LMFDB - Embedded newform 585.2.bt.b.571.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			571.7
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91643 + 1.10645i) q^{2} +(1.62047 - 0.611626i) q^{3} +(1.44848 - 2.50883i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.42878 + 2.96511i) q^{6} +(0.916933 - 0.529392i) q^{7} +1.98487i q^{8} +(2.25183 - 1.98224i) q^{9} +O(q^{10})$	\(q+(-1.91643 + 1.10645i) q^{2} +(1.62047 - 0.611626i) q^{3} +(1.44848 - 2.50883i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.42878 + 2.96511i) q^{6} +(0.916933 - 0.529392i) q^{7} +1.98487i q^{8} +(2.25183 - 1.98224i) q^{9} -2.21291 q^{10} +(-1.05983 + 0.611891i) q^{11} +(0.812740 - 4.95141i) q^{12} +(3.38513 - 1.24132i) q^{13} +(-1.17149 + 2.02909i) q^{14} +(1.70918 + 0.280550i) q^{15} +(0.700788 + 1.21380i) q^{16} -1.24095 q^{17} +(-2.12222 + 6.29037i) q^{18} -4.23962i q^{19} +(2.50883 - 1.44848i) q^{20} +(1.16207 - 1.41868i) q^{21} +(1.35406 - 2.34530i) q^{22} +(-0.567930 + 0.983684i) q^{23} +(1.21400 + 3.21641i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.11391 + 6.12440i) q^{26} +(2.43663 - 4.58943i) q^{27} -3.06724i q^{28} +(1.73591 + 3.00669i) q^{29} +(-3.58594 + 1.35347i) q^{30} +(1.71755 + 0.991626i) q^{31} +(-6.12392 - 3.53565i) q^{32} +(-1.34317 + 1.63977i) q^{33} +(2.37820 - 1.37306i) q^{34} +1.05878 q^{35} +(-1.71139 - 8.52069i) q^{36} -11.5907i q^{37} +(4.69094 + 8.12494i) q^{38} +(4.72627 - 4.08196i) q^{39} +(-0.992434 + 1.71895i) q^{40} +(3.01508 + 1.74076i) q^{41} +(-0.657326 + 4.00458i) q^{42} +(-2.57139 - 4.45377i) q^{43} +3.54524i q^{44} +(2.94126 - 0.590755i) q^{45} -2.51355i q^{46} +(4.19252 - 2.42055i) q^{47} +(1.87800 + 1.53830i) q^{48} +(-2.93949 + 5.09134i) q^{49} +(-1.91643 - 1.10645i) q^{50} +(-2.01092 + 0.758998i) q^{51} +(1.78901 - 10.2908i) q^{52} +3.53594 q^{53} +(0.408359 + 11.4913i) q^{54} -1.22378 q^{55} +(1.05077 + 1.81999i) q^{56} +(-2.59306 - 6.87016i) q^{57} +(-6.65352 - 3.84141i) q^{58} +(-0.233139 - 0.134603i) q^{59} +(3.17956 - 3.88167i) q^{60} +(5.60990 + 9.71663i) q^{61} -4.38875 q^{62} +(1.01540 - 3.00968i) q^{63} +12.8450 q^{64} +(3.55227 + 0.617550i) q^{65} +(0.759762 - 4.62865i) q^{66} +(4.51431 + 2.60634i) q^{67} +(-1.79749 + 3.11334i) q^{68} +(-0.318666 + 1.94139i) q^{69} +(-2.02909 + 1.17149i) q^{70} +5.36211i q^{71} +(3.93448 + 4.46958i) q^{72} +8.09939i q^{73} +(12.8246 + 22.2128i) q^{74} +(1.33992 + 1.09755i) q^{75} +(-10.6365 - 6.14098i) q^{76} +(-0.647860 + 1.12213i) q^{77} +(-4.54109 + 13.0522i) q^{78} +(3.73605 + 6.47103i) q^{79} +1.40158i q^{80} +(1.14146 - 8.92732i) q^{81} -7.70426 q^{82} +(-1.26565 + 0.730723i) q^{83} +(-1.87600 - 4.97037i) q^{84} +(-1.07470 - 0.620476i) q^{85} +(9.85578 + 5.69024i) q^{86} +(4.65196 + 3.81051i) q^{87} +(-1.21452 - 2.10362i) q^{88} +16.4481i q^{89} +(-4.98308 + 4.38651i) q^{90} +(2.44679 - 2.93027i) q^{91} +(1.64527 + 2.84968i) q^{92} +(3.38973 + 0.556402i) q^{93} +(-5.35645 + 9.27764i) q^{94} +(2.11981 - 3.67162i) q^{95} +(-12.0861 - 1.98385i) q^{96} +(3.53755 - 2.04240i) q^{97} -13.0096i q^{98} +(-1.17363 + 3.47870i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	−1.91643	+	1.10645i	−1.35512	+	0.782380i	−0.988962	−	0.148171i	$-0.952661\pi$
$2$	−1.91643	+	1.10645i	−1.35512	+	0.782380i	−0.366161	+	0.930552i	$0.619328\pi$
$3$	1.62047	−	0.611626i	0.935577	−	0.353122i
$3$	1.62047	−	0.611626i	0.935577	−	0.353122i
$4$	1.44848	−	2.50883i	0.724238	−	1.25442i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−2.42878	+	2.96511i	−0.991546	+	1.21050i
$7$	0.916933	−	0.529392i	0.346568	−	0.200091i	−0.316605	−	0.948558i	$-0.602543\pi$
$7$	0.916933	−	0.529392i	0.346568	−	0.200091i	0.663173	+	0.748466i	$0.269209\pi$
$8$			1.98487i			0.701757i
$9$	2.25183	−	1.98224i	0.750609	−	0.660746i
$10$	−2.21291			−0.699782
$11$	−1.05983	+	0.611891i	−0.319550	+	0.184492i	−0.651192	−	0.758913i	$-0.725731\pi$
$11$	−1.05983	+	0.611891i	−0.319550	+	0.184492i	0.331642	+	0.943405i	$0.392397\pi$
$12$	0.812740	−	4.95141i	0.234618	−	1.42935i
$13$	3.38513	−	1.24132i	0.938867	−	0.344281i
$13$	3.38513	−	1.24132i	0.938867	−	0.344281i
$14$	−1.17149	+	2.02909i	−0.313095	+	0.542296i
$15$	1.70918	+	0.280550i	0.441308	+	0.0724377i
$16$	0.700788	+	1.21380i	0.175197	+	0.303450i
$17$	−1.24095			−0.300975			−0.150488	−	0.988612i	$-0.548084\pi$
$17$	−1.24095			−0.300975			−0.150488	+	0.988612i	$0.548084\pi$
$18$	−2.12222	+	6.29037i	−0.500213	+	1.48265i
$19$		−	4.23962i		−	0.972635i	−0.873782	−	0.486317i	$-0.838340\pi$
$19$		−	4.23962i		−	0.972635i	0.873782	−	0.486317i	$-0.161660\pi$
$20$	2.50883	−	1.44848i	0.560992	−	0.323889i
$21$	1.16207	−	1.41868i	0.253585	−	0.309582i
$22$	1.35406	−	2.34530i	0.288686	−	0.500019i
$23$	−0.567930	+	0.983684i	−0.118422	+	0.205112i	−0.919142	−	0.393926i	$-0.871117\pi$
$23$	−0.567930	+	0.983684i	−0.118422	+	0.205112i	0.800721	+	0.599038i	$0.204450\pi$
$24$	1.21400	+	3.21641i	0.247806	+	0.656548i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−5.11391	+	6.12440i	−1.00292	+	1.20109i
$27$	2.43663	−	4.58943i	0.468929	−	0.883236i
$28$		−	3.06724i		−	0.579655i
$29$	1.73591	+	3.00669i	0.322351	+	0.558328i	0.980973	−	0.194146i	$-0.0621936\pi$
$29$	1.73591	+	3.00669i	0.322351	+	0.558328i	−0.658622	+	0.752474i	$0.728860\pi$
$30$	−3.58594	+	1.35347i	−0.654700	+	0.247109i
$31$	1.71755	+	0.991626i	0.308481	+	0.178101i	0.646246	−	0.763129i	$-0.276338\pi$
$31$	1.71755	+	0.991626i	0.308481	+	0.178101i	−0.337766	+	0.941230i	$0.609671\pi$
$32$	−6.12392	−	3.53565i	−1.08257	−	0.625020i
$33$	−1.34317	+	1.63977i	−0.233815	+	0.285447i
$34$	2.37820	−	1.37306i	0.407858	−	0.235477i
$35$	1.05878			0.178967
$36$	−1.71139	−	8.52069i	−0.285232	−	1.42011i
$37$		−	11.5907i		−	1.90550i	−0.303750	−	0.952752i	$-0.598239\pi$
$37$		−	11.5907i		−	1.90550i	0.303750	−	0.952752i	$-0.401761\pi$
$38$	4.69094	+	8.12494i	0.760970	+	1.31804i
$39$	4.72627	−	4.08196i	0.756809	−	0.653636i
$40$	−0.992434	+	1.71895i	−0.156918	+	0.271789i
$41$	3.01508	+	1.74076i	0.470876	+	0.271860i	0.716606	−	0.697478i	$-0.245694\pi$
$41$	3.01508	+	1.74076i	0.470876	+	0.271860i	−0.245730	+	0.969338i	$0.579028\pi$
$42$	−0.657326	+	4.00458i	−0.101428	+	0.617921i
$43$	−2.57139	−	4.45377i	−0.392133	−	0.679194i	0.600598	−	0.799551i	$-0.294929\pi$
$43$	−2.57139	−	4.45377i	−0.392133	−	0.679194i	−0.992731	+	0.120357i	$0.961596\pi$
$44$			3.54524i			0.534465i
$45$	2.94126	−	0.590755i	0.438457	−	0.0880646i
$46$		−	2.51355i		−	0.370603i
$47$	4.19252	−	2.42055i	0.611541	−	0.353074i	−0.162027	−	0.986786i	$-0.551803\pi$
$47$	4.19252	−	2.42055i	0.611541	−	0.353074i	0.773568	+	0.633713i	$0.218470\pi$
$48$	1.87800	+	1.53830i	0.271065	+	0.222035i
$49$	−2.93949	+	5.09134i	−0.419927	+	0.727335i
$50$	−1.91643	−	1.10645i	−0.271024	−	0.156476i
$51$	−2.01092	+	0.758998i	−0.281586	+	0.106281i
$52$	1.78901	−	10.2908i	0.248091	−	1.42707i
$53$	3.53594			0.485699			0.242849	−	0.970064i	$-0.421918\pi$
$53$	3.53594			0.485699			0.242849	+	0.970064i	$0.421918\pi$
$54$	0.408359	+	11.4913i	0.0555707	+	1.56377i
$55$	−1.22378			−0.165015
$56$	1.05077	+	1.81999i	0.140415	+	0.243207i
$57$	−2.59306	−	6.87016i	−0.343459	−	0.909975i
$58$	−6.65352	−	3.84141i	−0.873650	−	0.504402i
$59$	−0.233139	−	0.134603i	−0.0303521	−	0.0175238i	0.484747	−	0.874654i	$-0.338912\pi$
$59$	−0.233139	−	0.134603i	−0.0303521	−	0.0175238i	−0.515099	+	0.857131i	$0.672245\pi$
$60$	3.17956	−	3.88167i	0.410479	−	0.501122i
$61$	5.60990	+	9.71663i	0.718274	+	1.24409i	0.961683	+	0.274164i	$0.0884010\pi$
$61$	5.60990	+	9.71663i	0.718274	+	1.24409i	−0.243409	+	0.969924i	$0.578266\pi$
$62$	−4.38875			−0.557372
$63$	1.01540	−	3.00968i	0.127928	−	0.379184i
$64$	12.8450			1.60562
$65$	3.55227	+	0.617550i	0.440605	+	0.0765977i
$66$	0.759762	−	4.62865i	0.0935203	−	0.569748i
$67$	4.51431	+	2.60634i	0.551511	+	0.318415i	0.749731	−	0.661742i	$-0.230183\pi$
$67$	4.51431	+	2.60634i	0.551511	+	0.318415i	−0.198220	+	0.980158i	$0.563516\pi$
$68$	−1.79749	+	3.11334i	−0.217978	+	0.377548i
$69$	−0.318666	+	1.94139i	−0.0383629	+	0.233716i
$70$	−2.02909	+	1.17149i	−0.242522	+	0.140020i
$71$			5.36211i			0.636365i	0.948029	+	0.318183i	$0.103073\pi$
$71$			5.36211i			0.636365i	−0.948029	+	0.318183i	$0.896927\pi$
$72$	3.93448	+	4.46958i	0.463683	+	0.526745i
$73$			8.09939i			0.947962i	0.880535	+	0.473981i	$0.157183\pi$
$73$			8.09939i			0.947962i	−0.880535	+	0.473981i	$0.842817\pi$
$74$	12.8246	+	22.2128i	1.49083	+	2.58219i
$75$	1.33992	+	1.09755i	0.154720	+	0.126734i
$76$	−10.6365	−	6.14098i	−1.22009	−	0.704419i
$77$	−0.647860	+	1.12213i	−0.0738306	+	0.127878i
$78$	−4.54109	+	13.0522i	−0.514177	+	1.47787i
$79$	3.73605	+	6.47103i	0.420339	+	0.728048i	0.995972	−	0.0896596i	$-0.0285779\pi$
