LMFDB - Embedded newform 66.3.g.a.53.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(5,66)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("66.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.g (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			53.5
Character	$\chi$	$=$	66.53
Dual form			66.3.g.a.5.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34500 + 0.437016i) q^{2} +(-2.51921 - 1.62898i) q^{3} +(1.61803 + 1.17557i) q^{4} +(8.43444 - 2.74052i) q^{5} +(-2.67644 - 3.29191i) q^{6} +(-0.799737 - 0.581043i) q^{7} +(1.66251 + 2.28825i) q^{8} +(3.69284 + 8.20749i) q^{9} +12.5419 q^{10} +(-6.06969 - 9.17381i) q^{11} +(-2.16119 - 5.59726i) q^{12} +(-3.87315 + 11.9203i) q^{13} +(-0.821719 - 1.13100i) q^{14} +(-25.7124 - 6.83561i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-24.9252 + 8.09870i) q^{17} +(1.38005 + 12.6529i) q^{18} +(-1.71359 + 1.24499i) q^{19} +(16.8689 + 5.48103i) q^{20} +(1.06820 + 2.76653i) q^{21} +(-4.15462 - 14.9913i) q^{22} +13.1640i q^{23} +(-0.460697 - 8.47277i) q^{24} +(43.4039 - 31.5348i) q^{25} +(-10.4188 + 14.3402i) q^{26} +(4.06682 - 26.6920i) q^{27} +(-0.610945 - 1.88030i) q^{28} +(8.88514 - 12.2293i) q^{29} +(-31.5958 - 20.4306i) q^{30} +(-11.9183 + 36.6806i) q^{31} +5.65685i q^{32} +(0.346863 + 32.9982i) q^{33} -37.0636 q^{34} +(-8.33770 - 2.70908i) q^{35} +(-3.67335 + 17.6212i) q^{36} +(25.5186 + 18.5403i) q^{37} +(-2.84885 + 0.925648i) q^{38} +(29.1753 - 23.7205i) q^{39} +(20.2933 + 14.7439i) q^{40} +(-32.3701 - 44.5536i) q^{41} +(0.227706 + 4.18779i) q^{42} -0.435153 q^{43} +(0.963493 - 21.9789i) q^{44} +(53.6398 + 59.1053i) q^{45} +(-5.75289 + 17.7056i) q^{46} +(12.3550 + 17.0052i) q^{47} +(3.08310 - 11.5972i) q^{48} +(-14.8399 - 45.6724i) q^{49} +(72.1594 - 23.4460i) q^{50} +(75.9845 + 20.2004i) q^{51} +(-20.2801 + 14.7343i) q^{52} +(0.879055 + 0.285622i) q^{53} +(17.1347 - 34.1233i) q^{54} +(-76.3354 - 60.7419i) q^{55} -2.79598i q^{56} +(6.34496 - 0.344999i) q^{57} +(17.2949 - 12.5655i) q^{58} +(36.1462 - 49.7510i) q^{59} +(-33.5678 - 41.2870i) q^{60} +(4.81107 + 14.8069i) q^{61} +(-32.0601 + 44.1269i) q^{62} +(1.81561 - 8.70954i) q^{63} +(-2.47214 + 7.60845i) q^{64} +111.156i q^{65} +(-13.9542 + 44.5340i) q^{66} -26.5008 q^{67} +(-49.8505 - 16.1974i) q^{68} +(21.4439 - 33.1629i) q^{69} +(-10.0303 - 7.28741i) q^{70} +(41.9364 - 13.6260i) q^{71} +(-12.6414 + 22.0951i) q^{72} +(32.8530 + 23.8691i) q^{73} +(26.2200 + 36.0887i) q^{74} +(-160.713 + 8.73860i) q^{75} -4.23622 q^{76} +(-0.476221 + 10.8634i) q^{77} +(49.6069 - 19.1540i) q^{78} +(15.8723 - 48.8500i) q^{79} +(20.8511 + 28.6991i) q^{80} +(-53.7259 + 60.6179i) q^{81} +(-24.0670 - 74.0707i) q^{82} +(-108.904 + 35.3852i) q^{83} +(-1.52387 + 5.73208i) q^{84} +(-188.036 + 136.616i) q^{85} +(-0.585280 - 0.190169i) q^{86} +(-42.3049 + 16.3346i) q^{87} +(10.9010 - 29.1405i) q^{88} -149.971i q^{89} +(46.3154 + 102.938i) q^{90} +(10.0237 - 7.28267i) q^{91} +(-15.4752 + 21.2998i) q^{92} +(89.7767 - 72.9916i) q^{93} +(9.18590 + 28.2713i) q^{94} +(-11.0412 + 15.1969i) q^{95} +(9.21491 - 14.2508i) q^{96} +(28.0899 - 86.4517i) q^{97} -67.9145i q^{98} +(52.8796 - 83.6944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) $ 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	1.34500	+	0.437016i	0.672499	+	0.218508i
$2$	1.34500	+	0.437016i	0.672499	+	0.218508i
$3$	−2.51921	−	1.62898i	−0.839737	−	0.542994i
$3$	−2.51921	−	1.62898i	−0.839737	−	0.542994i
$4$	1.61803	+	1.17557i	0.404508	+	0.293893i
$5$	8.43444	−	2.74052i	1.68689	−	0.548103i	0.700660	−	0.713495i	$-0.252889\pi$
$5$	8.43444	−	2.74052i	1.68689	−	0.548103i	0.986228	+	0.165392i	$0.0528889\pi$
$6$	−2.67644	−	3.29191i	−0.446073	−	0.548652i
$7$	−0.799737	−	0.581043i	−0.114248	−	0.0830062i	0.529194	−	0.848501i	$-0.322494\pi$
$7$	−0.799737	−	0.581043i	−0.114248	−	0.0830062i	−0.643442	+	0.765495i	$0.722494\pi$
$8$	1.66251	+	2.28825i	0.207813	+	0.286031i
$9$	3.69284	+	8.20749i	0.410315	+	0.911944i
$10$	12.5419			1.25419
$11$	−6.06969	−	9.17381i	−0.551790	−	0.833983i
$11$	−6.06969	−	9.17381i	−0.551790	−	0.833983i
$12$	−2.16119	−	5.59726i	−0.180099	−	0.466438i
$13$	−3.87315	+	11.9203i	−0.297935	+	0.916949i	0.684285	+	0.729214i	$0.260114\pi$
$13$	−3.87315	+	11.9203i	−0.297935	+	0.916949i	−0.982220	+	0.187734i	$0.939886\pi$
$14$	−0.821719	−	1.13100i	−0.0586942	−	0.0807857i
$15$	−25.7124	−	6.83561i	−1.71416	−	0.455707i
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	−24.9252	+	8.09870i	−1.46619	+	0.476394i	−0.929955	−	0.367674i	$-0.880154\pi$
$17$	−24.9252	+	8.09870i	−1.46619	+	0.476394i	−0.536236	+	0.844068i	$0.680154\pi$
$18$	1.38005	+	12.6529i	0.0766695	+	0.702938i
$19$	−1.71359	+	1.24499i	−0.0901888	+	0.0655260i	−0.631966	−	0.774996i	$-0.717752\pi$
$19$	−1.71359	+	1.24499i	−0.0901888	+	0.0655260i	0.541777	+	0.840522i	$0.317752\pi$
$20$	16.8689	+	5.48103i	0.843444	+	0.274052i
$21$	1.06820	+	2.76653i	0.0508666	+	0.131739i
$22$	−4.15462	−	14.9913i	−0.188846	−	0.681423i
$23$			13.1640i			0.572349i	0.958178	+	0.286174i	$0.0923837\pi$
$23$			13.1640i			0.572349i	−0.958178	+	0.286174i	$0.907616\pi$
$24$	−0.460697	−	8.47277i	−0.0191957	−	0.353032i
$25$	43.4039	−	31.5348i	1.73616	−	1.26139i
$26$	−10.4188	+	14.3402i	−0.400721	+	0.551545i
$27$	4.06682	−	26.6920i	0.150623	−	0.988591i
$28$	−0.610945	−	1.88030i	−0.0218195	−	0.0671534i
$29$	8.88514	−	12.2293i	0.306384	−	0.421702i	−0.627865	−	0.778322i	$-0.716071\pi$
$29$	8.88514	−	12.2293i	0.306384	−	0.421702i	0.934249	+	0.356621i	$0.116071\pi$
$30$	−31.5958	−	20.4306i	−1.05319	−	0.681020i
$31$	−11.9183	+	36.6806i	−0.384460	+	1.18325i	0.552411	+	0.833572i	$0.313708\pi$
$31$	−11.9183	+	36.6806i	−0.384460	+	1.18325i	−0.936871	+	0.349675i	$0.886292\pi$
$32$			5.65685i			0.176777i
$33$	0.346863	+	32.9982i	0.0105110	+	0.999945i
$34$	−37.0636			−1.09011
$35$	−8.33770	−	2.70908i	−0.238220	−	0.0774023i
$36$	−3.67335	+	17.6212i	−0.102037	+	0.489478i
$37$	25.5186	+	18.5403i	0.689691	+	0.501090i	0.876558	−	0.481295i	$-0.159834\pi$
$37$	25.5186	+	18.5403i	0.689691	+	0.501090i	−0.186868	+	0.982385i	$0.559834\pi$
$38$	−2.84885	+	0.925648i	−0.0749698	+	0.0243591i
$39$	29.1753	−	23.7205i	0.748084	−	0.608219i
$40$	20.2933	+	14.7439i	0.507332	+	0.368599i
$41$	−32.3701	−	44.5536i	−0.789514	−	1.08667i	−0.994168	−	0.107839i	$-0.965607\pi$
$41$	−32.3701	−	44.5536i	−0.789514	−	1.08667i	0.204654	−	0.978834i	$-0.434393\pi$
$42$	0.227706	+	4.18779i	0.00542158	+	0.0997093i
$43$	−0.435153			−0.0101198			−0.00505992	−	0.999987i	$-0.501611\pi$
$43$	−0.435153			−0.0101198			−0.00505992	+	0.999987i	$0.501611\pi$
$44$	0.963493	−	21.9789i	0.0218976	−	0.499520i
$45$	53.6398	+	59.1053i	1.19200	+	1.31345i
$46$	−5.75289	+	17.7056i	−0.125063	+	0.384904i
$47$	12.3550	+	17.0052i	0.262872	+	0.361813i	0.919967	−	0.391995i	$-0.128215\pi$
$47$	12.3550	+	17.0052i	0.262872	+	0.361813i	−0.657095	+	0.753808i	$0.728215\pi$
$48$	3.08310	−	11.5972i	0.0642312	−	0.241608i
$49$	−14.8399	−	45.6724i	−0.302854	−	0.932090i
$50$	72.1594	−	23.4460i	1.44319	−	0.468920i
$51$	75.9845	+	20.2004i	1.48989	+	0.396087i
$52$	−20.2801	+	14.7343i	−0.390002	+	0.283353i
$53$	0.879055	+	0.285622i	0.0165859	+	0.00538910i	0.317298	−	0.948326i	$-0.397224\pi$
$53$	0.879055	+	0.285622i	0.0165859	+	0.00538910i	−0.300712	+	0.953715i	$0.597224\pi$
$54$	17.1347	−	34.1233i	0.317309	−	0.631914i
$55$	−76.3354	−	60.7419i	−1.38792	−	1.10440i
$56$		−	2.79598i		−	0.0499283i
$57$	6.34496	−	0.344999i	0.111315	−	0.00605262i
$58$	17.2949	−	12.5655i	0.298188	−	0.216646i
$59$	36.1462	−	49.7510i	0.612647	−	0.843237i	−0.384145	−	0.923273i	$-0.625504\pi$
$59$	36.1462	−	49.7510i	0.612647	−	0.843237i	0.996792	+	0.0800361i	$0.0255036\pi$
$60$	−33.5678	−	41.2870i	−0.559463	−	0.688116i
$61$	4.81107	+	14.8069i	0.0788700	+	0.242737i	0.982716	−	0.185122i	$-0.0592680\pi$
$61$	4.81107	+	14.8069i	0.0788700	+	0.242737i	−0.903846	+	0.427859i	$0.859268\pi$
$62$	−32.0601	+	44.1269i	−0.517098	+	0.711724i
$63$	1.81561	−	8.70954i	0.0288192	−	0.138247i
$64$	−2.47214	+	7.60845i	−0.0386271	+	0.118882i
$65$			111.156i			1.71009i
$66$	−13.9542	+	44.5340i	−0.211427	+	0.674758i
$67$	−26.5008			−0.395534			−0.197767	−	0.980249i	$-0.563369\pi$
$67$	−26.5008			−0.395534			−0.197767	+	0.980249i	$0.563369\pi$
$68$	−49.8505	−	16.1974i	−0.733095	−	0.238197i
$69$	21.4439	−	33.1629i	0.310782	−	0.480622i
$70$	−10.0303	−	7.28741i	−0.143289	−	0.104106i
$71$	41.9364	−	13.6260i	0.590654	−	0.191915i	0.00158602	−	0.999999i	$-0.499495\pi$
$71$	41.9364	−	13.6260i	0.590654	−	0.191915i	0.589068	+	0.808084i	$0.299495\pi$
$72$	−12.6414	+	22.0951i	−0.175575	+	0.306877i
$73$	32.8530	+	23.8691i	0.450040	+	0.326974i	0.789612	−	0.613607i	$-0.210282\pi$
$73$	32.8530	+	23.8691i	0.450040	+	0.326974i	−0.339571	+	0.940580i	$0.610282\pi$
$74$	26.2200	+	36.0887i	0.354324	+	0.487685i
$75$	−160.713	+	8.73860i	−2.14284	+	0.116515i
$76$	−4.23622			−0.0557397
$77$	−0.476221	+	10.8634i	−0.00618469	+	0.141083i
$78$	49.6069	−	19.1540i	0.635986	−	0.245564i
$79$	15.8723	−	48.8500i	0.200915	−	0.618354i	−0.798941	−	0.601409i	$-0.794606\pi$
$79$	15.8723	−	48.8500i	0.200915	−	0.618354i	0.999856	−	0.0169447i	$-0.00539393\pi$
