LMFDB - Embedded newform 77.2.m.a.9.1

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			9.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	77.9
Dual form			77.2.m.a.60.1

$q$-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 $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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	0.992319	−	0.123704i	$-0.0394772\pi$
$2$	1.08268	+	1.20243i	0.765568	+	0.850249i	−0.226752	+	0.973953i	$0.572811\pi$
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i	0.653139	−	0.757238i	$-0.273452\pi$
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i	−0.125703	+	0.992068i	$0.540119\pi$
$4$	−0.0646021	+	0.614648i	−0.0323011	+	0.307324i
$5$	−2.18720	−	0.464905i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−2.18720	−	0.464905i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$6$	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	0.304467	+	0.952523i	$0.401522\pi$
$13$	−1.80902	+	5.56758i	−0.501731	+	1.54417i	−0.806198	+	0.591646i	$0.798478\pi$
$14$	−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	−0.420943	−	0.907087i	$-0.638301\pi$
$17$	2.16535	−	2.40487i	0.525175	−	0.583266i	0.946118	+	0.323821i	$0.104968\pi$
$18$	0.338261	−	3.21834i	0.0797289	−	0.758570i
$19$	−0.119779	−	1.13962i	−0.0274792	−	0.261447i	−0.999633	−	0.0271019i	$-0.991372\pi$
$19$	−0.119779	−	1.13962i	−0.0274792	−	0.261447i	0.972153	−	0.234345i	$-0.0752945\pi$
$20$	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	−0.759304	−	0.650737i	$-0.774460\pi$
$23$	0.881966	−	1.52761i	0.183903	−	0.318529i	0.943206	+	0.332208i	$0.107794\pi$
$24$	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	0.992163	−	0.124947i	$-0.0398761\pi$
$29$	6.35410	+	4.61653i	1.17993	+	0.857267i	0.187764	+	0.982214i	$0.439876\pi$
$30$	−0.378188	−	3.59821i	−0.0690473	−	0.656941i
$31$	−4.28621	+	0.911062i	−0.769826	+	0.163632i	−0.576050	−	0.817414i	$-0.695407\pi$
$31$	−4.28621	+	0.911062i	−0.769826	+	0.163632i	−0.193776	+	0.981046i	$0.562073\pi$
$32$	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	−0.809430	−	0.587216i	$-0.800224\pi$
$37$	−5.56365	+	2.47710i	−0.914658	+	0.407232i	−0.105228	+	0.994448i	$0.533557\pi$
$38$	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	−0.427051	−	0.904228i	$-0.640447\pi$
$41$	1.92705	−	1.40008i	0.300955	−	0.218656i	0.728006	+	0.685571i	$0.240447\pi$
$42$	−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	0.990333	−	0.138712i	$-0.0442962\pi$
$47$	−0.0493516	−	0.469550i	−0.00719868	−	0.0684908i	−0.997531	+	0.0702211i	$0.977630\pi$
$48$	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	−0.597985	−	0.801507i	$-0.704032\pi$
$53$	−5.95709	+	1.26622i	−0.818269	+	0.173928i	−0.220284	+	0.975436i	$0.570698\pi$
$54$	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	−0.704707	−	0.709499i	$-0.748921\pi$
$59$	1.01478	−	9.65502i	0.132114	−	1.25698i	0.836820	−	0.547478i	$-0.184412\pi$
$60$	0.924716	−	1.02700i	0.119380	−	0.132585i
$61$	10.7051	+	2.27544i	1.37065	+	0.291341i	0.833674	−	0.552257i	$-0.186233\pi$
$61$	10.7051	+	2.27544i	1.37065	+	0.291341i	0.536976	+	0.843598i	$0.319567\pi$
$62$	−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	−0.999903	−	0.0139240i	$-0.995568\pi$
$67$	−4.19098	−	7.25900i	−0.512010	−	0.886827i	0.487893	−	0.872903i	$-0.337766\pi$
$68$	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	0.964087	−	0.265587i	$-0.0855657\pi$
$71$	0.236068	+	0.726543i	0.0280161	+	0.0862247i	−0.936071	+	0.351812i	$0.885566\pi$
$72$	−4.37441	−	0.929809i	−0.515529	−	0.109579i
$73$	−1.13456	+	10.7946i	−0.132791	+	1.26342i	0.701731	+	0.712442i	$0.252411\pi$
$73$	−1.13456	+	10.7946i	−0.132791	+	1.26342i	−0.834522	+	0.550975i	$0.814256\pi$
$74$	−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	−0.997989	−	0.0633893i	$-0.979809\pi$
$79$	−8.50345	−	9.44404i	−0.956713	−	1.06254i	0.0412762	−	0.999148i	$-0.486858\pi$
$80$	−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	−0.979576	−	0.201075i	$-0.935557\pi$
