LMFDB - Embedded newform 22.3.d.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,3,Mod(7,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	22.d (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.599456581593$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.1
Root			$-1.34500 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	22.13
Dual form			22.3.d.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 - 0.437016i) q^{2} +(2.48527 - 1.80565i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.399565 - 1.22973i) q^{5} +(-4.13178 + 1.34250i) q^{6} +(-6.48527 + 8.92621i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.135021 - 0.415553i) q^{9} +O(q^{10})$	\(q+(-1.34500 - 0.437016i) q^{2} +(2.48527 - 1.80565i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.399565 - 1.22973i) q^{5} +(-4.13178 + 1.34250i) q^{6} +(-6.48527 + 8.92621i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.135021 - 0.415553i) q^{9} +1.82860i q^{10} +(-4.82342 - 9.88608i) q^{11} +6.14392 q^{12} +(16.8835 + 5.48578i) q^{13} +(12.6236 - 9.17155i) q^{14} +(-3.21350 - 2.33474i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-4.75936 + 1.54641i) q^{17} +(-0.363207 + 0.499911i) q^{18} +(-17.1838 - 23.6514i) q^{19} +(0.799129 - 2.45947i) q^{20} +33.8942i q^{21} +(2.16710 + 15.4047i) q^{22} -4.83828 q^{23} +(-8.26355 - 2.68499i) q^{24} +(18.8728 - 13.7119i) q^{25} +(-20.3109 - 14.7567i) q^{26} +(8.12881 + 25.0179i) q^{27} +(-20.9868 + 6.81901i) q^{28} +(13.0262 - 17.9290i) q^{29} +(3.30182 + 4.54457i) q^{30} +(-1.77327 + 5.45757i) q^{31} -5.65685i q^{32} +(-29.8383 - 15.8602i) q^{33} +7.07714 q^{34} +(13.5681 + 4.40856i) q^{35} +(0.706982 - 0.513652i) q^{36} +(-6.94206 - 5.04370i) q^{37} +(12.7761 + 39.3207i) q^{38} +(51.8655 - 16.8521i) q^{39} +(-2.14965 + 2.95874i) q^{40} +(7.96811 + 10.9672i) q^{41} +(14.8123 - 45.5875i) q^{42} +2.42601i q^{43} +(3.81734 - 21.6663i) q^{44} -0.564970 q^{45} +(6.50748 + 2.11441i) q^{46} +(-25.2909 + 18.3749i) q^{47} +(9.94107 + 7.22261i) q^{48} +(-22.4766 - 69.1759i) q^{49} +(-31.3762 + 10.1948i) q^{50} +(-9.03601 + 12.4370i) q^{51} +(20.8692 + 28.7239i) q^{52} +(-29.4626 + 90.6765i) q^{53} -37.2014i q^{54} +(-10.2300 + 9.88165i) q^{55} +31.2072 q^{56} +(-85.4126 - 27.7522i) q^{57} +(-25.3554 + 18.4218i) q^{58} +(40.0587 + 29.1044i) q^{59} +(-2.45489 - 7.55539i) q^{60} +(9.49243 - 3.08428i) q^{61} +(4.77009 - 6.56546i) q^{62} +(2.83366 + 3.90020i) q^{63} +(-2.47214 + 7.60845i) q^{64} -22.9541i q^{65} +(33.2013 + 34.3717i) q^{66} +24.0980 q^{67} +(-9.51873 - 3.09282i) q^{68} +(-12.0244 + 8.73626i) q^{69} +(-16.3225 - 11.8590i) q^{70} +(-15.6399 - 48.1347i) q^{71} +(-1.17536 + 0.381898i) q^{72} +(25.8420 - 35.5685i) q^{73} +(7.13287 + 9.81756i) q^{74} +(22.1451 - 68.1556i) q^{75} -58.4696i q^{76} +(119.526 + 21.0591i) q^{77} -77.1235 q^{78} +(94.4452 + 30.6871i) q^{79} +(4.18430 - 3.04007i) q^{80} +(68.5573 + 49.8098i) q^{81} +(-5.92426 - 18.2330i) q^{82} +(12.4186 - 4.03505i) q^{83} +(-39.8450 + 54.8419i) q^{84} +(3.80335 + 5.23486i) q^{85} +(1.06021 - 3.26298i) q^{86} -68.0790i q^{87} +(-14.6028 + 27.4729i) q^{88} -165.275 q^{89} +(0.759883 + 0.246901i) q^{90} +(-158.461 + 115.129i) q^{91} +(-7.82851 - 5.68774i) q^{92} +(5.44742 + 16.7654i) q^{93} +(42.0464 - 13.6617i) q^{94} +(-22.2189 + 30.5818i) q^{95} +(-10.2143 - 14.0588i) q^{96} +(13.3891 - 41.2075i) q^{97} +102.864i q^{98} +(-4.75946 + 0.669553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9} - 4 q^{11} + 24 q^{12} + 30 q^{13} + 16 q^{14} + 42 q^{15} - 8 q^{16} + 30 q^{17} + 40 q^{18} - 30 q^{19} - 4 q^{20} + 24 q^{22} - 104 q^{23} - 40 q^{24} - 12 q^{25} - 96 q^{26} - 26 q^{27} - 40 q^{28} - 10 q^{29} - 60 q^{30} + 46 q^{31} - 14 q^{33} + 112 q^{34} + 70 q^{35} - 12 q^{36} + 6 q^{37} + 108 q^{38} + 130 q^{39} + 80 q^{40} + 250 q^{41} + 56 q^{42} - 12 q^{44} - 136 q^{45} - 160 q^{46} - 54 q^{47} - 8 q^{48} - 144 q^{49} - 80 q^{50} - 30 q^{51} - 40 q^{52} - 274 q^{53} - 26 q^{55} + 48 q^{56} - 130 q^{57} + 64 q^{58} + 50 q^{59} + 116 q^{60} + 50 q^{61} + 20 q^{62} - 20 q^{63} + 16 q^{64} - 136 q^{66} + 112 q^{67} + 60 q^{68} + 76 q^{69} + 4 q^{70} + 54 q^{71} - 80 q^{72} - 70 q^{73} - 40 q^{74} + 318 q^{75} + 266 q^{77} + 104 q^{78} + 370 q^{79} + 48 q^{80} + 180 q^{81} - 96 q^{82} - 150 q^{83} - 120 q^{84} - 330 q^{85} - 72 q^{86} + 72 q^{88} + 24 q^{89} + 160 q^{90} - 294 q^{91} - 112 q^{92} - 134 q^{93} - 20 q^{94} - 330 q^{95} - 18 q^{97} - 308 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9 - 4 * q^11 + 24 * q^12 + 30 * q^13 + 16 * q^14 + 42 * q^15 - 8 * q^16 + 30 * q^17 + 40 * q^18 - 30 * q^19 - 4 * q^20 + 24 * q^22 - 104 * q^23 - 40 * q^24 - 12 * q^25 - 96 * q^26 - 26 * q^27 - 40 * q^28 - 10 * q^29 - 60 * q^30 + 46 * q^31 - 14 * q^33 + 112 * q^34 + 70 * q^35 - 12 * q^36 + 6 * q^37 + 108 * q^38 + 130 * q^39 + 80 * q^40 + 250 * q^41 + 56 * q^42 - 12 * q^44 - 136 * q^45 - 160 * q^46 - 54 * q^47 - 8 * q^48 - 144 * q^49 - 80 * q^50 - 30 * q^51 - 40 * q^52 - 274 * q^53 - 26 * q^55 + 48 * q^56 - 130 * q^57 + 64 * q^58 + 50 * q^59 + 116 * q^60 + 50 * q^61 + 20 * q^62 - 20 * q^63 + 16 * q^64 - 136 * q^66 + 112 * q^67 + 60 * q^68 + 76 * q^69 + 4 * q^70 + 54 * q^71 - 80 * q^72 - 70 * q^73 - 40 * q^74 + 318 * q^75 + 266 * q^77 + 104 * q^78 + 370 * q^79 + 48 * q^80 + 180 * q^81 - 96 * q^82 - 150 * q^83 - 120 * q^84 - 330 * q^85 - 72 * q^86 + 72 * q^88 + 24 * q^89 + 160 * q^90 - 294 * q^91 - 112 * q^92 - 134 * q^93 - 20 * q^94 - 330 * q^95 - 18 * q^97 - 308 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i
$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i
$3$	2.48527	−	1.80565i	0.828423	−	0.601884i	−0.0906900	−	0.995879i	$-0.528907\pi$
$3$	2.48527	−	1.80565i	0.828423	−	0.601884i	0.919113	+	0.393995i	$0.128907\pi$
$4$	1.61803	+	1.17557i	0.404508	+	0.293893i
$5$	−0.399565	−	1.22973i	−0.0799129	−	0.245947i	0.903116	−	0.429396i	$-0.141274\pi$
$5$	−0.399565	−	1.22973i	−0.0799129	−	0.245947i	−0.983029	+	0.183450i	$0.941274\pi$
$6$	−4.13178	+	1.34250i	−0.688630	+	0.223749i
$7$	−6.48527	+	8.92621i	−0.926467	+	1.27517i	0.0347550	+	0.999396i	$0.488935\pi$
$7$	−6.48527	+	8.92621i	−0.926467	+	1.27517i	−0.961222	+	0.275776i	$0.911065\pi$
$8$	−1.66251	−	2.28825i	−0.207813	−	0.286031i
$9$	0.135021	−	0.415553i	0.0150024	−	0.0461726i
$10$			1.82860i			0.182860i
$11$	−4.82342	−	9.88608i	−0.438492	−	0.898735i
$11$	−4.82342	−	9.88608i	−0.438492	−	0.898735i
$12$	6.14392			0.511993
$13$	16.8835	+	5.48578i	1.29873	+	0.421983i	0.875140	−	0.483870i	$-0.160769\pi$
$13$	16.8835	+	5.48578i	1.29873	+	0.421983i	0.423592	+	0.905853i	$0.360769\pi$
$14$	12.6236	−	9.17155i	0.901683	−	0.655111i
$15$	−3.21350	−	2.33474i	−0.214233	−	0.155649i
$16$	1.23607	+	3.80423i	0.0772542	+	0.237764i
$17$	−4.75936	+	1.54641i	−0.279963	+	0.0909654i	−0.445633	−	0.895216i	$-0.647021\pi$
$17$	−4.75936	+	1.54641i	−0.279963	+	0.0909654i	0.165670	+	0.986181i	$0.447021\pi$
$18$	−0.363207	+	0.499911i	−0.0201782	+	0.0277729i
$19$	−17.1838	−	23.6514i	−0.904410	−	1.24481i	−0.969040	−	0.246904i	$-0.920587\pi$
$19$	−17.1838	−	23.6514i	−0.904410	−	1.24481i	0.0646304	−	0.997909i	$-0.479413\pi$
$20$	0.799129	−	2.45947i	0.0399565	−	0.122973i
$21$			33.8942i			1.61401i
$22$	2.16710	+	15.4047i	0.0985046	+	0.700212i
$23$	−4.83828			−0.210360			−0.105180	−	0.994453i	$-0.533542\pi$
$23$	−4.83828			−0.210360			−0.105180	+	0.994453i	$0.533542\pi$
$24$	−8.26355	−	2.68499i	−0.344315	−	0.111875i
$25$	18.8728	−	13.7119i	0.754913	−	0.548477i
$26$	−20.3109	−	14.7567i	−0.781188	−	0.567566i
$27$	8.12881	+	25.0179i	0.301067	+	0.926589i
$28$	−20.9868	+	6.81901i	−0.749527	+	0.243536i
$29$	13.0262	−	17.9290i	0.449178	−	0.618240i	−0.523043	−	0.852306i	$-0.675203\pi$
$29$	13.0262	−	17.9290i	0.449178	−	0.618240i	0.972221	+	0.234066i	$0.0752033\pi$
$30$	3.30182	+	4.54457i	0.110061	+	0.151486i
$31$	−1.77327	+	5.45757i	−0.0572023	+	0.176050i	−0.975575	−	0.219665i	$-0.929503\pi$
$31$	−1.77327	+	5.45757i	−0.0572023	+	0.176050i	0.918373	+	0.395716i	$0.129503\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−29.8383	−	15.8602i	−0.904191	−	0.480611i
$34$	7.07714			0.208151
$35$	13.5681	+	4.40856i	0.387661	+	0.125959i
$36$	0.706982	−	0.513652i	0.0196384	−	0.0142681i
$37$	−6.94206	−	5.04370i	−0.187623	−	0.136316i	0.490009	−	0.871718i	$-0.336994\pi$
$37$	−6.94206	−	5.04370i	−0.187623	−	0.136316i	−0.677632	+	0.735401i	$0.736994\pi$
$38$	12.7761	+	39.3207i	0.336213	+	1.03476i
$39$	51.8655	−	16.8521i	1.32988	−	0.432105i
$40$	−2.14965	+	2.95874i	−0.0537413	+	0.0739686i
$41$	7.96811	+	10.9672i	0.194344	+	0.267492i	0.895057	−	0.445951i	$-0.147135\pi$
$41$	7.96811	+	10.9672i	0.194344	+	0.267492i	−0.700713	+	0.713443i	$0.747135\pi$
$42$	14.8123	−	45.5875i	0.352674	−	1.08542i
$43$			2.42601i			0.0564188i	0.999602	+	0.0282094i	$0.00898053\pi$
$43$			2.42601i			0.0564188i	−0.999602	+	0.0282094i	$0.991019\pi$
$44$	3.81734	−	21.6663i	0.0867577	−	0.492416i
$45$	−0.564970			−0.0125549
$46$	6.50748	+	2.11441i	0.141467	+	0.0459654i
$47$	−25.2909	+	18.3749i	−0.538105	+	0.390956i	−0.823381	−	0.567489i	$-0.807915\pi$
$47$	−25.2909	+	18.3749i	−0.538105	+	0.390956i	0.285276	+	0.958446i	$0.407915\pi$
$48$	9.94107	+	7.22261i	0.207106	+	0.150471i
$49$	−22.4766	−	69.1759i	−0.458706	−	1.41175i
$50$	−31.3762	+	10.1948i	−0.627525	+	0.203895i
$51$	−9.03601	+	12.4370i	−0.177177	+	0.243863i
$52$	20.8692	+	28.7239i	0.401330	+	0.552384i
$53$	−29.4626	+	90.6765i	−0.555898	+	1.71088i	0.137662	+	0.990479i	$0.456041\pi$
