LMFDB - Embedded newform 45.3.k.a.13.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(7,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	45.13
Dual form			45.3.k.a.7.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62192 + 0.434591i) q^{2} +(-0.485971 + 2.96038i) q^{3} +(-1.02236 - 0.590260i) q^{4} +(4.97136 + 0.534392i) q^{5} +(-2.07476 + 4.59028i) q^{6} +(2.65078 + 0.710273i) q^{7} +(-6.15096 - 6.15096i) q^{8} +(-8.52766 - 2.87732i) q^{9} +(7.83089 + 3.02725i) q^{10} +(-7.26798 - 12.5885i) q^{11} +(2.24423 - 2.73972i) q^{12} +(5.67678 - 1.52109i) q^{13} +(3.99065 + 2.30401i) q^{14} +(-3.99794 + 14.4574i) q^{15} +(-4.94214 - 8.56004i) q^{16} +(5.66128 - 5.66128i) q^{17} +(-12.5807 - 8.37281i) q^{18} +30.5333i q^{19} +(-4.76709 - 3.48074i) q^{20} +(-3.39088 + 7.50212i) q^{21} +(-6.31720 - 23.5761i) q^{22} +(-21.8511 + 5.85498i) q^{23} +(21.1983 - 15.2200i) q^{24} +(24.4289 + 5.31331i) q^{25} +9.86831 q^{26} +(12.6621 - 23.8468i) q^{27} +(-2.29080 - 2.29080i) q^{28} +(-1.51233 + 0.873143i) q^{29} +(-12.7674 + 21.7112i) q^{30} +(-25.5269 + 44.2139i) q^{31} +(4.71001 + 17.5780i) q^{32} +(40.7988 - 15.3983i) q^{33} +(11.6425 - 6.72178i) q^{34} +(12.7984 + 4.94758i) q^{35} +(7.01998 + 7.97520i) q^{36} +(2.78899 - 2.78899i) q^{37} +(-13.2695 + 49.5224i) q^{38} +(1.74424 + 17.5446i) q^{39} +(-27.2916 - 33.8657i) q^{40} +(16.5617 - 28.6857i) q^{41} +(-8.76007 + 10.6942i) q^{42} +(10.2504 - 38.2550i) q^{43} +17.1600i q^{44} +(-40.8565 - 18.8613i) q^{45} -37.9852 q^{46} +(41.1513 + 11.0264i) q^{47} +(27.7427 - 10.4707i) q^{48} +(-35.9131 - 20.7345i) q^{49} +(37.3124 + 19.2343i) q^{50} +(14.0083 + 19.5107i) q^{51} +(-6.70155 - 1.79568i) q^{52} +(-4.77052 - 4.77052i) q^{53} +(30.9005 - 33.1747i) q^{54} +(-29.4046 - 66.4660i) q^{55} +(-11.9359 - 20.6737i) q^{56} +(-90.3900 - 14.8383i) q^{57} +(-2.83233 + 0.758920i) q^{58} +(-69.8599 - 40.3336i) q^{59} +(12.6210 - 12.4209i) q^{60} +(-7.61593 - 13.1912i) q^{61} +(-60.6174 + 60.6174i) q^{62} +(-20.5612 - 13.6841i) q^{63} +70.0941i q^{64} +(29.0342 - 4.52826i) q^{65} +(72.8641 - 7.24398i) q^{66} +(16.5707 + 61.8428i) q^{67} +(-9.12950 + 2.44624i) q^{68} +(-6.71395 - 67.5329i) q^{69} +(18.6077 + 13.5866i) q^{70} +45.4076 q^{71} +(34.7551 + 70.1516i) q^{72} +(92.0685 + 92.0685i) q^{73} +(5.73558 - 3.31144i) q^{74} +(-27.6011 + 69.7365i) q^{75} +(18.0226 - 31.2160i) q^{76} +(-10.3245 - 38.5316i) q^{77} +(-4.79571 + 29.2139i) q^{78} +(28.1913 - 16.2762i) q^{79} +(-19.9948 - 45.1961i) q^{80} +(64.4421 + 49.0736i) q^{81} +(39.3283 - 39.3283i) q^{82} +(-1.79188 + 6.68739i) q^{83} +(7.89490 - 5.66838i) q^{84} +(31.1696 - 25.1189i) q^{85} +(33.2505 - 57.5916i) q^{86} +(-1.84988 - 4.90138i) q^{87} +(-32.7264 + 122.136i) q^{88} -35.7887i q^{89} +(-58.0688 - 48.3473i) q^{90} +16.1283 q^{91} +(25.7957 + 6.91193i) q^{92} +(-118.484 - 97.0559i) q^{93} +(61.9519 + 35.7679i) q^{94} +(-16.3167 + 151.792i) q^{95} +(-54.3264 + 5.40100i) q^{96} +(-59.6982 - 15.9961i) q^{97} +(-49.2370 - 49.2370i) q^{98} +(25.7578 + 128.263i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

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

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.62192	+	0.434591i	0.810958	+	0.217295i	0.640389	−	0.768050i	$-0.278773\pi$
$2$	1.62192	+	0.434591i	0.810958	+	0.217295i	0.170568	+	0.985346i	$0.445440\pi$
$3$	−0.485971	+	2.96038i	−0.161990	+	0.986792i
$3$	−0.485971	+	2.96038i	−0.161990	+	0.986792i
$4$	−1.02236	−	0.590260i	−0.255590	−	0.147565i
$5$	4.97136	+	0.534392i	0.994272	+	0.106878i
$5$	4.97136	+	0.534392i	0.994272	+	0.106878i
$6$	−2.07476	+	4.59028i	−0.345793	+	0.765047i
$7$	2.65078	+	0.710273i	0.378682	+	0.101468i	0.443139	−	0.896453i	$-0.353865\pi$
$7$	2.65078	+	0.710273i	0.378682	+	0.101468i	−0.0644568	+	0.997920i	$0.520531\pi$
$8$	−6.15096	−	6.15096i	−0.768870	−	0.768870i
$9$	−8.52766	−	2.87732i	−0.947518	−	0.319702i
$10$	7.83089	+	3.02725i	0.783089	+	0.302725i
$11$	−7.26798	−	12.5885i	−0.660726	−	1.14441i	−0.980425	−	0.196891i	$-0.936915\pi$
$11$	−7.26798	−	12.5885i	−0.660726	−	1.14441i	0.319700	−	0.947519i	$-0.396418\pi$
$12$	2.24423	−	2.73972i	0.187019	−	0.228310i
$13$	5.67678	−	1.52109i	0.436675	−	0.117007i	−0.0337827	−	0.999429i	$-0.510755\pi$
$13$	5.67678	−	1.52109i	0.436675	−	0.117007i	0.470458	+	0.882422i	$0.344089\pi$
$14$	3.99065	+	2.30401i	0.285047	+	0.164572i
$15$	−3.99794	+	14.4574i	−0.266529	+	0.963827i
$16$	−4.94214	−	8.56004i	−0.308884	−	0.535003i
$17$	5.66128	−	5.66128i	0.333017	−	0.333017i	−0.520714	−	0.853731i	$-0.674334\pi$
$17$	5.66128	−	5.66128i	0.333017	−	0.333017i	0.853731	+	0.520714i	$0.174334\pi$
$18$	−12.5807	−	8.37281i	−0.698927	−	0.465156i
$19$			30.5333i			1.60701i	0.595295	+	0.803507i	$0.297035\pi$
$19$			30.5333i			1.60701i	−0.595295	+	0.803507i	$0.702965\pi$
$20$	−4.76709	−	3.48074i	−0.238355	−	0.174037i
$21$	−3.39088	+	7.50212i	−0.161470	+	0.357244i
$22$	−6.31720	−	23.5761i	−0.287145	−	1.07164i
$23$	−21.8511	+	5.85498i	−0.950048	+	0.254565i	−0.700383	−	0.713768i	$-0.746987\pi$
$23$	−21.8511	+	5.85498i	−0.950048	+	0.254565i	−0.249665	+	0.968332i	$0.580321\pi$
$24$	21.1983	−	15.2200i	0.883265	−	0.634165i
$25$	24.4289	+	5.31331i	0.977154	+	0.212532i
$26$	9.86831			0.379550
$27$	12.6621	−	23.8468i	0.468968	−	0.883215i
$28$	−2.29080	−	2.29080i	−0.0818144	−	0.0818144i
$29$	−1.51233	+	0.873143i	−0.0521492	+	0.0301084i	−0.525848	−	0.850579i	$-0.676252\pi$
$29$	−1.51233	+	0.873143i	−0.0521492	+	0.0301084i	0.473699	+	0.880687i	$0.342919\pi$
$30$	−12.7674	+	21.7112i	−0.425579	+	0.723707i
$31$	−25.5269	+	44.2139i	−0.823448	+	1.42625i	0.0796510	+	0.996823i	$0.474619\pi$
$31$	−25.5269	+	44.2139i	−0.823448	+	1.42625i	−0.903099	+	0.429432i	$0.858714\pi$
$32$	4.71001	+	17.5780i	0.147188	+	0.549312i
$33$	40.7988	−	15.3983i	1.23633	−	0.466615i
$34$	11.6425	−	6.72178i	0.342425	−	0.197699i
$35$	12.7984	+	4.94758i	0.365668	+	0.141359i
$36$	7.01998	+	7.97520i	0.195000	+	0.221533i
$37$	2.78899	−	2.78899i	0.0753782	−	0.0753782i	−0.668413	−	0.743791i	$-0.733026\pi$
$37$	2.78899	−	2.78899i	0.0753782	−	0.0753782i	0.743791	+	0.668413i	$0.233026\pi$
$38$	−13.2695	+	49.5224i	−0.349197	+	1.30322i
$39$	1.74424	+	17.5446i	0.0447242	+	0.449862i
$40$	−27.2916	−	33.8657i	−0.682290	−	0.846641i
$41$	16.5617	−	28.6857i	0.403944	−	0.699652i	−0.590254	−	0.807218i	$-0.700972\pi$
$41$	16.5617	−	28.6857i	0.403944	−	0.699652i	0.994198	+	0.107566i	$0.0343057\pi$
$42$	−8.76007	+	10.6942i	−0.208573	+	0.254623i
$43$	10.2504	−	38.2550i	0.238381	−	0.889650i	−0.738214	−	0.674566i	$-0.764331\pi$
$43$	10.2504	−	38.2550i	0.238381	−	0.889650i	0.976596	−	0.215084i	$-0.0690026\pi$
$44$			17.1600i			0.390000i
$45$	−40.8565	−	18.8613i	−0.907922	−	0.419140i
$46$	−37.9852			−0.825764
$47$	41.1513	+	11.0264i	0.875559	+	0.234605i	0.668490	−	0.743721i	$-0.266941\pi$
$47$	41.1513	+	11.0264i	0.875559	+	0.234605i	0.207069	+	0.978326i	$0.433608\pi$
$48$	27.7427	−	10.4707i	0.577973	−	0.218139i
$49$	−35.9131	−	20.7345i	−0.732921	−	0.423152i
$50$	37.3124	+	19.2343i	0.746248	+	0.384686i
$51$	14.0083	+	19.5107i	0.274673	+	0.382564i
$52$	−6.70155	−	1.79568i	−0.128876	−	0.0345322i
$53$	−4.77052	−	4.77052i	−0.0900098	−	0.0900098i	0.660668	−	0.750678i	$-0.270273\pi$
$53$	−4.77052	−	4.77052i	−0.0900098	−	0.0900098i	−0.750678	+	0.660668i	$0.770273\pi$
$54$	30.9005	−	33.1747i	0.572232	−	0.614345i
$55$	−29.4046	−	66.4660i	−0.534628	−	1.20847i
$56$	−11.9359	−	20.6737i	−0.213142	−	0.369173i
$57$	−90.3900	−	14.8383i	−1.58579	−	0.260321i
$58$	−2.83233	+	0.758920i	−0.0488332	+	0.0130848i
$59$	−69.8599	−	40.3336i	−1.18407	−	0.683620i	−0.227114	−	0.973868i	$-0.572929\pi$
$59$	−69.8599	−	40.3336i	−1.18407	−	0.683620i	−0.956952	+	0.290248i	$0.906262\pi$
$60$	12.6210	−	12.4209i	0.210349	−	0.207014i
$61$	−7.61593	−	13.1912i	−0.124851	−	0.216249i	0.796824	−	0.604212i	$-0.206512\pi$
$61$	−7.61593	−	13.1912i	−0.124851	−	0.216249i	−0.921675	+	0.387963i	$0.873179\pi$
$62$	−60.6174	+	60.6174i	−0.977700	+	0.977700i
$63$	−20.5612	−	13.6841i	−0.326369	−	0.217208i
$64$			70.0941i			1.09522i
$65$	29.0342	−	4.52826i	0.446680	−	0.0696655i
$66$	72.8641	−	7.24398i	1.10400	−	0.109757i
$67$	16.5707	+	61.8428i	0.247324	+	0.923027i	0.972201	+	0.234148i	$0.0752302\pi$
$67$	16.5707	+	61.8428i	0.247324	+	0.923027i	−0.724876	+	0.688879i	$0.758103\pi$
$68$	−9.12950	+	2.44624i	−0.134257	+	0.0359742i
$69$	−6.71395	−	67.5329i	−0.0973037	−	0.978737i
$70$	18.6077	+	13.5866i	0.265825	+	0.194095i
$71$	45.4076			0.639543			0.319772	−	0.947495i	$-0.396394\pi$
$71$	45.4076			0.639543			0.319772	+	0.947495i	$0.396394\pi$
$72$	34.7551	+	70.1516i	0.482709	+	0.974327i
$73$	92.0685	+	92.0685i	1.26121	+	1.26121i	0.950506	+	0.310707i	$0.100566\pi$
$73$	92.0685	+	92.0685i	1.26121	+	1.26121i	0.310707	+	0.950506i	$0.399434\pi$
$74$	5.73558	−	3.31144i	0.0775079	−	0.0447492i
$75$	−27.6011	+	69.7365i	−0.368015	+	0.929820i
$76$	18.0226	−	31.2160i	0.237139	−	0.410737i
$77$	−10.3245	−	38.5316i	−0.134084	−	0.500410i
$78$	−4.79571	+	29.2139i	−0.0614835	+	0.374537i
$79$	28.1913	−	16.2762i	0.356852	−	0.206028i	−0.310847	−	0.950460i	$-0.600613\pi$