$83$	−2.78115	−	8.55951i	−0.305271	−	0.939528i	0.674305	−	0.738453i	$-0.264443\pi$
$84$	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	−0.903670	−	0.428230i	$-0.859137\pi$
$89$	−0.763932	+	1.32317i	−0.0809766	+	0.140256i	0.822693	+	0.568486i	$0.192471\pi$
$90$	−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	−0.993137	−	0.116958i	$-0.962686\pi$
$97$	−1.19098	+	3.66547i	−0.120926	+	0.372172i	0.872211	+	0.489130i	$0.162686\pi$
$98$	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	0.597018	−	0.802228i	$-0.296352\pi$
$101$	14.7604	−	3.13742i	1.46872	−	0.312185i	0.871698	+	0.490043i	$0.163019\pi$
$102$	4.78339	+	2.12970i	0.473626	+	0.210872i
$103$	5.48127	−	2.44042i	0.540086	−	0.240462i	−0.118518	−	0.992952i	$-0.537814\pi$
$103$	5.48127	−	2.44042i	0.540086	−	0.240462i	0.658603	+	0.752490i	$0.271148\pi$
$104$	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	0.893274	+	0.449512i	$0.148402\pi$
$107$	1.16866	+	11.1191i	0.112979	+	1.07492i	−0.780295	+	0.625411i	$0.784931\pi$
$108$	3.02264	−	0.642482i	0.290854	−	0.0618229i
$109$	0.0729490	+	0.126351i	0.00698725	+	0.0121023i	0.869498	−	0.493937i	$-0.164443\pi$
$109$	0.0729490	+	0.126351i	0.00698725	+	0.0121023i	−0.862511	+	0.506039i	$0.831109\pi$
$110$	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	−0.664475	−	0.747311i	$-0.731345\pi$
$113$	−1.69098	+	1.22857i	−0.159074	+	0.115574i	0.505401	+	0.862885i	$0.331345\pi$
$114$	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	0.947768	−	0.318961i	$-0.103334\pi$
$127$	−0.0729490	−	0.224514i	−0.00647318	−	0.0199224i	−0.954241	+	0.299039i	$0.903334\pi$
$128$	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	−0.970478	−	0.241189i	$-0.922463\pi$
$131$	−3.16312	+	5.47868i	−0.276363	+	0.478675i	0.694115	+	0.719864i	$0.255796\pi$
$132$	−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	−0.733748	−	0.679422i	$-0.762230\pi$
$137$	0.218296	−	0.242442i	0.0186503	−	0.0207132i	0.752398	+	0.658709i	$0.228897\pi$
$138$	2.79173	+	0.593401i	0.237648	+	0.0505137i
$139$	−3.57295	−	2.59590i	−0.303054	−	0.220181i	0.425857	−	0.904791i	$-0.359973\pi$
$139$	−3.57295	−	2.59590i	−0.303054	−	0.220181i	−0.728910	+	0.684609i	$0.759973\pi$
$140$	−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	−0.708811	−	0.705399i	$-0.750768\pi$
$149$	−20.0585	−	4.26356i	−1.64325	−	0.349284i	−0.934442	+	0.356114i	$0.884101\pi$
$150$		0			0
$151$	−4.21878	−	1.87832i	−0.343320	−	0.152856i	0.227832	−	0.973701i	$-0.426836\pi$
$151$	−4.21878	−	1.87832i	−0.343320	−	0.152856i	−0.571151	+	0.820845i	$0.693503\pi$
$152$	−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	−0.0697118	−	0.997567i	$-0.522208\pi$
$157$	−10.7469	−	4.78482i	−0.857695	−	0.381870i	−0.787983	+	0.615697i	$0.788875\pi$
$158$	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	0.992798	+	0.119803i	$0.0382264\pi$
$163$	12.8714	+	14.2952i	1.00817	+	1.11969i	0.0153715	+	0.999882i	$0.495107\pi$
$164$	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	0.597278	+	0.802035i	$0.296249\pi$
$167$	−4.61803	+	14.2128i	−0.357354	+	1.09982i	−0.954632	+	0.297789i	$0.903751\pi$
$168$	−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	0.953237	+	0.302225i	$0.0977293\pi$
$173$	1.10046	+	10.4702i	0.0836665	+	0.796034i	−0.869570	+	0.493809i	$0.835604\pi$
$174$	−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	0.961400	−	0.275155i	$-0.0887292\pi$
$179$	18.7337	+	8.34078i	1.40022	+	0.623419i	0.438822	+	0.898574i	$0.355396\pi$
$180$	−2.52498	+	1.12419i	−0.188201	+	0.0837924i
$181$	−6.54508	−	20.1437i	−0.486492	−	1.49727i	−0.829808	−	0.558049i	$-0.811550\pi$
$181$	−6.54508	−	20.1437i	−0.486492	−	1.49727i	0.343315	−	0.939220i	$-0.388450\pi$
$182$	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	0.121875	−	0.992545i	$-0.461109\pi$
$191$	13.0053	−	5.79033i	0.941030	−	0.418974i	0.819155	+	0.573572i	$0.194443\pi$
$192$	2.83448	−	3.14801i	0.204561	−	0.227188i
