LMFDB - Embedded newform 350.2.q.a.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	350.81
Dual form			350.2.q.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 0.743145i) q^{2} +(0.169131 + 1.60917i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.373619 - 0.0794152i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 0.743145i) q^{2} +(0.169131 + 1.60917i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.373619 - 0.0794152i) q^{9} +(2.18720 + 0.464905i) q^{10} +(2.79173 + 0.593401i) q^{11} +(1.58268 - 0.336408i) q^{12} +(0.263932 - 0.812299i) q^{13} +(2.26531 + 1.36688i) q^{14} +(2.92705 - 2.12663i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(5.21470 - 2.32174i) q^{17} +(-0.190983 + 0.330792i) q^{18} +(0.627171 - 5.96713i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(4.09618 - 1.24400i) q^{21} +(-2.30902 + 1.67760i) q^{22} +(-4.99983 + 5.55288i) q^{23} +(-0.809017 + 1.40126i) q^{24} +(-2.50000 + 4.33013i) q^{25} +(0.427051 + 0.739674i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-2.53158 + 0.768834i) q^{28} +(4.42705 - 3.21644i) q^{29} +(-0.378188 + 3.59821i) q^{30} +(1.69381 - 0.754131i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.482716 + 4.59274i) q^{33} +(-1.76393 + 5.42882i) q^{34} +(-4.47214 + 3.87298i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(-2.56082 + 0.544320i) q^{37} +(4.01478 + 4.45887i) q^{38} +(1.35177 + 0.287327i) q^{39} +(0.233733 - 2.22382i) q^{40} +(3.59017 - 11.0494i) q^{41} +(-1.81641 + 3.87645i) q^{42} -2.23607 q^{43} +(0.298335 - 2.83847i) q^{44} +(-0.571506 - 0.634721i) q^{45} +(-0.781051 - 7.43120i) q^{46} +(4.35207 + 1.93767i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-1.54508 - 4.75528i) q^{50} +(4.61803 + 7.99867i) q^{51} +(-0.835438 - 0.177578i) q^{52} +(-0.442790 - 4.21286i) q^{53} +(-4.99904 - 2.22572i) q^{54} +(-1.97214 - 6.06961i) q^{55} +(1.12260 - 2.39578i) q^{56} +9.70820 q^{57} +(-0.571994 + 5.44216i) q^{58} +(6.90960 + 7.67389i) q^{59} +(-2.42094 - 2.68872i) q^{60} +(2.51856 - 2.79715i) q^{61} +(-0.572949 + 1.76336i) q^{62} +(-0.393136 - 0.930983i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.86810 + 0.397076i) q^{65} +(-3.09007 - 3.43187i) q^{66} +(-0.913545 + 0.406737i) q^{67} +(-2.85410 - 4.94345i) q^{68} +(-9.78115 - 7.10642i) q^{69} +(0.114256 - 5.91498i) q^{70} +(1.57295 - 1.14281i) q^{71} +(0.348943 + 0.155360i) q^{72} +(-7.45156 - 1.58388i) q^{73} +(1.30902 - 2.26728i) q^{74} +(-7.39074 - 3.29057i) q^{75} -6.00000 q^{76} +(0.145835 - 7.54984i) q^{77} +(-1.11803 + 0.812299i) q^{78} +(-8.17100 - 3.63796i) q^{79} +(1.49622 + 1.66172i) q^{80} +(-7.04179 + 3.13521i) q^{81} +(5.80902 + 10.0615i) q^{82} +(8.28115 + 6.01661i) q^{83} +(-1.66535 - 3.94371i) q^{84} +(-10.3262 - 7.50245i) q^{85} +(1.49622 - 1.66172i) q^{86} +(5.92455 + 6.57988i) q^{87} +(1.90977 + 2.12101i) q^{88} +(-11.4356 + 12.7005i) q^{89} +0.854102 q^{90} +(-2.24238 - 0.279566i) q^{91} +(6.04508 + 4.39201i) q^{92} +(1.50000 + 2.59808i) q^{93} +(-4.35207 + 1.93767i) q^{94} +(-12.2565 + 5.45694i) q^{95} +(1.47815 + 0.658114i) q^{96} +(5.47214 - 3.97574i) q^{97} +(2.41860 - 6.56889i) q^{98} +1.09017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$3$	0.169131	+	1.60917i	0.0976476	+	0.929055i	0.928192	+	0.372102i	$0.121363\pi$
$3$	0.169131	+	1.60917i	0.0976476	+	0.929055i	−0.830544	+	0.556953i	$0.811970\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i
$5$	−1.11803	−	1.93649i	−0.500000	−	0.866025i
$6$	−1.30902	−	0.951057i	−0.534404	−	0.388267i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.373619	−	0.0794152i	0.124540	−	0.0264717i
$10$	2.18720	+	0.464905i	0.691655	+	0.147016i
$11$	2.79173	+	0.593401i	0.841739	+	0.178917i	0.608551	−	0.793515i	$-0.291751\pi$
$11$	2.79173	+	0.593401i	0.841739	+	0.178917i	0.233188	+	0.972432i	$0.425084\pi$
$12$	1.58268	−	0.336408i	0.456879	−	0.0971127i
$13$	0.263932	−	0.812299i	0.0732016	−	0.225291i	−0.907761	−	0.419487i	$-0.862210\pi$
$13$	0.263932	−	0.812299i	0.0732016	−	0.225291i	0.980963	+	0.194196i	$0.0622098\pi$
$14$	2.26531	+	1.36688i	0.605430	+	0.365314i
$15$	2.92705	−	2.12663i	0.755761	−	0.549093i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	5.21470	−	2.32174i	1.26475	−	0.563104i	0.338840	−	0.940844i	$-0.389965\pi$
$17$	5.21470	−	2.32174i	1.26475	−	0.563104i	0.925912	+	0.377740i	$0.123299\pi$
$18$	−0.190983	+	0.330792i	−0.0450151	+	0.0779685i
$19$	0.627171	−	5.96713i	0.143883	−	1.36895i	−0.649561	−	0.760310i	$-0.725047\pi$
$19$	0.627171	−	5.96713i	0.143883	−	1.36895i	0.793443	−	0.608644i	$-0.208286\pi$
$20$	−1.80902	+	1.31433i	−0.404508	+	0.293893i
$21$	4.09618	−	1.24400i	0.893860	−	0.271463i
$22$	−2.30902	+	1.67760i	−0.492284	+	0.357665i
$23$	−4.99983	+	5.55288i	−1.04254	+	1.15786i	−0.0553214	+	0.998469i	$0.517618\pi$
$23$	−4.99983	+	5.55288i	−1.04254	+	1.15786i	−0.987216	+	0.159387i	$0.949048\pi$
$24$	−0.809017	+	1.40126i	−0.165140	+	0.286031i
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$	0.427051	+	0.739674i	0.0837516	+	0.145062i
$27$	1.69098	+	5.20431i	0.325430	+	1.00157i
$28$	−2.53158	+	0.768834i	−0.478424	+	0.145296i
$29$	4.42705	−	3.21644i	0.822083	−	0.597278i	−0.0952256	−	0.995456i	$-0.530357\pi$
$29$	4.42705	−	3.21644i	0.822083	−	0.597278i	0.917308	+	0.398178i	$0.130357\pi$
$30$	−0.378188	+	3.59821i	−0.0690473	+	0.656941i
$31$	1.69381	−	0.754131i	0.304217	−	0.135446i	−0.248951	−	0.968516i	$-0.580086\pi$
$31$	1.69381	−	0.754131i	0.304217	−	0.135446i	0.553167	+	0.833070i	$0.313419\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.482716	+	4.59274i	−0.0840301	+	0.799493i
$34$	−1.76393	+	5.42882i	−0.302512	+	0.931036i
$35$	−4.47214	+	3.87298i	−0.755929	+	0.654654i
$36$	−0.118034	−	0.363271i	−0.0196723	−	0.0605452i
$37$	−2.56082	+	0.544320i	−0.420997	+	0.0894856i	−0.413539	−	0.910487i	$-0.635707\pi$
$37$	−2.56082	+	0.544320i	−0.420997	+	0.0894856i	−0.00745814	+	0.999972i	$0.502374\pi$
$38$	4.01478	+	4.45887i	0.651284	+	0.723324i
$39$	1.35177	+	0.287327i	0.216456	+	0.0460091i
$40$	0.233733	−	2.22382i	0.0369564	−	0.351617i
$41$	3.59017	−	11.0494i	0.560690	−	1.72563i	−0.119731	−	0.992806i	$-0.538203\pi$
$41$	3.59017	−	11.0494i	0.560690	−	1.72563i	0.680421	−	0.732821i	$-0.261797\pi$
$42$	−1.81641	+	3.87645i	−0.280278	+	0.598150i
$43$	−2.23607			−0.340997			−0.170499	−	0.985358i	$-0.554538\pi$
$43$	−2.23607			−0.340997			−0.170499	+	0.985358i	$0.554538\pi$
$44$	0.298335	−	2.83847i	0.0449757	−	0.427915i
$45$	−0.571506	−	0.634721i	−0.0851950	−	0.0946187i
$46$	−0.781051	−	7.43120i	−0.115160	−	1.09567i
$47$	4.35207	+	1.93767i	0.634814	+	0.282638i	0.698804	−	0.715313i	$-0.253716\pi$
$47$	4.35207	+	1.93767i	0.634814	+	0.282638i	−0.0639898	+	0.997951i	$0.520383\pi$
$48$	−0.500000	−	1.53884i	−0.0721688	−	0.222113i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	−1.54508	−	4.75528i	−0.218508	−	0.672499i
$51$	4.61803	+	7.99867i	0.646654	+	1.12004i
$52$	−0.835438	−	0.177578i	−0.115854	−	0.0246256i
$53$	−0.442790	−	4.21286i	−0.0608218	−	0.578681i	−0.981913	−	0.189334i	$-0.939367\pi$
$53$	−0.442790	−	4.21286i	−0.0608218	−	0.578681i	0.921091	−	0.389347i	$-0.127299\pi$
$54$	−4.99904	−	2.22572i	−0.680284	−	0.302882i
$55$	−1.97214	−	6.06961i	−0.265923	−	0.818426i
$56$	1.12260	−	2.39578i	0.150014	−	0.320150i
$57$	9.70820			1.28588
$58$	−0.571994	+	5.44216i	−0.0751065	+	0.714590i
$59$	6.90960	+	7.67389i	0.899554	+	0.999055i	0.999992	+	0.00411210i	$0.00130893\pi$
$59$	6.90960	+	7.67389i	0.899554	+	0.999055i	−0.100438	+	0.994943i	$0.532024\pi$
$60$	−2.42094	−	2.68872i	−0.312542	−	0.347113i
$61$	2.51856	−	2.79715i	0.322469	−	0.358138i	−0.560013	−	0.828483i	$-0.689204\pi$
$61$	2.51856	−	2.79715i	0.322469	−	0.358138i	0.882482	+	0.470346i	$0.155871\pi$
$62$	−0.572949	+	1.76336i	−0.0727646	+	0.223946i
$63$	−0.393136	−	0.930983i	−0.0495305	−	0.117293i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.86810	+	0.397076i	−0.231709	+	0.0492512i
$66$	−3.09007	−	3.43187i	−0.380361	−	0.422434i
$67$	−0.913545	+	0.406737i	−0.111607	+	0.0496908i	−0.461781	−	0.886994i	$-0.652789\pi$
$67$	−0.913545	+	0.406737i	−0.111607	+	0.0496908i	0.350173	+	0.936685i	$0.386123\pi$
$68$	−2.85410	−	4.94345i	−0.346111	−	0.599481i
$69$	−9.78115	−	7.10642i	−1.17751	−	0.855513i
$70$	0.114256	−	5.91498i	0.0136561	−	0.706975i
$71$	1.57295	−	1.14281i	0.186675	−	0.135627i	−0.490523	−	0.871428i	$-0.663194\pi$
$71$	1.57295	−	1.14281i	0.186675	−	0.135627i	0.677198	+	0.735801i	$0.263194\pi$
$72$	0.348943	+	0.155360i	0.0411234	+	0.0183093i
$73$	−7.45156	−	1.58388i	−0.872139	−	0.185379i	−0.249962	−	0.968256i	$-0.580418\pi$
$73$	−7.45156	−	1.58388i	−0.872139	−	0.185379i	−0.622177	+	0.782877i	$0.713752\pi$
$74$	1.30902	−	2.26728i	0.152170	−	0.263566i
$75$	−7.39074	−	3.29057i	−0.853409	−	0.379962i
$76$	−6.00000			−0.688247
$77$	0.145835	−	7.54984i	0.0166194	−	0.860384i
$78$	−1.11803	+	0.812299i	−0.126592	+	0.0919748i
$79$	−8.17100	−	3.63796i	−0.919309	−	0.409303i	−0.108154	−	0.994134i	$-0.534494\pi$
$79$	−8.17100	−	3.63796i	−0.919309	−	0.409303i	−0.811155	+	0.584831i	$0.801161\pi$
$80$	1.49622	+	1.66172i	0.167283	+	0.185786i
$81$	−7.04179	+	3.13521i	−0.782422	+	0.348357i
$82$	5.80902	+	10.0615i	0.641499	+	1.11111i
$83$	8.28115	+	6.01661i	0.908975	+	0.660409i	0.940755	−	0.339086i	$-0.110118\pi$
$83$	8.28115	+	6.01661i	0.908975	+	0.660409i	−0.0317807	+	0.999495i	$0.510118\pi$
$84$	−1.66535	−	3.94371i	−0.181705	−	0.430294i
$85$	−10.3262	−	7.50245i	−1.12004	−	0.813755i