$53$	−29.4626	+	90.6765i	−0.555898	+	1.71088i	−0.693560	+	0.720399i	$0.743959\pi$
$54$		−	37.2014i		−	0.688915i
$55$	−10.2300	+	9.88165i	−0.186000	+	0.179666i
$56$	31.2072			0.557271
$57$	−85.4126	−	27.7522i	−1.49847	−	0.486881i
$58$	−25.3554	+	18.4218i	−0.437162	+	0.317617i
$59$	40.0587	+	29.1044i	0.678961	+	0.493294i	0.873013	−	0.487697i	$-0.162163\pi$
$59$	40.0587	+	29.1044i	0.678961	+	0.493294i	−0.194052	+	0.980991i	$0.562163\pi$
$60$	−2.45489	−	7.55539i	−0.0409149	−	0.125923i
$61$	9.49243	−	3.08428i	0.155614	−	0.0505619i	−0.230174	−	0.973149i	$-0.573930\pi$
$61$	9.49243	−	3.08428i	0.155614	−	0.0505619i	0.385788	+	0.922587i	$0.373930\pi$
$62$	4.77009	−	6.56546i	0.0769369	−	0.105895i
$63$	2.83366	+	3.90020i	0.0449788	+	0.0619080i
$64$	−2.47214	+	7.60845i	−0.0386271	+	0.118882i
$65$		−	22.9541i		−	0.353141i
$66$	33.2013	+	34.3717i	0.503050	+	0.520783i
$67$	24.0980			0.359671			0.179836	−	0.983697i	$-0.442443\pi$
$67$	24.0980			0.359671			0.179836	+	0.983697i	$0.442443\pi$
$68$	−9.51873	−	3.09282i	−0.139981	−	0.0454827i
$69$	−12.0244	+	8.73626i	−0.174267	+	0.126612i
$70$	−16.3225	−	11.8590i	−0.233179	−	0.169414i
$71$	−15.6399	−	48.1347i	−0.220280	−	0.677953i	−0.998736	−	0.0502541i	$-0.983997\pi$
$71$	−15.6399	−	48.1347i	−0.220280	−	0.677953i	0.778456	−	0.627699i	$-0.216003\pi$
$72$	−1.17536	+	0.381898i	−0.0163245	+	0.00530414i
$73$	25.8420	−	35.5685i	0.354000	−	0.487239i	−0.594465	−	0.804122i	$-0.702636\pi$
$73$	25.8420	−	35.5685i	0.354000	−	0.487239i	0.948465	+	0.316882i	$0.102636\pi$
$74$	7.13287	+	9.81756i	0.0963902	+	0.132670i
$75$	22.1451	−	68.1556i	0.295268	−	0.908741i
$76$		−	58.4696i		−	0.769337i
$77$	119.526	+	21.0591i	1.55229	+	0.273495i
$78$	−77.1235			−0.988763
$79$	94.4452	+	30.6871i	1.19551	+	0.388445i	0.838107	−	0.545506i	$-0.183662\pi$
$79$	94.4452	+	30.6871i	1.19551	+	0.388445i	0.357402	+	0.933951i	$0.383662\pi$
$80$	4.18430	−	3.04007i	0.0523037	−	0.0380009i
$81$	68.5573	+	49.8098i	0.846387	+	0.614936i
$82$	−5.92426	−	18.2330i	−0.0722471	−	0.222354i
$83$	12.4186	−	4.03505i	0.149622	−	0.0486151i	−0.233249	−	0.972417i	$-0.574936\pi$
$83$	12.4186	−	4.03505i	0.149622	−	0.0486151i	0.382870	+	0.923802i	$0.374936\pi$
$84$	−39.8450	+	54.8419i	−0.474345	+	0.652880i
$85$	3.80335	+	5.23486i	0.0447453	+	0.0615866i
$86$	1.06021	−	3.26298i	0.0123280	−	0.0379416i
$87$		−	68.0790i		−	0.782517i
$88$	−14.6028	+	27.4729i	−0.165941	+	0.312191i
$89$	−165.275			−1.85703			−0.928513	−	0.371301i	$-0.878912\pi$
$89$	−165.275			−1.85703			−0.928513	+	0.371301i	$0.878912\pi$
$90$	0.759883	+	0.246901i	0.00844314	+	0.00274334i
$91$	−158.461	+	115.129i	−1.74133	+	1.26515i
$92$	−7.82851	−	5.68774i	−0.0850925	−	0.0618233i
$93$	5.44742	+	16.7654i	0.0585744	+	0.180273i
$94$	42.0464	−	13.6617i	0.447302	−	0.145337i
$95$	−22.2189	+	30.5818i	−0.233884	+	0.321913i
$96$	−10.2143	−	14.0588i	−0.106399	−	0.146446i
$97$	13.3891	−	41.2075i	0.138032	−	0.424819i	−0.858017	−	0.513621i	$-0.828304\pi$
$97$	13.3891	−	41.2075i	0.138032	−	0.424819i	0.996049	+	0.0888017i	$0.0283037\pi$
$98$			102.864i			1.04963i
$99$	−4.75946	+	0.669553i	−0.0480753	+	0.00676316i
$100$	46.6562			0.466562
$101$	−56.1619	−	18.2481i	−0.556059	−	0.180674i	0.0174882	−	0.999847i	$-0.494433\pi$
$101$	−56.1619	−	18.2481i	−0.556059	−	0.180674i	−0.573547	+	0.819173i	$0.694433\pi$
$102$	17.5886	−	12.7789i	0.172437	−	0.125283i
$103$	−55.7874	−	40.5319i	−0.541626	−	0.393514i	0.283063	−	0.959101i	$-0.408650\pi$
$103$	−55.7874	−	40.5319i	−0.541626	−	0.393514i	−0.824688	+	0.565587i	$0.808650\pi$
$104$	−15.5161	−	47.7538i	−0.149194	−	0.459171i
$105$	41.6808	−	13.5429i	0.396960	−	0.128980i
$106$	79.2542	−	109.084i	0.747681	−	1.02909i
$107$	37.8813	+	52.1391i	0.354031	+	0.487281i	0.948473	−	0.316857i	$-0.102627\pi$
$107$	37.8813	+	52.1391i	0.354031	+	0.487281i	−0.594443	+	0.804138i	$0.702627\pi$
$108$	−16.2576	+	50.0358i	−0.150534	+	0.463295i
$109$			56.6982i			0.520167i	0.965586	+	0.260083i	$0.0837500\pi$
$109$			56.6982i			0.520167i	−0.965586	+	0.260083i	$0.916250\pi$
$110$	18.0777	−	8.82012i	0.164343	−	0.0801829i
$111$	−26.3601			−0.237478
$112$	−41.9735	−	13.6380i	−0.374764	−	0.121768i
$113$	138.617	−	100.711i	1.22670	−	0.891249i	0.230061	−	0.973176i	$-0.426108\pi$
$113$	138.617	−	100.711i	1.22670	−	0.891249i	0.996638	+	0.0819274i	$0.0261076\pi$
$114$	102.752	+	74.6534i	0.901329	+	0.654854i
$115$	1.93321	+	5.94980i	0.0168105	+	0.0517374i
$116$	42.1535	−	13.6965i	0.363392	−	0.118073i
$117$	4.55927	−	6.27530i	0.0389681	−	0.0536350i
$118$	−41.1598	−	56.6516i	−0.348812	−	0.480098i
$119$	17.0622	−	52.5120i	0.143380	−	0.441277i
$120$			11.2348i			0.0936233i
$121$	−74.4693	+	95.3694i	−0.615449	+	0.788177i
$122$	−14.1152			−0.115698
$123$	39.6058	+	12.8687i	0.321998	+	0.104624i
$124$	−9.28496	+	6.74592i	−0.0748787	+	0.0544026i
$125$	−50.5548	−	36.7302i	−0.404438	−	0.293842i
$126$	−2.10682	−	6.48412i	−0.0167208	−	0.0514613i
$127$	−141.566	+	45.9976i	−1.11469	+	0.362186i	−0.807740	−	0.589539i	$-0.799310\pi$
$127$	−141.566	+	45.9976i	−1.11469	+	0.362186i	−0.306954	+	0.951725i	$0.599310\pi$
$128$	6.65003	−	9.15298i	0.0519534	−	0.0715077i
$129$	4.38053	+	6.02928i	0.0339576	+	0.0467386i
$130$	−10.0313	+	30.8733i	−0.0771641	+	0.237487i
$131$		−	142.907i		−	1.09089i	−0.838145	−	0.545447i	$-0.816360\pi$
$131$		−	142.907i		−	1.09089i	0.838145	−	0.545447i	$-0.183640\pi$
$132$	−29.6347	−	60.7393i	−0.224505	−	0.460146i
$133$	322.559			2.42526
$134$	−32.4117	−	10.5312i	−0.241878	−	0.0785910i
$135$	27.5174	−	19.9925i	0.203832	−	0.148093i
$136$	11.4511	+	8.31968i	0.0841989	+	0.0611741i
$137$	43.7043	+	134.508i	0.319009	+	0.981810i	0.974073	+	0.226236i	$0.0726421\pi$
$137$	43.7043	+	134.508i	0.319009	+	0.981810i	−0.655063	+	0.755574i	$0.727358\pi$
$138$	19.9907	−	6.49537i	0.144860	−	0.0470679i
$139$	−39.4964	+	54.3621i	−0.284147	+	0.391094i	−0.927102	−	0.374809i	$-0.877708\pi$
$139$	−39.4964	+	54.3621i	−0.284147	+	0.391094i	0.642955	+	0.765904i	$0.277708\pi$
$140$	16.7711	+	23.0835i	0.119794	+	0.164882i
$141$	−29.6760	+	91.3333i	−0.210468	+	0.647754i
$142$			71.5759i			0.504056i
$143$	−27.2032	−	193.372i	−0.190233	−	1.35225i
$144$	1.74775			0.0121372
$145$	−27.2526	−	8.85492i	−0.187949	−	0.0610684i
$146$	−50.3014	+	36.5461i	−0.344530	+	0.250316i
$147$	−180.768	−	131.336i	−1.22971	−	0.893440i
$148$	−5.30326	−	16.3218i	−0.0358329	−	0.110282i
$149$	−119.845	+	38.9401i	−0.804331	+	0.261343i	−0.682195	−	0.731170i	$-0.738974\pi$
$149$	−119.845	+	38.9401i	−0.804331	+	0.261343i	−0.122136	+	0.992513i	$0.538974\pi$
$150$	−59.5701	+	81.9913i	−0.397134	+	0.546608i
$151$	61.7808	+	85.0339i	0.409144	+	0.563139i	0.963009	−	0.269468i	$-0.0868477\pi$
$151$	61.7808	+	85.0339i	0.409144	+	0.563139i	−0.553865	+	0.832606i	$0.686848\pi$
$152$	−25.5522	+	78.6414i	−0.168106	+	0.517378i
$153$			2.18657i			0.0142913i
$154$	−151.559	−	80.5594i	−0.984152	−	0.523113i
$155$	7.41989			0.0478702
$156$	103.731	+	33.7042i	0.664942	+	0.216053i
$157$	47.7355	−	34.6819i	0.304048	−	0.220904i	−0.425290	−	0.905057i	$-0.639828\pi$
$157$	47.7355	−	34.6819i	0.304048	−	0.220904i	0.729338	+	0.684153i	$0.239828\pi$
$158$	−113.618	−	82.5482i	−0.719100	−	0.522457i
$159$	90.5079	+	278.555i	0.569232	+	1.75192i
$160$	−6.95642	+	2.26028i	−0.0434777	+	0.0141267i
$161$	31.3776	−	43.1875i	0.194892	−	0.268245i
$162$	−70.4417	−	96.9547i	−0.434825	−	0.598486i
$163$	43.4560	−	133.744i	0.266601	−	0.820514i	−0.724719	−	0.689045i	$-0.758030\pi$
$163$	43.4560	−	133.744i	0.266601	−	0.820514i	0.991320	−	0.131470i	$-0.0419696\pi$
$164$			27.1123i			0.165319i
$165$	−7.58143	+	43.0303i	−0.0459481	+	0.260790i
$166$	−18.4664			−0.111243
$167$	36.4886	+	11.8559i	0.218494	+	0.0709932i	0.416219	−	0.909265i	$-0.363355\pi$
$167$	36.4886	+	11.8559i	0.218494	+	0.0709932i	−0.197724	+	0.980258i	$0.563355\pi$
$168$	77.5581	−	56.3493i	0.461656	−	0.335412i
$169$	118.235	+	85.9029i	0.699617	+	0.508301i
$170$	−2.82777	−	8.70300i	−0.0166340	−	0.0511941i
$171$	−12.1486	+	3.94732i	−0.0710445	+	0.0230838i
$172$	−2.85195	+	3.92537i	−0.0165811	+	0.0228219i
$173$	−166.526	−	229.204i	−0.962580	−	1.32488i	−0.945707	−	0.325019i	$-0.894629\pi$
$173$	−166.526	−	229.204i	−0.962580	−	1.32488i	−0.0168721	−	0.999858i	$-0.505371\pi$
$174$	−29.7516	+	91.5660i	−0.170986	+	0.526242i
$175$			257.388i			1.47079i
$176$	31.6468	−	30.5692i	0.179812	−	0.173689i
$177$	152.109			0.859373
$178$	222.295	+	72.2279i	1.24885	+	0.405775i
$179$	228.764	−	166.206i	1.27801	−	0.928528i	0.278518	−	0.960431i	$-0.410157\pi$
$179$	228.764	−	166.206i	1.27801	−	0.928528i	0.999491	+	0.0319036i	$0.0101570\pi$
$180$	−0.914140	−	0.664162i	−0.00507856	−	0.00368979i
$181$	−86.2701	−	265.512i	−0.476630	−	1.46692i	−0.843746	−	0.536742i	$-0.819655\pi$
$181$	−86.2701	−	265.512i	−0.476630	−	1.46692i	0.367116	−	0.930175i	$-0.380345\pi$
$182$	263.443	−	85.5979i	1.44749	−	0.470318i
$183$	18.0221	−	24.8053i	0.0984815	−	0.135548i
$184$	8.04368	+	11.0712i	0.0437157	+	0.0601695i
$185$	−3.42861	+	10.5522i	−0.0185330	+	0.0570388i
$186$		−	24.9301i		−	0.134033i
$187$	38.2443	+	39.5925i	0.204515	+	0.211725i
$188$	−62.5226			−0.332567
$189$	−276.032	−	89.6884i	−1.46049	−	0.474542i
$190$	43.2491	−	31.4223i	0.227627	−	0.165381i
$191$	18.1375	+	13.1777i	0.0949609	+	0.0689931i	0.634253	−	0.773126i	$-0.281308\pi$
$191$	18.1375	+	13.1777i	0.0949609	+	0.0689931i	−0.539292	+	0.842119i	$0.681308\pi$
$192$	7.59430	+	23.3729i	0.0395537	+	0.121734i
$193$	−245.239	+	79.6830i	−1.27067	+	0.412865i	−0.865285	−	0.501281i	$-0.832862\pi$