$193$	−12.1650	+	13.5106i	−0.875657	+	0.972516i	−0.999805	−	0.0197477i	$-0.993714\pi$
$193$	−12.1650	+	13.5106i	−0.875657	+	0.972516i	0.124148	+	0.992264i	$0.460380\pi$
$194$	−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	−0.940639	−	0.339408i	$-0.889773\pi$
$199$	−10.7812	−	18.6735i	−0.764256	−	1.32373i	0.176384	−	0.984322i	$-0.443560\pi$
$200$		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	0.808537	+	0.588445i	$0.200260\pi$
$211$	−2.78115	+	8.55951i	−0.191462	+	0.589261i	−1.00000		0.000815813i	$0.999740\pi$
$212$	−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	0.0674984	−	0.997719i	$-0.478498\pi$
$223$	15.4894	−	11.2537i	1.03724	−	0.753602i	0.969746	+	0.244117i	$0.0784982\pi$
$224$	−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	0.938202	+	0.346087i	$0.112490\pi$
$227$	−0.775226	+	7.37578i	−0.0514535	+	0.489548i	−0.989656	+	0.143461i	$0.954177\pi$
$228$	0.646976	+	0.288052i	0.0428471	+	0.0190767i
$229$	3.91716	+	4.35045i	0.258853	+	0.287486i	0.858537	−	0.512751i	$-0.171374\pi$
$229$	3.91716	+	4.35045i	0.258853	+	0.287486i	−0.599684	+	0.800237i	$0.704707\pi$
$230$	−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	0.671597	−	0.740916i	$-0.265609\pi$
$233$	−2.06773	−	2.29644i	−0.135461	−	0.150445i	−0.807059	+	0.590471i	$0.798942\pi$
$234$	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	−0.868359	−	0.495937i	$-0.834825\pi$
$239$	−10.2812	+	7.46969i	−0.665032	+	0.483174i	0.203326	+	0.979111i	$0.434825\pi$
$240$	−7.26281	−	8.06617i	−0.468812	−	0.520669i
$241$	0.791796	+	1.37143i	0.0510041	+	0.0883416i	0.890400	−	0.455178i	$-0.150425\pi$
$241$	0.791796	+	1.37143i	0.0510041	+	0.0883416i	−0.839396	+	0.543520i	$0.817091\pi$
$242$	−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	−0.933405	−	0.358824i	$-0.883178\pi$
$251$	0.517221	−	1.59184i	0.0326467	−	0.100476i	0.966052	+	0.258347i	$0.0831779\pi$
$252$	−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	−0.717784	−	0.696266i	$-0.754844\pi$
$257$	−10.9116	+	4.85817i	−0.680649	+	0.303045i	0.0371350	+	0.999310i	$0.488177\pi$
$258$	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	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$	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	−0.190747	−	0.981639i	$-0.561091\pi$
$269$	13.2104	−	14.6716i	0.805453	−	0.894546i	0.996200	+	0.0870932i	$0.0277578\pi$
$270$	−12.1047	+	13.4436i	−0.736668	+	0.818152i
$271$	13.8170	−	6.15173i	0.839324	−	0.373691i	0.0583819	−	0.998294i	$-0.481406\pi$
$271$	13.8170	−	6.15173i	0.839324	−	0.373691i	0.780942	+	0.624603i	$0.214739\pi$
$272$	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	−0.228676	−	0.973503i	$-0.573440\pi$
$277$	−0.692728	+	0.147244i	−0.0416220	+	0.00884703i	0.187054	+	0.982350i	$0.440106\pi$
$278$	−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	0.984737	−	0.174047i	$-0.0556846\pi$
$281$	1.43769	+	4.42477i	0.0857656	+	0.263959i	−0.898972	+	0.438007i	$0.855685\pi$
$282$	0.697887	−	0.310719i	0.0415585	−	0.0185031i
$283$	−18.6513	−	8.30410i	−1.10871	−	0.493628i	−0.231061	−	0.972939i	$-0.574220\pi$
$283$	−18.6513	−	8.30410i	−1.10871	−	0.493628i	−0.877645	+	0.479312i	$0.840886\pi$
$284$	−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	0.842127	−	0.539279i	$-0.181303\pi$
$293$	10.0902	+	7.33094i	0.589474	+	0.428278i	−0.252653	+	0.967557i	$0.581303\pi$
$294$	−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	0.0303671	−	0.999539i	$-0.490332\pi$
$311$	−12.2056	−	5.43428i	−0.692115	−	0.308150i	−0.722483	+	0.691389i	$0.756999\pi$
$312$	−1.36830	+	13.0185i	−0.0774645	+	0.737025i
$313$	−6.79252	−	1.44380i	−0.383936	−	0.0816081i	0.0119003	−	0.999929i	$-0.496212\pi$
$313$	−6.79252	−	1.44380i	−0.383936	−	0.0816081i	−0.395836	+	0.918321i	$0.629545\pi$
$314$	−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	0.735925	−	0.677064i	$-0.236748\pi$
$317$	−0.255585	−	0.283856i	−0.0143551	−	0.0159429i	−0.750280	+	0.661121i	$0.770081\pi$
