LMFDB - Embedded newform 45.3.i.a.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.11"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, 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:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 48x^{14} + 912x^{12} + 8704x^{10} + 43602x^{8} + 109032x^{6} + 117844x^{4} + 36000x^{2} + 81 $ x^16 + 48x^14 + 912x^12 + 8704x^10 + 43602x^8 + 109032x^6 + 117844x^4 + 36000*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.1
Root			$3.73655i$ of defining polynomial
Character	$\chi$	$=$	45.41
Dual form			45.3.i.a.11.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.23594 + 1.86827i) q^{2} +(2.62117 - 1.45927i) q^{3} +(4.98088 - 8.62715i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-5.75562 + 9.61919i) q^{6} +(3.63061 + 6.28840i) q^{7} +22.2764i q^{8} +(4.74103 - 7.65001i) q^{9} -8.35517 q^{10} +(6.50668 - 3.75663i) q^{11} +(0.466354 - 29.8817i) q^{12} +(-1.46668 + 2.54036i) q^{13} +(-23.4969 - 13.5659i) q^{14} +(6.70739 + 0.104680i) q^{15} +(-21.6949 - 37.5766i) q^{16} -1.90107i q^{17} +(-1.04942 + 33.6125i) q^{18} -7.38378 q^{19} +(19.2909 - 11.1376i) q^{20} +(18.6929 + 11.1849i) q^{21} +(-14.0368 + 24.3125i) q^{22} +(-30.6549 - 17.6986i) q^{23} +(32.5074 + 58.3902i) q^{24} +(2.50000 + 4.33013i) q^{25} -10.9606i q^{26} +(1.26358 - 26.9704i) q^{27} +72.3346 q^{28} +(-14.2015 + 8.19922i) q^{29} +(-21.9003 + 12.1925i) q^{30} +(-13.3206 + 23.0720i) q^{31} +(63.2391 + 36.5111i) q^{32} +(11.5731 - 19.3418i) q^{33} +(3.55172 + 6.15176i) q^{34} +16.2366i q^{35} +(-42.3832 - 79.0054i) q^{36} -44.6613 q^{37} +(23.8935 - 13.7949i) q^{38} +(-0.137323 + 8.79899i) q^{39} +(-24.9058 + 43.1381i) q^{40} +(14.8634 + 8.58140i) q^{41} +(-81.3857 - 1.27016i) q^{42} +(-20.5554 - 35.6031i) q^{43} -74.8454i q^{44} +(17.7339 - 9.51354i) q^{45} +132.263 q^{46} +(36.4950 - 21.0704i) q^{47} +(-111.701 - 66.8359i) q^{48} +(-1.86263 + 3.22616i) q^{49} +(-16.1797 - 9.34136i) q^{50} +(-2.77419 - 4.98303i) q^{51} +(14.6107 + 25.3065i) q^{52} +100.474i q^{53} +(46.2992 + 89.6354i) q^{54} +16.8002 q^{55} +(-140.083 + 80.8770i) q^{56} +(-19.3541 + 10.7750i) q^{57} +(30.6367 - 53.0644i) q^{58} +(-4.12003 - 2.37870i) q^{59} +(34.3118 - 57.3442i) q^{60} +(38.4629 + 66.6197i) q^{61} -99.5461i q^{62} +(65.3191 + 2.03933i) q^{63} -99.2915 q^{64} +(-5.68041 + 3.27959i) q^{65} +(-1.31425 + 84.2107i) q^{66} +(41.9225 - 72.6119i) q^{67} +(-16.4008 - 9.46903i) q^{68} +(-106.179 - 1.65710i) q^{69} +(-30.3343 - 52.5406i) q^{70} -23.1134i q^{71} +(170.415 + 105.613i) q^{72} -103.753 q^{73} +(144.521 - 83.4395i) q^{74} +(12.8718 + 7.70180i) q^{75} +(-36.7778 + 63.7010i) q^{76} +(47.2464 + 27.2777i) q^{77} +(-15.9945 - 28.7296i) q^{78} +(-40.2610 - 69.7340i) q^{79} -97.0225i q^{80} +(-36.0452 - 72.5379i) q^{81} -64.1296 q^{82} +(-17.1034 + 9.87463i) q^{83} +(189.601 - 105.556i) q^{84} +(2.12546 - 3.68141i) q^{85} +(133.032 + 76.8063i) q^{86} +(-25.2595 + 42.2153i) q^{87} +(83.6843 + 144.945i) q^{88} +29.0566i q^{89} +(-39.6121 + 63.9171i) q^{90} -21.2997 q^{91} +(-305.377 + 176.310i) q^{92} +(-1.24719 + 79.9139i) q^{93} +(-78.7306 + 136.365i) q^{94} +(-14.2986 - 8.25532i) q^{95} +(219.040 + 3.41849i) q^{96} +(47.7972 + 82.7872i) q^{97} -13.9196i q^{98} +(2.11011 - 67.5864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9} - 18 q^{11} - 22 q^{12} - 10 q^{13} - 54 q^{14} + 10 q^{15} - 32 q^{16} - 8 q^{18} - 52 q^{19} + 72 q^{21} - 24 q^{22} - 54 q^{23} + 108 q^{24} + 40 q^{25}+ \cdots - 824 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9 - 18 * q^11 - 22 * q^12 - 10 * q^13 - 54 * q^14 + 10 * q^15 - 32 * q^16 - 8 * q^18 - 52 * q^19 + 72 * q^21 - 24 * q^22 - 54 * q^23 + 108 * q^24 + 40 * q^25 + 34 * q^27 + 32 * q^28 - 54 * q^29 - 100 * q^30 + 32 * q^31 + 216 * q^32 + 62 * q^33 + 54 * q^34 - 86 * q^36 + 44 * q^37 + 252 * q^38 + 160 * q^39 - 30 * q^40 + 144 * q^41 - 270 * q^42 - 124 * q^43 + 140 * q^45 - 108 * q^46 - 216 * q^47 - 172 * q^48 - 54 * q^49 - 106 * q^51 + 62 * q^52 - 316 * q^54 - 18 * q^56 - 236 * q^57 + 90 * q^58 - 486 * q^59 - 10 * q^60 + 62 * q^61 - 132 * q^63 + 256 * q^64 - 90 * q^65 + 208 * q^66 + 14 * q^67 - 288 * q^68 + 90 * q^69 - 60 * q^70 + 804 * q^72 - 268 * q^73 + 540 * q^74 - 20 * q^75 - 106 * q^76 + 702 * q^77 + 290 * q^78 - 40 * q^79 - 112 * q^81 - 204 * q^82 + 522 * q^83 + 714 * q^84 + 30 * q^85 + 54 * q^86 + 106 * q^87 + 144 * q^88 + 250 * q^90 + 136 * q^91 - 1332 * q^92 + 90 * q^93 - 150 * q^94 + 180 * q^95 + 166 * q^96 - 142 * q^97 - 824 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−3.23594	+	1.86827i	−1.61797	+	0.934136i	−0.630528	+	0.776167i	$0.717161\pi$
$2$	−3.23594	+	1.86827i	−1.61797	+	0.934136i	−0.987444	+	0.157969i	$0.949505\pi$
$3$	2.62117	−	1.45927i	0.873722	−	0.486425i
$3$	2.62117	−	1.45927i	0.873722	−	0.486425i
$4$	4.98088	−	8.62715i	1.24522	−	2.15679i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$	−5.75562	+	9.61919i	−0.959271	+	1.60320i
$7$	3.63061	+	6.28840i	0.518658	+	0.898342i	0.999765	+	0.0216804i	$0.00690163\pi$
$7$	3.63061	+	6.28840i	0.518658	+	0.898342i	−0.481107	+	0.876662i	$0.659765\pi$
$8$			22.2764i			2.78455i
$9$	4.74103	−	7.65001i	0.526781	−	0.850001i
$10$	−8.35517			−0.835517
$11$	6.50668	−	3.75663i	0.591516	−	0.341512i	−0.174181	−	0.984714i	$-0.555728\pi$
$11$	6.50668	−	3.75663i	0.591516	−	0.341512i	0.765697	+	0.643202i	$0.222394\pi$
$12$	0.466354	−	29.8817i	0.0388628	−	2.49014i
$13$	−1.46668	+	2.54036i	−0.112821	+	0.195412i	−0.916907	−	0.399102i	$-0.869322\pi$
$13$	−1.46668	+	2.54036i	−0.112821	+	0.195412i	0.804085	+	0.594514i	$0.202655\pi$
$14$	−23.4969	−	13.5659i	−1.67835	−	0.968995i
$15$	6.70739	+	0.104680i	0.447159	+	0.00697867i
$16$	−21.6949	−	37.5766i	−1.35593	−	2.34854i
$17$		−	1.90107i		−	0.111828i	−0.998436	−	0.0559139i	$-0.982193\pi$
$17$		−	1.90107i		−	0.111828i	0.998436	−	0.0559139i	$-0.0178072\pi$
$18$	−1.04942	+	33.6125i	−0.0583009	+	1.86736i
$19$	−7.38378			−0.388620			−0.194310	−	0.980940i	$-0.562247\pi$
$19$	−7.38378			−0.388620			−0.194310	+	0.980940i	$0.562247\pi$
$20$	19.2909	−	11.1376i	0.964544	−	0.556880i
$21$	18.6929	+	11.1849i	0.890140	+	0.532614i
$22$	−14.0368	+	24.3125i	−0.638037	+	1.10511i
$23$	−30.6549	−	17.6986i	−1.33282	−	0.769506i	−0.347091	−	0.937831i	$-0.612831\pi$
$23$	−30.6549	−	17.6986i	−1.33282	−	0.769506i	−0.985731	+	0.168326i	$0.946164\pi$
$24$	32.5074	+	58.3902i	1.35448	+	2.43293i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$		−	10.9606i		−	0.421562i
$27$	1.26358	−	26.9704i	0.0467992	−	0.998904i
$28$	72.3346			2.58338
$29$	−14.2015	+	8.19922i	−0.489705	+	0.282732i	−0.724452	−	0.689325i	$-0.757907\pi$
$29$	−14.2015	+	8.19922i	−0.489705	+	0.282732i	0.234747	+	0.972057i	$0.424574\pi$
$30$	−21.9003	+	12.1925i	−0.730010	+	0.406416i
$31$	−13.3206	+	23.0720i	−0.429697	+	0.744257i	−0.996846	−	0.0793581i	$-0.974713\pi$
$31$	−13.3206	+	23.0720i	−0.429697	+	0.744257i	0.567149	+	0.823615i	$0.308046\pi$
$32$	63.2391	+	36.5111i	1.97622	+	1.14097i
$33$	11.5731	−	19.3418i	0.350701	−	0.586115i
$34$	3.55172	+	6.15176i	0.104462	+	0.180934i
$35$			16.2366i			0.463902i
$36$	−42.3832	−	79.0054i	−1.17731	−	2.19459i
$37$	−44.6613			−1.20706			−0.603531	−	0.797340i	$-0.706240\pi$
$37$	−44.6613			−1.20706			−0.603531	+	0.797340i	$0.706240\pi$
$38$	23.8935	−	13.7949i	0.628776	−	0.363024i
$39$	−0.137323	+	8.79899i	−0.00352110	+	0.225615i
$40$	−24.9058	+	43.1381i	−0.622645	+	1.07845i
$41$	14.8634	+	8.58140i	0.362522	+	0.209302i	0.670187	−	0.742193i	$-0.266214\pi$
$41$	14.8634	+	8.58140i	0.362522	+	0.209302i	−0.307664	+	0.951495i	$0.599547\pi$
$42$	−81.3857	−	1.27016i	−1.93775	−	0.0302419i
$43$	−20.5554	−	35.6031i	−0.478033	−	0.827978i	0.521650	−	0.853160i	$-0.325317\pi$
$43$	−20.5554	−	35.6031i	−0.478033	−	0.827978i	−0.999683	+	0.0251818i	$0.991984\pi$
$44$		−	74.8454i		−	1.70103i
$45$	17.7339	−	9.51354i	0.394088	−	0.211412i
$46$	132.263			2.87529
$47$	36.4950	−	21.0704i	0.776490	−	0.448307i	−0.0586949	−	0.998276i	$-0.518694\pi$
$47$	36.4950	−	21.0704i	0.776490	−	0.448307i	0.835185	+	0.549969i	$0.185361\pi$
$48$	−111.701	−	66.8359i	−2.32710	−	1.39241i
$49$	−1.86263	+	3.22616i	−0.0380128	+	0.0658401i
$50$	−16.1797	−	9.34136i	−0.323594	−	0.186827i
$51$	−2.77419	−	4.98303i	−0.0543959	−	0.0977065i
$52$	14.6107	+	25.3065i	0.280975	+	0.486663i
$53$			100.474i			1.89573i	0.318671	+	0.947865i	$0.396764\pi$
$53$			100.474i			1.89573i	−0.318671	+	0.947865i	$0.603236\pi$
$54$	46.2992	+	89.6354i	0.857393	+	1.65992i
$55$	16.8002			0.305458
$56$	−140.083	+	80.8770i	−2.50148	+	1.44423i
$57$	−19.3541	+	10.7750i	−0.339546	+	0.189035i
$58$	30.6367	−	53.0644i	0.528220	−	0.914903i
$59$	−4.12003	−	2.37870i	−0.0698310	−	0.0403169i	0.464678	−	0.885480i	$-0.346170\pi$
$59$	−4.12003	−	2.37870i	−0.0698310	−	0.0403169i	−0.534509	+	0.845163i	$0.679503\pi$
$60$	34.3118	−	57.3442i	0.571864	−	0.955737i
$61$	38.4629	+	66.6197i	0.630539	+	1.09213i	0.987442	+	0.157985i	$0.0504996\pi$
$61$	38.4629	+	66.6197i	0.630539	+	1.09213i	−0.356902	+	0.934142i	$0.616167\pi$
$62$		−	99.5461i		−	1.60558i
