LMFDB - Embedded newform 77.2.m.a.60.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(4,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("77.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.m (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:	$0.614848095564$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			60.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	77.60
Dual form			77.2.m.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.08268 - 1.20243i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.0646021 - 0.614648i) q^{4} +(-2.18720 + 0.464905i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-2.53158 + 0.768834i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-1.33826 + 1.48629i) q^{9} +O(q^{10})$	\(q+(1.08268 - 1.20243i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.0646021 - 0.614648i) q^{4} +(-2.18720 + 0.464905i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-2.53158 + 0.768834i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-1.33826 + 1.48629i) q^{9} +(-1.80902 + 3.13331i) q^{10} +(2.24724 - 2.43925i) q^{11} +(-0.309017 - 0.535233i) q^{12} +(-1.80902 - 5.56758i) q^{13} +(-1.81641 + 3.87645i) q^{14} +(-1.80902 + 1.31433i) q^{15} +(4.74803 - 1.00922i) q^{16} +(2.16535 + 2.40487i) q^{17} +(0.338261 + 3.21834i) q^{18} +(-0.119779 + 1.13962i) q^{19} +(0.427051 + 1.31433i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-0.500000 - 5.34307i) q^{22} +(0.881966 + 1.52761i) q^{23} +(2.18720 + 0.464905i) q^{24} +(-8.65323 - 3.85266i) q^{26} +(-1.54508 + 4.75528i) q^{27} +(0.636108 + 1.50636i) q^{28} +(6.35410 - 4.61653i) q^{29} +(-0.378188 + 3.59821i) q^{30} +(-4.28621 - 0.911062i) q^{31} +(1.69098 - 2.92887i) q^{32} +(1.06082 - 3.14240i) q^{33} +5.23607 q^{34} +(5.17965 - 2.85854i) q^{35} +(1.00000 + 0.726543i) q^{36} +(-5.56365 - 2.47710i) q^{37} +(1.24064 + 1.37787i) q^{38} +(-3.91716 - 4.35045i) q^{39} +(-4.56773 - 2.03368i) q^{40} +(1.92705 + 1.40008i) q^{41} +(-0.0826761 + 4.28012i) q^{42} +0.145898 q^{43} +(-1.64445 - 1.22368i) q^{44} +(2.23607 - 3.87298i) q^{45} +(2.79173 + 0.593401i) q^{46} +(-0.0493516 + 0.469550i) q^{47} +(3.92705 - 2.85317i) q^{48} +(5.81779 - 3.89273i) q^{49} +(2.95630 + 1.31623i) q^{51} +(-3.30524 + 1.47159i) q^{52} +(-5.95709 - 1.26622i) q^{53} +(4.04508 + 7.00629i) q^{54} +(-3.78115 + 6.37988i) q^{55} +(-5.59017 - 1.93649i) q^{56} +(0.354102 + 1.08981i) q^{57} +(1.32837 - 12.6386i) q^{58} +(1.01478 + 9.65502i) q^{59} +(0.924716 + 1.02700i) q^{60} +(10.7051 - 2.27544i) q^{61} +(-5.73607 + 4.16750i) q^{62} +(2.24520 - 4.79156i) q^{63} +(1.30902 + 4.02874i) q^{64} +(6.54508 + 11.3364i) q^{65} +(-2.62999 - 4.67777i) q^{66} +(-4.19098 + 7.25900i) q^{67} +(1.33826 - 1.48629i) q^{68} +(1.42705 + 1.03681i) q^{69} +(2.17068 - 9.32306i) q^{70} +(0.236068 - 0.726543i) q^{71} +(-4.37441 + 0.929809i) q^{72} +(-1.13456 - 10.7946i) q^{73} +(-9.00217 + 4.00802i) q^{74} +0.708204 q^{76} +(-3.81369 + 7.90290i) q^{77} -9.47214 q^{78} +(-8.50345 + 9.44404i) q^{79} +(-9.91572 + 4.41476i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(3.76988 - 0.801313i) q^{82} +(-2.78115 + 8.55951i) q^{83} +(1.19381 + 1.11740i) q^{84} +(-5.85410 - 4.25325i) q^{85} +(0.157960 - 0.175433i) q^{86} +(3.92705 - 6.80185i) q^{87} +(7.27126 - 1.45903i) q^{88} +(-0.763932 - 1.32317i) q^{89} +(-2.23607 - 6.88191i) q^{90} +(8.86022 + 12.7039i) q^{91} +(0.881966 - 0.640786i) q^{92} +(-4.28621 + 0.911062i) q^{93} +(0.511170 + 0.567712i) q^{94} +(-0.267834 - 2.54827i) q^{95} +(0.353512 - 3.36344i) q^{96} +(-1.19098 - 3.66547i) q^{97} +(1.61803 - 11.2101i) q^{98} +(0.618034 + 6.60440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} + 2 q^{12} - 10 q^{13} + 3 q^{14} - 10 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 3 q^{19} - 10 q^{20} - 16 q^{21} - 4 q^{22} + 16 q^{23} + 5 q^{24} - 15 q^{26} + 10 q^{27} - 12 q^{28} + 24 q^{29} + 5 q^{30} + 8 q^{31} + 18 q^{32} - 11 q^{33} + 24 q^{34} - 5 q^{35} + 8 q^{36} - 13 q^{37} - 9 q^{38} + 5 q^{39} - 5 q^{40} + 2 q^{41} + 10 q^{42} + 28 q^{43} - 12 q^{44} + 8 q^{46} + 6 q^{47} + 18 q^{48} - 11 q^{49} + 6 q^{51} - 5 q^{52} - 12 q^{53} + 10 q^{54} + 10 q^{55} - 24 q^{57} - 21 q^{58} - 18 q^{59} + 5 q^{60} + 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} + 30 q^{65} + 2 q^{66} - 38 q^{67} + 2 q^{68} - 2 q^{69} + 20 q^{70} - 16 q^{71} - 10 q^{72} + 15 q^{73} - 14 q^{74} - 48 q^{76} - 4 q^{77} - 40 q^{78} + 9 q^{79} - 15 q^{80} + q^{81} + 7 q^{82} + 18 q^{83} + 2 q^{84} - 20 q^{85} - 7 q^{86} + 18 q^{87} - 5 q^{88} - 24 q^{89} + 50 q^{91} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 15 q^{95} - 2 q^{96} - 14 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 + 2 * q^12 - 10 * q^13 + 3 * q^14 - 10 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 3 * q^19 - 10 * q^20 - 16 * q^21 - 4 * q^22 + 16 * q^23 + 5 * q^24 - 15 * q^26 + 10 * q^27 - 12 * q^28 + 24 * q^29 + 5 * q^30 + 8 * q^31 + 18 * q^32 - 11 * q^33 + 24 * q^34 - 5 * q^35 + 8 * q^36 - 13 * q^37 - 9 * q^38 + 5 * q^39 - 5 * q^40 + 2 * q^41 + 10 * q^42 + 28 * q^43 - 12 * q^44 + 8 * q^46 + 6 * q^47 + 18 * q^48 - 11 * q^49 + 6 * q^51 - 5 * q^52 - 12 * q^53 + 10 * q^54 + 10 * q^55 - 24 * q^57 - 21 * q^58 - 18 * q^59 + 5 * q^60 + 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 + 30 * q^65 + 2 * q^66 - 38 * q^67 + 2 * q^68 - 2 * q^69 + 20 * q^70 - 16 * q^71 - 10 * q^72 + 15 * q^73 - 14 * q^74 - 48 * q^76 - 4 * q^77 - 40 * q^78 + 9 * q^79 - 15 * q^80 + q^81 + 7 * q^82 + 18 * q^83 + 2 * q^84 - 20 * q^85 - 7 * q^86 + 18 * q^87 - 5 * q^88 - 24 * q^89 + 50 * q^91 + 16 * q^92 + 8 * q^93 + 8 * q^94 + 15 * q^95 - 2 * q^96 - 14 * q^97 + 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	1.08268	−	1.20243i	0.765568	−	0.850249i	−0.226752	−	0.973953i	$-0.572811\pi$
$2$	1.08268	−	1.20243i	0.765568	−	0.850249i	0.992319	+	0.123704i	$0.0394772\pi$
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i	−0.125703	−	0.992068i	$-0.540119\pi$
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i	0.653139	+	0.757238i	$0.273452\pi$
$4$	−0.0646021	−	0.614648i	−0.0323011	−	0.307324i
$5$	−2.18720	+	0.464905i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$5$	−2.18720	+	0.464905i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$6$	0.500000	−	1.53884i	0.204124	−	0.628230i
$7$	−2.53158	+	0.768834i	−0.956847	+	0.290592i
$7$	−2.53158	+	0.768834i	−0.956847	+	0.290592i
$8$	1.80902	+	1.31433i	0.639584	+	0.464685i
$9$	−1.33826	+	1.48629i	−0.446087	+	0.495430i
$10$	−1.80902	+	3.13331i	−0.572061	+	0.990839i
$11$	2.24724	−	2.43925i	0.677568	−	0.735460i
$11$	2.24724	−	2.43925i	0.677568	−	0.735460i
$12$	−0.309017	−	0.535233i	−0.0892055	−	0.154508i
$13$	−1.80902	−	5.56758i	−0.501731	−	1.54417i	−0.806198	−	0.591646i	$-0.798478\pi$
$13$	−1.80902	−	5.56758i	−0.501731	−	1.54417i	0.304467	−	0.952523i	$-0.401522\pi$
$14$	−1.81641	+	3.87645i	−0.485456	+	1.03603i
$15$	−1.80902	+	1.31433i	−0.467086	+	0.339358i
$16$	4.74803	−	1.00922i	1.18701	−	0.252306i
$17$	2.16535	+	2.40487i	0.525175	+	0.583266i	0.946118	−	0.323821i	$-0.104968\pi$
$17$	2.16535	+	2.40487i	0.525175	+	0.583266i	−0.420943	+	0.907087i	$0.638301\pi$
$18$	0.338261	+	3.21834i	0.0797289	+	0.758570i
$19$	−0.119779	+	1.13962i	−0.0274792	+	0.261447i	0.972153	+	0.234345i	$0.0752945\pi$
$19$	−0.119779	+	1.13962i	−0.0274792	+	0.261447i	−0.999633	+	0.0271019i	$0.991372\pi$
$20$	0.427051	+	1.31433i	0.0954915	+	0.293893i
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−0.500000	−	5.34307i	−0.106600	−	1.13915i
$23$	0.881966	+	1.52761i	0.183903	+	0.318529i	0.943206	−	0.332208i	$-0.107794\pi$
$23$	0.881966	+	1.52761i	0.183903	+	0.318529i	−0.759304	+	0.650737i	$0.774460\pi$
$24$	2.18720	+	0.464905i	0.446461	+	0.0948983i
$25$		0			0
$26$	−8.65323	−	3.85266i	−1.69704	−	0.755570i
$27$	−1.54508	+	4.75528i	−0.297352	+	0.915155i
$28$	0.636108	+	1.50636i	0.120213	+	0.284676i
$29$	6.35410	−	4.61653i	1.17993	−	0.857267i	0.187764	−	0.982214i	$-0.439876\pi$
$29$	6.35410	−	4.61653i	1.17993	−	0.857267i	0.992163	+	0.124947i	$0.0398761\pi$
$30$	−0.378188	+	3.59821i	−0.0690473	+	0.656941i
$31$	−4.28621	−	0.911062i	−0.769826	−	0.163632i	−0.193776	−	0.981046i	$-0.562073\pi$
$31$	−4.28621	−	0.911062i	−0.769826	−	0.163632i	−0.576050	+	0.817414i	$0.695407\pi$
$32$	1.69098	−	2.92887i	0.298926	−	0.517756i
$33$	1.06082	−	3.14240i	0.184666	−	0.547021i
$34$	5.23607			0.897978
$35$	5.17965	−	2.85854i	0.875520	−	0.483181i
$36$	1.00000	+	0.726543i	0.166667	+	0.121090i
$37$	−5.56365	−	2.47710i	−0.914658	−	0.407232i	−0.105228	−	0.994448i	$-0.533557\pi$
$37$	−5.56365	−	2.47710i	−0.914658	−	0.407232i	−0.809430	+	0.587216i	$0.800224\pi$
$38$	1.24064	+	1.37787i	0.201258	+	0.223519i
$39$	−3.91716	−	4.35045i	−0.627247	−	0.696629i
$40$	−4.56773	−	2.03368i	−0.722221	−	0.321554i
$41$	1.92705	+	1.40008i	0.300955	+	0.218656i	0.728006	−	0.685571i	$-0.240447\pi$
$41$	1.92705	+	1.40008i	0.300955	+	0.218656i	−0.427051	+	0.904228i	$0.640447\pi$
$42$	−0.0826761	+	4.28012i	−0.0127572	+	0.660436i
$43$	0.145898			0.0222492			0.0111246	−	0.999938i	$-0.496459\pi$
$43$	0.145898			0.0222492			0.0111246	+	0.999938i	$0.496459\pi$
$44$	−1.64445	−	1.22368i	−0.247911	−	0.184477i
$45$	2.23607	−	3.87298i	0.333333	−	0.577350i
$46$	2.79173	+	0.593401i	0.411619	+	0.0874922i
$47$	−0.0493516	+	0.469550i	−0.00719868	+	0.0684908i	−0.997531	−	0.0702211i	$-0.977630\pi$
$47$	−0.0493516	+	0.469550i	−0.00719868	+	0.0684908i	0.990333	+	0.138712i	$0.0442962\pi$
$48$	3.92705	−	2.85317i	0.566821	−	0.411820i
$49$	5.81779	−	3.89273i	0.831113	−	0.556104i
$50$		0			0
$51$	2.95630	+	1.31623i	0.413964	+	0.184309i
$52$	−3.30524	+	1.47159i	−0.458354	+	0.204072i
$53$	−5.95709	−	1.26622i	−0.818269	−	0.173928i	−0.220284	−	0.975436i	$-0.570698\pi$
$53$	−5.95709	−	1.26622i	−0.818269	−	0.173928i	−0.597985	+	0.801507i	$0.704032\pi$
$54$	4.04508	+	7.00629i	0.550466	+	0.953436i
$55$	−3.78115	+	6.37988i	−0.509851	+	0.860263i
