LMFDB - Embedded newform 170.2.k.b.161.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.4
Root			$1.88289i$ of defining polynomial
Character	$\chi$	$=$	170.161
Dual form			170.2.k.b.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.10324 - 2.66345i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(1.10324 + 2.66345i) q^{6} +(-0.0470744 + 0.0194989i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.75550 - 3.75550i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.10324 - 2.66345i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(1.10324 + 2.66345i) q^{6} +(-0.0470744 + 0.0194989i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.75550 - 3.75550i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(0.307817 + 0.743136i) q^{11} +(-2.66345 - 1.10324i) q^{12} -4.26661i q^{13} +(0.0194989 - 0.0470744i) q^{14} +(2.03851 - 2.03851i) q^{15} -1.00000 q^{16} +(2.43143 - 3.32989i) q^{17} +5.31107 q^{18} +(-4.53377 + 4.53377i) q^{19} +(0.382683 - 0.923880i) q^{20} +0.146892i q^{21} +(-0.743136 - 0.307817i) q^{22} +(3.28955 + 7.94167i) q^{23} +(2.66345 - 1.10324i) q^{24} +(0.707107 + 0.707107i) q^{25} +(3.01695 + 3.01695i) q^{26} +(-6.15542 + 2.54966i) q^{27} +(0.0194989 + 0.0470744i) q^{28} +(4.22074 + 1.74829i) q^{29} +2.88289i q^{30} +(-0.189238 + 0.456861i) q^{31} +(0.707107 - 0.707107i) q^{32} +2.31890 q^{33} +(0.635311 + 4.07387i) q^{34} -0.0509530 q^{35} +(-3.75550 + 3.75550i) q^{36} +(0.598098 - 1.44394i) q^{37} -6.41171i q^{38} +(-11.3639 - 4.70708i) q^{39} +(0.382683 + 0.923880i) q^{40} +(-7.95917 + 3.29679i) q^{41} +(-0.103868 - 0.103868i) q^{42} +(1.73504 + 1.73504i) q^{43} +(0.743136 - 0.307817i) q^{44} +(-2.03246 - 4.90679i) q^{45} +(-7.94167 - 3.28955i) q^{46} +8.22785i q^{47} +(-1.10324 + 2.66345i) q^{48} +(-4.94791 + 4.94791i) q^{49} -1.00000 q^{50} +(-6.18655 - 10.1496i) q^{51} -4.26661 q^{52} +(7.79336 - 7.79336i) q^{53} +(2.54966 - 6.15542i) q^{54} +0.804365i q^{55} +(-0.0470744 - 0.0194989i) q^{56} +(7.07363 + 17.0773i) q^{57} +(-4.22074 + 1.74829i) q^{58} +(7.13933 + 7.13933i) q^{59} +(-2.03851 - 2.03851i) q^{60} +(-5.73663 + 2.37619i) q^{61} +(-0.189238 - 0.456861i) q^{62} +(0.250016 + 0.103560i) q^{63} +1.00000i q^{64} +(1.63276 - 3.94183i) q^{65} +(-1.63971 + 1.63971i) q^{66} -0.822577 q^{67} +(-3.32989 - 2.43143i) q^{68} +24.7814 q^{69} +(0.0360292 - 0.0360292i) q^{70} +(4.17475 - 10.0787i) q^{71} -5.31107i q^{72} +(-6.19072 - 2.56428i) q^{73} +(0.598098 + 1.44394i) q^{74} +(2.66345 - 1.10324i) q^{75} +(4.53377 + 4.53377i) q^{76} +(-0.0289806 - 0.0289806i) q^{77} +(11.3639 - 4.70708i) q^{78} +(-3.14745 - 7.59862i) q^{79} +(-0.923880 - 0.382683i) q^{80} +3.27428i q^{81} +(3.29679 - 7.95917i) q^{82} +(-0.955109 + 0.955109i) q^{83} +0.146892 q^{84} +(3.52064 - 2.14595i) q^{85} -2.45372 q^{86} +(9.31294 - 9.31294i) q^{87} +(-0.307817 + 0.743136i) q^{88} +17.0535i q^{89} +(4.90679 + 2.03246i) q^{90} +(0.0831941 + 0.200848i) q^{91} +(7.94167 - 3.28955i) q^{92} +(1.00805 + 1.00805i) q^{93} +(-5.81797 - 5.81797i) q^{94} +(-5.92365 + 2.45366i) q^{95} +(-1.10324 - 2.66345i) q^{96} +(2.95171 + 1.22264i) q^{97} -6.99740i q^{98} +(1.63484 - 3.94685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.10324	−	2.66345i	0.636953	−	1.53774i	−0.193765	−	0.981048i	$-0.562070\pi$
$3$	1.10324	−	2.66345i	0.636953	−	1.53774i	0.830718	−	0.556693i	$-0.187930\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$6$	1.10324	+	2.66345i	0.450394	+	1.08735i
$7$	−0.0470744	+	0.0194989i	−0.0177925	+	0.00736988i	−0.391562	−	0.920152i	$-0.628065\pi$
$7$	−0.0470744	+	0.0194989i	−0.0177925	+	0.00736988i	0.373769	+	0.927522i	$0.378065\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−3.75550	−	3.75550i	−1.25183	−	1.25183i
$10$	−0.923880	+	0.382683i	−0.292156	+	0.121015i
$11$	0.307817	+	0.743136i	0.0928103	+	0.224064i	0.963467	−	0.267827i	$-0.0863057\pi$
$11$	0.307817	+	0.743136i	0.0928103	+	0.224064i	−0.870657	+	0.491891i	$0.836306\pi$
$12$	−2.66345	−	1.10324i	−0.768871	−	0.318477i
$13$		−	4.26661i		−	1.18335i	−0.806178	−	0.591673i	$-0.798468\pi$
$13$		−	4.26661i		−	1.18335i	0.806178	−	0.591673i	$-0.201532\pi$
$14$	0.0194989	−	0.0470744i	0.00521129	−	0.0125812i
$15$	2.03851	−	2.03851i	0.526342	−	0.526342i
$16$	−1.00000			−0.250000
$17$	2.43143	−	3.32989i	0.589707	−	0.807617i
$17$	2.43143	−	3.32989i	0.589707	−	0.807617i
$18$	5.31107			1.25183
$19$	−4.53377	+	4.53377i	−1.04012	+	1.04012i	−0.0409563	+	0.999161i	$0.513040\pi$
$19$	−4.53377	+	4.53377i	−1.04012	+	1.04012i	−0.999161	+	0.0409563i	$0.986960\pi$
$20$	0.382683	−	0.923880i	0.0855706	−	0.206586i
$21$			0.146892i			0.0320545i
$22$	−0.743136	−	0.307817i	−0.158437	−	0.0656268i
$23$	3.28955	+	7.94167i	0.685918	+	1.65595i	0.752847	+	0.658195i	$0.228680\pi$
$23$	3.28955	+	7.94167i	0.685918	+	1.65595i	−0.0669290	+	0.997758i	$0.521320\pi$
$24$	2.66345	−	1.10324i	0.543674	−	0.225197i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	3.01695	+	3.01695i	0.591673	+	0.591673i
$27$	−6.15542	+	2.54966i	−1.18461	+	0.490682i
$28$	0.0194989	+	0.0470744i	0.00368494	+	0.00889623i
$29$	4.22074	+	1.74829i	0.783772	+	0.324649i	0.738437	−	0.674323i	$-0.235564\pi$
$29$	4.22074	+	1.74829i	0.783772	+	0.324649i	0.0453353	+	0.998972i	$0.485564\pi$
$30$			2.88289i			0.526342i
$31$	−0.189238	+	0.456861i	−0.0339882	+	0.0820547i	−0.939962	−	0.341279i	$-0.889140\pi$
$31$	−0.189238	+	0.456861i	−0.0339882	+	0.0820547i	0.905974	+	0.423333i	$0.139140\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.31890			0.403668
$34$	0.635311	+	4.07387i	0.108955	+	0.698662i
$35$	−0.0509530			−0.00861263
$36$	−3.75550	+	3.75550i	−0.625916	+	0.625916i
$37$	0.598098	−	1.44394i	0.0983266	−	0.237381i	−0.867060	−	0.498203i	$-0.833993\pi$
$37$	0.598098	−	1.44394i	0.0983266	−	0.237381i	0.965387	+	0.260822i	$0.0839934\pi$
$38$		−	6.41171i		−	1.04012i
$39$	−11.3639	−	4.70708i	−1.81968	−	0.753736i
$40$	0.382683	+	0.923880i	0.0605076	+	0.146078i
$41$	−7.95917	+	3.29679i	−1.24301	+	0.514873i	−0.904655	−	0.426145i	$-0.859871\pi$
$41$	−7.95917	+	3.29679i	−1.24301	+	0.514873i	−0.338358	+	0.941018i	$0.609871\pi$
$42$	−0.103868	−	0.103868i	−0.0160272	−	0.0160272i
$43$	1.73504	+	1.73504i	0.264592	+	0.264592i	0.826916	−	0.562325i	$-0.190093\pi$
$43$	1.73504	+	1.73504i	0.264592	+	0.264592i	−0.562325	+	0.826916i	$0.690093\pi$
$44$	0.743136	−	0.307817i	0.112032	−	0.0464052i
$45$	−2.03246	−	4.90679i	−0.302981	−	0.731461i
$46$	−7.94167	−	3.28955i	−1.17094	−	0.485017i
$47$			8.22785i			1.20015i	0.799942	+	0.600077i	$0.204864\pi$
$47$			8.22785i			1.20015i	−0.799942	+	0.600077i	$0.795136\pi$
$48$	−1.10324	+	2.66345i	−0.159238	+	0.384435i
$49$	−4.94791	+	4.94791i	−0.706845	+	0.706845i
$50$	−1.00000			−0.141421
$51$	−6.18655	−	10.1496i	−0.866290	−	1.42123i
$52$	−4.26661			−0.591673
$53$	7.79336	−	7.79336i	1.07050	−	1.07050i	0.0731814	−	0.997319i	$-0.476685\pi$
$53$	7.79336	−	7.79336i	1.07050	−	1.07050i	0.997319	−	0.0731814i	$-0.0233152\pi$
$54$	2.54966	−	6.15542i	0.346964	−	0.837646i
$55$			0.804365i			0.108461i
$56$	−0.0470744	−	0.0194989i	−0.00629059	−	0.00260565i
$57$	7.07363	+	17.0773i	0.936925	+	2.26194i
$58$	−4.22074	+	1.74829i	−0.554210	+	0.229561i
$59$	7.13933	+	7.13933i	0.929462	+	0.929462i	0.997671	−	0.0682090i	$-0.0217285\pi$
$59$	7.13933	+	7.13933i	0.929462	+	0.929462i	−0.0682090	+	0.997671i	$0.521728\pi$
$60$	−2.03851	−	2.03851i	−0.263171	−	0.263171i
$61$	−5.73663	+	2.37619i	−0.734500	+	0.304240i	−0.718400	−	0.695630i	$-0.755125\pi$
$61$	−5.73663	+	2.37619i	−0.734500	+	0.304240i	−0.0161004	+	0.999870i	$0.505125\pi$
$62$	−0.189238	−	0.456861i	−0.0240333	−	0.0580214i
$63$	0.250016	+	0.103560i	0.0314990	+	0.0130473i
$64$			1.00000i			0.125000i
$65$	1.63276	−	3.94183i	0.202519	−	0.488924i
$66$	−1.63971	+	1.63971i	−0.201834	+	0.201834i
$67$	−0.822577			−0.100494			−0.0502469	−	0.998737i	$-0.516001\pi$
$67$	−0.822577			−0.100494			−0.0502469	+	0.998737i	$0.516001\pi$
$68$	−3.32989	−	2.43143i	−0.403809	−	0.294854i
$69$	24.7814			2.98333
$70$	0.0360292	−	0.0360292i	0.00430632	−	0.00430632i
$71$	4.17475	−	10.0787i	0.495452	−	1.19613i	−0.456457	−	0.889745i	$-0.650882\pi$
$71$	4.17475	−	10.0787i	0.495452	−	1.19613i	0.951909	−	0.306381i	$-0.0991181\pi$
$72$		−	5.31107i		−	0.625916i
$73$	−6.19072	−	2.56428i	−0.724569	−	0.300126i	−0.0102509	−	0.999947i	$-0.503263\pi$
$73$	−6.19072	−	2.56428i	−0.724569	−	0.300126i	−0.714318	+	0.699821i	$0.753263\pi$
$74$	0.598098	+	1.44394i	0.0695274	+	0.167854i
$75$	2.66345	−	1.10324i	0.307548	−	0.127391i
$76$	4.53377	+	4.53377i	0.520059	+	0.520059i
$77$	−0.0289806	−	0.0289806i	−0.00330265	−	0.00330265i
$78$	11.3639	−	4.70708i	1.28671	−	0.532972i
$79$	−3.14745	−	7.59862i	−0.354116	−	0.854912i	−0.996103	−	0.0881963i	$-0.971890\pi$
$79$	−3.14745	−	7.59862i	−0.354116	−	0.854912i	0.641987	−	0.766715i	$-0.278110\pi$