$80$	20.8511	+	28.6991i	0.260639	+	0.358738i
$81$	−53.7259	+	60.6179i	−0.663282	+	0.748369i
$82$	−24.0670	−	74.0707i	−0.293500	−	0.903301i
$83$	−108.904	+	35.3852i	−1.31210	+	0.426328i	−0.879776	−	0.475389i	$-0.842307\pi$
$83$	−108.904	+	35.3852i	−1.31210	+	0.426328i	−0.432327	+	0.901717i	$0.642307\pi$
$84$	−1.52387	+	5.73208i	−0.0181413	+	0.0682390i
$85$	−188.036	+	136.616i	−2.21219	+	1.60725i
$86$	−0.585280	−	0.190169i	−0.00680558	−	0.00221127i
$87$	−42.3049	+	16.3346i	−0.486263	+	0.187754i
$88$	10.9010	−	29.1405i	0.123875	−	0.331142i
$89$		−	149.971i		−	1.68506i	−0.538647	−	0.842531i	$-0.681064\pi$
$89$		−	149.971i		−	1.68506i	0.538647	−	0.842531i	$-0.318936\pi$
$90$	46.3154	+	102.938i	0.514615	+	1.14375i
$91$	10.0237	−	7.28267i	0.110151	−	0.0800293i
$92$	−15.4752	+	21.2998i	−0.168209	+	0.231520i
$93$	89.7767	−	72.9916i	0.965341	−	0.784856i
$94$	9.18590	+	28.2713i	0.0977223	+	0.300758i
$95$	−11.0412	+	15.1969i	−0.116223	+	0.159968i
$96$	9.21491	−	14.2508i	0.0959887	−	0.148446i
$97$	28.0899	−	86.4517i	0.289586	−	0.891255i	−0.695400	−	0.718623i	$-0.744773\pi$
$97$	28.0899	−	86.4517i	0.289586	−	0.891255i	0.984986	−	0.172632i	$-0.0552271\pi$
$98$		−	67.9145i		−	0.693005i
$99$	52.8796	−	83.6944i	0.534137	−	0.845398i
$100$	107.300			1.07300
$101$	−26.1786	−	8.50595i	−0.259194	−	0.0842173i	0.176537	−	0.984294i	$-0.443510\pi$
$101$	−26.1786	−	8.50595i	−0.259194	−	0.0842173i	−0.435732	+	0.900077i	$0.643510\pi$
$102$	93.3711	+	60.3760i	0.915403	+	0.591921i
$103$	4.96160	+	3.60481i	0.0481709	+	0.0349982i	0.611610	−	0.791159i	$-0.290522\pi$
$103$	4.96160	+	3.60481i	0.0481709	+	0.0349982i	−0.563439	+	0.826157i	$0.690522\pi$
$104$	−33.7158	+	10.9549i	−0.324190	+	0.105336i
$105$	16.5914	+	20.4067i	0.158013	+	0.194349i
$106$	1.05751	+	0.768322i	0.00997646	+	0.00724832i
$107$	104.004	+	143.149i	0.971998	+	1.33784i	0.941031	+	0.338320i	$0.109859\pi$
$107$	104.004	+	143.149i	0.971998	+	1.33784i	0.0309673	+	0.999520i	$0.490141\pi$
$108$	37.9585	−	38.4077i	0.351468	−	0.355627i
$109$	174.142			1.59764			0.798818	−	0.601573i	$-0.205459\pi$
$109$	174.142			1.59764			0.798818	+	0.601573i	$0.205459\pi$
$110$	−76.1258	−	115.057i	−0.692052	−	1.04598i
$111$	−34.0848	−	88.2762i	−0.307070	−	0.795281i
$112$	1.22189	−	3.76059i	0.0109097	−	0.0335767i
$113$	1.51946	+	2.09135i	0.0134465	+	0.0185075i	0.815687	−	0.578493i	$-0.196359\pi$
$113$	1.51946	+	2.09135i	0.0134465	+	0.0185075i	−0.802241	+	0.597001i	$0.796359\pi$
$114$	8.68472	+	2.30882i	0.0761817	+	0.0202528i
$115$	36.0762	+	111.031i	0.313706	+	0.965488i
$116$	28.7529	−	9.34239i	0.247870	−	0.0805378i
$117$	−112.139	+	12.2310i	−0.958453	+	0.104539i
$118$	70.3585	−	51.1184i	0.596259	−	0.433207i
$119$	24.6393	+	8.00581i	0.207053	+	0.0672757i
$120$	−27.1055	−	70.2005i	−0.225879	−	0.585004i
$121$	−47.3177	+	111.364i	−0.391055	+	0.920367i
$122$			22.0178i			0.180474i
$123$	8.97006	+	164.970i	0.0729273	+	1.34122i
$124$	−62.4048	+	45.3398i	−0.503265	+	0.365643i
$125$	149.347	−	205.559i	1.19478	−	1.64447i
$126$	6.24819	−	10.9209i	0.0495888	−	0.0866734i
$127$	−47.3258	−	145.654i	−0.372644	−	1.14688i	−0.945054	−	0.326914i	$-0.893991\pi$
$127$	−47.3258	−	145.654i	−0.372644	−	1.14688i	0.572410	−	0.819968i	$-0.306009\pi$
$128$	−6.65003	+	9.15298i	−0.0519534	+	0.0715077i
$129$	1.09624	+	0.708857i	0.00849801	+	0.00549501i
$130$	−48.5769	+	149.504i	−0.373668	+	1.15003i
$131$			110.277i			0.841808i	0.907105	+	0.420904i	$0.138287\pi$
$131$			110.277i			0.841808i	−0.907105	+	0.420904i	$0.861713\pi$
$132$	−38.2304	+	53.7999i	−0.289625	+	0.407575i
$133$	2.09381			0.0157430
$134$	−35.6434	−	11.5813i	−0.265996	−	0.0864273i
$135$	−38.8484	−	236.277i	−0.287766	−	1.75020i
$136$	−59.9702	−	43.5709i	−0.440957	−	0.320374i
$137$	−70.7950	+	23.0027i	−0.516752	+	0.167903i	−0.555771	−	0.831336i	$-0.687577\pi$
$137$	−70.7950	+	23.0027i	−0.516752	+	0.167903i	0.0390188	+	0.999238i	$0.487577\pi$
$138$	43.3348	−	35.2327i	0.314020	−	0.255309i
$139$	161.323	+	117.208i	1.16059	+	0.843221i	0.989853	−	0.142095i	$-0.0453838\pi$
$139$	161.323	+	117.208i	1.16059	+	0.843221i	0.170741	+	0.985316i	$0.445384\pi$
$140$	−10.3060	−	14.1849i	−0.0736140	−	0.101321i
$141$	−3.42369	−	62.9657i	−0.0242815	−	0.446566i
$142$	62.3591			0.439149
$143$	132.864	−	36.8212i	0.929117	−	0.257491i
$144$	−26.6586	+	24.1934i	−0.185129	+	0.168010i
$145$	41.4265	−	127.498i	0.285700	−	0.879294i
$146$	33.7560	+	46.4611i	0.231205	+	0.318227i
$147$	−37.0148	+	139.232i	−0.251801	+	0.947158i
$148$	19.4944	+	59.9977i	0.131719	+	0.405390i
$149$	−62.5185	+	20.3135i	−0.419588	+	0.136332i	−0.511199	−	0.859463i	$-0.670798\pi$
$149$	−62.5185	+	20.3135i	−0.419588	+	0.136332i	0.0916111	+	0.995795i	$0.470798\pi$
$150$	−219.978	−	58.4809i	−1.46652	−	0.389873i
$151$	149.698	−	108.762i	0.991374	−	0.720276i	0.0311528	−	0.999515i	$-0.490082\pi$
$151$	149.698	−	108.762i	0.991374	−	0.720276i	0.960222	+	0.279239i	$0.0900821\pi$
$152$	−5.69770	−	1.85130i	−0.0374849	−	0.0121796i
$153$	−158.515	−	174.667i	−1.03605	−	1.14161i
$154$	−5.38799	+	14.4031i	−0.0349870	+	0.0935267i
$155$			342.043i			2.20673i
$156$	75.0917	−	4.08303i	0.481357	−	0.0261732i
$157$	−76.4419	+	55.5383i	−0.486891	+	0.353747i	−0.803988	−	0.594646i	$-0.797292\pi$
$157$	−76.4419	+	55.5383i	−0.486891	+	0.353747i	0.317096	+	0.948393i	$0.397292\pi$
$158$	42.6964	−	58.7666i	0.270231	−	0.371941i
$159$	−1.74925	−	2.15151i	−0.0110016	−	0.0135315i
$160$	15.5027	+	47.7124i	0.0968919	+	0.298203i
$161$	7.64886	−	10.5278i	0.0475085	−	0.0653898i
$162$	−98.7521	+	58.0518i	−0.609581	+	0.358345i
$163$	20.6135	−	63.4418i	0.126463	−	0.389214i	−0.867702	−	0.497085i	$-0.834404\pi$
$163$	20.6135	−	63.4418i	0.126463	−	0.389214i	0.994165	+	0.107872i	$0.0344036\pi$
$164$		−	110.143i		−	0.671601i
$165$	93.3576	+	277.371i	0.565804	+	1.68103i
$166$	−161.940			−0.975543
$167$	−177.988	−	57.8320i	−1.06580	−	0.346299i	−0.276949	−	0.960885i	$-0.589323\pi$
$167$	−177.988	−	57.8320i	−1.06580	−	0.346299i	−0.788850	+	0.614586i	$0.789323\pi$
$168$	−4.55461	+	7.04367i	−0.0271108	+	0.0419266i
$169$	9.63085	+	6.99722i	0.0569873	+	0.0414037i
$170$	−312.611	+	101.573i	−1.83889	+	0.597491i
$171$	−16.5463	−	9.46669i	−0.0967618	−	0.0553607i
$172$	−0.704093	−	0.511553i	−0.00409356	−	0.00297415i
$173$	−99.1136	−	136.418i	−0.572911	−	0.788544i	0.419985	−	0.907531i	$-0.362035\pi$
$173$	−99.1136	−	136.418i	−0.572911	−	0.788544i	−0.992896	+	0.118987i	$0.962035\pi$
$174$	−64.0385	+	3.48202i	−0.368037	+	0.0200116i
$175$	−53.0348			−0.303056
$176$	27.3967	−	34.4299i	0.155663	−	0.195625i
$177$	−172.103	+	66.4517i	−0.972335	+	0.375433i
$178$	65.5395	−	201.710i	0.368200	−	1.13320i
$179$	−31.0224	−	42.6987i	−0.173310	−	0.238540i	0.713522	−	0.700633i	$-0.247099\pi$
$179$	−31.0224	−	42.6987i	−0.173310	−	0.238540i	−0.886832	+	0.462093i	$0.847099\pi$
$180$	17.3085	+	158.692i	0.0961585	+	0.881621i
$181$	−11.8929	−	36.6026i	−0.0657066	−	0.202224i	0.912813	−	0.408378i	$-0.133905\pi$
$181$	−11.8929	−	36.6026i	−0.0657066	−	0.202224i	−0.978520	+	0.206154i	$0.933905\pi$
$182$	16.6645	−	5.41463i	0.0915633	−	0.0297507i
$183$	12.0001	−	45.1390i	0.0655746	−	0.246661i
$184$	−30.1225	+	21.8853i	−0.163709	+	0.118942i
$185$	266.045	+	86.4432i	1.43808	+	0.467261i
$186$	152.648	−	58.9397i	0.820688	−	0.316880i
$187$	225.584	+	179.503i	1.20633	+	0.959908i
$188$			42.0392i			0.223613i
$189$	−18.7616	+	18.9836i	−0.0992676	+	0.100442i
$190$	−21.4917	+	15.6146i	−0.113114	+	0.0821823i
$191$	52.1553	−	71.7856i	0.273064	−	0.375841i	−0.650357	−	0.759629i	$-0.725381\pi$
$191$	52.1553	−	71.7856i	0.273064	−	0.375841i	0.923421	+	0.383788i	$0.125381\pi$
$192$	18.6219	−	15.1402i	0.0969888	−	0.0788553i
$193$	−5.89992	−	18.1581i	−0.0305695	−	0.0940834i	0.934608	−	0.355680i	$-0.115751\pi$
$193$	−5.89992	−	18.1581i	−0.0305695	−	0.0940834i	−0.965177	+	0.261597i	$0.915751\pi$
$194$	75.5615	−	104.002i	0.389493	−	0.536090i
$195$	181.071	−	280.025i	0.928568	−	1.43602i
$196$	29.6797	−	91.3448i	0.151427	−	0.466045i
$197$			219.988i			1.11669i	0.829608	+	0.558346i	$0.188564\pi$
$197$			219.988i			1.11669i	−0.829608	+	0.558346i	$0.811436\pi$
$198$	107.699	−	89.4595i	0.543933	−	0.451815i
$199$	16.7260			0.0840502			0.0420251	−	0.999117i	$-0.486619\pi$
$199$	16.7260			0.0840502			0.0420251	+	0.999117i	$0.486619\pi$
$200$	144.319	+	46.8920i	0.721594	+	0.234460i
$201$	66.7610	+	43.1692i	0.332144	+	0.214772i
$202$	−31.4929	−	22.8810i	−0.155906	−	0.113272i
$203$	−14.2116	+	4.61761i	−0.0700077	+	0.0227469i
$204$	99.1986	+	122.010i	0.486267	+	0.598089i
$205$	−395.123	−	287.074i	−1.92743	−	1.40036i
$206$	5.09798	+	7.01676i	0.0247475	+	0.0340620i
$207$	−108.044	+	48.6126i	−0.521950	+	0.234844i
$208$	−50.1351			−0.241034
$209$	21.8223	+	8.16339i	0.104413	+	0.0390593i
$210$	13.3973	+	34.6976i	0.0637966	+	0.165227i
$211$	−72.8199	+	224.117i	−0.345118	+	1.06216i	0.616403	+	0.787431i	$0.288589\pi$
$211$	−72.8199	+	224.117i	−0.345118	+	1.06216i	−0.961521	+	0.274733i	$0.911411\pi$
$212$	1.08657	+	1.49554i	0.00512534	+	0.00705442i
$213$	−127.843	−	33.9870i	−0.600202	−	0.159563i
$214$	77.3264	+	237.986i	0.361338	+	1.11209i
$215$	−3.67028	+	1.19254i	−0.0170710	+	0.00554672i
