LMFDB - Embedded newform 126.3.r.a.11.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(11,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.11"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.r (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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	126.11
Dual form			126.3.r.a.23.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.41421i q^{2} +(2.25313 + 1.98076i) q^{3} -2.00000 q^{4} +(2.56482 + 1.48080i) q^{5} +(-2.80121 + 3.18641i) q^{6} +(6.84216 - 1.47812i) q^{7} -2.82843i q^{8} +(1.15321 + 8.92581i) q^{9} +(-2.09417 + 3.62721i) q^{10} +(-9.06593 + 5.23422i) q^{11} +(-4.50626 - 3.96151i) q^{12} +(-1.61224 - 2.79249i) q^{13} +(2.09038 + 9.67628i) q^{14} +(2.84578 + 8.41673i) q^{15} +4.00000 q^{16} +(-4.26829 - 2.46430i) q^{17} +(-12.6230 + 1.63089i) q^{18} +(-10.3079 - 17.8539i) q^{19} +(-5.12965 - 2.96160i) q^{20} +(18.3441 + 10.2222i) q^{21} +(-7.40230 - 12.8212i) q^{22} +(12.7844 + 7.38107i) q^{23} +(5.60242 - 6.37282i) q^{24} +(-8.11446 - 14.0547i) q^{25} +(3.94917 - 2.28006i) q^{26} +(-15.0815 + 22.3953i) q^{27} +(-13.6843 + 2.95625i) q^{28} +(26.9302 + 15.5482i) q^{29} +(-11.9031 + 4.02454i) q^{30} +26.4957 q^{31} +5.65685i q^{32} +(-30.7944 - 6.16401i) q^{33} +(3.48504 - 6.03627i) q^{34} +(19.7377 + 6.34075i) q^{35} +(-2.30642 - 17.8516i) q^{36} +(-25.0484 - 43.3851i) q^{37} +(25.2492 - 14.5776i) q^{38} +(1.89864 - 9.48530i) q^{39} +(4.18834 - 7.25441i) q^{40} +(42.6147 - 24.6036i) q^{41} +(-14.4564 + 25.9425i) q^{42} +(26.9323 - 46.6481i) q^{43} +(18.1319 - 10.4684i) q^{44} +(-10.2596 + 24.6008i) q^{45} +(-10.4384 + 18.0799i) q^{46} +19.4878i q^{47} +(9.01253 + 7.92302i) q^{48} +(44.6303 - 20.2271i) q^{49} +(19.8763 - 11.4756i) q^{50} +(-4.73584 - 14.0068i) q^{51} +(3.22449 + 5.58497i) q^{52} +(-86.9554 - 50.2038i) q^{53} +(-31.6717 - 21.3285i) q^{54} -31.0033 q^{55} +(-4.18077 - 19.3526i) q^{56} +(12.1390 - 60.6447i) q^{57} +(-21.9884 + 38.0851i) q^{58} +27.8673i q^{59} +(-5.69156 - 16.8335i) q^{60} -40.6748 q^{61} +37.4706i q^{62} +(21.0839 + 59.3672i) q^{63} -8.00000 q^{64} -9.54964i q^{65} +(8.71723 - 43.5499i) q^{66} +76.1185 q^{67} +(8.53657 + 4.92859i) q^{68} +(14.1848 + 41.9533i) q^{69} +(-8.96718 + 27.9134i) q^{70} -2.51699i q^{71} +(25.2460 - 3.26177i) q^{72} +(-69.1461 + 119.765i) q^{73} +(61.3558 - 35.4238i) q^{74} +(9.55589 - 47.7397i) q^{75} +(20.6159 + 35.7078i) q^{76} +(-54.2937 + 49.2139i) q^{77} +(13.4142 + 2.68508i) q^{78} -32.6856 q^{79} +(10.2593 + 5.92320i) q^{80} +(-78.3402 + 20.5867i) q^{81} +(34.7948 + 60.2663i) q^{82} +(7.18301 + 4.14711i) q^{83} +(-36.6882 - 20.4445i) q^{84} +(-7.29826 - 12.6410i) q^{85} +(65.9704 + 38.0880i) q^{86} +(29.8802 + 88.3742i) q^{87} +(14.8046 + 25.6423i) q^{88} +(-107.053 + 61.8071i) q^{89} +(-34.7908 - 14.5092i) q^{90} +(-15.1589 - 16.7235i) q^{91} +(-25.5688 - 14.7621i) q^{92} +(59.6984 + 52.4816i) q^{93} -27.5599 q^{94} -61.0561i q^{95} +(-11.2048 + 12.7456i) q^{96} +(44.1237 - 76.4246i) q^{97} +(28.6055 + 63.1168i) q^{98} +(-57.1745 - 74.8846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) $ 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	2.25313	+	1.98076i	0.751044	+	0.660252i
$3$	2.25313	+	1.98076i	0.751044	+	0.660252i
$4$	−2.00000			−0.500000
$5$	2.56482	+	1.48080i	0.512965	+	0.296160i	0.734051	−	0.679094i	$-0.237627\pi$
$5$	2.56482	+	1.48080i	0.512965	+	0.296160i	−0.221087	+	0.975254i	$0.570960\pi$
$6$	−2.80121	+	3.18641i	−0.466869	+	0.531068i
$7$	6.84216	−	1.47812i	0.977451	−	0.211161i
$7$	6.84216	−	1.47812i	0.977451	−	0.211161i
$8$		−	2.82843i		−	0.353553i
$9$	1.15321	+	8.92581i	0.128134	+	0.991757i
$10$	−2.09417	+	3.62721i	−0.209417	+	0.362721i
$11$	−9.06593	+	5.23422i	−0.824175	+	0.475838i	−0.851854	−	0.523779i	$-0.824522\pi$
$11$	−9.06593	+	5.23422i	−0.824175	+	0.475838i	0.0276789	+	0.999617i	$0.491188\pi$
$12$	−4.50626	−	3.96151i	−0.375522	−	0.330126i
$13$	−1.61224	−	2.79249i	−0.124019	−	0.214807i	0.797330	−	0.603543i	$-0.206245\pi$
$13$	−1.61224	−	2.79249i	−0.124019	−	0.214807i	−0.921349	+	0.388737i	$0.872912\pi$
$14$	2.09038	+	9.67628i	0.149313	+	0.691163i
$15$	2.84578	+	8.41673i	0.189719	+	0.561115i
$16$	4.00000			0.250000
$17$	−4.26829	−	2.46430i	−0.251076	−	0.144959i	0.369181	−	0.929357i	$-0.379638\pi$
$17$	−4.26829	−	2.46430i	−0.251076	−	0.144959i	−0.620257	+	0.784399i	$0.712972\pi$
$18$	−12.6230	+	1.63089i	−0.701278	+	0.0906048i
$19$	−10.3079	−	17.8539i	−0.542524	−	0.939678i	−0.998758	−	0.0498189i	$-0.984136\pi$
$19$	−10.3079	−	17.8539i	−0.542524	−	0.939678i	0.456235	−	0.889859i	$-0.349198\pi$
$20$	−5.12965	−	2.96160i	−0.256482	−	0.148080i
$21$	18.3441	+	10.2222i	0.873528	+	0.486773i
$22$	−7.40230	−	12.8212i	−0.336468	−	0.582780i
$23$	12.7844	+	7.38107i	0.555843	+	0.320916i	0.751475	−	0.659761i	$-0.229343\pi$
$23$	12.7844	+	7.38107i	0.555843	+	0.320916i	−0.195632	+	0.980677i	$0.562676\pi$
$24$	5.60242	−	6.37282i	0.233434	−	0.265534i
$25$	−8.11446	−	14.0547i	−0.324578	−	0.562186i
$26$	3.94917	−	2.28006i	0.151891	−	0.0876945i
$27$	−15.0815	+	22.3953i	−0.558575	+	0.829454i
$28$	−13.6843	+	2.95625i	−0.488726	+	0.105580i
$29$	26.9302	+	15.5482i	0.928628	+	0.536144i	0.886377	−	0.462963i	$-0.153214\pi$
$29$	26.9302	+	15.5482i	0.928628	+	0.536144i	0.0422505	+	0.999107i	$0.486547\pi$
$30$	−11.9031	+	4.02454i	−0.396768	+	0.134151i
$31$	26.4957			0.854701			0.427350	−	0.904086i	$-0.359447\pi$
$31$	26.4957			0.854701			0.427350	+	0.904086i	$0.359447\pi$
$32$			5.65685i			0.176777i
$33$	−30.7944	−	6.16401i	−0.933165	−	0.186788i
$34$	3.48504	−	6.03627i	0.102501	−	0.177537i
$35$	19.7377	+	6.34075i	0.563935	+	0.181164i
$36$	−2.30642	−	17.8516i	−0.0640672	−	0.495878i
$37$	−25.0484	−	43.3851i	−0.676983	−	1.17257i	−0.975885	−	0.218286i	$-0.929954\pi$
$37$	−25.0484	−	43.3851i	−0.676983	−	1.17257i	0.298902	−	0.954284i	$-0.403380\pi$
$38$	25.2492	−	14.5776i	0.664453	−	0.383622i
$39$	1.89864	−	9.48530i	0.0486830	−	0.243213i
$40$	4.18834	−	7.25441i	0.104708	−	0.181360i
$41$	42.6147	−	24.6036i	1.03938	−	0.600088i	0.119725	−	0.992807i	$-0.461799\pi$
$41$	42.6147	−	24.6036i	1.03938	−	0.600088i	0.919659	+	0.392719i	$0.128465\pi$
$42$	−14.4564	+	25.9425i	−0.344201	+	0.617678i
$43$	26.9323	−	46.6481i	0.626332	−	1.08484i	−0.361949	−	0.932198i	$-0.617889\pi$
$43$	26.9323	−	46.6481i	0.626332	−	1.08484i	0.988282	−	0.152642i	$-0.0487781\pi$
$44$	18.1319	−	10.4684i	0.412088	−	0.237919i
$45$	−10.2596	+	24.6008i	−0.227990	+	0.546684i
$46$	−10.4384	+	18.0799i	−0.226922	+	0.393041i
$47$			19.4878i			0.414634i	0.978274	+	0.207317i	$0.0664732\pi$
$47$			19.4878i			0.414634i	−0.978274	+	0.207317i	$0.933527\pi$
$48$	9.01253	+	7.92302i	0.187761	+	0.165063i
$49$	44.6303	−	20.2271i	0.910822	−	0.412798i
$50$	19.8763	−	11.4756i	0.397526	−	0.229511i
$51$	−4.73584	−	14.0068i	−0.0928597	−	0.274643i
$52$	3.22449	+	5.58497i	0.0620093	+	0.107403i
$53$	−86.9554	−	50.2038i	−1.64067	−	0.947241i	−0.980596	−	0.196039i	$-0.937192\pi$
$53$	−86.9554	−	50.2038i	−1.64067	−	0.947241i	−0.660073	−	0.751202i	$-0.729475\pi$
$54$	−31.6717	−	21.3285i	−0.586513	−	0.394972i
$55$	−31.0033			−0.563697
$56$	−4.18077	−	19.3526i	−0.0746565	−	0.345581i
$57$	12.1390	−	60.6447i	0.212965	−	1.06394i
$58$	−21.9884	+	38.0851i	−0.379111	+	0.656639i
$59$			27.8673i			0.472327i	0.971713	+	0.236164i	$0.0758902\pi$
$59$			27.8673i			0.472327i	−0.971713	+	0.236164i	$0.924110\pi$
$60$	−5.69156	−	16.8335i	−0.0948593	−	0.280558i
$61$	−40.6748			−0.666799			−0.333400	−	0.942786i	$-0.608196\pi$
$61$	−40.6748			−0.666799			−0.333400	+	0.942786i	$0.608196\pi$
$62$			37.4706i			0.604365i
$63$	21.0839	+	59.3672i	0.334665	+	0.942337i
$64$	−8.00000			−0.125000
$65$		−	9.54964i		−	0.146918i
$66$	8.71723	−	43.5499i	0.132079	−	0.659847i
$67$	76.1185			1.13610			0.568049	−	0.822995i	$-0.307698\pi$
$67$	76.1185			1.13610			0.568049	+	0.822995i	$0.307698\pi$
$68$	8.53657	+	4.92859i	0.125538	+	0.0724793i
$69$	14.1848	+	41.9533i	0.205577	+	0.608019i
$70$	−8.96718	+	27.9134i	−0.128103	+	0.398762i
$71$		−	2.51699i		−	0.0354506i	−0.999843	−	0.0177253i	$-0.994358\pi$
$71$		−	2.51699i		−	0.0354506i	0.999843	−	0.0177253i	$-0.00564243\pi$
$72$	25.2460	−	3.26177i	0.350639	−	0.0453024i
$73$	−69.1461	+	119.765i	−0.947207	+	1.64061i	−0.195936	+	0.980617i	$0.562775\pi$
$73$	−69.1461	+	119.765i	−0.947207	+	1.64061i	−0.751271	+	0.659994i	$0.770559\pi$
$74$	61.3558	−	35.4238i	0.829132	−	0.478700i
$75$	9.55589	−	47.7397i	0.127412	−	0.636530i
$76$	20.6159	+	35.7078i	0.271262	+	0.469839i
$77$	−54.2937	+	49.2139i	−0.705113	+	0.639142i
$78$	13.4142	+	2.68508i	0.171977	+	0.0344241i
$79$	−32.6856			−0.413742			−0.206871	−	0.978368i	$-0.566328\pi$
$79$	−32.6856			−0.413742			−0.206871	+	0.978368i	$0.566328\pi$
$80$	10.2593	+	5.92320i	0.128241	+	0.0740401i
$81$	−78.3402	+	20.5867i	−0.967163	+	0.254156i
$82$	34.7948	+	60.2663i	0.424327	+	0.734955i