$63$	65.3191	+	2.03933i	1.03681	+	0.0323703i
$64$	−99.2915			−1.55143
$65$	−5.68041	+	3.27959i	−0.0873910	+	0.0504552i
$66$	−1.31425	+	84.2107i	−0.0199129	+	1.27592i
$67$	41.9225	−	72.6119i	0.625709	−	1.08376i	−0.362694	−	0.931908i	$-0.618143\pi$
$67$	41.9225	−	72.6119i	0.625709	−	1.08376i	0.988403	−	0.151852i	$-0.0485237\pi$
$68$	−16.4008	−	9.46903i	−0.241189	−	0.139250i
$69$	−106.179	−	1.65710i	−1.53882	−	0.0240159i
$70$	−30.3343	−	52.5406i	−0.433348	−	0.750580i
$71$		−	23.1134i		−	0.325540i	−0.986664	−	0.162770i	$-0.947957\pi$
$71$		−	23.1134i		−	0.325540i	0.986664	−	0.162770i	$-0.0520429\pi$
$72$	170.415	+	105.613i	2.36687	+	1.46685i
$73$	−103.753			−1.42127			−0.710637	−	0.703559i	$-0.751593\pi$
$73$	−103.753			−1.42127			−0.710637	+	0.703559i	$0.751593\pi$
$74$	144.521	−	83.4395i	1.95299	−	1.12756i
$75$	12.8718	+	7.70180i	0.171624	+	0.102691i
$76$	−36.7778	+	63.7010i	−0.483918	+	0.838171i
$77$	47.2464	+	27.2777i	0.613589	+	0.354256i
$78$	−15.9945	−	28.7296i	−0.205058	−	0.368328i
$79$	−40.2610	−	69.7340i	−0.509633	−	0.882709i	−0.999938	−	0.0111586i	$-0.996448\pi$
$79$	−40.2610	−	69.7340i	−0.509633	−	0.882709i	0.490305	−	0.871551i	$-0.336885\pi$
$80$		−	97.0225i		−	1.21278i
$81$	−36.0452	−	72.5379i	−0.445003	−	0.895529i
$82$	−64.1296			−0.782068
$83$	−17.1034	+	9.87463i	−0.206065	+	0.118971i	−0.599481	−	0.800389i	$-0.704626\pi$
$83$	−17.1034	+	9.87463i	−0.206065	+	0.118971i	0.393417	+	0.919360i	$0.371293\pi$
$84$	189.601	−	105.556i	2.25715	−	1.25662i
$85$	2.12546	−	3.68141i	0.0250055	−	0.0433107i
$86$	133.032	+	76.8063i	1.54689	+	0.893097i
$87$	−25.2595	+	42.2153i	−0.290339	+	0.485234i
$88$	83.6843	+	144.945i	0.950958	+	1.64711i
$89$			29.0566i			0.326478i	0.986587	+	0.163239i	$0.0521942\pi$
$89$			29.0566i			0.326478i	−0.986587	+	0.163239i	$0.947806\pi$
$90$	−39.6121	+	63.9171i	−0.440135	+	0.710190i
$91$	−21.2997			−0.234063
$92$	−305.377	+	176.310i	−3.31932	+	1.91641i
$93$	−1.24719	+	79.9139i	−0.0134107	+	0.859289i
$94$	−78.7306	+	136.365i	−0.837559	+	1.45070i
$95$	−14.2986	−	8.25532i	−0.150512	−	0.0868981i
$96$	219.040	+	3.41849i	2.28167	+	0.0356092i
$97$	47.7972	+	82.7872i	0.492755	+	0.853476i	0.999965	−	0.00834602i	$-0.00265665\pi$
$97$	47.7972	+	82.7872i	0.492755	+	0.853476i	−0.507210	+	0.861822i	$0.669323\pi$
$98$		−	13.9196i		−	0.142036i
$99$	2.11011	−	67.5864i	0.0213143	−	0.682691i
$100$	49.8088			0.498088
$101$	117.817	−	68.0219i	1.16651	−	0.673484i	0.213653	−	0.976910i	$-0.431464\pi$
$101$	117.817	−	68.0219i	1.16651	−	0.673484i	0.952855	+	0.303426i	$0.0981305\pi$
$102$	18.2868	+	10.9419i	0.179282	+	0.107273i
$103$	85.9401	−	148.853i	0.834370	−	1.44517i	−0.0601721	−	0.998188i	$-0.519165\pi$
$103$	85.9401	−	148.853i	0.834370	−	1.44517i	0.894542	−	0.446983i	$-0.147502\pi$
$104$	−56.5901	−	32.6723i	−0.544135	−	0.314157i
$105$	23.6936	+	42.5588i	0.225654	+	0.405322i
$106$	−187.712	−	325.127i	−1.77087	−	3.06724i
$107$			98.6056i			0.921548i	0.887518	+	0.460774i	$0.152428\pi$
$107$			98.6056i			0.921548i	−0.887518	+	0.460774i	$0.847572\pi$
$108$	−226.384	−	145.238i	−2.09615	−	1.34479i
$109$	2.62651			0.0240965			0.0120482	−	0.999927i	$-0.496165\pi$
$109$	2.62651			0.0240965			0.0120482	+	0.999927i	$0.496165\pi$
$110$	−54.3644	+	31.3873i	−0.494222	+	0.285339i
$111$	−117.065	+	65.1731i	−1.05464	+	0.587145i
$112$	157.531	−	272.852i	1.40653	−	2.43618i
$113$	2.36782	+	1.36706i	0.0209542	+	0.0120979i	0.510440	−	0.859913i	$-0.329482\pi$
$113$	2.36782	+	1.36706i	0.0209542	+	0.0120979i	−0.489486	+	0.872011i	$0.662816\pi$
$114$	42.4983	−	71.0260i	0.372792	−	0.623035i
$115$	−39.5753	−	68.5465i	−0.344133	−	0.596056i
$116$			163.357i			1.40825i
$117$	12.4802	+	23.2640i	0.106668	+	0.198838i
$118$	17.7762			0.150646
$119$	11.9547	−	6.90205i	0.100460	−	0.0580004i
$120$	−2.33190	+	149.417i	−0.0194325	+	1.24514i
$121$	−32.2754	+	55.9027i	−0.266739	+	0.462006i
$122$	−248.928	−	143.718i	−2.04039	−	1.17802i
$123$	51.4821	+	0.803465i	0.418554	+	0.00653224i
$124$	132.697	+	229.838i	1.07014	+	1.85353i
$125$			11.1803i			0.0894427i
$126$	−215.179	+	115.435i	−1.70777	+	0.916149i
$127$	193.060			1.52015			0.760077	−	0.649833i	$-0.225161\pi$
$127$	193.060			1.52015			0.760077	+	0.649833i	$0.225161\pi$
$128$	68.3455	−	39.4593i	0.533950	−	0.308276i
$129$	−105.834	−	63.3255i	−0.820418	−	0.490896i
$130$	12.2543	−	21.2251i	0.0942641	−	0.163270i
$131$	−201.259	−	116.197i	−1.53633	−	0.886999i	−0.999049	−	0.0435937i	$-0.986119\pi$
$131$	−201.259	−	116.197i	−1.53633	−	0.886999i	−0.537278	−	0.843405i	$-0.680547\pi$
$132$	−109.220	−	196.182i	−0.827424	−	1.48623i
$133$	−26.8076	−	46.4322i	−0.201561	−	0.349114i
$134$			313.291i			2.33799i
$135$	32.6007	−	50.8153i	0.241487	−	0.376409i
$136$	42.3491			0.311390
$137$	154.172	−	89.0111i	1.12534	−	0.649716i	0.182582	−	0.983191i	$-0.441555\pi$
$137$	154.172	−	89.0111i	1.12534	−	0.649716i	0.942759	+	0.333475i	$0.108221\pi$
$138$	346.685	−	193.009i	2.51221	−	1.39861i
$139$	−16.0343	+	27.7722i	−0.115355	+	0.199800i	−0.917922	−	0.396762i	$-0.870134\pi$
$139$	−16.0343	+	27.7722i	−0.115355	+	0.199800i	0.802567	+	0.596562i	$0.203467\pi$
$140$	140.075	+	80.8725i	1.00054	+	0.577661i
$141$	64.9120	−	108.485i	0.460369	−	0.769400i
$142$	43.1820	+	74.7935i	0.304099	+	0.526715i
$143$			22.0390i			0.154119i
$144$	−390.318	−	12.1861i	−2.71054	−	0.0846257i
$145$	−36.6680			−0.252883
$146$	335.739	−	193.839i	2.29958	−	1.32766i
$147$	−0.174395	+	11.1744i	−0.00118636	+	0.0760163i
$148$	−222.453	+	385.299i	−1.50306	+	2.60337i
$149$	80.4653	+	46.4567i	0.540036	+	0.311790i	0.745093	−	0.666960i	$-0.232405\pi$
$149$	80.4653	+	46.4567i	0.540036	+	0.311790i	−0.205058	+	0.978750i	$0.565738\pi$
$150$	−56.0414	−	0.874620i	−0.373609	−	0.00583080i
$151$	113.614	+	196.785i	0.752408	+	1.30321i	0.946653	+	0.322256i	$0.104441\pi$
$151$	113.614	+	196.785i	0.752408	+	1.30321i	−0.194245	+	0.980953i	$0.562226\pi$
$152$		−	164.484i		−	1.08213i
$153$	−14.5432	−	9.01305i	−0.0950537	−	0.0589088i
$154$	−203.849			−1.32369
$155$	−51.5905	+	29.7858i	−0.332842	+	0.192166i
$156$	75.2261	+	45.0114i	0.482219	+	0.288535i
$157$	0.792406	−	1.37249i	0.00504717	−	0.00874196i	−0.863491	−	0.504365i	$-0.831727\pi$
$157$	0.792406	−	1.37249i	0.00504717	−	0.00874196i	0.868538	+	0.495623i	$0.165060\pi$
$158$	260.564	+	150.437i	1.64914	+	0.952133i
$159$	146.619	+	263.358i	0.922131	+	1.65634i
$160$	81.6413	+	141.407i	0.510258	+	0.883793i
$161$		−	257.027i		−	1.59644i
$162$	252.161	+	167.386i	1.55655	+	1.03325i
$163$	−41.6801			−0.255706			−0.127853	−	0.991793i	$-0.540809\pi$
$163$	−41.6801			−0.255706			−0.127853	+	0.991793i	$0.540809\pi$
$164$	148.066	−	85.4859i	0.902841	−	0.521256i
$165$	44.0360	−	24.5161i	0.266885	−	0.148582i
$166$	36.8970	−	63.9075i	0.222271	−	0.384985i
$167$	8.01405	+	4.62692i	0.0479884	+	0.0277061i	0.523802	−	0.851840i	$-0.324513\pi$
$167$	8.01405	+	4.62692i	0.0479884	+	0.0277061i	−0.475814	+	0.879546i	$0.657846\pi$
$168$	−249.159	+	416.412i	−1.48309	+	2.47864i
$169$	80.1977	+	138.907i	0.474543	+	0.821932i
$170$			15.8838i			0.0934340i
$171$	−35.0068	+	56.4860i	−0.204718	+	0.330327i
$172$	−409.537			−2.38103
$173$	−127.637	+	73.6913i	−0.737787	+	0.425962i	−0.821264	−	0.570548i	$-0.806731\pi$
$173$	−127.637	+	73.6913i	−0.737787	+	0.425962i	0.0834771	+	0.996510i	$0.473397\pi$
$174$	2.86848	−	183.798i	0.0164855	−	1.05631i
$175$	−18.1530	+	31.4420i	−0.103732	+	0.179668i
$176$	−282.323	−	162.999i	−1.60411	−	0.926133i
$177$	−14.2705	−	0.222714i	−0.0806240	−	0.00125827i
$178$	−54.2856	−	94.0254i	−0.304975	−	0.528233i
$179$		−	160.022i		−	0.893977i	−0.894540	−	0.446988i	$-0.852496\pi$
$179$		−	160.022i		−	0.893977i	0.894540	−	0.446988i	$-0.147504\pi$
$180$	6.25603	−	200.379i	0.0347557	−	1.11322i
$181$	−30.3346			−0.167595			−0.0837973	−	0.996483i	$-0.526705\pi$
$181$	−30.3346			−0.167595			−0.0837973	+	0.996483i	$0.526705\pi$
$182$	68.9246	−	39.7937i	0.378707	−	0.218646i
$183$	198.034	+	118.493i	1.08215	+	0.647505i
$184$	394.262	−	682.882i	2.14273	−	3.71132i
$185$	−86.4862	−	49.9328i	−0.467493	−	0.269907i
$186$	−145.265	−	260.927i	−0.780995	−	1.40283i
$187$	−7.14163	−	12.3697i	−0.0381905	−	0.0661480i
$188$		−	419.797i		−	2.23296i
$189$	174.188	−	89.9731i	0.921631	−	0.476048i
$190$	61.6928			0.324699
$191$	−249.938	+	144.302i	−1.30857	+	0.755506i	−0.981858	−	0.189617i	$-0.939275\pi$
$191$	−249.938	+	144.302i	−1.30857	+	0.755506i	−0.326716	+	0.945122i	$0.605942\pi$
$192$	−260.260	+	144.894i	−1.35552	+	0.754654i
$193$	47.3339	−	81.9847i	0.245253	−	0.424791i	−0.716949	−	0.697125i	$-0.754462\pi$
$193$	47.3339	−	81.9847i	0.245253	−	0.424791i	0.962203	+	0.272334i	$0.0877955\pi$
$194$	−309.338	−	178.596i	−1.59453	−	0.920600i
$195$	−10.1035	+	16.8856i	−0.0518128	+	0.0865930i
$196$	18.5551	+	32.1383i	0.0946686	+	0.163971i
$197$		−	129.755i		−	0.658657i	−0.944215	−	0.329329i	$-0.893178\pi$
$197$		−	129.755i		−	0.658657i	0.944215	−	0.329329i	$-0.106822\pi$
$198$	119.442	+	222.648i	0.603241	+	1.12449i
$199$	136.428			0.685570			0.342785	−	0.939414i	$-0.388630\pi$
$199$	136.428			0.685570			0.342785	+	0.939414i	$0.388630\pi$
