LMFDB - Embedded newform 170.2.r.b.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(23,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([12, 15]))

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

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

chi := DirichletCharacter("170.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.r (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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	170.97
Dual form			170.2.r.b.163.5

$q$-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} +(0.567062 - 2.85081i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-2.18819 - 0.460262i) q^{5} +(-2.41680 - 1.61486i) q^{6} +(3.60477 + 2.40863i) q^{7} +(-0.923880 + 0.382683i) q^{8} +(-5.03395 - 2.08513i) q^{9} +(-1.26261 + 1.84549i) q^{10} +(-0.113862 + 0.170406i) q^{11} +(-2.41680 + 1.61486i) q^{12} +3.32855 q^{13} +(3.60477 - 2.40863i) q^{14} +(-2.55296 + 5.97712i) q^{15} +1.00000i q^{16} +(-4.05227 - 0.761002i) q^{17} +(-3.85282 + 3.85282i) q^{18} +(1.76021 - 0.729105i) q^{19} +(1.22183 + 1.87274i) q^{20} +(8.91069 - 8.91069i) q^{21} +(0.113862 + 0.170406i) q^{22} +(-0.769445 + 0.153052i) q^{23} +(0.567062 + 2.85081i) q^{24} +(4.57632 + 2.01428i) q^{25} +(1.27378 - 3.07518i) q^{26} +(-3.95431 + 5.91804i) q^{27} +(-0.845799 - 4.25212i) q^{28} +(8.95670 + 1.78160i) q^{29} +(4.54516 + 4.64597i) q^{30} +(-4.85565 - 7.26699i) q^{31} +(0.923880 + 0.382683i) q^{32} +(0.421230 + 0.421230i) q^{33} +(-2.25381 + 3.45258i) q^{34} +(-6.77931 - 6.92967i) q^{35} +(2.08513 + 5.03395i) q^{36} +(-1.88413 - 0.374777i) q^{37} -1.90524i q^{38} +(1.88750 - 9.48908i) q^{39} +(2.19776 - 0.412156i) q^{40} +(-3.42967 + 0.682203i) q^{41} +(-4.82243 - 11.6424i) q^{42} +(2.60772 + 6.29559i) q^{43} +(0.201008 - 0.0399830i) q^{44} +(10.0555 + 6.87959i) q^{45} +(-0.153052 + 0.769445i) q^{46} +11.8186i q^{47} +(2.85081 + 0.567062i) q^{48} +(4.51409 + 10.8980i) q^{49} +(3.61223 - 3.45713i) q^{50} +(-4.46736 + 11.1207i) q^{51} +(-2.35364 - 2.35364i) q^{52} +(4.78009 + 1.97998i) q^{53} +(3.95431 + 5.91804i) q^{54} +(0.327582 - 0.320474i) q^{55} +(-4.25212 - 0.845799i) q^{56} +(-1.08039 - 5.43149i) q^{57} +(5.07356 - 7.59313i) q^{58} +(-1.58062 + 3.81596i) q^{59} +(6.03167 - 2.42124i) q^{60} +(0.209544 + 1.05345i) q^{61} +(-8.57200 + 1.70508i) q^{62} +(-13.1239 - 19.6413i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-7.28349 - 1.53201i) q^{65} +(0.550364 - 0.227968i) q^{66} +(-5.49540 + 5.49540i) q^{67} +(2.32728 + 3.40350i) q^{68} +2.28034i q^{69} +(-8.99651 + 3.61139i) q^{70} +(-1.33556 + 0.892391i) q^{71} +5.44870 q^{72} +(-0.677883 + 0.452947i) q^{73} +(-1.06727 + 1.59729i) q^{74} +(8.33739 - 11.9040i) q^{75} +(-1.76021 - 0.729105i) q^{76} +(-0.820892 + 0.340025i) q^{77} +(-8.04446 - 5.37513i) q^{78} +(-10.3045 - 6.88525i) q^{79} +(0.460262 - 2.18819i) q^{80} +(3.07044 + 3.07044i) q^{81} +(-0.682203 + 3.42967i) q^{82} +(-0.269470 + 0.650559i) q^{83} -12.6016 q^{84} +(8.51686 + 3.53032i) q^{85} +6.81430 q^{86} +(10.1580 - 24.5236i) q^{87} +(0.0399830 - 0.201008i) q^{88} +(-3.70552 - 3.70552i) q^{89} +(10.2040 - 6.65737i) q^{90} +(11.9987 + 8.01725i) q^{91} +(0.652304 + 0.435856i) q^{92} +(-23.4703 + 9.72172i) q^{93} +(10.9189 + 4.52277i) q^{94} +(-4.18726 + 0.785257i) q^{95} +(1.61486 - 2.41680i) q^{96} +(0.124830 - 0.0834089i) q^{97} +11.7959 q^{98} +(0.928493 - 0.620400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44}+ \cdots + 160 q^{99}+O(q^{100}) $ 40 * q - 16 * q^10 - 16 * q^18 + 8 * q^25 - 8 * q^26 + 24 * q^27 - 8 * q^28 + 8 * q^29 + 16 * q^30 - 16 * q^31 - 32 * q^33 + 8 * q^34 - 32 * q^35 - 32 * q^39 - 56 * q^41 - 24 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^49 - 32 * q^51 - 16 * q^52 + 16 * q^53 - 24 * q^54 - 8 * q^55 - 8 * q^56 - 120 * q^57 + 16 * q^58 + 8 * q^60 + 24 * q^61 - 8 * q^62 - 24 * q^63 - 32 * q^65 + 16 * q^67 - 8 * q^70 + 24 * q^71 + 56 * q^72 + 88 * q^73 + 32 * q^74 + 8 * q^75 + 24 * q^77 + 32 * q^78 - 104 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 + 136 * q^85 + 96 * q^86 + 136 * q^87 - 16 * q^89 + 24 * q^90 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 136 * q^95 + 16 * q^97 + 72 * q^98 + 160 * q^99

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	0.567062	−	2.85081i	0.327394	−	1.64592i	−0.369855	−	0.929089i	$-0.620593\pi$
$3$	0.567062	−	2.85081i	0.327394	−	1.64592i	0.697249	−	0.716829i	$-0.254407\pi$
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$	−2.18819	−	0.460262i	−0.978587	−	0.205836i
$5$	−2.18819	−	0.460262i	−0.978587	−	0.205836i
$6$	−2.41680	−	1.61486i	−0.986656	−	0.659263i
$7$	3.60477	+	2.40863i	1.36248	+	0.910377i	0.999768	−	0.0215260i	$-0.00685247\pi$
$7$	3.60477	+	2.40863i	1.36248	+	0.910377i	0.362707	+	0.931903i	$0.381852\pi$
$8$	−0.923880	+	0.382683i	−0.326641	+	0.135299i
$9$	−5.03395	−	2.08513i	−1.67798	−	0.695043i
$10$	−1.26261	+	1.84549i	−0.399272	+	0.583594i
$11$	−0.113862	+	0.170406i	−0.0343306	+	0.0513794i	−0.848238	−	0.529615i	$-0.822336\pi$
$11$	−0.113862	+	0.170406i	−0.0343306	+	0.0513794i	0.813907	+	0.580995i	$0.197336\pi$
$12$	−2.41680	+	1.61486i	−0.697671	+	0.466169i
$13$	3.32855			0.923174			0.461587	−	0.887095i	$-0.347280\pi$
$13$	3.32855			0.923174			0.461587	+	0.887095i	$0.347280\pi$
$14$	3.60477	−	2.40863i	0.963416	−	0.643734i
$15$	−2.55296	+	5.97712i	−0.659171	+	1.54328i
$16$			1.00000i			0.250000i
$17$	−4.05227	−	0.761002i	−0.982819	−	0.184570i
$17$	−4.05227	−	0.761002i	−0.982819	−	0.184570i
$18$	−3.85282	+	3.85282i	−0.908117	+	0.908117i
$19$	1.76021	−	0.729105i	0.403821	−	0.167268i	−0.171522	−	0.985180i	$-0.554869\pi$
$19$	1.76021	−	0.729105i	0.403821	−	0.167268i	0.575343	+	0.817912i	$0.304869\pi$
$20$	1.22183	+	1.87274i	0.273209	+	0.418756i
$21$	8.91069	−	8.91069i	1.94447	−	1.94447i
$22$	0.113862	+	0.170406i	0.0242754	+	0.0363307i
$23$	−0.769445	+	0.153052i	−0.160440	+	0.0319136i	−0.274657	−	0.961542i	$-0.588564\pi$
$23$	−0.769445	+	0.153052i	−0.160440	+	0.0319136i	0.114216	+	0.993456i	$0.463564\pi$
$24$	0.567062	+	2.85081i	0.115751	+	0.581920i
$25$	4.57632	+	2.01428i	0.915263	+	0.402856i
$26$	1.27378	−	3.07518i	0.249809	−	0.603093i
$27$	−3.95431	+	5.91804i	−0.761007	+	1.13893i
$28$	−0.845799	−	4.25212i	−0.159841	−	0.803575i
$29$	8.95670	+	1.78160i	1.66322	+	0.330835i	0.935037	−	0.354550i	$-0.115366\pi$
$29$	8.95670	+	1.78160i	1.66322	+	0.330835i	0.728181	+	0.685385i	$0.240366\pi$
$30$	4.54516	+	4.64597i	0.829829	+	0.848234i
$31$	−4.85565	−	7.26699i	−0.872100	−	1.30519i	−0.951279	−	0.308330i	$-0.900230\pi$
$31$	−4.85565	−	7.26699i	−0.872100	−	1.30519i	0.0791791	−	0.996860i	$-0.474770\pi$
$32$	0.923880	+	0.382683i	0.163320	+	0.0676495i
$33$	0.421230	+	0.421230i	0.0733267	+	0.0733267i
$34$	−2.25381	+	3.45258i	−0.386525	+	0.592113i
$35$	−6.77931	−	6.92967i	−1.14591	−	1.17133i
$36$	2.08513	+	5.03395i	0.347521	+	0.838991i
$37$	−1.88413	−	0.374777i	−0.309749	−	0.0616129i	0.0377681	−	0.999287i	$-0.487975\pi$
$37$	−1.88413	−	0.374777i	−0.309749	−	0.0616129i	−0.347517	+	0.937674i	$0.612975\pi$
$38$		−	1.90524i		−	0.309071i
$39$	1.88750	−	9.48908i	0.302241	−	1.51947i
$40$	2.19776	−	0.412156i	0.347496	−	0.0651676i
$41$	−3.42967	+	0.682203i	−0.535624	+	0.106542i	−0.455488	−	0.890242i	$-0.650535\pi$
$41$	−3.42967	+	0.682203i	−0.535624	+	0.106542i	−0.0801355	+	0.996784i	$0.525535\pi$
$42$	−4.82243	−	11.6424i	−0.744117	−	1.79646i
$43$	2.60772	+	6.29559i	0.397674	+	0.960069i	0.988216	+	0.153063i	$0.0489137\pi$
$43$	2.60772	+	6.29559i	0.397674	+	0.960069i	−0.590543	+	0.807006i	$0.701086\pi$
$44$	0.201008	−	0.0399830i	0.0303031	−	0.00602766i
$45$	10.0555	+	6.87959i	1.49899	+	1.02555i
$46$	−0.153052	+	0.769445i	−0.0225663	+	0.113449i
$47$			11.8186i			1.72392i	0.506979	+	0.861958i	$0.330762\pi$
$47$			11.8186i			1.72392i	−0.506979	+	0.861958i	$0.669238\pi$
$48$	2.85081	+	0.567062i	0.411480	+	0.0818484i
$49$	4.51409	+	10.8980i	0.644870	+	1.55685i
$50$	3.61223	−	3.45713i	0.510847	−	0.488913i
$51$	−4.46736	+	11.1207i	−0.625556	+	1.55721i
$52$	−2.35364	−	2.35364i	−0.326391	−	0.326391i
$53$	4.78009	+	1.97998i	0.656596	+	0.271971i	0.686005	−	0.727597i	$-0.259363\pi$
$53$	4.78009	+	1.97998i	0.656596	+	0.271971i	−0.0294096	+	0.999567i	$0.509363\pi$
$54$	3.95431	+	5.91804i	0.538113	+	0.805343i
$55$	0.327582	−	0.320474i	0.0441712	−	0.0432128i
$56$	−4.25212	−	0.845799i	−0.568213	−	0.113025i
$57$	−1.08039	−	5.43149i	−0.143101	−	0.719419i
$58$	5.07356	−	7.59313i	0.666192	−	0.997026i
$59$	−1.58062	+	3.81596i	−0.205779	+	0.496795i	−0.992750	−	0.120195i	$-0.961648\pi$
$59$	−1.58062	+	3.81596i	−0.205779	+	0.496795i	0.786971	+	0.616990i	$0.211648\pi$
$60$	6.03167	−	2.42124i	0.778686	−	0.312581i
$61$	0.209544	+	1.05345i	0.0268294	+	0.134881i	0.991879	−	0.127188i	$-0.0405952\pi$
$61$	0.209544	+	1.05345i	0.0268294	+	0.134881i	−0.965049	+	0.262069i	$0.915595\pi$
$62$	−8.57200	+	1.70508i	−1.08865	+	0.216545i
$63$	−13.1239	−	19.6413i	−1.65346	−	2.47458i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	−7.28349	−	1.53201i	−0.903406	−	0.190022i
$66$	0.550364	−	0.227968i	0.0677451	−	0.0280609i
$67$	−5.49540	+	5.49540i	−0.671369	+	0.671369i	−0.958032	−	0.286662i	$-0.907454\pi$
$67$	−5.49540	+	5.49540i	−0.671369	+	0.671369i	0.286662	+	0.958032i	$0.407454\pi$
$68$	2.32728	+	3.40350i	0.282224	+	0.412734i
$69$			2.28034i			0.274520i
