LMFDB - Embedded newform 85.2.l.a.36.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, 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("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			36.4
Character	$\chi$	$=$	85.36
Dual form			85.2.l.a.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.213325 + 0.213325i) q^{2} +(0.980249 - 0.406032i) q^{3} -1.90899i q^{4} +(-0.382683 - 0.923880i) q^{5} +(0.295728 + 0.122495i) q^{6} +(-0.960473 + 2.31879i) q^{7} +(0.833883 - 0.833883i) q^{8} +(-1.32529 + 1.32529i) q^{9} +(0.115451 - 0.278722i) q^{10} +(2.25941 + 0.935880i) q^{11} +(-0.775110 - 1.87128i) q^{12} +5.61335i q^{13} +(-0.699548 + 0.289762i) q^{14} +(-0.750250 - 0.750250i) q^{15} -3.46219 q^{16} +(2.76113 - 3.06205i) q^{17} -0.565436 q^{18} +(-5.04243 - 5.04243i) q^{19} +(-1.76367 + 0.730537i) q^{20} +2.66297i q^{21} +(0.282343 + 0.681636i) q^{22} +(0.795280 + 0.329416i) q^{23} +(0.478830 - 1.15600i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-1.19747 + 1.19747i) q^{26} +(-1.97910 + 4.77798i) q^{27} +(4.42653 + 1.83353i) q^{28} +(-1.43561 - 3.46587i) q^{29} -0.320094i q^{30} +(-2.07626 + 0.860015i) q^{31} +(-2.40634 - 2.40634i) q^{32} +2.59479 q^{33} +(1.24223 - 0.0641935i) q^{34} +2.50984 q^{35} +(2.52997 + 2.52997i) q^{36} +(4.71693 - 1.95382i) q^{37} -2.15135i q^{38} +(2.27920 + 5.50249i) q^{39} +(-1.08952 - 0.451294i) q^{40} +(4.72598 - 11.4095i) q^{41} +(-0.568078 + 0.568078i) q^{42} +(-1.85272 + 1.85272i) q^{43} +(1.78658 - 4.31319i) q^{44} +(1.73158 + 0.717244i) q^{45} +(0.0993804 + 0.239926i) q^{46} +2.30114i q^{47} +(-3.39381 + 1.40576i) q^{48} +(0.495478 + 0.495478i) q^{49} -0.301687 q^{50} +(1.46330 - 4.12268i) q^{51} +10.7158 q^{52} +(1.96204 + 1.96204i) q^{53} +(-1.44145 + 0.597069i) q^{54} -2.44557i q^{55} +(1.13268 + 2.73452i) q^{56} +(-6.99022 - 2.89544i) q^{57} +(0.433105 - 1.04561i) q^{58} +(-5.26206 + 5.26206i) q^{59} +(-1.43222 + 1.43222i) q^{60} +(-0.346822 + 0.837303i) q^{61} +(-0.626380 - 0.259455i) q^{62} +(-1.80017 - 4.34599i) q^{63} +5.89773i q^{64} +(5.18606 - 2.14814i) q^{65} +(0.553532 + 0.553532i) q^{66} -6.69889 q^{67} +(-5.84541 - 5.27096i) q^{68} +0.913326 q^{69} +(0.535411 + 0.535411i) q^{70} +(0.222439 - 0.0921372i) q^{71} +2.21028i q^{72} +(-2.47116 - 5.96591i) q^{73} +(1.42304 + 0.589441i) q^{74} +(-0.406032 + 0.980249i) q^{75} +(-9.62592 + 9.62592i) q^{76} +(-4.34022 + 4.34022i) q^{77} +(-0.687606 + 1.66003i) q^{78} +(13.5899 + 5.62912i) q^{79} +(1.32492 + 3.19865i) q^{80} -0.135560i q^{81} +(3.44210 - 1.42577i) q^{82} +(-9.82767 - 9.82767i) q^{83} +5.08358 q^{84} +(-3.88561 - 1.37916i) q^{85} -0.790460 q^{86} +(-2.81451 - 2.81451i) q^{87} +(2.66450 - 1.10367i) q^{88} -0.395163i q^{89} +(0.216383 + 0.522395i) q^{90} +(-13.0162 - 5.39148i) q^{91} +(0.628850 - 1.51818i) q^{92} +(-1.68606 + 1.68606i) q^{93} +(-0.490889 + 0.490889i) q^{94} +(-2.72894 + 6.58825i) q^{95} +(-3.33586 - 1.38176i) q^{96} +(3.42855 + 8.27725i) q^{97} +0.211396i q^{98} +(-4.23471 + 1.75407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	0.213325	+	0.213325i	0.150843	+	0.150843i	0.778495	−	0.627651i	$-0.215984\pi$
$2$	0.213325	+	0.213325i	0.150843	+	0.150843i	−0.627651	+	0.778495i	$0.715984\pi$
$3$	0.980249	−	0.406032i	0.565947	−	0.234423i	−0.0813177	−	0.996688i	$-0.525913\pi$
$3$	0.980249	−	0.406032i	0.565947	−	0.234423i	0.647265	+	0.762265i	$0.275913\pi$
$4$		−	1.90899i		−	0.954493i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$5$	−0.382683	−	0.923880i	−0.171141	−	0.413171i
$6$	0.295728	+	0.122495i	0.120731	+	0.0500082i
$7$	−0.960473	+	2.31879i	−0.363025	+	0.876420i	0.631830	+	0.775107i	$0.282304\pi$
$7$	−0.960473	+	2.31879i	−0.363025	+	0.876420i	−0.994855	+	0.101312i	$0.967696\pi$
$8$	0.833883	−	0.833883i	0.294822	−	0.294822i
$9$	−1.32529	+	1.32529i	−0.441765	+	0.441765i
$10$	0.115451	−	0.278722i	0.0365087	−	0.0881397i
$11$	2.25941	+	0.935880i	0.681239	+	0.282179i	0.696345	−	0.717707i	$-0.254808\pi$
$11$	2.25941	+	0.935880i	0.681239	+	0.282179i	−0.0151056	+	0.999886i	$0.504808\pi$
$12$	−0.775110	−	1.87128i	−0.223755	−	0.540192i
$13$			5.61335i			1.55686i	0.627729	+	0.778432i	$0.283985\pi$
$13$			5.61335i			1.55686i	−0.627729	+	0.778432i	$0.716015\pi$
$14$	−0.699548	+	0.289762i	−0.186962	+	0.0774422i
$15$	−0.750250	−	0.750250i	−0.193714	−	0.193714i
$16$	−3.46219			−0.865549
$17$	2.76113	−	3.06205i	0.669673	−	0.742656i
$17$	2.76113	−	3.06205i	0.669673	−	0.742656i
$18$	−0.565436			−0.133275
$19$	−5.04243	−	5.04243i	−1.15681	−	1.15681i	−0.985157	−	0.171655i	$-0.945089\pi$
$19$	−5.04243	−	5.04243i	−1.15681	−	1.15681i	−0.171655	−	0.985157i	$-0.554911\pi$
$20$	−1.76367	+	0.730537i	−0.394369	+	0.163353i
$21$			2.66297i			0.581108i
$22$	0.282343	+	0.681636i	0.0601957	+	0.145325i
$23$	0.795280	+	0.329416i	0.165827	+	0.0686880i	0.464053	−	0.885807i	$-0.346395\pi$
$23$	0.795280	+	0.329416i	0.165827	+	0.0686880i	−0.298226	+	0.954495i	$0.596395\pi$
$24$	0.478830	−	1.15600i	0.0977407	−	0.235967i
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	−1.19747	+	1.19747i	−0.234843	+	0.234843i
$27$	−1.97910	+	4.77798i	−0.380879	+	0.919522i
$28$	4.42653	+	1.83353i	0.836536	+	0.346505i
$29$	−1.43561	−	3.46587i	−0.266586	−	0.643597i	0.732732	−	0.680518i	$-0.238245\pi$
$29$	−1.43561	−	3.46587i	−0.266586	−	0.643597i	−0.999318	+	0.0369210i	$0.988245\pi$
$30$		−	0.320094i		−	0.0584409i
$31$	−2.07626	+	0.860015i	−0.372907	+	0.154463i	−0.561263	−	0.827638i	$-0.689684\pi$
$31$	−2.07626	+	0.860015i	−0.372907	+	0.154463i	0.188356	+	0.982101i	$0.439684\pi$
$32$	−2.40634	−	2.40634i	−0.425385	−	0.425385i
$33$	2.59479			0.451694
$34$	1.24223	−	0.0641935i	0.213041	−	0.0110091i
$35$	2.50984			0.424240
$36$	2.52997	+	2.52997i	0.421661	+	0.421661i
$37$	4.71693	−	1.95382i	0.775459	−	0.321206i	0.0403776	−	0.999184i	$-0.487144\pi$
$37$	4.71693	−	1.95382i	0.775459	−	0.321206i	0.735081	+	0.677979i	$0.237144\pi$
$38$		−	2.15135i		−	0.348995i
$39$	2.27920	+	5.50249i	0.364965	+	0.881103i
$40$	−1.08952	−	0.451294i	−0.172268	−	0.0713559i
$41$	4.72598	−	11.4095i	0.738074	−	1.78187i	0.124518	−	0.992217i	$-0.460262\pi$
$41$	4.72598	−	11.4095i	0.738074	−	1.78187i	0.613556	−	0.789651i	$-0.289738\pi$
$42$	−0.568078	+	0.568078i	−0.0876564	+	0.0876564i
$43$	−1.85272	+	1.85272i	−0.282536	+	0.282536i	−0.834120	−	0.551583i	$-0.814024\pi$
$43$	−1.85272	+	1.85272i	−0.282536	+	0.282536i	0.551583	+	0.834120i	$0.314024\pi$
$44$	1.78658	−	4.31319i	0.269337	−	0.650238i
$45$	1.73158	+	0.717244i	0.258129	+	0.106920i
$46$	0.0993804	+	0.239926i	0.0146528	+	0.0353751i
$47$			2.30114i			0.335655i	0.985816	+	0.167828i	$0.0536752\pi$
$47$			2.30114i			0.335655i	−0.985816	+	0.167828i	$0.946325\pi$
$48$	−3.39381	+	1.40576i	−0.489855	+	0.202904i
$49$	0.495478	+	0.495478i	0.0707826	+	0.0707826i
$50$	−0.301687			−0.0426650
$51$	1.46330	−	4.12268i	0.204904	−	0.577291i
$52$	10.7158			1.48602
$53$	1.96204	+	1.96204i	0.269507	+	0.269507i	0.828902	−	0.559394i	$-0.188966\pi$
$53$	1.96204	+	1.96204i	0.269507	+	0.269507i	−0.559394	+	0.828902i	$0.688966\pi$
$54$	−1.44145	+	0.597069i	−0.196157	+	0.0812508i
$55$		−	2.44557i		−	0.329761i
$56$	1.13268	+	2.73452i	0.151360	+	0.365416i
$57$	−6.99022	−	2.89544i	−0.925877	−	0.383511i
$58$	0.433105	−	1.04561i	0.0568695	−	0.137295i
$59$	−5.26206	+	5.26206i	−0.685062	+	0.685062i	−0.961136	−	0.276075i	$-0.910966\pi$
$59$	−5.26206	+	5.26206i	−0.685062	+	0.685062i	0.276075	+	0.961136i	$0.410966\pi$
$60$	−1.43222	+	1.43222i	−0.184898	+	0.184898i
$61$	−0.346822	+	0.837303i	−0.0444061	+	0.107206i	−0.944526	−	0.328436i	$-0.893478\pi$
$61$	−0.346822	+	0.837303i	−0.0444061	+	0.107206i	0.900120	+	0.435642i	$0.143478\pi$
$62$	−0.626380	−	0.259455i	−0.0795504	−	0.0329508i
$63$	−1.80017	−	4.34599i	−0.226800	−	0.547543i
$64$			5.89773i			0.737216i
$65$	5.18606	−	2.14814i	0.643252	−	0.266444i
$66$	0.553532	+	0.553532i	0.0681351	+	0.0681351i
$67$	−6.69889			−0.818399			−0.409200	−	0.912445i	$-0.634192\pi$
$67$	−6.69889			−0.818399			−0.409200	+	0.912445i	$0.634192\pi$
$68$	−5.84541	−	5.27096i	−0.708860	−	0.639198i
$69$	0.913326			0.109952
$70$	0.535411	+	0.535411i	0.0639938	+	0.0639938i
$71$	0.222439	−	0.0921372i	0.0263986	−	0.0109347i	−0.369445	−	0.929253i	$-0.620452\pi$
$71$	0.222439	−	0.0921372i	0.0263986	−	0.0109347i	0.395844	+	0.918318i	$0.370452\pi$
$72$			2.21028i			0.260484i
$73$	−2.47116	−	5.96591i	−0.289228	−	0.698257i	0.710759	−	0.703436i	$-0.248352\pi$
$73$	−2.47116	−	5.96591i	−0.289228	−	0.698257i	−0.999987	+	0.00517825i	$0.998352\pi$
$74$	1.42304	+	0.589441i	0.165425	+	0.0685211i
$75$	−0.406032	+	0.980249i	−0.0468846	+	0.113189i
$76$	−9.62592	+	9.62592i	−1.10417	+	1.10417i
$77$	−4.34022	+	4.34022i	−0.494614	+	0.494614i
$78$	−0.687606	+	1.66003i	−0.0778560	+	0.187961i
$79$	13.5899	+	5.62912i	1.52898	+	0.633325i	0.979366	−	0.202093i	$-0.0647743\pi$