$83$	7.18301	+	4.14711i	0.0865422	+	0.0499652i	0.542647	−	0.839961i	$-0.317422\pi$
$83$	7.18301	+	4.14711i	0.0865422	+	0.0499652i	−0.456104	+	0.889926i	$0.650756\pi$
$84$	−36.6882	−	20.4445i	−0.436764	−	0.243387i
$85$	−7.29826	−	12.6410i	−0.0858619	−	0.148717i
$86$	65.9704	+	38.0880i	0.767097	+	0.442884i
$87$	29.8802	+	88.3742i	0.343451	+	1.01580i
$88$	14.8046	+	25.6423i	0.168234	+	0.291390i
$89$	−107.053	+	61.8071i	−1.20284	+	0.694461i	−0.961186	−	0.275900i	$-0.911024\pi$
$89$	−107.053	+	61.8071i	−1.20284	+	0.694461i	−0.241656	+	0.970362i	$0.577691\pi$
$90$	−34.7908	−	14.5092i	−0.386564	−	0.161214i
$91$	−15.1589	−	16.7235i	−0.166581	−	0.183775i
$92$	−25.5688	−	14.7621i	−0.277922	−	0.160458i
$93$	59.6984	+	52.4816i	0.641918	+	0.564318i
$94$	−27.5599			−0.293191
$95$		−	61.0561i		−	0.642696i
$96$	−11.2048	+	12.7456i	−0.116717	+	0.132767i
$97$	44.1237	−	76.4246i	0.454884	−	0.787882i	−0.543798	−	0.839216i	$-0.683014\pi$
$97$	44.1237	−	76.4246i	0.454884	−	0.787882i	0.998682	+	0.0513343i	$0.0163474\pi$
$98$	28.6055	+	63.1168i	0.291893	+	0.644049i
$99$	−57.1745	−	74.8846i	−0.577521	−	0.756410i
$100$	16.2289	+	28.1093i	0.162289	+	0.281093i
$101$	−64.3812	+	37.1705i	−0.637437	+	0.368025i	−0.783627	−	0.621232i	$-0.786632\pi$
$101$	−64.3812	+	37.1705i	−0.637437	+	0.368025i	0.146189	+	0.989257i	$0.453299\pi$
$102$	19.8086	−	6.69749i	0.194202	−	0.0656617i
$103$	−86.5789	+	149.959i	−0.840572	+	1.45591i	0.0488407	+	0.998807i	$0.484447\pi$
$103$	−86.5789	+	149.959i	−0.840572	+	1.45591i	−0.889412	+	0.457106i	$0.848886\pi$
$104$	−7.89834	+	4.56011i	−0.0759456	+	0.0438472i
$105$	31.9122	+	53.3822i	0.303926	+	0.508402i
$106$	70.9988	−	122.974i	0.669800	−	1.16013i
$107$	131.318	−	75.8164i	1.22727	−	0.708565i	0.260812	−	0.965390i	$-0.416010\pi$
$107$	131.318	−	75.8164i	1.22727	−	0.708565i	0.966458	+	0.256825i	$0.0826764\pi$
$108$	30.1630	−	44.7905i	0.279287	−	0.414727i
$109$	44.1319	−	76.4387i	0.404880	−	0.701272i	−0.589428	−	0.807821i	$-0.700647\pi$
$109$	44.1319	−	76.4387i	0.404880	−	0.701272i	0.994307	+	0.106549i	$0.0339800\pi$
$110$		−	43.8453i		−	0.398594i
$111$	29.4979	−	147.367i	0.265747	−	1.32763i
$112$	27.3686	−	5.91250i	0.244363	−	0.0527901i
$113$	−192.861	+	111.349i	−1.70674	+	0.985386i	−0.768201	+	0.640208i	$0.778848\pi$
$113$	−192.861	+	111.349i	−1.70674	+	0.985386i	−0.938537	+	0.345178i	$0.887819\pi$
$114$	85.7646	+	17.1672i	0.752321	+	0.150589i
$115$	21.8598	+	37.8623i	0.190085	+	0.329237i
$116$	−53.8604	−	31.0963i	−0.464314	−	0.268072i
$117$	23.0660	−	17.6109i	0.197145	−	0.150521i
$118$	−39.4103			−0.333986
$119$	−32.8468	−	10.5520i	−0.276024	−	0.0886727i
$120$	23.8061	−	8.04908i	0.198384	−	0.0670757i
$121$	−5.70597	+	9.88303i	−0.0471568	+	0.0816779i
$122$		−	57.5228i		−	0.471498i
$123$	144.750	+	28.9742i	1.17683	+	0.235562i
$124$	−52.9914			−0.427350
$125$		−	122.104i		−	0.976829i
$126$	−83.9580	+	29.8171i	−0.666333	+	0.236644i
$127$	142.808			1.12447			0.562237	−	0.826976i	$-0.309941\pi$
$127$	142.808			1.12447			0.562237	+	0.826976i	$0.309941\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	153.081	−	51.7580i	1.18667	−	0.401225i
$130$	13.5052			0.103886
$131$	−72.4912	−	41.8528i	−0.553368	−	0.319487i	0.197112	−	0.980381i	$-0.436844\pi$
$131$	−72.4912	−	41.8528i	−0.553368	−	0.319487i	−0.750479	+	0.660894i	$0.770177\pi$
$132$	61.5889	+	12.3280i	0.466582	+	0.0933941i
$133$	−96.9189	−	106.923i	−0.728713	−	0.803930i
$134$			107.648i			0.803342i
$135$	−71.8444	+	35.1071i	−0.532180	+	0.260053i
$136$	−6.97008	+	12.0725i	−0.0512506	+	0.0887686i
$137$	5.21255	−	3.00947i	0.0380478	−	0.0219669i	−0.480855	−	0.876800i	$-0.659674\pi$
$137$	5.21255	−	3.00947i	0.0380478	−	0.0219669i	0.518903	+	0.854833i	$0.326340\pi$
$138$	−59.3309	+	20.0604i	−0.429934	+	0.145365i
$139$	92.9625	+	161.016i	0.668795	+	1.15839i	0.978241	+	0.207470i	$0.0665228\pi$
$139$	92.9625	+	161.016i	0.668795	+	1.15839i	−0.309447	+	0.950917i	$0.600144\pi$
$140$	−39.4755	−	12.6815i	−0.281968	−	0.0905822i
$141$	−38.6006	+	43.9086i	−0.273763	+	0.311409i
$142$	3.55956			0.0250674
$143$	29.2330	+	16.8777i	0.204426	+	0.118026i
$144$	4.61284	+	35.7032i	0.0320336	+	0.247939i
$145$	46.0475	+	79.7566i	0.317569	+	0.550045i
$146$	−169.373	−	97.7874i	−1.16009	−	0.669777i
$147$	140.623	+	42.8274i	0.956619	+	0.291343i
$148$	50.0968	+	86.7702i	0.338492	+	0.586285i
$149$	−245.223	−	141.580i	−1.64579	−	0.950200i	−0.978718	−	0.205210i	$-0.934212\pi$
$149$	−245.223	−	141.580i	−1.64579	−	0.950200i	−0.667076	−	0.744989i	$-0.732454\pi$
$150$	67.5142	+	13.5141i	0.450095	+	0.0900938i
$151$	21.6207	+	37.4482i	0.143183	+	0.248001i	0.928694	−	0.370848i	$-0.120933\pi$
$151$	21.6207	+	37.4482i	0.143183	+	0.248001i	−0.785510	+	0.618849i	$0.787599\pi$
$152$	−50.4984	+	29.1553i	−0.332226	+	0.191811i
$153$	17.0736	−	40.9398i	0.111592	−	0.267580i
$154$	−69.5990	−	76.7829i	−0.451941	−	0.498590i
$155$	67.9568	+	39.2349i	0.438431	+	0.253128i
$156$	−3.79728	+	18.9706i	−0.0243415	+	0.121606i
$157$	115.241			0.734017			0.367009	−	0.930218i	$-0.380382\pi$
$157$	115.241			0.734017			0.367009	+	0.930218i	$0.380382\pi$
$158$		−	46.2244i		−	0.292559i
$159$	−96.4807	−	285.353i	−0.606797	−	1.79467i
$160$	−8.37668	+	14.5088i	−0.0523542	+	0.0906802i
$161$	98.3830	+	31.6056i	0.611075	+	0.196308i
$162$	−29.1140	−	110.790i	−0.179716	−	0.683888i
$163$	−45.0324	−	77.9983i	−0.276272	−	0.478517i	0.694183	−	0.719798i	$-0.255766\pi$
$163$	−45.0324	−	77.9983i	−0.276272	−	0.478517i	−0.970455	+	0.241281i	$0.922432\pi$
$164$	−85.2295	+	49.2072i	−0.519692	+	0.300044i
$165$	−69.8546	−	61.4100i	−0.423361	−	0.372182i
$166$	−5.86490	+	10.1583i	−0.0353307	+	0.0611946i
$167$	164.936	−	95.2257i	0.987639	−	0.570214i	0.0830712	−	0.996544i	$-0.473527\pi$
$167$	164.936	−	95.2257i	0.987639	−	0.570214i	0.904568	+	0.426330i	$0.140194\pi$
$168$	28.9129	−	51.8849i	0.172100	−	0.308839i
$169$	79.3013	−	137.354i	0.469239	−	0.812745i
$170$	17.8770	−	10.3213i	0.105159	−	0.0607136i
$171$	147.473	−	112.596i	0.862416	−	0.658457i
$172$	−53.8646	+	93.2962i	−0.313166	+	0.542420i
$173$		−	15.1191i		−	0.0873937i	−0.999045	−	0.0436968i	$-0.986086\pi$
$173$		−	15.1191i		−	0.0873937i	0.999045	−	0.0436968i	$-0.0139136\pi$
$174$	−124.980	+	42.2570i	−0.718276	+	0.242856i
$175$	−76.2949	−	84.1700i	−0.435971	−	0.480971i
$176$	−36.2637	+	20.9369i	−0.206044	+	0.118959i
$177$	−55.1984	+	62.7888i	−0.311855	+	0.354739i
$178$	−87.4084	−	151.396i	−0.491058	−	0.850538i
$179$	64.3594	+	37.1579i	0.359550	+	0.207586i	0.668883	−	0.743367i	$-0.266773\pi$
$179$	64.3594	+	37.1579i	0.359550	+	0.207586i	−0.309333	+	0.950954i	$0.600106\pi$
$180$	20.5191	−	49.2016i	0.113995	−	0.273342i
$181$	−168.354			−0.930134			−0.465067	−	0.885276i	$-0.653970\pi$
$181$	−168.354			−0.930134			−0.465067	+	0.885276i	$0.653970\pi$
$182$	23.6507	−	21.4379i	0.129949	−	0.117791i
$183$	−91.6456	−	80.5668i	−0.500796	−	0.440256i
$184$	20.8768	−	36.1597i	0.113461	−	0.196520i
$185$		−	148.367i		−	0.801982i
$186$	−74.2201	+	84.4262i	−0.399033	+	0.453904i
$187$	51.5946			0.275907
$188$		−	38.9756i		−	0.207317i
$189$	−70.0872	+	175.524i	−0.370832	+	0.928700i
$190$	86.3463			0.454454
$191$			94.8330i			0.496508i	0.968695	+	0.248254i	$0.0798567\pi$
$191$			94.8330i			0.496508i	−0.968695	+	0.248254i	$0.920143\pi$
$192$	−18.0251	−	15.8460i	−0.0938805	−	0.0825315i
$193$	−80.7967			−0.418636			−0.209318	−	0.977848i	$-0.567124\pi$
$193$	−80.7967			−0.418636			−0.209318	+	0.977848i	$0.567124\pi$
$194$	108.081	+	62.4004i	0.557117	+	0.321652i
$195$	18.9155	−	21.5166i	0.0970026	−	0.110342i
$196$	−89.2606	+	40.4542i	−0.455411	+	0.206399i
$197$			299.930i			1.52249i	0.648467	+	0.761243i	$0.275410\pi$
$197$			299.930i			1.52249i	−0.648467	+	0.761243i	$0.724590\pi$
$198$	105.903	−	80.8570i	0.534863	−	0.408369i
$199$	−166.251	+	287.955i	−0.835432	+	1.44701i	0.0582464	+	0.998302i	$0.481449\pi$
$199$	−166.251	+	287.955i	−0.835432	+	1.44701i	−0.893678	+	0.448708i	$0.851884\pi$
$200$	−39.7526	+	22.9511i	−0.198763	+	0.114756i
$201$	171.505	+	150.772i	0.853259	+	0.750111i
$202$	−52.5670	−	91.0487i	−0.260233	−	0.450736i
$203$	207.243	+	66.5768i	1.02090	+	0.327965i
$204$	9.47169	+	28.0136i	0.0464298	+	0.137322i
$205$	145.732			0.710889
$206$	−212.074	−	122.441i	−1.02949	−	0.594374i
$207$	−51.1390	+	122.623i	−0.247048	+	0.592382i
$208$	−6.44897	−	11.1699i	−0.0310047	−	0.0537017i
$209$	186.902	+	107.908i	0.894269	+	0.516306i
$210$	−75.4938	+	45.1307i	−0.359494	+	0.214908i
$211$	31.4009	+	54.3880i	0.148820	+	0.257763i	0.930791	−	0.365551i	$-0.119119\pi$
$211$	31.4009	+	54.3880i	0.148820	+	0.257763i	−0.781972	+	0.623314i	$0.785786\pi$
$212$	173.911	+	100.408i	0.820334	+	0.473620i
$213$	4.98555	−	5.67112i	0.0234063	−	0.0266250i
$214$	107.221	+	185.712i	0.501031	+	0.867811i
$215$	138.153	−	79.7627i	0.642573	−	0.370989i
$216$	63.3434	+	42.6570i	0.293256	+	0.197486i
$217$	181.288	−	39.1640i	0.835428	−	0.180479i
