LMFDB - Embedded newform 385.2.i.b.331.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 12 x^{9} + 49 x^{8} - 38 x^{7} + 136 x^{6} - 34 x^{5} + 113 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 13x^10 - 12x^9 + 49x^8 - 38x^7 + 136x^6 - 34x^5 + 113x^4 - 72x^3 + 58x^2 - 16*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.2
Root			$0.961975 - 1.66619i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.b.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.461975 + 0.800164i) q^{2} +(1.05339 + 1.82453i) q^{3} +(0.573158 + 0.992739i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.94657 q^{6} +(2.24596 + 1.39846i) q^{7} -2.90704 q^{8} +(-0.719279 + 1.24583i) q^{9} +O(q^{10})$	\(q+(-0.461975 + 0.800164i) q^{2} +(1.05339 + 1.82453i) q^{3} +(0.573158 + 0.992739i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.94657 q^{6} +(2.24596 + 1.39846i) q^{7} -2.90704 q^{8} +(-0.719279 + 1.24583i) q^{9} +(0.461975 + 0.800164i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.20752 + 2.09149i) q^{12} +2.69085 q^{13} +(-2.15657 + 1.15108i) q^{14} +2.10679 q^{15} +(0.196662 - 0.340629i) q^{16} +(-2.29781 - 3.97992i) q^{17} +(-0.664578 - 1.15108i) q^{18} +(-2.82607 + 4.89489i) q^{19} +1.14632 q^{20} +(-0.185649 + 5.57095i) q^{21} -0.923950 q^{22} +(3.40590 - 5.89919i) q^{23} +(-3.06226 - 5.30399i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.24310 + 2.15312i) q^{26} +3.28963 q^{27} +(-0.101013 + 3.03119i) q^{28} -2.78423 q^{29} +(-0.973283 + 1.68578i) q^{30} +(-4.35253 - 7.53881i) q^{31} +(-2.72533 - 4.72041i) q^{32} +(-1.05339 + 1.82453i) q^{33} +4.24611 q^{34} +(2.33408 - 1.24583i) q^{35} -1.64904 q^{36} +(-1.58777 + 2.75009i) q^{37} +(-2.61114 - 4.52264i) q^{38} +(2.83452 + 4.90954i) q^{39} +(-1.45352 + 2.51757i) q^{40} -10.0080 q^{41} +(-4.37191 - 2.72219i) q^{42} -1.01919 q^{43} +(-0.573158 + 0.992739i) q^{44} +(0.719279 + 1.24583i) q^{45} +(3.14688 + 5.45056i) q^{46} +(3.18739 - 5.52072i) q^{47} +0.828651 q^{48} +(3.08865 + 6.28174i) q^{49} +0.923950 q^{50} +(4.84099 - 8.38484i) q^{51} +(1.54228 + 2.67131i) q^{52} +(3.54644 + 6.14262i) q^{53} +(-1.51973 + 2.63224i) q^{54} +1.00000 q^{55} +(-6.52908 - 4.06536i) q^{56} -11.9079 q^{57} +(1.28625 - 2.22784i) q^{58} +(7.30306 + 12.6493i) q^{59} +(1.20752 + 2.09149i) q^{60} +(4.94059 - 8.55735i) q^{61} +8.04304 q^{62} +(-3.35771 + 1.79220i) q^{63} +5.82279 q^{64} +(1.34542 - 2.33034i) q^{65} +(-0.973283 - 1.68578i) q^{66} +(-2.93680 - 5.08669i) q^{67} +(2.63401 - 4.56224i) q^{68} +14.3510 q^{69} +(-0.0814179 + 2.44319i) q^{70} +4.84403 q^{71} +(2.09097 - 3.62167i) q^{72} +(-3.39271 - 5.87634i) q^{73} +(-1.46702 - 2.54095i) q^{74} +(1.05339 - 1.82453i) q^{75} -6.47914 q^{76} +(-0.0881194 + 2.64428i) q^{77} -5.23791 q^{78} +(-5.09280 + 8.82099i) q^{79} +(-0.196662 - 0.340629i) q^{80} +(5.62311 + 9.73952i) q^{81} +(4.62346 - 8.00808i) q^{82} +6.83735 q^{83} +(-5.63690 + 3.00873i) q^{84} -4.59561 q^{85} +(0.470839 - 0.815516i) q^{86} +(-2.93290 - 5.07992i) q^{87} +(-1.45352 - 2.51757i) q^{88} +(2.43420 - 4.21616i) q^{89} -1.32916 q^{90} +(6.04353 + 3.76303i) q^{91} +7.80848 q^{92} +(9.16987 - 15.8827i) q^{93} +(2.94499 + 5.10087i) q^{94} +(2.82607 + 4.89489i) q^{95} +(5.74170 - 9.94492i) q^{96} +7.44677 q^{97} +(-6.45330 - 0.430584i) q^{98} -1.43856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.461975	+	0.800164i	−0.326666	+	0.565801i	−0.981848	−	0.189669i	$-0.939258\pi$
$2$	−0.461975	+	0.800164i	−0.326666	+	0.565801i	0.655182	+	0.755471i	$0.272592\pi$
$3$	1.05339	+	1.82453i	0.608177	+	1.05339i	0.991541	+	0.129797i	$0.0414324\pi$
$3$	1.05339	+	1.82453i	0.608177	+	1.05339i	−0.383363	+	0.923598i	$0.625234\pi$
$4$	0.573158	+	0.992739i	0.286579	+	0.496370i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.94657			−0.794683
$7$	2.24596	+	1.39846i	0.848892	+	0.528566i
$7$	2.24596	+	1.39846i	0.848892	+	0.528566i
$8$	−2.90704			−1.02779
$9$	−0.719279	+	1.24583i	−0.239760	+	0.415276i
$10$	0.461975	+	0.800164i	0.146089	+	0.253034i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.20752	+	2.09149i	−0.348582	+	0.603762i
$13$	2.69085			0.746307			0.373153	−	0.927770i	$-0.378277\pi$
$13$	2.69085			0.746307			0.373153	+	0.927770i	$0.378277\pi$
$14$	−2.15657	+	1.15108i	−0.576367	+	0.307640i
$15$	2.10679			0.543970
$16$	0.196662	−	0.340629i	0.0491655	−	0.0851572i
$17$	−2.29781	−	3.97992i	−0.557300	−	0.965271i	−0.997721	−	0.0674799i	$-0.978504\pi$
$17$	−2.29781	−	3.97992i	−0.557300	−	0.965271i	0.440421	−	0.897791i	$-0.354829\pi$
$18$	−0.664578	−	1.15108i	−0.156642	−	0.271313i
$19$	−2.82607	+	4.89489i	−0.648344	+	1.12297i	0.335174	+	0.942156i	$0.391205\pi$
$19$	−2.82607	+	4.89489i	−0.648344	+	1.12297i	−0.983518	+	0.180809i	$0.942128\pi$
$20$	1.14632			0.256324
$21$	−0.185649	+	5.57095i	−0.0405119	+	1.21568i
$22$	−0.923950			−0.196987
$23$	3.40590	−	5.89919i	0.710179	−	1.23007i	−0.254610	−	0.967044i	$-0.581947\pi$
$23$	3.40590	−	5.89919i	0.710179	−	1.23007i	0.964790	−	0.263023i	$-0.0847195\pi$
$24$	−3.06226	−	5.30399i	−0.625081	−	1.08267i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.24310	+	2.15312i	−0.243793	+	0.422261i
$27$	3.28963			0.633089
$28$	−0.101013	+	3.03119i	−0.0190896	+	0.572840i
$29$	−2.78423			−0.517019			−0.258510	−	0.966009i	$-0.583231\pi$
$29$	−2.78423			−0.517019			−0.258510	+	0.966009i	$0.583231\pi$
$30$	−0.973283	+	1.68578i	−0.177696	+	0.307779i
$31$	−4.35253	−	7.53881i	−0.781738	−	1.35401i	−0.930928	−	0.365202i	$-0.881000\pi$
$31$	−4.35253	−	7.53881i	−0.781738	−	1.35401i	0.149190	−	0.988808i	$-0.452333\pi$
$32$	−2.72533	−	4.72041i	−0.481775	−	0.834459i
$33$	−1.05339	+	1.82453i	−0.183372	+	0.317610i
$34$	4.24611			0.728202
$35$	2.33408	−	1.24583i	0.394531	−	0.210583i
$36$	−1.64904			−0.274841
$37$	−1.58777	+	2.75009i	−0.261027	+	0.452113i	−0.966515	−	0.256609i	$-0.917395\pi$
$37$	−1.58777	+	2.75009i	−0.261027	+	0.452113i	0.705488	+	0.708722i	$0.250728\pi$
$38$	−2.61114	−	4.52264i	−0.423584	−	0.733668i
$39$	2.83452	+	4.90954i	0.453887	+	0.786155i
$40$	−1.45352	+	2.51757i	−0.229822	+	0.398063i
$41$	−10.0080			−1.56299			−0.781497	−	0.623909i	$-0.785544\pi$
$41$	−10.0080			−1.56299			−0.781497	+	0.623909i	$0.785544\pi$
$42$	−4.37191	−	2.72219i	−0.674600	−	0.420043i
$43$	−1.01919			−0.155425			−0.0777123	−	0.996976i	$-0.524762\pi$
$43$	−1.01919			−0.155425			−0.0777123	+	0.996976i	$0.524762\pi$
$44$	−0.573158	+	0.992739i	−0.0864069	+	0.149661i
$45$	0.719279	+	1.24583i	0.107224	+	0.185717i
$46$	3.14688	+	5.45056i	0.463982	+	0.803641i
$47$	3.18739	−	5.52072i	0.464929	−	0.805280i	−0.534270	−	0.845314i	$-0.679413\pi$
$47$	3.18739	−	5.52072i	0.464929	−	0.805280i	0.999198	+	0.0400339i	$0.0127466\pi$
$48$	0.828651			0.119605
$49$	3.08865	+	6.28174i	0.441235	+	0.897392i
$50$	0.923950			0.130666
$51$	4.84099	−	8.38484i	0.677874	−	1.17411i
$52$	1.54228	+	2.67131i	0.213876	+	0.370444i
$53$	3.54644	+	6.14262i	0.487141	+	0.843753i	0.999891	−	0.0147849i	$-0.00470635\pi$
$53$	3.54644	+	6.14262i	0.487141	+	0.843753i	−0.512749	+	0.858538i	$0.671373\pi$
$54$	−1.51973	+	2.63224i	−0.206808	+	0.358203i
$55$	1.00000			0.134840
$56$	−6.52908	−	4.06536i	−0.872486	−	0.543257i
$57$	−11.9079			−1.57723
$58$	1.28625	−	2.22784i	0.168892	−	0.292530i
$59$	7.30306	+	12.6493i	0.950777	+	1.64679i	0.743748	+	0.668460i	$0.233046\pi$
$59$	7.30306	+	12.6493i	0.950777	+	1.64679i	0.207029	+	0.978335i	$0.433620\pi$
$60$	1.20752	+	2.09149i	0.155891	+	0.270010i
$61$	4.94059	−	8.55735i	0.632577	−	1.09566i	−0.354446	−	0.935077i	$-0.615330\pi$
$61$	4.94059	−	8.55735i	0.632577	−	1.09566i	0.987023	−	0.160579i	$-0.0513363\pi$
$62$	8.04304			1.02147
$63$	−3.35771	+	1.79220i	−0.423031	+	0.225796i
$64$	5.82279			0.727849
$65$	1.34542	−	2.33034i	0.166879	−	0.289043i
$66$	−0.973283	−	1.68578i	−0.119803	−	0.207505i
$67$	−2.93680	−	5.08669i	−0.358788	−	0.621439i	0.628971	−	0.777429i	$-0.283476\pi$
$67$	−2.93680	−	5.08669i	−0.358788	−	0.621439i	−0.987759	+	0.155990i	$0.950143\pi$
$68$	2.63401	−	4.56224i	0.319421	−	0.553253i
$69$	14.3510			1.72766
$70$	−0.0814179	+	2.44319i	−0.00973130	+	0.292016i
$71$	4.84403			0.574880			0.287440	−	0.957799i	$-0.407196\pi$
$71$	4.84403			0.574880			0.287440	+	0.957799i	$0.407196\pi$
$72$	2.09097	−	3.62167i	0.246423	−	0.426818i
$73$	−3.39271	−	5.87634i	−0.397086	−	0.687774i	0.596279	−	0.802778i	$-0.296645\pi$
$73$	−3.39271	−	5.87634i	−0.397086	−	0.687774i	−0.993365	+	0.115004i	$0.963312\pi$
