LMFDB - Embedded newform 731.2.k.a.188.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(35,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("731.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.k (of order $7$, degree $6$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$30$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			188.2
Character	$\chi$	$=$	731.188
Dual form			731.2.k.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578512 - 2.53463i) q^{2} +(-0.698098 + 3.05857i) q^{3} +(-4.28771 + 2.06485i) q^{4} +(2.03783 + 2.55536i) q^{5} +8.15618 q^{6} +3.05620 q^{7} +(4.47222 + 5.60798i) q^{8} +(-6.16458 - 2.96870i) q^{9} +O(q^{10})$	\(q+(-0.578512 - 2.53463i) q^{2} +(-0.698098 + 3.05857i) q^{3} +(-4.28771 + 2.06485i) q^{4} +(2.03783 + 2.55536i) q^{5} +8.15618 q^{6} +3.05620 q^{7} +(4.47222 + 5.60798i) q^{8} +(-6.16458 - 2.96870i) q^{9} +(5.29796 - 6.64344i) q^{10} +(5.02063 + 2.41781i) q^{11} +(-3.32225 - 14.5557i) q^{12} +(-0.676568 - 0.848390i) q^{13} +(-1.76805 - 7.74632i) q^{14} +(-9.23833 + 4.44894i) q^{15} +(5.69253 - 7.13820i) q^{16} +(0.623490 - 0.781831i) q^{17} +(-3.95827 + 17.3423i) q^{18} +(3.90325 - 1.87971i) q^{19} +(-14.0141 - 6.74882i) q^{20} +(-2.13353 + 9.34759i) q^{21} +(3.22374 - 14.1241i) q^{22} +(-1.03092 - 0.496463i) q^{23} +(-20.2744 + 9.76365i) q^{24} +(-1.26450 + 5.54012i) q^{25} +(-1.75895 + 2.20565i) q^{26} +(7.51538 - 9.42398i) q^{27} +(-13.1041 + 6.31060i) q^{28} +(2.12087 + 9.29215i) q^{29} +(16.6209 + 20.8419i) q^{30} +(0.218326 + 0.956549i) q^{31} +(-8.46079 - 4.07450i) q^{32} +(-10.8999 + 13.6681i) q^{33} +(-2.34235 - 1.12801i) q^{34} +(6.22801 + 7.80968i) q^{35} +32.5619 q^{36} -5.02879 q^{37} +(-7.02244 - 8.80586i) q^{38} +(3.06717 - 1.47707i) q^{39} +(-5.21678 + 22.8562i) q^{40} +(-2.02132 - 8.85598i) q^{41} +24.9269 q^{42} +(5.59081 - 3.42678i) q^{43} -26.5194 q^{44} +(-4.97626 - 21.8024i) q^{45} +(-0.661950 + 2.90019i) q^{46} +(-7.76513 + 3.73949i) q^{47} +(17.8587 + 22.3941i) q^{48} +2.34035 q^{49} +14.7736 q^{50} +(1.95603 + 2.45278i) q^{51} +(4.65273 + 2.24064i) q^{52} +(2.59121 - 3.24927i) q^{53} +(-28.2340 - 13.5968i) q^{54} +(4.05282 + 17.7566i) q^{55} +(13.6680 + 17.1391i) q^{56} +(3.02436 + 13.2506i) q^{57} +(22.3252 - 10.7512i) q^{58} +(3.12715 - 3.92132i) q^{59} +(30.4249 - 38.1516i) q^{60} +(-0.743535 + 3.25764i) q^{61} +(2.29819 - 1.10675i) q^{62} +(-18.8402 - 9.07295i) q^{63} +(-1.36939 + 5.99968i) q^{64} +(0.789208 - 3.45775i) q^{65} +(40.9491 + 19.7201i) q^{66} +(-4.28531 + 2.06370i) q^{67} +(-1.05898 + 4.63969i) q^{68} +(2.23814 - 2.80654i) q^{69} +(16.1916 - 20.3037i) q^{70} +(-2.86068 + 1.37763i) q^{71} +(-10.9209 - 47.8475i) q^{72} +(3.10131 + 3.88892i) q^{73} +(2.90921 + 12.7461i) q^{74} +(-16.0621 - 7.73508i) q^{75} +(-12.8547 + 16.1193i) q^{76} +(15.3440 + 7.38930i) q^{77} +(-5.51821 - 6.91962i) q^{78} -15.6559 q^{79} +29.8410 q^{80} +(10.7793 + 13.5169i) q^{81} +(-21.2772 + 10.2466i) q^{82} +(0.428483 - 1.87731i) q^{83} +(-10.1535 - 44.4852i) q^{84} +3.26842 q^{85} +(-11.9200 - 12.1882i) q^{86} -29.9012 q^{87} +(8.89432 + 38.9686i) q^{88} +(2.26273 - 9.91369i) q^{89} +(-52.3821 + 25.2259i) q^{90} +(-2.06773 - 2.59285i) q^{91} +5.44539 q^{92} -3.07808 q^{93} +(13.9704 + 17.5184i) q^{94} +(12.7575 + 6.14368i) q^{95} +(18.3686 - 23.0335i) q^{96} +(7.96964 + 3.83798i) q^{97} +(-1.35392 - 5.93191i) q^{98} +(-23.7723 - 29.8095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) $ 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.578512	−	2.53463i	−0.409070	−	1.79225i	−0.588519	−	0.808484i	$-0.700289\pi$
$2$	−0.578512	−	2.53463i	−0.409070	−	1.79225i	0.179449	−	0.983767i	$-0.442569\pi$
$3$	−0.698098	+	3.05857i	−0.403047	+	1.76586i	0.211896	+	0.977292i	$0.432036\pi$
$3$	−0.698098	+	3.05857i	−0.403047	+	1.76586i	−0.614943	+	0.788572i	$0.710821\pi$
$4$	−4.28771	+	2.06485i	−2.14386	+	1.03243i
$5$	2.03783	+	2.55536i	0.911345	+	1.14279i	0.989309	+	0.145834i	$0.0465865\pi$
$5$	2.03783	+	2.55536i	0.911345	+	1.14279i	−0.0779645	+	0.996956i	$0.524842\pi$
$6$	8.15618			3.32975
$7$	3.05620			1.15513			0.577567	−	0.816343i	$-0.304002\pi$
$7$	3.05620			1.15513			0.577567	+	0.816343i	$0.304002\pi$
$8$	4.47222	+	5.60798i	1.58117	+	1.98272i
$9$	−6.16458	−	2.96870i	−2.05486	−	0.989568i
$10$	5.29796	−	6.64344i	1.67536	−	2.10084i
$11$	5.02063	+	2.41781i	1.51378	+	0.728996i	0.992252	−	0.124240i	$-0.0396492\pi$
$11$	5.02063	+	2.41781i	1.51378	+	0.728996i	0.521525	+	0.853236i	$0.325364\pi$
$12$	−3.32225	−	14.5557i	−0.959051	−	4.20188i
$13$	−0.676568	−	0.848390i	−0.187646	−	0.235301i	0.679106	−	0.734041i	$-0.262368\pi$
$13$	−0.676568	−	0.848390i	−0.187646	−	0.235301i	−0.866752	+	0.498740i	$0.833796\pi$
$14$	−1.76805	−	7.74632i	−0.472530	−	2.07029i
$15$	−9.23833	+	4.44894i	−2.38533	+	1.14871i
$16$	5.69253	−	7.13820i	1.42313	−	1.78455i
$17$	0.623490	−	0.781831i	0.151218	−	0.189622i
$17$	0.623490	−	0.781831i	0.151218	−	0.189622i
$18$	−3.95827	+	17.3423i	−0.932974	+	4.08763i
$19$	3.90325	−	1.87971i	0.895468	−	0.431235i	0.0712181	−	0.997461i	$-0.477311\pi$
$19$	3.90325	−	1.87971i	0.895468	−	0.431235i	0.824250	+	0.566226i	$0.191597\pi$
$20$	−14.0141	−	6.74882i	−3.13364	−	1.50908i
$21$	−2.13353	+	9.34759i	−0.465573	+	2.03981i
$22$	3.22374	−	14.1241i	0.687305	−	3.01128i
$23$	−1.03092	−	0.496463i	−0.214961	−	0.103520i	0.323305	−	0.946295i	$-0.395206\pi$
$23$	−1.03092	−	0.496463i	−0.214961	−	0.103520i	−0.538266	+	0.842775i	$0.680920\pi$
$24$	−20.2744	+	9.76365i	−4.13850	+	1.99300i
$25$	−1.26450	+	5.54012i	−0.252899	+	1.10802i
$26$	−1.75895	+	2.20565i	−0.344958	+	0.432564i
$27$	7.51538	−	9.42398i	1.44633	−	1.81365i
$28$	−13.1041	+	6.31060i	−2.47644	+	1.19259i
$29$	2.12087	+	9.29215i	0.393836	+	1.72551i	0.650944	+	0.759126i	$0.274373\pi$
$29$	2.12087	+	9.29215i	0.393836	+	1.72551i	−0.257108	+	0.966383i	$0.582769\pi$
$30$	16.6209	+	20.8419i	3.03455	+	3.80520i
$31$	0.218326	+	0.956549i	0.0392125	+	0.171801i	0.990742	−	0.135755i	$-0.0433460\pi$
$31$	0.218326	+	0.956549i	0.0392125	+	0.171801i	−0.951530	+	0.307556i	$0.900489\pi$
$32$	−8.46079	−	4.07450i	−1.49567	−	0.720277i
$33$	−10.8999	+	13.6681i	−1.89743	+	2.37930i
$34$	−2.34235	−	1.12801i	−0.401709	−	0.193453i
$35$	6.22801	+	7.80968i	1.05273	+	1.32008i
$36$	32.5619			5.42698
$37$	−5.02879			−0.826728			−0.413364	−	0.910566i	$-0.635646\pi$
$37$	−5.02879			−0.826728			−0.413364	+	0.910566i	$0.635646\pi$
$38$	−7.02244	−	8.80586i	−1.13919	−	1.42850i
$39$	3.06717	−	1.47707i	0.491140	−	0.236520i
$40$	−5.21678	+	22.8562i	−0.824846	+	3.61389i
$41$	−2.02132	−	8.85598i	−0.315677	−	1.38307i	−0.845052	−	0.534684i	$-0.820431\pi$
$41$	−2.02132	−	8.85598i	−0.315677	−	1.38307i	0.529375	−	0.848388i	$-0.322426\pi$
$42$	24.9269			3.84630
$43$	5.59081	−	3.42678i	0.852591	−	0.522579i
$43$	5.59081	−	3.42678i	0.852591	−	0.522579i
$44$	−26.5194			−3.99796
$45$	−4.97626	−	21.8024i	−0.741816	−	3.25011i
$46$	−0.661950	+	2.90019i	−0.0975992	+	0.427610i
$47$	−7.76513	+	3.73949i	−1.13266	+	0.545460i	−0.903781	−	0.427994i	$-0.859220\pi$
$47$	−7.76513	+	3.73949i	−1.13266	+	0.545460i	−0.228879	+	0.973455i	$0.573506\pi$
$48$	17.8587	+	22.3941i	2.57769	+	3.23231i
$49$	2.34035			0.334336
$50$	14.7736			2.08931
$51$	1.95603	+	2.45278i	0.273898	+	0.343458i
$52$	4.65273	+	2.24064i	0.645218	+	0.310721i
$53$	2.59121	−	3.24927i	0.355930	−	0.446322i	−0.571341	−	0.820713i	$-0.693577\pi$
$53$	2.59121	−	3.24927i	0.355930	−	0.446322i	0.927271	+	0.374391i	$0.122148\pi$
$54$	−28.2340	−	13.5968i	−3.84216	−	1.85029i
$55$	4.05282	+	17.7566i	0.546482	+	2.39430i
$56$	13.6680	+	17.1391i	1.82646	+	2.29031i
$57$	3.02436	+	13.2506i	0.400586	+	1.75508i
$58$	22.3252	−	10.7512i	2.93144	−	1.41171i
$59$	3.12715	−	3.92132i	0.407120	−	0.510512i	−0.535429	−	0.844580i	$-0.679850\pi$
$59$	3.12715	−	3.92132i	0.407120	−	0.510512i	0.942549	+	0.334068i	$0.108422\pi$
$60$	30.4249	−	38.1516i	3.92784	−	4.92535i
$61$	−0.743535	+	3.25764i	−0.0951999	+	0.417098i	−0.999961	−	0.00882124i	$-0.997192\pi$
$61$	−0.743535	+	3.25764i	−0.0951999	+	0.417098i	0.904761	+	0.425919i	$0.140049\pi$
$62$	2.29819	−	1.10675i	0.291870	−	0.140557i
$63$	−18.8402	−	9.07295i	−2.37364	−	1.14308i
$64$	−1.36939	+	5.99968i	−0.171174	+	0.749961i
$65$	0.789208	−	3.45775i	0.0978892	−	0.428881i
$66$	40.9491	+	19.7201i	5.04049	+	2.42737i
$67$	−4.28531	+	2.06370i	−0.523534	+	0.252121i	−0.676934	−	0.736044i	$-0.736692\pi$
$67$	−4.28531	+	2.06370i	−0.523534	+	0.252121i	0.153400	+	0.988164i	$0.450978\pi$
$68$	−1.05898	+	4.63969i	−0.128420	+	0.562644i
$69$	2.23814	−	2.80654i	0.269441	−	0.337868i
$70$	16.1916	−	20.3037i	1.93527	−	2.42675i
$71$	−2.86068	+	1.37763i	−0.339501	+	0.163495i	−0.595863	−	0.803086i	$-0.703190\pi$
$71$	−2.86068	+	1.37763i	−0.339501	+	0.163495i	0.256363	+	0.966581i	$0.417476\pi$
$72$	−10.9209	−	47.8475i	−1.28704	−	5.63889i
$73$	3.10131	+	3.88892i	0.362981	+	0.455164i	0.929466	−	0.368908i	$-0.120268\pi$
$73$	3.10131	+	3.88892i	0.362981	+	0.455164i	−0.566485	+	0.824072i	$0.691697\pi$
$74$	2.90921	+	12.7461i	0.338189	+	1.48170i
$75$	−16.0621	−	7.73508i	−1.85469	−	0.893171i
$76$	−12.8547	+	16.1193i	−1.47454	+	1.84901i