$70$	−8.99651	+	3.61139i	−1.07529	+	0.431644i
$71$	−1.33556	+	0.892391i	−0.158502	+	0.105907i	−0.632292	−	0.774730i	$-0.717886\pi$
$71$	−1.33556	+	0.892391i	−0.158502	+	0.105907i	0.473790	+	0.880638i	$0.342886\pi$
$72$	5.44870			0.642136
$73$	−0.677883	+	0.452947i	−0.0793403	+	0.0530135i	−0.594608	−	0.804016i	$-0.702693\pi$
$73$	−0.677883	+	0.452947i	−0.0793403	+	0.0530135i	0.515267	+	0.857029i	$0.327693\pi$
$74$	−1.06727	+	1.59729i	−0.124068	+	0.185681i
$75$	8.33739	−	11.9040i	0.962719	−	1.37456i
$76$	−1.76021	−	0.729105i	−0.201910	−	0.0836340i
$77$	−0.820892	+	0.340025i	−0.0935493	+	0.0387494i
$78$	−8.04446	−	5.37513i	−0.910855	−	0.608614i
$79$	−10.3045	−	6.88525i	−1.15935	−	0.774651i	−0.181380	−	0.983413i	$-0.558056\pi$
$79$	−10.3045	−	6.88525i	−1.15935	−	0.774651i	−0.977966	+	0.208762i	$0.933056\pi$
$80$	0.460262	−	2.18819i	0.0514589	−	0.244647i
$81$	3.07044	+	3.07044i	0.341160	+	0.341160i
$82$	−0.682203	+	3.42967i	−0.0753367	+	0.378743i
$83$	−0.269470	+	0.650559i	−0.0295782	+	0.0714081i	−0.937978	−	0.346693i	$-0.887304\pi$
$83$	−0.269470	+	0.650559i	−0.0295782	+	0.0714081i	0.908400	+	0.418102i	$0.137304\pi$
$84$	−12.6016			−1.37495
$85$	8.51686	+	3.53032i	0.923783	+	0.382917i
$86$	6.81430			0.734805
$87$	10.1580	−	24.5236i	1.08905	−	2.62921i
$88$	0.0399830	−	0.201008i	0.00426220	−	0.0214275i
$89$	−3.70552	−	3.70552i	−0.392784	−	0.392784i	0.482894	−	0.875679i	$-0.339585\pi$
$89$	−3.70552	−	3.70552i	−0.392784	−	0.392784i	−0.875679	+	0.482894i	$0.839585\pi$
$90$	10.2040	−	6.65737i	1.07559	−	0.701749i
$91$	11.9987	+	8.01725i	1.25780	+	0.840437i
$92$	0.652304	+	0.435856i	0.0680074	+	0.0454411i
$93$	−23.4703	+	9.72172i	−2.43376	+	1.00810i
$94$	10.9189	+	4.52277i	1.12620	+	0.466489i
$95$	−4.18726	+	0.785257i	−0.429603	+	0.0805656i
$96$	1.61486	−	2.41680i	0.164816	−	0.246664i
$97$	0.124830	−	0.0834089i	0.0126746	−	0.00846889i	−0.549217	−	0.835680i	$-0.685074\pi$
$97$	0.124830	−	0.0834089i	0.0126746	−	0.00846889i	0.561891	+	0.827211i	$0.310074\pi$
$98$	11.7959			1.19156
$99$	0.928493	−	0.620400i	0.0933171	−	0.0623525i
$100$	−1.81163	−	4.66026i	−0.181163	−	0.466026i
$101$		−	15.1577i		−	1.50824i	−0.656735	−	0.754122i	$-0.728063\pi$
$101$		−	15.1577i		−	1.50824i	0.656735	−	0.754122i	$-0.271937\pi$
$102$	8.56463	+	8.38302i	0.848025	+	0.830043i
$103$	−2.06188	+	2.06188i	−0.203163	+	0.203163i	−0.801354	−	0.598191i	$-0.795887\pi$
$103$	−2.06188	+	2.06188i	−0.203163	+	0.203163i	0.598191	+	0.801354i	$0.295887\pi$
$104$	−3.07518	+	1.27378i	−0.301546	+	0.124905i
$105$	−23.5995	+	15.3970i	−2.30308	+	1.50259i
$106$	3.65852	−	3.65852i	0.355347	−	0.355347i
$107$	−0.326739	−	0.488999i	−0.0315870	−	0.0472733i	0.815340	−	0.578982i	$-0.196550\pi$
$107$	−0.326739	−	0.488999i	−0.0315870	−	0.0472733i	−0.846927	+	0.531709i	$0.821550\pi$
$108$	6.98080	−	1.38857i	0.671728	−	0.133615i
$109$	0.693887	+	3.48840i	0.0664623	+	0.334129i	0.999683	−	0.0251750i	$-0.00801429\pi$
$109$	0.693887	+	3.48840i	0.0664623	+	0.334129i	−0.933221	+	0.359304i	$0.883014\pi$
$110$	−0.170719	−	0.425287i	−0.0162775	−	0.0405495i
$111$	−2.13684	+	5.15878i	−0.202820	+	0.489650i
$112$	−2.40863	+	3.60477i	−0.227594	+	0.340619i
$113$	−0.643843	−	3.23682i	−0.0605677	−	0.304494i	0.938613	−	0.344973i	$-0.112112\pi$
$113$	−0.643843	−	3.23682i	−0.0605677	−	0.304494i	−0.999180	+	0.0404784i	$0.987112\pi$
$114$	−5.43149	−	1.08039i	−0.508706	−	0.101188i
$115$	1.75413	+	0.0192399i	0.163574	+	0.00179413i
$116$	−5.07356	−	7.59313i	−0.471069	−	0.705004i
$117$	−16.7557	−	6.94046i	−1.54907	−	0.641646i
$118$	2.92061	+	2.92061i	0.268864	+	0.268864i
$119$	−12.7745	−	12.5037i	−1.17104	−	1.14621i
$120$	0.0712843	−	6.49911i	0.00650734	−	0.593285i
$121$	4.19344	+	10.1239i	0.381222	+	0.920352i
$122$	1.05345	+	0.209544i	0.0953749	+	0.0189713i
$123$			10.1642i			0.916474i
$124$	−1.70508	+	8.57200i	−0.153120	+	0.769789i
$125$	−9.08674	−	6.51392i	−0.812743	−	0.582623i
$126$	−23.1685	+	4.60851i	−2.06402	+	0.410558i
$127$	1.97507	+	4.76825i	0.175260	+	0.423114i	0.986961	−	0.160958i	$-0.0514585\pi$
$127$	1.97507	+	4.76825i	0.175260	+	0.423114i	−0.811702	+	0.584072i	$0.801458\pi$
$128$	−0.382683	−	0.923880i	−0.0338248	−	0.0816602i
$129$	19.4263	−	3.86413i	1.71039	−	0.340218i
$130$	−4.20266	+	6.14279i	−0.368598	+	0.538759i
$131$	2.13002	−	10.7084i	0.186101	−	0.935593i	−0.768985	−	0.639266i	$-0.779238\pi$
$131$	2.13002	−	10.7084i	0.186101	−	0.935593i	0.955087	−	0.296327i	$-0.0957618\pi$
$132$		−	0.595709i		−	0.0518498i
$133$	8.10132	+	1.61145i	0.702473	+	0.139731i
$134$	2.97409	+	7.18008i	0.256922	+	0.620264i
$135$	11.3766	−	11.1298i	0.979142	−	0.957896i
$136$	4.03503	−	0.847662i	0.346001	−	0.0726864i
$137$	12.3373	+	12.3373i	1.05405	+	1.05405i	0.998453	+	0.0555950i	$0.0177056\pi$
$137$	12.3373	+	12.3373i	1.05405	+	1.05405i	0.0555950	+	0.998453i	$0.482294\pi$
$138$	2.10676	+	0.872647i	0.179339	+	0.0742847i
$139$	−1.10884	−	1.65949i	−0.0940503	−	0.140756i	0.781461	−	0.623955i	$-0.214475\pi$
$139$	−1.10884	−	1.65949i	−0.0940503	−	0.140756i	−0.875511	+	0.483198i	$0.839475\pi$
$140$	−0.106324	+	9.69372i	−0.00898600	+	0.819268i
$141$	33.6926	+	6.70187i	2.83743	+	0.564399i
$142$	0.313366	+	1.57540i	0.0262971	+	0.132204i
$143$	−0.378995	+	0.567206i	−0.0316932	+	0.0474322i
$144$	2.08513	−	5.03395i	0.173761	−	0.419496i
$145$	−18.7789	−	8.02090i	−1.55951	−	0.666100i
$146$	0.159054	+	0.799618i	0.0131634	+	0.0661769i
$147$	33.6279	−	6.68900i	2.77358	−	0.551699i
$148$	1.06727	+	1.59729i	0.0877294	+	0.131296i
$149$	6.12503	−	6.12503i	0.501782	−	0.501782i	−0.410209	−	0.911991i	$-0.634544\pi$
$149$	6.12503	−	6.12503i	0.501782	−	0.501782i	0.911991	+	0.410209i	$0.134544\pi$
$150$	−7.80729	−	12.2582i	−0.637463	−	1.00088i
$151$	−20.9830	+	8.69145i	−1.70757	+	0.707300i	−0.707573	+	0.706640i	$0.750210\pi$
$151$	−20.9830	+	8.69145i	−1.70757	+	0.707300i	−1.00000		0.000659759i	$0.999790\pi$
$152$	−1.34721	+	1.34721i	−0.109273	+	0.109273i
$153$	18.8121	+	12.2803i	1.52087	+	0.992807i
$154$			0.888527i			0.0715995i
$155$	7.28034	+	18.1364i	0.584771	+	1.45675i
$156$	−8.04446	+	5.37513i	−0.644072	+	0.430355i
$157$	4.30033			0.343204			0.171602	−	0.985166i	$-0.445106\pi$
$157$	4.30033			0.343204			0.171602	+	0.985166i	$0.445106\pi$
$158$	−10.3045	+	6.88525i	−0.819782	+	0.547761i
$159$	8.35516	−	12.5044i	0.662607	−	0.991661i
$160$	−1.84549	−	1.26261i	−0.145898	−	0.0998180i
$161$	−3.14232	−	1.30159i	−0.247650	−	0.102580i
$162$	4.01173	−	1.66171i	0.315191	−	0.130556i
$163$	−3.31976	−	2.21819i	−0.260024	−	0.173742i	0.418724	−	0.908113i	$-0.362477\pi$
$163$	−3.31976	−	2.21819i	−0.260024	−	0.173742i	−0.678748	+	0.734371i	$0.737477\pi$
$164$	2.90753	+	1.94275i	0.227040	+	0.151703i
$165$	−0.727853	−	1.11561i	−0.0566633	−	0.0868498i
$166$	0.497916	+	0.497916i	0.0386458	+	0.0386458i
$167$	−2.41993	+	12.1658i	−0.187260	+	0.941419i	0.766819	+	0.641864i	$0.221838\pi$
$167$	−2.41993	+	12.1658i	−0.187260	+	0.941419i	−0.954079	+	0.299556i	$0.903162\pi$
$168$	−4.82243	+	11.6424i	−0.372059	+	0.898229i
$169$	−1.92074			−0.147750
$170$	6.52085	−	6.51755i	0.500126	−	0.499874i
$171$	−10.3811			−0.793863
$172$	2.60772	−	6.29559i	0.198837	−	0.480035i
$173$	2.69051	−	13.5261i	0.204556	−	1.02837i	−0.732919	−	0.680316i	$-0.761843\pi$
$173$	2.69051	−	13.5261i	0.204556	−	1.02837i	0.937474	−	0.348054i	$-0.113157\pi$
$174$	−18.7696	−	18.7696i	−1.42292	−	1.42292i
$175$	11.6449	+	18.2837i	0.880274	+	1.38212i
$176$	−0.170406	−	0.113862i	−0.0128449	−	0.00858266i
$177$	9.98227	+	6.66994i	0.750314	+	0.501344i
$178$	−4.84149	+	2.00541i	−0.362885	+	0.150312i
$179$	−17.1204	−	7.09151i	−1.27964	−	0.530044i	−0.363758	−	0.931493i	$-0.618507\pi$
$179$	−17.1204	−	7.09151i	−1.27964	−	0.530044i	−0.915881	+	0.401449i	$0.868507\pi$
$180$	−2.24571	−	11.9749i	−0.167386	−	0.892558i
$181$	11.0377	−	16.5190i	0.820422	−	1.22785i	−0.150537	−	0.988604i	$-0.548100\pi$
$181$	11.0377	−	16.5190i	0.820422	−	1.22785i	0.970959	−	0.239244i	$-0.0768997\pi$
$182$	11.9987	−	8.01725i	0.889400	−	0.594278i
$183$	3.12202			0.230786
$184$	0.652304	−	0.435856i	0.0480885	−	0.0321317i
$185$	3.95033	+	1.68728i	0.290434	+	0.124051i
$186$			25.4041i			1.86272i
$187$	0.591078	−	0.603883i	0.0432239	−	0.0441603i
$188$	8.35700	−	8.35700i	0.609497	−	0.609497i
$189$	−28.5087	+	11.8087i	−2.07371	+	0.858957i
$190$	−0.876911	+	4.16902i	−0.0636178	+	0.302453i
$191$	−4.91463	+	4.91463i	−0.355610	+	0.355610i	−0.862192	−	0.506582i	$-0.830909\pi$
$191$	−4.91463	+	4.91463i	−0.355610	+	0.355610i	0.506582	+	0.862192i	$0.330909\pi$
$192$	−1.61486	−	2.41680i	−0.116542	−	0.174418i
$193$	−18.1291	+	3.60610i	−1.30496	+	0.259573i	−0.798137	−	0.602476i	$-0.794181\pi$
$193$	−18.1291	+	3.60610i	−1.30496	+	0.259573i	−0.506825	+	0.862049i	$0.669181\pi$
$194$	−0.0292893	−	0.147247i	−0.00210285	−	0.0105717i
$195$	−8.49766	+	19.8951i	−0.608530	+	1.42472i
$196$	4.51409	−	10.8980i	0.322435	−	0.778427i
$197$	6.03705	−	9.03509i	0.430122	−	0.643723i	−0.551585	−	0.834118i	$-0.685977\pi$
$197$	6.03705	−	9.03509i	0.430122	−	0.643723i	0.981708	+	0.190395i	$0.0609769\pi$
$198$	−0.217855	−	1.09523i	−0.0154823	−	0.0778348i
$199$	15.2386	+	3.03114i	1.08024	+	0.214872i	0.702960	−	0.711229i	$-0.251861\pi$
$199$	15.2386	+	3.03114i	1.08024	+	0.214872i	0.377275	+	0.926101i	$0.376861\pi$
$200$	−4.99880	−	0.109670i	−0.353468	−	0.00775484i
$201$	12.5501	+	18.7826i	0.885217	+	1.32482i