$80$	−0.923880	−	0.382683i	−0.103293	−	0.0427853i
$81$			3.27428i			0.363809i
$82$	3.29679	−	7.95917i	0.364070	−	0.878943i
$83$	−0.955109	+	0.955109i	−0.104837	+	0.104837i	−0.757580	−	0.652743i	$-0.773618\pi$
$83$	−0.955109	+	0.955109i	−0.104837	+	0.104837i	0.652743	+	0.757580i	$0.273618\pi$
$84$	0.146892			0.0160272
$85$	3.52064	−	2.14595i	0.381867	−	0.232761i
$86$	−2.45372			−0.264592
$87$	9.31294	−	9.31294i	0.998452	−	0.998452i
$88$	−0.307817	+	0.743136i	−0.0328134	+	0.0792186i
$89$			17.0535i			1.80767i	0.427880	+	0.903835i	$0.359260\pi$
$89$			17.0535i			1.80767i	−0.427880	+	0.903835i	$0.640740\pi$
$90$	4.90679	+	2.03246i	0.517221	+	0.214240i
$91$	0.0831941	+	0.200848i	0.00872111	+	0.0210546i
$92$	7.94167	−	3.28955i	0.827977	−	0.342959i
$93$	1.00805	+	1.00805i	0.104530	+	0.104530i
$94$	−5.81797	−	5.81797i	−0.600077	−	0.600077i
$95$	−5.92365	+	2.45366i	−0.607754	+	0.251740i
$96$	−1.10324	−	2.66345i	−0.112598	−	0.271837i
$97$	2.95171	+	1.22264i	0.299700	+	0.124140i	0.527466	−	0.849576i	$-0.323142\pi$
$97$	2.95171	+	1.22264i	0.299700	+	0.124140i	−0.227766	+	0.973716i	$0.573142\pi$
$98$		−	6.99740i		−	0.706845i
$99$	1.63484	−	3.94685i	0.164307	−	0.396673i
$100$	0.707107	−	0.707107i	0.0707107	−	0.0707107i
$101$	10.6125			1.05598			0.527991	−	0.849250i	$-0.322945\pi$
$101$	10.6125			1.05598			0.527991	+	0.849250i	$0.322945\pi$
$102$	11.5514	+	2.80232i	1.14376	+	0.277471i
$103$	−6.47365			−0.637868			−0.318934	−	0.947777i	$-0.603325\pi$
$103$	−6.47365			−0.637868			−0.318934	+	0.947777i	$0.603325\pi$
$104$	3.01695	−	3.01695i	0.295836	−	0.295836i
$105$	−0.0562132	+	0.135711i	−0.00548584	+	0.0132440i
$106$			11.0215i			1.07050i
$107$	−13.5458	−	5.61084i	−1.30952	−	0.542420i	−0.384774	−	0.923011i	$-0.625721\pi$
$107$	−13.5458	−	5.61084i	−1.30952	−	0.542420i	−0.924744	+	0.380591i	$0.875721\pi$
$108$	2.54966	+	6.15542i	0.245341	+	0.592305i
$109$	3.57112	−	1.47921i	0.342051	−	0.141682i	−0.205044	−	0.978753i	$-0.565734\pi$
$109$	3.57112	−	1.47921i	0.342051	−	0.141682i	0.547095	+	0.837071i	$0.315734\pi$
$110$	−0.568772	−	0.568772i	−0.0542303	−	0.0542303i
$111$	−3.18600	−	3.18600i	−0.302402	−	0.302402i
$112$	0.0470744	−	0.0194989i	0.00444812	−	0.00184247i
$113$	−6.91657	−	16.6981i	−0.650656	−	1.57082i	−0.811828	−	0.583897i	$-0.801527\pi$
$113$	−6.91657	−	16.6981i	−0.650656	−	1.57082i	0.161171	−	0.986926i	$-0.448473\pi$
$114$	−17.0773	−	7.07363i	−1.59943	−	0.662506i
$115$			8.59600i			0.801581i
$116$	1.74829	−	4.22074i	0.162324	−	0.391886i
$117$	−16.0232	+	16.0232i	−1.48135	+	1.48135i
$118$	−10.0965			−0.929462
$119$	−0.0495289	+	0.204163i	−0.00454031	+	0.0187156i
$120$	2.88289			0.263171
$121$	7.32067	−	7.32067i	0.665516	−	0.665516i
$122$	2.37619	−	5.73663i	0.215130	−	0.519370i
$123$			24.8359i			2.23938i
$124$	0.456861	+	0.189238i	0.0410273	+	0.0169941i
$125$	0.382683	+	0.923880i	0.0342282	+	0.0826343i
$126$	−0.250016	+	0.103560i	−0.0222732	+	0.00922585i
$127$	−12.4567	−	12.4567i	−1.10535	−	1.10535i	−0.993754	−	0.111596i	$-0.964404\pi$
$127$	−12.4567	−	12.4567i	−1.10535	−	1.10535i	−0.111596	−	0.993754i	$-0.535596\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	6.53536	−	2.70703i	0.575406	−	0.238341i
$130$	1.63276	+	3.94183i	0.143203	+	0.345722i
$131$	−14.4504	−	5.98554i	−1.26253	−	0.522959i	−0.351848	−	0.936057i	$-0.614447\pi$
$131$	−14.4504	−	5.98554i	−1.26253	−	0.522959i	−0.910687	+	0.413098i	$0.864447\pi$
$132$		−	2.31890i		−	0.201834i
$133$	0.125021	−	0.301828i	0.0108407	−	0.0261718i
$134$	0.581649	−	0.581649i	0.0502469	−	0.0502469i
$135$	−6.66258			−0.573423
$136$	4.07387	−	0.635311i	0.349331	−	0.0544774i
$137$	−17.3384			−1.48132			−0.740661	−	0.671879i	$-0.765487\pi$
$137$	−17.3384			−1.48132			−0.740661	+	0.671879i	$0.765487\pi$
$138$	−17.5231	+	17.5231i	−1.49166	+	1.49166i
$139$	−4.21946	+	10.1867i	−0.357890	+	0.864023i	0.637706	+	0.770279i	$0.279883\pi$
$139$	−4.21946	+	10.1867i	−0.357890	+	0.864023i	−0.995596	+	0.0937432i	$0.970117\pi$
$140$			0.0509530i			0.00430632i
$141$	21.9144	+	9.07725i	1.84553	+	0.764442i
$142$	4.17475	+	10.0787i	0.350337	+	0.845789i
$143$	3.17067	−	1.31334i	0.265145	−	0.109827i
$144$	3.75550	+	3.75550i	0.312958	+	0.312958i
$145$	3.23042	+	3.23042i	0.268271	+	0.268271i
$146$	6.19072	−	2.56428i	0.512348	−	0.212221i
$147$	7.71978	+	18.6372i	0.636717	+	1.53717i
$148$	−1.44394	−	0.598098i	−0.118691	−	0.0491633i
$149$		−	11.4114i		−	0.934857i	−0.884031	−	0.467429i	$-0.845181\pi$
$149$		−	11.4114i		−	0.934857i	0.884031	−	0.467429i	$-0.154819\pi$
$150$	−1.10324	+	2.66345i	−0.0900788	+	0.217469i
$151$	4.48604	−	4.48604i	0.365069	−	0.365069i	−0.500606	−	0.865675i	$-0.666889\pi$
$151$	4.48604	−	4.48604i	0.365069	−	0.365069i	0.865675	+	0.500606i	$0.166889\pi$
$152$	−6.41171			−0.520059
$153$	−21.6366	+	3.37418i	−1.74922	+	0.272786i
$154$	0.0409848			0.00330265
$155$	−0.349666	+	0.349666i	−0.0280859	+	0.0280859i
$156$	−4.70708	+	11.3639i	−0.376868	+	0.909839i
$157$		−	15.7712i		−	1.25868i	−0.777130	−	0.629341i	$-0.783325\pi$
$157$		−	15.7712i		−	1.25868i	0.777130	−	0.629341i	$-0.216675\pi$
$158$	7.59862	+	3.14745i	0.604514	+	0.250398i
$159$	−12.1593	−	29.3551i	−0.964294	−	2.32801i
$160$	0.923880	−	0.382683i	0.0730391	−	0.0302538i
$161$	−0.309707	−	0.309707i	−0.0244084	−	0.0244084i
$162$	−2.31526	−	2.31526i	−0.181904	−	0.181904i
$163$	16.7371	−	6.93275i	1.31095	−	0.543015i	0.385791	−	0.922586i	$-0.373928\pi$
$163$	16.7371	−	6.93275i	1.31095	−	0.543015i	0.925163	+	0.379571i	$0.123928\pi$
$164$	3.29679	+	7.95917i	0.257436	+	0.621506i
$165$	2.14238	+	0.887404i	0.166784	+	0.0690843i
$166$		−	1.35073i		−	0.104837i
$167$	−1.76899	+	4.27073i	−0.136889	+	0.330479i	−0.977427	−	0.211273i	$-0.932239\pi$
$167$	−1.76899	+	4.27073i	−0.136889	+	0.330479i	0.840538	+	0.541752i	$0.182239\pi$
$168$	−0.103868	+	0.103868i	−0.00801362	+	0.00801362i
$169$	−5.20397			−0.400306
$170$	−0.972050	+	4.00688i	−0.0745529	+	0.307314i
$171$	34.0531			2.60410
$172$	1.73504	−	1.73504i	0.132296	−	0.132296i
$173$	−5.34485	+	12.9036i	−0.406361	+	0.981043i	0.579725	+	0.814812i	$0.303160\pi$
$173$	−5.34485	+	12.9036i	−0.406361	+	0.981043i	−0.986087	+	0.166231i	$0.946840\pi$
$174$			13.1705i			0.998452i
$175$	−0.0470744	−	0.0194989i	−0.00355849	−	0.00147398i
$176$	−0.307817	−	0.743136i	−0.0232026	−	0.0560160i
$177$	26.8916	−	11.1389i	2.02130	−	0.837248i
$178$	−12.0587	−	12.0587i	−0.903835	−	0.903835i
$179$	11.3082	+	11.3082i	0.845212	+	0.845212i	0.989531	−	0.144320i	$-0.0460993\pi$
$179$	11.3082	+	11.3082i	0.845212	+	0.845212i	−0.144320	+	0.989531i	$0.546099\pi$
$180$	−4.90679	+	2.03246i	−0.365731	+	0.151491i
$181$	−1.09451	−	2.64237i	−0.0813541	−	0.196406i	0.877968	−	0.478718i	$-0.158899\pi$
$181$	−1.09451	−	2.64237i	−0.0813541	−	0.196406i	−0.959323	+	0.282312i	$0.908899\pi$
$182$	−0.200848	−	0.0831941i	−0.0148879	−	0.00616676i
$183$			17.9007i			1.32326i
$184$	−3.28955	+	7.94167i	−0.242509	+	0.585468i
$185$	1.10514	−	1.10514i	0.0812515	−	0.0812515i
$186$	−1.42560			−0.104530
$187$	3.22300	+	0.781883i	0.235689	+	0.0571769i
$188$	8.22785			0.600077
$189$	0.240047	−	0.240047i	0.0174609	−	0.0174609i
$190$	2.45366	−	5.92365i	0.178007	−	0.429747i
$191$			14.2908i			1.03405i	0.855971	+	0.517023i	$0.172960\pi$
$191$			14.2908i			1.03405i	−0.855971	+	0.517023i	$0.827040\pi$
$192$	2.66345	+	1.10324i	0.192218	+	0.0796192i
$193$	3.34691	+	8.08015i	0.240916	+	0.581622i	0.997374	−	0.0724197i	$-0.0230721\pi$
$193$	3.34691	+	8.08015i	0.240916	+	0.581622i	−0.756459	+	0.654042i	$0.773072\pi$
$194$	−2.95171	+	1.22264i	−0.211920	+	0.0877802i
$195$	−8.69754	−	8.69754i	−0.622844	−	0.622844i
$196$	4.94791	+	4.94791i	0.353422	+	0.353422i
$197$	−11.5369	+	4.77874i	−0.821970	+	0.340471i	−0.753719	−	0.657197i	$-0.771742\pi$
$197$	−11.5369	+	4.77874i	−0.821970	+	0.340471i	−0.0682513	+	0.997668i	$0.521742\pi$
$198$	1.63484	+	3.94685i	0.116183	+	0.280490i
$199$	−7.06678	−	2.92716i	−0.500951	−	0.207501i	0.117875	−	0.993028i	$-0.462392\pi$
$199$	−7.06678	−	2.92716i	−0.500951	−	0.207501i	−0.618827	+	0.785528i	$0.712392\pi$
$200$			1.00000i			0.0707107i
$201$	−0.907496	+	2.19089i	−0.0640098	+	0.154533i
$202$	−7.50416	+	7.50416i	−0.527991	+	0.527991i
$203$	−0.232779			−0.0163379
$204$	−10.1496	+	6.18655i	−0.710616	+	0.433145i
$205$	−8.61494			−0.601693
$206$	4.57756	−	4.57756i	0.318934	−	0.318934i
$207$	17.4710	−	42.1788i	1.21432	−	2.93163i
$208$			4.26661i			0.295836i
$209$	−4.76477	−	1.97363i	−0.329586	−	0.136519i
$210$	−0.0562132	−	0.135711i	−0.00387908	−	0.00936492i
$211$	3.50089	−	1.45012i	0.241011	−	0.0998301i	−0.258909	−	0.965902i	$-0.583363\pi$
$211$	3.50089	−	1.45012i	0.241011	−	0.0998301i	0.499920	+	0.866072i	$0.333363\pi$
$212$	−7.79336	−	7.79336i	−0.535250	−	0.535250i
$213$	−22.2384	−	22.2384i	−1.52375	−	1.52375i
