LMFDB - Embedded newform 55.3.i.c.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(6,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("55.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.i (of order $10$, 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:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
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} - 2 x^{11} + 6 x^{10} + 5 x^{9} - 30 x^{8} + 88 x^{7} - 131 x^{6} - 12 x^{5} + 240 x^{4} + \cdots + 1331 $ x^12 - 2x^11 + 6x^10 + 5x^9 - 30x^8 + 88x^7 - 131x^6 - 12x^5 + 240x^4 - 925x^3 + 1386x^2 - 1452*x + 1331
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			6.3
Root			$1.54329 - 0.0151731i$ of defining polynomial
Character	$\chi$	$=$	55.6
Dual form			55.3.i.c.46.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.57580 - 0.512008i) q^{2} +(2.41303 + 1.75317i) q^{3} +(-1.01508 + 0.737497i) q^{4} +(0.690983 - 2.12663i) q^{5} +(4.70008 + 1.52715i) q^{6} +(-1.31003 - 1.80310i) q^{7} +(-5.11754 + 7.04369i) q^{8} +(-0.0320482 - 0.0986342i) q^{9} -3.70493i q^{10} +(-0.949049 - 10.9590i) q^{11} -3.74236 q^{12} +(-1.75040 + 0.568738i) q^{13} +(-2.98754 - 2.17058i) q^{14} +(5.39569 - 3.92020i) q^{15} +(-2.90689 + 8.94649i) q^{16} +(7.97437 + 2.59103i) q^{17} +(-0.101003 - 0.139019i) q^{18} +(-15.6197 + 21.4986i) q^{19} +(0.866979 + 2.66829i) q^{20} -6.64762i q^{21} +(-7.10660 - 16.7832i) q^{22} -7.63236 q^{23} +(-24.6975 + 8.02472i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(-2.46707 + 1.79243i) q^{26} +(8.39084 - 25.8243i) q^{27} +(2.65956 + 0.864143i) q^{28} +(31.8005 + 43.7696i) q^{29} +(6.49535 - 8.94009i) q^{30} +(1.08129 + 3.32786i) q^{31} -19.2397i q^{32} +(16.9228 - 28.1082i) q^{33} +13.8926 q^{34} +(-4.73973 + 1.54003i) q^{35} +(0.105274 + 0.0764859i) q^{36} +(37.8881 - 27.5273i) q^{37} +(-13.6060 + 41.8749i) q^{38} +(-5.22085 - 1.69636i) q^{39} +(11.4432 + 15.7502i) q^{40} +(-15.9749 + 21.9876i) q^{41} +(-3.40364 - 10.4753i) q^{42} -14.9713i q^{43} +(9.04557 + 10.4243i) q^{44} -0.231903 q^{45} +(-12.0271 + 3.90783i) q^{46} +(58.0480 + 42.1743i) q^{47} +(-22.6991 + 16.4919i) q^{48} +(13.6068 - 41.8775i) q^{49} +(-7.87900 - 2.56004i) q^{50} +(14.6999 + 20.2326i) q^{51} +(1.35734 - 1.86822i) q^{52} +(-12.1774 - 37.4781i) q^{53} -44.9902i q^{54} +(-23.9614 - 5.55420i) q^{55} +19.4046 q^{56} +(-75.3814 + 24.4929i) q^{57} +(72.5216 + 52.6900i) q^{58} +(-29.1317 + 21.1654i) q^{59} +(-2.58591 + 7.95861i) q^{60} +(-44.0546 - 14.3142i) q^{61} +(3.40779 + 4.69042i) q^{62} +(-0.135863 + 0.187000i) q^{63} +(-21.4785 - 66.1039i) q^{64} +4.11543i q^{65} +(12.2754 - 52.9574i) q^{66} -60.8461 q^{67} +(-10.0055 + 3.25097i) q^{68} +(-18.4171 - 13.3808i) q^{69} +(-6.68035 + 4.85356i) q^{70} +(-37.8919 + 116.619i) q^{71} +(0.858757 + 0.279027i) q^{72} +(-35.1241 - 48.3441i) q^{73} +(45.6098 - 62.7765i) q^{74} +(-4.60847 - 14.1834i) q^{75} -33.3422i q^{76} +(-18.5169 + 16.0678i) q^{77} -9.09555 q^{78} +(-81.5552 + 26.4989i) q^{79} +(17.0172 + 12.3638i) q^{80} +(64.7665 - 47.0556i) q^{81} +(-13.9155 + 42.8274i) q^{82} +(-43.6902 - 14.1958i) q^{83} +(4.90260 + 6.74785i) q^{84} +(11.0203 - 15.1681i) q^{85} +(-7.66545 - 23.5918i) q^{86} +161.369i q^{87} +(82.0485 + 49.3983i) q^{88} +121.940 q^{89} +(-0.365432 + 0.118736i) q^{90} +(3.31856 + 2.41107i) q^{91} +(7.74743 - 5.62884i) q^{92} +(-3.22512 + 9.92591i) q^{93} +(113.066 + 36.7372i) q^{94} +(34.9266 + 48.0724i) q^{95} +(33.7304 - 46.4259i) q^{96} +(-10.2685 - 31.6031i) q^{97} -72.9574i q^{98} +(-1.05051 + 0.444824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} + 7 q^{3} + 13 q^{4} + 15 q^{5} - 15 q^{6} - 40 q^{7} - 15 q^{8} - 16 q^{9} - 8 q^{11} + 68 q^{12} - 15 q^{13} - 5 q^{14} + 35 q^{15} + 77 q^{16} - 5 q^{17} - 115 q^{18} + 15 q^{19} - 20 q^{20}+ \cdots + 509 q^{99}+O(q^{100}) $ 12 * q - 5 * q^2 + 7 * q^3 + 13 * q^4 + 15 * q^5 - 15 * q^6 - 40 * q^7 - 15 * q^8 - 16 * q^9 - 8 * q^11 + 68 * q^12 - 15 * q^13 - 5 * q^14 + 35 * q^15 + 77 * q^16 - 5 * q^17 - 115 * q^18 + 15 * q^19 - 20 * q^20 - 90 * q^22 + 112 * q^23 - 235 * q^24 - 15 * q^25 + 80 * q^26 + 106 * q^27 + 110 * q^28 + 45 * q^29 - 10 * q^30 - 146 * q^31 - 133 * q^33 + 60 * q^34 - 70 * q^35 + 216 * q^36 + 8 * q^37 + 45 * q^38 + 195 * q^39 + 65 * q^40 - 145 * q^41 + 105 * q^42 - 167 * q^44 - 20 * q^45 - 475 * q^46 + 158 * q^47 + 227 * q^48 + 153 * q^49 + 25 * q^50 - 55 * q^51 + 60 * q^52 + 107 * q^53 - 60 * q^55 - 140 * q^56 + 125 * q^57 + 40 * q^58 - 59 * q^59 + 40 * q^60 + 210 * q^61 + 110 * q^62 - 640 * q^63 + 173 * q^64 + 195 * q^66 - 62 * q^67 - 225 * q^68 + 7 * q^69 - 15 * q^70 + 114 * q^71 - 795 * q^72 - 165 * q^73 - 30 * q^74 + 35 * q^75 - 430 * q^77 + 360 * q^78 - 355 * q^79 + 100 * q^80 + 145 * q^81 - 210 * q^82 + 105 * q^83 + 460 * q^84 + 70 * q^85 + 75 * q^86 + 270 * q^88 - 274 * q^89 - 265 * q^90 + 285 * q^91 + 428 * q^92 + 109 * q^93 + 410 * q^94 + 55 * q^95 - 75 * q^96 + 198 * q^97 + 509 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	1.57580	−	0.512008i	0.787900	−	0.256004i	0.112690	−	0.993630i	$-0.464053\pi$
$2$	1.57580	−	0.512008i	0.787900	−	0.256004i	0.675209	+	0.737626i	$0.264053\pi$
$3$	2.41303	+	1.75317i	0.804342	+	0.584389i	0.912185	−	0.409779i	$-0.134394\pi$
$3$	2.41303	+	1.75317i	0.804342	+	0.584389i	−0.107843	+	0.994168i	$0.534394\pi$
$4$	−1.01508	+	0.737497i	−0.253769	+	0.184374i
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$5$	0.690983	−	2.12663i	0.138197	−	0.425325i
$6$	4.70008	+	1.52715i	0.783347	+	0.254525i
$7$	−1.31003	−	1.80310i	−0.187147	−	0.257586i	0.705126	−	0.709082i	$-0.250890\pi$
$7$	−1.31003	−	1.80310i	−0.187147	−	0.257586i	−0.892273	+	0.451496i	$0.850890\pi$
$8$	−5.11754	+	7.04369i	−0.639693	+	0.880462i
$9$	−0.0320482	−	0.0986342i	−0.00356091	−	0.0109594i
$10$		−	3.70493i		−	0.370493i
$11$	−0.949049	−	10.9590i	−0.0862772	−	0.996271i
$11$	−0.949049	−	10.9590i	−0.0862772	−	0.996271i
$12$	−3.74236			−0.311864
$13$	−1.75040	+	0.568738i	−0.134646	+	0.0437491i	−0.375565	−	0.926796i	$-0.622551\pi$
$13$	−1.75040	+	0.568738i	−0.134646	+	0.0437491i	0.240919	+	0.970545i	$0.422551\pi$
$14$	−2.98754	−	2.17058i	−0.213396	−	0.155041i
$15$	5.39569	−	3.92020i	0.359713	−	0.261347i
$16$	−2.90689	+	8.94649i	−0.181681	+	0.559156i
$17$	7.97437	+	2.59103i	0.469080	+	0.152413i	0.534013	−	0.845476i	$-0.320683\pi$
$17$	7.97437	+	2.59103i	0.469080	+	0.152413i	−0.0649328	+	0.997890i	$0.520683\pi$
$18$	−0.101003	−	0.139019i	−0.00561128	−	0.00772326i
$19$	−15.6197	+	21.4986i	−0.822088	+	1.13151i	0.167257	+	0.985913i	$0.446509\pi$
$19$	−15.6197	+	21.4986i	−0.822088	+	1.13151i	−0.989344	+	0.145594i	$0.953491\pi$
$20$	0.866979	+	2.66829i	0.0433490	+	0.133414i
$21$		−	6.64762i		−	0.316553i
$22$	−7.10660	−	16.7832i	−0.323027	−	0.762874i
$23$	−7.63236			−0.331842			−0.165921	−	0.986139i	$-0.553060\pi$
$23$	−7.63236			−0.331842			−0.165921	+	0.986139i	$0.553060\pi$
$24$	−24.6975	+	8.02472i	−1.02906	+	0.334363i
$25$	−4.04508	−	2.93893i	−0.161803	−	0.117557i
$26$	−2.46707	+	1.79243i	−0.0948875	+	0.0689398i
$27$	8.39084	−	25.8243i	0.310772	−	0.956457i
$28$	2.65956	+	0.864143i	0.0949842	+	0.0308623i
$29$	31.8005	+	43.7696i	1.09657	+	1.50930i	0.839856	+	0.542809i	$0.182639\pi$
$29$	31.8005	+	43.7696i	1.09657	+	1.50930i	0.256713	+	0.966488i	$0.417361\pi$
$30$	6.49535	−	8.94009i	0.216512	−	0.298003i
$31$	1.08129	+	3.32786i	0.0348803	+	0.107350i	0.966981	−	0.254849i	$-0.0820258\pi$
$31$	1.08129	+	3.32786i	0.0348803	+	0.107350i	−0.932101	+	0.362200i	$0.882026\pi$
$32$		−	19.2397i		−	0.601241i
$33$	16.9228	−	28.1082i	0.512813	−	0.851762i
$34$	13.8926			0.408607
$35$	−4.73973	+	1.54003i	−0.135421	+	0.0440009i
$36$	0.105274	+	0.0764859i	0.00292427	+	0.00212461i
$37$	37.8881	−	27.5273i	1.02400	−	0.743981i	0.0569023	−	0.998380i	$-0.481878\pi$
$37$	37.8881	−	27.5273i	1.02400	−	0.743981i	0.967099	+	0.254399i	$0.0818776\pi$
$38$	−13.6060	+	41.8749i	−0.358052	+	1.10197i
$39$	−5.22085	−	1.69636i	−0.133868	−	0.0434963i
$40$	11.4432	+	15.7502i	0.286079	+	0.393754i
$41$	−15.9749	+	21.9876i	−0.389633	+	0.536283i	−0.958104	−	0.286419i	$-0.907535\pi$
$41$	−15.9749	+	21.9876i	−0.389633	+	0.536283i	0.568472	+	0.822703i	$0.307535\pi$
$42$	−3.40364	−	10.4753i	−0.0810390	−	0.249412i
$43$		−	14.9713i		−	0.348171i	−0.984731	−	0.174085i	$-0.944303\pi$
$43$		−	14.9713i		−	0.348171i	0.984731	−	0.174085i	$-0.0556969\pi$
$44$	9.04557	+	10.4243i	0.205581	+	0.236916i
$45$	−0.231903			−0.00515340
$46$	−12.0271	+	3.90783i	−0.261458	+	0.0849528i
$47$	58.0480	+	42.1743i	1.23506	+	0.897326i	0.997259	−	0.0739873i	$-0.0235724\pi$
$47$	58.0480	+	42.1743i	1.23506	+	0.897326i	0.237804	+	0.971313i	$0.423572\pi$
$48$	−22.6991	+	16.4919i	−0.472898	+	0.343580i
$49$	13.6068	−	41.8775i	0.277691	−	0.854644i
$50$	−7.87900	−	2.56004i	−0.157580	−	0.0512008i
$51$	14.6999	+	20.2326i	0.288232	+	0.396718i
$52$	1.35734	−	1.86822i	0.0261028	−	0.0359274i
$53$	−12.1774	−	37.4781i	−0.229762	−	0.707134i	−0.997773	−	0.0666977i	$-0.978754\pi$
$53$	−12.1774	−	37.4781i	−0.229762	−	0.707134i	0.768012	−	0.640436i	$-0.221246\pi$
$54$		−	44.9902i		−	0.833151i
$55$	−23.9614	−	5.55420i	−0.435663	−	0.100985i
$56$	19.4046			0.346511
$57$	−75.3814	+	24.4929i	−1.32248	+	0.429700i
$58$	72.5216	+	52.6900i	1.25037	+	0.908449i