$318$	−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	−0.847729	−	0.530430i	$-0.822030\pi$
$331$	0.645898	−	1.11873i	0.0355018	−	0.0614909i	0.883230	+	0.468939i	$0.155364\pi$
$332$	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	0.214464	−	0.976732i	$-0.431199\pi$
$337$	−11.8992	−	8.64527i	−0.648190	−	0.470938i	−0.862654	+	0.505794i	$0.831199\pi$
$338$	−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	0.288916	−	0.957354i	$-0.406705\pi$
$347$	22.5552	−	25.0501i	1.21083	−	1.34476i	0.921910	−	0.387404i	$-0.126628\pi$
$348$	−4.43444	+	1.97434i	−0.237711	+	0.105836i
$349$	−24.0623	+	17.4823i	−1.28803	+	0.935805i	−0.999764	−	0.0217461i	$-0.993077\pi$
$349$	−24.0623	+	17.4823i	−1.28803	+	0.935805i	−0.288262	+	0.957552i	$0.593077\pi$
$350$		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	0.800363	−	0.599515i	$-0.204640\pi$
$353$	−2.23607	−	3.87298i	−0.119014	−	0.206138i	−0.919377	+	0.393377i	$0.871307\pi$
$354$	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	−0.619059	−	0.785345i	$-0.712486\pi$
$359$	−8.51994	+	3.79332i	−0.449665	+	0.200204i	0.169394	+	0.985548i	$0.445819\pi$
$360$	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	0.624182	+	0.781279i	$0.285432\pi$
$367$	−2.85054	+	27.1211i	−0.148797	+	1.41571i	−0.772979	+	0.634432i	$0.781234\pi$
$368$	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	−0.380193	−	0.924907i	$-0.624142\pi$
$373$	11.7984	−	20.4354i	0.610897	−	1.05810i	0.991090	−	0.133197i	$-0.0425242\pi$
$374$	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	0.961810	+	0.273719i	$0.0882538\pi$
$379$	6.70820	+	20.6457i	0.344577	+	1.06050i	−0.617232	+	0.786781i	$0.711746\pi$
$380$	−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	0.214317	−	0.976764i	$-0.431247\pi$
$383$	−15.2551	−	16.9425i	−0.779499	−	0.865721i	−0.993816	+	0.111043i	$0.964581\pi$
$384$	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	−0.735903	−	0.677087i	$-0.763242\pi$
$389$	2.45933	−	23.3990i	0.124693	−	1.18638i	0.860596	−	0.509288i	$-0.170091\pi$
$390$	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	−0.00890435	+	0.999960i	$0.502834\pi$
$397$	−17.3435	+	30.0398i	−0.870443	+	1.50765i	−0.861539	+	0.507692i	$0.830499\pi$
$398$	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	0.624131	−	0.781319i	$-0.285453\pi$
$401$	17.5521	+	3.73082i	0.876512	+	0.186308i	0.252381	+	0.967628i	$0.418786\pi$
$402$	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	0.446231	−	0.894918i	$-0.352766\pi$
$409$	24.6301	−	5.23529i	1.21788	−	0.258868i	0.771648	+	0.636049i	$0.219433\pi$
$410$	−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	0.112688	−	0.993630i	$-0.464054\pi$
$421$	22.4164	−	16.2865i	1.09251	−	0.793754i	0.979821	+	0.199876i	$0.0640540\pi$
$422$	−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	0.233789	−	0.972287i	$-0.424887\pi$
$431$	17.4976	−	3.71924i	0.842831	−	0.179149i	0.609042	+	0.793138i	$0.291554\pi$
$432$	−2.53696	−	24.1376i	−0.122060	−	1.16132i
$433$	11.6631	+	8.47375i	0.560494	+	0.407223i	0.831640	−	0.555316i	$-0.187403\pi$
$433$	11.6631	+	8.47375i	0.560494	+	0.407223i	−0.271146	+	0.962538i	$0.587403\pi$
$434$	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	−0.757511	−	0.652823i	$-0.773585\pi$
$439$	3.90983	−	6.77202i	0.186606	−	0.323211i	0.944117	+	0.329612i	$0.106918\pi$
$440$	−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	−0.971274	−	0.237966i	$-0.923519\pi$
$443$	−1.48807	−	14.1581i	−0.0707005	−	0.672671i	0.900573	−	0.434705i	$-0.143147\pi$
$444$	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	−0.516092	−	0.856533i	$-0.672614\pi$
$449$	8.57953	−	26.4051i	0.404893	−	1.24613i	0.920985	−	0.389599i	$-0.127386\pi$
$450$		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	0.0415040	−	0.999138i	$-0.486785\pi$
$457$	−6.98974	−	1.48572i	−0.326966	−	0.0694989i	−0.368470	+	0.929639i	$0.620118\pi$
$458$	−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	0.264765	−	0.964313i	$-0.414705\pi$
