LMFDB - Embedded newform 71.2.c.a.5.4

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			5.4
Root			$-0.420063 + 1.29282i$ of defining polynomial
Character	$\chi$	$=$	71.5
Dual form			71.2.c.a.57.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.420063 + 1.29282i) q^{2} +(0.672312 + 2.06916i) q^{3} +(0.123097 - 0.0894354i) q^{4} +(-2.53185 - 1.83950i) q^{5} +(-2.39265 + 1.73836i) q^{6} +(-1.31457 - 4.04584i) q^{7} +(2.36681 + 1.71959i) q^{8} +(-1.40238 + 1.01889i) q^{9} +O(q^{10})$	\(q+(0.420063 + 1.29282i) q^{2} +(0.672312 + 2.06916i) q^{3} +(0.123097 - 0.0894354i) q^{4} +(-2.53185 - 1.83950i) q^{5} +(-2.39265 + 1.73836i) q^{6} +(-1.31457 - 4.04584i) q^{7} +(2.36681 + 1.71959i) q^{8} +(-1.40238 + 1.01889i) q^{9} +(1.31461 - 4.04595i) q^{10} +(0.802829 + 2.47085i) q^{11} +(0.267816 + 0.194580i) q^{12} +(-1.18431 + 3.64494i) q^{13} +(4.67835 - 3.39902i) q^{14} +(2.10403 - 6.47554i) q^{15} +(-1.13488 + 3.49279i) q^{16} +(-0.514419 + 1.58322i) q^{17} +(-1.90633 - 1.38503i) q^{18} +(-2.14855 - 6.61255i) q^{19} -0.476181 q^{20} +(7.48770 - 5.44013i) q^{21} +(-2.85714 + 2.07583i) q^{22} -4.87491 q^{23} +(-1.96688 + 6.05342i) q^{24} +(1.48144 + 4.55941i) q^{25} -5.20974 q^{26} +(2.22933 + 1.61970i) q^{27} +(-0.523662 - 0.380463i) q^{28} +(0.829618 + 0.602753i) q^{29} +9.25554 q^{30} +(-1.21584 - 3.74197i) q^{31} +0.858810 q^{32} +(-4.57285 + 3.32237i) q^{33} -2.26291 q^{34} +(-4.11402 + 12.6616i) q^{35} +(-0.0815044 + 0.250845i) q^{36} +6.90721 q^{37} +(7.64632 - 5.55538i) q^{38} -8.33819 q^{39} +(-2.82924 - 8.70751i) q^{40} -3.25301 q^{41} +(10.1784 + 7.39507i) q^{42} +(5.06571 + 3.68045i) q^{43} +(0.319808 + 0.232354i) q^{44} +5.42486 q^{45} +(-2.04777 - 6.30239i) q^{46} +(-0.919569 + 2.83014i) q^{47} -7.99014 q^{48} +(-8.97761 + 6.52262i) q^{49} +(-5.27221 + 3.83049i) q^{50} -3.62179 q^{51} +(0.180201 + 0.554601i) q^{52} +(2.74839 + 1.99682i) q^{53} +(-1.15753 + 3.56250i) q^{54} +(2.51249 - 7.73265i) q^{55} +(3.84584 - 11.8363i) q^{56} +(12.2379 - 8.89138i) q^{57} +(-0.430760 + 1.32574i) q^{58} +(0.332599 + 0.241648i) q^{59} +(-0.320142 - 0.985296i) q^{60} +(0.569635 - 1.75316i) q^{61} +(4.32698 - 3.14373i) q^{62} +(5.96579 + 4.33440i) q^{63} +(2.63051 + 8.09587i) q^{64} +(9.70337 - 7.04991i) q^{65} +(-6.21612 - 4.51627i) q^{66} +(-7.81299 + 5.67647i) q^{67} +(0.0782723 + 0.240897i) q^{68} +(-3.27746 - 10.0870i) q^{69} -18.0974 q^{70} +(2.18500 - 8.13792i) q^{71} -5.07124 q^{72} +(2.11717 + 6.51599i) q^{73} +(2.90147 + 8.92980i) q^{74} +(-8.43817 + 6.13069i) q^{75} +(-0.855876 - 0.621831i) q^{76} +(8.94131 - 6.49624i) q^{77} +(-3.50257 - 10.7798i) q^{78} +(-6.72113 - 4.88318i) q^{79} +(9.29833 - 6.75563i) q^{80} +(-3.45960 + 10.6476i) q^{81} +(-1.36647 - 4.20556i) q^{82} +(-5.85783 - 4.25596i) q^{83} +(0.435175 - 1.33933i) q^{84} +(4.21477 - 3.06221i) q^{85} +(-2.63025 + 8.09508i) q^{86} +(-0.689431 + 2.12185i) q^{87} +(-2.34871 + 7.22859i) q^{88} +(4.44552 + 3.22986i) q^{89} +(2.27879 + 7.01338i) q^{90} +16.3037 q^{91} +(-0.600088 + 0.435990i) q^{92} +(6.92533 - 5.03154i) q^{93} -4.04515 q^{94} +(-6.72397 + 20.6943i) q^{95} +(0.577388 + 1.77702i) q^{96} +13.7133 q^{97} +(-12.2038 - 8.86655i) q^{98} +(-3.64339 - 2.64708i) 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 $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.420063	+	1.29282i	0.297030	+	0.914164i	0.982532	+	0.186093i	$0.0595826\pi$
$2$	0.420063	+	1.29282i	0.297030	+	0.914164i	−0.685502	+	0.728070i	$0.740417\pi$
$3$	0.672312	+	2.06916i	0.388159	+	1.19463i	0.934162	+	0.356848i	$0.116149\pi$
$3$	0.672312	+	2.06916i	0.388159	+	1.19463i	−0.546003	+	0.837783i	$0.683851\pi$
$4$	0.123097	−	0.0894354i	0.0615487	−	0.0447177i
$5$	−2.53185	−	1.83950i	−1.13228	−	0.822650i	−0.146255	−	0.989247i	$-0.546722\pi$
$5$	−2.53185	−	1.83950i	−1.13228	−	0.822650i	−0.986025	+	0.166597i	$0.946722\pi$
$6$	−2.39265	+	1.73836i	−0.976794	+	0.709682i
$7$	−1.31457	−	4.04584i	−0.496862	−	1.52918i	−0.814035	−	0.580817i	$-0.802733\pi$
$7$	−1.31457	−	4.04584i	−0.496862	−	1.52918i	0.317172	−	0.948368i	$-0.397267\pi$
$8$	2.36681	+	1.71959i	0.836795	+	0.607967i
$9$	−1.40238	+	1.01889i	−0.467459	+	0.339629i
$10$	1.31461	−	4.04595i	0.415715	−	1.27944i
$11$	0.802829	+	2.47085i	0.242062	+	0.744990i	0.996106	+	0.0881662i	$0.0281007\pi$
$11$	0.802829	+	2.47085i	0.242062	+	0.744990i	−0.754044	+	0.656824i	$0.771899\pi$
$12$	0.267816	+	0.194580i	0.0773119	+	0.0561704i
$13$	−1.18431	+	3.64494i	−0.328469	+	1.01092i	0.641381	+	0.767222i	$0.278362\pi$
$13$	−1.18431	+	3.64494i	−0.328469	+	1.01092i	−0.969850	+	0.243701i	$0.921638\pi$
$14$	4.67835	−	3.39902i	1.25034	−	0.908427i
$15$	2.10403	−	6.47554i	0.543258	−	1.67198i
$16$	−1.13488	+	3.49279i	−0.283719	+	0.873197i
$17$	−0.514419	+	1.58322i	−0.124765	+	0.383987i	−0.993858	−	0.110661i	$-0.964703\pi$
$17$	−0.514419	+	1.58322i	−0.124765	+	0.383987i	0.869093	+	0.494648i	$0.164703\pi$
$18$	−1.90633	−	1.38503i	−0.449326	−	0.326454i
$19$	−2.14855	−	6.61255i	−0.492910	−	1.51702i	−0.820188	−	0.572094i	$-0.806131\pi$
$19$	−2.14855	−	6.61255i	−0.492910	−	1.51702i	0.327278	−	0.944928i	$-0.393869\pi$
$20$	−0.476181			−0.106477
$21$	7.48770	−	5.44013i	1.63395	−	1.18713i
$22$	−2.85714	+	2.07583i	−0.609143	+	0.442569i
$23$	−4.87491			−1.01649			−0.508244	−	0.861213i	$-0.669705\pi$
$23$	−4.87491			−1.01649			−0.508244	+	0.861213i	$0.669705\pi$
$24$	−1.96688	+	6.05342i	−0.401487	+	1.23565i
$25$	1.48144	+	4.55941i	0.296289	+	0.911882i
$26$	−5.20974			−1.02171
$27$	2.22933	+	1.61970i	0.429034	+	0.311711i
$28$	−0.523662	−	0.380463i	−0.0989628	−	0.0719007i
$29$	0.829618	+	0.602753i	0.154056	+	0.111928i	0.662143	−	0.749377i	$-0.269647\pi$
$29$	0.829618	+	0.602753i	0.154056	+	0.111928i	−0.508087	+	0.861306i	$0.669647\pi$
$30$	9.25554			1.68982
$31$	−1.21584	−	3.74197i	−0.218371	−	0.672078i	−0.998897	−	0.0469544i	$-0.985048\pi$
$31$	−1.21584	−	3.74197i	−0.218371	−	0.672078i	0.780526	−	0.625124i	$-0.214952\pi$
$32$	0.858810			0.151818
$33$	−4.57285	+	3.32237i	−0.796030	+	0.578350i
$34$	−2.26291			−0.388086
$35$	−4.11402	+	12.6616i	−0.695396	+	2.14021i
$36$	−0.0815044	+	0.250845i	−0.0135841	+	0.0418074i
$37$	6.90721			1.13554			0.567769	−	0.823188i	$-0.307807\pi$
$37$	6.90721			1.13554			0.567769	+	0.823188i	$0.307807\pi$
$38$	7.64632	−	5.55538i	1.24040	−	0.901201i
$39$	−8.33819			−1.33518
$40$	−2.82924	−	8.70751i	−0.447342	−	1.37678i
$41$	−3.25301			−0.508034			−0.254017	−	0.967200i	$-0.581752\pi$
$41$	−3.25301			−0.508034			−0.254017	+	0.967200i	$0.581752\pi$
$42$	10.1784	+	7.39507i	1.57057	+	1.14108i
$43$	5.06571	+	3.68045i	0.772513	+	0.561264i	0.902723	−	0.430223i	$-0.141565\pi$
$43$	5.06571	+	3.68045i	0.772513	+	0.561264i	−0.130210	+	0.991486i	$0.541565\pi$
$44$	0.319808	+	0.232354i	0.0482129	+	0.0350287i
$45$	5.42486			0.808691
$46$	−2.04777	−	6.30239i	−0.301927	−	0.929237i
$47$	−0.919569	+	2.83014i	−0.134133	+	0.412818i	−0.995454	−	0.0952422i	$-0.969637\pi$
$47$	−0.919569	+	2.83014i	−0.134133	+	0.412818i	0.861321	+	0.508061i	$0.169637\pi$
$48$	−7.99014			−1.15328
$49$	−8.97761	+	6.52262i	−1.28252	+	0.931802i
$50$	−5.27221	+	3.83049i	−0.745603	+	0.541712i
$51$	−3.62179			−0.507152
$52$	0.180201	+	0.554601i	0.0249894	+	0.0769094i
$53$	2.74839	+	1.99682i	0.377520	+	0.274285i	0.760322	−	0.649546i	$-0.225041\pi$
$53$	2.74839	+	1.99682i	0.377520	+	0.274285i	−0.382802	+	0.923830i	$0.625041\pi$
$54$	−1.15753	+	3.56250i	−0.157519	+	0.484795i
$55$	2.51249	−	7.73265i	0.338784	−	1.04267i
$56$	3.84584	−	11.8363i	0.513922	−	1.58169i
$57$	12.2379	−	8.89138i	1.62095	−	1.17769i
$58$	−0.430760	+	1.32574i	−0.0565616	+	0.174079i
$59$	0.332599	+	0.241648i	0.0433008	+	0.0314598i	0.609225	−	0.792997i	$-0.291481\pi$
$59$	0.332599	+	0.241648i	0.0433008	+	0.0314598i	−0.565924	+	0.824457i	$0.691481\pi$
$60$	−0.320142	−	0.985296i	−0.0413302	−	0.127201i
$61$	0.569635	−	1.75316i	0.0729343	−	0.224469i	−0.907944	−	0.419092i	$-0.862348\pi$
$61$	0.569635	−	1.75316i	0.0729343	−	0.224469i	0.980878	+	0.194623i	$0.0623485\pi$
$62$	4.32698	−	3.14373i	0.549527	−	0.399254i
$63$	5.96579	+	4.33440i	0.751618	+	0.546083i
$64$	2.63051	+	8.09587i	0.328813	+	1.01198i
$65$	9.70337	−	7.04991i	1.20355	−	0.874433i
$66$	−6.21612	−	4.51627i	−0.765151	−	0.555915i
$67$	−7.81299	+	5.67647i	−0.954508	+	0.693491i	−0.951869	−	0.306506i	$-0.900840\pi$
$67$	−7.81299	+	5.67647i	−0.954508	+	0.693491i	−0.00263931	+	0.999997i	$0.500840\pi$
$68$	0.0782723	+	0.240897i	0.00949191	+	0.0292131i
$69$	−3.27746	−	10.0870i	−0.394560	−	1.21433i
$70$	−18.0974			−2.16305
$71$	2.18500	−	8.13792i	0.259312	−	0.965794i
$71$	2.18500	−	8.13792i	0.259312	−	0.965794i
$72$	−5.07124			−0.597651
$73$	2.11717	+	6.51599i	0.247796	+	0.762639i	0.995164	+	0.0982279i	$0.0313174\pi$
$73$	2.11717	+	6.51599i	0.247796	+	0.762639i	−0.747368	+	0.664411i	$0.768683\pi$