$79$	13.5899	+	5.62912i	1.52898	+	0.633325i	0.549615	+	0.835418i	$0.314774\pi$
$80$	1.32492	+	3.19865i	0.148131	+	0.357620i
$81$		−	0.135560i		−	0.0150623i
$82$	3.44210	−	1.42577i	0.380117	−	0.157449i
$83$	−9.82767	−	9.82767i	−1.07873	−	1.07873i	−0.996624	−	0.0821031i	$-0.973836\pi$
$83$	−9.82767	−	9.82767i	−1.07873	−	1.07873i	−0.0821031	−	0.996624i	$-0.526164\pi$
$84$	5.08358			0.554664
$85$	−3.88561	−	1.37916i	−0.421453	−	0.149591i
$86$	−0.790460			−0.0852375
$87$	−2.81451	−	2.81451i	−0.301748	−	0.301748i
$88$	2.66450	−	1.10367i	0.284037	−	0.117652i
$89$		−	0.395163i		−	0.0418872i	−0.999781	−	0.0209436i	$-0.993333\pi$
$89$		−	0.395163i		−	0.0418872i	0.999781	−	0.0209436i	$-0.00666704\pi$
$90$	0.216383	+	0.522395i	0.0228088	+	0.0550653i
$91$	−13.0162	−	5.39148i	−1.36447	−	0.565181i
$92$	0.628850	−	1.51818i	0.0655621	−	0.158281i
$93$	−1.68606	+	1.68606i	−0.174836	+	0.174836i
$94$	−0.490889	+	0.490889i	−0.0506314	+	0.0506314i
$95$	−2.72894	+	6.58825i	−0.279983	+	0.675940i
$96$	−3.33586	−	1.38176i	−0.340465	−	0.141025i
$97$	3.42855	+	8.27725i	0.348116	+	0.840427i	0.996842	+	0.0794052i	$0.0253021\pi$
$97$	3.42855	+	8.27725i	0.348116	+	0.840427i	−0.648726	+	0.761022i	$0.724698\pi$
$98$			0.211396i			0.0213542i
$99$	−4.23471	+	1.75407i	−0.425604	+	0.176291i
$100$	1.34986	+	1.34986i	0.134986	+	0.134986i
$101$	15.2882			1.52124			0.760619	−	0.649199i	$-0.224896\pi$
$101$	15.2882			1.52124			0.760619	+	0.649199i	$0.224896\pi$
$102$	1.19163	−	0.567311i	0.117989	−	0.0561721i
$103$	−14.7746			−1.45579			−0.727894	−	0.685690i	$-0.759501\pi$
$103$	−14.7746			−1.45579			−0.727894	+	0.685690i	$0.759501\pi$
$104$	4.68088	+	4.68088i	0.458998	+	0.458998i
$105$	2.46027	−	1.01908i	0.240097	−	0.0994516i
$106$			0.837105i			0.0813068i
$107$	0.562841	+	1.35882i	0.0544119	+	0.131362i	0.948748	−	0.316034i	$-0.102351\pi$
$107$	0.562841	+	1.35882i	0.0544119	+	0.131362i	−0.894336	+	0.447396i	$0.852351\pi$
$108$	9.12109	+	3.77808i	0.877677	+	0.363546i
$109$	3.61166	−	8.71931i	0.345934	−	0.835158i	−0.651157	−	0.758943i	$-0.725716\pi$
$109$	3.61166	−	8.71931i	0.345934	−	0.835158i	0.997091	−	0.0762157i	$-0.0242838\pi$
$110$	0.521701	−	0.521701i	0.0497423	−	0.0497423i
$111$	3.83046	−	3.83046i	0.363571	−	0.363571i
$112$	3.32535	−	8.02809i	0.314216	−	0.758584i
$113$	13.8222	+	5.72534i	1.30028	+	0.538595i	0.922034	−	0.387109i	$-0.126526\pi$
$113$	13.8222	+	5.72534i	1.30028	+	0.538595i	0.378249	+	0.925704i	$0.376526\pi$
$114$	−0.873517	−	2.10886i	−0.0818124	−	0.197513i
$115$		−	0.860805i		−	0.0802705i
$116$	−6.61630	+	2.74056i	−0.614308	+	0.254455i
$117$	−7.43935	−	7.43935i	−0.687768	−	0.687768i
$118$	−2.24505			−0.206674
$119$	4.44825	+	9.34350i	0.407771	+	0.856517i
$120$	−1.25124			−0.114222
$121$	−3.54909	−	3.54909i	−0.322645	−	0.322645i
$122$	−0.252603	+	0.104632i	−0.0228696	+	0.00947291i
$123$		−	13.1031i		−	1.18146i
$124$	1.64176	+	3.96355i	0.147434	+	0.355937i
$125$	0.923880	+	0.382683i	0.0826343	+	0.0342282i
$126$	0.543087	−	1.31113i	0.0483820	−	0.116804i
$127$	4.21071	−	4.21071i	0.373640	−	0.373640i	−0.495161	−	0.868801i	$-0.664891\pi$
$127$	4.21071	−	4.21071i	0.373640	−	0.373640i	0.868801	+	0.495161i	$0.164891\pi$
$128$	−6.07081	+	6.07081i	−0.536589	+	0.536589i
$129$	−1.06386	+	2.56839i	−0.0936677	+	0.226134i
$130$	1.56457	+	0.648065i	0.137222	+	0.0568390i
$131$	−1.60241	−	3.86856i	−0.140003	−	0.337998i	0.838290	−	0.545225i	$-0.183556\pi$
$131$	−1.60241	−	3.86856i	−0.140003	−	0.337998i	−0.978293	+	0.207228i	$0.933556\pi$
$132$		−	4.95341i		−	0.431139i
$133$	16.5354	−	6.84920i	1.43380	−	0.593901i
$134$	−1.42904	−	1.42904i	−0.123450	−	0.123450i
$135$	5.17165			0.445104
$136$	−0.250931	−	4.85585i	−0.0215172	−	0.416386i
$137$	7.25998			0.620262			0.310131	−	0.950694i	$-0.399627\pi$
$137$	7.25998			0.620262			0.310131	+	0.950694i	$0.399627\pi$
$138$	0.194835	+	0.194835i	0.0165855	+	0.0165855i
$139$	9.60207	−	3.97731i	0.814437	−	0.337351i	0.0637140	−	0.997968i	$-0.479705\pi$
$139$	9.60207	−	3.97731i	0.814437	−	0.337351i	0.750723	+	0.660617i	$0.229705\pi$
$140$		−	4.79124i		−	0.404934i
$141$	0.934336	+	2.25569i	0.0786853	+	0.189963i
$142$	0.0671069	+	0.0277966i	0.00563149	+	0.00233264i
$143$	−5.25343	+	12.6829i	−0.439314	+	1.06060i
$144$	4.58843	−	4.58843i	0.382369	−	0.382369i
$145$	−2.65267	+	2.65267i	−0.220292	+	0.220292i
$146$	0.745517	−	1.79984i	0.0616994	−	0.148956i
$147$	0.686873	+	0.284512i	0.0566523	+	0.0234661i
$148$	−3.72981	−	9.00455i	−0.306588	−	0.740170i
$149$			6.01765i			0.492985i	0.969145	+	0.246492i	$0.0792781\pi$
$149$			6.01765i			0.492985i	−0.969145	+	0.246492i	$0.920722\pi$
$150$	−0.295728	+	0.122495i	−0.0241461	+	0.0100016i
$151$	7.36684	+	7.36684i	0.599505	+	0.599505i	0.940181	−	0.340676i	$-0.110656\pi$
$151$	7.36684	+	7.36684i	0.599505	+	0.599505i	−0.340676	+	0.940181i	$0.610656\pi$
$152$	−8.40959			−0.682108
$153$	0.398806	+	7.71743i	0.0322416	+	0.623917i
$154$	−1.85175			−0.149218
$155$	1.58910	+	1.58910i	0.127640	+	0.127640i
$156$	10.5042	−	4.35097i	0.841006	−	0.348356i
$157$			13.4073i			1.07002i	0.844847	+	0.535008i	$0.179691\pi$
$157$			13.4073i			1.07002i	−0.844847	+	0.535008i	$0.820309\pi$
$158$	1.69823	+	4.09989i	0.135104	+	0.326170i
$159$	2.71994	+	1.12664i	0.215706	+	0.0893482i
$160$	−1.30230	+	3.14403i	−0.102956	+	0.248558i
$161$	−1.52769	+	1.52769i	−0.120399	+	0.120399i
$162$	0.0289184	−	0.0289184i	0.00227204	−	0.00227204i
$163$	0.602777	−	1.45523i	0.0472132	−	0.113983i	−0.898513	−	0.438946i	$-0.855352\pi$
$163$	0.602777	−	1.45523i	0.0472132	−	0.113983i	0.945727	+	0.324963i	$0.105352\pi$
$164$	−21.7806	−	9.02182i	−1.70078	−	0.704486i
$165$	−0.992982	−	2.39727i	−0.0773035	−	0.186627i
$166$		−	4.19297i		−	0.325438i
$167$	−16.2648	+	6.73711i	−1.25861	+	0.521333i	−0.909482	−	0.415742i	$-0.863522\pi$
$167$	−16.2648	+	6.73711i	−1.25861	+	0.521333i	−0.349127	+	0.937075i	$0.613522\pi$
$168$	2.22061	+	2.22061i	0.171324	+	0.171324i
$169$	−18.5098			−1.42383
$170$	−0.534688	−	1.12310i	−0.0410087	−	0.0861382i
$171$	13.3654			1.02208
$172$	3.53681	+	3.53681i	0.269679	+	0.269679i
$173$	−17.4086	+	7.21087i	−1.32355	+	0.548232i	−0.928808	−	0.370560i	$-0.879166\pi$
$173$	−17.4086	+	7.21087i	−1.32355	+	0.548232i	−0.394741	+	0.918792i	$0.629166\pi$
$174$		−	1.20081i		−	0.0910333i
$175$	−0.960473	−	2.31879i	−0.0726050	−	0.175284i
$176$	−7.82253	−	3.24020i	−0.589646	−	0.244239i
$177$	−3.02156	+	7.29469i	−0.227114	+	0.548303i
$178$	0.0842980	−	0.0842980i	0.00631840	−	0.00631840i
$179$	2.34324	−	2.34324i	0.175142	−	0.175142i	−0.614092	−	0.789234i	$-0.710478\pi$
$179$	2.34324	−	2.34324i	0.175142	−	0.175142i	0.789234	+	0.614092i	$0.210478\pi$
$180$	1.36921	−	3.30556i	0.102055	−	0.246382i
$181$	−14.6575	−	6.07133i	−1.08948	−	0.451278i	−0.235656	−	0.971836i	$-0.575724\pi$
$181$	−14.6575	−	6.07133i	−1.08948	−	0.451278i	−0.853826	+	0.520558i	$0.825724\pi$
$182$	−1.62654	−	3.92681i	−0.120567	−	0.291075i
$183$			0.961587i			0.0710826i
$184$	0.937865	−	0.388477i	0.0691404	−	0.0286389i
$185$	−3.61018	−	3.61018i	−0.265426	−	0.265426i
$186$	−0.719356			−0.0527457
$187$	9.10425	−	4.33435i	0.665769	−	0.316959i
$188$	4.39284			0.320380
$189$	−9.17824	−	9.17824i	−0.667619	−	0.667619i
$190$	−1.98759	+	0.823286i	−0.144195	+	0.0597274i
$191$			27.4943i			1.98941i	0.102748	+	0.994707i	$0.467236\pi$
$191$			27.4943i			1.98941i	−0.102748	+	0.994707i	$0.532764\pi$
$192$	2.39467	+	5.78124i	0.172820	+	0.417225i
$193$	13.6376	+	5.64889i	0.981658	+	0.406616i	0.815040	−	0.579405i	$-0.196715\pi$
$193$	13.6376	+	5.64889i	0.981658	+	0.406616i	0.166619	+	0.986021i	$0.446715\pi$
$194$	−1.03435	+	2.49714i	−0.0742618	+	0.179284i
$195$	4.21142	−	4.21142i	0.301586	−	0.301586i
$196$	0.945861	−	0.945861i	0.0675615	−	0.0675615i
$197$	−0.144044	+	0.347754i	−0.0102627	+	0.0247764i	−0.928928	−	0.370261i	$-0.879268\pi$
$197$	−0.144044	+	0.347754i	−0.0102627	+	0.0247764i	0.918665	+	0.395037i	$0.129268\pi$
$198$	−1.27756	−	0.529181i	−0.0907919	−	0.0376072i
$199$	2.88162	+	6.95685i	0.204273	+	0.493158i	0.992503	−	0.122223i	$-0.0390022\pi$
$199$	2.88162	+	6.95685i	0.204273	+	0.493158i	−0.788230	+	0.615381i	$0.789002\pi$
$200$			1.17929i			0.0833883i
$201$	−6.56658	+	2.71996i	−0.463171	+	0.191852i
$202$	3.26136	+	3.26136i	0.229469	+	0.229469i
$203$	9.41549			0.660838
$204$	−7.87014	−	2.79343i	−0.551020	−	0.195579i
$205$	−12.3496			−0.862532
$206$	−3.15180	−	3.15180i	−0.219596	−	0.219596i
$207$	−1.49055	+	0.617408i	−0.103601	+	0.0429128i
$208$		−	19.4345i		−	1.34754i
$209$	−6.67383	−	16.1120i	−0.461638	−	1.11449i
$210$	0.742230	+	0.307442i	0.0512187	+	0.0212155i
$211$	3.32647	−	8.03080i	0.229003	−	0.552863i	−0.767053	−	0.641584i	$-0.778278\pi$
$211$	3.32647	−	8.03080i	0.229003	−	0.552863i	0.996057	+	0.0887204i	$0.0282778\pi$