$193$	−245.239	+	79.6830i	−1.27067	+	0.412865i	−0.405384	+	0.914146i	$0.632862\pi$
$194$	−36.0167	+	49.5727i	−0.185653	+	0.255529i
$195$	−41.4472	−	57.0472i	−0.212550	−	0.292550i
$196$	44.9532	−	138.352i	0.229353	−	0.705877i
$197$			153.374i			0.778547i	0.921122	+	0.389273i	$0.127274\pi$
$197$			153.374i			0.778547i	−0.921122	+	0.389273i	$0.872726\pi$
$198$	6.69406	+	1.17941i	0.0338084	+	0.00595663i
$199$	−235.505			−1.18344			−0.591721	−	0.806143i	$-0.701551\pi$
$199$	−235.505			−1.18344			−0.591721	+	0.806143i	$0.701551\pi$
$200$	−62.7525	−	20.3895i	−0.313762	−	0.101948i
$201$	59.8899	−	43.5126i	0.297960	−	0.216480i
$202$	67.5629	+	49.0873i	0.334470	+	0.243007i
$203$	75.5595	+	232.548i	0.372214	+	1.14556i
$204$	−29.2412	+	9.50103i	−0.143339	+	0.0465737i
$205$	10.3029	−	14.1807i	0.0502581	−	0.0691744i
$206$	57.3208	+	78.8953i	0.278256	+	0.382987i
$207$	−0.653272	+	2.01056i	−0.00315590	+	0.00971287i
$208$			71.0095i			0.341392i
$209$	−150.936	+	283.961i	−0.722180	+	1.35867i
$210$	−61.9790			−0.295138
$211$	239.140	+	77.7014i	1.13337	+	0.368253i	0.814855	−	0.579665i	$-0.196817\pi$
$211$	239.140	+	77.7014i	1.13337	+	0.368253i	0.318512	+	0.947919i	$0.396817\pi$
$212$	−154.268	+	112.082i	−0.727680	+	0.528690i
$213$	−125.784	−	91.3873i	−0.590535	−	0.429048i
$214$	−28.1646	−	86.6816i	−0.131610	−	0.405054i
$215$	2.98335	−	0.969348i	0.0138760	−	0.00450859i
$216$	43.7329	−	60.1932i	0.202467	−	0.278672i
$217$	−37.2152	−	51.2223i	−0.171499	−	0.236048i
$218$	24.7780	−	76.2588i	0.113661	−	0.349811i
$219$		−	135.059i		−	0.616707i
$220$	−28.1690	+	3.96277i	−0.128041	+	0.0180126i
$221$	−88.8381			−0.401982
$222$	35.4542	+	11.5198i	0.159704	+	0.0518908i
$223$	−11.1825	+	8.12457i	−0.0501458	+	0.0364330i	−0.612576	−	0.790412i	$-0.709867\pi$
$223$	−11.1825	+	8.12457i	−0.0501458	+	0.0364330i	0.562430	+	0.826845i	$0.309867\pi$
$224$	50.4942	+	36.6862i	0.225421	+	0.163778i
$225$	−3.14979	−	9.69407i	−0.0139991	−	0.0430848i
$226$	−230.452	+	74.8783i	−1.01970	+	0.331320i
$227$	−145.755	+	200.615i	−0.642094	+	0.883766i	−0.998725	−	0.0504789i	$-0.983925\pi$
$227$	−145.755	+	200.615i	−0.642094	+	0.883766i	0.356631	+	0.934245i	$0.383925\pi$
$228$	−105.576	−	145.313i	−0.463052	−	0.637336i
$229$	93.4415	−	287.583i	0.408042	−	1.25582i	−0.510287	−	0.860004i	$-0.670461\pi$
$229$	93.4415	−	287.583i	0.408042	−	1.25582i	0.918329	−	0.395819i	$-0.129539\pi$
$230$		−	8.84730i		−	0.0384665i
$231$	335.080	−	163.486i	1.45056	−	0.707730i
$232$	−62.6820			−0.270181
$233$	95.3175	+	30.9705i	0.409088	+	0.132921i	0.506329	−	0.862340i	$-0.331002\pi$
$233$	95.3175	+	30.9705i	0.409088	+	0.132921i	−0.0972417	+	0.995261i	$0.531002\pi$
$234$	−8.87461	+	6.44778i	−0.0379257	+	0.0275546i
$235$	32.7017	+	23.7591i	0.139156	+	0.101103i
$236$	30.6021	+	94.1837i	0.129670	+	0.399083i
$237$	290.132	−	94.2696i	1.22419	−	0.397762i
$238$	−45.8971	+	63.1720i	−0.192845	+	0.265429i
$239$	212.689	+	292.742i	0.889913	+	1.22486i	0.973575	+	0.228366i	$0.0733383\pi$
$239$	212.689	+	292.742i	0.889913	+	1.22486i	−0.0836623	+	0.996494i	$0.526662\pi$
$240$	4.90979	−	15.1108i	0.0204574	−	0.0629615i
$241$		−	161.370i		−	0.669586i	−0.942292	−	0.334793i	$-0.891334\pi$
$241$		−	161.370i		−	0.669586i	0.942292	−	0.334793i	$-0.108666\pi$
$242$	141.839	−	95.7272i	0.586111	−	0.395567i
$243$	23.5742			0.0970130
$244$	18.9849	+	6.16856i	0.0778068	+	0.0252810i
$245$	−76.0871	+	55.2805i	−0.310559	+	0.225635i
$246$	−47.6458	−	34.6167i	−0.193682	−	0.140718i
$247$	−160.376	−	493.586i	−0.649295	−	1.99832i
$248$	15.4363	−	5.01557i	0.0622432	−	0.0202241i
$249$	23.5777	−	32.4519i	0.0946894	−	0.130329i
$250$	51.9443	+	71.4952i	0.207777	+	0.285981i
$251$	−54.6106	+	168.074i	−0.217572	+	0.669618i	0.781389	+	0.624044i	$0.214512\pi$
$251$	−54.6106	+	168.074i	−0.217572	+	0.669618i	−0.998961	+	0.0455738i	$0.985488\pi$
$252$			9.64183i			0.0382612i
$253$	23.3370	+	47.8317i	0.0922413	+	0.189058i
$254$	210.508			0.828770
$255$	18.9047	+	6.14250i	0.0741360	+	0.0240882i
$256$	−12.9443	+	9.40456i	−0.0505636	+	0.0367366i
$257$	260.833	+	189.506i	1.01491	+	0.737378i	0.965234	−	0.261387i	$-0.0841798\pi$
$257$	260.833	+	189.506i	1.01491	+	0.737378i	0.0496800	+	0.998765i	$0.484180\pi$
$258$	−3.25691	−	10.0237i	−0.0126237	−	0.0388517i
$259$	90.0422	−	29.2565i	0.347653	−	0.112959i
$260$	26.9842	−	37.1406i	0.103785	−	0.142848i
$261$	−5.69163	−	7.83386i	−0.0218070	−	0.0300148i
$262$	−62.4527	+	192.210i	−0.238369	+	0.733624i
$263$		−	400.583i		−	1.52313i	−0.648089	−	0.761565i	$-0.724431\pi$
$263$		−	400.583i		−	1.52313i	0.648089	−	0.761565i	$-0.275569\pi$
$264$	13.3145	+	94.6450i	0.0504337	+	0.358504i
$265$	123.280			0.465208
$266$	−433.841	−	140.964i	−1.63098	−	0.529938i
$267$	−410.753	+	298.430i	−1.53840	+	1.11771i
$268$	38.9913	+	28.3289i	0.145490	+	0.105705i
$269$	28.5293	+	87.8043i	0.106057	+	0.326410i	0.989977	−	0.141228i	$-0.0451051\pi$
$269$	28.5293	+	87.8043i	0.106057	+	0.326410i	−0.883920	+	0.467638i	$0.845105\pi$
$270$	−45.7478	+	14.8644i	−0.169436	+	0.0550532i
$271$	91.5443	−	126.000i	0.337802	−	0.464944i	−0.605996	−	0.795468i	$-0.707225\pi$
$271$	91.5443	−	126.000i	0.337802	−	0.464944i	0.943798	+	0.330523i	$0.107225\pi$
$272$	−11.7658	−	16.1942i	−0.0432566	−	0.0595376i
$273$	−185.936	+	572.252i	−0.681084	+	2.09616i
$274$		−	200.012i		−	0.729972i
$275$	−226.589	−	120.440i	−0.823959	−	0.437964i
$276$	−29.7260			−0.107703
$277$	−283.332	−	92.0603i	−1.02286	−	0.332347i	−0.250897	−	0.968014i	$-0.580725\pi$
$277$	−283.332	−	92.0603i	−1.02286	−	0.332347i	−0.771964	+	0.635666i	$0.780725\pi$
$278$	76.8796	−	55.8563i	0.276545	−	0.200922i
$279$	2.02848	+	1.47378i	0.00727054	+	0.00528235i
$280$	−12.4693	−	38.3765i	−0.0445331	−	0.137059i
$281$	194.647	−	63.2446i	0.692694	−	0.225070i	0.0585494	−	0.998285i	$-0.481352\pi$
$281$	194.647	−	63.2446i	0.692694	−	0.225070i	0.634144	+	0.773215i	$0.281352\pi$
$282$	79.8282	−	109.874i	0.283079	−	0.389625i
$283$	54.0332	+	74.3704i	0.190930	+	0.262793i	0.893740	−	0.448585i	$-0.148072\pi$
$283$	54.0332	+	74.3704i	0.190930	+	0.262793i	−0.702810	+	0.711377i	$0.748072\pi$
$284$	31.2798	−	96.2693i	0.110140	−	0.338977i
$285$			116.124i			0.407451i
$286$	−47.9184	+	271.973i	−0.167547	+	0.950955i
$287$	−149.571			−0.521152
$288$	−2.35072	−	0.763797i	−0.00816224	−	0.00265207i
$289$	−213.546	+	155.150i	−0.738913	+	0.536851i
$290$	32.7850	+	23.8197i	0.113052	+	0.0821368i
$291$	−41.1308	−	126.588i	−0.141343	−	0.435009i
$292$	83.6265	−	27.1719i	0.286392	−	0.0930544i
$293$	58.0186	−	79.8558i	0.198016	−	0.272545i	−0.698450	−	0.715659i	$-0.746126\pi$
$293$	58.0186	−	79.8558i	0.198016	−	0.272545i	0.896465	+	0.443114i	$0.146126\pi$
$294$	185.737	+	255.645i	0.631757	+	0.869540i
$295$	19.7846	−	60.8906i	0.0670663	−	0.206409i
$296$			24.2703i			0.0819944i
$297$	208.120	−	201.034i	0.700742	−	0.676882i
$298$	178.209			0.598017
$299$	−81.6872	−	26.5418i	−0.273201	−	0.0887685i
$300$	115.953	−	84.2449i	0.386511	−	0.280816i
$301$	−21.6551	−	15.7333i	−0.0719437	−	0.0522702i
$302$	−45.9338	−	141.370i	−0.152099	−	0.468111i
$303$	−172.527	+	56.0575i	−0.569397	+	0.185008i
$304$	68.7351	−	94.6058i	0.226102	−	0.311203i
$305$	−7.58568	−	10.4408i	−0.0248711	−	0.0342321i
$306$	0.955566	−	2.94093i	0.00312276	−	0.00961088i
$307$			178.572i			0.581666i	0.956774	+	0.290833i	$0.0939325\pi$
$307$			178.572i			0.581666i	−0.956774	+	0.290833i	$0.906068\pi$
$308$	168.641	+	174.586i	0.547537	+	0.566838i
$309$	−211.833			−0.685545
$310$	−9.97973	−	3.24261i	−0.0321927	−	0.0104600i
$311$	−241.275	+	175.297i	−0.775805	+	0.563656i	−0.903717	−	0.428130i	$-0.859173\pi$
$311$	−241.275	+	175.297i	−0.775805	+	0.563656i	0.127912	+	0.991786i	$0.459173\pi$
$312$	−124.789	−	90.6642i	−0.399963	−	0.290590i
$313$	39.5599	+	121.753i	0.126390	+	0.388987i	0.994152	−	0.107993i	$-0.0344423\pi$
$313$	39.5599	+	121.753i	0.126390	+	0.388987i	−0.867762	+	0.496980i	$0.834442\pi$
$314$	−79.3607	+	25.7858i	−0.252741	+	0.0821205i
$315$	3.66398	−	5.04304i	0.0116317	−	0.0160096i
$316$	116.741	+	160.680i	0.369433	+	0.508480i
$317$	70.6393	−	217.405i	0.222837	−	0.685821i	−0.775667	−	0.631142i	$-0.782586\pi$
$317$	70.6393	−	217.405i	0.222837	−	0.685821i	0.998504	−	0.0546790i	$-0.0174136\pi$
$318$		−	414.209i		−	1.30254i
$319$	−240.078	−	42.2988i	−0.752595	−	0.132598i
$320$	10.3441			0.0323255
$321$	188.290	+	61.1792i	0.586574	+	0.190589i
$322$	−61.0764	+	44.3746i	−0.189678	+	0.137809i
$323$	118.359	+	85.9927i	0.366436	+	0.266231i
$324$	52.3731	+	161.188i	0.161646	+	0.497494i
$325$	393.860	−	127.973i	1.21188	−	0.393763i
$326$	−116.896	+	160.894i	−0.358578	+	0.493540i
$327$	102.377	+	140.910i	0.313080	+	0.430918i
$328$	11.8485	−	36.4660i	0.0361235	−	0.111177i
$329$		−	344.919i		−	1.04838i
$330$	29.0019	−	54.5625i	0.0878847	−	0.165341i
$331$	92.6536			0.279920			0.139960	−	0.990157i	$-0.455303\pi$
$331$	92.6536			0.279920			0.139960	+	0.990157i	$0.455303\pi$
$332$	24.8372	+	8.07010i	0.0748109	+	0.0243075i
$333$	−3.03325	+	2.20379i	−0.00910887	+	0.00661798i
$334$	−43.8958	−	31.8922i	−0.131425	−	0.0954856i
$335$	−9.62870	−	29.6341i	−0.0287424	−	0.0884600i
$336$	−128.941	+	41.8955i	−0.383753	+	0.124689i
$337$	143.163	−	197.048i	0.424817	−	0.584711i	−0.541937	−	0.840419i	$-0.682309\pi$
$337$	143.163	−	197.048i	0.424817	−	0.584711i	0.966754	+	0.255709i	$0.0823087\pi$
$338$	−121.485	−	167.210i	−0.359423	−	0.494704i
$339$	162.651	−	500.588i	0.479796	−	1.47666i
$340$			12.9413i			0.0380626i
$341$	62.5072	−	8.79340i	0.183305	−	0.0257871i
$342$	18.0649			0.0528213