$79$	3.73605	+	6.47103i	0.420339	+	0.728048i	−0.575634	+	0.817708i	$0.695245\pi$
$80$			1.40158i			0.156701i
$81$	1.14146	−	8.92732i	0.126829	−	0.991925i
$82$	−7.70426			−0.850793
$83$	−1.26565	+	0.730723i	−0.138923	+	0.0802073i	−0.567851	−	0.823132i	$-0.692225\pi$
$83$	−1.26565	+	0.730723i	−0.138923	+	0.0802073i	0.428928	+	0.903339i	$0.358892\pi$
$84$	−1.87600	−	4.97037i	−0.204689	−	0.542312i
$85$	−1.07470	−	0.620476i	−0.116567	−	0.0673001i
$86$	9.85578	+	5.69024i	1.06278	+	0.613594i
$87$	4.65196	+	3.81051i	0.498742	+	0.408530i
$88$	−1.21452	−	2.10362i	−0.129469	−	0.224246i
$89$			16.4481i			1.74349i	0.489955	+	0.871747i	$0.337013\pi$
$89$			16.4481i			1.74349i	−0.489955	+	0.871747i	$0.662987\pi$
$90$	−4.98308	+	4.38651i	−0.525263	+	0.462378i
$91$	2.44679	−	2.93027i	0.256494	−	0.307176i
$92$	1.64527	+	2.84968i	0.171531	+	0.297100i
$93$	3.38973	+	0.556402i	0.351499	+	0.0576962i
$94$	−5.35645	+	9.27764i	−0.552476	+	0.956916i
$95$	2.11981	−	3.67162i	0.217488	−	0.376700i
$96$	−12.0861	−	1.98385i	−1.23353	−	0.202476i
$97$	3.53755	−	2.04240i	0.359183	−	0.207375i	−0.309539	−	0.950887i	$-0.600175\pi$
$97$	3.53755	−	2.04240i	0.359183	−	0.207375i	0.668723	+	0.743512i	$0.266841\pi$
$98$		−	13.0096i		−	1.31417i
$99$	−1.17363	+	3.47870i	−0.117955	+	0.349623i
$100$	2.89695			0.289695
$101$	−6.61239	−	11.4530i	−0.657958	−	1.13962i	−0.981143	−	0.193281i	$-0.938087\pi$
$101$	−6.61239	−	11.4530i	−0.657958	−	1.13962i	0.323186	−	0.946336i	$-0.395246\pi$
$102$	3.01400	−	3.67956i	0.298431	−	0.364331i
$103$	1.09724	−	1.90048i	0.108114	−	0.187259i	−0.806892	−	0.590699i	$-0.798852\pi$
$103$	1.09724	−	1.90048i	0.108114	−	0.187259i	0.915006	+	0.403439i	$0.132185\pi$
$104$	2.46386	+	6.71904i	0.241601	+	0.658856i
$105$	1.71572	−	0.647579i	0.167437	−	0.0631972i
$106$	−6.77639	+	3.91235i	−0.658181	+	0.380001i
$107$	−14.1628			−1.36917			−0.684585	−	0.728933i	$-0.740017\pi$
$107$	−14.1628			−1.36917			−0.684585	+	0.728933i	$0.740017\pi$
$108$	−7.98472	−	12.7608i	−0.768330	−	1.22790i
$109$		−	0.673663i		−	0.0645252i	−0.999479	−	0.0322626i	$-0.989729\pi$
$109$		−	0.673663i		−	0.0645252i	0.999479	−	0.0322626i	$-0.0102713\pi$
$110$	2.34530	−	1.35406i	0.223615	−	0.129104i
$111$	−7.08919	−	18.7824i	−0.672876	−	1.78275i
$112$	1.28515	+	0.741983i	0.121435	+	0.0701108i
$113$	8.22843	−	14.2521i	0.774066	−	1.34072i	−0.161252	−	0.986913i	$-0.551553\pi$
$113$	8.22843	−	14.2521i	0.774066	−	1.34072i	0.935318	−	0.353808i	$-0.115113\pi$
$114$	12.5709	+	10.2971i	1.17738	+	0.964412i
$115$	−0.983684	+	0.567930i	−0.0917290	+	0.0529598i
$116$	10.0577			0.933834
$117$	5.16214	−	9.50538i	0.477240	−	0.878773i
$118$	0.595727			0.0548411
$119$	−1.13787	+	0.656950i	−0.104308	+	0.0602225i
$120$	−0.556855	+	3.39249i	−0.0508337	+	0.309691i
$121$	−4.75118	+	8.22928i	−0.431925	+	0.748116i
$122$	−21.5020	−	12.4142i	−1.94670	−	1.12393i
$123$	5.95053	+	0.976739i	0.536541	+	0.0880696i
$124$	4.97565	−	2.87269i	0.446826	−	0.257975i
$125$			1.00000i			0.0894427i
$126$	1.38413	+	6.89133i	0.123308	+	0.613929i
$127$	−18.7156			−1.66074			−0.830371	−	0.557211i	$-0.811871\pi$
$127$	−18.7156			−1.66074			−0.830371	+	0.557211i	$0.811871\pi$
$128$	−12.3686	+	7.14104i	−1.09324	+	0.631185i
$129$	−6.89089	−	5.64447i	−0.606709	−	0.496968i
$130$	−7.49098	+	2.74693i	−0.657002	+	0.240921i
$131$	7.24460	−	12.5480i	0.632963	−	1.09632i	−0.353979	−	0.935253i	$-0.615172\pi$
$131$	7.24460	−	12.5480i	0.632963	−	1.09632i	0.986943	−	0.161071i	$-0.0514950\pi$
$132$	2.16836	+	5.74494i	0.188731	+	0.500033i
$133$	−2.24442	−	3.88744i	−0.194616	−	0.337084i
$134$	−11.5352			−0.996487
$135$	4.40489	−	2.75625i	0.379113	−	0.237220i
$136$		−	2.46313i		−	0.211211i
$137$	−1.03496	+	0.597533i	−0.0884225	+	0.0510507i	−0.543559	−	0.839371i	$-0.682924\pi$
$137$	−1.03496	+	0.597533i	−0.0884225	+	0.0510507i	0.455137	+	0.890422i	$0.349590\pi$
$138$	−1.53735	−	4.07313i	−0.130868	−	0.346728i
$139$	3.18816	−	5.52206i	0.270416	−	0.468375i	−0.698552	−	0.715559i	$-0.746172\pi$
$139$	3.18816	−	5.52206i	0.270416	−	0.468375i	0.968968	+	0.247184i	$0.0795053\pi$
$140$	1.53362	−	2.65631i	0.129615	−	0.224499i
$141$	5.31336	−	6.48667i	0.447466	−	0.546276i
$142$	−5.93292	−	10.2761i	−0.497880	−	0.862353i
$143$	−2.82810	+	3.38692i	−0.236498	+	0.283228i
$144$	3.98410	+	1.34414i	0.332008	+	0.112012i
$145$			3.47182i			0.288319i
$146$	−8.96159	−	15.5219i	−0.741667	−	1.28460i
$147$	−1.64935	+	10.0482i	−0.136036	+	0.828764i
$148$	−29.0792	−	16.7889i	−2.39030	−	1.38004i
$149$	−14.4733	−	8.35614i	−1.18570	−	0.684561i	−0.228370	−	0.973574i	$-0.573340\pi$
$149$	−14.4733	−	8.35614i	−1.18570	−	0.684561i	−0.957325	+	0.289013i	$0.906673\pi$
$150$	−3.78225	−	0.620831i	−0.308819	−	0.0506906i
$151$	−6.42988	+	3.71229i	−0.523256	+	0.302102i	−0.738266	−	0.674510i	$-0.764355\pi$
$151$	−6.42988	+	3.71229i	−0.523256	+	0.302102i	0.215010	+	0.976612i	$0.431022\pi$
$152$	8.41508			0.682553
$153$	−2.79441	+	2.45986i	−0.225915	+	0.198868i
$154$		−	2.86731i		−	0.231054i
$155$	0.991626	+	1.71755i	0.0796493	+	0.137957i
$156$	−3.39506	−	17.7700i	−0.271822	−	1.42274i
$157$	−6.65410	+	11.5252i	−0.531055	+	0.919814i	0.468288	+	0.883576i	$0.344871\pi$
$157$	−6.65410	+	11.5252i	−0.531055	+	0.919814i	−0.999343	+	0.0362382i	$0.988463\pi$
$158$	−14.3198	−	8.26753i	−1.13922	−	0.657729i
$159$	5.72987	−	2.16267i	0.454409	−	0.171511i
$160$	−3.53565	−	6.12392i	−0.279517	−	0.484138i
$161$			1.20263i			0.0947805i
$162$	7.69013	+	18.3716i	0.604194	+	1.44341i
$163$			17.2668i			1.35244i	0.736699	+	0.676221i	$0.236384\pi$
$163$			17.2668i			1.35244i	−0.736699	+	0.676221i	$0.763616\pi$
$164$	8.73453	−	5.04288i	0.682052	−	0.393783i
$165$	−1.98310	+	0.748497i	−0.154384	+	0.0582704i
$166$	1.61702	−	2.80076i	0.125505	−	0.217381i
$167$	−17.1671	−	9.91143i	−1.32843	−	0.766969i	−0.343373	−	0.939199i	$-0.611570\pi$
$167$	−17.1671	−	9.91143i	−1.32843	−	0.766969i	−0.985057	+	0.172230i	$0.944903\pi$
$168$	2.81590	+	2.30656i	0.217251	+	0.177955i
$169$	9.91824	−	8.40408i	0.762942	−	0.646467i
$170$	2.74611			0.210617
$171$	−8.40393	−	9.54689i	−0.642665	−	0.730069i
$172$	−14.8984			−1.13599
$173$	−3.56636	−	6.17711i	−0.271145	−	0.469637i	0.698010	−	0.716088i	$-0.254069\pi$
$173$	−3.56636	−	6.17711i	−0.271145	−	0.469637i	−0.969155	+	0.246451i	$0.920736\pi$
$174$	−13.1313	−	2.15542i	−0.995482	−	0.163402i
$175$	0.916933	+	0.529392i	0.0693136	+	0.0400182i
$176$	−1.48543	−	0.857613i	−0.111968	−	0.0646450i
$177$	−0.460121	−	0.0755258i	−0.0345848	−	0.00567686i
$178$	−18.1990	−	31.5217i	−1.36408	−	2.36265i
$179$	−9.02185			−0.674325			−0.337162	−	0.941447i	$-0.609467\pi$
$179$	−9.02185			−0.674325			−0.337162	+	0.941447i	$0.609467\pi$
$180$	2.77824	−	8.23482i	0.207078	−	0.613788i
$181$	3.08861			0.229575			0.114787	−	0.993390i	$-0.463381\pi$
$181$	3.08861			0.229575			0.114787	+	0.993390i	$0.463381\pi$
$182$	−1.44691	+	8.32293i	−0.107252	+	0.616936i
$183$	15.0336	+	12.3143i	1.11132	+	0.910301i
$184$	−1.95248	−	1.12727i	−0.143939	−	0.0831032i
$185$	5.79536	−	10.0379i	0.426084	−	0.737998i
$186$	−7.11183	+	2.68427i	−0.521464	+	0.196820i
$187$	1.31520	−	0.759328i	0.0961766	−	0.0555276i
$188$		−	14.0244i		−	1.02284i
$189$	−0.195383	−	5.49813i	−0.0142120	−	0.399930i
$190$			9.38187i			0.680632i
$191$	10.2536	+	17.7598i	0.741927	+	1.28506i	0.951617	+	0.307287i	$0.0994212\pi$
$191$	10.2536	+	17.7598i	0.741927	+	1.28506i	−0.209690	+	0.977768i	$0.567245\pi$
$192$	20.8148	−	7.85630i	1.50218	−	0.566980i
$193$	−4.73010	−	2.73093i	−0.340480	−	0.196576i	0.320004	−	0.947416i	$-0.396316\pi$
$193$	−4.73010	−	2.73093i	−0.340480	−	0.196576i	−0.660484	+	0.750840i	$0.729649\pi$
$194$	−4.51965	+	7.82826i	−0.324492	+	0.562036i
$195$	6.13405	−	1.17194i	0.439268	−	0.0839244i
$196$	8.51556	+	14.7494i	0.608254	+	1.05353i
$197$			10.3771i			0.739340i	0.929163	+	0.369670i	$0.120529\pi$
$197$			10.3771i			0.739340i	−0.929163	+	0.369670i	$0.879471\pi$
$198$	−1.59983	−	7.96527i	−0.113695	−	0.566067i
$199$	−25.1188			−1.78062			−0.890311	−	0.455354i	$-0.849513\pi$
$199$	−25.1188			−1.78062			−0.890311	+	0.455354i	$0.849513\pi$
$200$	−1.71895	+	0.992434i	−0.121548	+	0.0701757i
$201$	8.90940	+	1.46242i	0.628421	+	0.103151i
$202$	25.3444	+	14.6326i	1.78323	+	1.02955i
$203$	3.18343	+	1.83795i	0.223433	+	0.128999i
$204$	−1.00857	+	6.14446i	−0.0706142	+	0.430198i
$205$	1.74076	+	3.01508i	0.121580	+	0.210582i
$206$			4.85618i			0.338346i
$207$	0.671015	+	3.34086i	0.0466388	+	0.232206i
$208$	3.87898	+	3.23897i	0.268959	+	0.224582i
$209$	2.59418	+	4.49326i	0.179444	+	0.310805i
$210$	−2.57155	+	3.13941i	−0.177454	+	0.216640i
$211$	−5.56068	+	9.63138i	−0.382813	+	0.663052i	−0.991463	−	0.130387i	$-0.958378\pi$