$86$	1.49622	−	1.66172i	0.161342	−	0.179188i
$87$	5.92455	+	6.57988i	0.635178	+	0.705437i
$88$	1.90977	+	2.12101i	0.203582	+	0.226101i
$89$	−11.4356	+	12.7005i	−1.21217	+	1.34625i	−0.291172	+	0.956671i	$0.594045\pi$
$89$	−11.4356	+	12.7005i	−1.21217	+	1.34625i	−0.920994	+	0.389577i	$0.872621\pi$
$90$	0.854102			0.0900303
$91$	−2.24238	−	0.279566i	−0.235065	−	0.0293065i
$92$	6.04508	+	4.39201i	0.630244	+	0.457899i
$93$	1.50000	+	2.59808i	0.155543	+	0.269408i
$94$	−4.35207	+	1.93767i	−0.448882	+	0.199855i
$95$	−12.2565	+	5.45694i	−1.25749	+	0.559871i
$96$	1.47815	+	0.658114i	0.150863	+	0.0671684i
$97$	5.47214	−	3.97574i	0.555611	−	0.403675i	−0.274239	−	0.961662i	$-0.588426\pi$
$97$	5.47214	−	3.97574i	0.555611	−	0.403675i	0.829850	+	0.557986i	$0.188426\pi$
$98$	2.41860	−	6.56889i	0.244316	−	0.663558i
$99$	1.09017			0.109566
$100$	4.56773	+	2.03368i	0.456773	+	0.203368i
$101$	4.35410	−	7.54153i	0.433249	−	0.750410i	−0.563902	−	0.825842i	$-0.690700\pi$
$101$	4.35410	−	7.54153i	0.433249	−	0.750410i	0.997151	+	0.0754321i	$0.0240336\pi$
$102$	−9.03424	−	1.92029i	−0.894523	−	0.190137i
$103$	−13.6523	−	6.07838i	−1.34520	−	0.598921i	−0.397357	−	0.917664i	$-0.630073\pi$
$103$	−13.6523	−	6.07838i	−1.34520	−	0.598921i	−0.947841	+	0.318743i	$0.896739\pi$
$104$	0.690983	−	0.502029i	0.0677565	−	0.0492279i
$105$	−6.98866	−	6.54139i	−0.682024	−	0.638374i
$106$	3.42705	+	2.48990i	0.332865	+	0.241840i
$107$	−2.28115	−	3.95107i	−0.220527	−	0.381965i	0.734441	−	0.678673i	$-0.237445\pi$
$107$	−2.28115	−	3.95107i	−0.220527	−	0.381965i	−0.954968	+	0.296708i	$0.904111\pi$
$108$	4.99904	−	2.22572i	0.481033	−	0.214170i
$109$	2.16535	+	2.40487i	0.207403	+	0.230344i	0.837867	−	0.545874i	$-0.183802\pi$
$109$	2.16535	+	2.40487i	0.207403	+	0.230344i	−0.630464	+	0.776218i	$0.717135\pi$
$110$	5.83022	+	2.59578i	0.555889	+	0.247498i
$111$	−1.30902	−	4.02874i	−0.124246	−	0.382391i
$112$	1.02924	+	2.43735i	0.0972544	+	0.230308i
$113$	−6.30902	+	19.4172i	−0.593502	+	1.82661i	−0.0314586	+	0.999505i	$0.510015\pi$
$113$	−6.30902	+	19.4172i	−0.593502	+	1.82661i	−0.562044	+	0.827107i	$0.689985\pi$
$114$	−6.49606	+	7.21460i	−0.608411	+	0.675709i
$115$	16.3431	+	3.47383i	1.52400	+	0.323936i
$116$	−3.66157	−	4.06659i	−0.339969	−	0.377573i
$117$	0.0341011	−	0.324451i	0.00315265	−	0.0299955i
$118$	−10.3262			−0.950607
$119$	−8.63940	−	12.3873i	−0.791972	−	1.13554i
$120$	3.61803			0.330280
$121$	−2.60735	−	1.16087i	−0.237032	−	0.105533i
$122$	0.393438	+	3.74331i	0.0356202	+	0.338904i
$123$	18.3876	+	3.90840i	1.65795	+	0.352409i
$124$	−0.927051	−	1.60570i	−0.0832516	−	0.144196i
$125$	11.1803			1.00000
$126$	0.954915	+	0.330792i	0.0850706	+	0.0294693i
$127$	2.78115	+	8.55951i	0.246787	+	0.759534i	0.995337	+	0.0964551i	$0.0307504\pi$
$127$	2.78115	+	8.55951i	0.246787	+	0.759534i	−0.748550	+	0.663078i	$0.769250\pi$
$128$	−0.913545	−	0.406737i	−0.0807468	−	0.0359508i
$129$	−0.378188	−	3.59821i	−0.0332976	−	0.316805i
$130$	0.954915	−	1.65396i	0.0837516	−	0.145062i
$131$	−1.86044	+	17.7009i	−0.162547	+	1.54653i	0.544133	+	0.838999i	$0.316859\pi$
$131$	−1.86044	+	17.7009i	−0.162547	+	1.54653i	−0.706680	+	0.707533i	$0.749808\pi$
$132$	4.61803			0.401948
$133$	−15.8166	+	1.35413i	−1.37148	+	0.117418i
$134$	0.309017	−	0.951057i	0.0266950	−	0.0821588i
$135$	8.18753	−	9.09317i	0.704670	−	0.782616i
$136$	5.58347	+	1.18680i	0.478778	+	0.101767i
$137$	−4.33070	−	4.80973i	−0.369997	−	0.410923i	0.529179	−	0.848510i	$-0.322500\pi$
$137$	−4.33070	−	4.80973i	−0.369997	−	0.410923i	−0.899176	+	0.437587i	$0.855833\pi$
$138$	11.8260	−	2.51369i	1.00669	−	0.213979i
$139$	1.85410	+	5.70634i	0.157263	+	0.484005i	0.998383	−	0.0568428i	$-0.0181034\pi$
$139$	1.85410	+	5.70634i	0.157263	+	0.484005i	−0.841120	+	0.540848i	$0.818103\pi$
$140$	4.31923	+	4.04280i	0.365042	+	0.341679i
$141$	−2.38197	+	7.33094i	−0.200598	+	0.617376i
$142$	−0.203232	+	1.93362i	−0.0170548	+	0.162266i
$143$	1.21885	−	2.11111i	0.101925	−	0.176539i
$144$	−0.348943	+	0.155360i	−0.0290786	+	0.0129466i
$145$	−11.1782	−	4.97686i	−0.928299	−	0.413305i
$146$	6.16312	−	4.47777i	0.510063	−	0.370583i
$147$	−5.28010	−	10.0202i	−0.435495	−	0.826452i
$148$	0.809017	+	2.48990i	0.0665008	+	0.204668i
$149$	4.61803	+	7.99867i	0.378324	+	0.655277i	0.990819	−	0.135198i	$-0.0431672\pi$
$149$	4.61803	+	7.99867i	0.378324	+	0.655277i	−0.612494	+	0.790475i	$0.709834\pi$
$150$	7.39074	−	3.29057i	0.603451	−	0.268674i
$151$	−7.69098	+	13.3212i	−0.625883	+	1.08406i	0.362486	+	0.931989i	$0.381928\pi$
$151$	−7.69098	+	13.3212i	−0.625883	+	1.08406i	−0.988369	+	0.152073i	$0.951405\pi$
$152$	4.01478	−	4.45887i	0.325642	−	0.361662i
$153$	1.76393	−	1.28157i	0.142605	−	0.103609i
$154$	5.51304	+	5.16020i	0.444253	+	0.415821i
$155$	−3.35410	−	2.43690i	−0.269408	−	0.195736i
$156$	0.144455	−	1.37440i	0.0115656	−	0.110040i
$157$	1.80902	−	3.13331i	0.144375	−	0.250065i	−0.784764	−	0.619794i	$-0.787216\pi$
$157$	1.80902	−	3.13331i	0.144375	−	0.250065i	0.929140	+	0.369729i	$0.120549\pi$
$158$	8.17100	−	3.63796i	0.650050	−	0.289421i
$159$	6.70432	−	1.42505i	0.531687	−	0.113014i
$160$	−2.23607			−0.176777
$161$	16.9267	+	10.2135i	1.33401	+	0.804938i
$162$	2.38197	−	7.33094i	0.187145	−	0.575973i
$163$	19.5084	−	4.14665i	1.52802	−	0.324790i	0.634183	−	0.773183i	$-0.281337\pi$
$163$	19.5084	−	4.14665i	1.52802	−	0.324790i	0.893837	+	0.448393i	$0.148003\pi$
$164$	−11.3642	−	2.41553i	−0.887391	−	0.188621i
$165$	9.43349	−	4.20006i	0.734396	−	0.326974i
$166$	−10.0124	+	2.12820i	−0.777112	+	0.165180i
$167$	−5.54508	−	4.02874i	−0.429092	−	0.311753i	0.352194	−	0.935927i	$-0.385436\pi$
$167$	−5.54508	−	4.02874i	−0.429092	−	0.311753i	−0.781286	+	0.624174i	$0.785436\pi$
$168$	4.04508	+	1.40126i	0.312085	+	0.108109i
$169$	9.92705	+	7.21242i	0.763619	+	0.554802i
$170$	12.4850	−	2.65377i	0.957557	−	0.203535i
$171$	−0.239558	−	2.27924i	−0.0183195	−	0.174298i
$172$	0.233733	+	2.22382i	0.0178220	+	0.169565i
$173$	2.48127	−	2.75573i	0.188648	−	0.209514i	−0.641400	−	0.767206i	$-0.721646\pi$
$173$	2.48127	−	2.75573i	0.188648	−	0.209514i	0.830048	+	0.557692i	$0.188313\pi$
$174$	−8.85410			−0.671228
$175$	12.5000	+	4.33013i	0.944911	+	0.327327i
$176$	−2.85410			−0.215136
$177$	−11.1800	+	12.4166i	−0.840338	+	0.933290i
$178$	−1.78641	−	16.9965i	−0.133897	−	1.27395i
$179$	1.06996	+	10.1800i	0.0799726	+	0.760888i	0.958864	+	0.283866i	$0.0916172\pi$
$179$	1.06996	+	10.1800i	0.0799726	+	0.760888i	−0.878891	+	0.477022i	$0.841716\pi$
$180$	−0.571506	+	0.634721i	−0.0425975	+	0.0473093i
$181$	−20.5623	−	14.9394i	−1.52838	−	1.11044i	−0.957128	−	0.289664i	$-0.906456\pi$
$181$	−20.5623	−	14.9394i	−1.52838	−	1.11044i	−0.571256	−	0.820772i	$-0.693544\pi$
$182$	1.70820	−	1.47935i	0.126620	−	0.109657i
$183$	4.92705	+	3.57971i	0.364218	+	0.264620i
$184$	−7.30885	+	1.55354i	−0.538816	+	0.114529i
$185$	3.91716	+	4.35045i	0.287995	+	0.319851i
$186$	−2.93444	−	0.623735i	−0.215164	−	0.0457345i
$187$	15.9358	−	3.38725i	1.16534	−	0.247701i
$188$	1.47214	−	4.53077i	0.107367	−	0.330440i
$189$	12.6757	−	6.99546i	0.922022	−	0.508845i
$190$	4.14590	−	12.7598i	0.300775	−	0.925690i
$191$	19.7939	−	4.20732i	1.43223	−	0.304431i	0.574491	−	0.818511i	$-0.305200\pi$
$191$	19.7939	−	4.20732i	1.43223	−	0.304431i	0.857742	+	0.514080i	$0.171867\pi$
$192$	−1.47815	+	0.658114i	−0.106676	+	0.0474953i
$193$	0.399187	−	0.691412i	0.0287341	−	0.0497689i	−0.851301	−	0.524678i	$-0.824186\pi$
$193$	0.399187	−	0.691412i	0.0287341	−	0.0497689i	0.880035	+	0.474909i	$0.157519\pi$
$194$	−0.707023	+	6.72688i	−0.0507613	+	0.482962i
$195$	−0.954915	−	2.93893i	−0.0683829	−	0.210461i
$196$	3.26328	+	6.19282i	0.233091	+	0.442344i
$197$	−13.8713	+	10.0781i	−0.988291	+	0.718035i	−0.959546	−	0.281551i	$-0.909151\pi$
$197$	−13.8713	+	10.0781i	−0.988291	+	0.718035i	−0.0287447	+	0.999587i	$0.509151\pi$
$198$	−0.729466	+	0.810154i	−0.0518409	+	0.0575751i
$199$	−2.20820	+	3.82472i	−0.156535	+	0.271127i	−0.933617	−	0.358273i	$-0.883366\pi$
$199$	−2.20820	+	3.82472i	−0.156535	+	0.271127i	0.777082	+	0.629400i	$0.216699\pi$
$200$	−4.56773	+	2.03368i	−0.322987	+	0.143803i
$201$	−0.809017	−	1.40126i	−0.0570637	−	0.0988372i
$202$	2.69098	+	8.28199i	0.189337	+	0.582719i
$203$	−10.5701	−	9.89360i	−0.741874	−	0.694394i
$204$	7.47214	−	5.42882i	0.523154	−	0.380094i
$205$	−25.4110	+	5.40128i	−1.77478	+	0.377242i
$206$	13.6523	−	6.07838i	0.951199	−	0.423501i
$207$	−1.42705	+	2.47172i	−0.0991869	+	0.171797i
$208$	−0.0892780	+	0.849423i	−0.00619031	+	0.0588969i
$209$	5.29180	−	16.2865i	0.366041	−	1.12656i
$210$	9.53753	−	0.816547i	0.658152	−	0.0563471i
$211$	7.19098	+	22.1316i	0.495048	+	1.52360i	0.816882	+	0.576804i	$0.195700\pi$
$211$	7.19098	+	22.1316i	0.495048	+	1.52360i	−0.321835	+	0.946796i	$0.604300\pi$
$212$	−4.14350	+	0.880728i	−0.284577	+	0.0604887i
$213$	2.10502	+	2.33786i	0.144233	+	0.160187i
$214$	4.46261	+	0.948557i	0.305058	+	0.0648420i
$215$	2.50000	+	4.33013i	0.170499	+	0.295312i
$216$	−1.69098	+	5.20431i	−0.115057	+	0.354108i
$217$	−2.80619	−	4.02357i	−0.190497	−	0.273138i
$218$	−3.23607			−0.219174
$219$	1.28844	−	12.2587i	0.0870649	−	0.828367i
$220$	−5.83022	+	2.59578i	−0.393073	+	0.175007i
$221$	−0.509617	−	4.84868i	−0.0342805	−	0.326158i
$222$	3.86984	+	1.72296i	0.259727	+	0.115638i
$223$	2.59017	+	7.97172i	0.173451	+	0.533826i	0.999559	−	0.0296847i	$-0.00945032\pi$
$223$	2.59017	+	7.97172i	0.173451	+	0.533826i	−0.826109	+	0.563511i	$0.809450\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	−0.590170	+	1.81636i	−0.0393447	+	0.121090i