$214$	13.5458	−	5.61084i	0.925969	−	0.383549i
$215$	0.938999	+	2.26694i	0.0640392	+	0.154604i
$216$	−6.15542	−	2.54966i	−0.418823	−	0.173482i
$217$		−	0.0251964i		−	0.00171044i
$218$	−1.47921	+	3.57112i	−0.100184	+	0.241867i
$219$	−13.6596	+	13.6596i	−0.923033	+	0.923033i
$220$	0.804365			0.0542303
$221$	−14.2073	−	10.3739i	−0.955690	−	0.697827i
$222$	4.50569			0.302402
$223$	10.6318	−	10.6318i	0.711959	−	0.711959i	−0.254986	−	0.966945i	$-0.582071\pi$
$223$	10.6318	−	10.6318i	0.711959	−	0.711959i	0.966945	+	0.254986i	$0.0820709\pi$
$224$	−0.0194989	+	0.0470744i	−0.00130282	+	0.00314529i
$225$		−	5.31107i		−	0.354072i
$226$	16.6981	+	6.91657i	1.11074	+	0.460084i
$227$	−0.407816	−	0.984554i	−0.0270677	−	0.0653472i	0.909768	−	0.415118i	$-0.136260\pi$
$227$	−0.407816	−	0.984554i	−0.0270677	−	0.0653472i	−0.936835	+	0.349770i	$0.886260\pi$
$228$	17.0773	−	7.07363i	1.13097	−	0.468463i
$229$	2.50936	+	2.50936i	0.165823	+	0.165823i	0.785141	−	0.619318i	$-0.212591\pi$
$229$	2.50936	+	2.50936i	0.165823	+	0.165823i	−0.619318	+	0.785141i	$0.712591\pi$
$230$	−6.07829	−	6.07829i	−0.400791	−	0.400791i
$231$	−0.109161	+	0.0452159i	−0.00718225	+	0.00297499i
$232$	1.74829	+	4.22074i	0.114781	+	0.277105i
$233$	−4.86575	−	2.01546i	−0.318766	−	0.132037i	0.217563	−	0.976046i	$-0.430189\pi$
$233$	−4.86575	−	2.01546i	−0.318766	−	0.132037i	−0.536329	+	0.844009i	$0.680189\pi$
$234$		−	22.6603i		−	1.48135i
$235$	−3.14866	+	7.60154i	−0.205396	+	0.495870i
$236$	7.13933	−	7.13933i	0.464731	−	0.464731i
$237$	−23.7109			−1.54019
$238$	−0.109343	−	0.179387i	−0.00708763	−	0.0116279i
$239$	−2.08566			−0.134910			−0.0674550	−	0.997722i	$-0.521488\pi$
$239$	−2.08566			−0.134910			−0.0674550	+	0.997722i	$0.521488\pi$
$240$	−2.03851	+	2.03851i	−0.131585	+	0.131585i
$241$	−1.86926	+	4.51280i	−0.120410	+	0.290695i	−0.972580	−	0.232571i	$-0.925286\pi$
$241$	−1.86926	+	4.51280i	−0.120410	+	0.290695i	0.852170	+	0.523265i	$0.175286\pi$
$242$			10.3530i			0.665516i
$243$	−9.74539	−	4.03667i	−0.625167	−	0.258953i
$244$	2.37619	+	5.73663i	0.152120	+	0.367250i
$245$	−6.46476	+	2.67779i	−0.413018	+	0.171078i
$246$	−17.5617	−	17.5617i	−1.11969	−	1.11969i
$247$	19.3438	+	19.3438i	1.23082	+	1.23082i
$248$	−0.456861	+	0.189238i	−0.0290107	+	0.0120166i
$249$	1.49017	+	3.59759i	0.0944357	+	0.227988i
$250$	−0.923880	−	0.382683i	−0.0584313	−	0.0242030i
$251$			2.73599i			0.172694i	0.996265	+	0.0863472i	$0.0275194\pi$
$251$			2.73599i			0.172694i	−0.996265	+	0.0863472i	$0.972481\pi$
$252$	0.103560	−	0.250016i	0.00652366	−	0.0157495i
$253$	−4.88916	+	4.88916i	−0.307379	+	0.307379i
$254$	17.6164			1.10535
$255$	−1.83153	−	11.7445i	−0.114695	−	0.735470i
$256$	1.00000			0.0625000
$257$	1.57156	−	1.57156i	0.0980315	−	0.0980315i	−0.656390	−	0.754422i	$-0.727917\pi$
$257$	1.57156	−	1.57156i	0.0980315	−	0.0980315i	0.754422	+	0.656390i	$0.227917\pi$
$258$	−2.70703	+	6.53536i	−0.168533	+	0.406874i
$259$			0.0796347i			0.00494826i
$260$	−3.94183	−	1.63276i	−0.244462	−	0.101260i
$261$	−9.28529	−	22.4167i	−0.574745	−	1.38756i
$262$	14.4504	−	5.98554i	0.892747	−	0.369788i
$263$	18.0243	+	18.0243i	1.11142	+	1.11142i	0.992958	+	0.118466i	$0.0377976\pi$
$263$	18.0243	+	18.0243i	1.11142	+	1.11142i	0.118466	+	0.992958i	$0.462202\pi$
$264$	1.63971	+	1.63971i	0.100917	+	0.100917i
$265$	10.1825	−	4.21774i	0.625507	−	0.259093i
$266$	0.125021	+	0.301828i	0.00766554	+	0.0185063i
$267$	45.4212	+	18.8141i	2.77973	+	1.15140i
$268$			0.822577i			0.0502469i
$269$	0.610716	−	1.47440i	0.0372360	−	0.0898957i	−0.904167	−	0.427178i	$-0.859508\pi$
$269$	0.610716	−	1.47440i	0.0372360	−	0.0898957i	0.941404	+	0.337282i	$0.109508\pi$
$270$	4.71115	−	4.71115i	0.286712	−	0.286712i
$271$	−18.6694			−1.13408			−0.567042	−	0.823689i	$-0.691912\pi$
$271$	−18.6694			−1.13408			−0.567042	+	0.823689i	$0.691912\pi$
$272$	−2.43143	+	3.32989i	−0.147427	+	0.201904i
$273$	0.626731			0.0379315
$274$	12.2601	−	12.2601i	0.740661	−	0.740661i
$275$	−0.307817	+	0.743136i	−0.0185621	+	0.0448128i
$276$		−	24.7814i		−	1.49166i
$277$	26.9671	+	11.1702i	1.62030	+	0.671150i	0.994095	−	0.108511i	$-0.0346081\pi$
$277$	26.9671	+	11.1702i	1.62030	+	0.671150i	0.626203	+	0.779660i	$0.284608\pi$
$278$	−4.21946	−	10.1867i	−0.253066	−	0.610956i
$279$	2.42642	−	1.00506i	0.145266	−	0.0601712i
$280$	−0.0360292	−	0.0360292i	−0.00215316	−	0.00215316i
$281$	−6.50098	−	6.50098i	−0.387816	−	0.387816i	0.486092	−	0.873908i	$-0.338422\pi$
$281$	−6.50098	−	6.50098i	−0.387816	−	0.387816i	−0.873908	+	0.486092i	$0.838422\pi$
$282$	−21.9144	+	9.07725i	−1.30498	+	0.540542i
$283$	0.128164	+	0.309415i	0.00761854	+	0.0183928i	0.927643	−	0.373468i	$-0.121831\pi$
$283$	0.128164	+	0.309415i	0.00761854	+	0.0183928i	−0.920024	+	0.391861i	$0.871831\pi$
$284$	−10.0787	−	4.17475i	−0.598063	−	0.247726i
$285$			18.4843i			1.09491i
$286$	−1.31334	+	3.17067i	−0.0776592	+	0.187486i
$287$	0.310389	−	0.310389i	0.0183217	−	0.0183217i
$288$	−5.31107			−0.312958
$289$	−5.17634	−	16.1928i	−0.304491	−	0.952515i
$290$	−4.56850			−0.268271
$291$	6.51285	−	6.51285i	0.381790	−	0.381790i
$292$	−2.56428	+	6.19072i	−0.150063	+	0.362285i
$293$			7.96292i			0.465199i	0.972573	+	0.232599i	$0.0747231\pi$
$293$			7.96292i			0.465199i	−0.972573	+	0.232599i	$0.925277\pi$
$294$	−18.6372	−	7.71978i	−1.08694	−	0.450227i
$295$	3.86378	+	9.32799i	0.224958	+	0.543096i
$296$	1.44394	−	0.598098i	0.0839270	−	0.0347637i
$297$	−3.78949	−	3.78949i	−0.219888	−	0.219888i
$298$	8.06907	+	8.06907i	0.467429	+	0.467429i
$299$	33.8840	−	14.0352i	1.95956	−	0.811678i
$300$	−1.10324	−	2.66345i	−0.0636953	−	0.153774i
$301$	−0.115508	−	0.0478448i	−0.00665775	−	0.00275773i
$302$			6.34422i			0.365069i
$303$	11.7081	−	28.2658i	0.672611	−	1.62383i
$304$	4.53377	−	4.53377i	0.260029	−	0.260029i
$305$	−6.20928			−0.355543
$306$	12.9135	−	17.6853i	0.738214	−	1.01100i
$307$	−8.53804			−0.487291			−0.243646	−	0.969864i	$-0.578343\pi$
$307$	−8.53804			−0.487291			−0.243646	+	0.969864i	$0.578343\pi$
$308$	−0.0289806	+	0.0289806i	−0.00165132	+	0.00165132i
$309$	−7.14196	+	17.2422i	−0.406292	+	0.980876i
$310$		−	0.494503i		−	0.0280859i
$311$	5.19639	+	2.15242i	0.294660	+	0.122052i	0.525116	−	0.851030i	$-0.324022\pi$
$311$	5.19639	+	2.15242i	0.294660	+	0.122052i	−0.230456	+	0.973083i	$0.574022\pi$
$312$	−4.70708	−	11.3639i	−0.266486	−	0.643354i
$313$	0.410794	−	0.170156i	0.0232194	−	0.00961780i	−0.371044	−	0.928615i	$-0.621000\pi$
$313$	0.410794	−	0.170156i	0.0232194	−	0.00961780i	0.394263	+	0.918998i	$0.371000\pi$
$314$	11.1519	+	11.1519i	0.629341	+	0.629341i
$315$	0.191354	+	0.191354i	0.0107816	+	0.0107816i
$316$	−7.59862	+	3.14745i	−0.427456	+	0.177058i
$317$	−0.649236	−	1.56739i	−0.0364647	−	0.0880336i	0.904598	−	0.426266i	$-0.140171\pi$
$317$	−0.649236	−	1.56739i	−0.0364647	−	0.0880336i	−0.941063	+	0.338232i	$0.890171\pi$
$318$	29.3551	+	12.1593i	1.64615	+	0.681859i
$319$			3.67474i			0.205746i
$320$	−0.382683	+	0.923880i	−0.0213927	+	0.0516464i
$321$	−29.8883	+	29.8883i	−1.66820	+	1.66820i
$322$	0.437992			0.0244084
$323$	4.07343	+	26.1205i	0.226652	+	1.45338i
$324$	3.27428			0.181904
$325$	3.01695	−	3.01695i	0.167350	−	0.167350i
$326$	−6.93275	+	16.7371i	−0.383970	+	0.926984i
$327$		−	11.1434i		−	0.616231i
$328$	−7.95917	−	3.29679i	−0.439471	−	0.182035i
$329$	−0.160434	−	0.387321i	−0.00884500	−	0.0213537i
$330$	−2.14238	+	0.887404i	−0.117934	+	0.0488500i
$331$	12.1261	+	12.1261i	0.666511	+	0.666511i	0.956907	−	0.290396i	$-0.0937870\pi$
$331$	12.1261	+	12.1261i	0.666511	+	0.666511i	−0.290396	+	0.956907i	$0.593787\pi$
$332$	0.955109	+	0.955109i	0.0524184	+	0.0524184i
$333$	−7.66885	+	3.17654i	−0.420250	+	0.174073i
$334$	−1.76899	−	4.27073i	−0.0967951	−	0.233684i
$335$	−0.759962	−	0.314786i	−0.0415211	−	0.0171986i
$336$		−	0.146892i		−	0.00801362i
$337$	12.4909	−	30.1556i	0.680420	−	1.64268i	−0.0828204	−	0.996564i	$-0.526393\pi$
$337$	12.4909	−	30.1556i	0.680420	−	1.64268i	0.763240	−	0.646115i	$-0.223607\pi$
$338$	3.67976	−	3.67976i	0.200153	−	0.200153i
$339$	−52.1050			−2.82996
$340$	−2.14595	−	3.52064i	−0.116381	−	0.190933i
$341$	−0.397761			−0.0215399
$342$	−24.0792	+	24.0792i	−1.30205	+	1.30205i
$343$	0.272934	−	0.658920i	0.0147370	−	0.0355783i
$344$			2.45372i			0.132296i
$345$	22.8950	+	9.48342i	1.23262	+	0.510570i
$346$	−5.34485	−	12.9036i	−0.287341	−	0.693702i
$347$	−24.4256	+	10.1174i	−1.31123	+	0.543131i	−0.925244	−	0.379372i	$-0.876140\pi$
$347$	−24.4256	+	10.1174i	−1.31123	+	0.543131i	−0.385990	+	0.922503i	$0.626140\pi$
$348$	−9.31294	−	9.31294i	−0.499226	−	0.499226i
$349$	14.8187	+	14.8187i	0.793228	+	0.793228i	0.982018	−	0.188789i	$-0.0604564\pi$
$349$	14.8187	+	14.8187i	0.793228	+	0.793228i	−0.188789	+	0.982018i	$0.560456\pi$
$350$	0.0470744	−	0.0194989i	0.00251623	−	0.00104226i
$351$	10.8784	+	26.2628i	0.580646	+	1.40180i
