.54197	−	1.84685i	−0.193263	−	0.140414i	−0.680209	+	0.733019i	$0.738111\pi$
$174$	14.9467			1.13310
$175$	−4.97506	+	0.498749i	−0.376079	+	0.0377019i
$176$	−2.41237			−0.181839
$177$	4.60111	+	3.34290i	0.345841	+	0.251268i
$178$	−3.15594	−	9.71298i	−0.236548	−	0.728019i
$179$	−2.55795	−	7.87257i	−0.191190	−	0.588424i	−1.00000		0.000353003i	$-0.999888\pi$
$179$	−2.55795	−	7.87257i	−0.191190	−	0.588424i	0.808809	−	0.588071i	$-0.200112\pi$
$180$	5.85451	+	3.82199i	0.436370	+	0.284874i
$181$	−7.24179	+	22.2879i	−0.538278	+	1.65665i	0.198179	+	0.980166i	$0.436497\pi$
$181$	−7.24179	+	22.2879i	−0.538278	+	1.65665i	−0.736457	+	0.676484i	$0.763503\pi$
$182$	0.719747			0.0533512
$183$	−0.109231	+	0.336177i	−0.00807455	+	0.0248509i
$184$	−4.65736	+	3.38377i	−0.343345	+	0.249455i
$185$	−8.47151	+	6.82647i	−0.622838	+	0.501892i
$186$	16.8738	+	12.2595i	1.23724	+	0.898911i
$187$	2.61482	−	1.89978i	0.191214	−	0.138925i
$188$	−2.79477	+	2.03052i	−0.203830	+	0.148091i
$189$	0.253824	+	0.184414i	0.0184630	+	0.0134142i
$190$	7.41695	−	5.97669i	0.538082	−	0.433595i
$191$	7.82854	−	5.68777i	0.566453	−	0.411552i	−0.267362	−	0.963596i	$-0.586152\pi$
$191$	7.82854	−	5.68777i	0.566453	−	0.411552i	0.833815	+	0.552044i	$0.186152\pi$
$192$	0.764888	−	2.35408i	0.0552010	−	0.169891i
$193$	−10.7534			−0.774044			−0.387022	−	0.922070i	$-0.626496\pi$
$193$	−10.7534			−0.774044			−0.387022	+	0.922070i	$0.626496\pi$
$194$	4.14808	−	12.7665i	0.297815	−	0.916579i
$195$	3.33574	+	2.17767i	0.238877	+	0.155946i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	3.32026	+	10.2187i	0.236559	+	0.728053i	0.996911	+	0.0785420i	$0.0250265\pi$
$197$	3.32026	+	10.2187i	0.236559	+	0.728053i	−0.760352	+	0.649511i	$0.774974\pi$
$198$	−6.10231	−	4.43359i	−0.433672	−	0.315081i
$199$	21.4180			1.51828			0.759141	−	0.650926i	$-0.225619\pi$
$199$	21.4180			1.51828			0.759141	+	0.650926i	$0.225619\pi$
$200$	−1.06304	+	4.88569i	−0.0751683	+	0.345470i
$201$	3.88781			0.274225
$202$	−3.51905	−	2.55674i	−0.247599	−	0.179891i
$203$	1.86600	+	5.74295i	0.130967	+	0.403076i
$204$	1.02480	+	3.15400i	0.0717502	+	0.220825i
$205$	16.9022	−	13.6200i	1.18050	−	0.951265i
$206$	2.00397	−	6.16759i	0.139623	−	0.429716i
$207$	−18.0001			−1.25110
$208$	0.222414	−	0.684520i	0.0154216	−	0.0474630i
$209$	−8.31373	+	6.04028i	−0.575073	+	0.417815i
$210$	−1.44534	+	5.34273i	−0.0997381	+	0.368683i
$211$	−0.0882604	−	0.0641249i	−0.00607610	−	0.00441454i	0.584743	−	0.811219i	$-0.301195\pi$
$211$	−0.0882604	−	0.0641249i	−0.00607610	−	0.00441454i	−0.590819	+	0.806804i	$0.701195\pi$
$212$	−10.3177	+	7.49624i	−0.708622	+	0.514844i
$213$	7.28120	−	5.29010i	0.498899	−	0.362472i
$214$	−13.3708	−	9.71446i	−0.914009	−	0.664067i
$215$	−17.7407	+	0.887029i	−1.20991	+	0.0604949i
$216$	0.253824	−	0.184414i	0.0172706	−	0.0125478i
$217$	−2.60388	+	8.01393i	−0.176763	+	0.544021i
$218$	17.7327			1.20101
$219$	−8.98655	+	27.6578i	−0.607255	+	1.86894i
$220$	1.40864	−	5.20704i	0.0949702	−	0.351059i
$221$	0.297991	+	0.917122i	0.0200451	+	0.0616923i
$222$	3.72159	+	11.4539i	0.249777	+	0.768733i
$223$	−22.5211	−	16.3625i	−1.50813	−	1.09572i	−0.967000	−	0.254775i	$-0.917999\pi$
$223$	−22.5211	−	16.3625i	−1.50813	−	1.09572i	−0.541125	−	0.840942i	$-0.682001\pi$
$224$	1.00000			0.0668153
$225$	−11.6683	+	10.4051i	−0.777885	+	0.693673i
$226$	5.97087			0.397176
$227$	13.5749	+	9.86272i	0.900996	+	0.654612i	0.938722	−	0.344676i	$-0.112011\pi$
$227$	13.5749	+	9.86272i	0.900996	+	0.654612i	−0.0377259	+	0.999288i	$0.512011\pi$
$228$	−3.25831	−	10.0281i	−0.215787	−	0.664124i
$229$	−8.34209	−	25.6743i	−0.551261	−	1.69661i	−0.705619	−	0.708591i	$-0.749331\pi$
$229$	−8.34209	−	25.6743i	−0.551261	−	1.69661i	0.154359	−	0.988015i	$-0.450669\pi$
$230$	−4.58426	−	12.0287i	−0.302277	−	0.793148i
$231$	1.84519	−	5.67891i	0.121404	−	0.373645i
$232$	6.03849			0.396447
$233$	−7.96921	+	24.5267i	−0.522081	+	1.60680i	0.247937	+	0.968776i	$0.420247\pi$
$233$	−7.96921	+	24.5267i	−0.522081	+	1.60680i	−0.770018	+	0.638022i	$0.779753\pi$
$234$	1.82067	−	1.32279i	0.119021	−	0.0864738i
$235$	−2.75091	−	7.21813i	−0.179449	−	0.470859i
$236$	1.85886	+	1.35054i	0.121002	+	0.0879129i
$237$	31.9650	−	23.2240i	2.07635	−	1.50856i
$238$	−1.08392	+	0.787516i	−0.0702603	+	0.0510471i
$239$	−2.51940	−	1.83045i	−0.162966	−	0.118402i	0.503313	−	0.864104i	$-0.332114\pi$
$239$	−2.51940	−	1.83045i	−0.162966	−	0.118402i	−0.666280	+	0.745702i	$0.732114\pi$
$240$	4.63460	+	3.02560i	0.299162	+	0.195301i
$241$	−14.1787	+	10.3014i	−0.913329	+	0.663572i	−0.941854	−	0.336021i	$-0.890919\pi$
$241$	−14.1787	+	10.3014i	−0.913329	+	0.663572i	0.0285259	+	0.999593i	$0.490919\pi$
$242$	1.60086	−	4.92694i	0.102907	−	0.316716i
$243$	−22.2373			−1.42652
$244$	−0.0441295	+	0.135817i	−0.00282510	+	0.00869476i
$245$	−2.23328	+	0.111663i	−0.142679	+	0.00713389i
$246$	−7.42524	−	22.8525i	−0.473416	−	1.45703i
$247$	−0.947453	−	2.91596i	−0.0602850	−	0.185538i
$248$	6.81706	+	4.95288i	0.432884	+	0.314508i
$249$	1.81556			0.115056
$250$	−9.92492	−	5.14742i	−0.627707	−	0.325551i
$251$	−5.36358			−0.338546			−0.169273	−	0.985569i	$-0.554142\pi$
$251$	−5.36358			−0.338546			−0.169273	+	0.985569i	$0.554142\pi$
$252$	2.52960	+	1.83786i	0.159350	+	0.115774i
$253$	4.29149	+	13.2078i	0.269803	+	0.830370i
$254$	−3.00179	−	9.23855i	−0.188349	−	0.579678i
$255$	−7.40626	+	0.370310i	−0.463798	+	0.0231897i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.51358			−0.156793			−0.0783965	−	0.996922i	$-0.524980\pi$
$257$	−2.51358			−0.156793			−0.0783965	+	0.996922i	$0.524980\pi$
$258$	−6.07612	+	18.7004i	−0.378283	+	1.16423i
$259$	−3.93630	+	2.85989i	−0.244590	+	0.177705i
$260$	1.34765	+	0.879784i	0.0835777	+	0.0545619i
$261$	15.2750	+	11.0979i	0.945496	+	0.686943i
$262$	0.688312	−	0.500088i	0.0425241	−	0.0308955i
$263$	−19.3063	+	14.0268i	−1.19048	+	0.864932i	−0.993315	−	0.115439i	$-0.963173\pi$
$263$	−19.3063	+	14.0268i	−1.19048	+	0.864932i	−0.197162	+	0.980371i	$0.563173\pi$
$264$	−4.83077	−	3.50976i	−0.297313	−	0.216011i
$265$	−10.1557	−	26.6478i	−0.623862	−	1.63696i
$266$	3.44630	−	2.50388i	0.211306	−	0.153523i
$267$	7.81167	−	24.0418i	0.478066	−	1.47134i
$268$	1.57069			0.0959451
$269$	4.61724	−	14.2104i	0.281518	−	0.866424i	−0.705903	−	0.708309i	$-0.749458\pi$
$269$	4.61724	−	14.2104i	0.281518	−	0.866424i	0.987421	−	0.158115i	$-0.0505416\pi$
$270$	0.249840	+	0.655559i	0.0152048	+	0.0398960i
$271$	−0.852653	−	2.62420i	−0.0517950	−	0.159409i	0.921813	−	0.387634i	$-0.126708\pi$
$271$	−0.852653	−	2.62420i	−0.0517950	−	0.159409i	−0.973608	+	0.228226i	$0.926708\pi$
$272$	0.414022	+	1.27423i	0.0251038	+	0.0772614i
$273$	1.44130	+	1.04716i	0.0872312	+	0.0633771i
$274$	8.55767			0.516988
$275$	10.4168	+	6.08102i	0.628154	+	0.366700i
$276$	−14.2494			−0.857715
$277$	21.2967	+	15.4729i	1.27959	+	0.929678i	0.999541	−	0.0303069i	$-0.00964847\pi$
$277$	21.2967	+	15.4729i	1.27959	+	0.929678i	0.280051	+	0.959985i	$0.409648\pi$
