LMFDB - Embedded newform 22.3.d.a.17.1

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			17.1
Root			$-1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	22.17
Dual form			22.3.d.a.13.1

$q$-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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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	0.919113	−	0.393995i	$-0.128907\pi$
$3$	2.48527	+	1.80565i	0.828423	+	0.601884i	−0.0906900	+	0.995879i	$0.528907\pi$
$4$	1.61803	−	1.17557i	0.404508	−	0.293893i
$5$	−0.399565	+	1.22973i	−0.0799129	+	0.245947i	−0.983029	−	0.183450i	$-0.941274\pi$
$5$	−0.399565	+	1.22973i	−0.0799129	+	0.245947i	0.903116	+	0.429396i	$0.141274\pi$
$6$	−4.13178	−	1.34250i	−0.688630	−	0.223749i
$7$	−6.48527	−	8.92621i	−0.926467	−	1.27517i	−0.961222	−	0.275776i	$-0.911065\pi$
$7$	−6.48527	−	8.92621i	−0.926467	−	1.27517i	0.0347550	−	0.999396i	$-0.488935\pi$
$8$	−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	0.423592	−	0.905853i	$-0.360769\pi$
$13$	16.8835	−	5.48578i	1.29873	−	0.421983i	0.875140	+	0.483870i	$0.160769\pi$
$14$	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	0.165670	−	0.986181i	$-0.447021\pi$
$17$	−4.75936	−	1.54641i	−0.279963	−	0.0909654i	−0.445633	+	0.895216i	$0.647021\pi$
$18$	−0.363207	−	0.499911i	−0.0201782	−	0.0277729i
$19$	−17.1838	+	23.6514i	−0.904410	+	1.24481i	0.0646304	+	0.997909i	$0.479413\pi$
$19$	−17.1838	+	23.6514i	−0.904410	+	1.24481i	−0.969040	+	0.246904i	$0.920587\pi$
$20$	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	0.972221	−	0.234066i	$-0.0752033\pi$
$29$	13.0262	+	17.9290i	0.449178	+	0.618240i	−0.523043	+	0.852306i	$0.675203\pi$
$30$	3.30182	−	4.54457i	0.110061	−	0.151486i
$31$	−1.77327	−	5.45757i	−0.0572023	−	0.176050i	0.918373	−	0.395716i	$-0.129503\pi$
$31$	−1.77327	−	5.45757i	−0.0572023	−	0.176050i	−0.975575	+	0.219665i	$0.929503\pi$
$32$			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	−0.677632	−	0.735401i	$-0.736994\pi$
$37$	−6.94206	+	5.04370i	−0.187623	+	0.136316i	0.490009	+	0.871718i	$0.336994\pi$
$38$	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	−0.700713	−	0.713443i	$-0.747135\pi$
$41$	7.96811	−	10.9672i	0.194344	−	0.267492i	0.895057	+	0.445951i	$0.147135\pi$
$42$	14.8123	+	45.5875i	0.352674	+	1.08542i
$43$		−	2.42601i		−	0.0564188i	−0.999602	−	0.0282094i	$-0.991019\pi$
$43$		−	2.42601i		−	0.0564188i	0.999602	−	0.0282094i	$-0.00898053\pi$
$44$	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	0.285276	−	0.958446i	$-0.407915\pi$
$47$	−25.2909	−	18.3749i	−0.538105	−	0.390956i	−0.823381	+	0.567489i	$0.807915\pi$
$48$	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	−0.693560	−	0.720399i	$-0.743959\pi$
$53$	−29.4626	−	90.6765i	−0.555898	−	1.71088i	0.137662	−	0.990479i	$-0.456041\pi$
$54$			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	−0.194052	−	0.980991i	$-0.562163\pi$
$59$	40.0587	−	29.1044i	0.678961	−	0.493294i	0.873013	+	0.487697i	$0.162163\pi$
$60$	−2.45489	+	7.55539i	−0.0409149	+	0.125923i
$61$	9.49243	+	3.08428i	0.155614	+	0.0505619i	0.385788	−	0.922587i	$-0.373930\pi$
$61$	9.49243	+	3.08428i	0.155614	+	0.0505619i	−0.230174	+	0.973149i	$0.573930\pi$
$62$	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	0.778456	+	0.627699i	$0.216003\pi$
$71$	−15.6399	+	48.1347i	−0.220280	+	0.677953i	−0.998736	+	0.0502541i	$0.983997\pi$
$72$	−1.17536	−	0.381898i	−0.0163245	−	0.00530414i
$73$	25.8420	+	35.5685i	0.354000	+	0.487239i	0.948465	−	0.316882i	$-0.102636\pi$
$73$	25.8420	+	35.5685i	0.354000	+	0.487239i	−0.594465	+	0.804122i	$0.702636\pi$
$74$	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	0.357402	−	0.933951i	$-0.383662\pi$
