LMFDB - Embedded newform 108.3.j.a.103.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,3,Mod(7,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.28
Character	$\chi$	$=$	108.103
Dual form			108.3.j.a.43.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.72865 + 1.00588i) q^{2} +(-0.482718 - 2.96091i) q^{3} +(1.97643 + 3.47760i) q^{4} +(-0.0274809 + 0.0100022i) q^{5} +(2.14386 - 5.60392i) q^{6} +(11.2305 - 1.98024i) q^{7} +(-0.0814860 + 7.99958i) q^{8} +(-8.53397 + 2.85857i) q^{9} +(-0.0575657 - 0.0103520i) q^{10} +(4.17143 - 11.4609i) q^{11} +(9.34281 - 7.53073i) q^{12} +(0.356957 + 0.299523i) q^{13} +(21.4055 + 7.87337i) q^{14} +(0.0428812 + 0.0765402i) q^{15} +(-8.18744 + 13.7465i) q^{16} +(-6.07992 + 10.5307i) q^{17} +(-17.6276 - 3.64266i) q^{18} +(-14.4475 + 8.34127i) q^{19} +(-0.0890979 - 0.0757989i) q^{20} +(-11.2845 - 32.2967i) q^{21} +(18.7391 - 15.6159i) q^{22} +(-43.8264 - 7.72777i) q^{23} +(23.7254 - 3.62027i) q^{24} +(-19.1505 + 16.0691i) q^{25} +(0.315770 + 0.876822i) q^{26} +(12.5835 + 23.8884i) q^{27} +(29.0829 + 35.1415i) q^{28} +(0.0229535 - 0.0192603i) q^{29} +(-0.00286346 + 0.175444i) q^{30} +(41.6937 + 7.35173i) q^{31} +(-27.9804 + 15.5272i) q^{32} +(-35.9483 - 6.81883i) q^{33} +(-21.1026 + 12.0883i) q^{34} +(-0.288818 + 0.166749i) q^{35} +(-26.8078 - 24.0280i) q^{36} +(11.7529 - 20.3566i) q^{37} +(-33.3649 - 0.113285i) q^{38} +(0.714549 - 1.20150i) q^{39} +(-0.0777744 - 0.220651i) q^{40} +(-3.36469 - 2.82331i) q^{41} +(12.9795 - 67.1803i) q^{42} +(12.3880 - 34.0357i) q^{43} +(48.1010 - 8.14511i) q^{44} +(0.205929 - 0.163915i) q^{45} +(-67.9871 - 57.4425i) q^{46} +(-45.6736 + 8.05348i) q^{47} +(44.6543 + 17.6066i) q^{48} +(76.1584 - 27.7194i) q^{49} +(-49.2679 + 8.51488i) q^{50} +(34.1154 + 12.9187i) q^{51} +(-0.336120 + 1.83334i) q^{52} +10.6210 q^{53} +(-2.27643 + 53.9520i) q^{54} +0.356679i q^{55} +(14.9260 + 90.0009i) q^{56} +(31.6718 + 38.7513i) q^{57} +(0.0590519 - 0.0102058i) q^{58} +(-16.2907 - 44.7583i) q^{59} +(-0.181425 + 0.300400i) q^{60} +(2.22565 + 12.6223i) q^{61} +(64.6788 + 54.6472i) q^{62} +(-90.1803 + 49.0026i) q^{63} +(-63.9867 - 1.30371i) q^{64} +(-0.0128054 - 0.00466078i) q^{65} +(-55.2830 - 47.9468i) q^{66} +(44.1264 - 52.5878i) q^{67} +(-48.6383 - 0.330289i) q^{68} +(-1.72546 + 133.496i) q^{69} +(-0.666993 - 0.00226466i) q^{70} +(-15.6606 - 9.04168i) q^{71} +(-22.1720 - 68.5011i) q^{72} +(66.0665 + 114.430i) q^{73} +(40.7927 - 23.3674i) q^{74} +(56.8235 + 48.9459i) q^{75} +(-57.5621 - 33.7567i) q^{76} +(24.1519 - 136.972i) q^{77} +(2.44376 - 1.35822i) q^{78} +(40.9769 + 48.8344i) q^{79} +(0.0875029 - 0.459658i) q^{80} +(64.6572 - 48.7898i) q^{81} +(-2.97646 - 8.26496i) q^{82} +(51.0828 + 60.8781i) q^{83} +(90.0120 - 103.075i) q^{84} +(0.0617509 - 0.350207i) q^{85} +(55.6500 - 46.3749i) q^{86} +(-0.0681080 - 0.0586659i) q^{87} +(91.3425 + 34.3036i) q^{88} +(36.4298 + 63.0983i) q^{89} +(0.520856 - 0.0762115i) q^{90} +(4.60194 + 2.65693i) q^{91} +(-59.7457 - 167.684i) q^{92} +(1.64150 - 127.000i) q^{93} +(-87.0542 - 32.0203i) q^{94} +(0.313599 - 0.373733i) q^{95} +(59.4814 + 75.3522i) q^{96} +(-113.701 - 41.3836i) q^{97} +(159.533 + 28.6888i) q^{98} +(-2.83707 + 109.731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	1.72865	+	1.00588i	0.864323	+	0.502938i
$2$	1.72865	+	1.00588i	0.864323	+	0.502938i
$3$	−0.482718	−	2.96091i	−0.160906	−	0.986970i
$3$	−0.482718	−	2.96091i	−0.160906	−	0.986970i
$4$	1.97643	+	3.47760i	0.494108	+	0.869401i
$5$	−0.0274809	+	0.0100022i	−0.00549618	+	0.00200045i	−0.344767	−	0.938688i	$-0.612042\pi$
$5$	−0.0274809	+	0.0100022i	−0.00549618	+	0.00200045i	0.339271	+	0.940689i	$0.389820\pi$
$6$	2.14386	−	5.60392i	0.357309	−	0.933986i
$7$	11.2305	−	1.98024i	1.60436	−	0.282892i	0.701450	−	0.712719i	$-0.252537\pi$
$7$	11.2305	−	1.98024i	1.60436	−	0.282892i	0.902911	+	0.429827i	$0.141425\pi$
$8$	−0.0814860	+	7.99958i	−0.0101858	+	0.999948i
$9$	−8.53397	+	2.85857i	−0.948219	+	0.317619i
$10$	−0.0575657	−	0.0103520i	−0.00575657	−	0.00103520i
$11$	4.17143	−	11.4609i	0.379220	−	1.04190i	−0.592460	−	0.805600i	$-0.701843\pi$
$11$	4.17143	−	11.4609i	0.379220	−	1.04190i	0.971680	−	0.236300i	$-0.0759347\pi$
$12$	9.34281	−	7.53073i	0.778567	−	0.627561i
$13$	0.356957	+	0.299523i	0.0274582	+	0.0230402i	0.656413	−	0.754401i	$-0.272073\pi$
$13$	0.356957	+	0.299523i	0.0274582	+	0.0230402i	−0.628955	+	0.777442i	$0.716517\pi$
$14$	21.4055	+	7.87337i	1.52896	+	0.562383i
$15$	0.0428812	+	0.0765402i	0.00285875	+	0.00510268i
$16$	−8.18744	+	13.7465i	−0.511715	+	0.859155i
$17$	−6.07992	+	10.5307i	−0.357642	+	0.619455i	−0.987566	−	0.157202i	$-0.949753\pi$
$17$	−6.07992	+	10.5307i	−0.357642	+	0.619455i	0.629924	+	0.776657i	$0.283086\pi$
$18$	−17.6276	−	3.64266i	−0.979309	−	0.202370i
$19$	−14.4475	+	8.34127i	−0.760395	+	0.439014i	−0.829437	−	0.558600i	$-0.811339\pi$
$19$	−14.4475	+	8.34127i	−0.760395	+	0.439014i	0.0690427	+	0.997614i	$0.478006\pi$
$20$	−0.0890979	−	0.0757989i	−0.00445489	−	0.00378995i
$21$	−11.2845	−	32.2967i	−0.537357	−	1.53794i
$22$	18.7391	−	15.6159i	0.851779	−	0.709813i
$23$	−43.8264	−	7.72777i	−1.90550	−	0.335990i	−0.908801	−	0.417231i	$-0.863001\pi$
$23$	−43.8264	−	7.72777i	−1.90550	−	0.335990i	−0.996695	+	0.0812406i	$0.974112\pi$
$24$	23.7254	−	3.62027i	0.988557	−	0.150845i
$25$	−19.1505	+	16.0691i	−0.766018	+	0.642766i
$26$	0.315770	+	0.876822i	0.0121450	+	0.0337239i
$27$	12.5835	+	23.8884i	0.466054	+	0.884756i
$28$	29.0829	+	35.1415i	1.03867	+	1.25505i
$29$	0.0229535	−	0.0192603i	0.000791500	−	0.000664147i	−0.642392	−	0.766376i	$-0.722058\pi$
$29$	0.0229535	−	0.0192603i	0.000791500	−	0.000664147i	0.643183	+	0.765712i	$0.277613\pi$
$30$	−0.00286346	+	0.175444i	−9.54487e−5	+	0.00584813i
$31$	41.6937	+	7.35173i	1.34496	+	0.237153i	0.799339	−	0.600880i	$-0.205183\pi$
$31$	41.6937	+	7.35173i	1.34496	+	0.237153i	0.545620	+	0.838033i	$0.316294\pi$
$32$	−27.9804	+	15.5272i	−0.874388	+	0.485227i
$33$	−35.9483	−	6.81883i	−1.08934	−	0.206631i
$34$	−21.1026	+	12.0883i	−0.620666	+	0.355537i
$35$	−0.288818	+	0.166749i	−0.00825195	+	0.00476426i
$36$	−26.8078	−	24.0280i	−0.744660	−	0.667444i
$37$	11.7529	−	20.3566i	0.317645	−	0.550178i	−0.662351	−	0.749194i	$-0.730441\pi$
$37$	11.7529	−	20.3566i	0.317645	−	0.550178i	0.979996	+	0.199016i	$0.0637746\pi$
$38$	−33.3649	−	0.113285i	−0.878023	−	0.00298117i
$39$	0.714549	−	1.20150i	0.0183218	−	0.0308077i
$40$	−0.0777744	−	0.220651i	−0.00194436	−	0.00551627i
$41$	−3.36469	−	2.82331i	−0.0820656	−	0.0688612i	0.600832	−	0.799375i	$-0.294836\pi$
$41$	−3.36469	−	2.82331i	−0.0820656	−	0.0688612i	−0.682898	+	0.730514i	$0.739280\pi$
$42$	12.9795	−	67.1803i	0.309036	−	1.59953i
$43$	12.3880	−	34.0357i	0.288092	−	0.791527i	−0.708241	−	0.705971i	$-0.750511\pi$
$43$	12.3880	−	34.0357i	0.288092	−	0.791527i	0.996333	−	0.0855564i	$-0.0272668\pi$
$44$	48.1010	−	8.14511i	1.09320	−	0.185116i
$45$	0.205929	−	0.163915i	0.00457620	−	0.00364255i
$46$	−67.9871	−	57.4425i	−1.47798	−	1.24875i
$47$	−45.6736	+	8.05348i	−0.971778	+	0.171351i	−0.636930	−	0.770922i	$-0.719796\pi$
$47$	−45.6736	+	8.05348i	−0.971778	+	0.171351i	−0.334848	+	0.942272i	$0.608685\pi$
$48$	44.6543	+	17.6066i	0.930298	+	0.366804i
$49$	76.1584	−	27.7194i	1.55425	−	0.565702i
$50$	−49.2679	+	8.51488i	−0.985358	+	0.170298i
$51$	34.1154	+	12.9187i	0.668930	+	0.253308i
$52$	−0.336120	+	1.83334i	−0.00646384	+	0.0352565i
$53$	10.6210			0.200397			0.100198	−	0.994967i	$-0.468052\pi$
$53$	10.6210			0.200397			0.100198	+	0.994967i	$0.468052\pi$
$54$	−2.27643	+	53.9520i	−0.0421562	+	0.999111i
$55$			0.356679i			0.00648508i
$56$	14.9260	+	90.0009i	0.266536	+	1.60716i
$57$	31.6718	+	38.7513i	0.555646	+	0.679847i
$58$	0.0590519	−	0.0102058i	0.00101814	−	0.000175963i
$59$	−16.2907	−	44.7583i	−0.276113	−	0.758615i	−0.997794	−	0.0663887i	$-0.978852\pi$
$59$	−16.2907	−	44.7583i	−0.276113	−	0.758615i	0.721681	−	0.692226i	$-0.243370\pi$
$60$	−0.181425	+	0.300400i	−0.00302374	+	0.00500667i
$61$	2.22565	+	12.6223i	0.0364861	+	0.206923i	0.997601	−	0.0692259i	$-0.0220529\pi$
$61$	2.22565	+	12.6223i	0.0364861	+	0.206923i	−0.961115	+	0.276149i	$0.910942\pi$
$62$	64.6788	+	54.6472i	1.04321	+	0.881407i
$63$	−90.1803	+	49.0026i	−1.43143	+	0.777818i
$64$	−63.9867	−	1.30371i	−0.999793	−	0.0203704i
$65$	−0.0128054	−	0.00466078i	−0.000197006	−	7.17043e-5i
$66$	−55.2830	−	47.9468i	−0.837621	−	0.726467i
$67$	44.1264	−	52.5878i	0.658603	−	0.784893i	−0.328581	−	0.944476i	$-0.606571\pi$
$67$	44.1264	−	52.5878i	0.658603	−	0.784893i	0.987185	+	0.159583i	$0.0510150\pi$
$68$	−48.6383	−	0.330289i	−0.715268	−	0.00485719i
$69$	−1.72546	+	133.496i	−0.0250067	+	1.93473i
$70$	−0.666993	−	0.00226466i	−0.00952847	−	3.23522e-5i
$71$	−15.6606	−	9.04168i	−0.220572	−	0.127348i	0.385643	−	0.922648i	$-0.373980\pi$
$71$	−15.6606	−	9.04168i	−0.220572	−	0.127348i	−0.606215	+	0.795301i	$0.707313\pi$
$72$	−22.1720	−	68.5011i	−0.307944	−	0.951405i
$73$	66.0665	+	114.430i	0.905020	+	1.56754i	0.820890	+	0.571086i	$0.193478\pi$
$73$	66.0665	+	114.430i	0.905020	+	1.56754i	0.0841297	+	0.996455i	$0.473189\pi$
$74$	40.7927	−	23.3674i	0.551253	−	0.315775i
$75$	56.8235	+	48.9459i	0.757647	+	0.652612i
$76$	−57.5621	−	33.7567i	−0.757396	−	0.444167i
$77$	24.1519	−	136.972i	0.313661	−	1.77886i
$78$	2.44376	−	1.35822i	0.0313303	−	0.0174131i
$79$	40.9769	+	48.8344i	0.518695	+	0.618157i	0.960272	−	0.279067i	$-0.0900251\pi$