$278$	5.13636	+	15.8081i	0.308059	+	0.948107i
$279$	8.14170	+	25.0576i	0.487431	+	1.50016i
$280$	−0.583923	+	2.15848i	−0.0348961	+	0.128994i
$281$	1.17052	−	3.60248i	0.0698273	−	0.214906i	−0.910053	−	0.414491i	$-0.863959\pi$
$281$	1.17052	−	3.60248i	0.0698273	−	0.214906i	0.979880	+	0.199585i	$0.0639595\pi$
$282$	−8.55075			−0.509190
$283$	2.81387	−	8.66019i	0.167267	−	0.514795i	−0.831929	−	0.554882i	$-0.812763\pi$
$283$	2.81387	−	8.66019i	0.167267	−	0.514795i	0.999196	+	0.0400868i	$0.0127635\pi$
$284$	2.94163	−	2.13722i	0.174553	−	0.126820i
$285$	23.5480	−	1.17739i	1.39486	−	0.0697424i
$286$	−1.40469	−	1.02057i	−0.0830611	−	0.0603474i
$287$	7.85364	−	5.70600i	0.463585	−	0.336815i
$288$	2.52960	−	1.83786i	0.149058	−	0.108297i
$289$	12.3010	+	8.93723i	0.723591	+	0.525720i
$290$	−3.52602	+	13.0340i	−0.207055	+	0.765381i
$291$	26.8805	−	19.5298i	1.57576	−	1.14486i
$292$	−3.63060	+	11.1738i	−0.212465	+	0.653899i
$293$	11.6032			0.677866			0.338933	−	0.940811i	$-0.389934\pi$
$293$	11.6032			0.677866			0.338933	+	0.940811i	$0.389934\pi$
$294$	−0.764888	+	2.35408i	−0.0446091	+	0.137293i
$295$	−4.00055	+	3.22370i	−0.232921	+	0.187691i
$296$	1.50353	+	4.62740i	0.0873911	+	0.268962i
$297$	−0.233884	−	0.719822i	−0.0135714	−	0.0417683i
$298$	−5.34059	−	3.88016i	−0.309372	−	0.224772i
$299$	−4.14345			−0.239622
$300$	−9.23694	+	8.23698i	−0.533295	+	0.475562i
$301$	−7.94381			−0.457873
$302$	−10.3374	−	7.51055i	−0.594850	−	0.432184i
$303$	−3.32709	−	10.2397i	−0.191137	−	0.588258i
$304$	−1.31637	−	4.05137i	−0.0754989	−	0.232362i
$305$	−0.267389	−	0.174559i	−0.0153107	−	0.00999522i
$306$	−1.29454	+	3.98420i	−0.0740042	+	0.227761i
$307$	6.37043			0.363579			0.181790	−	0.983337i	$-0.441811\pi$
$307$	6.37043			0.363579			0.181790	+	0.983337i	$0.441811\pi$
$308$	0.745462	−	2.29430i	0.0424766	−	0.130730i
$309$	12.9862	−	9.43503i	0.738759	−	0.536740i
$310$	−14.6713	+	11.8224i	−0.833276	+	0.671466i
$311$	18.2445	+	13.2554i	1.03455	+	0.751644i	0.969214	−	0.246219i	$-0.0791884\pi$
$311$	18.2445	+	13.2554i	1.03455	+	0.751644i	0.0653351	+	0.997863i	$0.479188\pi$
$312$	1.44130	−	1.04716i	0.0815973	−	0.0592839i
$313$	6.64564	−	4.82834i	0.375634	−	0.272914i	−0.383909	−	0.923371i	$-0.625422\pi$
$313$	6.64564	−	4.82834i	0.375634	−	0.272914i	0.759543	+	0.650457i	$0.225422\pi$
$314$	3.58570	+	2.60517i	0.202353	+	0.147018i
$315$	−5.44407	+	4.38691i	−0.306739	+	0.247175i
$316$	12.9140	−	9.38255i	0.726468	−	0.527810i
$317$	−5.85399	+	18.0167i	−0.328793	+	1.01192i	0.640906	+	0.767619i	$0.278559\pi$
$317$	−5.85399	+	18.0167i	−0.328793	+	1.01192i	−0.969699	+	0.244302i	$0.921441\pi$
$318$	−31.5675			−1.77022
$319$	4.50147	−	13.8541i	0.252034	−	0.775680i
$320$	1.87239	+	1.22235i	0.104670	+	0.0683315i
$321$	−12.6415	−	38.9064i	−0.705578	−	2.17154i
$322$	−1.77895	−	5.47506i	−0.0991372	−	0.305113i
$323$	4.61736	+	3.35471i	0.256917	+	0.186661i
$324$	−8.60367			−0.477982
$325$	−2.68592	+	2.39515i	−0.148988	+	0.132859i
$326$	13.8313			0.766045
$327$	35.5099	+	25.7994i	1.96370	+	1.42671i
$328$	−2.99982	−	9.23250i	−0.165637	−	0.509780i
$329$	−1.06751	−	3.28545i	−0.0588536	−	0.181133i
$330$	10.3965	−	8.37768i	0.572310	−	0.461176i
$331$	7.28088	−	22.4082i	0.400193	−	1.23167i	−0.524650	−	0.851318i	$-0.675804\pi$
$331$	7.28088	−	22.4082i	0.400193	−	1.23167i	0.924843	−	0.380350i	$-0.124196\pi$
$332$	0.733491			0.0402555
$333$	−4.70118	+	14.4687i	−0.257623	+	0.792882i
$334$	4.55051	−	3.30614i	0.248993	−	0.180904i
$335$	−0.917162	+	3.39030i	−0.0501099	+	0.185232i
$336$	2.00250	+	1.45490i	0.109245	+	0.0793714i
$337$	0.515013	−	0.374179i	0.0280545	−	0.0203828i	−0.573670	−	0.819087i	$-0.694481\pi$
$337$	0.515013	−	0.374179i	0.0280545	−	0.0203828i	0.601724	+	0.798704i	$0.294481\pi$
$338$	−10.0981	+	7.33671i	−0.549265	+	0.399065i
$339$	11.9567	+	8.68703i	0.649397	+	0.471815i
$340$	−2.99215	+	0.149606i	−0.162272	+	0.00811354i
$341$	16.4452	−	11.9482i	0.890559	−	0.647029i
$342$	4.11596	−	12.6676i	0.222566	−	0.684987i
$343$	−1.00000			−0.0539949
$344$	−2.45477	+	7.55501i	−0.132352	+	0.407339i
$345$	8.32057	−	30.7571i	0.447965	−	1.65591i
$346$	−0.970947	−	2.98827i	−0.0521984	−	0.160650i
$347$	9.19015	+	28.2844i	0.493353	+	1.51838i	0.819508	+	0.573068i	$0.194247\pi$
$347$	9.19015	+	28.2844i	0.493353	+	1.51838i	−0.326154	+	0.945317i	$0.605753\pi$
$348$	12.0921	+	8.78542i	0.648204	+	0.470948i
$349$	−12.7937			−0.684831			−0.342416	−	0.939549i	$-0.611245\pi$
$349$	−12.7937			−0.684831			−0.342416	+	0.939549i	$0.611245\pi$
$350$	−4.31807	−	2.52077i	−0.230810	−	0.134741i
$351$	0.225817			0.0120532
$352$	−1.95164	−	1.41795i	−0.104023	−	0.0755771i
$353$	6.03533	+	18.5748i	0.321228	+	0.988639i	0.973114	+	0.230322i	$0.0739781\pi$
$353$	6.03533	+	18.5748i	0.321228	+	0.988639i	−0.651886	+	0.758317i	$0.726022\pi$
$354$	1.75747	+	5.40893i	0.0934084	+	0.287481i
$355$	2.89545	+	7.59741i	0.153675	+	0.403229i
$356$	3.15594	−	9.71298i	0.167264	−	0.514787i
$357$	−3.31632			−0.175518
$358$	2.55795	−	7.87257i	0.135192	−	0.416078i
$359$	7.00263	−	5.08771i	0.369584	−	0.268519i	−0.387454	−	0.921889i	$-0.626645\pi$
$359$	7.00263	−	5.08771i	0.369584	−	0.268519i	0.757039	+	0.653370i	$0.226645\pi$
$360$	2.48989	+	6.53325i	0.131229	+	0.344333i
$361$	0.690578	+	0.501734i	0.0363462	+	0.0264071i
$362$	−18.9593	+	13.7747i	−0.996477	+	0.723983i
$363$	10.3739	−	7.53711i	0.544491	−	0.395596i
$364$	0.582288	+	0.423057i	0.0305202	+	0.0221742i
$365$	−21.9985	−	14.3612i	−1.15145	−	0.751701i
$366$	−0.285969	+	0.207769i	−0.0149478	+	0.0108602i
$367$	9.09782	−	28.0002i	0.474903	−	1.46160i	−0.371187	−	0.928558i	$-0.621049\pi$
$367$	9.09782	−	28.0002i	0.474903	−	1.46160i	0.846089	−	0.533041i	$-0.178951\pi$
$368$	−5.75682			−0.300095
$369$	9.37970	−	28.8678i	0.488288	−	1.50280i
$370$	−10.8661	+	0.543300i	−0.564901	+	0.0282448i
$371$	−3.94101	−	12.1292i	−0.204607	−	0.629715i
$372$	6.44521	+	19.8363i	0.334168	+	1.02846i
$373$	−18.6233	−	13.5306i	−0.964280	−	0.700590i	−0.0101392	−	0.999949i	$-0.503227\pi$
$373$	−18.6233	−	13.5306i	−0.964280	−	0.700590i	−0.954141	+	0.299358i	$0.903227\pi$
$374$	3.23209			0.167128
$375$	−12.3857	−	24.7475i	−0.639594	−	1.27796i
$376$	−3.45453			−0.178154
$377$	3.51614	+	2.55463i	0.181091	+	0.131570i
$378$	0.0969523	+	0.298389i	0.00498669	+	0.0153474i
$379$	5.87803	+	18.0907i	0.301934	+	0.929258i	0.980804	+	0.194999i	$0.0624702\pi$
$379$	5.87803	+	18.0907i	0.301934	+	0.929258i	−0.678869	+	0.734259i	$0.737530\pi$
$380$	9.51345	−	0.475668i	0.488030	−	0.0244013i
$381$	7.43011	−	22.8675i	0.380656	−	1.17154i
$382$	9.67661			0.495098
$383$	10.6193	−	32.6827i	0.542619	−	1.67001i	−0.183967	−	0.982932i	$-0.558894\pi$
$383$	10.6193	−	32.6827i	0.542619	−	1.67001i	0.726585	−	0.687076i	$-0.241106\pi$
$384$	2.00250	−	1.45490i	0.102190	−	0.0742452i
$385$	4.51690	+	2.94876i	0.230202	+	0.150283i
$386$	−8.69966	−	6.32067i	−0.442801	−	0.321714i
$387$	−20.0946	+	14.5996i	−1.02147	+	0.742139i
$388$	10.8598	−	7.89011i	0.551323	−	0.400560i
