LMFDB - Embedded newform 152.2.p.a.125.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(45,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("152.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.p (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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.14
Character	$\chi$	$=$	152.125
Dual form			152.2.p.a.45.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.837765 - 1.13936i) q^{2} +(2.05214 + 1.18481i) q^{3} +(-0.596300 - 1.90904i) q^{4} +(-0.164468 - 0.0949559i) q^{5} +(3.06914 - 1.34555i) q^{6} -1.69169 q^{7} +(-2.67465 - 0.919922i) q^{8} +(1.30753 + 2.26470i) q^{9} +O(q^{10})$	\(q+(0.837765 - 1.13936i) q^{2} +(2.05214 + 1.18481i) q^{3} +(-0.596300 - 1.90904i) q^{4} +(-0.164468 - 0.0949559i) q^{5} +(3.06914 - 1.34555i) q^{6} -1.69169 q^{7} +(-2.67465 - 0.919922i) q^{8} +(1.30753 + 2.26470i) q^{9} +(-0.245975 + 0.107839i) q^{10} +2.39629i q^{11} +(1.03814 - 4.62412i) q^{12} +(-0.577998 + 0.333707i) q^{13} +(-1.41724 + 1.92745i) q^{14} +(-0.225008 - 0.389726i) q^{15} +(-3.28885 + 2.27672i) q^{16} +(1.03237 - 1.78812i) q^{17} +(3.67572 + 0.407539i) q^{18} +(-0.150723 + 4.35629i) q^{19} +(-0.0832018 + 0.370599i) q^{20} +(-3.47158 - 2.00432i) q^{21} +(2.73025 + 2.00753i) q^{22} +(-1.43969 - 2.49362i) q^{23} +(-4.39883 - 5.05675i) q^{24} +(-2.48197 - 4.29889i) q^{25} +(-0.104012 + 0.938118i) q^{26} -0.912175i q^{27} +(1.00875 + 3.22950i) q^{28} +(-6.73551 + 3.88875i) q^{29} +(-0.632544 - 0.0701322i) q^{30} +7.83723 q^{31} +(-0.161271 + 5.65455i) q^{32} +(-2.83914 + 4.91753i) q^{33} +(-1.17244 - 2.67428i) q^{34} +(0.278229 + 0.160636i) q^{35} +(3.54372 - 3.84656i) q^{36} -6.55216i q^{37} +(4.83713 + 3.82128i) q^{38} -1.58151 q^{39} +(0.352543 + 0.405272i) q^{40} +(0.687251 - 1.19035i) q^{41} +(-5.19202 + 2.27625i) q^{42} +(8.88368 + 5.12899i) q^{43} +(4.57461 - 1.42891i) q^{44} -0.496629i q^{45} +(-4.04726 - 0.448733i) q^{46} +(5.45403 + 9.44666i) q^{47} +(-9.44666 + 0.775506i) q^{48} -4.13819 q^{49} +(-6.97731 - 0.773597i) q^{50} +(4.23716 - 2.44632i) q^{51} +(0.981720 + 0.904430i) q^{52} +(-2.54234 + 1.46782i) q^{53} +(-1.03930 - 0.764188i) q^{54} +(0.227542 - 0.394114i) q^{55} +(4.52467 + 1.55622i) q^{56} +(-5.47066 + 8.76116i) q^{57} +(-1.21207 + 10.9321i) q^{58} +(-10.4191 - 6.01545i) q^{59} +(-0.609829 + 0.661943i) q^{60} +(10.7112 - 6.18409i) q^{61} +(6.56576 - 8.92946i) q^{62} +(-2.21193 - 3.83117i) q^{63} +(6.30749 + 4.92093i) q^{64} +0.126750 q^{65} +(3.22433 + 7.35455i) q^{66} +(1.60208 - 0.924962i) q^{67} +(-4.02920 - 0.904582i) q^{68} -6.82301i q^{69} +(0.416113 - 0.182429i) q^{70} +(0.731563 - 1.26710i) q^{71} +(-1.41382 - 7.26010i) q^{72} +(4.43028 - 7.67347i) q^{73} +(-7.46530 - 5.48917i) q^{74} -11.7626i q^{75} +(8.40620 - 2.30992i) q^{76} -4.05378i q^{77} +(-1.32493 + 1.80192i) q^{78} +(1.95936 - 3.39372i) q^{79} +(0.757100 - 0.0621527i) q^{80} +(5.00333 - 8.66602i) q^{81} +(-0.780491 - 1.78026i) q^{82} -6.96015i q^{83} +(-1.75622 + 7.82256i) q^{84} +(-0.339586 + 0.196060i) q^{85} +(13.2862 - 5.82485i) q^{86} -18.4296 q^{87} +(2.20440 - 6.40924i) q^{88} +(2.12402 + 3.67892i) q^{89} +(-0.565841 - 0.416058i) q^{90} +(0.977791 - 0.564528i) q^{91} +(-3.90192 + 4.23537i) q^{92} +(16.0831 + 9.28559i) q^{93} +(15.3324 + 1.69995i) q^{94} +(0.438445 - 0.702160i) q^{95} +(-7.03050 + 11.4129i) q^{96} +(2.18817 - 3.79002i) q^{97} +(-3.46683 + 4.71491i) q^{98} +(-5.42689 + 3.13321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9	$ 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) $ 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.837765	−	1.13936i	0.592389	−	0.805652i
$2$	0.837765	−	1.13936i	0.592389	−	0.805652i
$3$	2.05214	+	1.18481i	1.18481	+	0.684048i	0.957121	−	0.289688i	$-0.0935514\pi$
$3$	2.05214	+	1.18481i	1.18481	+	0.684048i	0.227684	+	0.973735i	$0.426885\pi$
$4$	−0.596300	−	1.90904i	−0.298150	−	0.954519i
$5$	−0.164468	−	0.0949559i	−0.0735525	−	0.0424656i	0.462773	−	0.886477i	$-0.346855\pi$
$5$	−0.164468	−	0.0949559i	−0.0735525	−	0.0424656i	−0.536325	+	0.844011i	$0.680188\pi$
$6$	3.06914	−	1.34555i	1.25297	−	0.549318i
$7$	−1.69169			−0.639398			−0.319699	−	0.947519i	$-0.603582\pi$
$7$	−1.69169			−0.639398			−0.319699	+	0.947519i	$0.603582\pi$
$8$	−2.67465	−	0.919922i	−0.945631	−	0.325241i
$9$	1.30753	+	2.26470i	0.435842	+	0.754901i
$10$	−0.245975	+	0.107839i	−0.0777842	+	0.0341016i
$11$			2.39629i			0.722509i	0.932467	+	0.361255i	$0.117651\pi$
$11$			2.39629i			0.722509i	−0.932467	+	0.361255i	$0.882349\pi$
$12$	1.03814	−	4.62412i	0.299686	−	1.33487i
$13$	−0.577998	+	0.333707i	−0.160308	+	0.0925537i	−0.578008	−	0.816031i	$-0.696170\pi$
$13$	−0.577998	+	0.333707i	−0.160308	+	0.0925537i	0.417700	+	0.908585i	$0.362836\pi$
$14$	−1.41724	+	1.92745i	−0.378772	+	0.515132i
$15$	−0.225008	−	0.389726i	−0.0580969	−	0.100627i
$16$	−3.28885	+	2.27672i	−0.822213	+	0.569180i
$17$	1.03237	−	1.78812i	0.250387	−	0.433684i	−0.713245	−	0.700915i	$-0.752775\pi$
$17$	1.03237	−	1.78812i	0.250387	−	0.433684i	0.963632	+	0.267231i	$0.0861087\pi$
$18$	3.67572	+	0.407539i	0.866375	+	0.0960579i
$19$	−0.150723	+	4.35629i	−0.0345782	+	0.999402i
$19$	−0.150723	+	4.35629i	−0.0345782	+	0.999402i
$20$	−0.0832018	+	0.370599i	−0.0186045	+	0.0828684i
$21$	−3.47158	−	2.00432i	−0.757562	−	0.437378i
$22$	2.73025	+	2.00753i	0.582091	+	0.428007i
$23$	−1.43969	−	2.49362i	−0.300196	−	0.519955i	0.675984	−	0.736916i	$-0.263719\pi$
$23$	−1.43969	−	2.49362i	−0.300196	−	0.519955i	−0.976180	+	0.216961i	$0.930385\pi$
$24$	−4.39883	−	5.05675i	−0.897908	−	1.03220i
$25$	−2.48197	−	4.29889i	−0.496393	−	0.859779i
$26$	−0.104012	+	0.938118i	−0.0203985	+	0.183980i
$27$		−	0.912175i		−	0.175548i
$28$	1.00875	+	3.22950i	0.190637	+	0.610317i
$29$	−6.73551	+	3.88875i	−1.25075	+	0.722123i	−0.971259	−	0.238024i	$-0.923500\pi$
$29$	−6.73551	+	3.88875i	−1.25075	+	0.722123i	−0.279494	+	0.960147i	$0.590167\pi$
$30$	−0.632544	−	0.0701322i	−0.115486	−	0.0128043i
$31$	7.83723			1.40761			0.703804	−	0.710394i	$-0.251483\pi$
$31$	7.83723			1.40761			0.703804	+	0.710394i	$0.251483\pi$
$32$	−0.161271	+	5.65455i	−0.0285090	+	0.999594i
$33$	−2.83914	+	4.91753i	−0.494231	+	0.856032i
$34$	−1.17244	−	2.67428i	−0.201071	−	0.458635i
$35$	0.278229	+	0.160636i	0.0470293	+	0.0271524i
$36$	3.54372	−	3.84656i	0.590621	−	0.641093i
$37$		−	6.55216i		−	1.07717i	−0.842572	−	0.538584i	$-0.818959\pi$
$37$		−	6.55216i		−	1.07717i	0.842572	−	0.538584i	$-0.181041\pi$
$38$	4.83713	+	3.82128i	0.784686	+	0.619893i
$39$	−1.58151			−0.253245
$40$	0.352543	+	0.405272i	0.0557420	+	0.0640791i
$41$	0.687251	−	1.19035i	0.107331	−	0.185902i	−0.807357	−	0.590063i	$-0.799103\pi$
$41$	0.687251	−	1.19035i	0.107331	−	0.185902i	0.914688	+	0.404161i	$0.132436\pi$
$42$	−5.19202	+	2.27625i	−0.801146	+	0.351233i
$43$	8.88368	+	5.12899i	1.35475	+	0.782164i	0.988910	−	0.148515i	$-0.0474492\pi$
$43$	8.88368	+	5.12899i	1.35475	+	0.782164i	0.365838	+	0.930679i	$0.380783\pi$
$44$	4.57461	−	1.42891i	0.689649	−	0.215416i
$45$		−	0.496629i		−	0.0740331i
$46$	−4.04726	−	0.448733i	−0.596735	−	0.0661620i
$47$	5.45403	+	9.44666i	0.795552	+	1.37794i	0.922488	+	0.386026i	$0.126152\pi$
$47$	5.45403	+	9.44666i	0.795552	+	1.37794i	−0.126936	+	0.991911i	$0.540514\pi$
$48$	−9.44666	+	0.775506i	−1.36351	+	0.111935i
$49$	−4.13819			−0.591171
$50$	−6.97731	−	0.773597i	−0.986740	−	0.109403i
$51$	4.23716	−	2.44632i	0.593321	−	0.342554i
$52$	0.981720	+	0.904430i	0.136140	+	0.125422i
$53$	−2.54234	+	1.46782i	−0.349217	+	0.201621i	−0.664341	−	0.747430i	$-0.731288\pi$
$53$	−2.54234	+	1.46782i	−0.349217	+	0.201621i	0.315123	+	0.949051i	$0.397954\pi$
$54$	−1.03930	−	0.764188i	−0.141431	−	0.103993i
$55$	0.227542	−	0.394114i	0.0306818	−	0.0531424i
$56$	4.52467	+	1.55622i	0.604634	+	0.207959i
$57$	−5.47066	+	8.76116i	−0.724607	+	1.16044i
$58$	−1.21207	+	10.9321i	−0.159153	+	1.43545i
$59$	−10.4191	−	6.01545i	−1.35645	−	0.783145i	−0.367304	−	0.930101i	$-0.619719\pi$
$59$	−10.4191	−	6.01545i	−1.35645	−	0.783145i	−0.989143	+	0.146956i	$0.953052\pi$
$60$	−0.609829	+	0.661943i	−0.0787286	+	0.0854565i
$61$	10.7112	−	6.18409i	1.37142	−	0.791791i	0.380315	−	0.924857i	$-0.375815\pi$
$61$	10.7112	−	6.18409i	1.37142	−	0.791791i	0.991107	+	0.133066i	$0.0424822\pi$
$62$	6.56576	−	8.92946i	0.833852	−	1.13404i
$63$	−2.21193	−	3.83117i	−0.278676	−	0.482682i
$64$	6.30749	+	4.92093i	0.788436	+	0.615117i
$65$	0.126750			0.0157214
$66$	3.22433	+	7.35455i	0.396887	+	0.905282i
$67$	1.60208	−	0.924962i	0.195725	−	0.113002i	−0.398935	−	0.916979i	$-0.630620\pi$
$67$	1.60208	−	0.924962i	0.195725	−	0.113002i	0.594660	+	0.803977i	$0.297287\pi$
$68$	−4.02920	−	0.904582i	−0.488612	−	0.109697i
$69$		−	6.82301i		−	0.821393i
$70$	0.416113	−	0.182429i	0.0497350	−	0.0218045i
$71$	0.731563	−	1.26710i	0.0868205	−	0.150378i	−0.819345	−	0.573301i	$-0.805663\pi$
$71$	0.731563	−	1.26710i	0.0868205	−	0.150378i	0.906166	+	0.422923i	$0.138996\pi$
$72$	−1.41382	−	7.26010i	−0.166621	−	0.855611i
$73$	4.43028	−	7.67347i	0.518525	−	0.898112i	−0.481243	−	0.876587i	$-0.659815\pi$
$73$	4.43028	−	7.67347i	0.518525	−	0.898112i	0.999768	−	0.0215248i	$-0.00685209\pi$
