LMFDB - Embedded newform 126.3.q.a.29.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(29,126)] 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, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.29"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.q (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	126.29
Dual form			126.3.q.a.113.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(-1.47915 - 2.61001i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.47352 + 2.00544i) q^{5} +(-0.0339773 + 4.24250i) q^{6} +(-1.32288 + 2.29129i) q^{7} -2.82843i q^{8} +(-4.62426 + 7.72115i) q^{9} +5.67224 q^{10} +(-2.91437 - 1.68261i) q^{11} +(3.04152 - 5.17196i) q^{12} +(10.3947 + 18.0042i) q^{13} +(3.24037 - 1.87083i) q^{14} +(10.3720 + 6.09958i) q^{15} +(-2.00000 + 3.46410i) q^{16} +9.33226i q^{17} +(11.1232 - 6.18660i) q^{18} +9.84429 q^{19} +(-6.94704 - 4.01088i) q^{20} +(7.93700 + 0.0635658i) q^{21} +(2.37958 + 4.12155i) q^{22} +(-31.0433 + 17.9229i) q^{23} +(-7.38221 + 4.18365i) q^{24} +(-4.45643 + 7.71877i) q^{25} -29.4007i q^{26} +(26.9922 + 0.648636i) q^{27} -5.29150 q^{28} +(-24.8605 - 14.3532i) q^{29} +(-8.39006 - 14.8046i) q^{30} +(1.68794 + 2.92360i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-0.0808517 + 10.0954i) q^{33} +(6.59891 - 11.4296i) q^{34} -10.6118i q^{35} +(-17.9977 - 0.288298i) q^{36} -65.0515 q^{37} +(-12.0567 - 6.96096i) q^{38} +(31.6157 - 53.7611i) q^{39} +(5.67224 + 9.82460i) q^{40} +(21.0056 - 12.1276i) q^{41} +(-9.67585 - 5.69016i) q^{42} +(12.3344 - 21.3638i) q^{43} -6.73046i q^{44} +(0.578164 - 36.0933i) q^{45} +50.6935 q^{46} +(-40.6301 - 23.4578i) q^{47} +(11.9996 + 0.0961024i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(10.9160 - 6.30235i) q^{50} +(24.3573 - 13.8038i) q^{51} +(-20.7895 + 36.0084i) q^{52} +63.1893i q^{53} +(-32.5999 - 19.8808i) q^{54} +13.4975 q^{55} +(6.48074 + 3.74166i) q^{56} +(-14.5611 - 25.6936i) q^{57} +(20.2985 + 35.1581i) q^{58} +(43.7311 - 25.2482i) q^{59} +(-0.192728 + 24.0645i) q^{60} +(-18.8189 + 32.5953i) q^{61} -4.77422i q^{62} +(-11.5741 - 20.8096i) q^{63} -8.00000 q^{64} +(-72.2126 - 41.6920i) q^{65} +(7.23752 - 12.3071i) q^{66} +(26.8361 + 46.4815i) q^{67} +(-16.1640 + 9.33226i) q^{68} +(92.6964 + 54.5127i) q^{69} +(-7.50366 + 12.9967i) q^{70} +84.1279i q^{71} +(21.8387 + 13.0794i) q^{72} -119.438 q^{73} +(79.6715 + 45.9983i) q^{74} +(26.7377 + 0.214137i) q^{75} +(9.84429 + 17.0508i) q^{76} +(7.71071 - 4.45178i) q^{77} +(-76.7361 + 43.4879i) q^{78} +(73.0280 - 126.488i) q^{79} -16.0435i q^{80} +(-38.2324 - 71.4092i) q^{81} -34.3020 q^{82} +(84.8471 + 48.9865i) q^{83} +(7.82690 + 13.8109i) q^{84} +(-18.7153 - 32.4158i) q^{85} +(-30.2130 + 17.4435i) q^{86} +(-0.689690 + 86.1167i) q^{87} +(-4.75915 + 8.24310i) q^{88} +78.6860i q^{89} +(-26.2299 + 43.7962i) q^{90} -55.0037 q^{91} +(-62.0866 - 35.8457i) q^{92} +(5.13390 - 8.72996i) q^{93} +(33.1744 + 57.4597i) q^{94} +(-34.1943 + 19.7421i) q^{95} +(-14.6285 - 8.60271i) q^{96} +(45.7282 - 79.2035i) q^{97} +9.89949i q^{98} +(26.4686 - 14.7215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30}+ \cdots - 440 q^{99}+O(q^{100}) $ 24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	−1.47915	−	2.61001i	−0.493048	−	0.870002i
$3$	−1.47915	−	2.61001i	−0.493048	−	0.870002i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−3.47352	+	2.00544i	−0.694704	+	0.401088i	−0.805372	−	0.592770i	$-0.798034\pi$
$5$	−3.47352	+	2.00544i	−0.694704	+	0.401088i	0.110668	+	0.993857i	$0.464701\pi$
$6$	−0.0339773	+	4.24250i	−0.00566289	+	0.707084i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$		−	2.82843i		−	0.353553i
$9$	−4.62426	+	7.72115i	−0.513807	+	0.857906i
$10$	5.67224			0.567224
$11$	−2.91437	−	1.68261i	−0.264943	−	0.152965i	0.361644	−	0.932316i	$-0.382216\pi$
$11$	−2.91437	−	1.68261i	−0.264943	−	0.152965i	−0.626587	+	0.779351i	$0.715549\pi$
$12$	3.04152	−	5.17196i	0.253460	−	0.430997i
$13$	10.3947	+	18.0042i	0.799594	+	1.38494i	0.919881	+	0.392199i	$0.128285\pi$
$13$	10.3947	+	18.0042i	0.799594	+	1.38494i	−0.120286	+	0.992739i	$0.538381\pi$
$14$	3.24037	−	1.87083i	0.231455	−	0.133631i
$15$	10.3720	+	6.09958i	0.691470	+	0.406638i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			9.33226i			0.548957i	0.961593	+	0.274478i	$0.0885051\pi$
$17$			9.33226i			0.548957i	−0.961593	+	0.274478i	$0.911495\pi$
$18$	11.1232	−	6.18660i	0.617957	−	0.343700i
$19$	9.84429			0.518120			0.259060	−	0.965861i	$-0.416587\pi$
$19$	9.84429			0.518120			0.259060	+	0.965861i	$0.416587\pi$
$20$	−6.94704	−	4.01088i	−0.347352	−	0.200544i
$21$	7.93700	+	0.0635658i	0.377952	+	0.00302694i
$22$	2.37958	+	4.12155i	0.108163	+	0.187343i
$23$	−31.0433	+	17.9229i	−1.34971	+	0.779255i	−0.988208	−	0.153116i	$-0.951069\pi$
$23$	−31.0433	+	17.9229i	−1.34971	+	0.779255i	−0.361502	+	0.932372i	$0.617736\pi$
$24$	−7.38221	+	4.18365i	−0.307592	+	0.174319i
$25$	−4.45643	+	7.71877i	−0.178257	+	0.308751i
$26$		−	29.4007i		−	1.13080i
$27$	26.9922	+	0.648636i	0.999711	+	0.0240236i
$28$	−5.29150			−0.188982
$29$	−24.8605	−	14.3532i	−0.857260	−	0.494939i	0.00583393	−	0.999983i	$-0.498143\pi$
$29$	−24.8605	−	14.3532i	−0.857260	−	0.494939i	−0.863094	+	0.505044i	$0.831476\pi$
$30$	−8.39006	−	14.8046i	−0.279669	−	0.493486i
$31$	1.68794	+	2.92360i	0.0544497	+	0.0943096i	0.891966	−	0.452103i	$-0.149326\pi$
$31$	1.68794	+	2.92360i	0.0544497	+	0.0943096i	−0.837516	+	0.546413i	$0.815993\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	−0.0808517	+	10.0954i	−0.00245005	+	0.305920i
$34$	6.59891	−	11.4296i	0.194085	−	0.336166i
$35$		−	10.6118i		−	0.303194i
$36$	−17.9977	−	0.288298i	−0.499936	−	0.00800828i
$37$	−65.0515			−1.75815			−0.879074	−	0.476686i	$-0.841838\pi$
$37$	−65.0515			−1.75815			−0.879074	+	0.476686i	$0.841838\pi$
$38$	−12.0567	−	6.96096i	−0.317283	−	0.183183i
$39$	31.6157	−	53.7611i	0.810660	−	1.37849i
$40$	5.67224	+	9.82460i	0.141806	+	0.245615i
$41$	21.0056	−	12.1276i	0.512332	−	0.295795i	−0.221460	−	0.975170i	$-0.571082\pi$
$41$	21.0056	−	12.1276i	0.512332	−	0.295795i	0.733792	+	0.679374i	$0.237749\pi$
$42$	−9.67585	−	5.69016i	−0.230377	−	0.135480i
$43$	12.3344	−	21.3638i	0.286847	−	0.496833i	−0.686208	−	0.727405i	$-0.740726\pi$
$43$	12.3344	−	21.3638i	0.286847	−	0.496833i	0.973055	+	0.230572i	$0.0740596\pi$
$44$		−	6.73046i		−	0.152965i
$45$	0.578164	−	36.0933i	0.0128481	−	0.802073i
$46$	50.6935			1.10203
$47$	−40.6301	−	23.4578i	−0.864471	−	0.499102i	0.00103617	−	0.999999i	$-0.499670\pi$
$47$	−40.6301	−	23.4578i	−0.864471	−	0.499102i	−0.865507	+	0.500897i	$0.833004\pi$
$48$	11.9996	+	0.0961024i	0.249992	+	0.00200213i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	10.9160	−	6.30235i	0.218320	−	0.126047i
$51$	24.3573	−	13.8038i	0.477593	−	0.270662i
$52$	−20.7895	+	36.0084i	−0.399797	+	0.692469i
$53$			63.1893i			1.19225i	0.802891	+	0.596125i	$0.203294\pi$
$53$			63.1893i			1.19225i	−0.802891	+	0.596125i	$0.796706\pi$
$54$	−32.5999	−	19.8808i	−0.603702	−	0.368163i
$55$	13.4975			0.245410
$56$	6.48074	+	3.74166i	0.115728	+	0.0668153i
$57$	−14.5611	−	25.6936i	−0.255458	−	0.450766i
$58$	20.2985	+	35.1581i	0.349975	+	0.606174i
$59$	43.7311	−	25.2482i	0.741205	−	0.427935i	−0.0813024	−	0.996689i	$-0.525908\pi$
$59$	43.7311	−	25.2482i	0.741205	−	0.427935i	0.822507	+	0.568755i	$0.192575\pi$
$60$	−0.192728	+	24.0645i	−0.00321213	+	0.401075i
$61$	−18.8189	+	32.5953i	−0.308507	+	0.534349i	−0.978036	−	0.208436i	$-0.933163\pi$
$61$	−18.8189	+	32.5953i	−0.308507	+	0.534349i	0.669529	+	0.742786i	$0.266496\pi$
$62$		−	4.77422i		−	0.0770035i
$63$	−11.5741	−	20.8096i	−0.183715	−	0.330312i
$64$	−8.00000			−0.125000
$65$	−72.2126	−	41.6920i	−1.11096	−	0.641415i
$66$	7.23752	−	12.3071i	0.109659	−	0.186471i
$67$	26.8361	+	46.4815i	0.400539	+	0.693754i	0.993791	−	0.111263i	$-0.0354895\pi$
$67$	26.8361	+	46.4815i	0.400539	+	0.693754i	−0.593252	+	0.805017i	$0.702156\pi$
$68$	−16.1640	+	9.33226i	−0.237705	+	0.137239i
$69$	92.6964	+	54.5127i	1.34343	+	0.790040i
$70$	−7.50366	+	12.9967i	−0.107195	+	0.185668i
$71$			84.1279i			1.18490i	0.805607	+	0.592450i	$0.201839\pi$
$71$			84.1279i			1.18490i	−0.805607	+	0.592450i	$0.798161\pi$
$72$	21.8387	+	13.0794i	0.303316	+	0.181658i
$73$	−119.438			−1.63613			−0.818067	−	0.575122i	$-0.804954\pi$
$73$	−119.438			−1.63613			−0.818067	+	0.575122i	$0.804954\pi$
$74$	79.6715	+	45.9983i	1.07664	+	0.621599i
$75$	26.7377	+	0.214137i	0.356503	+	0.00285516i
$76$	9.84429	+	17.0508i	0.129530	+	0.224353i
$77$	7.71071	−	4.45178i	0.100139	−	0.0578153i
$78$	−76.7361	+	43.4879i	−0.983796	+	0.557538i
$79$	73.0280	−	126.488i	0.924405	−	1.60112i	0.131889	−	0.991264i	$-0.457896\pi$
$79$	73.0280	−	126.488i	0.924405	−	1.60112i	0.792516	−	0.609852i	$-0.208771\pi$