$74$	−1.46702	−	2.54095i	−0.170537	−	0.295379i
$75$	1.05339	−	1.82453i	0.121635	−	0.210679i
$76$	−6.47914			−0.743208
$77$	−0.0881194	+	2.64428i	−0.0100421	+	0.301344i
$78$	−5.23791			−0.593077
$79$	−5.09280	+	8.82099i	−0.572985	+	0.992439i	0.423273	+	0.906002i	$0.360881\pi$
$79$	−5.09280	+	8.82099i	−0.572985	+	0.992439i	−0.996257	+	0.0864364i	$0.972452\pi$
$80$	−0.196662	−	0.340629i	−0.0219875	−	0.0380834i
$81$	5.62311	+	9.73952i	0.624790	+	1.08217i
$82$	4.62346	−	8.00808i	0.510576	−	0.884344i
$83$	6.83735			0.750497			0.375249	−	0.926924i	$-0.377557\pi$
$83$	6.83735			0.750497			0.375249	+	0.926924i	$0.377557\pi$
$84$	−5.63690	+	3.00873i	−0.615037	+	0.328280i
$85$	−4.59561			−0.498464
$86$	0.470839	−	0.815516i	0.0507718	−	0.0879394i
$87$	−2.93290	−	5.07992i	−0.314439	−	0.544625i
$88$	−1.45352	−	2.51757i	−0.154946	−	0.268374i
$89$	2.43420	−	4.21616i	0.258025	−	0.446912i	−0.707688	−	0.706525i	$-0.750262\pi$
$89$	2.43420	−	4.21616i	0.258025	−	0.446912i	0.965713	+	0.259613i	$0.0835950\pi$
$90$	−1.32916			−0.140105
$91$	6.04353	+	3.76303i	0.633534	+	0.394473i
$92$	7.80848			0.814091
$93$	9.16987	−	15.8827i	0.950871	−	1.64696i
$94$	2.94499	+	5.10087i	0.303752	+	0.526115i
$95$	2.82607	+	4.89489i	0.289948	+	0.502205i
$96$	5.74170	−	9.94492i	0.586010	−	1.01500i
$97$	7.44677			0.756104			0.378052	−	0.925784i	$-0.376594\pi$
$97$	7.44677			0.756104			0.378052	+	0.925784i	$0.376594\pi$
$98$	−6.45330	−	0.430584i	−0.651882	−	0.0434956i
$99$	−1.43856			−0.144581
$100$	0.573158	−	0.992739i	0.0573158	−	0.0992739i
$101$	−5.83034	−	10.0984i	−0.580141	−	1.00483i	−0.995462	−	0.0951583i	$-0.969664\pi$
$101$	−5.83034	−	10.0984i	−0.580141	−	1.00483i	0.415322	−	0.909675i	$-0.363669\pi$
$102$	4.47283	+	7.74717i	0.442876	+	0.767084i
$103$	4.88804	−	8.46633i	0.481632	−	0.834212i	−0.518145	−	0.855293i	$-0.673377\pi$
$103$	4.88804	−	8.46633i	0.481632	−	0.834212i	0.999778	+	0.0210807i	$0.00671071\pi$
$104$	−7.82240			−0.767049
$105$	4.73176	+	2.94625i	0.461772	+	0.287525i
$106$	−6.55347			−0.636529
$107$	4.87162	−	8.43790i	0.470958	−	0.815722i	−0.528491	−	0.848939i	$-0.677242\pi$
$107$	4.87162	−	8.43790i	0.470958	−	0.815722i	0.999448	+	0.0332167i	$0.0105752\pi$
$108$	1.88548	+	3.26574i	0.181430	+	0.314246i
$109$	7.71940	+	13.3704i	0.739384	+	1.28065i	0.952773	+	0.303684i	$0.0982166\pi$
$109$	7.71940	+	13.3704i	0.739384	+	1.28065i	−0.213389	+	0.976967i	$0.568450\pi$
$110$	−0.461975	+	0.800164i	−0.0440476	+	0.0762926i
$111$	−6.69018			−0.635004
$112$	0.918049	−	0.490014i	0.0867474	−	0.0463020i
$113$	−18.6346			−1.75299			−0.876496	−	0.481409i	$-0.840125\pi$
$113$	−18.6346			−1.75299			−0.876496	+	0.481409i	$0.840125\pi$
$114$	5.50113	−	9.52824i	0.515228	−	0.892401i
$115$	−3.40590	−	5.89919i	−0.317602	−	0.550103i
$116$	−1.59581	−	2.76402i	−0.148167	−	0.256633i
$117$	−1.93547	+	3.35233i	−0.178934	+	0.309923i
$118$	−13.4953			−1.24234
$119$	0.404962	−	12.1521i	0.0371228	−	1.11398i
$120$	−6.12452			−0.559089
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	4.56485	+	7.90656i	0.413283	+	0.715826i
$123$	−10.5424	−	18.2600i	−0.950578	−	1.64645i
$124$	4.98938	−	8.64186i	0.448060	−	0.776062i
$125$	−1.00000			−0.0894427
$126$	0.117124	−	3.51466i	0.0104343	−	0.313111i
$127$	7.60714			0.675024			0.337512	−	0.941321i	$-0.390415\pi$
$127$	7.60714			0.675024			0.337512	+	0.941321i	$0.390415\pi$
$128$	2.76068	−	4.78164i	0.244012	−	0.422642i
$129$	−1.07361	−	1.85954i	−0.0945257	−	0.163723i
$130$	1.24310	+	2.15312i	0.109027	+	0.188841i
$131$	0.771450	−	1.33619i	0.0674019	−	0.116743i	−0.830355	−	0.557235i	$-0.811862\pi$
$131$	0.771450	−	1.33619i	0.0674019	−	0.116743i	0.897757	+	0.440491i	$0.145196\pi$
$132$	−2.41505			−0.210203
$133$	−13.1925	+	7.04159i	−1.14394	+	0.610583i
$134$	5.42692			0.468814
$135$	1.64481	−	2.84890i	0.141563	−	0.245194i
$136$	6.67981	+	11.5698i	0.572789	+	0.992099i
$137$	3.17649	+	5.50184i	0.271386	+	0.470054i	0.969217	−	0.246208i	$-0.0791847\pi$
$137$	3.17649	+	5.50184i	0.271386	+	0.470054i	−0.697831	+	0.716262i	$0.745851\pi$
$138$	−6.62981	+	11.4832i	−0.564367	+	0.977513i
$139$	4.54555			0.385549			0.192774	−	0.981243i	$-0.438251\pi$
$139$	4.54555			0.385549			0.192774	+	0.981243i	$0.438251\pi$
$140$	2.57458	+	1.60307i	0.217592	+	0.135484i
$141$	13.4303			1.13104
$142$	−2.23782	+	3.87601i	−0.187794	+	0.325268i
$143$	1.34542	+	2.33034i	0.112510	+	0.194873i
$144$	0.282910	+	0.490014i	0.0235758	+	0.0408345i
$145$	−1.39212	+	2.41122i	−0.115609	+	0.200241i
$146$	6.26938			0.518858
$147$	−8.20768	+	12.2525i	−0.676958	+	1.01057i
$148$	−3.64017			−0.299220
$149$	−1.90662	+	3.30237i	−0.156197	+	0.270540i	−0.933494	−	0.358593i	$-0.883257\pi$
$149$	−1.90662	+	3.30237i	−0.156197	+	0.270540i	0.777297	+	0.629133i	$0.216590\pi$
$150$	0.973283	+	1.68578i	0.0794683	+	0.137643i
$151$	8.07912	+	13.9934i	0.657469	+	1.13877i	0.981269	+	0.192644i	$0.0617064\pi$
$151$	8.07912	+	13.9934i	0.657469	+	1.13877i	−0.323799	+	0.946126i	$0.604960\pi$
$152$	8.21549	−	14.2296i	0.666364	−	1.15418i
$153$	6.61105			0.534472
$154$	−2.07515	−	1.29210i	−0.167220	−	0.104121i
$155$	−8.70507			−0.699208
$156$	−3.24926	+	5.62789i	−0.260149	+	0.450592i
$157$	4.64340	+	8.04261i	0.370584	+	0.641870i	0.989655	−	0.143464i	$-0.0458243\pi$
$157$	4.64340	+	8.04261i	0.370584	+	0.641870i	−0.619072	+	0.785335i	$0.712491\pi$
$158$	−4.70549	−	8.15015i	−0.374349	−	0.648391i
$159$	−7.47160	+	12.9412i	−0.592537	+	1.02630i
$160$	−5.45067			−0.430913
$161$	15.8993	−	8.48633i	1.25304	−	0.668817i
$162$	−10.3909			−0.816390
$163$	−6.43205	+	11.1406i	−0.503797	+	0.872602i	0.496193	+	0.868212i	$0.334731\pi$
$163$	−6.43205	+	11.1406i	−0.503797	+	0.872602i	−0.999990	+	0.00438986i	$0.998603\pi$
$164$	−5.73619	−	9.93538i	−0.447922	−	0.775823i
$165$	1.05339	+	1.82453i	0.0820066	+	0.142040i
$166$	−3.15869	+	5.47100i	−0.245162	+	0.424632i
$167$	−11.3734			−0.880101			−0.440050	−	0.897973i	$-0.645039\pi$
$167$	−11.3734			−0.880101			−0.440050	+	0.897973i	$0.645039\pi$
$168$	0.539689	−	16.1950i	0.0416379	−	1.24947i
$169$	−5.75934			−0.443026
$170$	2.12306	−	3.67724i	0.162831	−	0.282032i
$171$	−4.06546	−	7.04159i	−0.310894	−	0.538484i
$172$	−0.584155	−	1.01179i	−0.0445414	−	0.0771480i
$173$	−2.69032	+	4.65977i	−0.204541	+	0.354276i	−0.949986	−	0.312291i	$-0.898904\pi$
$173$	−2.69032	+	4.65977i	−0.204541	+	0.354276i	0.745445	+	0.666567i	$0.232237\pi$
$174$	5.41970			0.410866
$175$	0.0881194	−	2.64428i	0.00666120	−	0.199889i
$176$	0.393324			0.0296479
$177$	−15.3860	+	26.6493i	−1.15648	+	2.00309i
$178$	2.24908	+	3.89552i	0.168576	+	0.291982i
$179$	−1.25299	−	2.17024i	−0.0936530	−	0.162212i	0.815393	−	0.578908i	$-0.196521\pi$
$179$	−1.25299	−	2.17024i	−0.0936530	−	0.162212i	−0.909046	+	0.416697i	$0.863188\pi$
$180$	−0.824522	+	1.42811i	−0.0614562	+	0.106445i
$181$	−19.7391			−1.46719			−0.733596	−	0.679585i	$-0.762160\pi$
$181$	−19.7391			−1.46719			−0.733596	+	0.679585i	$0.762160\pi$
$182$	−5.80300	+	3.09739i	−0.430147	+	0.229594i
$183$	20.8175			1.53888
$184$	−9.90109	+	17.1492i	−0.729918	+	1.26425i
$185$	1.58777	+	2.75009i	0.116735	+	0.202191i
$186$	8.47250	+	14.6748i	0.621234	+	1.07601i
$187$	2.29781	−	3.97992i	0.168032	−	0.291040i
$188$	7.30752			0.532956
$189$	7.38836	+	4.60040i	0.537424	+	0.334630i
$190$	−5.22229			−0.378865
$191$	2.04147	−	3.53593i	0.147716	−	0.255851i	−0.782667	−	0.622440i	$-0.786141\pi$
$191$	2.04147	−	3.53593i	0.147716	−	0.255851i	0.930383	+	0.366590i	$0.119475\pi$
$192$	6.13369	+	10.6239i	0.442661	+	0.766712i
$193$	8.88659	+	15.3920i	0.639671	+	1.10794i	0.985505	+	0.169647i	$0.0542626\pi$
$193$	8.88659	+	15.3920i	0.639671	+	1.10794i	−0.345834	+	0.938296i	$0.612404\pi$
$194$	−3.44022	+	5.95863i	−0.246993	+	0.427805i
$195$	5.66905			0.405969
$196$	−4.46585	+	6.66665i	−0.318989	+	0.476189i
$197$	−10.1002			−0.719611			−0.359806	−	0.933027i	$-0.617157\pi$
$197$	−10.1002			−0.719611			−0.359806	+	0.933027i	$0.617157\pi$
$198$	0.664578	−	1.15108i	0.0472295	−	0.0818039i
$199$	−12.1309	−	21.0113i	−0.859935	−	1.48945i	−0.871990	−	0.489524i	$-0.837171\pi$
$199$	−12.1309	−	21.0113i	−0.859935	−	1.48945i	0.0120546	−	0.999927i	$-0.496163\pi$
$200$	1.45352	+	2.51757i	0.102779	+	0.178019i
$201$	6.18723	−	10.7166i	0.436413	−	0.755890i
$202$	10.7739			0.758048
$203$	−6.25327	−	3.89363i	−0.438893	−	0.273279i
$204$	11.0986			0.777059
$205$	−5.00402	+	8.66722i	−0.349496	+	0.605345i
$206$	4.51630	+	7.82246i	0.314665	+	0.545017i
