LMFDB - Embedded newform 108.3.j.a.43.28

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			43.28
Character	$\chi$	$=$	108.43
Dual form			108.3.j.a.103.28

$q$-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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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	0.339271	−	0.940689i	$-0.389820\pi$
$5$	−0.0274809	−	0.0100022i	−0.00549618	−	0.00200045i	−0.344767	+	0.938688i	$0.612042\pi$
$6$	2.14386	+	5.60392i	0.357309	+	0.933986i
$7$	11.2305	+	1.98024i	1.60436	+	0.282892i	0.902911	−	0.429827i	$-0.141425\pi$
$7$	11.2305	+	1.98024i	1.60436	+	0.282892i	0.701450	+	0.712719i	$0.252537\pi$
$8$	−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	0.971680	+	0.236300i	$0.0759347\pi$
$11$	4.17143	+	11.4609i	0.379220	+	1.04190i	−0.592460	+	0.805600i	$0.701843\pi$
$12$	9.34281	+	7.53073i	0.778567	+	0.627561i
$13$	0.356957	−	0.299523i	0.0274582	−	0.0230402i	−0.628955	−	0.777442i	$-0.716517\pi$
$13$	0.356957	−	0.299523i	0.0274582	−	0.0230402i	0.656413	+	0.754401i	$0.272073\pi$
$14$	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	0.629924	−	0.776657i	$-0.283086\pi$
$17$	−6.07992	−	10.5307i	−0.357642	−	0.619455i	−0.987566	+	0.157202i	$0.949753\pi$
$18$	−17.6276	+	3.64266i	−0.979309	+	0.202370i
$19$	−14.4475	−	8.34127i	−0.760395	−	0.439014i	0.0690427	−	0.997614i	$-0.478006\pi$
$19$	−14.4475	−	8.34127i	−0.760395	−	0.439014i	−0.829437	+	0.558600i	$0.811339\pi$
$20$	−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	−0.996695	−	0.0812406i	$-0.974112\pi$
$23$	−43.8264	+	7.72777i	−1.90550	+	0.335990i	−0.908801	+	0.417231i	$0.863001\pi$
$24$	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	0.643183	−	0.765712i	$-0.277613\pi$
$29$	0.0229535	+	0.0192603i	0.000791500	+	0.000664147i	−0.642392	+	0.766376i	$0.722058\pi$
$30$	−0.00286346	−	0.175444i	−9.54487e−5	−	0.00584813i
$31$	41.6937	−	7.35173i	1.34496	−	0.237153i	0.545620	−	0.838033i	$-0.316294\pi$
$31$	41.6937	−	7.35173i	1.34496	−	0.237153i	0.799339	+	0.600880i	$0.205183\pi$
$32$	−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	0.979996	−	0.199016i	$-0.0637746\pi$
$37$	11.7529	+	20.3566i	0.317645	+	0.550178i	−0.662351	+	0.749194i	$0.730441\pi$
$38$	−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	−0.682898	−	0.730514i	$-0.739280\pi$
$41$	−3.36469	+	2.82331i	−0.0820656	+	0.0688612i	0.600832	+	0.799375i	$0.294836\pi$
$42$	12.9795	+	67.1803i	0.309036	+	1.59953i
$43$	12.3880	+	34.0357i	0.288092	+	0.791527i	0.996333	+	0.0855564i	$0.0272668\pi$
$43$	12.3880	+	34.0357i	0.288092	+	0.791527i	−0.708241	+	0.705971i	$0.750511\pi$
$44$	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	−0.334848	−	0.942272i	$-0.608685\pi$
$47$	−45.6736	−	8.05348i	−0.971778	−	0.171351i	−0.636930	+	0.770922i	$0.719796\pi$
$48$	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	0.721681	+	0.692226i	$0.243370\pi$
$59$	−16.2907	+	44.7583i	−0.276113	+	0.758615i	−0.997794	+	0.0663887i	$0.978852\pi$
$60$	−0.181425	−	0.300400i	−0.00302374	−	0.00500667i
$61$	2.22565	−	12.6223i	0.0364861	−	0.206923i	−0.961115	−	0.276149i	$-0.910942\pi$
$61$	2.22565	−	12.6223i	0.0364861	−	0.206923i	0.997601	+	0.0692259i	$0.0220529\pi$
$62$	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	0.987185	−	0.159583i	$-0.0510150\pi$
$67$	44.1264	+	52.5878i	0.658603	+	0.784893i	−0.328581	+	0.944476i	$0.606571\pi$
$68$	−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	−0.606215	−	0.795301i	$-0.707313\pi$
$71$	−15.6606	+	9.04168i	−0.220572	+	0.127348i	0.385643	+	0.922648i	$0.373980\pi$
$72$	−22.1720	+	68.5011i	−0.307944	+	0.951405i
$73$	66.0665	−	114.430i	0.905020	−	1.56754i	0.0841297	−	0.996455i	$-0.473189\pi$
$73$	66.0665	−	114.430i	0.905020	−	1.56754i	0.820890	−	0.571086i	$-0.193478\pi$