$211$	−5.56068	+	9.63138i	−0.382813	+	0.663052i	0.608650	+	0.793439i	$0.291711\pi$
$212$	5.12172	−	8.87108i	0.351761	−	0.609268i
$213$	3.27960	+	8.68912i	0.224715	+	0.595369i
$214$	27.1421	−	15.6705i	1.85539	−	1.07121i
$215$		−	5.14277i		−	0.350734i
$216$	9.10941	+	4.83638i	0.619817	+	0.329074i
$217$	2.09983			0.142546
$218$	0.745376	+	1.29103i	0.0504832	+	0.0874395i
$219$	4.95380	+	13.1248i	0.334747	+	0.886892i
$220$	−1.77262	+	3.07027i	−0.119510	+	0.206997i
$221$	−4.20079	+	1.54042i	−0.282576	+	0.103620i
$222$	34.3678	+	28.1513i	2.30661	+	1.88939i
$223$	11.0073	−	6.35506i	0.737102	−	0.425566i	−0.0839124	−	0.996473i	$-0.526742\pi$
$223$	11.0073	−	6.35506i	0.737102	−	0.425566i	0.821015	+	0.570907i	$0.193408\pi$
$224$	−7.48697			−0.500244
$225$	2.84258	+	0.959021i	0.189506	+	0.0639347i
$226$			36.4175i			2.42246i
$227$	−12.8509	+	7.41948i	−0.852945	+	0.492448i	−0.861644	−	0.507514i	$-0.830565\pi$
$227$	−12.8509	+	7.41948i	−0.852945	+	0.492448i	0.00869815	+	0.999962i	$0.497231\pi$
$228$	−20.9921	−	3.44571i	−1.39023	−	0.228197i
$229$	8.61681	+	4.97492i	0.569415	+	0.328752i	0.756916	−	0.653513i	$-0.226705\pi$
$229$	8.61681	+	4.97492i	0.569415	+	0.328752i	−0.187501	+	0.982264i	$0.560039\pi$
$230$	1.25678	−	2.17680i	0.0828693	−	0.143534i
$231$	−0.363515	+	2.21462i	−0.0239175	+	0.145711i
$232$	−5.96788	+	3.44556i	−0.391810	+	0.226212i
$233$	14.2054			0.930628			0.465314	−	0.885146i	$-0.345941\pi$
$233$	14.2054			0.930628			0.465314	+	0.885146i	$0.345941\pi$
$234$	0.624367	+	23.9281i	0.0408161	+	1.56423i
$235$	4.84110			0.315799
$236$	−0.675393	+	0.389938i	−0.0439643	+	0.0253828i
$237$	10.0120	+	8.20103i	0.650349	+	0.532714i
$238$	1.45377	−	2.51800i	0.0942338	−	0.163218i
$239$	−7.62843	−	4.40428i	−0.493442	−	0.284889i	0.232559	−	0.972582i	$-0.425290\pi$
$239$	−7.62843	−	4.40428i	−0.493442	−	0.284889i	−0.726001	+	0.687693i	$0.758623\pi$
$240$	0.857240	+	2.27121i	0.0553346	+	0.146606i
$241$	−20.2820	+	11.7098i	−1.30648	+	0.754296i	−0.981507	−	0.191427i	$-0.938688\pi$
$241$	−20.2820	+	11.7098i	−1.30648	+	0.754296i	−0.324972	+	0.945724i	$0.605355\pi$
$242$		−	21.0278i		−	1.35172i
$243$	−3.61048	−	15.1646i	−0.231613	−	0.972808i
$244$	32.5032			2.08081
$245$	−5.09134	+	2.93949i	−0.325274	+	0.187797i
$246$	−12.4845	+	4.71212i	−0.795982	+	0.300434i
$247$	−5.26273	−	14.3517i	−0.334859	−	0.913174i
$248$	−1.96825	+	3.40910i	−0.124984	+	0.216478i
$249$	−1.60401	+	1.95822i	−0.101650	+	0.124097i
$250$	−1.10645	−	1.91643i	−0.0699782	−	0.121206i
$251$	7.47522			0.471832			0.235916	−	0.971774i	$-0.424191\pi$
$251$	7.47522			0.471832			0.235916	+	0.971774i	$0.424191\pi$
$252$	−6.08001	−	6.90690i	−0.383005	−	0.435094i
$253$		−	1.39005i		−	0.0873915i
$254$	35.8672	−	20.7079i	2.25051	−	1.29933i
$255$	−2.12101	−	0.348149i	−0.132823	−	0.0218020i
$256$	2.95749	−	5.12253i	0.184843	−	0.320158i
$257$	1.35692	−	2.35025i	0.0846420	−	0.146604i	−0.820597	−	0.571508i	$-0.806359\pi$
$257$	1.35692	−	2.35025i	0.0846420	−	0.146604i	0.905239	+	0.424904i	$0.139692\pi$
$258$	19.4513	+	3.19279i	1.21098	+	0.198775i
$259$	−6.13603	−	10.6279i	−0.381275	−	0.660387i
$260$	6.69471	−	8.01755i	0.415188	−	0.497227i
$261$	9.86895	+	3.32955i	0.610873	+	0.206094i
$262$			32.0632i			1.98087i
$263$	−11.3253	−	19.6160i	−0.698347	−	1.20957i	−0.969039	−	0.246907i	$-0.920586\pi$
$263$	−11.3253	−	19.6160i	−0.698347	−	1.20957i	0.270692	−	0.962666i	$-0.412747\pi$
$264$	−3.25472	−	2.66601i	−0.200314	−	0.164081i
$265$	3.06221	+	1.76797i	0.188110	+	0.108606i
$266$	8.60255	+	4.96668i	0.527456	+	0.304527i
$267$	10.0601	+	26.6536i	0.615667	+	1.63117i
$268$	13.0777	−	7.55044i	0.798850	−	0.461216i
$269$	−21.8510			−1.33228			−0.666139	−	0.745827i	$-0.732054\pi$
$269$	−21.8510			−1.33228			−0.666139	+	0.745827i	$0.732054\pi$
$270$	−5.39202	+	10.1560i	−0.328148	+	0.618073i
$271$		−	13.5318i		−	0.821999i	−0.911636	−	0.411000i	$-0.865180\pi$
$271$		−	13.5318i		−	0.821999i	0.911636	−	0.411000i	$-0.134820\pi$
$272$	−0.869645	−	1.50627i	−0.0527300	−	0.0913310i
$273$	2.17272	−	6.24493i	0.131499	−	0.377960i
$274$	1.32229	−	2.29026i	0.0798822	−	0.138360i
$275$	−1.05983	−	0.611891i	−0.0639100	−	0.0368984i
$276$	4.40904	+	3.61153i	0.265393	+	0.217389i
$277$	−0.0155003	−	0.0268472i	−0.000931320	−	0.00161309i	0.865559	−	0.500806i	$-0.166963\pi$
$277$	−0.0155003	−	0.0268472i	−0.000931320	−	0.00161309i	−0.866491	+	0.499193i	$0.833630\pi$
$278$			14.1102i			0.846274i
$279$	5.83326	−	1.17162i	0.349228	−	0.0701429i
$280$			2.10155i			0.125591i
$281$	9.91681	−	5.72548i	0.591588	−	0.341553i	−0.174137	−	0.984721i	$-0.555714\pi$
$281$	9.91681	−	5.72548i	0.591588	−	0.341553i	0.765725	+	0.643168i	$0.222380\pi$
$282$	−3.00551	+	18.3103i	−0.178975	+	1.09036i
$283$	−15.9080	+	27.5534i	−0.945631	+	1.63788i	−0.191147	+	0.981561i	$0.561221\pi$
$283$	−15.9080	+	27.5534i	−0.945631	+	1.63788i	−0.754484	+	0.656319i	$0.772113\pi$
$284$	13.4526	+	7.76688i	0.798267	+	0.460880i
$285$	1.18943	−	7.24626i	0.0704555	−	0.429231i
$286$	1.67240	−	9.61996i	0.0988909	−	0.568840i
$287$	3.68617			0.217588
$288$	−20.7985	+	4.17740i	−1.22556	+	0.246156i
$289$	−15.4600			−0.909414
$290$	−3.84141	−	6.65352i	−0.225575	−	0.390708i
$291$	4.48329	−	5.47330i	0.262815	−	0.320851i
$292$	20.3200	+	11.7318i	1.18914	+	0.686550i
$293$	24.7599	+	14.2951i	1.44649	+	0.835131i	0.998270	−	0.0587932i	$-0.0187252\pi$
$293$	24.7599	+	14.2951i	1.44649	+	0.835131i	0.448219	+	0.893924i	$0.352059\pi$
$294$	−7.95702	−	21.0817i	−0.464063	−	1.22951i
$295$	−0.134603	−	0.233139i	−0.00783689	−	0.0135739i
$296$	23.0061			1.33720
$297$	0.225831	+	6.35495i	0.0131041	+	0.368752i
$298$	36.9827			2.14235
$299$	−0.701451	+	4.03488i	−0.0405659	+	0.233343i
$300$	4.69441	−	1.77185i	0.271032	−	0.102298i
$301$	−4.71558	−	2.72254i	−0.271801	−	0.156925i
$302$	8.21495	−	14.2287i	0.472717	−	0.818770i
$303$	−17.7201	−	14.5149i	−1.01799	−	0.833860i
$304$	5.14605	−	2.97107i	0.295146	−	0.170403i
$305$			11.2198i			0.642444i
$306$	2.63358	−	7.80605i	0.150552	−	0.446242i
$307$			4.95115i			0.282577i	0.989968	+	0.141289i	$0.0451245\pi$
$307$			4.95115i			0.282577i	−0.989968	+	0.141289i	$0.954875\pi$
$308$	1.87682	+	3.25075i	0.106942	+	0.185229i
$309$	0.615662	−	3.75076i	0.0350238	−	0.213373i
$310$	−3.80077	−	2.19437i	−0.215869	−	0.124632i
$311$	−0.638413	+	1.10576i	−0.0362011	+	0.0627021i	−0.883558	−	0.468321i	$-0.844859\pi$
$311$	−0.638413	+	1.10576i	−0.0362011	+	0.0627021i	0.847357	+	0.531023i	$0.178192\pi$
$312$	8.10214	+	9.38103i	0.458694	+	0.531096i
$313$	7.67494	+	13.2934i	0.433813	+	0.751387i	0.997198	−	0.0748080i	$-0.0238344\pi$
$313$	7.67494	+	13.2934i	0.433813	+	0.751387i	−0.563385	+	0.826195i	$0.690501\pi$
$314$		−	29.4498i		−	1.66195i
$315$	2.38420	−	2.09876i	0.134334	−	0.118252i
$316$	21.6463			1.21770
$317$	1.90330	−	1.09887i	0.106900	−	0.0617186i	−0.445597	−	0.895234i	$-0.647009\pi$
$317$	1.90330	−	1.09887i	0.106900	−	0.0617186i	0.552497	+	0.833515i	$0.313675\pi$
$318$	−8.58802	+	10.4844i	−0.481592	+	0.587939i
$319$	−3.67953	−	2.12438i	−0.206014	−	0.118942i
$320$	11.1241	+	6.42248i	0.621853	+	0.359027i
$321$	−22.9504	+	8.66234i	−1.28096	+	0.483485i
$322$	−1.33065	−	2.30476i	−0.0741544	−	0.128439i
$323$			5.26116i			0.292739i
$324$	−20.7438	−	15.7947i	−1.15243	−	0.877485i
$325$	2.76758	+	2.31095i	0.153518	+	0.128188i
$326$	−19.1049	−	33.0907i	−1.05812	−	1.83273i
$327$	−0.412029	−	1.09165i	−0.0227853	−	0.0603683i
$328$	−3.45517	+	5.98453i	−0.190780	+	0.330440i
$329$	2.56284	−	4.43897i	0.141294	−	0.244728i
$330$	2.97230	−	3.62865i	0.163620	−	0.199751i
$331$	11.9839	−	6.91890i	0.658694	−	0.380297i	−0.133085	−	0.991105i	$-0.542488\pi$
$331$	11.9839	−	6.91890i	0.658694	−	0.380297i	0.791779	+	0.610807i	$0.209155\pi$
$332$			4.23374i			0.232357i
$333$	−22.9756	−	26.1003i	−1.25905	−	1.43029i
$334$	43.8661			2.40025
$335$	2.60634	+	4.51431i	0.142400	+	0.246643i
$336$	2.53636	+	0.416327i	0.138370	+	0.0227125i
$337$	6.57730	−	11.3922i	0.358289	−	0.620574i	−0.629386	−	0.777092i	$-0.716694\pi$
$337$	6.57730	−	11.3922i	0.358289	−	0.620574i	0.987675	+	0.156518i	$0.0500271\pi$
$338$	−9.70893	+	27.0799i	−0.528096	+	1.47295i
$339$	4.61698	−	28.1277i	0.250760	−	1.52769i
$340$	−3.11334	+	1.79749i	−0.168845	+	0.0974825i
$341$	−2.42707			−0.131433
$342$	26.6687	+	8.99741i	1.44208	+	0.486524i
$343$			13.6360i			0.736277i
$344$	8.84015	−	5.10386i	0.476629	−	0.275182i
$345$	−1.24667	+	1.52196i	−0.0671183	+	0.0819395i
$346$	13.6694	+	7.89201i	0.734870	+	0.424277i
$347$	−0.354154	+	0.613413i	−0.0190120	+	0.0329297i	−0.875375	−	0.483445i	$-0.839385\pi$
$347$	−0.354154	+	0.613413i	−0.0190120	+	0.0329297i	0.856363	+	0.516374i	$0.172719\pi$
$348$	16.2982	−	6.15155i	0.873674	−	0.329758i