$207$	4.89959	+	8.48633i	0.340545	+	0.589841i
$208$	0.529188	−	0.916580i	0.0366926	−	0.0635534i
$209$	−5.65214			−0.390966
$210$	−4.54344	+	2.42509i	−0.313527	+	0.167347i
$211$	−17.7589			−1.22257			−0.611287	−	0.791409i	$-0.709348\pi$
$211$	−17.7589			−1.22257			−0.611287	+	0.791409i	$0.709348\pi$
$212$	−4.06535	+	7.04139i	−0.279209	+	0.483604i
$213$	5.10267	+	8.83808i	0.349629	+	0.605575i
$214$	4.50113	+	7.79619i	0.307691	+	0.532937i
$215$	−0.509593	+	0.882642i	−0.0347540	+	0.0601957i
$216$	−9.56307			−0.650685
$217$	0.767085	−	23.0187i	0.0520731	−	1.56261i
$218$	−14.2647			−0.966125
$219$	7.14772	−	12.3802i	0.482998	−	0.836577i
$220$	0.573158	+	0.992739i	0.0386423	+	0.0669305i
$221$	−6.18304	−	10.7093i	−0.415917	−	0.720389i
$222$	3.09069	−	5.35324i	0.207434	−	0.359286i
$223$	5.23666			0.350673			0.175336	−	0.984509i	$-0.443899\pi$
$223$	5.23666			0.350673			0.175336	+	0.984509i	$0.443899\pi$
$224$	0.480309	−	14.4131i	0.0320920	−	0.963016i
$225$	1.43856			0.0959039
$226$	8.60870	−	14.9107i	0.572642	−	0.991845i
$227$	−8.08561	−	14.0047i	−0.536661	−	0.929524i	−0.999081	−	0.0428631i	$-0.986352\pi$
$227$	−8.08561	−	14.0047i	−0.536661	−	0.929524i	0.462420	−	0.886661i	$-0.346981\pi$
$228$	−6.82509	−	11.8214i	−0.452002	−	0.782891i
$229$	2.92044	−	5.05835i	0.192988	−	0.334265i	−0.753251	−	0.657733i	$-0.771515\pi$
$229$	2.92044	−	5.05835i	0.192988	−	0.334265i	0.946239	+	0.323468i	$0.104849\pi$
$230$	6.29376			0.414998
$231$	−4.91741	+	2.62470i	−0.323542	+	0.172692i
$232$	8.09387			0.531389
$233$	−10.7922	+	18.6927i	−0.707022	+	1.22460i	0.258935	+	0.965895i	$0.416629\pi$
$233$	−10.7922	+	18.6927i	−0.707022	+	1.22460i	−0.965957	+	0.258704i	$0.916705\pi$
$234$	−1.78828	−	3.09739i	−0.116903	−	0.202483i
$235$	−3.18739	−	5.52072i	−0.207922	−	0.360132i
$236$	−8.37162	+	14.5001i	−0.544946	+	0.943874i
$237$	−21.4589			−1.39391
$238$	9.53659	+	5.93800i	0.618165	+	0.384903i
$239$	−17.6469			−1.14149			−0.570743	−	0.821129i	$-0.693345\pi$
$239$	−17.6469			−1.14149			−0.570743	+	0.821129i	$0.693345\pi$
$240$	0.414325	−	0.717633i	0.0267446	−	0.0463230i
$241$	−3.40948	−	5.90539i	−0.219624	−	0.380400i	0.735069	−	0.677992i	$-0.237150\pi$
$241$	−3.40948	−	5.90539i	−0.219624	−	0.380400i	−0.954693	+	0.297592i	$0.903816\pi$
$242$	−0.461975	−	0.800164i	−0.0296969	−	0.0514365i
$243$	−6.91227	+	11.9724i	−0.443422	+	0.768030i
$244$	11.3270			0.725134
$245$	6.98447	+	0.466025i	0.446221	+	0.0297733i
$246$	19.4813			1.24208
$247$	−7.60452	+	13.1714i	−0.483864	+	0.838077i
$248$	12.6530	+	21.9156i	0.803465	+	1.39164i
$249$	7.20243	+	12.4750i	0.456435	+	0.790569i
$250$	0.461975	−	0.800164i	0.0292179	−	0.0506068i
$251$	−20.2641			−1.27906			−0.639529	−	0.768767i	$-0.720871\pi$
$251$	−20.2641			−1.27906			−0.639529	+	0.768767i	$0.720871\pi$
$252$	−3.70368	−	2.30611i	−0.233310	−	0.145272i
$253$	6.81180			0.428254
$254$	−3.51431	+	6.08696i	−0.220507	+	0.381930i
$255$	−4.84099	−	8.38484i	−0.303155	−	0.525079i
$256$	8.37352	+	14.5034i	0.523345	+	0.906460i
$257$	9.49369	−	16.4435i	0.592200	−	1.02572i	−0.401736	−	0.915756i	$-0.631593\pi$
$257$	9.49369	−	16.4435i	0.592200	−	1.02572i	0.993936	−	0.109965i	$-0.0350737\pi$
$258$	1.98391			0.123513
$259$	−7.41194	+	3.95617i	−0.460555	+	0.245824i
$260$	3.08456			0.191297
$261$	2.00264	−	3.46868i	0.123960	−	0.214706i
$262$	0.712781	+	1.23457i	0.0440357	+	0.0762721i
$263$	−0.0960194	−	0.166310i	−0.00592081	−	0.0102551i	0.863050	−	0.505119i	$-0.168551\pi$
$263$	−0.0960194	−	0.166310i	−0.00592081	−	0.0102551i	−0.868971	+	0.494864i	$0.835218\pi$
$264$	3.06226	−	5.30399i	0.188469	−	0.326438i
$265$	7.09288			0.435712
$266$	0.460185	−	13.8092i	0.0282158	−	0.846697i
$267$	10.2567			0.627700
$268$	3.36651	−	5.83096i	0.205642	−	0.356183i
$269$	0.676768	+	1.17220i	0.0412632	+	0.0714700i	0.885919	−	0.463839i	$-0.153528\pi$
$269$	0.676768	+	1.17220i	0.0412632	+	0.0714700i	−0.844656	+	0.535309i	$0.820195\pi$
$270$	1.51973	+	2.63224i	0.0924875	+	0.160193i
$271$	9.14689	−	15.8429i	0.555634	−	0.962386i	−0.442220	−	0.896907i	$-0.645809\pi$
$271$	9.14689	−	15.8429i	0.555634	−	0.962386i	0.997854	−	0.0654796i	$-0.0208577\pi$
$272$	−1.80756			−0.109600
$273$	−0.499553	+	14.9906i	−0.0302343	+	0.907270i
$274$	−5.86983			−0.354610
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	8.22541	+	14.2468i	0.495112	+	0.857558i
$277$	0.946310	+	1.63906i	0.0568583	+	0.0984814i	0.893054	−	0.449950i	$-0.148558\pi$
$277$	0.946310	+	1.63906i	0.0568583	+	0.0984814i	−0.836195	+	0.548432i	$0.815225\pi$
$278$	−2.09993	+	3.63719i	−0.125945	+	0.218144i
$279$	12.5227			0.749717
$280$	−6.78525	+	3.62167i	−0.405496	+	0.216436i
$281$	−10.1751			−0.606998			−0.303499	−	0.952832i	$-0.598155\pi$
$281$	−10.1751			−0.606998			−0.303499	+	0.952832i	$0.598155\pi$
$282$	−6.20447	+	10.7465i	−0.369471	+	0.639942i
$283$	−13.8764	−	24.0347i	−0.824867	−	1.42871i	−0.902021	−	0.431693i	$-0.857917\pi$
$283$	−13.8764	−	24.0347i	−0.824867	−	1.42871i	0.0771536	−	0.997019i	$-0.475417\pi$
$284$	2.77639	+	4.80886i	0.164749	+	0.285353i
$285$	−5.95393	+	10.3125i	−0.352680	+	0.610860i
$286$	−2.48621			−0.147013
$287$	−22.4776	−	13.9958i	−1.32681	−	0.826146i
$288$	7.84110			0.462041
$289$	−2.05982	+	3.56771i	−0.121166	+	0.209865i
$290$	−1.28625	−	2.22784i	−0.0755310	−	0.130823i
$291$	7.84438	+	13.5869i	0.459846	+	0.796476i
$292$	3.88912	−	6.73615i	0.227593	−	0.394203i
$293$	23.1246			1.35096			0.675478	−	0.737381i	$-0.263938\pi$
$293$	23.1246			1.35096			0.675478	+	0.737381i	$0.263938\pi$
$294$	−6.01225	−	12.2278i	−0.350642	−	0.713141i
$295$	14.6061			0.850401
$296$	4.61570	−	7.99463i	0.268282	−	0.464678i
$297$	1.64481	+	2.84890i	0.0954418	+	0.165310i
$298$	−1.76162	−	3.05122i	−0.102048	−	0.176753i
$299$	9.16476	−	15.8738i	0.530012	−	0.918007i
$300$	2.41505			0.139433
$301$	−2.28905	−	1.42529i	−0.131939	−	0.0821522i
$302$	−14.9294			−0.859090
$303$	12.2833	−	21.2753i	0.705657	−	1.22223i
$304$	1.11156	+	1.92528i	0.0637524	+	0.110422i
$305$	−4.94059	−	8.55735i	−0.282897	−	0.489992i
$306$	−3.05414	+	5.28993i	−0.174594	+	0.302405i
$307$	−0.633826			−0.0361744			−0.0180872	−	0.999836i	$-0.505758\pi$
$307$	−0.633826			−0.0361744			−0.0180872	+	0.999836i	$0.505758\pi$
$308$	−2.67559	+	1.42811i	−0.152456	+	0.0813743i
$309$	20.5961			1.17167
$310$	4.02152	−	6.96548i	0.228407	−	0.395613i
$311$	6.37597	+	11.0435i	0.361548	+	0.626220i	0.988216	−	0.153067i	$-0.0489150\pi$
$311$	6.37597	+	11.0435i	0.361548	+	0.626220i	−0.626668	+	0.779287i	$0.715582\pi$
$312$	−8.24007	−	14.2722i	−0.466502	−	0.808005i
$313$	8.76250	−	15.1771i	0.495286	−	0.857860i	−0.504699	−	0.863295i	$-0.668397\pi$
$313$	8.76250	−	15.1771i	0.495286	−	0.857860i	0.999985	+	0.00543504i	$0.00173003\pi$
$314$	−8.58054			−0.484228
$315$	−0.126765	+	3.80396i	−0.00714239	+	0.214329i
$316$	−11.6759			−0.656822
$317$	−9.30714	+	16.1204i	−0.522741	+	0.905414i	0.476909	+	0.878953i	$0.341757\pi$
$317$	−9.30714	+	16.1204i	−0.522741	+	0.905414i	−0.999650	+	0.0264615i	$0.991576\pi$
$318$	−6.90339	−	11.9570i	−0.387123	−	0.670516i
$319$	−1.39212	−	2.41122i	−0.0779436	−	0.135002i
$320$	2.91139	−	5.04268i	0.162752	−	0.281895i
$321$	20.5270			1.14570
$322$	−0.554603	+	16.6425i	−0.0309068	+	0.927450i
$323$	25.9750			1.44529
$324$	−6.44587	+	11.1646i	−0.358104	+	0.620254i
$325$	−1.34542	−	2.33034i	−0.0746307	−	0.129264i
$326$	−5.94289	−	10.2934i	−0.329146	−	0.570098i
$327$	−16.2631	+	28.1686i	−0.899354	+	1.55773i
$328$	29.0938			1.60643
$329$	14.8792	−	7.94188i	0.820318	−	0.437850i
$330$	−1.94657			−0.107155
$331$	6.37968	−	11.0499i	0.350659	−	0.607359i	−0.635706	−	0.771931i	$-0.719291\pi$
$331$	6.37968	−	11.0499i	0.350659	−	0.607359i	0.986365	+	0.164572i	$0.0526243\pi$
$332$	3.91889	+	6.78771i	0.215077	+	0.372524i
$333$	−2.28410	−	3.95617i	−0.125168	−	0.216797i
$334$	5.25423	−	9.10059i	0.287499	−	0.497962i
$335$	−5.87361			−0.320910
$336$	1.86111	+	1.15883i	0.101532	+	0.0632194i
$337$	19.4150			1.05760			0.528801	−	0.848746i	$-0.322642\pi$
$337$	19.4150			1.05760			0.528801	+	0.848746i	$0.322642\pi$
$338$	2.66067	−	4.60842i	0.144721	−	0.250665i
$339$	−19.6295	−	33.9994i	−1.06613	−	1.84659i
$340$	−2.63401	−	4.56224i	−0.142849	−	0.247422i
$341$	4.35253	−	7.53881i	0.235703	−	0.408249i
$342$	7.51257			0.406233
$343$	−1.84777	+	18.4279i	−0.0997702	+	0.995011i
$344$	2.96282			0.159744
$345$	7.17551	−	12.4284i	0.386317	−	0.669120i
$346$	−2.48572	−	4.30539i	−0.133633	−	0.231459i
