LMFDB - Embedded newform 380.2.n.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.785164 - 1.17623i) q^{2} +(1.08269 + 1.87527i) q^{3} +(-0.767036 + 1.84707i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.35566 - 2.74588i) q^{6} -3.94804i q^{7} +(2.77483 - 0.548038i) q^{8} +(-0.844418 + 1.46258i) q^{9} +O(q^{10})$	\(q+(-0.785164 - 1.17623i) q^{2} +(1.08269 + 1.87527i) q^{3} +(-0.767036 + 1.84707i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.35566 - 2.74588i) q^{6} -3.94804i q^{7} +(2.77483 - 0.548038i) q^{8} +(-0.844418 + 1.46258i) q^{9} +(-0.626064 + 1.26809i) q^{10} -3.27337i q^{11} +(-4.29420 + 0.561395i) q^{12} +(2.48768 + 1.43626i) q^{13} +(-4.64380 + 3.09986i) q^{14} +(1.08269 - 1.87527i) q^{15} +(-2.82331 - 2.83353i) q^{16} +(2.44844 + 4.24083i) q^{17} +(2.38333 - 0.155130i) q^{18} +(3.58606 - 2.47794i) q^{19} +(1.98312 - 0.259260i) q^{20} +(7.40363 - 4.27449i) q^{21} +(-3.85023 + 2.57013i) q^{22} +(-4.53719 - 2.61955i) q^{23} +(4.03198 + 4.61019i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.263860 - 4.05379i) q^{26} +2.83916 q^{27} +(7.29229 + 3.02829i) q^{28} +(3.15366 + 1.82076i) q^{29} +(-3.05583 + 0.198903i) q^{30} +10.1956 q^{31} +(-1.11613 + 5.54565i) q^{32} +(6.13844 - 3.54403i) q^{33} +(3.06576 - 6.20967i) q^{34} +(-3.41910 + 1.97402i) q^{35} +(-2.05378 - 2.68155i) q^{36} -5.70498i q^{37} +(-5.73027 - 2.27244i) q^{38} +6.22009i q^{39} +(-1.86203 - 2.12905i) q^{40} +(-5.08478 + 2.93570i) q^{41} +(-10.8408 - 5.35220i) q^{42} +(-8.05559 + 4.65090i) q^{43} +(6.04613 + 2.51079i) q^{44} +1.68884 q^{45} +(0.481244 + 7.39356i) q^{46} +(-3.70031 - 2.13638i) q^{47} +(2.25688 - 8.36229i) q^{48} -8.58701 q^{49} +(1.41123 - 0.0918564i) q^{50} +(-5.30179 + 9.18297i) q^{51} +(-4.56102 + 3.49325i) q^{52} +(-6.30379 - 3.63950i) q^{53} +(-2.22920 - 3.33950i) q^{54} +(-2.83482 + 1.63668i) q^{55} +(-2.16367 - 10.9551i) q^{56} +(8.52938 + 4.04199i) q^{57} +(-0.334498 - 5.13903i) q^{58} +(-2.14966 - 3.72333i) q^{59} +(2.63328 + 3.43819i) q^{60} +(4.29565 - 7.44029i) q^{61} +(-8.00524 - 11.9924i) q^{62} +(5.77430 + 3.33380i) q^{63} +(7.39931 - 3.04142i) q^{64} -2.87253i q^{65} +(-8.98827 - 4.43758i) q^{66} +(-5.43372 + 9.41147i) q^{67} +(-9.71113 + 1.26957i) q^{68} -11.3446i q^{69} +(5.00646 + 2.47172i) q^{70} +(2.83324 + 4.90732i) q^{71} +(-1.54157 + 4.52116i) q^{72} +(5.15017 + 8.92036i) q^{73} +(-6.71037 + 4.47934i) q^{74} -2.16537 q^{75} +(1.82628 + 8.52436i) q^{76} -12.9234 q^{77} +(7.31626 - 4.88379i) q^{78} +(1.15575 + 2.00182i) q^{79} +(-1.04226 + 3.86183i) q^{80} +(5.60717 + 9.71190i) q^{81} +(7.44545 + 3.67587i) q^{82} -8.63031i q^{83} +(2.21641 + 16.9537i) q^{84} +(2.44844 - 4.24083i) q^{85} +(11.7955 + 5.82352i) q^{86} +7.88527i q^{87} +(-1.79393 - 9.08302i) q^{88} +(-3.11895 - 1.80073i) q^{89} +(-1.32601 - 1.98646i) q^{90} +(5.67043 - 9.82147i) q^{91} +(8.31867 - 6.37121i) q^{92} +(11.0387 + 19.1195i) q^{93} +(0.392480 + 6.02983i) q^{94} +(-3.93899 - 1.86665i) q^{95} +(-11.6080 + 3.91116i) q^{96} +(-6.05217 + 3.49422i) q^{97} +(6.74220 + 10.1003i) q^{98} +(4.78755 + 2.76409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−0.785164	−	1.17623i	−0.555194	−	0.831721i
$2$	−0.785164	−	1.17623i	−0.555194	−	0.831721i
$3$	1.08269	+	1.87527i	0.625089	+	1.08269i	0.988524	+	0.151066i	$0.0482707\pi$
$3$	1.08269	+	1.87527i	0.625089	+	1.08269i	−0.363435	+	0.931620i	$0.618396\pi$
$4$	−0.767036	+	1.84707i	−0.383518	+	0.923533i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.35566	−	2.74588i	0.553446	−	1.12100i
$7$		−	3.94804i		−	1.49222i	−0.665824	−	0.746109i	$-0.731920\pi$
$7$		−	3.94804i		−	1.49222i	0.665824	−	0.746109i	$-0.268080\pi$
$8$	2.77483	−	0.548038i	0.981049	−	0.193761i
$9$	−0.844418	+	1.46258i	−0.281473	+	0.487525i
$10$	−0.626064	+	1.26809i	−0.197979	+	0.401004i
$11$		−	3.27337i		−	0.986957i	−0.869758	−	0.493479i	$-0.835725\pi$
$11$		−	3.27337i		−	0.986957i	0.869758	−	0.493479i	$-0.164275\pi$
$12$	−4.29420	+	0.561395i	−1.23963	+	0.162061i
$13$	2.48768	+	1.43626i	0.689959	+	0.398348i	0.803597	−	0.595174i	$-0.202917\pi$
$13$	2.48768	+	1.43626i	0.689959	+	0.398348i	−0.113638	+	0.993522i	$0.536250\pi$
$14$	−4.64380	+	3.09986i	−1.24111	+	0.828471i
$15$	1.08269	−	1.87527i	0.279548	−	0.484192i
$16$	−2.82331	−	2.83353i	−0.705828	−	0.708384i
$17$	2.44844	+	4.24083i	0.593834	+	1.02855i	0.993710	+	0.111982i	$0.0357199\pi$
$17$	2.44844	+	4.24083i	0.593834	+	1.02855i	−0.399876	+	0.916569i	$0.630947\pi$
$18$	2.38333	−	0.155130i	0.561757	−	0.0365646i
$19$	3.58606	−	2.47794i	0.822698	−	0.568478i
$19$	3.58606	−	2.47794i	0.822698	−	0.568478i
$20$	1.98312	−	0.259260i	0.443440	−	0.0579724i
$21$	7.40363	−	4.27449i	1.61560	−	0.932769i
$22$	−3.85023	+	2.57013i	−0.820873	+	0.547953i
$23$	−4.53719	−	2.61955i	−0.946070	−	0.546214i	−0.0542120	−	0.998529i	$-0.517265\pi$
$23$	−4.53719	−	2.61955i	−0.946070	−	0.546214i	−0.891858	+	0.452316i	$0.850598\pi$
$24$	4.03198	+	4.61019i	0.823025	+	0.941050i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.263860	−	4.05379i	−0.0517472	−	0.795014i
$27$	2.83916			0.546396
$28$	7.29229	+	3.02829i	1.37811	+	0.572293i
$29$	3.15366	+	1.82076i	0.585619	+	0.338108i	0.763363	−	0.645969i	$-0.223547\pi$
$29$	3.15366	+	1.82076i	0.585619	+	0.338108i	−0.177744	+	0.984077i	$0.556880\pi$
$30$	−3.05583	+	0.198903i	−0.557916	+	0.0363146i
$31$	10.1956			1.83119			0.915595	−	0.402101i	$-0.131720\pi$
$31$	10.1956			1.83119			0.915595	+	0.402101i	$0.131720\pi$
$32$	−1.11613	+	5.54565i	−0.197306	+	0.980342i
$33$	6.13844	−	3.54403i	1.06857	−	0.616936i
$34$	3.06576	−	6.20967i	0.525774	−	1.06495i
$35$	−3.41910	+	1.97402i	−0.577934	+	0.333670i
$36$	−2.05378	−	2.68155i	−0.342296	−	0.446924i
$37$		−	5.70498i		−	0.937893i	−0.883227	−	0.468946i	$-0.844634\pi$
$37$		−	5.70498i		−	0.937893i	0.883227	−	0.468946i	$-0.155366\pi$
$38$	−5.73027	−	2.27244i	−0.929573	−	0.368639i
$39$			6.22009i			0.996012i
$40$	−1.86203	−	2.12905i	−0.294412	−	0.336632i
$41$	−5.08478	+	2.93570i	−0.794110	+	0.458480i	−0.841407	−	0.540401i	$-0.818272\pi$
$41$	−5.08478	+	2.93570i	−0.794110	+	0.458480i	0.0472975	+	0.998881i	$0.484939\pi$
$42$	−10.8408	−	5.35220i	−1.67278	−	0.825863i
$43$	−8.05559	+	4.65090i	−1.22847	+	0.709256i	−0.966709	−	0.255878i	$-0.917635\pi$
$43$	−8.05559	+	4.65090i	−1.22847	+	0.709256i	−0.261758	+	0.965134i	$0.584302\pi$
$44$	6.04613	+	2.51079i	0.911488	+	0.378516i
$45$	1.68884			0.251757
$46$	0.481244	+	7.39356i	0.0709556	+	1.09012i
$47$	−3.70031	−	2.13638i	−0.539746	−	0.311623i	0.205230	−	0.978714i	$-0.434206\pi$
$47$	−3.70031	−	2.13638i	−0.539746	−	0.311623i	−0.744976	+	0.667091i	$0.767539\pi$
$48$	2.25688	−	8.36229i	0.325752	−	1.20699i
$49$	−8.58701			−1.22672
$50$	1.41123	−	0.0918564i	0.199578	−	0.0129905i
$51$	−5.30179	+	9.18297i	−0.742399	+	1.28587i
$52$	−4.56102	+	3.49325i	−0.632500	+	0.484427i
$53$	−6.30379	−	3.63950i	−0.865892	−	0.499923i	8.86935e−5	−	1.00000i	$-0.499972\pi$
$53$	−6.30379	−	3.63950i	−0.865892	−	0.499923i	−0.865981	+	0.500077i	$0.833305\pi$
$54$	−2.22920	−	3.33950i	−0.303356	−	0.454449i
$55$	−2.83482	+	1.63668i	−0.382247	+	0.220690i
$56$	−2.16367	−	10.9551i	−0.289133	−	1.46394i
$57$	8.52938	+	4.04199i	1.12974	+	0.535374i
$58$	−0.334498	−	5.13903i	−0.0439217	−	0.674787i
$59$	−2.14966	−	3.72333i	−0.279862	−	0.484736i	0.691488	−	0.722388i	$-0.256956\pi$
$59$	−2.14966	−	3.72333i	−0.279862	−	0.484736i	−0.971350	+	0.237652i	$0.923622\pi$
$60$	2.63328	+	3.43819i	0.339956	+	0.443869i
$61$	4.29565	−	7.44029i	0.550002	−	0.952632i	−0.448272	−	0.893897i	$-0.647960\pi$
$61$	4.29565	−	7.44029i	0.550002	−	0.952632i	0.998274	−	0.0587341i	$-0.0187064\pi$
$62$	−8.00524	−	11.9924i	−1.01667	−	1.52304i
$63$	5.77430	+	3.33380i	0.727494	+	0.420019i
$64$	7.39931	−	3.04142i	0.924914	−	0.380177i
$65$		−	2.87253i		−	0.356293i
$66$	−8.98827	−	4.43758i	−1.10638	−	0.546228i
$67$	−5.43372	+	9.41147i	−0.663834	+	1.14979i	0.315766	+	0.948837i	$0.397739\pi$
$67$	−5.43372	+	9.41147i	−0.663834	+	1.14979i	−0.979600	+	0.200957i	$0.935595\pi$
$68$	−9.71113	+	1.26957i	−1.17765	+	0.153958i
$69$		−	11.3446i		−	1.36573i
$70$	5.00646	+	2.47172i	0.598386	+	0.295427i
$71$	2.83324	+	4.90732i	0.336244	+	0.582391i	0.983723	−	0.179692i	$-0.0575101\pi$
$71$	2.83324	+	4.90732i	0.336244	+	0.582391i	−0.647479	+	0.762083i	$0.724177\pi$
$72$	−1.54157	+	4.52116i	−0.181675	+	0.532824i
$73$	5.15017	+	8.92036i	0.602782	+	1.04405i	0.992398	+	0.123072i	$0.0392746\pi$
$73$	5.15017	+	8.92036i	0.602782	+	1.04405i	−0.389616	+	0.920978i	$0.627392\pi$
$74$	−6.71037	+	4.47934i	−0.780065	+	0.520713i
$75$	−2.16537			−0.250036
$76$	1.82628	+	8.52436i	0.209489	+	0.977811i
$77$	−12.9234			−1.47276
$78$	7.31626	−	4.88379i	0.828404	−	0.552980i
$79$	1.15575	+	2.00182i	0.130032	+	0.225223i	0.923689	−	0.383144i	$-0.125159\pi$