$77$	15.3440	+	7.38930i	1.74862	+	0.842089i
$78$	−5.51821	−	6.91962i	−0.624814	−	0.783492i
$79$	−15.6559			−1.76142			−0.880711	−	0.473653i	$-0.842935\pi$
$79$	−15.6559			−1.76142			−0.880711	+	0.473653i	$0.842935\pi$
$80$	29.8410			3.33633
$81$	10.7793	+	13.5169i	1.19771	+	1.50187i
$82$	−21.2772	+	10.2466i	−2.34968	+	1.13155i
$83$	0.428483	−	1.87731i	0.0470321	−	0.206061i	−0.945952	−	0.324305i	$-0.894869\pi$
$83$	0.428483	−	1.87731i	0.0470321	−	0.206061i	0.992985	+	0.118244i	$0.0377266\pi$
$84$	−10.1535	−	44.4852i	−1.10783	−	4.85373i
$85$	3.26842			0.354510
$86$	−11.9200	−	12.1882i	−1.28536	−	1.31429i
$87$	−29.9012			−3.20575
$88$	8.89432	+	38.9686i	0.948138	+	4.15406i
$89$	2.26273	−	9.91369i	0.239849	−	1.05085i	−0.701302	−	0.712864i	$-0.747398\pi$
$89$	2.26273	−	9.91369i	0.239849	−	1.05085i	0.941152	−	0.337985i	$-0.109745\pi$
$90$	−52.3821	+	25.2259i	−5.52156	+	2.65904i
$91$	−2.06773	−	2.59285i	−0.216757	−	0.271804i
$92$	5.44539			0.567721
$93$	−3.07808			−0.319182
$94$	13.9704	+	17.5184i	1.44094	+	1.80688i
$95$	12.7575	+	6.14368i	1.30889	+	0.630329i
$96$	18.3686	−	23.0335i	1.87474	−	2.35084i
$97$	7.96964	+	3.83798i	0.809195	+	0.389688i	0.792271	−	0.610169i	$-0.208899\pi$
$97$	7.96964	+	3.83798i	0.809195	+	0.389688i	0.0169236	+	0.999857i	$0.494613\pi$
$98$	−1.35392	−	5.93191i	−0.136767	−	0.599214i
$99$	−23.7723	−	29.8095i	−2.38921	−	2.99597i
$100$	−6.01774	−	26.3654i	−0.601774	−	2.63654i
$101$	−13.2224	+	6.36758i	−1.31568	+	0.633598i	−0.954308	−	0.298825i	$-0.903405\pi$
$101$	−13.2224	+	6.36758i	−1.31568	+	0.633598i	−0.361371	+	0.932422i	$0.617691\pi$
$102$	5.08529	−	6.37676i	0.503519	−	0.631393i
$103$	−9.79172	+	12.2784i	−0.964807	+	1.20983i	0.0129132	+	0.999917i	$0.495889\pi$
$103$	−9.79172	+	12.2784i	−0.964807	+	1.20983i	−0.977720	+	0.209913i	$0.932682\pi$
$104$	1.73200	−	7.58837i	0.169836	−	0.744101i
$105$	−28.2342	+	13.5969i	−2.75537	+	1.32692i
$106$	−9.73473	−	4.68800i	−0.945521	−	0.455339i
$107$	3.23400	−	14.1691i	0.312642	−	1.36978i	−0.537518	−	0.843252i	$-0.680638\pi$
$107$	3.23400	−	14.1691i	0.312642	−	1.36978i	0.850161	−	0.526523i	$-0.176505\pi$
$108$	−12.7646	+	55.9255i	−1.22828	+	5.38143i
$109$	−3.90981	−	1.88286i	−0.374492	−	0.180346i	0.237164	−	0.971470i	$-0.423782\pi$
$109$	−3.90981	−	1.88286i	−0.374492	−	0.180346i	−0.611656	+	0.791124i	$0.709496\pi$
$110$	42.6617	−	20.5448i	4.06763	−	1.95887i
$111$	3.51059	−	15.3809i	0.333210	−	1.45989i
$112$	17.3975	−	21.8158i	1.64391	−	2.06140i
$113$	8.11514	−	10.1761i	0.763408	−	0.957283i	−0.236489	−	0.971634i	$-0.575997\pi$
$113$	8.11514	−	10.1761i	0.763408	−	0.957283i	0.999897	+	0.0143508i	$0.00456816\pi$
$114$	31.8356	−	15.3312i	2.98168	−	1.43590i
$115$	−0.832190	−	3.64606i	−0.0776021	−	0.339997i
$116$	−28.2806	−	35.4628i	−2.62579	−	3.29264i
$117$	1.65214	+	7.23850i	0.152740	+	0.669199i
$118$	−11.7482	−	5.65762i	−1.08151	−	0.520826i
$119$	1.90551	−	2.38943i	0.174678	−	0.219039i
$120$	−66.2654	−	31.9117i	−6.04918	−	2.91313i
$121$	12.5025	+	15.6777i	1.13659	+	1.42524i
$122$	8.68704			0.786488
$123$	28.4977			2.56955
$124$	−2.91125	−	3.65060i	−0.261438	−	0.327833i
$125$	−2.01006	+	0.967992i	−0.179785	+	0.0865798i
$126$	−12.0973	+	53.0016i	−1.07771	+	4.72176i
$127$	−2.16268	−	9.47531i	−0.191907	−	0.840798i	−0.975583	−	0.219629i	$-0.929515\pi$
$127$	−2.16268	−	9.47531i	−0.191907	−	0.840798i	0.783677	−	0.621169i	$-0.213342\pi$
$128$	−2.78237			−0.245929
$129$	6.57810	+	19.4921i	0.579169	+	1.71618i
$130$	−9.22066			−0.808705
$131$	0.579918	+	2.54079i	0.0506676	+	0.221989i	0.993923	−	0.110079i	$-0.0351105\pi$
$131$	0.579918	+	2.54079i	0.0506676	+	0.221989i	−0.943255	+	0.332069i	$0.892253\pi$
$132$	18.5132	−	81.1115i	1.61136	−	7.05985i
$133$	11.9291	−	5.74476i	1.03439	−	0.498134i
$134$	7.70980	+	9.66778i	0.666025	+	0.835169i
$135$	39.3967			3.39073
$136$	7.17288			0.615069
$137$	4.72593	+	5.92613i	0.403764	+	0.506303i	0.941594	−	0.336749i	$-0.109327\pi$
$137$	4.72593	+	5.92613i	0.403764	+	0.506303i	−0.537831	+	0.843053i	$0.680756\pi$
$138$	−8.40833	−	4.04924i	−0.715764	−	0.344694i
$139$	−6.18778	+	7.75924i	−0.524841	+	0.658130i	−0.971629	−	0.236510i	$-0.923996\pi$
$139$	−6.18778	+	7.75924i	−0.524841	+	0.658130i	0.446788	+	0.894640i	$0.352568\pi$
$140$	−42.8298	−	20.6257i	−3.61978	−	1.74319i
$141$	−6.01665	−	26.3607i	−0.506694	−	2.21997i
$142$	5.14672	+	6.45378i	0.431903	+	0.541589i
$143$	−1.34556	−	5.89526i	−0.112521	−	0.492987i
$144$	−56.2832	+	27.1046i	−4.69027	+	2.25872i
$145$	−19.4228	+	24.3554i	−1.61297	+	2.02261i
$146$	8.06282	−	10.1105i	0.667284	−	0.836748i
$147$	−1.63379	+	7.15812i	−0.134753	+	0.590392i
$148$	21.5620	−	10.3837i	1.77239	−	0.853536i
$149$	15.7019	+	7.56162i	1.28635	+	0.619472i	0.947013	−	0.321194i	$-0.104084\pi$
$149$	15.7019	+	7.56162i	1.28635	+	0.619472i	0.339334	+	0.940666i	$0.389798\pi$
$150$	−10.3134	+	45.1862i	−0.842089	+	3.68944i
$151$	1.31604	−	5.76596i	0.107098	−	0.469227i	−0.892728	−	0.450595i	$-0.851212\pi$
$151$	1.31604	−	5.76596i	0.107098	−	0.469227i	0.999826	−	0.0186321i	$-0.00593111\pi$
$152$	27.9976	+	13.4829i	2.27090	+	1.09361i
$153$	−6.16458	+	2.96870i	−0.498377	+	0.240006i
$154$	9.85240	−	43.1662i	0.793929	−	3.47843i
$155$	−1.99941	+	2.50718i	−0.160597	+	0.201382i
$156$	−10.1012	+	12.6665i	−0.808743	+	1.01413i
$157$	8.55776	−	4.12120i	0.682984	−	0.328908i	−0.0600179	−	0.998197i	$-0.519116\pi$
$157$	8.55776	−	4.12120i	0.682984	−	0.328908i	0.743002	+	0.669290i	$0.233402\pi$
$158$	9.05710	+	39.6818i	0.720545	+	3.15691i
$159$	8.12919	+	10.1937i	0.644687	+	0.808412i
$160$	−6.82983	−	29.9235i	−0.539946	−	2.36566i
$161$	−3.15068	−	1.51729i	−0.248308	−	0.119579i
$162$	28.0242	−	35.1413i	2.20179	−	2.76096i
$163$	−18.7775	−	9.04276i	−1.47077	−	0.708284i	−0.484706	−	0.874677i	$-0.661074\pi$
$163$	−18.7775	−	9.04276i	−1.47077	−	0.708284i	−0.986059	+	0.166393i	$0.946788\pi$
$164$	26.9531	+	33.7982i	2.10469	+	2.63919i
$165$	−57.1389			−4.44826
$166$	−5.00615			−0.388553
$167$	−0.634901	−	0.796141i	−0.0491301	−	0.0616072i	0.756659	−	0.653809i	$-0.226830\pi$
$167$	−0.634901	−	0.796141i	−0.0491301	−	0.0616072i	−0.805789	+	0.592202i	$0.798259\pi$
$168$	−61.9627	+	29.8397i	−4.78053	+	2.30218i
$169$	2.63075	−	11.5261i	0.202366	−	0.886621i
$170$	−1.89082	−	8.28423i	−0.145019	−	0.635371i
$171$	−29.6422			−2.26680
$172$	−16.8960	+	26.2373i	−1.28831	+	2.00057i
$173$	2.62288			0.199414			0.0997070	−	0.995017i	$-0.468209\pi$
$173$	2.62288			0.199414			0.0997070	+	0.995017i	$0.468209\pi$
$174$	17.2982	+	75.7884i	1.31137	+	5.74551i
$175$	−3.86455	+	16.9317i	−0.292132	+	1.27992i
$176$	45.8389	−	22.0748i	3.45524	−	1.66395i
$177$	9.81055	+	12.3020i	0.737406	+	0.924678i
$178$	−26.4365			−1.98150
$179$	14.5492			1.08746			0.543730	−	0.839260i	$-0.317011\pi$
$179$	14.5492			1.08746			0.543730	+	0.839260i	$0.317011\pi$
$180$	66.3555	+	83.2072i	4.94585	+	6.20190i
$181$	−2.37550	−	1.14398i	−0.176570	−	0.0850314i	0.343511	−	0.939149i	$-0.388384\pi$
$181$	−2.37550	−	1.14398i	−0.176570	−	0.0850314i	−0.520080	+	0.854117i	$0.674098\pi$
$182$	−5.37569	+	6.74091i	−0.398473	+	0.499669i
$183$	−9.44464	−	4.54830i	−0.698168	−	0.336220i
$184$	−1.82632	−	8.00164i	−0.134638	−	0.589889i
$185$	−10.2478	−	12.8503i	−0.753434	−	0.944776i
$186$	1.78071	+	7.80178i	0.130568	+	0.572054i
$187$	5.02063	−	2.41781i	0.367145	−	0.176808i
$188$	25.5731	−	32.0677i	1.86511	−	2.33878i
$189$	22.9685	−	28.8016i	1.67071	−	2.09501i
$190$	8.19158	−	35.8897i	0.594280	−	2.60371i
$191$	5.34490	−	2.57397i	0.386744	−	0.186246i	−0.230401	−	0.973096i	$-0.574004\pi$
$191$	5.34490	−	2.57397i	0.386744	−	0.186246i	0.617144	+	0.786850i	$0.288289\pi$
$192$	−17.3945	−	8.37673i	−1.25534	−	0.604539i
$193$	0.892707	−	3.91120i	0.0642584	−	0.281535i	−0.932583	−	0.360957i	$-0.882450\pi$
$193$	0.892707	−	3.91120i	0.0642584	−	0.281535i	0.996841	+	0.0794219i	$0.0253074\pi$
$194$	5.11731	−	22.4204i	0.367401	−	1.60969i
$195$	10.0248	+	4.82769i	0.717891	+	0.345718i
$196$	−10.0348	+	4.83248i	−0.716768	+	0.345177i
$197$	−1.44911	+	6.34897i	−0.103245	+	0.452346i	0.896708	+	0.442623i	$0.145952\pi$
$197$	−1.44911	+	6.34897i	−0.103245	+	0.452346i	−0.999953	+	0.00972263i	$0.996905\pi$
$198$	−61.8034	+	77.4991i	−4.39218	+	5.50762i
$199$	−0.233766	+	0.293133i	−0.0165712	+	0.0207796i	−0.790048	−	0.613045i	$-0.789944\pi$
$199$	−0.233766	+	0.293133i	−0.0165712	+	0.0207796i	0.773477	+	0.633825i	$0.218516\pi$
$200$	−36.7240	+	17.6853i	−2.59678	+	1.25054i
$201$	−3.32039	−	14.5476i	−0.234202	−	1.02611i
$202$	23.7887	+	29.8301i	1.67377	+	2.09884i
$203$	6.48181	+	28.3987i	0.454934	+	1.99319i
$204$	−13.4515	−	6.47791i	−0.941794	−	0.453544i
$205$	18.5111	−	23.2122i	1.29287	−	1.62121i
$206$	36.7858	+	17.7151i	2.56299	+	1.23427i
$207$	4.88131	+	6.12096i	0.339274	+	0.425436i
$208$	−9.90736			−0.686952
$209$	24.1416			1.66991
$210$	50.7967	+	63.6971i	3.50531	+	4.39552i
$211$	15.2032	−	7.32149i	1.04663	−	0.504032i	0.170127	−	0.985422i	$-0.445582\pi$
$211$	15.2032	−	7.32149i	1.04663	−	0.504032i	0.876507	+	0.481390i	$0.159868\pi$
$212$	−4.40108	+	19.2824i	−0.302268	+	1.32432i
$213$	−2.21654	−	9.71131i	−0.151875	−	0.665408i
$214$	−37.7842			−2.58287