$212$	3.74551	−	3.74551i	0.257243	−	0.257243i
$213$	0.180635	−	0.180635i	0.0123769	−	0.0123769i
$214$	−0.169802	+	0.409938i	−0.0116074	+	0.0280228i
$215$	2.42069	+	1.00268i	0.165090	+	0.0683824i
$216$	2.33394	+	5.63462i	0.158804	+	0.383387i
$217$		−	5.64043i		−	0.382897i
$218$	2.63050	−	1.08959i	0.178160	−	0.0737963i
$219$	−4.84471	−	4.84471i	−0.327375	−	0.327375i
$220$	−4.66856			−0.314754
$221$	17.1884	+	15.4992i	1.15622	+	1.04259i
$222$	1.63426			0.109684
$223$	4.57010	+	4.57010i	0.306037	+	0.306037i	0.843370	−	0.537333i	$-0.180568\pi$
$223$	4.57010	+	4.57010i	0.306037	+	0.306037i	−0.537333	+	0.843370i	$0.680568\pi$
$224$	7.89101	−	3.26856i	0.527241	−	0.218390i
$225$		−	1.87425i		−	0.124950i
$226$	1.72726	+	4.16997i	0.114896	+	0.277382i
$227$	2.82763	+	1.17124i	0.187676	+	0.0777381i	0.474543	−	0.880233i	$-0.342614\pi$
$227$	2.82763	+	1.17124i	0.187676	+	0.0777381i	−0.286866	+	0.957971i	$0.592614\pi$
$228$	−5.52736	+	13.3442i	−0.366058	+	0.883743i
$229$	5.34518	−	5.34518i	0.353219	−	0.353219i	−0.508087	−	0.861306i	$-0.669647\pi$
$229$	5.34518	−	5.34518i	0.353219	−	0.353219i	0.861306	+	0.508087i	$0.169647\pi$
$230$	0.183631	−	0.183631i	0.0121083	−	0.0121083i
$231$	−2.49222	+	6.01676i	−0.163976	+	0.395874i
$232$	−4.08727	−	1.69300i	−0.268342	−	0.111151i
$233$	8.55214	+	20.6467i	0.560270	+	1.35261i	0.909551	+	0.415593i	$0.136426\pi$
$233$	8.55214	+	20.6467i	0.560270	+	1.35261i	−0.349281	+	0.937018i	$0.613574\pi$
$234$		−	3.17400i		−	0.207491i
$235$	2.12597	−	0.880607i	0.138683	−	0.0574445i
$236$	10.0452	+	10.0452i	0.653886	+	0.653886i
$237$	15.6071			1.01379
$238$	−1.04428	+	2.94212i	−0.0676904	+	0.190709i
$239$	−3.45981			−0.223797			−0.111898	−	0.993720i	$-0.535693\pi$
$239$	−3.45981			−0.223797			−0.111898	+	0.993720i	$0.535693\pi$
$240$	2.59751	+	2.59751i	0.167669	+	0.167669i
$241$	−16.6541	+	6.89834i	−1.07278	+	0.444361i	−0.847972	−	0.530042i	$-0.822176\pi$
$241$	−16.6541	+	6.89834i	−1.07278	+	0.444361i	−0.224810	+	0.974403i	$0.572176\pi$
$242$		−	1.51422i		−	0.0973376i
$243$	−5.99235	−	14.4668i	−0.384410	−	0.928047i
$244$	1.59840	+	0.662079i	0.102327	+	0.0423853i
$245$	0.268151	−	0.647374i	0.0171315	−	0.0413592i
$246$	2.79521	−	2.79521i	0.178216	−	0.178216i
$247$	28.3049	−	28.3049i	1.80100	−	1.80100i
$248$	−1.01421	+	2.44851i	−0.0644022	+	0.155481i
$249$	−13.6239	−	5.64321i	−0.863381	−	0.357624i
$250$	0.115451	+	0.278722i	0.00730173	+	0.0176279i
$251$		−	24.0478i		−	1.51788i	−0.651159	−	0.758941i	$-0.725717\pi$
$251$		−	24.0478i		−	1.51788i	0.651159	−	0.758941i	$-0.274283\pi$
$252$	−8.29643	+	3.43649i	−0.522626	+	0.216479i
$253$	1.48857	+	1.48857i	0.0935859	+	0.0935859i
$254$	1.79650			0.112722
$255$	−4.36884	+	0.225765i	−0.273588	+	0.0141379i
$256$	9.20534			0.575334
$257$	−10.4664	−	10.4664i	−0.652873	−	0.652873i	0.300811	−	0.953684i	$-0.402743\pi$
$257$	−10.4664	−	10.4664i	−0.652873	−	0.652873i	−0.953684	+	0.300811i	$0.902743\pi$
$258$	−0.774848	+	0.320953i	−0.0482399	+	0.0199816i
$259$			12.8142i			0.796233i
$260$	−4.10076	−	9.90012i	−0.254319	−	0.613979i
$261$	6.49591	+	2.69070i	0.402087	+	0.166550i
$262$	0.483426	−	1.16709i	0.0298661	−	0.0721032i
$263$	17.3357	−	17.3357i	1.06896	−	1.06896i	0.0715243	−	0.997439i	$-0.477214\pi$
$263$	17.3357	−	17.3357i	1.06896	−	1.06896i	0.997439	−	0.0715243i	$-0.0227864\pi$
$264$	2.16375	−	2.16375i	0.133170	−	0.133170i
$265$	1.06185	−	2.56353i	0.0652289	−	0.157477i
$266$	4.98852	+	2.06631i	0.305866	+	0.126694i
$267$	−0.160449	−	0.387358i	−0.00981932	−	0.0237059i
$268$			12.7881i			0.781156i
$269$	6.09269	−	2.52367i	0.371478	−	0.153871i	−0.189131	−	0.981952i	$-0.560567\pi$
$269$	6.09269	−	2.52367i	0.371478	−	0.153871i	0.560609	+	0.828081i	$0.310567\pi$
$270$	1.10324	+	1.10324i	0.0671411	+	0.0671411i
$271$	−26.1956			−1.59127			−0.795634	−	0.605778i	$-0.792862\pi$
$271$	−26.1956			−1.59127			−0.795634	+	0.605778i	$0.792862\pi$
$272$	−9.55957	+	10.6014i	−0.579634	+	0.642805i
$273$	−14.9482			−0.904707
$274$	1.54873	+	1.54873i	0.0935624	+	0.0935624i
$275$	−2.25941	+	0.935880i	−0.136248	+	0.0564357i
$276$		−	1.74353i		−	0.104948i
$277$	3.66038	+	8.83695i	0.219931	+	0.530961i	0.994880	−	0.101063i	$-0.0322245\pi$
$277$	3.66038	+	8.83695i	0.219931	+	0.530961i	−0.774949	+	0.632024i	$0.782224\pi$
$278$	2.89682	+	1.19990i	0.173740	+	0.0719653i
$279$	1.61188	−	3.89143i	0.0965009	−	0.232974i
$280$	2.09291	−	2.09291i	0.125075	−	0.125075i
$281$	8.78037	−	8.78037i	0.523793	−	0.523793i	−0.394922	−	0.918715i	$-0.629228\pi$
$281$	8.78037	−	8.78037i	0.523793	−	0.523793i	0.918715	+	0.394922i	$0.129228\pi$
$282$	−0.281877	+	0.680511i	−0.0167855	+	0.0405238i
$283$	15.5612	+	6.44566i	0.925017	+	0.383155i	0.793786	−	0.608197i	$-0.208107\pi$
$283$	15.5612	+	6.44566i	0.925017	+	0.383155i	0.131231	+	0.991352i	$0.458107\pi$
$284$	−0.175889	−	0.424633i	−0.0104371	−	0.0251973i
$285$			7.56616i			0.448181i
$286$	−3.82626	+	1.58489i	−0.226252	+	0.0937165i
$287$	21.9171	+	21.9171i	1.29372	+	1.29372i
$288$	6.37822			0.375840
$289$	−1.75231	−	16.9094i	−0.103077	−	0.994673i
$290$	−1.13176			−0.0664591
$291$	6.72166	+	6.72166i	0.394031	+	0.394031i
$292$	−11.3888	+	4.71741i	−0.666482	+	0.276066i
$293$		−	20.8806i		−	1.21986i	−0.792456	−	0.609930i	$-0.791198\pi$
$293$		−	20.8806i		−	1.21986i	0.792456	−	0.609930i	$-0.208802\pi$
$294$	0.0858335	+	0.207220i	0.00500591	+	0.0120853i
$295$	6.87521	+	2.84781i	0.400290	+	0.165806i
$296$	2.30412	−	5.56263i	0.133924	−	0.323321i
$297$	−8.94323	+	8.94323i	−0.518939	+	0.518939i
$298$	−1.28371	+	1.28371i	−0.0743635	+	0.0743635i
$299$	−1.84913	+	4.46419i	−0.106938	+	0.258171i
$300$	1.87128	+	0.775110i	0.108038	+	0.0447510i
$301$	−2.51657	−	6.07554i	−0.145053	−	0.350188i
$302$			3.14306i			0.180863i
$303$	14.9863	−	6.20752i	0.860940	−	0.356613i
$304$	17.4579	+	17.4579i	1.00128	+	1.00128i
$305$	0.906291			0.0518941
$306$	−1.56124	+	1.73139i	−0.0892504	+	0.0989772i
$307$	−29.9529			−1.70950			−0.854751	−	0.519038i	$-0.826290\pi$
$307$	−29.9529			−1.70950			−0.854751	+	0.519038i	$0.826290\pi$
$308$	8.28541	+	8.28541i	0.472105	+	0.472105i
$309$	−14.4828	+	5.99898i	−0.823899	+	0.341270i
$310$			0.677989i			0.0385072i
$311$	0.0804873	+	0.194314i	0.00456402	+	0.0110185i	0.926145	−	0.377167i	$-0.123102\pi$
$311$	0.0804873	+	0.194314i	0.00456402	+	0.0110185i	−0.921581	+	0.388186i	$0.873102\pi$
$312$	6.48902	+	2.68784i	0.367369	+	0.152169i
$313$	−12.4082	+	29.9561i	−0.701354	+	1.69322i	0.0191979	+	0.999816i	$0.493889\pi$
$313$	−12.4082	+	29.9561i	−0.701354	+	1.69322i	−0.720551	+	0.693402i	$0.756111\pi$
$314$	−2.86010	+	2.86010i	−0.161405	+	0.161405i
$315$	−3.32627	+	3.32627i	−0.187414	+	0.187414i
$316$	10.7459	−	25.9429i	0.604504	−	1.45940i
$317$	−30.8937	−	12.7966i	−1.73516	−	0.718728i	−0.999127	−	0.0417842i	$-0.986696\pi$
$317$	−30.8937	−	12.7966i	−1.73516	−	0.718728i	−0.736035	−	0.676943i	$-0.763304\pi$
$318$	0.339892	+	0.820571i	0.0190602	+	0.0460154i
$319$		−	9.17441i		−	0.513668i
$320$	5.44879	−	2.25696i	0.304596	−	0.126168i
$321$	1.10345	+	1.10345i	0.0615886	+	0.0615886i
$322$	−0.651789			−0.0363228
$323$	−29.3630	+	1.51736i	−1.63380	+	0.0844283i
$324$	−0.258783			−0.0143768
$325$	−3.96924	−	3.96924i	−0.220174	−	0.220174i
$326$	0.439025	−	0.181850i	0.0243153	−	0.0100717i
$327$		−	10.0135i		−	0.553750i
$328$	−5.57330	−	13.4551i	−0.307734	−	0.742935i
$329$	−5.33585	−	2.21018i	−0.294175	−	0.121851i
$330$	0.299570	−	0.723225i	0.0164908	−	0.0398122i
$331$	0.626030	−	0.626030i	0.0344097	−	0.0344097i	−0.689693	−	0.724102i	$-0.742254\pi$
$331$	0.626030	−	0.626030i	0.0344097	−	0.0344097i	0.724102	+	0.689693i	$0.242254\pi$
$332$	−18.7609	+	18.7609i	−1.02964	+	1.02964i
$333$	−3.66194	+	8.84071i	−0.200673	+	0.484468i
$334$	−4.90688	−	2.03250i	−0.268493	−	0.111213i
$335$	2.56355	+	6.18896i	0.140062	+	0.338139i
$336$		−	9.21973i		−	0.502977i
$337$	15.8506	−	6.56551i	0.863434	−	0.357646i	0.0933847	−	0.995630i	$-0.470231\pi$
$337$	15.8506	−	6.56551i	0.863434	−	0.357646i	0.770050	+	0.637984i	$0.220231\pi$
$338$	−3.94859	−	3.94859i	−0.214775	−	0.214775i
$339$	15.8739			0.862150
$340$	−2.63279	+	7.41756i	−0.142783	+	0.402274i
$341$	−5.49600			−0.297625
$342$	2.85117	+	2.85117i	0.154174	+	0.154174i
$343$	−17.8563	+	7.39633i	−0.964151	+	0.399364i
$344$			3.08990i			0.166596i
$345$	−0.349515	−	0.843803i	−0.0188172	−	0.0454288i
$346$	−5.25194	−	2.17542i	−0.282346	−	0.116951i
$347$	11.8288	−	28.5572i	0.635003	−	1.53303i	−0.198257	−	0.980150i	$-0.563528\pi$
$347$	11.8288	−	28.5572i	0.635003	−	1.53303i	0.833260	−	0.552882i	$-0.186472\pi$
$348$	−5.37287	+	5.37287i	−0.288016	+	0.288016i
$349$	2.38415	−	2.38415i	0.127621	−	0.127621i	−0.640411	−	0.768032i	$-0.721236\pi$
$349$	2.38415	−	2.38415i	0.127621	−	0.127621i	0.768032	+	0.640411i	$0.221236\pi$
$350$	0.289762	−	0.699548i	0.0154884	−	0.0373924i
$351$	−26.8205	−	11.1094i	−1.43157	−	0.592976i