$59$	−29.1317	+	21.1654i	−0.493758	+	0.358736i	−0.806628	−	0.591060i	$-0.798710\pi$
$59$	−29.1317	+	21.1654i	−0.493758	+	0.358736i	0.312870	+	0.949796i	$0.398710\pi$
$60$	−2.58591	+	7.95861i	−0.0430985	+	0.132643i
$61$	−44.0546	−	14.3142i	−0.722207	−	0.234659i	−0.0752273	−	0.997166i	$-0.523968\pi$
$61$	−44.0546	−	14.3142i	−0.722207	−	0.234659i	−0.646980	+	0.762507i	$0.723968\pi$
$62$	3.40779	+	4.69042i	0.0549643	+	0.0756519i
$63$	−0.135863	+	0.187000i	−0.00215656	+	0.00296825i
$64$	−21.4785	−	66.1039i	−0.335601	−	1.03287i
$65$			4.11543i			0.0633143i
$66$	12.2754	−	52.9574i	0.185991	−	0.802386i
$67$	−60.8461			−0.908151			−0.454075	−	0.890963i	$-0.650030\pi$
$67$	−60.8461			−0.908151			−0.454075	+	0.890963i	$0.650030\pi$
$68$	−10.0055	+	3.25097i	−0.147139	+	0.0478084i
$69$	−18.4171	−	13.3808i	−0.266914	−	0.193925i
$70$	−6.68035	+	4.85356i	−0.0954336	+	0.0693365i
$71$	−37.8919	+	116.619i	−0.533688	+	1.64252i	0.212778	+	0.977101i	$0.431749\pi$
$71$	−37.8919	+	116.619i	−0.533688	+	1.64252i	−0.746466	+	0.665423i	$0.768251\pi$
$72$	0.858757	+	0.279027i	0.0119272	+	0.00387538i
$73$	−35.1241	−	48.3441i	−0.481152	−	0.662248i	0.497574	−	0.867422i	$-0.334224\pi$
$73$	−35.1241	−	48.3441i	−0.481152	−	0.662248i	−0.978726	+	0.205173i	$0.934224\pi$
$74$	45.6098	−	62.7765i	0.616348	−	0.848331i
$75$	−4.60847	−	14.1834i	−0.0614463	−	0.189112i
$76$		−	33.3422i		−	0.438713i
$77$	−18.5169	+	16.0678i	−0.240479	+	0.208673i
$78$	−9.09555			−0.116610
$79$	−81.5552	+	26.4989i	−1.03234	+	0.335429i	−0.775717	−	0.631081i	$-0.782611\pi$
$79$	−81.5552	+	26.4989i	−1.03234	+	0.335429i	−0.256627	+	0.966510i	$0.582611\pi$
$80$	17.0172	+	12.3638i	0.212716	+	0.154547i
$81$	64.7665	−	47.0556i	0.799587	−	0.580934i
$82$	−13.9155	+	42.8274i	−0.169701	+	0.522285i
$83$	−43.6902	−	14.1958i	−0.526388	−	0.171034i	0.0337544	−	0.999430i	$-0.489254\pi$
$83$	−43.6902	−	14.1958i	−0.526388	−	0.171034i	−0.560142	+	0.828396i	$0.689254\pi$
$84$	4.90260	+	6.74785i	0.0583643	+	0.0803315i
$85$	11.0203	−	15.1681i	0.129651	−	0.178449i
$86$	−7.66545	−	23.5918i	−0.0891331	−	0.274324i
$87$			161.369i			1.85481i
$88$	82.0485	+	49.3983i	0.932370	+	0.561344i
$89$	121.940			1.37011			0.685056	−	0.728490i	$-0.259778\pi$
$89$	121.940			1.37011			0.685056	+	0.728490i	$0.259778\pi$
$90$	−0.365432	+	0.118736i	−0.00406036	+	0.00131929i
$91$	3.31856	+	2.41107i	0.0364677	+	0.0264953i
$92$	7.74743	−	5.62884i	0.0842112	−	0.0611830i
$93$	−3.22512	+	9.92591i	−0.0346787	+	0.106730i
$94$	113.066	+	36.7372i	1.20282	+	0.390822i
$95$	34.9266	+	48.0724i	0.367649	+	0.506025i
$96$	33.7304	−	46.4259i	0.351358	−	0.483603i
$97$	−10.2685	−	31.6031i	−0.105861	−	0.325805i	0.884071	−	0.467353i	$-0.154792\pi$
$97$	−10.2685	−	31.6031i	−0.105861	−	0.325805i	−0.989931	+	0.141547i	$0.954792\pi$
$98$		−	72.9574i		−	0.744464i
$99$	−1.05051	+	0.444824i	−0.0106113	+	0.00449317i
$100$	6.27352			0.0627352
$101$	100.840	−	32.7650i	0.998420	−	0.324406i	0.236186	−	0.971708i	$-0.424103\pi$
$101$	100.840	−	32.7650i	0.998420	−	0.324406i	0.762234	+	0.647302i	$0.224103\pi$
$102$	33.5233	+	24.3561i	0.328660	+	0.238785i
$103$	158.992	−	115.514i	1.54361	−	1.12150i	0.595591	−	0.803288i	$-0.296918\pi$
$103$	158.992	−	115.514i	1.54361	−	1.12150i	0.948020	−	0.318211i	$-0.103082\pi$
$104$	4.95171	−	15.2398i	0.0476126	−	0.146537i
$105$	−14.1370	−	4.59339i	−0.134638	−	0.0437466i
$106$	−38.3782	−	52.8230i	−0.362058	−	0.498330i
$107$	−90.2208	+	124.178i	−0.843185	+	1.16054i	0.142139	+	0.989847i	$0.454602\pi$
$107$	−90.2208	+	124.178i	−0.843185	+	1.16054i	−0.985323	+	0.170697i	$0.945398\pi$
$108$	10.5280	+	32.4019i	0.0974816	+	0.300018i
$109$		−	35.9768i		−	0.330062i	−0.986288	−	0.165031i	$-0.947228\pi$
$109$		−	35.9768i		−	0.330062i	0.986288	−	0.165031i	$-0.0527725\pi$
$110$	−40.6022	+	3.51616i	−0.369111	+	0.0319651i
$111$	139.685			1.25842
$112$	19.9395	−	6.47874i	0.178031	−	0.0578459i
$113$	−107.159	−	77.8559i	−0.948314	−	0.688990i	0.00209353	−	0.999998i	$-0.499334\pi$
$113$	−107.159	−	77.8559i	−0.948314	−	0.688990i	−0.950407	+	0.311007i	$0.899334\pi$
$114$	−106.245	+	77.1918i	−0.931977	+	0.677121i
$115$	−5.27383	+	16.2312i	−0.0458594	+	0.141141i
$116$	−64.5599	−	20.9768i	−0.556551	−	0.180834i
$117$	0.112194	+	0.154422i	0.000958923	+	0.00131984i
$118$	−35.0689	+	48.2682i	−0.297194	+	0.409052i
$119$	−5.77476	−	17.7729i	−0.0485274	−	0.149352i
$120$			58.0674i			0.483895i
$121$	−119.199	+	20.8012i	−0.985112	+	0.171911i
$122$	−76.7503			−0.629101
$123$	−77.0959	+	25.0500i	−0.626796	+	0.203658i
$124$	−3.55188	−	2.58059i	−0.0286442	−	0.0208112i
$125$	−9.04508	+	6.57164i	−0.0723607	+	0.0525731i
$126$	−0.118348	+	0.364237i	−0.000939268	+	0.00289077i
$127$	−21.4191	−	6.95949i	−0.168654	−	0.0547991i	0.223473	−	0.974710i	$-0.428261\pi$
$127$	−21.4191	−	6.95949i	−0.168654	−	0.0547991i	−0.392127	+	0.919911i	$0.628261\pi$
$128$	−22.4562	−	30.9083i	−0.175439	−	0.241471i
$129$	26.2473	−	36.1262i	0.203467	−	0.280048i
$130$	2.10713	+	6.48509i	0.0162087	+	0.0498853i
$131$		−	69.8904i		−	0.533515i	−0.963764	−	0.266757i	$-0.914048\pi$
$131$		−	69.8904i		−	0.533515i	0.963764	−	0.266757i	$-0.0859522\pi$
$132$	3.55168	+	41.0125i	0.0269067	+	0.310701i
$133$	59.2264			0.445311
$134$	−95.8812	+	31.1537i	−0.715532	+	0.232490i
$135$	−49.1208	−	35.6884i	−0.363858	−	0.264358i
$136$	−59.0596	+	42.9093i	−0.434262	+	0.315509i
$137$	83.0828	−	255.703i	0.606444	−	1.86644i	0.119903	−	0.992786i	$-0.461742\pi$
$137$	83.0828	−	255.703i	0.606444	−	1.86644i	0.486541	−	0.873658i	$-0.338258\pi$
$138$	−35.8727	−	11.6557i	−0.259947	−	0.0844619i
$139$	−66.4957	−	91.5235i	−0.478386	−	0.658442i	0.499807	−	0.866137i	$-0.333404\pi$
$139$	−66.4957	−	91.5235i	−0.478386	−	0.658442i	−0.978194	+	0.207694i	$0.933404\pi$
$140$	3.67542	−	5.05878i	0.0262530	−	0.0361342i
$141$	66.1327	+	203.535i	0.469026	+	1.44351i
$142$			203.169i			1.43077i
$143$	7.89400	+	18.6428i	0.0552028	+	0.130369i
$144$	0.975591			0.00677493
$145$	115.055	−	37.3837i	0.793484	−	0.257819i
$146$	−80.1011	−	58.1968i	−0.548638	−	0.398609i
$147$	106.252	−	77.1966i	0.722803	−	0.525147i
$148$	−18.1580	+	55.8846i	−0.122689	+	0.377599i
$149$	185.247	+	60.1904i	1.24327	+	0.403962i	0.855504	−	0.517796i	$-0.173247\pi$
$149$	185.247	+	60.1904i	1.24327	+	0.403962i	0.387764	+	0.921759i	$0.373247\pi$
$150$	−14.5240	−	19.9906i	−0.0968270	−	0.133271i
$151$	−82.9127	+	114.120i	−0.549091	+	0.755758i	−0.989888	−	0.141848i	$-0.954696\pi$
$151$	−82.9127	+	114.120i	−0.549091	+	0.755758i	0.440798	+	0.897606i	$0.354696\pi$
$152$	−71.4954	−	220.040i	−0.470365	−	1.44763i
$153$		−	0.869583i		−	0.00568355i
$154$	−20.9520	+	34.8004i	−0.136052	+	0.225977i
$155$	7.82428			0.0504792
$156$	6.55062	−	2.12842i	0.0419911	−	0.0136437i
$157$	−39.8372	−	28.9434i	−0.253740	−	0.184353i	0.453643	−	0.891184i	$-0.350124\pi$
$157$	−39.8372	−	28.9434i	−0.253740	−	0.184353i	−0.707383	+	0.706831i	$0.750124\pi$
$158$	−114.947	+	83.5138i	−0.727512	+	0.528569i
$159$	36.3210	−	111.785i	0.228434	−	0.703048i
$160$	−40.9157	−	13.2943i	−0.255723	−	0.0830894i
$161$	9.99860	+	13.7619i	0.0621031	+	0.0854776i
$162$	77.9662	−	107.311i	0.481273	−	0.662415i
$163$	77.2981	+	237.899i	0.474222	+	1.45950i	0.847005	+	0.531586i	$0.178404\pi$
$163$	77.2981	+	237.899i	0.474222	+	1.45950i	−0.372783	+	0.927919i	$0.621596\pi$
$164$		−	34.1006i		−	0.207930i
$165$	−48.0822	−	55.4108i	−0.291407	−	0.335823i
$166$	−76.1154			−0.458526
$167$	263.329	−	85.5607i	1.57682	−	0.512340i	0.615585	−	0.788071i	$-0.288920\pi$
$167$	263.329	−	85.5607i	1.57682	−	0.512340i	0.961235	+	0.275731i	$0.0889199\pi$
$168$	46.8238	+	34.0195i	0.278713	+	0.202497i
$169$	−133.983	+	97.3447i	−0.792801	+	0.576004i
$170$	9.59957	−	29.5444i	0.0564681	−	0.173791i
$171$	2.62108	+	0.851641i	0.0153280	+	0.00498036i
$172$	11.0413	+	15.1971i	0.0641937	+	0.0883550i
$173$	−1.43083	+	1.96937i	−0.00827072	+	0.0113837i	−0.813132	−	0.582079i	$-0.802239\pi$
$173$	−1.43083	+	1.96937i	−0.00827072	+	0.0113837i	0.804862	+	0.593463i	$0.202239\pi$
$174$	82.6221	+	254.285i	0.474840	+	1.46141i
$175$			11.1438i			0.0636787i
$176$	100.803	+	23.3659i	0.572746	+	0.132761i
$177$	−107.402			−0.606792
$178$	192.153	−	62.4343i	1.07951	−	0.350754i
$179$	−117.428	−	85.3162i	−0.656020	−	0.476627i	0.209296	−	0.977852i	$-0.432883\pi$
$179$	−117.428	−	85.3162i	−0.656020	−	0.476627i	−0.865317	+	0.501226i	$0.832883\pi$
$180$	0.235399	−	0.171028i	0.00130777	−	0.000950153i
$181$	−49.3147	+	151.775i	−0.272457	+	0.838535i	0.717424	+	0.696636i	$0.245321\pi$
$181$	−49.3147	+	151.775i	−0.272457	+	0.838535i	−0.989881	+	0.141899i	$0.954679\pi$
$182$	6.46387	+	2.10024i	0.0355158	+	0.0115398i
$183$	−81.2098	−	111.776i	−0.443769	−	0.610796i
$184$	39.0589	−	53.7600i	0.212277	−	0.292174i
$185$	−32.3603	−	99.5947i	−0.174920	−	0.538350i
$186$			17.2925i			0.0929706i
$187$	20.8270	−	89.8499i	0.111374	−	0.480481i
$188$	−90.0266			−0.478865
$189$	−57.5561	+	18.7011i	−0.304529	+	0.0989476i
$190$	79.6508	+	57.8697i	0.419215	+	0.304578i
$191$	−59.2898	+	43.0766i	−0.310418	+	0.225532i	−0.732076	−	0.681223i	$-0.761448\pi$
$191$	−59.2898	+	43.0766i	−0.310418	+	0.225532i	0.421658	+	0.906755i	$0.361448\pi$
$192$	64.0630	−	197.166i	0.333662	−	1.02691i
$193$	250.612	+	81.4288i	1.29851	+	0.421911i	0.875062	−	0.484010i	$-0.160820\pi$
$193$	250.612	+	81.4288i	1.29851	+	0.421911i	0.423446	+	0.905921i	$0.360820\pi$