$352$	0.743136	+	0.307817i	0.0396093	+	0.0164067i
$353$			0.809224i			0.0430707i	0.999768	+	0.0215353i	$0.00685544\pi$
$353$			0.809224i			0.0430707i	−0.999768	+	0.0215353i	$0.993145\pi$
$354$	−11.1389	+	26.8916i	−0.592024	+	1.42927i
$355$	7.71393	−	7.71393i	0.409413	−	0.409413i
$356$	17.0535			0.903835
$357$	0.489135	+	0.357157i	0.0258877	+	0.0189028i
$358$	−15.9922			−0.845212
$359$	−3.05400	+	3.05400i	−0.161184	+	0.161184i	−0.783091	−	0.621907i	$-0.786358\pi$
$359$	−3.05400	+	3.05400i	−0.161184	+	0.161184i	0.621907	+	0.783091i	$0.286358\pi$
$360$	2.03246	−	4.90679i	0.107120	−	0.258611i
$361$		−	22.1101i		−	1.16369i
$362$	2.64237	+	1.09451i	0.138880	+	0.0575260i
$363$	−11.4218	−	27.5747i	−0.599489	−	1.44729i
$364$	0.200848	−	0.0831941i	0.0105273	−	0.00436056i
$365$	−4.73817	−	4.73817i	−0.248007	−	0.248007i
$366$	−12.6577	−	12.6577i	−0.661629	−	0.661629i
$367$	−26.9709	+	11.1717i	−1.40787	+	0.583158i	−0.951781	−	0.306778i	$-0.900749\pi$
$367$	−26.9709	+	11.1717i	−1.40787	+	0.583158i	−0.456086	+	0.889936i	$0.650749\pi$
$368$	−3.28955	−	7.94167i	−0.171480	−	0.413988i
$369$	42.2717	+	17.5095i	2.20058	+	0.911509i
$370$			1.56290i			0.0812515i
$371$	−0.214906	+	0.518830i	−0.0111574	+	0.0269363i
$372$	1.00805	−	1.00805i	0.0522650	−	0.0522650i
$373$	22.8584			1.18356			0.591782	−	0.806098i	$-0.298425\pi$
$373$	22.8584			1.18356			0.591782	+	0.806098i	$0.298425\pi$
$374$	−2.83188	+	1.72613i	−0.146433	+	0.0892559i
$375$	2.88289			0.148872
$376$	−5.81797	+	5.81797i	−0.300039	+	0.300039i
$377$	7.45927	−	18.0083i	0.384172	−	0.927473i
$378$			0.339478i			0.0174609i
$379$	−18.0134	−	7.46141i	−0.925288	−	0.383267i	−0.131399	−	0.991330i	$-0.541947\pi$
$379$	−18.0134	−	7.46141i	−0.925288	−	0.383267i	−0.793889	+	0.608063i	$0.791947\pi$
$380$	2.45366	+	5.92365i	0.125870	+	0.303877i
$381$	−46.9203	+	19.4350i	−2.40380	+	0.995686i
$382$	−10.1051	−	10.1051i	−0.517023	−	0.517023i
$383$	−13.7835	−	13.7835i	−0.704302	−	0.704302i	0.261029	−	0.965331i	$-0.415938\pi$
$383$	−13.7835	−	13.7835i	−0.704302	−	0.704302i	−0.965331	+	0.261029i	$0.915938\pi$
$384$	−2.66345	+	1.10324i	−0.135918	+	0.0562992i
$385$	−0.0156842	−	0.0378650i	−0.000799341	−	0.00192978i
$386$	−8.08015	−	3.34691i	−0.411269	−	0.170353i
$387$		−	13.0319i		−	0.662449i
$388$	1.22264	−	2.95171i	0.0620700	−	0.149850i
$389$	3.66713	−	3.66713i	0.185931	−	0.185931i	−0.608003	−	0.793934i	$-0.708029\pi$
$389$	3.66713	−	3.66713i	0.185931	−	0.185931i	0.793934	+	0.608003i	$0.208029\pi$
$390$	12.3002			0.622844
$391$	34.4432	+	8.35575i	1.74187	+	0.422568i
$392$	−6.99740			−0.353422
$393$	−31.8843	+	31.8843i	−1.60835	+	1.60835i
$394$	4.77874	−	11.5369i	0.240750	−	0.581221i
$395$		−	8.22469i		−	0.413829i
$396$	−3.94685	−	1.63484i	−0.198337	−	0.0821537i
$397$	5.42131	+	13.0882i	0.272088	+	0.656878i	0.999572	−	0.0292459i	$-0.00931059\pi$
$397$	5.42131	+	13.0882i	0.272088	+	0.656878i	−0.727484	+	0.686124i	$0.759311\pi$
$398$	7.06678	−	2.92716i	0.354226	−	0.146725i
$399$	−0.665974	−	0.665974i	−0.0333404	−	0.0333404i
$400$	−0.707107	−	0.707107i	−0.0353553	−	0.0353553i
$401$	−11.3109	+	4.68513i	−0.564840	+	0.233964i	−0.646785	−	0.762672i	$-0.723887\pi$
$401$	−11.3109	+	4.68513i	−0.564840	+	0.233964i	0.0819449	+	0.996637i	$0.473887\pi$
$402$	−0.907496	−	2.19089i	−0.0452618	−	0.109272i
$403$	1.94925	+	0.807405i	0.0970990	+	0.0402197i
$404$		−	10.6125i		−	0.527991i
$405$	−1.25301	+	3.02504i	−0.0622627	+	0.150315i
$406$	0.164599	−	0.164599i	0.00816893	−	0.00816893i
$407$	1.25714			0.0623144
$408$	2.80232	−	11.5514i	0.138735	−	0.571880i
$409$	−29.9188			−1.47939			−0.739694	−	0.672944i	$-0.765030\pi$
$409$	−29.9188			−1.47939			−0.739694	+	0.672944i	$0.765030\pi$
$410$	6.09168	−	6.09168i	0.300847	−	0.300847i
$411$	−19.1284	+	46.1799i	−0.943532	+	2.27789i
$412$			6.47365i			0.318934i
$413$	−0.475289	−	0.196871i	−0.0233874	−	0.00968740i
$414$	17.4710	+	42.1788i	0.858654	+	2.07297i
$415$	−1.24791	+	0.516901i	−0.0612575	+	0.0253737i
$416$	−3.01695	−	3.01695i	−0.147918	−	0.147918i
$417$	22.4766	+	22.4766i	1.10068	+	1.10068i
$418$	4.76477	−	1.97363i	0.233053	−	0.0965336i
$419$	−3.52147	−	8.50159i	−0.172035	−	0.415330i	0.814220	−	0.580556i	$-0.197165\pi$
$419$	−3.52147	−	8.50159i	−0.172035	−	0.415330i	−0.986256	+	0.165226i	$0.947165\pi$
$420$	0.135711	+	0.0562132i	0.00662200	+	0.00274292i
$421$			36.1293i			1.76083i	0.474200	+	0.880417i	$0.342738\pi$
$421$			36.1293i			1.76083i	−0.474200	+	0.880417i	$0.657262\pi$
$422$	−1.45012	+	3.50089i	−0.0705905	+	0.170421i
$423$	30.8996	−	30.8996i	1.50239	−	1.50239i
$424$	11.0215			0.535250
$425$	4.07387	−	0.635311i	0.197612	−	0.0308171i
$426$	31.4499			1.52375
$427$	0.223716	−	0.223716i	0.0108264	−	0.0108264i
$428$	−5.61084	+	13.5458i	−0.271210	+	0.654759i
$429$		−	9.89383i		−	0.477679i
$430$	−2.26694	−	0.938999i	−0.109322	−	0.0452825i
$431$	8.27632	+	19.9808i	0.398656	+	0.962442i	0.987985	+	0.154548i	$0.0493923\pi$
$431$	8.27632	+	19.9808i	0.398656	+	0.962442i	−0.589329	+	0.807893i	$0.700608\pi$
$432$	6.15542	−	2.54966i	0.296153	−	0.122670i
$433$	12.8615	+	12.8615i	0.618084	+	0.618084i	0.945040	−	0.326955i	$-0.106023\pi$
$433$	12.8615	+	12.8615i	0.618084	+	0.618084i	−0.326955	+	0.945040i	$0.606023\pi$
$434$	0.0178166	+	0.0178166i	0.000855222	+	0.000855222i
$435$	12.1679	−	5.04013i	0.583408	−	0.241656i
$436$	−1.47921	−	3.57112i	−0.0708411	−	0.171026i
$437$	−50.9197	−	21.0916i	−2.43582	−	1.00895i
$438$		−	19.3177i		−	0.923033i
$439$	10.1644	−	24.5389i	0.485118	−	1.17118i	−0.472031	−	0.881582i	$-0.656479\pi$
$439$	10.1644	−	24.5389i	0.485118	−	1.17118i	0.957149	−	0.289597i	$-0.0935212\pi$
$440$	−0.568772	+	0.568772i	−0.0271151	+	0.0271151i
$441$	37.1637			1.76970
$442$	17.3816	−	2.71062i	0.826758	−	0.128931i
$443$	28.5391			1.35593			0.677967	−	0.735092i	$-0.262861\pi$
$443$	28.5391			1.35593			0.677967	+	0.735092i	$0.262861\pi$
$444$	−3.18600	+	3.18600i	−0.151201	+	0.151201i
$445$	−6.52610	+	15.7554i	−0.309367	+	0.746878i
$446$			15.0356i			0.711959i
$447$	−30.3936	−	12.5894i	−1.43757	−	0.595460i
$448$	−0.0194989	−	0.0470744i	−0.000921235	−	0.00222406i
$449$	22.8467	−	9.46340i	1.07820	−	0.446605i	0.228323	−	0.973585i	$-0.426676\pi$
$449$	22.8467	−	9.46340i	1.07820	−	0.446605i	0.849878	+	0.526980i	$0.176676\pi$
$450$	3.75550	+	3.75550i	0.177036	+	0.177036i
$451$	−4.89993	−	4.89993i	−0.230729	−	0.230729i
$452$	−16.6981	+	6.91657i	−0.785412	+	0.325328i
$453$	−6.99917	−	16.8975i	−0.328850	−	0.793914i
$454$	0.984554	+	0.407816i	0.0462074	+	0.0191397i
$455$			0.217397i			0.0101917i
$456$	−7.07363	+	17.0773i	−0.331253	+	0.799716i
$457$	5.18233	−	5.18233i	0.242419	−	0.242419i	−0.575431	−	0.817850i	$-0.695166\pi$
$457$	5.18233	−	5.18233i	0.242419	−	0.242419i	0.817850	+	0.575431i	$0.195166\pi$
$458$	−3.54877			−0.165823
$459$	−6.47636	+	26.6962i	−0.302291	+	1.24607i
$460$	8.59600			0.400791
$461$	2.55232	−	2.55232i	0.118874	−	0.118874i	−0.645168	−	0.764041i	$-0.723212\pi$
$461$	2.55232	−	2.55232i	0.118874	−	0.118874i	0.764041	+	0.645168i	$0.223212\pi$
$462$	0.0452159	−	0.109161i	0.00210363	−	0.00507862i
$463$		−	37.3089i		−	1.73389i	−0.498402	−	0.866946i	$-0.666080\pi$
$463$		−	37.3089i		−	1.73389i	0.498402	−	0.866946i	$-0.333920\pi$
$464$	−4.22074	−	1.74829i	−0.195943	−	0.0811622i
$465$	0.545553	+	1.31708i	0.0252994	+	0.0610782i
$466$	4.86575	−	2.01546i	0.225401	−	0.0933643i
$467$	11.2923	+	11.2923i	0.522545	+	0.522545i	0.918339	−	0.395794i	$-0.129531\pi$
$467$	11.2923	+	11.2923i	0.522545	+	0.522545i	−0.395794	+	0.918339i	$0.629531\pi$
$468$	16.0232	+	16.0232i	0.740675	+	0.740675i
$469$	0.0387223	−	0.0160393i	0.00178803	−	0.000740627i
$470$	−3.14866	−	7.60154i	−0.145237	−	0.350633i
$471$	−42.0058	−	17.3994i	−1.93553	−	0.801721i
$472$			10.0965i			0.464731i
$473$	−0.755297	+	1.82345i	−0.0347286	+	0.0838423i
$474$	16.7661	−	16.7661i	0.770094	−	0.770094i
$475$	−6.41171			−0.294190
$476$	0.204163	+	0.0495289i	0.00935779	+	0.00227015i
$477$	−58.5358			−2.68017
$478$	1.47478	−	1.47478i	0.0674550	−	0.0674550i
$479$	2.55857	−	6.17694i	0.116904	−	0.282232i	−0.854587	−	0.519309i	$-0.826189\pi$
$479$	2.55857	−	6.17694i	0.116904	−	0.282232i	0.971491	+	0.237077i	$0.0761894\pi$
$480$		−	2.88289i		−	0.131585i
$481$	−6.16071	−	2.55185i	−0.280904	−	0.116354i
$482$	−1.86926	−	4.51280i	−0.0851425	−	0.205552i
$483$	−1.16657	+	0.483209i	−0.0530807	+	0.0219868i
$484$	−7.32067	−	7.32067i	−0.332758	−	0.332758i
$485$	2.25914	+	2.25914i	0.102582	+	0.102582i
$486$	9.74539	−	4.03667i	0.442060	−	0.183107i
$487$	−11.1332	−	26.8779i	−0.504494	−	1.21796i	−0.947013	−	0.321197i	$-0.895915\pi$
$487$	−11.1332	−	26.8779i	−0.504494	−	1.21796i	0.442519	−	0.896759i	$-0.354085\pi$
$488$	−5.73663	−	2.37619i	−0.259685	−	0.107565i
$489$		−	52.2269i		−	2.36178i
$490$	2.67779	−	6.46476i	0.120970	−	0.292048i