$216$	67.8389	−	35.0697i	0.314069	−	0.162360i
$217$	30.8445	−	22.4099i	0.142141	−	0.103271i
$218$	234.221	+	76.1030i	1.07441	+	0.349096i
$219$	−43.8812	−	113.648i	−0.200371	−	0.518941i
$220$	−52.1070	−	188.020i	−0.236850	−	0.854637i
$221$		−	328.485i		−	1.48636i
$222$	−7.26580	−	133.627i	−0.0327288	−	0.601923i
$223$	−289.044	+	210.002i	−1.29616	+	0.941715i	−0.999910	−	0.0133959i	$-0.995736\pi$
$223$	−289.044	+	210.002i	−1.29616	+	0.941715i	−0.296249	+	0.955111i	$0.595736\pi$
$224$	3.28688	−	4.52400i	0.0146736	−	0.0201964i
$225$	419.106	+	239.785i	1.86269	+	1.06571i
$226$	1.12971	+	3.47689i	0.00499872	+	0.0153845i
$227$	195.528	−	269.122i	0.861359	−	1.18556i	−0.119885	−	0.992788i	$-0.538253\pi$
$227$	195.528	−	269.122i	0.861359	−	1.18556i	0.981244	−	0.192771i	$-0.0617473\pi$
$228$	10.6719	+	6.90072i	0.0468067	+	0.0302663i
$229$	12.7938	−	39.3751i	0.0558679	−	0.171944i	−0.919229	−	0.393724i	$-0.871187\pi$
$229$	12.7938	−	39.3751i	0.0558679	−	0.171944i	0.975097	+	0.221780i	$0.0711867\pi$
$230$			165.102i			0.717837i
$231$	18.8960	−	26.5914i	0.0818007	−	0.115114i
$232$	42.7554			0.184290
$233$	−222.601	−	72.3276i	−0.955371	−	0.310419i	−0.210475	−	0.977599i	$-0.567501\pi$
$233$	−222.601	−	72.3276i	−0.955371	−	0.310419i	−0.744896	+	0.667180i	$0.767501\pi$
$234$	−156.172	−	32.5559i	−0.667401	−	0.139128i
$235$	150.811	+	109.570i	0.641747	+	0.466257i
$236$	116.972	−	38.0064i	0.495642	−	0.161044i
$237$	−119.561	+	97.2076i	−0.504479	+	0.410159i
$238$	29.6412	+	21.5356i	0.124543	+	0.0904856i
$239$	199.166	+	274.128i	0.833330	+	1.14698i	0.987294	+	0.158904i	$0.0507959\pi$
$239$	199.166	+	274.128i	0.833330	+	1.14698i	−0.153964	+	0.988076i	$0.549204\pi$
$240$	−5.77803	−	106.265i	−0.0240751	−	0.442771i
$241$	−406.779			−1.68788			−0.843940	−	0.536437i	$-0.819770\pi$
$241$	−406.779			−1.68788			−0.843940	+	0.536437i	$0.819770\pi$
$242$	−112.310	+	129.106i	−0.464092	+	0.533497i
$243$	234.092	−	65.1908i	0.963342	−	0.268275i
$244$	−9.62214	+	29.6139i	−0.0394350	+	0.121368i
$245$	−250.332	−	344.552i	−1.02176	−	1.40634i
$246$	−60.0299	+	225.804i	−0.244024	+	0.917904i
$247$	−8.20376	−	25.2486i	−0.0332136	−	0.102221i
$248$	−103.749	+	33.7099i	−0.418341	+	0.135927i
$249$	331.995	+	88.2606i	1.33331	+	0.354460i
$250$	290.704	−	211.209i	1.16282	−	0.844835i
$251$	−55.6077	−	18.0680i	−0.221545	−	0.0719842i	0.196141	−	0.980576i	$-0.437159\pi$
$251$	−55.6077	−	18.0680i	−0.221545	−	0.0719842i	−0.417686	+	0.908591i	$0.637159\pi$
$252$	13.1764	−	11.9580i	0.0522873	−	0.0474522i
$253$	120.764	−	79.9016i	0.477329	−	0.315816i
$254$		−	216.586i		−	0.852702i
$255$	696.247	−	37.8576i	2.73038	−	0.148461i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	−122.024	+	167.951i	−0.474801	+	0.653508i	−0.977495	−	0.210957i	$-0.932342\pi$
$257$	−122.024	+	167.951i	−0.474801	+	0.653508i	0.502694	+	0.864464i	$0.332342\pi$
$258$	1.16466	+	1.43249i	0.00451419	+	0.00555227i
$259$	−9.63542	−	29.6548i	−0.0372024	−	0.114497i
$260$	−130.671	+	179.854i	−0.502582	+	0.691745i
$261$	133.184	+	27.7637i	0.510282	+	0.106374i
$262$	−48.1928	+	148.322i	−0.183942	+	0.566115i
$263$			99.8714i			0.379739i	0.981809	+	0.189870i	$0.0608065\pi$
$263$			99.8714i			0.379739i	−0.981809	+	0.189870i	$0.939193\pi$
$264$	−74.9313	+	55.6534i	−0.283831	+	0.210808i
$265$	8.19709			0.0309324
$266$	2.81617	+	0.915030i	0.0105871	+	0.00343996i
$267$	−244.299	+	377.807i	−0.914979	+	1.41501i
$268$	−42.8791	−	31.1535i	−0.159997	−	0.116244i
$269$	−130.372	+	42.3603i	−0.484653	+	0.157473i	−0.541144	−	0.840930i	$-0.682009\pi$
$269$	−130.372	+	42.3603i	−0.484653	+	0.157473i	0.0564911	+	0.998403i	$0.482009\pi$
$270$	51.0058	−	334.769i	0.188910	−	1.23989i
$271$	−303.416	−	220.445i	−1.11962	−	0.813449i	−0.135465	−	0.990782i	$-0.543253\pi$
$271$	−303.416	−	220.445i	−1.11962	−	0.813449i	−0.984151	+	0.177333i	$0.943253\pi$
$272$	−61.6186	−	84.8107i	−0.226539	−	0.311804i
$273$	−37.1152	+	2.01810i	−0.135953	+	0.00739229i
$274$	−105.272			−0.384203
$275$	−552.743	−	206.773i	−2.00997	−	0.751902i
$276$	73.6824	−	28.4499i	0.266965	−	0.103079i
$277$	29.8797	−	91.9602i	0.107869	−	0.331986i	−0.882524	−	0.470267i	$-0.844158\pi$
$277$	29.8797	−	91.9602i	0.107869	−	0.331986i	0.990393	+	0.138281i	$0.0441576\pi$
$278$	165.757	+	228.145i	0.596247	+	0.820664i
$279$	−345.068	+	37.6367i	−1.23680	+	0.134898i
$280$	−7.66244	−	23.5826i	−0.0273659	−	0.0842234i
$281$	125.763	−	40.8630i	0.447556	−	0.145420i	−0.0765630	−	0.997065i	$-0.524395\pi$
$281$	125.763	−	40.8630i	0.447556	−	0.145420i	0.524119	+	0.851645i	$0.324395\pi$
$282$	22.9122	−	86.1850i	0.0812489	−	0.305620i
$283$	−127.510	+	92.6413i	−0.450565	+	0.327355i	−0.789819	−	0.613340i	$-0.789825\pi$
$283$	−127.510	+	92.6413i	−0.450565	+	0.327355i	0.339254	+	0.940695i	$0.389825\pi$
$284$	83.8728	+	27.2519i	0.295327	+	0.0959575i
$285$	52.5707	−	20.2983i	0.184459	−	0.0712222i
$286$	194.793	+	8.53917i	0.681094	+	0.0298572i
$287$			54.4396i			0.189685i
$288$	−46.4286	+	20.8899i	−0.161210	+	0.0725342i
$289$	321.873	−	233.854i	1.11375	−	0.809184i
$290$	111.437	−	153.380i	0.384265	−	0.528896i
$291$	−211.592	+	172.032i	−0.727122	+	0.591176i
$292$	25.0974	+	77.2419i	0.0859501	+	0.264527i
$293$	−114.882	+	158.122i	−0.392089	+	0.539665i	−0.958737	−	0.284296i	$-0.908240\pi$
$293$	−114.882	+	158.122i	−0.392089	+	0.539665i	0.566647	+	0.823961i	$0.308240\pi$
$294$	−110.631	+	171.091i	−0.376298	+	0.581942i
$295$	168.530	−	518.681i	0.571287	−	1.75824i
$296$			89.2162i			0.301406i
$297$	−269.551	+	124.704i	−0.907580	+	0.419878i
$298$	−92.9646			−0.311962
$299$	−156.920	−	50.9862i	−0.524814	−	0.170523i
$300$	−270.312	−	174.790i	−0.901041	−	0.582635i
$301$	0.348008	+	0.252843i	0.00115617	+	0.000840010i
$302$	248.873	−	80.8638i	0.824084	−	0.267761i
$303$	52.0934	+	64.0728i	0.171925	+	0.211461i
$304$	−6.85435	−	4.97997i	−0.0225472	−	0.0163815i
$305$	81.1573	+	111.704i	0.266090	+	0.366241i
$306$	−136.870	−	304.199i	−0.447288	−	0.994116i
$307$	−24.0379			−0.0782992			−0.0391496	−	0.999233i	$-0.512465\pi$
$307$	−24.0379			−0.0782992			−0.0391496	+	0.999233i	$0.512465\pi$
$308$	−13.5412	+	17.0175i	−0.0439650	+	0.0552516i
$309$	−6.62714	−	17.1636i	−0.0214471	−	0.0555458i
$310$	−149.478	+	460.047i	−0.482188	+	1.48402i
$311$	158.248	+	217.810i	0.508837	+	0.700354i	0.983723	−	0.179694i	$-0.0575107\pi$
$311$	158.248	+	217.810i	0.508837	+	0.700354i	−0.474886	+	0.880047i	$0.657511\pi$
$312$	102.783	+	27.3246i	0.329431	+	0.0875790i
$313$	186.136	+	572.869i	0.594685	+	1.83025i	0.556289	+	0.830989i	$0.312225\pi$
$313$	186.136	+	572.869i	0.594685	+	1.83025i	0.0383956	+	0.999263i	$0.487775\pi$
$314$	−127.085	+	41.2925i	−0.404730	+	0.131505i
$315$	−8.55500	−	78.4358i	−0.0271587	−	0.249002i
$316$	83.1085	−	60.3819i	0.263002	−	0.191082i
$317$	247.619	+	80.4564i	0.781133	+	0.253806i	0.672324	−	0.740257i	$-0.265296\pi$
$317$	247.619	+	80.4564i	0.781133	+	0.253806i	0.108809	+	0.994063i	$0.465296\pi$
$318$	−1.41249	−	3.65822i	−0.00444181	−	0.0115038i
$319$	−166.120	−	7.28223i	−0.520752	−	0.0228283i
$320$			70.9480i			0.221712i
$321$	−28.8204	−	530.043i	−0.0897833	−	1.65122i
$322$	14.8885	−	10.8171i	0.0462376	−	0.0335936i
$323$	32.6287	−	44.9096i	0.101018	−	0.139039i
$324$	−158.191	+	34.9233i	−0.488244	+	0.107788i
$325$	207.795	+	639.529i	0.639371	+	1.96778i
$326$	55.4502	−	76.3206i	0.170093	−	0.234112i
$327$	−438.701	−	283.675i	−1.34159	−	0.867506i
$328$	48.1341	−	148.141i	0.146750	−	0.451651i
$329$		−	20.7785i		−	0.0631565i
$330$	4.35033	+	413.861i	0.0131828	+	1.25413i
$331$	34.8349			0.105241			0.0526207	−	0.998615i	$-0.483243\pi$
$331$	34.8349			0.105241			0.0526207	+	0.998615i	$0.483243\pi$
$332$	−217.809	−	70.7704i	−0.656051	−	0.213164i
$333$	−57.9336	+	277.910i	−0.173975	+	0.834564i
$334$	−214.120	−	155.568i	−0.641079	−	0.465771i
$335$	−223.519	+	72.6257i	−0.667221	+	0.216793i
$336$	−9.20413	+	7.48328i	−0.0273932	+	0.0222717i
$337$	119.021	+	86.4739i	0.353178	+	0.256599i	0.750201	−	0.661210i	$-0.229957\pi$
$337$	119.021	+	86.4739i	0.353178	+	0.256599i	−0.397023	+	0.917809i	$0.629957\pi$
$338$	9.89557	+	13.6201i	0.0292768	+	0.0402961i
$339$	−0.421056	−	7.74372i	−0.00124205	−	0.0228428i
$340$	−464.850			−1.36721
$341$	408.842	−	113.304i	1.19895	−	0.332271i
$342$	−18.1176	−	19.9637i	−0.0529754	−	0.0583733i
$343$	−29.6378	+	91.2158i	−0.0864076	+	0.265935i
$344$	−0.723446	−	0.995738i	−0.00210304	−	0.00289459i
$345$	89.9842	−	338.478i	0.260824	−	0.981097i
$346$	−73.6906	−	226.796i	−0.212979	−	0.655481i
$347$	198.399	−	64.4637i	0.571755	−	0.185774i	−0.00884869	−	0.999961i	$-0.502817\pi$
$347$	198.399	−	64.4637i	0.571755	−	0.185774i	0.580604	+	0.814186i	$0.302817\pi$
$348$	−87.6532	−	23.3025i	−0.251877	−	0.0669613i
$349$	406.369	−	295.244i	1.16438	−	0.845972i	0.174055	−	0.984736i	$-0.444313\pi$
$349$	406.369	−	295.244i	1.16438	−	0.845972i	0.990325	+	0.138764i	$0.0443130\pi$
$350$	−71.3317	−	23.1771i	−0.203805	−	0.0662202i
$351$	302.426	+	151.860i	0.861612	+	0.432649i
$352$	51.8949	−	34.3354i	0.147429	−	0.0975437i
$353$			30.4003i			0.0861199i	0.999072	+	0.0430600i	$0.0137107\pi$
$353$			30.4003i			0.0861199i	−0.999072	+	0.0430600i	$0.986289\pi$
