LMFDB - Embedded newform 731.2.m.c.689.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.12
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.349181 + 0.349181i) q^{2} +(2.07415 + 0.859139i) q^{3} +1.75615i q^{4} +(0.898278 - 2.16864i) q^{5} +(-1.02425 + 0.424257i) q^{6} +(1.36146 + 3.28687i) q^{7} +(-1.31157 - 1.31157i) q^{8} +(1.44264 + 1.44264i) q^{9} +O(q^{10})$	\(q+(-0.349181 + 0.349181i) q^{2} +(2.07415 + 0.859139i) q^{3} +1.75615i q^{4} +(0.898278 - 2.16864i) q^{5} +(-1.02425 + 0.424257i) q^{6} +(1.36146 + 3.28687i) q^{7} +(-1.31157 - 1.31157i) q^{8} +(1.44264 + 1.44264i) q^{9} +(0.443585 + 1.07091i) q^{10} +(-3.34493 + 1.38551i) q^{11} +(-1.50877 + 3.64250i) q^{12} +1.47061i q^{13} +(-1.62311 - 0.672314i) q^{14} +(3.72632 - 3.72632i) q^{15} -2.59634 q^{16} +(0.519665 + 4.09023i) q^{17} -1.00748 q^{18} +(0.337940 - 0.337940i) q^{19} +(3.80844 + 1.57751i) q^{20} +7.98713i q^{21} +(0.684189 - 1.65178i) q^{22} +(-0.758292 + 0.314095i) q^{23} +(-1.59357 - 3.84722i) q^{24} +(-0.360544 - 0.360544i) q^{25} +(-0.513508 - 0.513508i) q^{26} +(-0.824602 - 1.99077i) q^{27} +(-5.77222 + 2.39093i) q^{28} +(1.73611 - 4.19135i) q^{29} +2.60232i q^{30} +(6.67583 + 2.76522i) q^{31} +(3.52974 - 3.52974i) q^{32} -8.12821 q^{33} +(-1.60969 - 1.24677i) q^{34} +8.35099 q^{35} +(-2.53348 + 2.53348i) q^{36} +(7.12681 + 2.95202i) q^{37} +0.236004i q^{38} +(-1.26346 + 3.05026i) q^{39} +(-4.02249 + 1.66617i) q^{40} +(-0.471612 - 1.13857i) q^{41} +(-2.78895 - 2.78895i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-2.43316 - 5.87418i) q^{44} +(4.42445 - 1.83267i) q^{45} +(0.155105 - 0.374457i) q^{46} -8.81831i q^{47} +(-5.38518 - 2.23062i) q^{48} +(-4.00016 + 4.00016i) q^{49} +0.251790 q^{50} +(-2.43621 + 8.93019i) q^{51} -2.58260 q^{52} +(3.67283 - 3.67283i) q^{53} +(0.983073 + 0.407202i) q^{54} +8.49850i q^{55} +(2.52531 - 6.09663i) q^{56} +(0.991274 - 0.410599i) q^{57} +(0.857321 + 2.06976i) q^{58} +(-1.34775 - 1.34775i) q^{59} +(6.54396 + 6.54396i) q^{60} +(3.39177 + 8.18847i) q^{61} +(-3.29664 + 1.36551i) q^{62} +(-2.77766 + 6.70587i) q^{63} -2.72764i q^{64} +(3.18922 + 1.32102i) q^{65} +(2.83822 - 2.83822i) q^{66} -5.85404 q^{67} +(-7.18303 + 0.912607i) q^{68} -1.84266 q^{69} +(-2.91601 + 2.91601i) q^{70} +(-8.98787 - 3.72290i) q^{71} -3.78426i q^{72} +(4.48179 - 10.8200i) q^{73} +(-3.51934 + 1.45776i) q^{74} +(-0.438063 - 1.05758i) q^{75} +(0.593471 + 0.593471i) q^{76} +(-9.10800 - 9.10800i) q^{77} +(-0.623916 - 1.50627i) q^{78} +(-1.51547 + 0.627729i) q^{79} +(-2.33223 + 5.63051i) q^{80} -10.9582i q^{81} +(0.562246 + 0.232890i) q^{82} +(2.03100 - 2.03100i) q^{83} -14.0266 q^{84} +(9.33701 + 2.54720i) q^{85} +0.493816 q^{86} +(7.20190 - 7.20190i) q^{87} +(6.20432 + 2.56991i) q^{88} +0.263388i q^{89} +(-0.905001 + 2.18487i) q^{90} +(-4.83370 + 2.00218i) q^{91} +(-0.551596 - 1.33167i) q^{92} +(11.4709 + 11.4709i) q^{93} +(3.07919 + 3.07919i) q^{94} +(-0.429304 - 1.03643i) q^{95} +(10.3537 - 4.28866i) q^{96} +(-3.31421 + 8.00120i) q^{97} -2.79356i q^{98} +(-6.82432 - 2.82672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.349181	+	0.349181i	−0.246908	+	0.246908i	−0.819701	−	0.572792i	$-0.805860\pi$
$2$	−0.349181	+	0.349181i	−0.246908	+	0.246908i	0.572792	+	0.819701i	$0.305860\pi$
$3$	2.07415	+	0.859139i	1.19751	+	0.496024i	0.890193	−	0.455583i	$-0.150569\pi$
$3$	2.07415	+	0.859139i	1.19751	+	0.496024i	0.307315	+	0.951608i	$0.400569\pi$
$4$			1.75615i			0.878073i
$5$	0.898278	−	2.16864i	0.401722	−	0.969844i	−0.585526	−	0.810654i	$-0.699112\pi$
$5$	0.898278	−	2.16864i	0.401722	−	0.969844i	0.987248	−	0.159190i	$-0.0508881\pi$
$6$	−1.02425	+	0.424257i	−0.418147	+	0.173202i
$7$	1.36146	+	3.28687i	0.514585	+	1.24232i	0.941189	+	0.337880i	$0.109710\pi$
$7$	1.36146	+	3.28687i	0.514585	+	1.24232i	−0.426604	+	0.904439i	$0.640290\pi$
$8$	−1.31157	−	1.31157i	−0.463711	−	0.463711i
$9$	1.44264	+	1.44264i	0.480880	+	0.480880i
$10$	0.443585	+	1.07091i	0.140274	+	0.338651i
$11$	−3.34493	+	1.38551i	−1.00853	+	0.417748i	−0.824919	−	0.565250i	$-0.808780\pi$
$11$	−3.34493	+	1.38551i	−1.00853	+	0.417748i	−0.183614	+	0.982998i	$0.558780\pi$
$12$	−1.50877	+	3.64250i	−0.435545	+	1.05150i
$13$			1.47061i			0.407873i	0.978984	+	0.203937i	$0.0653737\pi$
$13$			1.47061i			0.407873i	−0.978984	+	0.203937i	$0.934626\pi$
$14$	−1.62311	−	0.672314i	−0.433794	−	0.179683i
$15$	3.72632	−	3.72632i	0.962132	−	0.962132i
$16$	−2.59634			−0.649084
$17$	0.519665	+	4.09023i	0.126037	+	0.992026i
$17$	0.519665	+	4.09023i	0.126037	+	0.992026i
$18$	−1.00748			−0.237466
$19$	0.337940	−	0.337940i	0.0775287	−	0.0775287i	−0.667279	−	0.744808i	$-0.732541\pi$
$19$	0.337940	−	0.337940i	0.0775287	−	0.0775287i	0.744808	+	0.667279i	$0.232541\pi$
$20$	3.80844	+	1.57751i	0.851593	+	0.352741i
$21$			7.98713i			1.74293i
$22$	0.684189	−	1.65178i	0.145870	−	0.352160i
$23$	−0.758292	+	0.314095i	−0.158115	+	0.0654933i	−0.460337	−	0.887744i	$-0.652271\pi$
$23$	−0.758292	+	0.314095i	−0.158115	+	0.0654933i	0.302222	+	0.953237i	$0.402271\pi$
$24$	−1.59357	−	3.84722i	−0.325286	−	0.785311i
$25$	−0.360544	−	0.360544i	−0.0721088	−	0.0721088i
$26$	−0.513508	−	0.513508i	−0.100707	−	0.100707i
$27$	−0.824602	−	1.99077i	−0.158695	−	0.383123i
$28$	−5.77222	+	2.39093i	−1.09085	+	0.451843i
$29$	1.73611	−	4.19135i	0.322388	−	0.778314i	−0.676726	−	0.736235i	$-0.736602\pi$
$29$	1.73611	−	4.19135i	0.322388	−	0.778314i	0.999114	−	0.0420791i	$-0.0133982\pi$
$30$			2.60232i			0.475116i
$31$	6.67583	+	2.76522i	1.19902	+	0.496648i	0.890681	−	0.454630i	$-0.150228\pi$
$31$	6.67583	+	2.76522i	1.19902	+	0.496648i	0.308335	+	0.951278i	$0.400228\pi$
$32$	3.52974	−	3.52974i	0.623976	−	0.623976i
$33$	−8.12821			−1.41494
$34$	−1.60969	−	1.24677i	−0.276059	−	0.213820i
$35$	8.35099			1.41158
$36$	−2.53348	+	2.53348i	−0.422247	+	0.422247i
$37$	7.12681	+	2.95202i	1.17164	+	0.485310i	0.881735	−	0.471746i	$-0.156376\pi$
$37$	7.12681	+	2.95202i	1.17164	+	0.485310i	0.289906	+	0.957055i	$0.406376\pi$
$38$			0.236004i			0.0382849i
$39$	−1.26346	+	3.05026i	−0.202315	+	0.488432i
$40$	−4.02249	+	1.66617i	−0.636011	+	0.263444i
$41$	−0.471612	−	1.13857i	−0.0736535	−	0.177815i	0.882765	−	0.469815i	$-0.155679\pi$
$41$	−0.471612	−	1.13857i	−0.0736535	−	0.177815i	−0.956418	+	0.292000i	$0.905679\pi$
$42$	−2.78895	−	2.78895i	−0.430345	−	0.430345i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	−2.43316	−	5.87418i	−0.366813	−	0.885565i
$45$	4.42445	−	1.83267i	0.659558	−	0.273198i
$46$	0.155105	−	0.374457i	0.0228690	−	0.0552106i
$47$		−	8.81831i		−	1.28628i	−0.765747	−	0.643142i	$-0.777631\pi$
$47$		−	8.81831i		−	1.28628i	0.765747	−	0.643142i	$-0.222369\pi$
$48$	−5.38518	−	2.23062i	−0.777284	−	0.321962i
$49$	−4.00016	+	4.00016i	−0.571452	+	0.571452i
$50$	0.251790			0.0356085
$51$	−2.43621	+	8.93019i	−0.341138	+	1.25048i
$52$	−2.58260			−0.358143
$53$	3.67283	−	3.67283i	0.504502	−	0.504502i	−0.408332	−	0.912834i	$-0.633889\pi$
$53$	3.67283	−	3.67283i	0.504502	−	0.504502i	0.912834	+	0.408332i	$0.133889\pi$
$54$	0.983073	+	0.407202i	0.133779	+	0.0554132i
$55$			8.49850i			1.14594i
$56$	2.52531	−	6.09663i	0.337458	−	0.814697i
$57$	0.991274	−	0.410599i	0.131297	−	0.0543852i
$58$	0.857321	+	2.06976i	0.112572	+	0.271772i
$59$	−1.34775	−	1.34775i	−0.175462	−	0.175462i	0.613912	−	0.789374i	$-0.289595\pi$
$59$	−1.34775	−	1.34775i	−0.175462	−	0.175462i	−0.789374	+	0.613912i	$0.789595\pi$
$60$	6.54396	+	6.54396i	0.844822	+	0.844822i
$61$	3.39177	+	8.18847i	0.434272	+	1.04843i	0.977895	+	0.209096i	$0.0670522\pi$
$61$	3.39177	+	8.18847i	0.434272	+	1.04843i	−0.543623	+	0.839330i	$0.682948\pi$
$62$	−3.29664	+	1.36551i	−0.418673	+	0.173420i
$63$	−2.77766	+	6.70587i	−0.349952	+	0.844860i
$64$		−	2.72764i		−	0.340955i
$65$	3.18922	+	1.32102i	0.395573	+	0.163852i
$66$	2.83822	−	2.83822i	0.349360	−	0.349360i
$67$	−5.85404			−0.715185			−0.357593	−	0.933878i	$-0.616402\pi$
$67$	−5.85404			−0.715185			−0.357593	+	0.933878i	$0.616402\pi$
$68$	−7.18303	+	0.912607i	−0.871071	+	0.110670i
$69$	−1.84266			−0.221830
$70$	−2.91601	+	2.91601i	−0.348529	+	0.348529i
$71$	−8.98787	−	3.72290i	−1.06666	−	0.441827i	−0.220852	−	0.975307i	$-0.570884\pi$
$71$	−8.98787	−	3.72290i	−1.06666	−	0.441827i	−0.845812	+	0.533481i	$0.820884\pi$
$72$		−	3.78426i		−	0.445979i
$73$	4.48179	−	10.8200i	0.524554	−	1.26639i	−0.410494	−	0.911863i	$-0.634644\pi$
$73$	4.48179	−	10.8200i	0.524554	−	1.26639i	0.935048	−	0.354522i	$-0.115356\pi$
$74$	−3.51934	+	1.45776i	−0.409115	+	0.169461i
$75$	−0.438063	−	1.05758i	−0.0505832	−	0.122119i
$76$	0.593471	+	0.593471i	0.0680758	+	0.0680758i
$77$	−9.10800	−	9.10800i	−1.03795	−	1.03795i
$78$	−0.623916	−	1.50627i	−0.0706446	−	0.170551i