$491$	18.4774	−	18.4774i	0.833875	−	0.833875i	−0.154169	−	0.988044i	$-0.549270\pi$
$491$	18.4774	−	18.4774i	0.833875	−	0.833875i	0.988044	+	0.154169i	$0.0492701\pi$
$492$	24.8359			1.11969
$493$	16.0840	−	9.80377i	0.724388	−	0.441540i
$494$	−27.3563			−1.23082
$495$	3.02079	−	3.02079i	0.135774	−	0.135774i
$496$	0.189238	−	0.456861i	0.00849704	−	0.0205137i
$497$			0.555854i			0.0249335i
$498$	−3.59759	−	1.49017i	−0.161212	−	0.0667762i
$499$	−7.53159	−	18.1829i	−0.337160	−	0.813977i	−0.997986	−	0.0634373i	$-0.979794\pi$
$499$	−7.53159	−	18.1829i	−0.337160	−	0.813977i	0.660826	−	0.750540i	$-0.270206\pi$
$500$	0.923880	−	0.382683i	0.0413171	−	0.0171141i
$501$	9.42325	+	9.42325i	0.421000	+	0.421000i
$502$	−1.93464	−	1.93464i	−0.0863472	−	0.0863472i
$503$	−4.71622	+	1.95352i	−0.210286	+	0.0871032i	−0.485340	−	0.874326i	$-0.661304\pi$
$503$	−4.71622	+	1.95352i	−0.210286	+	0.0871032i	0.275054	+	0.961429i	$0.411304\pi$
$504$	0.103560	+	0.250016i	0.00461293	+	0.0111366i
$505$	9.80466	+	4.06122i	0.436302	+	0.180722i
$506$		−	6.91432i		−	0.307379i
$507$	−5.74121	+	13.8605i	−0.254976	+	0.615566i
$508$	−12.4567	+	12.4567i	−0.552675	+	0.552675i
$509$	42.8298			1.89840			0.949199	−	0.314677i	$-0.101896\pi$
$509$	42.8298			1.89840			0.949199	+	0.314677i	$0.101896\pi$
$510$	9.59972	+	7.00954i	0.425083	+	0.310388i
$511$	0.341425			0.0151038
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	16.3477	−	39.4668i	0.721767	−	1.74250i
$514$			2.22253i			0.0980315i
$515$	−5.98087	−	2.47736i	−0.263549	−	0.109166i
$516$	−2.70703	−	6.53536i	−0.119171	−	0.287703i
$517$	−6.11441	+	2.53267i	−0.268911	+	0.111387i
$518$	−0.0563102	−	0.0563102i	−0.00247413	−	0.00247413i
$519$	28.4714	+	28.4714i	1.24976	+	1.24976i
$520$	3.94183	−	1.63276i	0.172861	−	0.0716013i
$521$	−6.42569	−	15.5130i	−0.281515	−	0.679637i	0.718357	−	0.695675i	$-0.244895\pi$
$521$	−6.42569	−	15.5130i	−0.281515	−	0.679637i	−0.999871	+	0.0160384i	$0.994895\pi$
$522$	22.4167	+	9.28529i	0.981151	+	0.406406i
$523$			1.13554i			0.0496538i	0.999692	+	0.0248269i	$0.00790345\pi$
$523$			1.13554i			0.0496538i	−0.999692	+	0.0248269i	$0.992097\pi$
$524$	−5.98554	+	14.4504i	−0.261480	+	0.631267i
$525$	−0.103868	+	0.103868i	−0.00453319	+	0.00453319i
$526$	−25.4902			−1.11142
$527$	1.06118	+	1.74097i	0.0462257	+	0.0758377i
$528$	−2.31890			−0.100917
$529$	−35.9856	+	35.9856i	−1.56459	+	1.56459i
$530$	−4.21774	+	10.1825i	−0.183207	+	0.442300i
$531$		−	53.6235i		−	2.32706i
$532$	−0.301828	−	0.125021i	−0.0130859	−	0.00542036i
$533$	14.0661	+	33.9587i	0.609272	+	1.47091i
$534$	−45.4212	+	18.8141i	−1.96557	+	0.814164i
$535$	−10.3675	−	10.3675i	−0.448225	−	0.448225i
$536$	−0.581649	−	0.581649i	−0.0251234	−	0.0251234i
$537$	42.5942	−	17.6431i	1.83808	−	0.761356i
$538$	0.610716	+	1.47440i	0.0263298	+	0.0635659i
$539$	−5.20002	−	2.15392i	−0.223981	−	0.0927759i
$540$			6.66258i			0.286712i
$541$	5.08285	−	12.2711i	0.218529	−	0.527575i	−0.776156	−	0.630541i	$-0.782833\pi$
$541$	5.08285	−	12.2711i	0.218529	−	0.527575i	0.994685	+	0.102966i	$0.0328332\pi$
$542$	13.2012	−	13.2012i	0.567042	−	0.567042i
$543$	−8.24532			−0.353840
$544$	−0.635311	−	4.07387i	−0.0272387	−	0.174666i
$545$	3.86535			0.165573
$546$	−0.443166	+	0.443166i	−0.0189658	+	0.0189658i
$547$	−0.512357	+	1.23694i	−0.0219068	+	0.0528877i	−0.934454	−	0.356083i	$-0.884112\pi$
$547$	−0.512357	+	1.23694i	−0.0219068	+	0.0528877i	0.912548	+	0.408971i	$0.134112\pi$
$548$			17.3384i			0.740661i
$549$	30.4677	+	12.6201i	1.30033	+	0.538614i
$550$	−0.307817	−	0.743136i	−0.0131254	−	0.0316874i
$551$	−27.0622	+	11.2095i	−1.15289	+	0.477542i
$552$	17.5231	+	17.5231i	0.745831	+	0.745831i
$553$	0.296329	+	0.296329i	0.0126012	+	0.0126012i
$554$	−26.9671	+	11.1702i	−1.14572	+	0.474574i
$555$	−1.72425	−	4.16271i	−0.0731904	−	0.176697i
$556$	10.1867	+	4.21946i	0.432011	+	0.178945i
$557$		−	36.5401i		−	1.54825i	−0.633031	−	0.774127i	$-0.718189\pi$
$557$		−	36.5401i		−	1.54825i	0.633031	−	0.774127i	$-0.281811\pi$
$558$	−1.00506	+	2.42642i	−0.0425475	+	0.102719i
$559$	7.40276	−	7.40276i	0.313103	−	0.313103i
$560$	0.0509530			0.00215316
$561$	5.63823	−	7.72167i	0.238046	−	0.326009i
$562$	9.19377			0.387816
$563$	7.08309	−	7.08309i	0.298517	−	0.298517i	−0.541916	−	0.840433i	$-0.682301\pi$
$563$	7.08309	−	7.08309i	0.298517	−	0.298517i	0.840433	+	0.541916i	$0.182301\pi$
$564$	9.07725	−	21.9144i	0.382221	−	0.922764i
$565$		−	18.0739i		−	0.760374i
$566$	−0.309415	−	0.128164i	−0.0130057	−	0.00538712i
$567$	−0.0638447	−	0.154135i	−0.00268123	−	0.00647305i
$568$	10.0787	−	4.17475i	0.422895	−	0.175169i
$569$	8.63785	+	8.63785i	0.362118	+	0.362118i	0.864592	−	0.502474i	$-0.167577\pi$
$569$	8.63785	+	8.63785i	0.362118	+	0.362118i	−0.502474	+	0.864592i	$0.667577\pi$
$570$	−13.0704	−	13.0704i	−0.547457	−	0.547457i
$571$	−15.3745	+	6.36834i	−0.643405	+	0.266507i	−0.680436	−	0.732807i	$-0.738210\pi$
$571$	−15.3745	+	6.36834i	−0.643405	+	0.266507i	0.0370318	+	0.999314i	$0.488210\pi$
$572$	−1.31334	−	3.17067i	−0.0549133	−	0.132572i
$573$	38.0628	+	15.7661i	1.59010	+	0.658639i
$574$			0.438957i			0.0183217i
$575$	−3.28955	+	7.94167i	−0.137184	+	0.331191i
$576$	3.75550	−	3.75550i	0.156479	−	0.156479i
$577$	25.1510			1.04705			0.523525	−	0.852010i	$-0.324617\pi$
$577$	25.1510			1.04705			0.523525	+	0.852010i	$0.324617\pi$
$578$	15.1102	+	7.78979i	0.628503	+	0.324012i
$579$	25.2135			1.04784
$580$	3.23042	−	3.23042i	0.134136	−	0.134136i
$581$	0.0263377	−	0.0635848i	0.00109267	−	0.00263794i
$582$			9.21057i			0.381790i
$583$	8.19045	+	3.39260i	0.339214	+	0.140507i
$584$	−2.56428	−	6.19072i	−0.106111	−	0.256174i
$585$	−20.9354	+	8.67172i	−0.865571	+	0.358531i
$586$	−5.63063	−	5.63063i	−0.232599	−	0.232599i
$587$	21.9944	+	21.9944i	0.907808	+	0.907808i	0.996095	−	0.0882870i	$-0.0281393\pi$
$587$	21.9944	+	21.9944i	0.907808	+	0.907808i	−0.0882870	+	0.996095i	$0.528139\pi$
$588$	18.6372	−	7.71978i	0.768585	−	0.318359i
$589$	−1.21334	−	2.92926i	−0.0499948	−	0.120698i
$590$	−9.32799	−	3.86378i	−0.384027	−	0.159069i
$591$			36.0000i			1.48084i
$592$	−0.598098	+	1.44394i	−0.0245817	+	0.0593454i
$593$	−0.641202	+	0.641202i	−0.0263310	+	0.0263310i	−0.720150	−	0.693819i	$-0.755927\pi$
$593$	−0.641202	+	0.641202i	−0.0263310	+	0.0263310i	0.693819	+	0.720150i	$0.255927\pi$
$594$	5.35914			0.219888
$595$	−0.123888	+	0.169668i	−0.00507893	+	0.00695571i
$596$	−11.4114			−0.467429
$597$	−15.5927	+	15.5927i	−0.638165	+	0.638165i
$598$	−14.0352	+	33.8840i	−0.573943	+	1.38562i
$599$		−	12.8116i		−	0.523469i	−0.965140	−	0.261734i	$-0.915706\pi$
$599$		−	12.8116i		−	0.523469i	0.965140	−	0.261734i	$-0.0842944\pi$
$600$	2.66345	+	1.10324i	0.108735	+	0.0450394i
$601$	−9.94117	−	24.0001i	−0.405509	−	0.978985i	−0.986304	−	0.164935i	$-0.947258\pi$
$601$	−9.94117	−	24.0001i	−0.405509	−	0.978985i	0.580796	−	0.814049i	$-0.302742\pi$
$602$	0.115508	−	0.0478448i	0.00470774	−	0.00195001i
$603$	3.08918	+	3.08918i	0.125801	+	0.125801i
$604$	−4.48604	−	4.48604i	−0.182535	−	0.182535i
$605$	9.56492	−	3.96192i	0.388869	−	0.161075i
$606$	11.7081	+	28.2658i	0.475608	+	1.14822i
$607$	28.2966	+	11.7208i	1.14852	+	0.475734i	0.874038	−	0.485858i	$-0.161493\pi$
$607$	28.2966	+	11.7208i	1.14852	+	0.475734i	0.274485	+	0.961591i	$0.411493\pi$
$608$			6.41171i			0.260029i
$609$	−0.256810	+	0.619993i	−0.0104065	+	0.0251234i
$610$	4.39063	−	4.39063i	0.177771	−	0.177771i
$611$	35.1050			1.42020
$612$	3.37418	+	21.6366i	0.136393	+	0.874608i
$613$	−14.9109			−0.602244			−0.301122	−	0.953586i	$-0.597361\pi$
$613$	−14.9109			−0.602244			−0.301122	+	0.953586i	$0.597361\pi$
$614$	6.03730	−	6.03730i	0.243646	−	0.243646i
$615$	−9.50431	+	22.9454i	−0.383251	+	0.925249i
$616$		−	0.0409848i		−	0.00165132i
$617$	−27.6796	−	11.4653i	−1.11434	−	0.461575i	−0.251910	−	0.967751i	$-0.581059\pi$
$617$	−27.6796	−	11.4653i	−1.11434	−	0.461575i	−0.862430	+	0.506176i	$0.831059\pi$
$618$	−7.14196	−	17.2422i	−0.287292	−	0.693584i
$619$	−23.3334	+	9.66501i	−0.937848	+	0.388470i	−0.798651	−	0.601795i	$-0.794452\pi$
$619$	−23.3334	+	9.66501i	−0.937848	+	0.388470i	−0.139198	+	0.990265i	$0.544452\pi$
$620$	0.349666	+	0.349666i	0.0140429	+	0.0140429i
$621$	−40.4971	−	40.4971i	−1.62509	−	1.62509i
$622$	−5.19639	+	2.15242i	−0.208356	+	0.0863040i
$623$	−0.332525	−	0.802785i	−0.0133223	−	0.0321629i
$624$	11.3639	+	4.70708i	0.454920	+	0.188434i
$625$			1.00000i			0.0400000i
$626$	−0.170156	+	0.410794i	−0.00680081	+	0.0164186i
$627$	−10.5133	+	10.5133i	−0.419862	+	0.419862i
$628$	−15.7712			−0.629341
$629$	−3.35392	−	5.50242i	−0.133729	−	0.219396i
$630$	−0.270615			−0.0107816
$631$	−3.39306	+	3.39306i	−0.135076	+	0.135076i	−0.771412	−	0.636336i	$-0.780449\pi$
$631$	−3.39306	+	3.39306i	−0.135076	+	0.135076i	0.636336	+	0.771412i	$0.280449\pi$
$632$	3.14745	−	7.59862i	0.125199	−	0.302257i