$218$	108.101	+	62.4119i	0.495874	+	0.286293i
$219$	−393.020	+	132.884i	−1.79461	+	0.606776i
$220$	62.0067			0.281848
$221$			15.8922i			0.0719103i
$222$	208.408	+	41.7164i	0.938777	+	0.187912i
$223$	−184.727	+	319.956i	−0.828370	+	1.43478i	0.0709457	+	0.997480i	$0.477398\pi$
$223$	−184.727	+	319.956i	−0.828370	+	1.43478i	−0.899316	+	0.437299i	$0.855935\pi$
$224$	8.36153	+	38.7051i	0.0373283	+	0.172791i
$225$	116.091	−	88.6361i	0.515962	−	0.393938i
$226$	−157.471	−	272.747i	−0.696773	−	1.20685i
$227$	−164.291	+	94.8532i	−0.723747	+	0.417855i	−0.816130	−	0.577868i	$-0.803885\pi$
$227$	−164.291	+	94.8532i	−0.723747	+	0.417855i	0.0923833	+	0.995724i	$0.470551\pi$
$228$	−24.2781	+	121.289i	−0.106483	+	0.531971i
$229$	82.2100	−	142.392i	0.358996	−	0.621799i	−0.628798	−	0.777569i	$-0.716453\pi$
$229$	82.2100	−	142.392i	0.358996	−	0.621799i	0.987793	+	0.155770i	$0.0497859\pi$
$230$	−53.5454	+	30.9144i	−0.232806	+	0.134411i
$231$	−219.812	+	3.34285i	−0.951566	+	0.0144712i
$232$	43.9768	−	76.1701i	0.189555	−	0.328320i
$233$	327.491	−	189.077i	1.40554	−	0.811490i	0.410588	−	0.911821i	$-0.365324\pi$
$233$	327.491	−	189.077i	1.40554	−	0.811490i	0.994954	+	0.100331i	$0.0319903\pi$
$234$	24.9056	+	32.6202i	0.106434	+	0.139402i
$235$	−28.8576	+	49.9828i	−0.122798	+	0.212693i
$236$		−	55.7346i		−	0.236164i
$237$	−73.6450	−	64.7422i	−0.310738	−	0.273174i
$238$	14.9229	−	46.4524i	0.0627011	−	0.195178i
$239$	−99.8780	+	57.6646i	−0.417899	+	0.241274i	−0.694178	−	0.719803i	$-0.744232\pi$
$239$	−99.8780	+	57.6646i	−0.417899	+	0.241274i	0.276279	+	0.961078i	$0.410899\pi$
$240$	11.3831	+	33.6669i	0.0474297	+	0.140279i
$241$	136.139	+	235.800i	0.564892	+	0.978422i	0.997060	+	0.0766289i	$0.0244157\pi$
$241$	136.139	+	235.800i	0.564892	+	0.978422i	−0.432167	+	0.901793i	$0.642251\pi$
$242$	−13.9767	−	8.06946i	−0.0577550	−	0.0333449i
$243$	−217.288	−	108.788i	−0.894189	−	0.447689i
$244$	81.3495			0.333400
$245$	144.421	+	14.2096i	0.589474	+	0.0579984i
$246$	−40.9757	+	204.708i	−0.166568	+	0.832146i
$247$	−33.2378	+	57.5696i	−0.134566	+	0.233075i
$248$		−	74.9412i		−	0.302182i
$249$	7.96985	+	23.5718i	0.0320074	+	0.0946657i
$250$	172.681			0.690722
$251$		−	188.801i		−	0.752195i	−0.926580	−	0.376097i	$-0.877266\pi$
$251$		−	188.801i		−	0.752195i	0.926580	−	0.376097i	$-0.122734\pi$
$252$	−42.1678	−	118.734i	−0.167333	−	0.471169i
$253$	−154.537			−0.610816
$254$			201.961i			0.795123i
$255$	8.59471	−	42.9378i	0.0337048	−	0.168384i
$256$	16.0000			0.0625000
$257$	264.143	+	152.503i	1.02779	+	0.593396i	0.916351	−	0.400375i	$-0.131120\pi$
$257$	264.143	+	152.503i	1.02779	+	0.593396i	0.111441	+	0.993771i	$0.464454\pi$
$258$	73.1969	+	216.489i	0.283709	+	0.839103i
$259$	−235.514	−	259.823i	−0.909319	−	1.00318i
$260$			19.0993i			0.0734588i
$261$	−107.724	+	258.304i	−0.412735	+	0.989672i
$262$	59.1888	−	102.518i	0.225911	−	0.391290i
$263$	−16.6362	+	9.60493i	−0.0632556	+	0.0365206i	−0.531294	−	0.847187i	$-0.678294\pi$
$263$	−16.6362	+	9.60493i	−0.0632556	+	0.0365206i	0.468039	+	0.883708i	$0.344961\pi$
$264$	−17.4345	+	87.0998i	−0.0660396	+	0.329924i
$265$	−148.684	−	257.527i	−0.561070	−	0.971802i
$266$	151.212	−	137.064i	0.568465	−	0.515278i
$267$	−363.629	−	72.7863i	−1.36191	−	0.272608i
$268$	−152.237			−0.568049
$269$	−88.4256	−	51.0525i	−0.328720	−	0.189786i	0.326553	−	0.945179i	$-0.394113\pi$
$269$	−88.4256	−	51.0525i	−0.328720	−	0.189786i	−0.655273	+	0.755393i	$0.727446\pi$
$270$	−49.6490	−	101.603i	−0.183885	−	0.376308i
$271$	−3.15801	−	5.46983i	−0.0116532	−	0.0201839i	0.860140	−	0.510058i	$-0.170376\pi$
$271$	−3.15801	−	5.46983i	−0.0116532	−	0.0201839i	−0.871793	+	0.489874i	$0.837043\pi$
$272$	−17.0731	−	9.85718i	−0.0627689	−	0.0362396i
$273$	−1.02967	−	67.7064i	−0.00377167	−	0.248009i
$274$	4.25603	+	7.37166i	0.0155330	+	0.0269039i
$275$	147.130	+	84.9456i	0.535019	+	0.308893i
$276$	−28.3697	−	83.9066i	−0.102789	−	0.304009i
$277$	9.21161	+	15.9550i	0.0332549	+	0.0575992i	0.882174	−	0.470924i	$-0.156079\pi$
$277$	9.21161	+	15.9550i	0.0332549	+	0.0575992i	−0.848919	+	0.528523i	$0.822746\pi$
$278$	−227.711	+	131.469i	−0.819103	+	0.472909i
$279$	30.5551	+	236.496i	0.109517	+	0.847655i
$280$	17.9344	−	55.8267i	0.0640513	−	0.199381i
$281$	143.559	+	82.8838i	0.510886	+	0.294960i	0.733198	−	0.680015i	$-0.238027\pi$
$281$	143.559	+	82.8838i	0.510886	+	0.294960i	−0.222312	+	0.974976i	$0.571360\pi$
$282$	−62.0961	−	54.5895i	−0.220199	−	0.193580i
$283$	−299.240			−1.05739			−0.528693	−	0.848813i	$-0.677318\pi$
$283$	−299.240			−1.05739			−0.528693	+	0.848813i	$0.677318\pi$
$284$			5.03398i			0.0177253i
$285$	120.937	−	137.567i	0.424341	−	0.482693i
$286$	−23.8686	+	41.3416i	−0.0834567	+	0.144551i
$287$	255.210	−	231.332i	0.889232	−	0.806034i
$288$	−50.4920	+	6.52354i	−0.175319	+	0.0226512i
$289$	−132.354	−	229.245i	−0.457974	−	0.793234i
$290$	−112.793	+	65.1210i	−0.388941	+	0.224555i
$291$	250.795	−	84.7963i	0.861839	−	0.291396i
$292$	138.292	−	239.529i	0.473604	−	0.820305i
$293$	−299.230	+	172.760i	−1.02126	+	0.589626i	−0.914469	−	0.404656i	$-0.867391\pi$
$293$	−299.230	+	172.760i	−1.02126	+	0.589626i	−0.106792	+	0.994281i	$0.534058\pi$
$294$	−60.5670	+	198.871i	−0.206010	+	0.676432i
$295$	−41.2660	+	71.4747i	−0.139885	+	0.242287i
$296$	−122.712	+	70.8475i	−0.414566	+	0.239350i
$297$	19.5063	−	281.974i	0.0656779	−	0.949407i
$298$	200.224	−	346.798i	0.671893	−	1.16375i
$299$		−	47.6003i		−	0.159198i
$300$	−19.1118	+	95.4795i	−0.0637059	+	0.318265i
$301$	115.323	−	358.983i	0.383134	−	1.19263i
$302$	−52.9597	+	30.5763i	−0.175363	+	0.101246i
$303$	−218.685	−	43.7734i	−0.721733	−	0.144467i
$304$	−41.2318	−	71.4156i	−0.135631	−	0.234920i
$305$	−104.324	−	60.2312i	−0.342044	−	0.197479i
$306$	57.8976	+	24.1457i	0.189208	+	0.0789076i
$307$	153.935			0.501417			0.250708	−	0.968063i	$-0.419337\pi$
$307$	153.935			0.501417			0.250708	+	0.968063i	$0.419337\pi$
$308$	108.587	−	98.4278i	0.352557	−	0.319571i
$309$	−492.106	+	166.386i	−1.59258	+	0.538466i
$310$	−55.4865	+	96.1054i	−0.178989	+	0.310018i
$311$		−	503.595i		−	1.61928i	−0.586928	−	0.809639i	$-0.699663\pi$
$311$		−	503.595i		−	1.61928i	0.586928	−	0.809639i	$-0.300337\pi$
$312$	−26.8285	−	5.37016i	−0.0859887	−	0.0172121i
$313$	450.244			1.43848			0.719240	−	0.694762i	$-0.244490\pi$
$313$	450.244			1.43848			0.719240	+	0.694762i	$0.244490\pi$
$314$			162.975i			0.519029i
$315$	−33.8346	+	183.488i	−0.107411	+	0.582500i
$316$	65.3712			0.206871
$317$		−	338.490i		−	1.06779i	−0.845550	−	0.533896i	$-0.820727\pi$
$317$		−	338.490i		−	1.06779i	0.845550	−	0.533896i	$-0.179273\pi$
$318$	403.550	−	136.444i	1.26903	−	0.429070i
$319$	−325.530			−1.02047
$320$	−20.5186	−	11.8464i	−0.0641206	−	0.0370200i
$321$	446.050	+	89.2843i	1.38957	+	0.278144i
$322$	−44.6970	+	139.135i	−0.138811	+	0.432095i
$323$			101.607i			0.314574i
$324$	156.680	−	41.1734i	0.483582	−	0.127078i
$325$	−26.1649	+	45.3190i	−0.0805075	+	0.139443i
$326$	110.306	−	63.6854i	0.338363	−	0.195354i
$327$	250.841	−	84.8120i	0.767099	−	0.259364i
$328$	−69.5896	−	120.533i	−0.212163	−	0.367478i
$329$	28.8054	+	133.339i	0.0875544	+	0.405285i
$330$	86.8469	−	98.7893i	0.263172	−	0.299362i
$331$	−19.9228			−0.0601896			−0.0300948	−	0.999547i	$-0.509581\pi$
$331$	−19.9228			−0.0601896			−0.0300948	+	0.999547i	$0.509581\pi$
$332$	−14.3660	−	8.29422i	−0.0432711	−	0.0249826i
$333$	358.361	−	273.609i	1.07616	−	0.821649i
$334$	134.669	+	233.254i	0.403202	+	0.698366i
$335$	195.231	+	112.716i	0.582778	+	0.336467i
$336$	73.3764	+	40.8890i	0.218382	+	0.121693i
$337$	−35.6414	−	61.7327i	−0.105761	−	0.183183i	0.808288	−	0.588787i	$-0.200394\pi$
$337$	−35.6414	−	61.7327i	−0.105761	−	0.183183i	−0.914049	+	0.405604i	$0.867061\pi$
$338$	194.248	+	112.149i	0.574698	+	0.331802i
$339$	−655.097	−	131.128i	−1.93244	−	0.386809i
$340$	14.5965	+	25.2819i	0.0429310	+	0.0743586i
$341$	−240.208	+	138.684i	−0.704423	+	0.406699i
$342$	159.235	+	208.559i	0.465599	+	0.609821i
$343$	275.469	−	204.366i	0.803118	−	0.595820i
$344$	−131.941	−	76.1760i	−0.383549	−	0.221442i
$345$	−25.7429	+	128.608i	−0.0746172	+	0.372776i
$346$	21.3816			0.0617967
$347$			240.637i			0.693479i	0.937961	+	0.346740i	$0.112711\pi$
$347$			240.637i			0.693479i	−0.937961	+	0.346740i	$0.887289\pi$
$348$	−59.7604	−	176.748i	−0.171725	−	0.507898i
$349$	−190.956	+	330.745i	−0.547151	+	0.947693i	0.451318	+	0.892363i	$0.350954\pi$
$349$	−190.956	+	330.745i	−0.547151	+	0.947693i	−0.998468	+	0.0553292i	$0.982379\pi$
$350$	119.034	−	107.897i	0.340098	−	0.308278i
$351$	86.8535	+	6.00834i	0.247446	+	0.0171178i
$352$	−29.6092	−	51.2846i	−0.0841170	−	0.145695i
$353$	61.9024	−	35.7393i	0.175361	−	0.101245i	−0.409750	−	0.912198i	$-0.634384\pi$
$353$	61.9024	−	35.7393i	0.175361	−	0.101245i	0.585111	+	0.810953i	$0.301051\pi$
$354$	−88.7967	−	78.0623i	−0.250838	−	0.220515i