$74$	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	−0.441577	−	0.897223i	$-0.645581\pi$
$79$	40.9769	−	48.8344i	0.518695	−	0.618157i	0.960272	+	0.279067i	$0.0900251\pi$
$80$	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	−0.364827	−	0.931075i	$-0.618872\pi$
$83$	51.0828	−	60.8781i	0.615455	−	0.733471i	0.980282	+	0.197605i	$0.0633163\pi$
$84$	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	−0.585490	−	0.810680i	$-0.699098\pi$
$89$	36.4298	−	63.0983i	0.409324	−	0.708970i	0.994814	+	0.101709i	$0.0324312\pi$
$90$	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	−0.853431	−	0.521207i	$-0.825482\pi$
$97$	−113.701	+	41.3836i	−1.17217	+	0.426635i	−0.318741	+	0.947842i	$0.603260\pi$
$98$	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	−0.888451	−	0.458972i	$-0.848218\pi$
$101$	10.4431	−	59.2260i	0.103397	−	0.586396i	0.991848	−	0.127424i	$-0.0406710\pi$
$102$	45.9789	−	56.6478i	0.450773	−	0.555370i
$103$	−40.2223	+	110.510i	−0.390508	+	1.07291i	0.576262	+	0.817265i	$0.304511\pi$
$103$	−40.2223	+	110.510i	−0.390508	+	1.07291i	−0.966770	+	0.255647i	$0.917711\pi$
$104$	−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	$0.348972\pi$
$107$			190.361i			1.77907i	−0.456865	+	0.889536i	$0.651028\pi$
$108$	−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	0.811770	−	0.583978i	$-0.198504\pi$
$113$	119.582	+	43.5243i	1.05825	+	0.385171i	0.246478	+	0.969148i	$0.420727\pi$
$114$	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	0.0780954	−	0.996946i	$-0.475116\pi$
$127$	−94.7722	−	54.7167i	−0.746237	−	0.430840i	−0.824333	+	0.566106i	$0.808449\pi$
$128$	−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	0.312333	−	0.949973i	$-0.398890\pi$
$131$	121.927	−	21.4990i	0.930739	−	0.164114i	0.618407	+	0.785858i	$0.287779\pi$
$132$	−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	0.705486	−	0.708724i	$-0.250729\pi$
$137$	17.8149	+	14.9484i	0.130035	+	0.109113i	−0.575450	+	0.817837i	$0.695173\pi$
$138$	−137.263	−	229.032i	−0.994662	−	1.65965i
$139$	36.6332	−	6.45942i	0.263548	−	0.0464706i	−0.0403126	−	0.999187i	$-0.512835\pi$
$139$	36.6332	−	6.45942i	0.263548	−	0.0464706i	0.303861	+	0.952716i	$0.401724\pi$
$140$	−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	−0.218535	+	0.975829i	$0.570128\pi$
$149$	−181.406	+	152.217i	−1.21749	+	1.02159i	−0.998952	+	0.0457641i	$0.985428\pi$
$150$	48.9943	−	141.767i	0.326629	−	0.945117i
$151$	28.2544	+	77.6282i	0.187115	+	0.514094i	0.997410	−	0.0719283i	$-0.0229153\pi$
$151$	28.2544	+	77.6282i	0.187115	+	0.514094i	−0.810295	+	0.586022i	$0.800693\pi$
$152$	−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	0.977777	−	0.209650i	$-0.0672324\pi$
$157$	249.950	+	90.9743i	1.59204	+	0.579454i	0.614260	+	0.789104i	$0.289455\pi$
$158$	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	$0.0682130\pi$
$163$			69.3275i			0.425322i	−0.977126	+	0.212661i	$0.931787\pi$
$164$	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	−0.848687	−	0.528896i	$-0.822606\pi$
$167$	23.6159	−	64.8842i	0.141413	−	0.388528i	0.990099	+	0.140368i	$0.0448284\pi$
$168$	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	0.425516	−	0.904951i	$-0.360093\pi$
$173$	230.639	−	83.9456i	1.33317	−	0.485234i	0.907655	+	0.419717i	$0.137871\pi$
$174$	−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	0.184250	−	0.982879i	$-0.441014\pi$
$179$	201.836	−	116.530i	1.12757	−	0.651005i	0.943324	+	0.331874i	$0.107681\pi$
$180$	0.977035	−	0.392173i	0.00542797	−	0.00217874i
$181$	−33.8157	+	58.5706i	−0.186827	+	0.323594i	−0.944191	−	0.329399i	$-0.893154\pi$
$181$	−33.8157	+	58.5706i	−0.186827	+	0.323594i	0.757364	+	0.652993i	$0.226487\pi$
$182$	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	−0.887709	−	0.460406i	$-0.847704\pi$
