LMFDB - Embedded newform 22.3.d.a.19.1

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			19.1
Root			$-0.831254 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	22.19
Dual form			22.3.d.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831254 - 1.14412i) q^{2} +(-1.32276 - 4.07104i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(6.27955 + 4.56236i) q^{5} +(-3.55822 + 4.89747i) q^{6} +(-2.67724 - 0.869888i) q^{7} +(2.68999 - 0.874032i) q^{8} +(-7.54250 + 5.47994i) q^{9} +O(q^{10})$	\(q+(-0.831254 - 1.14412i) q^{2} +(-1.32276 - 4.07104i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(6.27955 + 4.56236i) q^{5} +(-3.55822 + 4.89747i) q^{6} +(-2.67724 - 0.869888i) q^{7} +(2.68999 - 0.874032i) q^{8} +(-7.54250 + 5.47994i) q^{9} -10.9771i q^{10} +(2.55337 + 10.6995i) q^{11} +8.56108 q^{12} +(-5.81594 - 8.00495i) q^{13} +(1.23021 + 3.78619i) q^{14} +(10.2672 - 31.5992i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-4.12316 + 5.67504i) q^{17} +(12.5395 + 4.07432i) q^{18} +(-16.8237 + 5.46635i) q^{19} +(-12.5591 + 9.12472i) q^{20} +12.0498i q^{21} +(10.1191 - 11.8154i) q^{22} +17.7682 q^{23} +(-7.11643 - 9.79493i) q^{24} +(10.8922 + 33.5228i) q^{25} +(-4.32413 + 13.3083i) q^{26} +(1.11869 + 0.812775i) q^{27} +(3.30925 - 4.55479i) q^{28} +(-29.6111 - 9.62124i) q^{29} +(-44.6880 + 14.5200i) q^{30} +(9.04205 - 6.56943i) q^{31} +5.65685i q^{32} +(40.1808 - 24.5478i) q^{33} +9.92033 q^{34} +(-12.8431 - 17.6770i) q^{35} +(-5.76195 - 17.7335i) q^{36} +(6.14453 - 18.9109i) q^{37} +(20.2389 + 14.7044i) q^{38} +(-24.8954 + 34.2655i) q^{39} +(20.8796 + 6.78420i) q^{40} +(76.0518 - 24.7107i) q^{41} +(13.7864 - 10.0164i) q^{42} +20.7470i q^{43} +(-21.9298 - 1.75588i) q^{44} -72.3650 q^{45} +(-14.7699 - 20.3291i) q^{46} +(-8.30906 - 25.5727i) q^{47} +(-5.29104 + 16.2841i) q^{48} +(-33.2309 - 24.1437i) q^{49} +(29.3000 - 40.3280i) q^{50} +(28.5572 + 9.27881i) q^{51} +(18.8208 - 6.11524i) q^{52} +(-52.0949 + 37.8492i) q^{53} -1.95554i q^{54} +(-32.7812 + 78.8378i) q^{55} -7.96207 q^{56} +(44.5074 + 61.2592i) q^{57} +(13.6065 + 41.8765i) q^{58} +(-11.0835 + 34.1116i) q^{59} +(53.7598 + 39.0588i) q^{60} +(30.4499 - 41.9107i) q^{61} +(-15.0325 - 4.88435i) q^{62} +(24.9600 - 8.11000i) q^{63} +(6.47214 - 4.70228i) q^{64} -76.8019i q^{65} +(-61.4861 - 25.5663i) q^{66} -17.1328 q^{67} +(-8.24631 - 11.3501i) q^{68} +(-23.5031 - 72.3352i) q^{69} +(-9.54881 + 29.3882i) q^{70} +(-25.5662 - 18.5749i) q^{71} +(-15.4996 + 21.3334i) q^{72} +(2.48055 + 0.805978i) q^{73} +(-26.7441 + 8.68968i) q^{74} +(122.065 - 88.6852i) q^{75} -35.3790i q^{76} +(2.47142 - 30.8664i) q^{77} +59.8983 q^{78} +(47.3809 + 65.2142i) q^{79} +(-9.59430 - 29.5282i) q^{80} +(-24.0997 + 74.1713i) q^{81} +(-91.4905 - 66.4717i) q^{82} +(31.8727 - 43.8690i) q^{83} +(-22.9201 - 7.44718i) q^{84} +(-51.7832 + 16.8254i) q^{85} +(23.7371 - 17.2460i) q^{86} +133.275i q^{87} +(16.2203 + 26.5500i) q^{88} +85.3100 q^{89} +(60.1537 + 82.7944i) q^{90} +(8.60725 + 26.4904i) q^{91} +(-10.9814 + 33.7972i) q^{92} +(-38.7049 - 28.1207i) q^{93} +(-22.3513 + 30.7640i) q^{94} +(-130.585 - 42.4296i) q^{95} +(23.0293 - 7.48266i) q^{96} +(12.3358 - 8.96251i) q^{97} +58.0898i q^{98} +(-77.8917 - 66.7089i) 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 $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i
$2$	−0.831254	−	1.14412i	−0.415627	−	0.572061i
$3$	−1.32276	−	4.07104i	−0.440920	−	1.35701i	−0.886897	−	0.461968i	$-0.847144\pi$
$3$	−1.32276	−	4.07104i	−0.440920	−	1.35701i	0.445977	−	0.895045i	$-0.352856\pi$
$4$	−0.618034	+	1.90211i	−0.154508	+	0.475528i
$5$	6.27955	+	4.56236i	1.25591	+	0.912472i	0.998549	−	0.0538429i	$-0.0171470\pi$
$5$	6.27955	+	4.56236i	1.25591	+	0.912472i	0.257361	+	0.966315i	$0.417147\pi$
$6$	−3.55822	+	4.89747i	−0.593036	+	0.816244i
$7$	−2.67724	−	0.869888i	−0.382463	−	0.124270i	0.111474	−	0.993767i	$-0.464443\pi$
$7$	−2.67724	−	0.869888i	−0.382463	−	0.124270i	−0.493937	+	0.869498i	$0.664443\pi$
$8$	2.68999	−	0.874032i	0.336249	−	0.109254i
$9$	−7.54250	+	5.47994i	−0.838055	+	0.608883i
$10$		−	10.9771i		−	1.09771i
$11$	2.55337	+	10.6995i	0.232125	+	0.972686i
$11$	2.55337	+	10.6995i	0.232125	+	0.972686i
$12$	8.56108			0.713424
$13$	−5.81594	−	8.00495i	−0.447380	−	0.615766i	0.524452	−	0.851440i	$-0.324270\pi$
$13$	−5.81594	−	8.00495i	−0.447380	−	0.615766i	−0.971832	+	0.235674i	$0.924270\pi$
$14$	1.23021	+	3.78619i	0.0878720	+	0.270442i
$15$	10.2672	−	31.5992i	0.684480	−	2.10661i
$16$	−3.23607	−	2.35114i	−0.202254	−	0.146946i
$17$	−4.12316	+	5.67504i	−0.242539	+	0.333826i	−0.912881	−	0.408226i	$-0.866147\pi$
$17$	−4.12316	+	5.67504i	−0.242539	+	0.333826i	0.670342	+	0.742052i	$0.266147\pi$
$18$	12.5395	+	4.07432i	0.696637	+	0.226351i
$19$	−16.8237	+	5.46635i	−0.885458	+	0.287703i	−0.716222	−	0.697873i	$-0.754130\pi$
$19$	−16.8237	+	5.46635i	−0.885458	+	0.287703i	−0.169236	+	0.985576i	$0.554130\pi$
$20$	−12.5591	+	9.12472i	−0.627955	+	0.456236i
$21$			12.0498i			0.573800i
$22$	10.1191	−	11.8154i	0.459959	−	0.537064i
$23$	17.7682			0.772532			0.386266	−	0.922387i	$-0.373765\pi$
$23$	17.7682			0.772532			0.386266	+	0.922387i	$0.373765\pi$
$24$	−7.11643	−	9.79493i	−0.296518	−	0.408122i
$25$	10.8922	+	33.5228i	0.435688	+	1.34091i
$26$	−4.32413	+	13.3083i	−0.166313	+	0.511857i
$27$	1.11869	+	0.812775i	0.0414329	+	0.0301028i
$28$	3.30925	−	4.55479i	0.118188	−	0.162671i
$29$	−29.6111	−	9.62124i	−1.02107	−	0.331767i	−0.249818	−	0.968293i	$-0.580371\pi$
$29$	−29.6111	−	9.62124i	−1.02107	−	0.331767i	−0.771256	+	0.636526i	$0.780371\pi$
$30$	−44.6880	+	14.5200i	−1.48960	+	0.484001i
$31$	9.04205	−	6.56943i	0.291679	−	0.211917i	−0.432316	−	0.901722i	$-0.642304\pi$
$31$	9.04205	−	6.56943i	0.291679	−	0.211917i	0.723995	+	0.689805i	$0.242304\pi$
$32$			5.65685i			0.176777i
$33$	40.1808	−	24.5478i	1.21760	−	0.743873i
$34$	9.92033			0.291774
$35$	−12.8431	−	17.6770i	−0.366946	−	0.505058i
$36$	−5.76195	−	17.7335i	−0.160054	−	0.492596i
$37$	6.14453	−	18.9109i	0.166068	−	0.511106i	−0.833045	−	0.553205i	$-0.813405\pi$
$37$	6.14453	−	18.9109i	0.166068	−	0.511106i	0.999113	+	0.0420992i	$0.0134045\pi$
$38$	20.2389	+	14.7044i	0.532604	+	0.386959i
$39$	−24.8954	+	34.2655i	−0.638343	+	0.878603i
$40$	20.8796	+	6.78420i	0.521990	+	0.169605i
$41$	76.0518	−	24.7107i	1.85492	−	0.602701i	0.859055	−	0.511883i	$-0.171052\pi$
$41$	76.0518	−	24.7107i	1.85492	−	0.602701i	0.995867	−	0.0908185i	$-0.0289483\pi$
$42$	13.7864	−	10.0164i	0.328249	−	0.238487i
$43$			20.7470i			0.482489i	0.970464	+	0.241244i	$0.0775556\pi$
$43$			20.7470i			0.482489i	−0.970464	+	0.241244i	$0.922444\pi$
$44$	−21.9298	−	1.75588i	−0.498405	−	0.0399064i
$45$	−72.3650			−1.60811
$46$	−14.7699	−	20.3291i	−0.321085	−	0.441936i
$47$	−8.30906	−	25.5727i	−0.176789	−	0.544099i	0.822922	−	0.568154i	$-0.192342\pi$
$47$	−8.30906	−	25.5727i	−0.176789	−	0.544099i	−0.999711	+	0.0240551i	$0.992342\pi$
$48$	−5.29104	+	16.2841i	−0.110230	+	0.339253i
$49$	−33.2309	−	24.1437i	−0.678182	−	0.492728i
$50$	29.3000	−	40.3280i	0.586000	−	0.806559i
$51$	28.5572	+	9.27881i	0.559946	+	0.181937i
$52$	18.8208	−	6.11524i	0.361938	−	0.117601i
$53$	−52.0949	+	37.8492i	−0.982923	+	0.714135i	−0.958360	−	0.285563i	$-0.907819\pi$
$53$	−52.0949	+	37.8492i	−0.982923	+	0.714135i	−0.0245630	+	0.999698i	$0.507819\pi$
$54$		−	1.95554i		−	0.0362137i
$55$	−32.7812	+	78.8378i	−0.596021	+	1.43341i
$56$	−7.96207			−0.142180
$57$	44.5074	+	61.2592i	0.780832	+	1.07472i
$58$	13.6065	+	41.8765i	0.234595	+	0.722008i
$59$	−11.0835	+	34.1116i	−0.187857	+	0.578164i	−0.999986	−	0.00531417i	$-0.998308\pi$
$59$	−11.0835	+	34.1116i	−0.187857	+	0.578164i	0.812129	+	0.583478i	$0.198308\pi$
$60$	53.7598	+	39.0588i	0.895996	+	0.650979i
$61$	30.4499	−	41.9107i	0.499178	−	0.687060i	−0.482869	−	0.875692i	$-0.660405\pi$
$61$	30.4499	−	41.9107i	0.499178	−	0.687060i	0.982048	+	0.188632i	$0.0604054\pi$
$62$	−15.0325	−	4.88435i	−0.242459	−	0.0787798i
$63$	24.9600	−	8.11000i	0.396191	−	0.128730i
$64$	6.47214	−	4.70228i	0.101127	−	0.0734732i
$65$		−	76.8019i		−	1.18157i
$66$	−61.4861	−	25.5663i	−0.931608	−	0.387367i
$67$	−17.1328			−0.255714			−0.127857	−	0.991793i	$-0.540810\pi$
$67$	−17.1328			−0.255714			−0.127857	+	0.991793i	$0.540810\pi$
$68$	−8.24631	−	11.3501i	−0.121269	−	0.166913i
$69$	−23.5031	−	72.3352i	−0.340625	−	1.04834i
$70$	−9.54881	+	29.3882i	−0.136412	+	0.419832i
$71$	−25.5662	−	18.5749i	−0.360087	−	0.261619i	0.393001	−	0.919538i	$-0.371437\pi$
$71$	−25.5662	−	18.5749i	−0.360087	−	0.261619i	−0.753088	+	0.657919i	$0.771437\pi$
$72$	−15.4996	+	21.3334i	−0.215273	+	0.296297i
$73$	2.48055	+	0.805978i	0.0339801	+	0.0110408i	0.325958	−	0.945384i	$-0.394313\pi$
$73$	2.48055	+	0.805978i	0.0339801	+	0.0110408i	−0.291978	+	0.956425i	$0.594313\pi$
$74$	−26.7441	+	8.68968i	−0.361407	+	0.117428i
$75$	122.065	−	88.6852i	1.62753	−	1.18247i
$76$		−	35.3790i		−	0.465513i
$77$	2.47142	−	30.8664i	0.0320963	−	0.400862i