$79$	94.4452	−	30.6871i	1.19551	−	0.388445i	0.838107	+	0.545506i	$0.183662\pi$
$80$	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	0.382870	−	0.923802i	$-0.374936\pi$
$83$	12.4186	+	4.03505i	0.149622	+	0.0486151i	−0.233249	+	0.972417i	$0.574936\pi$
$84$	−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	0.996049	−	0.0888017i	$-0.0283037\pi$
$97$	13.3891	+	41.2075i	0.138032	+	0.424819i	−0.858017	+	0.513621i	$0.828304\pi$
$98$		−	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	−0.573547	−	0.819173i	$-0.694433\pi$
$101$	−56.1619	+	18.2481i	−0.556059	+	0.180674i	0.0174882	+	0.999847i	$0.494433\pi$
$102$	17.5886	+	12.7789i	0.172437	+	0.125283i
$103$	−55.7874	+	40.5319i	−0.541626	+	0.393514i	−0.824688	−	0.565587i	$-0.808650\pi$
$103$	−55.7874	+	40.5319i	−0.541626	+	0.393514i	0.283063	+	0.959101i	$0.408650\pi$
$104$	−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	−0.594443	−	0.804138i	$-0.702627\pi$
$107$	37.8813	−	52.1391i	0.354031	−	0.487281i	0.948473	+	0.316857i	$0.102627\pi$
$108$	−16.2576	−	50.0358i	−0.150534	−	0.463295i
$109$		−	56.6982i		−	0.520167i	−0.965586	−	0.260083i	$-0.916250\pi$
$109$		−	56.6982i		−	0.520167i	0.965586	−	0.260083i	$-0.0837500\pi$
$110$	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	0.996638	−	0.0819274i	$-0.0261076\pi$
$113$	138.617	+	100.711i	1.22670	+	0.891249i	0.230061	+	0.973176i	$0.426108\pi$
$114$	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	−0.306954	−	0.951725i	$-0.599310\pi$
$127$	−141.566	−	45.9976i	−1.11469	−	0.362186i	−0.807740	+	0.589539i	$0.799310\pi$
$128$	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	$0.183640\pi$
$131$			142.907i			1.09089i	−0.838145	+	0.545447i	$0.816360\pi$
$132$	−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	−0.655063	−	0.755574i	$-0.727358\pi$
$137$	43.7043	−	134.508i	0.319009	−	0.981810i	0.974073	−	0.226236i	$-0.0726421\pi$
$138$	19.9907	+	6.49537i	0.144860	+	0.0470679i
$139$	−39.4964	−	54.3621i	−0.284147	−	0.391094i	0.642955	−	0.765904i	$-0.277708\pi$
$139$	−39.4964	−	54.3621i	−0.284147	−	0.391094i	−0.927102	+	0.374809i	$0.877708\pi$
$140$	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	−0.122136	−	0.992513i	$-0.538974\pi$
$149$	−119.845	−	38.9401i	−0.804331	−	0.261343i	−0.682195	+	0.731170i	$0.738974\pi$
$150$	−59.5701	−	81.9913i	−0.397134	−	0.546608i
$151$	61.7808	−	85.0339i	0.409144	−	0.563139i	−0.553865	−	0.832606i	$-0.686848\pi$
$151$	61.7808	−	85.0339i	0.409144	−	0.563139i	0.963009	+	0.269468i	$0.0868477\pi$
$152$	−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	0.729338	−	0.684153i	$-0.239828\pi$
$157$	47.7355	+	34.6819i	0.304048	+	0.220904i	−0.425290	+	0.905057i	$0.639828\pi$
$158$	−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	0.991320	+	0.131470i	$0.0419696\pi$
$163$	43.4560	+	133.744i	0.266601	+	0.820514i	−0.724719	+	0.689045i	$0.758030\pi$
$164$		−	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	−0.197724	−	0.980258i	$-0.563355\pi$
$167$	36.4886	−	11.8559i	0.218494	−	0.0709932i	0.416219	+	0.909265i	$0.363355\pi$
$168$	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	−0.0168721	+	0.999858i	$0.505371\pi$
$173$	−166.526	+	229.204i	−0.962580	+	1.32488i	−0.945707	+	0.325019i	$0.894629\pi$
$174$	−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	0.999491	−	0.0319036i	$-0.0101570\pi$
$179$	228.764	+	166.206i	1.27801	+	0.928528i	0.278518	+	0.960431i	$0.410157\pi$
$180$	−0.914140	+	0.664162i	−0.00507856	+	0.00368979i
$181$	−86.2701	+	265.512i	−0.476630	+	1.46692i	0.367116	+	0.930175i	$0.380345\pi$