$343$	249.069	+	80.9275i	0.726150	+	0.235940i
$344$	5.55131	−	4.03326i	0.0161375	−	0.0117246i
$345$	15.5478	+	11.2961i	0.0450661	+	0.0327424i
$346$	123.812	+	381.053i	0.357837	+	1.10131i
$347$	364.299	−	118.368i	1.04985	−	0.341118i	0.267242	−	0.963630i	$-0.413888\pi$
$347$	364.299	−	118.368i	1.04985	−	0.341118i	0.782610	+	0.622512i	$0.213888\pi$
$348$	80.0317	−	110.154i	0.229976	−	0.316535i
$349$	262.590	+	361.423i	0.752405	+	1.03560i	0.997808	+	0.0661760i	$0.0210799\pi$
$349$	262.590	+	361.423i	0.752405	+	1.03560i	−0.245402	+	0.969421i	$0.578920\pi$
$350$	112.483	−	346.186i	0.321379	−	0.989104i
$351$			466.983i			1.33044i
$352$	−55.9241	+	27.2854i	−0.158875	+	0.0775152i
$353$	−290.995			−0.824348			−0.412174	−	0.911105i	$-0.635230\pi$
$353$	−290.995			−0.824348			−0.412174	+	0.911105i	$0.635230\pi$
$354$	−204.586	−	66.4741i	−0.577927	−	0.187780i
$355$	−52.9437	+	38.4658i	−0.149137	+	0.108354i
$356$	−267.421	−	194.293i	−0.751182	−	0.545766i
$357$	−52.4143	−	161.315i	−0.146819	−	0.451862i
$358$	−380.321	+	123.574i	−1.06235	+	0.345178i
$359$	100.610	−	138.478i	0.280251	−	0.385732i	−0.645566	−	0.763704i	$-0.723379\pi$
$359$	100.610	−	138.478i	0.280251	−	0.385732i	0.925817	+	0.377972i	$0.123379\pi$
$360$	0.939266	+	1.29279i	0.00260907	+	0.00359108i
$361$	−152.553	+	469.511i	−0.422586	+	1.30059i
$362$			394.814i			1.09065i
$363$	−12.8722	+	371.484i	−0.0354607	+	1.02337i
$364$	−391.738			−1.07620
$365$	−54.0653	−	17.5669i	−0.148124	−	0.0481284i
$366$	−35.0800	+	25.4871i	−0.0958470	+	0.0696369i
$367$	−352.162	−	255.860i	−0.959569	−	0.697167i	−0.00651803	−	0.999979i	$-0.502075\pi$
$367$	−352.162	−	255.860i	−0.959569	−	0.697167i	−0.953050	+	0.302811i	$0.902075\pi$
$368$	−5.98045	−	18.4059i	−0.0162512	−	0.0500161i
$369$	5.63331	−	1.83037i	0.0152664	−	0.00496036i
$370$	9.22294	−	12.6943i	0.0249269	−	0.0343089i
$371$	−618.325	−	851.051i	−1.66664	−	2.29394i
$372$	−10.8948	+	33.5308i	−0.0292872	+	0.0901367i
$373$			449.027i			1.20383i	0.798561	+	0.601913i	$0.205595\pi$
$373$			449.027i			1.20383i	−0.798561	+	0.601913i	$0.794405\pi$
$374$	−34.1360	−	69.9652i	−0.0912727	−	0.187073i
$375$	−191.964			−0.511904
$376$	84.0928	+	27.3234i	0.223651	+	0.0726686i
$377$	318.282	−	231.245i	0.844248	−	0.613382i
$378$	332.068	+	241.261i	0.878486	+	0.638257i
$379$	−4.21499	−	12.9724i	−0.0111213	−	0.0342280i	0.945342	−	0.326081i	$-0.105728\pi$
$379$	−4.21499	−	12.9724i	−0.0111213	−	0.0342280i	−0.956463	+	0.291853i	$0.905728\pi$
$380$	−71.9020	+	23.3624i	−0.189216	+	0.0614800i
$381$	−268.774	+	369.936i	−0.705443	+	0.970960i
$382$	−18.6361	−	25.6503i	−0.0487855	−	0.0671475i
$383$	−206.948	+	636.921i	−0.540335	+	1.66298i	0.191495	+	0.981493i	$0.438666\pi$
$383$	−206.948	+	636.921i	−0.540335	+	1.66298i	−0.731830	+	0.681487i	$0.761334\pi$
$384$		−	34.7553i		−	0.0905085i
$385$	−21.8614	−	155.400i	−0.0567829	−	0.403637i
$386$	364.669			0.944738
$387$	1.00814	+	0.327563i	0.00260500	+	0.000846417i
$388$	70.1063	−	50.9352i	0.180686	−	0.131276i
$389$	253.174	+	183.942i	0.650833	+	0.472858i	0.863555	−	0.504255i	$-0.168233\pi$
$389$	253.174	+	183.942i	0.650833	+	0.472858i	−0.212722	+	0.977113i	$0.568233\pi$
$390$	30.8158	+	94.8414i	0.0790150	+	0.243183i
$391$	23.0272	−	7.48198i	0.0588930	−	0.0191355i
$392$	−120.924	+	166.437i	−0.308479	+	0.424585i
$393$	−258.041	−	355.162i	−0.656592	−	0.903721i
$394$	67.0268	−	206.287i	0.170119	−	0.523572i
$395$		−	128.404i		−	0.325073i
$396$	−8.48807	−	4.51172i	−0.0214345	−	0.0113932i
$397$	157.050			0.395593			0.197796	−	0.980243i	$-0.436622\pi$
$397$	157.050			0.395593			0.197796	+	0.980243i	$0.436622\pi$
$398$	316.753	+	102.919i	0.795863	+	0.258592i
$399$	801.646	−	582.430i	2.00914	−	1.45972i
$400$	75.4913	+	54.8477i	0.188728	+	0.137119i
$401$	−55.3351	−	170.304i	−0.137993	−	0.424698i	0.858051	−	0.513565i	$-0.171675\pi$
$401$	−55.3351	−	170.304i	−0.137993	−	0.424698i	−0.996044	+	0.0888670i	$0.971675\pi$
$402$	−99.5674	+	32.3514i	−0.247680	+	0.0804762i
$403$	−59.8781	+	82.4151i	−0.148581	+	0.204504i
$404$	−69.4200	−	95.5484i	−0.171832	−	0.236506i
$405$	33.8597	−	104.210i	0.0836043	−	0.257307i
$406$		−	345.797i		−	0.851718i
$407$	−16.3780	+	92.9577i	−0.0402408	+	0.228397i
$408$	43.4814			0.106572
$409$	38.6900	+	12.5711i	0.0945965	+	0.0307363i	0.355933	−	0.934512i	$-0.384163\pi$
$409$	38.6900	+	12.5711i	0.0945965	+	0.0307363i	−0.261336	+	0.965248i	$0.584163\pi$
$410$	−20.0546	+	14.5705i	−0.0489137	+	0.0355379i
$411$	351.492	+	255.374i	0.855211	+	0.621347i
$412$	−42.6178	−	131.164i	−0.103441	−	0.318360i
$413$	−519.583	+	168.823i	−1.25807	+	0.408772i
$414$	1.75730	−	2.41871i	0.00424468	−	0.00584230i
$415$	−9.92407	−	13.6593i	−0.0239134	−	0.0329140i
$416$	31.0323	−	95.5076i	0.0745968	−	0.229585i
$417$			206.421i			0.495015i
$418$	327.104	−	315.965i	0.782544	−	0.755898i
$419$	585.019			1.39623			0.698114	−	0.715987i	$-0.254023\pi$
$419$	585.019			1.39623			0.698114	+	0.715987i	$0.254023\pi$
$420$	83.3616	+	27.0858i	0.198480	+	0.0644900i
$421$	289.659	−	210.450i	0.688027	−	0.499881i	−0.187984	−	0.982172i	$-0.560195\pi$
$421$	289.659	−	210.450i	0.688027	−	0.499881i	0.876011	+	0.482291i	$0.160195\pi$
$422$	−287.686	−	209.016i	−0.681721	−	0.495300i
$423$	4.22095	+	12.9907i	0.00997860	+	0.0307110i
$424$	256.472	−	83.3328i	0.604887	−	0.196540i
$425$	−68.6184	+	94.4452i	−0.161455	+	0.222224i
$426$	129.241	+	177.885i	0.303383	+	0.417571i
$427$	−34.0301	+	104.734i	−0.0796957	+	0.245278i
$428$			128.895i			0.301156i
$429$	−416.770	−	431.462i	−0.971492	−	1.00574i
$430$	−4.43621			−0.0103168
$431$	59.9777	+	19.4879i	0.139159	+	0.0452156i	0.377769	−	0.925900i	$-0.376692\pi$
$431$	59.9777	+	19.4879i	0.139159	+	0.0452156i	−0.238609	+	0.971116i	$0.576692\pi$
$432$	−85.1260	+	61.8477i	−0.197051	+	0.143166i
$433$	−629.268	−	457.190i	−1.45327	−	1.05587i	−0.985053	−	0.172254i	$-0.944895\pi$
$433$	−629.268	−	457.190i	−1.45327	−	1.05587i	−0.468221	−	0.883611i	$-0.655105\pi$
$434$	27.6694	+	85.1576i	0.0637543	+	0.196216i
$435$	−83.7190	+	27.2020i	−0.192458	+	0.0625332i
$436$	−66.6527	+	91.7395i	−0.152873	+	0.210412i
$437$	83.1400	+	114.432i	0.190252	+	0.261859i
$438$	−59.0229	+	181.654i	−0.134755	+	0.414735i
$439$			190.905i			0.434863i	0.976076	+	0.217432i	$0.0697679\pi$
$439$			190.905i			0.434863i	−0.976076	+	0.217432i	$0.930232\pi$
$440$	39.6191	+	6.98040i	0.0900433	+	0.0158646i
$441$	−31.7811			−0.0720660
$442$	119.487	+	38.8237i	0.270332	+	0.0878363i
$443$	−432.952	+	314.558i	−0.977318	+	0.710063i	−0.957108	−	0.289732i	$-0.906434\pi$
$443$	−432.952	+	314.558i	−0.977318	+	0.710063i	−0.0202107	+	0.999796i	$0.506434\pi$
$444$	−42.6515	−	30.9881i	−0.0960619	−	0.0697930i
$445$	66.0381	+	203.245i	0.148400	+	0.456729i
$446$	18.5910	−	6.04059i	0.0416839	−	0.0135439i
$447$	−227.535	+	313.176i	−0.509028	+	0.700617i
$448$	−51.8821	−	71.4096i	−0.115808	−	0.159397i
$449$	157.485	−	484.690i	0.350747	−	1.07949i	−0.607688	−	0.794176i	$-0.707903\pi$
$449$	157.485	−	484.690i	0.350747	−	1.07949i	0.958435	−	0.285312i	$-0.0920971\pi$
$450$			14.4150i			0.0320333i
$451$	69.9888	−	131.673i	0.155186	−	0.291957i
$452$	342.680			0.758142
$453$	307.084	+	99.7775i	0.677889	+	0.220259i
$454$	283.712	−	206.129i	0.624917	−	0.454029i
$455$	204.893	+	148.864i	0.450315	+	0.327173i
$456$	78.4952	+	241.583i	0.172139	+	0.529788i
$457$	−770.822	+	250.455i	−1.68670	+	0.548042i	−0.986192	−	0.165604i	$-0.947043\pi$
$457$	−770.822	+	250.455i	−1.68670	+	0.548042i	−0.700507	+	0.713646i	$0.747043\pi$
$458$	−251.357	+	345.963i	−0.548815	+	0.755379i
$459$	−77.3759	−	106.499i	−0.168575	−	0.232024i
$460$	−3.86641	+	11.8996i	−0.00840525	+	0.0258687i
$461$		−	108.425i		−	0.235196i	−0.993061	−	0.117598i	$-0.962481\pi$
$461$		−	108.425i		−	0.235196i	0.993061	−	0.117598i	$-0.0375194\pi$
$462$	−522.128	+	73.4521i	−1.13015	+	0.158987i
$463$	320.444			0.692103			0.346051	−	0.938216i	$-0.387522\pi$
$463$	320.444			0.692103			0.346051	+	0.938216i	$0.387522\pi$
$464$	84.3070	+	27.3930i	0.181696	+	0.0590367i
$465$	18.4404	−	13.3977i	0.0396568	−	0.0288123i
$466$	−114.667	−	83.3105i	−0.246067	−	0.178778i
$467$	194.207	+	597.708i	0.415861	+	1.27989i	0.911478	+	0.411348i	$0.134942\pi$
$467$	194.207	+	597.708i	0.415861	+	1.27989i	−0.495617	+	0.868541i	$0.665058\pi$
$468$	14.7541	−	4.79390i	0.0315259	−	0.0102434i
$469$	−156.282	+	215.103i	−0.333223	+	0.458643i
$470$	−33.6005	−	46.2471i	−0.0714904	−	0.0983981i
$471$	56.0121	−	172.388i	0.118922	−	0.366003i
$472$		−	140.050i		−	0.296717i
$473$	23.9837	−	11.7017i	0.0507056	−	0.0247392i
$474$	−431.424			−0.910177
$475$	−648.613	−	210.747i	−1.36550	−	0.443678i
$476$	89.3387	−	64.9084i	0.187686	−	0.136362i
$477$	33.7029	+	24.4866i	0.0706559	+	0.0513345i
$478$	−158.134	−	486.685i	−0.330823	−	1.01817i
$479$	20.1138	−	6.53538i	0.0419913	−	0.0136438i	−0.287946	−	0.957647i	$-0.592972\pi$
$479$	20.1138	−	6.53538i	0.0419913	−	0.0136438i	0.329937	+	0.944003i	$0.392972\pi$
$480$	−13.2073	+	18.1783i	−0.0275152	+	0.0378714i
$481$	−89.5377	−	123.238i	−0.186149	−	0.256212i
$482$	−70.5214	+	217.042i	−0.146310	+	0.450296i
$483$		−	163.989i		−	0.339523i
$484$	−232.607	+	66.7670i	−0.480594	+	0.137948i
$485$	−56.0240			−0.115513
$486$	−31.7072	−	10.3023i	−0.0652411	−	0.0211981i
$487$	517.744	−	376.163i	1.06313	−	0.772409i	0.0884652	−	0.996079i	$-0.471804\pi$
$487$	517.744	−	376.163i	1.06313	−	0.772409i	0.974665	+	0.223670i	$0.0718038\pi$
$488$	−22.8388	−	16.5934i	−0.0468009	−	0.0340028i
$489$	−133.495	−	410.856i	−0.272996	−	0.840196i