$202$	−14.0039	−	5.80059i	−0.985308	−	0.408128i
$203$	27.9957	+	27.9957i	1.96491	+	1.96491i
$204$	11.0224	−	4.70464i	0.771726	−	0.329391i
$205$	7.81874	+	0.0857584i	0.546084	+	0.00598963i
$206$	1.11588	+	2.69398i	0.0777471	+	0.187698i
$207$	4.19248	+	0.833936i	0.291398	+	0.0579626i
$208$			3.32855i			0.230794i
$209$	−0.0761772	+	0.382969i	−0.00526929	+	0.0264905i
$210$	5.19383	+	27.6953i	0.358408	+	1.91116i
$211$	−17.6704	+	3.51487i	−1.21648	+	0.241973i	−0.761285	−	0.648417i	$-0.775431\pi$
$211$	−17.6704	+	3.51487i	−1.21648	+	0.241973i	−0.455197	+	0.890391i	$0.650431\pi$
$212$	−1.97998	−	4.78009i	−0.135985	−	0.328298i
$213$	1.78670	+	4.31347i	0.122422	+	0.295554i
$214$	−0.576814	+	0.114735i	−0.0394302	+	0.00784315i
$215$	−2.80855	−	14.9762i	−0.191542	−	1.02137i
$216$	1.38857	−	6.98080i	0.0944801	−	0.474983i
$217$		−	37.8913i		−	2.57223i
$218$	3.48840	+	0.693887i	0.236265	+	0.0469959i
$219$	0.906866	+	2.18937i	0.0612804	+	0.147944i
$220$	−0.458245	−	0.00502618i	−0.0308949	−	0.000338865i
$221$	−13.4882	−	2.53303i	−0.907313	−	0.170390i
$222$	3.94836	+	3.94836i	0.264997	+	0.264997i
$223$	−8.96939	−	3.71524i	−0.600635	−	0.248791i	0.0615836	−	0.998102i	$-0.480385\pi$
$223$	−8.96939	−	3.71524i	−0.600635	−	0.248791i	−0.662218	+	0.749311i	$0.730385\pi$
$224$	2.40863	+	3.60477i	0.160933	+	0.240854i
$225$	−18.8369	−	19.6820i	−1.25579	−	1.31213i
$226$	−3.23682	−	0.643843i	−0.215310	−	0.0428278i
$227$	−0.103244	−	0.519043i	−0.00685255	−	0.0344501i	0.977208	−	0.212285i	$-0.0680906\pi$
$227$	−0.103244	−	0.519043i	−0.00685255	−	0.0344501i	−0.984060	+	0.177835i	$0.943091\pi$
$228$	−3.07669	+	4.60460i	−0.203759	+	0.304947i
$229$	11.2020	−	27.0440i	0.740249	−	1.78712i	0.135382	−	0.990793i	$-0.456774\pi$
$229$	11.2020	−	27.0440i	0.740249	−	1.78712i	0.604867	−	0.796326i	$-0.293226\pi$
$230$	0.689053	−	1.61325i	0.0454348	−	0.106374i
$231$	0.503850	+	2.53303i	0.0331509	+	0.166661i
$232$	−8.95670	+	1.78160i	−0.588036	+	0.116968i
$233$	−4.49587	−	6.72855i	−0.294535	−	0.440802i	0.654459	−	0.756097i	$-0.272896\pi$
$233$	−4.49587	−	6.72855i	−0.294535	−	0.440802i	−0.948994	+	0.315295i	$0.897896\pi$
$234$	−12.8243	+	12.8243i	−0.838350	+	0.838350i
$235$	5.43964	−	25.8612i	0.354843	−	1.68700i
$236$	3.81596	−	1.58062i	0.248398	−	0.102890i
$237$	−25.4719	+	25.4719i	−1.65457	+	1.65457i
$238$	−16.4405	+	7.01718i	−1.06568	+	0.454856i
$239$			20.1335i			1.30233i	0.758937	+	0.651164i	$0.225719\pi$
$239$			20.1335i			1.30233i	−0.758937	+	0.651164i	$0.774281\pi$
$240$	−5.97712	−	2.55296i	−0.385821	−	0.164793i
$241$	−7.62327	+	5.09371i	−0.491058	+	0.328115i	−0.776324	−	0.630334i	$-0.782918\pi$
$241$	−7.62327	+	5.09371i	−0.491058	+	0.328115i	0.285266	+	0.958448i	$0.407918\pi$
$242$	10.9580			0.704407
$243$	−7.25971	+	4.85079i	−0.465711	+	0.311178i
$244$	0.596732	−	0.893072i	0.0382018	−	0.0571731i
$245$	−4.86174	−	25.9245i	−0.310605	−	1.65625i
$246$	9.39049	+	3.88967i	0.598716	+	0.247996i
$247$	5.85896	−	2.42686i	0.372797	−	0.154418i
$248$	7.26699	+	4.85565i	0.461454	+	0.308334i
$249$	1.70182	+	1.13712i	0.107848	+	0.0720619i
$250$	−9.49542	+	5.90228i	−0.600543	+	0.373293i
$251$	6.12489	+	6.12489i	0.386600	+	0.386600i	0.873473	−	0.486873i	$-0.161863\pi$
$251$	6.12489	+	6.12489i	0.386600	+	0.386600i	−0.486873	+	0.873473i	$0.661863\pi$
$252$	−4.60851	+	23.1685i	−0.290309	+	1.45948i
$253$	0.0615294	−	0.148545i	0.00386832	−	0.00933895i
$254$	5.16112			0.323837
$255$	14.8939	−	22.2781i	0.932691	−	1.39511i
$256$	−1.00000			−0.0625000
$257$	−1.52117	+	3.67244i	−0.0948882	+	0.229080i	−0.964196	−	0.265191i	$-0.914565\pi$
$257$	−1.52117	+	3.67244i	−0.0948882	+	0.229080i	0.869308	+	0.494271i	$0.164565\pi$
$258$	3.86413	−	19.4263i	0.240570	−	1.20943i
$259$	−5.88916	−	5.88916i	−0.365935	−	0.365935i
$260$	4.06691	+	6.23350i	0.252219	+	0.386585i
$261$	−41.3727	−	27.6444i	−2.56091	−	1.71114i
$262$	−9.07811	−	6.06580i	−0.560847	−	0.374746i
$263$	28.4288	−	11.7756i	1.75299	−	0.726113i	0.755514	−	0.655132i	$-0.227387\pi$
$263$	28.4288	−	11.7756i	1.75299	−	0.726113i	0.997478	−	0.0709807i	$-0.0226129\pi$
$264$	−0.550364	−	0.227968i	−0.0338725	−	0.0140305i
$265$	−9.54841	−	6.53265i	−0.586554	−	0.401298i
$266$	4.58903	−	6.86796i	0.281371	−	0.421102i
$267$	−12.6650	+	8.46248i	−0.775086	+	0.517896i
$268$	7.77166			0.474730
$269$	−13.2000	+	8.81994i	−0.804817	+	0.537761i	−0.888579	−	0.458724i	$-0.848307\pi$
$269$	−13.2000	+	8.81994i	−0.804817	+	0.537761i	0.0837617	+	0.996486i	$0.473307\pi$
$270$	−5.92891	−	14.7698i	−0.360822	−	0.898861i
$271$		−	19.7242i		−	1.19816i	−0.800690	−	0.599079i	$-0.795534\pi$
$271$		−	19.7242i		−	1.19816i	0.800690	−	0.599079i	$-0.204466\pi$
$272$	0.761002	−	4.05227i	0.0461425	−	0.245705i
$273$	29.6597	−	29.6597i	1.79509	−	1.79509i
$274$	16.1195	−	6.67691i	0.973814	−	0.403367i
$275$	−0.864314	+	0.550484i	−0.0521201	+	0.0331954i
$276$	1.61244	−	1.61244i	0.0970576	−	0.0970576i
$277$	7.52505	+	11.2620i	0.452136	+	0.676670i	0.985589	−	0.169160i	$-0.0541056\pi$
$277$	7.52505	+	11.2620i	0.452136	+	0.676670i	−0.533452	+	0.845830i	$0.679106\pi$
$278$	−1.95750	+	0.389372i	−0.117403	+	0.0233530i
$279$	9.29046	+	46.7063i	0.556205	+	2.79623i
$280$	8.91514	+	3.80785i	0.532781	+	0.227563i
$281$	6.96372	−	16.8119i	0.415421	−	1.00291i	−0.568237	−	0.822865i	$-0.692374\pi$
$281$	6.96372	−	16.8119i	0.415421	−	1.00291i	0.983658	−	0.180049i	$-0.0576258\pi$
$282$	19.0853	−	28.5632i	1.13651	−	1.70091i
$283$	−3.51053	−	17.6486i	−0.208679	−	1.04910i	−0.933065	−	0.359707i	$-0.882877\pi$
$283$	−3.51053	−	17.6486i	−0.208679	−	1.04910i	0.724386	−	0.689394i	$-0.242123\pi$
$284$	1.57540	+	0.313366i	0.0934827	+	0.0185949i
$285$	−0.135814	+	12.3824i	−0.00804492	+	0.733469i
$286$	0.378995	+	0.567206i	0.0224104	+	0.0335396i
$287$	−14.0063	−	5.80161i	−0.826768	−	0.342458i
$288$	−3.85282	−	3.85282i	−0.227029	−	0.227029i
$289$	15.8418	+	6.16757i	0.931868	+	0.362798i
$290$	−14.5967	+	14.2800i	−0.857150	+	0.838551i
$291$	−0.166997	−	0.403166i	−0.00978952	−	0.0236340i
$292$	0.799618	+	0.159054i	0.0467941	+	0.00930793i
$293$			16.4811i			0.962835i	0.876492	+	0.481417i	$0.159878\pi$
$293$			16.4811i			0.962835i	−0.876492	+	0.481417i	$0.840122\pi$
$294$	6.68900	−	33.6279i	0.390110	−	1.96122i
$295$	5.21503	−	7.62252i	0.303631	−	0.443800i
$296$	1.88413	−	0.374777i	0.109513	−	0.0217835i
$297$	−0.558226	−	1.34768i	−0.0323916	−	0.0782002i
$298$	−3.31484	−	8.00274i	−0.192024	−	0.463586i
$299$	−2.56114	+	0.509442i	−0.148114	+	0.0294618i
$300$	−14.3128	+	2.52198i	−0.826352	+	0.145607i
$301$	−5.76353	+	28.9752i	−0.332204	+	1.67010i
$302$			22.7118i			1.30692i
$303$	−43.2117	−	8.59534i	−2.48245	−	0.493789i
$304$	0.729105	+	1.76021i	0.0418170	+	0.100955i
$305$	0.0263414	−	2.40159i	0.00150831	−	0.137515i
$306$	18.5446	−	12.6806i	1.06013	−	0.724904i
$307$	−3.83948	−	3.83948i	−0.219130	−	0.219130i	0.589001	−	0.808132i	$-0.299521\pi$
$307$	−3.83948	−	3.83948i	−0.219130	−	0.219130i	−0.808132	+	0.589001i	$0.799521\pi$
$308$	0.820892	+	0.340025i	0.0467747	+	0.0193747i
$309$	4.70882	+	7.04725i	0.267876	+	0.400904i
$310$	19.5419	+	0.214342i	1.10991	+	0.0121738i
$311$	0.370233	+	0.0736439i	0.0209940	+	0.00417596i	0.205576	−	0.978641i	$-0.434093\pi$
$311$	0.370233	+	0.0736439i	0.0209940	+	0.00417596i	−0.184582	+	0.982817i	$0.559093\pi$
$312$	1.88750	+	9.48908i	0.106858	+	0.537214i
$313$	8.62342	−	12.9059i	0.487424	−	0.729482i	−0.503486	−	0.864003i	$-0.667950\pi$
$313$	8.62342	−	12.9059i	0.487424	−	0.729482i	0.990911	+	0.134521i	$0.0429496\pi$
$314$	1.64567	−	3.97299i	0.0928704	−	0.224209i
$315$	19.6774	+	49.0193i	1.10870	+	2.76193i
$316$	2.41778	+	12.1550i	0.136011	+	0.683771i
$317$	−22.8685	+	4.54883i	−1.28442	+	0.255488i	−0.789663	−	0.613541i	$-0.789745\pi$
$317$	−22.8685	+	4.54883i	−1.28442	+	0.255488i	−0.494761	+	0.869029i	$0.664745\pi$
$318$	−8.35516	−	12.5044i	−0.468534	−	0.701211i
$319$	−1.32342	+	1.32342i	−0.0740974	+	0.0740974i
$320$	−1.87274	+	1.22183i	−0.104689	+	0.0683022i
$321$	−1.57933	+	0.654179i	−0.0881495	+	0.0365127i
$322$	−2.40503	+	2.40503i	−0.134027	+	0.134027i
$323$	−7.68771	+	1.61500i	−0.427756	+	0.0898611i
$324$		−	4.34226i		−	0.241237i
$325$	15.2325	+	6.70463i	0.844948	+	0.371906i
$326$	−3.31976	+	2.21819i	−0.183865	+	0.122854i
$327$	10.3383			0.571708
$328$	2.90753	−	1.94275i	0.160542	−	0.107270i
$329$	−28.4666	+	42.6033i	−1.56941	+	2.34879i
$330$	−1.30922	+	0.245525i	−0.0720704	+	0.0135157i
$331$	−2.05592	−	0.851588i	−0.113003	−	0.0468075i	0.325465	−	0.945554i	$-0.394479\pi$
$331$	−2.05592	−	0.851588i	−0.113003	−	0.0468075i	−0.438469	+	0.898746i	$0.644479\pi$
$332$	0.650559	−	0.269470i	0.0357041	−	0.0147891i
$333$	8.70315	+	5.81526i	0.476930	+	0.318674i
$334$	10.3137	+	6.89138i	0.564340	+	0.377080i
$335$	14.5543	−	9.49563i	0.795185	−	0.518801i
$336$	8.91069	+	8.91069i	0.486118	+	0.486118i
$337$	4.78384	−	24.0500i	0.260592	−	1.31009i	−0.599676	−	0.800243i	$-0.704704\pi$
$337$	4.78384	−	24.0500i	0.260592	−	1.31009i	0.860268	−	0.509842i	$-0.170296\pi$
$338$	−0.735037	+	1.77454i	−0.0399808	+	0.0965221i
$339$	−9.59267			−0.521002
$340$	−3.52601	−	8.51864i	−0.191225	−	0.461988i
$341$	1.79121			0.0969997
$342$	−3.97268	+	9.59089i	−0.214818	+	0.518616i
$343$	−4.05635	+	20.3927i	−0.219022	+	1.10110i
$344$	−4.81844	−	4.81844i	−0.259793	−	0.259793i
$345$	1.04955	−	4.98980i	0.0565060	−	0.268642i
$346$	−11.4669	−	7.66192i	−0.616463	−	0.411907i
