LMFDB - Embedded newform 374.2.g.f.69.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [374,2,Mod(69,374)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("374.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(374, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$374 = 2 \cdot 11 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	374.g (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.98640503560$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 4 x^{15} + 10 x^{14} - 8 x^{13} + 68 x^{12} + 28 x^{11} + 306 x^{10} + 228 x^{9} + 1035 x^{8} + \cdots + 3481$ x^16 - 4x^15 + 10x^14 - 8x^13 + 68x^12 + 28x^11 + 306x^10 + 228x^9 + 1035x^8 + 264x^7 + 2972x^6 + 4642x^5 + 9487x^4 + 8098x^3 + 7793x^2 + 2124*x + 3481
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.4
Root			$3.02032 - 2.19439i$ of defining polynomial
Character	$\chi$	$=$	374.69
Dual form			374.2.g.f.103.4

$q$ -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} +(0.844641 + 2.59954i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.538167 - 0.391001i) q^{5} +(-2.21130 - 1.60660i) q^{6} +(0.0960172 - 0.295511i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-3.61712 + 2.62799i) q^{9} +0.665210 q^{10} +(-2.89066 + 1.62607i) q^{11} +2.73332 q^{12} +(-4.28903 + 3.11616i) q^{13} +(0.0960172 + 0.295511i) q^{14} +(0.561864 - 1.72924i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.809017 + 0.587785i) q^{17} +(1.38162 - 4.25219i) q^{18} +(2.30559 + 7.09588i) q^{19} +(-0.538167 + 0.391001i) q^{20} +0.849291 q^{21} +(1.38281 - 3.01461i) q^{22} -3.64343 q^{23} +(-2.21130 + 1.60660i) q^{24} +(-1.40834 - 4.33444i) q^{25} +(1.63826 - 5.04206i) q^{26} +(-3.25285 - 2.36333i) q^{27} +(-0.251376 - 0.182636i) q^{28} +(-0.922922 + 2.84046i) q^{29} +(0.561864 + 1.72924i) q^{30} +(7.68108 - 5.58063i) q^{31} +1.00000 q^{32} +(-6.66860 - 6.14092i) q^{33} -1.00000 q^{34} +(-0.167218 + 0.121491i) q^{35} +(1.38162 + 4.25219i) q^{36} +(0.704007 - 2.16671i) q^{37} +(-6.03612 - 4.38550i) q^{38} +(-11.7233 - 8.51746i) q^{39} +(0.205561 - 0.632653i) q^{40} +(0.909568 + 2.79936i) q^{41} +(-0.687091 + 0.499201i) q^{42} +9.41954 q^{43} +(0.653226 + 3.25166i) q^{44} +2.97416 q^{45} +(2.94760 - 2.14155i) q^{46} +(-1.86150 - 5.72910i) q^{47} +(0.844641 - 2.59954i) q^{48} +(5.58501 + 4.05775i) q^{49} +(3.68709 + 2.67883i) q^{50} +(-0.844641 + 2.59954i) q^{51} +(1.63826 + 5.04206i) q^{52} +(-8.23182 + 5.98076i) q^{53} +4.02074 q^{54} +(2.19145 + 0.255151i) q^{55} +0.310718 q^{56} +(-16.4986 + 11.9869i) q^{57} +(-0.922922 - 2.84046i) q^{58} +(0.0336496 - 0.103563i) q^{59} +(-1.47098 - 1.06873i) q^{60} +(3.52488 + 2.56097i) q^{61} +(-2.93391 + 9.02965i) q^{62} +(0.429294 + 1.32123i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.52664 q^{65} +(9.00455 + 1.04840i) q^{66} +0.391366 q^{67} +(0.809017 - 0.587785i) q^{68} +(-3.07739 - 9.47123i) q^{69} +(0.0638717 - 0.196577i) q^{70} +(8.09002 + 5.87774i) q^{71} +(-3.61712 - 2.62799i) q^{72} +(-3.19522 + 9.83388i) q^{73} +(0.704007 + 2.16671i) q^{74} +(10.0780 - 7.32208i) q^{75} +7.46105 q^{76} +(0.202969 + 1.01035i) q^{77} +14.4908 q^{78} +(6.54108 - 4.75238i) q^{79} +(0.205561 + 0.632653i) q^{80} +(-0.748775 + 2.30449i) q^{81} +(-2.38128 - 1.73010i) q^{82} +(-6.90684 - 5.01811i) q^{83} +(0.262445 - 0.807724i) q^{84} +(-0.205561 - 0.632653i) q^{85} +(-7.62057 + 5.53667i) q^{86} -8.16342 q^{87} +(-2.43975 - 2.24669i) q^{88} +10.6838 q^{89} +(-2.40615 + 1.74817i) q^{90} +(0.509039 + 1.56666i) q^{91} +(-1.12588 + 3.46511i) q^{92} +(20.9948 + 15.2536i) q^{93} +(4.87347 + 3.54078i) q^{94} +(1.53370 - 4.72026i) q^{95} +(0.844641 + 2.59954i) q^{96} +(6.88559 - 5.00267i) q^{97} -6.90345 q^{98} +(6.18255 - 13.4783i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 4 q^{2} + 5 q^{3} - 4 q^{4} - q^{5} + 2 q^{7} - 4 q^{8} - 13 q^{9} + 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{13} + 2 q^{14} - 6 q^{15} - 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} - q^{20} + 6 q^{22}+ \cdots + 65 q^{99}+O(q^{100})$ 16 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 - q^5 + 2 * q^7 - 4 * q^8 - 13 * q^9 + 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^13 + 2 * q^14 - 6 * q^15 - 4 * q^16 + 4 * q^17 + 2 * q^18 + 10 * q^19 - q^20 + 6 * q^22 - 24 * q^23 - 37 * q^25 + 15 * q^26 - 4 * q^27 - 13 * q^28 - 16 * q^29 - 6 * q^30 + 11 * q^31 + 16 * q^32 + 36 * q^33 - 16 * q^34 + 2 * q^36 + 5 * q^37 - 25 * q^38 - 30 * q^39 - q^40 + 4 * q^41 + 35 * q^42 + 16 * q^43 + 6 * q^44 + 6 * q^45 - 14 * q^46 - 14 * q^47 + 5 * q^48 + 2 * q^49 + 13 * q^50 - 5 * q^51 + 15 * q^52 + 5 * q^53 - 34 * q^54 + 81 * q^55 + 22 * q^56 - 12 * q^57 - 16 * q^58 + 17 * q^59 + 4 * q^60 - 30 * q^61 - 4 * q^62 + 72 * q^63 - 4 * q^64 + 6 * q^65 + 11 * q^66 + 26 * q^67 + 4 * q^68 - 73 * q^69 - 10 * q^70 - q^71 - 13 * q^72 - 43 * q^73 + 5 * q^74 + 67 * q^75 + 30 * q^76 + 40 * q^77 + 70 * q^78 - 13 * q^79 - q^80 - 39 * q^81 - 21 * q^82 - 24 * q^83 - 35 * q^84 + q^85 + 26 * q^86 - 92 * q^87 - 4 * q^88 + 24 * q^89 - 29 * q^90 - 10 * q^91 + 26 * q^92 + 11 * q^93 - 4 * q^94 - 39 * q^95 + 5 * q^96 + 3 * q^97 + 2 * q^98 + 65 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/374\mathbb{Z}\right)^\times$ .

$n$	$35$	$309$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.844641	+	2.59954i	0.487654	+	1.50084i	0.828100	+	0.560580i	$0.189422\pi$
$3$	0.844641	+	2.59954i	0.487654	+	1.50084i	−0.340447	+	0.940264i	$0.610578\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.538167	−	0.391001i	−0.240675	−	0.174861i	0.460909	−	0.887448i	$-0.347524\pi$
$5$	−0.538167	−	0.391001i	−0.240675	−	0.174861i	−0.701584	+	0.712587i	$0.747524\pi$
$6$	−2.21130	−	1.60660i	−0.902759	−	0.655893i
$7$	0.0960172	−	0.295511i	0.0362911	−	0.111693i	−0.931270	−	0.364330i	$-0.881298\pi$
$7$	0.0960172	−	0.295511i	0.0362911	−	0.111693i	0.967561	+	0.252638i	$0.0812980\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−3.61712	+	2.62799i	−1.20571	+	0.875998i
$10$	0.665210			0.210358
$11$	−2.89066	+	1.62607i	−0.871565	+	0.490279i
$11$	−2.89066	+	1.62607i	−0.871565	+	0.490279i
$12$	2.73332			0.789040
$13$	−4.28903	+	3.11616i	−1.18956	+	0.864269i	−0.993218	−	0.116266i	$-0.962907\pi$
$13$	−4.28903	+	3.11616i	−1.18956	+	0.864269i	−0.196345	+	0.980535i	$0.562907\pi$
$14$	0.0960172	+	0.295511i	0.0256617	+	0.0789785i
$15$	0.561864	−	1.72924i	0.145073	−	0.446488i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$18$	1.38162	−	4.25219i	0.325651	−	1.00225i
$19$	2.30559	+	7.09588i	0.528939	+	1.62791i	0.756392	+	0.654118i	$0.226960\pi$
$19$	2.30559	+	7.09588i	0.528939	+	1.62791i	−0.227453	+	0.973789i	$0.573040\pi$
$20$	−0.538167	+	0.391001i	−0.120338	+	0.0874305i
$21$	0.849291			0.185331
$22$	1.38281	−	3.01461i	0.294816	−	0.642716i
$23$	−3.64343			−0.759708			−0.379854	−	0.925047i	$-0.624026\pi$
$23$	−3.64343			−0.759708			−0.379854	+	0.925047i	$0.624026\pi$
$24$	−2.21130	+	1.60660i	−0.451379	+	0.327946i
$25$	−1.40834	−	4.33444i	−0.281669	−	0.866887i
$26$	1.63826	−	5.04206i	0.321290	−	0.988829i
$27$	−3.25285	−	2.36333i	−0.626011	−	0.454823i
$28$	−0.251376	−	0.182636i	−0.0475057	−	0.0345149i
$29$	−0.922922	+	2.84046i	−0.171382	+	0.527460i	−0.999450	−	0.0331680i	$-0.989440\pi$
$29$	−0.922922	+	2.84046i	−0.171382	+	0.527460i	0.828068	+	0.560628i	$0.189440\pi$
$30$	0.561864	+	1.72924i	0.102582	+	0.315714i
$31$	7.68108	−	5.58063i	1.37956	−	1.00231i	0.382641	−	0.923897i	$-0.375014\pi$
$31$	7.68108	−	5.58063i	1.37956	−	1.00231i	0.996921	−	0.0784138i	$-0.0249855\pi$
$32$	1.00000			0.176777
$33$	−6.66860	−	6.14092i	−1.16085	−	1.06900i
$34$	−1.00000			−0.171499
$35$	−0.167218	+	0.121491i	−0.0282650	+	0.0205358i
$36$	1.38162	+	4.25219i	0.230270	+	0.708698i
$37$	0.704007	−	2.16671i	0.115738	−	0.356205i	−0.876362	−	0.481653i	$-0.840037\pi$
$37$	0.704007	−	2.16671i	0.115738	−	0.356205i	0.992100	+	0.125448i	$0.0400367\pi$
$38$	−6.03612	−	4.38550i	−0.979188	−	0.711421i
$39$	−11.7233	−	8.51746i	−1.87723	−	1.36389i
$40$	0.205561	−	0.632653i	0.0325021	−	0.100031i
$41$	0.909568	+	2.79936i	0.142051	+	0.437187i	0.996620	−	0.0821505i	$-0.0261788\pi$
$41$	0.909568	+	2.79936i	0.142051	+	0.437187i	−0.854569	+	0.519337i	$0.826179\pi$
$42$	−0.687091	+	0.499201i	−0.106020	+	0.0770283i
$43$	9.41954			1.43647			0.718233	−	0.695802i	$-0.244951\pi$
$43$	9.41954			1.43647			0.718233	+	0.695802i	$0.244951\pi$
$44$	0.653226	+	3.25166i	0.0984775	+	0.490206i
$45$	2.97416			0.443362
$46$	2.94760	−	2.14155i	0.434599	−	0.315755i
$47$	−1.86150	−	5.72910i	−0.271527	−	0.835676i	−0.990117	−	0.140241i	$-0.955212\pi$
$47$	−1.86150	−	5.72910i	−0.271527	−	0.835676i	0.718590	−	0.695434i	$-0.244788\pi$
