LMFDB - Embedded newform 71.2.c.a.25.3

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			25.3
Root			$0.685174 + 0.497808i$ of defining polynomial
Character	$\chi$	$=$	71.25
Dual form			71.2.c.a.54.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.685174 + 0.497808i) q^{2} +(1.00262 - 0.728443i) q^{3} +(-0.396383 + 1.21994i) q^{4} +(0.467113 + 1.43763i) q^{5} +(-0.324342 + 0.998220i) q^{6} +(2.86367 - 2.08058i) q^{7} +(-0.859132 - 2.64414i) q^{8} +(-0.452442 + 1.39247i) q^{9} +O(q^{10})$	\(q+(-0.685174 + 0.497808i) q^{2} +(1.00262 - 0.728443i) q^{3} +(-0.396383 + 1.21994i) q^{4} +(0.467113 + 1.43763i) q^{5} +(-0.324342 + 0.998220i) q^{6} +(2.86367 - 2.08058i) q^{7} +(-0.859132 - 2.64414i) q^{8} +(-0.452442 + 1.39247i) q^{9} +(-1.03572 - 0.752493i) q^{10} +(-1.10266 + 0.801130i) q^{11} +(0.491238 + 1.51187i) q^{12} +(-3.28145 - 2.38411i) q^{13} +(-0.926385 + 2.85112i) q^{14} +(1.51556 + 1.10112i) q^{15} +(-0.170560 - 0.123919i) q^{16} +(-4.53547 - 3.29521i) q^{17} +(-0.383183 - 1.17932i) q^{18} +(3.19971 - 2.32472i) q^{19} -1.93898 q^{20} +(1.35558 - 4.17204i) q^{21} +(0.356706 - 1.09783i) q^{22} -3.61216 q^{23} +(-2.78748 - 2.02522i) q^{24} +(2.19651 - 1.59586i) q^{25} +3.43520 q^{26} +(1.70961 + 5.26163i) q^{27} +(1.40307 + 4.31822i) q^{28} +(1.00476 + 3.09235i) q^{29} -1.58657 q^{30} +(-4.91813 + 3.57323i) q^{31} +5.73897 q^{32} +(-0.521967 + 1.60645i) q^{33} +4.74797 q^{34} +(4.32876 + 3.14503i) q^{35} +(-1.51940 - 1.10391i) q^{36} +10.1421 q^{37} +(-1.03509 + 3.18568i) q^{38} -5.02672 q^{39} +(3.39997 - 2.47022i) q^{40} -6.99103 q^{41} +(1.14807 + 3.53339i) q^{42} +(-0.466627 - 1.43613i) q^{43} +(-0.540256 - 1.66274i) q^{44} -2.21320 q^{45} +(2.47496 - 1.79816i) q^{46} +(6.40533 + 4.65375i) q^{47} -0.261274 q^{48} +(1.70869 - 5.25880i) q^{49} +(-0.710560 + 2.18688i) q^{50} -6.94770 q^{51} +(4.20919 - 3.05816i) q^{52} +(-0.865214 - 2.66286i) q^{53} +(-3.79066 - 2.75408i) q^{54} +(-1.66679 - 1.21100i) q^{55} +(-7.96161 - 5.78445i) q^{56} +(1.51465 - 4.66161i) q^{57} +(-2.22784 - 1.61862i) q^{58} +(1.04569 + 3.21830i) q^{59} +(-1.94405 + 1.41243i) q^{60} +(-3.69213 - 2.68249i) q^{61} +(1.59099 - 4.89657i) q^{62} +(1.60151 + 4.92893i) q^{63} +(-3.59108 + 2.60907i) q^{64} +(1.89466 - 5.83115i) q^{65} +(-0.442065 - 1.36054i) q^{66} +(-3.52980 + 10.8636i) q^{67} +(5.81775 - 4.22684i) q^{68} +(-3.62160 + 2.63125i) q^{69} -4.53157 q^{70} +(8.41379 + 0.456169i) q^{71} +4.07060 q^{72} +(-9.86451 + 7.16698i) q^{73} +(-6.94908 + 5.04880i) q^{74} +(1.03976 - 3.20006i) q^{75} +(1.56772 + 4.82494i) q^{76} +(-1.49084 + 4.58834i) q^{77} +(3.44418 - 2.50234i) q^{78} +(-0.154617 - 0.475862i) q^{79} +(0.0984785 - 0.303086i) q^{80} +(1.99334 + 1.44825i) q^{81} +(4.79008 - 3.48020i) q^{82} +(-3.03657 - 9.34561i) q^{83} +(4.55232 + 3.30745i) q^{84} +(2.61871 - 8.05955i) q^{85} +(1.03464 + 0.751709i) q^{86} +(3.25999 + 2.36852i) q^{87} +(3.06563 + 2.22731i) q^{88} +(-3.04666 - 9.37667i) q^{89} +(1.51643 - 1.10175i) q^{90} -14.3573 q^{91} +(1.43180 - 4.40662i) q^{92} +(-2.32810 + 7.16515i) q^{93} -6.70545 q^{94} +(4.83672 + 3.51408i) q^{95} +(5.75398 - 4.18051i) q^{96} -15.0069 q^{97} +(1.44713 + 4.45379i) q^{98} +(-0.616662 - 1.89789i) 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 $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.685174	+	0.497808i	−0.484491	+	0.352004i	−0.803062	−	0.595896i	$-0.796797\pi$
$2$	−0.685174	+	0.497808i	−0.484491	+	0.352004i	0.318571	+	0.947899i	$0.396797\pi$
$3$	1.00262	−	0.728443i	0.578860	−	0.420567i	−0.259453	−	0.965756i	$-0.583542\pi$
$3$	1.00262	−	0.728443i	0.578860	−	0.420567i	0.838313	+	0.545189i	$0.183542\pi$
$4$	−0.396383	+	1.21994i	−0.198192	+	0.609971i
$5$	0.467113	+	1.43763i	0.208900	+	0.642927i	0.999531	+	0.0306339i	$0.00975259\pi$
$5$	0.467113	+	1.43763i	0.208900	+	0.642927i	−0.790631	+	0.612293i	$0.790247\pi$
$6$	−0.324342	+	0.998220i	−0.132412	+	0.407522i
$7$	2.86367	−	2.08058i	1.08237	−	0.786385i	0.104272	−	0.994549i	$-0.466749\pi$
$7$	2.86367	−	2.08058i	1.08237	−	0.786385i	0.978094	+	0.208164i	$0.0667487\pi$
$8$	−0.859132	−	2.64414i	−0.303749	−	0.934844i
$9$	−0.452442	+	1.39247i	−0.150814	+	0.464158i
$10$	−1.03572	−	0.752493i	−0.327523	−	0.237959i
$11$	−1.10266	+	0.801130i	−0.332465	+	0.241550i	−0.741476	−	0.670980i	$-0.765874\pi$
$11$	−1.10266	+	0.801130i	−0.332465	+	0.241550i	0.409011	+	0.912529i	$0.365874\pi$
$12$	0.491238	+	1.51187i	0.141808	+	0.436441i
$13$	−3.28145	−	2.38411i	−0.910110	−	0.661234i	0.0309325	−	0.999521i	$-0.490152\pi$
$13$	−3.28145	−	2.38411i	−0.910110	−	0.661234i	−0.941043	+	0.338288i	$0.890152\pi$
$14$	−0.926385	+	2.85112i	−0.247587	+	0.761994i
$15$	1.51556	+	1.10112i	0.391317	+	0.284308i
$16$	−0.170560	−	0.123919i	−0.0426400	−	0.0309797i
$17$	−4.53547	−	3.29521i	−1.10001	−	0.799206i	−0.118950	−	0.992900i	$-0.537953\pi$
$17$	−4.53547	−	3.29521i	−1.10001	−	0.799206i	−0.981062	+	0.193695i	$0.937953\pi$
$18$	−0.383183	−	1.17932i	−0.0903172	−	0.277968i
$19$	3.19971	−	2.32472i	0.734064	−	0.533328i	−0.156783	−	0.987633i	$-0.550112\pi$
$19$	3.19971	−	2.32472i	0.734064	−	0.533328i	0.890846	+	0.454305i	$0.150112\pi$
$20$	−1.93898			−0.433569
$21$	1.35558	−	4.17204i	0.295811	−	0.910414i
$22$	0.356706	−	1.09783i	0.0760499	−	0.234057i
$23$	−3.61216			−0.753187			−0.376593	−	0.926379i	$-0.622905\pi$
$23$	−3.61216			−0.753187			−0.376593	+	0.926379i	$0.622905\pi$
$24$	−2.78748	−	2.02522i	−0.568992	−	0.413397i
$25$	2.19651	−	1.59586i	0.439301	−	0.319171i
$26$	3.43520			0.673697
$27$	1.70961	+	5.26163i	0.329014	+	1.01260i
$28$	1.40307	+	4.31822i	0.265156	+	0.816067i
$29$	1.00476	+	3.09235i	0.186580	+	0.574235i	0.999972	−	0.00748157i	$-0.00238148\pi$
$29$	1.00476	+	3.09235i	0.186580	+	0.574235i	−0.813392	+	0.581716i	$0.802381\pi$
$30$	−1.58657			−0.289667
$31$	−4.91813	+	3.57323i	−0.883322	+	0.641771i	−0.934128	−	0.356938i	$-0.883821\pi$
$31$	−4.91813	+	3.57323i	−0.883322	+	0.641771i	0.0508064	+	0.998709i	$0.483821\pi$
$32$	5.73897			1.01452
$33$	−0.521967	+	1.60645i	−0.0908628	+	0.279647i
$34$	4.74797			0.814270
$35$	4.32876	+	3.14503i	0.731694	+	0.531607i
$36$	−1.51940	−	1.10391i	−0.253233	−	0.183984i
$37$	10.1421			1.66734			0.833672	−	0.552259i	$-0.186234\pi$
$37$	10.1421			1.66734			0.833672	+	0.552259i	$0.186234\pi$
$38$	−1.03509	+	3.18568i	−0.167914	+	0.516786i
$39$	−5.02672			−0.804919
$40$	3.39997	−	2.47022i	0.537583	−	0.390577i
$41$	−6.99103			−1.09182			−0.545908	−	0.837845i	$-0.683815\pi$
$41$	−6.99103			−1.09182			−0.545908	+	0.837845i	$0.683815\pi$
$42$	1.14807	+	3.53339i	0.177151	+	0.545215i
$43$	−0.466627	−	1.43613i	−0.0711600	−	0.219008i	0.909151	−	0.416466i	$-0.136731\pi$
$43$	−0.466627	−	1.43613i	−0.0711600	−	0.219008i	−0.980311	+	0.197458i	$0.936731\pi$
$44$	−0.540256	−	1.66274i	−0.0814466	−	0.250667i
$45$	−2.21320			−0.329925
$46$	2.47496	−	1.79816i	0.364912	−	0.265124i
$47$	6.40533	+	4.65375i	0.934314	+	0.678819i	0.947045	−	0.321100i	$-0.104053\pi$
$47$	6.40533	+	4.65375i	0.934314	+	0.678819i	−0.0127313	+	0.999919i	$0.504053\pi$
$48$	−0.261274			−0.0377116
$49$	1.70869	−	5.25880i	0.244098	−	0.751257i
$50$	−0.710560	+	2.18688i	−0.100488	+	0.309271i
$51$	−6.94770			−0.972872
$52$	4.20919	−	3.05816i	0.583710	−	0.424090i
$53$	−0.865214	−	2.66286i	−0.118846	−	0.365771i	0.873884	−	0.486135i	$-0.161594\pi$
$53$	−0.865214	−	2.66286i	−0.118846	−	0.365771i	−0.992730	+	0.120364i	$0.961594\pi$
$54$	−3.79066	−	2.75408i	−0.515844	−	0.374782i
$55$	−1.66679	−	1.21100i	−0.224750	−	0.163291i
$56$	−7.96161	−	5.78445i	−1.06392	−	0.772980i
$57$	1.51465	−	4.66161i	0.200620	−	0.617445i
$58$	−2.22784	−	1.61862i	−0.292529	−	0.212535i
$59$	1.04569	+	3.21830i	0.136137	+	0.418987i	0.995765	−	0.0919335i	$-0.0293047\pi$
$59$	1.04569	+	3.21830i	0.136137	+	0.418987i	−0.859628	+	0.510920i	$0.829305\pi$
$60$	−1.94405	+	1.41243i	−0.250976	+	0.182344i
$61$	−3.69213	−	2.68249i	−0.472728	−	0.343457i	0.325775	−	0.945447i	$-0.394375\pi$
$61$	−3.69213	−	2.68249i	−0.472728	−	0.343457i	−0.798504	+	0.601990i	$0.794375\pi$
$62$	1.59099	−	4.89657i	0.202056	−	0.621865i
$63$	1.60151	+	4.92893i	0.201771	+	0.620987i
$64$	−3.59108	+	2.60907i	−0.448885	+	0.326134i
$65$	1.89466	−	5.83115i	0.235003	−	0.723265i
$66$	−0.442065	−	1.36054i	−0.0544145	−	0.167471i
$67$	−3.52980	+	10.8636i	−0.431233	+	1.32720i	0.465664	+	0.884962i	$0.345816\pi$
$67$	−3.52980	+	10.8636i	−0.431233	+	1.32720i	−0.896897	+	0.442239i	$0.854184\pi$
$68$	5.81775	−	4.22684i	0.705505	−	0.512580i
$69$	−3.62160	+	2.63125i	−0.435990	+	0.316765i
$70$	−4.53157			−0.541627
$71$	8.41379	+	0.456169i	0.998533	+	0.0541373i
$71$	8.41379	+	0.456169i	0.998533	+	0.0541373i
$72$	4.07060			0.479725
$73$	−9.86451	+	7.16698i	−1.15455	+	0.838832i	−0.989080	−	0.147382i	$-0.952915\pi$