$79$	1.15575	+	2.00182i	0.130032	+	0.225223i	−0.793656	+	0.608366i	$0.791825\pi$
$80$	−1.04226	+	3.86183i	−0.116528	+	0.431765i
$81$	5.60717	+	9.71190i	0.623019	+	1.07910i
$82$	7.44545	+	3.67587i	0.822212	+	0.405932i
$83$		−	8.63031i		−	0.947299i	−0.880713	−	0.473650i	$-0.842936\pi$
$83$		−	8.63031i		−	0.947299i	0.880713	−	0.473650i	$-0.157064\pi$
$84$	2.21641	+	16.9537i	0.241830	+	1.84980i
$85$	2.44844	−	4.24083i	0.265571	−	0.459982i
$86$	11.7955	+	5.82352i	1.27194	+	0.627966i
$87$			7.88527i			0.845389i
$88$	−1.79393	−	9.08302i	−0.191234	−	0.968253i
$89$	−3.11895	−	1.80073i	−0.330608	−	0.190877i	0.325503	−	0.945541i	$-0.394466\pi$
$89$	−3.11895	−	1.80073i	−0.330608	−	0.190877i	−0.656111	+	0.754664i	$0.727800\pi$
$90$	−1.32601	−	1.98646i	−0.139774	−	0.209391i
$91$	5.67043	−	9.82147i	0.594422	−	1.02957i
$92$	8.31867	−	6.37121i	0.867282	−	0.664244i
$93$	11.0387	+	19.1195i	1.14466	+	1.98260i
$94$	0.392480	+	6.02983i	0.0404812	+	0.621929i
$95$	−3.93899	−	1.86665i	−0.404132	−	0.191514i
$96$	−11.6080	+	3.91116i	−1.18474	+	0.399181i
$97$	−6.05217	+	3.49422i	−0.614505	+	0.354785i	−0.774727	−	0.632296i	$-0.782112\pi$
$97$	−6.05217	+	3.49422i	−0.614505	+	0.354785i	0.160222	+	0.987081i	$0.448779\pi$
$98$	6.74220	+	10.1003i	0.681066	+	1.02028i
$99$	4.78755	+	2.76409i	0.481167	+	0.277802i
$100$	−1.21609	−	1.58781i	−0.121609	−	0.158781i
$101$	−4.36274	+	7.55649i	−0.434109	+	0.751899i	−0.997222	−	0.0744805i	$-0.976270\pi$
$101$	−4.36274	+	7.55649i	−0.434109	+	0.751899i	0.563113	+	0.826380i	$0.309603\pi$
$102$	14.9641	−	0.974006i	1.48166	−	0.0964410i
$103$	0.888621			0.0875584			0.0437792	−	0.999041i	$-0.486060\pi$
$103$	0.888621			0.0875584			0.0437792	+	0.999041i	$0.486060\pi$
$104$	7.69001	+	2.62204i	0.754068	+	0.257112i
$105$	−7.40363	−	4.27449i	−0.722520	−	0.417147i
$106$	0.668622	+	10.2723i	0.0649423	+	0.997735i
$107$	−14.9343			−1.44376			−0.721878	−	0.692021i	$-0.756721\pi$
$107$	−14.9343			−1.44376			−0.721878	+	0.692021i	$0.756721\pi$
$108$	−2.17774	+	5.24411i	−0.209553	+	0.504615i
$109$	9.85468	−	5.68960i	0.943907	−	0.544965i	0.0527241	−	0.998609i	$-0.483210\pi$
$109$	9.85468	−	5.68960i	0.943907	−	0.544965i	0.891183	+	0.453644i	$0.149876\pi$
$110$	4.15091	+	2.04934i	0.395774	+	0.195397i
$111$	10.6984	−	6.17670i	1.01544	−	0.586267i
$112$	−11.1869	+	11.1465i	−1.05706	+	1.05325i
$113$			16.1294i			1.51732i	0.651486	+	0.758661i	$0.274146\pi$
$113$			16.1294i			1.51732i	−0.651486	+	0.758661i	$0.725854\pi$
$114$	−1.94265	−	13.2061i	−0.181946	−	1.23687i
$115$			5.23910i			0.488548i
$116$	−5.78204	+	4.42842i	−0.536849	+	0.411169i
$117$	−4.20129	+	2.42562i	−0.388409	+	0.224248i
$118$	−2.69165	+	5.45192i	−0.247787	+	0.501890i
$119$	16.7429	−	9.66654i	1.53482	−	0.886131i
$120$	1.97655	−	5.79689i	0.180433	−	0.529181i
$121$	0.285065			0.0259150
$122$	−12.1243	+	0.789166i	−1.09768	+	0.0714478i
$123$	−11.0105	−	6.35689i	−0.992779	−	0.573181i
$124$	−7.82042	+	18.8320i	−0.702295	+	1.69117i
$125$	1.00000			0.0894427
$126$	−0.612461	−	9.40949i	−0.0545623	−	0.838264i
$127$	−2.57935	+	4.46757i	−0.228881	+	0.396433i	−0.957477	−	0.288511i	$-0.906840\pi$
$127$	−2.57935	+	4.46757i	−0.228881	+	0.396433i	0.728596	+	0.684944i	$0.240173\pi$
$128$	−9.38708	−	6.31528i	−0.829708	−	0.558197i
$129$	−17.4434	−	10.0709i	−1.53580	−	0.886696i
$130$	−3.37876	+	2.25541i	−0.296337	+	0.197812i
$131$	−5.65163	+	3.26297i	−0.493785	+	0.285087i	−0.726143	−	0.687543i	$-0.758689\pi$
$131$	−5.65163	+	3.26297i	−0.493785	+	0.285087i	0.232358	+	0.972630i	$0.425356\pi$
$132$	1.83765	+	14.0565i	0.159947	+	1.22346i
$133$	−9.78300	−	14.1579i	−0.848294	−	1.22765i
$134$	15.3364	−	0.998243i	1.32486	−	0.0862350i
$135$	−1.41958	−	2.45878i	−0.122178	−	0.211618i
$136$	9.11813	+	10.4257i	0.781873	+	0.893997i
$137$	5.44455	−	9.43024i	0.465159	−	0.805680i	−0.534049	−	0.845453i	$-0.679330\pi$
$137$	5.44455	−	9.43024i	0.465159	−	0.805680i	0.999209	+	0.0397735i	$0.0126636\pi$
$138$	−13.3439	+	8.90736i	−1.13590	+	0.758245i
$139$	12.7483	+	7.36021i	1.08129	+	0.624285i	0.931245	−	0.364394i	$-0.118724\pi$
$139$	12.7483	+	7.36021i	1.08129	+	0.624285i	0.150048	+	0.988679i	$0.452057\pi$
$140$	−1.02357	−	7.82945i	−0.0865075	−	0.661710i
$141$		−	9.25210i		−	0.779168i
$142$	3.54758	−	7.18559i	0.297706	−	0.603001i
$143$	4.70142	−	8.14310i	0.393153	−	0.680960i
$144$	6.52831	−	1.73662i	0.544026	−	0.144718i
$145$		−	3.64153i		−	0.302413i
$146$	6.44867	−	13.0617i	0.533696	−	1.08100i
$147$	−9.29703	−	16.1029i	−0.766806	−	1.32815i
$148$	10.5375	+	4.37593i	0.866175	+	0.359699i
$149$	−2.15970	−	3.74071i	−0.176929	−	0.306451i	0.763898	−	0.645337i	$-0.223283\pi$
$149$	−2.15970	−	3.74071i	−0.176929	−	0.306451i	−0.940827	+	0.338887i	$0.889950\pi$
$150$	1.70017	+	2.54698i	0.138818	+	0.207960i
$151$	−6.36061			−0.517619			−0.258810	−	0.965928i	$-0.583330\pi$
$151$	−6.36061			−0.517619			−0.258810	+	0.965928i	$0.583330\pi$
$152$	8.59268	−	8.84115i	0.696958	−	0.717112i
$153$	−8.27004			−0.668593
$154$	10.1470	+	15.2009i	0.817666	+	1.22492i
$155$	−5.09782	−	8.82968i	−0.409467	−	0.709217i
$156$	−11.4889	−	4.77104i	−0.919850	−	0.381989i
$157$	11.0461	+	19.1324i	0.881574	+	1.52693i	0.849591	+	0.527442i	$0.176849\pi$
$157$	11.0461	+	19.1324i	0.881574	+	1.52693i	0.0319830	+	0.999488i	$0.489818\pi$
$158$	1.44715	−	2.93119i	0.115129	−	0.233193i
$159$		−	15.7617i		−	1.24999i
$160$	5.36074	−	1.80623i	0.423804	−	0.142795i
$161$	−10.3421	+	17.9130i	−0.815070	+	1.41174i
$162$	7.02089	−	14.2208i	0.551613	−	1.11729i
$163$			15.8625i			1.24245i	0.783633	+	0.621224i	$0.213364\pi$
$163$			15.8625i			1.24245i	−0.783633	+	0.621224i	$0.786636\pi$
$164$	−1.52222	−	11.6437i	−0.118866	−	0.909222i
$165$	−6.13844	−	3.54403i	−0.477877	−	0.275902i
$166$	−10.1512	+	6.77620i	−0.787888	+	0.525935i
$167$	−1.48491	+	2.57193i	−0.114905	+	0.199022i	−0.917742	−	0.397177i	$-0.869990\pi$
$167$	−1.48491	+	2.57193i	−0.114905	+	0.199022i	0.802837	+	0.596199i	$0.203323\pi$
$168$	18.2012	−	15.9184i	1.40425	−	1.22813i
$169$	−2.37429	−	4.11239i	−0.182638	−	0.316338i
$170$	−6.91062	+	0.449810i	−0.530020	+	0.0344988i
$171$	0.596041	+	7.33730i	0.0455804	+	0.561097i
$172$	−2.41159	−	18.4466i	−0.183882	−	1.40654i
$173$	4.67239	−	2.69761i	0.355235	−	0.205095i	−0.311753	−	0.950163i	$-0.600916\pi$
$173$	4.67239	−	2.69761i	0.355235	−	0.205095i	0.666989	+	0.745068i	$0.267583\pi$
$174$	9.27489	−	6.19122i	0.703128	−	0.469355i
$175$	3.41910	+	1.97402i	0.258460	+	0.149222i
$176$	−9.27520	+	9.24173i	−0.699144	+	0.696622i
$177$	4.65482	−	8.06239i	0.349878	−	0.606006i
$178$	0.330816	+	5.08247i	0.0247957	+	0.380947i
$179$	10.2118			0.763267			0.381633	−	0.924314i	$-0.375362\pi$
$179$	10.2118			0.763267			0.381633	+	0.924314i	$0.375362\pi$
$180$	−1.29540	+	3.11939i	−0.0965534	+	0.232506i
$181$	0.907838	+	0.524141i	0.0674791	+	0.0389591i	0.533360	−	0.845888i	$-0.320929\pi$
$181$	0.907838	+	0.524141i	0.0674791	+	0.0389591i	−0.465881	+	0.884847i	$0.654262\pi$
$182$	−16.0045	+	1.04173i	−1.18633	+	0.0772181i
$183$	18.6034			1.37520
$184$	−14.0255	−	4.78224i	−1.03398	−	0.352551i
$185$	−4.94066	+	2.85249i	−0.363244	+	0.209719i
$186$	13.8218	−	27.9960i	1.01347	−	2.05277i
$187$	13.8818	−	8.01465i	1.01514	−	0.586089i
$188$	6.78431	−	5.19605i	0.494796	−	0.378961i
$189$		−	11.2091i		−	0.815342i
$190$	0.897142	+	6.09878i	0.0650855	+	0.442452i
$191$			18.6097i			1.34655i	0.739391	+	0.673276i	$0.235113\pi$
$191$			18.6097i			1.34655i	−0.739391	+	0.673276i	$0.764887\pi$
$192$	13.7146	+	10.5828i	0.989766	+	0.763746i
$193$	−3.12246	+	1.80275i	−0.224760	+	0.129765i	−0.608152	−	0.793820i	$-0.708089\pi$
$193$	−3.12246	+	1.80275i	−0.224760	+	0.129765i	0.383393	+	0.923586i	$0.374756\pi$
$194$	8.86196	+	4.37521i	0.636251	+	0.314122i
$195$	5.38676	−	3.11005i	0.385754	−	0.222715i
$196$	6.58655	−	15.8608i	0.470468	−	1.13291i
$197$	−14.0141			−0.998461			−0.499231	−	0.866469i	$-0.666384\pi$
$197$	−14.0141			−0.998461			−0.499231	+	0.866469i	$0.666384\pi$
$198$	−0.507799	−	7.80152i	−0.0360877	−	0.554430i
$199$	−9.33961	−	5.39222i	−0.662067	−	0.382245i	0.130997	−	0.991383i	$-0.458182\pi$
$199$	−9.33961	−	5.39222i	−0.662067	−	0.382245i	−0.793064	+	0.609138i	$0.791516\pi$
$200$	−0.912798	+	2.67709i	−0.0645445	+	0.189299i
$201$	−23.5320			−1.65982
$202$	12.3136	−	0.801491i	0.866385	−	0.0563927i
$203$	7.18845	−	12.4508i	0.504530	−	0.873872i
$204$	−12.8949	−	16.8364i	−0.902823	−	1.17879i
$205$	5.08478	+	2.93570i	0.355137	+	0.205038i
$206$	−0.697713	−	1.04522i	−0.0486120	−	0.0728242i
$207$	7.66258	−	4.42399i	0.532586	−	0.307489i
$208$	−2.95380	−	11.1040i	−0.204809	−	0.769921i
$209$	−8.11121	−	11.7385i	−0.561064	−	0.811968i
$210$	0.785277	+	12.0645i	0.0541893	+	0.832533i
$211$	−11.5911	−	20.0764i	−0.797965	−	1.38212i	−0.920940	−	0.389706i	$-0.872577\pi$
$211$	−11.5911	−	20.0764i	−0.797965	−	1.38212i	0.122975	−	0.992410i	$-0.460757\pi$