$74$	2.90147	+	8.92980i	0.337289	+	1.03807i
$75$	−8.43817	+	6.13069i	−0.974356	+	0.707911i
$76$	−0.855876	−	0.621831i	−0.0981758	−	0.0713289i
$77$	8.94131	−	6.49624i	1.01896	−	0.740315i
$78$	−3.50257	−	10.7798i	−0.396588	−	1.22057i
$79$	−6.72113	−	4.88318i	−0.756186	−	0.549401i	0.141552	−	0.989931i	$-0.454791\pi$
$79$	−6.72113	−	4.88318i	−0.756186	−	0.549401i	−0.897738	+	0.440530i	$0.854791\pi$
$80$	9.29833	−	6.75563i	1.03958	−	0.755302i
$81$	−3.45960	+	10.6476i	−0.384400	+	1.18306i
$82$	−1.36647	−	4.20556i	−0.150901	−	0.464427i
$83$	−5.85783	−	4.25596i	−0.642980	−	0.467153i	0.217892	−	0.975973i	$-0.430082\pi$
$83$	−5.85783	−	4.25596i	−0.642980	−	0.467153i	−0.860873	+	0.508820i	$0.830082\pi$
$84$	0.435175	−	1.33933i	0.0474815	−	0.146133i
$85$	4.21477	−	3.06221i	0.457156	−	0.332143i
$86$	−2.63025	+	8.09508i	−0.283627	+	0.872915i
$87$	−0.689431	+	2.12185i	−0.0739148	+	0.227486i
$88$	−2.34871	+	7.22859i	−0.250373	+	0.770570i
$89$	4.44552	+	3.22986i	0.471225	+	0.342365i	0.797918	−	0.602766i	$-0.205935\pi$
$89$	4.44552	+	3.22986i	0.471225	+	0.342365i	−0.326694	+	0.945130i	$0.605935\pi$
$90$	2.27879	+	7.01338i	0.240205	+	0.739275i
$91$	16.3037			1.70909
$92$	−0.600088	+	0.435990i	−0.0625635	+	0.0454551i
$93$	6.92533	−	5.03154i	0.718123	−	0.521747i
$94$	−4.04515			−0.417225
$95$	−6.72397	+	20.6943i	−0.689865	+	2.12319i
$96$	0.577388	+	1.77702i	0.0589294	+	0.181366i
$97$	13.7133			1.39238			0.696190	−	0.717858i	$-0.254877\pi$
$97$	13.7133			1.39238			0.696190	+	0.717858i	$0.254877\pi$
$98$	−12.2038	−	8.86655i	−1.23277	−	0.895656i
$99$	−3.64339	−	2.64708i	−0.366175	−	0.266041i
$100$	0.590135	+	0.428758i	0.0590135	+	0.0428758i
$101$	3.75113			0.373252			0.186626	−	0.982431i	$-0.440245\pi$
$101$	3.75113			0.373252			0.186626	+	0.982431i	$0.440245\pi$
$102$	−1.52138	−	4.68233i	−0.150639	−	0.463619i
$103$	4.58382			0.451657			0.225828	−	0.974167i	$-0.427491\pi$
$103$	4.58382			0.451657			0.225828	+	0.974167i	$0.427491\pi$
$104$	−9.07084	+	6.59035i	−0.889469	+	0.646237i
$105$	−28.9649			−2.82668
$106$	−1.42704	+	4.39197i	−0.138606	+	0.426586i
$107$	0.0622978	−	0.191733i	0.00602255	−	0.0185355i	−0.948000	−	0.318270i	$-0.896898\pi$
$107$	0.0622978	−	0.191733i	0.00602255	−	0.0185355i	0.954023	+	0.299735i	$0.0968981\pi$
$108$	0.419283			0.0403455
$109$	3.58093	−	2.60170i	0.342991	−	0.249198i	−0.402932	−	0.915230i	$-0.632009\pi$
$109$	3.58093	−	2.60170i	0.342991	−	0.249198i	0.745923	+	0.666032i	$0.232009\pi$
$110$	11.0523			1.05380
$111$	4.64380	+	14.2921i	0.440770	+	1.35655i
$112$	15.6231			1.47625
$113$	−10.2559	−	7.45138i	−0.964798	−	0.700967i	−0.0105379	−	0.999944i	$-0.503354\pi$
$113$	−10.2559	−	7.45138i	−0.964798	−	0.700967i	−0.954260	+	0.298978i	$0.903354\pi$
$114$	16.6357	+	12.0865i	1.55808	+	1.13201i
$115$	12.3426	+	8.96740i	1.15095	+	0.836214i
$116$	0.156031			0.0144871
$117$	−2.05293	−	6.31826i	−0.189793	−	0.584123i
$118$	−0.172695	+	0.531499i	−0.0158978	+	0.0489285i
$119$	7.08170			0.649178
$120$	16.1151	−	11.7083i	1.47110	−	1.06882i
$121$	3.43860	−	2.49829i	0.312600	−	0.227117i
$122$	2.50580			0.226865
$123$	−2.18703	−	6.73100i	−0.197198	−	0.606914i
$124$	−0.484332	−	0.351888i	−0.0434943	−	0.0316004i
$125$	−0.199171	+	0.612985i	−0.0178144	+	0.0548270i
$126$	−3.09760	+	9.53342i	−0.275956	+	0.849305i
$127$	−0.431074	+	1.32671i	−0.0382516	+	0.117726i	−0.968359	−	0.249561i	$-0.919714\pi$
$127$	−0.431074	+	1.32671i	−0.0382516	+	0.117726i	0.930107	+	0.367288i	$0.119714\pi$
$128$	−7.97195	+	5.79196i	−0.704628	+	0.511942i
$129$	−4.20972	+	12.9562i	−0.370645	+	1.14073i
$130$	13.1903	+	9.58332i	1.15687	+	0.840513i
$131$	−5.92233	−	18.2271i	−0.517436	−	1.59250i	−0.778805	−	0.627266i	$-0.784174\pi$
$131$	−5.92233	−	18.2271i	−0.517436	−	1.59250i	0.261369	−	0.965239i	$-0.415826\pi$
$132$	−0.265768	+	0.817949i	−0.0231321	+	0.0711933i
$133$	−23.9289	+	17.3854i	−2.07490	+	1.50750i
$134$	−10.6206	−	7.71633i	−0.917481	−	0.666589i
$135$	−2.66489	−	8.20169i	−0.229357	−	0.705889i
$136$	−3.94002	+	2.86259i	−0.337854	+	0.245465i
$137$	−15.8872	−	11.5427i	−1.35734	−	0.986163i	−0.998609	−	0.0527202i	$-0.983211\pi$
$137$	−15.8872	−	11.5427i	−1.35734	−	0.986163i	−0.358727	−	0.933442i	$-0.616789\pi$
$138$	11.6639	−	8.47434i	0.992900	−	0.721384i
$139$	−4.80264	−	14.7810i	−0.407355	−	1.25371i	−0.918913	−	0.394461i	$-0.870931\pi$
$139$	−4.80264	−	14.7810i	−0.407355	−	1.25371i	0.511558	−	0.859249i	$-0.329069\pi$
$140$	0.625975	+	1.92655i	0.0529046	+	0.162823i
$141$	−6.47426			−0.545231
$142$	11.4387	−	0.593622i	0.959917	−	0.0498157i
$143$	−9.95690			−0.832638
$144$	−1.96723	−	6.05452i	−0.163936	−	0.504543i
$145$	−0.991708	−	3.05216i	−0.0823569	−	0.253468i
$146$	−7.53467	+	5.47426i	−0.623573	+	0.453053i
$147$	−19.5321	−	14.1909i	−1.61098	−	1.17045i
$148$	0.850259	−	0.617750i	0.0698909	−	0.0507787i
$149$	2.07646	+	6.39069i	0.170110	+	0.523545i	0.999376	−	0.0353083i	$-0.0112413\pi$
$149$	2.07646	+	6.39069i	0.170110	+	0.523545i	−0.829266	+	0.558854i	$0.811241\pi$
$150$	−11.4705	−	8.33378i	−0.936559	−	0.680450i
$151$	8.10050	−	5.88536i	0.659210	−	0.478944i	−0.207186	−	0.978302i	$-0.566431\pi$
$151$	8.10050	−	5.88536i	0.659210	−	0.478944i	0.866396	+	0.499358i	$0.166431\pi$
$152$	6.28566	−	19.3453i	0.509835	−	1.56911i
$153$	−0.891712	−	2.74441i	−0.0720906	−	0.221872i
$154$	12.1544	+	8.83069i	0.979429	+	0.711597i
$155$	−3.80503	+	11.7107i	−0.305627	+	0.940624i
$156$	−1.02641	+	0.745730i	−0.0821785	+	0.0597062i
$157$	−2.83410	+	8.72247i	−0.226186	+	0.696129i	0.771983	+	0.635643i	$0.219265\pi$
$157$	−2.83410	+	8.72247i	−0.226186	+	0.696129i	−0.998169	+	0.0604858i	$0.980735\pi$
$158$	3.48979	−	10.7405i	0.277633	−	0.854466i
$159$	−2.28397	+	7.02935i	−0.181131	+	0.557464i
$160$	−2.17438	−	1.57978i	−0.171900	−	0.124893i
$161$	6.40843	+	19.7231i	0.505055	+	1.55440i
$162$	−15.2187			−1.19569
$163$	15.8141	−	11.4896i	1.23866	−	0.899939i	0.241151	−	0.970488i	$-0.422475\pi$
$163$	15.8141	−	11.4896i	1.23866	−	0.899939i	0.997508	+	0.0705489i	$0.0224751\pi$
$164$	−0.400437	+	0.290934i	−0.0312688	+	0.0227181i
$165$	17.6893			1.37711
$166$	3.04154	−	9.36091i	0.236070	−	0.726547i
$167$	−6.20089	−	19.0844i	−0.479840	−	1.47679i	−0.839318	−	0.543641i	$-0.817045\pi$
$167$	−6.20089	−	19.0844i	−0.479840	−	1.47679i	0.359478	−	0.933153i	$-0.382955\pi$
$168$	27.0768			2.08902
$169$	−1.36574	−	0.992271i	−0.105057	−	0.0763285i
$170$	5.72936	+	4.16262i	0.439422	+	0.319259i
$171$	9.75051	+	7.08416i	0.745640	+	0.541740i
$172$	0.952738			0.0726456
$173$	3.43572	+	10.5741i	0.261213	+	0.803932i	0.992542	+	0.121906i	$0.0389007\pi$
$173$	3.43572	+	10.5741i	0.261213	+	0.803932i	−0.731328	+	0.682025i	$0.761099\pi$
$174$	−3.03278			−0.229915
$175$	16.4992	−	11.9874i	1.24722	−	0.906160i
$176$	−9.54128			−0.719201
$177$	−0.276398	+	0.850665i	−0.0207753	+	0.0639399i
$178$	−2.30824	+	7.10402i	−0.173010	+	0.532469i
$179$	22.0389			1.64726			0.823632	−	0.567125i	$-0.191944\pi$
$179$	22.0389			1.64726			0.823632	+	0.567125i	$0.191944\pi$
$180$	0.667786	−	0.485175i	0.0497738	−	0.0361628i
$181$	−11.6108			−0.863025			−0.431513	−	0.902107i	$-0.642020\pi$
$181$	−11.6108			−0.863025			−0.431513	+	0.902107i	$0.642020\pi$
$182$	6.84859	+	21.0778i	0.507651	+	1.56239i
$183$	4.01054			0.296467
$184$	−11.5380	−	8.38285i	−0.850593	−	0.617992i
$185$	−17.4881	−	12.7058i	−1.28575	−	0.934150i
$186$	9.41397	+	6.83965i	0.690266	+	0.501507i
$187$	−4.32489			−0.316268
$188$	0.139918	+	0.430625i	0.0102046	+	0.0314065i
$189$	3.62244	−	11.1487i	0.263493	−	0.810949i
$190$	−29.5785			−2.14585
$191$	−4.51578	+	3.28091i	−0.326750	+	0.237398i	−0.739051	−	0.673650i	$-0.764726\pi$
$191$	−4.51578	+	3.28091i	−0.326750	+	0.237398i	0.412300	+	0.911048i	$0.364726\pi$
$192$	−14.9831	+	10.8859i	−1.08131	+	0.785621i
$193$	9.65947			0.695304			0.347652	−	0.937624i	$-0.386979\pi$
$193$	9.65947			0.695304			0.347652	+	0.937624i	$0.386979\pi$
$194$	5.76048	+	17.7289i	0.413578	+	1.27286i
$195$	21.1111	+	15.3381i	1.51180	+	1.09838i
$196$	−0.521767	+	1.60583i	−0.0372691	+	0.114702i
$197$	−0.300539	+	0.924963i	−0.0214125	+	0.0659009i	−0.961192	−	0.275881i	$-0.911030\pi$
$197$	−0.300539	+	0.924963i	−0.0214125	+	0.0659009i	0.939779	+	0.341782i	$0.111030\pi$
$198$	1.89175	−	5.82220i	0.134441	−	0.413766i
$199$	−12.7620	+	9.27215i	−0.904676	+	0.657285i	−0.939663	−	0.342103i	$-0.888861\pi$
$199$	−12.7620	+	9.27215i	−0.904676	+	0.657285i	0.0349871	+	0.999388i	$0.488861\pi$
$200$	−4.33402	+	13.3388i	−0.306462	+	0.943192i
$201$	−16.9983	−	12.3500i	−1.19897	−	0.871100i
$202$	1.57571	+	4.84955i	0.110867	+	0.341213i
$203$	1.34805	−	4.14887i	0.0946144	−	0.291193i
$204$	−0.445832	+	0.323916i	−0.0312145	+	0.0226787i
$205$	8.23614	+	5.98391i	0.575237	+	0.417934i
$206$	1.92549	+	5.92606i	0.134156	+	0.412888i