$74$	−7.46530	−	5.48917i	−0.867823	−	0.638103i
$75$		−	11.7626i		−	1.35823i
$76$	8.40620	−	2.30992i	0.964258	−	0.264966i
$77$		−	4.05378i		−	0.461971i
$78$	−1.32493	+	1.80192i	−0.150019	+	0.204027i
$79$	1.95936	−	3.39372i	0.220446	−	0.381823i	−0.734498	−	0.678611i	$-0.762582\pi$
$79$	1.95936	−	3.39372i	0.220446	−	0.381823i	0.954943	+	0.296788i	$0.0959155\pi$
$80$	0.757100	−	0.0621527i	0.0846464	−	0.00694889i
$81$	5.00333	−	8.66602i	0.555925	−	0.962891i
$82$	−0.780491	−	1.78026i	−0.0861908	−	0.196597i
$83$		−	6.96015i		−	0.763976i	−0.924167	−	0.381988i	$-0.875240\pi$
$83$		−	6.96015i		−	0.763976i	0.924167	−	0.381988i	$-0.124760\pi$
$84$	−1.75622	+	7.82256i	−0.191619	+	0.853511i
$85$	−0.339586	+	0.196060i	−0.0368332	+	0.0212657i
$86$	13.2862	−	5.82485i	1.43269	−	0.628110i
$87$	−18.4296			−1.97587
$88$	2.20440	−	6.40924i	0.234990	−	0.683227i
$89$	2.12402	+	3.67892i	0.225146	+	0.389964i	0.956363	−	0.292180i	$-0.0943807\pi$
$89$	2.12402	+	3.67892i	0.225146	+	0.389964i	−0.731217	+	0.682145i	$0.761047\pi$
$90$	−0.565841	−	0.416058i	−0.0596449	−	0.0438564i
$91$	0.977791	−	0.564528i	0.102500	−	0.0591786i
$92$	−3.90192	+	4.23537i	−0.406803	+	0.441567i
$93$	16.0831	+	9.28559i	1.66774	+	0.962871i
$94$	15.3324	+	1.69995i	1.58141	+	0.175337i
$95$	0.438445	−	0.702160i	0.0449835	−	0.0720401i
$96$	−7.03050	+	11.4129i	−0.717547	+	1.16482i
$97$	2.18817	−	3.79002i	0.222175	−	0.384818i	−0.733293	−	0.679913i	$-0.762018\pi$
$97$	2.18817	−	3.79002i	0.222175	−	0.384818i	0.955468	+	0.295094i	$0.0953510\pi$
$98$	−3.46683	+	4.71491i	−0.350203	+	0.476278i
$99$	−5.42689	+	3.13321i	−0.545423	+	0.314900i
$100$	−6.72675	+	7.30160i	−0.672675	+	0.730160i
$101$	−13.2059	+	7.62442i	−1.31403	+	0.758658i	−0.982762	−	0.184877i	$-0.940811\pi$
$101$	−13.2059	+	7.62442i	−1.31403	+	0.758658i	−0.331272	+	0.943535i	$0.607478\pi$
$102$	0.762488	−	6.87711i	0.0754975	−	0.680935i
$103$	−12.1757			−1.19971			−0.599856	−	0.800108i	$-0.704775\pi$
$103$	−12.1757			−1.19971			−0.599856	+	0.800108i	$0.704775\pi$
$104$	1.85293	−	0.360837i	0.181694	−	0.0353830i
$105$	0.380644	+	0.659295i	0.0371470	+	0.0643406i
$106$	−0.457501	+	4.12634i	−0.0444364	+	0.400786i
$107$			10.5673i			1.02158i	0.859706	+	0.510788i	$0.170646\pi$
$107$			10.5673i			1.02158i	−0.859706	+	0.510788i	$0.829354\pi$
$108$	−1.74138	+	0.543931i	−0.167564	+	0.0523397i
$109$	12.4245	+	7.17331i	1.19005	+	0.687079i	0.958319	−	0.285700i	$-0.0922261\pi$
$109$	12.4245	+	7.17331i	1.19005	+	0.687079i	0.231736	+	0.972779i	$0.425559\pi$
$110$	−0.258413	−	0.589428i	−0.0246387	−	0.0561998i
$111$	7.76304	−	13.4460i	0.736835	−	1.27624i
$112$	5.56371	−	3.85150i	0.525721	−	0.363932i
$113$	−3.61009			−0.339609			−0.169804	−	0.985478i	$-0.554314\pi$
$113$	−3.61009			−0.339609			−0.169804	+	0.985478i	$0.554314\pi$
$114$	5.39902	+	13.5729i	0.505664	+	1.27122i
$115$			0.546828i			0.0509920i
$116$	11.4402	+	10.5395i	1.06219	+	0.978567i
$117$	−1.51149	−	0.872662i	−0.139738	−	0.0806776i
$118$	−15.5825	+	6.83158i	−1.43449	+	0.628898i
$119$	−1.74645	+	3.02495i	−0.160097	+	0.277296i
$120$	0.243301	+	1.24937i	0.0222102	+	0.114051i
$121$	5.25779			0.477981
$122$	1.92750	−	17.3847i	0.174508	−	1.57394i
$123$	2.82067	−	1.62852i	0.254332	−	0.146838i
$124$	−4.67334	−	14.9616i	−0.419679	−	1.34359i
$125$			1.89227i			0.169250i
$126$	−6.21817	−	0.689429i	−0.553958	−	0.0614192i
$127$	9.11620	+	15.7897i	0.808932	+	1.40111i	0.913605	+	0.406604i	$0.133287\pi$
$127$	9.11620	+	15.7897i	0.808932	+	1.40111i	−0.104673	+	0.994507i	$0.533380\pi$
$128$	10.8909	−	3.06394i	0.962631	−	0.270817i
$129$	12.1537	+	21.0508i	1.07007	+	1.85342i
$130$	0.106187	−	0.144414i	0.00931318	−	0.0126660i
$131$	−13.1797	−	7.60929i	−1.15151	−	0.664826i	−0.202258	−	0.979332i	$-0.564828\pi$
$131$	−13.1797	−	7.60929i	−1.15151	−	0.664826i	−0.949256	+	0.314506i	$0.898161\pi$
$132$	11.0807	+	2.48770i	0.964454	+	0.216526i
$133$	0.254976	−	7.36948i	0.0221092	−	0.639015i
$134$	0.288299	−	2.60025i	0.0249052	−	0.224628i
$135$	−0.0866164	+	0.150024i	−0.00745475	+	0.0129120i
$136$	−4.40617	+	3.83290i	−0.377826	+	0.328668i
$137$	−6.40616	−	11.0958i	−0.547315	−	0.947978i	−0.998457	−	0.0555259i	$-0.982316\pi$
$137$	−6.40616	−	11.0958i	−0.547315	−	0.947978i	0.451142	−	0.892452i	$-0.351017\pi$
$138$	−7.77389	−	5.71607i	−0.661757	−	0.486584i
$139$	−9.81692	+	5.66780i	−0.832661	+	0.480737i	−0.854763	−	0.519019i	$-0.826297\pi$
$139$	−9.81692	+	5.66780i	−0.832661	+	0.480737i	0.0221021	+	0.999756i	$0.492964\pi$
$140$	0.140751	−	0.626937i	0.0118957	−	0.0529859i
$141$			25.8478i			2.17678i
$142$	−0.830815	−	1.89505i	−0.0697204	−	0.159029i
$143$	−0.799660	−	1.38505i	−0.0668709	−	0.115824i
$144$	−9.45635	−	4.47140i	−0.788029	−	0.372616i
$145$	1.47704			0.122661
$146$	−5.03134	−	11.4763i	−0.416397	−	0.949783i
$147$	−8.49216	−	4.90295i	−0.700422	−	0.404389i
$148$	−12.5083	+	3.90706i	−1.02818	+	0.321158i
$149$	−2.76967	−	1.59907i	−0.226901	−	0.131001i	0.382241	−	0.924063i	$-0.375152\pi$
$149$	−2.76967	−	1.59907i	−0.226901	−	0.131001i	−0.609141	+	0.793062i	$0.708486\pi$
$150$	−13.4019	−	9.85428i	−1.09426	−	0.804599i
$151$	1.86221			0.151545			0.0757723	−	0.997125i	$-0.475858\pi$
$151$	1.86221			0.151545			0.0757723	+	0.997125i	$0.475858\pi$
$152$	4.41058	−	11.5129i	0.357745	−	0.933819i
$153$	5.39942			0.436517
$154$	−4.61873	−	3.39611i	−0.372188	−	0.273666i
$155$	−1.28898	−	0.744191i	−0.103533	−	0.0597749i
$156$	0.943056	+	3.01917i	0.0755049	+	0.241727i
$157$	−1.28559	−	0.742237i	−0.102601	−	0.0592370i	0.447821	−	0.894123i	$-0.352200\pi$
$157$	−1.28559	−	0.742237i	−0.102601	−	0.0592370i	−0.550423	+	0.834886i	$0.685533\pi$
$158$	−2.22519	−	5.07556i	−0.177027	−	0.403790i
$159$	−6.95633			−0.551673
$160$	0.563457	−	0.914682i	0.0445452	−	0.0723120i
$161$	2.43550	+	4.21842i	0.191945	+	0.332458i
$162$	−5.68214	−	12.9607i	−0.446431	−	1.01829i
$163$			14.5040i			1.13604i	0.823014	+	0.568022i	$0.192291\pi$
$163$			14.5040i			1.13604i	−0.823014	+	0.568022i	$0.807709\pi$
$164$	−2.68224	−	0.602180i	−0.209448	−	0.0470223i
$165$	0.933897	−	0.539186i	0.0727038	−	0.0419756i
$166$	−7.93015	−	5.83097i	−0.615499	−	0.452571i
$167$	8.31489	+	14.4018i	0.643425	+	1.11445i	0.984663	+	0.174468i	$0.0558207\pi$
$167$	8.31489	+	14.4018i	0.643425	+	1.11445i	−0.341237	+	0.939977i	$0.610846\pi$
$168$	7.44145	+	8.55444i	0.574120	+	0.659989i
$169$	−6.27728	+	10.8726i	−0.482868	+	0.836351i
$170$	−0.0611094	+	0.551164i	−0.00468687	+	0.0422723i
$171$	−10.0628	+	5.35462i	−0.769520	+	0.409478i
$172$	4.49410	−	20.0177i	0.342672	−	1.52633i
$173$	14.5880	+	8.42236i	1.10910	+	0.640340i	0.938597	−	0.345017i	$-0.112127\pi$
$173$	14.5880	+	8.42236i	1.10910	+	0.640340i	0.170505	+	0.985357i	$0.445460\pi$
$174$	−15.4397	+	20.9981i	−1.17048	+	1.59186i
$175$	4.19871	+	7.27238i	0.317393	+	0.549740i
$176$	−5.45568	−	7.88105i	−0.411238	−	0.594056i
$177$	−14.2543	−	24.6891i	−1.07142	−	1.85575i
$178$	5.97106	+	0.662031i	0.447550	+	0.0496213i
$179$		−	12.0453i		−	0.900309i	−0.892951	−	0.450154i	$-0.851369\pi$
$179$		−	12.0453i		−	0.900309i	0.892951	−	0.450154i	$-0.148631\pi$
$180$	−0.948084	+	0.296140i	−0.0706660	+	0.0220730i
$181$	−9.94638	+	5.74254i	−0.739308	+	0.426840i	−0.821818	−	0.569750i	$-0.807040\pi$
$181$	−9.94638	+	5.74254i	−0.739308	+	0.426840i	0.0825094	+	0.996590i	$0.473707\pi$
$182$	0.175956	−	1.58700i	0.0130427	−	0.117636i
$183$	29.3077			2.16649
$184$	1.55673	+	7.99394i	0.114764	+	0.589321i
$185$	−0.622166	+	1.07762i	−0.0457426	+	0.0792285i
$186$	24.0535	−	10.5454i	1.76369	−	0.773225i
$187$	4.28487	+	2.47387i	0.313340	+	0.180907i
$188$	14.7818	−	16.0450i	1.07807	−	1.17020i
$189$			1.54312i			0.112245i
$190$	−0.432703	−	1.08779i	−0.0313916	−	0.0789168i
$191$	−10.6055			−0.767384			−0.383692	−	0.923461i	$-0.625348\pi$
$191$	−10.6055			−0.767384			−0.383692	+	0.923461i	$0.625348\pi$
$192$	7.11352	+	17.5716i	0.513374	+	1.26812i
$193$	−5.46214	+	9.46071i	−0.393174	+	0.680997i	−0.992866	−	0.119234i	$-0.961956\pi$
$193$	−5.46214	+	9.46071i	−0.393174	+	0.680997i	0.599692	+	0.800231i	$0.295290\pi$
$194$	−2.48504	−	5.66827i	−0.178416	−	0.406958i
$195$	0.260109	+	0.150174i	0.0186268	+	0.0107542i
$196$	2.46761	+	7.89997i	0.176258	+	0.564284i
$197$			8.20838i			0.584823i	0.956293	+	0.292412i	$0.0944577\pi$
$197$			8.20838i			0.584823i	−0.956293	+	0.292412i	$0.905542\pi$
$198$	−0.976583	+	8.80809i	−0.0694027	+	0.625964i
$199$	−8.74989	−	15.1553i	−0.620263	−	1.07433i	−0.989437	−	0.144967i	$-0.953692\pi$
$199$	−8.74989	−	15.1553i	−0.620263	−	1.07433i	0.369173	−	0.929361i	$-0.379641\pi$
$200$	2.68374	+	13.7812i	0.189769	+	0.974481i
$201$	4.38360			0.309195
$202$	−2.37643	+	21.4338i	−0.167205	+	1.50807i
$203$	11.3944	−	6.57855i	0.799729	−	0.461724i
$204$	−7.19674	−	6.63015i	−0.503873	−	0.464203i
$205$	−0.226062	+	0.130517i	−0.0157889	+	0.00911570i
$206$	−10.2004	+	13.8726i	−0.710696	+	0.966550i
$207$	3.76486	−	6.52093i	0.261676	−	0.453236i
$208$	1.14119	−	2.41345i	0.0791274	−	0.167343i
$209$	−10.4389	−	0.361176i	−0.722077	−	0.0249831i
$210$	1.07007	+	0.118642i	0.0738416	+	0.00818706i
$211$	−2.57636	−	1.48746i	−0.177364	−	0.102401i	0.408690	−	0.912673i	$-0.365986\pi$
$211$	−2.57636	−	1.48746i	−0.177364	−	0.102401i	−0.586053	+	0.810272i	$0.699319\pi$