$347$	3.66998	+	2.45220i	0.197015	+	0.131641i	0.650165	−	0.759793i	$-0.274700\pi$
$347$	3.66998	+	2.45220i	0.197015	+	0.131641i	−0.453150	+	0.891434i	$0.649700\pi$
$348$	−24.5236	+	10.1580i	−1.31460	+	0.544527i
$349$	2.43735	+	1.00958i	0.130468	+	0.0540418i	0.446963	−	0.894553i	$-0.352506\pi$
$349$	2.43735	+	1.00958i	0.130468	+	0.0540418i	−0.316494	+	0.948594i	$0.602506\pi$
$350$	21.3482	−	3.76165i	1.14111	−	0.201068i
$351$	−13.1621	+	19.6985i	−0.702542	+	1.05143i
$352$	−0.170406	+	0.113862i	−0.00908269	+	0.00606886i
$353$	−7.64333			−0.406813			−0.203407	−	0.979094i	$-0.565201\pi$
$353$	−7.64333			−0.406813			−0.203407	+	0.979094i	$0.565201\pi$
$354$	9.98227	−	6.66994i	0.530552	−	0.354503i
$355$	3.33318	−	1.33801i	0.176907	−	0.0710143i
$356$			5.24039i			0.277740i
$357$	−42.8896	+	29.3275i	−2.26996	+	1.55217i
$358$	−13.1034	+	13.1034i	−0.692536	+	0.692536i
$359$	15.2351	−	6.31059i	0.804079	−	0.333060i	0.0574900	−	0.998346i	$-0.481690\pi$
$359$	15.2351	−	6.31059i	0.804079	−	0.333060i	0.746589	+	0.665286i	$0.231690\pi$
$360$	−11.9228	−	2.50783i	−0.628386	−	0.132174i
$361$	−10.8683	+	10.8683i	−0.572014	+	0.572014i
$362$	−11.0377	−	16.5190i	−0.580126	−	0.868220i
$363$	31.2392	−	6.21387i	1.63963	−	0.326143i
$364$	−2.81529	−	14.1534i	−0.147561	−	0.741839i
$365$	1.69181	−	0.679129i	0.0885534	−	0.0355472i
$366$	1.19474	−	2.88437i	0.0624503	−	0.150768i
$367$	−0.510232	+	0.763616i	−0.0266339	+	0.0398605i	−0.844548	−	0.535480i	$-0.820131\pi$
$367$	−0.510232	+	0.763616i	−0.0266339	+	0.0398605i	0.817914	+	0.575341i	$0.195131\pi$
$368$	−0.153052	−	0.769445i	−0.00797840	−	0.0401101i
$369$	18.6872	+	3.71712i	0.972819	+	0.193506i
$370$	3.07057	−	3.00394i	0.159631	−	0.156167i
$371$	12.4621	+	18.6508i	0.647000	+	0.968303i
$372$	23.4703	+	9.72172i	1.21688	+	0.504048i
$373$	20.4777	+	20.4777i	1.06030	+	1.06030i	0.998061	+	0.0622355i	$0.0198230\pi$
$373$	20.4777	+	20.4777i	1.06030	+	1.06030i	0.0622355	+	0.998061i	$0.480177\pi$
$374$	−0.331719	−	0.777181i	−0.0171528	−	0.0401871i
$375$	−23.7227	+	22.2108i	−1.22504	+	1.14696i
$376$	−4.52277	−	10.9189i	−0.233244	−	0.563101i
$377$	29.8128	+	5.93014i	1.53544	+	0.305418i
$378$			30.8576i			1.58715i
$379$	−1.18087	+	5.93665i	−0.0606573	+	0.304945i	−0.999190	−	0.0402460i	$-0.987186\pi$
$379$	−1.18087	+	5.93665i	−0.0606573	+	0.304945i	0.938532	+	0.345191i	$0.112186\pi$
$380$	3.51610	+	2.40558i	0.180372	+	0.123403i
$381$	14.7134	−	2.92668i	0.753790	−	0.149938i
$382$	2.65978	+	6.42127i	0.136086	+	0.328541i
$383$	11.1820	+	26.9957i	0.571374	+	1.37942i	0.900386	+	0.435092i	$0.143284\pi$
$383$	11.1820	+	26.9957i	0.571374	+	1.37942i	−0.329012	+	0.944326i	$0.606716\pi$
$384$	−2.85081	+	0.567062i	−0.145480	+	0.0289378i
$385$	1.95276	−	0.366212i	0.0995221	−	0.0186639i
$386$	−3.60610	+	18.1291i	−0.183546	+	0.922747i
$387$		−	37.1291i		−	1.88738i
$388$	−0.147247	−	0.0292893i	−0.00747535	−	0.00148694i
$389$	−10.1663	−	24.5436i	−0.515451	−	1.24441i	−0.940672	−	0.339318i	$-0.889804\pi$
$389$	−10.1663	−	24.5436i	−0.515451	−	1.24441i	0.425221	−	0.905090i	$-0.360196\pi$
$390$	15.1288	+	15.4644i	0.766076	+	0.783068i
$391$	3.23447	−	0.0346593i	0.163574	−	0.00175279i
$392$	−8.34095	−	8.34095i	−0.421282	−	0.421282i
$393$	−29.3197	−	12.1446i	−1.47898	−	0.612615i
$394$	−6.03705	−	9.03509i	−0.304142	−	0.455181i
$395$	19.3791	+	19.8090i	0.975070	+	0.996697i
$396$	−1.09523	−	0.217855i	−0.0550375	−	0.0109476i
$397$	−3.71505	−	18.6768i	−0.186453	−	0.937363i	−0.954782	−	0.297307i	$-0.903911\pi$
$397$	−3.71505	−	18.6768i	−0.186453	−	0.937363i	0.768329	−	0.640055i	$-0.221089\pi$
$398$	8.63197	−	12.9187i	0.432681	−	0.647554i
$399$	9.18790	−	22.1816i	0.459970	−	1.11047i
$400$	−2.01428	+	4.57632i	−0.100714	+	0.228816i
$401$	−1.47933	−	7.43709i	−0.0738742	−	0.371391i	0.926109	−	0.377257i	$-0.123133\pi$
$401$	−1.47933	−	7.43709i	−0.0738742	−	0.371391i	−0.999983	+	0.00586632i	$0.998133\pi$
$402$	22.1556	−	4.40702i	1.10502	−	0.219802i
$403$	−16.1623	−	24.1886i	−0.805100	−	1.20492i
$404$	−10.7181	+	10.7181i	−0.533245	+	0.533245i
$405$	−5.30549	−	8.13191i	−0.263632	−	0.404078i
$406$	36.5781	−	15.1511i	1.81534	−	0.751938i
$407$	0.278395	−	0.278395i	0.0137995	−	0.0137995i
$408$	−0.128413	−	11.9838i	−0.00635741	−	0.593287i
$409$		−	10.2044i		−	0.504575i	−0.967652	−	0.252287i	$-0.918817\pi$
$409$		−	10.2044i		−	0.504575i	0.967652	−	0.252287i	$-0.0811828\pi$
$410$	3.07133	−	7.19075i	0.151682	−	0.355126i
$411$	42.1674	−	28.1754i	2.07997	−	1.38979i
$412$	2.91594			0.143658
$413$	−14.8890	+	9.94852i	−0.732640	+	0.489535i
$414$	2.37485	−	3.55421i	0.116717	−	0.174680i
$415$	0.889079	−	1.29952i	0.0436432	−	0.0637908i
$416$	3.07518	+	1.27378i	0.150773	+	0.0624523i
$417$	−5.35968	+	2.22005i	−0.262465	+	0.108716i
$418$	0.324665	+	0.216934i	0.0158799	+	0.0106106i
$419$	−6.68327	−	4.46562i	−0.326499	−	0.218160i	0.381507	−	0.924366i	$-0.375405\pi$
$419$	−6.68327	−	4.46562i	−0.326499	−	0.218160i	−0.708006	+	0.706206i	$0.750405\pi$
$420$	27.5747	+	5.80005i	1.34551	+	0.283013i
$421$	8.14770	+	8.14770i	0.397094	+	0.397094i	0.877207	−	0.480113i	$-0.159404\pi$
$421$	8.14770	+	8.14770i	0.397094	+	0.397094i	−0.480113	+	0.877207i	$0.659404\pi$
$422$	−3.51487	+	17.6704i	−0.171101	+	0.860183i
$423$	24.6433	−	59.4941i	1.19820	−	2.89270i
$424$	−5.17393			−0.251268
$425$	−17.0116	−	11.6450i	−0.825184	−	0.564865i
$426$	4.66887			0.226207
$427$	−1.78201	+	4.30216i	−0.0862377	+	0.208196i
$428$	−0.114735	+	0.576814i	−0.00554595	+	0.0278814i
$429$	1.40209	+	1.40209i	0.0676933	+	0.0676933i
$430$	−14.9110	−	3.13637i	−0.719070	−	0.151249i
$431$	8.95105	+	5.98090i	0.431157	+	0.288090i	0.752150	−	0.658992i	$-0.229017\pi$
$431$	8.95105	+	5.98090i	0.431157	+	0.288090i	−0.320993	+	0.947081i	$0.604017\pi$
$432$	−5.91804	−	3.95431i	−0.284732	−	0.190252i
$433$	−25.9274	+	10.7395i	−1.24599	+	0.516107i	−0.905582	−	0.424170i	$-0.860566\pi$
$433$	−25.9274	+	10.7395i	−1.24599	+	0.516107i	−0.340410	+	0.940277i	$0.610566\pi$
$434$	−35.0070	−	14.5004i	−1.68039	−	0.696040i
$435$	−33.5149	+	48.9869i	−1.60692	+	2.34874i
$436$	1.97602	−	2.95733i	0.0946343	−	0.141630i
$437$	−1.24280	+	0.830411i	−0.0594511	+	0.0397239i
$438$	2.36976			0.113231
$439$	4.11795	−	2.75152i	0.196539	−	0.131323i	−0.453407	−	0.891304i	$-0.649792\pi$
$439$	4.11795	−	2.75152i	0.196539	−	0.131323i	0.649946	+	0.759981i	$0.274792\pi$
$440$	−0.180007	+	0.421440i	−0.00858147	+	0.0200914i
$441$		−	64.2723i		−	3.06058i
$442$	−7.50192	+	11.4921i	−0.356830	+	0.546624i
$443$	14.5879	−	14.5879i	0.693094	−	0.693094i	−0.269818	−	0.962911i	$-0.586963\pi$
$443$	14.5879	−	14.5879i	0.693094	−	0.693094i	0.962911	+	0.269818i	$0.0869634\pi$
$444$	5.15878	−	2.13684i	0.244825	−	0.101410i
$445$	6.40285	+	9.81387i	0.303524	+	0.465222i
$446$	−6.86488	+	6.86488i	−0.325061	+	0.325061i
$447$	−13.9881	−	20.9346i	−0.661612	−	0.990173i
$448$	4.25212	−	0.845799i	0.200894	−	0.0399602i
$449$	5.09616	+	25.6201i	0.240503	+	1.20909i	0.892564	+	0.450922i	$0.148905\pi$
$449$	5.09616	+	25.6201i	0.240503	+	1.20909i	−0.652061	+	0.758166i	$0.726095\pi$
$450$	−25.3924	+	9.87106i	−1.19701	+	0.465326i
$451$	0.274256	−	0.662114i	0.0129142	−	0.0311777i
$452$	−1.83351	+	2.74404i	−0.0862411	+	0.129069i
$453$	12.8790	+	64.7473i	0.605110	+	3.04209i
$454$	−0.519043	−	0.103244i	−0.0243599	−	0.00484548i
$455$	−22.5653	−	23.0658i	−1.05788	−	1.08134i
$456$	3.07669	+	4.60460i	0.144079	+	0.215630i
$457$	32.7813	+	13.5785i	1.53344	+	0.635173i	0.980229	−	0.197865i	$-0.0634007\pi$
$457$	32.7813	+	13.5785i	1.53344	+	0.635173i	0.553215	+	0.833038i	$0.313401\pi$
$458$	−20.6986	−	20.6986i	−0.967182	−	0.967182i
$459$	20.5275	−	20.9722i	0.958144	−	0.978900i
$460$	−1.22676	−	1.25396i	−0.0571978	−	0.0584664i
$461$	−6.81224	−	16.4462i	−0.317277	−	0.765976i	−0.999397	−	0.0347345i	$-0.988941\pi$
$461$	−6.81224	−	16.4462i	−0.317277	−	0.765976i	0.682119	−	0.731241i	$-0.261059\pi$
$462$	2.53303	+	0.503850i	0.117847	+	0.0234412i
$463$		−	33.8924i		−	1.57511i	−0.616242	−	0.787557i	$-0.711346\pi$
$463$		−	33.8924i		−	1.57511i	0.616242	−	0.787557i	$-0.288654\pi$
$464$	−1.78160	+	8.95670i	−0.0827087	+	0.415804i
$465$	55.8319	−	10.4704i	2.58914	−	0.485555i
$466$	−7.93687	+	1.57874i	−0.367668	+	0.0731338i
$467$	4.98700	+	12.0397i	0.230771	+	0.557130i	0.996268	−	0.0863086i	$-0.0275071\pi$
$467$	4.98700	+	12.0397i	0.230771	+	0.557130i	−0.765498	+	0.643439i	$0.777507\pi$
$468$	6.94046	+	16.7557i	0.320823	+	0.774535i
$469$	−33.0460	+	6.57326i	−1.52592	+	0.303525i
$470$	−21.8110	−	14.9222i	−1.00607	−	0.688312i
$471$	2.43856	−	12.2595i	0.112363	−	0.564886i
$472$		−	4.13036i		−	0.190115i
$473$	−1.36973	−	0.272456i	−0.0629802	−	0.0125275i
$474$	13.7853	+	33.2806i	0.633178	+	1.52863i
$475$	9.52392	+	0.208948i	0.436987	+	0.00958719i
$476$	0.191534	+	17.8744i	0.00877897	+	0.819271i
$477$	−19.9342	−	19.9342i	−0.912724	−	0.912724i
$478$	18.6009	+	7.70476i	0.850787	+	0.352407i
$479$	−0.00324632	−	0.00485846i	−0.000148328	−	0.000221989i	0.831395	−	0.555681i	$-0.187542\pi$
$479$	−0.00324632	−	0.00485846i	−0.000148328	−	0.000221989i	−0.831544	+	0.555459i	$0.812542\pi$
$480$	−4.64597	+	4.54516i	−0.212059	+	0.207457i
$481$	−6.27142	−	1.24746i	−0.285952	−	0.0568795i
$482$	1.78867	+	8.99226i	0.0814718	+	0.409586i
$483$	−5.49249	+	8.22009i	−0.249917	+	0.374027i
$484$	4.19344	−	10.1239i	0.190611	−	0.460176i
$485$	−0.311542	+	0.125060i	−0.0141464	+	0.00567866i