$79$	28.1913	−	16.2762i	0.356852	−	0.206028i	0.667699	+	0.744431i	$0.267279\pi$
$80$	−19.9948	−	45.1961i	−0.249935	−	0.564951i
$81$	64.4421	+	49.0736i	0.795581	+	0.605847i
$82$	39.3283	−	39.3283i	0.479613	−	0.479613i
$83$	−1.79188	+	6.68739i	−0.0215889	+	0.0805709i	−0.975880	−	0.218308i	$-0.929946\pi$
$83$	−1.79188	+	6.68739i	−0.0215889	+	0.0805709i	0.954291	+	0.298879i	$0.0966128\pi$
$84$	7.89490	−	5.66838i	0.0939870	−	0.0674807i
$85$	31.1696	−	25.1189i	0.366701	−	0.295517i
$86$	33.2505	−	57.5916i	0.386634	−	0.669670i
$87$	−1.84988	−	4.90138i	−0.0212630	−	0.0563377i
$88$	−32.7264	+	122.136i	−0.371891	+	1.38791i
$89$		−	35.7887i		−	0.402121i	−0.979579	−	0.201060i	$-0.935561\pi$
$89$		−	35.7887i		−	0.402121i	0.979579	−	0.201060i	$-0.0644387\pi$
$90$	−58.0688	−	48.3473i	−0.645209	−	0.537192i
$91$	16.1283			0.177234
$92$	25.7957	+	6.91193i	0.280388	+	0.0751297i
$93$	−118.484	−	97.0559i	−1.27403	−	1.04361i
$94$	61.9519	+	35.7679i	0.659063	+	0.380510i
$95$	−16.3167	+	151.792i	−0.171755	+	1.59781i
$96$	−54.3264	+	5.40100i	−0.565900	+	0.0562604i
$97$	−59.6982	−	15.9961i	−0.615446	−	0.164908i	−0.0623891	−	0.998052i	$-0.519872\pi$
$97$	−59.6982	−	15.9961i	−0.615446	−	0.164908i	−0.553056	+	0.833144i	$0.686539\pi$
$98$	−49.2370	−	49.2370i	−0.502419	−	0.502419i
$99$	25.7578	+	128.263i	0.260179	+	1.29558i
$100$	−21.8389	−	19.8515i	−0.218389	−	0.198515i
$101$	−54.5879	−	94.5491i	−0.540475	−	0.936130i	−0.998877	−	0.0473847i	$-0.984911\pi$
$101$	−54.5879	−	94.5491i	−0.540475	−	0.936130i	0.458402	−	0.888745i	$-0.348422\pi$
$102$	14.2411	+	37.7327i	0.139619	+	0.369928i
$103$	113.280	−	30.3534i	1.09981	−	0.294693i	0.337122	−	0.941461i	$-0.390546\pi$
$103$	113.280	−	30.3534i	1.09981	−	0.294693i	0.762687	+	0.646768i	$0.223880\pi$
$104$	−44.2738	−	25.5615i	−0.425709	−	0.245783i
$105$	−20.8663	+	35.4837i	−0.198727	+	0.337940i
$106$	−5.66416	−	9.81061i	−0.0534354	−	0.0925529i
$107$	−24.4404	+	24.4404i	−0.228415	+	0.228415i	−0.812030	−	0.583615i	$-0.801638\pi$
$107$	−24.4404	+	24.4404i	−0.228415	+	0.228415i	0.583615	+	0.812030i	$0.301638\pi$
$108$	−27.0211	+	16.9061i	−0.250195	+	0.156538i
$109$		−	38.5655i		−	0.353812i	−0.984228	−	0.176906i	$-0.943391\pi$
$109$		−	38.5655i		−	0.353812i	0.984228	−	0.176906i	$-0.0566088\pi$
$110$	−18.8062	−	120.581i	−0.170965	−	1.09619i
$111$	6.90110	+	9.61184i	0.0621721	+	0.0865932i
$112$	−7.02054	−	26.2010i	−0.0626834	−	0.233938i
$113$	175.184	−	46.9404i	1.55030	−	0.415402i	0.620723	−	0.784030i	$-0.286839\pi$
$113$	175.184	−	46.9404i	1.55030	−	0.415402i	0.929577	+	0.368628i	$0.120173\pi$
$114$	−140.156	−	63.3491i	−1.22944	−	0.555694i
$115$	−111.759	+	17.4302i	−0.971814	+	0.151567i
$116$	2.06153			0.0177718
$117$	−52.7863	−	3.36256i	−0.451165	−	0.0287398i
$118$	−95.7782	−	95.7782i	−0.811679	−	0.811679i
$119$	19.0278	−	10.9857i	0.159898	−	0.0923170i
$120$	113.518	−	64.3357i	0.945984	−	0.536131i
$121$	−45.1471	+	78.1971i	−0.373117	+	0.646257i
$122$	−6.61963	−	24.7048i	−0.0542592	−	0.202498i
$123$	76.8720	+	62.9694i	0.624976	+	0.511946i
$124$	52.1954	−	30.1350i	0.420931	−	0.243024i
$125$	118.605	+	39.4689i	0.948842	+	0.315751i
$126$	−27.4016	−	31.1302i	−0.217473	−	0.247065i
$127$	71.5886	−	71.5886i	0.563690	−	0.563690i	−0.366664	−	0.930353i	$-0.619500\pi$
$127$	71.5886	−	71.5886i	0.563690	−	0.563690i	0.930353	+	0.366664i	$0.119500\pi$
$128$	−11.6222	+	43.3747i	−0.0907986	+	0.338865i
$129$	108.268	+	48.9358i	0.839285	+	0.379347i
$130$	49.0589	+	5.27354i	0.377376	+	0.0405657i
$131$	−93.6880	+	162.272i	−0.715176	+	1.23872i	0.247716	+	0.968833i	$0.420320\pi$
$131$	−93.6880	+	162.272i	−0.715176	+	1.23872i	−0.962892	+	0.269888i	$0.913013\pi$
$132$	−50.8001	−	8.33927i	−0.384849	−	0.0631763i
$133$	−21.6870	+	80.9368i	−0.163060	+	0.608548i
$134$			107.505i			0.802279i
$135$	75.6916	−	111.785i	0.560679	−	0.828034i
$136$	−69.6446			−0.512093
$137$	−36.9208	−	9.89289i	−0.269495	−	0.0722109i	0.121541	−	0.992586i	$-0.461216\pi$
$137$	−36.9208	−	9.89289i	−0.269495	−	0.0722109i	−0.391036	+	0.920376i	$0.627883\pi$
$138$	18.4597	−	112.450i	0.133766	−	0.814858i
$139$	−87.3985	−	50.4596i	−0.628766	−	0.363018i	0.151508	−	0.988456i	$-0.451587\pi$
$139$	−87.3985	−	50.4596i	−0.628766	−	0.363018i	−0.780274	+	0.625438i	$0.784920\pi$
$140$	−10.1642	−	12.6126i	−0.0726016	−	0.0900899i
$141$	−52.6408	+	116.465i	−0.373339	+	0.825991i
$142$	73.6473	+	19.7337i	0.518643	+	0.138970i
$143$	−60.4070	−	60.4070i	−0.422426	−	0.422426i
$144$	17.5150	+	87.2173i	0.121632	+	0.605676i
$145$	−7.98493	+	3.53253i	−0.0550685	+	0.0243623i
$146$	109.315	+	189.340i	0.748734	+	1.29685i
$147$	78.8345	−	96.2400i	0.536289	−	0.654694i
$148$	−4.49759	+	1.20513i	−0.0303891	+	0.00814274i
$149$	42.4235	+	24.4932i	0.284722	+	0.164384i	0.635559	−	0.772052i	$-0.280770\pi$
$149$	42.4235	+	24.4932i	0.284722	+	0.164384i	−0.350837	+	0.936436i	$0.614103\pi$
$150$	−75.0735	+	101.112i	−0.500490	+	0.674077i
$151$	−51.0998	−	88.5075i	−0.338409	−	0.586142i	0.645724	−	0.763571i	$-0.276556\pi$
$151$	−51.0998	−	88.5075i	−0.338409	−	0.586142i	−0.984134	+	0.177428i	$0.943222\pi$
$152$	187.809	−	187.809i	1.23559	−	1.23559i
$153$	−64.5668	+	31.9882i	−0.422005	+	0.209073i
$154$		−	66.9819i		−	0.434947i
$155$	−150.531	+	206.162i	−0.971167	+	1.33008i
$156$	8.57264	−	18.9665i	0.0549528	−	0.121580i
$157$	35.3571	+	131.954i	0.225204	+	0.840473i	0.982323	+	0.187196i	$0.0599399\pi$
$157$	35.3571	+	131.954i	0.225204	+	0.840473i	−0.757118	+	0.653278i	$0.773393\pi$
$158$	52.7974	−	14.1470i	0.334161	−	0.0895381i
$159$	16.4409	−	11.8042i	0.103402	−	0.0742403i
$160$	14.0216	+	89.9035i	0.0876351	+	0.561897i
$161$	−62.0810			−0.385596
$162$	83.1927	+	107.599i	0.513535	+	0.664192i
$163$	−150.604	−	150.604i	−0.923951	−	0.923951i	0.0733548	−	0.997306i	$-0.476629\pi$
$163$	−150.604	−	150.604i	−0.923951	−	0.923951i	−0.997306	+	0.0733548i	$0.976629\pi$
$164$	−33.8641	+	19.5514i	−0.206488	+	0.119216i
$165$	211.054	−	54.7480i	1.27912	−	0.331806i
$166$	−5.81255	+	10.0676i	−0.0350154	+	0.0606484i
$167$	−34.4600	−	128.607i	−0.206347	−	0.770099i	−0.989035	−	0.147684i	$-0.952818\pi$
$167$	−34.4600	−	128.607i	−0.206347	−	0.770099i	0.782687	−	0.622415i	$-0.213848\pi$
$168$	67.0024	−	25.2881i	0.398824	−	0.150524i
$169$	−116.446	+	67.2302i	−0.689031	+	0.397812i
$170$	61.4709	−	27.1948i	0.361594	−	0.159969i
$171$	87.8539	−	260.378i	0.513766	−	1.52268i
$172$	−33.0600	+	33.0600i	−0.192209	+	0.192209i
$173$	−37.9081	+	141.475i	−0.219122	+	0.817775i	0.765552	+	0.643373i	$0.222466\pi$
$173$	−37.9081	+	141.475i	−0.219122	+	0.817775i	−0.984675	+	0.174401i	$0.944201\pi$
$174$	−0.870259	−	8.75357i	−0.00500149	−	0.0503079i
$175$	60.9815	+	31.4355i	0.348466	+	0.179632i
$176$	−71.8388	+	124.428i	−0.408175	+	0.706980i
$177$	153.353	−	187.211i	0.866399	−	1.05769i
$178$	15.5535	−	58.0463i	0.0873790	−	0.326103i
$179$			141.161i			0.788611i	0.918979	+	0.394305i	$0.129015\pi$
$179$			141.161i			0.788611i	−0.918979	+	0.394305i	$0.870985\pi$
$180$	30.6370	+	43.3990i	0.170206	+	0.241106i
$181$	182.292			1.00714			0.503568	−	0.863956i	$-0.332020\pi$
$181$	182.292			1.00714			0.503568	+	0.863956i	$0.332020\pi$
$182$	26.1587	+	7.00919i	0.143729	+	0.0385120i
$183$	42.7520	−	16.1355i	0.233617	−	0.0881721i
$184$	170.419	+	98.3915i	0.926190	+	0.534736i
$185$	15.3555	−	12.3747i	0.0830027	−	0.0668901i
$186$	−149.992	−	208.909i	−0.806409	−	1.12317i
$187$	−112.413	−	30.1210i	−0.601140	−	0.161075i
$188$	−35.5630	−	35.5630i	−0.189165	−	0.189165i
$189$	50.5022	−	54.2189i	0.267208	−	0.286873i
$190$	−92.4317	+	239.103i	−0.486483	+	1.25843i
$191$	−109.084	−	188.938i	−0.571118	−	0.989206i	−0.996451	−	0.0841691i	$-0.973176\pi$
$191$	−109.084	−	188.938i	−0.571118	−	0.989206i	0.425333	−	0.905037i	$-0.360157\pi$
$192$	−207.505	−	34.0637i	−1.08075	−	0.177415i
$193$	−212.495	+	56.9379i	−1.10101	+	0.295015i	−0.763176	−	0.646191i	$-0.776361\pi$
$193$	−212.495	+	56.9379i	−1.10101	+	0.295015i	−0.337834	+	0.941206i	$0.609694\pi$
$194$	−89.8737	−	51.8886i	−0.463267	−	0.267467i
$195$	−0.704432	+	88.1527i	−0.00361247	+	0.452065i
$196$	24.4775	+	42.3962i	0.124885	+	0.216307i
$197$	−241.895	+	241.895i	−1.22789	+	1.22789i	−0.263133	+	0.964759i	$0.584756\pi$
$197$	−241.895	+	241.895i	−1.22789	+	1.22789i	−0.964759	+	0.263133i	$0.915244\pi$
$198$	−13.9650	+	219.226i	−0.0705302	+	1.10720i
$199$		−	126.744i		−	0.636904i	−0.947939	−	0.318452i	$-0.896837\pi$
$199$		−	126.744i		−	0.636904i	0.947939	−	0.318452i	$-0.103163\pi$
$200$	−117.579	−	182.943i	−0.587895	−	0.914714i
$201$	−191.131	+	19.0018i	−0.950900	+	0.0945362i
$202$	−47.4469	−	177.074i	−0.234885	−	0.876604i
$203$	−4.62901	+	1.24034i	−0.0228030	+	0.00611005i
$204$	−2.80512	−	28.2156i	−0.0137506	−	0.138312i
$205$	97.6637	−	133.757i	0.476408	−	0.652471i
$206$	196.922			0.955934
$207$	203.185	+	12.9432i	0.981572	+	0.0625275i
$208$	−41.0760	−	41.0760i	−0.197481	−	0.197481i
$209$	384.369	−	221.915i	1.83908	−	1.06180i
$210$	−49.2643	+	48.4832i	−0.234592	+	0.230873i
$211$	104.807	−	181.531i	0.496714	−	0.860334i	−0.503278	−	0.864124i	$-0.667873\pi$
$211$	104.807	−	181.531i	0.496714	−	0.860334i	0.999993	+	0.00378982i	$0.00120634\pi$
$212$	2.06135	+	7.69304i	0.00972333	+	0.0362879i