$48$	0.844641	−	2.59954i	0.121913	−	0.375211i
$49$	5.58501	+	4.05775i	0.797859	+	0.579678i
$50$	3.68709	+	2.67883i	0.521433	+	0.378844i
$51$	−0.844641	+	2.59954i	−0.118273	+	0.364008i
$52$	1.63826	+	5.04206i	0.227186	+	0.699208i
$53$	−8.23182	+	5.98076i	−1.13073	+	0.821521i	−0.985800	−	0.167921i	$-0.946295\pi$
$53$	−8.23182	+	5.98076i	−1.13073	+	0.821521i	−0.144926	+	0.989442i	$0.546295\pi$
$54$	4.02074			0.547153
$55$	2.19145	+	0.255151i	0.295495	+	0.0344045i
$56$	0.310718			0.0415215
$57$	−16.4986	+	11.9869i	−2.18529	+	1.58771i
$58$	−0.922922	−	2.84046i	−0.121186	−	0.372971i
$59$	0.0336496	−	0.103563i	0.00438081	−	0.0134827i	−0.948842	−	0.315751i	$-0.897744\pi$
$59$	0.0336496	−	0.103563i	0.00438081	−	0.0134827i	0.953223	+	0.302268i	$0.0977437\pi$
$60$	−1.47098	−	1.06873i	−0.189903	−	0.137972i
$61$	3.52488	+	2.56097i	0.451314	+	0.327899i	0.790114	−	0.612959i	$-0.210021\pi$
$61$	3.52488	+	2.56097i	0.451314	+	0.327899i	−0.338800	+	0.940858i	$0.610021\pi$
$62$	−2.93391	+	9.02965i	−0.372607	+	1.14677i
$63$	0.429294	+	1.32123i	0.0540860	+	0.166460i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	3.52664			0.437425
$66$	9.00455	+	1.04840i	1.10838	+	0.129049i
$67$	0.391366			0.0478130			0.0239065	−	0.999714i	$-0.492390\pi$
$67$	0.391366			0.0478130			0.0239065	+	0.999714i	$0.492390\pi$
$68$	0.809017	−	0.587785i	0.0981077	−	0.0712794i
$69$	−3.07739	−	9.47123i	−0.370474	−	1.14020i
$70$	0.0638717	−	0.196577i	0.00763413	−	0.0234954i
$71$	8.09002	+	5.87774i	0.960108	+	0.697560i	0.953176	−	0.302416i	$-0.0977933\pi$
$71$	8.09002	+	5.87774i	0.960108	+	0.697560i	0.00693242	+	0.999976i	$0.497793\pi$
$72$	−3.61712	−	2.62799i	−0.426282	−	0.309712i
$73$	−3.19522	+	9.83388i	−0.373973	+	1.15097i	0.570197	+	0.821508i	$0.306867\pi$
$73$	−3.19522	+	9.83388i	−0.373973	+	1.15097i	−0.944169	+	0.329461i	$0.893133\pi$
$74$	0.704007	+	2.16671i	0.0818391	+	0.251875i
$75$	10.0780	−	7.32208i	1.16371	−	0.845481i
$76$	7.46105			0.855841
$77$	0.202969	+	1.01035i	0.0231305	+	0.115140i
$78$	14.4908			1.64076
$79$	6.54108	−	4.75238i	0.735929	−	0.534684i	−0.155504	−	0.987835i	$-0.549700\pi$
$79$	6.54108	−	4.75238i	0.735929	−	0.534684i	0.891434	+	0.453151i	$0.149700\pi$
$80$	0.205561	+	0.632653i	0.0229825	+	0.0707327i
$81$	−0.748775	+	2.30449i	−0.0831973	+	0.256055i
$82$	−2.38128	−	1.73010i	−0.262968	−	0.191058i
$83$	−6.90684	−	5.01811i	−0.758124	−	0.550809i	0.140211	−	0.990122i	$-0.455222\pi$
$83$	−6.90684	−	5.01811i	−0.758124	−	0.550809i	−0.898334	+	0.439313i	$0.855222\pi$
$84$	0.262445	−	0.807724i	0.0286351	−	0.0881299i
$85$	−0.205561	−	0.632653i	−0.0222963	−	0.0686208i
$86$	−7.62057	+	5.53667i	−0.821747	+	0.597034i
$87$	−8.16342			−0.875211
$88$	−2.43975	−	2.24669i	−0.260078	−	0.239498i
$89$	10.6838			1.13248			0.566240	−	0.824241i	$-0.308398\pi$
$89$	10.6838			1.13248			0.566240	+	0.824241i	$0.308398\pi$
$90$	−2.40615	+	1.74817i	−0.253630	+	0.184273i
$91$	0.509039	+	1.56666i	0.0533618	+	0.164231i
$92$	−1.12588	+	3.46511i	−0.117381	+	0.361262i
$93$	20.9948	+	15.2536i	2.17706	+	1.58173i
$94$	4.87347	+	3.54078i	0.502660	+	0.365204i
$95$	1.53370	−	4.72026i	0.157355	−	0.484288i
$96$	0.844641	+	2.59954i	0.0862058	+	0.265314i
$97$	6.88559	−	5.00267i	0.699125	−	0.507944i	−0.180522	−	0.983571i	$-0.557779\pi$
$97$	6.88559	−	5.00267i	0.699125	−	0.507944i	0.879647	+	0.475627i	$0.157779\pi$
$98$	−6.90345			−0.697354
$99$	6.18255	−	13.4783i	0.621370	−	1.35462i
$100$	−4.55749			−0.455749
$101$	9.54081	−	6.93180i	0.949346	−	0.689740i	−0.00130608	−	0.999999i	$-0.500416\pi$
$101$	9.54081	−	6.93180i	0.949346	−	0.689740i	0.950652	+	0.310259i	$0.100416\pi$
$102$	−0.844641	−	2.59954i	−0.0836319	−	0.257393i
$103$	2.81556	−	8.66539i	0.277425	−	0.853826i	−0.711143	−	0.703048i	$-0.751822\pi$
$103$	2.81556	−	8.66539i	0.277425	−	0.853826i	0.988568	−	0.150778i	$-0.0481780\pi$
$104$	−4.28903	−	3.11616i	−0.420574	−	0.305565i
$105$	−0.457060	−	0.332074i	−0.0446045	−	0.0324071i
$106$	3.14427	−	9.67708i	0.305399	−	0.939921i
$107$	2.47127	+	7.60580i	0.238907	+	0.735280i	0.996579	+	0.0826447i	$0.0263366\pi$
$107$	2.47127	+	7.60580i	0.238907	+	0.735280i	−0.757672	+	0.652635i	$0.773663\pi$
$108$	−3.25285	+	2.36333i	−0.313005	+	0.227412i
$109$	−9.01904			−0.863867			−0.431934	−	0.901905i	$-0.642169\pi$
$109$	−9.01904			−0.863867			−0.431934	+	0.901905i	$0.642169\pi$
$110$	−1.92289	+	1.08168i	−0.183341	+	0.103134i
$111$	6.22707			0.591048
$112$	−0.251376	+	0.182636i	−0.0237528	+	0.0172574i
$113$	4.85401	+	14.9391i	0.456627	+	1.40535i	0.869215	+	0.494435i	$0.164625\pi$
$113$	4.85401	+	14.9391i	0.456627	+	1.40535i	−0.412588	+	0.910918i	$0.635375\pi$
$114$	6.30191	−	19.3953i	0.590228	−	1.81653i
$115$	1.96077	+	1.42458i	0.182843	+	0.132843i
$116$	2.41624	+	1.75550i	0.224342	+	0.162994i
$117$	7.32470	−	22.5431i	0.677169	−	2.08411i
$118$	0.0336496	+	0.103563i	0.00309770	+	0.00953374i
$119$	0.251376	−	0.182636i	0.0230436	−	0.0167422i
$120$	1.81823			0.165981
$121$	5.71177	−	9.40083i	0.519252	−	0.854621i
$122$	−4.35699			−0.394463
$123$	−6.50879	+	4.72891i	−0.586878	+	0.426392i
$124$	−2.93391	−	9.02965i	−0.263473	−	0.810886i
$125$	−1.96465	+	6.04658i	−0.175724	+	0.540822i
$126$	−1.12391	−	0.816566i	−0.100126	−	0.0727455i
$127$	−5.65072	−	4.10549i	−0.501421	−	0.364303i	0.308139	−	0.951341i	$-0.400294\pi$
$127$	−5.65072	−	4.10549i	−0.501421	−	0.364303i	−0.809559	+	0.587038i	$0.800294\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	7.95613	+	24.4864i	0.700498	+	2.15591i
$130$	−2.85311	+	2.07291i	−0.250234	+	0.181806i
$131$	−5.42141			−0.473671			−0.236835	−	0.971550i	$-0.576110\pi$
$131$	−5.42141			−0.473671			−0.236835	+	0.971550i	$0.576110\pi$
$132$	−7.90107	+	4.44457i	−0.687700	+	0.386850i
$133$	2.31829			0.201021
$134$	−0.316622	+	0.230039i	−0.0273520	+	0.0198724i
$135$	0.826509	+	2.54373i	0.0711345	+	0.218930i
$136$	−0.309017	+	0.951057i	−0.0264980	+	0.0815524i
$137$	−14.5752	−	10.5895i	−1.24524	−	0.904722i	−0.247307	−	0.968937i	$-0.579546\pi$
$137$	−14.5752	−	10.5895i	−1.24524	−	0.904722i	−0.997936	+	0.0642154i	$0.979546\pi$
$138$	8.05671	+	5.85354i	0.685833	+	0.498287i
$139$	−4.73007	+	14.5577i	−0.401200	+	1.23477i	0.522828	+	0.852438i	$0.324877\pi$
$139$	−4.73007	+	14.5577i	−0.401200	+	1.23477i	−0.924027	+	0.382327i	$0.875123\pi$
$140$	0.0638717	+	0.196577i	0.00539814	+	0.0166138i
$141$	13.3207	−	9.67807i	1.12181	−	0.815040i
$142$	−9.99981			−0.839165
$143$	7.33100	−	15.9820i	0.613049	−	1.33648i
$144$	4.47101			0.372584
$145$	1.60731	−	1.16778i	0.133480	−	0.0969787i
$146$	−3.19522	−	9.83388i	−0.264439	−	0.813858i
$147$	−5.83094	+	17.9458i	−0.480928	+	1.48014i
$148$	−1.84311	−	1.33910i	−0.151503	−	0.110073i
$149$	−11.8719	−	8.62547i	−0.972587	−	0.706626i	−0.0165477	−	0.999863i	$-0.505268\pi$
$149$	−11.8719	−	8.62547i	−0.972587	−	0.706626i	−0.956040	+	0.293237i	$0.905268\pi$
$150$	−3.84945	+	11.8474i	−0.314306	+	0.967334i
$151$	1.38514	+	4.26302i	0.112721	+	0.346920i	0.991465	−	0.130374i	$-0.0416178\pi$
$151$	1.38514	+	4.26302i	0.112721	+	0.346920i	−0.878744	+	0.477294i	$0.841618\pi$
$152$	−6.03612	+	4.38550i	−0.489594	+	0.355711i
$153$	−4.47101			−0.361460
$154$	−0.758075	−	0.698088i	−0.0610874	−	0.0562536i
$155$	−6.31573			−0.507292
$156$	−11.7233	+	8.51746i	−0.938613	+	0.681943i
$157$	0.197879	+	0.609009i	0.0157925	+	0.0486042i	0.958642	−	0.284614i	$-0.0918654\pi$
$157$	0.197879	+	0.609009i	0.0157925	+	0.0486042i	−0.942850	+	0.333218i	$0.891865\pi$
$158$	−2.49847	+	7.68950i	−0.198768	+	0.611744i
$159$	−22.5001	−	16.3473i	−1.78438	−	1.29643i
$160$	−0.538167	−	0.391001i	−0.0425458	−	0.0309113i
$161$	−0.349832	+	1.07667i	−0.0275706	+	0.0848537i
$162$	−0.748775	−	2.30449i	−0.0588293	−	0.181058i
$163$	−5.28120	+	3.83702i	−0.413656	+	0.300539i	−0.775080	−	0.631863i	$-0.782291\pi$
$163$	−5.28120	+	3.83702i	−0.413656	+	0.300539i	0.361424	+	0.932401i	$0.382291\pi$
$164$	2.94342			0.229843
$165$	1.18771	+	5.91227i	0.0924634	+	0.460269i
$166$	8.53732			0.662624
$167$	0.868935	−	0.631318i	0.0672402	−	0.0488528i	−0.553657	−	0.832745i	$-0.686768\pi$
$167$	0.868935	−	0.631318i	0.0672402	−	0.0488528i	0.620898	+	0.783892i	$0.286768\pi$
$168$	0.262445	+	0.807724i	0.0202481	+	0.0623172i
$169$	4.66810	−	14.3669i	0.359084	−	1.10515i
$170$	0.538167	+	0.391001i	0.0412755	+	0.0299884i
$171$	−26.9876	−	19.6076i	−2.06379	−	1.49943i
$172$	2.91080	−	8.95851i	0.221946	−	0.683080i
$173$	6.57448	+	20.2342i	0.499848	+	1.53837i	0.809262	+	0.587447i	$0.199867\pi$
$173$	6.57448	+	20.2342i	0.499848	+	1.53837i	−0.309414	+	0.950927i	$0.600133\pi$
$174$	6.60435	−	4.79834i	0.500674	−	0.363761i
$175$	−1.41610			−0.107047
$176$	3.29437	+	0.383564i	0.248323	+	0.0289122i
$177$	0.297638			0.0223718
$178$	−8.64336	+	6.27977i	−0.647848	+	0.470689i