$181$	−86.2701	+	265.512i	−0.476630	+	1.46692i	−0.843746	+	0.536742i	$0.819655\pi$
$182$	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	−0.539292	−	0.842119i	$-0.681308\pi$
$191$	18.1375	−	13.1777i	0.0949609	−	0.0689931i	0.634253	+	0.773126i	$0.281308\pi$
$192$	7.59430	−	23.3729i	0.0395537	−	0.121734i
$193$	−245.239	−	79.6830i	−1.27067	−	0.412865i	−0.405384	−	0.914146i	$-0.632862\pi$
$193$	−245.239	−	79.6830i	−1.27067	−	0.412865i	−0.865285	+	0.501281i	$0.832862\pi$
$194$	−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	$-0.872726\pi$
$197$		−	153.374i		−	0.778547i	0.921122	−	0.389273i	$-0.127274\pi$
$198$	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	0.318512	−	0.947919i	$-0.396817\pi$
$211$	239.140	−	77.7014i	1.13337	−	0.368253i	0.814855	+	0.579665i	$0.196817\pi$
$212$	−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	0.562430	−	0.826845i	$-0.309867\pi$
$223$	−11.1825	−	8.12457i	−0.0501458	−	0.0364330i	−0.612576	+	0.790412i	$0.709867\pi$
$224$	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	0.356631	−	0.934245i	$-0.383925\pi$
$227$	−145.755	−	200.615i	−0.642094	−	0.883766i	−0.998725	+	0.0504789i	$0.983925\pi$
$228$	−105.576	+	145.313i	−0.463052	+	0.637336i
$229$	93.4415	+	287.583i	0.408042	+	1.25582i	0.918329	+	0.395819i	$0.129539\pi$
$229$	93.4415	+	287.583i	0.408042	+	1.25582i	−0.510287	+	0.860004i	$0.670461\pi$
$230$			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	−0.0972417	−	0.995261i	$-0.531002\pi$
$233$	95.3175	−	30.9705i	0.409088	−	0.132921i	0.506329	+	0.862340i	$0.331002\pi$
$234$	−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	−0.0836623	−	0.996494i	$-0.526662\pi$
$239$	212.689	−	292.742i	0.889913	−	1.22486i	0.973575	−	0.228366i	$-0.0733383\pi$
$240$	4.90979	+	15.1108i	0.0204574	+	0.0629615i
$241$			161.370i			0.669586i	0.942292	+	0.334793i	$0.108666\pi$
$241$			161.370i			0.669586i	−0.942292	+	0.334793i	$0.891334\pi$
$242$	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	−0.998961	−	0.0455738i	$-0.985488\pi$
$251$	−54.6106	−	168.074i	−0.217572	−	0.669618i	0.781389	−	0.624044i	$-0.214512\pi$
$252$		−	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	0.0496800	−	0.998765i	$-0.484180\pi$
$257$	260.833	−	189.506i	1.01491	−	0.737378i	0.965234	+	0.261387i	$0.0841798\pi$
$258$	−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	$0.275569\pi$
$263$			400.583i			1.52313i	−0.648089	+	0.761565i	$0.724431\pi$
$264$	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	−0.883920	−	0.467638i	$-0.845105\pi$
$269$	28.5293	−	87.8043i	0.106057	−	0.326410i	0.989977	+	0.141228i	$0.0451051\pi$
$270$	−45.7478	−	14.8644i	−0.169436	−	0.0550532i
$271$	91.5443	+	126.000i	0.337802	+	0.464944i	0.943798	−	0.330523i	$-0.107225\pi$
$271$	91.5443	+	126.000i	0.337802	+	0.464944i	−0.605996	+	0.795468i	$0.707225\pi$
$272$	−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	−0.771964	−	0.635666i	$-0.780725\pi$
$277$	−283.332	+	92.0603i	−1.02286	+	0.332347i	−0.250897	+	0.968014i	$0.580725\pi$
$278$	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	0.634144	−	0.773215i	$-0.281352\pi$
$281$	194.647	+	63.2446i	0.692694	+	0.225070i	0.0585494	+	0.998285i	$0.481352\pi$
$282$	79.8282	+	109.874i	0.283079	+	0.389625i
$283$	54.0332	−	74.3704i	0.190930	−	0.262793i	−0.702810	−	0.711377i	$-0.748072\pi$
$283$	54.0332	−	74.3704i	0.190930	−	0.262793i	0.893740	+	0.448585i	$0.148072\pi$
$284$	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	0.896465	−	0.443114i	$-0.146126\pi$
$293$	58.0186	+	79.8558i	0.198016	+	0.272545i	−0.698450	+	0.715659i	$0.746126\pi$
$294$	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	$-0.906068\pi$