$194$	−32.3621	−	44.5426i	−0.166815	−	0.229601i
$195$	−7.21503	+	9.93064i	−0.0370002	+	0.0509263i
$196$	17.0726	+	52.5439i	0.0871049	+	0.268081i
$197$			219.288i			1.11313i	0.830803	+	0.556567i	$0.187882\pi$
$197$			219.288i			1.11313i	−0.830803	+	0.556567i	$0.812118\pi$
$198$	−1.42765	+	1.23883i	−0.00721034	+	0.00625670i
$199$	−108.109			−0.543261			−0.271630	−	0.962402i	$-0.587563\pi$
$199$	−108.109			−0.543261			−0.271630	+	0.962402i	$0.587563\pi$
$200$	41.4018	−	13.4523i	0.207009	−	0.0672613i
$201$	−146.823	−	106.673i	−0.730464	−	0.530713i
$202$	142.128	−	103.262i	0.703605	−	0.511199i
$203$	37.2614	−	114.679i	0.183554	−	0.564920i
$204$	−29.8430	−	9.69657i	−0.146289	−	0.0475322i
$205$	35.7211	+	49.1658i	0.174249	+	0.239833i
$206$	191.395	−	263.433i	0.929102	−	1.27880i
$207$	0.244603	+	0.752811i	0.00118166	+	0.00363677i
$208$		−	17.3132i		−	0.0832364i
$209$	250.427	+	150.772i	1.19822	+	0.721399i
$210$	−24.6290			−0.117281
$211$	237.612	−	77.2048i	1.12612	−	0.365900i	0.314022	−	0.949416i	$-0.398323\pi$
$211$	237.612	−	77.2048i	1.12612	−	0.365900i	0.812102	+	0.583516i	$0.198323\pi$
$212$	40.0009	+	29.0624i	0.188684	+	0.137087i
$213$	−295.887	+	214.974i	−1.38914	+	1.00927i
$214$	−78.5895	+	241.874i	−0.367241	+	1.13025i
$215$	−31.8385	−	10.3449i	−0.148086	−	0.0481160i
$216$	138.958	+	191.260i	0.643325	+	0.885461i
$217$	4.58395	−	6.30927i	0.0211242	−	0.0290750i
$218$	−18.4204	−	56.6922i	−0.0844973	−	0.260056i
$219$		−	178.234i		−	0.813854i
$220$	28.4189	−	12.0335i	0.129177	−	0.0546979i
$221$	−15.4319			−0.0698277
$222$	220.115	−	71.5198i	0.991510	−	0.322161i
$223$	−114.964	−	83.5261i	−0.515533	−	0.374557i	0.299385	−	0.954132i	$-0.403218\pi$
$223$	−114.964	−	83.5261i	−0.515533	−	0.374557i	−0.814919	+	0.579576i	$0.803218\pi$
$224$	−34.6911	+	25.2046i	−0.154871	+	0.112520i
$225$	−0.160241	+	0.493171i	−0.000712182	+	0.00219187i
$226$	−208.725	−	67.8188i	−0.923561	−	0.300083i
$227$	24.2567	+	33.3864i	0.106858	+	0.147077i	0.859097	−	0.511814i	$-0.171026\pi$
$227$	24.2567	+	33.3864i	0.106858	+	0.147077i	−0.752239	+	0.658890i	$0.771026\pi$
$228$	58.4545	−	80.4557i	0.256379	−	0.352876i
$229$	110.190	+	339.131i	0.481180	+	1.48092i	0.837438	+	0.546532i	$0.184052\pi$
$229$	110.190	+	339.131i	0.481180	+	1.48092i	−0.356258	+	0.934387i	$0.615948\pi$
$230$			28.2773i			0.122945i
$231$	−72.8512	+	6.30892i	−0.315373	+	0.0273113i
$232$	−471.040			−2.03035
$233$	−181.617	+	59.0111i	−0.779474	+	0.253266i	−0.671615	−	0.740900i	$-0.734399\pi$
$233$	−181.617	+	59.0111i	−0.779474	+	0.253266i	−0.107858	+	0.994166i	$0.534399\pi$
$234$	0.255861	+	0.185894i	0.00109342	+	0.000794417i
$235$	129.799	−	94.3046i	0.552337	−	0.401296i
$236$	13.9615	−	42.9691i	0.0591589	−	0.182073i
$237$	−243.252	−	79.0373i	−1.02638	−	0.333491i
$238$	−18.1997	−	25.0498i	−0.0764695	−	0.105251i
$239$	−165.024	+	227.136i	−0.690476	+	0.950359i	−1.00000		0.000532544i	$-0.999830\pi$
$239$	−165.024	+	227.136i	−0.690476	+	0.950359i	0.309523	+	0.950892i	$0.399830\pi$
$240$	19.3873	+	59.6681i	0.0807806	+	0.248617i
$241$		−	274.304i		−	1.13819i	−0.822271	−	0.569096i	$-0.807293\pi$
$241$		−	274.304i		−	1.13819i	0.822271	−	0.569096i	$-0.192707\pi$
$242$	−177.183	+	93.8092i	−0.732160	+	0.387641i
$243$	−5.60007			−0.0230455
$244$	55.2755	−	17.9601i	0.226539	−	0.0736070i
$245$	−79.6558	−	57.8733i	−0.325126	−	0.236218i
$246$	−108.662	+	78.9475i	−0.441715	+	0.320925i
$247$	15.1135	−	46.5146i	0.0611883	−	0.188318i
$248$	−28.9740	−	9.41422i	−0.116831	−	0.0379606i
$249$	−80.5380	−	110.851i	−0.323446	−	0.445185i
$250$	−10.8885	+	14.9867i	−0.0435540	+	0.0599470i
$251$	−37.0091	−	113.902i	−0.147447	−	0.453794i	0.849871	−	0.526991i	$-0.176680\pi$
$251$	−37.0091	−	113.902i	−0.147447	−	0.453794i	−0.997318	+	0.0731969i	$0.976680\pi$
$252$		−	0.290018i		−	0.00115086i
$253$	7.24348	+	83.6429i	0.0286304	+	0.330604i
$254$	−37.3155			−0.146911
$255$	53.1846	−	17.2807i	0.208567	−	0.0677675i
$256$	173.714	+	126.210i	0.678568	+	0.493009i
$257$	−29.6399	+	21.5347i	−0.115331	+	0.0837925i	−0.643955	−	0.765063i	$-0.722708\pi$
$257$	−29.6399	+	21.5347i	−0.115331	+	0.0837925i	0.528625	+	0.848856i	$0.322708\pi$
$258$	22.8635	−	70.3665i	0.0886181	−	0.272738i
$259$	−99.2689	−	32.2544i	−0.383277	−	0.124534i
$260$	−3.03511	−	4.17748i	−0.0116735	−	0.0160672i
$261$	3.29803	−	4.53935i	0.0126361	−	0.0173922i
$262$	−35.7845	−	110.133i	−0.136582	−	0.420356i
$263$		−	26.4631i		−	0.100620i	−0.998734	−	0.0503101i	$-0.983979\pi$
$263$		−	26.4631i		−	0.100620i	0.998734	−	0.0503101i	$-0.0160210\pi$
$264$	111.382	+	263.044i	0.421901	+	0.996379i
$265$	−88.1163			−0.332514
$266$	93.3289	−	30.3244i	0.350860	−	0.114001i
$267$	294.244	+	213.781i	1.10204	+	0.800678i
$268$	61.7635	−	44.8738i	0.230461	−	0.167440i
$269$	12.2133	−	37.5885i	0.0454024	−	0.139734i	−0.925786	−	0.378049i	$-0.876595\pi$
$269$	12.2133	−	37.5885i	0.0454024	−	0.139734i	0.971188	+	0.238315i	$0.0765950\pi$
$270$	−95.6773	−	31.0874i	−0.354360	−	0.115139i
$271$	−244.596	−	336.658i	−0.902568	−	1.24228i	−0.969642	−	0.244531i	$-0.921366\pi$
$271$	−244.596	−	336.658i	−0.902568	−	1.24228i	0.0670732	−	0.997748i	$-0.478634\pi$
$272$	−46.3612	+	63.8108i	−0.170446	+	0.234598i
$273$	3.78076	+	11.6360i	0.0138489	+	0.0426226i
$274$		−	445.475i		−	1.62582i
$275$	−28.3687	+	47.1192i	−0.103159	+	0.171343i
$276$	28.5630			0.103489
$277$	−114.108	+	37.0759i	−0.411942	+	0.133848i	−0.507654	−	0.861561i	$-0.669487\pi$
$277$	−114.108	+	37.0759i	−0.411942	+	0.133848i	0.0957120	+	0.995409i	$0.469487\pi$
$278$	−151.645	−	110.176i	−0.545484	−	0.396318i
$279$	0.293588	−	0.213304i	0.00105229	−	0.000764531i
$280$	13.4083	−	41.2664i	0.0478866	−	0.147380i
$281$	406.555	+	132.098i	1.44681	+	0.470098i	0.924014	−	0.382358i	$-0.124888\pi$
$281$	406.555	+	132.098i	1.44681	+	0.470098i	0.522799	+	0.852456i	$0.324888\pi$
$282$	208.424	+	286.871i	0.739091	+	1.01727i
$283$	119.366	−	164.293i	0.421787	−	0.580541i	−0.544256	−	0.838919i	$-0.683188\pi$
$283$	119.366	−	164.293i	0.421787	−	0.580541i	0.966044	+	0.258378i	$0.0831881\pi$
$284$	−47.5431	−	146.323i	−0.167405	−	0.515220i
$285$			177.232i			0.621867i
$286$	21.9846	+	25.3355i	0.0768693	+	0.0885857i
$287$	60.5735			0.211057
$288$	−1.89769	+	0.616598i	−0.00658921	+	0.00214096i
$289$	−176.929	−	128.546i	−0.612211	−	0.444797i
$290$	162.163	−	117.818i	0.559183	−	0.406271i
$291$	30.6274	−	94.2615i	0.105249	−	0.323923i
$292$	71.3073	+	23.1691i	0.244203	+	0.0793464i
$293$	240.571	+	331.117i	0.821061	+	1.13009i	0.989522	+	0.144385i	$0.0461205\pi$
$293$	240.571	+	331.117i	0.821061	+	1.13009i	−0.168460	+	0.985708i	$0.553880\pi$
$294$	127.907	−	176.048i	0.435056	−	0.598803i
$295$	24.8815	+	76.5773i	0.0843440	+	0.259584i
$296$			407.744i			1.37751i
$297$	−290.972	−	67.4465i	−0.979703	−	0.227092i
$298$	322.730			1.08299
$299$	13.3597	−	4.34081i	0.0446811	−	0.0145178i
$300$	15.1382	+	10.9985i	0.0504606	+	0.0366618i
$301$	−26.9948	+	19.6129i	−0.0896838	+	0.0651591i
$302$	−72.2236	+	222.281i	−0.239151	+	0.736031i
$303$	300.773	+	97.7271i	0.992651	+	0.322532i
$304$	−146.933	−	202.235i	−0.483331	−	0.665248i
$305$	−60.8820	+	83.7969i	−0.199613	+	0.274744i
$306$	−0.445233	−	1.37029i	−0.00145501	−	0.00447806i
$307$			548.367i			1.78621i	0.449846	+	0.893106i	$0.351479\pi$
$307$			548.367i			1.78621i	−0.449846	+	0.893106i	$0.648521\pi$
$308$	6.94608	−	29.9662i	0.0225522	−	0.0972928i
$309$	586.168			1.89698
$310$	12.3295	−	4.00610i	0.0397726	−	0.0129229i
$311$	−37.3991	−	27.1721i	−0.120254	−	0.0873700i	0.526032	−	0.850465i	$-0.323679\pi$
$311$	−37.3991	−	27.1721i	−0.120254	−	0.0873700i	−0.646287	+	0.763095i	$0.723679\pi$
$312$	38.6665	−	28.0929i	0.123931	−	0.0900412i
$313$	0.359023	−	1.10496i	0.00114704	−	0.00353022i	−0.950481	−	0.310782i	$-0.899409\pi$
$313$	0.359023	−	1.10496i	0.00114704	−	0.00353022i	0.951628	+	0.307251i	$0.0994092\pi$
$314$	−77.5947	−	25.2120i	−0.247117	−	0.0802931i
$315$	0.303799	+	0.418144i	0.000964442	+	0.00132744i
$316$	63.2419	−	87.0451i	0.200133	−	0.275459i
$317$	36.3906	+	111.999i	0.114797	+	0.353308i	0.991905	−	0.126985i	$-0.0405301\pi$
$317$	36.3906	+	111.999i	0.114797	+	0.353308i	−0.877108	+	0.480294i	$0.840530\pi$
$318$		−	194.747i		−	0.612411i
$319$	449.490	−	390.041i	1.40906	−	1.22270i
$320$	−155.420			−0.485686
$321$	−435.410	+	141.473i	−1.35642	+	0.440727i
$322$	22.8020	+	16.5666i	0.0708137	+	0.0514491i
$323$	−180.261	+	130.967i	−0.558082	+	0.405470i
$324$	−31.0396	+	95.5302i	−0.0958014	+	0.294846i
$325$	8.75198	+	2.84369i	0.0269292	+	0.00874982i
$326$	243.613	+	335.304i	0.747278	+	1.02854i
$327$	63.0733	−	86.8130i	0.192885	−	0.265483i
$328$	−73.1216	−	225.045i	−0.222932	−	0.686113i
$329$		−	159.916i		−	0.486066i
$330$	−104.139	−	62.6979i	−0.315572	−	0.189994i
$331$	−151.229			−0.456885			−0.228443	−	0.973557i	$-0.573363\pi$
$331$	−151.229			−0.456885			−0.228443	+	0.973557i	$0.573363\pi$
$332$	54.8183	−	17.8115i	0.165115	−	0.0536492i
$333$	−3.92937	−	2.85486i	−0.0117999	−	0.00857315i
$334$	371.146	−	269.653i	1.11121	−	0.807345i
$335$	−42.0436	+	129.397i	−0.125503	+	0.386260i
$336$	59.4729	+	19.3239i	0.177003	+	0.0575117i
$337$	−211.142	−	290.612i	−0.626534	−	0.862351i	0.371274	−	0.928523i	$-0.378921\pi$
$337$	−211.142	−	290.612i	−0.626534	−	0.862351i	−0.997808	+	0.0661727i	$0.978921\pi$