$486$	1.70337	+	8.56342i	0.0772664	+	0.388444i
$487$	−28.4214	+	5.65336i	−1.28790	+	0.256178i	−0.791099	−	0.611689i	$-0.790491\pi$
$487$	−28.4214	+	5.65336i	−1.28790	+	0.256178i	−0.496797	+	0.867867i	$0.665491\pi$
$488$	−0.596732	−	0.893072i	−0.0270128	−	0.0404275i
$489$	−8.20617	+	8.20617i	−0.371096	+	0.371096i
$490$	−25.8116	−	5.42920i	−1.16605	−	0.245266i
$491$	−28.8893	+	11.9663i	−1.30376	+	0.540034i	−0.923056	−	0.384665i	$-0.874317\pi$
$491$	−28.8893	+	11.9663i	−1.30376	+	0.540034i	−0.380700	+	0.924698i	$0.624317\pi$
$492$	7.18717	−	7.18717i	0.324023	−	0.324023i
$493$	−34.9392	−	14.0356i	−1.57358	−	0.632131i
$494$		−	6.34170i		−	0.285326i
$495$	−2.31726	+	0.930199i	−0.104153	+	0.0418093i
$496$	7.26699	−	4.85565i	0.326298	−	0.218025i
$497$	−6.96382			−0.312370
$498$	1.70182	−	1.13712i	0.0762602	−	0.0509555i
$499$	3.60412	−	5.39395i	0.161343	−	0.241466i	−0.741986	−	0.670415i	$-0.766116\pi$
$499$	3.60412	−	5.39395i	0.161343	−	0.241466i	0.903329	+	0.428949i	$0.141116\pi$
$500$	1.81926	+	11.0313i	0.0813596	+	0.493336i
$501$	33.3102	+	13.7976i	1.48819	+	0.616429i
$502$	8.00255	−	3.31477i	0.357171	−	0.147945i
$503$	21.7947	+	14.5628i	0.971779	+	0.649322i	0.936726	−	0.350063i	$-0.113840\pi$
$503$	21.7947	+	14.5628i	0.971779	+	0.649322i	0.0350533	+	0.999385i	$0.488840\pi$
$504$	19.6413	+	13.1239i	0.874895	+	0.584586i
$505$	−6.97650	+	33.1678i	−0.310450	+	1.47595i
$506$	−0.113692	−	0.113692i	−0.00505421	−	0.00505421i
$507$	−1.08918	+	5.47569i	−0.0483723	+	0.243184i
$508$	1.97507	−	4.76825i	0.0876298	−	0.211557i
$509$	37.2931			1.65299			0.826495	−	0.562944i	$-0.190331\pi$
$509$	37.2931			1.65299			0.826495	+	0.562944i	$0.190331\pi$
$510$	−14.8826	−	22.2856i	−0.659013	−	0.986823i
$511$	−3.53460			−0.156361
$512$	−0.382683	+	0.923880i	−0.0169124	+	0.0408301i
$513$	−2.64556	+	13.3001i	−0.116804	+	0.587215i
$514$	2.81076	+	2.81076i	0.123977	+	0.123977i
$515$	5.46078	−	3.56277i	0.240631	−	0.156994i
$516$	−16.4688	−	11.0041i	−0.725000	−	0.484429i
$517$	−2.01396	−	1.34569i	−0.0885739	−	0.0591832i
$518$	−7.69456	+	3.18719i	−0.338079	+	0.140037i
$519$	−37.0347	−	15.3403i	−1.62564	−	0.673364i
$520$	7.31534	−	1.37188i	0.320799	−	0.0601610i
$521$	−3.95806	+	5.92366i	−0.173406	+	0.259520i	−0.907985	−	0.419003i	$-0.862380\pi$
$521$	−3.95806	+	5.92366i	−0.173406	+	0.259520i	0.734579	+	0.678523i	$0.237380\pi$
$522$	−41.3727	+	27.6444i	−1.81083	+	1.20996i
$523$	−25.1852			−1.10127			−0.550637	−	0.834745i	$-0.685615\pi$
$523$	−25.1852			−1.10127			−0.550637	+	0.834745i	$0.685615\pi$
$524$	−9.07811	+	6.06580i	−0.396579	+	0.264986i
$525$	58.7268	−	22.8295i	2.56305	−	0.996363i
$526$		−	30.7711i		−	1.34168i
$527$	14.1462	+	33.1430i	0.616218	+	1.44373i
$528$	−0.421230	+	0.421230i	−0.0183317	+	0.0183317i
$529$	−20.6806	+	8.56619i	−0.899157	+	0.372443i
$530$	−9.68940	+	6.32165i	−0.420881	+	0.274595i
$531$	15.9135	−	15.9135i	0.690588	−	0.690588i
$532$	−4.58903	−	6.86796i	−0.198960	−	0.297764i
$533$	−11.4158	+	2.27075i	−0.494474	+	0.0983570i
$534$	2.97163	+	14.9394i	0.128595	+	0.646491i
$535$	0.489898	+	1.22041i	0.0211801	+	0.0527628i
$536$	2.97409	−	7.18008i	0.128461	−	0.310132i
$537$	−29.9249	+	44.7858i	−1.29136	+	1.93265i
$538$	3.09715	+	15.5704i	0.133528	+	0.671289i
$539$	−2.37107	−	0.471634i	−0.102129	−	0.0203147i
$540$	−15.9144	−	0.174554i	−0.684847	−	0.00751162i
$541$	3.83883	+	5.74521i	0.165044	+	0.247006i	0.904768	−	0.425904i	$-0.140044\pi$
$541$	3.83883	+	5.74521i	0.165044	+	0.247006i	−0.739724	+	0.672910i	$0.765044\pi$
$542$	−18.2228	−	7.54811i	−0.782734	−	0.324219i
$543$	−40.8336	−	40.8336i	−1.75234	−	1.75234i
$544$	−3.45258	−	2.25381i	−0.148028	−	0.0966313i
$545$	0.0872272	−	7.95265i	0.00373640	−	0.340654i
$546$	−16.0517	−	38.7523i	−0.686950	−	1.65844i
$547$	−29.6203	−	5.89185i	−1.26647	−	0.251917i	−0.484258	−	0.874925i	$-0.660910\pi$
$547$	−29.6203	−	5.89185i	−1.26647	−	0.251917i	−0.782215	+	0.623008i	$0.785910\pi$
$548$		−	17.4476i		−	0.745325i
$549$	1.14175	−	5.73994i	0.0487285	−	0.244975i
$550$	0.177822	+	1.00918i	0.00758236	+	0.0430317i
$551$	17.0647	−	3.39438i	0.726980	−	0.144605i
$552$	−0.872647	−	2.10676i	−0.0371423	−	0.0896695i
$553$	−20.5613	−	49.6395i	−0.874357	−	2.11089i
$554$	13.2845	−	2.64245i	0.564403	−	0.112267i
$555$	7.05019	−	10.3049i	0.299264	−	0.437418i
$556$	−0.389372	+	1.95750i	−0.0165130	+	0.0830166i
$557$		−	8.16499i		−	0.345962i	−0.984925	−	0.172981i	$-0.944660\pi$
$557$		−	8.16499i		−	0.345962i	0.984925	−	0.172981i	$-0.0553399\pi$
$558$	46.7063	+	9.29046i	1.97724	+	0.393297i
$559$	8.67993	+	20.9552i	0.367122	+	0.886311i
$560$	6.92967	−	6.77931i	0.292832	−	0.286478i
$561$	−1.38638	−	2.02749i	−0.0585330	−	0.0856009i
$562$	−12.8673	−	12.8673i	−0.542773	−	0.542773i
$563$	−0.665621	−	0.275709i	−0.0280526	−	0.0116198i	0.368613	−	0.929583i	$-0.379833\pi$
$563$	−0.665621	−	0.275709i	−0.0280526	−	0.0116198i	−0.396666	+	0.917963i	$0.629833\pi$
$564$	−19.0853	−	28.5632i	−0.803637	−	1.20273i
$565$	−0.0809363	+	7.37910i	−0.00340502	+	0.310441i
$566$	−17.6486	−	3.51053i	−0.741827	−	0.147559i
$567$	3.67268	+	18.4638i	0.154238	+	0.775407i
$568$	0.892391	−	1.33556i	0.0374439	−	0.0560388i
$569$	11.0704	−	26.7264i	0.464097	−	1.12043i	−0.502604	−	0.864517i	$-0.667624\pi$
$569$	11.0704	−	26.7264i	0.464097	−	1.12043i	0.966700	−	0.255911i	$-0.0823756\pi$
$570$	11.3879	+	4.86401i	0.476985	+	0.203731i
$571$	5.99542	+	30.1410i	0.250901	+	1.26136i	0.876570	+	0.481274i	$0.159826\pi$
$571$	5.99542	+	30.1410i	0.250901	+	1.26136i	−0.625670	+	0.780088i	$0.715174\pi$
$572$	0.669065	−	0.133085i	0.0279750	−	0.00556458i
$573$	11.2238	+	16.7976i	0.468881	+	0.701729i
$574$	−10.7200	+	10.7200i	−0.447444	+	0.447444i
$575$	−3.82952	−	0.849462i	−0.159702	−	0.0354250i
$576$	−5.03395	+	2.08513i	−0.209748	+	0.0868804i
$577$	14.2185	−	14.2185i	0.591924	−	0.591924i	−0.346227	−	0.938151i	$-0.612537\pi$
$577$	14.2185	−	14.2185i	0.591924	−	0.591924i	0.938151	+	0.346227i	$0.112537\pi$
$578$	11.7605	−	12.2756i	0.489171	−	0.510600i
$579$			53.7276i			2.23284i
$580$	7.60708	+	18.9503i	0.315867	+	0.786870i
$581$	−2.53834	+	1.69606i	−0.105308	+	0.0703645i
$582$	−0.436383			−0.0180887
$583$	−0.881670	+	0.589113i	−0.0365151	+	0.0243986i
$584$	0.452947	−	0.677883i	0.0187431	−	0.0280510i
$585$	33.4703	+	22.8991i	1.38383	+	0.946759i
$586$	15.2265	+	6.30703i	0.629002	+	0.260541i
$587$	11.2438	−	4.65734i	0.464082	−	0.192229i	−0.138376	−	0.990380i	$-0.544188\pi$
$587$	11.2438	−	4.65734i	0.464082	−	0.192229i	0.602458	+	0.798151i	$0.294188\pi$
$588$	−28.5083	−	19.0487i	−1.17566	−	0.785554i
$589$	−13.8454	−	9.25119i	−0.570489	−	0.381189i
$590$	−5.04659	−	7.73508i	−0.207765	−	0.318448i
$591$	−22.3340	−	22.3340i	−0.918697	−	0.918697i
$592$	0.374777	−	1.88413i	0.0154032	−	0.0774373i
$593$	3.31399	−	8.00069i	0.136089	−	0.328549i	−0.841113	−	0.540860i	$-0.818099\pi$
$593$	3.31399	−	8.00069i	0.136089	−	0.328549i	0.977202	+	0.212311i	$0.0680989\pi$
$594$	−1.45872			−0.0598518
$595$	22.1981	+	33.2400i	0.910033	+	1.36271i
$596$	−8.66210			−0.354814
$597$	17.2825	−	41.7235i	0.707324	−	1.70763i
$598$	−0.509442	+	2.56114i	−0.0208326	+	0.104733i
$599$	10.9709	+	10.9709i	0.448260	+	0.448260i	0.894776	−	0.446516i	$-0.147335\pi$
$599$	10.9709	+	10.9709i	0.448260	+	0.448260i	−0.446516	+	0.894776i	$0.647335\pi$
$600$	−3.14728	+	14.1885i	−0.128487	+	0.579241i
$601$	11.5196	+	7.69712i	0.469893	+	0.313972i	0.767876	−	0.640599i	$-0.221314\pi$
$601$	11.5196	+	7.69712i	0.469893	+	0.313972i	−0.297983	+	0.954571i	$0.596314\pi$
$602$	24.5640	+	16.4131i	1.00115	+	0.668950i
$603$	39.1221	−	16.2049i	1.59318	−	0.659915i
$604$	20.9830	+	8.69145i	0.853786	+	0.353650i
$605$	−4.51640	−	24.0830i	−0.183618	−	0.979113i
$606$	−24.4774	+	36.6331i	−0.994328	+	1.48812i
$607$	23.3412	−	15.5961i	0.947388	−	0.633025i	0.0170998	−	0.999854i	$-0.494557\pi$
$607$	23.3412	−	15.5961i	0.947388	−	0.633025i	0.930288	+	0.366829i	$0.119557\pi$
$608$	1.90524			0.0772678
$609$	95.6857	−	63.9351i	3.87738	−	2.59078i
$610$	−2.20870	−	0.943386i	−0.0894277	−	0.0381966i
$611$			39.3387i			1.59148i
$612$	−4.61866	−	21.9857i	−0.186698	−	0.888719i
$613$	13.6504	−	13.6504i	0.551333	−	0.551333i	−0.375492	−	0.926826i	$-0.622526\pi$
$613$	13.6504	−	13.6504i	0.551333	−	0.551333i	0.926826	+	0.375492i	$0.122526\pi$
$614$	−5.01652	+	2.07791i	−0.202450	+	0.0838576i
$615$	4.67819	−	22.2411i	0.188643	−	0.896850i
$616$	0.628283	−	0.628283i	0.0253143	−	0.0253143i
$617$	2.86892	+	4.29364i	0.115498	+	0.172856i	0.884715	−	0.466133i	$-0.154353\pi$
$617$	2.86892	+	4.29364i	0.115498	+	0.172856i	−0.769216	+	0.638988i	$0.779353\pi$
$618$	8.31280	−	1.65352i	0.334390	−	0.0665143i
$619$	−2.42896	−	12.2112i	−0.0976280	−	0.490809i	−0.998401	−	0.0565198i	$-0.982000\pi$
$619$	−2.42896	−	12.2112i	−0.0976280	−	0.490809i	0.900774	−	0.434289i	$-0.143000\pi$
$620$	7.67639	−	17.9724i	0.308291	−	0.721787i
$621$	2.13685	−	5.15882i	0.0857490	−	0.207016i
$622$	0.209720	−	0.313868i	0.00840900	−	0.0125850i
$623$	−4.43232	−	22.2828i	−0.177577	−	0.892740i
$624$	9.48908	+	1.88750i	0.379867	+	0.0755603i
$625$	16.8854	+	18.4360i	0.675415	+	0.737438i
$626$	−8.62342	−	12.9059i	−0.344661	−	0.515822i
$627$	1.04858	+	0.434334i	0.0418761	+	0.0173456i
$628$	−3.04080	−	3.04080i	−0.121341	−	0.121341i
$629$	7.34979	+	2.95252i	0.293055	+	0.117725i
$630$	52.8182	+	0.579327i	2.10433	+	0.0230809i