$200$	−96.4597	+	55.6911i	−0.482299	+	0.278455i
$201$	3.92515	−	251.504i	0.0195281	−	1.25127i
$202$	−254.167	+	440.230i	−1.25825	+	2.17936i
$203$	−103.120	−	59.5363i	−0.507980	−	0.293282i
$204$	−56.8072	−	0.886573i	−0.278467	−	0.00434594i
$205$	19.1886	+	33.2356i	0.0936029	+	0.162125i
$206$			642.238i			3.11766i
$207$	−280.731	+	150.601i	−1.35619	+	0.727539i
$208$	127.278			0.611911
$209$	−48.0439	+	27.7382i	−0.229875	+	0.132718i
$210$	−156.183	−	93.4516i	−0.743727	−	0.445008i
$211$	−79.1144	+	137.030i	−0.374950	+	0.649432i	−0.990320	−	0.138806i	$-0.955673\pi$
$211$	−79.1144	+	137.030i	−0.374950	+	0.649432i	0.615370	+	0.788239i	$0.289007\pi$
$212$	866.802	+	500.448i	4.08869	+	2.36060i
$213$	−33.7287	−	60.5840i	−0.158351	−	0.284432i
$214$	−184.222	−	319.082i	−0.860851	−	1.49104i
$215$		−	91.9267i		−	0.427566i
$216$	600.804	+	28.1480i	2.78150	+	0.130315i
$217$	−193.448			−0.891463
$218$	−8.49925	+	4.90704i	−0.0389874	+	0.0225094i
$219$	−271.954	+	151.404i	−1.24180	+	0.691343i
$220$	83.6797	−	144.937i	0.380362	−	0.658807i
$221$	4.82941	+	2.78826i	0.0218525	+	0.0126166i
$222$	257.054	−	429.605i	1.15790	−	1.93516i
$223$	103.124	+	178.616i	0.462440	+	0.800969i	0.999082	−	0.0428406i	$-0.0136407\pi$
$223$	103.124	+	178.616i	0.462440	+	0.800969i	−0.536642	+	0.843810i	$0.680307\pi$
$224$			530.230i			2.36710i
$225$	44.9781	+	1.40426i	0.199903	+	0.00624115i
$226$	−10.2162			−0.0452044
$227$	−127.562	+	73.6481i	−0.561948	+	0.324441i	−0.753927	−	0.656958i	$-0.771843\pi$
$227$	−127.562	+	73.6481i	−0.561948	+	0.324441i	0.191979	+	0.981399i	$0.438510\pi$
$228$	−3.44346	+	220.640i	−0.0151029	+	0.967718i
$229$	13.5751	−	23.5127i	0.0592798	−	0.102676i	−0.834863	−	0.550458i	$-0.814453\pi$
$229$	13.5751	−	23.5127i	0.0592798	−	0.102676i	0.894142	+	0.447783i	$0.147786\pi$
$230$	256.127	+	147.875i	1.11360	+	0.642935i
$231$	163.646	+	2.55398i	0.708426	+	0.0110562i
$232$	−182.649	−	316.358i	−0.787281	−	1.36361i
$233$			39.6011i			0.169962i	0.996383	+	0.0849808i	$0.0270829\pi$
$233$			39.6011i			0.169962i	−0.996383	+	0.0849808i	$0.972917\pi$
$234$	−83.8487	−	51.9646i	−0.358328	−	0.222071i
$235$	94.2298			0.400978
$236$	−41.0428	+	23.6960i	−0.173910	+	0.100407i
$237$	−207.292	−	124.033i	−0.874649	−	0.523345i
$238$	−25.7898	+	44.6693i	−0.108361	+	0.187686i
$239$	54.9394	+	31.7193i	0.229872	+	0.132717i	0.610513	−	0.792006i	$-0.290963\pi$
$239$	54.9394	+	31.7193i	0.229872	+	0.132717i	−0.380641	+	0.924723i	$0.624297\pi$
$240$	−141.582	−	254.312i	−0.589927	−	1.05963i
$241$	69.1161	+	119.713i	0.286789	+	0.496733i	0.973041	−	0.230630i	$-0.0740789\pi$
$241$	69.1161	+	119.713i	0.286789	+	0.496733i	−0.686253	+	0.727363i	$0.740746\pi$
$242$		−	241.197i		−	0.996683i
$243$	−200.333	−	137.534i	−0.824416	−	0.565984i
$244$	766.317			3.14064
$245$	−7.21392	+	4.16496i	−0.0294446	+	0.0169998i
$246$	−168.094	+	93.5827i	−0.683310	+	0.380417i
$247$	10.8296	−	18.7575i	0.0438446	−	0.0759411i
$248$	−513.961	−	296.735i	−2.07242	−	1.19651i
$249$	−30.4210	+	50.8415i	−0.122173	+	0.204183i
$250$	−20.8879	−	36.1789i	−0.0835517	−	0.144716i
$251$		−	186.477i		−	0.742936i	−0.928446	−	0.371468i	$-0.878855\pi$
$251$		−	186.477i		−	0.742936i	0.928446	−	0.371468i	$-0.121145\pi$
$252$	342.941	−	553.360i	1.36088	−	2.19587i
$253$	−265.949			−1.05118
$254$	−624.730	+	360.688i	−2.45957	+	1.42003i
$255$	0.199004	−	12.7512i	0.000780410	−	0.0500048i
$256$	51.1416	−	88.5798i	0.199772	−	0.346015i
$257$	201.713	+	116.459i	0.784877	+	0.453149i	0.838156	−	0.545431i	$-0.183634\pi$
$257$	201.713	+	116.459i	0.784877	+	0.453149i	−0.0532790	+	0.998580i	$0.516967\pi$
$258$	460.782	+	7.19128i	1.78598	+	0.0278732i
$259$	−162.148	−	280.848i	−0.626053	−	1.08435i
$260$			65.3410i			0.251312i
$261$	−4.60553	+	147.514i	−0.0176457	+	0.565188i
$262$	868.350			3.31431
$263$	−9.34728	+	5.39665i	−0.0355410	+	0.0205196i	−0.517665	−	0.855583i	$-0.673199\pi$
$263$	−9.34728	+	5.39665i	−0.0355410	+	0.0205196i	0.482124	+	0.876103i	$0.339865\pi$
$264$	430.866	+	257.808i	1.63207	+	0.976545i
$265$	−112.333	+	194.567i	−0.423898	+	0.734213i
$266$	173.496	+	100.168i	0.652240	+	0.376571i
$267$	42.4015	+	76.1622i	0.158807	+	0.285252i
$268$	−417.622	−	723.343i	−1.55829	−	2.69904i
$269$		−	58.4601i		−	0.217324i	−0.994079	−	0.108662i	$-0.965343\pi$
$269$		−	58.4601i		−	0.217324i	0.994079	−	0.108662i	$-0.0346566\pi$
$270$	−10.5574	+	225.342i	−0.0391015	+	0.834601i
$271$	−65.5995			−0.242065			−0.121032	−	0.992649i	$-0.538620\pi$
$271$	−65.5995			−0.242065			−0.121032	+	0.992649i	$0.538620\pi$
$272$	−71.4360	+	41.2436i	−0.262632	+	0.151631i
$273$	−55.8301	+	31.0821i	−0.204506	+	0.113854i
$274$	−332.594	+	576.069i	−1.21385	+	2.10244i
$275$	32.5334	+	18.7832i	0.118303	+	0.0683024i
$276$	−543.161	+	907.767i	−1.96797	+	3.28901i
$277$	−134.128	−	232.317i	−0.484218	−	0.838690i	0.515618	−	0.856819i	$-0.327562\pi$
$277$	−134.128	−	232.317i	−0.484218	−	0.838690i	−0.999836	+	0.0181286i	$0.994229\pi$
$278$		−	119.826i		−	0.431028i
$279$	113.347	+	211.288i	0.406263	+	0.757303i
$280$	−361.693			−1.29176
$281$	159.428	−	92.0461i	0.567361	−	0.327566i	−0.188734	−	0.982028i	$-0.560438\pi$
$281$	159.428	−	92.0461i	0.567361	−	0.327566i	0.756095	+	0.654462i	$0.227105\pi$
$282$	−7.37144	+	472.326i	−0.0261399	+	1.67491i
$283$	231.303	−	400.628i	0.817324	−	1.41565i	−0.0903234	−	0.995912i	$-0.528790\pi$
$283$	231.303	−	400.628i	0.817324	−	1.41565i	0.907647	−	0.419734i	$-0.137877\pi$
$284$	−199.402	−	115.125i	−0.702121	−	0.405370i
$285$	−49.5259	−	0.772935i	−0.173775	−	0.00271205i
$286$	−41.1750	−	71.3171i	−0.143968	−	0.249361i
$287$			124.623i			0.434226i
$288$	579.129	−	310.679i	2.01086	−	1.07875i
$289$	285.386			0.987495
$290$	118.656	−	68.5058i	0.409157	−	0.236227i
$291$	246.094	+	147.250i	0.845683	+	0.506013i
$292$	−516.782	+	895.093i	−1.76980	+	3.06539i
$293$	248.349	+	143.384i	0.847608	+	0.489367i	0.859843	−	0.510559i	$-0.170561\pi$
$293$	248.349	+	143.384i	0.847608	+	0.489367i	−0.0122351	+	0.999925i	$0.503895\pi$
$294$	−20.3125	−	36.4855i	−0.0690901	−	0.124100i
$295$	−5.31893	−	9.21266i	−0.0180303	−	0.0312294i
$296$		−	994.894i		−	3.36113i
$297$	−93.0962	−	180.235i	−0.313455	−	0.606850i
$298$	−347.175			−1.16502
$299$	89.9217	−	51.9163i	0.300741	−	0.173633i
$300$	130.557	−	72.6848i	0.435191	−	0.242283i
$301$	149.257	−	258.521i	0.495872	−	0.858875i
$302$	−735.294	−	424.522i	−2.43475	−	1.40570i
$303$	209.556	−	350.225i	0.691605	−	1.15586i
$304$	160.190	+	277.458i	0.526942	+	0.912690i
$305$			172.011i			0.563972i
$306$	63.8999	+	1.99502i	0.208823	+	0.00651966i
$307$	−236.738			−0.771133			−0.385567	−	0.922680i	$-0.625994\pi$
$307$	−236.738			−0.771133			−0.385567	+	0.922680i	$0.625994\pi$
$308$	470.658	−	271.734i	1.52811	−	0.882254i
$309$	8.04646	−	515.578i	0.0260403	−	1.66854i
$310$	111.296	−	192.770i	0.359019	−	0.621839i
$311$	448.597	+	258.997i	1.44243	+	0.832789i	0.998012	−	0.0630292i	$-0.0200761\pi$
$311$	448.597	+	258.997i	1.44243	+	0.832789i	0.444421	+	0.895818i	$0.353409\pi$
$312$	−196.010	−	3.05907i	−0.628237	−	0.00980470i
$313$	247.615	+	428.882i	0.791102	+	1.37023i	0.925285	+	0.379272i	$0.123826\pi$
$313$	247.615	+	428.882i	0.791102	+	1.37023i	−0.134183	+	0.990957i	$0.542841\pi$
$314$			5.92172i			0.0188590i
$315$	124.210	+	76.9781i	0.394317	+	0.244375i
$316$	−802.141			−2.53842
$317$	−189.840	+	109.604i	−0.598864	+	0.345754i	−0.768595	−	0.639736i	$-0.779044\pi$
$317$	−189.840	+	109.604i	−0.598864	+	0.345754i	0.169731	+	0.985491i	$0.445710\pi$
$318$	−966.475	−	578.289i	−3.03923	−	1.81852i
$319$	−61.6029	+	106.699i	−0.193112	+	0.334481i
$320$	−192.277	−	111.011i	−0.600866	−	0.346910i
$321$	143.893	+	258.462i	0.448264	+	0.805177i
$322$	480.197	+	831.725i	1.49129	+	2.58300i
$323$			14.0371i			0.0434586i
$324$	−805.332	−	50.3356i	−2.48559	−	0.155357i
$325$	−14.6668			−0.0451285
$326$	134.874	−	77.8697i	0.413725	−	0.238864i
$327$	6.88453	−	3.83281i	0.0210536	−	0.0117211i
$328$	−191.163	+	331.104i	−0.582813	+	1.00946i
$329$	264.998	+	152.997i	0.805466	+	0.465036i
$330$	−96.6954	+	161.604i	−0.293016	+	0.489709i
$331$	47.4838	+	82.2443i	0.143455	+	0.248472i	0.928796	−	0.370592i	$-0.120845\pi$
$331$	47.4838	+	82.2443i	0.143455	+	0.248472i	−0.785340	+	0.619064i	$0.787512\pi$
$332$			196.738i			0.592583i
$333$	−211.741	+	341.659i	−0.635858	+	1.02600i
$334$	−34.5774			−0.103525
$335$	162.365	−	93.7416i	0.484672	−	0.279826i
$336$	14.7494	−	945.072i	0.0438972	−	2.81272i
$337$	257.989	−	446.850i	0.765547	−	1.32597i	−0.174411	−	0.984673i	$-0.555802\pi$
$337$	257.989	−	446.850i	0.765547	−	1.32597i	0.939957	−	0.341293i	$-0.110865\pi$
$338$	−519.031	−	299.662i	−1.53559	−	0.886575i
$339$	8.20138	+	0.127996i	0.0241929	+	0.000377570i
$340$	−21.1734	−	36.6734i	−0.0622747	−	0.107863i
$341$			200.162i			0.586986i
$342$	7.74866	−	248.188i	0.0226569	−	0.725695i
$343$	328.750			0.958454
$344$	793.109	−	457.902i	2.30555	−	1.33111i
$345$	−203.762	−	121.921i	−0.590614	−	0.353393i
$346$	275.351	−	476.922i	0.795812	−	1.37839i
$347$	−96.4994	−	55.7140i	−0.278096	−	0.160559i	0.354465	−	0.935069i	$-0.384663\pi$