$79$	40.9769	+	48.8344i	0.518695	+	0.618157i	−0.441577	+	0.897223i	$0.645581\pi$
$80$	0.0875029	−	0.459658i	0.00109379	−	0.00574573i
$81$	64.6572	−	48.7898i	0.798237	−	0.602344i
$82$	−2.97646	−	8.26496i	−0.0362983	−	0.100792i
$83$	51.0828	+	60.8781i	0.615455	+	0.733471i	0.980282	−	0.197605i	$-0.0633163\pi$
$83$	51.0828	+	60.8781i	0.615455	+	0.733471i	−0.364827	+	0.931075i	$0.618872\pi$
$84$	90.0120	−	103.075i	1.07157	−	1.22708i
$85$	0.0617509	−	0.350207i	0.000726481	−	0.00412008i
$86$	55.6500	−	46.3749i	0.647093	−	0.539242i
$87$	−0.0681080	−	0.0586659i	−0.000782850	−	0.000674321i
$88$	91.3425	+	34.3036i	1.03798	+	0.389813i
$89$	36.4298	+	63.0983i	0.409324	+	0.708970i	0.994814	−	0.101709i	$-0.0324312\pi$
$89$	36.4298	+	63.0983i	0.409324	+	0.708970i	−0.585490	+	0.810680i	$0.699098\pi$
$90$	0.520856	−	0.0762115i	0.00578729	−	0.000846794i
$91$	4.60194	+	2.65693i	0.0505708	+	0.0291971i
$92$	−59.7457	−	167.684i	−0.649410	−	1.82265i
$93$	1.64150	−	127.000i	0.0176505	−	1.36559i
$94$	−87.0542	−	32.0203i	−0.926108	−	0.340641i
$95$	0.313599	−	0.373733i	0.00330104	−	0.00393403i
$96$	59.4814	+	75.3522i	0.619598	+	0.784919i
$97$	−113.701	−	41.3836i	−1.17217	−	0.426635i	−0.318741	−	0.947842i	$-0.603260\pi$
$97$	−113.701	−	41.3836i	−1.17217	−	0.426635i	−0.853431	+	0.521207i	$0.825482\pi$
$98$	159.533	+	28.6888i	1.62789	+	0.292743i
$99$	−2.83707	+	109.731i	−0.0286572	+	1.10840i
$100$	−93.7316	−	34.8381i	−0.937316	−	0.348381i
$101$	10.4431	+	59.2260i	0.103397	+	0.586396i	0.991848	+	0.127424i	$0.0406710\pi$
$101$	10.4431	+	59.2260i	0.103397	+	0.586396i	−0.888451	+	0.458972i	$0.848218\pi$
$102$	45.9789	+	56.6478i	0.450773	+	0.555370i
$103$	−40.2223	−	110.510i	−0.390508	−	1.07291i	−0.966770	−	0.255647i	$-0.917711\pi$
$103$	−40.2223	−	110.510i	−0.390508	−	1.07291i	0.576262	−	0.817265i	$-0.304511\pi$
$104$	−2.42514	+	2.83110i	−0.0233187	+	0.0272221i
$105$	0.633147	+	0.774671i	0.00602997	+	0.00737782i
$106$	18.3600	+	10.6834i	0.173208	+	0.100787i
$107$		−	190.361i		−	1.77907i	−0.456865	−	0.889536i	$-0.651028\pi$
$107$		−	190.361i		−	1.77907i	0.456865	−	0.889536i	$-0.348972\pi$
$108$	−58.2041	+	90.9741i	−0.538927	+	0.842352i
$109$	−141.475			−1.29794			−0.648970	−	0.760814i	$-0.724800\pi$
$109$	−141.475			−1.29794			−0.648970	+	0.760814i	$0.724800\pi$
$110$	−0.358775	+	0.616572i	−0.00326159	+	0.00560520i
$111$	−65.9473	−	24.9727i	−0.594120	−	0.224979i
$112$	−64.7279	+	170.593i	−0.577928	+	1.52316i
$113$	119.582	−	43.5243i	1.05825	−	0.385171i	0.246478	−	0.969148i	$-0.420727\pi$
$113$	119.582	−	43.5243i	1.05825	−	0.385171i	0.811770	+	0.583978i	$0.198504\pi$
$114$	15.7704	+	98.8451i	0.138337	+	0.867062i
$115$	1.28168	−	0.225995i	0.0111451	−	0.00196518i
$116$	0.112346	+	0.0417565i	0.000968496	+	0.000359970i
$117$	−3.90246	−	1.53573i	−0.0333544	−	0.0131259i
$118$	16.8604	−	93.7576i	0.142885	−	0.794556i
$119$	−47.4273	+	130.305i	−0.398549	+	1.09500i
$120$	−0.615784	+	0.336795i	−0.00513153	+	0.00280662i
$121$	−21.2600	−	17.8392i	−0.175702	−	0.147432i
$122$	−8.84908	+	24.0582i	−0.0725335	+	0.197198i
$123$	−6.73537	+	11.3254i	−0.0547591	+	0.0920764i
$124$	56.8384	+	159.524i	0.458374	+	1.28649i
$125$	0.731102	−	1.26631i	0.00584881	−	0.0101304i
$126$	−205.180	−	6.00205i	−1.62841	−	0.0476353i
$127$	−94.7722	+	54.7167i	−0.746237	+	0.430840i	−0.824333	−	0.566106i	$-0.808449\pi$
$127$	−94.7722	+	54.7167i	−0.746237	+	0.430840i	0.0780954	+	0.996946i	$0.475116\pi$
$128$	−109.299	−	66.6163i	−0.853898	−	0.520440i
$129$	−106.756	−	20.2500i	−0.827569	−	0.156977i
$130$	−0.0174478	−	0.0209375i	−0.000134214	−	0.000161057i
$131$	121.927	+	21.4990i	0.930739	+	0.164114i	0.618407	−	0.785858i	$-0.287779\pi$
$131$	121.927	+	21.4990i	0.930739	+	0.164114i	0.312333	+	0.949973i	$0.398890\pi$
$132$	−47.3361	−	138.491i	−0.358607	−	1.04917i
$133$	−145.735	+	122.286i	−1.09575	+	0.919447i
$134$	129.176	−	46.5200i	0.963998	−	0.347164i
$135$	−0.584742	−	0.530613i	−0.00433142	−	0.00393046i
$136$	−83.7461	−	49.4950i	−0.615780	−	0.363934i
$137$	17.8149	−	14.9484i	0.130035	−	0.109113i	−0.575450	−	0.817837i	$-0.695173\pi$
$137$	17.8149	−	14.9484i	0.130035	−	0.109113i	0.705486	+	0.708724i	$0.250729\pi$
$138$	−137.263	+	229.032i	−0.994662	+	1.65965i
$139$	36.6332	+	6.45942i	0.263548	+	0.0464706i	0.303861	−	0.952716i	$-0.401724\pi$
$139$	36.6332	+	6.45942i	0.263548	+	0.0464706i	−0.0403126	+	0.999187i	$0.512835\pi$
$140$	−1.15072	−	0.674826i	−0.00821940	−	0.00482019i
$141$	45.8931	+	131.348i	0.325483	+	0.931544i
$142$	−17.9769	−	31.3825i	−0.126598	−	0.221004i
$143$	4.92182	−	2.84161i	0.0344183	−	0.0198714i
$144$	30.5761	−	140.716i	0.212334	−	0.977197i
$145$	−0.000438137	0	0.000758876i	−3.02163e−6	0	5.23362e-6i
$146$	−0.897262	+	264.264i	−0.00614563	+	1.81003i
$147$	−118.838	−	212.117i	−0.808419	−	1.44298i
$148$	94.0208	+	0.638469i	0.635276	+	0.00431398i
$149$	−181.406	−	152.217i	−1.21749	−	1.02159i	−0.998952	−	0.0457641i	$-0.985428\pi$
$149$	−181.406	−	152.217i	−1.21749	−	1.02159i	−0.218535	−	0.975829i	$-0.570128\pi$
$150$	48.9943	+	141.767i	0.326629	+	0.945117i
$151$	28.2544	−	77.6282i	0.187115	−	0.514094i	−0.810295	−	0.586022i	$-0.800693\pi$
$151$	28.2544	−	77.6282i	0.187115	−	0.514094i	0.997410	+	0.0719283i	$0.0229153\pi$
$152$	−65.5494	−	116.254i	−0.431246	−	0.764827i
$153$	21.7830	−	107.249i	0.142373	−	0.700973i
$154$	179.527	−	212.483i	1.16576	−	1.37976i
$155$	−1.21932	+	0.214998i	−0.00786655	+	0.00138709i
$156$	5.59061	+	0.110234i	0.0358372	+	0.000706625i
$157$	249.950	−	90.9743i	1.59204	−	0.579454i	0.614260	−	0.789104i	$-0.289455\pi$
$157$	249.950	−	90.9743i	1.59204	−	0.579454i	0.977777	+	0.209650i	$0.0672324\pi$
$158$	21.7133	+	125.635i	0.137426	+	0.795158i
$159$	−5.12696	−	31.4479i	−0.0322451	−	0.197786i
$160$	0.613620	−	0.706570i	0.00383513	−	0.00441606i
$161$	−507.496			−3.15215
$162$	160.846	−	19.3033i	0.992876	−	0.119156i
$163$		−	69.3275i		−	0.425322i	−0.977126	−	0.212661i	$-0.931787\pi$
$163$		−	69.3275i		−	0.425322i	0.977126	−	0.212661i	$-0.0682130\pi$
$164$	3.16827	−	17.2811i	0.0193187	−	0.105373i
$165$	1.05610	−	0.172175i	0.00640058	−	0.00104349i
$166$	27.0683	+	156.619i	0.163062	+	0.943491i
$167$	23.6159	+	64.8842i	0.141413	+	0.388528i	0.990099	−	0.140368i	$-0.0448284\pi$
$167$	23.6159	+	64.8842i	0.141413	+	0.388528i	−0.848687	+	0.528896i	$0.822606\pi$
$168$	259.279	−	87.6396i	1.54333	−	0.521664i
$169$	−29.3088	−	166.219i	−0.173425	−	0.983542i
$170$	0.459010	−	0.543270i	0.00270006	−	0.00319570i
$171$	99.4504	−	112.483i	0.581581	−	0.657797i
$172$	142.846	−	24.1887i	0.830503	−	0.140632i
$173$	230.639	+	83.9456i	1.33317	+	0.485234i	0.907655	−	0.419717i	$-0.137871\pi$
$173$	230.639	+	83.9456i	1.33317	+	0.485234i	0.425516	+	0.904951i	$0.360093\pi$
$174$	−0.0587239	−	0.169921i	−0.000337494	−	0.000976556i
$175$	−183.249	+	218.387i	−1.04714	+	1.24793i
$176$	123.394	+	151.178i	0.701101	+	0.858965i
$177$	−124.661	+	69.8409i	−0.704302	+	0.394581i
$178$	−0.494761	+	145.719i	−0.00277956	+	0.818644i
$179$	201.836	+	116.530i	1.12757	+	0.651005i	0.943324	−	0.331874i	$-0.107681\pi$
$179$	201.836	+	116.530i	1.12757	+	0.651005i	0.184250	+	0.982879i	$0.441014\pi$
$180$	0.977035	+	0.392173i	0.00542797	+	0.00217874i
$181$	−33.8157	−	58.5706i	−0.186827	−	0.323594i	0.757364	−	0.652993i	$-0.226487\pi$
$181$	−33.8157	−	58.5706i	−0.186827	−	0.323594i	−0.944191	+	0.329399i	$0.893154\pi$
$182$	5.28259	+	9.22188i	0.0290252	+	0.0506696i
$183$	36.2991	−	12.6829i	0.198356	−	0.0693057i
$184$	65.3902	−	349.963i	0.355382	−	1.90197i
$185$	−0.119368	+	0.676972i	−0.000645235	+	0.00365931i
$186$	130.584	−	217.887i	0.702064	−	1.17144i
$187$	95.3297	+	113.610i	0.509785	+	0.607538i
$188$	−118.277	−	142.917i	−0.629135	−	0.760199i
$189$	188.624	+	243.361i	0.998009	+	1.28763i
$190$	0.918030	−	0.330610i	0.00483174	−	0.00174005i
$191$	−53.5083	−	63.7687i	−0.280148	−	0.333868i	0.607560	−	0.794274i	$-0.292148\pi$
$191$	−53.5083	−	63.7687i	−0.280148	−	0.333868i	−0.887709	+	0.460406i	$0.847704\pi$
$192$	27.0274	+	190.088i	0.140768	+	0.990043i
$193$	1.05357	−	5.97507i	0.00545889	−	0.0309589i	−0.981957	−	0.189106i	$-0.939441\pi$
$193$	1.05357	−	5.97507i	0.00545889	−	0.0309589i	0.987416	+	0.158147i	$0.0505521\pi$
$194$	−154.921	−	185.906i	−0.798563	−	0.958280i
$195$	−0.00761876	+	0.0401655i	−3.90706e−5	+	0.000205977i
$196$	246.919	+	210.063i	1.25979	+	1.07175i
$197$	116.454	+	201.704i	0.591137	+	1.02388i	0.994080	+	0.108654i	$0.0346539\pi$
$197$	116.454	+	201.704i	0.591137	+	1.02388i	−0.402943	+	0.915225i	$0.632013\pi$
$198$	−115.280	+	186.833i	−0.582223	+	0.943599i
$199$	−206.861	−	119.431i	−1.03950	−	0.600156i	−0.119809	−	0.992797i	$-0.538228\pi$
$199$	−206.861	−	119.431i	−1.03950	−	0.600156i	−0.919692	+	0.392641i	$0.871561\pi$
$200$	−126.986	−	154.505i	−0.634930	−	0.772526i
$201$	−177.008	−	105.269i	−0.880638	−	0.523728i
$202$	−41.5215	+	112.885i	−0.205552	+	0.558838i
$203$	0.219640	−	0.261756i	0.00108197	−	0.00128944i
$204$	22.5006	+	144.173i	0.110297	+	0.706730i
$205$	0.120704	+	0.0439327i	0.000588800	+	0.000214306i
$206$	41.6290	−	231.491i	0.202083	−	1.12374i
$207$	396.103	−	59.3321i	1.91354	−	0.286628i
$208$	−7.03995	+	2.45458i	−0.0338459	+	0.0118009i
$209$	35.3317	+	200.376i	0.169051	+	0.958738i
$210$	0.315264	+	1.97600i	0.00150126	+	0.00940952i
$211$	86.7160	+	238.250i	0.410976	+	1.12915i	0.956673	+	0.291165i	$0.0940430\pi$