$78$	59.8983			0.767927
$79$	47.3809	+	65.2142i	0.599758	+	0.825496i	0.995686	−	0.0927856i	$-0.0295771\pi$
$79$	47.3809	+	65.2142i	0.599758	+	0.825496i	−0.395928	+	0.918281i	$0.629577\pi$
$80$	−9.59430	−	29.5282i	−0.119929	−	0.369103i
$81$	−24.0997	+	74.1713i	−0.297527	+	0.915695i
$82$	−91.4905	−	66.4717i	−1.11574	−	0.810631i
$83$	31.8727	−	43.8690i	0.384009	−	0.528543i	−0.572632	−	0.819812i	$-0.694078\pi$
$83$	31.8727	−	43.8690i	0.384009	−	0.528543i	0.956641	+	0.291270i	$0.0940777\pi$
$84$	−22.9201	−	7.44718i	−0.272858	−	0.0886569i
$85$	−51.7832	+	16.8254i	−0.609214	+	0.197945i
$86$	23.7371	−	17.2460i	0.276013	−	0.200535i
$87$			133.275i			1.53189i
$88$	16.2203	+	26.5500i	0.184322	+	0.301704i
$89$	85.3100			0.958539			0.479269	−	0.877668i	$-0.340902\pi$
$89$	85.3100			0.958539			0.479269	+	0.877668i	$0.340902\pi$
$90$	60.1537	+	82.7944i	0.668374	+	0.919938i
$91$	8.60725	+	26.4904i	0.0945852	+	0.291103i
$92$	−10.9814	+	33.7972i	−0.119363	+	0.367361i
$93$	−38.7049	−	28.1207i	−0.416181	−	0.302373i
$94$	−22.3513	+	30.7640i	−0.237780	+	0.327276i
$95$	−130.585	−	42.4296i	−1.37458	−	0.446627i
$96$	23.0293	−	7.48266i	0.239888	−	0.0779444i
$97$	12.3358	−	8.96251i	0.127174	−	0.0923970i	−0.522380	−	0.852713i	$-0.674956\pi$
$97$	12.3358	−	8.96251i	0.127174	−	0.0923970i	0.649554	+	0.760316i	$0.274956\pi$
$98$			58.0898i			0.592753i
$99$	−77.8917	−	66.7089i	−0.786785	−	0.673828i
$100$	−70.4959			−0.704959
$101$	92.1317	+	126.808i	0.912195	+	1.25553i	0.966411	+	0.257000i	$0.0827341\pi$
$101$	92.1317	+	126.808i	0.912195	+	1.25553i	−0.0542159	+	0.998529i	$0.517266\pi$
$102$	−13.1222	−	40.3860i	−0.128649	−	0.395941i
$103$	40.5524	−	124.807i	0.393712	−	1.21172i	−0.536248	−	0.844061i	$-0.680159\pi$
$103$	40.5524	−	124.807i	0.393712	−	1.21172i	0.929960	−	0.367661i	$-0.119841\pi$
$104$	−22.6414	−	16.4500i	−0.217706	−	0.158173i
$105$	−54.9755	+	75.6673i	−0.523577	+	0.720641i
$106$	86.6082	+	28.1407i	0.817058	+	0.265478i
$107$	−90.4813	+	29.3991i	−0.845619	+	0.274758i	−0.699610	−	0.714525i	$-0.746643\pi$
$107$	−90.4813	+	29.3991i	−0.845619	+	0.274758i	−0.146009	+	0.989283i	$0.546643\pi$
$108$	−2.23738	+	1.62555i	−0.0207165	+	0.0150514i
$109$		−	105.607i		−	0.968875i	−0.874826	−	0.484437i	$-0.839024\pi$
$109$		−	105.607i		−	0.968875i	0.874826	−	0.484437i	$-0.160976\pi$
$110$	117.450	−	28.0285i	1.06772	−	0.254805i
$111$	−85.1148			−0.766800
$112$	6.61850	+	9.10958i	0.0590938	+	0.0813356i
$113$	33.9131	+	104.374i	0.300115	+	0.923661i	0.981455	+	0.191693i	$0.0613978\pi$
$113$	33.9131	+	104.374i	0.300115	+	0.923661i	−0.681339	+	0.731968i	$0.738602\pi$
$114$	33.0911	−	101.844i	0.290273	−	0.893368i
$115$	111.577	+	81.0652i	0.970231	+	0.704914i
$116$	36.6014	−	50.3775i	0.315529	−	0.434289i
$117$	87.7334	+	28.5063i	0.749858	+	0.243644i
$118$	48.2412	−	15.6745i	0.408823	−	0.132835i
$119$	15.9753	−	11.6068i	0.134246	−	0.0975357i
$120$		−	93.9755i		−	0.783129i
$121$	−107.961	+	54.6399i	−0.892236	+	0.451569i
$122$	−73.2625			−0.600513
$123$	−201.197	−	276.923i	−1.63575	−	2.25141i
$124$	6.90751	+	21.2591i	0.0557057	+	0.171445i
$125$	−24.5804	+	75.6508i	−0.196644	+	0.605207i
$126$	−30.0269	−	21.8158i	−0.238309	−	0.173142i
$127$	123.054	−	169.370i	0.968932	−	1.33362i	0.0263479	−	0.999653i	$-0.491612\pi$
$127$	123.054	−	169.370i	0.968932	−	1.33362i	0.942584	−	0.333968i	$-0.108388\pi$
$128$	−10.7600	−	3.49613i	−0.0840623	−	0.0273135i
$129$	84.4619	−	27.4433i	0.654743	−	0.212739i
$130$	−87.8708	+	63.8419i	−0.675930	+	0.491092i
$131$			80.8324i			0.617041i	0.951218	+	0.308521i	$0.0998339\pi$
$131$			80.8324i			0.617041i	−0.951218	+	0.308521i	$0.900166\pi$
$132$	21.8596	+	91.5997i	0.165603	+	0.693937i
$133$	49.7962			0.374407
$134$	14.2417	+	19.6020i	0.106281	+	0.146284i
$135$	3.31669	+	10.2077i	0.0245681	+	0.0756128i
$136$	−6.13110	+	18.8696i	−0.0450816	+	0.138747i
$137$	26.8831	+	19.5317i	0.196227	+	0.142567i	0.681560	−	0.731762i	$-0.261302\pi$
$137$	26.8831	+	19.5317i	0.196227	+	0.142567i	−0.485333	+	0.874329i	$0.661302\pi$
$138$	−63.2233	+	87.0194i	−0.458140	+	0.630575i
$139$	205.918	+	66.9069i	1.48143	+	0.481345i	0.934539	−	0.355861i	$-0.115812\pi$
$139$	205.918	+	66.9069i	1.48143	+	0.481345i	0.546888	+	0.837206i	$0.315812\pi$
$140$	41.5612	−	13.5041i	0.296866	−	0.0964576i
$141$	−93.1164	+	67.6530i	−0.660400	+	0.479808i
$142$			44.6913i			0.314728i
$143$	70.7991	−	82.6675i	0.495099	−	0.578095i
$144$	37.2922			0.258973
$145$	−142.049	−	195.514i	−0.979649	−	1.34837i
$146$	−1.13983	−	3.50802i	−0.00780702	−	0.0240275i
$147$	−54.3333	+	167.221i	−0.369614	+	1.13756i
$148$	32.1732	+	23.3752i	0.217386	+	0.157940i
$149$	−126.132	+	173.606i	−0.846522	+	1.16514i	0.138096	+	0.990419i	$0.455902\pi$
$149$	−126.132	+	173.606i	−0.846522	+	1.16514i	−0.984618	+	0.174719i	$0.944098\pi$
$150$	−202.933	−	65.9371i	−1.35289	−	0.439581i
$151$	−2.56100	+	0.832119i	−0.0169603	+	0.00551072i	−0.317485	−	0.948263i	$-0.602838\pi$
$151$	−2.56100	+	0.832119i	−0.0169603	+	0.00551072i	0.300525	+	0.953774i	$0.402838\pi$
$152$	−40.4779	+	29.4089i	−0.266302	+	0.193480i
$153$		−	65.3986i		−	0.427442i
$154$	−37.3693	+	22.8302i	−0.242658	+	0.148248i
$155$	86.7521			0.559691
$156$	−49.7907	−	68.5311i	−0.319171	−	0.439302i
$157$	−48.0880	−	148.000i	−0.306293	−	0.942672i	−0.979192	−	0.202938i	$-0.934951\pi$
$157$	−48.0880	−	148.000i	−0.306293	−	0.942672i	0.672899	−	0.739734i	$-0.265049\pi$
$158$	35.2275	−	108.419i	0.222959	−	0.686197i
$159$	222.994	+	162.015i	1.40248	+	1.01896i
$160$	−25.8086	+	35.5225i	−0.161304	+	0.222016i
$161$	−47.5698	−	15.4564i	−0.295465	−	0.0960024i
$162$	104.894	−	34.0821i	0.647494	−	0.210384i
$163$	−240.781	+	174.938i	−1.47719	+	1.07324i	−0.498737	+	0.866753i	$0.666203\pi$
$163$	−240.781	+	174.938i	−1.47719	+	1.07324i	−0.978450	+	0.206486i	$0.933797\pi$
$164$			159.931i			0.975191i
$165$	364.313	+	29.1699i	2.20796	+	0.176787i
$166$	−76.6859			−0.461963
$167$	3.79020	+	5.21677i	0.0226958	+	0.0312381i	0.820214	−	0.572057i	$-0.193854\pi$
$167$	3.79020	+	5.21677i	0.0226958	+	0.0312381i	−0.797518	+	0.603295i	$0.793854\pi$
$168$	10.5319	+	32.4139i	0.0626899	+	0.192940i
$169$	21.9698	−	67.6160i	0.129999	−	0.400094i
$170$	62.2952	+	45.2601i	0.366443	+	0.266236i
$171$	96.9373	−	133.423i	0.566885	−	0.780250i
$172$	−39.4632	−	12.8224i	−0.229437	−	0.0745486i
$173$	−130.724	+	42.4747i	−0.755629	+	0.245519i	−0.661401	−	0.750032i	$-0.730038\pi$
$173$	−130.724	+	42.4747i	−0.755629	+	0.245519i	−0.0942271	+	0.995551i	$0.530038\pi$
$174$	152.483	−	110.785i	0.876337	−	0.636696i
$175$		−	99.2235i		−	0.566991i
$176$	16.8933	−	40.6278i	0.0959844	−	0.230840i
$177$	153.531			0.867405
$178$	−70.9142	−	97.6051i	−0.398395	−	0.548343i
$179$	12.2847	+	37.8085i	0.0686298	+	0.211221i	0.979489	−	0.201495i	$-0.0645801\pi$
$179$	12.2847	+	37.8085i	0.0686298	+	0.211221i	−0.910860	+	0.412716i	$0.864580\pi$
$180$	44.7240	−	137.646i	0.248467	−	0.764702i
$181$	−252.810	−	183.677i	−1.39674	−	1.01479i	−0.995088	−	0.0989977i	$-0.968436\pi$
$181$	−252.810	−	183.677i	−1.39674	−	1.01479i	−0.401651	−	0.915793i	$-0.631564\pi$
$182$	23.1534	−	31.8680i	0.127217	−	0.175099i
$183$	−210.898	−	68.5248i	−1.15245	−	0.374453i
$184$	47.7965	−	15.5300i	0.259763	−	0.0844022i
$185$	124.863	−	90.7186i	0.674937	−	0.490371i
$186$			67.6586i			0.363756i
$187$	−71.2483	−	29.6254i	−0.381007	−	0.158425i
$188$	53.7774			0.286050
$189$	−2.28798	−	3.14913i	−0.0121057	−	0.0166621i
$190$	60.0044	+	184.675i	0.315813	+	0.971972i
$191$	53.9224	−	165.956i	0.282316	−	0.868880i	−0.704874	−	0.709332i	$-0.748997\pi$
$191$	53.9224	−	165.956i	0.282316	−	0.868880i	0.987190	−	0.159547i	$-0.0510035\pi$
$192$	−27.7042	−	20.1283i	−0.144293	−	0.104835i
$193$	−174.641	+	240.373i	−0.904877	+	1.24546i	0.0640085	+	0.997949i	$0.479612\pi$
$193$	−174.641	+	240.373i	−0.904877	+	1.24546i	−0.968886	+	0.247508i	$0.920388\pi$
$194$	−20.5084	−	6.66359i	−0.105714	−	0.0343484i
$195$	−312.664	+	101.591i	−1.60340	+	0.520977i
$196$	66.4618	−	48.2874i	0.339091	−	0.246364i
$197$		−	117.434i		−	0.596110i	−0.954549	−	0.298055i	$-0.903662\pi$
$197$		−	117.434i		−	0.596110i	0.954549	−	0.298055i	$-0.0963378\pi$
$198$	−11.5754	+	144.570i	−0.0584618	+	0.730150i
$199$	−68.1594			−0.342510			−0.171255	−	0.985227i	$-0.554782\pi$
$199$	−68.1594			−0.342510			−0.171255	+	0.985227i	$0.554782\pi$
$200$	58.6000	+	80.6559i	0.293000	+	0.403280i
$201$	22.6626	+	69.7483i	0.112749	+	0.347006i
$202$	68.4996	−	210.820i	0.339107	−	1.04366i
$203$	70.9067	+	51.5168i	0.349294	+	0.253777i
$204$	−35.2987	+	48.5845i	−0.173033	+	0.238159i
$205$	590.311	+	191.804i	2.87957	+	0.935627i
$206$	−176.504	+	57.3497i	−0.856816	+	0.278397i
$207$	−134.017	+	97.3690i	−0.647425	+	0.470382i
$208$			39.5787i			0.190282i
$209$	−101.445	−	166.048i	−0.485381	−	0.794489i
$210$	132.271			0.629864
$211$	200.036	+	275.326i	0.948037	+	1.30486i	0.952394	+	0.304871i	$0.0986133\pi$