$212$	4.31813	+	3.97816i	0.296570	+	0.273221i
$213$	3.00254	−	1.73352i	0.205731	−	0.118779i
$214$	12.0400	+	8.85289i	0.823035	+	0.605171i
$215$	−0.974056	−	1.68711i	−0.0664301	−	0.115060i
$216$	−0.839130	+	2.43975i	−0.0570956	+	0.166004i
$217$	−13.2581			−0.900021
$218$	18.5819	−	8.14652i	1.25852	−	0.551752i
$219$	18.1831	−	10.4980i	1.22870	−	0.709392i
$220$	−0.888062	−	0.199376i	−0.0598732	−	0.0134419i
$221$			1.37804i			0.0926971i
$222$	−8.81626	−	20.1095i	−0.591708	−	1.34966i
$223$	1.84870	−	3.20204i	0.123798	−	0.214425i	−0.797464	−	0.603366i	$-0.793826\pi$
$223$	1.84870	−	3.20204i	0.123798	−	0.214425i	0.921262	+	0.388941i	$0.127159\pi$
$224$	0.272821	−	9.56574i	0.0182286	−	0.639138i
$225$	6.49047	−	11.2418i	0.432698	−	0.749455i
$226$	−3.02441	+	4.11321i	−0.201181	+	0.273606i
$227$			17.3412i			1.15097i	0.817811	+	0.575486i	$0.195187\pi$
$227$			17.3412i			1.15097i	−0.817811	+	0.575486i	$0.804813\pi$
$228$	19.9875	+	5.21942i	1.32371	+	0.345665i
$229$		−	28.3602i		−	1.87410i	−0.349202	−	0.937048i	$-0.613547\pi$
$229$		−	28.3602i		−	1.87410i	0.349202	−	0.937048i	$-0.386453\pi$
$230$	0.623036	+	0.458113i	0.0410818	+	0.0302071i
$231$	4.80293	−	8.31893i	0.316010	−	0.547345i
$232$	21.5925	−	4.20490i	1.41762	−	0.276065i
$233$	1.15079	−	1.99323i	0.0753909	−	0.130581i	−0.825865	−	0.563867i	$-0.809313\pi$
$233$	1.15079	−	1.99323i	0.0753909	−	0.130581i	0.901256	+	0.433287i	$0.142646\pi$
$234$	−2.26056	+	0.991057i	−0.147777	+	0.0647874i
$235$		−	2.07157i		−	0.135134i
$236$	−5.27083	+	23.4774i	−0.343102	+	1.52825i
$237$	8.04178	−	4.64293i	0.522370	−	0.301590i
$238$	1.98340	+	4.52404i	0.128565	+	0.293250i
$239$	−14.0680			−0.909982			−0.454991	−	0.890496i	$-0.650358\pi$
$239$	−14.0680			−0.909982			−0.454991	+	0.890496i	$0.650358\pi$
$240$	1.62732	+	0.769470i	0.105043	+	0.0496691i
$241$	−7.57919	−	13.1275i	−0.488218	−	0.845619i	0.511690	−	0.859170i	$-0.329020\pi$
$241$	−7.57919	−	13.1275i	−0.488218	−	0.845619i	−0.999908	+	0.0135513i	$0.995686\pi$
$242$	4.40479	−	5.99053i	0.283151	−	0.385086i
$243$	18.1652	−	10.4877i	1.16530	−	0.672785i
$244$	−18.1927	−	16.7604i	−1.16467	−	1.07298i
$245$	0.680602	+	0.392946i	0.0434821	+	0.0251044i
$246$	0.507588	−	4.57809i	0.0323626	−	0.291888i
$247$	−1.36661	−	2.56822i	−0.0869552	−	0.163412i
$248$	−20.9618	−	7.20964i	−1.33108	−	0.457812i
$249$	8.24643	−	14.2832i	0.522596	−	0.905163i
$250$	2.15598	+	1.58528i	0.136356	+	0.100262i
$251$	−5.49240	+	3.17104i	−0.346677	+	0.200154i	−0.663221	−	0.748424i	$-0.730811\pi$
$251$	−5.49240	+	3.17104i	−0.346677	+	0.200154i	0.316544	+	0.948578i	$0.397478\pi$
$252$	−5.99487	+	6.50718i	−0.377641	+	0.409914i
$253$	5.97543	−	3.44992i	0.375672	−	0.216894i
$254$	25.6275	+	2.84140i	1.60801	+	0.178285i
$255$	−0.929171			−0.0581870
$256$	5.63309	−	14.9756i	0.352068	−	0.935974i
$257$	7.59341	+	13.1522i	0.473664	+	0.820410i	0.999545	−	0.0301476i	$-0.00959773\pi$
$257$	7.59341	+	13.1522i	0.473664	+	0.820410i	−0.525881	+	0.850558i	$0.676264\pi$
$258$	34.1665	+	3.78816i	2.12712	+	0.235840i
$259$			11.0842i			0.688739i
$260$	−0.0755810	−	0.241970i	−0.00468733	−	0.0150064i
$261$	−17.6137	−	10.1693i	−1.09026	−	0.629463i
$262$	−19.7112	+	8.64165i	−1.21776	+	0.533883i
$263$	8.63913	−	14.9634i	0.532711	−	0.922683i	−0.466559	−	0.884490i	$-0.654507\pi$
$263$	8.63913	−	14.9634i	0.532711	−	0.922683i	0.999270	−	0.0381930i	$-0.0121602\pi$
$264$	12.1174	−	10.5409i	0.745777	−	0.648747i
$265$	0.557513			0.0342478
$266$	−8.18291	−	6.46440i	−0.501727	−	0.396358i
$267$			10.0662i			0.616042i
$268$	−2.72111	−	2.50688i	−0.166218	−	0.153132i
$269$	−5.93419	−	3.42611i	−0.361814	−	0.208893i	0.308062	−	0.951366i	$-0.400320\pi$
$269$	−5.93419	−	3.42611i	−0.361814	−	0.208893i	−0.669876	+	0.742473i	$0.733653\pi$
$270$	0.0983678	+	0.224372i	0.00598647	+	0.0136549i
$271$	−9.27334	+	16.0619i	−0.563315	+	0.975691i	0.433889	+	0.900966i	$0.357141\pi$
$271$	−9.27334	+	16.0619i	−0.563315	+	0.975691i	−0.997204	+	0.0747245i	$0.976192\pi$
$272$	0.675733	+	8.23130i	0.0409723	+	0.499096i
$273$	2.67542			0.161924
$274$	−18.0090	−	1.99672i	−1.08796	−	0.120626i
$275$	10.3014	−	5.94752i	0.621198	−	0.358649i
$276$	−13.0254	+	4.06856i	−0.784035	+	0.244899i
$277$		−	15.5882i		−	0.936606i	−0.883568	−	0.468303i	$-0.844866\pi$
$277$		−	15.5882i		−	0.936606i	0.883568	−	0.468303i	$-0.155134\pi$
$278$	−1.76658	+	15.9333i	−0.105953	+	0.955618i
$279$	10.2474	+	17.7490i	0.613495	+	1.06260i
$280$	−0.596393	−	0.685593i	−0.0356413	−	0.0409720i
$281$	13.5170	+	23.4121i	0.806354	+	1.39665i	0.915373	+	0.402606i	$0.131896\pi$
$281$	13.5170	+	23.4121i	0.806354	+	1.39665i	−0.109019	+	0.994040i	$0.534771\pi$
$282$	29.4501	+	21.6544i	1.75373	+	1.28950i
$283$	−10.3932	−	6.00054i	−0.617814	−	0.356695i	0.158204	−	0.987407i	$-0.449430\pi$
$283$	−10.3932	−	6.00054i	−0.617814	−	0.356695i	−0.776017	+	0.630712i	$0.782763\pi$
$284$	−2.85518	−	0.641007i	−0.169424	−	0.0380367i
$285$	1.73167	−	0.921462i	0.102576	−	0.0545827i
$286$	−2.24800	−	0.249244i	−0.132927	−	0.0147381i
$287$	−1.16261	+	2.01371i	−0.0686269	+	0.118865i
$288$	−13.0167	+	7.02825i	−0.767019	+	0.414143i
$289$	6.36841	+	11.0304i	0.374612	+	0.648848i
$290$	1.23741	−	1.68289i	0.0726633	−	0.0988224i
$291$	8.98087	−	5.18511i	0.526468	−	0.303957i
$292$	−17.2907	−	3.88188i	−1.01186	−	0.227170i
$293$		−	10.0175i		−	0.585230i	−0.956230	−	0.292615i	$-0.905474\pi$
$293$		−	10.0175i		−	0.585230i	0.956230	−	0.292615i	$-0.0945255\pi$
$294$	−12.7007	+	5.56814i	−0.740719	+	0.324741i
$295$	1.14240	+	1.97870i	0.0665134	+	0.115205i
$296$	−6.02748	+	17.5247i	−0.350340	+	1.01860i
$297$	2.18584			0.126835
$298$	−4.14226	+	1.81602i	−0.239955	+	0.105199i
$299$	1.66427	+	0.960869i	0.0962475	+	0.0555685i
$300$	−22.4552	+	7.01404i	−1.29645	+	0.404956i
$301$	−15.0284	−	8.67665i	−0.866223	−	0.500114i
$302$	1.56009	−	2.12174i	0.0897733	−	0.122092i
$303$	−36.1338			−2.07583
$304$	−9.42235	−	14.6704i	−0.540409	−	0.841402i
$305$	−2.34886			−0.134495
$306$	4.52345	−	6.15191i	0.258588	−	0.351681i
$307$	1.23718	+	0.714285i	0.0706095	+	0.0407664i	0.534889	−	0.844922i	$-0.320353\pi$
$307$	1.23718	+	0.714285i	0.0706095	+	0.0407664i	−0.464280	+	0.885689i	$0.653687\pi$
$308$	−7.73881	+	2.41727i	−0.440960	+	0.137737i
$309$	−24.9864	−	14.4259i	−1.42143	−	0.820660i
$310$	−1.92776	+	0.845157i	−0.109490	+	0.0480017i
$311$	−22.0136			−1.24828			−0.624139	−	0.781313i	$-0.714550\pi$
$311$	−22.0136			−1.24828			−0.624139	+	0.781313i	$0.714550\pi$
$312$	4.22999	+	1.45487i	0.239476	+	0.0823656i
$313$	7.90105	+	13.6850i	0.446594	+	0.773523i	0.998162	−	0.0606068i	$-0.0193036\pi$
$313$	7.90105	+	13.6850i	0.446594	+	0.773523i	−0.551568	+	0.834130i	$0.685970\pi$
$314$	−1.92270	+	0.842938i	−0.108504	+	0.0475697i
$315$			0.840141i			0.0473366i
$316$	−7.64710	−	1.71682i	−0.430183	−	0.0965789i
$317$	−12.6842	+	7.32323i	−0.712416	+	0.411314i	−0.811955	−	0.583720i	$-0.801597\pi$
$317$	−12.6842	+	7.32323i	−0.712416	+	0.411314i	0.0995389	+	0.995034i	$0.468263\pi$
$318$	−5.82777	+	7.92579i	−0.326805	+	0.444456i
$319$	−9.31858	−	16.1403i	−0.521740	−	0.903681i
$320$	−0.570111	−	1.40827i	−0.0318702	−	0.0787248i
$321$	−12.5202	+	21.6856i	−0.698807	+	1.21037i
$322$	6.84669	+	0.759115i	0.381551	+	0.0423039i
$323$	7.63399	+	4.76683i	0.424766	+	0.265234i
$324$	−19.5272	−	4.38399i	−1.08485	−	0.243555i
$325$	2.86914	+	1.65650i	0.159151	+	0.0918861i
$326$	16.5254	+	12.1510i	0.915255	+	0.672980i
$327$	16.9980	+	29.4413i	0.939989	+	1.62811i
$328$	−2.93319	+	2.55156i	−0.161958	+	0.140886i
$329$	−9.22651	−	15.9808i	−0.508674	−	0.881049i
$330$	0.168057	−	1.51576i	0.00925125	−	0.0834398i
$331$		−	4.87906i		−	0.268177i	−0.990969	−	0.134089i	$-0.957189\pi$
$331$		−	4.87906i		−	0.268177i	0.990969	−	0.134089i	$-0.0428107\pi$
$332$	−13.2872	+	4.15034i	−0.729230	+	0.227780i
$333$	14.8387	−	8.56712i	0.813155	−	0.469476i
$334$	23.3748	+	2.59164i	1.27901	+	0.141808i
$335$	−0.351322			−0.0191948
$336$	15.9808	−	1.31191i	0.871824	−	0.0715708i
$337$	5.58021	−	9.66520i	0.303973	−	0.526497i	−0.673059	−	0.739589i	$-0.735020\pi$
$337$	5.58021	−	9.66520i	0.303973	−	0.526497i	0.977032	+	0.213092i	$0.0683533\pi$
$338$	7.12893	+	16.2608i	0.387762	+	0.884469i
$339$	−7.40842	−	4.27725i	−0.402370	−	0.232309i
$340$	0.576781	+	0.531371i	0.0312803	+	0.0288177i
$341$			18.7803i			1.01701i
$342$	−2.32938	+	15.9511i	−0.125958	+	0.862536i
$343$	18.8423			1.01739
$344$	−19.0424	−	21.8905i	−1.02670	−	1.18026i
$345$	−0.647884	+	1.12217i	−0.0348809	+	0.0604155i
$346$	21.8174	−	9.56503i	1.17291	−	0.514219i
$347$	1.59355	+	0.920039i	0.0855465	+	0.0493903i	0.542163	−	0.840273i	$-0.317606\pi$
$347$	1.59355	+	0.920039i	0.0855465	+	0.0493903i	−0.456617	+	0.889664i	$0.650939\pi$
$348$	10.9896	+	35.1829i	0.589105	+	1.88600i
$349$		−	11.1605i		−	0.597409i	−0.954346	−	0.298705i	$-0.903445\pi$
$349$		−	11.1605i		−	0.597409i	0.954346	−	0.298705i	$-0.0965545\pi$
$350$	11.8034	+	1.30868i	0.630919	+	0.0699521i
$351$	0.304399	+	0.527235i	0.0162476	+	0.0281417i
$352$	−13.5500	−	0.386453i	−0.722215	−	0.0205980i
$353$	31.3313			1.66760			0.833799	−	0.552068i	$-0.186161\pi$
$353$	31.3313			1.66760			0.833799	+	0.552068i	$0.186161\pi$
$354$	−40.0716	−	4.44287i	−2.12978	−	0.236136i