$211$	86.7160	+	238.250i	0.410976	+	1.12915i	−0.545696	+	0.837983i	$0.683735\pi$
$212$	20.9917	+	36.9358i	0.0990177	+	0.174225i
$213$	−19.2119	+	50.7343i	−0.0901968	+	0.238189i
$214$	191.479	−	329.066i	0.894762	−	1.53769i
$215$			1.05924i			0.00492669i
$216$	−192.123	+	98.7158i	−0.889458	+	0.457018i
$217$	482.801			2.22489
$218$	−244.561	−	142.307i	−1.12184	−	0.652782i
$219$	306.927	−	250.854i	1.40149	−	1.14545i
$220$	−1.24039	+	0.704952i	−0.00563813	+	0.00320433i
$221$	−5.32446	+	1.93795i	−0.0240926	+	0.00876899i
$222$	−88.8801	−	109.504i	−0.400361	−	0.493260i
$223$	−308.726	+	54.4367i	−1.38442	+	0.244111i	−0.815727	−	0.578438i	$-0.803663\pi$
$223$	−308.726	+	54.4367i	−1.38442	+	0.244111i	−0.568695	+	0.822548i	$0.692552\pi$
$224$	−283.487	+	229.787i	−1.26557	+	1.02584i
$225$	117.495	−	191.876i	0.522198	−	0.852784i
$226$	250.495	+	45.0465i	1.10838	+	0.199321i
$227$	0.171119	−	0.470145i	0.000753827	−	0.00207112i	−0.939315	−	0.343055i	$-0.888538\pi$
$227$	0.171119	−	0.470145i	0.000753827	−	0.00207112i	0.940069	+	0.340984i	$0.110760\pi$
$228$	−72.1644	+	186.731i	−0.316510	+	0.818996i
$229$	−145.884	−	122.411i	−0.637046	−	0.534545i	0.266063	−	0.963956i	$-0.414277\pi$
$229$	−145.884	−	122.411i	−0.637046	−	0.534545i	−0.903109	+	0.429410i	$0.858721\pi$
$230$	2.44290	+	0.898548i	0.0106213	+	0.00390673i
$231$	−417.221	−	5.39266i	−1.80615	−	0.0233449i
$232$	0.152204	+	0.185188i	0.000656051	+	0.000798223i
$233$	−28.2092	+	48.8598i	−0.121070	+	0.209699i	−0.920190	−	0.391473i	$-0.871966\pi$
$233$	−28.2092	+	48.8598i	−0.121070	+	0.209699i	0.799120	+	0.601171i	$0.205299\pi$
$234$	−5.20123	−	6.58012i	−0.0222275	−	0.0281202i
$235$	1.17460	−	0.678154i	0.00499829	−	0.00288576i
$236$	123.454	−	145.114i	0.523111	−	0.614891i
$237$	124.814	−	144.902i	0.526641	−	0.611401i
$238$	−213.056	+	177.546i	−0.895193	+	0.745991i
$239$	118.599	+	20.9122i	0.496230	+	0.0874987i	0.416162	−	0.909291i	$-0.363375\pi$
$239$	118.599	+	20.9122i	0.496230	+	0.0874987i	0.0800682	+	0.996789i	$0.474486\pi$
$240$	−1.40325	−	0.0372027i	−0.00584686	−	0.000155011i
$241$	95.8845	−	80.4566i	0.397861	−	0.333845i	−0.421805	−	0.906686i	$-0.638603\pi$
$241$	95.8845	−	80.4566i	0.397861	−	0.333845i	0.819666	+	0.572842i	$0.194159\pi$
$242$	−18.8069	−	52.2226i	−0.0777145	−	0.215796i
$243$	−175.673	−	167.892i	−0.722936	−	0.690915i
$244$	−39.4965	+	32.6870i	−0.161871	+	0.133963i
$245$	−1.81565	+	1.52351i	−0.00741080	+	0.00621840i
$246$	−23.0350	+	12.8027i	−0.0936382	+	0.0520433i
$247$	−7.65553	−	1.34988i	−0.0309941	−	0.00546509i
$248$	−62.2083	+	332.934i	−0.250840	+	1.34247i
$249$	155.596	−	180.638i	0.624883	−	0.725455i
$250$	2.53756	−	1.45360i	0.0101502	−	0.00581438i
$251$	−326.557	+	188.538i	−1.30102	+	0.751147i	−0.980580	−	0.196121i	$-0.937166\pi$
$251$	−326.557	+	188.538i	−1.30102	+	0.751147i	−0.320444	+	0.947267i	$0.603832\pi$
$252$	−348.646	−	216.761i	−1.38352	−	0.860163i
$253$	−271.386	+	470.054i	−1.07267	+	1.85792i
$254$	−218.866	−	0.743119i	−0.861676	−	0.00292567i
$255$	−1.06674	−	0.0137878i	−0.00418329	−	5.40698e-5i
$256$	−121.932	−	225.097i	−0.476295	−	0.879286i
$257$	204.733	+	171.791i	0.796627	+	0.668449i	0.947376	−	0.320123i	$-0.103724\pi$
$257$	204.733	+	171.791i	0.796627	+	0.668449i	−0.150749	+	0.988572i	$0.548169\pi$
$258$	−164.175	−	142.389i	−0.636337	−	0.551894i
$259$	91.6799	−	251.889i	0.353977	−	0.972543i
$260$	−0.00910062	−	0.0537438i	−3.50024e−5	−	0.000206707i
$261$	−0.140828	+	0.229981i	−0.000539569	+	0.000881152i
$262$	189.143	+	159.807i	0.721920	+	0.609951i
$263$	143.902	−	25.3738i	0.547156	−	0.0964784i	0.106765	−	0.994284i	$-0.465951\pi$
$263$	143.902	−	25.3738i	0.547156	−	0.0964784i	0.440391	+	0.897806i	$0.354840\pi$
$264$	57.4771	−	287.016i	0.217716	−	1.08718i
$265$	−0.291876	+	0.106234i	−0.00110142	+	0.000400883i
$266$	−374.929	+	64.7984i	−1.40951	+	0.243603i
$267$	169.243	−	138.324i	0.633869	−	0.518068i
$268$	270.092	+	49.5180i	1.00781	+	0.184769i
$269$	−28.5817			−0.106252			−0.0531258	−	0.998588i	$-0.516918\pi$
$269$	−28.5817			−0.106252			−0.0531258	+	0.998588i	$0.516918\pi$
$270$	−0.477082	−	1.50542i	−0.00176697	−	0.00557563i
$271$			456.679i			1.68516i	0.538569	+	0.842581i	$0.318965\pi$
$271$			456.679i			1.68516i	−0.538569	+	0.842581i	$0.681035\pi$
$272$	−94.9815	−	169.797i	−0.349197	−	0.624255i
$273$	5.64550	−	14.9085i	0.0206795	−	0.0546098i
$274$	45.8318	−	7.92103i	0.167269	−	0.0289089i
$275$	104.282	+	286.513i	0.379207	+	1.04186i
$276$	−467.657	+	257.846i	−1.69441	+	0.934223i
$277$	−36.6986	−	208.128i	−0.132486	−	0.751365i	−0.976577	−	0.215166i	$-0.930971\pi$
$277$	−36.6986	−	208.128i	−0.132486	−	0.751365i	0.844091	−	0.536199i	$-0.180140\pi$
$278$	56.8284	+	48.0145i	0.204419	+	0.172714i
$279$	−376.828	+	56.4449i	−1.35064	+	0.202312i
$280$	−1.31039	−	2.32401i	−0.00467996	−	0.00830005i
$281$	158.363	+	57.6394i	0.563569	+	0.205122i	0.608065	−	0.793887i	$-0.291946\pi$
$281$	158.363	+	57.6394i	0.563569	+	0.205122i	−0.0444958	+	0.999010i	$0.514168\pi$
$282$	−52.7865	+	273.216i	−0.187186	+	0.968852i
$283$	−0.932181	+	1.11093i	−0.00329393	+	0.00392555i	−0.767689	−	0.640823i	$-0.778593\pi$
$283$	−0.932181	+	1.11093i	−0.00329393	+	0.00392555i	0.764395	+	0.644748i	$0.223038\pi$
$284$	0.491185	−	72.3317i	0.00172952	−	0.254689i
$285$	−1.25797	−	0.748131i	−0.00441393	−	0.00262502i
$286$	11.3664	+	0.0385925i	0.0397426	+	0.000134939i
$287$	−43.3781	−	25.0443i	−0.151143	−	0.0872625i
$288$	194.398	−	212.493i	0.674994	−	0.737823i
$289$	70.5691	+	122.229i	0.244184	+	0.422939i
$290$	−0.00152072		0.000871116i	−5.24385e−6		3.00385e-6i
$291$	−67.6479	+	356.634i	−0.232467	+	1.22555i
$292$	−267.368	+	455.917i	−0.915644	+	1.56136i
$293$	43.8987	−	248.962i	0.149825	−	0.849699i	−0.813541	−	0.581508i	$-0.802463\pi$
$293$	43.8987	−	248.962i	0.149825	−	0.849699i	0.963366	−	0.268191i	$-0.0864259\pi$
$294$	7.93557	−	486.212i	0.0269917	−	1.65378i
$295$	0.895365	+	1.06705i	0.00303514	+	0.00361713i
$296$	161.886	+	95.6769i	0.546914	+	0.323233i
$297$	326.274	−	44.5689i	1.09856	−	0.150064i
$298$	−160.474	−	445.601i	−0.538504	−	1.49531i
$299$	−13.3295	−	15.8855i	−0.0445802	−	0.0531287i
$300$	−57.9066	+	294.348i	−0.193022	+	0.981160i
$301$	71.7245	−	406.770i	0.238287	−	1.35139i
$302$	126.926	−	105.771i	0.420285	−	0.350236i
$303$	170.322	−	59.5107i	0.562118	−	0.196405i
$304$	3.62500	−	266.896i	0.0119243	−	0.877947i
$305$	−0.187414	−	0.324610i	−0.000614472	−	0.00106430i
$306$	145.534	−	163.484i	0.475602	−	0.534262i
$307$	260.012	+	150.118i	0.846946	+	0.488985i	0.859619	−	0.510935i	$-0.170701\pi$
$307$	260.012	+	150.118i	0.846946	+	0.488985i	−0.0126731	+	0.999920i	$0.504034\pi$
$308$	524.070	−	186.726i	1.70153	−	0.606252i
$309$	−307.794	+	172.440i	−0.996097	+	0.558058i
$310$	−2.32403	−	0.854823i	−0.00749686	−	0.00275749i
$311$	204.701	−	243.953i	0.658203	−	0.784416i	−0.328924	−	0.944356i	$-0.606686\pi$
$311$	204.701	−	243.953i	0.658203	−	0.784416i	0.987127	+	0.159941i	$0.0511304\pi$
$312$	9.55329	+	5.81401i	0.0306195	+	0.0186346i
$313$	48.3252	+	17.5890i	0.154394	+	0.0561947i	0.418061	−	0.908419i	$-0.362710\pi$
$313$	48.3252	+	17.5890i	0.154394	+	0.0561947i	−0.263667	+	0.964614i	$0.584932\pi$
$314$	523.583	+	94.1559i	1.66746	+	0.299860i
$315$	1.98810	−	2.24864i	0.00631143	−	0.00713853i
$316$	−88.8385	+	239.019i	−0.281135	+	0.756390i
$317$	−22.2496	−	126.184i	−0.0701880	−	0.398056i	−0.999580	−	0.0289629i	$-0.990780\pi$
$317$	−22.2496	−	126.184i	−0.0701880	−	0.398056i	0.929393	−	0.369093i	$-0.120332\pi$
$318$	22.7700	−	59.5194i	0.0716037	−	0.187168i
$319$	−0.124991	−	0.343410i	−0.000391822	−	0.00107652i
$320$	1.77145	−	0.604183i	0.00553579	−	0.00188807i
$321$	−563.641	+	91.8905i	−1.75589	+	0.286263i
$322$	−877.281	−	510.478i	−2.72448	−	1.58533i
$323$		−	202.857i		−	0.628040i
$324$	297.462	+	128.422i	0.918093	+	0.396365i
$325$	−11.6490			−0.0358430
$326$	69.7348	−	119.843i	0.213910	−	0.367615i
$327$	68.2927	+	418.896i	0.208846	+	1.28103i
$328$	22.8595	−	26.6861i	0.0696935	−	0.0813599i
$329$	−496.990	+	180.890i	−1.51061	+	0.549817i
$330$	1.99880	+	0.764669i	0.00605697	+	0.00231718i
$331$	−577.538	+	101.836i	−1.74483	+	0.307660i	−0.952974	−	0.303051i	$-0.901995\pi$
$331$	−577.538	+	101.836i	−1.74483	+	0.307660i	−0.791854	+	0.610711i	$0.790884\pi$
$332$	−110.748	+	297.967i	−0.333579	+	0.897490i
$333$	−42.1080	+	207.319i	−0.126450	+	0.622579i
$334$	−24.4419	+	135.916i	−0.0731792	+	0.406936i
$335$	−0.686638	+	1.88652i	−0.00204967	+	0.00563141i
$336$	536.357	+	109.305i	1.59630	+	0.325312i
$337$	144.272	+	121.059i	0.428107	+	0.359224i	0.831237	−	0.555918i	$-0.187633\pi$
$337$	144.272	+	121.059i	0.428107	+	0.359224i	−0.403130	+	0.915143i	$0.632078\pi$
$338$	116.531	−	316.814i	0.344765	−	0.937320i
$339$	−186.596	−	333.062i	−0.550430	−	0.982483i
$340$	1.33993	−	0.477414i	0.00394096	−	0.00140416i
$341$	258.180	−	447.180i	0.757125	−	1.31138i
$342$	285.059	−	94.4090i	0.833505	−	0.276050i
$343$	316.486	−	182.723i	0.922699	−	0.532721i
$344$	271.262	+	101.872i	0.788552	+	0.296140i
$345$	−1.28784	−	3.68586i	−0.00373288	−	0.0106836i
$346$	314.254	+	377.106i	0.908247	+	1.08990i
$347$	−63.2707	−	11.1563i	−0.182336	−	0.0321508i	0.0817344	−	0.996654i	$-0.473954\pi$
$347$	−63.2707	−	11.1563i	−0.182336	−	0.0321508i	−0.264071	+	0.964503i	$0.585065\pi$
$348$	0.0694062	−	0.352802i	0.000199443	−	0.00101380i
$349$	−260.504	+	218.589i	−0.746431	+	0.626330i	−0.934556	−	0.355815i	$-0.884203\pi$