$79$	−1.51547	+	0.627729i	−0.170504	+	0.0706250i	−0.466303	−	0.884625i	$-0.654414\pi$
$79$	−1.51547	+	0.627729i	−0.170504	+	0.0706250i	0.295799	+	0.955250i	$0.404414\pi$
$80$	−2.33223	+	5.63051i	−0.260752	+	0.629510i
$81$		−	10.9582i		−	1.21758i
$82$	0.562246	+	0.232890i	0.0620897	+	0.0257184i
$83$	2.03100	−	2.03100i	0.222931	−	0.222931i	−0.586800	−	0.809732i	$-0.699613\pi$
$83$	2.03100	−	2.03100i	0.222931	−	0.222931i	0.809732	+	0.586800i	$0.199613\pi$
$84$	−14.0266			−1.53042
$85$	9.33701	+	2.54720i	1.01274	+	0.276282i
$86$	0.493816			0.0532496
$87$	7.20190	−	7.20190i	0.772125	−	0.772125i
$88$	6.20432	+	2.56991i	0.661383	+	0.273954i
$89$			0.263388i			0.0279191i	0.999903	+	0.0139595i	$0.00444360\pi$
$89$			0.263388i			0.0279191i	−0.999903	+	0.0139595i	$0.995556\pi$
$90$	−0.905001	+	2.18487i	−0.0953955	+	0.230305i
$91$	−4.83370	+	2.00218i	−0.506709	+	0.209886i
$92$	−0.551596	−	1.33167i	−0.0575079	−	0.138836i
$93$	11.4709	+	11.4709i	1.18948	+	1.18948i
$94$	3.07919	+	3.07919i	0.317594	+	0.317594i
$95$	−0.429304	−	1.03643i	−0.0440457	−	0.106336i
$96$	10.3537	−	4.28866i	1.05672	−	0.437709i
$97$	−3.31421	+	8.00120i	−0.336507	+	0.812399i	0.661539	+	0.749911i	$0.269904\pi$
$97$	−3.31421	+	8.00120i	−0.336507	+	0.812399i	−0.998046	+	0.0624882i	$0.980096\pi$
$98$		−	2.79356i		−	0.282192i
$99$	−6.82432	−	2.82672i	−0.685870	−	0.284096i
$100$	0.633168	−	0.633168i	0.0633168	−	0.0633168i
$101$	−0.108559			−0.0108020			−0.00540100	−	0.999985i	$-0.501719\pi$
$101$	−0.108559			−0.0108020			−0.00540100	+	0.999985i	$0.501719\pi$
$102$	−2.26757	−	3.96893i	−0.224523	−	0.392983i
$103$	−1.74202			−0.171646			−0.0858229	−	0.996310i	$-0.527352\pi$
$103$	−1.74202			−0.171646			−0.0858229	+	0.996310i	$0.527352\pi$
$104$	1.92881	−	1.92881i	0.189136	−	0.189136i
$105$	17.3212	+	7.17467i	1.69037	+	0.700176i
$106$			2.56496i			0.249131i
$107$	−0.338876	+	0.818119i	−0.0327604	+	0.0790906i	−0.939413	−	0.342787i	$-0.888629\pi$
$107$	−0.338876	+	0.818119i	−0.0327604	+	0.0790906i	0.906653	+	0.421878i	$0.138629\pi$
$108$	3.49607	−	1.44812i	0.336410	−	0.139346i
$109$	0.850779	+	2.05396i	0.0814898	+	0.196734i	0.959373	−	0.282141i	$-0.0910447\pi$
$109$	0.850779	+	2.05396i	0.0814898	+	0.196734i	−0.877883	+	0.478875i	$0.841045\pi$
$110$	−2.96751	−	2.96751i	−0.282941	−	0.282941i
$111$	12.2458	+	12.2458i	1.16232	+	1.16232i
$112$	−3.53482	−	8.53382i	−0.334009	−	0.806370i
$113$	11.1961	−	4.63758i	1.05324	−	0.436267i	0.212193	−	0.977228i	$-0.431939\pi$
$113$	11.1961	−	4.63758i	1.05324	−	0.436267i	0.841048	+	0.540961i	$0.181939\pi$
$114$	−0.202760	+	0.489507i	−0.0189903	+	0.0458465i
$115$			1.92660i			0.179657i
$116$	7.36062	+	3.04887i	0.683416	+	0.283080i
$117$	−2.12156	+	2.12156i	−0.196138	+	0.196138i
$118$	0.941217			0.0866460
$119$	−12.7365	+	7.27677i	−1.16756	+	0.667060i
$120$	−9.77469			−0.892303
$121$	1.49070	−	1.49070i	0.135519	−	0.135519i
$122$	−4.04360	−	1.67491i	−0.366090	−	0.151640i
$123$		−	2.76675i		−	0.249469i
$124$	−4.85613	+	11.7237i	−0.436093	+	1.05282i
$125$	9.73742	−	4.03337i	0.870942	−	0.360756i
$126$	−1.37165	−	3.31147i	−0.122197	−	0.295009i
$127$	−6.95141	−	6.95141i	−0.616838	−	0.616838i	0.327881	−	0.944719i	$-0.393665\pi$
$127$	−6.95141	−	6.95141i	−0.616838	−	0.616838i	−0.944719	+	0.327881i	$0.893665\pi$
$128$	8.01192	+	8.01192i	0.708160	+	0.708160i
$129$	−0.859139	−	2.07415i	−0.0756430	−	0.182618i
$130$	−1.57489	+	0.652339i	−0.138127	+	0.0572139i
$131$	−3.68104	+	8.88682i	−0.321614	+	0.776445i	0.677547	+	0.735480i	$0.263043\pi$
$131$	−3.68104	+	8.88682i	−0.321614	+	0.776445i	−0.999161	+	0.0409649i	$0.986957\pi$
$132$		−	14.2743i		−	1.24242i
$133$	1.57086	+	0.650670i	0.136211	+	0.0564202i
$134$	2.04412	−	2.04412i	0.176585	−	0.176585i
$135$	−5.05797			−0.435321
$136$	4.68306	−	6.04621i	0.401569	−	0.518459i
$137$	16.5355			1.41272			0.706360	−	0.707852i	$-0.250336\pi$
$137$	16.5355			1.41272			0.706360	+	0.707852i	$0.250336\pi$
$138$	0.643421	−	0.643421i	0.0547716	−	0.0547716i
$139$	−15.2185	−	6.30372i	−1.29082	−	0.534675i	−0.371590	−	0.928397i	$-0.621187\pi$
$139$	−15.2185	−	6.30372i	−1.29082	−	0.534675i	−0.919229	+	0.393722i	$0.871187\pi$
$140$			14.6656i			1.23947i
$141$	7.57616	−	18.2905i	0.638028	−	1.54034i
$142$	4.43836	−	1.83843i	0.372459	−	0.154277i
$143$	−2.03755	−	4.91908i	−0.170388	−	0.411354i
$144$	−3.74558	−	3.74558i	−0.312132	−	0.312132i
$145$	−7.53000	−	7.53000i	−0.625332	−	0.625332i
$146$	2.21318	+	5.34309i	0.183164	+	0.442198i
$147$	−11.7336	+	4.86022i	−0.967772	+	0.400864i
$148$	−5.18418	+	12.5157i	−0.426137	+	1.02879i
$149$			22.6620i			1.85654i	0.371904	+	0.928271i	$0.378705\pi$
$149$			22.6620i			1.85654i	−0.371904	+	0.928271i	$0.621295\pi$
$150$	0.522249	+	0.216323i	0.0426415	+	0.0176627i
$151$	11.9609	−	11.9609i	0.973365	−	0.973365i	−0.0262890	−	0.999654i	$-0.508369\pi$
$151$	11.9609	−	11.9609i	0.973365	−	0.973365i	0.999654	+	0.0262890i	$0.00836900\pi$
$152$	−0.886466			−0.0719019
$153$	−5.15103	+	6.65041i	−0.416436	+	0.537654i
$154$	6.36068			0.512558
$155$	11.9935	−	11.9935i	0.963342	−	0.963342i
$156$	−5.35669	−	2.21882i	−0.428879	−	0.177647i
$157$		−	11.5737i		−	0.923678i	−0.886964	−	0.461839i	$-0.847190\pi$
$157$		−	11.5737i		−	0.923678i	0.886964	−	0.461839i	$-0.152810\pi$
$158$	0.309983	−	0.748365i	0.0246609	−	0.0595367i
$159$	10.7735	−	4.46251i	0.854391	−	0.353900i
$160$	−4.48403	−	10.8254i	−0.354494	−	0.855824i
$161$	−2.06478	−	2.06478i	−0.162727	−	0.162727i
$162$	3.82639	+	3.82639i	0.300629	+	0.300629i
$163$	−2.47463	−	5.97428i	−0.193828	−	0.467942i	0.796848	−	0.604179i	$-0.206499\pi$
$163$	−2.47463	−	5.97428i	−0.193828	−	0.467942i	−0.990676	+	0.136237i	$0.956499\pi$
$164$	1.99950	−	0.828220i	0.156135	−	0.0646731i
$165$	−7.30140	+	17.6271i	−0.568413	+	1.37227i
$166$			1.41837i			0.110087i
$167$	−12.7225	−	5.26984i	−0.984498	−	0.407793i	−0.168408	−	0.985717i	$-0.553863\pi$
$167$	−12.7225	−	5.26984i	−0.984498	−	0.407793i	−0.816090	+	0.577925i	$0.803863\pi$
$168$	10.4757	−	10.4757i	0.808219	−	0.808219i
$169$	10.8373			0.833639
$170$	−4.14974	+	2.37087i	−0.318271	+	0.181838i
$171$	0.975050			0.0745639
$172$	1.24178	−	1.24178i	0.0946850	−	0.0946850i
$173$	−3.17700	−	1.31596i	−0.241543	−	0.100050i	0.258628	−	0.965977i	$-0.416730\pi$
$173$	−3.17700	−	1.31596i	−0.241543	−	0.100050i	−0.500171	+	0.865927i	$0.666730\pi$
$174$			5.02953i			0.381288i
$175$	0.694192	−	1.67593i	0.0524760	−	0.126688i
$176$	8.68456	−	3.59726i	0.654623	−	0.271154i
$177$	−1.63752	−	3.95333i	−0.123084	−	0.297151i
$178$	−0.0919700	−	0.0919700i	−0.00689344	−	0.00689344i
$179$	−6.59301	−	6.59301i	−0.492785	−	0.492785i	0.416398	−	0.909183i	$-0.363292\pi$
$179$	−6.59301	−	6.59301i	−0.492785	−	0.492785i	−0.909183	+	0.416398i	$0.863292\pi$
$180$	3.21843	+	7.76998i	0.239888	+	0.579140i
$181$	−5.72714	+	2.37226i	−0.425695	+	0.176329i	−0.585237	−	0.810863i	$-0.698998\pi$
$181$	−5.72714	+	2.37226i	−0.425695	+	0.176329i	0.159542	+	0.987191i	$0.448998\pi$
$182$	0.988710	−	2.38696i	0.0732881	−	0.176933i
$183$			19.8981i			1.47091i
$184$	1.40651	+	0.582597i	0.103690	+	0.0429496i
$185$	12.8037	−	12.8037i	0.941349	−	0.941349i
$186$	−8.01087			−0.587385
$187$	−7.40530	−	12.9615i	−0.541529	−	0.947839i
$188$	15.4862			1.12945
$189$	5.42072	−	5.42072i	0.394299	−	0.394299i
$190$	0.511807	+	0.211997i	0.0371304	+	0.0153799i
$191$		−	15.6653i		−	1.13350i	−0.823888	−	0.566752i	$-0.808200\pi$
$191$		−	15.6653i		−	1.13350i	0.823888	−	0.566752i	$-0.191800\pi$
$192$	2.34342	−	5.65752i	0.169122	−	0.408297i
$193$	19.6593	−	8.14317i	1.41511	−	0.586158i	0.461484	−	0.887149i	$-0.347317\pi$
$193$	19.6593	−	8.14317i	1.41511	−	0.586158i	0.953627	+	0.300990i	$0.0973172\pi$
$194$	−1.63661	−	3.95112i	−0.117502	−	0.283674i
$195$	5.47996	+	5.47996i	0.392428	+	0.392428i
$196$	−7.02487	−	7.02487i	−0.501776	−	0.501776i
$197$	1.52122	+	3.67256i	0.108383	+	0.261659i	0.968761	−	0.247997i	$-0.0797725\pi$
$197$	1.52122	+	3.67256i	0.108383	+	0.261659i	−0.860378	+	0.509657i	$0.829772\pi$
$198$	3.36996	−	1.39588i	0.239493	−	0.0992010i
$199$	7.14298	−	17.2447i	0.506352	−	1.22244i	−0.439616	−	0.898186i	$-0.644886\pi$
$199$	7.14298	−	17.2447i	0.506352	−	1.22244i	0.945969	−	0.324257i	$-0.105114\pi$
$200$			0.945760i			0.0668754i
$201$	−12.1421	−	5.02944i	−0.856441	−	0.354749i
$202$	0.0379066	−	0.0379066i	0.00266710	−	0.00266710i
$203$	16.1401			1.13281
$204$	−15.6827	−	4.27834i	−1.09801	−	0.299544i
$205$	−2.89279			−0.202041
$206$	0.608278	−	0.608278i	0.0423808	−	0.0423808i
$207$	−1.54707	−	0.640816i	−0.107529	−	0.0445398i
$208$		−	3.81820i		−	0.264744i
$209$	−0.662163	+	1.59860i	−0.0458028	+	0.110578i
$210$	−8.55348	+	3.54297i	−0.590246	+	0.244488i