$633$		−	10.9242i		−	0.434200i
$634$	1.56739	+	0.649236i	0.0622492	+	0.0257844i
$635$	−6.74150	−	16.2754i	−0.267528	−	0.645870i
$636$	−29.3551	+	12.1593i	−1.16401	+	0.482147i
$637$	21.1108	+	21.1108i	0.836441	+	0.836441i
$638$	−2.59843	−	2.59843i	−0.102873	−	0.102873i
$639$	−53.5289	+	22.1724i	−2.11757	+	0.877127i
$640$	−0.382683	−	0.923880i	−0.0151269	−	0.0365195i
$641$	12.0965	+	5.01052i	0.477781	+	0.197904i	0.608560	−	0.793508i	$-0.291748\pi$
$641$	12.0965	+	5.01052i	0.477781	+	0.197904i	−0.130778	+	0.991412i	$0.541748\pi$
$642$		−	42.2685i		−	1.66820i
$643$	−15.5696	+	37.5883i	−0.614004	+	1.48234i	0.244562	+	0.969634i	$0.421356\pi$
$643$	−15.5696	+	37.5883i	−0.614004	+	1.48234i	−0.858566	+	0.512703i	$0.828644\pi$
$644$	−0.309707	+	0.309707i	−0.0122042	+	0.0122042i
$645$	7.07382			0.278531
$646$	−21.3503	−	15.5896i	−0.840016	−	0.613365i
$647$	−6.37054			−0.250452			−0.125226	−	0.992128i	$-0.539966\pi$
$647$	−6.37054			−0.250452			−0.125226	+	0.992128i	$0.539966\pi$
$648$	−2.31526	+	2.31526i	−0.0909522	+	0.0909522i
$649$	−3.10789	+	7.50310i	−0.121995	+	0.294523i
$650$			4.26661i			0.167350i
$651$	−0.0671093	−	0.0277976i	−0.00263022	−	0.00108947i
$652$	−6.93275	−	16.7371i	−0.271507	−	0.655477i
$653$	−21.4786	+	8.89673i	−0.840523	+	0.348156i	−0.761060	−	0.648682i	$-0.775321\pi$
$653$	−21.4786	+	8.89673i	−0.840523	+	0.348156i	−0.0794631	+	0.996838i	$0.525321\pi$
$654$	7.87957	+	7.87957i	0.308116	+	0.308116i
$655$	−11.0598	−	11.0598i	−0.432144	−	0.432144i
$656$	7.95917	−	3.29679i	0.310753	−	0.128718i
$657$	13.6191	+	32.8794i	0.531331	+	1.28275i
$658$	0.387321	+	0.160434i	0.0150994	+	0.00625436i
$659$			20.8037i			0.810398i	0.914229	+	0.405199i	$0.132798\pi$
$659$			20.8037i			0.810398i	−0.914229	+	0.405199i	$0.867202\pi$
$660$	0.887404	−	2.14238i	0.0345421	−	0.0833921i
$661$	8.65808	−	8.65808i	0.336760	−	0.336760i	−0.518386	−	0.855147i	$-0.673467\pi$
$661$	8.65808	−	8.65808i	0.336760	−	0.336760i	0.855147	+	0.518386i	$0.173467\pi$
$662$	−17.1489			−0.666511
$663$	−43.3045	+	26.3956i	−1.68181	+	1.02512i
$664$	−1.35073			−0.0524184
$665$	0.231009	−	0.231009i	0.00895815	−	0.00895815i
$666$	3.17654	−	7.66885i	0.123088	−	0.297162i
$667$			39.2708i			1.52057i
$668$	4.27073	+	1.76899i	0.165240	+	0.0684445i
$669$	−16.5879	−	40.0466i	−0.641324	−	1.54829i
$670$	0.759962	−	0.314786i	0.0293599	−	0.0121613i
$671$	−3.53166	−	3.53166i	−0.136338	−	0.136338i
$672$	0.103868	+	0.103868i	0.00400681	+	0.00400681i
$673$	−31.2048	+	12.9254i	−1.20286	+	0.498239i	−0.891921	−	0.452192i	$-0.850642\pi$
$673$	−31.2048	+	12.9254i	−1.20286	+	0.498239i	−0.310936	+	0.950431i	$0.600642\pi$
$674$	12.4909	+	30.1556i	0.481130	+	1.16155i
$675$	−6.15542	−	2.54966i	−0.236922	−	0.0981364i
$676$			5.20397i			0.200153i
$677$	−4.90524	+	11.8423i	−0.188524	+	0.455136i	−0.989676	−	0.143325i	$-0.954221\pi$
$677$	−4.90524	+	11.8423i	−0.188524	+	0.455136i	0.801152	+	0.598461i	$0.204221\pi$
$678$	36.8438	−	36.8438i	1.41498	−	1.41498i
$679$	−0.162790			−0.00624730
$680$	4.00688	+	0.972050i	0.153657	+	0.0372764i
$681$	−3.07222			−0.117728
$682$	0.281259	−	0.281259i	0.0107700	−	0.0107700i
$683$	15.1051	−	36.4668i	0.577979	−	1.39536i	−0.316645	−	0.948544i	$-0.602556\pi$
$683$	15.1051	−	36.4668i	0.577979	−	1.39536i	0.894624	−	0.446820i	$-0.147444\pi$
$684$		−	34.0531i		−	1.30205i
$685$	−16.0186	−	6.63513i	−0.612040	−	0.253515i
$686$	0.272934	+	0.658920i	0.0104207	+	0.0251577i
$687$	9.45195	−	3.91513i	0.360614	−	0.149371i
$688$	−1.73504	−	1.73504i	−0.0661479	−	0.0661479i
$689$	−33.2512	−	33.2512i	−1.26677	−	1.26677i
$690$	−22.8950	+	9.48342i	−0.871597	+	0.361027i
$691$	4.09158	+	9.87795i	0.155651	+	0.375775i	0.982398	−	0.186799i	$-0.0598113\pi$
$691$	4.09158	+	9.87795i	0.155651	+	0.375775i	−0.826747	+	0.562574i	$0.809811\pi$
$692$	12.9036	+	5.34485i	0.490522	+	0.203181i
$693$			0.217673i			0.00826872i
$694$	10.1174	−	24.4256i	0.384052	−	0.927183i
$695$	−7.79655	+	7.79655i	−0.295740	+	0.295740i
$696$	13.1705			0.499226
$697$	−8.37415	+	34.5191i	−0.317194	+	1.30750i
$698$	−20.9568			−0.793228
$699$	−10.7361	+	10.7361i	−0.406078	+	0.406078i
$700$	−0.0194989	+	0.0470744i	−0.000736988	+	0.00177925i
$701$			4.10098i			0.154892i	0.996997	+	0.0774460i	$0.0246765\pi$
$701$			4.10098i			0.154892i	−0.996997	+	0.0774460i	$0.975323\pi$
$702$	−26.2628	−	10.8784i	−0.991225	−	0.410579i
$703$	3.83483	+	9.25810i	0.144633	+	0.349176i
$704$	−0.743136	+	0.307817i	−0.0280080	+	0.0116013i
$705$	16.7726	+	16.7726i	0.631692	+	0.631692i
$706$	−0.572208	−	0.572208i	−0.0215353	−	0.0215353i
$707$	−0.499577	+	0.206932i	−0.0187885	+	0.00778246i
$708$	−11.1389	−	26.8916i	−0.418624	−	1.01065i
$709$	13.6799	+	5.66639i	0.513759	+	0.212806i	0.624473	−	0.781046i	$-0.285314\pi$
$709$	13.6799	+	5.66639i	0.513759	+	0.212806i	−0.110714	+	0.993852i	$0.535314\pi$
$710$			10.9091i			0.409413i
$711$	−16.7163	+	40.3568i	−0.626912	+	1.51350i
$712$	−12.0587	+	12.0587i	−0.451918	+	0.451918i
$713$	−4.25075			−0.159192
$714$	−0.598419	+	0.0933221i	−0.0223953	+	0.00349249i
$715$	3.43191			0.128346
$716$	11.3082	−	11.3082i	0.422606	−	0.422606i
$717$	−2.30097	+	5.55504i	−0.0859314	+	0.207457i
$718$		−	4.31901i		−	0.161184i
$719$	20.0265	+	8.29523i	0.746861	+	0.309360i	0.723460	−	0.690366i	$-0.242551\pi$
$719$	20.0265	+	8.29523i	0.746861	+	0.309360i	0.0234008	+	0.999726i	$0.492551\pi$
$720$	2.03246	+	4.90679i	0.0757453	+	0.182865i
$721$	0.304744	−	0.126229i	0.0113492	−	0.00470101i
$722$	15.6342	+	15.6342i	0.581844	+	0.581844i
$723$	9.95736	+	9.95736i	0.370318	+	0.370318i
$724$	−2.64237	+	1.09451i	−0.0982030	+	0.0406770i
$725$	1.74829	+	4.22074i	0.0649298	+	0.156754i
$726$	27.5747	+	11.4218i	1.02339	+	0.423903i
$727$		−	28.3782i		−	1.05249i	−0.850333	−	0.526244i	$-0.823600\pi$
$727$		−	28.3782i		−	1.05249i	0.850333	−	0.526244i	$-0.176400\pi$
$728$	−0.0831941	+	0.200848i	−0.00308338	+	0.00744394i
$729$	−28.4487	+	28.4487i	−1.05366	+	1.05366i
$730$	6.70079			0.248007
$731$	9.99613	−	1.55888i	0.369720	−	0.0576571i
$732$	17.9007			0.661629
$733$	14.0314	−	14.0314i	0.518261	−	0.518261i	−0.398784	−	0.917045i	$-0.630568\pi$
$733$	14.0314	−	14.0314i	0.518261	−	0.518261i	0.917045	+	0.398784i	$0.130568\pi$
$734$	11.1717	−	26.9709i	0.412355	−	0.995512i
$735$			20.1728i			0.744084i
$736$	7.94167	+	3.28955i	0.292734	+	0.121254i
$737$	−0.253203	−	0.611286i	−0.00932685	−	0.0225170i
$738$	−42.2717	+	17.5095i	−1.55604	+	0.644534i
$739$	−15.3134	−	15.3134i	−0.563314	−	0.563314i	0.366933	−	0.930247i	$-0.380408\pi$
$739$	−15.3134	−	15.3134i	−0.563314	−	0.563314i	−0.930247	+	0.366933i	$0.880408\pi$
$740$	−1.10514	−	1.10514i	−0.0406258	−	0.0406258i
$741$	72.8620	−	30.1804i	2.67665	−	1.10871i
$742$	−0.214906	−	0.518830i	−0.00788946	−	0.0190468i
$743$	4.35374	+	1.80338i	0.159723	+	0.0661595i	0.461113	−	0.887342i	$-0.347450\pi$
$743$	4.35374	+	1.80338i	0.159723	+	0.0661595i	−0.301389	+	0.953501i	$0.597450\pi$
$744$			1.42560i			0.0522650i
$745$	4.36695	−	10.5427i	0.159993	−	0.386256i
$746$	−16.1633	+	16.1633i	−0.591782	+	0.591782i
$747$	7.17381			0.262476
$748$	0.781883	−	3.22300i	0.0285885	−	0.117844i
$749$	0.747064			0.0272971
$750$	−2.03851	+	2.03851i	−0.0744360	+	0.0744360i
$751$	−9.70037	+	23.4188i	−0.353971	+	0.854562i	0.642151	+	0.766579i	$0.278042\pi$
$751$	−9.70037	+	23.4188i	−0.353971	+	0.854562i	−0.996122	+	0.0879839i	$0.971958\pi$
$752$		−	8.22785i		−	0.300039i
$753$	7.28717	+	3.01845i	0.265559	+	0.109998i
$754$	7.45927	+	18.0083i	0.271650	+	0.655822i
$755$	5.86130	−	2.42783i	0.213314	−	0.0883578i
$756$	−0.240047	−	0.240047i	−0.00873044	−	0.00873044i
$757$	3.11150	+	3.11150i	0.113090	+	0.113090i	0.761387	−	0.648298i	$-0.224519\pi$
$757$	3.11150	+	3.11150i	0.113090	+	0.113090i	−0.648298	+	0.761387i	$0.724519\pi$
$758$	18.0134	−	7.46141i	0.654278	−	0.271011i
$759$	7.62812	+	18.4159i	0.276883	+	0.668456i
$760$	−5.92365	−	2.45366i	−0.214873	−	0.0890035i
$761$			12.4686i			0.451986i	0.974129	+	0.225993i	$0.0725627\pi$
$761$			12.4686i			0.451986i	−0.974129	+	0.225993i	$0.927437\pi$
$762$	19.4350	−	46.9203i	0.704056	−	1.69974i
$763$	−0.139266	+	0.139266i	−0.00504175	+	0.00504175i
$764$	14.2908			0.517023
$765$	−21.2809	−	5.16263i	−0.769411	−	0.186655i
$766$	19.4928			0.704302
$767$	30.4608	−	30.4608i	1.09987	−	1.09987i
$768$	1.10324	−	2.66345i	0.0398096	−	0.0961088i
$769$			21.0016i			0.757338i	0.925532	+	0.378669i	$0.123618\pi$
$769$			21.0016i			0.757338i	−0.925532	+	0.378669i	$0.876382\pi$
$770$	0.0378650	+	0.0156842i	0.00136456	+	0.000565219i
$771$	−2.45197	−	5.91958i	−0.0883056	−	0.213188i
$772$	8.08015	−	3.34691i	0.290811	−	0.120458i
$773$	−0.238588	−	0.238588i	−0.00858143	−	0.00858143i	0.702803	−	0.711384i	$-0.251932\pi$
$773$	−0.238588	−	0.238588i	−0.00858143	−	0.00858143i	−0.711384	+	0.702803i	$0.751932\pi$