$56$	−5.59017	−	1.93649i	−0.747018	−	0.258775i
$57$	0.354102	+	1.08981i	0.0469020	+	0.144349i
$58$	1.32837	−	12.6386i	0.174423	−	1.65953i
$59$	1.01478	+	9.65502i	0.132114	+	1.25698i	0.836820	+	0.547478i	$0.184412\pi$
$59$	1.01478	+	9.65502i	0.132114	+	1.25698i	−0.704707	+	0.709499i	$0.748921\pi$
$60$	0.924716	+	1.02700i	0.119380	+	0.132585i
$61$	10.7051	−	2.27544i	1.37065	−	0.291341i	0.536976	−	0.843598i	$-0.319567\pi$
$61$	10.7051	−	2.27544i	1.37065	−	0.291341i	0.833674	+	0.552257i	$0.186233\pi$
$62$	−5.73607	+	4.16750i	−0.728481	+	0.529273i
$63$	2.24520	−	4.79156i	0.282869	−	0.603680i
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	6.54508	+	11.3364i	0.811818	+	1.40611i
$66$	−2.62999	−	4.67777i	−0.323730	−	0.575793i
$67$	−4.19098	+	7.25900i	−0.512010	+	0.886827i	0.487893	+	0.872903i	$0.337766\pi$
$67$	−4.19098	+	7.25900i	−0.512010	+	0.886827i	−0.999903	+	0.0139240i	$0.995568\pi$
$68$	1.33826	−	1.48629i	0.162288	−	0.180239i
$69$	1.42705	+	1.03681i	0.171797	+	0.124818i
$70$	2.17068	−	9.32306i	0.259445	−	1.11432i
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	−0.936071	−	0.351812i	$-0.885566\pi$
$71$	0.236068	−	0.726543i	0.0280161	−	0.0862247i	0.964087	+	0.265587i	$0.0855657\pi$
$72$	−4.37441	+	0.929809i	−0.515529	+	0.109579i
$73$	−1.13456	−	10.7946i	−0.132791	−	1.26342i	−0.834522	−	0.550975i	$-0.814256\pi$
$73$	−1.13456	−	10.7946i	−0.132791	−	1.26342i	0.701731	−	0.712442i	$-0.252411\pi$
$74$	−9.00217	+	4.00802i	−1.04648	+	0.465923i
$75$		0			0
$76$	0.708204			0.0812366
$77$	−3.81369	+	7.90290i	−0.434610	+	0.900619i
$78$	−9.47214			−1.07251
$79$	−8.50345	+	9.44404i	−0.956713	+	1.06254i	0.0412762	+	0.999148i	$0.486858\pi$
$79$	−8.50345	+	9.44404i	−0.956713	+	1.06254i	−0.997989	+	0.0633893i	$0.979809\pi$
$80$	−9.91572	+	4.41476i	−1.10861	+	0.493585i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	3.76988	−	0.801313i	0.416314	−	0.0884902i
$83$	−2.78115	+	8.55951i	−0.305271	+	0.939528i	0.674305	+	0.738453i	$0.264443\pi$
$83$	−2.78115	+	8.55951i	−0.305271	+	0.939528i	−0.979576	+	0.201075i	$0.935557\pi$
$84$	1.19381	+	1.11740i	0.130255	+	0.121919i
$85$	−5.85410	−	4.25325i	−0.634967	−	0.461330i
$86$	0.157960	−	0.175433i	0.0170333	−	0.0189174i
$87$	3.92705	−	6.80185i	0.421024	−	0.729235i
$88$	7.27126	−	1.45903i	0.775119	−	0.155533i
$89$	−0.763932	−	1.32317i	−0.0809766	−	0.140256i	0.822693	−	0.568486i	$-0.192471\pi$
$89$	−0.763932	−	1.32317i	−0.0809766	−	0.140256i	−0.903670	+	0.428230i	$0.859137\pi$
$90$	−2.23607	−	6.88191i	−0.235702	−	0.725417i
$91$	8.86022	+	12.7039i	0.928803	+	1.33173i
$92$	0.881966	−	0.640786i	0.0919513	−	0.0668065i
$93$	−4.28621	+	0.911062i	−0.444459	+	0.0944727i
$94$	0.511170	+	0.567712i	0.0527232	+	0.0585550i
$95$	−0.267834	−	2.54827i	−0.0274792	−	0.261447i
$96$	0.353512	−	3.36344i	0.0360801	−	0.343280i
$97$	−1.19098	−	3.66547i	−0.120926	−	0.372172i	0.872211	−	0.489130i	$-0.162686\pi$
$97$	−1.19098	−	3.66547i	−0.120926	−	0.372172i	−0.993137	+	0.116958i	$0.962686\pi$
$98$	1.61803	−	11.2101i	0.163446	−	1.13239i
$99$	0.618034	+	6.60440i	0.0621148	+	0.663767i
$100$		0			0
$101$	14.7604	+	3.13742i	1.46872	+	0.312185i	0.871698	−	0.490043i	$-0.163019\pi$
$101$	14.7604	+	3.13742i	1.46872	+	0.312185i	0.597018	+	0.802228i	$0.296352\pi$
$102$	4.78339	−	2.12970i	0.473626	−	0.210872i
$103$	5.48127	+	2.44042i	0.540086	+	0.240462i	0.658603	−	0.752490i	$-0.271148\pi$
$103$	5.48127	+	2.44042i	0.540086	+	0.240462i	−0.118518	+	0.992952i	$0.537814\pi$
$104$	4.04508	−	12.4495i	0.396653	−	1.22077i
$105$	3.56917	−	4.71816i	0.348315	−	0.460445i
$106$	−7.97214	+	5.79210i	−0.774322	+	0.562578i
$107$	1.16866	−	11.1191i	0.112979	−	1.07492i	−0.780295	−	0.625411i	$-0.784931\pi$
$107$	1.16866	−	11.1191i	0.112979	−	1.07492i	0.893274	−	0.449512i	$-0.148402\pi$
$108$	3.02264	+	0.642482i	0.290854	+	0.0618229i
$109$	0.0729490	−	0.126351i	0.00698725	−	0.0121023i	−0.862511	−	0.506039i	$-0.831109\pi$
$109$	0.0729490	−	0.126351i	0.00698725	−	0.0121023i	0.869498	+	0.493937i	$0.164443\pi$
$110$	3.57762	+	11.4539i	0.341113	+	1.09209i
$111$	−6.09017			−0.578053
$112$	−11.2441	+	6.20538i	−1.06247	+	0.586353i
$113$	−1.69098	−	1.22857i	−0.159074	−	0.115574i	0.505401	−	0.862885i	$-0.331345\pi$
$113$	−1.69098	−	1.22857i	−0.159074	−	0.115574i	−0.664475	+	0.747311i	$0.731345\pi$
$114$	1.69381	+	0.754131i	0.158640	+	0.0706309i
$115$	−2.63923	−	2.93117i	−0.246110	−	0.273333i
$116$	−3.24803	−	3.60730i	−0.301572	−	0.334929i
$117$	10.6960	+	4.76216i	0.988843	+	0.440261i
$118$	12.7082	+	9.23305i	1.16988	+	0.849971i
$119$	−7.33070	−	4.42332i	−0.672005	−	0.405485i
$120$	−5.00000			−0.456435
$121$	−0.899840	−	10.9631i	−0.0818037	−	0.996648i
$122$	8.85410	−	15.3358i	0.801613	−	1.38843i
$123$	2.32991	+	0.495239i	0.210081	+	0.0446542i
$124$	−0.283084	+	2.69337i	−0.0254217	+	0.241872i
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$	−3.33070	−	7.88742i	−0.296723	−	0.702667i
$127$	−0.0729490	+	0.224514i	−0.00647318	+	0.0199224i	−0.954241	−	0.299039i	$-0.903334\pi$
$127$	−0.0729490	+	0.224514i	−0.00647318	+	0.0199224i	0.947768	+	0.318961i	$0.103334\pi$
$128$	12.4407	+	5.53895i	1.09961	+	0.489579i
$129$	0.133284	−	0.0593421i	0.0117350	−	0.00522478i
$130$	20.7175	+	4.40364i	1.81704	+	0.386225i
$131$	−3.16312	−	5.47868i	−0.276363	−	0.478675i	0.694115	−	0.719864i	$-0.255796\pi$
$131$	−3.16312	−	5.47868i	−0.276363	−	0.478675i	−0.970478	+	0.241189i	$0.922463\pi$
$132$	−2.00000	−	0.449028i	−0.174078	−	0.0390829i
$133$	−0.572949	−	2.97713i	−0.0496810	−	0.258150i
$134$	4.19098	+	12.8985i	0.362046	+	1.11426i
$135$	1.16866	−	11.1191i	0.100583	−	0.956979i
$136$	0.756375	+	7.19643i	0.0648586	+	0.617089i
$137$	0.218296	+	0.242442i	0.0186503	+	0.0207132i	0.752398	−	0.658709i	$-0.228897\pi$
$137$	0.218296	+	0.242442i	0.0186503	+	0.0207132i	−0.733748	+	0.679422i	$0.762230\pi$
$138$	2.79173	−	0.593401i	0.237648	−	0.0505137i
$139$	−3.57295	+	2.59590i	−0.303054	+	0.220181i	−0.728910	−	0.684609i	$-0.759973\pi$
$139$	−3.57295	+	2.59590i	−0.303054	+	0.220181i	0.425857	+	0.904791i	$0.359973\pi$
$140$	−2.09161	−	2.99899i	−0.176774	−	0.253461i
$141$	0.145898	+	0.449028i	0.0122868	+	0.0378150i
$142$	−0.618034	−	1.07047i	−0.0518643	−	0.0898315i
$143$	−17.6460	−	8.09905i	−1.47563	−	0.677276i
$144$	−4.85410	+	8.40755i	−0.404508	+	0.700629i
$145$	−11.7515	+	13.0513i	−0.975907	+	1.08385i
$146$	−14.2082	−	10.3229i	−1.17588	−	0.854326i
$147$	3.73150	−	5.92249i	0.307769	−	0.488479i
$148$	−1.16312	+	3.57971i	−0.0956078	+	0.294251i
$149$	−20.0585	+	4.26356i	−1.64325	+	0.349284i	−0.934442	−	0.356114i	$-0.884101\pi$
$149$	−20.0585	+	4.26356i	−1.64325	+	0.349284i	−0.708811	+	0.705399i	$0.750768\pi$
$150$		0			0
$151$	−4.21878	+	1.87832i	−0.343320	+	0.152856i	−0.571151	−	0.820845i	$-0.693503\pi$
$151$	−4.21878	+	1.87832i	−0.343320	+	0.152856i	0.227832	+	0.973701i	$0.426836\pi$
$152$	−1.71452	+	1.90416i	−0.139066	+	0.154448i
$153$	−6.47214			−0.523241
$154$	5.37372	+	13.1420i	0.433027	+	1.05901i
$155$	9.79837			0.787024
$156$	−2.42094	+	2.68872i	−0.193830	+	0.215270i
$157$	−10.7469	+	4.78482i	−0.857695	+	0.381870i	−0.787983	−	0.615697i	$-0.788875\pi$
$157$	−10.7469	+	4.78482i	−0.857695	+	0.381870i	−0.0697118	+	0.997567i	$0.522208\pi$
$158$	2.14935	+	20.4497i	0.170993	+	1.62689i
$159$	−5.95709	+	1.26622i	−0.472428	+	0.100418i
$160$	−2.33688	+	7.19218i	−0.184747	+	0.568592i
$161$	−3.40725	−	3.18918i	−0.268529	−	0.251343i
$162$	−1.30902	−	0.951057i	−0.102846	−	0.0747221i
$163$	12.8714	−	14.2952i	1.00817	−	1.11969i	0.0153715	−	0.999882i	$-0.495107\pi$
$163$	12.8714	−	14.2952i	1.00817	−	1.11969i	0.992798	−	0.119803i	$-0.0382264\pi$
$164$	0.736068	−	1.27491i	0.0574773	−	0.0995535i
$165$	−0.859324	+	7.36624i	−0.0668983	+	0.573461i
$166$	7.28115	+	12.6113i	0.565127	+	0.978829i
$167$	−4.61803	−	14.2128i	−0.357354	−	1.09982i	−0.954632	−	0.297789i	$-0.903751\pi$
$167$	−4.61803	−	14.2128i	−0.357354	−	1.09982i	0.597278	−	0.802035i	$-0.296249\pi$
$168$	−5.89452	+	0.504654i	−0.454772	+	0.0389349i
$169$	−17.2082	+	12.5025i	−1.32371	+	0.961730i
$170$	−11.4524	+	2.43427i	−0.878355	+	0.186700i
$171$	−1.53351	−	1.70314i	−0.117271	−	0.130242i
$172$	−0.00942533	−	0.0896760i	−0.000718674	−	0.00683773i
$173$	1.10046	−	10.4702i	0.0836665	−	0.796034i	−0.869570	−	0.493809i	$-0.835604\pi$
$173$	1.10046	−	10.4702i	0.0836665	−	0.796034i	0.953237	−	0.302225i	$-0.0977293\pi$
$174$	−3.92705	−	12.0862i	−0.297709	−	0.916254i
$175$		0			0
$176$	8.20820	−	13.8496i	0.618717	−	1.04395i
$177$	4.85410	+	8.40755i	0.364857	+	0.631950i
$178$	−2.41811	−	0.513986i	−0.181245	−	0.0385249i
$179$	18.7337	−	8.34078i	1.40022	−	0.623419i	0.438822	−	0.898574i	$-0.355396\pi$
$179$	18.7337	−	8.34078i	1.40022	−	0.623419i	0.961400	+	0.275155i	$0.0887292\pi$
$180$	−2.52498	−	1.12419i	−0.188201	−	0.0837924i
$181$	−6.54508	+	20.1437i	−0.486492	+	1.49727i	0.343315	+	0.939220i	$0.388450\pi$
$181$	−6.54508	+	20.1437i	−0.486492	+	1.49727i	−0.829808	+	0.558049i	$0.811550\pi$
$182$	24.8684	+	3.10043i	1.84337	+	0.229819i
$183$	8.85410	−	6.43288i	0.654514	−	0.475532i
$184$	−0.412289	+	3.92266i	−0.0303943	+	0.289183i
$185$	13.3204	+	2.83135i	0.979339	+	0.208165i
$186$	−3.54508	+	6.14027i	−0.259938	+	0.450226i
$187$	10.7321	+	0.122483i	0.784811	+	0.00895688i
$188$	0.291796			0.0212814
$189$	0.255483	−	13.2263i	0.0185837	−	0.962071i
$190$	−3.35410	−	2.43690i	−0.243332	−	0.176791i
$191$	13.0053	+	5.79033i	0.941030	+	0.418974i	0.819155	−	0.573572i	$-0.194443\pi$
$191$	13.0053	+	5.79033i	0.941030	+	0.418974i	0.121875	+	0.992545i	$0.461109\pi$
$192$	2.83448	+	3.14801i	0.204561	+	0.227188i
$193$	−12.1650	−	13.5106i	−0.875657	−	0.972516i	0.124148	−	0.992264i	$-0.460380\pi$
$193$	−12.1650	−	13.5106i	−0.875657	−	0.972516i	−0.999805	+	0.0197477i	$0.993714\pi$
$194$	−5.69693	−	2.53644i	−0.409016	−	0.182106i
$195$	10.5902	+	7.69421i	0.758378	+	0.550994i
$196$	−2.76850	−	3.32442i	−0.197750	−	0.237458i
$197$	2.38197			0.169708			0.0848540	−	0.996393i	$-0.472958\pi$