$226$	−10.2082	−	17.6811i	−0.679040	−	1.17613i
$227$	2.01081	+	0.427410i	0.133462	+	0.0283682i	0.274158	−	0.961685i	$-0.411601\pi$
$227$	2.01081	+	0.427410i	0.133462	+	0.0283682i	−0.140696	+	0.990053i	$0.544934\pi$
$228$	−1.01478	−	9.65502i	−0.0672057	−	0.639419i
$229$	−3.03867	−	1.35290i	−0.200801	−	0.0894023i	0.303872	−	0.952713i	$-0.401720\pi$
$229$	−3.03867	−	1.35290i	−0.200801	−	0.0894023i	−0.504673	+	0.863310i	$0.668387\pi$
$230$	−13.5172	+	9.82084i	−0.891299	+	0.647567i
$231$	12.1736	−	1.04224i	0.800966	−	0.0685740i
$232$	5.47214			0.359263
$233$	−2.90932	+	27.6803i	−0.190596	+	1.81340i	0.313321	+	0.949647i	$0.398559\pi$
$233$	−2.90932	+	27.6803i	−0.190596	+	1.81340i	−0.503917	+	0.863752i	$0.668108\pi$
$234$	0.218296	+	0.242442i	0.0142704	+	0.0158489i
$235$	−1.11349	−	10.5941i	−0.0726359	−	0.691084i
$236$	6.90960	−	7.67389i	0.449777	−	0.499528i
$237$	4.47214	−	13.7638i	0.290496	−	0.894056i
$238$	14.9865	+	1.86842i	0.971428	+	0.121112i
$239$	6.59017	+	20.2825i	0.426283	+	1.31196i	0.901761	+	0.432236i	$0.142275\pi$
$239$	6.59017	+	20.2825i	0.426283	+	1.31196i	−0.475478	+	0.879728i	$0.657725\pi$
$240$	−2.42094	+	2.68872i	−0.156271	+	0.173556i
$241$	−2.77415	−	3.08100i	−0.178699	−	0.198465i	0.647140	−	0.762371i	$-0.275965\pi$
$241$	−2.77415	−	3.08100i	−0.178699	−	0.198465i	−0.825839	+	0.563906i	$0.809298\pi$
$242$	2.60735	−	1.16087i	0.167607	−	0.0746234i
$243$	1.97214	+	3.41584i	0.126513	+	0.219126i
$244$	−3.04508	−	2.21238i	−0.194942	−	0.141633i
$245$	12.2984	+	9.68246i	0.785714	+	0.618590i
$246$	−15.2082	+	11.0494i	−0.969640	+	0.704484i
$247$	−4.68157	−	2.08437i	−0.297881	−	0.132625i
$248$	1.81359	+	0.385489i	0.115163	+	0.0244786i
$249$	−8.28115	+	14.3434i	−0.524797	+	0.908975i
$250$	−7.48111	+	8.30861i	−0.473147	+	0.525483i
$251$	8.81966			0.556692			0.278346	−	0.960481i	$-0.410214\pi$
$251$	8.81966			0.556692			0.278346	+	0.960481i	$0.410214\pi$
$252$	−0.884789	+	0.488297i	−0.0557365	+	0.0307598i
$253$	−17.2533	+	12.5352i	−1.08470	+	0.788084i
$254$	−8.22191	−	3.66063i	−0.515888	−	0.229688i
$255$	10.3262	−	17.8856i	0.646654	−	1.12004i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	0.482779	+	0.836198i	0.0301149	+	0.0521606i	0.880690	−	0.473693i	$-0.157079\pi$
$257$	0.482779	+	0.836198i	0.0301149	+	0.0521606i	−0.850575	+	0.525854i	$0.823746\pi$
$258$	2.92705	+	2.12663i	0.182230	+	0.132398i
$259$	2.69460	+	6.38106i	0.167434	+	0.396499i
$260$	0.590170	+	1.81636i	0.0366008	+	0.112646i
$261$	1.39860	−	1.55330i	0.0865710	−	0.0961468i
$262$	−11.9094	−	13.2268i	−0.735767	−	0.817153i
$263$	−11.1800	−	12.4166i	−0.689387	−	0.765641i	0.292262	−	0.956338i	$-0.405592\pi$
$263$	−11.1800	−	12.4166i	−0.689387	−	0.765641i	−0.981649	+	0.190697i	$0.938925\pi$
$264$	−3.09007	+	3.43187i	−0.190181	+	0.211217i
$265$	−7.66312	+	5.56758i	−0.470742	+	0.342014i
$266$	9.57709	−	12.6601i	0.587209	−	0.776243i
$267$	−22.3713	−	16.2537i	−1.36910	−	0.994711i
$268$	0.500000	+	0.866025i	0.0305424	+	0.0529009i
$269$	2.44260	−	1.08752i	0.148928	−	0.0663071i	−0.330919	−	0.943659i	$-0.607359\pi$
$269$	2.44260	−	1.08752i	0.148928	−	0.0663071i	0.479847	+	0.877352i	$0.340692\pi$
$270$	1.27902	+	12.1690i	0.0778385	+	0.740584i
$271$	0.831171	+	0.370061i	0.0504900	+	0.0224796i	0.431826	−	0.901957i	$-0.357869\pi$
$271$	0.831171	+	0.370061i	0.0504900	+	0.0224796i	−0.381336	+	0.924436i	$0.624536\pi$
$272$	−4.61803	+	3.35520i	−0.280009	+	0.203439i
$273$	0.0706138	−	3.65566i	0.00427374	−	0.221250i
$274$	6.47214			0.390996
$275$	−9.54883	+	10.6051i	−0.575816	+	0.639509i
$276$	−6.04508	+	10.4704i	−0.363871	+	0.630244i
$277$	19.9703	+	4.24481i	1.19990	+	0.255046i	0.764159	−	0.645028i	$-0.223154\pi$
$277$	19.9703	+	4.24481i	1.19990	+	0.255046i	0.435738	+	0.900074i	$0.356488\pi$
$278$	−5.48127	−	2.44042i	−0.328745	−	0.146367i
$279$	0.572949	−	0.416272i	0.0343016	−	0.0249215i
$280$	−5.89452	+	0.504654i	−0.352265	+	0.0301588i
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	0.0963896	−	0.995344i	$-0.469271\pi$
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	−0.916842	+	0.399250i	$0.869271\pi$
$282$	−3.85410	−	6.67550i	−0.229508	−	0.397520i
$283$	−7.82206	+	3.48260i	−0.464973	+	0.207019i	−0.625832	−	0.779958i	$-0.715240\pi$
$283$	−7.82206	+	3.48260i	−0.464973	+	0.207019i	0.160859	+	0.986977i	$0.448574\pi$
$284$	−1.30097	−	1.44488i	−0.0771985	−	0.0857376i
$285$	−10.8541	−	18.7999i	−0.642942	−	1.11361i
$286$	0.753289	+	2.31838i	0.0445429	+	0.137089i
$287$	−30.5023	−	3.80283i	−1.80049	−	0.224474i
$288$	0.118034	−	0.363271i	0.00695522	−	0.0214060i
$289$	10.4275	−	11.5809i	0.613380	−	0.681227i
$290$	11.1782	−	4.97686i	0.656407	−	0.292251i
$291$	7.32315	+	8.13318i	0.429290	+	0.476775i
$292$	−0.796301	+	7.57630i	−0.0466000	+	0.443370i
$293$	10.0902			0.589474			0.294737	−	0.955578i	$-0.404768\pi$
$293$	10.0902			0.589474			0.294737	+	0.955578i	$0.404768\pi$
$294$	10.9795	+	2.78094i	0.640339	+	0.162188i
$295$	7.13525	−	21.9601i	0.415431	−	1.27856i
$296$	−2.39169	−	1.06485i	−0.139014	−	0.0618932i
$297$	1.63253	+	15.5325i	0.0947289	+	0.901286i
$298$	−9.03424	−	1.92029i	−0.523339	−	0.111239i
$299$	3.19098	+	5.52694i	0.184539	+	0.319631i
$300$	−2.50000	+	7.69421i	−0.144338	+	0.444225i
$301$	1.11803	+	5.80948i	0.0644424	+	0.334853i
$302$	−4.75329	−	14.6291i	−0.273521	−	0.841811i
$303$	12.8720	+	5.73099i	0.739478	+	0.329237i
$304$	0.627171	+	5.96713i	0.0359707	+	0.342238i
$305$	−8.23249	−	1.74987i	−0.471391	−	0.100197i
$306$	−0.227908	+	2.16840i	−0.0130286	+	0.123959i
$307$	−27.1246			−1.54808			−0.774042	−	0.633135i	$-0.781768\pi$
$307$	−27.1246			−1.54808			−0.774042	+	0.633135i	$0.781768\pi$
$308$	−7.52372	+	0.644137i	−0.428704	+	0.0367031i
$309$	7.47214	−	22.9969i	0.425075	−	1.30825i
$310$	4.05530	−	0.861981i	0.230326	−	0.0489572i
$311$	−29.7517	−	6.32393i	−1.68707	−	0.358597i	−0.738275	−	0.674500i	$-0.764359\pi$
$311$	−29.7517	−	6.32393i	−1.68707	−	0.358597i	−0.948791	+	0.315903i	$0.897693\pi$
$312$	0.924716	+	1.02700i	0.0523517	+	0.0581425i
$313$	13.2322	−	2.81260i	0.747931	−	0.158978i	0.181849	−	0.983327i	$-0.441792\pi$
$313$	13.2322	−	2.81260i	0.747931	−	0.158978i	0.566082	+	0.824349i	$0.308459\pi$
$314$	1.11803	+	3.44095i	0.0630943	+	0.194184i
$315$	−1.36330	+	1.80218i	−0.0768134	+	0.101541i
$316$	−2.76393	+	8.50651i	−0.155483	+	0.478528i
$317$	1.75008	−	16.6509i	0.0982945	−	0.935209i	−0.828588	−	0.559858i	$-0.810856\pi$
$317$	1.75008	−	16.6509i	0.0982945	−	0.935209i	0.926883	−	0.375351i	$-0.122478\pi$
$318$	−3.42705	+	5.93583i	−0.192179	+	0.332865i
$319$	14.2678	−	6.35243i	0.798843	−	0.355668i
$320$	1.49622	−	1.66172i	0.0836413	−	0.0928931i
$321$	5.97214	−	4.33901i	0.333332	−	0.242180i
$322$	−18.9163	+	5.74483i	−1.05416	+	0.320147i
$323$	−10.5836	−	32.5729i	−0.588887	−	1.81241i
$324$	3.85410	+	6.67550i	0.214117	+	0.370861i
$325$	2.85753	+	3.17361i	0.158507	+	0.176040i
$326$	−9.97214	+	17.2722i	−0.552306	+	0.956621i
$327$	−3.50361	+	3.89116i	−0.193750	+	0.215181i
$328$	9.39919	−	6.82891i	0.518983	−	0.377063i
$329$	2.85817	−	12.2758i	0.157576	−	0.676789i
$330$	−3.19098	+	9.82084i	−0.175658	+	0.540619i
$331$	−0.993708	+	9.45450i	−0.0546191	+	0.519666i	0.932670	+	0.360731i	$0.117473\pi$
$331$	−0.993708	+	9.45450i	−0.0546191	+	0.519666i	−0.987289	+	0.158935i	$0.949194\pi$
$332$	5.11803	−	8.86469i	0.280889	−	0.486513i
$333$	−0.913545	+	0.406737i	−0.0500620	+	0.0222890i
$334$	6.70432	−	1.42505i	0.366844	−	0.0779752i
$335$	1.80902	+	1.31433i	0.0988372	+	0.0718094i
$336$	−3.74803	+	2.06846i	−0.204472	+	0.112844i
$337$	2.87132	−	8.83702i	0.156411	−	0.481383i	−0.841890	−	0.539649i	$-0.818557\pi$
$337$	2.87132	−	8.83702i	0.156411	−	0.481383i	0.998301	+	0.0582655i	$0.0185570\pi$
$338$	−12.0024	+	2.55118i	−0.652843	+	0.138766i
$339$	−32.3126	−	6.86825i	−1.75498	−	0.373032i
$340$	−6.38197	+	11.0539i	−0.346111	+	0.599481i
$341$	5.17616	−	1.10023i	0.280305	−	0.0595806i
$342$	1.85410	+	1.34708i	0.100258	+	0.0728420i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−1.80902	−	1.31433i	−0.0975357	−	0.0708638i
$345$	−2.82587	+	26.8863i	−0.152140	+	1.44751i
$346$	0.387613	+	3.68789i	0.0208382	+	0.198262i
$347$	−2.02957	−	19.3100i	−0.108953	−	1.03662i	−0.903258	−	0.429098i	$-0.858831\pi$
$347$	−2.02957	−	19.3100i	−0.108953	−	1.03662i	0.794305	−	0.607519i	$-0.207835\pi$
$348$	5.92455	−	6.57988i	0.317589	−	0.352719i
$349$	21.3820			1.14455			0.572275	−	0.820062i	$-0.306061\pi$
$349$	21.3820			1.14455			0.572275	+	0.820062i	$0.306061\pi$
$350$	−11.5820	+	6.39189i	−0.619086	+	0.341661i
$351$	4.67376			0.249467
$352$	1.90977	−	2.12101i	0.101791	−	0.113050i
$353$	−1.57153	−	14.9521i	−0.0836439	−	0.795819i	−0.953272	−	0.302112i	$-0.902308\pi$
$353$	−1.57153	−	14.9521i	−0.0836439	−	0.795819i	0.869628	−	0.493707i	$-0.164358\pi$
$354$	−1.74648	−	16.6167i	−0.0928245	−	0.883166i
$355$	−3.97166	−	1.76830i	−0.210794	−	0.0938515i
$356$	13.8262	+	10.0453i	0.732789	+	0.532402i
$357$	18.4721	−	15.9973i	0.977649	−	0.846669i
$358$	−8.28115	−	6.01661i	−0.437673	−	0.317988i
$359$	6.09979	−	1.29655i	0.321935	−	0.0684294i	−0.0441097	−	0.999027i	$-0.514045\pi$
$359$	6.09979	−	1.29655i	0.321935	−	0.0684294i	0.366045	+	0.930597i	$0.380712\pi$
$360$	−0.0892780	−	0.849423i	−0.00470536	−	0.0447685i
$361$	−16.6285	−	3.53450i	−0.875185	−	0.186026i
$362$	24.8610	−	5.28437i	1.30667	−	0.277740i
$363$	1.42705	−	4.39201i	0.0749008	−	0.230521i