$352$	−3.18487	−	7.68896i	−0.169754	−	0.409823i
$353$		−	23.7918i		−	1.26631i	−0.774025	−	0.633155i	$-0.781760\pi$
$353$		−	23.7918i		−	1.26631i	0.774025	−	0.633155i	$-0.218240\pi$
$354$	−2.20071	+	0.911565i	−0.116967	+	0.0484491i
$355$	−0.170247	−	0.170247i	−0.00903579	−	0.00903579i
$356$	−0.754360			−0.0399810
$357$	8.15416	+	7.35282i	0.431564	+	0.389152i
$358$	0.999743			0.0528381
$359$	22.4244	+	22.4244i	1.18351	+	1.18351i	0.978827	+	0.204688i	$0.0656178\pi$
$359$	22.4244	+	22.4244i	1.18351	+	1.18351i	0.204688	+	0.978827i	$0.434382\pi$
$360$	2.04203	−	0.845838i	0.107625	−	0.0445796i
$361$			31.8521i			1.67643i
$362$	−1.83164	−	4.42197i	−0.0962689	−	0.232414i
$363$	−4.92004	−	2.03795i	−0.258235	−	0.106964i
$364$	−10.2923	+	24.8477i	−0.539461	+	1.30237i
$365$	−4.56611	+	4.56611i	−0.239001	+	0.239001i
$366$	−0.205130	+	0.205130i	−0.0107223	+	0.0107223i
$367$	−1.72853	+	4.17304i	−0.0902286	+	0.217831i	−0.962551	−	0.271099i	$-0.912613\pi$
$367$	−1.72853	+	4.17304i	−0.0902286	+	0.217831i	0.872323	+	0.488930i	$0.162613\pi$
$368$	−2.75341	−	1.14050i	−0.143532	−	0.0594528i
$369$	8.85767	+	21.3843i	0.461112	+	1.11322i
$370$		−	1.54028i		−	0.0800755i
$371$	−6.43405	+	2.66507i	−0.334039	+	0.138364i
$372$	3.21866	+	3.21866i	0.166880	+	0.166880i
$373$	−5.12748			−0.265491			−0.132745	−	0.991150i	$-0.542379\pi$
$373$	−5.12748			−0.265491			−0.132745	+	0.991150i	$0.542379\pi$
$374$	2.86679	+	1.01754i	0.148238	+	0.0526156i
$375$	1.06101			0.0547905
$376$	1.91888	+	1.91888i	0.0989586	+	0.0989586i
$377$	19.4552	−	8.05860i	1.00199	−	0.415039i
$378$		−	3.91589i		−	0.201412i
$379$	2.11629	+	5.10917i	0.108706	+	0.262441i	0.968867	−	0.247584i	$-0.0796365\pi$
$379$	2.11629	+	5.10917i	0.108706	+	0.262441i	−0.860160	+	0.510024i	$0.829636\pi$
$380$	12.5769	+	5.20951i	0.645180	+	0.267242i
$381$	2.41786	−	5.83722i	0.123871	−	0.299050i
$382$	−5.86521	+	5.86521i	−0.300090	+	0.300090i
$383$	14.4493	−	14.4493i	0.738326	−	0.738326i	−0.233928	−	0.972254i	$-0.575158\pi$
$383$	14.4493	−	14.4493i	0.738326	−	0.738326i	0.972254	+	0.233928i	$0.0751580\pi$
$384$	−3.48596	+	8.41585i	−0.177892	+	0.429469i
$385$	5.67077	+	2.34891i	0.289009	+	0.119711i
$386$	1.70420	+	4.11429i	0.0867413	+	0.209412i
$387$		−	4.91079i		−	0.249629i
$388$	15.8011	−	6.54505i	0.802181	−	0.332274i
$389$	−3.66726	−	3.66726i	−0.185937	−	0.185937i	0.608000	−	0.793937i	$-0.291972\pi$
$389$	−3.66726	−	3.66726i	−0.185937	−	0.185937i	−0.793937	+	0.608000i	$0.791972\pi$
$390$	1.79680			0.0909845
$391$	3.20456	−	1.52563i	0.162062	−	0.0771543i
$392$	0.826343			0.0417366
$393$	−3.14152	−	3.14152i	−0.158469	−	0.158469i
$394$	−0.104913	+	0.0434563i	−0.00528543	+	0.00218930i
$395$		−	14.7096i		−	0.740120i
$396$	3.34850	+	8.08399i	0.168268	+	0.406236i
$397$	−5.70360	−	2.36251i	−0.286255	−	0.118571i	0.234936	−	0.972011i	$-0.424512\pi$
$397$	−5.70360	−	2.36251i	−0.286255	−	0.118571i	−0.521191	+	0.853440i	$0.674512\pi$
$398$	−0.869348	+	2.09879i	−0.0435765	+	0.105203i
$399$	13.4278	−	13.4278i	0.672233	−	0.672233i
$400$	2.44814	−	2.44814i	0.122407	−	0.122407i
$401$	−3.63413	+	8.77356i	−0.181480	+	0.438131i	−0.988272	−	0.152705i	$-0.951202\pi$
$401$	−3.63413	+	8.77356i	−0.181480	+	0.438131i	0.806792	+	0.590835i	$0.201202\pi$
$402$	−1.98105	−	0.820577i	−0.0988058	−	0.0409267i
$403$	−4.82757	−	11.6548i	−0.240478	−	0.580566i
$404$		−	29.1850i		−	1.45201i
$405$	−0.125241	+	0.0518767i	−0.00622329	+	0.00257777i
$406$	2.00856	+	2.00856i	0.0996831	+	0.0996831i
$407$	12.4860			0.618910
$408$	−2.21761	−	4.65806i	−0.109788	−	0.230608i
$409$	14.3886			0.711469			0.355734	−	0.934587i	$-0.384231\pi$
$409$	14.3886			0.711469			0.355734	+	0.934587i	$0.384231\pi$
$410$	−2.63447	−	2.63447i	−0.130107	−	0.130107i
$411$	7.11659	−	2.94779i	0.351035	−	0.145404i
$412$			28.2046i			1.38954i
$413$	−7.14753	−	17.2557i	−0.351707	−	0.849096i
$414$	−0.449680	−	0.186264i	−0.0221006	−	0.00915436i
$415$	−5.31870	+	12.8405i	−0.261085	+	0.630314i
$416$	13.5076	−	13.5076i	0.662266	−	0.662266i
$417$	7.79750	−	7.79750i	0.381845	−	0.381845i
$418$	2.01340	−	4.86079i	0.0984789	−	0.237749i
$419$	19.6078	+	8.12181i	0.957903	+	0.396776i	0.806196	−	0.591649i	$-0.201523\pi$
$419$	19.6078	+	8.12181i	0.957903	+	0.396776i	0.151707	+	0.988425i	$0.451523\pi$
$420$	−1.94540	−	4.69661i	−0.0949258	−	0.229171i
$421$			20.1672i			0.982887i	0.870909	+	0.491444i	$0.163531\pi$
$421$			20.1672i			0.982887i	−0.870909	+	0.491444i	$0.836469\pi$
$422$	2.42279	−	1.00355i	0.117939	−	0.0488521i
$423$	−3.04968	−	3.04968i	−0.148281	−	0.148281i
$424$	3.27223			0.158914
$425$	0.212782	+	4.11761i	0.0103214	+	0.199733i
$426$	0.0770678			0.00373395
$427$	−1.60842	−	1.60842i	−0.0778367	−	0.0778367i
$428$	2.59397	−	1.07446i	0.125384	−	0.0519358i
$429$			14.5655i			0.703227i
$430$	0.302496	+	0.730290i	0.0145877	+	0.0352177i
$431$	−18.4485	−	7.64163i	−0.888635	−	0.368085i	−0.108795	−	0.994064i	$-0.534699\pi$
$431$	−18.4485	−	7.64163i	−0.888635	−	0.368085i	−0.779839	+	0.625980i	$0.784699\pi$
$432$	6.85204	−	16.5423i	0.329669	−	0.795891i
$433$	12.8860	−	12.8860i	0.619263	−	0.619263i	−0.326080	−	0.945342i	$-0.605728\pi$
$433$	12.8860	−	12.8860i	0.619263	−	0.619263i	0.945342	+	0.326080i	$0.105728\pi$
$434$	1.20324	−	1.20324i	0.0577575	−	0.0577575i
$435$	−1.52320	+	3.67734i	−0.0730321	+	0.176315i
$436$	−16.6450	−	6.89460i	−0.797152	−	0.330191i
$437$	−2.34909	−	5.67120i	−0.112372	−	0.271290i
$438$		−	2.06699i		−	0.0987648i
$439$	13.6117	−	5.63815i	0.649651	−	0.269094i	−0.0334251	−	0.999441i	$-0.510642\pi$
$439$	13.6117	−	5.63815i	0.649651	−	0.269094i	0.683077	+	0.730347i	$0.260642\pi$
$440$	−2.03932	−	2.03932i	−0.0972209	−	0.0972209i
$441$	−1.31331			−0.0625386
$442$	0.360341	+	6.97307i	0.0171397	+	0.331675i
$443$	−23.3335			−1.10861			−0.554305	−	0.832314i	$-0.687016\pi$
$443$	−23.3335			−1.10861			−0.554305	+	0.832314i	$0.687016\pi$
$444$	−7.31228	−	7.31228i	−0.347026	−	0.347026i
$445$	−0.365083	+	0.151222i	−0.0173066	+	0.00716862i
$446$			1.94983i			0.0923272i
$447$	2.44336	+	5.89879i	0.115567	+	0.279003i
$448$	−13.6756	−	5.66461i	−0.646110	−	0.267628i
$449$	−0.655009	+	1.58133i	−0.0309118	+	0.0746277i	−0.938582	−	0.345057i	$-0.887859\pi$
$449$	−0.655009	+	1.58133i	−0.0309118	+	0.0746277i	0.907670	+	0.419685i	$0.137859\pi$
$450$	0.399824	−	0.399824i	0.0188479	−	0.0188479i
$451$	21.3559	−	21.3559i	1.00561	−	1.00561i
$452$	10.9296	−	26.3864i	0.514085	−	1.24111i
$453$	10.2125	+	4.23016i	0.479826	+	0.198750i
$454$	0.353348	+	0.853058i	0.0165835	+	0.0400360i
$455$			14.0886i			0.660484i
$456$	−8.24349	+	3.41457i	−0.386037	+	0.159902i
$457$	9.34572	+	9.34572i	0.437174	+	0.437174i	0.891060	−	0.453886i	$-0.149963\pi$
$457$	9.34572	+	9.34572i	0.437174	+	0.437174i	−0.453886	+	0.891060i	$0.649963\pi$
$458$	2.28052			0.106562
$459$	9.16585	+	19.2527i	0.427825	+	0.898641i
$460$	−1.64326			−0.0766176
$461$	−20.7116	−	20.7116i	−0.964634	−	0.964634i	0.0347616	−	0.999396i	$-0.488933\pi$
$461$	−20.7116	−	20.7116i	−0.964634	−	0.964634i	−0.999396	+	0.0347616i	$0.988933\pi$
$462$	−1.81518	+	0.751871i	−0.0844497	+	0.0349802i
$463$			9.80371i			0.455617i	0.973706	+	0.227808i	$0.0731560\pi$
$463$			9.80371i			0.455617i	−0.973706	+	0.227808i	$0.926844\pi$
$464$	4.97037	+	11.9995i	0.230744	+	0.557064i
$465$	2.20294	+	0.912488i	0.102159	+	0.0423156i
$466$	−2.58007	+	6.22884i	−0.119519	+	0.288545i
$467$	−9.67459	+	9.67459i	−0.447687	+	0.447687i	−0.894585	−	0.446898i	$-0.852529\pi$
$467$	−9.67459	+	9.67459i	−0.447687	+	0.447687i	0.446898	+	0.894585i	$0.352529\pi$
$468$	−14.2016	+	14.2016i	−0.656469	+	0.656469i
$469$	6.43410	−	15.5333i	0.297099	−	0.717261i
$470$	0.641378	+	0.265667i	0.0295846	+	0.0122543i
$471$	5.44378	+	13.1424i	0.250836	+	0.605572i
$472$			8.77589i			0.403943i
$473$	−5.91997	+	2.45213i	−0.272201	+	0.112749i
$474$	3.32938	+	3.32938i	0.152923	+	0.152923i
$475$	7.13107			0.327196
$476$	17.8366	−	8.49165i	0.817539	−	0.389214i
$477$	−5.20057			−0.238118
$478$	−0.738063	−	0.738063i	−0.0337582	−	0.0337582i
$479$	−10.1719	+	4.21334i	−0.464766	+	0.192513i	−0.602763	−	0.797920i	$-0.705934\pi$
$479$	−10.1719	+	4.21334i	−0.464766	+	0.192513i	0.137997	+	0.990433i	$0.455934\pi$
$480$			3.61071i			0.164806i
$481$	10.9675	+	26.4778i	0.500074	+	1.20728i
$482$	−5.02431	−	2.08114i	−0.228851	−	0.0947932i
$483$	−0.877226	+	2.11781i	−0.0399151	+	0.0963637i
$484$	−6.77516	+	6.77516i	−0.307962	+	0.307962i
$485$	6.33513	−	6.33513i	0.287663	−	0.287663i
$486$	1.80781	−	4.36445i	0.0820041	−	0.197975i
$487$	9.32586	+	3.86290i	0.422595	+	0.175045i	0.583838	−	0.811870i	$-0.301550\pi$
$487$	9.32586	+	3.86290i	0.422595	+	0.175045i	−0.161243	+	0.986915i	$0.551550\pi$
$488$	0.409004	+	0.987423i	0.0185147	+	0.0446985i
$489$		−	1.67124i		−	0.0755760i
$490$	0.195304	−	0.0808976i	0.00882294	−	0.00365458i