$73$	−9.86451	+	7.16698i	−1.15455	+	0.838832i	−0.165473	+	0.986214i	$0.552915\pi$
$74$	−6.94908	+	5.04880i	−0.807814	+	0.586911i
$75$	1.03976	−	3.20006i	0.120061	−	0.369511i
$76$	1.56772	+	4.82494i	0.179830	+	0.553459i
$77$	−1.49084	+	4.58834i	−0.169897	+	0.522890i
$78$	3.44418	−	2.50234i	0.389977	−	0.283335i
$79$	−0.154617	−	0.475862i	−0.0173958	−	0.0535387i	0.941982	−	0.335664i	$-0.108961\pi$
$79$	−0.154617	−	0.475862i	−0.0173958	−	0.0535387i	−0.959378	+	0.282125i	$0.908961\pi$
$80$	0.0984785	−	0.303086i	0.0110102	−	0.0338860i
$81$	1.99334	+	1.44825i	0.221483	+	0.160917i
$82$	4.79008	−	3.48020i	0.528976	−	0.384323i
$83$	−3.03657	−	9.34561i	−0.333307	−	1.02581i	−0.967550	−	0.252680i	$-0.918688\pi$
$83$	−3.03657	−	9.34561i	−0.333307	−	1.02581i	0.634243	−	0.773134i	$-0.281312\pi$
$84$	4.55232	+	3.30745i	0.496699	+	0.360873i
$85$	2.61871	−	8.05955i	0.284039	−	0.874181i
$86$	1.03464	+	0.751709i	0.111568	+	0.0810589i
$87$	3.25999	+	2.36852i	0.349508	+	0.253932i
$88$	3.06563	+	2.22731i	0.326797	+	0.237432i
$89$	−3.04666	−	9.37667i	−0.322946	−	0.993925i	−0.972359	−	0.233489i	$-0.924986\pi$
$89$	−3.04666	−	9.37667i	−0.322946	−	0.993925i	0.649414	−	0.760435i	$-0.275014\pi$
$90$	1.51643	−	1.10175i	0.159846	−	0.116135i
$91$	−14.3573			−1.50506
$92$	1.43180	−	4.40662i	0.149275	−	0.459422i
$93$	−2.32810	+	7.16515i	−0.241412	+	0.742991i
$94$	−6.70545			−0.691614
$95$	4.83672	+	3.51408i	0.496237	+	0.360537i
$96$	5.75398	−	4.18051i	0.587263	−	0.426672i
$97$	−15.0069			−1.52372			−0.761862	−	0.647740i	$-0.775714\pi$
$97$	−15.0069			−1.52372			−0.761862	+	0.647740i	$0.775714\pi$
$98$	1.44713	+	4.45379i	0.146182	+	0.449901i
$99$	−0.616662	−	1.89789i	−0.0619769	−	0.190745i
$100$	1.07619	+	3.31218i	0.107619	+	0.331218i
$101$	16.4452			1.63636			0.818179	−	0.574964i	$-0.194984\pi$
$101$	16.4452			1.63636			0.818179	+	0.574964i	$0.194984\pi$
$102$	4.76038	−	3.45862i	0.471348	−	0.342455i
$103$	10.9968			1.08355			0.541775	−	0.840523i	$-0.317752\pi$
$103$	10.9968			1.08355			0.541775	+	0.840523i	$0.317752\pi$
$104$	−3.48472	+	10.7249i	−0.341705	+	1.05166i
$105$	6.63105			0.647124
$106$	1.91841	+	1.39381i	0.186333	+	0.135379i
$107$	7.34106	+	5.33359i	0.709687	+	0.515618i	0.883073	−	0.469236i	$-0.155471\pi$
$107$	7.34106	+	5.33359i	0.709687	+	0.515618i	−0.173385	+	0.984854i	$0.555471\pi$
$108$	−7.09654			−0.682865
$109$	−0.809020	+	2.48991i	−0.0774901	+	0.238490i	−0.982296	−	0.187333i	$-0.940016\pi$
$109$	−0.809020	+	2.48991i	−0.0774901	+	0.238490i	0.904806	+	0.425823i	$0.140016\pi$
$110$	1.74489			0.166369
$111$	10.1686	−	7.38791i	0.965159	−	0.701229i
$112$	−0.746251			−0.0705141
$113$	2.23586	+	6.88128i	0.210332	+	0.647336i	0.999452	+	0.0330968i	$0.0105370\pi$
$113$	2.23586	+	6.88128i	0.210332	+	0.647336i	−0.789120	+	0.614239i	$0.789463\pi$
$114$	1.28279	+	3.94802i	0.120144	+	0.369766i
$115$	−1.68729	−	5.19293i	−0.157340	−	0.484244i
$116$	−4.17076			−0.387245
$117$	4.80448	−	3.49066i	0.444174	−	0.322712i
$118$	−2.31858	−	1.68454i	−0.213442	−	0.155075i
$119$	−19.8440			−1.81910
$120$	1.60945	−	4.95337i	0.146922	−	0.452179i
$121$	−2.82514	+	8.69487i	−0.256831	+	0.790443i
$122$	3.86512			0.349931
$123$	−7.00932	+	5.09257i	−0.632009	+	0.459181i
$124$	−2.40967	−	7.41620i	−0.216395	−	0.665994i
$125$	9.43486	+	6.85483i	0.843879	+	0.613114i
$126$	−3.55097	−	2.57993i	−0.316346	−	0.229839i
$127$	10.3622	+	7.52857i	0.919496	+	0.668053i	0.943398	−	0.331662i	$-0.107609\pi$
$127$	10.3622	+	7.52857i	0.919496	+	0.668053i	−0.0239027	+	0.999714i	$0.507609\pi$
$128$	−2.38518	+	7.34084i	−0.210822	+	0.648845i
$129$	−1.51399	−	1.09998i	−0.133299	−	0.0968474i
$130$	1.60463	+	4.93853i	0.140735	+	0.433138i
$131$	3.16651	−	2.30061i	0.276660	−	0.201005i	−0.440800	−	0.897606i	$-0.645305\pi$
$131$	3.16651	−	2.30061i	0.276660	−	0.201005i	0.717459	+	0.696601i	$0.245305\pi$
$132$	−1.75288	−	1.27354i	−0.152568	−	0.110847i
$133$	4.32614	−	13.3145i	0.375124	−	1.15451i
$134$	−2.98946	−	9.20063i	−0.258250	−	0.794813i
$135$	−6.76568	+	4.91556i	−0.582297	+	0.423064i
$136$	−4.81642	+	14.8234i	−0.413005	+	1.27110i
$137$	−6.42720	−	19.7809i	−0.549113	−	1.69000i	−0.711005	−	0.703187i	$-0.751760\pi$
$137$	−6.42720	−	19.7809i	−0.549113	−	1.69000i	0.161892	−	0.986808i	$-0.448240\pi$
$138$	1.17157	−	3.60573i	0.0997308	−	0.306940i
$139$	11.4656	−	8.33024i	0.972498	−	0.706561i	0.0164788	−	0.999864i	$-0.494754\pi$
$139$	11.4656	−	8.33024i	0.972498	−	0.706561i	0.956020	+	0.293303i	$0.0947544\pi$
$140$	−5.55260	+	4.03420i	−0.469280	+	0.340952i
$141$	9.81207			0.826326
$142$	−5.99200	+	3.87590i	−0.502838	+	0.325258i
$143$	5.52831			0.462300
$144$	0.249722	−	0.181434i	0.0208102	−	0.0151195i
$145$	−3.97630	+	2.88895i	−0.330214	+	0.239915i
$146$	3.19112	−	9.82127i	0.264099	−	0.812814i
$147$	−2.11758	−	6.51723i	−0.174655	−	0.537532i
$148$	−4.02014	+	12.3727i	−0.330454	+	1.01703i
$149$	−5.14634	+	3.73904i	−0.421605	+	0.306314i	−0.778283	−	0.627913i	$-0.783909\pi$
$149$	−5.14634	+	3.73904i	−0.421605	+	0.306314i	0.356678	+	0.934227i	$0.383909\pi$
$150$	0.880598	+	2.71020i	0.0719005	+	0.221287i
$151$	−5.17891	+	15.9390i	−0.421453	+	1.29710i	0.484896	+	0.874572i	$0.338857\pi$
$151$	−5.17891	+	15.9390i	−0.421453	+	1.29710i	−0.906350	+	0.422528i	$0.861143\pi$
$152$	−8.89587	−	6.46323i	−0.721550	−	0.524237i
$153$	6.64053	−	4.82463i	0.536855	−	0.390048i
$154$	−1.26263	−	3.88597i	−0.101745	−	0.313140i
$155$	−7.43430	−	5.40133i	−0.597137	−	0.433845i
$156$	1.99251	−	6.13231i	0.159528	−	0.490977i
$157$	−16.0484	−	11.6598i	−1.28080	−	0.930555i	−0.281222	−	0.959643i	$-0.590740\pi$
$157$	−16.0484	−	11.6598i	−1.28080	−	0.930555i	−0.999577	+	0.0290883i	$0.990740\pi$
$158$	0.342828	+	0.249079i	0.0272739	+	0.0198157i
$159$	−2.80721	−	2.03956i	−0.222627	−	0.161748i
$160$	2.68075	+	8.25050i	0.211932	+	0.652260i
$161$	−10.3440	+	7.51538i	−0.815224	+	0.592295i
$162$	−2.08674			−0.163950
$163$	4.58693	−	14.1171i	0.359276	−	1.10574i	−0.594213	−	0.804308i	$-0.702536\pi$
$163$	4.58693	−	14.1171i	0.359276	−	1.10574i	0.953488	−	0.301429i	$-0.0974638\pi$
$164$	2.77113	−	8.52866i	0.216389	−	0.665976i
$165$	−2.55329			−0.198774
$166$	6.73290	+	4.89174i	0.522575	+	0.379673i
$167$	0.824122	−	0.598760i	0.0637725	−	0.0463334i	−0.555442	−	0.831555i	$-0.687451\pi$
$167$	0.824122	−	0.598760i	0.0637725	−	0.0463334i	0.619215	+	0.785222i	$0.287451\pi$
$168$	−12.1961			−0.940947
$169$	1.06670	+	3.28295i	0.0820536	+	0.252535i
$170$	2.21784	+	6.82581i	0.170101	+	0.523516i
$171$	1.78944	+	5.50732i	0.136842	+	0.421155i
$172$	1.93696			0.147692
$173$	9.46388	−	6.87591i	0.719525	−	0.522766i	−0.166707	−	0.986006i	$-0.553313\pi$
$173$	9.46388	−	6.87591i	0.719525	−	0.522766i	0.886233	+	0.463241i	$0.153313\pi$
$174$	−3.41273			−0.258719
$175$	2.96977	−	9.14002i	0.224494	−	0.690920i
$176$	0.287345			0.0216594
$177$	3.39277	+	2.46499i	0.255016	+	0.185280i
$178$	6.75528	+	4.90800i	0.506330	+	0.367870i
$179$	−19.0058			−1.42056			−0.710280	−	0.703920i	$-0.751431\pi$
$179$	−19.0058			−1.42056			−0.710280	+	0.703920i	$0.751431\pi$
$180$	0.877276	−	2.69998i	0.0653883	−	0.201244i
$181$	−3.22913			−0.240019			−0.120010	−	0.992773i	$-0.538293\pi$
$181$	−3.22913			−0.240019			−0.120010	+	0.992773i	$0.538293\pi$
$182$	9.83728	−	7.14720i	0.729187	−	0.529786i
$183$	−5.65582			−0.418090
$184$	3.10332	+	9.55104i	0.228780	+	0.704112i
$185$	4.73749	+	14.5805i	0.348307	+	1.07198i
$186$	−1.97172	−	6.06832i	−0.144573	−	0.444951i
$187$	7.64097			0.558763
$188$	−8.21627	+	5.96947i	−0.599233	+	0.435368i
$189$	15.8430	+	11.5106i	1.15241	+	0.837273i
$190$	−5.06333			−0.367333
$191$	7.54914	−	23.2339i	0.546236	−	1.68114i	−0.171795	−	0.985133i	$-0.554957\pi$
$191$	7.54914	−	23.2339i	0.546236	−	1.68114i	0.718032	−	0.696010i	$-0.245043\pi$
$192$	−1.69991	+	5.23179i	−0.122681	+	0.377572i
$193$	−11.6772			−0.840543			−0.420271	−	0.907398i	$-0.638065\pi$
$193$	−11.6772			−0.840543			−0.420271	+	0.907398i	$0.638065\pi$
$194$	10.2824	−	7.47058i	0.738231	−	0.536356i
$195$	−2.34805	−	7.22655i	−0.168147	−	0.517504i
$196$	5.73813	+	4.16900i	0.409867	+	0.297786i
$197$	13.4031	+	9.73795i	0.954934	+	0.693800i	0.951969	−	0.306196i	$-0.0990562\pi$
$197$	13.4031	+	9.73795i	0.954934	+	0.693800i	0.00296518	+	0.999996i	$0.499056\pi$
$198$	1.36731	+	0.993407i	0.0971703	+	0.0705983i
$199$	1.90026	−	5.84841i	0.134706	−	0.414583i	−0.860838	−	0.508879i	$-0.830060\pi$
$199$	1.90026	−	5.84841i	0.134706	−	0.414583i	0.995544	+	0.0942962i	$0.0300601\pi$
$200$	−6.10675	−	4.43682i	−0.431813	−	0.313730i
$201$	4.37448	+	13.4633i	0.308552	+	0.949626i
$202$	−11.2678	+	8.18655i	−0.792801	+	0.576004i
$203$	9.31119	+	6.76498i	0.653517	+	0.474808i
$204$	2.75395	−	8.47579i	0.192815	−	0.593424i
$205$	−3.26561	−	10.0505i	−0.228080	−	0.701958i
$206$	−7.53475	+	5.47432i	−0.524971	+	0.381414i
$207$	1.63429	−	5.02983i	0.113591	−	0.349598i