$212$	11.5576	−	8.85190i	0.793781	−	0.607951i
$213$	−6.13502	+	10.6262i	−0.420365	+	0.728093i
$214$	11.7259	+	17.5662i	0.801565	+	1.20080i
$215$	8.05559	+	4.65090i	0.549387	+	0.317189i
$216$	7.87816	−	1.55597i	0.536041	−	0.105870i
$217$		−	40.2528i		−	2.73254i
$218$	−14.4298	−	7.12411i	−0.977311	−	0.482505i
$219$	−11.1520	+	19.3159i	−0.753585	+	1.30525i
$220$	−0.848655	−	6.49150i	−0.0572163	−	0.437657i
$221$			14.0664i			0.946211i
$222$	−15.6652	−	7.73402i	−1.05138	−	0.519073i
$223$	7.65621	+	13.2609i	0.512698	+	0.888019i	0.999892	+	0.0147248i	$0.00468721\pi$
$223$	7.65621	+	13.2609i	0.512698	+	0.888019i	−0.487194	+	0.873294i	$0.661979\pi$
$224$	21.8944	+	4.40652i	1.46288	+	0.294423i
$225$	−0.844418	−	1.46258i	−0.0562946	−	0.0975050i
$226$	18.9718	−	12.6642i	1.26199	−	0.842409i
$227$	−17.6163			−1.16923			−0.584617	−	0.811310i	$-0.698755\pi$
$227$	−17.6163			−1.16923			−0.584617	+	0.811310i	$0.698755\pi$
$228$	−14.0082	+	12.6540i	−0.927713	+	0.838030i
$229$	−17.5330			−1.15861			−0.579307	−	0.815110i	$-0.696677\pi$
$229$	−17.5330			−1.15861			−0.579307	+	0.815110i	$0.696677\pi$
$230$	6.16239	−	4.11355i	0.406336	−	0.271239i
$231$	−13.9920	−	24.2348i	−0.920604	−	1.59453i
$232$	9.74869	+	3.32398i	0.640033	+	0.218230i
$233$	5.57714	+	9.65990i	0.365371	+	0.632841i	0.988836	−	0.149011i	$-0.0476088\pi$
$233$	5.57714	+	9.65990i	0.365371	+	0.632841i	−0.623465	+	0.781851i	$0.714276\pi$
$234$	6.15178	+	3.03718i	0.402155	+	0.198547i
$235$			4.27275i			0.278724i
$236$	8.52610	−	1.11465i	0.555002	−	0.0725572i
$237$	−2.50263	+	4.33469i	−0.162564	+	0.281568i
$238$	−24.5160	−	12.1037i	−1.58914	−	0.784569i
$239$		−	1.42550i		−	0.0922080i	−0.998937	−	0.0461040i	$-0.985319\pi$
$239$		−	1.42550i		−	0.0922080i	0.998937	−	0.0461040i	$-0.0146806\pi$
$240$	−8.37039	+	2.22663i	−0.540307	+	0.143729i
$241$	13.4135	+	7.74428i	0.864038	+	0.498853i	0.865362	−	0.501146i	$-0.167088\pi$
$241$	13.4135	+	7.74428i	0.864038	+	0.498853i	−0.00132429	+	0.999999i	$0.500422\pi$
$242$	−0.223823	−	0.335302i	−0.0143879	−	0.0215541i
$243$	−7.88288	+	13.6535i	−0.505687	+	0.875875i
$244$	10.4478	+	13.6413i	0.668851	+	0.873297i
$245$	4.29350	+	7.43657i	0.274302	+	0.475105i
$246$	1.16784	+	17.9420i	0.0744588	+	1.14394i
$247$	12.4800	−	1.01380i	0.794080	−	0.0645066i
$248$	28.2911	−	5.58760i	1.79649	−	0.354813i
$249$	16.1841	−	9.34391i	1.02563	−	0.592146i
$250$	−0.785164	−	1.17623i	−0.0496581	−	0.0743913i
$251$	−3.07280	−	1.77408i	−0.193953	−	0.111979i	0.399879	−	0.916568i	$-0.369052\pi$
$251$	−3.07280	−	1.77408i	−0.193953	−	0.111979i	−0.593832	+	0.804589i	$0.702386\pi$
$252$	−10.5868	+	8.10838i	−0.666909	+	0.510780i
$253$	−8.57475	+	14.8519i	−0.539090	+	0.933731i
$254$	7.28011	−	0.473860i	0.456795	−	0.0297326i
$255$	10.6036			0.664022
$256$	−0.0578348	+	15.9999i	−0.00361468	+	0.999993i
$257$	22.8593	+	13.1978i	1.42593	+	0.823259i	0.996796	−	0.0799838i	$-0.0254869\pi$
$257$	22.8593	+	13.1978i	1.42593	+	0.823259i	0.429130	+	0.903243i	$0.358820\pi$
$258$	1.85016	+	28.4247i	0.115186	+	1.76965i
$259$	−22.5235			−1.39954
$260$	5.30575	+	2.20333i	0.329049	+	0.136645i
$261$	−5.32601	+	3.07497i	−0.329672	+	0.190336i
$262$	8.27546	+	4.08565i	0.511260	+	0.252413i
$263$	13.2686	−	7.66063i	0.818177	−	0.472375i	−0.0316106	−	0.999500i	$-0.510064\pi$
$263$	13.2686	−	7.66063i	0.818177	−	0.472375i	0.849787	+	0.527126i	$0.176730\pi$
$264$	15.0908	−	13.1982i	0.928777	−	0.812291i
$265$			7.27899i			0.447145i
$266$	−8.97169	+	22.6233i	−0.550090	+	1.38713i
$267$		−	7.79848i		−	0.477259i
$268$	−13.2158	−	17.2554i	−0.807281	−	1.05404i
$269$	5.16145	−	2.97997i	0.314699	−	0.181692i	−0.334328	−	0.942457i	$-0.608509\pi$
$269$	5.16145	−	2.97997i	0.314699	−	0.181692i	0.649027	+	0.760765i	$0.275176\pi$
$270$	−1.77749	+	3.60030i	−0.108175	+	0.219107i
$271$	−18.3221	+	10.5783i	−1.11299	+	0.642585i	−0.939602	−	0.342269i	$-0.888805\pi$
$271$	−18.3221	+	10.5783i	−1.11299	+	0.642585i	−0.173387	+	0.984854i	$0.555471\pi$
$272$	5.10381	−	18.9109i	0.309464	−	1.14664i
$273$	24.5572			1.48627
$274$	−15.3670	+	1.00023i	−0.928354	+	0.0604263i
$275$	2.83482	+	1.63668i	0.170946	+	0.0986957i
$276$	20.9542	+	8.70172i	1.26130	+	0.523782i
$277$	−5.50294			−0.330640			−0.165320	−	0.986240i	$-0.552866\pi$
$277$	−5.50294			−0.330640			−0.165320	+	0.986240i	$0.552866\pi$
$278$	−1.35216	−	20.7738i	−0.0810974	−	1.24593i
$279$	−8.60938	+	14.9119i	−0.515430	+	0.892751i
$280$	−8.40557	+	7.35136i	−0.502329	+	0.439328i
$281$	18.5036	+	10.6831i	1.10383	+	0.637299i	0.937226	−	0.348724i	$-0.113385\pi$
$281$	18.5036	+	10.6831i	1.10383	+	0.637299i	0.166609	+	0.986023i	$0.446718\pi$
$282$	−10.8826	+	7.26441i	−0.648050	+	0.432590i
$283$	−1.58472	+	0.914940i	−0.0942020	+	0.0543875i	−0.546361	−	0.837550i	$-0.683987\pi$
$283$	−1.58472	+	0.914940i	−0.0942020	+	0.0543875i	0.452159	+	0.891937i	$0.350654\pi$
$284$	−11.2373	+	1.46909i	−0.666813	+	0.0871747i
$285$	−0.764225	−	9.40765i	−0.0452688	−	0.557261i
$286$	−13.2695	+	0.863711i	−0.784645	+	0.0510723i
$287$	11.5903	+	20.0749i	0.684152	+	1.18499i
$288$	−7.16846	−	6.31527i	−0.422405	−	0.372131i
$289$	−3.48974	+	6.04440i	−0.205279	+	0.355553i
$290$	−4.28328	+	2.85920i	−0.251523	+	0.167898i
$291$	−13.1052	−	7.56629i	−0.768241	−	0.443544i
$292$	−20.4269	+	2.67047i	−1.19539	+	0.156278i
$293$			7.77927i			0.454470i	0.973840	+	0.227235i	$0.0729685\pi$
$293$			7.77927i			0.454470i	−0.973840	+	0.227235i	$0.927031\pi$
$294$	−11.6411	+	23.5789i	−0.678921	+	1.37515i
$295$	−2.14966	+	3.72333i	−0.125158	+	0.216780i
$296$	−3.12655	−	15.8303i	−0.181727	−	0.920119i
$297$		−	9.29360i		−	0.539269i
$298$	−2.70422	+	5.47737i	−0.156651	+	0.317295i
$299$	−7.52473	−	13.0332i	−0.435166	−	0.753730i
$300$	1.66092	−	3.99959i	0.0958932	−	0.230916i
$301$	18.3619	+	31.8038i	1.05836	+	1.83314i
$302$	4.99412	+	7.48155i	0.287379	+	0.430515i
$303$	−18.8939			−1.08543
$304$	−17.1459	−	3.16522i	−0.983384	−	0.181538i
$305$	−8.59131			−0.491937
$306$	6.49333	+	9.72747i	0.371199	+	0.556083i
$307$	1.71914	+	2.97764i	0.0981167	+	0.169943i	0.910905	−	0.412616i	$-0.135385\pi$
$307$	1.71914	+	2.97764i	0.0981167	+	0.169943i	−0.812788	+	0.582559i	$0.802052\pi$
$308$	9.91270	−	23.8703i	0.564829	−	1.36014i
$309$	0.962098	+	1.66640i	0.0547318	+	0.0947983i
$310$	−6.38312	+	12.9290i	−0.362537	+	0.734315i
$311$			15.7206i			0.891434i	0.895174	+	0.445717i	$0.147051\pi$
$311$			15.7206i			0.891434i	−0.895174	+	0.445717i	$0.852949\pi$
$312$	3.40885	+	17.2597i	0.192988	+	0.977137i
$313$	15.6032	−	27.0256i	0.881947	−	1.52758i	0.0327730	−	0.999463i	$-0.489566\pi$
$313$	15.6032	−	27.0256i	0.881947	−	1.52758i	0.849174	−	0.528114i	$-0.177101\pi$
$314$	13.8311	−	28.0148i	0.780535	−	1.58097i
$315$		−	6.66759i		−	0.375676i
$316$	−4.58400	+	0.599282i	−0.257870	+	0.0337122i
$317$	−5.56970	−	3.21567i	−0.312826	−	0.180610i	0.335365	−	0.942088i	$-0.391140\pi$
$317$	−5.56970	−	3.21567i	−0.312826	−	0.180610i	−0.648190	+	0.761478i	$0.724474\pi$
$318$	−18.5394	+	12.3755i	−1.03964	+	0.693985i
$319$	5.96003	−	10.3231i	0.333698	−	0.577981i
$320$	−6.33360	−	4.88728i	−0.354059	−	0.273207i
$321$	−16.1692	−	28.0058i	−0.902476	−	1.56313i
$322$	29.1900	−	1.89997i	1.62670	−	0.105881i
$323$	19.2888	+	9.14076i	1.07326	+	0.508605i
$324$	−22.2394	+	2.90743i	−1.23552	+	0.161524i
$325$	−2.48768	+	1.43626i	−0.137992	+	0.0796696i
$326$	18.6580	−	12.4547i	1.03337	−	0.689800i
$327$	21.3390	+	12.3201i	1.18005	+	0.681303i
$328$	−12.5005	+	10.9327i	−0.690225	+	0.603658i
$329$	−8.43450	+	14.6090i	−0.465009	+	0.805419i
$330$	0.651083	+	10.0029i	0.0358410	+	0.550639i
$331$	10.1401			0.557348			0.278674	−	0.960386i	$-0.410105\pi$
$331$	10.1401			0.557348			0.278674	+	0.960386i	$0.410105\pi$
$332$	15.9407	+	6.61976i	0.874862	+	0.363306i
$333$	8.34396	+	4.81739i	0.457246	+	0.263991i
$334$	4.19108	−	0.272796i	0.229326	−	0.0149267i
$335$	10.8674			0.593751
$336$	−33.0146	−	8.91023i	−1.80110	−	0.486093i
$337$	−17.7155	+	10.2280i	−0.965025	+	0.557157i	−0.897716	−	0.440575i	$-0.854775\pi$
$337$	−17.7155	+	10.2280i	−0.965025	+	0.557157i	−0.0673089	+	0.997732i	$0.521441\pi$
$338$	−2.97291	+	6.02161i	−0.161705	+	0.327532i
$339$	−30.2468	+	17.4630i	−1.64278	+	0.948461i
$340$	5.95504	+	7.77530i	0.322958	+	0.421675i
$341$		−	33.3741i		−	1.80731i
$342$	8.16237	−	6.46206i	0.441370	−	0.349428i
$343$			6.26556i			0.338309i
$344$	−19.8040	+	17.3202i	−1.06776	+	0.933843i
$345$	−9.82471	+	5.67230i	−0.528945	+	0.305386i
$346$	−6.84160	−	3.37775i	−0.367807	−	0.181589i
$347$	16.9414	−	9.78112i	0.909462	−	0.525078i	0.0292041	−	0.999573i	$-0.490703\pi$
$347$	16.9414	−	9.78112i	0.909462	−	0.525078i	0.880258	+	0.474495i	$0.157369\pi$
$348$	−14.5646	−	6.04829i	−0.780745	−	0.324222i
$349$	4.25268			0.227641			0.113820	−	0.993501i	$-0.463691\pi$