$207$	6.83647	−	4.96698i	0.475167	−	0.345229i
$208$	−11.3869	−	8.27310i	−0.789542	−	0.573636i
$209$	14.6137	−	10.6175i	1.01085	−	0.734427i
$210$	−12.1671	−	37.4465i	−0.839609	−	2.58405i
$211$	5.85429	+	18.0176i	0.403026	+	1.24039i	0.922533	+	0.385919i	$0.126116\pi$
$211$	5.85429	+	18.0176i	0.403026	+	1.24039i	−0.519507	+	0.854466i	$0.673884\pi$
$212$	0.516906			0.0355012
$213$	18.3077	−	0.950092i	1.25442	−	0.0650993i
$214$	0.274046			0.0187334
$215$	−6.05544	−	18.6367i	−0.412978	−	1.27101i
$216$	2.49118	+	7.66705i	0.169503	+	0.521677i
$217$	−13.5411	+	9.83820i	−0.919231	+	0.667860i
$218$	4.86776	+	3.53663i	0.329686	+	0.239531i
$219$	−12.0592	+	8.76155i	−0.814887	+	0.592050i
$220$	−0.382292	−	1.17657i	−0.0257741	−	0.0793246i
$221$	−5.16150	−	3.75005i	−0.347200	−	0.252256i
$222$	−16.5265	+	12.0072i	−1.10919	+	0.805871i
$223$	−8.76855	+	26.9868i	−0.587186	+	1.80717i	0.00312362	+	0.999995i	$0.499006\pi$
$223$	−8.76855	+	26.9868i	−0.587186	+	1.80717i	−0.590309	+	0.807177i	$0.700994\pi$
$224$	−1.12897	−	3.47461i	−0.0754324	−	0.232157i
$225$	−6.72307	−	4.88460i	−0.448205	−	0.325640i
$226$	5.32516	−	16.3892i	0.354225	−	1.09019i
$227$	2.39001	−	1.73644i	0.158630	−	0.115252i	−0.505638	−	0.862745i	$-0.668743\pi$
$227$	2.39001	−	1.73644i	0.158630	−	0.115252i	0.664269	+	0.747494i	$0.268743\pi$
$228$	0.711253	−	2.18901i	0.0471039	−	0.144971i
$229$	−5.95231	+	18.3193i	−0.393340	+	1.21058i	0.536907	+	0.843642i	$0.319593\pi$
$229$	−5.95231	+	18.3193i	−0.393340	+	1.21058i	−0.930247	+	0.366934i	$0.880407\pi$
$230$	−6.40859	+	19.7236i	−0.422570	+	1.30054i
$231$	19.4531	+	14.1335i	1.27992	+	0.929917i
$232$	0.927063	+	2.85321i	0.0608647	+	0.187322i
$233$	−24.2031			−1.58559			−0.792797	−	0.609485i	$-0.791376\pi$
$233$	−24.2031			−1.58559			−0.792797	+	0.609485i	$0.791376\pi$
$234$	7.30603	−	5.30814i	0.477610	−	0.347004i
$235$	7.53426	−	5.47396i	0.491481	−	0.357082i
$236$	0.0625540			0.00407192
$237$	5.58541	−	17.1901i	0.362811	−	1.11662i
$238$	2.97476	+	9.15537i	0.192825	+	0.593455i
$239$	−21.3521			−1.38115			−0.690576	−	0.723260i	$-0.742643\pi$
$239$	−21.3521			−1.38115			−0.690576	+	0.723260i	$0.742643\pi$
$240$	20.2299	+	14.6979i	1.30583	+	0.948743i
$241$	−2.79962	−	2.03404i	−0.180339	−	0.131024i	0.493953	−	0.869488i	$-0.335551\pi$
$241$	−2.79962	−	2.03404i	−0.180339	−	0.131024i	−0.674293	+	0.738464i	$0.735551\pi$
$242$	4.67428	+	3.39606i	0.300474	+	0.218307i
$243$	−16.0907			−1.03222
$244$	−0.0866738	−	0.266754i	−0.00554872	−	0.0170772i
$245$	34.7284			2.21871
$246$	7.78330	−	5.65490i	0.496245	−	0.360543i
$247$	26.6469			1.69550
$248$	3.55699	−	10.9473i	0.225869	−	0.695154i
$249$	4.86799	−	14.9821i	0.308496	−	0.949454i
$250$	−0.876145			−0.0554123
$251$	4.82004	−	3.50197i	0.304238	−	0.221042i	−0.425182	−	0.905108i	$-0.639790\pi$
$251$	4.82004	−	3.50197i	0.304238	−	0.221042i	0.729420	+	0.684066i	$0.239790\pi$
$252$	1.12202			0.0706807
$253$	−3.91372	−	12.0452i	−0.246053	−	0.757274i
$254$	−1.89628			−0.118983
$255$	9.16984	+	6.66228i	0.574238	+	0.417208i
$256$	2.93680	+	2.13371i	0.183550	+	0.133357i
$257$	16.6089	+	12.0671i	1.03603	+	0.752723i	0.969508	−	0.245062i	$-0.0788082\pi$
$257$	16.6089	+	12.0671i	1.03603	+	0.752723i	0.0665270	+	0.997785i	$0.478808\pi$
$258$	−18.5184			−1.15290
$259$	−9.08004	−	27.9455i	−0.564206	−	1.73645i
$260$	0.563947	−	1.73565i	0.0349745	−	0.107640i
$261$	−1.77758			−0.110029
$262$	21.0766	−	15.3130i	1.30212	−	0.946043i
$263$	11.8633	−	8.61917i	0.731521	−	0.531481i	−0.158523	−	0.987355i	$-0.550673\pi$
$263$	11.8633	−	8.61917i	0.731521	−	0.531481i	0.890044	+	0.455874i	$0.150673\pi$
$264$	−16.5362			−1.01773
$265$	−3.28537	−	10.1113i	−0.201819	−	0.621134i
$266$	−32.5278	−	23.6329i	−1.99441	−	1.44902i
$267$	−3.69433	+	11.3700i	−0.226089	+	0.695832i
$268$	−0.454080	+	1.39752i	−0.0277374	+	0.0853669i
$269$	−3.91608	+	12.0525i	−0.238768	+	0.734851i	0.757832	+	0.652450i	$0.226259\pi$
$269$	−3.91608	+	12.0525i	−0.238768	+	0.734851i	−0.996599	+	0.0824012i	$0.973741\pi$
$270$	9.48390	−	6.89046i	0.577172	−	0.419340i
$271$	0.481126	−	1.48075i	0.0292263	−	0.0899494i	−0.935379	−	0.353646i	$-0.884942\pi$
$271$	0.481126	−	1.48075i	0.0292263	−	0.0899494i	0.964606	+	0.263697i	$0.0849418\pi$
$272$	−4.94605	−	3.59351i	−0.299898	−	0.217889i
$273$	10.9612	+	33.7350i	0.663400	+	2.04173i
$274$	8.24907	−	25.3880i	0.498345	−	1.53375i
$275$	−10.0763	+	7.32086i	−0.607624	+	0.441464i
$276$	−1.30558	−	0.948559i	−0.0785867	−	0.0570965i
$277$	−4.29289	−	13.2122i	−0.257935	−	0.793842i	−0.993237	−	0.116102i	$-0.962960\pi$
$277$	−4.29289	−	13.2122i	−0.257935	−	0.793842i	0.735302	−	0.677739i	$-0.237040\pi$
$278$	17.0918	−	12.4179i	1.02510	−	0.744778i
$279$	5.51772	+	4.00886i	0.330337	+	0.240004i
$280$	−31.5100	+	22.8933i	−1.88308	+	1.36814i
$281$	−0.739039	−	2.27453i	−0.0440874	−	0.135687i	0.926590	−	0.376073i	$-0.122726\pi$
$281$	−0.739039	−	2.27453i	−0.0440874	−	0.135687i	−0.970677	+	0.240386i	$0.922726\pi$
$282$	−2.71960	−	8.37007i	−0.161950	−	0.498430i
$283$	−0.510962			−0.0303735			−0.0151868	−	0.999885i	$-0.504834\pi$
$283$	−0.510962			−0.0303735			−0.0151868	+	0.999885i	$0.504834\pi$
$284$	−0.458851	−	1.19717i	−0.0272278	−	0.0710392i
$285$	−47.3404			−2.80420
$286$	−4.18253	−	12.8725i	−0.247318	−	0.761167i
$287$	4.27632	+	13.1612i	0.252423	+	0.776878i
$288$	−1.20438	+	0.875031i	−0.0709686	+	0.0515617i
$289$	11.5113	+	8.36347i	0.677137	+	0.491969i
$290$	3.52933	−	2.56421i	0.207249	−	0.150575i
$291$	9.21964	+	28.3751i	0.540465	+	1.66338i
$292$	0.843378	+	0.612750i	0.0493550	+	0.0358585i
$293$	−5.20136	+	3.77901i	−0.303867	+	0.220772i	−0.729260	−	0.684236i	$-0.760136\pi$
$293$	−5.20136	+	3.77901i	−0.303867	+	0.220772i	0.425393	+	0.905009i	$0.360136\pi$
$294$	10.1416	−	31.2126i	0.591470	−	1.82036i
$295$	−0.397583	−	1.22363i	−0.0231482	−	0.0712427i
$296$	16.3481	+	11.8776i	0.950213	+	0.690370i
$297$	−2.21227	+	6.80868i	−0.128369	+	0.395080i
$298$	−7.38978	+	5.36899i	−0.428078	+	0.311017i
$299$	5.77341	−	17.7687i	0.333885	−	1.02759i
$300$	−0.490415	+	1.50934i	−0.0283141	+	0.0871420i
$301$	8.23128	−	25.3333i	0.474443	−	1.46019i
$302$	11.0115	+	8.00029i	0.633638	+	0.460365i
$303$	2.52193	+	7.76171i	0.144881	+	0.445898i
$304$	25.5346			1.46451
$305$	−4.66716	+	3.39089i	−0.267241	+	0.194162i
$306$	3.17346	−	2.30565i	0.181414	−	0.131805i
$307$	−18.0716			−1.03140			−0.515699	−	0.856770i	$-0.672468\pi$
$307$	−18.0716			−1.03140			−0.515699	+	0.856770i	$0.672468\pi$
$308$	0.519657	−	1.59934i	0.0296102	−	0.0911308i
$309$	3.08175	+	9.48466i	0.175315	+	0.539563i
$310$	−16.7382			−0.950664
$311$	−10.4703	−	7.60715i	−0.593718	−	0.431362i	0.249925	−	0.968265i	$-0.419594\pi$
$311$	−10.4703	−	7.60715i	−0.593718	−	0.431362i	−0.843644	+	0.536903i	$0.819594\pi$
$312$	−19.7349	−	14.3383i	−1.11727	−	0.811745i
$313$	3.02261	+	2.19605i	0.170848	+	0.124128i	0.669923	−	0.742430i	$-0.266327\pi$
$313$	3.02261	+	2.19605i	0.170848	+	0.124128i	−0.499075	+	0.866559i	$0.666327\pi$
$314$	−12.4671			−0.703560
$315$	−7.13138	−	21.9481i	−0.401808	−	1.23664i
$316$	−1.26408			−0.0711102
$317$	−17.3756	+	12.6241i	−0.975909	+	0.709039i	−0.956791	−	0.290778i	$-0.906086\pi$
$317$	−17.3756	+	12.6241i	−0.975909	+	0.709039i	−0.0191184	+	0.999817i	$0.506086\pi$
$318$	−10.0471			−0.563414
$319$	−0.823272	+	2.53377i	−0.0460944	+	0.141864i
$320$	8.23229	−	25.3364i	0.460199	−	1.41635i
$321$	0.438610			0.0244808
$322$	−22.8065	+	16.5699i	−1.27096	+	0.923405i
$323$	11.5744			0.644015
$324$	0.526402	+	1.62010i	0.0292445	+	0.0900054i
$325$	−18.3733			−1.01916
$326$	21.4970	+	15.6185i	1.19061	+	0.865029i
$327$	7.79084	+	5.66038i	0.430835	+	0.313020i
$328$	−7.69926	−	5.59384i	−0.425121	−	0.308868i
$329$	12.6591			0.697921
$330$	7.43062	+	22.8691i	0.409042	+	1.25890i
$331$	3.49059	−	10.7429i	0.191860	−	0.590485i	−0.808139	−	0.588992i	$-0.799525\pi$
$331$	3.49059	−	10.7429i	0.191860	−	0.590485i	0.999999	−	0.00149289i	$-0.000475203\pi$
$332$	−1.10172			−0.0604646
$333$	−9.68652	+	7.03767i	−0.530818	+	0.385662i
$334$	22.0680	−	16.0333i	1.20750	−	0.877304i
$335$	30.2232			1.65127
$336$	10.5036	+	32.3268i	0.573020	+	1.76357i
$337$	−18.4497	−	13.4045i	−1.00502	−	0.730191i	−0.0418624	−	0.999123i	$-0.513329\pi$
$337$	−18.4497	−	13.4045i	−1.00502	−	0.730191i	−0.963159	+	0.268933i	$0.913329\pi$
$338$	0.709131	−	2.18248i	0.0385716	−	0.118711i
$339$	8.52292	−	26.2309i	0.462902	−	1.42466i
$340$	0.244957	−	0.753899i	0.0132846	−	0.0408859i
$341$	8.26976	−	6.00833i	0.447832	−	0.325369i
$342$	−5.06273	+	15.5815i	−0.273761	+	0.842550i
$343$	14.1000	+	10.2443i	0.761329	+	0.553138i
$344$	5.66071	+	17.4219i	0.305205	+	0.939325i
$345$	−10.2569	+	31.5676i	−0.552216	+	1.69954i
$346$	−12.2272	+	8.88356i	−0.657337	+	0.477583i
$347$	7.49897	+	5.44832i	0.402566	+	0.292481i	0.770585	−	0.637337i	$-0.219964\pi$