$213$	−22.0668	+	134.424i	−0.103600	+	0.631097i
$214$	−50.2619	+	29.0187i	−0.234869	+	0.135601i
$215$	71.4015	−	184.701i	0.332100	−	0.859077i
$216$	−224.565	+	68.7964i	−1.03965	+	0.318502i
$217$	−99.0700	+	99.0700i	−0.456544	+	0.456544i
$218$	16.7602	−	62.5500i	0.0768817	−	0.286926i
$219$	−317.300	+	227.815i	−1.44886	+	1.04025i
$220$	−9.17016	+	85.3086i	−0.0416826	+	0.387766i
$221$	23.5265	−	40.7491i	0.106455	−	0.184385i
$222$	7.01578	+	18.5887i	0.0316026	+	0.0837331i
$223$	74.1657	−	276.790i	0.332582	−	1.24121i	−0.573885	−	0.818936i	$-0.694565\pi$
$223$	74.1657	−	276.790i	0.332582	−	1.24121i	0.906467	−	0.422276i	$-0.138769\pi$
$224$			49.9407i			0.222949i
$225$	−193.033	−	115.600i	−0.857924	−	0.513776i
$226$	304.533			1.34749
$227$	184.462	+	49.4265i	0.812609	+	0.217738i	0.641112	−	0.767447i	$-0.278473\pi$
$227$	184.462	+	49.4265i	0.812609	+	0.217738i	0.171496	+	0.985185i	$0.445140\pi$
$228$	83.6528	+	68.5237i	0.366898	+	0.300543i
$229$	−259.167	−	149.630i	−1.13173	−	0.653406i	−0.187363	−	0.982291i	$-0.559994\pi$
$229$	−259.167	−	149.630i	−1.13173	−	0.653406i	−0.944370	+	0.328885i	$0.893327\pi$
$230$	−188.838	−	20.2989i	−0.821035	−	0.0882563i
$231$	119.085	−	11.8392i	0.515521	−	0.0512519i
$232$	14.6729	+	3.93160i	0.0632454	+	0.0169466i
$233$	−54.0196	−	54.0196i	−0.231844	−	0.231844i	0.581618	−	0.813462i	$-0.302420\pi$
$233$	−54.0196	−	54.0196i	−0.231844	−	0.231844i	−0.813462	+	0.581618i	$0.802420\pi$
$234$	−84.1536	−	28.3942i	−0.359631	−	0.121343i
$235$	198.685	+	76.8073i	0.845469	+	0.326840i
$236$	47.6147	+	82.4710i	0.201757	+	0.349453i
$237$	34.4837	+	91.3666i	0.145501	+	0.385513i
$238$	35.6358	−	9.54860i	0.149730	−	0.0401202i
$239$	127.358	+	73.5301i	0.532878	+	0.307657i	0.742188	−	0.670192i	$-0.233788\pi$
$239$	127.358	+	73.5301i	0.532878	+	0.307657i	−0.209310	+	0.977849i	$0.567122\pi$
$240$	143.514	−	37.2280i	0.597977	−	0.155117i
$241$	194.950	+	337.663i	0.808921	+	1.40109i	0.913612	+	0.406587i	$0.133281\pi$
$241$	194.950	+	337.663i	0.808921	+	1.40109i	−0.104691	+	0.994505i	$0.533386\pi$
$242$	−107.209	+	107.209i	−0.443010	+	0.443010i
$243$	−176.593	+	166.925i	−0.726721	+	0.686932i
$244$			17.9815i			0.0736948i
$245$	−167.457	−	122.270i	−0.683497	−	0.499062i
$246$	97.3141	+	135.539i	0.395586	+	0.550971i
$247$	46.4438	+	173.331i	0.188032	+	0.701744i
$248$	428.973	−	114.943i	1.72973	−	0.463479i
$249$	−18.9264	−	8.55452i	−0.0760096	−	0.0343555i
$250$	175.215	+	115.560i	0.700859	+	0.462240i
$251$	−239.421			−0.953870			−0.476935	−	0.878938i	$-0.658252\pi$
$251$	−239.421			−0.953870			−0.476935	+	0.878938i	$0.658252\pi$
$252$	12.9438	+	26.1266i	0.0513644	+	0.103677i
$253$	232.519	+	232.519i	0.919047	+	0.919047i
$254$	147.222	−	84.9989i	0.579616	−	0.334641i
$255$	59.2140	+	104.481i	0.232212	+	0.409729i
$256$	102.488	−	177.514i	0.400342	−	0.693413i
$257$	−6.26563	−	23.3837i	−0.0243799	−	0.0909870i	0.952664	−	0.304025i	$-0.0983307\pi$
$257$	−6.26563	−	23.3837i	−0.0243799	−	0.0909870i	−0.977044	+	0.213038i	$0.931664\pi$
$258$	154.334	+	126.422i	0.598194	+	0.490008i
$259$	9.37394	−	5.41205i	0.0361928	−	0.0208959i
$260$	−32.3563	−	12.5082i	−0.124447	−	0.0481085i
$261$	15.4089	−	3.09442i	0.0590381	−	0.0118560i
$262$	−222.476	+	222.476i	−0.849146	+	0.849146i
$263$	−27.4221	+	102.341i	−0.104266	+	0.389128i	−0.998261	−	0.0589502i	$-0.981225\pi$
$263$	−27.4221	+	102.341i	−0.104266	+	0.389128i	0.893994	+	0.448078i	$0.147891\pi$
$264$	−345.666	−	156.237i	−1.30934	−	0.591808i
$265$	−21.1667	−	26.2653i	−0.0798742	−	0.0991144i
$266$	−70.3488	+	121.848i	−0.264469	+	0.458074i
$267$	105.948	+	17.3923i	0.396810	+	0.0651397i
$268$	19.5621	−	73.0067i	0.0729929	−	0.272413i
$269$		−	33.3603i		−	0.124016i	−0.998076	−	0.0620079i	$-0.980250\pi$
$269$		−	33.3603i		−	0.124016i	0.998076	−	0.0620079i	$-0.0197504\pi$
$270$	171.346	−	148.410i	0.634615	−	0.549667i
$271$	−89.2173			−0.329215			−0.164608	−	0.986359i	$-0.552636\pi$
$271$	−89.2173			−0.329215			−0.164608	+	0.986359i	$0.552636\pi$
$272$	−76.4397	−	20.4820i	−0.281028	−	0.0753013i
$273$	−7.83787	+	47.7457i	−0.0287101	+	0.174893i
$274$	−55.5830	−	32.0909i	−0.202858	−	0.117120i
$275$	−110.662	−	346.140i	−0.402407	−	1.25869i
$276$	−32.9979	+	73.0059i	−0.119558	+	0.264514i
$277$	91.9589	+	24.6403i	0.331982	+	0.0889542i	0.420960	−	0.907079i	$-0.361693\pi$
$277$	91.9589	+	24.6403i	0.331982	+	0.0889542i	−0.0889779	+	0.996034i	$0.528360\pi$
$278$	−119.824	−	119.824i	−0.431021	−	0.431021i
$279$	344.902	−	303.592i	1.23621	−	1.08814i
$280$	−48.2901	−	109.155i	−0.172465	−	0.389838i
$281$	149.830	+	259.513i	0.533202	+	0.923534i	0.999248	+	0.0387730i	$0.0123449\pi$
$281$	149.830	+	259.513i	0.533202	+	0.923534i	−0.466046	+	0.884761i	$0.654322\pi$
$282$	−135.993	+	166.019i	−0.482246	+	0.588719i
$283$	−4.07727	+	1.09250i	−0.0144073	+	0.00386043i	−0.266016	−	0.963969i	$-0.585707\pi$
$283$	−4.07727	+	1.09250i	−0.0144073	+	0.00386043i	0.251608	+	0.967829i	$0.419041\pi$
$284$	−46.4229	−	26.8023i	−0.163461	−	0.0943743i
$285$	−441.432	−	122.070i	−1.54888	−	0.428316i
$286$	−71.7227	−	124.227i	−0.250779	−	0.434361i
$287$	64.2761	−	64.2761i	0.223958	−	0.223958i
$288$	10.4121	−	163.451i	0.0361531	−	0.567539i
$289$			224.900i			0.778200i
$290$	−14.4861	+	2.25929i	−0.0499520	+	0.00779067i
$291$	76.3661	−	168.956i	0.262426	−	0.580603i
$292$	−39.7829	−	148.472i	−0.136243	−	0.508465i
$293$	−110.837	+	29.6986i	−0.378282	+	0.101360i	−0.442950	−	0.896546i	$-0.646068\pi$
$293$	−110.837	+	29.6986i	−0.378282	+	0.101360i	0.0646674	+	0.997907i	$0.479401\pi$
$294$	169.688	−	121.832i	0.577170	−	0.414396i
$295$	−325.745	−	237.845i	−1.10422	−	0.806256i
$296$	−34.3100			−0.115912
$297$	−392.224	+	13.9206i	−1.32062	+	0.0468706i
$298$	58.1629	+	58.1629i	0.195177	+	0.195177i
$299$	−115.138	+	66.4749i	−0.385077	+	0.222324i
$300$	69.3810	−	55.0040i	0.231270	−	0.183347i
$301$	54.3429	−	94.1247i	0.180541	−	0.312707i
$302$	−44.4150	−	165.759i	−0.147070	−	0.548872i
$303$	306.429	−	115.653i	1.01132	−	0.381692i
$304$	261.366	−	150.900i	0.859757	−	0.496381i
$305$	−30.8123	−	69.6480i	−0.101024	−	0.228354i
$306$	−118.624	+	23.8220i	−0.387659	+	0.0778497i
$307$	−148.857	+	148.857i	−0.484876	+	0.484876i	−0.906685	−	0.421809i	$-0.861395\pi$
$307$	−148.857	+	148.857i	−0.484876	+	0.484876i	0.421809	+	0.906685i	$0.361395\pi$
$308$	−12.1883	+	45.4873i	−0.0395724	+	0.147686i
$309$	34.8064	+	350.103i	0.112642	+	1.13302i
$310$	−333.745	+	268.958i	−1.07660	+	0.867605i
$311$	−17.4318	+	30.1928i	−0.0560510	+	0.0970831i	−0.892689	−	0.450672i	$-0.851184\pi$
$311$	−17.4318	+	30.1928i	−0.0560510	+	0.0970831i	0.836638	+	0.547756i	$0.184518\pi$
$312$	97.1874	−	118.645i	0.311498	−	0.380272i
$313$	43.5756	−	162.626i	0.139219	−	0.519573i	−0.860726	−	0.509069i	$-0.829990\pi$
$313$	43.5756	−	162.626i	0.139219	−	0.519573i	0.999945	−	0.0105038i	$-0.00334352\pi$
$314$			229.385i			0.730524i
$315$	−94.9047	−	79.0163i	−0.301285	−	0.250845i
$316$	−38.4289			−0.121610
$317$	−149.332	−	40.0134i	−0.471078	−	0.126225i	0.0154670	−	0.999880i	$-0.495077\pi$
$317$	−149.332	−	40.0134i	−0.471078	−	0.126225i	−0.486545	+	0.873655i	$0.661743\pi$
$318$	31.7957	−	12.0004i	0.0999865	−	0.0377370i
$319$	21.9831	+	12.6920i	0.0689127	+	0.0397868i
$320$	−37.4577	+	348.463i	−0.117055	+	1.08895i
$321$	−60.4755	−	84.2302i	−0.188397	−	0.262399i
$322$	−100.690	−	26.9798i	−0.312702	−	0.0837883i
$323$	172.857	+	172.857i	0.535162	+	0.535162i
$324$	−36.9169	−	88.2085i	−0.113941	−	0.272249i
$325$	146.759	−	6.99598i	0.451567	−	0.0215261i
$326$	−178.816	−	309.718i	−0.548515	−	0.950056i
$327$	114.168	+	18.7417i	0.349139	+	0.0573141i
$328$	−278.315	+	74.5743i	−0.848522	+	0.227361i
$329$	101.251	+	58.4573i	0.307754	+	0.177682i
$330$	366.105	+	2.92556i	1.10941	+	0.00886533i
$331$	74.6272	+	129.258i	0.225460	+	0.390508i	0.956457	−	0.291872i	$-0.0942782\pi$
$331$	74.6272	+	129.258i	0.225460	+	0.390508i	−0.730997	+	0.682380i	$0.760945\pi$
$332$	5.77925	−	5.77925i	0.0174074	−	0.0174074i
$333$	−31.8084	+	15.7588i	−0.0955207	+	0.0473237i
$334$		−	223.565i		−	0.669356i
$335$	49.3308	+	316.298i	0.147256	+	0.944174i
$336$	80.9767	−	8.05051i	0.241002	−	0.0239598i
$337$	−17.7797	−	66.3546i	−0.0527586	−	0.196898i	0.934516	−	0.355920i	$-0.115833\pi$
$337$	−17.7797	−	66.3546i	−0.0527586	−	0.196898i	−0.987275	+	0.159022i	$0.949166\pi$
$338$	−218.084	+	58.4353i	−0.645218	+	0.172886i
$339$	53.8269	+	541.422i	0.158781	+	1.59712i
$340$	−46.6933	+	7.28243i	−0.137333	+	0.0214189i
$341$	742.116			2.17629
$342$	255.649	−	384.130i	0.747513	−	1.12319i
$343$	−175.555	−	175.555i	−0.511822	−	0.511822i
$344$	−298.354	+	172.255i	−0.867309	+	0.500741i
$345$	2.71150	−	339.318i	0.00785943	−	0.983531i
$346$	−122.968	+	212.986i	−0.355398	+	0.615567i
$347$	5.27547	+	19.6883i	0.0152031	+	0.0567386i	0.973111	−	0.230338i	$-0.0739832\pi$
$347$	5.27547	+	19.6883i	0.0152031	+	0.0567386i	−0.957908	+	0.287077i	$0.907317\pi$
$348$	−1.00184	+	6.10290i	−0.00287886	+	0.0175371i
$349$	119.850	−	69.1957i	0.343411	−	0.198268i	−0.318368	−	0.947967i	$-0.603135\pi$
$349$	119.850	−	69.1957i	0.343411	−	0.198268i	0.661779	+	0.749699i	$0.269802\pi$
$350$	85.2452	+	77.4878i	0.243558	+	0.221394i
