LMFDB - Embedded newform 71.2.c.a.54.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(5,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("71.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.c (of order $5$, degree $4$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 28 x^{18} - 91 x^{17} + 268 x^{16} - 604 x^{15} + 1278 x^{14} - 1990 x^{13} + \cdots + 961 $ x^20 - 6x^19 + 28x^18 - 91x^17 + 268x^16 - 604x^15 + 1278x^14 - 1990x^13 + 3162x^12 - 4046x^11 + 6406x^10 - 8426x^9 + 12709x^8 - 13621x^7 + 17787x^6 - 13514x^5 + 9316x^4 - 1639x^3 - 228x^2 + 620*x + 961
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			54.1
Root			$2.18637 - 1.58849i$ of defining polynomial
Character	$\chi$	$=$	71.54
Dual form			71.2.c.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18637 - 1.58849i) q^{2} +(1.68338 + 1.22305i) q^{3} +(1.63889 + 5.04397i) q^{4} +(-0.994748 + 3.06152i) q^{5} +(-1.73770 - 5.34809i) q^{6} +(0.649950 + 0.472216i) q^{7} +(2.75886 - 8.49090i) q^{8} +(0.410878 + 1.26455i) q^{9} +O(q^{10})$	\(q+(-2.18637 - 1.58849i) q^{2} +(1.68338 + 1.22305i) q^{3} +(1.63889 + 5.04397i) q^{4} +(-0.994748 + 3.06152i) q^{5} +(-1.73770 - 5.34809i) q^{6} +(0.649950 + 0.472216i) q^{7} +(2.75886 - 8.49090i) q^{8} +(0.410878 + 1.26455i) q^{9} +(7.03810 - 5.11348i) q^{10} +(-1.76133 - 1.27968i) q^{11} +(-3.41015 + 10.4954i) q^{12} +(2.15960 - 1.56904i) q^{13} +(-0.670921 - 2.06488i) q^{14} +(-5.41893 + 3.93708i) q^{15} +(-10.9383 + 7.94715i) q^{16} +(1.63604 - 1.18865i) q^{17} +(1.11040 - 3.41746i) q^{18} +(-1.21303 - 0.881318i) q^{19} -17.0725 q^{20} +(0.516571 + 1.58984i) q^{21} +(1.81817 + 5.59574i) q^{22} +6.57862 q^{23} +(15.0290 - 10.9192i) q^{24} +(-4.33829 - 3.15195i) q^{25} -7.21412 q^{26} +(1.07404 - 3.30556i) q^{27} +(-1.31665 + 4.05224i) q^{28} +(-0.0382390 + 0.117688i) q^{29} +18.1018 q^{30} +(-0.464146 - 0.337222i) q^{31} +18.6835 q^{32} +(-1.39988 - 4.30840i) q^{33} -5.46515 q^{34} +(-2.09224 + 1.52010i) q^{35} +(-5.70498 + 4.14491i) q^{36} -5.83276 q^{37} +(1.25217 + 3.85378i) q^{38} +5.55446 q^{39} +(23.2507 + 16.8926i) q^{40} -8.59265 q^{41} +(1.39604 - 4.29656i) q^{42} +(0.557801 - 1.71674i) q^{43} +(3.56807 - 10.9814i) q^{44} -4.28017 q^{45} +(-14.3833 - 10.4501i) q^{46} +(8.39092 - 6.09636i) q^{47} -28.1331 q^{48} +(-1.96367 - 6.04356i) q^{49} +(4.47827 + 13.7827i) q^{50} +4.20785 q^{51} +(11.4536 + 8.32150i) q^{52} +(-4.03060 + 12.4049i) q^{53} +(-7.59912 + 5.52108i) q^{54} +(5.66986 - 4.11940i) q^{55} +(5.80266 - 4.21588i) q^{56} +(-0.964099 - 2.96719i) q^{57} +(0.270551 - 0.196567i) q^{58} +(-3.69817 + 11.3818i) q^{59} +(-28.7395 - 20.8805i) q^{60} +(1.35028 - 0.981037i) q^{61} +(0.479122 + 1.47459i) q^{62} +(-0.330092 + 1.01592i) q^{63} +(-18.9726 - 13.7844i) q^{64} +(2.65540 + 8.17247i) q^{65} +(-3.78320 + 11.6435i) q^{66} +(-0.173932 - 0.535308i) q^{67} +(8.67679 + 6.30406i) q^{68} +(11.0743 + 8.04597i) q^{69} +6.98908 q^{70} +(5.71386 - 6.19289i) q^{71} +11.8707 q^{72} +(-1.21771 - 0.884720i) q^{73} +(12.7526 + 9.26530i) q^{74} +(-3.44801 - 10.6119i) q^{75} +(2.45733 - 7.56287i) q^{76} +(-0.540492 - 1.66346i) q^{77} +(-12.1441 - 8.82323i) q^{78} +(-2.21557 + 6.81882i) q^{79} +(-13.4495 - 41.3933i) q^{80} +(9.07796 - 6.59552i) q^{81} +(18.7867 + 13.6494i) q^{82} +(3.61892 - 11.1379i) q^{83} +(-7.17252 + 5.21114i) q^{84} +(2.01163 + 6.19116i) q^{85} +(-3.94659 + 2.86736i) q^{86} +(-0.208309 + 0.151345i) q^{87} +(-15.7249 + 11.4248i) q^{88} +(1.52477 - 4.69276i) q^{89} +(9.35805 + 6.79902i) q^{90} +2.14456 q^{91} +(10.7816 + 33.1824i) q^{92} +(-0.368897 - 1.13535i) q^{93} -28.0297 q^{94} +(3.90483 - 2.83703i) q^{95} +(31.4516 + 22.8509i) q^{96} -12.6976 q^{97} +(-5.30684 + 16.3328i) q^{98} +(0.894534 - 2.75309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−2.18637	−	1.58849i	−1.54600	−	1.12323i	−0.946428	−	0.322914i	$-0.895338\pi$
$2$	−2.18637	−	1.58849i	−1.54600	−	1.12323i	−0.599572	−	0.800321i	$-0.704662\pi$
$3$	1.68338	+	1.22305i	0.971902	+	0.706128i	0.955884	−	0.293744i	$-0.0949013\pi$
$3$	1.68338	+	1.22305i	0.971902	+	0.706128i	0.0160174	+	0.999872i	$0.494901\pi$
$4$	1.63889	+	5.04397i	0.819443	+	2.52199i
$5$	−0.994748	+	3.06152i	−0.444865	+	1.36915i	0.437767	+	0.899088i	$0.355769\pi$
$5$	−0.994748	+	3.06152i	−0.444865	+	1.36915i	−0.882632	+	0.470065i	$0.844231\pi$
$6$	−1.73770	−	5.34809i	−0.709413	−	2.18335i
$7$	0.649950	+	0.472216i	0.245658	+	0.178481i	0.703800	−	0.710398i	$-0.251485\pi$
$7$	0.649950	+	0.472216i	0.245658	+	0.178481i	−0.458142	+	0.888879i	$0.651485\pi$
$8$	2.75886	−	8.49090i	0.975404	−	3.00198i
$9$	0.410878	+	1.26455i	0.136959	+	0.421517i
$10$	7.03810	−	5.11348i	2.22564	−	1.61702i
$11$	−1.76133	−	1.27968i	−0.531062	−	0.385839i	0.289693	−	0.957120i	$-0.406447\pi$
$11$	−1.76133	−	1.27968i	−0.531062	−	0.385839i	−0.820755	+	0.571280i	$0.806447\pi$
$12$	−3.41015	+	10.4954i	−0.984427	+	3.02975i
$13$	2.15960	−	1.56904i	0.598966	−	0.435175i	−0.246545	−	0.969131i	$-0.579295\pi$
$13$	2.15960	−	1.56904i	0.598966	−	0.435175i	0.845512	+	0.533957i	$0.179295\pi$
$14$	−0.670921	−	2.06488i	−0.179311	−	0.551863i
$15$	−5.41893	+	3.93708i	−1.39916	+	1.01655i
$16$	−10.9383	+	7.94715i	−2.73458	+	1.98679i
$17$	1.63604	−	1.18865i	0.396797	−	0.288290i	−0.371438	−	0.928458i	$-0.621135\pi$
$17$	1.63604	−	1.18865i	0.396797	−	0.288290i	0.768235	+	0.640168i	$0.221135\pi$
$18$	1.11040	−	3.41746i	0.261724	−	0.805503i
$19$	−1.21303	−	0.881318i	−0.278288	−	0.202188i	0.439882	−	0.898055i	$-0.355020\pi$
$19$	−1.21303	−	0.881318i	−0.278288	−	0.202188i	−0.718170	+	0.695867i	$0.755020\pi$
$20$	−17.0725			−3.81753
$21$	0.516571	+	1.58984i	0.112725	+	0.346932i
$22$	1.81817	+	5.59574i	0.387634	+	1.19302i
$23$	6.57862			1.37174			0.685868	−	0.727726i	$-0.259423\pi$
$23$	6.57862			1.37174			0.685868	+	0.727726i	$0.259423\pi$
$24$	15.0290	−	10.9192i	3.06778	−	2.22887i
$25$	−4.33829	−	3.15195i	−0.867659	−	0.630391i
$26$	−7.21412			−1.41481
$27$	1.07404	−	3.30556i	0.206699	−	0.636155i
$28$	−1.31665	+	4.05224i	−0.248824	+	0.765801i
$29$	−0.0382390	+	0.117688i	−0.00710080	+	0.0218540i	−0.954544	−	0.298070i	$-0.903657\pi$
$29$	−0.0382390	+	0.117688i	−0.00710080	+	0.0218540i	0.947443	+	0.319924i	$0.103657\pi$
$30$	18.1018			3.30493
$31$	−0.464146	−	0.337222i	−0.0833631	−	0.0605668i	0.545323	−	0.838226i	$-0.316407\pi$
$31$	−0.464146	−	0.337222i	−0.0833631	−	0.0605668i	−0.628686	+	0.777659i	$0.716407\pi$
$32$	18.6835			3.30282
$33$	−1.39988	−	4.30840i	−0.243688	−	0.749996i
$34$	−5.46515			−0.937265
$35$	−2.09224	+	1.52010i	−0.353652	+	0.256944i
$36$	−5.70498	+	4.14491i	−0.950830	+	0.690818i
$37$	−5.83276			−0.958899			−0.479450	−	0.877569i	$-0.659164\pi$
$37$	−5.83276			−0.958899			−0.479450	+	0.877569i	$0.659164\pi$
$38$	1.25217	+	3.85378i	0.203129	+	0.625166i
$39$	5.55446			0.889425
$40$	23.2507	+	16.8926i	3.67625	+	2.67096i
$41$	−8.59265			−1.34195			−0.670973	−	0.741482i	$-0.734123\pi$
$41$	−8.59265			−1.34195			−0.670973	+	0.741482i	$0.734123\pi$
$42$	1.39604	−	4.29656i	0.215413	−	0.662974i
$43$	0.557801	−	1.71674i	0.0850639	−	0.261800i	−0.899473	−	0.436976i	$-0.856049\pi$
$43$	0.557801	−	1.71674i	0.0850639	−	0.261800i	0.984537	+	0.175176i	$0.0560495\pi$
$44$	3.56807	−	10.9814i	0.537906	−	1.65551i
$45$	−4.28017			−0.638050
$46$	−14.3833	−	10.4501i	−2.12071	−	1.54078i
$47$	8.39092	−	6.09636i	1.22394	−	0.889246i	0.227521	−	0.973773i	$-0.426938\pi$
$47$	8.39092	−	6.09636i	1.22394	−	0.889246i	0.996421	+	0.0845275i	$0.0269381\pi$
$48$	−28.1331			−4.06067
$49$	−1.96367	−	6.04356i	−0.280525	−	0.863366i
$50$	4.47827	+	13.7827i	0.633323	+	1.94917i
$51$	4.20785			0.589217
$52$	11.4536	+	8.32150i	1.58832	+	1.15398i
$53$	−4.03060	+	12.4049i	−0.553646	+	1.70395i	0.145847	+	0.989307i	$0.453409\pi$
$53$	−4.03060	+	12.4049i	−0.553646	+	1.70395i	−0.699493	+	0.714639i	$0.746591\pi$
$54$	−7.59912	+	5.52108i	−1.03411	+	0.751324i
$55$	5.66986	−	4.11940i	0.764524	−	0.555459i
$56$	5.80266	−	4.21588i	0.775413	−	0.563371i
$57$	−0.964099	−	2.96719i	−0.127698	−	0.393014i
$58$	0.270551	−	0.196567i	0.0355250	−	0.0258105i
$59$	−3.69817	+	11.3818i	−0.481460	+	1.48178i	0.355582	+	0.934645i	$0.384283\pi$
$59$	−3.69817	+	11.3818i	−0.481460	+	1.48178i	−0.837043	+	0.547138i	$0.815717\pi$
$60$	−28.7395	−	20.8805i	−3.71026	−	2.69566i
$61$	1.35028	−	0.981037i	0.172886	−	0.125609i	−0.497977	−	0.867190i	$-0.665924\pi$
$61$	1.35028	−	0.981037i	0.172886	−	0.125609i	0.670863	+	0.741581i	$0.265924\pi$
$62$	0.479122	+	1.47459i	0.0608486	+	0.187273i
$63$	−0.330092	+	1.01592i	−0.0415877	+	0.127994i
$64$	−18.9726	−	13.7844i	−2.37157	−	1.72305i
$65$	2.65540	+	8.17247i	0.329362	+	1.01367i
$66$	−3.78320	+	11.6435i	−0.465679	+	1.43321i
$67$	−0.173932	−	0.535308i	−0.0212492	−	0.0653982i	0.939870	−	0.341533i	$-0.110946\pi$
$67$	−0.173932	−	0.535308i	−0.0212492	−	0.0653982i	−0.961119	+	0.276135i	$0.910946\pi$
$68$	8.67679	+	6.30406i	1.05222	+	0.764479i
$69$	11.0743	+	8.04597i	1.33319	+	0.968621i
$70$	6.98908			0.835355
$71$	5.71386	−	6.19289i	0.678110	−	0.734960i
$71$	5.71386	−	6.19289i	0.678110	−	0.734960i
$72$	11.8707			1.39898