$355$	−0.240638	+	0.138932i	−0.0127717	+	0.00737377i
$356$	5.75664	−	6.24858i	0.305101	−	0.331174i
$357$	−7.16794	+	4.13841i	−0.379368	+	0.219028i
$358$	−13.7240	−	10.0911i	−0.725335	−	0.533333i
$359$	12.2185	−	21.1630i	0.644866	−	1.11694i	−0.339467	−	0.940618i	$-0.610247\pi$
$359$	12.2185	−	21.1630i	0.644866	−	1.11694i	0.984333	−	0.176322i	$-0.0564200\pi$
$360$	−0.456860	+	1.32831i	−0.0240786	+	0.0700080i
$361$	−18.9546	−	1.31319i	−0.997609	−	0.0691151i
$362$	−1.78988	+	16.1434i	−0.0940739	+	0.848481i
$363$	10.7897	+	6.22945i	0.566314	+	0.326962i
$364$	−1.66076	−	1.53001i	−0.0870476	−	0.0801945i
$365$	−1.45728	+	0.841363i	−0.0762777	+	0.0440389i
$366$	24.5530	−	33.3922i	1.28341	−	1.74544i
$367$	−7.70902	−	13.3524i	−0.402407	−	0.696990i	0.591608	−	0.806225i	$-0.298493\pi$
$367$	−7.70902	−	13.3524i	−0.402407	−	0.696990i	−0.994016	+	0.109235i	$0.965160\pi$
$368$	10.4122	+	4.92336i	0.542773	+	0.256648i
$369$	3.59439			0.187117
$370$	0.706577	+	1.61167i	0.0367332	+	0.0837867i
$371$	4.30085	−	2.48309i	0.223289	−	0.128916i
$372$	8.13618	−	36.2403i	0.421841	−	1.87897i
$373$		−	31.6565i		−	1.63911i	−0.572998	−	0.819557i	$-0.694220\pi$
$373$		−	31.6565i		−	1.63911i	0.572998	−	0.819557i	$-0.305780\pi$
$374$	6.40835	−	2.80950i	0.331368	−	0.145276i
$375$	−2.24197	+	3.88320i	−0.115775	+	0.200528i
$376$	−5.89743	−	30.2838i	−0.304137	−	1.56177i
$377$	2.59541	−	4.49538i	0.133670	−	0.231524i
$378$	1.75817	+	1.29277i	0.0904305	+	0.0664928i
$379$			28.0274i			1.43967i	0.694144	+	0.719836i	$0.255783\pi$
$379$			28.0274i			1.43967i	−0.694144	+	0.719836i	$0.744217\pi$
$380$	−1.60190	−	0.418309i	−0.0821755	−	0.0214588i
$381$			43.2037i			2.21339i
$382$	−8.88488	+	12.0835i	−0.454590	+	0.618244i
$383$	9.71714	−	16.8306i	0.496523	−	0.860003i	−0.503469	−	0.864013i	$-0.667943\pi$
$383$	9.71714	−	16.8306i	0.496523	−	0.860003i	0.999992	+	0.00401044i	$0.00127657\pi$
$384$	25.9799	+	6.61598i	1.32578	+	0.337620i
$385$	−0.384930	+	0.666718i	−0.0196178	+	0.0339791i
$386$	6.20320	+	14.1492i	0.315735	+	0.720176i
$387$			26.8252i			1.36360i
$388$	−8.54010	−	1.91731i	−0.433558	−	0.0973366i
$389$	−13.6173	+	7.86194i	−0.690424	+	0.398616i	−0.803771	−	0.594939i	$-0.797176\pi$
$389$	−13.6173	+	7.86194i	−0.690424	+	0.398616i	0.113347	+	0.993555i	$0.463843\pi$
$390$	0.389013	−	0.170548i	0.0196984	−	0.00863604i
$391$	−5.94519			−0.300661
$392$	11.0682	+	3.80681i	0.559029	+	0.192273i
$393$	−18.0310	−	31.2307i	−0.909546	−	1.57538i
$394$	9.35234	+	6.87669i	0.471164	+	0.346443i
$395$	−0.644507	+	0.372106i	−0.0324286	+	0.0187227i
$396$	9.21748	+	8.49179i	0.463196	+	0.426729i
$397$	−11.2072	−	6.47045i	−0.562471	−	0.324743i	0.191666	−	0.981460i	$-0.438611\pi$
$397$	−11.2072	−	6.47045i	−0.562471	−	0.324743i	−0.754137	+	0.656718i	$0.771944\pi$
$398$	−24.5977	−	2.72723i	−1.23297	−	0.136704i
$399$	9.25465	−	14.8211i	0.463312	−	0.741985i
$400$	17.9502	+	8.48768i	0.897510	+	0.424384i
$401$	7.24910	−	12.5558i	0.362003	−	0.627007i	−0.626288	−	0.779592i	$-0.715426\pi$
$401$	7.24910	−	12.5558i	0.362003	−	0.627007i	0.988290	+	0.152585i	$0.0487598\pi$
$402$	3.67243	−	4.99451i	0.183164	−	0.249104i
$403$	−4.52990	+	2.61534i	−0.225650	+	0.130279i
$404$	22.4300	+	20.6641i	1.11593	+	1.02808i
$405$	−1.64578	+	0.950191i	−0.0817794	+	0.0472154i
$406$	2.05045	−	18.4936i	0.101762	−	0.917823i
$407$	15.7009			0.778264
$408$	−13.5833	+	2.64520i	−0.672475	+	0.130957i
$409$	7.55056	+	13.0779i	0.373351	+	0.646663i	0.990079	−	0.140514i	$-0.0448754\pi$
$409$	7.55056	+	13.0779i	0.373351	+	0.646663i	−0.616728	+	0.787177i	$0.711542\pi$
$410$	−0.0406805	+	0.366910i	−0.00200907	+	0.0181204i
$411$		−	30.3602i		−	1.49756i
$412$	7.26040	+	23.2440i	0.357694	+	1.14515i
$413$	17.6258	+	10.1763i	0.867309	+	0.500741i
$414$	−4.27565	−	9.75256i	−0.210137	−	0.479312i
$415$	−0.660908	+	1.14473i	−0.0324427	+	0.0561924i
$416$	−1.79375	−	3.32214i	−0.0879459	−	0.162881i
$417$	−26.8610			−1.31539
$418$	−9.15689	+	11.5912i	−0.447878	+	0.566943i
$419$			14.9627i			0.730975i	0.930816	+	0.365487i	$0.119098\pi$
$419$			14.9627i			0.730975i	−0.930816	+	0.365487i	$0.880902\pi$
$420$	1.03164	−	1.11980i	0.0503389	−	0.0546407i
$421$	13.6247	+	7.86623i	0.664028	+	0.383377i	0.793810	−	0.608166i	$-0.208094\pi$
$421$	13.6247	+	7.86623i	0.664028	+	0.383377i	−0.129782	+	0.991543i	$0.541428\pi$
$422$	−3.85314	+	1.68927i	−0.187568	+	0.0822321i
$423$	−14.2626	+	24.7035i	−0.693470	+	1.20113i
$424$	8.15015	−	1.58715i	0.395806	−	0.0770789i
$425$	−10.2493			−0.497163
$426$	0.540316	−	4.87327i	0.0261784	−	0.236111i
$427$	−18.1199	+	10.4615i	−0.876884	+	0.506269i
$428$	20.1733	−	6.30127i	0.975114	−	0.304583i
$429$		−	3.78976i		−	0.182971i
$430$	−2.73827	−	0.303601i	−0.132051	−	0.0146409i
$431$	17.5028	+	30.3157i	0.843080	+	1.46026i	0.887278	+	0.461235i	$0.152593\pi$
$431$	17.5028	+	30.3157i	0.843080	+	1.46026i	−0.0441982	+	0.999023i	$0.514073\pi$
$432$	2.07677	+	3.00001i	0.0999185	+	0.144338i
$433$	−0.852555	−	1.47667i	−0.0409712	−	0.0709641i	0.844813	−	0.535062i	$-0.179712\pi$
$433$	−0.852555	−	1.47667i	−0.0409712	−	0.0709641i	−0.885784	+	0.464098i	$0.846379\pi$
$434$	−11.1072	+	15.1059i	−0.533163	+	0.725104i
$435$	3.03109	+	1.75000i	0.145330	+	0.0839062i
$436$	6.28537	−	27.9964i	0.301014	−	1.34078i
$437$	11.0799	−	5.89586i	0.530024	−	0.282037i
$438$	3.27210	−	29.5121i	0.156347	−	1.41014i
$439$	3.75936	−	6.51141i	0.179425	−	0.310772i	−0.762259	−	0.647272i	$-0.775910\pi$
$439$	3.75936	−	6.51141i	0.179425	−	0.310772i	0.941684	+	0.336500i	$0.109243\pi$
$440$	−0.971149	+	0.844796i	−0.0462977	+	0.0402741i
$441$	−5.41080	−	9.37178i	−0.257657	−	0.446275i
$442$	1.57009	+	1.15448i	0.0746816	+	0.0549128i
$443$	14.4421	−	8.33817i	0.686166	−	0.396158i	−0.116008	−	0.993248i	$-0.537010\pi$
$443$	14.4421	−	8.33817i	0.686166	−	0.396158i	0.802174	+	0.597090i	$0.203677\pi$
$444$	−30.2980	−	6.80209i	−1.43788	−	0.322813i
$445$		−	0.806754i		−	0.0382438i
$446$	−2.09951	−	4.78890i	−0.0994149	−	0.226761i
$447$	−3.78918	−	6.56305i	−0.179222	−	0.310422i
$448$	−10.6703	−	8.32468i	−0.504124	−	0.393304i
$449$	−28.8395			−1.36102			−0.680510	−	0.732739i	$-0.738242\pi$
$449$	−28.8395			−1.36102			−0.680510	+	0.732739i	$0.738242\pi$
$450$	−7.37105	−	16.8130i	−0.347474	−	0.792573i
$451$	2.85243	+	1.64685i	0.134316	+	0.0775473i
$452$	2.15270	+	6.89180i	0.101254	+	0.324163i
$453$	3.82152	+	2.20636i	0.179551	+	0.103664i
$454$	19.7579	+	14.5278i	0.927283	+	0.681824i
$455$	−0.214421			−0.0100522
$456$	22.6917	−	18.4004i	1.06264	−	0.861679i
$457$	29.8262			1.39521			0.697606	−	0.716482i	$-0.254249\pi$
$457$	29.8262			1.39521			0.697606	+	0.716482i	$0.254249\pi$
$458$	−32.3126	−	23.7592i	−1.50987	−	1.11019i
$459$	−1.63108	−	0.941706i	−0.0761324	−	0.0439551i
$460$	1.04392	−	0.326074i	0.0486728	−	0.0152033i
$461$	8.11372	+	4.68446i	0.377893	+	0.218177i	0.676901	−	0.736074i	$-0.263322\pi$
$461$	8.11372	+	4.68446i	0.377893	+	0.218177i	−0.299008	+	0.954251i	$0.596656\pi$
$462$	−5.45456	−	12.4416i	−0.253769	−	0.578835i
$463$	1.77700			0.0825841			0.0412921	−	0.999147i	$-0.486853\pi$
$463$	1.77700			0.0825841			0.0412921	+	0.999147i	$0.486853\pi$
$464$	13.2985	−	28.1244i	0.617368	−	1.30564i
$465$	−1.76344	−	3.05437i	−0.0817777	−	0.141643i
$466$	−1.30692	−	2.98103i	−0.0605420	−	0.138093i
$467$		−	21.8590i		−	1.01151i	−0.862676	−	0.505757i	$-0.831213\pi$
$467$		−	21.8590i		−	1.01151i	0.862676	−	0.505757i	$-0.168787\pi$
$468$	−0.764640	+	3.40587i	−0.0353455	+	0.157436i
$469$	−2.71022	+	1.56475i	−0.125146	+	0.0722533i
$470$	−2.36027	−	1.73549i	−0.108871	−	0.0800521i
$471$	−1.75881	−	3.04635i	−0.0810418	−	0.140369i
$472$	22.3336	+	25.6739i	1.02799	+	1.18174i
$473$	−12.2906	+	21.2879i	−0.565121	+	0.978818i
$474$	1.44714	−	13.0522i	0.0664694	−	0.599507i
$475$	19.1013	−	10.1642i	0.876429	−	0.466367i
$476$	6.81615	+	1.53027i	0.312418	+	0.0701398i
$477$	−6.64836	−	3.83843i	−0.304407	−	0.175750i
$478$	−11.7857	+	16.0286i	−0.539064	+	0.733129i
$479$	0.781278	+	1.35321i	0.0356975	+	0.0618299i	0.883322	−	0.468766i	$-0.155301\pi$
$479$	0.781278	+	1.35321i	0.0356975	+	0.0618299i	−0.847625	+	0.530596i	$0.821968\pi$
$480$	2.24001	−	1.20947i	0.102242	−	0.0552045i
$481$	2.18650	+	3.78714i	0.0996960	+	0.172678i
$482$	−21.3066	−	2.36234i	−0.970490	−	0.107601i
$483$			11.5424i			0.525197i
$484$	−3.13522	−	10.0373i	−0.142510	−	0.456242i
$485$	−0.719770	+	0.415559i	−0.0326831	+	0.0188696i
$486$	3.26887	−	29.4830i	0.148279	−	1.33737i
$487$	32.4041			1.46837			0.734185	−	0.678950i	$-0.237564\pi$
$487$	32.4041			1.46837			0.734185	+	0.678950i	$0.237564\pi$
$488$	−34.3374	+	6.68684i	−1.55438	+	0.302699i
$489$	−17.1844	+	29.7643i	−0.777108	+	1.34599i
$490$	1.01789	−	0.446257i	0.0459837	−	0.0201599i
$491$	−8.21894	−	4.74521i	−0.370915	−	0.214148i	0.302943	−	0.953009i	$-0.402031\pi$
$491$	−8.21894	−	4.74521i	−0.370915	−	0.214148i	−0.673858	+	0.738861i	$0.735364\pi$
$492$	−4.79087	−	4.41369i	−0.215989	−	0.198984i
$493$			16.0586i			0.723242i
$494$	−4.07104	−	0.594504i	−0.183165	−	0.0267480i
$495$	1.19007			0.0534896
$496$	−25.7755	+	17.8432i	−1.15735	+	0.801182i
$497$	−1.23758	+	2.14354i	−0.0555129	+	0.0961511i
$498$	−9.36523	−	21.3617i	−0.419666	−	0.957239i