$197$	2.38197			0.169708			0.0848540	+	0.996393i	$0.472958\pi$
$198$	8.61048	+	6.40728i	0.611920	+	0.455345i
$199$	−10.7812	+	18.6735i	−0.764256	+	1.32373i	0.176384	+	0.984322i	$0.443560\pi$
$199$	−10.7812	+	18.6735i	−0.764256	+	1.32373i	−0.940639	+	0.339408i	$0.889773\pi$
$200$		0			0
$201$	−0.876154	+	8.33605i	−0.0617991	+	0.587980i
$202$	19.7533	−	14.3516i	1.38984	−	1.00978i
$203$	−12.5366	+	16.5723i	−0.879895	+	1.16315i
$204$	0.618034	−	1.90211i	0.0432710	−	0.133175i
$205$	−4.86576	−	2.16638i	−0.339839	−	0.151306i
$206$	8.86889	−	3.94868i	0.617925	−	0.275118i
$207$	−3.45077	−	0.733484i	−0.239845	−	0.0509807i
$208$	−14.2082	−	24.6093i	−0.985162	−	1.70635i
$209$	2.51064	+	2.85317i	0.173665	+	0.197358i
$210$	−1.80902	−	9.39993i	−0.124834	−	0.648657i
$211$	−2.78115	−	8.55951i	−0.191462	−	0.589261i	−1.00000		0.000815813i	$-0.999740\pi$
$211$	−2.78115	−	8.55951i	−0.191462	−	0.589261i	0.808537	−	0.588445i	$-0.200260\pi$
$212$	−0.393438	+	3.74331i	−0.0270214	+	0.257092i
$213$	−0.0798526	−	0.759747i	−0.00547141	−	0.0520570i
$214$	−12.1047	−	13.4436i	−0.827459	−	0.918987i
$215$	−0.319109	+	0.0678287i	−0.0217630	+	0.00462588i
$216$	−9.04508	+	6.57164i	−0.615440	+	0.447143i
$217$	11.5513	−	0.988957i	0.784156	−	0.0671348i
$218$	−0.0729490	−	0.224514i	−0.00494073	−	0.0152060i
$219$	−5.42705	−	9.39993i	−0.366726	−	0.635188i
$220$	4.16565	+	1.91193i	0.280848	+	0.128902i
$221$	9.47214	−	16.4062i	0.637165	−	1.10360i
$222$	−6.59368	+	7.32302i	−0.442539	+	0.491489i
$223$	15.4894	+	11.2537i	1.03724	+	0.753602i	0.969746	−	0.244117i	$-0.0784982\pi$
$223$	15.4894	+	11.2537i	1.03724	+	0.753602i	0.0674984	+	0.997719i	$0.478498\pi$
$224$	−2.02904	+	8.71475i	−0.135571	+	0.582279i
$225$		0			0
$226$	−3.30806	+	0.703150i	−0.220049	+	0.0467729i
$227$	−0.775226	−	7.37578i	−0.0514535	−	0.489548i	−0.989656	−	0.143461i	$-0.954177\pi$
$227$	−0.775226	−	7.37578i	−0.0514535	−	0.489548i	0.938202	−	0.346087i	$-0.112490\pi$
$228$	0.646976	−	0.288052i	0.0428471	−	0.0190767i
$229$	3.91716	−	4.35045i	0.258853	−	0.287486i	−0.599684	−	0.800237i	$-0.704707\pi$
$229$	3.91716	−	4.35045i	0.258853	−	0.287486i	0.858537	+	0.512751i	$0.171374\pi$
$230$	−6.38197			−0.420814
$231$	−0.269579	+	8.77082i	−0.0177370	+	0.577078i
$232$	17.5623			1.15302
$233$	−2.06773	+	2.29644i	−0.135461	+	0.150445i	−0.807059	−	0.590471i	$-0.798942\pi$
$233$	−2.06773	+	2.29644i	−0.135461	+	0.150445i	0.671597	+	0.740916i	$0.265609\pi$
$234$	17.3065	−	7.70533i	1.13136	−	0.503713i
$235$	−0.110354	−	1.04994i	−0.00719868	−	0.0684908i
$236$	5.86889	−	1.24747i	0.382032	−	0.0812034i
$237$	−3.92705	+	12.0862i	−0.255089	+	0.785084i
$238$	−13.2555	+	4.02567i	−0.859228	+	0.260945i
$239$	−10.2812	−	7.46969i	−0.665032	−	0.483174i	0.203326	−	0.979111i	$-0.434825\pi$
$239$	−10.2812	−	7.46969i	−0.665032	−	0.483174i	−0.868359	+	0.495937i	$0.834825\pi$
$240$	−7.26281	+	8.06617i	−0.468812	+	0.520669i
$241$	0.791796	−	1.37143i	0.0510041	−	0.0883416i	−0.839396	−	0.543520i	$-0.817091\pi$
$241$	0.791796	−	1.37143i	0.0510041	−	0.0883416i	0.890400	+	0.455178i	$0.150425\pi$
$242$	−14.1567	−	10.7875i	−0.910026	−	0.693448i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−2.09017	−	6.43288i	−0.133809	−	0.411823i
$245$	−10.9149	+	11.2189i	−0.697330	+	0.716750i
$246$	3.11803	−	2.26538i	0.198799	−	0.144436i
$247$	6.56161	−	1.39471i	0.417505	−	0.0887435i
$248$	−6.55639	−	7.28161i	−0.416331	−	0.462383i
$249$	0.940756	+	8.95070i	0.0596180	+	0.567227i
$250$	1.89094	−	17.9911i	0.119593	−	1.13786i
$251$	0.517221	+	1.59184i	0.0326467	+	0.100476i	0.966052	−	0.258347i	$-0.0831779\pi$
$251$	0.517221	+	1.59184i	0.0326467	+	0.100476i	−0.933405	+	0.358824i	$0.883178\pi$
$252$	−3.09017	−	1.07047i	−0.194662	−	0.0674330i
$253$	5.70820	+	1.28157i	0.358872	+	0.0805717i
$254$	0.190983	+	0.330792i	0.0119833	+	0.0207558i
$255$	−7.07794	−	1.50446i	−0.443238	−	0.0942131i
$256$	12.3898	−	5.51629i	0.774361	−	0.344768i
$257$	−10.9116	−	4.85817i	−0.680649	−	0.303045i	0.0371350	−	0.999310i	$-0.488177\pi$
$257$	−10.9116	−	4.85817i	−0.680649	−	0.303045i	−0.717784	+	0.696266i	$0.754844\pi$
$258$	0.0729490	−	0.224514i	0.00454161	−	0.0139776i
$259$	15.9893	+	1.99344i	0.993526	+	0.123867i
$260$	6.54508	−	4.75528i	0.405909	−	0.294910i
$261$	−1.64195	+	15.6222i	−0.101634	+	0.966987i
$262$	−10.0124	−	2.12820i	−0.618567	−	0.131481i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$	6.04919	−	4.29038i	0.372302	−	0.264055i
$265$	13.6180			0.836549
$266$	−4.20012	−	2.53433i	−0.257526	−	0.155390i
$267$	−1.23607	−	0.898056i	−0.0756461	−	0.0549601i
$268$	4.73248	+	2.10703i	0.289082	+	0.128708i
$269$	13.2104	+	14.6716i	0.805453	+	0.894546i	0.996200	−	0.0870932i	$-0.0277578\pi$
$269$	13.2104	+	14.6716i	0.805453	+	0.894546i	−0.190747	+	0.981639i	$0.561091\pi$
$270$	−12.1047	−	13.4436i	−0.736668	−	0.818152i
$271$	13.8170	+	6.15173i	0.839324	+	0.373691i	0.780942	−	0.624603i	$-0.214739\pi$
$271$	13.8170	+	6.15173i	0.839324	+	0.373691i	0.0583819	+	0.998294i	$0.481406\pi$
$272$	12.7082	+	9.23305i	0.770548	+	0.559836i
$273$	13.2614	+	8.00185i	0.802615	+	0.484294i
$274$	0.527864			0.0318894
$275$		0			0
$276$	0.545085	−	0.944115i	0.0328103	−	0.0568290i
$277$	−0.692728	−	0.147244i	−0.0416220	−	0.00884703i	0.187054	−	0.982350i	$-0.440106\pi$
$277$	−0.692728	−	0.147244i	−0.0416220	−	0.00884703i	−0.228676	+	0.973503i	$0.573440\pi$
$278$	−0.746950	+	7.10675i	−0.0447991	+	0.426235i
$279$	7.09017	−	5.15131i	0.424477	−	0.308401i
$280$	13.1271	+	1.63661i	0.784496	+	0.0978060i
$281$	1.43769	−	4.42477i	0.0857656	−	0.263959i	−0.898972	−	0.438007i	$-0.855685\pi$
$281$	1.43769	−	4.42477i	0.0857656	−	0.263959i	0.984737	+	0.174047i	$0.0556846\pi$
$282$	0.697887	+	0.310719i	0.0415585	+	0.0185031i
$283$	−18.6513	+	8.30410i	−1.10871	+	0.493628i	−0.877645	−	0.479312i	$-0.840886\pi$
$283$	−18.6513	+	8.30410i	−1.10871	+	0.493628i	−0.231061	+	0.972939i	$0.574220\pi$
$284$	−0.461819	−	0.0981626i	−0.0274039	−	0.00582488i
$285$	−1.28115	−	2.21902i	−0.0758890	−	0.131444i
$286$	−28.8435	+	12.4495i	−1.70555	+	0.736154i
$287$	−5.95492	−	2.06284i	−0.351508	−	0.121766i
$288$	2.09017	+	6.43288i	0.123164	+	0.379061i
$289$	0.682348	−	6.49210i	0.0401381	−	0.381888i
$290$	2.97032	+	28.2607i	0.174423	+	1.65953i
$291$	−2.57890	−	2.86416i	−0.151178	−	0.167900i
$292$	−6.56161	+	1.39471i	−0.383989	+	0.0816195i
$293$	10.0902	−	7.33094i	0.589474	−	0.428278i	−0.252653	−	0.967557i	$-0.581303\pi$
$293$	10.0902	−	7.33094i	0.589474	−	0.428278i	0.842127	+	0.539279i	$0.181303\pi$
$294$	−3.08140	−	10.8990i	−0.179711	−	0.635644i
$295$	−6.70820	−	20.6457i	−0.390567	−	1.20204i
$296$	−6.80902	−	11.7936i	−0.395766	−	0.685487i
$297$	8.12713	+	14.4551i	0.471584	+	0.838770i
$298$	−16.5902	+	28.7350i	−0.961043	+	1.66457i
$299$	6.90960	−	7.67389i	0.399593	−	0.443793i
$300$		0			0
$301$	−0.369352	+	0.112171i	−0.0212891	+	0.00646545i
$302$	−2.30902	+	7.10642i	−0.132869	+	0.408929i
$303$	14.7604	−	3.13742i	0.847964	−	0.180240i
$304$	0.581419	+	5.53184i	0.0333467	+	0.317272i
$305$	−22.3564	+	9.95371i	−1.28012	+	0.569948i
$306$	−7.00723	+	7.78231i	−0.400576	+	0.444885i
$307$	13.5066			0.770861			0.385431	−	0.922737i	$-0.374053\pi$
$307$	13.5066			0.770861			0.385431	+	0.922737i	$0.374053\pi$
$308$	5.10388	+	1.83353i	0.290820	+	0.104475i
$309$	6.00000			0.341328
$310$	10.6085	−	11.7819i	0.602520	−	0.669167i
$311$	−12.2056	+	5.43428i	−0.692115	+	0.308150i	−0.722483	−	0.691389i	$-0.756999\pi$
$311$	−12.2056	+	5.43428i	−0.692115	+	0.308150i	0.0303671	+	0.999539i	$0.490332\pi$
$312$	−1.36830	−	13.0185i	−0.0774645	−	0.737025i
$313$	−6.79252	+	1.44380i	−0.383936	+	0.0816081i	−0.395836	−	0.918321i	$-0.629545\pi$
$313$	−6.79252	+	1.44380i	−0.383936	+	0.0816081i	0.0119003	+	0.999929i	$0.496212\pi$
$314$	−5.88197	+	18.1028i	−0.331939	+	1.02160i
$315$	−2.68310	+	11.5239i	−0.151176	+	0.649300i
$316$	6.35410	+	4.61653i	0.357446	+	0.259700i
$317$	−0.255585	+	0.283856i	−0.0143551	+	0.0159429i	−0.750280	−	0.661121i	$-0.770081\pi$
$317$	−0.255585	+	0.283856i	−0.0143551	+	0.0159429i	0.735925	+	0.677064i	$0.236748\pi$
$318$	−4.92705	+	8.53390i	−0.276295	+	0.478557i
$319$	3.01834	−	25.8736i	0.168995	−	1.44865i
$320$	−4.73607	−	8.20311i	−0.264754	−	0.458568i
$321$	−3.45492	−	10.6331i	−0.192835	−	0.593484i
$322$	−7.52372	+	0.644137i	−0.419281	+	0.0358963i
$323$	−3.00000	+	2.17963i	−0.166924	+	0.121278i
$324$	−0.604528	+	0.128496i	−0.0335849	+	0.00713869i
$325$		0			0
$326$	−3.25341	−	30.9541i	−0.180190	−	1.71439i
$327$	0.0152505	−	0.145099i	0.000843354	−	0.00802398i
$328$	1.64590	+	5.06555i	0.0908795	+	0.279698i
$329$	−0.236068	−	1.22665i	−0.0130148	−	0.0676271i
$330$	7.92705	+	9.00854i	0.436370	+	0.495904i
$331$	0.645898	+	1.11873i	0.0355018	+	0.0614909i	0.883230	−	0.468939i	$-0.155364\pi$
$331$	0.645898	+	1.11873i	0.0355018	+	0.0614909i	−0.847729	+	0.530430i	$0.822030\pi$
$332$	5.44076	+	1.15647i	0.298600	+	0.0634695i
$333$	11.1273	−	4.95419i	0.609772	−	0.271488i
$334$	−22.0898	−	9.83503i	−1.20870	−	0.538149i
$335$	5.79180	−	17.8253i	0.316440	−	0.973901i
$336$	−7.74803	+	10.2423i	−0.422690	+	0.558762i
$337$	−11.8992	+	8.64527i	−0.648190	+	0.470938i	−0.862654	−	0.505794i	$-0.831199\pi$
$337$	−11.8992	+	8.64527i	−0.648190	+	0.470938i	0.214464	+	0.976732i	$0.431199\pi$
$338$	−3.59749	+	34.2279i	−0.195678	+	1.86175i
$339$	−2.04449	−	0.434571i	−0.111042	−	0.0236026i
$340$	−2.23607	+	3.87298i	−0.121268	+	0.210042i
$341$	−11.8544	+	8.40775i	−0.641954	+	0.455305i
$342$	−3.70820			−0.200517
$343$	−11.7353	+	14.3277i	−0.633648	+	0.773621i
$344$	0.263932	+	0.191758i	0.0142303	+	0.0103389i
$345$	−3.60327	−	1.60428i	−0.193994	−	0.0863715i
$346$	−11.3983	−	12.6591i	−0.612775	−	0.680555i
$347$	22.5552	+	25.0501i	1.21083	+	1.34476i	0.921910	+	0.387404i	$0.126628\pi$
$347$	22.5552	+	25.0501i	1.21083	+	1.34476i	0.288916	+	0.957354i	$0.406705\pi$
$348$	−4.43444	−	1.97434i	−0.237711	−	0.105836i
$349$	−24.0623	−	17.4823i	−1.28803	−	0.935805i	−0.288262	−	0.957552i	$-0.593077\pi$