$349$	−260.504	+	218.589i	−0.746431	+	0.626330i	0.188125	+	0.982145i	$0.439759\pi$
$350$	−536.443	+	193.189i	−1.53269	+	0.551969i
$351$	−2.66337	+	12.2962i	−0.00758794	+	0.0350318i
$352$	61.2379	+	385.452i	0.173971	+	1.09503i
$353$	109.064	−	91.5160i	0.308964	−	0.259252i	−0.475099	−	0.879932i	$-0.657588\pi$
$353$	109.064	−	91.5160i	0.308964	−	0.259252i	0.784064	+	0.620680i	$0.213143\pi$
$354$	−285.747	−	4.66373i	−0.807194	−	0.0131744i
$355$	0.520805	+	0.0918321i	0.00146706	+	0.000258682i
$356$	−147.430	+	251.398i	−0.414129	+	0.706174i
$357$	408.717	+	77.5272i	1.14486	+	0.217163i
$358$	231.688	+	404.460i	0.647173	+	1.12978i
$359$	−33.5032	+	19.3431i	−0.0933237	+	0.0538805i	−0.545936	−	0.837827i	$-0.683826\pi$
$359$	−33.5032	+	19.3431i	−0.0933237	+	0.0538805i	0.452612	+	0.891708i	$0.350492\pi$
$360$	1.29447	+	1.66070i	0.00359575	+	0.00461307i
$361$	−41.3465	+	71.6142i	−0.114533	+	0.198377i
$362$	0.459258	−	135.262i	0.00126867	−	0.373652i
$363$	−42.5578	+	71.5602i	−0.117239	+	0.197135i
$364$	−0.144337	+	21.2550i	−0.000396529	+	0.0583928i
$365$	−2.96013	−	2.48384i	−0.00810993	−	0.00680504i
$366$	75.5057	+	14.5880i	0.206300	+	0.0398580i
$367$	205.087	−	563.471i	0.558819	−	1.53534i	−0.262534	−	0.964923i	$-0.584558\pi$
$367$	205.087	−	563.471i	0.558819	−	1.53534i	0.821353	−	0.570420i	$-0.193220\pi$
$368$	465.056	−	539.188i	1.26374	−	1.46518i
$369$	36.7848	+	14.4758i	0.0996877	+	0.0392299i
$370$	−0.887295	+	1.05017i	−0.00239809	+	0.00283831i
$371$	119.280	−	21.0323i	0.321509	−	0.0566907i
$372$	444.901	−	245.299i	1.19597	−	0.659405i
$373$	−571.820	+	208.125i	−1.53303	+	0.557977i	−0.964361	−	0.264590i	$-0.914763\pi$
$373$	−571.820	+	208.125i	−1.53303	+	0.557977i	−0.568668	+	0.822567i	$0.692541\pi$
$374$	50.5143	+	292.280i	0.135065	+	0.781498i
$375$	−4.10233	−	1.55346i	−0.0109395	−	0.00414255i
$376$	−60.7027	−	366.026i	−0.161443	−	0.973473i
$377$	0.0139623			3.70353e−5
$378$	81.2726	+	610.417i	0.215007	+	1.61486i
$379$		−	529.969i		−	1.39834i	−0.714958	−	0.699168i	$-0.753554\pi$
$379$		−	529.969i		−	1.39834i	0.714958	−	0.699168i	$-0.246446\pi$
$380$	1.91950	+	0.351916i	0.00505132	+	0.000926095i
$381$	207.759	+	254.199i	0.545300	+	0.667189i
$382$	−28.3535	−	164.056i	−0.0742239	−	0.429467i
$383$	−120.922	−	332.231i	−0.315724	−	0.867445i	−0.991473	−	0.130313i	$-0.958402\pi$
$383$	−120.922	−	332.231i	−0.315724	−	0.867445i	0.675749	−	0.737132i	$-0.263820\pi$
$384$	−144.484	+	355.781i	−0.376261	+	0.926514i
$385$	0.706312	+	4.00570i	0.00183458	+	0.0104044i
$386$	7.83141	−	9.26902i	0.0202886	−	0.0240130i
$387$	−8.42529	+	325.871i	−0.0217708	+	0.842044i
$388$	−80.8055	−	477.197i	−0.208262	−	1.22989i
$389$	−271.255	−	98.7286i	−0.697313	−	0.253801i	−0.0310496	−	0.999518i	$-0.509885\pi$
$389$	−271.255	−	98.7286i	−0.697313	−	0.253801i	−0.666263	+	0.745717i	$0.732107\pi$
$390$	−0.0535716	+	0.0617683i	−0.000137363	+	0.000158380i
$391$	347.840	−	414.540i	0.889617	−	1.06020i
$392$	215.538	+	611.494i	0.549841	+	1.55993i
$393$	4.80031	−	371.392i	0.0122145	−	0.945018i
$394$	−1.58158	+	465.813i	−0.00401417	+	1.18227i
$395$	−1.61453	−	0.932152i	−0.00408743	−	0.00235988i
$396$	−387.209	+	207.010i	−0.977800	+	0.522752i
$397$	−10.6556	−	18.4561i	−0.0268404	−	0.0464889i	0.852293	−	0.523064i	$-0.175211\pi$
$397$	−10.6556	−	18.4561i	−0.0268404	−	0.0464889i	−0.879134	+	0.476575i	$0.841878\pi$
$398$	−237.456	−	414.530i	−0.596623	−	1.04153i
$399$	432.428	+	372.479i	1.08378	+	0.933532i
$400$	−64.1009	−	394.817i	−0.160252	−	0.987041i
$401$	−97.5887	+	553.453i	−0.243363	+	1.38018i	0.580899	+	0.813975i	$0.302701\pi$
$401$	−97.5887	+	553.453i	−0.243363	+	1.38018i	−0.824263	+	0.566207i	$0.808410\pi$
$402$	−200.097	−	360.021i	−0.497754	−	0.895576i
$403$	12.6809	+	15.1125i	0.0314662	+	0.0374999i
$404$	−185.324	+	153.373i	−0.458724	+	0.379637i
$405$	−1.28883	+	1.98750i	−0.00318230	+	0.00490742i
$406$	0.642974	−	0.231554i	0.00158368	−	0.000570330i
$407$	−184.278	−	219.614i	−0.452772	−	0.539593i
$408$	−106.124	+	271.857i	−0.260109	+	0.666315i
$409$	−26.8684	+	152.379i	−0.0656930	+	0.372564i	0.934183	+	0.356795i	$0.116131\pi$
$409$	−26.8684	+	152.379i	−0.0656930	+	0.372564i	−0.999876	+	0.0157685i	$0.994981\pi$
$410$	0.164464	+	0.197357i	0.000401131	+	0.000481359i
$411$	−52.8605	−	45.5323i	−0.128614	−	0.110784i
$412$	304.813	−	358.293i	0.739838	−	0.869642i
$413$	−271.585	−	470.400i	−0.657592	−	1.13898i
$414$	744.403	+	295.866i	1.79807	+	0.714653i
$415$	−2.01272	−	1.16204i	−0.00484992	−	0.00280010i
$416$	−14.6386	−	2.83821i	−0.0351889	−	0.00682262i
$417$	1.44226	−	111.586i	0.00345867	−	0.267591i
$418$	−140.477	+	381.919i	−0.336070	+	0.913681i
$419$	−174.492	+	207.951i	−0.416448	+	0.496304i	−0.932962	−	0.359975i	$-0.882785\pi$
$419$	−174.492	+	207.951i	−0.416448	+	0.496304i	0.516514	+	0.856279i	$0.327230\pi$
$420$	−1.44263	+	3.73292i	−0.00343483	+	0.00888790i
$421$	1.34786	+	0.490582i	0.00320158	+	0.00116528i	0.343620	−	0.939109i	$-0.388347\pi$
$421$	1.34786	+	0.490582i	0.00320158	+	0.00116528i	−0.340419	+	0.940274i	$0.610569\pi$
$422$	−89.7488	+	499.076i	−0.212675	+	1.18264i
$423$	366.755	−	199.289i	0.867034	−	0.471133i
$424$	−0.865466	+	84.9639i	−0.00204119	+	0.200387i
$425$	−52.7866	−	299.367i	−0.124204	−	0.704394i
$426$	−84.2430	+	68.3769i	−0.197753	+	0.160509i
$427$	49.9904	+	137.348i	0.117074	+	0.321657i
$428$	661.999	−	376.235i	1.54673	−	0.879053i
$429$	−10.7896	−	13.2014i	−0.0251506	−	0.0307724i
$430$	−1.06546	+	1.83105i	−0.00247782	+	0.00425825i
$431$			527.038i			1.22283i	0.791312	+	0.611413i	$0.209398\pi$
$431$			527.038i			1.22283i	−0.791312	+	0.611413i	$0.790602\pi$
$432$	−431.408	−	22.6069i	−0.998630	−	0.0523307i
$433$	−225.003			−0.519638			−0.259819	−	0.965657i	$-0.583663\pi$
$433$	−225.003			−0.519638			−0.259819	+	0.965657i	$0.583663\pi$
$434$	834.592	+	485.637i	1.92302	+	1.11898i
$435$	0.00245846		0.000930961i	5.65163e−6		2.14014e-6i
$436$	−279.616	−	491.995i	−0.641322	−	1.12843i
$437$	697.641	−	253.921i	1.59643	−	0.581054i
$438$	782.896	−	124.908i	1.78743	−	0.285179i
$439$	181.098	−	31.9325i	0.412524	−	0.0727391i	0.0364652	−	0.999335i	$-0.488390\pi$
$439$	181.098	−	31.9325i	0.412524	−	0.0727391i	0.376059	+	0.926596i	$0.377279\pi$
$440$	−2.85329	−	0.0290644i	−0.00648474	−	6.60554e-5i
$441$	−570.696	+	454.260i	−1.29409	+	1.03007i
$442$	−11.1534	−	2.00572i	−0.0252340	−	0.00453783i
$443$	214.678	−	589.822i	0.484600	−	1.33143i	−0.420911	−	0.907102i	$-0.638289\pi$
$443$	214.678	−	589.822i	0.484600	−	1.33143i	0.905510	−	0.424324i	$-0.139488\pi$
$444$	−43.4951	−	278.695i	−0.0979619	−	0.627692i
$445$	−1.63225	−	1.36962i	−0.00366798	−	0.00307780i
$446$	−588.434	−	216.438i	−1.31936	−	0.485287i
$447$	−363.134	+	610.604i	−0.812381	+	1.36600i
$448$	−721.186	+	112.068i	−1.60979	+	0.250152i
$449$	−111.868	+	193.761i	−0.249149	+	0.431539i	−0.963290	−	0.268463i	$-0.913484\pi$
$449$	−111.868	+	193.761i	−0.249149	+	0.431539i	0.714141	+	0.700002i	$0.246818\pi$
$450$	396.110	−	213.501i	0.880245	−	0.474447i
$451$	−46.3932	+	26.7851i	−0.102867	+	0.0593905i
$452$	387.706	+	329.836i	0.857756	+	0.729726i
$453$	−243.489	−	46.1861i	−0.537503	−	0.101956i
$454$	0.768711	−	0.640590i	0.00169320	−	0.00141099i
$455$	−0.153041	−	0.0269852i	−0.000336353	−	5.93082e-5i
$456$	−312.575	+	250.204i	−0.685471	+	0.548692i
$457$	142.077	−	119.217i	0.310892	−	0.260869i	−0.473969	−	0.880542i	$-0.657179\pi$
$457$	142.077	−	119.217i	0.310892	−	0.260869i	0.784860	+	0.619673i	$0.212735\pi$
$458$	−129.051	−	358.346i	−0.281771	−	0.782414i
$459$	−328.069	−	12.7267i	−0.714747	−	0.0277271i
$460$	3.31908	+	4.01052i	0.00721539	+	0.00871853i
$461$	281.321	−	236.057i	0.610241	−	0.512053i	−0.284478	−	0.958683i	$-0.591820\pi$
$461$	281.321	−	236.057i	0.610241	−	0.512053i	0.894719	+	0.446629i	$0.147376\pi$
$462$	−715.803	−	428.994i	−1.54936	−	0.928559i
$463$	22.7171	+	4.00564i	0.0490650	+	0.00865149i	0.198127	−	0.980176i	$-0.436514\pi$
$463$	22.7171	+	4.00564i	0.0490650	+	0.00865149i	−0.149062	+	0.988828i	$0.547625\pi$
$464$	0.0768305	+	0.473222i	0.000165583	+	0.00101988i
$465$	1.22518	+	3.50650i	0.00263479	+	0.00754086i
$466$	−97.9107	+	56.0864i	−0.210109	+	0.120357i
$467$	−419.567	+	242.237i	−0.898431	+	0.518709i	−0.876691	−	0.481054i	$-0.840254\pi$
$467$	−419.567	+	242.237i	−0.898431	+	0.518709i	−0.0217402	+	0.999764i	$0.506921\pi$
$468$	−2.37229	−	16.6065i	−0.00506900	−	0.0354839i
$469$	391.426	−	677.970i	0.834597	−	1.44556i
$470$	2.71260	+	0.00921016i	0.00577149	+	1.95961e-5i
$471$	−390.022	−	696.164i	−0.828071	−	1.47805i
$472$	359.375	−	126.672i	0.761388	−	0.268372i
$473$	−338.404	−	283.954i	−0.715441	−	0.600327i
$474$	361.512	−	124.937i	0.762684	−	0.263581i
$475$	142.639	−	391.898i	0.300293	−	0.825048i
$476$	−546.887	+	92.6063i	−1.14892	+	0.194551i
$477$	−90.6396	+	30.3609i	−0.190020	+	0.0636498i
$478$	183.980	+	155.445i	0.384896	+	0.325200i
$479$	−634.404	+	111.862i	−1.32443	+	0.233533i	−0.790744	−	0.612147i	$-0.790306\pi$
$479$	−634.404	+	111.862i	−1.32443	+	0.233533i	−0.533690	+	0.845680i	$0.679195\pi$
$480$	−2.38829	−	1.47580i	−0.00497561	−	0.00307458i
$481$	10.2925	−	3.74617i	0.0213982	−	0.00778830i
$482$	246.680	−	42.6332i	0.511783	−	0.0884506i
$483$	244.977	+	1502.65i	0.507200	+	3.11108i
$484$	20.0189	−	109.192i	0.0413614	−	0.225603i
$485$	3.53852			0.00729592
$486$	−134.798	−	466.932i	−0.277363	−	0.960765i
