LMFDB - Embedded newform 850.2.v.d.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(107,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("850.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.v (of order $16$, degree $8$, 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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			143.4
Character	$\chi$	$=$	850.143
Dual form			850.2.v.d.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.923880i) q^{2} +(1.27477 - 0.253568i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(0.722100 + 1.08070i) q^{6} +(0.128721 + 0.192645i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.21089 + 0.501569i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.923880i) q^{2} +(1.27477 - 0.253568i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(0.722100 + 1.08070i) q^{6} +(0.128721 + 0.192645i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.21089 + 0.501569i) q^{9} +(-3.12235 + 2.08629i) q^{11} +(-0.722100 + 1.08070i) q^{12} +6.31661 q^{13} +(-0.128721 + 0.192645i) q^{14} -1.00000i q^{16} +(2.15330 + 3.51615i) q^{17} +(-0.926779 - 0.926779i) q^{18} +(5.28368 + 2.18857i) q^{19} +(0.212939 + 0.212939i) q^{21} +(-3.12235 - 2.08629i) q^{22} +(-1.67699 + 8.43077i) q^{23} +(-1.27477 - 0.253568i) q^{24} +(2.41726 + 5.83578i) q^{26} +(-4.65853 + 3.11273i) q^{27} +(-0.227241 - 0.0452010i) q^{28} +(0.221089 + 1.11149i) q^{29} +(-1.28229 - 0.856800i) q^{31} +(0.923880 - 0.382683i) q^{32} +(-3.45127 + 3.45127i) q^{33} +(-2.42446 + 3.33496i) q^{34} +(0.501569 - 1.21089i) q^{36} +(-0.0492911 - 0.247803i) q^{37} +5.71901i q^{38} +(8.05222 - 1.60169i) q^{39} +(1.06798 - 5.36909i) q^{41} +(-0.115242 + 0.278218i) q^{42} +(3.68348 - 8.89270i) q^{43} +(0.732607 - 3.68307i) q^{44} +(-8.43077 + 1.67699i) q^{46} +4.58562i q^{47} +(-0.253568 - 1.27477i) q^{48} +(2.65824 - 6.41756i) q^{49} +(3.63655 + 3.93627i) q^{51} +(-4.46651 + 4.46651i) q^{52} +(5.77959 - 2.39399i) q^{53} +(-4.65853 - 3.11273i) q^{54} +(-0.0452010 - 0.227241i) q^{56} +(7.29043 + 1.45016i) q^{57} +(-0.942276 + 0.629608i) q^{58} +(-0.547416 - 1.32158i) q^{59} +(-10.1829 - 2.02550i) q^{61} +(0.300868 - 1.51257i) q^{62} +(-0.252493 - 0.168710i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-4.50930 - 1.86781i) q^{66} +(0.973313 + 0.973313i) q^{67} +(-4.00891 - 0.963677i) q^{68} +11.1725i q^{69} +(-1.06710 + 1.59702i) q^{71} +1.31066 q^{72} +(1.07259 - 1.60525i) q^{73} +(0.210077 - 0.140369i) q^{74} +(-5.28368 + 2.18857i) q^{76} +(-0.803827 - 0.332956i) q^{77} +(4.56122 + 6.82635i) q^{78} +(0.466756 + 0.698549i) q^{79} +(-2.36893 + 2.36893i) q^{81} +(5.36909 - 1.06798i) q^{82} +(-5.53052 - 13.3518i) q^{83} -0.301141 q^{84} +9.62539 q^{86} +(0.563676 + 1.36083i) q^{87} +(3.68307 - 0.732607i) q^{88} +(-9.96203 + 9.96203i) q^{89} +(0.813083 + 1.21686i) q^{91} +(-4.77565 - 7.14727i) q^{92} +(-1.85189 - 0.767076i) q^{93} +(-4.23656 + 1.75484i) q^{94} +(1.08070 - 0.722100i) q^{96} +(-2.79946 + 4.18968i) q^{97} +6.94632 q^{98} +(2.73442 - 4.09235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53} - 24 q^{54} - 8 q^{56} + 120 q^{57} - 16 q^{58} + 24 q^{61} + 8 q^{62} + 24 q^{63} - 16 q^{67} + 24 q^{71} - 56 q^{72} - 88 q^{73} + 32 q^{74} - 24 q^{77} - 32 q^{78} - 104 q^{79} + 48 q^{81} - 16 q^{82} - 16 q^{83} + 96 q^{86} - 136 q^{87} - 16 q^{89} + 48 q^{91} + 8 q^{92} + 8 q^{93} - 8 q^{94} - 16 q^{97} - 72 q^{98} + 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$3$	1.27477	−	0.253568i	0.735989	−	0.146397i	0.187157	−	0.982330i	$-0.440073\pi$
$3$	1.27477	−	0.253568i	0.735989	−	0.146397i	0.548832	+	0.835933i	$0.315073\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	0.722100	+	1.08070i	0.294796	+	0.441193i
$7$	0.128721	+	0.192645i	0.0486521	+	0.0728131i	0.854998	−	0.518631i	$-0.173558\pi$
$7$	0.128721	+	0.192645i	0.0486521	+	0.0728131i	−0.806346	+	0.591444i	$0.798558\pi$
$8$	−0.923880	−	0.382683i	−0.326641	−	0.135299i
$9$	−1.21089	+	0.501569i	−0.403632	+	0.167190i
$10$		0			0
$11$	−3.12235	+	2.08629i	−0.941425	+	0.629040i	−0.928681	−	0.370879i	$-0.879056\pi$
$11$	−3.12235	+	2.08629i	−0.941425	+	0.629040i	−0.0127435	+	0.999919i	$0.504056\pi$
$12$	−0.722100	+	1.08070i	−0.208452	+	0.311971i
$13$	6.31661			1.75191			0.875956	−	0.482392i	$-0.160232\pi$
$13$	6.31661			1.75191			0.875956	+	0.482392i	$0.160232\pi$
$14$	−0.128721	+	0.192645i	−0.0344023	+	0.0514866i
$15$		0			0
$16$		−	1.00000i		−	0.250000i
$17$	2.15330	+	3.51615i	0.522252	+	0.852791i
$17$	2.15330	+	3.51615i	0.522252	+	0.852791i
$18$	−0.926779	−	0.926779i	−0.218444	−	0.218444i
$19$	5.28368	+	2.18857i	1.21216	+	0.502092i	0.894909	−	0.446249i	$-0.147241\pi$
$19$	5.28368	+	2.18857i	1.21216	+	0.502092i	0.317250	+	0.948342i	$0.397241\pi$
$20$		0			0
$21$	0.212939	+	0.212939i	0.0464671	+	0.0464671i
$22$	−3.12235	−	2.08629i	−0.665688	−	0.444798i
$23$	−1.67699	+	8.43077i	−0.349676	+	1.75794i	0.260310	+	0.965525i	$0.416175\pi$
$23$	−1.67699	+	8.43077i	−0.349676	+	1.75794i	−0.609985	+	0.792413i	$0.708825\pi$
$24$	−1.27477	−	0.253568i	−0.260211	−	0.0517593i
$25$		0			0
$26$	2.41726	+	5.83578i	0.474064	+	1.14449i
$27$	−4.65853	+	3.11273i	−0.896534	+	0.599045i
$28$	−0.227241	−	0.0452010i	−0.0429444	−	0.00854218i
$29$	0.221089	+	1.11149i	0.0410552	+	0.206398i	0.995868	−	0.0908081i	$-0.0289450\pi$
$29$	0.221089	+	1.11149i	0.0410552	+	0.206398i	−0.954813	+	0.297207i	$0.903945\pi$
$30$		0			0
$31$	−1.28229	−	0.856800i	−0.230306	−	0.153886i	0.435063	−	0.900400i	$-0.356726\pi$
$31$	−1.28229	−	0.856800i	−0.230306	−	0.153886i	−0.665370	+	0.746514i	$0.731726\pi$
$32$	0.923880	−	0.382683i	0.163320	−	0.0676495i
$33$	−3.45127	+	3.45127i	−0.600789	+	0.600789i
$34$	−2.42446	+	3.33496i	−0.415792	+	0.571941i
$35$		0			0
$36$	0.501569	−	1.21089i	0.0835949	−	0.201816i
$37$	−0.0492911	−	0.247803i	−0.00810341	−	0.0407386i	0.976522	−	0.215418i	$-0.0691112\pi$
$37$	−0.0492911	−	0.247803i	−0.00810341	−	0.0407386i	−0.984625	+	0.174679i	$0.944111\pi$
$38$			5.71901i			0.927746i
$39$	8.05222	−	1.60169i	1.28939	−	0.256475i
$40$		0			0
$41$	1.06798	−	5.36909i	0.166790	−	0.838510i	−0.803264	−	0.595623i	$-0.796905\pi$
$41$	1.06798	−	5.36909i	0.166790	−	0.838510i	0.970054	−	0.242888i	$-0.0780947\pi$
$42$	−0.115242	+	0.278218i	−0.0177822	+	0.0429300i
$43$	3.68348	−	8.89270i	0.561725	−	1.35612i	−0.346661	−	0.937991i	$-0.612685\pi$
$43$	3.68348	−	8.89270i	0.561725	−	1.35612i	0.908386	−	0.418133i	$-0.137315\pi$
$44$	0.732607	−	3.68307i	0.110445	−	0.555243i
$45$		0			0
$46$	−8.43077	+	1.67699i	−1.24305	+	0.247258i
$47$			4.58562i			0.668882i	0.942417	+	0.334441i	$0.108547\pi$
$47$			4.58562i			0.668882i	−0.942417	+	0.334441i	$0.891453\pi$
$48$	−0.253568	−	1.27477i	−0.0365993	−	0.183997i
$49$	2.65824	−	6.41756i	0.379749	−	0.916795i
$50$		0			0
$51$	3.63655	+	3.93627i	0.509218	+	0.551189i
$52$	−4.46651	+	4.46651i	−0.619394	+	0.619394i
$53$	5.77959	−	2.39399i	0.793888	−	0.328839i	0.0513825	−	0.998679i	$-0.483637\pi$
$53$	5.77959	−	2.39399i	0.793888	−	0.328839i	0.742506	+	0.669840i	$0.233637\pi$
$54$	−4.65853	−	3.11273i	−0.633945	−	0.423589i
$55$		0			0
$56$	−0.0452010	−	0.227241i	−0.00604023	−	0.0303663i
$57$	7.29043	+	1.45016i	0.965641	+	0.192078i
$58$	−0.942276	+	0.629608i	−0.123727	+	0.0826716i
$59$	−0.547416	−	1.32158i	−0.0712674	−	0.172055i	0.884232	−	0.467048i	$-0.154683\pi$
$59$	−0.547416	−	1.32158i	−0.0712674	−	0.172055i	−0.955499	+	0.294993i	$0.904683\pi$
$60$		0			0
$61$	−10.1829	−	2.02550i	−1.30379	−	0.259339i	−0.506133	−	0.862456i	$-0.668925\pi$
$61$	−10.1829	−	2.02550i	−1.30379	−	0.259339i	−0.797653	+	0.603117i	$0.793925\pi$
$62$	0.300868	−	1.51257i	0.0382103	−	0.192096i
$63$	−0.252493	−	0.168710i	−0.0318111	−	0.0212555i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$		0			0
$66$	−4.50930	−	1.86781i	−0.555056	−	0.229912i
$67$	0.973313	+	0.973313i	0.118909	+	0.118909i	0.764057	−	0.645148i	$-0.223204\pi$
$67$	0.973313	+	0.973313i	0.118909	+	0.118909i	−0.645148	+	0.764057i	$0.723204\pi$
$68$	−4.00891	−	0.963677i	−0.486151	−	0.116863i
$69$			11.1725i			1.34501i
$70$		0			0
$71$	−1.06710	+	1.59702i	−0.126641	+	0.189532i	−0.889372	−	0.457184i	$-0.848858\pi$
$71$	−1.06710	+	1.59702i	−0.126641	+	0.189532i	0.762731	+	0.646716i	$0.223858\pi$
$72$	1.31066			0.154463
$73$	1.07259	−	1.60525i	0.125537	−	0.187880i	−0.763377	−	0.645953i	$-0.776460\pi$
$73$	1.07259	−	1.60525i	0.125537	−	0.187880i	0.888915	+	0.458073i	$0.151460\pi$