$347$	−9.83924	−	17.0421i	−0.528198	−	0.914866i	−0.999460	−	0.0328722i	$-0.989535\pi$
$347$	−9.83924	−	17.0421i	−0.528198	−	0.914866i	0.471262	−	0.881993i	$-0.343799\pi$
$348$	3.36203	−	5.82320i	0.180224	−	0.312156i
$349$	−7.95974			−0.426075			−0.213038	−	0.977044i	$-0.568336\pi$
$349$	−7.95974			−0.426075			−0.213038	+	0.977044i	$0.568336\pi$
$350$	2.07515	+	1.29210i	0.110922	+	0.0690658i
$351$	8.85189			0.472479
$352$	2.72533	−	4.72041i	0.145261	−	0.251599i
$353$	1.01995	+	1.76660i	0.0542863	+	0.0940267i	0.891892	−	0.452249i	$-0.149378\pi$
$353$	1.01995	+	1.76660i	0.0542863	+	0.0940267i	−0.837605	+	0.546276i	$0.816045\pi$
$354$	−14.2159	−	24.6227i	−0.755566	−	1.30868i
$355$	2.42201	−	4.19505i	0.128547	−	0.222650i
$356$	5.58073			0.295778
$357$	22.5985	−	12.0621i	1.19604	−	0.638393i
$358$	2.31540			0.122373
$359$	−15.4367	+	26.7371i	−0.814716	+	1.41113i	0.0948154	+	0.995495i	$0.469774\pi$
$359$	−15.4367	+	26.7371i	−0.814716	+	1.41113i	−0.909532	+	0.415635i	$0.863559\pi$
$360$	−2.09097	−	3.62167i	−0.110204	−	0.190879i
$361$	−6.47332	−	11.2121i	−0.340701	−	0.590111i
$362$	9.11895	−	15.7945i	0.479281	−	0.830140i
$363$	−2.10679			−0.110578
$364$	−0.271810	+	8.15646i	−0.0142467	+	0.427515i
$365$	−6.78542			−0.355165
$366$	−9.61718	+	16.6575i	−0.502698	+	0.870699i
$367$	7.69557	+	13.3291i	0.401705	+	0.695774i	0.993932	−	0.109997i	$-0.0350843\pi$
$367$	7.69557	+	13.3291i	0.401705	+	0.695774i	−0.592226	+	0.805772i	$0.701751\pi$
$368$	−1.33962	−	2.32030i	−0.0698327	−	0.120954i
$369$	7.19858	−	12.4683i	0.374743	−	0.649074i
$370$	−2.93403			−0.152533
$371$	−0.625021	+	18.7556i	−0.0324495	+	0.973742i
$372$	21.0231			1.09000
$373$	9.36591	−	16.2222i	0.484948	−	0.839955i	−0.514902	−	0.857249i	$-0.672172\pi$
$373$	9.36591	−	16.2222i	0.484948	−	0.839955i	0.999850	+	0.0172937i	$0.00550504\pi$
$374$	2.12306	+	3.67724i	0.109781	+	0.190146i
$375$	−1.05339	−	1.82453i	−0.0543970	−	0.0942185i
$376$	−9.26587	+	16.0490i	−0.477851	+	0.827662i
$377$	−7.49195			−0.385855
$378$	−7.09431	+	3.78663i	−0.364892	+	0.194763i
$379$	−17.7482			−0.911663			−0.455831	−	0.890066i	$-0.650658\pi$
$379$	−17.7482			−0.911663			−0.455831	+	0.890066i	$0.650658\pi$
$380$	−3.23957	+	5.61110i	−0.166186	+	0.287843i
$381$	8.01331	+	13.8795i	0.410535	+	0.711067i
$382$	1.88622	+	3.26702i	0.0965072	+	0.167155i
$383$	−14.7200	+	25.4958i	−0.752158	+	1.30278i	0.194617	+	0.980879i	$0.437654\pi$
$383$	−14.7200	+	25.4958i	−0.752158	+	1.30278i	−0.946775	+	0.321897i	$0.895680\pi$
$384$	11.6324			0.593611
$385$	2.24596	+	1.39846i	0.114465	+	0.0712719i
$386$	−16.4215			−0.835834
$387$	0.733080	−	1.26973i	0.0372645	−	0.0645441i
$388$	4.26818	+	7.39270i	0.216684	+	0.375307i
$389$	0.567235	+	0.982480i	0.0287600	+	0.0498137i	0.880047	−	0.474886i	$-0.157511\pi$
$389$	0.567235	+	0.982480i	0.0287600	+	0.0498137i	−0.851287	+	0.524700i	$0.824177\pi$
$390$	−2.61896	+	4.53617i	−0.132616	+	0.229698i
$391$	−31.3044			−1.58313
$392$	−8.97881	−	18.2613i	−0.453498	−	0.922333i
$393$	3.25056			0.163969
$394$	4.66605	−	8.08184i	0.235072	−	0.407157i
$395$	5.09280	+	8.82099i	0.256247	+	0.443832i
$396$	−0.824522	−	1.42811i	−0.0414338	−	0.0717654i
$397$	−6.12469	+	10.6083i	−0.307389	+	0.532414i	−0.977790	−	0.209585i	$-0.932789\pi$
$397$	−6.12469	+	10.6083i	−0.307389	+	0.532414i	0.670401	+	0.741999i	$0.266122\pi$
$398$	22.4166			1.12364
$399$	−26.7445	−	16.6526i	−1.33890	−	0.833673i
$400$	−0.393324			−0.0196662
$401$	11.7676	−	20.3820i	0.587644	−	1.01783i	−0.406896	−	0.913474i	$-0.633389\pi$
$401$	11.7676	−	20.3820i	0.587644	−	1.01783i	0.994540	−	0.104355i	$-0.0332778\pi$
$402$	5.71669	+	9.90159i	0.285122	+	0.493846i
$403$	−11.7120	−	20.2858i	−0.583416	−	1.01051i
$404$	6.68342	−	11.5760i	0.332512	−	0.575928i
$405$	11.2462			0.558829
$406$	6.00439	−	3.20488i	0.297993	−	0.159056i
$407$	−3.17553			−0.157405
$408$	−14.0729	+	24.3751i	−0.696715	+	1.20675i
$409$	2.09006	+	3.62009i	0.103347	+	0.179002i	0.913062	−	0.407822i	$-0.133711\pi$
$409$	2.09006	+	3.62009i	0.103347	+	0.179002i	−0.809715	+	0.586824i	$0.800378\pi$
$410$	−4.62346	−	8.00808i	−0.228337	−	0.395491i
$411$	−6.69219	+	11.5912i	−0.330102	+	0.571753i
$412$	11.2065			0.552103
$413$	−1.28708	+	38.6227i	−0.0633332	+	1.90050i
$414$	−9.05395			−0.444977
$415$	3.41868	−	5.92132i	0.167816	−	0.290666i
$416$	−7.33345	−	12.7019i	−0.359552	−	0.622763i
$417$	4.78826	+	8.29350i	0.234482	+	0.406135i
$418$	2.61114	−	4.52264i	0.127715	−	0.221209i
$419$	−5.43981			−0.265752			−0.132876	−	0.991133i	$-0.542421\pi$
$419$	−5.43981			−0.265752			−0.132876	+	0.991133i	$0.542421\pi$
$420$	−0.212813	+	6.38607i	−0.0103842	+	0.311608i
$421$	−4.94834			−0.241167			−0.120584	−	0.992703i	$-0.538477\pi$
$421$	−4.94834			−0.241167			−0.120584	+	0.992703i	$0.538477\pi$
$422$	8.20417	−	14.2100i	0.399373	−	0.691734i
$423$	4.58525	+	7.94188i	0.222942	+	0.386148i
$424$	−10.3096	−	17.8568i	−0.500681	−	0.867204i
$425$	−2.29781	+	3.97992i	−0.111460	+	0.193054i
$426$	−9.42922			−0.456847
$427$	23.0634	−	12.3102i	1.11612	−	0.595734i
$428$	11.1688			0.539867
$429$	−2.83452	+	4.90954i	−0.136852	+	0.237035i
$430$	−0.470839	−	0.815516i	−0.0227059	−	0.0393277i
$431$	7.53453	+	13.0502i	0.362925	+	0.628605i	0.988441	−	0.151606i	$-0.0484446\pi$
$431$	7.53453	+	13.0502i	0.362925	+	0.628605i	−0.625515	+	0.780212i	$0.715111\pi$
$432$	0.646945	−	1.12054i	0.0311262	−	0.0539121i
$433$	−36.4894			−1.75357			−0.876785	−	0.480883i	$-0.840316\pi$
$433$	−36.4894			−1.75357			−0.876785	+	0.480883i	$0.840316\pi$
$434$	18.0643	+	11.2478i	0.867116	+	0.539914i
$435$	−5.86579			−0.281243
$436$	−8.84888	+	15.3267i	−0.423784	+	0.734016i
$437$	19.2506	+	33.3430i	0.920882	+	1.59501i
$438$	6.60413	+	11.4387i	0.315558	+	0.546562i
$439$	−10.5365	+	18.2497i	−0.502879	+	0.871012i	0.497116	+	0.867684i	$0.334392\pi$
$439$	−10.5365	+	18.2497i	−0.502879	+	0.871012i	−0.999994	+	0.00332727i	$0.998941\pi$
$440$	−2.90704			−0.138588
$441$	−10.0476	−	0.670405i	−0.478456	−	0.0319240i
$442$	11.4256			0.543462
$443$	13.2759	−	22.9946i	0.630759	−	1.09251i	−0.356637	−	0.934243i	$-0.616077\pi$
$443$	13.2759	−	22.9946i	0.630759	−	1.09251i	0.987397	−	0.158264i	$-0.0505899\pi$
$444$	−3.83453	−	6.64160i	−0.181979	−	0.315197i
$445$	−2.43420	−	4.21616i	−0.115392	−	0.199865i
$446$	−2.41921	+	4.19019i	−0.114553	+	0.198411i
$447$	−8.03370			−0.379981
$448$	13.0777	+	8.14291i	0.617865	+	0.384716i
$449$	−24.5603			−1.15907			−0.579536	−	0.814947i	$-0.696766\pi$
$449$	−24.5603			−1.15907			−0.579536	+	0.814947i	$0.696766\pi$
$450$	−0.664578	+	1.15108i	−0.0313285	+	0.0542626i
$451$	−5.00402	−	8.66722i	−0.235630	−	0.408123i
$452$	−10.6806	−	18.4993i	−0.502371	−	0.870132i
$453$	−17.0210	+	29.4812i	−0.799716	+	1.38515i
$454$	14.9414			0.701235
$455$	6.28064	−	3.35233i	0.294441	−	0.157160i
$456$	34.6166			1.62107
$457$	13.0871	−	22.6675i	0.612187	−	1.06034i	−0.378684	−	0.925526i	$-0.623623\pi$
$457$	13.0871	−	22.6675i	0.612187	−	1.06034i	0.990871	−	0.134813i	$-0.0430435\pi$
$458$	2.69834	+	4.67366i	0.126085	+	0.218386i
$459$	−7.55892	−	13.0924i	−0.352820	−	0.611103i
$460$	3.90424	−	6.76234i	0.182036	−	0.315296i
$461$	12.3957			0.577324			0.288662	−	0.957431i	$-0.406790\pi$
$461$	12.3957			0.577324			0.288662	+	0.957431i	$0.406790\pi$
$462$	0.171530	−	5.14727i	0.00798031	−	0.239473i
$463$	11.0421			0.513168			0.256584	−	0.966522i	$-0.417403\pi$
$463$	11.0421			0.513168			0.256584	+	0.966522i	$0.417403\pi$
$464$	−0.547553	+	0.948390i	−0.0254195	+	0.0440279i
$465$	−9.16987	−	15.8827i	−0.425242	−	0.736542i
$466$	−9.97147	−	17.2711i	−0.461920	−	0.800068i
$467$	−10.4830	+	18.1571i	−0.485097	+	0.840212i	−0.999853	−	0.0171243i	$-0.994549\pi$
$467$	−10.4830	+	18.1571i	−0.485097	+	0.840212i	0.514757	+	0.857336i	$0.327882\pi$
$468$	−4.43732			−0.205115
$469$	0.517579	−	15.5315i	0.0238996	−	0.717177i
$470$	5.88998			0.271684
$471$	−9.78267	+	16.9441i	−0.450762	+	0.780742i
$472$	−21.2303	−	36.7719i	−0.977203	−	1.69256i
$473$	−0.509593	−	0.882642i	−0.0234311	−	0.0405839i
$474$	9.91348	−	17.1706i	0.455341	−	0.788674i
$475$	5.65214			0.259338
$476$	12.2960	−	6.56305i	0.563585	−	0.300817i
$477$	−10.2035			−0.467187
$478$	8.15244	−	14.1204i	0.372884	−	0.645854i
$479$	−5.68293	−	9.84313i	−0.259660	−	0.449744i	0.706491	−	0.707722i	$-0.250277\pi$
$479$	−5.68293	−	9.84313i	−0.259660	−	0.449744i	−0.966151	+	0.257978i	$0.916944\pi$
$480$	−5.74170	−	9.94492i	−0.262072	−	0.453921i
$481$	−4.27244	+	7.40008i	−0.194806	+	0.337415i
$482$	6.30038			0.286974