$354$	−260.519	+	14.1654i	−0.735929	+	0.0400153i
$355$	316.368	−	229.855i	0.891177	−	0.647478i
$356$	176.301	−	242.658i	0.495228	−	0.681622i
$357$	−49.0304	−	60.3053i	−0.137340	−	0.168922i
$358$	−23.0650	−	70.9869i	−0.0644275	−	0.198287i
$359$	374.903	−	516.009i	1.04430	−	1.43735i	0.150647	−	0.988588i	$-0.451864\pi$
$359$	374.903	−	516.009i	1.04430	−	1.43735i	0.893650	−	0.448764i	$-0.148136\pi$
$360$	−46.0709	+	221.004i	−0.127975	+	0.613900i
$361$	−110.169	+	339.065i	−0.305177	+	0.939237i
$362$		−	54.4277i		−	0.150353i
$363$	300.614	−	203.471i	0.828137	−	0.560526i
$364$	24.7800			0.0680770
$365$	342.510	+	111.288i	0.938383	+	0.304899i
$366$	35.8666	−	55.4675i	0.0979962	−	0.151551i
$367$	443.163	+	321.977i	1.20753	+	0.877321i	0.995004	−	0.0998347i	$-0.0318314\pi$
$367$	443.163	+	321.977i	1.20753	+	0.877321i	0.212525	+	0.977156i	$0.431831\pi$
$368$	−50.0789	+	16.2716i	−0.136084	+	0.0442164i
$369$	246.136	−	430.206i	0.667035	−	1.16587i
$370$	320.052	+	232.532i	0.865007	+	0.628464i
$371$	−0.537054	−	0.739192i	−0.00144759	−	0.00199243i
$372$	231.069	−	12.5641i	0.621152	−	0.0337744i
$373$	636.467			1.70634			0.853172	−	0.521629i	$-0.174676\pi$
$373$	636.467			1.70634			0.853172	+	0.521629i	$0.174676\pi$
$374$	224.965	+	340.015i	0.601510	+	0.909130i
$375$	−711.088	+	274.562i	−1.89623	+	0.732165i
$376$	−18.3718	+	56.5426i	−0.0488611	+	0.150379i
$377$	111.364	+	153.280i	0.295396	+	0.406578i
$378$	−33.5304	+	17.3337i	−0.0887047	+	0.0458564i
$379$	−182.521	−	561.743i	−0.481587	−	1.48217i	−0.836864	−	0.547411i	$-0.815613\pi$
$379$	−182.521	−	561.743i	−0.481587	−	1.48217i	0.355277	−	0.934761i	$-0.384387\pi$
$380$	−35.7301	+	11.6094i	−0.0940267	+	0.0305511i
$381$	−118.044	+	444.026i	−0.309826	+	1.16542i
$382$	101.520	−	73.7587i	0.265760	−	0.193086i
$383$	−510.991	−	166.031i	−1.33418	−	0.433501i	−0.446839	−	0.894615i	$-0.647450\pi$
$383$	−510.991	−	166.031i	−1.33418	−	0.433501i	−0.887341	+	0.461113i	$0.847450\pi$
$384$	31.6629	−	12.2255i	0.0824554	−	0.0318373i
$385$	25.7546	+	92.9317i	0.0668952	+	0.241381i
$386$		−	27.0009i		−	0.0699506i
$387$	−1.60695	−	3.57152i	−0.00415233	−	0.00922873i
$388$	147.080	−	106.860i	0.379073	−	0.275413i
$389$	23.6404	−	32.5383i	0.0607724	−	0.0836460i	−0.777549	−	0.628822i	$-0.783537\pi$
$389$	23.6404	−	32.5383i	0.0607724	−	0.0836460i	0.838321	+	0.545176i	$0.183537\pi$
$390$	365.915	−	297.502i	0.938243	−	0.762825i
$391$	−106.611	−	328.116i	−0.272664	−	0.839172i
$392$	79.8383	−	109.888i	0.203669	−	0.280326i
$393$	179.639	−	277.811i	0.457097	−	0.706897i
$394$	−96.1385	+	295.884i	−0.244006	+	0.750974i
$395$		−	455.521i		−	1.15322i
$396$	183.950	−	73.2566i	0.464519	−	0.184992i
$397$	372.194			0.937516			0.468758	−	0.883327i	$-0.344702\pi$
$397$	372.194			0.937516			0.468758	+	0.883327i	$0.344702\pi$
$398$	22.4964	+	7.30952i	0.0565236	+	0.0183656i
$399$	−5.27476	−	3.41078i	−0.0132199	−	0.00854833i
$400$	173.616	+	126.139i	0.434039	+	0.315348i
$401$	−467.895	+	152.028i	−1.16682	+	0.379123i	−0.827455	−	0.561532i	$-0.810212\pi$
$401$	−467.895	+	152.028i	−1.16682	+	0.379123i	−0.339365	+	0.940655i	$0.610212\pi$
$402$	70.9277	+	87.2381i	0.176437	+	0.217010i
$403$	−391.084	−	284.139i	−0.970432	−	0.705060i
$404$	−32.3586	−	44.5377i	−0.0800954	−	0.110242i
$405$	−287.023	+	658.515i	−0.708700	+	1.62596i
$406$	−21.1325			−0.0520504
$407$	15.1956	−	346.637i	0.0373356	−	0.851687i
$408$	80.1014	+	207.455i	0.196327	+	0.508467i
$409$	−89.6123	+	275.798i	−0.219101	+	0.674324i	0.779736	+	0.626109i	$0.215353\pi$
$409$	−89.6123	+	275.798i	−0.219101	+	0.674324i	−0.998837	+	0.0482152i	$0.984647\pi$
$410$	−405.984	−	558.789i	−0.990204	−	1.36290i
$411$	215.818	+	57.3751i	0.525106	+	0.139599i
$412$	3.79033	+	11.6654i	0.00919982	+	0.0283141i
$413$	−57.8149	+	18.7852i	−0.139988	+	0.0454848i
$414$	−166.563	+	18.1670i	−0.402326	+	0.0438817i
$415$	−821.575	+	596.909i	−1.97970	+	1.43834i
$416$	−67.4316	−	21.9098i	−0.162095	−	0.0526679i
$417$	−215.476	−	558.062i	−0.516730	−	1.33828i
$418$	25.7834	+	20.5164i	0.0616827	+	0.0490823i
$419$			490.966i			1.17176i	0.810399	+	0.585879i	$0.199250\pi$
$419$			490.966i			1.17176i	−0.810399	+	0.585879i	$0.800750\pi$
$420$	2.85588	+	52.5230i	0.00679971	+	0.125055i
$421$	−522.225	+	379.419i	−1.24044	+	0.901233i	−0.997628	−	0.0688404i	$-0.978070\pi$
$421$	−522.225	+	379.419i	−1.24044	+	0.901233i	−0.242813	+	0.970073i	$0.578070\pi$
$422$	−195.885	+	269.613i	−0.464183	+	0.638893i
$423$	−93.9450	+	164.201i	−0.222092	+	0.388182i
$424$	0.807862	+	2.48634i	0.00190533	+	0.00586402i
$425$	−826.463	+	1137.53i	−1.94462	+	2.67654i
$426$	−157.096	−	101.582i	−0.368769	−	0.238455i
$427$	4.75588	−	14.6371i	0.0111379	−	0.0342789i
$428$			353.884i			0.826831i
$429$	−394.693	−	123.672i	−0.920030	−	0.288280i
$430$	−5.45767			−0.0126923
$431$	337.422	+	109.635i	0.782881	+	0.254373i	0.673070	−	0.739579i	$-0.264975\pi$
$431$	337.422	+	109.635i	0.782881	+	0.254373i	0.109811	+	0.993952i	$0.464975\pi$
$432$	106.569	−	17.5220i	0.246688	−	0.0405602i
$433$	−301.103	−	218.764i	−0.695388	−	0.505229i	0.183039	−	0.983106i	$-0.441407\pi$
$433$	−301.103	−	218.764i	−0.695388	−	0.505229i	−0.878427	+	0.477877i	$0.841407\pi$
$434$	51.2793	−	16.6616i	0.118155	−	0.0383909i
$435$	−312.053	+	253.710i	−0.717364	+	0.583242i
$436$	281.768	+	204.717i	0.646257	+	0.469533i
$437$	−16.3891	−	22.5577i	−0.0375037	−	0.0516194i
$438$	−9.35410	−	172.033i	−0.0213564	−	0.392770i
$439$	403.316			0.918715			0.459358	−	0.888251i	$-0.348080\pi$
$439$	403.316			0.918715			0.459358	+	0.888251i	$0.348080\pi$
$440$	12.0841	−	275.658i	0.0274638	−	0.626496i
$441$	320.055	−	290.459i	0.725748	−	0.658637i
$442$	143.553	−	441.811i	0.324781	−	0.999572i
$443$	125.100	+	172.185i	0.282392	+	0.388680i	0.926524	−	0.376235i	$-0.122781\pi$
$443$	125.100	+	172.185i	0.282392	+	0.388680i	−0.644132	+	0.764914i	$0.722781\pi$
$444$	48.6246	−	182.903i	0.109515	−	0.411944i
$445$	−410.997	−	1264.92i	−0.923588	−	2.84251i
$446$	−480.537	+	156.136i	−1.07744	+	0.350081i
$447$	190.588	+	50.6676i	0.426371	+	0.113350i
$448$	6.39790	−	4.64835i	0.0142810	−	0.0103758i
$449$	280.393	+	91.1054i	0.624484	+	0.202907i	0.604130	−	0.796886i	$-0.293521\pi$
$449$	280.393	+	91.1054i	0.624484	+	0.202907i	0.0203541	+	0.999793i	$0.493521\pi$
$450$	458.906	+	505.665i	1.01979	+	1.12370i
$451$	−212.250	+	567.384i	−0.470620	+	1.25806i
$452$			5.17011i			0.0114383i
$453$	−554.290	+	30.1389i	−1.22360	+	0.0665317i
$454$	380.596	−	276.519i	0.838316	−	0.609072i
$455$	64.5863	−	88.8954i	0.141948	−	0.195375i
$456$	11.3380	+	13.9453i	0.0248640	+	0.0305817i
$457$	−119.583	−	368.039i	−0.261670	−	0.805337i	−0.992442	−	0.122715i	$-0.960840\pi$
$457$	−119.583	−	368.039i	−0.261670	−	0.805337i	0.730772	−	0.682622i	$-0.239160\pi$
$458$	34.4151	−	47.3683i	0.0751422	−	0.103424i
$459$	114.804	+	698.239i	0.250117	+	1.52122i
$460$	−72.1524	+	222.062i	−0.156853	+	0.482744i
$461$		−	108.108i		−	0.234507i	−0.993102	−	0.117253i	$-0.962591\pi$
$461$		−	108.108i		−	0.234507i	0.993102	−	0.117253i	$-0.0374090\pi$
$462$	37.0359	−	27.5075i	0.0801643	−	0.0595401i
$463$	40.7122			0.0879314			0.0439657	−	0.999033i	$-0.486001\pi$
$463$	40.7122			0.0879314			0.0439657	+	0.999033i	$0.486001\pi$
$464$	57.5058	+	18.6848i	0.123935	+	0.0402689i
$465$	557.182	−	861.678i	1.19824	−	1.85307i
$466$	−267.790	−	194.561i	−0.574657	−	0.417512i
$467$	873.302	−	283.753i	1.87003	−	0.607608i	0.878492	−	0.477757i	$-0.158550\pi$
$467$	873.302	−	283.753i	1.87003	−	0.607608i	0.991534	−	0.129851i	$-0.0414499\pi$
$468$	−195.823	−	112.037i	−0.418425	−	0.239395i
$469$	21.1936	+	15.3981i	0.0451890	+	0.0328317i
$470$	154.956	+	213.278i	0.329693	+	0.453784i
$471$	283.044	−	15.3902i	0.600943	−	0.0326756i
$472$	173.936			0.368508
$473$	2.64125	+	3.99202i	0.00558403	+	0.00843978i
$474$	−203.291	+	78.4937i	−0.428884	+	0.165599i
$475$	−35.1158	+	108.075i	−0.0739280	+	0.227527i
$476$	30.4559	+	41.9189i	0.0639830	+	0.0880650i
$477$	0.901966	+	8.26960i	0.00189091	+	0.0173367i
$478$	148.079	+	455.740i	0.309789	+	0.953432i
$479$	−528.773	+	171.809i	−1.10391	+	0.358682i	−0.803606	−	0.595162i	$-0.797088\pi$
$479$	−528.773	+	171.809i	−1.10391	+	0.358682i	−0.300304	+	0.953844i	$0.597088\pi$
$480$	38.6681	−	145.451i	0.0805585	−	0.303023i
$481$	−319.844	+	232.380i	−0.664956	+	0.483119i
$482$	−547.117	−	177.769i	−1.13510	−	0.368815i
$483$	−36.4186	+	14.0618i	−0.0754009	+	0.0291134i
$484$	−207.478	+	124.566i	−0.428674	+	0.257368i
$485$		−	806.152i		−	1.66217i
$486$	343.343	+	14.6207i	0.706467	+	0.0300837i
$487$	236.136	−	171.563i	0.484878	−	0.352285i	−0.318333	−	0.947979i	$-0.603123\pi$
$487$	236.136	−	171.563i	0.484878	−	0.352285i	0.803211	+	0.595694i	$0.203123\pi$
$488$	−25.8835	+	35.6256i	−0.0530399	+	0.0730032i
$489$	−155.275	+	126.244i	−0.317536	+	0.258168i
$490$	−186.121	−	572.821i	−0.379838	−	1.16902i
$491$	−177.221	+	243.924i	−0.360939	+	0.496790i	−0.950410	−	0.311000i	$-0.899336\pi$
$491$	−177.221	+	243.924i	−0.360939	+	0.496790i	0.589471	+	0.807789i	$0.299336\pi$
$492$	−179.420	+	277.472i	−0.364675	+	0.563968i
$493$	−122.422	+	376.777i	−0.248321	+	0.764254i
$494$		−	37.5444i		−	0.0760008i