$349$	−21.1121	+	12.1891i	−1.13010	+	0.652466i	−0.943961	−	0.330057i	$-0.892932\pi$
$349$	−21.1121	+	12.1891i	−1.13010	+	0.652466i	−0.186143	+	0.982523i	$0.559599\pi$
$350$	−2.34299			−0.125238
$351$	2.55134	−	18.5605i	0.136180	−	0.990684i
$352$	8.65373			0.461245
$353$	−19.1694	+	11.0675i	−1.02029	+	0.589063i	−0.914187	−	0.405293i	$-0.867170\pi$
$353$	−19.1694	+	11.0675i	−1.02029	+	0.589063i	−0.106100	+	0.994356i	$0.533836\pi$
$354$	0.965356	−	0.364362i	0.0513081	−	0.0193656i
$355$	−2.68105	+	4.64372i	−0.142296	+	0.246463i
$356$	41.2655	+	23.8247i	2.18707	+	1.26270i
$357$	−1.44207	+	1.76052i	−0.0763227	+	0.0931764i
$358$	17.2898	−	9.98225i	0.913793	−	0.527578i
$359$			2.42368i			0.127917i	0.997953	+	0.0639586i	$0.0203725\pi$
$359$			2.42368i			0.127917i	−0.997953	+	0.0639586i	$0.979627\pi$
$360$	1.17257	+	5.83801i	0.0617999	+	0.307690i
$361$	1.02566			0.0539819
$362$	−5.91911	+	3.41740i	−0.311102	+	0.179615i
$363$	−2.66589	+	16.2412i	−0.139923	+	0.852443i
$364$	−3.80744	−	10.3830i	−0.199564	−	0.544218i
$365$	−4.04970	+	7.01428i	−0.211971	+	0.367144i
$366$	−42.4361	−	6.96560i	−2.21817	−	0.364098i
$367$	−0.0405583	−	0.0702491i	−0.00211713	−	0.00366697i	0.864965	−	0.501832i	$-0.167341\pi$
$367$	−0.0405583	−	0.0702491i	−0.00211713	−	0.00366697i	−0.867082	+	0.498165i	$0.834007\pi$
$368$	−1.59199			−0.0829885
$369$	10.2400	−	2.05672i	0.533075	−	0.107069i
$370$			25.6492i			1.33344i
$371$	3.24222	−	1.87190i	0.168328	−	0.0971840i
$372$	6.30586	−	7.69834i	0.326944	−	0.399140i
$373$	4.12234	−	7.14011i	0.213447	−	0.369701i	−0.739344	−	0.673328i	$-0.764864\pi$
$373$	4.12234	−	7.14011i	0.213447	−	0.369701i	0.952791	+	0.303627i	$0.0981977\pi$
$374$	−1.68032	+	2.91040i	−0.0868874	+	0.150493i
$375$	0.611626	+	1.62047i	0.0315842	+	0.0836806i
$376$	4.80447	+	8.32159i	0.247772	+	0.429153i
$377$	9.60856	+	8.02321i	0.494866	+	0.413216i
$378$	6.45786	+	10.3206i	0.332156	+	0.530835i
$379$		−	28.1019i		−	1.44350i	−0.692154	−	0.721749i	$-0.743338\pi$
$379$		−	28.1019i		−	1.44350i	0.692154	−	0.721749i	$-0.256662\pi$
$380$	−6.14098	−	10.6365i	−0.315026	−	0.545640i
$381$	−30.3280	+	11.4469i	−1.55375	+	0.586445i
$382$	−39.3008	−	22.6903i	−2.01080	−	1.16094i
$383$	6.71744	+	3.87831i	0.343245	+	0.198173i	0.661706	−	0.749763i	$-0.269833\pi$
$383$	6.71744	+	3.87831i	0.343245	+	0.198173i	−0.318461	+	0.947936i	$0.603166\pi$
$384$	−15.6753	+	19.1368i	−0.799929	+	0.976571i
$385$	−1.12213	+	0.647860i	−0.0571889	+	0.0330180i
$386$	12.0866			0.615190
$387$	−14.6188	−	4.93203i	−0.743113	−	0.250709i
$388$		−	11.8335i		−	0.600754i
$389$	14.9645	+	25.9193i	0.758732	+	1.31416i	0.943497	+	0.331380i	$0.107514\pi$
$389$	14.9645	+	25.9193i	0.758732	+	1.31416i	−0.184765	+	0.982783i	$0.559152\pi$
$390$	−10.4588	+	9.03298i	−0.529602	+	0.457403i
$391$	0.704774	−	1.22070i	0.0356420	−	0.0617337i
$392$	−10.1056	−	5.83450i	−0.510412	−	0.294687i
$393$	4.06495	−	24.7646i	0.205049	−	1.24921i
$394$	−11.4818	−	19.8871i	−0.578445	−	1.00190i
$395$			7.47210i			0.375962i
$396$	7.02751	+	7.98327i	0.353146	+	0.401174i
$397$			36.7191i			1.84288i	0.388524	+	0.921439i	$0.372985\pi$
$397$			36.7191i			1.84288i	−0.388524	+	0.921439i	$0.627015\pi$
$398$	48.1384	−	27.7927i	2.41296	−	1.39312i
$399$	−6.01467	−	4.92673i	−0.301110	−	0.246645i
$400$	−0.700788	+	1.21380i	−0.0350394	+	0.0606900i
$401$	18.1252	+	10.4646i	0.905127	+	0.522576i	0.878860	−	0.477079i	$-0.158305\pi$
$401$	18.1252	+	10.4646i	0.905127	+	0.522576i	0.0262672	+	0.999655i	$0.491638\pi$
$402$	−18.6924	+	7.05521i	−0.932290	+	0.351882i
$403$	7.04505	+	1.22476i	0.350939	+	0.0610095i
$404$	−38.3116			−1.90607
$405$	5.45219	−	7.16056i	0.270922	−	0.355811i
$406$	−8.13444			−0.403705
$407$	7.09227	+	12.2842i	0.351551	+	0.608904i
$408$	−1.50651	−	3.99142i	−0.0745835	−	0.197605i
$409$	−17.5031	−	10.1054i	−0.865471	−	0.499680i	0.000369696	−	1.00000i	$-0.499882\pi$
$409$	−17.5031	−	10.1054i	−0.865471	−	0.499680i	−0.865840	+	0.500320i	$0.833216\pi$
$410$	−6.67208	−	3.85213i	−0.329511	−	0.190243i
$411$	−1.31165	+	1.60129i	−0.0646989	+	0.0789858i
$412$	−3.17865	−	5.50559i	−0.156601	−	0.271241i
$413$	−0.285031			−0.0140254
$414$	−4.98246	−	5.66009i	−0.244875	−	0.278178i
$415$	−1.46145			−0.0717396
$416$	−25.1192	−	4.36688i	−1.23157	−	0.214104i
$417$	1.78888	−	10.8983i	0.0876018	−	0.533691i
$418$	−9.94316	−	5.74069i	−0.486336	−	0.280786i
$419$	14.1445	−	24.4990i	0.691004	−	1.19685i	−0.280505	−	0.959852i	$-0.590502\pi$
$419$	14.1445	−	24.4990i	0.691004	−	1.19685i	0.971509	−	0.237002i	$-0.0761647\pi$
$420$	0.860516	−	5.24247i	0.0419889	−	0.255806i
$421$	−18.6160	+	10.7480i	−0.907289	+	0.523824i	−0.879558	−	0.475792i	$-0.842162\pi$
$421$	−18.6160	+	10.7480i	−0.907289	+	0.523824i	−0.0277313	+	0.999615i	$0.508828\pi$
$422$		−	24.6105i		−	1.19802i
$423$	4.64272	−	13.7612i	0.225737	−	0.669094i
$424$			7.01837i			0.340842i
$425$	−0.620476	−	1.07470i	−0.0300975	−	0.0521304i
$426$	−15.8992	−	13.0234i	−0.770321	−	0.630985i
$427$	10.2878	+	5.93967i	0.497862	+	0.287441i
$428$	−20.5145	+	35.5321i	−0.991605	+	1.71751i
$429$	−2.51132	+	7.21813i	−0.121248	+	0.348495i
$430$	5.69024	+	9.85578i	0.274408	+	0.475288i
$431$		−	34.6370i		−	1.66841i	−0.551457	−	0.834204i	$-0.685928\pi$
$431$		−	34.6370i		−	1.66841i	0.551457	−	0.834204i	$-0.314072\pi$
$432$	7.27821	−	0.258640i	0.350173	−	0.0124438i
$433$	36.2199			1.74062			0.870308	−	0.492508i	$-0.163920\pi$
$433$	36.2199			1.74062			0.870308	+	0.492508i	$0.163920\pi$
$434$	−4.02419	+	2.32337i	−0.193167	+	0.111525i
$435$	2.12346	+	5.62598i	0.101812	+	0.269745i
$436$	−1.69011	−	0.975784i	−0.0809415	−	0.0467316i
$437$	4.17044	+	2.40781i	0.199499	+	0.115181i
$438$	−24.0156	−	19.6716i	−1.14751	−	0.939948i
$439$	3.62173	+	6.27302i	0.172856	+	0.299395i	0.939417	−	0.342776i	$-0.111367\pi$
$439$	3.62173	+	6.27302i	0.172856	+	0.299395i	−0.766561	+	0.642171i	$0.778034\pi$
$440$		−	2.42905i		−	0.115800i
$441$	3.47304	+	17.2916i	0.165383	+	0.823410i
$442$	6.34612	−	7.60009i	0.301854	−	0.361499i
$443$	−13.9973	−	24.2440i	−0.665031	−	1.15187i	−0.979277	−	0.202525i	$-0.935085\pi$
$443$	−13.9973	−	24.2440i	−0.665031	−	1.15187i	0.314246	−	0.949341i	$-0.398248\pi$
$444$	−57.3904	−	9.42025i	−2.72363	−	0.447065i
$445$	−8.22405	+	14.2445i	−0.389857	+	0.675253i
$446$	−14.0631	+	24.3581i	−0.665909	+	1.15339i
$447$	−28.5643	−	4.68863i	−1.35104	−	0.221765i
$448$	11.7780	−	6.80001i	0.556456	−	0.321270i
$449$			32.0442i			1.51226i	0.654421	+	0.756130i	$0.272912\pi$
$449$			32.0442i			1.51226i	−0.654421	+	0.756130i	$0.727088\pi$
$450$	−6.50873	+	1.30729i	−0.306824	+	0.0616260i
$451$	−4.26061			−0.200625
$452$	−23.8374	−	41.2875i	−1.12122	−	1.94200i
$453$	−8.14887	+	9.94832i	−0.382867	+	0.467413i
$454$	16.4186	−	28.4379i	0.770564	−	1.33466i
$455$	3.58412	−	1.31429i	0.168026	−	0.0616149i
$456$	13.6364	−	5.14688i	0.638581	−	0.241025i
$457$	−22.0113	+	12.7083i	−1.02965	+	0.594467i	−0.916883	−	0.399155i	$-0.869304\pi$
$457$	−22.0113	+	12.7083i	−1.02965	+	0.594467i	−0.112763	+	0.993622i	$0.535970\pi$
$458$	−22.0180			−1.02884
$459$	−3.02374	+	5.69526i	−0.141136	+	0.265832i
$460$			3.29053i			0.153422i
$461$	7.27198	−	4.19848i	0.338690	−	0.195543i	−0.321003	−	0.947078i	$-0.604020\pi$
$461$	7.27198	−	4.19848i	0.338690	−	0.195543i	0.659692	+	0.751536i	$0.270687\pi$
$462$	−1.75372	−	4.64638i	−0.0815904	−	0.216169i
$463$	13.3439	+	7.70412i	0.620145	+	0.358041i	0.776926	−	0.629592i	$-0.216778\pi$
$463$	13.3439	+	7.70412i	0.620145	+	0.358041i	−0.156780	+	0.987634i	$0.550111\pi$
$464$	−2.43301	+	4.21410i	−0.112950	+	0.195635i
$465$	2.65739	+	2.17672i	0.123234	+	0.100943i
$466$	−27.2237	+	15.7176i	−1.26112	+	0.728105i
$467$	30.0028			1.38836			0.694182	−	0.719800i	$-0.255766\pi$
$467$	30.0028			1.38836			0.694182	+	0.719800i	$0.255766\pi$
$468$	−16.3702	−	26.7193i	−0.756712	−	1.23510i
$469$	5.51910			0.254848
$470$	−9.27764	+	5.35645i	−0.427946	+	0.247075i
$471$	−3.73362	+	22.7461i	−0.172036	+	1.04808i
$472$	0.267169	−	0.462750i	0.0122975	−	0.0212998i
$473$	5.45045	+	3.14682i	0.250612	+	0.144691i
$474$	−28.2614	−	4.63891i	−1.29809	−	0.213072i
$475$	3.67162	−	2.11981i	0.168465	−	0.0972635i
$476$			3.80630i			0.174462i
$477$	7.96233	−	7.00908i	0.364570	−	0.320924i
$478$	19.4925			0.891566
$479$	−0.742880	+	0.428902i	−0.0339431	+	0.0195970i	−0.516876	−	0.856061i	$-0.672905\pi$
$479$	−0.742880	+	0.428902i	−0.0339431	+	0.0195970i	0.482932	+	0.875658i	$0.339572\pi$
$480$	−9.47495	−	7.76112i	−0.432470	−	0.354245i
$481$	−14.3878	−	39.2361i	−0.656028	−	1.78901i
$482$	25.9127	−	44.8822i	1.18029	−	2.04433i
$483$	0.735559	+	1.94882i	0.0334691	+	0.0886745i
$484$	13.7639	+	23.8398i	0.625633	+	1.08363i
$485$	4.08481			0.185482
$486$	23.6981	+	25.0671i	1.07497	+	1.13706i