$351$	35.6071	−	154.633i	0.101445	−	0.440551i
$352$	187.048	−	187.048i	0.531388	−	0.531388i
$353$	−6.05222	+	22.5872i	−0.0171451	+	0.0639863i	−0.973968	−	0.226684i	$-0.927212\pi$
$353$	−6.05222	+	22.5872i	−0.0171451	+	0.0639863i	0.956823	+	0.290670i	$0.0938782\pi$
$354$	330.085	−	236.994i	0.932443	−	0.669475i
$355$	225.737	+	24.2654i	0.635880	+	0.0683533i
$356$	−21.1247	+	36.5890i	−0.0593390	+	0.102778i
$357$	23.2749	+	61.6683i	0.0651958	+	0.172740i
$358$	−61.3474	+	228.952i	−0.171362	+	0.639530i
$359$		−	401.663i		−	1.11884i	−0.828885	−	0.559419i	$-0.811024\pi$
$359$		−	401.663i		−	1.11884i	0.828885	−	0.559419i	$-0.188976\pi$
$360$	135.291	+	367.322i	0.375810	+	1.02034i
$361$	−571.281			−1.58250
$362$	295.662	+	79.2223i	0.816745	+	0.218846i
$363$	−209.553	−	171.654i	−0.577280	−	0.472876i
$364$	−16.4889	−	9.51987i	−0.0452992	−	0.0261535i
$365$	408.505	+	506.906i	1.11919	+	1.38878i
$366$	76.3524	−	7.59077i	0.208613	−	0.0207398i
$367$	607.153	+	162.686i	1.65437	+	0.443286i	0.960831	−	0.277135i	$-0.0893849\pi$
$367$	607.153	+	162.686i	1.65437	+	0.443286i	0.693537	+	0.720421i	$0.256052\pi$
$368$	158.110	+	158.110i	0.429647	+	0.429647i
$369$	−223.771	+	196.969i	−0.606424	+	0.533791i
$370$	30.2832	−	13.3973i	0.0818466	−	0.0362090i
$371$	−9.25721	−	16.0340i	−0.0249520	−	0.0432182i
$372$	63.8456	+	169.163i	0.171628	+	0.454739i
$373$	−360.865	+	96.6935i	−0.967467	+	0.259232i	−0.707758	−	0.706455i	$-0.750293\pi$
$373$	−360.865	+	96.6935i	−0.967467	+	0.259232i	−0.259709	+	0.965687i	$0.583627\pi$
$374$	−169.234	−	97.7075i	−0.452498	−	0.261250i
$375$	−174.482	+	331.935i	−0.465284	+	0.885161i
$376$	−185.297	−	320.943i	−0.492810	−	0.853572i
$377$	−7.25702	+	7.25702i	−0.0192494	+	0.0192494i
$378$	105.473	−	65.9907i	0.279030	−	0.174579i
$379$		−	223.796i		−	0.590491i	−0.955421	−	0.295246i	$-0.904599\pi$
$379$		−	223.796i		−	0.590491i	0.955421	−	0.295246i	$-0.0954015\pi$
$380$	106.278	−	145.555i	0.279680	−	0.383040i
$381$	177.139	+	246.719i	0.464932	+	0.647557i
$382$	−94.8135	−	353.849i	−0.248203	−	0.926306i
$383$	34.3604	−	9.20683i	0.0897138	−	0.0240387i	−0.213683	−	0.976903i	$-0.568546\pi$
$383$	34.3604	−	9.20683i	0.0897138	−	0.0240387i	0.303397	+	0.952864i	$0.401879\pi$
$384$	−122.758	−	55.4851i	−0.319681	−	0.144492i
$385$	−30.7359	−	197.072i	−0.0798335	−	0.511874i
$386$	−369.394			−0.956978
$387$	−197.483	+	296.732i	−0.510293	+	0.766749i
$388$	51.5913	+	51.5913i	0.132967	+	0.132967i
$389$	−180.301	+	104.097i	−0.463500	+	0.267602i	−0.713515	−	0.700640i	$-0.752898\pi$
$389$	−180.301	+	104.097i	−0.463500	+	0.267602i	0.250015	+	0.968242i	$0.419565\pi$
$390$	−39.4529	+	142.670i	−0.101161	+	0.365821i
$391$	−90.5585	+	156.852i	−0.231607	+	0.401156i
$392$	93.3634	+	348.437i	0.238172	+	0.888870i
$393$	−434.858	−	356.212i	−1.10651	−	0.906391i
$394$	−497.458	+	287.208i	−1.26258	+	0.728954i
$395$	148.847	−	65.8499i	0.376828	−	0.166709i
$396$	49.3748	−	146.335i	0.124684	−	0.369532i
$397$	231.955	−	231.955i	0.584269	−	0.584269i	−0.351805	−	0.936073i	$-0.614432\pi$
$397$	231.955	−	231.955i	0.584269	−	0.584269i	0.936073	+	0.351805i	$0.114432\pi$
$398$	55.0818	−	205.568i	0.138396	−	0.516502i
$399$	−229.064	−	103.535i	−0.574096	−	0.259485i
$400$	−75.2488	−	235.371i	−0.188122	−	0.588428i
$401$	47.0303	−	81.4589i	0.117283	−	0.203139i	−0.801407	−	0.598119i	$-0.795915\pi$
$401$	47.0303	−	81.4589i	0.117283	−	0.203139i	0.918690	+	0.394980i	$0.129248\pi$
$402$	−318.256	−	52.2445i	−0.791682	−	0.129961i
$403$	−77.6573	+	289.821i	−0.192698	+	0.719159i
$404$			128.884i			0.319021i
$405$	294.140	+	278.400i	0.726273	+	0.687407i
$406$	−8.04691			−0.0198200
$407$	−55.3796	−	14.8389i	−0.136068	−	0.0364593i
$408$	33.8453	−	206.174i	0.0829542	−	0.505329i
$409$	590.758	+	341.074i	1.44440	+	0.833922i	0.998139	−	0.0609834i	$-0.0194237\pi$
$409$	590.758	+	341.074i	1.44440	+	0.833922i	0.446256	+	0.894905i	$0.352757\pi$
$410$	216.532	−	174.498i	0.528126	−	0.425605i
$411$	47.2291	−	104.492i	0.114913	−	0.254238i
$412$	−133.730	−	35.8328i	−0.324587	−	0.0869728i
$413$	−156.535	−	156.535i	−0.379019	−	0.379019i
$414$	323.925	+	109.295i	0.782427	+	0.263998i
$415$	−12.4818	+	32.2878i	−0.0300765	+	0.0778020i
$416$	53.4753	+	92.6220i	0.128546	+	0.222649i
$417$	191.853	−	234.211i	0.460078	−	0.561656i
$418$	719.856	−	192.885i	1.72214	−	0.461447i
$419$	−181.648	−	104.875i	−0.433528	−	0.250298i	0.267320	−	0.963608i	$-0.413862\pi$
$419$	−181.648	−	104.875i	−0.433528	−	0.250298i	−0.700849	+	0.713310i	$0.747195\pi$
$420$	42.2775	−	23.9606i	0.100661	−	0.0570490i
$421$	2.94824	+	5.10651i	0.00700296	+	0.0121295i	0.869506	−	0.493923i	$-0.164438\pi$
$421$	2.94824	+	5.10651i	0.00700296	+	0.0121295i	−0.862503	+	0.506052i	$0.831104\pi$
$422$	248.879	−	248.879i	0.589761	−	0.589761i
$423$	−319.198	−	212.435i	−0.754604	−	0.502211i
$424$			58.6866i			0.138412i
$425$	168.379	−	108.218i	0.396185	−	0.254632i
$426$	−94.2097	+	208.434i	−0.221150	+	0.489281i
$427$	−10.8188	−	40.3762i	−0.0253367	−	0.0945579i
$428$	39.4132	−	10.5607i	0.0920868	−	0.0246746i
$429$	208.183	−	149.471i	0.485276	−	0.348418i
$430$	196.077	−	268.540i	0.455993	−	0.624511i
$431$	−623.625			−1.44693			−0.723463	−	0.690364i	$-0.757451\pi$
$431$	−623.625			−1.44693			−0.723463	+	0.690364i	$0.757451\pi$
$432$	−266.708	+	9.46583i	−0.617379	+	0.0219117i
$433$	342.585	+	342.585i	0.791190	+	0.791190i	0.981688	−	0.190497i	$-0.0610100\pi$
$433$	342.585	+	342.585i	0.791190	+	0.791190i	−0.190497	+	0.981688i	$0.561010\pi$
$434$	−203.738	+	117.628i	−0.469443	+	0.271033i
$435$	−6.57718	−	25.3551i	−0.0151200	−	0.0582876i
$436$	−22.7637	+	39.4278i	−0.0522103	+	0.0904308i
$437$	−178.772	−	667.186i	−0.409089	−	1.52674i
$438$	−613.640	+	231.601i	−1.40101	+	0.528769i
$439$	−407.092	+	235.035i	−0.927317	+	0.535387i	−0.885962	−	0.463758i	$-0.846501\pi$
$439$	−407.092	+	235.035i	−0.927317	+	0.535387i	−0.0413552	+	0.999145i	$0.513168\pi$
$440$	−227.963	+	589.696i	−0.518098	+	1.34022i
$441$	246.595	+	280.150i	0.559173	+	0.635260i
$442$	55.8673	−	55.8673i	0.126397	−	0.126397i
$443$	41.6735	−	155.528i	0.0940712	−	0.351078i	−0.902806	−	0.430048i	$-0.858496\pi$
$443$	41.6735	−	155.528i	0.0940712	−	0.351078i	0.996877	+	0.0789700i	$0.0251631\pi$
$444$	−1.38193	−	13.9002i	−0.00311245	−	0.0313068i
$445$	19.1252	−	177.919i	0.0429780	−	0.399817i
$446$	240.581	−	416.699i	0.539419	−	0.934302i
$447$	−93.1259	+	113.687i	−0.208335	+	0.254333i
$448$	−49.7859	+	185.804i	−0.111129	+	0.414740i
$449$		−	540.377i		−	1.20351i	−0.798680	−	0.601756i	$-0.794468\pi$
$449$		−	540.377i		−	1.20351i	0.798680	−	0.601756i	$-0.205532\pi$
$450$	−262.845	−	271.383i	−0.584099	−	0.603074i
$451$	−481.481			−1.06759
$452$	−206.808	−	55.4141i	−0.457540	−	0.122598i
$453$	286.849	−	108.263i	0.633220	−	0.238990i
$454$	277.702	+	160.331i	0.611678	+	0.353152i
$455$	80.1793	+	8.61880i	0.176218	+	0.0189424i
$456$	464.716	+	647.255i	1.01911	+	1.41942i
$457$	125.433	+	33.6098i	0.274471	+	0.0735444i	0.393429	−	0.919355i	$-0.371289\pi$
$457$	125.433	+	33.6098i	0.274471	+	0.0735444i	−0.118958	+	0.992899i	$0.537955\pi$
$458$	−355.319	−	355.319i	−0.775805	−	0.775805i
$459$	−63.3195	−	206.687i	−0.137951	−	0.450299i
$460$	124.546	+	48.1467i	0.270752	+	0.104667i
$461$	−383.986	−	665.083i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$461$	−383.986	−	665.083i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$462$	198.292	+	32.5513i	0.429203	+	0.0704573i
$463$	533.047	−	142.830i	1.15129	−	0.308487i	0.367808	−	0.929902i	$-0.380108\pi$
$463$	533.047	−	142.830i	1.15129	−	0.308487i	0.783482	+	0.621414i	$0.213442\pi$
$464$	14.9483	+	8.63040i	0.0322161	+	0.0186000i
$465$	−537.163	−	545.817i	−1.15519	−	1.17380i
$466$	−64.1388	−	111.092i	−0.137637	−	0.238394i
$467$	−118.969	+	118.969i	−0.254752	+	0.254752i	−0.822916	−	0.568163i	$-0.807654\pi$
$467$	−118.969	+	118.969i	−0.254752	+	0.254752i	0.568163	+	0.822916i	$0.307654\pi$
$468$	51.9819	+	34.5954i	0.111072	+	0.0739218i
$469$			175.701i			0.374629i
$470$	288.871	+	210.922i	0.614619	+	0.448770i
$471$	−407.817	+	40.5442i	−0.865854	+	0.0860811i
$472$	181.615	+	677.795i	0.384777	+	1.43601i
$473$	−556.073	+	148.999i	−1.17563	+	0.315009i
$474$	16.2225	+	163.175i	0.0342247	+	0.344252i
$475$	−162.233	+	745.893i	−0.341542	+	1.57030i
$476$	−25.9378			−0.0544911
$477$	26.9551	+	54.4077i	0.0565096	+	0.114062i
$478$	174.608	+	174.608i	0.365289	+	0.365289i
$479$	266.999	−	154.152i	0.557409	−	0.321820i	−0.194696	−	0.980864i	$-0.562372\pi$
$479$	266.999	−	154.152i	0.557409	−	0.321820i	0.752105	+	0.659043i	$0.229039\pi$
$480$	−272.962	−	2.18125i	−0.568672	−	0.00454428i
$481$	11.5902	−	20.0748i	0.0240960	−	0.0417355i
$482$	169.447	+	632.384i	0.351550	+	1.31200i
$483$	30.1696	−	183.783i	0.0624629	−	0.380503i
$484$	92.3133	−	53.2971i	0.190730	−	0.110118i
$485$	−288.233	−	111.425i	−0.594295	−	0.229741i
$486$	−358.963	+	193.992i	−0.738608	+	0.399160i
$487$	337.366	−	337.366i	0.692744	−	0.692744i	−0.270091	−	0.962835i	$-0.587054\pi$
$487$	337.366	−	337.366i	0.692744	−	0.692744i	0.962835	+	0.270091i	$0.0870538\pi$
$488$	−34.2931	+	127.984i	−0.0702728	+	0.262262i
$489$	519.034	−	372.655i	1.06142	−	0.762077i
$490$	−218.463	−	271.087i	−0.445843	−	0.553239i