$179$	−0.822197	−	2.53046i	−0.0614539	−	0.189136i	0.915616	−	0.402053i	$-0.131703\pi$
$179$	−0.822197	−	2.53046i	−0.0614539	−	0.189136i	−0.977070	+	0.212918i	$0.931703\pi$
$180$	0.919067	−	2.82860i	0.0685032	−	0.210831i
$181$	11.9502	+	8.68234i	0.888252	+	0.645353i	0.935422	−	0.353534i	$-0.115020\pi$
$181$	11.9502	+	8.68234i	0.888252	+	0.645353i	−0.0471693	+	0.998887i	$0.515020\pi$
$182$	−1.33268	−	0.968249i	−0.0987849	−	0.0717714i
$183$	−3.68009	+	11.3262i	−0.272040	+	0.837253i
$184$	−1.12588	−	3.46511i	−0.0830011	−	0.255451i
$185$	−1.22606	+	0.890783i	−0.0901416	+	0.0654917i
$186$	−25.9510			−1.90282
$187$	−3.29437	−	0.383564i	−0.240908	−	0.0280490i
$188$	−6.02394			−0.439341
$189$	−1.01072	+	0.734330i	−0.0735190	+	0.0534147i
$190$	1.53370	+	4.72026i	0.111267	+	0.342443i
$191$	−1.81696	+	5.59202i	−0.131471	+	0.404625i	−0.995024	−	0.0996320i	$-0.968233\pi$
$191$	−1.81696	+	5.59202i	−0.131471	+	0.404625i	0.863554	+	0.504257i	$0.168233\pi$
$192$	−2.21130	−	1.60660i	−0.159587	−	0.115947i
$193$	6.68561	+	4.85738i	0.481241	+	0.349642i	0.801806	−	0.597585i	$-0.203873\pi$
$193$	6.68561	+	4.85738i	0.481241	+	0.349642i	−0.320565	+	0.947227i	$0.603873\pi$
$194$	−2.63006	+	8.09449i	−0.188827	+	0.581151i
$195$	2.97874	+	9.16762i	0.213312	+	0.656507i
$196$	5.58501	−	4.05775i	0.398929	−	0.289839i
$197$	−1.48018			−0.105459			−0.0527293	−	0.998609i	$-0.516792\pi$
$197$	−1.48018			−0.105459			−0.0527293	+	0.998609i	$0.516792\pi$
$198$	2.92058	+	14.5382i	0.207557	+	1.03319i
$199$	−1.74882			−0.123971			−0.0619854	−	0.998077i	$-0.519743\pi$
$199$	−1.74882			−0.123971			−0.0619854	+	0.998077i	$0.519743\pi$
$200$	3.68709	−	2.67883i	0.260717	−	0.189422i
$201$	0.330564	+	1.01737i	0.0233162	+	0.0717598i
$202$	−3.64426	+	11.2159i	−0.256410	+	0.789148i
$203$	0.750770	+	0.545466i	0.0526937	+	0.0382842i
$204$	2.21130	+	1.60660i	0.154822	+	0.112485i
$205$	0.605054	−	1.86216i	0.0422588	−	0.130059i
$206$	2.81556	+	8.66539i	0.196169	+	0.603746i
$207$	13.1787	−	9.57491i	0.915986	−	0.665503i
$208$	5.30154			0.367595
$209$	−18.2031	−	16.7627i	−1.25913	−	1.15950i
$210$	0.564957			0.0389858
$211$	22.0001	−	15.9840i	1.51455	−	1.10038i	0.550440	−	0.834875i	$-0.314460\pi$
$211$	22.0001	−	15.9840i	1.51455	−	1.10038i	0.964108	−	0.265509i	$-0.0855400\pi$
$212$	3.14427	+	9.67708i	0.215950	+	0.664625i
$213$	−8.44625	+	25.9949i	−0.578727	+	1.78114i
$214$	−6.46988	−	4.70064i	−0.442272	−	0.321329i
$215$	−5.06928	−	3.68305i	−0.345722	−	0.251182i
$216$	1.24248	−	3.82395i	0.0845398	−	0.260187i
$217$	−0.911620	−	2.80568i	−0.0618848	−	0.190462i
$218$	7.29656	−	5.30126i	0.494185	−	0.359047i
$219$	−28.2624			−1.90979
$220$	0.919858	−	2.00535i	0.0620168	−	0.135200i
$221$	−5.30154			−0.356620
$222$	−5.03781	+	3.66018i	−0.338116	+	0.245655i
$223$	0.560264	+	1.72432i	0.0375181	+	0.115469i	0.968062	−	0.250713i	$-0.0806650\pi$
$223$	0.560264	+	1.72432i	0.0375181	+	0.115469i	−0.930543	+	0.366181i	$0.880665\pi$
$224$	0.0960172	−	0.295511i	0.00641542	−	0.0197446i
$225$	16.4850	+	11.9771i	1.09900	+	0.798472i
$226$	−12.7080	−	9.23287i	−0.845321	−	0.614161i
$227$	2.46376	−	7.58266i	0.163525	−	0.503279i	−0.835399	−	0.549644i	$-0.814764\pi$
$227$	2.46376	−	7.58266i	0.163525	−	0.503279i	0.998925	+	0.0463645i	$0.0147636\pi$
$228$	6.30191	+	19.3953i	0.417354	+	1.28448i
$229$	12.3093	−	8.94325i	0.813423	−	0.590986i	−0.101398	−	0.994846i	$-0.532332\pi$
$229$	12.3093	−	8.94325i	0.813423	−	0.590986i	0.914821	+	0.403859i	$0.132332\pi$
$230$	−2.42365			−0.159811
$231$	−2.45501	+	1.38101i	−0.161528	+	0.0908637i
$232$	−2.98664			−0.196082
$233$	−11.1915	+	8.13109i	−0.733179	+	0.532686i	−0.890568	−	0.454851i	$-0.849692\pi$
$233$	−11.1915	+	8.13109i	−0.733179	+	0.532686i	0.157389	+	0.987537i	$0.449692\pi$
$234$	7.32470	+	22.5431i	0.478831	+	1.47369i
$235$	−1.23829	+	3.81106i	−0.0807770	+	0.248606i
$236$	−0.0880959	−	0.0640054i	−0.00573455	−	0.00416640i
$237$	17.8788	+	12.9897i	1.16136	+	0.843774i
$238$	−0.0960172	+	0.295511i	−0.00622387	+	0.0191551i
$239$	−5.19389	−	15.9851i	−0.335965	−	1.03399i	−0.966245	−	0.257625i	$-0.917060\pi$
$239$	−5.19389	−	15.9851i	−0.335965	−	1.03399i	0.630280	−	0.776368i	$-0.282940\pi$
$240$	−1.47098	+	1.06873i	−0.0949513	+	0.0689861i
$241$	−21.0719			−1.35736			−0.678679	−	0.734435i	$-0.737447\pi$
$241$	−21.0719			−1.35736			−0.678679	+	0.734435i	$0.737447\pi$
$242$	0.904748	+	10.9627i	0.0581594	+	0.704711i
$243$	−18.6853			−1.19866
$244$	3.52488	−	2.56097i	0.225657	−	0.163950i
$245$	−1.41908	−	4.36749i	−0.0906619	−	0.279029i
$246$	2.48614	−	7.65154i	0.158510	−	0.487844i
$247$	−32.0007	−	23.2499i	−2.03616	−	1.47935i
$248$	7.68108	+	5.58063i	0.487749	+	0.354370i
$249$	7.21097	−	22.1931i	0.456977	−	1.40643i
$250$	−1.96465	−	6.04658i	−0.124255	−	0.382419i
$251$	14.7637	−	10.7265i	0.931876	−	0.677048i	−0.0145753	−	0.999894i	$-0.504640\pi$
$251$	14.7637	−	10.7265i	0.931876	−	0.677048i	0.946451	+	0.322846i	$0.104640\pi$
$252$	1.38923			0.0875130
$253$	10.5319	−	5.92448i	0.662135	−	0.372469i
$254$	6.98468			0.438258
$255$	1.47098	−	1.06873i	0.0921163	−	0.0669264i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	0.842879	−	2.59412i	0.0525774	−	0.161816i	−0.921320	−	0.388805i	$-0.872888\pi$
$257$	0.842879	−	2.59412i	0.0525774	−	0.161816i	0.973897	+	0.226989i	$0.0728880\pi$
$258$	−20.8294	−	15.1335i	−1.29678	−	0.942168i
$259$	−0.572689	−	0.416083i	−0.0355852	−	0.0258541i
$260$	1.08979	−	3.35403i	0.0675860	−	0.208008i
$261$	−4.12639	−	12.6997i	−0.255417	−	0.786094i
$262$	4.38601	−	3.18662i	0.270969	−	0.196870i
$263$	21.5679			1.32993			0.664966	−	0.746874i	$-0.268446\pi$
$263$	21.5679			1.32993			0.664966	+	0.746874i	$0.268446\pi$
$264$	3.77965	−	8.23987i	0.232621	−	0.507129i
$265$	6.76857			0.415790
$266$	−1.87553	+	1.36265i	−0.114996	+	0.0835497i
$267$	9.02396	+	27.7729i	0.552258	+	1.69967i
$268$	0.120939	−	0.372211i	0.00738751	−	0.0227364i
$269$	−23.9404	−	17.3937i	−1.45967	−	1.06051i	−0.983449	−	0.181187i	$-0.942006\pi$
$269$	−23.9404	−	17.3937i	−1.45967	−	1.06051i	−0.476222	−	0.879325i	$-0.657994\pi$
$270$	−2.16383	−	1.57211i	−0.131686	−	0.0956757i
$271$	4.44658	−	13.6852i	0.270111	−	0.831315i	−0.720361	−	0.693599i	$-0.756024\pi$
$271$	4.44658	−	13.6852i	0.270111	−	0.831315i	0.990472	−	0.137716i	$-0.0439761\pi$
$272$	−0.309017	−	0.951057i	−0.0187369	−	0.0576663i
$273$	−3.64264	+	2.64653i	−0.220462	+	0.160175i
$274$	18.0159			1.08838
$275$	11.1191	+	10.2393i	0.670510	+	0.617452i
$276$	−9.95864			−0.599440
$277$	9.20197	−	6.68562i	0.552893	−	0.401700i	−0.275958	−	0.961170i	$-0.588995\pi$
$277$	9.20197	−	6.68562i	0.552893	−	0.401700i	0.828851	+	0.559470i	$0.188995\pi$
$278$	−4.73007	−	14.5577i	−0.283691	−	0.873111i
$279$	−13.1176	+	40.3717i	−0.785327	+	2.41699i
$280$	−0.167218	−	0.121491i	−0.00999320	−	0.00726048i
$281$	−1.01414	−	0.736813i	−0.0604983	−	0.0439546i	0.557125	−	0.830429i	$-0.311904\pi$
$281$	−1.01414	−	0.736813i	−0.0604983	−	0.0439546i	−0.617623	+	0.786474i	$0.711904\pi$
$282$	−5.08806	+	15.6594i	−0.302990	+	0.932506i
$283$	−6.34339	−	19.5229i	−0.377075	−	1.16052i	−0.942068	−	0.335423i	$-0.891121\pi$
$283$	−6.34339	−	19.5229i	−0.377075	−	1.16052i	0.564992	−	0.825096i	$-0.308879\pi$
$284$	8.09002	−	5.87774i	0.480054	−	0.348780i
$285$	13.5659			0.803575
$286$	3.46310	+	17.2388i	0.204777	+	1.01935i
$287$	0.914576			0.0539857
$288$	−3.61712	+	2.62799i	−0.213141	+	0.154856i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−0.613937	+	1.88950i	−0.0360516	+	0.110956i
$291$	18.8205	+	13.6739i	1.10328	+	0.801577i
$292$	8.36520	+	6.07767i	0.489536	+	0.355669i
$293$	3.57855	−	11.0136i	0.209061	−	0.643424i	−0.790461	−	0.612512i	$-0.790159\pi$
$293$	3.57855	−	11.0136i	0.209061	−	0.643424i	0.999522	−	0.0309114i	$-0.00984098\pi$
$294$	−5.83094	−	17.9458i	−0.340067	−	1.04662i
$295$	−0.0586023	+	0.0425771i	−0.00341196	+	0.00247893i
$296$	2.27821			0.132418
$297$	13.2458	+	1.54221i	0.768600	+	0.0894881i
$298$	14.6745			0.850073
$299$	15.6268	−	11.3535i	0.903720	−	0.656591i
$300$	−3.84945	−	11.8474i	−0.222248	−	0.684009i
$301$	0.904438	−	2.78357i	0.0521309	−	0.160443i
$302$	−3.62634	−	2.63469i	−0.208672	−	0.151609i
$303$	26.0780	+	18.9468i	1.49814	+	1.08847i
$304$	2.30559	−	7.09588i	0.132235	−	0.406977i
$305$	−0.895628	−	2.75646i	−0.0512835	−	0.157834i
$306$	3.61712	−	2.62799i	0.206777	−	0.150232i
$307$	−20.7816			−1.18607			−0.593034	−	0.805177i	$-0.702070\pi$
$307$	−20.7816			−1.18607			−0.593034	+	0.805177i	$0.702070\pi$
$308$	1.02362	+	0.119180i	0.0583262	+	0.00679093i
$309$	24.9041			1.41675
$310$	5.10953	−	3.71229i	0.290202	−	0.210844i
$311$	3.64045	+	11.2042i	0.206431	+	0.635330i	0.999652	+	0.0263952i	$0.00840283\pi$