$349$	−24.0623	−	17.4823i	−1.28803	−	0.935805i	−0.999764	+	0.0217461i	$0.993077\pi$
$350$		0			0
$351$	29.2705			1.56234
$352$	−3.34419	−	10.7066i	−0.178246	−	0.570663i
$353$	−2.23607	+	3.87298i	−0.119014	+	0.206138i	−0.919377	−	0.393377i	$-0.871307\pi$
$353$	−2.23607	+	3.87298i	−0.119014	+	0.206138i	0.800363	+	0.599515i	$0.204640\pi$
$354$	15.3649	+	3.26592i	0.816637	+	0.173582i
$355$	−0.178556	+	1.69885i	−0.00947676	+	0.0901654i
$356$	−0.763932	+	0.555029i	−0.0404883	+	0.0294165i
$357$	−8.49606	−	1.05923i	−0.449659	−	0.0560606i
$358$	10.2533	−	31.5564i	0.541903	−	1.66781i
$359$	−8.51994	−	3.79332i	−0.449665	−	0.200204i	0.169394	−	0.985548i	$-0.445819\pi$
$359$	−8.51994	−	3.79332i	−0.449665	−	0.200204i	−0.619059	+	0.785345i	$0.712486\pi$
$360$	9.13545	−	4.06737i	0.481481	−	0.214369i
$361$	17.3004	+	3.67732i	0.910548	+	0.193543i
$362$	17.1353	+	29.6791i	0.900609	+	1.55990i
$363$	−5.28115	−	9.64932i	−0.277189	−	0.506458i
$364$	7.23607	−	6.26662i	0.379273	−	0.328460i
$365$	7.50000	+	23.0826i	0.392568	+	1.20820i
$366$	1.85101	−	17.6112i	0.0967539	−	0.920552i
$367$	−2.85054	−	27.1211i	−0.148797	−	1.41571i	−0.772979	−	0.634432i	$-0.781234\pi$
$367$	−2.85054	−	27.1211i	−0.148797	−	1.41571i	0.624182	−	0.781279i	$-0.285432\pi$
$368$	5.72930	+	6.36303i	0.298660	+	0.331696i
$369$	−4.65983	+	0.990477i	−0.242581	+	0.0515622i
$370$	17.8262	−	12.9515i	0.926742	−	0.673317i
$371$	16.0543	−	1.37448i	0.833500	−	0.0713594i
$372$	0.836881	+	2.57565i	0.0433903	+	0.133541i
$373$	11.7984	+	20.4354i	0.610897	+	1.05810i	0.991090	+	0.133197i	$0.0425242\pi$
$373$	11.7984	+	20.4354i	0.610897	+	1.05810i	−0.380193	+	0.924907i	$0.624142\pi$
$374$	11.7667	−	12.7721i	0.608441	−	0.660427i
$375$	5.59017	−	9.68246i	0.288675	−	0.500000i
$376$	−0.706420	+	0.784559i	−0.0364308	+	0.0404605i
$377$	−37.1976	−	27.0256i	−1.91577	−	1.39189i
$378$	−15.6271	−	14.6270i	−0.803773	−	0.752331i
$379$	6.70820	−	20.6457i	0.344577	−	1.06050i	−0.617232	−	0.786781i	$-0.711746\pi$
$379$	6.70820	−	20.6457i	0.344577	−	1.06050i	0.961810	−	0.273719i	$-0.0882538\pi$
$380$	−1.54899	+	0.329247i	−0.0794613	+	0.0168900i
$381$	0.0246758	+	0.234775i	0.00126418	+	0.0120279i
$382$	21.0430	−	9.36895i	1.07665	−	0.479357i
$383$	−15.2551	+	16.9425i	−0.779499	+	0.865721i	−0.993816	−	0.111043i	$-0.964581\pi$
$383$	−15.2551	+	16.9425i	−0.779499	+	0.865721i	0.214317	+	0.976764i	$0.431247\pi$
$384$	13.6180			0.694942
$385$	4.66722	−	19.0583i	0.237864	−	0.971299i
$386$	−29.4164			−1.49726
$387$	−0.195250	+	0.216847i	−0.00992510	+	0.0110229i
$388$	−2.17603	+	0.968833i	−0.110471	+	0.0491850i
$389$	2.45933	+	23.3990i	0.124693	+	1.18638i	0.860596	+	0.509288i	$0.170091\pi$
$389$	2.45933	+	23.3990i	0.124693	+	1.18638i	−0.735903	+	0.677087i	$0.763242\pi$
$390$	20.7175	−	4.40364i	1.04907	−	0.222987i
$391$	−1.76393	+	5.42882i	−0.0892059	+	0.274547i
$392$	15.6408	+	0.604471i	0.789980	+	0.0305304i
$393$	−5.11803	−	3.71847i	−0.258171	−	0.187572i
$394$	2.57890	−	2.86416i	0.129923	−	0.144294i
$395$	14.2082	−	24.6093i	0.714892	−	1.23823i
$396$	4.01945	−	0.806532i	0.201985	−	0.0405297i
$397$	−17.3435	−	30.0398i	−0.870443	−	1.50765i	−0.861539	−	0.507692i	$-0.830499\pi$
$397$	−17.3435	−	30.0398i	−0.870443	−	1.50765i	−0.00890435	−	0.999960i	$-0.502834\pi$
$398$	10.7812	+	33.1810i	0.540410	+	1.66321i
$399$	−1.73432	−	2.48670i	−0.0868247	−	0.124491i
$400$		0			0
$401$	17.5521	−	3.73082i	0.876512	−	0.186308i	0.252381	−	0.967628i	$-0.418786\pi$
$401$	17.5521	−	3.73082i	0.876512	−	0.186308i	0.624131	+	0.781319i	$0.285453\pi$
$402$	9.07495	+	10.0788i	0.452618	+	0.502683i
$403$	2.68141	+	25.5119i	0.133571	+	1.27084i
$404$	0.974857	−	9.27515i	0.0485010	−	0.461456i
$405$	0.690983	+	2.12663i	0.0343352	+	0.105673i
$406$	6.35410	+	33.0169i	0.315349	+	1.63860i
$407$	−18.5451	+	8.00448i	−0.919246	+	0.396767i
$408$	3.61803	+	6.26662i	0.179119	+	0.310244i
$409$	24.6301	+	5.23529i	1.21788	+	0.258868i	0.771648	−	0.636049i	$-0.219433\pi$
$409$	24.6301	+	5.23529i	1.21788	+	0.258868i	0.446231	+	0.894918i	$0.352766\pi$
$410$	−7.87297	+	3.50527i	−0.388818	+	0.173113i
$411$	0.298033	+	0.132693i	0.0147009	+	0.00654526i
$412$	1.14590	−	3.52671i	0.0564543	−	0.173749i
$413$	−9.99211	−	23.6623i	−0.491680	−	1.16434i
$414$	−4.61803	+	3.35520i	−0.226964	+	0.164899i
$415$	2.10359	−	20.0144i	0.103261	−	0.982467i
$416$	−19.3657	−	4.11631i	−0.949483	−	0.201819i
$417$	−2.20820	+	3.82472i	−0.108136	+	0.187297i
$418$	6.14896	+	0.0701768i	0.300755	+	0.00343246i
$419$	23.1803			1.13243			0.566217	−	0.824256i	$-0.308406\pi$
$419$	23.1803			1.13243			0.566217	+	0.824256i	$0.308406\pi$
$420$	−3.13058	−	1.88898i	−0.152757	−	0.0921729i
$421$	22.4164	+	16.2865i	1.09251	+	0.793754i	0.979821	−	0.199876i	$-0.0640540\pi$
$421$	22.4164	+	16.2865i	1.09251	+	0.793754i	0.112688	+	0.993630i	$0.464054\pi$
$422$	−13.3033	−	5.92302i	−0.647596	−	0.288328i
$423$	−0.631841	−	0.701731i	−0.0307212	−	0.0341193i
$424$	−9.11224	−	10.1202i	−0.442530	−	0.491479i
$425$		0			0
$426$	−1.00000	−	0.726543i	−0.0484502	−	0.0352011i
$427$	−25.3514	+	13.9909i	−1.22684	+	0.677068i
$428$	−6.90983			−0.333999
$429$	−19.4146	−	0.221575i	−0.937345	−	0.0106977i
$430$	−0.263932	+	0.457144i	−0.0127279	+	0.0220454i
$431$	17.4976	+	3.71924i	0.842831	+	0.179149i	0.609042	−	0.793138i	$-0.291554\pi$
$431$	17.4976	+	3.71924i	0.842831	+	0.179149i	0.233789	+	0.972287i	$0.424887\pi$
$432$	−2.53696	+	24.1376i	−0.122060	+	1.16132i
$433$	11.6631	−	8.47375i	0.560494	−	0.407223i	−0.271146	−	0.962538i	$-0.587403\pi$
$433$	11.6631	−	8.47375i	0.560494	−	0.407223i	0.831640	+	0.555316i	$0.187403\pi$
$434$	11.3172	−	14.9604i	0.543243	−	0.718124i
$435$	−5.42705	+	16.7027i	−0.260207	+	0.800835i
$436$	−0.0823743	−	0.0366754i	−0.00394502	−	0.00175643i
$437$	−1.84654	+	0.822131i	−0.0883318	+	0.0393279i
$438$	−17.1785	−	3.65141i	−0.820822	−	0.174471i
$439$	3.90983	+	6.77202i	0.186606	+	0.323211i	0.944117	−	0.329612i	$-0.106918\pi$
$439$	3.90983	+	6.77202i	0.186606	+	0.323211i	−0.757511	+	0.652823i	$0.773585\pi$
$440$	−15.2254	+	6.57164i	−0.725844	+	0.313291i
$441$	−2.00000	+	13.8564i	−0.0952381	+	0.659829i
$442$	−9.47214	−	29.1522i	−0.450544	−	1.38663i
$443$	−1.48807	+	14.1581i	−0.0707005	+	0.672671i	0.900573	+	0.434705i	$0.143147\pi$
$443$	−1.48807	+	14.1581i	−0.0707005	+	0.672671i	−0.971274	+	0.237966i	$0.923519\pi$
$444$	0.393438	+	3.74331i	0.0186717	+	0.177650i
$445$	2.28602	+	2.53889i	0.108368	+	0.120355i
$446$	30.3018	−	6.44084i	1.43483	−	0.304982i
$447$	−16.5902	+	12.0535i	−0.784688	+	0.570109i
$448$	−6.41131	−	9.19266i	−0.302906	−	0.434312i
$449$	8.57953	+	26.4051i	0.404893	+	1.24613i	0.920985	+	0.389599i	$0.127386\pi$
$449$	8.57953	+	26.4051i	0.404893	+	1.24613i	−0.516092	+	0.856533i	$0.672614\pi$
$450$		0			0
$451$	7.74569	−	1.55423i	0.364730	−	0.0731857i
$452$	−0.645898	+	1.11873i	−0.0303805	+	0.0526205i
$453$	−3.09007	+	3.43187i	−0.145184	+	0.161243i
$454$	−9.70820	−	7.05342i	−0.455629	−	0.331034i
$455$	−25.2852	−	23.6670i	−1.18539	−	1.10952i
$456$	−0.791796	+	2.43690i	−0.0370792	+	0.114118i
$457$	−6.98974	+	1.48572i	−0.326966	+	0.0694989i	−0.368470	−	0.929639i	$-0.620118\pi$
$457$	−6.98974	+	1.48572i	−0.326966	+	0.0694989i	0.0415040	+	0.999138i	$0.486785\pi$
$458$	−0.990108	−	9.42025i	−0.0462647	−	0.440179i
$459$	−14.7815	+	6.58114i	−0.689940	+	0.307181i
$460$	−1.63114	+	1.81156i	−0.0760521	+	0.0844644i
$461$	−7.90983			−0.368398			−0.184199	−	0.982889i	$-0.558969\pi$
$461$	−7.90983			−0.368398			−0.184199	+	0.982889i	$0.558969\pi$
$462$	10.2545	+	9.82011i	0.477081	+	0.456873i
$463$	−38.5967			−1.79374			−0.896871	−	0.442291i	$-0.854166\pi$
$463$	−38.5967			−1.79374			−0.896871	+	0.442291i	$0.854166\pi$
$464$	25.5103	−	28.3321i	1.18429	−	1.31529i
$465$	8.95126	−	3.98536i	0.415105	−	0.184817i
$466$	0.522642	+	4.97261i	0.0242109	+	0.230352i
$467$	2.47262	−	0.525572i	0.114419	−	0.0243206i	−0.150346	−	0.988633i	$-0.548039\pi$
$467$	2.47262	−	0.525572i	0.114419	−	0.0243206i	0.264765	+	0.964313i	$0.414705\pi$
$468$	2.23607	−	6.88191i	0.103362	−	0.318116i
$469$	5.02884	−	21.5989i	0.232210	−	0.997344i
$470$	−1.38197	−	1.00406i	−0.0637453	−	0.0463137i
$471$	−7.87161	+	8.74231i	−0.362705	+	0.402824i
$472$	−10.8541	+	18.7999i	−0.499601	+	0.865334i
$473$	0.327868	−	0.355881i	0.0150754	−	0.0163634i
$474$	10.2812	+	17.8075i	0.472229	+	0.817925i
$475$		0			0
$476$	−2.24520	+	4.79156i	−0.102909	+	0.219621i
$477$	9.85410	−	7.15942i	0.451188	−	0.327808i
$478$	−20.1130	+	4.27514i	−0.919946	+	0.195541i
$479$	−9.62341	−	10.6879i	−0.439705	−	0.488342i	0.482034	−	0.876152i	$-0.339898\pi$
$479$	−9.62341	−	10.6879i	−0.439705	−	0.488342i	−0.921739	+	0.387811i	$0.873231\pi$
$480$	0.790476	+	7.52088i	0.0360801	+	0.343280i
$481$	−3.72670	+	35.4572i	−0.169923	+	1.61671i
$482$	−0.791796	−	2.43690i	−0.0360653	−	0.110998i
$483$	−4.40983	−	1.52761i	−0.200654	−	0.0695087i
$484$	−6.68034	+	1.26133i	−0.303652	+	0.0573331i
$485$	4.30902	+	7.46344i	0.195662	+	0.338897i
$486$	−25.3228	−	5.38253i	−1.14867	−	0.244157i
$487$	−7.73968	+	3.44593i	−0.350718	+	0.156150i	−0.574532	−	0.818482i	$-0.694816\pi$
$487$	−7.73968	+	3.44593i	−0.350718	+	0.156150i	0.223814	+	0.974632i	$0.428149\pi$
$488$	22.3564	+	9.95371i	1.01203	+	0.450583i
$489$	5.94427	−	18.2946i	0.268809	−	0.827310i
$490$	1.67264	+	25.2709i	0.0755623	+	1.14162i
$491$	−10.0623	+	7.31069i	−0.454106	+	0.329927i	−0.791215	−	0.611539i	$-0.790551\pi$
$491$	−10.0623	+	7.31069i	−0.454106	+	0.329927i	0.337109	+	0.941466i	$0.390551\pi$
$492$	0.153880	−	1.46407i	0.00693745	−	0.0660054i
$493$	24.8610	+	5.28437i	1.11968	+	0.237996i
$494$	5.42705	−	9.39993i	0.244175	−	0.422923i
$495$	−4.42218	−	14.1578i	−0.198762	−	0.636347i
$496$	−21.2705			−0.955074
$497$	−0.0390343	+	2.02080i	−0.00175093	+	0.0906451i
$498$	11.7812	+	8.55951i	0.527926	+	0.383561i
$499$	−3.27377	−	1.45758i	−0.146554	−	0.0652502i	0.332149	−	0.943227i	$-0.392226\pi$
$499$	−3.27377	−	1.45758i	−0.146554	−	0.0652502i	−0.478703	+	0.877977i	$0.658893\pi$