$490$	126.495	−	41.1008i	0.258154	−	0.0838792i
$491$	270.808	−	372.735i	0.551544	−	0.759135i	−0.438677	−	0.898645i	$-0.644553\pi$
$491$	270.808	−	372.735i	0.551544	−	0.759135i	0.990221	+	0.139510i	$0.0445527\pi$
$492$	48.9554	+	67.3814i	0.0995029	+	0.136954i
$493$	−34.2707	+	105.474i	−0.0695145	+	0.213944i
$494$			733.958i			1.48575i
$495$	2.72508	+	5.58534i	0.00550522	+	0.0112835i
$496$	−22.9537			−0.0462776
$497$	531.089	+	172.561i	1.06859	+	0.347206i
$498$	−45.8939	+	33.3439i	−0.0921564	+	0.0669555i
$499$	422.667	+	307.085i	0.847028	+	0.615402i	0.924325	−	0.381607i	$-0.124629\pi$
$499$	422.667	+	307.085i	0.847028	+	0.615402i	−0.0772973	+	0.997008i	$0.524629\pi$
$500$	−38.6204	−	118.861i	−0.0772408	−	0.237723i
$501$	112.091	−	36.4207i	0.223735	−	0.0726960i
$502$	146.902	−	202.194i	0.292634	−	0.402776i
$503$	254.557	+	350.368i	0.506078	+	0.696557i	0.983252	−	0.182252i	$-0.0583387\pi$
$503$	254.557	+	350.368i	0.506078	+	0.696557i	−0.477173	+	0.878809i	$0.658339\pi$
$504$	4.21364	−	12.9682i	0.00836039	−	0.0257306i
$505$			76.3555i			0.151199i
$506$	−10.4851	−	74.5321i	−0.0207214	−	0.147297i
$507$	448.957			0.885517
$508$	−283.132	−	91.9952i	−0.557347	−	0.181093i
$509$	−147.166	+	106.922i	−0.289127	+	0.210063i	−0.722888	−	0.690965i	$-0.757186\pi$
$509$	−147.166	+	106.922i	−0.289127	+	0.210063i	0.433762	+	0.901028i	$0.357186\pi$
$510$	−22.7424	−	16.5233i	−0.0445929	−	0.0323986i
$511$	149.899	+	461.342i	0.293345	+	0.902822i
$512$	21.5200	−	6.99226i	0.0420312	−	0.0136568i
$513$	452.026	−	622.160i	0.881142	−	1.21279i
$514$	−268.002	−	368.873i	−0.521405	−	0.717653i
$515$	−27.5528	+	84.7988i	−0.0535006	+	0.164658i
$516$			14.9052i			0.0288861i
$517$	303.645	+	161.398i	0.587321	+	0.312183i
$518$	−133.892			−0.258479
$519$	−827.725	−	268.944i	−1.59485	−	0.518197i
$520$	−52.5247	+	38.1614i	−0.101009	+	0.0733874i
$521$	−547.116	−	397.503i	−1.05013	−	0.762961i	−0.0778899	−	0.996962i	$-0.524818\pi$
$521$	−547.116	−	397.503i	−1.05013	−	0.762961i	−0.972236	+	0.234000i	$0.924818\pi$
$522$	4.23170	+	13.0238i	0.00810671	+	0.0249499i
$523$	778.962	−	253.100i	1.48941	−	0.483939i	0.552502	−	0.833511i	$-0.313673\pi$
$523$	778.962	−	253.100i	1.48941	−	0.483939i	0.936909	+	0.349572i	$0.113673\pi$
$524$	167.997	−	231.229i	0.320606	−	0.441276i
$525$	464.754	+	639.679i	0.885245	+	1.21844i
$526$	−175.061	+	538.783i	−0.332816	+	1.02430i
$527$		−	28.7168i		−	0.0544910i
$528$	23.4534	−	133.116i	0.0444194	−	0.252113i
$529$	−505.591			−0.955749
$530$	−165.811	−	53.8754i	−0.312852	−	0.101652i
$531$	17.5032	−	12.7168i	0.0329627	−	0.0239488i
$532$	521.912	+	379.191i	0.981037	+	0.712765i
$533$	74.3662	+	228.876i	0.139524	+	0.429410i
$534$	682.880	−	221.881i	1.27880	−	0.415508i
$535$	48.9812	−	67.4168i	0.0915536	−	0.126013i
$536$	−40.0631	−	55.1421i	−0.0747445	−	0.102877i
$537$	268.428	−	826.135i	0.499865	−	1.53843i
$538$		−	130.564i		−	0.242685i
$539$	−575.465	+	555.870i	−1.06765	+	1.03130i
$540$	68.0267			0.125975
$541$	593.734	+	192.916i	1.09748	+	0.356591i	0.801131	−	0.598489i	$-0.204232\pi$
$541$	593.734	+	192.916i	1.09748	+	0.356591i	0.296345	+	0.955081i	$0.404232\pi$
$542$	−178.191	+	129.463i	−0.328765	+	0.238862i
$543$	−693.827	−	504.095i	−1.27777	−	0.928351i
$544$	8.74782	+	26.9230i	0.0160806	+	0.0494909i
$545$	69.7236	−	22.6546i	0.127933	−	0.0415680i
$546$	500.167	−	688.421i	0.916056	−	1.26084i
$547$	−525.682	−	723.539i	−0.961027	−	1.32274i	−0.946451	−	0.322847i	$-0.895360\pi$
$547$	−525.682	−	723.539i	−0.961027	−	1.32274i	−0.0145763	−	0.999894i	$-0.504640\pi$
$548$	−87.4086	+	269.016i	−0.159505	+	0.490905i
$549$		−	4.36106i		−	0.00794364i
$550$	252.127	+	261.015i	0.458412	+	0.474572i
$551$	−647.885			−1.17583
$552$	39.9814	+	12.9907i	0.0724301	+	0.0235340i
$553$	−886.422	+	644.023i	−1.60293	+	1.16460i
$554$	340.849	+	247.642i	0.615252	+	0.447006i
$555$	10.5325	+	32.4158i	0.0189776	+	0.0584069i
$556$	−127.813	+	41.5290i	−0.229879	+	0.0746924i
$557$	63.4979	−	87.3973i	0.114000	−	0.156907i	−0.748204	−	0.663469i	$-0.769084\pi$
$557$	63.4979	−	87.3973i	0.114000	−	0.156907i	0.862204	+	0.506561i	$0.169084\pi$
$558$	−2.08424	−	2.86870i	−0.00373519	−	0.00514105i
$559$	−13.3086	+	40.9596i	−0.0238078	+	0.0732729i
$560$			57.0655i			0.101903i
$561$	166.538	+	29.3420i	0.296859	+	0.0523029i
$562$	−289.439			−0.515015
$563$	133.507	+	43.3791i	0.237135	+	0.0770500i	0.425174	−	0.905112i	$-0.360213\pi$
$563$	133.507	+	43.3791i	0.237135	+	0.0770500i	−0.188038	+	0.982162i	$0.560213\pi$
$564$	−155.386	+	112.894i	−0.275506	+	0.200167i
$565$	−179.234	−	130.221i	−0.317229	−	0.230480i
$566$	−40.1735	−	123.641i	−0.0709779	−	0.218448i
$567$	−889.225	+	288.927i	−1.56830	+	0.509571i
$568$	−84.1425	+	115.812i	−0.148138	+	0.203895i
$569$	579.260	+	797.283i	1.01803	+	1.40120i	0.913575	+	0.406670i	$0.133310\pi$
$569$	579.260	+	797.283i	1.01803	+	1.40120i	0.104456	+	0.994529i	$0.466690\pi$
$570$	50.7479	−	156.186i	0.0890313	−	0.274010i
$571$		−	641.392i		−	1.12328i	−0.827382	−	0.561640i	$-0.810171\pi$
$571$		−	641.392i		−	1.12328i	0.827382	−	0.561640i	$-0.189829\pi$
$572$	183.307	−	344.862i	0.320466	−	0.602905i
$573$	68.8710			0.120194
$574$	201.172	+	65.3647i	0.350474	+	0.113876i
$575$	−91.3121	+	66.3421i	−0.158804	+	0.115378i
$576$	2.82793	+	2.05461i	0.00490959	+	0.00356703i
$577$	246.342	+	758.164i	0.426936	+	1.31398i	0.901128	+	0.433553i	$0.142740\pi$
$577$	246.342	+	758.164i	0.426936	+	1.31398i	−0.474191	+	0.880422i	$0.657260\pi$
$578$	355.021	−	115.353i	0.614224	−	0.199573i
$579$	−465.605	+	640.850i	−0.804154	+	1.10682i
$580$	−33.6861	−	46.3650i	−0.0580795	−	0.0799396i
$581$	−44.5203	+	137.019i	−0.0766270	+	0.235834i
$582$			188.235i			0.323428i
$583$	1038.55	−	146.101i	1.78138	−	0.250602i
$584$	−124.352			−0.212931
$585$	−9.53867	−	3.09930i	−0.0163054	−	0.00529795i
$586$	−112.933	+	82.0507i	−0.192719	+	0.140018i
$587$	−444.592	−	323.015i	−0.757397	−	0.550281i	0.140714	−	0.990050i	$-0.455060\pi$
$587$	−444.592	−	323.015i	−0.757397	−	0.550281i	−0.898111	+	0.439769i	$0.855060\pi$
$588$	−138.095	−	425.011i	−0.234855	−	0.722808i
$589$	159.551	−	51.8412i	0.270884	−	0.0880156i
$590$	−53.2204	+	73.2515i	−0.0902040	+	0.124155i
$591$	276.940	+	381.175i	0.468595	+	0.644966i
$592$	10.6065	−	32.6435i	0.0179164	−	0.0551411i
$593$		−	887.460i		−	1.49656i	−0.663383	−	0.748280i	$-0.730880\pi$
$593$		−	887.460i		−	1.49656i	0.663383	−	0.748280i	$-0.269120\pi$
$594$	−367.776	+	179.438i	−0.619152	+	0.302084i
$595$	−71.3932			−0.119989
$596$	−239.691	−	77.8802i	−0.402165	−	0.130671i
$597$	−585.293	+	425.240i	−0.980390	+	0.712295i
$598$	98.2698	+	71.3972i	0.164331	+	0.119393i
$599$	−326.276	−	1004.17i	−0.544701	−	1.67642i	−0.721701	−	0.692205i	$-0.756639\pi$
$599$	−326.276	−	1004.17i	−0.544701	−	1.67642i	0.177000	−	0.984211i	$-0.443361\pi$
$600$	−192.773	+	62.6358i	−0.321288	+	0.104393i
$601$	−518.251	+	713.311i	−0.862314	+	1.18687i	0.118699	+	0.992930i	$0.462128\pi$
$601$	−518.251	+	713.311i	−0.862314	+	1.18687i	−0.981013	+	0.193943i	$0.937872\pi$
$602$	22.2503	+	30.6249i	0.0369606	+	0.0508719i
$603$	3.25374	−	10.0140i	0.00539593	−	0.0166069i
$604$			210.215i			0.348039i
$605$	147.034	+	53.4712i	0.243032	+	0.0883822i
$606$	256.547			0.423344
$607$	−576.704	−	187.383i	−0.950090	−	0.308703i	−0.207338	−	0.978269i	$-0.566480\pi$
$607$	−576.704	−	187.383i	−0.950090	−	0.308703i	−0.742752	+	0.669567i	$0.766480\pi$
$608$	−133.793	+	97.2062i	−0.220054	+	0.159879i
$609$	607.687	+	441.510i	0.997844	+	0.724976i
$610$	5.63993	+	17.3579i	0.00924578	+	0.0284556i
$611$	−527.801	+	171.493i	−0.863831	+	0.280676i
$612$	−2.57047	+	3.53794i	−0.00420011	+	0.00578095i
$613$	25.3407	+	34.8785i	0.0413388	+	0.0568980i	0.829186	−	0.558973i	$-0.188804\pi$
$613$	25.3407	+	34.8785i	0.0413388	+	0.0568980i	−0.787847	+	0.615871i	$0.788804\pi$
$614$	78.0387	−	240.178i	0.127099	−	0.391170i
$615$		−	53.8464i		−	0.0875552i
$616$	−150.525	−	308.517i	−0.244359	−	0.500839i
$617$	608.797			0.986704			0.493352	−	0.869830i	$-0.335771\pi$
$617$	608.797			0.986704			0.493352	+	0.869830i	$0.335771\pi$
$618$	284.915	+	92.5746i	0.461028	+	0.149797i
$619$	−13.7867	+	10.0167i	−0.0222726	+	0.0161820i	−0.598866	−	0.800849i	$-0.704382\pi$
$619$	−13.7867	+	10.0167i	−0.0222726	+	0.0161820i	0.576593	+	0.817031i	$0.304382\pi$
$620$	12.0056	+	8.72260i	0.0193639	+	0.0140687i
$621$	−39.3295	−	121.044i	−0.0633325	−	0.194917i
$622$	401.122	−	130.333i	0.644891	−	0.209538i
$623$	1071.85	−	1475.28i	1.72047	−	2.36803i
$624$	128.218	+	176.478i	0.205478	+	0.282817i
$625$	155.251	−	477.814i	0.248402	−	0.764502i
$626$		−	181.046i		−	0.289210i
$627$	137.620	+	978.257i	0.219489	+	1.56022i
$628$	118.009			0.187912
$629$	40.8394	+	13.2695i	0.0649276	+	0.0210962i
$630$	−7.13193	+	5.18165i	−0.0113205	+	0.00822484i
$631$	886.305	+	643.939i	1.40460	+	1.02050i	0.994079	+	0.108655i	$0.0346545\pi$
$631$	886.305	+	643.939i	1.40460	+	1.02050i	0.410525	+	0.911849i	$0.365346\pi$
$632$	−86.7963	−	267.131i	−0.137336	−	0.422676i
$633$	734.630	−	238.696i	1.16055	−	0.377086i
$634$	−190.019	+	261.539i	−0.299715	+	0.412522i
$635$	113.130	+	155.710i	0.178157	+	0.245212i
$636$	−181.016	+	557.109i	−0.284616	+	0.875958i
$637$		−	1291.23i		−	2.02705i
$638$	304.419	+	161.810i	0.477145	+	0.253620i
$639$	−22.1142			−0.0346076
$640$	−13.9128	−	4.52056i	−0.0217388	−	0.00706337i
$641$	467.190	−	339.433i	0.728846	−	0.529537i	−0.160352	−	0.987060i	$-0.551263\pi$
$641$	467.190	−	339.433i	0.728846	−	0.529537i	0.889198	+	0.457523i	$0.151263\pi$
$642$	−226.513	−	164.572i	−0.352825	−	0.256342i