$467$	2.47262	+	0.525572i	0.114419	+	0.0243206i	−0.150346	+	0.988633i	$0.548039\pi$
$468$	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	−0.921739	−	0.387811i	$-0.873231\pi$
$479$	−9.62341	+	10.6879i	−0.439705	+	0.488342i	0.482034	+	0.876152i	$0.339898\pi$
$480$	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	0.223814	−	0.974632i	$-0.428149\pi$
$487$	−7.73968	−	3.44593i	−0.350718	−	0.156150i	−0.574532	+	0.818482i	$0.694816\pi$
$488$	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	0.337109	−	0.941466i	$-0.390551\pi$
$491$	−10.0623	−	7.31069i	−0.454106	−	0.329927i	−0.791215	+	0.611539i	$0.790551\pi$
$492$	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	−0.478703	−	0.877977i	$-0.658893\pi$
$499$	−3.27377	+	1.45758i	−0.146554	+	0.0652502i	0.332149	+	0.943227i	$0.392226\pi$
$500$	−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	0.0442222	−	0.999022i	$-0.485919\pi$
$503$	22.6074	−	16.4252i	1.00801	−	0.732365i	0.963792	+	0.266657i	$0.0859190\pi$
$504$	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	0.993877	−	0.110489i	$-0.0352416\pi$
$509$	−0.0282760	−	0.269028i	−0.00125331	−	0.0119245i	−0.995131	+	0.0985644i	$0.968575\pi$
$510$	−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	0.161475	+	0.986877i	$0.448375\pi$
$521$	−4.60285	+	43.7932i	−0.201655	+	1.91862i	−0.363129	+	0.931739i	$0.618292\pi$
$522$	17.0069	−	18.8881i	0.744372	−	0.826708i
$523$	24.2020	+	5.14429i	1.05828	+	0.224944i	0.704003	−	0.710197i	$-0.251394\pi$
$523$	24.2020	+	5.14429i	1.05828	+	0.224944i	0.354275	+	0.935141i	$0.384728\pi$
$524$	−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	0.955867	−	0.293799i	$-0.0949196\pi$
$541$	13.1128	+	14.5632i	0.563763	+	0.626122i	−0.392105	+	0.919921i	$0.628253\pi$
$542$	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	0.220411	−	0.975407i	$-0.429260\pi$
$547$	28.4443	−	20.6660i	1.21619	−	0.883613i	0.995778	+	0.0917938i	$0.0292601\pi$
$548$	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	0.920523	+	0.390689i	$0.127763\pi$
$557$	−1.44232	+	13.7228i	−0.0611132	+	0.581453i	−0.981636	+	0.190764i	$0.938903\pi$
$558$	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	−0.280053	−	0.959985i	$-0.590352\pi$
$563$	−3.45077	+	0.733484i	−0.145433	+	0.0309127i	0.134620	+	0.990897i	$0.457019\pi$
$564$	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	0.990742	+	0.135761i	$0.0433481\pi$
$569$	1.18974	+	11.3196i	0.0498765	+	0.474543i	−0.940865	+	0.338781i	$0.889985\pi$
$570$	−4.05530	+	0.861981i	−0.169858	+	0.0361044i
$571$	3.78115	+	6.54915i	0.158236	+	0.274073i	0.934233	−	0.356664i	$-0.116086\pi$
$571$	3.78115	+	6.54915i	0.158236	+	0.274073i	−0.775996	+	0.630737i	$0.782753\pi$
$572$	−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	−0.997536	−	0.0701539i	$-0.977651\pi$
$577$	−19.7810	+	21.9691i	−0.823496	+	0.914585i	0.174041	+	0.984738i	$0.444318\pi$
$578$	−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	−0.999872	−	0.0159972i	$-0.994908\pi$
$587$	−32.0795	−	23.3071i	−1.32406	−	0.961989i	−0.324192	−	0.945991i	$-0.605092\pi$
$588$	−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	−0.583050	−	0.812436i	$-0.698141\pi$
$593$	10.0344	−	17.3802i	0.412065	−	0.713718i	0.995115	+	0.0987183i	$0.0314743\pi$
$594$	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	−0.615767	−	0.787928i	$-0.711154\pi$
$599$	5.68321	−	6.31184i	0.232210	−	0.257895i	0.847977	+	0.530033i	$0.177821\pi$
$600$		0			0
$601$	15.4894	+	11.2537i	0.631824	+	0.459047i	0.857032	−	0.515264i	$-0.172306\pi$
$601$	15.4894	+	11.2537i	0.631824	+	0.459047i	−0.225208	+	0.974311i	$0.572306\pi$
$602$	−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	0.651952	−	0.758260i	$-0.273950\pi$
$607$	−4.19579	−	4.65990i	−0.170302	−	0.189139i	−0.822254	+	0.569121i	$0.807284\pi$
$608$	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	0.523619	−	0.851953i	$-0.324582\pi$
$613$	5.96350	+	2.65512i	0.240864	+	0.107239i	−0.282755	+	0.959192i	$0.591248\pi$