$74$	0.210077	−	0.140369i	0.0244210	−	0.0163176i
$75$		0			0
$76$	−5.28368	+	2.18857i	−0.606079	+	0.251046i
$77$	−0.803827	−	0.332956i	−0.0916046	−	0.0379439i
$78$	4.56122	+	6.82635i	0.516456	+	0.772931i
$79$	0.466756	+	0.698549i	0.0525141	+	0.0785929i	0.856798	−	0.515653i	$-0.172451\pi$
$79$	0.466756	+	0.698549i	0.0525141	+	0.0785929i	−0.804283	+	0.594246i	$0.797451\pi$
$80$		0			0
$81$	−2.36893	+	2.36893i	−0.263214	+	0.263214i
$82$	5.36909	−	1.06798i	0.592916	−	0.117938i
$83$	−5.53052	−	13.3518i	−0.607053	−	1.46556i	−0.866190	−	0.499715i	$-0.833438\pi$
$83$	−5.53052	−	13.3518i	−0.607053	−	1.46556i	0.259137	−	0.965841i	$-0.416562\pi$
$84$	−0.301141			−0.0328572
$85$		0			0
$86$	9.62539			1.03793
$87$	0.563676	+	1.36083i	0.0604324	+	0.145897i
$88$	3.68307	−	0.732607i	0.392616	−	0.0780962i
$89$	−9.96203	+	9.96203i	−1.05597	+	1.05597i	−0.0576355	+	0.998338i	$0.518356\pi$
$89$	−9.96203	+	9.96203i	−1.05597	+	1.05597i	−0.998338	+	0.0576355i	$0.981644\pi$
$90$		0			0
$91$	0.813083	+	1.21686i	0.0852342	+	0.127562i
$92$	−4.77565	−	7.14727i	−0.497896	−	0.745154i
$93$	−1.85189	−	0.767076i	−0.192032	−	0.0795421i
$94$	−4.23656	+	1.75484i	−0.436968	+	0.180998i
$95$		0			0
$96$	1.08070	−	0.722100i	0.110298	−	0.0736990i
$97$	−2.79946	+	4.18968i	−0.284242	+	0.425398i	−0.945925	−	0.324386i	$-0.894842\pi$
$97$	−2.79946	+	4.18968i	−0.284242	+	0.425398i	0.661683	+	0.749784i	$0.269842\pi$
$98$	6.94632			0.701684
$99$	2.73442	−	4.09235i	0.274820	−	0.411297i
$100$		0			0
$101$		−	17.9673i		−	1.78781i	−0.448252	−	0.893907i	$-0.647953\pi$
$101$		−	17.9673i		−	1.78781i	0.448252	−	0.893907i	$-0.352047\pi$
$102$	−2.24500	+	4.86608i	−0.222288	+	0.481814i
$103$	−2.05246	−	2.05246i	−0.202235	−	0.202235i	0.598722	−	0.800957i	$-0.295675\pi$
$103$	−2.05246	−	2.05246i	−0.202235	−	0.202235i	−0.800957	+	0.598722i	$0.795675\pi$
$104$	−5.83578	−	2.41726i	−0.572246	−	0.237032i
$105$		0			0
$106$	4.42351	+	4.42351i	0.429649	+	0.429649i
$107$	4.69092	+	3.13437i	0.453489	+	0.303011i	0.761257	−	0.648450i	$-0.224582\pi$
$107$	4.69092	+	3.13437i	0.453489	+	0.303011i	−0.307769	+	0.951461i	$0.599582\pi$
$108$	1.09304	−	5.49511i	0.105178	−	0.528767i
$109$	0.783289	+	0.155806i	0.0750255	+	0.0149235i	0.232460	−	0.972606i	$-0.425322\pi$
$109$	0.783289	+	0.155806i	0.0750255	+	0.0149235i	−0.157435	+	0.987529i	$0.550322\pi$
$110$		0			0
$111$	−0.125670	−	0.303394i	−0.0119280	−	0.0287968i
$112$	0.192645	−	0.128721i	0.0182033	−	0.0121630i
$113$	4.52373	+	0.899825i	0.425556	+	0.0846484i	0.403222	−	0.915102i	$-0.367890\pi$
$113$	4.52373	+	0.899825i	0.425556	+	0.0846484i	0.0223342	+	0.999751i	$0.492890\pi$
$114$	1.45016	+	7.29043i	0.135820	+	0.682811i
$115$		0			0
$116$	−0.942276	−	0.629608i	−0.0874881	−	0.0584577i
$117$	−7.64875	+	3.16821i	−0.707127	+	0.292902i
$118$	1.01149	−	1.01149i	0.0931154	−	0.0931154i
$119$	−0.400193	+	0.867427i	−0.0366856	+	0.0795169i
$120$		0			0
$121$	1.18696	−	2.86559i	0.107906	−	0.260508i
$122$	−2.02550	−	10.1829i	−0.183380	−	0.921916i
$123$		−	7.11516i		−	0.641552i
$124$	1.51257	−	0.300868i	0.135832	−	0.0270188i
$125$		0			0
$126$	0.0592432	−	0.297836i	0.00527781	−	0.0265333i
$127$	4.65967	−	11.2494i	0.413479	−	0.998227i	−0.570717	−	0.821146i	$-0.693335\pi$
$127$	4.65967	−	11.2494i	0.413479	−	0.998227i	0.984196	−	0.177080i	$-0.0566651\pi$
$128$	−0.382683	+	0.923880i	−0.0338248	+	0.0816602i
$129$	2.44069	−	12.2702i	0.214890	−	1.08033i
$130$		0			0
$131$	10.1457	−	2.01810i	0.886430	−	0.176322i	0.269181	−	0.963090i	$-0.413247\pi$
$131$	10.1457	−	2.01810i	0.886430	−	0.176322i	0.617249	+	0.786768i	$0.288247\pi$
$132$		−	4.88083i		−	0.424822i
$133$	0.258505	+	1.29959i	0.0224152	+	0.112689i
$134$	−0.526753	+	1.27169i	−0.0455045	+	0.109858i
$135$		0			0
$136$	−0.643820	−	4.07253i	−0.0552071	−	0.349217i
$137$	3.73375	−	3.73375i	0.318996	−	0.318996i	−0.529386	−	0.848381i	$-0.677578\pi$
$137$	3.73375	−	3.73375i	0.318996	−	0.318996i	0.848381	+	0.529386i	$0.177578\pi$
$138$	−10.3221	+	4.27554i	−0.878673	+	0.363958i
$139$	−6.87456	−	4.59343i	−0.583093	−	0.389610i	0.228751	−	0.973485i	$-0.426536\pi$
$139$	−6.87456	−	4.59343i	−0.583093	−	0.389610i	−0.811844	+	0.583875i	$0.801536\pi$
$140$		0			0
$141$	1.16277	+	5.84562i	0.0979225	+	0.492290i
$142$	−1.88382	−	0.374714i	−0.158086	−	0.0314453i
$143$	−19.7227	+	13.1783i	−1.64929	+	1.10202i
$144$	0.501569	+	1.21089i	0.0417974	+	0.100908i
$145$		0			0
$146$	1.89352	+	0.376644i	0.156709	+	0.0311713i
$147$	1.76136	−	8.85496i	0.145275	−	0.730345i
$148$	0.210077	+	0.140369i	0.0172683	+	0.0115383i
$149$	−4.98028	−	4.98028i	−0.408001	−	0.408001i	0.473040	−	0.881041i	$-0.343157\pi$
$149$	−4.98028	−	4.98028i	−0.408001	−	0.408001i	−0.881041	+	0.473040i	$0.843157\pi$
$150$		0			0
$151$	2.32478	+	0.962954i	0.189188	+	0.0783641i	0.475266	−	0.879842i	$-0.342352\pi$
$151$	2.32478	+	0.962954i	0.189188	+	0.0783641i	−0.286078	+	0.958206i	$0.592352\pi$
$152$	−4.04395	−	4.04395i	−0.328008	−	0.328008i
$153$	−4.37101	−	3.17766i	−0.353375	−	0.256898i
$154$		−	0.870057i		−	0.0701112i
$155$		0			0
$156$	−4.56122	+	6.82635i	−0.365190	+	0.546545i
$157$	−7.63886			−0.609647			−0.304824	−	0.952409i	$-0.598597\pi$
$157$	−7.63886			−0.609647			−0.304824	+	0.952409i	$0.598597\pi$
$158$	−0.466756	+	0.698549i	−0.0371331	+	0.0555736i
$159$	6.76062	−	4.51730i	0.536152	−	0.358245i
$160$		0			0
$161$	−1.84001	+	0.762158i	−0.145013	+	0.0600665i
$162$	−3.09516	−	1.28206i	−0.243178	−	0.100728i
$163$	12.9767	+	19.4210i	1.01641	+	1.52117i	0.844144	+	0.536116i	$0.180109\pi$
$163$	12.9767	+	19.4210i	1.01641	+	1.52117i	0.172267	+	0.985050i	$0.444891\pi$
$164$	3.04134	+	4.55169i	0.237489	+	0.355427i
$165$		0			0
$166$	10.2191	−	10.2191i	0.793153	−	0.793153i
$167$	0.898816	−	0.178786i	0.0695525	−	0.0138348i	−0.160191	−	0.987086i	$-0.551211\pi$
$167$	0.898816	−	0.178786i	0.0695525	−	0.0138348i	0.229744	+	0.973251i	$0.426211\pi$
$168$	−0.115242	−	0.278218i	−0.00889109	−	0.0214650i
$169$	26.8995			2.06919
$170$		0			0
$171$	−7.49570			−0.573210
$172$	3.68348	+	8.89270i	0.280862	+	0.678062i
$173$	5.35479	−	1.06513i	0.407117	−	0.0809807i	0.0127164	−	0.999919i	$-0.495952\pi$
$173$	5.35479	−	1.06513i	0.407117	−	0.0809807i	0.394401	+	0.918938i	$0.370952\pi$
$174$	−1.04154	+	1.04154i	−0.0789587	+	0.0789587i
$175$		0			0
$176$	2.08629	+	3.12235i	0.157260	+	0.235356i
$177$	−1.03294	−	1.54590i	−0.0776404	−	0.116197i
$178$	−13.0160	−	5.39141i	−0.975592	−	0.404103i
$179$	−4.10947	+	1.70220i	−0.307156	+	0.127228i	−0.530937	−	0.847411i	$-0.678160\pi$
$179$	−4.10947	+	1.70220i	−0.307156	+	0.127228i	0.223781	+	0.974639i	$0.428160\pi$
$180$		0			0
$181$	13.3461	−	8.91757i	0.992007	−	0.662838i	0.0501114	−	0.998744i	$-0.484042\pi$
$181$	13.3461	−	8.91757i	0.992007	−	0.662838i	0.941896	+	0.335906i	$0.109042\pi$
$182$	−0.813083	+	1.21686i	−0.0602697	+	0.0902000i
$183$	−13.4945			−0.997539
$184$	4.77565	−	7.14727i	0.352066	−	0.526903i
$185$		0			0
$186$		−	2.00447i		−	0.146975i
$187$	−14.0591	−	6.48624i	−1.02810	−	0.474321i
$188$	−3.24253	−	3.24253i	−0.236485	−	0.236485i
$189$	−1.19930	−	0.496768i	−0.0872366	−	0.0361346i
$190$		0			0
$191$	1.07106	+	1.07106i	0.0774988	+	0.0774988i	0.744794	−	0.667295i	$-0.232548\pi$
$191$	1.07106	+	1.07106i	0.0774988	+	0.0774988i	−0.667295	+	0.744794i	$0.732548\pi$
$192$	1.08070	+	0.722100i	0.0779927	+	0.0521130i
$193$	−0.838060	+	4.21321i	−0.0603249	+	0.303274i	−0.999155	−	0.0411078i	$-0.986911\pi$
$193$	−0.838060	+	4.21321i	−0.0603249	+	0.303274i	0.938830	+	0.344381i	$0.111911\pi$
$194$	−4.94207	−	0.983039i	−0.354820	−	0.0705781i
$195$		0			0
$196$	2.65824	+	6.41756i	0.189874	+	0.458397i
$197$	13.5854	−	9.07745i	0.967917	−	0.646742i	0.0321958	−	0.999482i	$-0.489750\pi$
$197$	13.5854	−	9.07745i	0.967917	−	0.646742i	0.935721	+	0.352740i	$0.114750\pi$
$198$	4.82726	+	0.960202i	0.343058	+	0.0682386i
$199$	2.47583	+	12.4469i	0.175507	+	0.882334i	0.963717	+	0.266927i	$0.0860083\pi$
$199$	2.47583	+	12.4469i	0.175507	+	0.882334i	−0.788209	+	0.615407i	$0.788992\pi$
$200$		0			0
$201$	1.48755	+	0.993950i	0.104924	+	0.0701078i
$202$	16.5996	−	6.87579i	1.16795	−	0.483779i
$203$	−0.185664	+	0.185664i	−0.0130311	+	0.0130311i
$204$	−5.35479	−	0.211939i	−0.374910	−	0.0148387i
$205$		0			0
$206$	1.11078	−	2.68167i	0.0773920	−	0.186841i
$207$	−2.19796	−	11.0499i	−0.152769	−	0.768022i
$208$		−	6.31661i		−	0.437978i
$209$	−21.0635	+	4.18979i	−1.45699	+	0.289814i
$210$		0			0
