LMFDB - Embedded newform 187.2.g.f.69.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.6
Character	$\chi$	$=$	187.69
Dual form			187.2.g.f.103.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.905302 - 0.657740i) q^{2} +(-0.440186 - 1.35475i) q^{3} +(-0.231085 + 0.711206i) q^{4} +(1.95004 + 1.41679i) q^{5} +(-1.28958 - 0.936932i) q^{6} +(1.26946 - 3.90701i) q^{7} +(0.950176 + 2.92434i) q^{8} +(0.785461 - 0.570671i) q^{9} +O(q^{10})$	\(q+(0.905302 - 0.657740i) q^{2} +(-0.440186 - 1.35475i) q^{3} +(-0.231085 + 0.711206i) q^{4} +(1.95004 + 1.41679i) q^{5} +(-1.28958 - 0.936932i) q^{6} +(1.26946 - 3.90701i) q^{7} +(0.950176 + 2.92434i) q^{8} +(0.785461 - 0.570671i) q^{9} +2.69726 q^{10} +(-2.08852 - 2.57645i) q^{11} +1.06523 q^{12} +(-3.08799 + 2.24355i) q^{13} +(-1.42055 - 4.37200i) q^{14} +(1.06102 - 3.26548i) q^{15} +(1.57368 + 1.14334i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.335726 - 1.03326i) q^{18} +(2.26712 + 6.97749i) q^{19} +(-1.45825 + 1.05948i) q^{20} -5.85183 q^{21} +(-3.58538 - 0.958756i) q^{22} -1.29415 q^{23} +(3.54351 - 2.57451i) q^{24} +(0.250291 + 0.770317i) q^{25} +(-1.31989 + 4.06219i) q^{26} +(-4.57613 - 3.32475i) q^{27} +(2.48533 + 1.80570i) q^{28} +(-2.52624 + 7.77496i) q^{29} +(-1.18729 - 3.65411i) q^{30} +(4.05953 - 2.94942i) q^{31} -3.97300 q^{32} +(-2.57111 + 3.96355i) q^{33} -1.11901 q^{34} +(8.01091 - 5.82027i) q^{35} +(0.224356 + 0.690498i) q^{36} +(-0.492977 + 1.51723i) q^{37} +(6.64180 + 4.82555i) q^{38} +(4.39875 + 3.19588i) q^{39} +(-2.29029 + 7.04879i) q^{40} +(2.87869 + 8.85968i) q^{41} +(-5.29767 + 3.84898i) q^{42} -4.68912 q^{43} +(2.31501 - 0.889993i) q^{44} +2.34020 q^{45} +(-1.17160 + 0.851218i) q^{46} +(-0.539452 - 1.66026i) q^{47} +(0.856237 - 2.63523i) q^{48} +(-7.99005 - 5.80511i) q^{49} +(0.733257 + 0.532742i) q^{50} +(-0.440186 + 1.35475i) q^{51} +(-0.882043 - 2.71465i) q^{52} +(1.92873 - 1.40131i) q^{53} -6.32960 q^{54} +(-0.422428 - 7.98318i) q^{55} +12.6316 q^{56} +(8.45481 - 6.14278i) q^{57} +(2.82690 + 8.70029i) q^{58} +(0.313462 - 0.964735i) q^{59} +(2.07724 + 1.50920i) q^{60} +(-11.7883 - 8.56469i) q^{61} +(1.73515 - 5.34024i) q^{62} +(-1.23250 - 3.79325i) q^{63} +(-6.74411 + 4.89989i) q^{64} -9.20035 q^{65} +(0.279355 + 5.27933i) q^{66} -8.31383 q^{67} +(0.604988 - 0.439550i) q^{68} +(0.569668 + 1.75326i) q^{69} +(3.42407 - 10.5382i) q^{70} +(3.32536 + 2.41601i) q^{71} +(2.41516 + 1.75472i) q^{72} +(3.99578 - 12.2977i) q^{73} +(0.551649 + 1.69780i) q^{74} +(0.933414 - 0.678165i) q^{75} -5.48633 q^{76} +(-12.7175 + 4.88917i) q^{77} +6.08425 q^{78} +(-1.35290 + 0.982938i) q^{79} +(1.44886 + 4.45914i) q^{80} +(-1.58981 + 4.89294i) q^{81} +(8.43345 + 6.12726i) q^{82} +(9.15884 + 6.65428i) q^{83} +(1.35227 - 4.16186i) q^{84} +(-0.744850 - 2.29241i) q^{85} +(-4.24507 + 3.08423i) q^{86} +11.6452 q^{87} +(5.54994 - 8.55563i) q^{88} +1.75309 q^{89} +(2.11859 - 1.53925i) q^{90} +(4.84550 + 14.9129i) q^{91} +(0.299060 - 0.920411i) q^{92} +(-5.78269 - 4.20137i) q^{93} +(-1.58039 - 1.14822i) q^{94} +(-5.46464 + 16.8184i) q^{95} +(1.74886 + 5.38242i) q^{96} +(13.8053 - 10.0301i) q^{97} -11.0517 q^{98} +(-3.11075 - 0.831839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.905302	−	0.657740i	0.640145	−	0.465093i	−0.219755	−	0.975555i	$-0.570526\pi$
$2$	0.905302	−	0.657740i	0.640145	−	0.465093i	0.859900	+	0.510463i	$0.170526\pi$
$3$	−0.440186	−	1.35475i	−0.254141	−	0.782167i	−0.993998	−	0.109402i	$-0.965107\pi$
$3$	−0.440186	−	1.35475i	−0.254141	−	0.782167i	0.739856	−	0.672765i	$-0.234893\pi$
$4$	−0.231085	+	0.711206i	−0.115542	+	0.355603i
$5$	1.95004	+	1.41679i	0.872086	+	0.633607i	0.931146	−	0.364647i	$-0.118810\pi$
$5$	1.95004	+	1.41679i	0.872086	+	0.633607i	−0.0590601	+	0.998254i	$0.518810\pi$
$6$	−1.28958	−	0.936932i	−0.526467	−	0.382501i
$7$	1.26946	−	3.90701i	0.479812	−	1.47671i	−0.359544	−	0.933128i	$-0.617068\pi$
$7$	1.26946	−	3.90701i	0.479812	−	1.47671i	0.839356	−	0.543582i	$-0.182932\pi$
$8$	0.950176	+	2.92434i	0.335938	+	1.03391i
$9$	0.785461	−	0.570671i	0.261820	−	0.190224i
$10$	2.69726			0.852947
$11$	−2.08852	−	2.57645i	−0.629713	−	0.776828i
$11$	−2.08852	−	2.57645i	−0.629713	−	0.776828i
$12$	1.06523			0.307505
$13$	−3.08799	+	2.24355i	−0.856454	+	0.622250i	−0.926918	−	0.375264i	$-0.877552\pi$
$13$	−3.08799	+	2.24355i	−0.856454	+	0.622250i	0.0704640	+	0.997514i	$0.477552\pi$
$14$	−1.42055	−	4.37200i	−0.379657	−	1.16847i
$15$	1.06102	−	3.26548i	0.273953	−	0.843142i
$16$	1.57368	+	1.14334i	0.393419	+	0.285836i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	0.335726	−	1.03326i	0.0791314	−	0.243541i
$19$	2.26712	+	6.97749i	0.520114	+	1.60075i	0.773781	+	0.633454i	$0.218363\pi$
$19$	2.26712	+	6.97749i	0.520114	+	1.60075i	−0.253667	+	0.967292i	$0.581637\pi$
$20$	−1.45825	+	1.05948i	−0.326076	+	0.236908i
$21$	−5.85183			−1.27697
$22$	−3.58538	−	0.958756i	−0.764405	−	0.204407i
$23$	−1.29415			−0.269850			−0.134925	−	0.990856i	$-0.543079\pi$
$23$	−1.29415			−0.269850			−0.134925	+	0.990856i	$0.543079\pi$
$24$	3.54351	−	2.57451i	0.723315	−	0.525519i
$25$	0.250291	+	0.770317i	0.0500582	+	0.154063i
$26$	−1.31989	+	4.06219i	−0.258851	+	0.796661i
$27$	−4.57613	−	3.32475i	−0.880676	−	0.639849i
$28$	2.48533	+	1.80570i	0.469684	+	0.341245i
$29$	−2.52624	+	7.77496i	−0.469111	+	1.44377i	0.384628	+	0.923072i	$0.374330\pi$
$29$	−2.52624	+	7.77496i	−0.469111	+	1.44377i	−0.853738	+	0.520702i	$0.825670\pi$
$30$	−1.18729	−	3.65411i	−0.216769	−	0.667147i
$31$	4.05953	−	2.94942i	0.729114	−	0.529732i	−0.160169	−	0.987090i	$-0.551204\pi$
$31$	4.05953	−	2.94942i	0.729114	−	0.529732i	0.889283	+	0.457357i	$0.151204\pi$
$32$	−3.97300			−0.702333
$33$	−2.57111	+	3.96355i	−0.447572	+	0.689965i
$34$	−1.11901			−0.191909
$35$	8.01091	−	5.82027i	1.35409	−	0.983805i
$36$	0.224356	+	0.690498i	0.0373927	+	0.115083i
$37$	−0.492977	+	1.51723i	−0.0810449	+	0.249431i	−0.983366	−	0.181633i	$-0.941862\pi$
$37$	−0.492977	+	1.51723i	−0.0810449	+	0.249431i	0.902321	+	0.431064i	$0.141862\pi$
$38$	6.64180	+	4.82555i	1.07744	+	0.782808i
$39$	4.39875	+	3.19588i	0.704364	+	0.511750i
$40$	−2.29029	+	7.04879i	−0.362127	+	1.11451i
$41$	2.87869	+	8.85968i	0.449575	+	1.38365i	0.877387	+	0.479783i	$0.159284\pi$
$41$	2.87869	+	8.85968i	0.449575	+	1.38365i	−0.427812	+	0.903868i	$0.640716\pi$
$42$	−5.29767	+	3.84898i	−0.817448	+	0.593911i
$43$	−4.68912			−0.715085			−0.357542	−	0.933897i	$-0.616385\pi$
$43$	−4.68912			−0.715085			−0.357542	+	0.933897i	$0.616385\pi$
$44$	2.31501	−	0.889993i	0.349001	−	0.134171i
$45$	2.34020			0.348857
$46$	−1.17160	+	0.851218i	−0.172743	+	0.125505i
$47$	−0.539452	−	1.66026i	−0.0786872	−	0.242174i	0.903973	−	0.427589i	$-0.140637\pi$
$47$	−0.539452	−	1.66026i	−0.0786872	−	0.242174i	−0.982660	+	0.185415i	$0.940637\pi$
$48$	0.856237	−	2.63523i	0.123587	−	0.380362i
$49$	−7.99005	−	5.80511i	−1.14144	−	0.829302i
$50$	0.733257	+	0.532742i	0.103698	+	0.0753412i
$51$	−0.440186	+	1.35475i	−0.0616383	+	0.189703i
$52$	−0.882043	−	2.71465i	−0.122317	−	0.376454i
$53$	1.92873	−	1.40131i	0.264932	−	0.192484i	−0.447387	−	0.894341i	$-0.647645\pi$
$53$	1.92873	−	1.40131i	0.264932	−	0.192484i	0.712318	+	0.701856i	$0.247645\pi$
$54$	−6.32960			−0.861350
$55$	−0.422428	−	7.98318i	−0.0569602	−	1.07645i
$56$	12.6316			1.68797
$57$	8.45481	−	6.14278i	1.11987	−	0.813631i
$58$	2.82690	+	8.70029i	0.371190	+	1.14240i
$59$	0.313462	−	0.964735i	0.0408092	−	0.125598i	−0.928576	−	0.371142i	$-0.878966\pi$
$59$	0.313462	−	0.964735i	0.0408092	−	0.125598i	0.969386	+	0.245544i	$0.0789665\pi$
$60$	2.07724	+	1.50920i	0.268171	+	0.194837i
$61$	−11.7883	−	8.56469i	−1.50933	−	1.09660i	−0.966471	−	0.256775i	$-0.917340\pi$
$61$	−11.7883	−	8.56469i	−1.50933	−	1.09660i	−0.542863	−	0.839821i	$-0.682660\pi$
$62$	1.73515	−	5.34024i	0.220364	−	0.678211i
$63$	−1.23250	−	3.79325i	−0.155280	−	0.477904i
$64$	−6.74411	+	4.89989i	−0.843014	+	0.612486i
$65$	−9.20035			−1.14116
$66$	0.279355	+	5.27933i	0.0343862	+	0.649840i
$67$	−8.31383			−1.01570			−0.507848	−	0.861447i	$-0.669559\pi$
$67$	−8.31383			−1.01570			−0.507848	+	0.861447i	$0.669559\pi$
$68$	0.604988	−	0.439550i	0.0733656	−	0.0533032i
$69$	0.569668	+	1.75326i	0.0685800	+	0.211068i
$70$	3.42407	−	10.5382i	0.409255	−	1.25956i
$71$	3.32536	+	2.41601i	0.394647	+	0.286728i	0.767357	−	0.641220i	$-0.221571\pi$
$71$	3.32536	+	2.41601i	0.394647	+	0.286728i	−0.372710	+	0.927948i	$0.621571\pi$
$72$	2.41516	+	1.75472i	0.284630	+	0.206796i
$73$	3.99578	−	12.2977i	0.467671	−	1.43934i	−0.387922	−	0.921692i	$-0.626807\pi$
$73$	3.99578	−	12.2977i	0.467671	−	1.43934i	0.855592	−	0.517650i	$-0.173193\pi$
$74$	0.551649	+	1.69780i	0.0641278	+	0.197365i
$75$	0.933414	−	0.678165i	0.107781	−	0.0783077i
$76$	−5.48633			−0.629325
$77$	−12.7175	+	4.88917i	−1.44929	+	0.557173i