$307$		−	178.572i		−	0.581666i	0.956774	−	0.290833i	$-0.0939325\pi$
$308$	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	0.127912	−	0.991786i	$-0.459173\pi$
$311$	−241.275	−	175.297i	−0.775805	−	0.563656i	−0.903717	+	0.428130i	$0.859173\pi$
$312$	−124.789	+	90.6642i	−0.399963	+	0.290590i
$313$	39.5599	−	121.753i	0.126390	−	0.388987i	−0.867762	−	0.496980i	$-0.834442\pi$
$313$	39.5599	−	121.753i	0.126390	−	0.388987i	0.994152	+	0.107993i	$0.0344423\pi$
$314$	−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	0.998504	+	0.0546790i	$0.0174136\pi$
$317$	70.6393	+	217.405i	0.222837	+	0.685821i	−0.775667	+	0.631142i	$0.782586\pi$
$318$			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	0.966754	−	0.255709i	$-0.0823087\pi$
$337$	143.163	+	197.048i	0.424817	+	0.584711i	−0.541937	+	0.840419i	$0.682309\pi$
$338$	−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	0.782610	−	0.622512i	$-0.213888\pi$
$347$	364.299	+	118.368i	1.04985	+	0.341118i	0.267242	+	0.963630i	$0.413888\pi$
$348$	80.0317	+	110.154i	0.229976	+	0.316535i
$349$	262.590	−	361.423i	0.752405	−	1.03560i	−0.245402	−	0.969421i	$-0.578920\pi$
$349$	262.590	−	361.423i	0.752405	−	1.03560i	0.997808	−	0.0661760i	$-0.0210799\pi$
$350$	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	0.925817	−	0.377972i	$-0.123379\pi$
$359$	100.610	+	138.478i	0.280251	+	0.385732i	−0.645566	+	0.763704i	$0.723379\pi$
$360$	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	−0.953050	−	0.302811i	$-0.902075\pi$
$367$	−352.162	+	255.860i	−0.959569	+	0.697167i	−0.00651803	+	0.999979i	$0.502075\pi$
$368$	−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	$-0.794405\pi$
$373$		−	449.027i		−	1.20383i	0.798561	−	0.601913i	$-0.205595\pi$
$374$	−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	−0.956463	−	0.291853i	$-0.905728\pi$
$379$	−4.21499	+	12.9724i	−0.0111213	+	0.0342280i	0.945342	+	0.326081i	$0.105728\pi$
$380$	−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	−0.731830	−	0.681487i	$-0.761334\pi$
$383$	−206.948	−	636.921i	−0.540335	−	1.66298i	0.191495	−	0.981493i	$-0.438666\pi$
$384$			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	−0.212722	−	0.977113i	$-0.568233\pi$
$389$	253.174	−	183.942i	0.650833	−	0.472858i	0.863555	+	0.504255i	$0.168233\pi$
$390$	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	−0.996044	−	0.0888670i	$-0.971675\pi$
$401$	−55.3351	+	170.304i	−0.137993	+	0.424698i	0.858051	+	0.513565i	$0.171675\pi$
$402$	−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	−0.261336	−	0.965248i	$-0.584163\pi$
$409$	38.6900	−	12.5711i	0.0945965	−	0.0307363i	0.355933	+	0.934512i	$0.384163\pi$
$410$	−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	0.876011	−	0.482291i	$-0.160195\pi$
$421$	289.659	+	210.450i	0.688027	+	0.499881i	−0.187984	+	0.982172i	$0.560195\pi$
$422$	−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	−0.238609	−	0.971116i	$-0.576692\pi$
$431$	59.9777	−	19.4879i	0.139159	−	0.0452156i	0.377769	+	0.925900i	$0.376692\pi$
$432$	−85.1260	−	61.8477i	−0.197051	−	0.143166i
$433$	−629.268	+	457.190i	−1.45327	+	1.05587i	−0.468221	+	0.883611i	$0.655105\pi$
$433$	−629.268	+	457.190i	−1.45327	+	1.05587i	−0.985053	+	0.172254i	$0.944895\pi$
$434$	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	$-0.930232\pi$
$439$		−	190.905i		−	0.434863i	0.976076	−	0.217432i	$-0.0697679\pi$
$440$	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	−0.0202107	−	0.999796i	$-0.506434\pi$
$443$	−432.952	−	314.558i	−0.977318	−	0.710063i	−0.957108	+	0.289732i	$0.906434\pi$
$444$	−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	0.958435	+	0.285312i	$0.0920971\pi$