$349$	4.25268			0.227641			0.113820	+	0.993501i	$0.463691\pi$
$350$	−0.362652	−	5.57158i	−0.0193846	−	0.297813i
$351$	7.06292	+	4.07778i	0.376991	+	0.217656i
$352$	18.1530	+	3.65350i	0.967556	+	0.194732i
$353$	30.7154			1.63482			0.817409	−	0.576058i	$-0.195410\pi$
$353$	30.7154			1.63482			0.817409	+	0.576058i	$0.195410\pi$
$354$	−13.1380	+	0.855150i	−0.698278	+	0.0454507i
$355$	2.83324	−	4.90732i	0.150373	−	0.260453i
$356$	5.71841	−	4.37968i	0.303075	−	0.232123i
$357$	36.2547	+	20.9317i	1.91880	+	1.10782i
$358$	−8.01794	−	12.0114i	−0.423762	−	0.634825i
$359$	−24.3194	+	14.0408i	−1.28353	+	0.741046i	−0.977492	−	0.210974i	$-0.932337\pi$
$359$	−24.3194	+	14.0408i	−1.28353	+	0.741046i	−0.306037	+	0.952020i	$0.599003\pi$
$360$	4.68623	−	0.925547i	0.246986	−	0.0487806i
$361$	6.71963	−	17.7721i	0.353665	−	0.935372i
$362$	−0.0962913	−	1.47936i	−0.00506096	−	0.0777536i
$363$	0.308636	+	0.534573i	0.0161992	+	0.0280578i
$364$	13.7915	+	18.0071i	0.722870	+	0.943827i
$365$	5.15017	−	8.92036i	0.269572	−	0.466913i
$366$	−14.6067	−	21.8819i	−0.763504	−	1.14378i
$367$	20.2665	+	11.7009i	1.05790	+	0.610781i	0.924852	−	0.380328i	$-0.124189\pi$
$367$	20.2665	+	11.7009i	1.05790	+	0.610781i	0.133052	+	0.991109i	$0.457522\pi$
$368$	5.38732	+	20.2521i	0.280833	+	1.05571i
$369$		−	9.91584i		−	0.516198i
$370$	7.23441	+	3.57168i	0.376099	+	0.185683i
$371$	−14.3689	+	24.8876i	−0.745994	+	1.29210i
$372$	−43.7821	+	5.72378i	−2.27000	+	0.296764i
$373$		−	30.4239i		−	1.57529i	−0.616130	−	0.787645i	$-0.711300\pi$
$373$		−	30.4239i		−	1.57529i	0.616130	−	0.787645i	$-0.288700\pi$
$374$	−20.3265	−	10.0354i	−1.05106	−	0.518916i
$375$	1.08269	+	1.87527i	0.0559097	+	0.0968384i
$376$	−11.4385	−	3.90016i	−0.589898	−	0.201135i
$377$	5.23020	+	9.05897i	0.269369	+	0.466561i
$378$	−13.1845	+	8.80098i	−0.678137	+	0.452673i
$379$	−4.20509			−0.216001			−0.108000	−	0.994151i	$-0.534445\pi$
$379$	−4.20509			−0.216001			−0.108000	+	0.994151i	$0.534445\pi$
$380$	6.46917	−	5.84379i	0.331861	−	0.299780i
$381$	−11.1705			−0.572283
$382$	21.8893	−	14.6117i	1.11996	−	0.747598i
$383$	−14.9952	−	25.9725i	−0.766220	−	1.32713i	−0.939599	−	0.342277i	$-0.888802\pi$
$383$	−14.9952	−	25.9725i	−0.766220	−	1.32713i	0.173379	−	0.984855i	$-0.444531\pi$
$384$	1.67958	−	24.4407i	0.0857108	−	1.24724i
$385$	6.46169	+	11.1920i	0.329318	+	0.570396i
$386$	4.57210	+	2.25728i	0.232714	+	0.114892i
$387$		−	15.7092i		−	0.798545i
$388$	−1.81183	−	13.8590i	−0.0919816	−	0.703582i
$389$	−11.8853	+	20.5860i	−0.602609	+	1.04375i	0.389815	+	0.920893i	$0.372539\pi$
$389$	−11.8853	+	20.5860i	−0.602609	+	1.04375i	−0.992424	+	0.122857i	$0.960794\pi$
$390$	−7.88762	−	3.89418i	−0.399405	−	0.197189i
$391$		−	25.6553i		−	1.29744i
$392$	−23.8274	+	4.70601i	−1.20347	+	0.237689i
$393$	−12.2379	−	7.06555i	−0.617320	−	0.356410i
$394$	11.0033	+	16.4838i	0.554340	+	0.830441i
$395$	1.15575	−	2.00182i	0.0581522	−	0.100723i
$396$	−8.77768	+	6.72276i	−0.441095	+	0.337831i
$397$	−8.44480	−	14.6268i	−0.423832	−	0.734099i	0.572478	−	0.819920i	$-0.305982\pi$
$397$	−8.44480	−	14.6268i	−0.423832	−	0.734099i	−0.996311	+	0.0858208i	$0.972649\pi$
$398$	0.990620	+	15.2193i	0.0496553	+	0.762875i
$399$	15.9579	−	33.6743i	0.798895	−	1.68582i
$400$	3.86557	−	1.02829i	0.193278	−	0.0514146i
$401$	13.8527	−	7.99788i	0.691773	−	0.399395i	−0.112503	−	0.993651i	$-0.535887\pi$
$401$	13.8527	−	7.99788i	0.691773	−	0.399395i	0.804276	+	0.594256i	$0.202553\pi$
$402$	18.4765	+	27.6791i	0.921524	+	1.38051i
$403$	25.3635	+	14.6436i	1.26345	+	0.729451i
$404$	−10.6110	−	13.8544i	−0.527915	−	0.689281i
$405$	5.60717	−	9.71190i	0.278623	−	0.482588i
$406$	−20.2891	+	1.32061i	−1.00693	+	0.0655407i
$407$	−18.6745			−0.925660
$408$	−9.67892	+	28.3867i	−0.479178	+	1.40535i
$409$	0.440286	+	0.254199i	0.0217707	+	0.0125693i	0.510846	−	0.859672i	$-0.329332\pi$
$409$	0.440286	+	0.254199i	0.0217707	+	0.0125693i	−0.489075	+	0.872242i	$0.662666\pi$
$410$	−0.539326	−	8.28589i	−0.0266354	−	0.409211i
$411$	23.5790			1.16306
$412$	−0.681605	+	1.64134i	−0.0335803	+	0.0808631i
$413$	−14.6998	+	8.48696i	−0.723332	+	0.417616i
$414$	−11.2200	−	5.53940i	−0.551433	−	0.272247i
$415$	−7.47406	+	4.31515i	−0.366887	+	0.211823i
$416$	−10.7416	+	12.1928i	−0.526650	+	0.597800i
$417$			31.8752i			1.56093i
$418$	−7.43854	+	18.7573i	−0.363831	+	0.917449i
$419$			1.19740i			0.0584969i	0.999572	+	0.0292484i	$0.00931139\pi$
$419$			1.19740i			0.0584969i	−0.999572	+	0.0292484i	$0.990689\pi$
$420$	13.5741	−	10.3963i	0.662349	−	0.507288i
$421$	26.5762	−	15.3438i	1.29524	−	0.747809i	0.315665	−	0.948871i	$-0.397772\pi$
$421$	26.5762	−	15.3438i	1.29524	−	0.747809i	0.979579	+	0.201062i	$0.0644391\pi$
$422$	−14.5135	+	29.3971i	−0.706508	+	1.43103i
$423$	6.24923	−	3.60799i	0.303848	−	0.175427i
$424$	−19.4865	−	6.64425i	−0.946348	−	0.322673i
$425$	−4.89688			−0.237534
$426$	17.3158	−	1.12708i	0.838954	−	0.0546073i
$427$	−29.3746	−	16.9594i	−1.42153	−	0.820723i
$428$	11.4552	−	27.5847i	0.553706	−	1.33336i
$429$	20.3607			0.983022
$430$	−0.854429	−	13.1270i	−0.0412042	−	0.633038i
$431$	15.4700	−	26.7949i	0.745165	−	1.29066i	−0.204953	−	0.978772i	$-0.565704\pi$
$431$	15.4700	−	26.7949i	0.745165	−	1.29066i	0.950118	−	0.311891i	$-0.100963\pi$
$432$	−8.01582	−	8.04485i	−0.385661	−	0.387058i
$433$	−18.7213	−	10.8088i	−0.899690	−	0.519436i	−0.0225906	−	0.999745i	$-0.507191\pi$
$433$	−18.7213	−	10.8088i	−0.899690	−	0.519436i	−0.877100	+	0.480308i	$0.840525\pi$
$434$	−47.3465	+	31.6050i	−2.27271	+	1.51709i
$435$	6.82884	−	3.94263i	0.327418	−	0.189035i
$436$	2.95018	+	22.5664i	0.141288	+	1.08073i
$437$	−22.7617	+	1.84903i	−1.08884	+	0.0884513i
$438$	31.4761	−	2.04877i	1.50399	−	0.0978941i
$439$	1.17251	+	2.03085i	0.0559609	+	0.0969270i	0.892649	−	0.450753i	$-0.148844\pi$
$439$	1.17251	+	2.03085i	0.0559609	+	0.0969270i	−0.836688	+	0.547680i	$0.815511\pi$
$440$	−6.96916	+	6.09510i	−0.332242	+	0.290572i
$441$	7.25103	−	12.5591i	0.345287	−	0.598055i
$442$	16.5454	−	11.0445i	0.786983	−	0.525331i
$443$	−12.2810	−	7.09045i	−0.583489	−	0.336877i	0.179030	−	0.983844i	$-0.442704\pi$
$443$	−12.2810	−	7.09045i	−0.583489	−	0.336877i	−0.762519	+	0.646966i	$0.776037\pi$
$444$	3.20275	+	24.4983i	0.151996	+	1.16264i
$445$			3.60145i			0.170725i
$446$	9.58655	−	19.4175i	0.453936	−	0.919444i
$447$	4.67655	−	8.10002i	0.221193	−	0.383118i
$448$	−12.0076	−	29.2128i	−0.567308	−	1.38017i
$449$		−	0.221704i		−	0.0104629i	−0.999986	−	0.00523144i	$-0.998335\pi$
$449$		−	0.221704i		−	0.0104629i	0.999986	−	0.00523144i	$-0.00166523\pi$
$450$	−1.05732	+	2.14159i	−0.0498425	+	0.100956i
$451$	9.60963	+	16.6444i	0.452500	+	0.783753i
$452$	−29.7920	−	12.3718i	−1.40130	−	0.581920i
$453$	−6.88655	−	11.9279i	−0.323558	−	0.560419i
$454$	13.8317	+	20.7208i	0.649152	+	0.972476i
$455$	−11.3409			−0.531667
$456$	25.8827	+	6.54138i	1.21207	+	0.306328i
$457$	−0.686147			−0.0320966			−0.0160483	−	0.999871i	$-0.505109\pi$
$457$	−0.686147			−0.0320966			−0.0160483	+	0.999871i	$0.505109\pi$
$458$	13.7663	+	20.6228i	0.643256	+	0.963642i
$459$	6.95151	+	12.0404i	0.324469	+	0.561996i
$460$	−9.67696	−	4.01858i	−0.451191	−	0.187367i
$461$	−0.885286	−	1.53336i	−0.0412319	−	0.0714157i	0.844673	−	0.535283i	$-0.179795\pi$
$461$	−0.885286	−	1.53336i	−0.0412319	−	0.0714157i	−0.885905	+	0.463867i	$0.846462\pi$
$462$	−17.5197	+	35.4861i	−0.815091	+	1.65096i
$463$		−	24.6835i		−	1.14714i	−0.819157	−	0.573570i	$-0.805558\pi$
$463$		−	24.6835i		−	1.14714i	0.819157	−	0.573570i	$-0.194442\pi$
$464$	−3.74455	−	14.0766i	−0.173837	−	0.653489i
$465$	11.0387	−	19.1195i	0.511906	−	0.886648i
$466$	6.98329	−	14.1446i	0.323495	−	0.655236i
$467$			5.61898i			0.260015i	0.991513	+	0.130008i	$0.0415002\pi$
$467$			5.61898i			0.260015i	−0.991513	+	0.130008i	$0.958500\pi$
$468$	−1.25773	−	9.62060i	−0.0581387	−	0.444712i
$469$	37.1569	+	21.4525i	1.71574	+	0.990585i
$470$	5.02574	−	3.35481i	0.231820	−	0.154746i
$471$	−23.9189	+	41.4287i	−1.10212	+	1.90894i
$472$	−8.00547	−	9.15348i	−0.368481	−	0.421323i
$473$	15.2241	+	26.3689i	0.700005	+	1.21244i
$474$	7.06357	−	0.459766i	0.324441	−	0.0211177i
$475$	0.352930	+	4.34459i	0.0161935	+	0.199343i
$476$	5.01230	+	38.3399i	0.229739	+	1.75731i
$477$	10.6461	−	6.14651i	0.487450	−	0.281430i
$478$	−1.67672	+	1.11925i	−0.0766913	+	0.0511934i
$479$	8.72341	+	5.03646i	0.398583	+	0.230122i	0.685872	−	0.727722i	$-0.259421\pi$
$479$	8.72341	+	5.03646i	0.398583	+	0.230122i	−0.287289	+	0.957844i	$0.592754\pi$
$480$	9.19116	+	8.09724i	0.419517	+	0.369587i
$481$	8.19386	−	14.1922i	0.373608	−	0.647108i
$482$	−1.42272	−	21.8579i	−0.0648032	−	0.995599i
$483$	−44.7889			−2.03797
$484$	−0.218655	+	0.526534i	−0.00993888	+	0.0239334i
$485$	6.05217	+	3.49422i	0.274815	+	0.158665i
$486$	22.2491	−	1.44818i	1.00924	−	0.0656910i