$364$	−0.0436417	+	2.25932i	−0.00228745	+	0.118421i
$365$	5.26393	+	16.2007i	0.275527	+	0.847984i
$366$	−5.95709	+	1.26622i	−0.311382	+	0.0661863i
$367$	−13.7541	+	6.12372i	−0.717958	+	0.319655i	−0.732997	−	0.680232i	$-0.761879\pi$
$367$	−13.7541	+	6.12372i	−0.717958	+	0.319655i	0.0150396	+	0.999887i	$0.495213\pi$
$368$	3.73607	−	6.47106i	0.194756	−	0.337327i
$369$	0.463865	−	4.41338i	0.0241479	−	0.229752i
$370$	−5.85410			−0.304340
$371$	−10.7239	+	3.25683i	−0.556759	+	0.169086i
$372$	2.42705	−	1.76336i	0.125837	−	0.0914257i
$373$	19.8414	−	22.0361i	1.02735	−	1.14099i	0.0374360	−	0.999299i	$-0.488081\pi$
$373$	19.8414	−	22.0361i	1.02735	−	1.14099i	0.989912	−	0.141686i	$-0.0452524\pi$
$374$	−8.14590	+	14.1091i	−0.421214	+	0.729565i
$375$	1.89094	+	17.9911i	0.0976476	+	0.929055i
$376$	2.38197	+	4.12569i	0.122841	+	0.212766i
$377$	−1.44427	−	4.44501i	−0.0743838	−	0.228930i
$378$	−3.28306	+	14.1008i	−0.168863	+	0.725265i
$379$	19.3713	−	14.0741i	0.995038	−	0.722937i	0.0340194	−	0.999421i	$-0.489169\pi$
$379$	19.3713	−	14.0741i	0.995038	−	0.722937i	0.961019	+	0.276484i	$0.0891692\pi$
$380$	6.70820	+	11.6190i	0.344124	+	0.596040i
$381$	−13.3033	+	5.92302i	−0.681550	+	0.303446i
$382$	−10.1180	+	17.5249i	−0.517684	+	0.896654i
$383$	−2.09057	+	19.8904i	−0.106823	+	1.01635i	0.801474	+	0.598029i	$0.204049\pi$
$383$	−2.09057	+	19.8904i	−0.106823	+	1.01635i	−0.908298	+	0.418325i	$0.862617\pi$
$384$	0.500000	−	1.53884i	0.0255155	−	0.0785287i
$385$	−14.7832	+	8.15856i	−0.753424	+	0.415799i
$386$	0.246711	+	0.759299i	0.0125573	+	0.0386473i
$387$	−0.835438	+	0.177578i	−0.0424677	+	0.00902679i
$388$	−4.52595	−	5.02658i	−0.229770	−	0.255186i
$389$	−4.00079	−	0.850394i	−0.202848	−	0.0431167i	0.105367	−	0.994433i	$-0.466398\pi$
$389$	−4.00079	−	0.850394i	−0.202848	−	0.0431167i	−0.308215	+	0.951317i	$0.599732\pi$
$390$	2.82301	+	1.25689i	0.142949	+	0.0636449i
$391$	−13.1803	+	40.5649i	−0.666558	+	2.05146i
$392$	−6.78572	−	1.71872i	−0.342731	−	0.0868083i
$393$	−28.7984			−1.45269
$394$	1.79223	−	17.0520i	0.0902915	−	0.859066i
$395$	2.09057	+	19.8904i	0.105188	+	1.00080i
$396$	−0.113954	−	1.08420i	−0.00572639	−	0.0544830i
$397$	25.2109	+	11.2246i	1.26530	+	0.563347i	0.926068	−	0.377357i	$-0.123167\pi$
$397$	25.2109	+	11.2246i	1.26530	+	0.563347i	0.339230	+	0.940703i	$0.389834\pi$
$398$	−1.36475	−	4.20025i	−0.0684085	−	0.210540i
$399$	−4.85410	−	25.2227i	−0.243009	−	1.26271i
$400$	1.54508	−	4.75528i	0.0772542	−	0.237764i
$401$	−5.76393	−	9.98342i	−0.287837	−	0.498548i	0.685456	−	0.728114i	$-0.259603\pi$
$401$	−5.76393	−	9.98342i	−0.287837	−	0.498548i	−0.973293	+	0.229566i	$0.926269\pi$
$402$	1.58268	+	0.336408i	0.0789367	+	0.0167785i
$403$	−0.165530	−	1.57492i	−0.00824566	−	0.0784522i
$404$	−7.95534	−	3.54195i	−0.395793	−	0.176218i
$405$	13.9443	+	10.1311i	0.692896	+	0.503419i
$406$	14.4251	−	1.23500i	0.715908	−	0.0612918i
$407$	−7.47214			−0.370380
$408$	−0.965432	+	9.18547i	−0.0477960	+	0.454749i
$409$	4.99983	+	5.55288i	0.247226	+	0.274572i	0.853967	−	0.520327i	$-0.174190\pi$
$409$	4.99983	+	5.55288i	0.247226	+	0.274572i	−0.606741	+	0.794900i	$0.707523\pi$
$410$	12.9894	−	22.4982i	0.641499	−	1.11111i
$411$	7.00723	−	7.78231i	0.345641	−	0.383873i
$412$	−4.61803	+	14.2128i	−0.227514	+	0.700217i
$413$	16.4826	−	21.7886i	0.811053	−	1.07215i
$414$	−0.881966	−	2.71441i	−0.0433463	−	0.133406i
$415$	2.39250	−	22.7632i	0.117443	−	1.11740i
$416$	−0.571506	−	0.634721i	−0.0280204	−	0.0311198i
$417$	−8.86889	+	3.94868i	−0.434311	+	0.193368i
$418$	8.56231	+	14.8303i	0.418796	+	0.725376i
$419$	6.28115	+	4.56352i	0.306854	+	0.222943i	0.730546	−	0.682864i	$-0.239266\pi$
$419$	6.28115	+	4.56352i	0.306854	+	0.222943i	−0.423691	+	0.905807i	$0.639266\pi$
$420$	−5.77504	+	7.63414i	−0.281793	+	0.372508i
$421$	−10.4443	+	7.58821i	−0.509023	+	0.369827i	−0.812453	−	0.583027i	$-0.801868\pi$
$421$	−10.4443	+	7.58821i	−0.509023	+	0.369827i	0.303430	+	0.952854i	$0.401868\pi$
$422$	−21.2587	−	9.46497i	−1.03486	−	0.460747i
$423$	1.77990	+	0.378329i	0.0865415	+	0.0183950i
$424$	2.11803	−	3.66854i	0.102861	−	0.178160i
$425$	−2.98335	+	28.3847i	−0.144714	+	1.37686i
$426$	−3.14590			−0.152419
$427$	−8.52648	−	5.14484i	−0.412625	−	0.248976i
$428$	−3.69098	+	2.68166i	−0.178410	+	0.129623i
$429$	3.60327	+	1.60428i	0.173968	+	0.0774554i
$430$	−4.89074	−	1.03956i	−0.235852	−	0.0501320i
$431$	1.85856	−	0.827482i	0.0895234	−	0.0398584i	−0.361486	−	0.932377i	$-0.617731\pi$
$431$	1.85856	−	0.827482i	0.0895234	−	0.0398584i	0.451010	+	0.892519i	$0.351064\pi$
$432$	−2.73607	−	4.73901i	−0.131639	−	0.228006i
$433$	−7.51722	−	5.46158i	−0.361255	−	0.262467i	0.392321	−	0.919829i	$-0.371672\pi$
$433$	−7.51722	−	5.46158i	−0.361255	−	0.262467i	−0.753575	+	0.657362i	$0.771672\pi$
$434$	4.86781	+	0.606887i	0.233662	+	0.0291315i
$435$	6.11803	−	18.8294i	0.293337	−	0.902799i
$436$	2.16535	−	2.40487i	0.103702	−	0.115172i
$437$	29.9990	+	33.3173i	1.43505	+	1.59378i
$438$	8.24786	+	9.16018i	0.394098	+	0.437690i
$439$	−9.33054	+	10.3626i	−0.445322	+	0.494581i	−0.923455	−	0.383707i	$-0.874647\pi$
$439$	−9.33054	+	10.3626i	−0.445322	+	0.494581i	0.478132	+	0.878288i	$0.341314\pi$
$440$	1.97214	−	6.06961i	0.0940179	−	0.289357i
$441$	−2.22220	+	1.48689i	−0.105819	+	0.0708043i
$442$	3.94427	+	2.86568i	0.187610	+	0.136307i
$443$	−4.92705	−	8.53390i	−0.234091	−	0.405458i	0.724917	−	0.688836i	$-0.241878\pi$
$443$	−4.92705	−	8.53390i	−0.234091	−	0.405458i	−0.959008	+	0.283378i	$0.908545\pi$
$444$	−3.86984	+	1.72296i	−0.183655	+	0.0817683i
$445$	37.3797	+	7.94530i	1.77197	+	0.376643i
$446$	−7.65731	−	3.40925i	−0.362584	−	0.161433i
$447$	−12.0902	+	8.78402i	−0.571845	+	0.415470i
$448$	2.31641	−	1.27838i	0.109440	−	0.0603977i
$449$	34.0344			1.60618			0.803092	−	0.595855i	$-0.203187\pi$
$449$	34.0344			1.60618			0.803092	+	0.595855i	$0.203187\pi$
$450$	−0.954915	−	1.65396i	−0.0450151	−	0.0779685i
$451$	16.5795	−	28.7166i	0.780699	−	1.35221i
$452$	19.9703	+	4.24481i	0.939322	+	0.199659i
$453$	−22.7368	−	10.1231i	−1.06827	−	0.475624i
$454$	−1.66312	+	1.20833i	−0.0780540	+	0.0567096i
$455$	1.96568	+	4.65492i	0.0921526	+	0.218226i
$456$	7.85410	+	5.70634i	0.367802	+	0.267224i
$457$	7.61803	+	13.1948i	0.356357	+	0.617228i	0.987349	−	0.158561i	$-0.0506855\pi$
$457$	7.61803	+	13.1948i	0.356357	+	0.617228i	−0.630993	+	0.775789i	$0.717352\pi$
$458$	3.03867	−	1.35290i	0.141988	−	0.0632170i
$459$	20.9010	+	23.2129i	0.975576	+	1.08349i
$460$	1.74648	−	16.6167i	0.0814302	−	0.774756i
$461$	−7.12868	−	21.9398i	−0.332016	−	1.02184i	−0.968173	−	0.250280i	$-0.919477\pi$
$461$	−7.12868	−	21.9398i	−0.332016	−	1.02184i	0.636158	−	0.771559i	$-0.280523\pi$
$462$	−7.37122	+	9.74417i	−0.342940	+	0.453340i
$463$	5.01722	−	15.4414i	0.233170	−	0.717624i	−0.764189	−	0.644993i	$-0.776860\pi$
$463$	5.01722	−	15.4414i	0.233170	−	0.717624i	0.997359	−	0.0726310i	$-0.0231395\pi$
$464$	−3.66157	+	4.06659i	−0.169984	+	0.188787i
$465$	3.35410	−	5.80948i	0.155543	−	0.269408i
$466$	−18.6238	−	20.6838i	−0.862730	−	0.958159i
$467$	3.55757	−	33.8480i	0.164625	−	1.56630i	−0.530673	−	0.847577i	$-0.678061\pi$
$467$	3.55757	−	33.8480i	0.164625	−	1.56630i	0.695298	−	0.718722i	$-0.255273\pi$
$468$	−0.326238			−0.0150804
$469$	1.51351	+	2.17009i	0.0698872	+	0.100206i
$470$	8.61803	+	6.26137i	0.397520	+	0.288815i
$471$	5.34799	+	2.38108i	0.246422	+	0.109714i
$472$	1.07939	+	10.2697i	0.0496828	+	0.472700i
$473$	−6.24250	−	1.32689i	−0.287031	−	0.0610103i
$474$	7.23607	+	12.5332i	0.332364	+	0.575671i
$475$	24.2705	+	17.6336i	1.11361	+	0.809083i
$476$	−11.4164	+	9.88690i	−0.523270	+	0.453165i
$477$	−0.500000	−	1.53884i	−0.0228934	−	0.0704587i
$478$	−19.4825	−	8.67416i	−0.891108	−	0.396747i
$479$	0.805727	+	7.66598i	0.0368146	+	0.350267i	0.997387	+	0.0722388i	$0.0230144\pi$
$479$	0.805727	+	7.66598i	0.0368146	+	0.350267i	−0.960573	+	0.278029i	$0.910319\pi$
$480$	−0.378188	−	3.59821i	−0.0172618	−	0.164235i
$481$	−0.233733	+	2.22382i	−0.0106573	+	0.101397i
$482$	4.14590			0.188840
$483$	−13.5725	+	28.9654i	−0.617568	+	1.31797i
$484$	−0.881966	+	2.71441i	−0.0400894	+	0.123382i
$485$	−13.8170	−	6.15173i	−0.627399	−	0.279336i
$486$	−3.85808	−	0.820060i	−0.175006	−	0.0371987i
$487$	−5.75235	−	6.38863i	−0.260664	−	0.289496i	0.598580	−	0.801063i	$-0.295732\pi$
$487$	−5.75235	−	6.38863i	−0.260664	−	0.289496i	−0.859244	+	0.511567i	$0.829065\pi$
$488$	3.68168	−	0.782565i	0.166662	−	0.0354251i
$489$	9.97214	+	30.6911i	0.450956	+	1.38790i
$490$	−15.4247	+	2.66064i	−0.696816	+	0.120196i
$491$	−8.60739	+	26.4908i	−0.388446	+	1.19551i	0.545503	+	0.838109i	$0.316339\pi$
$491$	−8.60739	+	26.4908i	−0.388446	+	1.19551i	−0.933949	+	0.357405i	$0.883661\pi$
$492$	1.96497	−	18.6954i	0.0885875	−	0.842853i
$493$	15.6180	−	27.0512i	0.703401	−	1.21833i
$494$	4.68157	−	2.08437i	0.210634	−	0.0937801i
$495$	−1.21885	−	2.11111i	−0.0547831	−	0.0948871i
$496$	−1.50000	+	1.08981i	−0.0673520	+	0.0489341i
$497$	−3.75559	−	3.51523i	−0.168461	−	0.157680i
$498$	−5.11803	−	15.7517i	−0.229345	−	0.705850i
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	0.699903	−	0.714238i	$-0.253227\pi$
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	−0.968500	+	0.249015i	$0.919893\pi$
$500$	−1.16866	−	11.1191i	−0.0522642	−	0.497261i
$501$	5.54508	−	9.60437i	0.247736	−	0.429092i
$502$	−5.90150	+	6.55428i	−0.263397	+	0.292532i
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	−0.402526	−	0.915409i	$-0.631868\pi$