$80$		−	16.0435i		−	0.200544i
$81$	−38.2324	−	71.4092i	−0.472006	−	0.881596i
$82$	−34.3020			−0.418318
$83$	84.8471	+	48.9865i	1.02225	+	0.590199i	0.914756	−	0.404006i	$-0.132383\pi$
$83$	84.8471	+	48.9865i	1.02225	+	0.590199i	0.107498	+	0.994205i	$0.465716\pi$
$84$	7.82690	+	13.8109i	0.0931774	+	0.164415i
$85$	−18.7153	−	32.4158i	−0.220180	−	0.381363i
$86$	−30.2130	+	17.4435i	−0.351314	+	0.202831i
$87$	−0.689690	+	86.1167i	−0.00792748	+	0.989847i
$88$	−4.75915	+	8.24310i	−0.0540813	+	0.0936715i
$89$			78.6860i			0.884112i	0.896987	+	0.442056i	$0.145751\pi$
$89$			78.6860i			0.884112i	−0.896987	+	0.442056i	$0.854249\pi$
$90$	−26.2299	+	43.7962i	−0.291443	+	0.486625i
$91$	−55.0037			−0.604436
$92$	−62.0866	−	35.8457i	−0.674855	−	0.389628i
$93$	5.13390	−	8.72996i	0.0552032	−	0.0938705i
$94$	33.1744	+	57.4597i	0.352919	+	0.611273i
$95$	−34.1943	+	19.7421i	−0.359940	+	0.207812i
$96$	−14.6285	−	8.60271i	−0.152380	−	0.0896116i
$97$	45.7282	−	79.2035i	0.471424	−	0.816531i	−0.528041	−	0.849219i	$-0.677073\pi$
$97$	45.7282	−	79.2035i	0.471424	−	0.816531i	0.999466	+	0.0326878i	$0.0104067\pi$
$98$			9.89949i			0.101015i
$99$	26.4686	−	14.7215i	0.267359	−	0.148702i
$100$	−17.8257			−0.178257
$101$	141.692	+	81.8059i	1.40289	+	0.809960i	0.994688	−	0.102931i	$-0.0328222\pi$
$101$	141.692	+	81.8059i	1.40289	+	0.809960i	0.408203	+	0.912891i	$0.366156\pi$
$102$	−39.5922	−	0.317085i	−0.388158	−	0.00310868i
$103$	28.6155	+	49.5635i	0.277820	+	0.481199i	0.970843	−	0.239717i	$-0.0770546\pi$
$103$	28.6155	+	49.5635i	0.277820	+	0.481199i	−0.693022	+	0.720916i	$0.743721\pi$
$104$	50.9235	−	29.4007i	0.489650	−	0.282699i
$105$	−27.6968	+	15.6964i	−0.263779	+	0.149489i
$106$	44.6816	−	77.3908i	0.421524	−	0.730101i
$107$			25.0726i			0.234324i	0.993113	+	0.117162i	$0.0373796\pi$
$107$			25.0726i			0.234324i	−0.993113	+	0.117162i	$0.962620\pi$
$108$	25.8687	+	47.4005i	0.239525	+	0.438894i
$109$	52.5383			0.482003			0.241002	−	0.970525i	$-0.422524\pi$
$109$	52.5383			0.482003			0.241002	+	0.970525i	$0.422524\pi$
$110$	−16.5310	−	9.54419i	−0.150282	−	0.0867654i
$111$	96.2206	+	169.785i	0.866852	+	1.52959i
$112$	−5.29150	−	9.16515i	−0.0472456	−	0.0818317i
$113$	77.4916	−	44.7398i	0.685767	−	0.395928i	−0.116258	−	0.993219i	$-0.537090\pi$
$113$	77.4916	−	44.7398i	0.685767	−	0.395928i	0.802024	+	0.597292i	$0.203756\pi$
$114$	−0.334483	+	41.7644i	−0.00293406	+	0.366355i
$115$	71.8864	−	124.511i	0.625099	−	1.08270i
$116$		−	57.4129i		−	0.494939i
$117$	−187.081	−	2.99678i	−1.59898	−	0.0256135i
$118$	−71.4126			−0.605191
$119$	−21.3829	−	12.3454i	−0.179688	−	0.103743i
$120$	17.2522	−	29.3366i	0.143768	−	0.244472i
$121$	−54.8376	−	94.9815i	−0.453203	−	0.784971i
$122$	46.0967	−	26.6140i	0.377842	−	0.218147i
$123$	−62.7235	−	36.8863i	−0.509947	−	0.299889i
$124$	−3.37588	+	5.84720i	−0.0272248	+	0.0471548i
$125$		−	136.020i		−	1.08816i
$126$	−0.539356	+	33.6706i	−0.00428061	+	0.267227i
$127$	−160.155			−1.26106			−0.630532	−	0.776163i	$-0.717163\pi$
$127$	−160.155			−1.26106			−0.630532	+	0.776163i	$0.717163\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	−74.0041	−	0.592684i	−0.573675	−	0.00459445i
$130$	58.9613	+	102.124i	0.453549	+	0.785570i
$131$	51.0527	−	29.4753i	0.389715	−	0.225002i	−0.292322	−	0.956320i	$-0.594428\pi$
$131$	51.0527	−	29.4753i	0.389715	−	0.225002i	0.682037	+	0.731318i	$0.261094\pi$
$132$	−17.5665	+	9.95533i	−0.133080	+	0.0754191i
$133$	−13.0228	+	22.5561i	−0.0979155	+	0.169595i
$134$		−	75.9040i		−	0.566448i
$135$	−95.0588	+	51.8782i	−0.704139	+	0.384283i
$136$	26.3956			0.194085
$137$	−125.476	−	72.4437i	−0.915885	−	0.528786i	−0.0335649	−	0.999437i	$-0.510686\pi$
$137$	−125.476	−	72.4437i	−0.915885	−	0.528786i	−0.882320	+	0.470650i	$0.844019\pi$
$138$	−74.9831	−	132.310i	−0.543356	−	0.958771i
$139$	−49.1724	−	85.1690i	−0.353758	−	0.612727i	0.633147	−	0.774032i	$-0.281763\pi$
$139$	−49.1724	−	85.1690i	−0.353758	−	0.612727i	−0.986905	+	0.161305i	$0.948430\pi$
$140$	18.3801	−	10.6118i	0.131287	−	0.0757985i
$141$	−1.12718	+	140.742i	−0.00799416	+	0.998173i
$142$	59.4874	−	103.035i	0.418925	−	0.725600i
$143$		−	69.9613i		−	0.489240i
$144$	−17.4983	−	31.4612i	−0.121516	−	0.218481i
$145$	115.138			0.794056
$146$	146.281	+	84.4553i	1.00192	+	0.578461i
$147$	−10.6453	+	18.1019i	−0.0724171	+	0.123142i
$148$	−65.0515	−	112.672i	−0.439537	−	0.761300i
$149$	−60.3560	+	34.8465i	−0.405074	+	0.233869i	−0.688671	−	0.725074i	$-0.741805\pi$
$149$	−60.3560	+	34.8465i	−0.405074	+	0.233869i	0.283597	+	0.958944i	$0.408472\pi$
$150$	−32.5955	−	19.1687i	−0.217303	−	0.127791i
$151$	66.3794	−	114.972i	0.439598	−	0.761407i	−0.558060	−	0.829801i	$-0.688454\pi$
$151$	66.3794	−	114.972i	0.439598	−	0.761407i	0.997658	+	0.0683938i	$0.0217874\pi$
$152$		−	27.8438i		−	0.183183i
$153$	−72.0558	−	43.1548i	−0.470953	−	0.282058i
$154$	−12.5915			−0.0817632
$155$	−11.7262	−	6.77012i	−0.0756529	−	0.0436782i
$156$	124.733	+	0.998958i	0.799569	+	0.00640358i
$157$	20.4647	+	35.4459i	0.130349	+	0.225770i	0.923811	−	0.382849i	$-0.125057\pi$
$157$	20.4647	+	35.4459i	0.130349	+	0.225770i	−0.793462	+	0.608619i	$0.791724\pi$
$158$	−178.881	+	103.277i	−1.13216	+	0.653653i
$159$	164.924	−	93.4661i	1.03726	−	0.587837i
$160$	−11.3445	+	19.6492i	−0.0709030	+	0.122808i
$161$		−	94.8389i		−	0.589062i
$162$	−3.66896	+	114.493i	−0.0226479	+	0.706744i
$163$	225.434			1.38303			0.691514	−	0.722363i	$-0.256944\pi$
$163$	225.434			1.38303			0.691514	+	0.722363i	$0.256944\pi$
$164$	42.0113	+	24.2552i	0.256166	+	0.147898i
$165$	−19.9648	−	35.2286i	−0.120999	−	0.213507i
$166$	−69.2774	−	119.992i	−0.417334	−	0.722843i
$167$	−138.606	+	80.0244i	−0.829978	+	0.479188i	−0.853845	−	0.520527i	$-0.825735\pi$
$167$	−138.606	+	80.0244i	−0.829978	+	0.479188i	0.0238673	+	0.999715i	$0.492402\pi$
$168$	0.179791	−	22.4492i	0.00107019	−	0.133626i
$169$	−131.601	+	227.939i	−0.778702	+	1.34875i
$170$			52.9348i			0.311381i
$171$	−45.5225	+	76.0093i	−0.266214	+	0.444499i
$172$	49.3377			0.286847
$173$	244.696	+	141.275i	1.41443	+	0.816621i	0.995802	−	0.0915378i	$-0.0291782\pi$
$173$	244.696	+	141.275i	1.41443	+	0.816621i	0.418627	+	0.908158i	$0.362512\pi$
$174$	61.7384	−	104.983i	0.354818	−	0.603352i
$175$	−11.7906	−	20.4219i	−0.0673749	−	0.116697i
$176$	11.6575	−	6.73046i	0.0662358	−	0.0382412i
$177$	−130.582	−	76.7927i	−0.737754	−	0.433857i
$178$	55.6394	−	96.3703i	0.312581	−	0.541406i
$179$			161.517i			0.902330i	0.892440	+	0.451165i	$0.148991\pi$
$179$			161.517i			0.902330i	−0.892440	+	0.451165i	$0.851009\pi$
$180$	63.0935	−	35.0919i	0.350520	−	0.194955i
$181$	−48.9442			−0.270410			−0.135205	−	0.990818i	$-0.543169\pi$
$181$	−48.9442			−0.270410			−0.135205	+	0.990818i	$0.543169\pi$
$182$	67.3655	+	38.8935i	0.370140	+	0.213701i
$183$	112.910	+	0.904271i	0.616994	+	0.00494137i
$184$	50.6935	+	87.8038i	0.275508	+	0.477194i
$185$	225.958	−	130.457i	1.22139	−	0.705171i
$186$	−12.4607	+	7.06176i	−0.0669932	+	0.0379664i
$187$	15.7026	−	27.1977i	0.0839711	−	0.145442i
$188$		−	93.8312i		−	0.499102i
$189$	−37.1935	+	60.9889i	−0.196791	+	0.322692i
$190$	55.8391			0.293890
$191$	−161.274	−	93.1116i	−0.844367	−	0.487495i	0.0143795	−	0.999897i	$-0.495423\pi$
$191$	−161.274	−	93.1116i	−0.844367	−	0.487495i	−0.858746	+	0.512401i	$0.828756\pi$
$192$	11.8332	+	20.8800i	0.0616310	+	0.108750i
$193$	158.411	+	274.376i	0.820783	+	1.42164i	0.905100	+	0.425199i	$0.139796\pi$
$193$	158.411	+	274.376i	0.820783	+	1.42164i	−0.0843170	+	0.996439i	$0.526871\pi$
$194$	−112.011	+	64.6694i	−0.577375	+	0.333347i
$195$	−2.00335	+	250.144i	−0.0102736	+	1.28279i
$196$	7.00000	−	12.1244i	0.0357143	−	0.0618590i
$197$			124.803i			0.633517i	0.948506	+	0.316758i	$0.102594\pi$
$197$			124.803i			0.633517i	−0.948506	+	0.316758i	$0.897406\pi$
$198$	−42.8269	−	0.686027i	−0.216297	−	0.00346478i
$199$	−349.881			−1.75820			−0.879098	−	0.476640i	$-0.841854\pi$
$199$	−349.881			−1.75820			−0.879098	+	0.476640i	$0.841854\pi$
$200$	21.8320	+	12.6047i	0.109160	+	0.0630235i
$201$	81.6225	−	138.795i	0.406082	−	0.690524i
$202$	−115.691	−	200.383i	−0.572728	−	0.991994i
$203$	65.7748	−	37.9751i	0.324014	−	0.187069i
$204$	48.2661	+	28.3842i	0.236598	+	0.139138i
$205$	−48.6423	+	84.2510i	−0.237280	+	0.410980i
$206$		−	80.9369i		−	0.392897i
$207$	5.16713	−	322.570i	0.0249620	−	1.55831i
$208$	−83.1578			−0.399797
$209$	−28.6899	−	16.5641i	−0.137272	−	0.0792543i
$210$	45.0205	+	0.360560i	0.214384	+	0.00171695i
$211$	−72.4171	−	125.430i	−0.343209	−	0.594456i	0.641818	−	0.766857i	$-0.278181\pi$
$211$	−72.4171	−	125.430i	−0.343209	−	0.594456i	−0.985027	+	0.172402i	$0.944847\pi$
$212$	−109.447	+	63.1893i	−0.516260	+	0.298063i
$213$	219.574	−	124.437i	1.03087	−	0.584213i
$214$	17.7290	−	30.7076i	0.0828460	−	0.143493i