$614$	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	0.997847	+	0.0655805i	$0.0208899\pi$
$619$	42.6506	+	18.9893i	1.71427	+	0.763244i	0.716426	+	0.697663i	$0.245777\pi$
$620$	−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	0.598582	−	0.801061i	$-0.295731\pi$
$631$	0.545085	+	0.396027i	0.0216995	+	0.0157656i	−0.576883	+	0.816827i	$0.695731\pi$
$632$	−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	−0.220067	−	0.975485i	$-0.570628\pi$
$641$	−27.6535	−	12.3121i	−1.09225	−	0.486300i	−0.872180	+	0.489185i	$0.837294\pi$
$642$	−16.5262	+	7.35793i	−0.652237	+	0.290395i
$643$	−5.87132	−	18.0701i	−0.231542	−	0.712614i	−0.997561	−	0.0697961i	$-0.977765\pi$
$643$	−5.87132	−	18.0701i	−0.231542	−	0.712614i	0.766019	−	0.642818i	$-0.222235\pi$
$644$	−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	−0.0760124	−	0.997107i	$-0.524219\pi$
$647$	6.61612	−	1.40630i	0.260107	−	0.0552874i	0.336119	+	0.941819i	$0.390886\pi$
$648$	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	0.644273	−	0.764796i	$-0.277160\pi$
$653$	42.0036	−	18.7012i	1.64373	−	0.731836i	0.999457	+	0.0329600i	$0.0104934\pi$
$654$	−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	0.770676	−	0.637228i	$-0.219919\pi$
$661$	−4.28115	−	7.41517i	−0.166518	−	0.288417i	−0.937193	+	0.348811i	$0.886586\pi$
$662$	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	−0.895676	−	0.444708i	$-0.853308\pi$
$673$	2.34346	−	7.21242i	0.0903337	−	0.278019i	0.986010	+	0.166689i	$0.0533076\pi$
$674$	−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	0.745948	−	0.666004i	$-0.231997\pi$
$677$	30.0917	+	6.39618i	1.15652	+	0.245825i	0.410569	+	0.911830i	$0.365330\pi$
$678$	−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	−0.993327	−	0.115329i	$-0.963208\pi$
$683$	−15.5902	−	27.0030i	−0.596541	−	1.03324i	0.396786	−	0.917911i	$-0.370125\pi$
$684$	−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	−0.982544	−	0.186030i	$-0.940438\pi$
$691$	−27.9916	−	31.0878i	−1.06485	−	1.18264i	−0.0823073	−	0.996607i	$-0.526229\pi$
$692$	−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	−0.903965	−	0.427606i	$-0.859357\pi$
$701$	−20.5623	+	14.9394i	−0.776628	+	0.564253i	0.127337	+	0.991859i	$0.459357\pi$
$702$	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	0.182458	−	0.983214i	$-0.441595\pi$
$709$	−1.35177	−	0.287327i	−0.0507667	−	0.0107908i	−0.233225	+	0.972423i	$0.574928\pi$
$710$	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	−0.316589	−	0.948563i	$-0.602538\pi$
$719$	4.73248	−	2.10703i	0.176492	−	0.0785791i	0.493080	+	0.869984i	$0.335871\pi$
$720$	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	−0.880607	−	0.473848i	$-0.842865\pi$
$733$	−30.2608	+	13.4730i	−1.11771	+	0.497636i	−0.237103	+	0.971485i	$0.576198\pi$
$734$	−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	−0.389311	−	0.921106i	$-0.627287\pi$
$739$	−10.0669	+	2.13978i	−0.370317	+	0.0787133i	0.0189943	+	0.999820i	$0.493954\pi$
$740$	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	−0.866589	−	0.499022i	$-0.833693\pi$
$743$	−12.5066	−	38.4913i	−0.458822	−	1.41211i	0.407767	−	0.913086i	$-0.366307\pi$
$744$	−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	0.999737	+	0.0229533i	$0.00730689\pi$
$751$	0.729474	+	6.94048i	0.0266189	+	0.253262i	−0.973118	+	0.230309i	$0.926026\pi$
$752$	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	−0.790413	−	0.612575i	$-0.790134\pi$
$757$	5.75329	−	17.7068i	0.209107	−	0.643565i	0.999520	−	0.0309902i	$-0.00986606\pi$
$758$	−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	0.151775	−	0.988415i	$-0.451501\pi$
$761$	−23.3680	−	25.9528i	−0.847091	−	0.940790i	−0.998865	+	0.0476256i	$0.984835\pi$
$762$	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	0.00394332	−	0.999992i	$-0.498745\pi$
$773$	−20.4784	−	9.11757i	−0.736557	−	0.327936i	−0.740500	+	0.672056i	$0.765411\pi$
$774$	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	−0.989118	−	0.147123i	$-0.952999\pi$