$211$	200.036	+	275.326i	0.948037	+	1.30486i	−0.00435633	+	0.999991i	$0.501387\pi$
$212$	−39.7970	−	122.482i	−0.187722	−	0.577748i
$213$	−41.8013	+	128.651i	−0.196250	+	0.603996i
$214$	108.849	+	79.0835i	0.508641	+	0.369549i
$215$	−94.6554	+	130.282i	−0.440258	+	0.605963i
$216$	3.71966	+	1.20859i	0.0172206	+	0.00559533i
$217$	−29.9224	+	9.72238i	−0.137891	+	0.0448036i
$218$	−120.828	+	87.7865i	−0.554256	+	0.402690i
$219$		−	11.1645i		−	0.0509795i
$220$	−129.698	−	111.078i	−0.589539	−	0.504900i
$221$	69.4084			0.314065
$222$	70.7520	+	97.3818i	0.318703	+	0.438657i
$223$	94.4494	+	290.685i	0.423540	+	1.30352i	0.904385	+	0.426717i	$0.140330\pi$
$223$	94.4494	+	290.685i	0.423540	+	1.30352i	−0.480845	+	0.876805i	$0.659670\pi$
$224$	4.92083	−	15.1448i	0.0219680	−	0.0676105i
$225$	−265.857	−	193.157i	−1.18159	−	0.858474i
$226$	91.2259	−	125.562i	0.403654	−	0.555583i
$227$	−187.559	−	60.9417i	−0.826252	−	0.268466i	−0.134786	−	0.990875i	$-0.543035\pi$
$227$	−187.559	−	60.9417i	−0.826252	−	0.268466i	−0.691466	+	0.722409i	$0.743035\pi$
$228$	−144.029	+	46.7979i	−0.631706	+	0.205254i
$229$	47.2886	−	34.3572i	0.206501	−	0.150031i	−0.479728	−	0.877417i	$-0.659265\pi$
$229$	47.2886	−	34.3572i	0.206501	−	0.150031i	0.686229	+	0.727386i	$0.259265\pi$
$230$		−	195.043i		−	0.848013i
$231$	−128.927	+	30.7676i	−0.558127	+	0.133193i
$232$	−88.0631			−0.379582
$233$	−163.455	−	224.976i	−0.701522	−	0.965563i	−0.999938	−	0.0111267i	$-0.996458\pi$
$233$	−163.455	−	224.976i	−0.701522	−	0.965563i	0.298416	−	0.954436i	$-0.403542\pi$
$234$	−40.3140	−	124.074i	−0.172282	−	0.530230i
$235$	64.4945	−	198.494i	0.274445	−	0.844655i
$236$	−58.0342	−	42.1643i	−0.245908	−	0.178662i
$237$	202.816	−	279.152i	0.855763	−	1.17786i
$238$	−26.5591	−	8.62957i	−0.111593	−	0.0362587i
$239$	312.226	−	101.448i	1.30638	−	0.424470i	0.428586	−	0.903501i	$-0.359012\pi$
$239$	312.226	−	101.448i	1.30638	−	0.424470i	0.877798	+	0.479031i	$0.159012\pi$
$240$	−107.520	+	78.1175i	−0.447998	+	0.325490i
$241$		−	81.8737i		−	0.339725i	−0.985468	−	0.169862i	$-0.945668\pi$
$241$		−	81.8737i		−	0.339725i	0.985468	−	0.169862i	$-0.0543323\pi$
$242$	152.257	+	78.1006i	0.629163	+	0.322730i
$243$	346.277			1.42501
$244$	60.8998	+	83.8213i	0.249589	+	0.343530i
$245$	−98.5231	−	303.223i	−0.402135	−	1.23764i
$246$	−149.589	+	460.387i	−0.608085	+	1.87149i
$247$	141.603	+	102.881i	0.573293	+	0.416522i
$248$	18.5812	−	25.5748i	0.0749240	−	0.103124i
$249$	−220.752	−	71.7268i	−0.886556	−	0.288059i
$250$	106.986	−	34.7620i	0.427946	−	0.139048i
$251$	393.701	−	286.041i	1.56853	−	1.13960i	0.639983	−	0.768389i	$-0.278941\pi$
$251$	393.701	−	286.041i	1.56853	−	1.13960i	0.928547	−	0.371215i	$-0.121059\pi$
$252$			52.4890i			0.208290i
$253$	45.3689	+	190.112i	0.179324	+	0.751431i
$254$	−296.069			−1.16563
$255$	136.993	+	188.555i	0.537229	+	0.739432i
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	−123.685	+	380.662i	−0.481263	+	1.48118i	0.356057	+	0.934464i	$0.384121\pi$
$257$	−123.685	+	380.662i	−0.481263	+	1.48118i	−0.837321	+	0.546712i	$0.815879\pi$
$258$	−101.608	−	73.8224i	−0.393829	−	0.286133i
$259$	−32.9008	+	45.2840i	−0.127030	+	0.174842i
$260$	146.086	+	47.4662i	0.561869	+	0.182562i
$261$	276.066	−	89.6992i	1.05772	−	0.343675i
$262$	92.4822	−	67.1923i	0.352986	−	0.256459i
$263$			90.5875i			0.344439i	0.985059	+	0.172220i	$0.0550939\pi$
$263$			90.5875i			0.344439i	−0.985059	+	0.172220i	$0.944906\pi$
$264$	86.6304	−	101.153i	0.328145	−	0.383154i
$265$	−499.814			−1.88609
$266$	−41.3933	−	56.9729i	−0.155614	−	0.214184i
$267$	−112.845	−	347.300i	−0.422639	−	1.30075i
$268$	10.5887	−	32.5885i	0.0395099	−	0.121599i
$269$	220.920	+	160.508i	0.821264	+	0.596683i	0.917074	−	0.398716i	$-0.130544\pi$
$269$	220.920	+	160.508i	0.821264	+	0.596683i	−0.0958103	+	0.995400i	$0.530544\pi$
$270$	8.92188	−	12.2799i	0.0330440	−	0.0454812i
$271$	−405.439	−	131.735i	−1.49608	−	0.486107i	−0.557211	−	0.830371i	$-0.688129\pi$
$271$	−405.439	−	131.735i	−1.49608	−	0.486107i	−0.938873	+	0.344263i	$0.888129\pi$
$272$	26.6856	−	8.67069i	0.0981089	−	0.0318775i
$273$	96.4580	−	70.0809i	0.353326	−	0.256706i
$274$		−	46.9934i		−	0.171509i
$275$	−330.867	+	202.138i	−1.20315	+	0.735047i
$276$	152.115			0.551143
$277$	111.277	+	153.160i	0.401723	+	0.552924i	0.961175	−	0.275938i	$-0.0889885\pi$
$277$	111.277	+	153.160i	0.401723	+	0.552924i	−0.559452	+	0.828863i	$0.688988\pi$
$278$	−94.6207	−	291.212i	−0.340362	−	1.04753i
$279$	−32.1995	+	99.0998i	−0.115410	+	0.355196i
$280$	−49.9982	−	36.3258i	−0.178565	−	0.129735i
$281$	−48.7922	+	67.1566i	−0.173638	+	0.238992i	−0.886962	−	0.461842i	$-0.847189\pi$
$281$	−48.7922	+	67.1566i	−0.173638	+	0.238992i	0.713324	+	0.700834i	$0.247189\pi$
$282$	154.807	+	50.2997i	0.548960	+	0.178368i
$283$	109.037	−	35.4282i	0.385289	−	0.125188i	−0.109967	−	0.993935i	$-0.535074\pi$
$283$	109.037	−	35.4282i	0.385289	−	0.125188i	0.495255	+	0.868747i	$0.335074\pi$
$284$	51.1324	−	37.1498i	0.180044	−	0.130809i
$285$			587.739i			2.06224i
$286$	−153.434	−	12.2852i	−0.536482	−	0.0429551i
$287$	−225.105			−0.784337
$288$	−30.9992	−	42.6668i	−0.107636	−	0.148149i
$289$	74.1003	+	228.057i	0.256402	+	0.789125i
$290$	−105.613	+	325.043i	−0.364183	+	1.12084i
$291$	−52.8041	−	38.3644i	−0.181457	−	0.131836i
$292$	−3.06612	+	4.22016i	−0.0105004	+	0.0144526i
$293$	−30.3234	−	9.85268i	−0.103493	−	0.0336269i	0.256813	−	0.966461i	$-0.417328\pi$
$293$	−30.3234	−	9.85268i	−0.103493	−	0.0336269i	−0.360306	+	0.932834i	$0.617328\pi$
$294$	236.486	−	76.8389i	0.804373	−	0.261357i
$295$	−225.229	+	163.639i	−0.763490	+	0.554708i
$296$		−	56.2408i		−	0.190003i
$297$	−5.83990	+	14.0448i	−0.0196630	+	0.0472888i
$298$	303.474			1.01837
$299$	−103.339	−	142.234i	−0.345615	−	0.475699i
$300$	93.2491	+	286.991i	0.310830	+	0.956638i
$301$	18.0476	−	55.5448i	0.0599588	−	0.184534i
$302$	3.08089	+	2.23840i	0.0102016	+	0.00741191i
$303$	394.374	−	542.809i	1.30156	−	1.79145i
$304$	67.2948	+	21.8654i	0.221364	+	0.0719256i
$305$	382.423	−	124.257i	1.25385	−	0.407399i
$306$	−74.8240	+	54.3628i	−0.244523	+	0.177656i
$307$		−	73.4747i		−	0.239331i	−0.992814	−	0.119666i	$-0.961818\pi$
$307$		−	73.4747i		−	0.239331i	0.992814	−	0.119666i	$-0.0381823\pi$
$308$	57.1840	+	23.7774i	0.185662	+	0.0771993i
$309$	−561.736			−1.81792
$310$	−72.1131	−	99.2551i	−0.232623	−	0.320178i
$311$	3.08269	+	9.48756i	0.00991220	+	0.0305066i	0.955890	−	0.293724i	$-0.0948946\pi$
$311$	3.08269	+	9.48756i	0.00991220	+	0.0305066i	−0.945978	+	0.324231i	$0.894895\pi$
$312$	−37.0192	+	113.933i	−0.118651	+	0.365171i
$313$	−180.747	−	131.320i	−0.577466	−	0.419554i	0.260344	−	0.965516i	$-0.416164\pi$
$313$	−180.747	−	131.320i	−0.577466	−	0.419554i	−0.837810	+	0.545962i	$0.816164\pi$
$314$	−129.356	+	178.044i	−0.411963	+	0.567018i
$315$	193.738	+	62.9494i	0.615043	+	0.199839i
$316$	−153.328	+	49.8192i	−0.485214	+	0.157656i
$317$	−17.4640	+	12.6884i	−0.0550916	+	0.0400264i	−0.614990	−	0.788535i	$-0.710840\pi$
$317$	−17.4640	+	12.6884i	−0.0550916	+	0.0400264i	0.559899	+	0.828561i	$0.310840\pi$
$318$		−	389.809i		−	1.22581i
$319$	27.3347	−	341.392i	0.0856886	−	1.07020i
$320$	62.0956			0.194049
$321$	239.370	+	329.465i	0.745701	+	1.02637i
$322$	21.8586	+	67.2739i	0.0678839	+	0.208925i
$323$	38.3450	−	118.014i	0.118715	−	0.365367i
$324$	−126.188	−	91.6808i	−0.389468	−	0.282965i
$325$	205.000	−	282.158i	0.630769	−	0.868178i
$326$	400.301	+	130.066i	1.22792	+	0.398974i
$327$	−429.931	+	139.693i	−1.31478	+	0.427196i
$328$	182.981	−	132.943i	0.557869	−	0.405316i
$329$			75.6921i			0.230067i
$330$	−269.463	−	441.067i	−0.816554	−	1.33657i
$331$	−211.248			−0.638212			−0.319106	−	0.947719i	$-0.603383\pi$
$331$	−211.248			−0.638212			−0.319106	+	0.947719i	$0.603383\pi$
$332$	63.7454	+	87.7381i	0.192004	+	0.264271i
$333$	57.2857	+	176.307i	0.172029	+	0.529451i
$334$	2.81800	−	8.67291i	0.00843713	−	0.0259668i
$335$	−107.586	−	78.1661i	−0.321153	−	0.233332i
$336$	28.3308	−	38.9940i	0.0843178	−	0.116053i
$337$	274.799	+	89.2875i	0.815426	+	0.264948i	0.686894	−	0.726757i	$-0.258973\pi$
$337$	274.799	+	89.2875i	0.815426	+	0.264948i	0.128532	+	0.991705i	$0.458973\pi$
$338$	−95.6234	+	31.0699i	−0.282909	+	0.0919229i
$339$	380.050	−	276.123i	1.12109	−	0.814521i
$340$		−	108.896i		−	0.320283i
$341$	93.3777	+	79.9716i	0.273835	+	0.234521i
$342$	−233.232			−0.681964
$343$	149.041	+	205.138i	0.434523	+	0.598070i
$344$	18.1336	+	55.8094i	0.0527138	+	0.162237i
$345$	182.430	−	561.462i	0.528783	−	1.62743i
$346$	157.261	+	114.257i	0.454511	+	0.330222i
$347$	−216.472	+	297.949i	−0.623840	+	0.858642i	−0.997625	−	0.0688734i	$-0.978060\pi$
$347$	−216.472	+	297.949i	−0.623840	+	0.858642i	0.373786	+	0.927515i	$0.378060\pi$
$348$	−253.503	−	82.3683i	−0.728458	−	0.236690i
$349$	−387.995	+	126.067i	−1.11173	+	0.361224i	−0.806607	−	0.591087i	$-0.798699\pi$
$349$	−387.995	+	126.067i	−1.11173	+	0.361224i	−0.305127	+	0.952312i	$0.598699\pi$
$350$	−113.524	+	82.4799i	−0.324354	+	0.235657i
