LMFDB - Embedded newform 92.2.h.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [92,2,Mod(7,92)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(92, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 19]))

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

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

chi := DirichletCharacter("92.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 92 = 2^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	92.h (of order $22$, degree $10$, 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:	$0.734623698596$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	92.11
Dual form			92.2.h.a.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.665666 - 1.24775i) q^{2} +(-0.837775 - 0.120454i) q^{3} +(-1.11378 + 1.66117i) q^{4} +(-0.870000 - 2.96295i) q^{5} +(0.407382 + 1.12552i) q^{6} +(-2.18927 - 2.52655i) q^{7} +(2.81414 + 0.283931i) q^{8} +(-2.19112 - 0.643371i) q^{9} +O(q^{10})$	\(q+(-0.665666 - 1.24775i) q^{2} +(-0.837775 - 0.120454i) q^{3} +(-1.11378 + 1.66117i) q^{4} +(-0.870000 - 2.96295i) q^{5} +(0.407382 + 1.12552i) q^{6} +(-2.18927 - 2.52655i) q^{7} +(2.81414 + 0.283931i) q^{8} +(-2.19112 - 0.643371i) q^{9} +(-3.11790 + 3.05788i) q^{10} +(3.72075 + 2.39118i) q^{11} +(1.13319 - 1.25753i) q^{12} +(-0.434836 + 0.501827i) q^{13} +(-1.69519 + 4.41351i) q^{14} +(0.371966 + 2.58708i) q^{15} +(-1.51900 - 3.70036i) q^{16} +(6.40622 - 2.92562i) q^{17} +(0.655787 + 3.16225i) q^{18} +(0.0351299 - 0.0769237i) q^{19} +(5.89096 + 1.85484i) q^{20} +(1.52978 + 2.38039i) q^{21} +(0.506826 - 6.23430i) q^{22} +(-1.16466 - 4.65227i) q^{23} +(-2.32342 - 0.576844i) q^{24} +(-3.81588 + 2.45232i) q^{25} +(0.915612 + 0.208518i) q^{26} +(4.06788 + 1.85774i) q^{27} +(6.63541 - 0.822745i) q^{28} +(0.868147 + 1.90098i) q^{29} +(2.98043 - 2.18625i) q^{30} +(1.07262 - 0.154220i) q^{31} +(-3.60598 + 4.35854i) q^{32} +(-2.82912 - 2.45145i) q^{33} +(-7.91486 - 6.04589i) q^{34} +(-5.58138 + 8.68480i) q^{35} +(3.50917 - 2.92326i) q^{36} +(-1.64073 + 5.58781i) q^{37} +(-0.119367 + 0.00737210i) q^{38} +(0.424742 - 0.368041i) q^{39} +(-1.60703 - 8.58517i) q^{40} +(-4.26295 + 1.25171i) q^{41} +(1.95182 - 3.49334i) q^{42} +(0.102673 - 0.714109i) q^{43} +(-8.11625 + 3.51757i) q^{44} +7.05190i q^{45} +(-5.02961 + 4.55006i) q^{46} -9.98624i q^{47} +(0.826861 + 3.28304i) q^{48} +(-0.594362 + 4.13388i) q^{49} +(5.60000 + 3.12886i) q^{50} +(-5.71938 + 1.67936i) q^{51} +(-0.349312 - 1.28126i) q^{52} +(4.68049 - 4.05566i) q^{53} +(-0.389851 - 6.31235i) q^{54} +(3.84789 - 13.1047i) q^{55} +(-5.44355 - 7.73168i) q^{56} +(-0.0386967 + 0.0602133i) q^{57} +(1.79405 - 2.34865i) q^{58} +(-2.44285 - 2.11674i) q^{59} +(-4.71188 - 2.26353i) q^{60} +(2.53891 - 0.365040i) q^{61} +(-0.906436 - 1.23571i) q^{62} +(3.17145 + 6.94450i) q^{63} +(7.83877 + 1.59804i) q^{64} +(1.86519 + 0.851805i) q^{65} +(-1.17555 + 5.16190i) q^{66} +(-7.53375 + 4.84165i) q^{67} +(-2.27513 + 13.9003i) q^{68} +(0.415337 + 4.03784i) q^{69} +(14.5518 + 1.18301i) q^{70} +(4.34061 + 6.75412i) q^{71} +(-5.98345 - 2.43266i) q^{72} +(2.98858 - 6.54407i) q^{73} +(8.06439 - 1.67239i) q^{74} +(3.49225 - 1.59486i) q^{75} +(0.0886569 + 0.144033i) q^{76} +(-2.10428 - 14.6356i) q^{77} +(-0.741960 - 0.284980i) q^{78} +(-3.21780 + 3.71354i) q^{79} +(-9.64242 + 7.72003i) q^{80} +(2.57912 + 1.65750i) q^{81} +(4.39953 + 4.48588i) q^{82} +(11.3746 + 3.33987i) q^{83} +(-5.65809 - 0.109985i) q^{84} +(-14.2419 - 16.4360i) q^{85} +(-0.959377 + 0.347247i) q^{86} +(-0.498332 - 1.69716i) q^{87} +(9.79178 + 7.78555i) q^{88} +(1.95542 + 0.281148i) q^{89} +(8.79904 - 4.69422i) q^{90} +2.21987 q^{91} +(9.02539 + 3.24689i) q^{92} -0.917193 q^{93} +(-12.4604 + 6.64750i) q^{94} +(-0.258484 - 0.0371644i) q^{95} +(3.54601 - 3.21712i) q^{96} +(3.87901 + 13.2107i) q^{97} +(5.55371 - 2.01017i) q^{98} +(-6.61419 - 7.63318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) $ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9	$ 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) $ 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/92\mathbb{Z}\right)^\times$.