$191$	−53.5083	+	63.7687i	−0.280148	+	0.333868i	0.607560	+	0.794274i	$0.292148\pi$
$192$	27.0274	−	190.088i	0.140768	−	0.990043i
$193$	1.05357	+	5.97507i	0.00545889	+	0.0309589i	0.987416	−	0.158147i	$-0.0505521\pi$
$193$	1.05357	+	5.97507i	0.00545889	+	0.0309589i	−0.981957	+	0.189106i	$0.939441\pi$
$194$	−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	−0.402943	−	0.915225i	$-0.632013\pi$
$197$	116.454	−	201.704i	0.591137	−	1.02388i	0.994080	−	0.108654i	$-0.0346539\pi$
$198$	−115.280	−	186.833i	−0.582223	−	0.943599i
$199$	−206.861	+	119.431i	−1.03950	+	0.600156i	−0.919692	−	0.392641i	$-0.871561\pi$
$199$	−206.861	+	119.431i	−1.03950	+	0.600156i	−0.119809	+	0.992797i	$0.538228\pi$
$200$	−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	−0.545696	−	0.837983i	$-0.683735\pi$
$211$	86.7160	−	238.250i	0.410976	−	1.12915i	0.956673	−	0.291165i	$-0.0940430\pi$
$212$	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	−0.568695	−	0.822548i	$-0.692552\pi$
$223$	−308.726	−	54.4367i	−1.38442	−	0.244111i	−0.815727	+	0.578438i	$0.803663\pi$
$224$	−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	0.940069	−	0.340984i	$-0.110760\pi$
$227$	0.171119	+	0.470145i	0.000753827	+	0.00207112i	−0.939315	+	0.343055i	$0.888538\pi$
$228$	−72.1644	−	186.731i	−0.316510	−	0.818996i
$229$	−145.884	+	122.411i	−0.637046	+	0.534545i	−0.903109	−	0.429410i	$-0.858721\pi$
$229$	−145.884	+	122.411i	−0.637046	+	0.534545i	0.266063	+	0.963956i	$0.414277\pi$
$230$	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	0.799120	−	0.601171i	$-0.205299\pi$
$233$	−28.2092	−	48.8598i	−0.121070	−	0.209699i	−0.920190	+	0.391473i	$0.871966\pi$
$234$	−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	0.0800682	−	0.996789i	$-0.474486\pi$
$239$	118.599	−	20.9122i	0.496230	−	0.0874987i	0.416162	+	0.909291i	$0.363375\pi$
$240$	−1.40325	+	0.0372027i	−0.00584686	+	0.000155011i
$241$	95.8845	+	80.4566i	0.397861	+	0.333845i	0.819666	−	0.572842i	$-0.194159\pi$
$241$	95.8845	+	80.4566i	0.397861	+	0.333845i	−0.421805	+	0.906686i	$0.638603\pi$
$242$	−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	−0.320444	−	0.947267i	$-0.603832\pi$
$251$	−326.557	−	188.538i	−1.30102	−	0.751147i	−0.980580	+	0.196121i	$0.937166\pi$
$252$	−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	−0.150749	−	0.988572i	$-0.548169\pi$
$257$	204.733	−	171.791i	0.796627	−	0.668449i	0.947376	+	0.320123i	$0.103724\pi$
$258$	−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	0.440391	−	0.897806i	$-0.354840\pi$
$263$	143.902	+	25.3738i	0.547156	+	0.0964784i	0.106765	+	0.994284i	$0.465951\pi$
$264$	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	$-0.681035\pi$
$271$		−	456.679i		−	1.68516i	0.538569	−	0.842581i	$-0.318965\pi$
$272$	−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	0.844091	+	0.536199i	$0.180140\pi$
$277$	−36.6986	+	208.128i	−0.132486	+	0.751365i	−0.976577	+	0.215166i	$0.930971\pi$
$278$	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	−0.0444958	−	0.999010i	$-0.514168\pi$
$281$	158.363	−	57.6394i	0.563569	−	0.205122i	0.608065	+	0.793887i	$0.291946\pi$
$282$	−52.7865	−	273.216i	−0.187186	−	0.968852i
$283$	−0.932181	−	1.11093i	−0.00329393	−	0.00392555i	0.764395	−	0.644748i	$-0.223038\pi$
$283$	−0.932181	−	1.11093i	−0.00329393	−	0.00392555i	−0.767689	+	0.640823i	$0.778593\pi$
$284$	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	0.963366	+	0.268191i	$0.0864259\pi$
$293$	43.8987	+	248.962i	0.149825	+	0.849699i	−0.813541	+	0.581508i	$0.802463\pi$
$294$	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	−0.0126731	−	0.999920i	$-0.504034\pi$
$307$	260.012	−	150.118i	0.846946	−	0.488985i	0.859619	+	0.510935i	$0.170701\pi$
$308$	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	0.987127	−	0.159941i	$-0.0511304\pi$