$347$	−96.4994	−	55.7140i	−0.278096	−	0.160559i	−0.632561	+	0.774510i	$0.717996\pi$
$348$	238.383	+	428.187i	0.685010	+	1.23042i
$349$	−310.131	−	537.162i	−0.888627	−	1.53915i	−0.841499	−	0.540258i	$-0.818327\pi$
$349$	−310.131	−	537.162i	−0.888627	−	1.53915i	−0.0471279	−	0.998889i	$-0.515007\pi$
$350$		−	135.659i		−	0.387598i
$351$	66.6613	+	42.7668i	0.189918	+	0.121843i
$352$	548.635			1.55862
$353$	488.067	−	281.786i	1.38263	−	0.798260i	0.390157	−	0.920748i	$-0.372421\pi$
$353$	488.067	−	281.786i	1.38263	−	0.798260i	0.992470	+	0.122488i	$0.0390873\pi$
$354$	46.5945	−	25.9404i	0.131623	−	0.0732780i
$355$	25.8415	−	44.7588i	0.0727930	−	0.126081i
$356$	250.675	+	144.727i	0.704144	+	0.406538i
$357$	21.2633	−	35.5366i	0.0595610	−	0.0995424i
$358$	298.964	+	517.822i	0.835096	+	1.44643i
$359$			415.128i			1.15635i	0.815915	+	0.578173i	$0.196234\pi$
$359$			415.128i			1.15635i	−0.815915	+	0.578173i	$0.803766\pi$
$360$	211.928	+	395.049i	0.588688	+	1.09736i
$361$	−306.480			−0.848974
$362$	98.1611	−	56.6733i	0.271163	−	0.156556i
$363$	−3.02191	+	193.629i	−0.00832482	+	0.533413i
$364$	−106.091	+	183.756i	−0.291460	+	0.504823i
$365$	−200.917	−	115.999i	−0.550457	−	0.317807i
$366$	−862.205	−	13.4562i	−2.35575	−	0.0367655i
$367$	−313.940	−	543.761i	−0.855423	−	1.48164i	−0.876252	−	0.481853i	$-0.839964\pi$
$367$	−313.940	−	543.761i	−0.855423	−	1.48164i	0.0208286	−	0.999783i	$-0.493370\pi$
$368$			1535.88i			4.17358i
$369$	136.116	−	73.0205i	0.368877	−	0.197888i
$370$	373.153			1.00852
$371$	−631.819	+	364.781i	−1.70302	+	0.983237i
$372$	683.217	+	408.802i	1.83660	+	1.09893i
$373$	−195.467	+	338.559i	−0.524040	+	0.907665i	0.475568	+	0.879679i	$0.342243\pi$
$373$	−195.467	+	338.559i	−0.524040	+	0.907665i	−0.999608	+	0.0279857i	$0.991091\pi$
$374$	46.2198	+	26.6850i	0.123582	+	0.0713503i
$375$	16.3152	+	29.3055i	0.0435072	+	0.0781481i
$376$	469.373	+	812.979i	1.24833	+	2.16218i
$377$		−	48.1024i		−	0.127593i
$378$	−395.569	+	616.579i	−1.04648	+	1.63116i
$379$	52.4430			0.138372			0.0691860	−	0.997604i	$-0.477960\pi$
$379$	52.4430			0.138372			0.0691860	+	0.997604i	$0.477960\pi$
$380$	−142.440	+	82.2376i	−0.374841	+	0.216415i
$381$	506.042	−	281.727i	1.32819	−	0.739441i
$382$	539.189	−	933.904i	1.41149	−	2.44477i
$383$	−96.0614	−	55.4610i	−0.250813	−	0.144807i	0.369324	−	0.929301i	$-0.379589\pi$
$383$	−96.0614	−	55.4610i	−0.250813	−	0.144807i	−0.620136	+	0.784494i	$0.712923\pi$
$384$	121.563	−	203.164i	0.316571	−	0.529074i
$385$	60.9948	+	105.646i	0.158428	+	0.274405i
$386$			353.731i			0.916400i
$387$	−369.818	−	11.5461i	−0.955601	−	0.0298348i
$388$	952.290			2.45435
$389$	−91.6114	+	52.8918i	−0.235505	+	0.135969i	−0.613109	−	0.789998i	$-0.710081\pi$
$389$	−91.6114	+	52.8918i	−0.235505	+	0.135969i	0.377604	+	0.925967i	$0.376748\pi$
$390$	1.14736	−	73.5170i	0.00294194	−	0.188505i
$391$	−33.6464	+	58.2773i	−0.0860521	+	0.149047i
$392$	−71.8674	−	41.4926i	−0.183335	−	0.105849i
$393$	−697.096	−	10.8794i	−1.77378	−	0.0276829i
$394$	242.419	+	419.881i	0.615276	+	1.06569i
$395$		−	180.053i		−	0.455829i
$396$	−572.568	−	354.844i	−1.44588	−	0.896072i
$397$	99.8892			0.251610			0.125805	−	0.992055i	$-0.459849\pi$
$397$	99.8892			0.251610			0.125805	+	0.992055i	$0.459849\pi$
$398$	−441.475	+	254.885i	−1.10923	+	0.640416i
$399$	−138.025	−	82.5868i	−0.345926	−	0.206984i
$400$	108.474	−	187.883i	0.271186	−	0.469708i
$401$	−136.080	−	78.5658i	−0.339352	−	0.195925i	0.320634	−	0.947203i	$-0.396104\pi$
$401$	−136.080	−	78.5658i	−0.339352	−	0.195925i	−0.659985	+	0.751279i	$0.729437\pi$
$402$	457.177	+	821.187i	1.13726	+	2.04275i
$403$	−39.0740	−	67.6782i	−0.0969579	−	0.167936i
$404$		−	1355.24i		−	3.35455i
$405$	11.2986	−	180.769i	0.0278977	−	0.446343i
$406$	444.920			1.09586
$407$	−290.597	+	167.776i	−0.713996	+	0.412226i
$408$	111.004	−	61.7990i	0.272069	−	0.151468i
$409$	−342.619	+	593.434i	−0.837700	+	1.45094i	0.0541134	+	0.998535i	$0.482767\pi$
$409$	−342.619	+	593.434i	−0.837700	+	1.45094i	−0.891813	+	0.452404i	$0.850567\pi$
$410$	−124.186	−	71.6990i	−0.302894	−	0.174876i
$411$	274.218	−	458.292i	0.667197	−	1.11506i
$412$	−856.116	−	1482.84i	−2.07795	−	3.59912i
$413$		−	34.5445i		−	0.0836428i
$414$	627.065	−	1011.82i	1.51465	−	2.44400i
$415$	−44.1607			−0.106411
$416$	−185.502	+	107.100i	−0.445919	+	0.257452i
$417$	−1.50127	+	96.1942i	−0.00360017	+	0.230681i
$418$	103.645	−	179.518i	0.247954	−	0.429469i
$419$	−44.6836	−	25.7981i	−0.106643	−	0.0615706i	0.445730	−	0.895168i	$-0.352944\pi$
$419$	−44.6836	−	25.7981i	−0.106643	−	0.0615706i	−0.552373	+	0.833597i	$0.686278\pi$
$420$	485.176	+	7.57199i	1.15518	+	0.0180285i
$421$	−7.37620	−	12.7760i	−0.0175207	−	0.0303467i	0.857132	−	0.515097i	$-0.172244\pi$
$421$	−7.37620	−	12.7760i	−0.0175207	−	0.0303467i	−0.874653	+	0.484750i	$0.838911\pi$
$422$		−	591.229i		−	1.40102i
$423$	11.8353	−	379.083i	0.0279795	−	0.896177i
$424$	−2238.20			−5.27876
$425$	8.23189	−	4.75268i	0.0193691	−	0.0111828i
$426$	222.332	+	133.032i	0.521905	+	0.312281i
$427$	−279.287	+	483.740i	−0.654069	+	1.13288i
$428$	850.685	+	491.143i	1.98758	+	1.14753i
$429$	32.1610	+	57.7680i	0.0749674	+	0.134657i
$430$	171.744	+	297.470i	0.399405	+	0.691790i
$431$			38.6810i			0.0897472i	0.998993	+	0.0448736i	$0.0142885\pi$
$431$			38.6810i			0.0897472i	−0.998993	+	0.0448736i	$0.985711\pi$
$432$	−1040.87	+	537.639i	−2.40942	+	1.24454i
$433$	−544.647			−1.25784			−0.628922	−	0.777468i	$-0.716504\pi$
$433$	−544.647			−1.25784			−0.628922	+	0.777468i	$0.716504\pi$
$434$	625.985	−	361.413i	1.44236	−	0.832748i
$435$	−96.1130	+	53.5087i	−0.220949	+	0.123009i
$436$	13.0824	−	22.6593i	0.0300054	−	0.0519709i
$437$	226.349	+	130.683i	0.517962	+	0.299045i
$438$	597.163	−	998.020i	1.36339	−	2.27858i
$439$	−125.709	−	217.735i	−0.286353	−	0.495978i	0.686583	−	0.727051i	$-0.259110\pi$
$439$	−125.709	−	217.735i	−0.286353	−	0.495978i	−0.972936	+	0.231073i	$0.925776\pi$
$440$			374.248i			0.850563i
$441$	15.8494	+	29.5444i	0.0359397	+	0.0669942i
$442$	−20.8369			−0.0471423
$443$	632.952	−	365.435i	1.42878	−	0.824909i	0.431760	−	0.901989i	$-0.357893\pi$
$443$	632.952	−	365.435i	1.42878	−	0.824909i	0.997025	+	0.0770796i	$0.0245596\pi$
$444$	−20.8280	+	1334.55i	−0.0469098	+	3.00575i
$445$	−32.4862	+	56.2678i	−0.0730028	+	0.126445i
$446$	−667.407	−	385.328i	−1.49643	−	0.863964i
$447$	278.706	+	4.34968i	0.623504	+	0.00973083i
$448$	−360.489	−	624.385i	−0.804662	−	1.39372i
$449$			94.7211i			0.210960i	0.994421	+	0.105480i	$0.0336379\pi$
$449$			94.7211i			0.210960i	−0.994421	+	0.105480i	$0.966362\pi$
$450$	−148.170	+	79.4872i	−0.329267	+	0.176638i
$451$	128.949			0.285917
$452$	23.5877	−	13.6184i	0.0521852	−	0.0301291i
$453$	584.963	+	350.012i	1.29131	+	0.772653i
$454$	275.190	−	476.642i	0.606144	−	1.04987i
$455$	−41.2467	−	23.8138i	−0.0906521	−	0.0523380i
$456$	−240.028	−	431.141i	−0.526377	−	0.945484i
$457$	204.206	+	353.695i	0.446840	+	0.773949i	0.998178	−	0.0603323i	$-0.0192160\pi$
$457$	204.206	+	353.695i	0.446840	+	0.773949i	−0.551339	+	0.834282i	$0.685883\pi$
$458$			101.448i			0.221502i
$459$	−51.2727	−	2.40215i	−0.111705	−	0.00523345i
$460$	−788.481			−1.71409
$461$	−511.735	+	295.450i	−1.11005	+	0.640890i	−0.938843	−	0.344344i	$-0.888101\pi$
$461$	−511.735	+	295.450i	−1.11005	+	0.640890i	−0.171211	+	0.985234i	$0.554768\pi$
$462$	−534.322	+	297.471i	−1.15654	+	0.643878i
$463$	−400.967	+	694.496i	−0.866020	+	1.49999i	1.04649e−5		1.00000i	$0.499997\pi$
$463$	−400.967	+	694.496i	−0.866020	+	1.49999i	−0.866031	+	0.499991i	$0.833337\pi$
$464$	616.198	+	355.762i	1.32801	+	0.766729i
$465$	−91.7616	+	153.358i	−0.197337	+	0.329803i
$466$	−73.9856	−	128.147i	−0.158767	−	0.274993i
$467$			20.6432i			0.0442039i	0.999756	+	0.0221019i	$0.00703584\pi$
$467$			20.6432i			0.0442039i	−0.999756	+	0.0221019i	$0.992964\pi$
$468$	262.864	+	8.20688i	0.561676	+	0.0175361i
$469$	608.817			1.29812
$470$	−304.922	+	176.047i	−0.648771	+	0.374568i
$471$	0.0741920	−	4.75386i	0.000157520	−	0.0100931i
$472$	52.9889	−	91.7795i	0.112265	−	0.194448i
$473$	−267.495	−	154.438i	−0.565529	−	0.326508i
$474$	902.512	+	14.0852i	1.90403	+	0.0297156i
$475$	−18.4595	−	31.9727i	−0.0388620	−	0.0673110i
$476$		−	137.513i		−	0.288893i
$477$	768.625	+	476.349i	1.61137	+	0.998636i
$478$	−237.041			−0.495902
$479$	435.378	−	251.366i	0.908931	−	0.524771i	0.0288439	−	0.999584i	$-0.490817\pi$
$479$	435.378	−	251.366i	0.908931	−	0.524771i	0.880087	+	0.474812i	$0.157484\pi$
$480$	420.347	+	251.514i	0.875723	+	0.523987i
$481$	65.5037	−	113.456i	0.136182	−	0.235875i
$482$	−447.312	−	258.255i	−0.928032	−	0.535800i
$483$	−375.073	−	673.711i	−0.776549	−	1.39485i
$484$	321.521	+	556.890i	0.664299	+	1.15060i
$485$			213.756i			0.440733i
$486$	905.218	+	70.7752i	1.86259	+	0.145628i
$487$	80.4336			0.165161			0.0825807	−	0.996584i	$-0.473684\pi$
$487$	80.4336			0.165161			0.0825807	+	0.996584i	$0.473684\pi$
$488$	−1484.05	+	856.816i	−3.04108	+	1.75577i
$489$	−109.250	+	60.8227i	−0.223416	+	0.124382i
$490$	15.5626	−	26.9551i	0.0317603	−	0.0550105i
$491$	−417.972	−	241.316i	−0.851267	−	0.491479i	0.00981129	−	0.999952i	$-0.496877\pi$