$208$	0.264247	+	0.813268i	0.0183222	+	0.0563900i
$209$	−1.66579	+	5.12676i	−0.115225	+	0.354626i
$210$	−4.54343	+	3.30099i	−0.313526	+	0.227790i
$211$	12.1765	−	8.84676i	0.838267	−	0.609036i	−0.0836193	−	0.996498i	$-0.526648\pi$
$211$	12.1765	−	8.84676i	0.838267	−	0.609036i	0.921886	+	0.387461i	$0.126648\pi$
$212$	3.59149			0.246664
$213$	8.76809	−	5.67160i	0.600780	−	0.388612i
$214$	−7.68502			−0.525337
$215$	1.84665	−	1.34167i	0.125941	−	0.0915013i
$216$	12.4437	−	9.04087i	0.846686	−	0.615153i
$217$	−6.64952	+	20.4651i	−0.451399	+	1.38926i
$218$	−0.685177	−	2.10876i	−0.0464061	−	0.142823i
$219$	−4.66957	+	14.3715i	−0.315540	+	0.971133i
$220$	2.13803	−	1.55337i	0.144146	−	0.104728i
$221$	7.02675	+	21.6261i	0.472671	+	1.45473i
$222$	−3.28949	+	10.1240i	−0.220776	+	0.679479i
$223$	−6.43836	−	4.67774i	−0.431144	−	0.313245i	0.350962	−	0.936390i	$-0.385855\pi$
$223$	−6.43836	−	4.67774i	−0.431144	−	0.313245i	−0.782106	+	0.623145i	$0.785855\pi$
$224$	16.4345	−	11.9404i	1.09808	−	0.797801i
$225$	1.22840	+	3.78061i	0.0818930	+	0.252041i
$226$	−4.95751	−	3.60184i	−0.329769	−	0.239591i
$227$	−0.423192	+	1.30245i	−0.0280882	+	0.0864467i	−0.964118	−	0.265474i	$-0.914471\pi$
$227$	−0.423192	+	1.30245i	−0.0280882	+	0.0864467i	0.936030	+	0.351921i	$0.114471\pi$
$228$	5.08651	+	3.69557i	0.336862	+	0.244745i
$229$	15.4221	+	11.2048i	1.01912	+	0.740433i	0.966102	−	0.258160i	$-0.0831163\pi$
$229$	15.4221	+	11.2048i	1.01912	+	0.740433i	0.0530168	+	0.998594i	$0.483116\pi$
$230$	3.74117	+	2.71812i	0.246686	+	0.179228i
$231$	1.84760	+	5.68634i	0.121563	+	0.374134i
$232$	7.31337	−	5.31347i	0.480146	−	0.348847i
$233$	−15.2009			−0.995845			−0.497923	−	0.867221i	$-0.665904\pi$
$233$	−15.2009			−0.995845			−0.497923	+	0.867221i	$0.665904\pi$
$234$	−1.55423	+	4.78342i	−0.101603	+	0.312702i
$235$	−3.69834	+	11.3823i	−0.241253	+	0.742500i
$236$	−4.34063			−0.282551
$237$	−0.501660	−	0.364477i	−0.0325863	−	0.0236753i
$238$	13.5966	−	9.87852i	0.881338	−	0.640330i
$239$	−16.0610			−1.03890			−0.519449	−	0.854502i	$-0.673863\pi$
$239$	−16.0610			−1.03890			−0.519449	+	0.854502i	$0.673863\pi$
$240$	−0.122045	−	0.375614i	−0.00787794	−	0.0242458i
$241$	−0.715972	−	2.20353i	−0.0461198	−	0.141942i	0.925345	−	0.379126i	$-0.123775\pi$
$241$	−0.715972	−	2.20353i	−0.0461198	−	0.141942i	−0.971465	+	0.237184i	$0.923775\pi$
$242$	−2.39267	−	7.36388i	−0.153807	−	0.473368i
$243$	−13.5437			−0.868828
$244$	4.73598	−	3.44089i	0.303190	−	0.220280i
$245$	8.35834			0.533995
$246$	2.26748	−	6.97859i	0.144569	−	0.444939i
$247$	−16.0421			−1.02073
$248$	13.6734	+	9.93433i	0.868264	+	0.630831i
$249$	−9.85225	−	7.15808i	−0.624361	−	0.453625i
$250$	−9.87691			−0.624671
$251$	0.649546	−	1.99910i	0.0409990	−	0.126182i	−0.928462	−	0.371427i	$-0.878869\pi$
$251$	0.649546	−	1.99910i	0.0409990	−	0.126182i	0.969461	+	0.245245i	$0.0788685\pi$
$252$	−6.64782			−0.418773
$253$	3.98298	−	2.89380i	0.250408	−	0.181932i
$254$	−10.8477			−0.680645
$255$	−3.24536	−	9.98820i	−0.203233	−	0.625485i
$256$	−4.76340	−	14.6602i	−0.297713	−	0.916266i
$257$	−0.415411	−	1.27850i	−0.0259126	−	0.0797508i	0.937264	−	0.348621i	$-0.113350\pi$
$257$	−0.415411	−	1.27850i	−0.0259126	−	0.0797508i	−0.963177	+	0.268870i	$0.913350\pi$
$258$	1.58492			0.0986729
$259$	29.0435	−	21.1014i	1.80468	−	1.31117i
$260$	6.36266	+	4.62274i	0.394595	+	0.286690i
$261$	−4.76061			−0.294674
$262$	−1.02435	+	3.15263i	−0.0632847	+	0.194770i
$263$	4.99363	−	15.3688i	0.307921	−	0.947683i	−0.670650	−	0.741774i	$-0.733985\pi$
$263$	4.99363	−	15.3688i	0.307921	−	0.947683i	0.978571	−	0.205909i	$-0.0660151\pi$
$264$	4.69611			0.289026
$265$	3.42404	−	2.48771i	0.210337	−	0.152819i
$266$	3.66391	+	11.2763i	0.224649	+	0.691397i
$267$	−9.88499	−	7.18187i	−0.604952	−	0.439523i
$268$	−11.8538	−	8.61230i	−0.724087	−	0.526080i
$269$	−3.34044	−	2.42697i	−0.203670	−	0.147975i	0.481275	−	0.876570i	$-0.340174\pi$
$269$	−3.34044	−	2.42697i	−0.203670	−	0.147975i	−0.684945	+	0.728595i	$0.740174\pi$
$270$	2.18867	−	6.73603i	0.133198	−	0.409941i
$271$	−15.5121	−	11.2702i	−0.942292	−	0.684615i	0.00667905	−	0.999978i	$-0.497874\pi$
$271$	−15.5121	−	11.2702i	−0.942292	−	0.684615i	−0.948971	+	0.315362i	$0.897874\pi$
$272$	0.365229	+	1.12406i	0.0221453	+	0.0681562i
$273$	−14.3949	+	10.4585i	−0.871218	+	0.632977i
$274$	14.2508	+	10.3538i	0.860925	+	0.625499i
$275$	−1.14351	+	3.51937i	−0.0689565	+	0.212226i
$276$	−1.77443	−	5.46113i	−0.106808	−	0.328721i
$277$	−3.67958	+	2.67337i	−0.221084	+	0.160627i	−0.692815	−	0.721116i	$-0.743630\pi$
$277$	−3.67958	+	2.67337i	−0.221084	+	0.160627i	0.471730	+	0.881743i	$0.343630\pi$
$278$	−3.70907	+	11.4153i	−0.222455	+	0.684646i
$279$	−2.75046	−	8.46505i	−0.164666	−	0.506789i
$280$	4.59691	−	14.1478i	0.274718	−	0.845494i
$281$	−20.4102	+	14.8289i	−1.21757	+	0.884618i	−0.995896	−	0.0905020i	$-0.971153\pi$
$281$	−20.4102	+	14.8289i	−1.21757	+	0.884618i	−0.221676	+	0.975120i	$0.571153\pi$
$282$	−6.72298	+	4.88453i	−0.400348	+	0.290870i
$283$	−0.438375			−0.0260587			−0.0130293	−	0.999915i	$-0.504147\pi$
$283$	−0.438375			−0.0260587			−0.0130293	+	0.999915i	$0.504147\pi$
$284$	−3.89159	+	10.0835i	−0.230923	+	0.598347i
$285$	7.40917			0.438881
$286$	−3.78785	+	2.75204i	−0.223981	+	0.162731i
$287$	−20.0200	+	14.5454i	−1.18174	+	0.858588i
$288$	−2.59655	+	7.99137i	−0.153003	+	0.470896i
$289$	4.45876	+	13.7227i	0.262280	+	0.807215i
$290$	1.28632	−	3.95888i	0.0755351	−	0.232473i
$291$	−15.0462	+	10.9317i	−0.882023	+	0.640827i
$292$	−4.83318	−	14.8750i	−0.282840	−	0.870493i
$293$	6.20929	−	19.1102i	0.362751	−	1.11643i	−0.588627	−	0.808405i	$-0.700331\pi$
$293$	6.20929	−	19.1102i	0.362751	−	1.11643i	0.951378	−	0.308027i	$-0.0996688\pi$
$294$	4.69524	+	3.41129i	0.273832	+	0.198951i
$295$	−4.13826	+	3.00662i	−0.240939	+	0.175052i
$296$	−8.71337	−	26.8170i	−0.506455	−	1.55871i
$297$	−6.10036	−	4.43217i	−0.353979	−	0.257181i
$298$	1.66482	−	5.12378i	0.0964404	−	0.296813i
$299$	11.8531	+	8.61179i	0.685483	+	0.498032i
$300$	3.49174	+	2.53690i	0.201596	+	0.146468i
$301$	−4.32425	−	3.14175i	−0.249246	−	0.181088i
$302$	−4.38613	−	13.4991i	−0.252393	−	0.776787i
$303$	16.4882	−	11.9794i	0.947222	−	0.688197i
$304$	−0.833820			−0.0478228
$305$	2.13178	−	6.56093i	0.122065	−	0.375678i
$306$	−2.14818	+	6.61142i	−0.122803	+	0.377950i
$307$	22.4071			1.27884			0.639420	−	0.768857i	$-0.279174\pi$
$307$	22.4071			1.27884			0.639420	+	0.768857i	$0.279174\pi$
$308$	−5.00657	−	3.63748i	−0.285276	−	0.207265i
$309$	11.0256	−	8.01057i	0.627224	−	0.455705i
$310$	7.78262			0.442023
$311$	5.61807	+	17.2906i	0.318572	+	0.980462i	0.974259	+	0.225430i	$0.0723788\pi$
$311$	5.61807	+	17.2906i	0.318572	+	0.980462i	−0.655688	+	0.755032i	$0.727621\pi$
$312$	4.31862	+	13.2913i	0.244494	+	0.752474i
$313$	−2.84692	−	8.76193i	−0.160918	−	0.495254i	0.837795	−	0.545985i	$-0.183845\pi$
$313$	−2.84692	−	8.76193i	−0.160918	−	0.495254i	−0.998712	+	0.0507318i	$0.983845\pi$
$314$	16.8003			0.948095
$315$	−6.33788	+	4.60474i	−0.357099	+	0.259448i
$316$	0.641812			0.0361047
$317$	−4.86332	+	14.9678i	−0.273151	+	0.840673i	0.716551	+	0.697534i	$0.245720\pi$
$317$	−4.86332	+	14.9678i	−0.273151	+	0.840673i	−0.989703	+	0.143139i	$0.954280\pi$
$318$	2.93874			0.164796
$319$	−3.58528	−	2.60486i	−0.200737	−	0.145844i
$320$	−5.42831	−	3.94390i	−0.303452	−	0.220471i
$321$	11.2455			0.627661
$322$	3.34625	−	10.2987i	0.186479	−	0.573923i
$323$	−22.1726			−1.23372
$324$	−2.55691	+	1.85770i	−0.142050	+	0.103206i
$325$	−11.0124			−0.610860
$326$	3.88477	+	11.9561i	0.215158	+	0.662187i
$327$	1.00262	+	3.08575i	0.0554450	+	0.170642i
$328$	6.00622	+	18.4853i	0.331638	+	1.02068i
$329$	28.0253			1.54508
$330$	1.74945	−	1.27105i	0.0963041	−	0.0699691i
$331$	24.6783	+	17.9298i	1.35644	+	0.985512i	0.998662	+	0.0517049i	$0.0164655\pi$
$331$	24.6783	+	17.9298i	1.35644	+	0.985512i	0.357778	+	0.933807i	$0.383534\pi$
$332$	12.6047			0.691775
$333$	−4.58870	+	14.1226i	−0.251459	+	0.773911i
$334$	−0.266600	+	0.820510i	−0.0145877	+	0.0448963i
$335$	−17.2666			−0.943377
$336$	−0.748202	+	0.543601i	−0.0408178	+	0.0296559i
$337$	1.15143	+	3.54372i	0.0627221	+	0.193039i	0.977507	−	0.210902i	$-0.0676401\pi$
$337$	1.15143	+	3.54372i	0.0627221	+	0.193039i	−0.914785	+	0.403941i	$0.867640\pi$
$338$	−2.36515	−	1.71839i	−0.128647	−	0.0934678i
$339$	7.25432	+	5.27057i	0.394001	+	0.286258i
$340$	8.79417	+	6.38934i	0.476931	+	0.346510i
$341$	2.56040	−	7.88011i	0.138654	−	0.426732i
$342$	−3.96766	−	2.88268i	−0.214547	−	0.155877i
$343$	1.60855	+	4.95060i	0.0868535	+	0.267308i
$344$	−3.39643	+	2.46765i	−0.183123	+	0.133047i
$345$	−5.47445	−	3.97742i	−0.294735	−	0.214137i
$346$	−3.06152	+	9.42240i	−0.164588	+	0.506551i
$347$	−4.09844	−	12.6137i	−0.220016	−	0.677139i	−0.998759	−	0.0497968i	$-0.984143\pi$