$499$	−2.66996	−	1.54150i	−0.119524	−	0.0690070i	0.439046	−	0.898464i	$-0.355316\pi$
$499$	−2.66996	−	1.54150i	−0.119524	−	0.0690070i	−0.558570	+	0.829457i	$0.688650\pi$
$500$	3.61241	−	1.12836i	0.161552	−	0.0504618i
$501$			39.4061i			1.76053i
$502$	−0.988372	+	8.91443i	−0.0441132	+	0.397870i
$503$	−6.04253	−	10.4660i	−0.269423	−	0.466655i	0.699290	−	0.714838i	$-0.253500\pi$
$503$	−6.04253	−	10.4660i	−0.269423	−	0.466655i	−0.968713	+	0.248184i	$0.920166\pi$
$504$	2.39175	+	12.2818i	0.106537	+	0.547076i
$505$	2.89593			0.128867
$506$	1.07529	−	9.69840i	0.0478027	−	0.431147i
$507$	−25.7637	+	14.8747i	−1.14421	+	0.660609i
$508$	24.7072	−	26.8186i	1.09620	−	1.18988i
$509$	35.3659	−	20.4185i	1.56757	−	0.905036i	0.571116	−	0.820869i	$-0.306511\pi$
$509$	35.3659	−	20.4185i	1.56757	−	0.905036i	0.996452	−	0.0841664i	$-0.0268227\pi$
$510$	−0.778427	+	1.05866i	−0.0344693	+	0.0468784i
$511$	−7.49465	+	12.9811i	−0.331544	+	0.574251i
$512$	−12.3434	−	18.9642i	−0.545508	−	0.838105i
$513$	3.97370	+	0.137486i	0.175443	+	0.00607015i
$514$	21.3466	+	2.36677i	0.941559	+	0.104394i
$515$	2.00253	+	1.15616i	0.0882418	+	0.0509465i
$516$	32.9396	−	35.7545i	1.45009	−	1.57401i
$517$	−22.6369	+	13.0694i	−0.995572	+	0.574794i
$518$	12.6289	+	9.28596i	0.554884	+	0.408002i
$519$	19.9577	+	34.5678i	0.876046	+	1.51736i
$520$	−0.339011	−	0.116600i	−0.0148666	−	0.00511324i
$521$	39.4916			1.73016			0.865079	−	0.501635i	$-0.167268\pi$
$521$	39.4916			1.73016			0.865079	+	0.501635i	$0.167268\pi$
$522$	−26.3427	+	11.5490i	−1.15299	+	0.505485i
$523$	−18.5865	+	10.7309i	−0.812732	+	0.469231i	−0.847904	−	0.530150i	$-0.822136\pi$
$523$	−18.5865	+	10.7309i	−0.812732	+	0.469231i	0.0351715	+	0.999381i	$0.488802\pi$
$524$	−6.66737	+	29.6979i	−0.291266	+	1.29736i
$525$			19.8986i			0.868447i
$526$	−9.81121	−	22.3789i	−0.427789	−	0.975767i
$527$	8.09095	−	14.0139i	0.352447	−	0.610457i
$528$	−1.85834	−	22.6370i	−0.0808738	−	0.985147i
$529$	7.35459	−	12.7385i	0.319765	−	0.553849i
$530$	0.467065	−	0.635210i	0.0202880	−	0.0275918i
$531$		−	31.4614i		−	1.36531i
$532$	−14.2207	+	3.90767i	−0.616544	+	0.169419i
$533$			0.917362i			0.0397354i
$534$	11.4691	+	8.43312i	0.496316	+	0.364937i
$535$	1.00342	−	1.73798i	0.0433818	−	0.0751395i
$536$	−5.13590	+	1.00016i	−0.221837	+	0.0432003i
$537$	14.2713	−	24.7187i	0.615854	−	1.06669i
$538$	−8.87504	+	3.89093i	−0.382630	+	0.167750i
$539$		−	9.91632i		−	0.427126i
$540$	0.338051	+	0.0758946i	0.0145474	+	0.00326599i
$541$	−0.0386684	+	0.0223252i	−0.00166249	+	0.000959837i	−0.500831	−	0.865545i	$-0.666972\pi$
$541$	−0.0386684	+	0.0223252i	−0.00166249	+	0.000959837i	0.499169	+	0.866505i	$0.333639\pi$
$542$	10.5315	+	24.0218i	0.452365	+	1.03182i
$543$	−27.2152			−1.16792
$544$	9.94455	+	6.12599i	0.426369	+	0.262650i
$545$	−1.36230	−	2.35957i	−0.0583544	−	0.101073i
$546$	2.24138	−	3.04828i	0.0959220	−	0.130454i
$547$	−26.8479	+	15.5006i	−1.14793	+	0.662759i	−0.948382	−	0.317129i	$-0.897281\pi$
$547$	−26.8479	+	15.5006i	−1.14793	+	0.662759i	−0.199549	+	0.979888i	$0.563948\pi$
$548$	−17.3623	+	18.8460i	−0.741681	+	0.805063i
$549$	28.0102	+	16.1717i	1.19545	+	0.690192i
$550$	1.85376	−	16.7197i	0.0790448	−	0.712929i
$551$	−15.9253	−	29.9280i	−0.678442	−	1.27498i
$552$	−6.27663	+	18.2491i	−0.267151	+	0.776735i
$553$	−3.31463	+	5.74111i	−0.140952	+	0.244137i
$554$	−17.7607	−	13.0593i	−0.754578	−	0.554835i
$555$	−2.55355	+	1.47429i	−0.108392	+	0.0625802i
$556$	16.6739	+	15.3612i	0.707130	+	0.651459i
$557$	31.3179	−	18.0814i	1.32698	−	0.766134i	0.342151	−	0.939645i	$-0.388845\pi$
$557$	31.3179	−	18.0814i	1.32698	−	0.766134i	0.984832	+	0.173511i	$0.0555113\pi$
$558$	28.8075	+	3.19398i	1.21952	+	0.135212i
$559$	−6.84633			−0.289569
$560$	−1.28078	+	0.105143i	−0.0541227	+	0.00444310i
$561$	5.86210	+	10.1535i	0.247498	+	0.428679i
$562$	37.9989	+	4.21306i	1.60289	+	0.177717i
$563$		−	31.7143i		−	1.33660i	−0.743893	−	0.668299i	$-0.767023\pi$
$563$		−	31.7143i		−	1.33660i	0.743893	−	0.668299i	$-0.232977\pi$
$564$	49.3445	−	15.4131i	2.07778	−	0.649008i
$565$	0.593746	+	0.342799i	0.0249791	+	0.0144217i
$566$	−15.5439	+	6.81464i	−0.653358	+	0.286441i
$567$	−8.46407	+	14.6602i	−0.355457	+	0.615670i
$568$	−3.12231	+	2.71608i	−0.131009	+	0.113964i
$569$	12.6400			0.529895			0.264947	−	0.964263i	$-0.414645\pi$
$569$	12.6400			0.529895			0.264947	+	0.964263i	$0.414645\pi$
$570$	0.400856	−	2.74498i	0.0167900	−	0.114974i
$571$		−	11.4543i		−	0.479348i	−0.970853	−	0.239674i	$-0.922959\pi$
$571$		−	11.4543i		−	0.479348i	0.970853	−	0.239674i	$-0.0770406\pi$
$572$	−2.16728	+	2.35249i	−0.0906184	+	0.0983624i
$573$	−21.7639	−	12.5654i	−0.909200	−	0.524927i
$574$	1.32035	+	3.01165i	0.0551102	+	0.125704i
$575$	−7.14652	+	12.3781i	−0.298031	+	0.516204i
$576$	−2.89724	+	20.7188i	−0.120718	+	0.863285i
$577$	18.1202			0.754354			0.377177	−	0.926141i	$-0.376895\pi$
$577$	18.1202			0.754354			0.377177	+	0.926141i	$0.376895\pi$
$578$	17.9029	+	1.98495i	0.744662	+	0.0825631i
$579$	−22.4182	+	12.9432i	−0.931669	+	0.537899i
$580$	−0.880759	−	2.81972i	−0.0365715	−	0.117083i
$581$			11.7744i			0.488485i
$582$	1.61613	−	14.5764i	0.0669908	−	0.604211i
$583$	−3.51733	−	6.09219i	−0.145673	−	0.252313i
$584$	−18.9084	+	16.4483i	−0.782437	+	0.680637i
$585$	0.165729	+	0.287051i	0.00685204	+	0.0118681i
$586$	−11.4136	−	8.39234i	−0.471492	−	0.346684i
$587$	12.2255	+	7.05842i	0.504602	+	0.291332i	0.730612	−	0.682793i	$-0.239235\pi$
$587$	12.2255	+	7.05842i	0.504602	+	0.291332i	−0.226010	+	0.974125i	$0.572568\pi$
$588$	−4.29604	+	19.1355i	−0.177166	+	0.789135i
$589$	−1.18125	+	34.1413i	−0.0486726	+	1.40677i
$590$	3.21153	+	0.356073i	0.132217	+	0.0146593i
$591$	−9.72533	+	16.8448i	−0.400047	+	0.692901i
$592$	14.9174	+	21.5491i	0.613103	+	0.885662i
$593$	−10.0302	−	17.3728i	−0.411891	−	0.713417i	0.583205	−	0.812325i	$-0.301798\pi$
$593$	−10.0302	−	17.3728i	−0.411891	−	0.713417i	−0.995097	+	0.0989082i	$0.968465\pi$
$594$	1.83122	−	2.49046i	0.0751358	−	0.102185i
$595$	0.574473	−	0.331672i	0.0235511	−	0.0135972i
$596$	−1.40113	+	6.24094i	−0.0573926	+	0.255639i
$597$		−	41.4677i		−	1.69716i
$598$	2.48905	−	1.09123i	0.101785	−	0.0446238i
$599$	−8.63575	−	14.9576i	−0.352847	−	0.611149i	0.633900	−	0.773415i	$-0.281453\pi$
$599$	−8.63575	−	14.9576i	−0.352847	−	0.611149i	−0.986747	+	0.162266i	$0.948120\pi$
$600$	−10.8207	+	31.4608i	−0.441752	+	1.28438i
$601$	−27.9233			−1.13901			−0.569507	−	0.821986i	$-0.692866\pi$
$601$	−27.9233			−1.13901			−0.569507	+	0.821986i	$0.692866\pi$
$602$	−22.4761	+	9.85383i	−0.916059	+	0.401612i
$603$	4.18953	+	2.41882i	0.170611	+	0.0985021i
$604$	−1.11044	−	3.55503i	−0.0451830	−	0.144652i
$605$	−0.864740	−	0.499258i	−0.0351567	−	0.0202977i
$606$	−30.2716	+	41.1695i	−1.22970	+	1.67240i
$607$	−8.30590			−0.337126			−0.168563	−	0.985691i	$-0.553913\pi$
$607$	−8.30590			−0.337126			−0.168563	+	0.985691i	$0.553913\pi$
$608$	−24.6086	−	1.55482i	−0.998010	−	0.0630561i
$609$	31.1772			1.26336
$610$	−1.96779	+	2.67621i	−0.0796736	+	0.108357i
$611$	−6.30483	−	3.64010i	−0.255066	−	0.147263i
$612$	−3.21968	−	10.3077i	−0.130148	−	0.416664i
$613$	16.9256	+	9.77202i	0.683620	+	0.394688i	0.801217	−	0.598373i	$-0.204186\pi$
$613$	16.9256	+	9.77202i	0.683620	+	0.394688i	−0.117598	+	0.993061i	$0.537519\pi$
$614$	1.85030	−	0.811193i	0.0746718	−	0.0327371i
$615$	−0.618549			−0.0249423
$616$	−3.72916	+	10.8424i	−0.150252	+	0.436854i
$617$	−3.52112	−	6.09876i	−0.141755	−	0.245527i	0.786403	−	0.617714i	$-0.211941\pi$
$617$	−3.52112	−	6.09876i	−0.141755	−	0.245527i	−0.928158	+	0.372187i	$0.878608\pi$
$618$	−37.3690	+	16.3831i	−1.50320	+	0.659024i
$619$		−	15.9039i		−	0.639231i	−0.947547	−	0.319615i	$-0.896446\pi$
$619$		−	15.9039i		−	0.639231i	0.947547	−	0.319615i	$-0.103554\pi$
$620$	−0.652072	+	2.90447i	−0.0261878	+	0.116646i
$621$	−2.27461	+	1.31325i	−0.0912771	+	0.0526989i
$622$	−18.4422	+	25.0815i	−0.739466	+	1.00568i
$623$	−3.59318	−	6.22358i	−0.143958	−	0.249342i
$624$	5.20136	−	3.60066i	0.208221	−	0.144142i
$625$	−12.2302	+	21.1832i	−0.489206	+	0.847330i
$626$	22.2114	+	2.46266i	0.887748	+	0.0984276i
$627$	−20.9943	−	13.1093i	−0.838431	−	0.523535i
$628$	−0.650360	+	2.89684i	−0.0259522	+	0.115597i
$629$	−11.7161	−	6.76428i	−0.467151	−	0.269710i
$630$	0.957227	+	0.703841i	0.0381368	+	0.0280417i
$631$	−17.8292	−	30.8810i	−0.709767	−	1.22935i	−0.964943	−	0.262458i	$-0.915467\pi$
$631$	−17.8292	−	30.8810i	−0.709767	−	1.22935i	0.255176	−	0.966895i	$-0.417867\pi$
$632$	−8.36256	+	7.27454i	−0.332645	+	0.289366i
$633$	−3.52470	−	6.10496i	−0.140094	−	0.242650i
$634$	−2.28256	+	20.5871i	−0.0906519	+	0.817617i
$635$		−	3.46255i		−	0.137407i
$636$	4.14806	+	13.2799i	0.164481	+	0.526582i
$637$	2.39187	−	1.38095i	0.0947692	−	0.0547150i
$638$	−26.1964	−	2.90448i	−1.03713	−	0.114990i
$639$	3.82615			0.151360
$640$	−2.08215	−	0.530236i	−0.0823043	−	0.0209594i
$641$	−5.98642	+	10.3688i	−0.236450	+	0.409543i	−0.959693	−	0.281051i	$-0.909317\pi$
$641$	−5.98642	+	10.3688i	−0.236450	+	0.409543i	0.723243	+	0.690593i	$0.242650\pi$
$642$	14.2188	+	32.4324i	0.561171	+	1.28001i
$643$	−8.69276	−	5.01877i	−0.342809	−	0.197921i	0.318705	−	0.947854i	$-0.396752\pi$