$78$	6.08425			0.688906
$79$	−1.35290	+	0.982938i	−0.152213	+	0.110589i	−0.661285	−	0.750135i	$-0.729989\pi$
$79$	−1.35290	+	0.982938i	−0.152213	+	0.110589i	0.509072	+	0.860724i	$0.329989\pi$
$80$	1.44886	+	4.45914i	0.161988	+	0.498547i
$81$	−1.58981	+	4.89294i	−0.176646	+	0.543660i
$82$	8.43345	+	6.12726i	0.931319	+	0.676643i
$83$	9.15884	+	6.65428i	1.00531	+	0.730403i	0.963221	−	0.268711i	$-0.0865977\pi$
$83$	9.15884	+	6.65428i	1.00531	+	0.730403i	0.0420921	+	0.999114i	$0.486598\pi$
$84$	1.35227	−	4.16186i	0.147545	−	0.454096i
$85$	−0.744850	−	2.29241i	−0.0807903	−	0.248647i
$86$	−4.24507	+	3.08423i	−0.457758	+	0.332581i
$87$	11.6452			1.24849
$88$	5.54994	−	8.55563i	0.591626	−	0.912034i
$89$	1.75309			0.185827			0.0929134	−	0.995674i	$-0.470382\pi$
$89$	1.75309			0.185827			0.0929134	+	0.995674i	$0.470382\pi$
$90$	2.11859	−	1.53925i	0.223319	−	0.162251i
$91$	4.84550	+	14.9129i	0.507946	+	1.56330i
$92$	0.299060	−	0.920411i	0.0311791	−	0.0959595i
$93$	−5.78269	−	4.20137i	−0.599637	−	0.435662i
$94$	−1.58039	−	1.14822i	−0.163005	−	0.118430i
$95$	−5.46464	+	16.8184i	−0.560660	+	1.72553i
$96$	1.74886	+	5.38242i	0.178492	+	0.549341i
$97$	13.8053	−	10.0301i	1.40171	−	1.01841i	0.407252	−	0.913316i	$-0.366487\pi$
$97$	13.8053	−	10.0301i	1.40171	−	1.01841i	0.994463	−	0.105090i	$-0.0335130\pi$
$98$	−11.0517			−1.11639
$99$	−3.11075	−	0.831839i	−0.312643	−	0.0836029i
$100$	−0.605693			−0.0605693
$101$	2.84221	−	2.06499i	0.282810	−	0.205474i	−0.437332	−	0.899300i	$-0.644076\pi$
$101$	2.84221	−	2.06499i	0.282810	−	0.205474i	0.720142	+	0.693826i	$0.244076\pi$
$102$	0.492574	+	1.51599i	0.0487721	+	0.150105i
$103$	4.67912	−	14.4009i	0.461048	−	1.41896i	−0.402838	−	0.915271i	$-0.631976\pi$
$103$	4.67912	−	14.4009i	0.461048	−	1.41896i	0.863886	−	0.503688i	$-0.168024\pi$
$104$	−9.49506	−	6.89856i	−0.931067	−	0.676460i
$105$	−11.4113	−	8.29080i	−1.11363	−	0.809100i
$106$	0.824390	−	2.53721i	0.0800718	−	0.246436i
$107$	−1.59714	−	4.91549i	−0.154401	−	0.475199i	0.843698	−	0.536818i	$-0.180374\pi$
$107$	−1.59714	−	4.91549i	−0.154401	−	0.475199i	−0.998100	+	0.0616189i	$0.980374\pi$
$108$	3.42206	−	2.48627i	0.329288	−	0.239242i
$109$	6.05406			0.579874			0.289937	−	0.957046i	$-0.406366\pi$
$109$	6.05406			0.579874			0.289937	+	0.957046i	$0.406366\pi$
$110$	−5.63328	−	6.94934i	−0.537112	−	0.662593i
$111$	2.27247			0.215693
$112$	6.46478	−	4.69694i	0.610864	−	0.443819i
$113$	3.53324	+	10.8742i	0.332379	+	1.02296i	0.967999	+	0.250955i	$0.0807446\pi$
$113$	3.53324	+	10.8742i	0.332379	+	1.02296i	−0.635620	+	0.772002i	$0.719255\pi$
$114$	3.61380	−	11.1221i	0.338464	−	1.04168i
$115$	−2.52366	−	1.83354i	−0.235332	−	0.170979i
$116$	−4.94583	−	3.59335i	−0.459208	−	0.333634i
$117$	−1.14516	+	3.52445i	−0.105870	+	0.325835i
$118$	−0.350768	−	1.07955i	−0.0322908	−	0.0993809i
$119$	−3.32350	+	2.41466i	−0.304665	+	0.221352i
$120$	10.5575			0.963765
$121$	−2.27615	+	10.7619i	−0.206922	+	0.978357i
$122$	−16.3053			−1.47621
$123$	10.7355	−	7.79981i	0.967989	−	0.703285i
$124$	1.15955	+	3.56873i	0.104131	+	0.320482i
$125$	3.12095	−	9.60530i	0.279146	−	0.859125i
$126$	−3.61076	−	2.62337i	−0.321672	−	0.233708i
$127$	−4.76374	−	3.46106i	−0.422713	−	0.307119i	0.356015	−	0.934480i	$-0.384135\pi$
$127$	−4.76374	−	3.46106i	−0.422713	−	0.307119i	−0.778729	+	0.627361i	$0.784135\pi$
$128$	−0.427160	+	1.31466i	−0.0377560	+	0.116201i
$129$	2.06409	+	6.35260i	0.181733	+	0.559315i
$130$	−8.32910	+	6.05144i	−0.730510	+	0.530747i
$131$	17.2321			1.50558			0.752790	−	0.658261i	$-0.228708\pi$
$131$	17.2321			1.50558			0.752790	+	0.658261i	$0.228708\pi$
$132$	−2.22475	−	2.74450i	−0.193640	−	0.238878i
$133$	30.1391			2.61339
$134$	−7.52652	+	5.46834i	−0.650193	+	0.472393i
$135$	−4.21318	−	12.9668i	−0.362612	−	1.11601i
$136$	0.950176	−	2.92434i	0.0814770	−	0.250760i
$137$	6.93290	+	5.03705i	0.592318	+	0.430344i	0.843144	−	0.537688i	$-0.180702\pi$
$137$	6.93290	+	5.03705i	0.592318	+	0.430344i	−0.250826	+	0.968032i	$0.580702\pi$
$138$	1.66891	+	1.21253i	0.142067	+	0.103218i
$139$	0.0623222	−	0.191808i	0.00528610	−	0.0162689i	−0.948379	−	0.317140i	$-0.897277\pi$
$139$	0.0623222	−	0.191808i	0.00528610	−	0.0162689i	0.953665	+	0.300871i	$0.0972774\pi$
$140$	2.28821	+	7.04239i	0.193389	+	0.595191i
$141$	−2.01179	+	1.46165i	−0.169423	+	0.123093i
$142$	4.59956			0.385987
$143$	12.2297	+	3.27032i	1.02270	+	0.273478i
$144$	1.88853			0.157378
$145$	−15.9418	+	11.5824i	−1.32389	+	0.961863i
$146$	−4.47134	−	13.7614i	−0.370050	−	1.13890i
$147$	−4.34738	+	13.3799i	−0.358566	+	1.10355i
$148$	−0.965142	−	0.701217i	−0.0793342	−	0.0576397i
$149$	−6.77253	−	4.92053i	−0.554827	−	0.403106i	0.274735	−	0.961520i	$-0.411410\pi$
$149$	−6.77253	−	4.92053i	−0.554827	−	0.403106i	−0.829562	+	0.558414i	$0.811410\pi$
$150$	0.398965	−	1.22789i	0.0325753	−	0.100257i
$151$	0.657551	+	2.02373i	0.0535107	+	0.164689i	0.974240	−	0.225512i	$-0.0724055\pi$
$151$	0.657551	+	2.02373i	0.0535107	+	0.164689i	−0.920730	+	0.390201i	$0.872406\pi$
$152$	−18.2504	+	13.2597i	−1.48030	+	1.07550i
$153$	−0.970883			−0.0784912
$154$	−8.29737	+	12.7910i	−0.668621	+	1.03073i
$155$	12.0950			0.971492
$156$	−3.28941	+	2.38990i	−0.263364	+	0.191345i
$157$	−1.22386	−	3.76666i	−0.0976748	−	0.300612i	0.890267	−	0.455440i	$-0.150518\pi$
$157$	−1.22386	−	3.76666i	−0.0976748	−	0.300612i	−0.987942	+	0.154827i	$0.950518\pi$
$158$	−0.578263	+	1.77971i	−0.0460042	+	0.141586i
$159$	−2.74742	−	1.99612i	−0.217885	−	0.158303i
$160$	−7.74751	−	5.62890i	−0.612495	−	0.445003i
$161$	−1.64288	+	5.05627i	−0.129477	+	0.398490i
$162$	1.77902	+	5.47527i	0.139773	+	0.430178i
$163$	5.55038	−	4.03259i	0.434739	−	0.315857i	−0.348802	−	0.937197i	$-0.613411\pi$
$163$	5.55038	−	4.03259i	0.434739	−	0.315857i	0.783541	+	0.621340i	$0.213411\pi$
$164$	−6.96628			−0.543975
$165$	−10.6293	+	4.08637i	−0.827488	+	0.318123i
$166$	12.6683			0.983251
$167$	−14.9144	+	10.8359i	−1.15411	+	0.838509i	−0.989022	−	0.147770i	$-0.952791\pi$
$167$	−14.9144	+	10.8359i	−1.15411	+	0.838509i	−0.165087	+	0.986279i	$0.552791\pi$
$168$	−5.56027	−	17.1127i	−0.428984	−	1.32028i
$169$	0.484913	−	1.49241i	0.0373010	−	0.114801i
$170$	−2.18213	−	1.58541i	−0.167361	−	0.121595i
$171$	5.76258	+	4.18676i	0.440676	+	0.320170i
$172$	1.08359	−	3.33494i	0.0826227	−	0.254286i
$173$	3.52560	+	10.8507i	0.268046	+	0.824961i	0.990976	+	0.134040i	$0.0427949\pi$
$173$	3.52560	+	10.8507i	0.268046	+	0.824961i	−0.722930	+	0.690921i	$0.757205\pi$
$174$	10.5424	−	7.65949i	0.799216	−	0.580664i
$175$	3.32737			0.251525
$176$	−0.340898	−	6.44239i	−0.0256962	−	0.485614i
$177$	−1.44496			−0.108610
$178$	1.58707	−	1.15308i	0.118956	−	0.0864267i
$179$	−2.71500	−	8.35590i	−0.202928	−	0.624549i	−0.999792	−	0.0203902i	$-0.993509\pi$
$179$	−2.71500	−	8.35590i	−0.202928	−	0.624549i	0.796864	−	0.604159i	$-0.206491\pi$
$180$	−0.540786	+	1.66437i	−0.0403078	+	0.124055i
$181$	−3.87677	−	2.81664i	−0.288158	−	0.209359i	0.434310	−	0.900764i	$-0.356992\pi$
$181$	−3.87677	−	2.81664i	−0.288158	−	0.209359i	−0.722468	+	0.691404i	$0.756992\pi$
$182$	14.1955	+	10.3136i	1.05224	+	0.764495i
$183$	−6.41400	+	19.7403i	−0.474136	+	1.45924i
$184$	−1.22968	−	3.78455i	−0.0906529	−	0.279001i
$185$	−3.11092	+	2.26021i	−0.228719	+	0.166174i
$186$	−7.99848			−0.586477
$187$	0.175253	+	3.31199i	0.0128158	+	0.242197i
$188$	1.30545			0.0952096
$189$	−18.7991	+	13.6583i	−1.36743	+	0.993496i
$190$	6.11501	+	18.8201i	0.443630	+	1.36535i
$191$	3.86448	−	11.8936i	0.279624	−	0.860594i	−0.708335	−	0.705877i	$-0.750553\pi$
$191$	3.86448	−	11.8936i	0.279624	−	0.860594i	0.987959	−	0.154717i	$-0.0494467\pi$
$192$	9.60679	+	6.97974i	0.693311	+	0.503720i
$193$	−9.53076	−	6.92450i	−0.686039	−	0.498437i	0.189317	−	0.981916i	$-0.439373\pi$
$193$	−9.53076	−	6.92450i	−0.686039	−	0.498437i	−0.875356	+	0.483480i	$0.839373\pi$
$194$	5.90073	−	18.1606i	0.423648	−	1.30385i
$195$	4.04986	+	12.4642i	0.290017	+	0.892580i
$196$	5.97501	−	4.34110i	0.426787	−	0.310079i
$197$	−2.10430			−0.149925			−0.0749626	−	0.997186i	$-0.523884\pi$
$197$	−2.10430			−0.149925			−0.0749626	+	0.997186i	$0.523884\pi$
$198$	−3.36331	+	1.29300i	−0.239020	+	0.0918898i
$199$	−12.3616			−0.876287			−0.438144	−	0.898905i	$-0.644364\pi$
$199$	−12.3616			−0.876287			−0.438144	+	0.898905i	$0.644364\pi$
$200$	−2.01485	+	1.46387i	−0.142471	+	0.103511i
$201$	3.65963	+	11.2632i	0.258130	+	0.794443i
$202$	1.21483	−	3.73887i	0.0854753	−	0.263066i
$203$	27.1699	+	19.7401i	1.90695	+	1.38548i
$204$	−0.861788	−	0.626126i	−0.0603372	−	0.0438376i
$205$	−6.93874	+	21.3553i	−0.484623	+	1.49152i
$206$	−5.23601	−	16.1148i	−0.364810	−	1.12277i
$207$	−1.01651	+	0.738536i	−0.0706522	+	0.0513318i
$208$	−7.42465			−0.514807
$209$	13.2422	−	20.4138i	0.915981	−	1.41205i
$210$	−15.7839			−1.08919