$338$	−161.290	+	221.996i	−0.477189	+	0.656794i
$339$	−122.084	−	375.737i	−0.360131	−	1.10837i
$340$			23.5243i			0.0691890i
$341$	35.4438	−	15.0081i	0.103941	−	0.0440121i
$342$	4.56635			0.0133519
$343$	−197.199	+	64.0737i	−0.574923	+	0.186804i
$344$	105.454	+	76.6165i	0.306551	+	0.222722i
$345$	−41.1819	+	29.9204i	−0.119368	+	0.0867257i
$346$	−1.24637	+	3.83594i	−0.00360223	+	0.0110865i
$347$	−73.4954	−	23.8801i	−0.211802	−	0.0688187i	0.201194	−	0.979551i	$-0.435518\pi$
$347$	−73.4954	−	23.8801i	−0.211802	−	0.0688187i	−0.412996	+	0.910733i	$0.635518\pi$
$348$	−119.009	−	163.802i	−0.341980	−	0.470695i
$349$	−246.959	+	339.910i	−0.707619	+	0.973954i	0.292226	+	0.956349i	$0.405604\pi$
$349$	−246.959	+	339.910i	−0.707619	+	0.973954i	−0.999845	+	0.0176044i	$0.994396\pi$
$350$	5.70570	+	17.5603i	0.0163020	+	0.0501724i
$351$			49.9750i			0.142379i
$352$	−210.848	+	18.2594i	−0.598999	+	0.0518734i
$353$	640.543			1.81457			0.907285	−	0.420516i	$-0.138151\pi$
$353$	640.543			1.81457			0.907285	+	0.420516i	$0.138151\pi$
$354$	−169.244	+	54.9908i	−0.478091	+	0.155341i
$355$	221.823	+	161.164i	0.624853	+	0.453982i
$356$	−123.778	+	89.9303i	−0.347692	+	0.252613i
$357$	17.2242	−	53.0106i	0.0482470	−	0.148489i
$358$	−228.725	−	74.3172i	−0.638896	−	0.207590i
$359$	−198.623	−	273.381i	−0.553268	−	0.761508i	0.437183	−	0.899372i	$-0.355976\pi$
$359$	−198.623	−	273.381i	−0.553268	−	0.761508i	−0.990451	+	0.137865i	$0.955976\pi$
$360$	1.18677	−	1.63345i	0.00329659	−	0.00453737i
$361$	−106.662	−	328.272i	−0.295462	−	0.909340i
$362$			264.416i			0.730432i
$363$	−324.097	−	158.781i	−0.892830	−	0.437414i
$364$	−5.14675			−0.0141394
$365$	−127.080	+	41.2908i	−0.348165	+	0.113126i
$366$	−185.200	−	134.556i	−0.506012	−	0.367639i
$367$	381.543	−	277.207i	1.03963	−	0.755333i	0.0694140	−	0.997588i	$-0.477887\pi$
$367$	381.543	−	277.207i	1.03963	−	0.755333i	0.970213	+	0.242255i	$0.0778871\pi$
$368$	22.1864	−	68.2828i	0.0602892	−	0.185551i
$369$	2.68070	+	0.871012i	0.00726477	+	0.00236047i
$370$	−101.987	−	140.372i	−0.275639	−	0.379385i
$371$	−51.6240	+	71.0543i	−0.139148	+	0.191521i
$372$	−4.04657	−	12.4541i	−0.0108779	−	0.0334787i
$373$		−	50.8370i		−	0.136292i	−0.997675	−	0.0681461i	$-0.978292\pi$
$373$		−	50.8370i		−	0.136292i	0.997675	−	0.0681461i	$-0.0217084\pi$
$374$	−13.1848	−	152.249i	−0.0352534	−	0.407083i
$375$	−33.3472			−0.0889259
$376$	−594.126	+	193.043i	−1.58012	+	0.513413i
$377$	−80.5569	−	58.5280i	−0.213679	−	0.155247i
$378$	−81.1217	+	58.9384i	−0.214608	+	0.155922i
$379$	−181.638	+	559.025i	−0.479256	+	1.47500i	0.360874	+	0.932615i	$0.382479\pi$
$379$	−181.638	+	559.025i	−0.479256	+	1.47500i	−0.840130	+	0.542385i	$0.817521\pi$
$380$	−70.9065	−	23.0389i	−0.186596	−	0.0606287i
$381$	−39.4837	−	54.3447i	−0.103632	−	0.142637i
$382$	−71.3733	+	98.2369i	−0.186841	+	0.257165i
$383$	−10.4312	−	32.1040i	−0.0272356	−	0.0838226i	0.936515	−	0.350628i	$-0.114032\pi$
$383$	−10.4312	−	32.1040i	−0.0272356	−	0.0838226i	−0.963750	+	0.266806i	$0.914032\pi$
$384$		−	113.952i		−	0.296750i
$385$	21.3754	+	50.4810i	0.0555205	+	0.131120i
$386$	436.607			1.13111
$387$	−1.47669	+	0.479804i	−0.00381573	+	0.00123980i
$388$	33.7305	+	24.5066i	0.0869342	+	0.0631614i
$389$	−418.883	+	304.337i	−1.07682	+	0.782356i	−0.977126	−	0.212662i	$-0.931787\pi$
$389$	−418.883	+	304.337i	−1.07682	+	0.782356i	−0.0996952	+	0.995018i	$0.531787\pi$
$390$	−6.28487	+	19.3428i	−0.0161151	+	0.0495970i
$391$	−60.8632	−	19.7757i	−0.155660	−	0.0505771i
$392$	225.339	+	310.153i	0.574845	+	0.791206i
$393$	122.530	−	168.647i	0.311780	−	0.429128i
$394$	112.277	+	345.553i	0.284967	+	0.877038i
$395$			191.748i			0.485437i
$396$	0.738297	−	1.22628i	0.00186439	−	0.00309667i
$397$	86.1063			0.216893			0.108446	−	0.994102i	$-0.465412\pi$
$397$	86.1063			0.216893			0.108446	+	0.994102i	$0.465412\pi$
$398$	−170.358	+	55.3526i	−0.428035	+	0.139077i
$399$	142.915	+	103.834i	0.358182	+	0.260235i
$400$	38.0517	−	27.6462i	0.0951293	−	0.0691155i
$401$	49.8340	−	153.373i	0.124274	−	0.382477i	−0.869494	−	0.493944i	$-0.835555\pi$
$401$	49.8340	−	153.373i	0.124274	−	0.382477i	0.993768	+	0.111467i	$0.0355548\pi$
$402$	−285.982	−	92.9211i	−0.711397	−	0.231147i
$403$	−3.78537	−	5.21011i	−0.00939297	−	0.0129283i
$404$	−78.1967	+	107.629i	−0.193556	+	0.266407i
$405$	−55.3172	−	170.249i	−0.136586	−	0.420368i
$406$		−	199.789i		−	0.492091i
$407$	−337.629	−	389.090i	−0.829555	−	0.955995i
$408$	−217.739			−0.533675
$409$	220.213	−	71.5515i	0.538418	−	0.174943i	−0.0271696	−	0.999631i	$-0.508649\pi$
$409$	220.213	−	71.5515i	0.538418	−	0.174943i	0.565588	+	0.824688i	$0.308649\pi$
$410$	81.4625	+	59.1860i	0.198689	+	0.144356i
$411$	648.771	−	471.359i	1.57852	−	1.14686i
$412$	−76.1976	+	234.512i	−0.184946	+	0.569204i
$413$	76.3268	+	24.8001i	0.184811	+	0.0600486i
$414$	0.770891	+	1.06104i	0.00186206	+	0.00256290i
$415$	−60.3784	+	83.1037i	−0.145490	+	0.200250i
$416$	10.9424	+	33.6771i	0.0263037	+	0.0809546i
$417$		−	337.427i		−	0.809177i
$418$	471.819	+	109.366i	1.12875	+	0.261642i
$419$	428.346			1.02231			0.511153	−	0.859490i	$-0.329219\pi$
$419$	428.346			1.02231			0.511153	+	0.859490i	$0.329219\pi$
$420$	17.7378	−	5.76335i	0.0422328	−	0.0137223i
$421$	423.964	+	308.028i	1.00704	+	0.731657i	0.963586	−	0.267398i	$-0.0861639\pi$
$421$	423.964	+	308.028i	1.00704	+	0.731657i	0.0434535	+	0.999055i	$0.486164\pi$
$422$	334.899	−	243.319i	0.793600	−	0.576584i
$423$	2.29950	−	7.07712i	0.00543616	−	0.0167308i
$424$	326.302	+	106.022i	0.769581	+	0.250052i
$425$	−24.6421	−	33.9170i	−0.0579815	−	0.0798047i
$426$	−356.190	+	490.253i	−0.836126	+	1.15083i
$427$	31.9029	+	98.1869i	0.0747140	+	0.229946i
$428$		−	192.588i		−	0.449972i
$429$	−13.6355	+	58.8251i	−0.0317844	+	0.137121i
$430$	−55.4677			−0.128995
$431$	8.66101	−	2.81413i	0.0200952	−	0.00652931i	−0.298952	−	0.954268i	$-0.596637\pi$
$431$	8.66101	−	2.81413i	0.0200952	−	0.00652931i	0.319047	+	0.947739i	$0.396637\pi$
$432$	206.646	+	150.137i	0.478347	+	0.347540i
$433$	159.214	−	115.676i	0.367700	−	0.267150i	−0.388556	−	0.921425i	$-0.627026\pi$
$433$	159.214	−	115.676i	0.367700	−	0.267150i	0.756257	+	0.654275i	$0.227026\pi$
$434$	3.99299	−	12.2892i	0.00920044	−	0.0283160i
$435$	343.171	+	111.503i	0.788899	+	0.256329i
$436$	26.5328	+	36.5192i	0.0608550	+	0.0837597i
$437$	119.215	−	164.085i	0.272803	−	0.375481i
$438$	−91.2573	−	280.861i	−0.208350	−	0.641235i
$439$			48.0326i			0.109414i	0.998502	+	0.0547069i	$0.0174224\pi$
$439$			48.0326i			0.109414i	−0.998502	+	0.0547069i	$0.982578\pi$
$440$	161.746	−	140.353i	0.367604	−	0.318985i
$441$	−4.56663			−0.0103552
$442$	−24.3176	+	7.90127i	−0.0550172	+	0.0178762i
$443$	102.069	+	74.1577i	0.230405	+	0.167399i	0.696998	−	0.717073i	$-0.254519\pi$
$443$	102.069	+	74.1577i	0.230405	+	0.167399i	−0.466593	+	0.884472i	$0.654519\pi$
$444$	−141.791	+	103.017i	−0.319349	+	0.232020i
$445$	84.2584	−	259.321i	0.189345	−	0.582743i
$446$	−223.926	−	72.7580i	−0.502076	−	0.163135i
$447$	341.482	+	470.010i	0.763942	+	1.05148i
$448$	−91.0545	+	125.326i	−0.203247	+	0.279745i
$449$	−13.6570	−	42.0320i	−0.0304165	−	0.0936124i	0.934696	−	0.355449i	$-0.115672\pi$
$449$	−13.6570	−	42.0320i	−0.0304165	−	0.0936124i	−0.965112	+	0.261836i	$0.915672\pi$
$450$			0.859183i			0.00190930i
$451$	256.123	+	154.202i	0.567900	+	0.341911i
$452$	166.194			0.367685
$453$	−400.141	+	130.014i	−0.883314	+	0.287006i
$454$	55.3177	+	40.1907i	0.121845	+	0.0885258i
$455$	7.42052	−	5.39133i	0.0163088	−	0.0118491i
$456$	213.247	−	656.307i	0.467647	−	1.43927i
$457$	−503.324	−	163.540i	−1.10137	−	0.357855i	−0.298738	−	0.954335i	$-0.596566\pi$
$457$	−503.324	−	163.540i	−1.10137	−	0.357855i	−0.802628	+	0.596480i	$0.796566\pi$
$458$	347.275	+	477.983i	0.758243	+	1.04363i
$459$	133.823	−	184.192i	0.291554	−	0.401289i
$460$	−6.61710	−	20.3653i	−0.0143850	−	0.0442725i
$461$		−	258.714i		−	0.561202i	−0.959825	−	0.280601i	$-0.909466\pi$
$461$		−	258.714i		−	0.561202i	0.959825	−	0.280601i	$-0.0905337\pi$
$462$	−111.569	+	47.2420i	−0.241491	+	0.102255i
$463$	−269.759			−0.582633			−0.291317	−	0.956627i	$-0.594093\pi$
$463$	−269.759			−0.582633			−0.291317	+	0.956627i	$0.594093\pi$
$464$	−484.025	+	157.269i	−1.04316	+	0.338942i
$465$	18.8802	+	13.7173i	0.0406026	+	0.0294995i
$466$	−255.978	+	185.979i	−0.549310	+	0.399097i
$467$	−39.5114	+	121.604i	−0.0846070	+	0.260393i	−0.984406	−	0.175911i	$-0.943713\pi$
$467$	−39.5114	+	121.604i	−0.0846070	+	0.260393i	0.899799	+	0.436304i	$0.143713\pi$
$468$	−0.227771	−	0.0740073i	−0.000486691	−	0.000158135i
$469$	79.7101	+	109.712i	0.169958	+	0.233927i
$470$	156.253	−	215.063i	0.332453	−	0.457582i
$471$	−45.3856	−	139.682i	−0.0963600	−	0.296566i
$472$		−	313.510i		−	0.664216i
$473$	−164.071	+	14.2085i	−0.346872	+	0.0300392i
$474$	−423.784			−0.894058
$475$	126.366	−	41.0587i	0.266033	−	0.0864394i
$476$	18.9693	+	13.7820i	0.0398514	+	0.0289537i
$477$	−3.30636	+	2.40221i	−0.00693157	+	0.00503608i
$478$	−143.749	+	442.414i	−0.300730	+	0.925553i
$479$	−478.561	−	155.494i	−0.999084	−	0.324622i	−0.236584	−	0.971611i	$-0.576028\pi$
$479$	−478.561	−	155.494i	−0.999084	−	0.324622i	−0.762499	+	0.646989i	$0.776028\pi$
$480$	−75.4235	−	103.812i	−0.157132	−	0.216274i
$481$	−50.6633	+	69.7320i	−0.105329	+	0.144973i
$482$	−140.446	−	432.249i	−0.291382	−	0.896781i