$491$	57.4522	−	99.5101i	0.117011	−	0.202668i	−0.801571	−	0.597899i	$-0.796002\pi$
$491$	57.4522	−	99.5101i	0.117011	−	0.202668i	0.918582	+	0.395231i	$0.129336\pi$
$492$	−41.4227	−	109.752i	−0.0841924	−	0.223073i
$493$	−3.61861	+	13.5048i	−0.00733997	+	0.0273932i
$494$			301.312i			0.609943i
$495$	59.5085	+	651.406i	0.120219	+	1.31597i
$496$	504.630			1.01740
$497$	120.365	+	32.2518i	0.242184	+	0.0648929i
$498$	−26.9793	−	22.0999i	−0.0541752	−	0.0443774i
$499$	367.018	+	211.898i	0.735507	+	0.424645i	0.820433	−	0.571742i	$-0.193732\pi$
$499$	367.018	+	211.898i	0.735507	+	0.424645i	−0.0849264	+	0.996387i	$0.527066\pi$
$500$	−97.9604	−	110.359i	−0.195921	−	0.220719i
$501$	397.470	−	39.5155i	0.793354	−	0.0788733i
$502$	−388.321	−	104.050i	−0.773549	−	0.207272i
$503$	429.215	+	429.215i	0.853309	+	0.853309i	0.990539	−	0.137230i	$-0.0438199\pi$
$503$	429.215	+	429.215i	0.853309	+	0.853309i	−0.137230	+	0.990539i	$0.543820\pi$
$504$	42.3011	+	210.642i	0.0839307	+	0.417940i
$505$	−220.850	−	499.209i	−0.437327	−	0.988533i
$506$	276.075	+	478.177i	0.545604	+	0.945013i
$507$	−142.437	−	377.397i	−0.280941	−	0.744372i
$508$	−115.445	+	30.9335i	−0.227254	+	0.0608926i
$509$	−254.721	−	147.063i	−0.500435	−	0.288926i	0.228458	−	0.973554i	$-0.426632\pi$
$509$	−254.721	−	147.063i	−0.500435	−	0.288926i	−0.728893	+	0.684627i	$0.759965\pi$
$510$	50.6336	+	195.193i	0.0992816	+	0.382731i
$511$	178.659	+	309.447i	0.349627	+	0.605571i
$512$	370.382	−	370.382i	0.723403	−	0.723403i
$513$	728.121	+	386.617i	1.41934	+	0.753639i
$514$		−	40.6493i		−	0.0790843i
$515$	579.378	−	90.3615i	1.12501	−	0.175459i
$516$	−81.8038	−	113.936i	−0.158535	−	0.220807i
$517$	−160.280	−	598.173i	−0.310019	−	1.15701i
$518$	17.5558	−	4.70405i	0.0338914	−	0.00908118i
$519$	−400.397	−	180.975i	−0.771478	−	0.348700i
$520$	−206.441	−	150.735i	−0.397002	−	0.289875i
$521$	659.361			1.26557			0.632784	−	0.774328i	$-0.281912\pi$
$521$	659.361			1.26557			0.632784	+	0.774328i	$0.281912\pi$
$522$	26.3368	+	1.67769i	0.0504536	+	0.00321397i
$523$	−179.405	−	179.405i	−0.343031	−	0.343031i	0.514475	−	0.857506i	$-0.327987\pi$
$523$	−179.405	−	179.405i	−0.343031	−	0.343031i	−0.857506	+	0.514475i	$0.827987\pi$
$524$	191.566	−	110.601i	0.365584	−	0.211070i
$525$	−122.696	+	165.251i	−0.233707	+	0.314765i
$526$	−88.9526	+	154.070i	−0.169111	+	0.292910i
$527$	105.792	+	394.822i	0.200744	+	0.749188i
$528$	−333.444	−	273.139i	−0.631522	−	0.517308i
$529$	−14.9377	+	8.62427i	−0.0282376	+	0.0163030i
$530$	−22.9159	−	51.7990i	−0.0432375	−	0.0977339i
$531$	479.689	+	544.960i	0.903369	+	1.02629i
$532$	69.9457	−	69.9457i	0.131477	−	0.131477i
$533$	50.3836	−	188.034i	0.0945284	−	0.352785i
$534$	164.280	+	74.2530i	0.307641	+	0.139051i
$535$	−134.563	+	108.441i	−0.251520	+	0.202694i
$536$	278.467	−	482.319i	0.519528	−	0.899848i
$537$	−417.891	−	68.6004i	−0.778195	−	0.127747i
$538$	14.4981	−	54.1075i	0.0269481	−	0.100572i
$539$			602.790i			1.11835i
$540$	−143.366	+	69.6064i	−0.265493	+	0.128901i
$541$	−423.058			−0.781992			−0.390996	−	0.920392i	$-0.627869\pi$
$541$	−423.058			−0.781992			−0.390996	+	0.920392i	$0.627869\pi$
$542$	−144.703	−	38.7730i	−0.266980	−	0.0715370i
$543$	−88.5885	+	539.652i	−0.163146	+	0.993834i
$544$	126.179	+	72.8493i	0.231946	+	0.133914i
$545$	20.6091	−	191.723i	0.0378148	−	0.351785i
$546$	−33.4622	+	74.0332i	−0.0612861	+	0.135592i
$547$	−469.487	−	125.799i	−0.858294	−	0.229979i	−0.197275	−	0.980348i	$-0.563209\pi$
$547$	−469.487	−	125.799i	−0.858294	−	0.229979i	−0.661019	+	0.750369i	$0.729876\pi$
$548$	31.9070	+	31.9070i	0.0582244	+	0.0582244i
$549$	26.9909	+	134.403i	0.0491637	+	0.244815i
$550$	−29.0548	−	609.502i	−0.0528270	−	1.10819i
$551$	−26.6599	−	46.1763i	−0.0483846	−	0.0838046i
$552$	−374.095	+	456.689i	−0.677708	+	0.827335i
$553$	86.2893	−	23.1212i	0.156039	−	0.0418104i
$554$	138.441	+	79.9290i	0.249894	+	0.144276i
$555$	29.1714	+	51.4718i	0.0525610	+	0.0927420i
$556$	59.5686	+	103.176i	0.107138	+	0.185568i
$557$	−771.430	+	771.430i	−1.38497	+	1.38497i	−0.549440	+	0.835533i	$0.685159\pi$
$557$	−771.430	+	771.430i	−1.38497	+	1.38497i	−0.835533	+	0.549440i	$0.814841\pi$
$558$	691.341	−	342.509i	1.23896	−	0.613816i
$559$		−	232.757i		−	0.416380i
$560$	−20.9000	−	134.006i	−0.0373215	−	0.239297i
$561$	143.799	−	318.147i	0.256327	−	0.567108i
$562$	130.229	+	486.023i	0.231725	+	0.864809i
$563$	−368.486	+	98.7354i	−0.654504	+	0.175374i	−0.570764	−	0.821114i	$-0.693353\pi$
$563$	−368.486	+	98.7354i	−0.654504	+	0.175374i	−0.0837395	+	0.996488i	$0.526686\pi$
$564$	122.562	−	87.9972i	0.217309	−	0.156023i
$565$	895.987	−	139.741i	1.58582	−	0.247329i
$566$	−7.08778			−0.0125226
$567$	135.966	+	175.855i	0.239799	+	0.310149i
$568$	−279.300	−	279.300i	−0.491726	−	0.491726i
$569$	−466.672	+	269.433i	−0.820162	+	0.473521i	−0.850472	−	0.526020i	$-0.823684\pi$
$569$	−466.672	+	269.433i	−0.820162	+	0.473521i	0.0303100	+	0.999541i	$0.490351\pi$
$570$	−662.915	−	389.830i	−1.16301	−	0.683912i
$571$	−149.200	+	258.422i	−0.261296	+	0.452579i	−0.966587	−	0.256340i	$-0.917483\pi$
$571$	−149.200	+	258.422i	−0.261296	+	0.452579i	0.705290	+	0.708919i	$0.250817\pi$
$572$	26.1019	+	97.4135i	0.0456327	+	0.170303i
$573$	612.340	−	231.110i	1.06866	−	0.403333i
$574$	132.184	−	76.3166i	0.230286	−	0.132956i
$575$	−564.907	+	26.9290i	−0.982446	+	0.0468330i
$576$	201.683	−	597.739i	0.350144	−	1.03774i
$577$	−616.326	+	616.326i	−1.06816	+	1.06816i	−0.0706547	+	0.997501i	$0.522509\pi$
$577$	−616.326	+	616.326i	−1.06816	+	1.06816i	−0.997501	+	0.0706547i	$0.977491\pi$
$578$	−97.7394	+	364.768i	−0.169099	+	0.631087i
$579$	−65.2911	−	656.736i	−0.112765	−	1.13426i
$580$	10.2486	+	1.10166i	0.0176700	+	0.00189942i
$581$	−9.49974	+	16.4540i	−0.0163507	+	0.0283202i
$582$	197.286	−	240.844i	0.338979	−	0.413821i
$583$	−25.3817	+	94.7258i	−0.0435364	+	0.162480i
$584$		−	1132.62i		−	1.93942i
$585$	−260.623	−	44.9251i	−0.445509	−	0.0767950i
$586$	−192.675			−0.328796
$587$	64.2180	+	17.2072i	0.109400	+	0.0293137i	0.313104	−	0.949719i	$-0.398631\pi$
$587$	64.2180	+	17.2072i	0.109400	+	0.0293137i	−0.203704	+	0.979033i	$0.565298\pi$
$588$	−137.404	+	51.8591i	−0.233680	+	0.0881958i
$589$	−1349.99	−	779.420i	−2.29201	−	1.32329i
$590$	−424.965	−	527.331i	−0.720279	−	0.893781i
$591$	−598.546	−	833.654i	−1.01277	−	1.41058i
$592$	−37.6575	−	10.0903i	−0.0636107	−	0.0170444i
$593$	687.903	+	687.903i	1.16004	+	1.16004i	0.984467	+	0.175572i	$0.0561776\pi$
$593$	687.903	+	687.903i	1.16004	+	1.16004i	0.175572	+	0.984467i	$0.443822\pi$
$594$	−642.204	−	147.879i	−1.08115	−	0.248955i
$595$	100.465	−	44.4457i	0.168849	−	0.0746987i
$596$	−28.9148	−	50.0819i	−0.0485147	−	0.0840300i
$597$	375.210	+	61.5939i	0.628492	+	0.103172i
$598$	−215.633	+	57.7788i	−0.360591	+	0.0966200i
$599$	657.040	+	379.342i	1.09690	+	0.633293i	0.935404	−	0.353581i	$-0.115036\pi$
$599$	657.040	+	379.342i	1.09690	+	0.633293i	0.161492	+	0.986874i	$0.448370\pi$
$600$	598.720	−	259.173i	0.997866	−	0.431955i
$601$	−506.677	−	877.590i	−0.843057	−	1.46022i	−0.887298	−	0.461196i	$-0.847421\pi$
$601$	−506.677	−	877.590i	−0.843057	−	1.46022i	0.0442418	−	0.999021i	$-0.485913\pi$
$602$	129.045	−	129.045i	0.214361	−	0.214361i
$603$	36.6318	−	575.054i	0.0607492	−	0.953655i
$604$			120.649i			0.199750i
$605$	−266.230	+	364.620i	−0.440050	+	0.602677i
$606$	547.264	−	54.4076i	0.903076	−	0.0897816i
$607$	−7.81169	−	29.1536i	−0.0128693	−	0.0480290i	0.959193	−	0.282754i	$-0.0912479\pi$
$607$	−7.81169	−	29.1536i	−0.0128693	−	0.0480290i	−0.972062	+	0.234725i	$0.924581\pi$
$608$	−536.714	+	143.812i	−0.882753	+	0.236533i
$609$	−1.42231	−	14.3064i	−0.00233548	−	0.0234916i
$610$	−19.7065	−	126.354i	−0.0323058	−	0.207138i
$611$	250.379			0.409785
$612$	84.8919	+	5.40774i	0.138712	+	0.00883617i
$613$	−280.031	−	280.031i	−0.456820	−	0.456820i	0.440790	−	0.897610i	$-0.354698\pi$
$613$	−280.031	−	280.031i	−0.456820	−	0.456820i	−0.897610	+	0.440790i	$0.854698\pi$
$614$	−306.125	+	176.741i	−0.498575	+	0.287853i
$615$	348.508	+	354.123i	0.566680	+	0.575810i
$616$	−173.501	+	300.512i	−0.281657	+	0.487844i
$617$	137.725	+	513.997i	0.223217	+	0.833058i	0.983111	+	0.183011i	$0.0585843\pi$
$617$	137.725	+	513.997i	0.223217	+	0.833058i	−0.759894	+	0.650047i	$0.774749\pi$
$618$	−95.6987	+	582.965i	−0.154852	+	0.943308i
$619$	252.742	−	145.921i	0.408307	−	0.235736i	−0.281755	−	0.959486i	$-0.590916\pi$
$619$	252.742	−	145.921i	0.408307	−	0.235736i	0.690062	+	0.723750i	$0.257583\pi$
$620$	275.586	−	121.919i	0.444494	−	0.196644i
$621$	−137.059	+	595.216i	−0.220707	+	0.958479i
$622$	−41.3945	+	41.3945i	−0.0665507	+	0.0665507i
$623$	25.4198	−	94.8679i	0.0408022	−	0.152276i
$624$	141.562	−	101.639i	0.226863	−	0.162883i
$625$	568.538	+	259.596i	0.909660	+	0.415353i
$626$	141.352	−	244.829i	0.225802	−	0.391100i
$627$	470.161	+	1245.72i	0.749858	+	1.98679i
$628$	41.7397	−	155.775i	0.0664645	−	0.248049i
$629$		−	31.5785i		−	0.0502044i
$630$	−119.588	−	169.402i	−0.189822	−	0.268893i
$631$	872.307			1.38242			0.691210	−	0.722654i	$-0.257078\pi$
$631$	872.307			1.38242			0.691210	+	0.722654i	$0.257078\pi$