$347$	7.49897	+	5.44832i	0.402566	+	0.292481i	−0.368019	+	0.929818i	$0.619964\pi$
$348$	0.104902	+	0.322854i	0.00562331	+	0.0173068i
$349$	21.0774	−	15.3136i	1.12825	−	0.819719i	0.142808	−	0.989750i	$-0.454387\pi$
$349$	21.0774	−	15.3136i	1.12825	−	0.819719i	0.985439	+	0.170031i	$0.0543869\pi$
$350$	22.4282	+	16.2951i	1.19884	+	0.871008i
$351$	−8.54392	+	6.20752i	−0.456041	+	0.331333i
$352$	0.689478	+	2.12199i	0.0367493	+	0.113103i
$353$	−4.20751	−	12.9494i	−0.223943	−	0.689226i	−0.998397	−	0.0565959i	$-0.981975\pi$
$353$	−4.20751	−	12.9494i	−0.223943	−	0.689226i	0.774454	−	0.632630i	$-0.218025\pi$
$354$	−1.21586			−0.0646224
$355$	−20.5018	+	16.5847i	−1.08812	+	0.880226i
$356$	0.836096			0.0443130
$357$	4.76111	+	14.6532i	0.251984	+	0.775528i
$358$	9.25773	+	28.4924i	0.489286	+	1.50587i
$359$	−10.8917	+	7.91328i	−0.574842	+	0.417647i	−0.836861	−	0.547416i	$-0.815612\pi$
$359$	−10.8917	+	7.91328i	−0.574842	+	0.417647i	0.262019	+	0.965063i	$0.415612\pi$
$360$	12.8396	+	9.32854i	0.676708	+	0.491657i
$361$	−23.7382	+	17.2468i	−1.24938	+	0.907727i
$362$	−4.87728	−	15.0107i	−0.256344	−	0.788946i
$363$	7.48118	+	5.43540i	0.392660	+	0.285284i
$364$	2.00694	−	1.45813i	0.105192	−	0.0764267i
$365$	6.62579	−	20.3921i	0.346809	−	1.06737i
$366$	1.68468	+	5.18491i	0.0880596	+	0.271020i
$367$	4.03067	+	2.92845i	0.210399	+	0.152864i	0.687994	−	0.725716i	$-0.258491\pi$
$367$	4.03067	+	2.92845i	0.210399	+	0.152864i	−0.477595	+	0.878580i	$0.658491\pi$
$368$	5.53242	−	17.0270i	0.288397	−	0.887595i
$369$	4.56195	−	3.31445i	0.237485	−	0.172543i
$370$	9.08027	−	27.9462i	0.472061	−	1.45285i
$371$	4.46586	−	13.7445i	0.231856	−	0.713580i
$372$	0.402491	−	1.23874i	0.0208682	−	0.0642256i
$373$	−16.0917	−	11.6913i	−0.833196	−	0.605352i	0.0872660	−	0.996185i	$-0.472187\pi$
$373$	−16.0917	−	11.6913i	−0.833196	−	0.605352i	−0.920462	+	0.390833i	$0.872187\pi$
$374$	−1.81673	−	5.59132i	−0.0939409	−	0.289120i
$375$	−1.40227			−0.0724129
$376$	−7.04313	+	5.11714i	−0.363222	+	0.263896i
$377$	−3.17952	+	2.31006i	−0.163754	+	0.118974i
$378$	15.9350			0.819606
$379$	−0.817062	+	2.51466i	−0.0419696	+	0.129169i	−0.969846	−	0.243719i	$-0.921633\pi$
$379$	−0.817062	+	2.51466i	−0.0419696	+	0.129169i	0.927876	+	0.372888i	$0.121633\pi$
$380$	1.02310	+	3.14877i	0.0524838	+	0.161528i
$381$	−3.03499			−0.155487
$382$	−6.13855	−	4.45991i	−0.314075	−	0.228189i
$383$	8.52545	+	6.19411i	0.435630	+	0.316504i	0.783896	−	0.620892i	$-0.213229\pi$
$383$	8.52545	+	6.19411i	0.435630	+	0.316504i	−0.348266	+	0.937396i	$0.613229\pi$
$384$	−17.3441	−	12.6013i	−0.885090	−	0.643055i
$385$	−34.5879			−1.76276
$386$	4.05759	+	12.4880i	0.206526	+	0.635622i
$387$	−10.8540			−0.551740
$388$	1.68808	−	1.22646i	0.0856991	−	0.0622640i
$389$	25.3752			1.28657			0.643286	−	0.765626i	$-0.277571\pi$
$389$	25.3752			1.28657			0.643286	+	0.765626i	$0.277571\pi$
$390$	−10.9614	+	33.7359i	−0.555054	+	1.70828i
$391$	2.50775	−	7.71805i	0.126822	−	0.390319i
$392$	−32.4646			−1.63971
$393$	33.7331	−	24.5085i	1.70161	−	1.23629i
$394$	−1.32206			−0.0666043
$395$	8.03430	+	24.7270i	0.404249	+	1.24415i
$396$	−0.685234			−0.0344343
$397$	9.99217	+	7.25974i	0.501493	+	0.364356i	0.809587	−	0.587000i	$-0.199691\pi$
$397$	9.99217	+	7.25974i	0.501493	+	0.364356i	−0.308094	+	0.951356i	$0.599691\pi$
$398$	−17.3481	−	12.6041i	−0.869582	−	0.631788i
$399$	−52.0608	−	37.8244i	−2.60630	−	1.89359i
$400$	−17.6063			−0.880316
$401$	3.45851	+	10.6442i	0.172710	+	0.531546i	0.999521	−	0.0309326i	$-0.00984771\pi$
$401$	3.45851	+	10.6442i	0.172710	+	0.531546i	−0.826812	+	0.562479i	$0.809848\pi$
$402$	8.82597	−	27.1635i	0.440199	−	1.35479i
$403$	15.0792			0.751148
$404$	0.461755	−	0.335484i	0.0229732	−	0.0166910i
$405$	28.3454	−	20.5941i	1.40849	−	1.02333i
$406$	5.93001			0.294302
$407$	5.54531	+	17.0667i	0.274871	+	0.845965i
$408$	−8.57210	−	6.22799i	−0.424382	−	0.308332i
$409$	1.09279	−	3.36327i	0.0540351	−	0.166303i	−0.920397	−	0.390985i	$-0.872134\pi$
$409$	1.09279	−	3.36327i	0.0540351	−	0.166303i	0.974432	+	0.224682i	$0.0721344\pi$
$410$	−4.27643	+	13.1615i	−0.211198	+	0.650000i
$411$	13.2026	−	40.6335i	0.651238	−	2.00430i
$412$	0.564256	−	0.409956i	0.0277989	−	0.0201971i
$413$	0.540442	−	1.66331i	0.0265934	−	0.0818461i
$414$	9.29318	+	6.75189i	0.456735	+	0.331837i
$415$	7.00233	+	21.5510i	0.343731	+	1.05789i
$416$	−1.01710	+	3.13031i	−0.0498674	+	0.153476i
$417$	27.3554	−	19.8749i	1.33960	−	0.973278i
$418$	19.8652	+	14.4329i	0.971640	+	0.705937i
$419$	6.45206	+	19.8574i	0.315204	+	0.970097i	0.975671	+	0.219242i	$0.0703584\pi$
$419$	6.45206	+	19.8574i	0.315204	+	0.970097i	−0.660467	+	0.750855i	$0.729642\pi$
$420$	−3.56550	+	2.59049i	−0.173979	+	0.126403i
$421$	−23.1026	−	16.7850i	−1.12595	−	0.818051i	−0.140851	−	0.990031i	$-0.544984\pi$
$421$	−23.1026	−	16.7850i	−1.12595	−	0.818051i	−0.985101	+	0.171979i	$0.944984\pi$
$422$	−20.8344	+	15.1371i	−1.01420	+	0.736863i
$423$	−1.59401	−	4.90586i	−0.0775035	−	0.238531i
$424$	3.07121	+	9.45221i	0.149151	+	0.459040i
$425$	−7.98063			−0.387117
$426$	8.91869	+	23.2695i	0.432112	+	1.12741i
$427$	−7.84182			−0.379492
$428$	−0.00947902	−	0.0291734i	−0.000458186	−	0.00141015i
$429$	−6.69414	−	20.6024i	−0.323196	−	0.994696i
$430$	21.5503	−	15.6572i	1.03925	−	0.755058i
$431$	−19.1459	−	13.9103i	−0.922225	−	0.670036i	0.0218515	−	0.999761i	$-0.493044\pi$
$431$	−19.1459	−	13.9103i	−0.922225	−	0.670036i	−0.944077	+	0.329725i	$0.893044\pi$
$432$	−8.18727	+	5.94840i	−0.393910	+	0.286193i
$433$	8.50707	+	26.1821i	0.408824	+	1.25823i	0.917660	+	0.397366i	$0.130076\pi$
$433$	8.50707	+	26.1821i	0.408824	+	1.25823i	−0.508836	+	0.860863i	$0.669924\pi$
$434$	−18.4072	−	13.3736i	−0.883573	−	0.641953i
$435$	5.64869	−	4.10401i	0.270834	−	0.196772i
$436$	0.208119	−	0.640525i	0.00996710	−	0.0306756i
$437$	10.4740	+	32.2356i	0.501038	+	1.54204i
$438$	−16.3928	−	11.9100i	−0.783277	−	0.569084i
$439$	−2.21774	+	6.82552i	−0.105847	+	0.325764i	−0.989928	−	0.141569i	$-0.954785\pi$
$439$	−2.21774	+	6.82552i	−0.105847	+	0.325764i	0.884081	+	0.467333i	$0.154785\pi$
$440$	19.2436	−	13.9813i	0.917402	−	0.666532i
$441$	5.94419	−	18.2944i	0.283057	−	0.871160i
$442$	2.67999	−	8.24816i	0.127474	−	0.392325i
$443$	−2.88709	+	8.88554i	−0.137170	+	0.422165i	−0.995921	−	0.0902274i	$-0.971241\pi$
$443$	−2.88709	+	8.88554i	−0.137170	+	0.422165i	0.858751	+	0.512392i	$0.171241\pi$
$444$	1.84986	+	1.34400i	0.0877906	+	0.0637836i
$445$	−5.31409	−	16.3551i	−0.251912	−	0.775305i
$446$	−38.5725			−1.82646
$447$	−11.8273	+	8.59306i	−0.559414	+	0.406438i
$448$	29.2966	−	21.2852i	1.38413	−	1.00563i
$449$	−2.94170			−0.138827			−0.0694137	−	0.997588i	$-0.522113\pi$
$449$	−2.94170			−0.138827			−0.0694137	+	0.997588i	$0.522113\pi$
$450$	3.49080	−	10.7436i	0.164558	−	0.506457i
$451$	−2.61161	−	8.03771i	−0.122976	−	0.378481i
$452$	−1.92890			−0.0907277
$453$	17.6238	+	12.8045i	0.828040	+	0.601606i
$454$	3.24887	+	2.36044i	0.152477	+	0.110781i
$455$	−41.2786	−	29.9907i	−1.93517	−	1.40598i
$456$	44.2545			2.07240
$457$	−10.9773	−	33.7846i	−0.513495	−	1.58038i	−0.786003	−	0.618222i	$-0.787853\pi$
$457$	−10.9773	−	33.7846i	−0.513495	−	1.58038i	0.272508	−	0.962154i	$-0.412147\pi$
$458$	−26.1840			−1.22350
$459$	−3.71115	+	2.69631i	−0.173221	+	0.125853i
$460$	2.32134			0.108233
$461$	9.60369	−	29.5571i	0.447288	−	1.37661i	−0.432666	−	0.901554i	$-0.642427\pi$
$461$	9.60369	−	29.5571i	0.447288	−	1.37661i	0.879955	−	0.475058i	$-0.157573\pi$
$462$	−10.1006	+	31.0864i	−0.469922	+	1.44627i
$463$	−13.8660			−0.644407			−0.322203	−	0.946670i	$-0.604424\pi$
$463$	−13.8660			−0.644407			−0.322203	+	0.946670i	$0.604424\pi$
$464$	−3.04680	+	2.21363i	−0.141444	+	0.102765i
$465$	−26.7894			−1.24233
$466$	−10.1668	−	31.2903i	−0.470969	−	1.44949i
$467$	−14.4287			−0.667681			−0.333840	−	0.942630i	$-0.608345\pi$
$467$	−14.4287			−0.667681			−0.333840	+	0.942630i	$0.608345\pi$
$468$	−0.817786	−	0.594156i	−0.0378022	−	0.0274649i
$469$	33.2368	+	24.1480i	1.53473	+	1.11505i
$470$	10.2417	+	7.44105i	0.472416	+	0.343230i
$471$	−19.9536			−0.919414
$472$	0.371666	+	1.14387i	0.0171073	+	0.0526509i
$473$	−5.02696	+	15.4714i	−0.231140	+	0.711375i
$474$	24.5700			1.12854
$475$	26.9664	−	19.5922i	1.23730	−	0.898953i
$476$	0.871738	−	0.633355i	0.0399560	−	0.0290298i
$477$	−5.88882			−0.269630
$478$	−8.96923	−	27.6045i	−0.410243	−	1.26260i
$479$	28.1213	+	20.4313i	1.28489	+	0.933530i	0.999689	−	0.0249364i	$-0.00793832\pi$
$479$	28.1213	+	20.4313i	1.28489	+	0.933530i	0.285205	+	0.958467i	$0.407938\pi$
$480$	1.80696	−	5.56126i	0.0824762	−	0.253835i
$481$	−8.18029	+	25.1763i	−0.372989	+	1.14794i
$482$	1.45364	−	4.47383i	0.0662113	−	0.203778i
$483$	−36.5019	+	26.5201i	−1.66089	+	1.20671i
$484$	0.199847	−	0.615066i	0.00908396	−	0.0279575i