$211$	−5.74658	+	4.17514i	−0.395611	+	0.287428i	−0.767751	−	0.640748i	$-0.778624\pi$
$211$	−5.74658	+	4.17514i	−0.395611	+	0.287428i	0.372140	+	0.928177i	$0.378624\pi$
$212$	0.550917	+	1.69555i	0.0378371	+	0.116451i
$213$	1.80933	−	5.56853i	0.123973	−	0.381549i
$214$	−4.67901	−	3.39950i	−0.319851	−	0.232385i
$215$	−9.14399	−	6.64350i	−0.623615	−	0.453083i
$216$	5.37458	−	16.5413i	0.365694	−	1.12549i
$217$	−6.36999	−	19.6048i	−0.432423	−	1.33086i
$218$	5.48075	−	3.98200i	0.371203	−	0.269695i
$219$	−18.4193			−1.24466
$220$	5.77530	+	1.54436i	0.389371	+	0.104121i
$221$	3.81696			0.256757
$222$	2.05727	−	1.49469i	0.138075	−	0.100317i
$223$	8.13508	+	25.0372i	0.544766	+	1.67662i	0.721547	+	0.692366i	$0.243431\pi$
$223$	8.13508	+	25.0372i	0.544766	+	1.67662i	−0.176781	+	0.984250i	$0.556569\pi$
$224$	−5.04357	+	15.5225i	−0.336988	+	1.03714i
$225$	0.636191	+	0.462220i	0.0424127	+	0.0308147i
$226$	10.3510	+	7.52047i	0.688541	+	0.500254i
$227$	4.32442	−	13.3092i	0.287022	−	0.883362i	−0.698764	−	0.715353i	$-0.746266\pi$
$227$	4.32442	−	13.3092i	0.287022	−	0.883362i	0.985785	−	0.168009i	$-0.0537339\pi$
$228$	2.41500	+	7.43262i	0.159938	+	0.492237i
$229$	−1.77193	+	1.28738i	−0.117092	+	0.0850726i	−0.644790	−	0.764359i	$-0.723055\pi$
$229$	−1.77193	+	1.28738i	−0.117092	+	0.0850726i	0.527698	+	0.849432i	$0.323055\pi$
$230$	−3.49067			−0.230168
$231$	12.2217	+	15.0769i	0.804127	+	0.991988i
$232$	−25.1370			−1.65033
$233$	−18.4825	+	13.4283i	−1.21083	+	0.879718i	−0.995306	−	0.0967806i	$-0.969145\pi$
$233$	−18.4825	+	13.4283i	−1.21083	+	0.879718i	−0.215523	+	0.976499i	$0.569145\pi$
$234$	1.28145	+	3.94391i	0.0837713	+	0.257821i
$235$	1.30029	−	4.00187i	0.0848214	−	0.261053i
$236$	0.613690	+	0.445872i	0.0399478	+	0.0290238i
$237$	1.92716	+	1.40017i	0.125183	+	0.0909506i
$238$	−1.42055	+	4.37200i	−0.0920805	+	0.283395i
$239$	0.208498	+	0.641691i	0.0134866	+	0.0415076i	0.957573	−	0.288190i	$-0.0930533\pi$
$239$	0.208498	+	0.641691i	0.0134866	+	0.0415076i	−0.944087	+	0.329697i	$0.893053\pi$
$240$	5.40326	−	3.92570i	0.348779	−	0.253403i
$241$	−5.84839			−0.376728			−0.188364	−	0.982099i	$-0.560318\pi$
$241$	−5.84839			−0.376728			−0.188364	+	0.982099i	$0.560318\pi$
$242$	5.01796	+	11.2399i	0.322566	+	0.722529i
$243$	−9.64069			−0.618451
$244$	8.81535	−	6.40473i	0.564345	−	0.410021i
$245$	−7.35632	−	22.6404i	−0.469978	−	1.44644i
$246$	4.58863	−	14.1224i	0.292561	−	0.900409i
$247$	−22.6552	−	16.4600i	−1.44152	−	1.04732i
$248$	12.4824	+	9.06899i	0.792633	+	0.575882i
$249$	4.98332	−	15.3371i	0.315805	−	0.971948i
$250$	−3.49239	−	10.7485i	−0.220878	−	0.679793i
$251$	3.40358	−	2.47284i	0.214832	−	0.156084i	−0.475165	−	0.879897i	$-0.657612\pi$
$251$	3.40358	−	2.47284i	0.214832	−	0.156084i	0.689997	+	0.723812i	$0.257612\pi$
$252$	2.98259			0.187886
$253$	2.70287	+	3.33432i	0.169928	+	0.209627i
$254$	−6.58909			−0.413437
$255$	−2.77778	+	2.01817i	−0.173951	+	0.126383i
$256$	−4.67405	−	14.3852i	−0.292128	−	0.899077i
$257$	4.73129	−	14.5614i	0.295130	−	0.908316i	−0.688048	−	0.725665i	$-0.741532\pi$
$257$	4.73129	−	14.5614i	0.295130	−	0.908316i	0.983178	−	0.182651i	$-0.0584678\pi$
$258$	6.04698	+	4.39339i	0.376469	+	0.273520i
$259$	5.30200	+	3.85213i	0.329450	+	0.239360i
$260$	2.12606	−	6.54335i	0.131853	−	0.405801i
$261$	2.45268	+	7.54858i	0.151817	+	0.467245i
$262$	15.6003	−	11.3343i	0.963789	−	0.700234i
$263$	−17.8237			−1.09906			−0.549528	−	0.835476i	$-0.685192\pi$
$263$	−17.8237			−1.09906			−0.549528	+	0.835476i	$0.685192\pi$
$264$	−14.0338	−	3.75273i	−0.863719	−	0.230965i
$265$	5.74647			0.353003
$266$	27.2850	−	19.8237i	1.67295	−	1.21547i
$267$	−0.771684	−	2.37500i	−0.0472263	−	0.145348i
$268$	1.92120	−	5.91285i	0.117356	−	0.361185i
$269$	13.9414	+	10.1290i	0.850022	+	0.617577i	0.925152	−	0.379596i	$-0.123937\pi$
$269$	13.9414	+	10.1290i	0.850022	+	0.617577i	−0.0751298	+	0.997174i	$0.523937\pi$
$270$	−12.3430	−	8.96771i	−0.751171	−	0.545757i
$271$	4.20810	−	12.9512i	0.255624	−	0.786730i	−0.738082	−	0.674711i	$-0.764268\pi$
$271$	4.20810	−	12.9512i	0.255624	−	0.786730i	0.993706	−	0.112019i	$-0.0357317\pi$
$272$	−0.601091	−	1.84997i	−0.0364465	−	0.112171i
$273$	18.0704	−	13.1289i	1.09367	−	0.794597i
$274$	9.58944			0.579319
$275$	1.46194	−	2.25368i	0.0881583	−	0.135902i
$276$	−1.37857			−0.0829802
$277$	11.1048	−	8.06813i	0.667224	−	0.484767i	−0.201871	−	0.979412i	$-0.564702\pi$
$277$	11.1048	−	8.06813i	0.667224	−	0.484767i	0.869095	+	0.494645i	$0.164702\pi$
$278$	−0.0697394	−	0.214636i	−0.00418269	−	0.0128730i
$279$	1.50545	−	4.63331i	0.0901292	−	0.277389i
$280$	24.6322	+	17.8964i	1.47206	+	1.06951i
$281$	11.2167	+	8.14939i	0.669130	+	0.486152i	0.869734	−	0.493521i	$-0.164290\pi$
$281$	11.2167	+	8.14939i	0.669130	+	0.486152i	−0.200604	+	0.979672i	$0.564290\pi$
$282$	−0.859888	+	2.64646i	−0.0512056	+	0.157595i
$283$	−4.90643	−	15.1004i	−0.291657	−	0.897627i	−0.984324	−	0.176370i	$-0.943565\pi$
$283$	−4.90643	−	15.1004i	−0.291657	−	0.897627i	0.692667	−	0.721257i	$-0.256435\pi$
$284$	−2.48672	+	1.80671i	−0.147560	+	0.107209i
$285$	25.1903			1.49214
$286$	13.2226	−	5.08336i	0.781870	−	0.300585i
$287$	38.2692			2.25896
$288$	−3.12063	+	2.26727i	−0.183885	+	0.133600i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−6.81391	+	20.9711i	−0.400127	+	1.23146i
$291$	−19.6652	−	14.2876i	−1.15280	−	0.837556i
$292$	7.82287	+	5.68365i	0.457799	+	0.332610i
$293$	−4.21356	+	12.9680i	−0.246159	+	0.757598i	0.749285	+	0.662248i	$0.230397\pi$
$293$	−4.21356	+	12.9680i	−0.246159	+	0.757598i	−0.995444	+	0.0953507i	$0.969603\pi$
$294$	4.86478	+	14.9723i	0.283720	+	0.873200i
$295$	1.97809	−	1.43717i	0.115169	−	0.0836751i
$296$	−4.90531			−0.285115
$297$	0.991305	+	18.7340i	0.0575213	+	1.08706i
$298$	−9.36761			−0.542651
$299$	3.99633	−	2.90351i	0.231114	−	0.167914i
$300$	0.266617	+	0.820563i	0.0153932	+	0.0473752i
$301$	−5.95267	+	18.3204i	−0.343106	+	1.05597i
$302$	1.92637	+	1.39959i	0.110850	+	0.0805374i
$303$	−4.04864	−	2.94151i	−0.232589	−	0.168985i
$304$	−4.40994	+	13.5724i	−0.252928	+	0.778431i
$305$	−10.8533	−	33.4030i	−0.621458	−	1.91265i
$306$	−0.878942	+	0.638589i	−0.0502458	+	0.0365057i
$307$	26.3596			1.50442			0.752212	−	0.658922i	$-0.228987\pi$
$307$	26.3596			1.50442			0.752212	+	0.658922i	$0.228987\pi$
$308$	−0.538386	−	10.1746i	−0.0306774	−	0.579750i
$309$	−21.5693			−1.22703
$310$	10.9496	−	7.95535i	0.621896	−	0.451834i
$311$	2.98106	+	9.17475i	0.169040	+	0.520253i	0.999311	−	0.0371074i	$-0.0118144\pi$
$311$	2.98106	+	9.17475i	0.169040	+	0.520253i	−0.830271	+	0.557360i	$0.811814\pi$
$312$	−5.16625	+	15.9001i	−0.292482	+	0.900166i
$313$	0.370676	+	0.269312i	0.0209518	+	0.0152224i	0.598212	−	0.801338i	$-0.295878\pi$
$313$	0.370676	+	0.269312i	0.0209518	+	0.0152224i	−0.577260	+	0.816560i	$0.695878\pi$
$314$	−3.58545	−	2.60498i	−0.202339	−	0.147008i
$315$	2.97080	−	9.14319i	0.167386	−	0.515160i
$316$	−0.386437	−	1.18933i	−0.0217388	−	0.0669052i
$317$	−6.75163	+	4.90534i	−0.379209	+	0.275512i	−0.761019	−	0.648729i	$-0.775301\pi$
$317$	−6.75163	+	4.90534i	−0.379209	+	0.275512i	0.381810	+	0.924241i	$0.375301\pi$
$318$	−3.80018			−0.213103
$319$	25.3079	−	9.72947i	1.41697	−	0.544746i
$320$	−20.0934			−1.12326
$321$	−5.95624	+	4.32746i	−0.332445	+	0.241535i
$322$	1.83841	+	5.65804i	0.102451	+	0.315310i
$323$	2.26712	−	6.97749i	0.126146	−	0.388238i
$324$	−3.11251	−	2.26137i	−0.172917	−	0.125632i
$325$	−2.50114	−	1.81719i	−0.138738	−	0.100799i
$326$	2.37237	−	7.30142i	0.131394	−	0.404388i
$327$	−2.66491	−	8.20175i	−0.147370	−	0.453558i
$328$	−23.1735	+	16.8365i	−1.27954	+	0.929642i
$329$	−7.17147			−0.395376
$330$	−6.93494	+	10.6907i	−0.381756	+	0.588504i
$331$	−21.5435			−1.18414			−0.592070	−	0.805886i	$-0.701689\pi$
$331$	−21.5435			−1.18414			−0.592070	+	0.805886i	$0.701689\pi$
$332$	−6.84904	+	4.97612i	−0.375890	+	0.273100i
$333$	0.478623	+	1.47305i	0.0262284	+	0.0807227i
$334$	−6.37478	+	19.6196i	−0.348813	+	1.07354i
$335$	−16.2123	−	11.7789i	−0.885774	−	0.643552i
$336$	−9.20889	−	6.69065i	−0.502386	−	0.365005i
$337$	7.72754	−	23.7829i	0.420946	−	1.29554i	−0.485878	−	0.874027i	$-0.661500\pi$
$337$	7.72754	−	23.7829i	0.420946	−	1.29554i	0.906823	−	0.421511i	$-0.138500\pi$
$338$	−0.542625	−	1.67003i	−0.0295149	−	0.0908375i
$339$	13.1765	−	9.57332i	0.715652	−	0.519951i
$340$	1.80250			0.0977544
$341$	−16.0775	−	4.29923i	−0.870643	−	0.232816i
$342$	7.97068			0.431005
$343$	−9.55920	+	6.94516i	−0.516148	+	0.375004i
$344$	−4.45550	−	13.7126i	−0.240224	−	0.739334i
$345$	−1.37312	+	4.22603i	−0.0739263	+	0.227522i
$346$	10.3286	+	7.50420i	0.555272	+	0.403428i
$347$	−4.02774	−	2.92633i	−0.216220	−	0.157093i	0.474403	−	0.880308i	$-0.342664\pi$
$347$	−4.02774	−	2.92633i	−0.216220	−	0.157093i	−0.690624	+	0.723214i	$0.742664\pi$