$311$	3.64045	+	11.2042i	0.206431	+	0.635330i	−0.793220	+	0.608935i	$0.791597\pi$
$312$	4.47789	−	13.7815i	0.253511	−	0.780226i
$313$	−17.4361	−	12.6681i	−0.985545	−	0.716041i	−0.0266044	−	0.999646i	$-0.508469\pi$
$313$	−17.4361	−	12.6681i	−0.985545	−	0.716041i	−0.958941	+	0.283605i	$0.908469\pi$
$314$	−0.518054	−	0.376388i	−0.0292355	−	0.0212408i
$315$	0.285571	−	0.878897i	0.0160901	−	0.0495202i
$316$	−2.49847	−	7.68950i	−0.140550	−	0.432568i
$317$	26.2174	−	19.0481i	1.47252	−	1.06985i	0.492644	−	0.870231i	$-0.336030\pi$
$317$	26.2174	−	19.0481i	1.47252	−	1.06985i	0.979874	−	0.199617i	$-0.0639697\pi$
$318$	27.8117			1.55960
$319$	−1.95095	−	9.71153i	−0.109232	−	0.543741i
$320$	0.665210			0.0371864
$321$	−17.6842	+	12.8483i	−0.987036	+	0.717124i
$322$	−0.349832	−	1.07667i	−0.0194954	−	0.0600006i
$323$	−2.30559	+	7.09588i	−0.128287	+	0.394825i
$324$	1.96032	+	1.42426i	0.108907	+	0.0791253i
$325$	19.5472	+	14.2019i	1.08429	+	0.787780i
$326$	2.01724	−	6.20843i	0.111725	−	0.343853i
$327$	−7.61785	−	23.4453i	−0.421268	−	1.29653i
$328$	−2.38128	+	1.73010i	−0.131484	+	0.0955288i
$329$	−1.87175			−0.103193
$330$	−4.43602	−	4.08500i	−0.244195	−	0.224872i
$331$	−16.1110			−0.885539			−0.442770	−	0.896635i	$-0.646004\pi$
$331$	−16.1110			−0.885539			−0.442770	+	0.896635i	$0.646004\pi$
$332$	−6.90684	+	5.01811i	−0.379062	+	0.275405i
$333$	3.14762	+	9.68738i	0.172489	+	0.530865i
$334$	−0.331903	+	1.02149i	−0.0181610	+	0.0558937i
$335$	−0.210620	−	0.153025i	−0.0115074	−	0.00836062i
$336$	−0.687091	−	0.499201i	−0.0374839	−	0.0272336i
$337$	−7.78866	+	23.9710i	−0.424275	+	1.30579i	0.479411	+	0.877591i	$0.340850\pi$
$337$	−7.78866	+	23.9710i	−0.424275	+	1.30579i	−0.903686	+	0.428195i	$0.859150\pi$
$338$	4.66810	+	14.3669i	0.253911	+	0.781458i
$339$	−34.7348	+	25.2363i	−1.88654	+	1.37065i
$340$	−0.665210			−0.0360761
$341$	−13.1288	+	28.6217i	−0.710966	+	1.54995i
$342$	33.3585			1.80382
$343$	3.49500	−	2.53927i	0.188712	−	0.137107i
$344$	2.91080	+	8.95851i	0.156940	+	0.483011i
$345$	−2.04711	+	6.30036i	−0.110213	+	0.339200i
$346$	−17.2122	−	12.5054i	−0.925334	−	0.672294i
$347$	0.344167	+	0.250052i	0.0184759	+	0.0134235i	0.596985	−	0.802252i	$-0.296365\pi$
$347$	0.344167	+	0.250052i	0.0184759	+	0.0134235i	−0.578509	+	0.815676i	$0.696365\pi$
$348$	−2.52264	+	7.76388i	−0.135227	+	0.416187i
$349$	10.8429	+	33.3711i	0.580408	+	1.78631i	0.616976	+	0.786982i	$0.288358\pi$
$349$	10.8429	+	33.3711i	0.580408	+	1.78631i	−0.0365672	+	0.999331i	$0.511642\pi$
$350$	1.14565	−	0.832361i	0.0612374	−	0.0444916i
$351$	21.3161			1.13777
$352$	−2.89066	+	1.62607i	−0.154072	+	0.0866700i
$353$	23.3174			1.24106			0.620530	−	0.784183i	$-0.286917\pi$
$353$	23.3174			1.24106			0.620530	+	0.784183i	$0.286917\pi$
$354$	−0.240794	+	0.174947i	−0.0127980	+	0.00929833i
$355$	−2.05557	−	6.32641i	−0.109099	−	0.335771i
$356$	3.30147	−	10.1609i	0.174978	−	0.538526i
$357$	0.687091	+	0.499201i	0.0363647	+	0.0264205i
$358$	2.15254	+	1.56391i	0.113765	+	0.0826553i
$359$	5.08778	−	15.6586i	0.268523	−	0.826428i	−0.722338	−	0.691540i	$-0.756933\pi$
$359$	5.08778	−	15.6586i	0.268523	−	0.826428i	0.990861	−	0.134888i	$-0.0430675\pi$
$360$	0.919067	+	2.82860i	0.0484391	+	0.149080i
$361$	−29.6645	+	21.5525i	−1.56129	+	1.13434i
$362$	−14.7713			−0.776361
$363$	29.2622	+	6.90764i	1.53587	+	0.362557i
$364$	1.64728			0.0863411
$365$	5.56462	−	4.04293i	0.291266	−	0.211617i
$366$	−3.68009	−	11.3262i	−0.192361	−	0.592027i
$367$	−1.66183	+	5.11459i	−0.0867469	+	0.266980i	−0.985015	−	0.172468i	$-0.944826\pi$
$367$	−1.66183	+	5.11459i	−0.0867469	+	0.266980i	0.898268	+	0.439448i	$0.144826\pi$
$368$	2.94760	+	2.14155i	0.153654	+	0.111636i
$369$	−10.6467	−	7.73530i	−0.554247	−	0.402684i
$370$	0.468313	−	1.44132i	0.0243464	−	0.0749305i
$371$	0.976983	+	3.00685i	0.0507224	+	0.156108i
$372$	20.9948	−	15.2536i	1.08853	−	0.790863i
$373$	−11.1079			−0.575143			−0.287571	−	0.957759i	$-0.592848\pi$
$373$	−11.1079			−0.575143			−0.287571	+	0.957759i	$0.592848\pi$
$374$	2.89066	−	1.62607i	0.149472	−	0.0840822i
$375$	−17.3777			−0.897382
$376$	4.87347	−	3.54078i	0.251330	−	0.182602i
$377$	−4.89290	−	15.0588i	−0.251997	−	0.775568i
$378$	0.386060	−	1.18817i	0.0198568	−	0.0611129i
$379$	25.3331	+	18.4056i	1.30127	+	0.945432i	0.999967	−	0.00809537i	$-0.00257686\pi$
$379$	25.3331	+	18.4056i	1.30127	+	0.945432i	0.301308	+	0.953527i	$0.402577\pi$
$380$	−4.01529	−	2.91728i	−0.205980	−	0.149653i
$381$	5.89955	−	18.1569i	0.302243	−	0.930208i
$382$	−1.81696	−	5.59202i	−0.0929637	−	0.286113i
$383$	14.4150	−	10.4731i	0.736571	−	0.535150i	−0.155064	−	0.987904i	$-0.549558\pi$
$383$	14.4150	−	10.4731i	0.736571	−	0.535150i	0.891635	+	0.452754i	$0.149558\pi$
$384$	2.73332			0.139484
$385$	0.285817	−	0.623098i	0.0145666	−	0.0317560i
$386$	−8.26387			−0.420620
$387$	−34.0716	+	24.7545i	−1.73196	+	1.25834i
$388$	−2.63006	−	8.09449i	−0.133521	−	0.410936i
$389$	−11.5457	+	35.5341i	−0.585392	+	1.80165i	0.0122981	+	0.999924i	$0.496085\pi$
$389$	−11.5457	+	35.5341i	−0.585392	+	1.80165i	−0.597690	+	0.801727i	$0.703915\pi$
$390$	−7.79845	−	5.66590i	−0.394890	−	0.286904i
$391$	−2.94760	−	2.14155i	−0.149066	−	0.108303i
$392$	−2.13328	+	6.56558i	−0.107747	+	0.331612i
$393$	−4.57914	−	14.0932i	−0.230987	−	0.710906i
$394$	1.19749	−	0.870030i	0.0603288	−	0.0438315i
$395$	−5.37838			−0.270615
$396$	−10.9081	−	10.0450i	−0.548155	−	0.504780i
$397$	3.52979			0.177155			0.0885777	−	0.996069i	$-0.471768\pi$
$397$	3.52979			0.177155			0.0885777	+	0.996069i	$0.471768\pi$
$398$	1.41483	−	1.02793i	0.0709189	−	0.0515256i
$399$	1.95812	+	6.02647i	0.0980285	+	0.301701i
$400$	−1.40834	+	4.33444i	−0.0704172	+	0.216722i
$401$	11.7186	+	8.51406i	0.585199	+	0.425172i	0.840595	−	0.541665i	$-0.182206\pi$
$401$	11.7186	+	8.51406i	0.585199	+	0.425172i	−0.255396	+	0.966837i	$0.582206\pi$
$402$	−0.865427	−	0.628770i	−0.0431636	−	0.0313602i
$403$	−15.5542	+	47.8710i	−0.774811	+	2.38462i
$404$	−3.64426	−	11.2159i	−0.181309	−	0.558012i
$405$	1.30402	−	0.947430i	0.0647975	−	0.0470782i
$406$	−0.928003			−0.0460560
$407$	1.48819	+	7.40798i	0.0737667	+	0.367200i
$408$	−2.73332			−0.135319
$409$	1.83151	−	1.33067i	0.0905623	−	0.0657973i	−0.541583	−	0.840647i	$-0.682175\pi$
$409$	1.83151	−	1.33067i	0.0905623	−	0.0657973i	0.632145	+	0.774850i	$0.282175\pi$
$410$	0.605054	+	1.86216i	0.0298815	+	0.0919658i
$411$	15.2170	−	46.8331i	0.750599	−	2.31011i
$412$	−7.37122	−	5.35550i	−0.363154	−	0.263847i
$413$	−0.0273730	−	0.0198877i	−0.00134694	−	0.000978607i
$414$	−5.03383	+	15.4925i	−0.247399	+	0.761417i
$415$	1.75494	+	5.40116i	0.0861468	+	0.265132i
$416$	−4.28903	+	3.11616i	−0.210287	+	0.152783i
$417$	−41.8384			−2.04884
$418$	24.5795	+	2.86179i	1.20222	+	0.139975i
$419$	18.4880			0.903199			0.451600	−	0.892221i	$-0.350854\pi$
$419$	18.4880			0.903199			0.451600	+	0.892221i	$0.350854\pi$
$420$	−0.457060	+	0.332074i	−0.0223022	+	0.0162035i
$421$	−5.30296	−	16.3208i	−0.258451	−	0.795429i	−0.993130	−	0.117015i	$-0.962668\pi$
$421$	−5.30296	−	16.3208i	−0.258451	−	0.795429i	0.734680	−	0.678414i	$-0.237332\pi$
$422$	−8.40329	+	25.8627i	−0.409066	+	1.25897i
$423$	21.7893	+	15.8309i	1.05943	+	0.769723i
$424$	−8.23182	−	5.98076i	−0.399772	−	0.290452i
$425$	1.40834	−	4.33444i	0.0683147	−	0.210251i
$426$	−8.44625	−	25.9949i	−0.409222	−	1.25946i
$427$	1.09524	−	0.795741i	0.0530026	−	0.0385086i
$428$	7.99721			0.386560
$429$	47.7380	+	5.55813i	2.30481	+	0.268349i
$430$	6.26598			0.302172
$431$	8.10989	−	5.89218i	0.390640	−	0.283816i	−0.375078	−	0.926993i	$-0.622384\pi$
$431$	8.10989	−	5.89218i	0.390640	−	0.283816i	0.765718	+	0.643177i	$0.222384\pi$
$432$	1.24248	+	3.82395i	0.0597787	+	0.183980i
$433$	−7.95265	+	24.4757i	−0.382180	+	1.17623i	0.556326	+	0.830964i	$0.312211\pi$
$433$	−7.95265	+	24.4757i	−0.382180	+	1.17623i	−0.938506	+	0.345264i	$0.887789\pi$
$434$	2.38665	+	1.73400i	0.114563	+	0.0832348i
$435$	4.39328	+	3.19191i	0.210642	+	0.153040i
$436$	−2.78704	+	8.57762i	−0.133475	+	0.410793i
$437$	−8.40026	−	25.8533i	−0.401839	−	1.23673i
$438$	22.8647	−	16.6122i	1.09252	−	0.793762i
$439$	35.8081			1.70903			0.854513	−	0.519430i	$-0.173856\pi$
$439$	35.8081			1.70903			0.854513	+	0.519430i	$0.173856\pi$
$440$	0.434533	+	2.16304i	0.0207155	+	0.103119i
$441$	−30.8654			−1.46978
$442$	4.28903	−	3.11616i	0.204008	−	0.148221i
$443$	−0.486395	−	1.49697i	−0.0231093	−	0.0711232i	0.938837	−	0.344362i	$-0.111905\pi$
$443$	−0.486395	−	1.49697i	−0.0231093	−	0.0711232i	−0.961946	+	0.273239i	$0.911905\pi$
$444$	1.92427	−	5.92230i	0.0913219	−	0.281060i
$445$	−5.74966	−	4.17737i	−0.272560	−	0.198026i
$446$	−1.46679	−	1.06569i	−0.0694545	−	0.0504617i
$447$	12.3947	−	38.1470i	0.586249	−	1.80429i