$787$	−20.7430	+	23.0375i	−0.739410	+	0.821198i	0.249708	+	0.968321i	$0.419665\pi$
$788$	−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	0.933649	−	0.358190i	$-0.116606\pi$
$797$	−0.909830	−	2.80017i	−0.0322278	−	0.0991871i	−0.965877	+	0.259003i	$0.916606\pi$
$798$	−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	−0.877660	−	0.479283i	$-0.840897\pi$
$809$	−8.79632	+	9.76931i	−0.309262	+	0.343471i	0.568398	+	0.822754i	$0.307563\pi$
$810$	3.30524	−	1.47159i	0.116134	−	0.0517063i
$811$	−31.5517	+	22.9236i	−1.10793	+	0.804957i	−0.982336	−	0.187125i	$-0.940083\pi$
$811$	−31.5517	+	22.9236i	−1.10793	+	0.804957i	−0.125593	+	0.992082i	$0.540083\pi$
$812$	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	−0.924428	−	0.381358i	$-0.875457\pi$
$821$	−36.0911	+	16.0688i	−1.25959	+	0.560804i	−0.335159	+	0.942162i	$0.608790\pi$
$822$	0.482228	+	0.214702i	0.0168196	+	0.00748858i
$823$	5.46158	−	1.16089i	0.190379	−	0.0404662i	−0.111736	−	0.993738i	$-0.535641\pi$
$823$	5.46158	−	1.16089i	0.190379	−	0.0404662i	0.302114	+	0.953272i	$0.402308\pi$
$824$	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	−0.995773	−	0.0918513i	$-0.970722\pi$
$827$	−3.91641	+	12.0535i	−0.136187	+	0.419140i	0.859586	+	0.510991i	$0.170722\pi$
$828$	−0.227908	−	2.16840i	−0.00792034	−	0.0753570i
$829$	1.06054	−	10.0903i	0.0368339	−	0.350451i	−0.960547	−	0.278119i	$-0.910289\pi$
$829$	1.06054	−	10.0903i	0.0368339	−	0.350451i	0.997381	−	0.0723324i	$-0.0230442\pi$
$830$	−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	0.0947715	−	0.995499i	$-0.469788\pi$
$839$	31.0172	−	22.5353i	1.07083	−	0.778006i	0.976062	+	0.217493i	$0.0697879\pi$
$840$	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	0.925239	+	0.379385i	$0.123865\pi$
$853$	11.6738	+	35.9281i	0.399702	+	1.23016i	−0.525537	+	0.850771i	$0.676135\pi$
$854$	−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	0.947208	−	0.320619i	$-0.103891\pi$
$857$	5.73607	+	9.93516i	0.195940	+	0.339379i	−0.751268	+	0.659997i	$0.770557\pi$
$858$	−21.2861	−	23.1049i	−0.726697	−	0.788787i
$859$	−4.14590	+	7.18091i	−0.141456	+	0.245009i	−0.928045	−	0.372468i	$-0.878512\pi$
$859$	−4.14590	+	7.18091i	−0.141456	+	0.245009i	0.786589	+	0.617477i	$0.211845\pi$
$860$	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	0.899546	−	0.436825i	$-0.143897\pi$
$863$	45.3476	+	9.63893i	1.54365	+	0.328113i	0.644104	+	0.764938i	$0.277231\pi$
$864$	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	0.999930	−	0.0118361i	$-0.00376765\pi$
$877$	0.574219	+	5.46333i	0.0193900	+	0.184484i	−0.980540	+	0.196320i	$0.937101\pi$
$878$	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	−0.933125	−	0.359553i	$-0.882929\pi$
$883$	−26.1353	+	18.9884i	−0.879521	+	0.639010i	0.0536035	+	0.998562i	$0.482929\pi$
$884$	−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	−0.593525	−	0.804816i	$-0.702264\pi$
$887$	−11.6919	+	5.20557i	−0.392575	+	0.174786i	0.200949	+	0.979602i	$0.435597\pi$
$888$	−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	−0.201947	+	0.979396i	$0.564727\pi$
$907$	−34.7805	+	38.6277i	−1.15487	+	1.28261i	−0.952922	+	0.303216i	$0.901940\pi$
$908$	−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	0.689192	+	0.724579i	$0.257966\pi$
$911$	−8.88197	+	27.3359i	−0.294273	+	0.905678i	−0.983465	+	0.181099i	$0.942034\pi$
$912$	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	0.112846	−	0.993612i	$-0.464003\pi$
$919$	−5.70535	−	1.21271i	−0.188202	−	0.0400036i	−0.301048	+	0.953609i	$0.597337\pi$
$920$	−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	0.0317077	−	0.999497i	$-0.489905\pi$
$929$	−10.5416	−	2.24068i	−0.345858	−	0.0735144i	−0.377566	+	0.925983i	$0.623239\pi$
$930$	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	−0.883481	−	0.468467i	$-0.844807\pi$
$937$	3.26393	−	10.0453i	0.106628	−	0.328167i	0.990109	+	0.140300i	$0.0448066\pi$