$348$	−2.69102	+	8.28211i	−0.144254	+	0.443968i
$349$	7.44875	+	22.9249i	0.398722	+	1.22714i	0.926025	+	0.377463i	$0.123204\pi$
$349$	7.44875	+	22.9249i	0.398722	+	1.22714i	−0.527302	+	0.849678i	$0.676796\pi$
$350$	3.01227	−	2.18854i	0.161013	−	0.116983i
$351$	21.5903			1.15240
$352$	8.29769	+	10.2362i	0.442268	+	0.545592i
$353$	22.0768			1.17503			0.587515	−	0.809213i	$-0.300106\pi$
$353$	22.0768			1.17503			0.587515	+	0.809213i	$0.300106\pi$
$354$	−1.30812	+	0.950407i	−0.0695260	+	0.0505136i
$355$	3.06161	+	9.42266i	0.162493	+	0.500103i
$356$	−0.405112	+	1.24681i	−0.0214709	+	0.0660806i
$357$	4.73423	+	3.43962i	0.250562	+	0.182044i
$358$	−7.95390	−	5.77885i	−0.420377	−	0.305422i
$359$	−1.44518	+	4.44781i	−0.0762737	+	0.234746i	−0.981923	−	0.189282i	$-0.939384\pi$
$359$	−1.44518	+	4.44781i	−0.0762737	+	0.234746i	0.905649	+	0.424028i	$0.139384\pi$
$360$	2.22360	+	6.84355i	0.117194	+	0.360687i
$361$	−28.1741	+	20.4697i	−1.48285	+	1.07735i
$362$	−5.36226			−0.281834
$363$	15.5817	−	1.65363i	0.817826	−	0.0867932i
$364$	−11.7259			−0.614603
$365$	25.2153	−	18.3200i	1.31983	−	0.958910i
$366$	7.17735	+	22.0896i	0.375166	+	1.15464i
$367$	−1.96008	+	6.03251i	−0.102315	+	0.314895i	−0.989091	−	0.147306i	$-0.952940\pi$
$367$	−1.96008	+	6.03251i	−0.102315	+	0.314895i	0.886776	+	0.462200i	$0.152940\pi$
$368$	−2.03658	−	1.47966i	−0.106164	−	0.0771328i
$369$	7.31706	+	5.31615i	0.380911	+	0.276748i
$370$	−1.32969	+	4.09235i	−0.0691271	+	0.212751i
$371$	−3.02646	−	9.31448i	−0.157126	−	0.483584i
$372$	4.32433	−	3.14181i	0.224206	−	0.162895i
$373$	−2.32164			−0.120210			−0.0601051	−	0.998192i	$-0.519144\pi$
$373$	−2.32164			−0.120210			−0.0601051	+	0.998192i	$0.519144\pi$
$374$	2.33709	+	2.88308i	0.120848	+	0.149081i
$375$	−14.3866			−0.742921
$376$	4.34260	−	3.15509i	0.223953	−	0.162711i
$377$	−9.64256	−	29.6767i	−0.496617	−	1.52843i
$378$	−8.03520	+	24.7298i	−0.413286	+	1.27196i
$379$	−21.1520	−	15.3678i	−1.08651	−	0.789392i	−0.107699	−	0.994184i	$-0.534348\pi$
$379$	−21.1520	−	15.3678i	−1.08651	−	0.789392i	−0.978806	+	0.204791i	$0.934348\pi$
$380$	−10.6986	−	7.77297i	−0.548826	−	0.398745i
$381$	−2.59195	+	7.97719i	−0.132789	+	0.408684i
$382$	−4.32441	−	13.3092i	−0.221256	−	0.680956i
$383$	−7.35273	+	5.34207i	−0.375707	+	0.272967i	−0.759574	−	0.650421i	$-0.774592\pi$
$383$	−7.35273	+	5.34207i	−0.375707	+	0.272967i	0.383866	+	0.923389i	$0.374592\pi$
$384$	1.96907			0.100484
$385$	−31.7266	−	8.48392i	−1.61694	−	0.432381i
$386$	−13.1827			−0.670984
$387$	−3.68312	+	2.67595i	−0.187224	+	0.136026i
$388$	3.94330	+	12.1362i	0.200191	+	0.616123i
$389$	−10.7541	+	33.0978i	−0.545256	+	1.67813i	0.175124	+	0.984546i	$0.443967\pi$
$389$	−10.7541	+	33.0978i	−0.545256	+	1.67813i	−0.720380	+	0.693580i	$0.756033\pi$
$390$	11.8646	+	8.62010i	0.600785	+	0.436496i
$391$	1.04699	+	0.760685i	0.0529487	+	0.0384695i
$392$	9.38418	−	28.8815i	0.473972	−	1.45874i
$393$	−7.58534	−	23.3453i	−0.382630	−	1.17761i
$394$	−1.90503	+	1.38408i	−0.0959738	+	0.0697291i
$395$	−4.03083			−0.202813
$396$	1.31046	−	2.02016i	0.0658530	−	0.101517i
$397$	−1.35056			−0.0677826			−0.0338913	−	0.999426i	$-0.510790\pi$
$397$	−1.35056			−0.0677826			−0.0338913	+	0.999426i	$0.510790\pi$
$398$	−11.1909	+	8.13069i	−0.560951	+	0.407555i
$399$	−13.2668	−	40.8310i	−0.664171	−	2.04411i
$400$	−0.486859	+	1.49840i	−0.0243430	+	0.0749199i
$401$	−3.10955	−	2.25922i	−0.155284	−	0.112820i	0.507430	−	0.861693i	$-0.330595\pi$
$401$	−3.10955	−	2.25922i	−0.155284	−	0.112820i	−0.662714	+	0.748873i	$0.730595\pi$
$402$	10.7213	+	7.78949i	0.534730	+	0.388504i
$403$	−5.91860	+	18.2156i	−0.294826	+	0.907382i
$404$	0.811839	+	2.49858i	0.0403905	+	0.124309i
$405$	−10.0325	+	7.28901i	−0.498517	+	0.362194i
$406$	37.5808			1.86510
$407$	4.93865	−	1.89864i	0.244800	−	0.0941118i
$408$	−4.38001			−0.216843
$409$	4.06864	−	2.95604i	0.201182	−	0.146167i	−0.482633	−	0.875823i	$-0.660320\pi$
$409$	4.06864	−	2.95604i	0.201182	−	0.146167i	0.683815	+	0.729656i	$0.260320\pi$
$410$	7.76455	+	23.8968i	0.383464	+	1.18018i
$411$	3.77219	−	11.6096i	0.186068	−	0.572659i
$412$	9.16071	+	6.65564i	0.451316	+	0.327900i
$413$	−3.37130	−	2.44939i	−0.165891	−	0.120527i
$414$	−0.434481	+	1.33720i	−0.0213536	+	0.0657196i
$415$	8.43241	+	25.9523i	0.413931	+	1.27395i
$416$	12.2686	−	8.91363i	0.601516	−	0.437027i
$417$	−0.287286			−0.0140684
$418$	−1.43878	−	27.1905i	−0.0703731	−	1.32993i
$419$	−3.08657			−0.150789			−0.0753945	−	0.997154i	$-0.524022\pi$
$419$	−3.08657			−0.150789			−0.0753945	+	0.997154i	$0.524022\pi$
$420$	8.53346	−	6.19992i	0.416390	−	0.302525i
$421$	−2.25853	−	6.95103i	−0.110074	−	0.338772i	0.880814	−	0.473463i	$-0.156996\pi$
$421$	−2.25853	−	6.95103i	−0.110074	−	0.338772i	−0.990888	+	0.134690i	$0.956996\pi$
$422$	−2.45624	+	7.55952i	−0.119568	+	0.367992i
$423$	−1.37118	−	0.996222i	−0.0666691	−	0.0484380i
$424$	5.93054	+	4.30879i	0.288012	+	0.209253i
$425$	0.250291	−	0.770317i	0.0121409	−	0.0373658i
$426$	−2.02466	−	6.23127i	−0.0980952	−	0.301906i
$427$	−48.4271	+	35.1843i	−2.34355	+	1.70269i
$428$	3.86500			0.186822
$429$	−0.952880	−	18.0078i	−0.0460055	−	0.869425i
$430$	−12.6478			−0.609930
$431$	−26.2151	+	19.0464i	−1.26274	+	0.917434i	−0.998889	−	0.0471300i	$-0.984993\pi$
$431$	−26.2151	+	19.0464i	−1.26274	+	0.917434i	−0.263850	+	0.964564i	$0.584993\pi$
$432$	−3.40002	−	10.4642i	−0.163583	−	0.503458i
$433$	−2.39913	+	7.38377i	−0.115295	+	0.354841i	−0.992008	−	0.126172i	$-0.959731\pi$
$433$	−2.39913	+	7.38377i	−0.115295	+	0.354841i	0.876714	+	0.481013i	$0.159731\pi$
$434$	−18.6616	−	13.5585i	−0.895787	−	0.650827i
$435$	22.7086	+	16.4987i	1.08879	+	0.791054i
$436$	−1.39900	+	4.30569i	−0.0670001	+	0.206205i
$437$	−2.93401	−	9.02995i	−0.140353	−	0.431961i
$438$	−16.6750	+	12.1151i	−0.796763	+	0.578882i
$439$	−5.96173			−0.284538			−0.142269	−	0.989828i	$-0.545440\pi$
$439$	−5.96173			−0.284538			−0.142269	+	0.989828i	$0.545440\pi$
$440$	22.9442	−	8.82075i	1.09382	−	0.420513i
$441$	−9.58868			−0.456604
$442$	3.45550	−	2.51057i	0.164362	−	0.119416i
$443$	1.33343	+	4.10389i	0.0633534	+	0.194982i	0.977723	−	0.209898i	$-0.0673133\pi$
$443$	1.33343	+	4.10389i	0.0633534	+	0.194982i	−0.914370	+	0.404880i	$0.867313\pi$
$444$	−0.525133	+	1.61619i	−0.0249217	+	0.0767012i
$445$	3.41860	+	2.48375i	0.162057	+	0.117741i
$446$	23.8327	+	17.3155i	1.12851	+	0.819911i
$447$	−3.68493	+	11.3410i	−0.174291	+	0.536413i
$448$	10.5825	+	32.5695i	0.499975	+	1.53877i
$449$	28.7466	−	20.8856i	1.35663	−	0.985653i	0.357983	−	0.933728i	$-0.383464\pi$
$449$	28.7466	−	20.8856i	1.35663	−	0.985653i	0.998651	−	0.0519245i	$-0.0165355\pi$
$450$	0.879965			0.0414820
$451$	16.8143	−	25.9204i	0.791754	−	1.22055i
$452$	−8.55027			−0.402171
$453$	2.45221	−	1.78164i	0.115215	−	0.0837086i
$454$	−4.83909	−	14.8932i	−0.227110	−	0.698971i
$455$	−11.6795	+	35.9459i	−0.547544	+	1.68517i
$456$	25.9971	+	18.8880i	1.21743	+	0.884513i
$457$	−3.66758	−	2.66466i	−0.171562	−	0.124647i	0.498691	−	0.866780i	$-0.333814\pi$
$457$	−3.66758	−	2.66466i	−0.171562	−	0.124647i	−0.670253	+	0.742133i	$0.733814\pi$
$458$	−0.757368	+	2.33094i	−0.0353895	+	0.108918i
$459$	1.74793	+	5.37956i	0.0815862	+	0.251096i
$460$	1.88721	−	1.37114i	0.0879915	−	0.0639296i
$461$	27.7415			1.29205			0.646026	−	0.763316i	$-0.276430\pi$
$461$	27.7415			1.29205			0.646026	+	0.763316i	$0.276430\pi$
$462$	20.9810	+	5.61047i	0.976124	+	0.261023i
$463$	32.1332			1.49336			0.746679	−	0.665185i	$-0.231647\pi$
$463$	32.1332			1.49336			0.746679	+	0.665185i	$0.231647\pi$
$464$	−12.8649	+	9.34692i	−0.597240	+	0.433920i
$465$	−5.32403	−	16.3857i	−0.246896	−	0.759868i
$466$	−7.89989	+	24.3134i	−0.365955	+	1.12629i
$467$	11.3472	+	8.24425i	0.525087	+	0.381498i	0.818517	−	0.574482i	$-0.194797\pi$
$467$	11.3472	+	8.24425i	0.525087	+	0.381498i	−0.293430	+	0.955981i	$0.594797\pi$
$468$	−2.24198	−	1.62889i	−0.103636	−	0.0752957i
$469$	−10.5541	+	32.4822i	−0.487343	+	1.49989i
$470$	−1.45504	−	4.47815i	−0.0671160	−	0.206562i
$471$	−4.56416	+	3.31606i	−0.210306	+	0.152796i
$472$	3.11906			0.143566
$473$	9.79334	+	12.0813i	0.450298	+	0.555498i
$474$	2.66561			0.122436
$475$	−4.80743	+	3.49280i	−0.220580	+	0.160261i
$476$	−0.949313	−	2.92169i	−0.0435117	−	0.133915i
$477$	0.715260	−	2.20134i	0.0327495	−	0.100793i
$478$	0.610820	+	0.443787i	0.0279383	+	0.0202983i
$479$	−11.2738	−	8.19087i	−0.515112	−	0.374250i	0.299648	−	0.954050i	$-0.403131\pi$
$479$	−11.2738	−	8.19087i	−0.515112	−	0.374250i	−0.814759	+	0.579799i	$0.803131\pi$
$480$	−4.21542	+	12.9737i	−0.192407	+	0.592166i
$481$	−1.88168	−	5.79120i	−0.0857970	−	0.264056i
$482$	−5.29456	+	3.84672i	−0.241160	+	0.175213i
$483$	7.57317			0.344591
$484$	−7.12797	−	4.10573i	−0.323999	−	0.186624i
$485$	41.1315			1.86768