$491$	−417.972	−	241.316i	−0.851267	−	0.491479i	−0.861078	+	0.508473i	$0.830210\pi$
$492$	263.358	−	440.142i	0.535281	−	0.894597i
$493$	15.5873	+	26.9980i	0.0316173	+	0.0547627i
$494$			80.9307i			0.163827i
$495$	79.6501	−	128.521i	0.160909	−	0.259639i
$496$	1155.96			2.33056
$497$	145.346	−	83.9155i	0.292447	−	0.168844i
$498$	3.45462	−	221.355i	0.00693698	−	0.444488i
$499$	17.5059	−	30.3212i	0.0350820	−	0.0607638i	−0.847951	−	0.530074i	$-0.822164\pi$
$499$	17.5059	−	30.3212i	0.0350820	−	0.0607638i	0.883033	+	0.469310i	$0.155497\pi$
$500$	96.4544	+	55.6880i	0.192909	+	0.111376i
$501$	27.7581	+	0.433212i	0.0554054	+	0.000864695i
$502$	348.390	+	603.429i	0.694004	+	1.20205i
$503$		−	211.016i		−	0.419514i	−0.977754	−	0.209757i	$-0.932733\pi$
$503$		−	211.016i		−	0.419514i	0.977754	−	0.209757i	$-0.0672673\pi$
$504$	−45.4289	+	1455.08i	−0.0901367	+	2.88706i
$505$	304.203			0.602382
$506$	860.595	−	496.865i	1.70078	−	0.981947i
$507$	412.914	+	247.067i	0.814427	+	0.487311i
$508$	961.608	−	1665.55i	1.89293	−	3.27865i
$509$	−732.292	−	422.789i	−1.43869	−	0.830627i	−0.440930	−	0.897542i	$-0.645351\pi$
$509$	−732.292	−	422.789i	−1.43869	−	0.830627i	−0.997759	+	0.0669144i	$0.978685\pi$
$510$	23.1788	+	41.6341i	0.0454487	+	0.0816354i
$511$	−376.687	−	652.440i	−0.737156	−	1.27679i
$512$			697.860i			1.36301i
$513$	−9.32998	+	199.144i	−0.0181871	+	0.388194i
$514$	−870.311			−1.69321
$515$	332.845	−	192.168i	0.646300	−	0.373142i
$516$	−1073.46	+	597.627i	−2.08036	+	1.15819i
$517$	158.308	−	274.197i	0.306204	−	0.530361i
$518$	1049.40	+	605.872i	2.02587	+	1.16964i
$519$	−227.022	+	379.415i	−0.437423	+	0.731050i
$520$	−73.0575	−	126.539i	−0.140495	−	0.243345i
$521$		−	260.960i		−	0.500883i	−0.968132	−	0.250442i	$-0.919424\pi$
$521$		−	260.960i		−	0.500883i	0.968132	−	0.250442i	$-0.0805758\pi$
$522$	−260.693	−	485.951i	−0.499412	−	0.930941i
$523$	553.330			1.05799			0.528996	−	0.848624i	$-0.322569\pi$
$523$	553.330			1.05799			0.528996	+	0.848624i	$0.322569\pi$
$524$	−2004.89	+	1157.53i	−3.82613	+	2.20902i
$525$	−1.69965	+	108.905i	−0.00323742	+	0.207438i
$526$	20.1648	−	34.9265i	0.0383362	−	0.0664003i
$527$	43.8615	+	25.3234i	0.0832286	+	0.0480521i
$528$	−977.877	−	15.2614i	−1.85204	−	0.0289042i
$529$	361.983	+	626.973i	0.684278	+	1.18520i
$530$		−	839.475i		−	1.58392i
$531$	−37.7302	+	20.2407i	−0.0710551	+	0.0381182i
$532$	−534.103			−1.00395
$533$	−43.5996	+	25.1723i	−0.0818005	+	0.0472275i
$534$	−279.501	−	167.239i	−0.523409	−	0.313181i
$535$	−110.244	+	190.949i	−0.206064	+	0.356914i
$536$	1617.53	+	933.884i	3.01779	+	1.74232i
$537$	−233.516	−	419.444i	−0.434853	−	0.781088i
$538$	109.219	+	189.174i	0.203010	+	0.351624i
$539$			27.9888i			0.0519273i
$540$	−276.010	−	534.356i	−0.511130	−	0.989549i
$541$	−795.168			−1.46981			−0.734906	−	0.678169i	$-0.762774\pi$
$541$	−795.168			−1.46981			−0.734906	+	0.678169i	$0.762774\pi$
$542$	212.276	−	122.558i	0.391654	−	0.226121i
$543$	−79.5121	+	44.2665i	−0.146431	+	0.0815222i
$544$	69.4102	−	120.222i	0.127592	−	0.220996i
$545$	5.08622	+	2.93653i	0.00933252	+	0.00538813i
$546$	122.593	−	204.886i	0.224529	−	0.375249i
$547$	303.604	+	525.858i	0.555035	+	0.961348i	0.997901	+	0.0647606i	$0.0206284\pi$
$547$	303.604	+	525.858i	0.555035	+	0.961348i	−0.442866	+	0.896588i	$0.646038\pi$
$548$		−	1773.42i		−	3.23616i
$549$	691.995	+	21.6048i	1.26046	+	0.0393529i
$550$	−140.368			−0.255215
$551$	104.861	−	60.5412i	0.190309	−	0.109875i
$552$	36.9143	−	2365.28i	0.0668736	−	4.28494i
$553$	292.344	−	506.354i	0.528650	−	0.915649i
$554$	868.064	+	501.177i	1.56690	+	0.904651i
$555$	−299.561	−	4.67515i	−0.539749	−	0.00842369i
$556$	159.730	+	276.661i	0.287284	+	0.497591i
$557$			686.808i			1.23305i	0.787336	+	0.616524i	$0.211460\pi$
$557$			686.808i			1.23305i	−0.787336	+	0.616524i	$0.788540\pi$
$558$	−761.528	−	471.951i	−1.36475	−	0.845791i
$559$	120.593			0.215729
$560$	610.116	−	352.251i	1.08949	−	0.629019i
$561$	−36.7702	−	22.0014i	−0.0655439	−	0.0392181i
$562$	−343.934	+	595.712i	−0.611983	+	1.05999i
$563$	−208.976	−	120.652i	−0.371182	−	0.214302i	0.302792	−	0.953057i	$-0.402081\pi$
$563$	−208.976	−	120.652i	−0.371182	−	0.214302i	−0.673975	+	0.738754i	$0.735414\pi$
$564$	−612.600	−	1100.36i	−1.08617	−	1.95099i
$565$	3.05685	+	5.29461i	0.00541035	+	0.00937099i
$566$			1728.55i			3.05397i
$567$	325.281	−	490.023i	0.573688	−	0.864238i
$568$	514.883			0.906484
$569$	−666.084	+	384.564i	−1.17062	+	0.675859i	−0.953827	−	0.300358i	$-0.902894\pi$
$569$	−666.084	+	384.564i	−1.17062	+	0.675859i	−0.216796	+	0.976217i	$0.569561\pi$
$570$	161.707	−	90.0267i	0.283697	−	0.157942i
$571$	−48.7253	+	84.3947i	−0.0853333	+	0.147802i	−0.905533	−	0.424275i	$-0.860529\pi$
$571$	−48.7253	+	84.3947i	−0.0853333	+	0.147802i	0.820200	+	0.572077i	$0.193862\pi$
$572$	190.134	+	109.774i	0.332402	+	0.191913i
$573$	−444.553	+	742.966i	−0.775834	+	1.29663i
$574$	−232.829	−	403.272i	−0.405626	−	0.702565i
$575$		−	176.986i		−	0.307802i
$576$	−470.745	+	759.581i	−0.817265	+	1.31872i
$577$	277.283			0.480560			0.240280	−	0.970704i	$-0.422761\pi$
$577$	277.283			0.480560			0.240280	+	0.970704i	$0.422761\pi$
$578$	−923.493	+	533.179i	−1.59774	+	0.922454i
$579$	4.43181	−	283.969i	0.00765425	−	0.490447i
$580$	−182.639	+	316.340i	−0.314895	+	0.545414i
$581$	−124.191	−	71.7018i	−0.213754	−	0.123411i
$582$	−1071.45	−	16.7218i	−1.84098	−	0.0287315i
$583$	377.443	+	653.750i	0.647415	+	1.12136i
$584$		−	2311.25i		−	3.95761i
$585$	−1.84216	+	59.0038i	−0.00314899	+	0.100861i
$586$	−1071.52			−1.82854
$587$	405.017	−	233.836i	0.689977	−	0.398358i	−0.113626	−	0.993524i	$-0.536247\pi$
$587$	405.017	−	233.836i	0.689977	−	0.398358i	0.803603	+	0.595165i	$0.202913\pi$
$588$	95.5345	+	57.1629i	0.162474	+	0.0972158i
$589$	98.3565	−	170.358i	0.166989	−	0.289233i
$590$	34.4235	+	19.8744i	0.0583449	+	0.0336855i
$591$	−189.349	−	340.111i	−0.320387	−	0.575483i
$592$	968.922	+	1678.22i	1.63669	+	2.83483i
$593$		−	254.411i		−	0.429023i	−0.976721	−	0.214512i	$-0.931184\pi$
$593$		−	254.411i		−	0.429023i	0.976721	−	0.214512i	$-0.0688160\pi$
$594$	637.981	+	409.300i	1.07404	+	0.689057i
$595$	30.8669			0.0518772
$596$	801.577	−	462.791i	1.34493	−	0.776495i
$597$	357.602	−	199.087i	0.598998	−	0.333478i
$598$	−193.988	+	335.997i	−0.324394	+	0.561867i
$599$	352.081	+	203.274i	0.587780	+	0.339355i	0.764219	−	0.644956i	$-0.223124\pi$
$599$	352.081	+	203.274i	0.587780	+	0.339355i	−0.176439	+	0.984312i	$0.556458\pi$
$600$	−171.569	+	286.737i	−0.285948	+	0.477895i
$601$	−249.967	−	432.956i	−0.415919	−	0.720393i	0.579605	−	0.814897i	$-0.303207\pi$
$601$	−249.967	−	432.956i	−0.415919	−	0.720393i	−0.995524	+	0.0945042i	$0.969873\pi$
$602$			1115.41i			1.85285i
$603$	−356.726	−	664.963i	−0.591585	−	1.10276i
$604$	2263.59			3.74766
$605$	−125.002	+	72.1701i	−0.206615	+	0.119289i
$606$	−23.7973	+	1524.81i	−0.0392695	+	2.51620i
$607$	−29.9627	+	51.8970i	−0.0493620	+	0.0854975i	−0.889651	−	0.456642i	$-0.849052\pi$
$607$	−29.9627	+	51.8970i	−0.0493620	+	0.0854975i	0.840289	+	0.542139i	$0.182385\pi$
$608$	−466.944	−	269.590i	−0.767999	−	0.443405i
$609$	−357.174	−	5.57430i	−0.586493	−	0.00915321i
$610$	−321.364	−	556.619i	−0.526826	−	0.912490i
$611$			123.614i			0.202314i
$612$	−150.195	+	80.5735i	−0.245417	+	0.131656i
$613$	−373.866			−0.609896			−0.304948	−	0.952369i	$-0.598639\pi$
$613$	−373.866			−0.609896			−0.304948	+	0.952369i	$0.598639\pi$
$614$	766.071	−	442.291i	1.24767	−	0.720344i
$615$	98.7964	+	59.1147i	0.160645	+	0.0961214i
$616$	−607.650	+	1052.48i	−0.986444	+	1.70857i
$617$	−320.088	−	184.803i	−0.518782	−	0.299519i	0.217654	−	0.976026i	$-0.430159\pi$
$617$	−320.088	−	184.803i	−0.518782	−	0.299519i	−0.736436	+	0.676507i	$0.763493\pi$
$618$	937.202	+	1683.41i	1.51651	+	2.72397i
$619$	−598.225	−	1036.16i	−0.966438	−	1.67392i	−0.705701	−	0.708510i	$-0.749368\pi$
$619$	−598.225	−	1036.16i	−0.966438	−	1.67392i	−0.260738	−	0.965410i	$-0.583966\pi$
$620$			593.438i			0.957158i
$621$	−516.074	+	804.413i	−0.831037	+	1.29535i
$622$	−1935.51			−3.11175
$623$	−182.719	+	105.493i	−0.293289	+	0.169331i
$624$	333.616	−	185.733i	0.534640	−	0.297649i
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	−1602.54	−	925.224i	−2.55996	−	1.47799i
$627$	−85.4535	+	142.816i	−0.136289	+	0.227776i
$628$	−7.89377	−	13.6724i	−0.0125697	−	0.0217713i
$629$			84.9044i			0.134983i
$630$	−545.752	−	17.0389i	−0.866273	−	0.0270459i
$631$	628.525			0.996078			0.498039	−	0.867155i	$-0.334054\pi$
$631$	628.525			0.996078			0.498039	+	0.867155i	$0.334054\pi$
$632$	1553.43	−	896.870i	2.45795	−	1.41910i
$633$	−7.40738	+	474.629i	−0.0117020	+	0.749808i
$634$	409.541	−	709.345i	0.645963	−	1.11884i
$635$	373.858	+	215.847i	0.588753	+	0.339917i
$636$	3002.32	+	46.8563i	4.72063	+	0.0736734i
$637$	−5.46374	−	9.46347i	−0.00857730	−	0.0148563i
$638$		−	460.364i		−	0.721573i
$639$	−176.817	−	109.581i	−0.276709	−	0.171489i
$640$	176.467			0.275730
$641$	824.417	−	475.977i	1.28614	−	0.742554i	0.308178	−	0.951329i	$-0.400281\pi$