$355$	3.72716	−	6.45564i	0.0104991	−	0.0181849i
$356$	214.106	−	123.614i	0.601421	−	0.347231i
$357$	−53.1072	−	88.8367i	−0.148760	−	0.248842i
$358$	−52.5492	+	91.0180i	−0.146786	+	0.254240i
$359$	−215.975	+	124.693i	−0.601603	+	0.347335i	−0.769672	−	0.638440i	$-0.779580\pi$
$359$	−215.975	+	124.693i	−0.601603	+	0.347335i	0.168069	+	0.985775i	$0.446247\pi$
$360$	69.5816	+	29.0184i	0.193282	+	0.0806068i
$361$	−32.0076	+	55.4388i	−0.0886637	+	0.153570i
$362$		−	238.089i		−	0.657704i
$363$	−32.4322	+	10.9656i	−0.0893448	+	0.0302084i
$364$	30.3177	+	33.4471i	0.0832905	+	0.0918876i
$365$	−354.695	+	204.783i	−0.971767	+	0.561050i
$366$	113.939	−	129.606i	0.311308	−	0.354116i
$367$	−37.3613	−	64.7117i	−0.101802	−	0.176326i	0.810625	−	0.585565i	$-0.199127\pi$
$367$	−37.3613	−	64.7117i	−0.101802	−	0.176326i	−0.912427	+	0.409239i	$0.865794\pi$
$368$	51.1376	+	29.5243i	0.138961	+	0.0802291i
$369$	268.751	+	351.998i	0.728323	+	0.953924i
$370$	209.822			0.567087
$371$	−669.170	−	214.971i	−1.80369	−	0.579437i
$372$	−119.397	−	104.963i	−0.320959	−	0.282159i
$373$	−65.4399	+	113.345i	−0.175442	+	0.303874i	−0.940314	−	0.340308i	$-0.889469\pi$
$373$	−65.4399	+	113.345i	−0.175442	+	0.303874i	0.764872	+	0.644182i	$0.222802\pi$
$374$			72.9658i			0.195096i
$375$	241.858	−	275.116i	0.644953	−	0.733642i
$376$	55.1198			0.146595
$377$		−	100.270i		−	0.265967i
$378$	−248.229	−	99.1183i	−0.656690	−	0.262218i
$379$	712.886			1.88097			0.940483	−	0.339839i	$-0.110373\pi$
$379$	712.886			1.88097			0.940483	+	0.339839i	$0.110373\pi$
$380$			122.112i			0.321348i
$381$	321.766	+	282.868i	0.844529	+	0.742436i
$382$	−134.114			−0.351084
$383$	262.429	+	151.514i	0.685194	+	0.395597i	0.801809	−	0.597580i	$-0.203871\pi$
$383$	262.429	+	151.514i	0.685194	+	0.395597i	−0.116615	+	0.993177i	$0.537204\pi$
$384$	22.4097	−	25.4913i	0.0583586	−	0.0663835i
$385$	−212.130	+	45.8268i	−0.550986	+	0.119031i
$386$		−	114.264i		−	0.296020i
$387$	447.431	+	186.597i	1.15615	+	0.482164i
$388$	−88.2475	+	152.849i	−0.227442	+	0.393941i
$389$	−124.187	+	71.6992i	−0.319246	+	0.184317i	−0.651056	−	0.759029i	$-0.725674\pi$
$389$	−124.187	+	71.6992i	−0.319246	+	0.184317i	0.331811	+	0.943346i	$0.392341\pi$
$390$	30.4291	+	26.7506i	0.0780233	+	0.0685912i
$391$	−36.3783	−	63.0091i	−0.0930391	−	0.161148i
$392$	−57.2109	−	126.234i	−0.145946	−	0.322024i
$393$	−80.4320	−	237.887i	−0.204662	−	0.605311i
$394$	−424.164			−1.07656
$395$	−83.8327	−	48.4009i	−0.212235	−	0.122534i
$396$	114.349	+	149.769i	0.288760	+	0.378205i
$397$	42.3608	+	73.3711i	0.106702	+	0.184814i	0.914432	−	0.404739i	$-0.132637\pi$
$397$	42.3608	+	73.3711i	0.106702	+	0.184814i	−0.807730	+	0.589552i	$0.799304\pi$
$398$	−407.230	−	235.114i	−1.02319	−	0.590740i
$399$	−6.58322	−	432.884i	−0.0164993	−	1.08492i
$400$	−32.4578	−	56.2186i	−0.0811446	−	0.140547i
$401$	−422.345	−	243.841i	−1.05323	−	0.608082i	−0.129677	−	0.991556i	$-0.541394\pi$
$401$	−422.345	−	243.841i	−1.05323	−	0.608082i	−0.923552	+	0.383474i	$0.874727\pi$
$402$	−213.224	+	242.545i	−0.530408	+	0.603345i
$403$	−42.7175	−	73.9889i	−0.105999	−	0.183595i
$404$	128.762	−	74.3410i	0.318719	−	0.184012i
$405$	−231.414	−	63.2051i	−0.571391	−	0.156062i
$406$	−94.1539	+	293.086i	−0.231906	+	0.721886i
$407$	454.174	+	262.217i	1.11591	+	0.644269i
$408$	−39.6173	+	13.3950i	−0.0971011	+	0.0328309i
$409$	505.001			1.23472			0.617361	−	0.786680i	$-0.288202\pi$
$409$	505.001			1.23472			0.617361	+	0.786680i	$0.288202\pi$
$410$			206.097i			0.502675i
$411$	17.7056	+	3.54406i	0.0430793	+	0.00862303i
$412$	173.158	−	299.918i	0.420286	−	0.727956i
$413$	41.1914	+	190.673i	0.0997370	+	0.461677i
$414$	−173.415	−	72.3214i	−0.418877	−	0.174689i
$415$	12.2821	+	21.2732i	0.0295954	+	0.0512607i
$416$	15.7967	−	9.12022i	0.0379728	−	0.0219236i
$417$	−109.476	+	546.926i	−0.262533	+	1.31157i
$418$	−152.605	+	264.320i	−0.365084	+	0.632344i
$419$	−146.816	+	84.7643i	−0.350396	+	0.202301i	−0.664860	−	0.746968i	$-0.731509\pi$
$419$	−146.816	+	84.7643i	−0.350396	+	0.202301i	0.314463	+	0.949270i	$0.398175\pi$
$420$	−63.8245	−	106.764i	−0.151963	−	0.254201i
$421$	−116.481	+	201.751i	−0.276677	+	0.479219i	−0.970557	−	0.240872i	$-0.922567\pi$
$421$	−116.481	+	201.751i	−0.276677	+	0.479219i	0.693880	+	0.720091i	$0.255900\pi$
$422$	−76.9162	+	44.4076i	−0.182266	+	0.105231i
$423$	−173.944	+	22.4735i	−0.411216	+	0.0531289i
$424$	−141.998	+	245.947i	−0.334900	+	0.580064i
$425$			79.9857i			0.188202i
$426$	8.02017	+	7.05063i	0.0188267	+	0.0165508i
$427$	−278.303	+	60.1224i	−0.651764	+	0.140802i
$428$	−262.636	+	151.633i	−0.613635	+	0.354282i
$429$	32.4352	+	95.9309i	0.0756065	+	0.223615i
$430$	112.802	+	195.378i	0.262329	+	0.454367i
$431$	88.5091	+	51.1007i	0.205357	+	0.118563i	0.599152	−	0.800635i	$-0.295505\pi$
$431$	88.5091	+	51.1007i	0.205357	+	0.118563i	−0.393795	+	0.919198i	$0.628838\pi$
$432$	−60.3261	+	89.5810i	−0.139644	+	0.207364i
$433$	230.096			0.531400			0.265700	−	0.964056i	$-0.414397\pi$
$433$	230.096			0.531400			0.265700	+	0.964056i	$0.414397\pi$
$434$	55.3862	+	256.380i	0.127618	+	0.590737i
$435$	−54.2273	+	270.911i	−0.124660	+	0.622784i
$436$	−88.2638	+	152.877i	−0.202440	+	0.350636i
$437$		−	304.335i		−	0.696418i
$438$	−187.926	−	555.814i	−0.429055	−	1.26898i
$439$	−195.422			−0.445152			−0.222576	−	0.974915i	$-0.571447\pi$
$439$	−195.422			−0.445152			−0.222576	+	0.974915i	$0.571447\pi$
$440$			87.6907i			0.199297i
$441$	232.012	+	375.035i	0.526103	+	0.850421i
$442$	−22.4749			−0.0508483
$443$		−	297.116i		−	0.670691i	−0.942095	−	0.335346i	$-0.891147\pi$
$443$		−	297.116i		−	0.670691i	0.942095	−	0.335346i	$-0.108853\pi$
$444$	−58.9959	+	294.734i	−0.132874	+	0.663816i
$445$	−366.096			−0.822687
$446$	−452.486	−	261.243i	−1.01454	−	0.585746i
$447$	−272.086	−	804.726i	−0.608693	−	1.80028i
$448$	−54.7373	+	11.8250i	−0.122181	+	0.0263951i
$449$		−	324.700i		−	0.723162i	−0.932341	−	0.361581i	$-0.882237\pi$
$449$		−	324.700i		−	0.723162i	0.932341	−	0.361581i	$-0.117763\pi$
$450$	125.350	+	164.178i	0.278556	+	0.364840i
$451$	−257.561	+	446.109i	−0.571089	+	0.989156i
$452$	385.723	−	222.697i	0.853369	−	0.492693i
$453$	−25.4614	+	127.201i	−0.0562061	+	0.280797i
$454$	−134.143	−	232.342i	−0.295468	−	0.511766i
$455$	−14.1156	−	65.3402i	−0.0310232	−	0.143605i
$456$	−171.529	−	34.3344i	−0.376160	−	0.0752947i
$457$	602.773			1.31898			0.659489	−	0.751714i	$-0.270773\pi$
$457$	602.773			1.31898			0.659489	+	0.751714i	$0.270773\pi$
$458$	201.373	+	116.263i	0.439678	+	0.253848i
$459$	119.561	−	58.4240i	0.260481	−	0.127286i
$460$	−43.7196	−	75.7246i	−0.0950426	−	0.164619i
$461$	212.964	+	122.955i	0.461961	+	0.266713i	0.712868	−	0.701298i	$-0.247396\pi$
$461$	212.964	+	122.955i	0.461961	+	0.266713i	−0.250908	+	0.968011i	$0.580729\pi$
$462$	−4.72751	−	310.861i	−0.0102327	−	0.672858i
$463$	422.033	+	730.982i	0.911518	+	1.57879i	0.811921	+	0.583767i	$0.198422\pi$
$463$	422.033	+	730.982i	0.911518	+	1.57879i	0.0995964	+	0.995028i	$0.468245\pi$
$464$	107.721	+	62.1927i	0.232157	+	0.134036i
$465$	75.4010	+	223.007i	0.162153	+	0.479586i
$466$	267.395	+	463.142i	0.573810	+	0.993868i
$467$	−611.287	+	352.927i	−1.30897	+	0.755732i	−0.981924	−	0.189278i	$-0.939385\pi$
$467$	−611.287	+	352.927i	−1.30897	+	0.755732i	−0.327042	+	0.945010i	$0.606052\pi$
$468$	−46.1319	+	35.2218i	−0.0985724	+	0.0752603i
$469$	520.815	−	112.513i	1.11048	−	0.239899i
$470$	−70.6863	−	40.8108i	−0.150396	−	0.0868314i
$471$	259.653	+	228.264i	0.551279	+	0.484636i
$472$	78.8207			0.166993
$473$			563.878i			1.19213i
$474$	91.5593	−	104.150i	0.193163	−	0.219725i
$475$	−167.287	+	289.749i	−0.352183	+	0.609998i
$476$	65.6937	+	21.1041i	0.138012	+	0.0443363i
$477$	347.831	−	834.043i	0.729206	−	1.74852i
$478$	−81.5500	−	141.249i	−0.170607	−	0.295500i
$479$	287.728	−	166.120i	0.600685	−	0.346806i	−0.168626	−	0.985680i	$-0.553933\pi$
$479$	287.728	−	166.120i	0.600685	−	0.346806i	0.769311	+	0.638874i	$0.220600\pi$
$480$	−47.6122	+	16.0982i	−0.0991921	+	0.0335378i
$481$	−80.7682	+	139.895i	−0.167917	+	0.290841i
$482$	−333.471	+	192.530i	−0.691849	+	0.399439i
$483$	159.067	+	266.084i	0.329331	+	0.550899i
$484$	11.4119	−	19.7661i	0.0235784	−	0.0408390i
$485$	226.339	−	130.677i	0.466679	−	0.269437i
$486$	153.850	−	307.292i	0.316564	−	0.632287i
$487$	217.311	−	376.393i	0.446223	−	0.772881i	−0.551913	−	0.833901i	$-0.686102\pi$
$487$	217.311	−	376.393i	0.446223	−	0.772881i	0.998137	+	0.0610203i	$0.0194354\pi$
$488$			115.046i			0.235749i
$489$	53.0318	−	264.939i	0.108450	−	0.541797i
$490$	−20.0954	+	204.242i	−0.0410111	+	0.416821i
$491$	712.780	−	411.523i	1.45169	−	0.838133i	0.453112	−	0.891454i	$-0.350314\pi$
$491$	712.780	−	411.523i	1.45169	−	0.838133i	0.998577	+	0.0533201i	$0.0169804\pi$
$492$	−289.501	−	57.9483i	−0.588416	−	0.117781i
$493$	−76.6306	−	132.728i	−0.155437	−	0.269225i
$494$	−81.4157	−	47.0054i	−0.164809	−	0.0951526i