$483$			50.7370i			0.105046i
$484$	105.655	−	109.023i	0.218295	−	0.225255i
$485$	−74.3034			−0.153203
$486$	−8.82458	+	2.86728i	−0.0181576	+	0.00589975i
$487$	166.147	+	120.713i	0.341164	+	0.247870i	0.745153	−	0.666894i	$-0.232377\pi$
$487$	166.147	+	120.713i	0.341164	+	0.247870i	−0.403989	+	0.914764i	$0.632377\pi$
$488$	326.277	−	237.054i	0.668599	−	0.485766i
$489$	−230.554	+	709.574i	−0.471481	+	1.45107i
$490$	−155.153	−	50.4123i	−0.316639	−	0.102882i
$491$	−56.3909	−	77.6154i	−0.114849	−	0.158076i	0.747722	−	0.664011i	$-0.231147\pi$
$491$	−56.3909	−	77.6154i	−0.114849	−	0.158076i	−0.862571	+	0.505935i	$0.831147\pi$
$492$	59.7840	−	82.2856i	0.121512	−	0.167247i
$493$	140.180	+	431.431i	0.284342	+	0.875113i
$494$		−	81.0360i		−	0.164040i
$495$	0.220087	+	2.54142i	0.000444620	+	0.00513418i
$496$	−32.9159			−0.0663627
$497$	259.915	−	84.4516i	0.522969	−	0.169923i
$498$	−183.668	−	133.443i	−0.368812	−	0.267958i
$499$	−183.447	+	133.282i	−0.367630	+	0.267099i	−0.756227	−	0.654309i	$-0.772960\pi$
$499$	−183.447	+	133.282i	−0.367630	+	0.267099i	0.388598	+	0.921408i	$0.372960\pi$
$500$	4.33490	−	13.3414i	0.00866979	−	0.0266829i
$501$	785.422	+	255.199i	1.56771	+	0.509379i
$502$	−116.638	−	160.538i	−0.232346	−	0.319797i
$503$	56.2423	−	77.4109i	0.111814	−	0.153898i	−0.749442	−	0.662070i	$-0.769678\pi$
$503$	56.2423	−	77.4109i	0.111814	−	0.153898i	0.861256	+	0.508171i	$0.169678\pi$
$504$	−0.621882	−	1.91396i	−0.00123389	−	0.00379753i
$505$		−	237.090i		−	0.469485i
$506$	54.2401	+	128.096i	0.107194	+	0.253154i
$507$	−493.967			−0.974294
$508$	26.8746	−	8.73210i	0.0529028	−	0.0171892i
$509$	80.9705	+	58.8285i	0.159078	+	0.115577i	0.664476	−	0.747309i	$-0.268655\pi$
$509$	80.9705	+	58.8285i	0.159078	+	0.115577i	−0.505399	+	0.862886i	$0.668655\pi$
$510$	74.9603	−	54.4619i	0.146981	−	0.106788i
$511$	−41.1557	+	126.664i	−0.0805396	+	0.247875i
$512$	483.698	+	157.163i	0.944723	+	0.306959i
$513$	424.126	+	583.759i	0.826756	+	1.13793i
$514$	−35.6807	+	49.1102i	−0.0694177	+	0.0955452i
$515$	−135.795	−	417.935i	−0.263680	−	0.811524i
$516$			56.0282i			0.108582i
$517$	407.097	−	676.172i	0.787422	−	1.30788i
$518$	−172.942			−0.333865
$519$	−6.90528	+	2.24366i	−0.0133050	+	0.00432305i
$520$	−28.9878	−	21.0609i	−0.0557458	−	0.0405017i
$521$	−398.168	+	289.286i	−0.764237	+	0.555251i	−0.900207	−	0.435462i	$-0.856585\pi$
$521$	−398.168	+	289.286i	−0.764237	+	0.555251i	0.135970	+	0.990713i	$0.456585\pi$
$522$	2.87285	−	8.84173i	0.00550355	−	0.0169382i
$523$	−423.738	−	137.681i	−0.810206	−	0.263252i	−0.125521	−	0.992091i	$-0.540060\pi$
$523$	−423.738	−	137.681i	−0.810206	−	0.263252i	−0.684685	+	0.728839i	$0.740060\pi$
$524$	51.5440	+	70.9442i	0.0983663	+	0.135390i
$525$	−19.5369	+	26.8902i	−0.0372131	+	0.0512194i
$526$	−13.5493	−	41.7006i	−0.0257592	−	0.0792787i
$527$			29.3393i			0.0556722i
$528$	202.277	+	233.107i	0.383100	+	0.441491i
$529$	−470.747			−0.889881
$530$	−138.854	+	45.1162i	−0.261988	+	0.0851250i
$531$	3.02126	+	2.19507i	0.00568975	+	0.00413384i
$532$	−60.1193	+	43.6792i	−0.113006	+	0.0821039i
$533$	15.4573	−	47.5726i	0.0290005	−	0.0892544i
$534$	573.128	+	186.220i	1.07327	+	0.348728i
$535$	201.740	+	277.671i	0.377084	+	0.519011i
$536$	311.383	−	428.581i	0.580938	−	0.799592i
$537$	−133.783	−	411.740i	−0.249130	−	0.766742i
$538$		−	65.4853i		−	0.121720i
$539$	−471.849	−	109.373i	−0.875415	−	0.202919i
$540$	76.1815			0.141077
$541$	−102.718	+	33.3750i	−0.189866	+	0.0616913i	−0.402407	−	0.915461i	$-0.631826\pi$
$541$	−102.718	+	33.3750i	−0.189866	+	0.0616913i	0.212541	+	0.977152i	$0.431826\pi$
$542$	−557.806	−	405.270i	−1.02916	−	0.747730i
$543$	−385.084	+	279.780i	−0.709179	+	0.515249i
$544$	49.8506	−	153.424i	0.0916372	−	0.282030i
$545$	−76.5093	−	24.8594i	−0.140384	−	0.0456135i
$546$	11.9154	+	16.4002i	0.0218231	+	0.0300370i
$547$	−18.4002	+	25.3257i	−0.0336384	+	0.0462993i	−0.825505	−	0.564395i	$-0.809110\pi$
$547$	−18.4002	+	25.3257i	−0.0336384	+	0.0462993i	0.791867	+	0.610694i	$0.209110\pi$
$548$	104.244	+	320.831i	0.190227	+	0.585459i
$549$			4.80404i			0.00875052i
$550$	−20.5779	+	88.7754i	−0.0374144	+	0.161410i
$551$	−1437.70			−2.60926
$552$	188.500	−	61.2475i	0.341486	−	0.110956i
$553$	154.620	+	112.338i	0.279602	+	0.203142i
$554$	−160.828	+	116.848i	−0.290303	+	0.210918i
$555$	96.5198	−	297.058i	0.173910	−	0.535239i
$556$	134.997	+	43.8630i	0.242799	+	0.0788903i
$557$	75.6402	+	104.110i	0.135799	+	0.186912i	0.871501	−	0.490394i	$-0.163147\pi$
$557$	75.6402	+	104.110i	0.135799	+	0.186912i	−0.735701	+	0.677306i	$0.763147\pi$
$558$	0.353422	−	0.486444i	0.000633373	−	0.000871763i
$559$	8.51477	+	26.2058i	0.0152322	+	0.0468797i
$560$		−	46.8806i		−	0.0837154i
$561$	207.778	−	180.297i	0.370371	−	0.321385i
$562$	708.284			1.26029
$563$	281.575	−	91.4894i	0.500134	−	0.162503i	−0.0480767	−	0.998844i	$-0.515309\pi$
$563$	281.575	−	91.4894i	0.500134	−	0.162503i	0.548211	+	0.836340i	$0.315309\pi$
$564$	−217.237	−	157.832i	−0.385171	−	0.279843i
$565$	−239.616	+	174.091i	−0.424099	+	0.308126i
$566$	103.977	−	320.009i	0.183705	−	0.565387i
$567$	−169.692	−	55.1363i	−0.299280	−	0.0972421i
$568$	−627.517	−	863.703i	−1.10478	−	1.52060i
$569$	355.335	−	489.077i	0.624491	−	0.859538i	−0.373179	−	0.927759i	$-0.621732\pi$
$569$	355.335	−	489.077i	0.624491	−	0.859538i	0.997670	+	0.0682211i	$0.0217323\pi$
$570$	90.7443	+	279.282i	0.159201	+	0.489969i
$571$			612.659i			1.07296i	0.843914	+	0.536479i	$0.180246\pi$
$571$			612.659i			1.07296i	−0.843914	+	0.536479i	$0.819754\pi$
$572$	−21.7620	−	13.1021i	−0.0380455	−	0.0229057i
$573$	−218.588			−0.381481
$574$	95.4517	−	31.0141i	0.166292	−	0.0540316i
$575$	30.8735	+	22.4309i	0.0536931	+	0.0390103i
$576$	−5.83176	+	4.23702i	−0.0101246	+	0.00735594i
$577$	−148.690	+	457.620i	−0.257694	+	0.793101i	0.735593	+	0.677424i	$0.236904\pi$
$577$	−148.690	+	457.620i	−0.257694	+	0.793101i	−0.993287	+	0.115677i	$0.963096\pi$
$578$	−344.621	−	111.974i	−0.596230	−	0.193727i
$579$	461.976	+	635.855i	0.797885	+	1.09819i
$580$	−89.2196	+	122.800i	−0.153827	+	0.211724i
$581$	31.6390	+	97.3747i	0.0544560	+	0.167598i
$582$		−	164.219i		−	0.282163i
$583$	−399.165	+	169.020i	−0.684674	+	0.289914i
$584$	520.270			0.890874
$585$	0.405922	−	0.131892i	0.000693884	−	0.000225456i
$586$	548.626	+	398.600i	0.936222	+	0.680205i
$587$	−298.317	+	216.740i	−0.508206	+	0.369233i	−0.812143	−	0.583459i	$-0.801699\pi$
$587$	−298.317	+	216.740i	−0.508206	+	0.369233i	0.303937	+	0.952692i	$0.401699\pi$
$588$	−50.9217	+	156.721i	−0.0866016	+	0.266532i
$589$	−88.4339	−	28.7339i	−0.150142	−	0.0487842i
$590$	78.4164	+	107.931i	0.132909	+	0.182934i
$591$	−384.448	+	529.147i	−0.650503	+	0.895341i
$592$	136.136	+	418.984i	0.229960	+	0.707744i
$593$		−	881.291i		−	1.48616i	−0.669204	−	0.743079i	$-0.733365\pi$
$593$		−	881.291i		−	1.48616i	0.669204	−	0.743079i	$-0.266635\pi$
$594$	−493.046	+	42.6979i	−0.830044	+	0.0718819i
$595$	−41.7866			−0.0702295
$596$	−232.430	+	75.5211i	−0.389984	+	0.126713i
$597$	−260.870	−	189.533i	−0.436967	−	0.317475i
$598$	18.8296	−	13.6805i	0.0314876	−	0.0228771i
$599$	276.534	−	851.084i	0.461659	−	1.42084i	−0.401477	−	0.915869i	$-0.631503\pi$
$599$	276.534	−	851.084i	0.461659	−	1.42084i	0.863136	−	0.504972i	$-0.168497\pi$
$600$	123.488	+	40.1236i	0.205813	+	0.0668726i
$601$	−449.838	−	619.149i	−0.748483	−	1.03020i	−0.998085	−	0.0618498i	$-0.980300\pi$
$601$	−449.838	−	619.149i	−0.748483	−	1.03020i	0.249603	−	0.968348i	$-0.419700\pi$
$602$	−32.4964	+	44.7275i	−0.0539808	+	0.0742982i
$603$	1.95001	+	6.00150i	0.00323384	+	0.00995274i
$604$		−	176.988i		−	0.293026i
$605$	−38.1278	+	267.864i	−0.0630211	+	0.442751i
$606$	523.995			0.864679
$607$	1053.73	−	342.377i	1.73596	−	0.564048i	0.741672	−	0.670763i	$-0.234033\pi$
$607$	1053.73	−	342.377i	1.73596	−	0.564048i	0.994290	+	0.106715i	$0.0340332\pi$
$608$	413.627	+	300.518i	0.680308	+	0.494273i
$609$	290.964	−	211.398i	0.477773	−	0.347123i
$610$	−53.0331	+	163.219i	−0.0869396	+	0.267572i
$611$	−125.593	−	40.8077i	−0.205553	−	0.0667883i
$612$	0.641314	+	0.882693i	0.00104790	+	0.00144231i
$613$	75.0479	−	103.295i	0.122427	−	0.168507i	−0.743404	−	0.668842i	$-0.766790\pi$
$613$	75.0479	−	103.295i	0.122427	−	0.168507i	0.865831	+	0.500336i	$0.166790\pi$
$614$	280.769	+	864.117i	0.457278	+	1.40736i
$615$			181.263i			0.294737i
$616$	−18.4159	−	212.655i	−0.0298960	−	0.345219i
$617$	182.872			0.296389			0.148195	−	0.988958i	$-0.452654\pi$
$617$	182.872			0.296389			0.148195	+	0.988958i	$0.452654\pi$
$618$	923.683	−	300.123i	1.49463	−	0.485635i
$619$	−93.6587	−	68.0470i	−0.151306	−	0.109931i	0.509556	−	0.860437i	$-0.329810\pi$
$619$	−93.6587	−	68.0470i	−0.151306	−	0.109931i	−0.660863	+	0.750507i	$0.729810\pi$
$620$	−7.94225	+	5.77038i	−0.0128101	+	0.00930706i
$621$	−64.0419	+	197.101i	−0.103127	+	0.317392i
$622$	−72.8458	−	23.6690i	−0.117116	−	0.0380531i
$623$	−159.745	−	219.870i	−0.256412	−	0.352921i
$624$	30.3529	−	41.7771i	0.0486424	−	0.0669505i
$625$	7.72542	+	23.7764i	0.0123607	+	0.0380423i
$626$		−	1.92501i		−	0.00307510i
$627$	339.958	+	802.858i	0.542197	+	1.28048i
$628$	61.7835			0.0983813
$629$	373.457	−	121.344i	0.593732	−	0.192915i
$630$	0.692820	+	0.503363i	0.00109971	+	0.000798989i
$631$	675.353	−	490.673i	1.07029	−	0.777611i	0.0943258	−	0.995541i	$-0.469930\pi$