$211$	−6.70858	−	16.1960i	−0.461838	−	1.11498i	−0.967642	−	0.252327i	$-0.918804\pi$
$211$	−6.70858	−	16.1960i	−0.461838	−	1.11498i	0.505804	−	0.862648i	$-0.331196\pi$
$212$	6.45003	+	6.45003i	0.442990	+	0.442990i
$213$	−15.4437	−	15.4437i	−1.05818	−	1.05818i
$214$	−0.167343	−	0.404001i	−0.0114393	−	0.0276169i
$215$	−2.16864	+	0.898278i	−0.147900	+	0.0612621i
$216$	−1.52951	+	3.69256i	−0.104070	+	0.251247i
$217$			25.7073i			1.74513i
$218$	−1.01428	−	0.420128i	−0.0686957	−	0.0284547i
$219$	18.5918	−	18.5918i	1.25632	−	1.25632i
$220$	−14.9246			−1.00622
$221$	−6.01512	+	0.764223i	−0.404621	+	0.0514072i
$222$	−8.55203			−0.573975
$223$	−8.51733	+	8.51733i	−0.570362	+	0.570362i	−0.932230	−	0.361867i	$-0.882139\pi$
$223$	−8.51733	+	8.51733i	−0.570362	+	0.570362i	0.361867	+	0.932230i	$0.382139\pi$
$224$	16.4074	+	6.79617i	1.09627	+	0.454088i
$225$		−	1.04027i		−	0.0693513i
$226$	−2.29011	+	5.52882i	−0.152336	+	0.367772i
$227$	−18.6052	+	7.70651i	−1.23487	+	0.511499i	−0.902107	−	0.431512i	$-0.857980\pi$
$227$	−18.6052	+	7.70651i	−1.23487	+	0.511499i	−0.332761	+	0.943011i	$0.607980\pi$
$228$	0.721071	+	1.74082i	0.0477541	+	0.115289i
$229$	−20.5319	−	20.5319i	−1.35679	−	1.35679i	−0.877849	−	0.478937i	$-0.841022\pi$
$229$	−20.5319	−	20.5319i	−1.35679	−	1.35679i	−0.478937	−	0.877849i	$-0.658978\pi$
$230$	−0.672733	−	0.672733i	−0.0443587	−	0.0443587i
$231$	−11.0663	−	26.7163i	−0.728107	−	1.75781i
$232$	−7.77431	+	3.22022i	−0.510408	+	0.211418i
$233$	−3.28507	+	7.93085i	−0.215212	+	0.519567i	−0.994209	−	0.107460i	$-0.965728\pi$
$233$	−3.28507	+	7.93085i	−0.215212	+	0.519567i	0.778998	+	0.627027i	$0.215728\pi$
$234$		−	1.48161i		−	0.0968562i
$235$	−19.1237	−	7.92130i	−1.24749	−	0.516729i
$236$	2.36684	−	2.36684i	0.154068	−	0.154068i
$237$	−3.68261			−0.239212
$238$	1.90644	−	6.98826i	0.123576	−	0.452982i
$239$	1.89849			0.122803			0.0614015	−	0.998113i	$-0.480443\pi$
$239$	1.89849			0.122803			0.0614015	+	0.998113i	$0.480443\pi$
$240$	−9.67479	+	9.67479i	−0.624505	+	0.624505i
$241$	12.3913	+	5.13264i	0.798194	+	0.330623i	0.744233	−	0.667920i	$-0.232815\pi$
$241$	12.3913	+	5.13264i	0.798194	+	0.330623i	0.0539610	+	0.998543i	$0.482815\pi$
$242$			1.04105i			0.0669213i
$243$	6.94080	−	16.7566i	0.445252	−	1.07493i
$244$	−14.3801	+	5.95645i	−0.920594	+	0.381323i
$245$	5.08164	+	12.2682i	0.324654	+	0.783784i
$246$	0.966095	+	0.966095i	0.0615960	+	0.0615960i
$247$	0.496977	+	0.496977i	0.0316219	+	0.0316219i
$248$	−5.12906	−	12.3826i	−0.325696	−	0.786299i
$249$	5.95750	−	2.46768i	0.377541	−	0.156383i
$250$	−1.99175	+	4.80850i	−0.125969	+	0.304116i
$251$			25.1842i			1.58961i	0.606862	+	0.794807i	$0.292428\pi$
$251$			25.1842i			1.58961i	−0.606862	+	0.794807i	$0.707572\pi$
$252$	−11.7765	−	4.87798i	−0.741848	−	0.307284i
$253$	2.10125	−	2.10125i	0.132104	−	0.132104i
$254$	4.85460			0.304605
$255$	17.1779	+	13.3051i	1.07572	+	0.833195i
$256$	−0.139937			−0.00874606
$257$	17.3778	−	17.3778i	1.08400	−	1.08400i	0.0878663	−	0.996132i	$-0.471995\pi$
$257$	17.3778	−	17.3778i	1.08400	−	1.08400i	0.996132	−	0.0878663i	$-0.0280048\pi$
$258$	1.02425	+	0.424257i	0.0637668	+	0.0264131i
$259$			27.4440i			1.70528i
$260$	−2.31990	+	5.60073i	−0.143874	+	0.347342i
$261$	8.55119	−	3.54202i	0.529305	−	0.219245i
$262$	−1.81776	−	4.38845i	−0.112301	−	0.271120i
$263$	17.4532	+	17.4532i	1.07621	+	1.07621i	0.996846	+	0.0793657i	$0.0252895\pi$
$263$	17.4532	+	17.4532i	1.07621	+	1.07621i	0.0793657	+	0.996846i	$0.474711\pi$
$264$	10.6608	+	10.6608i	0.656124	+	0.656124i
$265$	−4.66581	−	11.2643i	−0.286618	−	0.691958i
$266$	−0.775714	+	0.321311i	−0.0475621	+	0.0197009i
$267$	−0.226287	+	0.546305i	−0.0138485	+	0.0334333i
$268$		−	10.2806i		−	0.627985i
$269$	6.23023	+	2.58065i	0.379864	+	0.157345i	0.564441	−	0.825473i	$-0.309092\pi$
$269$	6.23023	+	2.58065i	0.379864	+	0.157345i	−0.184578	+	0.982818i	$0.559092\pi$
$270$	1.76615	−	1.76615i	0.107484	−	0.107484i
$271$	5.55343			0.337347			0.168673	−	0.985672i	$-0.446052\pi$
$271$	5.55343			0.337347			0.168673	+	0.985672i	$0.446052\pi$
$272$	−1.34922	−	10.6196i	−0.0818088	−	0.643908i
$273$	−11.7459			−0.710897
$274$	−5.77387	+	5.77387i	−0.348812	+	0.348812i
$275$	1.70553	+	0.706454i	0.102847	+	0.0426008i
$276$		−	3.23598i		−	0.194783i
$277$	−10.3317	+	24.9429i	−0.620771	+	1.49867i	0.230028	+	0.973184i	$0.426118\pi$
$277$	−10.3317	+	24.9429i	−0.620771	+	1.49867i	−0.850800	+	0.525490i	$0.823882\pi$
$278$	7.51516	−	3.11288i	0.450729	−	0.186698i
$279$	5.64160	+	13.6200i	0.337754	+	0.815410i
$280$	−10.9529	−	10.9529i	−0.654564	−	0.654564i
$281$	3.53607	+	3.53607i	0.210944	+	0.210944i	0.804669	−	0.593724i	$-0.202343\pi$
$281$	3.53607	+	3.53607i	0.210944	+	0.210944i	−0.593724	+	0.804669i	$0.702343\pi$
$282$	3.74123	+	9.03213i	0.222787	+	0.537856i
$283$	−1.04945	+	0.434697i	−0.0623834	+	0.0258400i	−0.413657	−	0.910433i	$-0.635749\pi$
$283$	−1.04945	+	0.434697i	−0.0623834	+	0.0258400i	0.351274	+	0.936273i	$0.385749\pi$
$284$	6.53795	−	15.7840i	0.387956	−	0.936609i
$285$		−	2.51854i		−	0.149186i
$286$	2.42912	+	1.00617i	0.143637	+	0.0594963i
$287$	3.10025	−	3.10025i	0.183002	−	0.183002i
$288$	10.1843			0.600114
$289$	−16.4599	+	4.25109i	−0.968229	+	0.250064i
$290$	5.25866			0.308799
$291$	−13.7483	+	13.7483i	−0.805939	+	0.805939i
$292$	19.0015	+	7.87068i	1.11198	+	0.460597i
$293$			4.47479i			0.261420i	0.991421	+	0.130710i	$0.0417257\pi$
$293$			4.47479i			0.261420i	−0.991421	+	0.130710i	$0.958274\pi$
$294$	2.40006	−	5.79425i	0.139974	−	0.337927i
$295$	−4.13343	+	1.71212i	−0.240658	+	0.0996837i
$296$	−5.47555	−	13.2191i	−0.318260	−	0.768347i
$297$	5.51646	+	5.51646i	0.320098	+	0.320098i
$298$	−7.91313	−	7.91313i	−0.458395	−	0.458395i
$299$	−0.461910	−	1.11515i	−0.0267130	−	0.0644908i
$300$	1.85726	−	0.769303i	0.107229	−	0.0444157i
$301$	1.36146	−	3.28687i	0.0784735	−	0.189452i
$302$			8.35305i			0.480664i
$303$	−0.225167	−	0.0932671i	−0.0129355	−	0.00535806i
$304$	−0.877406	+	0.877406i	−0.0503227	+	0.0503227i
$305$	20.8046			1.19127
$306$	−0.523554	−	4.12084i	−0.0299296	−	0.235573i
$307$	17.2838			0.986441			0.493221	−	0.869904i	$-0.335820\pi$
$307$	17.2838			0.986441			0.493221	+	0.869904i	$0.335820\pi$
$308$	15.9950	−	15.9950i	0.911398	−	0.911398i
$309$	−3.61319	−	1.49663i	−0.205547	−	0.0851405i
$310$			8.37581i			0.475714i
$311$	0.685183	−	1.65418i	0.0388532	−	0.0937999i	−0.903262	−	0.429090i	$-0.858834\pi$
$311$	0.685183	−	1.65418i	0.0388532	−	0.0937999i	0.942115	+	0.335290i	$0.108834\pi$
$312$	5.65776	−	2.34352i	0.320307	−	0.132676i
$313$	−1.95471	−	4.71908i	−0.110486	−	0.266738i	0.858959	−	0.512044i	$-0.171112\pi$
$313$	−1.95471	−	4.71908i	−0.110486	−	0.266738i	−0.969446	+	0.245306i	$0.921112\pi$
$314$	4.04130	+	4.04130i	0.228064	+	0.228064i
$315$	12.0475	+	12.0475i	0.678798	+	0.678798i
$316$	−1.10238	−	2.66139i	−0.0620139	−	0.149715i
$317$	−25.1684	+	10.4251i	−1.41360	+	0.585533i	−0.953244	−	0.302202i	$-0.902278\pi$
$317$	−25.1684	+	10.4251i	−1.41360	+	0.585533i	−0.460357	+	0.887734i	$0.652278\pi$
$318$	−2.20366	+	5.32011i	−0.123575	+	0.298337i
$319$			16.4252i			0.919632i
$320$	−5.91526	−	2.45018i	−0.330673	−	0.136969i
$321$	−1.40576	+	1.40576i	−0.0784617	+	0.0784617i
$322$	1.44196			0.0803573
$323$	1.55787	+	1.20663i	0.0866819	+	0.0671389i
$324$	19.2442			1.06912
$325$	0.530219	−	0.530219i	0.0294113	−	0.0294113i
$326$	2.95020	+	1.22201i	0.163396	+	0.0676810i
$327$			4.99115i			0.276011i
$328$	−0.874768	+	2.11188i	−0.0483010	+	0.116609i
$329$	28.9846	−	12.0058i	1.59797	−	0.661903i
$330$	−3.60555	−	8.70456i	−0.198479	−	0.479171i
$331$	10.4156	+	10.4156i	0.572495	+	0.572495i	0.932825	−	0.360330i	$-0.117336\pi$
$331$	10.4156	+	10.4156i	0.572495	+	0.572495i	−0.360330	+	0.932825i	$0.617336\pi$
$332$	3.56673	+	3.56673i	0.195750	+	0.195750i
$333$	6.02272	+	14.5401i	0.330043	+	0.796794i
$334$	6.28259	−	2.60233i	0.343768	−	0.142393i
$335$	−5.25856	+	12.6953i	−0.287306	+	0.693618i
$336$		−	20.7373i		−	1.13131i
$337$	−22.5066	−	9.32255i	−1.22601	−	0.507831i	−0.326697	−	0.945129i	$-0.605936\pi$
$337$	−22.5066	−	9.32255i	−1.22601	−	0.507831i	−0.899317	+	0.437298i	$0.855936\pi$
$338$	−3.78418	+	3.78418i	−0.205832	+	0.205832i
$339$	27.2067			1.47766
$340$	−4.47325	+	16.3972i	−0.242596	+	0.889261i
$341$	−26.1614			−1.41672
$342$	−0.340469	+	0.340469i	−0.0184104	+	0.0184104i
$343$	4.41399	+	1.82833i	0.238333	+	0.0987208i
$344$			1.85485i			0.100007i
$345$	−1.65522	+	3.99606i	−0.0891141	+	0.215140i
$346$	1.56885	−	0.649840i	0.0843421	−	0.0349356i
$347$	5.39078	+	13.0145i	0.289392	+	0.698654i	0.999988	−	0.00494627i	$-0.00157445\pi$
$347$	5.39078	+	13.0145i	0.289392	+	0.698654i	−0.710596	+	0.703601i	$0.751574\pi$