$495$	−35.7534	−	276.730i	−0.0722290	−	0.559050i
$496$	105.983			0.213675
$497$	−3.72043	−	17.2217i	−0.00748577	−	0.0346512i
$498$	−33.3355	+	11.2711i	−0.0669388	+	0.0226327i
$499$	−48.0240	+	83.1801i	−0.0962405	+	0.166693i	−0.910126	−	0.414332i	$-0.864015\pi$
$499$	−48.0240	+	83.1801i	−0.0962405	+	0.166693i	0.813885	+	0.581026i	$0.197348\pi$
$500$			244.207i			0.488415i
$501$	560.241	+	112.141i	1.11825	+	0.223835i
$502$	267.005			0.531882
$503$			165.477i			0.328980i	0.986379	+	0.164490i	$0.0525978\pi$
$503$			165.477i			0.328980i	−0.986379	+	0.164490i	$0.947402\pi$
$504$	167.916	−	59.6343i	0.333166	−	0.118322i
$505$	−220.168			−0.435977
$506$		−	218.548i		−	0.431912i
$507$	450.741	−	152.400i	0.889036	−	0.300592i
$508$	−285.616			−0.562237
$509$	−543.179	−	313.604i	−1.06715	−	0.616119i	−0.139748	−	0.990187i	$-0.544629\pi$
$509$	−543.179	−	313.604i	−1.06715	−	0.616119i	−0.927401	+	0.374068i	$0.877963\pi$
$510$	60.7233	+	12.1548i	0.119065	+	0.0238329i
$511$	−296.082	+	921.655i	−0.579417	+	1.80363i
$512$			22.6274i			0.0441942i
$513$	555.302	+	38.4146i	1.08246	+	0.0748823i
$514$	−215.671	+	373.554i	−0.419594	+	0.726759i
$515$	−444.119	+	256.412i	−0.862367	+	0.497888i
$516$	−306.161	+	103.516i	−0.593335	+	0.200613i
$517$	−102.003	−	176.675i	−0.197299	−	0.341731i
$518$	367.445	−	333.067i	0.709354	−	0.642986i
$519$	29.9473	−	34.0654i	0.0577019	−	0.0656365i
$520$	−27.0105			−0.0519432
$521$	−413.754	−	238.881i	−0.794153	−	0.458505i	0.0472693	−	0.998882i	$-0.484948\pi$
$521$	−413.754	−	238.881i	−0.794153	−	0.458505i	−0.841423	+	0.540377i	$0.818281\pi$
$522$	−365.297	−	152.344i	−0.699803	−	0.291848i
$523$	−285.017	−	493.664i	−0.544965	−	0.943908i	−0.998609	−	0.0527246i	$-0.983209\pi$
$523$	−285.017	−	493.664i	−0.544965	−	0.943908i	0.453644	−	0.891183i	$-0.350124\pi$
$524$	144.982	+	83.7056i	0.276684	+	0.159743i
$525$	−5.18233	−	340.768i	−0.00987111	−	0.649081i
$526$	−13.5834	−	23.5272i	−0.0258240	−	0.0447285i
$527$	−113.091	−	65.2933i	−0.214594	−	0.123896i
$528$	−123.178	−	24.6560i	−0.233291	−	0.0466971i
$529$	−155.540	−	269.402i	−0.294026	−	0.509267i
$530$	364.199	−	210.270i	0.687168	−	0.396736i
$531$	−248.738	+	32.1369i	−0.468434	+	0.0605214i
$532$	193.838	+	213.845i	0.364357	+	0.401965i
$533$	−137.411	−	79.3340i	−0.257806	−	0.148844i
$534$	102.935	−	514.249i	0.192763	−	0.963014i
$535$	449.076			0.839395
$536$		−	215.296i		−	0.401671i
$537$	71.4095	+	211.202i	0.132979	+	0.393300i
$538$	72.1992	−	125.053i	0.134199	−	0.232440i
$539$	−298.742	+	416.982i	−0.554252	+	0.773622i
$540$	143.689	−	70.2143i	0.266090	−	0.130026i
$541$	−21.3831	−	37.0366i	−0.0395252	−	0.0684596i	0.845586	−	0.533839i	$-0.179251\pi$
$541$	−21.3831	−	37.0366i	−0.0395252	−	0.0684596i	−0.885111	+	0.465379i	$0.845918\pi$
$542$	7.73550	−	4.46610i	0.0142721	−	0.00824003i
$543$	−379.324	−	333.469i	−0.698571	−	0.614123i
$544$	13.9402	−	24.1451i	0.0256253	−	0.0443843i
$545$	226.381	−	130.701i	0.415378	−	0.239819i
$546$	95.7513	−	1.45617i	0.175369	−	0.00266697i
$547$	339.046	−	587.244i	0.619828	−	1.07357i	−0.369689	−	0.929156i	$-0.620536\pi$
$547$	339.046	−	587.244i	0.619828	−	1.07357i	0.989517	−	0.144418i	$-0.0461309\pi$
$548$	−10.4251	+	6.01894i	−0.0190239	+	0.0109835i
$549$	−46.9066	−	363.055i	−0.0854400	−	0.661303i
$550$	−120.131	+	208.073i	−0.218420	+	0.378315i
$551$		−	641.079i		−	1.16348i
$552$	118.662	−	40.1207i	0.214967	−	0.0726825i
$553$	−223.640	+	48.3134i	−0.404412	+	0.0873659i
$554$	−22.5637	+	13.0272i	−0.0407288	+	0.0235148i
$555$	293.878	−	334.290i	0.529510	−	0.602324i
$556$	−185.925	−	322.031i	−0.334397	−	0.579193i
$557$	19.6576	+	11.3493i	0.0352918	+	0.0203758i	0.517542	−	0.855658i	$-0.326847\pi$
$557$	19.6576	+	11.3493i	0.0352918	+	0.0203758i	−0.482250	+	0.876033i	$0.660180\pi$
$558$	−334.456	+	43.2115i	−0.599383	+	0.0774399i
$559$	−173.686			−0.310708
$560$	78.9509	+	25.3630i	0.140984	+	0.0452911i
$561$	116.250	+	102.196i	0.207218	+	0.182168i
$562$	−117.215	+	203.023i	−0.208568	+	0.361251i
$563$			330.783i			0.587536i	0.955877	+	0.293768i	$0.0949093\pi$
$563$			330.783i			0.587536i	−0.955877	+	0.293768i	$0.905091\pi$
$564$	77.2012	−	87.8172i	0.136882	−	0.155704i
$565$	−659.541			−1.16733
$566$		−	423.189i		−	0.747685i
$567$	−505.587	+	256.654i	−0.891687	+	0.452652i
$568$	−7.11913			−0.0125337
$569$		−	145.968i		−	0.256535i	−0.991740	−	0.128267i	$-0.959058\pi$
$569$		−	145.968i		−	0.256535i	0.991740	−	0.128267i	$-0.0409416\pi$
$570$	194.550	+	171.031i	0.341315	+	0.300054i
$571$	417.093			0.730461			0.365230	−	0.930917i	$-0.380990\pi$
$571$	417.093			0.730461			0.365230	+	0.930917i	$0.380990\pi$
$572$	−58.4659	−	33.7553i	−0.102213	−	0.0590128i
$573$	−187.841	+	213.671i	−0.327820	+	0.372899i
$574$	327.153	+	360.921i	0.569952	+	0.628782i
$575$		−	239.574i		−	0.416650i
$576$	−9.22568	−	71.4065i	−0.0160168	−	0.123970i
$577$	416.092	−	720.693i	0.721131	−	1.24903i	−0.239416	−	0.970917i	$-0.576956\pi$
$577$	416.092	−	720.693i	0.721131	−	1.24903i	0.960547	−	0.278118i	$-0.0897106\pi$
$578$	324.201	−	187.178i	0.560901	−	0.323837i
$579$	−182.046	−	160.039i	−0.314414	−	0.276405i
$580$	−92.0949	−	159.513i	−0.158784	−	0.275023i
$581$	55.2772	+	17.7578i	0.0951415	+	0.0305642i
$582$	119.920	+	354.678i	0.206048	+	0.609412i
$583$	1051.11			1.80293
$584$	338.745	+	195.575i	0.580043	+	0.334888i
$585$	85.2383	−	11.0127i	0.145707	−	0.0188252i
$586$	−244.320	−	423.175i	−0.416928	−	0.722141i
$587$	−110.455	−	63.7713i	−0.188169	−	0.108639i	0.402956	−	0.915219i	$-0.367983\pi$
$587$	−110.455	−	63.7713i	−0.188169	−	0.108639i	−0.591125	+	0.806580i	$0.701316\pi$
$588$	−281.246	−	85.6547i	−0.478309	−	0.145671i
$589$	−273.116	−	473.052i	−0.463695	−	0.803144i
$590$	−101.081	−	58.3589i	−0.171323	−	0.0989134i
$591$	−594.087	+	675.781i	−1.00522	+	1.14345i
$592$	−100.194	−	173.540i	−0.169246	−	0.293142i
$593$	−634.357	+	366.246i	−1.06974	+	0.617616i	−0.928111	−	0.372304i	$-0.878568\pi$
$593$	−634.357	+	366.246i	−1.06974	+	0.617616i	−0.141631	+	0.989920i	$0.545235\pi$
$594$	398.771	+	27.5861i	0.671332	+	0.0464413i
$595$	−68.6208	−	75.7038i	−0.115329	−	0.127233i
$596$	490.447	+	283.160i	0.822897	+	0.475100i
$597$	−944.954	+	319.498i	−1.58284	+	0.535173i
$598$	67.3170			0.112570
$599$		−	374.842i		−	0.625779i	−0.949790	−	0.312889i	$-0.898703\pi$
$599$		−	374.842i		−	0.625779i	0.949790	−	0.312889i	$-0.101297\pi$
$600$	−135.028	−	27.0281i	−0.225047	−	0.0450469i
$601$	−12.0771	+	20.9181i	−0.0200949	+	0.0348054i	−0.875898	−	0.482496i	$-0.839730\pi$
$601$	−12.0771	+	20.9181i	−0.0200949	+	0.0348054i	0.855803	+	0.517302i	$0.173064\pi$
$602$	507.679	+	163.092i	0.843320	+	0.270917i
$603$	87.7807	+	679.420i	0.145573	+	1.12673i
$604$	−43.2414	−	74.8963i	−0.0715917	−	0.124001i
$605$	−29.2696	+	16.8988i	−0.0483795	+	0.0279319i
$606$	61.9049	−	309.267i	0.102153	−	0.510342i
$607$	201.354	−	348.755i	0.331720	−	0.574556i	−0.651129	−	0.758967i	$-0.725704\pi$
$607$	201.354	−	348.755i	0.331720	−	0.574556i	0.982849	+	0.184411i	$0.0590378\pi$
$608$	100.997	−	58.3106i	0.166113	−	0.0959055i
$609$	335.073	+	560.504i	0.550202	+	0.920368i
$610$	85.1798	−	147.536i	0.139639	−	0.241862i
$611$	54.4194	−	31.4191i	0.0890662	−	0.0514224i
$612$	−34.1472	+	81.8795i	−0.0557961	+	0.133790i
$613$	50.5577	−	87.5686i	0.0824759	−	0.142852i	−0.821837	−	0.569723i	$-0.807051\pi$
$613$	50.5577	−	87.5686i	0.0824759	−	0.142852i	0.904313	+	0.426870i	$0.140384\pi$
$614$			217.697i			0.354555i
$615$	328.354	+	288.660i	0.533909	+	0.469366i
$616$	139.198	+	153.566i	0.225971	+	0.249295i
$617$	129.541	−	74.7908i	0.209954	−	0.121217i	−0.391336	−	0.920248i	$-0.627987\pi$
$617$	129.541	−	74.7908i	0.209954	−	0.121217i	0.601290	+	0.799031i	$0.294654\pi$
$618$	−235.305	−	695.943i	−0.380753	−	1.12612i
$619$	−490.963	−	850.373i	−0.793155	−	1.37378i	−0.924004	−	0.382382i	$-0.875104\pi$
$619$	−490.963	−	850.373i	−0.793155	−	1.37378i	0.130849	−	0.991402i	$-0.458230\pi$
$620$	−135.914	−	78.4698i	−0.219216	−	0.126564i
$621$	−358.109	+	174.992i	−0.576665	+	0.281791i
$622$	712.191			1.14500
$623$	−641.115	+	581.131i	−1.02908	+	0.932795i
$624$	7.59455	−	37.9412i	0.0121708	−	0.0608032i
$625$	−22.0502	+	38.1921i	−0.0352804	+	0.0611074i
$626$			636.742i			1.01716i
$627$	207.376	+	613.339i	0.330743	+	0.978212i
$628$	−230.481			−0.367009
$629$			246.907i			0.392538i
$630$	−259.491	−	47.8493i	−0.411890	−	0.0759513i
$631$	−1084.15			−1.71814			−0.859072	−	0.511855i	$-0.828959\pi$
$631$	−1084.15			−1.71814			−0.859072	+	0.511855i	$0.828959\pi$
$632$			92.4488i			0.146280i
$633$	−36.9789	+	184.741i	−0.0584185	+	0.291850i
$634$	478.697			0.755043
$635$	366.278	+	211.470i	0.576815	+	0.333024i
$636$	192.961	+	570.706i	0.303399	+	0.897337i
$637$	−128.439	−	92.0185i	−0.201631	−	0.144456i
$638$		−	460.369i		−	0.721581i
$639$	22.4662	−	2.90262i	0.0351584	−	0.00454244i
$640$	16.7534	−	29.0177i	0.0261771	−	0.0453401i