$211$	−2.36187	+	11.8739i	−0.162598	+	0.817434i	0.810267	+	0.586061i	$0.199322\pi$
$211$	−2.36187	+	11.8739i	−0.162598	+	0.817434i	−0.972865	+	0.231373i	$0.925678\pi$
$212$	−2.39399	+	5.77959i	−0.164420	+	0.396944i
$213$	−0.955350	+	2.30642i	−0.0654595	+	0.158033i
$214$	−1.10065	+	5.53332i	−0.0752386	+	0.378250i
$215$		0			0
$216$	5.49511	−	1.09304i	0.373895	−	0.0743723i
$217$		−	0.357316i		−	0.0242562i
$218$	0.155806	+	0.783289i	0.0105525	+	0.0530511i
$219$	0.960270	−	2.31830i	0.0648890	−	0.156656i
$220$		0			0
$221$	13.6016	+	22.2101i	0.914940	+	1.49401i
$222$	0.232207	−	0.232207i	0.0155847	−	0.0155847i
$223$	−5.11747	+	2.11973i	−0.342691	+	0.141947i	−0.547390	−	0.836878i	$-0.684379\pi$
$223$	−5.11747	+	2.11973i	−0.342691	+	0.141947i	0.204699	+	0.978825i	$0.434379\pi$
$224$	0.192645	+	0.128721i	0.0128717	+	0.00860056i
$225$		0			0
$226$	0.899825	+	4.52373i	0.0598555	+	0.300914i
$227$	23.3969	+	4.65394i	1.55291	+	0.308893i	0.895646	−	0.444769i	$-0.146714\pi$
$227$	23.3969	+	4.65394i	1.55291	+	0.308893i	0.657263	+	0.753661i	$0.271714\pi$
$228$	−6.18052	+	4.12969i	−0.409315	+	0.273496i
$229$	−9.50419	−	22.9451i	−0.628055	−	1.51626i	−0.842037	−	0.539420i	$-0.818643\pi$
$229$	−9.50419	−	22.9451i	−0.628055	−	1.51626i	0.213982	−	0.976838i	$-0.431357\pi$
$230$		0			0
$231$	−1.10912	−	0.220618i	−0.0729749	−	0.0145156i
$232$	0.221089	−	1.11149i	0.0145152	−	0.0729729i
$233$	16.2366	+	10.8489i	1.06369	+	0.710738i	0.958897	−	0.283755i	$-0.0915803\pi$
$233$	16.2366	+	10.8489i	1.06369	+	0.710738i	0.104798	+	0.994494i	$0.466580\pi$
$234$	−5.85410	−	5.85410i	−0.382694	−	0.382694i
$235$		0			0
$236$	1.32158	+	0.547416i	0.0860274	+	0.0356337i
$237$	0.772136	+	0.772136i	0.0501556	+	0.0501556i
$238$	−0.954545	−	0.0377802i	−0.0618740	−	0.00244893i
$239$		−	9.42167i		−	0.609437i	−0.952442	−	0.304718i	$-0.901438\pi$
$239$		−	9.42167i		−	0.609437i	0.952442	−	0.304718i	$-0.0985624\pi$
$240$		0			0
$241$	15.3100	−	22.9131i	0.986206	−	1.47596i	0.110054	−	0.993926i	$-0.464898\pi$
$241$	15.3100	−	22.9131i	0.986206	−	1.47596i	0.876152	−	0.482035i	$-0.160102\pi$
$242$	3.10169			0.199384
$243$	6.91903	−	10.3551i	0.443856	−	0.664277i
$244$	8.63264	−	5.76815i	0.552648	−	0.369268i
$245$		0			0
$246$	6.57355	−	2.72285i	0.419114	−	0.173603i
$247$	33.3749	+	13.8243i	2.12359	+	0.879621i
$248$	0.856800	+	1.28229i	0.0544069	+	0.0814256i
$249$	−10.4357	−	15.6182i	−0.661338	−	0.989762i
$250$		0			0
$251$	−16.1723	+	16.1723i	−1.02079	+	1.02079i	−0.0210077	+	0.999779i	$0.506687\pi$
$251$	−16.1723	+	16.1723i	−1.02079	+	1.02079i	−0.999779	+	0.0210077i	$0.993313\pi$
$252$	0.297836	−	0.0592432i	0.0187619	−	0.00373197i
$253$	−12.3529	−	29.8225i	−0.776620	−	1.87493i
$254$	12.1763			0.764010
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−6.76367	−	16.3289i	−0.421906	−	1.01857i	−0.981785	−	0.189996i	$-0.939152\pi$
$257$	−6.76367	−	16.3289i	−0.421906	−	1.01857i	0.559879	−	0.828574i	$-0.310848\pi$
$258$	12.2702	−	2.44069i	0.763907	−	0.151951i
$259$	0.0413933	−	0.0413933i	0.00257205	−	0.00257205i
$260$		0			0
$261$	−0.825205	−	1.23501i	−0.0510789	−	0.0764450i
$262$	5.74705	+	8.60107i	0.355054	+	0.531376i
$263$	−6.10353	−	2.52816i	−0.376360	−	0.155893i	0.186481	−	0.982459i	$-0.440292\pi$
$263$	−6.10353	−	2.52816i	−0.376360	−	0.155893i	−0.562841	+	0.826565i	$0.690292\pi$
$264$	4.50930	−	1.86781i	0.277528	−	0.114956i
$265$		0			0
$266$	−1.10174	+	0.736159i	−0.0675520	+	0.0451368i
$267$	−10.1733	+	15.2254i	−0.622593	+	0.931776i
$268$	−1.37647			−0.0840814
$269$	5.36879	−	8.03497i	0.327341	−	0.489901i	−0.630899	−	0.775865i	$-0.717314\pi$
$269$	5.36879	−	8.03497i	0.327341	−	0.489901i	0.958240	+	0.285964i	$0.0923139\pi$
$270$		0			0
$271$		−	26.8606i		−	1.63167i	−0.578287	−	0.815833i	$-0.696279\pi$
$271$		−	26.8606i		−	1.63167i	0.578287	−	0.815833i	$-0.303721\pi$
$272$	3.51615	−	2.15330i	0.213198	−	0.130563i
$273$	1.34505	+	1.34505i	0.0814062	+	0.0814062i
$274$	4.87838	+	2.02069i	0.294713	+	0.122074i
$275$		0			0
$276$	−7.90017	−	7.90017i	−0.475535	−	0.475535i
$277$	−18.0672	−	12.0722i	−1.08556	−	0.725345i	−0.121913	−	0.992541i	$-0.538903\pi$
$277$	−18.0672	−	12.0722i	−1.08556	−	0.725345i	−0.963642	+	0.267196i	$0.913903\pi$
$278$	1.61300	−	8.10910i	0.0967413	−	0.486351i
$279$	1.98247	+	0.394337i	0.118687	+	0.0236083i
$280$		0			0
$281$	0.789615	+	1.90630i	0.0471045	+	0.113720i	0.945680	−	0.325098i	$-0.105397\pi$
$281$	0.789615	+	1.90630i	0.0471045	+	0.113720i	−0.898576	+	0.438818i	$0.855397\pi$
$282$	−4.95568	+	3.31128i	−0.295106	+	0.197184i
$283$	−5.91527	−	1.17662i	−0.351627	−	0.0699429i	0.0161170	−	0.999870i	$-0.494870\pi$
$283$	−5.91527	−	1.17662i	−0.351627	−	0.0699429i	−0.367744	+	0.929927i	$0.619870\pi$
$284$	−0.374714	−	1.88382i	−0.0222352	−	0.111784i
$285$		0			0
$286$	−19.7227	−	13.1783i	−1.16623	−	0.779247i
$287$	1.17180	−	0.485376i	0.0691692	−	0.0286508i
$288$	−0.926779	+	0.926779i	−0.0546110	+	0.0546110i
$289$	−7.72658	+	15.1427i	−0.454505	+	0.890744i
$290$		0			0
$291$	−2.50630	+	6.05074i	−0.146922	+	0.354701i
$292$	0.376644	+	1.89352i	0.0220414	+	0.110810i
$293$			22.6254i			1.32179i	0.750478	+	0.660895i	$0.229823\pi$
$293$			22.6254i			1.32179i	−0.750478	+	0.660895i	$0.770177\pi$
$294$	8.85496	−	1.76136i	0.516432	−	0.102725i
$295$		0			0
$296$	−0.0492911	+	0.247803i	−0.00286499	+	0.0144033i
$297$	8.05151	−	19.4381i	0.467196	−	1.12791i
$298$	2.69531	−	6.50705i	0.156135	−	0.376943i
$299$	−10.5929	+	53.2539i	−0.612601	+	3.07975i
$300$		0			0
$301$	2.18728	−	0.435077i	0.126073	−	0.0250774i
$302$			2.51632i			0.144798i
$303$	−4.55593	−	22.9042i	−0.261731	−	1.31581i
$304$	2.18857	−	5.28368i	0.125523	−	0.303040i
$305$		0			0
$306$	1.26306	−	5.25433i	0.0722041	−	0.300370i
$307$	−16.4310	+	16.4310i	−0.937764	+	0.937764i	−0.998174	−	0.0604092i	$-0.980759\pi$
$307$	−16.4310	+	16.4310i	−0.937764	+	0.937764i	0.0604092	+	0.998174i	$0.480759\pi$
$308$	0.803827	−	0.332956i	0.0458023	−	0.0189719i
$309$	−3.13685	−	2.09598i	−0.178449	−	0.119236i
$310$		0			0
$311$	1.11477	+	5.60431i	0.0632126	+	0.317791i	0.999435	−	0.0336174i	$-0.0107028\pi$
$311$	1.11477	+	5.60431i	0.0632126	+	0.317791i	−0.936222	+	0.351409i	$0.885703\pi$
$312$	−8.05222	−	1.60169i	−0.455867	−	0.0906777i
$313$	11.8948	−	7.94787i	0.672335	−	0.449240i	−0.171970	−	0.985102i	$-0.555013\pi$
$313$	11.8948	−	7.94787i	0.672335	−	0.449240i	0.844306	+	0.535862i	$0.180013\pi$
$314$	−2.92326	−	7.05738i	−0.164969	−	0.398271i
$315$		0			0
$316$	−0.823995	−	0.163903i	−0.0463533	−	0.00922025i
$317$	2.10050	−	10.5599i	0.117976	−	0.593105i	−0.875890	−	0.482511i	$-0.839725\pi$
$317$	2.10050	−	10.5599i	0.117976	−	0.593105i	0.993866	−	0.110594i	$-0.0352752\pi$
$318$	6.76062	+	4.51730i	0.379117	+	0.253318i
$319$	−3.00921	−	3.00921i	−0.168483	−	0.168483i
$320$		0			0
$321$	6.77462	+	2.80614i	0.378123	+	0.156624i
$322$	−1.40828	−	1.40828i	−0.0784806	−	0.0784806i
$323$	3.68201	+	23.2908i	0.204873	+	1.29594i
$324$		−	3.35017i		−	0.186121i
$325$		0			0
$326$	−12.9767	+	19.4210i	−0.718711	+	1.07563i
$327$	1.03802			0.0574027
$328$	−3.04134	+	4.55169i	−0.167930	+	0.251325i
$329$	−0.883399	+	0.590268i	−0.0487033	+	0.0325425i
$330$		0			0
$331$	5.90858	−	2.44742i	0.324765	−	0.134522i	−0.214344	−	0.976758i	$-0.568761\pi$
$331$	5.90858	−	2.44742i	0.324765	−	0.134522i	0.539109	+	0.842236i	$0.318761\pi$
$332$	13.3518	+	5.53052i	0.732778	+	0.303527i
$333$	0.183977	+	0.275341i	0.0100819	+	0.0150886i
$334$	0.509138	+	0.761979i	0.0278588	+	0.0416937i
$335$		0			0
$336$	0.212939	−	0.212939i	0.0116168	−	0.0116168i
$337$	−22.8272	+	4.54062i	−1.24348	+	0.247343i	−0.772622	−	0.634866i	$-0.781055\pi$
$337$	−22.8272	+	4.54062i	−1.24348	+	0.247343i	−0.470857	+	0.882210i	$0.656055\pi$
$338$	10.2940	+	24.8519i	0.559920	+	1.35177i
$339$	5.99488			0.325597
$340$		0			0
$341$	5.79130			0.313617
$342$	−2.86848	−	6.92512i	−0.155110	−	0.374468i
$343$	3.16917	−	0.630387i	0.171119	−	0.0340377i
$344$	−6.80618	+	6.80618i	−0.366964	+	0.366964i
$345$		0			0
$346$	3.03325	+	4.53957i	0.163068	+	0.244049i
$347$	−11.7115	−	17.5275i	−0.628706	−	0.940925i	−0.999923	−	0.0123793i	$-0.996059\pi$
$347$	−11.7115	−	17.5275i	−0.628706	−	0.940925i	0.371217	−	0.928546i	$-0.378941\pi$
$348$	−1.36083	−	0.563676i	−0.0729483	−	0.0302162i
$349$	27.4890	−	11.3863i	1.47145	−	0.609495i	0.504262	−	0.863551i	$-0.331765\pi$
$349$	27.4890	−	11.3863i	1.47145	−	0.609495i	0.967190	+	0.254055i	$0.0817646\pi$
$350$		0			0