$215$	20.1498	+	7.30333i	1.37420	+	0.498083i
$216$	86.4599			5.88285
$217$	0.667248	+	2.92340i	0.0452957	+	0.198454i
$218$	−2.51049	+	10.9992i	−0.170032	+	0.744957i
$219$	−14.0596	+	6.77072i	−0.950056	+	0.457523i
$220$	−54.0421	−	67.7666i	−3.64352	−	4.56882i
$221$	−1.08513			−0.0729938
$222$	−41.0157			−2.75279
$223$	−4.52613	−	5.67559i	−0.303092	−	0.380065i	0.606839	−	0.794825i	$-0.292437\pi$
$223$	−4.52613	−	5.67559i	−0.303092	−	0.380065i	−0.909931	+	0.414759i	$0.863866\pi$
$224$	−25.8578	−	12.4525i	−1.72770	−	0.832016i
$225$	24.2420	−	30.3986i	1.61614	−	2.02657i
$226$	−30.4872	−	14.6819i	−2.02798	−	0.976623i
$227$	−5.59685	−	24.5214i	−0.371476	−	1.62754i	−0.722637	−	0.691228i	$-0.757070\pi$
$227$	−5.59685	−	24.5214i	−0.371476	−	1.62754i	0.351161	−	0.936315i	$-0.385787\pi$
$228$	−40.3281	−	50.5698i	−2.67079	−	3.34907i
$229$	2.50197	+	10.9618i	0.165335	+	0.724378i	0.987821	+	0.155594i	$0.0497291\pi$
$229$	2.50197	+	10.9618i	0.165335	+	0.724378i	−0.822487	+	0.568785i	$0.807414\pi$
$230$	−8.75997	+	4.21858i	−0.577615	+	0.278165i
$231$	−33.3123	+	41.7723i	−2.19179	+	2.74842i
$232$	−42.6252	+	53.4503i	−2.79848	+	3.50919i
$233$	4.28239	−	18.7624i	0.280549	−	1.22917i	−0.616543	−	0.787321i	$-0.711467\pi$
$233$	4.28239	−	18.7624i	0.280549	−	1.22917i	0.897092	−	0.441844i	$-0.145676\pi$
$234$	17.3911	−	8.37511i	1.13689	−	0.547498i
$235$	−25.3797	−	12.2222i	−1.65559	−	0.797290i
$236$	−5.31136	+	23.2706i	−0.345740	+	1.51479i
$237$	10.9293	−	47.8845i	0.709936	−	3.11043i
$238$	−7.15868	−	3.44744i	−0.464028	−	0.223464i
$239$	−2.86543	+	1.37992i	−0.185349	+	0.0892594i	−0.524257	−	0.851560i	$-0.675657\pi$
$239$	−2.86543	+	1.37992i	−0.185349	+	0.0892594i	0.338908	+	0.940820i	$0.389943\pi$
$240$	−20.8320	+	91.2708i	−1.34470	+	5.89151i
$241$	−7.72827	+	9.69094i	−0.497821	+	0.624248i	−0.965736	−	0.259525i	$-0.916434\pi$
$241$	−7.72827	+	9.69094i	−0.497821	+	0.624248i	0.467915	+	0.883774i	$0.345005\pi$
$242$	32.5042	−	40.7590i	2.08945	−	2.62009i
$243$	−16.2872	+	7.84350i	−1.04482	+	0.503161i
$244$	−3.53848	−	15.5031i	−0.226528	−	0.992485i
$245$	4.76923	+	5.98043i	0.304695	+	0.382076i
$246$	−16.4862	−	72.2309i	−1.05112	−	4.60528i
$247$	−4.23554	−	2.03973i	−0.269501	−	0.129785i
$248$	−4.38791	+	5.50226i	−0.278632	+	0.349394i
$249$	5.44274	+	2.62109i	0.344920	+	0.166105i
$250$	3.61634	+	4.53474i	0.228717	+	0.286802i
$251$	−13.1826			−0.832077			−0.416039	−	0.909347i	$-0.636582\pi$
$251$	−13.1826			−0.832077			−0.416039	+	0.909347i	$0.636582\pi$
$252$	99.5156			6.26889
$253$	−3.97549	−	4.98511i	−0.249937	−	0.313411i
$254$	−22.7652	+	10.9632i	−1.42842	+	0.687890i
$255$	−2.28168	+	9.99669i	−0.142884	+	0.626017i
$256$	4.34841	+	19.0516i	0.271776	+	1.19073i
$257$	−7.04564			−0.439495			−0.219747	−	0.975557i	$-0.570523\pi$
$257$	−7.04564			−0.439495			−0.219747	+	0.975557i	$0.570523\pi$
$258$	45.5997	−	27.9494i	2.83891	−	1.74005i
$259$	−15.3690			−0.954982
$260$	3.75584	+	16.4554i	0.232928	+	1.02052i
$261$	14.5114	−	63.5784i	0.898231	−	3.93541i
$262$	6.10445	−	2.93975i	0.377134	−	0.181618i
$263$	6.01134	+	7.53798i	0.370675	+	0.464812i	0.931828	−	0.362900i	$-0.118213\pi$
$263$	6.01134	+	7.53798i	0.370675	+	0.464812i	−0.561153	+	0.827712i	$0.689642\pi$
$264$	−125.397			−7.71765
$265$	13.5835			0.834427
$266$	−21.4620	−	26.9124i	−1.31592	−	1.65011i
$267$	28.7421	+	13.8414i	1.75899	+	0.847083i
$268$	14.1129	−	17.6971i	0.862085	−	1.08102i
$269$	6.00647	+	2.89256i	0.366221	+	0.176363i	0.607939	−	0.793984i	$-0.291997\pi$
$269$	6.00647	+	2.89256i	0.366221	+	0.176363i	−0.241718	+	0.970347i	$0.577711\pi$
$270$	−22.7914	−	99.8558i	−1.38704	−	6.07703i
$271$	−0.579135	−	0.726213i	−0.0351800	−	0.0441143i	0.763930	−	0.645299i	$-0.223267\pi$
$271$	−0.579135	−	0.726213i	−0.0351800	−	0.0441143i	−0.799110	+	0.601184i	$0.794696\pi$
$272$	−2.03164	−	8.90119i	−0.123186	−	0.539714i
$273$	9.37387	−	4.51422i	0.567333	−	0.273213i
$274$	12.2865	−	15.4068i	0.742256	−	0.930759i
$275$	−19.7435	+	24.7576i	−1.19058	+	1.49294i
$276$	−3.80142	+	16.6551i	−0.228818	+	1.00252i
$277$	−16.5262	+	7.95860i	−0.992963	+	0.478186i	−0.858545	−	0.512739i	$-0.828631\pi$
$277$	−16.5262	+	7.95860i	−0.992963	+	0.478186i	−0.134418	+	0.990925i	$0.542917\pi$
$278$	23.2465	+	11.1949i	1.39423	+	0.671426i
$279$	1.49382	−	6.54487i	0.0894328	−	0.391831i
$280$	−15.9435	+	69.8531i	−0.952808	+	4.17452i
$281$	−6.42561	−	3.09441i	−0.383320	−	0.184597i	0.232293	−	0.972646i	$-0.425377\pi$
$281$	−6.42561	−	3.09441i	−0.383320	−	0.184597i	−0.615613	+	0.788049i	$0.711091\pi$
$282$	−63.3338	+	30.4999i	−3.77147	+	1.81624i
$283$	2.89652	−	12.6905i	0.172180	−	0.754372i	−0.812918	−	0.582379i	$-0.802122\pi$
$283$	2.89652	−	12.6905i	0.172180	−	0.754372i	0.985098	−	0.171993i	$-0.0550207\pi$
$284$	9.42118	−	11.8138i	0.559044	−	0.701019i
$285$	−27.6968	+	34.7307i	−1.64062	+	2.05727i
$286$	−14.1639	+	6.82096i	−0.837527	+	0.403332i
$287$	−6.17755	−	27.0656i	−0.364649	−	1.59763i
$288$	40.0612	+	50.2351i	2.36063	+	2.96013i
$289$	−0.222521	−	0.974928i	−0.0130895	−	0.0573487i
$290$	72.9681	+	35.1396i	4.28483	+	2.06347i
$291$	−17.3023	+	21.6964i	−1.01428	+	1.27187i
$292$	−21.3276	−	10.2708i	−1.24810	−	0.601055i
$293$	−12.2343	−	15.3413i	−0.714733	−	0.896247i	0.283294	−	0.959033i	$-0.408573\pi$
$293$	−12.2343	−	15.3413i	−0.714733	−	0.896247i	−0.998027	+	0.0627860i	$0.980001\pi$
$294$	19.0883			1.11325
$295$	16.3929			0.954434
$296$	−22.4898	−	28.2014i	−1.30720	−	1.63917i
$297$	60.5173	−	29.1436i	3.51157	−	1.69108i
$298$	10.0822	−	44.1728i	0.584044	−	2.55886i
$299$	0.276291	+	1.21051i	0.0159783	+	0.0700055i
$300$	84.8414			4.89832
$301$	17.0866	−	10.4729i	0.984857	−	0.603649i
$302$	−15.3759			−0.884784
$303$	−10.2451	−	44.8868i	−0.588567	−	2.57868i
$304$	8.80164	−	38.5625i	0.504809	−	2.21171i
$305$	−9.83963	+	4.73851i	−0.563415	+	0.271327i
$306$	11.0908	+	13.9075i	0.634021	+	0.795037i
$307$	17.2360			0.983708			0.491854	−	0.870678i	$-0.336319\pi$
$307$	17.2360			0.983708			0.491854	+	0.870678i	$0.336319\pi$
$308$	−81.0487			−4.61818
$309$	−30.7188	−	38.5202i	−1.74753	−	2.19134i
$310$	7.51145	+	3.61733i	0.426622	+	0.205450i
$311$	11.3547	−	14.2384i	0.643868	−	0.807385i	−0.347613	−	0.937638i	$-0.613008\pi$
$311$	11.3547	−	14.2384i	0.643868	−	0.807385i	0.991481	+	0.130253i	$0.0415790\pi$
$312$	22.0004	+	10.5948i	1.24553	+	0.599815i
$313$	3.15377	+	13.8176i	0.178262	+	0.781015i	0.982433	+	0.186617i	$0.0597524\pi$
$313$	3.15377	+	13.8176i	0.178262	+	0.781015i	−0.804171	+	0.594398i	$0.797390\pi$
$314$	−15.3965	−	19.3066i	−0.868873	−	1.08953i
$315$	−15.2084	−	66.6325i	−0.856898	−	3.75431i
$316$	67.1279	−	32.3271i	3.77624	−	1.81854i
$317$	16.7348	−	20.9847i	0.939918	−	1.17862i	−0.0438258	−	0.999039i	$-0.513955\pi$
$317$	16.7348	−	20.9847i	0.939918	−	1.17862i	0.983743	−	0.179580i	$-0.0574739\pi$
$318$	21.1343	−	26.5016i	1.18516	−	1.48614i
$319$	−11.8185	+	51.7803i	−0.661710	+	2.89914i
$320$	−18.1219	+	8.72705i	−1.01305	+	0.487857i
$321$	41.0794	+	19.7828i	2.29283	+	1.10417i
$322$	−2.02305	+	8.86357i	−0.112740	+	0.493947i
$323$	0.964024	−	4.22367i	0.0536398	−	0.235011i
$324$	−74.1291	−	35.6987i	−4.11829	−	1.98326i
$325$	5.55570	−	2.67548i	0.308175	−	0.148409i
$326$	−12.0570	+	52.8252i	−0.667776	+	2.92572i
$327$	8.48829	−	10.6440i	0.469404	−	0.588613i
$328$	40.6244	−	50.9414i	2.24311	−	2.81277i
$329$	−23.7318	+	11.4286i	−1.30838	+	0.630080i
$330$	33.0555	+	144.826i	1.81965	+	7.97240i
$331$	3.69090	+	4.62825i	0.202870	+	0.254391i	0.872851	−	0.487988i	$-0.162269\pi$
$331$	3.69090	+	4.62825i	0.202870	+	0.254391i	−0.669980	+	0.742379i	$0.733697\pi$
$332$	2.03915	+	8.93411i	0.111913	+	0.490323i
$333$	31.0004	+	14.9290i	1.69881	+	0.818104i
$334$	−1.65062	+	2.06981i	−0.0903180	+	0.113255i
$335$	−14.0062	−	6.74503i	−0.765241	−	0.368520i
$336$	54.5798	+	68.4409i	2.97757	+	3.73376i
$337$	−9.85050			−0.536591			−0.268296	−	0.963337i	$-0.586460\pi$
$337$	−9.85050			−0.536591			−0.268296	+	0.963337i	$0.586460\pi$
$338$	−30.7362			−1.67183
$339$	25.4590	+	31.9246i	1.38274	+	1.73390i
$340$	−14.0141	+	6.74882i	−0.760019	+	0.366006i
$341$	−1.21662	+	5.33035i	−0.0658835	+	0.288655i
$342$	17.1484	+	75.1319i	0.927278	+	4.06267i
$343$	−14.2408			−0.768932
$344$	44.2206	+	16.0279i	2.38422	+	0.864165i
$345$	11.7327			0.631666
$346$	−1.51737	−	6.64802i	−0.0815742	−	0.357400i
$347$	0.507760	−	2.22464i	0.0272580	−	0.119425i	−0.959469	−	0.281816i	$-0.909063\pi$
$347$	0.507760	−	2.22464i	0.0272580	−	0.119425i	0.986727	+	0.162391i	$0.0519205\pi$
$348$	128.208	−	61.7417i	6.87267	−	3.30970i
$349$	15.9840	+	20.0433i	0.855606	+	1.07290i	0.996560	+	0.0828794i	$0.0264116\pi$
$349$	15.9840	+	20.0433i	0.855606	+	1.07290i	−0.140954	+	0.990016i	$0.545017\pi$
$350$	45.1512			2.41343
$351$	−13.0799			−0.698152
$352$	−32.6271	−	40.9131i	−1.73903	−	2.18068i
$353$	12.7941	+	6.16130i	0.680960	+	0.327933i	0.742189	−	0.670191i	$-0.233788\pi$
$353$	12.7941	+	6.16130i	0.680960	+	0.327933i	−0.0612292	+	0.998124i	$0.519502\pi$
$354$	25.5056	−	31.9830i	1.35560	−	1.69987i
$355$	−9.34992	−	4.50269i	−0.496242	−	0.238978i
$356$	10.7684	+	47.1793i	0.570722	+	2.50050i
$357$	5.97801	+	7.49618i	0.316390	+	0.396740i