$641$	−402.810	+	232.562i	−0.628408	+	0.362812i	−0.780135	−	0.625611i	$-0.784850\pi$
$641$	−402.810	+	232.562i	−0.628408	+	0.362812i	0.151727	+	0.988422i	$0.451517\pi$
$642$	−126.267	+	630.811i	−0.196678	+	0.982571i
$643$	−477.440	−	826.950i	−0.742519	−	1.28608i	−0.951345	−	0.308128i	$-0.900297\pi$
$643$	−477.440	−	826.950i	−0.742519	−	1.28608i	0.208825	−	0.977953i	$-0.433036\pi$
$644$	−196.766	−	63.2111i	−0.305537	−	0.0981539i
$645$	469.268	+	93.9316i	0.727547	+	0.145630i
$646$	−143.694			−0.222437
$647$	853.653	+	492.857i	1.31940	+	0.761757i	0.983632	−	0.180187i	$-0.0576702\pi$
$647$	853.653	+	492.857i	1.31940	+	0.761757i	0.335770	+	0.941944i	$0.391004\pi$
$648$	58.2279	+	221.580i	0.0898579	+	0.341944i
$649$	−145.864	−	252.643i	−0.224751	−	0.389281i
$650$	−64.0908	−	37.0028i	−0.0986012	−	0.0569274i
$651$	486.040	+	270.846i	0.746605	+	0.416045i
$652$	90.0647	+	155.997i	0.138136	+	0.239259i
$653$	848.101	+	489.651i	1.29878	+	0.749849i	0.980193	−	0.198046i	$-0.0634594\pi$
$653$	848.101	+	489.651i	1.29878	+	0.749849i	0.318584	+	0.947895i	$0.396793\pi$
$654$	119.942	+	354.743i	0.183398	+	0.542421i
$655$	−123.951	−	214.690i	−0.189239	−	0.327771i
$656$	170.459	−	98.4145i	0.259846	−	0.150022i
$657$	−1148.74	−	479.071i	−1.74846	−	0.729180i
$658$	−188.569	+	40.7370i	−0.286580	+	0.0619103i
$659$	−752.133	−	434.244i	−1.14132	−	0.658944i	−0.194566	−	0.980889i	$-0.562330\pi$
$659$	−752.133	−	434.244i	−1.14132	−	0.658944i	−0.946758	+	0.321945i	$0.895663\pi$
$660$	139.709	+	122.820i	0.211681	+	0.186091i
$661$	715.343			1.08221			0.541107	−	0.840954i	$-0.318005\pi$
$661$	715.343			1.08221			0.541107	+	0.840954i	$0.318005\pi$
$662$		−	28.1750i		−	0.0425605i
$663$	−31.4785	+	35.8072i	−0.0474789	+	0.0540078i
$664$	11.7298	−	20.3166i	0.0176654	−	0.0305973i
$665$	−90.2485	−	417.755i	−0.135712	−	0.628204i
$666$	386.942	+	506.799i	0.580994	+	0.760959i
$667$	229.524	+	397.548i	0.344114	+	0.596024i
$668$	−329.871	+	190.451i	−0.493819	+	0.285107i
$669$	−1049.97	+	355.004i	−1.56946	+	0.530649i
$670$	−159.405	+	276.098i	−0.237918	+	0.412086i
$671$	368.755	−	212.901i	0.549560	−	0.317288i
$672$	−57.8257	+	103.770i	−0.0860502	+	0.154419i
$673$	113.251	−	196.156i	0.168278	−	0.291465i	−0.769537	−	0.638603i	$-0.779513\pi$
$673$	113.251	−	196.156i	0.168278	−	0.291465i	0.937814	+	0.347137i	$0.112846\pi$
$674$	87.3033	−	50.4046i	0.129530	−	0.0747842i
$675$	437.136	+	30.2401i	0.647609	+	0.0448002i
$676$	−158.603	+	274.708i	−0.234619	+	0.406373i
$677$			986.694i			1.45745i	0.684806	+	0.728725i	$0.259887\pi$
$677$			986.694i			1.45745i	−0.684806	+	0.728725i	$0.740113\pi$
$678$	185.444	−	926.447i	0.273516	−	1.36644i
$679$	188.937	−	588.130i	0.278257	−	0.866170i
$680$	−35.7540	+	20.6426i	−0.0525795	+	0.0303568i
$681$	−558.049	−	111.703i	−0.819456	−	0.164027i
$682$	−196.129	−	339.706i	−0.287579	−	0.498102i
$683$	545.995	+	315.230i	0.799407	+	0.461538i	0.843264	−	0.537500i	$-0.180631\pi$
$683$	545.995	+	315.230i	0.799407	+	0.461538i	−0.0438569	+	0.999038i	$0.513965\pi$
$684$	−294.946	+	225.192i	−0.431208	+	0.329228i
$685$	17.8257			0.0260229
$686$	289.018	+	389.573i	0.421308	+	0.567890i
$687$	467.274	−	157.990i	0.680166	−	0.229971i
$688$	107.729	−	186.592i	0.156583	−	0.271210i
$689$			323.763i			0.469902i
$690$	−181.879	−	36.4060i	−0.263592	−	0.0527623i
$691$	512.489			0.741663			0.370831	−	0.928700i	$-0.379073\pi$
$691$	512.489			0.741663			0.370831	+	0.928700i	$0.379073\pi$
$692$			30.2382i			0.0436968i
$693$	−501.886	−	427.861i	−0.724222	−	0.617405i
$694$	−340.313			−0.490364
$695$			550.636i			0.792281i
$696$	249.960	−	84.5140i	0.359138	−	0.121428i
$697$	−242.522			−0.347952
$698$	−467.744	−	270.052i	−0.670120	−	0.386894i
$699$	1112.40	+	222.664i	1.59141	+	0.318547i
$700$	152.590	+	168.340i	0.217986	+	0.240486i
$701$		−	1245.31i		−	1.77648i	−0.459378	−	0.888241i	$-0.651928\pi$
$701$		−	1245.31i		−	1.77648i	0.459378	−	0.888241i	$-0.348072\pi$
$702$	−8.49708	+	122.829i	−0.0121041	+	0.174971i
$703$	−516.395	+	894.422i	−0.734559	+	1.27229i
$704$	72.5274	−	41.8737i	0.103022	−	0.0594797i
$705$	−164.024	+	55.4580i	−0.232658	+	0.0786638i
$706$	50.5431	+	87.5432i	0.0715908	+	0.123999i
$707$	−385.564	+	349.490i	−0.545352	+	0.494328i
$708$	110.397	−	125.578i	0.155928	−	0.177369i
$709$	898.046			1.26664			0.633319	−	0.773891i	$-0.281692\pi$
$709$	898.046			1.26664			0.633319	+	0.773891i	$0.281692\pi$
$710$	9.12965	+	5.27101i	0.0128587	+	0.00742395i
$711$	−37.6934	−	291.745i	−0.0530146	−	0.410331i
$712$	174.817	+	302.792i	0.245529	+	0.425269i
$713$	338.732	+	195.567i	0.475079	+	0.274287i
$714$	125.634	−	75.1049i	0.175958	−	0.105189i
$715$	49.9849	+	86.5764i	0.0699089	+	0.121086i
$716$	−128.719	−	74.3159i	−0.179775	−	0.103793i
$717$	−339.258	−	67.9080i	−0.473163	−	0.0947113i
$718$	−176.343	−	305.435i	−0.245603	−	0.425397i
$719$	928.510	−	536.076i	1.29139	−	0.745585i	0.312490	−	0.949921i	$-0.398837\pi$
$719$	928.510	−	536.076i	1.29139	−	0.745585i	0.978901	+	0.204336i	$0.0655034\pi$
$720$	−41.0383	+	98.4032i	−0.0569976	+	0.136671i
$721$	−370.728	+	1154.02i	−0.514186	+	1.60058i
$722$	−78.4022	−	45.2656i	−0.108590	−	0.0626947i
$723$	−160.323	+	800.946i	−0.221746	+	1.10781i
$724$	336.708			0.465067
$725$		−	504.660i		−	0.696082i
$726$	−15.5078	−	45.8660i	−0.0213605	−	0.0631763i
$727$	−369.111	+	639.319i	−0.507718	+	0.879394i	0.492242	+	0.870458i	$0.336178\pi$
$727$	−369.111	+	639.319i	−0.507718	+	0.879394i	−0.999960	+	0.00893533i	$0.997156\pi$
$728$	−47.3013	+	42.8757i	−0.0649743	+	0.0588953i
$729$	−274.096	−	675.509i	−0.375988	−	0.926624i
$730$	−289.607	−	501.615i	−0.396722	−	0.687143i
$731$	−229.909	+	132.738i	−0.314514	+	0.181585i
$732$	183.291	+	161.134i	0.250398	+	0.220128i
$733$	−460.261	+	797.195i	−0.627913	+	1.08758i	0.360056	+	0.932931i	$0.382757\pi$
$733$	−460.261	+	797.195i	−0.627913	+	1.08758i	−0.987970	+	0.154647i	$0.950576\pi$
$734$	91.5162	−	52.8369i	0.124681	−	0.0719848i
$735$	297.254	+	318.079i	0.404427	+	0.432761i
$736$	−41.7537	+	72.3195i	−0.0567305	+	0.0982601i
$737$	−690.085	+	398.421i	−0.936344	+	0.540598i
$738$	−497.800	+	380.071i	−0.674526	+	0.515002i
$739$	174.909	−	302.951i	0.236683	−	0.409948i	−0.723077	−	0.690767i	$-0.757273\pi$
$739$	174.909	−	302.951i	0.236683	−	0.409948i	0.959761	+	0.280820i	$0.0906063\pi$
$740$			296.733i			0.400991i
$741$	−188.921	+	63.8759i	−0.254954	+	0.0862023i
$742$	304.015	−	946.350i	0.409724	−	1.27540i
$743$	780.241	−	450.472i	1.05012	−	0.606288i	0.127439	−	0.991846i	$-0.459324\pi$
$743$	780.241	−	450.472i	1.05012	−	0.606288i	0.922684	+	0.385558i	$0.125991\pi$
$744$	148.440	−	168.852i	0.199516	−	0.226952i
$745$	−419.303	−	726.254i	−0.562823	−	0.974837i
$746$	−160.294	−	92.5459i	−0.214872	−	0.124056i
$747$	−28.7328	+	68.8966i	−0.0384643	+	0.0922311i
$748$	−103.189			−0.137954
$749$	786.432	−	712.852i	1.04998	−	0.951739i
$750$	389.072	+	342.038i	0.518763	+	0.456051i
$751$	124.709	−	216.001i	0.166057	−	0.287618i	−0.770973	−	0.636867i	$-0.780230\pi$
$751$	124.709	−	216.001i	0.166057	−	0.287618i	0.937030	+	0.349249i	$0.113563\pi$
$752$			77.9512i			0.103659i
$753$	373.968	−	425.393i	0.496638	−	0.564931i
$754$	141.803			0.188067
$755$			128.064i			0.169621i
$756$	140.174	−	351.049i	0.185416	−	0.464350i
$757$	−1393.33			−1.84060			−0.920299	−	0.391215i	$-0.872055\pi$
$757$	−1393.33			−1.84060			−0.920299	+	0.391215i	$0.872055\pi$
$758$			1008.17i			1.33004i
$759$	−348.191	−	306.099i	−0.458750	−	0.403293i
$760$	−172.693			−0.227227
$761$	1225.68	+	707.645i	1.61061	+	0.929889i	0.989228	+	0.146384i	$0.0467637\pi$
$761$	1225.68	+	707.645i	1.61061	+	0.929889i	0.621387	+	0.783504i	$0.286570\pi$
$762$	−400.036	+	455.045i	−0.524981	+	0.597172i
$763$	188.972	−	588.238i	0.247669	−	0.770954i
$764$		−	189.666i		−	0.248254i
$765$	104.414	−	79.7206i	0.136489	−	0.104210i
$766$	−214.273	+	371.131i	−0.279729	+	0.484505i
$767$	77.8191	−	44.9289i	0.101459	−	0.0585774i
$768$	36.0501	+	31.6921i	0.0469403	+	0.0412658i
$769$	599.927	+	1039.10i	0.780139	+	1.35124i	0.931860	+	0.362818i	$0.118185\pi$
$769$	599.927	+	1039.10i	0.780139	+	1.35124i	−0.151721	+	0.988423i	$0.548481\pi$
$770$	−64.8088	−	299.997i	−0.0841673	−	0.389606i
$771$	293.077	+	866.811i	0.380126	+	1.12427i
$772$	161.593			0.209318
$773$	621.344	+	358.733i	0.803808	+	0.464079i	0.844801	−	0.535081i	$-0.179719\pi$
$773$	621.344	+	358.733i	0.803808	+	0.464079i	−0.0409928	+	0.999159i	$0.513052\pi$
$774$	−263.889	+	632.763i	−0.340941	+	0.817523i
$775$	−214.998	−	372.388i	−0.277417	−	0.480501i
$776$	−216.161	−	124.801i	−0.278558	−	0.160826i
$777$	−15.9973	−	1051.91i	−0.0205885	−	1.35381i
$778$	−101.398	−	175.626i	−0.130332	−	0.225741i
$779$	−878.541	−	507.226i	−1.12778	−	0.651124i
$780$	−37.8310	+	43.0332i	−0.0485013	+	0.0551708i
$781$	13.1745	+	22.8189i	0.0168687	+	0.0292175i
$782$	89.1083	−	51.4467i	0.113949	−	0.0657886i
$783$	−754.354	+	368.619i	−0.963415	+	0.470778i