$503$	7.70820	−	5.60034i	0.343692	−	0.249707i	0.746218	+	0.665702i	$0.231868\pi$
$504$	0.229164	−	0.984261i	0.0102078	−	0.0438425i
$505$	−19.4721			−0.866499
$506$	2.22920	−	21.2094i	0.0991000	−	0.942873i
$507$	−9.92705	+	17.1942i	−0.440876	+	0.763619i
$508$	8.22191	−	3.66063i	0.364788	−	0.162414i
$509$	−31.7962	+	6.75850i	−1.40934	+	0.299565i	−0.848867	−	0.528606i	$-0.822715\pi$
$509$	−31.7962	+	6.75850i	−1.40934	+	0.299565i	−0.560476	+	0.828171i	$0.689382\pi$
$510$	6.38197	+	19.6417i	0.282598	+	0.869748i
$511$	−0.389256	+	20.1517i	−0.0172197	+	0.891457i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	32.1153	−	6.82633i	1.41793	−	0.301390i
$514$	−0.944458	−	0.200751i	−0.0416583	−	0.00885474i
$515$	3.49297	+	33.2333i	0.153918	+	1.46444i
$516$	−3.53897	+	0.752232i	−0.155795	+	0.0331151i
$517$	11.0000	+	7.99197i	0.483779	+	0.351486i
$518$	−6.54508	−	2.26728i	−0.287575	−	0.0996187i
$519$	4.85410	+	3.52671i	0.213071	+	0.154805i
$520$	−1.74472	−	0.776798i	−0.0765109	−	0.0340648i
$521$	1.92144	+	18.2813i	0.0841798	+	0.800917i	0.952423	+	0.304779i	$0.0985825\pi$
$521$	1.92144	+	18.2813i	0.0841798	+	0.800917i	−0.868243	+	0.496138i	$0.834751\pi$
$522$	0.218482	+	2.07872i	0.00956271	+	0.0909831i
$523$	13.0294	−	14.4706i	0.569736	−	0.632756i	−0.387567	−	0.921841i	$-0.626685\pi$
$523$	13.0294	−	14.4706i	0.569736	−	0.632756i	0.957303	+	0.289086i	$0.0933512\pi$
$524$	17.7984			0.777526
$525$	−4.85378	+	20.8470i	−0.211836	+	0.909837i
$526$	16.7082			0.728512
$527$	7.08181	−	7.86514i	0.308488	−	0.342611i
$528$	−0.482716	−	4.59274i	−0.0210075	−	0.199873i
$529$	−3.43196	−	32.6530i	−0.149216	−	1.41969i
$530$	0.990108	−	9.42025i	0.0430075	−	0.409189i
$531$	3.19098	+	2.31838i	0.138477	+	0.100609i
$532$	3.00000	+	15.5885i	0.130066	+	0.675845i
$533$	−8.02786	−	5.83258i	−0.347725	−	0.252637i
$534$	27.0482	−	5.74927i	1.17049	−	0.248795i
$535$	−5.10081	+	8.83487i	−0.220527	+	0.381965i
$536$	−0.978148	−	0.207912i	−0.0422495	−	0.00898042i
$537$	−16.2004	+	3.44350i	−0.699098	+	0.148598i
$538$	−0.826238	+	2.54290i	−0.0356216	+	0.109632i
$539$	−19.6880	+	3.39603i	−0.848021	+	0.146277i
$540$	−9.89919	−	7.19218i	−0.425993	−	0.309502i
$541$	19.3320	−	4.10915i	0.831149	−	0.176666i	0.227361	−	0.973811i	$-0.426990\pi$
$541$	19.3320	−	4.10915i	0.831149	−	0.176666i	0.603789	+	0.797144i	$0.293657\pi$
$542$	−0.831171	+	0.370061i	−0.0357019	+	0.0158955i
$543$	20.5623	−	35.6150i	0.882413	−	1.52838i
$544$	0.596670	−	5.67693i	0.0255820	−	0.243397i
$545$	2.23607	−	6.88191i	0.0957826	−	0.294789i
$546$	2.66943	+	2.49859i	0.114241	+	0.106930i
$547$	34.5066	−	25.0705i	1.47539	−	1.07194i	0.496390	−	0.868100i	$-0.334659\pi$
$547$	34.5066	−	25.0705i	1.47539	−	1.07194i	0.979005	−	0.203837i	$-0.0653414\pi$
$548$	−4.33070	+	4.80973i	−0.184999	+	0.205462i
$549$	0.718847	−	1.24508i	0.0306796	−	0.0531387i
$550$	−1.49167	−	14.1923i	−0.0636052	−	0.605163i
$551$	−16.4164	−	28.4341i	−0.699362	−	1.21133i
$552$	−3.73607	−	11.4984i	−0.159018	−	0.489406i
$553$	−5.36621	+	23.0479i	−0.228194	+	0.980095i
$554$	−16.5172	+	12.0005i	−0.701749	+	0.509851i
$555$	−6.33810	+	7.03917i	−0.269037	+	0.298796i
$556$	5.48127	−	2.44042i	0.232458	−	0.103497i
$557$	−14.0902	+	24.4049i	−0.597020	+	1.03407i	0.396239	+	0.918147i	$0.370315\pi$
$557$	−14.0902	+	24.4049i	−0.597020	+	1.03407i	−0.993258	+	0.115921i	$0.963018\pi$
$558$	−0.0740275	+	0.704324i	−0.00313383	+	0.0298164i
$559$	−0.590170	+	1.81636i	−0.0249615	+	0.0768237i
$560$	3.56917	−	4.71816i	0.150825	−	0.199379i
$561$	8.14590	+	25.0705i	0.343920	+	1.05848i
$562$	16.6285	−	3.53450i	0.701431	−	0.149094i
$563$	−26.6906	−	29.6430i	−1.12488	−	1.24930i	−0.965024	−	0.262161i	$-0.915565\pi$
$563$	−26.6906	−	29.6430i	−1.12488	−	1.24930i	−0.159852	−	0.987141i	$-0.551102\pi$
$564$	7.53976	+	1.60263i	0.317481	+	0.0674827i
$565$	44.6549	−	9.49168i	1.87864	−	0.399318i
$566$	2.64590	−	8.14324i	0.111215	−	0.342286i
$567$	11.6664	+	16.7275i	0.489943	+	0.702490i
$568$	1.94427			0.0815798
$569$	0.759975	−	7.23068i	0.0318598	−	0.303126i	−0.966975	−	0.254870i	$-0.917967\pi$
$569$	0.759975	−	7.23068i	0.0318598	−	0.303126i	0.998835	−	0.0482555i	$-0.0153662\pi$
$570$	21.2338	+	4.51339i	0.889387	+	0.189045i
$571$	−3.14888	−	29.9596i	−0.131777	−	1.25377i	−0.837956	−	0.545737i	$-0.816250\pi$
$571$	−3.14888	−	29.9596i	−0.131777	−	1.25377i	0.706180	−	0.708032i	$-0.250417\pi$
$572$	−2.22694	−	0.991500i	−0.0931132	−	0.0414567i
$573$	10.1180	+	31.1401i	0.422687	+	1.30090i
$574$	23.2361	−	20.1230i	0.969855	−	0.839919i
$575$	−11.5451	−	35.5321i	−0.481463	−	1.48179i
$576$	0.190983	+	0.330792i	0.00795763	+	0.0137830i
$577$	11.9687	+	2.54402i	0.498263	+	0.105909i	0.450186	−	0.892935i	$-0.351358\pi$
$577$	11.9687	+	2.54402i	0.498263	+	0.105909i	0.0480764	+	0.998844i	$0.484691\pi$
$578$	1.62893	+	15.4982i	0.0677545	+	0.644641i
$579$	1.18011	+	0.525421i	0.0490439	+	0.0218357i
$580$	−3.78115	+	11.6372i	−0.157004	+	0.483208i
$581$	11.4910	−	24.5234i	0.476728	−	1.01740i
$582$	−10.9443			−0.453655
$583$	1.26377	−	12.0239i	0.0523399	−	0.497981i
$584$	−5.09746	−	5.66130i	−0.210934	−	0.234266i
$585$	−0.666422	+	0.296710i	−0.0275532	+	0.0122675i
$586$	−6.75164	+	7.49846i	−0.278908	+	0.309758i
$587$	−1.20820	+	3.71847i	−0.0498679	+	0.153478i	−0.972889	−	0.231271i	$-0.925712\pi$
$587$	−1.20820	+	3.71847i	−0.0498679	+	0.153478i	0.923022	+	0.384748i	$0.125712\pi$
$588$	−9.41338	+	6.29857i	−0.388201	+	0.259748i
$589$	−3.43769	−	10.5801i	−0.141648	−	0.435947i
$590$	11.5451	+	19.9967i	0.475304	+	0.823250i
$591$	−18.5635	−	20.6168i	−0.763598	−	0.848062i
$592$	2.39169	−	1.06485i	0.0982980	−	0.0437651i
$593$	−19.4443	−	33.6785i	−0.798481	−	1.38301i	−0.920605	−	0.390494i	$-0.872304\pi$
$593$	−19.4443	−	33.6785i	−0.798481	−	1.38301i	0.122125	−	0.992515i	$-0.461029\pi$
$594$	−12.6353	−	9.18005i	−0.518431	−	0.376662i
$595$	−14.3288	+	30.5796i	−0.587424	+	1.25364i
$596$	7.47214	−	5.42882i	0.306071	−	0.222373i
$597$	−6.52810	−	2.90650i	−0.267177	−	0.118955i
$598$	−6.24250	−	1.32689i	−0.255275	−	0.0542604i
$599$	−19.9443	+	34.5445i	−0.814901	+	1.41145i	0.0944982	+	0.995525i	$0.469875\pi$
$599$	−19.9443	+	34.5445i	−0.814901	+	1.41145i	−0.909399	+	0.415925i	$0.863458\pi$
$600$	−4.04508	−	7.00629i	−0.165140	−	0.286031i
$601$	−3.85410			−0.157212			−0.0786060	−	0.996906i	$-0.525047\pi$
$601$	−3.85410			−0.157212			−0.0786060	+	0.996906i	$0.525047\pi$
$602$	−5.06539	−	3.05644i	−0.206450	−	0.124571i
$603$	−0.309017	+	0.224514i	−0.0125841	+	0.00914292i
$604$	14.0521	+	6.25641i	0.571773	+	0.254570i
$605$	0.667097	+	6.34700i	0.0271214	+	0.258042i
$606$	−12.8720	+	5.73099i	−0.522890	+	0.232805i
$607$	−6.89919	−	11.9497i	−0.280029	−	0.485025i	0.691362	−	0.722508i	$-0.257011\pi$
$607$	−6.89919	−	11.9497i	−0.280029	−	0.485025i	−0.971392	+	0.237483i	$0.923678\pi$
$608$	−4.85410	−	3.52671i	−0.196860	−	0.143027i
$609$	14.1328	−	18.6824i	0.572688	−	0.757048i
$610$	6.80902	−	4.94704i	0.275689	−	0.200300i
$611$	2.72261	−	3.02377i	0.110145	−	0.122329i
$612$	−1.45893	−	1.62031i	−0.0589738	−	0.0654971i
$613$	8.69870	+	9.66088i	0.351337	+	0.390199i	0.892746	−	0.450560i	$-0.148776\pi$
$613$	8.69870	+	9.66088i	0.351337	+	0.390199i	−0.541409	+	0.840759i	$0.682109\pi$
$614$	18.1499	−	20.1575i	0.732471	−	0.813491i
$615$	−12.9894	−	39.9771i	−0.523781	−	1.61203i
$616$	4.55567	−	6.02223i	0.183553	−	0.242642i
$617$	31.1246	+	22.6134i	1.25303	+	0.910379i	0.998394	−	0.0566576i	$-0.0180443\pi$
$617$	31.1246	+	22.6134i	1.25303	+	0.910379i	0.254636	+	0.967037i	$0.418044\pi$
$618$	12.0902	+	20.9408i	0.486338	+	0.842362i
$619$	−8.90035	+	3.96269i	−0.357735	+	0.159274i	−0.577732	−	0.816227i	$-0.696062\pi$
$619$	−8.90035	+	3.96269i	−0.357735	+	0.159274i	0.219997	+	0.975501i	$0.429395\pi$
$620$	−2.07295	+	3.59045i	−0.0832516	+	0.144196i
$621$	−37.3535	−	16.6309i	−1.49895	−	0.667374i
$622$	24.6074	−	17.8783i	0.986666	−	0.716855i
$623$	38.7146	+	23.3602i	1.55107	+	0.935907i
$624$	−1.38197			−0.0553229
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	−6.76393	+	11.7155i	−0.270341	+	0.468245i
$627$	27.1027	+	5.76086i	1.08238	+	0.230067i
$628$	−3.30524	−	1.47159i	−0.131893	−	0.0587227i
$629$	−12.0902	+	8.78402i	−0.482067	+	0.350242i
$630$	−0.427051	−	2.21902i	−0.0170141	−	0.0884080i
$631$	−20.3992	−	14.8209i	−0.812079	−	0.590010i	0.102354	−	0.994748i	$-0.467363\pi$
$631$	−20.3992	−	14.8209i	−0.812079	−	0.590010i	−0.914433	+	0.404738i	$0.867363\pi$
$632$	−4.47214	−	7.74597i	−0.177892	−	0.308118i
$633$	−34.3972	+	15.3146i	−1.36717	+	0.608702i
$634$	11.2030	+	12.4422i	0.444929	+	0.494143i
$635$	13.4660	−	14.9555i	0.534382	−	0.593491i
$636$	−2.11803	−	6.51864i	−0.0839855	−	0.258481i
$637$	0.394857	+	5.96566i	0.0156448	+	0.236368i
$638$	−4.82624	+	14.8536i	−0.191073	+	0.588061i
$639$	0.496927	−	0.551893i	0.0196581	−	0.0218326i
$640$	0.233733	+	2.22382i	0.00923910	+	0.0879041i
$641$	29.4878	+	32.7496i	1.16470	+	1.29353i	0.948354	+	0.317213i	$0.102747\pi$
$641$	29.4878	+	32.7496i	1.16470	+	1.29353i	0.216345	+	0.976317i	$0.430586\pi$
$642$	−0.771626	+	7.34153i	−0.0304536	+	0.289747i
$643$	5.94427			0.234419			0.117210	−	0.993107i	$-0.462605\pi$
$643$	5.94427			0.234419			0.117210	+	0.993107i	$0.462605\pi$
$644$	8.38824	−	17.9016i	0.330543	−	0.705422i
$645$	−6.54508	+	4.75528i	−0.257712	+	0.187239i
$646$	31.2882	+	13.9304i	1.23102	+	0.548085i
$647$	3.65627	+	34.7871i	0.143743	+	1.36762i	0.794005	+	0.607912i	$0.207993\pi$
$647$	3.65627	+	34.7871i	0.143743	+	1.36762i	−0.650262	+	0.759710i	$0.725341\pi$