$938$	−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	−0.857953	−	0.513728i	$-0.828264\pi$
$941$	−7.89465	+	8.76790i	−0.257358	+	0.285825i	0.600595	+	0.799554i	$0.294931\pi$
$942$	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	−0.999387	−	0.0350079i	$-0.988854\pi$
$947$	−14.4443	+	25.0182i	−0.469376	+	0.812983i	0.530011	+	0.847991i	$0.322188\pi$
$948$	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	0.569813	−	0.821774i	$-0.307016\pi$
$953$	−1.10081	−	0.799788i	−0.0356588	−	0.0259077i	−0.605472	+	0.795867i	$0.707016\pi$
$954$	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	0.982328	+	0.187168i	$0.0599308\pi$
$971$	1.88151	+	17.9014i	0.0603806	+	0.574483i	−0.921947	+	0.387315i	$0.873403\pi$
$972$	−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	−0.145236	−	0.989397i	$-0.546394\pi$
$977$	3.89177	−	0.827221i	0.124509	−	0.0264651i	0.269745	+	0.962932i	$0.413061\pi$
$978$	−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	−0.958711	−	0.284383i	$-0.908211\pi$
$983$	1.19694	−	11.3881i	0.0381764	−	0.363225i	0.996887	−	0.0788415i	$-0.0251221\pi$
$984$	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	0.814116	−	0.580702i	$-0.197222\pi$
$991$	−3.01722	−	5.22598i	−0.0958452	−	0.166009i	−0.909961	+	0.414694i	$0.863889\pi$
$992$	−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	0.505958	+	0.862558i	$0.331139\pi$
$997$	−5.31348	+	50.5543i	−0.168279	+	1.60107i	−0.674238	+	0.738514i	$0.735528\pi$
$998$	−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.9.1	✓	8
3.2	odd	2		693.2.by.a.163.1		8
7.2	even	3		539.2.f.a.295.1		4
7.3	odd	6		539.2.q.a.361.1		8
7.4	even	3	inner	77.2.m.a.53.1	yes	8
7.5	odd	6		539.2.f.b.295.1		4
7.6	odd	2		539.2.q.a.471.1		8
11.2	odd	10		847.2.n.a.366.1		8
11.3	even	5		847.2.n.c.807.1		8
11.4	even	5		847.2.e.a.485.1		4
11.5	even	5	inner	77.2.m.a.16.1	yes	8
11.6	odd	10		847.2.n.b.632.1		8
11.7	odd	10		847.2.e.b.485.2		4
11.8	odd	10		847.2.n.a.807.1		8
11.9	even	5		847.2.n.c.366.1		8
11.10	odd	2		847.2.n.b.9.1		8
21.11	odd	6		693.2.by.a.361.1		8
33.5	odd	10		693.2.by.a.478.1		8
77.4	even	15		847.2.e.a.606.1		4
77.5	odd	30		539.2.f.b.148.1		4
77.16	even	15		539.2.f.a.148.1		4
77.18	odd	30		847.2.e.b.606.2		4
77.25	even	15		847.2.n.c.81.1		8
77.26	odd	30		5929.2.a.o.1.2		2
77.27	odd	10		539.2.q.a.324.1		8
77.32	odd	6		847.2.n.b.130.1		8
77.37	even	15		5929.2.a.q.1.2		2
77.38	odd	30		539.2.q.a.214.1		8
77.39	odd	30		847.2.n.b.753.1		8
77.40	even	30		5929.2.a.j.1.1		2
77.46	odd	30		847.2.n.a.487.1		8
77.51	odd	30		5929.2.a.l.1.1		2
77.53	even	15		847.2.n.c.487.1		8
77.60	even	15	inner	77.2.m.a.60.1	yes	8
77.74	odd	30		847.2.n.a.81.1		8
231.137	odd	30		693.2.by.a.676.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.a.9.1	✓	8	1.1	even	1	trivial
77.2.m.a.16.1	yes	8	11.5	even	5	inner
77.2.m.a.53.1	yes	8	7.4	even	3	inner
77.2.m.a.60.1	yes	8	77.60	even	15	inner
539.2.f.a.148.1		4	77.16	even	15
539.2.f.a.295.1		4	7.2	even	3
539.2.f.b.148.1		4	77.5	odd	30
539.2.f.b.295.1		4	7.5	odd	6
539.2.q.a.214.1		8	77.38	odd	30
539.2.q.a.324.1		8	77.27	odd	10
539.2.q.a.361.1		8	7.3	odd	6
539.2.q.a.471.1		8	7.6	odd	2
693.2.by.a.163.1		8	3.2	odd	2
693.2.by.a.361.1		8	21.11	odd	6
693.2.by.a.478.1		8	33.5	odd	10
693.2.by.a.676.1		8	231.137	odd	30
847.2.e.a.485.1		4	11.4	even	5
847.2.e.a.606.1		4	77.4	even	15
847.2.e.b.485.2		4	11.7	odd	10
847.2.e.b.606.2		4	77.18	odd	30
847.2.n.a.81.1		8	77.74	odd	30
847.2.n.a.366.1		8	11.2	odd	10
847.2.n.a.487.1		8	77.46	odd	30
847.2.n.a.807.1		8	11.8	odd	10
847.2.n.b.9.1		8	11.10	odd	2
847.2.n.b.130.1		8	77.32	odd	6
847.2.n.b.632.1		8	11.6	odd	10
847.2.n.b.753.1		8	77.39	odd	30
847.2.n.c.81.1		8	77.25	even	15
847.2.n.c.366.1		8	11.9	even	5
847.2.n.c.487.1		8	77.53	even	15
847.2.n.c.807.1		8	11.3	even	5
5929.2.a.j.1.1		2	77.40	even	30
5929.2.a.l.1.1		2	77.51	odd	30
5929.2.a.o.1.2		2	77.26	odd	30
5929.2.a.q.1.2		2	77.37	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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