$448$	0.0960172	+	0.295511i	0.00453639	+	0.0139616i
$449$	1.67414	−	1.21634i	0.0790076	−	0.0574024i	−0.547580	−	0.836753i	$-0.684451\pi$
$449$	1.67414	−	1.21634i	0.0790076	−	0.0574024i	0.626588	+	0.779351i	$0.284451\pi$
$450$	−20.3766			−0.960563
$451$	−7.18121	−	6.61297i	−0.338150	−	0.311392i
$452$	15.7079			0.738837
$453$	−9.91193	+	7.20144i	−0.465703	+	0.338353i
$454$	2.46376	+	7.58266i	0.115630	+	0.355872i
$455$	0.338618	−	1.04216i	0.0158747	−	0.0488572i
$456$	−16.4986	−	11.9869i	−0.772618	−	0.561340i
$457$	−18.5282	−	13.4615i	−0.866713	−	0.629704i	0.0629902	−	0.998014i	$-0.479936\pi$
$457$	−18.5282	−	13.4615i	−0.866713	−	0.629704i	−0.929703	+	0.368311i	$0.879936\pi$
$458$	−4.70174	+	14.4705i	−0.219698	+	0.676161i
$459$	−1.24248	−	3.82395i	−0.0579939	−	0.178487i
$460$	1.96077	−	1.42458i	0.0914215	−	0.0664216i
$461$	−30.7520			−1.43226			−0.716132	−	0.697964i	$-0.754089\pi$
$461$	−30.7520			−1.43226			−0.716132	+	0.697964i	$0.754089\pi$
$462$	1.17441	−	2.56028i	0.0546383	−	0.119115i
$463$	−23.7747			−1.10490			−0.552451	−	0.833545i	$-0.686308\pi$
$463$	−23.7747			−1.10490			−0.552451	+	0.833545i	$0.686308\pi$
$464$	2.41624	−	1.75550i	0.112171	−	0.0814971i
$465$	−5.33452	−	16.4180i	−0.247383	−	0.761365i
$466$	4.27477	−	13.1564i	0.198025	−	0.609458i
$467$	7.93914	+	5.76812i	0.367379	+	0.266917i	0.756123	−	0.654429i	$-0.227091\pi$
$467$	7.93914	+	5.76812i	0.367379	+	0.266917i	−0.388744	+	0.921346i	$0.627091\pi$
$468$	−19.1763	−	13.9324i	−0.886425	−	0.644026i
$469$	0.0375779	−	0.115653i	0.00173519	−	0.00534035i
$470$	−1.23829	−	3.81106i	−0.0571180	−	0.175791i
$471$	−1.41600	+	1.02879i	−0.0652460	+	0.0474040i
$472$	0.108892			0.00501218
$473$	−27.2286	+	15.3169i	−1.25197	+	0.704270i
$474$	−22.0995			−1.01506
$475$	27.5096	−	19.9869i	1.26223	−	0.917061i
$476$	−0.0960172	−	0.295511i	−0.00440094	−	0.0135447i
$477$	14.0581	−	43.2663i	0.643676	−	1.98103i
$478$	13.5978	+	9.87936i	0.621948	+	0.451872i
$479$	−7.23809	−	5.25878i	−0.330717	−	0.240280i	0.410018	−	0.912077i	$-0.365522\pi$
$479$	−7.23809	−	5.25878i	−0.330717	−	0.240280i	−0.740735	+	0.671798i	$0.765522\pi$
$480$	0.561864	−	1.72924i	0.0256455	−	0.0789286i
$481$	3.73232	+	11.4869i	0.170179	+	0.523757i
$482$	17.0475	−	12.3857i	0.776492	−	0.564155i
$483$	−3.09433			−0.140797
$484$	−7.17569	−	8.33724i	−0.326168	−	0.378965i
$485$	−5.66164			−0.257082
$486$	15.1167	−	10.9829i	0.685708	−	0.498196i
$487$	−1.47135	−	4.52834i	−0.0666730	−	0.205198i	0.912170	−	0.409813i	$-0.134406\pi$
$487$	−1.47135	−	4.52834i	−0.0666730	−	0.205198i	−0.978843	+	0.204614i	$0.934406\pi$
$488$	−1.34638	+	4.14374i	−0.0609479	+	0.187578i
$489$	−14.4352	−	10.4878i	−0.652782	−	0.474274i
$490$	3.71521	+	2.69926i	0.167836	+	0.121940i
$491$	−2.12648	+	6.54462i	−0.0959665	+	0.295355i	−0.987504	−	0.157592i	$-0.949627\pi$
$491$	−2.12648	+	6.54462i	−0.0959665	+	0.295355i	0.891538	+	0.452946i	$0.149627\pi$
$492$	2.48614	+	7.65154i	0.112084	+	0.344958i
$493$	−2.41624	+	1.75550i	−0.108822	+	0.0790638i
$494$	39.5550			1.77967
$495$	−8.59728	+	4.83621i	−0.386419	+	0.217371i
$496$	−9.49433			−0.426308
$497$	2.51372	−	1.82632i	0.112756	−	0.0819217i
$498$	7.21097	+	22.1931i	0.323131	+	0.994496i
$499$	5.56199	−	17.1180i	0.248989	−	0.766309i	−0.745966	−	0.665984i	$-0.768012\pi$
$499$	5.56199	−	17.1180i	0.248989	−	0.766309i	0.994955	−	0.100325i	$-0.0319881\pi$
$500$	5.14352	+	3.73699i	0.230025	+	0.167123i
$501$	2.37507	+	1.72559i	0.106110	+	0.0770937i
$502$	−5.63923	+	17.3558i	−0.251691	+	0.774626i
$503$	8.49331	+	26.1397i	0.378698	+	1.16551i	0.940950	+	0.338546i	$0.109935\pi$
$503$	8.49331	+	26.1397i	0.378698	+	1.16551i	−0.562252	+	0.826966i	$0.690065\pi$
$504$	−1.12391	+	0.816566i	−0.0500628	+	0.0363727i
$505$	−7.84489			−0.349093
$506$	−5.03816	+	10.9835i	−0.223974	+	0.488276i
$507$	41.2902			1.83376
$508$	−5.65072	+	4.10549i	−0.250710	+	0.182152i
$509$	−12.5731	−	38.6959i	−0.557291	−	1.71517i	−0.689815	−	0.723986i	$-0.742308\pi$
$509$	−12.5731	−	38.6959i	−0.557291	−	1.71517i	0.132524	−	0.991180i	$-0.457692\pi$
$510$	−0.561864	+	1.72924i	−0.0248798	+	0.0765720i
$511$	2.59922	+	1.88844i	0.114983	+	0.0835399i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	9.27018	−	28.5307i	0.409289	−	1.25966i
$514$	0.842879	+	2.59412i	0.0371778	+	0.114422i
$515$	−4.90341	+	3.56254i	−0.216070	+	0.156984i
$516$	25.7466			1.13343
$517$	14.6969	+	13.5339i	0.646368	+	0.595222i
$518$	0.707882			0.0311026
$519$	−47.0464	+	34.1812i	−2.06511	+	1.50039i
$520$	1.08979	+	3.35403i	0.0477905	+	0.147084i
$521$	3.08251	−	9.48699i	0.135047	−	0.415633i	−0.860550	−	0.509366i	$-0.829880\pi$
$521$	3.08251	−	9.48699i	0.135047	−	0.415633i	0.995597	+	0.0937331i	$0.0298800\pi$
$522$	10.8030	+	7.84887i	0.472836	+	0.343536i
$523$	−33.0481	−	24.0108i	−1.44509	−	1.04992i	−0.986947	−	0.161044i	$-0.948514\pi$
$523$	−33.0481	−	24.0108i	−1.44509	−	1.04992i	−0.458145	−	0.888877i	$-0.651486\pi$
$524$	−1.67531	+	5.15607i	−0.0731862	+	0.225244i
$525$	−1.19609	−	3.68120i	−0.0522018	−	0.160661i
$526$	−17.4488	+	12.6773i	−0.760802	+	0.552755i
$527$	9.49433			0.413580
$528$	1.78547	+	8.88781i	0.0777027	+	0.386792i
$529$	−9.72542			−0.422844
$530$	−5.47589	+	3.97847i	−0.237857	+	0.172814i
$531$	0.150448	+	0.463031i	0.00652888	+	0.0200938i
$532$	0.716390	−	2.20482i	0.0310594	−	0.0955911i
$533$	−12.6244	−	9.17219i	−0.546825	−	0.397292i
$534$	−23.6250	−	17.1646i	−1.02236	−	0.742785i
$535$	1.64392	−	5.05946i	0.0710727	−	0.218739i
$536$	0.120939	+	0.372211i	0.00522376	+	0.0160771i
$537$	5.88357	−	4.27466i	0.253895	−	0.184465i
$538$	29.5919			1.27580
$539$	−22.7425	−	2.64792i	−0.979590	−	0.114054i
$540$	2.67464			0.115098
$541$	−14.9104	+	10.8331i	−0.641049	+	0.465750i	−0.860211	−	0.509939i	$-0.829668\pi$
$541$	−14.9104	+	10.8331i	−0.641049	+	0.465750i	0.219161	+	0.975689i	$0.429668\pi$
$542$	4.44658	+	13.6852i	0.190997	+	0.587828i
$543$	−12.4764	+	38.3985i	−0.535415	+	1.64784i
$544$	0.809017	+	0.587785i	0.0346863	+	0.0252011i
$545$	4.85375	+	3.52645i	0.207912	+	0.151057i
$546$	1.39136	−	4.28218i	0.0595449	−	0.183260i
$547$	12.2795	+	37.7924i	0.525034	+	1.61589i	0.764249	+	0.644921i	$0.223110\pi$
$547$	12.2795	+	37.7924i	0.525034	+	1.61589i	−0.239215	+	0.970967i	$0.576890\pi$
$548$	−14.5752	+	10.5895i	−0.622621	+	0.452361i
$549$	−19.4801			−0.831392
$550$	−15.0141	−	1.74809i	−0.640202	−	0.0745388i
$551$	−22.2835			−0.949307
$552$	8.05671	−	5.85354i	0.342916	−	0.249143i
$553$	−0.776321	−	2.38927i	−0.0330125	−	0.101602i
$554$	−3.51484	+	10.8176i	−0.149331	+	0.459594i
$555$	−3.35120	−	2.43479i	−0.142251	−	0.103351i
$556$	12.3835	+	8.99713i	0.525177	+	0.381563i
$557$	−0.337890	+	1.03992i	−0.0143168	+	0.0440627i	−0.957960	−	0.286903i	$-0.907374\pi$
$557$	−0.337890	+	1.03992i	−0.0143168	+	0.0440627i	0.943643	+	0.330965i	$0.107374\pi$
$558$	−13.1176	−	40.3717i	−0.555310	−	1.70907i
$559$	−40.4007	+	29.3528i	−1.70877	+	1.24149i
$560$	0.206693			0.00873438
$561$	−1.78547	−	8.88781i	−0.0753827	−	0.375244i
$562$	1.25354			0.0528774
$563$	33.0383	−	24.0038i	1.39240	−	1.01164i	0.396803	−	0.917904i	$-0.370120\pi$
$563$	33.0383	−	24.0038i	1.39240	−	1.01164i	0.995597	−	0.0937341i	$-0.0298804\pi$
$564$	−5.08806	−	15.6594i	−0.214246	−	0.659382i
$565$	3.22894	−	9.93764i	0.135842	−	0.418080i
$566$	16.6072	+	12.0658i	0.698053	+	0.507165i
$567$	0.609107	+	0.442542i	0.0255801	+	0.0185850i
$568$	−3.09011	+	9.51038i	−0.129658	+	0.399047i
$569$	−0.0822207	−	0.253049i	−0.00344687	−	0.0106084i	0.949318	−	0.314316i	$-0.101775\pi$
$569$	−0.0822207	−	0.253049i	−0.00344687	−	0.0106084i	−0.952765	+	0.303708i	$0.901775\pi$
$570$	−10.9751	+	7.97384i	−0.459694	+	0.333987i
$571$	27.3690			1.14536			0.572679	−	0.819780i	$-0.305904\pi$
$571$	27.3690			1.14536			0.572679	+	0.819780i	$0.305904\pi$
$572$	−12.9344	−	11.9109i	−0.540815	−	0.498021i
$573$	−16.0714			−0.671390
$574$	−0.739907	+	0.537574i	−0.0308831	+	0.0224379i
$575$	5.13120	+	15.7922i	0.213986	+	0.658581i
$576$	1.38162	−	4.25219i	0.0575674	−	0.177174i
$577$	−3.43170	−	2.49328i	−0.142863	−	0.103796i	0.514058	−	0.857756i	$-0.328142\pi$
$577$	−3.43170	−	2.49328i	−0.142863	−	0.103796i	−0.656921	+	0.753959i	$0.728142\pi$
$578$	−0.809017	−	0.587785i	−0.0336507	−	0.0244486i
$579$	−6.98000	+	21.4822i	−0.290079	+	0.892772i
$580$	−0.613937	−	1.88950i	−0.0254924	−	0.0784574i
$581$	−2.14608	+	1.55922i	−0.0890344	+	0.0646873i
$582$	−23.2634			−0.964299
$583$	14.0702	−	30.6739i	0.582727	−	1.27038i
$584$	−10.3400			−0.427870
$585$	−12.7563	+	9.26798i	−0.527408	+	0.383184i
$586$	3.57855	+	11.0136i	0.147828	+	0.454969i
$587$	7.01848	−	21.6006i	0.289684	−	0.891554i	−0.695272	−	0.718747i	$-0.744716\pi$
$587$	7.01848	−	21.6006i	0.289684	−	0.891554i	0.984956	−	0.172808i	$-0.0552839\pi$