$347$	−4.09844	−	12.6137i	−0.220016	−	0.677139i	0.778743	−	0.627342i	$-0.215857\pi$
$348$	−4.18166	+	3.03816i	−0.224161	+	0.162862i
$349$	−4.80058	+	14.7747i	−0.256969	+	0.790870i	0.736466	+	0.676474i	$0.236493\pi$
$349$	−4.80058	+	14.7747i	−0.256969	+	0.790870i	−0.993435	+	0.114395i	$0.963507\pi$
$350$	2.51516	+	7.74088i	0.134441	+	0.413768i
$351$	6.93433	−	21.3417i	0.370127	−	1.13913i
$352$	−6.32814	+	4.59766i	−0.337291	+	0.245056i
$353$	21.1159	−	15.3416i	1.12388	−	0.816549i	0.139090	−	0.990280i	$-0.455582\pi$
$353$	21.1159	−	15.3416i	1.12388	−	0.816549i	0.984793	+	0.173731i	$0.0555822\pi$
$354$	−3.55173			−0.188772
$355$	3.27439	+	12.3090i	0.173787	+	0.653293i
$356$	12.6466			0.670270
$357$	−19.8959	+	14.4552i	−1.05300	+	0.765052i
$358$	13.0223	−	9.46124i	0.688249	−	0.500042i
$359$	−5.28433	+	16.2635i	−0.278896	+	0.858355i	0.709266	+	0.704941i	$0.249027\pi$
$359$	−5.28433	+	16.2635i	−0.278896	+	0.858355i	−0.988162	+	0.153414i	$0.950973\pi$
$360$	1.90143	+	5.85201i	0.100214	+	0.308428i
$361$	−1.03753	+	3.19319i	−0.0546068	+	0.168062i
$362$	2.21252	−	1.60749i	0.116287	−	0.0844877i
$363$	3.50119	+	10.7756i	0.183765	+	0.565570i
$364$	5.69100	−	17.5151i	0.298290	−	0.918041i
$365$	−14.9113	−	10.8337i	−0.780493	−	0.567061i
$366$	3.87522	−	2.81552i	0.202561	−	0.147169i
$367$	−2.04717	−	6.30053i	−0.106861	−	0.328885i	0.883302	−	0.468805i	$-0.155315\pi$
$367$	−2.04717	−	6.30053i	−0.106861	−	0.328885i	−0.990163	+	0.139920i	$0.955315\pi$
$368$	0.616089	+	0.447615i	0.0321158	+	0.0233335i
$369$	3.16304	−	9.73484i	0.164661	−	0.506775i
$370$	−10.5043	−	7.63183i	−0.546093	−	0.396760i
$371$	−8.01797	−	5.82540i	−0.416272	−	0.302440i
$372$	−7.81824	−	5.68029i	−0.405357	−	0.294509i
$373$	−6.99439	−	21.5265i	−0.362156	−	1.11460i	−0.951743	−	0.306896i	$-0.900710\pi$
$373$	−6.99439	−	21.5265i	−0.362156	−	1.11460i	0.589588	−	0.807704i	$-0.299290\pi$
$374$	−5.23540	+	3.80374i	−0.270716	+	0.196687i
$375$	14.4529			0.746344
$376$	6.80212	−	20.9348i	0.350792	−	1.07963i
$377$	4.07542	−	12.5429i	0.209895	−	0.645990i
$378$	−16.5853			−0.853055
$379$	1.45438	+	1.05667i	0.0747066	+	0.0542775i	0.624512	−	0.781015i	$-0.285298\pi$
$379$	1.45438	+	1.05667i	0.0747066	+	0.0542775i	−0.549805	+	0.835293i	$0.685298\pi$
$380$	−6.20417	+	4.50759i	−0.318267	+	0.231235i
$381$	15.8734			0.813220
$382$	6.39353	+	19.6773i	0.327122	+	1.00678i
$383$	5.24285	+	16.1358i	0.267897	+	0.824502i	0.991012	+	0.133774i	$0.0427098\pi$
$383$	5.24285	+	16.1358i	0.267897	+	0.824502i	−0.723115	+	0.690728i	$0.757290\pi$
$384$	2.95596	+	9.09750i	0.150846	+	0.464255i
$385$	−7.29272			−0.371672
$386$	8.00091	−	5.81300i	0.407236	−	0.295874i
$387$	2.21090			0.112386
$388$	5.94850	−	18.3076i	0.301989	−	0.929427i
$389$	15.5456			0.788193			0.394096	−	0.919069i	$-0.371058\pi$
$389$	15.5456			0.788193			0.394096	+	0.919069i	$0.371058\pi$
$390$	5.20626	+	3.78257i	0.263629	+	0.191538i
$391$	16.3828	+	11.9028i	0.828514	+	0.601951i
$392$	−15.3730			−0.776452
$393$	1.49893	−	4.61325i	0.0756113	−	0.232708i
$394$	−14.0311			−0.706877
$395$	0.611889	−	0.444563i	0.0307875	−	0.0223684i
$396$	2.55975			0.128632
$397$	−7.32551	−	22.5456i	−0.367657	−	1.13153i	−0.948300	−	0.317374i	$-0.897199\pi$
$397$	−7.32551	−	22.5456i	−0.367657	−	1.13153i	0.580643	−	0.814158i	$-0.302801\pi$
$398$	1.60938	+	4.95315i	0.0806707	+	0.248279i
$399$	−5.36139	−	16.5007i	−0.268405	−	0.826067i
$400$	−0.572393			−0.0286196
$401$	−6.44669	+	4.68379i	−0.321932	+	0.233898i	−0.737000	−	0.675893i	$-0.763758\pi$
$401$	−6.44669	+	4.68379i	−0.321932	+	0.233898i	0.415067	+	0.909791i	$0.363758\pi$
$402$	−9.69941	−	7.04703i	−0.483763	−	0.351474i
$403$	24.6576			1.22828
$404$	−6.51860	+	20.0622i	−0.324312	+	0.998130i
$405$	−1.15093	+	3.54218i	−0.0571899	+	0.176013i
$406$	−9.74745			−0.483758
$407$	−11.1832	+	8.12510i	−0.554333	+	0.402746i
$408$	5.96899	+	18.3707i	0.295509	+	0.909484i
$409$	−8.97938	−	6.52390i	−0.444002	−	0.322586i	0.343221	−	0.939255i	$-0.388482\pi$
$409$	−8.97938	−	6.52390i	−0.444002	−	0.322586i	−0.787223	+	0.616668i	$0.788482\pi$
$410$	7.24073	+	5.26070i	0.357594	+	0.259808i
$411$	−20.8532	−	15.1508i	−1.02861	−	0.747332i
$412$	−4.35896	+	13.4155i	−0.214751	+	0.660934i
$413$	9.69044	+	7.04051i	0.476835	+	0.346441i
$414$	1.38412	+	4.25988i	0.0680257	+	0.209362i
$415$	12.0171	−	8.73092i	0.589895	−	0.428584i
$416$	−18.8321	−	13.6824i	−0.923322	−	0.670833i
$417$	5.42747	−	16.7040i	0.265785	−	0.818001i
$418$	−1.41079	−	4.34197i	−0.0690041	−	0.212373i
$419$	8.18093	−	5.94379i	0.399665	−	0.290373i	−0.369740	−	0.929135i	$-0.620553\pi$
$419$	8.18093	−	5.94379i	0.399665	−	0.290373i	0.769404	+	0.638762i	$0.220553\pi$
$420$	−2.62844	+	8.08950i	−0.128255	+	0.394727i
$421$	5.93237	+	18.2580i	0.289126	+	0.889839i	0.985131	+	0.171802i	$0.0549590\pi$
$421$	5.93237	+	18.2580i	0.289126	+	0.889839i	−0.696005	+	0.718037i	$0.745041\pi$
$422$	−3.93905	+	12.1232i	−0.191750	+	0.590146i
$423$	−9.37827	+	6.81371i	−0.455987	+	0.331294i
$424$	−6.29762	+	4.57549i	−0.305840	+	0.222205i
$425$	−15.2209			−0.738320
$426$	−3.18430	+	8.25087i	−0.154280	+	0.399756i
$427$	−16.1542			−0.781755
$428$	−9.41655	+	6.84152i	−0.455166	+	0.330698i
$429$	5.54276	−	4.02705i	0.267607	−	0.194428i
$430$	−0.597384	+	1.83856i	−0.0288084	+	0.0886632i
$431$	−5.04358	−	15.5225i	−0.242941	−	0.747694i	−0.995968	−	0.0897055i	$-0.971407\pi$
$431$	−5.04358	−	15.5225i	−0.242941	−	0.747694i	0.753028	−	0.657989i	$-0.228593\pi$
$432$	0.360425	−	1.10928i	0.0173410	−	0.0533700i
$433$	16.4551	−	11.9553i	0.790780	−	0.574535i	−0.117415	−	0.993083i	$-0.537461\pi$
$433$	16.4551	−	11.9553i	0.790780	−	0.574535i	0.908195	+	0.418548i	$0.137461\pi$
$434$	−5.63162	−	17.3324i	−0.270327	−	0.831980i
$435$	−1.88227	+	5.79302i	−0.0902478	+	0.277754i
$436$	−2.71686	−	1.97392i	−0.130114	−	0.0945334i
$437$	−11.5578	+	8.39727i	−0.552887	+	0.401696i
$438$	−3.95476	−	12.1715i	−0.188966	−	0.581577i
$439$	2.90816	+	2.11290i	0.138799	+	0.100843i	0.655018	−	0.755613i	$-0.272661\pi$
$439$	2.90816	+	2.11290i	0.138799	+	0.100843i	−0.516219	+	0.856457i	$0.672661\pi$
$440$	−1.77004	+	5.44764i	−0.0843836	+	0.259706i
$441$	6.54966	+	4.75861i	0.311889	+	0.226600i
$442$	−15.5802	−	11.3197i	−0.741075	−	0.538423i
$443$	15.3923	+	11.1832i	0.731310	+	0.531328i	0.889977	−	0.456004i	$-0.150720\pi$
$443$	15.3923	+	11.1832i	0.731310	+	0.531328i	−0.158668	+	0.987332i	$0.550720\pi$
$444$	4.98216	+	15.3335i	0.236443	+	0.727697i
$445$	12.0570	−	8.75993i	0.571557	−	0.415261i
$446$	6.74002			0.319149
$447$	−2.43613	+	7.49763i	−0.115225	+	0.354626i
$448$	−4.85529	+	14.9430i	−0.229391	+	0.705992i
$449$	19.7921			0.934047			0.467023	−	0.884245i	$-0.345326\pi$
$449$	19.7921			0.934047			0.467023	+	0.884245i	$0.345326\pi$
$450$	−2.72369	−	1.97887i	−0.128396	−	0.0932850i
$451$	7.70874	−	5.60072i	0.362990	−	0.263728i
$452$	−9.28101			−0.436542
$453$	6.41822	+	19.7533i	0.301554	+	0.928089i
$454$	−0.358411	−	1.10308i	−0.0168211	−	0.0517699i
$455$	−6.70650	−	20.6405i	−0.314406	−	0.967641i
$456$	−13.6272			−0.638153
$457$	−8.82100	+	6.40883i	−0.412629	+	0.299792i	−0.774665	−	0.632372i	$-0.782082\pi$
$457$	−8.82100	+	6.40883i	−0.412629	+	0.299792i	0.362036	+	0.932164i	$0.382082\pi$
$458$	−16.1446			−0.754390
$459$	9.58430	−	29.4974i	0.447357	−	1.37682i
$460$	7.00389			0.326558
$461$	−9.67720	−	7.03090i	−0.450712	−	0.327461i	0.339165	−	0.940727i	$-0.389856\pi$
$461$	−9.67720	−	7.03090i	−0.450712	−	0.327461i	−0.789877	+	0.613266i	$0.789856\pi$
$462$	−4.09664	−	2.97638i	−0.190593	−	0.138474i
$463$	−2.04266			−0.0949303			−0.0474652	−	0.998873i	$-0.515114\pi$
$463$	−2.04266			−0.0949303			−0.0474652	+	0.998873i	$0.515114\pi$
$464$	0.211828	−	0.651940i	0.00983387	−	0.0302655i
$465$	−11.3883			−0.528120
$466$	10.4153	−	7.56714i	0.482479	−	0.350541i
$467$	4.63214			0.214350			0.107175	−	0.994240i	$-0.465819\pi$
$467$	4.63214			0.214350			0.107175	+	0.994240i	$0.465819\pi$
$468$	2.35399	+	7.24483i	0.108813	+	0.334892i
$469$	12.4944	+	38.4538i	0.576938	+	1.77563i
$470$	−3.13220	−	9.63993i	−0.144478	−	0.444657i
$471$	−24.5838			−1.13276
$472$	7.61124	−	5.52989i	0.350336	−	0.254534i
$473$	1.66506	+	1.20974i	0.0765594	+	0.0556237i
$474$	0.525164			0.0241216
$475$	3.31826	−	10.2125i	0.152252	−	0.468584i
$476$	7.86584	−	24.2086i	0.360530	−	1.10960i
$477$	4.09942			0.187699
$478$	11.0046	−	7.99528i	0.503337	−	0.365696i
$479$	−3.62376	−	11.1528i	−0.165574	−	0.509584i	0.833504	−	0.552513i	$-0.186331\pi$
$479$	−3.62376	−	11.1528i	−0.165574	−	0.509584i	−0.999078	+	0.0429288i	$0.986331\pi$
$480$	8.69778	+	6.31931i	0.396998	+	0.288436i
$481$	−33.2807	−	24.1798i	−1.51747	−	1.10250i
$482$	1.58750	+	1.15339i	0.0723088	+	0.0525354i
$483$	−4.89656	+	15.0701i	−0.222801	+	0.685712i
$484$	−9.48741	−	6.89300i	−0.431246	−	0.313318i