$485$	−34.7202	−	25.2257i	−1.57656	−	1.14544i
$486$	−6.75910	−	20.8024i	−0.306599	−	0.943615i
$487$	−0.742357	+	2.28474i	−0.0336394	+	0.103531i	−0.966466	−	0.256793i	$-0.917334\pi$
$487$	−0.742357	+	2.28474i	−0.0336394	+	0.103531i	0.932827	+	0.360325i	$0.117334\pi$
$488$	4.36293	−	3.16986i	0.197501	−	0.143493i
$489$	34.4060	+	24.9974i	1.55589	+	1.13042i
$490$	14.5881	+	44.8976i	0.659024	+	2.02827i
$491$	−11.0234	+	8.00900i	−0.497481	+	0.361441i	−0.808054	−	0.589109i	$-0.799479\pi$
$491$	−11.0234	+	8.00900i	−0.497481	+	0.361441i	0.310573	+	0.950550i	$0.399479\pi$
$492$	−0.871208	−	0.632970i	−0.0392771	−	0.0285365i
$493$	−1.38106	+	1.00340i	−0.0621998	+	0.0451908i
$494$	11.1934	+	34.4497i	0.503614	+	1.54996i
$495$	4.35524	+	13.4040i	0.195753	+	0.602467i
$496$	14.4497			0.648813
$497$	−35.7971	+	1.85772i	−1.60572	+	0.0833301i
$498$	21.4141			0.959589
$499$	5.35792	+	16.4900i	0.239853	+	0.738193i	0.996440	+	0.0843000i	$0.0268654\pi$
$499$	5.35792	+	16.4900i	0.239853	+	0.738193i	−0.756587	+	0.653893i	$0.773135\pi$
$500$	0.0303052	+	0.0932697i	0.00135529	+	0.00417115i
$501$	35.3198	−	25.6613i	1.57797	−	1.14646i
$502$	6.55214	+	4.76041i	0.292437	+	0.212468i
$503$	7.59835	−	5.52053i	0.338794	−	0.246148i	−0.405359	−	0.914158i	$-0.632853\pi$
$503$	7.59835	−	5.52053i	0.338794	−	0.246148i	0.744153	+	0.668010i	$0.232853\pi$
$504$	6.66652	+	20.5174i	0.296950	+	0.913919i
$505$	−9.49733	−	6.90021i	−0.422626	−	0.307055i
$506$	13.9283	−	10.1195i	0.619188	−	0.449866i
$507$	1.13496	−	3.49306i	0.0504055	−	0.155132i
$508$	0.0655908	+	0.201868i	0.00291012	+	0.00895643i
$509$	22.7231	+	16.5093i	1.00718	+	0.731760i	0.963616	−	0.267290i	$-0.0861283\pi$
$509$	22.7231	+	16.5093i	1.00718	+	0.731760i	0.0435656	+	0.999051i	$0.486128\pi$
$510$	−4.76123	+	14.6536i	−0.210831	+	0.648870i
$511$	23.5795	−	17.1315i	1.04309	−	0.757852i
$512$	−7.61490	+	23.4362i	−0.336534	+	1.03575i
$513$	5.92053	−	18.2215i	0.261398	−	0.804500i
$514$	−8.62379	+	26.5413i	−0.380379	+	1.17069i
$515$	−11.6056	−	8.43193i	−0.511402	−	0.371555i
$516$	0.640537	+	1.97137i	0.0281981	+	0.0867847i
$517$	−7.73112			−0.340014
$518$	32.3144	−	23.4778i	1.41981	−	1.03155i
$519$	−19.5696	+	14.2181i	−0.859010	+	0.624107i
$520$	35.0890			1.53876
$521$	0.905965	−	2.78827i	0.0396910	−	0.122156i	−0.929248	−	0.369457i	$-0.879544\pi$
$521$	0.905965	−	2.78827i	0.0396910	−	0.122156i	0.968939	+	0.247301i	$0.0795436\pi$
$522$	−0.746694	−	2.29809i	−0.0326819	−	0.100585i
$523$	−34.8019			−1.52178			−0.760891	−	0.648880i	$-0.775238\pi$
$523$	−34.8019			−1.52178			−0.760891	+	0.648880i	$0.775238\pi$
$524$	−2.35917	−	1.71404i	−0.103061	−	0.0748780i
$525$	35.8964	+	26.0803i	1.56665	+	1.13824i
$526$	16.1264	+	11.7165i	0.703144	+	0.510864i
$527$	6.54981			0.285314
$528$	−6.41471	−	19.7425i	−0.279165	−	0.859180i
$529$	0.764739			0.0332495
$530$	11.6921	−	8.49480i	0.507872	−	0.368990i
$531$	−0.712642			−0.0309260
$532$	−1.39072	+	4.28018i	−0.0602952	+	0.185569i
$533$	3.85257	−	11.8570i	0.166874	−	0.513584i
$534$	−16.2512			−0.703259
$535$	−0.510422	+	0.370843i	−0.0220675	+	0.0160329i
$536$	−28.2531			−1.22035
$537$	14.8170	+	45.6020i	0.639401	+	1.96787i
$538$	−17.2267			−0.742696
$539$	−23.3239	−	16.9458i	−1.00463	−	0.729908i
$540$	−1.06156	−	0.771270i	−0.0456824	−	0.0331902i
$541$	20.1847	+	14.6650i	0.867808	+	0.630499i	0.929998	−	0.367565i	$-0.119808\pi$
$541$	20.1847	+	14.6650i	0.867808	+	0.630499i	−0.0621900	+	0.998064i	$0.519808\pi$
$542$	2.11646			0.0909096
$543$	−7.80609	−	24.0247i	−0.334991	−	1.03100i
$544$	−0.441788	+	1.35968i	−0.0189415	+	0.0582960i
$545$	−13.8522			−0.593364
$546$	−39.0090	+	28.3417i	−1.66943	+	1.21291i
$547$	−22.6668	+	16.4684i	−0.969161	+	0.704137i	−0.955260	−	0.295767i	$-0.904425\pi$
$547$	−22.6668	+	16.4684i	−0.969161	+	0.704137i	−0.0139006	+	0.999903i	$0.504425\pi$
$548$	−2.98800			−0.127641
$549$	0.987425	+	3.03898i	0.0421423	+	0.129701i
$550$	−13.6973	−	9.95164i	−0.584053	−	0.424339i
$551$	2.20326	−	6.78093i	0.0938619	−	0.288877i
$552$	9.58834	−	29.5099i	0.408107	−	1.25602i
$553$	−10.9212	+	33.6119i	−0.464416	+	1.42932i
$554$	15.2777	−	11.0999i	0.649087	−	0.471589i
$555$	14.5330	−	44.7279i	0.616890	−	1.89859i
$556$	−1.91314	−	1.38998i	−0.0811352	−	0.0589482i
$557$	4.61095	+	14.1910i	0.195372	+	0.601294i	0.999972	+	0.00747629i	$0.00237980\pi$
$557$	4.61095	+	14.1910i	0.195372	+	0.601294i	−0.804600	+	0.593817i	$0.797620\pi$
$558$	−2.86495	+	8.81740i	−0.121283	+	0.373270i
$559$	−19.4144	+	14.1054i	−0.821141	+	0.596594i
$560$	−39.5555	−	28.7388i	−1.67153	−	1.21444i
$561$	−2.90768	−	8.94891i	−0.122762	−	0.377823i
$562$	2.63012	−	1.91089i	0.110945	−	0.0806062i
$563$	28.2214	+	20.5040i	1.18939	+	0.864142i	0.993200	−	0.116424i	$-0.0371432\pi$
$563$	28.2214	+	20.5040i	1.18939	+	0.864142i	0.196190	+	0.980566i	$0.437143\pi$
$564$	−0.796964	+	0.579028i	−0.0335582	+	0.0243815i
$565$	12.2597	+	37.7316i	0.515771	+	1.58738i
$566$	−0.214636	−	0.660583i	−0.00902184	−	0.0277664i
$567$	47.6262			2.00011
$568$	19.1654	−	15.5036i	0.804162	−	0.650518i
$569$	34.1769			1.43277			0.716386	−	0.697704i	$-0.245795\pi$
$569$	34.1769			1.43277			0.716386	+	0.697704i	$0.245795\pi$
$570$	−19.8860	−	61.2027i	−0.832931	−	2.56350i
$571$	−9.96289	−	30.6626i	−0.416934	−	1.28319i	−0.910510	−	0.413488i	$-0.864310\pi$
$571$	−9.96289	−	30.6626i	−0.416934	−	1.28319i	0.493575	−	0.869703i	$-0.335690\pi$
$572$	−1.22567	+	0.890500i	−0.0512478	+	0.0372337i
$573$	−9.82474	−	7.13809i	−0.410434	−	0.298198i
$574$	−15.2187	+	11.0570i	−0.635217	+	0.461512i
$575$	−7.22190	−	22.2267i	−0.301174	−	0.926918i
$576$	−11.9377	−	8.67328i	−0.497406	−	0.361387i
$577$	12.6178	−	9.16735i	0.525285	−	0.381642i	−0.293306	−	0.956019i	$-0.594756\pi$
$577$	12.6178	−	9.16735i	0.525285	−	0.381642i	0.818591	+	0.574377i	$0.194756\pi$
$578$	−5.97700	+	18.3953i	−0.248610	+	0.765144i
$579$	6.49418	+	19.9870i	0.269889	+	0.830632i
$580$	−0.395048	−	0.287019i	−0.0164035	−	0.0119178i
$581$	−9.51840	+	29.2946i	−0.394890	+	1.21535i
$582$	−32.8112	+	23.8387i	−1.36007	+	0.988147i
$583$	−2.72737	+	8.39397i	−0.112956	+	0.347643i
$584$	−6.19388	+	19.0628i	−0.256305	+	0.788824i
$585$	−6.42473	+	19.7733i	−0.265630	+	0.817524i
$586$	−7.07050	−	5.13702i	−0.292080	−	0.212208i
$587$	12.4939	+	38.4522i	0.515677	+	1.58709i	0.782047	+	0.623219i	$0.214176\pi$
$587$	12.4939	+	38.4522i	0.515677	+	1.58709i	−0.266370	+	0.963871i	$0.585824\pi$
$588$	−3.67352			−0.151493
$589$	−22.1317	+	16.0796i	−0.911920	+	0.662549i
$590$	1.41493	−	1.02801i	0.0582518	−	0.0423224i
$591$	−2.11595			−0.0870387
$592$	−7.83883	+	24.1254i	−0.322174	+	0.991549i
$593$	−11.3245	−	34.8533i	−0.465042	−	1.43125i	−0.858929	−	0.512094i	$-0.828870\pi$
$593$	−11.3245	−	34.8533i	−0.465042	−	1.43125i	0.393887	−	0.919159i	$-0.371130\pi$
$594$	−9.73171			−0.399297
$595$	−17.9298	−	13.0268i	−0.735051	−	0.534046i
$596$	0.827161	+	0.600967i	0.0338818	+	0.0246166i
$597$	−27.7656	−	20.1729i	−1.13637	−	0.825622i
$598$	25.3970			1.03856
$599$	−10.9894	−	33.8218i	−0.449013	−	1.38192i	−0.878022	−	0.478620i	$-0.841137\pi$
$599$	−10.9894	−	33.8218i	−0.449013	−	1.38192i	0.429009	−	0.903300i	$-0.358863\pi$
$600$	−30.5139			−1.24572
$601$	24.4315	−	17.7505i	0.996582	−	0.724059i	0.0352296	−	0.999379i	$-0.488784\pi$
$601$	24.4315	−	17.7505i	0.996582	−	0.724059i	0.961353	+	0.275320i	$0.0887838\pi$
$602$	36.2091			1.47577
$603$	5.17308	−	15.9211i	0.210664	−	0.648358i
$604$	0.470791	−	1.44894i	0.0191562	−	0.0589567i
$605$	−13.3017			−0.540789
$606$	−8.97514	+	6.52082i	−0.364590	+	0.264890i
$607$	46.6582			1.89380			0.946898	−	0.321533i	$-0.104198\pi$
$607$	46.6582			1.89380			0.946898	+	0.321533i	$0.104198\pi$
$608$	−1.84519	−	5.67892i	−0.0748325	−	0.230311i
$609$	9.49098			0.384594
$610$	−6.34433	−	4.60942i	−0.256874	−	0.186630i
$611$	−9.22663	−	6.70354i	−0.373269	−	0.271196i
$612$	−0.355215	−	0.258079i	−0.0143587	−	0.0104322i
$613$	5.57638			0.225228			0.112614	−	0.993639i	$-0.464078\pi$
$613$	5.57638			0.225228			0.112614	+	0.993639i	$0.464078\pi$
$614$	−7.59120	−	23.3633i	−0.306356	−	0.942867i
$615$	−6.84442	+	21.0650i	−0.275994	+	0.849421i
$616$	32.3333			1.30274
$617$	16.5620	−	12.0330i	0.666762	−	0.484431i	−0.202177	−	0.979349i	$-0.564802\pi$
$617$	16.5620	−	12.0330i	0.666762	−	0.484431i	0.868940	+	0.494918i	$0.164802\pi$
$618$	−10.9674	+	7.96832i	−0.441175	+	0.320533i
$619$	29.0786			1.16877			0.584383	−	0.811478i	$-0.301337\pi$
$619$	29.0786			1.16877			0.584383	+	0.811478i	$0.301337\pi$
$620$	0.578960	+	1.78186i	0.0232516	+	0.0715611i
$621$	−10.8678	−	7.89589i	−0.436108	−	0.316851i
$622$	5.43648	−	16.7318i	0.217983	−	0.670883i
$623$	7.22354	−	22.2318i	0.289405	−	0.890697i
$624$	9.46281	−	29.1235i	0.378816	−	1.16587i
$625$	21.0242	−	15.2750i	0.840968	−	0.610999i
$626$	−1.56942	+	4.83018i	−0.0627266	+	0.193053i