$351$		−	13.6821i		−	0.0389804i
$352$	−60.5258	+	14.4441i	−0.171948	+	0.0410342i
$353$	387.049			1.09646			0.548228	−	0.836329i	$-0.315303\pi$
$353$	387.049			1.09646			0.548228	+	0.836329i	$0.315303\pi$
$354$	−127.623	−	175.658i	−0.360517	−	0.496209i
$355$	−75.7987	−	233.284i	−0.213517	−	0.657139i
$356$	−52.7244	+	162.269i	−0.148102	+	0.455812i
$357$	−68.3830	−	49.6832i	−0.191549	−	0.139169i
$358$	33.0458	−	45.4837i	0.0923068	−	0.127049i
$359$	172.594	+	56.0791i	0.480762	+	0.156209i	0.539365	−	0.842072i	$-0.318664\pi$
$359$	172.594	+	56.0791i	0.480762	+	0.156209i	−0.0586025	+	0.998281i	$0.518664\pi$
$360$	−194.661	+	63.2493i	−0.540726	+	0.175693i
$361$	−38.8995	+	28.2621i	−0.107755	+	0.0782884i
$362$			441.928i			1.22079i
$363$	365.247	+	367.236i	1.00619	+	1.01167i
$364$	−55.7073			−0.153042
$365$	11.8996	+	16.3783i	0.0326015	+	0.0448721i
$366$	96.9087	+	298.254i	0.264778	+	0.814903i
$367$	−9.52625	+	29.3188i	−0.0259571	+	0.0798877i	−0.963196	−	0.268800i	$-0.913373\pi$
$367$	−9.52625	+	29.3188i	−0.0259571	+	0.0798877i	0.937239	+	0.348688i	$0.113373\pi$
$368$	−57.4992	−	41.7756i	−0.156248	−	0.113521i
$369$	−438.207	+	603.140i	−1.18755	+	1.63453i
$370$	−207.586	−	67.4489i	−0.561044	−	0.182294i
$371$	172.395	−	56.0146i	0.464677	−	0.150983i
$372$	77.4097	−	56.2415i	0.208091	−	0.151187i
$373$		−	93.3419i		−	0.250246i	−0.992141	−	0.125123i	$-0.960067\pi$
$373$		−	93.3419i		−	0.250246i	0.992141	−	0.125123i	$-0.0399326\pi$
$374$	25.3303	+	106.143i	0.0677281	+	0.283805i
$375$	340.491			0.907977
$376$	−44.7026	−	61.5279i	−0.118890	−	0.163638i
$377$	95.1990	+	292.992i	0.252517	+	0.777168i
$378$	−1.70110	+	5.23545i	−0.00450027	+	0.0138504i
$379$	−279.896	−	203.357i	−0.738513	−	0.536561i	0.153732	−	0.988113i	$-0.450871\pi$
$379$	−279.896	−	203.357i	−0.738513	−	0.536561i	−0.892245	+	0.451551i	$0.850871\pi$
$380$	161.412	−	222.164i	0.424767	−	0.584642i
$381$	−852.282	−	276.923i	−2.23696	−	0.726833i
$382$	−234.697	+	76.2578i	−0.614391	+	0.199628i
$383$	−58.2427	+	42.3158i	−0.152070	+	0.110485i	−0.661218	−	0.750193i	$-0.729960\pi$
$383$	−58.2427	+	42.3158i	−0.152070	+	0.110485i	0.509149	+	0.860679i	$0.329960\pi$
$384$			48.4288i			0.126117i
$385$	156.343	−	182.552i	0.406086	−	0.474160i
$386$	420.188			1.08857
$387$	−113.693	−	156.484i	−0.293779	−	0.404352i
$388$	9.42374	+	29.0033i	0.0242880	+	0.0747507i
$389$	71.1079	−	218.847i	0.182797	−	0.562590i	−0.817107	−	0.576486i	$-0.804423\pi$
$389$	71.1079	−	218.847i	0.182797	−	0.562590i	0.999903	+	0.0138963i	$0.00442346\pi$
$390$	376.135	+	273.278i	0.964448	+	0.700713i
$391$	−73.2612	+	100.835i	−0.187369	+	0.257891i
$392$	−110.493	−	35.9015i	−0.281871	−	0.0915854i
$393$	329.072	−	106.922i	0.837333	−	0.272066i
$394$	−134.358	+	97.6171i	−0.341011	+	0.247759i
$395$			625.685i			1.58401i
$396$	175.028	−	106.930i	0.441989	−	0.270026i
$397$	535.814			1.34966			0.674829	−	0.737975i	$-0.264218\pi$
$397$	535.814			1.34966			0.674829	+	0.737975i	$0.264218\pi$
$398$	56.6578	+	77.9827i	0.142356	+	0.195937i
$399$	−65.8684	−	202.722i	−0.165084	−	0.508075i
$400$	43.5688	−	134.091i	0.108922	−	0.335228i
$401$	56.2403	+	40.8609i	0.140250	+	0.101898i	0.655698	−	0.755023i	$-0.272374\pi$
$401$	56.2403	+	40.8609i	0.140250	+	0.101898i	−0.515448	+	0.856921i	$0.672374\pi$
$402$	60.9622	−	83.9073i	0.151647	−	0.208725i
$403$	−105.176	−	34.1737i	−0.260983	−	0.0847984i
$404$	−298.145	+	96.8730i	−0.737982	+	0.239785i
$405$	−489.732	+	355.811i	−1.20921	+	0.878545i
$406$		−	123.950i		−	0.305294i
$407$	218.028	+	17.4571i	0.535694	+	0.0428921i
$408$	84.9288			0.208159
$409$	−62.6529	−	86.2344i	−0.153186	−	0.210842i	0.725526	−	0.688195i	$-0.241596\pi$
$409$	−62.6529	−	86.2344i	−0.153186	−	0.210842i	−0.878712	+	0.477353i	$0.841596\pi$
$410$	−271.251	−	834.826i	−0.661589	−	2.03616i
$411$	43.9545	−	135.278i	0.106945	−	0.329143i
$412$	212.335	+	154.270i	0.515376	+	0.374443i
$413$	59.3466	−	81.6836i	0.143696	−	0.197781i
$414$	222.804	+	72.3934i	0.538174	+	0.174863i
$415$	400.293	−	130.063i	0.964561	−	0.313405i
$416$	45.2828	−	32.8999i	0.108853	−	0.0790863i
$417$		−	926.803i		−	2.22255i
$418$	−105.653	+	254.093i	−0.252759	+	0.607879i
$419$	−367.987			−0.878251			−0.439126	−	0.898426i	$-0.644712\pi$
$419$	−367.987			−0.878251			−0.439126	+	0.898426i	$0.644712\pi$
$420$	−109.951	−	151.335i	−0.261788	−	0.360321i
$421$	−76.3511	−	234.984i	−0.181357	−	0.558158i	0.818510	−	0.574492i	$-0.194800\pi$
$421$	−76.3511	−	234.984i	−0.181357	−	0.558158i	−0.999867	+	0.0163342i	$0.994800\pi$
$422$	148.726	−	457.731i	0.352431	−	1.08467i
$423$	202.808	+	147.348i	0.479451	+	0.348342i
$424$	−107.054	+	147.347i	−0.252485	+	0.347516i
$425$	−235.153	−	76.4059i	−0.553302	−	0.179779i
$426$	181.940	−	59.1159i	0.427089	−	0.138770i
$427$	−117.979	+	85.7169i	−0.276298	+	0.200742i
$428$		−	190.275i		−	0.444568i
$429$	−430.193	−	178.876i	−1.00278	−	0.416961i
$430$	227.741			0.529631
$431$	−423.447	−	582.824i	−0.982475	−	1.35226i	−0.935485	−	0.353366i	$-0.885037\pi$
$431$	−423.447	−	582.824i	−0.982475	−	1.35226i	−0.0469898	−	0.998895i	$-0.514963\pi$
$432$	−1.70920	−	5.26039i	−0.00395649	−	0.0121768i
$433$	−136.159	+	419.054i	−0.314455	+	0.967792i	0.661524	+	0.749924i	$0.269910\pi$
$433$	−136.159	+	419.054i	−0.314455	+	0.967792i	−0.975978	+	0.217868i	$0.930090\pi$
$434$	35.9967	+	26.1531i	0.0829417	+	0.0602607i
$435$	−608.047	+	836.905i	−1.39781	+	1.92392i
$436$	200.877	+	65.2689i	0.460727	+	0.149699i
$437$	−298.927	+	97.1274i	−0.684045	+	0.222260i
$438$	−12.7736	+	9.28054i	−0.0291634	+	0.0211885i
$439$		−	458.772i		−	1.04504i	−0.852627	−	0.522520i	$-0.824992\pi$
$439$		−	458.772i		−	1.04504i	0.852627	−	0.522520i	$-0.175008\pi$
$440$	−19.2744	+	240.725i	−0.0438055	+	0.547102i
$441$	382.950			0.868368
$442$	−57.6960	−	79.4118i	−0.130534	−	0.179665i
$443$	233.341	+	718.151i	0.526730	+	1.62111i	0.760870	+	0.648905i	$0.224773\pi$
$443$	233.341	+	718.151i	0.526730	+	1.62111i	−0.234140	+	0.972203i	$0.575227\pi$
$444$	52.6038	−	161.898i	0.118477	−	0.364635i
$445$	535.708	+	389.215i	1.20384	+	0.874640i
$446$	254.068	−	349.695i	0.569660	−	0.784070i
$447$	873.597	+	283.849i	1.95436	+	0.635009i
$448$	−21.4179	+	6.95910i	−0.0478079	+	0.0155337i
$449$	−189.284	+	137.523i	−0.421567	+	0.306286i	−0.778268	−	0.627932i	$-0.783902\pi$
$449$	−189.284	+	137.523i	−0.421567	+	0.306286i	0.356701	+	0.934219i	$0.383902\pi$
$450$			464.736i			1.03275i
$451$	458.582	+	750.624i	1.01681	+	1.66436i
$452$	−219.490			−0.485597
$453$	6.77518	+	9.32523i	0.0149562	+	0.0205855i
$454$	86.1846	+	265.249i	0.189834	+	0.584248i
$455$	−66.8091	+	205.617i	−0.146833	+	0.451906i
$456$	173.267	+	125.886i	0.379972	+	0.276066i
$457$	327.023	−	450.109i	0.715587	−	0.984920i	−0.284072	−	0.958803i	$-0.591686\pi$
$457$	327.023	−	450.109i	0.715587	−	0.984920i	0.999659	−	0.0261176i	$-0.00831444\pi$
$458$	−78.6177	−	25.5444i	−0.171654	−	0.0557739i
$459$	−9.22506	+	2.99740i	−0.0200982	+	0.00653029i
$460$	−223.153	+	162.130i	−0.485116	+	0.352457i
$461$		−	661.204i		−	1.43428i	−0.696928	−	0.717141i	$-0.745450\pi$
$461$		−	661.204i		−	1.43428i	0.696928	−	0.717141i	$-0.254550\pi$
$462$	142.373	+	121.933i	0.308167	+	0.263924i
$463$	−63.9989			−0.138227			−0.0691133	−	0.997609i	$-0.522017\pi$
$463$	−63.9989			−0.138227			−0.0691133	+	0.997609i	$0.522017\pi$
$464$	73.2028	+	100.755i	0.157765	+	0.217144i
$465$	−114.752	−	353.171i	−0.246779	−	0.759508i
$466$	−121.528	+	374.025i	−0.260790	+	0.802628i
$467$	−548.155	−	398.258i	−1.17378	−	0.852801i	−0.182324	−	0.983239i	$-0.558362\pi$
$467$	−548.155	−	398.258i	−1.17378	−	0.852801i	−0.991457	+	0.130437i	$0.958362\pi$
$468$	−108.444	+	149.261i	−0.231719	+	0.318934i
$469$	45.8686	+	14.9036i	0.0978009	+	0.0317774i
$470$	−280.713	+	91.2091i	−0.597261	+	0.194062i
$471$	−538.903	+	391.536i	−1.14417	+	0.831286i
$472$			101.448i			0.214931i
$473$	−221.984	+	52.9749i	−0.469310	+	0.111998i
$474$	−487.976			−1.02948
$475$	−366.494	−	504.436i	−0.771567	−	1.06197i
$476$	12.2041	+	37.5602i	0.0256388	+	0.0789081i
$477$	185.514	−	570.954i	0.388919	−	1.19697i
$478$	−375.608	−	272.895i	−0.785791	−	0.570911i
$479$	−81.4459	+	112.101i	−0.170033	+	0.234031i	−0.885526	−	0.464589i	$-0.846202\pi$
$479$	−81.4459	+	112.101i	−0.170033	+	0.234031i	0.715493	+	0.698620i	$0.246202\pi$
$480$	178.752	+	58.0801i	0.372400	+	0.121000i
$481$	−187.117	+	60.7981i	−0.389017	+	0.126399i
$482$	−93.6736	+	68.0578i	−0.194343	+	0.141199i
$483$			214.104i			0.443279i
$484$	−37.2079	−	239.123i	−0.0768758	−	0.494055i
$485$	118.354			0.244028
$486$	−287.844	−	396.184i	−0.592272	−	0.815193i
$487$	22.8809	+	70.4203i	0.0469835	+	0.144600i	0.971796	−	0.235823i	$-0.0757785\pi$
$487$	22.8809	+	70.4203i	0.0469835	+	0.144600i	−0.924813	+	0.380423i	$0.875778\pi$
$488$	45.2787	−	139.354i	0.0927843	−	0.285561i
$489$	1030.68	+	748.829i	2.10772	+	1.53135i
$490$	−265.027	+	364.778i	−0.540871	+	0.744445i