$631$	675.353	−	490.673i	1.07029	−	0.777611i	0.975964	+	0.217930i	$0.0699305\pi$
$632$	230.712	−	710.059i	0.365051	−	1.12351i
$633$	708.717	+	230.276i	1.11962	+	0.363785i
$634$	114.689	+	157.855i	0.180897	+	0.248983i
$635$	−29.6005	+	40.7415i	−0.0466149	+	0.0641599i
$636$	45.5721	+	140.257i	0.0716543	+	0.220529i
$637$			81.0410i			0.127223i
$638$	508.602	−	844.768i	0.797183	−	1.32409i
$639$	12.7170			0.0199014
$640$	−81.2473	+	26.3989i	−0.126949	+	0.0412482i
$641$	−20.3823	−	14.8086i	−0.0317976	−	0.0231023i	0.571773	−	0.820412i	$-0.306256\pi$
$641$	−20.3823	−	14.8086i	−0.0317976	−	0.0231023i	−0.603571	+	0.797310i	$0.706256\pi$
$642$	−613.684	+	445.867i	−0.955893	+	0.694497i
$643$	126.790	−	390.218i	0.197184	−	0.606871i	−0.802760	−	0.596303i	$-0.796636\pi$
$643$	126.790	−	390.218i	0.197184	−	0.606871i	0.999944	−	0.0105686i	$-0.00336414\pi$
$644$	−20.2987	−	6.59545i	−0.0315197	−	0.0102414i
$645$	−58.6906	−	80.7807i	−0.0909932	−	0.125241i
$646$	−216.998	+	298.672i	−0.335911	+	0.462341i
$647$	213.067	+	655.754i	0.329316	+	1.01353i	0.969455	+	0.245270i	$0.0788767\pi$
$647$	213.067	+	655.754i	0.329316	+	1.01353i	−0.640139	+	0.768259i	$0.721123\pi$
$648$			697.005i			1.07563i
$649$	259.599	+	299.167i	0.399999	+	0.460966i
$650$	15.2474			0.0234575
$651$	22.1224	−	7.18800i	0.0339822	−	0.0110415i
$652$	−253.913	−	184.479i	−0.389438	−	0.282943i
$653$	291.983	−	212.138i	0.447140	−	0.324866i	−0.341325	−	0.939945i	$-0.610876\pi$
$653$	291.983	−	212.138i	0.447140	−	0.324866i	0.788466	+	0.615079i	$0.210876\pi$
$654$	54.9419	−	169.094i	0.0840091	−	0.258553i
$655$	−148.631	−	48.2931i	−0.226917	−	0.0737299i
$656$	−150.275	−	206.835i	−0.229077	−	0.315298i
$657$	−3.64272	+	5.01378i	−0.00554448	+	0.00763132i
$658$	−81.8782	−	251.995i	−0.124435	−	0.382971i
$659$			464.630i			0.705053i	0.935802	+	0.352527i	$0.114677\pi$
$659$			464.630i			0.705053i	−0.935802	+	0.352527i	$0.885323\pi$
$660$	89.6724	+	20.7858i	0.135867	+	0.0314937i
$661$	103.487			0.156562			0.0782808	−	0.996931i	$-0.475057\pi$
$661$	103.487			0.156562			0.0782808	+	0.996931i	$0.475057\pi$
$662$	−238.307	+	77.4305i	−0.359980	+	0.116964i
$663$	−37.2376	−	27.0547i	−0.0561653	−	0.0408065i
$664$	323.577	−	235.093i	0.487315	−	0.354055i
$665$	40.9244	−	125.952i	0.0615405	−	0.189402i
$666$	−7.65362	−	2.48681i	−0.0114919	−	0.00373395i
$667$	−242.713	−	334.065i	−0.363887	−	0.500848i
$668$	−204.198	+	281.055i	−0.305686	+	0.420741i
$669$	−130.976	−	403.102i	−0.195778	−	0.602544i
$670$			225.430i			0.336463i
$671$	−115.059	+	496.379i	−0.171474	+	0.739760i
$672$	−127.898			−0.190325
$673$	−220.508	+	71.6473i	−0.327649	+	0.106460i	−0.468222	−	0.883611i	$-0.655105\pi$
$673$	−220.508	+	71.6473i	−0.327649	+	0.106460i	0.140573	+	0.990070i	$0.455105\pi$
$674$	−481.513	−	349.840i	−0.714412	−	0.519050i
$675$	−109.837	+	79.8016i	−0.162722	+	0.118225i
$676$	64.2122	−	197.625i	0.0949884	−	0.292344i
$677$	−201.949	−	65.6172i	−0.298300	−	0.0969235i	0.156043	−	0.987750i	$-0.450126\pi$
$677$	−201.949	−	65.6172i	−0.298300	−	0.0969235i	−0.454343	+	0.890827i	$0.650126\pi$
$678$	−384.761	−	529.578i	−0.567494	−	0.781088i
$679$	−43.5316	+	59.9161i	−0.0641113	+	0.0882416i
$680$	50.4429	+	155.247i	0.0741807	+	0.228305i
$681$			123.088i			0.180746i
$682$	48.1681	−	41.7973i	0.0706276	−	0.0612864i
$683$	−537.182			−0.786504			−0.393252	−	0.919431i	$-0.628650\pi$
$683$	−537.182			−0.786504			−0.393252	+	0.919431i	$0.628650\pi$
$684$	−3.28868	+	1.06856i	−0.00480802	+	0.00156222i
$685$	−486.375	−	353.372i	−0.710037	−	0.515872i
$686$	−277.939	+	201.935i	−0.405159	+	0.294365i
$687$	−328.660	+	1011.51i	−0.478399	+	1.47236i
$688$	133.941	+	43.5201i	0.194682	+	0.0632559i
$689$	42.6304	+	58.6758i	0.0618729	+	0.0851608i
$690$	−49.5749	+	68.2339i	−0.0718476	+	0.0988898i
$691$	142.052	+	437.192i	0.205575	+	0.632695i	0.999689	+	0.0249265i	$0.00793517\pi$
$691$	142.052	+	437.192i	0.205575	+	0.632695i	−0.794114	+	0.607769i	$0.792065\pi$
$692$		−	3.05430i		−	0.00441373i
$693$	2.17827	+	1.31145i	0.00314324	+	0.00189242i
$694$	−128.041			−0.184497
$695$	−240.584	+	78.1704i	−0.346164	+	0.112475i
$696$	−1136.63	−	825.812i	−1.63309	−	1.18651i
$697$	−184.361	+	133.946i	−0.264506	+	0.192175i
$698$	−215.121	+	662.075i	−0.308196	+	0.948531i
$699$	−541.704	−	176.010i	−0.774970	−	0.251803i
$700$	−8.21849	−	11.3118i	−0.0117407	−	0.0161597i
$701$	256.752	−	353.389i	0.366265	−	0.504121i	−0.585616	−	0.810589i	$-0.699147\pi$
$701$	256.752	−	353.389i	0.366265	−	0.504121i	0.951881	+	0.306468i	$0.0991472\pi$
$702$	25.5876	+	78.7506i	0.0364496	+	0.112180i
$703$			1244.51i			1.77028i
$704$	−704.047	+	298.118i	−1.00007	+	0.423463i
$705$	478.541			0.678781
$706$	1009.37	−	327.963i	1.42970	−	0.464537i
$707$	−191.182	−	138.902i	−0.270414	−	0.196467i
$708$	109.022	−	79.2088i	0.153985	−	0.111877i
$709$	401.098	−	1234.45i	0.565724	−	1.74112i	−0.100067	−	0.994981i	$-0.531906\pi$
$709$	401.098	−	1234.45i	0.565724	−	1.74112i	0.665791	−	0.746138i	$-0.268094\pi$
$710$	432.066	+	140.387i	0.608543	+	0.197728i
$711$	5.22739	+	7.19489i	0.00735217	+	0.0101194i
$712$	−624.033	+	858.908i	−0.876451	+	1.20633i
$713$	−8.25278	−	25.3995i	−0.0115747	−	0.0356234i
$714$		−	92.3529i		−	0.129346i
$715$	45.1009	−	3.90574i	0.0630782	−	0.00546258i
$716$	182.118			0.254355
$717$	−796.414	+	258.771i	−1.11076	+	0.360907i
$718$	−452.964	−	329.097i	−0.630869	−	0.458353i
$719$	597.870	−	434.378i	0.831530	−	0.604142i	−0.0884615	−	0.996080i	$-0.528195\pi$
$719$	597.870	−	434.378i	0.831530	−	0.604142i	0.919992	+	0.391937i	$0.128195\pi$
$720$	0.674117	−	2.07472i	0.000936273	−	0.00288155i
$721$	−416.568	−	135.351i	−0.577764	−	0.187727i
$722$	−336.156	−	462.678i	−0.465589	−	0.640829i
$723$	480.901	−	661.904i	0.665147	−	0.915496i
$724$	−61.8753	−	190.433i	−0.0854631	−	0.263028i
$725$		−	270.511i		−	0.373119i
$726$	−592.010	−	84.2666i	−0.815440	−	0.116070i
$727$	721.746			0.992773			0.496386	−	0.868102i	$-0.334660\pi$
$727$	721.746			0.992773			0.496386	+	0.868102i	$0.334660\pi$
$728$	−33.9657	+	11.0361i	−0.0466562	+	0.0151595i
$729$	−596.412	−	433.319i	−0.818123	−	0.594402i
$730$	−179.111	+	130.132i	−0.245358	+	0.178263i
$731$	38.7912	−	119.387i	0.0530659	−	0.163320i
$732$	164.868	+	53.5690i	0.225230	+	0.0731817i
$733$	−705.403	−	970.904i	−0.962351	−	1.32456i	−0.945818	−	0.324699i	$-0.894737\pi$
$733$	−705.403	−	970.904i	−0.962351	−	1.32456i	−0.0165330	−	0.999863i	$-0.505263\pi$
$734$	459.303	−	632.176i	0.625753	−	0.861275i
$735$	−90.7500	−	279.300i	−0.123469	−	0.380000i
$736$			146.844i			0.199517i
$737$	57.7459	+	666.811i	0.0783527	+	0.904764i
$738$	4.67021			0.00632820
$739$	7.68044	−	2.49552i	0.0103930	−	0.00337689i	−0.303816	−	0.952731i	$-0.598261\pi$
$739$	7.68044	−	2.49552i	0.0103930	−	0.00337689i	0.314209	+	0.949354i	$0.398261\pi$
$740$	106.299	+	77.2307i	0.143647	+	0.104366i
$741$	118.017	−	85.7445i	0.159267	−	0.115715i
$742$	−44.9687	+	138.399i	−0.0606047	+	0.186522i
$743$	−246.178	−	79.9879i	−0.331329	−	0.107655i	0.138628	−	0.990345i	$-0.455731\pi$
$743$	−246.178	−	79.9879i	−0.331329	−	0.107655i	−0.469957	+	0.882689i	$0.655731\pi$
$744$	−53.4103	−	73.5130i	−0.0717881	−	0.0988078i
$745$	256.005	−	352.361i	0.343631	−	0.472967i
$746$	−26.0290	−	80.1089i	−0.0348914	−	0.107385i
$747$			4.76430i			0.00637791i
$748$	45.1230	+	106.564i	0.0603249	+	0.142466i
$749$	342.097			0.456739
$750$	−52.5485	+	17.0740i	−0.0700647	+	0.0227654i
$751$	381.165	+	276.932i	0.507543	+	0.368751i	0.811891	−	0.583810i	$-0.198439\pi$
$751$	381.165	+	276.932i	0.507543	+	0.368751i	−0.304348	+	0.952561i	$0.598439\pi$
$752$	−546.051	+	396.730i	−0.726132	+	0.527566i
$753$	110.386	−	339.732i	0.146595	−	0.451172i
$754$	−156.908	−	50.9826i	−0.208101	−	0.0676162i
$755$	185.398	+	255.179i	0.245561	+	0.337985i
$756$	44.6318	−	61.4305i	0.0590368	−	0.0812572i
$757$	268.783	+	827.228i	0.355063	+	1.09277i	0.955973	+	0.293455i	$0.0948050\pi$
$757$	268.783	+	827.228i	0.355063	+	1.09277i	−0.600910	+	0.799317i	$0.705195\pi$
$758$			973.911i			1.28484i
$759$	−129.161	+	214.532i	−0.170173	+	0.282650i
$760$	−517.346			−0.680718
$761$	614.545	−	199.678i	0.807549	−	0.262389i	0.123990	−	0.992284i	$-0.460431\pi$
$761$	614.545	−	199.678i	0.807549	−	0.262389i	0.683559	+	0.729895i	$0.260431\pi$
$762$	−90.0433	−	65.4203i	−0.118167	−	0.0858534i
$763$	−64.8698	+	47.1306i	−0.0850193	+	0.0617702i
$764$	28.4149	−	87.4521i	0.0371923	−	0.114466i
$765$	−1.84928	−	0.600867i	−0.00241736	−	0.000785447i
$766$	−32.8751	−	45.2487i	−0.0429179	−	0.0590714i
$767$	38.9545	−	53.6162i	0.0507881	−	0.0699038i
$768$	197.908	+	609.097i	0.257692	+	0.793096i
$769$			152.670i			0.198530i	0.995061	+	0.0992650i	$0.0316492\pi$
$769$			152.670i			0.198530i	−0.995061	+	0.0992650i	$0.968351\pi$
$770$	59.5300	+	68.6036i	0.0773117	+	0.0890955i
$771$	−109.276			−0.141733
$772$	−314.444	+	102.169i	−0.407311	+	0.132343i
$773$	579.036	+	420.694i	0.749076	+	0.544235i	0.895540	−	0.444981i	$-0.146789\pi$
$773$	579.036	+	420.694i	0.749076	+	0.544235i	−0.146464	+	0.989216i	$0.546789\pi$
$774$	−2.08130	+	1.51215i	−0.00268901	+	0.00195368i
$775$	5.40644	−	16.6393i	0.00697606	−	0.0214701i
$776$	275.152	+	89.4023i	0.354577	+	0.115209i
$777$	−182.991	−	251.866i	−0.235510	−	0.324151i
$778$	−504.253	+	694.045i	−0.648141	+	0.892089i