$449$	157.485	+	484.690i	0.350747	+	1.07949i	−0.607688	+	0.794176i	$0.707903\pi$
$450$		−	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	−0.700507	−	0.713646i	$-0.747043\pi$
$457$	−770.822	−	250.455i	−1.68670	−	0.548042i	−0.986192	+	0.165604i	$0.947043\pi$
$458$	−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	$0.0375194\pi$
$461$			108.425i			0.235196i	−0.993061	+	0.117598i	$0.962481\pi$
$462$	−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	−0.495617	−	0.868541i	$-0.665058\pi$
$467$	194.207	−	597.708i	0.415861	−	1.27989i	0.911478	−	0.411348i	$-0.134942\pi$
$468$	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	0.329937	−	0.944003i	$-0.392972\pi$
$479$	20.1138	+	6.53538i	0.0419913	+	0.0136438i	−0.287946	+	0.957647i	$0.592972\pi$
$480$	−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	0.974665	−	0.223670i	$-0.0718038\pi$
$487$	517.744	+	376.163i	1.06313	+	0.772409i	0.0884652	+	0.996079i	$0.471804\pi$
$488$	−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	0.990221	−	0.139510i	$-0.0445527\pi$
$491$	270.808	+	372.735i	0.551544	+	0.759135i	−0.438677	+	0.898645i	$0.644553\pi$
$492$	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	−0.0772973	−	0.997008i	$-0.524629\pi$
$499$	422.667	−	307.085i	0.847028	−	0.615402i	0.924325	+	0.381607i	$0.124629\pi$
$500$	−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	−0.477173	−	0.878809i	$-0.658339\pi$
$503$	254.557	−	350.368i	0.506078	−	0.696557i	0.983252	+	0.182252i	$0.0583387\pi$
$504$	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	0.433762	−	0.901028i	$-0.357186\pi$
$509$	−147.166	−	106.922i	−0.289127	−	0.210063i	−0.722888	+	0.690965i	$0.757186\pi$
$510$	−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	−0.972236	−	0.234000i	$-0.924818\pi$
$521$	−547.116	+	397.503i	−1.05013	+	0.762961i	−0.0778899	+	0.996962i	$0.524818\pi$
$522$	4.23170	−	13.0238i	0.00810671	−	0.0249499i
$523$	778.962	+	253.100i	1.48941	+	0.483939i	0.936909	−	0.349572i	$-0.113673\pi$
$523$	778.962	+	253.100i	1.48941	+	0.483939i	0.552502	+	0.833511i	$0.313673\pi$
$524$	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	0.296345	−	0.955081i	$-0.404232\pi$
$541$	593.734	−	192.916i	1.09748	−	0.356591i	0.801131	+	0.598489i	$0.204232\pi$
$542$	−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	−0.0145763	+	0.999894i	$0.504640\pi$
$547$	−525.682	+	723.539i	−0.961027	+	1.32274i	−0.946451	+	0.322847i	$0.895360\pi$
$548$	−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	0.862204	−	0.506561i	$-0.169084\pi$
$557$	63.4979	+	87.3973i	0.114000	+	0.156907i	−0.748204	+	0.663469i	$0.769084\pi$
$558$	−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	−0.188038	−	0.982162i	$-0.560213\pi$
$563$	133.507	−	43.3791i	0.237135	−	0.0770500i	0.425174	+	0.905112i	$0.360213\pi$
$564$	−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	0.104456	−	0.994529i	$-0.466690\pi$
$569$	579.260	−	797.283i	1.01803	−	1.40120i	0.913575	−	0.406670i	$-0.133310\pi$
$570$	50.7479	+	156.186i	0.0890313	+	0.274010i
$571$			641.392i			1.12328i	0.827382	+	0.561640i	$0.189829\pi$
$571$			641.392i			1.12328i	−0.827382	+	0.561640i	$0.810171\pi$
$572$	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	−0.474191	−	0.880422i	$-0.657260\pi$
$577$	246.342	−	758.164i	0.426936	−	1.31398i	0.901128	−	0.433553i	$-0.142740\pi$
$578$	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	−0.898111	−	0.439769i	$-0.855060\pi$
$587$	−444.592	+	323.015i	−0.757397	+	0.550281i	0.140714	+	0.990050i	$0.455060\pi$
$588$	−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	$0.269120\pi$