$348$	12.6476	+	12.6476i	0.677982	+	0.677982i
$349$	9.26265	+	9.26265i	0.495818	+	0.495818i	0.910133	−	0.414315i	$-0.135979\pi$
$349$	9.26265	+	9.26265i	0.495818	+	0.495818i	−0.414315	+	0.910133i	$0.635979\pi$
$350$	0.342803	+	0.827601i	0.0183236	+	0.0442371i
$351$	2.92764	−	1.21267i	0.156266	−	0.0647274i
$352$	−6.91621	+	16.6972i	−0.368635	+	0.889965i
$353$			3.12184i			0.166159i	0.996543	+	0.0830794i	$0.0264755\pi$
$353$			3.12184i			0.166159i	−0.996543	+	0.0830794i	$0.973524\pi$
$354$	1.95222	+	0.808636i	0.103759	+	0.0429785i
$355$	−16.1472	+	16.1472i	−0.857006	+	0.857006i
$356$	−0.462548			−0.0245150
$357$	−32.6692	+	4.15063i	−1.72904	+	0.219675i
$358$	4.60431			0.243345
$359$	−20.0998	+	20.0998i	−1.06083	+	1.06083i	−0.0627991	+	0.998026i	$0.520003\pi$
$359$	−20.0998	+	20.0998i	−1.06083	+	1.06083i	−0.998026	+	0.0627991i	$0.979997\pi$
$360$	−8.20667	−	3.39932i	−0.432530	−	0.179160i
$361$			18.7716i			0.987979i
$362$	1.17146	−	2.82815i	0.0615706	−	0.148644i
$363$	4.37266	−	1.81121i	0.229505	−	0.0950641i
$364$	−3.51612	−	8.48867i	−0.184295	−	0.444927i
$365$	−19.4387	−	19.4387i	−1.01747	−	1.01747i
$366$	−6.94803	−	6.94803i	−0.363179	−	0.363179i
$367$	10.8939	+	26.3003i	0.568658	+	1.37286i	0.902686	+	0.430299i	$0.141592\pi$
$367$	10.8939	+	26.3003i	0.568658	+	1.37286i	−0.334028	+	0.942563i	$0.608408\pi$
$368$	1.96878	−	0.815496i	0.102630	−	0.0425107i
$369$	0.962183	−	2.32292i	0.0500893	−	0.120926i
$370$			8.94163i			0.464853i
$371$	17.0725	+	7.07168i	0.886362	+	0.367143i
$372$	−20.1446	+	20.1446i	−1.04445	+	1.04445i
$373$	−6.84073			−0.354200			−0.177100	−	0.984193i	$-0.556672\pi$
$373$	−6.84073			−0.354200			−0.177100	+	0.984193i	$0.556672\pi$
$374$	7.11170	+	1.94012i	0.367737	+	0.100321i
$375$	23.6621			1.22190
$376$	−11.5659	+	11.5659i	−0.596464	+	0.596464i
$377$	6.16383	+	2.55314i	0.317454	+	0.131494i
$378$			3.78562i			0.194711i
$379$	5.29952	−	12.7942i	0.272218	−	0.657192i	−0.727360	−	0.686257i	$-0.759253\pi$
$379$	5.29952	−	12.7942i	0.272218	−	0.657192i	0.999578	+	0.0290643i	$0.00925275\pi$
$380$	1.82013	−	0.753921i	0.0933705	−	0.0386753i
$381$	−8.44601	−	20.3905i	−0.432702	−	1.04464i
$382$	5.47004	+	5.47004i	0.279871	+	0.279871i
$383$	−23.9054	−	23.9054i	−1.22151	−	1.22151i	−0.967096	−	0.254412i	$-0.918118\pi$
$383$	−23.9054	−	23.9054i	−1.22151	−	1.22151i	−0.254412	−	0.967096i	$-0.581882\pi$
$384$	9.73453	+	23.5012i	0.496763	+	1.19929i
$385$	−27.9334	+	11.5704i	−1.42362	+	0.589683i
$386$	−4.02123	+	9.70811i	−0.204675	+	0.494130i
$387$		−	2.04020i		−	0.103709i
$388$	−14.0513	−	5.82023i	−0.713345	−	0.295477i
$389$	−21.0543	+	21.0543i	−1.06749	+	1.06749i	−0.0699425	+	0.997551i	$0.522282\pi$
$389$	−21.0543	+	21.0543i	−1.06749	+	1.06749i	−0.997551	+	0.0699425i	$0.977718\pi$
$390$	−3.82699			−0.193787
$391$	−1.67878	−	2.93836i	−0.0848993	−	0.148599i
$392$	10.4930			0.529977
$393$	−15.2700	+	15.2700i	−0.770271	+	0.770271i
$394$	−1.81357	−	0.751205i	−0.0913663	−	0.0378452i
$395$			3.85038i			0.193734i
$396$	4.96414	−	11.9845i	0.249457	−	0.602243i
$397$	−5.61458	+	2.32564i	−0.281788	+	0.116720i	−0.519101	−	0.854713i	$-0.673733\pi$
$397$	−5.61458	+	2.32564i	−0.281788	+	0.116720i	0.237313	+	0.971433i	$0.423733\pi$
$398$	3.52732	+	8.51570i	0.176809	+	0.426854i
$399$	2.69917	+	2.69917i	0.135127	+	0.135127i
$400$	0.936094	+	0.936094i	0.0468047	+	0.0468047i
$401$	−9.02368	−	21.7851i	−0.450621	−	1.08790i	−0.972086	−	0.234623i	$-0.924614\pi$
$401$	−9.02368	−	21.7851i	−0.450621	−	1.08790i	0.521466	−	0.853272i	$-0.325386\pi$
$402$	5.99599	−	2.48362i	0.299053	−	0.123872i
$403$	−4.06656	+	9.81754i	−0.202570	+	0.489046i
$404$		−	0.190645i		−	0.00948494i
$405$	−23.7643	−	9.84350i	−1.18086	−	0.489127i
$406$	−5.63580	+	5.63580i	−0.279700	+	0.279700i
$407$	−27.9287			−1.38438
$408$	14.9079	−	8.51733i	0.738050	−	0.421671i
$409$	4.07509			0.201500			0.100750	−	0.994912i	$-0.467876\pi$
$409$	4.07509			0.201500			0.100750	+	0.994912i	$0.467876\pi$
$410$	1.01011	−	1.01011i	0.0498856	−	0.0498856i
$411$	34.2970	+	14.2063i	1.69175	+	0.700744i
$412$		−	3.05923i		−	0.150718i
$413$	2.59496	−	6.26479i	0.127690	−	0.308270i
$414$	0.763967	−	0.316445i	0.0375469	−	0.0155524i
$415$	−2.58010	−	6.22890i	−0.126652	−	0.305765i
$416$	5.19087	+	5.19087i	0.254503	+	0.254503i
$417$	−26.1497	−	26.1497i	−1.28056	−	1.28056i
$418$	−0.326987	−	0.789416i	−0.0159935	−	0.0386116i
$419$	11.9721	−	4.95901i	0.584876	−	0.242264i	−0.0705683	−	0.997507i	$-0.522481\pi$
$419$	11.9721	−	4.95901i	0.584876	−	0.242264i	0.655445	+	0.755243i	$0.272481\pi$
$420$	−12.5998	+	30.4185i	−0.614805	+	1.48427i
$421$			39.9136i			1.94527i	0.232341	+	0.972635i	$0.425362\pi$
$421$			39.9136i			1.94527i	−0.232341	+	0.972635i	$0.574638\pi$
$422$	7.99782	+	3.31281i	0.389328	+	0.161265i
$423$	12.7216	−	12.7216i	0.618548	−	0.618548i
$424$	−9.63438			−0.467887
$425$	1.28734	−	1.66207i	0.0624454	−	0.0806222i
$426$	10.7853			0.522548
$427$	−22.2966	+	22.2966i	−1.07901	+	1.07901i
$428$	−1.43674	−	0.595116i	−0.0694473	−	0.0287660i
$429$		−	11.9534i		−	0.577116i
$430$	0.443585	−	1.07091i	0.0213915	−	0.0516438i
$431$	5.26248	−	2.17979i	0.253485	−	0.104997i	−0.252323	−	0.967643i	$-0.581195\pi$
$431$	5.26248	−	2.17979i	0.253485	−	0.104997i	0.505808	+	0.862646i	$0.331195\pi$
$432$	2.14095	+	5.16870i	0.103006	+	0.248679i
$433$	−19.5117	−	19.5117i	−0.937674	−	0.937674i	0.0604941	−	0.998169i	$-0.480732\pi$
$433$	−19.5117	−	19.5117i	−0.937674	−	0.937674i	−0.998169	+	0.0604941i	$0.980732\pi$
$434$	−8.97651	−	8.97651i	−0.430886	−	0.430886i
$435$	−9.14899	−	22.0876i	−0.438661	−	1.05902i
$436$	−3.60706	+	1.49409i	−0.172747	+	0.0715540i
$437$	−0.150112	+	0.362402i	−0.00718082	+	0.0173360i
$438$			12.9838i			0.620389i
$439$	−18.7076	−	7.74894i	−0.892865	−	0.369837i	−0.111393	−	0.993776i	$-0.535531\pi$
$439$	−18.7076	−	7.74894i	−0.892865	−	0.369837i	−0.781473	+	0.623940i	$0.785531\pi$
$440$	11.1464	−	11.1464i	0.531385	−	0.531385i
$441$	−11.5416			−0.549599
$442$	1.83351	−	2.36722i	0.0872113	−	0.112597i
$443$	−33.4695			−1.59019			−0.795093	−	0.606488i	$-0.792578\pi$
$443$	−33.4695			−1.59019			−0.795093	+	0.606488i	$0.792578\pi$
$444$	−21.5055	+	21.5055i	−1.02061	+	1.02061i
$445$	0.571193	+	0.236596i	0.0270771	+	0.0112157i
$446$		−	5.94818i		−	0.281654i
$447$	−19.4698	+	47.0043i	−0.920890	+	2.22322i
$448$	8.96539	−	3.71359i	0.423575	−	0.175450i
$449$	12.5594	+	30.3211i	0.592715	+	1.43094i	0.880871	+	0.473357i	$0.156958\pi$
$449$	12.5594	+	30.3211i	0.592715	+	1.43094i	−0.288156	+	0.957583i	$0.593042\pi$
$450$	0.363242	+	0.363242i	0.0171234	+	0.0171234i
$451$	3.15502	+	3.15502i	0.148564	+	0.148564i
$452$	8.14426	+	19.6620i	0.383074	+	0.924822i
$453$	35.0848	−	14.5326i	1.64843	−	0.682800i
$454$	3.80560	−	9.18754i	0.178606	−	0.431192i
$455$			12.2810i			0.575744i
$456$	−1.83866	−	0.761598i	−0.0861031	−	0.0356651i
$457$	6.67770	−	6.67770i	0.312370	−	0.312370i	−0.533457	−	0.845827i	$-0.679108\pi$
$457$	6.67770	−	6.67770i	0.312370	−	0.312370i	0.845827	+	0.533457i	$0.179108\pi$
$458$	14.3387			0.670003
$459$	7.71416	−	4.40734i	0.360066	−	0.205717i
$460$	−3.38340			−0.157752
$461$	20.7414	−	20.7414i	0.966022	−	0.966022i	−0.0334197	−	0.999441i	$-0.510640\pi$
$461$	20.7414	−	20.7414i	0.966022	−	0.966022i	0.999441	+	0.0334197i	$0.0106398\pi$
$462$	13.1930	+	5.46471i	0.613792	+	0.254241i
$463$		−	31.9157i		−	1.48325i	−0.670814	−	0.741625i	$-0.734055\pi$
$463$		−	31.9157i		−	1.48325i	0.670814	−	0.741625i	$-0.265945\pi$
$464$	−4.50754	+	10.8822i	−0.209257	+	0.505192i
$465$	35.1804	−	14.5722i	1.63145	−	0.675769i
$466$	−1.62222	−	3.91638i	−0.0751478	−	0.181423i
$467$	−0.405595	−	0.405595i	−0.0187687	−	0.0187687i	0.697660	−	0.716429i	$-0.254225\pi$
$467$	−0.405595	−	0.405595i	−0.0187687	−	0.0187687i	−0.716429	+	0.697660i	$0.754225\pi$
$468$	−3.72576	−	3.72576i	−0.172223	−	0.172223i
$469$	−7.97008	−	19.2415i	−0.368024	−	0.888488i
$470$	9.44360	−	3.91167i	0.435601	−	0.180432i
$471$	9.94338	−	24.0054i	0.458167	−	1.10611i
$472$			3.53535i			0.162728i
$473$	3.34493	+	1.38551i	0.153800	+	0.0637060i
$474$	1.28590	−	1.28590i	0.0590633	−	0.0590633i
$475$	−0.243684			−0.0111810
$476$	−12.7791	−	22.3672i	−0.585727	−	1.02520i
$477$	10.5971			0.485210
$478$	−0.662916	+	0.662916i	−0.0303211	+	0.0303211i
$479$	−2.83541	−	1.17447i	−0.129553	−	0.0536628i	0.316965	−	0.948437i	$-0.397336\pi$
$479$	−2.83541	−	1.17447i	−0.129553	−	0.0536628i	−0.446518	+	0.894774i	$0.647336\pi$
$480$		−	26.3059i		−	1.20069i
$481$	−4.34127	+	10.4808i	−0.197945	+	0.477881i
$482$	−6.11903	+	2.53458i	−0.278714	+	0.115447i
$483$	−2.50871	−	6.05657i	−0.114150	−	0.275584i
$484$	2.61789	+	2.61789i	0.118995	+	0.118995i