$351$	−29.4261	+	19.6619i	−1.57065	+	1.04947i
$352$	−2.08629	+	3.12235i	−0.111200	+	0.166422i
$353$	−7.24952			−0.385853			−0.192926	−	0.981213i	$-0.561798\pi$
$353$	−7.24952			−0.385853			−0.192926	+	0.981213i	$0.561798\pi$
$354$	1.03294	−	1.54590i	0.0549001	−	0.0821638i
$355$		0			0
$356$		−	14.0884i		−	0.746686i
$357$	−0.290203	+	1.20725i	−0.0153592	+	0.0638942i
$358$	−3.14525	−	3.14525i	−0.166232	−	0.166232i
$359$	19.2554	+	7.97584i	1.01626	+	0.420949i	0.827735	−	0.561120i	$-0.189629\pi$
$359$	19.2554	+	7.97584i	1.01626	+	0.420949i	0.188525	+	0.982068i	$0.439629\pi$
$360$		0			0
$361$	9.69237	+	9.69237i	0.510125	+	0.510125i
$362$	13.3461	+	8.91757i	0.701455	+	0.468697i
$363$	0.786488	−	3.95394i	0.0412799	−	0.207528i
$364$	−1.43539	−	0.285517i	−0.0752348	−	0.0149651i
$365$		0			0
$366$	−5.16410	−	12.4673i	−0.269932	−	0.651674i
$367$	−20.1941	+	13.4933i	−1.05412	+	0.704342i	−0.956752	−	0.290906i	$-0.906043\pi$
$367$	−20.1941	+	13.4933i	−1.05412	+	0.704342i	−0.0973712	+	0.995248i	$0.531043\pi$
$368$	8.43077	+	1.67699i	0.439485	+	0.0874189i
$369$	1.39976	+	7.03706i	0.0728686	+	0.366335i
$370$		0			0
$371$	1.20515	+	0.805254i	0.0625681	+	0.0418067i
$372$	1.85189	−	0.767076i	0.0960158	−	0.0397710i
$373$	5.48095	−	5.48095i	0.283793	−	0.283793i	−0.550827	−	0.834620i	$-0.685688\pi$
$373$	5.48095	−	5.48095i	0.283793	−	0.283793i	0.834620	+	0.550827i	$0.185688\pi$
$374$	0.612334	−	15.4711i	0.0316630	−	0.799990i
$375$		0			0
$376$	1.75484	−	4.23656i	0.0904991	−	0.218484i
$377$	1.39653	+	7.02084i	0.0719251	+	0.361592i
$378$		−	1.29812i		−	0.0667680i
$379$	−24.4160	+	4.85664i	−1.25416	+	0.249469i	−0.777088	−	0.629392i	$-0.783304\pi$
$379$	−24.4160	+	4.85664i	−1.25416	+	0.249469i	−0.477077	+	0.878861i	$0.658304\pi$
$380$		0			0
$381$	3.08752	−	15.5220i	0.158178	−	0.795216i
$382$	−0.579651	+	1.39940i	−0.0296575	+	0.0715996i
$383$	−7.60872	+	18.3691i	−0.388788	+	0.938616i	0.601410	+	0.798941i	$0.294606\pi$
$383$	−7.60872	+	18.3691i	−0.388788	+	0.938616i	−0.990197	+	0.139675i	$0.955394\pi$
$384$	−0.253568	+	1.27477i	−0.0129398	+	0.0650529i
$385$		0			0
$386$	−4.21321	+	0.838060i	−0.214447	+	0.0426561i
$387$			12.6156i			0.641289i
$388$	−0.983039	−	4.94207i	−0.0499062	−	0.250896i
$389$	3.92126	−	9.46676i	0.198816	−	0.479984i	−0.792757	−	0.609538i	$-0.791355\pi$
$389$	3.92126	−	9.46676i	0.198816	−	0.479984i	0.991572	+	0.129555i	$0.0413548\pi$
$390$		0			0
$391$	−33.2549	+	12.2575i	−1.68177	+	0.619887i
$392$	−4.91179	+	4.91179i	−0.248083	+	0.248083i
$393$	12.4217	−	5.14522i	0.626590	−	0.259542i
$394$	13.5854	+	9.07745i	0.684421	+	0.457315i
$395$		0			0
$396$	0.960202	+	4.82726i	0.0482519	+	0.242579i
$397$	17.9852	+	3.57747i	0.902650	+	0.179548i	0.624533	−	0.780999i	$-0.285290\pi$
$397$	17.9852	+	3.57747i	0.902650	+	0.179548i	0.278118	+	0.960547i	$0.410290\pi$
$398$	−10.5519	+	7.05058i	−0.528921	+	0.353414i
$399$	0.659069	+	1.59113i	0.0329947	+	0.0796562i
$400$		0			0
$401$	−7.09217	−	1.41072i	−0.354166	−	0.0704480i	0.0148011	−	0.999890i	$-0.495289\pi$
$401$	−7.09217	−	1.41072i	−0.354166	−	0.0704480i	−0.368967	+	0.929442i	$0.620289\pi$
$402$	−0.349029	+	1.75469i	−0.0174080	+	0.0875158i
$403$	−8.09973	−	5.41207i	−0.403476	−	0.269594i
$404$	12.7048	+	12.7048i	0.632088	+	0.632088i
$405$		0			0
$406$	−0.242582	−	0.100481i	−0.0120391	−	0.00498678i
$407$	0.670893	+	0.670893i	0.0332549	+	0.0332549i
$408$	−1.85338	−	5.02829i	−0.0917562	−	0.248937i
$409$			5.46288i			0.270122i	0.990837	+	0.135061i	$0.0431231\pi$
$409$			5.46288i			0.270122i	−0.990837	+	0.135061i	$0.956877\pi$
$410$		0			0
$411$	3.81291	−	5.70643i	0.188077	−	0.281477i
$412$	2.90262			0.143002
$413$	0.184132	−	0.275572i	0.00906053	−	0.0135600i
$414$	9.36766	−	6.25927i	0.460395	−	0.307626i
$415$		0			0
$416$	5.83578	−	2.41726i	0.286123	−	0.118516i
$417$	−9.92823	−	4.11241i	−0.486188	−	0.201386i
$418$	−11.9315	−	17.8568i	−0.583589	−	0.873403i
$419$	5.00808	+	7.49513i	0.244661	+	0.366161i	0.933393	−	0.358855i	$-0.116833\pi$
$419$	5.00808	+	7.49513i	0.244661	+	0.366161i	−0.688733	+	0.725015i	$0.741833\pi$
$420$		0			0
$421$	16.4962	−	16.4962i	0.803973	−	0.803973i	−0.179741	−	0.983714i	$-0.557526\pi$
$421$	16.4962	−	16.4962i	0.803973	−	0.803973i	0.983714	+	0.179741i	$0.0575258\pi$
$422$	−11.8739	+	2.36187i	−0.578013	+	0.114974i
$423$	−2.30001	−	5.55271i	−0.111830	−	0.269982i
$424$	−6.25579			−0.303808
$425$		0			0
$426$	−2.49645			−0.120953
$427$	−0.920553	−	2.22241i	−0.0445487	−	0.107550i
$428$	−5.53332	+	1.10065i	−0.267463	+	0.0532017i
$429$	−21.8003	+	21.8003i	−1.05253	+	1.05253i
$430$		0			0
$431$	−7.38136	−	11.0470i	−0.355547	−	0.532114i	0.609980	−	0.792417i	$-0.291178\pi$
$431$	−7.38136	−	11.0470i	−0.355547	−	0.532114i	−0.965527	+	0.260303i	$0.916178\pi$
$432$	3.11273	+	4.65853i	0.149761	+	0.224133i
$433$	14.7508	+	6.11000i	0.708880	+	0.293628i	0.707841	−	0.706372i	$-0.249669\pi$
$433$	14.7508	+	6.11000i	0.708880	+	0.293628i	0.00103885	+	0.999999i	$0.499669\pi$
$434$	0.330117	−	0.136739i	0.0158461	−	0.00656368i
$435$		0			0
$436$	−0.664041	+	0.443698i	−0.0318018	+	0.0212493i
$437$	−27.3120	+	40.8753i	−1.30651	+	1.95533i
$438$	2.50931			0.119899
$439$	−3.79978	+	5.68677i	−0.181353	+	0.271415i	−0.910997	−	0.412413i	$-0.864686\pi$
$439$	−3.79978	+	5.68677i	−0.181353	+	0.271415i	0.729643	+	0.683828i	$0.239686\pi$
$440$		0			0
$441$			9.10428i			0.433537i
$442$	−15.3144	+	21.0656i	−0.728431	+	1.00199i
$443$	20.2583	+	20.2583i	0.962499	+	0.962499i	0.999322	−	0.0368225i	$-0.0117236\pi$
$443$	20.2583	+	20.2583i	0.962499	+	0.962499i	−0.0368225	+	0.999322i	$0.511724\pi$
$444$	0.303394	+	0.125670i	0.0143984	+	0.00596402i
$445$		0			0
$446$	−3.91675	−	3.91675i	−0.185463	−	0.185463i
$447$	−7.61156	−	5.08588i	−0.360014	−	0.240554i
$448$	−0.0452010	+	0.227241i	−0.00213554	+	0.0107361i
$449$	−32.0536	−	6.37587i	−1.51271	−	0.300896i	−0.632152	−	0.774844i	$-0.717828\pi$
$449$	−32.0536	−	6.37587i	−1.51271	−	0.300896i	−0.880553	+	0.473948i	$0.842828\pi$
$450$		0			0
$451$	7.86686	+	18.9923i	0.370436	+	0.894312i
$452$	−3.83503	+	2.56249i	−0.180385	+	0.120529i
$453$	3.20773	+	0.638057i	0.150712	+	0.0299786i
$454$	4.65394	+	23.3969i	0.218420	+	1.09807i
$455$		0			0
$456$	−6.18052	−	4.12969i	−0.289430	−	0.193391i
$457$	19.5403	−	8.09384i	0.914054	−	0.378614i	0.124447	−	0.992226i	$-0.460284\pi$
$457$	19.5403	−	8.09384i	0.914054	−	0.378614i	0.789607	+	0.613612i	$0.210284\pi$
$458$	17.5615	−	17.5615i	0.820593	−	0.820593i
$459$	−20.9760	−	9.67742i	−0.979077	−	0.451703i
$460$		0			0
$461$	−14.0929	+	34.0234i	−0.656374	+	1.58463i	0.146990	+	0.989138i	$0.453041\pi$
$461$	−14.0929	+	34.0234i	−0.656374	+	1.58463i	−0.803364	+	0.595488i	$0.796959\pi$
$462$	−0.220618	−	1.10912i	−0.0102641	−	0.0516011i
$463$		−	6.44868i		−	0.299696i	−0.988709	−	0.149848i	$-0.952122\pi$
$463$		−	6.44868i		−	0.299696i	0.988709	−	0.149848i	$-0.0478784\pi$
$464$	1.11149	−	0.221089i	0.0515996	−	0.0102638i
$465$		0			0
$466$	−3.80964	+	19.1524i	−0.176478	+	0.887217i
$467$	−10.5568	+	25.4863i	−0.488509	+	1.17937i	0.466961	+	0.884278i	$0.345349\pi$
$467$	−10.5568	+	25.4863i	−0.488509	+	1.17937i	−0.955470	+	0.295087i	$0.904651\pi$
$468$	3.16821	−	7.64875i	0.146451	−	0.353563i
$469$	−0.0622179	+	0.312790i	−0.00287295	+	0.0144433i
$470$		0			0
$471$	−9.73779	+	1.93697i	−0.448694	+	0.0892507i
$472$			1.43047i			0.0658425i
$473$	7.05163	+	35.4509i	0.324234	+	1.63004i
$474$	−0.417877	+	1.00884i	−0.0191937	+	0.0463378i
$475$		0			0
$476$	−0.330384	−	0.896343i	−0.0151431	−	0.0410838i
$477$	−5.79773	+	5.79773i	−0.265460	+	0.265460i
$478$	8.70448	−	3.60552i	0.398134	−	0.164912i
$479$	−21.9066	−	14.6376i	−1.00094	−	0.668807i	−0.0568119	−	0.998385i	$-0.518094\pi$
$479$	−21.9066	−	14.6376i	−1.00094	−	0.668807i	−0.944128	+	0.329578i	$0.893094\pi$
$480$		0			0
$481$	−0.311353	−	1.56527i	−0.0141965	−	0.0713704i
$482$	27.0278	+	5.37617i	1.23108	+	0.244878i
$483$	−2.15234	+	1.43814i	−0.0979347	+	0.0654378i
$484$	1.18696	+	2.86559i	0.0539529	+	0.130254i
$485$		0			0
$486$	12.2146	+	2.42964i	0.554066	+	0.110211i
$487$	−3.03751	+	15.2706i	−0.137643	+	0.691978i	0.848910	+	0.528537i	$0.177259\pi$
$487$	−3.03751	+	15.2706i	−0.137643	+	0.691978i	−0.986553	+	0.163441i	$0.947741\pi$
$488$	8.63264	+	5.76815i	0.390781	+	0.261112i
$489$	21.4668	+	21.4668i	0.970762	+	0.970762i
$490$		0			0
$491$	−27.1621	−	11.2509i	−1.22581	−	0.507747i	−0.326558	−	0.945177i	$-0.605889\pi$