$487$		−	141.644i		−	0.290850i	−0.989369	−	0.145425i	$-0.953545\pi$
$487$		−	141.644i		−	0.290850i	0.989369	−	0.145425i	$-0.0464549\pi$
$488$	−101.154	+	16.7757i	−0.207284	+	0.0343765i
$489$	−205.272	+	33.4656i	−0.419780	+	0.0684368i
$490$	−4.67107	+	0.807292i	−0.00953279	+	0.00164753i
$491$	−45.4768	−	124.946i	−0.0926207	−	0.254473i	0.884728	−	0.466107i	$-0.154344\pi$
$491$	−45.4768	−	124.946i	−0.0926207	−	0.254473i	−0.977349	+	0.211634i	$0.932122\pi$
$492$	−52.6972	−	1.03906i	−0.107108	−	0.00211192i
$493$	0.0632693	+	0.358818i	0.000128335	+	0.000727826i
$494$	−11.8759	−	10.0340i	−0.0240403	−	0.0203117i
$495$	−1.01959	−	3.04389i	−0.00205978	−	0.00614927i
$496$	−442.426	+	512.950i	−0.891987	+	1.03417i
$497$	−193.782	−	70.5309i	−0.389903	−	0.141913i
$498$	450.670	−	155.750i	0.904959	−	0.312750i
$499$	−240.997	+	287.208i	−0.482959	+	0.575568i	−0.951412	−	0.307920i	$-0.900367\pi$
$499$	−240.997	+	287.208i	−0.482959	+	0.575568i	0.468453	+	0.883488i	$0.344811\pi$
$500$	5.84868	+	0.0397167i	0.0116974	+	7.94335e-5i
$501$	180.716	−	101.245i	0.360711	−	0.202087i
$502$	−754.147	−	2.56057i	−1.50228	−	0.00510074i
$503$	103.876	+	59.9729i	0.206513	+	0.119230i	0.599690	−	0.800233i	$-0.295291\pi$
$503$	103.876	+	59.9729i	0.206513	+	0.119230i	−0.393177	+	0.919463i	$0.628624\pi$
$504$	−384.652	−	725.398i	−0.763198	−	1.43928i
$505$	−0.879379	−	1.52313i	−0.00174135	−	0.00301610i
$506$	−941.945	+	539.576i	−1.86155	+	1.06636i
$507$	−478.011	+	167.018i	−0.942822	+	0.329423i
$508$	−377.594	−	221.436i	−0.743295	−	0.435898i
$509$	−53.3303	+	302.451i	−0.104775	+	0.594206i	0.886535	+	0.462661i	$0.153105\pi$
$509$	−53.3303	+	302.451i	−0.104775	+	0.594206i	−0.991310	+	0.131546i	$0.958006\pi$
$510$	−1.83014	−	1.09684i	−0.00358852	−	0.00215067i
$511$	968.561	+	1154.29i	1.89542	+	2.25888i
$512$	15.6431	−	511.761i	0.0305530	−	0.999533i
$513$	−381.059	−	240.166i	−0.742805	−	0.468160i
$514$	181.110	+	502.902i	0.352354	+	0.978409i
$515$	2.21069	+	2.63460i	0.00429261	+	0.00511573i
$516$	−140.575	−	411.279i	−0.272432	−	0.797053i
$517$	−98.2237	+	557.054i	−0.189988	+	1.07747i
$518$	411.851	−	343.207i	0.795078	−	0.662563i
$519$	137.222	−	723.422i	0.264397	−	1.39388i
$520$	0.0383278	−	0.102058i	7.37073e−5	−	0.000196265i
$521$	439.923	+	761.970i	0.844383	+	1.46251i	0.886156	+	0.463387i	$0.153366\pi$
$521$	439.923	+	761.970i	0.844383	+	1.46251i	−0.0417736	+	0.999127i	$0.513301\pi$
$522$	−0.474773	+	0.255900i	−0.000909526	+	0.000490230i
$523$	77.7561	+	44.8925i	0.148673	+	0.0858366i	0.572491	−	0.819911i	$-0.305977\pi$
$523$	77.7561	+	44.8925i	0.148673	+	0.0858366i	−0.423818	+	0.905747i	$0.639310\pi$
$524$	166.215	+	466.504i	0.317204	+	0.890275i
$525$	735.083	+	437.164i	1.40016	+	0.832693i
$526$	274.279	+	100.885i	0.521442	+	0.191797i
$527$	−330.914	+	394.368i	−0.627920	+	0.748326i
$528$	388.060	−	438.334i	0.734961	−	0.830178i
$529$	1363.94	+	496.432i	2.57833	+	0.938435i
$530$	−0.611408	−	0.109949i	−0.00115360	−	0.000207452i
$531$	266.969	+	335.398i	0.502766	+	0.631634i
$532$	−713.299	−	265.119i	−1.34079	−	0.498344i
$533$	−0.355405	−	2.01560i	−0.000666800	−	0.00378161i
$534$	431.698	−	68.8760i	0.808424	−	0.128981i
$535$	1.90403	+	5.23128i	0.00355894	+	0.00977810i
$536$	417.085	+	357.278i	0.778144	+	0.666564i
$537$	247.605	−	653.868i	0.461089	−	1.21763i
$538$	−49.4076	−	28.7496i	−0.0918357	−	0.0534380i
$539$		−	988.473i		−	1.83390i
$540$	0.689558	−	3.08222i	0.00127696	−	0.00570782i
$541$	−509.281			−0.941369			−0.470684	−	0.882302i	$-0.655993\pi$
$541$	−509.281			−0.941369			−0.470684	+	0.882302i	$0.655993\pi$
$542$	−459.362	+	789.436i	−0.847531	+	1.45652i
$543$	−157.099	+	128.398i	−0.289316	+	0.236461i
$544$	6.60551	−	389.059i	0.0121425	−	0.715182i
$545$	3.88787	−	1.41507i	0.00713371	−	0.00259646i
$546$	24.7551	−	20.0928i	0.0453391	−	0.0368000i
$547$	−587.142	+	103.529i	−1.07339	+	0.189267i	−0.682289	−	0.731083i	$-0.739015\pi$
$547$	−587.142	+	103.529i	−1.07339	+	0.189267i	−0.391097	+	0.920350i	$0.627904\pi$
$548$	87.1946	+	32.4084i	0.159114	+	0.0591395i
$549$	−55.0753	−	101.356i	−0.100319	−	0.184619i
$550$	−107.929	+	600.173i	−0.196235	+	1.09122i
$551$	−0.170966	+	0.469724i	−0.000310282	+	0.000852494i
$552$	−1067.77	−	24.6811i	−1.93437	−	0.0447121i
$553$	556.896	+	467.291i	1.00705	+	0.845011i
$554$	145.912	−	396.694i	0.263379	−	0.716054i
$555$	2.06207	+	0.0266527i	0.00371545	+	4.80228e-5i
$556$	49.9397	+	140.162i	0.0898195	+	0.252090i
$557$	333.205	−	577.127i	0.598213	−	1.03613i	−0.394872	−	0.918736i	$-0.629211\pi$
$557$	333.205	−	577.127i	0.598213	−	1.03613i	0.993085	−	0.117399i	$-0.0374556\pi$
$558$	−708.179	−	281.469i	−1.26914	−	0.504425i
$559$	14.6164	−	8.43879i	0.0261474	−	0.0150962i
$560$	0.0724669	−	5.33548i	0.000129405	−	0.00952765i
$561$	290.370	−	337.104i	0.517594	−	0.600898i
$562$	215.775	+	258.932i	0.383942	+	0.460732i
$563$	−594.943	−	104.904i	−1.05674	−	0.186331i	−0.381829	−	0.924233i	$-0.624706\pi$
$563$	−594.943	−	104.904i	−1.05674	−	0.186331i	−0.674908	+	0.737902i	$0.735817\pi$
$564$	−366.071	+	419.197i	−0.649062	+	0.743258i
$565$	−2.85088	+	2.39217i	−0.00504581	+	0.00423394i
$566$	−2.72887	+	0.982747i	−0.00482132	+	0.00173630i
$567$	629.518	−	675.973i	1.11026	−	1.19219i
$568$	73.6058	−	124.542i	0.129588	−	0.219264i
$569$	−639.699	+	536.771i	−1.12425	+	0.943359i	−0.998811	−	0.0487421i	$-0.984479\pi$
$569$	−639.699	+	536.771i	−1.12425	+	0.943359i	−0.125440	+	0.992101i	$0.540034\pi$
$570$	−1.42206	−	2.55861i	−0.00249483	−	0.00448879i
$571$	−221.543	−	39.0640i	−0.387991	−	0.0684132i	−0.0237497	−	0.999718i	$-0.507560\pi$
$571$	−221.543	−	39.0640i	−0.387991	−	0.0684132i	−0.364241	+	0.931305i	$0.618672\pi$
$572$	19.6096	+	11.4999i	0.0342826	+	0.0201047i
$573$	−162.984	+	189.216i	−0.284440	+	0.330219i
$574$	−49.7938	−	86.9257i	−0.0867488	−	0.151438i
$575$	963.474	−	556.262i	1.67561	−	0.967412i
$576$	549.787	−	171.785i	0.954492	−	0.298237i
$577$	418.572	−	724.989i	0.725429	−	1.25648i	−0.233369	−	0.972388i	$-0.574975\pi$
$577$	418.572	−	724.989i	0.725429	−	1.25648i	0.958797	−	0.284091i	$-0.0916918\pi$
$578$	−0.958414	+	282.275i	−0.00165816	+	0.488365i
$579$	−18.2002	−	0.235241i	−0.0314339	−	0.000406288i
$580$	−0.00350502		2.38016e-5i	−6.04313e−6		4.10372e-8i
$581$	694.240	+	582.536i	1.19490	+	1.00264i
$582$	−475.668	+	548.448i	−0.817299	+	0.942351i
$583$	44.3049	−	121.727i	0.0759946	−	0.208794i
$584$	−920.780	+	519.180i	−1.57668	+	0.889006i
$585$	0.122604	+	0.00316989i	0.000209579	+	5.41861e-6i
$586$	326.310	−	386.210i	0.556843	−	0.659062i
$587$	−8.15169	+	1.43736i	−0.0138870	+	0.00244866i	−0.180587	−	0.983559i	$-0.557800\pi$
$587$	−8.15169	+	1.43736i	−0.0138870	+	0.00244866i	0.166700	+	0.986008i	$0.446689\pi$
$588$	502.786	−	832.506i	0.855078	−	1.41583i
$589$	−663.693	+	241.565i	−1.12681	+	0.410127i
$590$	0.474445	+	2.74519i	0.000804145	+	0.00465286i
$591$	541.013	−	442.176i	0.915420	−	0.748182i
$592$	183.605	+	328.229i	0.310144	+	0.554441i
$593$	921.853			1.55456			0.777279	−	0.629156i	$-0.216599\pi$
$593$	921.853			1.55456			0.777279	+	0.629156i	$0.216599\pi$
$594$	608.842	+	251.147i	1.02499	+	0.422806i
$595$		−	4.05529i		−	0.00681561i
$596$	170.816	−	931.704i	0.286604	−	1.56326i
$597$	−253.769	+	670.147i	−0.425074	+	1.12252i
$598$	−7.06317	−	40.8682i	−0.0118113	−	0.0683414i
$599$	−127.402	−	350.033i	−0.212690	−	0.584362i	0.786769	−	0.617248i	$-0.211752\pi$
$599$	−127.402	−	350.033i	−0.212690	−	0.584362i	−0.999459	+	0.0328858i	$0.989530\pi$
$600$	−396.177	+	450.576i	−0.660295	+	0.750960i
$601$	47.9969	+	272.204i	0.0798617	+	0.452918i	0.998348	+	0.0574643i	$0.0183015\pi$
$601$	47.9969	+	272.204i	0.0798617	+	0.452918i	−0.918486	+	0.395454i	$0.870587\pi$
$602$	533.146	−	631.015i	0.885624	−	1.04820i
$603$	−226.248	+	574.921i	−0.375203	+	0.953434i
$604$	325.803	−	55.1693i	0.539409	−	0.0913400i
$605$	0.762675	+	0.277591i	0.00126062	+	0.000458828i
$606$	354.286	+	68.4496i	0.584631	+	0.112953i
$607$	342.336	−	407.980i	0.563980	−	0.672126i	−0.406403	−	0.913694i	$-0.633217\pi$
$607$	342.336	−	407.980i	0.563980	−	0.672126i	0.970384	+	0.241568i	$0.0776617\pi$
$608$	274.730	−	457.722i	0.451859	−	0.752833i
$609$	−0.881061	−	0.523979i	−0.00144673	−	0.000860392i
$610$	0.00254531	−	0.749651i	4.17263e−6	−	0.00122894i
$611$	−18.7157	−	10.8055i	−0.0306313	−	0.0176850i
$612$	416.021	−	136.217i	0.679774	−	0.222577i
$613$	−99.4269	−	172.213i	−0.162197	−	0.280934i	0.773459	−	0.633846i	$-0.218525\pi$
$613$	−99.4269	−	172.213i	−0.162197	−	0.280934i	−0.935656	+	0.352912i	$0.885191\pi$
$614$	298.469	+	521.041i	0.486106	+	0.848602i
$615$	0.0718147	−	0.378601i	0.000116772	−	0.000615611i
$616$	1093.75	+	204.367i	1.77557	+	0.331764i
$617$	61.3734	−	348.066i	0.0994707	−	0.564126i	−0.893815	−	0.448436i	$-0.851981\pi$
$617$	61.3734	−	348.066i	0.0994707	−	0.564126i	0.993285	−	0.115690i	$-0.0369079\pi$
$618$	−705.519	−	11.5149i	−1.14162	−	0.0186326i
$619$	376.578	+	448.788i	0.608365	+	0.725021i	0.979023	−	0.203748i	$-0.0653124\pi$
$619$	376.578	+	448.788i	0.608365	+	0.725021i	−0.370659	+	0.928769i	$0.620868\pi$
$620$	−3.15757	−	3.81537i	−0.00509286	−	0.00615381i
$621$	−366.883	−	1144.19i	−0.590794	−	1.84249i
$622$	599.242	−	215.805i	0.963412	−	0.346953i
$623$	534.077	+	636.488i	0.857266	+	1.02165i
$624$	10.6661	+	19.6598i	0.0170931	+	0.0315060i
$625$	108.519	−	615.442i	0.173630	−	0.984707i
$626$	65.8449	+	79.0142i	0.105184	+	0.126221i