$487$	−9.47822			−0.429499			−0.214749	−	0.976669i	$-0.568894\pi$
$487$	−9.47822			−0.429499			−0.214749	+	0.976669i	$0.568894\pi$
$488$	7.84213	−	22.9997i	0.354996	−	1.04115i
$489$	−29.7465	+	17.1741i	−1.34518	+	0.776641i
$490$	5.37601	−	10.8891i	0.242864	−	0.491918i
$491$	−30.0353	+	17.3409i	−1.35548	+	0.782584i	−0.989010	−	0.147848i	$-0.952766\pi$
$491$	−30.0353	+	17.3409i	−1.35548	+	0.782584i	−0.366465	+	0.930432i	$0.619432\pi$
$492$	20.1870	−	15.4611i	0.910101	−	0.697039i
$493$			17.8321i			0.803120i
$494$	−10.9913	−	13.8833i	−0.494521	−	0.624639i
$495$		−	5.52818i		−	0.248473i
$496$	−28.7854	−	28.8897i	−1.29250	−	1.29719i
$497$	19.3743	−	11.1857i	0.869055	−	0.501749i
$498$	−23.6978	−	11.6998i	−1.06192	−	0.524279i
$499$	29.8481	−	17.2328i	1.33618	−	0.771447i	0.349945	−	0.936770i	$-0.386200\pi$
$499$	29.8481	−	17.2328i	1.33618	−	0.771447i	0.986239	+	0.165323i	$0.0528668\pi$
$500$	−0.767036	+	1.84707i	−0.0343029	+	0.0826033i
$501$	−6.43075			−0.287305
$502$	0.325921	+	5.00726i	0.0145466	+	0.223485i
$503$	−4.58096	−	2.64482i	−0.204255	−	0.117927i	0.394384	−	0.918946i	$-0.370958\pi$
$503$	−4.58096	−	2.64482i	−0.204255	−	0.117927i	−0.598639	+	0.801019i	$0.704291\pi$
$504$	17.8497	+	6.08616i	0.795090	+	0.271099i
$505$	8.72549			0.388279
$506$	24.2018	−	1.57529i	1.07590	−	0.0700302i
$507$	5.14122	−	8.90485i	0.228330	−	0.395478i
$508$	−6.27345	−	8.19103i	−0.278339	−	0.363418i
$509$	−18.3731	−	10.6077i	−0.814373	−	0.470178i	0.0340992	−	0.999418i	$-0.489144\pi$
$509$	−18.3731	−	10.6077i	−0.814373	−	0.470178i	−0.848472	+	0.529240i	$0.822477\pi$
$510$	−8.32554	−	12.4723i	−0.368661	−	0.552281i
$511$	35.2179	−	20.3331i	1.55795	−	0.899483i
$512$	18.8650	−	12.4945i	0.833722	−	0.552184i
$513$	10.1814	−	7.03526i	0.449519	−	0.310614i
$514$	−2.42461	−	37.2503i	−0.106945	−	1.64304i
$515$	−0.444311	−	0.769569i	−0.0195787	−	0.0339112i
$516$	31.9814	−	24.4943i	1.40790	−	1.07830i
$517$	−6.99315	+	12.1125i	−0.307558	+	0.532706i
$518$	17.6846	+	26.4928i	0.777017	+	1.16403i
$519$	10.1175	+	5.84132i	0.444108	+	0.256406i
$520$	−1.57425	−	7.97077i	−0.0690356	−	0.349541i
$521$			25.0477i			1.09736i	0.836032	+	0.548680i	$0.184870\pi$
$521$			25.0477i			1.09736i	−0.836032	+	0.548680i	$0.815130\pi$
$522$	7.79867	+	3.85026i	0.341338	+	0.168521i
$523$	−5.53411	+	9.58537i	−0.241990	+	0.419139i	−0.961281	−	0.275570i	$-0.911133\pi$
$523$	−5.53411	+	9.58537i	−0.241990	+	0.419139i	0.719291	+	0.694709i	$0.244467\pi$
$524$	−1.69192	−	12.9418i	−0.0739118	−	0.565363i
$525$			8.54897i			0.373108i
$526$	−19.4287	−	9.59208i	−0.847131	−	0.418235i
$527$	24.9634	+	43.2379i	1.08742	+	1.88347i
$528$	−27.3728	−	7.38758i	−1.19125	−	0.321503i
$529$	2.22407	+	3.85221i	0.0966988	+	0.167487i
$530$	8.56177	−	5.71520i	0.371900	−	0.248252i
$531$	7.26086			0.315095
$532$	33.6545	−	7.21024i	1.45911	−	0.312603i
$533$	−16.8658			−0.730538
$534$	−9.17281	+	6.12309i	−0.396947	+	0.264972i
$535$	7.46716	+	12.9335i	0.322834	+	0.559164i
$536$	−9.91977	+	29.0931i	−0.428469	+	1.25663i
$537$	11.0562	+	19.1499i	0.477110	+	0.826378i
$538$	−7.55771	−	3.73130i	−0.325836	−	0.160868i
$539$			28.1084i			1.21072i
$540$	5.63040	−	0.736081i	0.242294	−	0.0316759i
$541$	−17.7878	+	30.8094i	−0.764757	+	1.32460i	0.175618	+	0.984458i	$0.443808\pi$
$541$	−17.7878	+	30.8094i	−0.764757	+	1.32460i	−0.940375	+	0.340140i	$0.889526\pi$
$542$	26.8283	+	13.2454i	1.15238	+	0.568937i
$543$			2.26992i			0.0974116i
$544$	−26.2509	+	8.84490i	−1.12550	+	0.379222i
$545$	−9.85468	−	5.68960i	−0.422128	−	0.243716i
$546$	−19.2814	−	28.8849i	−0.825168	−	1.23616i
$547$	−12.9116	+	22.3636i	−0.552061	+	0.956197i	0.446065	+	0.895001i	$0.352825\pi$
$547$	−12.9116	+	22.3636i	−0.552061	+	0.956197i	−0.998126	+	0.0611966i	$0.980508\pi$
$548$	13.2421	+	17.2898i	0.565675	+	0.738583i
$549$	7.25466	+	12.5654i	0.309621	+	0.536280i
$550$	−0.300680	−	4.61947i	−0.0128210	−	0.196975i
$551$	15.8209	−	1.28520i	0.673995	−	0.0547516i
$552$	−6.21727	−	31.4793i	−0.264625	−	1.33985i
$553$	7.90327	−	4.56296i	0.336081	−	0.194037i
$554$	4.32071	+	6.47272i	0.183569	+	0.275000i
$555$	−10.6984	−	6.17670i	−0.454120	−	0.262186i
$556$	−23.3732	+	17.9013i	−0.991243	+	0.759185i
$557$	6.03429	−	10.4517i	0.255681	−	0.442852i	−0.709399	−	0.704807i	$-0.751034\pi$
$557$	6.03429	−	10.4517i	0.255681	−	0.442852i	0.965080	+	0.261954i	$0.0843670\pi$
$558$	24.2996	−	1.58165i	1.02868	−	0.0669567i
$559$	−26.7197			−1.13012
$560$	15.2466	+	4.11487i	0.644288	+	0.173885i
$561$	30.0592	+	17.3547i	1.26910	+	0.732716i
$562$	−1.96262	−	30.1525i	−0.0827881	−	1.27191i
$563$	−10.6952			−0.450749			−0.225374	−	0.974272i	$-0.572360\pi$
$563$	−10.6952			−0.450749			−0.225374	+	0.974272i	$0.572360\pi$
$564$	17.0892	+	7.09670i	0.719587	+	0.298825i
$565$	13.9684	−	8.06468i	0.587656	−	0.339283i
$566$	2.32045	+	1.14562i	0.0975356	+	0.0481541i
$567$	38.3430	−	22.1373i	1.61025	−	0.929680i
$568$	10.5511	+	12.0642i	0.442716	+	0.506203i
$569$		−	26.6437i		−	1.11696i	−0.829518	−	0.558481i	$-0.811385\pi$
$569$		−	26.6437i		−	1.11696i	0.829518	−	0.558481i	$-0.188615\pi$
$570$	−10.4655	+	8.28545i	−0.438352	+	0.347039i
$571$			15.9522i			0.667580i	0.942647	+	0.333790i	$0.108328\pi$
$571$			15.9522i			0.667580i	−0.942647	+	0.333790i	$0.891672\pi$
$572$	11.4347	+	14.9299i	0.478108	+	0.624250i
$573$	−34.8982	+	20.1485i	−1.45789	+	0.841715i
$574$	14.5125	−	29.3949i	0.605739	−	1.22692i
$575$	4.53719	−	2.61955i	0.189214	−	0.109243i
$576$	−1.79981	+	13.3903i	−0.0749920	+	0.557928i
$577$	−29.4017			−1.22401			−0.612005	−	0.790854i	$-0.709637\pi$
$577$	−29.4017			−1.22401			−0.612005	+	0.790854i	$0.709637\pi$
$578$	9.84963	−	0.641109i	0.409690	−	0.0266666i
$579$	−6.76129	−	3.90363i	−0.280990	−	0.162230i
$580$	6.72615	+	2.79319i	0.279288	+	0.115981i
$581$	−34.0728			−1.41358
$582$	1.39002	+	21.3555i	0.0576184	+	0.885215i
$583$	−11.9134	+	20.6346i	−0.493403	+	0.854599i
$584$	19.1795	+	21.9300i	0.793655	+	0.907468i
$585$	4.20129	+	2.42562i	0.173702	+	0.100287i
$586$	9.15021	−	6.10800i	0.377992	−	0.252319i
$587$	−33.2812	+	19.2149i	−1.37366	+	0.793085i	−0.991387	−	0.130963i	$-0.958193\pi$
$587$	−33.2812	+	19.2149i	−1.37366	+	0.793085i	−0.382276	+	0.924048i	$0.624860\pi$
$588$	36.8744	−	4.82070i	1.52067	−	0.198803i
$589$	36.5621	−	25.2642i	1.50652	−	1.04099i
$590$	6.06733	−	0.394921i	0.249788	−	0.0162586i
$591$	−15.1728	−	26.2801i	−0.624127	−	1.08102i
$592$	−16.1653	+	16.1069i	−0.664388	+	0.661991i
$593$	−16.5728	+	28.7050i	−0.680564	+	1.17877i	0.294245	+	0.955730i	$0.404932\pi$
$593$	−16.5728	+	28.7050i	−0.680564	+	1.17877i	−0.974809	+	0.223042i	$0.928401\pi$
$594$	−10.9314	+	7.29700i	−0.448522	+	0.299399i
$595$	−16.7429	−	9.66654i	−0.686394	−	0.396290i
$596$	8.56590	−	1.11985i	0.350873	−	0.0458708i
$597$		−	23.3523i		−	0.955748i
$598$	−9.42192	+	19.0840i	−0.385291	+	0.780404i
$599$	18.5991	−	32.2146i	0.759940	−	1.31625i	−0.182941	−	0.983124i	$-0.558562\pi$
$599$	18.5991	−	32.2146i	0.759940	−	1.31625i	0.942881	−	0.333131i	$-0.108105\pi$
$600$	−6.00853	+	1.18671i	−0.245297	+	0.0484471i
$601$		−	5.66226i		−	0.230968i	−0.993309	−	0.115484i	$-0.963158\pi$
$601$		−	5.66226i		−	0.230968i	0.993309	−	0.115484i	$-0.0368419\pi$
$602$	22.9915	−	46.5690i	0.937063	−	1.89801i
$603$	−9.17666	−	15.8944i	−0.373703	−	0.647272i
$604$	4.87882	−	11.7485i	0.198516	−	0.478039i
$605$	−0.142533	−	0.246874i	−0.00579477	−	0.0100368i
$606$	14.8348	+	22.2236i	0.602623	+	0.902773i
$607$	15.3239			0.621978			0.310989	−	0.950414i	$-0.399340\pi$
$607$	15.3239			0.621978			0.310989	+	0.950414i	$0.399340\pi$
$608$	9.73929	+	22.6527i	0.394980	+	0.918690i
$609$	31.1313			1.26151
$610$	6.74558	+	10.1054i	0.273121	+	0.409154i
$611$	−6.13680	−	10.6293i	−0.248269	−	0.430014i
$612$	6.34342	−	15.2753i	0.256418	−	0.617468i
$613$	−23.4137	−	40.5538i	−0.945672	−	1.63795i	−0.754399	−	0.656416i	$-0.772072\pi$
$613$	−23.4137	−	40.5538i	−0.945672	−	1.63795i	−0.191273	−	0.981537i	$-0.561262\pi$
$614$	2.15259	−	4.36004i	0.0868713	−	0.175957i
$615$			12.7138i			0.512669i
$616$	−35.8601	+	7.08250i	−1.44485	+	0.285362i
$617$	−1.55860	+	2.69958i	−0.0627471	+	0.108681i	−0.895692	−	0.444674i	$-0.853319\pi$
$617$	−1.55860	+	2.69958i	−0.0627471	+	0.108681i	0.832945	+	0.553355i	$0.186653\pi$
$618$	1.20467	−	2.44005i	0.0484589	−	0.0981531i
$619$		−	38.6088i		−	1.55182i	−0.630844	−	0.775909i	$-0.717291\pi$
$619$		−	38.6088i		−	1.55182i	0.630844	−	0.775909i	$-0.282709\pi$
$620$	20.2192	−	2.64332i	0.812023	−	0.106158i
$621$	−12.8818	−	7.43731i	−0.516929	−	0.298449i
$622$	18.4911	−	12.3433i	0.741424	−	0.494919i
$623$	−7.10933	+	12.3137i	−0.284829	+	0.493339i
$624$	17.6249	−	17.5613i	0.705559	−	0.703013i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−44.0394	+	2.86651i	−1.76017	+	0.114569i
$627$	13.2309	−	27.9198i	0.528392	−	1.11501i
$628$	−43.8115	+	5.72763i	−1.74827	+	0.228557i