$487$		−	19.2888i		−	0.874058i	−0.899448	−	0.437029i	$-0.856031\pi$
$487$		−	19.2888i		−	0.874058i	0.899448	−	0.437029i	$-0.143969\pi$
$488$	−19.2862	+	11.1349i	−0.873047	+	0.504054i
$489$	10.5608	+	27.9803i	0.477578	+	1.26531i
$490$	6.50481	−	11.2667i	0.293857	−	0.508976i
$491$	−8.18301	+	14.1734i	−0.369294	+	0.639636i	−0.989455	−	0.144838i	$-0.953734\pi$
$491$	−8.18301	+	14.1734i	−0.369294	+	0.639636i	0.620161	+	0.784474i	$0.287067\pi$
$492$	11.0697	−	13.5141i	0.499059	−	0.609262i
$493$	−2.15418	−	3.73116i	−0.0970196	−	0.168043i
$494$	25.9651	+	21.6810i	1.16822	+	0.975476i
$495$	−2.75575	+	2.42583i	−0.123862	+	0.109033i
$496$			2.77968i			0.124811i
$497$	2.83866	+	4.91670i	0.127331	+	0.220544i
$498$	0.907311	−	5.52756i	0.0406576	−	0.247696i
$499$	−23.1110	−	13.3432i	−1.03459	−	0.597322i	−0.116296	−	0.993215i	$-0.537102\pi$
$499$	−23.1110	−	13.3432i	−1.03459	−	0.597322i	−0.918297	+	0.395892i	$0.870435\pi$
$500$	2.50883	+	1.44848i	0.112198	+	0.0647778i
$501$	−33.8808	−	5.56131i	−1.51368	−	0.248461i
$502$	−14.3258	+	8.27098i	−0.639390	+	0.369152i
$503$	−29.6619			−1.32256			−0.661280	−	0.750139i	$-0.729987\pi$
$503$	−29.6619			−1.32256			−0.661280	+	0.750139i	$0.729987\pi$
$504$	5.97382	+	2.01543i	0.266095	+	0.0897742i
$505$		−	13.2248i		−	0.588495i
$506$	1.53802	+	2.66393i	0.0683734	+	0.118426i
$507$	10.9320	−	19.6848i	0.485509	−	0.874232i
$508$	−27.1091	+	46.9543i	−1.20277	+	2.08326i
$509$	−4.38296	−	2.53051i	−0.194271	−	0.112163i	0.399709	−	0.916642i	$-0.369111\pi$
$509$	−4.38296	−	2.53051i	−0.194271	−	0.112163i	−0.593981	+	0.804479i	$0.702444\pi$
$510$	4.44998	−	1.67959i	0.197049	−	0.0743736i
$511$	4.28775	+	7.42660i	0.189679	+	0.328533i
$512$		−	15.4748i		−	0.683898i
$513$	−19.4574	−	10.3304i	−0.859066	−	0.456096i
$514$			6.00545i			0.264889i
$515$	1.90048	−	1.09724i	0.0837450	−	0.0483502i
$516$	−24.1423	+	9.11222i	−1.06281	+	0.401143i
$517$	−2.96223	+	5.13073i	−0.130279	+	0.225649i
$518$	23.5186	+	13.5785i	1.03335	+	0.596603i
$519$	−9.55725	−	7.82853i	−0.419517	−	0.343634i
$520$	−1.22576	+	7.05079i	−0.0537529	+	0.309198i
$521$	14.4458			0.632881			0.316441	−	0.948612i	$-0.397512\pi$
$521$	14.4458			0.632881			0.316441	+	0.948612i	$0.397512\pi$
$522$	−22.5972	+	4.53867i	−0.989051	+	0.198652i
$523$	29.4092			1.28597			0.642987	−	0.765877i	$-0.277695\pi$
$523$	29.4092			1.28597			0.642987	+	0.765877i	$0.277695\pi$
$524$	−20.9872	−	36.3510i	−0.916832	−	1.58800i
$525$	1.80965	+	0.297042i	0.0789796	+	0.0129640i
$526$	43.4083	+	25.0618i	1.89269	+	1.09275i
$527$	−2.13139	−	1.23056i	−0.0928450	−	0.0536041i
$528$	−2.93163	−	0.481207i	−0.127583	−	0.0209418i
$529$	10.8549	+	18.8013i	0.471953	+	0.817446i
$530$	−7.82470			−0.339883
$531$	−0.791804	+	0.159035i	−0.0343614	+	0.00690152i
$532$	−13.0039			−0.563792
$533$	12.3673	+	2.15001i	0.535686	+	0.0931272i
$534$	−48.7704	−	39.9488i	−2.11050	−	1.72875i
$535$	−12.2654	−	7.08140i	−0.530277	−	0.306156i
$536$	−5.17324	+	8.96032i	−0.223450	+	0.387027i
$537$	−14.6196	+	5.51800i	−0.630883	+	0.238119i
$538$	41.8759	−	24.1771i	1.80540	−	1.04235i
$539$		−	7.19459i		−	0.309893i
$540$	−0.534590	−	15.0435i	−0.0230051	−	0.647369i
$541$		−	27.4422i		−	1.17983i	−0.807465	−	0.589915i	$-0.799161\pi$
$541$		−	27.4422i		−	1.17983i	0.807465	−	0.589915i	$-0.200839\pi$
$542$	14.9723	+	25.9328i	0.643116	+	1.11391i
$543$	5.00499	−	1.88907i	0.214785	−	0.0810679i
$544$	7.59949	+	4.38757i	0.325826	+	0.188115i
$545$	0.336831	−	0.583409i	0.0144283	−	0.0249905i
$546$	2.74584	+	14.3720i	0.117511	+	0.615065i
$547$	−10.0951	−	17.4852i	−0.431635	−	0.747614i	0.565379	−	0.824831i	$-0.308730\pi$
$547$	−10.0951	−	17.4852i	−0.431635	−	0.747614i	−0.997014	+	0.0772173i	$0.975396\pi$
$548$			3.46205i			0.147891i
$549$	31.8932	+	10.7600i	1.36117	+	0.459227i
$550$	2.70812			0.115474
$551$	12.7472	−	7.35960i	0.543049	−	0.313530i
$552$	−3.85340	−	0.632510i	−0.164012	−	0.0269214i
$553$	6.85142	+	3.95567i	0.291352	+	0.168212i
$554$	0.0594104	+	0.0343006i	0.00252411	+	0.00145729i
$555$	3.25178	−	19.8106i	0.138030	−	0.840914i
$556$	−9.23595	−	15.9971i	−0.391692	−	0.678430i
$557$			4.02815i			0.170678i	0.996352	+	0.0853391i	$0.0271974\pi$
$557$			4.02815i			0.170678i	−0.996352	+	0.0853391i	$0.972803\pi$
$558$	−9.88271	+	8.69955i	−0.418368	+	0.368281i
$559$	−14.2330	−	11.8847i	−0.601994	−	0.502669i
$560$	0.741983	+	1.28515i	0.0313545	+	0.0543076i
$561$	1.66681	−	2.03487i	0.0703726	−	0.0859124i
$562$	−12.6699	+	21.9450i	−0.534449	+	0.925693i
$563$	−18.1141	+	31.3746i	−0.763419	+	1.32228i	0.177659	+	0.984092i	$0.443147\pi$
$563$	−18.1141	+	31.3746i	−0.763419	+	1.32228i	−0.941078	+	0.338188i	$0.890186\pi$
$564$	−8.57770	−	22.7261i	−0.361186	−	0.956943i
$565$	14.2521	−	8.22843i	0.599589	−	0.346173i
$566$		−	70.4057i		−	2.95937i
$567$	−3.67941	−	8.79004i	−0.154521	−	0.369147i
$568$	−10.6431			−0.446574
$569$	4.33283	+	7.50468i	0.181642	+	0.314613i	0.942440	−	0.334376i	$-0.108526\pi$
$569$	4.33283	+	7.50468i	0.181642	+	0.314613i	−0.760798	+	0.648989i	$0.775192\pi$
$570$	5.73819	+	15.2030i	0.240346	+	0.636784i
$571$	19.0500	−	32.9956i	0.797219	−	1.38082i	−0.124202	−	0.992257i	$-0.539637\pi$
$571$	19.0500	−	32.9956i	0.797219	−	1.38082i	0.921421	−	0.388567i	$-0.127030\pi$
$572$	4.40078	+	12.0011i	0.184006	+	0.501791i
$573$	27.4780	+	22.5078i	1.14791	+	0.940277i
$574$	−7.06429	+	4.07857i	−0.294858	+	0.170236i
$575$	−1.13586			−0.0473686
$576$	28.9246	−	25.4618i	1.20519	−	1.06091i
$577$			4.98879i			0.207686i	0.994594	+	0.103843i	$0.0331140\pi$
$577$			4.98879i			0.207686i	−0.994594	+	0.103843i	$0.966886\pi$
$578$	29.6281	−	17.1058i	1.23237	−	0.711508i
$579$	−9.33528	−	1.53232i	−0.387961	−	0.0636812i
$580$	8.71023	+	5.02885i	0.361673	+	0.208812i
$581$	−0.773678	+	1.34005i	−0.0320976	+	0.0555946i
$582$	−2.53598	+	15.4498i	−0.105120	+	0.640413i
$583$	−3.74748	+	2.16361i	−0.155205	+	0.0896076i
$584$	−16.0762			−0.665239
$585$	9.22324	−	5.65083i	0.381334	−	0.233633i
$586$	−63.2676			−2.61356
$587$	30.8788	−	17.8279i	1.27450	−	0.735835i	0.298671	−	0.954356i	$-0.403457\pi$
$587$	30.8788	−	17.8279i	1.27450	−	0.735835i	0.975832	+	0.218521i	$0.0701232\pi$
$588$	22.8203	+	18.6925i	0.941092	+	0.770868i
$589$	4.20411	−	7.28174i	0.173228	−	0.300039i
$590$	0.515915	+	0.297864i	0.0212399	+	0.0122628i
$591$	6.34692	+	16.8158i	0.261078	+	0.691710i
$592$	14.0688	−	8.12264i	0.578225	−	0.333839i
$593$		−	4.39457i		−	0.180463i	−0.995921	−	0.0902317i	$-0.971239\pi$
$593$		−	4.39457i		−	0.180463i	0.995921	−	0.0902317i	$-0.0287608\pi$
$594$	−7.46424	−	11.9290i	−0.306262	−	0.489451i
$595$	−1.31390			−0.0538646
$596$	−41.9283	+	24.2073i	−1.71745	+	0.991571i
$597$	−40.7041	+	15.3633i	−1.66591	+	0.628777i
$598$	−3.12013	−	8.50870i	−0.127591	−	0.347947i
$599$	−19.6062	+	33.9589i	−0.801088	+	1.38752i	0.117813	+	0.993036i	$0.462412\pi$
$599$	−19.6062	+	33.9589i	−0.801088	+	1.38752i	−0.918901	+	0.394489i	$0.870922\pi$
$600$	−2.17850	+	2.65956i	−0.0889368	+	0.108576i
$601$	17.9811	+	31.1443i	0.733466	+	1.27040i	0.955393	+	0.295338i	$0.0954321\pi$
$601$	17.9811	+	31.1443i	0.733466	+	1.27040i	−0.221927	+	0.975063i	$0.571235\pi$
$602$	12.0495			0.491099
$603$	15.3318	−	3.07942i	0.624361	−	0.125404i
$604$			21.5087i			0.875175i
$605$	−8.22928	+	4.75118i	−0.334568	+	0.193163i
$606$	50.0195	+	8.21036i	2.03190	+	0.333523i
$607$	−6.31059	+	10.9303i	−0.256139	+	0.443645i	−0.965204	−	0.261497i	$-0.915784\pi$
$607$	−6.31059	+	10.9303i	−0.256139	+	0.443645i	0.709065	+	0.705143i	$0.249117\pi$
$608$	−14.9898	+	25.9631i	−0.607916	+	1.05294i
$609$	6.28279	+	1.03128i	0.254591	+	0.0417895i
$610$	−12.4142	−	21.5020i	−0.502635	−	0.870590i
$611$	11.1875	−	13.3981i	0.452599	−	0.542031i
$612$	2.12375	+	10.5738i	0.0858476	+	0.427419i
$613$		−	13.6583i		−	0.551652i	−0.961208	−	0.275826i	$-0.911049\pi$
$613$		−	13.6583i		−	0.551652i	0.961208	−	0.275826i	$-0.0889513\pi$
$614$	−5.47821	−	9.48854i	−0.221083	−	0.382926i
$615$	4.66494	+	3.82114i	0.188108	+	0.154083i
$616$	−2.22727	−	1.28592i	−0.0897395	−	0.0518111i
$617$	−10.1696	−	5.87142i	−0.409413	−	0.236375i	0.281125	−	0.959671i	$-0.409293\pi$
$617$	−10.1696	−	5.87142i	−0.409413	−	0.236375i	−0.690537	+	0.723297i	$0.742626\pi$
$618$	2.97016	+	7.86928i	0.119478	+	0.316549i
$619$	15.4901	−	8.94321i	0.622600	−	0.359458i	−0.155281	−	0.987870i	$-0.549628\pi$
$619$	15.4901	−	8.94321i	0.622600	−	0.359458i	0.777880	+	0.628412i	$0.216295\pi$
$620$	5.74538			0.230740
$621$	3.13071	+	5.00334i	0.125631	+	0.200777i
$622$		−	2.82550i		−	0.113292i
$623$	8.70749	+	15.0818i	0.348858	+	0.604240i
$624$	8.26680	+	2.87617i	0.330937	+	0.115139i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−29.4170	−	16.9839i	−1.17574	−	0.678814i