$593$			887.460i			1.49656i	−0.663383	+	0.748280i	$0.730880\pi$
$594$	−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	0.177000	+	0.984211i	$0.443361\pi$
$599$	−326.276	+	1004.17i	−0.544701	+	1.67642i	−0.721701	+	0.692205i	$0.756639\pi$
$600$	−192.773	−	62.6358i	−0.321288	−	0.104393i
$601$	−518.251	−	713.311i	−0.862314	−	1.18687i	−0.981013	−	0.193943i	$-0.937872\pi$
$601$	−518.251	−	713.311i	−0.862314	−	1.18687i	0.118699	−	0.992930i	$-0.462128\pi$
$602$	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	−0.742752	−	0.669567i	$-0.766480\pi$
$607$	−576.704	+	187.383i	−0.950090	+	0.308703i	−0.207338	+	0.978269i	$0.566480\pi$
$608$	−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	−0.787847	−	0.615871i	$-0.788804\pi$
$613$	25.3407	−	34.8785i	0.0413388	−	0.0568980i	0.829186	+	0.558973i	$0.188804\pi$
$614$	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	0.576593	−	0.817031i	$-0.304382\pi$
$619$	−13.7867	−	10.0167i	−0.0222726	−	0.0161820i	−0.598866	+	0.800849i	$0.704382\pi$
$620$	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	0.410525	−	0.911849i	$-0.365346\pi$
$631$	886.305	−	643.939i	1.40460	−	1.02050i	0.994079	−	0.108655i	$-0.0346545\pi$
$632$	−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	0.889198	−	0.457523i	$-0.151263\pi$
$641$	467.190	+	339.433i	0.728846	+	0.529537i	−0.160352	+	0.987060i	$0.551263\pi$
$642$	−226.513	+	164.572i	−0.352825	+	0.256342i
$643$	−137.849	+	424.256i	−0.214384	+	0.659808i	0.784812	+	0.619734i	$0.212759\pi$
$643$	−137.849	+	424.256i	−0.214384	+	0.659808i	−0.999197	+	0.0400739i	$0.987241\pi$
$644$	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	−0.999824	−	0.0187464i	$-0.994032\pi$
$647$	−130.673	−	402.172i	−0.201968	−	0.621594i	0.797856	−	0.602848i	$-0.205968\pi$
$648$			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	−0.0508038	−	0.998709i	$-0.516178\pi$
$653$	576.811	−	419.078i	0.883325	−	0.641773i	0.934129	+	0.356935i	$0.116178\pi$
$654$	−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	$-0.781641\pi$
$659$		−	834.878i		−	1.26689i	0.773789	−	0.633443i	$-0.218359\pi$
$660$	−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	−0.994928	−	0.100590i	$-0.967927\pi$
$673$	−1171.50	+	380.644i	−1.74072	+	0.565593i	−0.745788	+	0.666183i	$0.767927\pi$
$674$	−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	−0.438180	−	0.898887i	$-0.644377\pi$
$677$	−894.336	−	290.587i	−1.32103	−	0.429228i	−0.882848	+	0.469659i	$0.844377\pi$
$678$	−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	0.943242	−	0.332108i	$-0.107760\pi$
$691$	−10.4098	−	32.0381i	−0.0150649	−	0.0463649i	−0.958306	+	0.285743i	$0.907760\pi$
$692$			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	−0.235951	+	0.971765i	$0.575820\pi$
$701$	−762.156	+	1049.02i	−1.08724	+	1.49646i	−0.851291	+	0.524694i	$0.824180\pi$
$702$	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	−0.110888	−	0.993833i	$-0.535369\pi$
$709$	399.155	−	1228.47i	0.562983	−	1.73268i	0.673870	−	0.738850i	$-0.264631\pi$
$710$	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	−0.621771	−	0.783199i	$-0.713586\pi$
$719$	−49.6409	+	36.0662i	−0.0690416	+	0.0501617i	0.552729	+	0.833361i	$0.313586\pi$
$720$	−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	0.990439	+	0.137948i	$0.0440507\pi$
$733$	597.815	+	822.822i	0.815573	+	1.12254i	−0.174866	+	0.984592i	$0.555949\pi$
$734$	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	−0.514927	−	0.857234i	$-0.672181\pi$
$739$	−316.027	+	102.683i	−0.427641	+	0.138949i	0.0872852	+	0.996183i	$0.472181\pi$
$740$	−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	−0.0221495	−	0.999755i	$-0.507051\pi$