$73$	−1.21771	−	0.884720i	−0.142523	−	0.103549i	0.514239	−	0.857647i	$-0.328074\pi$
$73$	−1.21771	−	0.884720i	−0.142523	−	0.103549i	−0.656762	+	0.754098i	$0.728074\pi$
$74$	12.7526	+	9.26530i	1.48246	+	1.07707i
$75$	−3.44801	−	10.6119i	−0.398142	−	1.22536i
$76$	2.45733	−	7.56287i	0.281875	−	0.867521i
$77$	−0.540492	−	1.66346i	−0.0615947	−	0.189569i
$78$	−12.1441	−	8.82323i	−1.37505	−	0.999034i
$79$	−2.21557	+	6.81882i	−0.249271	+	0.767178i	0.745633	+	0.666356i	$0.232147\pi$
$79$	−2.21557	+	6.81882i	−0.249271	+	0.767178i	−0.994905	+	0.100821i	$0.967853\pi$
$80$	−13.4495	−	41.3933i	−1.50370	−	4.62791i
$81$	9.07796	−	6.59552i	1.00866	−	0.732836i
$82$	18.7867	+	13.6494i	2.07465	+	1.50732i
$83$	3.61892	−	11.1379i	0.397228	−	1.22254i	−0.529985	−	0.848007i	$-0.677803\pi$
$83$	3.61892	−	11.1379i	0.397228	−	1.22254i	0.927213	−	0.374534i	$-0.122197\pi$
$84$	−7.17252	+	5.21114i	−0.782586	+	0.568582i
$85$	2.01163	+	6.19116i	0.218192	+	0.671526i
$86$	−3.94659	+	2.86736i	−0.425571	+	0.309196i
$87$	−0.208309	+	0.151345i	−0.0223330	+	0.0162259i
$88$	−15.7249	+	11.4248i	−1.67628	+	1.21789i
$89$	1.52477	−	4.69276i	0.161625	−	0.497432i	−0.837146	−	0.546979i	$-0.815778\pi$
$89$	1.52477	−	4.69276i	0.161625	−	0.497432i	0.998772	+	0.0495471i	$0.0157778\pi$
$90$	9.35805	+	6.79902i	0.986425	+	0.716680i
$91$	2.14456			0.224811
$92$	10.7816	+	33.1824i	1.12406	+	3.45950i
$93$	−0.368897	−	1.13535i	−0.0382528	−	0.117730i
$94$	−28.0297			−2.89105
$95$	3.90483	−	2.83703i	0.400627	−	0.291073i
$96$	31.4516	+	22.8509i	3.21001	+	2.33221i
$97$	−12.6976			−1.28925			−0.644625	−	0.764499i	$-0.722986\pi$
$97$	−12.6976			−1.28925			−0.644625	+	0.764499i	$0.722986\pi$
$98$	−5.30684	+	16.3328i	−0.536072	+	1.64986i
$99$	0.894534	−	2.75309i	0.0899040	−	0.276696i
$100$	8.78840	−	27.0479i	0.878840	−	2.70479i
$101$	−17.0916			−1.70068			−0.850340	−	0.526234i	$-0.823604\pi$
$101$	−17.0916			−1.70068			−0.850340	+	0.526234i	$0.823604\pi$
$102$	−9.19994	−	6.68415i	−0.910930	−	0.661829i
$103$	3.78232			0.372683			0.186342	−	0.982485i	$-0.440337\pi$
$103$	3.78232			0.372683			0.186342	+	0.982485i	$0.440337\pi$
$104$	−7.36455	−	22.6657i	−0.722153	−	2.22256i
$105$	−5.38119			−0.525150
$106$	28.5175	−	20.7192i	2.76987	−	2.01243i
$107$	−3.21296	+	2.33435i	−0.310609	+	0.225670i	−0.732158	−	0.681135i	$-0.761487\pi$
$107$	−3.21296	+	2.33435i	−0.310609	+	0.225670i	0.421549	+	0.906806i	$0.361487\pi$
$108$	18.4334			1.77375
$109$	2.73849	+	8.42822i	0.262300	+	0.807277i	0.992303	+	0.123833i	$0.0395187\pi$
$109$	2.73849	+	8.42822i	0.262300	+	0.807277i	−0.730003	+	0.683444i	$0.760481\pi$
$110$	−18.9401			−1.80587
$111$	−9.81876	−	7.13375i	−0.931956	−	0.677105i
$112$	−10.8621			−1.02638
$113$	−4.98009	+	15.3271i	−0.468487	+	1.44186i	0.386056	+	0.922475i	$0.373837\pi$
$113$	−4.98009	+	15.3271i	−0.468487	+	1.44186i	−0.854543	+	0.519380i	$0.826163\pi$
$114$	−2.60548	+	8.01886i	−0.244026	+	0.751035i
$115$	−6.54407	+	20.1406i	−0.610237	+	1.87812i
$116$	−0.656282			−0.0609342
$117$	2.87147	+	2.08624i	0.265467	+	0.192873i
$118$	26.1655	−	19.0103i	2.40873	−	1.75004i
$119$	1.62464			0.148931
$120$	18.4793	+	56.8734i	1.68692	+	5.19181i
$121$	−1.93448	−	5.95371i	−0.175862	−	0.541247i
$122$	−4.51059			−0.408370
$123$	−14.4647	−	10.5092i	−1.30424	−	0.947586i
$124$	0.940255	−	2.89381i	0.0844374	−	0.259872i
$125$	0.943860	−	0.685755i	0.0844214	−	0.0613358i
$126$	2.33548	−	1.69683i	0.208061	−	0.151166i
$127$	8.08780	−	5.87613i	0.717676	−	0.521422i	−0.167965	−	0.985793i	$-0.553720\pi$
$127$	8.08780	−	5.87613i	0.717676	−	0.521422i	0.885641	+	0.464371i	$0.153720\pi$
$128$	8.03770	+	24.7375i	0.710439	+	2.18651i
$129$	3.03865	−	2.20771i	0.267538	−	0.194378i
$130$	7.17623	−	22.0862i	0.629397	−	1.93709i
$131$	1.33155	+	0.967427i	0.116338	+	0.0845245i	0.644433	−	0.764661i	$-0.277093\pi$
$131$	1.33155	+	0.967427i	0.116338	+	0.0845245i	−0.528095	+	0.849185i	$0.677093\pi$
$132$	19.4372	−	14.1219i	1.69179	−	1.22916i
$133$	−0.372236	−	1.14563i	−0.0322770	−	0.0993383i
$134$	−0.470052	+	1.44667i	−0.0406063	+	0.124973i
$135$	9.05163	+	6.57640i	0.779040	+	0.566006i
$136$	−5.57911	−	17.1707i	−0.478404	−	1.47238i
$137$	4.06552	−	12.5124i	0.347341	−	1.06901i	−0.612978	−	0.790100i	$-0.710028\pi$
$137$	4.06552	−	12.5124i	0.347341	−	1.06901i	0.960319	−	0.278905i	$-0.0899716\pi$
$138$	−11.4317	−	35.1830i	−0.973127	−	2.99498i
$139$	−3.43840	−	2.49814i	−0.291641	−	0.211890i	0.432338	−	0.901712i	$-0.357689\pi$
$139$	−3.43840	−	2.49814i	−0.291641	−	0.211890i	−0.723979	+	0.689822i	$0.757689\pi$
$140$	−11.0963	−	8.06191i	−0.937806	−	0.681356i
$141$	21.5813			1.81747
$142$	−22.3300	+	4.46354i	−1.87389	+	0.374572i
$143$	−5.81167			−0.485996
$144$	−14.5439	−	10.5668i	−1.21199	−	0.880563i
$145$	−0.322265	−	0.234139i	−0.0267626	−	0.0194442i
$146$	1.25700	+	3.86866i	0.104030	+	0.320173i
$147$	4.08596	−	12.5753i	0.337004	−	1.03719i
$148$	−9.55922	−	29.4203i	−0.785763	−	2.41833i
$149$	8.28637	+	6.02040i	0.678846	+	0.493210i	0.872975	−	0.487766i	$-0.162188\pi$
$149$	8.28637	+	6.02040i	0.678846	+	0.493210i	−0.194129	+	0.980976i	$0.562188\pi$
$150$	−9.31828	+	28.6787i	−0.760835	+	2.34161i
$151$	6.67915	+	20.5563i	0.543542	+	1.67285i	0.724432	+	0.689347i	$0.242102\pi$
$151$	6.67915	+	20.5563i	0.543542	+	1.67285i	−0.180890	+	0.983503i	$0.557898\pi$
$152$	−10.8298	+	7.86828i	−0.878409	+	0.638202i
$153$	2.17532	+	1.58046i	0.175864	+	0.127773i
$154$	−1.46068	+	4.49552i	−0.117705	+	0.362259i
$155$	1.49412	−	1.08554i	0.120011	−	0.0871928i
$156$	9.10312	+	28.0165i	0.728833	+	2.24312i
$157$	1.11495	−	0.810062i	0.0889830	−	0.0646500i	−0.542404	−	0.840118i	$-0.682486\pi$
$157$	1.11495	−	0.810062i	0.0889830	−	0.0646500i	0.631387	+	0.775468i	$0.282486\pi$
$158$	15.6757	−	11.3891i	1.24709	−	0.906067i
$159$	−21.9569	+	15.9526i	−1.74129	+	1.26512i
$160$	−18.5854	+	57.2001i	−1.46931	+	4.52206i
$161$	4.27577	+	3.10653i	0.336978	+	0.244829i
$162$	−30.3248			−2.38254
$163$	2.23462	+	6.87745i	0.175029	+	0.538684i	0.999635	−	0.0270241i	$-0.00860307\pi$
$163$	2.23462	+	6.87745i	0.175029	+	0.538684i	−0.824606	+	0.565708i	$0.808603\pi$
$164$	−14.0824	−	43.3411i	−1.09965	−	3.38437i
$165$	14.5828			1.13527
$166$	−25.6048	+	18.6029i	−1.98731	+	1.44387i
$167$	−12.3293	−	8.95775i	−0.954069	−	0.693172i	−0.00230308	−	0.999997i	$-0.500733\pi$
$167$	−12.3293	−	8.95775i	−0.954069	−	0.693172i	−0.951766	+	0.306826i	$0.900733\pi$
$168$	14.9243			1.15144
$169$	−1.81523	+	5.58671i	−0.139633	+	0.429747i
$170$	5.43645	−	16.7317i	0.416956	−	1.28326i
$171$	0.616065	−	1.89605i	0.0471117	−	0.144995i
$172$	9.57334			0.729960
$173$	−5.73772	−	4.16870i	−0.436231	−	0.316940i	0.347905	−	0.937530i	$-0.386893\pi$
$173$	−5.73772	−	4.16870i	−0.436231	−	0.316940i	−0.784135	+	0.620590i	$0.786893\pi$
$174$	0.695851			0.0527523
$175$	−1.33127	−	4.09723i	−0.100635	−	0.309721i
$176$	29.4359			2.21881
$177$	−20.1459	+	14.6369i	−1.51426	+	1.10017i
$178$	−10.7881	+	7.83805i	−0.808606	+	0.587486i
$179$	3.97301			0.296957			0.148478	−	0.988916i	$-0.452562\pi$
$179$	3.97301			0.296957			0.148478	+	0.988916i	$0.452562\pi$
$180$	−7.01471	−	21.5890i	−0.522845	−	1.60915i
$181$	−0.0838084			−0.00622943			−0.00311471	−	0.999995i	$-0.500991\pi$
$181$	−0.0838084			−0.00622943			−0.00311471	+	0.999995i	$0.500991\pi$
$182$	−4.68882	−	3.40663i	−0.347558	−	0.252516i
$183$	3.47290			0.256724
$184$	18.1495	−	55.8584i	1.33800	−	4.11793i
$185$	5.80212	−	17.8571i	0.426581	−	1.31288i
$186$	−0.996946	+	3.06828i	−0.0730996	+	0.224977i
$187$	−4.40270			−0.321958
$188$	44.5016	+	32.3323i	3.24562	+	2.35808i
$189$	2.25901	−	1.64127i	0.164319	−	0.119385i
$190$	−13.0440			−0.946313
$191$	2.17771	+	6.70231i	0.157574	+	0.484962i	0.998413	−	0.0563233i	$-0.0179377\pi$
$191$	2.17771	+	6.70231i	0.157574	+	0.484962i	−0.840839	+	0.541286i	$0.817938\pi$
$192$	−15.0791	−	46.4088i	−1.08824	−	3.34927i
$193$	−16.1491			−1.16244			−0.581219	−	0.813748i	$-0.697424\pi$
$193$	−16.1491			−1.16244			−0.581219	+	0.813748i	$0.697424\pi$
$194$	27.7618	+	20.1701i	1.99318	+	1.44813i
$195$	−5.52529	+	17.0051i	−0.395674	+	1.21776i
$196$	27.2653	−	19.8094i	1.94752	−	1.41496i
$197$	10.7093	−	7.78076i	0.763006	−	0.554356i	−0.136825	−	0.990595i	$-0.543690\pi$
$197$	10.7093	−	7.78076i	0.763006	−	0.554356i	0.899831	+	0.436239i	$0.143690\pi$
$198$	−6.32906	+	4.59833i	−0.449786	+	0.326789i
$199$	0.791882	+	2.43716i	0.0561350	+	0.172766i	0.975193	−	0.221357i	$-0.0710485\pi$
$199$	0.791882	+	2.43716i	0.0561350	+	0.172766i	−0.919058	+	0.394123i	$0.871049\pi$
$200$	−38.7317	+	28.1402i	−2.73874	+	1.98981i
$201$	0.361913	−	1.11386i	0.0255274	−	0.0785653i
$202$	37.3687	+	27.1499i	2.62925	+	1.91026i
$203$	−0.0804274	+	0.0584339i	−0.00564490	+	0.00410126i
$204$	6.89619	+	21.2243i	0.482830	+	1.48600i
$205$	8.54752	−	26.3066i	0.596985	−	1.83733i
$206$	−8.26957	−	6.00820i	−0.576168	−	0.418611i
$207$	2.70301	+	8.31900i	0.187872	+	0.578210i
$208$	−11.1530	+	34.3254i	−0.773322	+	2.38004i
$209$	1.00874	+	3.10459i	0.0697762	+	0.214749i
$210$	11.7653	+	8.54799i	0.811883	+	0.589867i
$211$	−8.36072	−	6.07442i	−0.575576	−	0.418180i	0.261551	−	0.965190i	$-0.415766\pi$