$486$	−8.72774	+	6.34107i	−0.395898	+	0.287637i
$487$	5.07367	+	15.6152i	0.229910	+	0.707591i	0.997756	+	0.0669559i	$0.0213287\pi$
$487$	5.07367	+	15.6152i	0.229910	+	0.707591i	−0.767846	+	0.640635i	$0.778671\pi$
$488$	13.8451	−	42.6109i	0.626740	−	1.92891i
$489$	−7.90636	−	5.74430i	−0.357538	−	0.259766i
$490$	−21.5512	−	15.6579i	−0.973585	−	0.707351i
$491$	4.28579	−	13.1903i	0.193415	−	0.595270i	−0.806576	−	0.591130i	$-0.798682\pi$
$491$	4.28579	−	13.1903i	0.193415	−	0.595270i	0.999991	−	0.00414044i	$-0.00131795\pi$
$492$	3.06646	+	9.43759i	0.138247	+	0.425479i
$493$	6.61378	−	4.80519i	0.297870	−	0.216415i
$494$	−31.3362			−1.40988
$495$	−4.88757	−	6.02940i	−0.219680	−	0.271002i
$496$	9.76060			0.438264
$497$	13.6608	−	9.92516i	0.612771	−	0.445204i
$498$	−5.57640	−	17.1624i	−0.249885	−	0.769066i
$499$	6.03599	−	18.5769i	0.270208	−	0.831614i	−0.720240	−	0.693725i	$-0.755968\pi$
$499$	6.03599	−	18.5769i	0.270208	−	0.831614i	0.990448	−	0.137889i	$-0.0440318\pi$
$500$	6.11015	+	4.43928i	0.273254	+	0.198531i
$501$	21.2451	+	15.4355i	0.949161	+	0.689606i
$502$	1.45478	−	4.47734i	0.0649298	−	0.199833i
$503$	−7.66909	−	23.6030i	−0.341948	−	1.05241i	−0.963198	−	0.268794i	$-0.913375\pi$
$503$	−7.66909	−	23.6030i	−0.341948	−	1.05241i	0.621250	−	0.783613i	$-0.286625\pi$
$504$	9.92166	−	7.20851i	0.441946	−	0.321092i
$505$	8.46808			0.376825
$506$	4.64003	+	1.24078i	0.206275	+	0.0551593i
$507$	−2.23530			−0.0992730
$508$	3.56235	−	2.58820i	0.158054	−	0.114833i
$509$	3.41797	+	10.5194i	0.151499	+	0.466265i	0.997789	−	0.0664564i	$-0.0211693\pi$
$509$	3.41797	+	10.5194i	0.151499	+	0.466265i	−0.846291	+	0.532721i	$0.821169\pi$
$510$	−1.18729	+	3.65411i	−0.0525742	+	0.161807i
$511$	−42.9749	−	31.2231i	−1.90110	−	1.38123i
$512$	−15.9298	−	11.5737i	−0.704005	−	0.511489i
$513$	12.8238	−	39.4675i	0.566183	−	1.74253i
$514$	−5.29438	−	16.2944i	−0.233525	−	0.718716i
$515$	29.5275	−	21.4530i	1.30114	−	0.945330i
$516$	−4.99499			−0.219892
$517$	−3.15092	+	4.85737i	−0.138577	+	0.213627i
$518$	7.33361			0.322220
$519$	13.1480	−	9.55262i	0.577135	−	0.419313i
$520$	−8.74196	−	26.9050i	−0.383360	−	1.17986i
$521$	5.41798	−	16.6748i	0.237366	−	0.730538i	−0.759433	−	0.650586i	$-0.774523\pi$
$521$	5.41798	−	16.6748i	0.237366	−	0.730538i	0.996799	−	0.0799518i	$-0.0254767\pi$
$522$	7.18542	+	5.22051i	0.314497	+	0.228496i
$523$	15.5254	+	11.2799i	0.678880	+	0.493235i	0.872986	−	0.487746i	$-0.162181\pi$
$523$	15.5254	+	11.2799i	0.678880	+	0.493235i	−0.194106	+	0.980981i	$0.562181\pi$
$524$	−3.98209	+	12.2556i	−0.173958	+	0.535389i
$525$	−1.46466	−	4.50776i	−0.0639230	−	0.196735i
$526$	−16.1358	+	11.7233i	−0.703555	+	0.511162i
$527$	−5.01786			−0.218581
$528$	−8.57779	+	3.29768i	−0.373300	+	0.143513i
$529$	−21.3252			−0.927181
$530$	5.20229	−	3.77968i	0.225973	−	0.164179i
$531$	−0.304334	−	0.936645i	−0.0132070	−	0.0406469i
$532$	−6.96470	+	21.4351i	−0.301958	+	0.929331i
$533$	−28.7665	−	20.9001i	−1.24602	−	0.905284i
$534$	−2.26074	−	1.64252i	−0.0978317	−	0.0710789i
$535$	3.84972	−	11.8482i	0.166438	−	0.512244i
$536$	−7.89960	−	24.3125i	−0.341211	−	1.05014i
$537$	−10.1251	+	7.35630i	−0.436929	+	0.317448i
$538$	19.2834			0.831368
$539$	1.73085	+	32.7100i	0.0745528	+	1.40892i
$540$	10.1957			0.438752
$541$	−15.4796	+	11.2466i	−0.665521	+	0.483530i	−0.868523	−	0.495649i	$-0.834930\pi$
$541$	−15.4796	+	11.2466i	−0.665521	+	0.483530i	0.203002	+	0.979178i	$0.434930\pi$
$542$	−4.70893	−	14.4926i	−0.202266	−	0.622510i
$543$	−2.10935	+	6.49191i	−0.0905208	+	0.278594i
$544$	3.21422	+	2.33527i	0.137809	+	0.100124i
$545$	11.8057	+	8.57733i	0.505700	+	0.367412i
$546$	7.72374	−	23.7712i	0.330545	−	1.01731i
$547$	−0.636688	−	1.95953i	−0.0272228	−	0.0837833i	0.936522	−	0.350609i	$-0.114025\pi$
$547$	−0.636688	−	1.95953i	−0.0272228	−	0.0837833i	−0.963745	+	0.266825i	$0.914025\pi$
$548$	−5.18447	+	3.76674i	−0.221470	+	0.160907i
$549$	−14.1468			−0.603773
$550$	−0.158842	−	3.00184i	−0.00677304	−	0.127999i
$551$	−59.9770			−2.55511
$552$	−4.58584	+	3.33181i	−0.195186	+	0.141811i
$553$	2.12289	+	6.53359i	0.0902745	+	0.277836i
$554$	4.74649	−	14.6082i	0.201659	−	0.620642i
$555$	4.43141	+	3.21961i	0.188103	+	0.136665i
$556$	0.122013	+	0.0886479i	0.00517452	+	0.00375951i
$557$	−6.60520	+	20.3287i	−0.279871	+	0.861355i	0.708018	+	0.706194i	$0.249589\pi$
$557$	−6.60520	+	20.3287i	−0.279871	+	0.861355i	−0.987889	+	0.155161i	$0.950411\pi$
$558$	−1.68463	−	5.18474i	−0.0713159	−	0.219488i
$559$	14.4800	−	10.5203i	0.612437	−	0.444962i
$560$	19.2612			0.813933
$561$	4.40978	−	1.69532i	0.186181	−	0.0715763i
$562$	15.5146			0.654446
$563$	−14.5866	+	10.5978i	−0.614750	+	0.446642i	−0.851084	−	0.525030i	$-0.824054\pi$
$563$	−14.5866	+	10.5978i	−0.614750	+	0.446642i	0.236333	+	0.971672i	$0.424054\pi$
$564$	−0.574640	−	1.76856i	−0.0241967	−	0.0744698i
$565$	−8.51646	+	26.2110i	−0.358290	+	1.10270i
$566$	−14.3740	−	10.4433i	−0.604182	−	0.438964i
$567$	17.0985	+	12.4228i	0.718071	+	0.521709i
$568$	−3.90558	+	12.0201i	−0.163874	+	0.504353i
$569$	5.37103	+	16.5303i	0.225165	+	0.692988i	0.998275	+	0.0587150i	$0.0187003\pi$
$569$	5.37103	+	16.5303i	0.225165	+	0.692988i	−0.773109	+	0.634273i	$0.781300\pi$
$570$	22.8048	−	16.5687i	0.955188	−	0.693984i
$571$	11.8005			0.493835			0.246918	−	0.969036i	$-0.420582\pi$
$571$	11.8005			0.493835			0.246918	+	0.969036i	$0.420582\pi$
$572$	−5.15198	+	7.94214i	−0.215415	+	0.332078i
$573$	−17.8140			−0.744192
$574$	34.6452	−	25.1712i	1.44606	−	1.05063i
$575$	−0.323915	−	0.996909i	−0.0135082	−	0.0415740i
$576$	−2.50102	+	7.69734i	−0.104209	+	0.320722i
$577$	0.392811	+	0.285394i	0.0163530	+	0.0118811i	0.595932	−	0.803035i	$-0.296783\pi$
$577$	0.392811	+	0.285394i	0.0163530	+	0.0118811i	−0.579579	+	0.814916i	$0.696783\pi$
$578$	0.905302	+	0.657740i	0.0376556	+	0.0273584i
$579$	−5.18568	+	15.9599i	−0.215510	+	0.663270i
$580$	−4.55355	−	14.0144i	−0.189076	−	0.581916i
$581$	37.6251	−	27.3363i	1.56095	−	1.13410i
$582$	−27.2005			−1.12750
$583$	−7.63859	−	2.04262i	−0.316358	−	0.0845965i
$584$	39.7595			1.64526
$585$	−7.22652	+	5.25037i	−0.298780	+	0.217076i
$586$	4.71503	+	14.5114i	0.194776	+	0.599459i
$587$	−7.10914	+	21.8797i	−0.293426	+	0.903071i	0.690320	+	0.723504i	$0.257470\pi$
$587$	−7.10914	+	21.8797i	−0.293426	+	0.903071i	−0.983746	+	0.179567i	$0.942530\pi$
$588$	−8.51123	−	6.18377i	−0.350997	−	0.255014i
$589$	29.7830	+	21.6386i	1.22719	+	0.891604i
$590$	0.845486	−	2.60214i	0.0348081	−	0.107128i
$591$	0.926283	+	2.85080i	0.0381022	+	0.117266i
$592$	−2.51050	+	1.82398i	−0.103181	+	0.0749653i
$593$	9.05044			0.371657			0.185829	−	0.982582i	$-0.440503\pi$
$593$	9.05044			0.371657			0.185829	+	0.982582i	$0.440503\pi$
$594$	13.2195	+	16.3079i	0.542403	+	0.669120i
$595$	−9.90203			−0.405944
$596$	5.06454	−	3.67961i	0.207452	−	0.150723i
$597$	5.44138	+	16.7468i	0.222701	+	0.685403i
$598$	1.70814	−	5.25710i	0.0698509	−	0.214979i
$599$	−32.4647	−	23.5870i	−1.32647	−	0.963739i	−0.999827	−	0.0185922i	$-0.994082\pi$
$599$	−32.4647	−	23.5870i	−1.32647	−	0.963739i	−0.326646	−	0.945147i	$-0.605918\pi$
$600$	2.87009	+	2.08524i	0.117171	+	0.0851298i
$601$	−1.13251	+	3.48551i	−0.0461960	+	0.142177i	−0.971494	−	0.237064i	$-0.923815\pi$
$601$	−1.13251	+	3.48551i	−0.0461960	+	0.142177i	0.925298	+	0.379241i	$0.123815\pi$
$602$	6.66113	+	20.5008i	0.271487	+	0.835552i
$603$	−6.53019	+	4.74446i	−0.265930	+	0.193209i
$604$	−1.59124			−0.0647467
$605$	−19.6860	+	17.7614i	−0.800348	+	0.722104i
$606$	−5.60000			−0.227484
$607$	17.3058	−	12.5734i	0.702419	−	0.510337i	−0.178300	−	0.983976i	$-0.557060\pi$
$607$	17.3058	−	12.5734i	0.702419	−	0.510337i	0.880719	+	0.473639i	$0.157060\pi$
$608$	−9.00727	−	27.7215i	−0.365293	−	1.12426i
$609$	14.7831	−	45.4977i	0.599042	−	1.84366i
$610$	−31.7960	−	23.1012i	−1.28738	−	0.935338i
$611$	5.39071	+	3.91658i	0.218085	+	0.158448i
$612$	0.224356	−	0.690498i	0.00906907	−	0.0279117i
$613$	12.0580	+	37.1106i	0.487017	+	1.49888i	0.829039	+	0.559191i	$0.188888\pi$
$613$	12.0580	+	37.1106i	0.487017	+	1.49888i	−0.342022	+	0.939692i	$0.611112\pi$
$614$	23.8634	−	17.3378i	0.963049	−	0.699696i
$615$	31.9854			1.28978
$616$	−26.3815	−	32.5447i	−1.06294	−	1.31126i
$617$	17.7677			0.715300			0.357650	−	0.933856i	$-0.383578\pi$
$617$	17.7677			0.715300			0.357650	+	0.933856i	$0.383578\pi$
$618$	−19.5267	+	14.1870i	−0.785479	+	0.570684i
$619$	−2.08192	−	6.40751i	−0.0836796	−	0.257539i	0.900459	−	0.434941i	$-0.143231\pi$
$619$	−2.08192	−	6.40751i	−0.0836796	−	0.257539i	−0.984139	+	0.177402i	$0.943231\pi$
$620$	−2.79497	+	8.60202i	−0.112249	+	0.345466i
$621$	5.92222	+	4.30274i	0.237650	+	0.172663i
$622$	8.73336	+	6.34516i	0.350176	+	0.254418i
$623$	2.22548	−	6.84932i	0.0891620	−	0.274412i
$624$	3.26823	+	10.0586i	0.130834	+	0.402665i
$625$	22.9710	−	16.6894i	0.918841	−	0.667577i