$629$	24.1938	−	13.9683i	0.964671	−	0.556953i
$630$	−7.84263	+	5.23515i	−0.312458	+	0.208573i
$631$	22.3773	+	12.9196i	0.890827	+	0.514319i	0.874213	−	0.485542i	$-0.161378\pi$
$631$	22.3773	+	12.9196i	0.890827	+	0.514319i	0.0166144	+	0.999862i	$0.494711\pi$
$632$	4.30409	+	4.92131i	0.171207	+	0.195759i
$633$	25.0991	−	43.4728i	0.997598	−	1.72789i
$634$	0.590759	+	9.07608i	0.0234620	+	0.360457i
$635$	5.15871			0.204717
$636$	29.1130	+	12.0898i	1.15440	+	0.479392i
$637$	−21.3617	−	12.3332i	−0.846383	−	0.488660i
$638$	−16.8219	+	1.09493i	−0.665986	+	0.0433488i
$639$	−9.56976			−0.378574
$640$	−0.775655	+	11.2871i	−0.0306605	+	0.446161i
$641$	−14.9270	+	8.61808i	−0.589579	+	0.340394i	−0.764931	−	0.644112i	$-0.777227\pi$
$641$	−14.9270	+	8.61808i	−0.589579	+	0.340394i	0.175352	+	0.984506i	$0.443894\pi$
$642$	−20.2459	+	41.0079i	−0.799041	+	1.61845i
$643$	12.5722	−	7.25858i	0.495800	−	0.286250i	−0.231177	−	0.972912i	$-0.574258\pi$
$643$	12.5722	−	7.25858i	0.495800	−	0.286250i	0.726978	+	0.686661i	$0.240924\pi$
$644$	−25.1538	−	32.8424i	−0.991197	−	1.29417i
$645$			20.1419i			0.793085i
$646$	−4.39320	−	29.8650i	−0.172848	−	1.17502i
$647$			9.61299i			0.377926i	0.981984	+	0.188963i	$0.0605126\pi$
$647$			9.61299i			0.377926i	−0.981984	+	0.188963i	$0.939487\pi$
$648$	20.8814	+	23.8759i	0.820299	+	0.937934i
$649$	−12.1878	+	7.03664i	−0.478414	+	0.276212i
$650$	3.64262	+	1.79839i	0.142875	+	0.0705385i
$651$	75.4847	−	43.5811i	2.95848	−	1.70808i
$652$	−29.2991	−	12.1671i	−1.14744	−	0.476501i
$653$	20.6157			0.806757			0.403378	−	0.915033i	$-0.367836\pi$
$653$	20.6157			0.806757			0.403378	+	0.915033i	$0.367836\pi$
$654$	−2.26336	−	34.7729i	−0.0885044	−	1.35973i
$655$	5.65163	+	3.26297i	0.220827	+	0.127495i
$656$	22.6743	+	6.11951i	0.885284	+	0.238927i
$657$	−17.3956			−0.678667
$658$	23.8060	−	1.54952i	0.928054	−	0.0604068i
$659$	3.21420	−	5.56716i	0.125207	−	0.216866i	−0.796607	−	0.604498i	$-0.793374\pi$
$659$	3.21420	−	5.56716i	0.125207	−	0.216866i	0.921814	+	0.387632i	$0.126707\pi$
$660$	11.2545	−	8.61971i	0.438079	−	0.335522i
$661$	−29.3700	−	16.9568i	−1.14236	−	0.659543i	−0.195347	−	0.980734i	$-0.562583\pi$
$661$	−29.3700	−	16.9568i	−1.14236	−	0.659543i	−0.947014	+	0.321192i	$0.895917\pi$
$662$	−7.96161	−	11.9271i	−0.309437	−	0.463558i
$663$	−26.3783	+	15.2295i	−1.02445	+	0.591466i
$664$	−4.72974	−	23.9476i	−0.183549	−	0.929347i
$665$	−7.36960	+	15.5513i	−0.285781	+	0.603053i
$666$	−0.885016	−	13.5969i	−0.0342937	−	0.526868i
$667$	−9.53916	−	16.5223i	−0.369358	−	0.639747i
$668$	−3.61155	−	4.71548i	−0.139735	−	0.182448i
$669$	−16.5785	+	28.7149i	−0.640964	+	1.11018i
$670$	−8.53271	−	12.7826i	−0.329647	−	0.493835i
$671$	−24.3548	−	14.0613i	−0.940207	−	0.542829i
$672$	15.4414	+	45.8288i	0.595665	+	1.76789i
$673$			32.9224i			1.26906i	0.772897	+	0.634532i	$0.218807\pi$
$673$			32.9224i			1.26906i	−0.772897	+	0.634532i	$0.781193\pi$
$674$	25.9401	+	12.8068i	0.999176	+	0.493300i
$675$	−1.41958	+	2.45878i	−0.0546396	+	0.0946385i
$676$	9.41702	−	1.23112i	0.362193	−	0.0473507i
$677$			11.4373i			0.439570i	0.975548	+	0.219785i	$0.0705357\pi$
$677$			11.4373i			0.439570i	−0.975548	+	0.219785i	$0.929464\pi$
$678$	44.2893	+	21.8659i	1.70092	+	0.839756i
$679$	13.7953	+	23.8942i	0.529416	+	0.916976i
$680$	4.46987	−	13.1094i	0.171411	−	0.502722i
$681$	−19.0729	−	33.0352i	−0.730875	−	1.26591i
$682$	−39.2556	+	26.2041i	−1.50317	+	1.00341i
$683$	50.7926			1.94353			0.971763	−	0.235961i	$-0.0758237\pi$
$683$	50.7926			1.94353			0.971763	+	0.235961i	$0.0758237\pi$
$684$	−14.0097	−	4.52705i	−0.535673	−	0.173096i
$685$	−10.8891			−0.416051
$686$	7.36975	−	4.91949i	0.281378	−	0.187827i
$687$	−18.9827	−	32.8791i	−0.724236	−	1.25441i
$688$	35.9219	+	9.69487i	1.36951	+	0.369613i
$689$	−10.4546	−	18.1078i	−0.398287	−	0.689853i
$690$	14.3859	+	7.10244i	0.547663	+	0.270385i
$691$		−	19.9100i		−	0.757413i	−0.925517	−	0.378707i	$-0.876369\pi$
$691$		−	19.9100i		−	0.757413i	0.925517	−	0.378707i	$-0.123631\pi$
$692$	1.39877	+	10.6994i	0.0531731	+	0.406730i
$693$	10.9127	−	18.9014i	0.414541	−	0.718006i
$694$	−24.8066	−	12.2472i	−0.941647	−	0.464898i
$695$		−	14.7204i		−	0.558377i
$696$	4.32143	+	21.8802i	0.163803	+	0.829368i
$697$	−24.8996	−	14.3758i	−0.943140	−	0.544522i
$698$	−3.33905	−	5.00214i	−0.126385	−	0.189334i
$699$	−12.0766	+	20.9173i	−0.456779	+	0.791164i
$700$	−6.26872	+	4.80116i	−0.236935	+	0.181467i
$701$	−8.95850	−	15.5166i	−0.338358	−	0.586053i	0.645766	−	0.763535i	$-0.276538\pi$
$701$	−8.95850	−	15.5166i	−0.338358	−	0.586053i	−0.984124	+	0.177482i	$0.943205\pi$
$702$	−0.749140	−	11.5093i	−0.0282745	−	0.434392i
$703$	−14.1366	−	20.4584i	−0.533172	−	0.771603i
$704$	−9.95568	−	24.2207i	−0.375219	−	0.912850i
$705$	−8.01256	+	4.62605i	−0.301770	+	0.174227i
$706$	−24.1166	−	36.1284i	−0.907642	−	1.35971i
$707$	29.8333	+	17.2243i	1.12200	+	0.647786i
$708$	11.3214	+	14.7819i	0.425482	+	0.555538i
$709$	−17.3771	+	30.0980i	−0.652611	+	1.13036i	0.329876	+	0.944024i	$0.392993\pi$
$709$	−17.3771	+	30.0980i	−0.652611	+	1.13036i	−0.982487	+	0.186331i	$0.940340\pi$
$710$	−7.99669	+	0.520502i	−0.300110	+	0.0195341i
$711$	−3.90376			−0.146402
$712$	−9.64140	−	3.28740i	−0.361327	−	0.123200i
$713$	−46.2596	−	26.7080i	−1.73243	−	1.00022i
$714$	−3.84541	−	59.0787i	−0.143911	−	2.21096i
$715$	−9.40284			−0.351646
$716$	−7.83283	+	18.8619i	−0.292727	+	0.704902i
$717$	2.67319	−	1.54337i	0.0998323	−	0.0576382i
$718$	35.6099	+	17.5809i	1.32895	+	0.656113i
$719$	6.06739	−	3.50301i	0.226275	−	0.130640i	−0.382577	−	0.923924i	$-0.624963\pi$
$719$	6.06739	−	3.50301i	0.226275	−	0.130640i	0.608853	+	0.793283i	$0.291630\pi$
$720$	−4.76811	−	4.78538i	−0.177697	−	0.178340i
$721$		−	3.50831i		−	0.130656i
$722$	−26.1801	+	6.05016i	−0.974321	+	0.225163i
$723$			33.5385i			1.24731i
$724$	−1.66447	+	1.27480i	−0.0618595	+	0.0473777i
$725$	−3.15366	+	1.82076i	−0.117124	+	0.0676215i
$726$	0.386452	−	0.782755i	0.0143426	−	0.0290508i
$727$	−17.8443	+	10.3024i	−0.661810	+	0.382096i	−0.792966	−	0.609266i	$-0.791464\pi$
$727$	−17.8443	+	10.3024i	−0.661810	+	0.382096i	0.131156	+	0.991362i	$0.458131\pi$
$728$	10.3519	−	30.3605i	0.383667	−	1.12523i
$729$	−0.495701			−0.0183593
$730$	−14.5361	+	0.946152i	−0.538006	+	0.0350187i
$731$	−39.4473	−	22.7749i	−1.45901	−	0.842361i
$732$	−14.2695	+	34.3617i	−0.527415	+	1.27004i
$733$	−40.0849			−1.48057			−0.740285	−	0.672293i	$-0.765309\pi$
$733$	−40.0849			−1.48057			−0.740285	+	0.672293i	$0.765309\pi$
$734$	−2.14960	−	33.0252i	−0.0793432	−	1.21898i
$735$	−9.29703	+	16.1029i	−0.342926	+	0.593966i
$736$	19.5912	−	22.2379i	0.722141	−	0.819701i
$737$	30.8072	+	17.7866i	1.13480	+	0.655176i
$738$	−11.6633	+	7.78556i	−0.429333	+	0.286590i
$739$	−4.68755	+	2.70636i	−0.172434	+	0.0995550i	−0.583733	−	0.811946i	$-0.698409\pi$
$739$	−4.68755	+	2.70636i	−0.172434	+	0.0995550i	0.411299	+	0.911501i	$0.365075\pi$
$740$	−1.47908	−	11.3137i	−0.0543719	−	0.415899i
$741$	15.4130	+	22.3056i	0.566211	+	0.819417i
$742$	40.5555	−	2.63974i	1.48884	−	0.0969080i
$743$	−4.94123	−	8.55846i	−0.181276	−	0.313980i	0.761039	−	0.648706i	$-0.224689\pi$
$743$	−4.94123	−	8.55846i	−0.181276	−	0.313980i	−0.942315	+	0.334726i	$0.891356\pi$
$744$	41.1086	+	47.0038i	1.50712	+	1.72324i
$745$	−2.15970	+	3.74071i	−0.0791252	+	0.137049i
$746$	−35.7855	+	23.8877i	−1.31020	+	0.874592i
$747$	12.6225	+	7.28759i	0.461832	+	0.266639i
$748$	4.15576	+	31.7881i	0.151950	+	1.16229i
$749$			58.9613i			2.15440i
$750$	1.35566	−	2.74588i	0.0495017	−	0.100265i
$751$	−19.2599	+	33.3592i	−0.702805	+	1.21729i	0.264673	+	0.964338i	$0.414736\pi$
$751$	−19.2599	+	33.3592i	−0.702805	+	1.21729i	−0.967478	+	0.252956i	$0.918597\pi$
$752$	4.39364	+	16.5166i	0.160219	+	0.602299i
$753$		−	7.68309i		−	0.279988i
$754$	6.54888	−	13.2647i	0.238496	−	0.483072i
$755$	3.18031	+	5.50845i	0.115743	+	0.200473i
$756$	20.7040	+	8.59779i	0.752995	+	0.312698i
$757$	10.0966	+	17.4878i	0.366967	+	0.635606i	0.989090	−	0.147314i	$-0.0470628\pi$
$757$	10.0966	+	17.4878i	0.366967	+	0.635606i	−0.622123	+	0.782920i	$0.713729\pi$
$758$	3.30168	+	4.94615i	0.119922	+	0.179652i
$759$	−37.1350			−1.34792
$760$	−11.9530	−	3.02091i	−0.433581	−	0.109580i
$761$	19.8935			0.721138			0.360569	−	0.932733i	$-0.382583\pi$
$761$	19.8935			0.721138			0.360569	+	0.932733i	$0.382583\pi$
$762$	8.77069	+	13.1391i	0.317729	+	0.475980i
$763$	−22.4628	−	38.9066i	−0.813207	−	1.40852i
$764$	−34.3734	−	14.2743i	−1.24359	−	0.516427i
$765$	4.13502	+	7.16206i	0.149502	+	0.258945i
$766$	−18.7759	+	38.0305i	−0.678402	+	1.37410i
$767$		−	12.3499i		−	0.445931i
$768$	−30.0667	+	17.2144i	−1.08494	+	0.621171i
$769$	−18.0305	+	31.2297i	−0.650196	+	1.12617i	0.332879	+	0.942970i	$0.391980\pi$
$769$	−18.0305	+	31.2297i	−0.650196	+	1.12617i	−0.983075	+	0.183203i	$0.941353\pi$