$491$	−12.0793	−	12.0793i	−0.545132	−	0.545132i	0.379897	−	0.925029i	$-0.375959\pi$
$491$	−12.0793	−	12.0793i	−0.545132	−	0.545132i	−0.925029	+	0.379897i	$0.875959\pi$
$492$	−25.0136			−1.12770
$493$	−14.5766	−	5.17382i	−0.656497	−	0.233017i
$494$	12.0763			0.543338
$495$	3.24110	+	3.24110i	0.145677	+	0.145677i
$496$	7.18841	−	2.97754i	0.322769	−	0.133695i
$497$			0.604284i			0.0271059i
$498$	−1.70248	−	4.11016i	−0.0762901	−	0.184180i
$499$	−28.9724	−	12.0008i	−1.29698	−	0.537227i	−0.375923	−	0.926651i	$-0.622674\pi$
$499$	−28.9724	−	12.0008i	−1.29698	−	0.537227i	−0.921059	+	0.389424i	$0.872674\pi$
$500$	0.730537	−	1.76367i	0.0326706	−	0.0788738i
$501$	−13.2081	+	13.2081i	−0.590094	+	0.590094i
$502$	5.12999	−	5.12999i	0.228963	−	0.228963i
$503$	−3.31991	+	8.01498i	−0.148028	+	0.357370i	−0.980449	−	0.196773i	$-0.936954\pi$
$503$	−3.31991	+	8.01498i	−0.148028	+	0.357370i	0.832422	+	0.554143i	$0.186954\pi$
$504$	−5.12518	−	2.12292i	−0.228293	−	0.0945623i
$505$	−5.85056	−	14.1245i	−0.260346	−	0.628532i
$506$			0.635099i			0.0282336i
$507$	−18.1442	+	7.51556i	−0.805811	+	0.333778i
$508$	−8.03817	−	8.03817i	−0.356636	−	0.356636i
$509$	−14.1196			−0.625840			−0.312920	−	0.949780i	$-0.601307\pi$
$509$	−14.1196			−0.625840			−0.312920	+	0.949780i	$0.601307\pi$
$510$	−0.980144	−	0.883821i	−0.0434015	−	0.0391363i
$511$	16.2072			0.716963
$512$	14.1053	+	14.1053i	0.623374	+	0.623374i
$513$	34.0721	−	14.1131i	1.50432	−	0.623109i
$514$		−	4.46546i		−	0.196963i
$515$	5.65401	+	13.6500i	0.249145	+	0.601490i
$516$	4.90301	+	2.03089i	0.215843	+	0.0894051i
$517$	−2.15359	+	5.19922i	−0.0947147	+	0.228662i
$518$	−2.73358	+	2.73358i	−0.120106	+	0.120106i
$519$	−14.1369	+	14.1369i	−0.620541	+	0.620541i
$520$	2.53328	−	6.11587i	0.111091	−	0.268199i
$521$	−16.2808	−	6.74373i	−0.713275	−	0.295448i	−0.00361608	−	0.999993i	$-0.501151\pi$
$521$	−16.2808	−	6.74373i	−0.713275	−	0.295448i	−0.709659	+	0.704545i	$0.751151\pi$
$522$	0.811747	+	1.95973i	0.0355292	+	0.0857751i
$523$			26.3853i			1.15375i	0.816833	+	0.576875i	$0.195728\pi$
$523$			26.3853i			1.15375i	−0.816833	+	0.576875i	$0.804272\pi$
$524$	−7.38502	+	3.05898i	−0.322616	+	0.133632i
$525$	−1.88301	−	1.88301i	−0.0821811	−	0.0821811i
$526$	7.39626			0.322492
$527$	−3.09942	+	8.73223i	−0.135013	+	0.380382i
$528$	−8.98366			−0.390963
$529$	−15.7395	−	15.7395i	−0.684326	−	0.684326i
$530$	0.773384	−	0.320346i	0.0335937	−	0.0139150i
$531$		−	13.9476i		−	0.605272i
$532$	−13.0750	−	31.5659i	−0.566874	−	1.36856i
$533$	64.0457	+	26.5286i	2.77413	+	1.14908i
$534$	0.0484053	−	0.116861i	0.00209470	−	0.00505706i
$535$	1.04000	−	1.04000i	0.0449629	−	0.0449629i
$536$	−5.58609	+	5.58609i	−0.241282	+	0.241282i
$537$	1.34553	−	3.24839i	0.0580638	−	0.140178i
$538$	1.83808	+	0.761359i	0.0792454	+	0.0328245i
$539$	0.655783	+	1.58320i	0.0282466	+	0.0681932i
$540$		−	9.87260i		−	0.424849i
$541$	−4.07266	+	1.68695i	−0.175097	+	0.0725277i	−0.468510	−	0.883458i	$-0.655209\pi$
$541$	−4.07266	+	1.68695i	−0.175097	+	0.0725277i	0.293413	+	0.955986i	$0.405209\pi$
$542$	−5.58816	−	5.58816i	−0.240032	−	0.240032i
$543$	−16.8331			−0.722379
$544$	−14.0125	+	0.724113i	−0.600783	+	0.0310461i
$545$	−9.43771			−0.404267
$546$	−3.18882	−	3.18882i	−0.136469	−	0.136469i
$547$	−20.9386	+	8.67306i	−0.895271	+	0.370833i	−0.782400	−	0.622776i	$-0.786005\pi$
$547$	−20.9386	+	8.67306i	−0.895271	+	0.370833i	−0.112871	+	0.993610i	$0.536005\pi$
$548$		−	13.8592i		−	0.592035i
$549$	−0.650032	−	1.56932i	−0.0277427	−	0.0669768i
$550$	−0.681636	−	0.282343i	−0.0290650	−	0.0120391i
$551$	−10.2374	+	24.7154i	−0.436130	+	1.05291i
$552$	0.761607	−	0.761607i	0.0324162	−	0.0324162i
$553$	−26.1055	+	26.1055i	−1.11012	+	1.11012i
$554$	−1.10429	+	2.66599i	−0.0469167	+	0.113267i
$555$	−5.00473	−	2.07303i	−0.212439	−	0.0879951i
$556$	−7.59262	−	18.3302i	−0.321999	−	0.777374i
$557$		−	11.4954i		−	0.487076i	−0.969891	−	0.243538i	$-0.921692\pi$
$557$		−	11.4954i		−	0.487076i	0.969891	−	0.243538i	$-0.0783080\pi$
$558$	1.17399	−	0.486284i	0.0496991	−	0.0205860i
$559$	−10.4000	−	10.4000i	−0.439871	−	0.439871i
$560$	−8.68955			−0.367200
$561$	7.16455	−	7.94537i	0.302487	−	0.335454i
$562$	3.74614			0.158021
$563$	9.57715	+	9.57715i	0.403629	+	0.403629i	0.879510	−	0.475881i	$-0.157871\pi$
$563$	9.57715	+	9.57715i	0.403629	+	0.403629i	−0.475881	+	0.879510i	$0.657871\pi$
$564$	4.30607	−	1.78363i	0.181318	−	0.0751045i
$565$		−	14.9610i		−	0.629415i
$566$	1.94457	+	4.69461i	0.0817364	+	0.197329i
$567$	0.314336	+	0.130202i	0.0132009	+	0.00546797i
$568$	0.108656	−	0.262320i	0.00455912	−	0.0110067i
$569$	−11.2263	+	11.2263i	−0.470632	+	0.470632i	−0.902119	−	0.431487i	$-0.857989\pi$
$569$	−11.2263	+	11.2263i	−0.470632	+	0.470632i	0.431487	+	0.902119i	$0.357989\pi$
$570$	−1.61405	+	1.61405i	−0.0676051	+	0.0676051i
$571$	1.35486	−	3.27093i	0.0566993	−	0.136884i	−0.892991	−	0.450074i	$-0.851398\pi$
$571$	1.35486	−	3.27093i	0.0566993	−	0.136884i	0.949691	+	0.313190i	$0.101398\pi$
$572$	24.2115	+	10.0287i	1.01233	+	0.419322i
$573$	11.1636	+	26.9512i	0.466364	+	1.12590i
$574$			9.35092i			0.390300i
$575$	−0.795280	+	0.329416i	−0.0331655	+	0.0137376i
$576$	−7.81622	−	7.81622i	−0.325676	−	0.325676i
$577$	18.5078			0.770492			0.385246	−	0.922814i	$-0.374117\pi$
$577$	18.5078			0.770492			0.385246	+	0.922814i	$0.374117\pi$
$578$	3.23339	−	3.98101i	0.134491	−	0.165588i
$579$	15.6619			0.650887
$580$	5.06390	+	5.06390i	0.210267	+	0.210267i
$581$	32.2275	−	13.3491i	1.33702	−	0.553813i
$582$			2.86779i			0.118874i
$583$	2.59683	+	6.26931i	0.107550	+	0.259648i
$584$	−7.03554	−	2.91422i	−0.291133	−	0.120591i
$585$	−4.02615	+	9.71998i	−0.166461	+	0.401872i
$586$	4.45436	−	4.45436i	0.184008	−	0.184008i
$587$	−9.70579	+	9.70579i	−0.400601	+	0.400601i	−0.878445	−	0.477844i	$-0.841418\pi$
$587$	−9.70579	+	9.70579i	−0.400601	+	0.400601i	0.477844	+	0.878445i	$0.341418\pi$
$588$	0.543129	−	1.31123i	0.0223983	−	0.0540742i
$589$	14.8059	+	6.13282i	0.610068	+	0.252699i
$590$	0.859145	+	2.07416i	0.0353705	+	0.0853918i
$591$			0.399372i			0.0164280i
$592$	−16.3309	+	6.76450i	−0.671197	+	0.278019i
$593$	−14.3711	−	14.3711i	−0.590150	−	0.590150i	0.347522	−	0.937672i	$-0.387023\pi$
$593$	−14.3711	−	14.3711i	−0.590150	−	0.590150i	−0.937672	+	0.347522i	$0.887023\pi$
$594$	−3.81563			−0.156557
$595$	6.92999	−	7.68525i	0.284102	−	0.315065i
$596$	11.4876			0.470550
$597$	5.64942	+	5.64942i	0.231215	+	0.231215i
$598$	−1.34679	+	0.557858i	−0.0550742	+	0.0228125i
$599$		−	26.7277i		−	1.09206i	−0.837764	−	0.546032i	$-0.816138\pi$
$599$		−	26.7277i		−	1.09206i	0.837764	−	0.546032i	$-0.183862\pi$
$600$	0.478830	+	1.15600i	0.0195481	+	0.0471934i
$601$	25.5537	+	10.5847i	1.04236	+	0.431758i	0.837157	−	0.546962i	$-0.184216\pi$
$601$	25.5537	+	10.5847i	1.04236	+	0.431758i	0.205199	+	0.978720i	$0.434216\pi$
$602$	0.759216	−	1.83291i	0.0309433	−	0.0747038i
$603$	8.87800	−	8.87800i	0.361540	−	0.361540i
$604$	14.0632	−	14.0632i	0.572223	−	0.572223i
$605$	−1.92075	+	4.63711i	−0.0780898	+	0.188525i
$606$	4.52117	+	1.87273i	0.183660	+	0.0760744i
$607$	−9.03844	−	21.8207i	−0.366859	−	0.885676i	−0.994261	−	0.106981i	$-0.965882\pi$
$607$	−9.03844	−	21.8207i	−0.366859	−	0.885676i	0.627402	−	0.778696i	$-0.284118\pi$
$608$			24.2676i			0.984180i
$609$	9.22953	−	3.82300i	0.373999	−	0.154916i
$610$	0.193334	+	0.193334i	0.00782788	+	0.00782788i
$611$	−12.9171			−0.522570
$612$	14.7325	−	0.761315i	0.595524	−	0.0307744i
$613$	12.0396			0.486275			0.243137	−	0.969992i	$-0.421823\pi$
$613$	12.0396			0.486275			0.243137	+	0.969992i	$0.421823\pi$
$614$	−6.38969	−	6.38969i	−0.257867	−	0.257867i
$615$	−12.1057	+	5.01433i	−0.488147	+	0.202197i
$616$			7.23847i			0.291646i
$617$	5.94989	+	14.3643i	0.239534	+	0.578285i	0.997235	−	0.0743165i	$-0.0236775\pi$
$617$	5.94989	+	14.3643i	0.239534	+	0.578285i	−0.757701	+	0.652602i	$0.773678\pi$
$618$	−4.36928	−	1.80981i	−0.175758	−	0.0728014i
$619$	12.8172	−	30.9434i	0.515166	−	1.24372i	−0.425676	−	0.904876i	$-0.639964\pi$
$619$	12.8172	−	30.9434i	0.515166	−	1.24372i	0.940842	−	0.338845i	$-0.110036\pi$
$620$	3.03357	−	3.03357i	0.121831	−	0.121831i
$621$	−3.14788	+	3.14788i	−0.126320	+	0.126320i
$622$	−0.0242820	+	0.0586218i	−0.000973618	+	0.00235052i
$623$	0.916299	+	0.379543i	0.0367107	+	0.0152061i
$624$	−7.89105	−	19.0507i	−0.315895	−	0.762637i
$625$		−	1.00000i		−	0.0400000i
$626$	−9.03735	+	3.74339i	−0.361205	+	0.149616i
$627$	−13.0840	−	13.0840i	−0.522525	−	0.522525i
$628$	25.5942			1.02132
$629$	7.04138	−	19.8382i	0.280758	−	0.791002i
$630$	−1.41915			−0.0565404
$631$	−0.385100	−	0.385100i	−0.0153306	−	0.0153306i	0.699400	−	0.714731i	$-0.253451\pi$
$631$	−0.385100	−	0.385100i	−0.0153306	−	0.0153306i	−0.714731	+	0.699400i	$0.753451\pi$
$632$	16.0264	−	6.63836i	0.637496	−	0.264060i