$485$	14.3746	+	14.3746i	0.652718	+	0.652718i
$486$	3.42748	+	8.27467i	0.155474	+	0.375347i
$487$	−13.1774	+	5.45824i	−0.597124	+	0.247337i	−0.660712	−	0.750640i	$-0.729746\pi$
$487$	−13.1774	+	5.45824i	−0.597124	+	0.247337i	0.0635884	+	0.997976i	$0.479746\pi$
$488$	6.29122	−	15.1883i	0.284790	−	0.687544i
$489$		−	14.5176i		−	0.656508i
$490$	−6.05821	−	2.50939i	−0.273682	−	0.113363i
$491$	−10.7432	+	10.7432i	−0.484832	+	0.484832i	−0.906671	−	0.421839i	$-0.861385\pi$
$491$	−10.7432	+	10.7432i	−0.484832	+	0.484832i	0.421839	+	0.906671i	$0.361385\pi$
$492$	4.85881			0.219052
$493$	18.0458	+	4.92300i	0.812740	+	0.221721i
$494$	−0.347070			−0.0156154
$495$	−12.2603	+	12.2603i	−0.551058	+	0.551058i
$496$	−17.3327	−	7.17945i	−0.778262	−	0.322367i
$497$		−	34.6105i		−	1.55249i
$498$	−1.21858	+	2.94191i	−0.0546058	+	0.131830i
$499$	14.8775	−	6.16245i	0.666007	−	0.275869i	−0.0239569	−	0.999713i	$-0.507626\pi$
$499$	14.8775	−	6.16245i	0.666007	−	0.275869i	0.689964	+	0.723844i	$0.257626\pi$
$500$	7.08319	+	17.1003i	0.316770	+	0.764750i
$501$	−21.8608	−	21.8608i	−0.976670	−	0.976670i
$502$	−8.79385	−	8.79385i	−0.392489	−	0.392489i
$503$	−0.832371	−	2.00952i	−0.0371136	−	0.0896001i	0.904236	−	0.427033i	$-0.140441\pi$
$503$	−0.832371	−	2.00952i	−0.0371136	−	0.0896001i	−0.941349	+	0.337433i	$0.890441\pi$
$504$	12.4383	−	5.15213i	0.554048	−	0.229494i
$505$	−0.0975160	+	0.235424i	−0.00433941	+	0.0104763i
$506$			1.46743i			0.0652352i
$507$	22.4782	+	9.31076i	0.998290	+	0.413505i
$508$	12.2077	−	12.2077i	0.541629	−	0.541629i
$509$	−37.4180			−1.65852			−0.829262	−	0.558860i	$-0.811239\pi$
$509$	−37.4180			−1.65852			−0.829262	+	0.558860i	$0.811239\pi$
$510$	−10.6441	+	1.35233i	−0.471328	+	0.0598823i
$511$	41.6657			1.84318
$512$	−15.9750	+	15.9750i	−0.706001	+	0.706001i
$513$	−0.951425	−	0.394093i	−0.0420064	−	0.0173996i
$514$			12.1360i			0.535296i
$515$	−1.56481	+	3.77780i	−0.0689540	+	0.166470i
$516$	3.64250	−	1.50877i	0.160352	−	0.0664200i
$517$	12.2179	+	29.4966i	0.537342	+	1.29726i
$518$	−9.58291	−	9.58291i	−0.421049	−	0.421049i
$519$	−5.45897	−	5.45897i	−0.239622	−	0.239622i
$520$	−2.45028	−	5.91550i	−0.107452	−	0.259412i
$521$	28.8907	−	11.9669i	1.26573	−	0.524281i	0.354064	−	0.935221i	$-0.384800\pi$
$521$	28.8907	−	11.9669i	1.26573	−	0.524281i	0.911662	+	0.410941i	$0.134800\pi$
$522$	−1.74911	+	4.22272i	−0.0765563	+	0.184823i
$523$			4.49861i			0.196711i	0.995151	+	0.0983553i	$0.0313582\pi$
$523$			4.49861i			0.196711i	−0.995151	+	0.0983553i	$0.968642\pi$
$524$	−15.6065	−	6.46444i	−0.681775	−	0.282400i
$525$	2.87971	−	2.87971i	0.125681	−	0.125681i
$526$	−12.1887			−0.531451
$527$	−7.84118	+	28.7427i	−0.341567	+	1.25205i
$528$	21.1036			0.918415
$529$	−15.7871	+	15.7871i	−0.686396	+	0.686396i
$530$	5.56247	+	2.30405i	0.241618	+	0.100082i
$531$		−	3.88863i		−	0.168752i
$532$	−1.14267	+	2.75865i	−0.0495411	+	0.119603i
$533$	1.67440	−	0.693557i	0.0725261	−	0.0300413i
$534$	−0.111744	−	0.269774i	−0.00483564	−	0.0116743i
$535$	1.46980	+	1.46980i	0.0635449	+	0.0635449i
$536$	7.67801	+	7.67801i	0.331640	+	0.331640i
$537$	−8.01055	−	19.3392i	−0.345681	−	0.834547i
$538$	−3.07659	+	1.27436i	−0.132641	+	0.0549418i
$539$	7.83796	−	18.9225i	0.337605	−	0.815051i
$540$		−	8.88253i		−	0.382243i
$541$	35.3707	+	14.6510i	1.52071	+	0.629897i	0.977733	−	0.209853i	$-0.0672986\pi$
$541$	35.3707	+	14.6510i	1.52071	+	0.629897i	0.542973	+	0.839750i	$0.317299\pi$
$542$	−1.93915	+	1.93915i	−0.0832937	+	0.0832937i
$543$	−13.9170			−0.597236
$544$	16.2717	+	12.6032i	0.697644	+	0.540356i
$545$	5.21853			0.223537
$546$	4.10146	−	4.10146i	0.175526	−	0.175526i
$547$	−16.5746	−	6.86541i	−0.708678	−	0.293544i	−0.000920364	−	1.00000i	$-0.500293\pi$
$547$	−16.5746	−	6.86541i	−0.708678	−	0.293544i	−0.707757	+	0.706456i	$0.750293\pi$
$548$			29.0387i			1.24047i
$549$	−6.91990	+	16.7061i	−0.295334	+	0.712999i
$550$	−0.842219	+	0.348859i	−0.0359123	+	0.0148754i
$551$	−0.829722	−	2.00313i	−0.0353473	−	0.0853360i
$552$	2.41678	+	2.41678i	0.102865	+	0.102865i
$553$	−4.12652	−	4.12652i	−0.175478	−	0.175478i
$554$	−5.10196	−	12.3172i	−0.216761	−	0.523308i
$555$	37.5570	−	15.5566i	1.59420	−	0.660341i
$556$	11.0703	−	26.7260i	0.469483	−	1.13343i
$557$			32.1089i			1.36050i	0.732981	+	0.680250i	$0.238129\pi$
$557$			32.1089i			1.36050i	−0.732981	+	0.680250i	$0.761871\pi$
$558$	−6.72580	−	2.78592i	−0.284726	−	0.117937i
$559$	1.03988	−	1.03988i	0.0439821	−	0.0439821i
$560$	−21.6820			−0.916232
$561$	−4.22394	−	33.2462i	−0.178335	−	1.40366i
$562$	−2.46946			−0.104168
$563$	14.4927	−	14.4927i	0.610796	−	0.610796i	−0.332358	−	0.943153i	$-0.607844\pi$
$563$	14.4927	−	14.4927i	0.610796	−	0.610796i	0.943153	+	0.332358i	$0.107844\pi$
$564$	32.1207	+	13.3048i	1.35253	+	0.560235i
$565$		−	28.4461i		−	1.19674i
$566$	0.214660	−	0.518236i	0.00902285	−	0.0217831i
$567$	36.0181	−	14.9192i	1.51262	−	0.626547i
$568$	6.90540	+	16.6711i	0.289744	+	0.699504i
$569$	−25.9741	−	25.9741i	−1.08889	−	1.08889i	−0.995643	−	0.0932500i	$-0.970274\pi$
$569$	−25.9741	−	25.9741i	−1.08889	−	1.08889i	−0.0932500	−	0.995643i	$-0.529726\pi$
$570$	0.879427	+	0.879427i	0.0368352	+	0.0368352i
$571$	3.30602	+	7.98144i	0.138353	+	0.334013i	0.977836	−	0.209373i	$-0.0671422\pi$
$571$	3.30602	+	7.98144i	0.138353	+	0.334013i	−0.839483	+	0.543385i	$0.817142\pi$
$572$	8.63861	−	3.57823i	0.361199	−	0.149613i
$573$	13.4587	−	32.4922i	0.562246	−	1.35738i
$574$			2.16510i			0.0903695i
$575$	0.386642	+	0.160153i	0.0161241	+	0.00667882i
$576$	3.93500	−	3.93500i	0.163958	−	0.163958i
$577$	−39.9974			−1.66511			−0.832556	−	0.553940i	$-0.813124\pi$
$577$	−39.9974			−1.66511			−0.832556	+	0.553940i	$0.813124\pi$
$578$	4.26308	−	7.23188i	0.177321	−	0.300807i
$579$	47.7725			1.98536
$580$	13.2238	−	13.2238i	0.549087	−	0.549087i
$581$	9.44076	+	3.91049i	0.391669	+	0.162234i
$582$		−	9.60128i		−	0.397986i
$583$	−7.19659	+	17.3741i	−0.298052	+	0.719562i
$584$	−20.0694	+	8.31303i	−0.830479	+	0.343996i
$585$	2.69514	+	6.50664i	0.111430	+	0.269016i
$586$	−1.56251	−	1.56251i	−0.0645468	−	0.0645468i
$587$	−9.06836	−	9.06836i	−0.374291	−	0.374291i	0.494746	−	0.869038i	$-0.335261\pi$
$587$	−9.06836	−	9.06836i	−0.374291	−	0.374291i	−0.869038	+	0.494746i	$0.835261\pi$
$588$	−8.53526	−	20.6059i	−0.351988	−	0.849774i
$589$	3.19051	−	1.32155i	0.131463	−	0.0544536i
$590$	0.845475	−	2.04116i	0.0348076	−	0.0840331i
$591$			8.92437i			0.367099i
$592$	−18.5036	−	7.66445i	−0.760494	−	0.315007i
$593$	8.83959	−	8.83959i	0.362998	−	0.362998i	−0.501917	−	0.864916i	$-0.667372\pi$
$593$	8.83959	−	8.83959i	0.362998	−	0.362998i	0.864916	+	0.501917i	$0.167372\pi$
$594$	−3.85249			−0.158069
$595$	4.33972	+	34.1574i	0.177911	+	1.40032i
$596$	−39.7977			−1.63018
$597$	29.6312	−	29.6312i	1.21272	−	1.21272i
$598$	0.550679	+	0.228099i	0.0225190	+	0.00932766i
$599$		−	37.5401i		−	1.53385i	−0.641739	−	0.766923i	$-0.721787\pi$
$599$		−	37.5401i		−	1.53385i	0.641739	−	0.766923i	$-0.278213\pi$
$600$	−0.812540	+	1.96164i	−0.0331718	+	0.0800838i
$601$	42.0424	−	17.4145i	1.71495	−	0.710354i	0.715009	−	0.699115i	$-0.246422\pi$
$601$	42.0424	−	17.4145i	1.71495	−	0.710354i	0.999937	−	0.0112389i	$-0.00357754\pi$
$602$	0.672314	+	1.62311i	0.0274015	+	0.0661530i
$603$	−8.44527	−	8.44527i	−0.343918	−	0.343918i
$604$	21.0051	+	21.0051i	0.854686	+	0.854686i
$605$	−1.89373	−	4.57186i	−0.0769910	−	0.185873i
$606$	0.111191	−	0.0460568i	0.00451683	−	0.00187093i
$607$	10.4460	−	25.2190i	0.423992	−	1.02361i	−0.557166	−	0.830401i	$-0.688111\pi$
$607$	10.4460	−	25.2190i	0.423992	−	1.02361i	0.981158	−	0.193206i	$-0.0618886\pi$
$608$		−	2.38568i		−	0.0967520i
$609$	33.4768	+	13.8666i	1.35655	+	0.561902i
$610$	−7.26456	+	7.26456i	−0.294133	+	0.294133i
$611$	12.9683			0.524641
$612$	−11.6791	−	9.04596i	−0.472099	−	0.365661i
$613$	22.9450			0.926740			0.463370	−	0.886165i	$-0.346640\pi$
$613$	22.9450			0.926740			0.463370	+	0.886165i	$0.346640\pi$
$614$	−6.03519	+	6.03519i	−0.243560	+	0.243560i
$615$	−6.00007	−	2.48531i	−0.241946	−	0.100217i
$616$			23.8916i			0.962621i
$617$	−0.372732	+	0.899854i	−0.0150056	+	0.0362268i	−0.931205	−	0.364496i	$-0.881241\pi$
$617$	−0.372732	+	0.899854i	−0.0150056	+	0.0362268i	0.916199	+	0.400723i	$0.131241\pi$
$618$	1.78425	−	0.739062i	0.0717732	−	0.0297294i
$619$	−10.2765	−	24.8096i	−0.413046	−	0.997182i	−0.984315	−	0.176419i	$-0.943549\pi$
$619$	−10.2765	−	24.8096i	−0.413046	−	0.997182i	0.571269	−	0.820763i	$-0.306451\pi$
$620$	21.0624	+	21.0624i	0.845885	+	0.845885i
$621$	1.25058	+	1.25058i	0.0501840	+	0.0501840i
$622$	0.338355	+	0.816861i	0.0135668	+	0.0327531i
$623$	−0.865721	+	0.358593i	−0.0346844	+	0.0143667i
$624$	3.28036	−	7.91950i	0.131320	−	0.317034i