$627$	31.7943	+	23.0999i	1.26974	+	0.922521i
$628$	0.431228	+	1.32718i	0.0172079	+	0.0529603i
$629$	−3.55320	+	10.9356i	−0.141675	+	0.436032i
$630$	25.3794	−	18.4392i	1.01114	−	0.734636i
$631$	−0.233735	−	0.169818i	−0.00930483	−	0.00676036i	0.583123	−	0.812384i	$-0.301831\pi$
$631$	−0.233735	−	0.169818i	−0.00930483	−	0.00676036i	−0.592428	+	0.805623i	$0.701831\pi$
$632$	−7.51058	−	23.1152i	−0.298755	−	0.919472i
$633$	−33.3455	+	24.2269i	−1.32537	+	0.962934i
$634$	−23.6195	−	17.1606i	−0.938052	−	0.681535i
$635$	3.53190	−	2.56608i	0.140159	−	0.101832i
$636$	0.347522	+	1.06956i	0.0137801	+	0.0424109i
$637$	−13.1422	−	40.4476i	−0.520714	−	1.60259i
$638$	−3.62154			−0.143378
$639$	5.22742	+	13.6387i	0.206794	+	0.539539i
$640$	30.8381			1.21898
$641$	6.06671	+	18.6714i	0.239621	+	0.737477i	0.996475	+	0.0838929i	$0.0267354\pi$
$641$	6.06671	+	18.6714i	0.239621	+	0.737477i	−0.756854	+	0.653584i	$0.773265\pi$
$642$	0.184244	+	0.567045i	0.00727153	+	0.0223795i
$643$	6.53321	−	4.74666i	0.257645	−	0.187190i	−0.451463	−	0.892290i	$-0.649098\pi$
$643$	6.53321	−	4.74666i	0.257645	−	0.187190i	0.709108	+	0.705100i	$0.249098\pi$
$644$	2.55281	+	1.85472i	0.100595	+	0.0730863i
$645$	34.4913	−	25.0594i	1.35809	−	0.986712i
$646$	4.86197	+	14.9636i	0.191292	+	0.588735i
$647$	14.3021	+	10.3910i	0.562272	+	0.408514i	0.832290	−	0.554341i	$-0.187030\pi$
$647$	14.3021	+	10.3910i	0.562272	+	0.408514i	−0.270018	+	0.962855i	$0.587030\pi$
$648$	−26.4977	+	19.2517i	−1.04093	+	0.756278i
$649$	−0.330055	+	1.01581i	−0.0129558	+	0.0398739i
$650$	−7.71793	−	23.7534i	−0.302722	−	0.931683i
$651$	−29.4607	−	21.4044i	−1.15466	−	0.838906i
$652$	0.919097	−	2.82869i	0.0359946	−	0.110780i
$653$	−10.1047	+	7.34150i	−0.395428	+	0.287295i	−0.767676	−	0.640838i	$-0.778587\pi$
$653$	−10.1047	+	7.34150i	−0.395428	+	0.287295i	0.372248	+	0.928133i	$0.378587\pi$
$654$	−4.04522	+	12.4499i	−0.158180	+	0.486829i
$655$	−18.5342	+	57.0424i	−0.724191	+	2.22883i
$656$	3.69176	−	11.3621i	0.144139	−	0.443614i
$657$	−9.60813	−	6.98072i	−0.374849	−	0.272344i
$658$	5.31764	+	16.3660i	0.207303	+	0.638014i
$659$	8.95269			0.348747			0.174374	−	0.984680i	$-0.444210\pi$
$659$	8.95269			0.348747			0.174374	+	0.984680i	$0.444210\pi$
$660$	2.17750	−	1.58205i	0.0847592	−	0.0615811i
$661$	−19.4196	+	14.1092i	−0.755336	+	0.548784i	−0.897476	−	0.441063i	$-0.854602\pi$
$661$	−19.4196	+	14.1092i	−0.755336	+	0.548784i	0.142140	+	0.989847i	$0.454602\pi$
$662$	15.3550			0.596788
$663$	4.28932	−	13.2012i	0.166584	−	0.512691i
$664$	−6.54588	−	20.1461i	−0.254029	−	0.781822i
$665$	92.5649			3.58951
$666$	−13.1674	−	9.56669i	−0.510227	−	0.370702i
$667$	−4.04431	−	2.93836i	−0.156596	−	0.113774i
$668$	−2.47013	−	1.79466i	−0.0955724	−	0.0694374i
$669$	−61.7353			−2.38683
$670$	12.6957	+	39.0732i	0.490476	+	1.50953i
$671$	4.78911			0.184882
$672$	6.43051	−	4.67204i	0.248062	−	0.180228i
$673$	−5.51593			−0.212623			−0.106312	−	0.994333i	$-0.533904\pi$
$673$	−5.51593			−0.212623			−0.106312	+	0.994333i	$0.533904\pi$
$674$	9.57960	−	29.4830i	0.368993	−	1.13564i
$675$	−4.08226	+	12.5639i	−0.157126	+	0.483585i
$676$	−0.256864			−0.00987937
$677$	16.7555	−	12.1736i	0.643967	−	0.467869i	−0.217244	−	0.976117i	$-0.569707\pi$
$677$	16.7555	−	12.1736i	0.643967	−	0.467869i	0.861211	+	0.508248i	$0.169707\pi$
$678$	37.4920			1.43987
$679$	−18.0272	−	55.4820i	−0.691821	−	2.12920i
$680$	15.2413			0.584478
$681$	5.19981	+	3.77788i	0.199257	+	0.144769i
$682$	11.2415	+	8.16745i	0.430460	+	0.312748i
$683$	−6.36427	−	4.62391i	−0.243522	−	0.176929i	0.459329	−	0.888266i	$-0.348090\pi$
$683$	−6.36427	−	4.62391i	−0.243522	−	0.176929i	−0.702851	+	0.711337i	$0.748090\pi$
$684$	1.83384			0.0701185
$685$	18.9913	+	58.4491i	0.725619	+	2.23322i
$686$	−7.32111	+	22.5321i	−0.279521	+	0.860278i
$687$	−41.9075			−1.59887
$688$	−18.6040	+	13.5166i	−0.709270	+	0.515315i
$689$	−10.5332	+	7.65284i	−0.401284	+	0.291550i
$690$	−45.1199			−1.71769
$691$	0.374453	+	1.15245i	0.0142449	+	0.0438412i	0.957926	−	0.287014i	$-0.0926627\pi$
$691$	0.374453	+	1.15245i	0.0142449	+	0.0438412i	−0.943681	+	0.330855i	$0.892663\pi$
$692$	1.36862	+	0.994364i	0.0520273	+	0.0378001i
$693$	−5.92016	+	18.2204i	−0.224888	+	0.692134i
$694$	−3.89367	+	11.9835i	−0.147802	+	0.454887i
$695$	−15.0301	+	46.2579i	−0.570124	+	1.75466i
$696$	−5.28047	+	3.83649i	−0.200156	+	0.145422i
$697$	1.67341	−	5.15022i	0.0633849	−	0.195079i
$698$	28.6516	+	20.8166i	1.08448	+	0.787921i
$699$	−16.2720	−	50.0800i	−0.615463	−	1.89420i
$700$	0.958911	−	2.95123i	0.0362434	−	0.111546i
$701$	−11.7317	+	8.52359i	−0.443101	+	0.321932i	−0.786866	−	0.617124i	$-0.788298\pi$
$701$	−11.7317	+	8.52359i	−0.443101	+	0.321932i	0.343765	+	0.939056i	$0.388298\pi$
$702$	−11.6142	−	8.43822i	−0.438350	−	0.318480i
$703$	−14.8405	−	45.6743i	−0.559719	−	1.72264i
$704$	−17.8919	+	12.9992i	−0.674325	+	0.489926i
$705$	16.3919	+	11.9094i	0.617354	+	0.448534i
$706$	14.9738	−	10.8791i	0.563548	−	0.409441i
$707$	−4.93114	−	15.1765i	−0.185455	−	0.570771i
$708$	0.0420558	+	0.129434i	0.00158055	+	0.00486444i
$709$	−14.4150			−0.541365			−0.270683	−	0.962669i	$-0.587249\pi$
$709$	−14.4150			−0.541365			−0.270683	+	0.962669i	$0.587249\pi$
$710$	−30.0532	−	19.5386i	−1.12788	−	0.733270i
$711$	14.4010			0.540079
$712$	4.96769	+	15.2890i	0.186172	+	0.572978i
$713$	5.92711	+	18.2418i	0.221972	+	0.683160i
$714$	−16.9440	+	12.3105i	−0.634113	+	0.460710i
$715$	25.2094	+	18.3157i	0.942779	+	0.684969i
$716$	2.71293	−	1.97106i	0.101387	−	0.0736619i
$717$	−14.3553	−	44.1809i	−0.536107	−	1.64997i
$718$	−14.8057	−	10.7569i	−0.552543	−	0.401446i
$719$	11.5105	−	8.36284i	0.429268	−	0.311881i	−0.352088	−	0.935967i	$-0.614528\pi$
$719$	11.5105	−	8.36284i	0.429268	−	0.311881i	0.781356	+	0.624086i	$0.214528\pi$
$720$	−6.15654	+	18.9479i	−0.229441	+	0.706146i
$721$	−6.02576	−	18.5454i	−0.224411	−	0.690667i
$722$	−32.2686	−	23.4445i	−1.20091	−	0.872515i
$723$	2.32655	−	7.16037i	0.0865252	−	0.266297i
$724$	−1.42926	+	1.03842i	−0.0531181	+	0.0385925i
$725$	−1.51917	+	4.67551i	−0.0564204	+	0.173644i
$726$	−3.88443	+	11.9551i	−0.144165	+	0.443694i
$727$	5.41315	−	16.6600i	0.200763	−	0.617884i	−0.799098	−	0.601200i	$-0.794689\pi$
$727$	5.41315	−	16.6600i	0.200763	−	0.617884i	0.999861	−	0.0166832i	$-0.00531068\pi$
$728$	38.5878	+	28.0357i	1.43016	+	1.03907i
$729$	−0.439135	−	1.35152i	−0.0162643	−	0.0500563i
$730$	29.1466			1.07876
$731$	−8.43286	+	6.12683i	−0.311900	+	0.226609i
$732$	0.493686	−	0.358684i	0.0182472	−	0.0132573i
$733$	−52.1367			−1.92571			−0.962857	−	0.270013i	$-0.912972\pi$
$733$	−52.1367			−1.92571			−0.962857	+	0.270013i	$0.912972\pi$
$734$	−2.09283	+	6.44107i	−0.0772478	+	0.237744i
$735$	23.3483	+	71.8586i	0.861214	+	2.65055i
$736$	−4.18662			−0.154321
$737$	−20.2982	−	14.7475i	−0.747694	−	0.543232i
$738$	6.20130	+	4.50551i	0.228273	+	0.165850i
$739$	10.3657	+	7.53112i	0.381309	+	0.277037i	0.761885	−	0.647713i	$-0.224274\pi$
$739$	10.3657	+	7.53112i	0.381309	+	0.277037i	−0.380576	+	0.924750i	$0.624274\pi$
$740$	−3.28908			−0.120909
$741$	17.9150	+	55.1367i	0.658124	+	2.02550i
$742$	19.6452			0.721197
$743$	11.0213	−	8.00746i	0.404333	−	0.293765i	−0.366971	−	0.930233i	$-0.619605\pi$
$743$	11.0213	−	8.00746i	0.404333	−	0.293765i	0.771304	+	0.636467i	$0.219605\pi$
$744$	25.0432			0.918127
$745$	6.49837	−	19.9999i	0.238082	−	0.732741i
$746$	8.35523	−	25.7148i	0.305907	−	0.941485i
$747$	12.5512			0.459226
$748$	−0.532383	+	0.386799i	−0.0194658	+	0.0141428i
$749$	−0.857616			−0.0313366
$750$	−0.589042	−	1.81289i	−0.0215088	−	0.0661972i
$751$	−7.07488			−0.258166			−0.129083	−	0.991634i	$-0.541203\pi$
$751$	−7.07488			−0.258166			−0.129083	+	0.991634i	$0.541203\pi$
$752$	−8.84149	−	6.42372i	−0.322416	−	0.234249i
$753$	10.4867	+	7.61904i	0.382157	+	0.277653i
$754$	−4.32209	−	3.14019i	−0.157401	−	0.114359i
$755$	−31.3354			−1.14041
$756$	−0.551178	−	1.69635i	−0.0200461	−	0.0616957i
$757$	−14.1831	+	43.6512i	−0.515495	+	1.58653i	0.266884	+	0.963729i	$0.414006\pi$
$757$	−14.1831	+	43.6512i	−0.515495	+	1.58653i	−0.782379	+	0.622803i	$0.785994\pi$
$758$	−3.59422			−0.130548
$759$	22.2922	−	16.1962i	0.809156	−	0.587886i
$760$	−51.5001	+	37.4170i	−1.86810	+	1.35726i
$761$	18.8748			0.684211			0.342105	−	0.939662i	$-0.388860\pi$
$761$	18.8748			0.684211			0.342105	+	0.939662i	$0.388860\pi$
$762$	−1.27489	−	3.92371i	−0.0461844	−	0.142141i
$763$	−15.2335	−	11.0678i	−0.551489	−	0.400680i
$764$	−0.262451	+	0.807742i	−0.00949515	+	0.0292231i
$765$	−2.79065	+	8.58874i	−0.100896	+	0.310527i
$766$	−4.42665	+	13.6238i	−0.159941	+	0.492249i
$767$	−1.27469	+	0.926118i	−0.0460264	+	0.0334402i
$768$	−2.44055	+	7.51124i	−0.0880658	+	0.271039i
$769$	25.0734	+	18.2169i	0.904168	+	0.656917i	0.939533	−	0.342458i	$-0.111259\pi$