$215$			98.9437i			0.460203i
$216$	1.83462	−	76.3455i	0.00849361	−	0.353451i
$217$	−8.93174			−0.0411601
$218$	−64.3461	−	37.1502i	−0.295165	−	0.170414i
$219$	176.666	+	311.733i	0.806694	+	1.42344i
$220$	13.4975	+	23.3784i	0.0613524	+	0.106265i
$221$	−168.020	+	97.0063i	−0.760271	+	0.438943i
$222$	2.21028	−	275.981i	0.00995620	−	1.24316i
$223$	−143.953	+	249.333i	−0.645527	+	1.11809i	0.338652	+	0.940912i	$0.390029\pi$
$223$	−143.953	+	249.333i	−0.645527	+	1.11809i	−0.984179	+	0.177175i	$0.943304\pi$
$224$			14.9666i			0.0668153i
$225$	−38.9901	−	70.1024i	−0.173289	−	0.311566i
$226$	−126.543			−0.559926
$227$	−195.541	−	112.895i	−0.861412	−	0.497337i	0.00307261	−	0.999995i	$-0.499022\pi$
$227$	−195.541	−	112.895i	−0.861412	−	0.497337i	−0.864485	+	0.502659i	$0.832355\pi$
$228$	29.9416	−	50.9143i	0.131323	−	0.223308i
$229$	210.223	+	364.117i	0.918004	+	1.59003i	0.802443	+	0.596729i	$0.203533\pi$
$229$	210.223	+	364.117i	0.918004	+	1.59003i	0.115561	+	0.993300i	$0.463133\pi$
$230$	−176.085	+	101.663i	−0.765587	+	0.442012i
$231$	−23.0244	−	13.5402i	−0.0996729	−	0.0586154i
$232$	−40.5971	+	70.3162i	−0.174987	+	0.303087i
$233$			33.5752i			0.144100i	0.997401	+	0.0720498i	$0.0229541\pi$
$233$			33.5752i			0.144100i	−0.997401	+	0.0720498i	$0.977046\pi$
$234$	227.008	+	135.957i	0.970118	+	0.581011i
$235$	188.173			0.800735
$236$	87.4622	+	50.4963i	0.370602	+	0.213967i
$237$	−438.154	−	3.50908i	−1.84875	−	0.0148063i
$238$	17.4591	+	30.2400i	0.0733574	+	0.127059i
$239$	314.355	−	181.493i	1.31529	−	0.759386i	0.332327	−	0.943164i	$-0.392166\pi$
$239$	314.355	−	181.493i	1.31529	−	0.759386i	0.982968	+	0.183778i	$0.0588328\pi$
$240$	−41.8736	+	23.7307i	−0.174474	+	0.0988778i
$241$	−146.429	+	253.623i	−0.607590	+	1.05238i	0.384046	+	0.923314i	$0.374530\pi$
$241$	−146.429	+	253.623i	−0.607590	+	1.05238i	−0.991636	+	0.129064i	$0.958803\pi$
$242$			155.104i			0.640926i
$243$	−129.827	+	205.412i	−0.534268	+	0.845315i
$244$	−75.2756			−0.308507
$245$	24.3147	+	14.0381i	0.0992435	+	0.0572982i
$246$	50.7377	+	89.5285i	0.206251	+	0.363937i
$247$	102.329	+	177.238i	0.414286	+	0.717565i
$248$	8.26918	−	4.77422i	0.0333435	−	0.0192509i
$249$	2.35386	−	293.910i	0.00945326	−	1.18036i
$250$	−96.1809	+	166.590i	−0.384724	+	0.666361i
$251$		−	201.905i		−	0.804404i	−0.915551	−	0.402202i	$-0.868245\pi$
$251$		−	201.905i		−	0.804404i	0.915551	−	0.402202i	$-0.131755\pi$
$252$	24.4693	−	40.8565i	0.0971003	−	0.162129i
$253$	120.629			0.476795
$254$	196.149	+	113.247i	0.772241	+	0.445854i
$255$	−56.9228	+	96.7947i	−0.223227	+	0.379587i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−226.134	+	130.558i	−0.879897	+	0.508009i	−0.870625	−	0.491948i	$-0.836285\pi$
$257$	−226.134	+	130.558i	−0.879897	+	0.508009i	−0.00927277	+	0.999957i	$0.502952\pi$
$258$	90.2171	+	53.0547i	0.349679	+	0.205638i
$259$	86.0550	−	149.052i	0.332259	−	0.575489i
$260$		−	166.768i		−	0.641415i
$261$	225.785	−	125.579i	0.865077	−	0.481145i
$262$	−83.3686			−0.318201
$263$	−146.320	−	84.4780i	−0.556350	−	0.321209i	0.195329	−	0.980738i	$-0.437423\pi$
$263$	−146.320	−	84.4780i	−0.556350	−	0.321209i	−0.751679	+	0.659529i	$0.770756\pi$
$264$	28.5540	+	0.228683i	0.108159	+	0.000866224i
$265$	−126.722	−	219.489i	−0.478197	−	0.828262i
$266$	31.8991	−	18.4170i	0.119922	−	0.0692367i
$267$	205.371	−	116.388i	0.769180	−	0.435910i
$268$	−53.6722	+	92.9631i	−0.200270	+	0.346877i
$269$		−	284.702i		−	1.05837i	−0.848506	−	0.529185i	$-0.822498\pi$
$269$		−	284.702i		−	1.05837i	0.848506	−	0.529185i	$-0.177502\pi$
$270$	153.106	+	3.67922i	0.567060	+	0.0136267i
$271$	483.986			1.78592			0.892962	−	0.450131i	$-0.148623\pi$
$271$	483.986			1.78592			0.892962	+	0.450131i	$0.148623\pi$
$272$	−32.3279	−	18.6645i	−0.118853	−	0.0686196i
$273$	81.3585	+	143.560i	0.298016	+	0.525861i
$274$	102.451	+	177.450i	0.373908	+	0.647628i
$275$	25.9754	−	14.9969i	0.0944561	−	0.0545342i
$276$	−1.72243	+	215.068i	−0.00624069	+	0.779230i
$277$	27.2899	−	47.2676i	0.0985196	−	0.170641i	−0.812552	−	0.582888i	$-0.801923\pi$
$277$	27.2899	−	47.2676i	0.0985196	−	0.170641i	0.911072	+	0.412247i	$0.135256\pi$
$278$			139.080i			0.500289i
$279$	−30.3790	−	0.486630i	−0.108885	−	0.00174419i
$280$	−30.0147			−0.107195
$281$	169.436	+	97.8240i	0.602976	+	0.348128i	0.770211	−	0.637789i	$-0.220151\pi$
$281$	169.436	+	97.8240i	0.602976	+	0.348128i	−0.167236	+	0.985917i	$0.553484\pi$
$282$	100.900	−	171.576i	0.357803	−	0.608427i
$283$	−44.3105	−	76.7481i	−0.156574	−	0.271195i	0.777057	−	0.629430i	$-0.216712\pi$
$283$	−44.3105	−	76.7481i	−0.156574	−	0.271195i	−0.933631	+	0.358236i	$0.883378\pi$
$284$	−145.714	+	84.1279i	−0.513077	+	0.296225i
$285$	102.105	+	60.0460i	0.358265	+	0.210688i
$286$	−49.4701	+	85.6847i	−0.172972	+	0.299597i
$287$			64.1733i			0.223600i
$288$	−0.815430	+	50.9052i	−0.00283135	+	0.176754i
$289$	201.909			0.698647
$290$	−141.015	−	81.4150i	−0.486258	−	0.280741i
$291$	−274.360	−	2.19729i	−0.942818	−	0.00755084i
$292$	−119.438	−	206.872i	−0.409034	−	0.708467i
$293$	399.075	−	230.406i	1.36203	−	0.786369i	0.372136	−	0.928178i	$-0.378625\pi$
$293$	399.075	−	230.406i	1.36203	−	0.786369i	0.989894	+	0.141810i	$0.0452921\pi$
$294$	25.8377	−	14.6428i	0.0878835	−	0.0498054i
$295$	−101.267	+	175.400i	−0.343279	+	0.594576i
$296$			183.993i			0.621599i
$297$	−77.5740	−	47.3079i	−0.261192	−	0.159286i
$298$	98.5609			0.330741
$299$	−645.374	−	372.607i	−2.15844	−	1.24618i
$300$	26.3668	+	46.5253i	0.0878895	+	0.155084i
$301$	32.6338	+	56.5234i	0.108418	+	0.187785i
$302$	−162.596	+	93.8746i	−0.538396	+	0.310843i
$303$	3.93087	−	490.820i	0.0129732	−	1.61987i
$304$	−19.6886	+	34.1016i	−0.0647650	+	0.112176i
$305$		−	150.961i		−	0.494953i
$306$	57.7350	+	103.805i	0.188676	+	0.339231i
$307$	−36.6995			−0.119542			−0.0597712	−	0.998212i	$-0.519037\pi$
$307$	−36.6995			−0.119542			−0.0597712	+	0.998212i	$0.519037\pi$
$308$	15.4214	+	8.90356i	0.0500695	+	0.0289077i
$309$	87.0346	−	147.998i	0.281665	−	0.478959i
$310$	9.57440	+	16.5833i	0.0308852	+	0.0534947i
$311$	−172.442	+	99.5593i	−0.554475	+	0.320126i	−0.750925	−	0.660388i	$-0.770392\pi$
$311$	−172.442	+	99.5593i	−0.554475	+	0.320126i	0.196450	+	0.980514i	$0.437059\pi$
$312$	−152.059	−	89.4228i	−0.487370	−	0.286612i
$313$	47.7951	−	82.7836i	0.152700	−	0.264484i	−0.779519	−	0.626378i	$-0.784536\pi$
$313$	47.7951	−	82.7836i	0.152700	−	0.264484i	0.932219	+	0.361894i	$0.117870\pi$
$314$		−	57.8830i		−	0.184341i
$315$	81.9352	+	49.0716i	0.260112	+	0.155783i
$316$	292.112			0.924405
$317$	−47.4997	−	27.4240i	−0.149841	−	0.0865109i	0.423205	−	0.906034i	$-0.360905\pi$
$317$	−47.4997	−	27.4240i	−0.149841	−	0.0865109i	−0.573046	+	0.819523i	$0.694238\pi$
$318$	−268.081	−	2.14700i	−0.843022	−	0.00675159i
$319$	48.3019	+	83.6614i	0.151417	+	0.262261i
$320$	27.7882	−	16.0435i	0.0868380	−	0.0501360i
$321$	65.4397	−	37.0861i	0.203862	−	0.115533i
$322$	−67.0612	+	116.153i	−0.208265	+	0.360725i
$323$			91.8695i			0.284426i
$324$	85.4520	−	137.630i	0.263741	−	0.424783i
$325$	−185.294			−0.570134
$326$	−276.099	−	159.406i	−0.846928	−	0.488974i
$327$	−77.7118	−	137.125i	−0.237651	−	0.419344i
$328$	−34.3020	−	59.4129i	−0.104579	−	0.181137i
$329$	107.497	−	62.0635i	0.326739	−	0.188643i
$330$	−0.458610	+	57.2633i	−0.00138973	+	0.173525i
$331$	111.327	−	192.824i	0.336336	−	0.582551i	−0.647404	−	0.762147i	$-0.724146\pi$
$331$	111.327	−	192.824i	0.336336	−	0.582551i	0.983741	+	0.179595i	$0.0574788\pi$
$332$			195.946i			0.590199i
$333$	300.815	−	502.272i	0.903348	−	1.50833i
$334$	226.343			0.677674
$335$	−186.432	−	107.636i	−0.556513	−	0.321303i
$336$	−16.0942	+	27.3674i	−0.0478994	+	0.0814507i
$337$	−120.850	−	209.318i	−0.358605	−	0.621121i	0.629123	−	0.777305i	$-0.283414\pi$
$337$	−120.850	−	209.318i	−0.358605	−	0.621121i	−0.987728	+	0.156184i	$0.950081\pi$
$338$	322.354	−	186.111i	0.953711	−	0.550625i
$339$	−231.393	−	136.077i	−0.682574	−	0.401407i
$340$	37.4306	−	64.8316i	0.110090	−	0.190681i
$341$		−	11.3606i		−	0.0333156i
$342$	109.500	−	60.9027i	0.320176	−	0.178078i
$343$	18.5203			0.0539949
$344$	−60.4261	−	34.8870i	−0.175657	−	0.101416i
$345$	−431.305	−	3.45423i	−1.25016	−	0.0100123i
$346$	−199.794	−	346.053i	−0.577438	−	1.00015i
$347$	−474.285	+	273.829i	−1.36682	+	0.789132i	−0.990520	−	0.137368i	$-0.956136\pi$
$347$	−474.285	+	273.829i	−1.36682	+	0.789132i	−0.376296	+	0.926500i	$0.622802\pi$
$348$	−149.848	+	84.9221i	−0.430598	+	0.244029i
$349$	12.2170	−	21.1605i	0.0350058	−	0.0606318i	−0.847992	−	0.530009i	$-0.822188\pi$
$349$	12.2170	−	21.1605i	0.0350058	−	0.0606318i	0.882998	+	0.469378i	$0.155522\pi$
$350$			33.3489i			0.0952825i
$351$	268.898	+	492.715i	0.766092	+	1.40375i
$352$	−19.0366			−0.0540813