$627$	6.95199	+	5.69451i	0.277636	+	0.227417i
$628$	19.2766	+	33.3880i	0.769220	+	1.33233i
$629$			14.3835i			0.573509i
$630$	−2.24697	+	6.66014i	−0.0895216	+	0.265346i
$631$		−	40.4209i		−	1.60913i	−0.593864	−	0.804565i	$-0.702398\pi$
$631$		−	40.4209i		−	1.60913i	0.593864	−	0.804565i	$-0.297602\pi$
$632$	−12.8441	+	7.41557i	−0.510913	+	0.294976i
$633$	−3.12010	+	19.0084i	−0.124013	+	0.755516i
$634$	−2.43169	+	4.21181i	−0.0965748	+	0.167272i
$635$	−16.2082	−	9.35780i	−0.643202	−	0.371353i
$636$	2.87380	−	17.5079i	0.113954	−	0.694232i
$637$	−3.63056	+	20.8837i	−0.143848	+	0.827443i
$638$	9.40210			0.372233
$639$	10.6290	+	12.0745i	0.420476	+	0.477662i
$640$	−14.2821			−0.564549
$641$	17.7262	+	30.7027i	0.700143	+	1.21268i	0.968416	+	0.249340i	$0.0802137\pi$
$641$	17.7262	+	30.7027i	0.700143	+	1.21268i	−0.268273	+	0.963343i	$0.586453\pi$
$642$	34.3984	−	41.9943i	1.35759	−	1.65738i
$643$	28.5026	+	16.4560i	1.12403	+	0.648961i	0.942428	−	0.334410i	$-0.108537\pi$
$643$	28.5026	+	16.4560i	1.12403	+	0.648961i	0.181606	+	0.983371i	$0.441870\pi$
$644$	3.01720	+	1.74198i	0.118894	+	0.0686436i
$645$	−3.14545	−	8.33370i	−0.123852	−	0.328139i
$646$	−5.82123	−	10.0827i	−0.229033	−	0.396697i
$647$	−37.7889			−1.48564			−0.742818	−	0.669494i	$-0.766511\pi$
$647$	−37.7889			−1.48564			−0.742818	+	0.669494i	$0.766511\pi$
$648$	17.7196	+	2.26564i	0.696090	+	0.0890029i
$649$	0.329450			0.0129320
$650$	−7.86084	−	1.36658i	−0.308328	−	0.0536017i
$651$	3.40271	−	1.28431i	0.133363	−	0.0503362i
$652$	43.3196	+	25.0106i	1.69653	+	0.979490i
$653$	11.3362	−	19.6348i	0.443618	−	0.768369i	−0.554337	−	0.832292i	$-0.687028\pi$
$653$	11.3362	−	19.6348i	0.443618	−	0.768369i	0.997955	+	0.0639234i	$0.0203613\pi$
$654$	1.99748	+	1.63618i	0.0781078	+	0.0639797i
$655$	12.5480	−	7.24460i	0.490291	−	0.283070i
$656$			4.87960i			0.190517i
$657$	16.0549	+	18.2384i	0.626362	+	0.711549i
$658$			11.3426i			0.442182i
$659$	24.4766	+	42.3947i	0.953472	+	1.65146i	0.737827	+	0.674990i	$0.235852\pi$
$659$	24.4766	+	42.3947i	0.953472	+	1.65146i	0.215646	+	0.976472i	$0.430814\pi$
$660$	−0.994618	+	6.05945i	−0.0387154	+	0.235864i
$661$	30.9756	+	17.8838i	1.20481	+	0.695597i	0.961621	−	0.274381i	$-0.0884731\pi$
$661$	30.9756	+	17.8838i	1.20481	+	0.695597i	0.243189	+	0.969979i	$0.421806\pi$
$662$	−15.3109	+	26.5192i	−0.595074	+	1.03070i
$663$	−5.86508	+	5.06551i	−0.227781	+	0.196728i
$664$	−1.45039	−	2.51215i	−0.0562860	−	0.0974903i
$665$		−	4.48883i		−	0.174070i
$666$	72.9099	+	24.5981i	2.82520	+	0.953157i
$667$	−3.94351			−0.152693
$668$	−49.7322	+	28.7129i	−1.92420	+	1.11094i
$669$	13.9500	−	17.0305i	0.539339	−	0.658437i
$670$	−9.98975	−	5.76758i	−0.385938	−	0.222821i
$671$	−11.8910	−	6.86530i	−0.459049	−	0.265032i
$672$	−12.1324	+	4.57922i	−0.468017	+	0.176647i
$673$	15.0753	+	26.1112i	0.581111	+	1.00651i	0.995348	+	0.0963447i	$0.0307151\pi$
$673$	15.0753	+	26.1112i	0.581111	+	1.00651i	−0.414237	+	0.910169i	$0.635952\pi$
$674$			29.1099i			1.12127i
$675$	5.19287	−	0.184535i	0.199874	−	0.00710277i
$676$	−6.71810	−	37.0563i	−0.258388	−	1.42524i
$677$	−8.73261	−	15.1253i	−0.335621	−	0.581313i	0.647983	−	0.761655i	$-0.275613\pi$
$677$	−8.73261	−	15.1253i	−0.335621	−	0.581313i	−0.983604	+	0.180342i	$0.942280\pi$
$678$	22.2739	+	59.0133i	0.855423	+	2.26639i
$679$	2.16246	−	3.74550i	0.0829877	−	0.143739i
$680$	1.23156	−	2.13313i	0.0472283	−	0.0818018i
$681$	−16.2865	+	19.8830i	−0.624102	+	0.761917i
$682$	4.65132	−	2.68544i	0.178108	−	0.102831i
$683$			20.0805i			0.768360i	0.923258	+	0.384180i	$0.125516\pi$
$683$			20.0805i			0.768360i	−0.923258	+	0.384180i	$0.874484\pi$
$684$	−36.1244	+	7.25563i	−1.38125	+	0.277426i
$685$	−1.19507			−0.0456612
$686$	−15.0876	−	26.1326i	−0.576049	−	0.997746i
$687$	17.0060	+	2.79143i	0.648821	+	0.106500i
$688$	3.60399	−	6.24230i	0.137401	−	0.237986i
$689$	11.9696	−	4.38924i	0.456006	−	0.167217i
$690$	0.705177	−	4.29611i	0.0268456	−	0.163550i
$691$	−15.6067	+	9.01055i	−0.593708	+	0.342778i	−0.766562	−	0.642170i	$-0.778034\pi$
$691$	−15.6067	+	9.01055i	−0.593708	+	0.342778i	0.172854	+	0.984947i	$0.444701\pi$
$692$	−20.6631			−0.785494
$693$	0.765454	+	3.81105i	0.0290772	+	0.144770i
$694$		−	1.56742i		−	0.0594984i
$695$	5.52206	−	3.18816i	0.209464	−	0.120934i
$696$	−7.56336	+	9.23352i	−0.286688	+	0.349996i
$697$	−3.74157	−	2.16020i	−0.141722	−	0.0818232i
$698$	26.9733	−	46.7191i	1.02095	−	1.76834i
$699$	23.0194	−	8.68840i	0.870675	−	0.328626i
$700$	2.65631	−	1.53362i	0.100399	−	0.0579655i
$701$	23.9457			0.904417			0.452209	−	0.891912i	$-0.350636\pi$
$701$	23.9457			0.904417			0.452209	+	0.891912i	$0.350636\pi$
$702$	15.6468	+	38.3928i	0.590550	+	1.44904i
$703$	−49.1402			−1.85336
$704$	−13.6134	+	7.85972i	−0.513075	+	0.296224i
$705$	7.84484	−	2.96094i	0.295454	−	0.111516i
$706$	24.4913	−	42.4202i	0.921742	−	1.59650i
$707$	−12.1262	−	7.00109i	−0.456054	−	0.263303i
$708$	−0.855955	+	1.04497i	−0.0321688	+	0.0392724i
$709$	−38.8600	+	22.4358i	−1.45942	+	0.842595i	−0.998983	−	0.0450989i	$-0.985640\pi$
$709$	−38.8600	+	22.4358i	−1.45942	+	0.842595i	−0.460434	+	0.887694i	$0.652306\pi$
$710$		−	11.8658i		−	0.445317i
$711$	21.2401	+	7.16590i	0.796565	+	0.268742i
$712$	−32.6473			−1.22351
$713$	−1.95089	+	1.12635i	−0.0730615	+	0.0421821i
$714$	0.815710	−	4.96950i	0.0305272	−	0.185979i
$715$	−4.14267	+	1.51911i	−0.154927	+	0.0568114i
$716$	−13.0679	+	22.6343i	−0.488371	+	0.845884i
$717$	−15.0554	−	2.47124i	−0.562254	−	0.0922902i
$718$	−2.68169	−	4.64483i	−0.100080	−	0.173343i
$719$	4.04721			0.150935			0.0754677	−	0.997148i	$-0.475955\pi$
$719$	4.04721			0.150935			0.0754677	+	0.997148i	$0.475955\pi$
$720$	2.77826	+	3.15611i	0.103540	+	0.117621i
$721$		−	2.32348i		−	0.0865309i
$722$	−1.96560	+	1.13484i	−0.0731521	+	0.0422344i
$723$	−25.7043	+	31.3804i	−0.955953	+	1.16705i
$724$	4.47378	−	7.74881i	0.166267	−	0.287982i
$725$	−1.73591	+	3.00669i	−0.0644702	+	0.111666i
$726$	−12.8612	−	34.0749i	−0.477322	−	1.26464i
$727$	−17.0401	−	29.5143i	−0.631981	−	1.09462i	−0.987146	−	0.159820i	$-0.948909\pi$
$727$	−17.0401	−	29.5143i	−0.631981	−	1.09462i	0.355165	−	0.934804i	$-0.384425\pi$
$728$	5.81620	+	4.85657i	0.215563	+	0.179996i
$729$	−15.1257	−	22.3654i	−0.560212	−	0.828349i
$730$		−	17.9232i		−	0.663367i
$731$	3.19097	+	5.52692i	0.118022	+	0.204421i
$732$	52.6704	−	19.8798i	1.94675	−	0.734779i
$733$	−16.5146	−	9.53474i	−0.609982	−	0.352174i	0.162976	−	0.986630i	$-0.447891\pi$
$733$	−16.5146	−	9.53474i	−0.609982	−	0.352174i	−0.772959	+	0.634456i	$0.781224\pi$
$734$	0.155455	+	0.0897518i	0.00573794	+	0.00331280i
$735$	−6.45249	+	7.87734i	−0.238004	+	0.290560i
$736$	6.95592	−	4.01600i	0.256398	−	0.148032i
$737$	−6.37919			−0.234980
$738$	−17.3487	+	15.2717i	−0.638613	+	0.562158i
$739$		−	46.8060i		−	1.72179i	−0.508786	−	0.860893i	$-0.669906\pi$
$739$		−	46.8060i		−	1.72179i	0.508786	−	0.860893i	$-0.330094\pi$
$740$	−16.7889	−	29.0792i	−0.617172	−	1.06897i
$741$	−17.3059	−	20.0376i	−0.635749	−	0.736099i
$742$	−4.14233	+	7.17473i	−0.152070	+	0.263393i
$743$	−16.5257	−	9.54111i	−0.606269	−	0.350029i	0.165235	−	0.986254i	$-0.447162\pi$
$743$	−16.5257	−	9.54111i	−0.606269	−	0.350029i	−0.771504	+	0.636225i	$0.780495\pi$
$744$	−1.10438	+	6.72817i	−0.0404887	+	0.246667i
$745$	−8.35614	−	14.4733i	−0.306145	−	0.530259i
$746$			18.2447i			0.667986i
$747$	−1.40156	+	4.15428i	−0.0512803	+	0.151997i
$748$		−	4.39947i		−	0.160861i
$749$	−12.9863	+	7.49767i	−0.474511	+	0.273959i
$750$	−2.96511	−	2.42878i	−0.108271	−	0.0886865i
$751$	14.0126	−	24.2705i	0.511326	−	0.885643i	−0.488587	−	0.872515i	$-0.662488\pi$
$751$	14.0126	−	24.2705i	0.511326	−	0.885643i	0.999914	−	0.0131283i	$-0.00417899\pi$
$752$	5.87613	+	3.39259i	0.214280	+	0.123715i
$753$	12.1133	−	4.57204i	0.441435	−	0.166614i
$754$	−27.2915	−	4.74453i	−0.993896	−	0.172785i
$755$	−7.42458			−0.270208
$756$	−14.0769	−	7.47372i	−0.511972	−	0.271817i
$757$	−2.77014			−0.100682			−0.0503412	−	0.998732i	$-0.516031\pi$
$757$	−2.77014			−0.100682			−0.0503412	+	0.998732i	$0.516031\pi$
$758$	31.0935	+	53.8554i	1.12937	+	1.95612i
$759$	−0.850188	−	2.25252i	−0.0308599	−	0.0817615i
$760$	7.28767	+	4.20754i	0.264352	+	0.152624i
$761$	−24.7126	−	14.2678i	−0.895831	−	0.517208i	−0.0199856	−	0.999800i	$-0.506362\pi$
$761$	−24.7126	−	14.2678i	−0.895831	−	0.517208i	−0.875845	+	0.482592i	$0.839695\pi$
$762$	45.4561	−	55.4938i	1.64670	−	2.01033i
$763$	−0.356631	−	0.617704i	−0.0129109	−	0.0223624i
$764$	59.4086			2.14933
$765$	−3.64996	+	0.733099i	−0.131965	+	0.0265053i
$766$	−17.1647			−0.620185
$767$	−0.956292	−	0.166248i	−0.0345297	−	0.00600287i
$768$	1.65945	−	10.1098i	0.0598803	−	0.364805i