$389$	−6.75247	−	4.90595i	−0.342364	−	0.248742i	0.403295	−	0.915070i	$-0.367865\pi$
$389$	−6.75247	−	4.90595i	−0.342364	−	0.248742i	−0.745658	+	0.666328i	$0.767865\pi$
$390$	1.41867	+	3.72247i	0.0718373	+	0.188495i
$391$	6.23994	−	4.53359i	0.315568	−	0.229273i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$	2.10593			0.106230
$394$	−3.32026	+	10.2187i	−0.167272	+	0.514811i
$395$	12.7113	+	33.3532i	0.639574	+	1.67818i
$396$	−2.33088	−	7.17370i	−0.117131	−	0.360492i
$397$	6.06961	+	18.6803i	0.304625	+	0.937540i	0.979817	+	0.199897i	$0.0640609\pi$
$397$	6.06961	+	18.6803i	0.304625	+	0.937540i	−0.675192	+	0.737642i	$0.735939\pi$
$398$	17.3275	+	12.5892i	0.868550	+	0.631039i
$399$	10.5441			0.527866
$400$	−3.73175	+	3.32776i	−0.186588	+	0.166388i
$401$	−32.0190			−1.59895			−0.799477	−	0.600697i	$-0.794890\pi$
$401$	−32.0190			−1.59895			−0.799477	+	0.600697i	$0.794890\pi$
$402$	3.14531	+	2.28520i	0.156874	+	0.113975i
$403$	1.87414	+	5.76801i	0.0933575	+	0.287325i
$404$	−1.34416	−	4.13689i	−0.0668743	−	0.205818i
$405$	5.02388	−	18.5709i	0.249639	−	0.922793i
$406$	−1.86600	+	5.74295i	−0.0926079	+	0.285018i
$407$	11.7374			0.581804
$408$	−1.02480	+	3.15400i	−0.0507351	+	0.156147i
$409$	16.9327	−	12.3023i	0.837267	−	0.608310i	−0.0843387	−	0.996437i	$-0.526878\pi$
$409$	16.9327	−	12.3023i	0.837267	−	0.608310i	0.921606	+	0.388127i	$0.126878\pi$
$410$	21.6798	−	1.08398i	1.07069	−	0.0535341i
$411$	17.1367	+	12.4506i	0.845293	+	0.614142i
$412$	5.24647	−	3.81178i	0.258475	−	0.187793i
$413$	−1.85886	+	1.35054i	−0.0914687	+	0.0664559i
$414$	−14.5624	−	10.5802i	−0.715704	−	0.519989i
$415$	−0.428302	+	1.58322i	−0.0210245	+	0.0777174i
$416$	0.582288	−	0.423057i	0.0285490	−	0.0207421i
$417$	−12.7137	+	39.1287i	−0.622591	+	1.91614i
$418$	−10.2763			−0.502632
$419$	8.44085	−	25.9783i	0.412363	−	1.26912i	−0.502226	−	0.864736i	$-0.667485\pi$
$419$	8.44085	−	25.9783i	0.412363	−	1.26912i	0.914589	−	0.404385i	$-0.132515\pi$
$420$	−4.30968	+	3.47281i	−0.210291	+	0.169456i
$421$	1.27074	+	3.91093i	0.0619320	+	0.190607i	0.977235	−	0.212158i	$-0.0680492\pi$
$421$	1.27074	+	3.91093i	0.0619320	+	0.190607i	−0.915303	+	0.402765i	$0.868049\pi$
$422$	−0.0337125	−	0.103756i	−0.00164110	−	0.00505078i
$423$	−8.73857	−	6.34894i	−0.424884	−	0.308696i
$424$	−12.7534			−0.619358
$425$	1.42426	−	6.54586i	0.0690870	−	0.317521i
$426$	9.00005			0.436054
$427$	−0.115532	−	0.0839393i	−0.00559101	−	0.00406211i
$428$	−5.10719	−	15.7183i	−0.246865	−	0.759774i
$429$	−1.32807	−	4.08738i	−0.0641198	−	0.197340i
$430$	−14.8739	−	9.71012i	−0.717285	−	0.468263i
$431$	−8.77193	+	26.9972i	−0.422529	+	1.30041i	0.482811	+	0.875724i	$0.339616\pi$
$431$	−8.77193	+	26.9972i	−0.422529	+	1.30041i	−0.905340	+	0.424686i	$0.860384\pi$
$432$	0.313744			0.0150950
$433$	2.63569	−	8.11181i	0.126663	−	0.389829i	−0.867537	−	0.497372i	$-0.834298\pi$
$433$	2.63569	−	8.11181i	0.126663	−	0.389829i	0.994200	+	0.107543i	$0.0342984\pi$
$434$	−6.81706	+	4.95288i	−0.327229	+	0.237746i
$435$	−26.0240	+	20.9705i	−1.24776	+	1.00546i
$436$	14.3461	+	10.4230i	0.687053	+	0.499173i
$437$	−19.8397	+	14.4144i	−0.949062	+	0.689534i
$438$	−23.5271	+	17.0934i	−1.12417	+	0.816756i
$439$	32.2159	+	23.4062i	1.53758	+	1.11712i	0.951831	+	0.306624i	$0.0991995\pi$
$439$	32.2159	+	23.4062i	1.53758	+	1.11712i	0.585749	+	0.810493i	$0.300800\pi$
$440$	4.20023	−	3.38461i	0.200238	−	0.161355i
$441$	−2.52960	+	1.83786i	−0.120457	+	0.0875171i
$442$	−0.297991	+	0.917122i	−0.0141740	+	0.0436231i
$443$	29.2372			1.38910			0.694551	−	0.719444i	$-0.255603\pi$
$443$	29.2372			1.38910			0.694551	+	0.719444i	$0.255603\pi$
$444$	−3.72159	+	11.4539i	−0.176619	+	0.543576i
$445$	19.1224	+	12.4837i	0.906491	+	0.591782i
$446$	−8.60230	−	26.4752i	−0.407331	−	1.25363i
$447$	−5.04927	−	15.5401i	−0.238822	−	0.735020i
$448$	0.809017	+	0.587785i	0.0382225	+	0.0277702i
$449$	−19.2120			−0.906670			−0.453335	−	0.891340i	$-0.649766\pi$
$449$	−19.2120			−0.906670			−0.453335	+	0.891340i	$0.649766\pi$
$450$	−15.5558	+	1.55947i	−0.733307	+	0.0735139i
$451$	−23.4183			−1.10273
$452$	4.83053	+	3.50959i	0.227209	+	0.165077i
$453$	−9.77352	−	30.0798i	−0.459200	−	1.41327i
$454$	5.18514	+	15.9582i	0.243351	+	0.748956i
$455$	−1.25317	+	1.00982i	−0.0587496	+	0.0473413i
$456$	3.25831	−	10.0281i	0.152584	−	0.469607i
$457$	−22.4341			−1.04942			−0.524711	−	0.851280i	$-0.675827\pi$
$457$	−22.4341			−1.04942			−0.524711	+	0.851280i	$0.675827\pi$
$458$	8.34209	−	25.6743i	0.389800	−	1.19968i
$459$	−0.340075	+	0.247079i	−0.0158733	+	0.0115326i
$460$	3.36154	−	12.4260i	0.156732	−	0.579364i
$461$	−22.8376	−	16.5925i	−1.06365	−	0.772789i	−0.0888926	−	0.996041i	$-0.528333\pi$
$461$	−22.8376	−	16.5925i	−1.06365	−	0.772789i	−0.974761	+	0.223252i	$0.928333\pi$
$462$	4.83077	−	3.50976i	0.224748	−	0.163289i
$463$	−14.4212	+	10.4776i	−0.670212	+	0.486937i	−0.870096	−	0.492882i	$-0.835943\pi$
$463$	−14.4212	+	10.4776i	−0.670212	+	0.486937i	0.199884	+	0.979820i	$0.435943\pi$
$464$	4.88524	+	3.54934i	0.226792	+	0.164774i
$465$	−46.5798	+	2.32897i	−2.16008	+	0.108003i
$466$	−20.8637	+	15.1583i	−0.966491	+	0.702197i
$467$	0.599693	−	1.84567i	0.0277505	−	0.0854073i	−0.936222	−	0.351409i	$-0.885703\pi$
$467$	0.599693	−	1.84567i	0.0277505	−	0.0854073i	0.963973	+	0.266002i	$0.0857027\pi$
$468$	2.25047			0.104028
$469$	−0.485370	+	1.49381i	−0.0224123	+	0.0689779i
$470$	2.01718	−	7.45653i	0.0930455	−	0.343944i
$471$	3.39011	+	10.4337i	0.156208	+	0.480759i
$472$	0.710023	+	2.18522i	0.0326814	+	0.100583i
$473$	15.5035	+	11.2639i	0.712851	+	0.517917i
$474$	39.5110			1.81480
$475$	−4.52840	+	20.8123i	−0.207777	+	0.954936i
$476$	−1.33980			−0.0614098
$477$	−32.2609	−	23.4389i	−1.47712	−	1.07319i
$478$	−0.962325	−	2.96173i	−0.0440157	−	0.135466i
$479$	5.18083	+	15.9450i	0.236718	+	0.728544i	0.996889	+	0.0788204i	$0.0251154\pi$
$479$	5.18083	+	15.9450i	0.236718	+	0.728544i	−0.760171	+	0.649724i	$0.774885\pi$
$480$	1.97107	+	5.17191i	0.0899666	+	0.236064i
$481$	−1.08216	+	3.33056i	−0.0493424	+	0.151860i
$482$	−17.5258			−0.798278
$483$	4.40332	−	13.5520i	0.200358	−	0.616638i
$484$	4.19111	−	3.04502i	0.190505	−	0.138410i
$485$	10.6894	+	28.0479i	0.485378	+	1.27359i
$486$	−17.9903	−	13.0707i	−0.816058	−	0.592901i
$487$	−25.1875	+	18.2998i	−1.14135	+	0.829242i	−0.987307	−	0.158821i	$-0.949231\pi$
$487$	−25.1875	+	18.2998i	−1.14135	+	0.829242i	−0.154047	+	0.988064i	$0.549231\pi$
$488$	−0.115532	+	0.0839393i	−0.00522991	+	0.00379975i
$489$	27.6972	+	20.1232i	1.25251	+	0.910003i
$490$	−1.87239	−	1.22235i	−0.0845861	−	0.0552202i
$491$	32.7765	−	23.8135i	1.47918	−	1.07469i	0.501366	−	0.865236i	$-0.332831\pi$
$491$	32.7765	−	23.8135i	1.47918	−	1.07469i	0.977818	−	0.209454i	$-0.0671688\pi$
$492$	7.42524	−	22.8525i	0.334756	−	1.03027i
$493$	−8.09039			−0.364373
$494$	0.947453	−	2.91596i	0.0426279	−	0.131195i
$495$	16.8453	−	0.842260i	0.757141	−	0.0378568i
$496$	2.60388	+	8.01393i	0.116918	+	0.359836i
