LMFDB - Embedded newform 304.2.k.b.77.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.5
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30576 + 0.543132i) q^{2} +(0.641204 + 0.641204i) q^{3} +(1.41002 - 1.41840i) q^{4} +(2.46245 - 2.46245i) q^{5} +(-1.18552 - 0.489000i) q^{6} +0.804840i q^{7} +(-1.07076 + 2.61791i) q^{8} -2.17771i q^{9} +O(q^{10})$	\(q+(-1.30576 + 0.543132i) q^{2} +(0.641204 + 0.641204i) q^{3} +(1.41002 - 1.41840i) q^{4} +(2.46245 - 2.46245i) q^{5} +(-1.18552 - 0.489000i) q^{6} +0.804840i q^{7} +(-1.07076 + 2.61791i) q^{8} -2.17771i q^{9} +(-1.87793 + 4.55280i) q^{10} +(2.23973 - 2.23973i) q^{11} +(1.81359 - 0.00537592i) q^{12} +(-3.45404 - 3.45404i) q^{13} +(-0.437134 - 1.05093i) q^{14} +3.15787 q^{15} +(-0.0237137 - 3.99993i) q^{16} -3.81469 q^{17} +(1.18279 + 2.84357i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-0.0206454 - 6.96483i) q^{20} +(-0.516067 + 0.516067i) q^{21} +(-1.70808 + 4.14102i) q^{22} +6.41707i q^{23} +(-2.36520 + 0.992040i) q^{24} -7.12733i q^{25} +(6.38614 + 2.63414i) q^{26} +(3.31997 - 3.31997i) q^{27} +(1.14158 + 1.13484i) q^{28} +(6.51038 + 6.51038i) q^{29} +(-4.12342 + 1.71514i) q^{30} +7.13377 q^{31} +(2.20345 + 5.21007i) q^{32} +2.87225 q^{33} +(4.98107 - 2.07188i) q^{34} +(1.98188 + 1.98188i) q^{35} +(-3.08887 - 3.07061i) q^{36} +(-1.33491 + 1.33491i) q^{37} +(1.30736 + 0.539259i) q^{38} -4.42949i q^{39} +(3.80978 + 9.08318i) q^{40} +5.62347i q^{41} +(0.393567 - 0.954151i) q^{42} +(-0.204323 + 0.204323i) q^{43} +(-0.0187781 - 6.33489i) q^{44} +(-5.36251 - 5.36251i) q^{45} +(-3.48531 - 8.37914i) q^{46} -6.17814 q^{47} +(2.54957 - 2.57998i) q^{48} +6.35223 q^{49} +(3.87108 + 9.30658i) q^{50} +(-2.44600 - 2.44600i) q^{51} +(-9.76944 + 0.0289589i) q^{52} +(-3.93648 + 3.93648i) q^{53} +(-2.53190 + 6.13827i) q^{54} -11.0305i q^{55} +(-2.10700 - 0.861792i) q^{56} -0.906800i q^{57} +(-12.0370 - 4.96499i) q^{58} +(0.172991 - 0.172991i) q^{59} +(4.45264 - 4.47912i) q^{60} +(3.14024 + 3.14024i) q^{61} +(-9.31499 + 3.87458i) q^{62} +1.75271 q^{63} +(-5.70693 - 5.60633i) q^{64} -17.0108 q^{65} +(-3.75047 + 1.56001i) q^{66} +(4.31703 + 4.31703i) q^{67} +(-5.37878 + 5.41076i) q^{68} +(-4.11465 + 4.11465i) q^{69} +(-3.66428 - 1.51143i) q^{70} +13.3115i q^{71} +(5.70106 + 2.33181i) q^{72} -11.8720i q^{73} +(1.01804 - 2.46811i) q^{74} +(4.57007 - 4.57007i) q^{75} +(-1.99999 + 0.00592845i) q^{76} +(1.80262 + 1.80262i) q^{77} +(2.40580 + 5.78384i) q^{78} -10.7952 q^{79} +(-9.90802 - 9.79124i) q^{80} -2.27558 q^{81} +(-3.05429 - 7.34290i) q^{82} +(11.0430 + 11.0430i) q^{83} +(0.00432675 + 1.45965i) q^{84} +(-9.39350 + 9.39350i) q^{85} +(0.155822 - 0.377771i) q^{86} +8.34897i q^{87} +(3.46520 + 8.26164i) q^{88} -15.4339i q^{89} +(9.91470 + 4.08960i) q^{90} +(2.77994 - 2.77994i) q^{91} +(9.10196 + 9.04816i) q^{92} +(4.57421 + 4.57421i) q^{93} +(8.06717 - 3.35555i) q^{94} -3.48243 q^{95} +(-1.92785 + 4.75358i) q^{96} -9.57400 q^{97} +(-8.29449 + 3.45010i) q^{98} +(-4.87749 - 4.87749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.30576	+	0.543132i	−0.923311	+	0.384052i
$2$	−1.30576	+	0.543132i	−0.923311	+	0.384052i
$3$	0.641204	+	0.641204i	0.370200	+	0.370200i	0.867550	−	0.497350i	$-0.165694\pi$
$3$	0.641204	+	0.641204i	0.370200	+	0.370200i	−0.497350	+	0.867550i	$0.665694\pi$
$4$	1.41002	−	1.41840i	0.705008	−	0.709200i
$5$	2.46245	−	2.46245i	1.10124	−	1.10124i	0.106980	−	0.994261i	$-0.465882\pi$
$5$	2.46245	−	2.46245i	1.10124	−	1.10124i	0.994261	−	0.106980i	$-0.0341182\pi$
$6$	−1.18552	−	0.489000i	−0.483985	−	0.199633i
$7$			0.804840i			0.304201i	0.988365	+	0.152100i	$0.0486037\pi$
$7$			0.804840i			0.304201i	−0.988365	+	0.152100i	$0.951396\pi$
$8$	−1.07076	+	2.61791i	−0.378572	+	0.925572i
$9$		−	2.17771i		−	0.725905i
$10$	−1.87793	+	4.55280i	−0.593854	+	1.43972i
$11$	2.23973	−	2.23973i	0.675305	−	0.675305i	−0.283629	−	0.958934i	$-0.591539\pi$
$11$	2.23973	−	2.23973i	0.675305	−	0.675305i	0.958934	+	0.283629i	$0.0915386\pi$
$12$	1.81359	−	0.00537592i	0.523539	−	0.00155189i
$13$	−3.45404	−	3.45404i	−0.957977	−	0.957977i	0.0411750	−	0.999152i	$-0.486890\pi$
$13$	−3.45404	−	3.45404i	−0.957977	−	0.957977i	−0.999152	+	0.0411750i	$0.986890\pi$
$14$	−0.437134	−	1.05093i	−0.116829	−	0.280872i
$15$	3.15787			0.815358
$16$	−0.0237137	−	3.99993i	−0.00592842	−	0.999982i
$17$	−3.81469			−0.925199			−0.462600	−	0.886567i	$-0.653083\pi$
$17$	−3.81469			−0.925199			−0.462600	+	0.886567i	$0.653083\pi$
$18$	1.18279	+	2.84357i	0.278785	+	0.670236i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	−0.0206454	−	6.96483i	−0.00461645	−	1.55738i
$21$	−0.516067	+	0.516067i	−0.112615	+	0.112615i
$22$	−1.70808	+	4.14102i	−0.364164	+	0.882869i
$23$			6.41707i			1.33805i	0.743240	+	0.669025i	$0.233288\pi$
$23$			6.41707i			1.33805i	−0.743240	+	0.669025i	$0.766712\pi$
$24$	−2.36520	+	0.992040i	−0.482793	+	0.202499i
$25$		−	7.12733i		−	1.42547i
$26$	6.38614	+	2.63414i	1.25242	+	0.516598i
$27$	3.31997	−	3.31997i	0.638929	−	0.638929i
$28$	1.14158	+	1.13484i	0.215739	+	0.214464i
$29$	6.51038	+	6.51038i	1.20895	+	1.20895i	0.971368	+	0.237579i	$0.0763538\pi$
$29$	6.51038	+	6.51038i	1.20895	+	1.20895i	0.237579	+	0.971368i	$0.423646\pi$
$30$	−4.12342	+	1.71514i	−0.752830	+	0.313140i
$31$	7.13377			1.28126			0.640632	−	0.767848i	$-0.278673\pi$
$31$	7.13377			1.28126			0.640632	+	0.767848i	$0.278673\pi$
$32$	2.20345	+	5.21007i	0.389519	+	0.921018i
$33$	2.87225			0.499995
$34$	4.98107	−	2.07188i	0.854247	−	0.355325i
$35$	1.98188	+	1.98188i	0.334999	+	0.334999i
$36$	−3.08887	−	3.07061i	−0.514811	−	0.511768i
$37$	−1.33491	+	1.33491i	−0.219459	+	0.219459i	−0.808270	−	0.588812i	$-0.799596\pi$
$37$	−1.33491	+	1.33491i	−0.219459	+	0.219459i	0.588812	+	0.808270i	$0.299596\pi$
$38$	1.30736	+	0.539259i	0.212082	+	0.0874794i
$39$		−	4.42949i		−	0.709285i
$40$	3.80978	+	9.08318i	0.602379	+	1.43618i
$41$			5.62347i			0.878239i	0.898429	+	0.439120i	$0.144710\pi$
$41$			5.62347i			0.878239i	−0.898429	+	0.439120i	$0.855290\pi$
$42$	0.393567	−	0.954151i	0.0607287	−	0.147229i
$43$	−0.204323	+	0.204323i	−0.0311589	+	0.0311589i	−0.722515	−	0.691356i	$-0.757014\pi$
$43$	−0.204323	+	0.204323i	−0.0311589	+	0.0311589i	0.691356	+	0.722515i	$0.257014\pi$
$44$	−0.0187781	−	6.33489i	−0.00283091	−	0.955021i
$45$	−5.36251	−	5.36251i	−0.799396	−	0.799396i
$46$	−3.48531	−	8.37914i	−0.513882	−	1.23544i
$47$	−6.17814			−0.901175			−0.450587	−	0.892732i	$-0.648785\pi$
$47$	−6.17814			−0.901175			−0.450587	+	0.892732i	$0.648785\pi$
$48$	2.54957	−	2.57998i	0.367998	−	0.372388i
$49$	6.35223			0.907462
$50$	3.87108	+	9.30658i	0.547453	+	1.31615i
$51$	−2.44600	−	2.44600i	−0.342508	−	0.342508i
$52$	−9.76944	+	0.0289589i	−1.35478	+	0.00401588i
$53$	−3.93648	+	3.93648i	−0.540717	+	0.540717i	−0.923739	−	0.383022i	$-0.874883\pi$
$53$	−3.93648	+	3.93648i	−0.540717	+	0.540717i	0.383022	+	0.923739i	$0.374883\pi$
$54$	−2.53190	+	6.13827i	−0.344548	+	0.835313i
$55$		−	11.0305i		−	1.48735i
$56$	−2.10700	−	0.861792i	−0.281560	−	0.115162i
$57$		−	0.906800i		−	0.120109i
$58$	−12.0370	−	4.96499i	−1.58053	−	0.651936i
$59$	0.172991	−	0.172991i	0.0225215	−	0.0225215i	−0.695756	−	0.718278i	$-0.744931\pi$
$59$	0.172991	−	0.172991i	0.0225215	−	0.0225215i	0.718278	+	0.695756i	$0.244931\pi$
$60$	4.45264	−	4.47912i	0.574834	−	0.578252i
$61$	3.14024	+	3.14024i	0.402066	+	0.402066i	0.878961	−	0.476895i	$-0.158238\pi$
$61$	3.14024	+	3.14024i	0.402066	+	0.402066i	−0.476895	+	0.878961i	$0.658238\pi$
$62$	−9.31499	+	3.87458i	−1.18301	+	0.492072i
$63$	1.75271			0.220821
$64$	−5.70693	−	5.60633i	−0.713367	−	0.700791i
$65$	−17.0108			−2.10993
$66$	−3.75047	+	1.56001i	−0.461651	+	0.192024i
$67$	4.31703	+	4.31703i	0.527410	+	0.527410i	0.919799	−	0.392390i	$-0.128351\pi$
$67$	4.31703	+	4.31703i	0.527410	+	0.527410i	−0.392390	+	0.919799i	$0.628351\pi$
$68$	−5.37878	+	5.41076i	−0.652273	+	0.656151i
$69$	−4.11465	+	4.11465i	−0.495346	+	0.495346i
$70$	−3.66428	−	1.51143i	−0.437965	−	0.180651i
$71$			13.3115i			1.57979i	0.613245	+	0.789893i	$0.289864\pi$
$71$			13.3115i			1.57979i	−0.613245	+	0.789893i	$0.710136\pi$
$72$	5.70106	+	2.33181i	0.671877	+	0.274807i
$73$		−	11.8720i		−	1.38951i	−0.719248	−	0.694753i	$-0.755514\pi$
$73$		−	11.8720i		−	1.38951i	0.719248	−	0.694753i	$-0.244486\pi$
$74$	1.01804	−	2.46811i	0.118345	−	0.286912i
$75$	4.57007	−	4.57007i	0.527707	−	0.527707i
$76$	−1.99999	+	0.00592845i	−0.229415	+	0.000680040i
$77$	1.80262	+	1.80262i	0.205428	+	0.205428i
$78$	2.40580	+	5.78384i	0.272403	+	0.654891i