$358$	−8.41690	−	36.8769i	−0.444847	−	1.94900i
$359$	−5.74330	+	2.76583i	−0.303120	+	0.145975i	−0.579261	−	0.815142i	$-0.696659\pi$
$359$	−5.74330	+	2.76583i	−0.303120	+	0.145975i	0.276141	+	0.961117i	$0.410944\pi$
$360$	100.013	−	125.412i	5.27113	−	6.60978i
$361$	−0.144211	+	0.180835i	−0.00759005	+	0.00951762i
$362$	−1.52531	+	6.68281i	−0.0801684	+	0.351241i
$363$	−56.6792	+	27.2953i	−2.97489	+	1.43263i
$364$	14.2197	+	6.84783i	0.745314	+	0.358924i
$365$	−3.61764	+	15.8499i	−0.189356	+	0.829623i
$366$	−6.06440	+	26.5699i	−0.316991	+	1.38883i
$367$	−17.2063	−	8.28612i	−0.898162	−	0.432532i	−0.0729370	−	0.997337i	$-0.523237\pi$
$367$	−17.2063	−	8.28612i	−0.898162	−	0.432532i	−0.825225	+	0.564805i	$0.808951\pi$
$368$	−9.41236	+	4.53276i	−0.490653	+	0.236286i
$369$	−13.8302	+	60.5941i	−0.719972	+	3.15440i
$370$	−26.6423	+	33.4084i	−1.38507	+	1.73682i
$371$	7.91925	−	9.93042i	0.411147	−	0.515562i
$372$	13.1979	−	6.35579i	0.684281	−	0.329532i
$373$	4.72009	+	20.6801i	0.244397	+	1.07077i	0.936966	+	0.349422i	$0.113622\pi$
$373$	4.72009	+	20.6801i	0.244397	+	1.07077i	−0.692568	+	0.721352i	$0.743521\pi$
$374$	−9.03273	−	11.3267i	−0.467071	−	0.585689i
$375$	−1.55745	−	6.82364i	−0.0804265	−	0.352371i
$376$	−55.6983	−	26.8229i	−2.87242	−	1.38329i
$377$	6.44845	−	8.08610i	0.332112	−	0.416455i
$378$	−86.2887	−	41.5545i	−4.43821	−	2.13733i
$379$	10.9432	+	13.7224i	0.562116	+	0.704872i	0.978947	−	0.204112i	$-0.0654308\pi$
$379$	10.9432	+	13.7224i	0.562116	+	0.704872i	−0.416831	+	0.908984i	$0.636859\pi$
$380$	−67.3863			−3.45684
$381$	30.4906			1.56208
$382$	−9.61614	−	12.0583i	−0.492004	−	0.616954i
$383$	12.2819	−	5.91465i	0.627575	−	0.302224i	−0.0929312	−	0.995673i	$-0.529624\pi$
$383$	12.2819	−	5.91465i	0.627575	−	0.302224i	0.720506	+	0.693448i	$0.243909\pi$
$384$	1.94236	−	8.51005i	0.0991209	−	0.434277i
$385$	12.3862	+	54.2676i	0.631261	+	2.76573i
$386$	−10.4299			−0.530867
$387$	−44.6381	+	4.52718i	−2.26908	+	0.230130i
$388$	−42.0964			−2.13712
$389$	6.25983	+	27.4261i	0.317386	+	1.39056i	0.842119	+	0.539291i	$0.181308\pi$
$389$	6.25983	+	27.4261i	0.317386	+	1.39056i	−0.524734	+	0.851267i	$0.675835\pi$
$390$	6.43692	−	28.2020i	0.325946	−	1.42806i
$391$	−1.03092	+	0.496463i	−0.0521356	+	0.0251072i
$392$	10.4666	+	13.1246i	0.528641	+	0.662895i
$393$	−8.17600			−0.412425
$394$	16.9306			0.852951
$395$	−31.9040	−	40.0063i	−1.60526	−	2.01294i
$396$	163.481	+	78.7284i	8.21524	+	3.95625i
$397$	14.9894	−	18.7961i	0.752295	−	0.943348i	−0.247378	−	0.968919i	$-0.579569\pi$
$397$	14.9894	−	18.7961i	0.752295	−	0.943348i	0.999673	+	0.0255708i	$0.00814033\pi$
$398$	0.878218	+	0.422927i	0.0440211	+	0.0211994i
$399$	9.24304	+	40.4964i	0.462731	+	2.02736i
$400$	32.3483	+	40.5635i	1.61742	+	2.02817i
$401$	−1.81294	−	7.94299i	−0.0905337	−	0.396654i	0.909275	−	0.416195i	$-0.136637\pi$
$401$	−1.81294	−	7.94299i	−0.0905337	−	0.396654i	−0.999809	+	0.0195410i	$0.993780\pi$
$402$	−34.9517	+	16.8319i	−1.74323	+	0.839497i
$403$	0.663814	−	0.832396i	0.0330669	−	0.0414646i
$404$	43.5458	−	54.6047i	2.16648	−	2.71668i
$405$	−12.5740	+	55.0901i	−0.624805	+	2.73745i
$406$	68.2302	−	32.8579i	3.38621	−	1.63071i
$407$	−25.2477	−	12.1586i	−1.25148	−	0.602682i
$408$	−5.00737	+	21.9387i	−0.247902	+	1.08613i
$409$	−7.22014	+	31.6335i	−0.357013	+	1.56418i	0.403578	+	0.914945i	$0.367766\pi$
$409$	−7.22014	+	31.6335i	−0.357013	+	1.56418i	−0.760591	+	0.649231i	$0.775091\pi$
$410$	−69.5430	−	33.4901i	−3.43448	−	1.65396i
$411$	−21.4246	+	10.3176i	−1.05680	+	0.508927i
$412$	16.6309	−	72.8649i	0.819347	−	3.58979i
$413$	9.55718	−	11.9843i	0.470278	−	0.589710i
$414$	12.6905	−	15.9133i	0.623702	−	0.782098i
$415$	5.67036	−	2.73070i	0.278347	−	0.134045i
$416$	2.26754	+	9.93472i	0.111175	+	0.487090i
$417$	−19.4125	−	24.3424i	−0.950632	−	1.19205i
$418$	−13.9662	−	61.1898i	−0.683108	−	2.99289i
$419$	−9.13689	−	4.40009i	−0.446366	−	0.214959i	0.197178	−	0.980368i	$-0.436822\pi$
$419$	−9.13689	−	4.40009i	−0.446366	−	0.214959i	−0.643544	+	0.765409i	$0.722537\pi$
$420$	92.9845	−	116.599i	4.53718	−	5.68944i
$421$	−4.65030	−	2.23947i	−0.226642	−	0.109145i	0.317117	−	0.948386i	$-0.397285\pi$
$421$	−4.65030	−	2.23947i	−0.226642	−	0.109145i	−0.543759	+	0.839241i	$0.682999\pi$
$422$	−27.3525	−	34.2989i	−1.33150	−	1.66965i
$423$	58.9702			2.86723
$424$	29.8103			1.44772
$425$	3.54304	+	4.44283i	0.171863	+	0.215509i
$426$	−23.3322	+	11.2362i	−1.13045	+	0.544396i
$427$	−2.27239	+	9.95599i	−0.109969	+	0.481804i
$428$	15.3906	+	67.4306i	0.743933	+	3.25938i
$429$	18.9704			0.915899
$430$	6.85433	−	55.2972i	0.330545	−	2.66667i
$431$	32.7587			1.57793			0.788965	−	0.614438i	$-0.210617\pi$
$431$	32.7587			1.57793			0.788965	+	0.614438i	$0.210617\pi$
$432$	−24.4888	−	107.293i	−1.17822	−	5.16212i
$433$	−0.466667	+	2.04460i	−0.0224266	+	0.0982572i	−0.984903	−	0.173110i	$-0.944619\pi$
$433$	−0.466667	+	2.04460i	−0.0224266	+	0.0982572i	0.962476	+	0.271367i	$0.0874756\pi$
$434$	7.02372	−	3.38245i	0.337149	−	0.162363i
$435$	−60.9336	−	76.4083i	−2.92154	−	3.66350i
$436$	20.6520			0.989050
$437$	−4.95713			−0.237132
$438$	25.2949	+	31.7188i	1.20864	+	1.51558i
$439$	15.7625	+	7.59084i	0.752305	+	0.362291i	0.770413	−	0.637545i	$-0.220050\pi$
$439$	15.7625	+	7.59084i	0.752305	+	0.362291i	−0.0181081	+	0.999836i	$0.505764\pi$
$440$	−81.4535	+	102.139i	−3.88314	+	4.86931i
$441$	−14.4273	−	6.94781i	−0.687013	−	0.330848i
$442$	0.627761	+	2.75040i	0.0298596	+	0.130823i
$443$	−6.47425	−	8.11846i	−0.307601	−	0.385719i	0.603871	−	0.797082i	$-0.293624\pi$
$443$	−6.47425	−	8.11846i	−0.307601	−	0.385719i	−0.911472	+	0.411363i	$0.865053\pi$
$444$	16.7069	+	73.1977i	0.792874	+	3.47381i
$445$	29.9441	−	14.4203i	1.41949	−	0.683588i
$446$	−11.7671	+	14.7554i	−0.557187	+	0.698690i
$447$	−34.0892	+	42.7464i	−1.61236	+	2.02184i
$448$	−4.18512	+	18.3362i	−0.197729	+	0.866305i
$449$	18.0773	−	8.70555i	0.853119	−	0.410840i	0.0443847	−	0.999015i	$-0.485867\pi$
$449$	18.0773	−	8.70555i	0.853119	−	0.410840i	0.808734	+	0.588174i	$0.200153\pi$
$450$	−91.0733	−	43.8586i	−4.29324	−	2.06751i
$451$	11.2638	−	49.3498i	0.530390	−	2.32379i
$452$	−13.7833	+	60.3886i	−0.648312	+	2.84044i
$453$	16.7168	+	8.05041i	0.785426	+	0.378241i
$454$	−58.9148	+	28.3719i	−2.76501	+	1.33156i
$455$	2.41198	−	10.5676i	0.113075	−	0.495415i
$456$	−60.7835	+	76.2200i	−2.84645	+	3.56933i
$457$	17.8386	−	22.3689i	0.834454	−	1.04637i	−0.163752	−	0.986501i	$-0.552360\pi$
$457$	17.8386	−	22.3689i	0.834454	−	1.04637i	0.998206	−	0.0598704i	$-0.0190687\pi$
$458$	26.3367	−	12.6831i	1.23063	−	0.592642i
$459$	−2.68221	−	11.7515i	−0.125195	−	0.548514i
$460$	11.0968	+	13.9149i	0.517390	+	0.648786i
$461$	6.71422	+	29.4169i	0.312712	+	1.37008i	0.850044	+	0.526711i	$0.176575\pi$
$461$	6.71422	+	29.4169i	0.312712	+	1.37008i	−0.537332	+	0.843371i	$0.680568\pi$
$462$	125.149	+	60.2684i	5.82245	+	2.80394i
$463$	17.7062	−	22.2029i	0.822877	−	1.03185i	−0.175996	−	0.984391i	$-0.556315\pi$
$463$	17.7062	−	22.2029i	0.822877	−	1.03185i	0.998873	−	0.0474638i	$-0.0151139\pi$
$464$	78.4024	+	37.7566i	3.63974	+	1.75281i
$465$	−6.27260	−	7.86559i	−0.290885	−	0.364758i
$466$	−50.0331			−2.31774
$467$	11.1186			0.514509			0.257255	−	0.966344i	$-0.417182\pi$
$467$	11.1186			0.514509			0.257255	+	0.966344i	$0.417182\pi$
$468$	−22.0303	−	27.6252i	−1.01835	−	1.27697i
$469$	−13.0968	+	6.30707i	−0.604752	+	0.291233i
$470$	−16.2963	+	71.3988i	−0.751693	+	3.29338i
$471$	6.63081	+	29.0515i	0.305532	+	1.33862i
$472$	35.9759			1.65593
$473$	36.3547	−	3.68708i	1.67159	−	0.169532i
$474$	−127.692			−5.86509
$475$	5.47816	+	24.0014i	0.251355	+	1.10126i
$476$	−3.23645	+	14.1798i	−0.148342	+	0.649930i
$477$	−25.6198	+	12.3379i	−1.17305	+	0.564912i
$478$	5.15526	+	6.46449i	0.235796	+	0.295679i
$479$	20.4372			0.933801			0.466901	−	0.884310i	$-0.345371\pi$
$479$	20.4372			0.933801			0.466901	+	0.884310i	$0.345371\pi$
$480$	96.2908			4.39505
$481$	3.40232	+	4.26637i	0.155132	+	0.194530i
$482$	29.0338	+	13.9819i	1.32245	+	0.636860i
$483$	6.84021	−	8.57735i	0.311240	−	0.390283i
$484$	−85.9794	−	41.4055i	−3.90816	−	1.88207i
$485$	6.43337	+	28.1864i	0.292124	+	1.27988i
$486$	29.3027	+	36.7444i	1.32920	+	1.66676i
$487$	−2.58386	−	11.3206i	−0.117086	−	0.512987i	−0.999126	−	0.0418117i	$-0.986687\pi$
$487$	−2.58386	−	11.3206i	−0.117086	−	0.512987i	0.882040	−	0.471175i	$-0.156170\pi$
$488$	−21.5940	+	10.3991i	−0.977516	+	0.470747i
$489$	40.7664	−	51.1194i	1.84352	−	2.31170i
$490$	12.3991	−	15.5480i	0.560134	−	0.702386i
$491$	1.24488	−	5.45420i	0.0561809	−	0.246144i	−0.939038	−	0.343813i	$-0.888281\pi$
$491$	1.24488	−	5.45420i	0.0561809	−	0.246144i	0.995219	+	0.0976686i	$0.0311385\pi$
$492$	−122.190	+	58.8435i	−5.50874	+	2.65287i
$493$	8.58724	+	4.13540i	0.386750	+	0.186249i
$494$	−2.71964	+	11.9155i	−0.122362	+	0.536105i
$495$	27.7301	−	121.493i	1.24637	−	5.46072i
$496$	8.07087	+	3.88673i	0.362393	+	0.174519i
$497$	−8.74282	+	4.21032i	−0.392169	+	0.188859i
$498$	3.49478	−	15.3116i	0.156605	−	0.686131i
$499$	−14.2995	+	17.9310i	−0.640132	+	0.802700i	−0.991020	−	0.133717i	$-0.957309\pi$