$625$		−	27.2894i		−	1.09158i
$626$	2.33036	+	0.965266i	0.0931398	+	0.0385798i
$627$	−2.74685	+	2.74685i	−0.109698	+	0.109698i
$628$	20.3250			0.811056
$629$	−8.37089	+	30.6843i	−0.333769	+	1.22346i
$630$	−8.41349			−0.335201
$631$	−25.7227	+	25.7227i	−1.02401	+	1.02401i	−0.0243013	+	0.999705i	$0.507736\pi$
$631$	−25.7227	+	25.7227i	−1.02401	+	1.02401i	−0.999705	+	0.0243013i	$0.992264\pi$
$632$	2.81097	+	1.16434i	0.111814	+	0.0463150i
$633$		−	39.3564i		−	1.56428i
$634$	5.14809	−	12.4286i	0.204457	−	0.493602i
$635$	−21.3194	+	8.83078i	−0.846034	+	0.350439i
$636$	7.83682	+	18.9198i	0.310750	+	0.750217i
$637$	−5.88267	−	5.88267i	−0.233080	−	0.233080i
$638$	−5.73535	−	5.73535i	−0.227065	−	0.227065i
$639$	−7.59546	−	18.3371i	−0.300472	−	0.725403i
$640$	24.5719	−	10.1780i	0.971288	−	0.402321i
$641$	15.0049	−	36.2250i	0.592657	−	1.43080i	−0.288270	−	0.957549i	$-0.593080\pi$
$641$	15.0049	−	36.2250i	0.592657	−	1.43080i	0.880927	−	0.473252i	$-0.156920\pi$
$642$		−	0.981727i		−	0.0387457i
$643$	24.3498	+	10.0860i	0.960264	+	0.397754i	0.807079	−	0.590443i	$-0.201047\pi$
$643$	24.3498	+	10.0860i	0.960264	+	0.397754i	0.153185	+	0.988198i	$0.451047\pi$
$644$	3.62605	−	3.62605i	0.142886	−	0.142886i
$645$	−5.26981			−0.207499
$646$	−0.965310	+	0.122643i	−0.0379796	+	0.00482533i
$647$	−43.2311			−1.69959			−0.849795	−	0.527113i	$-0.823274\pi$
$647$	−43.2311			−1.69959			−0.849795	+	0.527113i	$0.823274\pi$
$648$	−14.3725	+	14.3725i	−0.564604	+	0.564604i
$649$	6.37545	+	2.64080i	0.250258	+	0.103660i
$650$			0.370285i			0.0145238i
$651$	−22.0862	+	53.3207i	−0.865625	+	2.08980i
$652$	10.4917	−	4.34581i	0.410887	−	0.170195i
$653$	4.98399	+	12.0324i	0.195039	+	0.470865i	0.990898	−	0.134617i	$-0.0429805\pi$
$653$	4.98399	+	12.0324i	0.195039	+	0.470865i	−0.795859	+	0.605482i	$0.792980\pi$
$654$	−1.74282	−	1.74282i	−0.0681495	−	0.0681495i
$655$	15.9657	+	15.9657i	0.623830	+	0.623830i
$656$	1.22446	+	2.95612i	0.0478073	+	0.115417i
$657$	22.0750	−	9.14375i	0.861226	−	0.356732i
$658$	−5.92867	+	14.3131i	−0.231124	+	0.557982i
$659$			30.5072i			1.18839i	0.804321	+	0.594195i	$0.202529\pi$
$659$			30.5072i			1.18839i	−0.804321	+	0.594195i	$0.797471\pi$
$660$	−30.9558	−	12.8223i	−1.20495	−	0.499108i
$661$	−10.2695	+	10.2695i	−0.399436	+	0.399436i	−0.878034	−	0.478598i	$-0.841145\pi$
$661$	−10.2695	+	10.2695i	−0.399436	+	0.399436i	0.478598	+	0.878034i	$0.341145\pi$
$662$	−7.27388			−0.282707
$663$	−13.1328	−	3.58272i	−0.510036	−	0.139141i
$664$	−5.32761			−0.206751
$665$	2.82213	−	2.82213i	0.109438	−	0.109438i
$666$	−7.18015	−	2.97412i	−0.278225	−	0.115245i
$667$			3.72357i			0.144177i
$668$	9.25461	−	22.3426i	0.358071	−	0.864461i
$669$	−24.9837	+	10.3486i	−0.965927	+	0.400100i
$670$	−2.59676	−	6.26914i	−0.100322	−	0.242198i
$671$	−22.6905	−	22.6905i	−0.875956	−	0.875956i
$672$	28.1925	+	28.1925i	1.08755	+	1.08755i
$673$	−1.89427	−	4.57316i	−0.0730186	−	0.176282i	0.883156	−	0.469079i	$-0.155414\pi$
$673$	−1.89427	−	4.57316i	−0.0730186	−	0.176282i	−0.956175	+	0.292797i	$0.905414\pi$
$674$	11.1141	−	4.60363i	0.428100	−	0.177325i
$675$	−0.420453	+	1.01506i	−0.0161833	+	0.0390698i
$676$			19.0319i			0.731996i
$677$	−44.3754	−	18.3809i	−1.70548	−	0.706434i	−0.705486	−	0.708724i	$-0.749271\pi$
$677$	−44.3754	−	18.3809i	−1.70548	−	0.706434i	−0.999997	+	0.00228946i	$0.999271\pi$
$678$	−9.50005	+	9.50005i	−0.364847	+	0.364847i
$679$	−30.8111			−1.18242
$680$	−8.90535	−	15.5870i	−0.341504	−	0.597735i
$681$	−45.2108			−1.73248
$682$	9.13507	−	9.13507i	0.349800	−	0.349800i
$683$	3.06064	+	1.26776i	0.117112	+	0.0485095i	0.440470	−	0.897767i	$-0.354812\pi$
$683$	3.06064	+	1.26776i	0.117112	+	0.0485095i	−0.323358	+	0.946277i	$0.604812\pi$
$684$			1.71233i			0.0654726i
$685$	14.8535	−	35.8594i	0.567521	−	1.37012i
$686$	−2.17970	+	0.902862i	−0.0832214	+	0.0344714i
$687$	−24.9464	−	60.2259i	−0.951764	−	2.29776i
$688$	1.83589	+	1.83589i	0.0699926	+	0.0699926i
$689$	5.40130	+	5.40130i	0.205773	+	0.205773i
$690$	−0.817375	−	1.97332i	−0.0311169	−	0.0751229i
$691$	5.18233	−	2.14659i	0.197145	−	0.0816602i	−0.281926	−	0.959436i	$-0.590973\pi$
$691$	5.18233	−	2.14659i	0.197145	−	0.0816602i	0.479072	+	0.877776i	$0.340973\pi$
$692$	2.31101	−	5.57927i	0.0878514	−	0.212092i
$693$		−	26.2791i		−	0.998261i
$694$	−6.42677	−	2.66205i	−0.243957	−	0.101050i
$695$	−27.3410	+	27.3410i	−1.03710	+	1.03710i
$696$	−18.8917			−0.716087
$697$	4.41194	−	2.52068i	0.167114	−	0.0954774i
$698$	−6.46868			−0.244843
$699$	−13.6274	+	13.6274i	−0.515436	+	0.515436i
$700$	2.94317	+	1.21910i	0.111242	+	0.0460777i
$701$		−	39.5851i		−	1.49511i	−0.664201	−	0.747554i	$-0.731228\pi$
$701$		−	39.5851i		−	1.49511i	0.664201	−	0.747554i	$-0.268772\pi$
$702$	−0.598835	+	1.44572i	−0.0226016	+	0.0545650i
$703$	3.40604	−	1.41083i	0.128461	−	0.0532104i
$704$	3.77918	+	9.12375i	0.142433	+	0.343864i
$705$	−32.8599	−	32.8599i	−1.23757	−	1.23757i
$706$	−1.09009	−	1.09009i	−0.0410260	−	0.0410260i
$707$	−0.147799	−	0.356818i	−0.00555855	−	0.0134195i
$708$	6.94263	−	2.87573i	0.260920	−	0.108077i
$709$	−10.0416	+	24.2425i	−0.377118	+	0.910444i	0.615385	+	0.788227i	$0.289001\pi$
$709$	−10.0416	+	24.2425i	−0.377118	+	0.910444i	−0.992503	+	0.122218i	$0.960999\pi$
$710$		−	11.2766i		−	0.423203i
$711$	−3.09186	−	1.28069i	−0.115954	−	0.0480297i
$712$	0.345453	−	0.345453i	0.0129464	−	0.0129464i
$713$	−5.93077			−0.222109
$714$	9.95813	−	12.8568i	0.372673	−	0.481152i
$715$	−12.4980			−0.467398
$716$	11.5783	−	11.5783i	0.432701	−	0.432701i
$717$	3.93774	+	1.63107i	0.147058	+	0.0609133i
$718$		−	14.0369i		−	0.523853i
$719$	−1.30910	+	3.16046i	−0.0488213	+	0.117865i	−0.946409	−	0.322972i	$-0.895318\pi$
$719$	−1.30910	+	3.16046i	−0.0488213	+	0.117865i	0.897587	+	0.440837i	$0.145318\pi$
$720$	−11.4874	+	4.75822i	−0.428109	+	0.177329i
$721$	−2.37169	−	5.72577i	−0.0883265	−	0.213239i
$722$	−6.55468	−	6.55468i	−0.243940	−	0.243940i
$723$	21.2917	+	21.2917i	0.791847	+	0.791847i
$724$	−4.16603	−	10.0577i	−0.154829	−	0.373791i
$725$	−2.13711	+	0.885220i	−0.0793703	+	0.0328763i
$726$	−0.894407	+	2.15929i	−0.0331946	+	0.0801388i
$727$			51.2362i			1.90024i	0.311878	+	0.950122i	$0.399042\pi$
$727$			51.2362i			1.90024i	−0.311878	+	0.950122i	$0.600958\pi$
$728$	8.96576	+	3.71374i	0.332293	+	0.137640i
$729$	5.54664	−	5.54664i	0.205431	−	0.205431i
$730$	13.5753			0.502444
$731$	2.52477	−	3.25968i	0.0933819	−	0.120564i
$732$	−34.9439			−1.29156
$733$	2.15810	−	2.15810i	0.0797114	−	0.0797114i	−0.666127	−	0.745838i	$-0.732049\pi$
$733$	2.15810	−	2.15810i	0.0797114	−	0.0797114i	0.745838	+	0.666127i	$0.232049\pi$
$734$	−12.9875	−	5.37960i	−0.479377	−	0.198565i
$735$			29.8118i			1.09962i
$736$	−1.56790	+	3.78524i	−0.0577936	+	0.139526i
$737$	19.5813	−	8.11086i	0.721288	−	0.298767i
$738$	0.475142	+	1.14709i	0.0174902	+	0.0422251i
$739$	3.36503	+	3.36503i	0.123785	+	0.123785i	0.766285	−	0.642500i	$-0.222103\pi$
$739$	3.36503	+	3.36503i	0.123785	+	0.123785i	−0.642500	+	0.766285i	$0.722103\pi$
$740$	22.4852	+	22.4852i	0.826572	+	0.826572i
$741$	0.603830	+	1.45778i	0.0221823	+	0.0535527i
$742$	−8.43070	+	3.49211i	−0.309501	+	0.128199i
$743$	−3.41211	+	8.23757i	−0.125178	+	0.302207i	−0.974028	−	0.226427i	$-0.927296\pi$
$743$	−3.41211	+	8.23757i	−0.125178	+	0.302207i	0.848850	+	0.528634i	$0.177296\pi$
$744$		−	30.0900i		−	1.10315i
$745$	49.1456	+	20.3568i	1.80056	+	0.745814i
$746$	2.38865	−	2.38865i	0.0874548	−	0.0874548i
$747$	5.86000			0.214406
$748$	22.7623	−	13.0048i	0.832271	−	0.475502i
$749$	−3.15042			−0.115114
$750$	−8.26234	+	8.26234i	−0.301698	+	0.301698i
$751$	−48.1684	−	19.9520i	−1.75769	−	0.728058i	−0.996867	−	0.0790969i	$-0.974796\pi$
$751$	−48.1684	−	19.9520i	−1.75769	−	0.728058i	−0.760821	−	0.648961i	$-0.775204\pi$
$752$			22.8953i			0.834907i
$753$	−21.6368	+	52.2358i	−0.788487	+	1.90358i
$754$	−3.04380	+	1.26078i	−0.110849	+	0.0459151i
$755$	−15.1946	−	36.6831i	−0.552990	−	1.33503i
$756$	9.51956	+	9.51956i	0.346223	+	0.346223i
$757$	−29.1718	−	29.1718i	−1.06027	−	1.06027i	−0.998063	−	0.0622039i	$-0.980187\pi$
$757$	−29.1718	−	29.1718i	−1.06027	−	1.06027i	−0.0622039	−	0.998063i	$-0.519813\pi$
$758$	2.61699	+	6.31797i	0.0950533	+	0.229479i
$759$	6.16355	−	2.55303i	0.223723	−	0.0926690i
$760$	−0.796293	+	1.92242i	−0.0288846	+	0.0697336i
$761$			32.9776i			1.19544i	0.801706	+	0.597718i	$0.203926\pi$
$761$			32.9776i			1.19544i	−0.801706	+	0.597718i	$0.796074\pi$
$762$	10.0691	+	4.17078i	0.364767	+	0.151091i
$763$	−5.59279	+	5.59279i	−0.202473	+	0.202473i
$764$	27.5106			0.995299
$765$	9.79525	+	17.1446i	0.354148	+	0.619865i
$766$	16.6946			0.603201
$767$	1.98201	−	1.98201i	0.0715663	−	0.0715663i