$633$		−	9.22284i		−	0.366575i
$634$	−3.86056	−	9.32021i	−0.153322	−	0.370153i
$635$	−5.50155	−	2.27882i	−0.218322	−	0.0904321i
$636$	2.15074	−	5.19233i	0.0852822	−	0.205889i
$637$	−2.78130	+	2.78130i	−0.110199	+	0.110199i
$638$	1.95713	−	1.95713i	0.0774835	−	0.0774835i
$639$	−0.172688	+	0.416906i	−0.00683144	+	0.0164926i
$640$	7.93189	+	3.28550i	0.313536	+	0.129871i
$641$	4.75450	+	11.4784i	0.187792	+	0.453369i	0.989534	−	0.144301i	$-0.0460933\pi$
$641$	4.75450	+	11.4784i	0.187792	+	0.453369i	−0.801742	+	0.597670i	$0.796093\pi$
$642$			0.470786i			0.0185805i
$643$	35.4438	−	14.6813i	1.39777	−	0.578975i	0.448597	−	0.893734i	$-0.351924\pi$
$643$	35.4438	−	14.6813i	1.39777	−	0.578975i	0.949171	+	0.314760i	$0.101924\pi$
$644$	2.91634	+	2.91634i	0.114920	+	0.114920i
$645$	2.78000			0.109462
$646$	−6.58754	−	5.94016i	−0.259183	−	0.233712i
$647$	19.6602			0.772923			0.386462	−	0.922305i	$-0.373697\pi$
$647$	19.6602			0.772923			0.386462	+	0.922305i	$0.373697\pi$
$648$	−0.113041	−	0.113041i	−0.00444069	−	0.00444069i
$649$	−16.8138	+	6.96452i	−0.660001	+	0.273381i
$650$		−	1.69348i		−	0.0664236i
$651$	−2.29020	−	5.52902i	−0.0897599	−	0.216700i
$652$	−2.77802	−	1.15069i	−0.108796	−	0.0450646i
$653$	11.9119	−	28.7578i	0.466147	−	1.12538i	−0.499684	−	0.866208i	$-0.666551\pi$
$653$	11.9119	−	28.7578i	0.466147	−	1.12538i	0.965831	−	0.259171i	$-0.0834494\pi$
$654$	2.13614	−	2.13614i	0.0835296	−	0.0835296i
$655$	−2.96087	+	2.96087i	−0.115691	+	0.115691i
$656$	−16.3623	+	39.5020i	−0.638839	+	1.54229i
$657$	11.1816	+	4.63158i	0.436236	+	0.180695i
$658$	−0.666782	−	1.60975i	−0.0259939	−	0.0627548i
$659$			4.15956i			0.162033i	0.996713	+	0.0810167i	$0.0258167\pi$
$659$			4.15956i			0.162033i	−0.996713	+	0.0810167i	$0.974183\pi$
$660$	−4.57635	+	1.89559i	−0.178134	+	0.0737857i
$661$	4.85106	+	4.85106i	0.188685	+	0.188685i	0.795127	−	0.606443i	$-0.207404\pi$
$661$	4.85106	+	4.85106i	0.188685	+	0.188685i	−0.606443	+	0.795127i	$0.707404\pi$
$662$	0.267095			0.0103810
$663$	23.1421	+	8.21405i	0.898764	+	0.319007i
$664$	−16.3903			−0.636066
$665$	−12.6557	−	12.6557i	−0.490766	−	0.490766i
$666$	−2.66713	+	1.10476i	−0.103349	+	0.0428086i
$667$		−	3.22925i		−	0.125037i
$668$	12.8610	+	31.0493i	0.497608	+	1.20133i
$669$	6.33545	+	2.62423i	0.244943	+	0.101459i
$670$	−0.773390	+	1.86713i	−0.0298787	+	0.0721335i
$671$	−1.56723	+	1.56723i	−0.0605023	+	0.0605023i
$672$	6.40801	−	6.40801i	0.247195	−	0.247195i
$673$	−6.61298	+	15.9651i	−0.254912	+	0.615411i	−0.998588	−	0.0531290i	$-0.983081\pi$
$673$	−6.61298	+	15.9651i	−0.254912	+	0.615411i	0.743676	+	0.668540i	$0.233081\pi$
$674$	4.78190	+	1.98073i	0.184192	+	0.0762948i
$675$	−1.97910	−	4.77798i	−0.0761757	−	0.183904i
$676$			35.3348i			1.35903i
$677$	7.51469	−	3.11269i	0.288813	−	0.119630i	−0.233573	−	0.972339i	$-0.575042\pi$
$677$	7.51469	−	3.11269i	0.288813	−	0.119630i	0.522386	+	0.852709i	$0.325042\pi$
$678$	3.38629	+	3.38629i	0.130050	+	0.130050i
$679$	−22.4862			−0.862942
$680$	−4.39020	+	2.09009i	−0.168356	+	0.0801511i
$681$	3.24734			0.124438
$682$	−1.17243	−	1.17243i	−0.0448948	−	0.0448948i
$683$	−26.9190	+	11.1502i	−1.03003	+	0.426652i	−0.832723	−	0.553690i	$-0.813219\pi$
$683$	−26.9190	+	11.1502i	−1.03003	+	0.426652i	−0.197306	+	0.980342i	$0.563219\pi$
$684$		−	25.5143i		−	0.975566i
$685$	−2.77827	−	6.70735i	−0.106152	−	0.256275i
$686$	−5.38702	−	2.23138i	−0.205677	−	0.0851943i
$687$	3.06929	−	7.40992i	0.117101	−	0.282706i
$688$	6.41446	−	6.41446i	0.244549	−	0.244549i
$689$	−11.0136	+	11.0136i	−0.419587	+	0.419587i
$690$	0.105444	−	0.254564i	0.00401418	−	0.00969110i
$691$	34.5393	+	14.3066i	1.31394	+	0.544250i	0.926031	−	0.377448i	$-0.123198\pi$
$691$	34.5393	+	14.3066i	1.31394	+	0.544250i	0.387906	+	0.921699i	$0.373198\pi$
$692$	13.7654	+	33.2327i	0.523283	+	1.26332i
$693$		−	11.5041i		−	0.437006i
$694$	8.61534	−	3.56859i	0.327034	−	0.135462i
$695$	−7.34910	−	7.34910i	−0.278767	−	0.278767i
$696$	−4.69395			−0.177924
$697$	−21.8875	−	45.9744i	−0.829048	−	1.74140i
$698$	1.01720			0.0385015
$699$	16.7665	+	16.7665i	0.634166	+	0.634166i
$700$	−4.42653	+	1.83353i	−0.167307	+	0.0693009i
$701$			14.6423i			0.553031i	0.961009	+	0.276515i	$0.0891797\pi$
$701$			14.6423i			0.553031i	−0.961009	+	0.276515i	$0.910820\pi$
$702$	−3.35156	−	8.09139i	−0.126497	−	0.305390i
$703$	−33.6368	−	13.9328i	−1.26863	−	0.525486i
$704$	−5.51956	+	13.3254i	−0.208026	+	0.502220i
$705$	1.72643	−	1.72643i	0.0650210	−	0.0650210i
$706$	5.07538	−	5.07538i	0.191014	−	0.191014i
$707$	−14.6840	+	35.4502i	−0.552247	+	1.33324i
$708$	13.9255	+	5.76812i	0.523351	+	0.216779i
$709$	−10.8526	−	26.2006i	−0.407579	−	0.983983i	−0.985773	−	0.168083i	$-0.946242\pi$
$709$	−10.8526	−	26.2006i	−0.407579	−	0.983983i	0.578194	−	0.815899i	$-0.303758\pi$
$710$		−	0.0726360i		−	0.00272598i
$711$	−25.4708	+	10.5504i	−0.955231	+	0.395670i
$712$	−0.329520	−	0.329520i	−0.0123493	−	0.0123493i
$713$	−1.93451			−0.0724480
$714$	0.170946	+	3.30802i	0.00639748	+	0.123800i
$715$	13.7279			0.513393
$716$	−4.47321	−	4.47321i	−0.167172	−	0.167172i
$717$	−3.39148	+	1.40480i	−0.126657	+	0.0524631i
$718$			9.56736i			0.357051i
$719$	−4.83536	−	11.6736i	−0.180329	−	0.435352i	0.807706	−	0.589586i	$-0.200709\pi$
$719$	−4.83536	−	11.6736i	−0.180329	−	0.435352i	−0.988034	+	0.154234i	$0.950709\pi$
$720$	−5.99507	−	2.48324i	−0.223423	−	0.0925449i
$721$	14.1906	−	34.2593i	0.528487	−	1.27588i
$722$	−6.79485	+	6.79485i	−0.252878	+	0.252878i
$723$	−13.5242	+	13.5242i	−0.502969	+	0.502969i
$724$	−11.5901	+	27.9809i	−0.430742	+	1.03990i
$725$	3.46587	+	1.43561i	0.128719	+	0.0533173i
$726$	−0.614822	−	1.48431i	−0.0228182	−	0.0550879i
$727$			15.0242i			0.557218i	0.960405	+	0.278609i	$0.0898734\pi$
$727$			15.0242i			0.557218i	−0.960405	+	0.278609i	$0.910127\pi$
$728$	−15.3498	+	6.35811i	−0.568903	+	0.235647i
$729$	−11.4604	−	11.4604i	−0.424460	−	0.424460i
$730$	−1.94813			−0.0721035
$731$	0.557517	+	10.7887i	0.0206205	+	0.399035i
$732$	1.83566			0.0678478
$733$	−1.24931	−	1.24931i	−0.0461442	−	0.0461442i	0.683658	−	0.729802i	$-0.260388\pi$
$733$	−1.24931	−	1.24931i	−0.0461442	−	0.0461442i	−0.729802	+	0.683658i	$0.760388\pi$
$734$	−1.25895	+	0.521475i	−0.0464688	+	0.0192480i
$735$		−	0.743466i		−	0.0274231i
$736$	−1.12103	−	2.70640i	−0.0413216	−	0.0997592i
$737$	−15.1356	−	6.26935i	−0.557526	−	0.230935i
$738$	−2.67224	+	6.45136i	−0.0983665	+	0.237478i
$739$	−13.9406	+	13.9406i	−0.512812	+	0.512812i	−0.915387	−	0.402575i	$-0.868115\pi$
$739$	−13.9406	+	13.9406i	−0.512812	+	0.512812i	0.402575	+	0.915387i	$0.368115\pi$
$740$	−6.89179	+	6.89179i	−0.253347	+	0.253347i
$741$	16.2532	−	39.2386i	0.597075	−	1.44147i
$742$	−1.94107	−	0.804017i	−0.0712589	−	0.0295164i
$743$	−10.8535	−	26.2027i	−0.398176	−	0.961282i	−0.988099	−	0.153822i	$-0.950842\pi$
$743$	−10.8535	−	26.2027i	−0.398176	−	0.961282i	0.589922	−	0.807460i	$-0.299158\pi$
$744$			2.81195i			0.103091i
$745$	5.55958	−	2.30285i	0.203687	−	0.0843700i
$746$	−1.09382	−	1.09382i	−0.0400475	−	0.0400475i
$747$	26.0491			0.953087
$748$	−8.27422	−	17.3799i	−0.302535	−	0.635472i
$749$	−3.69141			−0.134881
$750$	0.226341	+	0.226341i	0.00826479	+	0.00826479i
$751$	16.5853	−	6.86987i	0.605207	−	0.250685i	−0.0589704	−	0.998260i	$-0.518782\pi$
$751$	16.5853	−	6.86987i	0.605207	−	0.250685i	0.664178	+	0.747575i	$0.268782\pi$
$752$		−	7.96698i		−	0.290526i
$753$	−9.76418	−	23.5728i	−0.355826	−	0.859041i
$754$	5.86937	+	2.43117i	0.213750	+	0.0885381i
$755$	3.98690	−	9.62524i	0.145098	−	0.350298i
$756$	−17.5211	+	17.5211i	−0.637237	+	0.637237i
$757$	−31.0649	+	31.0649i	−1.12907	+	1.12907i	−0.138743	+	0.990328i	$0.544306\pi$
$757$	−31.0649	+	31.0649i	−1.12907	+	1.12907i	−0.990328	+	0.138743i	$0.955694\pi$
$758$	−0.638456	+	1.54137i	−0.0231898	+	0.0559851i
$759$	2.06358	+	0.854764i	0.0749033	+	0.0310260i
$760$	3.21821	+	7.76945i	0.116737	+	0.281828i
$761$		−	13.2781i		−	0.481331i	−0.970608	−	0.240666i	$-0.922634\pi$
$761$		−	13.2781i		−	0.481331i	0.970608	−	0.240666i	$-0.0773657\pi$
$762$	1.76101	−	0.729435i	0.0637948	−	0.0264247i
$763$	16.7493	+	16.7493i	0.606367	+	0.606367i
$764$	52.4861			1.89888
$765$	6.97736	−	3.32178i	0.252267	−	0.120099i
$766$	6.16480			0.222743
$767$	−29.5378	−	29.5378i	−1.06655	−	1.06655i
$768$	9.02353	−	3.73767i	0.325609	−	0.134871i
$769$			24.8906i			0.897578i	0.893638	+	0.448789i	$0.148144\pi$
$769$			24.8906i			0.897578i	−0.893638	+	0.448789i	$0.851856\pi$
$770$	0.708635	+	1.71080i	0.0255374	+	0.0616528i
$771$	−14.5093	−	6.00995i	−0.522540	−	0.216443i
$772$	10.7836	−	26.0340i	0.388112	−	0.936985i
$773$	−37.9750	+	37.9750i	−1.36587	+	1.36587i	−0.499624	+	0.866242i	$0.666529\pi$
$773$	−37.9750	+	37.9750i	−1.36587	+	1.36587i	−0.866242	+	0.499624i	$0.833471\pi$
$774$	1.04759	−	1.04759i	0.0376549	−	0.0376549i