$588$	15.2656	+	11.0911i	0.629543	+	0.457389i
$589$	57.3089	+	41.6374i	2.36137	+	1.71564i
$590$	0.0223841	−	0.0688911i	0.000921538	−	0.00283620i
$591$	−1.25022	−	3.84779i	−0.0514273	−	0.158277i
$592$	−1.84311	+	1.33910i	−0.0757515	+	0.0550367i
$593$	0.435881			0.0178995			0.00894975	−	0.999960i	$-0.497151\pi$
$593$	0.435881			0.0178995			0.00894975	+	0.999960i	$0.497151\pi$
$594$	−11.6226	+	6.53802i	−0.476880	+	0.268258i
$595$	−0.206693			−0.00847359
$596$	−11.8719	+	8.62547i	−0.486294	+	0.353313i
$597$	−1.47713	−	4.54613i	−0.0604548	−	0.186061i
$598$	−5.96890	+	18.3704i	−0.244087	+	0.751221i
$599$	24.2153	+	17.5934i	0.989408	+	0.718847i	0.959791	−	0.280714i	$-0.0905713\pi$
$599$	24.2153	+	17.5934i	0.989408	+	0.718847i	0.0296169	+	0.999561i	$0.490571\pi$
$600$	10.0780	+	7.32208i	0.411432	+	0.298923i
$601$	4.78427	−	14.7245i	0.195155	−	0.600624i	−0.804820	−	0.593519i	$-0.797738\pi$
$601$	4.78427	−	14.7245i	0.195155	−	0.600624i	0.999975	−	0.00710523i	$-0.00226168\pi$
$602$	0.904438	+	2.78357i	0.0368621	+	0.113450i
$603$	−1.41562	+	1.02851i	−0.0576485	+	0.0418841i
$604$	4.48240			0.182386
$605$	−6.74962	+	2.82590i	−0.274411	+	0.114889i
$606$	−32.2342			−1.30943
$607$	4.68113	−	3.40104i	0.190001	−	0.138044i	−0.488718	−	0.872442i	$-0.662535\pi$
$607$	4.68113	−	3.40104i	0.190001	−	0.138044i	0.678719	+	0.734398i	$0.262535\pi$
$608$	2.30559	+	7.09588i	0.0935041	+	0.287776i
$609$	−0.783829	+	2.41238i	−0.0317624	+	0.0977545i
$610$	2.34479	+	1.70359i	0.0949376	+	0.0689762i
$611$	25.8369	+	18.7716i	1.04525	+	0.759417i
$612$	−1.38162	+	4.25219i	−0.0558486	+	0.171884i
$613$	5.04448	+	15.5253i	0.203745	+	0.627061i	0.999763	+	0.0217884i	$0.00693603\pi$
$613$	5.04448	+	15.5253i	0.203745	+	0.627061i	−0.796018	+	0.605273i	$0.793064\pi$
$614$	16.8127	−	12.2151i	0.678504	−	0.492962i
$615$	5.35182			0.215806
$616$	−0.898179	+	0.505251i	−0.0361887	+	0.0203571i
$617$	7.09064			0.285458			0.142729	−	0.989762i	$-0.454412\pi$
$617$	7.09064			0.285458			0.142729	+	0.989762i	$0.454412\pi$
$618$	−20.1479	+	14.6383i	−0.810466	+	0.588838i
$619$	6.26545	+	19.2831i	0.251830	+	0.775052i	0.994438	+	0.105326i	$0.0335886\pi$
$619$	6.26545	+	19.2831i	0.251830	+	0.775052i	−0.742608	+	0.669726i	$0.766411\pi$
$620$	−1.95167	+	6.00662i	−0.0783809	+	0.241232i
$621$	11.8515	+	8.61063i	0.475585	+	0.345533i
$622$	−9.53083	−	6.92455i	−0.382152	−	0.277649i
$623$	1.02583	−	3.15717i	0.0410989	−	0.126489i
$624$	4.47789	+	13.7815i	0.179259	+	0.551703i
$625$	−15.0139	+	10.9083i	−0.600557	+	0.436330i
$626$	21.5522			0.861398
$627$	28.2002	−	61.4781i	1.12621	−	2.45520i
$628$	0.640350			0.0255527
$629$	1.84311	−	1.33910i	0.0734897	−	0.0533934i
$630$	0.285571	+	0.878897i	0.0113774	+	0.0350161i
$631$	−12.6703	+	38.9952i	−0.504397	+	1.55237i	0.297386	+	0.954757i	$0.403885\pi$
$631$	−12.6703	+	38.9952i	−0.504397	+	1.55237i	−0.801783	+	0.597616i	$0.796115\pi$
$632$	6.54108	+	4.75238i	0.260190	+	0.189039i
$633$	60.1332	+	43.6893i	2.39008	+	1.73649i
$634$	−10.0142	+	30.8205i	−0.397714	+	1.22404i
$635$	1.43578	+	4.41888i	0.0569772	+	0.175358i
$636$	−22.5001	+	16.3473i	−0.892189	+	0.648213i
$637$	−36.5989			−1.45010
$638$	7.28665	+	6.71006i	0.288481	+	0.265654i
$639$	−44.7093			−1.76867
$640$	−0.538167	+	0.391001i	−0.0212729	+	0.0154557i
$641$	−14.8264	−	45.6309i	−0.585606	−	1.80231i	−0.596821	−	0.802374i	$-0.703570\pi$
$641$	−14.8264	−	45.6309i	−0.585606	−	1.80231i	0.0112149	−	0.999937i	$-0.496430\pi$
$642$	6.75477	−	20.7890i	0.266589	−	0.820478i
$643$	−16.4901	−	11.9808i	−0.650306	−	0.472475i	0.213069	−	0.977037i	$-0.431654\pi$
$643$	−16.4901	−	11.9808i	−0.650306	−	0.472475i	−0.863375	+	0.504562i	$0.831654\pi$
$644$	0.915872	+	0.665420i	0.0360904	+	0.0262212i
$645$	5.29250	−	16.2886i	0.208392	−	0.641365i
$646$	−2.30559	−	7.09588i	−0.0907123	−	0.279184i
$647$	−19.4272	+	14.1147i	−0.763762	+	0.554906i	−0.900062	−	0.435762i	$-0.856479\pi$
$647$	−19.4272	+	14.1147i	−0.763762	+	0.554906i	0.136300	+	0.990668i	$0.456479\pi$
$648$	−2.42309			−0.0951879
$649$	0.0711314	+	0.354081i	0.00279215	+	0.0138989i
$650$	−24.1617			−0.947701
$651$	6.52347	−	4.73958i	0.255675	−	0.185759i
$652$	2.01724	+	6.20843i	0.0790012	+	0.243141i
$653$	−3.05220	+	9.39372i	−0.119442	+	0.367605i	−0.992848	−	0.119389i	$-0.961906\pi$
$653$	−3.05220	+	9.39372i	−0.119442	+	0.367605i	0.873406	+	0.486993i	$0.161906\pi$
$654$	19.9438	+	14.4900i	0.779864	+	0.566604i
$655$	2.91762	+	2.11978i	0.114001	+	0.0828265i
$656$	0.909568	−	2.79936i	0.0355127	−	0.109297i
$657$	−14.2859	−	43.9674i	−0.557345	−	1.71533i
$658$	1.51428	−	1.10019i	0.0590326	−	0.0428897i
$659$	32.8645			1.28022			0.640110	−	0.768283i	$-0.278889\pi$
$659$	32.8645			1.28022			0.640110	+	0.768283i	$0.278889\pi$
$660$	5.98992	+	0.697407i	0.233157	+	0.0271465i
$661$	−34.4794			−1.34109			−0.670547	−	0.741867i	$-0.733941\pi$
$661$	−34.4794			−1.34109			−0.670547	+	0.741867i	$0.733941\pi$
$662$	13.0341	−	9.46979i	0.506583	−	0.368054i
$663$	−4.47789	−	13.7815i	−0.173907	−	0.535231i
$664$	2.63818	−	8.11947i	0.102381	−	0.315097i
$665$	−1.24762	−	0.906452i	−0.0483808	−	0.0351507i
$666$	−8.24058	−	5.98713i	−0.319316	−	0.231997i
$667$	3.36260	−	10.3490i	0.130200	−	0.400716i
$668$	−0.331903	−	1.02149i	−0.0128417	−	0.0395228i
$669$	−4.00920	+	2.91286i	−0.155005	+	0.112617i
$670$	0.260341			0.0100578
$671$	−14.3535	−	1.67118i	−0.554112	−	0.0645153i
$672$	0.849291			0.0327621
$673$	−19.7358	+	14.3389i	−0.760759	+	0.552724i	−0.899143	−	0.437655i	$-0.855809\pi$
$673$	−19.7358	+	14.3389i	−0.760759	+	0.552724i	0.138384	+	0.990379i	$0.455809\pi$
$674$	−7.78866	−	23.9710i	−0.300008	−	0.923330i
$675$	−5.66258	+	17.4276i	−0.217953	+	0.670790i
$676$	−12.2212	−	8.87925i	−0.470048	−	0.341510i
$677$	−28.9453	−	21.0300i	−1.11246	−	0.808247i	−0.129408	−	0.991591i	$-0.541308\pi$
$677$	−28.9453	−	21.0300i	−1.11246	−	0.808247i	−0.983049	+	0.183344i	$0.941308\pi$
$678$	13.2675	−	40.8333i	0.509536	−	1.56819i
$679$	−0.817208	−	2.51511i	−0.0313616	−	0.0965210i
$680$	0.538167	−	0.391001i	0.0206377	−	0.0149942i
$681$	21.7924			0.835087
$682$	−6.20194	−	30.8724i	−0.237485	−	1.18216i
$683$	36.6612			1.40280			0.701401	−	0.712767i	$-0.252558\pi$
$683$	36.6612			1.40280			0.701401	+	0.712767i	$0.252558\pi$
$684$	−26.9876	+	19.6076i	−1.03189	+	0.749716i
$685$	3.70338	+	11.3978i	0.141499	+	0.435489i
$686$	−1.33497	+	4.10862i	−0.0509694	+	0.156868i
$687$	33.6453	+	24.4447i	1.28365	+	0.932624i
$688$	−7.62057	−	5.53667i	−0.290531	−	0.211083i
$689$	16.6695	−	51.3034i	0.635057	−	1.95450i
$690$	−2.04711	−	6.30036i	−0.0779322	−	0.239851i
$691$	−29.9476	+	21.7582i	−1.13926	+	0.827720i	−0.987016	−	0.160623i	$-0.948650\pi$
$691$	−29.9476	+	21.7582i	−1.13926	+	0.827720i	−0.152243	+	0.988343i	$0.548650\pi$
$692$	21.2755			0.808771
$693$	−3.38936	−	3.12116i	−0.128751	−	0.118563i
$694$	−0.425414			−0.0161485
$695$	8.23763	−	5.98499i	0.312471	−	0.227024i
$696$	−2.52264	−	7.76388i	−0.0956203	−	0.294289i
$697$	−0.909568	+	2.79936i	−0.0344523	+	0.106033i
$698$	−28.3871	−	20.6245i	−1.07447	−	0.780648i
$699$	−30.5899	−	22.2248i	−1.15702	−	0.840621i
$700$	−0.437598	+	1.34679i	−0.0165397	+	0.0509038i
$701$	5.34871	+	16.4616i	0.202018	+	0.621747i	0.999823	+	0.0188313i	$0.00599453\pi$
$701$	5.34871	+	16.4616i	0.202018	+	0.621747i	−0.797805	+	0.602916i	$0.794005\pi$
$702$	−17.2451	+	12.5293i	−0.650874	+	0.472887i
$703$	16.9979			0.641087
$704$	1.38281	−	3.01461i	0.0521165	−	0.113617i
$705$	−10.9529			−0.412510
$706$	−18.8642	+	13.7056i	−0.709963	+	0.515818i
$707$	−1.13234	−	3.48498i	−0.0425860	−	0.131066i
$708$	0.0919750	−	0.283070i	0.00345663	−	0.0106384i
$709$	−2.07548	−	1.50793i	−0.0779463	−	0.0566313i	0.548130	−	0.836393i	$-0.315340\pi$
$709$	−2.07548	−	1.50793i	−0.0779463	−	0.0566313i	−0.626076	+	0.779762i	$0.715340\pi$
$710$	5.38156	+	3.90994i	0.201966	+	0.146737i
$711$	−11.1707	+	34.3799i	−0.418934	+	1.28935i
$712$	3.30147	+	10.1609i	0.123728	+	0.380795i
$713$	−27.9855	+	20.3326i	−1.04806	+	0.761463i
$714$	−0.849291			−0.0317839
$715$	−10.1943	+	5.73457i	−0.381245	+	0.214461i
$716$	−2.66068			−0.0994344
$717$	37.1670	−	27.0034i	1.38803	−	1.00846i
$718$	5.08778	+	15.6586i	0.189874	+	0.584373i
$719$	−10.4470	+	32.1527i	−0.389609	+	1.19909i	0.543472	+	0.839427i	$0.317109\pi$
$719$	−10.4470	+	32.1527i	−0.389609	+	1.19909i	−0.933081	+	0.359666i	$0.882891\pi$
$720$	−2.40615	−	1.74817i	−0.0896719	−	0.0651504i
$721$	−2.29037	−	1.66405i	−0.0852979	−	0.0619726i
$722$	11.3308	−	34.8727i	0.421689	−	1.29783i
$723$	−17.7982	−	54.7771i	−0.661921	−	2.03718i
$724$	11.9502	−	8.68234i	0.444126	−	0.322677i
$725$	13.6116			0.505522
$726$	−27.7338	+	11.6115i	−1.02930	+	0.430943i