$632$	−273.518	−	73.2889i	−0.432782	−	0.115963i
$633$	486.466	+	398.486i	0.768508	+	0.629520i
$634$	−224.814	−	129.797i	−0.354597	−	0.204726i
$635$	394.149	−	317.636i	0.620707	−	0.500215i
$636$	−23.7761	+	2.36376i	−0.0373838	+	0.00371660i
$637$	−235.410	−	63.0779i	−0.369560	−	0.0990233i
$638$	30.1390	+	30.1390i	0.0472398	+	0.0472398i
$639$	−387.221	−	130.652i	−0.605979	−	0.204463i
$640$	−80.9574	+	209.421i	−0.126496	+	0.327220i
$641$	508.796	+	881.261i	0.793754	+	1.37482i	0.923627	+	0.383291i	$0.125209\pi$
$641$	508.796	+	881.261i	0.793754	+	1.37482i	−0.129874	+	0.991531i	$0.541457\pi$
$642$	−61.4805	−	162.896i	−0.0957640	−	0.253733i
$643$	306.101	−	82.0195i	0.476051	−	0.127558i	−0.0128120	−	0.999918i	$-0.504078\pi$
$643$	306.101	−	82.0195i	0.476051	−	0.127558i	0.488863	+	0.872360i	$0.337412\pi$
$644$	63.4692	+	36.6439i	0.0985546	+	0.0569005i
$645$	512.087	+	301.135i	0.793933	+	0.466876i
$646$	205.238	+	355.483i	0.317706	+	0.550283i
$647$	638.406	−	638.406i	0.986717	−	0.986717i	−0.0131963	−	0.999913i	$-0.504201\pi$
$647$	638.406	−	638.406i	0.986717	−	0.986717i	0.999913	+	0.0131963i	$0.00420064\pi$
$648$	−94.5311	−	698.230i	−0.145881	−	1.07752i
$649$			1172.58i			1.80674i
$650$	241.071	+	52.4333i	0.370879	+	0.0806667i
$651$	−245.139	−	341.430i	−0.376558	−	0.524470i
$652$	65.0761	+	242.867i	0.0998100	+	0.372496i
$653$	−629.363	+	168.637i	−0.963803	+	0.258250i	−0.706209	−	0.708003i	$-0.749596\pi$
$653$	−629.363	+	168.637i	−0.963803	+	0.258250i	−0.257593	+	0.966253i	$0.582930\pi$
$654$	177.026	+	80.0140i	0.270683	+	0.122346i
$655$	−552.474	+	756.648i	−0.843472	+	1.15519i
$656$	−327.401			−0.499088
$657$	−520.219	−	1050.04i	−0.791810	−	1.59823i
$658$	138.815	+	138.815i	0.210966	+	0.210966i
$659$	−434.653	+	250.947i	−0.659565	+	0.380800i	−0.792111	−	0.610377i	$-0.791018\pi$
$659$	−434.653	+	250.947i	−0.659565	+	0.380800i	0.132547	+	0.991177i	$0.457685\pi$
$660$	−248.089	−	68.6047i	−0.375893	−	0.103946i
$661$	484.464	−	839.117i	0.732926	−	1.26947i	−0.222701	−	0.974887i	$-0.571487\pi$
$661$	484.464	−	839.117i	0.732926	−	1.26947i	0.955627	−	0.294579i	$-0.0951793\pi$
$662$	64.8646	+	242.078i	0.0979828	+	0.365677i
$663$	109.200	+	89.4503i	0.164705	+	0.134918i
$664$	52.1556	−	30.1121i	0.0785476	−	0.0453495i
$665$	−151.066	+	390.777i	−0.227166	+	0.587634i
$666$	−58.4392	+	11.7358i	−0.0877465	+	0.0176213i
$667$	27.9338	−	27.9338i	0.0418798	−	0.0418798i
$668$	−40.6808	+	151.823i	−0.0608994	+	0.227279i
$669$	783.361	+	354.071i	1.17094	+	0.529254i
$670$	−57.4499	+	534.448i	−0.0857462	+	0.797683i
$671$	−110.705	+	191.746i	−0.164985	+	0.285762i
$672$	−147.843	−	24.2697i	−0.220005	−	0.0361157i
$673$	104.673	−	390.643i	0.155531	−	0.580450i	−0.843528	−	0.537085i	$-0.819525\pi$
$673$	104.673	−	390.643i	0.155531	−	0.580450i	0.999059	−	0.0433653i	$-0.0138079\pi$
$674$		−	115.348i		−	0.171140i
$675$	436.027	−	515.272i	0.645966	−	0.763366i
$676$	158.733			0.234813
$677$	122.427	+	32.8042i	0.180837	+	0.0484552i	0.348101	−	0.937457i	$-0.386827\pi$
$677$	122.427	+	32.8042i	0.180837	+	0.0484552i	−0.167264	+	0.985912i	$0.553493\pi$
$678$	−147.994	+	901.533i	−0.218281	+	1.32970i
$679$	−146.885	−	84.8041i	−0.216325	−	0.124896i
$680$	−346.229	−	37.2175i	−0.509160	−	0.0547316i
$681$	−235.964	+	522.058i	−0.346497	+	0.766605i
$682$	1203.65	+	322.517i	1.76488	+	0.472899i
$683$	−227.456	−	227.456i	−0.333025	−	0.333025i	0.520709	−	0.853734i	$-0.325668\pi$
$683$	−227.456	−	227.456i	−0.333025	−	0.333025i	−0.853734	+	0.520709i	$0.825668\pi$
$684$	−243.509	+	214.343i	−0.356007	+	0.313367i
$685$	−178.260	−	68.9112i	−0.260233	−	0.100600i
$686$	−208.441	−	361.030i	−0.303850	−	0.526283i
$687$	568.909	−	694.515i	0.828106	−	1.01094i
$688$	−378.123	+	101.318i	−0.549597	+	0.147264i
$689$	−34.3376	−	19.8248i	−0.0498368	−	0.0287733i
$690$	151.862	−	549.167i	0.220090	−	0.795894i
$691$	514.537	+	891.204i	0.744626	+	1.28973i	0.950369	+	0.311124i	$0.100706\pi$
$691$	514.537	+	891.204i	0.744626	+	1.28973i	−0.205743	+	0.978606i	$0.565961\pi$
$692$	122.263	−	122.263i	0.176681	−	0.176681i
$693$	−22.8236	+	358.291i	−0.0329346	+	0.517015i
$694$			34.2254i			0.0493162i
$695$	−407.524	−	297.558i	−0.586366	−	0.428141i
$696$	−18.7696	+	41.5268i	−0.0269679	+	0.0596649i
$697$	−68.6375	−	256.158i	−0.0984756	−	0.367516i
$698$	224.459	−	60.1436i	0.321575	−	0.0861657i
$699$	186.170	−	133.666i	0.266338	−	0.191225i
$700$	−43.7899	−	68.1334i	−0.0625571	−	0.0973335i
$701$	−921.196			−1.31412			−0.657058	−	0.753840i	$-0.728200\pi$
$701$	−921.196			−1.31412			−0.657058	+	0.753840i	$0.728200\pi$
$702$	124.954	−	235.328i	0.177997	−	0.335224i
$703$	85.1571	+	85.1571i	0.121134	+	0.121134i
$704$	882.380	−	509.443i	1.25338	−	0.723640i
$705$	−323.934	+	550.857i	−0.459481	+	0.781358i
$706$	−19.6324	+	34.0043i	−0.0278079	+	0.0481647i
$707$	−77.5447	−	289.401i	−0.109681	−	0.409336i
$708$	−267.285	+	100.879i	−0.377521	+	0.142484i
$709$	896.021	−	517.318i	1.26378	−	0.729645i	0.289977	−	0.957033i	$-0.406352\pi$
$709$	896.021	−	517.318i	1.26378	−	0.729645i	0.973804	+	0.227389i	$0.0730188\pi$
$710$	355.582	+	137.460i	0.500819	+	0.193606i
$711$	−287.238	+	57.6831i	−0.403991	+	0.0811295i
$712$	−220.135	+	220.135i	−0.309179	+	0.309179i
$713$	298.919	−	1115.58i	0.419242	−	1.56463i
$714$	10.9494	+	110.136i	0.0153354	+	0.154252i
$715$	−268.024	−	332.586i	−0.374858	−	0.465155i
$716$	83.3219	−	144.318i	0.116371	−	0.201561i
$717$	−279.569	+	341.294i	−0.389915	+	0.476002i
$718$	174.559	−	651.463i	0.243118	−	0.907330i
$719$			111.687i			0.155336i	0.996979	+	0.0776681i	$0.0247475\pi$
$719$			111.687i			0.155336i	−0.996979	+	0.0776681i	$0.975253\pi$
$720$	40.4651	+	442.948i	0.0562015	+	0.615206i
$721$	321.840			0.446380
$722$	−926.570	−	248.274i	−1.28334	−	0.343869i
$723$	−1094.35	+	413.031i	−1.51362	+	0.571273i
$724$	−186.368	−	107.600i	−0.257414	−	0.148618i
$725$	−41.5837	+	13.2944i	−0.0573568	+	0.0183371i
$726$	−265.277	−	369.478i	−0.365396	−	0.508923i
$727$	−1326.37	−	355.399i	−1.82444	−	0.488857i	−0.827120	−	0.562025i	$-0.810022\pi$
$727$	−1326.37	−	355.399i	−1.82444	−	0.488857i	−0.997320	+	0.0731679i	$0.976689\pi$
$728$	−99.2042	−	99.2042i	−0.136270	−	0.136270i
$729$	−408.340	−	603.903i	−0.560138	−	0.828400i
$730$	442.264	+	999.692i	0.605841	+	1.36944i
$731$	−158.542	−	274.602i	−0.216883	−	0.375653i
$732$	−53.2321	−	8.73851i	−0.0727214	−	0.0119379i
$733$	−370.352	+	99.2355i	−0.505255	+	0.135383i	−0.502438	−	0.864613i	$-0.667563\pi$
$733$	−370.352	+	99.2355i	−0.505255	+	0.135383i	−0.00281726	+	0.999996i	$0.500897\pi$
$734$	914.049	+	527.726i	1.24530	+	0.718973i
$735$	443.345	−	436.315i	0.603190	−	0.593626i
$736$	−205.838	−	356.521i	−0.279671	−	0.484404i
$737$	658.073	−	658.073i	0.892908	−	0.892908i
$738$	−448.538	+	222.218i	−0.607775	+	0.301109i
$739$			108.074i			0.146243i	0.997323	+	0.0731215i	$0.0232961\pi$
$739$			108.074i			0.146243i	−0.997323	+	0.0731215i	$0.976704\pi$
$740$	−23.0031	+	3.58764i	−0.0310853	+	0.00484816i
$741$	−535.694	+	53.2574i	−0.722934	+	0.0718724i
$742$	−8.04620	−	30.0288i	−0.0108439	−	0.0404701i
$743$	1095.25	−	293.471i	1.47409	−	0.394981i	0.569758	−	0.821812i	$-0.307037\pi$
$743$	1095.25	−	293.471i	1.47409	−	0.394981i	0.904331	+	0.426831i	$0.140370\pi$
$744$	131.806	+	1325.78i	0.177158	+	1.78196i
$745$	197.814	+	144.436i	0.265522	+	0.193873i
$746$	−627.315			−0.840905
$747$	34.5223	−	51.8720i	0.0462146	−	0.0694404i
$748$	97.1476	+	97.1476i	0.129876	+	0.129876i
$749$	−82.1455	+	47.4267i	−0.109673	+	0.0633200i
$750$	−427.251	+	462.543i	−0.569668	+	0.616724i
$751$	123.908	−	214.615i	0.164991	−	0.285773i	−0.771661	−	0.636034i	$-0.780574\pi$
$751$	123.908	−	214.615i	0.164991	−	0.285773i	0.936652	+	0.350261i	$0.113907\pi$
$752$	−108.989	−	406.751i	−0.144932	−	0.540892i
$753$	116.352	−	708.778i	0.154518	−	0.941272i
$754$	−14.9241	+	8.61644i	−0.0197933	+	0.0114276i
$755$	−206.738	−	467.310i	−0.273825	−	0.618954i
$756$	−83.6348	+	25.6219i	−0.110628	+	0.0338913i
$757$	794.781	−	794.781i	1.04991	−	1.04991i	0.0512222	−	0.998687i	$-0.483688\pi$
$757$	794.781	−	794.781i	1.04991	−	1.04991i	0.998687	−	0.0512222i	$-0.0163117\pi$
$758$	97.2598	−	362.978i	0.128311	−	0.478863i
$759$	−801.341	+	575.346i	−1.05579	+	0.758032i
$760$	1034.03	−	833.303i	1.36057	−	1.09645i
$761$	−735.111	+	1273.25i	−0.965980	+	1.67313i	−0.259021	+	0.965872i	$0.583400\pi$
$761$	−735.111	+	1273.25i	−0.965980	+	1.67313i	−0.706959	+	0.707255i	$0.749933\pi$
$762$	180.083	+	477.141i	0.236329	+	0.626169i
$763$	27.3920	−	102.228i	0.0359004	−	0.133982i
$764$			257.551i			0.337109i
$765$	−338.079	+	124.521i	−0.441933	+	0.162772i
$766$	59.7308			0.0779776
$767$	−457.930	−	122.702i	−0.597040	−	0.159976i
$768$	475.702	+	389.669i	0.619403	+	0.507381i
$769$	−330.109	−	190.589i	−0.429271	−	0.247840i	0.269765	−	0.962926i	$-0.413054\pi$
$769$	−330.109	−	190.589i	−0.429271	−	0.247840i	−0.699036	+	0.715087i	$0.746387\pi$
$770$	35.7945	−	332.991i	0.0464864	−	0.432456i
$771$	72.2694	−	7.18485i	0.0937346	−	0.00931887i
$772$	250.855	+	67.2163i	0.324941	+	0.0870678i
$773$	−325.772	−	325.772i	−0.421438	−	0.421438i	0.464260	−	0.885699i	$-0.346320\pi$
$773$	−325.772	−	325.772i	−0.421438	−	0.421438i	−0.885699	+	0.464260i	$0.846320\pi$