$483$	32.2318	+	20.0693i	1.46660	+	0.913183i
$484$	−1.14632			−0.0521053
$485$	3.72338	−	6.44909i	0.169070	−	0.292838i
$486$	−6.38659	−	11.0619i	−0.289702	−	0.501778i
$487$	8.09570	+	14.0222i	0.366851	+	0.635405i	0.989071	−	0.147437i	$-0.0471025\pi$
$487$	8.09570	+	14.0222i	0.366851	+	0.635405i	−0.622220	+	0.782842i	$0.713769\pi$
$488$	−14.3625	+	24.8765i	−0.650159	+	1.12611i
$489$	−27.1019			−1.22559
$490$	−3.59955	+	5.37343i	−0.162611	+	0.242747i
$491$	24.7164			1.11543			0.557717	−	0.830031i	$-0.311677\pi$
$491$	24.7164			1.11543			0.557717	+	0.830031i	$0.311677\pi$
$492$	12.0849	−	20.9317i	0.544832	−	0.943676i
$493$	6.39763	+	11.0810i	0.288135	+	0.499064i
$494$	−7.02619	−	12.1697i	−0.316123	−	0.547542i
$495$	−0.719279	+	1.24583i	−0.0323292	+	0.0559958i
$496$	−3.42391			−0.153738
$497$	10.8795	+	6.77415i	0.488011	+	0.303862i
$498$	−13.3094			−0.596407
$499$	10.7053	−	18.5421i	0.479234	−	0.830057i	−0.520482	−	0.853872i	$-0.674248\pi$
$499$	10.7053	−	18.5421i	0.479234	−	0.830057i	0.999716	+	0.0238149i	$0.00758123\pi$
$500$	−0.573158	−	0.992739i	−0.0256324	−	0.0443967i
$501$	−11.9807	−	20.7512i	−0.535257	−	0.927093i
$502$	9.36151	−	16.2146i	0.417824	−	0.723693i
$503$	0.824380			0.0367573			0.0183786	−	0.999831i	$-0.494150\pi$
$503$	0.824380			0.0367573			0.0183786	+	0.999831i	$0.494150\pi$
$504$	9.76098	−	5.20998i	0.434789	−	0.232071i
$505$	−11.6607			−0.518894
$506$	−3.14688	+	5.45056i	−0.139896	+	0.242307i
$507$	−6.06686	−	10.5081i	−0.269439	−	0.466681i
$508$	4.36009	+	7.55190i	0.193448	+	0.335062i
$509$	−15.8770	+	27.4998i	−0.703736	+	1.21891i	0.263409	+	0.964684i	$0.415153\pi$
$509$	−15.8770	+	27.4998i	−0.703736	+	1.21891i	−0.967146	+	0.254223i	$0.918180\pi$
$510$	8.94566			0.396121
$511$	0.597927	−	17.9426i	0.0264507	−	0.793732i
$512$	−4.43070			−0.195811
$513$	−9.29671	+	16.1024i	−0.410460	+	0.710937i
$514$	8.77169	+	15.1930i	0.386903	+	0.670135i
$515$	−4.88804	−	8.46633i	−0.215393	−	0.373071i
$516$	1.23069	−	2.13162i	0.0541782	−	0.0938394i
$517$	6.37478			0.280363
$518$	0.258545	−	7.75842i	0.0113598	−	0.340885i
$519$	−11.3359			−0.497589
$520$	−3.91120	+	6.77439i	−0.171517	+	0.297077i
$521$	18.5367	+	32.1064i	0.812106	+	1.40661i	0.911388	+	0.411549i	$0.135012\pi$
$521$	18.5367	+	32.1064i	0.812106	+	1.40661i	−0.0992821	+	0.995059i	$0.531655\pi$
$522$	1.85034	+	3.20488i	0.0809872	+	0.140274i
$523$	12.1580	−	21.0583i	0.531632	−	0.920813i	−0.467686	−	0.883894i	$-0.654912\pi$
$523$	12.1580	−	21.0583i	0.531632	−	0.920813i	0.999318	−	0.0369189i	$-0.0117543\pi$
$524$	1.76865			0.0772639
$525$	4.91741	−	2.62470i	0.214613	−	0.114551i
$526$	0.177434			0.00773650
$527$	−20.0025	+	34.6454i	−0.871325	+	1.50918i
$528$	0.414325	+	0.717633i	0.0180312	+	0.0312310i
$529$	−11.7003	−	20.2656i	−0.508710	−	0.881111i
$530$	−3.27673	+	5.67547i	−0.142332	+	0.246527i
$531$	−21.0118			−0.911832
$532$	−14.5519	−	9.06079i	−0.630903	−	0.392835i
$533$	−26.9301			−1.16647
$534$	−4.73834	+	8.20704i	−0.205048	+	0.355153i
$535$	−4.87162	−	8.43790i	−0.210619	−	0.364802i
$536$	8.53740	+	14.7872i	0.368760	+	0.638711i
$537$	2.63979	−	4.57225i	0.113915	−	0.197307i
$538$	−1.25060			−0.0539171
$539$	−3.89582	+	5.81572i	−0.167805	+	0.250501i
$540$	3.77096			0.162276
$541$	−12.5227	+	21.6899i	−0.538392	+	0.932522i	0.460599	+	0.887608i	$0.347635\pi$
$541$	−12.5227	+	21.6899i	−0.538392	+	0.932522i	−0.998991	+	0.0449138i	$0.985699\pi$
$542$	8.45127	+	14.6380i	0.363013	+	0.628757i
$543$	−20.7930	−	36.0146i	−0.892314	−	1.54553i
$544$	−12.5246	+	21.6932i	−0.536986	+	0.930088i
$545$	15.4388			0.661325
$546$	−11.7641	−	7.32499i	−0.503458	−	0.313481i
$547$	40.3748			1.72630			0.863151	−	0.504946i	$-0.168487\pi$
$547$	40.3748			1.72630			0.863151	+	0.504946i	$0.168487\pi$
$548$	−3.64126	+	6.30685i	−0.155547	+	0.269415i
$549$	7.10732	+	12.3102i	0.303333	+	0.525388i
$550$	0.461975	+	0.800164i	0.0196987	+	0.0341191i
$551$	7.86843	−	13.6285i	0.335206	−	0.580595i
$552$	−41.7190			−1.77568
$553$	−23.7740	+	12.6895i	−1.01097	+	0.539613i
$554$	−1.74869			−0.0742946
$555$	−3.34509	+	5.79386i	−0.141991	+	0.245936i
$556$	2.60532	+	4.51255i	0.110490	+	0.191375i
$557$	3.17818	+	5.50476i	0.134664	+	0.233244i	0.925469	−	0.378824i	$-0.123671\pi$
$557$	3.17818	+	5.50476i	0.134664	+	0.233244i	−0.790805	+	0.612068i	$0.790338\pi$
$558$	−5.78519	+	10.0203i	−0.244907	+	0.424191i
$559$	−2.74248			−0.115994
$560$	0.0346595	−	1.04006i	0.00146463	−	0.0439506i
$561$	9.68198			0.408774
$562$	4.70066	−	8.14178i	0.198285	−	0.343440i
$563$	10.7132	+	18.5558i	0.451509	+	0.782036i	0.998480	−	0.0551155i	$-0.0175527\pi$
$563$	10.7132	+	18.5558i	0.451509	+	0.782036i	−0.546971	+	0.837151i	$0.684219\pi$
$564$	7.69770	+	13.3328i	0.324132	+	0.561412i
$565$	−9.31728	+	16.1380i	−0.391981	+	0.678931i
$566$	25.6422			1.07782
$567$	−0.991011	+	29.7382i	−0.0416185	+	1.24889i
$568$	−14.0818			−0.590858
$569$	17.0097	−	29.4617i	0.713083	−	1.23510i	−0.250611	−	0.968088i	$-0.580631\pi$
$569$	17.0097	−	29.4617i	0.713083	−	1.23510i	0.963694	−	0.267009i	$-0.0860353\pi$
$570$	−5.50113	−	9.52824i	−0.230417	−	0.399094i
$571$	19.4229	+	33.6414i	0.812821	+	1.40785i	0.910882	+	0.412668i	$0.135403\pi$
$571$	19.4229	+	33.6414i	0.812821	+	1.40785i	−0.0980602	+	0.995180i	$0.531264\pi$
$572$	−1.54228	+	2.67131i	−0.0644860	+	0.111693i
$573$	8.60189			0.359349
$574$	21.5830	−	11.5201i	0.900859	−	0.480839i
$575$	−6.81180			−0.284072
$576$	−4.18821	+	7.25419i	−0.174509	+	0.302258i
$577$	0.943109	+	1.63351i	0.0392621	+	0.0680040i	0.884989	−	0.465612i	$-0.154166\pi$
$577$	0.943109	+	1.63351i	0.0392621	+	0.0680040i	−0.845727	+	0.533616i	$0.820833\pi$
$578$	−1.90317	−	3.29638i	−0.0791614	−	0.137112i
$579$	−18.7222	+	32.4277i	−0.778067	+	1.34765i
$580$	−3.19161			−0.132525
$581$	15.3564	+	9.56173i	0.637091	+	0.396688i
$582$	−14.4956			−0.600863
$583$	−3.54644	+	6.14262i	−0.146879	+	0.254401i
$584$	9.86273	+	17.0828i	0.408123	+	0.706889i
$585$	1.93547	+	3.35233i	0.0800219	+	0.138602i
$586$	−10.6830	+	18.5035i	−0.441311	+	0.764372i
$587$	−21.8489			−0.901799			−0.450900	−	0.892575i	$-0.648897\pi$
$587$	−21.8489			−0.901799			−0.450900	+	0.892575i	$0.648897\pi$
$588$	−16.8678	−	1.12547i	−0.695617	−	0.0464137i
$589$	49.2022			2.02734
$590$	−6.74766	+	11.6873i	−0.277797	+	0.481158i
$591$	−10.6395	−	18.4282i	−0.437652	−	0.758035i
$592$	0.624507	+	1.08168i	0.0256671	+	0.0444567i
$593$	−16.0995	+	27.8852i	−0.661128	+	1.14511i	0.319192	+	0.947690i	$0.396589\pi$
$593$	−16.0995	+	27.8852i	−0.661128	+	1.14511i	−0.980320	+	0.197417i	$0.936745\pi$
$594$	−3.03945			−0.124710
$595$	−10.3215	−	6.42676i	−0.423142	−	0.263471i
$596$	−4.37119			−0.179051
$597$	25.5572	−	44.2664i	1.04599	−	1.81170i
$598$	8.46778	+	14.6666i	0.346273	+	0.599763i
$599$	−1.35950	−	2.35472i	−0.0555475	−	0.0962111i	0.836915	−	0.547334i	$-0.184357\pi$
$599$	−1.35950	−	2.35472i	−0.0555475	−	0.0962111i	−0.892462	+	0.451122i	$0.851024\pi$
$600$	−3.06226	+	5.30399i	−0.125016	+	0.216534i
$601$	7.46800			0.304626			0.152313	−	0.988332i	$-0.451328\pi$
$601$	7.46800			0.304626			0.152313	+	0.988332i	$0.451328\pi$
$602$	2.19795	−	1.17317i	0.0895816	−	0.0478148i
$603$	8.44953			0.344091
$604$	−9.26123	+	16.0409i	−0.376834	+	0.652696i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	11.3491	+	19.6573i	0.461028	+	0.798523i
$607$	1.79103	−	3.10215i	0.0726956	−	0.125912i	−0.827386	−	0.561633i	$-0.810173\pi$
$607$	1.79103	−	3.10215i	0.0726956	−	0.125912i	0.900082	+	0.435721i	$0.143507\pi$
$608$	30.8079			1.24943
$609$	0.516890	−	15.5108i	0.0209454	−	0.628530i
$610$	9.12971			0.369651
$611$	8.57678	−	14.8554i	0.346979	−	0.600986i
$612$	3.78918	+	6.56305i	0.153169	+	0.265296i
$613$	1.73685	+	3.00832i	0.0701508	+	0.121505i	0.898967	−	0.438016i	$-0.144319\pi$
$613$	1.73685	+	3.00832i	0.0701508	+	0.121505i	−0.828816	+	0.559521i	$0.810985\pi$
$614$	0.292812	−	0.507165i	0.0118169	−	0.0204675i
$615$	−21.0848			−0.850223
$616$	0.256167	−	7.68703i	0.0103212	−	0.309719i
$617$	−16.5920			−0.667969			−0.333985	−	0.942579i	$-0.608393\pi$
$617$	−16.5920			−0.667969			−0.333985	+	0.942579i	$0.608393\pi$
$618$	−9.51489	+	16.4803i	−0.382745	+	0.662934i
$619$	14.4753	+	25.0719i	0.581811	+	1.00773i	0.995265	+	0.0972008i	$0.0309889\pi$
$619$	14.4753	+	25.0719i	0.581811	+	1.00773i	−0.413454	+	0.910525i	$0.635678\pi$
$620$	−4.98938	−	8.64186i	−0.200378	−	0.347066i
$621$	11.2041	−	19.4061i	0.449607	−	0.778742i
$622$	−11.7822			−0.472421