$727$	7.21894			0.267736			0.133868	−	0.990999i	$-0.457260\pi$
$727$	7.21894			0.267736			0.133868	+	0.990999i	$0.457260\pi$
$728$	−1.33268	+	0.968249i	−0.0493924	+	0.0358857i
$729$	−13.5360	−	41.6596i	−0.501334	−	1.54295i
$730$	−2.12550	+	6.54160i	−0.0786681	+	0.242116i
$731$	7.62057	+	5.53667i	0.281857	+	0.204781i
$732$	9.63460	+	6.99995i	0.356105	+	0.258726i
$733$	0.813943	−	2.50506i	0.0300637	−	0.0925264i	−0.934899	−	0.354914i	$-0.884510\pi$
$733$	0.813943	−	2.50506i	0.0300637	−	0.0925264i	0.964962	+	0.262388i	$0.0845100\pi$
$734$	−1.66183	−	5.11459i	−0.0613393	−	0.188783i
$735$	10.1548	−	7.37792i	0.374567	−	0.272139i
$736$	−3.64343			−0.134299
$737$	−1.13130	+	0.636390i	−0.0416721	+	0.0234417i
$738$	13.1601			0.484429
$739$	36.3500	−	26.4098i	1.33716	−	0.971500i	0.337612	−	0.941286i	$-0.390381\pi$
$739$	36.3500	−	26.4098i	1.33716	−	0.971500i	0.999543	−	0.0302145i	$-0.00961903\pi$
$740$	0.468313	+	1.44132i	0.0172155	+	0.0529839i
$741$	33.4098	−	102.825i	1.22734	−	3.77736i
$742$	−2.55778	−	1.85833i	−0.0938989	−	0.0682215i
$743$	23.7330	+	17.2430i	0.870678	+	0.632585i	0.930769	−	0.365608i	$-0.119139\pi$
$743$	23.7330	+	17.2430i	0.870678	+	0.632585i	−0.0600909	+	0.998193i	$0.519139\pi$
$744$	−8.01930	+	24.6809i	−0.294002	+	0.904845i
$745$	3.01652	+	9.28388i	0.110517	+	0.340135i
$746$	8.98644	−	6.52903i	0.329017	−	0.239045i
$747$	38.1705			1.39658
$748$	−1.38281	+	3.01461i	−0.0505604	+	0.110225i
$749$	2.48488			0.0907955
$750$	14.0589	−	10.2144i	0.513357	−	0.372976i
$751$	11.3307	+	34.8723i	0.413463	+	1.27251i	0.913619	+	0.406572i	$0.133276\pi$
$751$	11.3307	+	34.8723i	0.413463	+	1.27251i	−0.500156	+	0.865935i	$0.666724\pi$
$752$	−1.86150	+	5.72910i	−0.0678819	+	0.208919i
$753$	40.3538	+	29.3188i	1.47058	+	1.06844i
$754$	12.8098	+	9.30685i	0.466505	+	0.338936i
$755$	0.921409	−	2.83580i	0.0335335	−	0.103206i
$756$	0.386060	+	1.18817i	0.0140409	+	0.0432134i
$757$	10.3195	−	7.49758i	0.375070	−	0.272504i	−0.384240	−	0.923233i	$-0.625537\pi$
$757$	10.3195	−	7.49758i	0.375070	−	0.272504i	0.759310	+	0.650729i	$0.225537\pi$
$758$	−31.3135			−1.13736
$759$	24.2966	+	22.3740i	0.881910	+	0.812125i
$760$	4.96317			0.180033
$761$	−9.19524	+	6.68073i	−0.333327	+	0.242176i	−0.741841	−	0.670576i	$-0.766047\pi$
$761$	−9.19524	+	6.68073i	−0.333327	+	0.242176i	0.408514	+	0.912752i	$0.366047\pi$
$762$	5.89955	+	18.1569i	0.213718	+	0.657756i
$763$	−0.865983	+	2.66522i	−0.0313507	+	0.0964875i
$764$	4.75686	+	3.45606i	0.172097	+	0.125036i
$765$	2.40615	+	1.74817i	0.0869945	+	0.0632052i
$766$	−5.50603	+	16.9458i	−0.198941	+	0.612277i
$767$	0.178395	+	0.549042i	0.00644146	+	0.0198248i
$768$	−2.21130	+	1.60660i	−0.0797934	+	0.0579733i
$769$	37.7545			1.36146			0.680731	−	0.732534i	$-0.261662\pi$
$769$	37.7545			1.36146			0.680731	+	0.732534i	$0.261662\pi$
$770$	0.135017	+	0.672096i	0.00486568	+	0.0242206i
$771$	7.45543			0.268501
$772$	6.68561	−	4.85738i	0.240620	−	0.174821i
$773$	−5.92121	−	18.2236i	−0.212971	−	0.655457i	−0.999291	−	0.0376384i	$-0.988016\pi$
$773$	−5.92121	−	18.2236i	−0.212971	−	0.655457i	0.786320	−	0.617819i	$-0.211984\pi$
$774$	13.0142	−	40.0536i	0.467786	−	1.43970i
$775$	−35.0065	−	25.4337i	−1.25747	−	0.913605i
$776$	6.88559	+	5.00267i	0.247178	+	0.179585i
$777$	0.597906	−	1.84017i	0.0214498	−	0.0660156i
$778$	−11.5457	−	35.5341i	−0.413935	−	1.27396i
$779$	−17.7669	+	12.9084i	−0.636563	+	0.462490i
$780$	9.63941			0.345146
$781$	−32.9431	−	3.83557i	−1.17880	−	0.137247i
$782$	3.64343			0.130289
$783$	9.71507	−	7.05841i	0.347188	−	0.252247i
$784$	−2.13328	−	6.56558i	−0.0761887	−	0.234485i
$785$	0.131631	−	0.405119i	0.00469812	−	0.0144593i
$786$	11.9884	+	8.71005i	0.427610	+	0.310677i
$787$	−17.4501	−	12.6782i	−0.622029	−	0.451931i	0.231601	−	0.972811i	$-0.425604\pi$
$787$	−17.4501	−	12.6782i	−0.622029	−	0.451931i	−0.853630	+	0.520880i	$0.825604\pi$
$788$	−0.457402	+	1.40774i	−0.0162943	+	0.0501486i
$789$	18.2171	+	56.0665i	0.648546	+	1.99602i
$790$	4.35120	−	3.16133i	0.154809	−	0.112475i
$791$	4.88073			0.173539
$792$	14.7292	+	1.71492i	0.523378	+	0.0609370i
$793$	−23.0987			−0.820260
$794$	−2.85566	+	2.07476i	−0.101344	+	0.0736305i
$795$	5.71701	+	17.5952i	0.202762	+	0.624036i
$796$	−0.540416	+	1.66323i	−0.0191545	+	0.0589516i
$797$	34.2100	+	24.8550i	1.21178	+	0.880410i	0.995391	−	0.0958968i	$-0.0305719\pi$
$797$	34.2100	+	24.8550i	1.21178	+	0.880410i	0.216390	+	0.976307i	$0.430572\pi$
$798$	−5.12642	−	3.72456i	−0.181473	−	0.131848i
$799$	1.86150	−	5.72910i	0.0658551	−	0.202681i
$800$	−1.40834	−	4.33444i	−0.0497925	−	0.153245i
$801$	−38.6446	+	28.0769i	−1.36544	+	0.992050i
$802$	−14.4850			−0.511483
$803$	−6.75433	−	33.6220i	−0.238355	−	1.18650i
$804$	1.06973			0.0377264
$805$	0.609248	−	0.442644i	0.0214732	−	0.0156012i
$806$	−15.5542	−	47.8710i	−0.547874	−	1.68618i
$807$	24.9946	−	76.9253i	0.879850	−	2.70790i
$808$	9.54081	+	6.93180i	0.335645	+	0.243860i
$809$	−7.49770	−	5.44740i	−0.263605	−	0.191520i	0.448130	−	0.893968i	$-0.352090\pi$
$809$	−7.49770	−	5.44740i	−0.263605	−	0.191520i	−0.711735	+	0.702448i	$0.752090\pi$
$810$	−0.498093	+	1.53297i	−0.0175012	+	0.0538632i
$811$	−10.9281	−	33.6332i	−0.383737	−	1.18102i	−0.937392	−	0.348275i	$-0.886767\pi$
$811$	−10.9281	−	33.6332i	−0.383737	−	1.18102i	0.553655	−	0.832746i	$-0.313233\pi$
$812$	0.750770	−	0.545466i	0.0263469	−	0.0191421i
$813$	39.3309			1.37939
$814$	−5.55827	−	5.11844i	−0.194817	−	0.179401i
$815$	4.34245			0.152109
$816$	2.21130	−	1.60660i	0.0774109	−	0.0562423i
$817$	21.7176	+	66.8399i	0.759803	+	2.33843i
$818$	−0.699574	+	2.15307i	−0.0244600	+	0.0752802i
$819$	−5.95843	−	4.32905i	−0.208204	−	0.151269i
$820$	−1.58405	−	1.15088i	−0.0553175	−	0.0401905i
$821$	11.3161	−	34.8274i	0.394934	−	1.21548i	−0.534078	−	0.845435i	$-0.679341\pi$
$821$	11.3161	−	34.8274i	0.394934	−	1.21548i	0.929013	−	0.370048i	$-0.120659\pi$
$822$	15.2170	+	46.8331i	0.530753	+	1.63349i
$823$	38.1345	−	27.7063i	1.32928	−	0.965782i	0.329518	−	0.944149i	$-0.393114\pi$
$823$	38.1345	−	27.7063i	1.32928	−	0.965782i	0.999766	−	0.0216325i	$-0.00688637\pi$
$824$	9.11133			0.317408
$825$	−17.2257	+	37.5531i	−0.599723	+	1.30743i
$826$	0.0338349			0.00117727
$827$	−32.0174	+	23.2620i	−1.11335	+	0.808898i	−0.983188	−	0.182594i	$-0.941551\pi$
$827$	−32.0174	+	23.2620i	−1.11335	+	0.808898i	−0.130164	+	0.991492i	$0.541551\pi$
$828$	−5.03383	−	15.4925i	−0.174938	−	0.538403i
$829$	14.5671	−	44.8329i	0.505936	−	1.55711i	−0.293256	−	0.956034i	$-0.594739\pi$
$829$	14.5671	−	44.8329i	0.505936	−	1.55711i	0.799191	−	0.601077i	$-0.205261\pi$
$830$	−4.59450	−	3.33810i	−0.159477	−	0.115867i
$831$	25.1519	+	18.2739i	0.872509	+	0.633915i
$832$	1.63826	−	5.04206i	0.0567966	−	0.174802i
$833$	2.13328	+	6.56558i	0.0739139	+	0.227484i
$834$	33.8480	−	24.5920i	1.17206	−	0.851551i
$835$	−0.714477			−0.0247255
$836$	−21.5673	+	12.1322i	−0.745922	+	0.419601i
$837$	−38.1742			−1.31949
$838$	−14.9571	+	10.8670i	−0.516685	+	0.375394i
$839$	−12.7570	−	39.2621i	−0.440421	−	1.35548i	−0.887428	−	0.460947i	$-0.847510\pi$
$839$	−12.7570	−	39.2621i	−0.440421	−	1.35548i	0.447006	−	0.894531i	$-0.352490\pi$
$840$	0.174581	−	0.537306i	0.00602363	−	0.0185388i
$841$	16.2451	+	11.8027i	0.560174	+	0.406991i
$842$	13.8833	+	10.0868i	0.478451	+	0.347615i
$843$	1.05879	−	3.25863i	0.0364667	−	0.112233i
$844$	−8.40329	−	25.8627i	−0.289253	−	0.890229i
$845$	−8.12969	+	5.90657i	−0.279670	+	0.203192i
$846$	−26.9331			−0.925979
$847$	−2.22962	−	2.59053i	−0.0766106	−	0.0890117i
$848$	10.1751			0.349414
$849$	45.3927	−	32.9798i	1.55787	−	1.13186i
$850$	1.40834	+	4.33444i	0.0483058	+	0.148670i
$851$	−2.56500	+	7.89425i	−0.0879270	+	0.270611i
$852$	22.1126	+	16.0657i	0.757564	+	0.550402i
$853$	−2.79525	−	2.03087i	−0.0957076	−	0.0695356i	0.538902	−	0.842368i	$-0.318839\pi$
$853$	−2.79525	−	2.03087i	−0.0957076	−	0.0695356i	−0.634610	+	0.772833i	$0.718839\pi$
$854$	−0.418346	+	1.28754i	−0.0143155	+	0.0440586i
$855$	6.85721	+	21.1043i	0.234512	+	0.721752i
$856$	−6.46988	+	4.70064i	−0.221136	+	0.160665i
$857$	8.27598			0.282702			0.141351	−	0.989960i	$-0.454855\pi$
$857$	8.27598			0.282702			0.141351	+	0.989960i	$0.454855\pi$
$858$	−41.8878	+	23.5630i	−1.43003	+	0.804429i
$859$	−40.9427			−1.39695			−0.698473	−	0.715636i	$-0.746137\pi$
$859$	−40.9427			−1.39695			−0.698473	+	0.715636i	$0.746137\pi$
$860$	−5.06928	+	3.68305i	−0.172861	+	0.125591i
$861$	0.772488	+	2.37747i	0.0263263	+	0.0810241i
$862$	−3.09770	+	9.53375i	−0.105508	+	0.324721i
$863$	−0.386735	−	0.280980i	−0.0131646	−	0.00956465i	0.581183	−	0.813773i	$-0.302590\pi$
$863$	−0.386735	−	0.280980i	−0.0131646	−	0.00956465i	−0.594348	+	0.804208i	$0.702590\pi$
$864$	−3.25285	−	2.36333i	−0.110664	−	0.0804022i