$627$	576.241	−	201.339i	0.919044	−	0.321115i
$628$	810.381	+	689.422i	1.29041	+	1.09780i
$629$	142.913	+	247.533i	0.227207	+	0.393534i
$630$	5.69857	−	1.88732i	0.00904535	−	0.00299574i
$631$	284.892	+	164.483i	0.451493	+	0.260670i	0.708461	−	0.705750i	$-0.249390\pi$
$631$	284.892	+	164.483i	0.451493	+	0.260670i	−0.256968	+	0.966420i	$0.582723\pi$
$632$	−393.994	+	323.819i	−0.623408	+	0.512372i
$633$	663.578	−	371.766i	1.04831	−	0.587308i
$634$	88.4634	−	240.507i	0.139532	−	0.379349i
$635$	2.05713	−	2.45160i	0.00323958	−	0.00386078i
$636$	99.2303	−	79.9842i	0.156023	−	0.125761i
$637$	35.4879	+	12.9165i	0.0557109	+	0.0202771i
$638$	0.129363	−	0.719360i	0.000202763	−	0.00112752i
$639$	159.494	+	32.3944i	0.249599	+	0.0506954i
$640$	3.66995	+	0.737442i	0.00573429	+	0.00115225i
$641$	109.356	+	620.190i	0.170602	+	0.967534i	0.943098	+	0.332514i	$0.107897\pi$
$641$	109.356	+	620.190i	0.170602	+	0.967534i	−0.772496	+	0.635020i	$0.780992\pi$
$642$	−1066.77	−	408.106i	−1.66163	−	0.635679i
$643$	−146.675	−	402.987i	−0.228111	−	0.626729i	0.771848	−	0.635807i	$-0.219333\pi$
$643$	−146.675	−	402.987i	−0.228111	−	0.626729i	−0.999959	+	0.00907777i	$0.997110\pi$
$644$	−1003.03	−	1764.87i	−1.55750	−	2.74048i
$645$	3.13631	−	0.511313i	0.00486249	−	0.000792733i
$646$	204.049	−	350.668i	0.315865	−	0.542830i
$647$			676.594i			1.04574i	0.852412	+	0.522870i	$0.175139\pi$
$647$			676.594i			1.04574i	−0.852412	+	0.522870i	$0.824861\pi$
$648$	385.030	+	521.206i	0.594182	+	0.804331i
$649$	−580.925			−0.895108
$650$	−20.1369	−	11.7174i	−0.0309799	−	0.0180268i
$651$	−233.057	−	1429.53i	−0.357998	−	2.19590i
$652$	241.093	−	137.021i	0.369775	−	0.210155i
$653$	−942.066	+	342.884i	−1.44267	+	0.525091i	−0.940535	−	0.339696i	$-0.889676\pi$
$653$	−942.066	+	342.884i	−1.44267	+	0.525091i	−0.502139	+	0.864787i	$0.667454\pi$
$654$	−303.303	+	792.816i	−0.463766	+	1.21226i
$655$	−3.56570	+	0.628729i	−0.00544381	+	0.000959891i
$656$	66.3588	−	23.1369i	0.101157	−	0.0352697i
$657$	−890.916	−	787.690i	−1.35604	−	1.19892i
$658$	−1041.07	−	187.216i	−1.58218	−	0.284523i
$659$	−269.613	+	740.757i	−0.409125	+	1.12406i	0.548527	+	0.836133i	$0.315189\pi$
$659$	−269.613	+	740.757i	−0.409125	+	1.12406i	−0.957652	+	0.287929i	$0.907033\pi$
$660$	2.68606	+	3.33239i	0.00406978	+	0.00504907i
$661$	189.550	+	159.052i	0.286763	+	0.240623i	0.774809	−	0.632195i	$-0.217846\pi$
$661$	189.550	+	159.052i	0.286763	+	0.240623i	−0.488046	+	0.872818i	$0.662290\pi$
$662$	−1100.79	−	404.894i	−1.66283	−	0.611622i
$663$	8.30830	+	14.8298i	0.0125314	+	0.0223677i
$664$	−491.162	+	403.680i	−0.739701	+	0.607952i
$665$	2.78180	−	4.81822i	0.00418316	−	0.00724544i
$666$	−281.327	+	316.025i	−0.422412	+	0.474512i
$667$	−1.15481	+	0.666728i	−0.00173135	+	0.000999593i
$668$	−178.966	+	210.366i	−0.267914	+	0.314919i
$669$	310.210	+	887.832i	0.463692	+	1.32710i
$670$	−3.08456	+	2.57046i	−0.00460382	+	0.00383650i
$671$	153.947	+	27.1450i	0.229429	+	0.0404545i
$672$	817.224	+	728.457i	1.21611	+	1.08401i
$673$	57.9800	−	48.6510i	0.0861515	−	0.0722897i	−0.598695	−	0.800977i	$-0.704314\pi$
$673$	57.9800	−	48.6510i	0.0861515	−	0.0722897i	0.684846	+	0.728688i	$0.259869\pi$
$674$	127.625	+	354.387i	0.189355	+	0.525797i
$675$	−624.845	−	255.269i	−0.925697	−	0.378176i
$676$	520.116	−	430.444i	0.769402	−	0.636752i
$677$	−388.600	+	326.074i	−0.574003	+	0.481646i	−0.882972	−	0.469427i	$-0.844461\pi$
$677$	−388.600	+	326.074i	−0.574003	+	0.481646i	0.308968	+	0.951072i	$0.400016\pi$
$678$	12.4602	−	763.438i	0.0183779	−	1.12601i
$679$	−1358.87	−	239.605i	−2.00128	−	0.352879i
$680$	2.79648	+	0.522519i	0.00411247	+	0.000768410i
$681$	−1.47466	−	0.279720i	−0.00216543	−	0.000410749i
$682$	896.109	−	513.320i	1.31394	−	0.752668i
$683$	−412.872	+	238.372i	−0.604498	+	0.349007i	−0.770809	−	0.637066i	$-0.780148\pi$
$683$	−412.872	+	238.372i	−0.604498	+	0.349007i	0.166311	+	0.986073i	$0.446814\pi$
$684$	587.729	+	123.534i	0.859253	+	0.180605i
$685$	−0.340051	+	0.588985i	−0.000496424	+	0.000859832i
$686$	730.888	+	2.48160i	1.06544	+	0.00361750i
$687$	−292.027	+	491.038i	−0.425075	+	0.714757i
$688$	366.445	+	448.956i	0.532623	+	0.652552i
$689$	3.79125	+	3.18124i	0.00550255	+	0.00461718i
$690$	1.48129	−	7.66695i	0.00214679	−	0.0111115i
$691$	−302.988	+	832.454i	−0.438478	+	1.20471i	0.502004	+	0.864865i	$0.332596\pi$
$691$	−302.988	+	832.454i	−0.438478	+	1.20471i	−0.940482	+	0.339844i	$0.889626\pi$
$692$	163.912	+	967.982i	0.236867	+	1.39882i
$693$	185.433	+	1237.96i	0.267580	+	1.78637i
$694$	−98.1507	−	82.9277i	−0.141427	−	0.119492i
$695$	−1.07132	+	0.188903i	−0.00154147	+	0.000271803i
$696$	0.474853	−	0.540055i	0.000682260	−	0.000775941i
$697$	50.1886	−	18.2671i	0.0720065	−	0.0262082i
$698$	−670.193	+	115.828i	−0.960162	+	0.165943i
$699$	158.287	+	59.9395i	0.226447	+	0.0857503i
$700$	−1121.64	−	205.639i	−1.60235	−	0.293770i
$701$	−32.2592			−0.0460189			−0.0230094	−	0.999735i	$-0.507325\pi$
$701$	−32.2592			−0.0460189			−0.0230094	+	0.999735i	$0.507325\pi$
$702$	−16.9724	+	18.5767i	−0.0241772	+	0.0264625i
$703$			392.135i			0.557803i
$704$	−281.857	+	727.907i	−0.400366	+	1.03396i
$705$	−2.57495	−	3.15052i	−0.00365242	−	0.00446882i
$706$	280.587	−	48.4934i	0.397433	−	0.0686876i
$707$	234.564	+	644.459i	0.331774	+	0.911541i
$708$	−489.263	−	295.487i	−0.691050	−	0.417355i
$709$	−118.464	−	671.843i	−0.167086	−	0.947592i	−0.946887	−	0.321565i	$-0.895791\pi$
$709$	−118.464	−	671.843i	−0.167086	−	0.947592i	0.779801	−	0.626027i	$-0.215320\pi$
$710$	0.807916	+	0.682610i	0.00113791	+	0.000961423i
$711$	−489.292	−	299.616i	−0.688174	−	0.421400i
$712$	−507.729	+	286.282i	−0.713103	+	0.402082i
$713$	−1770.47	−	644.400i	−2.48313	−	0.903786i
$714$	628.543	+	545.135i	0.880313	+	0.763494i
$715$	−0.106833	+	0.127319i	−0.000149417	+	0.000178069i
$716$	−6.33043	+	932.218i	−0.00884139	+	1.30198i
$717$	4.66929	−	361.255i	0.00651226	−	0.503843i
$718$	−77.3719	−	0.262702i	−0.107760	−	0.000365881i
$719$	−154.479	−	89.1882i	−0.214852	−	0.124045i	0.388712	−	0.921359i	$-0.372920\pi$
$719$	−154.479	−	89.1882i	−0.214852	−	0.124045i	−0.603564	+	0.797314i	$0.706253\pi$
$720$	0.567218	+	4.17284i	0.000787803	+	0.00579561i
$721$	−670.555	−	1161.43i	−0.930034	−	1.61087i
$722$	−143.508	+	82.2062i	−0.198765	+	0.113859i
$723$	−284.510	−	245.067i	−0.393513	−	0.338959i
$724$	136.851	−	233.358i	0.189020	−	0.322318i
$725$	−0.130074	+	0.737686i	−0.000179412	+	0.00101750i
$726$	−145.548	+	80.8943i	−0.200479	+	0.111425i
$727$	92.5811	+	110.334i	0.127347	+	0.151766i	0.825950	−	0.563743i	$-0.190639\pi$
$727$	92.5811	+	110.334i	0.127347	+	0.151766i	−0.698603	+	0.715509i	$0.746195\pi$
$728$	−21.6294	+	36.5971i	−0.0297107	+	0.0502708i
$729$	−412.313	+	601.198i	−0.565588	+	0.824688i
$730$	−2.61857	−	7.27120i	−0.00358709	−	0.00996054i
$731$	283.103	+	337.389i	0.387281	+	0.461544i
$732$	115.849	+	101.167i	0.158263	+	0.138206i
$733$	−123.401	+	699.844i	−0.168351	+	0.954767i	0.777190	+	0.629265i	$0.216644\pi$
$733$	−123.401	+	699.844i	−0.168351	+	0.954767i	−0.945542	+	0.325501i	$0.894467\pi$
$734$	921.304	−	767.750i	1.25518	−	1.04598i
$735$	5.38741	+	4.64054i	0.00732981	+	0.00631366i
$736$	1346.27	−	464.277i	1.82917	−	0.630811i
$737$	−418.633	−	725.094i	−0.568024	−	0.983846i
$738$	49.0269	+	62.0245i	0.0664321	+	0.0840440i
$739$	−431.977	−	249.402i	−0.584543	−	0.337486i	0.178394	−	0.983959i	$-0.442910\pi$
$739$	−431.977	−	249.402i	−0.584543	−	0.337486i	−0.762937	+	0.646473i	$0.776243\pi$
$740$	−2.59016	+	0.922872i	−0.00350022	+	0.00124712i
$741$	−0.301402	+	23.3190i	−0.000406750	+	0.0314696i
$742$	227.348	+	83.6233i	0.306399	+	0.112700i
$743$	758.718	−	904.205i	1.02115	−	1.21696i	0.0452027	−	0.998978i	$-0.485607\pi$
$743$	758.718	−	904.205i	1.02115	−	1.21696i	0.975952	−	0.217987i	$-0.0699489\pi$
$744$	1015.82	+	23.4801i	1.36534	+	0.0315592i
$745$	6.50770	+	2.36861i	0.00873517	+	0.00317934i
$746$	−1197.82	−	215.404i	−1.60566	−	0.288746i
$747$	−609.963	−	373.508i	−0.816550	−	0.500011i
$748$	−206.676	+	556.060i	−0.276305	+	0.743396i
$749$	−376.961	−	2137.85i	−0.503285	−	2.85427i
$750$	−5.52889	−	6.81181i	−0.00737185	−	0.00908241i
$751$	−302.047	−	829.866i	−0.402192	−	1.10501i	−0.961200	−	0.275852i	$-0.911040\pi$
$751$	−302.047	−	829.866i	−0.402192	−	1.10501i	0.559008	−	0.829162i	$-0.311182\pi$
$752$	263.243	−	693.788i	0.350057	−	0.922591i
$753$	715.878	+	875.895i	0.950702	+	1.16321i
$754$	0.0241359	+	0.0140443i	3.20104e−5	+	1.86264e-5i
$755$			2.41590i			0.00319987i
$756$	−473.512	+	1136.95i	−0.626339	+	1.50390i
$757$	431.216			0.569638			0.284819	−	0.958581i	$-0.408067\pi$
$757$	431.216			0.569638			0.284819	+	0.958581i	$0.408067\pi$
$758$	533.083	−	916.129i	0.703275	−	1.20861i
$759$	1522.79	+	576.645i	2.00631	+	0.759743i
$760$	2.96415	+	2.53912i	0.00390020	+	0.00334094i
$761$	104.477	−	38.0267i	0.137290	−	0.0499694i	−0.272461	−	0.962167i	$-0.587838\pi$
$761$	104.477	−	38.0267i	0.137290	−	0.0499694i	0.409751	+	0.912197i	$0.365616\pi$
$762$	103.450	+	648.400i	0.135761	+	0.850919i
$763$	−1588.84	+	280.156i	−2.08236	+	0.367177i
$764$	116.007	−	312.115i	0.151841	−	0.408528i
$765$	0.474109	+	3.16517i	0.000619751	+	0.00413748i
$766$	125.151	−	695.943i	0.163383	−	0.908542i
$767$	7.59104	−	20.8562i	0.00989705	−	0.0271919i
$768$	−607.634	+	469.687i	−0.791190	+	0.611571i
$769$	−524.769	−	440.334i	−0.682405	−	0.572606i	0.234303	−	0.972164i	$-0.424719\pi$