$631$	6.61850	+	15.9785i	0.263478	+	0.636093i	0.999149	−	0.0412464i	$-0.0131329\pi$
$631$	6.61850	+	15.9785i	0.263478	+	0.636093i	−0.735671	+	0.677339i	$0.763133\pi$
$632$	12.1550	+	2.41778i	0.483499	+	0.0961740i
$633$			52.3683i			2.08145i
$634$	−4.54883	+	22.8685i	−0.180657	+	0.908225i
$635$	−2.12718	−	11.3429i	−0.0844148	−	0.450128i
$636$	−14.7499	+	2.93394i	−0.584872	+	0.116338i
$637$	15.0254	+	36.2745i	0.595327	+	1.43725i
$638$	0.716231	+	1.72913i	0.0283559	+	0.0684571i
$639$	8.58388	−	1.70744i	0.339573	−	0.0675452i
$640$	0.412156	+	2.19776i	0.0162919	+	0.0868739i
$641$	−3.24162	+	16.2967i	−0.128036	+	0.643683i	0.862458	+	0.506129i	$0.168924\pi$
$641$	−3.24162	+	16.2967i	−0.128036	+	0.643683i	−0.990494	+	0.137554i	$0.956076\pi$
$642$			1.70945i			0.0674667i
$643$	28.6070	+	5.69028i	1.12815	+	0.224403i	0.723671	−	0.690145i	$-0.242453\pi$
$643$	28.6070	+	5.69028i	1.12815	+	0.224403i	0.404478	+	0.914548i	$0.367453\pi$
$644$	1.30159	+	3.14232i	0.0512899	+	0.123825i
$645$	−44.2869	−	0.485753i	−1.74380	−	0.0191265i
$646$	−1.44989	+	7.72055i	−0.0570453	+	0.303761i
$647$	−24.7423	−	24.7423i	−0.972719	−	0.972719i	0.0269187	−	0.999638i	$-0.491430\pi$
$647$	−24.7423	−	24.7423i	−0.972719	−	0.972719i	−0.999638	+	0.0269187i	$0.991430\pi$
$648$	−4.01173	−	1.66171i	−0.157596	−	0.0652782i
$649$	−0.470291	−	0.703840i	−0.0184605	−	0.0276281i
$650$	12.0235	−	11.5073i	0.471600	−	0.451352i
$651$	−108.021	−	21.4867i	−4.23368	−	0.842132i
$652$	0.778926	+	3.91593i	0.0305051	+	0.153360i
$653$	−1.37339	+	2.05543i	−0.0537451	+	0.0804352i	−0.857369	−	0.514702i	$-0.827902\pi$
$653$	−1.37339	+	2.05543i	−0.0537451	+	0.0804352i	0.803624	+	0.595138i	$0.202902\pi$
$654$	3.95629	−	9.55132i	0.154703	−	0.373486i
$655$	−9.58954	+	22.4515i	−0.374694	+	0.877253i
$656$	−0.682203	−	3.42967i	−0.0266355	−	0.133906i
$657$	4.35688	−	0.866638i	0.169978	−	0.0338108i
$658$	28.4666	+	42.6033i	1.10974	+	1.66085i
$659$	−6.38040	+	6.38040i	−0.248545	+	0.248545i	−0.820373	−	0.571828i	$-0.806234\pi$
$659$	−6.38040	+	6.38040i	−0.248545	+	0.248545i	0.571828	+	0.820373i	$0.306234\pi$
$660$	−0.274182	+	1.30352i	−0.0106725	+	0.0507395i
$661$	−36.7694	+	15.2304i	−1.43016	+	0.592394i	−0.957392	−	0.288791i	$-0.906747\pi$
$661$	−36.7694	+	15.2304i	−1.43016	+	0.592394i	−0.472772	+	0.881185i	$0.656747\pi$
$662$	−1.57353	+	1.57353i	−0.0611570	+	0.0611570i
$663$	−14.8698	+	37.0159i	−0.577497	+	1.43758i
$664$		−	0.704160i		−	0.0273267i
$665$	−16.9855	−	7.25489i	−0.658669	−	0.281332i
$666$	8.70315	−	5.81526i	0.337240	−	0.225337i
$667$	−7.16437			−0.277406
$668$	10.3137	−	6.89138i	0.399048	−	0.266636i
$669$	−15.6777	+	23.4633i	−0.606134	+	0.907144i
$670$	−3.20314	−	17.0802i	−0.123748	−	0.659866i
$671$	−0.203374	−	0.0842402i	−0.00785116	−	0.00325206i
$672$	11.6424	−	4.82243i	0.449115	−	0.186029i
$673$	24.5399	+	16.3970i	0.945944	+	0.632059i	0.929900	−	0.367812i	$-0.119893\pi$
$673$	24.5399	+	16.3970i	0.945944	+	0.632059i	0.0160435	+	0.999871i	$0.494893\pi$
$674$	−20.3886	−	13.6232i	−0.785339	−	0.524747i
$675$	−30.0167	+	19.1177i	−1.15534	+	0.735842i
$676$	1.35817	+	1.35817i	0.0522374	+	0.0522374i
$677$	−3.91750	+	19.6946i	−0.150562	+	0.756925i	0.829543	+	0.558443i	$0.188601\pi$
$677$	−3.91750	+	19.6946i	−0.150562	+	0.756925i	−0.980105	+	0.198482i	$0.936399\pi$
$678$	−3.67095	+	8.86247i	−0.140982	+	0.340361i
$679$	0.650886			0.0249787
$680$	−9.21954	−	0.00232981i	−0.353553	−	8.93441e-5i
$681$	−1.53824			−0.0589455
$682$	0.685468	−	1.65487i	0.0262479	−	0.0633681i
$683$	3.32933	−	16.7376i	0.127393	−	0.640448i	−0.863340	−	0.504623i	$-0.831631\pi$
$683$	3.32933	−	16.7376i	0.127393	−	0.640448i	0.990733	−	0.135825i	$-0.0433685\pi$
$684$	7.34055	+	7.34055i	0.280673	+	0.280673i
$685$	−21.3180	−	32.6748i	−0.814517	−	1.24844i
$686$	17.2881	+	11.5515i	0.660061	+	0.441039i
$687$	−70.7453	−	47.2705i	−2.69910	−	1.80348i
$688$	−6.29559	+	2.60772i	−0.240017	+	0.0994184i
$689$	15.9108	+	6.59046i	0.606152	+	0.251076i
$690$	−4.20833	−	2.87917i	−0.160208	−	0.109608i
$691$	6.72848	−	10.0699i	0.255963	−	0.383076i	−0.681126	−	0.732166i	$-0.738509\pi$
$691$	6.72848	−	10.0699i	0.255963	−	0.383076i	0.937089	+	0.349090i	$0.113509\pi$
$692$	−11.4669	+	7.66192i	−0.435905	+	0.291262i
$693$	4.84132			0.183907
$694$	3.66998	−	2.45220i	0.139311	−	0.0930843i
$695$	1.66254	+	4.14163i	0.0630637	+	0.157101i
$696$			26.5442i			1.00615i
$697$	14.4171	−	0.154488i	0.546086	−	0.00585163i
$698$	1.86547	−	1.86547i	0.0706090	−	0.0706090i
$699$	−21.7313	+	9.00140i	−0.821953	+	0.340464i
$700$	4.69431	−	21.1627i	0.177428	−	0.799875i
$701$	14.2960	−	14.2960i	0.539954	−	0.539954i	−0.383561	−	0.923515i	$-0.625303\pi$
$701$	14.2960	−	14.2960i	0.539954	−	0.539954i	0.923515	+	0.383561i	$0.125303\pi$
$702$	13.1621	+	19.6985i	0.496772	+	0.743472i
$703$	−3.58972	+	0.714041i	−0.135389	+	0.0269305i
$704$	0.0399830	+	0.201008i	0.00150691	+	0.00757577i
$705$	−70.6410	−	30.1724i	−2.66049	−	1.13636i
$706$	−2.92498	+	7.06152i	−0.110083	+	0.265764i
$707$	36.5092	−	54.6399i	1.37307	−	2.05494i
$708$	−2.34217	−	11.7749i	−0.0880242	−	0.442528i
$709$	−23.2275	−	4.62024i	−0.872327	−	0.173517i	−0.261426	−	0.965224i	$-0.584193\pi$
$709$	−23.2275	−	4.62024i	−0.872327	−	0.173517i	−0.610901	+	0.791707i	$0.709193\pi$
$710$	0.0393927	−	3.59149i	0.00147838	−	0.134786i
$711$	37.5157	+	56.1462i	1.40695	+	2.10565i
$712$	4.84149	+	2.00541i	0.181443	+	0.0751560i
$713$	4.84839	+	4.84839i	0.181574	+	0.181574i
$714$	10.6819	+	50.8479i	0.399761	+	1.90294i
$715$	1.09038	−	1.06672i	0.0407777	−	0.0398929i
$716$	7.09151	+	17.1204i	0.265022	+	0.639820i
$717$	57.3969	+	11.4169i	2.14353	+	0.426374i
$718$		−	16.4904i		−	0.615415i
$719$	−4.20295	+	21.1297i	−0.156744	+	0.788003i	0.819794	+	0.572658i	$0.194088\pi$
$719$	−4.20295	+	21.1297i	−0.156744	+	0.788003i	−0.976538	+	0.215345i	$0.930912\pi$
$720$	−6.87959	+	10.0555i	−0.256387	+	0.374747i
$721$	−12.3989	+	2.46630i	−0.461760	+	0.0918497i
$722$	5.88186	+	14.2001i	0.218900	+	0.528472i
$723$	10.1983	+	24.6210i	0.379281	+	0.915664i
$724$	−19.4855	+	3.87591i	−0.724173	+	0.144047i
$725$	37.4001	+	26.1945i	1.38900	+	0.972838i
$726$	6.21387	−	31.2392i	0.230618	−	1.15940i
$727$			16.4509i			0.610131i	0.952331	+	0.305065i	$0.0986783\pi$
$727$			16.4509i			0.610131i	−0.952331	+	0.305065i	$0.901322\pi$
$728$	−14.1534	−	2.81529i	−0.524560	−	0.104341i
$729$	14.6971	+	35.4820i	0.544338	+	1.31415i
$730$	0.0199944	−	1.82292i	0.000740025	−	0.0674693i
$731$	−5.77622	−	27.4959i	−0.213641	−	1.01697i
$732$	−2.20760	−	2.20760i	−0.0815952	−	0.0815952i
$733$	36.0246	+	14.9219i	1.33060	+	0.551152i	0.930826	−	0.365462i	$-0.119089\pi$
$733$	36.0246	+	14.9219i	1.33060	+	0.551152i	0.399773	+	0.916614i	$0.369089\pi$
$734$	0.510232	+	0.763616i	0.0188330	+	0.0281856i
$735$	−76.6628	−	0.840862i	−2.82775	−	0.0310156i
$736$	−0.769445	−	0.153052i	−0.0283621	−	0.00564158i
$737$	−0.310734	−	1.56217i	−0.0114460	−	0.0575431i
$738$	10.5855	−	15.8423i	0.389656	−	0.583162i
$739$	−12.2812	+	29.6494i	−0.451771	+	1.09067i	0.519877	+	0.854241i	$0.325978\pi$
$739$	−12.2812	+	29.6494i	−0.451771	+	1.09067i	−0.971648	+	0.236431i	$0.924022\pi$
$740$	−1.60022	−	3.98639i	−0.0588254	−	0.146543i
$741$	−3.59614	−	18.0790i	−0.132107	−	0.664149i
$742$	22.0002	−	4.37610i	0.807651	−	0.160652i
$743$	28.4498	+	42.5782i	1.04372	+	1.56204i	0.807078	+	0.590445i	$0.201048\pi$
$743$	28.4498	+	42.5782i	1.04372	+	1.56204i	0.236645	+	0.971596i	$0.423952\pi$
$744$	17.9634	−	17.9634i	0.658570	−	0.658570i
$745$	−16.2218	+	10.5836i	−0.594322	+	0.387753i
$746$	26.7555	−	11.0825i	0.979587	−	0.405758i
$747$	2.71300	−	2.71300i	0.0992634	−	0.0992634i
$748$	−0.844965	+	0.00905430i	−0.0308950	+	0.000331058i
$749$		−	2.54972i		−	0.0931649i
$750$	11.4418	+	30.4167i	0.417796	+	1.11066i
$751$	22.9913	−	15.3623i	0.838965	−	0.560578i	−0.0602011	−	0.998186i	$-0.519174\pi$
$751$	22.9913	−	15.3623i	0.838965	−	0.560578i	0.899166	+	0.437608i	$0.144174\pi$
$752$	−11.8186			−0.430979
$753$	20.9341	−	13.9877i	0.762882	−	0.509741i
$754$	16.8876	−	25.2741i	0.615011	−	0.920429i
$755$	49.9151	−	9.36082i	1.81660	−	0.340675i
$756$	28.5087	+	11.8087i	1.03685	+	0.429479i
$757$	28.7956	−	11.9275i	1.04659	−	0.433513i	0.207919	−	0.978146i	$-0.433331\pi$
$757$	28.7956	−	11.9275i	1.04659	−	0.433513i	0.838675	+	0.544633i	$0.183331\pi$
$758$	5.03285	+	3.36284i	0.182801	+	0.122144i
$759$	−0.388584	−	0.259643i	−0.0141047	−	0.00942446i
$760$	3.56802	−	2.32788i	0.129426	−	0.0844409i
$761$	−27.3997	−	27.3997i	−0.993237	−	0.993237i	0.00674063	−	0.999977i	$-0.497854\pi$
$761$	−27.3997	−	27.3997i	−0.993237	−	0.993237i	−0.999977	+	0.00674063i	$0.997854\pi$
$762$	2.92668	−	14.7134i	0.106022	−	0.533010i
$763$	−5.90098	+	14.2462i	−0.213630	+	0.515748i
$764$	6.95033			0.251454
$765$	−35.5122	−	35.5302i	−1.28395	−	1.28460i
$766$	29.2200			1.05576
$767$	−5.26118	+	12.7016i	−0.189970	+	0.458629i
$768$	−0.567062	+	2.85081i	−0.0204621	+	0.102870i
$769$	−16.7358	−	16.7358i	−0.603507	−	0.603507i	0.337735	−	0.941241i	$-0.390339\pi$
$769$	−16.7358	−	16.7358i	−0.603507	−	0.603507i	−0.941241	+	0.337735i	$0.890339\pi$
$770$	0.408955	−	1.94426i	0.0147377	−	0.0700664i
$771$	9.60684	+	6.41909i	0.345982	+	0.231178i
$772$	15.3691	+	10.2693i	0.553146	+	0.369601i
$773$	3.33513	−	1.38145i	0.119956	−	0.0496875i	−0.321898	−	0.946774i	$-0.604321\pi$
$773$	3.33513	−	1.38145i	0.119956	−	0.0496875i	0.441854	+	0.897087i	$0.354321\pi$