$491$	484.225	+	157.334i	0.986201	+	0.320436i	0.757339	−	0.653022i	$-0.226499\pi$
$491$	484.225	+	157.334i	0.986201	+	0.320436i	0.228863	+	0.973459i	$0.426499\pi$
$492$	651.086	−	211.551i	1.32335	−	0.429981i
$493$	176.692	−	128.374i	0.358402	−	0.260394i
$494$		−	247.532i		−	0.501077i
$495$	−184.775	−	774.273i	−0.373282	−	1.56419i
$496$	−44.7063			−0.0901337
$497$	52.2887	+	71.9692i	0.105209	+	0.144807i
$498$	101.437	+	312.191i	0.203689	+	0.626890i
$499$	87.3543	−	268.849i	0.175059	−	0.538775i	−0.824577	−	0.565749i	$-0.808587\pi$
$499$	87.3543	−	268.849i	0.175059	−	0.538775i	0.999636	+	0.0269739i	$0.00858711\pi$
$500$	−128.705	−	93.5096i	−0.257410	−	0.187019i
$501$	16.2241	−	22.3306i	0.0323835	−	0.0445720i
$502$	−654.531	−	212.670i	−1.30385	−	0.423646i
$503$	−124.944	+	40.5967i	−0.248397	+	0.0807092i	−0.430569	−	0.902557i	$-0.641687\pi$
$503$	−124.944	+	40.5967i	−0.248397	+	0.0807092i	0.182172	+	0.983267i	$0.441687\pi$
$504$	60.0539	−	43.6317i	0.119155	−	0.0865708i
$505$			1216.64i			2.40919i
$506$	179.799	−	209.939i	0.355333	−	0.414899i
$507$	−304.328			−0.600252
$508$	246.109	+	338.740i	0.484466	+	0.666810i
$509$	46.4157	+	142.853i	0.0911900	+	0.280654i	0.986242	−	0.165308i	$-0.0528617\pi$
$509$	46.4157	+	142.853i	0.0911900	+	0.280654i	−0.895052	+	0.445962i	$0.852862\pi$
$510$	101.854	−	313.474i	0.199714	−	0.614656i
$511$	−5.93991	−	4.31559i	−0.0116241	−	0.00844539i
$512$	13.3001	−	18.3060i	0.0259767	−	0.0357538i
$513$	−23.2634	−	7.55874i	−0.0453478	−	0.0147344i
$514$	538.338	−	174.917i	1.04735	−	0.340305i
$515$	824.067	−	598.720i	1.60013	−	1.16256i
$516$			177.617i			0.344219i
$517$	252.400	−	154.200i	0.488201	−	0.298259i
$518$	79.1594			0.152817
$519$	345.832	+	475.997i	0.666344	+	0.917143i
$520$	−67.1273	−	206.597i	−0.129091	−	0.397301i
$521$	104.285	−	320.956i	0.200163	−	0.616039i	−0.799714	−	0.600381i	$-0.795016\pi$
$521$	104.285	−	320.956i	0.200163	−	0.616039i	0.999877	−	0.0156581i	$-0.00498433\pi$
$522$	−332.108	−	241.290i	−0.636222	−	0.462242i
$523$	468.968	−	645.479i	0.896688	−	1.23419i	−0.0748239	−	0.997197i	$-0.523839\pi$
$523$	468.968	−	645.479i	0.896688	−	1.23419i	0.971512	−	0.236989i	$-0.0761605\pi$
$524$	−153.752	−	49.9572i	−0.293421	−	0.0953381i
$525$	−403.943	+	131.249i	−0.769414	+	0.249998i
$526$	103.643	−	75.3012i	0.197040	−	0.143158i
$527$			78.4007i			0.148768i
$528$	−187.743	−	15.0322i	−0.355574	−	0.0284701i
$529$	−213.290			−0.403194
$530$	415.473	+	571.849i	0.783911	+	1.07896i
$531$	−103.332	−	318.024i	−0.194599	−	0.598916i
$532$	−30.7757	+	94.7179i	−0.0578491	+	0.178041i
$533$	−640.121	−	465.075i	−1.20098	−	0.872561i
$534$	−303.551	+	417.803i	−0.568448	+	0.782402i
$535$	−702.311	−	228.195i	−1.31273	−	0.426532i
$536$	−46.0872	+	14.9746i	−0.0859835	+	0.0279377i
$537$	137.670	−	100.023i	0.256369	−	0.186263i
$538$		−	386.182i		−	0.717811i
$539$	173.475	−	417.204i	0.321847	−	0.774033i
$540$	−21.4661			−0.0397520
$541$	−157.810	−	217.207i	−0.291700	−	0.401491i	0.637865	−	0.770148i	$-0.279818\pi$
$541$	−157.810	−	217.207i	−0.291700	−	0.401491i	−0.929566	+	0.368657i	$0.879818\pi$
$542$	186.302	+	573.377i	0.343730	+	1.05789i
$543$	−413.349	+	1272.16i	−0.761233	+	2.34283i
$544$	−32.1029	−	23.3241i	−0.0590126	−	0.0428752i
$545$	481.819	−	663.167i	0.884072	−	1.21682i
$546$	−160.362	−	52.1048i	−0.293704	−	0.0954301i
$547$	−208.929	+	67.8851i	−0.381954	+	0.124104i	−0.493700	−	0.869632i	$-0.664356\pi$
$547$	−208.929	+	67.8851i	−0.381954	+	0.124104i	0.111746	+	0.993737i	$0.464356\pi$
$548$	−53.7662	+	39.0634i	−0.0981135	+	0.0712837i
$549$			482.975i			0.879735i
$550$	506.305	+	210.524i	0.920554	+	0.382771i
$551$	550.762			0.999568
$552$	−126.447	−	174.039i	−0.229070	−	0.315288i
$553$	−70.1209	−	215.810i	−0.126801	−	0.390253i
$554$	82.7342	−	254.630i	0.149340	−	0.459621i
$555$	−534.483	−	388.325i	−0.963032	−	0.699684i
$556$	−254.529	+	350.329i	−0.457786	+	0.630088i
$557$	−315.980	−	102.668i	−0.567289	−	0.184323i	0.0113094	−	0.999936i	$-0.496400\pi$
$557$	−315.980	−	102.668i	−0.567289	−	0.184323i	−0.578598	+	0.815613i	$0.696400\pi$
$558$	140.148	−	45.5369i	0.251162	−	0.0816074i
$559$	166.079	−	120.663i	0.297100	−	0.215856i
$560$			87.4001i			0.156072i
$561$	−26.3618	+	329.242i	−0.0469907	+	0.586884i
$562$	117.394			0.208886
$563$	−138.173	−	190.179i	−0.245423	−	0.337796i	0.668479	−	0.743731i	$-0.266946\pi$
$563$	−138.173	−	190.179i	−0.245423	−	0.337796i	−0.913902	+	0.405936i	$0.866946\pi$
$564$	−71.1346	−	218.930i	−0.126125	−	0.388173i
$565$	−263.232	+	810.143i	−0.465897	+	1.43388i
$566$	−131.171	−	95.3016i	−0.231751	−	0.168377i
$567$	129.041	−	177.610i	0.227586	−	0.313246i
$568$	−85.0080	−	27.6208i	−0.149662	−	0.0486281i
$569$	−806.921	+	262.184i	−1.41814	+	0.460781i	−0.915010	−	0.403431i	$-0.867818\pi$
$569$	−806.921	+	262.184i	−1.41814	+	0.460781i	−0.503128	+	0.864212i	$0.667818\pi$
$570$	672.446	−	488.561i	1.17973	−	0.857124i
$571$			457.660i			0.801506i	0.916186	+	0.400753i	$0.131251\pi$
$571$			457.660i			0.801506i	−0.916186	+	0.400753i	$0.868749\pi$
$572$	113.487	+	185.759i	0.198403	+	0.324754i
$573$	−746.940			−1.30356
$574$	187.119	+	257.547i	0.325991	+	0.448689i
$575$	193.535	+	595.641i	0.336583	+	1.03590i
$576$	−23.0478	+	70.9339i	−0.0400136	+	0.123149i
$577$	435.656	+	316.522i	0.755036	+	0.548566i	0.897384	−	0.441251i	$-0.145465\pi$
$577$	435.656	+	316.522i	0.755036	+	0.548566i	−0.142348	+	0.989817i	$0.545465\pi$
$578$	199.329	−	274.353i	0.344860	−	0.474660i
$579$	1209.58	+	393.015i	2.08908	+	0.678783i
$580$	459.681	−	149.359i	0.792553	−	0.257516i
$581$	−123.492	+	89.7222i	−0.212551	+	0.154427i
$582$			92.3049i			0.158599i
$583$	−537.987	−	460.749i	−0.922790	−	0.790307i
$584$	7.37711			0.0126320
$585$	420.870	+	579.278i	0.719436	+	0.990219i
$586$	13.9338	+	42.8838i	0.0237778	+	0.0731806i
$587$	−95.4324	+	293.711i	−0.162577	+	0.500359i	−0.998850	−	0.0479541i	$-0.984730\pi$
$587$	−95.4324	+	293.711i	−0.162577	+	0.500359i	0.836273	+	0.548313i	$0.184730\pi$
$588$	−284.493	−	206.696i	−0.483831	−	0.351524i
$589$	−116.210	+	159.949i	−0.197300	+	0.271560i
$590$	374.446	+	121.665i	0.634654	+	0.206211i
$591$	−478.076	+	155.336i	−0.808928	+	0.262837i
$592$	−64.3464	+	46.7504i	−0.108693	+	0.0789702i
$593$			137.892i			0.232533i	0.993218	+	0.116266i	$0.0370927\pi$
$593$			137.892i			0.232533i	−0.993218	+	0.116266i	$0.962907\pi$
$594$	20.9234	−	4.99322i	0.0352246	−	0.00840610i
$595$	153.272			0.257600
$596$	−252.264	−	347.211i	−0.423261	−	0.582569i
$597$	90.1586	+	277.480i	0.151019	+	0.464790i
$598$	−76.8321	+	236.465i	−0.128482	+	0.395426i
$599$	326.403	+	237.145i	0.544912	+	0.395902i	0.825906	−	0.563808i	$-0.190664\pi$
$599$	326.403	+	237.145i	0.544912	+	0.395902i	−0.280994	+	0.959710i	$0.590664\pi$
$600$	250.840	−	345.251i	0.418066	−	0.575418i
$601$	−186.353	−	60.5497i	−0.310071	−	0.100748i	0.149848	−	0.988709i	$-0.452122\pi$
$601$	−186.353	−	60.5497i	−0.310071	−	0.100748i	−0.459919	+	0.887961i	$0.652122\pi$
$602$	−78.5522	+	25.5231i	−0.130485	+	0.0423972i
$603$	129.224	−	93.8868i	0.214302	−	0.155700i
$604$		−	5.38559i		−	0.00891654i
$605$	−927.231	−	149.441i	−1.53261	−	0.247011i
$606$	−948.865			−1.56578
$607$	226.112	+	311.216i	0.372507	+	0.512712i	0.953580	−	0.301140i	$-0.0973670\pi$
$607$	226.112	+	311.216i	0.372507	+	0.512712i	−0.581073	+	0.813851i	$0.697367\pi$
$608$	−30.9223	−	95.1692i	−0.0508591	−	0.156528i
$609$	115.934	−	356.808i	0.190368	−	0.585892i
$610$	−460.056	−	334.250i	−0.754190	−	0.547951i
$611$	−156.383	+	215.243i	−0.255946	+	0.352279i
$612$	124.396	+	40.4186i	0.203261	+	0.0660434i
$613$	771.255	−	250.596i	1.25816	−	0.408802i	0.397324	−	0.917678i	$-0.369939\pi$
$613$	771.255	−	250.596i	1.25816	−	0.408802i	0.860840	+	0.508876i	$0.169939\pi$
$614$	−84.0641	+	61.0761i	−0.136912	+	0.0994725i
$615$		−	2656.89i		−	4.32014i
$616$	−20.3301	−	85.1905i	−0.0330035	−	0.138296i
$617$	193.591			0.313762			0.156881	−	0.987617i	$-0.449856\pi$
$617$	193.591			0.313762			0.156881	+	0.987617i	$0.449856\pi$
$618$	466.945	+	642.695i	0.755575	+	1.03996i
$619$	−342.042	−	1052.70i	−0.552572	−	1.70064i	−0.702270	−	0.711911i	$-0.747830\pi$
$619$	−342.042	−	1052.70i	−0.552572	−	1.70064i	0.149698	−	0.988732i	$-0.452170\pi$
$620$	−53.6158	+	165.012i	−0.0864770	+	0.266149i
$621$	19.8771	+	14.4416i	0.0320083	+	0.0232554i
$622$	8.29243	−	11.4135i	0.0133319	−	0.0183498i
$623$	−228.395	−	74.2101i	−0.366605	−	0.119117i
$624$	161.126	−	52.3531i	0.258215	−	0.0838992i
$625$	213.404	−	155.047i	0.341446	−	0.248075i
$626$			315.957i			0.504724i
$627$	−541.802	+	632.627i	−0.864118	+	1.00897i
$628$	311.232			0.495592
$629$	81.9853	+	112.843i	0.130342	+	0.179401i
$630$	−89.0239	−	273.988i	−0.141308	−	0.434901i
$631$	−18.0339	+	55.5027i	−0.0285799	+	0.0879599i	−0.964329	−	0.264706i	$-0.914725\pi$
$631$	−18.0339	+	55.5027i	−0.0285799	+	0.0879599i	0.935749	+	0.352666i	$0.114725\pi$
$632$	184.454	+	134.013i	0.291857	+	0.212046i
$633$	856.262	−	1178.54i	1.35270	−	1.86184i