$774$	9.21494	+	9.21494i	0.331224	+	0.331224i
$775$	−0.456861	+	0.189238i	−0.0164109	+	0.00679763i
$776$	1.22264	+	2.95171i	0.0438901	+	0.105960i
$777$	0.212103	+	0.0878558i	0.00760914	+	0.00315181i
$778$			5.18611i			0.185931i
$779$	21.1381	−	51.0319i	0.757351	−	1.82841i
$780$	−8.69754	+	8.69754i	−0.311422	+	0.311422i
$781$	8.77493			0.313992
$782$	−30.2634	+	18.4466i	−1.08222	+	0.659649i
$783$	−30.4380			−1.08776
$784$	4.94791	−	4.94791i	0.176711	−	0.176711i
$785$	6.03539	−	14.5707i	0.215412	−	0.520051i
$786$		−	45.0912i		−	1.60835i
$787$	−17.5495	−	7.26922i	−0.625570	−	0.259120i	0.0472993	−	0.998881i	$-0.484939\pi$
$787$	−17.5495	−	7.26922i	−0.625570	−	0.259120i	−0.672870	+	0.739761i	$0.734939\pi$
$788$	4.77874	+	11.5369i	0.170236	+	0.410985i
$789$	67.8917	−	28.1217i	2.41701	−	1.00116i
$790$	5.81573	+	5.81573i	0.206915	+	0.206915i
$791$	0.651188	+	0.651188i	0.0231536	+	0.0231536i
$792$	3.94685	−	1.63484i	0.140245	−	0.0580915i
$793$	10.1383	+	24.4760i	0.360021	+	0.869167i
$794$	−13.0882	−	5.42131i	−0.464483	−	0.192395i
$795$		−	31.7737i		−	1.12690i
$796$	−2.92716	+	7.06678i	−0.103750	+	0.250476i
$797$	27.7507	−	27.7507i	0.982981	−	0.982981i	−0.0168766	−	0.999858i	$-0.505372\pi$
$797$	27.7507	−	27.7507i	0.982981	−	0.982981i	0.999858	+	0.0168766i	$0.00537225\pi$
$798$	0.941830			0.0333404
$799$	27.3978	+	20.0054i	0.969265	+	0.707740i
$800$	1.00000			0.0353553
$801$	64.0445	−	64.0445i	2.26290	−	2.26290i
$802$	4.68513	−	11.3109i	0.165438	−	0.399402i
$803$		−	5.38988i		−	0.190205i
$804$	2.19089	+	0.907496i	0.0772667	+	0.0320049i
$805$	−0.167612	−	0.404652i	−0.00590756	−	0.0142621i
$806$	−1.94925	+	0.807405i	−0.0686594	+	0.0284396i
$807$	−3.25322	−	3.25322i	−0.114519	−	0.114519i
$808$	7.50416	+	7.50416i	0.263996	+	0.263996i
$809$	−48.6210	+	20.1395i	−1.70942	+	0.708066i	−0.709429	+	0.704777i	$0.751047\pi$
$809$	−48.6210	+	20.1395i	−1.70942	+	0.708066i	−0.999995	+	0.00328894i	$0.998953\pi$
$810$	−1.25301	−	3.02504i	−0.0440264	−	0.106289i
$811$	−29.2374	−	12.1105i	−1.02667	−	0.425259i	−0.195158	−	0.980772i	$-0.562522\pi$
$811$	−29.2374	−	12.1105i	−1.02667	−	0.425259i	−0.831508	+	0.555513i	$0.812522\pi$
$812$			0.232779i			0.00816893i
$813$	−20.5967	+	49.7249i	−0.722358	+	1.74393i
$814$	−0.888936	+	0.888936i	−0.0311572	+	0.0311572i
$815$	18.1161			0.634581
$816$	6.18655	+	10.1496i	0.216573	+	0.355308i
$817$	−15.7326			−0.550413
$818$	21.1558	−	21.1558i	0.739694	−	0.739694i
$819$	0.441850	−	1.06672i	0.0154395	−	0.0372742i
$820$			8.61494i			0.300847i
$821$	46.7664	+	19.3713i	1.63216	+	0.676062i	0.995471	−	0.0950605i	$-0.0303045\pi$
$821$	46.7664	+	19.3713i	1.63216	+	0.676062i	0.636687	+	0.771123i	$0.280304\pi$
$822$	−19.1284	−	46.1799i	−0.667178	−	1.61071i
$823$	−11.5618	+	4.78907i	−0.403021	+	0.166937i	−0.574980	−	0.818167i	$-0.694990\pi$
$823$	−11.5618	+	4.78907i	−0.403021	+	0.166937i	0.171959	+	0.985104i	$0.444990\pi$
$824$	−4.57756	−	4.57756i	−0.159467	−	0.159467i
$825$	1.63971	+	1.63971i	0.0570873	+	0.0570873i
$826$	0.475289	−	0.196871i	0.0165374	−	0.00685002i
$827$	1.01832	+	2.45843i	0.0354103	+	0.0854881i	0.940595	−	0.339530i	$-0.110268\pi$
$827$	1.01832	+	2.45843i	0.0354103	+	0.0854881i	−0.905185	+	0.425018i	$0.860268\pi$
$828$	−42.1788	−	17.4710i	−1.46581	−	0.607160i
$829$			52.0086i			1.80633i	0.429290	+	0.903167i	$0.358764\pi$
$829$			52.0086i			1.80633i	−0.429290	+	0.903167i	$0.641236\pi$
$830$	0.516901	−	1.24791i	0.0179419	−	0.0433156i
$831$	59.5022	−	59.5022i	2.06411	−	2.06411i
$832$	4.26661			0.147918
$833$	4.44552	+	28.5065i	0.154028	+	0.987691i
$834$	−31.7867			−1.10068
$835$	−3.26868	+	3.26868i	−0.113117	+	0.113117i
$836$	−1.97363	+	4.76477i	−0.0682596	+	0.164793i
$837$		−	3.29466i		−	0.113880i
$838$	8.50159	+	3.52147i	0.293683	+	0.121647i
$839$	3.37778	+	8.15467i	0.116614	+	0.281531i	0.971400	−	0.237450i	$-0.0763116\pi$
$839$	3.37778	+	8.15467i	0.116614	+	0.281531i	−0.854786	+	0.518981i	$0.826312\pi$
$840$	−0.135711	+	0.0562132i	−0.00468246	+	0.00193954i
$841$	−5.74795	−	5.74795i	−0.198205	−	0.198205i
$842$	−25.5473	−	25.5473i	−0.880417	−	0.880417i
$843$	−24.4871	+	10.1429i	−0.843381	+	0.349340i
$844$	−1.45012	−	3.50089i	−0.0499151	−	0.120506i
$845$	−4.80784	−	1.99147i	−0.165395	−	0.0685088i
$846$			43.6987i			1.50239i
$847$	−0.201872	+	0.487362i	−0.00693640	+	0.0167459i
$848$	−7.79336	+	7.79336i	−0.267625	+	0.267625i
$849$	0.965504			0.0331360
$850$	−2.43143	+	3.32989i	−0.0833972	+	0.114214i
$851$	13.4347			0.460537
$852$	−22.2384	+	22.2384i	−0.761877	+	0.761877i
$853$	−2.74760	+	6.63328i	−0.0940759	+	0.227119i	−0.963912	−	0.266222i	$-0.914225\pi$
$853$	−2.74760	+	6.63328i	−0.0940759	+	0.227119i	0.869836	+	0.493341i	$0.164225\pi$
$854$			0.316382i			0.0108264i
$855$	31.4609	+	13.0315i	1.07594	+	0.445670i
$856$	−5.61084	−	13.5458i	−0.191774	−	0.462984i
$857$	21.8316	−	9.04294i	0.745753	−	0.308901i	0.0227457	−	0.999741i	$-0.492759\pi$
$857$	21.8316	−	9.04294i	0.745753	−	0.308901i	0.723007	+	0.690840i	$0.242759\pi$
$858$	6.99600	+	6.99600i	0.238839	+	0.238839i
$859$	−31.5996	−	31.5996i	−1.07816	−	1.07816i	−0.996674	−	0.0814888i	$-0.974033\pi$
$859$	−31.5996	−	31.5996i	−1.07816	−	1.07816i	−0.0814888	−	0.996674i	$-0.525967\pi$
$860$	2.26694	−	0.938999i	0.0773021	−	0.0320196i
$861$	−0.484273	−	1.16914i	−0.0165040	−	0.0398441i
$862$	−19.9808	−	8.27632i	−0.680549	−	0.281893i
$863$			8.63241i			0.293851i	0.989148	+	0.146925i	$0.0469377\pi$
$863$			8.63241i			0.293851i	−0.989148	+	0.146925i	$0.953062\pi$
$864$	−2.54966	+	6.15542i	−0.0867411	+	0.209412i
$865$	−9.87599	+	9.87599i	−0.335794	+	0.335794i
$866$	−18.1889			−0.618084
$867$	−48.8393	−	4.07753i	−1.65867	−	0.138480i
$868$	−0.0251964			−0.000855222
$869$	4.67797	−	4.67797i	0.158689	−	0.158689i
$870$	−5.04013	+	12.1679i	−0.170876	+	0.412532i
$871$			3.50961i			0.118919i
$872$	3.57112	+	1.47921i	0.120933	+	0.0500922i
$873$	−6.49351	−	15.6767i	−0.219772	−	0.530577i
$874$	50.9197	−	21.0916i	1.72239	−	0.713435i
$875$	−0.0360292	−	0.0360292i	−0.00121801	−	0.00121801i
$876$	13.6596	+	13.6596i	0.461517	+	0.461517i
$877$	34.2801	−	14.1993i	1.15756	−	0.479476i	0.280496	−	0.959855i	$-0.409501\pi$
$877$	34.2801	−	14.1993i	1.15756	−	0.479476i	0.877061	+	0.480379i	$0.159501\pi$
$878$	10.1644	+	24.5389i	0.343030	+	0.828148i
$879$	21.2088	+	8.78497i	0.715355	+	0.296310i
$880$		−	0.804365i		−	0.0271151i
$881$	−7.55523	+	18.2399i	−0.254542	+	0.614519i	−0.998560	−	0.0536402i	$-0.982918\pi$
$881$	−7.55523	+	18.2399i	−0.254542	+	0.614519i	0.744018	+	0.668159i	$0.232918\pi$
$882$	−26.2787	+	26.2787i	−0.884851	+	0.884851i
$883$	−24.5536			−0.826296			−0.413148	−	0.910664i	$-0.635571\pi$
$883$	−24.5536			−0.826296			−0.413148	+	0.910664i	$0.635571\pi$
$884$	−10.3739	+	14.2073i	−0.348914	+	0.477845i
$885$	29.1073			0.978430
$886$	−20.1802	+	20.1802i	−0.677967	+	0.677967i
$887$	−2.96436	+	7.15660i	−0.0995334	+	0.240295i	−0.965801	−	0.259286i	$-0.916513\pi$
$887$	−2.96436	+	7.15660i	−0.0995334	+	0.240295i	0.866267	+	0.499581i	$0.166513\pi$
$888$		−	4.50569i		−	0.151201i
$889$	0.829281	+	0.343500i	0.0278132	+	0.0115206i
$890$	−6.52610	−	15.7554i	−0.218755	−	0.528122i
$891$	−2.43323	+	1.00788i	−0.0815164	+	0.0337652i
$892$	−10.6318	−	10.6318i	−0.355979	−	0.355979i
$893$	−37.3031	−	37.3031i	−1.24830	−	1.24830i
$894$	30.3936	−	12.5894i	1.01651	−	0.421054i
$895$	6.11993	+	14.7748i	0.204567	+	0.493868i
$896$	0.0470744	+	0.0194989i	0.00157265	+	0.000651412i
$897$		−	105.732i		−	3.53030i
$898$	−9.46340	+	22.8467i	−0.315798	+	0.762403i
$899$	−1.59745	+	1.59745i	−0.0532779	+	0.0532779i
$900$	−5.31107			−0.177036
$901$	−7.00206	−	44.9000i	−0.233272	−	1.49584i
$902$	6.92955			0.230729
$903$	−0.254864	+	0.254864i	−0.00848135	+	0.00848135i
$904$	6.91657	−	16.6981i	0.230042	−	0.555370i
$905$		−	2.86008i		−	0.0950724i
$906$	16.8975	+	6.99917i	0.561382	+	0.232532i
$907$	−6.31292	−	15.2407i	−0.209617	−	0.506060i	0.783746	−	0.621081i	$-0.213306\pi$
$907$	−6.31292	−	15.2407i	−0.209617	−	0.506060i	−0.993363	+	0.115021i	$0.963306\pi$
$908$	−0.984554	+	0.407816i	−0.0326736	+	0.0135338i
$909$	−39.8552	−	39.8552i	−1.32191	−	1.32191i
$910$	−0.153723	−	0.153723i	−0.00509586	−	0.00509586i
$911$	−27.2844	+	11.3016i	−0.903974	+	0.374438i	−0.785747	−	0.618548i	$-0.787721\pi$
$911$	−27.2844	+	11.3016i	−0.903974	+	0.374438i	−0.118227	+	0.992987i	$0.537721\pi$
$912$	−7.07363	−	17.0773i	−0.234231	−	0.565484i
$913$	−1.00377	−	0.415777i	−0.0332201	−	0.0137602i
$914$			7.32892i			0.242419i
$915$	−6.85030	+	16.5381i	−0.226464	+	0.546732i
$916$	2.50936	−	2.50936i	0.0829115	−	0.0829115i
$917$	0.796955			0.0263178
$918$	−14.2976	−	23.4565i	−0.471890	−	0.774181i
$919$	−24.9725			−0.823767			−0.411884	−	0.911236i	$-0.635129\pi$
$919$	−24.9725			−0.823767			−0.411884	+	0.911236i	$0.635129\pi$
$920$	−6.07829	+	6.07829i	−0.200395	+	0.200395i