$770$	8.09086	−	16.3880i	0.291574	−	0.590581i
$771$			57.1565i			2.05844i
$772$	−0.934766	−	7.15017i	−0.0336430	−	0.257340i
$773$	22.5711	+	13.0314i	0.811827	+	0.468708i	0.847590	−	0.530652i	$-0.178053\pi$
$773$	22.5711	+	13.0314i	0.811827	+	0.468708i	−0.0357632	+	0.999360i	$0.511386\pi$
$774$	−18.4777	+	12.3343i	−0.664166	+	0.443348i
$775$	−5.09782	+	8.82968i	−0.183119	+	0.317171i
$776$	−14.8788	+	13.0127i	−0.534116	+	0.467128i
$777$	−24.3859	−	42.2375i	−0.874838	−	1.51526i
$778$	33.5458	−	2.18348i	1.20267	−	0.0782817i
$779$	−10.9598	+	23.1274i	−0.392677	+	0.828625i
$780$	1.61262	+	12.3352i	0.0577412	+	0.441672i
$781$	16.0634	−	9.27424i	0.574795	−	0.331858i
$782$	−30.1765	+	20.1436i	−1.07911	+	0.720333i
$783$	8.95373	+	5.16944i	0.319980	+	0.184741i
$784$	24.2438	+	24.3316i	0.865849	+	0.868985i
$785$	11.0461	−	19.1324i	0.394252	−	0.682864i
$786$	1.29803	+	19.9422i	0.0462992	+	0.711314i
$787$	21.7354			0.774784			0.387392	−	0.921915i	$-0.373376\pi$
$787$	21.7354			0.774784			0.387392	+	0.921915i	$0.373376\pi$
$788$	10.7493	−	25.8849i	0.382928	−	0.922112i
$789$	28.7315	+	16.5881i	1.02287	+	0.590552i
$790$	−3.26206	+	0.212326i	−0.116059	+	0.00755424i
$791$	63.6793			2.26418
$792$	14.7994	+	5.04611i	0.525875	+	0.179306i
$793$	21.3724	−	12.3394i	0.758958	−	0.438185i
$794$	−10.5740	+	21.4175i	−0.375256	+	0.760078i
$795$	−13.6501	+	7.88086i	−0.484118	+	0.279505i
$796$	17.1236	−	13.1148i	0.606930	−	0.464843i
$797$		−	30.3028i		−	1.07338i	−0.843779	−	0.536691i	$-0.819674\pi$
$797$		−	30.3028i		−	1.07338i	0.843779	−	0.536691i	$-0.180326\pi$
$798$	−52.1383	+	7.66965i	−1.84568	+	0.271503i
$799$		−	20.9232i		−	0.740209i
$800$	−4.24461	−	3.73942i	−0.150070	−	0.132209i
$801$	5.26740	−	3.04113i	0.186114	−	0.107453i
$802$	−20.2840	−	10.0144i	−0.716254	−	0.353620i
$803$	29.1996	−	16.8584i	1.03043	−	0.594920i
$804$	18.0499	−	43.4652i	0.636572	−	1.53290i
$805$	20.6842			0.729021
$806$	−2.69022	−	41.3310i	−0.0947590	−	1.45582i
$807$	11.1765	+	6.45273i	0.393430	+	0.227147i
$808$	−7.96460	+	23.3589i	−0.280194	+	0.821763i
$809$	−20.3469			−0.715359			−0.357679	−	0.933844i	$-0.616432\pi$
$809$	−20.3469			−0.715359			−0.357679	+	0.933844i	$0.616432\pi$
$810$	−15.8260	+	1.03011i	−0.556068	+	0.0361943i
$811$	9.57310	−	16.5811i	0.336157	−	0.582241i	−0.647549	−	0.762024i	$-0.724206\pi$
$811$	9.57310	−	16.5811i	0.336157	−	0.582241i	0.983706	+	0.179782i	$0.0575393\pi$
$812$	17.4836	+	22.8277i	0.613553	+	0.801096i
$813$	−39.6742	−	22.9059i	−1.39143	−	0.803345i
$814$	14.6625	+	21.9655i	0.513922	+	0.769891i
$815$	13.7373	−	7.93126i	0.481198	−	0.277820i
$816$	40.9889	−	10.9036i	1.43490	−	0.381701i
$817$	−17.3632	+	36.6397i	−0.607461	+	1.28186i
$818$	−0.0466996	−	0.717465i	−0.00163281	−	0.0250856i
$819$	9.57643	+	16.5869i	0.334627	+	0.579592i
$820$	−9.32265	+	7.14015i	−0.325561	+	0.249345i
$821$	−9.61633	+	16.6560i	−0.335612	+	0.581297i	−0.983602	−	0.180351i	$-0.942277\pi$
$821$	−9.61633	+	16.6560i	−0.335612	+	0.581297i	0.647990	+	0.761649i	$0.275610\pi$
$822$	−18.5133	−	27.7343i	−0.645727	−	0.967345i
$823$	−25.8383	−	14.9177i	−0.900666	−	0.520000i	−0.0232501	−	0.999730i	$-0.507401\pi$
$823$	−25.8383	−	14.9177i	−0.900666	−	0.520000i	−0.877416	+	0.479730i	$0.840735\pi$
$824$	2.46577	−	0.486998i	0.0858991	−	0.0169654i
$825$			7.08806i			0.246775i
$826$	21.5244	+	10.6267i	0.748929	+	0.369752i
$827$	12.4356	−	21.5391i	0.432429	−	0.748989i	−0.564653	−	0.825328i	$-0.690990\pi$
$827$	12.4356	−	21.5391i	0.432429	−	0.748989i	0.997082	+	0.0763398i	$0.0243234\pi$
$828$	2.29393	+	17.5467i	0.0797196	+	0.609788i
$829$		−	39.8433i		−	1.38382i	−0.721985	−	0.691908i	$-0.756770\pi$
$829$		−	39.8433i		−	1.38382i	0.721985	−	0.691908i	$-0.243230\pi$
$830$	10.9440	+	5.40312i	0.379871	+	0.187545i
$831$	−5.95796	−	10.3195i	−0.206679	−	0.357979i
$832$	22.7754	+	3.06128i	0.789595	+	0.106131i
$833$	−21.0248	−	36.4160i	−0.728466	−	1.26174i
$834$	37.4926	−	25.0272i	1.29826	−	0.866622i
$835$	2.96981			0.102775
$836$	27.9034	−	5.97810i	0.965058	−	0.206757i
$837$	28.9470			1.00055
$838$	1.40842	−	0.940156i	0.0486530	−	0.0324771i
$839$	−1.17583	−	2.03660i	−0.0405943	−	0.0703114i	0.845014	−	0.534744i	$-0.179592\pi$
$839$	−1.17583	−	2.03660i	−0.0405943	−	0.0703114i	−0.885609	+	0.464432i	$0.846258\pi$
$840$	−22.8864	−	7.80348i	−0.789654	−	0.269246i
$841$	−7.86963	−	13.6306i	−0.271367	−	0.470021i
$842$	−38.9144	−	19.2123i	−1.34108	−	0.662101i
$843$			46.2657i			1.59348i
$844$	45.9732	−	6.01023i	1.58246	−	0.206881i
$845$	−2.37429	+	4.11239i	−0.0816780	+	0.141470i
$846$	−9.15049	−	4.51767i	−0.314600	−	0.155321i
$847$		−	1.12545i		−	0.0386709i
$848$	7.48492	+	28.1374i	0.257033	+	0.966244i
$849$	−3.43151	−	1.98119i	−0.117769	−	0.0679941i
$850$	3.84486	+	5.75986i	0.131877	+	0.197562i
$851$	−14.9445	+	25.8846i	−0.512290	+	0.887312i
$852$	−14.9215	−	19.4824i	−0.511201	−	0.667458i
$853$	12.8231	+	22.2103i	0.439056	+	0.760468i	0.997617	−	0.0689959i	$-0.0219795\pi$
$853$	12.8231	+	22.2103i	0.439056	+	0.760468i	−0.558561	+	0.829464i	$0.688646\pi$
$854$	3.11566	+	47.8672i	0.106616	+	1.63798i
$855$	6.05627	−	4.18484i	0.207120	−	0.143118i
$856$	−41.4401	+	8.18458i	−1.41639	+	0.279743i
$857$	−41.6368	+	24.0390i	−1.42229	+	0.821158i	−0.996494	−	0.0836626i	$-0.973338\pi$
$857$	−41.6368	+	24.0390i	−1.42229	+	0.821158i	−0.425793	+	0.904821i	$0.640005\pi$
$858$	−15.9864	−	23.9488i	−0.545768	−	0.817599i
$859$	10.6843	+	6.16856i	0.364542	+	0.210469i	0.671071	−	0.741393i	$-0.265834\pi$
$859$	10.6843	+	6.16856i	0.364542	+	0.210469i	−0.306529	+	0.951861i	$0.599168\pi$
$860$	−14.7695	+	11.3118i	−0.503634	+	0.385730i
$861$	−25.0972	+	43.4697i	−0.855311	+	1.48144i
$862$	−43.6634	+	2.84204i	−1.48718	+	0.0968003i
$863$	18.7366			0.637801			0.318900	−	0.947788i	$-0.396686\pi$
$863$	18.7366			0.637801			0.318900	+	0.947788i	$0.396686\pi$
$864$	−3.16886	+	15.7450i	−0.107807	+	0.535655i
$865$	−4.67239	−	2.69761i	−0.158866	−	0.0917214i
$866$	1.98571	+	30.5073i	0.0674771	+	1.03668i
$867$	−15.1132			−0.513270
$868$	74.3495	+	30.8753i	2.52359	+	1.04798i
$869$	6.55270	−	3.78320i	0.222285	−	0.128336i
$870$	−9.99920	−	4.93668i	−0.339005	−	0.167369i
$871$	−27.0347	+	15.6085i	−0.916037	+	0.528874i
$872$	24.2269	−	21.1884i	0.820426	−	0.717529i
$873$		−	11.8023i		−	0.399449i
$874$	20.0466	+	25.3212i	0.678085	+	0.856503i
$875$		−	3.94804i		−	0.133468i
$876$	−27.1237	−	35.4146i	−0.916426	−	1.19655i
$877$	31.8009	−	18.3602i	1.07384	−	0.619981i	0.144611	−	0.989489i	$-0.453807\pi$
$877$	31.8009	−	18.3602i	1.07384	−	0.619981i	0.929228	+	0.369507i	$0.120474\pi$
$878$	1.46813	−	2.97369i	0.0495471	−	0.100357i
$879$	−14.5882	+	8.42251i	−0.492048	+	0.284084i
$880$	12.6412	+	3.41169i	0.426134	+	0.115008i
$881$	−19.0565			−0.642028			−0.321014	−	0.947074i	$-0.604024\pi$
$881$	−19.0565			−0.642028			−0.321014	+	0.947074i	$0.604024\pi$
$882$	−20.4657	+	1.33211i	−0.689116	+	0.0448543i
$883$	−8.42170	−	4.86227i	−0.283413	−	0.163629i	0.351555	−	0.936167i	$-0.385653\pi$
$883$	−8.42170	−	4.86227i	−0.283413	−	0.163629i	−0.634967	+	0.772539i	$0.718987\pi$
$884$	−25.9817	−	10.7895i	−0.873858	−	0.362889i
$885$	−9.30964			−0.312940
$886$	1.30261	+	20.0125i	0.0437619	+	0.672332i
$887$	−10.3039	+	17.8469i	−0.345971	+	0.599240i	−0.985530	−	0.169503i	$-0.945784\pi$
$887$	−10.3039	+	17.8469i	−0.345971	+	0.599240i	0.639558	+	0.768742i	$0.279117\pi$
$888$	26.3010	−	23.0024i	0.882604	−	0.771909i
$889$	17.6381	+	10.1834i	0.591564	+	0.341540i
$890$	4.23614	−	2.82773i	0.141996	−	0.0947857i
$891$	31.7906	−	18.3543i	1.06503	−	0.614893i
$892$	−30.3664	+	3.96990i	−1.01674	+	0.132922i
$893$	−18.5634	+	1.50798i	−0.621199	+	0.0504627i
$894$	−13.1993	+	0.859141i	−0.441452	+	0.0287340i
$895$	−5.10591	−	8.84369i	−0.170672	−	0.295612i
$896$	−24.9330	+	37.0605i	−0.832952	+	1.23811i
$897$	16.2938	−	28.2218i	0.544035	−	0.942297i
$898$	−0.260775	+	0.174074i	−0.00870219	+	0.00580893i
$899$	32.1535	+	18.5639i	1.07238	+	0.619139i
$900$	3.34917	−	0.437849i	0.111639	−	0.0145950i
$901$		−	35.6444i		−	1.18749i
$902$	12.0325	−	24.3717i	0.400638	−	0.811489i
$903$	−39.7604	+	68.8671i	−1.32314	+	2.29175i
$904$	8.83950	+	44.7561i	0.293997	+	1.48857i
$905$		−	1.04828i		−	0.0348461i
$906$	−8.62284	+	17.4655i	−0.286475	+	0.580252i
$907$	−25.7223	−	44.5523i	−0.854093	−	1.47933i	−0.877483	−	0.479607i	$-0.840779\pi$
$907$	−25.7223	−	44.5523i	−0.854093	−	1.47933i	0.0233900	−	0.999726i	$-0.492554\pi$
$908$	13.5123	−	32.5384i	0.448422	−	1.07983i
$909$	−7.36796	−	12.7617i	−0.244380	−	0.423278i
$910$	8.90443	+	13.3395i	0.295179	+	0.442199i
$911$	15.8133			0.523918			0.261959	−	0.965079i	$-0.415632\pi$
$911$	15.8133			0.523918			0.261959	+	0.965079i	$0.415632\pi$
$912$	−12.6280	−	35.5801i	−0.418154	−	1.17817i
$913$	−28.2502			−0.934944