$485$	−7.00994	−	21.5744i	−0.318305	−	0.979642i
$486$	9.27979	−	6.74216i	0.420940	−	0.305831i
$487$	13.4659	+	9.78356i	0.610199	+	0.443335i	0.849484	−	0.527614i	$-0.176913\pi$
$487$	13.4659	+	9.78356i	0.610199	+	0.443335i	−0.239285	+	0.970949i	$0.576913\pi$
$488$	−3.92084	+	12.0671i	−0.177488	+	0.546252i
$489$	−5.68458	−	17.4953i	−0.257066	−	0.791167i
$490$	−5.72692	+	4.16085i	−0.258716	+	0.187968i
$491$	−4.99240	+	15.3650i	−0.225304	+	0.693413i	0.772957	+	0.634458i	$0.218777\pi$
$491$	−4.99240	+	15.3650i	−0.225304	+	0.693413i	−0.998261	+	0.0589549i	$0.981223\pi$
$492$	−3.43426	−	10.5696i	−0.154828	−	0.476513i
$493$	5.63286	−	17.3361i	0.253691	−	0.780781i
$494$	10.9916	−	7.98589i	0.494537	−	0.359302i
$495$	2.44041	−	1.77306i	0.109688	−	0.0796932i
$496$	1.28163			0.0575467
$497$	25.0434	−	16.1992i	1.12335	−	0.726635i
$498$	10.3139			0.462175
$499$	17.4787	−	12.6990i	0.782452	−	0.568485i	−0.123262	−	0.992374i	$-0.539335\pi$
$499$	17.4787	−	12.6990i	0.782452	−	0.568485i	0.905714	+	0.423889i	$0.139335\pi$
$500$	−12.1023	+	8.79284i	−0.541232	+	0.393228i
$501$	0.390115	−	1.20065i	0.0174291	−	0.0536411i
$502$	0.550115	+	1.69308i	0.0245528	+	0.0755659i
$503$	−0.488083	+	1.50217i	−0.0217626	+	0.0669783i	−0.961348	−	0.275336i	$-0.911211\pi$
$503$	−0.488083	+	1.50217i	−0.0217626	+	0.0669783i	0.939585	+	0.342314i	$0.111211\pi$
$504$	11.6569	−	8.46921i	0.519238	−	0.377249i
$505$	7.68177	+	23.6421i	0.341834	+	1.05206i
$506$	−1.28848	+	3.96552i	−0.0572798	+	0.176289i
$507$	3.46093	+	2.51451i	0.153705	+	0.111673i
$508$	−13.2918	+	9.65707i	−0.589729	+	0.428463i
$509$	8.24522	+	25.3762i	0.365463	+	1.12478i	0.949691	+	0.313190i	$0.101398\pi$
$509$	8.24522	+	25.3762i	0.365463	+	1.12478i	−0.584228	+	0.811590i	$0.698602\pi$
$510$	7.19585	+	5.22809i	0.318638	+	0.231504i
$511$	−13.3372	+	41.0478i	−0.590004	+	1.81585i
$512$	−1.92722	−	1.40021i	−0.0851720	−	0.0618811i
$513$	17.7021	+	12.8613i	0.781566	+	0.567841i
$514$	0.921078	+	0.669202i	0.0406270	+	0.0295173i
$515$	5.13677	+	15.8094i	0.226353	+	0.696643i
$516$	1.94202	−	1.41096i	0.0854929	−	0.0621142i
$517$	−10.7912			−0.474595
$518$	−9.39545	+	28.9162i	−0.412812	+	1.27051i
$519$	4.47992	−	13.7878i	0.196647	−	0.605217i
$520$	−17.0461			−0.747522
$521$	−22.2671	−	16.1780i	−0.975540	−	0.708772i	−0.0188328	−	0.999823i	$-0.505995\pi$
$521$	−22.2671	−	16.1780i	−0.975540	−	0.708772i	−0.956708	+	0.291051i	$0.905995\pi$
$522$	3.26185	−	2.36987i	0.142767	−	0.103727i
$523$	1.57114			0.0687012			0.0343506	−	0.999410i	$-0.489064\pi$
$523$	1.57114			0.0687012			0.0343506	+	0.999410i	$0.489064\pi$
$524$	1.55145	+	4.77488i	0.0677756	+	0.208592i
$525$	−3.68044	−	11.3272i	−0.160628	−	0.494361i
$526$	4.22922	+	13.0162i	0.184403	+	0.567533i
$527$	34.0805			1.48457
$528$	0.288096	−	0.209314i	0.0125378	−	0.00910923i
$529$	−9.95233			−0.432710
$530$	−1.10766	+	3.40903i	−0.0481138	+	0.148079i
$531$	−4.95451			−0.215008
$532$	14.5281	+	10.5553i	0.629873	+	0.457630i
$533$	22.9407	+	16.6674i	0.993673	+	0.721946i
$534$	10.3481			0.447808
$535$	−4.23861	+	13.0451i	−0.183251	+	0.563989i
$536$	31.7574			1.37171
$537$	−19.0555	+	13.8446i	−0.822305	+	0.597440i
$538$	3.49695			0.150764
$539$	2.32888	+	7.16755i	0.100312	+	0.308728i
$540$	−3.31489	−	10.2022i	−0.142650	−	0.439032i
$541$	−1.12828	−	3.47248i	−0.0485085	−	0.149294i	0.923868	−	0.382711i	$-0.125009\pi$
$541$	−1.12828	−	3.47248i	−0.0485085	−	0.149294i	−0.972377	+	0.233417i	$0.925009\pi$
$542$	16.2389			0.697520
$543$	−3.23757	+	2.35224i	−0.138938	+	0.100944i
$544$	−26.0289	−	18.9111i	−1.11598	−	0.810807i
$545$	−3.95747			−0.169519
$546$	4.65668	−	14.3318i	0.199287	−	0.613344i
$547$	−10.4527	+	32.1700i	−0.446923	+	1.37549i	0.433438	+	0.901184i	$0.357300\pi$
$547$	−10.4527	+	32.1700i	−0.446923	+	1.37549i	−0.880361	+	0.474305i	$0.842700\pi$
$548$	26.6792			1.13968
$549$	5.40577	−	3.92752i	0.230713	−	0.167623i
$550$	−0.968467	−	2.98064i	−0.0412956	−	0.127095i
$551$	10.4038	+	7.55881i	0.443217	+	0.322016i
$552$	10.0688	+	7.31542i	0.428557	+	0.311365i
$553$	−1.43284	−	1.04102i	−0.0609306	−	0.0442687i
$554$	1.19033	−	3.66345i	0.0505721	−	0.155645i
$555$	15.3709	+	11.1676i	0.652460	+	0.474040i
$556$	5.61764	+	17.2893i	0.238241	+	0.733230i
$557$	12.5334	−	9.10608i	0.531059	−	0.385837i	−0.289695	−	0.957119i	$-0.593554\pi$
$557$	12.5334	−	9.10608i	0.531059	−	0.385837i	0.820754	+	0.571282i	$0.193554\pi$
$558$	6.09852	+	4.43083i	0.258171	+	0.187572i
$559$	−1.89268	+	5.82508i	−0.0800520	+	0.246375i
$560$	−0.348584	−	1.07283i	−0.0147304	−	0.0453354i
$561$	7.66095	−	5.56601i	0.323446	−	0.234997i
$562$	6.60262	−	20.3208i	0.278515	−	0.857180i
$563$	−10.8893	−	33.5138i	−0.458929	−	1.41244i	−0.866460	−	0.499246i	$-0.833610\pi$
$563$	−10.8893	−	33.5138i	−0.458929	−	1.41244i	0.407532	−	0.913191i	$-0.366390\pi$
$564$	−3.88934	+	11.9702i	−0.163771	+	0.504035i
$565$	−8.84831	+	6.42867i	−0.372251	+	0.270456i
$566$	0.300363	−	0.218227i	0.0126252	−	0.00917276i
$567$	8.72148			0.366268
$568$	−6.02239	−	22.6391i	−0.252694	−	0.949917i
$569$	−11.2480			−0.471542			−0.235771	−	0.971809i	$-0.575762\pi$
$569$	−11.2480			−0.471542			−0.235771	+	0.971809i	$0.575762\pi$
$570$	−5.07657	+	3.68835i	−0.212634	+	0.154488i
$571$	−24.7227	+	17.9621i	−1.03461	+	0.751690i	−0.969227	−	0.246170i	$-0.920828\pi$
$571$	−24.7227	+	17.9621i	−1.03461	+	0.751690i	−0.0653858	+	0.997860i	$0.520828\pi$
$572$	−2.19133	+	6.74421i	−0.0916240	+	0.281990i
$573$	−9.35565	−	28.7937i	−0.390838	−	1.20288i
$574$	6.47639	−	19.9323i	0.270319	−	0.831957i
$575$	−7.93413	+	5.76448i	−0.330876	+	0.240395i
$576$	−2.00831	−	6.18094i	−0.0836795	−	0.257539i
$577$	5.01852	−	15.4454i	0.208924	−	0.643002i	−0.790606	−	0.612326i	$-0.790234\pi$
$577$	5.01852	−	15.4454i	0.208924	−	0.643002i	0.999529	−	0.0306757i	$-0.00976592\pi$
$578$	−9.88628	−	7.18280i	−0.411215	−	0.298765i
$579$	−11.7077	+	8.50617i	−0.486557	+	0.353504i
$580$	−1.94822	−	5.99599i	−0.0808953	−	0.248970i
$581$	−28.1400	−	20.4449i	−1.16745	−	0.848199i
$582$	4.86737	−	14.9802i	0.201759	−	0.620951i
$583$	3.08733	+	2.24308i	0.127864	+	0.0928987i
$584$	27.4254	+	19.9257i	1.13487	+	0.824532i
$585$	7.26251	+	5.27652i	0.300268	+	0.218157i
$586$	5.25879	+	16.1849i	0.217239	+	0.668592i
$587$	−24.7430	+	17.9768i	−1.02125	+	0.741984i	−0.966539	−	0.256518i	$-0.917425\pi$
$587$	−24.7430	+	17.9768i	−1.02125	+	0.741984i	−0.0547136	+	0.998502i	$0.517425\pi$
$588$	8.79002			0.362494
$589$	−7.42980	+	22.8666i	−0.306140	+	0.942201i
$590$	1.33871	−	4.12012i	0.0551137	−	0.169623i
$591$	20.5317			0.844562
$592$	−1.72983	−	1.25679i	−0.0710955	−	0.0516539i
$593$	−17.4909	+	12.7079i	−0.718265	+	0.521850i	−0.885829	−	0.464011i	$-0.846410\pi$
$593$	−17.4909	+	12.7079i	−0.718265	+	0.521850i	0.167564	+	0.985861i	$0.446410\pi$
$594$	6.38618			0.262028
$595$	−9.26941	−	28.5283i	−0.380009	−	1.16955i
$596$	−2.52148	−	7.76033i	−0.103284	−	0.317876i
$597$	−2.35500	−	7.24794i	−0.0963836	−	0.296638i
$598$	−12.4085			−0.507420
$599$	25.5704	−	18.5780i	1.04478	−	0.759077i	0.0735668	−	0.997290i	$-0.476562\pi$
$599$	25.5704	−	18.5780i	1.04478	−	0.759077i	0.971213	+	0.238213i	$0.0765618\pi$
$600$	−9.35469			−0.381904
$601$	−10.5885	+	32.5882i	−0.431916	+	1.32930i	0.464299	+	0.885678i	$0.346306\pi$
$601$	−10.5885	+	32.5882i	−0.431916	+	1.32930i	−0.896215	+	0.443621i	$0.853694\pi$
$602$	4.52686			0.184501
$603$	−13.5303	−	9.83031i	−0.550995	−	0.400321i
$604$	−17.3919	−	12.6359i	−0.707665	−	0.514149i
$605$	−13.8196			−0.561849
$606$	−5.33386	+	16.4159i	−0.216673	+	0.666851i
$607$	16.8652			0.684539			0.342269	−	0.939602i	$-0.388804\pi$
$607$	16.8652			0.684539			0.342269	+	0.939602i	$0.388804\pi$
$608$	18.3630	−	13.3415i	0.744720	−	0.541071i
$609$	14.2634			0.577984
$610$	1.80545	+	5.55660i	0.0731004	+	0.224980i
$611$	−9.92372	−	30.5421i	−0.401471	−	1.23560i
$612$	3.25357	+	10.0135i	0.131518	+	0.404770i
$613$	−4.97336			−0.200872			−0.100436	−	0.994944i	$-0.532024\pi$
$613$	−4.97336			−0.200872			−0.100436	+	0.994944i	$0.532024\pi$
$614$	−15.3528	+	11.1544i	−0.619587	+	0.450157i
$615$	−10.5954	−	7.69798i	−0.427246	−	0.310413i
$616$	13.4130			0.540427
$617$	−8.00879	+	24.6485i	−0.322422	+	0.992312i	0.650169	+	0.759790i	$0.274698\pi$
$617$	−8.00879	+	24.6485i	−0.322422	+	0.992312i	−0.972591	+	0.232523i	$0.925302\pi$
$618$	−3.56673	+	10.9773i	−0.143475	+	0.441571i
$619$	−15.2256			−0.611970			−0.305985	−	0.952036i	$-0.598986\pi$
$619$	−15.2256			−0.611970			−0.305985	+	0.952036i	$0.598986\pi$
$620$	9.53614	−	6.92841i	0.382981	−	0.278252i
$621$	−6.17537	−	19.0058i	−0.247809	−	0.762677i
$622$	−12.4568	−	9.05038i	−0.499472	−	0.362887i
$623$	−28.2335	−	20.5129i	−1.13115	−	0.821831i
$624$	0.857357	+	0.622906i	0.0343217	+	0.0249362i
$625$	−1.25258	+	3.85505i	−0.0501033	+	0.154202i
$626$	6.31240	+	4.58623i	0.252294	+	0.183303i