$775$	0.860015	−	2.07626i	0.0308926	−	0.0745814i
$776$	9.76127	+	4.04325i	0.350409	+	0.145144i
$777$	5.20296	+	12.5611i	0.186655	+	0.450626i
$778$		−	1.56463i		−	0.0560949i
$779$	−81.3621	+	33.7013i	−2.91510	+	1.20747i
$780$	−8.03954	−	8.03954i	−0.287862	−	0.287862i
$781$	0.588811			0.0210693
$782$	1.00907	+	0.358158i	0.0360841	+	0.0128077i
$783$	19.4011			0.693339
$784$	−1.71544	−	1.71544i	−0.0612658	−	0.0612658i
$785$	12.3867	−	5.13073i	0.442100	−	0.183124i
$786$		−	1.34033i		−	0.0478079i
$787$	19.6997	+	47.5592i	0.702217	+	1.69530i	0.718588	+	0.695436i	$0.244789\pi$
$787$	19.6997	+	47.5592i	0.702217	+	1.69530i	−0.0163714	+	0.999866i	$0.505211\pi$
$788$	0.663857	+	0.274979i	0.0236489	+	0.00979571i
$789$	9.95443	−	24.0321i	0.354387	−	0.855566i
$790$	3.13792	−	3.13792i	0.111642	−	0.111642i
$791$	−26.5517	+	26.5517i	−0.944070	+	0.944070i
$792$	−2.06856	+	4.99394i	−0.0735031	+	0.177452i
$793$	−4.70008	−	1.94684i	−0.166905	−	0.0691342i
$794$	−0.712737	−	1.72070i	−0.0252941	−	0.0610654i
$795$		−	2.94405i		−	0.104415i
$796$	13.2805	−	5.50097i	0.470716	−	0.194977i
$797$	13.3772	+	13.3772i	0.473846	+	0.473846i	0.903157	−	0.429311i	$-0.141244\pi$
$797$	13.3772	+	13.3772i	0.473846	+	0.473846i	−0.429311	+	0.903157i	$0.641244\pi$
$798$	5.72898			0.202804
$799$	7.04620	+	6.35374i	0.249276	+	0.224779i
$800$	3.40308			0.120317
$801$	0.523707	+	0.523707i	0.0185043	+	0.0185043i
$802$	−2.64687	+	1.09637i	−0.0934642	+	0.0387141i
$803$		−	15.7922i		−	0.557294i
$804$	5.19237	+	12.5355i	0.183121	+	0.442093i
$805$	1.99602	+	0.826780i	0.0703506	+	0.0291402i
$806$	1.45641	−	3.51609i	0.0513000	−	0.123849i
$807$	4.94766	−	4.94766i	0.174166	−	0.174166i
$808$	12.7486	−	12.7486i	0.448495	−	0.448495i
$809$	11.5703	−	27.9333i	0.406791	−	0.982081i	−0.579185	−	0.815196i	$-0.696629\pi$
$809$	11.5703	−	27.9333i	0.406791	−	0.982081i	0.985976	−	0.166885i	$-0.0533709\pi$
$810$	−0.0377837	−	0.0156505i	−0.00132758	−	0.000549903i
$811$	−6.57121	−	15.8643i	−0.230746	−	0.557071i	0.765519	−	0.643413i	$-0.222482\pi$
$811$	−6.57121	−	15.8643i	−0.230746	−	0.557071i	−0.996266	+	0.0863422i	$0.972482\pi$
$812$		−	17.9740i		−	0.630765i
$813$	−25.6782	+	10.6362i	−0.900573	+	0.373030i
$814$	2.66358	+	2.66358i	0.0933586	+	0.0933586i
$815$	−1.57513			−0.0551745
$816$	−5.06624	+	14.2735i	−0.177354	+	0.499673i
$817$	18.6844			0.653683
$818$	3.06944	+	3.06944i	0.107320	+	0.107320i
$819$	24.3956	−	10.1050i	0.852450	−	0.353096i
$820$			23.5752i			0.823280i
$821$	−16.7555	−	40.4514i	−0.584771	−	1.41176i	−0.888443	−	0.458986i	$-0.848213\pi$
$821$	−16.7555	−	40.4514i	−0.584771	−	1.41176i	0.303672	−	0.952777i	$-0.401787\pi$
$822$	2.14698	+	0.889309i	0.0748846	+	0.0310182i
$823$	9.67025	−	23.3460i	0.337084	−	0.813792i	−0.660909	−	0.750466i	$-0.729829\pi$
$823$	9.67025	−	23.3460i	0.337084	−	0.813792i	0.997993	−	0.0633260i	$-0.0201708\pi$
$824$	−12.3203	+	12.3203i	−0.429199	+	0.429199i
$825$	−1.83479	+	1.83479i	−0.0638792	+	0.0638792i
$826$	2.15632	−	5.20581i	0.0750278	−	0.181133i
$827$	−20.3879	−	8.44496i	−0.708958	−	0.293660i	−0.00108492	−	0.999999i	$-0.500345\pi$
$827$	−20.3879	−	8.44496i	−0.708958	−	0.293660i	−0.707874	+	0.706339i	$0.750345\pi$
$828$	1.17862	+	2.84544i	0.0409599	+	0.0988860i
$829$			20.9555i			0.727816i	0.931435	+	0.363908i	$0.118558\pi$
$829$			20.9555i			0.727816i	−0.931435	+	0.363908i	$0.881442\pi$
$830$	−3.87380	+	1.60458i	−0.134462	+	0.0556958i
$831$	7.17617	+	7.17617i	0.248939	+	0.248939i
$832$	−33.1060			−1.14774
$833$	2.88526	−	0.149099i	0.0999684	−	0.00516597i
$834$	3.32680			0.115198
$835$	12.4486	+	12.4486i	0.430800	+	0.430800i
$836$	−30.7576	+	12.7402i	−1.06378	+	0.440630i
$837$		−	11.6224i		−	0.401728i
$838$	2.45024	+	5.91541i	0.0846422	+	0.204344i
$839$	18.6855	+	7.73980i	0.645096	+	0.267207i	0.681152	−	0.732142i	$-0.261479\pi$
$839$	18.6855	+	7.73980i	0.645096	+	0.267207i	−0.0360558	+	0.999350i	$0.511479\pi$
$840$	1.20178	−	2.90137i	0.0414655	−	0.100107i
$841$	10.5548	−	10.5548i	0.363958	−	0.363958i
$842$	−4.30216	+	4.30216i	−0.148262	+	0.148262i
$843$	5.04183	−	12.1721i	0.173650	−	0.419228i
$844$	−15.3307	−	6.35018i	−0.527704	−	0.218582i
$845$	7.08338	+	17.1008i	0.243676	+	0.588285i
$846$		−	1.30115i		−	0.0447343i
$847$	11.6384	−	4.82078i	0.399900	−	0.165644i
$848$	−6.79298	−	6.79298i	−0.233272	−	0.233272i
$849$	17.8710			0.613331
$850$	−0.832997	+	0.923780i	−0.0285716	+	0.0316854i
$851$	4.39490			0.150655
$852$	−0.344829	−	0.344829i	−0.0118137	−	0.0118137i
$853$	10.6192	−	4.39863i	0.363595	−	0.150606i	−0.193404	−	0.981119i	$-0.561953\pi$
$853$	10.6192	−	4.39863i	0.363595	−	0.150606i	0.556999	+	0.830513i	$0.311953\pi$
$854$		−	0.686230i		−	0.0234823i
$855$	−5.11472	−	12.3480i	−0.174920	−	0.422293i
$856$	1.60244	+	0.663753i	0.0547703	+	0.0226866i
$857$	−10.7482	+	25.9484i	−0.367151	+	0.886380i	0.627064	+	0.778968i	$0.284256\pi$
$857$	−10.7482	+	25.9484i	−0.367151	+	0.886380i	−0.994215	+	0.107412i	$0.965744\pi$
$858$	−3.10717	+	3.10717i	−0.106077	+	0.106077i
$859$	−2.22749	+	2.22749i	−0.0760011	+	0.0760011i	−0.744086	−	0.668084i	$-0.767115\pi$
$859$	−2.22749	+	2.22749i	−0.0760011	+	0.0760011i	0.668084	+	0.744086i	$0.267115\pi$
$860$	1.91411	−	4.62106i	0.0652705	−	0.157577i
$861$	30.3833	+	12.5852i	1.03546	+	0.428901i
$862$	−2.30538	−	5.56568i	−0.0785216	−	0.189568i
$863$			34.5368i			1.17565i	0.808989	+	0.587823i	$0.200015\pi$
$863$			34.5368i			1.17565i	−0.808989	+	0.587823i	$0.799985\pi$
$864$	16.2598	−	6.73504i	0.553171	−	0.229131i
$865$	13.3239	+	13.3239i	0.453028	+	0.453028i
$866$	5.49781			0.186823
$867$	−8.58348	−	15.8640i	−0.291510	−	0.538769i
$868$	−10.7675			−0.365473
$869$	25.4370	+	25.4370i	0.862892	+	0.862892i
$870$	−1.10941	+	0.459531i	−0.0376124	+	0.0155795i
$871$		−	37.6032i		−	1.27414i
$872$	−4.25919	−	10.2826i	−0.144234	−	0.348212i
$873$	−15.5136	−	6.42595i	−0.525057	−	0.217486i
$874$	0.708688	−	1.71093i	0.0239717	−	0.0578729i
$875$	−1.77472	+	1.77472i	−0.0599966	+	0.0599966i
$876$	−9.24848	+	9.24848i	−0.312477	+	0.312477i
$877$	−6.05591	+	14.6203i	−0.204493	+	0.493691i	−0.992539	−	0.121926i	$-0.961093\pi$
$877$	−6.05591	+	14.6203i	−0.204493	+	0.493691i	0.788046	+	0.615617i	$0.211093\pi$
$878$	4.10647	+	1.70096i	0.138587	+	0.0574045i
$879$	−8.47821	−	20.4682i	−0.285963	−	0.690376i
$880$			8.46705i			0.285424i
$881$	29.1623	−	12.0794i	0.982504	−	0.406967i	0.167152	−	0.985931i	$-0.446543\pi$
$881$	29.1623	−	12.0794i	0.982504	−	0.406967i	0.815353	+	0.578965i	$0.196543\pi$
$882$	−0.280162	−	0.280162i	−0.00943353	−	0.00943353i
$883$	−20.2779			−0.682406			−0.341203	−	0.939990i	$-0.610834\pi$
$883$	−20.2779			−0.682406			−0.341203	+	0.939990i	$0.610834\pi$
$884$	29.5878	−	32.8124i	0.995144	−	1.10360i
$885$	7.89572			0.265412
$886$	−4.97762	−	4.97762i	−0.167226	−	0.167226i
$887$	45.1215	−	18.6899i	1.51503	−	0.627547i	0.538443	−	0.842662i	$-0.319013\pi$
$887$	45.1215	−	18.6899i	1.51503	−	0.627547i	0.976589	+	0.215115i	$0.0690126\pi$
$888$		−	6.38831i		−	0.214378i
$889$	5.71946	+	13.8080i	0.191825	+	0.463106i
$890$	−0.110141	−	0.0456218i	−0.00369192	−	0.00152925i
$891$	0.126868	−	0.306287i	0.00425024	−	0.0102610i
$892$	8.72426	−	8.72426i	0.292110	−	0.292110i
$893$	11.6033	−	11.6033i	0.388290	−	0.388290i
$894$	−0.737129	+	1.77959i	−0.0246533	+	0.0595183i
$895$	−3.06159	−	1.26815i	−0.102338	−	0.0423897i
$896$	−8.24607	−	19.9078i	−0.275482	−	0.665072i
$897$			5.12682i			0.171180i
$898$	−0.477067	+	0.197608i	−0.0159199	+	0.00659425i
$899$	5.96141	+	5.96141i	0.198824	+	0.198824i
$900$	−3.57791			−0.119264
$901$	11.4253	−	0.590416i	0.380633	−	0.0196696i
$902$	9.11148			0.303379
$903$	−4.93373	−	4.93373i	−0.164184	−	0.164184i
$904$	16.3004	−	6.75183i	0.542142	−	0.224563i
$905$			15.8652i			0.527375i
$906$	1.27618	+	3.08098i	0.0423984	+	0.102359i
$907$	−38.5317	−	15.9603i	−1.27942	−	0.529955i	−0.363608	−	0.931552i	$-0.618455\pi$
$907$	−38.5317	−	15.9603i	−1.27942	−	0.529955i	−0.915816	+	0.401598i	$0.868455\pi$
$908$	2.23588	−	5.39790i	0.0742004	−	0.179136i
$909$	−20.2614	+	20.2614i	−0.672029	+	0.672029i
$910$	−3.00545	+	3.00545i	−0.0996297	+	0.0996297i
$911$	2.44973	−	5.91417i	0.0811632	−	0.195945i	−0.878088	−	0.478498i	$-0.841181\pi$
$911$	2.44973	−	5.91417i	0.0811632	−	0.195945i	0.959252	+	0.282553i	$0.0911813\pi$
$912$	24.2015	+	10.0246i	0.801392	+	0.331947i
$913$	−13.0073	−	31.4023i	−0.430478	−	1.03926i
$914$			3.98735i			0.131890i
$915$	0.888391	−	0.367983i	0.0293693	−	0.0121652i
$916$	−10.2039	−	10.2039i	−0.337145	−	0.337145i
$917$	10.5094			0.347052
$918$	−2.15178	+	6.06239i	−0.0710195	+	0.200089i
$919$	−23.6812			−0.781170			−0.390585	−	0.920567i	$-0.627727\pi$
$919$	−23.6812			−0.781170			−0.390585	+	0.920567i	$0.627727\pi$
$920$	−0.717811	−	0.717811i	−0.0236655	−	0.0236655i
$921$	−29.3613	+	12.1618i	−0.967488	+	0.400746i
$922$		−	8.83658i		−	0.291017i