$769$	−524.769	−	440.334i	−0.682405	−	0.572606i	−0.916708	+	0.399558i	$0.869164\pi$
$770$	−2.80827	+	7.63489i	−0.00364710	+	0.00991544i
$771$	409.831	−	689.123i	0.531557	−	0.893804i
$772$	22.8612	−	8.14542i	0.0296130	−	0.0105511i
$773$	−327.341	+	566.971i	−0.423468	+	0.733468i	−0.996276	−	0.0862217i	$-0.972521\pi$
$773$	−327.341	+	566.971i	−0.423468	+	0.733468i	0.572808	+	0.819689i	$0.305854\pi$
$774$	−342.350	+	554.841i	−0.442313	+	0.716849i
$775$	−916.590	+	529.194i	−1.18270	+	0.682830i
$776$	340.317	−	906.185i	0.438553	−	1.16776i
$777$	−790.075	−	149.865i	−1.01683	−	0.192876i
$778$	−369.594	−	443.515i	−0.475057	−	0.570071i
$779$	72.1613	+	12.7240i	0.0926333	+	0.0163337i
$780$	−0.154737	+	0.0528892i	−0.000198381	+	6.78067e-5i
$781$	−168.953	+	141.768i	−0.216329	+	0.181522i
$782$	1018.27	−	366.709i	1.30213	−	0.468937i
$783$	0.748932	+	0.305962i	0.000956490	+	0.000390756i
$784$	−242.499	+	1273.86i	−0.309309	+	1.62482i
$785$	−5.95890	+	5.00011i	−0.00759095	+	0.00636957i
$786$	381.872	−	637.177i	0.485843	−	0.810658i
$787$	1342.11	+	236.650i	1.70535	+	0.300698i	0.939557	−	0.342393i	$-0.111238\pi$
$787$	1342.11	+	236.650i	1.70535	+	0.300698i	0.765789	+	0.643092i	$0.222349\pi$
$788$	−471.284	+	803.635i	−0.598076	+	1.01984i
$789$	−144.594	−	413.833i	−0.183262	−	0.524503i
$790$	−1.85333	−	3.23538i	−0.00234599	−	0.00409542i
$791$	1256.78	−	725.602i	1.58885	−	0.917323i
$792$	−877.573	−	31.6369i	−1.10805	−	0.0399456i
$793$	−2.98620	+	5.17225i	−0.00376570	+	0.00652238i
$794$	0.144716	−	42.6223i	0.000182263	−	0.0536805i
$795$	0.455443	+	0.812936i	0.000572884	+	0.00102256i
$796$	6.48803	−	955.426i	0.00815080	−	1.20028i
$797$	210.572	+	176.691i	0.264206	+	0.221695i	0.765261	−	0.643720i	$-0.222610\pi$
$797$	210.572	+	176.691i	0.264206	+	0.221695i	−0.501055	+	0.865416i	$0.667054\pi$
$798$	372.847	+	1078.85i	0.467227	+	1.35195i
$799$	192.883	−	529.941i	0.241405	−	0.663255i
$800$	286.328	−	746.975i	0.357911	−	0.933719i
$801$	−491.262	−	434.342i	−0.613311	−	0.542250i
$802$	−725.401	+	858.562i	−0.904490	+	1.07053i
$803$	1587.07	−	279.843i	1.97642	−	0.348497i
$804$	16.2399	−	823.622i	0.0201989	−	1.02441i
$805$	13.9465	−	5.07609i	0.0173248	−	0.00630571i
$806$	6.71947	+	38.8795i	0.00833681	+	0.0482375i
$807$	13.7969	+	84.6278i	0.0170965	+	0.104867i
$808$	−474.635	+	78.7147i	−0.587419	+	0.0974192i
$809$	787.388			0.973286			0.486643	−	0.873601i	$-0.338221\pi$
$809$	787.388			0.973286			0.486643	+	0.873601i	$0.338221\pi$
$810$	−4.22711	+	2.13929i	−0.00521866	+	0.00264110i
$811$		−	343.690i		−	0.423785i	−0.977293	−	0.211893i	$-0.932037\pi$
$811$		−	343.690i		−	0.423785i	0.977293	−	0.211893i	$-0.0679627\pi$
$812$	1.34439	+	0.246476i	0.00165565	+	0.000303542i
$813$	1352.18	−	220.447i	1.66320	−	0.271153i
$814$	−97.6473	−	564.996i	−0.119960	−	0.694099i
$815$	0.693429	+	1.90518i	0.000850834	+	0.00233765i
$816$	−456.905	+	363.196i	−0.559933	+	0.445093i
$817$	104.925	+	595.062i	0.128428	+	0.728350i
$818$	−199.720	+	236.382i	−0.244156	+	0.288976i
$819$	−46.8679	−	9.51922i	−0.0572257	−	0.0116230i
$820$	0.0857828	+	0.506591i	0.000104613	+	0.000617794i
$821$	381.598	+	138.890i	0.464796	+	0.169172i	0.563794	−	0.825916i	$-0.309341\pi$
$821$	381.598	+	138.890i	0.464796	+	0.169172i	−0.0989974	+	0.995088i	$0.531564\pi$
$822$	−45.5773	−	131.880i	−0.0554468	−	0.160438i
$823$	99.2596	−	118.293i	0.120607	−	0.143734i	−0.702362	−	0.711820i	$-0.747871\pi$
$823$	99.2596	−	118.293i	0.120607	−	0.143734i	0.822969	+	0.568086i	$0.192316\pi$
$824$	887.311	−	312.757i	1.07683	−	0.379559i
$825$	797.999	−	447.074i	0.967272	−	0.541908i
$826$	3.68846	−	1086.33i	0.00446544	−	1.31518i
$827$	780.782	+	450.785i	0.944114	+	0.545084i	0.891248	−	0.453517i	$-0.149831\pi$
$827$	780.782	+	450.785i	0.944114	+	0.545084i	0.0528664	+	0.998602i	$0.483164\pi$
$828$	989.204	+	1260.22i	1.19469	+	1.52201i
$829$	−94.0098	−	162.830i	−0.113401	−	0.196417i	0.803738	−	0.594983i	$-0.202841\pi$
$829$	−94.0098	−	162.830i	−0.113401	−	0.196417i	−0.917140	+	0.398566i	$0.869508\pi$
$830$	−2.31040	−	4.03330i	−0.00278362	−	0.00485940i
$831$	−598.534	+	209.128i	−0.720257	+	0.251659i
$832$	−22.4500	−	19.6308i	−0.0269832	−	0.0235947i
$833$	−171.132	+	970.536i	−0.205440	+	1.16511i
$834$	114.734	−	191.441i	0.137571	−	0.229546i
$835$	−1.29797	−	1.54686i	−0.00155446	−	0.00185253i
$836$	−626.998	+	518.900i	−0.749998	+	0.620693i
$837$	349.030	+	1088.51i	0.417001	+	1.30049i
$838$	−510.808	+	183.957i	−0.609556	+	0.219519i
$839$	−639.149	−	761.708i	−0.761798	−	0.907876i	0.236162	−	0.971714i	$-0.424110\pi$
$839$	−639.149	−	761.708i	−0.761798	−	0.907876i	−0.997960	+	0.0638379i	$0.979666\pi$
$840$	−6.24864	+	5.00179i	−0.00743886	+	0.00595451i
$841$	−146.038	+	828.222i	−0.173648	+	0.984807i
$842$	1.83651	+	2.20383i	0.00218113	+	0.00261737i
$843$	94.2205	−	496.722i	0.111768	−	0.589231i
$844$	−657.152	+	772.449i	−0.778616	+	0.915224i
$845$	2.46799	+	4.27469i	0.00292070	+	0.00505880i
$846$	834.450	+	24.4098i	0.986347	+	0.0288532i
$847$	−274.087	−	158.244i	−0.323597	−	0.186829i
$848$	−86.9592	+	146.002i	−0.102546	+	0.172172i
$849$	3.73934	+	2.22384i	0.00440441	+	0.00261936i
$850$	209.877	−	570.597i	0.246914	−	0.671291i
$851$	−672.397	+	801.331i	−0.790126	+	0.941635i
$852$	−214.405	+	33.4615i	−0.251649	+	0.0392740i
$853$	−789.347	−	287.299i	−0.925377	−	0.336810i	−0.165001	−	0.986293i	$-0.552763\pi$
$853$	−789.347	−	287.299i	−0.925377	−	0.336810i	−0.760376	+	0.649484i	$0.774985\pi$
$854$	−51.7388	+	287.709i	−0.0605840	+	0.336896i
$855$	−1.60790	+	4.08587i	−0.00188059	+	0.00477879i
$856$	1522.81	+	15.5117i	1.77898	+	0.0181212i
$857$	208.651	+	1183.32i	0.243466	+	1.38077i	0.824028	+	0.566549i	$0.191722\pi$
$857$	208.651	+	1183.32i	0.243466	+	1.38077i	−0.580562	+	0.814216i	$0.697167\pi$
$858$	−5.37249	−	33.6735i	−0.00626164	−	0.0392464i
$859$	129.769	+	356.538i	0.151070	+	0.415062i	0.992025	−	0.126044i	$-0.0402280\pi$
$859$	129.769	+	356.538i	0.151070	+	0.415062i	−0.840954	+	0.541106i	$0.818006\pi$
$860$	−3.68361	+	2.09351i	−0.00428327	+	0.00243431i
$861$	−53.2146	+	140.528i	−0.0618056	+	0.163215i
$862$	−530.134	+	911.062i	−0.615005	+	1.05692i
$863$			1664.89i			1.92918i	0.263745	+	0.964592i	$0.415042\pi$
$863$			1664.89i			1.92918i	−0.263745	+	0.964592i	$0.584958\pi$
$864$	−723.012	−	473.022i	−0.836819	−	0.547479i
$865$	−7.17780			−0.00829803
$866$	−388.951	−	226.325i	−0.449135	−	0.261346i
$867$	327.845	−	267.951i	0.378137	−	0.309055i
$868$	954.222	+	1678.99i	1.09933	+	1.93432i
$869$	730.618	−	265.923i	0.840757	−	0.306010i
$870$	0.00331337	+	0.00408220i	3.80847e−6	+	4.69219e-6i
$871$	31.5025	−	5.55473i	0.0361682	−	0.00637742i
$872$	11.5283	−	1131.74i	0.0132205	−	1.29787i
$873$	1088.62	+	28.1458i	1.24698	+	0.0322403i
$874$	1461.39	+	262.801i	1.67207	+	0.300688i
$875$	5.70306	−	15.6690i	0.00651778	−	0.0179075i
$876$	1478.99	+	571.573i	1.68835	+	0.652481i
$877$	−651.110	−	546.346i	−0.742429	−	0.622972i	0.191060	−	0.981578i	$-0.438807\pi$
$877$	−651.110	−	546.346i	−0.742429	−	0.622972i	−0.933489	+	0.358607i	$0.883252\pi$
$878$	345.174	+	126.962i	0.393137	+	0.144604i
$879$	−758.344	−	9.80174i	−0.862735	−	0.0111510i
$880$	−4.90309	−	2.92029i	−0.00557169	−	0.00331851i
$881$	77.5520	−	134.324i	0.0880272	−	0.152468i	−0.818650	−	0.574293i	$-0.805277\pi$
$881$	77.5520	−	134.324i	0.0880272	−	0.152468i	0.906677	+	0.421825i	$0.138610\pi$
$882$	−1443.46	+	211.207i	−1.63658	+	0.239463i
$883$	421.366	−	243.276i	0.477199	−	0.275511i	−0.242050	−	0.970264i	$-0.577820\pi$
$883$	421.366	−	243.276i	0.477199	−	0.275511i	0.719248	+	0.694753i	$0.244486\pi$
$884$	−17.2628	−	14.6862i	−0.0195281	−	0.0166133i
$885$	2.72724	−	3.16618i	0.00308163	−	0.00357761i
$886$	964.389	−	803.654i	1.08847	−	0.907059i
$887$	−677.148	−	119.399i	−0.763414	−	0.134610i	−0.221633	−	0.975130i	$-0.571139\pi$
$887$	−677.148	−	119.399i	−0.763414	−	0.134610i	−0.541781	+	0.840520i	$0.682250\pi$
$888$	205.145	−	525.516i	0.231019	−	0.591797i
$889$	−955.989	+	802.170i	−1.07535	+	0.902328i
$890$	−1.44391	−	4.00943i	−0.00162238	−	0.00450497i
$891$	−289.463	−	944.552i	−0.324874	−	1.06010i
$892$	−799.485	−	966.036i	−0.896284	−	1.08300i
$893$	592.692	−	497.328i	0.663709	−	0.556918i
$894$	−1241.92	+	690.250i	−1.38917	+	0.772091i
$895$	−6.71219	−	1.18354i	−0.00749965	−	0.00132239i
$896$	−1359.40	−	531.697i	−1.51719	−	0.593412i
$897$	−40.6011	+	47.1356i	−0.0452632	+	0.0525481i
$898$	−388.279	+	222.419i	−0.432382	+	0.247682i
$899$	1.09861	−	0.634285i	0.00122204	−	0.000705545i
$900$	899.490	+	29.3694i	0.999433	+	0.0326326i
$901$	−64.5751	+	111.847i	−0.0716705	+	0.124137i
$902$	−107.140	−	0.363774i	−0.118780	−	0.000403298i
$903$	−1239.03	−	16.0147i	−1.37213	−	0.0177350i
$904$	338.432	+	960.153i	0.374372	+	1.06212i
$905$	1.51512	+	1.27134i	0.00167417	+	0.00140479i
$906$	−374.449	−	324.759i	−0.413299	−	0.358453i
$907$	486.942	−	1337.86i	0.536871	−	1.47504i	−0.313874	−	0.949465i	$-0.601627\pi$
$907$	486.942	−	1337.86i	0.536871	−	1.47504i	0.850746	−	0.525578i	$-0.176151\pi$
$908$	1.97318	−	0.334126i	0.00217311	−	0.000367980i
$909$	−258.423	−	475.580i	−0.284294	−	0.523191i
$910$	−0.237410	−	0.200588i	−0.000260890	−	0.000220426i
$911$	483.356	−	85.2286i	0.530577	−	0.0935550i	0.0980594	−	0.995181i	$-0.468736\pi$
$911$	483.356	−	85.2286i	0.530577	−	0.0935550i	0.432518	+	0.901626i	$0.357625\pi$
$912$	−792.005	+	118.102i	−0.868426	+	0.129498i