$79$	−10.7952			−1.21456			−0.607278	−	0.794489i	$-0.707739\pi$
$79$	−10.7952			−1.21456			−0.607278	+	0.794489i	$0.707739\pi$
$80$	−9.90802	−	9.79124i	−1.10775	−	1.09469i
$81$	−2.27558			−0.252842
$82$	−3.05429	−	7.34290i	−0.337290	−	0.810888i
$83$	11.0430	+	11.0430i	1.21213	+	1.21213i	0.970326	+	0.241800i	$0.0777378\pi$
$83$	11.0430	+	11.0430i	1.21213	+	1.21213i	0.241800	+	0.970326i	$0.422262\pi$
$84$	0.00432675	+	1.45965i	0.000472087	+	0.159261i
$85$	−9.39350	+	9.39350i	−1.01887	+	1.01887i
$86$	0.155822	−	0.377771i	0.0168027	−	0.0407361i
$87$			8.34897i			0.895103i
$88$	3.46520	+	8.26164i	0.369392	+	0.880694i
$89$		−	15.4339i		−	1.63599i	−0.575228	−	0.817993i	$-0.695087\pi$
$89$		−	15.4339i		−	1.63599i	0.575228	−	0.817993i	$-0.304913\pi$
$90$	9.91470	+	4.08960i	1.04510	+	0.431082i
$91$	2.77994	−	2.77994i	0.291417	−	0.291417i
$92$	9.10196	+	9.04816i	0.948945	+	0.943336i
$93$	4.57421	+	4.57421i	0.474323	+	0.474323i
$94$	8.06717	−	3.35555i	0.832065	−	0.346098i
$95$	−3.48243			−0.357290
$96$	−1.92785	+	4.75358i	−0.196761	+	0.485160i
$97$	−9.57400			−0.972092			−0.486046	−	0.873933i	$-0.661561\pi$
$97$	−9.57400			−0.972092			−0.486046	+	0.873933i	$0.661561\pi$
$98$	−8.29449	+	3.45010i	−0.837870	+	0.348513i
$99$	−4.87749	−	4.87749i	−0.490207	−	0.490207i
$100$	−10.1094	−	10.0496i	−1.01094	−	1.00496i
$101$	−3.61068	+	3.61068i	−0.359276	+	0.359276i	−0.863546	−	0.504270i	$-0.831762\pi$
$101$	−3.61068	+	3.61068i	−0.359276	+	0.359276i	0.504270	+	0.863546i	$0.331762\pi$
$102$	4.52239	+	1.86539i	0.447783	+	0.184701i
$103$		−	5.49544i		−	0.541482i	−0.962652	−	0.270741i	$-0.912731\pi$
$103$		−	5.49544i		−	0.541482i	0.962652	−	0.270741i	$-0.0872687\pi$
$104$	12.7408	−	5.34391i	1.24934	−	0.524014i
$105$			2.54158i			0.248033i
$106$	3.00207	−	7.27812i	0.291587	−	0.706914i
$107$	0.358864	−	0.358864i	0.0346926	−	0.0346926i	−0.689548	−	0.724240i	$-0.742191\pi$
$107$	0.358864	−	0.358864i	0.0346926	−	0.0346926i	0.724240	+	0.689548i	$0.242191\pi$
$108$	−0.0278350	−	9.39026i	−0.00267842	−	0.903578i
$109$	−3.18381	−	3.18381i	−0.304954	−	0.304954i	0.537995	−	0.842948i	$-0.319182\pi$
$109$	−3.18381	−	3.18381i	−0.304954	−	0.304954i	−0.842948	+	0.537995i	$0.819182\pi$
$110$	5.99099	+	14.4031i	0.571219	+	1.37328i
$111$	−1.71191			−0.162487
$112$	3.21930	−	0.0190857i	0.304195	−	0.00180343i
$113$	4.42591			0.416355			0.208177	−	0.978091i	$-0.433247\pi$
$113$	4.42591			0.416355			0.208177	+	0.978091i	$0.433247\pi$
$114$	0.492512	+	1.18406i	0.0461280	+	0.110898i
$115$	15.8017	+	15.8017i	1.47352	+	1.47352i
$116$	18.4141	−	0.0545836i	1.70970	−	0.00506796i
$117$	−7.52190	+	7.52190i	−0.695400	+	0.695400i
$118$	−0.131928	+	0.319842i	−0.0121449	+	0.0294438i
$119$		−	3.07022i		−	0.281446i
$120$	−3.38133	+	8.26703i	−0.308672	+	0.754673i
$121$			0.967203i			0.0879276i
$122$	−5.80595	−	2.39483i	−0.525646	−	0.216818i
$123$	−3.60580	+	3.60580i	−0.325124	+	0.325124i
$124$	10.0587	−	10.1185i	0.903301	−	0.908672i
$125$	−5.23844	−	5.23844i	−0.468540	−	0.468540i
$126$	−2.28862	+	0.951953i	−0.203886	+	0.0848067i
$127$	−13.9037			−1.23375			−0.616875	−	0.787061i	$-0.711602\pi$
$127$	−13.9037			−1.23375			−0.616875	+	0.787061i	$0.711602\pi$
$128$	10.4969	+	4.22090i	0.927800	+	0.373078i
$129$	−0.262025			−0.0230701
$130$	22.2120	−	9.23910i	1.94812	−	0.810323i
$131$	2.56012	+	2.56012i	0.223679	+	0.223679i	0.810046	−	0.586367i	$-0.199442\pi$
$131$	2.56012	+	2.56012i	0.223679	+	0.223679i	−0.586367	+	0.810046i	$0.699442\pi$
$132$	4.04992	−	4.07400i	0.352500	−	0.354596i
$133$	0.569108	−	0.569108i	0.0493479	−	0.0493479i
$134$	−7.98173	−	3.29229i	−0.689516	−	0.284410i
$135$		−	16.3505i		−	1.40723i
$136$	4.08463	−	9.98654i	0.350254	−	0.856338i
$137$		−	17.7739i		−	1.51853i	−0.650784	−	0.759263i	$-0.725560\pi$
$137$		−	17.7739i		−	1.51853i	0.650784	−	0.759263i	$-0.274440\pi$
$138$	3.13795	−	7.60754i	0.267120	−	0.647597i
$139$	−4.92726	+	4.92726i	−0.417924	+	0.417924i	−0.884488	−	0.466563i	$-0.845492\pi$
$139$	−4.92726	+	4.92726i	−0.417924	+	0.417924i	0.466563	+	0.884488i	$0.345492\pi$
$140$	5.60557	−	0.0166162i	0.473757	−	0.00140433i
$141$	−3.96145	−	3.96145i	−0.333615	−	0.333615i
$142$	−7.22991	−	17.3816i	−0.606720	−	1.45863i
$143$	−15.4722			−1.29385
$144$	−8.71070	+	0.0516416i	−0.725892	+	0.00430347i
$145$	32.0630			2.66269
$146$	6.44804	+	15.5019i	0.533643	+	1.28295i
$147$	4.07308	+	4.07308i	0.335942	+	0.335942i
$148$	0.0111920	+	3.77569i	0.000919980	+	0.310360i
$149$	−4.92764	+	4.92764i	−0.403688	+	0.403688i	−0.879530	−	0.475843i	$-0.842143\pi$
$149$	−4.92764	+	4.92764i	−0.403688	+	0.403688i	0.475843	+	0.879530i	$0.342143\pi$
$150$	−3.48526	+	8.44957i	−0.284571	+	0.689905i
$151$			16.4283i			1.33692i	0.743749	+	0.668459i	$0.233046\pi$
$151$			16.4283i			1.33692i	−0.743749	+	0.668459i	$0.766954\pi$
$152$	2.60829	−	1.09400i	0.211560	−	0.0887351i
$153$			8.30731i			0.671606i
$154$	−3.33286	−	1.37473i	−0.268569	−	0.110779i
$155$	17.5666	−	17.5666i	1.41098	−	1.41098i
$156$	−6.28278	−	6.24564i	−0.503025	−	0.500052i
$157$	−0.415749	−	0.415749i	−0.0331804	−	0.0331804i	0.690322	−	0.723502i	$-0.257469\pi$
$157$	−0.415749	−	0.415749i	−0.0331804	−	0.0331804i	−0.723502	+	0.690322i	$0.757469\pi$
$158$	14.0960	−	5.86323i	1.12141	−	0.466453i
$159$	−5.04818			−0.400346
$160$	18.2554	+	7.40363i	1.44322	+	0.585309i
$161$	−5.16471			−0.407036
$162$	2.97136	−	1.23594i	0.233452	−	0.0971045i
$163$	8.76975	+	8.76975i	0.686900	+	0.686900i	0.961545	−	0.274646i	$-0.0885606\pi$
$163$	8.76975	+	8.76975i	0.686900	+	0.686900i	−0.274646	+	0.961545i	$0.588561\pi$
$164$	7.97633	+	7.92919i	0.622847	+	0.619165i
$165$	7.07278	−	7.07278i	0.550615	−	0.550615i
$166$	−20.4173	−	8.42169i	−1.58469	−	0.653650i
$167$		−	0.675485i		−	0.0522706i	−0.999658	−	0.0261353i	$-0.991680\pi$
$167$		−	0.675485i		−	0.0522706i	0.999658	−	0.0261353i	$-0.00832007\pi$
$168$	−0.798433	−	1.90360i	−0.0616004	−	0.146866i
$169$			10.8607i			0.835440i
$170$	7.16374	−	17.3676i	0.549434	−	1.33203i
$171$	−1.53988	+	1.53988i	−0.117757	+	0.117757i
$172$	0.00171306	+	0.577910i	0.000130620	+	0.0440652i
$173$	12.9792	+	12.9792i	0.986790	+	0.986790i	0.999914	−	0.0131242i	$-0.00417769\pi$
$173$	12.9792	+	12.9792i	0.986790	+	0.986790i	−0.0131242	+	0.999914i	$0.504178\pi$
$174$	−4.53459	−	10.9017i	−0.343767	−	0.826459i
$175$	5.73636			0.433628
$176$	−9.01188	−	8.90566i	−0.679296	−	0.671289i
$177$	0.221845			0.0166749
$178$	8.38263	+	20.1529i	0.628304	+	1.51053i
$179$	−1.27856	−	1.27856i	−0.0955642	−	0.0955642i	0.657708	−	0.753273i	$-0.271526\pi$
$179$	−1.27856	−	1.27856i	−0.0955642	−	0.0955642i	−0.753273	+	0.657708i	$0.771526\pi$
$180$	−15.1674	+	0.0449598i	−1.13051	+	0.00335111i
$181$	6.45799	−	6.45799i	0.480019	−	0.480019i	−0.425119	−	0.905138i	$-0.639768\pi$
$181$	6.45799	−	6.45799i	0.480019	−	0.480019i	0.905138	+	0.425119i	$0.139768\pi$
$182$	−2.12006	+	5.13982i	−0.157149	+	0.380988i
$183$			4.02707i			0.297689i
$184$	−16.7993	−	6.87116i	−1.23846	−	0.506548i
$185$			6.57432i			0.483354i
$186$	−8.45721	−	3.48842i	−0.620113	−	0.255783i
$187$	−8.54389	+	8.54389i	−0.624791	+	0.624791i
$188$	−8.71128	+	8.76307i	−0.635335	+	0.639113i
$189$	2.67205	+	2.67205i	0.194363	+	0.194363i
$190$	4.54722	−	1.89142i	0.329890	−	0.137218i
$191$	10.7065			0.774697			0.387349	−	0.921933i	$-0.373391\pi$
$191$	10.7065			0.774697			0.387349	+	0.921933i	$0.373391\pi$
$192$	−0.0645102	−	7.25411i	−0.00465563	−	0.523521i
$193$	0.327108			0.0235457			0.0117729	−	0.999931i	$-0.496252\pi$
$193$	0.327108			0.0235457			0.0117729	+	0.999931i	$0.496252\pi$
$194$	12.5013	−	5.19995i	0.897544	−	0.373334i
$195$	−10.9074	−	10.9074i	−0.781094	−	0.781094i
$196$	8.95675	−	9.01000i	0.639768	−	0.643572i
$197$	14.3829	−	14.3829i	1.02474	−	1.02474i	0.0250533	−	0.999686i	$-0.492024\pi$
$197$	14.3829	−	14.3829i	1.02474	−	1.02474i	0.999686	−	0.0250533i	$-0.00797554\pi$
$198$	9.01796	+	3.71971i	0.640878	+	0.264348i
$199$		−	23.8399i		−	1.68997i	−0.534791	−	0.844984i	$-0.679610\pi$
$199$		−	23.8399i		−	1.68997i	0.534791	−	0.844984i	$-0.320390\pi$
$200$	18.6587	+	7.63168i	1.31937	+	0.539641i
$201$			5.53620i			0.390494i
$202$	2.75360	−	6.67575i	0.193743	−	0.469704i
$203$	−5.23981	+	5.23981i	−0.367763	+	0.367763i
$204$	−6.91830	+	0.0205075i	−0.484378	+	0.00143581i
$205$	13.8475	+	13.8475i	0.967153	+	0.967153i
$206$	2.98475	+	7.17572i	0.207957	+	0.499956i
$207$	13.9745			0.971297
$208$	−13.7340	+	13.8978i	−0.952281	+	0.963639i
$209$	−3.16746			−0.219098
$210$	−1.38041	−	3.31869i	−0.0952575	−	0.229011i