$643$	−137.849	−	424.256i	−0.214384	−	0.659808i	−0.999197	−	0.0400739i	$-0.987241\pi$
$643$	−137.849	−	424.256i	−0.214384	−	0.659808i	0.784812	−	0.619734i	$-0.212759\pi$
$644$	101.540	−	32.9923i	0.157671	−	0.0512303i
$645$	5.66411	−	7.79598i	0.00878156	−	0.0120868i
$646$	−121.612	−	167.385i	−0.188254	−	0.259109i
$647$	−130.673	+	402.172i	−0.201968	+	0.621594i	0.797856	+	0.602848i	$0.205968\pi$
$647$	−130.673	+	402.172i	−0.201968	+	0.621594i	−0.999824	+	0.0187464i	$0.994032\pi$
$648$		−	239.685i		−	0.369885i
$649$	94.5083	−	536.406i	0.145621	−	0.826512i
$650$	−585.667			−0.901026
$651$	−184.980	−	60.1035i	−0.284147	−	0.0923249i
$652$	227.539	−	165.316i	0.348986	−	0.253553i
$653$	576.811	+	419.078i	0.883325	+	0.641773i	0.934129	−	0.356935i	$-0.116178\pi$
$653$	576.811	+	419.078i	0.883325	+	0.641773i	−0.0508038	+	0.998709i	$0.516178\pi$
$654$	−76.1170	−	234.264i	−0.116387	−	0.358202i
$655$	−175.738	+	57.1006i	−0.268302	+	0.0871765i
$656$	−31.8724	+	43.8687i	−0.0485861	+	0.0668730i
$657$	−11.2914	−	15.5412i	−0.0171863	−	0.0236548i
$658$	−150.735	+	463.914i	−0.229080	+	0.705037i
$659$			834.878i			1.26689i	0.773789	+	0.633443i	$0.218359\pi$
$659$			834.878i			1.26689i	−0.773789	+	0.633443i	$0.781641\pi$
$660$	−62.8522	+	60.7120i	−0.0952306	+	0.0919879i
$661$	−160.201			−0.242361			−0.121181	−	0.992630i	$-0.538668\pi$
$661$	−160.201			−0.242361			−0.121181	+	0.992630i	$0.538668\pi$
$662$	−124.619	−	40.4911i	−0.188246	−	0.0611648i
$663$	−220.786	+	160.411i	−0.333011	+	0.241947i
$664$	−29.8792	−	21.7085i	−0.0449988	−	0.0326936i
$665$	−128.883	−	396.662i	−0.193809	−	0.596484i
$666$	5.04281	−	1.63851i	0.00757178	−	0.00246022i
$667$	−63.0242	+	86.7454i	−0.0944891	+	0.130053i
$668$	45.1024	+	62.0781i	0.0675185	+	0.0929312i
$669$	−13.1214	+	40.3835i	−0.0196134	+	0.0603639i
$670$			44.0656i			0.0657696i
$671$	−76.2774	−	78.9662i	−0.113677	−	0.117684i
$672$	191.734			0.285319
$673$	−1171.50	−	380.644i	−1.74072	−	0.565593i	−0.745788	−	0.666183i	$-0.767927\pi$
$673$	−1171.50	−	380.644i	−1.74072	−	0.565593i	−0.994928	+	0.100590i	$0.967927\pi$
$674$	−278.667	+	202.464i	−0.413453	+	0.300391i
$675$	496.457	+	360.697i	0.735492	+	0.534366i
$676$	90.3237	+	277.988i	0.133615	+	0.411224i
$677$	−894.336	+	290.587i	−1.32103	+	0.429228i	−0.882848	−	0.469659i	$-0.844377\pi$
$677$	−894.336	+	290.587i	−1.32103	+	0.429228i	−0.438180	+	0.898887i	$0.644377\pi$
$678$	−437.530	+	602.209i	−0.645325	+	0.888213i
$679$	280.994	+	386.756i	0.413836	+	0.569596i
$680$	5.65555	−	17.4060i	0.00831698	−	0.0255970i
$681$			761.765i			1.11860i
$682$	−87.9148	−	15.4895i	−0.128907	−	0.0227119i
$683$	350.306			0.512893			0.256446	−	0.966558i	$-0.417448\pi$
$683$	350.306			0.512893			0.256446	+	0.966558i	$0.417448\pi$
$684$	−24.2972	−	7.89465i	−0.0355223	−	0.0115419i
$685$	147.946	−	107.489i	0.215980	−	0.156919i
$686$	−299.631	−	217.695i	−0.436780	−	0.317339i
$687$	−287.049	−	883.445i	−0.417829	−	1.28595i
$688$	−9.22909	+	2.99871i	−0.0134144	+	0.00435859i
$689$	−994.864	+	1369.31i	−1.44392	+	1.98739i
$690$	−15.9752	−	21.9879i	−0.0231524	−	0.0318666i
$691$	−10.4098	+	32.0381i	−0.0150649	+	0.0463649i	−0.958306	−	0.285743i	$-0.907760\pi$
$691$	−10.4098	+	32.0381i	−0.0150649	+	0.0463649i	0.943242	+	0.332108i	$0.107760\pi$
$692$		−	566.623i		−	0.818819i
$693$	24.8898	−	46.8261i	0.0359160	−	0.0675702i
$694$	−541.709			−0.780561
$695$	82.6323	+	26.8489i	0.118895	+	0.0386314i
$696$	−155.781	+	113.182i	−0.223824	+	0.162618i
$697$	−54.8829	−	39.8748i	−0.0787416	−	0.0572091i
$698$	−195.234	−	600.869i	−0.279705	−	0.860844i
$699$	292.811	−	95.1402i	0.418900	−	0.136109i
$700$	−302.578	+	416.463i	−0.432254	+	0.594947i
$701$	−762.156	−	1049.02i	−1.08724	−	1.49646i	−0.851291	−	0.524694i	$-0.824180\pi$
$701$	−762.156	−	1049.02i	−1.08724	−	1.49646i	−0.235951	−	0.971765i	$-0.575820\pi$
$702$	204.079	−	628.091i	0.290711	−	0.894716i
$703$			250.860i			0.356842i
$704$	87.1419	−	12.2590i	0.123781	−	0.0174133i
$705$	124.173			0.176132
$706$	391.387	+	127.169i	0.554373	+	0.180127i
$707$	527.112	−	382.969i	0.745561	−	0.541682i
$708$	246.118	+	178.815i	0.347624	+	0.252563i
$709$	399.155	+	1228.47i	0.562983	+	1.73268i	0.673870	+	0.738850i	$0.264631\pi$
$709$	399.155	+	1228.47i	0.562983	+	1.73268i	−0.110888	+	0.993833i	$0.535369\pi$
$710$	88.0193	−	28.5992i	0.123971	−	0.0402806i
$711$	25.5043	−	35.1036i	0.0358710	−	0.0493722i
$712$	274.771	+	378.190i	0.385915	+	0.531166i
$713$	8.57958	−	26.4052i	0.0120331	−	0.0370340i
$714$			239.874i			0.335957i
$715$	−226.927	+	110.717i	−0.317380	+	0.154849i
$716$	565.535			0.789853
$717$	1057.18	+	343.498i	1.47445	+	0.479077i
$718$	−195.837	+	142.284i	−0.272754	+	0.198167i
$719$	−49.6409	−	36.0662i	−0.0690416	−	0.0501617i	0.552729	−	0.833361i	$-0.313586\pi$
$719$	−49.6409	−	36.0662i	−0.0690416	−	0.0501617i	−0.621771	+	0.783199i	$0.713586\pi$
$720$	−0.698341	−	2.14927i	−0.000969918	−	0.00298510i
$721$	723.593	−	235.110i	1.00360	−	0.326088i
$722$	410.368	−	564.823i	0.568377	−	0.782303i
$723$	−291.379	−	401.048i	−0.403013	−	0.554700i
$724$	172.540	−	531.024i	0.238315	−	0.733459i
$725$		−	516.984i		−	0.713081i
$726$	179.658	−	494.020i	0.247462	−	0.680468i
$727$	−768.090			−1.05652			−0.528260	−	0.849083i	$-0.677155\pi$
$727$	−768.090			−1.05652			−0.528260	+	0.849083i	$0.677155\pi$
$728$	526.886	+	171.196i	0.723745	+	0.235159i
$729$	−558.428	+	405.722i	−0.766019	+	0.556545i
$730$	65.0406	+	47.2548i	0.0890968	+	0.0647326i
$731$	−3.75161	−	11.5463i	−0.00513216	−	0.0157952i
$732$	58.3208	−	18.9496i	0.0796732	−	0.0258874i
$733$	597.815	−	822.822i	0.815573	−	1.12254i	−0.174866	−	0.984592i	$-0.555949\pi$
$733$	597.815	−	822.822i	0.815573	−	1.12254i	0.990439	−	0.137948i	$-0.0440507\pi$
$734$	361.841	+	498.032i	0.492972	+	0.678517i
$735$	−89.2794	+	274.774i	−0.121469	+	0.373842i
$736$			27.3695i			0.0371868i
$737$	−116.235	−	238.235i	−0.157713	−	0.323249i
$738$	−8.37669			−0.0113505
$739$	−316.027	−	102.683i	−0.427641	−	0.138949i	0.0872852	−	0.996183i	$-0.472181\pi$
$739$	−316.027	−	102.683i	−0.427641	−	0.138949i	−0.514927	+	0.857234i	$0.672181\pi$
$740$	−17.9524	+	13.0432i	−0.0242600	+	0.0176259i
$741$	−1289.82	−	937.110i	−1.74065	−	1.26466i
$742$	459.722	+	1414.88i	0.619571	+	1.90684i
$743$	−466.388	+	151.539i	−0.627710	+	0.203955i	−0.605560	−	0.795799i	$-0.707051\pi$
$743$	−466.388	+	151.539i	−0.627710	+	0.203955i	−0.0221495	+	0.999755i	$0.507051\pi$
$744$	29.3070	−	40.3377i	0.0393912	−	0.0542173i
$745$	95.7719	+	131.819i	0.128553	+	0.176938i
$746$	196.232	−	603.941i	0.263046	−	0.809572i
$747$		−	5.70541i		−	0.00763777i
$748$	15.3369	+	109.021i	0.0205039	+	0.145750i
$749$	−711.074			−0.949365
$750$	258.191	+	83.8914i	0.344255	+	0.111855i
$751$	783.181	−	569.014i	1.04285	−	0.757675i	0.0720106	−	0.997404i	$-0.477058\pi$
$751$	783.181	−	569.014i	1.04285	−	0.757675i	0.970840	+	0.239729i	$0.0770584\pi$
$752$	−101.164	−	73.4998i	−0.134526	−	0.0977391i
$753$	167.762	+	516.317i	0.222791	+	0.685680i
$754$	−529.146	+	171.930i	−0.701785	+	0.228024i
$755$	79.8837	−	109.950i	0.105806	−	0.145630i
$756$	−341.195	−	469.615i	−0.451316	−	0.621183i
$757$	−65.6453	+	202.035i	−0.0867176	+	0.266889i	−0.985007	−	0.172515i	$-0.944811\pi$
$757$	−65.6453	+	202.035i	−0.0867176	+	0.266889i	0.898289	+	0.439405i	$0.144811\pi$
$758$			19.2899i			0.0254484i
$759$	144.366	+	76.7359i	0.190206	+	0.101101i
$760$	106.918			0.140681
$761$	355.806	+	115.608i	0.467550	+	0.151916i	0.533311	−	0.845919i	$-0.320947\pi$
$761$	355.806	+	115.608i	0.467550	+	0.151916i	−0.0657608	+	0.997835i	$0.520947\pi$
$762$	523.168	−	380.104i	0.686572	−	0.498824i
$763$	−506.099	−	367.703i	−0.663302	−	0.481917i
$764$	13.8558	+	42.6439i	0.0181359	+	0.0558166i
$765$	2.68890	−	0.873676i	0.00351490	−	0.00114206i
$766$	556.690	−	766.218i	0.726749	−	1.00028i
$767$	516.671	+	711.137i	0.673626	+	0.927167i
$768$	−15.1886	+	46.7457i	−0.0197768	+	0.0608668i
$769$			642.305i			0.835248i	0.908620	+	0.417624i	$0.137137\pi$
$769$			642.305i			0.835248i	−0.908620	+	0.417624i	$0.862863\pi$
$770$	−38.5088	+	218.566i	−0.0500114	+	0.283852i
$771$	990.422			1.28459
$772$	−490.478	−	159.366i	−0.635335	−	0.206433i
$773$	−106.829	+	77.6155i	−0.138200	+	0.100408i	−0.654737	−	0.755856i	$-0.727221\pi$
$773$	−106.829	+	77.6155i	−0.138200	+	0.100408i	0.516537	+	0.856265i	$0.327221\pi$
$774$	−1.21279	−	0.881144i	−0.00156691	−	0.00113843i
$775$	41.3670	+	127.315i	0.0533768	+	0.164277i
$776$	−116.552	+	37.8702i	−0.150196	+	0.0488017i
$777$	170.952	−	235.295i	0.220015	−	0.302825i
$778$	−260.133	−	358.042i	−0.334361	−	0.460208i
$779$	122.467	−	376.915i	0.157211	−	0.483844i
$780$		−	141.028i		−	0.180806i
$781$	−400.426	+	386.791i	−0.512709	+	0.495251i
$782$	−34.2412			−0.0437867
$783$	554.432	+	180.146i	0.708087	+	0.230071i
$784$	235.378	−	171.012i	0.300227	−	0.218128i
$785$	−61.7229	−	44.8443i	−0.0786279	−	0.0571265i
$786$	191.852	+	590.460i	0.244087	+	0.751222i
$787$	783.369	−	254.532i	0.995387	−	0.323421i	0.234366	−	0.972148i	$-0.424699\pi$
$787$	783.369	−	254.532i	0.995387	−	0.323421i	0.761021	+	0.648728i	$0.224699\pi$
$788$	−180.302	+	248.164i	−0.228809	+	0.314929i
$789$	−723.314	−	995.556i	−0.916748	−	1.26180i
$790$	−56.1146	+	172.703i	−0.0710311	+	0.218611i
$791$			1890.46i			2.38996i
$792$	9.44474	+	9.77768i	0.0119252	+	0.0123456i
$793$	177.185			0.223437
$794$	−211.232	−	68.6335i	−0.266036	−	0.0864402i
$795$	306.384	−	222.601i	0.385389	−	0.280002i
$796$	−381.055	−	276.853i	−0.478712	−	0.347805i