$500$	−4.62358	−	5.13500i	−0.206773	−	0.229644i
$501$	−9.99967	−	11.1058i	−0.446752	−	0.496169i
$502$	2.47407	+	1.10153i	0.110423	+	0.0491635i
$503$	22.6074	+	16.4252i	1.00801	+	0.732365i	0.963792	−	0.266657i	$-0.0859190\pi$
$503$	22.6074	+	16.4252i	1.00801	+	0.732365i	0.0442222	+	0.999022i	$0.485919\pi$
$504$	10.3593	−	5.71708i	0.461440	−	0.254659i
$505$	−33.7426			−1.50153
$506$	7.72114	−	5.47621i	0.343247	−	0.243447i
$507$	−10.6353	+	18.4208i	−0.472328	+	0.818097i
$508$	0.142710	+	0.0303339i	0.00633172	+	0.00134585i
$509$	−0.0282760	+	0.269028i	−0.00125331	+	0.0119245i	−0.995131	−	0.0985644i	$-0.968575\pi$
$509$	−0.0282760	+	0.269028i	−0.00125331	+	0.0119245i	0.993877	+	0.110489i	$0.0352416\pi$
$510$	−9.47214	+	6.88191i	−0.419433	+	0.304736i
$511$	11.1715	+	26.4552i	0.494199	+	1.17031i
$512$	−1.63525	+	5.03280i	−0.0722687	+	0.222420i
$513$	−5.23415	−	2.33039i	−0.231093	−	0.102889i
$514$	−17.6554	+	7.86069i	−0.778746	+	0.346720i
$515$	−13.1232	−	2.78943i	−0.578278	−	0.122917i
$516$	−0.0450850	−	0.0780895i	−0.00198476	−	0.00343770i
$517$	1.03444	+	1.17557i	0.0454947	+	0.0517015i
$518$	19.7082	−	17.0678i	0.865929	−	0.749916i
$519$	−3.25329	−	10.0126i	−0.142804	−	0.439504i
$520$	−3.05960	+	29.1102i	−0.134172	+	1.27657i
$521$	−4.60285	−	43.7932i	−0.201655	−	1.91862i	−0.363129	−	0.931739i	$-0.618292\pi$
$521$	−4.60285	−	43.7932i	−0.201655	−	1.91862i	0.161475	−	0.986877i	$-0.448375\pi$
$522$	17.0069	+	18.8881i	0.744372	+	0.826708i
$523$	24.2020	−	5.14429i	1.05828	−	0.224944i	0.354275	−	0.935141i	$-0.384728\pi$
$523$	24.2020	−	5.14429i	1.05828	−	0.224944i	0.704003	+	0.710197i	$0.251394\pi$
$524$	−3.16312	+	2.29814i	−0.138181	+	0.100395i
$525$		0			0
$526$	6.00000	+	18.4661i	0.261612	+	0.805160i
$527$	−7.09017	−	12.2805i	−0.308853	−	0.534948i
$528$	1.86544	−	15.9908i	0.0811827	−	0.695910i
$529$	9.94427	−	17.2240i	0.432360	−	0.748869i
$530$	14.7439	−	16.3748i	0.640435	−	0.711275i
$531$	−15.7082	−	11.4127i	−0.681678	−	0.495268i
$532$	−1.79287	+	0.544491i	−0.0777310	+	0.0236067i
$533$	4.30902	−	13.2618i	0.186644	−	0.574432i
$534$	−2.41811	+	0.513986i	−0.104642	+	0.0222423i
$535$	2.61321	+	24.8630i	0.112979	+	1.07492i
$536$	−17.1223	+	7.62332i	−0.739569	+	0.329277i
$537$	13.7216	−	15.2394i	0.592130	−	0.657627i
$538$	31.9443			1.37722
$539$	3.57864	−	22.9389i	0.154143	−	0.988049i
$540$	−6.90983			−0.297352
$541$	13.1128	−	14.5632i	0.563763	−	0.626122i	−0.392105	−	0.919921i	$-0.628253\pi$
$541$	13.1128	−	14.5632i	0.563763	−	0.626122i	0.955867	+	0.293799i	$0.0949196\pi$
$542$	22.3564	−	9.95371i	0.960290	−	0.427549i
$543$	2.21395	+	21.0643i	0.0950096	+	0.903956i
$544$	10.7051	−	2.27544i	0.458978	−	0.0975588i
$545$	−0.100813	+	0.310271i	−0.00431836	+	0.0132905i
$546$	23.9795	−	7.28250i	1.02623	−	0.311662i
$547$	28.4443	+	20.6660i	1.21619	+	0.883613i	0.995778	−	0.0917938i	$-0.0292601\pi$
$547$	28.4443	+	20.6660i	1.21619	+	0.883613i	0.220411	+	0.975407i	$0.429260\pi$
$548$	0.134914	−	0.149837i	0.00576325	−	0.00640074i
$549$	−10.9443	+	18.9560i	−0.467090	+	0.809024i
$550$		0			0
$551$	4.50000	+	7.79423i	0.191706	+	0.332045i
$552$	1.21885	+	3.75123i	0.0518776	+	0.159663i
$553$	14.2663	−	30.4461i	0.606663	−	1.29470i
$554$	−0.927051	+	0.673542i	−0.0393866	+	0.0286161i
$555$	13.3204	−	2.83135i	0.565421	−	0.120184i
$556$	1.82639	+	2.02841i	0.0774560	+	0.0860236i
$557$	−1.44232	−	13.7228i	−0.0611132	−	0.581453i	−0.981636	−	0.190764i	$-0.938903\pi$
$557$	−1.44232	−	13.7228i	−0.0611132	−	0.581453i	0.920523	−	0.390689i	$-0.127763\pi$
$558$	1.48225	−	14.1027i	0.0627486	−	0.597013i
$559$	−0.263932	−	0.812299i	−0.0111631	−	0.0343566i
$560$	21.7082	−	18.7999i	0.917339	−	0.794439i
$561$	9.85410	−	4.25325i	0.416041	−	0.179573i
$562$	−3.76393	−	6.51932i	−0.158772	−	0.275001i
$563$	−3.45077	−	0.733484i	−0.145433	−	0.0309127i	0.134620	−	0.990897i	$-0.457019\pi$
$563$	−3.45077	−	0.733484i	−0.145433	−	0.0309127i	−0.280053	+	0.959985i	$0.590352\pi$
$564$	0.266569	−	0.118684i	0.0112246	−	0.00499750i
$565$	4.26969	+	1.90099i	0.179627	+	0.0799753i
$566$	−10.2082	+	31.4176i	−0.429083	+	1.32058i
$567$	1.02924	+	2.43735i	0.0432242	+	0.102359i
$568$	1.38197	−	1.00406i	0.0579860	−	0.0421293i
$569$	1.18974	−	11.3196i	0.0498765	−	0.474543i	−0.940865	−	0.338781i	$-0.889985\pi$
$569$	1.18974	−	11.3196i	0.0498765	−	0.474543i	0.990742	−	0.135761i	$-0.0433481\pi$
$570$	−4.05530	−	0.861981i	−0.169858	−	0.0361044i
$571$	3.78115	−	6.54915i	0.158236	−	0.274073i	−0.775996	−	0.630737i	$-0.782753\pi$
$571$	3.78115	−	6.54915i	0.158236	−	0.274073i	0.934233	+	0.356664i	$0.116086\pi$
$572$	−3.83810	+	11.3693i	−0.160479	+	0.475374i
$573$	14.2361			0.594720
$574$	−8.92768	+	4.92700i	−0.372634	+	0.205649i
$575$		0			0
$576$	−7.73968	−	3.44593i	−0.322487	−	0.143580i
$577$	−19.7810	−	21.9691i	−0.823496	−	0.914585i	0.174041	−	0.984738i	$-0.444318\pi$
$577$	−19.7810	−	21.9691i	−0.823496	−	0.914585i	−0.997536	+	0.0701539i	$0.977651\pi$
$578$	−7.06756	−	7.84932i	−0.293972	−	0.326489i
$579$	−16.6086	−	7.39461i	−0.690228	−	0.307310i
$580$	8.78115	+	6.37988i	0.364618	+	0.264910i
$581$	0.459870	−	23.8073i	0.0190786	−	0.987694i
$582$	−6.23607			−0.258493
$583$	−16.4756	+	11.6853i	−0.682350	+	0.483956i
$584$	12.1353	−	21.0189i	0.502160	−	0.869767i
$585$	−25.6082	−	5.44320i	−1.05877	−	0.225049i
$586$	2.10942	−	20.0698i	0.0871393	−	0.829075i
$587$	−32.0795	+	23.3071i	−1.32406	+	0.961989i	−0.324192	+	0.945991i	$0.605092\pi$
$587$	−32.0795	+	23.3071i	−1.32406	+	0.961989i	−0.999872	+	0.0159972i	$0.994908\pi$
$588$	−3.88131	−	1.91095i	−0.160063	−	0.0788064i
$589$	1.55166	−	4.77553i	0.0639352	−	0.196772i
$590$	−32.0879	−	14.2865i	−1.32104	−	0.588165i
$591$	2.17603	−	0.968833i	0.0895101	−	0.0398525i
$592$	−28.9163	−	6.14635i	−1.18845	−	0.252613i
$593$	10.0344	+	17.3802i	0.412065	+	0.713718i	0.995115	−	0.0987183i	$-0.0314743\pi$
$593$	10.0344	+	17.3802i	0.412065	+	0.713718i	−0.583050	+	0.812436i	$0.698141\pi$
$594$	26.1803	+	5.87785i	1.07419	+	0.241171i
$595$	18.0902	+	6.26662i	0.741625	+	0.256906i
$596$	3.91641	+	12.0535i	0.160422	+	0.493729i
$597$	−2.25387	+	21.4442i	−0.0922450	+	0.877652i
$598$	−1.74648	−	16.6167i	−0.0714190	−	0.679506i
$599$	5.68321	+	6.31184i	0.232210	+	0.257895i	0.847977	−	0.530033i	$-0.177821\pi$
$599$	5.68321	+	6.31184i	0.232210	+	0.257895i	−0.615767	+	0.787928i	$0.711154\pi$
$600$		0			0
$601$	15.4894	−	11.2537i	0.631824	−	0.459047i	−0.225208	−	0.974311i	$-0.572306\pi$
$601$	15.4894	−	11.2537i	0.631824	−	0.459047i	0.857032	+	0.515264i	$0.172306\pi$
$602$	−0.265010	+	0.565567i	−0.0108010	+	0.0230508i
$603$	−5.18034	−	15.9434i	−0.210960	−	0.649267i
$604$	1.42705	+	2.47172i	0.0580659	+	0.100573i
$605$	7.06495	+	23.5603i	0.287231	+	0.957861i
$606$	12.2082	−	21.1452i	0.495924	−	0.858966i
$607$	−4.19579	+	4.65990i	−0.170302	+	0.189139i	−0.822254	−	0.569121i	$-0.807284\pi$
$607$	−4.19579	+	4.65990i	−0.170302	+	0.189139i	0.651952	+	0.758260i	$0.273950\pi$
$608$	3.13525	+	2.27790i	0.127151	+	0.0923809i
$609$	−4.71215	+	20.2387i	−0.190946	+	0.820113i
$610$	−12.2361	+	37.6587i	−0.495424	+	1.52476i
$611$	2.70353	−	0.574654i	0.109373	−	0.0232480i
$612$	0.418114	+	3.97809i	0.0169013	+	0.160805i
$613$	5.96350	−	2.65512i	0.240864	−	0.107239i	−0.282755	−	0.959192i	$-0.591248\pi$
$613$	5.96350	−	2.65512i	0.240864	−	0.107239i	0.523619	+	0.851953i	$0.324582\pi$
$614$	14.6232	−	16.2408i	0.590146	−	0.655424i
$615$	−5.32624			−0.214775
$616$	−17.2860	+	9.28404i	−0.696474	+	0.374065i
$617$	16.5279			0.665387			0.332693	−	0.943035i	$-0.392043\pi$
$617$	16.5279			0.665387			0.332693	+	0.943035i	$0.392043\pi$
$618$	6.49606	−	7.21460i	0.261310	−	0.290214i
$619$	42.6506	−	18.9893i	1.71427	−	0.763244i	0.716426	−	0.697663i	$-0.245777\pi$
$619$	42.6506	−	18.9893i	1.71427	−	0.763244i	0.997847	−	0.0655805i	$-0.0208899\pi$
$620$	−0.632996	−	6.02255i	−0.0254217	−	0.241872i
$621$	−8.62693	+	1.83371i	−0.346187	+	0.0735843i
$622$	−6.68034	+	20.5600i	−0.267857	+	0.824380i
$623$	2.95125	+	2.76237i	0.118239	+	0.110672i
$624$	−22.9894	−	16.7027i	−0.920311	−	0.668645i
$625$	−16.7283	+	18.5786i	−0.669131	+	0.743145i
$626$	−5.61803	+	9.73072i	−0.224542	+	0.388918i
$627$	3.45408	+	1.58533i	0.137942	+	0.0633120i
$628$	3.63525	+	6.29645i	0.145062	+	0.251256i
$629$	−6.09017	−	18.7436i	−0.242831	−	0.747357i
$630$	10.9518	+	15.7029i	0.436331	+	0.625620i
$631$	0.545085	−	0.396027i	0.0216995	−	0.0157656i	−0.576883	−	0.816827i	$-0.695731\pi$
$631$	0.545085	−	0.396027i	0.0216995	−	0.0157656i	0.598582	+	0.801061i	$0.295731\pi$
$632$	−27.7954	+	5.90810i	−1.10564	+	0.235012i
$633$	−6.02218	−	6.68830i	−0.239360	−	0.265836i
$634$	0.0646021	+	0.614648i	0.00256568	+	0.0244108i
$635$	0.0551768	−	0.524972i	0.00218963	−	0.0208329i
$636$	1.16312	+	3.57971i	0.0461207	+	0.141945i
$637$	−32.1976	−	25.3490i	−1.27571	−	1.00436i
$638$	−27.8435	−	31.6421i	−1.10233	−	1.25272i
$639$	0.763932	+	1.32317i	0.0302207	+	0.0523438i
$640$	−29.7854	−	6.33109i	−1.17737	−	0.250258i
$641$	−27.6535	+	12.3121i	−1.09225	+	0.486300i	−0.872180	−	0.489185i	$-0.837294\pi$
$641$	−27.6535	+	12.3121i	−1.09225	+	0.486300i	−0.220067	+	0.975485i	$0.570628\pi$
$642$	−16.5262	−	7.35793i	−0.652237	−	0.290395i
$643$	−5.87132	+	18.0701i	−0.231542	+	0.712614i	0.766019	+	0.642818i	$0.222235\pi$
$643$	−5.87132	+	18.0701i	−0.231542	+	0.712614i	−0.997561	+	0.0697961i	$0.977765\pi$
$644$	−1.74011	+	2.30029i	−0.0685699	+	0.0906439i
$645$	−0.263932	+	0.191758i	−0.0103923	+	0.00755046i
$646$	−0.627171	+	5.96713i	−0.0246757	+	0.234774i
$647$	6.61612	+	1.40630i	0.260107	+	0.0552874i	0.336119	−	0.941819i	$-0.390886\pi$
$647$	6.61612	+	1.40630i	0.260107	+	0.0552874i	−0.0760124	+	0.997107i	$0.524219\pi$
$648$	1.11803	−	1.93649i	0.0439205	−	0.0760726i
$649$	25.8314	+	19.2218i	1.01397	+	0.754523i
$650$		0			0
$651$	10.1504	−	5.60181i	0.397827	−	0.219552i
$652$	−9.61803	−	6.98791i	−0.376671	−	0.273668i
$653$	42.0036	+	18.7012i	1.64373	+	0.731836i	0.999457	−	0.0329600i	$-0.0104934\pi$