$641$	824.417	−	475.977i	1.28614	−	0.742554i	0.977964	+	0.208774i	$0.0669474\pi$
$642$	−948.506	−	567.537i	−1.47742	−	0.884014i
$643$	35.7759	−	61.9656i	0.0556390	−	0.0963696i	−0.836864	−	0.547410i	$-0.815614\pi$
$643$	35.7759	−	61.9656i	0.0556390	−	0.0963696i	0.892503	+	0.451041i	$0.148947\pi$
$644$	−2217.41	−	1280.22i	−3.44318	−	1.98792i
$645$	−134.146	−	240.955i	−0.207979	−	0.373574i
$646$	−26.2252	−	45.4233i	−0.0405962	−	0.0703147i
$647$		−	900.292i		−	1.39149i	−0.718290	−	0.695744i	$-0.755075\pi$
$647$		−	900.292i		−	1.39149i	0.718290	−	0.695744i	$-0.244925\pi$
$648$	1615.88	−	802.958i	2.49365	−	1.23913i
$649$	−35.7436			−0.0550748
$650$	47.4608	−	27.4015i	0.0730166	−	0.0421562i
$651$	−507.058	+	282.293i	−0.778892	+	0.433630i
$652$	−207.604	+	359.580i	−0.318410	+	0.551503i
$653$	−222.825	−	128.648i	−0.341233	−	0.197011i	0.319584	−	0.947558i	$-0.396457\pi$
$653$	−222.825	−	128.648i	−0.341233	−	0.197011i	−0.660817	+	0.750547i	$0.729790\pi$
$654$	−15.1172	+	25.2649i	−0.0231150	+	0.0386314i
$655$	−259.824	−	450.029i	−0.396678	−	0.687066i
$656$		−	744.690i		−	1.13520i
$657$	−491.897	+	793.711i	−0.748701	+	1.20808i
$658$	−1143.36			−1.73763
$659$	477.967	−	275.954i	0.725291	−	0.418747i	−0.0914057	−	0.995814i	$-0.529136\pi$
$659$	477.967	−	275.954i	0.725291	−	0.418747i	0.816697	+	0.577067i	$0.195803\pi$
$660$	7.83482	−	502.017i	0.0118709	−	0.760632i
$661$	523.413	−	906.578i	0.791851	−	1.37153i	−0.132969	−	0.991120i	$-0.542451\pi$
$661$	523.413	−	906.578i	0.791851	−	1.37153i	0.924820	−	0.380405i	$-0.124216\pi$
$662$	−307.309	−	177.425i	−0.464214	−	0.268014i
$663$	16.7275	+	0.261061i	0.0252300	+	0.000393757i
$664$	−219.971	−	381.002i	−0.331282	−	0.573798i
$665$		−	119.887i		−	0.180282i
$666$	46.8683	−	1501.18i	0.0703728	−	2.25402i
$667$	580.460			0.870254
$668$	79.8342	−	46.0923i	0.119512	−	0.0690004i
$669$	530.956	+	317.696i	0.793656	+	0.474883i
$670$	−350.270	+	606.685i	−0.522791	+	0.905500i
$671$	500.531	+	288.982i	0.745948	+	0.430673i
$672$	773.751	+	1389.82i	1.15142	+	2.06819i
$673$	−118.875	−	205.898i	−0.176635	−	0.305940i	0.764091	−	0.645108i	$-0.223188\pi$
$673$	−118.875	−	205.898i	−0.176635	−	0.305940i	−0.940726	+	0.339168i	$0.889854\pi$
$674$			1927.98i			2.86050i
$675$	119.944	−	61.9546i	0.177695	−	0.0917846i
$676$	1597.82			2.36364
$677$	−145.591	+	84.0570i	−0.215053	+	0.124161i	−0.603658	−	0.797244i	$-0.706291\pi$
$677$	−145.591	+	84.0570i	−0.215053	+	0.124161i	0.388605	+	0.921405i	$0.372957\pi$
$678$	−26.7783	+	14.9082i	−0.0394961	+	0.0219885i
$679$	−347.066	+	601.136i	−0.511143	+	0.885325i
$680$	82.0087	+	47.3477i	0.120601	+	0.0696290i
$681$	−226.889	+	379.192i	−0.333171	+	0.556817i
$682$	−373.958	−	647.714i	−0.548325	−	0.949727i
$683$			995.446i			1.45746i	0.684800	+	0.728731i	$0.259889\pi$
$683$			995.446i			1.45746i	−0.684800	+	0.728731i	$0.740111\pi$
$684$	312.948	+	583.359i	0.457527	+	0.852864i
$685$	398.070			0.581123
$686$	−1063.82	+	614.194i	−1.55075	+	0.895327i
$687$	1.27102	−	81.4405i	0.00185010	−	0.118545i
$688$	−891.896	+	1544.81i	−1.29636	+	2.24536i
$689$	−255.239	−	147.362i	−0.370449	−	0.213879i
$690$	887.142	+	13.8453i	1.28571	+	0.0200657i
$691$	298.570	+	517.138i	0.432084	+	0.748391i	0.997053	−	0.0767211i	$-0.0244451\pi$
$691$	298.570	+	517.138i	0.432084	+	0.748391i	−0.564969	+	0.825112i	$0.691112\pi$
$692$			1468.19i			2.12167i
$693$	432.671	−	232.111i	0.624345	−	0.334936i
$694$	416.355			0.599936
$695$	−62.1006	+	35.8538i	−0.0893534	+	0.0515882i
$696$	−940.407	−	562.691i	−1.35116	−	0.808464i
$697$	16.3139	−	28.2564i	0.0234058	−	0.0405401i
$698$	2007.13	+	1158.82i	2.87555	+	1.66020i
$699$	57.7888	+	103.801i	0.0826736	+	0.148499i
$700$	180.836	+	313.218i	0.258338	+	0.447454i
$701$			413.729i			0.590199i	0.955467	+	0.295099i	$0.0953528\pi$
$701$			413.729i			0.590199i	−0.955467	+	0.295099i	$0.904647\pi$
$702$	−295.612	−	13.8496i	−0.421100	−	0.0197287i
$703$	329.769			0.469089
$704$	−646.058	+	373.002i	−0.917696	+	0.529832i
$705$	246.992	−	137.507i	0.350343	−	0.195046i
$706$	−1052.91	+	1823.69i	−1.49137	+	2.58312i
$707$	855.497	+	493.921i	1.21004	+	0.698616i
$708$	−73.0009	+	122.004i	−0.103109	+	0.172322i
$709$	328.568	+	569.096i	0.463424	+	0.802674i	0.999129	−	0.0417311i	$-0.0132873\pi$
$709$	328.568	+	569.096i	0.463424	+	0.802674i	−0.535705	+	0.844405i	$0.679954\pi$
$710$			193.116i			0.271994i
$711$	−724.345	−	22.6147i	−1.01877	−	0.0318070i
$712$	−647.277			−0.909096
$713$	816.684	−	471.513i	1.14542	−	0.661308i
$714$	−2.41467	+	154.720i	−0.00338189	+	0.216695i
$715$	−24.6404	+	42.6784i	−0.0344621	+	0.0596901i
$716$	−1380.53	−	797.051i	−1.92812	−	1.11320i
$717$	190.293	+	2.96984i	0.265401	+	0.00414203i
$718$	−775.572	−	1343.33i	−1.08018	−	1.87093i
$719$		−	217.226i		−	0.302122i	−0.988524	−	0.151061i	$-0.951731\pi$
$719$		−	217.226i		−	0.302122i	0.988524	−	0.151061i	$-0.0482690\pi$
$720$	−742.223	−	459.987i	−1.03086	−	0.638871i
$721$	1248.06			1.73101
$722$	991.751	−	572.588i	1.37362	−	0.793058i
$723$	355.858	+	212.927i	0.492197	+	0.294505i
$724$	−151.093	+	261.701i	−0.208692	+	0.361466i
$725$	−71.0073	−	40.9961i	−0.0979411	−	0.0565463i
$726$	−351.973	−	632.218i	−0.484812	−	0.870824i
$727$	−304.437	−	527.300i	−0.418757	−	0.725309i	0.577057	−	0.816704i	$-0.304201\pi$
$727$	−304.437	−	527.300i	−0.418757	−	0.725309i	−0.995815	+	0.0913946i	$0.970868\pi$
$728$		−	474.481i		−	0.651760i
$729$	−725.807	−	68.1584i	−0.995620	−	0.0934958i
$730$	866.874			1.18750
$731$	−67.6840	+	39.0774i	−0.0925910	+	0.0534574i
$732$	2008.65	−	1118.27i	2.74405	−	1.52769i
$733$	440.351	−	762.709i	0.600751	−	1.04053i	−0.391957	−	0.919984i	$-0.628202\pi$
$733$	440.351	−	762.709i	0.600751	−	1.04053i	0.992708	−	0.120548i	$-0.0384650\pi$
$734$	2031.79	+	1173.05i	2.76810	+	1.59816i
$735$	−12.8311	+	21.4441i	−0.0174572	+	0.0291757i
$736$	−1292.39	−	2238.49i	−1.75597	−	3.04143i
$737$		−	629.950i		−	0.854749i
$738$	−304.040	+	490.592i	−0.411979	+	0.664758i
$739$	−917.157			−1.24108			−0.620540	−	0.784175i	$-0.713086\pi$
$739$	−917.157			−1.24108			−0.620540	+	0.784175i	$0.713086\pi$
$740$	−861.556	+	497.419i	−1.16426	+	0.672188i
$741$	1.01396	−	64.9698i	0.00136837	−	0.0876786i
$742$	1363.02	−	2360.82i	1.83695	−	3.18170i
$743$	−956.492	−	552.231i	−1.28734	−	0.743245i	−0.309159	−	0.951010i	$-0.600048\pi$
$743$	−956.492	−	552.231i	−1.28734	−	0.743245i	−0.978179	+	0.207765i	$0.933381\pi$
$744$	−1780.20	−	27.7830i	−2.39274	−	0.0373427i
$745$	103.880	+	179.926i	0.139437	+	0.241511i
$746$		−	1460.74i		−	1.95810i
$747$	−5.54662	+	177.657i	−0.00742519	+	0.237827i
$748$	−142.287			−0.190223
$749$	−620.071	+	357.998i	−0.827866	+	0.477968i
$750$	−107.546	−	64.3498i	−0.143394	−	0.0857998i
$751$	−330.239	+	571.990i	−0.439732	+	0.761638i	−0.997669	−	0.0682453i	$-0.978260\pi$
$751$	−330.239	+	571.990i	−0.439732	+	0.761638i	0.557936	+	0.829884i	$0.311593\pi$
$752$	−1583.51	−	914.241i	−2.10573	−	1.21575i
$753$	−272.121	−	488.787i	−0.361383	−	0.649120i
$754$	89.8684	+	155.657i	0.119189	+	0.206441i
$755$			508.096i			0.672974i
$756$	91.4003	−	1950.89i	0.120900	−	2.58055i
$757$	−353.728			−0.467276			−0.233638	−	0.972324i	$-0.575063\pi$
$757$	−353.728			−0.467276			−0.233638	+	0.972324i	$0.575063\pi$
$758$	−169.702	+	97.9778i	−0.223882	+	0.129258i
$759$	−697.096	+	388.093i	−0.918441	+	0.511321i
$760$	183.899	−	318.522i	0.241972	−	0.419108i
$761$	708.380	+	408.983i	0.930854	+	0.537429i	0.887081	−	0.461613i	$-0.152729\pi$
$761$	708.380	+	408.983i	0.930854	+	0.537429i	0.0437722	+	0.999042i	$0.486062\pi$
$762$	−1111.18	+	1857.08i	−1.45824	+	2.43711i
$763$	9.53584	+	16.5166i	0.0124978	+	0.0216469i
$764$			2875.00i			3.76309i
$765$	−18.0859	−	33.7135i	−0.0236417	−	0.0440700i
$766$	414.465			0.541078
$767$	12.0855	−	6.97756i	0.0157568	−	0.00909721i
$768$	4.78832	−	306.812i	0.00623479	−	0.399495i
$769$	500.408	−	866.732i	0.650725	−	1.12709i	−0.332222	−	0.943201i	$-0.607798\pi$
$769$	500.408	−	866.732i	0.650725	−	1.12709i	0.982947	−	0.183888i	$-0.0588684\pi$
$770$	−394.751	−	227.910i	−0.512664	−	0.295987i
$771$	698.670	+	10.9039i	0.906187	+	0.0141426i
$772$	−471.530	−	816.713i	−0.610790	−	1.05792i
$773$			860.440i			1.11312i	0.830808	+	0.556559i	$0.187879\pi$
$773$			860.440i			1.11312i	−0.830808	+	0.556559i	$0.812121\pi$
$774$	1218.28	−	653.558i	1.57401	−	0.844390i
$775$	−133.206			−0.171879
$776$	−1844.20	+	1064.75i	−2.37655	+	1.37210i
$777$	−834.850	−	499.531i	−1.07445	−	0.642898i
$778$	197.633	−	342.310i	0.254027	−	0.439987i
$779$	−109.748	−	63.3632i	−0.140884	−	0.0813391i
$780$	95.3505	+	171.270i	0.122244	+	0.219577i
$781$	−86.8283	−	150.391i	−0.111176	−	0.192562i
$782$		−	251.442i		−	0.321538i
$783$	203.192	+	393.380i	0.259504	+	0.502401i
$784$	161.638			0.206171
$785$	3.06898	−	1.77187i	0.00390952	−	0.00225716i
$786$	2276.09	−	1267.16i	2.89579	−	1.61216i
$787$	−463.491	+	802.789i	−0.588933	+	1.02006i	0.405439	+	0.914122i	$0.367119\pi$
$787$	−463.491	+	802.789i	−0.588933	+	1.02006i	−0.994372	+	0.105940i	$0.966215\pi$
$788$	−1119.42	−	646.297i	−1.42058	−	0.820174i
$789$	−16.6256	+	27.7858i	−0.0210717	+	0.0352165i
$790$	336.387	+	582.640i	0.425807	+	0.737519i