$643$	−8.69276	−	5.01877i	−0.342809	−	0.197921i	−0.661513	+	0.749933i	$0.730086\pi$
$644$	6.60083	−	7.16491i	0.260109	−	0.282337i
$645$		−	4.61627i		−	0.181765i
$646$	11.8266	−	4.70440i	0.465313	−	0.185092i
$647$	−40.2359			−1.58184			−0.790918	−	0.611922i	$-0.790397\pi$
$647$	−40.2359			−1.58184			−0.790918	+	0.611922i	$0.790397\pi$
$648$	−21.3542	+	18.5759i	−0.838872	+	0.729730i
$649$	14.4148	−	24.9671i	0.565829	−	0.980045i
$650$	4.29102	−	1.88124i	0.168308	−	0.0737883i
$651$	−27.2076	−	15.7083i	−1.06635	−	0.615657i
$652$	27.6887	−	8.64876i	1.08437	−	0.338711i
$653$		−	43.7050i		−	1.71031i	−0.518375	−	0.855153i	$-0.673463\pi$
$653$		−	43.7050i		−	1.71031i	0.518375	−	0.855153i	$-0.326537\pi$
$654$	47.7847	+	5.29804i	1.86853	+	0.207170i
$655$	1.44509	+	2.50297i	0.0564645	+	0.0977993i
$656$	0.449835	+	5.47957i	0.0175631	+	0.213941i
$657$	23.1708			0.903980
$658$	−25.9376	−	2.87579i	−1.01115	−	0.112110i
$659$	4.18148	−	2.41418i	0.162888	−	0.0940432i	−0.416340	−	0.909209i	$-0.636688\pi$
$659$	4.18148	−	2.41418i	0.162888	−	0.0940432i	0.579228	+	0.815166i	$0.303354\pi$
$660$	−1.58621	−	1.46133i	−0.0617431	−	0.0568821i
$661$	9.74688	−	5.62737i	0.379110	−	0.218879i	−0.298321	−	0.954466i	$-0.596427\pi$
$661$	9.74688	−	5.62737i	0.379110	−	0.218879i	0.677431	+	0.735586i	$0.263093\pi$
$662$	−5.55902	−	4.08750i	−0.216058	−	0.158865i
$663$	−1.63271	+	2.82794i	−0.0634093	+	0.109828i
$664$	−6.40280	+	18.6160i	−0.248477	+	0.722440i
$665$	−0.741711	+	1.18784i	−0.0287623	+	0.0460623i
$666$	2.67026	−	24.0839i	0.103471	−	0.933232i
$667$	19.3941	+	11.1972i	0.750942	+	0.433557i
$668$	22.5354	−	24.4612i	0.871922	−	0.946434i
$669$	7.58759	−	4.38070i	0.293353	−	0.169368i
$670$	−0.294326	+	0.400284i	−0.0113708	+	0.0154643i
$671$	14.8189	+	25.6670i	0.572076	+	0.990865i
$672$	11.8934	−	19.3070i	0.458798	−	0.744785i
$673$	−20.3750			−0.785400			−0.392700	−	0.919667i	$-0.628459\pi$
$673$	−20.3750			−0.785400			−0.392700	+	0.919667i	$0.628459\pi$
$674$	−6.33728	−	14.4551i	−0.244103	−	0.556788i
$675$	−3.92134	+	2.26399i	−0.150933	+	0.0871410i
$676$	24.4993	+	5.50025i	0.942280	+	0.211548i
$677$			23.5908i			0.906667i	0.891341	+	0.453333i	$0.149765\pi$
$677$			23.5908i			0.906667i	−0.891341	+	0.453333i	$0.850235\pi$
$678$	−11.0799	+	4.85756i	−0.425520	+	0.186553i
$679$	−3.70170	+	6.41153i	−0.142058	+	0.246052i
$680$	1.08863	−	0.211999i	0.0417471	−	0.00812980i
$681$	−20.5459	+	35.5865i	−0.787320	+	1.36368i
$682$	21.3976	+	15.7335i	0.819356	+	0.602465i
$683$			16.2258i			0.620863i	0.950596	+	0.310431i	$0.100473\pi$
$683$			16.2258i			0.620863i	−0.950596	+	0.310431i	$0.899527\pi$
$684$	16.2226	+	16.0173i	0.620287	+	0.612435i
$685$			2.43321i			0.0929682i
$686$	15.7854	−	21.4683i	0.602691	−	0.819663i
$687$	33.6013	−	58.1992i	1.28197	−	2.22044i
$688$	−40.8944	+	3.35715i	−1.55908	+	0.127990i
$689$	0.979645	−	1.69679i	0.0373215	−	0.0646427i
$690$	0.735784	+	1.67829i	0.0280108	+	0.0638914i
$691$		−	29.1062i		−	1.10725i	−0.832765	−	0.553626i	$-0.813244\pi$
$691$		−	29.1062i		−	1.10725i	0.832765	−	0.553626i	$-0.186756\pi$
$692$	7.37980	−	32.8712i	0.280538	−	1.24958i
$693$	9.18059	−	5.30042i	0.348742	−	0.201346i
$694$	2.38328	−	1.04486i	0.0904682	−	0.0396624i
$695$	2.15277			0.0816590
$696$	49.2928	+	16.9538i	1.86844	+	0.642633i
$697$	−1.41900	−	2.45778i	−0.0537484	−	0.0930950i
$698$	−12.7159	−	9.34989i	−0.481304	−	0.353899i
$699$	4.72318	−	2.72693i	0.178647	−	0.103142i
$700$	11.3796	−	12.3520i	0.430107	−	0.466863i
$701$	−41.0190	−	23.6824i	−1.54927	−	0.894470i	−0.998198	−	0.0600112i	$-0.980886\pi$
$701$	−41.0190	−	23.6824i	−1.54927	−	0.894470i	−0.551070	−	0.834459i	$-0.685780\pi$
$702$	0.855728	+	0.0948774i	0.0322974	+	0.00358092i
$703$	28.5431	+	0.987562i	1.07652	+	0.0372466i
$704$	−11.7920	+	15.1146i	−0.444427	+	0.569652i
$705$	2.45441	−	4.25115i	0.0924383	−	0.160108i
$706$	26.2483	−	35.6978i	0.987867	−	1.34350i
$707$	22.3402	−	12.8981i	0.840190	−	0.485084i
$708$	−38.6327	+	41.9341i	−1.45190	+	1.57598i
$709$	−15.0641	+	8.69724i	−0.565743	+	0.326632i	−0.755447	−	0.655210i	$-0.772580\pi$
$709$	−15.0641	+	8.69724i	−0.565743	+	0.326632i	0.189705	+	0.981841i	$0.439247\pi$
$710$	−0.0433034	+	0.390567i	−0.00162515	+	0.0146577i
$711$	10.2477			0.384318
$712$	−2.29670	−	11.7937i	−0.0860725	−	0.441989i
$713$	−11.2832	−	19.5430i	−0.422558	−	0.731892i
$714$	−1.28989	+	11.6339i	−0.0482729	+	0.435388i
$715$			0.303730i			0.0113588i
$716$	−22.9949	+	7.18262i	−0.859362	+	0.268427i
$717$	−28.8695	−	16.6678i	−1.07815	−	0.622471i
$718$	−13.8762	−	31.6509i	−0.517853	−	1.18120i
$719$	−9.36490	+	16.2205i	−0.349252	+	0.604922i	−0.986117	−	0.166054i	$-0.946897\pi$
$719$	−9.36490	+	16.2205i	−0.349252	+	0.604922i	0.636865	+	0.770975i	$0.280231\pi$
$720$	1.13069	+	1.63334i	0.0421382	+	0.0608710i
$721$	20.5976			0.767093
$722$	−17.3757	+	20.4960i	−0.646655	+	0.762782i
$723$		−	35.9194i		−	1.33586i
$724$	16.8938	+	15.5637i	0.627852	+	0.578422i
$725$	33.4346	+	19.3035i	1.24173	+	0.716914i
$726$	16.1369	−	7.07461i	0.598895	−	0.262564i
$727$	−10.4941	+	18.1763i	−0.389205	+	0.674123i	−0.992343	−	0.123514i	$-0.960584\pi$
$727$	−10.4941	+	18.1763i	−0.389205	+	0.674123i	0.603138	+	0.797637i	$0.293917\pi$
$728$	−3.13457	+	0.610423i	−0.116175	+	0.0226238i
$729$	19.6834			0.729016
$730$	−0.262242	+	2.36524i	−0.00970601	+	0.0875414i
$731$	18.3425	−	10.5901i	0.678424	−	0.391688i
$732$	−17.4762	−	55.9496i	−0.645940	−	2.06796i
$733$			17.9327i			0.662358i	0.943568	+	0.331179i	$0.107446\pi$
$733$			17.9327i			0.662358i	−0.943568	+	0.331179i	$0.892554\pi$
$734$	−21.6716	−	2.40280i	−0.799913	−	0.0886890i
$735$	0.931129	+	1.61276i	0.0343452	+	0.0594876i
$736$	14.3325	−	7.73865i	0.528302	−	0.285251i
$737$	2.21648	+	3.83905i	0.0816450	+	0.141413i
$738$	3.01126	−	4.09532i	0.110846	−	0.150751i
$739$	38.6989	+	22.3428i	1.42356	+	0.821893i	0.996601	−	0.0823770i	$-0.0262512\pi$
$739$	38.6989	+	22.3428i	1.42356	+	0.821893i	0.426960	+	0.904270i	$0.359584\pi$
$740$	2.42822	+	0.545152i	0.0892632	+	0.0200402i
$741$	0.238370	−	6.88953i	0.00875675	−	0.253093i
$742$	0.773949	−	6.98048i	0.0284126	−	0.256261i
$743$	−8.74997	+	15.1554i	−0.321005	+	0.555997i	−0.980696	−	0.195540i	$-0.937354\pi$
$743$	−8.74997	+	15.1554i	−0.321005	+	0.555997i	0.659690	+	0.751537i	$0.270687\pi$
$744$	−34.4747	−	39.6309i	−1.26390	−	1.45294i
$745$	0.303683	+	0.525994i	0.0111261	+	0.0192709i
$746$	−36.0683	−	26.5207i	−1.32056	−	0.970993i
$747$	15.7627	−	9.10058i	0.576726	−	0.332973i
$748$	2.16764	−	9.65514i	0.0792568	−	0.353027i
$749$		−	17.8765i		−	0.653194i
$750$	2.54614	+	5.80763i	0.0929719	+	0.212065i
$751$	24.1697	+	41.8632i	0.881966	+	1.52761i	0.849152	+	0.528149i	$0.177114\pi$
$751$	24.1697	+	41.8632i	0.881966	+	1.52761i	0.0328148	+	0.999461i	$0.489553\pi$
$752$	−39.4449	−	18.6514i	−1.43841	−	0.680145i
$753$	−15.0282			−0.547660
$754$	−2.94753	−	6.72318i	−0.107343	−	0.244844i
$755$	−0.306275	−	0.176828i	−0.0111465	−	0.00643542i
$756$	2.94587	−	0.920160i	0.107140	−	0.0334659i
$757$	45.8916	+	26.4955i	1.66796	+	0.962996i	0.968737	+	0.248090i	$0.0798028\pi$
$757$	45.8916	+	26.4955i	1.66796	+	0.962996i	0.699221	+	0.714906i	$0.253531\pi$
$758$	31.9334	+	23.4804i	1.15988	+	0.852846i
$759$	16.3499			0.593464
$760$	−1.81862	+	1.47470i	−0.0659682	+	0.0534929i
$761$	−36.4487			−1.32127			−0.660633	−	0.750709i	$-0.729712\pi$
$761$	−36.4487			−1.32127			−0.660633	+	0.750709i	$0.729712\pi$
$762$	49.2247	+	36.1945i	1.78322	+	1.31119i
$763$	−21.0184	−	12.1350i	−0.760918	−	0.439316i
$764$	6.32404	+	20.2462i	0.228796	+	0.732483i
$765$	−0.888035	−	0.512707i	−0.0321070	−	0.0185370i
$766$	−11.0355	−	25.1714i	−0.398728	−	0.909481i
$767$	8.02960			0.289932
$768$	29.3031	−	24.0579i	1.05738	−	0.868116i
$769$	−20.7706	−	35.9758i	−0.749008	−	1.29732i	−0.948298	−	0.317380i	$-0.897197\pi$
$769$	−20.7706	−	35.9758i	−0.749008	−	1.29732i	0.199290	−	0.979941i	$-0.436136\pi$
$770$	0.437154	+	0.997128i	0.0157539	+	0.0359340i
$771$			35.9869i			1.29604i
$772$	21.3179	+	4.78601i	0.767249	+	0.172252i
$773$	37.4904	−	21.6451i	1.34844	−	0.778519i	0.360407	−	0.932795i	$-0.382638\pi$
$773$	37.4904	−	21.6451i	1.34844	−	0.778519i	0.988028	+	0.154276i	$0.0493043\pi$
$774$	30.5636	+	22.4732i	1.09859	+	0.807782i
$775$	−19.4517	−	33.6914i	−0.698727	−	1.21023i
$776$	−9.33911	+	8.12403i	−0.335254	+	0.291636i
$777$	−13.1326	+	22.7464i	−0.471130	+	0.816022i
$778$	−2.45047	+	22.1015i	−0.0878535	+	0.792377i
$779$	5.08194	+	3.17328i	0.182079	+	0.113695i
$780$	0.131585	−	0.586106i	0.00471149	−	0.0209860i
$781$	3.03635	+	1.75304i	0.108649	+	0.0627286i
$782$	−4.98067	+	6.77373i	−0.178108	+	0.242228i
$783$	3.54722	+	6.14397i	0.126767	+	0.219568i
$784$	13.6099	−	9.42151i	0.486068	−	0.336482i
$785$	0.140960	+	0.244149i	0.00503106	+	0.00871406i
$786$	−50.6889	−	5.62005i	−1.80801	−	0.200460i
$787$			22.6592i			0.807713i	0.914822	+	0.403856i	$0.132330\pi$
$787$			22.6592i			0.807713i	−0.914822	+	0.403856i	$0.867670\pi$
$788$	15.6701	−	4.89466i	0.558225	−	0.174365i
$789$	35.4574	−	20.4714i	1.26232	−	0.728800i
$790$	−0.115981	+	1.04606i	−0.00412641	+	0.0372173i
$791$	6.10714			0.217145
$792$	17.3973	−	3.38794i	0.618187	−	0.120385i
$793$	−4.12735	+	7.14878i	−0.146566	+	0.253860i