$211$	−14.6021	−	14.6021i	−1.00525	−	1.00525i	−0.999986	−	0.00526137i	$-0.998325\pi$
$211$	−14.6021	−	14.6021i	−1.00525	−	1.00525i	−0.00526137	−	0.999986i	$-0.501675\pi$
$212$	0.0330038	+	11.1340i	0.00226671	+	0.764686i
$213$	−8.53540	+	8.53540i	−0.584836	+	0.584836i
$214$	−0.273679	+	0.663500i	−0.0187083	+	0.0453559i
$215$			1.00627i			0.0686270i
$216$	5.13650	+	12.2463i	0.349494	+	0.833255i
$217$			5.74154i			0.389761i
$218$	5.88652	+	2.42806i	0.398686	+	0.164449i
$219$	7.61235	−	7.61235i	0.514395	−	0.514395i
$220$	−15.6456	−	15.5531i	−1.05483	−	1.04859i
$221$	13.1761	+	13.1761i	0.886320	+	0.886320i
$222$	2.23534	−	0.929791i	0.150026	−	0.0624035i
$223$	−13.4186			−0.898575			−0.449287	−	0.893387i	$-0.648322\pi$
$223$	−13.4186			−0.898575			−0.449287	+	0.893387i	$0.648322\pi$
$224$	−4.19327	+	1.77343i	−0.280175	+	0.118492i
$225$	−15.5213			−1.03475
$226$	−5.77917	+	2.40385i	−0.384425	+	0.159902i
$227$	−3.28097	−	3.28097i	−0.217766	−	0.217766i	0.589790	−	0.807556i	$-0.299210\pi$
$227$	−3.28097	−	3.28097i	−0.217766	−	0.217766i	−0.807556	+	0.589790i	$0.799210\pi$
$228$	−1.28620	−	1.27860i	−0.0851810	−	0.0846775i
$229$	−5.21272	+	5.21272i	−0.344466	+	0.344466i	−0.858043	−	0.513577i	$-0.828320\pi$
$229$	−5.21272	+	5.21272i	−0.344466	+	0.344466i	0.513577	+	0.858043i	$0.328320\pi$
$230$	−29.2156	−	12.0508i	−1.92642	−	0.794607i
$231$			2.31170i			0.152099i
$232$	−24.0147	+	10.0725i	−1.57664	+	0.661294i
$233$		−	9.52523i		−	0.624019i	−0.950079	−	0.312009i	$-0.898998\pi$
$233$		−	9.52523i		−	0.624019i	0.950079	−	0.312009i	$-0.101002\pi$
$234$	5.73641	−	13.9072i	0.375001	−	0.909140i
$235$	−15.2134	+	15.2134i	−0.992411	+	0.992411i
$236$	−0.00145037	−	0.489291i	−9.44113e−5	−	0.0318501i
$237$	−6.92194	−	6.92194i	−0.449628	−	0.449628i
$238$	1.66753	+	4.00897i	0.108090	+	0.259863i
$239$	−27.5037			−1.77907			−0.889533	−	0.456871i	$-0.848970\pi$
$239$	−27.5037			−1.77907			−0.889533	+	0.456871i	$0.848970\pi$
$240$	−0.0748847	−	12.6313i	−0.00483379	−	0.815344i
$241$	−2.85057			−0.183622			−0.0918108	−	0.995776i	$-0.529266\pi$
$241$	−2.85057			−0.183622			−0.0918108	+	0.995776i	$0.529266\pi$
$242$	−0.525319	−	1.26293i	−0.0337688	−	0.0811845i
$243$	−11.4190	−	11.4190i	−0.732531	−	0.732531i
$244$	8.88189	−	0.0263280i	0.568605	−	0.00168548i
$245$	15.6421	−	15.6421i	0.999335	−	0.999335i
$246$	2.74988	−	6.66673i	0.175326	−	0.425055i
$247$			4.88474i			0.310809i
$248$	−7.63858	+	18.6756i	−0.485050	+	1.18590i
$249$			14.1616i			0.897457i
$250$	9.68531	+	3.99498i	0.612553	+	0.252665i
$251$	−19.9618	+	19.9618i	−1.25997	+	1.25997i	−0.308871	+	0.951104i	$0.599951\pi$
$251$	−19.9618	+	19.9618i	−1.25997	+	1.25997i	−0.951104	+	0.308871i	$0.900049\pi$
$252$	2.47135	−	2.48604i	0.155680	−	0.156606i
$253$	14.3725	+	14.3725i	0.903592	+	0.903592i
$254$	18.1548	−	7.55152i	1.13914	−	0.473824i
$255$	−12.0463			−0.754369
$256$	−15.9989	+	0.189706i	−0.999930	+	0.0118566i
$257$	−1.20771			−0.0753346			−0.0376673	−	0.999290i	$-0.511993\pi$
$257$	−1.20771			−0.0753346			−0.0376673	+	0.999290i	$0.511993\pi$
$258$	0.342142	−	0.142314i	0.0213008	−	0.00886011i
$259$	−1.07439	−	1.07439i	−0.0667595	−	0.0667595i
$260$	−23.9855	+	24.1281i	−1.48752	+	1.49636i
$261$	14.1777	−	14.1777i	0.877580	−	0.877580i
$262$	−4.73339	−	1.95242i	−0.292430	−	0.120621i
$263$			21.0147i			1.29582i	0.761715	+	0.647912i	$0.224358\pi$
$263$			21.0147i			1.29582i	−0.761715	+	0.647912i	$0.775642\pi$
$264$	−3.07550	+	7.51931i	−0.189284	+	0.462781i
$265$			19.3868i			1.19092i
$266$	−0.434017	+	1.05222i	−0.0266113	+	0.0645156i
$267$	9.89626	−	9.89626i	0.605642	−	0.605642i
$268$	12.2104	−	0.0361944i	0.745867	−	0.00221093i
$269$	−20.2510	−	20.2510i	−1.23473	−	1.23473i	−0.962128	−	0.272598i	$-0.912117\pi$
$269$	−20.2510	−	20.2510i	−1.23473	−	1.23473i	−0.272598	−	0.962128i	$-0.587883\pi$
$270$	8.88050	+	21.3499i	0.540450	+	1.29931i
$271$	11.3960			0.692256			0.346128	−	0.938187i	$-0.387496\pi$
$271$	11.3960			0.692256			0.346128	+	0.938187i	$0.387496\pi$
$272$	0.0904605	+	15.2585i	0.00548497	+	0.925183i
$273$	3.56503			0.215765
$274$	9.65357	+	23.2084i	0.583194	+	1.40207i
$275$	−15.9633	−	15.9633i	−0.962623	−	0.962623i
$276$	0.0344976	+	11.6379i	0.00207651	+	0.700522i
$277$	15.8820	−	15.8820i	0.954257	−	0.954257i	−0.0447420	−	0.998999i	$-0.514247\pi$
$277$	15.8820	−	15.8820i	0.954257	−	0.954257i	0.998999	+	0.0447420i	$0.0142466\pi$
$278$	3.75766	−	9.10996i	0.225370	−	0.546379i
$279$		−	15.5353i		−	0.930075i
$280$	−7.31051	+	3.06626i	−0.436886	+	0.183244i
$281$		−	23.9384i		−	1.42804i	−0.700124	−	0.714021i	$-0.746872\pi$
$281$		−	23.9384i		−	1.42804i	0.700124	−	0.714021i	$-0.253128\pi$
$282$	7.32430	+	3.02111i	0.436156	+	0.179905i
$283$	10.4536	−	10.4536i	0.621404	−	0.621404i	−0.324487	−	0.945890i	$-0.605191\pi$
$283$	10.4536	−	10.4536i	0.621404	−	0.621404i	0.945890	+	0.324487i	$0.105191\pi$
$284$	18.8810	+	18.7694i	1.12038	+	1.11376i
$285$	−2.23295	−	2.23295i	−0.132269	−	0.132269i
$286$	20.2030	−	8.40346i	1.19463	−	0.496907i
$287$	−4.52600			−0.267161
$288$	11.3460	−	4.79849i	0.668571	−	0.282754i
$289$	−2.44811			−0.144006
$290$	−41.8665	+	17.4144i	−2.45849	+	1.02261i
$291$	−6.13889	−	6.13889i	−0.359868	−	0.359868i
$292$	−16.8392	−	16.7396i	−0.985438	−	0.979613i
$293$	−11.2054	+	11.2054i	−0.654624	+	0.654624i	−0.954103	−	0.299479i	$-0.903187\pi$
$293$	−11.2054	+	11.2054i	−0.654624	+	0.654624i	0.299479	+	0.954103i	$0.403187\pi$
$294$	−7.53068	−	3.10624i	−0.439198	−	0.181160i
$295$		−	0.851964i		−	0.0496033i
$296$	−2.06531	−	4.92407i	−0.120044	−	0.286206i
$297$		−	14.8717i		−	0.862943i
$298$	3.75795	−	9.11067i	0.217692	−	0.527767i
$299$	22.1648	−	22.1648i	1.28182	−	1.28182i
$300$	−0.0383159	−	12.9261i	−0.00221217	−	0.746287i
$301$	−0.164447	−	0.164447i	−0.00947857	−	0.00947857i
$302$	−8.92275	−	21.4514i	−0.513446	−	1.23439i
$303$	−4.63036			−0.266007
$304$	−2.81161	+	2.84515i	−0.161257	+	0.163180i
$305$	15.4654			0.885543
$306$	−4.51197	−	10.8474i	−0.257932	−	0.620102i
$307$	−12.6311	−	12.6311i	−0.720894	−	0.720894i	0.247893	−	0.968787i	$-0.420262\pi$
$307$	−12.6311	−	12.6311i	−0.720894	−	0.720894i	−0.968787	+	0.247893i	$0.920262\pi$
$308$	5.09857	−	0.0151134i	0.290518	−	0.000861164i
$309$	3.52370	−	3.52370i	0.200456	−	0.200456i
$310$	−13.3967	+	32.4787i	−0.760884	+	1.84466i
$311$		−	5.24139i		−	0.297212i	−0.988896	−	0.148606i	$-0.952521\pi$
$311$		−	5.24139i		−	0.297212i	0.988896	−	0.148606i	$-0.0474786\pi$
$312$	11.5960	+	4.74293i	0.656495	+	0.268515i
$313$			19.9685i			1.12868i	0.825541	+	0.564342i	$0.190870\pi$
$313$			19.9685i			1.12868i	−0.825541	+	0.564342i	$0.809130\pi$
$314$	0.768675	+	0.317062i	0.0433788	+	0.0178928i
$315$	4.31596	−	4.31596i	0.243177	−	0.243177i
$316$	−15.2214	+	15.3119i	−0.856272	+	0.861363i
$317$	13.8554	+	13.8554i	0.778197	+	0.778197i	0.979524	−	0.201327i	$-0.0645255\pi$
$317$	13.8554	+	13.8554i	0.778197	+	0.778197i	−0.201327	+	0.979524i	$0.564526\pi$
$318$	6.59170	−	2.74183i	0.369644	−	0.153754i
$319$	29.1630			1.63281
$320$	−27.8583	+	0.247742i	−1.55733	+	0.0138492i
$321$	0.460210			0.0256864
$322$	6.74387	−	2.80512i	0.375821	−	0.156323i
$323$	2.69740	+	2.69740i	0.150087	+	0.150087i
$324$	−3.20860	+	3.22768i	−0.178256	+	0.179315i
$325$	−24.6180	+	24.6180i	−1.36556	+	1.36556i
$326$	−16.2143	−	6.68805i	−0.898028	−	0.370417i
$327$		−	4.08295i		−	0.225788i
$328$	−14.7218	−	6.02141i	−0.812874	−	0.332477i
$329$		−	4.97241i		−	0.274138i
$330$	−5.39390	+	13.0768i	−0.296924	+	0.719854i
$331$	1.84476	−	1.84476i	0.101397	−	0.101397i	−0.654588	−	0.755986i	$-0.727158\pi$
$331$	1.84476	−	1.84476i	0.101397	−	0.101397i	0.755986	+	0.654588i	$0.227158\pi$
$332$	31.2342	−	0.0925855i	1.71420	−	0.00508129i
$333$	2.90706	+	2.90706i	0.159306	+	0.159306i
$334$	0.366877	+	0.882020i	0.0200746	+	0.0482620i
$335$	21.2610			1.16161
$336$	2.07647	+	2.05199i	0.113281	+	0.111945i
$337$	6.12355			0.333571			0.166786	−	0.985993i	$-0.446661\pi$
$337$	6.12355			0.333571			0.166786	+	0.985993i	$0.446661\pi$
$338$	−5.89880	−	14.1815i	−0.320853	−	0.771371i
$339$	2.83791	+	2.83791i	0.154134	+	0.154134i
$340$	0.0787559	+	26.5687i	0.00427114	+	1.44089i
$341$	15.9777	−	15.9777i	0.865243	−	0.865243i
$342$	1.17435	−	2.84706i	0.0635017	−	0.153952i
$343$			10.7464i			0.580251i
$344$	−0.316118	−	0.753681i	−0.0170439	−	0.0406357i
$345$			20.2643i			1.09099i
$346$	−23.9971	−	9.89829i	−1.29009	−	0.532135i
$347$	5.41366	−	5.41366i	0.290621	−	0.290621i	−0.546705	−	0.837325i	$-0.684118\pi$
$347$	5.41366	−	5.41366i	0.290621	−	0.290621i	0.837325	+	0.546705i	$0.184118\pi$
$348$	11.8422	+	11.7722i	0.634807	+	0.631055i