$311$	204.701	+	243.953i	0.658203	+	0.784416i	−0.328924	+	0.944356i	$0.606686\pi$
$312$	9.55329	−	5.81401i	0.0306195	−	0.0186346i
$313$	48.3252	−	17.5890i	0.154394	−	0.0561947i	−0.263667	−	0.964614i	$-0.584932\pi$
$313$	48.3252	−	17.5890i	0.154394	−	0.0561947i	0.418061	+	0.908419i	$0.362710\pi$
$314$	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	0.929393	+	0.369093i	$0.120332\pi$
$317$	−22.2496	+	126.184i	−0.0701880	+	0.398056i	−0.999580	+	0.0289629i	$0.990780\pi$
$318$	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	−0.791854	−	0.610711i	$-0.790884\pi$
$331$	−577.538	−	101.836i	−1.74483	−	0.307660i	−0.952974	+	0.303051i	$0.901995\pi$
$332$	−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	−0.403130	−	0.915143i	$-0.632078\pi$
$337$	144.272	−	121.059i	0.428107	−	0.359224i	0.831237	+	0.555918i	$0.187633\pi$
$338$	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	−0.264071	−	0.964503i	$-0.585065\pi$
$347$	−63.2707	+	11.1563i	−0.182336	+	0.0321508i	0.0817344	+	0.996654i	$0.473954\pi$
$348$	0.0694062	+	0.352802i	0.000199443	+	0.00101380i
$349$	−260.504	−	218.589i	−0.746431	−	0.626330i	0.188125	−	0.982145i	$-0.439759\pi$
$349$	−260.504	−	218.589i	−0.746431	−	0.626330i	−0.934556	+	0.355815i	$0.884203\pi$
$350$	−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	0.784064	−	0.620680i	$-0.213143\pi$
$353$	109.064	+	91.5160i	0.308964	+	0.259252i	−0.475099	+	0.879932i	$0.657588\pi$
$354$	−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	0.452612	−	0.891708i	$-0.350492\pi$
$359$	−33.5032	−	19.3431i	−0.0933237	−	0.0538805i	−0.545936	+	0.837827i	$0.683826\pi$
$360$	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	0.821353	+	0.570420i	$0.193220\pi$
$367$	205.087	+	563.471i	0.558819	+	1.53534i	−0.262534	+	0.964923i	$0.584558\pi$
$368$	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	−0.568668	−	0.822567i	$-0.692541\pi$
$373$	−571.820	−	208.125i	−1.53303	−	0.557977i	−0.964361	+	0.264590i	$0.914763\pi$
$374$	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	$0.246446\pi$
$379$			529.969i			1.39834i	−0.714958	+	0.699168i	$0.753554\pi$
$380$	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	0.675749	+	0.737132i	$0.263820\pi$
$383$	−120.922	+	332.231i	−0.315724	+	0.867445i	−0.991473	+	0.130313i	$0.958402\pi$
$384$	−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	−0.666263	−	0.745717i	$-0.732107\pi$
$389$	−271.255	+	98.7286i	−0.697313	+	0.253801i	−0.0310496	+	0.999518i	$0.509885\pi$
$390$	−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	−0.879134	−	0.476575i	$-0.841878\pi$
$397$	−10.6556	+	18.4561i	−0.0268404	+	0.0464889i	0.852293	+	0.523064i	$0.175211\pi$
$398$	−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	−0.824263	−	0.566207i	$-0.808410\pi$
$401$	−97.5887	−	553.453i	−0.243363	−	1.38018i	0.580899	−	0.813975i	$-0.302701\pi$
$402$	−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	−0.999876	−	0.0157685i	$-0.994981\pi$
$409$	−26.8684	−	152.379i	−0.0656930	−	0.372564i	0.934183	−	0.356795i	$-0.116131\pi$
$410$	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	0.516514	−	0.856279i	$-0.327230\pi$
$419$	−174.492	−	207.951i	−0.416448	−	0.496304i	−0.932962	+	0.359975i	$0.882785\pi$
$420$	−1.44263	−	3.73292i	−0.00343483	−	0.00888790i
$421$	1.34786	−	0.490582i	0.00320158	−	0.00116528i	−0.340419	−	0.940274i	$-0.610569\pi$
$421$	1.34786	−	0.490582i	0.00320158	−	0.00116528i	0.343620	+	0.939109i	$0.388347\pi$
$422$	−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	$-0.790602\pi$
$431$		−	527.038i		−	1.22283i	0.791312	−	0.611413i	$-0.209398\pi$
$432$	−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	0.376059	−	0.926596i	$-0.377279\pi$
$439$	181.098	+	31.9325i	0.412524	+	0.0727391i	0.0364652	+	0.999335i	$0.488390\pi$