$497$	1.12360	+	3.45809i	0.0504004	+	0.155116i
$498$	1.46882	+	1.06716i	0.0658192	+	0.0478205i
$499$	−19.2997			−0.863973			−0.431987	−	0.901880i	$-0.642187\pi$
$499$	−19.2997			−0.863973			−0.431987	+	0.901880i	$0.642187\pi$
$500$	−5.00386	−	9.99807i	−0.223779	−	0.447127i
$501$	13.9225			0.622012
$502$	−4.33922	−	3.15263i	−0.193669	−	0.140709i
$503$	0.838149	+	2.57956i	0.0373712	+	0.115017i	0.968002	−	0.250943i	$-0.0807407\pi$
$503$	0.838149	+	2.57956i	0.0373712	+	0.115017i	−0.930631	+	0.365960i	$0.880741\pi$
$504$	0.966220	+	2.97372i	0.0430389	+	0.132460i
$505$	9.71428	−	0.485710i	0.432280	−	0.0216138i
$506$	−4.29149	+	13.2078i	−0.190780	+	0.587160i
$507$	−30.8957			−1.37213
$508$	3.00179	−	9.23855i	0.133183	−	0.409895i
$509$	7.09657	−	5.15596i	0.314550	−	0.228534i	−0.419296	−	0.907849i	$-0.637723\pi$
$509$	7.09657	−	5.15596i	0.314550	−	0.228534i	0.733846	+	0.679316i	$0.237723\pi$
$510$	−6.20945	−	4.05370i	−0.274959	−	0.179501i
$511$	−9.50503	−	6.90581i	−0.420478	−	0.305495i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	1.08126	−	0.785579i	0.0477386	−	0.0346841i
$514$	−2.03353	−	1.47745i	−0.0896953	−	0.0651674i
$515$	5.16412	+	13.5502i	0.227558	+	0.597092i
$516$	−15.9075	+	11.5575i	−0.700288	+	0.508789i
$517$	−2.57522	+	7.92571i	−0.113258	+	0.348572i
$518$	−4.86554			−0.213779
$519$	2.40332	−	7.39664i	0.105494	−	0.324677i
$520$	0.573148	+	1.50389i	0.0251342	+	0.0659499i
$521$	1.45861	+	4.48913i	0.0639027	+	0.196672i	0.977910	−	0.209025i	$-0.0670289\pi$
$521$	1.45861	+	4.48913i	0.0639027	+	0.196672i	−0.914008	+	0.405697i	$0.867029\pi$
$522$	5.83451	+	17.9568i	0.255370	+	0.785947i
$523$	1.23171	+	0.894889i	0.0538589	+	0.0391308i	0.614389	−	0.789003i	$-0.289403\pi$
$523$	1.23171	+	0.894889i	0.0538589	+	0.0391308i	−0.560530	+	0.828134i	$0.689403\pi$
$524$	0.850801			0.0371674
$525$	−4.97946	−	11.3302i	−0.217321	−	0.494491i
$526$	−23.8639			−1.04052
$527$	−9.13351	−	6.63588i	−0.397862	−	0.289064i
$528$	−1.84519	−	5.67891i	−0.0803015	−	0.247143i
$529$	3.13372	+	9.64459i	0.136249	+	0.419330i
$530$	7.44699	−	27.5279i	0.323476	−	1.19573i
$531$	−2.22007	+	6.83266i	−0.0963426	+	0.296512i
$532$	4.25986			0.184688
$533$	2.15911	−	6.64507i	0.0935216	−	0.287830i
$534$	20.4512	−	14.8587i	0.885010	−	0.642998i
$535$	36.9099	−	1.84548i	1.59575	−	0.0797870i
$536$	1.27071	+	0.923228i	0.0548865	+	0.0398774i
$537$	16.5761	−	12.0433i	0.715313	−	0.519705i
$538$	12.0881	−	8.78251i	0.521155	−	0.378641i
$539$	1.95164	+	1.41795i	0.0840633	+	0.0610756i
$540$	−0.183203	+	0.677211i	−0.00788378	+	0.0291425i
$541$	−19.5026	+	14.1695i	−0.838484	+	0.609195i	−0.921947	−	0.387316i	$-0.873402\pi$
$541$	−19.5026	+	14.1695i	−0.838484	+	0.609195i	0.0834625	+	0.996511i	$0.473402\pi$
$542$	0.852653	−	2.62420i	0.0366246	−	0.112719i
$543$	−58.0068			−2.48931
$544$	−0.414022	+	1.27423i	−0.0177510	+	0.0546321i
$545$	−30.8749	+	24.8795i	−1.32254	+	1.06572i
$546$	0.550526	+	1.69434i	0.0235603	+	0.0725112i
$547$	6.15426	+	18.9409i	0.263137	+	0.809853i	0.992117	+	0.125318i	$0.0399950\pi$
$547$	6.15426	+	18.9409i	0.263137	+	0.809853i	−0.728979	+	0.684536i	$0.760005\pi$
$548$	6.92330	+	5.03007i	0.295749	+	0.214874i
$549$	−0.446519			−0.0190570
$550$	4.85300	+	11.0425i	0.206933	+	0.470852i
$551$	25.7231			1.09584
$552$	−11.5280	−	8.37560i	−0.490666	−	0.356489i
$553$	4.93270	+	15.1813i	0.209760	+	0.645574i
$554$	8.13460	+	25.0357i	0.345606	+	1.06367i
$555$	−22.5498	−	14.7211i	−0.957186	−	0.624878i
$556$	−5.13636	+	15.8081i	−0.217830	+	0.670413i
$557$	−20.7209			−0.877971			−0.438985	−	0.898494i	$-0.644662\pi$
$557$	−20.7209			−0.877971			−0.438985	+	0.898494i	$0.644662\pi$
$558$	−8.14170	+	25.0576i	−0.344666	+	1.06077i
$559$	−4.62558	+	3.36068i	−0.195641	+	0.142142i
$560$	−1.74113	+	1.40303i	−0.0735760	+	0.0592886i
$561$	6.47227	+	4.70238i	0.273260	+	0.198535i
$562$	3.06446	−	2.22646i	0.129266	−	0.0939175i
$563$	−13.6016	+	9.88211i	−0.573237	+	0.416481i	−0.836280	−	0.548303i	$-0.815274\pi$
$563$	−13.6016	+	9.88211i	−0.573237	+	0.416481i	0.263043	+	0.964784i	$0.415274\pi$
$564$	−6.91770	−	5.02600i	−0.291288	−	0.211633i
$565$	−10.3960	+	8.37728i	−0.437364	+	0.352435i
$566$	7.36680	−	5.35229i	0.309650	−	0.224974i
$567$	2.65868	−	8.18258i	0.111654	−	0.343636i
$568$	3.63605			0.152565
$569$	7.96957	−	24.5278i	0.334102	−	1.02826i	−0.633061	−	0.774102i	$-0.718202\pi$
$569$	7.96957	−	24.5278i	0.334102	−	1.02826i	0.967163	−	0.254158i	$-0.0817983\pi$
$570$	19.7427	+	12.8886i	0.826933	+	0.539845i
$571$	3.76114	+	11.5756i	0.157399	+	0.484423i	0.998396	−	0.0566159i	$-0.0180310\pi$
$571$	3.76114	+	11.5756i	0.157399	+	0.484423i	−0.840997	+	0.541039i	$0.818031\pi$
$572$	−0.536544	−	1.65131i	−0.0224340	−	0.0690449i
$573$	19.3774	+	14.0785i	0.809503	+	0.588139i
$574$	9.70763			0.405189
$575$	24.8583	+	14.5116i	1.03666	+	0.605176i
$576$	3.12675			0.130281
$577$	−6.45529	−	4.69004i	−0.268737	−	0.195249i	0.445253	−	0.895405i	$-0.353114\pi$
$577$	−6.45529	−	4.69004i	−0.268737	−	0.195249i	−0.713990	+	0.700156i	$0.753114\pi$
$578$	4.69858	+	14.4607i	0.195435	+	0.601488i
$579$	−8.22512	−	25.3143i	−0.341824	−	1.05203i
$580$	−10.5138	+	8.47216i	−0.436561	+	0.351787i
$581$	−0.226661	+	0.697591i	−0.00940348	+	0.0289409i
$582$	33.2261			1.37727
$583$	−9.50715	+	29.2600i	−0.393746	+	1.21183i
$584$	−9.50503	+	6.90581i	−0.393321	+	0.285764i
$585$	−1.31410	+	4.85760i	−0.0543315	+	0.200837i
$586$	9.38718	+	6.82018i	0.387781	+	0.281739i
$587$	−16.0256	+	11.6433i	−0.661446	+	0.480569i	−0.867151	−	0.498045i	$-0.834051\pi$
$587$	−16.0256	+	11.6433i	−0.661446	+	0.480569i	0.205705	+	0.978614i	$0.434051\pi$
$588$	−2.00250	+	1.45490i	−0.0825818	+	0.0599992i
$589$	29.0397	+	21.0986i	1.19656	+	0.869352i
$590$	−5.13136	+	0.256566i	−0.211255	+	0.0105627i
$591$	−21.5161	+	15.6323i	−0.885053	+	0.643028i
$592$	−1.50353	+	4.62740i	−0.0617948	+	0.190185i
$593$	−31.9392			−1.31159			−0.655793	−	0.754941i	$-0.727665\pi$
$593$	−31.9392			−1.31159			−0.655793	+	0.754941i	$0.727665\pi$
$594$	0.233884	−	0.719822i	0.00959639	−	0.0295347i
$595$	0.782342	−	2.89194i	0.0320729	−	0.118558i
$596$	−2.03992	−	6.27823i	−0.0835585	−	0.257167i
$597$	16.3824	+	50.4197i	0.670485	+	2.06354i
$598$	−3.35212	−	2.43546i	−0.137079	−	0.0995934i
$599$	−24.9633			−1.01997			−0.509987	−	0.860182i	$-0.670350\pi$
$599$	−24.9633			−1.01997			−0.509987	+	0.860182i	$0.670350\pi$
$600$	−12.3144	+	1.23452i	−0.502734	+	0.0503990i
$601$	−21.5723			−0.879952			−0.439976	−	0.898010i	$-0.645013\pi$
$601$	−21.5723			−0.879952			−0.439976	+	0.898010i	$0.645013\pi$
$602$	−6.42667	−	4.66925i	−0.261932	−	0.190304i
$603$	1.51763	+	4.67079i	0.0618027	+	0.190209i
$604$	−3.94853	−	12.1523i	−0.160663	−	0.494471i
$605$	4.12532	+	10.8245i	0.167718	+	0.440077i
$606$	3.32709	−	10.2397i	0.135154	−	0.415961i
$607$	−12.9944			−0.527425			−0.263712	−	0.964601i	$-0.584947\pi$
$607$	−12.9944			−0.527425			−0.263712	+	0.964601i	$0.584947\pi$
$608$	1.31637	−	4.05137i	0.0533858	−	0.164305i