$653$	42.0036	+	18.7012i	1.64373	+	0.731836i	0.644273	+	0.764796i	$0.277160\pi$
$654$	−0.157960	−	0.175433i	−0.00617674	−	0.00685996i
$655$	9.46545	+	10.5125i	0.369846	+	0.410755i
$656$	10.5627	+	4.70281i	0.412404	+	0.183614i
$657$	17.5623	+	12.7598i	0.685171	+	0.497806i
$658$	−1.73054	−	1.04420i	−0.0674636	−	0.0407073i
$659$	−14.5623			−0.567267			−0.283633	−	0.958933i	$-0.591540\pi$
$659$	−14.5623			−0.567267			−0.283633	+	0.958933i	$0.591540\pi$
$660$	4.58316	+	0.0523067i	0.178399	+	0.00203603i
$661$	−4.28115	+	7.41517i	−0.166518	+	0.288417i	−0.937193	−	0.348811i	$-0.886586\pi$
$661$	−4.28115	+	7.41517i	−0.166518	+	0.288417i	0.770676	+	0.637228i	$0.219919\pi$
$662$	2.04449	+	0.434571i	0.0794615	+	0.0168901i
$663$	1.98022	−	18.8405i	0.0769052	−	0.731704i
$664$	−16.2812	+	11.8290i	−0.631831	+	0.459052i
$665$	2.63724	+	6.24523i	0.102268	+	0.242179i
$666$	6.09017	−	18.7436i	0.235989	−	0.726300i
$667$	12.6564	+	5.63497i	0.490056	+	0.218187i
$668$	−8.43757	+	3.75665i	−0.326459	+	0.145349i
$669$	18.7275	+	3.98066i	0.724048	+	0.153901i
$670$	−15.1631	−	26.2633i	−0.585802	−	1.01464i
$671$	18.5066	−	31.2259i	0.714439	−	1.20546i
$672$	1.69098	+	8.78661i	0.0652311	+	0.338951i
$673$	2.34346	+	7.21242i	0.0903337	+	0.278019i	0.986010	−	0.166689i	$-0.0533076\pi$
$673$	2.34346	+	7.21242i	0.0903337	+	0.278019i	−0.895676	+	0.444708i	$0.853308\pi$
$674$	−2.48761	+	23.6680i	−0.0958191	+	0.911657i
$675$		0			0
$676$	8.79632	+	9.76931i	0.338320	+	0.375743i
$677$	30.0917	−	6.39618i	1.15652	−	0.245825i	0.410569	−	0.911830i	$-0.365330\pi$
$677$	30.0917	−	6.39618i	1.15652	−	0.245825i	0.745948	+	0.666004i	$0.231997\pi$
$678$	−2.73607	+	1.98787i	−0.105078	+	0.0763437i
$679$	5.83320	+	8.36376i	0.223858	+	0.320972i
$680$	−5.00000	−	15.3884i	−0.191741	−	0.590119i
$681$	−3.70820	−	6.42280i	−0.142099	−	0.246122i
$682$	−2.72476	+	23.3570i	−0.104336	+	0.894387i
$683$	−15.5902	+	27.0030i	−0.596541	+	1.03324i	0.396786	+	0.917911i	$0.370125\pi$
$683$	−15.5902	+	27.0030i	−0.596541	+	1.03324i	−0.993327	+	0.115329i	$0.963208\pi$
$684$	−0.947762	+	1.05260i	−0.0362386	+	0.0402470i
$685$	−0.590170	−	0.428784i	−0.0225492	−	0.0163830i
$686$	4.52250	+	29.6232i	0.172670	+	1.13102i
$687$	1.80902	−	5.56758i	0.0690183	−	0.212416i
$688$	0.692728	−	0.147244i	0.0264100	−	0.00561362i
$689$	3.72670	+	35.4572i	0.141976	+	1.35081i
$690$	−5.83022	+	2.59578i	−0.221953	+	0.0988196i
$691$	−27.9916	+	31.0878i	−1.06485	+	1.18264i	−0.0823073	+	0.996607i	$0.526229\pi$
$691$	−27.9916	+	31.0878i	−1.06485	+	1.18264i	−0.982544	+	0.186030i	$0.940438\pi$
$692$	−6.50658			−0.247343
$693$	−6.64228	−	16.2444i	−0.252320	−	0.617073i
$694$	54.5410			2.07035
$695$	6.60792	−	7.33884i	0.250653	−	0.278378i
$696$	16.0440	−	7.14323i	0.608145	−	0.270764i
$697$	0.805727	+	7.66598i	0.0305191	+	0.290370i
$698$	−47.0730	+	10.0057i	−1.78174	+	0.378720i
$699$	−0.954915	+	2.93893i	−0.0361182	+	0.111160i
$700$		0			0
$701$	−20.5623	−	14.9394i	−0.776628	−	0.564253i	0.127337	−	0.991859i	$-0.459357\pi$
$701$	−20.5623	−	14.9394i	−0.776628	−	0.564253i	−0.903965	+	0.427606i	$0.859357\pi$
$702$	31.6905	−	35.1958i	1.19608	−	1.32838i
$703$	3.48936	−	6.04374i	0.131604	−	0.227944i
$704$	12.7688	+	5.86052i	0.481241	+	0.220877i
$705$	−0.527864	−	0.914287i	−0.0198805	−	0.0344341i
$706$	2.23607	+	6.88191i	0.0841555	+	0.259004i
$707$	−39.7793	+	3.40567i	−1.49606	+	0.128083i
$708$	4.85410	−	3.52671i	0.182428	−	0.132542i
$709$	−1.35177	+	0.287327i	−0.0507667	+	0.0107908i	−0.233225	−	0.972423i	$-0.574928\pi$
$709$	−1.35177	+	0.287327i	−0.0507667	+	0.0107908i	0.182458	+	0.983214i	$0.441595\pi$
$710$	1.84943	+	2.05400i	0.0694079	+	0.0770853i
$711$	−2.65674	−	25.2772i	−0.0996355	−	0.947968i
$712$	0.357112	−	3.39769i	0.0133833	−	0.127334i
$713$	−2.38854	−	7.35118i	−0.0894517	−	0.275304i
$714$	−10.4721	+	9.06914i	−0.391910	+	0.339404i
$715$	42.3607	+	9.51057i	1.58420	+	0.355675i
$716$	−6.33688	−	10.9758i	−0.236820	−	0.410185i
$717$	−12.4305	−	2.64218i	−0.464225	−	0.0986742i
$718$	−13.7856	+	6.13773i	−0.514472	+	0.229058i
$719$	4.73248	+	2.10703i	0.176492	+	0.0785791i	0.493080	−	0.869984i	$-0.335871\pi$
$719$	4.73248	+	2.10703i	0.176492	+	0.0785791i	−0.316589	+	0.948563i	$0.602538\pi$
$720$	6.70820	−	20.6457i	0.250000	−	0.769421i
$721$	−15.7526	−	1.96393i	−0.586656	−	0.0731405i
$722$	23.1525	−	16.8213i	0.861646	−	0.626022i
$723$	0.165530	−	1.57492i	0.00615614	−	0.0585718i
$724$	12.8041	+	2.72160i	0.475861	+	0.101147i
$725$		0			0
$726$	−17.3204	−	4.09685i	−0.642822	−	0.152049i
$727$	−1.58359			−0.0587322			−0.0293661	−	0.999569i	$-0.509349\pi$
$727$	−1.58359			−0.0587322			−0.0293661	+	0.999569i	$0.509349\pi$
$728$	−0.668863	+	34.6269i	−0.0247897	+	1.28336i
$729$	−10.5172	−	7.64121i	−0.389527	−	0.283008i
$730$	35.8754	+	15.9728i	1.32781	+	0.591178i
$731$	0.315921	+	0.350865i	0.0116847	+	0.0129772i
$732$	−4.52595	−	5.02658i	−0.167284	−	0.185788i
$733$	−30.2608	−	13.4730i	−1.11771	−	0.497636i	−0.237103	−	0.971485i	$-0.576198\pi$
$733$	−30.2608	−	13.4730i	−1.11771	−	0.497636i	−0.880607	+	0.473848i	$0.842865\pi$
$734$	−35.6976	−	25.9358i	−1.31762	−	0.957308i
$735$	−5.40816	+	14.6885i	−0.199483	+	0.541793i
$736$	5.96556			0.219893
$737$	8.28834	+	26.5355i	0.305305	+	0.977449i
$738$	−3.85410	+	6.67550i	−0.141871	+	0.245729i
$739$	−10.0669	−	2.13978i	−0.370317	−	0.0787133i	0.0189943	−	0.999820i	$-0.493954\pi$
$739$	−10.0669	−	2.13978i	−0.370317	−	0.0787133i	−0.389311	+	0.921106i	$0.627287\pi$
$740$	0.879754	−	8.37030i	0.0323404	−	0.307698i
$741$	5.42705	−	3.94298i	0.199368	−	0.144849i
$742$	15.7289	−	20.7924i	0.577427	−	0.763313i
$743$	−12.5066	+	38.4913i	−0.458822	+	1.41211i	0.407767	+	0.913086i	$0.366307\pi$
$743$	−12.5066	+	38.4913i	−0.458822	+	1.41211i	−0.866589	+	0.499022i	$0.833693\pi$
$744$	−8.95126	−	3.98536i	−0.328169	−	0.146110i
$745$	41.8898	−	18.6505i	1.53472	−	0.683303i
$746$	37.3460	+	7.93814i	1.36733	+	0.290636i
$747$	−9.00000	−	15.5885i	−0.329293	−	0.570352i
$748$	−0.618034	−	6.60440i	−0.0225976	−	0.241481i
$749$	5.59017	+	29.0474i	0.204260	+	1.06137i
$750$	−5.59017	−	17.2048i	−0.204124	−	0.628230i
$751$	0.729474	−	6.94048i	0.0266189	−	0.253262i	−0.973118	−	0.230309i	$-0.926026\pi$
$751$	0.729474	−	6.94048i	0.0266189	−	0.253262i	0.999737	−	0.0229533i	$-0.00730689\pi$
$752$	0.239558	+	2.27924i	0.00873578	+	0.0831154i
$753$	1.11997	+	1.24385i	0.0408138	+	0.0453283i
$754$	−72.7694	+	15.4676i	−2.65011	+	0.563297i
$755$	8.35410	−	6.06961i	0.304037	−	0.220896i
$756$	−8.14602	+	0.697414i	−0.296268	+	0.0253647i
$757$	5.75329	+	17.7068i	0.209107	+	0.643565i	0.999520	+	0.0309902i	$0.00986606\pi$
$757$	5.75329	+	17.7068i	0.209107	+	0.643565i	−0.790413	+	0.612575i	$0.790134\pi$
$758$	−17.5623	−	30.4188i	−0.637892	−	1.10486i
$759$	5.73597	−	1.15096i	0.208202	−	0.0417773i
$760$	2.86475	−	4.96188i	0.103915	−	0.179986i
$761$	−23.3680	+	25.9528i	−0.847091	+	0.940790i	−0.998865	−	0.0476256i	$-0.984835\pi$
$761$	−23.3680	+	25.9528i	−0.847091	+	0.940790i	0.151775	+	0.988415i	$0.451501\pi$
$762$	0.309017	+	0.224514i	0.0111945	+	0.00813328i
$763$	−0.0875330	+	0.375954i	−0.00316891	+	0.0136105i
$764$	2.71885	−	8.36775i	0.0983644	−	0.302735i
$765$	14.1559	−	3.00893i	0.511807	−	0.108788i
$766$	3.85590	+	36.6865i	0.139319	+	1.32554i
$767$	51.9194	−	23.1160i	1.87470	−	0.834670i
$768$	9.07495	−	10.0788i	0.327464	−	0.363686i
$769$	−12.4721			−0.449757			−0.224878	−	0.974387i	$-0.572198\pi$
$769$	−12.4721			−0.449757			−0.224878	+	0.974387i	$0.572198\pi$
$770$	−17.8632	−	26.2459i	−0.643745	−	0.945838i
$771$	−11.9443			−0.430162
$772$	−7.51840	+	8.35003i	−0.270593	+	0.300524i
$773$	−20.4784	+	9.11757i	−0.736557	+	0.327936i	−0.740500	−	0.672056i	$-0.765411\pi$
$773$	−20.4784	+	9.11757i	−0.736557	+	0.327936i	0.00394332	+	0.999992i	$0.498745\pi$
$774$	0.0493516	+	0.469550i	0.00177391	+	0.0168776i
$775$		0			0
$776$	2.66312	−	8.19624i	0.0956004	−	0.294228i
$777$	15.4177	−	4.68233i	0.553109	−	0.167978i
$778$	30.7984	+	22.3763i	1.10418	+	0.802230i
$779$	−1.82639	+	2.02841i	−0.0654370	+	0.0726752i
$780$	4.04508	−	7.00629i	0.144837	−	0.250866i
$781$	−1.24171	−	2.20854i	−0.0444320	−	0.0790278i
$782$	4.61803	+	7.99867i	0.165141	+	0.286032i
$783$	12.1353	+	37.3485i	0.433679	+	1.33473i
$784$	23.6944	−	24.3542i	0.846228	−	0.869794i
$785$	21.2812	−	15.4617i	0.759557	−	0.551850i
$786$	−10.0124	+	2.12820i	−0.357130	+	0.0759103i
$787$	−20.7430	−	23.0375i	−0.739410	−	0.821198i	0.249708	−	0.968321i	$-0.419665\pi$
$787$	−20.7430	−	23.0375i	−0.739410	−	0.821198i	−0.989118	+	0.147123i	$0.952999\pi$
$788$	−0.153880	−	1.46407i	−0.00548175	−	0.0521554i
$789$	−1.25434	+	11.9343i	−0.0446557	+	0.424871i
$790$	−14.2082	−	43.7284i	−0.505505	−	1.55579i
$791$	5.22542	+	1.81014i	0.185795	+	0.0643612i
$792$	−7.56231	+	12.7598i	−0.268715	+	0.453398i
$793$	−32.0344	−	55.4853i	−1.13758	−	1.97034i
$794$	−54.8982	−	11.6690i	−1.94826	−	0.414116i
$795$	12.4407	−	5.53895i	0.441226	−	0.196446i
$796$	12.1741	+	5.42027i	0.431500	+	0.192116i
$797$	−0.909830	+	2.80017i	−0.0322278	+	0.0991871i	−0.965877	−	0.259003i	$-0.916606\pi$
$797$	−0.909830	+	2.80017i	−0.0322278	+	0.0991871i	0.933649	+	0.358190i	$0.116606\pi$
$798$	−4.86781	−	0.606887i	−0.172319	−	0.0214836i
$799$	−1.23607	+	0.898056i	−0.0437289	+	0.0317709i
$800$		0			0
$801$	2.98895	+	0.635322i	0.105609	+	0.0224480i
$802$	14.5172	−	25.1446i	0.512621	−	0.887885i
$803$	−28.8804	−	21.4907i	−1.01917	−	0.758389i
$804$	5.18034			0.182697
$805$	8.93501	+	5.39135i	0.314918	+	0.190020i
$806$	33.5795	+	24.3970i	1.18279	+	0.859346i
$807$	18.0358	+	8.03006i	0.634890	+	0.282671i
$808$	22.5782	+	25.0757i	0.794300	+	0.882159i
$809$	−8.79632	−	9.76931i	−0.309262	−	0.343471i	0.568398	−	0.822754i	$-0.307563\pi$
$809$	−8.79632	−	9.76931i	−0.309262	−	0.343471i	−0.877660	+	0.479283i	$0.840897\pi$
$810$	3.30524	+	1.47159i	0.116134	+	0.0517063i
$811$	−31.5517	−	22.9236i	−1.10793	−	0.804957i	−0.125593	−	0.992082i	$-0.540083\pi$
$811$	−31.5517	−	22.9236i	−1.10793	−	0.804957i	−0.982336	+	0.187125i	$0.940083\pi$