$499$	−14.2995	+	17.9310i	−0.640132	+	0.802700i	0.350887	+	0.936418i	$0.385880\pi$
$500$	6.61978	−	8.30094i	0.296046	−	0.371230i
$501$	2.87827	−	1.38610i	0.128592	−	0.0619265i
$502$	7.62628	+	33.4129i	0.340377	+	1.49129i
$503$	8.08404	+	10.1371i	0.360450	+	0.451990i	0.928681	−	0.370879i	$-0.120944\pi$
$503$	8.08404	+	10.1371i	0.360450	+	0.451990i	−0.568231	+	0.822869i	$0.692372\pi$
$504$	−33.3764	−	146.232i	−1.48670	−	6.51367i
$505$	−43.2164	−	20.8119i	−1.92311	−	0.926119i
$506$	−10.3355	+	12.9603i	−0.459470	+	0.576157i
$507$	33.4167	+	16.0927i	1.48409	+	0.714700i
$508$	28.8381	+	36.1618i	1.27948	+	1.60442i
$509$	16.9734			0.752332			0.376166	−	0.926552i	$-0.377242\pi$
$509$	16.9734			0.752332			0.376166	+	0.926552i	$0.377242\pi$
$510$	26.6578			1.18043
$511$	9.47823	+	11.8853i	0.419292	+	0.525776i
$512$	40.7595	−	19.6287i	1.80133	−	0.867476i
$513$	11.6201	−	50.9109i	0.513039	−	2.24777i
$514$	4.07598	+	17.8581i	0.179784	+	0.787685i
$515$	−51.3296			−2.26185
$516$	−68.4533	−	69.9937i	−3.01349	−	3.08130i
$517$	−48.0272			−2.11223
$518$	8.89114	+	38.9546i	0.390654	+	1.71157i
$519$	−1.83103	+	8.02225i	−0.0803732	+	0.352138i
$520$	22.9205	−	11.0379i	1.00513	−	0.484045i
$521$	−6.16077	−	7.72536i	−0.269908	−	0.338454i	0.628343	−	0.777936i	$-0.283733\pi$
$521$	−6.16077	−	7.72536i	−0.269908	−	0.338454i	−0.898251	+	0.439482i	$0.855162\pi$
$522$	−169.543			−7.42067
$523$	−31.9448			−1.39685			−0.698424	−	0.715685i	$-0.746115\pi$
$523$	−31.9448			−1.39685			−0.698424	+	0.715685i	$0.746115\pi$
$524$	−7.73287	−	9.69672i	−0.337812	−	0.423603i
$525$	−49.0889	−	23.6400i	−2.14241	−	1.03173i
$526$	15.6283	−	19.5973i	0.681428	−	0.854483i
$527$	0.883984	+	0.425704i	0.0385070	+	0.0185440i
$528$	35.5173	+	155.612i	1.54569	+	6.77213i
$529$	−13.5240	−	16.9585i	−0.587998	−	0.737326i
$530$	−7.85820	−	34.4290i	−0.341339	−	1.49550i
$531$	−30.9188	+	14.8897i	−1.34176	+	0.646158i
$532$	−39.2866	+	49.2638i	−1.70329	+	2.13586i
$533$	−6.14576	+	7.70654i	−0.266202	+	0.333807i
$534$	18.4553	−	80.8578i	0.798637	−	3.49906i
$535$	42.7973	−	20.6101i	1.85029	−	0.891053i
$536$	−30.7380	−	14.8026i	−1.32768	−	0.639377i
$537$	−10.1568	+	44.4998i	−0.438298	+	1.92031i
$538$	3.85675	−	16.8975i	0.166276	−	0.728504i
$539$	11.7500	+	5.65852i	0.506110	+	0.243730i
$540$	−168.922	+	81.3484i	−7.26923	+	3.50068i
$541$	6.45136	−	28.2652i	0.277365	−	1.21522i	−0.623745	−	0.781628i	$-0.714390\pi$
$541$	6.45136	−	28.2652i	0.277365	−	1.21522i	0.901110	−	0.433590i	$-0.142753\pi$
$542$	−1.50564	+	1.88801i	−0.0646728	+	0.0810971i
$543$	5.15727	−	6.46701i	0.221320	−	0.277526i
$544$	−8.46079	+	4.07450i	−0.362753	+	0.174693i
$545$	−3.15613	−	13.8279i	−0.135194	−	0.592322i
$546$	−16.8648	−	21.1477i	−0.721745	−	0.905039i
$547$	6.57706	+	28.8160i	0.281215	+	1.23208i	0.896238	+	0.443573i	$0.146289\pi$
$547$	6.57706	+	28.8160i	0.281215	+	1.23208i	−0.615024	+	0.788509i	$0.710854\pi$
$548$	−32.5000	−	15.6512i	−1.38833	−	0.668586i
$549$	14.2545	−	17.8746i	0.608369	−	0.762871i
$550$	74.1730	+	35.7198i	3.16275	+	1.52310i
$551$	25.7448	+	32.2830i	1.09677	+	1.37530i
$552$	25.7485			1.09593
$553$	−47.8474			−2.03468
$554$	29.7327	+	37.2836i	1.26322	+	1.58403i
$555$	46.4576	−	22.3728i	1.97202	−	0.949673i
$556$	10.5098	−	46.0462i	0.445713	−	1.95280i
$557$	−6.18054	−	27.0787i	−0.261878	−	1.14736i	−0.919212	−	0.393763i	$-0.871173\pi$
$557$	−6.18054	−	27.0787i	−0.261878	−	1.14736i	0.657334	−	0.753599i	$-0.271684\pi$
$558$	−17.4530			−0.738844
$559$	−6.68981	−	2.42474i	−0.282949	−	0.102555i
$560$	91.2002			3.85391
$561$	3.89013	+	17.0438i	0.164242	+	0.719589i
$562$	−4.12588	+	18.0767i	−0.174040	+	0.762518i
$563$	−25.3664	+	12.2158i	−1.06907	+	0.514835i	−0.883806	−	0.467854i	$-0.845027\pi$
$563$	−25.3664	+	12.2158i	−1.06907	+	0.514835i	−0.185261	+	0.982689i	$0.559313\pi$
$564$	80.2287	+	100.604i	3.37824	+	4.23617i
$565$	42.5407			1.78970
$566$	−33.8413			−1.42246
$567$	32.9438	+	41.3103i	1.38351	+	1.73487i
$568$	−20.5193	−	9.88159i	−0.860972	−	0.414622i
$569$	−17.8385	+	22.3688i	−0.747831	+	0.937750i	−0.999548	−	0.0300506i	$-0.990433\pi$
$569$	−17.8385	+	22.3688i	−0.747831	+	0.937750i	0.251718	+	0.967801i	$0.419005\pi$
$570$	104.052	+	50.1090i	4.35827	+	2.09883i
$571$	−2.06561	−	9.05003i	−0.0864431	−	0.378732i	0.913139	−	0.407649i	$-0.133651\pi$
$571$	−2.06561	−	9.05003i	−0.0864431	−	0.378732i	−0.999582	+	0.0289169i	$0.990794\pi$
$572$	17.9422	+	22.4988i	0.750202	+	0.940723i
$573$	4.14139	+	18.1446i	0.173009	+	0.758002i
$574$	−65.0275	+	31.3156i	−2.71419	+	1.30709i
$575$	4.05405	−	5.08361i	0.169065	−	0.212001i
$576$	26.2530	−	32.9202i	1.09387	−	1.37168i
$577$	−6.98899	+	30.6208i	−0.290956	+	1.27476i	0.592243	+	0.805760i	$0.298243\pi$
$577$	−6.98899	+	30.6208i	−0.290956	+	1.27476i	−0.883198	+	0.469000i	$0.844614\pi$
$578$	−2.34235	+	1.12801i	−0.0974288	+	0.0469192i
$579$	11.3395	+	5.46081i	0.471253	+	0.226943i
$580$	32.9890	−	144.534i	1.36979	−	6.00145i
$581$	1.30953	−	5.73742i	0.0543284	−	0.238028i
$582$	65.0018	+	31.3032i	2.69441	+	1.29756i
$583$	20.8656	−	10.0483i	0.864165	−	0.416160i
$584$	−7.93927	+	34.7842i	−0.328529	+	1.43938i
$585$	−15.1302	+	18.9726i	−0.625555	+	0.784421i
$586$	−31.8067	+	39.8844i	−1.31392	+	1.64761i
$587$	−21.0589	+	10.1414i	−0.869194	+	0.418582i	−0.814666	−	0.579931i	$-0.803080\pi$
$587$	−21.0589	+	10.1414i	−0.869194	+	0.418582i	−0.0545280	+	0.998512i	$0.517365\pi$
$588$	−7.77523	−	34.0655i	−0.320645	−	1.40484i
$589$	2.65022	+	3.32326i	0.109200	+	0.136933i
$590$	−9.48351	−	41.5500i	−0.390430	−	1.71059i
$591$	−18.4071	−	8.86441i	−0.757168	−	0.364633i
$592$	−28.6265	+	35.8965i	−1.17654	+	1.47534i
$593$	−39.4472	−	18.9968i	−1.61990	−	0.780104i	−0.619914	−	0.784670i	$-0.712833\pi$
$593$	−39.4472	−	18.9968i	−1.61990	−	0.780104i	−0.999990	+	0.00456528i	$0.998547\pi$
$594$	−108.878	−	136.529i	−4.46732	−	5.60184i
$595$	9.98895			0.409507
$596$	−82.9388			−3.39730
$597$	−0.733375	−	0.919623i	−0.0300150	−	0.0376377i
$598$	2.90835	−	1.40059i	0.118931	−	0.0572743i
$599$	2.00351	−	8.77794i	0.0818611	−	0.358657i	−0.917363	−	0.398053i	$-0.869686\pi$
$599$	2.00351	−	8.77794i	0.0818611	−	0.358657i	0.999224	+	0.0393956i	$0.0125433\pi$
$600$	−28.4548	−	124.669i	−1.16166	−	5.08958i
$601$	14.7655			0.602298			0.301149	−	0.953577i	$-0.402630\pi$
$601$	14.7655			0.602298			0.301149	+	0.953577i	$0.402630\pi$
$602$	−36.4297	−	37.2495i	−1.48477	−	1.51818i
$603$	32.5436			1.32528
$604$	6.26305	+	27.4402i	0.254840	+	1.11653i
$605$	−14.5840	+	63.8969i	−0.592926	+	2.59778i
$606$	−107.844	+	51.9351i	−4.38088	+	2.10972i
$607$	5.52784	+	6.93169i	0.224368	+	0.281348i	0.881256	−	0.472640i	$-0.156699\pi$
$607$	5.52784	+	6.93169i	0.224368	+	0.281348i	−0.656888	+	0.753988i	$0.728127\pi$
$608$	−40.6835			−1.64993
$609$	−91.3841			−3.70307
$610$	17.7027	+	22.1985i	0.716761	+	0.898790i
$611$	8.42618	+	4.05784i	0.340887	+	0.164162i
$612$	20.3020	−	25.4579i	0.820660	−	1.02907i
$613$	44.1139	+	21.2441i	1.78174	+	0.858043i	0.955646	+	0.294518i	$0.0951590\pi$
$613$	44.1139	+	21.2441i	1.78174	+	0.858043i	0.826099	+	0.563525i	$0.190555\pi$
$614$	−9.97121	−	43.6867i	−0.402405	−	1.76305i
$615$	58.0734	+	72.8217i	2.34174	+	2.93645i
$616$	27.1828	+	119.096i	1.09523	+	4.79850i
$617$	27.3088	−	13.1512i	1.09941	−	0.529449i	0.205939	−	0.978565i	$-0.433975\pi$
$617$	27.3088	−	13.1512i	1.09941	−	0.529449i	0.893474	+	0.449116i	$0.148261\pi$
$618$	−79.8630	+	100.145i	−3.21256	+	4.02842i
$619$	−6.66892	+	8.36256i	−0.268046	+	0.336120i	−0.897578	−	0.440855i	$-0.854675\pi$
$619$	−6.66892	+	8.36256i	−0.268046	+	0.336120i	0.629532	+	0.776975i	$0.283247\pi$
$620$	3.39594	−	14.8786i	0.136384	−	0.597538i
$621$	−12.4264	+	5.98422i	−0.498653	+	0.240139i
$622$	−42.6579	−	20.5429i	−1.71042	−	0.823697i
$623$	6.91537	−	30.2982i	0.277058	−	1.21387i
$624$	6.91631	−	30.3023i	0.276874	−	1.21306i
$625$	19.0295	+	9.16411i	0.761179	+	0.366564i
$626$	33.1979	−	15.9872i	1.32685	−	0.638979i
$627$	−16.8532	+	73.8386i	−0.673051	+	2.94883i
$628$	−28.1835	+	35.3411i	−1.12465	+	1.41026i
$629$	−3.13540	+	3.93167i	−0.125017	+	0.156766i
$630$	−160.090	+	77.0953i	−6.37814	+	3.07155i
$631$	7.46603	+	32.7108i	0.297218	+	1.30220i	0.874250	+	0.485476i	$0.161354\pi$
$631$	7.46603	+	32.7108i	0.297218	+	1.30220i	−0.577032	+	0.816721i	$0.695789\pi$
$632$	−70.0164	−	87.7978i	−2.78510	−	3.49241i
$633$	11.7799	+	51.6112i	0.468210	+	2.05136i
$634$	−62.8697	−	30.2764i	−2.49687	−	1.20243i
$635$	19.8056	−	24.8355i	0.785962	−	0.985566i
$636$	−55.9041	−	26.9220i	−2.21674	−	1.06753i
$637$	−1.58341	−	1.98553i	−0.0627369	−	0.0786696i
$638$	138.081			5.46667
$639$	21.7247			0.859415
$640$	−5.66999	−	7.10994i	−0.224126	−	0.281045i
$641$	−38.4812	+	18.5316i	−1.51992	+	0.731954i	−0.993017	−	0.117973i	$-0.962360\pi$
$641$	−38.4812	+	18.5316i	−1.51992	+	0.731954i	−0.526901	+	0.849927i	$0.676646\pi$
$642$	26.3771	−	115.565i	1.04102	−	4.56100i
$643$	−2.40938	−	10.5562i	−0.0950169	−	0.416296i	0.904940	−	0.425538i	$-0.139915\pi$
$643$	−2.40938	−	10.5562i	−0.0950169	−	0.416296i	−0.999957	+	0.00924220i	$0.997058\pi$
$644$	16.6422			0.655795
$645$	−36.4042	+	56.5309i	−1.43341	+	2.22590i
$646$	−11.2631			−0.443141