$627$	2.06441	+	6.35360i	0.0824446	+	0.253738i
$628$	20.5856	−	14.9563i	0.821455	−	0.596822i
$629$	−45.9990	−	33.4202i	−1.83410	−	1.33255i
$630$	2.05028	−	6.31010i	0.0816850	−	0.251400i
$631$	8.75483	+	26.9446i	0.348524	+	1.07265i	0.959670	+	0.281129i	$0.0907090\pi$
$631$	8.75483	+	26.9446i	0.348524	+	1.07265i	−0.611146	+	0.791518i	$0.709291\pi$
$632$	−1.12541	+	0.817657i	−0.0447664	+	0.0325247i
$633$	5.76401	−	17.7398i	0.229099	−	0.705094i
$634$	−4.11885	−	12.6765i	−0.163581	−	0.503449i
$635$	−5.98296	+	18.4137i	−0.237427	+	0.730724i
$636$	3.60088	−	2.61619i	0.142784	−	0.103739i
$637$	−18.1445	+	13.1828i	−0.718913	+	0.522321i
$638$	3.75327			0.148593
$639$	−4.44196	+	11.5096i	−0.175721	+	0.455313i
$640$	−11.6675			−0.461200
$641$	36.1798	−	26.2862i	1.42902	−	1.03824i	0.438819	−	0.898576i	$-0.355397\pi$
$641$	36.1798	−	26.2862i	1.42902	−	1.03824i	0.990199	−	0.139666i	$-0.0446030\pi$
$642$	−7.70512	+	5.59809i	−0.304097	+	0.220939i
$643$	4.78511	−	14.7270i	0.188706	−	0.580778i	−0.811286	−	0.584649i	$-0.801232\pi$
$643$	4.78511	−	14.7270i	0.188706	−	0.580778i	0.999993	+	0.00387120i	$0.00123224\pi$
$644$	−5.06812	−	15.5981i	−0.199712	−	0.614651i
$645$	0.874151	−	2.69036i	0.0344197	−	0.105933i
$646$	15.1921	−	11.0377i	0.597726	−	0.434273i
$647$	4.31239	+	13.2722i	0.169538	+	0.521783i	0.999342	−	0.0362713i	$-0.0115481\pi$
$647$	4.31239	+	13.2722i	0.169538	+	0.521783i	−0.829804	+	0.558054i	$0.811548\pi$
$648$	2.11682	−	6.51492i	0.0831567	−	0.255930i
$649$	−3.73131	−	2.71096i	−0.146467	−	0.106414i
$650$	7.54543	−	5.48208i	0.295956	−	0.215025i
$651$	8.24075	+	25.3624i	0.322980	+	0.994032i
$652$	15.4039	+	11.1916i	0.603262	+	0.438296i
$653$	2.16093	−	6.65065i	0.0845636	−	0.260260i	−0.899830	−	0.436241i	$-0.856310\pi$
$653$	2.16093	−	6.65065i	0.0845636	−	0.260260i	0.984394	+	0.175981i	$0.0563096\pi$
$654$	−2.22308	−	1.61516i	−0.0869293	−	0.0631578i
$655$	4.78654	+	3.47762i	0.187025	+	0.135882i
$656$	1.19239	+	0.866322i	0.0465550	+	0.0338242i
$657$	−5.51672	−	16.9787i	−0.215228	−	0.662403i
$658$	−19.2022	+	13.9512i	−0.748580	+	0.543875i
$659$	13.1609			0.512675			0.256337	−	0.966587i	$-0.417484\pi$
$659$	13.1609			0.512675			0.256337	+	0.966587i	$0.417484\pi$
$660$	1.01208	−	3.11487i	0.0393953	−	0.121246i
$661$	−5.66295	+	17.4288i	−0.220263	+	0.677900i	0.778475	+	0.627676i	$0.215994\pi$
$661$	−5.66295	+	17.4288i	−0.220263	+	0.677900i	−0.998738	+	0.0502244i	$0.984006\pi$
$662$	−25.8345			−1.00409
$663$	22.7985	+	16.5641i	0.885421	+	0.643296i
$664$	−22.1023	+	16.0582i	−0.857734	+	0.623180i
$665$	21.1621			0.820631
$666$	−3.88627	−	11.9607i	−0.150590	−	0.463468i
$667$	−3.62937	−	11.1700i	−0.140530	−	0.432506i
$668$	0.403784	+	1.24272i	0.0156229	+	0.0480823i
$669$	−9.86266			−0.381313
$670$	11.8307	−	8.59547i	0.457058	−	0.332072i
$671$	6.22018			0.240127
$672$	7.77963	−	23.9432i	0.300106	−	0.923630i
$673$	−33.4428			−1.28913			−0.644563	−	0.764551i	$-0.722961\pi$
$673$	−33.4428			−1.28913			−0.644563	+	0.764551i	$0.722961\pi$
$674$	−2.55302	−	1.85488i	−0.0983387	−	0.0714473i
$675$	12.1520	+	8.82892i	0.467729	+	0.339825i
$676$	−4.42783			−0.170301
$677$	−1.05468	+	3.24598i	−0.0405348	+	0.124753i	−0.969276	−	0.245975i	$-0.920892\pi$
$677$	−1.05468	+	3.24598i	−0.0405348	+	0.124753i	0.928741	+	0.370728i	$0.120892\pi$
$678$	−7.59421			−0.291654
$679$	−42.9749	+	31.2231i	−1.64923	+	1.19823i
$680$	−23.5604			−0.903499
$681$	0.524462	+	1.61413i	0.0200974	+	0.0618536i
$682$	2.16846	+	6.67384i	0.0830347	+	0.255555i
$683$	−2.61283	−	8.04146i	−0.0999771	−	0.307698i	0.888542	−	0.458796i	$-0.151719\pi$
$683$	−2.61283	−	8.04146i	−0.0999771	−	0.307698i	−0.988519	+	0.151098i	$0.951719\pi$
$684$	−7.42791			−0.284013
$685$	25.4353	−	18.4798i	0.971833	−	0.706078i
$686$	−3.56659	−	2.59128i	−0.136173	−	0.0989355i
$687$	23.6244			0.901329
$688$	−0.0983760	+	0.302770i	−0.00375055	+	0.0115430i
$689$	−3.50939	+	10.8008i	−0.133697	+	0.411477i
$690$	5.73095			0.218174
$691$	−12.0106	+	8.72621i	−0.456905	+	0.331961i	−0.792316	−	0.610111i	$-0.791125\pi$
$691$	−12.0106	+	8.72621i	−0.456905	+	0.331961i	0.335411	+	0.942072i	$0.391125\pi$
$692$	4.63689	+	14.2709i	0.176268	+	0.542497i
$693$	−5.71463	−	4.15192i	−0.217081	−	0.157718i
$694$	9.08736	+	6.60235i	0.344951	+	0.250622i
$695$	17.3315	+	12.5921i	0.657422	+	0.477645i
$696$	3.46193	−	10.6547i	0.131224	−	0.403867i
$697$	31.7076	+	23.0369i	1.20101	+	0.872586i
$698$	−4.06572	−	12.5130i	−0.153890	−	0.473624i
$699$	−15.2407	+	11.0730i	−0.576455	+	0.418819i
$700$	9.97312	+	7.24590i	0.376949	+	0.273869i
$701$	1.33295	−	4.10240i	0.0503449	−	0.154946i	−0.922723	−	0.385463i	$-0.874042\pi$
$701$	1.33295	−	4.10240i	0.0503449	−	0.154946i	0.973068	+	0.230517i	$0.0740418\pi$
$702$	5.87283	+	18.0747i	0.221656	+	0.682187i
$703$	32.4516	−	23.5775i	1.22394	−	0.889242i
$704$	1.86953	−	5.75384i	0.0704607	−	0.216856i
$705$	4.58335	+	14.1061i	0.172619	+	0.531267i
$706$	−6.83088	+	21.0233i	−0.257084	+	0.791222i
$707$	47.0936	−	34.2155i	1.77114	−	1.28681i
$708$	−4.35198	+	3.16190i	−0.163558	+	0.118832i
$709$	3.49544			0.131274			0.0656370	−	0.997844i	$-0.479092\pi$
$709$	3.49544			0.131274			0.0656370	+	0.997844i	$0.479092\pi$
$710$	−8.37105	−	6.80378i	−0.314160	−	0.255341i
$711$	0.732581			0.0274739
$712$	−22.1757	+	16.1116i	−0.831070	+	0.603808i
$713$	17.7650	−	12.9071i	0.665306	−	0.483373i
$714$	6.43624	−	19.8087i	0.240870	−	0.741323i
$715$	2.58235	+	7.94765i	0.0965743	+	0.297225i
$716$	7.53357	−	23.1860i	0.281543	−	0.866500i
$717$	−16.1030	+	11.6995i	−0.601376	+	0.436925i
$718$	−4.47542	−	13.7739i	−0.167021	−	0.514038i
$719$	−8.46371	+	26.0486i	−0.315643	+	0.971449i	0.659846	+	0.751401i	$0.270622\pi$
$719$	−8.46371	+	26.0486i	−0.315643	+	0.971449i	−0.975489	+	0.220048i	$0.929378\pi$
$720$	0.377483	+	0.274258i	0.0140680	+	0.0102210i
$721$	31.4913	−	22.8798i	1.17280	−	0.852088i
$722$	−0.878706	−	2.70438i	−0.0327021	−	0.100647i
$723$	−2.32299	−	1.68775i	−0.0863930	−	0.0627682i
$724$	1.27997	−	3.93935i	0.0475698	−	0.146405i
$725$	7.14191	+	5.18890i	0.265244	+	0.192711i
$726$	−7.76309	−	5.64022i	−0.288115	−	0.209328i
$727$	−13.5593	−	9.85143i	−0.502888	−	0.365369i	0.307231	−	0.951635i	$-0.400598\pi$
$727$	−13.5593	−	9.85143i	−0.502888	−	0.365369i	−0.810119	+	0.586266i	$0.800598\pi$
$728$	12.3348	+	37.9628i	0.457160	+	1.40699i
$729$	−19.5591	+	14.2105i	−0.724413	+	0.526317i
$730$	15.6099			0.577750
$731$	−2.61598	+	8.05115i	−0.0967555	+	0.297783i
$732$	2.24187	−	6.89977i	0.0828620	−	0.255023i
$733$	16.2429			0.599945			0.299972	−	0.953948i	$-0.403023\pi$
$733$	16.2429			0.599945			0.299972	+	0.953948i	$0.403023\pi$
$734$	4.53912	+	3.29786i	0.167542	+	0.121726i
$735$	8.38020	−	6.08857i	0.309108	−	0.224580i
$736$	−20.7301			−0.764120
$737$	−4.81098	−	14.8067i	−0.177215	−	0.545411i
$738$	2.67885	+	8.24465i	0.0986098	+	0.303490i
$739$	−5.02304	−	15.4593i	−0.184775	−	0.568680i	0.815169	−	0.579223i	$-0.196644\pi$
$739$	−5.02304	−	15.4593i	−0.184775	−	0.568680i	−0.999944	+	0.0105430i	$0.996644\pi$
$740$	−19.6652			−0.722908
$741$	−16.0840	+	11.6857i	−0.590862	+	0.429286i
$742$	8.39364			0.308140
$743$	−12.4893	+	38.4380i	−0.458187	+	1.41016i	0.409165	+	0.912460i	$0.365820\pi$
$743$	−12.4893	+	38.4380i	−0.458187	+	1.41016i	−0.867352	+	0.497695i	$0.834180\pi$
$744$	20.9458			0.767909
$745$	−7.77927	−	5.65197i	−0.285010	−	0.207072i
$746$	15.5084	+	11.2675i	0.567805	+	0.412534i
$747$	14.3874			0.526407
$748$	−3.02875	+	9.32154i	−0.110742	+	0.340829i
$749$	32.1194			1.17362
$750$	−9.90274	+	7.19477i	−0.361597	+	0.262716i
$751$	37.1025			1.35389			0.676944	−	0.736034i	$-0.263304\pi$
$751$	37.1025			1.35389			0.676944	+	0.736034i	$0.263304\pi$
$752$	−0.515805	−	1.58748i	−0.0188095	−	0.0578896i
$753$	−0.804983	−	2.47748i	−0.0293352	−	0.0902845i
$754$	3.45156	+	10.6228i	0.125699	+	0.386860i
$755$	−25.3335			−0.921982
$756$	−20.3222	+	14.7649i	−0.739110	+	0.536995i
$757$	−19.9909	−	14.5242i	−0.726581	−	0.527892i	0.161899	−	0.986807i	$-0.448238\pi$
$757$	−19.9909	−	14.5242i	−0.726581	−	0.527892i	−0.888480	+	0.458916i	$0.848238\pi$
$758$	−1.52252			−0.0553006
$759$	1.88543	−	5.80275i	0.0684366	−	0.210626i
$760$	5.13633	−	15.8080i	0.186314	−	0.573416i
$761$	40.3697			1.46340			0.731701	−	0.681626i	$-0.238727\pi$
$761$	40.3697			1.46340			0.731701	+	0.681626i	$0.238727\pi$
$762$	−10.8761	+	7.90192i	−0.393998	+	0.286256i
$763$	2.86368	+	8.81351i	0.103672	+	0.319071i
$764$	25.3516	+	18.4190i	0.917189	+	0.666377i
$765$	10.0379	+	7.29296i	0.362921	+	0.263678i
$766$	−11.6248	−	8.44592i	−0.420022	−	0.305164i
$767$	4.24141	−	13.0537i	0.153149	−	0.471343i
$768$	−15.4550	−	11.2287i	−0.557685	−	0.405182i
$769$	12.9786	+	39.9440i	0.468021	+	1.44042i	0.855144	+	0.518391i	$0.173469\pi$
$769$	12.9786	+	39.9440i	0.468021	+	1.44042i	−0.387123	+	0.922028i	$0.626531\pi$