$784$	178.521	−	80.9085i	0.227706	−	0.103200i
$785$	295.572	+	170.649i	0.376525	+	0.217387i
$786$	336.423	−	113.748i	0.428019	−	0.144718i
$787$	999.151			1.26957			0.634784	−	0.772689i	$-0.281089\pi$
$787$	999.151			1.26957			0.634784	+	0.772689i	$0.281089\pi$
$788$		−	599.859i		−	0.761243i
$789$	−56.5086	−	11.3111i	−0.0716206	−	0.0143360i
$790$	68.4491	−	118.557i	0.0866445	−	0.150073i
$791$	−1155.00	+	1046.94i	−1.46018	+	1.32356i
$792$	−211.806	+	161.714i	−0.267431	+	0.204184i
$793$	65.5776	+	113.584i	0.0826956	+	0.143233i
$794$	−103.762	+	59.9073i	−0.130683	+	0.0754500i
$795$	175.095	−	874.749i	0.220246	−	1.10031i
$796$	332.502	−	575.910i	0.417716	−	0.723505i
$797$	−655.287	+	378.330i	−0.822192	+	0.474693i	−0.851172	−	0.524887i	$-0.824107\pi$
$797$	−655.287	+	378.330i	−0.822192	+	0.474693i	0.0289800	+	0.999580i	$0.490774\pi$
$798$	612.190	−	9.31007i	0.767155	−	0.0116668i
$799$	48.0237	−	83.1795i	0.0601048	−	0.104105i
$800$	79.5051	−	45.9023i	0.0993814	−	0.0573779i
$801$	−675.133	−	884.258i	−0.842862	−	1.10394i
$802$	344.843	−	597.286i	0.429979	−	0.744745i
$803$		−	1447.70i		−	1.80287i
$804$	−343.010	−	301.545i	−0.426630	−	0.375055i
$805$	205.533	+	226.748i	0.255321	+	0.281675i
$806$	104.636	−	60.4117i	0.129822	−	0.0749525i
$807$	−98.1119	−	290.178i	−0.121576	−	0.359576i
$808$	105.134	+	182.097i	0.130116	+	0.225368i
$809$	125.257	+	72.3172i	0.154829	+	0.0893908i	0.575413	−	0.817863i	$-0.304841\pi$
$809$	125.257	+	72.3172i	0.154829	+	0.0893908i	−0.420584	+	0.907254i	$0.638175\pi$
$810$	89.3855	−	327.268i	0.110352	−	0.404035i
$811$	379.249			0.467631			0.233816	−	0.972281i	$-0.424879\pi$
$811$	379.249			0.467631			0.233816	+	0.972281i	$0.424879\pi$
$812$	−414.486	−	133.154i	−0.510451	−	0.163982i
$813$	3.71899	−	18.5795i	0.00457440	−	0.0228530i
$814$	−370.831	+	642.299i	−0.455567	+	0.789065i
$815$		−	266.736i		−	0.327283i
$816$	−18.9434	−	56.0273i	−0.0232149	−	0.0686609i
$817$	−1110.47			−1.35920
$818$			714.180i			0.873080i
$819$	131.790	−	154.591i	0.160916	−	0.188756i
$820$	−291.465			−0.355445
$821$		−	190.491i		−	0.232023i	−0.993248	−	0.116012i	$-0.962989\pi$
$821$		−	190.491i		−	0.232023i	0.993248	−	0.116012i	$-0.0370110\pi$
$822$	−5.01206	+	25.0395i	−0.00609740	+	0.0304617i
$823$	276.753			0.336273			0.168136	−	0.985764i	$-0.446225\pi$
$823$	276.753			0.336273			0.168136	+	0.985764i	$0.446225\pi$
$824$	424.148	+	244.882i	0.514743	+	0.297187i
$825$	163.247	+	482.823i	0.197875	+	0.585240i
$826$	−269.652	+	58.2534i	−0.326455	+	0.0705247i
$827$			583.798i			0.705923i	0.935638	+	0.352962i	$0.114825\pi$
$827$			583.798i			0.705923i	−0.935638	+	0.352962i	$0.885175\pi$
$828$	102.278	−	245.246i	0.123524	−	0.296191i
$829$	−74.7220	+	129.422i	−0.0901351	+	0.156119i	−0.907568	−	0.419906i	$-0.862063\pi$
$829$	−74.7220	+	129.422i	−0.0901351	+	0.156119i	0.817433	+	0.576024i	$0.195397\pi$
$830$	−30.0849	+	17.3695i	−0.0362468	+	0.0209271i
$831$	−10.8479	+	54.1946i	−0.0130541	+	0.0652162i
$832$	12.8979	+	22.3399i	0.0155023	+	0.0268508i
$833$	−240.340	−	23.6471i	−0.288524	−	0.0283879i
$834$	−773.470	−	154.823i	−0.927422	−	0.185639i
$835$	564.041			0.675498
$836$	−373.804	−	215.816i	−0.447134	−	0.258153i
$837$	−399.596	+	593.379i	−0.477414	+	0.708935i
$838$	−119.875	−	207.629i	−0.143049	−	0.247768i
$839$	1054.23	+	608.660i	1.25653	+	0.725459i	0.972398	−	0.233326i	$-0.0749610\pi$
$839$	1054.23	+	608.660i	1.25653	+	0.725459i	0.284133	+	0.958785i	$0.408294\pi$
$840$	150.988	−	90.2615i	0.179747	−	0.107454i
$841$	62.9908	+	109.103i	0.0748998	+	0.129730i
$842$	−285.319	−	164.729i	−0.338859	−	0.195640i
$843$	159.285	+	471.103i	0.188950	+	0.558842i
$844$	−62.8018	−	108.776i	−0.0744098	−	0.128882i
$845$	406.788	−	234.859i	0.481406	−	0.277940i
$846$	−31.7824	−	245.995i	−0.0375678	−	0.290774i
$847$	−24.4328	+	76.0554i	−0.0288463	+	0.0897939i
$848$	−347.822	−	200.815i	−0.410167	−	0.236810i
$849$	−674.228	−	592.722i	−0.794143	−	0.698141i
$850$	−113.117			−0.133079
$851$		−	739.536i		−	0.869020i
$852$	−9.97109	+	11.3422i	−0.0117032	+	0.0133125i
$853$	−288.526	+	499.741i	−0.338248	+	0.585863i	−0.984103	−	0.177597i	$-0.943168\pi$
$853$	−288.526	+	499.741i	−0.338248	+	0.585863i	0.645855	+	0.763460i	$0.276501\pi$
$854$	−85.0259	−	393.580i	−0.0995619	−	0.460867i
$855$	544.975	−	70.4105i	0.637398	−	0.0823515i
$856$	−214.441	−	371.423i	−0.250515	−	0.433905i
$857$	1067.61	−	616.387i	1.24576	−	0.719238i	0.275496	−	0.961302i	$-0.411158\pi$
$857$	1067.61	−	616.387i	1.24576	−	0.719238i	0.970260	+	0.242064i	$0.0778245\pi$
$858$	−135.667	+	45.8703i	−0.158120	+	0.0534619i
$859$	−138.541	+	239.960i	−0.161282	+	0.279348i	−0.935329	−	0.353780i	$-0.884896\pi$
$859$	−138.541	+	239.960i	−0.161282	+	0.279348i	0.774047	+	0.633128i	$0.218229\pi$
$860$	−276.306	+	159.525i	−0.321286	+	0.185495i
$861$	1033.23	−	15.7132i	1.20004	−	0.0182500i
$862$	−72.2673	+	125.171i	−0.0838368	+	0.145210i
$863$	−391.421	+	225.987i	−0.453559	+	0.261862i	−0.709332	−	0.704874i	$-0.751003\pi$
$863$	−391.421	+	225.987i	−0.453559	+	0.261862i	0.255773	+	0.966737i	$0.417670\pi$
$864$	−126.687	−	85.3140i	−0.146628	−	0.0987430i
$865$	22.3884	−	38.7778i	0.0258825	−	0.0448299i
$866$			325.405i			0.375757i
$867$	155.866	−	778.681i	0.179776	−	0.898132i
$868$	−362.576	+	78.3279i	−0.417714	+	0.0902395i
$869$	296.325	−	171.083i	0.340996	−	0.196874i
$870$	−383.126	−	76.6889i	−0.440375	−	0.0881482i
$871$	−122.722	−	212.560i	−0.140897	−	0.244041i
$872$	−216.201	−	124.824i	−0.247937	−	0.143147i
$873$	733.035	+	305.707i	0.839674	+	0.350179i
$874$	430.395			0.492442
$875$	−180.484	−	835.453i	−0.206268	−	0.954803i
$876$	786.040	−	265.768i	0.897305	−	0.303388i
$877$	−747.574	+	1294.84i	−0.852422	+	1.47644i	0.0265935	+	0.999646i	$0.491534\pi$
$877$	−747.574	+	1294.84i	−0.852422	+	1.47644i	−0.879016	+	0.476792i	$0.841799\pi$
$878$		−	276.368i		−	0.314770i
$879$	−1016.40	−	203.449i	−1.15631	−	0.231455i
$880$	−124.013			−0.140924
$881$		−	1486.39i		−	1.68716i	−0.537004	−	0.843580i	$-0.680444\pi$
$881$		−	1486.39i		−	1.68716i	0.537004	−	0.843580i	$-0.319556\pi$
$882$	−530.380	+	328.114i	−0.601338	+	0.372011i
$883$	153.053			0.173333			0.0866665	−	0.996237i	$-0.472379\pi$
$883$	153.053			0.173333			0.0866665	+	0.996237i	$0.472379\pi$
$884$		−	31.7843i		−	0.0359551i
$885$	−234.552	+	79.3042i	−0.265030	+	0.0896093i
$886$	420.186			0.474250
$887$	−149.232	−	86.1590i	−0.168243	−	0.0971352i	0.413514	−	0.910498i	$-0.364301\pi$
$887$	−149.232	−	86.1590i	−0.168243	−	0.0971352i	−0.581757	+	0.813363i	$0.697635\pi$
$888$	−416.817	−	83.4327i	−0.469389	−	0.0939558i
$889$	977.116	−	211.088i	1.09912	−	0.237444i
$890$		−	517.738i		−	0.581728i
$891$	602.472	−	596.687i	0.676175	−	0.669682i
$892$	369.453	−	639.912i	0.414185	−	0.717390i
$893$	347.933	−	200.879i	0.389623	−	0.224949i
$894$	1138.05	−	384.787i	1.27299	−	0.430411i
$895$	110.047	+	190.607i	0.122958	+	0.212969i
$896$	−16.7231	−	77.4102i	−0.0186641	−	0.0863953i
$897$	94.2847	−	107.250i	0.105111	−	0.119565i
$898$	459.195			0.511353
$899$	713.535	+	411.960i	0.793699	+	0.458242i
$900$	−232.183	+	177.272i	−0.257981	+	0.196969i
$901$	247.434	+	428.568i	0.274621	+	0.475658i
$902$	−630.894	−	364.247i	−0.699439	−	0.403821i
$903$	970.897	−	580.409i	1.07519	−	0.642756i
$904$	314.941	+	545.495i	0.348387	+	0.603423i
$905$	−431.799	−	249.299i	−0.477126	−	0.275469i
$906$	−179.889	−	36.0078i	−0.198553	−	0.0397437i
$907$	18.1686	+	31.4689i	0.0200315	+	0.0346956i	0.875867	−	0.482552i	$-0.160290\pi$
$907$	18.1686	+	31.4689i	0.0200315	+	0.0346956i	−0.855836	+	0.517247i	$0.826957\pi$
$908$	328.581	−	189.706i	0.361873	−	0.208928i
$909$	−406.022	−	531.789i	−0.446669	−	0.585026i
$910$	92.4050	−	19.9624i	0.101544	−	0.0219367i
$911$	−1310.92	−	756.860i	−1.43899	−	0.830801i	−0.441210	−	0.897404i	$-0.645451\pi$
$911$	−1310.92	−	756.860i	−1.43899	−	0.830801i	−0.997780	+	0.0666029i	$0.978784\pi$
$912$	48.5561	−	242.579i	0.0532414	−	0.265986i
$913$	−86.8275			−0.0951013
$914$			852.449i			0.932658i
$915$	−115.751	−	342.348i	−0.126504	−	0.374151i
$916$	−164.420	+	284.784i	−0.179498	+	0.310899i
$917$	−557.860	−	179.213i	−0.608353	−	0.195434i
$918$	82.6241	+	169.084i	0.0900044	+	0.184188i
$919$	2.39355	+	4.14575i	0.00260452	+	0.00451115i	0.867325	−	0.497743i	$-0.165838\pi$
$919$	2.39355	+	4.14575i	0.00260452	+	0.00451115i	−0.864720	+	0.502254i	$0.832504\pi$
$920$	107.091	−	61.8289i	0.116403	−	0.0672053i
$921$	346.836	+	304.907i	0.376586	+	0.331061i
$922$	−173.884	+	301.176i	−0.188595	+	0.326656i
$923$	−7.02867	+	4.05800i	−0.00761502	+	0.00439654i
$924$	439.623	−	6.68571i	0.475783	−	0.00723562i
$925$	−406.508	+	704.093i	−0.439468	+	0.761181i
$926$	−1033.76	+	596.844i	−1.11638	+	0.644540i
$927$	−1438.35	−	599.852i	−1.55162	−	0.647090i
$928$	−87.9537	+	152.340i	−0.0947777	+	0.164160i
$929$		−	856.513i		−	0.921973i	−0.887407	−	0.460986i	$-0.847496\pi$
$929$		−	856.513i		−	0.921973i	0.887407	−	0.460986i	$-0.152504\pi$