$774$	−449.259	+	395.449i	−0.580437	+	0.510917i
$775$	−858.515	+	944.462i	−1.10776	+	1.21866i
$776$	268.810	+	465.593i	0.346405	+	0.599991i
$777$	11.4662	+	30.3805i	0.0147571	+	0.0390997i
$778$	−337.673	+	90.4793i	−0.434028	+	0.116297i
$779$	875.869	+	505.683i	1.12435	+	0.649144i
$780$	52.7532	−	89.7081i	0.0676323	−	0.115010i
$781$	−330.021	−	571.614i	−0.422563	−	0.731900i
$782$	−215.045	+	215.045i	−0.274993	+	0.274993i
$783$	1.67236	+	47.1201i	0.00213583	+	0.0601789i
$784$			409.891i			0.522820i
$785$	105.257	+	674.887i	0.134086	+	0.859729i
$786$	−550.496	−	766.730i	−0.700377	−	0.975484i
$787$	−90.6626	−	338.358i	−0.115200	−	0.429933i	0.884102	−	0.467295i	$-0.154771\pi$
$787$	−90.6626	−	338.358i	−0.115200	−	0.429933i	−0.999302	+	0.0373615i	$0.988105\pi$
$788$	390.085	−	104.523i	0.495032	−	0.132643i
$789$	−289.640	−	130.914i	−0.367098	−	0.165924i
$790$	270.035	−	42.1154i	0.341816	−	0.0533107i
$791$	497.714			0.629221
$792$	630.505	−	947.375i	0.796092	−	1.19618i
$793$	−63.2989	−	63.2989i	−0.0798220	−	0.0798220i
$794$	477.017	−	275.406i	0.600776	−	0.346858i
$795$	88.0416	−	49.8971i	0.110744	−	0.0627636i
$796$	−74.8119	+	129.578i	−0.0939848	+	0.162787i
$797$	−32.4527	−	121.115i	−0.0407186	−	0.151964i	0.942573	−	0.333999i	$-0.108398\pi$
$797$	−32.4527	−	121.115i	−0.0407186	−	0.151964i	−0.983292	+	0.182035i	$0.941732\pi$
$798$	−326.528	−	267.474i	−0.409183	−	0.335180i
$799$	295.393	−	170.545i	0.369703	−	0.213448i
$800$	21.6629	+	454.436i	0.0270786	+	0.568045i
$801$	−102.976	+	305.194i	−0.128559	+	0.381017i
$802$	111.680	−	111.680i	0.139252	−	0.139252i
$803$	489.853	−	1828.16i	0.610029	−	2.27666i
$804$	206.621	+	93.3904i	0.256991	+	0.116157i
$805$	−308.627	−	33.1756i	−0.383388	−	0.0412119i
$806$	−251.907	+	436.316i	−0.312540	+	0.541335i
$807$	98.7590	+	16.2121i	0.122378	+	0.0200894i
$808$	−245.799	+	917.336i	−0.304207	+	1.13532i
$809$		−	717.779i		−	0.887242i	−0.896214	−	0.443621i	$-0.853694\pi$
$809$		−	717.779i		−	0.887242i	0.896214	−	0.443621i	$-0.146306\pi$
$810$	356.081	+	579.372i	0.439606	+	0.715274i
$811$	771.312			0.951063			0.475532	−	0.879699i	$-0.342256\pi$
$811$	771.312			0.951063			0.475532	+	0.879699i	$0.342256\pi$
$812$	5.46464	+	1.46425i	0.00672986	+	0.00180326i
$813$	43.3571	−	264.117i	0.0533297	−	0.324867i
$814$	−83.3722	−	48.1350i	−0.102423	−	0.0591339i
$815$	−668.225	−	829.189i	−0.819909	−	1.01741i
$816$	97.7818	−	216.337i	0.119831	−	0.265118i
$817$	1168.05	+	312.978i	1.42968	+	0.383082i
$818$	809.931	+	809.931i	0.990136	+	0.990136i
$819$	−137.536	−	46.4061i	−0.167932	−	0.0566619i
$820$	−178.799	+	79.1006i	−0.218047	+	0.0964641i
$821$	303.667	+	525.966i	0.369874	+	0.640641i	0.989546	−	0.144220i	$-0.0460674\pi$
$821$	303.667	+	525.966i	0.369874	+	0.640641i	−0.619671	+	0.784861i	$0.712734\pi$
$822$	122.013	−	148.951i	0.148434	−	0.181206i
$823$	−528.599	+	141.638i	−0.642283	+	0.172099i	−0.565237	−	0.824928i	$-0.691215\pi$
$823$	−528.599	+	141.638i	−0.642283	+	0.172099i	−0.0770455	+	0.997028i	$0.524549\pi$
$824$	−883.485	−	510.080i	−1.07219	−	0.619029i
$825$	1078.48	−	159.387i	1.30725	−	0.193196i
$826$	−185.858	−	321.915i	−0.225009	−	0.389728i
$827$	−54.4673	+	54.4673i	−0.0658613	+	0.0658613i	−0.739270	−	0.673409i	$-0.764829\pi$
$827$	−54.4673	+	54.4673i	−0.0658613	+	0.0658613i	0.673409	+	0.739270i	$0.264829\pi$
$828$	−200.089	−	133.165i	−0.241653	−	0.160827i
$829$		−	533.549i		−	0.643605i	−0.946807	−	0.321803i	$-0.895711\pi$
$829$		−	533.549i		−	0.643605i	0.946807	−	0.321803i	$-0.104289\pi$
$830$	−34.2764	+	46.9437i	−0.0412968	+	0.0565587i
$831$	−117.634	+	260.259i	−0.141557	+	0.313187i
$832$	106.619	+	397.909i	0.128148	+	0.478256i
$833$	−320.698	+	85.9307i	−0.384991	+	0.103158i
$834$	412.954	−	296.493i	0.495149	−	0.355507i
$835$	−102.587	−	657.765i	−0.122859	−	0.787742i
$836$	−523.951			−0.626736
$837$	731.135	+	1168.58i	0.873518	+	1.39615i
$838$	−249.041	−	249.041i	−0.297185	−	0.297185i
$839$	−1319.75	+	761.957i	−1.57300	+	0.908173i	−0.577204	+	0.816600i	$0.695856\pi$
$839$	−1319.75	+	761.957i	−1.57300	+	0.908173i	−0.995798	+	0.0915732i	$0.970810\pi$
$840$	346.607	−	89.9107i	0.412627	−	0.107037i
$841$	−418.975	+	725.686i	−0.498187	+	0.862885i
$842$	2.56256	+	9.56361i	0.00304342	+	0.0113582i
$843$	−841.069	+	317.437i	−0.997710	+	0.376556i
$844$	−214.301	+	123.727i	−0.253911	+	0.146595i
$845$	−614.823	+	271.998i	−0.727601	+	0.321891i
$846$	−425.389	−	483.272i	−0.502824	−	0.571244i
$847$	−175.216	+	175.216i	−0.206867	+	0.206867i
$848$	−17.2593	+	64.4125i	−0.0203529	+	0.0759581i
$849$	−1.25278	−	12.6012i	−0.00147559	−	0.0148424i
$850$	320.127	−	102.345i	0.376620	−	0.120406i
$851$	−44.6131	+	77.2721i	−0.0524243	+	0.0908015i
$852$	101.905	−	124.404i	0.119607	−	0.146014i
$853$	−188.905	+	705.002i	−0.221459	+	0.826497i	0.762333	+	0.647185i	$0.224054\pi$
$853$	−188.905	+	705.002i	−0.221459	+	0.826497i	−0.983792	+	0.179312i	$0.942613\pi$
$854$		−	70.1886i		−	0.0821880i
$855$	575.897	−	1247.48i	0.673564	−	1.45904i
$856$	300.664			0.351243
$857$	1160.15	+	310.861i	1.35373	+	0.362731i	0.861511	−	0.507739i	$-0.169518\pi$
$857$	1160.15	+	310.861i	1.35373	+	0.362731i	0.492221	+	0.870470i	$0.336185\pi$
$858$	402.615	−	151.955i	0.469248	−	0.177104i
$859$	987.915	+	570.373i	1.15008	+	0.663996i	0.948906	−	0.315560i	$-0.102192\pi$
$859$	987.915	+	570.373i	1.15008	+	0.663996i	0.201170	+	0.979556i	$0.435526\pi$
$860$	−182.020	+	146.686i	−0.211651	+	0.170565i
$861$	159.045	+	221.518i	0.184721	+	0.257280i
$862$	−1011.47	−	271.022i	−1.17340	−	0.314410i
$863$	1189.86	+	1189.86i	1.37874	+	1.37874i	0.846744	+	0.532000i	$0.178559\pi$
$863$	1189.86	+	1189.86i	1.37874	+	1.37874i	0.532000	+	0.846744i	$0.321441\pi$
$864$	478.818	+	110.256i	0.554187	+	0.127612i
$865$	−264.058	+	683.066i	−0.305269	+	0.789671i
$866$	406.760	+	704.529i	0.469700	+	0.813544i
$867$	−665.788	−	109.295i	−0.767922	−	0.126061i
$868$	159.762	−	42.8082i	0.184058	−	0.0493182i
$869$	−409.787	−	236.591i	−0.471562	−	0.272256i
$870$	0.351464	−	43.9822i	0.000403981	−	0.0505543i
$871$	188.137	+	325.862i	0.216001	+	0.374125i
$872$	−237.215	+	237.215i	−0.272035	+	0.272035i
$873$	463.061	+	308.180i	0.530424	+	0.353013i
$874$		−	1159.81i		−	1.32702i
$875$	286.362	+	188.865i	0.327271	+	0.215846i
$876$	458.865	−	45.6193i	0.523819	−	0.0520768i
$877$	375.154	+	1400.09i	0.427769	+	1.59646i	0.757800	+	0.652487i	$0.226274\pi$
$877$	375.154	+	1400.09i	0.427769	+	1.59646i	−0.330031	+	0.943970i	$0.607059\pi$
$878$	−762.413	+	204.288i	−0.868352	+	0.232674i
$879$	−34.0556	−	342.551i	−0.0387436	−	0.389706i
$880$	−423.630	+	580.189i	−0.481398	+	0.659305i
$881$	127.177			0.144355			0.0721777	−	0.997392i	$-0.477005\pi$
$881$	127.177			0.144355			0.0721777	+	0.997392i	$0.477005\pi$
$882$	278.206	+	561.548i	0.315427	+	0.636675i
$883$	−363.077	−	363.077i	−0.411186	−	0.411186i	0.470966	−	0.882151i	$-0.343905\pi$
$883$	−363.077	−	363.077i	−0.411186	−	0.411186i	−0.882151	+	0.470966i	$0.843905\pi$
$884$	−48.1052	+	27.7736i	−0.0544177	+	0.0314181i
$885$	862.415	−	848.741i	0.974480	−	0.959029i
$886$	135.182	−	234.142i	0.152575	−	0.264268i
$887$	−399.719	−	1491.77i	−0.450642	−	1.68182i	−0.700594	−	0.713560i	$-0.747082\pi$
$887$	−399.719	−	1491.77i	−0.450642	−	1.68182i	0.249952	−	0.968258i	$-0.419585\pi$
$888$	16.6737	−	101.570i	0.0187766	−	0.114381i
$889$	240.613	−	138.918i	0.270655	−	0.156263i
$890$	108.341	−	280.258i	0.121732	−	0.314896i
$891$	149.399	−	1167.90i	0.167676	−	1.31077i
$892$	−239.202	+	239.202i	−0.268164	+	0.268164i
$893$	−336.674	+	1256.48i	−0.377014	+	1.40704i
$894$	−200.449	+	143.919i	−0.224216	+	0.160983i
$895$	−75.4354	+	701.764i	−0.0842854	+	0.784094i
$896$	−61.6158	+	106.722i	−0.0687677	+	0.119109i
$897$	−140.837	−	373.157i	−0.157009	−	0.416005i
$898$	234.843	−	876.446i	0.261518	−	0.975997i
$899$		−	89.1545i		−	0.0991708i
$900$	129.115	+	232.124i	0.143462	+	0.257916i
$901$	−54.0145			−0.0599495
$902$	−780.921	−	209.247i	−0.865766	−	0.231981i
$903$	252.236	+	206.617i	0.279331	+	0.228812i
$904$	−1366.28	−	788.821i	−1.51137	−	0.872589i
$905$	906.237	+	97.4151i	1.00137	+	0.107641i
$906$	512.294	−	50.9310i	0.565446	−	0.0562153i
$907$	332.129	+	88.9936i	0.366184	+	0.0981186i	0.437219	−	0.899355i	$-0.355964\pi$
$907$	332.129	+	88.9936i	0.366184	+	0.0981186i	−0.0710351	+	0.997474i	$0.522630\pi$
$908$	−159.412	−	159.412i	−0.175564	−	0.175564i
$909$	193.460	+	963.350i	0.212827	+	1.05979i
$910$	126.298	+	48.8242i	0.138790	+	0.0536530i
$911$	−9.64078	−	16.6983i	−0.0105826	−	0.0183297i	0.860686	−	0.509137i	$-0.170035\pi$
$911$	−9.64078	−	16.6983i	−0.0105826	−	0.0183297i	−0.871268	+	0.490807i	$0.836702\pi$
$912$	319.704	+	847.076i	0.350553	+	0.928811i
$913$	97.2076	−	26.0467i	0.106471	−	0.0285287i
$914$	188.836	+	109.024i	0.206604	+	0.119283i
$915$	221.158	−	57.3690i	0.241703	−	0.0626984i
$916$	176.641	+	305.952i	0.192840	+	0.334008i
$917$	−363.604	+	363.604i	−0.396514	+	0.396514i
$918$	−12.8744	−	362.748i	−0.0140244	−	0.395150i
$919$		−	947.679i		−	1.03121i	−0.856827	−	0.515603i	$-0.827568\pi$
$919$		−	947.679i		−	1.03121i	0.856827	−	0.515603i	$-0.172432\pi$
$920$	794.635	+	580.210i	0.863733	+	0.630663i