$495$	216.644	−	850.833i	0.437665	−	1.71885i
$496$	−154.273			−0.311035
$497$	−41.4554	−	13.4697i	−0.0834112	−	0.0271020i
$498$	407.961	+	263.797i	0.819199	+	0.529714i
$499$	−465.283	−	338.048i	−0.932431	−	0.677451i	0.0141560	−	0.999900i	$-0.495494\pi$
$499$	−465.283	−	338.048i	−0.932431	−	0.677451i	−0.946587	+	0.322449i	$0.895494\pi$
$500$	483.297	−	157.033i	0.966595	−	0.314066i
$501$	354.183	+	435.631i	0.706952	+	0.869522i
$502$	−66.8962	−	48.6029i	−0.133259	−	0.0968186i
$503$	−192.227	−	264.578i	−0.382161	−	0.526000i	0.573994	−	0.818859i	$-0.305393\pi$
$503$	−192.227	−	264.578i	−0.382161	−	0.526000i	−0.956155	+	0.292860i	$0.905393\pi$
$504$	22.9480	−	10.3251i	0.0455318	−	0.0204863i
$505$	−244.113			−0.483391
$506$	197.346	−	54.6915i	0.390012	−	0.108086i
$507$	−12.8638	−	33.3160i	−0.0253724	−	0.0657119i
$508$	94.6516	−	291.308i	0.186322	−	0.573441i
$509$	316.671	+	435.860i	0.622143	+	0.856306i	0.997507	−	0.0705715i	$-0.0224823\pi$
$509$	316.671	+	435.860i	0.622143	+	0.856306i	−0.375364	+	0.926877i	$0.622482\pi$
$510$	952.994	+	253.353i	1.86862	+	0.496770i
$511$	−12.4048	−	38.1780i	−0.0242755	−	0.0747123i
$512$	−21.5200	+	6.99226i	−0.0420312	+	0.0136568i
$513$	26.2625	+	50.8021i	0.0511939	+	0.0990295i
$514$	−237.519	+	172.568i	−0.462100	+	0.335735i
$515$	51.7274	+	16.8072i	0.100442	+	0.0326354i
$516$	0.940447	+	2.43566i	0.00182257	+	0.00472028i
$517$	81.0115	−	216.559i	0.156695	−	0.418876i
$518$		−	44.0964i		−	0.0851282i
$519$	27.4653	+	505.120i	0.0529197	+	0.973257i
$520$	−254.352	+	184.797i	−0.489138	+	0.355379i
$521$	−502.912	+	692.199i	−0.965282	+	1.32860i	−0.0208875	+	0.999782i	$0.506649\pi$
$521$	−502.912	+	692.199i	−0.965282	+	1.32860i	−0.944394	+	0.328815i	$0.893351\pi$
$522$	166.998	+	95.5455i	0.319920	+	0.183037i
$523$	−48.0566	−	147.903i	−0.0918864	−	0.282797i	0.894543	−	0.446981i	$-0.147501\pi$
$523$	−48.0566	−	147.903i	−0.0918864	−	0.282797i	−0.986430	+	0.164184i	$0.947501\pi$
$524$	−129.638	+	178.432i	−0.247401	+	0.340519i
$525$	133.606	+	86.3928i	0.254487	+	0.164558i
$526$	−43.6454	+	134.327i	−0.0829761	+	0.255374i
$527$		−	1010.80i		−	1.91802i
$528$	−125.104	+	42.1075i	−0.236939	+	0.0797491i
$529$	355.709			0.672417
$530$	11.0251	+	3.58226i	0.0208020	+	0.00675898i
$531$	541.813	+	112.947i	1.02036	+	0.212707i
$532$	3.38786	+	2.46143i	0.00636816	+	0.00462674i
$533$	656.468	−	213.299i	1.23165	−	0.400186i
$534$	−493.690	+	401.387i	−0.924513	+	0.751661i
$535$	1269.52	+	922.357i	2.37293	+	1.72403i
$536$	−44.0577	−	60.6402i	−0.0821972	−	0.113135i
$537$	8.59660	+	158.102i	0.0160086	+	0.294417i
$538$	−193.862			−0.360338
$539$	−328.917	+	413.356i	−0.610235	+	0.766894i
$540$	214.902	−	427.973i	0.397967	−	0.792543i
$541$	−69.2149	+	213.022i	−0.127939	+	0.393755i	−0.994425	−	0.105446i	$-0.966373\pi$
$541$	−69.2149	+	213.022i	−0.127939	+	0.393755i	0.866486	+	0.499201i	$0.166373\pi$
$542$	−311.756	−	429.095i	−0.575195	−	0.791688i
$543$	−29.6642	+	111.583i	−0.0546302	+	0.205493i
$544$	−45.8132	−	140.998i	−0.0842154	−	0.259188i
$545$	1468.79	−	477.240i	2.69503	−	0.875669i
$546$	−50.8018	−	13.5056i	−0.0930436	−	0.0247355i
$547$	−101.190	+	73.5189i	−0.184991	+	0.134404i	−0.676426	−	0.736510i	$-0.736472\pi$
$547$	−101.190	+	73.5189i	−0.184991	+	0.134404i	0.491436	+	0.870914i	$0.336472\pi$
$548$	−141.590	−	46.0054i	−0.258376	−	0.0839514i
$549$	−103.761	+	94.1665i	−0.189001	+	0.171524i
$550$	−653.075	−	519.667i	−1.18741	−	0.944848i
$551$			32.0180i			0.0581089i
$552$	111.536	−	6.06462i	0.202057	−	0.0109866i
$553$	−41.0776	+	29.8446i	−0.0742814	+	0.0539686i
$554$	80.3762	−	110.628i	0.145083	−	0.199690i
$555$	−529.408	−	651.151i	−0.953889	−	1.17324i
$556$	123.240	+	379.292i	0.221654	+	0.682180i
$557$	210.638	−	289.919i	0.378166	−	0.520500i	−0.576932	−	0.816792i	$-0.695750\pi$
$557$	210.638	−	289.919i	0.378166	−	0.520500i	0.955097	+	0.296292i	$0.0957502\pi$
$558$	−480.564	−	100.179i	−0.861225	−	0.179533i
$559$	1.68541	−	5.18717i	0.00301505	−	0.00927938i
$560$		−	35.0671i		−	0.0626198i
$561$	−275.888	−	819.678i	−0.491779	−	1.46110i
$562$	187.009			0.332756
$563$	138.482	+	44.9956i	0.245972	+	0.0799210i	0.429408	−	0.903111i	$-0.358722\pi$
$563$	138.482	+	44.9956i	0.245972	+	0.0799210i	−0.183437	+	0.983032i	$0.558722\pi$
$564$	68.4810	−	105.906i	0.121420	−	0.187776i
$565$	18.5472	+	13.4753i	0.0328268	+	0.0238501i
$566$	−211.986	+	68.8785i	−0.374534	+	0.121693i
$567$	78.1882	−	17.2613i	0.137898	−	0.0304433i
$568$	100.899	+	73.3075i	0.177639	+	0.129063i
$569$	−0.785884	−	1.08168i	−0.00138117	−	0.00190101i	0.808326	−	0.588735i	$-0.200374\pi$
$569$	−0.785884	−	1.08168i	−0.00138117	−	0.00190101i	−0.809707	+	0.586834i	$0.800374\pi$
$570$	79.5781	−	4.32697i	0.139611	−	0.00759117i
$571$	−63.3495			−0.110945			−0.0554724	−	0.998460i	$-0.517666\pi$
$571$	−63.3495			−0.110945			−0.0554724	+	0.998460i	$0.517666\pi$
$572$	258.264	+	96.6127i	0.451510	+	0.168903i
$573$	−248.328	+	95.8830i	−0.433382	+	0.167335i
$574$	−23.7910	+	73.2211i	−0.0414477	+	0.127563i
$575$	415.125	+	571.370i	0.721956	+	0.993688i
$576$	−71.5755	+	7.80675i	−0.124263	+	0.0135534i
$577$	−99.6407	−	306.663i	−0.172688	−	0.531478i	0.826833	−	0.562448i	$-0.190140\pi$
$577$	−99.6407	−	306.663i	−0.172688	−	0.531478i	−0.999520	+	0.0309701i	$0.990140\pi$
$578$	535.116	−	173.870i	0.925806	−	0.300812i
$579$	−14.7161	+	55.3549i	−0.0254163	+	0.0956043i
$580$	216.912	−	157.596i	0.373986	−	0.271717i
$581$	107.655	+	34.9793i	0.185293	+	0.0602054i
$582$	−359.772	+	138.913i	−0.618165	+	0.238683i
$583$	−2.71535	−	9.79793i	−0.00465755	−	0.0168061i
$584$			114.858i			0.196675i
$585$	−912.310	+	410.480i	−1.55950	+	0.701676i
$586$	−223.618	+	162.468i	−0.381601	+	0.277249i
$587$	179.958	−	247.691i	0.306573	−	0.421961i	−0.627736	−	0.778426i	$-0.716018\pi$
$587$	179.958	−	247.691i	0.306573	−	0.421961i	0.934309	+	0.356465i	$0.116018\pi$
$588$	−223.568	+	181.769i	−0.380218	+	0.309131i
$589$	−25.2442	−	77.6936i	−0.0428594	−	0.131908i
$590$	453.344	−	623.974i	0.768379	−	1.05758i
$591$	358.357	−	554.197i	0.606357	−	0.937728i
$592$	−38.9889	+	119.995i	−0.0658596	+	0.202695i
$593$			658.253i			1.11004i	0.831838	+	0.555019i	$0.187289\pi$
$593$			658.253i			1.11004i	−0.831838	+	0.555019i	$0.812711\pi$
$594$	−417.043	+	49.9280i	−0.702093	+	0.0840539i
$595$	229.759			0.386150
$596$	−125.037	−	40.6270i	−0.209794	−	0.0681661i
$597$	−42.1363	−	27.2463i	−0.0705800	−	0.0456387i
$598$	−188.774	−	137.153i	−0.315676	−	0.229352i
$599$	−987.836	+	320.967i	−1.64914	+	0.535839i	−0.978554	−	0.205991i	$-0.933958\pi$
$599$	−987.836	+	320.967i	−1.64914	+	0.535839i	−0.670588	+	0.741830i	$0.733958\pi$
$600$	−287.183	−	353.223i	−0.478639	−	0.588706i
$601$	−266.984	−	193.975i	−0.444232	−	0.322754i	0.343082	−	0.939305i	$-0.388529\pi$
$601$	−266.984	−	193.975i	−0.444232	−	0.322754i	−0.787314	+	0.616552i	$0.788529\pi$
$602$	0.357574	+	0.492158i	0.000593976	+	0.000817538i
$603$	−97.8630	−	217.505i	−0.162294	−	0.360704i
$604$	370.073			0.612703
$605$	−93.9019	+	1068.97i	−0.155210	+	1.76690i
$606$	42.0647	+	108.943i	0.0694136	+	0.179774i
$607$	137.424	−	422.949i	0.226399	−	0.696785i	−0.771747	−	0.635929i	$-0.780617\pi$
$607$	137.424	−	422.949i	0.226399	−	0.696785i	0.998147	−	0.0608560i	$-0.0193830\pi$
$608$	−7.04275	−	9.69351i	−0.0115835	−	0.0159433i
$609$	43.3239	+	11.5176i	0.0711394	+	0.0189123i
$610$	60.3402	+	185.708i	0.0989183	+	0.304439i
$611$	−250.560	+	81.4120i	−0.410083	+	0.133244i
$612$	−51.1497	−	468.962i	−0.0835780	−	0.766277i
$613$	61.0274	−	44.3390i	0.0995553	−	0.0723312i	−0.536894	−	0.843650i	$-0.680402\pi$
$613$	61.0274	−	44.3390i	0.0995553	−	0.0723312i	0.636449	+	0.771319i	$0.280402\pi$
$614$	−32.3308	−	10.5049i	−0.0526561	−	0.0171090i
$615$	527.761	+	1366.85i	0.858147	+	2.22252i
$616$	−25.6498	+	16.9708i	−0.0416393	+	0.0275499i
$617$			244.757i			0.396688i	0.980132	+	0.198344i	$0.0635563\pi$
$617$			244.757i			0.396688i	−0.980132	+	0.198344i	$0.936444\pi$
$618$	−1.41270	−	25.9812i	−0.00228592	−	0.0420408i
$619$	112.069	−	81.4229i	0.181049	−	0.131539i	−0.493570	−	0.869706i	$-0.664308\pi$
$619$	112.069	−	81.4229i	0.181049	−	0.131539i	0.674618	+	0.738167i	$0.264308\pi$
$620$	−402.096	+	553.437i	−0.648541	+	0.892641i
$621$	351.374	+	53.5357i	0.565819	+	0.0862088i
$622$	117.657	+	362.111i	0.189159	+	0.582172i
$623$	−87.1394	+	119.937i	−0.139871	+	0.192515i
$624$	126.301	+	81.6692i	0.202405	+	0.130880i
$625$	281.852	−	867.450i	0.450963	−	1.38792i
$626$			851.851i			1.36078i
$627$	−41.6769	−	56.1134i	−0.0664703	−	0.0894950i
$628$	−188.975			−0.300915
$629$	−786.209	−	255.455i	−1.24993	−	0.406128i
$630$	22.7712	−	109.235i	0.0361448	−	0.173388i
$631$	174.516	+	126.793i	0.276571	+	0.200940i	0.717420	−	0.696641i	$-0.245323\pi$
$631$	174.516	+	126.793i	0.276571	+	0.200940i	−0.440849	+	0.897581i	$0.645323\pi$
$632$	138.169	−	44.8937i	0.218621	−	0.0710343i
$633$	548.530	−	445.975i	0.866557	−	0.704541i
$634$	297.886	+	216.427i	0.469853	+	0.341368i
$635$	−798.334	−	1098.81i	−1.25722	−	1.73041i
$636$	−0.301099	−	5.53758i	−0.000473427	−	0.00870689i
$637$	601.907			0.944909
$638$	−220.248	−	82.3916i	−0.345217	−	0.129140i
$639$	266.699	+	293.874i	0.417370	+	0.459897i