$812$	10.9961	+	6.63497i	0.385886	+	0.232842i
$813$	15.1246			0.530443
$814$	−10.4535	+	30.9655i	−0.366394	+	1.08534i
$815$	−21.5066	+	37.2505i	−0.753343	+	1.30483i
$816$	15.3649	+	3.26592i	0.537881	+	0.114330i
$817$	−0.0174755	+	0.166268i	−0.000611391	+	0.00581700i
$818$	32.9615	−	23.9479i	1.15247	−	0.837320i
$819$	−30.7390	−	3.83235i	−1.07411	−	0.133913i
$820$	−1.01722	+	3.13068i	−0.0355229	+	0.109328i
$821$	−36.0911	−	16.0688i	−1.25959	−	0.560804i	−0.335159	−	0.942162i	$-0.608790\pi$
$821$	−36.0911	−	16.0688i	−1.25959	−	0.560804i	−0.924428	+	0.381358i	$0.875457\pi$
$822$	0.482228	−	0.214702i	0.0168196	−	0.00748858i
$823$	5.46158	+	1.16089i	0.190379	+	0.0404662i	0.302114	−	0.953272i	$-0.402308\pi$
$823$	5.46158	+	1.16089i	0.190379	+	0.0404662i	−0.111736	+	0.993738i	$0.535641\pi$
$824$	6.70820	+	11.6190i	0.233691	+	0.404765i
$825$		0			0
$826$	−39.2705	−	13.6037i	−1.36640	−	0.473333i
$827$	−3.91641	−	12.0535i	−0.136187	−	0.419140i	0.859586	−	0.510991i	$-0.170722\pi$
$827$	−3.91641	−	12.0535i	−0.136187	−	0.419140i	−0.995773	+	0.0918513i	$0.970722\pi$
$828$	−0.227908	+	2.16840i	−0.00792034	+	0.0753570i
$829$	1.06054	+	10.0903i	0.0368339	+	0.350451i	0.997381	+	0.0723324i	$0.0230442\pi$
$829$	1.06054	+	10.0903i	0.0368339	+	0.350451i	−0.960547	+	0.278119i	$0.910289\pi$
$830$	−21.7884	−	24.1985i	−0.756288	−	0.839943i
$831$	−0.692728	+	0.147244i	−0.0240305	+	0.00510783i
$832$	20.0623	−	14.5761i	0.695535	−	0.505336i
$833$	21.9591	+	5.56188i	0.760836	+	0.192708i
$834$	2.20820	+	6.79615i	0.0764638	+	0.235332i
$835$	16.7082	+	28.9395i	0.578211	+	1.00149i
$836$	1.59150	−	1.72748i	0.0550433	−	0.0597463i
$837$	10.9549	−	18.9745i	0.378657	−	0.655854i
$838$	25.0968	−	27.8728i	0.866955	−	0.962851i
$839$	31.0172	+	22.5353i	1.07083	+	0.778006i	0.976062	−	0.217493i	$-0.0697879\pi$
$839$	31.0172	+	22.5353i	1.07083	+	0.778006i	0.0947715	+	0.995499i	$0.469788\pi$
$840$	12.6579	−	3.84417i	0.436739	−	0.132636i
$841$	10.1008	−	31.0871i	0.348304	−	1.07197i
$842$	43.8531	−	9.32127i	1.51128	−	0.321232i
$843$	−0.486316	−	4.62699i	−0.0167496	−	0.159362i
$844$	−5.08142	+	2.26239i	−0.174910	+	0.0778748i
$845$	31.8254	−	35.3457i	1.09483	−	1.21593i
$846$	−1.52786			−0.0525290
$847$	10.7068	+	27.0622i	0.367892	+	0.929869i
$848$	−29.5623			−1.01517
$849$	−13.6612	+	15.1723i	−0.468853	+	0.520714i
$850$		0			0
$851$	−1.12291	−	10.6838i	−0.0384929	−	0.366236i
$852$	−0.461819	+	0.0981626i	−0.0158216	+	0.00336299i
$853$	11.6738	−	35.9281i	0.399702	−	1.23016i	−0.525537	−	0.850771i	$-0.676135\pi$
$853$	11.6738	−	35.9281i	0.399702	−	1.23016i	0.925239	−	0.379385i	$-0.123865\pi$
$854$	−10.6242	+	45.6310i	−0.363553	+	1.56146i
$855$	4.14590	+	3.01217i	0.141787	+	0.103014i
$856$	16.7283	−	18.5786i	0.571760	−	0.635004i
$857$	5.73607	−	9.93516i	0.195940	−	0.339379i	−0.751268	−	0.659997i	$-0.770557\pi$
$857$	5.73607	−	9.93516i	0.195940	−	0.339379i	0.947208	+	0.320619i	$0.103891\pi$
$858$	−21.2861	+	23.1049i	−0.726697	+	0.788787i
$859$	−4.14590	−	7.18091i	−0.141456	−	0.245009i	0.786589	−	0.617477i	$-0.211845\pi$
$859$	−4.14590	−	7.18091i	−0.141456	−	0.245009i	−0.928045	+	0.372468i	$0.878512\pi$
$860$	0.0623059	+	0.191758i	0.00212461	+	0.00653889i
$861$	−6.27912	+	0.537581i	−0.213992	+	0.0183207i
$862$	23.4164	−	17.0130i	0.797566	−	0.579466i
$863$	45.3476	−	9.63893i	1.54365	−	0.328113i	0.644104	−	0.764938i	$-0.277231\pi$
$863$	45.3476	−	9.63893i	1.54365	−	0.328113i	0.899546	+	0.436825i	$0.143897\pi$
$864$	11.3149	+	12.5665i	0.384940	+	0.427519i
$865$	2.46071	+	23.4121i	0.0836665	+	0.796034i
$866$	2.43826	−	23.1985i	0.0828553	−	0.788316i
$867$	−2.01722	−	6.20837i	−0.0685084	−	0.210847i
$868$	−1.35410	−	7.03612i	−0.0459612	−	0.238821i
$869$	3.92705	+	41.9650i	0.133216	+	1.42357i
$870$	14.2082	+	24.6093i	0.481703	+	0.834334i
$871$	47.9966	+	10.2020i	1.62630	+	0.345681i
$872$	0.298033	−	0.132693i	0.0100927	−	0.00449355i
$873$	7.04179	+	3.13521i	0.238329	+	0.106111i
$874$	−1.01064	+	3.11044i	−0.0341855	+	0.105212i
$875$	−17.8459	+	23.5908i	−0.603300	+	0.797514i
$876$	−5.42705	+	3.94298i	−0.183363	+	0.133221i
$877$	0.574219	−	5.46333i	0.0193900	−	0.184484i	−0.980540	−	0.196320i	$-0.937101\pi$
$877$	0.574219	−	5.46333i	0.0193900	−	0.184484i	0.999930	+	0.0118361i	$0.00376765\pi$
$878$	12.3760	+	2.63060i	0.417669	+	0.0887784i
$879$	6.23607	−	10.8012i	0.210337	−	0.364315i
$880$	−11.5143	+	34.1079i	−0.388147	+	1.14978i
$881$	0.652476			0.0219825			0.0109912	−	0.999940i	$-0.496501\pi$
$881$	0.652476			0.0219825			0.0109912	+	0.999940i	$0.496501\pi$
$882$	14.4961	+	17.4069i	0.488108	+	0.586120i
$883$	−26.1353	−	18.9884i	−0.879521	−	0.639010i	0.0536035	−	0.998562i	$-0.482929\pi$
$883$	−26.1353	−	18.9884i	−0.879521	−	0.639010i	−0.933125	+	0.359553i	$0.882929\pi$
$884$	−10.6960	−	4.76216i	−0.359745	−	0.160169i
$885$	−14.5256	−	16.1323i	−0.488273	−	0.542283i
$886$	15.4131	+	17.1179i	0.517812	+	0.575088i
$887$	−11.6919	−	5.20557i	−0.392575	−	0.174786i	0.200949	−	0.979602i	$-0.435597\pi$
$887$	−11.6919	−	5.20557i	−0.392575	−	0.174786i	−0.593525	+	0.804816i	$0.702264\pi$
$888$	−11.0172	−	8.00448i	−0.369714	−	0.268613i
$889$	0.0120623	−	0.624461i	0.000404556	−	0.0209437i
$890$	5.52786			0.185294
$891$	−2.66078	−	1.97996i	−0.0891396	−	0.0663311i
$892$	5.91641	−	10.2475i	0.198096	−	0.343112i
$893$	−0.529197	−	0.112484i	−0.0177089	−	0.00376414i
$894$	−3.46829	+	32.9986i	−0.115997	+	1.10364i
$895$	−37.0967	+	26.9524i	−1.24001	+	0.900918i
$896$	−35.7531	−	4.45747i	−1.19443	−	0.148914i
$897$	3.19098	−	9.82084i	0.106544	−	0.327908i
$898$	41.0392	+	18.2718i	1.36950	+	0.609739i
$899$	−31.4410	+	13.9984i	−1.04861	+	0.466873i
$900$		0			0
$901$	−9.85410	−	17.0678i	−0.328288	−	0.568611i
$902$	6.51722	−	10.9964i	0.217000	−	0.366140i
$903$	−0.291796	+	0.252703i	−0.00971037	+	0.00840942i
$904$	−1.44427	−	4.44501i	−0.0480358	−	0.147839i
$905$	4.95054	−	47.1012i	0.164561	−	1.56570i
$906$	0.781051	+	7.43120i	0.0259487	+	0.246885i
$907$	−34.7805	−	38.6277i	−1.15487	−	1.28261i	−0.952922	−	0.303216i	$-0.901940\pi$
$907$	−34.7805	−	38.6277i	−1.15487	−	1.28261i	−0.201947	−	0.979396i	$-0.564727\pi$
$908$	−4.48343	+	0.952982i	−0.148788	+	0.0316258i
$909$	−24.4164	+	17.7396i	−0.809841	+	0.588384i
$910$	−55.8337	+	4.78015i	−1.85087	+	0.158460i
$911$	−8.88197	−	27.3359i	−0.294273	−	0.905678i	−0.983465	−	0.181099i	$-0.942034\pi$
$911$	−8.88197	−	27.3359i	−0.294273	−	0.905678i	0.689192	−	0.724579i	$-0.257966\pi$
$912$	2.78115	+	4.81710i	0.0920932	+	0.159510i
$913$	14.6288	+	26.0192i	0.484144	+	0.861109i
$914$	−5.78115	+	10.0133i	−0.191224	+	0.331209i
$915$	−16.3751	+	18.1863i	−0.541343	+	0.601222i
$916$	−2.92705	−	2.12663i	−0.0967125	−	0.0702657i
$917$	12.2199	+	11.4378i	0.403536	+	0.377710i
$918$	−8.09017	+	24.8990i	−0.267015	+	0.821789i
$919$	−5.70535	+	1.21271i	−0.188202	+	0.0400036i	−0.301048	−	0.953609i	$-0.597337\pi$
$919$	−5.70535	+	1.21271i	−0.188202	+	0.0400036i	0.112846	+	0.993612i	$0.464003\pi$
$920$	−0.921906	−	8.77135i	−0.0303943	−	0.289183i
$921$	12.3389	−	5.49362i	0.406580	−	0.181021i
$922$	−8.56378	+	9.51105i	−0.282033	+	0.313230i
$923$	−4.47214			−0.147202
$924$	5.40839	−	0.400918i	0.177923	−	0.0131892i
$925$		0			0
$926$	−41.7878	+	46.4100i	−1.37323	+	1.52513i
$927$	−10.9625	+	4.88084i	−0.360057	+	0.160308i
$928$	−2.77652	−	26.4168i	−0.0911436	−	0.867174i
$929$	−10.5416	+	2.24068i	−0.345858	+	0.0735144i	−0.377566	−	0.925983i	$-0.623239\pi$
$929$	−10.5416	+	2.24068i	−0.345858	+	0.0735144i	0.0317077	+	0.999497i	$0.489905\pi$
$930$	4.89919	−	15.0781i	0.160651	−	0.494432i
$931$	3.73938	+	7.09634i	0.122553	+	0.232573i
$932$	1.54508	+	1.12257i	0.0506109	+	0.0367710i
$933$	−8.94004	+	9.92892i	−0.292684	+	0.325058i
$934$	2.04508	−	3.54219i	0.0669172	−	0.115904i
$935$	−23.5303	+	4.72152i	−0.769523	+	0.154410i
$936$	13.0902	+	22.6728i	0.427866	+	0.741085i
$937$	3.26393	+	10.0453i	0.106628	+	0.328167i	0.990109	−	0.140300i	$-0.0448066\pi$
$937$	3.26393	+	10.0453i	0.106628	+	0.328167i	−0.883481	+	0.468467i	$0.844807\pi$
$938$	−20.5266	−	29.4315i	−0.670218	−	0.960971i
$939$	−5.61803	+	4.08174i	−0.183338	+	0.133203i
$940$	−0.638218	+	0.135657i	−0.0208164	+	0.00442466i
$941$	−7.89465	−	8.76790i	−0.257358	−	0.285825i	0.600595	−	0.799554i	$-0.294931\pi$
$941$	−7.89465	−	8.76790i	−0.257358	−	0.285825i	−0.857953	+	0.513728i	$0.828264\pi$
$942$	1.98964	+	18.9302i	0.0648260	+	0.616778i
$943$	−0.439190	+	4.17861i	−0.0143020	+	0.136074i
$944$	14.5623	+	44.8182i	0.473963	+	1.45871i
$945$	5.59017	+	29.0474i	0.181848	+	0.944911i
$946$	−0.0729490	−	0.779543i	−0.00237178	−	0.0253451i
$947$	−14.4443	−	25.0182i	−0.469376	−	0.812983i	0.530011	−	0.847991i	$-0.322188\pi$
$947$	−14.4443	−	25.0182i	−0.469376	−	0.812983i	−0.999387	+	0.0350079i	$0.988854\pi$
$948$	7.68247	+	1.63296i	0.249515	+	0.0530361i
$949$	−58.0476	+	25.8445i	−1.88431	+	0.838947i
$950$		0			0
$951$	−0.118034	+	0.363271i	−0.00382751	+	0.0117799i
$952$	−7.44768	−	17.6368i	−0.241381	−	0.571612i
$953$	−1.10081	+	0.799788i	−0.0356588	+	0.0259077i	−0.605472	−	0.795867i	$-0.707016\pi$
$953$	−1.10081	+	0.799788i	−0.0356588	+	0.0259077i	0.569813	+	0.821774i	$0.307016\pi$
$954$	2.06007	−	19.6002i	0.0666972	−	0.634581i
$955$	−31.1372	−	6.61841i	−1.00758	−	0.214167i
$956$	−3.92705	+	6.80185i	−0.127010	+	0.219988i
$957$	−7.76637	−	24.8644i	−0.251051	−	0.803753i
$958$	−23.2705			−0.751836
$959$	−0.739031	−	0.445928i	−0.0238645	−	0.0143998i
$960$	−7.66312	−	5.56758i	−0.247326	−	0.179693i
$961$	−10.7784	−	4.79883i	−0.347689	−	0.154801i
$962$	38.6001	+	42.8697i	1.24452	+	1.38218i
$963$	14.9622	+	16.6172i	0.482151	+	0.535483i
$964$	−0.894100	−	0.398079i	−0.0287970	−	0.0128213i
$965$	32.8885	+	23.8949i	1.05872	+	0.769205i
$966$	−6.61127	+	3.64862i	−0.212714	+	0.117392i
$967$	7.97871			0.256578			0.128289	−	0.991737i	$-0.459051\pi$
$967$	7.97871			0.256578			0.128289	+	0.991737i	$0.459051\pi$
$968$	12.7813	−	21.0152i	0.410807	−	0.675453i
$969$	−1.85410	+	3.21140i	−0.0595623	+	0.103165i