$769$	43.3223	+	25.0121i	1.56224	+	0.901961i	0.997030	+	0.0770150i	$0.0245389\pi$
$769$	43.3223	+	25.0121i	1.56224	+	0.901961i	0.565212	+	0.824946i	$0.308794\pi$
$770$	1.43365	−	2.48316i	0.0516653	−	0.0894869i
$771$	0.761366	−	4.63842i	0.0274199	−	0.167049i
$772$	−13.7029	+	7.91136i	−0.493177	+	0.284736i
$773$		−	51.3118i		−	1.84556i	−0.385332	−	0.922778i	$-0.625913\pi$
$773$		−	51.3118i		−	1.84556i	0.385332	−	0.922778i	$-0.374087\pi$
$774$	33.4729	−	6.72307i	1.20316	−	0.241656i
$775$			1.98325i			0.0712405i
$776$	4.05390	+	7.02156i	0.145527	+	0.252059i
$777$	−16.4436	−	13.4692i	−0.589909	−	0.483206i
$778$	−57.3571	−	33.1151i	−2.05635	−	1.18723i
$779$	7.38014	−	12.7828i	0.264421	−	0.457990i
$780$	5.94482	−	17.0868i	0.212859	−	0.611807i
$781$	−3.28103	−	5.68291i	−0.117404	−	0.203350i
$782$			3.11920i			0.111542i
$783$	18.0287	−	0.640674i	0.644295	−	0.0228958i
$784$	−8.23984			−0.294280
$785$	−11.5252	+	6.65410i	−0.411353	+	0.237495i
$786$	19.6107	+	51.9574i	0.699490	+	1.85326i
$787$	−2.53351	−	1.46272i	−0.0903098	−	0.0521404i	0.454165	−	0.890918i	$-0.349938\pi$
$787$	−2.53351	−	1.46272i	−0.0903098	−	0.0521404i	−0.544475	+	0.838777i	$0.683271\pi$
$788$	26.0345	+	15.0310i	0.927441	+	0.535458i
$789$	−30.3499	−	24.8602i	−1.08048	−	0.885046i
$790$	−8.26753	−	14.3198i	−0.294146	−	0.509475i
$791$		−	17.4243i		−	0.619535i
$792$	−6.90477	−	2.32951i	−0.245350	−	0.0827754i
$793$	31.0517	+	25.9284i	1.10268	+	0.920744i
$794$	−40.6279	−	70.3696i	−1.44183	−	2.49732i
$795$	6.04355	+	0.992009i	0.214343	+	0.0351829i
$796$	−36.3839	+	63.0188i	−1.28959	+	2.23364i
$797$	0.0823808	−	0.142688i	0.00291808	−	0.00505426i	−0.864563	−	0.502525i	$-0.832404\pi$
$797$	0.0823808	−	0.142688i	0.00291808	−	0.00505426i	0.867481	+	0.497471i	$0.165738\pi$
$798$	16.9779	+	2.78681i	0.601011	+	0.0986519i
$799$	−5.20271	+	3.00379i	−0.184059	+	0.106266i
$800$		−	7.07129i		−	0.250008i
$801$	32.6041	+	37.0383i	1.15201	+	1.30868i
$802$	−46.3142			−1.63541
$803$	−4.95595	−	8.58395i	−0.174892	−	0.302921i
$804$	16.5740	−	20.2339i	0.584520	−	0.713595i
$805$	−0.601315	+	1.04151i	−0.0211936	+	0.0367083i
$806$	−14.8565	+	5.44785i	−0.523298	+	0.191892i
$807$	−35.4088	+	13.3646i	−1.24645	+	0.470457i
$808$	22.7327	−	13.1247i	0.799734	−	0.461726i
$809$	32.2178			1.13272			0.566360	−	0.824158i	$-0.308351\pi$
$809$	32.2178			1.13272			0.566360	+	0.824158i	$0.308351\pi$
$810$	−2.52594	+	19.7553i	−0.0887524	+	0.694131i
$811$			25.5331i			0.896587i	0.893886	+	0.448294i	$0.147968\pi$
$811$			25.5331i			0.896587i	−0.893886	+	0.448294i	$0.852032\pi$
$812$	9.22224	−	5.32446i	0.323637	−	0.186852i
$813$	−8.27641	−	21.9279i	−0.290266	−	0.769044i
$814$	−27.1837	−	15.6945i	−0.952788	−	0.550093i
$815$	−8.63342	+	14.9535i	−0.302415	+	0.523799i
$816$	−2.33050	−	1.90896i	−0.0815840	−	0.0668271i
$817$	−18.8823	+	10.9017i	−0.660608	+	0.381402i
$818$	44.7246			1.56376
$819$	−0.298734	−	11.4486i	−0.0104386	−	0.400046i
$820$	10.0858			0.352210
$821$	21.3774	−	12.3422i	0.746076	−	0.430747i	−0.0781981	−	0.996938i	$-0.524917\pi$
$821$	21.3774	−	12.3422i	0.746076	−	0.430747i	0.824274	+	0.566190i	$0.191583\pi$
$822$	0.741935	−	4.52004i	0.0258779	−	0.157655i
$823$	−0.855265	+	1.48136i	−0.0298127	+	0.0516371i	−0.880547	−	0.473959i	$-0.842824\pi$
$823$	−0.855265	+	1.48136i	−0.0298127	+	0.0516371i	0.850734	+	0.525596i	$0.176158\pi$
$824$	3.77219	+	2.17788i	0.131411	+	0.0758700i
$825$	−2.09166	−	0.343333i	−0.0728224	−	0.0119533i
$826$	0.546242	−	0.315373i	0.0190062	−	0.0109732i
$827$			18.3595i			0.638423i	0.947683	+	0.319212i	$0.103418\pi$
$827$			18.3595i			0.638423i	−0.947683	+	0.319212i	$0.896582\pi$
$828$	9.35361	+	3.15569i	0.325060	+	0.109668i
$829$	−29.8986			−1.03842			−0.519211	−	0.854646i	$-0.673774\pi$
$829$	−29.8986			−1.03842			−0.519211	+	0.854646i	$0.673774\pi$
$830$	2.80076	−	1.61702i	0.0972159	−	0.0561276i
$831$	−0.0415381	−	0.0340247i	−0.00144094	−	0.00118030i
$832$	43.4819	−	15.9447i	1.50746	−	0.552784i
$833$	3.64777	−	6.31812i	0.126388	−	0.218910i
$834$	8.63016	+	22.8651i	0.298838	+	0.791754i
$835$	−9.91143	−	17.1671i	−0.342999	−	0.594092i
$836$	15.0305			0.519839
$837$	8.73602	−	5.46634i	0.301961	−	0.188944i
$838$			62.6009i			2.16251i
$839$	−19.7284	+	11.3902i	−0.681101	+	0.393234i	−0.800270	−	0.599640i	$-0.795310\pi$
$839$	−19.7284	+	11.3902i	−0.681101	+	0.393234i	0.119169	+	0.992874i	$0.461977\pi$
$840$	1.28536	+	3.40549i	0.0443491	+	0.117500i
$841$	8.47322	−	14.6760i	0.292180	−	0.506071i
$842$	23.7842	−	41.1955i	0.819659	−	1.41969i
$843$	12.5680	−	15.3433i	0.432866	−	0.528452i
$844$	16.1090	+	27.9016i	0.554495	+	0.960414i
$845$	12.7915	−	2.31902i	0.440041	−	0.0797768i
$846$	6.32870	+	31.5094i	0.217585	+	1.08332i
$847$			10.0609i			0.345698i
$848$	2.47794	+	4.29193i	0.0850930	+	0.147385i
$849$	−8.92597	+	54.3791i	−0.306338	+	1.86629i
$850$	2.37820	+	1.37306i	0.0815716	+	0.0470954i
$851$	11.4016	+	6.58272i	0.390842	+	0.225653i
$852$	26.5500	+	4.35800i	0.909587	+	0.149303i
$853$	−41.1579	+	23.7625i	−1.40922	+	0.813614i	−0.995313	−	0.0967050i	$-0.969170\pi$
$853$	−41.1579	+	23.7625i	−1.40922	+	0.813614i	−0.413908	+	0.910319i	$0.635836\pi$
$854$	−26.2879			−0.899552
$855$	−2.50458	−	12.4698i	−0.0856547	−	0.426459i
$856$		−	28.1113i		−	0.960825i
$857$	−1.21310	−	2.10115i	−0.0414387	−	0.0717739i	0.844562	−	0.535457i	$-0.179861\pi$
$857$	−1.21310	−	2.10115i	−0.0414387	−	0.0717739i	−0.886001	+	0.463684i	$0.846527\pi$
$858$	−3.17375	−	16.6117i	−0.108350	−	0.567115i
$859$	6.75571	−	11.7012i	0.230502	−	0.399241i	−0.727454	−	0.686156i	$-0.759297\pi$
$859$	6.75571	−	11.7012i	0.230502	−	0.399241i	0.957956	+	0.286915i	$0.0926299\pi$
$860$	−12.9024	−	7.44918i	−0.439967	−	0.254015i
$861$	5.97331	−	2.25455i	0.203570	−	0.0768350i
$862$	38.3242	+	66.3795i	1.30533	+	2.26090i
$863$			11.2875i			0.384230i	0.981372	+	0.192115i	$0.0615346\pi$
$863$			11.2875i			0.384230i	−0.981372	+	0.192115i	$0.938465\pi$
$864$	−31.1483	+	19.4902i	−1.05969	+	0.663072i
$865$		−	7.13271i		−	0.242520i
$866$	−69.4129	+	40.0756i	−2.35875	+	1.36182i
$867$	−25.0525	+	9.45576i	−0.850827	+	0.321134i
$868$	3.04156	−	5.26813i	0.103237	−	0.178812i
$869$	−7.91914	−	4.57212i	−0.268638	−	0.155098i
$870$	−10.2943	−	8.43230i	−0.349011	−	0.285882i
$871$	18.5169	+	3.21909i	0.627420	+	0.109075i
$872$	1.33713			0.0452810
$873$	3.91742	−	11.6114i	0.132584	−	0.392987i
$874$	−10.6565			−0.360461
$875$	0.529392	+	0.916933i	0.0178967	+	0.0309980i
$876$	40.1034	+	6.58270i	1.35497	+	0.222409i
$877$	−23.2929	−	13.4482i	−0.786546	−	0.454112i	0.0521995	−	0.998637i	$-0.483377\pi$
$877$	−23.2929	−	13.4482i	−0.786546	−	0.454112i	−0.838745	+	0.544524i	$0.816710\pi$
$878$	−13.8816	−	8.01455i	−0.468481	−	0.270478i
$879$	48.8659	+	8.02101i	1.64821	+	0.270542i
$880$	−0.857613	−	1.48543i	−0.0289101	−	0.0500738i
$881$	19.3845			0.653082			0.326541	−	0.945183i	$-0.394117\pi$
$881$	19.3845			0.653082			0.326541	+	0.945183i	$0.394117\pi$
$882$	−25.7882	−	29.2954i	−0.868333	−	0.986429i
$883$	−41.9619			−1.41213			−0.706065	−	0.708147i	$-0.749531\pi$
$883$	−41.9619			−1.41213			−0.706065	+	0.708147i	$0.749531\pi$
$884$	−2.22008	+	12.7703i	−0.0746693	+	0.429513i
$885$	−0.360714	−	0.295468i	−0.0121253	−	0.00993204i
$886$	53.6497	+	30.9747i	1.80240	+	1.04061i
$887$	25.0333	−	43.3589i	0.840536	−	1.45585i	−0.0489071	−	0.998803i	$-0.515574\pi$
$887$	25.0333	−	43.3589i	0.840536	−	1.45585i	0.889443	−	0.457047i	$-0.151093\pi$
$888$	37.2806	−	14.0711i	1.25105	−	0.472195i
$889$	−17.1610	+	9.90789i	−0.575560	+	0.332300i
$890$		−	36.3981i		−	1.22007i
$891$	4.25280	+	10.1599i	0.142474	+	0.340368i
$892$		−	36.8206i		−	1.23284i
$893$	−10.2622	−	17.7747i	−0.343412	−	0.594806i
$894$	59.9292	−	22.6196i	2.00433	−	0.756511i
$895$	−7.81315	−	4.51093i	−0.261165	−	0.150784i
$896$	−7.56081	+	13.0957i	−0.252589	+	0.437497i
$897$	1.33116	+	6.96742i	0.0444462	+	0.232635i
$898$	−35.4554	−	61.4106i	−1.18316	−	2.04930i
$899$			6.88550i			0.229644i
$900$	6.52344	−	5.74245i	0.217448	−	0.191415i
$901$	−4.38793			−0.146183
$902$	8.16518	−	4.71417i	0.271871	−	0.156965i
$903$	−9.30662	−	1.52762i	−0.309705	−	0.0508360i
$904$	28.2885	+	16.3324i	0.940860	+	0.543206i
$905$	2.67481	+	1.54430i	0.0889138	+	0.0513344i
$906$	4.60941	−	28.0816i	0.153137	−	0.932950i
$907$	−5.69329	−	9.86106i	−0.189043	−	0.327431i	0.755889	−	0.654700i	$-0.227205\pi$
$907$	−5.69329	−	9.86106i	−0.189043	−	0.327431i	−0.944931	+	0.327269i	$0.893872\pi$
$908$			42.9877i			1.42660i
$909$	−37.5926	−	12.6828i	−1.24687	−	0.420663i
$910$	−5.41453	+	6.48441i	−0.179490	+	0.214956i
$911$	−9.28246	−	16.0777i	−0.307542	−	0.532678i	0.670282	−	0.742106i	$-0.266173\pi$
$911$	−9.28246	−	16.0777i	−0.307542	−	0.532678i	−0.977824	+	0.209428i	$0.932840\pi$