$743$	−466.388	−	151.539i	−0.627710	−	0.203955i	−0.605560	+	0.795799i	$0.707051\pi$
$744$	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	0.970840	−	0.239729i	$-0.0770584\pi$
$751$	783.181	+	569.014i	1.04285	+	0.757675i	0.0720106	+	0.997404i	$0.477058\pi$
$752$	−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	0.898289	−	0.439405i	$-0.144811\pi$
$757$	−65.6453	−	202.035i	−0.0867176	−	0.266889i	−0.985007	+	0.172515i	$0.944811\pi$
$758$		−	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	−0.0657608	−	0.997835i	$-0.520947\pi$
$761$	355.806	−	115.608i	0.467550	−	0.151916i	0.533311	+	0.845919i	$0.320947\pi$
$762$	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	$-0.862863\pi$
$769$		−	642.305i		−	0.835248i	0.908620	−	0.417624i	$-0.137137\pi$
$770$	−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	0.516537	−	0.856265i	$-0.327221\pi$
$773$	−106.829	−	77.6155i	−0.138200	−	0.100408i	−0.654737	+	0.755856i	$0.727221\pi$
$774$	−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	0.761021	−	0.648728i	$-0.224699\pi$
$787$	783.369	+	254.532i	0.995387	+	0.323421i	0.234366	+	0.972148i	$0.424699\pi$
$788$	−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	−0.999447	−	0.0332558i	$-0.989412\pi$
$797$	−136.550	+	420.258i	−0.171330	+	0.527300i	0.828117	+	0.560556i	$0.189412\pi$
$798$	−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	0.585425	−	0.810727i	$-0.300928\pi$
$809$	471.251	+	153.119i	0.582511	+	0.189269i	−0.00291426	+	0.999996i	$0.500928\pi$
$810$	−91.0825	−	125.364i	−0.112447	−	0.154771i
$811$	−509.110	+	700.729i	−0.627755	+	0.864031i	−0.997889	−	0.0649476i	$-0.979312\pi$
$811$	−509.110	+	700.729i	−0.627755	+	0.864031i	0.370133	+	0.928979i	$0.379312\pi$
$812$	−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	0.697230	−	0.716847i	$-0.254416\pi$
$821$	−164.190	−	225.988i	−0.199988	−	0.275260i	−0.897218	+	0.441587i	$0.854416\pi$
$822$	−361.153	+	497.084i	−0.439359	+	0.604725i
$823$	−407.602	−	1254.47i	−0.495264	−	1.52426i	−0.816545	−	0.577281i	$-0.804114\pi$
$823$	−407.602	−	1254.47i	−0.495264	−	1.52426i	0.321282	−	0.946984i	$-0.395886\pi$
$824$		−	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	−0.251434	−	0.967874i	$-0.580902\pi$
$827$	94.3228	−	30.6473i	0.114054	−	0.0370585i	0.365488	+	0.930816i	$0.380902\pi$
$828$	−3.42058	−	2.48519i	−0.00413113	−	0.00300144i
$829$	−181.366	+	131.770i	−0.218777	+	0.158951i	−0.691776	−	0.722112i	$-0.743171\pi$
$829$	−181.366	+	131.770i	−0.218777	+	0.158951i	0.472999	+	0.881063i	$0.343171\pi$
$830$	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	0.996952	−	0.0780117i	$-0.0248571\pi$
$839$	1032.67	+	750.279i	1.23083	+	0.894253i	0.233882	+	0.972265i	$0.424857\pi$
$840$	−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	0.779538	−	0.626355i	$-0.215454\pi$
$853$	888.856	+	288.807i	1.04203	+	0.338578i	0.262497	+	0.964933i	$0.415454\pi$
$854$	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	$-0.701068\pi$
$857$		−	1383.27i		−	1.61408i	0.590497	−	0.807040i	$-0.298932\pi$
$858$	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	−0.710911	−	0.703282i	$-0.751717\pi$
$863$	239.575	−	737.336i	0.277607	−	0.854386i	0.988518	−	0.151104i	$-0.0482829\pi$
$864$	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	−0.942999	−	0.332795i	$-0.892008\pi$
$877$	−293.874	+	404.483i	−0.335090	+	0.461212i	0.607909	+	0.794007i	$0.292008\pi$
$878$	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	0.0647360	−	0.997902i	$-0.479379\pi$
$883$	−763.195	−	554.494i	−0.864321	−	0.627966i	−0.929057	+	0.369936i	$0.879379\pi$