$353$	145.238	+	83.8531i	0.411439	+	0.237544i	0.691408	−	0.722465i	$-0.256991\pi$
$353$	145.238	+	83.8531i	0.411439	+	0.237544i	−0.279969	+	0.960009i	$0.590324\pi$
$354$	105.630	+	186.387i	0.298389	+	0.526518i
$355$	−168.713	−	292.220i	−0.475249	−	0.823155i
$356$	−136.288	+	78.6860i	−0.382832	+	0.221028i
$357$	−0.593213	+	74.0702i	−0.00166166	+	0.207479i
$358$	114.210	−	197.817i	0.319022	−	0.552562i
$359$			54.4528i			0.151679i	0.997120	+	0.0758396i	$0.0241637\pi$
$359$			54.4528i			0.151679i	−0.997120	+	0.0758396i	$0.975836\pi$
$360$	−102.087	−	1.63529i	−0.283575	−	0.00454249i
$361$	−264.090			−0.731551
$362$	59.9442	+	34.6088i	0.165592	+	0.0956044i
$363$	−166.790	+	283.618i	−0.459475	+	0.781317i
$364$	−55.0037	−	95.2692i	−0.151109	−	0.261729i
$365$	414.870	−	239.525i	1.13663	−	0.656234i
$366$	−137.646	−	80.9468i	−0.376083	−	0.221166i
$367$	83.9105	−	145.337i	0.228639	−	0.396014i	−0.728766	−	0.684763i	$-0.759906\pi$
$367$	83.9105	−	145.337i	0.228639	−	0.396014i	0.957405	+	0.288748i	$0.0932391\pi$
$368$		−	143.383i		−	0.389628i
$369$	−3.49636	+	218.269i	−0.00947524	+	0.591515i
$370$	−368.987			−0.997263
$371$	−144.785	−	83.5916i	−0.390256	−	0.225314i
$372$	20.2546	+	0.162215i	0.0544479	+	0.000436062i
$373$	263.215	+	455.902i	0.705670	+	1.22226i	0.966449	+	0.256858i	$0.0826874\pi$
$373$	263.215	+	455.902i	0.705670	+	1.22226i	−0.260779	+	0.965399i	$0.583979\pi$
$374$	−38.4634	+	22.2068i	−0.102843	+	0.0593766i
$375$	−355.014	+	201.194i	−0.946704	+	0.536517i
$376$	−66.3487	+	114.919i	−0.176459	+	0.305637i
$377$		−	596.792i		−	1.58300i
$378$	88.6782	−	48.3960i	0.234599	−	0.128032i
$379$	88.4297			0.233324			0.116662	−	0.993172i	$-0.462781\pi$
$379$	88.4297			0.233324			0.116662	+	0.993172i	$0.462781\pi$
$380$	−68.3887	−	39.4842i	−0.179970	−	0.103906i
$381$	236.893	+	418.006i	0.621766	+	1.09713i
$382$	131.680	+	228.076i	0.344711	+	0.597057i
$383$	61.9482	−	35.7658i	0.161745	−	0.0933833i	−0.416943	−	0.908933i	$-0.636898\pi$
$383$	61.9482	−	35.7658i	0.161745	−	0.0933833i	0.578687	+	0.815549i	$0.303565\pi$
$384$	0.271819	−	33.9400i	0.000707861	−	0.0883855i
$385$	−17.8555	+	30.9267i	−0.0463780	+	0.0803291i
$386$		−	448.054i		−	1.16076i
$387$	107.916	+	194.028i	0.278853	+	0.501364i
$388$	182.913			0.471424
$389$	509.363	+	294.081i	1.30942	+	0.755991i	0.981999	−	0.188888i	$-0.0604885\pi$
$389$	509.363	+	294.081i	1.30942	+	0.755991i	0.327417	+	0.944880i	$0.393822\pi$
$390$	179.332	−	304.946i	0.459826	−	0.781912i
$391$	−167.261	−	289.704i	−0.427777	−	0.740932i
$392$	−17.1464	+	9.89949i	−0.0437409	+	0.0252538i
$393$	−152.445	−	89.6495i	−0.387901	−	0.228116i
$394$	88.2489	−	152.852i	0.223982	−	0.387948i
$395$			585.813i			1.48307i
$396$	51.9669	+	31.1234i	0.131230	+	0.0785944i
$397$	696.775			1.75510			0.877551	−	0.479484i	$-0.159176\pi$
$397$	696.775			1.75510			0.877551	+	0.479484i	$0.159176\pi$
$398$	428.515	+	247.403i	1.07667	+	0.621616i
$399$	78.1341	+	0.625760i	0.195825	+	0.00156832i
$400$	−17.8257	−	30.8751i	−0.0445643	−	0.0771877i
$401$	537.160	−	310.130i	1.33955	−	0.773390i	0.352811	−	0.935695i	$-0.385226\pi$
$401$	537.160	−	310.130i	1.33955	−	0.773390i	0.986741	+	0.162304i	$0.0518927\pi$
$402$	−198.110	+	112.273i	−0.492811	+	0.279286i
$403$	−35.0914	+	60.7800i	−0.0870753	+	0.150819i
$404$			327.224i			0.809960i
$405$	276.008	+	171.369i	0.681501	+	0.423133i
$406$	−107.410			−0.264556
$407$	189.584	+	109.457i	0.465809	+	0.268935i
$408$	−39.0430	−	68.8927i	−0.0956935	−	0.168855i
$409$	−53.2078	−	92.1586i	−0.130092	−	0.225327i	0.793620	−	0.608414i	$-0.208194\pi$
$409$	−53.2078	−	92.1586i	−0.130092	−	0.225327i	−0.923712	+	0.383088i	$0.874861\pi$
$410$	119.149	−	68.7906i	0.290607	−	0.167782i
$411$	−3.48101	+	434.648i	−0.00846961	+	1.05754i
$412$	−57.2310	+	99.1270i	−0.138910	+	0.240600i
$413$			133.601i			0.323488i
$414$	−234.420	+	391.413i	−0.566232	+	0.945441i
$415$	−392.958			−0.946886
$416$	101.847	+	58.8014i	0.244825	+	0.141350i
$417$	−149.559	+	254.317i	−0.358654	+	0.609874i
$418$	23.4252	+	40.5737i	0.0560412	+	0.0970663i
$419$	−162.096	+	93.5864i	−0.386865	+	0.223356i	−0.680801	−	0.732469i	$-0.738368\pi$
$419$	−162.096	+	93.5864i	−0.386865	+	0.223356i	0.293936	+	0.955825i	$0.405035\pi$
$420$	−54.8837	−	32.2759i	−0.130676	−	0.0768474i
$421$	−190.208	+	329.449i	−0.451800	+	0.782540i	−0.998498	−	0.0547895i	$-0.982551\pi$
$421$	−190.208	+	329.449i	−0.451800	+	0.782540i	0.546698	+	0.837330i	$0.315885\pi$
$422$			204.827i			0.485371i
$423$	369.006	−	205.236i	0.872354	−	0.485193i
$424$	178.726			0.421524
$425$	−72.0336	−	41.5886i	−0.169491	−	0.0978555i
$426$	−356.913	−	2.85844i	−0.837824	−	0.00670996i
$427$	−49.7901	−	86.2391i	−0.116605	−	0.201965i
$428$	−43.4271	+	25.0726i	−0.101465	+	0.0585809i
$429$	−182.599	+	103.483i	−0.425639	+	0.241219i
$430$	69.9637	−	121.181i	0.162706	−	0.281816i
$431$			630.398i			1.46264i	0.682035	+	0.731320i	$0.261095\pi$
$431$			630.398i			1.46264i	−0.682035	+	0.731320i	$0.738905\pi$
$432$	−56.2314	+	92.2065i	−0.130165	+	0.213441i
$433$	228.885			0.528603			0.264301	−	0.964440i	$-0.414859\pi$
$433$	228.885			0.528603			0.264301	+	0.964440i	$0.414859\pi$
$434$	10.9391	+	6.31569i	0.0252053	+	0.0145523i
$435$	−170.306	−	300.511i	−0.391508	−	0.690830i
$436$	52.5383	+	90.9991i	0.120501	+	0.208713i
$437$	−305.599	+	176.438i	−0.699312	+	0.403748i
$438$	4.05818	−	506.716i	0.00926525	−	1.15689i
$439$	−245.842	+	425.811i	−0.560004	+	0.969956i	0.437491	+	0.899223i	$0.355867\pi$
$439$	−245.842	+	425.811i	−0.560004	+	0.969956i	−0.997495	+	0.0707333i	$0.977466\pi$
$440$		−	38.1768i		−	0.0867654i
$441$	62.9919	+	1.00904i	0.142839	+	0.00228808i
$442$	274.375			0.620759
$443$	299.012	+	172.635i	0.674971	+	0.389695i	0.797958	−	0.602713i	$-0.205914\pi$
$443$	299.012	+	172.635i	0.674971	+	0.389695i	−0.122986	+	0.992408i	$0.539247\pi$
$444$	−197.855	+	336.444i	−0.445620	+	0.757756i
$445$	−157.800	−	273.318i	−0.354607	−	0.614197i
$446$	352.610	−	203.580i	0.790606	−	0.456457i
$447$	180.225	+	105.986i	0.403188	+	0.237106i
$448$	10.5830	−	18.3303i	0.0236228	−	0.0409159i
$449$			811.155i			1.80658i	0.429030	+	0.903290i	$0.358856\pi$
$449$			811.155i			1.80658i	−0.429030	+	0.903290i	$0.641144\pi$
$450$	−1.81695	+	113.428i	−0.00403768	+	0.252062i
$451$	−81.6243			−0.180985
$452$	154.983	+	89.4796i	0.342883	+	0.197964i
$453$	−398.263	−	3.18961i	−0.879169	−	0.00704108i
$454$	159.658	+	276.536i	0.351670	+	0.609111i
$455$	191.057	−	110.307i	0.419905	−	0.242432i
$456$	−72.6726	+	41.1851i	−0.159370	+	0.0903182i
$457$	−211.628	+	366.551i	−0.463081	+	0.802080i	−0.999113	−	0.0421179i	$-0.986589\pi$
$457$	−211.628	+	366.551i	−0.463081	+	0.802080i	0.536032	+	0.844198i	$0.319923\pi$
$458$		−	594.600i		−	1.29825i
$459$	−6.05324	+	251.898i	−0.0131879	+	0.548798i
$460$	287.546			0.625099
$461$	245.509	+	141.745i	0.532557	+	0.307472i	0.742057	−	0.670337i	$-0.233850\pi$
$461$	245.509	+	141.745i	0.532557	+	0.307472i	−0.209500	+	0.977809i	$0.567184\pi$
$462$	18.6247	+	32.8640i	0.0403132	+	0.0711342i
$463$	−323.479	−	560.282i	−0.698659	−	1.21011i	−0.968932	−	0.247329i	$-0.920447\pi$
$463$	−323.479	−	560.282i	−0.698659	−	1.21011i	0.270273	−	0.962784i	$-0.412886\pi$
$464$	99.4421	−	57.4129i	0.214315	−	0.123735i
$465$	−0.325313	+	40.6194i	−0.000699597	+	0.0873536i
$466$	23.7413	−	41.1211i	0.0509469	−	0.0882427i
$467$		−	526.799i		−	1.12805i	−0.825758	−	0.564025i	$-0.809252\pi$
$467$		−	526.799i		−	1.12805i	0.825758	−	0.564025i	$-0.190748\pi$
$468$	−181.890	−	327.031i	−0.388655	−	0.698784i
$469$	−142.003			−0.302779
$470$	−230.464	−	133.058i	−0.490348	−	0.283103i
$471$	62.2438	−	105.843i	0.132152	−	0.224719i
$472$	−71.4126	−	123.690i	−0.151298	−	0.262055i
$473$	−71.8942	+	41.5081i	−0.151996	+	0.0877551i
$474$	534.145	+	314.119i	1.12689	+	0.662699i
$475$	−43.8704	+	75.9858i	−0.0923587	+	0.159970i
$476$		−	49.3817i		−	0.103743i
$477$	−487.894	−	292.204i	−1.02284	−	0.612586i
$478$	−513.340			−1.07393
$479$	595.527	+	343.828i	1.24327	+	0.717803i	0.969759	−	0.244065i	$-0.0784810\pi$
$479$	595.527	+	343.828i	1.24327	+	0.717803i	0.273513	+	0.961868i	$0.411814\pi$
$480$	68.0647	+	0.545116i	0.141801	+	0.00113566i
$481$	−676.192	−	1171.20i	−1.40580	−	2.43493i
$482$	358.677	−	207.082i	0.744143	−	0.429631i
$483$	−247.530	+	140.281i	−0.512485	+	0.290436i
$484$	109.675	−	189.963i	0.226602	−	0.392486i
$485$			366.820i			0.756330i
$486$	304.253	−	159.775i	0.626035	−	0.328755i
$487$	211.195			0.433666			0.216833	−	0.976209i	$-0.430427\pi$
$487$	211.195			0.433666			0.216833	+	0.976209i	$0.430427\pi$
$488$	92.1934	+	53.2279i	0.188921	+	0.109074i
$489$	−333.449	−	588.383i	−0.681900	−	1.20324i
$490$	−19.8528	−	34.3861i	−0.0405160	−	0.0701757i
$491$	−233.574	+	134.854i	−0.475711	+	0.274652i	−0.718627	−	0.695395i	$-0.755229\pi$