$970$	13.6396	+	2.89918i	0.437940	+	0.0930870i
$971$	1.88151	−	17.9014i	0.0603806	−	0.574483i	−0.921947	−	0.387315i	$-0.873403\pi$
$971$	1.88151	−	17.9014i	0.0603806	−	0.574483i	0.982328	−	0.187168i	$-0.0599308\pi$
$972$	−8.00000	+	5.81234i	−0.256600	+	0.186431i
$973$	7.04939	−	9.31873i	0.225993	−	0.298745i
$974$	−4.23607	+	13.0373i	−0.135732	+	0.417741i
$975$		0			0
$976$	48.5317	−	21.6077i	1.55346	−	0.691646i
$977$	3.89177	+	0.827221i	0.124509	+	0.0264651i	0.269745	−	0.962932i	$-0.413061\pi$
$977$	3.89177	+	0.827221i	0.124509	+	0.0264651i	−0.145236	+	0.989397i	$0.546394\pi$
$978$	−15.5623	−	26.9547i	−0.497628	−	0.861916i
$979$	−4.94427	−	1.11006i	−0.158020	−	0.0354776i
$980$	7.60081	+	5.98409i	0.242799	+	0.191155i
$981$	0.0901699	+	0.277515i	0.00287890	+	0.00886036i
$982$	−2.10359	+	20.0144i	−0.0671284	+	0.638684i
$983$	1.19694	+	11.3881i	0.0381764	+	0.363225i	0.996887	+	0.0788415i	$0.0251221\pi$
$983$	1.19694	+	11.3881i	0.0381764	+	0.363225i	−0.958711	+	0.284383i	$0.908211\pi$
$984$	3.56395	+	3.95817i	0.113615	+	0.126182i
$985$	−5.20985	+	1.10739i	−0.166000	+	0.0352843i
$986$	33.2705	−	24.1724i	1.05955	−	0.769807i
$987$	−0.714580	−	1.02458i	−0.0227453	−	0.0326127i
$988$	−1.28115	−	3.94298i	−0.0407589	−	0.125443i
$989$	0.128677	+	0.222875i	0.00409169	+	0.00708702i
$990$	−21.8116	−	10.0110i	−0.693220	−	0.318170i
$991$	−3.01722	+	5.22598i	−0.0958452	+	0.166009i	−0.909961	−	0.414694i	$-0.863889\pi$
$991$	−3.01722	+	5.22598i	−0.0958452	+	0.166009i	0.814116	+	0.580702i	$0.197222\pi$
$992$	−9.91629	+	11.0132i	−0.314842	+	0.349668i
$993$	1.04508	+	0.759299i	0.0331648	+	0.0240956i
$994$	2.38761	+	2.23480i	0.0757305	+	0.0708837i
$995$	14.8992	−	45.8550i	0.472336	−	1.45370i
$996$	5.44076	−	1.15647i	0.172397	−	0.0366441i
$997$	−5.31348	−	50.5543i	−0.168279	−	1.60107i	−0.674238	−	0.738514i	$-0.735528\pi$
$997$	−5.31348	−	50.5543i	−0.168279	−	1.60107i	0.505958	−	0.862558i	$-0.331139\pi$
$998$	−5.29708	+	2.35841i	−0.167676	+	0.0746542i
$999$	20.3756	−	22.6294i	0.644655	−	0.715962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.m.a.60.1	yes	8
3.2	odd	2		693.2.by.a.676.1		8
7.2	even	3	inner	77.2.m.a.16.1	yes	8
7.3	odd	6		539.2.f.b.148.1		4
7.4	even	3		539.2.f.a.148.1		4
7.5	odd	6		539.2.q.a.324.1		8
7.6	odd	2		539.2.q.a.214.1		8
11.2	odd	10		847.2.n.b.130.1		8
11.3	even	5		847.2.e.a.606.1		4
11.4	even	5		847.2.n.c.487.1		8
11.5	even	5		847.2.n.c.81.1		8
11.6	odd	10		847.2.n.a.81.1		8
11.7	odd	10		847.2.n.a.487.1		8
11.8	odd	10		847.2.e.b.606.2		4
11.9	even	5	inner	77.2.m.a.53.1	yes	8
11.10	odd	2		847.2.n.b.753.1		8
21.2	odd	6		693.2.by.a.478.1		8
33.20	odd	10		693.2.by.a.361.1		8
77.2	odd	30		847.2.n.b.9.1		8
77.3	odd	30		5929.2.a.o.1.2		2
77.9	even	15	inner	77.2.m.a.9.1	✓	8
77.16	even	15		847.2.n.c.807.1		8
77.20	odd	10		539.2.q.a.361.1		8
77.25	even	15		5929.2.a.q.1.2		2
77.30	odd	30		847.2.e.b.485.2		4
77.31	odd	30		539.2.f.b.295.1		4
77.37	even	15		847.2.n.c.366.1		8
77.51	odd	30		847.2.n.a.366.1		8
77.52	even	30		5929.2.a.j.1.1		2
77.53	even	15		539.2.f.a.295.1		4
77.58	even	15		847.2.e.a.485.1		4
77.65	odd	6		847.2.n.b.632.1		8
77.72	odd	30		847.2.n.a.807.1		8
77.74	odd	30		5929.2.a.l.1.1		2
77.75	odd	30		539.2.q.a.471.1		8
231.86	odd	30		693.2.by.a.163.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.a.9.1	✓	8	77.9	even	15	inner
77.2.m.a.16.1	yes	8	7.2	even	3	inner
77.2.m.a.53.1	yes	8	11.9	even	5	inner
77.2.m.a.60.1	yes	8	1.1	even	1	trivial
539.2.f.a.148.1		4	7.4	even	3
539.2.f.a.295.1		4	77.53	even	15
539.2.f.b.148.1		4	7.3	odd	6
539.2.f.b.295.1		4	77.31	odd	30
539.2.q.a.214.1		8	7.6	odd	2
539.2.q.a.324.1		8	7.5	odd	6
539.2.q.a.361.1		8	77.20	odd	10
539.2.q.a.471.1		8	77.75	odd	30
693.2.by.a.163.1		8	231.86	odd	30
693.2.by.a.361.1		8	33.20	odd	10
693.2.by.a.478.1		8	21.2	odd	6
693.2.by.a.676.1		8	3.2	odd	2
847.2.e.a.485.1		4	77.58	even	15
847.2.e.a.606.1		4	11.3	even	5
847.2.e.b.485.2		4	77.30	odd	30
847.2.e.b.606.2		4	11.8	odd	10
847.2.n.a.81.1		8	11.6	odd	10
847.2.n.a.366.1		8	77.51	odd	30
847.2.n.a.487.1		8	11.7	odd	10
847.2.n.a.807.1		8	77.72	odd	30
847.2.n.b.9.1		8	77.2	odd	30
847.2.n.b.130.1		8	11.2	odd	10
847.2.n.b.632.1		8	77.65	odd	6
847.2.n.b.753.1		8	11.10	odd	2
847.2.n.c.81.1		8	11.5	even	5
847.2.n.c.366.1		8	77.37	even	15
847.2.n.c.487.1		8	11.4	even	5
847.2.n.c.807.1		8	77.16	even	15
5929.2.a.j.1.1		2	77.52	even	30
5929.2.a.l.1.1		2	77.74	odd	30
5929.2.a.o.1.2		2	77.3	odd	30
5929.2.a.q.1.2		2	77.25	even	15

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.08268 - 1.20243i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.0646021 - 0.614648i) q^{4} +(-2.18720 + 0.464905i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-2.53158 + 0.768834i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-1.33826 + 1.48629i) q^{9} +O(q^{10})\)	\(q+(1.08268 - 1.20243i) q^{2} +(0.913545 - 0.406737i) q^{3} +(-0.0646021 - 0.614648i) q^{4} +(-2.18720 + 0.464905i) q^{5} +(0.500000 - 1.53884i) q^{6} +(-2.53158 + 0.768834i) q^{7} +(1.80902 + 1.31433i) q^{8} +(-1.33826 + 1.48629i) q^{9} +(-1.80902 + 3.13331i) q^{10} +(2.24724 - 2.43925i) q^{11} +(-0.309017 - 0.535233i) q^{12} +(-1.80902 - 5.56758i) q^{13} +(-1.81641 + 3.87645i) q^{14} +(-1.80902 + 1.31433i) q^{15} +(4.74803 - 1.00922i) q^{16} +(2.16535 + 2.40487i) q^{17} +(0.338261 + 3.21834i) q^{18} +(-0.119779 + 1.13962i) q^{19} +(0.427051 + 1.31433i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-0.500000 - 5.34307i) q^{22} +(0.881966 + 1.52761i) q^{23} +(2.18720 + 0.464905i) q^{24} +(-8.65323 - 3.85266i) q^{26} +(-1.54508 + 4.75528i) q^{27} +(0.636108 + 1.50636i) q^{28} +(6.35410 - 4.61653i) q^{29} +(-0.378188 + 3.59821i) q^{30} +(-4.28621 - 0.911062i) q^{31} +(1.69098 - 2.92887i) q^{32} +(1.06082 - 3.14240i) q^{33} +5.23607 q^{34} +(5.17965 - 2.85854i) q^{35} +(1.00000 + 0.726543i) q^{36} +(-5.56365 - 2.47710i) q^{37} +(1.24064 + 1.37787i) q^{38} +(-3.91716 - 4.35045i) q^{39} +(-4.56773 - 2.03368i) q^{40} +(1.92705 + 1.40008i) q^{41} +(-0.0826761 + 4.28012i) q^{42} +0.145898 q^{43} +(-1.64445 - 1.22368i) q^{44} +(2.23607 - 3.87298i) q^{45} +(2.79173 + 0.593401i) q^{46} +(-0.0493516 + 0.469550i) q^{47} +(3.92705 - 2.85317i) q^{48} +(5.81779 - 3.89273i) q^{49} +(2.95630 + 1.31623i) q^{51} +(-3.30524 + 1.47159i) q^{52} +(-5.95709 - 1.26622i) q^{53} +(4.04508 + 7.00629i) q^{54} +(-3.78115 + 6.37988i) q^{55} +(-5.59017 - 1.93649i) q^{56} +(0.354102 + 1.08981i) q^{57} +(1.32837 - 12.6386i) q^{58} +(1.01478 + 9.65502i) q^{59} +(0.924716 + 1.02700i) q^{60} +(10.7051 - 2.27544i) q^{61} +(-5.73607 + 4.16750i) q^{62} +(2.24520 - 4.79156i) q^{63} +(1.30902 + 4.02874i) q^{64} +(6.54508 + 11.3364i) q^{65} +(-2.62999 - 4.67777i) q^{66} +(-4.19098 + 7.25900i) q^{67} +(1.33826 - 1.48629i) q^{68} +(1.42705 + 1.03681i) q^{69} +(2.17068 - 9.32306i) q^{70} +(0.236068 - 0.726543i) q^{71} +(-4.37441 + 0.929809i) q^{72} +(-1.13456 - 10.7946i) q^{73} +(-9.00217 + 4.00802i) q^{74} +0.708204 q^{76} +(-3.81369 + 7.90290i) q^{77} -9.47214 q^{78} +(-8.50345 + 9.44404i) q^{79} +(-9.91572 + 4.41476i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(3.76988 - 0.801313i) q^{82} +(-2.78115 + 8.55951i) q^{83} +(1.19381 + 1.11740i) q^{84} +(-5.85410 - 4.25325i) q^{85} +(0.157960 - 0.175433i) q^{86} +(3.92705 - 6.80185i) q^{87} +(7.27126 - 1.45903i) q^{88} +(-0.763932 - 1.32317i) q^{89} +(-2.23607 - 6.88191i) q^{90} +(8.86022 + 12.7039i) q^{91} +(0.881966 - 0.640786i) q^{92} +(-4.28621 + 0.911062i) q^{93} +(0.511170 + 0.567712i) q^{94} +(-0.267834 - 2.54827i) q^{95} +(0.353512 - 3.36344i) q^{96} +(-1.19098 - 3.66547i) q^{97} +(1.61803 - 11.2101i) q^{98} +(0.618034 + 6.60440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + q^{3} + 2 q^{4} - 5 q^{5} + 4 q^{6} - 5 q^{7} + 10 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} + 2 q^{12} - 10 q^{13} + 3 q^{14} - 10 q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 3 q^{19} - 10 q^{20} - 16 q^{21} - 4 q^{22} + 16 q^{23} + 5 q^{24} - 15 q^{26} + 10 q^{27} - 12 q^{28} + 24 q^{29} + 5 q^{30} + 8 q^{31} + 18 q^{32} - 11 q^{33} + 24 q^{34} - 5 q^{35} + 8 q^{36} - 13 q^{37} - 9 q^{38} + 5 q^{39} - 5 q^{40} + 2 q^{41} + 10 q^{42} + 28 q^{43} - 12 q^{44} + 8 q^{46} + 6 q^{47} + 18 q^{48} - 11 q^{49} + 6 q^{51} - 5 q^{52} - 12 q^{53} + 10 q^{54} + 10 q^{55} - 24 q^{57} - 21 q^{58} - 18 q^{59} + 5 q^{60} + 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} + 30 q^{65} + 2 q^{66} - 38 q^{67} + 2 q^{68} - 2 q^{69} + 20 q^{70} - 16 q^{71} - 10 q^{72} + 15 q^{73} - 14 q^{74} - 48 q^{76} - 4 q^{77} - 40 q^{78} + 9 q^{79} - 15 q^{80} + q^{81} + 7 q^{82} + 18 q^{83} + 2 q^{84} - 20 q^{85} - 7 q^{86} + 18 q^{87} - 5 q^{88} - 24 q^{89} + 50 q^{91} + 16 q^{92} + 8 q^{93} + 8 q^{94} + 15 q^{95} - 2 q^{96} - 14 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + q^3 + 2 * q^4 - 5 * q^5 + 4 * q^6 - 5 * q^7 + 10 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 + 2 * q^12 - 10 * q^13 + 3 * q^14 - 10 * q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 3 * q^19 - 10 * q^20 - 16 * q^21 - 4 * q^22 + 16 * q^23 + 5 * q^24 - 15 * q^26 + 10 * q^27 - 12 * q^28 + 24 * q^29 + 5 * q^30 + 8 * q^31 + 18 * q^32 - 11 * q^33 + 24 * q^34 - 5 * q^35 + 8 * q^36 - 13 * q^37 - 9 * q^38 + 5 * q^39 - 5 * q^40 + 2 * q^41 + 10 * q^42 + 28 * q^43 - 12 * q^44 + 8 * q^46 + 6 * q^47 + 18 * q^48 - 11 * q^49 + 6 * q^51 - 5 * q^52 - 12 * q^53 + 10 * q^54 + 10 * q^55 - 24 * q^57 - 21 * q^58 - 18 * q^59 + 5 * q^60 + 18 * q^61 - 28 * q^62 - 2 * q^63 + 6 * q^64 + 30 * q^65 + 2 * q^66 - 38 * q^67 + 2 * q^68 - 2 * q^69 + 20 * q^70 - 16 * q^71 - 10 * q^72 + 15 * q^73 - 14 * q^74 - 48 * q^76 - 4 * q^77 - 40 * q^78 + 9 * q^79 - 15 * q^80 + q^81 + 7 * q^82 + 18 * q^83 + 2 * q^84 - 20 * q^85 - 7 * q^86 + 18 * q^87 - 5 * q^88 - 24 * q^89 + 50 * q^91 + 16 * q^92 + 8 * q^93 + 8 * q^94 + 15 * q^95 - 2 * q^96 - 14 * q^97 + 4 * q^98 - 4 * q^99

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