$623$	11.3632	−	6.06520i	0.455258	−	0.242997i
$624$	2.22977			0.0892624
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.09611	+	14.0229i	0.323586	+	0.560467i
$627$	−5.95393	−	10.3125i	−0.237777	−	0.411842i
$628$	−5.32281	+	9.21938i	−0.212403	+	0.367893i
$629$	14.5935			0.581882
$630$	−2.98523	−	1.85876i	−0.118934	−	0.0740550i
$631$	−24.3141			−0.967929			−0.483964	−	0.875088i	$-0.660804\pi$
$631$	−24.3141			−0.967929			−0.483964	+	0.875088i	$0.660804\pi$
$632$	14.8050	−	25.6430i	0.588910	−	1.02002i
$633$	−18.7071	−	32.4017i	−0.743541	−	1.28785i
$634$	−8.59933	−	14.8945i	−0.341523	−	0.591535i
$635$	3.80357	−	6.58797i	0.150940	−	0.261436i
$636$	−17.1296			−0.679235
$637$	8.31107	+	16.9032i	0.329297	+	0.669729i
$638$	2.57249			0.101846
$639$	−3.48421	+	6.03482i	−0.137833	+	0.238734i
$640$	−2.76068	−	4.78164i	−0.109126	−	0.189011i
$641$	−8.89976	−	15.4148i	−0.351519	−	0.608849i	0.634997	−	0.772515i	$-0.281001\pi$
$641$	−8.89976	−	15.4148i	−0.351519	−	0.608849i	−0.986516	+	0.163666i	$0.947668\pi$
$642$	−9.48294	+	16.4249i	−0.374262	+	0.648240i
$643$	14.2247			0.560967			0.280483	−	0.959859i	$-0.409505\pi$
$643$	14.2247			0.560967			0.280483	+	0.959859i	$0.409505\pi$
$644$	17.5375	+	10.9198i	0.691075	+	0.430301i
$645$	−2.14721			−0.0845463
$646$	−11.9998	+	20.7843i	−0.472126	+	0.817746i
$647$	−3.55840	−	6.16333i	−0.139895	−	0.242306i	0.787562	−	0.616236i	$-0.211343\pi$
$647$	−3.55840	−	6.16333i	−0.139895	−	0.242306i	−0.927457	+	0.373930i	$0.878010\pi$
$648$	−16.3466	−	28.3132i	−0.642155	−	1.11225i
$649$	−7.30306	+	12.6493i	−0.286670	+	0.496527i
$650$	2.48621			0.0975171
$651$	42.8063	−	22.8482i	1.67771	−	0.895490i
$652$	−14.7463			−0.577511
$653$	−7.70623	+	13.3476i	−0.301568	+	0.522331i	−0.976491	−	0.215557i	$-0.930843\pi$
$653$	−7.70623	+	13.3476i	−0.301568	+	0.522331i	0.674923	+	0.737888i	$0.264177\pi$
$654$	−15.0263	−	26.0264i	−0.587576	−	1.01771i
$655$	−0.771450	−	1.33619i	−0.0301430	−	0.0522093i
$656$	−1.96820	+	3.40903i	−0.0768454	+	0.133100i
$657$	9.76122			0.380821
$658$	−0.519021	+	15.5748i	−0.0202336	+	0.607168i
$659$	−17.1319			−0.667364			−0.333682	−	0.942686i	$-0.608291\pi$
$659$	−17.1319			−0.667364			−0.333682	+	0.942686i	$0.608291\pi$
$660$	−1.20752	+	2.09149i	−0.0470028	+	0.0814112i
$661$	24.9653	+	43.2411i	0.971036	+	1.68188i	0.692439	+	0.721476i	$0.256536\pi$
$661$	24.9653	+	43.2411i	0.971036	+	1.68188i	0.278597	+	0.960408i	$0.410131\pi$
$662$	5.89450	+	10.2096i	0.229096	+	0.396807i
$663$	13.0264	−	22.5623i	0.505902	−	0.876248i
$664$	−19.8765			−0.771356
$665$	−0.498063	+	14.9458i	−0.0193140	+	0.579575i
$666$	4.22078			0.163552
$667$	−9.48282	+	16.4247i	−0.367176	+	0.635968i
$668$	−6.51876	−	11.2908i	−0.252219	−	0.436855i
$669$	5.51627	+	9.55446i	0.213271	+	0.369397i
$670$	2.71346	−	4.69985i	0.104830	−	0.181571i
$671$	9.88117			0.381459
$672$	26.8031	−	14.3063i	1.03395	−	0.551879i
$673$	−24.5485			−0.946276			−0.473138	−	0.880988i	$-0.656879\pi$
$673$	−24.5485			−0.946276			−0.473138	+	0.880988i	$0.656879\pi$
$674$	−8.96923	+	15.5352i	−0.345482	+	0.598392i
$675$	−1.64481	−	2.84890i	−0.0633089	−	0.109654i
$676$	−3.30101	−	5.71752i	−0.126962	−	0.219905i
$677$	−20.2528	+	35.0789i	−0.778380	+	1.34819i	0.154496	+	0.987993i	$0.450625\pi$
$677$	−20.2528	+	35.0789i	−0.778380	+	1.34819i	−0.932875	+	0.360200i	$0.882709\pi$
$678$	36.2734			1.39307
$679$	16.7251	+	10.4140i	0.641851	+	0.399651i
$680$	13.3596			0.512318
$681$	17.0347	−	29.5049i	0.652770	−	1.13063i
$682$	4.02152	+	6.96548i	0.153992	+	0.266722i
$683$	4.41929	+	7.65443i	0.169099	+	0.292889i	0.938103	−	0.346355i	$-0.112581\pi$
$683$	4.41929	+	7.65443i	0.169099	+	0.292889i	−0.769004	+	0.639244i	$0.779247\pi$
$684$	4.66031	−	8.07189i	0.178191	−	0.308637i
$685$	6.35298			0.242735
$686$	−13.8917	−	9.99172i	−0.530387	−	0.381486i
$687$	12.3055			0.469484
$688$	−0.200435	+	0.347164i	−0.00764153	+	0.0132355i
$689$	9.54293	+	16.5288i	0.363557	+	0.629699i
$690$	6.62981	+	11.4832i	0.252393	+	0.437157i
$691$	21.7568	−	37.6838i	0.827666	−	1.43356i	−0.0721987	−	0.997390i	$-0.523002\pi$
$691$	21.7568	−	37.6838i	0.827666	−	1.43356i	0.899865	−	0.436169i	$-0.143665\pi$
$692$	−6.16792			−0.234469
$693$	−3.23094	−	2.01176i	−0.122733	−	0.0764204i
$694$	18.1819			0.690176
$695$	2.27277	−	3.93656i	0.0862113	−	0.149322i
$696$	8.52604	+	14.7675i	0.323179	+	0.559762i
$697$	22.9965	+	39.8312i	0.871056	+	1.50871i
$698$	3.67720	−	6.36910i	0.139184	−	0.241074i
$699$	−45.4739			−1.71998
$700$	2.67559	−	1.42811i	0.101128	−	0.0539776i
$701$	25.6790			0.969882			0.484941	−	0.874547i	$-0.338841\pi$
$701$	25.6790			0.969882			0.484941	+	0.874547i	$0.338841\pi$
$702$	−4.08935	+	7.08296i	−0.154343	+	0.267329i
$703$	−8.97427	−	15.5439i	−0.338471	−	0.586249i
$704$	2.91139	+	5.04268i	0.109727	+	0.190053i
$705$	6.71516	−	11.6310i	0.252908	−	0.438049i
$706$	−1.88476			−0.0709339
$707$	1.02753	−	30.8341i	0.0386443	−	1.15964i
$708$	−35.2745			−1.32570
$709$	12.7875	−	22.1485i	0.480243	−	0.831805i	−0.519500	−	0.854470i	$-0.673882\pi$
$709$	12.7875	−	22.1485i	0.480243	−	0.831805i	0.999743	+	0.0226654i	$0.00721522\pi$
$710$	2.23782	+	3.87601i	0.0839838	+	0.145464i
$711$	−7.32629	−	12.6895i	−0.274757	−	0.475894i
$712$	−7.07632	+	12.2565i	−0.265196	+	0.459333i
$713$	−59.2972			−2.22070
$714$	−0.788286	+	23.6549i	−0.0295009	+	0.885261i
$715$	2.69085			0.100632
$716$	1.43632	−	2.48779i	0.0536780	−	0.0929730i
$717$	−18.5892	−	32.1974i	−0.694226	−	1.20243i
$718$	−14.2627	−	24.7037i	−0.532279	−	0.921935i
$719$	6.66263	−	11.5400i	0.248474	−	0.430370i	−0.714628	−	0.699504i	$-0.753404\pi$
$719$	6.66263	−	11.5400i	0.248474	−	0.430370i	0.963103	+	0.269134i	$0.0867375\pi$
$720$	0.565820			0.0210869
$721$	22.8181	−	12.1793i	0.849790	−	0.453581i
$722$	11.9620			0.445181
$723$	7.18305	−	12.4414i	0.267141	−	0.462701i
$724$	−11.3136	−	19.5957i	−0.420467	−	0.728270i
$725$	1.39212	+	2.41122i	0.0517019	+	0.0895503i
$726$	0.973283	−	1.68578i	0.0361219	−	0.0625650i
$727$	18.3479			0.680484			0.340242	−	0.940338i	$-0.389491\pi$
$727$	18.3479			0.680484			0.340242	+	0.940338i	$0.389491\pi$
$728$	−17.5688	−	10.9393i	−0.651142	−	0.405436i
$729$	4.61330			0.170863
$730$	3.13469	−	5.42945i	0.116020	−	0.200953i
$731$	2.34189	+	4.05628i	0.0866180	+	0.150027i
$732$	11.9318	+	20.6664i	0.441010	+	0.763852i
$733$	14.6751	−	25.4180i	0.542036	−	0.938835i	−0.456751	−	0.889595i	$-0.650987\pi$
$733$	14.6751	−	25.4180i	0.542036	−	0.938835i	0.998787	−	0.0492398i	$-0.0156799\pi$
$734$	−14.2206			−0.524893
$735$	6.50712	+	13.2343i	0.240019	+	0.488155i
$736$	−37.1289			−1.36859
$737$	2.93680	−	5.08669i	0.108179	−	0.187371i
$738$	6.65112	+	11.5201i	0.244831	+	0.424060i
$739$	7.92348	+	13.7239i	0.291470	+	0.504841i	0.974158	−	0.225869i	$-0.0725223\pi$
$739$	7.92348	+	13.7239i	0.291470	+	0.504841i	−0.682687	+	0.730710i	$0.739189\pi$
$740$	−1.82008	+	3.15248i	−0.0669076	+	0.115887i
$741$	−32.0422			−1.17710
$742$	−14.7188	−	9.16473i	−0.540344	−	0.336448i
$743$	17.2227			0.631838			0.315919	−	0.948786i	$-0.397687\pi$
$743$	17.2227			0.631838			0.315919	+	0.948786i	$0.397687\pi$
$744$	−26.6572	+	46.1716i	−0.977299	+	1.69273i
$745$	1.90662	+	3.30237i	0.0698533	+	0.120989i
$746$	8.65363	+	14.9885i	0.316832	+	0.548769i
$747$	−4.91797	+	8.51817i	−0.179939	+	0.311663i
$748$	5.26803			0.192618
$749$	22.7415	−	12.1384i	0.830956	−	0.443528i
$750$	1.94657			0.0710786
$751$	−9.06617	+	15.7031i	−0.330829	+	0.573013i	−0.982675	−	0.185339i	$-0.940662\pi$
$751$	−9.06617	+	15.7031i	−0.330829	+	0.573013i	0.651845	+	0.758352i	$0.273995\pi$
$752$	−1.25368	−	2.17143i	−0.0457169	−	0.0791840i
$753$	−21.3461	−	36.9725i	−0.777895	−	1.34735i
$754$	3.46109	−	5.99479i	0.126045	−	0.218317i
$755$	16.1582			0.588058
$756$	−0.332294	+	9.97147i	−0.0120854	+	0.362659i
$757$	−50.4925			−1.83518			−0.917591	−	0.397525i	$-0.869869\pi$
$757$	−50.4925			−1.83518			−0.917591	+	0.397525i	$0.869869\pi$
$758$	8.19921	−	14.2015i	0.297809	−	0.515820i
$759$	7.17551	+	12.4284i	0.260455	+	0.451121i
$760$	−8.21549	−	14.2296i	−0.298007	−	0.516163i
$761$	−6.59070	+	11.4154i	−0.238913	+	0.413809i	−0.960403	−	0.278616i	$-0.910124\pi$
$761$	−6.59070	+	11.4154i	−0.238913	+	0.413809i	0.721490	+	0.692425i	$0.243458\pi$
$762$	−14.8078			−0.536430
$763$	−1.36046	+	40.8246i	−0.0492519	+	1.47795i
$764$	4.68034			0.169329
$765$	3.30553	−	5.72534i	0.119512	−	0.207000i
$766$	−13.6006	−	23.5569i	−0.491408	−	0.851144i
$767$	19.6514	+	34.0373i	0.709572	+	1.22901i