$n$	$5$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.665666	−	1.24775i	−0.470697	−	0.882295i
$2$	−0.665666	−	1.24775i	−0.470697	−	0.882295i
$3$	−0.837775	−	0.120454i	−0.483690	−	0.0695441i	−0.103843	−	0.994594i	$-0.533114\pi$
$3$	−0.837775	−	0.120454i	−0.483690	−	0.0695441i	−0.379846	+	0.925050i	$0.624023\pi$
$4$	−1.11378	+	1.66117i	−0.556888	+	0.830587i
$5$	−0.870000	−	2.96295i	−0.389076	−	1.32507i	−0.888565	−	0.458750i	$-0.848297\pi$
$5$	−0.870000	−	2.96295i	−0.389076	−	1.32507i	0.499490	−	0.866320i	$-0.333521\pi$
$6$	0.407382	+	1.12552i	0.166313	+	0.459491i
$7$	−2.18927	−	2.52655i	−0.827467	−	0.954948i	0.172079	−	0.985083i	$-0.444952\pi$
$7$	−2.18927	−	2.52655i	−0.827467	−	0.954948i	−0.999546	+	0.0301353i	$0.990406\pi$
$8$	2.81414	+	0.283931i	0.994949	+	0.100385i
$9$	−2.19112	−	0.643371i	−0.730373	−	0.214457i
$10$	−3.11790	+	3.05788i	−0.985966	+	0.966986i
$11$	3.72075	+	2.39118i	1.12185	+	0.720968i	0.963843	−	0.266470i	$-0.0858575\pi$
$11$	3.72075	+	2.39118i	1.12185	+	0.720968i	0.158005	+	0.987438i	$0.449494\pi$
$12$	1.13319	−	1.25753i	0.327124	−	0.363018i
$13$	−0.434836	+	0.501827i	−0.120602	+	0.139182i	−0.812840	−	0.582488i	$-0.802079\pi$
$13$	−0.434836	+	0.501827i	−0.120602	+	0.139182i	0.692238	+	0.721669i	$0.256625\pi$
$14$	−1.69519	+	4.41351i	−0.453059	+	1.17956i
$15$	0.371966	+	2.58708i	0.0960411	+	0.667981i
$16$	−1.51900	−	3.70036i	−0.379751	−	0.925089i
$17$	6.40622	−	2.92562i	1.55374	−	0.709568i	0.560771	−	0.827971i	$-0.310505\pi$
$17$	6.40622	−	2.92562i	1.55374	−	0.709568i	0.992966	+	0.118403i	$0.0377776\pi$
$18$	0.655787	+	3.16225i	0.154570	+	0.745349i
$19$	0.0351299	−	0.0769237i	0.00805935	−	0.0176475i	−0.905560	−	0.424219i	$-0.860549\pi$
$19$	0.0351299	−	0.0769237i	0.00805935	−	0.0176475i	0.913619	+	0.406572i	$0.133276\pi$
$20$	5.89096	+	1.85484i	1.31726	+	0.414755i
$21$	1.52978	+	2.38039i	0.333826	+	0.519444i
$22$	0.506826	−	6.23430i	0.108056	−	1.32916i
$23$	−1.16466	−	4.65227i	−0.242848	−	0.970064i
$23$	−1.16466	−	4.65227i	−0.242848	−	0.970064i
$24$	−2.32342	−	0.576844i	−0.474265	−	0.117748i
$25$	−3.81588	+	2.45232i	−0.763177	+	0.490464i
$26$	0.915612	+	0.208518i	0.179566	+	0.0408938i
$27$	4.06788	+	1.85774i	0.782864	+	0.357522i
$28$	6.63541	−	0.822745i	1.25397	−	0.155484i
$29$	0.868147	+	1.90098i	0.161211	+	0.353002i	0.972949	−	0.231019i	$-0.0742058\pi$
$29$	0.868147	+	1.90098i	0.161211	+	0.353002i	−0.811739	+	0.584021i	$0.801479\pi$
$30$	2.98043	−	2.18625i	0.544150	−	0.399153i
$31$	1.07262	−	0.154220i	0.192649	−	0.0276987i	−0.0453151	−	0.998973i	$-0.514429\pi$
$31$	1.07262	−	0.154220i	0.192649	−	0.0276987i	0.237964	+	0.971274i	$0.423520\pi$
$32$	−3.60598	+	4.35854i	−0.637454	+	0.770489i
$33$	−2.82912	−	2.45145i	−0.492487	−	0.426743i
$34$	−7.91486	−	6.04589i	−1.35739	−	1.03686i
$35$	−5.58138	+	8.68480i	−0.943425	+	1.46800i
$36$	3.50917	−	2.92326i	0.584862	−	0.487210i
$37$	−1.64073	+	5.58781i	−0.269734	+	0.918631i	0.707544	+	0.706669i	$0.249803\pi$
$37$	−1.64073	+	5.58781i	−0.269734	+	0.918631i	−0.977278	+	0.211961i	$0.932015\pi$
$38$	−0.119367	+	0.00737210i	−0.0193638	+	0.00119591i
$39$	0.424742	−	0.368041i	0.0680131	−	0.0589337i
$40$	−1.60703	−	8.58517i	−0.254094	−	1.35743i
$41$	−4.26295	+	1.25171i	−0.665760	+	0.195485i	−0.597114	−	0.802156i	$-0.703686\pi$
$41$	−4.26295	+	1.25171i	−0.665760	+	0.195485i	−0.0686462	+	0.997641i	$0.521868\pi$
$42$	1.95182	−	3.49334i	0.301172	−	0.539034i
$43$	0.102673	−	0.714109i	0.0156575	−	0.108901i	−0.980494	−	0.196550i	$-0.937026\pi$
$43$	0.102673	−	0.714109i	0.0156575	−	0.108901i	0.996151	+	0.0876491i	$0.0279354\pi$
$44$	−8.11625	+	3.51757i	−1.22357	+	0.530294i
$45$			7.05190i			1.05124i
$46$	−5.02961	+	4.55006i	−0.741575	+	0.670870i
$47$		−	9.98624i		−	1.45664i	−0.685236	−	0.728321i	$-0.740301\pi$
$47$		−	9.98624i		−	1.45664i	0.685236	−	0.728321i	$-0.259699\pi$
$48$	0.826861	+	3.28304i	0.119347	+	0.473866i
$49$	−0.594362	+	4.13388i	−0.0849089	+	0.590554i
$50$	5.60000	+	3.12886i	0.791959	+	0.442487i
$51$	−5.71938	+	1.67936i	−0.800873	+	0.235157i
$52$	−0.349312	−	1.28126i	−0.0484409	−	0.177679i
$53$	4.68049	−	4.05566i	0.642914	−	0.557088i	−0.271211	−	0.962520i	$-0.587424\pi$
$53$	4.68049	−	4.05566i	0.642914	−	0.557088i	0.914125	+	0.405432i	$0.132879\pi$
$54$	−0.389851	−	6.31235i	−0.0530520	−	0.859002i
$55$	3.84789	−	13.1047i	0.518849	−	1.76704i
$56$	−5.44355	−	7.73168i	−0.727425	−	1.03319i
$57$	−0.0386967	+	0.0602133i	−0.00512551	+	0.00797544i
$58$	1.79405	−	2.34865i	0.235571	−	0.308393i
$59$	−2.44285	−	2.11674i	−0.318032	−	0.275577i	0.481185	−	0.876619i	$-0.340207\pi$
$59$	−2.44285	−	2.11674i	−0.318032	−	0.275577i	−0.799217	+	0.601043i	$0.794752\pi$
$60$	−4.71188	−	2.26353i	−0.608301	−	0.292220i
$61$	2.53891	−	0.365040i	0.325074	−	0.0467386i	0.0221542	−	0.999755i	$-0.492948\pi$