$349$	4.17862	+	4.17862i	0.223676	+	0.223676i	0.810045	−	0.586368i	$-0.199443\pi$
$349$	4.17862	+	4.17862i	0.223676	+	0.223676i	−0.586368	+	0.810045i	$0.699443\pi$
$350$	−7.49030	+	3.11560i	−0.400373	+	0.166536i
$351$	−22.9346			−1.22416
$352$	16.6043	+	6.73400i	0.885012	+	0.358924i
$353$	15.2615			0.812287			0.406143	−	0.913809i	$-0.366873\pi$
$353$	15.2615			0.812287			0.406143	+	0.913809i	$0.366873\pi$
$354$	−0.289677	+	0.120491i	−0.0153961	+	0.00640404i
$355$	32.7789	+	32.7789i	1.73973	+	1.73973i
$356$	−21.8914	−	21.7620i	−1.16024	−	1.15338i
$357$	1.96864	−	1.96864i	0.104191	−	0.104191i
$358$	2.36392	+	0.975067i	0.124937	+	0.0515339i
$359$			19.1684i			1.01167i	0.862630	+	0.505835i	$0.168816\pi$
$359$			19.1684i			1.01167i	−0.862630	+	0.505835i	$0.831184\pi$
$360$	19.7806	−	8.29661i	1.04253	−	0.437270i
$361$			1.00000i			0.0526316i
$362$	−4.92504	+	11.9401i	−0.258855	+	0.627559i
$363$	−0.620175	+	0.620175i	−0.0325507	+	0.0325507i
$364$	−0.0233073	−	7.86284i	−0.00122163	−	0.412125i
$365$	−29.2341	−	29.2341i	−1.53018	−	1.53018i
$366$	−2.18723	−	5.25838i	−0.114328	−	0.274860i
$367$	17.7871			0.928481			0.464240	−	0.885709i	$-0.346327\pi$
$367$	17.7871			0.928481			0.464240	+	0.885709i	$0.346327\pi$
$368$	25.6678	−	0.152172i	1.33803	−	0.00793253i
$369$	12.2463			0.637518
$370$	−3.57073	−	8.58448i	−0.185633	−	0.446286i
$371$	−3.16824	−	3.16824i	−0.164487	−	0.164487i
$372$	12.9378	−	0.0383506i	0.670791	−	0.00198838i
$373$	1.50380	−	1.50380i	0.0778636	−	0.0778636i	−0.667102	−	0.744966i	$-0.732466\pi$
$373$	1.50380	−	1.50380i	0.0778636	−	0.0778636i	0.744966	+	0.667102i	$0.232466\pi$
$374$	6.51581	−	15.7967i	0.336924	−	0.816829i
$375$		−	6.71782i		−	0.346907i
$376$	6.61533	−	16.1738i	0.341159	−	0.834102i
$377$		−	44.9742i		−	2.31629i
$378$	−4.94032	−	2.03778i	−0.254103	−	0.104812i
$379$	−18.9214	+	18.9214i	−0.971925	+	0.971925i	−0.999617	−	0.0276912i	$-0.991184\pi$
$379$	−18.9214	+	18.9214i	−0.971925	+	0.971925i	0.0276912	+	0.999617i	$0.491184\pi$
$380$	−4.91028	+	4.93948i	−0.251892	+	0.253390i
$381$	−8.91509	−	8.91509i	−0.456734	−	0.456734i
$382$	−13.9802	+	5.81506i	−0.715287	+	0.297524i
$383$	6.27197			0.320483			0.160241	−	0.987078i	$-0.448773\pi$
$383$	6.27197			0.320483			0.160241	+	0.987078i	$0.448773\pi$
$384$	4.02418	+	9.43709i	0.205358	+	0.481584i
$385$	8.87775			0.452452
$386$	−0.427124	+	0.177663i	−0.0217401	+	0.00904280i
$387$	0.444957	+	0.444957i	0.0226184	+	0.0226184i
$388$	−13.4995	+	13.5798i	−0.685333	+	0.689408i
$389$	12.0536	−	12.0536i	0.611140	−	0.611140i	−0.332103	−	0.943243i	$-0.607758\pi$
$389$	12.0536	−	12.0536i	0.611140	−	0.611140i	0.943243	+	0.332103i	$0.107758\pi$
$390$	20.1666	+	8.31827i	1.02117	+	0.421212i
$391$		−	24.4791i		−	1.23796i
$392$	−6.80173	+	16.6296i	−0.343539	+	0.839921i
$393$			3.28312i			0.165612i
$394$	−10.9688	+	26.5924i	−0.552600	+	1.33971i
$395$	−26.5827	+	26.5827i	−1.33752	+	1.33752i
$396$	−13.7956	+	0.0408934i	−0.693254	+	0.00205497i
$397$	4.51253	+	4.51253i	0.226477	+	0.226477i	0.811219	−	0.584742i	$-0.198804\pi$
$397$	4.51253	+	4.51253i	0.226477	+	0.226477i	−0.584742	+	0.811219i	$0.698804\pi$
$398$	12.9482	+	31.1292i	0.649036	+	1.56037i
$399$	0.729829			0.0365371
$400$	−28.5088	+	0.169015i	−1.42544	+	0.00845076i
$401$	6.01435			0.300342			0.150171	−	0.988660i	$-0.452017\pi$
$401$	6.01435			0.300342			0.150171	+	0.988660i	$0.452017\pi$
$402$	−3.00689	−	7.22895i	−0.149970	−	0.360547i
$403$	−24.6403	−	24.6403i	−1.22742	−	1.22742i
$404$	0.0302722	+	10.2125i	0.00150610	+	0.508090i
$405$	−5.60350	+	5.60350i	−0.278440	+	0.278440i
$406$	3.99602	−	9.68784i	0.198319	−	0.480800i
$407$			5.97970i			0.296403i
$408$	9.02250	−	3.78433i	0.446680	−	0.187352i
$409$			21.5864i			1.06738i	0.845680	+	0.533690i	$0.179195\pi$
$409$			21.5864i			1.06738i	−0.845680	+	0.533690i	$0.820805\pi$
$410$	−25.6026	−	10.5605i	−1.26442	−	0.521546i
$411$	11.3967	−	11.3967i	0.562158	−	0.562158i
$412$	−7.79473	−	7.74866i	−0.384019	−	0.381749i
$413$	0.139230	+	0.139230i	0.00685107	+	0.00685107i
$414$	−18.2474	+	7.59002i	−0.896810	+	0.373029i
$415$	54.3857			2.66969
$416$	10.3849	−	25.6066i	0.509164	−	1.25546i
$417$	−6.31876			−0.309431
$418$	4.13594	−	1.72035i	0.202295	−	0.0841450i
$419$	−7.73445	−	7.73445i	−0.377853	−	0.377853i	0.492474	−	0.870327i	$-0.336093\pi$
$419$	−7.73445	−	7.73445i	−0.377853	−	0.377853i	−0.870327	+	0.492474i	$0.836093\pi$
$420$	3.60497	+	3.58366i	0.175905	+	0.174865i
$421$	−8.12312	+	8.12312i	−0.395897	+	0.395897i	−0.876783	−	0.480886i	$-0.840315\pi$
$421$	−8.12312	+	8.12312i	−0.395897	+	0.395897i	0.480886	+	0.876783i	$0.340315\pi$
$422$	26.9976	+	11.1359i	1.31422	+	0.542089i
$423$			13.4542i			0.654167i
$424$	−6.09033	−	14.5204i	−0.295772	−	0.705173i
$425$			27.1886i			1.31884i
$426$	6.50933	−	15.7810i	0.315378	−	0.764593i
$427$	−2.52739	+	2.52739i	−0.122309	+	0.122309i
$428$	−0.00300874	−	1.01501i	−0.000145433	−	0.0490626i
$429$	−9.92086	−	9.92086i	−0.478984	−	0.478984i
$430$	−0.546537	−	1.31395i	−0.0263564	−	0.0633641i
$431$	12.6801			0.610777			0.305388	−	0.952228i	$-0.401214\pi$
$431$	12.6801			0.610777			0.305388	+	0.952228i	$0.401214\pi$
$432$	−13.3584	−	13.2009i	−0.642706	−	0.635130i
$433$	4.08579			0.196351			0.0981753	−	0.995169i	$-0.468699\pi$
$433$	4.08579			0.196351			0.0981753	+	0.995169i	$0.468699\pi$
$434$	−3.11842	−	7.49707i	−0.149689	−	0.359871i
$435$	20.5589	+	20.5589i	0.985725	+	0.985725i
$436$	−9.00514	+	0.0266934i	−0.431268	+	0.00127838i
$437$	4.53755	−	4.53755i	0.217061	−	0.217061i
$438$	−5.80539	+	14.0744i	−0.277392	+	0.672501i
$439$		−	31.3499i		−	1.49625i	−0.663557	−	0.748126i	$-0.730954\pi$
$439$		−	31.3499i		−	1.49625i	0.663557	−	0.748126i	$-0.269046\pi$
$440$	28.8768	+	11.8110i	1.37665	+	0.563068i
$441$		−	13.8333i		−	0.658731i
$442$	−24.3612	−	10.0484i	−1.15874	−	0.477956i
$443$	−6.31119	+	6.31119i	−0.299854	+	0.299854i	−0.840956	−	0.541103i	$-0.818007\pi$
$443$	−6.31119	+	6.31119i	−0.299854	+	0.299854i	0.541103	+	0.840956i	$0.318007\pi$
$444$	−2.41381	+	2.42817i	−0.114555	+	0.115236i
$445$	−38.0051	−	38.0051i	−1.80162	−	1.80162i
$446$	17.5214	−	7.28806i	0.829664	−	0.345100i
$447$	−6.31925			−0.298890
$448$	4.51219	−	4.59317i	0.213181	−	0.217007i
$449$	−21.6350			−1.02102			−0.510510	−	0.859872i	$-0.670543\pi$
$449$	−21.6350			−1.02102			−0.510510	+	0.859872i	$0.670543\pi$
$450$	20.2671	−	8.43010i	0.955398	−	0.397399i
$451$	12.5951	+	12.5951i	0.593079	+	0.593079i
$452$	6.24060	−	6.27771i	0.293533	−	0.295279i
$453$	−10.5339	+	10.5339i	−0.494927	+	0.494927i
$454$	6.06616	+	2.50216i	0.284699	+	0.117432i
$455$		−	13.6910i		−	0.641842i
$456$	2.37392	+	0.970968i	0.111169	+	0.0454697i
$457$		−	13.6711i		−	0.639506i	−0.947501	−	0.319753i	$-0.896400\pi$
$457$		−	13.6711i		−	0.639506i	0.947501	−	0.319753i	$-0.103600\pi$
$458$	3.97536	−	9.63775i	0.185756	−	0.450342i
$459$	−12.6647	+	12.6647i	−0.591137	+	0.591137i
$460$	44.6938	−	0.132483i	2.08386	−	0.00617705i
$461$	17.0209	+	17.0209i	0.792744	+	0.792744i	0.981939	−	0.189195i	$-0.0605880\pi$
$461$	17.0209	+	17.0209i	0.792744	+	0.792744i	−0.189195	+	0.981939i	$0.560588\pi$
$462$	−1.25556	−	3.01853i	−0.0584139	−	0.140435i
$463$	13.4679			0.625906			0.312953	−	0.949769i	$-0.398682\pi$
$463$	13.4679			0.625906			0.312953	+	0.949769i	$0.398682\pi$
$464$	25.8867	−	26.1954i	1.20176	−	1.21609i
$465$	22.5275			1.04469
$466$	5.17346	+	12.4377i	0.239656	+	0.576164i
$467$	−14.8235	−	14.8235i	−0.685951	−	0.685951i	0.275383	−	0.961335i	$-0.411195\pi$
$467$	−14.8235	−	14.8235i	−0.685951	−	0.685951i	−0.961335	+	0.275383i	$0.911195\pi$
$468$	0.0630643	+	21.2751i	0.00291515	+	0.983440i
$469$	−3.47452	+	3.47452i	−0.160438	+	0.160438i
$470$	11.6021	−	28.1279i	0.535167	−	1.29744i
$471$		−	0.533160i		−	0.0245667i
$472$	0.267643	+	0.638108i	0.0123193	+	0.0293713i
$473$			0.915257i			0.0420835i
$474$	12.7979	+	5.27886i	0.587828	+	0.242466i
$475$	−5.03978	+	5.03978i	−0.231241	+	0.231241i
$476$	−4.35479	−	4.32905i	−0.199602	−	0.198422i
$477$	8.57253	+	8.57253i	0.392509	+	0.392509i
$478$	35.9132	−	14.9381i	1.64263	−	0.683254i
$479$	−27.1174			−1.23903			−0.619514	−	0.784986i	$-0.712670\pi$
$479$	−27.1174			−1.23903			−0.619514	+	0.784986i	$0.712670\pi$
$480$	6.95822	+	16.4527i	0.317598	+	0.750960i
$481$	9.22168			0.420473
$482$	3.72217	−	1.54824i	0.169540	−	0.0705203i
$483$	−3.31163	−	3.31163i	−0.150685	−	0.150685i
$484$	1.37188	+	1.36377i	0.0623582	+	0.0619896i
$485$	−23.5755	+	23.5755i	−1.07051	+	1.07051i
$486$	21.1125	+	8.70847i	0.957685	+	0.395024i