$921$	−9.41946	+	22.7406i	−0.310382	+	0.749328i
$922$			3.60953i			0.118874i
$923$	−43.0021	−	17.8120i	−1.41543	−	0.586290i
$924$	0.0452159	+	0.109161i	0.00148749	+	0.00359113i
$925$	1.44394	−	0.598098i	0.0474763	−	0.0196653i
$926$	26.3814	+	26.3814i	0.866946	+	0.866946i
$927$	24.3118	+	24.3118i	0.798503	+	0.798503i
$928$	4.22074	−	1.74829i	0.138553	−	0.0573904i
$929$	−6.69633	−	16.1664i	−0.219699	−	0.530401i	0.775149	−	0.631779i	$-0.217675\pi$
$929$	−6.69633	−	16.1664i	−0.219699	−	0.530401i	−0.994848	+	0.101378i	$0.967675\pi$
$930$	−1.31708	−	0.545553i	−0.0431888	−	0.0178894i
$931$		−	44.8653i		−	1.47040i
$932$	−2.01546	+	4.86575i	−0.0660185	+	0.159383i
$933$	11.4657	−	11.4657i	0.375370	−	0.375370i
$934$	−15.9697			−0.522545
$935$	2.67845	+	1.95575i	0.0875945	+	0.0639600i
$936$	−22.6603			−0.740675
$937$	−34.0590	+	34.0590i	−1.11266	+	1.11266i	−0.119869	+	0.992790i	$0.538247\pi$
$937$	−34.0590	+	34.0590i	−1.11266	+	1.11266i	−0.992790	+	0.119869i	$0.961753\pi$
$938$	−0.0160393	+	0.0387223i	−0.000523702	+	0.00126433i
$939$		−	1.28185i		−	0.0418316i
$940$	7.60154	+	3.14866i	0.247935	+	0.102698i
$941$	−0.0516215	−	0.124625i	−0.00168281	−	0.00406267i	0.923036	−	0.384714i	$-0.125700\pi$
$941$	−0.0516215	−	0.124625i	−0.00168281	−	0.00406267i	−0.924719	+	0.380651i	$0.875700\pi$
$942$	42.0058	−	17.3994i	1.36862	−	0.566902i
$943$	−52.3641	−	52.3641i	−1.70521	−	1.70521i
$944$	−7.13933	−	7.13933i	−0.232366	−	0.232366i
$945$	0.313637	−	0.129913i	0.0102026	−	0.00422606i
$946$	−0.755297	−	1.82345i	−0.0245568	−	0.0592855i
$947$	−4.06279	−	1.68286i	−0.132023	−	0.0546857i	0.315694	−	0.948861i	$-0.397763\pi$
$947$	−4.06279	−	1.68286i	−0.132023	−	0.0546857i	−0.447717	+	0.894175i	$0.647763\pi$
$948$			23.7109i			0.770094i
$949$	−10.9408	+	26.4134i	−0.355153	+	0.857415i
$950$	4.53377	−	4.53377i	0.147095	−	0.147095i
$951$	−4.89093			−0.158599
$952$	−0.179387	+	0.109343i	−0.00581397	+	0.00354382i
$953$	−42.0828			−1.36320			−0.681598	−	0.731727i	$-0.738715\pi$
$953$	−42.0828			−1.36320			−0.681598	+	0.731727i	$0.738715\pi$
$954$	41.3911	−	41.3911i	1.34009	−	1.34009i
$955$	−5.46885	+	13.2030i	−0.176968	+	0.427238i
$956$			2.08566i			0.0674550i
$957$	9.78746	+	4.05410i	0.316384	+	0.131050i
$958$	2.55857	+	6.17694i	0.0826638	+	0.199568i
$959$	0.816196	−	0.338080i	0.0263564	−	0.0109172i
$960$	2.03851	+	2.03851i	0.0657927	+	0.0657927i
$961$	21.7474	+	21.7474i	0.701529	+	0.701529i
$962$	6.16071	−	2.55185i	0.198629	−	0.0822749i
$963$	29.7996	+	71.9425i	0.960277	+	2.31831i
$964$	4.51280	+	1.86926i	0.145347	+	0.0602049i
$965$			8.74589i			0.281540i
$966$	0.483209	−	1.16657i	0.0155470	−	0.0375337i
$967$	13.0357	−	13.0357i	0.419201	−	0.419201i	−0.465727	−	0.884928i	$-0.654207\pi$
$967$	13.0357	−	13.0357i	0.419201	−	0.419201i	0.884928	+	0.465727i	$0.154207\pi$
$968$	10.3530			0.332758
$969$	74.0644	+	17.9677i	2.37929	+	0.577204i
$970$	−3.19490			−0.102582
$971$	2.66396	−	2.66396i	0.0854905	−	0.0854905i	−0.663068	−	0.748559i	$-0.730746\pi$
$971$	2.66396	−	2.66396i	0.0854905	−	0.0854905i	0.748559	+	0.663068i	$0.230746\pi$
$972$	−4.03667	+	9.74539i	−0.129476	+	0.312584i
$973$		−	0.561807i		−	0.0180107i
$974$	26.8779	+	11.1332i	0.861225	+	0.356731i
$975$	−4.70708	−	11.3639i	−0.150747	−	0.363936i
$976$	5.73663	−	2.37619i	0.183625	−	0.0760600i
$977$	29.7970	+	29.7970i	0.953290	+	0.953290i	0.998957	−	0.0456670i	$-0.0145413\pi$
$977$	29.7970	+	29.7970i	0.953290	+	0.953290i	−0.0456670	+	0.998957i	$0.514541\pi$
$978$	36.9300	+	36.9300i	1.18089	+	1.18089i
$979$	−12.6731	+	5.24937i	−0.405034	+	0.167770i
$980$	2.67779	+	6.46476i	0.0855389	+	0.206509i
$981$	−18.9665	−	7.85617i	−0.605553	−	0.250828i
$982$			26.1311i			0.833875i
$983$	9.13655	−	22.0576i	0.291411	−	0.703527i	−0.708587	−	0.705623i	$-0.750667\pi$
$983$	9.13655	−	22.0576i	0.291411	−	0.703527i	0.999998	+	0.00209587i	$0.000667138\pi$
$984$	−17.5617	+	17.5617i	−0.559845	+	0.559845i
$985$	−12.4875			−0.397883
$986$	−4.44081	+	18.3054i	−0.141424	+	0.582964i
$987$	−1.20861			−0.0384703
$988$	19.3438	−	19.3438i	0.615409	−	0.615409i
$989$	−8.07164	+	19.4867i	−0.256663	+	0.619640i
$990$			4.27204i			0.135774i
$991$	37.1719	+	15.3971i	1.18080	+	0.489105i	0.884750	−	0.466066i	$-0.154329\pi$
$991$	37.1719	+	15.3971i	1.18080	+	0.489105i	0.296054	+	0.955171i	$0.404329\pi$
$992$	0.189238	+	0.456861i	0.00600831	+	0.0145054i
$993$	45.6752	−	18.9193i	1.44946	−	0.600385i
$994$	−0.393048	−	0.393048i	−0.0124667	−	0.0124667i
$995$	−5.40868	−	5.40868i	−0.171467	−	0.171467i
$996$	3.59759	−	1.49017i	0.113994	−	0.0472179i
$997$	7.73984	+	18.6856i	0.245123	+	0.591780i	0.997777	−	0.0666363i	$-0.0212267\pi$
$997$	7.73984	+	18.6856i	0.245123	+	0.591780i	−0.752654	+	0.658416i	$0.771227\pi$
$998$	18.1829	+	7.53159i	0.575569	+	0.238408i
$999$			10.4130i			0.329452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.161.4	yes	16
5.2	odd	4		850.2.o.j.399.1		16
5.3	odd	4		850.2.o.g.399.4		16
5.4	even	2		850.2.l.e.501.1		16
17.6	odd	16		2890.2.b.r.2311.1		16
17.7	odd	16		2890.2.a.bi.1.1		8
17.10	odd	16		2890.2.a.bj.1.8		8
17.11	odd	16		2890.2.b.r.2311.16		16
17.15	even	8	inner	170.2.k.b.151.4	✓	16
85.32	odd	8		850.2.o.g.49.4		16
85.49	even	8		850.2.l.e.151.1		16
85.83	odd	8		850.2.o.j.49.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.151.4	✓	16	17.15	even	8	inner
170.2.k.b.161.4	yes	16	1.1	even	1	trivial
850.2.l.e.151.1		16	85.49	even	8
850.2.l.e.501.1		16	5.4	even	2
850.2.o.g.49.4		16	85.32	odd	8
850.2.o.g.399.4		16	5.3	odd	4
850.2.o.j.49.1		16	85.83	odd	8
850.2.o.j.399.1		16	5.2	odd	4
2890.2.a.bi.1.1		8	17.7	odd	16
2890.2.a.bj.1.8		8	17.10	odd	16
2890.2.b.r.2311.1		16	17.6	odd	16
2890.2.b.r.2311.16		16	17.11	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.10324 - 2.66345i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(1.10324 + 2.66345i) q^{6} +(-0.0470744 + 0.0194989i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.75550 - 3.75550i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.10324 - 2.66345i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(1.10324 + 2.66345i) q^{6} +(-0.0470744 + 0.0194989i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.75550 - 3.75550i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(0.307817 + 0.743136i) q^{11} +(-2.66345 - 1.10324i) q^{12} -4.26661i q^{13} +(0.0194989 - 0.0470744i) q^{14} +(2.03851 - 2.03851i) q^{15} -1.00000 q^{16} +(2.43143 - 3.32989i) q^{17} +5.31107 q^{18} +(-4.53377 + 4.53377i) q^{19} +(0.382683 - 0.923880i) q^{20} +0.146892i q^{21} +(-0.743136 - 0.307817i) q^{22} +(3.28955 + 7.94167i) q^{23} +(2.66345 - 1.10324i) q^{24} +(0.707107 + 0.707107i) q^{25} +(3.01695 + 3.01695i) q^{26} +(-6.15542 + 2.54966i) q^{27} +(0.0194989 + 0.0470744i) q^{28} +(4.22074 + 1.74829i) q^{29} +2.88289i q^{30} +(-0.189238 + 0.456861i) q^{31} +(0.707107 - 0.707107i) q^{32} +2.31890 q^{33} +(0.635311 + 4.07387i) q^{34} -0.0509530 q^{35} +(-3.75550 + 3.75550i) q^{36} +(0.598098 - 1.44394i) q^{37} -6.41171i q^{38} +(-11.3639 - 4.70708i) q^{39} +(0.382683 + 0.923880i) q^{40} +(-7.95917 + 3.29679i) q^{41} +(-0.103868 - 0.103868i) q^{42} +(1.73504 + 1.73504i) q^{43} +(0.743136 - 0.307817i) q^{44} +(-2.03246 - 4.90679i) q^{45} +(-7.94167 - 3.28955i) q^{46} +8.22785i q^{47} +(-1.10324 + 2.66345i) q^{48} +(-4.94791 + 4.94791i) q^{49} -1.00000 q^{50} +(-6.18655 - 10.1496i) q^{51} -4.26661 q^{52} +(7.79336 - 7.79336i) q^{53} +(2.54966 - 6.15542i) q^{54} +0.804365i q^{55} +(-0.0470744 - 0.0194989i) q^{56} +(7.07363 + 17.0773i) q^{57} +(-4.22074 + 1.74829i) q^{58} +(7.13933 + 7.13933i) q^{59} +(-2.03851 - 2.03851i) q^{60} +(-5.73663 + 2.37619i) q^{61} +(-0.189238 - 0.456861i) q^{62} +(0.250016 + 0.103560i) q^{63} +1.00000i q^{64} +(1.63276 - 3.94183i) q^{65} +(-1.63971 + 1.63971i) q^{66} -0.822577 q^{67} +(-3.32989 - 2.43143i) q^{68} +24.7814 q^{69} +(0.0360292 - 0.0360292i) q^{70} +(4.17475 - 10.0787i) q^{71} -5.31107i q^{72} +(-6.19072 - 2.56428i) q^{73} +(0.598098 + 1.44394i) q^{74} +(2.66345 - 1.10324i) q^{75} +(4.53377 + 4.53377i) q^{76} +(-0.0289806 - 0.0289806i) q^{77} +(11.3639 - 4.70708i) q^{78} +(-3.14745 - 7.59862i) q^{79} +(-0.923880 - 0.382683i) q^{80} +3.27428i q^{81} +(3.29679 - 7.95917i) q^{82} +(-0.955109 + 0.955109i) q^{83} +0.146892 q^{84} +(3.52064 - 2.14595i) q^{85} -2.45372 q^{86} +(9.31294 - 9.31294i) q^{87} +(-0.307817 + 0.743136i) q^{88} +17.0535i q^{89} +(4.90679 + 2.03246i) q^{90} +(0.0831941 + 0.200848i) q^{91} +(7.94167 - 3.28955i) q^{92} +(1.00805 + 1.00805i) q^{93} +(-5.81797 - 5.81797i) q^{94} +(-5.92365 + 2.45366i) q^{95} +(-1.10324 - 2.66345i) q^{96} +(2.95171 + 1.22264i) q^{97} -6.99740i q^{98} +(1.63484 - 3.94685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

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