$648$	−7.53976	−	1.60263i	−0.296190	−	0.0629571i
$649$	14.7361	+	25.5236i	0.578441	+	1.00189i
$650$	−4.27051			−0.167503
$651$	6.00000	−	5.19615i	0.235159	−	0.203653i
$652$	−6.16312	−	18.9681i	−0.241366	−	0.742849i
$653$	−19.3686	−	8.62348i	−0.757954	−	0.337463i	−0.00888987	−	0.999960i	$-0.502830\pi$
$653$	−19.3686	−	8.62348i	−0.757954	−	0.337463i	−0.749064	+	0.662498i	$0.769496\pi$
$654$	−0.547318	−	5.20738i	−0.0214018	−	0.203625i
$655$	36.3576	−	16.1875i	1.42061	−	0.632496i
$656$	−1.21442	+	11.5544i	−0.0474149	+	0.451123i
$657$	−2.90983			−0.113523
$658$	7.21024	+	10.3382i	0.281084	+	0.403024i
$659$	−12.6074	+	38.8016i	−0.491114	+	1.51149i	0.331812	+	0.943346i	$0.392340\pi$
$659$	−12.6074	+	38.8016i	−0.491114	+	1.51149i	−0.822926	+	0.568149i	$0.807660\pi$
$660$	−5.16312	−	8.94278i	−0.200974	−	0.348097i
$661$	−39.6214	−	8.42179i	−1.54109	−	0.327570i	−0.642478	−	0.766304i	$-0.722093\pi$
$661$	−39.6214	−	8.42179i	−1.54109	−	0.327570i	−0.898617	+	0.438735i	$0.855427\pi$
$662$	−6.36114	−	7.06476i	−0.247233	−	0.274580i
$663$	7.71616	−	1.64012i	0.299671	−	0.0636970i
$664$	3.16312	+	9.73508i	0.122753	+	0.377794i
$665$	20.3058	+	29.1148i	0.787425	+	1.12903i
$666$	0.309017	−	0.951057i	0.0119742	−	0.0368527i
$667$	−4.27402	+	40.6646i	−0.165491	+	1.57454i
$668$	−3.42705	+	5.93583i	−0.132597	+	0.229664i
$669$	−12.3898	+	5.51629i	−0.479017	+	0.213272i
$670$	−2.18720	+	0.464905i	−0.0844991	+	0.0179608i
$671$	8.69098	−	6.31437i	0.335512	−	0.243764i
$672$	0.970756	−	4.16940i	0.0374477	−	0.160838i
$673$	4.89261	+	15.0579i	0.188596	+	0.580439i	0.999992	−	0.00405796i	$-0.00129169\pi$
$673$	4.89261	+	15.0579i	0.188596	+	0.580439i	−0.811396	+	0.584497i	$0.801292\pi$
$674$	4.64590	+	8.04693i	0.178953	+	0.309956i
$675$	−26.7628	−	5.68861i	−1.03010	−	0.218955i
$676$	6.13525	−	10.6266i	0.235971	−	0.408714i
$677$	−15.8639	+	17.6186i	−0.609699	+	0.677139i	−0.966389	−	0.257084i	$-0.917238\pi$
$677$	−15.8639	+	17.6186i	−0.609699	+	0.677139i	0.356691	+	0.934223i	$0.383905\pi$
$678$	26.7254	−	19.4172i	1.02638	−	0.745711i
$679$	−13.0653	−	12.2292i	−0.501402	−	0.469312i
$680$	−3.94427	−	12.1392i	−0.151256	−	0.465518i
$681$	−0.347687	+	3.30802i	−0.0133234	+	0.126763i
$682$	−2.64590	+	4.58283i	−0.101317	+	0.175486i
$683$	−17.5221	+	7.80135i	−0.670465	+	0.298510i	−0.713594	−	0.700559i	$-0.752934\pi$
$683$	−17.5221	+	7.80135i	−0.670465	+	0.298510i	0.0431292	+	0.999070i	$0.486267\pi$
$684$	−2.24171	+	0.476491i	−0.0857141	+	0.0182191i
$685$	−4.47214	+	13.7638i	−0.170872	+	0.525888i
$686$	−18.2758	−	2.99927i	−0.697773	−	0.114512i
$687$	1.66312	−	5.11855i	0.0634519	−	0.195285i
$688$	2.18720	−	0.464905i	0.0833864	−	0.0177243i
$689$	−3.53897	−	0.752232i	−0.134824	−	0.0286577i
$690$	−18.0896	−	20.0905i	−0.688658	−	0.764832i
$691$	−6.01160	+	1.27780i	−0.228692	+	0.0486100i	−0.320832	−	0.947136i	$-0.603963\pi$
$691$	−6.01160	+	1.27780i	−0.228692	+	0.0486100i	0.0921402	+	0.995746i	$0.470629\pi$
$692$	−3.00000	−	2.17963i	−0.114043	−	0.0828570i
$693$	−0.545085	−	2.83234i	−0.0207061	−	0.107592i
$694$	15.7082	+	11.4127i	0.596275	+	0.433219i
$695$	8.97733	−	9.97033i	0.340530	−	0.378196i
$696$	0.925506	+	8.80560i	0.0350812	+	0.333775i
$697$	−6.93213	−	65.9548i	−0.262573	−	2.49822i
$698$	−14.3073	+	15.8899i	−0.541540	+	0.601441i
$699$	−45.0344			−1.70336
$700$	2.99980	−	12.8841i	0.113382	−	0.486975i
$701$	41.0132			1.54905			0.774523	−	0.632546i	$-0.217990\pi$
$701$	41.0132			1.54905			0.774523	+	0.632546i	$0.217990\pi$
$702$	−3.12736	+	3.47328i	−0.118034	+	0.131091i
$703$	1.64195	+	15.6222i	0.0619275	+	0.589201i
$704$	0.298335	+	2.83847i	0.0112439	+	0.106979i
$705$	16.8594	−	3.58358i	0.634962	−	0.134965i
$706$	12.1631	+	8.83702i	0.457765	+	0.332586i
$707$	−21.7705	−	7.54153i	−0.818764	−	0.283628i
$708$	13.5172	+	9.82084i	0.508008	+	0.369090i
$709$	7.41787	−	1.57672i	0.278584	−	0.0592149i	−0.0665008	−	0.997786i	$-0.521183\pi$
$709$	7.41787	−	1.57672i	0.278584	−	0.0592149i	0.345085	+	0.938572i	$0.387850\pi$
$710$	3.97166	−	1.76830i	0.149054	−	0.0663630i
$711$	−3.34175	−	0.710311i	−0.125325	−	0.0266387i
$712$	−16.7167	+	3.55325i	−0.626485	+	0.133164i
$713$	−4.28115	+	13.1760i	−0.160330	+	0.493446i
$714$	−0.471932	+	24.4318i	−0.0176616	+	0.914336i
$715$	−5.45085			−0.203850
$716$	10.0124	−	2.12820i	0.374180	−	0.0795345i
$717$	−31.5233	+	14.0351i	−1.17726	+	0.524150i
$718$	−3.11803	+	5.40059i	−0.116364	+	0.201548i
$719$	−3.87698	+	36.8870i	−0.144587	+	1.37565i	0.646016	+	0.763324i	$0.276434\pi$
$719$	−3.87698	+	36.8870i	−0.144587	+	1.37565i	−0.790603	+	0.612329i	$0.790233\pi$
$720$	0.690983	+	0.502029i	0.0257514	+	0.0187095i
$721$	−8.96597	+	38.5088i	−0.333910	+	1.43414i
$722$	13.7533	−	9.99235i	0.511844	−	0.371877i
$723$	4.48866	−	4.98517i	0.166935	−	0.185400i
$724$	−12.7082	+	22.0113i	−0.472297	+	0.818042i
$725$	2.85997	+	27.2108i	0.106217	+	1.01058i
$726$	2.30902	+	3.99933i	0.0856957	+	0.148429i
$727$	−0.583592	−	1.79611i	−0.0216442	−	0.0666141i	0.939651	−	0.342134i	$-0.111150\pi$
$727$	−0.583592	−	1.79611i	−0.0216442	−	0.0666141i	−0.961295	+	0.275520i	$0.911150\pi$
$728$	−1.64980	−	1.54421i	−0.0611457	−	0.0572323i
$729$	−23.8713	+	17.3435i	−0.884123	+	0.642353i
$730$	−15.5617	−	6.92853i	−0.575966	−	0.256436i
$731$	−11.6604	+	5.19156i	−0.431277	+	0.192017i
$732$	3.04508	−	5.27424i	0.112550	−	0.194942i
$733$	−1.53743	+	14.6276i	−0.0567861	+	0.540284i	0.928737	+	0.370740i	$0.120896\pi$
$733$	−1.53743	+	14.6276i	−0.0567861	+	0.540284i	−0.985523	+	0.169544i	$0.945771\pi$
$734$	4.65248	−	14.3188i	0.171726	−	0.528518i
$735$	−13.5007	+	21.4278i	−0.497981	+	0.790375i
$736$	2.30902	+	7.10642i	0.0851115	+	0.261946i
$737$	−2.79173	+	0.593401i	−0.102835	+	0.0218582i
$738$	2.96940	+	3.29785i	0.109305	+	0.121396i
$739$	−37.9297	−	8.06221i	−1.39527	−	0.296573i	−0.551900	−	0.833910i	$-0.686097\pi$
$739$	−37.9297	−	8.06221i	−1.39527	−	0.296573i	−0.843367	+	0.537337i	$0.819430\pi$
$740$	3.91716	−	4.35045i	0.143998	−	0.159926i
$741$	2.56231	−	7.88597i	0.0941287	−	0.289698i
$742$	4.75542	−	10.1487i	0.174577	−	0.372570i
$743$	−31.7639			−1.16531			−0.582653	−	0.812721i	$-0.697985\pi$
$743$	−31.7639			−1.16531			−0.582653	+	0.812721i	$0.697985\pi$
$744$	−0.313585	+	2.98357i	−0.0114966	+	0.109383i
$745$	10.3262	−	17.8856i	0.378324	−	0.655277i
$746$	3.09953	+	29.4900i	0.113482	+	1.07971i
$747$	3.57181	+	1.59027i	0.130686	+	0.0581850i
$748$	−5.03444	−	15.4944i	−0.184077	−	0.566532i
$749$	−9.12461	+	7.90215i	−0.333406	+	0.288738i
$750$	−14.6353	−	10.6331i	−0.534404	−	0.388267i
$751$	2.75329	+	4.76884i	0.100469	+	0.174017i	0.911878	−	0.410461i	$-0.134632\pi$
$751$	2.75329	+	4.76884i	0.100469	+	0.174017i	−0.811409	+	0.584479i	$0.801299\pi$
$752$	−4.65983	−	0.990477i	−0.169926	−	0.0361190i
$753$	1.49167	+	14.1923i	0.0543596	+	0.517197i
$754$	4.26969	+	1.90099i	0.155493	+	0.0692300i
$755$	34.3951			1.25177
$756$	−8.28211	−	11.8750i	−0.301217	−	0.431891i
$757$	38.7984			1.41015			0.705075	−	0.709132i	$-0.250913\pi$
$757$	38.7984			1.41015			0.705075	+	0.709132i	$0.250913\pi$
$758$	−2.50286	+	23.8131i	−0.0909079	+	0.864931i
$759$	−23.0894	−	25.6434i	−0.838092	−	0.930796i
$760$	−13.1232	−	2.78943i	−0.476029	−	0.101183i
$761$	10.8641	−	12.0657i	0.393822	−	0.437383i	−0.513327	−	0.858193i	$-0.671587\pi$
$761$	10.8641	−	12.0657i	0.393822	−	0.437383i	0.907149	+	0.420810i	$0.138254\pi$
$762$	4.50000	−	13.8496i	0.163018	−	0.501717i
$763$	5.16535	−	6.82818i	0.186998	−	0.247197i
$764$	−6.25329	−	19.2456i	−0.226236	−	0.696283i
$765$	−4.45389	−	1.98300i	−0.161031	−	0.0716955i
$766$	−13.3826	−	14.8629i	−0.483533	−	0.537018i
$767$	8.05716	−	3.58728i	0.290927	−	0.129529i
$768$	0.809017	+	1.40126i	0.0291929	+	0.0505636i
$769$	−23.3713	−	16.9803i	−0.842791	−	0.612324i	0.0803576	−	0.996766i	$-0.474394\pi$
$769$	−23.3713	−	16.9803i	−0.842791	−	0.612324i	−0.923149	+	0.384442i	$0.874394\pi$
$770$	3.82892	−	16.4452i	0.137985	−	0.592645i
$771$	−1.26393	+	0.918300i	−0.0455194	+	0.0330718i
$772$	−0.729351	−	0.324728i	−0.0262499	−	0.0116872i
$773$	49.5248	+	10.5268i	1.78128	+	0.378623i	0.976597	−	0.215078i	$-0.0690006\pi$
$773$	49.5248	+	10.5268i	1.78128	+	0.378623i	0.804686	+	0.593701i	$0.202334\pi$
$774$	0.427051	−	0.739674i	0.0153500	−	0.0265870i
$775$	−0.969032	+	9.21973i	−0.0348087	+	0.331182i
$776$	6.76393			0.242811
$777$	−9.81247	+	5.41530i	−0.352020	+	0.194273i
$778$	3.30902	−	2.40414i	0.118634	−	0.0861927i
$779$	−63.6816	−	28.3529i	−2.28163	−	1.01585i
$780$	−2.82301	+	1.25689i	−0.101080	+	0.0450037i
$781$	5.06940	−	2.25704i	0.181397	−	0.0807633i
$782$	−21.3262	−	36.9381i	−0.762625	−	1.32090i
$783$	24.2254	+	17.6008i	0.865746	+	0.629001i
$784$	5.81779	−	3.89273i	0.207778	−	0.139026i
$785$	−8.09017			−0.288751
$786$	19.2699	−	21.4014i	0.687334	−	0.763361i
$787$	−15.4131	−	17.1179i	−0.549416	−	0.610188i	0.402922	−	0.915234i	$-0.367995\pi$
$787$	−15.4131	−	17.1179i	−0.549416	−	0.610188i	−0.952338	+	0.305046i	$0.901328\pi$
$788$	11.4728	+	12.7419i	0.408703	+	0.453911i
$789$	18.0896	−	20.0905i	0.644006	−	0.715241i
$790$	−16.1803	−	11.7557i	−0.575671	−	0.418249i
$791$	53.6018	+	6.68273i	1.90586	+	0.237610i
$792$	0.881966	+	0.640786i	0.0313393	+	0.0227693i
$793$	−1.60739	−	2.78408i	−0.0570801	−	0.0988657i
$794$	−25.2109	+	11.2246i	−0.894701	+	0.398346i
$795$	−10.2553	−	11.3896i	−0.363716	−	0.403948i
$796$	4.03459	+	1.79631i	0.143002	+	0.0636687i
$797$	−13.1910	+	9.58381i	−0.467249	+	0.339476i	−0.796368	−	0.604812i	$-0.793248\pi$