$774$	−34.3028	−	14.2087i	−1.23299	−	0.510721i
$775$	−7.58324	−	43.0367i	−0.272398	−	1.54592i
$776$	−0.0834089	+	0.124830i	−0.00299420	+	0.00448114i
$777$	−20.1284	+	13.4494i	−0.722103	+	0.482494i
$778$	−26.5658			−0.952429
$779$	−5.53955	+	3.70141i	−0.198475	+	0.132617i
$780$	20.0767	−	8.05923i	0.718863	−	0.288567i
$781$		−	0.329197i		−	0.0117796i
$782$	1.20576	−	3.00153i	0.0431178	−	0.107334i
$783$	−45.9611	+	45.9611i	−1.64252	+	1.64252i
$784$	−10.8980	+	4.51409i	−0.389213	+	0.161217i
$785$	−9.40993	−	1.97928i	−0.335855	−	0.0706436i
$786$	−22.4403	+	22.4403i	−0.800419	+	0.800419i
$787$	24.8711	+	37.2222i	0.886557	+	1.32683i	0.944502	+	0.328507i	$0.106545\pi$
$787$	24.8711	+	37.2222i	0.886557	+	1.32683i	−0.0579442	+	0.998320i	$0.518455\pi$
$788$	−10.6576	+	2.11993i	−0.379662	+	0.0755194i
$789$	−17.4491	−	87.7226i	−0.621205	−	3.12301i
$790$	25.7172	−	10.3234i	0.914976	−	0.367291i
$791$	5.47539	−	13.2188i	0.194683	−	0.470005i
$792$	−0.620400	+	0.928493i	−0.0220449	+	0.0329926i
$793$	0.697479	+	3.50646i	0.0247682	+	0.124518i
$794$	−18.6768	−	3.71505i	−0.662816	−	0.131842i
$795$	−24.0379	+	23.5163i	−0.852537	+	0.834039i
$796$	−8.63197	−	12.9187i	−0.305952	−	0.457890i
$797$	−15.2682	−	6.32428i	−0.540826	−	0.224017i	0.0955114	−	0.995428i	$-0.469551\pi$
$797$	−15.2682	−	6.32428i	−0.540826	−	0.224017i	−0.636337	+	0.771411i	$0.719551\pi$
$798$	−16.9770	−	16.9770i	−0.600980	−	0.600980i
$799$	8.99396	−	47.8920i	0.318183	−	1.69430i
$800$	3.45713	+	3.61223i	0.122228	+	0.127712i
$801$	10.9269	+	26.3799i	0.386083	+	0.932086i
$802$	−7.43709	−	1.47933i	−0.262613	−	0.0522370i
$803$		−	0.167089i		−	0.00589644i
$804$	4.40702	−	22.1556i	0.155424	−	0.781367i
$805$	6.27691	+	4.29442i	0.221232	+	0.151358i
$806$	−28.5324	+	5.67544i	−1.00501	+	0.199909i
$807$	17.6588	+	42.6321i	0.621620	+	1.50072i
$808$	5.80059	+	14.0039i	0.204064	+	0.492654i
$809$	13.8880	−	2.76250i	0.488276	−	0.0971242i	0.0551885	−	0.998476i	$-0.482424\pi$
$809$	13.8880	−	2.76250i	0.488276	−	0.0971242i	0.433088	+	0.901352i	$0.357424\pi$
$810$	−9.54323	+	1.78969i	−0.335315	+	0.0628833i
$811$	2.59779	−	13.0600i	0.0912209	−	0.458598i	−0.907994	−	0.418983i	$-0.862387\pi$
$811$	2.59779	−	13.0600i	0.0912209	−	0.458598i	0.999215	−	0.0396154i	$-0.0126133\pi$
$812$		−	39.5918i		−	1.38940i
$813$	−56.2299	−	11.1848i	−1.97207	−	0.392269i
$814$	−0.150666	−	0.363740i	−0.00528085	−	0.0127491i
$815$	6.24331	+	6.38178i	0.218694	+	0.223544i
$816$	−11.1207	−	4.46736i	−0.389303	−	0.156389i
$817$	9.18029	+	9.18029i	0.321178	+	0.321178i
$818$	−9.42763	−	3.90505i	−0.329629	−	0.136537i
$819$	−43.6836	−	65.3772i	−1.52643	−	2.28446i
$820$	−5.46804	−	5.58932i	−0.190952	−	0.195188i
$821$	34.1291	+	6.78870i	1.19111	+	0.236927i	0.750562	−	0.660800i	$-0.229783\pi$
$821$	34.1291	+	6.78870i	1.19111	+	0.236927i	0.440552	+	0.897727i	$0.354783\pi$
$822$	−9.89388	−	49.7399i	−0.345089	−	1.73488i
$823$	−11.5439	+	17.2766i	−0.402394	+	0.602226i	−0.976228	−	0.216746i	$-0.930456\pi$
$823$	−11.5439	+	17.2766i	−0.402394	+	0.602226i	0.573834	+	0.818972i	$0.305456\pi$
$824$	1.11588	−	2.69398i	0.0388736	−	0.0938491i
$825$	1.07921	+	2.77616i	0.0375732	+	0.0966534i
$826$	3.49346	+	17.5628i	0.121553	+	0.611087i
$827$	−16.5320	+	3.28843i	−0.574875	+	0.114350i	−0.473962	−	0.880545i	$-0.657177\pi$
$827$	−16.5320	+	3.28843i	−0.574875	+	0.114350i	−0.100914	+	0.994895i	$0.532177\pi$
$828$	−2.37485	−	3.55421i	−0.0825317	−	0.123517i
$829$	6.04684	−	6.04684i	0.210015	−	0.210015i	−0.594259	−	0.804274i	$-0.702554\pi$
$829$	6.04684	−	6.04684i	0.210015	−	0.210015i	0.804274	+	0.594259i	$0.202554\pi$
$830$	−0.860362	−	1.31871i	−0.0298636	−	0.0457729i
$831$	36.3731	−	15.0662i	1.26177	−	0.522642i
$832$	2.35364	−	2.35364i	0.0815978	−	0.0815978i
$833$	−9.99892	−	47.5967i	−0.346442	−	1.64913i
$834$			5.80128i			0.200882i
$835$	10.8947	−	25.5073i	0.377028	−	0.882715i
$836$	0.324665	−	0.216934i	0.0112288	−	0.00750283i
$837$	62.2071			2.15019
$838$	−6.68327	+	4.46562i	−0.230870	+	0.154262i
$839$	−7.84414	+	11.7396i	−0.270810	+	0.405295i	−0.941802	−	0.336169i	$-0.890869\pi$
$839$	−7.84414	+	11.7396i	−0.270810	+	0.405295i	0.670992	+	0.741465i	$0.265869\pi$
$840$	15.9109	−	23.2561i	0.548979	−	0.802412i
$841$	50.2559	+	20.8167i	1.73296	+	0.717817i
$842$	10.6455	−	4.40950i	0.366867	−	0.151961i
$843$	−43.9788	−	29.3857i	−1.51471	−	1.01210i
$844$	14.9803	+	10.0095i	0.515642	+	0.344541i
$845$	4.20295	+	0.884046i	0.144586	+	0.0304121i
$846$	−45.5348	−	45.5348i	−1.56552	−	1.56552i
$847$	−9.26826	+	46.5947i	−0.318461	+	1.60101i
$848$	−1.97998	+	4.78009i	−0.0679927	+	0.164149i
$849$	−52.3036			−1.79506
$850$	−17.2686	+	11.2603i	−0.592309	+	0.386226i
$851$	1.50710			0.0516626
$852$	1.78670	−	4.31347i	0.0612112	−	0.147777i
$853$	−1.08474	+	5.45336i	−0.0371408	+	0.186720i	−0.994902	−	0.100845i	$-0.967845\pi$
$853$	−1.08474	+	5.45336i	−0.0371408	+	0.186720i	0.957761	+	0.287564i	$0.0928455\pi$
$854$	3.29273	+	3.29273i	0.112675	+	0.112675i
$855$	22.7158	+	4.77803i	0.776863	+	0.163405i
$856$	0.488999	+	0.326739i	0.0167136	+	0.0111677i
$857$	6.94199	+	4.63849i	0.237134	+	0.158448i	0.668460	−	0.743748i	$-0.266954\pi$
$857$	6.94199	+	4.63849i	0.237134	+	0.158448i	−0.431326	+	0.902196i	$0.641954\pi$
$858$	1.83191	−	0.758803i	0.0625405	−	0.0259051i
$859$	−25.9674	−	10.7561i	−0.885997	−	0.366992i	−0.107177	−	0.994240i	$-0.534181\pi$
$859$	−25.9674	−	10.7561i	−0.885997	−	0.366992i	−0.778819	+	0.627248i	$0.784181\pi$
$860$	−8.60380	+	12.5757i	−0.293387	+	0.428828i
$861$	−24.4818	+	36.6396i	−0.834337	+	1.24867i
$862$	8.95105	−	5.98090i	0.304874	−	0.203710i
$863$	6.00314			0.204349			0.102175	−	0.994766i	$-0.467420\pi$
$863$	6.00314			0.204349			0.102175	+	0.994766i	$0.467420\pi$
$864$	−5.91804	+	3.95431i	−0.201336	+	0.134528i
$865$	−12.1129	+	28.3593i	−0.411850	+	0.964244i
$866$			28.0636i			0.953641i
$867$	26.5658	−	41.6645i	0.902224	−	1.41500i
$868$	−26.7932	+	26.7932i	−0.909421	+	0.909421i
$869$	2.34658	−	0.971985i	0.0796022	−	0.0329723i
$870$	32.4324	+	49.7102i	1.09956	+	1.68533i
$871$	−18.2917	+	18.2917i	−0.619791	+	0.619791i
$872$	−1.97602	−	2.95733i	−0.0669166	−	0.100148i
$873$	−0.802307	+	0.159589i	−0.0271540	+	0.00540126i
$874$	0.291602	+	1.46598i	0.00986357	+	0.0495875i
$875$	−17.0660	−	45.3678i	−0.576935	−	1.53371i
$876$	0.906866	−	2.18937i	0.0306402	−	0.0739719i
$877$	−7.68846	+	11.5066i	−0.259621	+	0.388550i	−0.938265	−	0.345917i	$-0.887568\pi$
$877$	−7.68846	+	11.5066i	−0.259621	+	0.388550i	0.678644	+	0.734467i	$0.262568\pi$
$878$	−0.966207	−	4.85745i	−0.0326079	−	0.163931i
$879$	46.9845	+	9.34579i	1.58475	+	0.315226i
$880$	0.320474	+	0.327582i	0.0108032	+	0.0110428i
$881$	8.61265	+	12.8897i	0.290168	+	0.434267i	0.947701	−	0.319159i	$-0.103400\pi$
$881$	8.61265	+	12.8897i	0.290168	+	0.434267i	−0.657534	+	0.753425i	$0.728400\pi$
$882$	−59.3798	−	24.5959i	−1.99942	−	0.828188i
$883$	−15.7079	−	15.7079i	−0.528614	−	0.528614i	0.391545	−	0.920159i	$-0.371941\pi$
$883$	−15.7079	−	15.7079i	−0.528614	−	0.528614i	−0.920159	+	0.391545i	$0.871941\pi$
$884$	7.74646	+	11.3287i	0.260542	+	0.381026i
$885$	−18.7732	−	19.1895i	−0.631053	−	0.645049i
$886$	−7.89494	−	19.0601i	−0.265236	−	0.640335i
$887$	−19.3307	−	3.84511i	−0.649061	−	0.129106i	−0.140430	−	0.990091i	$-0.544848\pi$
$887$	−19.3307	−	3.84511i	−0.649061	−	0.129106i	−0.508631	+	0.860984i	$0.669848\pi$
$888$		−	5.58383i		−	0.187381i
$889$	−4.36527	+	21.9457i	−0.146406	+	0.736035i
$890$	11.5171	−	2.15986i	0.386054	−	0.0723986i
$891$	−0.872829	+	0.173617i	−0.0292409	+	0.00581637i
$892$	3.71524	+	8.96939i	0.124396	+	0.300317i
$893$	8.61698	+	20.8032i	0.288356	+	0.696154i
$894$	−24.6941	+	4.91195i	−0.825893	+	0.164280i
$895$	34.1987	+	23.3974i	1.14314	+	0.782089i
$896$	0.845799	−	4.25212i	0.0282562	−	0.142053i
$897$			7.59022i			0.253430i
$898$	25.6201	+	5.09616i	0.854954	+	0.170061i
$899$	−30.5437	−	73.7391i	−1.01869	−	2.45934i
$900$	−0.597559	+	27.2370i	−0.0199186	+	0.907899i
$901$	−17.8634	−	11.6611i	−0.595117	−	0.388486i
$902$	−0.506760	−	0.506760i	−0.0168733	−	0.0168733i
$903$	79.3347	+	32.8615i	2.64009	+	1.09356i
$904$	1.83351	+	2.74404i	0.0609816	+	0.0912655i
$905$	−31.7555	+	31.0665i	−1.05559	+	1.03268i
$906$	64.7473	+	12.8790i	2.15108	+	0.427877i
$907$	−6.60837	−	33.2225i	−0.219427	−	1.10314i	−0.920708	−	0.390251i	$-0.872388\pi$
$907$	−6.60837	−	33.2225i	−0.219427	−	1.10314i	0.701281	−	0.712885i	$-0.252612\pi$
$908$	−0.294014	+	0.440023i	−0.00975721	+	0.0146027i
$909$	−31.6057	+	76.3028i	−1.04829	+	2.53081i
$910$	−29.9454	+	12.0207i	−0.992679	+	0.398483i
$911$	−11.2044	−	56.3285i	−0.371220	−	1.86625i	−0.487636	−	0.873047i	$-0.662141\pi$
$911$	−11.2044	−	56.3285i	−0.371220	−	1.86625i	0.116416	−	0.993200i	$-0.462859\pi$
$912$	5.43149	−	1.08039i	0.179855	−	0.0357753i
$913$	−0.0801770	−	0.119993i	−0.00265347	−	0.00397120i
$914$	25.0897	−	25.0897i	0.829894	−	0.829894i
$915$	−6.83156	−	1.43695i	−0.225844	−	0.0475040i
$916$	−27.0440	+	11.2020i	−0.893560	+	0.370125i
$917$	33.4707	−	33.4707i	1.10530	−	1.10530i
$918$	−11.5203	−	26.9907i	−0.380226	−	0.890826i
$919$		−	52.4129i		−	1.72894i	−0.502682	−	0.864472i	$-0.667653\pi$
$919$		−	52.4129i		−	1.72894i	0.502682	−	0.864472i	$-0.332347\pi$
$920$	−1.62797	+	0.653503i	−0.0536726	+	0.0215453i
$921$	−13.1229	+	8.76841i	−0.432413	+	0.288929i
$922$	−17.8012			−0.586252
$923$	−4.44547	+	2.97037i	−0.146325	+	0.0977709i