$770$	4.99679	−	3.63038i	0.180072	−	0.130830i
$771$	−1.34781	−	0.979243i	−0.0485403	−	0.0352666i
$772$	4.62864	−	14.2455i	0.166589	−	0.512707i
$773$	7.46865	+	22.9861i	0.268629	+	0.826754i	0.990835	+	0.135076i	$0.0431280\pi$
$773$	7.46865	+	22.9861i	0.268629	+	0.826754i	−0.722207	+	0.691677i	$0.756872\pi$
$774$	−1.51485	+	1.10060i	−0.0544501	+	0.0395603i
$775$	−5.10034	+	15.6972i	−0.183210	+	0.563862i
$776$	12.8929	+	39.6804i	0.462830	+	1.42444i
$777$	13.7484	−	42.3131i	0.493220	−	1.51797i
$778$	−10.6514	+	7.73873i	−0.381873	+	0.277447i
$779$	−22.3693	+	16.2522i	−0.801463	+	0.582297i
$780$	9.74670			0.348988
$781$	−9.64301	+	6.23754i	−0.345054	+	0.223197i
$782$	−17.1504			−0.613297
$783$	−14.5530	+	10.5734i	−0.520083	+	0.377862i
$784$	−0.943098	+	0.685201i	−0.0336821	+	0.0244715i
$785$	9.26607	−	28.5180i	0.330720	−	1.01785i
$786$	1.26948	+	3.90706i	0.0452809	+	0.139360i
$787$	8.78976	−	27.0521i	0.313321	−	0.964303i	−0.663119	−	0.748514i	$-0.730768\pi$
$787$	8.78976	−	27.0521i	0.313321	−	0.964303i	0.976440	−	0.215789i	$-0.0692323\pi$
$788$	−17.1925	+	12.4911i	−0.612458	+	0.444977i
$789$	−6.18861	−	19.0466i	−0.220321	−	0.678077i
$790$	−0.197943	+	0.609207i	−0.00704251	+	0.0216746i
$791$	20.7198	+	15.0538i	0.736712	+	0.535252i
$792$	−4.48849	+	3.26108i	−0.159492	+	0.115877i
$793$	5.72018	+	17.6049i	0.203129	+	0.625168i
$794$	16.2426	+	11.8010i	0.576430	+	0.418801i
$795$	1.62084	−	4.98844i	0.0574853	−	0.176922i
$796$	6.38149	+	4.63642i	0.226186	+	0.164334i
$797$	−16.7664	−	12.1815i	−0.593897	−	0.431492i	0.249810	−	0.968295i	$-0.419632\pi$
$797$	−16.7664	−	12.1815i	−0.593897	−	0.431492i	−0.843707	+	0.536803i	$0.819632\pi$
$798$	11.8877	+	8.63689i	0.420819	+	0.305743i
$799$	−13.7161	−	42.2138i	−0.485241	−	1.49342i
$800$	12.6057	−	9.15857i	0.445679	−	0.323804i
$801$	14.4352			0.510043
$802$	2.08548	−	6.41843i	0.0736407	−	0.226643i
$803$	5.13552	−	15.8055i	0.181228	−	0.557764i
$804$	−18.1584			−0.640397
$805$	−15.6361	−	11.3603i	−0.551102	−	0.400399i
$806$	−16.8947	+	12.2747i	−0.595092	+	0.432359i
$807$	−5.11709			−0.180130
$808$	−14.1286	−	43.4833i	−0.497042	−	1.52974i
$809$	−10.9734	−	33.7726i	−0.385804	−	1.18738i	−0.935896	−	0.352278i	$-0.885407\pi$
$809$	−10.9734	−	33.7726i	−0.385804	−	1.18738i	0.550092	−	0.835104i	$-0.314593\pi$
$810$	−0.974744	−	2.99995i	−0.0342490	−	0.105408i
$811$	−19.7488			−0.693474			−0.346737	−	0.937962i	$-0.612710\pi$
$811$	−19.7488			−0.693474			−0.346737	+	0.937962i	$0.612710\pi$
$812$	−11.9437	+	8.67759i	−0.419141	+	0.304524i
$813$	−23.7623			−0.833382
$814$	3.61773	−	11.1342i	0.126801	−	0.390254i
$815$	22.4378			0.785961
$816$	1.18500	+	0.860952i	0.0414832	+	0.0301393i
$817$	−4.83168	−	3.51042i	−0.169039	−	0.122814i
$818$	9.40010			0.328667
$819$	6.49586	−	19.9922i	0.226984	−	0.698584i
$820$	13.5555			0.473377
$821$	3.41060	−	2.47795i	0.119031	−	0.0864809i	−0.526677	−	0.850065i	$-0.676562\pi$
$821$	3.41060	−	2.47795i	0.119031	−	0.0864809i	0.645708	+	0.763584i	$0.276562\pi$
$822$	21.8303			0.761419
$823$	−12.9508	−	39.8586i	−0.451438	−	1.38938i	−0.875267	−	0.483640i	$-0.839314\pi$
$823$	−12.9508	−	39.8586i	−0.451438	−	1.38938i	0.423829	−	0.905742i	$-0.360686\pi$
$824$	−9.44774	−	29.0772i	−0.329128	−	1.01295i
$825$	1.41716	+	4.36156i	0.0493391	+	0.151850i
$826$	−10.1445			−0.352971
$827$	9.61515	−	6.98582i	0.334352	−	0.242921i	−0.407923	−	0.913016i	$-0.633747\pi$
$827$	9.61515	−	6.98582i	0.334352	−	0.242921i	0.742275	+	0.670096i	$0.233747\pi$
$828$	5.48830	+	3.98748i	0.190732	+	0.138575i
$829$	−40.1733			−1.39528			−0.697639	−	0.716449i	$-0.745766\pi$
$829$	−40.1733			−1.39528			−0.697639	+	0.716449i	$0.745766\pi$
$830$	−3.88747	+	11.9644i	−0.134936	+	0.415291i
$831$	−1.74180	+	5.36072i	−0.0604225	+	0.185961i
$832$	18.0043			0.624185
$833$	−25.0785	+	18.2206i	−0.868920	+	0.631307i
$834$	4.59665	+	14.1470i	0.159169	+	0.489871i
$835$	1.24575	+	0.905092i	0.0431110	+	0.0313220i
$836$	−5.59406	−	4.06433i	−0.193475	−	0.140568i
$837$	−27.2091	−	19.7685i	−0.940483	−	0.683301i
$838$	−2.64649	+	8.14507i	−0.0914216	+	0.281367i
$839$	−11.8700	−	8.62403i	−0.409797	−	0.297735i	0.363723	−	0.931507i	$-0.381506\pi$
$839$	−11.8700	−	8.62403i	−0.409797	−	0.297735i	−0.773520	+	0.633772i	$0.781506\pi$
$840$	−5.69695	−	17.5334i	−0.196563	−	0.604960i
$841$	14.9084	−	10.8316i	0.514084	−	0.373504i
$842$	−13.1537	−	9.55671i	−0.453306	−	0.329346i
$843$	−9.66161	+	29.7354i	−0.332763	+	1.02414i
$844$	5.96597	+	18.3614i	0.205357	+	0.632024i
$845$	−4.22140	+	3.06702i	−0.145220	+	0.105509i
$846$	3.03383	−	9.33716i	0.104305	−	0.321018i
$847$	10.0001	+	30.7772i	0.343608	+	1.05752i
$848$	−0.182408	+	0.561393i	−0.00626390	+	0.0192783i
$849$	−0.439522	+	0.319331i	−0.0150843	+	0.0109594i
$850$	10.4289	−	7.57707i	0.357710	−	0.259891i
$851$	−36.6347			−1.25582
$852$	3.44350	+	12.9447i	0.117972	+	0.443478i
$853$	−4.29914			−0.147200			−0.0735998	−	0.997288i	$-0.523449\pi$
$853$	−4.29914			−0.147200			−0.0735998	+	0.997288i	$0.523449\pi$
$854$	11.0684	−	8.04168i	0.378754	−	0.275181i
$855$	−7.08160	+	5.14508i	−0.242186	+	0.175958i
$856$	7.79581	−	23.9930i	0.266455	−	0.820065i
$857$	5.18382	+	15.9541i	0.177076	+	0.544983i	0.999722	−	0.0235701i	$-0.00750330\pi$
$857$	5.18382	+	15.9541i	0.177076	+	0.544983i	−0.822646	+	0.568553i	$0.807503\pi$
$858$	−1.79306	+	5.51847i	−0.0612140	+	0.188397i
$859$	−1.07518	+	0.781164i	−0.0366847	+	0.0266530i	−0.605977	−	0.795483i	$-0.707217\pi$
$859$	−1.07518	+	0.781164i	−0.0366847	+	0.0266530i	0.569292	+	0.822136i	$0.307217\pi$
$860$	0.904780	+	2.78463i	0.0308527	+	0.0949549i
$861$	−9.47690	+	29.1669i	−0.322972	+	0.994005i
$862$	11.1830	+	8.12491i	0.380894	+	0.276736i
$863$	−24.4290	+	17.7487i	−0.831573	+	0.604173i	−0.920004	−	0.391909i	$-0.871815\pi$
$863$	−24.4290	+	17.7487i	−0.831573	+	0.604173i	0.0884311	+	0.996082i	$0.471815\pi$
$864$	9.81139	+	30.1963i	0.333790	+	1.02730i
$865$	14.3057	+	10.3937i	0.486408	+	0.353396i
$866$	−5.32314	+	16.3829i	−0.180888	+	0.556715i
$867$	14.4666	+	10.5106i	0.491311	+	0.356958i
$868$	−22.3305	−	16.2240i	−0.757946	−	0.550680i
$869$	0.551717	+	0.400846i	0.0187157	+	0.0135978i
$870$	−1.59413	−	4.90624i	−0.0540462	−	0.166337i
$871$	37.4829	−	27.2329i	1.27006	−	0.922752i
$872$	7.27872			0.246488
$873$	6.78977	−	20.8968i	0.229799	−	0.707249i
$874$	3.73891	−	11.5072i	0.126471	−	0.389236i
$875$	41.2804			1.39553
$876$	−15.6814	−	11.3932i	−0.529825	−	0.384941i
$877$	−12.2582	+	8.90609i	−0.413929	+	0.300737i	−0.775191	−	0.631727i	$-0.782346\pi$
$877$	−12.2582	+	8.90609i	−0.413929	+	0.300737i	0.361261	+	0.932465i	$0.382346\pi$
$878$	−3.04442			−0.102744
$879$	−7.69518	−	23.6833i	−0.259552	−	0.798819i
$880$	0.134223	+	0.413095i	0.00452464	+	0.0139254i
$881$	5.01735	+	15.4418i	0.169039	+	0.520248i	0.999311	−	0.0371097i	$-0.0118151\pi$
$881$	5.01735	+	15.4418i	0.169039	+	0.520248i	−0.830272	+	0.557358i	$0.811815\pi$
$882$	−6.85653			−0.230871
$883$	−16.4069	+	11.9203i	−0.552136	+	0.401150i	−0.828572	−	0.559882i	$-0.810846\pi$
$883$	−16.4069	+	11.9203i	−0.552136	+	0.401150i	0.276437	+	0.961032i	$0.410846\pi$
$884$	−29.1679			−0.981023
$885$	−1.95893	+	6.02897i	−0.0658487	+	0.202662i
$886$	−16.1135			−0.541343
$887$	−39.8872	−	28.9798i	−1.33928	−	0.973046i	−0.999470	−	0.0325526i	$-0.989636\pi$
$887$	−39.8872	−	28.9798i	−1.33928	−	0.973046i	−0.339813	−	0.940493i	$-0.610364\pi$
$888$	−28.2708	−	20.5399i	−0.948706	−	0.689275i
$889$	45.3377			1.52058
$890$	−3.90039	+	12.0042i	−0.130741	+	0.402381i
$891$	−3.35822			−0.112505
$892$	8.25863	−	6.00025i	0.276519	−	0.200903i
$893$	31.3139			1.04788
$894$	−2.06321	−	6.34991i	−0.0690041	−	0.212373i
$895$	−8.87786	−	27.3232i	−0.296754	−	0.913315i
$896$	8.44282	+	25.9843i	0.282055	+	0.868075i
$897$	18.1573			0.606254
$898$	−13.5610	+	9.85267i	−0.452538	+	0.328788i
$899$	−15.9912	−	11.6183i	−0.533337	−	0.387492i
$900$	−5.09904			−0.169968
$901$	−4.85052	+	14.9284i	−0.161594	+	0.497336i
$902$	−2.49374	+	7.67495i	−0.0830325	+	0.255548i
$903$	−6.62414			−0.220438
$904$	16.2741	−	11.8239i	0.541270	−	0.393255i
$905$	−1.50837	−	4.64228i	−0.0501399	−	0.154315i
$906$	−14.2309	−	10.3394i	−0.472791	−	0.343503i
$907$	33.4366	+	24.2931i	1.11024	+	0.806640i	0.982702	−	0.185193i	$-0.0592911\pi$
$907$	33.4366	+	24.2931i	1.11024	+	0.806640i	0.127542	+	0.991833i	$0.459291\pi$
$908$	−1.42117	−	1.03254i	−0.0471631	−	0.0342660i
$909$	−7.44050	+	22.8995i	−0.246786	+	0.759528i
$910$	14.8701	+	10.8038i	0.492940	+	0.358142i
$911$	−10.2545	−	31.5601i	−0.339747	−	1.04563i	−0.964336	−	0.264680i	$-0.914734\pi$
$911$	−10.2545	−	31.5601i	−0.339747	−	1.04563i	0.624590	−	0.780953i	$-0.285266\pi$
$912$	−0.836000	+	0.607390i	−0.0276827	+	0.0201127i
$913$	10.8354	+	7.87234i	0.358598	+	0.260537i
$914$	2.85355	−	8.78233i	0.0943871	−	0.290494i