$487$		−	7.14404i		−	0.323727i	−0.986813	−	0.161864i	$-0.948250\pi$
$487$		−	7.14404i		−	0.323727i	0.986813	−	0.161864i	$-0.0517505\pi$
$488$	−11.5833	+	4.85842i	−0.524352	+	0.219930i
$489$			11.2464i			0.508580i
$490$	−11.9291	+	28.9205i	−0.538900	+	1.30649i
$491$	−22.5130	+	22.5130i	−1.01600	+	1.01600i	−0.0161273	+	0.999870i	$0.505134\pi$
$491$	−22.5130	+	22.5130i	−1.01600	+	1.01600i	−0.999870	+	0.0161273i	$0.994866\pi$
$492$	0.0302313	+	10.1987i	0.00136293	+	0.459792i
$493$	−24.8351	−	24.8351i	−1.11852	−	1.11852i
$494$	−2.65306	−	6.37830i	−0.119367	−	0.286973i
$495$	−24.0212			−1.07967
$496$	−0.169168	−	28.5346i	−0.00759587	−	1.28124i
$497$	−10.7136			−0.480572
$498$	−7.69164	−	18.4917i	−0.344671	−	0.828632i
$499$	23.3244	+	23.3244i	1.04414	+	1.04414i	0.998980	+	0.0451638i	$0.0143810\pi$
$499$	23.3244	+	23.3244i	1.04414	+	1.04414i	0.0451638	+	0.998980i	$0.485619\pi$
$500$	−14.8165	+	0.0439196i	−0.662613	+	0.00196414i
$501$	0.433124	−	0.433124i	0.0193505	−	0.0193505i
$502$	15.2234	−	36.9071i	0.679453	−	1.64725i
$503$			14.7499i			0.657664i	0.944388	+	0.328832i	$0.106655\pi$
$503$			14.7499i			0.657664i	−0.944388	+	0.328832i	$0.893345\pi$
$504$	−1.87674	+	4.58844i	−0.0835965	+	0.204385i
$505$			17.7822i			0.791299i
$506$	−26.5732	−	10.9609i	−1.18132	−	0.487270i
$507$	−6.96394	+	6.96394i	−0.309279	+	0.309279i
$508$	−19.6044	+	19.7209i	−0.869803	+	0.874975i
$509$	27.2157	+	27.2157i	1.20631	+	1.20631i	0.972212	+	0.234101i	$0.0752145\pi$
$509$	27.2157	+	27.2157i	1.20631	+	1.20631i	0.234101	+	0.972212i	$0.424785\pi$
$510$	15.7296	−	6.54273i	0.696517	−	0.289717i
$511$	9.55502			0.422689
$512$	20.7876	−	8.93721i	0.918693	−	0.394973i
$513$	−4.69515			−0.207296
$514$	1.57697	−	0.655943i	0.0695573	−	0.0289324i
$515$	−13.5323	−	13.5323i	−0.596302	−	0.596302i
$516$	−0.369460	+	0.371657i	−0.0162646	+	0.0163613i
$517$	−13.8374	+	13.8374i	−0.608567	+	0.608567i
$518$	1.98643	+	0.819361i	0.0872789	+	0.0360007i
$519$			16.6446i			0.730618i
$520$	18.2145	−	44.5327i	0.798759	−	1.95289i
$521$			7.41411i			0.324818i	0.986724	+	0.162409i	$0.0519264\pi$
$521$			7.41411i			0.324818i	−0.986724	+	0.162409i	$0.948074\pi$
$522$	−10.8123	+	26.2131i	−0.473243	+	1.14732i
$523$	30.5329	−	30.5329i	1.33511	−	1.33511i	0.434380	−	0.900730i	$-0.356967\pi$
$523$	30.5329	−	30.5329i	1.33511	−	1.33511i	0.900730	−	0.434380i	$-0.143033\pi$
$524$	7.24108	−	0.0214643i	0.316328	−	0.000937672i
$525$	3.67818	+	3.67818i	0.160529	+	0.160529i
$526$	−11.4138	−	27.4402i	−0.497665	−	1.19645i
$527$	−27.2132			−1.18542
$528$	−0.0681117	−	11.4888i	−0.00296418	−	0.499986i
$529$	−18.1787			−0.790380
$530$	−10.5296	−	25.3145i	−0.457376	−	1.09959i
$531$	−0.376725	−	0.376725i	−0.0163485	−	0.0163485i
$532$	−0.00477145	−	1.60967i	−0.000206869	−	0.0697881i
$533$	19.4237	−	19.4237i	0.841333	−	0.841333i
$534$	−7.54716	+	18.2971i	−0.326598	+	0.791794i
$535$		−	1.76737i		−	0.0764100i
$536$	−15.9241	+	6.67910i	−0.687818	+	0.288493i
$537$		−	1.63964i		−	0.0707557i
$538$	37.4419	+	15.4440i	1.61424	+	0.665837i
$539$	14.2273	−	14.2273i	0.612813	−	0.612813i
$540$	−23.1916	−	23.0545i	−0.998007	−	0.992108i
$541$	12.0212	+	12.0212i	0.516833	+	0.516833i	0.916612	−	0.399779i	$-0.130913\pi$
$541$	12.0212	+	12.0212i	0.516833	+	0.516833i	−0.399779	+	0.916612i	$0.630913\pi$
$542$	−14.8804	+	6.18952i	−0.639168	+	0.265863i
$543$	8.28179			0.355406
$544$	−8.40550	−	19.8748i	−0.360383	−	0.852125i
$545$	−15.6800			−0.671656
$546$	−4.65507	+	1.93628i	−0.199218	+	0.0828651i
$547$	−17.5909	−	17.5909i	−0.752133	−	0.752133i	0.222744	−	0.974877i	$-0.428499\pi$
$547$	−17.5909	−	17.5909i	−0.752133	−	0.752133i	−0.974877	+	0.222744i	$0.928499\pi$
$548$	−25.2105	−	25.0615i	−1.07694	−	1.07057i
$549$	6.83853	−	6.83853i	0.291862	−	0.291862i
$550$	29.5144	+	12.1741i	1.25850	+	0.519103i
$551$		−	9.20707i		−	0.392234i
$552$	−6.36598	−	15.1776i	−0.270954	−	0.646002i
$553$		−	8.68842i		−	0.369469i
$554$	−12.1120	+	29.3641i	−0.514591	+	1.24756i
$555$	−4.21549	+	4.21549i	−0.178937	+	0.178937i
$556$	0.0413106	+	13.9363i	0.00175196	+	0.591032i
$557$	−12.3742	−	12.3742i	−0.524314	−	0.524314i	0.394558	−	0.918871i	$-0.370898\pi$
$557$	−12.3742	−	12.3742i	−0.524314	−	0.524314i	−0.918871	+	0.394558i	$0.870898\pi$
$558$	8.43773	+	20.2854i	0.357197	+	0.858749i
$559$	1.41148			0.0596991
$560$	7.88038	−	7.97437i	0.333007	−	0.336979i
$561$	−10.9568			−0.462595
$562$	13.0017	+	31.2577i	0.548443	+	1.31853i
$563$	5.03251	+	5.03251i	0.212095	+	0.212095i	0.805157	−	0.593062i	$-0.202081\pi$
$563$	5.03251	+	5.03251i	0.212095	+	0.212095i	−0.593062	+	0.805157i	$0.702081\pi$
$564$	−11.2046	+	0.0332132i	−0.471800	+	0.00139853i
$565$	10.8986	−	10.8986i	0.458507	−	0.458507i
$566$	−7.97223	+	19.3276i	−0.335098	+	0.812401i
$567$		−	1.83148i		−	0.0769147i
$568$	−34.8484	−	14.2535i	−1.46221	−	0.598062i
$569$		−	23.4978i		−	0.985079i	−0.870290	−	0.492540i	$-0.836069\pi$
$569$		−	23.4978i		−	0.985079i	0.870290	−	0.492540i	$-0.163931\pi$
$570$	4.12848	+	1.70291i	0.172923	+	0.0713270i
$571$	28.4418	−	28.4418i	1.19025	−	1.19025i	0.213256	−	0.976996i	$-0.431593\pi$
$571$	28.4418	−	28.4418i	1.19025	−	1.19025i	0.976996	−	0.213256i	$-0.0684067\pi$
$572$	−21.8161	+	21.9458i	−0.912176	+	0.917600i
$573$	6.86507	+	6.86507i	0.286793	+	0.286793i
$574$	5.90986	−	2.45821i	0.246673	−	0.102604i
$575$	45.7365			1.90735
$576$	−12.2090	+	12.4281i	−0.508707	+	0.517836i
$577$	6.00071			0.249813			0.124906	−	0.992169i	$-0.460137\pi$
$577$	6.00071			0.249813			0.124906	+	0.992169i	$0.460137\pi$
$578$	3.19664	−	1.32965i	0.132963	−	0.0553059i
$579$	0.209743	+	0.209743i	0.00871662	+	0.00871662i
$580$	45.2093	−	45.4781i	1.87721	−	1.88838i
$581$	−8.88784	+	8.88784i	−0.368730	+	0.368730i
$582$	11.3501	+	4.68169i	0.470479	+	0.194062i
$583$			17.6333i			0.730297i
$584$	31.0797	+	12.7120i	1.28609	+	0.526028i
$585$			37.0446i			1.53161i
$586$	8.54551	−	20.7175i	0.353012	−	0.855832i
$587$	−13.8810	+	13.8810i	−0.572929	+	0.572929i	−0.932946	−	0.360017i	$-0.882771\pi$
$587$	−13.8810	+	13.8810i	−0.572929	+	0.572929i	0.360017	+	0.932946i	$0.382771\pi$
$588$	11.5204	−	0.0341491i	0.475092	−	0.00140828i
$589$	−5.04434	−	5.04434i	−0.207848	−	0.207848i
$590$	0.462729	+	1.11246i	0.0190503	+	0.0457993i
$591$	18.4448			0.758716
$592$	5.37122	+	5.30791i	0.220756	+	0.218154i
$593$	−21.7124			−0.891623			−0.445811	−	0.895127i	$-0.647085\pi$
$593$	−21.7124			−0.891623			−0.445811	+	0.895127i	$0.647085\pi$
$594$	8.07730	+	19.4189i	0.331415	+	0.796765i
$595$	−7.56026	−	7.56026i	−0.309940	−	0.309940i
$596$	0.0413138	+	13.9374i	0.00169228	+	0.570898i
$597$	15.2863	−	15.2863i	0.625626	−	0.625626i
$598$	−16.9035	+	40.9803i	−0.691234	+	1.67581i
$599$		−	12.9083i		−	0.527417i	−0.964602	−	0.263709i	$-0.915054\pi$
$599$		−	12.9083i		−	0.527417i	0.964602	−	0.263709i	$-0.0849457\pi$
$600$	7.07059	+	16.8575i	0.288656	+	0.688205i
$601$			26.7077i			1.08943i	0.838621	+	0.544716i	$0.183362\pi$
$601$			26.7077i			1.08943i	−0.838621	+	0.544716i	$0.816638\pi$
$602$	0.304045	+	0.125412i	0.0123919	+	0.00511141i
$603$	9.40126	−	9.40126i	0.382849	−	0.382849i
$604$	23.3019	+	23.1642i	0.948142	+	0.942538i
$605$	2.38169	+	2.38169i	0.0968295	+	0.0968295i
$606$	6.04614	−	2.51490i	0.245608	−	0.102161i
$607$	−32.0851			−1.30229			−0.651147	−	0.758952i	$-0.725712\pi$
$607$	−32.0851			−1.30229			−0.651147	+	0.758952i	$0.725712\pi$
$608$	2.12600	−	5.24215i	0.0862205	−	0.212597i
$609$	−6.71958			−0.272291
$610$	−20.1940	+	8.39973i	−0.817632	+	0.340095i
$611$	21.3395	+	21.3395i	0.863305	+	0.863305i
$612$	11.7831	+	11.7134i	0.476303	+	0.473488i
$613$	−4.63526	+	4.63526i	−0.187216	+	0.187216i	−0.794492	−	0.607275i	$-0.792263\pi$
$613$	−4.63526	+	4.63526i	−0.187216	+	0.187216i	0.607275	+	0.794492i	$0.292263\pi$
$614$	23.3535	+	9.63281i	0.942471	+	0.388749i
$615$			17.7582i			0.716080i
$616$	−6.64930	+	2.78893i	−0.267908	+	0.112369i
$617$			40.9298i			1.64777i	0.566757	+	0.823885i	$0.308198\pi$
$617$			40.9298i			1.64777i	−0.566757	+	0.823885i	$0.691802\pi$
$618$	−2.68727	+	6.51494i	−0.108098	+	0.262069i
$619$	5.50312	−	5.50312i	0.221189	−	0.221189i	−0.587810	−	0.808999i	$-0.700010\pi$
$619$	5.50312	−	5.50312i	0.221189	−	0.221189i	0.808999	+	0.587810i	$0.200010\pi$
$620$	−0.147280	−	49.6855i	−0.00591489	−	1.99542i
$621$	21.3045	+	21.3045i	0.854920	+	0.854920i
$622$	2.84677	+	6.84399i	0.114145	+	0.274419i
$623$	12.4218			0.497668
$624$	−17.7176	+	0.105039i	−0.709273	+	0.00420494i
$625$	9.83783			0.393513
$626$	−10.8455	−	26.0740i	−0.433474	−	1.04213i
$627$	−2.03099	−	2.03099i	−0.0811099	−	0.0811099i