$640$	−31.0054	+	95.4248i	−0.0484459	+	0.149101i
$641$	−553.519	−	761.853i	−0.863524	−	1.18854i	−0.980718	−	0.195430i	$-0.937390\pi$
$641$	−553.519	−	761.853i	−0.863524	−	1.18854i	0.117194	−	0.993109i	$-0.462610\pi$
$642$	192.874	−	725.501i	0.300426	−	1.13006i
$643$	33.7509	+	103.874i	0.0524897	+	0.161547i	0.973865	−	0.227127i	$-0.0729333\pi$
$643$	33.7509	+	103.874i	0.0524897	+	0.161547i	−0.921375	+	0.388674i	$0.872933\pi$
$644$	24.7522	−	8.04249i	0.0384352	−	0.0124883i
$645$	11.1888	+	2.97454i	0.0173470	+	0.00461169i
$646$	63.5117	−	46.1440i	0.0983154	−	0.0714303i
$647$	−634.054	−	206.017i	−0.979991	−	0.318418i	−0.225149	−	0.974324i	$-0.572287\pi$
$647$	−634.054	−	206.017i	−0.979991	−	0.318418i	−0.754843	+	0.655906i	$0.772287\pi$
$648$	−228.028	−	22.1603i	−0.351896	−	0.0341980i
$649$	−675.802	−	29.6253i	−1.04130	−	0.0456476i
$650$			950.974i			1.46304i
$651$	−114.209	+	6.20998i	−0.175436	+	0.00953915i
$652$	107.934	−	78.4184i	0.165542	−	0.120274i
$653$	87.6509	−	120.641i	0.134228	−	0.184749i	−0.736612	−	0.676316i	$-0.763576\pi$
$653$	87.6509	−	120.641i	0.134228	−	0.184749i	0.870840	+	0.491567i	$0.163576\pi$
$654$	−466.081	−	573.261i	−0.712662	−	0.876545i
$655$	302.216	+	930.124i	0.461398	+	1.42004i
$656$	129.480	−	178.214i	0.197379	−	0.271668i
$657$	−74.5845	+	357.785i	−0.113523	+	0.544574i
$658$	9.08053	−	27.9470i	0.0138002	−	0.0424726i
$659$		−	191.395i		−	0.290433i	−0.989400	−	0.145216i	$-0.953612\pi$
$659$		−	191.395i		−	0.290433i	0.989400	−	0.145216i	$-0.0463878\pi$
$660$	−175.013	+	558.544i	−0.265171	+	0.846278i
$661$	−446.353			−0.675269			−0.337635	−	0.941277i	$-0.609627\pi$
$661$	−446.353			−0.675269			−0.337635	+	0.941277i	$0.609627\pi$
$662$	46.8529	+	15.2234i	0.0707747	+	0.0229961i
$663$	−535.095	+	827.522i	−0.807082	+	1.24815i
$664$	−262.025	−	190.372i	−0.394615	−	0.286705i
$665$	17.6601	−	5.73813i	0.0265566	−	0.00862877i
$666$	−199.372	+	348.470i	−0.299357	+	0.523228i
$667$	160.987	+	116.964i	0.241360	+	0.175359i
$668$	−220.006	−	302.812i	−0.329350	−	0.453311i
$669$	1070.25	−	58.1937i	1.59978	−	0.0869860i
$670$	−332.371			−0.496076
$671$	106.634	−	134.009i	0.158919	−	0.199716i
$672$	−15.6498	+	6.04264i	−0.0232885	+	0.00899202i
$673$	135.227	−	416.185i	0.200931	−	0.618403i	−0.798925	−	0.601431i	$-0.794597\pi$
$673$	135.227	−	416.185i	0.200931	−	0.618403i	0.999856	−	0.0169719i	$-0.00540259\pi$
$674$	122.293	+	168.321i	0.181443	+	0.249735i
$675$	−665.210	−	1286.78i	−0.985497	−	1.90635i
$676$	7.35732	+	22.6435i	0.0108836	+	0.0334963i
$677$	30.9201	−	10.0466i	0.0456723	−	0.0148398i	−0.286092	−	0.958202i	$-0.592356\pi$
$677$	30.9201	−	10.0466i	0.0456723	−	0.0148398i	0.331764	+	0.943362i	$0.392356\pi$
$678$	2.81781	−	10.5993i	0.00415607	−	0.0156332i
$679$	−72.6967	+	52.8172i	−0.107064	+	0.0777868i
$680$	−625.222	−	203.147i	−0.919444	−	0.298746i
$681$	−930.971	+	359.462i	−1.36707	+	0.527844i
$682$	599.407	+	26.2763i	0.878895	+	0.0385283i
$683$			238.996i			0.349921i	0.984575	+	0.174961i	$0.0559799\pi$
$683$			238.996i			0.349921i	−0.984575	+	0.174961i	$0.944020\pi$
$684$	−15.6437	−	34.7687i	−0.0228709	−	0.0508315i
$685$	−534.077	+	388.030i	−0.779675	+	0.566467i
$686$	−79.7255	+	109.733i	−0.116218	+	0.159960i
$687$	−96.3715	+	78.3534i	−0.140279	+	0.114052i
$688$	−0.537879	−	1.65542i	−0.000781801	−	0.00240614i
$689$	−6.80943	+	9.37237i	−0.00988306	+	0.0136029i
$690$	268.949	−	415.928i	0.389781	−	0.602794i
$691$	22.7256	−	69.9421i	0.0328879	−	0.101219i	−0.933265	−	0.359188i	$-0.883054\pi$
$691$	22.7256	−	69.9421i	0.0328879	−	0.101219i	0.966153	+	0.257970i	$0.0830535\pi$
$692$		−	337.244i		−	0.487347i
$693$	−90.9198	+	36.2082i	−0.131197	+	0.0522485i
$694$	295.018			0.425097
$695$	1681.88	+	546.475i	2.41997	+	0.786294i
$696$	−107.710	−	69.6477i	−0.154755	−	0.100069i
$697$	1167.66	+	848.353i	1.67526	+	1.21715i
$698$	675.591	−	219.513i	0.967896	−	0.314488i
$699$	442.960	+	544.822i	0.633705	+	0.779431i
$700$	−85.8122	−	62.3462i	−0.122589	−	0.0890660i
$701$	−631.093	−	868.625i	−0.900276	−	1.23912i	−0.970380	−	0.241584i	$-0.922333\pi$
$701$	−631.093	−	868.625i	−0.900276	−	1.23912i	0.0701042	−	0.997540i	$-0.477667\pi$
$702$	340.396	+	336.416i	0.484895	+	0.479225i
$703$	−66.8108			−0.0950367
$704$	84.8036	−	23.5021i	0.120460	−	0.0333836i
$705$	−201.436	−	521.698i	−0.285724	−	0.739997i
$706$	−13.2854	+	40.8884i	−0.0188179	+	0.0579155i
$707$	15.9937	+	22.0134i	0.0226219	+	0.0311364i
$708$	−356.588	−	94.7985i	−0.503655	−	0.133896i
$709$	223.211	+	686.973i	0.314825	+	0.968933i	0.975826	+	0.218548i	$0.0701319\pi$
$709$	223.211	+	686.973i	0.314825	+	0.968933i	−0.661001	+	0.750385i	$0.729868\pi$
$710$	525.964	−	170.896i	0.740795	−	0.240699i
$711$	459.550	−	50.1231i	0.646343	−	0.0704967i
$712$	343.170	−	249.327i	0.481980	−	0.350179i
$713$	−482.865	−	156.892i	−0.677230	−	0.220045i
$714$	−39.5913	−	102.538i	−0.0554500	−	0.143610i
$715$	1019.72	−	674.681i	1.42618	−	0.943610i
$716$		−	105.557i		−	0.147426i
$717$	−55.1907	−	1015.02i	−0.0769745	−	1.41565i
$718$	729.747	−	530.192i	1.01636	−	0.738430i
$719$	−457.238	+	629.334i	−0.635936	+	0.875291i	−0.998391	−	0.0567107i	$-0.981939\pi$
$719$	−457.238	+	629.334i	−0.635936	+	0.875291i	0.362455	+	0.932001i	$0.381939\pi$
$720$	−158.548	+	277.116i	−0.220205	+	0.384884i
$721$	−1.87342	−	5.76581i	−0.00259837	−	0.00799696i
$722$	−296.353	+	407.895i	−0.410462	+	0.564952i
$723$	1024.76	+	662.636i	1.41738	+	0.916509i
$724$	23.7858	−	73.2051i	0.0328533	−	0.101112i
$725$		−	810.993i		−	1.11861i
$726$	493.245	−	142.295i	0.679400	−	0.195998i
$727$	−1122.23			−1.54364			−0.771820	−	0.635841i	$-0.780653\pi$
$727$	−1122.23			−1.54364			−0.771820	+	0.635841i	$0.780653\pi$
$728$	33.3291	+	10.8293i	0.0457817	+	0.0148754i
$729$	−695.922	−	217.103i	−0.954626	−	0.297809i
$730$	412.040	+	299.365i	0.564438	+	0.410089i
$731$	10.8463	−	3.52418i	0.0148376	−	0.00482104i
$732$	72.4807	−	58.9293i	0.0990173	−	0.0805046i
$733$	−1065.65	−	774.243i	−1.45383	−	1.05627i	−0.984918	−	0.173020i	$-0.944648\pi$
$733$	−1065.65	−	774.243i	−1.45383	−	1.05627i	−0.468908	−	0.883247i	$-0.655352\pi$
$734$	455.344	+	626.727i	0.620360	+	0.853852i
$735$	69.3694	+	1275.79i	0.0943801	+	1.73576i
$736$	−74.4670			−0.101178
$737$	160.851	+	243.113i	0.218252	+	0.329868i
$738$	519.059	−	471.061i	0.703332	−	0.638294i
$739$	−36.9675	+	113.774i	−0.0500237	+	0.153957i	−0.972948	−	0.231024i	$-0.925792\pi$
$739$	−36.9675	+	113.774i	−0.0500237	+	0.153957i	0.922924	+	0.384982i	$0.125792\pi$
$740$	328.850	+	452.623i	0.444391	+	0.611652i
$741$	−20.4625	+	76.9702i	−0.0276147	+	0.103873i
$742$	−0.399298	−	1.22891i	−0.000538137	−	0.00165622i
$743$	−447.502	+	145.402i	−0.602290	+	0.195696i	−0.594262	−	0.804272i	$-0.702556\pi$
$743$	−447.502	+	145.402i	−0.602290	+	0.195696i	−0.00802872	+	0.999968i	$0.502556\pi$
$744$	316.277	+	84.0820i	0.425104	+	0.113013i
$745$	−471.639	+	342.666i	−0.633073	+	0.459955i
$746$	856.046	+	278.146i	1.14751	+	0.372850i
$747$	−692.591	−	763.161i	−0.927163	−	1.02163i
$748$	153.985	+	555.632i	0.205863	+	0.742824i
$749$		−	174.912i		−	0.233528i
$750$	−1076.40	+	58.5279i	−1.43520	+	0.0780372i
$751$	363.580	−	264.157i	0.484128	−	0.351740i	−0.318793	−	0.947824i	$-0.603278\pi$
$751$	363.580	−	264.157i	0.484128	−	0.351740i	0.802922	+	0.596084i	$0.203278\pi$
$752$	−49.4200	+	68.0208i	−0.0657181	+	0.0904532i
$753$	110.655	+	136.101i	0.146952	+	0.180745i
$754$	82.7990	+	254.829i	0.109813	+	0.337970i
$755$	964.552	−	1327.59i	1.27755	−	1.75840i
$756$	−52.6734	+	8.66051i	−0.0696738	+	0.0114557i
$757$	−298.262	+	917.955i	−0.394005	+	1.21262i	0.535729	+	0.844390i	$0.320037\pi$
$757$	−298.262	+	917.955i	−0.394005	+	1.21262i	−0.929734	+	0.368232i	$0.879963\pi$
$758$		−	835.308i		−	1.10199i
$759$	−434.389	+	4.56611i	−0.572317	+	0.00601595i
$760$	−53.1304			−0.0699085
$761$	618.469	+	200.953i	0.812706	+	0.264064i	0.685743	−	0.727843i	$-0.259477\pi$
$761$	618.469	+	200.953i	0.812706	+	0.264064i	0.126962	+	0.991908i	$0.459477\pi$
$762$	−352.815	+	545.626i	−0.463012	+	0.716045i
$763$	−139.268	−	101.184i	−0.182527	−	0.132614i
$764$	168.778	−	54.8393i	0.220914	−	0.0717792i
$765$	−1815.66	−	1038.80i	−2.37341	−	1.35791i
$766$	−614.723	−	446.622i	−0.802510	−	0.583058i
$767$	453.048	+	623.568i	0.590676	+	0.812996i
$768$	47.9292	−	2.60609i	0.0624078	−	0.00339335i
$769$	1118.20			1.45410			0.727048	−	0.686587i	$-0.240892\pi$
$769$	1118.20			1.45410			0.727048	+	0.686587i	$0.240892\pi$
$770$	−5.97274	+	136.248i	−0.00775680	+	0.176946i
$771$	580.993	−	224.330i	0.753558	−	0.290960i
$772$	11.7998	−	36.3162i	0.0152848	−	0.0470417i
$773$	−88.9963	−	122.493i	−0.115131	−	0.158464i	0.747562	−	0.664192i	$-0.231224\pi$
$773$	−88.9963	−	122.493i	−0.115131	−	0.158464i	−0.862693	+	0.505727i	$0.831224\pi$
$774$	−0.600534	−	5.50594i	−0.000775884	−	0.00711362i
$775$	639.418	+	1967.93i	0.825055	+	2.53926i
$776$	244.522	−	79.4501i	0.315106	−	0.102384i
$777$	−24.0334	+	90.4025i	−0.0309310	+	0.116348i
$778$	46.0161	−	33.4326i	0.0591466	−	0.0429725i
$779$	110.938	+	36.0459i	0.142411	+	0.0462720i
$780$	622.167	−	240.228i	0.797650	−	0.307985i
$781$	−379.543	−	302.011i	−0.485971	−	0.386698i