$491$	−27.1621	−	11.2509i	−1.22581	−	0.507747i	−0.899252	+	0.437430i	$0.855889\pi$
$492$	5.03118	+	5.03118i	0.226823	+	0.226823i
$493$	−3.43209	+	3.17075i	−0.154574	+	0.142804i
$494$			36.1247i			1.62533i
$495$		0			0
$496$	−0.856800	+	1.28229i	−0.0384715	+	0.0575766i
$497$	−0.445017			−0.0199617
$498$	10.4357	−	15.6182i	0.467637	−	0.699868i
$499$	−1.84513	+	1.23288i	−0.0825994	+	0.0551912i	−0.596184	−	0.802848i	$-0.703317\pi$
$499$	−1.84513	+	1.23288i	−0.0825994	+	0.0551912i	0.513585	+	0.858039i	$0.328317\pi$
$500$		0			0
$501$	1.10045	−	0.455821i	0.0491645	−	0.0203646i
$502$	−21.1301	−	8.75239i	−0.943084	−	0.390638i
$503$	−6.36947	−	9.53258i	−0.284000	−	0.425037i	0.661852	−	0.749635i	$-0.269771\pi$
$503$	−6.36947	−	9.53258i	−0.284000	−	0.425037i	−0.945852	+	0.324598i	$0.894771\pi$
$504$	0.168710	+	0.252493i	0.00751496	+	0.0112469i
$505$		0			0
$506$	22.8252	−	22.8252i	1.01470	−	1.01470i
$507$	34.2907	−	6.82085i	1.52290	−	0.302924i
$508$	4.65967	+	11.2494i	0.206739	+	0.499113i
$509$	10.4091			0.461376			0.230688	−	0.973028i	$-0.425902\pi$
$509$	10.4091			0.461376			0.230688	+	0.973028i	$0.425902\pi$
$510$		0			0
$511$	0.447309			0.0197878
$512$	−0.382683	−	0.923880i	−0.0169124	−	0.0408301i
$513$	−31.4266	+	6.25113i	−1.38752	+	0.275994i
$514$	12.4976	−	12.4976i	0.551247	−	0.551247i
$515$		0			0
$516$	6.95049	+	10.4021i	0.305978	+	0.457929i
$517$	−9.56694	−	14.3179i	−0.420753	−	0.629702i
$518$	0.0540829	+	0.0224019i	0.00237627	+	0.000984282i
$519$	6.55605	−	2.71560i	0.287779	−	0.119202i
$520$		0			0
$521$	−23.6046	+	15.7721i	−1.03414	+	0.690989i	−0.952146	−	0.305644i	$-0.901128\pi$
$521$	−23.6046	+	15.7721i	−1.03414	+	0.690989i	−0.0819920	+	0.996633i	$0.526128\pi$
$522$	0.825205	−	1.23501i	0.0361182	−	0.0540547i
$523$	2.22356			0.0972295			0.0486148	−	0.998818i	$-0.484519\pi$
$523$	2.22356			0.0972295			0.0486148	+	0.998818i	$0.484519\pi$
$524$	−5.74705	+	8.60107i	−0.251061	+	0.375739i
$525$		0			0
$526$		−	6.60641i		−	0.288053i
$527$	0.251474	−	6.35368i	0.0109544	−	0.276771i
$528$	3.45127	+	3.45127i	0.150197	+	0.150197i
$529$	−47.0165	−	19.4749i	−2.04419	−	0.846733i
$530$		0			0
$531$	1.32573	+	1.32573i	0.0575316	+	0.0575316i
$532$	−1.10174	−	0.736159i	−0.0477665	−	0.0319165i
$533$	6.74599	−	33.9144i	0.292201	−	1.46900i
$534$	−17.9595	−	3.57237i	−0.777185	−	0.154592i
$535$		0			0
$536$	−0.526753	−	1.27169i	−0.0227523	−	0.0549288i
$537$	−4.80701	+	3.21194i	−0.207438	+	0.138605i
$538$	9.47789	+	1.88527i	0.408621	+	0.0812797i
$539$	5.08892	+	25.5837i	0.219195	+	1.10197i
$540$		0			0
$541$	−13.9050	−	9.29106i	−0.597825	−	0.399454i	0.219515	−	0.975609i	$-0.429552\pi$
$541$	−13.9050	−	9.29106i	−0.597825	−	0.399454i	−0.817340	+	0.576155i	$0.804552\pi$
$542$	24.8160	−	10.2791i	1.06594	−	0.441526i
$543$	14.7520	−	14.7520i	0.633069	−	0.633069i
$544$	3.33496	+	2.42446i	0.142985	+	0.103948i
$545$		0			0
$546$	−0.727936	+	1.75739i	−0.0311528	+	0.0752095i
$547$	−1.12716	−	5.66660i	−0.0481937	−	0.242286i	0.949178	−	0.314740i	$-0.101917\pi$
$547$	−1.12716	−	5.66660i	−0.0481937	−	0.242286i	−0.997372	+	0.0724533i	$0.976917\pi$
$548$			5.28032i			0.225564i
$549$	13.3463	−	2.65475i	0.569608	−	0.113302i
$550$		0			0
$551$	−1.26441	+	6.35662i	−0.0538657	+	0.270801i
$552$	4.27554	−	10.3221i	0.181979	−	0.439337i
$553$	−0.0744907	+	0.179837i	−0.00316767	+	0.00764743i
$554$	4.23918	−	21.3118i	0.180105	−	0.905451i
$555$		0			0
$556$	8.10910	−	1.61300i	0.343902	−	0.0684064i
$557$		−	6.57780i		−	0.278710i	−0.990242	−	0.139355i	$-0.955497\pi$
$557$		−	6.57780i		−	0.278710i	0.990242	−	0.139355i	$-0.0445030\pi$
$558$	0.394337	+	1.98247i	0.0166936	+	0.0839245i
$559$	23.2671	−	56.1717i	0.984092	−	2.37581i
$560$		0			0
$561$	−19.5668	−	4.70355i	−0.826110	−	0.198584i
$562$	−1.45902	+	1.45902i	−0.0615450	+	0.0615450i
$563$	1.12543	−	0.466167i	0.0474311	−	0.0196466i	−0.358842	−	0.933398i	$-0.616828\pi$
$563$	1.12543	−	0.466167i	0.0474311	−	0.0196466i	0.406273	+	0.913752i	$0.366828\pi$
$564$	−4.95568	−	3.31128i	−0.208672	−	0.139430i
$565$		0			0
$566$	−1.17662	−	5.91527i	−0.0494571	−	0.248638i
$567$	−0.761295	−	0.151431i	−0.0319714	−	0.00635950i
$568$	1.59702	−	1.06710i	0.0670096	−	0.0447744i
$569$	4.32635	+	10.4447i	0.181370	+	0.437866i	0.988249	−	0.152850i	$-0.0488452\pi$
$569$	4.32635	+	10.4447i	0.181370	+	0.437866i	−0.806879	+	0.590716i	$0.798845\pi$
$570$		0			0
$571$	41.9951	+	8.35335i	1.75744	+	0.349577i	0.965377	−	0.260860i	$-0.0840059\pi$
$571$	41.9951	+	8.35335i	1.75744	+	0.349577i	0.792065	+	0.610436i	$0.209006\pi$
$572$	4.62759	−	23.2645i	0.193489	−	0.972737i
$573$	1.63693	+	1.09376i	0.0683839	+	0.0456927i
$574$	0.896857	+	0.896857i	0.0374341	+	0.0374341i
$575$		0			0
$576$	−1.21089	−	0.501569i	−0.0504540	−	0.0208987i
$577$	23.2398	+	23.2398i	0.967488	+	0.967488i	0.999488	−	0.0320003i	$-0.0101878\pi$
$577$	23.2398	+	23.2398i	0.967488	+	0.967488i	−0.0320003	+	0.999488i	$0.510188\pi$
$578$	−16.9468	−	1.34359i	−0.704895	−	0.0558860i
$579$			5.58338i			0.232037i
$580$		0			0
$581$	1.86027	−	2.78410i	0.0771772	−	0.115504i
$582$	−6.54927			−0.271476
$583$	−13.0514	+	19.5328i	−0.540533	+	0.808965i
$584$	−1.60525	+	1.07259i	−0.0664256	+	0.0443842i
$585$		0			0
$586$	−20.9031	+	8.65837i	−0.863501	+	0.357674i
$587$	−0.798310	−	0.330671i	−0.0329498	−	0.0136482i	0.366148	−	0.930557i	$-0.380676\pi$
$587$	−0.798310	−	0.330671i	−0.0329498	−	0.0136482i	−0.399097	+	0.916909i	$0.630676\pi$
$588$	5.01593	+	7.50688i	0.206854	+	0.309578i
$589$	−4.90005	−	7.33344i	−0.201903	−	0.302169i
$590$		0			0
$591$	15.0165	−	15.0165i	0.617695	−	0.617695i
$592$	−0.247803	+	0.0492911i	−0.0101846	+	0.00202585i
$593$	−6.76356	−	16.3287i	−0.277746	−	0.670538i	0.722026	−	0.691865i	$-0.243211\pi$
$593$	−6.76356	−	16.3287i	−0.277746	−	0.670538i	−0.999773	+	0.0213270i	$0.993211\pi$
$594$	21.0396			0.863266
$595$		0			0
$596$	7.04318			0.288500
$597$	6.31224	+	15.2391i	0.258343	+	0.623695i
$598$	−53.2539	+	10.5929i	−2.17771	+	0.433174i
$599$	30.5345	−	30.5345i	1.24761	−	1.24761i	0.290833	−	0.956774i	$-0.406068\pi$
$599$	30.5345	−	30.5345i	1.24761	−	1.24761i	0.956774	−	0.290833i	$-0.0939324\pi$
$600$		0			0
$601$	9.33973	+	13.9779i	0.380976	+	0.570170i	0.971556	−	0.236808i	$-0.0761013\pi$
$601$	9.33973	+	13.9779i	0.380976	+	0.570170i	−0.590581	+	0.806979i	$0.701101\pi$
$602$	1.23899	+	1.85429i	0.0504976	+	0.0755750i
$603$	−1.66676	−	0.690396i	−0.0678759	−	0.0281151i
$604$	−2.32478	+	0.962954i	−0.0945938	+	0.0391821i
$605$		0			0
$606$	19.4172	−	12.9742i	0.788772	−	0.527040i
$607$	12.8899	−	19.2912i	0.523186	−	0.783004i	−0.471938	−	0.881632i	$-0.656445\pi$
$607$	12.8899	−	19.2912i	0.523186	−	0.783004i	0.995124	+	0.0986279i	$0.0314453\pi$
$608$	5.71901			0.231936
$609$	−0.189601	+	0.283758i	−0.00768302	+	0.0114985i
$610$		0			0
$611$			28.9656i			1.17182i
$612$	5.33771	−	0.843831i	0.215764	−	0.0341099i
$613$	5.22573	+	5.22573i	0.211065	+	0.211065i	0.804720	−	0.593655i	$-0.202315\pi$
$613$	5.22573	+	5.22573i	0.211065	+	0.211065i	−0.593655	+	0.804720i	$0.702315\pi$
$614$	−21.4681	−	8.89237i	−0.866381	−	0.358867i
$615$		0			0
$616$	0.615223	+	0.615223i	0.0247880	+	0.0247880i
$617$	6.06006	+	4.04920i	0.243969	+	0.163015i	0.671543	−	0.740965i	$-0.265632\pi$
$617$	6.06006	+	4.04920i	0.243969	+	0.163015i	−0.427574	+	0.903980i	$0.640632\pi$
$618$	0.736010	−	3.70017i	0.0296067	−	0.148843i
$619$	14.5332	+	2.89082i	0.584137	+	0.116192i	0.478308	−	0.878192i	$-0.341250\pi$
$619$	14.5332	+	2.89082i	0.584137	+	0.116192i	0.105829	+	0.994384i	$0.466250\pi$
$620$		0			0
$621$	−18.4304	−	44.4950i	−0.739588	−	1.78552i
$622$	−4.75111	+	3.17459i	−0.190502	+	0.127289i
$623$	−3.20146	−	0.636811i	−0.128264	−	0.0255133i
$624$	−1.60169	−	8.05222i	−0.0641188	−	0.322347i
$625$		0			0
$626$	11.8948	+	7.94787i	0.475413	+	0.317661i
$627$	−25.7887	+	10.6820i	−1.02990	+	0.426600i
$628$	5.40149	−	5.40149i	0.215543	−	0.215543i
$629$	0.765174	−	0.706910i	0.0305095	−	0.0281863i
$630$		0			0
$631$	−1.21200	+	2.92604i	−0.0482491	+	0.116484i	−0.946166	−	0.323680i	$-0.895080\pi$
$631$	−1.21200	+	2.92604i	−0.0482491	+	0.116484i	0.897917	+	0.440164i	$0.145080\pi$
$632$	−0.163903	−	0.823995i	−0.00651970	−	0.0327768i
$633$			15.7354i			0.625426i
$634$	10.5599	−	2.10050i	0.419388	−	0.0834215i
$635$		0			0
$636$	−1.58626	+	7.97469i	−0.0628995	+	0.316217i
$637$	16.7911	−	40.5372i	0.665286	−	1.60614i
$638$	1.62857	−	3.93172i	0.0644758	−	0.155658i
$639$	0.491125	−	2.46905i	0.0194286	−	0.0976741i