$609$	−12.0921	+	8.78542i	−0.489996	+	0.356003i
$610$	−0.113719	−	0.298389i	−0.00460435	−	0.0120814i
$611$	−2.01153	−	1.46146i	−0.0813778	−	0.0591244i
$612$	−3.38916	+	2.46237i	−0.136999	+	0.0995354i
$613$	−5.68959	+	4.13373i	−0.229800	+	0.166960i	−0.696727	−	0.717336i	$-0.745361\pi$
$613$	−5.68959	+	4.13373i	−0.229800	+	0.166960i	0.466927	+	0.884296i	$0.345361\pi$
$614$	5.15378	+	3.74444i	0.207990	+	0.151113i
$615$	44.9910	+	29.3714i	1.81421	+	1.18437i
$616$	1.95164	−	1.41795i	0.0786340	−	0.0571310i
$617$	12.6382	−	38.8964i	0.508795	−	1.56591i	−0.285501	−	0.958378i	$-0.592160\pi$
$617$	12.6382	−	38.8964i	0.508795	−	1.56591i	0.794296	−	0.607531i	$-0.207840\pi$
$618$	16.0518			0.645699
$619$	13.3203	−	40.9957i	0.535389	−	1.64776i	−0.207419	−	0.978252i	$-0.566506\pi$
$619$	13.3203	−	40.9957i	0.535389	−	1.64776i	0.742808	−	0.669505i	$-0.233494\pi$
$620$	−18.8184	+	0.940911i	−0.755764	+	0.0377879i
$621$	−0.558137	−	1.71777i	−0.0223972	−	0.0689316i
$622$	6.96877	+	21.4477i	0.279422	+	0.859973i
$623$	8.26235	+	6.00295i	0.331024	+	0.240503i
$624$	1.78154			0.0713186
$625$	24.5025	−	4.96261i	0.980100	−	0.198505i
$626$	8.21447			0.328316
$627$	−20.5784	−	14.9511i	−0.821821	−	0.597088i
$628$	1.36962	+	4.21525i	0.0546537	+	0.168207i
$629$	−2.01444	−	6.19980i	−0.0803209	−	0.247202i
$630$	−6.98291	+	0.349143i	−0.278206	+	0.0139102i
$631$	−9.36051	+	28.8087i	−0.372636	+	1.14686i	0.572424	+	0.819958i	$0.306003\pi$
$631$	−9.36051	+	28.8087i	−0.372636	+	1.14686i	−0.945060	+	0.326898i	$0.893997\pi$
$632$	15.9626			0.634956
$633$	0.0834461	−	0.256821i	0.00331668	−	0.0102077i
$634$	−15.3260	+	11.1350i	−0.608671	+	0.442226i
$635$	18.1884	+	11.8739i	0.721785	+	0.471201i
$636$	−25.5386	−	18.5549i	−1.01267	−	0.735750i
$637$	−0.582288	+	0.423057i	−0.0230711	+	0.0167621i
$638$	11.7850	−	8.56230i	0.466572	−	0.338985i
$639$	9.19774	+	6.68255i	0.363857	+	0.264358i
$640$	0.796319	+	2.08947i	0.0314773	+	0.0825935i
$641$	15.9982	−	11.6234i	0.631892	−	0.459097i	−0.225163	−	0.974321i	$-0.572291\pi$
$641$	15.9982	−	11.6234i	0.631892	−	0.459097i	0.857055	+	0.515224i	$0.172291\pi$
$642$	12.6415	−	38.9064i	0.498919	−	1.53551i
$643$	37.9049			1.49482			0.747411	−	0.664362i	$-0.231297\pi$
$643$	37.9049			1.49482			0.747411	+	0.664362i	$0.231297\pi$
$644$	1.77895	−	5.47506i	0.0701006	−	0.215747i
$645$	−15.6578	−	41.0846i	−0.616525	−	1.61771i
$646$	1.76367	+	5.42803i	0.0693908	+	0.213563i
$647$	−7.34458	−	22.6043i	−0.288745	−	0.888667i	−0.985251	−	0.171115i	$-0.945263\pi$
$647$	−7.34458	−	22.6043i	−0.288745	−	0.888667i	0.696506	−	0.717551i	$-0.254737\pi$
$648$	−6.96052	−	5.05711i	−0.273435	−	0.198662i
$649$	5.54285			0.217576
$650$	−3.58079	+	0.358973i	−0.140450	+	0.0140801i
$651$	−20.8571			−0.817455
$652$	11.1898	+	8.12984i	0.438225	+	0.318389i
$653$	−11.6150	−	35.7472i	−0.454528	−	1.39889i	−0.871688	−	0.490061i	$-0.836974\pi$
$653$	−11.6150	−	35.7472i	−0.454528	−	1.39889i	0.417160	−	0.908833i	$-0.363026\pi$
$654$	13.5636	+	41.7443i	0.530377	+	1.63233i
$655$	−0.496802	+	1.83644i	−0.0194117	+	0.0717555i
$656$	2.99982	−	9.23250i	0.117123	−	0.360469i
$657$	−36.7358			−1.43320
$658$	1.06751	−	3.28545i	0.0416158	−	0.128080i
$659$	4.35747	−	3.16589i	0.169743	−	0.123325i	−0.499670	−	0.866216i	$-0.666546\pi$
$659$	4.35747	−	3.16589i	0.169743	−	0.123325i	0.669413	+	0.742890i	$0.266546\pi$
$660$	13.3353	−	0.666757i	0.519074	−	0.0259535i
$661$	−22.8790	−	16.6225i	−0.889889	−	0.646542i	0.0459603	−	0.998943i	$-0.485365\pi$
$661$	−22.8790	−	16.6225i	−0.889889	−	0.646542i	−0.935849	+	0.352401i	$0.885365\pi$
$662$	19.0616	−	13.8490i	0.740849	−	0.538259i
$663$	−1.93105	+	1.40299i	−0.0749958	+	0.0544877i
$664$	0.593406	+	0.431135i	0.0230286	+	0.0167313i
$665$	−2.48743	+	9.19482i	−0.0964584	+	0.356560i
$666$	−12.3078	+	8.94217i	−0.476919	+	0.346502i
$667$	10.7422	−	33.0611i	0.415940	−	1.28013i
$668$	5.62474			0.217628
$669$	21.2927	−	65.5320i	0.823222	−	2.53362i
$670$	−2.73477	+	2.20372i	−0.105653	+	0.0851370i
$671$	0.106456	+	0.327639i	0.00410970	+	0.0126484i
$672$	0.764888	+	2.35408i	0.0295062	+	0.0908107i
$673$	−16.8780	−	12.2626i	−0.650600	−	0.472688i	0.212876	−	0.977079i	$-0.431717\pi$
$673$	−16.8780	−	12.2626i	−0.650600	−	0.472688i	−0.863475	+	0.504391i	$0.831717\pi$
$674$	0.636591			0.0245206
$675$	−1.35477	−	0.790878i	−0.0521451	−	0.0304409i
$676$	−12.4820			−0.480076
$677$	−30.1857	−	21.9312i	−1.16013	−	0.842883i	−0.170335	−	0.985386i	$-0.554485\pi$
$677$	−30.1857	−	21.9312i	−1.16013	−	0.842883i	−0.989794	+	0.142503i	$0.954485\pi$
$678$	4.56704	+	14.0559i	0.175396	+	0.539814i
$679$	4.14808	+	12.7665i	0.159189	+	0.489932i
$680$	−2.50864	−	1.63771i	−0.0962019	−	0.0628033i
$681$	−12.8344	+	39.5002i	−0.491815	+	1.51365i
$682$	20.3274			0.778377
$683$	4.87616	−	15.0073i	0.186581	−	0.574237i	−0.813391	−	0.581717i	$-0.802381\pi$
$683$	4.87616	−	15.0073i	0.186581	−	0.574237i	0.999972	+	0.00748009i	$0.00238101\pi$
$684$	10.7757	−	7.82902i	0.412020	−	0.299350i
$685$	−14.9000	+	12.0066i	−0.569299	+	0.458750i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	54.0587	−	39.2759i	2.06247	−	1.49847i
$688$	−6.42667	+	4.66925i	−0.245015	+	0.178014i
$689$	−7.42613	−	5.39540i	−0.282913	−	0.205548i
$690$	24.8101	−	19.9923i	0.944503	−	0.761094i
$691$	22.7265	−	16.5118i	0.864558	−	0.628138i	−0.0645635	−	0.997914i	$-0.520565\pi$
$691$	22.7265	−	16.5118i	0.864558	−	0.628138i	0.929121	+	0.369776i	$0.120565\pi$
$692$	0.970947	−	2.98827i	0.0369099	−	0.113597i
$693$	7.54287			0.286530
$694$	−9.19015	+	28.2844i	−0.348853	+	1.07366i
$695$	−31.1222	−	20.3175i	−1.18053	−	0.770685i
$696$	4.61877	+	14.2151i	0.175074	+	0.538822i
$697$	4.01917	+	12.3697i	0.152237	+	0.468537i
$698$	−10.3503	−	7.51995i	−0.391765	−	0.284634i
$699$	−63.8334			−2.41440
$700$	−2.01172	−	4.57744i	−0.0760358	−	0.173011i
$701$	36.5750			1.38142			0.690710	−	0.723132i	$-0.257298\pi$
$701$	36.5750			1.38142			0.690710	+	0.723132i	$0.257298\pi$
$702$	0.182689	+	0.132732i	0.00689517	+	0.00500963i
$703$	6.40484	+	19.7121i	0.241563	+	0.743455i
$704$	−0.745462	−	2.29430i	−0.0280957	−	0.0864695i
$705$	14.8879	−	11.9969i	0.560712	−	0.451830i
$706$	−6.03533	+	18.5748i	−0.227143	+	0.699074i
$707$	4.34978			0.163590
$708$	−1.75747	+	5.40893i	−0.0660497	+	0.203280i
$709$	−1.21399	+	0.882014i	−0.0455923	+	0.0331247i	−0.610348	−	0.792133i	$-0.708970\pi$
$709$	−1.21399	+	0.882014i	−0.0455923	+	0.0331247i	0.564756	+	0.825258i	$0.308970\pi$
$710$	−2.12317	+	7.84834i	−0.0796813	+	0.294543i
$711$	40.3788	+	29.3369i	1.51432	+	1.10022i
$712$	8.26235	−	6.00295i	0.309645	−	0.224970i
$713$	39.2445	−	28.5128i	1.46972	−	1.06781i
$714$	−2.68296	−	1.94928i	−0.100407	−	0.0729501i
$715$	3.87763	−	0.193880i	0.145015	−	0.00725069i
$716$	6.69681	−	4.86552i	0.250272	−	0.181833i
$717$	2.38197	−	7.33096i	0.0889565	−	0.273780i
$718$	8.65572			0.323029
$719$	−4.52153	+	13.9158i	−0.168625	+	0.518973i	−0.999285	−	0.0378060i	$-0.987963\pi$
$719$	−4.52153	+	13.9158i	−0.168625	+	0.518973i	0.830660	+	0.556779i	$0.187963\pi$