$626$	0.512711			0.0204920
$627$	−33.4846	−	8.95403i	−1.33725	−	0.357589i
$628$	2.96169			0.118184
$629$	1.29063	−	0.937698i	0.0514608	−	0.0373885i
$630$	−3.32437	−	10.2314i	−0.132446	−	0.407627i
$631$	−8.02856	+	24.7094i	−0.319612	+	0.983664i	0.654202	+	0.756320i	$0.273004\pi$
$631$	−8.02856	+	24.7094i	−0.319612	+	0.983664i	−0.973814	+	0.227345i	$0.926996\pi$
$632$	−4.15994	−	3.02237i	−0.165474	−	0.120224i
$633$	8.18584	+	5.94736i	0.325358	+	0.236386i
$634$	−2.88582	+	8.88163i	−0.114610	+	0.352735i
$635$	−4.38590	−	13.4984i	−0.174049	−	0.535668i
$636$	2.05454	−	1.49271i	0.0814679	−	0.0591899i
$637$	37.6973			1.49362
$638$	16.5118	−	25.4541i	0.653708	−	1.00774i
$639$	3.99069			0.157869
$640$	−2.69558	+	1.95846i	−0.106552	+	0.0774147i
$641$	0.124103	+	0.381950i	0.00490177	+	0.0150861i	0.953477	−	0.301464i	$-0.0974754\pi$
$641$	0.124103	+	0.381950i	0.00490177	+	0.0150861i	−0.948576	+	0.316550i	$0.897475\pi$
$642$	−2.54585	+	7.83531i	−0.100477	+	0.309235i
$643$	−38.6210	−	28.0598i	−1.52306	−	1.10657i	−0.959943	−	0.280197i	$-0.909600\pi$
$643$	−38.6210	−	28.0598i	−1.52306	−	1.10657i	−0.563121	−	0.826374i	$-0.690400\pi$
$644$	−3.21641	−	2.33686i	−0.126744	−	0.0920851i
$645$	−4.97524	+	15.3122i	−0.195900	+	0.602918i
$646$	−2.53694	−	7.80791i	−0.0998147	−	0.307198i
$647$	−31.6531	+	22.9974i	−1.24441	+	0.904119i	−0.997884	−	0.0650160i	$-0.979290\pi$
$647$	−31.6531	+	22.9974i	−1.24441	+	0.904119i	−0.246529	+	0.969135i	$0.579290\pi$
$648$	−15.8192			−0.621438
$649$	−3.14026	+	1.20725i	−0.123266	+	0.0473889i
$650$	−3.45953			−0.135694
$651$	−23.7557	+	17.2595i	−0.931059	+	0.676454i
$652$	1.58539	+	4.87934i	0.0620888	+	0.191090i
$653$	2.14039	−	6.58745i	0.0837600	−	0.257787i	−0.900402	−	0.435059i	$-0.856727\pi$
$653$	2.14039	−	6.58745i	0.0837600	−	0.257787i	0.984162	+	0.177272i	$0.0567274\pi$
$654$	−7.80717	−	5.67224i	−0.305284	−	0.221802i
$655$	33.6034	+	24.4143i	1.31299	+	0.953946i
$656$	−5.59954	+	17.2336i	−0.218625	+	0.672859i
$657$	−3.87943	−	11.9397i	−0.151351	−	0.465811i
$658$	−6.49235	+	4.71697i	−0.253098	+	0.183887i
$659$	−46.6797			−1.81838			−0.909191	−	0.416379i	$-0.863299\pi$
$659$	−46.6797			−1.81838			−0.909191	+	0.416379i	$0.863299\pi$
$660$	−0.449983	−	8.50391i	−0.0175156	−	0.331014i
$661$	−9.83818			−0.382661			−0.191330	−	0.981526i	$-0.561280\pi$
$661$	−9.83818			−0.382661			−0.191330	+	0.981526i	$0.561280\pi$
$662$	−19.5034	+	14.1701i	−0.758022	+	0.550735i
$663$	−1.68017	−	5.17104i	−0.0652525	−	0.200827i
$664$	−10.7569	+	33.1063i	−0.417448	+	1.28477i
$665$	58.7726	+	42.7008i	2.27910	+	1.65587i
$666$	1.40218	+	1.01875i	0.0543335	+	0.0394756i
$667$	3.26934	−	10.0620i	0.126589	−	0.389602i
$668$	−4.26009	−	13.1112i	−0.164828	−	0.507288i
$669$	30.3383	−	22.0420i	1.17295	−	0.852195i
$670$	−22.4245			−0.866335
$671$	2.55364	+	48.2594i	0.0985821	+	1.86303i
$672$	23.2493			0.896860
$673$	35.6813	−	25.9240i	1.37541	−	0.999297i	0.378122	−	0.925756i	$-0.376570\pi$
$673$	35.6813	−	25.9240i	1.37541	−	0.999297i	0.997292	−	0.0735412i	$-0.0234300\pi$
$674$	−8.64722	−	26.6134i	−0.333079	−	1.02511i
$675$	1.41575	−	4.35722i	0.0544922	−	0.167710i
$676$	0.949355	+	0.689747i	0.0365136	+	0.0265287i
$677$	−4.71215	−	3.42358i	−0.181103	−	0.131579i	0.493540	−	0.869723i	$-0.335702\pi$
$677$	−4.71215	−	3.42358i	−0.181103	−	0.131579i	−0.674643	+	0.738144i	$0.735702\pi$
$678$	5.63199	−	17.3335i	0.216295	−	0.665689i
$679$	−21.6625	−	66.6703i	−0.831330	−	2.55857i
$680$	5.99606	−	4.35639i	0.229938	−	0.167060i
$681$	−19.9342			−0.763880
$682$	−17.3827	+	6.68269i	−0.665619	+	0.255893i
$683$	16.3840			0.626917			0.313458	−	0.949602i	$-0.398512\pi$
$683$	16.3840			0.626917			0.313458	+	0.949602i	$0.398512\pi$
$684$	−4.30930	+	3.13089i	−0.164770	+	0.119712i
$685$	6.38302	+	19.6449i	0.243883	+	0.750594i
$686$	−4.08585	+	12.5749i	−0.155998	+	0.480113i
$687$	2.52406	+	1.83384i	0.0962990	+	0.0699653i
$688$	−7.37917	−	5.36128i	−0.281328	−	0.204397i
$689$	−2.81200	+	8.65444i	−0.107129	+	0.329708i
$690$	1.53654	+	4.72899i	0.0584951	+	0.180030i
$691$	−20.3229	+	14.7654i	−0.773119	+	0.561704i	−0.902906	−	0.429838i	$-0.858571\pi$
$691$	−20.3229	+	14.7654i	−0.773119	+	0.561704i	0.129787	+	0.991542i	$0.458571\pi$
$692$	−8.53178			−0.324329
$693$	−7.19899	+	11.0978i	−0.273467	+	0.421569i
$694$	−5.57108			−0.211475
$695$	0.393282	−	0.285736i	0.0149180	−	0.0108386i
$696$	11.0650	+	34.0544i	0.419416	+	1.29083i
$697$	2.87869	−	8.85968i	0.109038	−	0.335584i
$698$	21.8220	+	15.8546i	0.825974	+	0.600105i
$699$	26.3278	+	19.1282i	0.995808	+	0.723497i
$700$	−0.768905	+	2.36645i	−0.0290619	+	0.0894432i
$701$	−0.846476	−	2.60519i	−0.0319710	−	0.0983965i	0.933798	−	0.357802i	$-0.116474\pi$
$701$	−0.846476	−	2.60519i	−0.0319710	−	0.0983965i	−0.965769	+	0.259405i	$0.916474\pi$
$702$	19.5457	−	14.2008i	0.737706	−	0.535975i
$703$	−11.7041			−0.441427
$704$	26.7095	+	7.14232i	1.00665	+	0.269186i
$705$	−5.99392			−0.225744
$706$	19.9862	−	14.5208i	0.752190	−	0.546498i
$707$	−4.45983	−	13.7260i	−0.167729	−	0.516218i
$708$	0.333908	−	1.02766i	0.0125490	−	0.0386220i
$709$	37.9908	+	27.6019i	1.42677	+	1.03661i	0.990606	+	0.136746i	$0.0436645\pi$
$709$	37.9908	+	27.6019i	1.42677	+	1.03661i	0.436168	+	0.899865i	$0.356335\pi$
$710$	8.96934	+	6.51661i	0.336613	+	0.244564i
$711$	−0.501715	+	1.54412i	−0.0188158	+	0.0579090i
$712$	1.66574	+	5.12663i	0.0624263	+	0.192128i
$713$	−5.25366	+	3.81701i	−0.196751	+	0.142948i
$714$	6.54828			0.245063
$715$	19.2151	+	23.7042i	0.718606	+	0.886487i
$716$	6.57016			0.245539
$717$	0.777555	−	0.564927i	0.0290383	−	0.0210976i
$718$	1.61718	+	4.97716i	0.0603525	+	0.185746i
$719$	0.212162	−	0.652966i	0.00791229	−	0.0243515i	−0.947022	−	0.321167i	$-0.895925\pi$
$719$	0.212162	−	0.652966i	0.00791229	−	0.0243515i	0.954935	+	0.296816i	$0.0959248\pi$
$720$	3.68272	+	2.67566i	0.137247	+	0.0997158i
$721$	−50.3243	−	36.5627i	−1.87417	−	1.36167i
$722$	−12.0423	+	37.0625i	−0.448170	+	1.37932i
$723$	2.57438	+	7.92312i	0.0957421	+	0.294664i
$724$	2.89907	−	2.10630i	0.107743	−	0.0782800i
$725$	−6.62148			−0.245915
$726$	13.0185	−	11.7457i	0.483160	−	0.435925i
$727$	13.9595			0.517730			0.258865	−	0.965914i	$-0.416652\pi$
$727$	13.9595			0.517730			0.258865	+	0.965914i	$0.416652\pi$
$728$	−39.0064	+	28.3398i	−1.44567	+	1.05034i
$729$	9.01313	+	27.7396i	0.333820	+	1.02739i
$730$	10.7776	−	33.1702i	0.398898	−	1.22768i
$731$	3.79358	+	2.75620i	0.140311	+	0.101942i
$732$	−12.5572	−	9.12335i	−0.464128	−	0.337209i
$733$	12.2076	−	37.5712i	0.450899	−	1.38772i	−0.424985	−	0.905201i	$-0.639721\pi$
$733$	12.2076	−	37.5712i	0.450899	−	1.38772i	0.875883	−	0.482523i	$-0.160279\pi$
$734$	2.19336	+	6.75047i	0.0809584	+	0.249164i
$735$	−27.4340	+	19.9320i	−1.01192	+	0.735202i
$736$	5.14167			0.189524
$737$	17.3636	+	21.4201i	0.639597	+	0.789021i
$738$	10.1208			0.372551
$739$	34.4605	−	25.0370i	1.26765	−	0.921000i	0.268542	−	0.963268i	$-0.413458\pi$
$739$	34.4605	−	25.0370i	1.26765	−	0.921000i	0.999106	+	0.0422676i	$0.0134582\pi$
$740$	−0.888592	−	2.73481i	−0.0326653	−	0.100533i
$741$	−12.3267	+	37.9377i	−0.452832	+	1.39367i
$742$	−8.86637	−	6.44179i	−0.325495	−	0.236486i
$743$	−17.0937	−	12.4193i	−0.627108	−	0.455621i	0.228289	−	0.973593i	$-0.426687\pi$
$743$	−17.0937	−	12.4193i	−0.627108	−	0.455621i	−0.855397	+	0.517973i	$0.826687\pi$
$744$	6.79166	−	20.9026i	0.248994	−	0.766326i
$745$	−6.23537	−	19.1905i	−0.228446	−	0.703085i
$746$	−2.10179	+	1.52704i	−0.0769520	+	0.0559089i
$747$	10.9913			0.402151
$748$	−2.39601	−	0.640710i	−0.0876067	−	0.0234267i
$749$	−21.2324			−0.775814
$750$	−13.0242	+	9.46265i	−0.475577	+	0.345527i
$751$	9.20198	+	28.3208i	0.335785	+	1.03344i	0.966334	+	0.257290i	$0.0828297\pi$
$751$	9.20198	+	28.3208i	0.335785	+	1.03344i	−0.630549	+	0.776149i	$0.717170\pi$
$752$	1.04933	−	3.22950i	0.0382650	−	0.117768i
$753$	−4.84830	−	3.52249i	−0.176682	−	0.128367i
$754$	−28.2490	−	20.5241i	−1.02877	−	0.747444i
$755$	−1.58495	+	4.87798i	−0.0576822	+	0.177528i
$756$	−5.36970	−	16.5262i	−0.195294	−	0.601054i
$757$	9.41278	−	6.83878i	0.342113	−	0.248560i	−0.403440	−	0.915006i	$-0.632185\pi$
$757$	9.41278	−	6.83878i	0.342113	−	0.248560i	0.745553	+	0.666446i	$0.232185\pi$
$758$	−29.2570			−1.06266
$759$	3.32741	−	5.12944i	0.120777	−	0.186187i
$760$	−54.3752			−1.97240
$761$	−38.9528	+	28.3009i	−1.41204	+	1.02591i	−0.419015	+	0.907979i	$0.637625\pi$
$761$	−38.9528	+	28.3009i	−1.41204	+	1.02591i	−0.993022	+	0.117926i	$0.962375\pi$
$762$	2.90043	+	8.92659i	0.105071	+	0.323376i
$763$	7.68541	−	23.6533i	0.278231	−	0.856305i
$764$	7.56581	+	5.49688i	0.273721	+	0.198870i
$765$	−1.89326	−	1.37554i	−0.0684511	−	0.0497326i
$766$	−3.14275	+	9.67238i	−0.113552	+	0.349477i
$767$	1.19647	+	3.68236i	0.0432021	+	0.132962i