$491$	−233.574	+	134.854i	−0.475711	+	0.274652i	0.242916	+	0.970047i	$0.421896\pi$
$492$	1.16549	−	145.527i	0.00236889	−	0.295786i
$493$	133.948	−	232.005i	0.271700	−	0.470598i
$494$		−	289.429i		−	0.585889i
$495$	−62.4160	+	104.216i	−0.126093	+	0.210538i
$496$	−13.5035			−0.0272248
$497$	−192.761	−	111.291i	−0.387849	−	0.223925i
$498$	−210.708	+	358.300i	−0.423109	+	0.719478i
$499$	−43.3403	−	75.0676i	−0.0868543	−	0.150436i	0.819326	−	0.573329i	$-0.194348\pi$
$499$	−43.3403	−	75.0676i	−0.0868543	−	0.150436i	−0.906180	+	0.422892i	$0.861015\pi$
$500$	235.594	−	136.020i	0.471188	−	0.272041i
$501$	413.883	+	243.396i	0.826114	+	0.485819i
$502$	−142.769	+	247.283i	−0.284400	+	0.492595i
$503$			796.451i			1.58340i	0.610909	+	0.791701i	$0.290804\pi$
$503$			796.451i			1.58340i	−0.610909	+	0.791701i	$0.709196\pi$
$504$	−58.8585	+	32.7364i	−0.116783	+	0.0649532i
$505$	−656.227			−1.29946
$506$	−147.740	−	85.2977i	−0.291976	−	0.168573i
$507$	789.579	+	6.32357i	1.55735	+	0.0124725i
$508$	−160.155	−	277.397i	−0.315266	−	0.546057i
$509$	−429.587	+	248.022i	−0.843982	+	0.487273i	−0.858616	−	0.512620i	$-0.828675\pi$
$509$	−429.587	+	248.022i	−0.843982	+	0.487273i	0.0146337	+	0.999893i	$0.495342\pi$
$510$	138.160	−	78.2983i	0.270902	−	0.153526i
$511$	158.001	−	273.667i	0.309200	−	0.535551i
$512$			22.6274i			0.0441942i
$513$	265.719	+	6.38536i	0.517971	+	0.0124471i
$514$	369.275			0.718433
$515$	−198.793	−	114.773i	−0.386006	−	0.222861i
$516$	−72.9776	−	128.772i	−0.141429	−	0.249557i
$517$	78.9409	+	136.730i	0.152690	+	0.264467i
$518$	−210.791	+	121.700i	−0.406932	+	0.234942i
$519$	6.78845	−	847.625i	0.0130799	−	1.63319i
$520$	−117.923	+	204.248i	−0.226774	+	0.392785i
$521$		−	759.191i		−	1.45718i	−0.684950	−	0.728590i	$-0.740176\pi$
$521$		−	759.191i		−	1.45718i	0.684950	−	0.728590i	$-0.259824\pi$
$522$	−365.327	−	5.85203i	−0.699860	−	0.0112108i
$523$	153.141			0.292813			0.146407	−	0.989224i	$-0.453229\pi$
$523$	153.141			0.292813			0.146407	+	0.989224i	$0.453229\pi$
$524$	102.105	+	58.9505i	0.194857	+	0.112501i
$525$	−35.8613	+	60.9806i	−0.0683073	+	0.116153i
$526$	119.470	+	206.928i	0.227129	+	0.393399i
$527$	−27.2838	+	15.7523i	−0.0517719	+	0.0298905i
$528$	−34.8097	−	20.4708i	−0.0659274	−	0.0387705i
$529$	377.959	−	654.644i	0.714478	−	1.23751i
$530$			358.425i			0.676273i
$531$	−7.27899	+	454.408i	−0.0137081	+	0.855760i
$532$	−52.0911			−0.0979155
$533$	436.695	+	252.126i	0.819316	+	0.473032i
$534$	−333.826	−	2.67354i	−0.625142	−	0.00500663i
$535$	−50.2816	−	87.0904i	−0.0939844	−	0.162786i
$536$	131.470	−	75.9040i	0.245279	−	0.141612i
$537$	421.561	−	238.907i	0.785029	−	0.444892i
$538$	−201.314	+	348.687i	−0.374190	+	0.648117i
$539$			23.5566i			0.0437043i
$540$	−184.914	−	112.769i	−0.342434	−	0.208831i
$541$	−513.041			−0.948320			−0.474160	−	0.880439i	$-0.657248\pi$
$541$	−513.041			−0.948320			−0.474160	+	0.880439i	$0.657248\pi$
$542$	−592.759	−	342.229i	−1.09365	−	0.631420i
$543$	72.3956	+	127.745i	0.133325	+	0.235257i
$544$	26.3956	+	45.7186i	0.0485214	+	0.0840415i
$545$	−182.493	+	105.362i	−0.334850	+	0.193326i
$546$	1.86888	−	233.354i	0.00342286	−	0.427387i
$547$	99.8344	−	172.918i	0.182513	−	0.316121i	−0.760223	−	0.649662i	$-0.774910\pi$
$547$	99.8344	−	172.918i	0.182513	−	0.316121i	0.942736	+	0.333541i	$0.108244\pi$
$548$		−	289.775i		−	0.528786i
$549$	−164.650	−	296.033i	−0.299909	−	0.539222i
$550$	−42.4177			−0.0771231
$551$	−244.734	−	141.297i	−0.444164	−	0.256438i
$552$	154.185	−	262.185i	0.279321	−	0.474973i
$553$	193.214	+	334.656i	0.349392	+	0.605165i
$554$	−66.8464	+	38.5938i	−0.120661	+	0.0696639i
$555$	−674.717	−	396.786i	−1.21571	−	0.714930i
$556$	98.3447	−	170.338i	0.176879	−	0.306363i
$557$		−	53.8854i		−	0.0967421i	−0.998829	−	0.0483711i	$-0.984597\pi$
$557$		−	53.8854i		−	0.0967421i	0.998829	−	0.0483711i	$-0.0154030\pi$
$558$	36.8625	+	22.0772i	0.0660618	+	0.0395649i
$559$	512.852			0.917445
$560$	36.7603	+	21.2236i	0.0656434	+	0.0378992i
$561$	−94.2126	−	0.754529i	−0.167937	−	0.00134497i
$562$	−138.344	−	239.619i	−0.246164	−	0.426368i
$563$	183.647	−	106.029i	0.326194	−	0.188328i	−0.327956	−	0.944693i	$-0.606360\pi$
$563$	183.647	−	106.029i	0.326194	−	0.188328i	0.654150	+	0.756365i	$0.273026\pi$
$564$	−244.900	+	138.790i	−0.434220	+	0.246082i
$565$	−179.446	+	310.809i	−0.317603	+	0.550105i
$566$			125.329i			0.221430i
$567$	214.196	+	6.86400i	0.377771	+	0.0121058i
$568$	237.950			0.418925
$569$	−419.953	−	242.460i	−0.738055	−	0.426116i	0.0833068	−	0.996524i	$-0.473452\pi$
$569$	−419.953	−	242.460i	−0.738055	−	0.426116i	−0.821362	+	0.570408i	$0.806785\pi$
$570$	−82.5942	−	145.740i	−0.144902	−	0.255685i
$571$	355.259	+	615.326i	0.622169	+	1.07763i	0.989081	+	0.147373i	$0.0470817\pi$
$571$	355.259	+	615.326i	0.622169	+	1.07763i	−0.366912	+	0.930256i	$0.619585\pi$
$572$	121.176	−	69.9613i	0.211847	−	0.122310i
$573$	−4.47413	+	558.652i	−0.00780825	+	0.974959i
$574$	45.3773	−	78.5959i	0.0790546	−	0.136927i
$575$		−	319.488i		−	0.555632i
$576$	36.9941	−	61.7692i	0.0642258	−	0.107238i
$577$	664.563			1.15175			0.575877	−	0.817536i	$-0.304661\pi$
$577$	664.563			1.15175			0.575877	+	0.817536i	$0.304661\pi$
$578$	−247.287	−	142.771i	−0.427832	−	0.247009i
$579$	481.810	−	819.296i	0.832142	−	1.41502i
$580$	115.138	+	199.425i	0.198514	+	0.343836i
$581$	−224.484	+	129.606i	−0.386376	+	0.223074i
$582$	334.467	+	196.693i	0.574686	+	0.337961i
$583$	106.323	−	184.157i	0.182373	−	0.315879i
$584$			337.821i			0.578461i
$585$	655.840	−	364.770i	1.12109	−	0.623539i
$586$	−651.687			−1.11209
$587$	−116.045	−	66.9986i	−0.197692	−	0.114137i	0.397887	−	0.917435i	$-0.369744\pi$
$587$	−116.045	−	66.9986i	−0.197692	−	0.114137i	−0.595578	+	0.803297i	$0.703077\pi$
$588$	−41.9987	−	0.336359i	−0.0714263	−	0.000572038i
$589$	16.6166	+	28.7807i	0.0282115	+	0.0488637i
$590$	248.053	−	143.214i	0.420429	−	0.242735i
$591$	325.736	−	184.602i	0.551161	−	0.312355i
$592$	130.103	−	225.345i	0.219768	−	0.380650i
$593$			37.8229i			0.0637823i	0.999491	+	0.0318911i	$0.0101530\pi$
$593$			37.8229i			0.0637823i	−0.999491	+	0.0318911i	$0.989847\pi$
$594$	61.5566	+	112.793i	0.103631	+	0.189887i
$595$	99.0319			0.166440
$596$	−120.712	−	69.6931i	−0.202537	−	0.116935i
$597$	517.525	+	913.192i	0.866876	+	1.52963i
$598$	526.945	+	912.696i	0.881180	+	1.52625i
$599$	700.983	−	404.713i	1.17026	−	0.675647i	0.216515	−	0.976279i	$-0.430531\pi$
$599$	700.983	−	404.713i	1.17026	−	0.675647i	0.953740	+	0.300632i	$0.0971976\pi$
$600$	0.605671	−	75.6257i	0.00100945	−	0.126043i
$601$	160.964	−	278.797i	0.267827	−	0.463889i	−0.700474	−	0.713678i	$-0.747028\pi$
$601$	160.964	−	278.797i	0.267827	−	0.463889i	0.968300	+	0.249789i	$0.0803612\pi$
$602$		−	92.3023i		−	0.153326i
$603$	−482.988	−	7.73680i	−0.800976	−	0.0128305i
$604$	265.517			0.439598
$605$	380.959	+	219.947i	0.629685	+	0.363549i
$606$	−351.876	+	598.350i	−0.580654	+	0.987376i
$607$	−304.992	−	528.262i	−0.502459	−	0.870284i	−0.999996	−	0.00284120i	$-0.999096\pi$
$607$	−304.992	−	528.262i	−0.502459	−	0.870284i	0.497537	−	0.867443i	$-0.334238\pi$
$608$	48.2270	−	27.8438i	0.0793207	−	0.0457958i
$609$	−196.406	−	115.502i	−0.322505	−	0.189658i
$610$	−106.745	+	184.888i	−0.174992	+	0.303096i
$611$		−	975.350i		−	1.59632i
$612$	2.69047	−	167.959i	0.00439620	−	0.274443i
$613$	−960.151			−1.56632			−0.783158	−	0.621823i	$-0.786392\pi$
$613$	−960.151			−1.56632			−0.783158	+	0.621823i	$0.786392\pi$
$614$	44.9476	+	25.9505i	0.0732045	+	0.0422646i
$615$	291.845	+	2.33732i	0.474544	+	0.00380053i
$616$	−12.5915	−	21.8092i	−0.0204408	−	0.0354045i
$617$	−748.615	+	432.213i	−1.21331	+	0.700507i	−0.963480	−	0.267782i	$-0.913709\pi$
$617$	−748.615	+	432.213i	−1.21331	+	0.700507i	−0.249834	+	0.968289i	$0.580376\pi$
$618$	−211.246	+	119.717i	−0.341822	+	0.193717i
$619$	7.62254	−	13.2026i	0.0123143	−	0.0213290i	−0.859803	−	0.510627i	$-0.829413\pi$
$619$	7.62254	−	13.2026i	0.0123143	−	0.0213290i	0.872117	+	0.489298i	$0.162747\pi$
$620$		−	27.0805i		−	0.0436782i
$621$	−849.553	+	463.642i	−1.36804	+	0.746606i
$622$	281.596			0.452727
$623$	−180.292	−	104.092i	−0.289394	−	0.167082i
$624$	123.002	+	217.042i	0.197119	+	0.347824i
$625$	161.370	+	279.500i	0.258191	+	0.447201i
$626$	−117.074	+	67.5925i	−0.187019	+	0.107975i
$627$	−0.795927	+	99.3817i	−0.00126942	+	0.158503i
$628$	−40.9295	+	70.8919i	−0.0651743	+	0.112885i
$629$		−	607.077i		−	0.965147i
$630$	−65.6508	−	118.037i	−0.104208	−	0.187361i
$631$	−716.934			−1.13619			−0.568094	−	0.822964i	$-0.692319\pi$
$631$	−716.934			−1.13619			−0.568094	+	0.822964i	$0.692319\pi$
$632$	−357.763	−	206.554i	−0.566080	−	0.326826i
$633$	−220.258	+	374.539i	−0.347959	+	0.591688i
$634$	38.7833	+	67.1747i	0.0611725	+	0.105954i
$635$	556.303	−	321.181i	0.876067	−	0.505798i