$61$	2.53891	−	0.365040i	0.325074	−	0.0467386i	0.302920	+	0.953016i	$0.402038\pi$
$62$	−0.906436	−	1.23571i	−0.115118	−	0.156935i
$63$	3.17145	+	6.94450i	0.399565	+	0.874925i
$64$	7.83877	+	1.59804i	0.979846	+	0.199755i
$65$	1.86519	+	0.851805i	0.231349	+	0.105653i
$66$	−1.17555	+	5.16190i	−0.144701	+	0.635386i
$67$	−7.53375	+	4.84165i	−0.920394	+	0.591502i	−0.912772	−	0.408469i	$-0.866063\pi$
$67$	−7.53375	+	4.84165i	−0.920394	+	0.591502i	−0.00762244	+	0.999971i	$0.502426\pi$
$68$	−2.27513	+	13.9003i	−0.275900	+	1.68566i
$69$	0.415337	+	4.03784i	0.0500006	+	0.486099i
$70$	14.5518	+	1.18301i	1.73928	+	0.141397i
$71$	4.34061	+	6.75412i	0.515135	+	0.801566i	0.997217	−	0.0745602i	$-0.0237553\pi$
$71$	4.34061	+	6.75412i	0.515135	+	0.801566i	−0.482081	+	0.876127i	$0.660119\pi$
$72$	−5.98345	−	2.43266i	−0.705156	−	0.286692i
$73$	2.98858	−	6.54407i	0.349786	−	0.765925i	−0.650195	−	0.759768i	$-0.725313\pi$
$73$	2.98858	−	6.54407i	0.349786	−	0.765925i	0.999981	−	0.00615760i	$-0.00196004\pi$
$74$	8.06439	−	1.67239i	0.937466	−	0.194412i
$75$	3.49225	−	1.59486i	0.403250	−	0.184158i
$76$	0.0886569	+	0.144033i	0.0101696	+	0.0165217i
$77$	−2.10428	−	14.6356i	−0.239805	−	1.66788i
$78$	−0.741960	−	0.284980i	−0.0840104	−	0.0322677i
$79$	−3.21780	+	3.71354i	−0.362031	+	0.417806i	−0.907319	−	0.420443i	$-0.861875\pi$
$79$	−3.21780	+	3.71354i	−0.362031	+	0.417806i	0.545288	+	0.838249i	$0.316420\pi$
$80$	−9.64242	+	7.72003i	−1.07806	+	0.863126i
$81$	2.57912	+	1.65750i	0.286569	+	0.184167i
$82$	4.39953	+	4.48588i	0.485847	+	0.495383i
$83$	11.3746	+	3.33987i	1.24852	+	0.366598i	0.838210	−	0.545348i	$-0.183603\pi$
$83$	11.3746	+	3.33987i	1.24852	+	0.366598i	0.410309	+	0.911946i	$0.365421\pi$
$84$	−5.65809	−	0.109985i	−0.617348	−	0.0120004i
$85$	−14.2419	−	16.4360i	−1.54475	−	1.78273i
$86$	−0.959377	+	0.347247i	−0.103452	+	0.0374446i
$87$	−0.498332	−	1.69716i	−0.0534268	−	0.181955i
$88$	9.79178	+	7.78555i	1.04381	+	0.829942i
$89$	1.95542	+	0.281148i	0.207275	+	0.0298016i	0.245170	−	0.969480i	$-0.421156\pi$
$89$	1.95542	+	0.281148i	0.207275	+	0.0298016i	−0.0378953	+	0.999282i	$0.512065\pi$
$90$	8.79904	−	4.69422i	0.927500	−	0.494814i
$91$	2.21987			0.232705
$92$	9.02539	+	3.24689i	0.940962	+	0.338512i
$93$	−0.917193			−0.0951084
$94$	−12.4604	+	6.64750i	−1.28519	+	0.685637i
$95$	−0.258484	−	0.0371644i	−0.0265199	−	0.00381298i
$96$	3.54601	−	3.21712i	0.361913	−	0.328346i
$97$	3.87901	+	13.2107i	0.393854	+	1.34134i	0.883095	+	0.469194i	$0.155455\pi$
$97$	3.87901	+	13.2107i	0.393854	+	1.34134i	−0.489242	+	0.872148i	$0.662726\pi$
$98$	5.55371	−	2.01017i	0.561010	−	0.203058i
$99$	−6.61419	−	7.63318i	−0.664751	−	0.767164i
$100$	0.176312	−	9.07019i	0.0176312	−	0.907019i
$101$	7.96253	+	2.33801i	0.792301	+	0.232641i	0.652749	−	0.757574i	$-0.273616\pi$
$101$	7.96253	+	2.33801i	0.792301	+	0.232641i	0.139552	+	0.990215i	$0.455434\pi$
$102$	5.90262	+	6.01848i	0.584447	+	0.595918i
$103$	8.29024	+	5.32781i	0.816861	+	0.524965i	0.881078	−	0.472971i	$-0.156818\pi$
$103$	8.29024	+	5.32781i	0.816861	+	0.524965i	−0.0642166	+	0.997936i	$0.520455\pi$
$104$	−1.36617	+	1.28875i	−0.133964	+	0.126372i
$105$	5.72206	−	6.60361i	0.558416	−	0.644446i
$106$	−8.17611	−	3.14037i	−0.794134	−	0.305020i
$107$	1.82050	+	12.6618i	0.175994	+	1.22407i	0.865919	+	0.500185i	$0.166735\pi$
$107$	1.82050	+	12.6618i	0.175994	+	1.22407i	−0.689924	+	0.723881i	$0.742356\pi$
$108$	−7.61674	+	4.68836i	−0.732921	+	0.451137i
$109$	−0.583810	+	0.266617i	−0.0559189	+	0.0255373i	−0.443178	−	0.896434i	$-0.646149\pi$
$109$	−0.583810	+	0.266617i	−0.0559189	+	0.0255373i	0.387259	+	0.921971i	$0.373422\pi$
$110$	−18.9128	+	3.92214i	−1.80327	+	0.373962i
$111$	2.04764	−	4.48370i	0.194353	−	0.425574i
$112$	−6.02364	+	11.9389i	−0.569181	+	1.12812i
$113$	−9.30246	−	14.4749i	−0.875102	−	1.36169i	−0.931677	−	0.363287i	$-0.881654\pi$
$113$	−9.30246	−	14.4749i	−0.875102	−	1.36169i	0.0565754	−	0.998398i	$-0.481982\pi$
$114$	0.100890	+	0.00820202i	0.00944926	+	0.000768190i
$115$	−12.7712	+	7.49828i	−1.19092	+	0.699218i
$116$	−4.12478	−	0.675120i	−0.382976	−	0.0626833i
$117$	1.27564	−	0.819803i	0.117933	−	0.0757908i
$118$	−1.01505	+	4.45712i	−0.0934429	+	0.410311i
$119$	−21.4167	−	9.78068i	−1.96327	−	0.896594i
$120$	0.312212	+	7.38601i	0.0285009	+	0.674248i
$121$	3.55666	+	7.78801i	0.323333	+	0.708001i
$122$	−2.14555	−	2.92494i	−0.194249	−	0.264812i
$123$	3.72217	−	0.535167i	0.335616	−	0.0482544i
$124$	−0.938475	+	1.95358i	−0.0842776	+	0.175437i
$125$	−1.08299	−	0.938417i	−0.0968656	−	0.0839345i
$126$	6.55390	−	8.57990i	0.583868	−	0.764358i
$127$	5.21515	−	8.11493i	0.462770	−	0.720084i	−0.528929	−	0.848666i	$-0.677406\pi$
$127$	5.21515	−	8.11493i	0.462770	−	0.720084i	0.991699	+	0.128582i	$0.0410426\pi$
$128$	−3.22404	−	10.8446i	−0.284968	−	0.958537i