$779$	−223.180	−	686.879i	−0.286496	−	0.881744i
$780$		−	15.4014i		−	0.0197454i
$781$	1313.99	+	304.579i	1.68244	+	0.389986i
$782$	−106.034			−0.135593
$783$	1397.15	−	453.963i	1.78436	−	0.579774i
$784$	335.104	+	243.467i	0.427428	+	0.310545i
$785$	−89.0786	+	64.7194i	−0.113476	+	0.0824451i
$786$	106.733	−	328.491i	0.135793	−	0.417927i
$787$	582.331	+	189.211i	0.739938	+	0.240421i	0.654646	−	0.755935i	$-0.272818\pi$
$787$	582.331	+	189.211i	0.739938	+	0.240421i	0.0852922	+	0.996356i	$0.472818\pi$
$788$	−161.724	−	222.594i	−0.205233	−	0.282479i
$789$	46.3943	−	63.8562i	0.0588014	−	0.0809331i
$790$	98.1764	+	302.156i	0.124274	+	0.382476i
$791$			295.213i			0.373214i
$792$	2.24285	−	9.67591i	0.00283188	−	0.0122171i
$793$	85.2541			0.107508
$794$	135.686	−	44.0871i	0.170890	−	0.0555254i
$795$	−212.627	−	154.482i	−0.267455	−	0.194318i
$796$	109.739	−	79.7299i	0.137863	−	0.100163i
$797$	−35.3761	+	108.877i	−0.0443866	+	0.136608i	−0.970794	−	0.239915i	$-0.922880\pi$
$797$	−35.3761	+	108.877i	−0.0443866	+	0.136608i	0.926407	+	0.376523i	$0.122880\pi$
$798$	278.369	+	90.4475i	0.348833	+	0.113343i
$799$	353.621	+	486.717i	0.442579	+	0.609158i
$800$	−56.5441	+	77.8263i	−0.0706801	+	0.0972828i
$801$	−3.90795	−	12.0274i	−0.00487884	−	0.0150155i
$802$		−	267.201i		−	0.333168i
$803$	−496.468	+	430.805i	−0.618267	+	0.536494i
$804$	227.708			0.283219
$805$	36.1753	−	11.7541i	0.0449382	−	0.0146013i
$806$	−8.63260	−	6.27195i	−0.0107104	−	0.00778158i
$807$	95.3699	−	69.2903i	0.118178	−	0.0858615i
$808$	−285.268	+	877.966i	−0.353055	+	1.08659i
$809$	660.065	+	214.468i	0.815902	+	0.265103i	0.687096	−	0.726567i	$-0.258885\pi$
$809$	660.065	+	214.468i	0.815902	+	0.265103i	0.128807	+	0.991670i	$0.458885\pi$
$810$	−174.338	−	239.955i	−0.215232	−	0.296241i
$811$	754.445	−	1038.40i	0.930266	−	1.28040i	−0.0294904	−	0.999565i	$-0.509388\pi$
$811$	754.445	−	1038.40i	0.930266	−	1.28040i	0.959756	−	0.280836i	$-0.0906116\pi$
$812$	46.7521	+	143.888i	0.0575764	+	0.177202i
$813$		−	1241.18i		−	1.52667i
$814$	−731.252	−	440.259i	−0.898344	−	0.540859i
$815$	559.335			0.686300
$816$	−223.742	+	72.6981i	−0.274193	+	0.0890908i
$817$	321.863	+	233.847i	0.393958	+	0.286227i
$818$	310.376	−	225.502i	0.379433	−	0.275674i
$819$	0.131461	−	0.404594i	0.000160513	−	0.000494010i
$820$	−72.5193	−	23.5629i	−0.0884381	−	0.0287353i
$821$	−208.579	−	287.084i	−0.254054	−	0.349676i	0.662872	−	0.748733i	$-0.269337\pi$
$821$	−208.579	−	287.084i	−0.254054	−	0.349676i	−0.916926	+	0.399057i	$0.869337\pi$
$822$	780.992	−	1074.94i	0.950112	−	1.30772i
$823$	−199.071	−	612.677i	−0.241884	−	0.744444i	−0.996133	−	0.0878551i	$-0.971999\pi$
$823$	−199.071	−	612.677i	−0.241884	−	0.744444i	0.754249	−	0.656589i	$-0.228001\pi$
$824$			1711.04i			2.07651i
$825$	−151.062	+	63.9649i	−0.183106	+	0.0775332i
$826$	132.974			0.160985
$827$	−693.571	+	225.355i	−0.838660	+	0.272497i	−0.696688	−	0.717374i	$-0.745344\pi$
$827$	−693.571	+	225.355i	−0.838660	+	0.272497i	−0.141971	+	0.989871i	$0.545344\pi$
$828$	−0.803487	−	0.583767i	−0.000970395	−	0.000705033i
$829$	−899.621	+	653.613i	−1.08519	+	0.788435i	−0.978580	−	0.205866i	$-0.933999\pi$
$829$	−899.621	+	653.613i	−1.08519	+	0.788435i	−0.106608	+	0.994301i	$0.533999\pi$
$830$	−52.5944	+	161.869i	−0.0633668	+	0.195023i
$831$	−340.346	−	110.585i	−0.409562	−	0.133075i
$832$	75.1916	+	103.492i	0.0903745	+	0.124390i
$833$	217.012	−	298.691i	0.260518	−	0.358573i
$834$	−172.765	−	531.717i	−0.207153	−	0.637550i
$835$		−	619.123i		−	0.741465i
$836$	−365.397	+	31.6434i	−0.437078	+	0.0378510i
$837$	95.0128			0.113516
$838$	674.987	−	219.317i	0.805474	−	0.261714i
$839$	487.599	+	354.261i	0.581167	+	0.422242i	0.839145	−	0.543908i	$-0.183056\pi$
$839$	487.599	+	354.261i	0.581167	+	0.422242i	−0.257978	+	0.966151i	$0.583056\pi$
$840$	104.701	−	76.0699i	0.124644	−	0.0905594i
$841$	−644.625	+	1983.95i	−0.766498	+	2.35904i
$842$	825.794	+	268.317i	0.980753	+	0.318666i
$843$	749.438	+	1031.51i	0.889013	+	1.22362i
$844$	−184.256	+	253.607i	−0.218313	+	0.300482i
$845$	114.436	+	352.196i	0.135427	+	0.416800i
$846$		−	12.3295i		−	0.0145739i
$847$	193.660	+	187.677i	0.228643	+	0.221578i
$848$	370.696			0.437141
$849$	576.066	−	187.175i	0.678523	−	0.220465i
$850$	−56.1969	−	40.8294i	−0.0661139	−	0.0480346i
$851$	−289.175	+	210.098i	−0.339806	+	0.246884i
$852$	141.805	−	436.431i	0.166438	−	0.512243i
$853$	−1552.04	−	504.288i	−1.81951	−	0.591194i	−0.999831	−	0.0183661i	$-0.994154\pi$
$853$	−1552.04	−	504.288i	−1.81951	−	0.591194i	−0.819676	−	0.572828i	$-0.805846\pi$
$854$	100.545	+	138.388i	0.117734	+	0.162047i
$855$	3.62225	−	4.98559i	0.00423654	−	0.00583110i
$856$	−412.965	−	1270.97i	−0.482436	−	1.48478i
$857$		−	1580.81i		−	1.84459i	−0.386486	−	0.922295i	$-0.626311\pi$
$857$		−	1580.81i		−	1.84459i	0.386486	−	0.922295i	$-0.373689\pi$
$858$	8.63212	+	99.6780i	0.0100608	+	0.116175i
$859$	−1222.90			−1.42364			−0.711819	−	0.702363i	$-0.752128\pi$
$859$	−1222.90			−1.42364			−0.711819	+	0.702363i	$0.752128\pi$
$860$	39.9478	−	12.9798i	0.0464510	−	0.0150928i
$861$	146.165	+	106.195i	0.169762	+	0.123340i
$862$	12.2072	−	8.86902i	0.0141614	−	0.0102889i
$863$	361.176	−	1111.58i	0.418512	−	1.28805i	−0.490560	−	0.871408i	$-0.663208\pi$
$863$	361.176	−	1111.58i	0.418512	−	1.28805i	0.909072	−	0.416640i	$-0.136792\pi$
$864$	−496.853	−	161.437i	−0.575061	−	0.186849i
$865$	3.19944	+	4.40365i	0.00369878	+	0.00509093i
$866$	191.663	−	263.801i	0.221320	−	0.304620i
$867$	−201.571	−	620.371i	−0.232492	−	0.715538i
$868$			9.78504i			0.0112731i
$869$	367.801	+	868.613i	0.423246	+	0.999555i
$870$	597.859			0.687195
$871$	106.505	−	34.6055i	0.122279	−	0.0397308i
$872$	253.410	+	184.113i	0.290607	+	0.211139i
$873$	−2.78806	+	2.02565i	−0.00319366	+	0.00232033i
$874$	103.846	−	319.604i	0.118817	−	0.365680i
$875$	23.6986	+	7.70015i	0.0270842	+	0.00880017i
$876$	131.447	+	180.921i	0.150054	+	0.206531i
$877$	320.830	−	441.585i	0.365827	−	0.503517i	−0.585934	−	0.810359i	$-0.699272\pi$
$877$	320.830	−	441.585i	0.365827	−	0.503517i	0.951761	+	0.306842i	$0.0992722\pi$
$878$	24.5931	+	75.6898i	0.0280104	+	0.0862071i
$879$			1220.76i			1.38880i
$880$	119.344	−	198.225i	0.135618	−	0.225256i
$881$	−445.171			−0.505302			−0.252651	−	0.967557i	$-0.581302\pi$
$881$	−445.171			−0.505302			−0.252651	+	0.967557i	$0.581302\pi$
$882$	−7.19609	+	2.33815i	−0.00815884	+	0.00265097i
$883$	−499.994	−	363.267i	−0.566244	−	0.411401i	0.267495	−	0.963559i	$-0.413804\pi$
$883$	−499.994	−	363.267i	−0.566244	−	0.411401i	−0.833739	+	0.552159i	$0.813804\pi$
$884$	15.6646	−	11.3810i	0.0177201	−	0.0128744i
$885$	−74.2131	+	228.404i	−0.0838566	+	0.258084i
$886$	198.810	+	64.5973i	0.224391	+	0.0729089i
$887$	−717.869	−	988.062i	−0.809323	−	1.11394i	−0.991427	−	0.130658i	$-0.958291\pi$
$887$	−717.869	−	988.062i	−0.809323	−	1.11394i	0.182105	−	0.983279i	$-0.441709\pi$
$888$	−714.843	+	983.897i	−0.805004	+	1.10799i
$889$	15.5110	+	47.7379i	0.0174477	+	0.0536984i
$890$		−	451.779i		−	0.507616i
$891$	−577.149	−	665.117i	−0.647754	−	0.746484i
$892$	178.297			0.199885
$893$	−1813.38	+	589.203i	−2.03066	+	0.659802i
$894$	778.756	+	565.799i	0.871092	+	0.632885i
$895$	−262.576	+	190.773i	−0.293381	+	0.213154i
$896$	−26.3125	+	80.9815i	−0.0293666	+	0.0903812i
$897$	39.8474	+	12.9472i	0.0444229	+	0.0144339i
$898$	−43.0414	−	59.2415i	−0.0479303	−	0.0659704i
$899$	−111.274	+	153.155i	−0.123775	+	0.170362i
$900$	−0.201055	−	0.618784i	−0.000223394	−	0.000687537i
$901$		−	330.416i		−	0.366721i
$902$	482.551	+	111.854i	0.534979	+	0.124007i
$903$	−99.5238			−0.110215
$904$	1096.79	−	356.368i	1.21326	−	0.394212i
$905$	288.693	+	209.748i	0.318998	+	0.231766i
$906$	−563.974	+	409.751i	−0.622488	+	0.452264i
$907$	309.050	−	951.157i	0.340738	−	1.04868i	−0.623088	−	0.782152i	$-0.714122\pi$
$907$	309.050	−	951.157i	0.340738	−	1.04868i	0.963826	−	0.266532i	$-0.0858779\pi$
$908$	−49.2447	−	16.0006i	−0.0542343	−	0.0176218i
$909$	−6.46351	−	8.89625i	−0.00711057	−	0.00978686i
$910$	8.93285	−	12.2950i	0.00981632	−	0.0135110i
$911$	390.823	+	1202.83i	0.429004	+	1.32034i	0.899107	+	0.437728i	$0.144217\pi$
$911$	390.823	+	1202.83i	0.429004	+	1.32034i	−0.470103	+	0.882611i	$0.655783\pi$
$912$		−	745.597i		−	0.817541i
$913$	−114.107	+	492.273i	−0.124981	+	0.539182i
$914$	−876.872			−0.959378
$915$	−293.820	+	95.4678i	−0.321115	+	0.104336i
$916$	−361.959	−	262.979i	−0.395152	−	0.287095i
$917$	−126.019	+	91.5584i	−0.137426	+	0.0998456i
$918$	116.571	−	358.768i	0.126983	−	0.390815i
$919$	−410.290	−	133.311i	−0.446452	−	0.145061i	0.0771583	−	0.997019i	$-0.475415\pi$
$919$	−410.290	−	133.311i	−0.446452	−	0.145061i	−0.523611	+	0.851958i	$0.675415\pi$
$920$	−87.3384	−	120.211i	−0.0949331	−	0.130664i
$921$	−961.379	+	1323.22i	−1.04384	+	1.43673i
$922$	−132.464	−	407.681i	−0.143670	−	0.442171i
$923$		−	225.680i		−	0.244507i
$924$	69.2968	−	60.1315i	0.0749965	−	0.0650774i
$925$	−234.161			−0.253147
$926$	−425.086	+	138.119i	−0.459057	+	0.149156i
$927$	−16.4891	−	11.9800i	−0.0177876	−	0.0129234i
$928$	842.115	−	611.832i	0.907451	−	0.659302i
$929$	−394.187	+	1213.18i	−0.424313	+	1.30590i	0.479338	+	0.877630i	$0.340877\pi$
$929$	−394.187	+	1213.18i	−0.424313	+	1.30590i	−0.903651	+	0.428270i	$0.859123\pi$
$930$	36.7747	+	11.9488i	0.0395427	+	0.0128482i