$440$	−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	0.905510	+	0.424324i	$0.139488\pi$
$443$	214.678	+	589.822i	0.484600	+	1.33143i	−0.420911	+	0.907102i	$0.638289\pi$
$444$	−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	0.714141	−	0.700002i	$-0.246818\pi$
$449$	−111.868	−	193.761i	−0.249149	−	0.431539i	−0.963290	+	0.268463i	$0.913484\pi$
$450$	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	0.784860	−	0.619673i	$-0.212735\pi$
$457$	142.077	+	119.217i	0.310892	+	0.260869i	−0.473969	+	0.880542i	$0.657179\pi$
$458$	−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	0.894719	−	0.446629i	$-0.147376\pi$
$461$	281.321	+	236.057i	0.610241	+	0.512053i	−0.284478	+	0.958683i	$0.591820\pi$
$462$	−715.803	+	428.994i	−1.54936	+	0.928559i
$463$	22.7171	−	4.00564i	0.0490650	−	0.00865149i	−0.149062	−	0.988828i	$-0.547625\pi$
$463$	22.7171	−	4.00564i	0.0490650	−	0.00865149i	0.198127	+	0.980176i	$0.436514\pi$
$464$	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	−0.0217402	−	0.999764i	$-0.506921\pi$
$467$	−419.567	−	242.237i	−0.898431	−	0.518709i	−0.876691	+	0.481054i	$0.840254\pi$
$468$	−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	−0.533690	−	0.845680i	$-0.679195\pi$
$479$	−634.404	−	111.862i	−1.32443	−	0.233533i	−0.790744	+	0.612147i	$0.790306\pi$
$480$	−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	$0.0464549\pi$
$487$			141.644i			0.290850i	−0.989369	+	0.145425i	$0.953545\pi$
$488$	−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	−0.977349	−	0.211634i	$-0.932122\pi$
$491$	−45.4768	+	124.946i	−0.0926207	+	0.254473i	0.884728	+	0.466107i	$0.154344\pi$
$492$	−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	0.468453	−	0.883488i	$-0.344811\pi$
$499$	−240.997	−	287.208i	−0.482959	−	0.575568i	−0.951412	+	0.307920i	$0.900367\pi$
$500$	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	−0.393177	−	0.919463i	$-0.628624\pi$
$503$	103.876	−	59.9729i	0.206513	−	0.119230i	0.599690	+	0.800233i	$0.295291\pi$
$504$	−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	−0.991310	−	0.131546i	$-0.958006\pi$
$509$	−53.3303	−	302.451i	−0.104775	−	0.594206i	0.886535	−	0.462661i	$-0.153105\pi$
$510$	−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	−0.0417736	−	0.999127i	$-0.513301\pi$
$521$	439.923	−	761.970i	0.844383	−	1.46251i	0.886156	−	0.463387i	$-0.153366\pi$
$522$	−0.474773	−	0.255900i	−0.000909526	−	0.000490230i
$523$	77.7561	−	44.8925i	0.148673	−	0.0858366i	−0.423818	−	0.905747i	$-0.639310\pi$
$523$	77.7561	−	44.8925i	0.148673	−	0.0858366i	0.572491	+	0.819911i	$0.305977\pi$
$524$	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	−0.391097	−	0.920350i	$-0.627904\pi$
$547$	−587.142	−	103.529i	−1.07339	−	0.189267i	−0.682289	+	0.731083i	$0.739015\pi$
$548$	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	0.993085	+	0.117399i	$0.0374556\pi$
$557$	333.205	+	577.127i	0.598213	+	1.03613i	−0.394872	+	0.918736i	$0.629211\pi$
$558$	−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	−0.674908	−	0.737902i	$-0.735817\pi$
$563$	−594.943	+	104.904i	−1.05674	+	0.186331i	−0.381829	+	0.924233i	$0.624706\pi$
$564$	−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	−0.125440	−	0.992101i	$-0.540034\pi$
$569$	−639.699	−	536.771i	−1.12425	−	0.943359i	−0.998811	+	0.0487421i	$0.984479\pi$
$570$	−1.42206	+	2.55861i	−0.00249483	+	0.00448879i
$571$	−221.543	+	39.0640i	−0.387991	+	0.0684132i	−0.364241	−	0.931305i	$-0.618672\pi$
$571$	−221.543	+	39.0640i	−0.387991	+	0.0684132i	−0.0237497	+	0.999718i	$0.507560\pi$
$572$	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	0.958797	+	0.284091i	$0.0916918\pi$
$577$	418.572	+	724.989i	0.725429	+	1.25648i	−0.233369	+	0.972388i	$0.574975\pi$
$578$	−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	0.166700	−	0.986008i	$-0.446689\pi$