$912$	6.52182	−	7.96198i	0.215959	−	0.263648i
$913$	0.894247	−	1.54888i	0.0295952	−	0.0512605i
$914$	28.1222	−	48.7090i	0.930198	−	1.61115i
$915$	6.86232	+	18.1813i	0.226861	+	0.601056i
$916$	24.9625	−	14.4121i	0.824783	−	0.476189i
$917$		−	15.3409i		−	0.506602i
$918$	−0.506754	−	14.2602i	−0.0167254	−	0.470657i
$919$	35.4777			1.17030			0.585151	−	0.810925i	$-0.301035\pi$
$919$	35.4777			1.17030			0.585151	+	0.810925i	$0.301035\pi$
$920$	−1.12727	−	1.95248i	−0.0371649	−	0.0643714i
$921$	3.02825	+	8.02318i	0.0997842	+	0.264373i
$922$	−9.29083	+	16.0922i	−0.305977	+	0.529968i
$923$	6.65610	+	18.1514i	0.219088	+	0.597462i
$924$	5.02957	+	4.11982i	0.165461	+	0.135532i
$925$	10.0379	−	5.79536i	0.330043	−	0.190550i
$926$	−34.0970			−1.12050
$927$	−1.29640	−	6.45454i	−0.0425794	−	0.211995i
$928$		−	24.5503i		−	0.805903i
$929$	20.4710	−	11.8189i	0.671632	−	0.387767i	−0.125063	−	0.992149i	$-0.539913\pi$
$929$	20.4710	−	11.8189i	0.671632	−	0.387767i	0.796695	+	0.604382i	$0.206580\pi$
$930$	−7.50116	−	1.23126i	−0.245973	−	0.0403748i
$931$	21.5853	+	12.4623i	0.707431	+	0.408436i
$932$	20.5762	−	35.6390i	0.673996	−	1.16740i
$933$	−0.358214	+	2.18232i	−0.0117274	+	0.0714461i
$934$	−57.4983	+	33.1967i	−1.88140	+	1.08623i
$935$	1.51866			0.0496654
$936$	18.8669	+	10.2462i	0.616685	+	0.334906i
$937$	−15.7766			−0.515398			−0.257699	−	0.966225i	$-0.582964\pi$
$937$	−15.7766			−0.515398			−0.257699	+	0.966225i	$0.582964\pi$
$938$	−10.5770	+	6.10662i	−0.345351	+	0.199388i
$939$	20.5676	+	16.8473i	0.671197	+	0.549791i
$940$	7.01222	−	12.1455i	0.228713	−	0.396143i
$941$	39.4024	+	22.7490i	1.28448	+	0.741595i	0.977664	−	0.210174i	$-0.0674031\pi$
$941$	39.4024	+	22.7490i	1.28448	+	0.741595i	0.306816	+	0.951769i	$0.400736\pi$
$942$	−18.0122	−	47.7224i	−0.586871	−	1.55488i
$943$	−3.42471	+	1.97726i	−0.111524	+	0.0643883i
$944$		−	0.377313i		−	0.0122805i
$945$	2.57986	−	4.85921i	0.0839228	−	0.158070i
$946$	−13.9272			−0.452813
$947$	23.1767	−	13.3811i	0.753142	−	0.434827i	−0.0736859	−	0.997281i	$-0.523476\pi$
$947$	23.1767	−	13.3811i	0.753142	−	0.434827i	0.826828	+	0.562455i	$0.190143\pi$
$948$	35.0772	−	13.2394i	1.13925	−	0.429997i
$949$	10.0539	+	27.4175i	0.326365	+	0.890010i
$950$	−4.69094	+	8.12494i	−0.152194	+	0.263608i
$951$	2.41213	−	2.94478i	0.0782187	−	0.0954912i
$952$	−1.30396	−	2.25852i	−0.0422616	−	0.0731992i
$953$	1.14387			0.0370536			0.0185268	−	0.999828i	$-0.494102\pi$
$953$	1.14387			0.0370536			0.0185268	+	0.999828i	$0.494102\pi$
$954$	−7.50405	+	22.2424i	−0.242953	+	0.720123i
$955$			20.5073i			0.663600i
$956$	−22.0992	+	12.7590i	−0.714739	+	0.412655i
$957$	−7.26189	−	1.19199i	−0.234744	−	0.0385316i
$958$	0.949120	−	1.64392i	0.0306647	−	0.0531128i
$959$	−0.632658	+	1.09580i	−0.0204296	+	0.0353851i
$960$	21.9543	+	3.60365i	0.708572	+	0.116307i
$961$	−13.5334	−	23.4405i	−0.436560	−	0.756144i
$962$	70.9862	+	59.2740i	2.28869	+	1.91107i
$963$	−31.8922	+	28.0741i	−1.02771	+	0.904674i
$964$			67.8456i			2.18516i
$965$	−2.73093	−	4.73010i	−0.0879116	−	0.152267i
$966$	−3.56593	−	2.92092i	−0.114732	−	0.0939792i
$967$	−36.6240	−	21.1449i	−1.17775	−	0.679974i	−0.222257	−	0.974988i	$-0.571342\pi$
$967$	−36.6240	−	21.1449i	−1.17775	−	0.679974i	−0.955493	+	0.295014i	$0.904676\pi$
$968$	−16.3340	−	9.43046i	−0.524996	−	0.303107i
$969$	3.21786	+	8.52554i	0.103373	+	0.273880i
$970$	−7.82826	+	4.51965i	−0.251350	+	0.145117i
$971$	−48.9893			−1.57214			−0.786071	−	0.618136i	$-0.787888\pi$
$971$	−48.9893			−1.57214			−0.786071	+	0.618136i	$0.787888\pi$
$972$	−43.2751	−	12.9074i	−1.38805	−	0.414006i
$973$		−	6.75115i		−	0.216432i
$974$	21.3421	+	36.9656i	0.683845	+	1.18446i
$975$	5.89821	+	2.05209i	0.188894	+	0.0657196i
$976$	−7.86270	+	13.6186i	−0.251679	+	0.435921i
$977$	36.9860	+	21.3539i	1.18329	+	0.683172i	0.956773	−	0.290836i	$-0.0939334\pi$
$977$	36.9860	+	21.3539i	1.18329	+	0.683172i	0.226515	+	0.974008i	$0.427267\pi$
$978$	−51.1980	−	41.9373i	−1.63713	−	1.34101i
$979$	−10.0645	−	17.4321i	−0.321661	−	0.557134i
$980$			17.0311i			0.544039i
$981$	−1.33536	−	1.51697i	−0.0426348	−	0.0484332i
$982$		−	36.2165i		−	1.15571i
$983$	−14.1606	+	8.17563i	−0.451653	+	0.260762i	−0.708528	−	0.705683i	$-0.750640\pi$
$983$	−14.1606	+	8.17563i	−0.451653	+	0.260762i	0.256875	+	0.966445i	$0.417307\pi$
$984$	−1.93870	+	11.8110i	−0.0618034	+	0.376521i
$985$	−5.18857	+	8.98686i	−0.165322	+	0.286345i
$986$	8.25670	+	4.76701i	0.262947	+	0.151812i
$987$	1.43801	−	8.76070i	0.0457723	−	0.278856i
$988$	−43.6289	−	7.58473i	−1.38802	−	0.241302i
$989$	5.84147			0.185748
$990$	2.59714	−	7.69805i	0.0825425	−	0.244660i
$991$	14.5897			0.463458			0.231729	−	0.972780i	$-0.425562\pi$
$991$	14.5897			0.463458			0.231729	+	0.972780i	$0.425562\pi$
$992$	−7.01208	−	12.1453i	−0.222634	−	0.385613i
$993$	15.1877	−	18.5415i	0.481968	−	0.588397i
$994$	−10.8802	−	6.28168i	−0.345098	−	0.199243i
$995$	−21.7535	−	12.5594i	−0.689632	−	0.398159i
$996$	2.58946	+	6.86064i	0.0820503	+	0.217388i
$997$	16.2063	+	28.0701i	0.513259	+	0.888991i	0.999882	+	0.0153784i	$0.00489528\pi$
$997$	16.2063	+	28.0701i	0.513259	+	0.888991i	−0.486623	+	0.873612i	$0.661771\pi$
$998$	59.0543			1.86933
$999$	−53.1948	−	28.2423i	−1.68301	−	0.893545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.7	yes	108
9.7	even	3	inner	585.2.bt.b.376.48	yes	108
13.12	even	2	inner	585.2.bt.b.571.48	yes	108
117.25	even	6	inner	585.2.bt.b.376.7	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.7	✓	108	117.25	even	6	inner
585.2.bt.b.376.48	yes	108	9.7	even	3	inner
585.2.bt.b.571.7	yes	108	1.1	even	1	trivial
585.2.bt.b.571.48	yes	108	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91643 + 1.10645i) q^{2} +(1.62047 - 0.611626i) q^{3} +(1.44848 - 2.50883i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.42878 + 2.96511i) q^{6} +(0.916933 - 0.529392i) q^{7} +1.98487i q^{8} +(2.25183 - 1.98224i) q^{9} +O(q^{10})\)	\(q+(-1.91643 + 1.10645i) q^{2} +(1.62047 - 0.611626i) q^{3} +(1.44848 - 2.50883i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-2.42878 + 2.96511i) q^{6} +(0.916933 - 0.529392i) q^{7} +1.98487i q^{8} +(2.25183 - 1.98224i) q^{9} -2.21291 q^{10} +(-1.05983 + 0.611891i) q^{11} +(0.812740 - 4.95141i) q^{12} +(3.38513 - 1.24132i) q^{13} +(-1.17149 + 2.02909i) q^{14} +(1.70918 + 0.280550i) q^{15} +(0.700788 + 1.21380i) q^{16} -1.24095 q^{17} +(-2.12222 + 6.29037i) q^{18} -4.23962i q^{19} +(2.50883 - 1.44848i) q^{20} +(1.16207 - 1.41868i) q^{21} +(1.35406 - 2.34530i) q^{22} +(-0.567930 + 0.983684i) q^{23} +(1.21400 + 3.21641i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-5.11391 + 6.12440i) q^{26} +(2.43663 - 4.58943i) q^{27} -3.06724i q^{28} +(1.73591 + 3.00669i) q^{29} +(-3.58594 + 1.35347i) q^{30} +(1.71755 + 0.991626i) q^{31} +(-6.12392 - 3.53565i) q^{32} +(-1.34317 + 1.63977i) q^{33} +(2.37820 - 1.37306i) q^{34} +1.05878 q^{35} +(-1.71139 - 8.52069i) q^{36} -11.5907i q^{37} +(4.69094 + 8.12494i) q^{38} +(4.72627 - 4.08196i) q^{39} +(-0.992434 + 1.71895i) q^{40} +(3.01508 + 1.74076i) q^{41} +(-0.657326 + 4.00458i) q^{42} +(-2.57139 - 4.45377i) q^{43} +3.54524i q^{44} +(2.94126 - 0.590755i) q^{45} -2.51355i q^{46} +(4.19252 - 2.42055i) q^{47} +(1.87800 + 1.53830i) q^{48} +(-2.93949 + 5.09134i) q^{49} +(-1.91643 - 1.10645i) q^{50} +(-2.01092 + 0.758998i) q^{51} +(1.78901 - 10.2908i) q^{52} +3.53594 q^{53} +(0.408359 + 11.4913i) q^{54} -1.22378 q^{55} +(1.05077 + 1.81999i) q^{56} +(-2.59306 - 6.87016i) q^{57} +(-6.65352 - 3.84141i) q^{58} +(-0.233139 - 0.134603i) q^{59} +(3.17956 - 3.88167i) q^{60} +(5.60990 + 9.71663i) q^{61} -4.38875 q^{62} +(1.01540 - 3.00968i) q^{63} +12.8450 q^{64} +(3.55227 + 0.617550i) q^{65} +(0.759762 - 4.62865i) q^{66} +(4.51431 + 2.60634i) q^{67} +(-1.79749 + 3.11334i) q^{68} +(-0.318666 + 1.94139i) q^{69} +(-2.02909 + 1.17149i) q^{70} +5.36211i q^{71} +(3.93448 + 4.46958i) q^{72} +8.09939i q^{73} +(12.8246 + 22.2128i) q^{74} +(1.33992 + 1.09755i) q^{75} +(-10.6365 - 6.14098i) q^{76} +(-0.647860 + 1.12213i) q^{77} +(-4.54109 + 13.0522i) q^{78} +(3.73605 + 6.47103i) q^{79} +1.40158i q^{80} +(1.14146 - 8.92732i) q^{81} -7.70426 q^{82} +(-1.26565 + 0.730723i) q^{83} +(-1.87600 - 4.97037i) q^{84} +(-1.07470 - 0.620476i) q^{85} +(9.85578 + 5.69024i) q^{86} +(4.65196 + 3.81051i) q^{87} +(-1.21452 - 2.10362i) q^{88} +16.4481i q^{89} +(-4.98308 + 4.38651i) q^{90} +(2.44679 - 2.93027i) q^{91} +(1.64527 + 2.84968i) q^{92} +(3.38973 + 0.556402i) q^{93} +(-5.35645 + 9.27764i) q^{94} +(2.11981 - 3.67162i) q^{95} +(-12.0861 - 1.98385i) q^{96} +(3.53755 - 2.04240i) q^{97} -13.0096i q^{98} +(-1.17363 + 3.47870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more