$931$	687.776	+	946.642i	0.738749	+	1.01680i
$932$	140.835	−	193.843i	0.151111	−	0.207986i
$933$	−42.6080	−	131.134i	−0.0456677	−	0.140551i
$934$			211.853i			0.226824i
$935$	−176.686	−	106.376i	−0.188969	−	0.113771i
$936$	−1.66186			−0.00177549
$937$	−802.209	+	260.654i	−0.856146	+	0.278179i	−0.704018	−	0.710182i	$-0.748613\pi$
$937$	−802.209	+	260.654i	−0.856146	+	0.278179i	−0.152128	+	0.988361i	$0.548613\pi$
$938$	181.780	+	132.071i	0.193796	+	0.140801i
$939$	2.80351	−	2.03687i	0.00298563	−	0.00216919i
$940$	−62.2068	+	191.453i	−0.0661775	+	0.203673i
$941$	−1486.45	−	482.975i	−1.57964	−	0.513258i	−0.617679	−	0.786430i	$-0.711927\pi$
$941$	−1486.45	−	482.975i	−1.57964	−	0.513258i	−0.961965	+	0.273172i	$0.911927\pi$
$942$	−143.037	−	196.874i	−0.151844	−	0.208995i
$943$	121.926	−	167.817i	0.129296	−	0.177961i
$944$	−104.674	−	322.153i	−0.110883	−	0.341263i
$945$			135.322i			0.143198i
$946$	−251.268	+	106.395i	−0.265611	+	0.112469i
$947$	−986.562			−1.04178			−0.520888	−	0.853625i	$-0.674399\pi$
$947$	−986.562			−1.04178			−0.520888	+	0.853625i	$0.674399\pi$
$948$	305.209	−	99.1684i	0.321950	−	0.104608i
$949$	88.9762	+	64.6450i	0.0937579	+	0.0681191i
$950$	178.105	−	129.401i	0.187479	−	0.136211i
$951$	−108.541	+	334.055i	−0.114134	+	0.351267i
$952$	154.739	+	50.2779i	0.162541	+	0.0528129i
$953$	995.156	+	1369.71i	1.04424	+	1.43727i	0.893702	+	0.448661i	$0.148099\pi$
$953$	995.156	+	1369.71i	1.04424	+	1.43727i	0.150533	+	0.988605i	$0.451901\pi$
$954$	−3.98020	+	5.47828i	−0.00417212	+	0.00574243i
$955$	50.6396	+	155.853i	0.0530257	+	0.163196i
$956$		−	352.265i		−	0.368478i
$957$	1768.44	−	153.147i	1.84790	−	0.160028i
$958$	−833.730			−0.870282
$959$	−569.898	+	185.171i	−0.594263	+	0.193088i
$960$	−375.032	−	272.476i	−0.390658	−	0.283830i
$961$	767.560	−	557.665i	0.798710	−	0.580296i
$962$	−44.1318	+	135.824i	−0.0458751	+	0.141189i
$963$	15.1396	+	4.91916i	0.0157213	+	0.00510817i
$964$	202.299	+	278.440i	0.209853	+	0.288838i
$965$	346.338	−	476.693i	0.358899	−	0.493982i
$966$	25.9778	+	79.9514i	0.0268921	+	0.0827654i
$967$		−	1364.74i		−	1.41132i	−0.708552	−	0.705658i	$-0.750651\pi$
$967$		−	1364.74i		−	1.41132i	0.708552	−	0.705658i	$-0.249349\pi$
$968$	463.487	−	946.050i	0.478808	−	0.977324i
$969$	−664.580			−0.685841
$970$	−117.087	+	38.0439i	−0.120708	+	0.0392206i
$971$	66.9491	+	48.6413i	0.0689486	+	0.0500941i	0.621726	−	0.783235i	$-0.286432\pi$
$971$	66.9491	+	48.6413i	0.0689486	+	0.0500941i	−0.552777	+	0.833329i	$0.686432\pi$
$972$	5.68450	−	4.13003i	0.00584825	−	0.00424900i
$973$	−77.9147	+	239.797i	−0.0800767	+	0.246451i
$974$	323.620	+	105.151i	0.332259	+	0.107957i
$975$	16.1333	+	22.2056i	0.0165470	+	0.0227750i
$976$	256.124	−	352.525i	0.262422	−	0.361193i
$977$	392.445	+	1207.82i	0.401684	+	1.23626i	0.923633	+	0.383279i	$0.125205\pi$
$977$	392.445	+	1207.82i	0.401684	+	1.23626i	−0.521949	+	0.852977i	$0.674795\pi$
$978$			1236.19i			1.26400i
$979$	−115.727	−	1336.34i	−0.118209	−	1.36500i
$980$	123.538			0.126059
$981$	−3.54854	+	1.15299i	−0.00361727	+	0.00117532i
$982$	−128.600	−	93.4336i	−0.130958	−	0.0951463i
$983$	303.303	−	220.362i	0.308548	−	0.224173i	−0.422725	−	0.906258i	$-0.638926\pi$
$983$	303.303	−	220.362i	0.308548	−	0.224173i	0.731273	+	0.682085i	$0.238926\pi$
$984$	218.097	−	671.234i	0.221644	−	0.682149i
$985$	466.343	+	151.524i	0.473444	+	0.153831i
$986$	441.792	+	608.075i	0.448065	+	0.616709i
$987$	280.359	−	385.881i	0.284052	−	0.390964i
$988$	18.9630	+	58.3621i	0.0191933	+	0.0590709i
$989$			114.267i			0.115538i
$990$	1.64804	+	3.89208i	0.00166469	+	0.00393139i
$991$	885.269			0.893309			0.446655	−	0.894707i	$-0.352615\pi$
$991$	885.269			0.893309			0.446655	+	0.894707i	$0.352615\pi$
$992$	64.0271	−	20.8037i	0.0645435	−	0.0209715i
$993$	−364.920	−	265.130i	−0.367492	−	0.266999i
$994$	366.335	−	266.158i	0.368546	−	0.267764i
$995$	−74.7014	+	229.907i	−0.0750768	+	0.231063i
$996$	163.505	+	53.1259i	0.164161	+	0.0533392i
$997$	−43.8072	−	60.2954i	−0.0439390	−	0.0604769i	0.786482	−	0.617613i	$-0.211900\pi$
$997$	−43.8072	−	60.2954i	−0.0439390	−	0.0604769i	−0.830421	+	0.557136i	$0.811900\pi$
$998$	−220.834	+	303.952i	−0.221277	+	0.304561i
$999$	−392.961	−	1209.41i	−0.393355	−	1.21062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.c.6.3	✓	12
5.2	odd	4		275.3.q.e.149.4		24
5.3	odd	4		275.3.q.e.149.3		24
5.4	even	2		275.3.x.g.226.1		12
11.2	odd	10	inner	55.3.i.c.46.3	yes	12
11.3	even	5		605.3.c.c.241.6		12
11.8	odd	10		605.3.c.c.241.7		12
55.2	even	20		275.3.q.e.24.3		24
55.13	even	20		275.3.q.e.24.4		24
55.24	odd	10		275.3.x.g.101.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.c.6.3	✓	12	1.1	even	1	trivial
55.3.i.c.46.3	yes	12	11.2	odd	10	inner
275.3.q.e.24.3		24	55.2	even	20
275.3.q.e.24.4		24	55.13	even	20
275.3.q.e.149.3		24	5.3	odd	4
275.3.q.e.149.4		24	5.2	odd	4
275.3.x.g.101.1		12	55.24	odd	10
275.3.x.g.226.1		12	5.4	even	2
605.3.c.c.241.6		12	11.3	even	5
605.3.c.c.241.7		12	11.8	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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57580 - 0.512008i) q^{2} +(2.41303 + 1.75317i) q^{3} +(-1.01508 + 0.737497i) q^{4} +(0.690983 - 2.12663i) q^{5} +(4.70008 + 1.52715i) q^{6} +(-1.31003 - 1.80310i) q^{7} +(-5.11754 + 7.04369i) q^{8} +(-0.0320482 - 0.0986342i) q^{9} -3.70493i q^{10} +(-0.949049 - 10.9590i) q^{11} -3.74236 q^{12} +(-1.75040 + 0.568738i) q^{13} +(-2.98754 - 2.17058i) q^{14} +(5.39569 - 3.92020i) q^{15} +(-2.90689 + 8.94649i) q^{16} +(7.97437 + 2.59103i) q^{17} +(-0.101003 - 0.139019i) q^{18} +(-15.6197 + 21.4986i) q^{19} +(0.866979 + 2.66829i) q^{20} -6.64762i q^{21} +(-7.10660 - 16.7832i) q^{22} -7.63236 q^{23} +(-24.6975 + 8.02472i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(-2.46707 + 1.79243i) q^{26} +(8.39084 - 25.8243i) q^{27} +(2.65956 + 0.864143i) q^{28} +(31.8005 + 43.7696i) q^{29} +(6.49535 - 8.94009i) q^{30} +(1.08129 + 3.32786i) q^{31} -19.2397i q^{32} +(16.9228 - 28.1082i) q^{33} +13.8926 q^{34} +(-4.73973 + 1.54003i) q^{35} +(0.105274 + 0.0764859i) q^{36} +(37.8881 - 27.5273i) q^{37} +(-13.6060 + 41.8749i) q^{38} +(-5.22085 - 1.69636i) q^{39} +(11.4432 + 15.7502i) q^{40} +(-15.9749 + 21.9876i) q^{41} +(-3.40364 - 10.4753i) q^{42} -14.9713i q^{43} +(9.04557 + 10.4243i) q^{44} -0.231903 q^{45} +(-12.0271 + 3.90783i) q^{46} +(58.0480 + 42.1743i) q^{47} +(-22.6991 + 16.4919i) q^{48} +(13.6068 - 41.8775i) q^{49} +(-7.87900 - 2.56004i) q^{50} +(14.6999 + 20.2326i) q^{51} +(1.35734 - 1.86822i) q^{52} +(-12.1774 - 37.4781i) q^{53} -44.9902i q^{54} +(-23.9614 - 5.55420i) q^{55} +19.4046 q^{56} +(-75.3814 + 24.4929i) q^{57} +(72.5216 + 52.6900i) q^{58} +(-29.1317 + 21.1654i) q^{59} +(-2.58591 + 7.95861i) q^{60} +(-44.0546 - 14.3142i) q^{61} +(3.40779 + 4.69042i) q^{62} +(-0.135863 + 0.187000i) q^{63} +(-21.4785 - 66.1039i) q^{64} +4.11543i q^{65} +(12.2754 - 52.9574i) q^{66} -60.8461 q^{67} +(-10.0055 + 3.25097i) q^{68} +(-18.4171 - 13.3808i) q^{69} +(-6.68035 + 4.85356i) q^{70} +(-37.8919 + 116.619i) q^{71} +(0.858757 + 0.279027i) q^{72} +(-35.1241 - 48.3441i) q^{73} +(45.6098 - 62.7765i) q^{74} +(-4.60847 - 14.1834i) q^{75} -33.3422i q^{76} +(-18.5169 + 16.0678i) q^{77} -9.09555 q^{78} +(-81.5552 + 26.4989i) q^{79} +(17.0172 + 12.3638i) q^{80} +(64.7665 - 47.0556i) q^{81} +(-13.9155 + 42.8274i) q^{82} +(-43.6902 - 14.1958i) q^{83} +(4.90260 + 6.74785i) q^{84} +(11.0203 - 15.1681i) q^{85} +(-7.66545 - 23.5918i) q^{86} +161.369i q^{87} +(82.0485 + 49.3983i) q^{88} +121.940 q^{89} +(-0.365432 + 0.118736i) q^{90} +(3.31856 + 2.41107i) q^{91} +(7.74743 - 5.62884i) q^{92} +(-3.22512 + 9.92591i) q^{93} +(113.066 + 36.7372i) q^{94} +(34.9266 + 48.0724i) q^{95} +(33.7304 - 46.4259i) q^{96} +(-10.2685 - 31.6031i) q^{97} -72.9574i q^{98} +(-1.05051 + 0.444824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} + 7 q^{3} + 13 q^{4} + 15 q^{5} - 15 q^{6} - 40 q^{7} - 15 q^{8} - 16 q^{9} - 8 q^{11} + 68 q^{12} - 15 q^{13} - 5 q^{14} + 35 q^{15} + 77 q^{16} - 5 q^{17} - 115 q^{18} + 15 q^{19} - 20 q^{20}+ \cdots + 509 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 + 7 * q^3 + 13 * q^4 + 15 * q^5 - 15 * q^6 - 40 * q^7 - 15 * q^8 - 16 * q^9 - 8 * q^11 + 68 * q^12 - 15 * q^13 - 5 * q^14 + 35 * q^15 + 77 * q^16 - 5 * q^17 - 115 * q^18 + 15 * q^19 - 20 * q^20 - 90 * q^22 + 112 * q^23 - 235 * q^24 - 15 * q^25 + 80 * q^26 + 106 * q^27 + 110 * q^28 + 45 * q^29 - 10 * q^30 - 146 * q^31 - 133 * q^33 + 60 * q^34 - 70 * q^35 + 216 * q^36 + 8 * q^37 + 45 * q^38 + 195 * q^39 + 65 * q^40 - 145 * q^41 + 105 * q^42 - 167 * q^44 - 20 * q^45 - 475 * q^46 + 158 * q^47 + 227 * q^48 + 153 * q^49 + 25 * q^50 - 55 * q^51 + 60 * q^52 + 107 * q^53 - 60 * q^55 - 140 * q^56 + 125 * q^57 + 40 * q^58 - 59 * q^59 + 40 * q^60 + 210 * q^61 + 110 * q^62 - 640 * q^63 + 173 * q^64 + 195 * q^66 - 62 * q^67 - 225 * q^68 + 7 * q^69 - 15 * q^70 + 114 * q^71 - 795 * q^72 - 165 * q^73 - 30 * q^74 + 35 * q^75 - 430 * q^77 + 360 * q^78 - 355 * q^79 + 100 * q^80 + 145 * q^81 - 210 * q^82 + 105 * q^83 + 460 * q^84 + 70 * q^85 + 75 * q^86 + 270 * q^88 - 274 * q^89 - 265 * q^90 + 285 * q^91 + 428 * q^92 + 109 * q^93 + 410 * q^94 + 55 * q^95 - 75 * q^96 + 198 * q^97 + 509 * q^99

Introduction

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