$768$	−0.290250	−	0.120225i	−0.0104735	−	0.00433826i
$769$		−	12.3695i		−	0.446055i	−0.974812	−	0.223027i	$-0.928406\pi$
$769$		−	12.3695i		−	0.446055i	0.974812	−	0.223027i	$-0.0715939\pi$
$770$	5.71366	−	13.7940i	0.205906	−	0.497101i
$771$	50.9741	−	21.1142i	1.83579	−	0.760408i
$772$	14.3006	+	34.5247i	0.514689	+	1.24257i
$773$	−3.75739	−	3.75739i	−0.135144	−	0.135144i	0.636299	−	0.771443i	$-0.280465\pi$
$773$	−3.75739	−	3.75739i	−0.135144	−	0.135144i	−0.771443	+	0.636299i	$0.780465\pi$
$774$	0.712399	+	0.712399i	0.0256066	+	0.0256066i
$775$	−1.40995	−	3.40392i	−0.0506468	−	0.122272i
$776$	14.8410	−	6.14734i	0.532761	−	0.220677i
$777$	−23.5782	+	56.9228i	−0.845863	+	2.04209i
$778$		−	14.7035i		−	0.527146i
$779$	−0.544146	−	0.225392i	−0.0194960	−	0.00807552i
$780$	−9.62361	+	9.62361i	−0.344580	+	0.344580i
$781$	35.2219			1.26034
$782$	1.61222	+	0.439823i	0.0576527	+	0.0157280i
$783$	−9.77560			−0.349351
$784$	10.3858	−	10.3858i	0.370920	−	0.370920i
$785$	−25.0990	−	10.3964i	−0.895823	−	0.371062i
$786$		−	10.6640i		−	0.380372i
$787$	−15.6150	+	37.6980i	−0.556616	+	1.34379i	0.355814	+	0.934557i	$0.384204\pi$
$787$	−15.6150	+	37.6980i	−0.556616	+	1.34379i	−0.912430	+	0.409233i	$0.865796\pi$
$788$	−6.44955	+	2.67149i	−0.229756	+	0.0951679i
$789$	21.2058	+	51.1952i	0.754945	+	1.82260i
$790$	−1.34448	−	1.34448i	−0.0478344	−	0.0478344i
$791$	30.4862	+	30.4862i	1.08396	+	1.08396i
$792$	5.24314	+	12.6581i	0.186307	+	0.449784i
$793$	−12.0420	+	4.98797i	−0.427625	+	0.177128i
$794$	1.14844	−	2.77257i	0.0407565	−	0.0983949i
$795$		−	27.3723i		−	0.970795i
$796$	30.2842	+	12.5441i	1.07339	+	0.444614i
$797$	8.01103	−	8.01103i	0.283765	−	0.283765i	−0.550843	−	0.834609i	$-0.685694\pi$
$797$	8.01103	−	8.01103i	0.283765	−	0.283765i	0.834609	+	0.550843i	$0.185694\pi$
$798$	−1.88500			−0.0667281
$799$	36.0689	−	4.58257i	1.27603	−	0.162120i
$800$	−2.54525			−0.0899883
$801$	−0.379974	+	0.379974i	−0.0134257	+	0.0134257i
$802$	10.7578	+	4.45604i	0.379872	+	0.157348i
$803$			42.4017i			1.49632i
$804$	8.83243	−	21.3234i	0.311496	−	0.752017i
$805$	−6.33249	+	2.62300i	−0.223191	+	0.0924487i
$806$	−2.00813	−	4.84806i	−0.0707335	−	0.170766i
$807$	10.7053	+	10.7053i	0.376843	+	0.376843i
$808$	0.142383	+	0.142383i	0.00500901	+	0.00500901i
$809$	2.01021	+	4.85307i	0.0706751	+	0.170625i	0.955270	−	0.295736i	$-0.0955649\pi$
$809$	2.01021	+	4.85307i	0.0706751	+	0.170625i	−0.884595	+	0.466361i	$0.845565\pi$
$810$	11.7352	−	4.86088i	0.412333	−	0.170794i
$811$	−14.8778	+	35.9183i	−0.522432	+	1.26126i	0.413957	+	0.910296i	$0.364146\pi$
$811$	−14.8778	+	35.9183i	−0.522432	+	1.26126i	−0.936389	+	0.350965i	$0.885854\pi$
$812$			28.3443i			0.994690i
$813$	11.5186	+	4.77117i	0.403976	+	0.167332i
$814$	9.75218	−	9.75218i	0.341814	−	0.341814i
$815$	−15.1790			−0.531695
$816$	6.32523	−	23.1858i	0.221427	−	0.811665i
$817$	−0.477919			−0.0167203
$818$	−1.42294	+	1.42294i	−0.0497520	+	0.0497520i
$819$	−9.86170	−	4.08485i	−0.344596	−	0.142736i
$820$		−	5.08016i		−	0.177407i
$821$	9.09208	−	21.9502i	0.317316	−	0.766068i	−0.682079	−	0.731279i	$-0.738924\pi$
$821$	9.09208	−	21.9502i	0.317316	−	0.766068i	0.999395	−	0.0347896i	$-0.0110761\pi$
$822$	−16.9364	+	7.01529i	−0.590725	+	0.244686i
$823$	−9.56400	−	23.0895i	−0.333380	−	0.804851i	−0.998319	−	0.0579534i	$-0.981543\pi$
$823$	−9.56400	−	23.0895i	−0.333380	−	0.804851i	0.664939	−	0.746898i	$-0.268457\pi$
$824$	2.28478	+	2.28478i	0.0795942	+	0.0795942i
$825$	2.93058	+	2.93058i	0.102030	+	0.102030i
$826$	1.28143	+	3.09365i	0.0445868	+	0.107642i
$827$	5.92798	−	2.45545i	0.206136	−	0.0853844i	−0.277226	−	0.960805i	$-0.589415\pi$
$827$	5.92798	−	2.45545i	0.206136	−	0.0853844i	0.483363	+	0.875420i	$0.339415\pi$
$828$	1.12537	−	2.71687i	0.0391092	−	0.0944179i
$829$		−	40.2898i		−	1.39932i	−0.714475	−	0.699661i	$-0.753334\pi$
$829$		−	40.2898i		−	1.39932i	0.714475	−	0.699661i	$-0.246666\pi$
$830$	3.07593	+	1.27409i	0.106767	+	0.0442244i
$831$	−42.8589	+	42.8589i	−1.48676	+	1.48676i
$832$	4.01129			0.139067
$833$	−18.4403	−	14.2828i	−0.638919	−	0.494870i
$834$	18.2619			0.632359
$835$	−22.8567	+	22.8567i	−0.790990	+	0.790990i
$836$	−2.80738	−	1.16285i	−0.0970953	−	0.0402182i
$837$		−	15.5702i		−	0.538186i
$838$	−2.44884	+	5.91203i	−0.0845939	+	0.204228i
$839$	25.4597	−	10.5457i	0.878965	−	0.364079i	0.102870	−	0.994695i	$-0.467197\pi$
$839$	25.4597	−	10.5457i	0.878965	−	0.364079i	0.776095	+	0.630615i	$0.217197\pi$
$840$	−13.3079	−	32.1281i	−0.459166	−	1.10853i
$841$	5.95278	+	5.95278i	0.205268	+	0.205268i
$842$	−13.9371	−	13.9371i	−0.480303	−	0.480303i
$843$	4.29635	+	10.3723i	0.147974	+	0.357241i
$844$	28.4424	−	11.7812i	0.979029	−	0.405527i
$845$	9.73492	−	23.5022i	0.334891	−	0.808500i
$846$			8.88431i			0.305449i
$847$	6.92929	+	2.87020i	0.238093	+	0.0986214i
$848$	−9.53591	+	9.53591i	−0.327464	+	0.327464i
$849$	−2.55018			−0.0875219
$850$	0.130846	+	1.02988i	0.00448800	+	0.0353245i
$851$	−6.33142			−0.217038
$852$	27.1213	−	27.1213i	0.929161	−	0.929161i
$853$	−24.8703	−	10.3016i	−0.851542	−	0.352720i	−0.0861480	−	0.996282i	$-0.527456\pi$
$853$	−24.8703	−	10.3016i	−0.851542	−	0.352720i	−0.765394	+	0.643562i	$0.777456\pi$
$854$		−	15.5711i		−	0.532832i
$855$	0.875867	−	2.11453i	0.0299540	−	0.0723154i
$856$	1.51749	−	0.628563i	0.0518666	−	0.0214838i
$857$	−19.5445	−	47.1845i	−0.667626	−	1.61179i	−0.785570	−	0.618773i	$-0.787630\pi$
$857$	−19.5445	−	47.1845i	−0.667626	−	1.61179i	0.117944	−	0.993020i	$-0.462370\pi$
$858$	4.17390	+	4.17390i	0.142495	+	0.142495i
$859$	11.1398	+	11.1398i	0.380085	+	0.380085i	0.871133	−	0.491047i	$-0.163386\pi$
$859$	11.1398	+	11.1398i	0.380085	+	0.380085i	−0.491047	+	0.871133i	$0.663386\pi$
$860$	−1.57751	−	3.80844i	−0.0537926	−	0.129867i
$861$	9.09393	−	3.76683i	0.309920	−	0.128373i
$862$	−1.07642	+	2.59870i	−0.0366629	+	0.0885121i
$863$			54.9174i			1.86941i	0.355424	+	0.934705i	$0.384337\pi$
$863$			54.9174i			1.86941i	−0.355424	+	0.934705i	$0.615663\pi$
$864$	−9.93751	−	4.11625i	−0.338081	−	0.140038i
$865$	−5.70766	+	5.70766i	−0.194066	+	0.194066i
$866$	13.6263			0.463039
$867$	−37.7925	−	5.32396i	−1.28350	−	0.180811i
$868$	−45.1458			−1.53235
$869$	4.19941	−	4.19941i	0.142455	−	0.142455i
$870$	10.9072	+	4.51792i	0.369790	+	0.153172i
$871$		−	8.60901i		−	0.291705i
$872$	1.57806	−	3.80978i	0.0534400	−	0.129016i
$873$	−16.3240	+	6.76164i	−0.552485	+	0.228847i
$874$	−0.0741277	−	0.178960i	−0.00250741	−	0.00605341i
$875$	26.5143	+	26.5143i	0.896348	+	0.896348i
$876$	32.6499	+	32.6499i	1.10314	+	1.10314i
$877$	−18.0791	−	43.6468i	−0.610487	−	1.47385i	−0.862467	−	0.506114i	$-0.831081\pi$
$877$	−18.0791	−	43.6468i	−0.610487	−	1.47385i	0.251979	−	0.967733i	$-0.418919\pi$
$878$	9.23812	−	3.82655i	0.311771	−	0.129140i
$879$	−3.84447	+	9.28137i	−0.129671	+	0.313053i
$880$		−	22.0650i		−	0.743810i
$881$	−7.11361	−	2.94655i	−0.239664	−	0.0992719i	0.259619	−	0.965711i	$-0.416403\pi$
$881$	−7.11361	−	2.94655i	−0.239664	−	0.0992719i	−0.499283	+	0.866439i	$0.666403\pi$
$882$	4.03010	−	4.03010i	0.135700	−	0.135700i
$883$	−0.0616120			−0.00207341			−0.00103670	−	0.999999i	$-0.500330\pi$
$883$	−0.0616120			−0.00207341			−0.00103670	+	0.999999i	$0.500330\pi$
$884$	−1.34209	−	10.5634i	−0.0451393	−	0.355287i
$885$	−10.0443			−0.337635
$886$	11.6869	−	11.6869i	0.392630	−	0.392630i
$887$	8.18489	+	3.39029i	0.274822	+	0.113835i	0.515838	−	0.856686i	$-0.327481\pi$
$887$	8.18489	+	3.39029i	0.274822	+	0.113835i	−0.241016	+	0.970521i	$0.577481\pi$
$888$		−	32.1227i		−	1.07797i
$889$	13.3843	−	32.3125i	0.448894	−	1.08373i
$890$	−0.282064	+	0.116835i	−0.00945481	+	0.00391631i
$891$	15.1827	+	36.6543i	0.508640	+	1.22797i
$892$	−14.9577	−	14.9577i	−0.500820	−	0.500820i
$893$	−2.98006	−	2.98006i	−0.0997239	−	0.0997239i
$894$	−9.61450	−	23.2115i	−0.321557	−	0.776308i
$895$	−20.2202	+	8.37548i	−0.675887	+	0.279961i
$896$	−15.4262	+	37.2421i	−0.515352	+	1.24417i
$897$		−	2.70983i		−	0.0904786i
$898$	−14.9730	−	6.20204i	−0.499657	−	0.206965i
$899$	23.1800	−	23.1800i	0.773097	−	0.773097i
$900$	1.82686			0.0608955
$901$	16.9313	+	13.1141i	0.564065	+	0.436893i
$902$	−2.20334			−0.0733633
$903$	5.64775	−	5.64775i	0.187945	−	0.187945i
$904$	−20.7670	−	8.60199i	−0.690702	−	0.286098i
$905$			14.5510i			0.483692i
$906$	−7.17643	+	17.3254i	−0.238421	+	0.575599i
$907$	2.59596	−	1.07528i	0.0861975	−	0.0357042i	−0.339168	−	0.940726i	$-0.610146\pi$
$907$	2.59596	−	1.07528i	0.0861975	−	0.0357042i	0.425366	+	0.905022i	$0.360146\pi$
$908$	−13.5338	−	32.6734i	−0.449134	−	1.08430i
$909$	−0.156611	−	0.156611i	−0.00519446	−	0.00519446i
$910$	−4.28831	−	4.28831i	−0.142156	−	0.142156i