$628$	−1.17591	+	0.00348568i	−0.0469240	+	0.000139094i
$629$	5.09229	−	5.09229i	0.203043	−	0.203043i
$630$	−3.29147	+	7.97975i	−0.131135	+	0.317921i
$631$			17.8827i			0.711899i	0.934505	+	0.355949i	$0.115842\pi$
$631$			17.8827i			0.711899i	−0.934505	+	0.355949i	$0.884158\pi$
$632$	11.5591	−	28.2609i	0.459797	−	1.12416i
$633$		−	18.7258i		−	0.744284i
$634$	−25.6171	−	10.5665i	−1.01739	−	0.419650i
$635$	−34.2371	+	34.2371i	−1.35866	+	1.35866i
$636$	−7.11801	+	7.16033i	−0.282247	+	0.283926i
$637$	−21.9408	−	21.9408i	−0.869328	−	0.869328i
$638$	−38.0799	+	15.8394i	−1.50760	+	0.627086i
$639$	28.9887			1.14677
$640$	36.2417	−	15.4543i	1.43258	−	0.610883i
$641$	7.27894			0.287501			0.143750	−	0.989614i	$-0.454084\pi$
$641$	7.27894			0.287501			0.143750	+	0.989614i	$0.454084\pi$
$642$	−0.600923	+	0.249955i	−0.0237165	+	0.00986492i
$643$	9.58100	+	9.58100i	0.377838	+	0.377838i	0.870322	−	0.492484i	$-0.163911\pi$
$643$	9.58100	+	9.58100i	0.377838	+	0.377838i	−0.492484	+	0.870322i	$0.663911\pi$
$644$	−7.28232	+	7.32562i	−0.286964	+	0.288670i
$645$	−0.645225	+	0.645225i	−0.0254057	+	0.0254057i
$646$	−4.98719	−	2.05711i	−0.196218	−	0.0809358i
$647$			46.8177i			1.84059i	0.391222	+	0.920296i	$0.372052\pi$
$647$			46.8177i			1.84059i	−0.391222	+	0.920296i	$0.627948\pi$
$648$	2.43660	−	5.95726i	0.0957188	−	0.234023i
$649$		−	0.774908i		−	0.0304178i
$650$	18.7744	−	45.5161i	0.736392	−	1.78529i
$651$	−3.68150	+	3.68150i	−0.144289	+	0.144289i
$652$	24.8045	−	0.0735264i	0.971419	−	0.00287952i
$653$	−30.9292	−	30.9292i	−1.21035	−	1.21035i	−0.970910	−	0.239443i	$-0.923035\pi$
$653$	−30.9292	−	30.9292i	−1.21035	−	1.21035i	−0.239443	−	0.970910i	$-0.576965\pi$
$654$	2.21758	+	5.33135i	0.0867142	+	0.208472i
$655$	12.6083			0.492649
$656$	22.4935	−	0.133353i	0.878224	−	0.00520657i
$657$	−25.8537			−1.00865
$658$	2.70068	+	6.49278i	0.105283	+	0.253115i
$659$	−23.4911	−	23.4911i	−0.915084	−	0.915084i	0.0815823	−	0.996667i	$-0.474003\pi$
$659$	−23.4911	−	23.4911i	−0.915084	−	0.915084i	−0.996667	+	0.0815823i	$0.974003\pi$
$660$	−0.0592988	−	20.0048i	−0.00230820	−	0.778684i
$661$	−9.89350	+	9.89350i	−0.384813	+	0.384813i	−0.872833	−	0.488020i	$-0.837719\pi$
$661$	−9.89350	+	9.89350i	−0.384813	+	0.384813i	0.488020	+	0.872833i	$0.337719\pi$
$662$	−1.40687	+	3.41077i	−0.0546794	+	0.132563i
$663$			16.8971i			0.656230i
$664$	−40.7340	+	17.0852i	−1.58079	+	0.663033i
$665$		−	2.80280i		−	0.108688i
$666$	−5.37484	−	2.21701i	−0.208271	−	0.0859072i
$667$	−41.7775	+	41.7775i	−1.61763	+	1.61763i
$668$	−0.958107	−	0.952444i	−0.0370703	−	0.0368512i
$669$	−8.60406	−	8.60406i	−0.332652	−	0.332652i
$670$	−27.7617	+	11.5475i	−1.07253	+	0.446119i
$671$	14.0666			0.543034
$672$	−3.82587	−	1.55161i	−0.147586	−	0.0598548i
$673$	−41.8111			−1.61170			−0.805849	−	0.592121i	$-0.798291\pi$
$673$	−41.8111			−1.61170			−0.805849	+	0.592121i	$0.798291\pi$
$674$	−7.99589	+	3.32590i	−0.307990	+	0.128109i
$675$	−23.6625	−	23.6625i	−0.910772	−	0.910772i
$676$	15.4048	+	15.3138i	0.592494	+	0.588991i
$677$	26.7463	−	26.7463i	1.02794	−	1.02794i	0.0283467	−	0.999598i	$-0.490976\pi$
$677$	26.7463	−	26.7463i	1.02794	−	1.02794i	0.999598	−	0.0283467i	$-0.00902424\pi$
$678$	−5.24699	−	2.16427i	−0.201510	−	0.0831183i
$679$		−	7.70553i		−	0.295711i
$680$	−14.5332	−	34.6496i	−0.557321	−	1.32875i
$681$		−	4.20755i		−	0.161234i
$682$	−12.1851	+	29.5411i	−0.466590	+	1.13119i
$683$	10.8804	−	10.8804i	0.416326	−	0.416326i	−0.467609	−	0.883935i	$-0.654885\pi$
$683$	10.8804	−	10.8804i	0.416326	−	0.416326i	0.883935	+	0.467609i	$0.154885\pi$
$684$	0.0129105	+	4.35541i	0.000493644	+	0.166533i
$685$	−43.7673	−	43.7673i	−1.67226	−	1.67226i
$686$	−5.83672	−	14.0322i	−0.222847	−	0.535753i
$687$	−6.68484			−0.255042
$688$	0.822122	+	0.812432i	0.0313431	+	0.0309737i
$689$	27.1935			1.03599
$690$	−11.0062	−	26.4602i	−0.418998	−	1.00732i
$691$	5.98794	+	5.98794i	0.227792	+	0.227792i	0.811770	−	0.583978i	$-0.198504\pi$
$691$	5.98794	+	5.98794i	0.227792	+	0.227792i	−0.583978	+	0.811770i	$0.698504\pi$
$692$	36.7105	−	0.108819i	1.39553	−	0.00413667i
$693$	3.92560	−	3.92560i	0.149121	−	0.149121i
$694$	−4.12861	+	10.0093i	−0.156720	+	0.379947i
$695$			24.2663i			0.920472i
$696$	−21.8569	−	8.93976i	−0.828483	−	0.338861i
$697$		−	21.4518i		−	0.812546i
$698$	−7.72582	−	3.18673i	−0.292426	−	0.120620i
$699$	6.10762	−	6.10762i	0.231011	−	0.231011i
$700$	8.08835	−	8.13644i	0.305711	−	0.307529i
$701$	−34.6817	−	34.6817i	−1.30991	−	1.30991i	−0.921476	−	0.388435i	$-0.873016\pi$
$701$	−34.6817	−	34.6817i	−1.30991	−	1.30991i	−0.388435	−	0.921476i	$-0.626984\pi$
$702$	29.9471	−	12.4565i	1.13028	−	0.470141i
$703$	1.88785			0.0712018
$704$	−25.3387	+	0.225335i	−0.954987	+	0.00849262i
$705$	−19.5098			−0.734780
$706$	−19.9278	+	8.28900i	−0.749994	+	0.311961i
$707$	−2.90602	−	2.90602i	−0.109292	−	0.109292i
$708$	0.312805	−	0.314665i	0.0117559	−	0.0118258i
$709$	−30.3930	+	30.3930i	−1.14143	+	1.14143i	−0.153243	+	0.988188i	$0.548972\pi$
$709$	−30.3930	+	30.3930i	−1.14143	+	1.14143i	−0.988188	+	0.153243i	$0.951028\pi$
$710$	−60.6047	−	24.9981i	−2.27445	−	0.938163i
$711$			23.5089i			0.881652i
$712$	40.4045	+	16.5260i	1.51422	+	0.619338i
$713$			45.7779i			1.71440i
$714$	−1.50134	+	3.63980i	−0.0561861	+	0.136216i
$715$	−38.0996	+	38.0996i	−1.42484	+	1.42484i
$716$	−3.61630	+	0.0107196i	−0.135148	+	0.000400610i
$717$	−17.6355	−	17.6355i	−0.658610	−	0.658610i
$718$	−10.4110	−	25.0293i	−0.388534	−	0.934086i
$719$	−10.6422			−0.396886			−0.198443	−	0.980112i	$-0.563589\pi$
$719$	−10.6422			−0.396886			−0.198443	+	0.980112i	$0.563589\pi$
$720$	−21.3225	+	21.5768i	−0.794643	+	0.804121i
$721$	4.42295			0.164719
$722$	−0.543132	−	1.30576i	−0.0202133	−	0.0485953i
$723$	−1.82780	−	1.82780i	−0.0679767	−	0.0679767i
$724$	−0.0541444	−	18.2659i	−0.00201226	−	0.678846i
$725$	46.4016	−	46.4016i	1.72331	−	1.72331i
$726$	0.472962	−	1.14664i	0.0175533	−	0.0425557i
$727$		−	28.8605i		−	1.07037i	−0.844733	−	0.535187i	$-0.820241\pi$
$727$		−	28.8605i		−	1.07037i	0.844733	−	0.535187i	$-0.179759\pi$
$728$	4.30099	+	10.2543i	0.159405	+	0.380050i
$729$		−	7.81713i		−	0.289523i
$730$	54.0507	+	22.2947i	2.00050	+	0.825165i
$731$	0.779429	−	0.779429i	0.0288282	−	0.0288282i
$732$	5.71199	+	5.67822i	0.211121	+	0.209873i
$733$	4.78662	+	4.78662i	0.176798	+	0.176798i	0.789958	−	0.613160i	$-0.210102\pi$
$733$	4.78662	+	4.78662i	0.176798	+	0.176798i	−0.613160	+	0.789958i	$0.710102\pi$
$734$	−23.2257	+	9.66076i	−0.857277	+	0.356585i
$735$	20.0595			0.739907
$736$	−33.4333	+	14.1397i	−1.23237	+	0.521197i
$737$	19.3380			0.712324
$738$	−15.9907	+	6.65137i	−0.588627	+	0.244840i
$739$	−5.00473	−	5.00473i	−0.184102	−	0.184102i	0.609039	−	0.793141i	$-0.291555\pi$
$739$	−5.00473	−	5.00473i	−0.184102	−	0.184102i	−0.793141	+	0.609039i	$0.791555\pi$
$740$	9.32502	+	9.26990i	0.342794	+	0.340768i
$741$	−3.13212	+	3.13212i	−0.115061	+	0.115061i
$742$	5.85772	+	2.41618i	0.215044	+	0.0887009i
$743$		−	2.84870i		−	0.104509i	−0.998634	−	0.0522543i	$-0.983359\pi$
$743$		−	2.84870i		−	0.104509i	0.998634	−	0.0522543i	$-0.0166407\pi$
$744$	−16.8728	+	7.07698i	−0.618586	+	0.259455i
$745$			24.2681i			0.889115i
$746$	−1.14684	+	2.78036i	−0.0419887	+	0.101796i
$747$	24.0485	−	24.0485i	0.879888	−	0.879888i
$748$	0.0716328	+	24.1657i	0.00261915	+	0.883584i
$749$	0.288828	+	0.288828i	0.0105535	+	0.0105535i
$750$	3.64866	+	8.77186i	0.133230	+	0.320303i
$751$	−50.7488			−1.85185			−0.925924	−	0.377710i	$-0.876712\pi$
$751$	−50.7488			−1.85185			−0.925924	+	0.377710i	$0.876712\pi$
$752$	0.146507	+	24.7121i	0.00534254	+	0.901159i
$753$	−25.5991			−0.932884
$754$	24.4269	+	58.7254i	0.889575	+	2.13865i
$755$	40.4539	+	40.4539i	1.47227	+	1.47227i
$756$	7.55765	−	0.0224027i	0.274869	−	0.000814777i
$757$	6.98410	−	6.98410i	0.253841	−	0.253841i	−0.568702	−	0.822544i	$-0.692554\pi$
$757$	6.98410	−	6.98410i	0.253841	−	0.253841i	0.822544	+	0.568702i	$0.192554\pi$
$758$	14.4300	−	34.9836i	0.524120	−	1.27066i
$759$			18.4314i			0.669019i
$760$	3.72886	−	9.11670i	0.135260	−	0.330698i
$761$		−	23.2624i		−	0.843261i	−0.906768	−	0.421630i	$-0.861458\pi$
$761$		−	23.2624i		−	0.843261i	0.906768	−	0.421630i	$-0.138542\pi$
$762$	16.4830	+	6.79889i	0.597117	+	0.246298i
$763$	2.56246	−	2.56246i	0.0927672	−	0.0927672i
$764$	15.0964	−	15.1861i	0.546167	−	0.549415i
$765$	20.4563	+	20.4563i	0.739601	+	0.739601i
$766$	−8.18968	+	3.40651i	−0.295905	+	0.123082i
$767$	−1.19503			−0.0431502
$768$	−10.3802	−	10.1369i	−0.374563	−	0.365784i