$636$	326.812	+	192.191i	0.513856	+	0.302188i
$637$	72.7631	−	126.029i	0.114228	−	0.197848i
$638$		−	136.618i		−	0.214136i
$639$	−649.564	−	389.029i	−1.01653	−	0.608809i
$640$	−45.3779			−0.0709030
$641$	279.229	+	161.213i	0.435615	+	0.251502i	0.701736	−	0.712437i	$-0.252409\pi$
$641$	279.229	+	161.213i	0.435615	+	0.251502i	−0.266121	+	0.963940i	$0.585742\pi$
$642$	−106.371	−	0.851902i	−0.165687	−	0.00132695i
$643$	429.688	+	744.241i	0.668254	+	1.15745i	0.978392	+	0.206759i	$0.0662915\pi$
$643$	429.688	+	744.241i	0.668254	+	1.15745i	−0.310138	+	0.950692i	$0.600375\pi$
$644$	164.266	−	94.8389i	0.255071	−	0.147265i
$645$	258.244	−	146.352i	0.400378	−	0.226902i
$646$	64.9615	−	112.517i	0.100560	−	0.174174i
$647$			523.408i			0.808977i	0.914543	+	0.404489i	$0.132550\pi$
$647$			523.408i			0.808977i	−0.914543	+	0.404489i	$0.867450\pi$
$648$	−201.976	+	108.138i	−0.311691	+	0.166879i
$649$	−169.932			−0.261836
$650$	226.937	+	131.022i	0.349134	+	0.201573i
$651$	13.2113	+	23.3119i	0.0202939	+	0.0358094i
$652$	225.434	+	390.462i	0.345757	+	0.598869i
$653$	−1061.65	+	612.945i	−1.62581	+	0.938660i	−0.640482	+	0.767974i	$0.721265\pi$
$653$	−1061.65	+	612.945i	−1.62581	+	0.938660i	−0.985325	+	0.170687i	$0.945401\pi$
$654$	−1.78511	+	222.894i	−0.00272953	+	0.340817i
$655$	−118.222	+	204.766i	−0.180491	+	0.312620i
$656$			97.0208i			0.147898i
$657$	552.312	−	922.198i	0.840657	−	1.40365i
$658$	−175.542			−0.266781
$659$	−745.244	−	430.267i	−1.13087	−	0.652909i	−0.186717	−	0.982414i	$-0.559785\pi$
$659$	−745.244	−	430.267i	−1.13087	−	0.652909i	−0.944154	+	0.329505i	$0.893118\pi$
$660$	41.0529	−	69.8086i	0.0622014	−	0.105771i
$661$	306.814	+	531.417i	0.464166	+	0.803960i	0.999163	−	0.0408940i	$-0.0130206\pi$
$661$	306.814	+	531.417i	0.464166	+	0.803960i	−0.534997	+	0.844854i	$0.679687\pi$
$662$	−272.695	+	157.441i	−0.411926	+	0.237826i
$663$	501.713	+	295.046i	0.756731	+	0.445017i
$664$	138.555	−	239.984i	0.208667	−	0.361421i
$665$		−	104.465i		−	0.157091i
$666$	−723.582	+	402.447i	−1.08646	+	0.604275i
$667$	1029.00			1.54274
$668$	−277.213	−	160.049i	−0.414989	−	0.239594i
$669$	863.688	+	6.91710i	1.29101	+	0.0103395i
$670$	152.221	+	263.654i	0.227195	+	0.393514i
$671$	109.691	−	63.3299i	0.163473	−	0.0943814i
$672$	39.0630	−	22.1378i	0.0581294	−	0.0329432i
$673$	−497.647	+	861.950i	−0.739446	+	1.28076i	0.213299	+	0.976987i	$0.431579\pi$
$673$	−497.647	+	861.950i	−0.739446	+	1.28076i	−0.952745	+	0.303771i	$0.901754\pi$
$674$			341.815i			0.507144i
$675$	−125.296	+	205.456i	−0.185623	+	0.304379i
$676$	−526.403			−0.778702
$677$	−393.511	−	227.194i	−0.581258	−	0.335589i	0.180375	−	0.983598i	$-0.442269\pi$
$677$	−393.511	−	227.194i	−0.581258	−	0.335589i	−0.761633	+	0.648009i	$0.775602\pi$
$678$	187.176	+	330.279i	0.276071	+	0.487137i
$679$	120.985	+	209.553i	0.178182	+	0.308620i
$680$	−91.6858	+	52.9348i	−0.134832	+	0.0778453i
$681$	−5.42476	+	677.351i	−0.00796588	+	0.994641i
$682$	−8.03317	+	13.9139i	−0.0117788	+	0.0204015i
$683$		−	1103.35i		−	1.61544i	−0.589567	−	0.807720i	$-0.700701\pi$
$683$		−	1103.35i		−	1.61544i	0.589567	−	0.807720i	$-0.299299\pi$
$684$	−177.174	−	2.83809i	−0.259027	−	0.00414925i
$685$	581.126			0.848359
$686$	−22.6826	−	13.0958i	−0.0330650	−	0.0190901i
$687$	639.397	−	1087.26i	0.930708	−	1.58263i
$688$	49.3377	+	85.4553i	0.0717117	+	0.124208i
$689$	−1137.67	+	656.835i	−1.65119	+	0.953317i
$690$	525.796	+	309.209i	0.762023	+	0.448129i
$691$	−54.9059	+	95.0998i	−0.0794586	+	0.137626i	−0.903016	−	0.429606i	$-0.858652\pi$
$691$	−54.9059	+	95.0998i	−0.0794586	+	0.137626i	0.823558	+	0.567232i	$0.191986\pi$
$692$			565.101i			0.816621i
$693$	−1.28344	+	80.1218i	−0.00185201	+	0.115616i
$694$	774.504			1.11600
$695$	341.603	+	197.224i	0.491514	+	0.283776i
$696$	243.575	+	1.95074i	0.349964	+	0.00280279i
$697$	113.178	+	196.030i	0.162379	+	0.281248i
$698$	−29.9255	+	17.2775i	−0.0428732	+	0.0247528i
$699$	87.6315	−	49.6626i	0.125367	−	0.0710481i
$700$	23.5812	−	40.8439i	0.0336875	−	0.0583484i
$701$		−	435.772i		−	0.621644i	−0.950468	−	0.310822i	$-0.899396\pi$
$701$		−	435.772i		−	0.621644i	0.950468	−	0.310822i	$-0.100604\pi$
$702$	19.0704	−	793.590i	0.0271658	−	1.13047i
$703$	−640.385			−0.910932
$704$	23.3150	+	13.4609i	0.0331179	+	0.0191206i
$705$	−278.335	−	491.132i	−0.394801	−	0.696641i
$706$	−118.586	−	205.397i	−0.167969	−	0.290931i
$707$	−374.882	+	216.438i	−0.530243	+	0.306136i
$708$	2.42641	−	302.968i	0.00342713	−	0.427921i
$709$	388.936	−	673.657i	0.548570	−	0.950151i	−0.449803	−	0.893128i	$-0.648506\pi$
$709$	388.936	−	673.657i	0.548570	−	0.950151i	0.998373	−	0.0570231i	$-0.0181609\pi$
$710$			477.193i			0.672103i
$711$	638.934	+	1148.77i	0.898642	+	1.61572i
$712$	222.558			0.312581
$713$	−104.799	−	60.5055i	−0.146983	−	0.0848604i
$714$	53.1020	−	90.2976i	0.0743726	−	0.126467i
$715$	140.303	+	243.012i	0.196228	+	0.339877i
$716$	−279.756	+	161.517i	−0.390720	+	0.225583i
$717$	−938.676	−	552.015i	−1.30917	−	0.769895i
$718$	38.5040	−	66.6908i	0.0536267	−	0.0928841i
$719$			47.2047i			0.0656533i	0.999461	+	0.0328267i	$0.0104509\pi$
$719$			47.2047i			0.0656533i	−0.999461	+	0.0328267i	$0.989549\pi$
$720$	123.874	+	74.1893i	0.172048	+	0.103041i
$721$	−151.419			−0.210013
$722$	323.443	+	186.740i	0.447982	+	0.258642i
$723$	878.548	+	7.03611i	1.21514	+	0.00973182i
$724$	−48.9442	−	84.7739i	−0.0676025	−	0.117091i
$725$	221.579	−	127.928i	0.305626	−	0.176453i
$726$	404.823	−	229.422i	0.557607	−	0.316008i
$727$	−130.458	+	225.960i	−0.179447	+	0.310812i	−0.941691	−	0.336478i	$-0.890764\pi$
$727$	−130.458	+	225.960i	−0.179447	+	0.310812i	0.762244	+	0.647290i	$0.224098\pi$
$728$			155.574i			0.213701i
$729$	728.159	+	35.0162i	0.998846	+	0.0480332i
$730$	−677.480			−0.928055
$731$	199.373	+	115.108i	0.272740	+	0.157466i
$732$	111.344	+	196.470i	0.152109	+	0.268401i
$733$	56.4059	+	97.6979i	0.0769521	+	0.133285i	0.901934	−	0.431875i	$-0.142148\pi$
$733$	56.4059	+	97.6979i	0.0769521	+	0.133285i	−0.824981	+	0.565160i	$0.808814\pi$
$734$	−205.538	+	118.667i	−0.280025	+	0.161672i
$735$	0.674546	−	84.2257i	0.000917750	−	0.114593i
$736$	−101.387	+	175.608i	−0.137754	+	0.238597i
$737$		−	180.619i		−	0.245074i
$738$	158.622	−	264.851i	0.214934	−	0.358877i
$739$	−703.950			−0.952571			−0.476285	−	0.879291i	$-0.658017\pi$
$739$	−703.950			−0.952571			−0.476285	+	0.879291i	$0.658017\pi$
$740$	451.915	+	260.913i	0.610696	+	0.352586i
$741$	311.234	−	529.240i	0.420019	−	0.714224i
$742$	118.216	+	204.757i	0.159321	+	0.275952i
$743$	166.506	−	96.1325i	0.224100	−	0.129384i	−0.383747	−	0.923438i	$-0.625367\pi$
$743$	166.506	−	96.1325i	0.224100	−	0.129384i	0.607847	+	0.794054i	$0.292033\pi$
$744$	−24.6921	−	14.5209i	−0.0331882	−	0.0195173i
$745$	139.765	−	242.080i	0.187604	−	0.324940i
$746$		−	744.485i		−	0.997969i
$747$	−770.587	+	428.591i	−1.03158	+	0.573750i
$748$	62.8104			0.0839711
$749$	−57.4486	−	33.1680i	−0.0767005	−	0.0442830i
$750$	577.067	+	4.62161i	0.769423	+	0.00616215i
$751$	−274.777	−	475.928i	−0.365882	−	0.633726i	0.623036	−	0.782193i	$-0.285899\pi$
$751$	−274.777	−	475.928i	−0.365882	−	0.633726i	−0.988917	+	0.148468i	$0.952566\pi$
$752$	162.520	−	93.8312i	0.216118	−	0.124776i
$753$	−526.974	+	298.647i	−0.699833	+	0.396610i
$754$	−421.996	+	730.918i	−0.559676	+	0.969387i
$755$			532.479i			0.705270i
$756$	−142.829	−	3.43226i	−0.188928	−	0.00454003i
$757$	741.823			0.979952			0.489976	−	0.871736i	$-0.337006\pi$
$757$	741.823			0.979952			0.489976	+	0.871736i	$0.337006\pi$
$758$	−108.304	−	62.5292i	−0.142881	−	0.0824924i
$759$	−178.428	−	314.843i	−0.235083	−	0.414813i
$760$	55.8391	+	96.7162i	0.0734725	+	0.127258i
$761$	−293.314	+	169.345i	−0.385433	+	0.222530i	−0.680179	−	0.733046i	$-0.738098\pi$
$761$	−293.314	+	169.345i	−0.385433	+	0.222530i	0.294746	+	0.955575i	$0.404765\pi$
$762$	5.44165	−	679.459i	0.00714127	−	0.891679i
$763$	−69.5017	+	120.380i	−0.0910900	+	0.157773i
$764$		−	372.446i		−	0.487495i
$765$	336.832	+	5.39558i	0.440303	+	0.00705304i
$766$	−101.161			−0.132064
$767$	909.145	+	524.895i	1.18533	+	0.684348i
$768$	−24.3321	+	41.3757i	−0.0316825	+	0.0538746i
$769$	342.939	+	593.987i	0.445954	+	0.772415i	0.998118	−	0.0613201i	$-0.0195311\pi$
$769$	342.939	+	593.987i	0.445954	+	0.772415i	−0.552164	+	0.833736i	$0.686198\pi$
$770$	43.7370	−	25.2516i	0.0568013	−	0.0327942i
$771$	675.242	+	397.095i	0.875801	+	0.515039i
$772$	−316.822	+	548.752i	−0.410391	+	0.710819i
$773$		−	611.346i		−	0.790874i	−0.918493	−	0.395437i	$-0.870593\pi$
$773$		−	611.346i		−	0.790874i	0.918493	−	0.395437i	$-0.129407\pi$
$774$	5.02893	−	313.943i	0.00649732	−	0.405611i
$775$	−30.0888			−0.0388242
$776$	−224.021	−	129.339i	−0.288687	−	0.166674i
$777$	−516.313	−	4.13505i	−0.664496	−	0.00532181i