$640$		0			0
$641$	43.7038	−	8.69323i	1.72620	−	0.343362i	0.770438	−	0.637515i	$-0.220038\pi$
$641$	43.7038	−	8.69323i	1.72620	−	0.343362i	0.955758	+	0.294153i	$0.0950376\pi$
$642$			7.33280i			0.289403i
$643$	6.34291	+	31.8880i	0.250140	+	1.25754i	0.877791	+	0.479043i	$0.159016\pi$
$643$	6.34291	+	31.8880i	0.250140	+	1.25754i	−0.627651	+	0.778495i	$0.715984\pi$
$644$	0.762158	−	1.84001i	0.0300332	−	0.0725067i
$645$		0			0
$646$	−20.1089	+	12.3148i	−0.791173	+	0.484518i
$647$	−16.2490	+	16.2490i	−0.638814	+	0.638814i	−0.950263	−	0.311449i	$-0.899186\pi$
$647$	−16.2490	+	16.2490i	−0.638814	+	0.638814i	0.311449	+	0.950263i	$0.399186\pi$
$648$	3.09516	−	1.28206i	0.121589	−	0.0503639i
$649$	4.46642	+	2.98437i	0.175322	+	0.117147i
$650$		0			0
$651$	−0.0906038	−	0.455496i	−0.00355104	−	0.0178523i
$652$	−22.9086	−	4.55680i	−0.897169	−	0.178458i
$653$	23.0875	−	15.4266i	0.903483	−	0.603688i	−0.0146798	−	0.999892i	$-0.504673\pi$
$653$	23.0875	−	15.4266i	0.903483	−	0.603688i	0.918162	+	0.396205i	$0.129673\pi$
$654$	0.397234	+	0.959007i	0.0155331	+	0.0375001i
$655$		0			0
$656$	−5.36909	−	1.06798i	−0.209628	−	0.0416975i
$657$	−0.493654	+	2.48176i	−0.0192593	+	0.0968228i
$658$	−0.883399	−	0.590268i	−0.0344385	−	0.0230110i
$659$	28.1330	+	28.1330i	1.09591	+	1.09591i	0.994884	+	0.101024i	$0.0322118\pi$
$659$	28.1330	+	28.1330i	1.09591	+	1.09591i	0.101024	+	0.994884i	$0.467788\pi$
$660$		0			0
$661$	−34.0520	−	14.1048i	−1.32447	−	0.548614i	−0.395398	−	0.918510i	$-0.629393\pi$
$661$	−34.0520	−	14.1048i	−1.32447	−	0.548614i	−0.929073	+	0.369896i	$0.879393\pi$
$662$	4.52223	+	4.52223i	0.175762	+	0.175762i
$663$	22.9706	+	24.8639i	0.892105	+	0.965633i
$664$			14.4519i			0.560844i
$665$		0			0
$666$	−0.183977	+	0.275341i	−0.00712896	+	0.0106692i
$667$	−9.74148			−0.377192
$668$	−0.509138	+	0.761979i	−0.0196992	+	0.0294819i
$669$	−5.98611	+	3.99979i	−0.231436	+	0.154641i
$670$		0			0
$671$	36.0204	−	14.9201i	1.39055	−	0.575985i
$672$	0.278218	+	0.115242i	0.0107325	+	0.00444555i
$673$	−9.40166	−	14.0706i	−0.362407	−	0.542381i	0.604797	−	0.796379i	$-0.293254\pi$
$673$	−9.40166	−	14.0706i	−0.362407	−	0.542381i	−0.967205	+	0.253999i	$0.918254\pi$
$674$	−12.9306	−	19.3520i	−0.498068	−	0.745411i
$675$		0			0
$676$	−19.0208	+	19.0208i	−0.731570	+	0.731570i
$677$	24.5991	−	4.89306i	0.945420	−	0.188056i	0.301774	−	0.953379i	$-0.402421\pi$
$677$	24.5991	−	4.89306i	0.945420	−	0.188056i	0.643645	+	0.765324i	$0.277421\pi$
$678$	2.29414	+	5.53855i	0.0881060	+	0.212707i
$679$	−1.16747			−0.0448035
$680$		0			0
$681$	31.0058			1.18814
$682$	2.21624	+	5.35046i	0.0848640	+	0.204880i
$683$	−36.3106	+	7.22263i	−1.38939	+	0.276366i	−0.832409	−	0.554161i	$-0.813039\pi$
$683$	−36.3106	+	7.22263i	−1.38939	+	0.276366i	−0.556978	+	0.830527i	$0.688039\pi$
$684$	5.30026	−	5.30026i	0.202660	−	0.202660i
$685$		0			0
$686$	1.79519	+	2.68669i	0.0685407	+	0.102578i
$687$	−17.9338	−	26.8398i	−0.684217	−	1.02400i
$688$	−8.89270	−	3.68348i	−0.339031	−	0.140431i
$689$	36.5074	−	15.1219i	1.39082	−	0.576097i
$690$		0			0
$691$	−14.5848	+	9.74523i	−0.554831	+	0.370726i	−0.801151	−	0.598463i	$-0.795779\pi$
$691$	−14.5848	+	9.74523i	−0.554831	+	0.370726i	0.246320	+	0.969189i	$0.420779\pi$
$692$	−3.03325	+	4.53957i	−0.115307	+	0.172569i
$693$	1.14035			0.0433184
$694$	11.7115	−	17.5275i	0.444562	−	0.665335i
$695$		0			0
$696$		−	1.47296i		−	0.0558322i
$697$	21.1782	−	7.80610i	0.802181	−	0.295677i
$698$	21.0392	+	21.0392i	0.796344	+	0.796344i
$699$	23.4489	+	9.71284i	0.886918	+	0.367374i
$700$		0			0
$701$	−8.37457	−	8.37457i	−0.316303	−	0.316303i	0.531042	−	0.847345i	$-0.321801\pi$
$701$	−8.37457	−	8.37457i	−0.316303	−	0.316303i	−0.847345	+	0.531042i	$0.821801\pi$
$702$	−29.4261	−	19.6619i	−1.11062	−	0.742090i
$703$	0.281896	−	1.41719i	0.0106319	−	0.0534503i
$704$	−3.68307	−	0.732607i	−0.138811	−	0.0276112i
$705$		0			0
$706$	−2.77427	−	6.69768i	−0.104411	−	0.252071i
$707$	3.46132	−	2.31278i	0.130176	−	0.0869810i
$708$	1.82352	+	0.362720i	0.0685319	+	0.0136318i
$709$	−1.41979	−	7.13777i	−0.0533213	−	0.268064i	0.944923	−	0.327292i	$-0.106136\pi$
$709$	−1.41979	−	7.13777i	−0.0533213	−	0.268064i	−0.998244	+	0.0592278i	$0.981136\pi$
$710$		0			0
$711$	−0.915563	−	0.611760i	−0.0343363	−	0.0229428i
$712$	13.0160	−	5.39141i	0.487796	−	0.202052i
$713$	9.37387	−	9.37387i	0.351054	−	0.351054i
$714$	−1.22641	+	0.193881i	−0.0458971	+	0.00725580i
$715$		0			0
$716$	1.70220	−	4.10947i	0.0636141	−	0.153578i
$717$	−2.38903	−	12.0105i	−0.0892200	−	0.448539i
$718$			20.8419i			0.777812i
$719$	−32.9536	+	6.55488i	−1.22896	+	0.244456i	−0.766536	−	0.642201i	$-0.778021\pi$
$719$	−32.9536	+	6.55488i	−1.22896	+	0.244456i	−0.462427	+	0.886657i	$0.653021\pi$
$720$		0			0
$721$	0.131201	−	0.659592i	0.00488618	−	0.0245645i
$722$	−5.24547	+	12.6637i	−0.195216	+	0.471294i
$723$	13.7068	−	33.0910i	0.509760	−	1.23067i
$724$	−3.13143	+	15.7428i	−0.116379	+	0.585076i
$725$		0			0
$726$	3.95394	−	0.786488i	0.146745	−	0.0291893i
$727$		−	12.7660i		−	0.473466i	−0.971575	−	0.236733i	$-0.923923\pi$
$727$		−	12.7660i		−	0.473466i	0.971575	−	0.236733i	$-0.0760767\pi$
$728$	−0.285517	−	1.43539i	−0.0105820	−	0.0531991i
$729$	10.0406	−	24.2402i	0.371875	−	0.897786i
$730$		0			0
$731$	39.1997	−	6.19702i	1.44985	−	0.229205i
$732$	9.54202	−	9.54202i	0.352683	−	0.352683i
$733$	2.63452	−	1.09125i	0.0973081	−	0.0403063i	−0.333498	−	0.942751i	$-0.608229\pi$
$733$	2.63452	−	1.09125i	0.0973081	−	0.0403063i	0.430806	+	0.902444i	$0.358229\pi$
$734$	−20.1941	−	13.4933i	−0.745377	−	0.498045i
$735$		0			0
$736$	1.67699	+	8.43077i	0.0618145	+	0.310762i
$737$	−5.06964	−	1.00841i	−0.186743	−	0.0371454i
$738$	−5.96574	+	3.98618i	−0.219602	+	0.146733i
$739$	9.96231	+	24.0512i	0.366470	+	0.884736i	0.994323	+	0.106404i	$0.0339338\pi$
$739$	9.96231	+	24.0512i	0.366470	+	0.884736i	−0.627853	+	0.778332i	$0.716066\pi$
$740$		0			0
$741$	46.0507	+	9.16006i	1.69172	+	0.336503i
$742$	−0.282768	+	1.42157i	−0.0103807	+	0.0521874i
$743$	−28.5582	−	19.0820i	−1.04770	−	0.700049i	−0.0924080	−	0.995721i	$-0.529456\pi$
$743$	−28.5582	−	19.0820i	−1.04770	−	0.700049i	−0.955289	+	0.295672i	$0.904456\pi$
$744$	1.41737	+	1.41737i	0.0519634	+	0.0519634i
$745$		0			0
$746$	7.16120	+	2.96627i	0.262190	+	0.108603i
$747$	13.3938	+	13.3938i	0.490052	+	0.490052i
$748$	14.5277	−	5.35480i	0.531186	−	0.195791i
$749$			1.30714i			0.0477620i
$750$		0			0
$751$	−19.9211	+	29.8140i	−0.726929	+	1.08793i	0.265380	+	0.964144i	$0.414503\pi$
$751$	−19.9211	+	29.8140i	−0.726929	+	1.08793i	−0.992309	+	0.123783i	$0.960497\pi$
$752$	4.58562			0.167220
$753$	−16.5152	+	24.7168i	−0.601848	+	0.900729i
$754$	−5.95198	+	3.97699i	−0.216758	+	0.144833i
$755$		0			0
$756$	1.19930	−	0.496768i	0.0436183	−	0.0180673i
$757$	2.33308	+	0.966392i	0.0847971	+	0.0351241i	0.424679	−	0.905344i	$-0.360387\pi$
$757$	2.33308	+	0.966392i	0.0847971	+	0.0351241i	−0.339882	+	0.940468i	$0.610387\pi$
$758$	−13.8305	−	20.6989i	−0.502348	−	0.751817i
$759$	−23.3091	−	34.8846i	−0.846068	−	1.26623i
$760$		0			0
$761$	−13.0853	+	13.0853i	−0.474342	+	0.474342i	−0.903316	−	0.428975i	$-0.858875\pi$
$761$	−13.0853	+	13.0853i	−0.474342	+	0.474342i	0.428975	+	0.903316i	$0.358875\pi$
$762$	15.5220	−	3.08752i	0.562303	−	0.111849i
$763$	0.0708109	+	0.170953i	0.00256353	+	0.00618890i
$764$	−1.51470			−0.0547999
$765$		0			0
$766$	−19.8825			−0.718386
$767$	−3.45781	−	8.34789i	−0.124854	−	0.301425i
$768$	−1.27477	+	0.253568i	−0.0459993	+	0.00914983i
$769$	−9.78371	+	9.78371i	−0.352810	+	0.352810i	−0.861154	−	0.508344i	$-0.830258\pi$
$769$	−9.78371	+	9.78371i	−0.352810	+	0.352810i	0.508344	+	0.861154i	$0.330258\pi$
$770$		0			0
$771$	−12.7626	−	19.1006i	−0.459634	−	0.687891i
$772$	−2.38659	−	3.57179i	−0.0858953	−	0.128551i
$773$	−34.2492	−	14.1865i	−1.23186	−	0.510252i	−0.330696	−	0.943737i	$-0.607284\pi$
$773$	−34.2492	−	14.1865i	−1.23186	−	0.510252i	−0.901161	+	0.433485i	$0.857284\pi$
$774$	−11.6553	+	4.82780i	−0.418942	+	0.173532i
$775$		0			0
$776$	4.18968	−	2.79946i	0.150401	−	0.100495i
$777$	0.0422709	−	0.0632629i	0.00151646	−	0.00226955i
$778$	10.2467			0.367364
$779$	17.3935	−	26.0312i	0.623186	−	0.932664i
$780$		0			0
$781$		−	7.21274i		−	0.258092i
$782$	−24.0505	−	26.0328i	−0.860045	−	0.930931i
$783$	−4.48971	−	4.48971i	−0.160449	−	0.160449i
$784$	−6.41756	−	2.65824i	−0.229199	−	0.0949372i
$785$		0			0
$786$	9.50713	+	9.50713i	0.339108	+	0.339108i