$797$	−136.550	−	420.258i	−0.171330	−	0.527300i	0.828117	−	0.560556i	$-0.189412\pi$
$797$	−136.550	−	420.258i	−0.171330	−	0.527300i	−0.999447	+	0.0332558i	$0.989412\pi$
$798$	−1332.74	+	433.034i	−1.67010	+	0.542649i
$799$	91.9536	−	126.563i	0.115086	−	0.158402i
$800$	−77.5663	−	106.761i	−0.0969579	−	0.133451i
$801$	−22.3157	+	68.6807i	−0.0278598	+	0.0857437i
$802$			253.240i			0.315761i
$803$	−476.280	−	83.9147i	−0.593125	−	0.104502i
$804$	148.056			0.184149
$805$	−65.6465	−	21.3298i	−0.0815484	−	0.0264967i
$806$	116.553	−	84.6804i	0.144606	−	0.105062i
$807$	229.447	+	166.703i	0.284321	+	0.206571i
$808$	51.6135	+	158.850i	0.0638781	+	0.196596i
$809$	471.251	−	153.119i	0.582511	−	0.189269i	−0.00291426	−	0.999996i	$-0.500928\pi$
$809$	471.251	−	153.119i	0.582511	−	0.189269i	0.585425	+	0.810727i	$0.300928\pi$
$810$	−91.0825	+	125.364i	−0.112447	+	0.154771i
$811$	−509.110	−	700.729i	−0.627755	−	0.864031i	0.370133	−	0.928979i	$-0.379312\pi$
$811$	−509.110	−	700.729i	−0.627755	−	0.864031i	−0.997889	+	0.0649476i	$0.979312\pi$
$812$	−151.119	+	465.097i	−0.186107	+	0.572779i
$813$		−	478.441i		−	0.588488i
$814$	62.6524	−	117.870i	0.0769685	−	0.144804i
$815$	−181.833			−0.223108
$816$	−58.4823	−	19.0021i	−0.0716695	−	0.0232868i
$817$	57.3786	−	41.6880i	0.0702309	−	0.0510257i
$818$	−46.5441	−	33.8163i	−0.0568999	−	0.0413402i
$819$	26.4465	+	81.3940i	0.0322912	+	0.0993822i
$820$	33.3409	−	10.8331i	0.0406597	−	0.0132111i
$821$	−164.190	+	225.988i	−0.199988	+	0.275260i	−0.897218	−	0.441587i	$-0.854416\pi$
$821$	−164.190	+	225.988i	−0.199988	+	0.275260i	0.697230	+	0.716847i	$0.254416\pi$
$822$	−361.153	−	497.084i	−0.439359	−	0.604725i
$823$	−407.602	+	1254.47i	−0.495264	+	1.52426i	0.321282	+	0.946984i	$0.395886\pi$
$823$	−407.602	+	1254.47i	−0.495264	+	1.52426i	−0.816545	+	0.577281i	$0.804114\pi$
$824$			195.040i			0.236699i
$825$	−780.607	+	109.814i	−0.946190	+	0.133108i
$826$	772.616			0.935370
$827$	94.3228	+	30.6473i	0.114054	+	0.0370585i	0.365488	−	0.930816i	$-0.380902\pi$
$827$	94.3228	+	30.6473i	0.114054	+	0.0370585i	−0.251434	+	0.967874i	$0.580902\pi$
$828$	−3.42058	+	2.48519i	−0.00413113	+	0.00300144i
$829$	−181.366	−	131.770i	−0.218777	−	0.158951i	0.472999	−	0.881063i	$-0.343171\pi$
$829$	−181.366	−	131.770i	−0.218777	−	0.158951i	−0.691776	+	0.722112i	$0.743171\pi$
$830$	7.37851	+	22.7087i	0.00888977	+	0.0273599i
$831$	−870.386	+	282.805i	−1.04740	+	0.340319i
$832$	−83.4767	+	114.896i	−0.100333	+	0.138096i
$833$	213.949	+	294.475i	0.256841	+	0.353512i
$834$	90.2094	−	277.636i	0.108165	−	0.332897i
$835$		−	49.6084i		−	0.0594113i
$836$	−578.035	+	282.023i	−0.691430	+	0.337348i
$837$	−150.951			−0.180348
$838$	−786.849	−	255.663i	−0.938961	−	0.305087i
$839$	1032.67	−	750.279i	1.23083	−	0.894253i	0.233882	−	0.972265i	$-0.424857\pi$
$839$	1032.67	−	750.279i	1.23083	−	0.894253i	0.996952	+	0.0780117i	$0.0248571\pi$
$840$	−100.284	−	72.8607i	−0.119386	−	0.0867389i
$841$	108.116	+	332.748i	0.128557	+	0.395657i
$842$	−481.561	+	156.469i	−0.571925	+	0.185830i
$843$	369.552	−	508.645i	0.438377	−	0.603374i
$844$	295.594	+	406.850i	0.350230	+	0.482050i
$845$	58.3951	−	179.722i	0.0691066	−	0.212688i
$846$		−	19.3171i		−	0.0228335i
$847$	−368.333	−	1283.22i	−0.434868	−	1.51502i
$848$	−381.372			−0.449731
$849$	268.574	+	87.2650i	0.316342	+	0.102786i
$850$	133.566	−	97.0411i	0.157136	−	0.114166i
$851$	33.5877	+	24.4029i	0.0394684	+	0.0286755i
$852$	−96.0903	−	295.736i	−0.112782	−	0.347107i
$853$	888.856	−	288.807i	1.04203	−	0.338578i	0.262497	−	0.964933i	$-0.415454\pi$
$853$	888.856	−	288.807i	1.04203	−	0.338578i	0.779538	+	0.626355i	$0.215454\pi$
$854$	91.5407	−	125.995i	0.107191	−	0.147535i
$855$	9.70832	+	13.3624i	0.0113548	+	0.0156285i
$856$	56.3291	−	173.363i	0.0658051	−	0.202527i
$857$			1383.27i			1.61408i	0.590497	+	0.807040i	$0.298932\pi$
$857$			1383.27i			1.61408i	−0.590497	+	0.807040i	$0.701068\pi$
$858$	371.999	+	762.450i	0.433565	+	0.888636i
$859$	515.755			0.600413			0.300206	−	0.953874i	$-0.402944\pi$
$859$	515.755			0.600413			0.300206	+	0.953874i	$0.402944\pi$
$860$	5.96669	+	1.93870i	0.00693801	+	0.00225430i
$861$	−371.723	+	270.072i	−0.431734	+	0.313673i
$862$	−72.1532	−	52.4224i	−0.0837044	−	0.0608148i
$863$	239.575	+	737.336i	0.277607	+	0.854386i	0.988518	+	0.151104i	$0.0482829\pi$
$863$	239.575	+	737.336i	0.277607	+	0.854386i	−0.710911	+	0.703282i	$0.751717\pi$
$864$	141.523	−	45.9835i	0.163799	−	0.0532216i
$865$	−215.322	+	296.365i	−0.248927	+	0.342618i
$866$	646.564	+	889.919i	0.746609	+	1.02762i
$867$	−250.571	+	771.179i	−0.289009	+	0.889480i
$868$		−	126.629i		−	0.145885i
$869$	−152.173	−	1081.71i	−0.175113	−	1.24478i
$870$	124.490			0.143091
$871$	406.858	+	132.196i	0.467116	+	0.151775i
$872$	129.739	−	94.2611i	0.148784	−	0.108098i
$873$	−15.3161	−	11.1278i	−0.0175442	−	0.0127466i
$874$	−61.8143	−	190.245i	−0.0707257	−	0.217671i
$875$	655.722	−	213.057i	0.749397	−	0.243494i
$876$	158.771	−	218.530i	0.181246	−	0.249463i
$877$	−293.874	−	404.483i	−0.335090	−	0.461212i	0.607909	−	0.794007i	$-0.292008\pi$
$877$	−293.874	−	404.483i	−0.335090	−	0.461212i	−0.942999	+	0.332795i	$0.892008\pi$
$878$	83.4285	−	256.767i	0.0950211	−	0.292445i
$879$		−	303.224i		−	0.344965i
$880$	−50.2370	−	26.7028i	−0.0570875	−	0.0303441i
$881$	636.290			0.722236			0.361118	−	0.932520i	$-0.382395\pi$
$881$	636.290			0.722236			0.361118	+	0.932520i	$0.382395\pi$
$882$	42.7455	+	13.8888i	0.0484643	+	0.0157470i
$883$	−763.195	+	554.494i	−0.864321	+	0.627966i	−0.929057	−	0.369936i	$-0.879379\pi$
$883$	−763.195	+	554.494i	−0.864321	+	0.627966i	0.0647360	+	0.997902i	$0.479379\pi$
$884$	−143.743	−	104.435i	−0.162605	−	0.118140i
$885$	−60.7774	−	187.054i	−0.0686750	−	0.211360i
$886$	719.786	−	233.873i	0.812400	−	0.263965i
$887$	−334.312	+	460.141i	−0.376902	+	0.518761i	−0.954761	−	0.297376i	$-0.903889\pi$
$887$	−334.312	+	460.141i	−0.376902	+	0.518761i	0.577858	+	0.816137i	$0.303889\pi$
$888$	43.8238	+	60.3183i	0.0493511	+	0.0679260i
$889$	507.510	−	1561.96i	0.570877	−	1.75698i
$890$		−	302.223i		−	0.339576i
$891$	161.744	−	918.017i	0.181530	−	1.03032i
$892$	−27.6447			−0.0309918
$893$	869.188	+	282.416i	0.973335	+	0.316256i
$894$	442.897	−	321.784i	0.495411	−	0.359937i
$895$	−295.795	−	214.908i	−0.330498	−	0.240121i
$896$	38.5742	+	118.719i	0.0430515	+	0.132499i
$897$	−250.940	+	81.5353i	−0.279755	+	0.0908977i
$898$	−423.634	+	583.083i	−0.471753	+	0.649313i
$899$	74.7496	+	102.884i	0.0831475	+	0.114443i
$900$	6.29959	−	19.3881i	0.00699954	−	0.0215424i
$901$		−	477.124i		−	0.529549i
$902$	−151.678	+	146.513i	−0.168157	+	0.162431i
$903$	−82.2276			−0.0910604
$904$	−460.904	−	149.757i	−0.509849	−	0.165660i
$905$	−292.039	+	212.178i	−0.322695	+	0.234451i
$906$	−369.422	−	268.401i	−0.407751	−	0.296248i
$907$	86.1215	+	265.055i	0.0949521	+	0.292232i	0.987241	−	0.159232i	$-0.0509018\pi$
$907$	86.1215	+	265.055i	0.0949521	+	0.292232i	−0.892289	+	0.451464i	$0.850902\pi$
$908$	−471.674	+	153.256i	−0.519465	+	0.168784i
$909$	−15.1661	+	20.8744i	−0.0166844	+	0.0229641i
$910$	−210.525	−	289.763i	−0.231346	−	0.318421i
$911$	153.490	−	472.395i	0.168486	−	0.518545i	−0.830791	−	0.556585i	$-0.812111\pi$
$911$	153.490	−	472.395i	0.168486	−	0.518545i	0.999276	+	0.0380397i	$0.0121113\pi$
$912$		−	359.233i		−	0.393895i
$913$	−99.7910	−	103.309i	−0.109300	−	0.113153i
$914$	1146.21			1.25405
$915$	−37.7049	−	12.2511i	−0.0412076	−	0.0133891i
$916$	489.266	−	355.473i	0.534133	−	0.388071i
$917$	1275.62	+	926.791i	1.39108	+	1.01068i
$918$	57.5287	+	177.055i	0.0626674	+	0.192871i
$919$	−189.624	+	61.6127i	−0.206338	+	0.0670432i	−0.410362	−	0.911923i	$-0.634598\pi$
$919$	−189.624	+	61.6127i	−0.206338	+	0.0670432i	0.204025	+	0.978966i	$0.434598\pi$
$920$	10.4006	−	14.3152i	0.0113050	−	0.0155600i
$921$	322.438	+	443.798i	0.350096	+	0.481866i
$922$	−47.3836	+	145.832i	−0.0513921	+	0.158169i
$923$		−	898.479i		−	0.973434i
$924$	734.360	+	129.385i	0.794762	+	0.140028i
$925$	−200.175			−0.216406
$926$	−430.996	−	140.039i	−0.465438	−	0.151230i
$927$	−24.3757	+	17.7100i	−0.0262952	+	0.0191046i
$928$	−101.422	−	73.6871i	−0.109290	−	0.0794042i
$929$	−333.204	−	1025.50i	−0.358669	−	1.10387i	−0.953851	−	0.300280i	$-0.902920\pi$
$929$	−333.204	−	1025.50i	−0.358669	−	1.10387i	0.595182	−	0.803591i	$-0.297080\pi$
$930$	−30.6573	+	9.96117i	−0.0329649	+	0.0107109i
$931$	−1249.88	+	1720.31i	−1.34251	+	1.84781i
$932$	117.819	+	162.164i	0.126415	+	0.173995i
$933$	−283.109	+	871.319i	−0.303439	+	0.933890i
$934$		−	888.787i		−	0.951592i
$935$	33.4071	−	62.8501i	0.0357296	−	0.0672194i
$936$	−21.9393			−0.0234394
$937$	191.210	+	62.1278i	0.204066	+	0.0663051i	0.409266	−	0.912415i	$-0.365785\pi$
$937$	191.210	+	62.1278i	0.204066	+	0.0663051i	−0.205200	+	0.978720i	$0.565785\pi$
$938$	304.202	−	221.016i	0.324309	−	0.235625i
$939$	318.161	+	231.157i	0.338829	+	0.246174i
$940$	24.9818	+	76.8862i	0.0265764	+	0.0817938i
$941$	−1503.07	+	488.376i	−1.59731	+	0.518997i	−0.966440	−	0.256893i	$-0.917301\pi$
$941$	−1503.07	+	488.376i	−1.59731	+	0.518997i	−0.630869	+	0.775890i	$0.717301\pi$
$942$	−150.672	+	207.383i	−0.159949	+	0.220151i
$943$	−38.5520	−	53.0622i	−0.0408823	−	0.0562696i
$944$	−61.2043	+	188.367i	−0.0648350	+	0.199542i
$945$			375.283i			0.397125i
$946$	−37.3719	+	5.25741i	−0.0395051	+	0.00555752i
$947$	−1589.44			−1.67839			−0.839195	−	0.543830i	$-0.816974\pi$
$947$	−1589.44			−1.67839			−0.839195	+	0.543830i	$0.816974\pi$
$948$	580.264	+	188.539i	0.612093	+	0.198881i