$129$	−0.172034	+	0.585895i	−0.0151468	+	0.0515852i
$130$	−0.178753	−	2.89432i	−0.0156777	−	0.253849i
$131$	12.1850	−	10.5584i	1.06461	−	0.922488i	0.0674421	−	0.997723i	$-0.478516\pi$
$131$	12.1850	−	10.5584i	1.06461	−	0.922488i	0.997166	+	0.0752352i	$0.0239707\pi$
$132$	7.22330	−	1.96930i	0.628708	−	0.171406i
$133$	−0.271261	+	0.0796494i	−0.0235213	+	0.00690648i
$134$	11.0561	+	6.17734i	0.955106	+	0.533641i
$135$	1.96533	−	13.6691i	0.169148	−	1.17645i
$136$	18.8587	−	6.41419i	1.61712	−	0.550012i
$137$		−	0.724845i		−	0.0619277i	−0.999521	−	0.0309639i	$-0.990142\pi$
$137$		−	0.724845i		−	0.0619277i	0.999521	−	0.0309639i	$-0.00985768\pi$
$138$	4.76175	−	3.20609i	0.405347	−	0.272921i
$139$			13.8324i			1.17325i	0.809859	+	0.586625i	$0.199544\pi$
$139$			13.8324i			1.17325i	−0.809859	+	0.586625i	$0.800456\pi$
$140$	−8.21055	−	18.9446i	−0.693918	−	1.60111i
$141$	−1.20288	+	8.36622i	−0.101301	+	0.704563i
$142$	5.53808	−	9.91200i	0.464745	−	0.831796i
$143$	−2.81787	+	0.827402i	−0.235642	+	0.0691908i
$144$	0.947616	+	9.08521i	0.0789680	+	0.757101i
$145$	4.87720	−	4.22612i	0.405030	−	0.350960i
$146$	−10.1548	+	0.627160i	−0.840415	+	0.0519041i
$147$	0.995884	−	3.39167i	0.0821392	−	0.279740i
$148$	−7.45492	−	8.94911i	−0.612791	−	0.735613i
$149$	0.563831	−	0.877337i	0.0461908	−	0.0718743i	−0.817390	−	0.576084i	$-0.804580\pi$
$149$	0.563831	−	0.877337i	0.0461908	−	0.0718743i	0.863581	+	0.504210i	$0.168216\pi$
$150$	−4.31466	−	3.29582i	−0.352290	−	0.269103i
$151$	−6.75094	−	5.84972i	−0.549384	−	0.476044i	0.335380	−	0.942083i	$-0.391135\pi$
$151$	−6.75094	−	5.84972i	−0.549384	−	0.476044i	−0.884764	+	0.466039i	$0.845681\pi$
$152$	0.120701	−	0.206500i	0.00979018	−	0.0167493i
$153$	−15.9191	+	2.28882i	−1.28698	+	0.185040i
$154$	−16.8609	+	12.3681i	−1.35869	+	0.996647i
$155$	−1.39013	−	3.04395i	−0.111658	−	0.244496i
$156$	0.138312	+	1.11548i	0.0110739	+	0.0893103i
$157$	9.20866	+	4.20546i	0.734931	+	0.335632i	0.747475	−	0.664289i	$-0.231266\pi$
$157$	9.20866	+	4.20546i	0.734931	+	0.335632i	−0.0125441	+	0.999921i	$0.503993\pi$
$158$	6.77556	+	1.54304i	0.539035	+	0.122758i
$159$	−4.40972	+	2.83395i	−0.349713	+	0.224747i
$160$	16.0513	+	6.89240i	1.26897	+	0.544892i
$161$	−9.20445	+	13.1276i	−0.725413	+	1.03460i
$162$	0.351318	−	4.32145i	0.0276021	−	0.339525i
$163$	2.37384	+	3.69377i	0.185934	+	0.289318i	0.921689	−	0.387929i	$-0.126809\pi$
$163$	2.37384	+	3.69377i	0.185934	+	0.289318i	−0.735756	+	0.677247i	$0.763173\pi$
$164$	2.66866	−	8.47563i	0.208387	−	0.661835i
$165$	−4.80218	+	10.5153i	−0.373849	+	0.818615i
$166$	−3.40432	−	16.4159i	−0.264227	−	1.27412i
$167$	−21.0674	+	9.62118i	−1.63025	+	0.744509i	−0.999504	−	0.0314819i	$-0.989977\pi$
$167$	−21.0674	+	9.62118i	−1.63025	+	0.744509i	−0.630744	+	0.775991i	$0.717250\pi$
$168$	3.62916	+	7.13311i	0.279996	+	0.550331i
$169$	1.78734	+	12.4313i	0.137488	+	0.956250i
$170$	−11.0277	+	28.7112i	−0.845789	+	2.20205i
$171$	−0.126464	+	0.145948i	−0.00967097	+	0.0111609i
$172$	1.07190	+	0.965916i	0.0817319	+	0.0736504i
$173$	1.60994	+	1.03465i	0.122401	+	0.0786627i	0.600409	−	0.799693i	$-0.295004\pi$
$173$	1.60994	+	1.03465i	0.122401	+	0.0786627i	−0.478008	+	0.878356i	$0.658641\pi$
$174$	−1.78592	+	1.75154i	−0.135390	+	0.132784i
$175$	14.5499	+	4.27224i	1.09987	+	0.322951i
$176$	3.19639	−	17.4003i	0.240937	−	1.31160i
$177$	1.79159	+	2.06761i	0.134664	+	0.155411i
$178$	−0.950857	−	2.62704i	−0.0712698	−	0.196905i
$179$	−1.18494	−	4.03554i	−0.0885667	−	0.301630i	0.903283	−	0.429046i	$-0.141150\pi$
$179$	−1.18494	−	4.03554i	−0.0885667	−	0.301630i	−0.991849	+	0.127415i	$0.959332\pi$
$180$	−11.7144	−	7.85425i	−0.873143	−	0.585421i
$181$	5.66335	+	0.814266i	0.420953	+	0.0605239i	0.349537	−	0.936923i	$-0.386339\pi$
$181$	5.66335	+	0.814266i	0.420953	+	0.0605239i	0.0714164	+	0.997447i	$0.477248\pi$
$182$	−1.47769	−	2.76985i	−0.109534	−	0.205315i
$183$	−2.17101			−0.160486
$184$	−1.95658	−	13.4228i	−0.144241	−	0.989543i
$185$	17.9838			1.32220
$186$	0.610544	+	1.14443i	0.0447673	+	0.0839137i
$187$	30.8316	+	4.43292i	2.25463	+	0.324167i
$188$	16.5889	+	11.1224i	1.20987	+	0.811187i
$189$	−4.21202	−	14.3448i	−0.306379	−	1.04343i
$190$	0.125692	+	0.347263i	0.00911866	+	0.0251931i
$191$	14.1160	+	16.2907i	1.02140	+	1.17875i	0.983765	+	0.179463i	$0.0574359\pi$
$191$	14.1160	+	16.2907i	1.02140	+	1.17875i	0.0376315	+	0.999292i	$0.488019\pi$
$192$	−6.37464	−	2.28301i	−0.460050	−	0.164762i
$193$	−16.8140	−	4.93704i	−1.21030	−	0.355376i	−0.386516	−	0.922283i	$-0.626322\pi$
$193$	−16.8140	−	4.93704i	−1.21030	−	0.355376i	−0.823782	+	0.566907i	$0.808140\pi$
$194$	13.9016	−	13.6340i	0.998073	−	0.978861i
$195$	−1.46001	−	0.938291i	−0.104553	−	0.0671924i
$196$	−6.20511	−	5.59156i	−0.443222	−	0.399397i
$197$	−14.8161	+	17.0987i	−1.05560	+	1.21823i	−0.0804339	+	0.996760i	$0.525631\pi$