$787$	−0.927549	−	0.619768i	−0.0330635	−	0.0220924i	0.538929	−	0.842351i	$-0.318829\pi$
$787$	−0.927549	−	0.619768i	−0.0330635	−	0.0220924i	−0.571992	+	0.820259i	$0.693829\pi$
$788$	−3.18758	+	16.0250i	−0.113553	+	0.570868i
$789$	−8.42166	−	1.67517i	−0.299819	−	0.0596377i
$790$		0			0
$791$	0.408954	+	0.987301i	0.0145407	+	0.0351044i
$792$	−4.09235	+	2.73442i	−0.145415	+	0.0971635i
$793$	−64.3213	−	12.7943i	−2.28412	−	0.454339i
$794$	3.57747	+	17.9852i	0.126960	+	0.638270i
$795$		0			0
$796$	−10.5519	−	7.05058i	−0.374003	−	0.249901i
$797$	29.7784	−	12.3346i	1.05481	−	0.436915i	0.213201	−	0.977008i	$-0.431611\pi$
$797$	29.7784	−	12.3346i	1.05481	−	0.436915i	0.841605	+	0.540094i	$0.181611\pi$
$798$	−1.21780	+	1.21780i	−0.0431096	+	0.0431096i
$799$	−16.1237	+	9.87423i	−0.570417	+	0.349325i
$800$		0			0
$801$	7.06633	−	17.0596i	0.249676	−	0.602772i
$802$	−1.41072	−	7.09217i	−0.0498143	−	0.250433i
$803$			7.24988i			0.255843i
$804$	−1.75469	+	0.349029i	−0.0618830	+	0.0123093i
$805$		0			0
$806$	1.90047	−	9.55429i	0.0669411	−	0.336535i
$807$	4.80657	−	11.6041i	0.169199	−	0.408483i
$808$	−6.87579	+	16.5996i	−0.241890	+	0.583973i
$809$	−9.35143	+	47.0128i	−0.328779	+	1.65288i	0.363753	+	0.931495i	$0.381495\pi$
$809$	−9.35143	+	47.0128i	−0.328779	+	1.65288i	−0.692532	+	0.721387i	$0.743505\pi$
$810$		0			0
$811$	23.4134	−	4.65722i	0.822157	−	0.163537i	0.233951	−	0.972248i	$-0.424834\pi$
$811$	23.4134	−	4.65722i	0.822157	−	0.163537i	0.588206	+	0.808711i	$0.299834\pi$
$812$		−	0.262569i		−	0.00921437i
$813$	−6.81099	−	34.2411i	−0.238872	−	1.20089i
$814$	−0.363085	+	0.876564i	−0.0127261	+	0.0307236i
$815$		0			0
$816$	3.93627	−	3.63655i	0.137797	−	0.127305i
$817$	38.9246	−	38.9246i	1.36180	−	1.36180i
$818$	−5.04705	+	2.09055i	−0.176466	+	0.0730945i
$819$	−1.59490	−	1.06568i	−0.0557303	−	0.0372378i
$820$		0			0
$821$	−0.922689	−	4.63867i	−0.0322021	−	0.161891i	0.961338	−	0.275370i	$-0.0888004\pi$
$821$	−0.922689	−	4.63867i	−0.0322021	−	0.161891i	−0.993540	+	0.113479i	$0.963800\pi$
$822$	6.73119	+	1.33892i	0.234777	+	0.0467001i
$823$	39.4255	−	26.3433i	1.37429	−	0.918268i	0.374326	−	0.927297i	$-0.377874\pi$
$823$	39.4255	−	26.3433i	1.37429	−	0.918268i	0.999959	+	0.00902870i	$0.00287396\pi$
$824$	1.11078	+	2.68167i	0.0386960	+	0.0934204i
$825$		0			0
$826$	0.325060	+	0.0646584i	0.0113103	+	0.00224975i
$827$	−4.29568	+	21.5958i	−0.149375	+	0.750961i	0.831378	+	0.555708i	$0.187553\pi$
$827$	−4.29568	+	21.5958i	−0.149375	+	0.750961i	−0.980753	+	0.195253i	$0.937447\pi$
$828$	9.36766	+	6.25927i	0.325549	+	0.217525i
$829$	−25.4470	−	25.4470i	−0.883812	−	0.883812i	0.110108	−	0.993920i	$-0.464880\pi$
$829$	−25.4470	−	25.4470i	−0.883812	−	0.883812i	−0.993920	+	0.110108i	$0.964880\pi$
$830$		0			0
$831$	−26.0927	−	10.8080i	−0.905146	−	0.374924i
$832$	4.46651	+	4.46651i	0.154849	+	0.154849i
$833$	28.2891	−	4.47218i	0.980159	−	0.154952i
$834$		−	10.7462i		−	0.372112i
$835$		0			0
$836$	11.9315	−	17.8568i	0.412660	−	0.617589i
$837$	8.64058			0.298662
$838$	−5.00808	+	7.49513i	−0.173001	+	0.258915i
$839$	−0.105053	+	0.0701939i	−0.00362682	+	0.00242336i	−0.557382	−	0.830256i	$-0.688194\pi$
$839$	−0.105053	+	0.0701939i	−0.00362682	+	0.00242336i	0.553756	+	0.832679i	$0.313194\pi$
$840$		0			0
$841$	25.6060	−	10.6063i	0.882965	−	0.365736i
$842$	21.5533	+	8.92766i	0.742775	+	0.307667i
$843$	1.48995	+	2.22987i	0.0513167	+	0.0768009i
$844$	−6.72603	−	10.0662i	−0.231520	−	0.346494i
$845$		0			0
$846$	4.24986	−	4.24986i	0.146113	−	0.146113i
$847$	0.704829	−	0.140199i	0.0242182	−	0.00481730i
$848$	−2.39399	−	5.77959i	−0.0822098	−	0.198472i
$849$	−7.83897			−0.269033
$850$		0			0
$851$	2.17183			0.0744495
$852$	−0.955350	−	2.30642i	−0.0327298	−	0.0790166i
$853$	37.0917	−	7.37800i	1.27000	−	0.252618i	0.486316	−	0.873783i	$-0.338340\pi$
$853$	37.0917	−	7.37800i	1.27000	−	0.252618i	0.783680	+	0.621165i	$0.213340\pi$
$854$	1.70096	−	1.70096i	0.0582057	−	0.0582057i
$855$		0			0
$856$	−3.13437	−	4.69092i	−0.107131	−	0.160332i
$857$	4.67457	+	6.99598i	0.159680	+	0.238978i	0.902679	−	0.430314i	$-0.141597\pi$
$857$	4.67457	+	6.99598i	0.159680	+	0.238978i	−0.742999	+	0.669293i	$0.766597\pi$
$858$	−28.4835	−	11.7982i	−0.972409	−	0.402785i
$859$	−30.9791	+	12.8320i	−1.05699	+	0.437821i	−0.842383	−	0.538879i	$-0.818848\pi$
$859$	−30.9791	+	12.8320i	−1.05699	+	0.437821i	−0.214610	+	0.976700i	$0.568848\pi$
$860$		0			0
$861$	1.37070	−	0.915873i	0.0467134	−	0.0312129i
$862$	7.38136	−	11.0470i	0.251410	−	0.376262i
$863$	−26.1614			−0.890545			−0.445273	−	0.895395i	$-0.646893\pi$
$863$	−26.1614			−0.890545			−0.445273	+	0.895395i	$0.646893\pi$
$864$	−3.11273	+	4.65853i	−0.105897	+	0.158486i
$865$		0			0
$866$			15.9662i			0.542553i
$867$	−6.00994	+	21.2626i	−0.204108	+	0.722116i
$868$	0.252661	+	0.252661i	0.00857586	+	0.00857586i
$869$	−2.91475	−	1.20733i	−0.0988762	−	0.0409559i
$870$		0			0
$871$	6.14803	+	6.14803i	0.208318	+	0.208318i
$872$	−0.664041	−	0.443698i	−0.0224873	−	0.0150255i
$873$	1.28843	−	6.47739i	0.0436068	−	0.219226i
$874$	−48.2157	−	9.59070i	−1.63092	−	0.324410i
$875$		0			0
$876$	0.960270	+	2.31830i	0.0324445	+	0.0783280i
$877$	−22.0398	+	14.7265i	−0.744231	+	0.497279i	−0.868942	−	0.494914i	$-0.835200\pi$
$877$	−22.0398	+	14.7265i	−0.744231	+	0.497279i	0.124711	+	0.992193i	$0.460200\pi$
$878$	−6.70800	−	1.33430i	−0.226384	−	0.0450306i
$879$	5.73707	+	28.8422i	0.193507	+	0.972823i
$880$		0			0
$881$	−7.94047	−	5.30565i	−0.267521	−	0.178752i	0.414574	−	0.910016i	$-0.363931\pi$
$881$	−7.94047	−	5.30565i	−0.267521	−	0.178752i	−0.682095	+	0.731264i	$0.738931\pi$
$882$	−8.41126	+	3.48406i	−0.283222	+	0.117314i
$883$	−0.220809	+	0.220809i	−0.00743081	+	0.00743081i	−0.710812	−	0.703382i	$-0.751673\pi$
$883$	−0.220809	+	0.220809i	−0.00743081	+	0.00743081i	0.703382	+	0.710812i	$0.251673\pi$
$884$	−25.3227	−	6.08717i	−0.851694	−	0.204734i
$885$		0			0
$886$	−10.9637	+	26.4687i	−0.368333	+	0.889233i
$887$	−7.18445	−	36.1187i	−0.241230	−	1.21275i	−0.891492	−	0.453036i	$-0.850341\pi$
$887$	−7.18445	−	36.1187i	−0.241230	−	1.21275i	0.650262	−	0.759710i	$-0.274659\pi$
$888$			0.328391i			0.0110201i
$889$	2.76695	−	0.550381i	0.0928006	−	0.0184592i
$890$		0			0
$891$	2.45436	−	12.3389i	0.0822242	−	0.413369i
$892$	2.11973	−	5.11747i	0.0709737	−	0.171346i
$893$	−10.0360	+	24.2290i	−0.335841	+	0.810791i
$894$	1.78592	−	8.97844i	0.0597302	−	0.300284i
$895$		0			0
$896$	−0.227241	+	0.0452010i	−0.00759157	+	0.00151006i
$897$			70.5725i			2.35635i
$898$	−6.37587	−	32.0536i	−0.212765	−	1.06964i
$899$	0.668824	−	1.61468i	0.0223065	−	0.0538527i
$900$		0			0
$901$	20.8628	+	15.1669i	0.695041	+	0.505284i
$902$	−14.5361	+	14.5361i	−0.483998	+	0.483998i
$903$	2.67796	−	1.10925i	0.0891168	−	0.0369134i
$904$	−3.83503	−	2.56249i	−0.127551	−	0.0852270i
$905$		0			0
$906$	0.638057	+	3.20773i	0.0211980	+	0.106570i
$907$	−50.7536	−	10.0955i	−1.68525	−	0.335216i	−0.742785	−	0.669530i	$-0.766495\pi$
$907$	−50.7536	−	10.0955i	−1.68525	−	0.335216i	−0.942462	+	0.334314i	$0.891495\pi$
$908$	−19.8350	+	13.2533i	−0.658246	+	0.439826i
$909$	9.01185	+	21.7565i	0.298904	+	0.721618i
$910$		0			0
$911$	−35.9361	−	7.14813i	−1.19061	−	0.236828i	−0.440264	−	0.897868i	$-0.645115\pi$
$911$	−35.9361	−	7.14813i	−1.19061	−	0.236828i	−0.750351	+	0.661040i	$0.770115\pi$
$912$	1.45016	−	7.29043i	0.0480195	−	0.241410i
$913$	45.1240	+	30.1509i	1.49339	+	0.997850i
$914$	14.9555	+	14.9555i	0.494683	+	0.494683i
$915$		0			0
$916$	22.9451	+	9.50419i	0.758129	+	0.314027i
$917$	1.69474	+	1.69474i	0.0559652	+	0.0559652i
$918$	0.913597	−	23.0827i	0.0301532	−	0.761843i
$919$			28.6462i			0.944952i	0.881343	+	0.472476i	$0.156640\pi$
$919$			28.6462i			0.944952i	−0.881343	+	0.472476i	$0.843360\pi$
$920$		0			0
$921$	−16.7793	+	25.1121i	−0.552898	+	0.827471i
$922$	−36.8266			−1.21282
$923$	−6.74043	+	10.0878i	−0.221864	+	0.332043i
$924$	0.940269	−	0.628267i	0.0309326	−	0.0206685i
$925$		0			0
$926$	5.95780	−	2.46780i	0.195786	−	0.0810970i
$927$	3.51476	+	1.45586i	0.115440	+	0.0478168i
$928$	0.629608	+	0.942276i	0.0206679	+	0.0309317i
$929$	−14.1081	−	21.1142i	−0.462870	−	0.692734i	0.524456	−	0.851438i	$-0.324269\pi$
$929$	−14.1081	−	21.1142i	−0.462870	−	0.692734i	−0.987326	+	0.158703i	$0.949269\pi$
$930$		0			0
$931$	28.0906	−	28.0906i	0.920631	−	0.920631i
$932$	−19.1524	+	3.80964i	−0.627357	+	0.124789i
$933$	2.84214	+	6.86154i	0.0930476	+	0.224637i