$949$	631.425	−	458.757i	0.665358	−	0.483411i
$950$	780.283	+	566.909i	0.821351	+	0.596746i
$951$	−217.001	−	667.861i	−0.228182	−	0.702272i
$952$	−148.526	+	48.2591i	−0.156015	+	0.0506923i
$953$	−258.366	+	355.610i	−0.271108	+	0.373148i	−0.922763	−	0.385367i	$-0.874075\pi$
$953$	−258.366	+	355.610i	−0.271108	+	0.373148i	0.651655	+	0.758515i	$0.274075\pi$
$954$	−34.6292	−	47.6630i	−0.0362990	−	0.0499612i
$955$	8.95793	−	27.5697i	0.00938003	−	0.0288688i
$956$			723.697i			0.757005i
$957$	−673.035	+	328.373i	−0.703275	+	0.343128i
$958$	−29.9091			−0.0312204
$959$	−1484.08	−	482.207i	−1.54753	−	0.502823i
$960$	25.7080	−	18.6779i	0.0267791	−	0.0194562i
$961$	750.825	+	545.506i	0.781295	+	0.567644i
$962$	66.5709	+	204.884i	0.0692005	+	0.212977i
$963$	26.7814	−	8.70179i	0.0278103	−	0.00903613i
$964$	189.702	−	261.103i	0.196786	−	0.270853i
$965$	195.978	+	269.740i	0.203086	+	0.279524i
$966$	−71.6660	+	220.565i	−0.0741884	+	0.228329i
$967$		−	293.276i		−	0.303285i	−0.988435	−	0.151642i	$-0.951544\pi$
$967$		−	293.276i		−	0.303285i	0.988435	−	0.151642i	$-0.0484562\pi$
$968$	342.034	+	11.8518i	0.353341	+	0.0122436i
$969$	449.426			0.463804
$970$	75.3522	+	24.4834i	0.0776826	+	0.0252406i
$971$	−1256.93	+	913.212i	−1.29447	+	0.940487i	−0.999885	−	0.0151392i	$-0.995181\pi$
$971$	−1256.93	+	913.212i	−1.29447	+	0.940487i	−0.294583	+	0.955626i	$0.595181\pi$
$972$	38.1438	+	27.7131i	0.0392426	+	0.0285114i
$973$	−229.103	−	705.106i	−0.235460	−	0.724672i
$974$	−860.754	+	279.676i	−0.883731	+	0.287142i
$975$	747.774	−	1029.22i	0.766947	−	1.05561i
$976$	23.4666	+	32.2990i	0.0240436	+	0.0330932i
$977$	−254.761	+	784.074i	−0.260759	+	0.802532i	0.731882	+	0.681432i	$0.238642\pi$
$977$	−254.761	+	784.074i	−0.260759	+	0.802532i	−0.992640	+	0.121101i	$0.961358\pi$
$978$			610.939i			0.624682i
$979$	797.191	+	1633.92i	0.814291	+	1.66897i
$980$	−188.098			−0.191936
$981$	23.5611	+	7.65547i	0.0240174	+	0.00780374i
$982$	−527.127	+	382.980i	−0.536789	+	0.390000i
$983$	−1218.19	−	885.064i	−1.23925	−	0.900370i	−0.241705	−	0.970350i	$-0.577707\pi$
$983$	−1218.19	−	885.064i	−1.23925	−	0.900370i	−0.997548	+	0.0699794i	$0.977707\pi$
$984$	−36.3982	−	112.022i	−0.0369900	−	0.113844i
$985$	188.609	−	61.2827i	0.191481	−	0.0622160i
$986$	92.1879	−	126.886i	0.0934969	−	0.128687i
$987$	−622.803	−	857.215i	−0.631006	−	0.868506i
$988$	320.752	−	987.172i	0.324647	−	0.999162i
$989$		−	11.7377i		−	0.0118683i
$990$	−1.22435	−	8.70317i	−0.00123671	−	0.00879108i
$991$	−1303.62			−1.31545			−0.657727	−	0.753256i	$-0.728482\pi$
$991$	−1303.62			−1.31545			−0.657727	+	0.753256i	$0.728482\pi$
$992$	30.8727	+	10.0311i	0.0311216	+	0.0101120i
$993$	230.269	−	167.300i	0.231892	−	0.168480i
$994$	−638.901	−	464.189i	−0.642758	−	0.466991i
$995$	94.0995	+	289.608i	0.0945723	+	0.291064i
$996$	76.2989	−	24.7910i	0.0766054	−	0.0248906i
$997$	196.761	−	270.818i	0.197353	−	0.271633i	−0.698859	−	0.715260i	$-0.746308\pi$
$997$	196.761	−	270.818i	0.197353	−	0.271633i	0.896212	+	0.443627i	$0.146308\pi$
$998$	−434.284	−	597.741i	−0.435155	−	0.598939i
$999$	69.7522	−	214.675i	0.0698220	−	0.214890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.3.d.a.13.1	✓	8
3.2	odd	2		198.3.j.a.145.2		8
4.3	odd	2		176.3.n.b.145.1		8
11.2	odd	10		242.3.d.e.239.1		8
11.3	even	5		242.3.d.e.161.1		8
11.4	even	5		242.3.b.d.241.2		8
11.5	even	5		242.3.d.c.215.2		8
11.6	odd	10	inner	22.3.d.a.17.1	yes	8
11.7	odd	10		242.3.b.d.241.6		8
11.8	odd	10		242.3.d.d.161.2		8
11.9	even	5		242.3.d.d.239.2		8
11.10	odd	2		242.3.d.c.233.2		8
33.17	even	10		198.3.j.a.127.2		8
33.26	odd	10		2178.3.d.l.1693.6		8
33.29	even	10		2178.3.d.l.1693.2		8
44.39	even	10		176.3.n.b.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.3.d.a.13.1	✓	8	1.1	even	1	trivial
22.3.d.a.17.1	yes	8	11.6	odd	10	inner
176.3.n.b.17.1		8	44.39	even	10
176.3.n.b.145.1		8	4.3	odd	2
198.3.j.a.127.2		8	33.17	even	10
198.3.j.a.145.2		8	3.2	odd	2
242.3.b.d.241.2		8	11.4	even	5
242.3.b.d.241.6		8	11.7	odd	10
242.3.d.c.215.2		8	11.5	even	5
242.3.d.c.233.2		8	11.10	odd	2
242.3.d.d.161.2		8	11.8	odd	10
242.3.d.d.239.2		8	11.9	even	5
242.3.d.e.161.1		8	11.3	even	5
242.3.d.e.239.1		8	11.2	odd	10
2178.3.d.l.1693.2		8	33.29	even	10
2178.3.d.l.1693.6		8	33.26	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	22.d (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(2.48527 - 1.80565i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.399565 - 1.22973i) q^{5} +(-4.13178 + 1.34250i) q^{6} +(-6.48527 + 8.92621i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.135021 - 0.415553i) q^{9} +O(q^{10})\)	\(q+(-1.34500 - 0.437016i) q^{2} +(2.48527 - 1.80565i) q^{3} +(1.61803 + 1.17557i) q^{4} +(-0.399565 - 1.22973i) q^{5} +(-4.13178 + 1.34250i) q^{6} +(-6.48527 + 8.92621i) q^{7} +(-1.66251 - 2.28825i) q^{8} +(0.135021 - 0.415553i) q^{9} +1.82860i q^{10} +(-4.82342 - 9.88608i) q^{11} +6.14392 q^{12} +(16.8835 + 5.48578i) q^{13} +(12.6236 - 9.17155i) q^{14} +(-3.21350 - 2.33474i) q^{15} +(1.23607 + 3.80423i) q^{16} +(-4.75936 + 1.54641i) q^{17} +(-0.363207 + 0.499911i) q^{18} +(-17.1838 - 23.6514i) q^{19} +(0.799129 - 2.45947i) q^{20} +33.8942i q^{21} +(2.16710 + 15.4047i) q^{22} -4.83828 q^{23} +(-8.26355 - 2.68499i) q^{24} +(18.8728 - 13.7119i) q^{25} +(-20.3109 - 14.7567i) q^{26} +(8.12881 + 25.0179i) q^{27} +(-20.9868 + 6.81901i) q^{28} +(13.0262 - 17.9290i) q^{29} +(3.30182 + 4.54457i) q^{30} +(-1.77327 + 5.45757i) q^{31} -5.65685i q^{32} +(-29.8383 - 15.8602i) q^{33} +7.07714 q^{34} +(13.5681 + 4.40856i) q^{35} +(0.706982 - 0.513652i) q^{36} +(-6.94206 - 5.04370i) q^{37} +(12.7761 + 39.3207i) q^{38} +(51.8655 - 16.8521i) q^{39} +(-2.14965 + 2.95874i) q^{40} +(7.96811 + 10.9672i) q^{41} +(14.8123 - 45.5875i) q^{42} +2.42601i q^{43} +(3.81734 - 21.6663i) q^{44} -0.564970 q^{45} +(6.50748 + 2.11441i) q^{46} +(-25.2909 + 18.3749i) q^{47} +(9.94107 + 7.22261i) q^{48} +(-22.4766 - 69.1759i) q^{49} +(-31.3762 + 10.1948i) q^{50} +(-9.03601 + 12.4370i) q^{51} +(20.8692 + 28.7239i) q^{52} +(-29.4626 + 90.6765i) q^{53} -37.2014i q^{54} +(-10.2300 + 9.88165i) q^{55} +31.2072 q^{56} +(-85.4126 - 27.7522i) q^{57} +(-25.3554 + 18.4218i) q^{58} +(40.0587 + 29.1044i) q^{59} +(-2.45489 - 7.55539i) q^{60} +(9.49243 - 3.08428i) q^{61} +(4.77009 - 6.56546i) q^{62} +(2.83366 + 3.90020i) q^{63} +(-2.47214 + 7.60845i) q^{64} -22.9541i q^{65} +(33.2013 + 34.3717i) q^{66} +24.0980 q^{67} +(-9.51873 - 3.09282i) q^{68} +(-12.0244 + 8.73626i) q^{69} +(-16.3225 - 11.8590i) q^{70} +(-15.6399 - 48.1347i) q^{71} +(-1.17536 + 0.381898i) q^{72} +(25.8420 - 35.5685i) q^{73} +(7.13287 + 9.81756i) q^{74} +(22.1451 - 68.1556i) q^{75} -58.4696i q^{76} +(119.526 + 21.0591i) q^{77} -77.1235 q^{78} +(94.4452 + 30.6871i) q^{79} +(4.18430 - 3.04007i) q^{80} +(68.5573 + 49.8098i) q^{81} +(-5.92426 - 18.2330i) q^{82} +(12.4186 - 4.03505i) q^{83} +(-39.8450 + 54.8419i) q^{84} +(3.80335 + 5.23486i) q^{85} +(1.06021 - 3.26298i) q^{86} -68.0790i q^{87} +(-14.6028 + 27.4729i) q^{88} -165.275 q^{89} +(0.759883 + 0.246901i) q^{90} +(-158.461 + 115.129i) q^{91} +(-7.82851 - 5.68774i) q^{92} +(5.44742 + 16.7654i) q^{93} +(42.0464 - 13.6617i) q^{94} +(-22.2189 + 30.5818i) q^{95} +(-10.2143 - 14.0588i) q^{96} +(13.3891 - 41.2075i) q^{97} +102.864i q^{98} +(-4.75946 + 0.669553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9} - 4 q^{11} + 24 q^{12} + 30 q^{13} + 16 q^{14} + 42 q^{15} - 8 q^{16} + 30 q^{17} + 40 q^{18} - 30 q^{19} - 4 q^{20} + 24 q^{22} - 104 q^{23} - 40 q^{24} - 12 q^{25} - 96 q^{26} - 26 q^{27} - 40 q^{28} - 10 q^{29} - 60 q^{30} + 46 q^{31} - 14 q^{33} + 112 q^{34} + 70 q^{35} - 12 q^{36} + 6 q^{37} + 108 q^{38} + 130 q^{39} + 80 q^{40} + 250 q^{41} + 56 q^{42} - 12 q^{44} - 136 q^{45} - 160 q^{46} - 54 q^{47} - 8 q^{48} - 144 q^{49} - 80 q^{50} - 30 q^{51} - 40 q^{52} - 274 q^{53} - 26 q^{55} + 48 q^{56} - 130 q^{57} + 64 q^{58} + 50 q^{59} + 116 q^{60} + 50 q^{61} + 20 q^{62} - 20 q^{63} + 16 q^{64} - 136 q^{66} + 112 q^{67} + 60 q^{68} + 76 q^{69} + 4 q^{70} + 54 q^{71} - 80 q^{72} - 70 q^{73} - 40 q^{74} + 318 q^{75} + 266 q^{77} + 104 q^{78} + 370 q^{79} + 48 q^{80} + 180 q^{81} - 96 q^{82} - 150 q^{83} - 120 q^{84} - 330 q^{85} - 72 q^{86} + 72 q^{88} + 24 q^{89} + 160 q^{90} - 294 q^{91} - 112 q^{92} - 134 q^{93} - 20 q^{94} - 330 q^{95} - 18 q^{97} - 308 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 + 2 * q^5 - 20 * q^6 - 30 * q^7 - 4 * q^9 - 4 * q^11 + 24 * q^12 + 30 * q^13 + 16 * q^14 + 42 * q^15 - 8 * q^16 + 30 * q^17 + 40 * q^18 - 30 * q^19 - 4 * q^20 + 24 * q^22 - 104 * q^23 - 40 * q^24 - 12 * q^25 - 96 * q^26 - 26 * q^27 - 40 * q^28 - 10 * q^29 - 60 * q^30 + 46 * q^31 - 14 * q^33 + 112 * q^34 + 70 * q^35 - 12 * q^36 + 6 * q^37 + 108 * q^38 + 130 * q^39 + 80 * q^40 + 250 * q^41 + 56 * q^42 - 12 * q^44 - 136 * q^45 - 160 * q^46 - 54 * q^47 - 8 * q^48 - 144 * q^49 - 80 * q^50 - 30 * q^51 - 40 * q^52 - 274 * q^53 - 26 * q^55 + 48 * q^56 - 130 * q^57 + 64 * q^58 + 50 * q^59 + 116 * q^60 + 50 * q^61 + 20 * q^62 - 20 * q^63 + 16 * q^64 - 136 * q^66 + 112 * q^67 + 60 * q^68 + 76 * q^69 + 4 * q^70 + 54 * q^71 - 80 * q^72 - 70 * q^73 - 40 * q^74 + 318 * q^75 + 266 * q^77 + 104 * q^78 + 370 * q^79 + 48 * q^80 + 180 * q^81 - 96 * q^82 - 150 * q^83 - 120 * q^84 - 330 * q^85 - 72 * q^86 + 72 * q^88 + 24 * q^89 + 160 * q^90 - 294 * q^91 - 112 * q^92 - 134 * q^93 - 20 * q^94 - 330 * q^95 - 18 * q^97 - 308 * q^99

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