$634$	29.0341	+	9.43375i	0.0457951	+	0.0148797i
$635$	1545.45	−	502.148i	2.43378	−	0.790785i
$636$	−445.989	+	324.030i	−0.701240	+	0.509481i
$637$			406.430i			0.638038i
$638$	−413.317	+	252.510i	−0.647832	+	0.395783i
$639$	294.622			0.461068
$640$	−51.6172	−	71.0450i	−0.0806519	−	0.111008i
$641$	107.021	+	329.377i	0.166960	+	0.513849i	0.999175	−	0.0406028i	$-0.0129278\pi$
$641$	107.021	+	329.377i	0.166960	+	0.513849i	−0.832216	+	0.554452i	$0.812928\pi$
$642$	177.971	−	547.737i	0.277213	−	0.853174i
$643$	−429.292	−	311.899i	−0.667640	−	0.485069i	0.201595	−	0.979469i	$-0.435388\pi$
$643$	−429.292	−	311.899i	−0.667640	−	0.485069i	−0.869234	+	0.494400i	$0.835388\pi$
$644$	58.7996	−	80.9307i	0.0913037	−	0.125669i
$645$	655.589	+	213.014i	1.01642	+	0.330254i
$646$	−166.897	+	54.2280i	−0.258354	+	0.0839442i
$647$	−849.915	+	617.499i	−1.31362	+	0.954404i	−0.313636	+	0.949543i	$0.601547\pi$
$647$	−849.915	+	617.499i	−1.31362	+	0.954404i	−0.999988	+	0.00486101i	$0.998453\pi$
$648$			220.584i			0.340408i
$649$	−393.280	−	31.4892i	−0.605978	−	0.0485195i
$650$	−493.230			−0.758816
$651$	79.1603	+	108.955i	0.121598	+	0.167365i
$652$	−183.941	−	566.111i	−0.282118	−	0.868269i
$653$	−216.285	+	665.655i	−0.331217	+	1.01938i	0.637339	+	0.770584i	$0.280035\pi$
$653$	−216.285	+	665.655i	−0.331217	+	1.01938i	−0.968556	+	0.248797i	$0.919965\pi$
$654$	517.208	+	375.774i	0.790839	+	0.574578i
$655$	−368.787	+	507.591i	−0.563033	+	0.774949i
$656$	−304.207	−	98.8430i	−0.463731	−	0.150675i
$657$	−23.1262	+	7.51417i	−0.0351997	+	0.0114371i
$658$	86.6011	−	62.9193i	0.131613	−	0.0956221i
$659$		−	682.215i		−	1.03523i	−0.855614	−	0.517614i	$-0.826820\pi$
$659$		−	682.215i		−	1.03523i	0.855614	−	0.517614i	$-0.173180\pi$
$660$	−280.642	+	674.937i	−0.425216	+	1.02263i
$661$	499.139			0.755128			0.377564	−	0.925984i	$-0.376762\pi$
$661$	499.139			0.755128			0.377564	+	0.925984i	$0.376762\pi$
$662$	175.601	+	241.694i	0.265258	+	0.365096i
$663$	−91.8107	−	282.564i	−0.138478	−	0.426190i
$664$	47.3945	−	145.865i	0.0713772	−	0.219677i
$665$	312.698	+	227.188i	0.470222	+	0.341636i
$666$	154.098	−	212.098i	0.231379	−	0.318465i
$667$	−526.138	−	170.953i	−0.788813	−	0.256301i
$668$	−12.2654	+	3.98525i	−0.0183613	+	0.00596595i
$669$	1058.46	−	769.014i	1.58215	−	1.14950i
$670$			188.068i			0.280698i
$671$	526.175	+	218.786i	0.784165	+	0.326060i
$672$	−68.1639			−0.101434
$673$	−534.669	−	735.909i	−0.794457	−	1.09348i	−0.993539	−	0.113493i	$-0.963796\pi$
$673$	−534.669	−	735.909i	−0.794457	−	1.09348i	0.199082	−	0.979983i	$-0.436204\pi$
$674$	−126.272	−	388.624i	−0.187347	−	0.576594i
$675$	−15.0615	+	46.3545i	−0.0223133	+	0.0686733i
$676$	115.035	+	83.5779i	0.170170	+	0.123636i
$677$	−629.409	+	866.307i	−0.929703	+	1.27963i	0.0302719	+	0.999542i	$0.490363\pi$
$677$	−629.409	+	866.307i	−0.929703	+	1.27963i	−0.959975	+	0.280085i	$0.909637\pi$
$678$	−631.836	−	205.296i	−0.931912	−	0.302797i
$679$	−40.8224	+	13.2640i	−0.0601213	+	0.0195346i
$680$	−124.590	+	90.5203i	−0.183221	+	0.133118i
$681$			844.172i			1.23961i
$682$	13.8768	−	173.312i	0.0203472	−	0.254123i
$683$	−910.450			−1.33302			−0.666508	−	0.745498i	$-0.732212\pi$
$683$	−910.450			−1.33302			−0.666508	+	0.745498i	$0.732212\pi$
$684$	193.875	+	266.846i	0.283443	+	0.390125i
$685$	79.7031	+	245.301i	0.116355	+	0.358104i
$686$	110.812	−	341.044i	0.161533	−	0.497148i
$687$	−202.421	−	147.067i	−0.294645	−	0.214072i
$688$	48.7792	−	67.1388i	0.0709000	−	0.0975854i
$689$	605.962	+	196.889i	0.879480	+	0.285760i
$690$	−794.028	+	257.995i	−1.15076	+	0.373906i
$691$	289.151	−	210.081i	0.418453	−	0.304024i	−0.358562	−	0.933506i	$-0.616733\pi$
$691$	289.151	−	210.081i	0.418453	−	0.304024i	0.777015	+	0.629482i	$0.216733\pi$
$692$		−	274.902i		−	0.397257i
$693$	150.505	+	246.353i	0.217180	+	0.355488i
$694$	520.833			0.750480
$695$	987.821	+	1359.62i	1.42133	+	1.95629i
$696$	116.486	+	358.508i	0.167365	+	0.515098i
$697$	−173.339	+	533.483i	−0.248693	+	0.765399i
$698$	466.759	+	339.120i	0.668709	+	0.485846i
$699$	−699.675	+	963.020i	−1.00097	+	1.37771i
$700$	188.734	+	61.3235i	0.269620	+	0.0876050i
$701$	462.389	−	150.239i	0.659613	−	0.214321i	0.0399648	−	0.999201i	$-0.487275\pi$
$701$	462.389	−	150.239i	0.659613	−	0.214321i	0.619648	+	0.784880i	$0.287275\pi$
$702$	−15.6540	+	11.3733i	−0.0222992	+	0.0162013i
$703$			351.740i			0.500341i
$704$	66.8381	+	57.2422i	0.0949404	+	0.0813100i
$705$	−893.387			−1.26721
$706$	−321.736	−	442.832i	−0.455717	−	0.627240i
$707$	−136.350	−	419.641i	−0.192857	−	0.593552i
$708$	−94.8872	+	292.033i	−0.134021	+	0.412476i
$709$	224.323	+	162.980i	0.316394	+	0.229873i	0.734635	−	0.678462i	$-0.237353\pi$
$709$	224.323	+	162.980i	0.316394	+	0.229873i	−0.418241	+	0.908336i	$0.637353\pi$
$710$	−203.898	+	280.642i	−0.287180	+	0.395270i
$711$	−714.740	−	232.233i	−1.00526	−	0.326629i
$712$	229.483	−	74.5636i	0.322308	−	0.104724i
$713$	160.661	−	116.727i	0.225331	−	0.163713i
$714$			119.538i			0.167420i
$715$	821.746	−	196.104i	1.14929	−	0.274271i
$716$	−79.5084			−0.111045
$717$	−826.000	−	1136.89i	−1.15202	−	1.58562i
$718$	−79.3078	−	244.084i	−0.110457	−	0.339950i
$719$	64.3187	−	197.953i	0.0894558	−	0.275317i	−0.896313	−	0.443421i	$-0.853765\pi$
$719$	64.3187	−	197.953i	0.0894558	−	0.275317i	0.985769	+	0.168105i	$0.0537646\pi$
$720$	234.178	+	170.140i	0.325247	+	0.236306i
$721$	−217.137	+	298.863i	−0.301161	+	0.414512i
$722$	64.6707	+	21.0128i	0.0895716	+	0.0291036i
$723$	−333.311	+	108.299i	−0.461011	+	0.149792i
$724$	505.620	−	367.354i	0.698370	−	0.507395i
$725$		−	1097.44i		−	1.51372i
$726$	116.550	−	723.154i	0.160538	−	0.996079i
$727$	1019.99			1.40302			0.701508	−	0.712661i	$-0.252510\pi$
$727$	1019.99			1.40302			0.701508	+	0.712661i	$0.252510\pi$
$728$	46.3069	+	63.7360i	0.0636084	+	0.0875494i
$729$	−241.144	−	742.166i	−0.330788	−	1.01806i
$730$	8.84727	−	27.2291i	0.0121196	−	0.0373001i
$731$	−117.740	−	85.5432i	−0.161067	−	0.117022i
$732$	260.684	−	358.801i	0.356126	−	0.490165i
$733$	−217.763	−	70.7554i	−0.297084	−	0.0965285i	0.156683	−	0.987649i	$-0.449920\pi$
$733$	−217.763	−	70.7554i	−0.297084	−	0.0965285i	−0.453767	+	0.891121i	$0.649920\pi$
$734$	41.4630	−	13.4722i	0.0564891	−	0.0183544i
$735$	−1104.11	+	802.183i	−1.50219	+	1.09140i
$736$			100.512i			0.136566i
$737$	−43.7464	−	183.313i	−0.0593574	−	0.248729i
$738$	1054.33			1.42863
$739$	603.027	+	829.995i	0.816004	+	1.12313i	0.990369	+	0.138452i	$0.0442125\pi$
$739$	603.027	+	829.995i	0.816004	+	1.12313i	−0.174366	+	0.984681i	$0.555787\pi$
$740$	95.3871	+	293.571i	0.128902	+	0.396718i
$741$	231.525	−	712.559i	0.312449	−	0.961619i
$742$	−207.392	−	150.679i	−0.279504	−	0.203071i
$743$	628.381	−	864.893i	0.845735	−	1.16405i	−0.139051	−	0.990285i	$-0.544405\pi$
$743$	628.381	−	864.893i	0.845735	−	1.16405i	0.984786	−	0.173769i	$-0.0555947\pi$
$744$	−128.694	−	41.8153i	−0.172976	−	0.0562034i
$745$	−1584.10	+	514.706i	−2.12631	+	0.690881i
$746$	−106.795	+	77.5908i	−0.143156	+	0.104009i
$747$			505.543i			0.676764i
$748$	100.385	−	117.213i	0.134204	−	0.156702i
$749$	267.814			0.357562
$750$	−283.035	−	389.564i	−0.377380	−	0.519418i
$751$	8.02272	+	24.6914i	0.0106827	+	0.0328780i	0.956256	−	0.292532i	$-0.0944977\pi$
$751$	8.02272	+	24.6914i	0.0106827	+	0.0328780i	−0.945573	+	0.325410i	$0.894498\pi$
$752$	−33.2362	+	102.291i	−0.0441971	+	0.136025i
$753$	−1685.25	−	1224.41i	−2.23805	−	1.62604i
$754$	256.085	−	352.470i	0.339635	−	0.467467i
$755$	−19.8784	−	6.45887i	−0.0263290	−	0.00855480i
$756$	7.40405	−	2.40572i	0.00979371	−	0.00318217i
$757$	426.698	−	310.014i	0.563670	−	0.409530i	−0.269130	−	0.963104i	$-0.586736\pi$
$757$	426.698	−	310.014i	0.563670	−	0.409530i	0.832800	+	0.553574i	$0.186736\pi$
$758$			489.277i			0.645484i
$759$	713.941	−	436.171i	0.940634	−	0.574666i
$760$	−388.357			−0.510996
$761$	−273.817	−	376.876i	−0.359812	−	0.495238i	0.590285	−	0.807195i	$-0.299015\pi$
$761$	−273.817	−	376.876i	−0.359812	−	0.495238i	−0.950096	+	0.311957i	$0.899015\pi$
$762$	391.629	+	1205.31i	0.513948	+	1.58177i
$763$	−91.8666	+	282.736i	−0.120402	+	0.370559i
$764$	282.341	+	205.133i	0.369557	+	0.268499i
$765$	298.372	−	410.674i	0.390029	−	0.536829i
$766$	96.8290	+	31.4616i	0.126409	+	0.0410726i
$767$	337.523	−	109.668i	0.440056	−	0.142983i
$768$	55.4085	−	40.2566i	0.0721465	−	0.0524175i
$769$			389.868i			0.506981i	0.967338	+	0.253490i	$0.0815786\pi$
$769$			389.868i			0.506981i	−0.967338	+	0.253490i	$0.918421\pi$
$770$	−338.822	−	27.1289i	−0.440029	−	0.0352323i
$771$	1713.30			2.22217
$772$	−349.283	−	480.746i	−0.452439	−	0.622728i
$773$	237.431	+	730.738i	0.307156	+	0.945328i	0.978864	+	0.204512i	$0.0655608\pi$
$773$	237.431	+	730.738i	0.307156	+	0.945328i	−0.671708	+	0.740816i	$0.734439\pi$
$774$	−84.5299	+	260.156i	−0.109212	+	0.336119i
$775$	318.713	+	231.559i	0.411243	+	0.298786i
$776$	25.3498	−	34.8910i	0.0326673	−	0.0449626i
$777$	227.873	+	74.0403i	0.293273	+	0.0952900i