$197$	−14.8161	+	17.0987i	−1.05560	+	1.21823i	−0.975167	+	0.221469i	$0.928915\pi$
$198$	−5.12149	+	13.3340i	−0.363968	+	0.947609i
$199$	1.12382	+	7.81633i	0.0796654	+	0.554085i	0.990093	+	0.140416i	$0.0448439\pi$
$199$	1.12382	+	7.81633i	0.0796654	+	0.554085i	−0.910427	+	0.413669i	$0.864247\pi$
$200$	−11.4347	+	5.81772i	−0.808557	+	0.411375i
$201$	6.89479	−	3.14874i	0.486321	−	0.222095i
$202$	−2.38313	−	11.4916i	−0.167676	−	0.808546i
$203$	2.90231	−	6.35517i	0.203702	−	0.446046i
$204$	3.58040	−	11.3713i	0.250678	−	0.796151i
$205$	7.41752	+	11.5419i	0.518062	+	0.806121i
$206$	1.12926	−	13.8907i	0.0786795	−	0.967812i
$207$	−0.441231	+	10.9430i	−0.0306677	+	0.760590i
$208$	2.51745	+	0.846770i	0.174554	+	0.0587129i
$209$	0.314648	−	0.202212i	0.0217647	−	0.0139873i
$210$	−12.0487	−	2.74392i	−0.831437	−	0.189348i
$211$	−12.6417	−	5.77328i	−0.870292	−	0.397449i	−0.0703473	−	0.997523i	$-0.522411\pi$
$211$	−12.6417	−	5.77328i	−0.870292	−	0.397449i	−0.799945	+	0.600073i	$0.795138\pi$
$212$	1.52415	+	12.2922i	0.104679	+	0.844232i
$213$	−2.82290	−	6.18128i	−0.193422	−	0.423534i
$214$	14.5870	−	10.7001i	0.997147	−	0.731443i
$215$	−2.20519	+	0.317059i	−0.150393	+	0.0216232i
$216$	10.9201	+	6.38294i	0.743020	+	0.434304i
$217$	−2.73791	−	2.37241i	−0.185861	−	0.161050i
$218$	0.721295	+	0.550973i	0.0488523	+	0.0373166i
$219$	−3.29201	+	5.12247i	−0.222454	+	0.346145i
$220$	17.4835	+	20.9877i	1.17874	+	1.41499i
$221$	−1.31750	+	4.48698i	−0.0886243	+	0.301827i
$222$	−6.95759	+	0.429702i	−0.466963	+	0.0288397i
$223$	6.41897	−	5.56207i	0.429846	−	0.372464i	−0.412899	−	0.910777i	$-0.635484\pi$
$223$	6.41897	−	5.56207i	0.429846	−	0.372464i	0.842745	+	0.538313i	$0.180938\pi$
$224$	18.9066	−	0.431323i	1.26325	−	0.0288190i
$225$	9.93881	−	2.91830i	0.662588	−	0.194553i
$226$	−11.8688	+	21.2426i	−0.789500	+	1.41304i
$227$	3.73456	−	25.9745i	0.247872	−	1.72399i	−0.362597	−	0.931946i	$-0.618110\pi$
$227$	3.73456	−	25.9745i	0.247872	−	1.72399i	0.610469	−	0.792040i	$-0.290981\pi$
$228$	−0.0569253	−	0.131346i	−0.00376997	−	0.00869861i
$229$		−	3.21581i		−	0.212507i	−0.994339	−	0.106253i	$-0.966115\pi$
$229$		−	3.21581i		−	0.212507i	0.994339	−	0.106253i	$-0.0338855\pi$
$230$	17.8573	+	10.9439i	1.17748	+	0.721620i
$231$			12.5148i			0.823415i
$232$	1.90334	+	5.59611i	0.124960	+	0.367402i
$233$	3.27930	−	22.8080i	0.214834	−	1.49420i	−0.541879	−	0.840456i	$-0.682287\pi$
$233$	3.27930	−	22.8080i	0.214834	−	1.49420i	0.756713	−	0.653747i	$-0.226804\pi$
$234$	−1.87206	−	1.04597i	−0.122380	−	0.0683770i
$235$	−29.5887	+	8.68802i	−1.93015	+	0.566744i
$236$	6.23707	−	1.70042i	0.405999	−	0.110688i
$237$	3.14310	−	2.72352i	0.204167	−	0.176911i
$238$	2.05250	+	33.2334i	0.133044	+	2.15420i
$239$	6.83449	−	23.2761i	0.442087	−	1.50561i	−0.373862	−	0.927484i	$-0.621967\pi$
$239$	6.83449	−	23.2761i	0.442087	−	1.50561i	0.815949	−	0.578124i	$-0.196215\pi$
$240$	9.00809	−	5.30618i	0.581470	−	0.342513i
$241$	−1.20466	+	1.87448i	−0.0775987	+	0.120746i	−0.877884	−	0.478874i	$-0.841045\pi$
$241$	−1.20466	+	1.87448i	−0.0775987	+	0.120746i	0.800285	+	0.599620i	$0.204682\pi$
$242$	7.34996	−	9.62205i	0.472473	−	0.618529i
$243$	−12.1002	−	10.4849i	−0.776230	−	0.672607i
$244$	−2.22139	+	4.62415i	−0.142210	+	0.296031i
$245$	12.7656	−	1.83541i	0.815562	−	0.117260i
$246$	−3.14548	−	4.28810i	−0.200548	−	0.273399i
$247$	0.0233267	+	0.0510783i	0.00148424	+	0.00325003i
$248$	3.06230	−	0.129445i	0.194456	−	0.00821980i
$249$	−9.12702	−	4.16817i	−0.578401	−	0.264147i
$250$	−0.450002	+	1.97598i	−0.0284606	+	0.124972i
$251$	6.45187	−	4.14636i	0.407238	−	0.261716i	−0.320946	−	0.947097i	$-0.604001\pi$
$251$	6.45187	−	4.14636i	0.407238	−	0.261716i	0.728184	+	0.685381i	$0.240364\pi$
$252$	−15.0683	−	2.46630i	−0.949214	−	0.155362i
$253$	6.79101	−	20.0948i	0.426947	−	1.26335i
$254$	−13.5970	−	1.10538i	−0.853151	−	0.0693580i
$255$	9.95171	+	15.4852i	0.623200	+	0.969718i
$256$	−11.3853	+	11.2417i	−0.711579	+	0.702606i
$257$	−4.74126	+	10.3819i	−0.295751	+	0.647605i	−0.997924	−	0.0644015i	$-0.979486\pi$
$257$	−4.74126	+	10.3819i	−0.295751	+	0.647605i	0.702173	+	0.712007i	$0.252213\pi$
$258$	0.845570	−	0.175354i	0.0526429	−	0.0109171i
$259$	17.7099	−	8.08785i	1.10044	−	0.502554i
$260$	−3.49241	+	2.14969i	−0.216590	+	0.133318i
$261$	−0.679181	−	4.72381i	−0.0420403	−	0.292396i
$262$	−21.2854	−	8.17553i	−1.31501	−	0.505086i
$263$	−8.96316	+	10.3440i	−0.552692	+	0.637840i	−0.961508	−	0.274776i	$-0.911396\pi$
$263$	−8.96316	+	10.3440i	−0.552692	+	0.637840i	0.408816	+	0.912617i	$0.365942\pi$
$264$	−7.26551	−	7.70200i	−0.447161	−	0.474025i
$265$	−16.0887	−	10.3396i	−0.988323	−	0.635157i
$266$	0.279952	+	0.285447i	0.0171650	+	0.0175019i
$267$	−1.60434	−	0.471077i	−0.0981841	−	0.0288295i
$268$	0.348095	−	17.9074i	0.0212633	−	1.09387i