$720$	−1.82578	+	6.74903i	−0.0680429	+	0.251522i
$721$	2.00397	+	6.16759i	0.0746318	+	0.229693i
$722$	0.263777	+	0.811823i	0.00981677	+	0.0302129i
$723$	−35.0954	−	25.4983i	−1.30521	−	0.948293i
$724$	−23.4349			−0.870953
$725$	−12.1477	−	27.6409i	−0.451156	−	1.02656i
$726$	12.8229			0.475902
$727$	30.8307	+	22.3998i	1.14345	+	0.830763i	0.987596	−	0.157018i	$-0.0501879\pi$
$727$	30.8307	+	22.3998i	1.14345	+	0.830763i	0.155851	+	0.987781i	$0.450188\pi$
$728$	0.222414	+	0.684520i	0.00824322	+	0.0253700i
$729$	−9.03298	−	27.8006i	−0.334555	−	1.02965i
$730$	−9.35584	−	24.5489i	−0.346275	−	0.908594i
$731$	3.28891	−	10.1222i	0.121645	−	0.374384i
$732$	−0.353477			−0.0130649
$733$	9.14065	−	28.1320i	0.337618	−	1.03908i	−0.627801	−	0.778374i	$-0.716045\pi$
$733$	9.14065	−	28.1320i	0.337618	−	1.03908i	0.965418	−	0.260706i	$-0.0839553\pi$
$734$	23.8184	−	17.3051i	0.879154	−	0.638743i
$735$	−1.97107	−	5.17191i	−0.0727040	−	0.190769i
$736$	−4.65736	−	3.38377i	−0.171673	−	0.124727i
$737$	3.06543	−	2.22716i	0.112916	−	0.0820386i
$738$	24.5564	−	17.8413i	0.903933	−	0.656746i
$739$	−29.0839	−	21.1307i	−1.06987	−	0.777306i	−0.0939806	−	0.995574i	$-0.529959\pi$
$739$	−29.0839	−	21.1307i	−1.06987	−	0.777306i	−0.975889	+	0.218268i	$0.929959\pi$
$740$	−9.11020	−	5.94739i	−0.334898	−	0.218630i
$741$	6.13971	−	4.46076i	0.225548	−	0.163870i
$742$	3.94101	−	12.1292i	0.144679	−	0.445276i
$743$	0.901242			0.0330634			0.0165317	−	0.999863i	$-0.494738\pi$
$743$	0.901242			0.0330634			0.0165317	+	0.999863i	$0.494738\pi$
$744$	−6.44521	+	19.8363i	−0.236293	+	0.727234i
$745$	14.7426	−	0.737124i	0.540127	−	0.0270061i
$746$	−7.11348	−	21.8930i	−0.260443	−	0.801561i
$747$	0.708713	+	2.18120i	0.0259305	+	0.0798058i
$748$	2.61482	+	1.89978i	0.0956072	+	0.0694627i
$749$	16.5272			0.603891
$750$	4.52599	−	27.3013i	0.165266	−	0.996902i
$751$	2.29539			0.0837599			0.0418800	−	0.999123i	$-0.486665\pi$
$751$	2.29539			0.0837599			0.0418800	+	0.999123i	$0.486665\pi$
$752$	−2.79477	−	2.03052i	−0.101915	−	0.0740455i
$753$	−4.10253	−	12.6263i	−0.149505	−	0.460128i
$754$	1.34305	+	4.13347i	0.0489109	+	0.150532i
$755$	28.5362	−	1.42680i	1.03854	−	0.0519265i
$756$	−0.0969523	+	0.298389i	−0.00352612	+	0.0108523i
$757$	−6.33099			−0.230104			−0.115052	−	0.993359i	$-0.536703\pi$
$757$	−6.33099			−0.230104			−0.115052	+	0.993359i	$0.536703\pi$
$758$	−5.87803	+	18.0907i	−0.213500	+	0.657084i
$759$	−27.8098	+	20.2050i	−1.00943	+	0.733396i
$760$	7.97613	+	5.20704i	0.289325	+	0.188879i
$761$	−34.7825	−	25.2709i	−1.26086	−	0.916071i	−0.262064	−	0.965051i	$-0.584403\pi$
$761$	−34.7825	−	25.2709i	−1.26086	−	0.916071i	−0.998800	+	0.0489797i	$0.984403\pi$
$762$	19.4523	−	14.1329i	0.704682	−	0.511981i
$763$	−14.3461	+	10.4230i	−0.519363	+	0.377340i
$764$	7.82854	+	5.68777i	0.283227	+	0.205776i
$765$	−3.33596	−	8.75327i	−0.120612	−	0.316475i
$766$	27.8016	−	20.1990i	1.00451	−	0.729821i
$767$	−0.511037	+	1.57281i	−0.0184525	+	0.0567909i
$768$	2.47523			0.0893171
$769$	−10.0322	+	30.8759i	−0.361770	+	1.11341i	0.590209	+	0.807251i	$0.299045\pi$
$769$	−10.0322	+	30.8759i	−0.361770	+	1.11341i	−0.951979	+	0.306164i	$0.900955\pi$
$770$	1.92101	+	5.04056i	0.0692285	+	0.181649i
$771$	−1.92261	−	5.91718i	−0.0692411	−	0.213102i
$772$	−3.32297	−	10.2271i	−0.119596	−	0.368080i
$773$	29.7281	+	21.5987i	1.06925	+	0.776852i	0.975777	−	0.218770i	$-0.0702043\pi$
$773$	29.7281	+	21.5987i	1.06925	+	0.776852i	0.0934692	+	0.995622i	$0.470204\pi$
$774$	−24.8383			−0.892795
$775$	8.95755	−	41.1685i	0.321765	−	1.47882i
$776$	13.4235			0.481874
$777$	−9.74324	−	7.07888i	−0.349537	−	0.253953i
$778$	−2.57921	−	7.93800i	−0.0924693	−	0.284591i
$779$	−12.7788	−	39.3292i	−0.457849	−	1.40911i
$780$	−1.04028	+	3.84542i	−0.0372481	+	0.137688i
$781$	2.71054	−	8.34218i	0.0969906	−	0.298506i
$782$	7.71300			0.275816
$783$	−0.585446	+	1.80182i	−0.0209221	+	0.0643917i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−9.89828	+	0.494910i	−0.353285	+	0.0176641i
$786$	1.70373	+	1.23783i	0.0607700	+	0.0441520i
$787$	−4.66996	+	3.39293i	−0.166466	+	0.120945i	−0.667899	−	0.744252i	$-0.732806\pi$
$787$	−4.66996	+	3.39293i	−0.166466	+	0.120945i	0.501433	+	0.865196i	$0.332806\pi$
$788$	−8.69256	+	6.31551i	−0.309660	+	0.224981i
$789$	−47.7875	−	34.7196i	−1.70128	−	1.23605i
$790$	−9.32090	+	34.4548i	−0.331623	+	1.22585i
$791$	−4.83053	+	3.50959i	−0.171754	+	0.124787i
$792$	2.33088	−	7.17370i	0.0828241	−	0.254906i
$793$	−0.102784			−0.00364998
$794$	−6.06961	+	18.6803i	−0.215402	+	0.662941i
$795$	54.9630	−	44.2900i	1.94934	−	1.57080i
$796$	6.61853	+	20.3697i	0.234587	+	0.721986i
$797$	5.34483	+	16.4497i	0.189324	+	0.582678i	0.999996	−	0.00282186i	$-0.000898227\pi$
$797$	5.34483	+	16.4497i	0.189324	+	0.582678i	−0.810672	+	0.585500i	$0.800898\pi$
$798$	8.53037	+	6.19768i	0.301972	+	0.219395i
$799$	4.62839			0.163741
$800$	−4.97506	+	0.498749i	−0.175895	+	0.0176334i
$801$	31.9330			1.12830
$802$	−25.9039	−	18.8203i	−0.914699	−	0.664568i
$803$	8.75833	+	26.9554i	0.309075	+	0.951234i
$804$	1.20140	+	3.69753i	0.0423701	+	0.130402i
$805$	10.7790	+	7.03685i	0.379911	+	0.248016i
$806$	−1.87414	+	5.76801i	−0.0660137	+	0.203169i
$807$	36.9841			1.30190
$808$	1.34416	−	4.13689i	0.0472873	−	0.145535i
$809$	−18.7162	+	13.5981i	−0.658025	+	0.478083i	−0.865995	−	0.500052i	$-0.833314\pi$
$809$	−18.7162	+	13.5981i	−0.658025	+	0.478083i	0.207971	+	0.978135i	$0.433314\pi$
$810$	14.9801	−	12.0712i	0.526346	−	0.424138i
$811$	18.5638	+	13.4874i	0.651862	+	0.473605i	0.863905	−	0.503655i	$-0.168012\pi$
$811$	18.5638	+	13.4874i	0.651862	+	0.473605i	−0.212043	+	0.977260i	$0.568012\pi$
$812$	−4.88524	+	3.54934i	−0.171438	+	0.124557i
$813$	5.52539	−	4.01443i	0.193784	−	0.140792i
$814$	9.49580	+	6.89910i	0.332827	+	0.241813i
$815$	−24.0820	+	19.4057i	−0.843557	+	0.679751i
$816$	−2.68296	+	1.94928i	−0.0939223	+	0.0682385i
$817$	−10.4570	+	32.1833i	−0.365843	+	1.12595i
$818$	20.9299			0.731798
$819$	−0.695434	+	2.14033i	−0.0243004	+	0.0747891i
$820$	18.1765	+	11.8661i	0.634751	+	0.414383i
$821$	14.1451	+	43.5342i	0.493668	+	1.51936i	0.819022	+	0.573763i	$0.194517\pi$
$821$	14.1451	+	43.5342i	0.493668	+	1.51936i	−0.325353	+	0.945593i	$0.605483\pi$
$822$	6.54565	+	20.1455i	0.228306	+	0.702653i
$823$	9.32644	+	6.77605i	0.325099	+	0.236198i	0.738348	−	0.674420i	$-0.235606\pi$
$823$	9.32644	+	6.77605i	0.325099	+	0.236198i	−0.413249	+	0.910618i	$0.635606\pi$
$824$	6.48499			0.225915
$825$	−6.34758	+	29.1732i	−0.220994	+	1.01568i
$826$	−2.29768			−0.0799466
$827$	−17.3379	−	12.5967i	−0.602897	−	0.438030i	0.244009	−	0.969773i	$-0.421537\pi$
$827$	−17.3379	−	12.5967i	−0.602897	−	0.438030i	−0.846906	+	0.531743i	$0.821537\pi$
$828$	−5.56235	−	17.1192i	−0.193305	−	0.594932i
$829$	10.1372	+	31.1991i	0.352080	+	1.08359i	0.957683	+	0.287824i	$0.0929319\pi$
$829$	10.1372	+	31.1991i	0.352080	+	1.08359i	−0.605603	+	0.795767i	$0.707068\pi$