$794$	−16.7612	+	7.34831i	−0.594831	+	0.260782i
$795$	1.14410	+	0.660544i	0.0405769	+	0.0234271i
$796$	−23.7144	+	25.7410i	−0.840534	+	0.912364i
$797$		−	40.3106i		−	1.42788i	−0.700209	−	0.713938i	$-0.746910\pi$
$797$		−	40.3106i		−	1.42788i	0.700209	−	0.713938i	$-0.253090\pi$
$798$	−9.13345	−	22.9610i	−0.323321	−	0.812812i
$799$	22.5224			0.796785
$800$	24.7086	−	13.3411i	0.873581	−	0.471680i
$801$	−5.55443	+	9.62056i	−0.196256	+	0.339926i
$802$	−8.23259	−	18.7782i	−0.290703	−	0.663080i
$803$	18.3879	+	10.6162i	0.648894	+	0.374639i
$804$	−2.61394	−	8.36846i	−0.0921866	−	0.295133i
$805$		−	0.925062i		−	0.0326041i
$806$	−0.815168	+	7.35225i	−0.0287131	+	0.258972i
$807$	−8.11854	−	14.0617i	−0.285786	−	0.494996i
$808$	42.3349	−	8.24426i	1.48934	−	0.290032i
$809$	8.87371			0.311983			0.155991	−	0.987758i	$-0.450143\pi$
$809$	8.87371			0.311983			0.155991	+	0.987758i	$0.450143\pi$
$810$	−0.296162	+	2.67118i	−0.0104061	+	0.0938556i
$811$	22.8552	−	13.1954i	0.802554	−	0.463355i	−0.0418093	−	0.999126i	$-0.513312\pi$
$811$	22.8552	−	13.1954i	0.802554	−	0.463355i	0.844364	+	0.535771i	$0.179979\pi$
$812$	−19.3532	−	17.8295i	−0.679163	−	0.625693i
$813$	−38.0604	+	21.9742i	−1.33484	+	0.770669i
$814$	13.1537	−	17.8890i	0.461035	−	0.627010i
$815$	1.37724	−	2.38545i	0.0482427	−	0.0835588i
$816$	−8.36579	+	17.6924i	−0.292861	+	0.619358i
$817$	−23.6824	+	37.9268i	−0.828541	+	1.32689i
$818$	21.2261	+	2.35341i	0.742154	+	0.0822851i
$819$	2.55698	+	1.47627i	0.0893480	+	0.0515851i
$820$	0.383963	+	0.353734i	0.0134086	+	0.0123529i
$821$	−48.9615	+	28.2679i	−1.70877	+	0.986558i	−0.772678	+	0.634799i	$0.781083\pi$
$821$	−48.9615	+	28.2679i	−1.70877	+	0.986558i	−0.936091	+	0.351759i	$0.885584\pi$
$822$	−34.5913	−	25.4347i	−1.20651	−	0.887138i
$823$	14.4813	+	25.0823i	0.504786	+	0.874315i	0.999985	+	0.00553538i	$0.00176198\pi$
$823$	14.4813	+	25.0823i	0.504786	+	0.874315i	−0.495199	+	0.868780i	$0.664905\pi$
$824$	32.5658	+	11.2007i	1.13448	+	0.390196i
$825$	28.1866			0.981331
$826$	26.3607	−	11.5569i	0.917208	−	0.402116i
$827$	−37.8270	+	21.8394i	−1.31537	+	0.759431i	−0.982980	−	0.183711i	$-0.941189\pi$
$827$	−37.8270	+	21.8394i	−1.31537	+	0.759431i	−0.332392	+	0.943141i	$0.607856\pi$
$828$	−14.6937	−	3.29883i	−0.510641	−	0.114642i
$829$			43.0872i			1.49648i	0.663428	+	0.748240i	$0.269101\pi$
$829$			43.0872i			1.49648i	−0.663428	+	0.748240i	$0.730899\pi$
$830$	0.750574	+	1.71202i	0.0260528	+	0.0594253i
$831$	18.4690	−	31.9893i	0.640683	−	1.10970i
$832$	−5.28787	−	0.739434i	−0.183324	−	0.0256353i
$833$	−4.27216	+	7.39960i	−0.148022	+	0.256381i
$834$	−22.5032	+	30.6044i	−0.779221	+	1.05974i
$835$		−	3.15819i		−	0.109294i
$836$	5.53525	+	20.1437i	0.191441	+	0.696685i
$837$		−	7.14893i		−	0.247103i
$838$	17.0479	+	12.5352i	0.588911	+	0.433021i
$839$	−13.1507	+	22.7776i	−0.454011	+	0.786370i	−0.998631	−	0.0523129i	$-0.983341\pi$
$839$	−13.1507	+	22.7776i	−0.454011	+	0.786370i	0.544620	+	0.838683i	$0.316674\pi$
$840$	−0.411589	−	2.11354i	−0.0142012	−	0.0729242i
$841$	15.7448	−	27.2707i	0.542923	−	0.940370i
$842$	20.3768	−	8.93345i	0.702231	−	0.307867i
$843$			64.0598i			2.20634i
$844$	−1.30333	+	5.80533i	−0.0448626	+	0.199828i
$845$	2.06483	−	1.19213i	0.0710323	−	0.0410105i
$846$	16.1976	+	36.9460i	0.556885	+	1.27023i
$847$	−8.89453			−0.305620
$848$	5.01956	−	10.6156i	0.172373	−	0.364543i
$849$	−14.2189	−	24.6279i	−0.487993	−	0.845228i
$850$	−8.58648	+	11.6776i	−0.294514	+	0.400540i
$851$	−16.3386	+	9.43308i	−0.560079	+	0.323362i
$852$	−5.09977	−	4.69827i	−0.174715	−	0.160960i
$853$	−26.0077	−	15.0156i	−0.890488	−	0.514123i	−0.0163857	−	0.999866i	$-0.505216\pi$
$853$	−26.0077	−	15.0156i	−0.890488	−	0.514123i	−0.874102	+	0.485742i	$0.838549\pi$
$854$	−3.26073	+	29.4095i	−0.111580	+	1.00637i
$855$	2.16346	+	0.0748535i	0.0739888	+	0.00255993i
$856$	9.72106	−	28.2637i	0.332259	−	0.966035i
$857$	−1.18354	+	2.04995i	−0.0404289	+	0.0700248i	−0.885532	−	0.464579i	$-0.846206\pi$
$857$	−1.18354	+	2.04995i	−0.0404289	+	0.0700248i	0.845103	+	0.534604i	$0.179539\pi$
$858$	−4.31792	−	3.17493i	−0.147411	−	0.108390i
$859$	26.6130	−	15.3650i	0.908023	−	0.524247i	0.0282283	−	0.999602i	$-0.491013\pi$
$859$	26.6130	−	15.3650i	0.908023	−	0.524247i	0.879794	+	0.475354i	$0.157680\pi$
$860$	−2.63994	+	2.86554i	−0.0900211	+	0.0977140i
$861$	−4.77170	+	2.75494i	−0.162619	+	0.0938881i
$862$	49.2039	+	5.45540i	1.67589	+	0.185812i
$863$	25.6392			0.872769			0.436385	−	0.899760i	$-0.356259\pi$
$863$	25.6392			0.872769			0.436385	+	0.899760i	$0.356259\pi$
$864$	5.15795	+	0.147108i	0.175477	+	0.00500470i
$865$	−1.59950	−	2.77042i	−0.0543848	−	0.0941972i
$866$	−2.39670	−	0.265730i	−0.0814433	−	0.00902989i
$867$			30.1813i			1.02501i
$868$	7.90584	+	25.3103i	0.268342	+	0.859088i
$869$	8.13233	+	4.69520i	0.275870	+	0.159274i
$870$	4.53324	−	1.98743i	0.153691	−	0.0673802i
$871$	−0.617333	+	1.06925i	−0.0209175	+	0.0362302i
$872$	−26.6324	−	30.6157i	−0.901887	−	1.03678i
$873$	11.4444			0.387333
$874$	2.56483	−	17.5634i	0.0867565	−	0.594091i
$875$		−	3.20113i		−	0.108218i
$876$	−30.8838	−	28.4523i	−1.04347	−	0.961315i
$877$	−38.0835	−	21.9875i	−1.28599	−	0.742466i	−0.308053	−	0.951369i	$-0.599677\pi$
$877$	−38.0835	−	21.9875i	−1.28599	−	0.742466i	−0.977936	+	0.208903i	$0.933011\pi$
$878$	−4.26940	−	9.73831i	−0.144085	−	0.328652i
$879$	11.8688	−	20.5574i	0.400325	−	0.693384i
$880$	0.148936	+	1.81423i	0.00502063	+	0.0611578i
$881$	−19.5761			−0.659537			−0.329768	−	0.944062i	$-0.606971\pi$
$881$	−19.5761			−0.659537			−0.329768	+	0.944062i	$0.606971\pi$
$882$	−15.2108	−	1.68648i	−0.512176	−	0.0567866i
$883$	25.9549	−	14.9851i	0.873452	−	0.504288i	0.00495812	−	0.999988i	$-0.498422\pi$
$883$	25.9549	−	14.9851i	0.873452	−	0.504288i	0.868494	+	0.495700i	$0.165088\pi$
$884$	2.63073	−	0.821727i	0.0884812	−	0.0276377i
$885$			5.41411i			0.181993i
$886$	2.59890	−	23.4403i	0.0873117	−	0.787491i
$887$	0.508968	+	0.881558i	0.0170895	+	0.0295998i	0.874444	−	0.485127i	$-0.161227\pi$
$887$	0.508968	+	0.881558i	0.0170895	+	0.0295998i	−0.857354	+	0.514727i	$0.827893\pi$
$888$	−33.1326	+	28.8219i	−1.11186	+	0.967198i
$889$	−15.4218	−	26.7113i	−0.517229	−	0.895867i
$890$	−0.919187	−	0.675870i	−0.0308112	−	0.0226552i
$891$	20.7663	+	11.9894i	0.695698	+	0.401661i
$892$	−7.21520	−	1.61986i	−0.241583	−	0.0542369i
$893$	−41.9744	+	22.3355i	−1.40462	+	0.747430i
$894$	−10.6521	−	1.18104i	−0.356261	−	0.0394998i
$895$	−1.14377	+	1.98107i	−0.0382321	+	0.0662200i
$896$	−18.4240	+	5.18323i	−0.615504	+	0.173160i
$897$	2.27689	+	3.94368i	0.0760230	+	0.131676i
$898$	−24.1607	+	32.8587i	−0.806253	+	1.09651i
$899$	−52.7878	+	30.4770i	−1.76057	+	1.01647i
$900$	−25.3314	−	5.68705i	−0.844378	−	0.189568i
$901$			6.06136i			0.201933i
$902$	4.26603	−	1.87028i	0.142043	−	0.0622736i
$903$	−20.5603	−	35.6115i	−0.684203	−	1.18507i
$904$	9.65572	+	3.32100i	0.321145	+	0.110455i
$905$	2.18115			0.0725040
$906$	5.71538	−	2.50570i	0.189881	−	0.0832462i
$907$	−0.437148	−	0.252387i	−0.0145153	−	0.00838039i	0.492725	−	0.870185i	$-0.336001\pi$
$907$	−0.437148	−	0.252387i	−0.0145153	−	0.00838039i	−0.507240	+	0.861805i	$0.669334\pi$
$908$	33.1049	−	10.3405i	1.09863	−	0.343163i
$909$	−34.5341	−	19.9383i	−1.14542	−	0.661310i
$910$	−0.179634	+	0.244304i	−0.00595482	+	0.00809859i
$911$	30.7395			1.01845			0.509223	−	0.860634i	$-0.329933\pi$
$911$	30.7395			1.01845			0.509223	+	0.860634i	$0.329933\pi$
$912$	−1.95450	−	41.2693i	−0.0647200	−	1.36656i
$913$	16.6786			0.551980
$914$	24.9874	−	33.9829i	0.826508	−	1.12405i
$915$	−4.82020	−	2.78294i	−0.159351	−	0.0920013i
$916$	−54.1407	+	16.9112i	−1.78886	+	0.558762i
$917$	22.2959	+	12.8725i	0.736275	+	0.425089i
$918$	−2.43941	+	1.06947i	−0.0805125	+	0.0352977i
$919$	−37.9965			−1.25339			−0.626694	−	0.779266i	$-0.715592\pi$
$919$	−37.9965			−1.25339			−0.626694	+	0.779266i	$0.715592\pi$
$920$	0.503039	−	1.46257i	0.0165847	−	0.0482196i
$921$	1.69258	+	2.93163i	0.0557723	+	0.0966005i
$922$	12.1347	−	5.32000i	0.399635	−	0.175205i
$923$			0.976511i			0.0321423i
$924$	−18.7451	−	4.20840i	−0.616670	−	0.138446i
$925$	−28.1670	+	16.2622i	−0.926127	+	0.534699i
$926$	1.48871	−	2.02465i	0.0489219	−	0.0665341i
$927$	−15.9201	−	27.5744i	−0.522885	−	0.905663i
$928$	−20.9029	−	38.7135i	−0.686172	−	1.27083i
$929$	16.2656	−	28.1728i	0.533656	−	0.924319i	−0.465572	−	0.885010i	$-0.654151\pi$
$929$	16.2656	−	28.1728i	0.533656	−	0.924319i	0.999227	−	0.0393083i	$-0.0125155\pi$
$930$	−4.95739	−	0.549643i	−0.162559	−	0.0180235i
$931$	0.623721	−	18.0272i	0.0204416	−	0.590817i
$932$	−4.49137	−	1.00834i	−0.147120	−	0.0330293i
$933$	−45.1751	−	26.0819i	−1.47897	−	0.853882i
$934$	−24.9053	−	18.3127i	−0.814928	−	0.599210i
$935$	−0.469817	−	0.813746i	−0.0153646	−	0.0266124i
$936$	3.23994	+	3.72452i	0.105901	+	0.121740i
$937$	17.2886	+	29.9447i	0.564794	+	0.978252i	0.997069	+	0.0765097i	$0.0243776\pi$
$937$	17.2886	+	29.9447i	0.564794	+	0.978252i	−0.432275	+	0.901742i	$0.642289\pi$
$938$	−0.487711	+	4.39882i	−0.0159243	+	0.143626i
$939$			37.4448i			1.22197i
$940$	−3.95470	+	1.23528i	−0.128988	+	0.0402903i
$941$	4.84790	−	2.79894i	0.158037	−	0.0912427i	−0.418896	−	0.908034i	$-0.637583\pi$