$930$	−315.380	+	106.633i	−0.339118	+	0.114659i
$931$	−821.180	−	588.324i	−0.882040	−	0.631927i
$932$	−654.982	+	378.154i	−0.702771	+	0.405745i
$933$	997.500	−	1134.67i	1.06913	−	1.21615i
$934$	−499.114	−	864.491i	−0.534383	−	0.925579i
$935$	132.331	+	76.4014i	0.141531	+	0.0817127i
$936$	−49.8111	−	65.2404i	−0.0532170	−	0.0697012i
$937$	664.605			0.709290			0.354645	−	0.935001i	$-0.384602\pi$
$937$	664.605			0.709290			0.354645	+	0.935001i	$0.384602\pi$
$938$	159.117	+	736.544i	0.169634	+	0.785228i
$939$	1014.46	+	891.824i	1.08036	+	0.949759i
$940$	57.7151	−	99.9655i	0.0613991	−	0.106346i
$941$			535.737i			0.569327i	0.958628	+	0.284663i	$0.0918819\pi$
$941$			535.737i			0.569327i	−0.958628	+	0.284663i	$0.908118\pi$
$942$	−322.814	+	367.204i	−0.342690	+	0.389813i
$943$	726.405			0.770312
$944$			111.469i			0.118082i
$945$	−439.678	+	346.404i	−0.465268	+	0.366565i
$946$	−797.444			−0.842964
$947$			679.955i			0.718009i	0.933336	+	0.359005i	$0.116884\pi$
$947$			679.955i			0.718009i	−0.933336	+	0.359005i	$0.883116\pi$
$948$	147.290	+	129.484i	0.155369	+	0.136587i
$949$	445.921			0.469885
$950$	−409.767	−	236.579i	−0.431334	−	0.249031i
$951$	670.466	−	762.663i	0.705012	−	0.801959i
$952$	−29.8457	+	92.9049i	−0.0313505	+	0.0975891i
$953$			1272.32i			1.33507i	0.744579	+	0.667534i	$0.232650\pi$
$953$			1272.32i			1.33507i	−0.744579	+	0.667534i	$0.767350\pi$
$954$	1179.52	+	491.908i	1.23639	+	0.515627i
$955$	−140.429	+	243.230i	−0.147046	+	0.254691i
$956$	199.756	−	115.329i	0.208950	−	0.120637i
$957$	−733.462	−	644.795i	−0.766418	−	0.673767i
$958$	234.929	+	406.909i	0.245229	+	0.424749i
$959$	31.2167	−	28.2961i	0.0325513	−	0.0295058i
$960$	−22.7662	−	67.3338i	−0.0237148	−	0.0701394i
$961$	−258.977			−0.269487
$962$	−197.841	−	114.223i	−0.205656	−	0.118735i
$963$	828.160	+	1084.69i	0.859979	+	1.12636i
$964$	−272.278	−	471.600i	−0.282446	−	0.489211i
$965$	−207.229	−	119.644i	−0.214745	−	0.123983i
$966$	−376.300	+	224.955i	−0.389544	+	0.232872i
$967$	745.822	+	1291.80i	0.771275	+	1.33589i	0.936865	+	0.349692i	$0.113714\pi$
$967$	745.822	+	1291.80i	0.771275	+	1.33589i	−0.165590	+	0.986195i	$0.552953\pi$
$968$	27.9534	+	16.1389i	0.0288775	+	0.0166724i
$969$	−201.259	+	228.935i	−0.207698	+	0.236259i
$970$	184.805	+	320.092i	0.190521	+	0.329992i
$971$	390.142	−	225.249i	0.401795	−	0.231976i	−0.285463	−	0.958390i	$-0.592148\pi$
$971$	390.142	−	225.249i	0.401795	−	0.231976i	0.687258	+	0.726413i	$0.258814\pi$
$972$	434.576	+	217.577i	0.447095	+	0.223844i
$973$	874.065	+	964.285i	0.898320	+	0.991043i
$974$	532.300	+	307.324i	0.546509	+	0.315527i
$975$	−148.719	+	50.2834i	−0.152532	+	0.0515727i
$976$	−162.699			−0.166700
$977$			1297.96i			1.32852i	0.747502	+	0.664259i	$0.231253\pi$
$977$			1297.96i			1.32852i	−0.747502	+	0.664259i	$0.768747\pi$
$978$	374.680	+	74.9983i	0.383108	+	0.0766854i
$979$	647.023	−	1120.68i	0.660902	−	1.14472i
$980$	−288.842	−	28.4192i	−0.294737	−	0.0289992i
$981$	733.171	+	305.763i	0.747371	+	0.311685i
$982$	581.982	+	1008.02i	0.592650	+	1.02650i
$983$	376.130	−	217.159i	0.382634	−	0.220914i	−0.296329	−	0.955086i	$-0.595763\pi$
$983$	376.130	−	217.159i	0.382634	−	0.220914i	0.678964	+	0.734172i	$0.262429\pi$
$984$	81.9513	−	409.416i	0.0832838	−	0.416073i
$985$	−444.136	+	769.266i	−0.450900	+	0.780981i
$986$	187.706	−	108.372i	0.190371	−	0.109911i
$987$	−199.209	+	357.486i	−0.201833	+	0.362195i
$988$	66.4757	−	115.139i	0.0672831	−	0.116538i
$989$	688.626	−	397.578i	0.696285	−	0.402000i
$990$	391.355	−	50.5629i	0.395308	−	0.0510736i
$991$	−497.425	+	861.565i	−0.501942	+	0.869389i	0.498055	+	0.867145i	$0.334048\pi$
$991$	−497.425	+	861.565i	−0.501942	+	0.869389i	−0.999997	+	0.00224416i	$0.999286\pi$
$992$			149.882i			0.151091i
$993$	−44.8886	−	39.4621i	−0.0452050	−	0.0397403i
$994$	24.3551	−	5.26148i	0.0245021	−	0.00529324i
$995$	−852.808	+	492.369i	−0.857094	+	0.494843i
$996$	−15.9397	−	47.1435i	−0.0160037	−	0.0473329i
$997$	−818.276	−	1417.30i	−0.820739	−	1.42156i	−0.905133	−	0.425129i	$-0.860229\pi$
$997$	−818.276	−	1417.30i	−0.820739	−	1.42156i	0.0843943	−	0.996432i	$-0.473104\pi$
$998$	−117.634	−	67.9162i	−0.117870	−	0.0680523i
$999$	1349.39	+	93.3477i	1.35074	+	0.0934412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.r.a.11.16	yes	32
3.2	odd	2		378.3.r.a.305.3		32
7.2	even	3		126.3.i.a.65.10	✓	32
9.4	even	3		378.3.i.a.179.3		32
9.5	odd	6		126.3.i.a.95.10	yes	32
21.2	odd	6		378.3.i.a.359.6		32
63.23	odd	6	inner	126.3.r.a.23.8	yes	32
63.58	even	3		378.3.r.a.233.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.10	✓	32	7.2	even	3
126.3.i.a.95.10	yes	32	9.5	odd	6
126.3.r.a.11.16	yes	32	1.1	even	1	trivial
126.3.r.a.23.8	yes	32	63.23	odd	6	inner
378.3.i.a.179.3		32	9.4	even	3
378.3.i.a.359.6		32	21.2	odd	6
378.3.r.a.233.11		32	63.58	even	3
378.3.r.a.305.3		32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(2.25313 + 1.98076i) q^{3} -2.00000 q^{4} +(2.56482 + 1.48080i) q^{5} +(-2.80121 + 3.18641i) q^{6} +(6.84216 - 1.47812i) q^{7} -2.82843i q^{8} +(1.15321 + 8.92581i) q^{9} +(-2.09417 + 3.62721i) q^{10} +(-9.06593 + 5.23422i) q^{11} +(-4.50626 - 3.96151i) q^{12} +(-1.61224 - 2.79249i) q^{13} +(2.09038 + 9.67628i) q^{14} +(2.84578 + 8.41673i) q^{15} +4.00000 q^{16} +(-4.26829 - 2.46430i) q^{17} +(-12.6230 + 1.63089i) q^{18} +(-10.3079 - 17.8539i) q^{19} +(-5.12965 - 2.96160i) q^{20} +(18.3441 + 10.2222i) q^{21} +(-7.40230 - 12.8212i) q^{22} +(12.7844 + 7.38107i) q^{23} +(5.60242 - 6.37282i) q^{24} +(-8.11446 - 14.0547i) q^{25} +(3.94917 - 2.28006i) q^{26} +(-15.0815 + 22.3953i) q^{27} +(-13.6843 + 2.95625i) q^{28} +(26.9302 + 15.5482i) q^{29} +(-11.9031 + 4.02454i) q^{30} +26.4957 q^{31} +5.65685i q^{32} +(-30.7944 - 6.16401i) q^{33} +(3.48504 - 6.03627i) q^{34} +(19.7377 + 6.34075i) q^{35} +(-2.30642 - 17.8516i) q^{36} +(-25.0484 - 43.3851i) q^{37} +(25.2492 - 14.5776i) q^{38} +(1.89864 - 9.48530i) q^{39} +(4.18834 - 7.25441i) q^{40} +(42.6147 - 24.6036i) q^{41} +(-14.4564 + 25.9425i) q^{42} +(26.9323 - 46.6481i) q^{43} +(18.1319 - 10.4684i) q^{44} +(-10.2596 + 24.6008i) q^{45} +(-10.4384 + 18.0799i) q^{46} +19.4878i q^{47} +(9.01253 + 7.92302i) q^{48} +(44.6303 - 20.2271i) q^{49} +(19.8763 - 11.4756i) q^{50} +(-4.73584 - 14.0068i) q^{51} +(3.22449 + 5.58497i) q^{52} +(-86.9554 - 50.2038i) q^{53} +(-31.6717 - 21.3285i) q^{54} -31.0033 q^{55} +(-4.18077 - 19.3526i) q^{56} +(12.1390 - 60.6447i) q^{57} +(-21.9884 + 38.0851i) q^{58} +27.8673i q^{59} +(-5.69156 - 16.8335i) q^{60} -40.6748 q^{61} +37.4706i q^{62} +(21.0839 + 59.3672i) q^{63} -8.00000 q^{64} -9.54964i q^{65} +(8.71723 - 43.5499i) q^{66} +76.1185 q^{67} +(8.53657 + 4.92859i) q^{68} +(14.1848 + 41.9533i) q^{69} +(-8.96718 + 27.9134i) q^{70} -2.51699i q^{71} +(25.2460 - 3.26177i) q^{72} +(-69.1461 + 119.765i) q^{73} +(61.3558 - 35.4238i) q^{74} +(9.55589 - 47.7397i) q^{75} +(20.6159 + 35.7078i) q^{76} +(-54.2937 + 49.2139i) q^{77} +(13.4142 + 2.68508i) q^{78} -32.6856 q^{79} +(10.2593 + 5.92320i) q^{80} +(-78.3402 + 20.5867i) q^{81} +(34.7948 + 60.2663i) q^{82} +(7.18301 + 4.14711i) q^{83} +(-36.6882 - 20.4445i) q^{84} +(-7.29826 - 12.6410i) q^{85} +(65.9704 + 38.0880i) q^{86} +(29.8802 + 88.3742i) q^{87} +(14.8046 + 25.6423i) q^{88} +(-107.053 + 61.8071i) q^{89} +(-34.7908 - 14.5092i) q^{90} +(-15.1589 - 16.7235i) q^{91} +(-25.5688 - 14.7621i) q^{92} +(59.6984 + 52.4816i) q^{93} -27.5599 q^{94} -61.0561i q^{95} +(-11.2048 + 12.7456i) q^{96} +(44.1237 - 76.4246i) q^{97} +(28.6055 + 63.1168i) q^{98} +(-57.1745 - 74.8846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 8 q^{6} + 2 q^{7} - 20 q^{9} - 36 q^{11} + 10 q^{13} + 36 q^{14} + 10 q^{15} + 128 q^{16} - 54 q^{17} + 28 q^{19} + 28 q^{21} - 126 q^{23} - 16 q^{24} + 80 q^{25} - 72 q^{26} - 126 q^{27}+ \cdots + 394 q^{99}+O(q^{100}) \) 32 * q - 64 * q^4 + 8 * q^6 + 2 * q^7 - 20 * q^9 - 36 * q^11 + 10 * q^13 + 36 * q^14 + 10 * q^15 + 128 * q^16 - 54 * q^17 + 28 * q^19 + 28 * q^21 - 126 * q^23 - 16 * q^24 + 80 * q^25 - 72 * q^26 - 126 * q^27 - 4 * q^28 + 36 * q^29 + 76 * q^30 + 16 * q^31 - 40 * q^33 - 90 * q^35 + 40 * q^36 + 22 * q^37 + 46 * q^39 + 72 * q^41 + 120 * q^42 + 16 * q^43 + 72 * q^44 + 464 * q^45 - 12 * q^46 + 2 * q^49 - 288 * q^50 - 286 * q^51 - 20 * q^52 - 72 * q^53 - 160 * q^54 - 24 * q^55 - 72 * q^56 - 282 * q^57 - 24 * q^58 - 20 * q^60 + 124 * q^61 + 66 * q^63 - 256 * q^64 - 16 * q^66 - 140 * q^67 + 108 * q^68 + 218 * q^69 + 72 * q^70 + 196 * q^73 + 216 * q^74 + 658 * q^75 - 56 * q^76 + 486 * q^77 + 32 * q^78 + 76 * q^79 - 380 * q^81 - 56 * q^84 + 60 * q^85 - 144 * q^86 - 740 * q^87 - 486 * q^89 + 296 * q^90 - 122 * q^91 + 252 * q^92 + 238 * q^93 - 336 * q^94 + 32 * q^96 - 38 * q^97 + 288 * q^98 + 394 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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