$797$	−13.1910	+	9.58381i	−0.467249	+	0.339476i	0.329119	+	0.944288i	$0.393248\pi$
$798$	21.9921	+	13.2699i	0.778512	+	0.469751i
$799$	27.1935			0.962037
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	−3.26393	+	5.65330i	−0.115325	+	0.199749i
$802$	11.2760	+	2.39678i	0.398168	+	0.0846332i
$803$	−19.8629	−	8.84353i	−0.700946	−	0.312081i
$804$	−1.30902	+	0.951057i	−0.0461655	+	0.0335412i
$805$	0.853733	−	44.1975i	0.0300901	−	1.55776i
$806$	1.28115	+	0.930812i	0.0451267	+	0.0327865i
$807$	2.16312	+	3.74663i	0.0761454	+	0.131888i
$808$	7.95534	−	3.54195i	0.279868	−	0.124605i
$809$	−20.3898	−	22.6452i	−0.716869	−	0.796163i	0.269097	−	0.963113i	$-0.413275\pi$
$809$	−20.3898	−	22.6452i	−0.716869	−	0.796163i	−0.985965	+	0.166950i	$0.946608\pi$
$810$	−16.8594	+	3.58358i	−0.592380	+	0.125914i
$811$	−6.51722	−	20.0579i	−0.228851	−	0.704330i	−0.997878	−	0.0651137i	$-0.979259\pi$
$811$	−6.51722	−	20.0579i	−0.228851	−	0.704330i	0.769027	−	0.639216i	$-0.220741\pi$
$812$	−8.73452	+	11.5463i	−0.306522	+	0.405197i
$813$	−0.454915	+	1.40008i	−0.0159546	+	0.0491031i
$814$	4.99983	−	5.55288i	0.175244	−	0.194628i
$815$	−29.8410	−	33.1418i	−1.04529	−	1.16091i
$816$	−6.18014	−	6.86374i	−0.216348	−	0.240279i
$817$	−1.40240	+	13.3429i	−0.0490636	+	0.466809i
$818$	−7.47214			−0.261257
$819$	−0.859998	+	0.0736280i	−0.0300508	+	0.00257277i
$820$	8.02786	+	24.7072i	0.280345	+	0.862814i
$821$	21.9566	+	9.77569i	0.766289	+	0.341174i	0.752380	−	0.658729i	$-0.228906\pi$
$821$	21.9566	+	9.77569i	0.766289	+	0.341174i	0.0139091	+	0.999903i	$0.495572\pi$
$822$	1.09464	+	10.4148i	0.0381798	+	0.363257i
$823$	−33.6643	−	7.15557i	−1.17346	−	0.249428i	−0.420378	−	0.907349i	$-0.638103\pi$
$823$	−33.6643	−	7.15557i	−1.17346	−	0.249428i	−0.753087	+	0.657921i	$0.771436\pi$
$824$	−7.47214	−	12.9421i	−0.260304	−	0.450860i
$825$	−18.6803	−	13.5721i	−0.650366	−	0.472519i
$826$	5.16312	+	26.8284i	0.179648	+	0.933478i
$827$	−16.1631	−	49.7450i	−0.562047	−	1.72980i	−0.676567	−	0.736381i	$-0.736533\pi$
$827$	−16.1631	−	49.7450i	−0.562047	−	1.72980i	0.114520	−	0.993421i	$-0.463467\pi$
$828$	2.60735	+	1.16087i	0.0906117	+	0.0403429i
$829$	3.32966	+	31.6796i	0.115644	+	1.10028i	0.886327	+	0.463060i	$0.153248\pi$
$829$	3.32966	+	31.6796i	0.115644	+	1.10028i	−0.770683	+	0.637218i	$0.780085\pi$
$830$	15.3154	+	17.0095i	0.531606	+	0.590408i
$831$	−3.45304	+	32.8535i	−0.119785	+	1.13967i
$832$	0.854102			0.0296107
$833$	−27.8635	+	28.6395i	−0.965414	+	0.992299i
$834$	3.00000	−	9.23305i	0.103882	−	0.319714i
$835$	−1.60203	+	15.2423i	−0.0554405	+	0.527481i
$836$	−16.7504	−	3.56041i	−0.579325	−	0.123139i
$837$	6.78893	+	7.53987i	0.234660	+	0.260616i
$838$	−7.59427	+	1.61421i	−0.262340	+	0.0557620i
$839$	0.0557281	+	0.171513i	0.00192395	+	0.00592130i	0.952014	−	0.306055i	$-0.0990091\pi$
$839$	0.0557281	+	0.171513i	0.00192395	+	0.00592130i	−0.950090	+	0.311976i	$0.899009\pi$
$840$	−1.80902	−	9.39993i	−0.0624170	−	0.324328i
$841$	0.291796	−	0.898056i	0.0100619	−	0.0309674i
$842$	1.34944	−	12.8391i	0.0465049	−	0.442465i
$843$	13.7533	−	23.8214i	0.473688	−	0.820452i
$844$	21.2587	−	9.46497i	0.731754	−	0.325798i
$845$	2.86802	−	27.2874i	0.0986629	−	0.938715i
$846$	−1.47214	+	1.06957i	−0.0506131	+	0.0367726i
$847$	−1.71235	+	7.35453i	−0.0588369	+	0.252705i
$848$	1.30902	+	4.02874i	0.0449518	+	0.138348i
$849$	−6.92705	−	11.9980i	−0.237736	−	0.411770i
$850$	−19.0977	−	21.2101i	−0.655045	−	0.727501i
$851$	9.78115	−	16.9415i	0.335294	−	0.580746i
$852$	2.10502	−	2.33786i	0.0721167	−	0.0800937i
$853$	−0.972136	+	0.706298i	−0.0332853	+	0.0241832i	−0.604304	−	0.796754i	$-0.706549\pi$
$853$	−0.972136	+	0.706298i	−0.0332853	+	0.0241832i	0.571018	+	0.820937i	$0.306549\pi$
$854$	9.52869	−	2.89384i	0.326065	−	0.0990251i
$855$	−4.14590	+	3.01217i	−0.141787	+	0.103014i
$856$	0.476891	−	4.53731i	0.0162998	−	0.155082i
$857$	10.2082	−	17.6811i	0.348706	−	0.603976i	−0.637314	−	0.770604i	$-0.719955\pi$
$857$	10.2082	−	17.6811i	0.348706	−	0.603976i	0.986020	+	0.166628i	$0.0532880\pi$
$858$	−3.60327	+	1.60428i	−0.123014	+	0.0547692i
$859$	19.1556	−	4.07166i	0.653582	−	0.138923i	0.130826	−	0.991405i	$-0.458237\pi$
$859$	19.1556	−	4.07166i	0.653582	−	0.138923i	0.522756	+	0.852482i	$0.324904\pi$
$860$	4.04508	−	2.93893i	0.137936	−	0.100217i
$861$	0.960533	−	49.7265i	0.0327349	−	1.69468i
$862$	−0.628677	+	1.93487i	−0.0214128	+	0.0659019i
$863$	5.90257	−	1.25463i	0.200926	−	0.0427081i	−0.106349	−	0.994329i	$-0.533916\pi$
$863$	5.90257	−	1.25463i	0.200926	−	0.0427081i	0.307275	+	0.951621i	$0.400583\pi$
$864$	5.35256	+	1.13772i	0.182098	+	0.0387061i
$865$	−8.11060	−	1.72396i	−0.275769	−	0.0586164i
$866$	9.08875	−	1.93187i	0.308848	−	0.0656477i
$867$	20.3992	+	14.8209i	0.692793	+	0.503343i
$868$	−3.70820	+	3.21140i	−0.125865	+	0.109002i
$869$	−20.6525	−	15.0049i	−0.700587	−	0.509006i
$870$	9.89919	+	17.1459i	0.335614	+	0.581300i
$871$	0.0892780	+	0.849423i	0.00302507	+	0.0287816i
$872$	0.338261	+	3.21834i	0.0114550	+	0.108987i
$873$	1.72876	−	1.91998i	0.0585097	−	0.0649816i
$874$	−44.8328			−1.51649
$875$	−5.59017	−	29.0474i	−0.188982	−	0.981981i
$876$	−12.3262			−0.416465
$877$	−16.7513	+	18.6042i	−0.565652	+	0.628220i	−0.956324	−	0.292310i	$-0.905576\pi$
$877$	−16.7513	+	18.6042i	−0.565652	+	0.628220i	0.390672	+	0.920530i	$0.372243\pi$
$878$	−1.45757	−	13.8679i	−0.0491907	−	0.468018i
$879$	1.70656	+	16.2368i	0.0575607	+	0.547654i
$880$	3.19098	+	5.52694i	0.107568	+	0.186313i
$881$	0.236068	+	0.171513i	0.00795333	+	0.00577843i	0.591755	−	0.806118i	$-0.298435\pi$
$881$	0.236068	+	0.171513i	0.00795333	+	0.00577843i	−0.583801	+	0.811896i	$0.698435\pi$
$882$	0.381966	−	2.64634i	0.0128615	−	0.0891068i
$883$	13.9721	+	10.1514i	0.470200	+	0.341620i	0.797519	−	0.603294i	$-0.206145\pi$
$883$	13.9721	+	10.1514i	0.470200	+	0.341620i	−0.327319	+	0.944914i	$0.606145\pi$
$884$	−4.76885	+	1.01365i	−0.160394	+	0.0340927i
$885$	36.5443	+	7.76772i	1.22842	+	0.261109i
$886$	9.63877	+	2.04878i	0.323821	+	0.0688302i
$887$	−10.6377	+	2.26112i	−0.357180	+	0.0759210i	−0.383007	−	0.923745i	$-0.625111\pi$
$887$	−10.6377	+	2.26112i	−0.357180	+	0.0759210i	0.0258268	+	0.999666i	$0.491778\pi$
$888$	1.30902	−	4.02874i	0.0439277	−	0.135196i
$889$	20.8477	−	11.5054i	0.699209	−	0.385879i
$890$	−30.9164	+	22.4621i	−1.03632	+	0.752931i
$891$	−21.5192	+	4.57406i	−0.720922	+	0.153237i
$892$	7.65731	−	3.40925i	0.256386	−	0.114150i
$893$	14.2918	−	24.7541i	0.478257	−	0.828365i
$894$	1.56210	−	14.8624i	0.0522445	−	0.497073i
$895$	18.5172	−	13.4535i	0.618962	−	0.449703i
$896$	−0.599960	+	2.57683i	−0.0200433	+	0.0860858i
$897$	−8.35410	+	6.06961i	−0.278935	+	0.202658i
$898$	−22.7735	+	25.2925i	−0.759961	+	0.844022i
$899$	5.07295	−	8.78661i	0.169192	−	0.293050i
$900$	1.86810	+	0.397076i	0.0622699	+	0.0132359i
$901$	−12.0902	−	20.9408i	−0.402782	−	0.697639i
$902$	10.2467	+	31.5361i	0.341178	+	1.05004i
$903$	−9.15934	+	2.78167i	−0.304804	+	0.0925681i
$904$	−16.5172	+	12.0005i	−0.549355	+	0.399129i
$905$	−5.94065	+	56.5215i	−0.197474	+	1.87884i
$906$	22.7368	−	10.1231i	0.755380	−	0.336317i
$907$	−0.364745	+	0.631757i	−0.0121112	+	0.0209771i	−0.872017	−	0.489475i	$-0.837189\pi$
$907$	−0.364745	+	0.631757i	−0.0121112	+	0.0209771i	0.859906	+	0.510452i	$0.170522\pi$
$908$	0.214882	−	2.04447i	0.00713111	−	0.0678480i
$909$	1.02786	−	3.16344i	0.0340921	−	0.104925i
$910$	−4.77458	−	1.65396i	−0.158276	−	0.0548283i
$911$	2.17376	+	6.69015i	0.0720200	+	0.221655i	0.980587	−	0.196084i	$-0.0628227\pi$
$911$	2.17376	+	6.69015i	0.0720200	+	0.221655i	−0.908567	+	0.417739i	$0.862823\pi$
$912$	−9.49606	+	2.01845i	−0.314446	+	0.0668375i
$913$	19.5485	+	21.7108i	0.646961	+	0.718523i
$914$	−14.9031	−	3.16776i	−0.492952	−	0.104780i
$915$	1.42347	−	13.5434i	0.0470585	−	0.447732i
$916$	−1.02786	+	3.16344i	−0.0339616	+	0.104523i
$917$	46.9184	−	4.01688i	1.54938	−	0.132649i
$918$	−31.2361			−1.03094
$919$	3.99093	−	37.9712i	0.131649	−	1.25255i	−0.706737	−	0.707476i	$-0.749834\pi$
$919$	3.99093	−	37.9712i	0.131649	−	1.25255i	0.838386	−	0.545077i	$-0.183500\pi$
$920$	11.1800	+	12.4166i	0.368593	+	0.409364i
$921$	−4.58760	−	43.6481i	−0.151167	−	1.43825i
$922$	21.0745	+	9.38296i	0.694051	+	0.309011i
$923$	−0.513156	−	1.57933i	−0.0168907	−	0.0519843i
$924$	−2.30902	−	11.9980i	−0.0759611	−	0.394705i
$925$	4.04508	−	12.4495i	0.133002	−	0.409337i
$926$	8.11803	+	14.0608i	0.266775	+	0.462068i
$927$	−5.58347	−	1.18680i	−0.183385	−	0.0389797i
$928$	−0.571994	−	5.44216i	−0.0187766	−	0.178648i
$929$	30.4450	+	13.5550i	0.998869	+	0.444725i	0.840007	−	0.542576i	$-0.182551\pi$
$929$	30.4450	+	13.5550i	0.998869	+	0.444725i	0.158862	+	0.987301i	$0.449217\pi$
$930$	2.07295	+	6.37988i	0.0679747	+	0.209205i
$931$	11.4265	+	40.4158i	0.374487	+	1.32457i
$932$	27.8328			0.911694
$933$	5.14435	−	48.9452i	0.168418	−	1.60239i
$934$	22.7735	+	25.2925i	0.745171	+	0.827597i
$935$	−24.3761	−	27.0724i	−0.797185	−	0.885364i
$936$	0.218296	−	0.242442i	0.00713522	−	0.00792447i
$937$	−8.31966	+	25.6053i	−0.271791	+	0.836488i	0.718259	+	0.695776i	$0.244939\pi$
$937$	−8.31966	+	25.6053i	−0.271791	+	0.836488i	−0.990051	+	0.140712i	$0.955061\pi$
$938$	−2.62543	−	0.327321i	−0.0857232	−	0.0106874i
$939$	6.76393	+	20.8172i	0.220733	+	0.679345i
$940$	−10.4197	+	2.21477i	−0.339853	+	0.0722380i
$941$	2.59314	+	2.87997i	0.0845340	+	0.0938845i	0.783928	−	0.620852i	$-0.213213\pi$
$941$	2.59314	+	2.87997i	0.0845340	+	0.0938845i	−0.699394	+	0.714737i	$0.746547\pi$