$830$	−1.27710	+	1.02911i	−0.0443288	+	0.0357208i
$831$	−20.1350	+	61.9691i	−0.698475	+	2.14968i
$832$	0.719747			0.0249528
$833$	0.414022	−	1.27423i	0.0143450	−	0.0441494i
$834$	−33.2848	+	24.1828i	−1.15256	+	0.837383i
$835$	−3.28441	+	12.1409i	−0.113662	+	0.420153i
$836$	−8.31373	−	6.04028i	−0.287536	−	0.208907i
$837$	−2.13881	+	1.55394i	−0.0739282	+	0.0537120i
$838$	22.0984	−	16.0555i	0.763378	−	0.554627i
$839$	−20.3924	−	14.8160i	−0.704025	−	0.511504i	0.177215	−	0.984172i	$-0.443291\pi$
$839$	−20.3924	−	14.8160i	−0.704025	−	0.511504i	−0.881241	+	0.472668i	$0.843291\pi$
$840$	−5.52787	+	0.276391i	−0.190730	+	0.00953641i
$841$	−6.03803	+	4.38689i	−0.208208	+	0.151272i
$842$	−1.27074	+	3.91093i	−0.0437925	+	0.134780i
$843$	9.37586			0.322922
$844$	0.0337125	−	0.103756i	0.00116043	−	0.00357144i
$845$	7.28851	−	26.9421i	0.250732	−	0.926835i
$846$	−3.33784	−	10.2728i	−0.114757	−	0.353186i
$847$	1.60086	+	4.92694i	0.0550062	+	0.169292i
$848$	−10.3177	−	7.49624i	−0.354311	−	0.257422i
$849$	22.5391			0.773540
$850$	4.99981	−	4.45855i	0.171492	−	0.152927i
$851$	28.0100			0.960170
$852$	7.28120	+	5.29010i	0.249450	+	0.181236i
$853$	1.57155	+	4.83673i	0.0538088	+	0.165606i	0.974349	−	0.225040i	$-0.0722514\pi$
$853$	1.57155	+	4.83673i	0.0538088	+	0.165606i	−0.920541	+	0.390647i	$0.872251\pi$
$854$	−0.0441295	−	0.135817i	−0.00151008	−	0.00464755i
$855$	10.6066	+	27.8307i	0.362738	+	0.951791i
$856$	5.10719	−	15.7183i	0.174560	−	0.537241i
$857$	13.8374			0.472676			0.236338	−	0.971671i	$-0.424053\pi$
$857$	13.8374			0.472676			0.236338	+	0.971671i	$0.424053\pi$
$858$	1.32807	−	4.08738i	0.0453395	−	0.139541i
$859$	−33.1705	+	24.0998i	−1.13176	+	0.822273i	−0.985950	−	0.167039i	$-0.946579\pi$
$859$	−33.1705	+	24.0998i	−1.13176	+	0.822273i	−0.145812	+	0.989312i	$0.546579\pi$
$860$	−6.32580	−	16.5983i	−0.215708	−	0.565998i
$861$	19.4395	+	14.1237i	0.662498	+	0.481333i
$862$	−22.9652	+	16.6852i	−0.782198	+	0.568300i
$863$	−5.72731	+	4.16113i	−0.194960	+	0.141647i	−0.680983	−	0.732299i	$-0.738447\pi$
$863$	−5.72731	+	4.16113i	−0.194960	+	0.141647i	0.486023	+	0.873946i	$0.338447\pi$
$864$	0.253824	+	0.184414i	0.00863528	+	0.00627390i
$865$	5.88316	+	3.84069i	0.200033	+	0.130587i
$866$	6.90031	−	5.01337i	0.234482	−	0.170361i
$867$	−11.6301	+	35.7936i	−0.394978	+	1.21562i
$868$	−8.42635			−0.286009
$869$	11.8995	−	36.6228i	0.403662	−	1.24234i
$870$	−33.3800	+	1.66899i	−1.13169	+	0.0565840i
$871$	0.349344	+	1.07517i	0.0118371	+	0.0364307i
$872$	5.47972	+	16.8648i	0.185567	+	0.571116i
$873$	33.9559	+	24.6704i	1.14923	+	0.834968i
$874$	−24.5232			−0.829510
$875$	11.0550	−	1.66938i	0.373727	−	0.0564352i
$876$	−29.0811			−0.982559
$877$	7.42087	+	5.39158i	0.250585	+	0.182061i	0.705986	−	0.708226i	$-0.250504\pi$
$877$	7.42087	+	5.39158i	0.250585	+	0.182061i	−0.455401	+	0.890286i	$0.650504\pi$
$878$	12.3054	+	37.8720i	0.415286	+	1.27812i
$879$	8.87514	+	27.3149i	0.299351	+	0.921307i
$880$	5.38748	−	0.269372i	0.181612	−	0.00908052i
$881$	15.3905	−	47.3671i	0.518519	−	1.59584i	−0.258268	−	0.966073i	$-0.583152\pi$
$881$	15.3905	−	47.3671i	0.518519	−	1.59584i	0.776787	−	0.629764i	$-0.216848\pi$
$882$	−3.12675			−0.105283
$883$	−12.3275	+	37.9400i	−0.414852	+	1.27678i	0.497531	+	0.867446i	$0.334240\pi$
$883$	−12.3275	+	37.9400i	−0.414852	+	1.27678i	−0.912383	+	0.409338i	$0.865760\pi$
$884$	−0.780151	+	0.566813i	−0.0262393	+	0.0190640i
$885$	−10.6488	−	6.95186i	−0.357957	−	0.233684i
$886$	23.6534	+	17.1852i	0.794651	+	0.577348i
$887$	−12.3117	+	8.94495i	−0.413385	+	0.300342i	−0.774971	−	0.631997i	$-0.782236\pi$
$887$	−12.3117	+	8.94495i	−0.413385	+	0.300342i	0.361586	+	0.932339i	$0.382236\pi$
$888$	−9.74324	+	7.07888i	−0.326962	+	0.237552i
$889$	7.85878	+	5.70974i	0.263575	+	0.191499i
$890$	8.13267	+	21.3394i	0.272608	+	0.715298i
$891$	−16.7913	+	12.1996i	−0.562530	+	0.408702i
$892$	8.60230	−	26.4752i	0.288026	−	0.886454i
$893$	−14.7158			−0.492446
$894$	5.04927	−	15.5401i	0.168873	−	0.519737i
$895$	6.59170	+	17.2960i	0.220336	+	0.578142i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	−3.16928	−	9.75403i	−0.105819	−	0.325677i
$898$	−15.5428	−	11.2925i	−0.518671	−	0.376837i
$899$	−50.8824			−1.69702
$900$	−13.5015	−	7.88183i	−0.450051	−	0.262728i
$901$	17.0870			0.569250
$902$	−18.9458	−	13.7650i	−0.630827	−	0.458323i
$903$	−6.07612	−	18.7004i	−0.202201	−	0.622309i
$904$	1.84510	+	5.67863i	0.0613671	+	0.188868i
$905$	13.6842	−	50.5838i	0.454878	−	1.68146i
$906$	9.77352	−	30.0798i	0.324703	−	0.999334i
$907$	−35.3648			−1.17427			−0.587134	−	0.809490i	$-0.699744\pi$
$907$	−35.3648			−1.17427			−0.587134	+	0.809490i	$0.699744\pi$
$908$	−5.18514	+	15.9582i	−0.172075	+	0.529592i
$909$	11.0032	−	7.99429i	0.364953	−	0.265154i
$910$	−1.60740	+	0.0803691i	−0.0532847	+	0.00266421i
$911$	36.0531	+	26.1941i	1.19449	+	0.867849i	0.993732	−	0.111791i	$-0.0356588\pi$
$911$	36.0531	+	26.1941i	1.19449	+	0.867849i	0.200760	+	0.979640i	$0.435659\pi$
$912$	8.53037	−	6.19768i	0.282469	−	0.205226i
$913$	1.43151	−	1.04006i	0.0473762	−	0.0344208i
$914$	−18.1496	−	13.1864i	−0.600334	−	0.436168i
$915$	0.206404	−	0.762974i	0.00682349	−	0.0252231i
$916$	21.8399	−	15.8676i	0.721610	−	0.524280i
$917$	−0.262912	+	0.809159i	−0.00868211	+	0.0267208i
$918$	−0.420355			−0.0138738
$919$	−12.7552	+	39.2565i	−0.420756	+	1.29495i	0.486244	+	0.873823i	$0.338367\pi$
$919$	−12.7552	+	39.2565i	−0.420756	+	1.29495i	−0.907000	+	0.421131i	$0.861633\pi$
$920$	10.0233	−	8.07696i	0.330460	−	0.266289i
$921$	4.87266	+	14.9965i	0.160560	+	0.494152i
$922$	−8.72319	−	26.8472i	−0.287283	−	0.884166i
$923$	2.11723	+	1.53826i	0.0696894	+	0.0506323i
$924$	5.97116			0.196437
$925$	18.1570	−	16.1914i	0.596998	−	0.532369i
$926$	−17.8256			−0.585787
$927$	16.4044	+	11.9185i	0.538791	+	0.391455i
$928$	1.86600	+	5.74295i	0.0612544	+	0.188522i
$929$	11.3224	+	34.8468i	0.371477	+	1.14329i	0.945825	+	0.324677i	$0.105256\pi$
$929$	11.3224	+	34.8468i	0.371477	+	1.14329i	−0.574348	+	0.818611i	$0.694744\pi$
$930$	−39.0528	−	25.4947i	−1.28059	−	0.836005i
$931$	−1.31637	+	4.05137i	−0.0431422	+	0.132778i
$932$	−25.7889			−0.844744
$933$	−17.2493	+	53.0879i	−0.564716	+	1.73802i
$934$	1.57002	−	1.14068i	0.0513725	−	0.0373243i
$935$	−5.62748	+	4.53471i	−0.184038	+	0.148301i
$936$	1.82067	+	1.32279i	0.0595105	+	0.0432369i
$937$	28.4344	−	20.6588i	0.928913	−	0.674895i	−0.0168137	−	0.999859i	$-0.505352\pi$
$937$	28.4344	−	20.6588i	0.928913	−	0.674895i	0.945726	+	0.324964i	$0.105352\pi$
$938$	−1.27071	+	0.923228i	−0.0414903	+	0.0301445i
$939$	16.4495	+	11.9512i	0.536809	+	0.390014i
$940$	6.01477	−	4.84679i	0.196180	−	0.158085i
$941$	16.8295	−	12.2274i	0.548626	−	0.398600i	−0.278652	−	0.960392i	$-0.589888\pi$
$941$	16.8295	−	12.2274i	0.548626	−	0.398600i	0.827279	+	0.561792i	$0.189888\pi$
$942$	−3.39011	+	10.4337i	−0.110456	+	0.339948i
$943$	−55.8850			−1.81987
$944$	−0.710023	+	2.18522i	−0.0231093	+	0.0711230i
$945$	−0.587453	−	0.383506i	−0.0191098	−	0.0124754i