$768$	−17.4310	+	12.6643i	−0.628986	+	0.456985i
$769$	34.7592			1.25345			0.626724	−	0.779241i	$-0.284395\pi$
$769$	34.7592			1.25345			0.626724	+	0.779241i	$0.284395\pi$
$770$	−34.3023	+	13.1873i	−1.23617	+	0.475239i
$771$	−21.8097			−0.785459
$772$	7.12716	−	5.17819i	0.256512	−	0.186367i
$773$	−5.43724	−	16.7341i	−0.195564	−	0.601884i	−0.999970	−	0.00780327i	$-0.997516\pi$
$773$	−5.43724	−	16.7341i	−0.195564	−	0.601884i	0.804406	−	0.594080i	$-0.202484\pi$
$774$	−1.57426	+	4.84508i	−0.0565856	+	0.174153i
$775$	3.28805	+	2.38891i	0.118110	+	0.0858122i
$776$	42.4490	+	30.8410i	1.52383	+	1.10713i
$777$	2.88482	−	8.87855i	0.103492	−	0.318516i
$778$	12.0340	+	37.0369i	0.431441	+	1.32784i
$779$	−55.2920	+	40.1720i	−1.98104	+	1.43931i
$780$	−9.80048			−0.350914
$781$	−0.720356	−	13.6135i	−0.0257764	−	0.487130i
$782$	1.44818			0.0517867
$783$	37.4102	−	27.1801i	1.33693	−	0.971338i
$784$	−5.93652	−	18.2707i	−0.212019	−	0.652527i
$785$	2.94998	−	9.07910i	0.105289	−	0.324047i
$786$	−22.2222	−	16.1453i	−0.792638	−	0.575885i
$787$	−26.1300	−	18.9845i	−0.931433	−	0.676725i	0.0149105	−	0.999889i	$-0.495254\pi$
$787$	−26.1300	−	18.9845i	−0.931433	−	0.676725i	−0.946343	+	0.323163i	$0.895254\pi$
$788$	0.486272	−	1.49659i	0.0173227	−	0.0533139i
$789$	7.84573	+	24.1467i	0.279315	+	0.859644i
$790$	−3.64911	+	2.65124i	−0.129830	+	0.0943268i
$791$	46.9708			1.67009
$792$	−0.523185	−	9.88731i	−0.0185906	−	0.351330i
$793$	55.6174			1.97503
$794$	−1.22266	+	0.888317i	−0.0433907	+	0.0315252i
$795$	−2.52951	−	7.78504i	−0.0897126	−	0.276107i
$796$	2.85657	−	8.79162i	0.101248	−	0.311611i
$797$	13.8247	+	10.0442i	0.489697	+	0.355785i	0.805068	−	0.593183i	$-0.202129\pi$
$797$	13.8247	+	10.0442i	0.489697	+	0.355785i	−0.315371	+	0.948968i	$0.602129\pi$
$798$	−38.8667	−	28.2383i	−1.37587	−	0.999625i
$799$	−0.539452	+	1.66026i	−0.0190844	+	0.0587359i
$800$	−0.994405	−	3.06046i	−0.0351575	−	0.108204i
$801$	1.37698	−	1.00044i	0.0486532	−	0.0353486i
$802$	−4.30107			−0.151876
$803$	−40.0298	+	15.3892i	−1.41262	+	0.543073i
$804$	−8.85613			−0.312332
$805$	−10.3674	+	7.53233i	−0.365402	+	0.265480i
$806$	6.62300	+	20.3835i	0.233285	+	0.717978i
$807$	7.58551	−	23.3458i	0.267023	−	0.821811i
$808$	8.73933	+	6.34949i	0.307448	+	0.223374i
$809$	−35.9603	−	26.1267i	−1.26430	−	0.918567i	−0.265338	−	0.964155i	$-0.585484\pi$
$809$	−35.9603	−	26.1267i	−1.26430	−	0.918567i	−0.998960	+	0.0455888i	$0.985484\pi$
$810$	−4.28813	+	13.1975i	−0.150669	+	0.463713i
$811$	11.0868	+	34.1218i	0.389311	+	1.19818i	0.933304	+	0.359087i	$0.116912\pi$
$811$	11.0868	+	34.1218i	0.389311	+	1.19818i	−0.543993	+	0.839090i	$0.683088\pi$
$812$	−20.3178	+	14.7617i	−0.713015	+	0.518036i
$813$	−19.3980			−0.680318
$814$	3.22216	−	4.96719i	0.112937	−	0.174100i
$815$	16.5368			0.579259
$816$	−2.24166	+	1.62866i	−0.0784737	+	0.0570145i
$817$	−10.6308	−	32.7183i	−0.371925	−	1.14467i
$818$	1.73904	−	5.35222i	0.0608042	−	0.187136i
$819$	12.3163	+	8.94832i	0.430367	+	0.312680i
$820$	−13.5846	−	9.86976i	−0.474393	−	0.344667i
$821$	−6.38382	+	19.6474i	−0.222797	+	0.685698i	0.775711	+	0.631088i	$0.217391\pi$
$821$	−6.38382	+	19.6474i	−0.222797	+	0.685698i	−0.998508	+	0.0546096i	$0.982609\pi$
$822$	−4.22113	−	12.9913i	−0.147229	−	0.453124i
$823$	−19.7773	+	14.3691i	−0.689394	+	0.500874i	−0.876461	−	0.481473i	$-0.840102\pi$
$823$	−19.7773	+	14.3691i	−0.689394	+	0.500874i	0.187067	+	0.982347i	$0.440102\pi$
$824$	46.5590			1.62196
$825$	−3.69671	−	0.988527i	−0.128703	−	0.0344161i
$826$	−4.66311			−0.162250
$827$	41.6618	−	30.2691i	1.44872	−	1.05256i	0.462595	−	0.886570i	$-0.346918\pi$
$827$	41.6618	−	30.2691i	1.44872	−	1.05256i	0.986128	−	0.165989i	$-0.0530815\pi$
$828$	−0.290352	−	0.893611i	−0.0100904	−	0.0310551i
$829$	10.1816	−	31.3356i	0.353620	−	1.08833i	−0.603185	−	0.797601i	$-0.706102\pi$
$829$	10.1816	−	31.3356i	0.353620	−	1.08833i	0.956805	−	0.290730i	$-0.0938981\pi$
$830$	24.7037	+	17.9483i	0.857479	+	0.622995i
$831$	−15.8185	−	11.4928i	−0.548738	−	0.398681i
$832$	9.83258	−	30.2616i	0.340883	−	1.04913i
$833$	3.05193	+	9.39287i	0.105743	+	0.325444i
$834$	−0.260080	+	0.188959i	−0.00900584	+	0.00654312i
$835$	−44.4359			−1.53777
$836$	11.4583	+	14.1352i	0.396294	+	0.488877i
$837$	−28.3831			−0.981062
$838$	−2.79428	+	2.03016i	−0.0965268	+	0.0701308i
$839$	6.43838	+	19.8153i	0.222278	+	0.684100i	0.998557	+	0.0537107i	$0.0171049\pi$
$839$	6.43838	+	19.8153i	0.222278	+	0.684100i	−0.776279	+	0.630390i	$0.782895\pi$
$840$	13.4024	−	41.2483i	0.462426	−	1.42320i
$841$	−30.6067	−	22.2370i	−1.05540	−	0.766794i
$842$	−6.61662	−	4.80726i	−0.228024	−	0.165669i
$843$	6.10298	−	18.7830i	0.210198	−	0.646923i
$844$	−1.64144	−	5.05182i	−0.0565005	−	0.173891i
$845$	3.06003	−	2.22324i	0.105268	−	0.0764819i
$846$	−1.89659			−0.0652061
$847$	39.1575	+	22.5548i	1.34547	+	0.774992i
$848$	4.63738			0.159248
$849$	−18.2976	+	13.2940i	−0.627972	+	0.456248i
$850$	−0.280079	−	0.861995i	−0.00960664	−	0.0295662i
$851$	0.637989	−	1.96353i	0.0218700	−	0.0673088i
$852$	3.54227	+	2.57361i	0.121356	+	0.0881703i
$853$	1.69456	+	1.23117i	0.0580206	+	0.0421544i	0.616418	−	0.787419i	$-0.288583\pi$
$853$	1.69456	+	1.23117i	0.0580206	+	0.0421544i	−0.558397	+	0.829574i	$0.688583\pi$
$854$	−20.6990	+	63.7049i	−0.708304	+	2.17994i
$855$	5.30553	+	16.3287i	0.181445	+	0.558431i
$856$	12.8570	−	9.34117i	0.439444	−	0.319275i
$857$	33.9148			1.15851			0.579254	−	0.815147i	$-0.303344\pi$
$857$	33.9148			1.15851			0.579254	+	0.815147i	$0.303344\pi$
$858$	−12.7071	−	15.6757i	−0.433813	−	0.535161i
$859$	−2.45598			−0.0837971			−0.0418985	−	0.999122i	$-0.513341\pi$
$859$	−2.45598			−0.0837971			−0.0418985	+	0.999122i	$0.513341\pi$
$860$	6.83794	−	4.96805i	0.233172	−	0.169409i
$861$	−16.8456	−	51.8453i	−0.574096	−	1.76688i
$862$	−11.2050	+	34.4855i	−0.381645	+	1.17458i
$863$	6.52329	+	4.73944i	0.222055	+	0.161333i	0.693251	−	0.720696i	$-0.256178\pi$
$863$	6.52329	+	4.73944i	0.222055	+	0.161333i	−0.471196	+	0.882028i	$0.656178\pi$
$864$	18.1809	+	13.2092i	0.618528	+	0.449387i
$865$	−8.49804	+	26.1543i	−0.288942	+	0.889273i
$866$	2.68466	+	8.26254i	0.0912286	+	0.280773i
$867$	1.15242	−	0.837283i	0.0391383	−	0.0284356i
$868$	15.4151			0.523222
$869$	5.35805	+	1.43278i	0.181759	+	0.0486038i
$870$	31.4100			1.06490
$871$	25.6730	−	18.6525i	0.869897	−	0.632017i
$872$	5.75242	+	17.7041i	0.194802	+	0.599538i
$873$	5.11961	−	15.7565i	0.173273	−	0.533278i
$874$	−8.59552	−	6.24501i	−0.290748	−	0.211241i
$875$	−33.5661	−	24.3872i	−1.13474	−	0.824437i
$876$	4.25642	−	13.0999i	0.143811	−	0.442605i
$877$	10.0254	+	30.8550i	0.338534	+	1.04190i	0.964955	+	0.262415i	$0.0845190\pi$
$877$	10.0254	+	30.8550i	0.338534	+	1.04190i	−0.626421	+	0.779485i	$0.715481\pi$
$878$	−5.39717	+	3.92127i	−0.182146	+	0.132336i
$879$	19.4232			0.655127
$880$	8.46275	−	13.0459i	0.285279	−	0.439778i
$881$	6.65827			0.224323			0.112161	−	0.993690i	$-0.464223\pi$
$881$	6.65827			0.224323			0.112161	+	0.993690i	$0.464223\pi$
$882$	−8.68065	+	6.30686i	−0.292293	+	0.212363i
$883$	12.6406	+	38.9037i	0.425389	+	1.30921i	0.902621	+	0.430436i	$0.141640\pi$
$883$	12.6406	+	38.9037i	0.425389	+	1.30921i	−0.477232	+	0.878777i	$0.658360\pi$
$884$	−0.882043	+	2.71465i	−0.0296663	+	0.0913035i
$885$	−2.81773	−	2.04720i	−0.0947170	−	0.0688159i
$886$	3.90645	+	2.83820i	0.131240	+	0.0953513i
$887$	−7.02933	+	21.6341i	−0.236022	+	0.726401i	0.760962	+	0.648796i	$0.224727\pi$
$887$	−7.02933	+	21.6341i	−0.236022	+	0.726401i	−0.996984	+	0.0776046i	$0.975273\pi$
$888$	2.15925	+	6.64548i	0.0724596	+	0.223008i
$889$	−19.5698	+	14.2183i	−0.656349	+	0.476865i
$890$	4.72853			0.158501
$891$	15.9267	−	6.12294i	0.533566	−	0.205126i
$892$	−19.6865			−0.659153
$893$	10.3615	−	7.52804i	0.346733	−	0.251916i
$894$	4.12349	+	12.6908i	0.137910	+	0.424444i
$895$	6.54419	−	20.1409i	0.218748	−	0.673237i
$896$	4.59414	+	3.33784i	0.153479	+	0.111509i
$897$	−5.69266	−	4.13596i	−0.190072	−	0.138096i
$898$	12.2870	−	37.8155i	0.410023	−	1.26192i
$899$	12.6763	+	39.0137i	0.422778	+	1.30118i
$900$	−0.475748	+	0.345651i	−0.0158583	+	0.0115217i
$901$	−2.38405			−0.0794241
$902$	−1.82690	−	34.5252i	−0.0608290	−	1.14956i
$903$	27.4399			0.913144
$904$	−28.4426	+	20.6648i	−0.945988	+	0.687301i
$905$	−3.56929	−	10.9851i	−0.118647	−	0.365158i
$906$	1.04814	−	3.22584i	0.0348220	−	0.107171i
$907$	12.4342	+	9.03399i	0.412871	+	0.299969i	0.774763	−	0.632251i	$-0.217869\pi$
$907$	12.4342	+	9.03399i	0.412871	+	0.299969i	−0.361892	+	0.932220i	$0.617869\pi$
$908$	8.46627	+	6.15111i	0.280963	+	0.204132i
$909$	1.05402	−	3.24393i	0.0349595	−	0.107594i
$910$	13.0695	+	40.2239i	0.433251	+	1.33341i
$911$	6.24833	−	4.53968i	0.207017	−	0.150406i	−0.479446	−	0.877571i	$-0.659162\pi$
$911$	6.24833	−	4.53968i	0.207017	−	0.150406i	0.686463	+	0.727165i	$0.259162\pi$