$211$	−8.36072	−	6.07442i	−0.575576	−	0.418180i	−0.837126	+	0.547010i	$0.815766\pi$
$212$	−69.1757			−4.75101
$213$	17.1928	−	3.43667i	1.17803	−	0.235477i
$214$	10.7328			0.733682
$215$	4.70095	+	3.41544i	0.320602	+	0.232931i
$216$	−25.1040	−	18.2391i	−1.70811	−	1.24102i
$217$	−0.142430	−	0.438355i	−0.00966878	−	0.0297575i
$218$	7.40080	−	22.7773i	0.501245	−	1.54267i
$219$	−0.967821	−	2.97865i	−0.0653993	−	0.201278i
$220$	30.0704	+	21.8474i	2.02734	+	1.47295i
$221$	1.66815	−	5.13403i	0.112212	−	0.345352i
$222$	10.1356	+	31.1941i	0.680255	+	2.09361i
$223$	−10.0778	+	7.32196i	−0.674861	+	0.490315i	−0.871649	−	0.490131i	$-0.836949\pi$
$223$	−10.0778	+	7.32196i	−0.674861	+	0.490315i	0.196788	+	0.980446i	$0.436949\pi$
$224$	12.1434	+	8.82268i	0.811363	+	0.589490i
$225$	2.20330	−	6.78106i	0.146887	−	0.452071i
$226$	35.2354	−	25.6000i	2.34382	−	1.70289i
$227$	3.61176	+	11.1158i	0.239721	+	0.737785i	0.996460	+	0.0840678i	$0.0267912\pi$
$227$	3.61176	+	11.1158i	0.239721	+	0.737785i	−0.756739	+	0.653717i	$0.773209\pi$
$228$	13.3864	−	9.72578i	0.886535	−	0.644105i
$229$	0.299083	−	0.217296i	0.0197639	−	0.0143593i	−0.577859	−	0.816136i	$-0.696112\pi$
$229$	0.299083	−	0.217296i	0.0197639	−	0.0143593i	0.597623	+	0.801777i	$0.296112\pi$
$230$	46.3010	−	33.6396i	3.05299	−	2.21813i
$231$	1.12464	−	3.46129i	0.0739960	−	0.227736i
$232$	0.893777	+	0.649367i	0.0586793	+	0.0426330i
$233$	−2.04412			−0.133915			−0.0669575	−	0.997756i	$-0.521329\pi$
$233$	−2.04412			−0.133915			−0.0669575	+	0.997756i	$0.521329\pi$
$234$	−2.96412	−	9.12262i	−0.193771	−	0.596365i
$235$	10.3173	+	31.7533i	0.673025	+	2.07136i
$236$	−63.4703			−4.13156
$237$	−12.0694	+	8.76894i	−0.783992	+	0.569604i
$238$	−3.55207	−	2.58073i	−0.230247	−	0.167284i
$239$	−16.8727			−1.09140			−0.545701	−	0.837980i	$-0.683737\pi$
$239$	−16.8727			−1.09140			−0.545701	+	0.837980i	$0.683737\pi$
$240$	27.9854	−	86.1302i	1.80645	−	5.55968i
$241$	−1.80922	+	5.56822i	−0.116542	+	0.358681i	−0.992266	−	0.124133i	$-0.960385\pi$
$241$	−1.80922	+	5.56822i	−0.116542	+	0.358681i	0.875723	+	0.482814i	$0.160385\pi$
$242$	−5.22794	+	16.0900i	−0.336065	+	1.03430i
$243$	12.9213			0.828903
$244$	7.16128	+	5.20297i	0.458454	+	0.333086i
$245$	20.4558			1.30688
$246$	14.9314	+	45.9542i	0.951994	+	2.92993i
$247$	−4.00249			−0.254672
$248$	−4.14383	+	3.01067i	−0.263133	+	0.191178i
$249$	19.7142	−	14.3232i	1.24934	−	0.907696i
$250$	−3.15295			−0.199410
$251$	−0.707562	−	2.17765i	−0.0446609	−	0.137452i	0.926240	−	0.376935i	$-0.123022\pi$
$251$	−0.707562	−	2.17765i	−0.0446609	−	0.137452i	−0.970901	+	0.239483i	$0.923022\pi$
$252$	−5.66525			−0.356877
$253$	−11.5872	−	8.41856i	−0.728478	−	0.529270i
$254$	−27.0171			−1.69521
$255$	−4.18575	+	12.8824i	−0.262122	+	0.806729i
$256$	7.22816	−	22.2460i	0.451760	−	1.39037i
$257$	6.31563	−	19.4375i	0.393958	−	1.21248i	−0.535811	−	0.844338i	$-0.679994\pi$
$257$	6.31563	−	19.4375i	0.393958	−	1.21248i	0.929770	−	0.368142i	$-0.120006\pi$
$258$	−10.1505			−0.631945
$259$	−3.79100	−	2.75432i	−0.235561	−	0.171145i
$260$	−36.8698	+	26.7875i	−2.28657	+	1.66129i
$261$	−0.164533			−0.0101844
$262$	−1.37451	−	4.23032i	−0.0849177	−	0.261350i
$263$	−6.58723	−	20.2734i	−0.406186	−	1.25011i	−0.919901	−	0.392151i	$-0.871731\pi$
$263$	−6.58723	−	20.2734i	−0.406186	−	1.25011i	0.513714	−	0.857961i	$-0.328269\pi$
$264$	−40.4442			−2.48917
$265$	−33.9685	−	24.6795i	−2.08667	−	1.51605i
$266$	−1.00597	+	3.09606i	−0.0616801	+	0.189832i
$267$	8.30625	−	6.03485i	0.508334	−	0.369327i
$268$	2.41502	−	1.75462i	0.147521	−	0.107180i
$269$	−8.77545	+	6.37574i	−0.535049	+	0.388736i	−0.822243	−	0.569137i	$-0.807277\pi$
$269$	−8.77545	+	6.37574i	−0.535049	+	0.388736i	0.287194	+	0.957872i	$0.407277\pi$
$270$	−9.34369	−	28.7569i	−0.568639	−	1.75009i
$271$	10.7141	−	7.78425i	0.650835	−	0.472859i	−0.212720	−	0.977113i	$-0.568232\pi$
$271$	10.7141	−	7.78425i	0.650835	−	0.472859i	0.863556	+	0.504254i	$0.168232\pi$
$272$	−8.44910	+	26.0037i	−0.512302	+	1.57670i
$273$	3.61012	+	2.62291i	0.218494	+	0.158746i
$274$	−28.7646	+	20.8987i	−1.73773	+	1.26254i
$275$	3.60768	+	11.1033i	0.217551	+	0.669554i
$276$	−22.4341	+	69.0451i	−1.35037	+	4.15602i
$277$	18.0498	+	13.1139i	1.08451	+	0.787941i	0.978463	−	0.206421i	$-0.0661816\pi$
$277$	18.0498	+	13.1139i	1.08451	+	0.787941i	0.106044	+	0.994361i	$0.466182\pi$
$278$	3.54934	+	10.9238i	0.212875	+	0.655163i
$279$	0.235727	−	0.725493i	0.0141126	−	0.0434341i
$280$	7.13481	+	21.9587i	0.426387	+	1.31228i
$281$	22.6734	+	16.4732i	1.35258	+	0.982706i	0.998878	+	0.0473473i	$0.0150767\pi$
$281$	22.6734	+	16.4732i	1.35258	+	0.982706i	0.353700	+	0.935359i	$0.384923\pi$
$282$	−47.1848	−	34.2817i	−2.80981	−	2.04145i
$283$	−2.76030			−0.164083			−0.0820414	−	0.996629i	$-0.526144\pi$
$283$	−2.76030			−0.164083			−0.0820414	+	0.996629i	$0.526144\pi$
$284$	40.6011	+	18.6711i	2.40923	+	1.10793i
$285$	10.0432			0.594905
$286$	12.7065	+	9.23180i	0.751350	+	0.545888i
$287$	−5.58479	−	4.05759i	−0.329660	−	0.239512i
$288$	7.67665	+	23.6263i	0.452351	+	1.39219i
$289$	−3.98956	+	12.2786i	−0.234680	+	0.722271i
$290$	0.332663	+	1.02383i	0.0195346	+	0.0601214i
$291$	−21.3750	−	15.5298i	−1.25302	−	0.910375i
$292$	2.46681	−	7.59207i	0.144359	−	0.444292i
$293$	−3.52100	−	10.8365i	−0.205699	−	0.633076i	−0.999684	−	0.0251387i	$-0.991997\pi$
$293$	−3.52100	−	10.8365i	−0.205699	−	0.633076i	0.793985	−	0.607937i	$-0.208003\pi$
$294$	−28.9092	+	21.0038i	−1.68602	+	1.22497i
$295$	−31.1668	−	22.6440i	−1.81460	−	1.31839i
$296$	−16.0918	+	49.5253i	−0.935314	+	2.87860i
$297$	−6.12182	+	4.44776i	−0.355224	+	0.258085i
$298$	−8.55374	−	26.3257i	−0.495505	−	1.52501i
$299$	14.2072	−	10.3221i	0.821624	−	0.596945i
$300$	47.8752	−	34.7834i	2.76408	−	2.00822i
$301$	1.17321	−	0.852390i	0.0676229	−	0.0491309i
$302$	18.0505	−	55.5536i	1.03869	−	3.19675i
$303$	−28.7717	−	20.9039i	−1.65289	−	1.20090i
$304$	20.2725			1.16271
$305$	1.66027	+	5.10980i	0.0950670	+	0.292586i
$306$	−2.24551	−	6.91096i	−0.128367	−	0.395073i
$307$	31.7326			1.81108			0.905538	−	0.424265i	$-0.139468\pi$
$307$	31.7326			1.81108			0.905538	+	0.424265i	$0.139468\pi$
$308$	7.50465	−	5.45245i	0.427617	−	0.310682i
$309$	6.36710	+	4.62597i	0.362211	+	0.263162i
$310$	−4.99108			−0.283474
$311$	2.81721	−	8.67049i	0.159749	−	0.491658i	−0.838862	−	0.544345i	$-0.816778\pi$
$311$	2.81721	−	8.67049i	0.159749	−	0.491658i	0.998611	+	0.0526864i	$0.0167784\pi$
$312$	15.3240	−	47.1623i	0.867549	−	2.67004i
$313$	4.90296	−	15.0898i	0.277132	−	0.852924i	−0.711516	−	0.702670i	$-0.751991\pi$
$313$	4.90296	−	15.0898i	0.277132	−	0.852924i	0.988647	−	0.150254i	$-0.0480090\pi$
$314$	−3.72449			−0.210185
$315$	−2.78190	−	2.02117i	−0.156742	−	0.113880i
$316$	−38.0250			−2.13907
$317$	4.04671	+	12.4545i	0.227286	+	0.699513i	0.998052	+	0.0623949i	$0.0198738\pi$
$317$	4.04671	+	12.4545i	0.227286	+	0.699513i	−0.770766	+	0.637119i	$0.780126\pi$
$318$	73.3466			4.11307
$319$	0.217955	−	0.158353i	0.0122031	−	0.00886608i
$320$	61.0742	−	44.3730i	3.41415	−	2.48052i
$321$	−8.26368			−0.461233
$322$	−4.41374	−	13.5841i	−0.245968	−	0.757011i
$323$	−3.03214			−0.168713
$324$	48.1454	+	34.9797i	2.67474	+	1.94331i
$325$	−14.3146			−0.794029
$326$	6.03908	−	18.5864i	0.334473	−	1.02940i
$327$	−5.69819	+	17.5372i	−0.315111	+	0.969811i
$328$	−23.7059	+	72.9593i	−1.30894	+	4.02850i
$329$	8.33248			0.459385
$330$	−31.8834	−	23.1647i	−1.75512	−	1.27517i
$331$	3.67800	−	2.67223i	0.202161	−	0.146879i	−0.482099	−	0.876117i	$-0.660125\pi$
$331$	3.67800	−	2.67223i	0.202161	−	0.146879i	0.684260	+	0.729238i	$0.260125\pi$
$332$	62.1101			3.40874
$333$	−2.39655	−	7.37582i	−0.131330	−	0.404192i
$334$	12.7271	+	39.1700i	0.696396	+	2.14329i
$335$	1.81187			0.0989932
$336$	−18.2851	−	13.2849i	−0.997536	−	0.724752i
$337$	3.62864	−	11.1678i	0.197665	−	0.608349i	−0.802271	−	0.596960i	$-0.796375\pi$
$337$	3.62864	−	11.1678i	0.197665	−	0.608349i	0.999935	−	0.0113883i	$-0.00362509\pi$
$338$	12.8432	−	9.33115i	0.698579	−	0.507547i
$339$	−27.1292	+	19.7105i	−1.47346	+	1.07053i
$340$	−27.9312	+	20.2932i	−1.51478	+	1.10055i
$341$	0.385979	+	1.18792i	0.0209019	+	0.0643295i
$342$	−4.35882	+	3.16687i	−0.235698	+	0.171244i
$343$	3.31539	−	10.2037i	0.179014	−	0.550949i
$344$	−13.0377	−	9.47247i	−0.702947	−	0.510721i
$345$	−35.6491	+	25.9006i	−1.91928	+	1.39444i
$346$	5.92285	+	18.2287i	0.318414	+	0.979979i
$347$	3.71612	−	11.4370i	0.199492	−	0.613972i	−0.800403	−	0.599462i	$-0.795381\pi$
$347$	3.71612	−	11.4370i	0.199492	−	0.613972i	0.999895	−	0.0145098i	$-0.00461876\pi$
$348$	−1.10477	−	0.802665i	−0.0592221	−	0.0430274i
$349$	5.55230	+	17.0882i	0.297208	+	0.914712i	0.982471	+	0.186416i	$0.0596873\pi$
$349$	5.55230	+	17.0882i	0.297208	+	0.914712i	−0.685263	+	0.728296i	$0.740313\pi$
$350$	−3.59777	+	11.0728i	−0.192309	+	0.591865i
$351$	−2.86706	−	8.82392i	−0.153033	−	0.470986i
$352$	−32.9080	−	23.9091i	−1.75400	−	1.27436i
$353$	12.5884	+	9.14598i	0.670011	+	0.486791i	0.870029	−	0.493001i	$-0.164100\pi$
$353$	12.5884	+	9.14598i	0.670011	+	0.486791i	−0.200018	+	0.979792i	$0.564100\pi$