$913$	910.805	−	331.506i	0.997596	−	0.363095i
$914$	365.519	−	63.1720i	0.399911	−	0.0691160i
$915$	−0.870674	+	0.711611i	−0.000951556	+	0.000777716i
$916$	137.368	−	749.262i	0.149965	−	0.817971i
$917$	1411.88			1.53967
$918$	−554.314	−	351.996i	−0.603827	−	0.383438i
$919$			798.127i			0.868473i	0.900799	+	0.434237i	$0.142982\pi$
$919$			798.127i			0.868473i	−0.900799	+	0.434237i	$0.857018\pi$
$920$	1.70343	+	10.2714i	0.00185155	+	0.0111645i
$921$	318.974	−	842.338i	0.346334	−	0.914591i
$922$	723.748	−	125.084i	0.784976	−	0.135666i
$923$	−2.88199	−	7.91820i	−0.00312242	−	0.00857877i
$924$	−805.855	−	1461.59i	−0.872138	−	1.58181i
$925$	102.040	+	578.696i	0.110313	+	0.625618i
$926$	35.2406	+	29.7749i	0.0380569	+	0.0321543i
$927$	659.156	+	828.110i	0.711064	+	0.893323i
$928$	−0.343190	+	0.895315i	−0.000369816	+	0.000964779i
$929$	1243.88	+	452.736i	1.33895	+	0.487337i	0.909481	−	0.415745i	$-0.136479\pi$
$929$	1243.88	+	452.736i	1.33895	+	0.487337i	0.429467	+	0.903083i	$0.358702\pi$
$930$	−1.40921	+	7.29387i	−0.00151527	+	0.00784287i
$931$	−869.084	+	1035.73i	−0.933495	+	1.11250i
$932$	−225.669	−	1.53245i	−0.242134	−	0.00164426i
$933$	−821.136	−	488.341i	−0.880103	−	0.523409i
$934$	−968.944	−	3.28988i	−1.03741	−	0.00352235i
$935$	−3.75609	−	2.16858i	−0.00401721	−	0.00231934i
$936$	12.6032	−	31.0930i	0.0134650	−	0.0332190i
$937$	248.718	+	430.792i	0.265441	+	0.459757i	0.967679	−	0.252185i	$-0.0811492\pi$
$937$	248.718	+	430.792i	0.265441	+	0.459757i	−0.702238	+	0.711942i	$0.747816\pi$
$938$	1358.59	−	778.244i	1.44839	−	0.829684i
$939$	28.7518	−	151.577i	0.0306196	−	0.161424i
$940$	4.67986	+	2.74446i	0.00497858	+	0.00291964i
$941$	−65.2086	+	369.816i	−0.0692971	+	0.393004i	0.930356	+	0.366658i	$0.119498\pi$
$941$	−65.2086	+	369.816i	−0.0692971	+	0.393004i	−0.999653	+	0.0263455i	$0.991613\pi$
$942$	26.0443	−	1595.73i	0.0276479	−	1.69398i
$943$	125.644	+	149.737i	0.133239	+	0.158788i
$944$	748.648	+	142.516i	0.793059	+	0.150971i
$945$	−7.61771	−	4.80113i	−0.00806106	−	0.00508056i
$946$	−299.357	−	831.249i	−0.316445	−	0.878698i
$947$	−278.093	−	331.419i	−0.293657	−	0.349967i	0.598963	−	0.800777i	$-0.295580\pi$
$947$	−278.093	−	331.419i	−0.293657	−	0.349967i	−0.892620	+	0.450810i	$0.851135\pi$
$948$	750.598	+	147.664i	0.791770	+	0.155764i
$949$	−10.6916	+	60.6352i	−0.0112662	+	0.0638937i
$950$	640.773	−	533.975i	0.674498	−	0.562079i
$951$	−362.878	+	126.790i	−0.381575	+	0.133323i
$952$	−1038.52	−	390.017i	−1.09089	−	0.409681i
$953$	−701.965	−	1215.84i	−0.736585	−	1.27580i	−0.954024	−	0.299729i	$-0.903104\pi$
$953$	−701.965	−	1215.84i	−0.736585	−	1.27580i	0.217440	−	0.976074i	$-0.430229\pi$
$954$	−187.223	−	38.6888i	−0.196251	−	0.0405543i
$955$	2.10829	+	1.21722i	0.00220763	+	0.00127458i
$956$	161.678	+	453.771i	0.169119	+	0.474656i
$957$	−0.956471	+	0.535858i	−0.000999448	+	0.000559935i
$958$	−1209.18	−	444.760i	−1.26219	−	0.464259i
$959$	170.469	−	203.157i	0.177757	−	0.211842i
$960$	−2.64404	−	4.95346i	−0.00275421	−	0.00515986i
$961$	781.275	+	284.361i	0.812982	+	0.295901i
$962$	21.5603	+	3.87719i	0.0224120	+	0.00403034i
$963$	544.159	+	1624.53i	0.565066	+	1.68695i
$964$	469.305	+	174.431i	0.486831	+	0.180945i
$965$	0.0308111	+	0.174738i	3.19286e−5	+	0.000181076i
$966$	−1088.00	+	2843.97i	−1.12629	+	2.94406i
$967$	116.860	+	321.071i	0.120848	+	0.332028i	0.985336	−	0.170626i	$-0.0545791\pi$
$967$	116.860	+	321.071i	0.120848	+	0.332028i	−0.864488	+	0.502654i	$0.832357\pi$
$968$	144.439	−	168.617i	0.149214	−	0.174191i
$969$	−600.641	+	97.9227i	−0.619857	+	0.101055i
$970$	6.11685	+	3.55931i	0.00630603	+	0.00366939i
$971$			459.145i			0.472858i	0.971649	+	0.236429i	$0.0759771\pi$
$971$			459.145i			0.472858i	−0.971649	+	0.236429i	$0.924023\pi$
$972$	236.657	−	942.750i	0.243474	−	0.969907i
$973$	424.201			0.435972
$974$	142.476	−	244.852i	0.146279	−	0.251388i
$975$	5.62316	+	34.4915i	0.00576734	+	0.0353759i
$976$	−191.734	−	72.7494i	−0.196449	−	0.0745383i
$977$	−557.923	+	203.067i	−0.571057	+	0.207848i	−0.611378	−	0.791339i	$-0.709384\pi$
$977$	−557.923	+	203.067i	−0.571057	+	0.207848i	0.0403203	+	0.999187i	$0.487162\pi$
$978$	−388.505	−	148.628i	−0.397245	−	0.151972i
$979$	875.128	−	154.309i	0.893900	−	0.157619i
$980$	−8.88665	−	3.30299i	−0.00906801	−	0.00337040i
$981$	1207.35	−	404.417i	1.23073	−	0.412250i
$982$	47.0672	−	261.732i	0.0479300	−	0.266529i
$983$	−15.8459	+	43.5363i	−0.0161200	+	0.0442892i	−0.947492	−	0.319781i	$-0.896391\pi$
$983$	−15.8459	+	43.5363i	−0.0161200	+	0.0442892i	0.931372	+	0.364070i	$0.118613\pi$
$984$	−90.0496	−	54.8030i	−0.0915139	−	0.0556941i
$985$	−5.21775	−	4.37821i	−0.00529721	−	0.00444488i
$986$	−0.251556	+	0.683910i	−0.000255128	+	0.000693621i
$987$	775.504	+	1384.22i	0.785718	+	1.40246i
$988$	−10.4363	−	29.2908i	−0.0105631	−	0.0296466i
$989$	−805.940	+	1395.93i	−0.814904	+	1.41145i
$990$	1.29926	−	6.28739i	0.00131238	−	0.00635090i
$991$	−608.358	+	351.236i	−0.613883	+	0.354426i	−0.774484	−	0.632594i	$-0.781990\pi$
$991$	−608.358	+	351.236i	−0.613883	+	0.354426i	0.160600	+	0.987019i	$0.448657\pi$
$992$	−1280.76	+	441.684i	−1.29109	+	0.445246i
$993$	580.314	+	1660.88i	0.584404	+	1.67259i
$994$	−264.035	−	316.843i	−0.265629	−	0.318756i
$995$	6.87929	+	1.21300i	0.00691386	+	0.00121910i
$996$	935.713	+	184.081i	0.939471	+	0.184821i
$997$	1345.84	−	1129.29i	1.34989	−	1.13269i	0.370927	−	0.928662i	$-0.379040\pi$
$997$	1345.84	−	1129.29i	1.34989	−	1.13269i	0.978964	−	0.204031i	$-0.0654043\pi$
$998$	−705.493	+	254.069i	−0.706907	+	0.254578i
$999$	634.178	+	24.6016i	0.634813	+	0.0246262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.103.28	yes	204
3.2	odd	2		324.3.j.a.199.7		204
4.3	odd	2	inner	108.3.j.a.103.14	yes	204
12.11	even	2		324.3.j.a.199.21		204
27.11	odd	18		324.3.j.a.127.21		204
27.16	even	9	inner	108.3.j.a.43.14	✓	204
108.11	even	18		324.3.j.a.127.7		204
108.43	odd	18	inner	108.3.j.a.43.28	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.14	✓	204	27.16	even	9	inner
108.3.j.a.43.28	yes	204	108.43	odd	18	inner
108.3.j.a.103.14	yes	204	4.3	odd	2	inner
108.3.j.a.103.28	yes	204	1.1	even	1	trivial
324.3.j.a.127.7		204	108.11	even	18
324.3.j.a.127.21		204	27.11	odd	18
324.3.j.a.199.7		204	3.2	odd	2
324.3.j.a.199.21		204	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72865 + 1.00588i) q^{2} +(-0.482718 - 2.96091i) q^{3} +(1.97643 + 3.47760i) q^{4} +(-0.0274809 + 0.0100022i) q^{5} +(2.14386 - 5.60392i) q^{6} +(11.2305 - 1.98024i) q^{7} +(-0.0814860 + 7.99958i) q^{8} +(-8.53397 + 2.85857i) q^{9} +(-0.0575657 - 0.0103520i) q^{10} +(4.17143 - 11.4609i) q^{11} +(9.34281 - 7.53073i) q^{12} +(0.356957 + 0.299523i) q^{13} +(21.4055 + 7.87337i) q^{14} +(0.0428812 + 0.0765402i) q^{15} +(-8.18744 + 13.7465i) q^{16} +(-6.07992 + 10.5307i) q^{17} +(-17.6276 - 3.64266i) q^{18} +(-14.4475 + 8.34127i) q^{19} +(-0.0890979 - 0.0757989i) q^{20} +(-11.2845 - 32.2967i) q^{21} +(18.7391 - 15.6159i) q^{22} +(-43.8264 - 7.72777i) q^{23} +(23.7254 - 3.62027i) q^{24} +(-19.1505 + 16.0691i) q^{25} +(0.315770 + 0.876822i) q^{26} +(12.5835 + 23.8884i) q^{27} +(29.0829 + 35.1415i) q^{28} +(0.0229535 - 0.0192603i) q^{29} +(-0.00286346 + 0.175444i) q^{30} +(41.6937 + 7.35173i) q^{31} +(-27.9804 + 15.5272i) q^{32} +(-35.9483 - 6.81883i) q^{33} +(-21.1026 + 12.0883i) q^{34} +(-0.288818 + 0.166749i) q^{35} +(-26.8078 - 24.0280i) q^{36} +(11.7529 - 20.3566i) q^{37} +(-33.3649 - 0.113285i) q^{38} +(0.714549 - 1.20150i) q^{39} +(-0.0777744 - 0.220651i) q^{40} +(-3.36469 - 2.82331i) q^{41} +(12.9795 - 67.1803i) q^{42} +(12.3880 - 34.0357i) q^{43} +(48.1010 - 8.14511i) q^{44} +(0.205929 - 0.163915i) q^{45} +(-67.9871 - 57.4425i) q^{46} +(-45.6736 + 8.05348i) q^{47} +(44.6543 + 17.6066i) q^{48} +(76.1584 - 27.7194i) q^{49} +(-49.2679 + 8.51488i) q^{50} +(34.1154 + 12.9187i) q^{51} +(-0.336120 + 1.83334i) q^{52} +10.6210 q^{53} +(-2.27643 + 53.9520i) q^{54} +0.356679i q^{55} +(14.9260 + 90.0009i) q^{56} +(31.6718 + 38.7513i) q^{57} +(0.0590519 - 0.0102058i) q^{58} +(-16.2907 - 44.7583i) q^{59} +(-0.181425 + 0.300400i) q^{60} +(2.22565 + 12.6223i) q^{61} +(64.6788 + 54.6472i) q^{62} +(-90.1803 + 49.0026i) q^{63} +(-63.9867 - 1.30371i) q^{64} +(-0.0128054 - 0.00466078i) q^{65} +(-55.2830 - 47.9468i) q^{66} +(44.1264 - 52.5878i) q^{67} +(-48.6383 - 0.330289i) q^{68} +(-1.72546 + 133.496i) q^{69} +(-0.666993 - 0.00226466i) q^{70} +(-15.6606 - 9.04168i) q^{71} +(-22.1720 - 68.5011i) q^{72} +(66.0665 + 114.430i) q^{73} +(40.7927 - 23.3674i) q^{74} +(56.8235 + 48.9459i) q^{75} +(-57.5621 - 33.7567i) q^{76} +(24.1519 - 136.972i) q^{77} +(2.44376 - 1.35822i) q^{78} +(40.9769 + 48.8344i) q^{79} +(0.0875029 - 0.459658i) q^{80} +(64.6572 - 48.7898i) q^{81} +(-2.97646 - 8.26496i) q^{82} +(51.0828 + 60.8781i) q^{83} +(90.0120 - 103.075i) q^{84} +(0.0617509 - 0.350207i) q^{85} +(55.6500 - 46.3749i) q^{86} +(-0.0681080 - 0.0586659i) q^{87} +(91.3425 + 34.3036i) q^{88} +(36.4298 + 63.0983i) q^{89} +(0.520856 - 0.0762115i) q^{90} +(4.60194 + 2.65693i) q^{91} +(-59.7457 - 167.684i) q^{92} +(1.64150 - 127.000i) q^{93} +(-87.0542 - 32.0203i) q^{94} +(0.313599 - 0.373733i) q^{95} +(59.4814 + 75.3522i) q^{96} +(-113.701 - 41.3836i) q^{97} +(159.533 + 28.6888i) q^{98} +(-2.83707 + 109.731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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