$647$	−7.78806	−	34.1217i	−0.306180	−	1.34146i	−0.860624	−	0.509242i	$-0.829926\pi$
$647$	−7.78806	−	34.1217i	−0.306180	−	1.34146i	0.554444	−	0.832221i	$-0.312931\pi$
$648$	−27.5948	+	120.901i	−1.08403	+	4.74943i
$649$	25.1812	−	12.1266i	0.988450	−	0.476012i
$650$	−9.99538	−	12.5338i	−0.392051	−	0.491616i
$651$	−9.40723			−0.368698
$652$	99.1844			3.88436
$653$	−1.03837	−	1.30207i	−0.0406346	−	0.0509541i	0.761099	−	0.648636i	$-0.224660\pi$
$653$	−1.03837	−	1.30207i	−0.0406346	−	0.0509541i	−0.801734	+	0.597682i	$0.796089\pi$
$654$	−31.8891	−	15.3570i	−1.24696	−	0.600505i
$655$	−5.31084	+	6.65958i	−0.207512	+	0.260211i
$656$	−74.7222	−	35.9843i	−2.91741	−	1.40495i
$657$	−7.57322	−	33.1805i	−0.295460	−	1.29449i
$658$	42.6964	+	53.5396i	1.66448	+	2.08719i
$659$	6.87673	+	30.1289i	0.267879	+	1.17366i	0.912475	+	0.409133i	$0.134169\pi$
$659$	6.87673	+	30.1289i	0.267879	+	1.17366i	−0.644596	+	0.764524i	$0.722974\pi$
$660$	244.995	−	117.984i	9.53643	−	4.59250i
$661$	16.6686	−	20.9018i	0.648334	−	0.812985i	−0.343683	−	0.939086i	$-0.611675\pi$
$661$	16.6686	−	20.9018i	0.648334	−	0.812985i	0.992017	+	0.126100i	$0.0402461\pi$
$662$	9.59564	−	12.0326i	0.372945	−	0.467658i
$663$	0.757528	−	3.31895i	0.0294199	−	0.128897i
$664$	12.4442	−	5.99280i	0.482928	−	0.232566i
$665$	38.9894	+	18.7763i	1.51194	+	0.728114i
$666$	19.9053	−	87.2109i	0.771316	−	3.37935i
$667$	2.42676	−	10.6324i	0.0939647	−	0.411686i
$668$	4.36619	+	2.10265i	0.168933	+	0.0813538i
$669$	20.5188	−	9.88135i	0.793304	−	0.382035i
$670$	−8.99338	+	39.4026i	−0.347444	+	1.52225i
$671$	−11.6094	+	14.5577i	−0.448174	+	0.561993i
$672$	56.1380	−	70.3949i	2.16557	−	2.71554i
$673$	13.7435	−	6.61854i	0.529774	−	0.255126i	−0.149821	−	0.988713i	$-0.547870\pi$
$673$	13.7435	−	6.61854i	0.529774	−	0.255126i	0.679595	+	0.733587i	$0.262155\pi$
$674$	5.69863	+	24.9673i	0.219503	+	0.961706i
$675$	42.7068	+	53.5526i	1.64379	+	2.06124i
$676$	12.5198	+	54.8526i	0.481529	+	2.10972i
$677$	34.0626	+	16.4037i	1.30913	+	0.630445i	0.952711	−	0.303879i	$-0.0982820\pi$
$677$	34.0626	+	16.4037i	1.30913	+	0.630445i	0.356423	+	0.934325i	$0.383996\pi$
$678$	66.1885	−	82.9978i	2.54195	−	3.18751i
$679$	24.3568	+	11.7296i	0.934729	+	0.450142i
$680$	14.6171	+	18.3293i	0.560540	+	0.702895i
$681$	78.9075			3.02374
$682$	14.2143			0.544292
$683$	−9.36565	−	11.7441i	−0.358366	−	0.449377i	0.569666	−	0.821876i	$-0.307072\pi$
$683$	−9.36565	−	11.7441i	−0.358366	−	0.449377i	−0.928033	+	0.372499i	$0.878501\pi$
$684$	127.097	−	61.2069i	4.85969	−	2.34030i
$685$	−5.51274	+	24.1529i	−0.210631	+	0.922834i
$686$	8.23848	+	36.0951i	0.314547	+	1.37812i
$687$	−35.2741			−1.34579
$688$	7.36480	−	59.4154i	0.280780	−	2.26519i
$689$	−4.50978			−0.171809
$690$	−6.78749	−	29.7379i	−0.258395	−	1.13210i
$691$	4.30444	−	18.8590i	0.163749	−	0.717429i	−0.824662	−	0.565626i	$-0.808635\pi$
$691$	4.30444	−	18.8590i	0.163749	−	0.717429i	0.988411	−	0.151804i	$-0.0485081\pi$
$692$	−11.2462	+	5.41587i	−0.427515	+	0.205880i
$693$	−72.6529	−	91.1038i	−2.75986	−	3.46075i
$694$	−5.93238			−0.225190
$695$	−32.4373			−1.23042
$696$	−133.725	−	167.686i	−5.06882	−	6.35611i
$697$	−8.18416	−	3.94128i	−0.309997	−	0.149287i
$698$	41.5554	−	52.1088i	1.57290	−	1.97235i
$699$	54.3965	+	26.1960i	2.05746	+	0.990823i
$700$	−18.3914	−	80.5780i	−0.695130	−	3.04556i
$701$	−6.02103	−	7.55013i	−0.227411	−	0.285165i	0.655015	−	0.755616i	$-0.272662\pi$
$701$	−6.02103	−	7.55013i	−0.227411	−	0.285165i	−0.882426	+	0.470452i	$0.844091\pi$
$702$	7.56686	+	33.1526i	0.285593	+	1.25126i
$703$	−19.6286	+	9.45266i	−0.740308	+	0.356514i
$704$	−21.3813	+	26.8113i	−0.805837	+	1.01049i
$705$	55.1000	−	69.0932i	2.07519	−	2.60220i
$706$	8.21507	−	35.9926i	0.309178	−	1.35460i
$707$	−40.4103	+	19.4606i	−1.51979	+	0.731890i
$708$	−67.4668	−	32.4903i	−2.53556	−	1.22106i
$709$	−7.52265	+	32.9589i	−0.282519	+	1.23780i	0.612033	+	0.790832i	$0.290352\pi$
$709$	−7.52265	+	32.9589i	−0.282519	+	1.23780i	−0.894552	+	0.446964i	$0.852505\pi$
$710$	−6.00358	+	26.3034i	−0.225310	+	0.987149i
$711$	96.5118	+	46.4776i	3.61948	+	1.74305i
$712$	65.7152	−	31.6468i	2.46278	−	1.18601i
$713$	0.249815	−	1.09451i	0.00935565	−	0.0409898i
$714$	15.5417	−	19.4886i	0.581632	−	0.729344i
$715$	12.3225	−	15.4519i	0.460835	−	0.577869i
$716$	−62.3829	+	30.0420i	−2.33136	+	1.12272i
$717$	−2.22022	−	9.72741i	−0.0829156	−	0.363277i
$718$	10.3329	+	12.9571i	0.385621	+	0.483553i
$719$	−4.53652	−	19.8758i	−0.169184	−	0.741243i	−0.986326	−	0.164806i	$-0.947300\pi$
$719$	−4.53652	−	19.8758i	−0.169184	−	0.741243i	0.817142	−	0.576436i	$-0.195557\pi$
$720$	−183.957	−	88.5892i	−6.85569	−	3.30153i
$721$	−29.9254	+	37.5253i	−1.11448	+	1.39752i
$722$	0.541776	+	0.260906i	0.0201628	+	0.00970990i
$723$	−24.2453	−	30.4026i	−0.901692	−	1.13069i
$724$	12.5476			0.466329
$725$	−54.1614			−2.01150
$726$	101.973	+	127.870i	3.78457	+	4.74570i
$727$	−32.3984	+	15.6022i	−1.20159	+	0.578655i	−0.924129	−	0.382082i	$-0.875207\pi$
$727$	−32.3984	+	15.6022i	−1.20159	+	0.578655i	−0.277461	+	0.960737i	$0.589493\pi$
$728$	5.29332	−	23.1916i	0.196184	−	0.859536i
$729$	−1.07849	−	4.72516i	−0.0399440	−	0.175006i
$730$	42.2665			1.56435
$731$	0.806650	−	6.50764i	0.0298350	−	0.240694i
$732$	49.8875			1.84390
$733$	−0.952236	−	4.17202i	−0.0351716	−	0.154097i	0.954293	−	0.298873i	$-0.0966108\pi$
$733$	−0.952236	−	4.17202i	−0.0351716	−	0.154097i	−0.989464	+	0.144776i	$0.953754\pi$
$734$	−11.0482	+	48.4051i	−0.407795	+	1.78667i
$735$	−21.6209	+	10.4121i	−0.797500	+	0.384056i
$736$	6.69952	+	8.40093i	0.246947	+	0.309662i
$737$	−26.5046			−0.976308
$738$	161.584			5.94800
$739$	−24.7608	−	31.0490i	−0.910840	−	1.14216i	−0.989395	−	0.145247i	$-0.953602\pi$
$739$	−24.7608	−	31.0490i	−0.910840	−	1.14216i	0.0785555	−	0.996910i	$-0.474969\pi$
$740$	70.4738	+	33.9384i	2.59067	+	1.24760i
$741$	9.19547	−	11.5308i	0.337804	−	0.423593i
$742$	−29.7513	−	14.3275i	−1.09220	−	0.525978i
$743$	−6.34017	−	27.7781i	−0.232598	−	1.01908i	−0.947475	−	0.319829i	$-0.896374\pi$
$743$	−6.34017	−	27.7781i	−0.232598	−	1.01908i	0.714877	−	0.699250i	$-0.246483\pi$
$744$	−13.7658	−	17.2618i	−0.504680	−	0.632849i
$745$	12.6751	+	55.5332i	0.464379	+	2.03458i
$746$	49.6856	−	23.9273i	1.81912	−	0.876042i
$747$	−8.21458	+	10.3008i	−0.300556	+	0.376885i
$748$	−16.5346	+	20.7337i	−0.604565	+	0.758100i
$749$	9.88374	−	43.3035i	0.361144	−	1.58227i
$750$	−16.3944	+	7.89511i	−0.598638	+	0.288289i
$751$	8.86327	+	4.26833i	0.323425	+	0.155753i	0.588550	−	0.808461i	$-0.299699\pi$
$751$	8.86327	+	4.26833i	0.323425	+	0.155753i	−0.265125	+	0.964214i	$0.585413\pi$
$752$	−17.5100	+	76.7162i	−0.638523	+	2.79755i
$753$	9.20273	−	40.3198i	0.335366	−	1.46933i
$754$	−24.2257	−	11.6665i	−0.882250	−	0.424869i
$755$	17.4160	−	8.38708i	0.633832	−	0.305237i
$756$	−39.0113	+	170.919i	−1.41883	+	6.21628i
$757$	−21.3740	+	26.8022i	−0.776852	+	0.974142i	−1.00000		0.000643037i	$-0.999795\pi$
$757$	−21.3740	+	26.8022i	−0.776852	+	0.974142i	0.223148	+	0.974785i	$0.428367\pi$
$758$	28.4503	−	35.6756i	1.03336	−	1.29580i
$759$	18.0226	−	8.67921i	0.654178	−	0.315035i
$760$	22.6006	+	99.0197i	0.819810	+	3.59182i
$761$	20.0959	+	25.1994i	0.728474	+	0.913478i	0.998784	−	0.0492955i	$-0.0156976\pi$
$761$	20.0959	+	25.1994i	0.728474	+	0.913478i	−0.270310	+	0.962773i	$0.587126\pi$
$762$	−17.6392	−	77.2823i	−0.639000	−	2.79964i
$763$	−11.9491	−	5.75441i	−0.432588	−	0.208324i
$764$	−17.6025	+	22.0729i	−0.636838	+	0.798569i
$765$	−20.1484	−	9.70298i	−0.728469	−	0.350812i
$766$	−22.0966	−	27.7083i	−0.798384	−	1.00114i
$767$	−5.44253			−0.196518
$768$	−61.3063			−2.21220
$769$	−13.4204	−	16.8286i	−0.483950	−	0.606855i	0.478575	−	0.878047i	$-0.341154\pi$
$769$	−13.4204	−	16.8286i	−0.483950	−	0.606855i	−0.962525	+	0.271192i	$0.912582\pi$
$770$	130.383	−	62.7889i	4.69866	−	2.26276i
$771$	4.91854	−	21.5495i	0.177137	−	0.776088i
$772$	4.24839	+	18.6134i	0.152903	+	0.669912i
$773$	−18.9092			−0.680118			−0.340059	−	0.940404i	$-0.610447\pi$
$773$	−18.9092			−0.680118			−0.340059	+	0.940404i	$0.610447\pi$
$774$	37.2984	+	110.522i	1.34066	+	3.97263i
$775$	−5.57546			−0.200277
$776$	14.1187	+	61.8579i	0.506830	+	2.22057i
$777$	10.7290	−	47.0070i	0.384902	−	1.68637i
$778$	65.8935	−	31.7326i	2.36240	−	1.13767i
$779$	−24.5364	−	30.7677i	−0.879107	−	1.10237i
$780$	−52.9519			−1.89598
$781$	−17.6933			−0.633115
$782$	1.85474	+	2.32577i	0.0663255	+	0.0831695i
$783$	103.508	+	49.8469i	3.69908	+	1.78138i
$784$	13.3225	−	16.7059i	0.475804	−	0.596639i
$785$	27.9704	+	13.4698i	0.998306	+	0.480759i
$786$	4.72991	+	20.7231i	0.168710	+	0.739168i
$787$	8.29716	+	10.4043i	0.295762	+	0.370874i	0.907403	−	0.420262i	$-0.138062\pi$
$787$	8.29716	+	10.4043i	0.295762	+	0.370874i	−0.611641	+	0.791135i	$0.709490\pi$
$788$	−6.89633	−	30.2148i	−0.245672	−	1.07636i
$789$	−27.2519	+	13.1238i	−0.970194	+	0.467221i
$790$	−82.9442	+	104.009i	−2.95102	+	3.70047i
$791$	24.8015	−	31.1001i	0.881839	−	1.10579i
$792$	60.8564	−	266.629i	2.16244	−	9.47426i
$793$	3.26680	−	1.57321i	0.116007	−	0.0558663i
$794$	−56.3126	−	27.1187i	−1.99846	−	0.962407i
$795$	−9.48260	+	41.5460i	−0.336313	+	1.47348i