$778$	−309.497	+	100.562i	−0.397811	+	0.129257i
$779$	−1144.40	+	831.452i	−1.46906	+	1.06733i
$780$		−	657.508i		−	0.842959i
$781$	133.463	−	320.975i	0.170888	−	0.410980i
$782$	176.267			0.225405
$783$	−25.3058	−	34.8304i	−0.0323190	−	0.0444833i
$784$	50.7723	+	156.261i	0.0647606	+	0.199313i
$785$	373.257	−	1148.77i	0.475486	−	1.46340i
$786$	−395.874	−	287.619i	−0.503656	−	0.365928i
$787$	−461.438	+	635.114i	−0.586325	+	0.807007i	−0.994371	−	0.105954i	$-0.966210\pi$
$787$	−461.438	+	635.114i	−0.586325	+	0.807007i	0.408046	+	0.912961i	$0.366210\pi$
$788$	223.372	+	72.5779i	0.283467	+	0.0921040i
$789$	368.785	−	119.826i	0.467408	−	0.151870i
$790$	715.860	−	520.103i	0.906152	−	0.658358i
$791$		−	308.934i		−	0.390561i
$792$	−267.834	−	111.367i	−0.338174	−	0.140615i
$793$	−512.587			−0.646390
$794$	−445.397	−	613.037i	−0.560954	−	0.772087i
$795$	661.135	+	2034.76i	0.831616	+	2.55945i
$796$	42.1248	−	129.647i	0.0529206	−	0.162873i
$797$	957.809	+	695.889i	1.20177	+	0.873136i	0.994458	−	0.105139i	$-0.0335288\pi$
$797$	957.809	+	695.889i	1.20177	+	0.873136i	0.207311	+	0.978275i	$0.433529\pi$
$798$	−177.186	+	243.875i	−0.222037	+	0.305608i
$799$	179.385	+	58.2858i	0.224512	+	0.0729485i
$800$	−189.633	+	61.6156i	−0.237042	+	0.0770196i
$801$	−643.450	+	467.494i	−0.803308	+	0.583638i
$802$		−	98.3116i		−	0.122583i
$803$	−2.28984	+	28.5987i	−0.00285161	+	0.0356148i
$804$	−146.675			−0.182432
$805$	−228.200	−	314.090i	−0.283478	−	0.390174i
$806$	48.3290	+	148.741i	0.0599615	+	0.184543i
$807$	361.209	−	1111.69i	0.447595	−	1.37756i
$808$	358.669	+	260.588i	0.443897	+	0.322510i
$809$	143.287	−	197.218i	0.177116	−	0.243780i	−0.711224	−	0.702966i	$-0.751859\pi$
$809$	143.287	−	197.218i	0.177116	−	0.243780i	0.888340	+	0.459186i	$0.151859\pi$
$810$	814.183	+	264.544i	1.00516	+	0.326598i
$811$	−1200.10	+	389.937i	−1.47978	+	0.480810i	−0.934047	−	0.357149i	$-0.883749\pi$
$811$	−1200.10	+	389.937i	−1.47978	+	0.480810i	−0.545733	+	0.837959i	$0.683749\pi$
$812$	−141.813	+	103.034i	−0.174647	+	0.126889i
$813$			1824.81i			2.24454i
$814$	−161.263	−	263.962i	−0.198112	−	0.324277i
$815$	−2310.13			−2.83452
$816$	−70.5974	−	97.1689i	−0.0865164	−	0.119080i
$817$	−113.410	−	349.042i	−0.138813	−	0.427223i
$818$	−46.5822	+	143.365i	−0.0569465	+	0.175263i
$819$	−210.086	−	152.636i	−0.256515	−	0.186369i
$820$	−729.664	+	1004.30i	−0.889835	+	1.22475i
$821$	258.452	+	83.9760i	0.314801	+	0.102285i	0.462156	−	0.886799i	$-0.347076\pi$
$821$	258.452	+	83.9760i	0.314801	+	0.102285i	−0.147355	+	0.989084i	$0.547076\pi$
$822$	−191.312	+	62.1610i	−0.232739	+	0.0756216i
$823$	18.3666	−	13.3441i	0.0223167	−	0.0162140i	−0.576571	−	0.817047i	$-0.695610\pi$
$823$	18.3666	−	13.3441i	0.0223167	−	0.0162140i	0.598888	+	0.800833i	$0.295610\pi$
$824$		−	371.175i		−	0.450455i
$825$	1260.57	+	1079.59i	1.52796	+	1.30859i
$826$	−142.788			−0.172867
$827$	−637.912	−	878.010i	−0.771357	−	1.06168i	−0.996184	−	0.0872826i	$-0.972182\pi$
$827$	−637.912	−	878.010i	−0.771357	−	1.06168i	0.224827	−	0.974399i	$-0.427818\pi$
$828$	−102.380	−	315.093i	−0.123647	−	0.380547i
$829$	451.578	−	1389.81i	0.544726	−	1.67650i	−0.176913	−	0.984226i	$-0.556611\pi$
$829$	451.578	−	1389.81i	0.544726	−	1.67650i	0.721640	−	0.692269i	$-0.243389\pi$
$830$	−481.553	−	349.869i	−0.580184	−	0.421529i
$831$	476.327	−	655.608i	0.573198	−	0.788939i
$832$	−75.2831	−	24.4610i	−0.0904845	−	0.0294002i
$833$	274.033	−	89.0386i	0.328971	−	0.106889i
$834$	−1060.38	+	770.409i	−1.27143	+	0.923751i
$835$			50.0512i			0.0599416i
$836$	378.539	−	90.3356i	0.452798	−	0.108057i
$837$	15.4547			0.0184644
$838$	305.891	+	421.023i	0.365025	+	0.502414i
$839$	−10.0002	−	30.7775i	−0.0119192	−	0.0366836i	0.944920	−	0.327301i	$-0.106139\pi$
$839$	−10.0002	−	30.7775i	−0.0119192	−	0.0366836i	−0.956839	+	0.290618i	$0.906139\pi$
$840$	−81.7482	+	251.595i	−0.0973193	+	0.299518i
$841$	103.868	+	75.4648i	0.123506	+	0.0897322i
$842$	−205.384	+	282.687i	−0.243924	+	0.335733i
$843$	337.938	+	109.803i	0.400875	+	0.130252i
$844$	−647.330	+	210.330i	−0.766978	+	0.249206i
$845$	446.449	−	324.364i	0.528342	−	0.383863i
$846$		−	354.521i		−	0.419056i
$847$	336.567	−	52.3704i	0.397364	−	0.0618304i
$848$	257.571			0.303740
$849$	−288.459	−	397.029i	−0.339763	−	0.467644i
$850$	108.054	+	332.557i	0.127123	+	0.391243i
$851$	109.178	−	336.014i	0.128293	−	0.394846i
$852$	−218.874	−	159.021i	−0.256895	−	0.186645i
$853$	−192.414	+	264.834i	−0.225573	+	0.310474i	−0.906770	−	0.421626i	$-0.861460\pi$
$853$	−192.414	+	264.834i	−0.225573	+	0.310474i	0.681197	+	0.732100i	$0.261460\pi$
$854$	196.141	+	63.7302i	0.229674	+	0.0746255i
$855$	1217.45	−	395.572i	1.42391	−	0.462658i
$856$	−217.698	+	158.167i	−0.254320	+	0.184775i
$857$		−	77.8781i		−	0.0908729i	−0.998967	−	0.0454365i	$-0.985532\pi$
$857$		−	77.8781i		−	0.0908729i	0.998967	−	0.0454365i	$-0.0144679\pi$
$858$	152.943	+	640.885i	0.178255	+	0.746952i
$859$	−311.381			−0.362492			−0.181246	−	0.983438i	$-0.558013\pi$
$859$	−311.381			−0.362492			−0.181246	+	0.983438i	$0.558013\pi$
$860$	−189.311	−	260.564i	−0.220129	−	0.302981i
$861$	297.759	+	916.409i	0.345830	+	1.06435i
$862$	−314.831	+	968.950i	−0.365233	+	1.12407i
$863$	558.472	+	405.754i	0.647129	+	0.470167i	0.862292	−	0.506411i	$-0.169028\pi$
$863$	558.472	+	405.754i	0.647129	+	0.470167i	−0.215163	+	0.976578i	$0.569028\pi$
$864$	−4.59775	+	6.32826i	−0.00532147	+	0.00732438i
$865$	−1014.67	−	329.687i	−1.17303	−	0.381141i
$866$	592.632	−	192.558i	0.684332	−	0.222353i
$867$	830.412	−	603.330i	0.957800	−	0.695882i
$868$		−	62.9245i		−	0.0724937i
$869$	−576.781	+	673.470i	−0.663730	+	0.774994i
$870$	1462.96			1.68157
$871$	99.6433	+	137.147i	0.114401	+	0.157460i
$872$	−92.3042	−	284.083i	−0.105853	−	0.325783i
$873$	−43.9289	+	135.199i	−0.0503195	+	0.154868i
$874$	359.610	+	261.272i	0.411453	+	0.298938i
$875$	131.615	−	181.153i	0.150418	−	0.207032i
$876$	21.2362	+	6.90005i	0.0242422	+	0.00787677i
$877$	1437.49	−	467.069i	1.63910	−	0.532575i	0.662762	−	0.748830i	$-0.269384\pi$
$877$	1437.49	−	467.069i	1.63910	−	0.532575i	0.976337	+	0.216255i	$0.0693843\pi$
$878$	−524.892	+	381.356i	−0.597827	+	0.434346i
$879$			136.481i			0.155268i
$880$	291.441	−	178.051i	0.331183	−	0.202331i
$881$	479.209			0.543937			0.271969	−	0.962306i	$-0.412325\pi$
$881$	479.209			0.543937			0.271969	+	0.962306i	$0.412325\pi$
$882$	−318.329	−	438.142i	−0.360917	−	0.496760i
$883$	−435.327	−	1339.80i	−0.493009	−	1.51732i	−0.820037	−	0.572310i	$-0.806047\pi$
$883$	−435.327	−	1339.80i	−0.493009	−	1.51732i	0.327029	−	0.945014i	$-0.393953\pi$
$884$	−42.8968	+	132.023i	−0.0485257	+	0.149347i
$885$	964.104	+	700.462i	1.08938	+	0.791483i
$886$	627.687	−	863.937i	0.708450	−	0.975098i
$887$	−974.679	−	316.692i	−1.09885	−	0.357038i	−0.297190	−	0.954819i	$-0.596049\pi$
$887$	−974.679	−	316.692i	−1.09885	−	0.357038i	−0.801660	+	0.597781i	$0.796049\pi$
$888$	−228.958	+	74.3931i	−0.257836	+	0.0837760i
$889$	−476.779	+	346.400i	−0.536309	+	0.389651i
$890$		−	936.453i		−	1.05219i
$891$	−855.135	−	68.4691i	−0.959747	−	0.0768452i
$892$	−611.289			−0.685302
$893$	279.578	+	384.806i	0.313077	+	0.430914i
$894$	−401.423	−	1235.45i	−0.449019	−	1.38194i
$895$	−95.3535	+	293.468i	−0.106540	+	0.327897i
$896$	25.7658	+	18.7199i	0.0287565	+	0.0208928i
$897$	−442.347	+	608.838i	−0.493140	+	0.678749i
$898$	314.685	+	102.248i	0.350429	+	0.113861i
$899$	−330.951	+	107.533i	−0.368133	+	0.119614i
$900$	531.715	−	386.313i	0.590794	−	0.429237i
$901$		−	451.699i		−	0.501330i
$902$	477.608	−	1148.63i	0.529499	−	1.27343i
$903$	−249.997			−0.276852
$904$	182.452	+	251.123i	0.201827	+	0.277791i
$905$	−749.531	−	2306.82i	−0.828211	−	2.54897i
$906$	5.03732	−	15.5033i	0.00555995	−	0.0171118i
$907$	368.251	+	267.550i	0.406010	+	0.294983i	0.771984	−	0.635642i	$-0.219264\pi$
$907$	368.251	+	267.550i	0.406010	+	0.294983i	−0.365975	+	0.930625i	$0.619264\pi$
$908$	231.836	−	319.095i	0.255326	−	0.351426i
$909$	−1389.81	−	451.576i	−1.52894	−	0.496783i
$910$	290.787	−	94.4823i	0.319546	−	0.103827i
$911$	−575.580	+	418.184i	−0.631812	+	0.459038i	−0.857027	−	0.515271i	$-0.827691\pi$
$911$	−575.580	+	418.184i	−0.631812	+	0.459038i	0.225216	+	0.974309i	$0.427691\pi$
$912$		−	302.882i		−	0.332108i
$913$	550.762	+	229.010i	0.603244	+	0.250832i
$914$	−786.819			−0.860852
$915$	−1011.71	−	1392.50i	−1.10569	−	1.52185i
$916$	36.1253	+	111.182i	0.0394381	+	0.121378i
$917$	70.3152	−	216.408i	0.0766796	−	0.235995i
$918$	11.0978	+	8.06300i	0.0120891	+	0.00878322i
$919$	−854.905	+	1176.68i	−0.930256	+	1.28039i	0.0295034	+	0.999565i	$0.490607\pi$
$919$	−854.905	+	1176.68i	−0.930256	+	1.28039i	−0.959760	+	0.280823i	$0.909393\pi$
$920$	370.994	+	120.543i	0.403254	+	0.131025i
$921$	−299.118	+	97.1894i	−0.324775	+	0.105526i
$922$	−756.499	+	549.628i	−0.820497	+	0.596126i
$923$			312.687i			0.338772i
$924$	21.1580	−	264.250i	0.0228983	−	0.285985i
$925$	700.874			0.757702