$354$	67.2971			3.57680
$355$	13.2758	+	23.6534i	0.704606	+	1.25539i
$356$	26.1691			1.38696
$357$	2.73489	+	1.98702i	0.144746	+	0.105164i
$358$	−8.68649	−	6.31111i	−0.459096	−	0.333552i
$359$	−7.25902	−	22.3410i	−0.383117	−	1.17911i	−0.937837	−	0.347075i	$-0.887175\pi$
$359$	−7.25902	−	22.3410i	−0.383117	−	1.17911i	0.554721	−	0.832037i	$-0.312825\pi$
$360$	−11.8084	+	36.3425i	−0.622356	+	1.91542i
$361$	−5.17660	−	15.9319i	−0.272453	−	0.838523i
$362$	0.183236	+	0.133129i	0.00963069	+	0.00699711i
$363$	4.02522	−	12.3883i	0.211269	−	0.650219i
$364$	3.51469	+	10.8171i	0.184220	+	0.566971i
$365$	3.91991	−	2.84798i	0.205177	−	0.149070i
$366$	−7.59305	−	5.51668i	−0.396895	−	0.288361i
$367$	1.52675	−	4.69885i	0.0796956	−	0.245278i	−0.903268	−	0.429076i	$-0.858839\pi$
$367$	1.52675	−	4.69885i	0.0796956	−	0.245278i	0.982964	+	0.183798i	$0.0588393\pi$
$368$	−71.9590	+	52.2813i	−3.75112	+	2.72535i
$369$	−3.53053	−	10.8658i	−0.183792	−	0.565653i
$370$	−41.0515	+	29.8257i	−2.13417	+	1.55056i
$371$	−8.47750	+	6.15926i	−0.440130	+	0.319773i
$372$	5.12208	−	3.72141i	0.265567	−	0.192946i
$373$	−10.9518	+	33.7063i	−0.567064	+	1.74524i	0.0946728	+	0.995508i	$0.469820\pi$
$373$	−10.9518	+	33.7063i	−0.567064	+	1.74524i	−0.661737	+	0.749736i	$0.730180\pi$
$374$	9.62596	+	6.99367i	0.497746	+	0.361634i
$375$	2.42759			0.125360
$376$	−28.6142	−	88.0654i	−1.47566	−	4.54163i
$377$	0.102076	+	0.314157i	0.00525717	+	0.0161799i
$378$	−7.54619			−0.388134
$379$	15.3141	−	11.1263i	0.786632	−	0.571521i	−0.120330	−	0.992734i	$-0.538395\pi$
$379$	15.3141	−	11.1263i	0.786632	−	0.571521i	0.906962	+	0.421212i	$0.138395\pi$
$380$	20.7095	+	15.0463i	1.06237	+	0.771859i
$381$	20.8017			1.06570
$382$	5.88529	−	18.1131i	0.301118	−	0.926744i
$383$	−10.3898	+	31.9765i	−0.530893	+	1.63392i	0.221467	+	0.975168i	$0.428916\pi$
$383$	−10.3898	+	31.9765i	−0.530893	+	1.63392i	−0.752360	+	0.658753i	$0.771084\pi$
$384$	−16.7246	+	51.4732i	−0.853476	+	2.62673i
$385$	5.63038			0.286951
$386$	35.3080	+	25.6527i	1.79713	+	1.30569i
$387$	2.40009			0.122003
$388$	−20.8100	−	64.0465i	−1.05647	−	3.25147i
$389$	−14.7667			−0.748703			−0.374351	−	0.927287i	$-0.622135\pi$
$389$	−14.7667			−0.748703			−0.374351	+	0.927287i	$0.622135\pi$
$390$	39.0928	−	28.4026i	1.97954	−	1.43822i
$391$	10.7629	−	7.81967i	0.544301	−	0.395458i
$392$	−56.7327			−2.86544
$393$	1.05830	+	3.25710i	0.0533840	+	0.164299i
$394$	−35.7742			−1.80228
$395$	−18.6720	−	13.5660i	−0.939492	−	0.682581i
$396$	15.3526			0.771495
$397$	−4.76432	+	14.6631i	−0.239114	+	0.735918i	0.757435	+	0.652911i	$0.226452\pi$
$397$	−4.76432	+	14.6631i	−0.239114	+	0.735918i	−0.996549	+	0.0830072i	$0.973548\pi$
$398$	2.14007	−	6.58645i	0.107272	−	0.330149i
$399$	0.774540	−	2.38379i	0.0387755	−	0.119339i
$400$	72.5027			3.62514
$401$	−7.11518	−	5.16948i	−0.355315	−	0.258151i	0.395780	−	0.918345i	$-0.370474\pi$
$401$	−7.11518	−	5.16948i	−0.355315	−	0.258151i	−0.751095	+	0.660194i	$0.770474\pi$
$402$	−2.56063	+	1.86041i	−0.127713	+	0.0927887i
$403$	−1.53149			−0.0762888
$404$	−28.0112	−	86.2096i	−1.39361	−	4.28909i
$405$	11.1620	+	34.3532i	0.554646	+	1.70703i
$406$	0.268666			0.0133337
$407$	10.2734	+	7.46409i	0.509235	+	0.369981i
$408$	11.6089	−	35.7284i	0.574725	−	1.76882i
$409$	19.3961	−	14.0921i	0.959077	−	0.696810i	0.00614102	−	0.999981i	$-0.498045\pi$
$409$	19.3961	−	14.0921i	0.959077	−	0.696810i	0.952936	+	0.303171i	$0.0980452\pi$
$410$	−60.4759	+	43.9383i	−2.98669	+	2.16996i
$411$	22.1471	−	16.0908i	1.09244	−	0.793701i
$412$	6.19879	+	19.0779i	0.305393	+	0.939902i
$413$	−7.77829	+	5.65126i	−0.382745	+	0.278080i
$414$	7.30489	−	22.4822i	0.359016	−	1.10494i
$415$	30.4989	+	22.1588i	1.49713	+	1.08773i
$416$	40.3491	−	29.3153i	1.97828	−	1.43730i
$417$	−2.73279	−	8.41066i	−0.133825	−	0.411872i
$418$	2.72614	−	8.39018i	0.133340	−	0.410377i
$419$	2.47713	+	1.79974i	0.121016	+	0.0879232i	0.646647	−	0.762789i	$-0.276171\pi$
$419$	2.47713	+	1.79974i	0.121016	+	0.0879232i	−0.525631	+	0.850713i	$0.676171\pi$
$420$	−8.81916	−	27.1426i	−0.430331	−	1.32442i
$421$	0.370934	−	1.14162i	0.0180782	−	0.0556391i	−0.941610	−	0.336704i	$-0.890688\pi$
$421$	0.370934	−	1.14162i	0.0180782	−	0.0556391i	0.959689	+	0.281065i	$0.0906877\pi$
$422$	8.63048	+	26.5619i	0.420125	+	1.29301i
$423$	11.1568	+	8.10589i	0.542462	+	0.394122i
$424$	94.2090	+	68.4468i	4.57519	+	3.32407i
$425$	−10.8442			−0.526020
$426$	−43.0491	−	19.7968i	−2.08573	−	0.959160i
$427$	1.34088			0.0648896
$428$	−17.0401	−	12.3804i	−0.823664	−	0.598427i
$429$	−9.78326	−	7.10796i	−0.472340	−	0.343175i
$430$	−4.85263	−	14.9349i	−0.234015	−	0.720223i
$431$	1.07088	−	3.29583i	0.0515825	−	0.158755i	−0.921947	−	0.387316i	$-0.873402\pi$
$431$	1.07088	−	3.29583i	0.0515825	−	0.158755i	0.973529	+	0.228562i	$0.0734022\pi$
$432$	14.5216	+	44.6928i	0.698670	+	2.15028i
$433$	2.93122	+	2.12965i	0.140865	+	0.102345i	0.655986	−	0.754773i	$-0.272253\pi$
$433$	2.93122	+	2.12965i	0.140865	+	0.102345i	−0.515121	+	0.857118i	$0.672253\pi$
$434$	−0.384918	+	1.18466i	−0.0184767	+	0.0568653i
$435$	−0.256131	−	0.788291i	−0.0122806	−	0.0377957i
$436$	−38.0236	+	27.6258i	−1.82100	+	1.32303i
$437$	−7.98006	−	5.79785i	−0.381738	−	0.277349i
$438$	−2.61554	+	8.04981i	−0.124975	+	0.384635i
$439$	−15.2832	+	11.1039i	−0.729425	+	0.529959i	−0.889382	−	0.457166i	$-0.848865\pi$
$439$	−15.2832	+	11.1039i	−0.729425	+	0.529959i	0.159956	+	0.987124i	$0.448865\pi$
$440$	−19.3350	−	59.5071i	−0.921761	−	2.83689i
$441$	6.83556	−	4.96633i	0.325503	−	0.236492i
$442$	−11.8026	+	8.57506i	−0.561391	+	0.407874i
$443$	−8.89584	+	6.46321i	−0.422654	+	0.307076i	−0.778705	−	0.627390i	$-0.784123\pi$
$443$	−8.89584	+	6.46321i	−0.422654	+	0.307076i	0.356051	+	0.934467i	$0.384123\pi$
$444$	19.8906	−	61.2170i	0.943966	−	2.90523i
$445$	12.8502	+	9.33623i	0.609159	+	0.442580i
$446$	33.6648			1.59407
$447$	6.58589	+	20.2693i	0.311502	+	0.958704i
$448$	−5.82202	−	17.9183i	−0.275065	−	0.846562i
$449$	25.5235			1.20453			0.602264	−	0.798297i	$-0.294266\pi$
$449$	25.5235			1.20453			0.602264	+	0.798297i	$0.294266\pi$
$450$	−15.5889	+	11.3260i	−0.734869	+	0.533913i
$451$	15.1345	+	10.9959i	0.712657	+	0.517776i
$452$	−85.4714			−4.02024
$453$	−13.8978	+	42.7731i	−0.652977	+	2.00966i
$454$	9.76080	−	30.0407i	0.458097	−	1.40988i
$455$	−2.13330	+	6.56562i	−0.100011	+	0.307801i
$456$	−27.8539			−1.30438
$457$	2.84572	+	2.06753i	0.133117	+	0.0967151i	0.652351	−	0.757917i	$-0.273783\pi$
$457$	2.84572	+	2.06753i	0.133117	+	0.0967151i	−0.519234	+	0.854632i	$0.673783\pi$
$458$	−0.999081			−0.0466840
$459$	−2.17198	−	6.68467i	−0.101379	−	0.312014i
$460$	−112.313			−5.23664
$461$	−12.8877	+	9.36344i	−0.600239	+	0.436099i	−0.845964	−	0.533241i	$-0.820974\pi$
$461$	−12.8877	+	9.36344i	−0.600239	+	0.436099i	0.245725	+	0.969340i	$0.420974\pi$
$462$	−7.95713	+	5.78119i	−0.370199	+	0.268965i
$463$	16.6512			0.773848			0.386924	−	0.922112i	$-0.373538\pi$
$463$	16.6512			0.773848			0.386924	+	0.922112i	$0.373538\pi$
$464$	−0.517011	−	1.59119i	−0.0240016	−	0.0738694i
$465$	3.84285			0.178208
$466$	4.46922	+	3.24708i	0.207032	+	0.150418i
$467$	21.9803			1.01713			0.508563	−	0.861025i	$-0.330177\pi$
$467$	21.9803			1.01713			0.508563	+	0.861025i	$0.330177\pi$
$468$	−5.81695	+	17.9027i	−0.268889	+	0.827554i
$469$	0.139734	−	0.430057i	0.00645231	−	0.0198582i
$470$	27.8825	−	85.8136i	1.28612	−	3.95828i
$471$	2.86764			0.132134
$472$	86.4388	+	62.8015i	3.97867	+	2.89067i
$473$	−3.17936	+	2.30994i	−0.146187	+	0.106211i
$474$	40.3177			1.85185
$475$	2.48461	+	7.64683i	0.114002	+	0.350861i
$476$	2.66260	+	8.19465i	0.122040	+	0.375601i
$477$	−17.3427			−0.794069
$478$	36.8900	+	26.8021i	1.68731	+	1.22590i
$479$	−9.07264	+	27.9227i	−0.414539	+	1.27582i	0.498123	+	0.867106i	$0.334023\pi$
$479$	−9.07264	+	27.9227i	−0.414539	+	1.27582i	−0.912662	+	0.408714i	$0.865977\pi$
$480$	−101.245	+	73.5587i	−4.62117	+	3.35748i
$481$	−12.5964	+	9.15185i	−0.574348	+	0.417289i
$482$	12.8007	−	9.30027i	0.583057	−	0.423616i
$483$	3.39832	+	10.4590i	0.154629	+	0.475899i
$484$	26.8600	−	19.5149i	1.22091	−	0.887042i
$485$	12.6310	−	38.8741i	0.573542	−	1.76518i
$486$	−28.2508	−	20.5254i	−1.28148	−	0.931053i
$487$	2.69667	−	1.95925i	0.122198	−	0.0887819i	−0.525008	−	0.851097i	$-0.675938\pi$
$487$	2.69667	−	1.95925i	0.122198	−	0.0887819i	0.647206	+	0.762316i	$0.275938\pi$
$488$	−4.60464	−	14.1716i	−0.208442	−	0.641520i
$489$	−4.64974	+	14.3104i	−0.210269	+	0.647140i
$490$	−44.7241	−	32.4940i	−2.02043	−	1.46793i
$491$	−6.89716	−	21.2273i	−0.311264	−	0.957974i	−0.977265	−	0.212022i	$-0.931995\pi$
$491$	−6.89716	−	21.2273i	−0.311264	−	0.957974i	0.666000	−	0.745951i	$-0.268005\pi$
$492$	29.3023	−	90.1831i	1.32105	−	4.06577i
$493$	0.0773289	+	0.237994i	0.00348272	+	0.0107187i
$494$	8.75095	+	6.35793i	0.393724	+	0.286057i
$495$	7.53881	+	5.47727i	0.338844	+	0.246185i
$496$	7.75693			0.348296
$497$	6.63810	−	1.32689i	0.297760	−	0.0595191i
$498$	−65.8549			−2.95103
$499$	−11.9628	−	8.69145i	−0.535527	−	0.389083i	0.286894	−	0.957962i	$-0.407377\pi$