$791$			19.8531i			0.0250987i
$792$	1505.58	+	47.0058i	1.90099	+	0.0593507i
$793$	−225.651			−0.284553
$794$	−323.236	+	186.620i	−0.407098	+	0.235038i
$795$	−10.5176	+	673.916i	−0.0132297	+	0.847693i
$796$	679.534	−	1176.99i	0.853686	−	1.47863i
$797$	−825.230	−	476.447i	−1.03542	−	0.597800i	−0.116888	−	0.993145i	$-0.537292\pi$
$797$	−825.230	−	476.447i	−1.03542	−	0.597800i	−0.918533	+	0.395345i	$0.870625\pi$
$798$	600.934	+	9.37859i	0.753050	+	0.0117526i
$799$	−40.0564	−	69.3797i	−0.0501332	−	0.0868332i
$800$			365.111i			0.456389i
$801$	222.283	+	137.758i	0.277507	+	0.171983i
$802$	587.129			0.732082
$803$	−675.087	+	389.762i	−0.840707	+	0.485382i
$804$	−2150.21	−	1286.58i	−2.67440	−	1.60022i
$805$	287.365	−	497.731i	0.356975	−	0.618299i
$806$	252.883	+	146.002i	0.313750	+	0.181144i
$807$	−85.3094	−	153.234i	−0.105712	−	0.189881i
$808$	1515.28	+	2624.55i	1.87535	+	3.24820i
$809$		−	1425.22i		−	1.76171i	−0.473387	−	0.880855i	$-0.656969\pi$
$809$		−	1425.22i		−	1.76171i	0.473387	−	0.880855i	$-0.343031\pi$
$810$	301.164	+	606.066i	0.371807	+	0.748230i
$811$	−473.774			−0.584185			−0.292093	−	0.956390i	$-0.594352\pi$
$811$	−473.774			−0.584185			−0.292093	+	0.956390i	$0.594352\pi$
$812$	−1027.26	+	593.087i	−1.26509	+	0.730402i
$813$	−171.947	+	95.7277i	−0.211497	+	0.117746i
$814$	626.903	−	1085.83i	0.770151	−	1.33394i
$815$	−80.7131	−	46.5997i	−0.0990345	−	0.0571776i
$816$	−127.060	+	212.351i	−0.155711	+	0.260234i
$817$	151.777	+	262.885i	0.185773	+	0.321769i
$818$		−	2560.42i		−	3.13010i
$819$	−100.983	+	162.943i	−0.123300	+	0.198953i
$820$	382.305			0.466225
$821$	−63.4905	+	36.6562i	−0.0773331	+	0.0446483i	−0.538168	−	0.842838i	$-0.680883\pi$
$821$	−63.4905	+	36.6562i	−0.0773331	+	0.0446483i	0.460835	+	0.887486i	$0.347550\pi$
$822$	−31.1403	+	1995.32i	−0.0378836	+	2.42740i
$823$	−316.027	+	547.374i	−0.383994	+	0.665096i	−0.991629	−	0.129120i	$-0.958785\pi$
$823$	−316.027	+	547.374i	−0.383994	+	0.665096i	0.607635	+	0.794216i	$0.292118\pi$
$824$	3315.90	+	1914.44i	4.02416	+	2.32335i
$825$	112.685	+	1.75864i	0.136588	+	0.00213169i
$826$	64.5385	+	111.784i	0.0781338	+	0.135332i
$827$			226.153i			0.273462i	0.990608	+	0.136731i	$0.0436597\pi$
$827$			226.153i			0.273462i	−0.990608	+	0.136731i	$0.956340\pi$
$828$	−99.0338	+	3172.03i	−0.119606	+	3.83095i
$829$	−522.396			−0.630152			−0.315076	−	0.949067i	$-0.602030\pi$
$829$	−522.396			−0.630152			−0.315076	+	0.949067i	$0.602030\pi$
$830$	142.901	−	82.5042i	0.172170	−	0.0994026i
$831$	−690.588	−	413.212i	−0.831032	−	0.497247i
$832$	145.629	−	252.236i	0.175034	−	0.303168i
$833$	6.13317	+	3.54099i	0.00736275	+	0.00425089i
$834$	−174.859	−	314.084i	−0.209663	−	0.376599i
$835$	10.3461	+	17.9200i	0.0123905	+	0.0214610i
$836$			552.642i			0.661055i
$837$	605.429	+	388.415i	0.723332	+	0.464057i
$838$	192.792			0.230061
$839$	511.329	−	295.216i	0.609450	−	0.351866i	−0.163300	−	0.986576i	$-0.552214\pi$
$839$	511.329	−	295.216i	0.609450	−	0.351866i	0.772750	+	0.634710i	$0.218881\pi$
$840$	−948.057	+	527.809i	−1.12864	+	0.628344i
$841$	−286.046	+	495.446i	−0.340126	+	0.589115i
$842$	47.7379	+	27.5615i	0.0566959	+	0.0327334i
$843$	283.568	−	473.918i	0.336380	−	0.562180i
$844$	788.120	+	1365.06i	0.933791	+	1.61737i
$845$			358.655i			0.424444i
$846$	669.931	+	1248.80i	0.791881	+	1.47613i
$847$	−468.718			−0.553386
$848$	3775.47	−	2179.77i	4.45220	−	2.57048i
$849$	21.6566	−	1387.65i	0.0255083	−	1.63445i
$850$	−17.7586	+	30.7588i	−0.0208925	+	0.0361868i
$851$	1369.09	+	790.444i	1.60880	+	0.928841i
$852$	−690.666	−	10.7790i	−0.810640	−	0.0126514i
$853$	−693.749	−	1201.61i	−0.813305	−	1.40869i	−0.910538	−	0.413424i	$-0.864333\pi$
$853$	−693.749	−	1201.61i	−0.813305	−	1.40869i	0.0972332	−	0.995262i	$-0.469001\pi$
$854$		−	2087.14i		−	2.44396i
$855$	−130.944	+	70.2459i	−0.153150	+	0.0821590i
$856$	−2196.58			−2.56610
$857$	−683.058	+	394.363i	−0.797033	+	0.460167i	−0.842433	−	0.538801i	$-0.818877\pi$
$857$	−683.058	+	394.363i	−0.797033	+	0.460167i	0.0453994	+	0.998969i	$0.485544\pi$
$858$	−211.998	−	126.848i	−0.247084	−	0.147842i
$859$	−413.601	+	716.378i	−0.481491	+	0.833968i	−0.999774	−	0.0212416i	$-0.993238\pi$
$859$	−413.601	+	716.378i	−0.481491	+	0.833968i	0.518283	+	0.855209i	$0.326571\pi$
$860$	−793.065	−	457.876i	−0.922169	−	0.532414i
$861$	181.859	+	326.657i	0.211218	+	0.379393i
$862$	−72.2667	−	125.170i	−0.0838361	−	0.145208i
$863$			1089.70i			1.26268i	0.775504	+	0.631342i	$0.217496\pi$
$863$			1089.70i			1.26268i	−0.775504	+	0.631342i	$0.782504\pi$
$864$	1064.63	−	1659.45i	1.23221	−	1.92066i
$865$	−329.558			−0.380992
$866$	1762.45	−	1017.55i	2.03516	−	1.17500i
$867$	748.044	−	416.457i	0.862796	−	0.480342i
$868$	−963.540	+	1668.90i	−1.11007	+	1.92270i
$869$	−523.930	−	302.491i	−0.602912	−	0.348091i
$870$	211.047	−	352.716i	0.242583	−	0.405421i
$871$	122.974	+	212.996i	0.141187	+	0.244542i
$872$			58.5093i			0.0670979i
$873$	859.931	+	26.8479i	0.985029	+	0.0307536i
$874$	−976.605			−1.11740
$875$	−70.3064	+	40.5914i	−0.0803502	+	0.0463902i
$876$	−48.3856	+	3100.31i	−0.0552347	+	3.53917i
$877$	−213.875	+	370.443i	−0.243872	+	0.422398i	−0.961814	−	0.273705i	$-0.911751\pi$
$877$	−213.875	+	370.443i	−0.243872	+	0.422398i	0.717942	+	0.696103i	$0.245084\pi$
$878$	813.575	+	469.718i	0.926623	+	0.534986i
$879$	860.202	+	13.4249i	0.978614	+	0.0152729i
$880$	−364.478	−	631.294i	−0.414179	−	0.717379i
$881$		−	1113.87i		−	1.26432i	−0.774837	−	0.632161i	$-0.782168\pi$
$881$		−	1113.87i		−	1.26432i	0.774837	−	0.632161i	$-0.217832\pi$
$882$	−106.485	−	65.9932i	−0.120731	−	0.0748222i
$883$	−408.581			−0.462719			−0.231359	−	0.972868i	$-0.574317\pi$
$883$	−408.581			−0.462719			−0.231359	+	0.972868i	$0.574317\pi$
$884$	48.1094	−	27.7760i	0.0544224	−	0.0314208i
$885$	−27.3856	−	16.3861i	−0.0309442	−	0.0185154i
$886$	−1365.46	+	2365.05i	−1.54116	+	2.66936i
$887$	−755.098	−	435.956i	−0.851294	−	0.491495i	0.00979311	−	0.999952i	$-0.496883\pi$
$887$	−755.098	−	435.956i	−0.851294	−	0.491495i	−0.861087	+	0.508457i	$0.830216\pi$
$888$	−1451.82	−	2607.78i	−1.63494	−	2.93669i
$889$	700.924	+	1214.04i	0.788441	+	1.36562i
$890$		−	242.773i		−	0.272778i
$891$	−507.033	−	336.572i	−0.569060	−	0.377746i
$892$	2054.60			2.30336
$893$	−269.471	+	155.579i	−0.301760	+	0.174221i
$894$	−910.004	+	506.624i	−1.01790	+	0.566693i
$895$	178.910	−	309.881i	0.199899	−	0.346236i
$896$	496.272	+	286.523i	0.553875	+	0.319780i
$897$	159.940	−	267.302i	0.178305	−	0.297995i
$898$	−176.965	−	306.512i	−0.197066	−	0.341328i
$899$		−	436.874i		−	0.485956i
$900$	236.145	−	381.038i	0.262384	−	0.423376i
$901$	191.008			0.211995
$902$	−417.270	+	240.911i	−0.462606	+	0.267085i
$903$	13.9748	−	895.436i	0.0154759	−	0.991623i
$904$	−30.4533	+	52.7466i	−0.0336872	+	0.0583480i
$905$	−58.7427	−	33.9151i	−0.0649091	−	0.0374753i
$906$	−2546.82	−	39.7475i	−2.81106	−	0.0438714i
$907$	843.097	+	1460.29i	0.929544	+	1.61002i	0.784085	+	0.620653i	$0.213133\pi$
$907$	843.097	+	1460.29i	0.929544	+	1.61002i	0.145459	+	0.989364i	$0.453534\pi$
$908$			1467.33i			1.61600i
$909$	38.2081	−	1223.80i	0.0420332	−	1.34631i
$910$	177.963			0.195563
$911$	−383.084	+	221.173i	−0.420509	+	0.242781i	−0.695295	−	0.718724i	$-0.744726\pi$
$911$	−383.084	+	221.173i	−0.420509	+	0.242781i	0.274786	+	0.961505i	$0.411393\pi$
$912$	824.773	+	493.502i	0.904356	+	0.541120i
$913$	−74.1907	+	128.502i	−0.0812603	+	0.140747i
$914$	−1321.60	−	763.024i	−1.44595	−	0.834819i
$915$	251.012	+	450.870i	0.274330	+	0.492755i
$916$	−135.232	−	234.228i	−0.147633	−	0.255708i
$917$		−	1687.46i		−	1.84020i
$918$	170.404	−	88.0182i	0.185625	−	0.0958804i
$919$	−182.236			−0.198298			−0.0991489	−	0.995073i	$-0.531612\pi$
$919$	−182.236			−0.198298			−0.0991489	+	0.995073i	$0.531612\pi$
$920$	1526.97	−	881.597i	1.65975	−	0.958258i
$921$	−620.530	+	345.466i	−0.673757	+	0.375099i
$922$	1103.96	−	1912.12i	1.19736	−	2.07388i
$923$	58.7162	+	33.8998i	0.0636145	+	0.0367279i
$924$	837.137	−	1399.08i	0.905992	−	1.51416i
$925$	−111.653	−	193.389i	−0.120706	−	0.209069i
$926$		−	2996.47i		−	3.23592i
$927$	−731.279	−	1363.16i	−0.788866	−	1.47050i
$928$	−1197.45			−1.29035
$929$	−1150.27	+	664.111i	−1.23819	+	0.714867i	−0.968723	−	0.248144i	$-0.920179\pi$
$929$	−1150.27	+	664.111i	−1.23819	+	0.714867i	−0.269463	+	0.963011i	$0.586846\pi$
$930$	10.4205	−	667.694i	0.0112048	−	0.717951i
$931$	13.7532	−	23.8213i	0.0147725	−	0.0255868i
$932$	341.644	+	197.248i	0.366571	+	0.211640i
$933$	1553.79	+	24.2496i	1.66537	+	0.0259910i
$934$	−38.5671	−	66.8003i	−0.0412924	−	0.0715206i
$935$		−	31.9383i		−	0.0341587i
$936$	−518.239	+	278.014i	−0.553674	+	0.297024i
$937$	−276.582			−0.295178			−0.147589	−	0.989049i	$-0.547151\pi$
$937$	−276.582			−0.295178			−0.147589	+	0.989049i	$0.547151\pi$
$938$	−1970.10	+	1137.44i	−2.10032	+	1.21262i
$939$	1274.90	+	762.832i	1.35772	+	0.812388i
$940$	469.348	−	812.934i	0.499306	−	0.864823i
$941$	1083.50	+	625.557i	1.15143	+	0.664779i	0.949236	−	0.314566i	$-0.101859\pi$
$941$	1083.50	+	625.557i	1.15143	+	0.664779i	0.202196	+	0.979345i	$0.435192\pi$