$912$	20.3284			0.673142
$913$	−1.98403	−	37.4949i	−0.0656619	−	1.24090i
$914$	−5.07292			−0.167797
$915$	−40.4753	+	29.4071i	−1.33807	+	0.972167i
$916$	−0.506128	−	1.55770i	−0.0167230	−	0.0514680i
$917$	21.8756	−	67.3261i	0.722395	−	2.22330i
$918$	5.12075	+	3.72045i	0.169010	+	0.122793i
$919$	12.8874	+	9.36322i	0.425115	+	0.308864i	0.779693	−	0.626163i	$-0.215375\pi$
$919$	12.8874	+	9.36322i	0.425115	+	0.308864i	−0.354578	+	0.935027i	$0.615375\pi$
$920$	2.96399	−	9.12223i	0.0977199	−	0.300751i
$921$	−11.6031	−	35.7108i	−0.382336	−	1.17671i
$922$	25.1144	−	18.2467i	0.827100	−	0.600923i
$923$	−15.6891			−0.516414
$924$	−13.5470	+	5.20808i	−0.445665	+	0.171333i
$925$	−1.29213			−0.0424851
$926$	29.0903	−	21.1353i	0.955966	−	0.694550i
$927$	−4.54288	−	13.9815i	−0.149208	−	0.459214i
$928$	10.0367	−	30.8899i	0.329472	−	1.01401i
$929$	5.80288	+	4.21604i	0.190386	+	0.138324i	0.678895	−	0.734235i	$-0.262459\pi$
$929$	5.80288	+	4.21604i	0.190386	+	0.138324i	−0.488509	+	0.872559i	$0.662459\pi$
$930$	−15.5974	−	11.3322i	−0.511458	−	0.371596i
$931$	22.3907	−	68.9114i	0.733824	−	2.25848i
$932$	−5.27928	−	16.2479i	−0.172929	−	0.532219i
$933$	11.1173	−	8.07719i	0.363964	−	0.264435i
$934$	15.6952			0.513564
$935$	−4.35064	+	6.70682i	−0.142281	+	0.219337i
$936$	−11.3948			−0.372451
$937$	−41.1896	+	29.9260i	−1.34561	+	0.977640i	−0.346388	+	0.938091i	$0.612592\pi$
$937$	−41.1896	+	29.9260i	−1.34561	+	0.977640i	−0.999218	+	0.0395481i	$0.987408\pi$
$938$	11.8102	+	36.3480i	0.385616	+	1.18681i
$939$	0.201685	−	0.620721i	0.00658173	−	0.0202565i
$940$	2.54568	+	1.84955i	0.0830310	+	0.0603255i
$941$	39.0790	+	28.3926i	1.27394	+	0.925571i	0.999352	−	0.0359905i	$-0.0114586\pi$
$941$	39.0790	+	28.3926i	1.27394	+	0.925571i	0.274588	+	0.961562i	$0.411459\pi$
$942$	−1.95084	+	6.00407i	−0.0635618	+	0.195623i
$943$	−3.72546	−	11.4658i	−0.121318	−	0.373378i
$944$	1.59631	−	1.15979i	0.0519555	−	0.0377479i
$945$	−56.0099			−1.82200
$946$	16.8123	+	4.49572i	0.546614	+	0.146169i
$947$	5.07275			0.164842			0.0824211	−	0.996598i	$-0.473735\pi$
$947$	5.07275			0.164842			0.0824211	+	0.996598i	$0.473735\pi$
$948$	−1.44115	+	1.04705i	−0.0468063	+	0.0340067i
$949$	15.2517	+	46.9400i	0.495093	+	1.52374i
$950$	−2.05482	+	6.32408i	−0.0666671	+	0.205180i
$951$	9.61749	+	6.98752i	0.311869	+	0.226586i
$952$	−10.2192	−	7.42469i	−0.331207	−	0.240636i
$953$	−4.90411	+	15.0933i	−0.158860	+	0.488920i	−0.998532	−	0.0541741i	$-0.982747\pi$
$953$	−4.90411	+	15.0933i	−0.158860	+	0.488920i	0.839672	+	0.543094i	$0.182747\pi$
$954$	−0.800386	−	2.46333i	−0.0259135	−	0.0797534i
$955$	24.3867	−	17.7180i	0.789135	−	0.573340i
$956$	−0.504556			−0.0163185
$957$	−24.3212	−	30.0031i	−0.786192	−	0.969863i
$958$	−15.5936			−0.503807
$959$	28.4809	−	20.6926i	0.919695	−	0.668197i
$960$	8.84483	+	27.2216i	0.285466	+	0.878573i
$961$	−1.79882	+	5.53619i	−0.0580264	+	0.178587i
$962$	−5.51259	−	4.00513i	−0.177733	−	0.129131i
$963$	−4.05962	−	2.94949i	−0.130819	−	0.0950459i
$964$	1.35147	−	4.15941i	0.0435281	−	0.133966i
$965$	−8.77483	−	27.0062i	−0.282472	−	0.869359i
$966$	6.85600	−	4.98118i	0.220588	−	0.160267i
$967$	−44.9022			−1.44396			−0.721978	−	0.691916i	$-0.756767\pi$
$967$	−44.9022			−1.44396			−0.721978	+	0.691916i	$0.756767\pi$
$968$	−33.6343	+	3.56950i	−1.08105	+	0.114728i
$969$	−10.4507			−0.335725
$970$	37.2364	−	27.0538i	1.19559	−	0.868646i
$971$	−13.8840	−	42.7307i	−0.445560	−	1.37129i	−0.881868	−	0.471496i	$-0.843714\pi$
$971$	−13.8840	−	42.7307i	−0.445560	−	1.37129i	0.436308	−	0.899798i	$-0.356286\pi$
$972$	2.22782	−	6.85652i	0.0714573	−	0.219923i
$973$	−0.670279	−	0.486986i	−0.0214882	−	0.0156121i
$974$	14.8639	+	10.7993i	0.476271	+	0.346031i
$975$	−1.36087	+	4.18833i	−0.0435827	+	0.134134i
$976$	−8.75857	−	26.9561i	−0.280355	−	0.862844i
$977$	30.6041	−	22.2352i	0.979111	−	0.711366i	0.0216012	−	0.999767i	$-0.493124\pi$
$977$	30.6041	−	22.2352i	0.979111	−	0.711366i	0.957510	+	0.288401i	$0.0931236\pi$
$978$	−10.9359			−0.349691
$979$	−3.66136	−	4.51673i	−0.117018	−	0.144355i
$980$	17.8020			0.568663
$981$	4.75523	−	3.45487i	0.151823	−	0.110306i
$982$	−4.79586	−	14.7601i	−0.153042	−	0.471015i
$983$	5.66637	−	17.4393i	0.180729	−	0.556228i	−0.819119	−	0.573623i	$-0.805537\pi$
$983$	5.66637	−	17.4393i	0.180729	−	0.556228i	0.999849	+	0.0173955i	$0.00553744\pi$
$984$	33.0100	+	23.9831i	1.05232	+	0.764554i
$985$	−4.10347	−	2.98135i	−0.130748	−	0.0949937i
$986$	2.82690	−	8.70029i	0.0900267	−	0.277074i
$987$	3.15678	+	9.71557i	0.100481	+	0.309250i
$988$	16.9417	−	12.3089i	0.538988	−	0.391598i
$989$	6.06845			0.192966
$990$	−8.39050	−	2.24368i	−0.266668	−	0.0713089i
$991$	32.4908			1.03210			0.516052	−	0.856557i	$-0.327401\pi$
$991$	32.4908			1.03210			0.516052	+	0.856557i	$0.327401\pi$
$992$	−16.1285	+	11.7180i	−0.512081	+	0.372048i
$993$	9.48316	+	29.1862i	0.300939	+	0.926195i
$994$	5.83898	−	17.9705i	0.185201	−	0.569990i
$995$	−24.1056	−	17.5137i	−0.764198	−	0.555222i
$996$	9.75625	+	7.08833i	0.309139	+	0.224602i
$997$	−13.4869	+	41.5085i	−0.427135	+	1.31459i	0.473800	+	0.880633i	$0.342882\pi$
$997$	−13.4869	+	41.5085i	−0.427135	+	1.31459i	−0.900935	+	0.433954i	$0.857118\pi$
$998$	−6.75436	−	20.7878i	−0.213805	−	0.658026i
$999$	7.30033	−	5.30400i	0.230972	−	0.167811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.69.6	✓	36
11.2	odd	10		2057.2.a.be.1.12		18
11.4	even	5	inner	187.2.g.f.103.6	yes	36
11.9	even	5		2057.2.a.bd.1.7		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.69.6	✓	36	1.1	even	1	trivial
187.2.g.f.103.6	yes	36	11.4	even	5	inner
2057.2.a.bd.1.7		18	11.9	even	5
2057.2.a.be.1.12		18	11.2	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.905302 - 0.657740i) q^{2} +(-0.440186 - 1.35475i) q^{3} +(-0.231085 + 0.711206i) q^{4} +(1.95004 + 1.41679i) q^{5} +(-1.28958 - 0.936932i) q^{6} +(1.26946 - 3.90701i) q^{7} +(0.950176 + 2.92434i) q^{8} +(0.785461 - 0.570671i) q^{9} +O(q^{10})\)	\(q+(0.905302 - 0.657740i) q^{2} +(-0.440186 - 1.35475i) q^{3} +(-0.231085 + 0.711206i) q^{4} +(1.95004 + 1.41679i) q^{5} +(-1.28958 - 0.936932i) q^{6} +(1.26946 - 3.90701i) q^{7} +(0.950176 + 2.92434i) q^{8} +(0.785461 - 0.570671i) q^{9} +2.69726 q^{10} +(-2.08852 - 2.57645i) q^{11} +1.06523 q^{12} +(-3.08799 + 2.24355i) q^{13} +(-1.42055 - 4.37200i) q^{14} +(1.06102 - 3.26548i) q^{15} +(1.57368 + 1.14334i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.335726 - 1.03326i) q^{18} +(2.26712 + 6.97749i) q^{19} +(-1.45825 + 1.05948i) q^{20} -5.85183 q^{21} +(-3.58538 - 0.958756i) q^{22} -1.29415 q^{23} +(3.54351 - 2.57451i) q^{24} +(0.250291 + 0.770317i) q^{25} +(-1.31989 + 4.06219i) q^{26} +(-4.57613 - 3.32475i) q^{27} +(2.48533 + 1.80570i) q^{28} +(-2.52624 + 7.77496i) q^{29} +(-1.18729 - 3.65411i) q^{30} +(4.05953 - 2.94942i) q^{31} -3.97300 q^{32} +(-2.57111 + 3.96355i) q^{33} -1.11901 q^{34} +(8.01091 - 5.82027i) q^{35} +(0.224356 + 0.690498i) q^{36} +(-0.492977 + 1.51723i) q^{37} +(6.64180 + 4.82555i) q^{38} +(4.39875 + 3.19588i) q^{39} +(-2.29029 + 7.04879i) q^{40} +(2.87869 + 8.85968i) q^{41} +(-5.29767 + 3.84898i) q^{42} -4.68912 q^{43} +(2.31501 - 0.889993i) q^{44} +2.34020 q^{45} +(-1.17160 + 0.851218i) q^{46} +(-0.539452 - 1.66026i) q^{47} +(0.856237 - 2.63523i) q^{48} +(-7.99005 - 5.80511i) q^{49} +(0.733257 + 0.532742i) q^{50} +(-0.440186 + 1.35475i) q^{51} +(-0.882043 - 2.71465i) q^{52} +(1.92873 - 1.40131i) q^{53} -6.32960 q^{54} +(-0.422428 - 7.98318i) q^{55} +12.6316 q^{56} +(8.45481 - 6.14278i) q^{57} +(2.82690 + 8.70029i) q^{58} +(0.313462 - 0.964735i) q^{59} +(2.07724 + 1.50920i) q^{60} +(-11.7883 - 8.56469i) q^{61} +(1.73515 - 5.34024i) q^{62} +(-1.23250 - 3.79325i) q^{63} +(-6.74411 + 4.89989i) q^{64} -9.20035 q^{65} +(0.279355 + 5.27933i) q^{66} -8.31383 q^{67} +(0.604988 - 0.439550i) q^{68} +(0.569668 + 1.75326i) q^{69} +(3.42407 - 10.5382i) q^{70} +(3.32536 + 2.41601i) q^{71} +(2.41516 + 1.75472i) q^{72} +(3.99578 - 12.2977i) q^{73} +(0.551649 + 1.69780i) q^{74} +(0.933414 - 0.678165i) q^{75} -5.48633 q^{76} +(-12.7175 + 4.88917i) q^{77} +6.08425 q^{78} +(-1.35290 + 0.982938i) q^{79} +(1.44886 + 4.45914i) q^{80} +(-1.58981 + 4.89294i) q^{81} +(8.43345 + 6.12726i) q^{82} +(9.15884 + 6.65428i) q^{83} +(1.35227 - 4.16186i) q^{84} +(-0.744850 - 2.29241i) q^{85} +(-4.24507 + 3.08423i) q^{86} +11.6452 q^{87} +(5.54994 - 8.55563i) q^{88} +1.75309 q^{89} +(2.11859 - 1.53925i) q^{90} +(4.84550 + 14.9129i) q^{91} +(0.299060 - 0.920411i) q^{92} +(-5.78269 - 4.20137i) q^{93} +(-1.58039 - 1.14822i) q^{94} +(-5.46464 + 16.8184i) q^{95} +(1.74886 + 5.38242i) q^{96} +(13.8053 - 10.0301i) q^{97} -11.0517 q^{98} +(-3.11075 - 0.831839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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