$499$	−11.9628	−	8.69145i	−0.535527	−	0.389083i	−0.822421	+	0.568879i	$0.807377\pi$
$500$	5.00581	+	3.63693i	0.223866	+	0.162649i
$501$	−9.79914	−	30.1586i	−0.437793	−	1.34739i
$502$	−1.91219	+	5.88512i	−0.0853453	+	0.262666i
$503$	1.92585	+	5.92716i	0.0858695	+	0.264279i	0.984767	−	0.173880i	$-0.0556306\pi$
$503$	1.92585	+	5.92716i	0.0858695	+	0.264279i	−0.898897	+	0.438159i	$0.855631\pi$
$504$	7.71538	+	5.60555i	0.343670	+	0.249691i
$505$	17.0019	−	52.3263i	0.756572	−	2.32849i
$506$	11.9610	+	36.8122i	0.531732	+	1.63650i
$507$	−9.88854	+	7.18445i	−0.439166	+	0.319073i
$508$	42.8940	+	31.1643i	1.90311	+	1.38269i
$509$	11.7126	−	36.0478i	0.519153	−	1.59779i	−0.256443	−	0.966559i	$-0.582550\pi$
$509$	11.7126	−	36.0478i	0.519153	−	1.59779i	0.775596	−	0.631230i	$-0.217450\pi$
$510$	29.6153	−	21.5168i	1.31139	−	0.952778i
$511$	−0.373673	−	1.15005i	−0.0165303	−	0.0508751i
$512$	−9.05515	+	6.57895i	−0.400185	+	0.290751i
$513$	−4.21609	+	3.06317i	−0.186145	+	0.135242i
$514$	−44.6847	+	32.4654i	−1.97096	+	1.43199i
$515$	−3.76246	+	11.5797i	−0.165794	+	0.510260i
$516$	16.1156	+	11.7087i	0.709450	+	0.515445i
$517$	−22.5806			−0.993096
$518$	3.91332	+	12.0440i	0.171941	+	0.529181i
$519$	−4.56026	−	14.0350i	−0.200173	−	0.616069i
$520$	76.7175			3.36428
$521$	−33.9065	+	24.6345i	−1.48547	+	1.07926i	−0.509729	+	0.860335i	$0.670254\pi$
$521$	−33.9065	+	24.6345i	−1.48547	+	1.07926i	−0.975742	+	0.218923i	$0.929746\pi$
$522$	0.359732	+	0.261360i	0.0157450	+	0.0114394i
$523$	27.5169			1.20323			0.601615	−	0.798786i	$-0.294524\pi$
$523$	27.5169			1.20323			0.601615	+	0.798786i	$0.294524\pi$
$524$	−2.69742	+	8.30180i	−0.117837	+	0.362666i
$525$	2.77007	−	8.52541i	0.120896	−	0.372079i
$526$	−17.8020	+	54.7891i	−0.776206	+	2.38892i
$527$	−1.16020			−0.0505390
$528$	49.5519	+	36.0015i	2.15647	+	1.56677i
$529$	20.2782			0.881662
$530$	35.0645	+	107.917i	1.52310	+	4.68763i
$531$	−15.9123			−0.690537
$532$	5.16845	−	3.75510i	0.224081	−	0.162804i
$533$	−18.5567	+	13.4822i	−0.803781	+	0.583981i
$534$	−27.7469			−1.20073
$535$	−3.95058	−	12.1586i	−0.170799	−	0.525664i
$536$	−5.02510			−0.217051
$537$	6.68810	+	4.85919i	0.288613	+	0.209690i
$538$	29.3142			1.26383
$539$	−4.27517	+	13.1576i	−0.184145	+	0.566739i
$540$	−18.3366	+	56.4341i	−0.789080	+	2.42854i
$541$	−2.41286	+	7.42600i	−0.103737	+	0.319269i	−0.989432	−	0.144998i	$-0.953682\pi$
$541$	−2.41286	+	7.42600i	−0.103737	+	0.319269i	0.885695	+	0.464267i	$0.153682\pi$
$542$	−35.7903			−1.53732
$543$	−0.141082	−	0.102502i	−0.00605439	−	0.00439877i
$544$	30.5670	−	22.2082i	1.31055	−	0.952168i
$545$	−28.5273			−1.22197
$546$	−3.72661	−	11.4693i	−0.159484	−	0.490841i
$547$	−3.02696	−	9.31603i	−0.129424	−	0.398325i	0.865258	−	0.501328i	$-0.167155\pi$
$547$	−3.02696	−	9.31603i	−0.129424	−	0.398325i	−0.994681	+	0.103003i	$0.967155\pi$
$548$	69.7751			2.98064
$549$	1.79537	+	1.30441i	0.0766246	+	0.0556710i
$550$	9.74978	−	30.0067i	0.415732	−	1.27949i
$551$	0.150105	−	0.109058i	0.00639470	−	0.00464602i
$552$	98.8701	−	71.8333i	4.20819	−	3.05743i
$553$	−4.65997	+	3.38567i	−0.198162	+	0.143973i
$554$	−18.6322	−	57.3440i	−0.791606	−	2.43631i
$555$	31.6073	−	22.9641i	1.34166	−	0.974770i
$556$	6.96542	−	21.4374i	0.295400	−	0.909147i
$557$	−21.6249	−	15.7114i	−0.916275	−	0.665713i	0.0263187	−	0.999654i	$-0.491622\pi$
$557$	−21.6249	−	15.7114i	−0.916275	−	0.665713i	−0.942594	+	0.333941i	$0.891622\pi$
$558$	−1.66783	+	1.21175i	−0.0706048	+	0.0512974i
$559$	−1.48900	−	4.58269i	−0.0629782	−	0.193827i
$560$	10.8051	−	33.2546i	0.456598	−	1.40527i
$561$	−7.41144	−	5.38472i	−0.312911	−	0.227343i
$562$	−23.4049	−	72.0330i	−0.987277	−	3.03853i
$563$	−5.94357	+	18.2924i	−0.250492	+	0.770934i	0.744193	+	0.667965i	$0.232834\pi$
$563$	−5.94357	+	18.2924i	−0.250492	+	0.770934i	−0.994685	+	0.102969i	$0.967166\pi$
$564$	35.3693	+	108.855i	1.48931	+	4.58364i
$565$	−41.9704	−	30.4933i	−1.76571	−	1.28286i
$566$	6.03505	+	4.38472i	0.253672	+	0.184304i
$567$	9.01473			0.378583
$568$	−36.8194	−	65.6011i	−1.54491	−	2.75256i
$569$	31.5773			1.32379			0.661895	−	0.749597i	$-0.269753\pi$
$569$	31.5773			1.32379			0.661895	+	0.749597i	$0.269753\pi$
$570$	−21.9581	−	15.9535i	−0.919723	−	0.668218i
$571$	−26.4082	−	19.1867i	−1.10515	−	0.802937i	−0.123255	−	0.992375i	$-0.539333\pi$
$571$	−26.4082	−	19.1867i	−1.10515	−	0.802937i	−0.981893	+	0.189439i	$0.939333\pi$
$572$	−9.52466	−	29.3139i	−0.398246	−	1.22568i
$573$	−4.53133	+	13.9460i	−0.189299	+	0.582603i
$574$	5.76499	+	17.7428i	0.240626	+	0.740571i
$575$	−28.5400	−	20.7355i	−1.19020	−	0.864730i
$576$	9.63566	−	29.6555i	0.401486	−	1.23565i
$577$	−1.82728	−	5.62380i	−0.0760708	−	0.234122i	0.905789	−	0.423728i	$-0.139279\pi$
$577$	−1.82728	−	5.62380i	−0.0760708	−	0.234122i	−0.981860	+	0.189606i	$0.939279\pi$
$578$	28.2272	−	20.5082i	1.17410	−	0.853031i
$579$	−27.1851	−	19.7511i	−1.12977	−	0.820829i
$580$	0.652835	−	2.00922i	0.0271075	−	0.0834283i
$581$	7.61160	−	5.53015i	0.315783	−	0.229429i
$582$	22.0647	+	67.9081i	0.914610	+	2.81488i
$583$	22.9736	−	16.6913i	0.951470	−	0.691284i
$584$	−10.8716	+	7.89866i	−0.449869	+	0.326849i
$585$	−9.24347	+	6.71577i	−0.382170	+	0.277663i
$586$	−9.51552	+	29.2858i	−0.393082	+	1.20978i
$587$	25.8856	+	18.8070i	1.06841	+	0.776248i	0.975626	−	0.219438i	$-0.0704224\pi$
$587$	25.8856	+	18.8070i	1.06841	+	0.776248i	0.0927872	+	0.995686i	$0.470422\pi$
$588$	70.1259			2.89194
$589$	0.265823	+	0.818121i	0.0109531	+	0.0337101i
$590$	32.1724	+	99.0166i	1.32452	+	4.07645i
$591$	27.5441			1.13301
$592$	63.8005	−	46.3538i	2.62219	−	1.90513i
$593$	−17.4065	−	12.6465i	−0.714798	−	0.519331i	0.169920	−	0.985458i	$-0.445649\pi$
$593$	−17.4065	−	12.6465i	−0.714798	−	0.519331i	−0.884718	+	0.466127i	$0.845649\pi$
$594$	20.4498			0.839067
$595$	−1.61611	+	4.97387i	−0.0662540	+	0.203909i
$596$	−16.7863	+	51.6630i	−0.687594	+	2.11620i
$597$	−1.64773	+	5.07119i	−0.0674370	+	0.207550i
$598$	−47.4589			−1.94074
$599$	−28.3598	−	20.6046i	−1.15875	−	0.841882i	−0.169131	−	0.985593i	$-0.554096\pi$
$599$	−28.3598	−	20.6046i	−1.15875	−	0.841882i	−0.989620	+	0.143712i	$0.954096\pi$
$600$	−99.6171			−4.06685
$601$	−0.633336	−	1.94921i	−0.0258343	−	0.0795098i	0.937308	−	0.348502i	$-0.113309\pi$
$601$	−0.633336	−	1.94921i	−0.0258343	−	0.0795098i	−0.963142	+	0.268992i	$0.913309\pi$
$602$	−3.91910			−0.159731
$603$	0.605459	−	0.439892i	0.0246562	−	0.0179138i
$604$	−92.7391	+	67.3789i	−3.77350	+	2.74161i
$605$	20.1517			0.819284
$606$	29.7001	+	91.4075i	1.20648	+	3.71317i
$607$	−35.3755			−1.43585			−0.717924	−	0.696121i	$-0.754908\pi$
$607$	−35.3755			−1.43585			−0.717924	+	0.696121i	$0.754908\pi$
$608$	−22.6637	−	16.4661i	−0.919135	−	0.667791i
$609$	−0.206858			−0.00838230
$610$	4.48690	−	13.8093i	0.181669	−	0.559121i
$611$	8.55561	−	26.3315i	0.346123	−	1.06526i
$612$	−4.40670	+	13.5624i	−0.178130	+	0.548229i
$613$	9.51044			0.384123			0.192062	−	0.981383i	$-0.438483\pi$
$613$	9.51044			0.384123			0.192062	+	0.981383i	$0.438483\pi$
$614$	−69.3794	−	50.4071i	−2.79992	−	2.03426i
$615$	46.5630	−	33.8300i	1.87760	−	1.36416i
$616$	−15.6154			−0.629163
$617$	6.86929	+	21.1415i	0.276547	+	0.851124i	0.988806	+	0.149207i	$0.0476722\pi$
$617$	6.86929	+	21.1415i	0.276547	+	0.851124i	−0.712259	+	0.701917i	$0.752328\pi$
$618$	−6.57254	−	20.2282i	−0.264386	−	0.813697i
$619$	15.4976			0.622903			0.311451	−	0.950262i	$-0.399185\pi$
$619$	15.4976			0.622903			0.311451	+	0.950262i	$0.399185\pi$
$620$	7.92413	+	5.75722i	0.318241	+	0.231215i
$621$	7.06571	−	21.7460i	0.283537	−	0.872637i
$622$	−19.9325	+	14.4818i	−0.799220	+	0.580668i
$623$	3.20702	−	2.33004i	0.128487	−	0.0933511i
$624$	−60.7564	+	44.1421i	−2.43220	+	1.76710i
$625$	−7.12486	−	21.9281i	−0.284994	−	0.877122i
$626$	−34.6897	+	25.2035i	−1.38648	+	1.00734i
$627$	−2.09897	+	6.45996i	−0.0838247	+	0.257986i
$628$	5.91321	+	4.29620i	0.235963	+	0.171437i
$629$	−9.54260	+	6.93310i	−0.380488	+	0.276441i
$630$	2.87166	+	8.83805i	0.114410	+	0.352116i
$631$	−9.31583	+	28.6712i	−0.370857	+	1.14138i	0.575374	+	0.817891i	$0.304857\pi$
$631$	−9.31583	+	28.6712i	−0.370857	+	1.14138i	−0.946231	+	0.323491i	$0.895143\pi$
$632$	51.7855	+	37.6243i	2.05992	+	1.49662i
$633$	−6.64498	−	20.4511i	−0.264114	−	0.812860i
$634$	10.9363	−	33.6583i	0.434334	−	1.33674i
$635$	9.94456	+	30.6062i	0.394638	+	1.21457i
$636$	−116.449	−	84.6054i	−4.61751	−	3.35482i
$637$	−13.7234	−	9.97061i	−0.543740	−	0.395050i
$638$	−0.728074			−0.0288247
$639$	10.1789	+	4.68095i	0.402672	+	0.185175i
$640$	−83.7298			−3.30971
$641$	24.2494	+	17.6182i	0.957795	+	0.695878i	0.952637	−	0.304108i	$-0.0983585\pi$
$641$	24.2494	+	17.6182i	0.957795	+	0.695878i	0.00515704	+	0.999987i	$0.498358\pi$
$642$	18.0675	+	13.1268i	0.713067	+	0.518073i
$643$	9.67064	+	29.7632i	0.381373	+	1.17374i	0.939078	+	0.343705i	$0.111682\pi$
$643$	9.67064	+	29.7632i	0.381373	+	1.17374i	−0.557705	+	0.830039i	$0.688318\pi$
$644$	−8.66175	+	26.6581i	−0.341321	+	1.05048i
$645$	3.73625	+	11.4990i	0.147115	+	0.452772i
$646$	6.62939	+	4.81653i	0.260830	+	0.189504i