$769$	25.0734	+	18.2169i	0.904168	+	0.656917i	−0.0353649	+	0.999374i	$0.511259\pi$
$770$	−14.5291	−	44.7160i	−0.523593	−	1.61145i
$771$	−13.8024	+	42.4793i	−0.497080	+	1.52986i
$772$	1.18906	−	0.863899i	0.0427950	−	0.0310924i
$773$	−15.4968	−	11.2591i	−0.557382	−	0.404962i	0.273118	−	0.961981i	$-0.411945\pi$
$773$	−15.4968	−	11.2591i	−0.557382	−	0.404962i	−0.830500	+	0.557019i	$0.811945\pi$
$774$	−4.55937	−	14.0323i	−0.163883	−	0.504381i
$775$	15.2600	−	11.0870i	0.548155	−	0.398258i
$776$	32.4569	+	23.5813i	1.16514	+	0.846521i
$777$	51.7191	−	37.5761i	1.85541	−	1.34804i
$778$	10.6592	+	32.8056i	0.382150	+	1.17614i
$779$	6.98924	+	21.5107i	0.250415	+	0.770700i
$780$	3.97049			0.142166
$781$	21.8618	−	1.13454i	0.782277	−	0.0405969i
$782$	11.0315			0.394485
$783$	0.873210	+	2.68746i	0.0312060	+	0.0960421i
$784$	−12.5936	−	38.7593i	−0.449773	−	1.38426i
$785$	23.2205	−	16.8707i	0.828776	−	0.602141i
$786$	45.8552	+	33.3157i	1.63560	+	1.18833i
$787$	20.5087	−	14.9005i	0.731057	−	0.531144i	−0.158841	−	0.987304i	$-0.550776\pi$
$787$	20.5087	−	14.9005i	0.731057	−	0.531144i	0.889898	+	0.456160i	$0.150776\pi$
$788$	0.0457289	+	0.140739i	0.00162903	+	0.00501363i
$789$	25.8103	+	18.7523i	0.918870	+	0.667598i
$790$	−28.5927	+	20.7738i	−1.01728	+	0.739100i
$791$	−16.6649	+	51.2893i	−0.592536	+	1.82364i
$792$	−4.07134	−	12.5303i	−0.144669	−	0.445244i
$793$	5.71552	+	4.15257i	0.202964	+	0.147462i
$794$	−5.18820	+	15.9677i	−0.184122	+	0.566671i
$795$	18.7132	−	13.5959i	0.663688	−	0.482198i
$796$	−0.741712	+	2.28275i	−0.0262893	+	0.0809101i
$797$	16.7231	−	51.4685i	0.592364	−	1.82311i	0.0249312	−	0.999689i	$-0.492063\pi$
$797$	16.7231	−	51.4685i	0.592364	−	1.82311i	0.567433	−	0.823420i	$-0.307937\pi$
$798$	27.0314	−	83.1940i	0.956900	−	2.94504i
$799$	−4.00769	−	2.91176i	−0.141782	−	0.103011i
$800$	1.27228	+	3.91567i	0.0449818	+	0.138440i
$801$	−9.52517			−0.336555
$802$	−12.3083	+	8.94249i	−0.434620	+	0.315770i
$803$	−14.4003	+	10.4624i	−0.508176	+	0.369212i
$804$	−3.19697			−0.112748
$805$	20.0555	−	61.7244i	0.706862	−	2.17550i
$806$	6.33422	+	19.4947i	0.223113	+	0.686672i
$807$	−27.5713			−0.970557
$808$	8.87824	+	6.45042i	0.312335	+	0.226925i
$809$	−24.4217	−	17.7434i	−0.858623	−	0.623826i	0.0688871	−	0.997624i	$-0.478055\pi$
$809$	−24.4217	−	17.7434i	−0.858623	−	0.623826i	−0.927510	+	0.373798i	$0.878055\pi$
$810$	38.5314	+	27.9947i	1.35386	+	0.983634i
$811$	12.6854			0.445444			0.222722	−	0.974882i	$-0.428506\pi$
$811$	12.6854			0.445444			0.222722	+	0.974882i	$0.428506\pi$
$812$	−0.205114	−	0.631278i	−0.00719811	−	0.0221535i
$813$	3.38739			0.118801
$814$	−19.7348	+	14.3382i	−0.691706	+	0.502554i
$815$	−61.1743			−2.14284
$816$	4.11028	−	12.6501i	0.143889	−	0.442843i
$817$	13.4532	−	41.4048i	0.470670	−	1.44857i
$818$	4.80715			0.168078
$819$	−22.8640	+	16.6116i	−0.798931	+	0.580457i
$820$	1.54902			0.0540942
$821$	−4.01586	−	12.3596i	−0.140155	−	0.431351i	0.856202	−	0.516642i	$-0.172818\pi$
$821$	−4.01586	−	12.3596i	−0.140155	−	0.431351i	−0.996356	+	0.0852906i	$0.972818\pi$
$822$	58.0779			2.02570
$823$	7.17127	+	5.21024i	0.249975	+	0.181617i	0.705716	−	0.708495i	$-0.250626\pi$
$823$	7.17127	+	5.21024i	0.249975	+	0.181617i	−0.455741	+	0.890113i	$0.650626\pi$
$824$	10.8490	+	7.88229i	0.377944	+	0.274593i
$825$	−21.9225	−	15.9276i	−0.763242	−	0.554528i
$826$	2.37738			0.0827197
$827$	14.4672	+	44.5256i	0.503075	+	1.54831i	0.803983	+	0.594653i	$0.202710\pi$
$827$	14.4672	+	44.5256i	0.503075	+	1.54831i	−0.300907	+	0.953653i	$0.597290\pi$
$828$	0.397326	−	1.22284i	0.0138080	−	0.0424968i
$829$	−4.81689			−0.167298			−0.0836488	−	0.996495i	$-0.526657\pi$
$829$	−4.81689			−0.167298			−0.0836488	+	0.996495i	$0.526657\pi$
$830$	−24.9201	+	18.1055i	−0.864991	+	0.628453i
$831$	24.4519	−	17.7654i	0.848228	−	0.616274i
$832$	−32.6243			−1.13104
$833$	−5.70848	−	17.5689i	−0.197787	−	0.608726i
$834$	37.1857	+	27.0170i	1.28764	+	0.935523i
$835$	−19.4060	+	59.7254i	−0.671571	+	2.06688i
$836$	0.849330	−	2.61397i	0.0293747	−	0.0904060i
$837$	3.35037	−	10.3114i	0.115806	−	0.356413i
$838$	−22.9618	+	16.6827i	−0.793203	+	0.576295i
$839$	−1.45521	+	4.47866i	−0.0502393	+	0.154621i	−0.973029	−	0.230684i	$-0.925904\pi$
$839$	−1.45521	+	4.47866i	−0.0502393	+	0.154621i	0.922789	+	0.385305i	$0.125904\pi$
$840$	−68.5545	−	49.8078i	−2.36536	−	1.71853i
$841$	−8.63654	−	26.5805i	−0.297812	−	0.916570i
$842$	11.9955	−	36.9183i	0.413392	−	1.27229i
$843$	4.20950	−	3.05838i	0.144983	−	0.105336i
$844$	2.33206	+	1.69434i	0.0802729	+	0.0583217i
$845$	1.63258	+	5.02457i	0.0561625	+	0.172850i
$846$	5.67283	−	4.12155i	0.195036	−	0.141702i
$847$	−14.6280	−	10.6279i	−0.502624	−	0.365177i
$848$	−10.0936	+	7.33340i	−0.346614	+	0.251830i
$849$	−0.343526	−	1.05726i	−0.0117898	−	0.0362852i
$850$	−3.35237	−	10.3175i	−0.114985	−	0.353889i
$851$	−33.6720			−1.15426
$852$	2.16865	−	1.75431i	0.0742969	−	0.0601017i
$853$	−38.7893			−1.32812			−0.664060	−	0.747679i	$-0.731168\pi$
$853$	−38.7893			−1.32812			−0.664060	+	0.747679i	$0.731168\pi$
$854$	−3.29406	−	10.1381i	−0.112720	−	0.346918i
$855$	−11.6556	−	35.8721i	−0.398612	−	1.22680i
$856$	0.477149	−	0.346669i	0.0163086	−	0.0118489i
$857$	−42.6515	−	30.9881i	−1.45695	−	1.05853i	−0.984145	−	0.177366i	$-0.943242\pi$
$857$	−42.6515	−	30.9881i	−1.45695	−	1.05853i	−0.472802	−	0.881169i	$-0.656758\pi$
$858$	23.8233	−	17.3087i	0.813316	−	0.590908i
$859$	−3.37561	−	10.3891i	−0.115174	−	0.354470i	0.876809	−	0.480839i	$-0.159668\pi$
$859$	−3.37561	−	10.3891i	−0.115174	−	0.354470i	−0.991983	+	0.126369i	$0.959668\pi$
$860$	−2.41219	−	1.75256i	−0.0822551	−	0.0597618i
$861$	−24.3575	+	17.6968i	−0.830103	+	0.603105i
$862$	9.94107	−	30.5955i	0.338594	−	1.04209i
$863$	−9.37471	−	28.8524i	−0.319119	−	0.982147i	−0.974026	−	0.226437i	$-0.927292\pi$
$863$	−9.37471	−	28.8524i	−0.319119	−	0.982147i	0.654907	−	0.755709i	$-0.272708\pi$
$864$	1.91457	+	1.39101i	0.0651349	+	0.0473233i
$865$	10.7522	−	33.0920i	0.365587	−	1.12516i
$866$	−30.2753	+	21.9963i	−1.02879	+	0.747463i
$867$	−9.56618	+	29.4417i	−0.324885	+	0.999892i
$868$	−0.786992	+	2.42211i	−0.0267122	+	0.0822118i
$869$	6.66972	−	20.5273i	0.226255	−	0.696340i
$870$	7.67856	+	5.57880i	0.260328	+	0.189139i
$871$	−11.4373	−	35.2005i	−0.387540	−	1.19272i
$872$	12.9493			0.438517
$873$	−19.2313	+	13.9724i	−0.650881	+	0.472893i
$874$	−37.2751	+	27.0820i	−1.26085	+	0.916061i
$875$	2.74186			0.0926919
$876$	−0.700867	+	2.15705i	−0.0236801	+	0.0728798i
$877$	−0.536197	−	1.65024i	−0.0181061	−	0.0557248i	0.941595	−	0.336747i	$-0.109327\pi$
$877$	−0.536197	−	1.65024i	−0.0181061	−	0.0557248i	−0.959701	+	0.281022i	$0.909327\pi$
$878$	−9.75577			−0.329241
$879$	−11.3163	−	8.22179i	−0.381690	−	0.277314i
$880$	24.1571	+	17.5512i	0.814337	+	0.591650i
$881$	17.0005	+	12.3516i	0.572760	+	0.416134i	0.836107	−	0.548567i	$-0.184826\pi$
$881$	17.0005	+	12.3516i	0.572760	+	0.416134i	−0.263347	+	0.964701i	$0.584826\pi$
$882$	26.1483			0.880459
$883$	14.5034	+	44.6369i	0.488078	+	1.50215i	0.827473	+	0.561506i	$0.189778\pi$
$883$	14.5034	+	44.6369i	0.488078	+	1.50215i	−0.339394	+	0.940644i	$0.610222\pi$
$884$	−0.970754			−0.0326500
$885$	2.26460	−	1.64533i	0.0761236	−	0.0553070i
$886$	−12.7002			−0.426671
$887$	2.05032	−	6.31024i	0.0688431	−	0.211877i	−0.910716	−	0.413032i	$-0.864470\pi$
$887$	2.05032	−	6.31024i	0.0688431	−	0.211877i	0.979559	+	0.201155i	$0.0644696\pi$
$888$	−13.5856	+	41.8123i	−0.455904	+	1.40313i
$889$	5.93434			0.199031
$890$	18.9120	−	13.7403i	0.633931	−	0.460577i
$891$	−29.0860			−0.974419
$892$	1.33419	+	4.10623i	0.0446721	+	0.137487i
$893$	20.6902			0.692370
$894$	−16.0775	−	11.6810i	−0.537713	−	0.390672i
$895$	−55.7993	−	40.5405i	−1.86516	−	1.35512i
$896$	33.9131	+	24.6393i	1.13296	+	0.823141i
$897$	40.6479			1.35719
$898$	−1.23570	−	3.80310i	−0.0412359	−	0.126911i
$899$	1.24680	−	3.83726i	0.0415831	−	0.127980i
$900$	−1.26445			−0.0421483
$901$	−4.57523	+	3.32410i	−0.152423	+	0.110742i
$902$	9.29429	−	6.75269i	0.309466	−	0.224840i
$903$	57.9526			1.92854
$904$	−11.4606	−	35.2721i	−0.381173	−	1.17313i
$905$	29.3969	+	21.3581i	0.977186	+	0.709967i
$906$	−9.15077	+	28.1632i	−0.304014	+	0.935659i
$907$	12.7624	−	39.2786i	0.423768	−	1.30423i	−0.480400	−	0.877049i	$-0.659509\pi$
$907$	12.7624	−	39.2786i	0.423768	−	1.30423i	0.904169	−	0.427176i	$-0.140491\pi$
$908$	0.138904	−	0.427503i	0.00460969	−	0.0141872i
$909$	−5.26051	+	3.82198i	−0.174480	+	0.126767i
$910$	21.4330	−	65.9639i	0.710496	−	2.18668i
$911$	22.3677	+	16.2511i	0.741075	+	0.538423i	0.893048	−	0.449962i	$-0.148563\pi$
$911$	22.3677	+	16.2511i	0.741075	+	0.538423i	−0.151972	+	0.988385i	$0.548563\pi$
$912$	17.1672	+	52.8351i	0.568462	+	1.74955i
$913$	5.81303	−	17.8907i	0.192383	−	0.592094i
$914$	39.0663	−	28.3833i	1.29220	−	0.938837i