$914$	0.538737	+	0.807067i	0.0178198	+	0.0266954i
$915$	−9.30169	−	16.1110i	−0.307504	−	0.532613i
$916$	13.4484	−	32.3846i	0.444349	−	1.07002i
$917$	12.8823	+	22.3129i	0.425412	+	0.736835i
$918$	8.70418	−	17.6302i	0.287281	−	0.581885i
$919$			10.8775i			0.358815i	0.983775	+	0.179407i	$0.0574180\pi$
$919$			10.8775i			0.358815i	−0.983775	+	0.179407i	$0.942582\pi$
$920$	2.87122	+	14.5376i	0.0946615	+	0.479290i
$921$	−3.72258	+	6.44770i	−0.122663	+	0.212459i
$922$	−1.10849	+	2.24524i	−0.0365062	+	0.0739431i
$923$			16.2771i			0.535768i
$924$	55.4956	−	7.25512i	1.82567	−	0.238676i
$925$	4.94066	+	2.85249i	0.162448	+	0.0937893i
$926$	−29.0335	+	19.3806i	−0.954099	+	0.636885i
$927$	−0.750368	+	1.29968i	−0.0246453	+	0.0426869i
$928$	−13.6172	+	15.4569i	−0.447007	+	0.507397i
$929$	26.2417	+	45.4520i	0.860964	+	1.49123i	0.871000	+	0.491283i	$0.163472\pi$
$929$	26.2417	+	45.4520i	0.860964	+	1.49123i	−0.0100359	+	0.999950i	$0.503195\pi$
$930$	−31.1562	+	2.02794i	−1.02165	+	0.0664989i
$931$	−30.7935	+	21.2781i	−1.00922	+	0.697361i
$932$	−22.1203	+	2.89187i	−0.724576	+	0.0947262i
$933$	−29.4804	+	17.0205i	−0.965144	+	0.557226i
$934$	6.60921	−	4.41182i	0.216260	−	0.144359i
$935$	−13.8818	−	8.01465i	−0.453983	−	0.262107i
$936$	−10.3285	+	9.03313i	−0.337598	+	0.295257i
$937$	12.9757	−	22.4746i	0.423899	−	0.734215i	−0.572418	−	0.819962i	$-0.693994\pi$
$937$	12.9757	−	22.4746i	0.423899	−	0.734215i	0.996317	+	0.0857475i	$0.0273278\pi$
$938$	−3.94110	−	60.5488i	−0.128682	−	1.97699i
$939$	67.5736			2.20518
$940$	−7.89206	−	3.27736i	−0.257411	−	0.106896i
$941$	−43.7587	−	25.2641i	−1.42649	−	0.823586i	−0.429651	−	0.902995i	$-0.641364\pi$
$941$	−43.7587	−	25.2641i	−1.42649	−	0.823586i	−0.996842	+	0.0794083i	$0.974697\pi$
$942$	67.5100	−	4.39420i	2.19959	−	0.143171i
$943$	30.7609			1.00171
$944$	−4.48101	+	16.6033i	−0.145844	+	0.540390i
$945$	−9.70736	+	5.60455i	−0.315781	+	0.182316i
$946$	19.0625	−	38.6110i	0.619776	−	1.25535i
$947$	−24.4340	+	14.1070i	−0.793998	+	0.458415i	−0.841368	−	0.540462i	$-0.818249\pi$
$947$	−24.4340	+	14.1070i	−0.793998	+	0.458415i	0.0473701	+	0.998877i	$0.484916\pi$
$948$	−6.08685	−	7.94740i	−0.197692	−	0.258120i
$949$			29.5880i			0.960469i
$950$	4.83313	−	3.82634i	0.156807	−	0.124143i
$951$		−	13.9262i		−	0.451589i
$952$	41.1611	−	35.9987i	1.33404	−	1.16673i
$953$	37.6612	−	21.7437i	1.21997	−	0.704348i	0.255055	−	0.966926i	$-0.417906\pi$
$953$	37.6612	−	21.7437i	1.21997	−	0.704348i	0.964911	+	0.262579i	$0.0845730\pi$
$954$	−15.5886	−	7.69622i	−0.504700	−	0.249174i
$955$	16.1165	−	9.30486i	0.521517	−	0.301098i
$956$	2.63299	+	1.09341i	0.0851571	+	0.0353634i
$957$	25.8114			0.834363
$958$	−0.925262	−	14.2152i	−0.0298939	−	0.459272i
$959$	−37.2310	−	21.4953i	−1.20225	−	0.694119i
$960$	2.30766	−	17.1686i	0.0744792	−	0.554114i
$961$	72.9510			2.35326
$962$	−23.1268	+	1.50532i	−0.745638	+	0.0485333i
$963$	12.6108	−	21.8426i	0.406378	−	0.703867i
$964$	−24.5928	+	18.8355i	−0.792081	+	0.606649i
$965$	3.12246	+	1.80275i	0.100516	+	0.0580327i
$966$	35.1666	+	52.6821i	1.13147	+	1.69502i
$967$	−46.6515	+	26.9343i	−1.50021	+	0.866148i	−0.500213	+	0.865903i	$0.666745\pi$
$967$	−46.6515	+	26.9343i	−1.50021	+	0.866148i	−1.00000		0.000245616i	$0.999922\pi$
$968$	0.791006	−	0.156227i	0.0254239	−	0.00502131i
$969$	3.74232	+	46.0682i	0.120221	+	1.47992i
$970$	−0.641933	−	9.86229i	−0.0206112	−	0.316659i
$971$	21.5228	+	37.2785i	0.690698	+	1.19632i	0.971609	+	0.236590i	$0.0760300\pi$
$971$	21.5228	+	37.2785i	0.690698	+	1.19632i	−0.280911	+	0.959734i	$0.590637\pi$
$972$	−19.1726	−	25.0330i	−0.614960	−	0.802933i
$973$	29.0584	−	50.3306i	0.931569	−	1.61352i
$974$	7.44195	+	11.1486i	0.238455	+	0.357223i
$975$	−5.38676	−	3.11005i	−0.172514	−	0.0996012i
$976$	−33.2103	+	8.83437i	−1.06304	+	0.282781i
$977$		−	8.99767i		−	0.287861i	−0.989588	−	0.143930i	$-0.954026\pi$
$977$		−	8.99767i		−	0.287861i	0.989588	−	0.143930i	$-0.0459742\pi$
$978$	43.5566	+	21.5042i	1.39279	+	0.687628i
$979$	−5.89444	+	10.2095i	−0.188387	+	0.326296i
$980$	−17.0291	+	2.22627i	−0.543975	+	0.0711156i
$981$			19.2176i			0.613571i
$982$	43.9796	+	21.7130i	1.40344	+	0.692890i
$983$	−3.94801	−	6.83816i	−0.125922	−	0.218103i	0.796171	−	0.605072i	$-0.206856\pi$
$983$	−3.94801	−	6.83816i	−0.125922	−	0.218103i	−0.922093	+	0.386968i	$0.873522\pi$
$984$	−34.0359	−	11.6051i	−1.08502	−	0.369957i
$985$	7.00704	+	12.1365i	0.223263	+	0.386702i
$986$	20.9747	−	14.0012i	0.667971	−	0.445888i
$987$	−36.5277			−1.16269
$988$	−7.70002	+	23.8289i	−0.244970	+	0.758099i
$989$	48.7330			1.54962
$990$	−6.50242	+	4.34053i	−0.206660	+	0.137951i
$991$	−26.8727	−	46.5450i	−0.853641	−	1.47855i	−0.877900	−	0.478844i	$-0.841056\pi$
$991$	−26.8727	−	46.5450i	−0.853641	−	1.47855i	0.0242592	−	0.999706i	$-0.492277\pi$
$992$	−11.3796	+	56.5414i	−0.361304	+	1.79519i
$993$	10.9785	+	19.0153i	0.348392	+	0.603433i
$994$	−28.3690	−	14.0060i	−0.899809	−	0.444242i
$995$			10.7844i			0.341890i
$996$	4.84501	+	37.0603i	0.153520	+	1.17430i
$997$	13.4769	−	23.3426i	0.426817	−	0.739269i	−0.569771	−	0.821803i	$-0.692968\pi$
$997$	13.4769	−	23.3426i	0.426817	−	0.739269i	0.996588	+	0.0825347i	$0.0263015\pi$
$998$	−43.7054	−	21.5777i	−1.38347	−	0.683029i
$999$		−	16.1973i		−	0.512461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.6	✓	40
4.3	odd	2	inner	380.2.n.b.31.13	yes	40
19.8	odd	6	inner	380.2.n.b.331.13	yes	40
76.27	even	6	inner	380.2.n.b.331.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.6	✓	40	1.1	even	1	trivial
380.2.n.b.31.13	yes	40	4.3	odd	2	inner
380.2.n.b.331.6	yes	40	76.27	even	6	inner
380.2.n.b.331.13	yes	40	19.8	odd	6	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.785164 - 1.17623i) q^{2} +(1.08269 + 1.87527i) q^{3} +(-0.767036 + 1.84707i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.35566 - 2.74588i) q^{6} -3.94804i q^{7} +(2.77483 - 0.548038i) q^{8} +(-0.844418 + 1.46258i) q^{9} +O(q^{10})\)	\(q+(-0.785164 - 1.17623i) q^{2} +(1.08269 + 1.87527i) q^{3} +(-0.767036 + 1.84707i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.35566 - 2.74588i) q^{6} -3.94804i q^{7} +(2.77483 - 0.548038i) q^{8} +(-0.844418 + 1.46258i) q^{9} +(-0.626064 + 1.26809i) q^{10} -3.27337i q^{11} +(-4.29420 + 0.561395i) q^{12} +(2.48768 + 1.43626i) q^{13} +(-4.64380 + 3.09986i) q^{14} +(1.08269 - 1.87527i) q^{15} +(-2.82331 - 2.83353i) q^{16} +(2.44844 + 4.24083i) q^{17} +(2.38333 - 0.155130i) q^{18} +(3.58606 - 2.47794i) q^{19} +(1.98312 - 0.259260i) q^{20} +(7.40363 - 4.27449i) q^{21} +(-3.85023 + 2.57013i) q^{22} +(-4.53719 - 2.61955i) q^{23} +(4.03198 + 4.61019i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.263860 - 4.05379i) q^{26} +2.83916 q^{27} +(7.29229 + 3.02829i) q^{28} +(3.15366 + 1.82076i) q^{29} +(-3.05583 + 0.198903i) q^{30} +10.1956 q^{31} +(-1.11613 + 5.54565i) q^{32} +(6.13844 - 3.54403i) q^{33} +(3.06576 - 6.20967i) q^{34} +(-3.41910 + 1.97402i) q^{35} +(-2.05378 - 2.68155i) q^{36} -5.70498i q^{37} +(-5.73027 - 2.27244i) q^{38} +6.22009i q^{39} +(-1.86203 - 2.12905i) q^{40} +(-5.08478 + 2.93570i) q^{41} +(-10.8408 - 5.35220i) q^{42} +(-8.05559 + 4.65090i) q^{43} +(6.04613 + 2.51079i) q^{44} +1.68884 q^{45} +(0.481244 + 7.39356i) q^{46} +(-3.70031 - 2.13638i) q^{47} +(2.25688 - 8.36229i) q^{48} -8.58701 q^{49} +(1.41123 - 0.0918564i) q^{50} +(-5.30179 + 9.18297i) q^{51} +(-4.56102 + 3.49325i) q^{52} +(-6.30379 - 3.63950i) q^{53} +(-2.22920 - 3.33950i) q^{54} +(-2.83482 + 1.63668i) q^{55} +(-2.16367 - 10.9551i) q^{56} +(8.52938 + 4.04199i) q^{57} +(-0.334498 - 5.13903i) q^{58} +(-2.14966 - 3.72333i) q^{59} +(2.63328 + 3.43819i) q^{60} +(4.29565 - 7.44029i) q^{61} +(-8.00524 - 11.9924i) q^{62} +(5.77430 + 3.33380i) q^{63} +(7.39931 - 3.04142i) q^{64} -2.87253i q^{65} +(-8.98827 - 4.43758i) q^{66} +(-5.43372 + 9.41147i) q^{67} +(-9.71113 + 1.26957i) q^{68} -11.3446i q^{69} +(5.00646 + 2.47172i) q^{70} +(2.83324 + 4.90732i) q^{71} +(-1.54157 + 4.52116i) q^{72} +(5.15017 + 8.92036i) q^{73} +(-6.71037 + 4.47934i) q^{74} -2.16537 q^{75} +(1.82628 + 8.52436i) q^{76} -12.9234 q^{77} +(7.31626 - 4.88379i) q^{78} +(1.15575 + 2.00182i) q^{79} +(-1.04226 + 3.86183i) q^{80} +(5.60717 + 9.71190i) q^{81} +(7.44545 + 3.67587i) q^{82} -8.63031i q^{83} +(2.21641 + 16.9537i) q^{84} +(2.44844 - 4.24083i) q^{85} +(11.7955 + 5.82352i) q^{86} +7.88527i q^{87} +(-1.79393 - 9.08302i) q^{88} +(-3.11895 - 1.80073i) q^{89} +(-1.32601 - 1.98646i) q^{90} +(5.67043 - 9.82147i) q^{91} +(8.31867 - 6.37121i) q^{92} +(11.0387 + 19.1195i) q^{93} +(0.392480 + 6.02983i) q^{94} +(-3.93899 - 1.86665i) q^{95} +(-11.6080 + 3.91116i) q^{96} +(-6.05217 + 3.49422i) q^{97} +(6.74220 + 10.1003i) q^{98} +(4.78755 + 2.76409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

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