$942$	−5.34799	+	2.38108i	−0.174247	+	0.0775797i
$943$	43.4058	+	75.1810i	1.41349	+	2.44823i
$944$	−8.35410	−	6.06961i	−0.271903	−	0.197549i
$945$	−27.7185	−	16.7252i	−0.901683	−	0.544072i
$946$	5.16312	−	3.75123i	0.167867	−	0.121963i
$947$	44.7128	+	19.9074i	1.45297	+	0.646905i	0.973089	−	0.230428i	$-0.0740128\pi$
$947$	44.7128	+	19.9074i	1.45297	+	0.646905i	0.479882	+	0.877333i	$0.340679\pi$
$948$	−14.1559	−	3.00893i	−0.459762	−	0.0977254i
$949$	−3.25329	+	5.63486i	−0.105606	+	0.182915i
$950$	−29.3444	+	6.23735i	−0.952059	+	0.202366i
$951$	27.0902			0.878459
$952$	0.291670	−	15.0997i	0.00945308	−	0.489383i
$953$	−32.1074	+	23.3274i	−1.04006	+	0.755648i	−0.970297	−	0.241915i	$-0.922224\pi$
$953$	−32.1074	+	23.3274i	−1.04006	+	0.755648i	−0.0697631	+	0.997564i	$0.522224\pi$
$954$	1.47815	+	0.658114i	0.0478568	+	0.0213072i
$955$	−30.2776	−	33.6267i	−0.979761	−	1.08814i
$956$	19.4825	−	8.67416i	0.630109	−	0.280542i
$957$	12.6353	+	21.8849i	0.408440	+	0.707438i
$958$	−6.23607	−	4.53077i	−0.201478	−	0.146382i
$959$	−10.3307	+	13.6564i	−0.333596	+	0.440987i
$960$	2.92705	+	2.12663i	0.0944702	+	0.0686366i
$961$	−18.4428	+	20.4828i	−0.594928	+	0.660735i
$962$	−1.49622	−	1.66172i	−0.0482401	−	0.0535761i
$963$	−1.16606	−	1.29504i	−0.0375757	−	0.0417320i
$964$	−2.77415	+	3.08100i	−0.0893493	+	0.0992324i
$965$	−1.78522			−0.0574682
$966$	−12.4437	−	29.4679i	−0.400371	−	0.948115i
$967$	−10.1910	−	7.40418i	−0.327720	−	0.238102i	0.411743	−	0.911300i	$-0.364920\pi$
$967$	−10.1910	−	7.40418i	−0.327720	−	0.238102i	−0.739463	+	0.673198i	$0.764920\pi$
$968$	−1.42705	−	2.47172i	−0.0458672	−	0.0794442i
$969$	50.6254	−	22.5399i	1.62632	−	0.724085i
$970$	13.8170	−	6.15173i	0.443638	−	0.197520i
$971$	21.2901	+	9.47898i	0.683233	+	0.304195i	0.718845	−	0.695171i	$-0.244671\pi$
$971$	21.2901	+	9.47898i	0.683233	+	0.304195i	−0.0356117	+	0.999366i	$0.511338\pi$
$972$	3.19098	−	2.31838i	0.102351	−	0.0743622i
$973$	13.8985	−	7.67027i	0.445564	−	0.245897i
$974$	8.59675			0.275458
$975$	−4.62358	+	5.13500i	−0.148073	+	0.164452i
$976$	−1.88197	+	3.25966i	−0.0602403	+	0.104339i
$977$	−41.5569	−	8.83319i	−1.32952	−	0.282599i	−0.512243	−	0.858840i	$-0.671185\pi$
$977$	−41.5569	−	8.83319i	−1.32952	−	0.282599i	−0.817279	+	0.576242i	$0.804519\pi$
$978$	−29.4806	−	13.1256i	−0.942685	−	0.419710i
$979$	−39.4615	+	28.6705i	−1.26119	+	0.916312i
$980$	8.34389	−	13.2431i	0.266536	−	0.423035i
$981$	1.00000	+	0.726543i	0.0319275	+	0.0231967i
$982$	−13.9271	−	24.1224i	−0.444430	−	0.769775i
$983$	45.8226	−	20.4015i	1.46151	−	0.650708i	0.486667	−	0.873587i	$-0.338212\pi$
$983$	45.8226	−	20.4015i	1.46151	−	0.650708i	0.974846	+	0.222880i	$0.0715458\pi$
$984$	12.5786	+	13.9699i	0.400990	+	0.445345i
$985$	35.0248	+	15.5940i	1.11598	+	0.496867i
$986$	9.65248	+	29.7073i	0.307397	+	0.946072i
$987$	20.2373	+	2.52306i	0.644161	+	0.0803099i
$988$	−1.58359	+	4.87380i	−0.0503808	+	0.155056i
$989$	11.1800	−	12.4166i	0.355502	−	0.394825i
$990$	2.38442	+	0.506825i	0.0757820	+	0.0161080i
$991$	14.8788	+	16.5246i	0.472642	+	0.524922i	0.931575	−	0.363549i	$-0.118435\pi$
$991$	14.8788	+	16.5246i	0.472642	+	0.524922i	−0.458933	+	0.888471i	$0.651768\pi$
$992$	0.193806	−	1.84395i	0.00615336	−	0.0585453i
$993$	−15.3820			−0.488132
$994$	5.12531	−	0.438799i	0.162565	−	0.0139179i
$995$	9.87539			0.313071
$996$	15.1304	+	6.73650i	0.479426	+	0.213454i
$997$	−2.28438	−	21.7344i	−0.0723469	−	0.688335i	−0.969245	−	0.246098i	$-0.920852\pi$
$997$	−2.28438	−	21.7344i	−0.0723469	−	0.688335i	0.896898	−	0.442237i	$-0.145815\pi$
$998$	11.7378	+	2.49494i	0.371553	+	0.0789760i
$999$	−7.16312	−	12.4069i	−0.226631	−	0.392537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.a.81.1	✓	8
7.2	even	3	inner	350.2.q.a.331.1	yes	8
25.21	even	5	inner	350.2.q.a.221.1	yes	8
175.121	even	15	inner	350.2.q.a.121.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.a.81.1	✓	8	1.1	even	1	trivial
350.2.q.a.121.1	yes	8	175.121	even	15	inner
350.2.q.a.221.1	yes	8	25.21	even	5	inner
350.2.q.a.331.1	yes	8	7.2	even	3	inner

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.169131 + 1.60917i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.373619 - 0.0794152i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 0.743145i) q^{2} +(0.169131 + 1.60917i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-1.11803 - 1.93649i) q^{5} +(-1.30902 - 0.951057i) q^{6} +(-0.500000 - 2.59808i) q^{7} +(0.809017 + 0.587785i) q^{8} +(0.373619 - 0.0794152i) q^{9} +(2.18720 + 0.464905i) q^{10} +(2.79173 + 0.593401i) q^{11} +(1.58268 - 0.336408i) q^{12} +(0.263932 - 0.812299i) q^{13} +(2.26531 + 1.36688i) q^{14} +(2.92705 - 2.12663i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(5.21470 - 2.32174i) q^{17} +(-0.190983 + 0.330792i) q^{18} +(0.627171 - 5.96713i) q^{19} +(-1.80902 + 1.31433i) q^{20} +(4.09618 - 1.24400i) q^{21} +(-2.30902 + 1.67760i) q^{22} +(-4.99983 + 5.55288i) q^{23} +(-0.809017 + 1.40126i) q^{24} +(-2.50000 + 4.33013i) q^{25} +(0.427051 + 0.739674i) q^{26} +(1.69098 + 5.20431i) q^{27} +(-2.53158 + 0.768834i) q^{28} +(4.42705 - 3.21644i) q^{29} +(-0.378188 + 3.59821i) q^{30} +(1.69381 - 0.754131i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.482716 + 4.59274i) q^{33} +(-1.76393 + 5.42882i) q^{34} +(-4.47214 + 3.87298i) q^{35} +(-0.118034 - 0.363271i) q^{36} +(-2.56082 + 0.544320i) q^{37} +(4.01478 + 4.45887i) q^{38} +(1.35177 + 0.287327i) q^{39} +(0.233733 - 2.22382i) q^{40} +(3.59017 - 11.0494i) q^{41} +(-1.81641 + 3.87645i) q^{42} -2.23607 q^{43} +(0.298335 - 2.83847i) q^{44} +(-0.571506 - 0.634721i) q^{45} +(-0.781051 - 7.43120i) q^{46} +(4.35207 + 1.93767i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(-1.54508 - 4.75528i) q^{50} +(4.61803 + 7.99867i) q^{51} +(-0.835438 - 0.177578i) q^{52} +(-0.442790 - 4.21286i) q^{53} +(-4.99904 - 2.22572i) q^{54} +(-1.97214 - 6.06961i) q^{55} +(1.12260 - 2.39578i) q^{56} +9.70820 q^{57} +(-0.571994 + 5.44216i) q^{58} +(6.90960 + 7.67389i) q^{59} +(-2.42094 - 2.68872i) q^{60} +(2.51856 - 2.79715i) q^{61} +(-0.572949 + 1.76336i) q^{62} +(-0.393136 - 0.930983i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.86810 + 0.397076i) q^{65} +(-3.09007 - 3.43187i) q^{66} +(-0.913545 + 0.406737i) q^{67} +(-2.85410 - 4.94345i) q^{68} +(-9.78115 - 7.10642i) q^{69} +(0.114256 - 5.91498i) q^{70} +(1.57295 - 1.14281i) q^{71} +(0.348943 + 0.155360i) q^{72} +(-7.45156 - 1.58388i) q^{73} +(1.30902 - 2.26728i) q^{74} +(-7.39074 - 3.29057i) q^{75} -6.00000 q^{76} +(0.145835 - 7.54984i) q^{77} +(-1.11803 + 0.812299i) q^{78} +(-8.17100 - 3.63796i) q^{79} +(1.49622 + 1.66172i) q^{80} +(-7.04179 + 3.13521i) q^{81} +(5.80902 + 10.0615i) q^{82} +(8.28115 + 6.01661i) q^{83} +(-1.66535 - 3.94371i) q^{84} +(-10.3262 - 7.50245i) q^{85} +(1.49622 - 1.66172i) q^{86} +(5.92455 + 6.57988i) q^{87} +(1.90977 + 2.12101i) q^{88} +(-11.4356 + 12.7005i) q^{89} +0.854102 q^{90} +(-2.24238 - 0.279566i) q^{91} +(6.04508 + 4.39201i) q^{92} +(1.50000 + 2.59808i) q^{93} +(-4.35207 + 1.93767i) q^{94} +(-12.2565 + 5.45694i) q^{95} +(1.47815 + 0.658114i) q^{96} +(5.47214 - 3.97574i) q^{97} +(2.41860 - 6.56889i) q^{98} +1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 8 q - q^{2} - 3 q^{3} + q^{4} - 6 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 5 q^{10} + 8 q^{11} + 2 q^{12} + 20 q^{13} - 4 q^{14} + 10 q^{15} + q^{16} + 14 q^{17} - 6 q^{18} - 6 q^{19} - 10 q^{20} + 15 q^{21} - 14 q^{22} + 7 q^{23} - 2 q^{24} - 20 q^{25} - 10 q^{26} + 18 q^{27} - 5 q^{28} + 22 q^{29} + 5 q^{30} + 6 q^{31} + 4 q^{32} + 6 q^{33} - 32 q^{34} + 8 q^{36} - q^{37} + 6 q^{38} - 5 q^{39} - 5 q^{40} - 16 q^{41} + 3 q^{42} - 7 q^{44} + 10 q^{45} + 13 q^{46} + 2 q^{47} - 4 q^{48} - 52 q^{49} + 10 q^{50} + 28 q^{51} - 10 q^{52} + 7 q^{53} - 11 q^{54} + 20 q^{55} - q^{56} + 24 q^{57} + 11 q^{58} - 15 q^{59} + 11 q^{61} - 18 q^{62} - 16 q^{63} - 2 q^{64} + 20 q^{65} - q^{66} - q^{67} + 4 q^{68} - 38 q^{69} - 25 q^{70} + 26 q^{71} - q^{72} + 4 q^{73} + 6 q^{74} - 15 q^{75} - 48 q^{76} - 40 q^{77} - 20 q^{79} - 5 q^{80} - 16 q^{81} + 42 q^{82} + 26 q^{83} + 8 q^{84} - 20 q^{85} - 5 q^{86} - 2 q^{87} - 8 q^{88} + q^{89} - 20 q^{90} - 10 q^{91} + 26 q^{92} + 12 q^{93} - 2 q^{94} - 30 q^{95} + 3 q^{96} + 8 q^{97} + 11 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - q^2 - 3 * q^3 + q^4 - 6 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 5 * q^10 + 8 * q^11 + 2 * q^12 + 20 * q^13 - 4 * q^14 + 10 * q^15 + q^16 + 14 * q^17 - 6 * q^18 - 6 * q^19 - 10 * q^20 + 15 * q^21 - 14 * q^22 + 7 * q^23 - 2 * q^24 - 20 * q^25 - 10 * q^26 + 18 * q^27 - 5 * q^28 + 22 * q^29 + 5 * q^30 + 6 * q^31 + 4 * q^32 + 6 * q^33 - 32 * q^34 + 8 * q^36 - q^37 + 6 * q^38 - 5 * q^39 - 5 * q^40 - 16 * q^41 + 3 * q^42 - 7 * q^44 + 10 * q^45 + 13 * q^46 + 2 * q^47 - 4 * q^48 - 52 * q^49 + 10 * q^50 + 28 * q^51 - 10 * q^52 + 7 * q^53 - 11 * q^54 + 20 * q^55 - q^56 + 24 * q^57 + 11 * q^58 - 15 * q^59 + 11 * q^61 - 18 * q^62 - 16 * q^63 - 2 * q^64 + 20 * q^65 - q^66 - q^67 + 4 * q^68 - 38 * q^69 - 25 * q^70 + 26 * q^71 - q^72 + 4 * q^73 + 6 * q^74 - 15 * q^75 - 48 * q^76 - 40 * q^77 - 20 * q^79 - 5 * q^80 - 16 * q^81 + 42 * q^82 + 26 * q^83 + 8 * q^84 - 20 * q^85 - 5 * q^86 - 2 * q^87 - 8 * q^88 + q^89 - 20 * q^90 - 10 * q^91 + 26 * q^92 + 12 * q^93 - 2 * q^94 - 30 * q^95 + 3 * q^96 + 8 * q^97 + 11 * q^98 - 36 * q^99

Introduction

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