$884$	−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	0.577858	−	0.816137i	$-0.303889\pi$
$887$	−334.312	−	460.141i	−0.376902	−	0.518761i	−0.954761	+	0.297376i	$0.903889\pi$
$888$	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	−0.892289	−	0.451464i	$-0.850902\pi$
$907$	86.1215	−	265.055i	0.0949521	−	0.292232i	0.987241	+	0.159232i	$0.0509018\pi$
$908$	−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	0.999276	−	0.0380397i	$-0.0121113\pi$
$911$	153.490	+	472.395i	0.168486	+	0.518545i	−0.830791	+	0.556585i	$0.812111\pi$
$912$			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	0.204025	−	0.978966i	$-0.434598\pi$
$919$	−189.624	−	61.6127i	−0.206338	−	0.0670432i	−0.410362	+	0.911923i	$0.634598\pi$
$920$	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	0.595182	+	0.803591i	$0.297080\pi$
$929$	−333.204	+	1025.50i	−0.358669	+	1.10387i	−0.953851	+	0.300280i	$0.902920\pi$
$930$	−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	−0.205200	−	0.978720i	$-0.565785\pi$
$937$	191.210	−	62.1278i	0.204066	−	0.0663051i	0.409266	+	0.912415i	$0.365785\pi$
$938$	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	−0.630869	−	0.775890i	$-0.717301\pi$
$941$	−1503.07	−	488.376i	−1.59731	−	0.518997i	−0.966440	+	0.256893i	$0.917301\pi$
$942$	−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	0.651655	−	0.758515i	$-0.274075\pi$
$953$	−258.366	−	355.610i	−0.271108	−	0.373148i	−0.922763	+	0.385367i	$0.874075\pi$
$954$	−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	$0.0484562\pi$
$967$			293.276i			0.303285i	−0.988435	+	0.151642i	$0.951544\pi$
$968$	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	−0.294583	−	0.955626i	$-0.595181\pi$
$971$	−1256.93	−	913.212i	−1.29447	−	0.940487i	−0.999885	+	0.0151392i	$0.995181\pi$
$972$	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	−0.992640	−	0.121101i	$-0.961358\pi$
$977$	−254.761	−	784.074i	−0.260759	−	0.802532i	0.731882	−	0.681432i	$-0.238642\pi$
$978$		−	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	−0.997548	−	0.0699794i	$-0.977707\pi$
$983$	−1218.19	+	885.064i	−1.23925	+	0.900370i	−0.241705	+	0.970350i	$0.577707\pi$
$984$	−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	0.896212	−	0.443627i	$-0.146308\pi$
$997$	196.761	+	270.818i	0.197353	+	0.271633i	−0.698859	+	0.715260i	$0.746308\pi$
$998$	−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.17.1	yes	8
3.2	odd	2		198.3.j.a.127.2		8
4.3	odd	2		176.3.n.b.17.1		8
11.2	odd	10	inner	22.3.d.a.13.1	✓	8
11.3	even	5		242.3.b.d.241.6		8
11.4	even	5		242.3.d.e.239.1		8
11.5	even	5		242.3.d.d.161.2		8
11.6	odd	10		242.3.d.e.161.1		8
11.7	odd	10		242.3.d.d.239.2		8
11.8	odd	10		242.3.b.d.241.2		8
11.9	even	5		242.3.d.c.233.2		8
11.10	odd	2		242.3.d.c.215.2		8
33.2	even	10		198.3.j.a.145.2		8
33.8	even	10		2178.3.d.l.1693.6		8
33.14	odd	10		2178.3.d.l.1693.2		8
44.35	even	10		176.3.n.b.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.3.d.a.13.1	✓	8	11.2	odd	10	inner
22.3.d.a.17.1	yes	8	1.1	even	1	trivial
176.3.n.b.17.1		8	4.3	odd	2
176.3.n.b.145.1		8	44.35	even	10
198.3.j.a.127.2		8	3.2	odd	2
198.3.j.a.145.2		8	33.2	even	10
242.3.b.d.241.2		8	11.8	odd	10
242.3.b.d.241.6		8	11.3	even	5
242.3.d.c.215.2		8	11.10	odd	2
242.3.d.c.233.2		8	11.9	even	5
242.3.d.d.161.2		8	11.5	even	5
242.3.d.d.239.2		8	11.7	odd	10
242.3.d.e.161.1		8	11.6	odd	10
242.3.d.e.239.1		8	11.4	even	5
2178.3.d.l.1693.2		8	33.14	odd	10
2178.3.d.l.1693.6		8	33.8	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 $\F_{q}$

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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