$924$	1.43484	−	2.14740i	0.0472029	−	0.0706441i
$925$	−7.86747	−	5.51026i	−0.258681	−	0.181176i
$926$	−31.3125	−	12.9701i	−1.02899	−	0.426223i
$927$	14.6787	−	6.08011i	0.482111	−	0.199697i
$928$	7.59313	+	5.07356i	0.249257	+	0.166548i
$929$	2.80819	+	1.87637i	0.0921337	+	0.0615617i	0.600784	−	0.799412i	$-0.294855\pi$
$929$	2.80819	+	1.87637i	0.0921337	+	0.0615617i	−0.508650	+	0.860973i	$0.669855\pi$
$930$	11.6925	−	55.5888i	0.383413	−	1.82283i
$931$	15.8915	+	15.8915i	0.520824	+	0.520824i
$932$	−1.57874	+	7.93687i	−0.0517134	+	0.259981i
$933$	0.419890	−	1.01370i	0.0137466	−	0.0331872i
$934$	13.0317			0.426409
$935$	−1.57133	+	1.04936i	−0.0513881	+	0.0343177i
$936$	18.1363			0.592803
$937$	−3.23192	+	7.80256i	−0.105582	+	0.254898i	−0.967838	−	0.251575i	$-0.919051\pi$
$937$	−3.23192	+	7.80256i	−0.105582	+	0.254898i	0.862255	+	0.506474i	$0.169051\pi$
$938$	−6.57326	+	33.0460i	−0.214625	+	1.07899i
$939$	−31.9022	−	31.9022i	−1.04109	−	1.04109i
$940$	−22.1331	+	14.4403i	−0.721901	+	0.470989i
$941$	7.93491	+	5.30194i	0.258671	+	0.172838i	0.678143	−	0.734930i	$-0.262785\pi$
$941$	7.93491	+	5.30194i	0.258671	+	0.172838i	−0.419472	+	0.907768i	$0.637785\pi$
$942$	−10.3931	−	6.94442i	−0.338624	−	0.226262i
$943$	2.53453	−	1.04984i	0.0825356	−	0.0341874i
$944$	−3.81596	−	1.58062i	−0.124199	−	0.0514448i
$945$	67.8175	−	12.7182i	2.20610	−	0.413722i
$946$	−0.775889	+	1.16120i	−0.0252263	+	0.0377539i
$947$	−19.5020	+	13.0308i	−0.633730	+	0.423445i	−0.830511	−	0.557003i	$-0.811951\pi$
$947$	−19.5020	+	13.0308i	−0.633730	+	0.423445i	0.196781	+	0.980448i	$0.436951\pi$
$948$	36.0226			1.16996
$949$	−2.25637	+	1.50766i	−0.0732449	+	0.0489407i
$950$	3.83769	−	8.71899i	0.124511	−	0.282882i
$951$			67.7734i			2.19770i
$952$	16.5871	+	6.66327i	0.537590	+	0.215958i
$953$	14.9101	−	14.9101i	0.482986	−	0.482986i	−0.423098	−	0.906084i	$-0.639057\pi$
$953$	14.9101	−	14.9101i	0.482986	−	0.482986i	0.906084	+	0.423098i	$0.139057\pi$
$954$	−26.0453	+	10.7883i	−0.843247	+	0.349284i
$955$	13.0161	−	8.49210i	0.421192	−	0.274798i
$956$	14.2365	−	14.2365i	0.460442	−	0.460442i
$957$	3.02237	+	4.52330i	0.0976993	+	0.146217i
$958$	−0.00573095	+	0.00113996i	−0.000185158	+	3.68303e-5i
$959$	14.7572	+	74.1893i	0.476534	+	2.39570i
$960$	2.42124	+	6.03167i	0.0781453	+	0.194671i
$961$	−17.3687	+	41.9317i	−0.560279	+	1.35263i
$962$	−3.55248	+	5.31666i	−0.114536	+	0.171416i
$963$	0.625159	+	3.14289i	0.0201455	+	0.101278i
$964$	8.99226	+	1.78867i	0.289621	+	0.0576093i
$965$	41.3296	+	0.453316i	1.33045	+	0.0145928i
$966$	5.49249	+	8.22009i	0.176718	+	0.264477i
$967$	21.6193	+	8.95502i	0.695231	+	0.287974i	0.702178	−	0.712002i	$-0.252211\pi$
$967$	21.6193	+	8.95502i	0.695231	+	0.287974i	−0.00694687	+	0.999976i	$0.502211\pi$
$968$	−7.74847	−	7.74847i	−0.249045	−	0.249045i
$969$	0.244659	+	22.8320i	0.00785957	+	0.733471i
$970$	−0.00368190	+	0.335685i	−0.000118219	+	0.0107782i
$971$	−15.8385	−	38.2375i	−0.508281	−	1.22710i	−0.944872	−	0.327439i	$-0.893814\pi$
$971$	−15.8385	−	38.2375i	−0.508281	−	1.22710i	0.436591	−	0.899660i	$-0.356186\pi$
$972$	8.56342	+	1.70337i	0.274672	+	0.0546356i
$973$		−	8.65286i		−	0.277398i
$974$	−5.65336	+	28.4214i	−0.181145	+	0.910680i
$975$	27.7514	−	39.6231i	0.888757	−	1.26896i
$976$	−1.05345	+	0.209544i	−0.0337201	+	0.00670735i
$977$	−17.9798	−	43.4070i	−0.575223	−	1.38871i	−0.897057	−	0.441916i	$-0.854299\pi$
$977$	−17.9798	−	43.4070i	−0.575223	−	1.38871i	0.321833	−	0.946796i	$-0.395701\pi$
$978$	4.44115	+	10.7219i	0.142012	+	0.342848i
$979$	1.05336	−	0.209526i	0.0336655	−	0.00669649i
$980$	−14.8936	+	21.7691i	−0.475758	+	0.695389i
$981$	3.78078	−	19.0073i	0.120711	−	0.606856i
$982$			31.2696i			0.997852i
$983$	−46.5284	−	9.25506i	−1.48402	−	0.295191i	−0.614435	−	0.788967i	$-0.710616\pi$
$983$	−46.5284	−	9.25506i	−1.48402	−	0.295191i	−0.869589	+	0.493777i	$0.835616\pi$
$984$	−3.88967	−	9.39049i	−0.123998	−	0.299358i
$985$	−17.3687	+	16.9918i	−0.553413	+	0.541405i
$986$	−26.3378	+	26.9084i	−0.838767	+	0.856938i
$987$	105.312	+	105.312i	3.35211	+	3.35211i
$988$	−5.85896	−	2.42686i	−0.186398	−	0.0772088i
$989$	−2.97005	−	4.44500i	−0.0944422	−	0.141343i
$990$	−0.0273862	+	2.49684i	−0.000870390	+	0.0793549i
$991$	44.9876	+	8.94859i	1.42908	+	0.284261i	0.848177	−	0.529712i	$-0.177700\pi$
$991$	44.9876	+	8.94859i	1.42908	+	0.284261i	0.580902	+	0.813974i	$0.302700\pi$
$992$	−1.70508	−	8.57200i	−0.0541363	−	0.272161i
$993$	−3.59355	+	5.37813i	−0.114038	+	0.170670i
$994$	−2.66494	+	6.43373i	−0.0845267	+	0.204066i
$995$	−31.9498	−	13.6465i	−1.01288	−	0.432622i
$996$	−0.399303	−	2.00743i	−0.0126524	−	0.0636078i
$997$	39.4467	−	7.84644i	1.24929	−	0.248499i	0.474238	−	0.880397i	$-0.342724\pi$
$997$	39.4467	−	7.84644i	1.24929	−	0.248499i	0.775052	+	0.631897i	$0.217724\pi$
$998$	−3.60412	−	5.39395i	−0.114087	−	0.170743i
$999$	9.66837	−	9.66837i	0.305894	−	0.305894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.r.b.97.5	yes	40
5.2	odd	4		850.2.s.d.743.1		40
5.3	odd	4		170.2.o.b.63.5	yes	40
5.4	even	2		850.2.v.d.607.1		40
17.10	odd	16		170.2.o.b.27.5	✓	40
85.27	even	16		850.2.v.d.843.1		40
85.44	odd	16		850.2.s.d.707.1		40
85.78	even	16	inner	170.2.r.b.163.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.27.5	✓	40	17.10	odd	16
170.2.o.b.63.5	yes	40	5.3	odd	4
170.2.r.b.97.5	yes	40	1.1	even	1	trivial
170.2.r.b.163.5	yes	40	85.78	even	16	inner
850.2.s.d.707.1		40	85.44	odd	16
850.2.s.d.743.1		40	5.2	odd	4
850.2.v.d.607.1		40	5.4	even	2
850.2.v.d.843.1		40	85.27	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 - 0.923880i) q^{2} +(0.567062 - 2.85081i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-2.18819 - 0.460262i) q^{5} +(-2.41680 - 1.61486i) q^{6} +(3.60477 + 2.40863i) q^{7} +(-0.923880 + 0.382683i) q^{8} +(-5.03395 - 2.08513i) q^{9} +(-1.26261 + 1.84549i) q^{10} +(-0.113862 + 0.170406i) q^{11} +(-2.41680 + 1.61486i) q^{12} +3.32855 q^{13} +(3.60477 - 2.40863i) q^{14} +(-2.55296 + 5.97712i) q^{15} +1.00000i q^{16} +(-4.05227 - 0.761002i) q^{17} +(-3.85282 + 3.85282i) q^{18} +(1.76021 - 0.729105i) q^{19} +(1.22183 + 1.87274i) q^{20} +(8.91069 - 8.91069i) q^{21} +(0.113862 + 0.170406i) q^{22} +(-0.769445 + 0.153052i) q^{23} +(0.567062 + 2.85081i) q^{24} +(4.57632 + 2.01428i) q^{25} +(1.27378 - 3.07518i) q^{26} +(-3.95431 + 5.91804i) q^{27} +(-0.845799 - 4.25212i) q^{28} +(8.95670 + 1.78160i) q^{29} +(4.54516 + 4.64597i) q^{30} +(-4.85565 - 7.26699i) q^{31} +(0.923880 + 0.382683i) q^{32} +(0.421230 + 0.421230i) q^{33} +(-2.25381 + 3.45258i) q^{34} +(-6.77931 - 6.92967i) q^{35} +(2.08513 + 5.03395i) q^{36} +(-1.88413 - 0.374777i) q^{37} -1.90524i q^{38} +(1.88750 - 9.48908i) q^{39} +(2.19776 - 0.412156i) q^{40} +(-3.42967 + 0.682203i) q^{41} +(-4.82243 - 11.6424i) q^{42} +(2.60772 + 6.29559i) q^{43} +(0.201008 - 0.0399830i) q^{44} +(10.0555 + 6.87959i) q^{45} +(-0.153052 + 0.769445i) q^{46} +11.8186i q^{47} +(2.85081 + 0.567062i) q^{48} +(4.51409 + 10.8980i) q^{49} +(3.61223 - 3.45713i) q^{50} +(-4.46736 + 11.1207i) q^{51} +(-2.35364 - 2.35364i) q^{52} +(4.78009 + 1.97998i) q^{53} +(3.95431 + 5.91804i) q^{54} +(0.327582 - 0.320474i) q^{55} +(-4.25212 - 0.845799i) q^{56} +(-1.08039 - 5.43149i) q^{57} +(5.07356 - 7.59313i) q^{58} +(-1.58062 + 3.81596i) q^{59} +(6.03167 - 2.42124i) q^{60} +(0.209544 + 1.05345i) q^{61} +(-8.57200 + 1.70508i) q^{62} +(-13.1239 - 19.6413i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-7.28349 - 1.53201i) q^{65} +(0.550364 - 0.227968i) q^{66} +(-5.49540 + 5.49540i) q^{67} +(2.32728 + 3.40350i) q^{68} +2.28034i q^{69} +(-8.99651 + 3.61139i) q^{70} +(-1.33556 + 0.892391i) q^{71} +5.44870 q^{72} +(-0.677883 + 0.452947i) q^{73} +(-1.06727 + 1.59729i) q^{74} +(8.33739 - 11.9040i) q^{75} +(-1.76021 - 0.729105i) q^{76} +(-0.820892 + 0.340025i) q^{77} +(-8.04446 - 5.37513i) q^{78} +(-10.3045 - 6.88525i) q^{79} +(0.460262 - 2.18819i) q^{80} +(3.07044 + 3.07044i) q^{81} +(-0.682203 + 3.42967i) q^{82} +(-0.269470 + 0.650559i) q^{83} -12.6016 q^{84} +(8.51686 + 3.53032i) q^{85} +6.81430 q^{86} +(10.1580 - 24.5236i) q^{87} +(0.0399830 - 0.201008i) q^{88} +(-3.70552 - 3.70552i) q^{89} +(10.2040 - 6.65737i) q^{90} +(11.9987 + 8.01725i) q^{91} +(0.652304 + 0.435856i) q^{92} +(-23.4703 + 9.72172i) q^{93} +(10.9189 + 4.52277i) q^{94} +(-4.18726 + 0.785257i) q^{95} +(1.61486 - 2.41680i) q^{96} +(0.124830 - 0.0834089i) q^{97} +11.7959 q^{98} +(0.928493 - 0.620400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44}+ \cdots + 160 q^{99}+O(q^{100}) \) 40 * q - 16 * q^10 - 16 * q^18 + 8 * q^25 - 8 * q^26 + 24 * q^27 - 8 * q^28 + 8 * q^29 + 16 * q^30 - 16 * q^31 - 32 * q^33 + 8 * q^34 - 32 * q^35 - 32 * q^39 - 56 * q^41 - 24 * q^42 + 16 * q^43 + 16 * q^44 + 24 * q^45 + 16 * q^49 - 32 * q^51 - 16 * q^52 + 16 * q^53 - 24 * q^54 - 8 * q^55 - 8 * q^56 - 120 * q^57 + 16 * q^58 + 8 * q^60 + 24 * q^61 - 8 * q^62 - 24 * q^63 - 32 * q^65 + 16 * q^67 - 8 * q^70 + 24 * q^71 + 56 * q^72 + 88 * q^73 + 32 * q^74 + 8 * q^75 + 24 * q^77 + 32 * q^78 - 104 * q^79 + 8 * q^80 + 48 * q^81 + 16 * q^82 + 16 * q^83 + 136 * q^85 + 96 * q^86 + 136 * q^87 - 16 * q^89 + 24 * q^90 + 48 * q^91 - 8 * q^92 - 8 * q^93 - 8 * q^94 - 136 * q^95 + 16 * q^97 + 72 * q^98 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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