$647$	7.76116	−	23.8864i	0.305123	−	0.939071i	−0.674509	−	0.738267i	$-0.735644\pi$
$647$	7.76116	−	23.8864i	0.305123	−	0.939071i	0.979631	−	0.200804i	$-0.0643556\pi$
$648$	−30.9571	−	95.2761i	−1.21611	−	3.74280i
$649$	21.0788	−	15.3147i	0.827416	−	0.601153i
$650$	31.2970	+	22.7386i	1.22757	+	0.891881i
$651$	0.296365	−	0.912118i	0.0116155	−	0.0357487i
$652$	−31.0274	+	22.5427i	−1.21513	+	0.882841i
$653$	14.0346	+	43.1940i	0.549216	+	1.69031i	0.710750	+	0.703445i	$0.248356\pi$
$653$	14.0346	+	43.1940i	0.549216	+	1.69031i	−0.161534	+	0.986867i	$0.551644\pi$
$654$	40.3162	−	29.2914i	1.57649	−	1.14538i
$655$	−4.28635	+	3.11422i	−0.167482	+	0.121683i
$656$	93.9891	−	68.2871i	3.66966	−	2.66616i
$657$	0.618443	−	1.90337i	0.0241278	−	0.0742576i
$658$	−18.2179	−	13.2361i	−0.710209	−	0.515997i
$659$	−30.6346			−1.19336			−0.596678	−	0.802481i	$-0.703513\pi$
$659$	−30.6346			−1.19336			−0.596678	+	0.802481i	$0.703513\pi$
$660$	23.8995	+	73.5551i	0.930287	+	2.86313i
$661$	−9.66176	−	29.7358i	−0.375799	−	1.15659i	−0.942938	−	0.332968i	$-0.891950\pi$
$661$	−9.66176	−	29.7358i	−0.375799	−	1.15659i	0.567139	−	0.823622i	$-0.308050\pi$
$662$	−12.2863			−0.477521
$663$	9.08730	−	6.60231i	0.352921	−	0.256412i
$664$	−84.5865	−	61.4557i	−3.28259	−	2.38494i
$665$	3.87764			0.150368
$666$	−6.47669	+	19.9332i	−0.250967	+	0.772396i
$667$	−0.251560	+	0.774221i	−0.00974043	+	0.0299780i
$668$	24.9763	−	76.8693i	0.966364	−	2.97416i
$669$	−25.9200			−1.00212
$670$	−3.96143	−	2.87815i	−0.153044	−	0.111193i
$671$	−3.63372			−0.140278
$672$	9.65138	+	29.7039i	0.372310	+	1.14585i
$673$	49.8702			1.92235			0.961177	−	0.275933i	$-0.0889868\pi$
$673$	49.8702			1.92235			0.961177	+	0.275933i	$0.0889868\pi$
$674$	−25.6735	+	18.6529i	−0.988908	+	0.718484i
$675$	−15.0785	+	10.9552i	−0.580371	+	0.421664i
$676$	−31.1541			−1.19824
$677$	8.84440	+	27.2203i	0.339918	+	1.04616i	0.964249	+	0.265000i	$0.0853718\pi$
$677$	8.84440	+	27.2203i	0.339918	+	1.04616i	−0.624331	+	0.781160i	$0.714628\pi$
$678$	90.6247			3.48042
$679$	−8.25283	−	5.99603i	−0.316715	−	0.230107i
$680$	58.1183			2.22874
$681$	−7.51526	+	23.1296i	−0.287985	+	0.886328i
$682$	1.04311	−	3.21037i	0.0399428	−	0.122931i
$683$	5.81552	−	17.8983i	0.222525	−	0.684860i	−0.776009	−	0.630722i	$-0.782759\pi$
$683$	5.81552	−	17.8983i	0.222525	−	0.684860i	0.998533	−	0.0541384i	$-0.0172412\pi$
$684$	10.5733			0.404280
$685$	34.2628	+	24.8934i	1.30911	+	0.951126i
$686$	−23.4572	+	17.0427i	−0.895602	+	0.650693i
$687$	0.769235			0.0293481
$688$	7.54176	+	23.2111i	0.287527	+	0.884916i
$689$	10.7594	+	33.1139i	0.409899	+	1.26154i
$690$	119.085			4.53349
$691$	−0.0770430	−	0.0559750i	−0.00293085	−	0.00212939i	0.586319	−	0.810080i	$-0.300577\pi$
$691$	−0.0770430	−	0.0559750i	−0.00293085	−	0.00212939i	−0.589250	+	0.807951i	$0.700577\pi$
$692$	11.6233	−	35.7729i	0.441852	−	1.35988i
$693$	1.88146	−	1.36696i	0.0714707	−	0.0519265i
$694$	−26.2925	+	19.1026i	−0.998048	+	0.725125i
$695$	11.0685	−	8.04170i	0.419850	−	0.305039i
$696$	0.710361	+	2.18627i	0.0269262	+	0.0828702i
$697$	−14.0579	+	10.2136i	−0.532480	+	0.386870i
$698$	15.0051	−	46.1811i	0.567953	−	1.74798i
$699$	−3.44104	−	2.50006i	−0.130152	−	0.0945610i
$700$	18.4845	−	13.4298i	0.698648	−	0.507598i
$701$	−5.11812	−	15.7519i	−0.193309	−	0.594943i	−0.999992	−	0.00395900i	$-0.998740\pi$
$701$	−5.11812	−	15.7519i	−0.193309	−	0.594943i	0.806684	−	0.590984i	$-0.201260\pi$
$702$	−7.74826	+	23.8467i	−0.292439	+	0.900036i
$703$	7.07531	+	5.14051i	0.266850	+	0.193878i
$704$	15.7774	+	48.5579i	0.594634	+	1.83009i
$705$	−21.4679	+	66.0715i	−0.808529	+	2.48840i
$706$	−12.9945	−	39.9931i	−0.489056	−	1.50516i
$707$	−11.1087	−	8.07094i	−0.417786	−	0.303539i
$708$	−106.845	−	77.6273i	−4.01547	−	2.91741i
$709$	37.7053			1.41605			0.708027	−	0.706186i	$-0.249586\pi$
$709$	37.7053			1.41605			0.708027	+	0.706186i	$0.249586\pi$
$710$	8.54750	−	72.8038i	0.320782	−	2.73228i
$711$	−9.53308			−0.357518
$712$	−35.6391	−	25.8933i	−1.33563	−	0.970394i
$713$	−3.05344	−	2.21845i	−0.114352	−	0.0830817i
$714$	−2.82314	−	8.68872i	−0.105653	−	0.325167i
$715$	5.78115	−	17.7925i	0.216203	−	0.665403i
$716$	6.51132	+	20.0398i	0.243339	+	0.748921i
$717$	−28.4032	−	20.6361i	−1.06074	−	0.770669i
$718$	−19.6176	+	60.3766i	−0.732121	+	2.25324i
$719$	−0.796320	−	2.45082i	−0.0296977	−	0.0914002i	0.935109	−	0.354360i	$-0.115301\pi$
$719$	−0.796320	−	2.45082i	−0.0296977	−	0.0914002i	−0.964807	+	0.262960i	$0.915301\pi$
$720$	46.8178	−	34.0151i	1.74480	−	1.26767i
$721$	2.45832	+	1.78607i	0.0915526	+	0.0665169i
$722$	−13.9898	+	43.0562i	−0.520647	+	1.60239i
$723$	−9.85583	+	7.16068i	−0.366542	+	0.266308i
$724$	−0.137352	−	0.422727i	−0.00510466	−	0.0157105i
$725$	0.536838	−	0.390035i	0.0199377	−	0.0144856i
$726$	−28.4794	+	20.6915i	−1.05697	+	0.767935i
$727$	26.8471	−	19.5055i	0.995703	−	0.723421i	0.0345404	−	0.999403i	$-0.489003\pi$
$727$	26.8471	−	19.5055i	0.995703	−	0.723421i	0.961163	+	0.275983i	$0.0890033\pi$
$728$	5.91655	−	18.2093i	0.219282	−	0.674880i
$729$	−5.48235	−	3.98316i	−0.203050	−	0.147524i
$730$	−13.0944			−0.484645
$731$	−1.12801	−	3.47167i	−0.0417211	−	0.128404i
$732$	5.69168	+	17.5172i	0.210371	+	0.647454i
$733$	−1.45359			−0.0536895			−0.0268447	−	0.999640i	$-0.508546\pi$
$733$	−1.45359			−0.0536895			−0.0268447	+	0.999640i	$0.508546\pi$
$734$	−10.8021	+	7.84821i	−0.398714	+	0.289683i
$735$	34.4350	+	25.0185i	1.27015	+	0.922821i
$736$	122.912			4.53059
$737$	−0.378673	+	1.16543i	−0.0139486	+	0.0429293i
$738$	−9.54127	+	29.3650i	−0.351219	+	1.08094i
$739$	−6.40984	+	19.7275i	−0.235790	+	0.725686i	0.761226	+	0.648487i	$0.224598\pi$
$739$	−6.40984	+	19.7275i	−0.235790	+	0.725686i	−0.997016	+	0.0771995i	$0.975402\pi$
$740$	99.5797			3.66062
$741$	−6.73773	−	4.89525i	−0.247517	−	0.179831i
$742$	28.3189			1.03962
$743$	10.9937	+	33.8350i	0.403318	+	1.24129i	0.922291	+	0.386496i	$0.126315\pi$
$743$	10.9937	+	33.8350i	0.403318	+	1.24129i	−0.518973	+	0.854791i	$0.673685\pi$
$744$	−10.6578			−0.390736
$745$	−26.6744	+	19.3801i	−0.977275	+	0.710032i
$746$	77.4870	−	56.2976i	2.83700	−	2.06120i
$747$	15.5714			0.569726
$748$	−7.21553	−	22.2071i	−0.263826	−	0.811972i
$749$	−3.19059			−0.116581
$750$	−5.30762	−	3.85621i	−0.193807	−	0.140809i
$751$	44.1032			1.60935			0.804674	−	0.593717i	$-0.202340\pi$
$751$	44.1032			1.60935			0.804674	+	0.593717i	$0.202340\pi$
$752$	−43.3339	+	133.368i	−1.58022	+	4.86343i
$753$	1.47228	−	4.53121i	0.0536528	−	0.165126i
$754$	0.275861	−	0.849012i	0.0100463	−	0.0309192i
$755$	−69.5777			−2.53219
$756$	11.9808	+	8.70454i	0.435737	+	0.316581i
$757$	−4.09456	+	2.97487i	−0.148819	+	0.108124i	−0.659703	−	0.751526i	$-0.729318\pi$
$757$	−4.09456	+	2.97487i	−0.148819	+	0.108124i	0.510884	+	0.859650i	$0.329318\pi$
$758$	−51.1564			−1.85809
$759$	−9.20930	−	28.3433i	−0.334276	−	1.02880i
$760$	−13.3160	−	40.9825i	−0.483023	−	1.48659i
$761$	−23.4507			−0.850087			−0.425043	−	0.905173i	$-0.639741\pi$
$761$	−23.4507			−0.850087			−0.425043	+	0.905173i	$0.639741\pi$
$762$	−45.4802	−	33.0433i	−1.64757	−	1.19703i
$763$	−2.20006	+	6.77108i	−0.0796474	+	0.245130i
$764$	−30.2373	+	21.9687i	−1.09395	+	0.794798i
$765$	−7.00251	+	5.08762i	−0.253176	+	0.183943i
$766$	73.5104	−	53.4084i	2.65604	−	1.92972i
$767$	9.87195	+	30.3827i	0.356456	+	1.09706i
$768$	39.3757	−	28.6081i	1.42085	−	1.03231i
$769$	−1.48005	+	4.55514i	−0.0533721	+	0.164262i	−0.974190	−	0.225731i	$-0.927523\pi$
$769$	−1.48005	+	4.55514i	−0.0533721	+	0.164262i	0.920817	+	0.389994i	$0.127523\pi$
$770$	−12.3101	−	8.94382i	−0.443626	−	0.322313i
$771$	34.4047	−	24.9965i	1.23905	−	0.900226i
$772$	−26.4665	−	81.4556i	−0.952551	−	2.93165i
$773$	−4.23166	+	13.0237i	−0.152202	+	0.468430i	−0.997867	−	0.0652847i	$-0.979204\pi$
$773$	−4.23166	+	13.0237i	−0.152202	+	0.468430i	0.845664	+	0.533715i	$0.179204\pi$
$774$	−5.24749	−	3.81253i	−0.188617	−	0.137038i
$775$	0.950694	+	2.92593i	0.0341499	+	0.105103i
$776$	−35.0310	+	107.814i	−1.25754	+	3.87031i
$777$	−3.01303	−	9.27316i	−0.108092	−	0.332673i
$778$	32.2856	+	23.4569i	1.15749	+	0.840969i
$779$	10.4231	+	7.57286i	0.373448	+	0.271326i
$780$	−94.8285			−3.39540
$781$	−17.9890	+	3.59581i	−0.643696	+	0.128668i
$782$	−35.9531			−1.28568
$783$	0.347953	+	0.252803i	0.0124348	+	0.00903442i
$784$	69.5084	+	50.5008i	2.48244	+	1.80360i
$785$	1.37092	+	4.21926i	0.0489303	+	0.150592i
$786$	2.86005	−	8.80234i	0.102015	−	0.313969i
$787$	−4.11562	−	12.6666i	−0.146706	−	0.451514i	0.850521	−	0.525942i	$-0.176287\pi$
$787$	−4.11562	−	12.6666i	−0.146706	−	0.451514i	−0.997226	+	0.0744275i	$0.976287\pi$
$788$	56.7973	+	41.2656i	2.02332	+	1.47003i
$789$	13.7066	−	42.1844i	0.487966	−	1.50181i
$790$	19.2745	+	59.3208i	0.685756	+	2.11054i
$791$	−10.4745	+	7.61019i	−0.372431	+	0.270587i
$792$	−20.9083	−	15.1908i	−0.742945	−	0.539781i
$793$	1.37678	−	4.23730i	0.0488910	−	0.150471i
$794$	33.7088	−	24.4909i	1.19628	−	0.869148i
$795$	−26.9976	−	83.0902i	−0.957508	−	2.94691i
$796$	−10.9952	+	7.98846i	−0.389714	+	0.283143i
$797$	39.7583	−	28.8861i	1.40831	−	1.02320i	0.414745	−	0.909937i	$-0.363871\pi$