$269$	12.9093	+	14.8981i	0.787091	+	0.908351i	0.997600	−	0.0692405i	$-0.0220576\pi$
$269$	12.9093	+	14.8981i	0.787091	+	0.908351i	−0.210509	+	0.977592i	$0.567512\pi$
$270$	−18.3640	+	6.64685i	−1.11760	+	0.404514i
$271$	−0.208669	−	0.710661i	−0.0126757	−	0.0431696i	0.952912	−	0.303246i	$-0.0980704\pi$
$271$	−0.208669	−	0.710661i	−0.0126757	−	0.0431696i	−0.965588	+	0.260076i	$0.916252\pi$
$272$	−20.5569	−	19.2613i	−1.24645	−	1.16789i
$273$	−1.85975	−	0.267392i	−0.112557	−	0.0161833i
$274$	−0.904428	+	0.482505i	−0.0546385	+	0.0291492i
$275$	−20.0619			−1.20978
$276$	−7.17015	−	3.80731i	−0.431592	−	0.229173i
$277$	−19.6083			−1.17815			−0.589074	−	0.808079i	$-0.700508\pi$
$277$	−19.6083			−1.17815			−0.589074	+	0.808079i	$0.700508\pi$
$278$	17.2594	−	9.20777i	1.03515	−	0.552245i
$279$	−2.44946	−	0.352180i	−0.146646	−	0.0210844i
$280$	−18.1727	+	22.8555i	−1.08602	+	1.36588i
$281$	0.951494	+	3.24049i	0.0567614	+	0.193312i	0.982993	−	0.183644i	$-0.0587892\pi$
$281$	0.951494	+	3.24049i	0.0567614	+	0.193312i	−0.926231	+	0.376955i	$0.876971\pi$
$282$	11.2397	−	4.06821i	0.669314	−	0.242259i
$283$	−9.07704	−	10.4755i	−0.539574	−	0.622702i	0.418848	−	0.908056i	$-0.362434\pi$
$283$	−9.07704	−	10.4755i	−0.539574	−	0.622702i	−0.958422	+	0.285355i	$0.907889\pi$
$284$	−16.0542	−	0.312072i	−0.952644	−	0.0185181i
$285$	0.212075	+	0.0622708i	0.0125622	+	0.00368860i
$286$	2.90816	+	2.96524i	0.171963	+	0.175338i
$287$	12.4953	+	8.03023i	0.737573	+	0.474009i
$288$	10.7053	−	7.23011i	0.630816	−	0.426038i
$289$	21.3478	−	24.6366i	1.25575	−	1.44921i
$290$	−8.51975	−	3.27236i	−0.500297	−	0.192160i
$291$	−1.65846	−	11.5348i	−0.0972205	−	0.676184i
$292$	7.54223	+	12.2532i	0.441376	+	0.717063i
$293$	4.75294	−	2.17060i	0.277670	−	0.126808i	−0.271713	−	0.962378i	$-0.587590\pi$
$293$	4.75294	−	2.17060i	0.277670	−	0.126808i	0.549383	+	0.835571i	$0.314863\pi$
$294$	−4.89490	+	1.01510i	−0.285476	+	0.0592020i
$295$	−4.14652	+	9.07961i	−0.241420	+	0.528635i
$296$	−6.20379	+	15.2590i	−0.360588	+	0.886913i
$297$	10.6934	+	16.6392i	0.620493	+	0.965505i
$298$	−1.47002	−	0.119507i	−0.0851562	−	0.00692288i
$299$	2.84107	+	1.43851i	0.164303	+	0.0831914i
$300$	−1.24025	+	7.57754i	−0.0716058	+	0.437490i
$301$	−2.02901	+	1.30397i	−0.116950	+	0.0751595i
$302$	−2.80514	+	12.3175i	−0.161418	+	0.708791i
$303$	−6.38919	−	2.91784i	−0.367049	−	0.167626i
$304$	−0.338008	−	0.0131458i	−0.0193861	−	0.000753961i
$305$	−3.29045	−	7.20508i	−0.188410	−	0.412561i
$306$	13.4527	+	18.3395i	0.769037	+	1.04840i
$307$	−15.7492	+	2.26440i	−0.898856	+	0.129236i	−0.576227	−	0.817290i	$-0.695476\pi$
$307$	−15.7492	+	2.26440i	−0.898856	+	0.129236i	−0.322629	+	0.946526i	$0.604567\pi$
$308$	26.6560	+	12.8052i	1.51887	+	0.729646i
$309$	−6.30360	−	5.46210i	−0.358599	−	0.310728i
$310$	−2.87274	+	3.76079i	−0.163161	+	0.213598i
$311$	−3.21032	+	4.99535i	−0.182041	+	0.283261i	−0.920266	−	0.391294i	$-0.872028\pi$
$311$	−3.21032	+	4.99535i	−0.182041	+	0.283261i	0.738225	+	0.674554i	$0.235664\pi$
$312$	1.29978	−	0.915121i	0.0735856	−	0.0518085i
$313$	3.98799	−	13.5819i	0.225415	−	0.767692i	−0.766661	−	0.642052i	$-0.778083\pi$
$313$	3.98799	−	13.5819i	0.225415	−	0.767692i	0.992076	−	0.125640i	$-0.0400984\pi$
$314$	−0.882525	−	14.2896i	−0.0498038	−	0.806407i
$315$	17.8170	−	15.4385i	1.00388	−	0.869863i
$316$	−2.58493	−	9.48138i	−0.145413	−	0.533369i
$317$	−22.8502	+	6.70943i	−1.28340	+	0.376839i	−0.851153	−	0.524918i	$-0.824096\pi$
$317$	−22.8502	+	6.70943i	−1.28340	+	0.376839i	−0.432243	+	0.901757i	$0.642278\pi$
$318$	6.47147	+	3.61577i	0.362902	+	0.202762i
$319$	−1.31542	+	9.14895i	−0.0736494	+	0.512243i
$320$	−2.08481	−	24.6161i	−0.116544	−	1.37608i
$321$		−	10.8271i		−	0.604308i
$322$	22.5072	+	2.74626i	1.25427	+	0.153043i
$323$		−	0.595567i		−	0.0331382i
$324$	−5.62596	+	2.43828i	−0.312553	+	0.135460i
$325$	0.428642	−	2.98127i	0.0237768	−	0.165371i
$326$	3.02873	−	5.42078i	0.167746	−	0.300229i
$327$	0.521217	−	0.153043i	0.0288233	−	0.00846330i
$328$	−12.3519	+	2.31212i	−0.682021	+	0.127665i
$329$	−25.2308	+	21.8626i	−1.39102	+	1.20532i
$330$	16.3172	−	1.00775i	0.898230	−	0.0554748i
$331$	0.494233	−	1.68320i	0.0271655	−	0.0925172i	−0.944794	−	0.327664i	$-0.893739\pi$
$331$	0.494233	−	1.68320i	0.0271655	−	0.0925172i	0.971960	+	0.235146i	$0.0755569\pi$
$332$	−18.2168	+	15.1752i	−0.999778	+	0.832850i
$333$	7.19007	−	11.1880i	0.394013	−	0.613097i
$334$	26.0288	+	19.8825i	1.42423	+	1.08792i
$335$	20.8999	+	18.1099i	1.14188	+	0.989448i
$336$	6.48455	−	9.27657i	0.353761	−	0.506078i
$337$	14.0531	−	2.02054i	0.765524	−	0.110066i	0.251518	−	0.967853i	$-0.419070\pi$
$337$	14.0531	−	2.02054i	0.765524	−	0.110066i	0.514005	+	0.857787i	$0.328161\pi$
$338$	14.3214	−	10.5052i	0.778980	−	0.571409i
$339$	6.04981	+	13.2472i	0.328581	+	0.719492i
$340$	43.1653	−	5.35220i	2.34097	−	0.290264i