$587$	−8.15169	−	1.43736i	−0.0138870	−	0.00244866i	−0.180587	+	0.983559i	$0.557800\pi$
$588$	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	−0.999459	−	0.0328858i	$-0.989530\pi$
$599$	−127.402	+	350.033i	−0.212690	+	0.584362i	0.786769	+	0.617248i	$0.211752\pi$
$600$	−396.177	−	450.576i	−0.660295	−	0.750960i
$601$	47.9969	−	272.204i	0.0798617	−	0.452918i	−0.918486	−	0.395454i	$-0.870587\pi$
$601$	47.9969	−	272.204i	0.0798617	−	0.452918i	0.998348	−	0.0574643i	$-0.0183015\pi$
$602$	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	0.970384	−	0.241568i	$-0.0776617\pi$
$607$	342.336	+	407.980i	0.563980	+	0.672126i	−0.406403	+	0.913694i	$0.633217\pi$
$608$	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	−0.935656	−	0.352912i	$-0.885191\pi$
$613$	−99.4269	+	172.213i	−0.162197	+	0.280934i	0.773459	+	0.633846i	$0.218525\pi$
$614$	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	0.993285	+	0.115690i	$0.0369079\pi$
$617$	61.3734	+	348.066i	0.0994707	+	0.564126i	−0.893815	+	0.448436i	$0.851981\pi$
$618$	−705.519	+	11.5149i	−1.14162	+	0.0186326i
$619$	376.578	−	448.788i	0.608365	−	0.725021i	−0.370659	−	0.928769i	$-0.620868\pi$
$619$	376.578	−	448.788i	0.608365	−	0.725021i	0.979023	+	0.203748i	$0.0653124\pi$
$620$	−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	−0.256968	−	0.966420i	$-0.582723\pi$
$631$	284.892	−	164.483i	0.451493	−	0.260670i	0.708461	+	0.705750i	$0.249390\pi$
$632$	−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	−0.772496	−	0.635020i	$-0.780992\pi$
$641$	109.356	−	620.190i	0.170602	−	0.967534i	0.943098	−	0.332514i	$-0.107897\pi$
$642$	−1066.77	+	408.106i	−1.66163	+	0.635679i
$643$	−146.675	+	402.987i	−0.228111	+	0.626729i	−0.999959	−	0.00907777i	$-0.997110\pi$
$643$	−146.675	+	402.987i	−0.228111	+	0.626729i	0.771848	+	0.635807i	$0.219333\pi$
$644$	−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	$-0.824861\pi$
$647$		−	676.594i		−	1.04574i	0.852412	−	0.522870i	$-0.175139\pi$
$648$	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	−0.502139	−	0.864787i	$-0.667454\pi$
$653$	−942.066	−	342.884i	−1.44267	−	0.525091i	−0.940535	+	0.339696i	$0.889676\pi$
$654$	−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	−0.957652	−	0.287929i	$-0.907033\pi$
$659$	−269.613	−	740.757i	−0.409125	−	1.12406i	0.548527	−	0.836133i	$-0.315189\pi$
$660$	2.68606	−	3.33239i	0.00406978	−	0.00504907i
$661$	189.550	−	159.052i	0.286763	−	0.240623i	−0.488046	−	0.872818i	$-0.662290\pi$
$661$	189.550	−	159.052i	0.286763	−	0.240623i	0.774809	+	0.632195i	$0.217846\pi$
$662$	−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	0.684846	−	0.728688i	$-0.259869\pi$
$673$	57.9800	+	48.6510i	0.0861515	+	0.0722897i	−0.598695	+	0.800977i	$0.704314\pi$
$674$	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	0.308968	−	0.951072i	$-0.400016\pi$
$677$	−388.600	−	326.074i	−0.574003	−	0.481646i	−0.882972	+	0.469427i	$0.844461\pi$
$678$	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	0.166311	−	0.986073i	$-0.446814\pi$
$683$	−412.872	−	238.372i	−0.604498	−	0.349007i	−0.770809	+	0.637066i	$0.780148\pi$
$684$	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	−0.940482	−	0.339844i	$-0.889626\pi$
$691$	−302.988	−	832.454i	−0.438478	−	1.20471i	0.502004	−	0.864865i	$-0.332596\pi$
$692$	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	0.779801	+	0.626027i	$0.215320\pi$
$709$	−118.464	+	671.843i	−0.167086	+	0.947592i	−0.946887	+	0.321565i	$0.895791\pi$
$710$	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	−0.603564	−	0.797314i	$-0.706253\pi$
$719$	−154.479	+	89.1882i	−0.214852	+	0.124045i	0.388712	+	0.921359i	$0.372920\pi$
$720$	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	−0.698603	−	0.715509i	$-0.746195\pi$