$797$	39.7583	−	28.8861i	1.40831	−	1.02320i	0.993565	−	0.113260i	$-0.0361294\pi$
$798$	−5.48007	+	3.98150i	−0.193992	+	0.140944i
$799$	6.48141	−	19.9477i	0.229296	−	0.705700i
$800$	−81.0547	−	58.8897i	−2.86572	−	2.08207i
$801$	6.56073			0.231812
$802$	7.34475	+	22.6048i	0.259352	+	0.798204i
$803$	1.01264	+	3.11658i	0.0357352	+	0.109982i
$804$	6.21139			0.219059
$805$	−13.7640	+	10.0001i	−0.485118	+	0.352459i
$806$	3.34841	+	2.43276i	0.117943	+	0.0856903i
$807$	−22.5703			−0.794512
$808$	−47.1534	+	145.123i	−1.65885	+	5.10541i
$809$	−6.23242	+	19.1814i	−0.219120	+	0.674383i	0.779715	+	0.626134i	$0.215364\pi$
$809$	−6.23242	+	19.1814i	−0.219120	+	0.674383i	−0.998835	+	0.0482482i	$0.984636\pi$
$810$	30.1655	−	92.8399i	1.05991	−	3.26206i
$811$	14.0717			0.494123			0.247061	−	0.969000i	$-0.420535\pi$
$811$	14.0717			0.494123			0.247061	+	0.969000i	$0.420535\pi$
$812$	−0.426550	−	0.309907i	−0.0149690	−	0.0108756i
$813$	27.5565			0.966447
$814$	−10.6049	−	32.6386i	−0.371702	−	1.14398i
$815$	−23.2783			−0.815405
$816$	−46.0268	+	33.4404i	−1.61126	+	1.17065i
$817$	−2.18962	+	1.59085i	−0.0766051	+	0.0556569i
$818$	−64.7925			−2.26542
$819$	0.881153	+	2.71191i	0.0307900	+	0.0947618i
$820$	146.698			5.12291
$821$	−7.42463	−	5.39431i	−0.259122	−	0.188263i	0.450638	−	0.892707i	$-0.351196\pi$
$821$	−7.42463	−	5.39431i	−0.259122	−	0.188263i	−0.709760	+	0.704444i	$0.751196\pi$
$822$	−73.9820			−2.58042
$823$	−5.29317	+	16.2907i	−0.184508	+	0.567859i	−0.999940	−	0.0109955i	$-0.996500\pi$
$823$	−5.29317	+	16.2907i	−0.184508	+	0.567859i	0.815431	+	0.578854i	$0.196500\pi$
$824$	10.4349	−	32.1153i	0.363517	−	1.11879i
$825$	−7.50677	+	23.1035i	−0.261352	+	0.804360i
$826$	25.9832			0.904073
$827$	21.9489	+	15.9468i	0.763237	+	0.554524i	0.899901	−	0.436093i	$-0.143638\pi$
$827$	21.9489	+	15.9468i	0.763237	+	0.554524i	−0.136665	+	0.990617i	$0.543638\pi$
$828$	−37.5309	+	27.2678i	−1.30429	+	0.947621i
$829$	9.22240			0.320307			0.160154	−	0.987092i	$-0.448801\pi$
$829$	9.22240			0.320307			0.160154	+	0.987092i	$0.448801\pi$
$830$	−31.4830	−	96.8947i	−1.09279	−	3.36326i
$831$	14.3457	+	44.1516i	0.497648	+	1.53160i
$832$	−62.6016			−2.17032
$833$	−10.3963	−	7.55337i	−0.360211	−	0.261709i
$834$	−7.38539	+	22.7299i	−0.255735	+	0.787071i
$835$	39.6889	−	28.8356i	1.37349	−	0.997899i
$836$	−14.0063	+	10.1761i	−0.484417	+	0.351949i
$837$	−1.61322	+	1.17207i	−0.0557610	+	0.0405127i
$838$	−2.55706	−	7.86982i	−0.0883322	−	0.271859i
$839$	−1.44252	+	1.04805i	−0.0498013	+	0.0361828i	−0.612407	−	0.790542i	$-0.709799\pi$
$839$	−1.44252	+	1.04805i	−0.0498013	+	0.0361828i	0.562606	+	0.826725i	$0.309799\pi$
$840$	−14.8459	+	45.6911i	−0.512234	+	1.57649i
$841$	23.4491	+	17.0368i	0.808590	+	0.587475i
$842$	−2.62446	+	1.90678i	−0.0904447	+	0.0657119i
$843$	18.0205	+	55.4613i	0.620657	+	1.91019i
$844$	16.9369	−	52.1265i	0.582993	−	1.79427i
$845$	−15.2981	−	11.1147i	−0.526271	−	0.382358i
$846$	−11.5168	−	35.4450i	−0.395955	−	1.21863i
$847$	1.55413	−	4.78311i	0.0534004	−	0.164350i
$848$	−54.4958	−	167.721i	−1.87139	−	5.75955i
$849$	−4.64664	−	3.37598i	−0.159472	−	0.115863i
$850$	23.7094	+	17.2259i	0.813227	+	0.590844i
$851$	−38.3715			−1.31536
$852$	45.5115	+	81.0878i	1.55920	+	2.77802i
$853$	−41.3280			−1.41504			−0.707522	−	0.706691i	$-0.750187\pi$
$853$	−41.3280			−1.41504			−0.707522	+	0.706691i	$0.750187\pi$
$854$	−2.93166	−	2.12998i	−0.100319	−	0.0728862i
$855$	5.19197	+	3.77219i	0.177562	+	0.129006i
$856$	10.9566	+	33.7211i	0.374490	+	1.15256i
$857$	−12.1657	+	37.4421i	−0.415572	+	1.27900i	0.496167	+	0.868227i	$0.334740\pi$
$857$	−12.1657	+	37.4421i	−0.415572	+	1.27900i	−0.911739	+	0.410771i	$0.865260\pi$
$858$	10.0989	+	31.0813i	0.344772	+	1.06110i
$859$	−19.6337	−	14.2647i	−0.669894	−	0.486707i	0.200095	−	0.979776i	$-0.435875\pi$
$859$	−19.6337	−	14.2647i	−0.669894	−	0.486707i	−0.869990	+	0.493070i	$0.835875\pi$
$860$	−9.52306	+	29.3090i	−0.324734	+	0.999428i
$861$	−4.43871	−	13.6610i	−0.151271	−	0.465564i
$862$	−7.57675	+	5.50483i	−0.258065	+	0.187495i
$863$	23.5135	+	17.0836i	0.800410	+	0.581532i	0.911034	−	0.412330i	$-0.135285\pi$
$863$	23.5135	+	17.0836i	0.800410	+	0.581532i	−0.110624	+	0.993862i	$0.535285\pi$
$864$	20.0669	−	61.7596i	0.682690	−	2.10110i
$865$	18.4701	−	13.4193i	0.628003	−	0.456271i
$866$	−3.02580	−	9.31245i	−0.102821	−	0.316450i
$867$	−21.7333	+	15.7902i	−0.738102	+	0.536263i
$868$	1.97762	−	1.43683i	0.0671249	−	0.0487691i
$869$	12.6283	−	9.17500i	0.428386	−	0.311241i
$870$	−0.692196	+	2.13036i	−0.0234677	+	0.0722260i
$871$	−1.21555	−	0.883146i	−0.0411872	−	0.0299242i
$872$	79.1182			2.67928
$873$	−5.21717	−	16.0568i	−0.176575	−	0.543441i
$874$	8.23755	+	25.3526i	0.278639	+	0.857563i
$875$	0.937287			0.0316861
$876$	13.4381	−	9.76332i	0.454030	−	0.329872i
$877$	−30.3631	−	22.0601i	−1.02529	−	0.744917i	−0.0579292	−	0.998321i	$-0.518450\pi$
$877$	−30.3631	−	22.0601i	−1.02529	−	0.744917i	−0.967361	+	0.253404i	$0.918450\pi$
$878$	51.0531			1.72296
$879$	7.32640	−	22.5484i	0.247113	−	0.760537i
$880$	−29.2813	+	90.1186i	−0.987072	+	3.03790i
$881$	−10.7515	+	33.0896i	−0.362226	+	1.11482i	0.589473	+	0.807788i	$0.299335\pi$
$881$	−10.7515	+	33.0896i	−0.362226	+	1.11482i	−0.951700	+	0.307030i	$0.900665\pi$
$882$	−22.8341			−0.768864
$883$	−30.2371	−	21.9685i	−1.01756	−	0.739300i	−0.0517784	−	0.998659i	$-0.516489\pi$
$883$	−30.2371	−	21.9685i	−1.01756	−	0.739300i	−0.965781	+	0.259358i	$0.916489\pi$
$884$	28.6298			0.962924
$885$	−24.7709	−	76.2371i	−0.832666	−	2.56268i
$886$	29.7164			0.998342
$887$	45.3545	−	32.9520i	1.52285	−	1.10642i	0.562805	−	0.826590i	$-0.309722\pi$
$887$	45.3545	−	32.9520i	1.52285	−	1.10642i	0.960050	−	0.279829i	$-0.0902777\pi$
$888$	−87.6605	+	63.6891i	−2.94169	+	2.13727i
$889$	8.03147			0.269367
$890$	−13.2648	−	40.8250i	−0.444639	−	1.36846i
$891$	−24.4295			−0.818420
$892$	−53.4482	−	38.8324i	−1.78958	−	1.30020i
$893$	−15.5513			−0.520404
$894$	17.7984	−	54.7779i	0.595268	−	1.83205i
$895$	−3.95215	+	12.1635i	−0.132106	+	0.406580i
$896$	−6.45734	+	19.8737i	−0.215725	+	0.663932i
$897$	36.5407			1.22006
$898$	−55.8039	−	40.5439i	−1.86220	−	1.35297i
$899$	0.0574353	−	0.0417292i	0.00191557	−	0.00139175i
$900$	37.8144			1.26048
$901$	8.15089	+	25.0859i	0.271546	+	0.835731i
$902$	−15.6229	−	48.0822i	−0.520184	−	1.60096i
$903$	3.01748			0.100416
$904$	116.402	+	84.5708i	3.87146	+	2.81278i
$905$	0.0833682	−	0.256581i	0.00277125	−	0.00852904i
$906$	98.3307	−	71.4414i	3.26682	−	2.37348i
$907$	−36.8950	+	26.8058i	−1.22508	+	0.890071i	−0.996511	−	0.0834575i	$-0.973404\pi$
$907$	−36.8950	+	26.8058i	−1.22508	+	0.890071i	−0.228566	+	0.973528i	$0.573404\pi$
$908$	−50.1488	+	36.4352i	−1.66424	+	1.20914i
$909$	−7.02256	−	21.6132i	−0.232924	−	0.716865i
$910$	15.0936	−	10.9662i	0.500349	−	0.363525i
$911$	−14.1308	+	43.4902i	−0.468175	+	1.44090i	0.386770	+	0.922176i	$0.373591\pi$
$911$	−14.1308	+	43.4902i	−0.468175	+	1.44090i	−0.854945	+	0.518719i	$0.826409\pi$
$912$	34.1263	+	24.7942i	1.13004	+	0.821019i
$913$	−20.6271	+	14.9865i	−0.682657	+	0.495980i
$914$	−2.93754	−	9.04081i	−0.0971650	−	0.299043i
$915$	−3.45466	+	10.6323i	−0.114207	+	0.351494i
$916$	1.58620	+	1.15244i	0.0524095	+	0.0380777i
$917$	0.408606	+	1.25756i	0.0134933	+	0.0415283i
$918$	−5.86980	+	18.0654i	−0.193732	+	0.596246i
$919$	−0.453311	−	1.39515i	−0.0149534	−	0.0460217i	0.943301	−	0.331937i	$-0.107702\pi$
$919$	−0.453311	−	1.39515i	−0.0149534	−	0.0460217i	−0.958255	+	0.285916i	$0.907702\pi$
$920$	152.957	+	111.130i	5.04285	+	3.66385i
$921$	53.4181	+	38.8106i	1.76019	+	1.27885i
$922$	43.0510			1.41781
$923$	2.62276	−	22.3395i	0.0863291	−	0.735313i
$924$	19.3018			0.634983
$925$	25.3042	+	18.3846i	0.831997	+	0.604481i
$926$	−36.4058	−	26.4504i	−1.19637	−	0.869213i
$927$	1.55407	+	4.78294i	0.0510424	+	0.157092i
$928$	−0.714440	+	2.19882i	−0.0234526	+	0.0721798i
$929$	−12.5780	−	38.7110i	−0.412670	−	1.27007i	−0.914318	−	0.404996i	$-0.867273\pi$
$929$	−12.5780	−	38.7110i	−0.412670	−	1.27007i	0.501648	−	0.865072i	$-0.332727\pi$
$930$	−8.40190	−	6.10434i	−0.275509	−	0.200169i
$931$	−2.94431	+	9.06164i	−0.0964957	+	0.296983i
$932$	−3.35008	−	10.3105i	−0.109736	−	0.337731i
$933$	15.3469	−	11.1502i	0.502434	−	0.365040i
$934$	−48.0571	−	34.9155i	−1.57248	−	1.14247i
$935$	4.37958	−	13.4790i	0.143228	−	0.440809i
$936$	25.6361	−	18.6257i	0.837941	−	0.608800i
$937$	−10.2760	−	31.6264i	−0.335704	−	1.03319i	−0.966374	−	0.257139i	$-0.917220\pi$
$937$	−10.2760	−	31.6264i	−0.335704	−	1.03319i	0.630670	−	0.776051i	$-0.282780\pi$
$938$	−0.988653	+	0.718299i	−0.0322807	+	0.0234533i
$939$	26.7091	−	19.4053i	0.871618	−	0.633268i
$940$	−143.254	+	104.080i	−4.67243	+	3.39472i
$941$	−18.7554	+	57.7231i	−0.611407	+	1.88172i	−0.166805	+	0.985990i	$0.553345\pi$
$941$	−18.7554	+	57.7231i	−0.611407	+	1.88172i	−0.444602	+	0.895728i	$0.646655\pi$
$942$	−6.26973	−	4.55523i	−0.204279	−	0.148417i
$943$	−56.5278			−1.84080
$944$	−50.0011	−	153.887i	−1.62740	−	5.00861i
$945$	2.77763	+	8.54866i	0.0903562	+	0.278088i
$946$	10.6206			0.345305