$768$	−17.6412	+	30.5555i	−0.636573	+	1.10258i
$769$	2.07828			0.0749446			0.0374723	−	0.999298i	$-0.488069\pi$
$769$	2.07828			0.0749446			0.0374723	+	0.999298i	$0.488069\pi$
$770$	−2.15657	+	1.15108i	−0.0777174	+	0.0414821i
$771$	40.0024			1.44065
$772$	−10.1868	+	17.6441i	−0.366633	+	0.635026i
$773$	−17.6316	−	30.5388i	−0.634164	−	1.09840i	−0.986692	−	0.162603i	$-0.948011\pi$
$773$	−17.6316	−	30.5388i	−0.634164	−	1.09840i	0.352528	−	0.935801i	$-0.385322\pi$
$774$	0.677329	+	1.17317i	0.0243461	+	0.0421687i
$775$	−4.35253	+	7.53881i	−0.156348	+	0.270802i
$776$	−21.6480			−0.777119
$777$	−15.0259	−	9.35592i	−0.539050	−	0.335642i
$778$	−1.04819			−0.0375796
$779$	28.2834	−	48.9883i	1.01336	−	1.75519i
$780$	3.24926	+	5.62789i	0.116342	+	0.201511i
$781$	2.42201	+	4.19505i	0.0866664	+	0.150111i
$782$	14.4618	−	25.0486i	0.517154	−	0.895738i
$783$	−9.15909			−0.327319
$784$	2.74716	+	0.183299i	0.0981129	+	0.00654639i
$785$	9.28680			0.331460
$786$	−1.50168	+	2.60098i	−0.0535631	+	0.0927740i
$787$	−25.5236	−	44.2082i	−0.909819	−	1.57585i	−0.814314	−	0.580424i	$-0.802887\pi$
$787$	−25.5236	−	44.2082i	−0.909819	−	1.57585i	−0.0955050	−	0.995429i	$-0.530447\pi$
$788$	−5.78903	−	10.0269i	−0.206226	−	0.357193i
$789$	0.202293	−	0.350381i	0.00720181	−	0.0124739i
$790$	−9.41098			−0.334828
$791$	−41.8524	−	26.0596i	−1.48810	−	0.926573i
$792$	4.18194			0.148599
$793$	13.2944	−	23.0265i	0.472097	−	0.817696i
$794$	−5.65891	−	9.80151i	−0.200827	−	0.347843i
$795$	7.47160	+	12.9412i	0.264990	+	0.458977i
$796$	13.9058	−	24.0856i	0.492879	−	0.853692i
$797$	6.41816			0.227343			0.113671	−	0.993518i	$-0.463739\pi$
$797$	6.41816			0.227343			0.113671	+	0.993518i	$0.463739\pi$
$798$	25.6801	−	13.7069i	0.909066	−	0.485220i
$799$	−29.2960			−1.03642
$800$	−2.72533	+	4.72041i	−0.0963551	+	0.166892i
$801$	3.50174	+	6.06520i	0.123728	+	0.214303i
$802$	10.8726	+	18.8320i	0.383926	+	0.664980i
$803$	3.39271	−	5.87634i	0.119726	−	0.207372i
$804$	14.1850			0.500268
$805$	0.600252	−	18.0123i	0.0211561	−	0.634851i
$806$	21.6426			0.762328
$807$	−1.42581	+	2.46957i	−0.0501908	+	0.0869329i
$808$	16.9490	+	29.3566i	0.596265	+	1.03276i
$809$	8.34764	+	14.4585i	0.293487	+	0.508335i	0.974632	−	0.223814i	$-0.0718508\pi$
$809$	8.34764	+	14.4585i	0.293487	+	0.508335i	−0.681144	+	0.732149i	$0.738517\pi$
$810$	−5.19547	+	8.99882i	−0.182550	+	0.316186i
$811$	−4.77237			−0.167580			−0.0837902	−	0.996483i	$-0.526703\pi$
$811$	−4.77237			−0.167580			−0.0837902	+	0.996483i	$0.526703\pi$
$812$	0.281243	−	8.43953i	0.00986970	−	0.296169i
$813$	38.5411			1.35170
$814$	1.46702	−	2.54095i	0.0514189	−	0.0890602i
$815$	6.43205	+	11.1406i	0.225305	+	0.390239i
$816$	−1.90408	−	3.29796i	−0.0666561	−	0.115452i
$817$	2.88029	−	4.98881i	0.100769	−	0.174536i
$818$	−3.86223			−0.135040
$819$	−9.03507	+	4.82253i	−0.315711	+	0.168513i
$820$	−11.4724			−0.400633
$821$	−11.6284	+	20.1409i	−0.405833	+	0.702923i	−0.994418	−	0.105512i	$-0.966352\pi$
$821$	−11.6284	+	20.1409i	−0.405833	+	0.702923i	0.588585	+	0.808435i	$0.299685\pi$
$822$	−6.18325	−	10.7097i	−0.215666	−	0.373544i
$823$	−11.9422	−	20.6845i	−0.416279	−	0.721017i	0.579283	−	0.815127i	$-0.303333\pi$
$823$	−11.9422	−	20.6845i	−0.416279	−	0.721017i	−0.995562	+	0.0941102i	$0.969999\pi$
$824$	−14.2097	+	24.6119i	−0.495019	+	0.857397i
$825$	2.10679			0.0733490
$826$	−30.3099	−	18.8726i	−1.05462	−	0.656662i
$827$	46.3332			1.61116			0.805581	−	0.592486i	$-0.201853\pi$
$827$	46.3332			1.61116			0.805581	+	0.592486i	$0.201853\pi$
$828$	−5.61648	+	9.72803i	−0.195186	+	0.338072i
$829$	−2.06802	−	3.58192i	−0.0718254	−	0.124405i	0.827876	−	0.560911i	$-0.189549\pi$
$829$	−2.06802	−	3.58192i	−0.0718254	−	0.124405i	−0.899701	+	0.436506i	$0.856216\pi$
$830$	3.15869	+	5.47100i	0.109640	+	0.189901i
$831$	−1.99368	+	3.45315i	−0.0691598	+	0.119788i
$832$	15.6682			0.543198
$833$	17.9037	−	26.7268i	0.620326	−	0.926028i
$834$	−8.84822			−0.306389
$835$	−5.68670	+	9.84966i	−0.196797	+	0.340862i
$836$	−3.23957	−	5.61110i	−0.112043	−	0.194064i
$837$	−14.3182	−	24.7999i	−0.494910	−	0.857209i
$838$	2.51306	−	4.35274i	0.0868121	−	0.150363i
$839$	−19.9857			−0.689982			−0.344991	−	0.938606i	$-0.612118\pi$
$839$	−19.9857			−0.689982			−0.344991	+	0.938606i	$0.612118\pi$
$840$	−13.7554	−	8.56486i	−0.474606	−	0.295516i
$841$	−21.2480			−0.732691
$842$	2.28601	−	3.95948i	0.0787811	−	0.136453i
$843$	−10.7184	−	18.5649i	−0.369163	−	0.639408i
$844$	−10.1787	−	17.6300i	−0.350364	−	0.606848i
$845$	−2.87967	+	4.98774i	−0.0990637	+	0.171583i
$846$	−8.47308			−0.291310
$847$	−2.33408	+	1.24583i	−0.0801998	+	0.0428072i
$848$	2.78980			0.0958022
$849$	29.2347	−	50.6359i	1.00333	−	1.73782i
$850$	−2.12306	−	3.67724i	−0.0728202	−	0.126128i
$851$	10.8156	+	18.7331i	0.370752	+	0.642162i
$852$	−5.84927	+	10.1312i	−0.200393	+	0.347091i
$853$	−2.03016			−0.0695114			−0.0347557	−	0.999396i	$-0.511065\pi$
$853$	−2.03016			−0.0695114			−0.0347557	+	0.999396i	$0.511065\pi$
$854$	−0.804504	+	24.1415i	−0.0275296	+	0.826106i
$855$	−8.13093			−0.278072
$856$	−14.1620	+	24.5293i	−0.484047	+	0.838394i
$857$	1.12741	+	1.95274i	0.0385117	+	0.0667042i	0.884639	−	0.466277i	$-0.154405\pi$
$857$	1.12741	+	1.95274i	0.0385117	+	0.0667042i	−0.846127	+	0.532981i	$0.821072\pi$
$858$	−2.61896	−	4.53617i	−0.0894097	−	0.154862i
$859$	28.4037	−	49.1966i	0.969121	−	1.67857i	0.271013	−	0.962576i	$-0.412641\pi$
$859$	28.4037	−	49.1966i	0.969121	−	1.67857i	0.698109	−	0.715992i	$-0.254025\pi$
$860$	−1.16831			−0.0398391
$861$	1.85798	−	55.7543i	0.0633199	−	1.90010i
$862$	−13.9231			−0.474221
$863$	21.8464	−	37.8391i	0.743661	−	1.28806i	−0.207157	−	0.978308i	$-0.566421\pi$
$863$	21.8464	−	37.8391i	0.743661	−	1.28806i	0.950818	−	0.309751i	$-0.100246\pi$
$864$	−8.96533	−	15.5284i	−0.305007	−	0.528287i
$865$	2.69032	+	4.65977i	0.0914736	+	0.158437i
$866$	16.8572	−	29.1975i	0.572831	−	0.992172i
$867$	−8.67920			−0.294761
$868$	23.2912	−	12.4318i	0.790555	−	0.421964i
$869$	−10.1856			−0.345523
$870$	2.70985	−	4.69359i	0.0918724	−	0.159128i
$871$	−7.90249	−	13.6875i	−0.267766	−	0.463784i
$872$	−22.4406	−	38.8682i	−0.759934	−	1.31624i
$873$	−5.35630	+	9.27739i	−0.181283	+	0.313992i
$874$	−35.5732			−1.20328
$875$	−2.24596	−	1.39846i	−0.0759272	−	0.0472764i
$876$	16.3871			0.553669
$877$	9.32614	−	16.1533i	0.314921	−	0.545460i	−0.664500	−	0.747289i	$-0.731355\pi$
$877$	9.32614	−	16.1533i	0.314921	−	0.545460i	0.979421	+	0.201829i	$0.0646886\pi$
$878$	−9.73518	−	16.8618i	−0.328546	−	0.569059i
$879$	24.3594	+	42.1916i	0.821621	+	1.42309i
$880$	0.196662	−	0.340629i	0.00662948	−	0.0114826i
$881$	1.62610			0.0547848			0.0273924	−	0.999625i	$-0.491280\pi$
$881$	1.62610			0.0547848			0.0273924	+	0.999625i	$0.491280\pi$
$882$	5.17816	−	7.72999i	0.174358	−	0.260282i
$883$	−2.08494			−0.0701638			−0.0350819	−	0.999384i	$-0.511169\pi$
$883$	−2.08494			−0.0701638			−0.0350819	+	0.999384i	$0.511169\pi$
$884$	7.08773	−	12.2763i	0.238386	−	0.412897i
$885$	15.3860	+	26.6493i	0.517195	+	0.895808i
$886$	12.2663	+	21.2459i	0.412095	+	0.713769i
$887$	−2.42156	+	4.19426i	−0.0813079	+	0.140829i	−0.903812	−	0.427930i	$-0.859243\pi$
$887$	−2.42156	+	4.19426i	−0.0813079	+	0.140829i	0.822504	+	0.568759i	$0.192576\pi$
$888$	19.4486			0.652653
$889$	17.0853	+	10.6382i	0.573023	+	0.356795i
$890$	4.49816			0.150779
$891$	−5.62311	+	9.73952i	−0.188381	+	0.326286i
$892$	3.00144	+	5.19864i	0.100496	+	0.174063i
$893$	18.0156	+	31.2039i	0.602868	+	1.04420i
$894$	3.71137	−	6.42828i	0.124127	−	0.214994i
$895$	−2.50598			−0.0837657
$896$	12.8873	−	6.87867i	0.430534	−	0.229800i
$897$	38.6164			1.28936
$898$	11.3462	−	19.6523i	0.378629	−	0.655805i
$899$	12.1185	+	20.9898i	0.404174	+	0.700049i
$900$	0.824522	+	1.42811i	0.0274841	+	0.0476038i
$901$	16.2981	−	28.2291i	0.542967	−	0.940447i
$902$	9.24693			0.307889
$903$	0.189211	−	5.67783i	0.00629655	−	0.188946i
$904$	54.1714			1.80171
$905$	−9.86953	+	17.0945i	−0.328074	+	0.568241i
$906$	−15.7265	−	27.2392i	−0.522479	−	0.904961i
$907$	−9.18602	−	15.9106i	−0.305017	−	0.528304i	0.672248	−	0.740326i	$-0.265329\pi$
$907$	−9.18602	−	15.9106i	−0.305017	−	0.528304i	−0.977265	+	0.212021i	$0.931995\pi$
$908$	9.26867	−	16.0538i	0.307592	−	0.532765i
$909$	16.7746			0.556377
$910$	−0.219083	+	6.57424i	−0.00726254	+	0.217934i
$911$	40.6812			1.34783			0.673914	−	0.738809i	$-0.264612\pi$
$911$	40.6812			1.34783			0.673914	+	0.738809i	$0.264612\pi$