$934$	−27.5862			−0.902647
$935$		0			0
$936$	8.27894			0.270606
$937$	−10.3892	−	25.0817i	−0.339400	−	0.819385i	−0.997774	−	0.0666932i	$-0.978755\pi$
$937$	−10.3892	−	25.0817i	−0.339400	−	0.819385i	0.658373	−	0.752692i	$-0.271245\pi$
$938$	−0.312790	+	0.0622179i	−0.0102130	+	0.00203149i
$939$	13.1479	−	13.1479i	0.429064	−	0.429064i
$940$		0			0
$941$	−3.84639	−	5.75653i	−0.125389	−	0.187657i	0.763464	−	0.645850i	$-0.223497\pi$
$941$	−3.84639	−	5.75653i	−0.125389	−	0.187657i	−0.888853	+	0.458193i	$0.848497\pi$
$942$	−5.51601	−	8.25530i	−0.179721	−	0.268972i
$943$	43.4746	+	18.0078i	1.41573	+	0.586413i
$944$	−1.32158	+	0.547416i	−0.0430137	+	0.0178169i
$945$		0			0
$946$	−30.0539	+	20.0813i	−0.977135	+	0.652901i
$947$	7.08749	−	10.6072i	0.230312	−	0.344687i	−0.698256	−	0.715848i	$-0.746040\pi$
$947$	7.08749	−	10.6072i	0.230312	−	0.344687i	0.928568	+	0.371161i	$0.121040\pi$
$948$	−1.09197			−0.0354654
$949$	6.77514	−	10.1397i	0.219930	−	0.329149i
$950$		0			0
$951$		−	13.9941i		−	0.453790i
$952$	0.701680	−	0.648251i	0.0227416	−	0.0210099i
$953$	−8.80491	−	8.80491i	−0.285219	−	0.285219i	0.549967	−	0.835186i	$-0.314640\pi$
$953$	−8.80491	−	8.80491i	−0.285219	−	0.285219i	−0.835186	+	0.549967i	$0.814640\pi$
$954$	−7.57510	−	3.13771i	−0.245253	−	0.101587i
$955$		0			0
$956$	6.66212	+	6.66212i	0.215468	+	0.215468i
$957$	−4.59909	−	3.07301i	−0.148667	−	0.0993364i
$958$	5.14003	−	25.8407i	0.166067	−	0.834874i
$959$	1.19990	+	0.238675i	0.0387469	+	0.00770723i
$960$		0			0
$961$	−10.9530	−	26.4429i	−0.353323	−	0.852998i
$962$	1.32698	−	0.886657i	0.0427834	−	0.0285870i
$963$	−7.25232	−	1.44258i	−0.233703	−	0.0464864i
$964$	5.37617	+	27.0278i	0.173155	+	0.870507i
$965$		0			0
$966$	−2.15234	−	1.43814i	−0.0692503	−	0.0462715i
$967$	20.6427	−	8.55048i	0.663824	−	0.274965i	−0.0252226	−	0.999682i	$-0.508029\pi$
$967$	20.6427	−	8.55048i	0.663824	−	0.274965i	0.689047	+	0.724717i	$0.258029\pi$
$968$	−2.19322	+	2.19322i	−0.0704929	+	0.0704929i
$969$	10.5995	+	28.7568i	0.340506	+	0.923803i
$970$		0			0
$971$	22.0127	−	53.1434i	0.706421	−	1.70545i	−0.00233344	−	0.999997i	$-0.500743\pi$
$971$	22.0127	−	53.1434i	0.706421	−	1.70545i	0.708755	−	0.705455i	$-0.249257\pi$
$972$	2.42964	+	12.2146i	0.0779307	+	0.391784i
$973$		−	1.91562i		−	0.0614121i
$974$	−15.2706	+	3.03751i	−0.489302	+	0.0973282i
$975$		0			0
$976$	−2.02550	+	10.1829i	−0.0648348	+	0.325946i
$977$	−10.9310	+	26.3897i	−0.349713	+	0.844282i	0.646941	+	0.762540i	$0.276048\pi$
$977$	−10.9310	+	26.3897i	−0.349713	+	0.844282i	−0.996654	+	0.0817415i	$0.973952\pi$
$978$	−11.6177	+	28.0477i	−0.371495	+	0.896867i
$979$	10.3213	−	51.8887i	0.329870	−	1.65837i
$980$		0			0
$981$	−1.02663	+	0.204209i	−0.0327777	+	0.00651990i
$982$		−	29.4001i		−	0.938195i
$983$	−8.03048	−	40.3720i	−0.256133	−	1.28767i	−0.867944	−	0.496662i	$-0.834559\pi$
$983$	−8.03048	−	40.3720i	−0.256133	−	1.28767i	0.611812	−	0.791004i	$-0.290441\pi$
$984$	−2.72285	+	6.57355i	−0.0868014	+	0.209557i
$985$		0			0
$986$	−4.24280	−	1.95744i	−0.135118	−	0.0623377i
$987$	−0.976458	+	0.976458i	−0.0310810	+	0.0310810i
$988$	−33.3749	+	13.8243i	−1.06180	+	0.439811i
$989$	68.7952	+	45.9675i	2.18756	+	1.46168i
$990$		0			0
$991$	1.32060	+	6.63910i	0.0419502	+	0.210898i	0.996075	−	0.0885106i	$-0.0282107\pi$
$991$	1.32060	+	6.63910i	0.0419502	+	0.210898i	−0.954125	+	0.299408i	$0.903211\pi$
$992$	−1.51257	−	0.300868i	−0.0480240	−	0.00955258i
$993$	6.91150	−	4.61812i	0.219330	−	0.146552i
$994$	−0.170301	−	0.411142i	−0.00540161	−	0.0130406i
$995$		0			0
$996$	18.4229	+	3.66454i	0.583752	+	0.116116i
$997$	3.41136	−	17.1501i	0.108039	−	0.543148i	−0.888417	−	0.459037i	$-0.848195\pi$
$997$	3.41136	−	17.1501i	0.108039	−	0.543148i	0.996456	−	0.0841118i	$-0.0268053\pi$
$998$	−1.84513	−	1.23288i	−0.0584066	−	0.0390261i
$999$	1.00097	+	1.00097i	0.0316692	+	0.0316692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.v.d.143.4		40
5.2	odd	4		850.2.s.d.7.2		40
5.3	odd	4		170.2.o.b.7.4	✓	40
5.4	even	2		170.2.r.b.143.2	yes	40
17.5	odd	16		850.2.s.d.243.2		40
85.22	even	16	inner	850.2.v.d.107.4		40
85.39	odd	16		170.2.o.b.73.4	yes	40
85.73	even	16		170.2.r.b.107.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.7.4	✓	40	5.3	odd	4
170.2.o.b.73.4	yes	40	85.39	odd	16
170.2.r.b.107.2	yes	40	85.73	even	16
170.2.r.b.143.2	yes	40	5.4	even	2
850.2.s.d.7.2		40	5.2	odd	4
850.2.s.d.243.2		40	17.5	odd	16
850.2.v.d.107.4		40	85.22	even	16	inner
850.2.v.d.143.4		40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.v (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{2} +(1.27477 - 0.253568i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(0.722100 + 1.08070i) q^{6} +(0.128721 + 0.192645i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.21089 + 0.501569i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.923880i) q^{2} +(1.27477 - 0.253568i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(0.722100 + 1.08070i) q^{6} +(0.128721 + 0.192645i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(-1.21089 + 0.501569i) q^{9} +(-3.12235 + 2.08629i) q^{11} +(-0.722100 + 1.08070i) q^{12} +6.31661 q^{13} +(-0.128721 + 0.192645i) q^{14} -1.00000i q^{16} +(2.15330 + 3.51615i) q^{17} +(-0.926779 - 0.926779i) q^{18} +(5.28368 + 2.18857i) q^{19} +(0.212939 + 0.212939i) q^{21} +(-3.12235 - 2.08629i) q^{22} +(-1.67699 + 8.43077i) q^{23} +(-1.27477 - 0.253568i) q^{24} +(2.41726 + 5.83578i) q^{26} +(-4.65853 + 3.11273i) q^{27} +(-0.227241 - 0.0452010i) q^{28} +(0.221089 + 1.11149i) q^{29} +(-1.28229 - 0.856800i) q^{31} +(0.923880 - 0.382683i) q^{32} +(-3.45127 + 3.45127i) q^{33} +(-2.42446 + 3.33496i) q^{34} +(0.501569 - 1.21089i) q^{36} +(-0.0492911 - 0.247803i) q^{37} +5.71901i q^{38} +(8.05222 - 1.60169i) q^{39} +(1.06798 - 5.36909i) q^{41} +(-0.115242 + 0.278218i) q^{42} +(3.68348 - 8.89270i) q^{43} +(0.732607 - 3.68307i) q^{44} +(-8.43077 + 1.67699i) q^{46} +4.58562i q^{47} +(-0.253568 - 1.27477i) q^{48} +(2.65824 - 6.41756i) q^{49} +(3.63655 + 3.93627i) q^{51} +(-4.46651 + 4.46651i) q^{52} +(5.77959 - 2.39399i) q^{53} +(-4.65853 - 3.11273i) q^{54} +(-0.0452010 - 0.227241i) q^{56} +(7.29043 + 1.45016i) q^{57} +(-0.942276 + 0.629608i) q^{58} +(-0.547416 - 1.32158i) q^{59} +(-10.1829 - 2.02550i) q^{61} +(0.300868 - 1.51257i) q^{62} +(-0.252493 - 0.168710i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-4.50930 - 1.86781i) q^{66} +(0.973313 + 0.973313i) q^{67} +(-4.00891 - 0.963677i) q^{68} +11.1725i q^{69} +(-1.06710 + 1.59702i) q^{71} +1.31066 q^{72} +(1.07259 - 1.60525i) q^{73} +(0.210077 - 0.140369i) q^{74} +(-5.28368 + 2.18857i) q^{76} +(-0.803827 - 0.332956i) q^{77} +(4.56122 + 6.82635i) q^{78} +(0.466756 + 0.698549i) q^{79} +(-2.36893 + 2.36893i) q^{81} +(5.36909 - 1.06798i) q^{82} +(-5.53052 - 13.3518i) q^{83} -0.301141 q^{84} +9.62539 q^{86} +(0.563676 + 1.36083i) q^{87} +(3.68307 - 0.732607i) q^{88} +(-9.96203 + 9.96203i) q^{89} +(0.813083 + 1.21686i) q^{91} +(-4.77565 - 7.14727i) q^{92} +(-1.85189 - 0.767076i) q^{93} +(-4.23656 + 1.75484i) q^{94} +(1.08070 - 0.722100i) q^{96} +(-2.79946 + 4.18968i) q^{97} +6.94632 q^{98} +(2.73442 - 4.09235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} + 8 q^{28} + 8 q^{29} - 16 q^{31} + 32 q^{33} + 8 q^{34} - 32 q^{39} - 56 q^{41} + 24 q^{42} - 16 q^{43} + 16 q^{44} + 16 q^{49} - 32 q^{51} + 16 q^{52} - 16 q^{53} - 24 q^{54} - 8 q^{56} + 120 q^{57} - 16 q^{58} + 24 q^{61} + 8 q^{62} + 24 q^{63} - 16 q^{67} + 24 q^{71} - 56 q^{72} - 88 q^{73} + 32 q^{74} - 24 q^{77} - 32 q^{78} - 104 q^{79} + 48 q^{81} - 16 q^{82} - 16 q^{83} + 96 q^{86} - 136 q^{87} - 16 q^{89} + 48 q^{91} + 8 q^{92} + 8 q^{93} - 8 q^{94} - 16 q^{97} - 72 q^{98} + 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 + 8 * q^28 + 8 * q^29 - 16 * q^31 + 32 * q^33 + 8 * q^34 - 32 * q^39 - 56 * q^41 + 24 * q^42 - 16 * q^43 + 16 * q^44 + 16 * q^49 - 32 * q^51 + 16 * q^52 - 16 * q^53 - 24 * q^54 - 8 * q^56 + 120 * q^57 - 16 * q^58 + 24 * q^61 + 8 * q^62 + 24 * q^63 - 16 * q^67 + 24 * q^71 - 56 * q^72 - 88 * q^73 + 32 * q^74 - 24 * q^77 - 32 * q^78 - 104 * q^79 + 48 * q^81 - 16 * q^82 - 16 * q^83 + 96 * q^86 - 136 * q^87 - 16 * q^89 + 48 * q^91 + 8 * q^92 + 8 * q^93 - 8 * q^94 - 16 * q^97 - 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

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Database

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