$911$	−17.1443	−	41.3901i	−0.568017	−	1.37131i	−0.903224	−	0.429170i	$-0.858806\pi$
$911$	−17.1443	−	41.3901i	−0.568017	−	1.37131i	0.335206	−	0.942145i	$-0.391194\pi$
$912$	−2.57368	+	1.06605i	−0.0852231	+	0.0353006i
$913$	−3.97956	+	9.60752i	−0.131704	+	0.317962i
$914$			4.66345i			0.154253i
$915$	43.1517	+	17.8740i	1.42655	+	0.590897i
$916$	36.0570	−	36.0570i	1.19136	−	1.19136i
$917$	−34.2214			−1.13009
$918$	−1.15468	+	4.23260i	−0.0381101	+	0.139697i
$919$	39.4420			1.30107			0.650536	−	0.759476i	$-0.274544\pi$
$919$	39.4420			1.30107			0.650536	+	0.759476i	$0.274544\pi$
$920$	2.52688	−	2.52688i	0.0833089	−	0.0833089i
$921$	35.8492	+	14.8492i	1.18127	+	0.489299i
$922$			14.4850i			0.477037i
$923$	5.47493	−	13.2176i	0.180209	−	0.435064i
$924$	46.9178	−	19.4340i	1.54348	−	0.639331i
$925$	−1.50520	−	3.63386i	−0.0494905	−	0.119481i
$926$	11.1444	+	11.1444i	0.366227	+	0.366227i
$927$	−2.51310	−	2.51310i	−0.0825410	−	0.0825410i
$928$	−8.66634	−	20.9224i	−0.284487	−	0.686811i
$929$	15.0988	−	6.25411i	0.495374	−	0.205191i	−0.120987	−	0.992654i	$-0.538606\pi$
$929$	15.0988	−	6.25411i	0.495374	−	0.205191i	0.616362	+	0.787463i	$0.288606\pi$
$930$	−7.19599	+	17.3727i	−0.235966	+	0.569672i
$931$			2.70363i			0.0886078i
$932$	−13.9277	−	5.76905i	−0.456218	−	0.188972i
$933$	2.84234	−	2.84234i	0.0930540	−	0.0930540i
$934$	0.283252			0.00926830
$935$	−34.7608	+	4.41637i	−1.13680	+	0.144431i
$936$	5.56516			0.181903
$937$	−23.8970	+	23.8970i	−0.780680	+	0.780680i	−0.979946	−	0.199266i	$-0.936144\pi$
$937$	−23.8970	+	23.8970i	−0.780680	+	0.780680i	0.199266	+	0.979946i	$0.436144\pi$
$938$	9.50175	+	3.93575i	0.310243	+	0.128507i
$939$		−	11.4674i		−	0.374225i
$940$	13.9110	−	33.5840i	0.453725	−	1.09539i
$941$	−29.3895	+	12.1735i	−0.958070	+	0.396845i	−0.806258	−	0.591564i	$-0.798511\pi$
$941$	−29.3895	+	12.1735i	−0.958070	+	0.396845i	−0.151812	+	0.988409i	$0.548511\pi$
$942$	4.91020	+	11.8543i	0.159983	+	0.386233i
$943$	0.715239	+	0.715239i	0.0232914	+	0.0232914i
$944$	3.49921	+	3.49921i	0.113890	+	0.113890i
$945$	−6.88625	−	16.6249i	−0.224010	−	0.540807i
$946$	−1.65178	+	0.684189i	−0.0537040	+	0.0222449i
$947$	−2.46637	+	5.95435i	−0.0801463	+	0.193490i	−0.958873	−	0.283834i	$-0.908393\pi$
$947$	−2.46637	+	5.95435i	−0.0801463	+	0.193490i	0.878727	+	0.477325i	$0.158393\pi$
$948$		−	6.46721i		−	0.210045i
$949$	15.9120	+	6.59096i	0.516525	+	0.213952i
$950$	0.0850899	−	0.0850899i	0.00276068	−	0.00276068i
$951$	−61.1596			−1.98324
$952$	26.2489	+	7.16087i	0.850732	+	0.232085i
$953$	−8.44238			−0.273475			−0.136738	−	0.990607i	$-0.543662\pi$
$953$	−8.44238			−0.273475			−0.136738	+	0.990607i	$0.543662\pi$
$954$	−3.70032	+	3.70032i	−0.119802	+	0.119802i
$955$	−33.9724	−	14.0718i	−1.09932	−	0.455354i
$956$			3.33402i			0.107830i
$957$	−14.1115	+	34.0682i	−0.456160	+	1.10127i
$958$	1.40017	−	0.579971i	0.0452376	−	0.0187380i
$959$	22.5125	+	54.3499i	0.726965	+	1.75505i
$960$	−10.1641	−	10.1641i	−0.328044	−	0.328044i
$961$	15.0000	+	15.0000i	0.483871	+	0.483871i
$962$	−2.14379	−	5.17557i	−0.0691186	−	0.166867i
$963$	−1.66913	+	0.691375i	−0.0537869	+	0.0222792i
$964$	−9.01367	+	21.7609i	−0.290311	+	0.700872i
$965$		−	49.9488i		−	1.60791i
$966$	2.99083	+	1.23884i	0.0962285	+	0.0398592i
$967$	−3.16542	+	3.16542i	−0.101793	+	0.101793i	−0.756169	−	0.654376i	$-0.772931\pi$
$967$	−3.16542	+	3.16542i	−0.101793	+	0.101793i	0.654376	+	0.756169i	$0.272931\pi$
$968$	−3.91034			−0.125683
$969$	2.19457	+	3.84116i	0.0704998	+	0.123396i
$970$	−10.0387			−0.322323
$971$	29.7684	−	29.7684i	0.955312	−	0.955312i	−0.0437311	−	0.999043i	$-0.513924\pi$
$971$	29.7684	−	29.7684i	0.955312	−	0.955312i	0.999043	+	0.0437311i	$0.0139245\pi$
$972$	29.4270	+	12.1891i	0.943871	+	0.390964i
$973$		−	58.6036i		−	1.87875i
$974$	2.69537	−	6.50720i	0.0863652	−	0.208504i
$975$	1.55528	−	0.644220i	0.0498089	−	0.0206315i
$976$	−8.80619	−	21.2600i	−0.281879	−	0.680517i
$977$	−5.90805	−	5.90805i	−0.189015	−	0.189015i	0.606255	−	0.795270i	$-0.292671\pi$
$977$	−5.90805	−	5.90805i	−0.189015	−	0.189015i	−0.795270	+	0.606255i	$0.792671\pi$
$978$	5.06926	+	5.06926i	0.162097	+	0.162097i
$979$	−0.364928	−	0.881013i	−0.0116631	−	0.0281573i
$980$	−21.5447	+	8.92409i	−0.688219	+	0.285070i
$981$	−1.73576	+	4.19049i	−0.0554185	+	0.133792i
$982$		−	7.50262i		−	0.239418i
$983$	10.5470	+	4.36871i	0.336397	+	0.139340i	0.544486	−	0.838770i	$-0.316725\pi$
$983$	10.5470	+	4.36871i	0.336397	+	0.139340i	−0.208090	+	0.978110i	$0.566725\pi$
$984$	−3.62879	+	3.62879i	−0.115682	+	0.115682i
$985$	9.33093			0.297308
$986$	−8.02025	+	4.58222i	−0.255417	+	0.145928i
$987$	70.4330			2.24191
$988$	−0.872764	+	0.872764i	−0.0277663	+	0.0277663i
$989$	0.758292	+	0.314095i	0.0241123	+	0.00998763i
$990$		−	8.56210i		−	0.272122i
$991$	22.0510	−	53.2359i	0.700474	−	1.69109i	−0.0220582	−	0.999757i	$-0.507022\pi$
$991$	22.0510	−	53.2359i	0.700474	−	1.69109i	0.722532	−	0.691337i	$-0.242978\pi$
$992$	33.3245	−	13.8034i	1.05805	−	0.438260i
$993$	12.6551	+	30.5520i	0.401596	+	0.969539i
$994$	12.0853	+	12.0853i	0.383324	+	0.383324i
$995$	−30.9810	−	30.9810i	−0.982165	−	0.982165i
$996$	4.33360	+	10.4622i	0.137315	+	0.331509i
$997$	−39.8694	+	16.5144i	−1.26268	+	0.523018i	−0.910730	−	0.413003i	$-0.864480\pi$
$997$	−39.8694	+	16.5144i	−1.26268	+	0.523018i	−0.351946	+	0.936020i	$0.614480\pi$
$998$	−3.04312	+	7.34674i	−0.0963282	+	0.232557i
$999$		−	16.6221i		−	0.525899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.12	yes	128
17.2	even	8	inner	731.2.m.c.87.12	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.12	✓	128	17.2	even	8	inner
731.2.m.c.689.12	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.349181 + 0.349181i) q^{2} +(2.07415 + 0.859139i) q^{3} +1.75615i q^{4} +(0.898278 - 2.16864i) q^{5} +(-1.02425 + 0.424257i) q^{6} +(1.36146 + 3.28687i) q^{7} +(-1.31157 - 1.31157i) q^{8} +(1.44264 + 1.44264i) q^{9} +O(q^{10})\)	\(q+(-0.349181 + 0.349181i) q^{2} +(2.07415 + 0.859139i) q^{3} +1.75615i q^{4} +(0.898278 - 2.16864i) q^{5} +(-1.02425 + 0.424257i) q^{6} +(1.36146 + 3.28687i) q^{7} +(-1.31157 - 1.31157i) q^{8} +(1.44264 + 1.44264i) q^{9} +(0.443585 + 1.07091i) q^{10} +(-3.34493 + 1.38551i) q^{11} +(-1.50877 + 3.64250i) q^{12} +1.47061i q^{13} +(-1.62311 - 0.672314i) q^{14} +(3.72632 - 3.72632i) q^{15} -2.59634 q^{16} +(0.519665 + 4.09023i) q^{17} -1.00748 q^{18} +(0.337940 - 0.337940i) q^{19} +(3.80844 + 1.57751i) q^{20} +7.98713i q^{21} +(0.684189 - 1.65178i) q^{22} +(-0.758292 + 0.314095i) q^{23} +(-1.59357 - 3.84722i) q^{24} +(-0.360544 - 0.360544i) q^{25} +(-0.513508 - 0.513508i) q^{26} +(-0.824602 - 1.99077i) q^{27} +(-5.77222 + 2.39093i) q^{28} +(1.73611 - 4.19135i) q^{29} +2.60232i q^{30} +(6.67583 + 2.76522i) q^{31} +(3.52974 - 3.52974i) q^{32} -8.12821 q^{33} +(-1.60969 - 1.24677i) q^{34} +8.35099 q^{35} +(-2.53348 + 2.53348i) q^{36} +(7.12681 + 2.95202i) q^{37} +0.236004i q^{38} +(-1.26346 + 3.05026i) q^{39} +(-4.02249 + 1.66617i) q^{40} +(-0.471612 - 1.13857i) q^{41} +(-2.78895 - 2.78895i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-2.43316 - 5.87418i) q^{44} +(4.42445 - 1.83267i) q^{45} +(0.155105 - 0.374457i) q^{46} -8.81831i q^{47} +(-5.38518 - 2.23062i) q^{48} +(-4.00016 + 4.00016i) q^{49} +0.251790 q^{50} +(-2.43621 + 8.93019i) q^{51} -2.58260 q^{52} +(3.67283 - 3.67283i) q^{53} +(0.983073 + 0.407202i) q^{54} +8.49850i q^{55} +(2.52531 - 6.09663i) q^{56} +(0.991274 - 0.410599i) q^{57} +(0.857321 + 2.06976i) q^{58} +(-1.34775 - 1.34775i) q^{59} +(6.54396 + 6.54396i) q^{60} +(3.39177 + 8.18847i) q^{61} +(-3.29664 + 1.36551i) q^{62} +(-2.77766 + 6.70587i) q^{63} -2.72764i q^{64} +(3.18922 + 1.32102i) q^{65} +(2.83822 - 2.83822i) q^{66} -5.85404 q^{67} +(-7.18303 + 0.912607i) q^{68} -1.84266 q^{69} +(-2.91601 + 2.91601i) q^{70} +(-8.98787 - 3.72290i) q^{71} -3.78426i q^{72} +(4.48179 - 10.8200i) q^{73} +(-3.51934 + 1.45776i) q^{74} +(-0.438063 - 1.05758i) q^{75} +(0.593471 + 0.593471i) q^{76} +(-9.10800 - 9.10800i) q^{77} +(-0.623916 - 1.50627i) q^{78} +(-1.51547 + 0.627729i) q^{79} +(-2.33223 + 5.63051i) q^{80} -10.9582i q^{81} +(0.562246 + 0.232890i) q^{82} +(2.03100 - 2.03100i) q^{83} -14.0266 q^{84} +(9.33701 + 2.54720i) q^{85} +0.493816 q^{86} +(7.20190 - 7.20190i) q^{87} +(6.20432 + 2.56991i) q^{88} +0.263388i q^{89} +(-0.905001 + 2.18487i) q^{90} +(-4.83370 + 2.00218i) q^{91} +(-0.551596 - 1.33167i) q^{92} +(11.4709 + 11.4709i) q^{93} +(3.07919 + 3.07919i) q^{94} +(-0.429304 - 1.03643i) q^{95} +(10.3537 - 4.28866i) q^{96} +(-3.31421 + 8.00120i) q^{97} -2.79356i q^{98} +(-6.82432 - 2.82672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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