$778$	−415.893	−	720.348i	−0.534567	−	0.925897i
$779$	206.785	−	119.388i	0.265450	−	0.153258i
$780$	−435.265	+	246.674i	−0.558032	+	0.316249i
$781$	141.555	−	245.180i	0.181248	−	0.313931i
$782$			473.085i			0.604968i
$783$	−661.731	−	403.551i	−0.845122	−	0.515391i
$784$	28.0000			0.0357143
$785$	−142.169	−	82.0815i	−0.181107	−	0.104562i
$786$	123.314	+	217.593i	0.156888	+	0.276835i
$787$	494.442	+	856.398i	0.628261	+	1.08818i	0.987901	+	0.155089i	$0.0495664\pi$
$787$	494.442	+	856.398i	0.628261	+	1.08818i	−0.359639	+	0.933091i	$0.617100\pi$
$788$	−216.165	+	124.803i	−0.274321	+	0.158379i
$789$	−4.05927	+	506.852i	−0.00514483	+	0.642397i
$790$	414.232	−	717.471i	0.524344	−	0.908191i
$791$			236.741i			0.299293i
$792$	−41.6387	−	74.8644i	−0.0525741	−	0.0945257i
$793$	−782.470			−0.986721
$794$	−853.372	−	492.694i	−1.07478	−	0.620522i
$795$	−385.428	+	655.402i	−0.484815	+	0.824405i
$796$	−349.881	−	606.012i	−0.439549	−	0.761321i
$797$	−451.755	+	260.821i	−0.566819	+	0.327253i	−0.755878	−	0.654713i	$-0.772790\pi$
$797$	−451.755	+	260.821i	−0.566819	+	0.327253i	0.189059	+	0.981966i	$0.439456\pi$
$798$	−95.2519	−	56.0155i	−0.119363	−	0.0701949i
$799$	218.914	−	379.171i	0.273986	−	0.474557i
$800$			50.4188i			0.0630235i
$801$	−607.547	−	363.865i	−0.758485	−	0.454263i
$802$	−877.179			−1.09374
$803$	348.087	+	200.968i	0.433483	+	0.250271i
$804$	322.023	+	2.57902i	0.400526	+	0.00320773i
$805$	190.194	+	329.425i	0.236265	+	0.409224i
$806$	85.9559	−	49.6267i	0.106645	−	0.0615715i
$807$	−743.073	+	421.115i	−0.920784	+	0.521828i
$808$	231.382	−	400.766i	0.286364	−	0.495997i
$809$			117.417i			0.145139i	0.997363	+	0.0725694i	$0.0231199\pi$
$809$			117.417i			0.145139i	−0.997363	+	0.0725694i	$0.976880\pi$
$810$	−216.864	−	405.050i	−0.267733	−	0.500062i
$811$	−103.595			−0.127737			−0.0638684	−	0.997958i	$-0.520344\pi$
$811$	−103.595			−0.127737			−0.0638684	+	0.997958i	$0.520344\pi$
$812$	131.550	+	75.9502i	0.162007	+	0.0935347i
$813$	−715.885	−	1263.21i	−0.880547	−	1.55376i
$814$	−154.795	−	268.113i	−0.190166	−	0.329377i
$815$	−783.048	+	452.093i	−0.960795	+	0.554715i
$816$	−0.896853	+	111.984i	−0.00109908	+	0.137235i
$817$	121.424	−	210.312i	0.148621	−	0.257420i
$818$			150.494i			0.183978i
$819$	254.351	−	424.692i	0.310563	−	0.518550i
$820$	−194.569			−0.237280
$821$	503.527	+	290.711i	0.613309	+	0.354094i	0.774260	−	0.632868i	$-0.218123\pi$
$821$	503.527	+	290.711i	0.613309	+	0.354094i	−0.160950	+	0.986963i	$0.551456\pi$
$822$	311.606	−	529.872i	0.379083	−	0.644613i
$823$	590.769	+	1023.24i	0.717824	+	1.24331i	0.961860	+	0.273541i	$0.0881950\pi$
$823$	590.769	+	1023.24i	0.717824	+	1.24331i	−0.244037	+	0.969766i	$0.578472\pi$
$824$	140.187	−	80.9369i	0.170130	−	0.0982244i
$825$	−77.5635	−	45.6134i	−0.0940163	−	0.0552889i
$826$	94.4699	−	163.627i	0.114370	−	0.198095i
$827$			772.787i			0.934447i	0.884139	+	0.467223i	$0.154746\pi$
$827$			772.787i			0.934447i	−0.884139	+	0.467223i	$0.845254\pi$
$828$	563.875	−	313.621i	0.681009	−	0.378769i
$829$	−692.394			−0.835216			−0.417608	−	0.908627i	$-0.637131\pi$
$829$	−692.394			−0.835216			−0.417608	+	0.908627i	$0.637131\pi$
$830$	481.273	+	277.863i	0.579847	+	0.334775i
$831$	−163.734	−	1.31131i	−0.197033	−	0.00157800i
$832$	−83.1578	−	144.034i	−0.0999493	−	0.173117i
$833$	56.5738	−	32.6629i	0.0679158	−	0.0392112i
$834$	363.001	−	205.720i	0.435253	−	0.246667i
$835$	320.968	−	555.933i	0.384393	−	0.665788i
$836$		−	66.2566i		−	0.0792543i
$837$	43.6649	+	80.0092i	0.0521683	+	0.0955905i
$838$	264.702			0.315874
$839$	−51.8471	−	29.9340i	−0.0617964	−	0.0356781i	0.468783	−	0.883313i	$-0.344692\pi$
$839$	−51.8471	−	29.9340i	−0.0617964	−	0.0356781i	−0.530580	+	0.847635i	$0.678026\pi$
$840$	44.3960	+	78.3384i	0.0528524	+	0.0932600i
$841$	−8.46925	−	14.6692i	−0.0100705	−	0.0174425i
$842$	465.912	−	268.994i	0.553340	−	0.319471i
$843$	4.70056	−	586.925i	0.00557599	−	0.696234i
$844$	144.834	−	250.860i	0.171605	−	0.297228i
$845$		−	1055.67i		−	1.24931i
$846$	−597.062	−	9.56410i	−0.705747	−	0.0113051i
$847$	290.173			0.342590
$848$	−218.894	−	126.379i	−0.258130	−	0.149031i
$849$	−134.771	+	229.172i	−0.158741	+	0.269932i
$850$	58.8151	+	101.871i	0.0691943	+	0.119848i
$851$	2019.41	−	1165.91i	2.37299	−	1.37005i
$852$	435.106	+	255.876i	0.510688	+	0.300324i
$853$	354.754	−	614.451i	0.415889	−	0.720341i	−0.579632	−	0.814878i	$-0.696804\pi$
$853$	354.754	−	614.451i	0.415889	−	0.720341i	0.995521	+	0.0945369i	$0.0301370\pi$
$854$			140.828i			0.164904i
$855$	5.69161	−	355.312i	0.00665686	−	0.415570i
$856$	70.9161			0.0828460
$857$	464.496	+	268.177i	0.542002	+	0.312925i	0.745890	−	0.666069i	$-0.232024\pi$
$857$	464.496	+	268.177i	0.542002	+	0.312925i	−0.203888	+	0.978994i	$0.565358\pi$
$858$	296.811	+	2.37710i	0.345934	+	0.00277051i
$859$	46.6609	+	80.8191i	0.0543200	+	0.0940851i	0.891907	−	0.452219i	$-0.149368\pi$
$859$	46.6609	+	80.8191i	0.0543200	+	0.0940851i	−0.837587	+	0.546304i	$0.816034\pi$
$860$	−171.375	+	98.9437i	−0.199274	+	0.115051i
$861$	167.493	−	94.9215i	0.194533	−	0.110246i
$862$	445.758	−	772.076i	0.517121	−	0.895680i
$863$		−	400.285i		−	0.463830i	−0.972736	−	0.231915i	$-0.925501\pi$
$863$		−	400.285i		−	0.463830i	0.972736	−	0.231915i	$-0.0744991\pi$
$864$	134.069	−	73.1678i	0.155172	−	0.0846850i
$865$	−1133.28			−1.31015
$866$	−280.326	−	161.846i	−0.323702	−	0.186889i
$867$	−298.653	−	526.983i	−0.344467	−	0.607824i
$868$	−8.93174	−	15.4702i	−0.0102900	−	0.0178228i
$869$	−425.662	+	245.756i	−0.489829	+	0.282803i
$870$	−3.91209	+	488.474i	−0.00449665	+	0.561464i
$871$	−557.908	+	966.325i	−0.640538	+	1.10944i
$872$		−	148.601i		−	0.170414i
$873$	400.084	+	719.332i	0.458286	+	0.823977i
$874$	499.042			0.570986
$875$	311.662	+	179.938i	0.356185	+	0.205643i
$876$	−363.272	+	617.728i	−0.414694	+	0.705169i
$877$	150.061	+	259.913i	0.171107	+	0.296366i	0.938807	−	0.344443i	$-0.111932\pi$
$877$	150.061	+	259.913i	0.171107	+	0.296366i	−0.767700	+	0.640809i	$0.778599\pi$
$878$	602.187	−	347.673i	0.685863	−	0.395983i
$879$	−1191.65	−	700.784i	−1.35569	−	0.797251i
$880$	−26.9950	+	46.7568i	−0.0306762	+	0.0531327i
$881$		−	9.45241i		−	0.0107292i	−0.999986	−	0.00536459i	$-0.998292\pi$
$881$		−	9.45241i		−	0.0107292i	0.999986	−	0.00536459i	$-0.00170761\pi$
$882$	−76.4355	−	45.7778i	−0.0866616	−	0.0519023i
$883$	264.964			0.300072			0.150036	−	0.988681i	$-0.452061\pi$
$883$	264.964			0.300072			0.150036	+	0.988681i	$0.452061\pi$
$884$	−336.040	−	194.013i	−0.380135	−	0.219471i
$885$	607.584	+	4.86601i	0.686536	+	0.00549832i
$886$	−244.143	−	422.867i	−0.275556	−	0.477277i
$887$	1433.09	−	827.395i	1.61566	−	0.932801i	0.627634	−	0.778508i	$-0.284023\pi$
$887$	1433.09	−	827.395i	1.61566	−	0.932801i	0.988025	−	0.154293i	$-0.0493100\pi$
$888$	480.224	−	272.153i	0.540792	−	0.306478i
$889$	211.865	−	366.962i	0.238319	−	0.412780i
$890$			446.326i			0.501490i
$891$	−8.73058	+	272.444i	−0.00979863	+	0.305773i
$892$	−575.810			−0.645527
$893$	−399.975	−	230.925i	−0.447900	−	0.258595i
$894$	−145.786	−	257.245i	−0.163071	−	0.287746i
$895$	−323.913	−	561.033i	−0.361914	−	0.626853i
$896$	−25.9230	+	14.9666i	−0.0289319	+	0.0167038i
$897$	−17.9042	+	2235.57i	−0.0199601	+	2.49227i
$898$	573.573	−	993.458i	0.638723	−	1.10630i
$899$		−	96.9096i		−	0.107797i
$900$	82.4308	−	137.635i	0.0915898	−	0.152928i
$901$	−589.699			−0.654494
$902$	99.9690	+	57.7171i	0.110830	+	0.0639879i
$903$	99.2563	−	168.781i	0.109918	−	0.186911i
$904$	−126.543	−	219.179i	−0.139982	−	0.242455i
$905$	170.009	−	98.1546i	0.187855	−	0.108458i
$906$	485.516	+	285.521i	0.535889	+	0.315145i
$907$	52.8627	−	91.5609i	0.0582830	−	0.100949i	−0.835412	−	0.549625i	$-0.814771\pi$
$907$	52.8627	−	91.5609i	0.0582830	−	0.100949i	0.893695	+	0.448675i	$0.148104\pi$
$908$		−	451.582i		−	0.497337i
$909$	−1286.86	+	715.734i	−1.41568	+	0.787386i
$910$	−311.994			−0.342851
$911$	517.915	+	299.018i	0.568512	+	0.328231i	0.756555	−	0.653930i	$-0.226881\pi$
$911$	517.915	+	299.018i	0.568512	+	0.328231i	−0.188043	+	0.982161i	$0.560214\pi$
$912$	118.128	+	0.946060i	0.129526	+	0.00103735i
$913$	−164.851	−	285.530i	−0.180559	−	0.312738i
$914$	518.381	−	299.287i	0.567156	−	0.327448i
$915$	−394.008	+	223.293i	−0.430610	+	0.244036i
$916$	−420.446	+	728.233i	−0.459002	+	0.795015i
$917$			155.968i			0.170086i
$918$	185.533	−	304.231i	0.202105	−	0.331406i
$919$	−1453.58			−1.58169			−0.790847	−	0.612014i	$-0.790359\pi$
$919$	−1453.58			−1.58169			−0.790847	+	0.612014i	$0.790359\pi$
$920$	−352.170	−	203.326i	−0.382794	−	0.221006i
$921$	54.2839	+	95.7860i	0.0589402	+	0.104002i
$922$	−200.457	−	347.202i	−0.217415	−	0.376575i
$923$	−1514.65	+	874.486i	−1.64101	+	0.947439i
$924$	0.427827	−	53.4197i	0.000463016	−	0.0578135i