$912$	−2.34182	+	4.05616i	−0.0775455	+	0.134313i
$913$	3.41868	+	5.92132i	0.113142	+	0.195967i
$914$	12.0918	+	20.9436i	0.399961	+	0.692753i
$915$	10.4088	−	18.0285i	0.344103	−	0.596005i
$916$	6.69550			0.221226
$917$	3.60125	−	1.92219i	0.118924	−	0.0634762i
$918$	13.9681			0.461017
$919$	10.0865	−	17.4703i	0.332723	−	0.576293i	−0.650322	−	0.759659i	$-0.725366\pi$
$919$	10.0865	−	17.4703i	0.332723	−	0.576293i	0.983045	+	0.183366i	$0.0586993\pi$
$920$	9.90109	+	17.1492i	0.326429	+	0.565392i
$921$	−0.667669	−	1.15644i	−0.0220004	−	0.0381059i
$922$	−5.72649	+	9.91856i	−0.188592	+	0.326651i
$923$	13.0345			0.429037
$924$	−5.42409	−	3.37734i	−0.178440	−	0.111106i
$925$	3.17553			0.104411
$926$	−5.10116	+	8.83546i	−0.167634	+	0.290351i
$927$	7.03172	+	12.1793i	0.230952	+	0.400021i
$928$	7.58796	+	13.1427i	0.249087	+	0.431431i
$929$	2.37505	−	4.11372i	0.0779230	−	0.134967i	−0.824431	−	0.565963i	$-0.808504\pi$
$929$	2.37505	−	4.11372i	0.0779230	−	0.134967i	0.902354	+	0.430996i	$0.141838\pi$
$930$	16.9450			0.555648
$931$	−39.4772	−	2.63404i	−1.29381	−	0.0863271i
$932$	−24.7426			−0.810471
$933$	−13.4328	+	23.2663i	−0.439771	+	0.761706i
$934$	−9.68579	−	16.7763i	−0.316929	−	0.548937i
$935$	−2.29781	−	3.97992i	−0.0751463	−	0.130157i
$936$	5.62649	−	9.74536i	0.183908	−	0.318537i
$937$	4.80117			0.156847			0.0784237	−	0.996920i	$-0.475011\pi$
$937$	4.80117			0.156847			0.0784237	+	0.996920i	$0.475011\pi$
$938$	12.1886	+	7.58930i	0.397973	+	0.247800i
$939$	36.9215			1.20489
$940$	3.65376	−	6.32850i	0.119173	−	0.206413i
$941$	15.9649	+	27.6520i	0.520441	+	0.901430i	0.999718	+	0.0237664i	$0.00756578\pi$
$941$	15.9649	+	27.6520i	0.520441	+	0.901430i	−0.479276	+	0.877664i	$0.659101\pi$
$942$	−9.03869	−	15.6555i	−0.294497	−	0.510083i
$943$	−34.0864	+	59.0394i	−1.11001	+	1.92259i
$944$	5.74494			0.186982
$945$	7.67824	−	4.09831i	0.249773	−	0.133318i
$946$	0.941677			0.0306166
$947$	−26.4402	+	45.7958i	−0.859192	+	1.48816i	0.0135087	+	0.999909i	$0.495700\pi$
$947$	−26.4402	+	45.7958i	−0.859192	+	1.48816i	−0.872701	+	0.488255i	$0.837633\pi$
$948$	−12.2994	−	21.3031i	−0.399464	−	0.691893i
$949$	−9.12926	−	15.8123i	−0.296348	−	0.513290i
$950$	−2.61114	+	4.52264i	−0.0847167	+	0.146734i
$951$	−39.2164			−1.27168
$952$	−1.17724	+	35.3266i	−0.0381546	+	1.14494i
$953$	−27.0875			−0.877450			−0.438725	−	0.898621i	$-0.644570\pi$
$953$	−27.0875			−0.877450			−0.438725	+	0.898621i	$0.644570\pi$
$954$	4.71377	−	8.16449i	0.152614	−	0.264335i
$955$	−2.04147	−	3.53593i	−0.0660604	−	0.114420i
$956$	−10.1145	−	17.5188i	−0.327126	−	0.566599i
$957$	2.93290	−	5.07992i	0.0948070	−	0.164211i
$958$	10.5015			0.339288
$959$	−0.559821	+	16.7991i	−0.0180776	+	0.542471i
$960$	12.2674			0.395928
$961$	−22.3891	+	38.7790i	−0.722229	+	1.25094i
$962$	−3.94752	−	6.83730i	−0.127273	−	0.220443i
$963$	7.00811	+	12.1384i	0.225833	+	0.391155i
$964$	3.90834	−	6.76945i	0.125879	−	0.218029i
$965$	17.7732			0.572139
$966$	−30.9490	+	16.5192i	−0.995767	+	0.531497i
$967$	47.6631			1.53274			0.766371	−	0.642398i	$-0.222061\pi$
$967$	47.6631			1.53274			0.766371	+	0.642398i	$0.222061\pi$
$968$	1.45352	−	2.51757i	0.0467179	−	0.0809177i
$969$	27.3619	+	47.3923i	0.878992	+	1.52246i
$970$	3.44022	+	5.95863i	0.110459	+	0.191320i
$971$	−13.1151	+	22.7160i	−0.420882	+	0.728990i	−0.996026	−	0.0890628i	$-0.971613\pi$
$971$	−13.1151	+	22.7160i	−0.420882	+	0.728990i	0.575144	+	0.818052i	$0.304946\pi$
$972$	−15.8473			−0.508302
$973$	10.2091	+	6.35675i	0.327289	+	0.203788i
$974$	−14.9600			−0.479351
$975$	2.83452	−	4.90954i	0.0907774	−	0.157231i
$976$	−1.94325	−	3.36581i	−0.0622020	−	0.107737i
$977$	26.5531	+	45.9912i	0.849508	+	1.47139i	0.881648	+	0.471907i	$0.156434\pi$
$977$	26.5531	+	45.9912i	0.849508	+	1.47139i	−0.0321407	+	0.999483i	$0.510232\pi$
$978$	12.5204	−	21.6860i	0.400359	−	0.693442i
$979$	4.86840			0.155595
$980$	3.54057	+	7.20087i	0.113099	+	0.230023i
$981$	−22.2096			−0.709098
$982$	−11.4183	+	19.7771i	−0.364374	+	0.631114i
$983$	24.6477	+	42.6911i	0.786140	+	1.36163i	0.928316	+	0.371793i	$0.121257\pi$
$983$	24.6477	+	42.6911i	0.786140	+	1.36163i	−0.142176	+	0.989841i	$0.545410\pi$
$984$	30.6472	+	53.0825i	0.976997	+	1.69221i
$985$	−5.05011	+	8.74705i	−0.160910	+	0.278704i
$986$	−11.8222			−0.376495
$987$	30.1639	+	18.7817i	0.960128	+	0.597828i
$988$	−17.4344			−0.554661
$989$	−3.47125	+	6.01238i	−0.110379	+	0.191183i
$990$	−0.664578	−	1.15108i	−0.0211217	−	0.0365838i
$991$	−11.9602	−	20.7157i	−0.379929	−	0.658056i	0.611123	−	0.791536i	$-0.290718\pi$
$991$	−11.9602	−	20.7157i	−0.379929	−	0.658056i	−0.991051	+	0.133480i	$0.957385\pi$
$992$	−23.7242	+	41.0915i	−0.753244	+	1.30466i
$993$	26.8813			0.853051
$994$	−10.4465	+	5.57587i	−0.331342	+	0.176856i
$995$	−24.2618			−0.769149
$996$	−8.25627	+	14.3003i	−0.261610	+	0.453121i
$997$	−12.2830	−	21.2748i	−0.389007	−	0.673780i	0.603309	−	0.797507i	$-0.293848\pi$
$997$	−12.2830	−	21.2748i	−0.389007	−	0.673780i	−0.992316	+	0.123727i	$0.960515\pi$
$998$	9.89114	+	17.1320i	0.313098	+	0.542302i
$999$	−5.22316	+	9.04678i	−0.165254	+	0.286228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.b.331.2	yes	12
7.2	even	3		2695.2.a.r.1.5		6
7.4	even	3	inner	385.2.i.b.221.2	✓	12
7.5	odd	6		2695.2.a.q.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.b.221.2	✓	12	7.4	even	3	inner
385.2.i.b.331.2	yes	12	1.1	even	1	trivial
2695.2.a.q.1.5		6	7.5	odd	6
2695.2.a.r.1.5		6	7.2	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.461975 + 0.800164i) q^{2} +(1.05339 + 1.82453i) q^{3} +(0.573158 + 0.992739i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.94657 q^{6} +(2.24596 + 1.39846i) q^{7} -2.90704 q^{8} +(-0.719279 + 1.24583i) q^{9} +O(q^{10})\)	\(q+(-0.461975 + 0.800164i) q^{2} +(1.05339 + 1.82453i) q^{3} +(0.573158 + 0.992739i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.94657 q^{6} +(2.24596 + 1.39846i) q^{7} -2.90704 q^{8} +(-0.719279 + 1.24583i) q^{9} +(0.461975 + 0.800164i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.20752 + 2.09149i) q^{12} +2.69085 q^{13} +(-2.15657 + 1.15108i) q^{14} +2.10679 q^{15} +(0.196662 - 0.340629i) q^{16} +(-2.29781 - 3.97992i) q^{17} +(-0.664578 - 1.15108i) q^{18} +(-2.82607 + 4.89489i) q^{19} +1.14632 q^{20} +(-0.185649 + 5.57095i) q^{21} -0.923950 q^{22} +(3.40590 - 5.89919i) q^{23} +(-3.06226 - 5.30399i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.24310 + 2.15312i) q^{26} +3.28963 q^{27} +(-0.101013 + 3.03119i) q^{28} -2.78423 q^{29} +(-0.973283 + 1.68578i) q^{30} +(-4.35253 - 7.53881i) q^{31} +(-2.72533 - 4.72041i) q^{32} +(-1.05339 + 1.82453i) q^{33} +4.24611 q^{34} +(2.33408 - 1.24583i) q^{35} -1.64904 q^{36} +(-1.58777 + 2.75009i) q^{37} +(-2.61114 - 4.52264i) q^{38} +(2.83452 + 4.90954i) q^{39} +(-1.45352 + 2.51757i) q^{40} -10.0080 q^{41} +(-4.37191 - 2.72219i) q^{42} -1.01919 q^{43} +(-0.573158 + 0.992739i) q^{44} +(0.719279 + 1.24583i) q^{45} +(3.14688 + 5.45056i) q^{46} +(3.18739 - 5.52072i) q^{47} +0.828651 q^{48} +(3.08865 + 6.28174i) q^{49} +0.923950 q^{50} +(4.84099 - 8.38484i) q^{51} +(1.54228 + 2.67131i) q^{52} +(3.54644 + 6.14262i) q^{53} +(-1.51973 + 2.63224i) q^{54} +1.00000 q^{55} +(-6.52908 - 4.06536i) q^{56} -11.9079 q^{57} +(1.28625 - 2.22784i) q^{58} +(7.30306 + 12.6493i) q^{59} +(1.20752 + 2.09149i) q^{60} +(4.94059 - 8.55735i) q^{61} +8.04304 q^{62} +(-3.35771 + 1.79220i) q^{63} +5.82279 q^{64} +(1.34542 - 2.33034i) q^{65} +(-0.973283 - 1.68578i) q^{66} +(-2.93680 - 5.08669i) q^{67} +(2.63401 - 4.56224i) q^{68} +14.3510 q^{69} +(-0.0814179 + 2.44319i) q^{70} +4.84403 q^{71} +(2.09097 - 3.62167i) q^{72} +(-3.39271 - 5.87634i) q^{73} +(-1.46702 - 2.54095i) q^{74} +(1.05339 - 1.82453i) q^{75} -6.47914 q^{76} +(-0.0881194 + 2.64428i) q^{77} -5.23791 q^{78} +(-5.09280 + 8.82099i) q^{79} +(-0.196662 - 0.340629i) q^{80} +(5.62311 + 9.73952i) q^{81} +(4.62346 - 8.00808i) q^{82} +6.83735 q^{83} +(-5.63690 + 3.00873i) q^{84} -4.59561 q^{85} +(0.470839 - 0.815516i) q^{86} +(-2.93290 - 5.07992i) q^{87} +(-1.45352 - 2.51757i) q^{88} +(2.43420 - 4.21616i) q^{89} -1.32916 q^{90} +(6.04353 + 3.76303i) q^{91} +7.80848 q^{92} +(9.16987 - 15.8827i) q^{93} +(2.94499 + 5.10087i) q^{94} +(2.82607 + 4.89489i) q^{95} +(5.74170 - 9.94492i) q^{96} +7.44677 q^{97} +(-6.45330 - 0.430584i) q^{98} -1.43856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

Introduction

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