$926$	53.1993	+	73.2226i	0.0574507	+	0.0790741i
$927$	378.071	+	1163.58i	0.407844	+	1.25521i
$928$	54.4260	−	167.506i	0.0586487	−	0.180502i
$929$	16.3821	+	11.9023i	0.0176341	+	0.0128119i	0.596567	−	0.802563i	$-0.296531\pi$
$929$	16.3821	+	11.9023i	0.0176341	+	0.0128119i	−0.578933	+	0.815375i	$0.696531\pi$
$930$	−308.683	+	424.866i	−0.331917	+	0.456845i
$931$	691.045	+	224.534i	0.742261	+	0.241175i
$932$	528.951	−	171.866i	0.567543	−	0.184406i
$933$	34.5465	−	25.0995i	0.0370274	−	0.0269020i
$934$			958.211i			1.02592i
$935$	−312.245	−	511.095i	−0.333952	−	0.546625i
$936$	260.918			0.278758
$937$	633.411	+	871.815i	0.675999	+	0.930433i	0.999877	−	0.0156661i	$-0.00498688\pi$
$937$	633.411	+	871.815i	0.675999	+	0.930433i	−0.323878	+	0.946099i	$0.604987\pi$
$938$	−21.0769	−	64.8680i	−0.0224700	−	0.0691557i
$939$	−295.525	+	909.532i	−0.314723	+	0.968618i
$940$	337.698	+	245.352i	0.359253	+	0.261013i
$941$	−711.851	+	979.779i	−0.756484	+	1.04121i	0.241014	+	0.970522i	$0.422520\pi$
$941$	−711.851	+	979.779i	−0.756484	+	1.04121i	−0.997498	+	0.0706893i	$0.977480\pi$
$942$	895.930	+	291.105i	0.951093	+	0.309029i
$943$	1351.31	−	439.066i	1.43299	−	0.465606i
$944$	116.068	−	84.3286i	0.122954	−	0.0893312i
$945$		−	30.2137i		−	0.0319722i
$946$	245.135	+	209.941i	0.259127	+	0.221925i
$947$	1088.36			1.14928			0.574638	−	0.818408i	$-0.305143\pi$
$947$	1088.36			1.14928			0.574638	+	0.818408i	$0.305143\pi$
$948$	405.632	+	558.304i	0.427881	+	0.588928i
$949$	−7.97488	−	24.5442i	−0.00840346	−	0.0258632i
$950$	−272.487	+	838.629i	−0.286829	+	0.882768i
$951$	74.7556	+	54.3131i	0.0786073	+	0.0571116i
$952$	32.8289	−	45.1850i	0.0344841	−	0.0474633i
$953$	681.751	+	221.514i	0.715374	+	0.232439i	0.644016	−	0.765012i	$-0.277267\pi$
$953$	681.751	+	221.514i	0.715374	+	0.232439i	0.0713576	+	0.997451i	$0.477267\pi$
$954$	−807.451	+	262.357i	−0.846385	+	0.275007i
$955$	1095.76	−	796.116i	1.14739	−	0.833630i
$956$			656.587i			0.686807i
$957$	−1425.98	+	340.300i	−1.49005	+	0.355590i
$958$	195.959			0.204550
$959$	−54.9821	−	75.6764i	−0.0573328	−	0.0789118i
$960$	−82.1376	−	252.794i	−0.0855600	−	0.263327i
$961$	−258.364	+	795.163i	−0.268849	+	0.827433i
$962$	225.102	+	163.546i	0.233994	+	0.170007i
$963$	521.349	−	717.575i	0.541380	−	0.745146i
$964$	155.733	+	50.6007i	0.161549	+	0.0524904i
$965$	−2193.34	+	712.659i	−2.27289	+	0.738507i
$966$	244.961	−	177.975i	0.253583	−	0.184239i
$967$			60.5985i			0.0626665i	0.999509	+	0.0313333i	$0.00997532\pi$
$967$			60.5985i			0.0626665i	−0.999509	+	0.0313333i	$0.990025\pi$
$968$	−242.656	+	241.342i	−0.250678	+	0.249320i
$969$	−531.159			−0.548152
$970$	−98.3820	−	135.411i	−0.101425	−	0.139599i
$971$	28.2144	+	86.8350i	0.0290571	+	0.0894284i	0.964533	−	0.263961i	$-0.0850290\pi$
$971$	28.2144	+	86.8350i	0.0290571	+	0.0894284i	−0.935476	+	0.353389i	$0.885029\pi$
$972$	−214.011	+	658.658i	−0.220176	+	0.677632i
$973$	−493.091	−	358.252i	−0.506774	−	0.368193i
$974$	61.5496	−	84.7157i	0.0631926	−	0.0869772i
$975$	−1419.84	−	461.334i	−1.45625	−	0.473163i
$976$	−197.076	+	64.0338i	−0.201922	+	0.0656084i
$977$	136.847	−	99.4251i	0.140069	−	0.101766i	−0.515544	−	0.856863i	$-0.672410\pi$
$977$	136.847	−	99.4251i	0.140069	−	0.101766i	0.655613	+	0.755097i	$0.272410\pi$
$978$		−	1801.69i		−	1.84221i
$979$	217.828	+	912.778i	0.222501	+	0.932357i
$980$	637.655			0.650668
$981$	578.722	+	796.543i	0.589931	+	0.811971i
$982$	−222.504	−	684.797i	−0.226583	−	0.697350i
$983$	416.033	−	1280.42i	0.423228	−	1.30256i	−0.481453	−	0.876472i	$-0.659891\pi$
$983$	416.033	−	1280.42i	0.423228	−	1.30256i	0.904681	−	0.426089i	$-0.140109\pi$
$984$	−783.258	−	569.070i	−0.795994	−	0.578323i
$985$	535.775	−	737.430i	0.543934	−	0.748660i
$986$	−293.752	−	95.4459i	−0.297923	−	0.0968011i
$987$	308.145	−	100.122i	0.312204	−	0.101441i
$988$	−283.207	+	205.762i	−0.286647	+	0.208261i
$989$			368.638i			0.372738i
$990$	−732.268	+	855.022i	−0.739665	+	0.863659i
$991$	−745.776			−0.752549			−0.376275	−	0.926508i	$-0.622795\pi$
$991$	−745.776			−0.752549			−0.376275	+	0.926508i	$0.622795\pi$
$992$	37.1623	+	51.1495i	0.0374620	+	0.0515620i
$993$	279.431	+	859.999i	0.281400	+	0.866062i
$994$	38.8765	−	119.649i	0.0391111	−	0.120372i
$995$	−428.011	−	310.968i	−0.430161	−	0.312531i
$996$	272.865	−	375.566i	0.273961	−	0.377075i
$997$	−243.533	−	79.1286i	−0.244265	−	0.0793667i	0.184326	−	0.982865i	$-0.440990\pi$
$997$	−243.533	−	79.1286i	−0.244265	−	0.0793667i	−0.428591	+	0.903499i	$0.640990\pi$
$998$	−380.210	+	123.538i	−0.380972	+	0.123785i
$999$	22.2442	−	16.1613i	0.0222664	−	0.0161775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.3.d.a.19.1	yes	8
3.2	odd	2		198.3.j.a.19.2		8
4.3	odd	2		176.3.n.b.129.2		8
11.2	odd	10		242.3.b.d.241.1		8
11.3	even	5		242.3.d.d.215.1		8
11.4	even	5		242.3.d.c.161.2		8
11.5	even	5		242.3.d.e.233.2		8
11.6	odd	10		242.3.d.d.233.1		8
11.7	odd	10	inner	22.3.d.a.7.1	✓	8
11.8	odd	10		242.3.d.e.215.2		8
11.9	even	5		242.3.b.d.241.5		8
11.10	odd	2		242.3.d.c.239.2		8
33.2	even	10		2178.3.d.l.1693.7		8
33.20	odd	10		2178.3.d.l.1693.3		8
33.29	even	10		198.3.j.a.73.2		8
44.7	even	10		176.3.n.b.161.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.3.d.a.7.1	✓	8	11.7	odd	10	inner
22.3.d.a.19.1	yes	8	1.1	even	1	trivial
176.3.n.b.129.2		8	4.3	odd	2
176.3.n.b.161.2		8	44.7	even	10
198.3.j.a.19.2		8	3.2	odd	2
198.3.j.a.73.2		8	33.29	even	10
242.3.b.d.241.1		8	11.2	odd	10
242.3.b.d.241.5		8	11.9	even	5
242.3.d.c.161.2		8	11.4	even	5
242.3.d.c.239.2		8	11.10	odd	2
242.3.d.d.215.1		8	11.3	even	5
242.3.d.d.233.1		8	11.6	odd	10
242.3.d.e.215.2		8	11.8	odd	10
242.3.d.e.233.2		8	11.5	even	5
2178.3.d.l.1693.3		8	33.20	odd	10
2178.3.d.l.1693.7		8	33.2	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)

\(f(q)\)	\(=\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-1.32276 - 4.07104i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(6.27955 + 4.56236i) q^{5} +(-3.55822 + 4.89747i) q^{6} +(-2.67724 - 0.869888i) q^{7} +(2.68999 - 0.874032i) q^{8} +(-7.54250 + 5.47994i) q^{9} +O(q^{10})\)	\(q+(-0.831254 - 1.14412i) q^{2} +(-1.32276 - 4.07104i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(6.27955 + 4.56236i) q^{5} +(-3.55822 + 4.89747i) q^{6} +(-2.67724 - 0.869888i) q^{7} +(2.68999 - 0.874032i) q^{8} +(-7.54250 + 5.47994i) q^{9} -10.9771i q^{10} +(2.55337 + 10.6995i) q^{11} +8.56108 q^{12} +(-5.81594 - 8.00495i) q^{13} +(1.23021 + 3.78619i) q^{14} +(10.2672 - 31.5992i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-4.12316 + 5.67504i) q^{17} +(12.5395 + 4.07432i) q^{18} +(-16.8237 + 5.46635i) q^{19} +(-12.5591 + 9.12472i) q^{20} +12.0498i q^{21} +(10.1191 - 11.8154i) q^{22} +17.7682 q^{23} +(-7.11643 - 9.79493i) q^{24} +(10.8922 + 33.5228i) q^{25} +(-4.32413 + 13.3083i) q^{26} +(1.11869 + 0.812775i) q^{27} +(3.30925 - 4.55479i) q^{28} +(-29.6111 - 9.62124i) q^{29} +(-44.6880 + 14.5200i) q^{30} +(9.04205 - 6.56943i) q^{31} +5.65685i q^{32} +(40.1808 - 24.5478i) q^{33} +9.92033 q^{34} +(-12.8431 - 17.6770i) q^{35} +(-5.76195 - 17.7335i) q^{36} +(6.14453 - 18.9109i) q^{37} +(20.2389 + 14.7044i) q^{38} +(-24.8954 + 34.2655i) q^{39} +(20.8796 + 6.78420i) q^{40} +(76.0518 - 24.7107i) q^{41} +(13.7864 - 10.0164i) q^{42} +20.7470i q^{43} +(-21.9298 - 1.75588i) q^{44} -72.3650 q^{45} +(-14.7699 - 20.3291i) q^{46} +(-8.30906 - 25.5727i) q^{47} +(-5.29104 + 16.2841i) q^{48} +(-33.2309 - 24.1437i) q^{49} +(29.3000 - 40.3280i) q^{50} +(28.5572 + 9.27881i) q^{51} +(18.8208 - 6.11524i) q^{52} +(-52.0949 + 37.8492i) q^{53} -1.95554i q^{54} +(-32.7812 + 78.8378i) q^{55} -7.96207 q^{56} +(44.5074 + 61.2592i) q^{57} +(13.6065 + 41.8765i) q^{58} +(-11.0835 + 34.1116i) q^{59} +(53.7598 + 39.0588i) q^{60} +(30.4499 - 41.9107i) q^{61} +(-15.0325 - 4.88435i) q^{62} +(24.9600 - 8.11000i) q^{63} +(6.47214 - 4.70228i) q^{64} -76.8019i q^{65} +(-61.4861 - 25.5663i) q^{66} -17.1328 q^{67} +(-8.24631 - 11.3501i) q^{68} +(-23.5031 - 72.3352i) q^{69} +(-9.54881 + 29.3882i) q^{70} +(-25.5662 - 18.5749i) q^{71} +(-15.4996 + 21.3334i) q^{72} +(2.48055 + 0.805978i) q^{73} +(-26.7441 + 8.68968i) q^{74} +(122.065 - 88.6852i) q^{75} -35.3790i q^{76} +(2.47142 - 30.8664i) q^{77} +59.8983 q^{78} +(47.3809 + 65.2142i) q^{79} +(-9.59430 - 29.5282i) q^{80} +(-24.0997 + 74.1713i) q^{81} +(-91.4905 - 66.4717i) q^{82} +(31.8727 - 43.8690i) q^{83} +(-22.9201 - 7.44718i) q^{84} +(-51.7832 + 16.8254i) q^{85} +(23.7371 - 17.2460i) q^{86} +133.275i q^{87} +(16.2203 + 26.5500i) q^{88} +85.3100 q^{89} +(60.1537 + 82.7944i) q^{90} +(8.60725 + 26.4904i) q^{91} +(-10.9814 + 33.7972i) q^{92} +(-38.7049 - 28.1207i) q^{93} +(-22.3513 + 30.7640i) q^{94} +(-130.585 - 42.4296i) q^{95} +(23.0293 - 7.48266i) q^{96} +(12.3358 - 8.96251i) q^{97} +58.0898i q^{98} +(-77.8917 - 66.7089i) 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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