$915$	−10.1541	−	7.37738i	−0.335684	−	0.243889i
$916$	0.905684	+	2.78741i	0.0299247	+	0.0920986i
$917$	−65.9584	+	47.9216i	−2.17814	+	1.58251i
$918$	−5.04476	−	3.66523i	−0.166502	−	0.120971i
$919$	28.2965	−	20.5586i	0.933415	−	0.678166i	−0.0134112	−	0.999910i	$-0.504269\pi$
$919$	28.2965	−	20.5586i	0.933415	−	0.678166i	0.946827	+	0.321744i	$0.104269\pi$
$920$	13.7923	+	42.4483i	0.454718	+	1.39948i
$921$	−12.1497	−	37.3930i	−0.400347	−	1.23214i
$922$	42.2463			1.39131
$923$	27.0745	+	17.6020i	0.891167	+	0.579378i
$924$	3.65866			0.120361
$925$	10.2326	+	31.4928i	0.336447	+	1.03548i
$926$	−5.82459	−	17.9263i	−0.191408	−	0.589093i
$927$	−6.42824	+	4.67039i	−0.211131	+	0.153396i
$928$	0.712484	+	0.517650i	0.0233884	+	0.0169927i
$929$	−24.6643	+	17.9196i	−0.809208	+	0.587924i	−0.913601	−	0.406612i	$-0.866710\pi$
$929$	−24.6643	+	17.9196i	−0.809208	+	0.587924i	0.104393	+	0.994536i	$0.466710\pi$
$930$	−11.2533	−	34.6340i	−0.369009	−	1.13569i
$931$	62.4199	+	45.3507i	2.04573	+	1.48631i
$932$	−2.97933	+	2.16461i	−0.0975913	+	0.0709042i
$933$	8.70109	−	26.7792i	0.284861	−	0.876712i
$934$	−6.06097	−	18.6538i	−0.198321	−	0.610370i
$935$	10.9500	+	7.95564i	0.358103	+	0.260177i
$936$	6.00592	−	18.4843i	0.196310	−	0.604179i
$937$	−32.0039	+	23.2522i	−1.04552	+	0.759617i	−0.971356	−	0.237629i	$-0.923630\pi$
$937$	−32.0039	+	23.2522i	−1.04552	+	0.759617i	−0.0741668	+	0.997246i	$0.523630\pi$
$938$	−17.2575	+	53.1130i	−0.563476	+	1.73420i
$939$	−2.51186	+	7.73069i	−0.0819713	+	0.252282i
$940$	0.437881	−	1.34766i	0.0142821	−	0.0439558i
$941$	12.3627	+	8.98200i	0.403011	+	0.292805i	0.770766	−	0.637118i	$-0.219874\pi$
$941$	12.3627	+	8.98200i	0.403011	+	0.292805i	−0.367755	+	0.929923i	$0.619874\pi$
$942$	−8.38178	−	25.7965i	−0.273093	−	0.840494i
$943$	15.8581			0.516411
$944$	−1.22148	+	0.887459i	−0.0397559	+	0.0288843i
$945$	−29.6795	+	21.5634i	−0.965475	+	0.701459i
$946$	−22.1134			−0.718969
$947$	−10.2733	+	31.6180i	−0.333838	+	1.02745i	0.633454	+	0.773781i	$0.281637\pi$
$947$	−10.2733	+	31.6180i	−0.333838	+	1.02745i	−0.967292	+	0.253667i	$0.918363\pi$
$948$	−0.849857	−	2.61559i	−0.0276021	−	0.0849505i
$949$	−26.2577			−0.852362
$950$	36.6569	+	26.6328i	1.18931	+	0.864081i
$951$	−37.8031	−	27.4655i	−1.22585	−	0.890631i
$952$	16.7611	+	12.1776i	0.543229	+	0.394679i
$953$	41.3447			1.33929			0.669643	−	0.742683i	$-0.266447\pi$
$953$	41.3447			1.33929			0.669643	+	0.742683i	$0.266447\pi$
$954$	−2.47368	−	7.61319i	−0.0800882	−	0.246486i
$955$	17.4685			0.565268
$956$	−2.62839	+	1.90963i	−0.0850081	+	0.0617620i
$957$	−5.79628			−0.187367
$958$	−14.6013	+	44.9383i	−0.471748	+	1.45189i
$959$	−25.8152	+	79.4509i	−0.833616	+	2.56560i
$960$	57.9597			1.87064
$961$	12.5554	−	9.12206i	0.405014	−	0.294260i
$962$	−35.9848			−1.16020
$963$	0.107989	+	0.332356i	0.00347990	+	0.0107100i
$964$	−0.526541			−0.0169587
$965$	−24.4564	−	17.7686i	−0.787279	−	0.571992i
$966$	−49.6189	−	36.0503i	−1.59646	−	1.15990i
$967$	−26.2780	−	19.0921i	−0.845042	−	0.613959i	0.0787323	−	0.996896i	$-0.474913\pi$
$967$	−26.2780	−	19.0921i	−0.845042	−	0.613959i	−0.923775	+	0.382937i	$0.874913\pi$
$968$	12.4346			0.399662
$969$	7.78158	+	23.9492i	0.249980	+	0.769360i
$970$	18.0277	−	55.4835i	0.578834	−	1.78147i
$971$	24.6783			0.791965			0.395983	−	0.918258i	$-0.370404\pi$
$971$	24.6783			0.791965			0.395983	+	0.918258i	$0.370404\pi$
$972$	−1.98072	+	1.43908i	−0.0635316	+	0.0461584i
$973$	−53.4882	+	38.8615i	−1.71475	+	1.24584i
$974$	−3.26560			−0.104637
$975$	−12.3526	−	38.0172i	−0.395598	−	1.21753i
$976$	5.47694	+	3.97923i	0.175313	+	0.127372i
$977$	16.9332	−	52.1152i	0.541743	−	1.66731i	−0.186869	−	0.982385i	$-0.559834\pi$
$977$	16.9332	−	52.1152i	0.541743	−	1.66731i	0.728611	−	0.684927i	$-0.240166\pi$
$978$	−17.8645	+	54.9813i	−0.571244	+	1.75811i
$979$	−4.41152	+	13.5773i	−0.140993	+	0.433931i
$980$	4.27497	−	3.10595i	0.136559	−	0.0992158i
$981$	−2.37098	+	7.29714i	−0.0756997	+	0.232980i
$982$	−14.9848	−	10.8871i	−0.478183	−	0.347420i
$983$	−4.75703	−	14.6406i	−0.151726	−	0.466964i	0.846089	−	0.533042i	$-0.178951\pi$
$983$	−4.75703	−	14.6406i	−0.151726	−	0.466964i	−0.997814	+	0.0660781i	$0.978951\pi$
$984$	6.39826	−	19.6918i	0.203969	−	0.627753i
$985$	2.46239	−	1.78903i	0.0784582	−	0.0570032i
$986$	−1.87735	−	1.36397i	−0.0597870	−	0.0434378i
$987$	8.51089	+	26.1938i	0.270905	+	0.833758i
$988$	3.28016	−	2.38317i	0.104356	−	0.0758188i
$989$	−24.6949	−	17.9419i	−0.785251	−	0.570518i
$990$	−15.4996	+	11.2611i	−0.492609	+	0.357901i
$991$	−5.58837	−	17.1992i	−0.177520	−	0.546351i	0.822219	−	0.569171i	$-0.192736\pi$
$991$	−5.58837	−	17.1992i	−0.177520	−	0.546351i	−0.999740	+	0.0228194i	$0.992736\pi$
$992$	−1.04418	−	3.21365i	−0.0331526	−	0.102033i
$993$	24.5756			0.779885
$994$	−17.4388	−	45.4989i	−0.553124	−	1.44314i
$995$	49.3677			1.56506
$996$	−0.740697	−	2.27963i	−0.0234699	−	0.0722329i
$997$	18.5106	+	56.9698i	0.586237	+	1.80425i	0.594244	+	0.804285i	$0.297451\pi$
$997$	18.5106	+	56.9698i	0.586237	+	1.80425i	−0.00800667	+	0.999968i	$0.502549\pi$
$998$	−19.0680	+	13.8537i	−0.603586	+	0.438531i
$999$	15.3984	+	11.1876i	0.487184	+	0.353960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.c.a.5.4	✓	20
3.2	odd	2		639.2.f.c.289.2		20
71.25	even	5		5041.2.a.i.1.7		10
71.46	odd	10		5041.2.a.j.1.7		10
71.57	even	5	inner	71.2.c.a.57.4	yes	20
213.128	odd	10		639.2.f.c.199.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.c.a.5.4	✓	20	1.1	even	1	trivial
71.2.c.a.57.4	yes	20	71.57	even	5	inner
639.2.f.c.199.2		20	213.128	odd	10
639.2.f.c.289.2		20	3.2	odd	2
5041.2.a.i.1.7		10	71.25	even	5
5041.2.a.j.1.7		10	71.46	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)

\(f(q)\)	\(=\)	\(q+(0.420063 + 1.29282i) q^{2} +(0.672312 + 2.06916i) q^{3} +(0.123097 - 0.0894354i) q^{4} +(-2.53185 - 1.83950i) q^{5} +(-2.39265 + 1.73836i) q^{6} +(-1.31457 - 4.04584i) q^{7} +(2.36681 + 1.71959i) q^{8} +(-1.40238 + 1.01889i) q^{9} +O(q^{10})\)	\(q+(0.420063 + 1.29282i) q^{2} +(0.672312 + 2.06916i) q^{3} +(0.123097 - 0.0894354i) q^{4} +(-2.53185 - 1.83950i) q^{5} +(-2.39265 + 1.73836i) q^{6} +(-1.31457 - 4.04584i) q^{7} +(2.36681 + 1.71959i) q^{8} +(-1.40238 + 1.01889i) q^{9} +(1.31461 - 4.04595i) q^{10} +(0.802829 + 2.47085i) q^{11} +(0.267816 + 0.194580i) q^{12} +(-1.18431 + 3.64494i) q^{13} +(4.67835 - 3.39902i) q^{14} +(2.10403 - 6.47554i) q^{15} +(-1.13488 + 3.49279i) q^{16} +(-0.514419 + 1.58322i) q^{17} +(-1.90633 - 1.38503i) q^{18} +(-2.14855 - 6.61255i) q^{19} -0.476181 q^{20} +(7.48770 - 5.44013i) q^{21} +(-2.85714 + 2.07583i) q^{22} -4.87491 q^{23} +(-1.96688 + 6.05342i) q^{24} +(1.48144 + 4.55941i) q^{25} -5.20974 q^{26} +(2.22933 + 1.61970i) q^{27} +(-0.523662 - 0.380463i) q^{28} +(0.829618 + 0.602753i) q^{29} +9.25554 q^{30} +(-1.21584 - 3.74197i) q^{31} +0.858810 q^{32} +(-4.57285 + 3.32237i) q^{33} -2.26291 q^{34} +(-4.11402 + 12.6616i) q^{35} +(-0.0815044 + 0.250845i) q^{36} +6.90721 q^{37} +(7.64632 - 5.55538i) q^{38} -8.33819 q^{39} +(-2.82924 - 8.70751i) q^{40} -3.25301 q^{41} +(10.1784 + 7.39507i) q^{42} +(5.06571 + 3.68045i) q^{43} +(0.319808 + 0.232354i) q^{44} +5.42486 q^{45} +(-2.04777 - 6.30239i) q^{46} +(-0.919569 + 2.83014i) q^{47} -7.99014 q^{48} +(-8.97761 + 6.52262i) q^{49} +(-5.27221 + 3.83049i) q^{50} -3.62179 q^{51} +(0.180201 + 0.554601i) q^{52} +(2.74839 + 1.99682i) q^{53} +(-1.15753 + 3.56250i) q^{54} +(2.51249 - 7.73265i) q^{55} +(3.84584 - 11.8363i) q^{56} +(12.2379 - 8.89138i) q^{57} +(-0.430760 + 1.32574i) q^{58} +(0.332599 + 0.241648i) q^{59} +(-0.320142 - 0.985296i) q^{60} +(0.569635 - 1.75316i) q^{61} +(4.32698 - 3.14373i) q^{62} +(5.96579 + 4.33440i) q^{63} +(2.63051 + 8.09587i) q^{64} +(9.70337 - 7.04991i) q^{65} +(-6.21612 - 4.51627i) q^{66} +(-7.81299 + 5.67647i) q^{67} +(0.0782723 + 0.240897i) q^{68} +(-3.27746 - 10.0870i) q^{69} -18.0974 q^{70} +(2.18500 - 8.13792i) q^{71} -5.07124 q^{72} +(2.11717 + 6.51599i) q^{73} +(2.90147 + 8.92980i) q^{74} +(-8.43817 + 6.13069i) q^{75} +(-0.855876 - 0.621831i) q^{76} +(8.94131 - 6.49624i) q^{77} +(-3.50257 - 10.7798i) q^{78} +(-6.72113 - 4.88318i) q^{79} +(9.29833 - 6.75563i) q^{80} +(-3.45960 + 10.6476i) q^{81} +(-1.36647 - 4.20556i) q^{82} +(-5.85783 - 4.25596i) q^{83} +(0.435175 - 1.33933i) q^{84} +(4.21477 - 3.06221i) q^{85} +(-2.63025 + 8.09508i) q^{86} +(-0.689431 + 2.12185i) q^{87} +(-2.34871 + 7.22859i) q^{88} +(4.44552 + 3.22986i) q^{89} +(2.27879 + 7.01338i) q^{90} +16.3037 q^{91} +(-0.600088 + 0.435990i) q^{92} +(6.92533 - 5.03154i) q^{93} -4.04515 q^{94} +(-6.72397 + 20.6943i) q^{95} +(0.577388 + 1.77702i) q^{96} +13.7133 q^{97} +(-12.2038 - 8.86655i) q^{98} +(-3.64339 - 2.64708i) 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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