$925$	289.897	−	502.117i	0.313403	−	0.542829i
$926$			914.937i			0.988053i
$927$	−515.013	−	8.24980i	−0.555570	−	0.00889946i
$928$	−162.388			−0.174987
$929$	999.556	+	577.094i	1.07595	+	0.621199i	0.929800	−	0.368064i	$-0.119979\pi$
$929$	999.556	+	577.094i	1.07595	+	0.621199i	0.146147	+	0.989263i	$0.453313\pi$
$930$	29.1207	−	49.5184i	0.0313126	−	0.0532456i
$931$	−34.4550	−	59.6778i	−0.0370086	−	0.0641008i
$932$	−58.1540	+	33.5752i	−0.0623970	+	0.0360249i
$933$	514.917	+	302.811i	0.551893	+	0.324557i
$934$	−372.503	+	645.195i	−0.398826	+	0.690787i
$935$			125.962i			0.134719i
$936$	−8.47617	+	529.145i	−0.00905574	+	0.565326i
$937$	1700.25			1.81457			0.907286	−	0.420513i	$-0.138150\pi$
$937$	1700.25			1.81457			0.907286	+	0.420513i	$0.138150\pi$
$938$	173.918	+	100.412i	0.185414	+	0.107049i
$939$	−286.762	−	2.29661i	−0.305390	−	0.00244581i
$940$	188.173	+	325.925i	0.200184	+	0.346729i
$941$	994.455	−	574.149i	1.05681	−	0.610148i	0.132259	−	0.991215i	$-0.457777\pi$
$941$	994.455	−	574.149i	1.05681	−	0.610148i	0.924547	+	0.381068i	$0.124443\pi$
$942$	−151.075	+	85.6173i	−0.160377	+	0.0908889i
$943$	−434.723	+	752.962i	−0.461000	+	0.798475i
$944$			201.985i			0.213967i
$945$	6.88318	−	286.435i	0.00728379	−	0.303106i
$946$	117.403			0.124104
$947$	−868.085	−	501.189i	−0.916668	−	0.529239i	−0.0340977	−	0.999419i	$-0.510856\pi$
$947$	−868.085	−	501.189i	−0.916668	−	0.529239i	−0.882571	+	0.470180i	$0.844189\pi$
$948$	−432.076	−	762.414i	−0.455776	−	0.804234i
$949$	−1241.52	−	2150.38i	−1.30824	−	2.26595i
$950$	107.460	−	62.0421i	0.113116	−	0.0653075i
$951$	−1.31775	+	164.538i	−0.00138565	+	0.173016i
$952$	−34.9181	+	60.4800i	−0.0366787	+	0.0635294i
$953$		−	140.777i		−	0.147719i	−0.997269	−	0.0738597i	$-0.976468\pi$
$953$		−	140.777i		−	0.147719i	0.997269	−	0.0738597i	$-0.0235317\pi$
$954$	390.927	+	702.868i	0.409776	+	0.736759i
$955$	746.918			0.782114
$956$	628.711	+	362.986i	0.657647	+	0.379693i
$957$	146.911	−	249.816i	0.153512	−	0.261040i
$958$	−486.246	−	842.203i	−0.507564	−	0.879126i
$959$	331.979	−	191.668i	0.346172	−	0.199862i
$960$	−82.9764	−	48.7966i	−0.0864337	−	0.0508298i
$961$	474.802	−	822.381i	0.494070	−	0.855755i
$962$			1912.56i			1.98811i
$963$	−193.590	−	115.942i	−0.201028	−	0.120397i
$964$	−585.717			−0.607590
$965$	−1100.49	−	635.368i	−1.14040	−	0.658412i
$966$	402.355	+	3.22237i	0.416516	+	0.00333579i
$967$	522.129	+	904.354i	0.539947	+	0.935216i	0.998906	+	0.0467584i	$0.0148891\pi$
$967$	522.129	+	904.354i	0.539947	+	0.935216i	−0.458959	+	0.888457i	$0.651778\pi$
$968$	−268.648	+	155.104i	−0.277529	+	0.160232i
$969$	239.780	−	135.888i	0.247451	−	0.140236i
$970$	259.381	−	449.261i	0.267403	−	0.463156i
$971$		−	698.841i		−	0.719712i	−0.933008	−	0.359856i	$-0.882826\pi$
$971$		−	698.841i		−	0.719712i	0.933008	−	0.359856i	$-0.117174\pi$
$972$	−485.610	−	19.4558i	−0.499599	−	0.0200162i
$973$	260.196			0.267416
$974$	−258.660	−	149.338i	−0.265565	−	0.153324i
$975$	274.076	+	483.617i	0.281104	+	0.496018i
$976$	−75.2756	−	130.381i	−0.0771267	−	0.133587i
$977$	−306.627	+	177.031i	−0.313845	+	0.181199i	−0.648646	−	0.761090i	$-0.724664\pi$
$977$	−306.627	+	177.031i	−0.313845	+	0.181199i	0.334801	+	0.942289i	$0.391331\pi$
$978$	−7.65963	+	956.403i	−0.00783194	+	0.977917i
$979$	132.398	−	229.320i	0.135238	−	0.234240i
$980$			56.1523i			0.0572982i
$981$	−242.951	+	405.657i	−0.247656	+	0.413513i
$982$	381.425			0.388417
$983$	550.281	+	317.705i	0.559797	+	0.323199i	0.753064	−	0.657947i	$-0.228575\pi$
$983$	550.281	+	317.705i	0.559797	+	0.323199i	−0.193267	+	0.981146i	$0.561908\pi$
$984$	−104.330	+	177.409i	−0.106027	+	0.180294i
$985$	−250.284	−	433.505i	−0.254096	−	0.440107i
$986$	−328.105	+	189.431i	−0.332763	+	0.192121i
$987$	−320.990	−	188.767i	−0.325218	−	0.191254i
$988$	−204.657	+	354.477i	−0.207143	+	0.358782i
$989$			884.273i			0.894108i
$990$	150.136	−	83.5038i	0.151652	−	0.0843472i
$991$	−1564.14			−1.57835			−0.789175	−	0.614169i	$-0.789491\pi$
$991$	−1564.14			−1.57835			−0.789175	+	0.614169i	$0.789491\pi$
$992$	16.5384	+	9.54843i	0.0166717	+	0.00962544i
$993$	−667.942	−	5.34941i	−0.672651	−	0.00538712i
$994$	157.389	+	272.605i	0.158339	+	0.274251i
$995$	1215.32	−	701.665i	1.22143	−	0.705191i
$996$	511.420	−	289.833i	0.513474	−	0.290997i
$997$	186.336	−	322.743i	0.186896	−	0.323714i	−0.757317	−	0.653047i	$-0.773490\pi$
$997$	186.336	−	322.743i	0.186896	−	0.323714i	0.944214	+	0.329333i	$0.106824\pi$
$998$			122.585i			0.122831i
$999$	−1755.88	−	42.1947i	−1.75764	−	0.0422370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.q.a.29.2	✓	24
3.2	odd	2		378.3.q.a.197.11		24
9.2	odd	6		1134.3.b.c.323.9		24
9.4	even	3		378.3.q.a.71.11		24
9.5	odd	6	inner	126.3.q.a.113.2	yes	24
9.7	even	3		1134.3.b.c.323.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.q.a.29.2	✓	24	1.1	even	1	trivial
126.3.q.a.113.2	yes	24	9.5	odd	6	inner
378.3.q.a.71.11		24	9.4	even	3
378.3.q.a.197.11		24	3.2	odd	2
1134.3.b.c.323.9		24	9.2	odd	6
1134.3.b.c.323.16		24	9.7	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-1.47915 - 2.61001i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-3.47352 + 2.00544i) q^{5} +(-0.0339773 + 4.24250i) q^{6} +(-1.32288 + 2.29129i) q^{7} -2.82843i q^{8} +(-4.62426 + 7.72115i) q^{9} +5.67224 q^{10} +(-2.91437 - 1.68261i) q^{11} +(3.04152 - 5.17196i) q^{12} +(10.3947 + 18.0042i) q^{13} +(3.24037 - 1.87083i) q^{14} +(10.3720 + 6.09958i) q^{15} +(-2.00000 + 3.46410i) q^{16} +9.33226i q^{17} +(11.1232 - 6.18660i) q^{18} +9.84429 q^{19} +(-6.94704 - 4.01088i) q^{20} +(7.93700 + 0.0635658i) q^{21} +(2.37958 + 4.12155i) q^{22} +(-31.0433 + 17.9229i) q^{23} +(-7.38221 + 4.18365i) q^{24} +(-4.45643 + 7.71877i) q^{25} -29.4007i q^{26} +(26.9922 + 0.648636i) q^{27} -5.29150 q^{28} +(-24.8605 - 14.3532i) q^{29} +(-8.39006 - 14.8046i) q^{30} +(1.68794 + 2.92360i) q^{31} +(4.89898 - 2.82843i) q^{32} +(-0.0808517 + 10.0954i) q^{33} +(6.59891 - 11.4296i) q^{34} -10.6118i q^{35} +(-17.9977 - 0.288298i) q^{36} -65.0515 q^{37} +(-12.0567 - 6.96096i) q^{38} +(31.6157 - 53.7611i) q^{39} +(5.67224 + 9.82460i) q^{40} +(21.0056 - 12.1276i) q^{41} +(-9.67585 - 5.69016i) q^{42} +(12.3344 - 21.3638i) q^{43} -6.73046i q^{44} +(0.578164 - 36.0933i) q^{45} +50.6935 q^{46} +(-40.6301 - 23.4578i) q^{47} +(11.9996 + 0.0961024i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(10.9160 - 6.30235i) q^{50} +(24.3573 - 13.8038i) q^{51} +(-20.7895 + 36.0084i) q^{52} +63.1893i q^{53} +(-32.5999 - 19.8808i) q^{54} +13.4975 q^{55} +(6.48074 + 3.74166i) q^{56} +(-14.5611 - 25.6936i) q^{57} +(20.2985 + 35.1581i) q^{58} +(43.7311 - 25.2482i) q^{59} +(-0.192728 + 24.0645i) q^{60} +(-18.8189 + 32.5953i) q^{61} -4.77422i q^{62} +(-11.5741 - 20.8096i) q^{63} -8.00000 q^{64} +(-72.2126 - 41.6920i) q^{65} +(7.23752 - 12.3071i) q^{66} +(26.8361 + 46.4815i) q^{67} +(-16.1640 + 9.33226i) q^{68} +(92.6964 + 54.5127i) q^{69} +(-7.50366 + 12.9967i) q^{70} +84.1279i q^{71} +(21.8387 + 13.0794i) q^{72} -119.438 q^{73} +(79.6715 + 45.9983i) q^{74} +(26.7377 + 0.214137i) q^{75} +(9.84429 + 17.0508i) q^{76} +(7.71071 - 4.45178i) q^{77} +(-76.7361 + 43.4879i) q^{78} +(73.0280 - 126.488i) q^{79} -16.0435i q^{80} +(-38.2324 - 71.4092i) q^{81} -34.3020 q^{82} +(84.8471 + 48.9865i) q^{83} +(7.82690 + 13.8109i) q^{84} +(-18.7153 - 32.4158i) q^{85} +(-30.2130 + 17.4435i) q^{86} +(-0.689690 + 86.1167i) q^{87} +(-4.75915 + 8.24310i) q^{88} +78.6860i q^{89} +(-26.2299 + 43.7962i) q^{90} -55.0037 q^{91} +(-62.0866 - 35.8457i) q^{92} +(5.13390 - 8.72996i) q^{93} +(33.1744 + 57.4597i) q^{94} +(-34.1943 + 19.7421i) q^{95} +(-14.6285 - 8.60271i) q^{96} +(45.7282 - 79.2035i) q^{97} +9.89949i q^{98} +(26.4686 - 14.7215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30}+ \cdots - 440 q^{99}+O(q^{100}) \) 24 * q + 24 * q^4 + 36 * q^5 + 8 * q^6 - 32 * q^9 - 24 * q^12 - 44 * q^15 - 48 * q^16 + 48 * q^18 + 24 * q^19 + 72 * q^20 + 28 * q^21 + 24 * q^22 - 72 * q^23 - 16 * q^24 + 72 * q^25 - 108 * q^29 - 56 * q^30 - 60 * q^31 + 104 * q^33 - 48 * q^34 - 80 * q^36 - 168 * q^37 + 144 * q^38 + 64 * q^39 + 108 * q^41 + 60 * q^43 + 116 * q^45 - 324 * q^47 - 48 * q^48 - 84 * q^49 + 144 * q^50 - 268 * q^51 - 208 * q^54 + 264 * q^55 + 60 * q^57 - 432 * q^59 - 32 * q^60 - 192 * q^64 - 180 * q^65 - 112 * q^66 + 72 * q^67 + 72 * q^68 + 536 * q^69 + 96 * q^72 + 24 * q^73 + 288 * q^74 + 76 * q^75 + 24 * q^76 - 64 * q^78 + 12 * q^79 + 544 * q^81 - 288 * q^82 + 756 * q^83 + 112 * q^84 - 156 * q^85 + 360 * q^86 + 280 * q^87 - 48 * q^88 + 80 * q^90 - 168 * q^91 - 144 * q^92 + 436 * q^93 - 936 * q^95 - 64 * q^96 + 48 * q^97 - 440 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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