$923$	0.517199	+	1.24863i	0.0170238	+	0.0410991i
$924$	11.4859	+	4.75762i	0.377859	+	0.156514i
$925$	−1.95382	+	4.71693i	−0.0642411	+	0.155092i
$926$	−2.09137	+	2.09137i	−0.0687268	+	0.0687268i
$927$	19.5807	−	19.5807i	0.643116	−	0.643116i
$928$	−4.88550	+	11.7946i	−0.160374	+	0.387178i
$929$	50.7164	+	21.0074i	1.66395	+	0.689232i	0.998369	−	0.0570920i	$-0.0181828\pi$
$929$	50.7164	+	21.0074i	1.66395	+	0.689232i	0.665583	+	0.746324i	$0.268183\pi$
$930$	0.275286	+	0.664598i	0.00902697	+	0.0217930i
$931$		−	4.99683i		−	0.163764i
$932$	39.4142	−	16.3259i	1.29106	−	0.534773i
$933$	0.157795	+	0.157795i	0.00516598	+	0.00516598i
$934$	−4.12766			−0.135061
$935$	−7.48847	−	6.75255i	−0.244899	−	0.220832i
$936$	−12.4071			−0.405539
$937$	4.78966	+	4.78966i	0.156471	+	0.156471i	0.781001	−	0.624530i	$-0.214709\pi$
$937$	4.78966	+	4.78966i	0.156471	+	0.156471i	−0.624530	+	0.781001i	$0.714709\pi$
$938$	4.68619	−	1.94108i	0.153010	−	0.0633786i
$939$			34.4025i			1.12268i
$940$	−1.68107	−	4.05845i	−0.0548303	−	0.132372i
$941$	−23.2992	−	9.65084i	−0.759532	−	0.314608i	−0.0309078	−	0.999522i	$-0.509840\pi$
$941$	−23.2992	−	9.65084i	−0.759532	−	0.314608i	−0.728624	+	0.684914i	$0.759840\pi$
$942$	−1.64232	+	3.96490i	−0.0535096	+	0.129184i
$943$	7.51696	−	7.51696i	0.244786	−	0.244786i
$944$	18.2183	−	18.2183i	0.592954	−	0.592954i
$945$	−4.96723	+	11.9920i	−0.161584	+	0.390098i
$946$	−1.78598	−	0.739776i	−0.0580671	−	0.0240522i
$947$	9.37621	+	22.6362i	0.304686	+	0.735577i	0.999860	+	0.0167354i	$0.00532731\pi$
$947$	9.37621	+	22.6362i	0.304686	+	0.735577i	−0.695174	+	0.718841i	$0.744673\pi$
$948$		−	29.7937i		−	0.967654i
$949$	33.4888	−	13.8715i	1.08709	−	0.450288i
$950$	1.52123	+	1.52123i	0.0493553	+	0.0493553i
$951$	−35.4793			−1.15050
$952$	11.5007	+	4.08206i	0.372740	+	0.132300i
$953$	30.3936			0.984545			0.492272	−	0.870441i	$-0.336166\pi$
$953$	30.3936			0.984545			0.492272	+	0.870441i	$0.336166\pi$
$954$	−1.10941	−	1.10941i	−0.0359185	−	0.0359185i
$955$	25.4014	−	10.5216i	0.821969	−	0.340471i
$956$			6.60473i			0.213612i
$957$	−3.72511	−	8.99320i	−0.120416	−	0.290709i
$958$	−3.06873	−	1.27111i	−0.0991462	−	0.0410677i
$959$	−6.97302	+	16.8344i	−0.225171	+	0.543610i
$960$	4.42477	−	4.42477i	0.142809	−	0.142809i
$961$	−18.3491	+	18.3491i	−0.591906	+	0.591906i
$962$	−3.30874	+	7.98801i	−0.106678	+	0.257544i
$963$	−2.54677	−	1.05491i	−0.0820684	−	0.0339939i
$964$	13.1688	+	31.7923i	0.424139	+	1.02396i
$965$		−	14.7613i		−	0.475182i
$966$	−0.638915	+	0.264647i	−0.0205568	+	0.00851489i
$967$	−31.0785	−	31.0785i	−0.999416	−	0.999416i	0.000584066	−	1.00000i	$-0.499814\pi$
$967$	−31.0785	−	31.0785i	−0.999416	−	0.999416i	−1.00000		0.000584066i	$0.999814\pi$
$968$	−5.91906			−0.190246
$969$	−28.1669	+	13.4097i	−0.904852	+	0.430782i
$970$	2.70288			0.0867843
$971$	29.9769	+	29.9769i	0.962005	+	0.962005i	0.999304	−	0.0372988i	$-0.0118753\pi$
$971$	29.9769	+	29.9769i	0.962005	+	0.962005i	−0.0372988	+	0.999304i	$0.511875\pi$
$972$	−27.6169	+	11.4393i	−0.885814	+	0.366916i
$973$			26.0853i			0.836255i
$974$	1.16538	+	2.81349i	0.0373413	+	0.0901500i
$975$	−5.50249	−	2.27920i	−0.176221	−	0.0729929i
$976$	1.20077	−	2.89891i	0.0384356	−	0.0927918i
$977$	16.7792	−	16.7792i	0.536813	−	0.536813i	−0.385778	−	0.922591i	$-0.626067\pi$
$977$	16.7792	−	16.7792i	0.536813	−	0.536813i	0.922591	+	0.385778i	$0.126067\pi$
$978$	0.356517	−	0.356517i	0.0114001	−	0.0114001i
$979$	0.369825	−	0.892837i	0.0118197	−	0.0285352i
$980$	−1.23583	−	0.511896i	−0.0394770	−	0.0163519i
$981$	6.76915	+	16.3422i	0.216122	+	0.521765i
$982$		−	5.15363i		−	0.164459i
$983$	−25.9264	+	10.7391i	−0.826925	+	0.342524i	−0.755685	−	0.654935i	$-0.772696\pi$
$983$	−25.9264	+	10.7391i	−0.826925	+	0.342524i	−0.0712405	+	0.997459i	$0.522696\pi$
$984$	−10.9264	−	10.9264i	−0.348322	−	0.348322i
$985$	0.376406			0.0119933
$986$	−2.00585	−	4.21325i	−0.0638791	−	0.134177i
$987$	−6.12786			−0.195052
$988$	−54.0337	−	54.0337i	−1.71904	−	1.71904i
$989$	−2.08374	+	0.863114i	−0.0662591	+	0.0274454i
$990$			1.38282i			0.0439488i
$991$	17.0472	+	41.1557i	0.541523	+	1.30735i	0.923648	+	0.383242i	$0.125193\pi$
$991$	17.0472	+	41.1557i	0.541523	+	1.30735i	−0.382124	+	0.924111i	$0.624807\pi$
$992$	7.06567	+	2.92670i	0.224335	+	0.0929227i
$993$	0.359477	−	0.867854i	0.0114076	−	0.0275405i
$994$	−0.128909	+	0.128909i	−0.00408874	+	0.00408874i
$995$	5.32454	−	5.32454i	0.168799	−	0.168799i
$996$	−10.7728	+	26.0079i	−0.341349	+	0.824090i
$997$	−18.9837	−	7.86332i	−0.601221	−	0.249034i	0.0612487	−	0.998123i	$-0.480492\pi$
$997$	−18.9837	−	7.86332i	−0.601221	−	0.249034i	−0.662470	+	0.749089i	$0.730492\pi$
$998$	−3.62047	−	8.74058i	−0.114604	−	0.276678i
$999$			26.4042i			0.835392i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.36.4	yes	24
3.2	odd	2		765.2.be.b.631.3		24
5.2	odd	4		425.2.n.c.274.3		24
5.3	odd	4		425.2.n.f.274.4		24
5.4	even	2		425.2.m.b.376.3		24
17.3	odd	16		1445.2.a.p.1.7		12
17.5	odd	16		1445.2.d.j.866.12		24
17.9	even	8	inner	85.2.l.a.26.4	✓	24
17.12	odd	16		1445.2.d.j.866.11		24
17.14	odd	16		1445.2.a.q.1.7		12
51.26	odd	8		765.2.be.b.451.3		24
85.9	even	8		425.2.m.b.26.3		24
85.14	odd	16		7225.2.a.bq.1.6		12
85.43	odd	8		425.2.n.c.349.3		24
85.54	odd	16		7225.2.a.bs.1.6		12
85.77	odd	8		425.2.n.f.349.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.4	✓	24	17.9	even	8	inner
85.2.l.a.36.4	yes	24	1.1	even	1	trivial
425.2.m.b.26.3		24	85.9	even	8
425.2.m.b.376.3		24	5.4	even	2
425.2.n.c.274.3		24	5.2	odd	4
425.2.n.c.349.3		24	85.43	odd	8
425.2.n.f.274.4		24	5.3	odd	4
425.2.n.f.349.4		24	85.77	odd	8
765.2.be.b.451.3		24	51.26	odd	8
765.2.be.b.631.3		24	3.2	odd	2
1445.2.a.p.1.7		12	17.3	odd	16
1445.2.a.q.1.7		12	17.14	odd	16
1445.2.d.j.866.11		24	17.12	odd	16
1445.2.d.j.866.12		24	17.5	odd	16
7225.2.a.bq.1.6		12	85.14	odd	16
7225.2.a.bs.1.6		12	85.54	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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.213325 + 0.213325i) q^{2} +(0.980249 - 0.406032i) q^{3} -1.90899i q^{4} +(-0.382683 - 0.923880i) q^{5} +(0.295728 + 0.122495i) q^{6} +(-0.960473 + 2.31879i) q^{7} +(0.833883 - 0.833883i) q^{8} +(-1.32529 + 1.32529i) q^{9} +(0.115451 - 0.278722i) q^{10} +(2.25941 + 0.935880i) q^{11} +(-0.775110 - 1.87128i) q^{12} +5.61335i q^{13} +(-0.699548 + 0.289762i) q^{14} +(-0.750250 - 0.750250i) q^{15} -3.46219 q^{16} +(2.76113 - 3.06205i) q^{17} -0.565436 q^{18} +(-5.04243 - 5.04243i) q^{19} +(-1.76367 + 0.730537i) q^{20} +2.66297i q^{21} +(0.282343 + 0.681636i) q^{22} +(0.795280 + 0.329416i) q^{23} +(0.478830 - 1.15600i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(-1.19747 + 1.19747i) q^{26} +(-1.97910 + 4.77798i) q^{27} +(4.42653 + 1.83353i) q^{28} +(-1.43561 - 3.46587i) q^{29} -0.320094i q^{30} +(-2.07626 + 0.860015i) q^{31} +(-2.40634 - 2.40634i) q^{32} +2.59479 q^{33} +(1.24223 - 0.0641935i) q^{34} +2.50984 q^{35} +(2.52997 + 2.52997i) q^{36} +(4.71693 - 1.95382i) q^{37} -2.15135i q^{38} +(2.27920 + 5.50249i) q^{39} +(-1.08952 - 0.451294i) q^{40} +(4.72598 - 11.4095i) q^{41} +(-0.568078 + 0.568078i) q^{42} +(-1.85272 + 1.85272i) q^{43} +(1.78658 - 4.31319i) q^{44} +(1.73158 + 0.717244i) q^{45} +(0.0993804 + 0.239926i) q^{46} +2.30114i q^{47} +(-3.39381 + 1.40576i) q^{48} +(0.495478 + 0.495478i) q^{49} -0.301687 q^{50} +(1.46330 - 4.12268i) q^{51} +10.7158 q^{52} +(1.96204 + 1.96204i) q^{53} +(-1.44145 + 0.597069i) q^{54} -2.44557i q^{55} +(1.13268 + 2.73452i) q^{56} +(-6.99022 - 2.89544i) q^{57} +(0.433105 - 1.04561i) q^{58} +(-5.26206 + 5.26206i) q^{59} +(-1.43222 + 1.43222i) q^{60} +(-0.346822 + 0.837303i) q^{61} +(-0.626380 - 0.259455i) q^{62} +(-1.80017 - 4.34599i) q^{63} +5.89773i q^{64} +(5.18606 - 2.14814i) q^{65} +(0.553532 + 0.553532i) q^{66} -6.69889 q^{67} +(-5.84541 - 5.27096i) q^{68} +0.913326 q^{69} +(0.535411 + 0.535411i) q^{70} +(0.222439 - 0.0921372i) q^{71} +2.21028i q^{72} +(-2.47116 - 5.96591i) q^{73} +(1.42304 + 0.589441i) q^{74} +(-0.406032 + 0.980249i) q^{75} +(-9.62592 + 9.62592i) q^{76} +(-4.34022 + 4.34022i) q^{77} +(-0.687606 + 1.66003i) q^{78} +(13.5899 + 5.62912i) q^{79} +(1.32492 + 3.19865i) q^{80} -0.135560i q^{81} +(3.44210 - 1.42577i) q^{82} +(-9.82767 - 9.82767i) q^{83} +5.08358 q^{84} +(-3.88561 - 1.37916i) q^{85} -0.790460 q^{86} +(-2.81451 - 2.81451i) q^{87} +(2.66450 - 1.10367i) q^{88} -0.395163i q^{89} +(0.216383 + 0.522395i) q^{90} +(-13.0162 - 5.39148i) q^{91} +(0.628850 - 1.51818i) q^{92} +(-1.68606 + 1.68606i) q^{93} +(-0.490889 + 0.490889i) q^{94} +(-2.72894 + 6.58825i) q^{95} +(-3.33586 - 1.38176i) q^{96} +(3.42855 + 8.27725i) q^{97} +0.211396i q^{98} +(-4.23471 + 1.75407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Introduction

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