$942$	8.64142	+	15.5218i	0.00917348	+	0.0164775i
$943$	−303.758	−	526.124i	−0.322119	−	0.557926i
$944$			206.422i			0.218668i
$945$	437.907	+	20.5162i	0.463394	+	0.0217102i
$946$	1154.13			1.22001
$947$	−935.323	+	540.009i	−0.987670	+	0.570232i	−0.904577	−	0.426310i	$-0.859813\pi$
$947$	−935.323	+	540.009i	−0.987670	+	0.570232i	−0.0830930	+	0.996542i	$0.526480\pi$
$948$	−2102.55	+	1170.54i	−2.21788	+	1.23475i
$949$	152.172	−	263.570i	0.160350	−	0.277734i
$950$	119.468	+	68.9746i	0.125755	+	0.0726048i
$951$	−337.660	+	564.319i	−0.355057	+	0.593396i
$952$	153.753	+	266.308i	0.161505	+	0.279735i
$953$		−	328.534i		−	0.344737i	−0.985033	−	0.172369i	$-0.944858\pi$
$953$		−	328.534i		−	0.344737i	0.985033	−	0.172369i	$-0.0551420\pi$
$954$	−3377.18	−	105.439i	−3.54002	−	0.110523i
$955$	−645.336			−0.675745
$956$	547.294	−	315.980i	0.572483	−	0.330523i
$957$	−5.76780	+	369.572i	−0.00602696	+	0.386178i
$958$	−939.239	+	1626.81i	−0.980416	+	1.69813i
$959$	1119.47	+	646.328i	1.16733	+	0.673961i
$960$	−665.987	−	10.3938i	−0.693736	−	0.0108269i
$961$	125.623	+	217.585i	0.130721	+	0.226416i
$962$			489.515i			0.508851i
$963$	754.334	+	467.493i	0.783316	+	0.485454i
$964$	1377.04			1.42846
$965$	183.323	−	105.842i	0.189972	−	0.109681i
$966$	2472.39	+	1479.35i	2.55941	+	1.53142i
$967$	298.854	−	517.631i	0.309053	−	0.535296i	−0.669102	−	0.743170i	$-0.733321\pi$
$967$	298.854	−	517.631i	0.309053	−	0.535296i	0.978155	+	0.207875i	$0.0666546\pi$
$968$	−1245.31	−	718.981i	−1.28648	−	0.742749i
$969$	20.4840	+	36.7936i	0.0211393	+	0.0379707i
$970$	−399.354	−	691.701i	−0.411705	−	0.713094i
$971$		−	711.597i		−	0.732850i	−0.930448	−	0.366425i	$-0.880582\pi$
$971$		−	711.597i		−	0.732850i	0.930448	−	0.366425i	$-0.119418\pi$
$972$	−2184.36	+	1043.26i	−2.24729	+	1.07332i
$973$	−232.857			−0.239319
$974$	−260.279	+	150.272i	−0.267226	+	0.154283i
$975$	−38.4440	+	21.4028i	−0.0394298	+	0.0219516i
$976$	1668.90	−	2890.61i	1.70994	−	2.96169i
$977$	292.262	+	168.738i	0.299142	+	0.172710i	0.642058	−	0.766656i	$-0.278081\pi$
$977$	292.262	+	168.738i	0.299142	+	0.172710i	−0.342915	+	0.939366i	$0.611414\pi$
$978$	239.895	−	400.928i	0.245291	−	0.409947i
$979$	109.155	+	189.062i	0.111496	+	0.193117i
$980$			82.9807i			0.0846742i
$981$	12.4524	−	20.0928i	0.0126936	−	0.0204820i
$982$	1803.38			1.83643
$983$	−274.504	+	158.485i	−0.279252	+	0.161226i	−0.633085	−	0.774083i	$-0.718211\pi$
$983$	−274.504	+	158.485i	−0.279252	+	0.161226i	0.353833	+	0.935309i	$0.384878\pi$
$984$	−17.8983	+	1146.84i	−0.0181894	+	1.16549i
$985$	145.071	−	251.270i	0.147280	−	0.255097i
$986$	−100.879	−	58.2427i	−0.102312	−	0.0590697i
$987$	917.869	+	14.3249i	0.929959	+	0.0145136i
$988$	−107.882	−	186.857i	−0.109193	−	0.189127i
$989$			1455.21i			1.47140i
$990$	−17.6304	+	564.696i	−0.0178084	+	0.570400i
$991$	685.922			0.692152			0.346076	−	0.938207i	$-0.387514\pi$
$991$	685.922			0.692152			0.346076	+	0.938207i	$0.387514\pi$
$992$	−1684.76	+	972.700i	−1.69835	+	0.980544i
$993$	244.480	+	146.284i	0.246203	+	0.147315i
$994$	−313.554	+	543.092i	−0.315447	+	0.546370i
$995$	264.192	+	152.532i	0.265520	+	0.153298i
$996$	287.094	+	515.682i	0.288247	+	0.517753i
$997$	−293.035	−	507.551i	−0.293917	−	0.509078i	0.680816	−	0.732455i	$-0.261625\pi$
$997$	−293.035	−	507.551i	−0.293917	−	0.509078i	−0.974732	+	0.223376i	$0.928292\pi$
$998$			130.823i			0.131086i
$999$	−56.4330	+	1204.53i	−0.0564895	+	1.20574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.i.a.41.1	yes	16
3.2	odd	2		135.3.i.a.71.8		16
4.3	odd	2		720.3.bs.c.401.2		16
5.2	odd	4		225.3.i.b.149.1		32
5.3	odd	4		225.3.i.b.149.16		32
5.4	even	2		225.3.j.b.176.8		16
9.2	odd	6	inner	45.3.i.a.11.1	✓	16
9.4	even	3		405.3.c.a.161.1		16
9.5	odd	6		405.3.c.a.161.16		16
9.7	even	3		135.3.i.a.116.8		16
12.11	even	2		2160.3.bs.c.881.1		16
15.2	even	4		675.3.i.c.449.16		32
15.8	even	4		675.3.i.c.449.1		32
15.14	odd	2		675.3.j.b.476.1		16
36.7	odd	6		2160.3.bs.c.1601.1		16
36.11	even	6		720.3.bs.c.641.2		16
45.2	even	12		225.3.i.b.74.16		32
45.7	odd	12		675.3.i.c.224.1		32
45.29	odd	6		225.3.j.b.101.8		16
45.34	even	6		675.3.j.b.251.1		16
45.38	even	12		225.3.i.b.74.1		32
45.43	odd	12		675.3.i.c.224.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.i.a.11.1	✓	16	9.2	odd	6	inner
45.3.i.a.41.1	yes	16	1.1	even	1	trivial
135.3.i.a.71.8		16	3.2	odd	2
135.3.i.a.116.8		16	9.7	even	3
225.3.i.b.74.1		32	45.38	even	12
225.3.i.b.74.16		32	45.2	even	12
225.3.i.b.149.1		32	5.2	odd	4
225.3.i.b.149.16		32	5.3	odd	4
225.3.j.b.101.8		16	45.29	odd	6
225.3.j.b.176.8		16	5.4	even	2
405.3.c.a.161.1		16	9.4	even	3
405.3.c.a.161.16		16	9.5	odd	6
675.3.i.c.224.1		32	45.7	odd	12
675.3.i.c.224.16		32	45.43	odd	12
675.3.i.c.449.1		32	15.8	even	4
675.3.i.c.449.16		32	15.2	even	4
675.3.j.b.251.1		16	45.34	even	6
675.3.j.b.476.1		16	15.14	odd	2
720.3.bs.c.401.2		16	4.3	odd	2
720.3.bs.c.641.2		16	36.11	even	6
2160.3.bs.c.881.1		16	12.11	even	2
2160.3.bs.c.1601.1		16	36.7	odd	6

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23594 + 1.86827i) q^{2} +(2.62117 - 1.45927i) q^{3} +(4.98088 - 8.62715i) q^{4} +(1.93649 + 1.11803i) q^{5} +(-5.75562 + 9.61919i) q^{6} +(3.63061 + 6.28840i) q^{7} +22.2764i q^{8} +(4.74103 - 7.65001i) q^{9} -8.35517 q^{10} +(6.50668 - 3.75663i) q^{11} +(0.466354 - 29.8817i) q^{12} +(-1.46668 + 2.54036i) q^{13} +(-23.4969 - 13.5659i) q^{14} +(6.70739 + 0.104680i) q^{15} +(-21.6949 - 37.5766i) q^{16} -1.90107i q^{17} +(-1.04942 + 33.6125i) q^{18} -7.38378 q^{19} +(19.2909 - 11.1376i) q^{20} +(18.6929 + 11.1849i) q^{21} +(-14.0368 + 24.3125i) q^{22} +(-30.6549 - 17.6986i) q^{23} +(32.5074 + 58.3902i) q^{24} +(2.50000 + 4.33013i) q^{25} -10.9606i q^{26} +(1.26358 - 26.9704i) q^{27} +72.3346 q^{28} +(-14.2015 + 8.19922i) q^{29} +(-21.9003 + 12.1925i) q^{30} +(-13.3206 + 23.0720i) q^{31} +(63.2391 + 36.5111i) q^{32} +(11.5731 - 19.3418i) q^{33} +(3.55172 + 6.15176i) q^{34} +16.2366i q^{35} +(-42.3832 - 79.0054i) q^{36} -44.6613 q^{37} +(23.8935 - 13.7949i) q^{38} +(-0.137323 + 8.79899i) q^{39} +(-24.9058 + 43.1381i) q^{40} +(14.8634 + 8.58140i) q^{41} +(-81.3857 - 1.27016i) q^{42} +(-20.5554 - 35.6031i) q^{43} -74.8454i q^{44} +(17.7339 - 9.51354i) q^{45} +132.263 q^{46} +(36.4950 - 21.0704i) q^{47} +(-111.701 - 66.8359i) q^{48} +(-1.86263 + 3.22616i) q^{49} +(-16.1797 - 9.34136i) q^{50} +(-2.77419 - 4.98303i) q^{51} +(14.6107 + 25.3065i) q^{52} +100.474i q^{53} +(46.2992 + 89.6354i) q^{54} +16.8002 q^{55} +(-140.083 + 80.8770i) q^{56} +(-19.3541 + 10.7750i) q^{57} +(30.6367 - 53.0644i) q^{58} +(-4.12003 - 2.37870i) q^{59} +(34.3118 - 57.3442i) q^{60} +(38.4629 + 66.6197i) q^{61} -99.5461i q^{62} +(65.3191 + 2.03933i) q^{63} -99.2915 q^{64} +(-5.68041 + 3.27959i) q^{65} +(-1.31425 + 84.2107i) q^{66} +(41.9225 - 72.6119i) q^{67} +(-16.4008 - 9.46903i) q^{68} +(-106.179 - 1.65710i) q^{69} +(-30.3343 - 52.5406i) q^{70} -23.1134i q^{71} +(170.415 + 105.613i) q^{72} -103.753 q^{73} +(144.521 - 83.4395i) q^{74} +(12.8718 + 7.70180i) q^{75} +(-36.7778 + 63.7010i) q^{76} +(47.2464 + 27.2777i) q^{77} +(-15.9945 - 28.7296i) q^{78} +(-40.2610 - 69.7340i) q^{79} -97.0225i q^{80} +(-36.0452 - 72.5379i) q^{81} -64.1296 q^{82} +(-17.1034 + 9.87463i) q^{83} +(189.601 - 105.556i) q^{84} +(2.12546 - 3.68141i) q^{85} +(133.032 + 76.8063i) q^{86} +(-25.2595 + 42.2153i) q^{87} +(83.6843 + 144.945i) q^{88} +29.0566i q^{89} +(-39.6121 + 63.9171i) q^{90} -21.2997 q^{91} +(-305.377 + 176.310i) q^{92} +(-1.24719 + 79.9139i) q^{93} +(-78.7306 + 136.365i) q^{94} +(-14.2986 - 8.25532i) q^{95} +(219.040 + 3.41849i) q^{96} +(47.7972 + 82.7872i) q^{97} -13.9196i q^{98} +(2.11011 - 67.5864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 16 q^{4} - 22 q^{6} + 2 q^{7} + 8 q^{9} - 18 q^{11} - 22 q^{12} - 10 q^{13} - 54 q^{14} + 10 q^{15} - 32 q^{16} - 8 q^{18} - 52 q^{19} + 72 q^{21} - 24 q^{22} - 54 q^{23} + 108 q^{24} + 40 q^{25}+ \cdots - 824 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 + 16 * q^4 - 22 * q^6 + 2 * q^7 + 8 * q^9 - 18 * q^11 - 22 * q^12 - 10 * q^13 - 54 * q^14 + 10 * q^15 - 32 * q^16 - 8 * q^18 - 52 * q^19 + 72 * q^21 - 24 * q^22 - 54 * q^23 + 108 * q^24 + 40 * q^25 + 34 * q^27 + 32 * q^28 - 54 * q^29 - 100 * q^30 + 32 * q^31 + 216 * q^32 + 62 * q^33 + 54 * q^34 - 86 * q^36 + 44 * q^37 + 252 * q^38 + 160 * q^39 - 30 * q^40 + 144 * q^41 - 270 * q^42 - 124 * q^43 + 140 * q^45 - 108 * q^46 - 216 * q^47 - 172 * q^48 - 54 * q^49 - 106 * q^51 + 62 * q^52 - 316 * q^54 - 18 * q^56 - 236 * q^57 + 90 * q^58 - 486 * q^59 - 10 * q^60 + 62 * q^61 - 132 * q^63 + 256 * q^64 - 90 * q^65 + 208 * q^66 + 14 * q^67 - 288 * q^68 + 90 * q^69 - 60 * q^70 + 804 * q^72 - 268 * q^73 + 540 * q^74 - 20 * q^75 - 106 * q^76 + 702 * q^77 + 290 * q^78 - 40 * q^79 - 112 * q^81 - 204 * q^82 + 522 * q^83 + 714 * q^84 + 30 * q^85 + 54 * q^86 + 106 * q^87 + 144 * q^88 + 250 * q^90 + 136 * q^91 - 1332 * q^92 + 90 * q^93 - 150 * q^94 + 180 * q^95 + 166 * q^96 - 142 * q^97 - 824 * q^99

Introduction

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