$921$	−368.332	−	513.013i	−0.399927	−	0.557017i
$922$	−333.753	−	1245.58i	−0.361988	−	1.35096i
$923$	257.769	−	69.0689i	0.279273	−	0.0748309i
$924$	−128.736	−	58.1875i	−0.139325	−	0.0629734i
$925$	82.9507	−	53.3131i	0.0896764	−	0.0576358i
$926$	926.630			1.00068
$927$	−1053.35	−	67.1001i	−1.13630	−	0.0723841i
$928$	−22.4712	−	22.4712i	−0.0242146	−	0.0242146i
$929$	−216.919	+	125.239i	−0.233498	+	0.134810i	−0.612185	−	0.790715i	$-0.709709\pi$
$929$	−216.919	+	125.239i	−0.233498	+	0.134810i	0.378687	+	0.925525i	$0.376376\pi$
$930$	−634.026	−	1118.72i	−0.681748	−	1.20292i
$931$	633.091	−	1096.55i	0.680012	−	1.17781i
$932$	23.3419	+	87.1132i	0.0250450	+	0.0934691i
$933$	−80.9108	−	66.2777i	−0.0867211	−	0.0710372i
$934$	−244.661	+	141.255i	−0.261950	+	0.151237i
$935$	−542.750	−	209.815i	−0.580481	−	0.224401i
$936$	304.003	+	345.369i	0.324790	+	0.368984i
$937$	−773.708	+	773.708i	−0.825729	+	0.825729i	−0.986923	−	0.161194i	$-0.948466\pi$
$937$	−773.708	+	773.708i	−0.825729	+	0.825729i	0.161194	+	0.986923i	$0.448466\pi$
$938$	−76.3581	+	284.972i	−0.0814053	+	0.303809i
$939$	460.259	+	208.032i	0.490158	+	0.221546i
$940$	−157.792	−	195.801i	−0.167864	−	0.208299i
$941$	711.412	−	1232.20i	0.756017	−	1.30946i	−0.188850	−	0.982006i	$-0.560476\pi$
$941$	711.412	−	1232.20i	0.756017	−	1.30946i	0.944867	−	0.327454i	$-0.106191\pi$
$942$	−679.065	−	111.474i	−0.720876	−	0.118338i
$943$	−193.937	+	723.783i	−0.205660	+	0.767533i
$944$			797.338i			0.844638i
$945$	280.039	−	242.554i	0.296338	−	0.256671i
$946$	−966.657			−1.02184
$947$	974.990	+	261.248i	1.02956	+	0.275869i	0.733779	−	0.679388i	$-0.237755\pi$
$947$	974.990	+	261.248i	1.02956	+	0.275869i	0.295778	+	0.955257i	$0.404421\pi$
$948$	18.6753	−	113.764i	0.0196997	−	0.120004i
$949$	662.697	+	382.608i	0.698311	+	0.403170i
$950$	−587.286	+	1139.27i	−0.618196	+	1.19923i
$951$	191.026	−	422.633i	0.200868	−	0.444409i
$952$	−184.612	−	49.4667i	−0.193920	−	0.0519608i
$953$	−1340.68	−	1340.68i	−1.40680	−	1.40680i	−0.775700	−	0.631102i	$-0.782603\pi$
$953$	−1340.68	−	1340.68i	−1.40680	−	1.40680i	−0.631102	−	0.775700i	$-0.717397\pi$
$954$	20.0738	+	99.9591i	0.0210417	+	0.104779i
$955$	−441.327	−	997.574i	−0.462122	−	1.04458i
$956$	−86.8038	−	150.349i	−0.0907989	−	0.157268i
$957$	−48.2562	+	58.9105i	−0.0504245	+	0.0615574i
$958$	500.043	−	133.986i	0.521966	−	0.139860i
$959$	−90.8420	−	52.4476i	−0.0947257	−	0.0546899i
$960$	−1013.38	−	280.232i	−1.05560	−	0.291908i
$961$	−822.745	−	1425.04i	−0.856134	−	1.48287i
$962$	27.5226	−	27.5226i	0.0286098	−	0.0286098i
$963$	278.743	−	138.097i	0.289452	−	0.143403i
$964$		−	460.285i		−	0.477474i
$965$	−1086.82	+	169.503i	−1.12623	+	0.175651i
$966$	128.803	−	284.969i	0.133336	−	0.294999i
$967$	224.840	+	839.114i	0.232513	+	0.867750i	0.979254	+	0.202635i	$0.0649506\pi$
$967$	224.840	+	839.114i	0.232513	+	0.867750i	−0.746741	+	0.665114i	$0.768383\pi$
$968$	758.685	−	203.289i	0.783766	−	0.210009i
$969$	−595.727	+	427.720i	−0.614785	+	0.441403i
$970$	−419.066	−	305.985i	−0.432027	−	0.315448i
$971$	−35.3368			−0.0363922			−0.0181961	−	0.999834i	$-0.505792\pi$
$971$	−35.3368			−0.0363922			−0.0181961	+	0.999834i	$0.505792\pi$
$972$	279.071	−	66.4211i	0.287110	−	0.0683345i
$973$	−195.834	−	195.834i	−0.201268	−	0.201268i
$974$	693.796	−	400.563i	0.712316	−	0.411256i
$975$	−50.6100	+	437.862i	−0.0519077	+	0.449090i
$976$	−75.2780	+	130.385i	−0.0771291	+	0.133592i
$977$	181.759	+	678.332i	0.186037	+	0.694301i	0.994406	+	0.105625i	$0.0336842\pi$
$977$	181.759	+	678.332i	0.186037	+	0.694301i	−0.808369	+	0.588677i	$0.799649\pi$
$978$	1003.78	−	378.848i	1.02636	−	0.387370i
$979$	−450.527	+	260.112i	−0.460191	+	0.265691i
$980$	99.0301	+	223.847i	0.101051	+	0.228416i
$981$	−110.965	+	328.873i	−0.113114	+	0.335243i
$982$	136.429	−	136.429i	0.138929	−	0.138929i
$983$	−10.8240	+	40.3956i	−0.0110112	+	0.0410942i	−0.971213	−	0.238213i	$-0.923438\pi$
$983$	−10.8240	+	40.3956i	−0.0110112	+	0.0410942i	0.960202	+	0.279308i	$0.0901049\pi$
$984$	−85.5149	−	860.159i	−0.0869054	−	0.874145i
$985$	−1331.81	+	1073.28i	−1.35209	+	1.08962i
$986$	−11.7381	+	20.3311i	−0.0119048	+	0.0206197i
$987$	−222.261	+	271.332i	−0.225188	+	0.274906i
$988$	54.8279	−	204.620i	0.0554938	−	0.207106i
$989$			895.929i			0.905894i
$990$	−186.577	+	1082.39i	−0.188462	+	1.09332i
$991$	805.965			0.813284			0.406642	−	0.913588i	$-0.366700\pi$
$991$	805.965			0.813284			0.406642	+	0.913588i	$0.366700\pi$
$992$	−897.423	−	240.464i	−0.904660	−	0.242403i
$993$	−418.919	+	158.109i	−0.421873	+	0.159223i
$994$	181.206	+	104.619i	0.182300	+	0.105251i
$995$	67.7309	−	630.090i	0.0680712	−	0.633256i
$996$	14.3002	+	19.9173i	0.0143576	+	0.0199973i
$997$	−204.376	−	54.7624i	−0.204991	−	0.0549271i	0.154862	−	0.987936i	$-0.450507\pi$
$997$	−204.376	−	54.7624i	−0.204991	−	0.0549271i	−0.359853	+	0.933009i	$0.617173\pi$
$998$	503.183	+	503.183i	0.504192	+	0.504192i
$999$	−31.1939	−	101.823i	−0.0312252	−	0.101925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.13.7	yes	40
3.2	odd	2		135.3.l.a.118.4		40
5.2	odd	4	inner	45.3.k.a.22.4	yes	40
5.3	odd	4		225.3.o.b.157.7		40
5.4	even	2		225.3.o.b.193.4		40
9.2	odd	6		135.3.l.a.73.7		40
9.4	even	3		405.3.g.h.163.4		20
9.5	odd	6		405.3.g.g.163.7		20
9.7	even	3	inner	45.3.k.a.43.4	yes	40
15.2	even	4		135.3.l.a.37.7		40
45.2	even	12		135.3.l.a.127.4		40
45.7	odd	12	inner	45.3.k.a.7.7	✓	40
45.22	odd	12		405.3.g.h.82.4		20
45.32	even	12		405.3.g.g.82.7		20
45.34	even	6		225.3.o.b.43.7		40
45.43	odd	12		225.3.o.b.7.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.7	✓	40	45.7	odd	12	inner
45.3.k.a.13.7	yes	40	1.1	even	1	trivial
45.3.k.a.22.4	yes	40	5.2	odd	4	inner
45.3.k.a.43.4	yes	40	9.7	even	3	inner
135.3.l.a.37.7		40	15.2	even	4
135.3.l.a.73.7		40	9.2	odd	6
135.3.l.a.118.4		40	3.2	odd	2
135.3.l.a.127.4		40	45.2	even	12
225.3.o.b.7.4		40	45.43	odd	12
225.3.o.b.43.7		40	45.34	even	6
225.3.o.b.157.7		40	5.3	odd	4
225.3.o.b.193.4		40	5.4	even	2
405.3.g.g.82.7		20	45.32	even	12
405.3.g.g.163.7		20	9.5	odd	6
405.3.g.h.82.4		20	45.22	odd	12
405.3.g.h.163.4		20	9.4	even	3

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.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62192 + 0.434591i) q^{2} +(-0.485971 + 2.96038i) q^{3} +(-1.02236 - 0.590260i) q^{4} +(4.97136 + 0.534392i) q^{5} +(-2.07476 + 4.59028i) q^{6} +(2.65078 + 0.710273i) q^{7} +(-6.15096 - 6.15096i) q^{8} +(-8.52766 - 2.87732i) q^{9} +(7.83089 + 3.02725i) q^{10} +(-7.26798 - 12.5885i) q^{11} +(2.24423 - 2.73972i) q^{12} +(5.67678 - 1.52109i) q^{13} +(3.99065 + 2.30401i) q^{14} +(-3.99794 + 14.4574i) q^{15} +(-4.94214 - 8.56004i) q^{16} +(5.66128 - 5.66128i) q^{17} +(-12.5807 - 8.37281i) q^{18} +30.5333i q^{19} +(-4.76709 - 3.48074i) q^{20} +(-3.39088 + 7.50212i) q^{21} +(-6.31720 - 23.5761i) q^{22} +(-21.8511 + 5.85498i) q^{23} +(21.1983 - 15.2200i) q^{24} +(24.4289 + 5.31331i) q^{25} +9.86831 q^{26} +(12.6621 - 23.8468i) q^{27} +(-2.29080 - 2.29080i) q^{28} +(-1.51233 + 0.873143i) q^{29} +(-12.7674 + 21.7112i) q^{30} +(-25.5269 + 44.2139i) q^{31} +(4.71001 + 17.5780i) q^{32} +(40.7988 - 15.3983i) q^{33} +(11.6425 - 6.72178i) q^{34} +(12.7984 + 4.94758i) q^{35} +(7.01998 + 7.97520i) q^{36} +(2.78899 - 2.78899i) q^{37} +(-13.2695 + 49.5224i) q^{38} +(1.74424 + 17.5446i) q^{39} +(-27.2916 - 33.8657i) q^{40} +(16.5617 - 28.6857i) q^{41} +(-8.76007 + 10.6942i) q^{42} +(10.2504 - 38.2550i) q^{43} +17.1600i q^{44} +(-40.8565 - 18.8613i) q^{45} -37.9852 q^{46} +(41.1513 + 11.0264i) q^{47} +(27.7427 - 10.4707i) q^{48} +(-35.9131 - 20.7345i) q^{49} +(37.3124 + 19.2343i) q^{50} +(14.0083 + 19.5107i) q^{51} +(-6.70155 - 1.79568i) q^{52} +(-4.77052 - 4.77052i) q^{53} +(30.9005 - 33.1747i) q^{54} +(-29.4046 - 66.4660i) q^{55} +(-11.9359 - 20.6737i) q^{56} +(-90.3900 - 14.8383i) q^{57} +(-2.83233 + 0.758920i) q^{58} +(-69.8599 - 40.3336i) q^{59} +(12.6210 - 12.4209i) q^{60} +(-7.61593 - 13.1912i) q^{61} +(-60.6174 + 60.6174i) q^{62} +(-20.5612 - 13.6841i) q^{63} +70.0941i q^{64} +(29.0342 - 4.52826i) q^{65} +(72.8641 - 7.24398i) q^{66} +(16.5707 + 61.8428i) q^{67} +(-9.12950 + 2.44624i) q^{68} +(-6.71395 - 67.5329i) q^{69} +(18.6077 + 13.5866i) q^{70} +45.4076 q^{71} +(34.7551 + 70.1516i) q^{72} +(92.0685 + 92.0685i) q^{73} +(5.73558 - 3.31144i) q^{74} +(-27.6011 + 69.7365i) q^{75} +(18.0226 - 31.2160i) q^{76} +(-10.3245 - 38.5316i) q^{77} +(-4.79571 + 29.2139i) q^{78} +(28.1913 - 16.2762i) q^{79} +(-19.9948 - 45.1961i) q^{80} +(64.4421 + 49.0736i) q^{81} +(39.3283 - 39.3283i) q^{82} +(-1.79188 + 6.68739i) q^{83} +(7.89490 - 5.66838i) q^{84} +(31.1696 - 25.1189i) q^{85} +(33.2505 - 57.5916i) q^{86} +(-1.84988 - 4.90138i) q^{87} +(-32.7264 + 122.136i) q^{88} -35.7887i q^{89} +(-58.0688 - 48.3473i) q^{90} +16.1283 q^{91} +(25.7957 + 6.91193i) q^{92} +(-118.484 - 97.0559i) q^{93} +(61.9519 + 35.7679i) q^{94} +(-16.3167 + 151.792i) q^{95} +(-54.3264 + 5.40100i) q^{96} +(-59.6982 - 15.9961i) q^{97} +(-49.2370 - 49.2370i) q^{98} +(25.7578 + 128.263i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

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