$947$	23.8705	−	17.3429i	0.775686	−	0.563569i	−0.127995	−	0.991775i	$-0.540854\pi$
$947$	23.8705	−	17.3429i	0.775686	−	0.563569i	0.903681	+	0.428206i	$0.140854\pi$
$948$	−64.0107	−	46.5065i	−2.07897	−	1.51046i
$949$	−4.01794			−0.130428
$950$	6.71467	−	20.6656i	0.217853	−	0.670481i
$951$	−8.42029	+	25.9150i	−0.273047	+	0.840351i
$952$	4.48216	−	13.7947i	0.145268	−	0.447088i
$953$	47.4945			1.53850			0.769249	−	0.638949i	$-0.220630\pi$
$953$	47.4945			1.53850			0.769249	+	0.638949i	$0.220630\pi$
$954$	37.9177	+	27.5488i	1.22763	+	0.891926i
$955$	−22.6855			−0.734087
$956$	−27.6524	−	85.1052i	−0.894342	−	2.75250i
$957$	0.560575			0.0181208
$958$	64.1912	−	46.6376i	2.07392	−	1.50679i
$959$	8.55094	−	6.21262i	0.276124	−	0.200616i
$960$	157.082			5.06978
$961$	−9.47781	−	29.1697i	−0.305736	−	0.940958i
$962$	42.0782			1.35666
$963$	−4.27204	−	3.10382i	−0.137665	−	0.100019i
$964$	−31.0511			−1.00009
$965$	16.0643	−	49.4408i	0.517127	−	1.59155i
$966$	9.18399	−	28.2654i	0.295490	−	0.909425i
$967$	−4.20800	+	12.9509i	−0.135320	+	0.416473i	−0.995640	−	0.0932825i	$-0.970264\pi$
$967$	−4.20800	+	12.9509i	−0.135320	+	0.416473i	0.860320	+	0.509755i	$0.170264\pi$
$968$	−55.8893			−1.79635
$969$	−5.10425	−	3.70846i	−0.163972	−	0.119133i
$970$	−89.3672	+	64.9291i	−2.86941	+	2.08475i
$971$	−7.67596			−0.246333			−0.123167	−	0.992386i	$-0.539305\pi$
$971$	−7.67596			−0.246333			−0.123167	+	0.992386i	$0.539305\pi$
$972$	21.1766	+	65.1748i	0.679239	+	2.09048i
$973$	−1.05512	−	3.24734i	−0.0338257	−	0.104105i
$974$	−9.00818			−0.288641
$975$	−24.0969	−	17.5074i	−0.771718	−	0.560686i
$976$	−6.97336	+	21.4618i	−0.223212	+	0.686975i
$977$	−25.3157	+	18.3929i	−0.809920	+	0.588441i	−0.913807	−	0.406148i	$-0.866872\pi$
$977$	−25.3157	+	18.3929i	−0.809920	+	0.588441i	0.103888	+	0.994589i	$0.466872\pi$
$978$	32.8981	−	23.9019i	1.05197	−	0.764298i
$979$	−8.69089	+	6.31430i	−0.277762	+	0.201806i
$980$	33.5248	+	103.179i	1.07091	+	3.29592i
$981$	−9.53273	+	6.92593i	−0.304357	+	0.221128i
$982$	−18.6396	+	57.3669i	−0.594814	+	1.83065i
$983$	−30.8170	−	22.3899i	−0.982910	−	0.714126i	−0.0245533	−	0.999699i	$-0.507816\pi$
$983$	−30.8170	−	22.3899i	−0.982910	−	0.714126i	−0.958357	+	0.285572i	$0.907816\pi$
$984$	−129.139	+	93.8249i	−4.11680	+	2.99103i
$985$	13.1679	+	40.5266i	0.419564	+	1.29129i
$986$	0.208982	−	0.643180i	0.00665534	−	0.0204830i
$987$	14.0268	+	10.1910i	0.446477	+	0.324384i
$988$	−6.55963	−	20.1885i	−0.208690	−	0.642280i
$989$	3.66956	−	11.2938i	0.116685	−	0.359120i
$990$	−7.78206	−	23.9507i	−0.247330	−	0.761203i
$991$	39.2423	+	28.5112i	1.24657	+	0.905689i	0.998018	−	0.0629288i	$-0.0200441\pi$
$991$	39.2423	+	28.5112i	1.24657	+	0.905689i	0.248556	+	0.968618i	$0.420044\pi$
$992$	−8.67190	−	6.30050i	−0.275333	−	0.200041i
$993$	9.45975			0.300196
$994$	−16.6211	−	7.64351i	−0.527190	−	0.242437i
$995$	−8.24914			−0.261515
$996$	104.555	+	75.9638i	3.31296	+	2.40700i
$997$	−14.9817	−	10.8848i	−0.474474	−	0.344726i	0.324708	−	0.945814i	$-0.394734\pi$
$997$	−14.9817	−	10.8848i	−0.474474	−	0.344726i	−0.799182	+	0.601089i	$0.794734\pi$
$998$	12.3487	+	38.0055i	0.390893	+	1.20304i
$999$	−6.26462	+	19.2805i	−0.198204	+	0.610009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.c.a.54.1	yes	20
3.2	odd	2		639.2.f.c.622.5		20
71.5	even	5		5041.2.a.i.1.10		10
71.25	even	5	inner	71.2.c.a.25.1	✓	20
71.66	odd	10		5041.2.a.j.1.10		10
213.167	odd	10		639.2.f.c.451.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.c.a.25.1	✓	20	71.25	even	5	inner
71.2.c.a.54.1	yes	20	1.1	even	1	trivial
639.2.f.c.451.5		20	213.167	odd	10
639.2.f.c.622.5		20	3.2	odd	2
5041.2.a.i.1.10		10	71.5	even	5
5041.2.a.j.1.10		10	71.66	odd	10

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.18637 - 1.58849i) q^{2} +(1.68338 + 1.22305i) q^{3} +(1.63889 + 5.04397i) q^{4} +(-0.994748 + 3.06152i) q^{5} +(-1.73770 - 5.34809i) q^{6} +(0.649950 + 0.472216i) q^{7} +(2.75886 - 8.49090i) q^{8} +(0.410878 + 1.26455i) q^{9} +O(q^{10})\)	\(q+(-2.18637 - 1.58849i) q^{2} +(1.68338 + 1.22305i) q^{3} +(1.63889 + 5.04397i) q^{4} +(-0.994748 + 3.06152i) q^{5} +(-1.73770 - 5.34809i) q^{6} +(0.649950 + 0.472216i) q^{7} +(2.75886 - 8.49090i) q^{8} +(0.410878 + 1.26455i) q^{9} +(7.03810 - 5.11348i) q^{10} +(-1.76133 - 1.27968i) q^{11} +(-3.41015 + 10.4954i) q^{12} +(2.15960 - 1.56904i) q^{13} +(-0.670921 - 2.06488i) q^{14} +(-5.41893 + 3.93708i) q^{15} +(-10.9383 + 7.94715i) q^{16} +(1.63604 - 1.18865i) q^{17} +(1.11040 - 3.41746i) q^{18} +(-1.21303 - 0.881318i) q^{19} -17.0725 q^{20} +(0.516571 + 1.58984i) q^{21} +(1.81817 + 5.59574i) q^{22} +6.57862 q^{23} +(15.0290 - 10.9192i) q^{24} +(-4.33829 - 3.15195i) q^{25} -7.21412 q^{26} +(1.07404 - 3.30556i) q^{27} +(-1.31665 + 4.05224i) q^{28} +(-0.0382390 + 0.117688i) q^{29} +18.1018 q^{30} +(-0.464146 - 0.337222i) q^{31} +18.6835 q^{32} +(-1.39988 - 4.30840i) q^{33} -5.46515 q^{34} +(-2.09224 + 1.52010i) q^{35} +(-5.70498 + 4.14491i) q^{36} -5.83276 q^{37} +(1.25217 + 3.85378i) q^{38} +5.55446 q^{39} +(23.2507 + 16.8926i) q^{40} -8.59265 q^{41} +(1.39604 - 4.29656i) q^{42} +(0.557801 - 1.71674i) q^{43} +(3.56807 - 10.9814i) q^{44} -4.28017 q^{45} +(-14.3833 - 10.4501i) q^{46} +(8.39092 - 6.09636i) q^{47} -28.1331 q^{48} +(-1.96367 - 6.04356i) q^{49} +(4.47827 + 13.7827i) q^{50} +4.20785 q^{51} +(11.4536 + 8.32150i) q^{52} +(-4.03060 + 12.4049i) q^{53} +(-7.59912 + 5.52108i) q^{54} +(5.66986 - 4.11940i) q^{55} +(5.80266 - 4.21588i) q^{56} +(-0.964099 - 2.96719i) q^{57} +(0.270551 - 0.196567i) q^{58} +(-3.69817 + 11.3818i) q^{59} +(-28.7395 - 20.8805i) q^{60} +(1.35028 - 0.981037i) q^{61} +(0.479122 + 1.47459i) q^{62} +(-0.330092 + 1.01592i) q^{63} +(-18.9726 - 13.7844i) q^{64} +(2.65540 + 8.17247i) q^{65} +(-3.78320 + 11.6435i) q^{66} +(-0.173932 - 0.535308i) q^{67} +(8.67679 + 6.30406i) q^{68} +(11.0743 + 8.04597i) q^{69} +6.98908 q^{70} +(5.71386 - 6.19289i) q^{71} +11.8707 q^{72} +(-1.21771 - 0.884720i) q^{73} +(12.7526 + 9.26530i) q^{74} +(-3.44801 - 10.6119i) q^{75} +(2.45733 - 7.56287i) q^{76} +(-0.540492 - 1.66346i) q^{77} +(-12.1441 - 8.82323i) q^{78} +(-2.21557 + 6.81882i) q^{79} +(-13.4495 - 41.3933i) q^{80} +(9.07796 - 6.59552i) q^{81} +(18.7867 + 13.6494i) q^{82} +(3.61892 - 11.1379i) q^{83} +(-7.17252 + 5.21114i) q^{84} +(2.01163 + 6.19116i) q^{85} +(-3.94659 + 2.86736i) q^{86} +(-0.208309 + 0.151345i) q^{87} +(-15.7249 + 11.4248i) q^{88} +(1.52477 - 4.69276i) q^{89} +(9.35805 + 6.79902i) q^{90} +2.14456 q^{91} +(10.7816 + 33.1824i) q^{92} +(-0.368897 - 1.13535i) q^{93} -28.0297 q^{94} +(3.90483 - 2.83703i) q^{95} +(31.4516 + 22.8509i) q^{96} -12.6976 q^{97} +(-5.30684 + 16.3328i) q^{98} +(0.894534 - 2.75309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9	\( 20 q - 6 q^{2} - q^{3} - 10 q^{4} - q^{5} - 8 q^{6} - q^{7} - q^{8} - 10 q^{9} + 15 q^{10} - q^{11} + 4 q^{12} + 3 q^{13} + 5 q^{14} - 5 q^{15} - 16 q^{16} - 2 q^{17} + 36 q^{18} + 3 q^{19} - 72 q^{20} + 25 q^{21} + 10 q^{22} - 22 q^{23} + 19 q^{24} + 14 q^{25} - 42 q^{26} + 2 q^{27} + 4 q^{28} - q^{29} + 20 q^{30} + 6 q^{31} + 52 q^{32} + 10 q^{33} - 34 q^{34} + 3 q^{35} + 20 q^{36} - 6 q^{37} + 25 q^{38} - 86 q^{39} + 65 q^{40} - 60 q^{41} + 27 q^{42} + 23 q^{43} + 37 q^{44} - 44 q^{45} - 19 q^{46} + 29 q^{47} - 96 q^{48} + 22 q^{49} + 36 q^{50} + 34 q^{51} + 43 q^{52} + 2 q^{53} + 4 q^{54} + 10 q^{55} + 31 q^{56} - 18 q^{57} - 33 q^{58} + 31 q^{59} - 38 q^{60} - 2 q^{61} + 5 q^{62} + 23 q^{63} - 65 q^{64} + 54 q^{65} - 94 q^{66} - 38 q^{67} - 3 q^{68} + 11 q^{69} - 34 q^{70} + 45 q^{71} - 10 q^{72} - 21 q^{73} + 21 q^{74} + 13 q^{75} - q^{76} - 12 q^{77} - 6 q^{78} - 59 q^{79} - 16 q^{80} - 35 q^{81} + 53 q^{82} - 15 q^{83} - 33 q^{84} + 13 q^{85} - 19 q^{86} + 49 q^{87} - 64 q^{88} + 16 q^{89} + 86 q^{90} - 18 q^{91} + 86 q^{92} - 62 q^{94} + 15 q^{95} + 107 q^{96} - 58 q^{97} - 30 q^{98} + 30 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - q^3 - 10 * q^4 - q^5 - 8 * q^6 - q^7 - q^8 - 10 * q^9 + 15 * q^10 - q^11 + 4 * q^12 + 3 * q^13 + 5 * q^14 - 5 * q^15 - 16 * q^16 - 2 * q^17 + 36 * q^18 + 3 * q^19 - 72 * q^20 + 25 * q^21 + 10 * q^22 - 22 * q^23 + 19 * q^24 + 14 * q^25 - 42 * q^26 + 2 * q^27 + 4 * q^28 - q^29 + 20 * q^30 + 6 * q^31 + 52 * q^32 + 10 * q^33 - 34 * q^34 + 3 * q^35 + 20 * q^36 - 6 * q^37 + 25 * q^38 - 86 * q^39 + 65 * q^40 - 60 * q^41 + 27 * q^42 + 23 * q^43 + 37 * q^44 - 44 * q^45 - 19 * q^46 + 29 * q^47 - 96 * q^48 + 22 * q^49 + 36 * q^50 + 34 * q^51 + 43 * q^52 + 2 * q^53 + 4 * q^54 + 10 * q^55 + 31 * q^56 - 18 * q^57 - 33 * q^58 + 31 * q^59 - 38 * q^60 - 2 * q^61 + 5 * q^62 + 23 * q^63 - 65 * q^64 + 54 * q^65 - 94 * q^66 - 38 * q^67 - 3 * q^68 + 11 * q^69 - 34 * q^70 + 45 * q^71 - 10 * q^72 - 21 * q^73 + 21 * q^74 + 13 * q^75 - q^76 - 12 * q^77 - 6 * q^78 - 59 * q^79 - 16 * q^80 - 35 * q^81 + 53 * q^82 - 15 * q^83 - 33 * q^84 + 13 * q^85 - 19 * q^86 + 49 * q^87 - 64 * q^88 + 16 * q^89 + 86 * q^90 - 18 * q^91 + 86 * q^92 - 62 * q^94 + 15 * q^95 + 107 * q^96 - 58 * q^97 - 30 * q^98 + 30 * q^99

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