$915$	−2.64191	−	8.13096i	−0.0873389	−	0.268801i
$916$	−19.7822	+	14.3726i	−0.653624	+	0.474885i
$917$	4.28126	−	13.1764i	0.141380	−	0.435122i
$918$	8.11716	+	24.9820i	0.267906	+	0.824530i
$919$	−3.07111	+	9.45189i	−0.101306	+	0.311789i	−0.988846	−	0.148943i	$-0.952413\pi$
$919$	−3.07111	+	9.45189i	−0.101306	+	0.311789i	0.887539	+	0.460732i	$0.152413\pi$
$920$	−12.2812	+	8.92284i	−0.404900	+	0.294177i
$921$	22.4657	−	16.3223i	0.740270	−	0.537838i
$922$	10.1306			0.333634
$923$	−26.5219	−	21.5563i	−0.872978	−	0.709535i
$924$	−7.66936			−0.252303
$925$	22.2771	−	16.1853i	0.732467	−	0.532168i
$926$	1.39958	−	1.01685i	0.0459929	−	0.0334158i
$927$	−4.97543	+	15.3128i	−0.163415	+	0.502939i
$928$	5.76632	+	17.7469i	0.189289	+	0.582570i
$929$	−12.4145	+	38.2078i	−0.407306	+	1.25356i	0.511649	+	0.859195i	$0.329035\pi$
$929$	−12.4145	+	38.2078i	−0.407306	+	1.25356i	−0.918954	+	0.394364i	$0.870965\pi$
$930$	7.80297	−	5.66919i	0.255869	−	0.185900i
$931$	−6.75796	−	20.7989i	−0.221483	−	0.681655i
$932$	6.02539	−	18.5442i	0.197368	−	0.607437i
$933$	18.2280	+	13.2434i	0.596758	+	0.433570i
$934$	−3.17383	+	2.30592i	−0.103851	+	0.0754520i
$935$	3.56920	+	10.9849i	0.116725	+	0.359243i
$936$	−13.3575	−	9.70477i	−0.436603	−	0.317210i
$937$	−0.350705	+	1.07936i	−0.0114570	+	0.0352611i	−0.956622	−	0.291333i	$-0.905901\pi$
$937$	−0.350705	+	1.07936i	−0.0114570	+	0.0352611i	0.945165	+	0.326594i	$0.105901\pi$
$938$	−27.7035	−	20.1278i	−0.904551	−	0.657194i
$939$	−9.23693	−	6.71102i	−0.301436	−	0.219006i
$940$	−12.4198	−	9.02351i	−0.405089	−	0.294315i
$941$	3.06294	+	9.42677i	0.0998491	+	0.307304i	0.988487	−	0.151305i	$-0.0483477\pi$
$941$	3.06294	+	9.42677i	0.0998491	+	0.307304i	−0.888638	+	0.458609i	$0.848348\pi$
$942$	16.8442	−	12.2380i	0.548814	−	0.398737i
$943$	25.2527			0.822341
$944$	0.220456	−	0.678493i	0.00717523	−	0.0220831i
$945$	−9.14749	+	28.1531i	−0.297568	+	0.915820i
$946$	−1.74307			−0.0566721
$947$	41.3687	+	30.0561i	1.34430	+	0.976693i	0.999274	+	0.0381014i	$0.0121310\pi$
$947$	41.3687	+	30.0561i	1.34430	+	0.976693i	0.345029	+	0.938592i	$0.387869\pi$
$948$	0.643490	−	0.467523i	0.0208996	−	0.0151844i
$949$	49.4568			1.60543
$950$	2.81031	+	8.64923i	0.0911784	+	0.280618i
$951$	6.02711	+	18.5496i	0.195443	+	0.601510i
$952$	17.0486	+	52.4703i	0.552550	+	1.70057i
$953$	9.21136			0.298385			0.149193	−	0.988808i	$-0.452333\pi$
$953$	9.21136			0.298385			0.149193	+	0.988808i	$0.452333\pi$
$954$	−2.80882	+	2.04072i	−0.0909388	+	0.0660709i
$955$	36.9279			1.19496
$956$	6.36629	−	19.5934i	0.205901	−	0.633697i
$957$	−5.49215			−0.177536
$958$	8.03487	+	5.83767i	0.259595	+	0.188607i
$959$	−59.5611	−	43.2737i	−1.92333	−	1.39738i
$960$	−8.31541			−0.268379
$961$	1.84049	−	5.66444i	0.0593705	−	0.182724i
$962$	34.8400			1.12329
$963$	−10.7483	+	7.80910i	−0.346359	+	0.251645i
$964$	2.97198			0.0957211
$965$	−5.45457	−	16.7875i	−0.175589	−	0.540407i
$966$	−4.14701	−	12.7632i	−0.133428	−	0.410648i
$967$	−5.28310	−	16.2597i	−0.169893	−	0.522877i	0.829471	−	0.558550i	$-0.188642\pi$
$967$	−5.28310	−	16.2597i	−0.169893	−	0.522877i	−0.999363	+	0.0356738i	$0.988642\pi$
$968$	25.4176			0.816953
$969$	−22.2306	+	16.1515i	−0.714150	+	0.518860i
$970$	15.5429	+	11.2926i	0.499054	+	0.362584i
$971$	−33.6234			−1.07903			−0.539513	−	0.841977i	$-0.681392\pi$
$971$	−33.6234			−1.07903			−0.539513	+	0.841977i	$0.681392\pi$
$972$	5.36849	−	16.5225i	0.172194	−	0.529960i
$973$	15.5020	−	47.7101i	0.496970	−	1.52952i
$974$	−14.0968			−0.451692
$975$	−11.0412	+	8.02192i	−0.353602	+	0.256907i
$976$	0.297318	+	0.915049i	0.00951690	+	0.0292900i
$977$	−30.8622	−	22.4227i	−0.987371	−	0.717367i	−0.0280269	−	0.999607i	$-0.508922\pi$
$977$	−30.8622	−	22.4227i	−0.987371	−	0.717367i	−0.959344	+	0.282240i	$0.908922\pi$
$978$	12.6043	+	9.15753i	0.403040	+	0.292826i
$979$	10.8714	+	7.89850i	0.347450	+	0.252437i
$980$	−3.31311	+	10.1967i	−0.105833	+	0.325721i
$981$	−3.10110	−	2.25308i	−0.0990105	−	0.0719353i
$982$	−4.22817	−	13.0130i	−0.134926	−	0.415261i
$983$	−3.93287	+	2.85740i	−0.125439	+	0.0911368i	−0.648736	−	0.761014i	$-0.724702\pi$
$983$	−3.93287	+	2.85740i	−0.125439	+	0.0911368i	0.523297	+	0.852151i	$0.324702\pi$
$984$	19.4874	+	14.1584i	0.621235	+	0.451354i
$985$	−7.73876	+	23.8174i	−0.246577	+	0.758887i
$986$	4.77059	+	14.6824i	0.151927	+	0.467582i
$987$	28.0986	−	20.4148i	0.894387	−	0.649810i
$988$	6.35881	−	19.5704i	0.202301	−	0.622618i
$989$	1.68553	+	5.18753i	0.0535967	+	0.164954i
$990$	−0.789461	+	2.42971i	−0.0250907	+	0.0772213i
$991$	−9.22511	+	6.70244i	−0.293045	+	0.212910i	−0.724587	−	0.689183i	$-0.757970\pi$
$991$	−9.22511	+	6.70244i	−0.293045	+	0.212910i	0.431542	+	0.902093i	$0.357970\pi$
$992$	−28.2250	+	20.5067i	−0.896145	+	0.651087i
$993$	37.8036			1.19966
$994$	−9.09500	+	23.5661i	−0.288476	+	0.747473i
$995$	9.29547			0.294686
$996$	12.6377	−	9.18183i	0.400441	−	0.290938i
$997$	43.3128	−	31.4686i	1.37173	−	0.996620i	0.374130	−	0.927376i	$-0.377941\pi$
$997$	43.3128	−	31.4686i	1.37173	−	0.996620i	0.997600	−	0.0692439i	$-0.0220587\pi$
$998$	−5.65427	+	17.4020i	−0.178983	+	0.550852i
$999$	17.3389	+	53.3638i	0.548580	+	1.68835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.c.a.25.3	✓	20
3.2	odd	2		639.2.f.c.451.3		20
71.14	odd	10		5041.2.a.j.1.6		10
71.54	even	5	inner	71.2.c.a.54.3	yes	20
71.57	even	5		5041.2.a.i.1.6		10
213.125	odd	10		639.2.f.c.622.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.c.a.25.3	✓	20	1.1	even	1	trivial
71.2.c.a.54.3	yes	20	71.54	even	5	inner
639.2.f.c.451.3		20	3.2	odd	2
639.2.f.c.622.3		20	213.125	odd	10
5041.2.a.i.1.6		10	71.57	even	5
5041.2.a.j.1.6		10	71.14	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)

\(f(q)\)	\(=\)	\(q+(-0.685174 + 0.497808i) q^{2} +(1.00262 - 0.728443i) q^{3} +(-0.396383 + 1.21994i) q^{4} +(0.467113 + 1.43763i) q^{5} +(-0.324342 + 0.998220i) q^{6} +(2.86367 - 2.08058i) q^{7} +(-0.859132 - 2.64414i) q^{8} +(-0.452442 + 1.39247i) q^{9} +O(q^{10})\)	\(q+(-0.685174 + 0.497808i) q^{2} +(1.00262 - 0.728443i) q^{3} +(-0.396383 + 1.21994i) q^{4} +(0.467113 + 1.43763i) q^{5} +(-0.324342 + 0.998220i) q^{6} +(2.86367 - 2.08058i) q^{7} +(-0.859132 - 2.64414i) q^{8} +(-0.452442 + 1.39247i) q^{9} +(-1.03572 - 0.752493i) q^{10} +(-1.10266 + 0.801130i) q^{11} +(0.491238 + 1.51187i) q^{12} +(-3.28145 - 2.38411i) q^{13} +(-0.926385 + 2.85112i) q^{14} +(1.51556 + 1.10112i) q^{15} +(-0.170560 - 0.123919i) q^{16} +(-4.53547 - 3.29521i) q^{17} +(-0.383183 - 1.17932i) q^{18} +(3.19971 - 2.32472i) q^{19} -1.93898 q^{20} +(1.35558 - 4.17204i) q^{21} +(0.356706 - 1.09783i) q^{22} -3.61216 q^{23} +(-2.78748 - 2.02522i) q^{24} +(2.19651 - 1.59586i) q^{25} +3.43520 q^{26} +(1.70961 + 5.26163i) q^{27} +(1.40307 + 4.31822i) q^{28} +(1.00476 + 3.09235i) q^{29} -1.58657 q^{30} +(-4.91813 + 3.57323i) q^{31} +5.73897 q^{32} +(-0.521967 + 1.60645i) q^{33} +4.74797 q^{34} +(4.32876 + 3.14503i) q^{35} +(-1.51940 - 1.10391i) q^{36} +10.1421 q^{37} +(-1.03509 + 3.18568i) q^{38} -5.02672 q^{39} +(3.39997 - 2.47022i) q^{40} -6.99103 q^{41} +(1.14807 + 3.53339i) q^{42} +(-0.466627 - 1.43613i) q^{43} +(-0.540256 - 1.66274i) q^{44} -2.21320 q^{45} +(2.47496 - 1.79816i) q^{46} +(6.40533 + 4.65375i) q^{47} -0.261274 q^{48} +(1.70869 - 5.25880i) q^{49} +(-0.710560 + 2.18688i) q^{50} -6.94770 q^{51} +(4.20919 - 3.05816i) q^{52} +(-0.865214 - 2.66286i) q^{53} +(-3.79066 - 2.75408i) q^{54} +(-1.66679 - 1.21100i) q^{55} +(-7.96161 - 5.78445i) q^{56} +(1.51465 - 4.66161i) q^{57} +(-2.22784 - 1.61862i) q^{58} +(1.04569 + 3.21830i) q^{59} +(-1.94405 + 1.41243i) q^{60} +(-3.69213 - 2.68249i) q^{61} +(1.59099 - 4.89657i) q^{62} +(1.60151 + 4.92893i) q^{63} +(-3.59108 + 2.60907i) q^{64} +(1.89466 - 5.83115i) q^{65} +(-0.442065 - 1.36054i) q^{66} +(-3.52980 + 10.8636i) q^{67} +(5.81775 - 4.22684i) q^{68} +(-3.62160 + 2.63125i) q^{69} -4.53157 q^{70} +(8.41379 + 0.456169i) q^{71} +4.07060 q^{72} +(-9.86451 + 7.16698i) q^{73} +(-6.94908 + 5.04880i) q^{74} +(1.03976 - 3.20006i) q^{75} +(1.56772 + 4.82494i) q^{76} +(-1.49084 + 4.58834i) q^{77} +(3.44418 - 2.50234i) q^{78} +(-0.154617 - 0.475862i) q^{79} +(0.0984785 - 0.303086i) q^{80} +(1.99334 + 1.44825i) q^{81} +(4.79008 - 3.48020i) q^{82} +(-3.03657 - 9.34561i) q^{83} +(4.55232 + 3.30745i) q^{84} +(2.61871 - 8.05955i) q^{85} +(1.03464 + 0.751709i) q^{86} +(3.25999 + 2.36852i) q^{87} +(3.06563 + 2.22731i) q^{88} +(-3.04666 - 9.37667i) q^{89} +(1.51643 - 1.10175i) q^{90} -14.3573 q^{91} +(1.43180 - 4.40662i) q^{92} +(-2.32810 + 7.16515i) q^{93} -6.70545 q^{94} +(4.83672 + 3.51408i) q^{95} +(5.75398 - 4.18051i) q^{96} -15.0069 q^{97} +(1.44713 + 4.45379i) q^{98} +(-0.616662 - 1.89789i) 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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