$946$	5.92181	+	18.2254i	0.192534	+	0.592560i
$947$	−1.94407	−	5.98323i	−0.0631738	−	0.194429i	0.914488	−	0.404613i	$-0.132594\pi$
$947$	−1.94407	−	5.98323i	−0.0631738	−	0.194429i	−0.977662	+	0.210184i	$0.932594\pi$
$948$	31.9650	+	23.2240i	1.03818	+	0.754279i
$949$	−8.45621			−0.274500
$950$	−15.8967	+	14.1758i	−0.515758	+	0.459924i
$951$	−46.8905			−1.52053
$952$	−1.08392	−	0.787516i	−0.0351302	−	0.0255235i
$953$	−14.0794	−	43.3319i	−0.456076	−	1.40366i	−0.869868	−	0.493285i	$-0.835796\pi$
$953$	−14.0794	−	43.3319i	−0.456076	−	1.40366i	0.413792	−	0.910371i	$-0.364204\pi$
$954$	−12.3226	−	37.9249i	−0.398958	−	1.22787i
$955$	−16.8482	+	13.5765i	−0.545195	+	0.439326i
$956$	0.962325	−	2.96173i	0.0311238	−	0.0957893i
$957$	36.0568			1.16555
$958$	−5.18083	+	15.9450i	−0.167385	+	0.515158i
$959$	−6.92330	+	5.03007i	−0.223565	+	0.162430i
$960$	−1.44534	+	5.34273i	−0.0466482	+	0.172436i
$961$	−32.3634	−	23.5134i	−1.04398	−	0.758495i
$962$	−2.83314	+	2.05840i	−0.0913442	+	0.0663654i
$963$	41.8072	−	30.3747i	1.34722	−	0.978811i
$964$	−14.1787	−	10.3014i	−0.456664	−	0.331786i
$965$	24.0153	−	1.20075i	0.773079	−	0.0386536i
$966$	11.5280	−	8.37560i	0.370908	−	0.269481i
$967$	10.9129	−	33.5864i	0.350935	−	1.08007i	−0.607395	−	0.794400i	$-0.707785\pi$
$967$	10.9129	−	33.5864i	0.350935	−	1.08007i	0.958329	−	0.285666i	$-0.0922147\pi$
$968$	5.18049			0.166507
$969$	−4.36550	+	13.4356i	−0.140240	+	0.431614i
$970$	−7.83827	+	28.9743i	−0.251672	+	0.930308i
$971$	11.0506	+	34.0102i	0.354630	+	1.09144i	0.956224	+	0.292637i	$0.0945328\pi$
$971$	11.0506	+	34.0102i	0.354630	+	1.09144i	−0.601593	+	0.798803i	$0.705467\pi$
$972$	−6.87170	−	21.1489i	−0.220410	−	0.678352i
$973$	−13.4472	−	9.76994i	−0.431097	−	0.313210i
$974$	−31.1334			−0.997580
$975$	−7.69281	−	4.49085i	−0.246367	−	0.143822i
$976$	−0.142806			−0.00457111
$977$	−0.372070	−	0.270325i	−0.0119036	−	0.00864845i	0.581818	−	0.813319i	$-0.302342\pi$
$977$	−0.372070	−	0.270325i	−0.0119036	−	0.00864845i	−0.593721	+	0.804671i	$0.702342\pi$
$978$	10.5794	+	32.5600i	0.338292	+	1.04115i
$979$	−7.61328	−	23.4313i	−0.243321	−	0.748866i
$980$	−0.796319	−	2.08947i	−0.0254375	−	0.0667456i
$981$	−17.1337	+	52.7322i	−0.547038	+	1.68361i
$982$	40.5140			1.29285
$983$	2.84751	−	8.76375i	0.0908216	−	0.279520i	−0.895321	−	0.445422i	$-0.853054\pi$
$983$	2.84751	−	8.76375i	0.0908216	−	0.279520i	0.986142	+	0.165902i	$0.0530536\pi$
$984$	19.4395	−	14.1237i	0.619710	−	0.450246i
$985$	−8.55612	−	22.4505i	−0.272621	−	0.715332i
$986$	−6.54526	−	4.75541i	−0.208444	−	0.151443i
$987$	6.91770	−	5.02600i	0.220193	−	0.159979i
$988$	2.48046	−	1.80216i	0.0789141	−	0.0573344i
$989$	36.9972	+	26.8800i	1.17644	+	0.854735i
$990$	14.1232	+	9.22004i	0.448866	+	0.293032i
$991$	23.2329	−	16.8797i	0.738016	−	0.536200i	−0.154073	−	0.988059i	$-0.549239\pi$
$991$	23.2329	−	16.8797i	0.738016	−	0.536200i	0.892089	+	0.451859i	$0.149239\pi$
$992$	−2.60388	+	8.01393i	−0.0826734	+	0.254443i
$993$	58.3199			1.85072
$994$	−1.12360	+	3.45809i	−0.0356385	+	0.109684i
$995$	−47.8323	+	2.39160i	−1.51639	+	0.0758187i
$996$	0.561038	+	1.72670i	0.0177772	+	0.0547125i
$997$	−17.3934	−	53.5315i	−0.550855	−	1.69536i	−0.706645	−	0.707568i	$-0.749792\pi$
$997$	−17.3934	−	53.5315i	−0.550855	−	1.69536i	0.155789	−	0.987790i	$-0.450208\pi$
$998$	−15.6138	−	11.3441i	−0.494246	−	0.359091i
$999$	−1.52653			−0.0482974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.b.141.3	✓	12
25.6	even	5		8750.2.a.p.1.5		6
25.11	even	5	inner	350.2.h.b.211.3	yes	12
25.19	even	10		8750.2.a.q.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.b.141.3	✓	12	1.1	even	1	trivial
350.2.h.b.211.3	yes	12	25.11	even	5	inner
8750.2.a.p.1.5		6	25.6	even	5
8750.2.a.q.1.2		6	25.19	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.764888 + 2.35408i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23328 + 0.111663i) q^{5} +(-0.764888 + 2.35408i) q^{6} -1.00000 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.52960 + 1.83786i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.764888 + 2.35408i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.23328 + 0.111663i) q^{5} +(-0.764888 + 2.35408i) q^{6} -1.00000 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.52960 + 1.83786i) q^{9} +(-1.87239 - 1.22235i) q^{10} +(1.95164 + 1.41795i) q^{11} +(-2.00250 + 1.45490i) q^{12} +(-0.582288 + 0.423057i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.97107 - 5.17191i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.414022 - 1.27423i) q^{17} -3.12675 q^{18} +(-1.31637 + 4.05137i) q^{19} +(-0.796319 - 2.08947i) q^{20} +(-0.764888 - 2.35408i) q^{21} +(0.745462 + 2.29430i) q^{22} +(4.65736 + 3.38377i) q^{23} -2.47523 q^{24} +(4.97506 - 0.498749i) q^{25} -0.719747 q^{26} +(-0.253824 - 0.184414i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-1.86600 - 5.74295i) q^{29} +(1.44534 - 5.34273i) q^{30} +(2.60388 - 8.01393i) q^{31} -1.00000 q^{32} +(-1.84519 + 5.67891i) q^{33} +(1.08392 - 0.787516i) q^{34} +(2.23328 - 0.111663i) q^{35} +(-2.52960 - 1.83786i) q^{36} +(3.93630 - 2.85989i) q^{37} +(-3.44630 + 2.50388i) q^{38} +(-1.44130 - 1.04716i) q^{39} +(0.583923 - 2.15848i) q^{40} +(-7.85364 + 5.70600i) q^{41} +(0.764888 - 2.35408i) q^{42} +7.94381 q^{43} +(-0.745462 + 2.29430i) q^{44} +(5.44407 - 4.38691i) q^{45} +(1.77895 + 5.47506i) q^{46} +(1.06751 + 3.28545i) q^{47} +(-2.00250 - 1.45490i) q^{48} +1.00000 q^{49} +(4.31807 + 2.52077i) q^{50} +3.31632 q^{51} +(-0.582288 - 0.423057i) q^{52} +(3.94101 + 12.1292i) q^{53} +(-0.0969523 - 0.298389i) q^{54} +(-4.51690 - 2.94876i) q^{55} +(0.309017 - 0.951057i) q^{56} -10.5441 q^{57} +(1.86600 - 5.74295i) q^{58} +(1.85886 - 1.35054i) q^{59} +(4.30968 - 3.47281i) q^{60} +(0.115532 + 0.0839393i) q^{61} +(6.81706 - 4.95288i) q^{62} +(2.52960 - 1.83786i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.25317 - 1.00982i) q^{65} +(-4.83077 + 3.50976i) q^{66} +(0.485370 - 1.49381i) q^{67} +1.33980 q^{68} +(-4.40332 + 13.5520i) q^{69} +(1.87239 + 1.22235i) q^{70} +(-1.12360 - 3.45809i) q^{71} +(-0.966220 - 2.97372i) q^{72} +(9.50503 + 6.90581i) q^{73} +4.86554 q^{74} +(4.97946 + 11.3302i) q^{75} -4.25986 q^{76} +(-1.95164 - 1.41795i) q^{77} +(-0.550526 - 1.69434i) q^{78} +(-4.93270 - 15.1813i) q^{79} +(1.74113 - 1.40303i) q^{80} +(-2.65868 + 8.18258i) q^{81} -9.70763 q^{82} +(0.226661 - 0.697591i) q^{83} +(2.00250 - 1.45490i) q^{84} +(-0.782342 + 2.89194i) q^{85} +(6.42667 + 4.66925i) q^{86} +(12.0921 - 8.78542i) q^{87} +(-1.95164 + 1.41795i) q^{88} +(-8.26235 - 6.00295i) q^{89} +(6.98291 - 0.349143i) q^{90} +(0.582288 - 0.423057i) q^{91} +(-1.77895 + 5.47506i) q^{92} +20.8571 q^{93} +(-1.06751 + 3.28545i) q^{94} +(2.48743 - 9.19482i) q^{95} +(-0.764888 - 2.35408i) q^{96} +(-4.14808 - 12.7665i) q^{97} +(0.809017 + 0.587785i) q^{98} -7.54287 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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