$865$	4.37341	−	13.4600i	0.148700	−	0.457653i
$866$	−7.95265	−	24.4757i	−0.270242	−	0.831719i
$867$	−2.21130	+	1.60660i	−0.0750996	+	0.0545631i
$868$	−2.95006			−0.100132
$869$	−11.1803	+	24.3738i	−0.379266	+	0.826823i
$870$	−5.43039			−0.184108
$871$	−1.67858	+	1.21956i	−0.0568766	+	0.0413233i
$872$	−2.78704	−	8.57762i	−0.0943810	−	0.290475i
$873$	−11.7590	+	36.1906i	−0.397983	+	1.22487i
$874$	21.9922	+	15.9782i	0.743896	+	0.540472i
$875$	1.59819	+	1.16115i	0.0540286	+	0.0392541i
$876$	−8.73355	+	26.8791i	−0.295079	+	0.908161i
$877$	−2.52734	−	7.77836i	−0.0853423	−	0.262657i	0.899274	−	0.437385i	$-0.144095\pi$
$877$	−2.52734	−	7.77836i	−0.0853423	−	0.262657i	−0.984617	+	0.174728i	$0.944095\pi$
$878$	−28.9693	+	21.0475i	−0.977668	+	0.710317i
$879$	31.6530			1.06763
$880$	−1.62295	−	1.49452i	−0.0547095	−	0.0503804i
$881$	54.0571			1.82123			0.910615	−	0.413255i	$-0.135608\pi$
$881$	54.0571			1.82123			0.910615	+	0.413255i	$0.135608\pi$
$882$	24.9707	−	18.1422i	0.840806	−	0.610881i
$883$	1.28114	+	3.94294i	0.0431137	+	0.132690i	0.970296	−	0.241919i	$-0.0777768\pi$
$883$	1.28114	+	3.94294i	0.0431137	+	0.132690i	−0.927183	+	0.374609i	$0.877777\pi$
$884$	−1.63826	+	5.04206i	−0.0551008	+	0.169583i
$885$	−0.160179	−	0.116377i	−0.00538434	−	0.00391195i
$886$	1.27340	+	0.925178i	0.0427807	+	0.0310820i
$887$	−10.8491	+	33.3901i	−0.364277	+	1.12113i	0.586155	+	0.810199i	$0.300641\pi$
$887$	−10.8491	+	33.3901i	−0.364277	+	1.12113i	−0.950432	+	0.310931i	$0.899359\pi$
$888$	1.92427	+	5.92230i	0.0645743	+	0.198739i
$889$	−1.75578	+	1.27565i	−0.0588871	+	0.0427840i
$890$	7.10697			0.238226
$891$	−1.58282	−	7.87906i	−0.0530266	−	0.263958i
$892$	1.81305			0.0607055
$893$	36.3612	−	26.4179i	1.21678	−	0.884043i
$894$	12.3947	+	38.1470i	0.414541	+	1.27583i
$895$	−0.546934	+	1.68329i	−0.0182820	+	0.0562661i
$896$	−0.251376	−	0.182636i	−0.00839790	−	0.00610143i
$897$	42.7129	+	31.0328i	1.42614	+	1.03615i
$898$	−0.639465	+	1.96807i	−0.0213392	+	0.0656754i
$899$	8.76253	+	26.9683i	0.292247	+	0.899443i
$900$	16.4850	−	11.9771i	0.549501	−	0.399236i
$901$	−10.1751			−0.338981
$902$	9.69673	+	1.12899i	0.322866	+	0.0375913i
$903$	7.99993			0.266221
$904$	−12.7080	+	9.23287i	−0.422660	+	0.307081i
$905$	−3.03640	−	9.34509i	−0.100933	−	0.310641i
$906$	3.78602	−	11.6522i	0.125782	−	0.387118i
$907$	5.30363	+	3.85331i	0.176104	+	0.127947i	0.672345	−	0.740237i	$-0.265287\pi$
$907$	5.30363	+	3.85331i	0.176104	+	0.127947i	−0.496242	+	0.868185i	$0.665287\pi$
$908$	−6.45020	−	4.68634i	−0.214057	−	0.155522i
$909$	−16.2936	+	50.1464i	−0.540423	+	1.66325i
$910$	0.338618	+	1.04216i	0.0112251	+	0.0345472i
$911$	−16.9612	+	12.3230i	−0.561950	+	0.408281i	−0.832172	−	0.554517i	$-0.812903\pi$
$911$	−16.9612	+	12.3230i	−0.561950	+	0.408281i	0.270222	+	0.962798i	$0.412903\pi$
$912$	20.3934			0.675293
$913$	28.1251	+	3.27461i	0.930805	+	0.108374i
$914$	22.9021			0.757535
$915$	6.40904	−	4.65644i	0.211876	−	0.153937i
$916$	−4.70174	−	14.4705i	−0.155350	−	0.478118i
$917$	−0.520549	+	1.60208i	−0.0171900	+	0.0529055i
$918$	3.25285	+	2.36333i	0.107360	+	0.0780016i
$919$	5.66760	+	4.11775i	0.186957	+	0.135832i	0.677327	−	0.735682i	$-0.263138\pi$
$919$	5.66760	+	4.11775i	0.186957	+	0.135832i	−0.490370	+	0.871514i	$0.663138\pi$
$920$	−0.748948	+	2.30503i	−0.0246921	+	0.0759945i
$921$	−17.5530	−	54.0225i	−0.578390	−	1.78010i
$922$	24.8789	−	18.0756i	0.819343	−	0.595288i
$923$	−53.0143			−1.74499
$924$	0.554779	+	2.76161i	0.0182509	+	0.0908502i
$925$	−10.3829			−0.341389
$926$	19.2341	−	13.9744i	0.632072	−	0.459227i
$927$	12.5884	+	38.7431i	0.413457	+	1.27249i
$928$	−0.922922	+	2.84046i	−0.0302964	+	0.0932427i
$929$	−8.81389	−	6.40366i	−0.289174	−	0.210097i	0.433735	−	0.901041i	$-0.357195\pi$
$929$	−8.81389	−	6.40366i	−0.289174	−	0.210097i	−0.722909	+	0.690943i	$0.757195\pi$
$930$	13.9660	+	10.1469i	0.457962	+	0.332729i
$931$	−15.9165	+	48.9861i	−0.521644	+	1.60545i
$932$	4.27477	+	13.1564i	0.140025	+	0.430952i
$933$	−26.0508	+	18.9270i	−0.852864	+	0.619642i
$934$	−9.81331			−0.321101
$935$	1.62295	+	1.49452i	0.0530760	+	0.0488761i
$936$	23.7032			0.774764
$937$	−9.30461	+	6.76019i	−0.303968	+	0.220846i	−0.729304	−	0.684190i	$-0.760156\pi$
$937$	−9.30461	+	6.76019i	−0.303968	+	0.220846i	0.425336	+	0.905036i	$0.360156\pi$
$938$	0.0375779	+	0.115653i	0.00122696	+	0.00377620i
$939$	18.2039	−	56.0257i	0.594060	−	1.82833i
$940$	3.24188	+	2.35536i	0.105738	+	0.0768235i
$941$	−1.19133	−	0.865551i	−0.0388362	−	0.0282162i	0.568198	−	0.822892i	$-0.307641\pi$
$941$	−1.19133	−	0.865551i	−0.0388362	−	0.0282162i	−0.607034	+	0.794676i	$0.707641\pi$
$942$	0.540865	−	1.66461i	0.0176223	−	0.0542360i
$943$	−3.31395	−	10.1993i	−0.107917	−	0.332134i
$944$	−0.0880959	+	0.0640054i	−0.00286728	+	0.00208320i
$945$	0.831059			0.0270344
$946$	13.0254	−	28.3962i	0.423493	−	0.923240i
$947$	31.9456			1.03809			0.519046	−	0.854747i	$-0.326287\pi$
$947$	31.9456			1.03809			0.519046	+	0.854747i	$0.326287\pi$
$948$	17.8788	−	12.9897i	0.580678	−	0.421887i
$949$	−16.9396	−	52.1347i	−0.549882	−	1.69236i
$950$	−10.5077	+	32.3394i	−0.340916	+	1.04923i
$951$	71.6605	+	52.0644i	2.32375	+	1.68830i
$952$	0.251376	+	0.182636i	0.00814716	+	0.00591925i
$953$	−8.27588	+	25.4705i	−0.268082	+	0.825072i	0.722885	+	0.690968i	$0.242816\pi$
$953$	−8.27588	+	25.4705i	−0.268082	+	0.825072i	−0.990967	+	0.134104i	$0.957184\pi$
$954$	14.0581	+	43.2663i	0.455147	+	1.40080i
$955$	3.16431	−	2.29901i	0.102395	−	0.0743942i
$956$	−16.8078			−0.543602
$957$	23.5976	−	13.2743i	0.762803	−	0.429098i
$958$	8.94677			0.289057
$959$	−4.52878	+	3.29035i	−0.146242	+	0.106251i
$960$	0.561864	+	1.72924i	0.0181341	+	0.0558110i
$961$	18.2760	−	56.2478i	0.589548	−	1.81444i
$962$	−9.77133	−	7.09929i	−0.315040	−	0.228890i
$963$	−28.9269	−	21.0166i	−0.932156	−	0.677251i
$964$	−6.51156	+	20.0405i	−0.209723	+	0.645462i
$965$	−1.69873	−	5.22816i	−0.0546841	−	0.168300i
$966$	2.50337	−	1.81880i	0.0805445	−	0.0585190i
$967$	−51.6181			−1.65993			−0.829963	−	0.557819i	$-0.811638\pi$
$967$	−51.6181			−1.65993			−0.829963	+	0.557819i	$0.811638\pi$
$968$	10.7058	+	2.52720i	0.344096	+	0.0812274i
$969$	−20.3934			−0.655131
$970$	4.58036	−	3.32783i	0.147067	−	0.106850i
$971$	18.2614	+	56.2029i	0.586037	+	1.80364i	0.595065	+	0.803678i	$0.297126\pi$
$971$	18.2614	+	56.2029i	0.586037	+	1.80364i	−0.00902778	+	0.999959i	$0.502874\pi$
$972$	−5.77407	+	17.7708i	−0.185203	+	0.569997i
$973$	3.84778	+	2.79557i	0.123354	+	0.0896220i
$974$	3.85203	+	2.79867i	0.123427	+	0.0896750i
$975$	−20.4080	+	62.8093i	−0.653578	+	2.01151i
$976$	−1.34638	−	4.14374i	−0.0430967	−	0.132638i
$977$	−23.7199	+	17.2335i	−0.758867	+	0.551349i	−0.898562	−	0.438846i	$-0.855388\pi$
$977$	−23.7199	+	17.2335i	−0.758867	+	0.551349i	0.139696	+	0.990194i	$0.455388\pi$
$978$	17.8429			0.570552
$979$	−30.8831	+	17.3726i	−0.987029	+	0.555231i
$980$	−4.59225			−0.146694
$981$	32.6230	−	23.7020i	1.04157	−	0.756746i
$982$	−2.12648	−	6.54462i	−0.0678586	−	0.208847i
$983$	4.06734	−	12.5180i	0.129728	−	0.399262i	−0.865005	−	0.501764i	$-0.832685\pi$
$983$	4.06734	−	12.5180i	0.129728	−	0.399262i	0.994733	+	0.102502i	$0.0326848\pi$
$984$	−6.50879	−	4.72891i	−0.207493	−	0.150752i
$985$	0.796585	+	0.578753i	0.0253813	+	0.0184406i
$986$	0.922922	−	2.84046i	0.0293918	−	0.0904587i
$987$	−1.58095	−	4.86568i	−0.0503223	−	0.154876i
$988$	−32.0007	+	23.2499i	−1.01808	+	0.739677i
$989$	−34.3194			−1.09129
$990$	4.11270	−	8.96593i	0.130710	−	0.284956i
$991$	48.8810			1.55275			0.776377	−	0.630268i	$-0.217055\pi$
$991$	48.8810			1.55275			0.776377	+	0.630268i	$0.217055\pi$
$992$	7.68108	−	5.58063i	0.243874	−	0.177185i
$993$	−13.6080	−	41.8811i	−0.431836	−	1.32906i
$994$	−0.960154	+	2.95505i	−0.0304542	+	0.0937285i
$995$	0.941158	+	0.683791i	0.0298367	+	0.0216776i
$996$	−18.8786	−	13.7161i	−0.598190	−	0.434611i
$997$	−15.0594	+	46.3481i	−0.476936	+	1.46786i	0.366392	+	0.930461i	$0.380593\pi$
$997$	−15.0594	+	46.3481i	−0.476936	+	1.46786i	−0.843328	+	0.537399i	$0.819407\pi$
$998$	5.56199	+	17.1180i	0.176062	+	0.541862i
$999$	−7.41068	+	5.38417i	−0.234463	+	0.170348i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	374.2.g.f.69.4	✓	16
11.2	odd	10		4114.2.a.bg.1.8		8
11.4	even	5	inner	374.2.g.f.103.4	yes	16
11.9	even	5		4114.2.a.bi.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
374.2.g.f.69.4	✓	16	1.1	even	1	trivial
374.2.g.f.103.4	yes	16	11.4	even	5	inner
4114.2.a.bg.1.8		8	11.2	odd	10
4114.2.a.bi.1.8		8	11.9	even	5

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	374.2.g.f.69.4

Level	$374$
Weight	$2$
Character	374.69
Analytic conductor	$2.986$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$