$341$	4.35972	+	1.99102i	0.236092	+	0.107820i
$342$	0.266290	+	0.0606439i	0.0143993	+	0.00327925i
$343$	−7.94113	+	5.10345i	−0.428781	+	0.275561i
$344$	0.491694	−	1.98045i	0.0265104	−	0.106779i
$345$	11.6026	−	4.74354i	0.624661	−	0.255384i
$346$	0.219300	−	2.69754i	0.0117896	−	0.145020i
$347$	−1.79443	−	2.79219i	−0.0963301	−	0.149893i	0.789743	−	0.613437i	$-0.210214\pi$
$347$	−1.79443	−	2.79219i	−0.0963301	−	0.149893i	−0.886073	+	0.463545i	$0.846577\pi$
$348$	3.37431	+	1.06244i	0.180882	+	0.0569530i
$349$	5.85411	−	12.8187i	0.313363	−	0.686169i	−0.685769	−	0.727819i	$-0.740534\pi$
$349$	5.85411	−	12.8187i	0.313363	−	0.686169i	0.999132	+	0.0416496i	$0.0132613\pi$
$350$	−4.35469	−	20.9986i	−0.232768	−	1.12242i
$351$	−2.70112	+	1.23356i	−0.144175	+	0.0658426i
$352$	−23.8390	+	7.59449i	−1.27062	+	0.404787i
$353$	2.72653	+	18.9635i	0.145119	+	1.00932i	0.924066	+	0.382233i	$0.124845\pi$
$353$	2.72653	+	18.9635i	0.145119	+	1.00932i	−0.778947	+	0.627090i	$0.784246\pi$
$354$	1.38726	−	3.61180i	0.0737321	−	0.191965i
$355$	16.2358	−	18.7371i	0.861705	−	0.994460i
$356$	−2.64494	+	2.93517i	−0.140182	+	0.155563i
$357$	16.7643	+	10.7737i	0.887259	+	0.570207i
$358$	−4.24658	+	4.16484i	−0.224439	+	0.220119i
$359$	13.1988	+	3.87551i	0.696606	+	0.204542i	0.610817	−	0.791772i	$-0.290841\pi$
$359$	13.1988	+	3.87551i	0.696606	+	0.204542i	0.0857882	+	0.996313i	$0.472659\pi$
$360$	−2.00225	+	19.8450i	−0.105528	+	1.04593i
$361$	12.4377	+	14.3538i	0.654614	+	0.755465i
$362$	−2.75390	−	7.60849i	−0.144742	−	0.399893i
$363$	−2.04159	−	6.95301i	−0.107156	−	0.364939i
$364$	−2.47244	+	3.68759i	−0.129591	+	0.193282i
$365$	−21.9898	−	3.16165i	−1.15100	−	0.165488i
$366$	1.44517	+	2.70888i	0.0755401	+	0.141596i
$367$	5.36619			0.280113			0.140056	−	0.990144i	$-0.455272\pi$
$367$	5.36619			0.280113			0.140056	+	0.990144i	$0.455272\pi$
$368$	−15.4459	+	11.3764i	−0.805174	+	0.593038i
$369$	10.1459			0.528177
$370$	−11.9712	−	22.4394i	−0.622354	−	1.16657i
$371$	−20.4937	−	2.94655i	−1.06398	−	0.152977i
$372$	1.02155	−	1.52362i	0.0529648	−	0.0789959i
$373$	5.02020	+	17.0972i	0.259936	+	0.885261i	0.981264	+	0.192668i	$0.0617139\pi$
$373$	5.02020	+	17.0972i	0.259936	+	0.885261i	−0.721328	+	0.692594i	$0.756468\pi$
$374$	−14.9924	−	41.4211i	−0.775238	−	2.14183i
$375$	0.794267	+	0.916633i	0.0410158	+	0.0473347i
$376$	2.83540	−	28.1027i	0.146225	−	1.44928i
$377$	−1.33146	−	0.390953i	−0.0685738	−	0.0201351i
$378$	−15.0950	+	14.8044i	−0.776403	+	0.761458i
$379$	27.9347	+	17.9525i	1.43491	+	0.922159i	0.999762	+	0.0217988i	$0.00693932\pi$
$379$	27.9347	+	17.9525i	1.43491	+	0.922159i	0.435145	+	0.900360i	$0.356697\pi$
$380$	0.349630	−	0.387994i	0.0179356	−	0.0199037i
$381$	−5.34660	+	6.17031i	−0.273915	+	0.316114i
$382$	10.9303	−	28.4574i	0.559240	−	1.45601i
$383$	1.34026	+	9.32169i	0.0684839	+	0.476316i	0.994985	+	0.100024i	$0.0318920\pi$
$383$	1.34026	+	9.32169i	0.0684839	+	0.476316i	−0.926501	+	0.376292i	$0.877199\pi$
$384$	1.39475	+	9.47370i	0.0711753	+	0.483453i
$385$	−41.5338	+	18.9679i	−2.11676	+	0.966692i
$386$	5.03231	+	24.2661i	0.256138	+	1.23511i
$387$	−0.684406	+	1.49864i	−0.0347903	+	0.0761802i
$388$	−26.2656	−	8.27005i	−1.33343	−	0.419848i
$389$	−4.17937	−	6.50322i	−0.211902	−	0.329727i	0.718990	−	0.695021i	$-0.244605\pi$
$389$	−4.17937	−	6.50322i	−0.211902	−	0.329727i	−0.930892	+	0.365294i	$0.880968\pi$
$390$	−0.198877	+	2.44632i	−0.0100705	+	0.123874i
$391$	−21.0718	−	26.3961i	−1.06565	−	1.33491i
$392$	−2.84636	+	11.4646i	−0.143763	+	0.579048i
$393$	−11.4801	+	7.37780i	−0.579094	+	0.372161i
$394$	31.1975	+	7.10480i	1.57171	+	0.357935i
$395$	13.8025	+	6.30339i	0.694479	+	0.317158i
$396$	20.0468	−	2.48566i	1.00739	−	0.124909i
$397$	0.814423	+	1.78334i	0.0408747	+	0.0895032i	0.928968	−	0.370160i	$-0.120697\pi$
$397$	0.814423	+	1.78334i	0.0408747	+	0.0895032i	−0.888093	+	0.459664i	$0.847970\pi$
$398$	9.00477	−	6.60532i	0.451368	−	0.331095i
$399$	0.236850	−	0.0340539i	0.0118573	−	0.00170483i
$400$	14.8708	+	10.3950i	0.743540	+	0.519752i
$401$	25.2805	+	21.9057i	1.26245	+	1.09392i	0.991333	+	0.131373i	$0.0419386\pi$
$401$	25.2805	+	21.9057i	1.26245	+	1.09392i	0.271117	+	0.962546i	$0.412607\pi$
$402$	−8.51849	−	6.50698i	−0.424863	−	0.324539i
$403$	−0.389022	+	0.605331i	−0.0193786	+	0.0301537i
$404$	−12.7523	+	10.6231i	−0.634452	+	0.528520i
$405$	2.66725	−	9.08381i	0.132537	−	0.451378i
$406$	−9.86166	+	0.609057i	−0.489426	+	0.0302270i
$407$	−19.4662	+	16.8676i	−0.964904	+	0.836094i
$408$	−16.5719	+	3.10205i	−0.820434	+	0.153574i
$409$	14.5213	−	4.26384i	0.718033	−	0.210833i	0.0977491	−	0.995211i	$-0.468836\pi$
$409$	14.5213	−	4.26384i	0.718033	−	0.210833i	0.620284	+	0.784378i	$0.287018\pi$
$410$	9.46384	−	16.9383i	0.467386	−	0.836522i
$411$	−0.0873104	+	0.607257i	−0.00430671	+	0.0299538i