$782$		−	487.906i		−	0.623921i
$783$	−290.291	−	286.896i	−0.370742	−	0.366407i
$784$	155.405	−	112.908i	0.198221	−	0.144016i
$785$	−492.541	+	677.925i	−0.627441	+	0.863599i
$786$	363.022	−	295.149i	0.461860	−	0.375508i
$787$	−296.143	−	911.433i	−0.376293	−	1.15811i	−0.942602	−	0.333918i	$-0.891629\pi$
$787$	−296.143	−	911.433i	−0.376293	−	1.15811i	0.566309	−	0.824193i	$-0.308371\pi$
$788$	−258.612	+	355.949i	−0.328188	+	0.451712i
$789$	162.689	−	251.597i	0.206196	−	0.318881i
$790$	199.070	−	612.674i	0.251987	−	0.775537i
$791$		−	2.55540i		−	0.00323060i
$792$	279.426	−	18.1410i	0.352811	−	0.0229053i
$793$	−195.138			−0.246075
$794$	500.599	+	162.655i	0.630478	+	0.204855i
$795$	−20.6502	−	13.3529i	−0.0259751	−	0.0167961i
$796$	27.0632	+	19.6626i	0.0339990	+	0.0247017i
$797$	676.115	−	219.683i	0.848325	−	0.275637i	0.147580	−	0.989050i	$-0.452851\pi$
$797$	676.115	−	219.683i	0.848325	−	0.275637i	0.700744	+	0.713413i	$0.252851\pi$
$798$	−5.60396	−	6.89265i	−0.00702251	−	0.00863740i
$799$	−445.671	−	323.799i	−0.557786	−	0.405256i
$800$	178.388	+	245.530i	0.222985	+	0.306912i
$801$	1230.88	−	553.817i	1.53668	−	0.691407i
$802$	−695.756			−0.867526
$803$	19.5630	−	446.265i	0.0243624	−	0.555747i
$804$	57.2730	+	148.332i	0.0712351	+	0.184492i
$805$	35.6624	−	109.758i	0.0443011	−	0.136345i
$806$	−401.834	−	553.077i	−0.498553	−	0.686199i
$807$	397.438	+	105.659i	0.492488	+	0.130928i
$808$	−24.0585	−	74.0443i	−0.0297753	−	0.0916390i
$809$	−731.760	+	237.763i	−0.904524	+	0.293898i	−0.724103	−	0.689692i	$-0.757746\pi$
$809$	−731.760	+	237.763i	−0.904524	+	0.293898i	−0.180421	+	0.983589i	$0.557746\pi$
$810$	−673.827	+	760.267i	−0.831885	+	0.938601i
$811$	1031.27	−	749.265i	1.27161	−	0.923878i	0.272343	−	0.962200i	$-0.412202\pi$
$811$	1031.27	−	749.265i	1.27161	−	0.923878i	0.999265	+	0.0383228i	$0.0122015\pi$
$812$	−28.4231	−	9.23523i	−0.0350038	−	0.0113734i
$813$	405.268	+	1049.61i	0.498485	+	1.29103i
$814$	171.924	−	459.584i	0.211209	−	0.564600i
$815$		−	591.588i		−	0.725875i
$816$	17.0751	+	314.031i	0.0209254	+	0.384842i
$817$	0.745673	−	0.541763i	0.000912696	−	0.000663113i
$818$	−241.057	+	331.786i	−0.294690	+	0.405606i
$819$	96.7885	+	55.3760i	0.118179	+	0.0676141i
$820$	−301.847	−	928.991i	−0.368107	−	1.13292i
$821$	−187.589	+	258.194i	−0.228488	+	0.314487i	−0.907833	−	0.419333i	$-0.862264\pi$
$821$	−187.589	+	258.194i	−0.228488	+	0.314487i	0.679345	+	0.733819i	$0.262264\pi$
$822$	265.201	+	171.486i	0.322629	+	0.208620i
$823$	273.948	−	843.126i	0.332866	−	1.02445i	−0.634898	−	0.772596i	$-0.718958\pi$
$823$	273.948	−	843.126i	0.332866	−	1.02445i	0.967764	−	0.251859i	$-0.0810419\pi$
$824$			17.3464i			0.0210514i
$825$	1055.65	+	1421.31i	1.27957	+	1.72280i
$826$	−85.9703			−0.104080
$827$	51.2627	+	16.6563i	0.0619864	+	0.0201406i	0.339846	−	0.940481i	$-0.389625\pi$
$827$	51.2627	+	16.6563i	0.0619864	+	0.0201406i	−0.277860	+	0.960622i	$0.589625\pi$
$828$	−231.966	−	48.3560i	−0.280152	−	0.0584010i
$829$	129.000	+	93.7238i	0.155609	+	0.113056i	0.662865	−	0.748739i	$-0.269340\pi$
$829$	129.000	+	93.7238i	0.155609	+	0.113056i	−0.507256	+	0.861795i	$0.669340\pi$
$830$	−1365.87	+	443.800i	−1.64563	+	0.534698i
$831$	−225.075	+	182.994i	−0.270848	+	0.220209i
$832$	−81.1203	−	58.9374i	−0.0975004	−	0.0708382i
$833$	739.774	+	1018.21i	0.888084	+	1.22234i
$834$	−45.9328	−	844.759i	−0.0550753	−	1.01290i
$835$	−1659.72			−1.98769
$836$	25.7125	+	38.8623i	0.0307566	+	0.0464860i
$837$	930.609	+	467.295i	1.11184	+	0.558298i
$838$	−214.560	+	660.348i	−0.256038	+	0.788005i
$839$	−682.963	−	940.018i	−0.814021	−	1.12040i	−0.990691	−	0.136133i	$-0.956533\pi$
$839$	−682.963	−	940.018i	−0.814021	−	1.12040i	0.176670	−	0.984270i	$-0.443467\pi$
$840$	−19.1123	+	71.8914i	−0.0227527	+	0.0855850i
$841$	189.272	+	582.520i	0.225056	+	0.692651i
$842$	−868.204	+	282.097i	−1.03112	+	0.335032i
$843$	−383.389	−	101.924i	−0.454791	−	0.120906i
$844$	−381.290	+	277.023i	−0.451765	+	0.328227i
$845$	100.407	+	32.6242i	0.118825	+	0.0386085i
$846$	−198.114	+	179.794i	−0.234178	+	0.212523i
$847$	102.549	−	61.5687i	0.121073	−	0.0726903i
$848$			3.69717i			0.00435987i
$849$	472.135	−	25.6718i	0.556107	−	0.0302377i
$850$	−1608.71	+	1168.79i	−1.89260	+	1.37505i
$851$	−244.065	+	335.927i	−0.286798	+	0.394744i
$852$	−166.900	−	205.281i	−0.195892	−	0.240940i
$853$	47.0512	+	144.809i	0.0551597	+	0.169764i	0.974841	−	0.222902i	$-0.0715529\pi$
$853$	47.0512	+	144.809i	0.0551597	+	0.169764i	−0.919681	+	0.392666i	$0.871553\pi$
$854$	12.7933	−	17.6085i	0.0149804	−	0.0206188i
$855$	−165.502	−	34.5009i	−0.193570	−	0.0403519i
$856$	−154.653	+	475.973i	−0.180669	+	0.556043i
$857$		−	693.917i		−	0.809704i	−0.914382	−	0.404852i	$-0.867323\pi$
$857$		−	693.917i		−	0.809704i	0.914382	−	0.404852i	$-0.132677\pi$
$858$	−476.814	−	338.826i	−0.555727	−	0.394902i
$859$	−1416.30			−1.64878			−0.824391	−	0.566021i	$-0.808482\pi$
$859$	−1416.30			−1.64878			−0.824391	+	0.566021i	$0.808482\pi$
$860$	−7.34055	−	2.38509i	−0.00853552	−	0.00277336i
$861$	88.6811	−	137.145i	0.102998	−	0.159285i
$862$	405.919	+	294.917i	0.470904	+	0.342131i
$863$	−158.215	+	51.4070i	−0.183331	+	0.0595678i	−0.399244	−	0.916845i	$-0.630727\pi$
$863$	−158.215	+	51.4070i	−0.183331	+	0.0595678i	0.215913	+	0.976413i	$0.430727\pi$
$864$	150.993	+	23.0054i	0.174760	+	0.0266266i
$865$	−1209.82	−	878.989i	−1.39864	−	1.01617i
$866$	−309.379	−	425.824i	−0.357251	−	0.491714i
$867$	−1191.81	+	64.8032i	−1.37464	+	0.0747442i
$868$	76.2518			0.0878478
$869$	−544.481	+	150.895i	−0.626560	+	0.173642i
$870$	−530.586	+	204.867i	−0.609869	+	0.235480i
$871$	102.641	−	315.898i	0.117843	−	0.362684i
$872$	289.513	+	398.480i	0.332010	+	0.456973i
$873$	813.283	−	88.7049i	0.931596	−	0.101609i
$874$	−12.1852	−	37.5023i	−0.0139419	−	0.0429088i
$875$	−238.877	+	77.6158i	−0.273002	+	0.0887038i
$876$	62.6000	−	235.472i	0.0714612	−	0.268804i
$877$	213.374	−	155.026i	0.243300	−	0.176768i	−0.459452	−	0.888203i	$-0.651954\pi$
$877$	213.374	−	155.026i	0.243300	−	0.176768i	0.702752	+	0.711435i	$0.251954\pi$
$878$	542.459	+	176.256i	0.617835	+	0.200747i
$879$	546.990	−	211.201i	0.622287	−	0.240274i
$880$	136.720	−	365.478i	0.155364	−	0.415316i
$881$			751.643i			0.853170i	0.904447	+	0.426585i	$0.140284\pi$
$881$			751.643i			0.853170i	−0.904447	+	0.426585i	$0.859716\pi$
$882$	557.408	−	250.797i	0.631982	−	0.284351i
$883$	48.6257	−	35.3286i	0.0550687	−	0.0400098i	−0.559910	−	0.828553i	$-0.689164\pi$
$883$	48.6257	−	35.3286i	0.0550687	−	0.0400098i	0.614979	+	0.788543i	$0.289164\pi$
$884$	386.157	−	531.499i	0.436829	−	0.601243i
$885$	−1269.48	+	1032.13i	−1.43444	+	1.16625i
$886$	93.0112	+	286.259i	0.104979	+	0.323091i
$887$	−982.906	+	1352.85i	−1.10812	+	1.52520i	−0.283972	+	0.958833i	$0.591652\pi$
$887$	−982.906	+	1352.85i	−1.10812	+	1.52520i	−0.824152	+	0.566369i	$0.808348\pi$
$888$	145.331	−	224.754i	0.163662	−	0.253102i
$889$	−46.7830	+	143.983i	−0.0526243	+	0.161961i
$890$		−	1880.92i		−	2.11340i
$891$	882.197	+	124.939i	0.990120	+	0.140223i
$892$	−714.555			−0.801070
$893$	−42.3427	−	13.7580i	−0.0474163	−	0.0154065i
$894$	234.197	+	151.438i	0.261966	+	0.169393i
$895$	−378.673	−	275.122i	−0.423098	−	0.307399i
$896$	10.6366	−	3.45603i	0.0118712	−	0.00385717i
$897$	312.258	+	384.064i	0.348113	+	0.428165i
$898$	337.314	+	245.073i	0.375628	+	0.272910i
$899$	342.685	+	471.665i	0.381185	+	0.524656i
$900$	396.243	+	880.668i	0.440270	+	0.978520i
$901$	−24.2238			−0.0268855
$902$	−533.431	+	670.373i	−0.591387	+	0.743207i
$903$	−0.464830	−	1.20386i	−0.000514762	−	0.00133318i
$904$	−2.25942	+	6.95378i	−0.00249936	+	0.00769223i
$905$	−200.620	−	276.130i	−0.221679	−	0.305116i
$906$	−758.690	−	201.697i	−0.837406	−	0.222624i
$907$	−115.700	−	356.087i	−0.127563	−	0.392599i	0.866796	−	0.498662i	$-0.166175\pi$
$907$	−115.700	−	356.087i	−0.127563	−	0.392599i	−0.994359	+	0.106064i	$0.966175\pi$
$908$	632.743	−	205.591i	0.696854	−	0.226421i
$909$	−26.8609	−	246.272i	−0.0295500	−	0.270926i
$910$	125.717	−	91.3388i	0.138151	−	0.100372i
$911$	−1306.25	−	424.425i	−1.43386	−	0.465889i	−0.513882	−	0.857861i	$-0.671793\pi$
$911$	−1306.25	−	424.425i	−1.43386	−	0.465889i	−0.919977	+	0.391972i	$0.871793\pi$
$912$	9.15525	+	23.7112i	0.0100387	+	0.0259991i
$913$	985.634	+	784.292i	1.07956	+	0.859027i
$914$		−	547.271i		−	0.598765i
$915$	−22.4895	−	413.608i	−0.0245787	−	0.452031i
$916$	66.9890	−	48.6703i	0.0731321	−	0.0531335i
$917$	64.0756	−	88.1925i	0.0698753	−	0.0961751i
$918$	−150.731	+	989.301i	−0.164195	+	1.07767i
$919$	−39.6257	−	121.955i	−0.0431183	−	0.132705i	0.927180	−	0.374616i	$-0.122226\pi$
$919$	−39.6257	−	121.955i	−0.0431183	−	0.132705i	−0.970298	+	0.241912i	$0.922226\pi$
$920$	−194.090	+	267.141i	−0.210967	+	0.290371i
$921$	60.5564	+	39.1572i	0.0657507	+	0.0425160i
$922$	47.2448	−	145.404i	0.0512416	−	0.157706i
$923$			552.671i			0.598777i
$924$	61.8344	−	20.8123i	0.0669203	−	0.0225241i
$925$	1692.27			1.82948
$926$	54.7578	+	17.7919i	0.0591337	+	0.0192137i
$927$	−11.2641	+	54.0343i	−0.0121511	+	0.0582894i
$928$	69.1796	+	50.2619i	0.0745470	+	0.0541616i
$929$	1181.51	−	383.897i	1.27181	−	0.413236i	0.406122	−	0.913819i	$-0.366881\pi$