$727$	92.5811	−	110.334i	0.127347	−	0.151766i	0.825950	+	0.563743i	$0.190639\pi$
$728$	−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	−0.945542	−	0.325501i	$-0.894467\pi$
$733$	−123.401	−	699.844i	−0.168351	−	0.954767i	0.777190	−	0.629265i	$-0.216644\pi$
$734$	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	−0.762937	−	0.646473i	$-0.776243\pi$
$739$	−431.977	+	249.402i	−0.584543	+	0.337486i	0.178394	+	0.983959i	$0.442910\pi$
$740$	−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	0.975952	+	0.217987i	$0.0699489\pi$
$743$	758.718	+	904.205i	1.02115	+	1.21696i	0.0452027	+	0.998978i	$0.485607\pi$
$744$	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	0.559008	+	0.829162i	$0.311182\pi$
$751$	−302.047	+	829.866i	−0.402192	+	1.10501i	−0.961200	+	0.275852i	$0.911040\pi$
$752$	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	0.409751	−	0.912197i	$-0.365616\pi$
$761$	104.477	+	38.0267i	0.137290	+	0.0499694i	−0.272461	+	0.962167i	$0.587838\pi$
$762$	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	−0.916708	−	0.399558i	$-0.869164\pi$
$769$	−524.769	+	440.334i	−0.682405	+	0.572606i	0.234303	+	0.972164i	$0.424719\pi$
$770$	−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	0.572808	−	0.819689i	$-0.305854\pi$
$773$	−327.341	−	566.971i	−0.423468	−	0.733468i	−0.996276	+	0.0862217i	$0.972521\pi$
$774$	−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	0.765789	−	0.643092i	$-0.222349\pi$
$787$	1342.11	−	236.650i	1.70535	−	0.300698i	0.939557	+	0.342393i	$0.111238\pi$
$788$	−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	−0.501055	−	0.865416i	$-0.667054\pi$
$797$	210.572	−	176.691i	0.264206	−	0.221695i	0.765261	+	0.643720i	$0.222610\pi$
$798$	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	$0.0679627\pi$
$811$			343.690i			0.423785i	−0.977293	+	0.211893i	$0.932037\pi$
$812$	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	−0.0989974	−	0.995088i	$-0.531564\pi$
$821$	381.598	−	138.890i	0.464796	−	0.169172i	0.563794	+	0.825916i	$0.309341\pi$
$822$	−45.5773	+	131.880i	−0.0554468	+	0.160438i
$823$	99.2596	+	118.293i	0.120607	+	0.143734i	0.822969	−	0.568086i	$-0.192316\pi$
$823$	99.2596	+	118.293i	0.120607	+	0.143734i	−0.702362	+	0.711820i	$0.747871\pi$
$824$	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	0.0528664	−	0.998602i	$-0.483164\pi$
$827$	780.782	−	450.785i	0.944114	−	0.545084i	0.891248	+	0.453517i	$0.149831\pi$
$828$	989.204	−	1260.22i	1.19469	−	1.52201i
$829$	−94.0098	+	162.830i	−0.113401	+	0.196417i	−0.917140	−	0.398566i	$-0.869508\pi$
$829$	−94.0098	+	162.830i	−0.113401	+	0.196417i	0.803738	+	0.594983i	$0.202841\pi$
$830$	−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	−0.997960	−	0.0638379i	$-0.979666\pi$
$839$	−639.149	+	761.708i	−0.761798	+	0.907876i	0.236162	+	0.971714i	$0.424110\pi$
$840$	−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	−0.760376	−	0.649484i	$-0.774985\pi$
$853$	−789.347	+	287.299i	−0.925377	+	0.336810i	−0.165001	+	0.986293i	$0.552763\pi$
$854$	−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	−0.580562	−	0.814216i	$-0.697167\pi$
$857$	208.651	−	1183.32i	0.243466	−	1.38077i	0.824028	−	0.566549i	$-0.191722\pi$
$858$	−5.37249	+	33.6735i	−0.00626164	+	0.0392464i
$859$	129.769	−	356.538i	0.151070	−	0.415062i	−0.840954	−	0.541106i	$-0.818006\pi$
$859$	129.769	−	356.538i	0.151070	−	0.415062i	0.992025	+	0.126044i	$0.0402280\pi$
$860$	−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	$-0.584958\pi$
$863$		−	1664.89i		−	1.92918i	0.263745	−	0.964592i	$-0.415042\pi$
$864$	−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	−0.933489	−	0.358607i	$-0.883252\pi$
$877$	−651.110	+	546.346i	−0.742429	+	0.622972i	0.191060	+	0.981578i	$0.438807\pi$
$878$	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	0.906677	−	0.421825i	$-0.138610\pi$