$769$	−23.0481			−0.831137			−0.415568	−	0.909562i	$-0.636417\pi$
$769$	−23.0481			−0.831137			−0.415568	+	0.909562i	$0.636417\pi$
$770$	−11.5922	+	4.82179i	−0.417754	+	0.173765i
$771$	−0.774386	−	0.774386i	−0.0278888	−	0.0278888i
$772$	0.461227	−	0.463970i	0.0165999	−	0.0166986i
$773$	−2.17649	+	2.17649i	−0.0782828	+	0.0782828i	−0.745164	−	0.666881i	$-0.767629\pi$
$773$	−2.17649	+	2.17649i	−0.0782828	+	0.0782828i	0.666881	+	0.745164i	$0.267629\pi$
$774$	−0.822676	−	0.339336i	−0.0295705	−	0.0121972i
$775$		−	50.8447i		−	1.82640i
$776$	10.2515	−	25.0639i	0.368007	−	0.899741i
$777$		−	1.37781i		−	0.0494287i
$778$	−9.19238	+	22.2857i	−0.329563	+	0.798982i
$779$	3.97640	−	3.97640i	0.142469	−	0.142469i
$780$	−30.8506	+	0.0914485i	−1.10463	+	0.00327438i
$781$	29.8142	+	29.8142i	1.06684	+	1.06684i
$782$	13.2954	+	31.9639i	0.475443	+	1.14303i
$783$	43.2286			1.54486
$784$	−0.150635	−	25.4085i	−0.00537982	−	0.907446i
$785$	−2.04752			−0.0730793
$786$	−1.78317	−	4.28697i	−0.0636035	−	0.152911i
$787$	29.0078	+	29.0078i	1.03402	+	1.03402i	0.999401	+	0.0346154i	$0.0110206\pi$
$787$	29.0078	+	29.0078i	1.03402	+	1.03402i	0.0346154	+	0.999401i	$0.488979\pi$
$788$	−0.120588	−	40.6808i	−0.00429575	−	1.44919i
$789$	−13.4748	+	13.4748i	−0.479714	+	0.479714i
$790$	20.2727	−	49.1485i	0.721270	−	1.74863i
$791$			3.56215i			0.126655i
$792$	17.9915	−	7.54622i	0.639300	−	0.268143i
$793$		−	21.6930i		−	0.770340i
$794$	−8.34318	−	3.44138i	−0.296088	−	0.122130i
$795$	−12.4309	+	12.4309i	−0.440878	+	0.440878i
$796$	−33.8146	−	33.6147i	−1.19853	−	1.19144i
$797$	−19.9343	−	19.9343i	−0.706110	−	0.706110i	0.259605	−	0.965715i	$-0.416408\pi$
$797$	−19.9343	−	19.9343i	−0.706110	−	0.706110i	−0.965715	+	0.259605i	$0.916408\pi$
$798$	−0.952981	+	0.396393i	−0.0337351	+	0.0140322i
$799$	23.5677			0.833766
$800$	37.1339	−	15.7047i	1.31288	−	0.555246i
$801$	−33.6105			−1.18757
$802$	−7.85330	+	3.26659i	−0.277310	+	0.115347i
$803$	−26.5900	−	26.5900i	−0.938340	−	0.938340i
$804$	7.85255	+	7.80613i	0.276938	+	0.275301i
$805$	−12.7178	+	12.7178i	−0.448245	+	0.448245i
$806$	45.5572	+	18.7914i	1.60469	+	0.661898i
$807$		−	25.9701i		−	0.914190i
$808$	−5.58626	−	13.3186i	−0.196524	−	0.468547i
$809$			43.3860i			1.52537i	0.646770	+	0.762685i	$0.276119\pi$
$809$			43.3860i			1.52537i	−0.646770	+	0.762685i	$0.723881\pi$
$810$	4.27338	−	10.3603i	0.150151	−	0.364022i
$811$	6.75874	−	6.75874i	0.237331	−	0.237331i	−0.578413	−	0.815744i	$-0.696328\pi$
$811$	6.75874	−	6.75874i	0.237331	−	0.237331i	0.815744	+	0.578413i	$0.196328\pi$
$812$	0.0439311	+	14.8204i	0.00154168	+	0.520093i
$813$	7.30715	+	7.30715i	0.256273	+	0.256273i
$814$	−3.24777	−	7.80805i	−0.113834	−	0.273672i
$815$	43.1902			1.51289
$816$	−9.72582	+	9.84183i	−0.340472	+	0.344533i
$817$	0.288956			0.0101093
$818$	−11.7243	−	28.1867i	−0.409930	−	0.985524i
$819$	−6.05392	−	6.05392i	−0.211541	−	0.211541i
$820$	39.1666	−	0.116099i	1.36776	−	0.00405435i
$821$	6.95595	−	6.95595i	0.242764	−	0.242764i	−0.575228	−	0.817993i	$-0.695087\pi$
$821$	6.95595	−	6.95595i	0.242764	−	0.242764i	0.817993	+	0.575228i	$0.195087\pi$
$822$	−8.69144	+	21.0713i	−0.303149	+	0.734945i
$823$		−	8.46071i		−	0.294922i	−0.989068	−	0.147461i	$-0.952890\pi$
$823$		−	8.46071i		−	0.294922i	0.989068	−	0.147461i	$-0.0471101\pi$
$824$	14.3866	+	5.88431i	0.501180	+	0.204990i
$825$		−	20.4715i		−	0.712726i
$826$	−0.257421	−	0.106181i	−0.00895684	−	0.00369450i
$827$	−14.8002	+	14.8002i	−0.514654	+	0.514654i	−0.915949	−	0.401295i	$-0.868560\pi$
$827$	−14.8002	+	14.8002i	−0.514654	+	0.514654i	0.401295	+	0.915949i	$0.368560\pi$
$828$	19.7043	−	19.8215i	0.684772	−	0.688844i
$829$	15.7348	+	15.7348i	0.546493	+	0.546493i	0.925425	−	0.378932i	$-0.123709\pi$
$829$	15.7348	+	15.7348i	0.546493	+	0.546493i	−0.378932	+	0.925425i	$0.623709\pi$
$830$	−71.0146	+	29.5386i	−2.46495	+	1.02530i
$831$	20.3672			0.706531
$832$	0.347503	+	39.0764i	0.0120475	+	1.35473i
$833$	−24.2318			−0.839583
$834$	8.25078	−	3.43192i	0.285701	−	0.118838i
$835$	−1.66335	−	1.66335i	−0.0575625	−	0.0575625i
$836$	−4.46617	+	4.49272i	−0.154466	+	0.155384i
$837$	23.6839	−	23.6839i	0.818637	−	0.818637i
$838$	14.3002	+	5.89851i	0.493991	+	0.203761i
$839$		−	26.6370i		−	0.919611i	−0.888020	−	0.459806i	$-0.847919\pi$
$839$		−	26.6370i		−	0.919611i	0.888020	−	0.459806i	$-0.152081\pi$
$840$	−6.65363	−	2.72143i	−0.229572	−	0.0938982i
$841$			55.7701i			1.92311i
$842$	6.19491	−	15.0188i	0.213491	−	0.517581i
$843$	15.3494	−	15.3494i	0.528661	−	0.528661i
$844$	−41.3007	+	0.122425i	−1.42163	+	0.00421404i
$845$	26.7440	+	26.7440i	0.920021	+	0.920021i
$846$	−7.30742	−	17.5680i	−0.251234	−	0.604000i
$847$	−0.778444			−0.0267476
$848$	15.8390	+	15.6523i	0.543913	+	0.537502i
$849$	13.4058			0.460087
$850$	−14.7670	−	35.5017i	−0.506503	−	1.21770i
$851$	−8.56624	−	8.56624i	−0.293647	−	0.293647i
$852$	0.0715616	+	24.1417i	0.00245166	+	0.827079i
$853$	32.1066	−	32.1066i	1.09931	−	1.09931i	0.104819	−	0.994491i	$-0.466574\pi$
$853$	32.1066	−	32.1066i	1.09931	−	1.09931i	0.994491	−	0.104819i	$-0.0334264\pi$
$854$	1.92745	−	4.67286i	0.0659561	−	0.159902i
$855$			7.58374i			0.259358i
$856$	0.555216	+	1.32373i	0.0189769	+	0.0452442i
$857$		−	54.1832i		−	1.85086i	−0.378915	−	0.925432i	$-0.623703\pi$
$857$		−	54.1832i		−	1.85086i	0.378915	−	0.925432i	$-0.376297\pi$
$858$	18.3426	+	7.56592i	0.626206	+	0.258296i
$859$	37.7627	−	37.7627i	1.28845	−	1.28845i	0.352714	−	0.935731i	$-0.385259\pi$
$859$	37.7627	−	37.7627i	1.28845	−	1.28845i	0.935731	−	0.352714i	$-0.114741\pi$
$860$	1.42729	+	1.41886i	0.0486703	+	0.0483826i
$861$	−2.90209	−	2.90209i	−0.0989029	−	0.0989029i
$862$	−16.5571	+	6.88694i	−0.563937	+	0.234570i
$863$	−39.3537			−1.33962			−0.669808	−	0.742534i	$-0.733624\pi$
$863$	−39.3537			−1.33962			−0.669808	+	0.742534i	$0.733624\pi$
$864$	24.6127	+	9.98187i	0.837341	+	0.339590i
$865$	63.9212			2.17339
$866$	−5.33506	+	2.21912i	−0.181293	+	0.0754089i
$867$	−1.56974	−	1.56974i	−0.0533111	−	0.0533111i
$868$	8.14380	+	8.09566i	0.276419	+	0.274785i
$869$	−24.1784	+	24.1784i	−0.820196	+	0.820196i
$870$	−38.0112	−	15.6788i	−1.28870	−	0.531561i
$871$		−	29.8224i		−	1.01049i
$872$	11.7440	−	4.92583i	0.397704	−	0.166810i
$873$			20.8494i			0.705646i
$874$	−3.46046	+	8.38944i	−0.117052	+	0.283777i
$875$	4.21611	−	4.21611i	0.142530	−	0.142530i
$876$	−0.0638226	−	21.5309i	−0.00215637	−	0.727461i
$877$	17.4252	+	17.4252i	0.588408	+	0.588408i	0.937200	−	0.348792i	$-0.113408\pi$
$877$	17.4252	+	17.4252i	0.588408	+	0.588408i	−0.348792	+	0.937200i	$0.613408\pi$
$878$	17.0272	+	40.9355i	0.574639	+	1.38151i
$879$	−14.3699			−0.484683
$880$	−44.1211	+	0.261573i	−1.48732	+	0.00881762i
$881$	−45.0982			−1.51940			−0.759698	−	0.650276i	$-0.774653\pi$
$881$	−45.0982			−1.51940			−0.759698	+	0.650276i	$0.774653\pi$
$882$	7.51333	+	18.0630i	0.252987	+	0.608214i
$883$	2.58218	+	2.58218i	0.0868974	+	0.0868974i	0.749219	−	0.662322i	$-0.230429\pi$
$883$	2.58218	+	2.58218i	0.0868974	+	0.0868974i	−0.662322	+	0.749219i	$0.730429\pi$
$884$	37.2674	−	0.110470i	1.25344	−	0.00371549i
$885$	0.546283	−	0.546283i	0.0183631	−	0.0183631i
$886$	4.81309	−	11.6687i	0.161699	−	0.392018i
$887$		−	4.17256i		−	0.140101i	−0.997543	−	0.0700505i	$-0.977684\pi$
$887$		−	4.17256i		−	0.140101i	0.997543	−	0.0700505i	$-0.0223160\pi$
$888$	1.83305	−	4.48162i	0.0615130	−	0.150393i
$889$		−	11.1902i		−	0.375308i
$890$	70.2674	+	28.9838i	2.35537	+	0.971538i
$891$	−5.09668	+	5.09668i	−0.170745	+	0.170745i
$892$	−18.9204	+	19.0329i	−0.633502	+	0.637269i
$893$	4.36861	+	4.36861i	0.146190	+	0.146190i
$894$	8.25141	−	3.43218i	0.275969	−	0.114789i
$895$	−6.29679			−0.210479
$896$	−3.39714	+	8.44829i	−0.113491	+	0.282238i
$897$	28.4243			0.949060
$898$	28.2501	−	11.7507i	0.942719	−	0.392125i
$899$	46.4436	+	46.4436i	1.54898	+	1.54898i
$900$	−21.8852	+	22.0154i	−0.729508	+	0.733846i
$901$	15.0165	−	15.0165i	0.500271	−	0.500271i
$902$	−23.2869	−	9.60535i	−0.775370	−	0.319823i
$903$		−	0.210888i		−	0.00701793i
$904$	−4.73910	+	11.5866i	−0.157620	+	0.385366i
$905$		−	31.8050i		−	1.05723i
$906$	8.03345	−	19.4761i	0.266894	−	0.647049i
$907$	0.762883	−	0.762883i	0.0253311	−	0.0253311i	−0.694328	−	0.719659i	$-0.744298\pi$
$907$	0.762883	−	0.762883i	0.0253311	−	0.0253311i	0.719659	+	0.694328i	$0.244298\pi$
$908$	−9.27995	+	0.0275080i	−0.307966	+	0.000912884i
$909$	7.86302	+	7.86302i	0.260800	+	0.260800i
$910$	7.43599	+	17.8771i	0.246501	+	0.592620i
$911$	41.8322			1.38596			0.692981	−	0.720956i	$-0.256297\pi$
$911$	41.8322			1.38596			0.692981	+	0.720956i	$0.256297\pi$