$796$	0.397043	−	1.73956i	0.0140728	−	0.0616571i
$797$	−11.1560	−	5.37243i	−0.395165	−	0.190301i	0.225739	−	0.974188i	$-0.427520\pi$
$797$	−11.1560	−	5.37243i	−0.395165	−	0.190301i	−0.620904	+	0.783886i	$0.713234\pi$
$798$	97.2960	−	46.8553i	3.44424	−	1.65866i
$799$	−1.91783	+	8.40255i	−0.0678479	+	0.297261i
$800$	33.2718	−	41.7216i	1.17634	−	1.47508i
$801$	−43.3796	+	54.3963i	−1.53274	+	1.92200i
$802$	−19.0837	+	9.19023i	−0.673869	+	0.324518i
$803$	6.16788	+	27.0232i	0.217660	+	0.953629i
$804$	44.2755	+	55.5197i	1.56147	+	1.95803i
$805$	−2.54334	−	11.1431i	−0.0896408	−	0.392742i
$806$	−2.49384	−	1.20097i	−0.0878417	−	0.0423023i
$807$	−13.0402	+	16.3519i	−0.459037	+	0.575614i
$808$	−94.8427	−	45.6739i	−3.33656	−	1.60680i
$809$	26.4100	+	33.1171i	0.928527	+	1.16434i	0.986126	+	0.165996i	$0.0530838\pi$
$809$	26.4100	+	33.1171i	0.928527	+	1.16434i	−0.0575998	+	0.998340i	$0.518345\pi$
$810$	146.907			5.16179
$811$	8.36297			0.293664			0.146832	−	0.989161i	$-0.453092\pi$
$811$	8.36297			0.293664			0.146832	+	0.989161i	$0.453092\pi$
$812$	−86.4312	−	108.381i	−3.03314	−	3.80344i
$813$	2.62546	−	1.26436i	0.0920790	−	0.0443429i
$814$	−16.2115	+	71.0274i	−0.568214	+	2.48951i
$815$	−15.1578	−	66.4107i	−0.530955	−	2.32627i
$816$	28.6432			1.00271
$817$	15.3810	−	23.8847i	0.538114	−	0.835620i
$818$	84.3561			2.94944
$819$	5.04927	+	22.1223i	0.176436	+	0.773015i
$820$	−31.4405	+	137.750i	−1.09795	+	4.81043i
$821$	−22.3477	+	10.7621i	−0.779940	+	0.375599i	−0.781105	−	0.624400i	$-0.785344\pi$
$821$	−22.3477	+	10.7621i	−0.779940	+	0.375599i	0.00116480	+	0.999999i	$0.499629\pi$
$822$	38.5455	+	48.3346i	1.34443	+	1.68586i
$823$	−34.4533			−1.20097			−0.600484	−	0.799637i	$-0.705025\pi$
$823$	−34.4533			−1.20097			−0.600484	+	0.799637i	$0.705025\pi$
$824$	−112.648			−3.92428
$825$	−61.9397	−	77.6700i	−2.15647	−	2.70412i
$826$	−35.9047	−	17.2908i	−1.24928	−	0.601624i
$827$	−15.2496	+	19.1223i	−0.530279	+	0.664949i	−0.972756	−	0.231831i	$-0.925528\pi$
$827$	−15.2496	+	19.1223i	−0.530279	+	0.664949i	0.442477	+	0.896780i	$0.354100\pi$
$828$	−33.5685	−	16.1658i	−1.16659	−	0.561799i
$829$	−9.17568	−	40.2013i	−0.318685	−	1.39625i	−0.839862	−	0.542800i	$-0.817364\pi$
$829$	−9.17568	−	40.2013i	−0.318685	−	1.39625i	0.521177	−	0.853448i	$-0.325493\pi$
$830$	−10.2017	−	12.7925i	−0.354105	−	0.444034i
$831$	−12.8050	−	56.1023i	−0.444200	−	1.94617i
$832$	6.01656	−	2.89742i	0.208587	−	0.100450i
$833$	1.45919	−	1.82976i	0.0505578	−	0.0633974i
$834$	−50.4687	+	63.2857i	−1.74759	+	2.19140i
$835$	0.740604	−	3.24480i	0.0256297	−	0.112291i
$836$	−103.512	+	49.8488i	−3.58004	+	1.72406i
$837$	10.6553	+	5.13132i	0.368301	+	0.177364i
$838$	−5.86679	+	25.7041i	−0.202665	+	0.887933i
$839$	−5.24235	+	22.9682i	−0.180986	+	0.792952i	0.800176	+	0.599765i	$0.204739\pi$
$839$	−5.24235	+	22.9682i	−0.180986	+	0.792952i	−0.981162	+	0.193186i	$0.938118\pi$
$840$	−202.520	−	97.5286i	−6.98761	−	3.36506i
$841$	−55.7178	+	26.8323i	−1.92131	+	0.925252i
$842$	−2.98596	+	13.0823i	−0.102903	+	0.450847i
$843$	13.9502	−	17.4930i	0.480469	−	0.602489i
$844$	−50.0693	+	62.7849i	−1.72346	+	2.16115i
$845$	34.8142	−	16.7657i	1.19765	−	0.576756i
$846$	−34.1149	−	149.467i	−1.17290	−	5.13879i
$847$	38.2102	+	47.9141i	1.31292	+	1.64635i
$848$	−8.44344	−	36.9931i	−0.289949	−	1.27035i
$849$	36.7927	+	17.7184i	1.26272	+	0.608094i
$850$	9.21122	−	11.5505i	0.315942	−	0.396179i
$851$	5.18425	+	2.49661i	0.177714	+	0.0855825i
$852$	29.5563	+	37.0625i	1.01258	+	1.26974i
$853$	−6.01443			−0.205930			−0.102965	−	0.994685i	$-0.532833\pi$
$853$	−6.01443			−0.205930			−0.102965	+	0.994685i	$0.532833\pi$
$854$	26.5493			0.908499
$855$	−60.4058	−	75.7464i	−2.06583	−	2.59047i
$856$	93.9230	−	45.2309i	3.21022	−	1.54596i
$857$	7.74345	−	33.9263i	0.264511	−	1.15890i	−0.651787	−	0.758402i	$-0.725980\pi$
$857$	7.74345	−	33.9263i	0.264511	−	1.15890i	0.916298	−	0.400497i	$-0.131163\pi$
$858$	−10.9746	−	48.0828i	−0.374666	−	1.64152i
$859$	−29.3745			−1.00224			−0.501122	−	0.865377i	$-0.667079\pi$
$859$	−29.3745			−1.00224			−0.501122	+	0.865377i	$0.667079\pi$
$860$	−101.477	+	10.2917i	−3.46033	+	0.350945i
$861$	87.0946			2.96817
$862$	−18.9513	−	83.0310i	−0.645483	−	2.82805i
$863$	10.3062	−	45.1544i	0.350827	−	1.53707i	−0.424449	−	0.905452i	$-0.639532\pi$
$863$	10.3062	−	45.1544i	0.350827	−	1.53707i	0.775276	−	0.631622i	$-0.217611\pi$
$864$	−101.984	+	49.1129i	−3.46957	+	1.67086i
$865$	5.34498	+	6.70240i	0.181735	+	0.227888i
$866$	5.45227			0.185276
$867$	3.13722			0.106546
$868$	−8.89737	−	11.1569i	−0.301996	−	0.378691i
$869$	−78.6023	−	37.8529i	−2.66640	−	1.28407i
$870$	−158.416	+	198.647i	−5.37079	+	6.73476i
$871$	4.65012	+	2.23938i	0.157563	+	0.0758785i
$872$	−6.92644	−	30.3467i	−0.234559	−	1.02767i
$873$	−37.7357	−	47.3190i	−1.27716	−	1.60151i
$874$	2.86776	+	12.5645i	0.0970034	+	0.424999i
$875$	−6.14313	+	2.95838i	−0.207676	+	0.100011i
$876$	46.3028	−	58.0618i	1.56443	−	1.96173i
$877$	−7.31978	+	9.17872i	−0.247171	+	0.309943i	−0.889904	−	0.456147i	$-0.849229\pi$
$877$	−7.31978	+	9.17872i	−0.247171	+	0.309943i	0.642733	+	0.766090i	$0.277800\pi$
$878$	10.1211	−	44.3435i	0.341571	−	1.49652i
$879$	55.4630	−	26.7096i	1.87072	−	0.900892i
$880$	149.821	+	72.1499i	5.05046	+	2.43217i
$881$	−5.16284	+	22.6199i	−0.173941	+	0.762083i	0.810410	+	0.585863i	$0.199244\pi$
$881$	−5.16284	+	22.6199i	−0.173941	+	0.762083i	−0.984351	+	0.176220i	$0.943613\pi$
$882$	−9.26375	+	40.5871i	−0.311927	+	1.36664i
$883$	−11.5851	−	5.57910i	−0.389871	−	0.187752i	0.228671	−	0.973504i	$-0.426562\pi$
$883$	−11.5851	−	5.57910i	−0.389871	−	0.187752i	−0.618542	+	0.785752i	$0.712276\pi$
$884$	4.65273	−	2.24064i	0.156488	−	0.0753608i
$885$	−11.4439	+	50.1389i	−0.384682	+	1.68540i
$886$	−16.8318	+	21.1064i	−0.565476	+	0.709084i
$887$	11.0572	−	13.8653i	0.371264	−	0.465551i	−0.560743	−	0.827990i	$-0.689484\pi$
$887$	11.0572	−	13.8653i	0.371264	−	0.465551i	0.932007	+	0.362439i	$0.118056\pi$
$888$	101.956	−	49.0993i	3.42141	−	1.64767i
$889$	−6.60957	−	28.9584i	−0.221678	−	0.971235i
$890$	−53.8731	−	67.5547i	−1.80583	−	2.26444i
$891$	21.4379	+	93.9256i	0.718197	+	3.14663i
$892$	31.1260	+	14.9895i	1.04218	+	0.501885i
$893$	−23.2801	+	29.1924i	−0.779040	+	0.976885i
$894$	128.067	+	61.6739i	4.28321	+	2.06268i
$895$	29.6488	+	37.1785i	0.991051	+	1.24274i
$896$	−8.50347			−0.284081
$897$	−3.89530			−0.130060
$898$	−32.5232	−	40.7828i	−1.08531	−	1.36094i
$899$	−8.42535	+	4.05744i	−0.281001	+	0.135323i
$900$	−41.1744	+	180.397i	−1.37248	+	6.01322i
$901$	−0.924791	−	4.05178i	−0.0308093	−	0.134984i
$902$	−131.599			−4.38178
$903$	20.1040	+	59.5717i	0.669018	+	1.98242i
$904$	93.3598			3.10510
$905$	−1.91758	−	8.40149i	−0.0637427	−	0.279275i
$906$	10.7339	−	47.0282i	0.356609	−	1.56241i
$907$	−12.4841	+	6.01201i	−0.414526	+	0.199625i	−0.629510	−	0.776992i	$-0.716744\pi$
$907$	−12.4841	+	6.01201i	−0.414526	+	0.199625i	0.214984	+	0.976618i	$0.431030\pi$
$908$	74.6308	+	93.5841i	2.47671	+	3.10570i
$909$	100.414			3.33052
$910$	−28.1802			−0.934163
$911$	8.52151	+	10.6856i	0.282330	+	0.354031i	0.902694	−	0.430283i	$-0.141586\pi$
$911$	8.52151	+	10.6856i	0.282330	+	0.354031i	−0.620364	+	0.784314i	$0.713015\pi$
$912$	111.802	+	53.8408i	3.70212	+	1.78285i
$913$	6.69022	−	8.38927i	0.221414	−	0.277644i
$914$	−67.0166	−	32.2735i	−2.21671	−	1.06751i
$915$	−7.62404	−	33.4031i	−0.252043	−	1.10427i
$916$	−33.3623	−	41.8350i	−1.10232	−	1.38227i
$917$	1.77234	+	7.76515i	0.0585280	+	0.256428i
$918$	−28.2340	+	13.5968i	−0.931861	+	0.448761i
$919$	−32.7050	+	41.0108i	−1.07884	+	1.35282i	−0.147335	+	0.989087i	$0.547070\pi$
$919$	−32.7050	+	41.0108i	−1.07884	+	1.35282i	−0.931503	+	0.363733i	$0.881502\pi$
$920$	16.7253	−	20.9729i	0.551417	−	0.691455i
$921$	−12.0324	+	52.7173i	−0.396481	+	1.73709i
$922$	70.6766	−	34.0360i	2.32761	−	1.12092i
$923$	3.10422	+	1.49491i	0.102177	+	0.0492056i
$924$	56.5799	−	247.893i	1.86134	−	8.15507i
$925$	6.35888	−	27.8601i	0.209079	−	0.916034i
$926$	−66.5192	−	32.0340i	−2.18596	−	1.05270i
$927$	96.8129	−	46.6226i	3.17975	−	1.53129i
$928$	19.9166	−	87.2604i	0.653795	−	2.86446i
$929$	24.0377	−	30.1424i	0.788652	−	0.988939i	−0.211281	−	0.977425i	$-0.567764\pi$
$929$	24.0377	−	30.1424i	0.788652	−	0.988939i	0.999934	−	0.0115136i	$-0.00366498\pi$
$930$	−16.3076	+	20.4490i	−0.534746	+	0.670550i
$931$	9.13499	−	4.39918i	0.299387	−	0.144177i
$932$	20.3799	+	89.2903i	0.667567	+	2.92480i
$933$	35.6223	+	44.6690i	1.16622	+	1.46240i
$934$	−6.43226	−	28.1816i	−0.210470	−	0.922130i
$935$	16.4095	+	7.90242i	0.536649	+	0.258437i
$936$	−33.2046	+	41.6373i	−1.08533	+	1.36096i
$937$	24.9094	+	11.9957i	0.813756	+	0.391884i	0.793998	−	0.607921i	$-0.207996\pi$
$937$	24.9094	+	11.9957i	0.813756	+	0.391884i	0.0197578	+	0.999805i	$0.493710\pi$
$938$	23.5627	+	29.5467i	0.769349	+	0.964733i
$939$	−44.4636			−1.45101
$940$	134.058			4.37249
$941$	26.6474	+	33.4148i	0.868681	+	1.08929i	0.995252	+	0.0973334i	$0.0310313\pi$
$941$	26.6474	+	33.4148i	0.868681	+	1.08929i	−0.126571	+	0.991958i	$0.540397\pi$
$942$	69.7986	−	33.6132i	2.27416	−	1.09518i
$943$	−2.31285	+	10.1333i	−0.0753169	+	0.329985i