$881$	77.5520	+	134.324i	0.0880272	+	0.152468i	−0.818650	+	0.574293i	$0.805277\pi$
$882$	−1443.46	−	211.207i	−1.63658	−	0.239463i
$883$	421.366	+	243.276i	0.477199	+	0.275511i	0.719248	−	0.694753i	$-0.244486\pi$
$883$	421.366	+	243.276i	0.477199	+	0.275511i	−0.242050	+	0.970264i	$0.577820\pi$
$884$	−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	−0.541781	−	0.840520i	$-0.682250\pi$
$887$	−677.148	+	119.399i	−0.763414	+	0.134610i	−0.221633	+	0.975130i	$0.571139\pi$
$888$	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	0.850746	+	0.525578i	$0.176151\pi$
$907$	486.942	+	1337.86i	0.536871	+	1.47504i	−0.313874	+	0.949465i	$0.601627\pi$
$908$	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	0.432518	−	0.901626i	$-0.357625\pi$
$911$	483.356	+	85.2286i	0.530577	+	0.0935550i	0.0980594	+	0.995181i	$0.468736\pi$
$912$	−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	$-0.857018\pi$
$919$		−	798.127i		−	0.868473i	0.900799	−	0.434237i	$-0.142982\pi$
$920$	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	0.429467	−	0.903083i	$-0.358702\pi$
$929$	1243.88	−	452.736i	1.33895	−	0.487337i	0.909481	+	0.415745i	$0.136479\pi$
$930$	−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	−0.702238	−	0.711942i	$-0.747816\pi$
$937$	248.718	−	430.792i	0.265441	−	0.459757i	0.967679	+	0.252185i	$0.0811492\pi$
$938$	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	−0.999653	−	0.0263455i	$-0.991613\pi$
$941$	−65.2086	−	369.816i	−0.0692971	−	0.393004i	0.930356	−	0.366658i	$-0.119498\pi$
$942$	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	−0.892620	−	0.450810i	$-0.851135\pi$
$947$	−278.093	+	331.419i	−0.293657	+	0.349967i	0.598963	+	0.800777i	$0.295580\pi$
$948$	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	0.217440	+	0.976074i	$0.430229\pi$
$953$	−701.965	+	1215.84i	−0.736585	+	1.27580i	−0.954024	+	0.299729i	$0.903104\pi$
$954$	−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	−0.864488	−	0.502654i	$-0.832357\pi$
$967$	116.860	−	321.071i	0.120848	−	0.332028i	0.985336	+	0.170626i	$0.0545791\pi$
$968$	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	$-0.924023\pi$
$971$		−	459.145i		−	0.472858i	0.971649	−	0.236429i	$-0.0759771\pi$
$972$	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	0.0403203	−	0.999187i	$-0.487162\pi$
$977$	−557.923	−	203.067i	−0.571057	−	0.207848i	−0.611378	+	0.791339i	$0.709384\pi$
$978$	−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	0.931372	−	0.364070i	$-0.118613\pi$
$983$	−15.8459	−	43.5363i	−0.0161200	−	0.0442892i	−0.947492	+	0.319781i	$0.896391\pi$
$984$	−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	0.160600	−	0.987019i	$-0.448657\pi$
$991$	−608.358	−	351.236i	−0.613883	−	0.354426i	−0.774484	+	0.632594i	$0.781990\pi$
$992$	−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	0.978964	+	0.204031i	$0.0654043\pi$
$997$	1345.84	+	1129.29i	1.34989	+	1.13269i	0.370927	+	0.928662i	$0.379040\pi$
$998$	−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.43.28	yes	204
3.2	odd	2		324.3.j.a.127.7		204
4.3	odd	2	inner	108.3.j.a.43.14	✓	204
12.11	even	2		324.3.j.a.127.21		204
27.5	odd	18		324.3.j.a.199.21		204
27.22	even	9	inner	108.3.j.a.103.14	yes	204
108.59	even	18		324.3.j.a.199.7		204
108.103	odd	18	inner	108.3.j.a.103.28	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.14	✓	204	4.3	odd	2	inner
108.3.j.a.43.28	yes	204	1.1	even	1	trivial
108.3.j.a.103.14	yes	204	27.22	even	9	inner
108.3.j.a.103.28	yes	204	108.103	odd	18	inner
324.3.j.a.127.7		204	3.2	odd	2
324.3.j.a.127.21		204	12.11	even	2
324.3.j.a.199.7		204	108.59	even	18
324.3.j.a.199.21		204	27.5	odd	18

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

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