$941$	4.84790	−	2.79894i	0.158037	−	0.0912427i	0.576933	+	0.816792i	$0.304249\pi$
$942$	−4.94438	−	0.548199i	−0.161096	−	0.0178613i
$943$	−3.95771			−0.128881
$944$	47.9623	−	3.93737i	1.56104	−	0.128151i
$945$	0.146528	−	0.253794i	0.00476655	−	0.00825591i
$946$	13.9580	+	31.8377i	0.453815	+	1.03513i
$947$	48.0463	+	27.7395i	1.56129	+	0.901413i	0.997127	+	0.0757524i	$0.0241358\pi$
$947$	48.0463	+	27.7395i	1.56129	+	0.901413i	0.564167	+	0.825661i	$0.309197\pi$
$948$	−13.6588	−	12.5835i	−0.443619	−	0.408693i
$949$			5.91367i			0.191966i
$950$	4.42166	−	30.2786i	0.143457	−	0.982367i
$951$	−34.7064			−1.12543
$952$	7.45386	−	6.48407i	0.241581	−	0.210150i
$953$	−14.6941	+	25.4509i	−0.475987	+	0.824434i	−0.999622	−	0.0275091i	$-0.991242\pi$
$953$	−14.6941	+	25.4509i	−0.475987	+	0.824434i	0.523634	+	0.851943i	$0.324576\pi$
$954$	−9.94313	+	4.35920i	−0.321921	+	0.141134i
$955$	1.74426	+	1.00705i	0.0564430	+	0.0325874i
$956$	8.38875	+	26.8563i	0.271311	+	0.868595i
$957$		−	44.1628i		−	1.42758i
$958$	2.19633	+	0.243514i	0.0709601	+	0.00786759i
$959$	10.8372	+	18.7706i	0.349952	+	0.606135i
$960$	0.498578	−	3.56544i	0.0160915	−	0.115074i
$961$	30.4222			0.981361
$962$	6.14670	+	0.681505i	0.198178	+	0.0219726i
$963$	−23.9317	+	13.8170i	−0.771189	+	0.445246i
$964$	−20.5415	+	22.2969i	−0.661597	+	0.718135i
$965$	1.79670	−	1.03733i	0.0578378	−	0.0333927i
$966$	13.1510	+	9.66981i	0.423126	+	0.311121i
$967$	3.42120	−	5.92569i	0.110018	−	0.190557i	−0.805759	−	0.592243i	$-0.798242\pi$
$967$	3.42120	−	5.92569i	0.110018	−	0.190557i	0.915777	+	0.401686i	$0.131576\pi$
$968$	−14.0627	−	4.83675i	−0.451993	−	0.155459i
$969$	10.0183	+	18.8270i	0.321833	+	0.604811i
$970$	−0.129525	+	1.16822i	−0.00415878	+	0.0375093i
$971$	10.1781	+	5.87632i	0.326630	+	0.188580i	0.654344	−	0.756197i	$-0.272945\pi$
$971$	10.1781	+	5.87632i	0.326630	+	0.188580i	−0.327714	+	0.944777i	$0.606278\pi$
$972$	−30.8533	−	28.4242i	−0.989619	−	0.911708i
$973$	16.6072	−	9.58815i	0.532401	−	0.307382i
$974$	27.1470	−	36.9201i	0.869846	−	1.18300i
$975$	3.92526	+	6.79875i	0.125709	+	0.217734i
$976$	−21.1480	+	44.7248i	−0.676930	+	1.43161i
$977$	29.7901			0.953069			0.476535	−	0.879156i	$-0.341893\pi$
$977$	29.7901			0.953069			0.476535	+	0.879156i	$0.341893\pi$
$978$	19.5159	+	44.5148i	0.624049	+	1.42343i
$979$	−8.81576	+	5.08978i	−0.281753	+	0.162670i
$980$	0.344305	−	1.53361i	0.0109984	−	0.0489894i
$981$			37.5172i			1.19783i
$982$	−12.2921	+	5.38899i	−0.392255	+	0.171970i
$983$	−6.27747	+	10.8729i	−0.200220	+	0.346791i	−0.948599	−	0.316480i	$-0.897499\pi$
$983$	−6.27747	+	10.8729i	−0.200220	+	0.346791i	0.748379	+	0.663271i	$0.230832\pi$
$984$	−9.04242	+	1.76091i	−0.288262	+	0.0561358i
$985$	0.779434	−	1.35002i	0.0248348	−	0.0430152i
$986$	18.2966	+	13.4533i	0.582681	+	0.428441i
$987$		−	43.7265i		−	1.39183i
$988$	−4.08793	+	4.14034i	−0.130054	+	0.131722i
$989$		−	29.5366i		−	0.939210i
$990$	0.996997	−	1.35592i	0.0316867	−	0.0430940i
$991$	−18.1756	+	31.4811i	−0.577367	+	1.00003i	0.418413	+	0.908257i	$0.362587\pi$
$991$	−18.1756	+	31.4811i	−0.577367	+	1.00003i	−0.995780	+	0.0917723i	$0.970747\pi$
$992$	−1.26392	+	44.3161i	−0.0401295	+	1.40704i
$993$	5.78073	−	10.0125i	0.183446	−	0.317738i
$994$	1.40548	+	3.20583i	0.0445791	+	0.101683i
$995$			3.32341i			0.105359i
$996$	−32.1846	−	7.22565i	−1.01981	−	0.228953i
$997$	−13.9442	+	8.05070i	−0.441618	+	0.254968i	−0.704284	−	0.709919i	$-0.748732\pi$
$997$	−13.9442	+	8.05070i	−0.441618	+	0.254968i	0.262666	+	0.964887i	$0.415398\pi$
$998$	−3.99313	+	1.75064i	−0.126400	+	0.0554155i
$999$	−5.97672			−0.189095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.p.a.125.14	yes	36
4.3	odd	2		608.2.t.a.49.3		36
8.3	odd	2		608.2.t.a.49.16		36
8.5	even	2	inner	152.2.p.a.125.11	yes	36
19.7	even	3	inner	152.2.p.a.45.11	✓	36
76.7	odd	6		608.2.t.a.273.16		36
152.45	even	6	inner	152.2.p.a.45.14	yes	36
152.83	odd	6		608.2.t.a.273.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.p.a.45.11	✓	36	19.7	even	3	inner
152.2.p.a.45.14	yes	36	152.45	even	6	inner
152.2.p.a.125.11	yes	36	8.5	even	2	inner
152.2.p.a.125.14	yes	36	1.1	even	1	trivial
608.2.t.a.49.3		36	4.3	odd	2
608.2.t.a.49.16		36	8.3	odd	2
608.2.t.a.273.3		36	152.83	odd	6
608.2.t.a.273.16		36	76.7	odd	6

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.837765 - 1.13936i) q^{2} +(2.05214 + 1.18481i) q^{3} +(-0.596300 - 1.90904i) q^{4} +(-0.164468 - 0.0949559i) q^{5} +(3.06914 - 1.34555i) q^{6} -1.69169 q^{7} +(-2.67465 - 0.919922i) q^{8} +(1.30753 + 2.26470i) q^{9} +O(q^{10})\)	\(q+(0.837765 - 1.13936i) q^{2} +(2.05214 + 1.18481i) q^{3} +(-0.596300 - 1.90904i) q^{4} +(-0.164468 - 0.0949559i) q^{5} +(3.06914 - 1.34555i) q^{6} -1.69169 q^{7} +(-2.67465 - 0.919922i) q^{8} +(1.30753 + 2.26470i) q^{9} +(-0.245975 + 0.107839i) q^{10} +2.39629i q^{11} +(1.03814 - 4.62412i) q^{12} +(-0.577998 + 0.333707i) q^{13} +(-1.41724 + 1.92745i) q^{14} +(-0.225008 - 0.389726i) q^{15} +(-3.28885 + 2.27672i) q^{16} +(1.03237 - 1.78812i) q^{17} +(3.67572 + 0.407539i) q^{18} +(-0.150723 + 4.35629i) q^{19} +(-0.0832018 + 0.370599i) q^{20} +(-3.47158 - 2.00432i) q^{21} +(2.73025 + 2.00753i) q^{22} +(-1.43969 - 2.49362i) q^{23} +(-4.39883 - 5.05675i) q^{24} +(-2.48197 - 4.29889i) q^{25} +(-0.104012 + 0.938118i) q^{26} -0.912175i q^{27} +(1.00875 + 3.22950i) q^{28} +(-6.73551 + 3.88875i) q^{29} +(-0.632544 - 0.0701322i) q^{30} +7.83723 q^{31} +(-0.161271 + 5.65455i) q^{32} +(-2.83914 + 4.91753i) q^{33} +(-1.17244 - 2.67428i) q^{34} +(0.278229 + 0.160636i) q^{35} +(3.54372 - 3.84656i) q^{36} -6.55216i q^{37} +(4.83713 + 3.82128i) q^{38} -1.58151 q^{39} +(0.352543 + 0.405272i) q^{40} +(0.687251 - 1.19035i) q^{41} +(-5.19202 + 2.27625i) q^{42} +(8.88368 + 5.12899i) q^{43} +(4.57461 - 1.42891i) q^{44} -0.496629i q^{45} +(-4.04726 - 0.448733i) q^{46} +(5.45403 + 9.44666i) q^{47} +(-9.44666 + 0.775506i) q^{48} -4.13819 q^{49} +(-6.97731 - 0.773597i) q^{50} +(4.23716 - 2.44632i) q^{51} +(0.981720 + 0.904430i) q^{52} +(-2.54234 + 1.46782i) q^{53} +(-1.03930 - 0.764188i) q^{54} +(0.227542 - 0.394114i) q^{55} +(4.52467 + 1.55622i) q^{56} +(-5.47066 + 8.76116i) q^{57} +(-1.21207 + 10.9321i) q^{58} +(-10.4191 - 6.01545i) q^{59} +(-0.609829 + 0.661943i) q^{60} +(10.7112 - 6.18409i) q^{61} +(6.56576 - 8.92946i) q^{62} +(-2.21193 - 3.83117i) q^{63} +(6.30749 + 4.92093i) q^{64} +0.126750 q^{65} +(3.22433 + 7.35455i) q^{66} +(1.60208 - 0.924962i) q^{67} +(-4.02920 - 0.904582i) q^{68} -6.82301i q^{69} +(0.416113 - 0.182429i) q^{70} +(0.731563 - 1.26710i) q^{71} +(-1.41382 - 7.26010i) q^{72} +(4.43028 - 7.67347i) q^{73} +(-7.46530 - 5.48917i) q^{74} -11.7626i q^{75} +(8.40620 - 2.30992i) q^{76} -4.05378i q^{77} +(-1.32493 + 1.80192i) q^{78} +(1.95936 - 3.39372i) q^{79} +(0.757100 - 0.0621527i) q^{80} +(5.00333 - 8.66602i) q^{81} +(-0.780491 - 1.78026i) q^{82} -6.96015i q^{83} +(-1.75622 + 7.82256i) q^{84} +(-0.339586 + 0.196060i) q^{85} +(13.2862 - 5.82485i) q^{86} -18.4296 q^{87} +(2.20440 - 6.40924i) q^{88} +(2.12402 + 3.67892i) q^{89} +(-0.565841 - 0.416058i) q^{90} +(0.977791 - 0.564528i) q^{91} +(-3.90192 + 4.23537i) q^{92} +(16.0831 + 9.28559i) q^{93} +(15.3324 + 1.69995i) q^{94} +(0.438445 - 0.702160i) q^{95} +(-7.03050 + 11.4129i) q^{96} +(2.18817 - 3.79002i) q^{97} +(-3.46683 + 4.71491i) q^{98} +(-5.42689 + 3.13321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9	\( 36 q - q^{2} + q^{4} - 3 q^{6} - 8 q^{7} + 2 q^{8} + 12 q^{9} - 10 q^{10} - 10 q^{12} - 6 q^{15} - 3 q^{16} - 2 q^{17} - 20 q^{18} + 16 q^{20} - 9 q^{22} - 2 q^{23} + 21 q^{24} + 8 q^{25} - 24 q^{26} + 8 q^{28} - 28 q^{30} - 48 q^{31} + 9 q^{32} + 12 q^{33} + 10 q^{34} + 4 q^{36} - 30 q^{38} - 20 q^{39} - 10 q^{40} + 2 q^{41} - 16 q^{42} + 3 q^{44} + 8 q^{46} + 10 q^{47} + 39 q^{48} - 12 q^{49} - 26 q^{50} - 12 q^{52} - 11 q^{54} + 8 q^{55} - 8 q^{56} - 6 q^{57} + 24 q^{58} + 34 q^{60} + 42 q^{62} - 28 q^{63} + 46 q^{64} - 28 q^{65} + 33 q^{66} + 44 q^{68} + 8 q^{70} - 30 q^{71} - 36 q^{72} - 10 q^{73} + 6 q^{74} + 39 q^{76} - 32 q^{78} + 34 q^{79} + 8 q^{80} - 2 q^{81} + 27 q^{82} - 40 q^{84} + 46 q^{86} + 36 q^{87} + 66 q^{88} - 2 q^{89} + 30 q^{90} + 22 q^{92} - 4 q^{94} + 38 q^{95} - 62 q^{96} - 18 q^{97} + 39 q^{98}+O(q^{100}) \) 36 * q - q^2 + q^4 - 3 * q^6 - 8 * q^7 + 2 * q^8 + 12 * q^9 - 10 * q^10 - 10 * q^12 - 6 * q^15 - 3 * q^16 - 2 * q^17 - 20 * q^18 + 16 * q^20 - 9 * q^22 - 2 * q^23 + 21 * q^24 + 8 * q^25 - 24 * q^26 + 8 * q^28 - 28 * q^30 - 48 * q^31 + 9 * q^32 + 12 * q^33 + 10 * q^34 + 4 * q^36 - 30 * q^38 - 20 * q^39 - 10 * q^40 + 2 * q^41 - 16 * q^42 + 3 * q^44 + 8 * q^46 + 10 * q^47 + 39 * q^48 - 12 * q^49 - 26 * q^50 - 12 * q^52 - 11 * q^54 + 8 * q^55 - 8 * q^56 - 6 * q^57 + 24 * q^58 + 34 * q^60 + 42 * q^62 - 28 * q^63 + 46 * q^64 - 28 * q^65 + 33 * q^66 + 44 * q^68 + 8 * q^70 - 30 * q^71 - 36 * q^72 - 10 * q^73 + 6 * q^74 + 39 * q^76 - 32 * q^78 + 34 * q^79 + 8 * q^80 - 2 * q^81 + 27 * q^82 - 40 * q^84 + 46 * q^86 + 36 * q^87 + 66 * q^88 - 2 * q^89 + 30 * q^90 + 22 * q^92 - 4 * q^94 + 38 * q^95 - 62 * q^96 - 18 * q^97 + 39 * q^98

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