$944$	−10.1898	−	44.6444i	−0.331650	−	1.45305i
$945$	120.404			3.91675
$946$	−30.3770	−	90.0125i	−0.987641	−	2.92656i
$947$	39.8483			1.29490			0.647449	−	0.762109i	$-0.275836\pi$
$947$	39.8483			1.29490			0.647449	+	0.762109i	$0.275836\pi$
$948$	52.0127	+	227.883i	1.68929	+	7.40128i
$949$	1.20107	−	5.26225i	0.0389885	−	0.170820i
$950$	57.6653	−	27.7701i	1.87091	−	0.900983i
$951$	52.5007	+	65.8337i	1.70245	+	2.13481i
$952$	21.9217			0.710488
$953$	−39.0426			−1.26471			−0.632356	−	0.774678i	$-0.717912\pi$
$953$	−39.0426			−1.26471			−0.632356	+	0.774678i	$0.717912\pi$
$954$	46.0932	+	57.7991i	1.49232	+	1.87131i
$955$	17.4694	+	8.41282i	0.565297	+	0.272232i
$956$	9.43680	−	11.8334i	0.305208	−	0.382719i
$957$	−150.123	−	72.2954i	−4.85279	−	2.33698i
$958$	−11.8232	−	51.8007i	−0.381990	−	1.67361i
$959$	14.4434	+	18.1114i	0.466401	+	0.584849i
$960$	−14.0414	−	61.5194i	−0.453184	−	1.98553i
$961$	27.0627	−	13.0327i	0.872991	−	0.420410i
$962$	8.84538	−	11.0918i	0.285186	−	0.357612i
$963$	−62.0000	+	77.7455i	−1.99792	+	2.50532i
$964$	13.1262	−	57.5097i	0.422767	−	1.85226i
$965$	11.8137	−	5.68918i	0.380297	−	0.183141i
$966$	−25.6975	−	12.3753i	−0.826804	−	0.398168i
$967$	−5.25078	+	23.0052i	−0.168854	+	0.739796i	0.817604	+	0.575781i	$0.195302\pi$
$967$	−5.25078	+	23.0052i	−0.168854	+	0.739796i	−0.986458	+	0.164015i	$0.947555\pi$
$968$	−32.0061	+	140.228i	−1.02872	+	4.50710i
$969$	12.2454	+	5.89706i	0.393378	+	0.189441i
$970$	67.7202	−	32.6124i	2.17437	−	1.04712i
$971$	7.48816	−	32.8078i	0.240307	−	1.05285i	−0.700432	−	0.713719i	$-0.747009\pi$
$971$	7.48816	−	32.8078i	0.240307	−	1.05285i	0.940739	−	0.339133i	$-0.110134\pi$
$972$	53.6391	−	67.2613i	1.72048	−	2.15741i
$973$	−18.9111	+	23.7138i	−0.606262	+	0.760228i
$974$	−27.1988	+	13.0982i	−0.871505	+	0.419695i
$975$	4.30472	+	18.8602i	0.137861	+	0.604010i
$976$	19.0211	+	23.8517i	0.608851	+	0.763474i
$977$	−4.38539	−	19.2136i	−0.140301	−	0.614699i	−0.995364	−	0.0961755i	$-0.969339\pi$
$977$	−4.38539	−	19.2136i	−0.140301	−	0.614699i	0.855063	−	0.518524i	$-0.173518\pi$
$978$	−153.152	−	73.7543i	−4.89728	−	2.35840i
$979$	35.3297	−	44.3021i	1.12914	−	1.41590i
$980$	−32.7978	−	15.7946i	−1.04769	−	0.504540i
$981$	18.5126	+	23.2141i	0.591063	+	0.741170i
$982$	−14.5445			−0.464134
$983$	−29.1108			−0.928490			−0.464245	−	0.885707i	$-0.653674\pi$
$983$	−29.1108			−0.928490			−0.464245	+	0.885707i	$0.653674\pi$
$984$	127.448	+	159.814i	4.06289	+	5.09470i
$985$	−19.1769	+	9.23512i	−0.611028	+	0.294255i
$986$	5.51386	−	24.1578i	0.175597	−	0.769341i
$987$	−18.3881	−	80.5635i	−0.585299	−	2.56436i
$988$	22.3725			0.711766
$989$	−7.46492	+	0.757090i	−0.237371	+	0.0240741i
$990$	−323.983			−10.2968
$991$	−2.85215	−	12.4961i	−0.0906016	−	0.396952i	0.909210	−	0.416337i	$-0.136686\pi$
$991$	−2.85215	−	12.4961i	−0.0906016	−	0.396952i	−0.999812	+	0.0193852i	$0.993829\pi$
$992$	2.05025	−	8.98273i	0.0650955	−	0.285202i
$993$	−16.7324	+	8.05790i	−0.530987	+	0.255710i
$994$	15.7294	+	19.7240i	0.498906	+	0.625609i
$995$	−1.22543			−0.0388488
$996$	−28.7491			−0.910950
$997$	−6.15592	−	7.71928i	−0.194960	−	0.244472i	0.674737	−	0.738058i	$-0.264257\pi$
$997$	−6.15592	−	7.71928i	−0.194960	−	0.244472i	−0.869697	+	0.493586i	$0.835686\pi$
$998$	53.7207	+	25.8705i	1.70050	+	0.818917i
$999$	−37.7932	+	47.3912i	−1.19573	+	1.49939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.k.a.188.2	yes	180
43.35	even	7	inner	731.2.k.a.35.2	✓	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.k.a.35.2	✓	180	43.35	even	7	inner
731.2.k.a.188.2	yes	180	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.578512 - 2.53463i) q^{2} +(-0.698098 + 3.05857i) q^{3} +(-4.28771 + 2.06485i) q^{4} +(2.03783 + 2.55536i) q^{5} +8.15618 q^{6} +3.05620 q^{7} +(4.47222 + 5.60798i) q^{8} +(-6.16458 - 2.96870i) q^{9} +O(q^{10})\)	\(q+(-0.578512 - 2.53463i) q^{2} +(-0.698098 + 3.05857i) q^{3} +(-4.28771 + 2.06485i) q^{4} +(2.03783 + 2.55536i) q^{5} +8.15618 q^{6} +3.05620 q^{7} +(4.47222 + 5.60798i) q^{8} +(-6.16458 - 2.96870i) q^{9} +(5.29796 - 6.64344i) q^{10} +(5.02063 + 2.41781i) q^{11} +(-3.32225 - 14.5557i) q^{12} +(-0.676568 - 0.848390i) q^{13} +(-1.76805 - 7.74632i) q^{14} +(-9.23833 + 4.44894i) q^{15} +(5.69253 - 7.13820i) q^{16} +(0.623490 - 0.781831i) q^{17} +(-3.95827 + 17.3423i) q^{18} +(3.90325 - 1.87971i) q^{19} +(-14.0141 - 6.74882i) q^{20} +(-2.13353 + 9.34759i) q^{21} +(3.22374 - 14.1241i) q^{22} +(-1.03092 - 0.496463i) q^{23} +(-20.2744 + 9.76365i) q^{24} +(-1.26450 + 5.54012i) q^{25} +(-1.75895 + 2.20565i) q^{26} +(7.51538 - 9.42398i) q^{27} +(-13.1041 + 6.31060i) q^{28} +(2.12087 + 9.29215i) q^{29} +(16.6209 + 20.8419i) q^{30} +(0.218326 + 0.956549i) q^{31} +(-8.46079 - 4.07450i) q^{32} +(-10.8999 + 13.6681i) q^{33} +(-2.34235 - 1.12801i) q^{34} +(6.22801 + 7.80968i) q^{35} +32.5619 q^{36} -5.02879 q^{37} +(-7.02244 - 8.80586i) q^{38} +(3.06717 - 1.47707i) q^{39} +(-5.21678 + 22.8562i) q^{40} +(-2.02132 - 8.85598i) q^{41} +24.9269 q^{42} +(5.59081 - 3.42678i) q^{43} -26.5194 q^{44} +(-4.97626 - 21.8024i) q^{45} +(-0.661950 + 2.90019i) q^{46} +(-7.76513 + 3.73949i) q^{47} +(17.8587 + 22.3941i) q^{48} +2.34035 q^{49} +14.7736 q^{50} +(1.95603 + 2.45278i) q^{51} +(4.65273 + 2.24064i) q^{52} +(2.59121 - 3.24927i) q^{53} +(-28.2340 - 13.5968i) q^{54} +(4.05282 + 17.7566i) q^{55} +(13.6680 + 17.1391i) q^{56} +(3.02436 + 13.2506i) q^{57} +(22.3252 - 10.7512i) q^{58} +(3.12715 - 3.92132i) q^{59} +(30.4249 - 38.1516i) q^{60} +(-0.743535 + 3.25764i) q^{61} +(2.29819 - 1.10675i) q^{62} +(-18.8402 - 9.07295i) q^{63} +(-1.36939 + 5.99968i) q^{64} +(0.789208 - 3.45775i) q^{65} +(40.9491 + 19.7201i) q^{66} +(-4.28531 + 2.06370i) q^{67} +(-1.05898 + 4.63969i) q^{68} +(2.23814 - 2.80654i) q^{69} +(16.1916 - 20.3037i) q^{70} +(-2.86068 + 1.37763i) q^{71} +(-10.9209 - 47.8475i) q^{72} +(3.10131 + 3.88892i) q^{73} +(2.90921 + 12.7461i) q^{74} +(-16.0621 - 7.73508i) q^{75} +(-12.8547 + 16.1193i) q^{76} +(15.3440 + 7.38930i) q^{77} +(-5.51821 - 6.91962i) q^{78} -15.6559 q^{79} +29.8410 q^{80} +(10.7793 + 13.5169i) q^{81} +(-21.2772 + 10.2466i) q^{82} +(0.428483 - 1.87731i) q^{83} +(-10.1535 - 44.4852i) q^{84} +3.26842 q^{85} +(-11.9200 - 12.1882i) q^{86} -29.9012 q^{87} +(8.89432 + 38.9686i) q^{88} +(2.26273 - 9.91369i) q^{89} +(-52.3821 + 25.2259i) q^{90} +(-2.06773 - 2.59285i) q^{91} +5.44539 q^{92} -3.07808 q^{93} +(13.9704 + 17.5184i) q^{94} +(12.7575 + 6.14368i) q^{95} +(18.3686 - 23.0335i) q^{96} +(7.96964 + 3.83798i) q^{97} +(-1.35392 - 5.93191i) q^{98} +(-23.7723 - 29.8095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9}+O(q^{10}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9	\( 180 q - 4 q^{2} - 6 q^{3} - 34 q^{4} - 6 q^{5} - 14 q^{6} + 66 q^{7} + 2 q^{8} - 26 q^{9} - 8 q^{10} - 12 q^{11} - 24 q^{12} - 5 q^{13} - 8 q^{14} - q^{15} - 58 q^{16} - 30 q^{17} + 36 q^{18} - 24 q^{19} - 36 q^{20} - 28 q^{21} + 5 q^{22} + 27 q^{23} - 46 q^{24} - 38 q^{25} + 6 q^{26} - 36 q^{27} - 54 q^{28} + 28 q^{29} - 21 q^{30} + 36 q^{31} + 11 q^{32} + 5 q^{33} - 4 q^{34} + 6 q^{35} + 192 q^{36} + 164 q^{37} + 32 q^{38} - 34 q^{39} + 2 q^{40} + 42 q^{41} - 2 q^{42} - 22 q^{43} + 14 q^{44} + 58 q^{45} - 53 q^{46} + 21 q^{47} - 20 q^{48} + 166 q^{49} + 18 q^{50} - 6 q^{51} + 54 q^{52} + 8 q^{53} - 154 q^{54} - 5 q^{55} - 35 q^{56} + 8 q^{57} + 9 q^{58} - 13 q^{59} - 88 q^{60} - 34 q^{61} - 36 q^{62} - 31 q^{63} - 18 q^{64} + 9 q^{65} + 222 q^{66} - 48 q^{67} - 27 q^{68} + 2 q^{69} - 64 q^{70} - 42 q^{71} + 77 q^{72} - 44 q^{73} - 35 q^{74} - 21 q^{75} + 44 q^{76} - 32 q^{77} + 124 q^{78} - 96 q^{79} + 490 q^{80} - 12 q^{81} - 130 q^{82} - 8 q^{83} + 170 q^{84} + 22 q^{85} - 12 q^{86} - 90 q^{87} - 122 q^{88} - 81 q^{89} + 49 q^{90} - 27 q^{91} - 116 q^{92} + 18 q^{93} - 124 q^{94} + 117 q^{95} + 52 q^{96} - 79 q^{97} - 54 q^{98} - 39 q^{99}+O(q^{100}) \) 180 * q - 4 * q^2 - 6 * q^3 - 34 * q^4 - 6 * q^5 - 14 * q^6 + 66 * q^7 + 2 * q^8 - 26 * q^9 - 8 * q^10 - 12 * q^11 - 24 * q^12 - 5 * q^13 - 8 * q^14 - q^15 - 58 * q^16 - 30 * q^17 + 36 * q^18 - 24 * q^19 - 36 * q^20 - 28 * q^21 + 5 * q^22 + 27 * q^23 - 46 * q^24 - 38 * q^25 + 6 * q^26 - 36 * q^27 - 54 * q^28 + 28 * q^29 - 21 * q^30 + 36 * q^31 + 11 * q^32 + 5 * q^33 - 4 * q^34 + 6 * q^35 + 192 * q^36 + 164 * q^37 + 32 * q^38 - 34 * q^39 + 2 * q^40 + 42 * q^41 - 2 * q^42 - 22 * q^43 + 14 * q^44 + 58 * q^45 - 53 * q^46 + 21 * q^47 - 20 * q^48 + 166 * q^49 + 18 * q^50 - 6 * q^51 + 54 * q^52 + 8 * q^53 - 154 * q^54 - 5 * q^55 - 35 * q^56 + 8 * q^57 + 9 * q^58 - 13 * q^59 - 88 * q^60 - 34 * q^61 - 36 * q^62 - 31 * q^63 - 18 * q^64 + 9 * q^65 + 222 * q^66 - 48 * q^67 - 27 * q^68 + 2 * q^69 - 64 * q^70 - 42 * q^71 + 77 * q^72 - 44 * q^73 - 35 * q^74 - 21 * q^75 + 44 * q^76 - 32 * q^77 + 124 * q^78 - 96 * q^79 + 490 * q^80 - 12 * q^81 - 130 * q^82 - 8 * q^83 + 170 * q^84 + 22 * q^85 - 12 * q^86 - 90 * q^87 - 122 * q^88 - 81 * q^89 + 49 * q^90 - 27 * q^91 - 116 * q^92 + 18 * q^93 - 124 * q^94 + 117 * q^95 + 52 * q^96 - 79 * q^97 - 54 * q^98 - 39 * q^99

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