$912$	−3.62714	+	0.0215036i	−0.120106	+	0.000712054i
$913$	49.4667			1.63711
$914$	7.42520	+	17.8511i	0.245604	+	0.590463i
$915$	9.91645	+	9.91645i	0.327828	+	0.327828i
$916$	0.0437039	+	14.7437i	0.00144402	+	0.487146i
$917$	−2.06049	+	2.06049i	−0.0680433	+	0.0680433i
$918$	9.65843	−	23.4156i	0.318776	−	0.772831i
$919$		−	31.0064i		−	1.02281i	−0.859341	−	0.511403i	$-0.829126\pi$
$919$		−	31.0064i		−	1.02281i	0.859341	−	0.511403i	$-0.170874\pi$
$920$	−58.2874	+	24.4476i	−1.92168	+	0.806014i
$921$		−	16.1982i		−	0.533749i
$922$	−31.4699	−	12.9806i	−1.03640	−	0.427494i
$923$	45.9784	−	45.9784i	1.51340	−	1.51340i
$924$	3.27892	+	3.25954i	0.107868	+	0.107231i
$925$	9.51437	+	9.51437i	0.312831	+	0.312831i
$926$	−17.5858	+	7.31484i	−0.577906	+	0.240380i
$927$	−11.9675			−0.393064
$928$	−19.5742	+	48.2648i	−0.642554	+	1.58437i
$929$	43.5848			1.42997			0.714985	−	0.699139i	$-0.246433\pi$
$929$	43.5848			1.42997			0.714985	+	0.699139i	$0.246433\pi$
$930$	−29.4155	+	12.2354i	−0.964573	+	0.401215i
$931$	−4.49171	−	4.49171i	−0.147210	−	0.147210i
$932$	−13.5106	−	13.4307i	−0.442554	−	0.439938i
$933$	3.36080	−	3.36080i	0.110028	−	0.110028i
$934$	27.4071	+	11.3048i	0.896788	+	0.369905i
$935$			42.0778i			1.37609i
$936$	−11.6375	−	27.7458i	−0.380384	−	0.906901i
$937$		−	46.3969i		−	1.51572i	−0.652417	−	0.757860i	$-0.726245\pi$
$937$		−	46.3969i		−	1.51572i	0.652417	−	0.757860i	$-0.273755\pi$
$938$	2.64976	−	6.42401i	0.0865179	−	0.209751i
$939$	−12.8039	+	12.8039i	−0.417838	+	0.417838i
$940$	0.127550	+	43.0297i	0.00416023	+	1.40348i
$941$	2.25521	+	2.25521i	0.0735178	+	0.0735178i	0.742910	−	0.669392i	$-0.233445\pi$
$941$	2.25521	+	2.25521i	0.0735178	+	0.0735178i	−0.669392	+	0.742910i	$0.733445\pi$
$942$	0.289576	+	0.696179i	0.00943491	+	0.0226827i
$943$	−36.0862			−1.17513
$944$	−0.696055	−	0.687850i	−0.0226547	−	0.0223876i
$945$	13.1596			0.428081
$946$	−0.497105	−	1.19511i	−0.0161623	−	0.0388562i
$947$	14.9480	+	14.9480i	0.485744	+	0.485744i	0.906960	−	0.421216i	$-0.138397\pi$
$947$	14.9480	+	14.9480i	0.485744	+	0.485744i	−0.421216	+	0.906960i	$0.638397\pi$
$948$	−19.5781	+	0.0580342i	−0.635868	+	0.00188486i
$949$	−41.0061	+	41.0061i	−1.33112	+	1.33112i
$950$	3.84348	−	9.31801i	0.124699	−	0.302316i
$951$			17.7683i			0.576176i
$952$	8.03756	+	3.28747i	0.260499	+	0.106548i
$953$			15.2316i			0.493400i	0.969092	+	0.246700i	$0.0793462\pi$
$953$			15.2316i			0.493400i	−0.969092	+	0.246700i	$0.920654\pi$
$954$	−15.8497	−	6.53764i	−0.513152	−	0.211664i
$955$	26.3643	−	26.3643i	0.853129	−	0.853129i
$956$	−38.7806	+	39.0112i	−1.25426	+	1.26171i
$957$	18.6995	+	18.6995i	0.604467	+	0.604467i
$958$	35.4089	−	14.7284i	1.14401	−	0.475852i
$959$	14.3051			0.461937
$960$	−18.0218	−	17.7040i	−0.581650	−	0.571396i
$961$	19.8907			0.641636
$962$	−12.0413	+	5.00859i	−0.388227	+	0.161483i
$963$	−0.781502	−	0.781502i	−0.0251835	−	0.0251835i
$964$	−4.01935	+	4.04325i	−0.129455	+	0.130224i
$965$	0.805487	−	0.805487i	0.0259296	−	0.0259296i
$966$	6.12285	+	2.52554i	0.197000	+	0.0812580i
$967$		−	20.2650i		−	0.651678i	−0.945425	−	0.325839i	$-0.894353\pi$
$967$		−	20.2650i		−	0.651678i	0.945425	−	0.325839i	$-0.105647\pi$
$968$	−2.53205	−	1.03565i	−0.0813833	−	0.0332869i
$969$			3.45917i			0.111124i
$970$	17.9793	−	43.5885i	0.577281	−	1.39954i
$971$	33.5103	−	33.5103i	1.07540	−	1.07540i	0.0784821	−	0.996916i	$-0.474993\pi$
$971$	33.5103	−	33.5103i	1.07540	−	1.07540i	0.996916	−	0.0784821i	$-0.0250073\pi$
$972$	−32.2978	+	0.0957382i	−1.03595	+	0.00307080i
$973$	−3.96565	−	3.96565i	−0.127133	−	0.127133i
$974$	3.88016	+	9.32839i	0.124328	+	0.298901i
$975$	−31.5704			−1.01106
$976$	12.4863	−	12.6352i	0.399675	−	0.404443i
$977$	−23.2192			−0.742847			−0.371423	−	0.928464i	$-0.621130\pi$
$977$	−23.2192			−0.742847			−0.371423	+	0.928464i	$0.621130\pi$
$978$	−6.10828	−	14.6851i	−0.195321	−	0.469578i
$979$	−34.5677	−	34.5677i	−1.10479	−	1.10479i
$980$	−0.131144	−	44.2422i	−0.00418926	−	1.41327i
$981$	−6.93343	+	6.93343i	−0.221367	+	0.221367i
$982$	17.1690	−	41.6241i	0.547886	−	1.32828i
$983$		−	28.1286i		−	0.897165i	−0.893742	−	0.448582i	$-0.851929\pi$
$983$		−	28.1286i		−	0.897165i	0.893742	−	0.448582i	$-0.148071\pi$
$984$	−5.57871	−	13.3006i	−0.177843	−	0.424008i
$985$		−	70.8344i		−	2.25697i
$986$	45.9174	+	18.9399i	1.46231	+	0.603170i
$987$	3.18833	−	3.18833i	0.101486	−	0.101486i
$988$	6.92852	+	6.88756i	0.220425	+	0.219123i
$989$	−1.31115	−	1.31115i	−0.0416922	−	0.0416922i
$990$	31.3659	−	13.0467i	0.996873	−	0.414650i
$991$	−51.3769			−1.63204			−0.816021	−	0.578022i	$-0.803825\pi$
$991$	−51.3769			−1.63204			−0.816021	+	0.578022i	$0.803825\pi$
$992$	15.7189	+	37.1674i	0.499077	+	1.18007i
$993$	2.36574			0.0750745
$994$	13.9894	−	5.81892i	0.443718	−	0.184565i
$995$	−58.7047	−	58.7047i	−1.86106	−	1.86106i
$996$	20.0869	+	19.9681i	0.636476	+	0.632714i
$997$	−13.0813	+	13.0813i	−0.414289	+	0.414289i	−0.883230	−	0.468941i	$-0.844636\pi$
$997$	−13.0813	+	13.0813i	−0.414289	+	0.414289i	0.468941	+	0.883230i	$0.344636\pi$
$998$	−43.1243	−	17.7878i	−1.36508	−	0.563064i
$999$			8.86376i			0.280437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.5	✓	68
4.3	odd	2		1216.2.k.b.913.14		68
16.5	even	4	inner	304.2.k.b.229.5	yes	68
16.11	odd	4		1216.2.k.b.305.14		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.5	✓	68	1.1	even	1	trivial
304.2.k.b.229.5	yes	68	16.5	even	4	inner
1216.2.k.b.305.14		68	16.11	odd	4
1216.2.k.b.913.14		68	4.3	odd	2

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30576 + 0.543132i) q^{2} +(0.641204 + 0.641204i) q^{3} +(1.41002 - 1.41840i) q^{4} +(2.46245 - 2.46245i) q^{5} +(-1.18552 - 0.489000i) q^{6} +0.804840i q^{7} +(-1.07076 + 2.61791i) q^{8} -2.17771i q^{9} +O(q^{10})\)	\(q+(-1.30576 + 0.543132i) q^{2} +(0.641204 + 0.641204i) q^{3} +(1.41002 - 1.41840i) q^{4} +(2.46245 - 2.46245i) q^{5} +(-1.18552 - 0.489000i) q^{6} +0.804840i q^{7} +(-1.07076 + 2.61791i) q^{8} -2.17771i q^{9} +(-1.87793 + 4.55280i) q^{10} +(2.23973 - 2.23973i) q^{11} +(1.81359 - 0.00537592i) q^{12} +(-3.45404 - 3.45404i) q^{13} +(-0.437134 - 1.05093i) q^{14} +3.15787 q^{15} +(-0.0237137 - 3.99993i) q^{16} -3.81469 q^{17} +(1.18279 + 2.84357i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(-0.0206454 - 6.96483i) q^{20} +(-0.516067 + 0.516067i) q^{21} +(-1.70808 + 4.14102i) q^{22} +6.41707i q^{23} +(-2.36520 + 0.992040i) q^{24} -7.12733i q^{25} +(6.38614 + 2.63414i) q^{26} +(3.31997 - 3.31997i) q^{27} +(1.14158 + 1.13484i) q^{28} +(6.51038 + 6.51038i) q^{29} +(-4.12342 + 1.71514i) q^{30} +7.13377 q^{31} +(2.20345 + 5.21007i) q^{32} +2.87225 q^{33} +(4.98107 - 2.07188i) q^{34} +(1.98188 + 1.98188i) q^{35} +(-3.08887 - 3.07061i) q^{36} +(-1.33491 + 1.33491i) q^{37} +(1.30736 + 0.539259i) q^{38} -4.42949i q^{39} +(3.80978 + 9.08318i) q^{40} +5.62347i q^{41} +(0.393567 - 0.954151i) q^{42} +(-0.204323 + 0.204323i) q^{43} +(-0.0187781 - 6.33489i) q^{44} +(-5.36251 - 5.36251i) q^{45} +(-3.48531 - 8.37914i) q^{46} -6.17814 q^{47} +(2.54957 - 2.57998i) q^{48} +6.35223 q^{49} +(3.87108 + 9.30658i) q^{50} +(-2.44600 - 2.44600i) q^{51} +(-9.76944 + 0.0289589i) q^{52} +(-3.93648 + 3.93648i) q^{53} +(-2.53190 + 6.13827i) q^{54} -11.0305i q^{55} +(-2.10700 - 0.861792i) q^{56} -0.906800i q^{57} +(-12.0370 - 4.96499i) q^{58} +(0.172991 - 0.172991i) q^{59} +(4.45264 - 4.47912i) q^{60} +(3.14024 + 3.14024i) q^{61} +(-9.31499 + 3.87458i) q^{62} +1.75271 q^{63} +(-5.70693 - 5.60633i) q^{64} -17.0108 q^{65} +(-3.75047 + 1.56001i) q^{66} +(4.31703 + 4.31703i) q^{67} +(-5.37878 + 5.41076i) q^{68} +(-4.11465 + 4.11465i) q^{69} +(-3.66428 - 1.51143i) q^{70} +13.3115i q^{71} +(5.70106 + 2.33181i) q^{72} -11.8720i q^{73} +(1.01804 - 2.46811i) q^{74} +(4.57007 - 4.57007i) q^{75} +(-1.99999 + 0.00592845i) q^{76} +(1.80262 + 1.80262i) q^{77} +(2.40580 + 5.78384i) q^{78} -10.7952 q^{79} +(-9.90802 - 9.79124i) q^{80} -2.27558 q^{81} +(-3.05429 - 7.34290i) q^{82} +(11.0430 + 11.0430i) q^{83} +(0.00432675 + 1.45965i) q^{84} +(-9.39350 + 9.39350i) q^{85} +(0.155822 - 0.377771i) q^{86} +8.34897i q^{87} +(3.46520 + 8.26164i) q^{88} -15.4339i q^{89} +(9.91470 + 4.08960i) q^{90} +(2.77994 - 2.77994i) q^{91} +(9.10196 + 9.04816i) q^{92} +(4.57421 + 4.57421i) q^{93} +(8.06717 - 3.35555i) q^{94} -3.48243 q^{95} +(-1.92785 + 4.75358i) q^{96} -9.57400 q^{97} +(-8.29449 + 3.45010i) q^{98} +(-4.87749 - 4.87749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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