$929$	1181.51	−	383.897i	1.27181	−	0.413236i	0.865689	+	0.500582i	$0.166881\pi$
$930$	1125.97	−	915.457i	1.21073	−	0.984363i
$931$	82.2912	+	59.7881i	0.0883901	+	0.0642192i
$932$	−275.151	−	378.712i	−0.295226	−	0.406344i
$933$	−43.8521	−	806.492i	−0.0470012	−	0.864408i
$934$	1298.59			1.39036
$935$	2394.61	+	895.788i	2.56108	+	0.958062i
$936$	−214.419	−	236.267i	−0.229081	−	0.252422i
$937$	427.500	−	1315.71i	0.456243	−	1.40417i	−0.413426	−	0.910538i	$-0.635668\pi$
$937$	427.500	−	1315.71i	0.456243	−	1.40417i	0.869669	−	0.493635i	$-0.164332\pi$
$938$	21.7762	+	29.9723i	0.0232155	+	0.0319535i
$939$	464.276	−	1746.39i	0.494437	−	1.85984i
$940$	115.209	+	354.577i	0.122563	+	0.377210i
$941$	786.750	−	255.631i	0.836079	−	0.271658i	0.140475	−	0.990084i	$-0.455137\pi$
$941$	786.750	−	255.631i	0.836079	−	0.271658i	0.695604	+	0.718426i	$0.255137\pi$
$942$	387.419	+	102.995i	0.411273	+	0.109337i
$943$	586.504	−	426.120i	0.621956	−	0.451877i
$944$	233.943	+	76.0127i	0.247821	+	0.0805220i
$945$	−106.219	+	211.532i	−0.112401	+	0.223844i
$946$	1.80790	+	6.52352i	0.00191109	+	0.00689589i
$947$			1065.81i			1.12546i	0.826640	+	0.562731i	$0.190249\pi$
$947$			1065.81i			1.12546i	−0.826640	+	0.562731i	$0.809751\pi$
$948$	−307.729	+	16.7324i	−0.324609	+	0.0176502i
$949$	−411.772	+	299.170i	−0.433901	+	0.315247i
$950$	−94.4612	+	130.015i	−0.0994329	+	0.136858i
$951$	−492.743	−	606.054i	−0.518132	−	0.637281i
$952$	22.6438	+	69.6906i	0.0237855	+	0.0732044i
$953$	447.497	−	615.927i	0.469567	−	0.646303i	−0.506891	−	0.862010i	$-0.669205\pi$
$953$	447.497	−	615.927i	0.469567	−	0.646303i	0.976458	+	0.215707i	$0.0692055\pi$
$954$	−2.40080	+	11.5168i	−0.00251657	+	0.0120721i
$955$	243.171	−	748.404i	0.254630	−	0.783669i
$956$			677.682i			0.708873i
$957$	406.628	+	288.952i	0.424899	+	0.301935i
$958$	−786.281			−0.820753
$959$	69.9830	+	22.7388i	0.0729749	+	0.0237110i
$960$	115.573	−	178.733i	0.120388	−	0.186180i
$961$	−425.960	−	309.478i	−0.443246	−	0.322037i
$962$	−531.743	+	172.774i	−0.552748	+	0.179599i
$963$	−790.825	+	1382.24i	−0.821210	+	1.43534i
$964$	−658.183	−	478.198i	−0.682762	−	0.496056i
$965$	−99.5251	−	136.985i	−0.103135	−	0.141953i
$966$	−55.1282	+	2.99753i	−0.0570685	+	0.00310303i
$967$	−1750.16			−1.80988			−0.904941	−	0.425538i	$-0.860085\pi$
$967$	−1750.16			−1.80988			−0.904941	+	0.425538i	$0.860085\pi$
$968$	−333.495	+	76.8698i	−0.344520	+	0.0794110i
$969$	−155.355	+	59.9851i	−0.160326	+	0.0619041i
$970$	352.302	−	1084.27i	0.363197	−	1.11781i
$971$	217.975	+	300.017i	0.224485	+	0.308977i	0.906372	−	0.422480i	$-0.138841\pi$
$971$	217.975	+	300.017i	0.224485	+	0.308977i	−0.681887	+	0.731457i	$0.738841\pi$
$972$	455.405	+	169.711i	0.468524	+	0.174600i
$973$	−60.9130	−	187.471i	−0.0626032	−	0.192673i
$974$	392.577	−	127.556i	0.403057	−	0.130961i
$975$	518.300	−	1949.60i	0.531590	−	1.99959i
$976$	−50.3822	+	36.6048i	−0.0516211	+	0.0375049i
$977$	−416.889	−	135.456i	−0.426703	−	0.138644i	0.0877894	−	0.996139i	$-0.472020\pi$
$977$	−416.889	−	135.456i	−0.426703	−	0.138644i	−0.514493	+	0.857495i	$0.672020\pi$
$978$	−264.016	+	101.940i	−0.269955	+	0.104234i
$979$	−1375.80	+	910.275i	−1.40531	+	0.929801i
$980$		−	851.780i		−	0.869163i
$981$	643.079	+	1429.27i	0.655534	+	1.45695i
$982$	−344.960	+	250.628i	−0.351283	+	0.255222i
$983$	1065.06	−	1465.93i	1.08348	−	1.49128i	0.227843	−	0.973698i	$-0.426833\pi$
$983$	1065.06	−	1465.93i	1.08348	−	1.49128i	0.855634	−	0.517581i	$-0.173167\pi$
$984$	−362.579	+	294.790i	−0.368475	+	0.299583i
$985$	602.882	+	1855.48i	0.612063	+	1.88374i
$986$	−329.316	+	453.264i	−0.333991	+	0.459700i
$987$	−33.8478	+	52.3454i	−0.0342936	+	0.0530348i
$988$	16.4075	−	50.4971i	0.0166068	−	0.0511105i
$989$		−	5.72837i		−	0.00579208i
$990$	663.213	−	1049.69i	0.669912	−	1.06029i
$991$	804.635			0.811942			0.405971	−	0.913886i	$-0.366933\pi$
$991$	804.635			0.811942			0.405971	+	0.913886i	$0.366933\pi$
$992$	−207.497	−	67.4199i	−0.209170	−	0.0679636i
$993$	−87.7565	−	56.7455i	−0.0883751	−	0.0571455i
$994$	−49.8709	−	36.2333i	−0.0501719	−	0.0364520i
$995$	141.074	−	45.8378i	0.141783	−	0.0460682i
$996$	433.423	+	533.092i	0.435164	+	0.535233i
$997$	1037.33	+	753.662i	1.04045	+	0.755930i	0.970373	−	0.241611i	$-0.0776759\pi$
$997$	1037.33	+	753.662i	1.04045	+	0.755930i	0.0700756	+	0.997542i	$0.477676\pi$
$998$	−478.072	−	658.009i	−0.479030	−	0.659328i
$999$	598.657	−	605.740i	0.599256	−	0.606347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.g.a.53.5	yes	32
3.2	odd	2	inner	66.3.g.a.53.3	yes	32
11.4	even	5		726.3.c.h.485.13		16
11.5	even	5	inner	66.3.g.a.5.3	✓	32
11.7	odd	10		726.3.c.i.485.5		16
33.5	odd	10	inner	66.3.g.a.5.5	yes	32
33.26	odd	10		726.3.c.h.485.5		16
33.29	even	10		726.3.c.i.485.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.g.a.5.3	✓	32	11.5	even	5	inner
66.3.g.a.5.5	yes	32	33.5	odd	10	inner
66.3.g.a.53.3	yes	32	3.2	odd	2	inner
66.3.g.a.53.5	yes	32	1.1	even	1	trivial
726.3.c.h.485.5		16	33.26	odd	10
726.3.c.h.485.13		16	11.4	even	5
726.3.c.i.485.5		16	11.7	odd	10
726.3.c.i.485.13		16	33.29	even	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34500 + 0.437016i) q^{2} +(-2.51921 - 1.62898i) q^{3} +(1.61803 + 1.17557i) q^{4} +(8.43444 - 2.74052i) q^{5} +(-2.67644 - 3.29191i) q^{6} +(-0.799737 - 0.581043i) q^{7} +(1.66251 + 2.28825i) q^{8} +(3.69284 + 8.20749i) q^{9} +12.5419 q^{10} +(-6.06969 - 9.17381i) q^{11} +(-2.16119 - 5.59726i) q^{12} +(-3.87315 + 11.9203i) q^{13} +(-0.821719 - 1.13100i) q^{14} +(-25.7124 - 6.83561i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-24.9252 + 8.09870i) q^{17} +(1.38005 + 12.6529i) q^{18} +(-1.71359 + 1.24499i) q^{19} +(16.8689 + 5.48103i) q^{20} +(1.06820 + 2.76653i) q^{21} +(-4.15462 - 14.9913i) q^{22} +13.1640i q^{23} +(-0.460697 - 8.47277i) q^{24} +(43.4039 - 31.5348i) q^{25} +(-10.4188 + 14.3402i) q^{26} +(4.06682 - 26.6920i) q^{27} +(-0.610945 - 1.88030i) q^{28} +(8.88514 - 12.2293i) q^{29} +(-31.5958 - 20.4306i) q^{30} +(-11.9183 + 36.6806i) q^{31} +5.65685i q^{32} +(0.346863 + 32.9982i) q^{33} -37.0636 q^{34} +(-8.33770 - 2.70908i) q^{35} +(-3.67335 + 17.6212i) q^{36} +(25.5186 + 18.5403i) q^{37} +(-2.84885 + 0.925648i) q^{38} +(29.1753 - 23.7205i) q^{39} +(20.2933 + 14.7439i) q^{40} +(-32.3701 - 44.5536i) q^{41} +(0.227706 + 4.18779i) q^{42} -0.435153 q^{43} +(0.963493 - 21.9789i) q^{44} +(53.6398 + 59.1053i) q^{45} +(-5.75289 + 17.7056i) q^{46} +(12.3550 + 17.0052i) q^{47} +(3.08310 - 11.5972i) q^{48} +(-14.8399 - 45.6724i) q^{49} +(72.1594 - 23.4460i) q^{50} +(75.9845 + 20.2004i) q^{51} +(-20.2801 + 14.7343i) q^{52} +(0.879055 + 0.285622i) q^{53} +(17.1347 - 34.1233i) q^{54} +(-76.3354 - 60.7419i) q^{55} -2.79598i q^{56} +(6.34496 - 0.344999i) q^{57} +(17.2949 - 12.5655i) q^{58} +(36.1462 - 49.7510i) q^{59} +(-33.5678 - 41.2870i) q^{60} +(4.81107 + 14.8069i) q^{61} +(-32.0601 + 44.1269i) q^{62} +(1.81561 - 8.70954i) q^{63} +(-2.47214 + 7.60845i) q^{64} +111.156i q^{65} +(-13.9542 + 44.5340i) q^{66} -26.5008 q^{67} +(-49.8505 - 16.1974i) q^{68} +(21.4439 - 33.1629i) q^{69} +(-10.0303 - 7.28741i) q^{70} +(41.9364 - 13.6260i) q^{71} +(-12.6414 + 22.0951i) q^{72} +(32.8530 + 23.8691i) q^{73} +(26.2200 + 36.0887i) q^{74} +(-160.713 + 8.73860i) q^{75} -4.23622 q^{76} +(-0.476221 + 10.8634i) q^{77} +(49.6069 - 19.1540i) q^{78} +(15.8723 - 48.8500i) q^{79} +(20.8511 + 28.6991i) q^{80} +(-53.7259 + 60.6179i) q^{81} +(-24.0670 - 74.0707i) q^{82} +(-108.904 + 35.3852i) q^{83} +(-1.52387 + 5.73208i) q^{84} +(-188.036 + 136.616i) q^{85} +(-0.585280 - 0.190169i) q^{86} +(-42.3049 + 16.3346i) q^{87} +(10.9010 - 29.1405i) q^{88} -149.971i q^{89} +(46.3154 + 102.938i) q^{90} +(10.0237 - 7.28267i) q^{91} +(-15.4752 + 21.2998i) q^{92} +(89.7767 - 72.9916i) q^{93} +(9.18590 + 28.2713i) q^{94} +(-11.0412 + 15.1969i) q^{95} +(9.21491 - 14.2508i) q^{96} +(28.0899 - 86.4517i) q^{97} -67.9145i q^{98} +(52.8796 - 83.6944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 16 q^{4} + 12 q^{6} - 8 q^{7} + 26 q^{9} + 16 q^{10} - 24 q^{12} + 8 q^{13} - 82 q^{15} - 32 q^{16} - 8 q^{18} - 4 q^{19} - 100 q^{21} - 24 q^{24} - 88 q^{25} - 106 q^{27} - 24 q^{28} - 36 q^{30}+ \cdots + 470 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 16 * q^4 + 12 * q^6 - 8 * q^7 + 26 * q^9 + 16 * q^10 - 24 * q^12 + 8 * q^13 - 82 * q^15 - 32 * q^16 - 8 * q^18 - 4 * q^19 - 100 * q^21 - 24 * q^24 - 88 * q^25 - 106 * q^27 - 24 * q^28 - 36 * q^30 - 148 * q^31 + 78 * q^33 - 32 * q^34 + 8 * q^36 + 96 * q^37 + 362 * q^39 + 48 * q^40 + 152 * q^42 + 560 * q^43 - 20 * q^45 + 176 * q^46 + 8 * q^48 + 208 * q^49 - 82 * q^51 + 24 * q^52 - 176 * q^54 - 108 * q^55 - 142 * q^57 - 144 * q^58 - 36 * q^60 - 384 * q^61 + 506 * q^63 + 64 * q^64 + 400 * q^66 - 680 * q^67 + 136 * q^69 - 400 * q^70 + 16 * q^72 - 92 * q^73 + 90 * q^75 + 128 * q^76 + 152 * q^78 + 320 * q^79 - 198 * q^81 - 328 * q^82 - 240 * q^84 - 1024 * q^85 - 1332 * q^87 - 736 * q^90 - 264 * q^91 - 226 * q^93 - 64 * q^94 - 32 * q^96 - 248 * q^97 + 470 * q^99

Introduction

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