$412$	−18.0839	+	7.83754i	−0.890930	+	0.386128i
$413$			10.8061i			0.531735i
$414$	13.9479	−	6.73383i	0.685500	−	0.330949i
$415$		−	36.6079i		−	1.79701i
$416$	−0.619225	−	3.70483i	−0.0303600	−	0.181644i
$417$	1.66617	−	11.5885i	0.0815926	−	0.567489i
$418$	−0.461761	−	0.257997i	−0.0225855	−	0.0126191i
$419$	21.7194	−	6.37740i	1.06106	−	0.311556i	0.295784	−	0.955255i	$-0.404419\pi$
$419$	21.7194	−	6.37740i	1.06106	−	0.311556i	0.765279	+	0.643698i	$0.222601\pi$
$420$	4.59665	+	16.8603i	0.224294	+	0.822698i
$421$	−9.54230	+	8.26845i	−0.465063	+	0.402980i	−0.855624	−	0.517597i	$-0.826827\pi$
$421$	−9.54230	+	8.26845i	−0.465063	+	0.402980i	0.390561	+	0.920577i	$0.372281\pi$
$422$	1.21154	+	19.6168i	0.0589767	+	0.954933i
$423$	−6.42485	+	21.8810i	−0.312387	+	1.06389i
$424$	14.3231	−	10.0843i	0.695590	−	0.489736i
$425$	−17.2708	+	26.8739i	−0.837758	+	1.30358i
$426$	−5.83360	+	7.63695i	−0.282639	+	0.370011i
$427$	−6.48066	−	5.61553i	−0.313621	−	0.271754i
$428$	−23.0612	−	11.0783i	−1.11470	−	0.535490i
$429$	2.46041	−	0.353753i	0.118790	−	0.0170794i
$430$	1.86353	+	2.54048i	0.0898675	+	0.122513i
$431$	7.90072	+	17.3002i	0.380564	+	0.833319i	0.998877	+	0.0473869i	$0.0150894\pi$
$431$	7.90072	+	17.3002i	0.380564	+	0.833319i	−0.618312	+	0.785932i	$0.712183\pi$
$432$	0.695174	−	17.8745i	0.0334466	−	0.859988i
$433$	−14.4190	−	6.58493i	−0.692932	−	0.316452i	0.0376357	−	0.999292i	$-0.488017\pi$
$433$	−14.4190	−	6.58493i	−0.692932	−	0.316452i	−0.730568	+	0.682840i	$0.760745\pi$
$434$	−1.13765	+	4.99546i	−0.0546089	+	0.239790i
$435$	−4.59505	+	2.95306i	−0.220316	+	0.141588i
$436$	0.207336	−	1.26676i	0.00992962	−	0.0606669i
$437$	−0.398784	−	0.0738439i	−0.0190764	−	0.00353243i
$438$	8.58297	+	0.697763i	0.410110	+	0.0333404i
$439$	−15.9982	−	24.8937i	−0.763553	−	1.18811i	−0.977432	−	0.211251i	$-0.932246\pi$
$439$	−15.9982	−	24.8937i	−0.763553	−	1.18811i	0.213879	−	0.976860i	$-0.431390\pi$
$440$	14.5493	−	35.7859i	0.693612	−	1.70603i
$441$	3.96194	−	8.67544i	0.188664	−	0.413116i
$442$	6.47565	−	1.34292i	0.308015	−	0.0638762i
$443$	−22.4811	+	10.2668i	−1.06811	+	0.487789i	−0.870335	−	0.492459i	$-0.836098\pi$
$443$	−22.4811	+	10.2668i	−1.06811	+	0.487789i	−0.197773	+	0.980248i	$0.563371\pi$
$444$	5.16760	+	8.39532i	0.245243	+	0.398424i
$445$	−0.868193	−	6.03842i	−0.0411563	−	0.286248i
$446$	−11.2130	−	4.30681i	−0.530950	−	0.203933i
$447$	−0.578042	+	0.667096i	−0.0273405	+	0.0315526i
$448$	−13.1237	−	23.3036i	−0.620034	−	1.10099i
$449$	−13.4420	−	8.63865i	−0.634367	−	0.407683i	0.183557	−	0.983009i	$-0.441239\pi$
$449$	−13.4420	−	8.63865i	−0.634367	−	0.407683i	−0.817924	+	0.575326i	$0.804875\pi$
$450$	−10.2572	−	10.4586i	−0.483531	−	0.493022i
$451$	−18.8544	−	5.53616i	−0.887820	−	0.260688i
$452$	34.4062	+	0.668809i	1.61833	+	0.0314581i
$453$	4.95115	+	5.71393i	0.232625	+	0.268464i
$454$	−34.8957	+	12.6305i	−1.63774	+	0.592779i
$455$	−1.93128	−	6.57735i	−0.0905399	−	0.308351i
$456$	−0.125994	+	0.158461i	−0.00590023	+	0.00742064i
$457$	7.56544	+	1.08775i	0.353896	+	0.0508826i	0.316970	−	0.948435i	$-0.397334\pi$
$457$	7.56544	+	1.08775i	0.353896	+	0.0508826i	0.0369258	+	0.999318i	$0.488243\pi$
$458$	−4.01254	+	2.14066i	−0.187494	+	0.100026i
$459$	31.4948			1.47005
$460$	1.76827	−	29.5665i	0.0824460	−	1.37855i
$461$	−36.0717			−1.68003			−0.840013	−	0.542567i	$-0.817453\pi$
$461$	−36.0717			−1.68003			−0.840013	+	0.542567i	$0.817453\pi$
$462$	15.6154	−	8.33070i	0.726495	−	0.387579i
$463$	−3.14515	−	0.452204i	−0.146168	−	0.0210157i	0.0688426	−	0.997628i	$-0.478069\pi$
$463$	−3.14515	−	0.452204i	−0.146168	−	0.0210157i	−0.215010	+	0.976612i	$0.568978\pi$
$464$	5.71557	−	6.10004i	0.265339	−	0.283187i
$465$	0.797957	+	2.71759i	0.0370044	+	0.126025i
$466$	−30.6417	+	11.0908i	−1.41945	+	0.513770i
$467$	−8.73659	−	10.0826i	−0.404281	−	0.466565i	0.516703	−	0.856164i	$-0.327159\pi$
$467$	−8.73659	−	10.0826i	−0.404281	−	0.466565i	−0.920985	+	0.389599i	$0.872614\pi$
$468$	−0.0589405	+	3.03213i	−0.00272452	+	0.140160i
$469$	28.7261	+	8.43475i	1.32645	+	0.389481i
$470$	30.5367	+	31.1361i	1.40855	+	1.43620i
$471$	−7.20823	−	4.63245i	−0.332138	−	0.213452i
$472$	−6.27352	−	6.65042i	−0.288762	−	0.306110i
$473$	2.08958	−	2.41151i	0.0960792	−	0.110881i
$474$	−5.49053	−	2.10887i	−0.252189	−	0.0968635i
$475$	0.0545900	+	0.379682i	0.00250476	+	0.0174210i
$476$	40.1008	−	24.6834i	1.83802	−	1.13136i
$477$	−12.8648	+	5.87516i	−0.589039	+	0.269005i
$478$	−33.5924	+	6.96638i	−1.53648	+	0.318635i
$479$	−1.92972	+	4.22550i	−0.0881713	+	0.193068i	−0.948581	−	0.316535i	$-0.897481\pi$
$479$	−1.92972	+	4.22550i	−0.0881713	+	0.193068i	0.860410	+	0.509603i	$0.170208\pi$
$480$	−12.6172	−	7.70773i	−0.575893	−	0.351808i
$481$	−2.09067	−	3.25314i	−0.0953262	−	0.148330i
$482$	3.14079	+	0.255335i	0.143059	+	0.0116302i
$483$	9.29254	−	9.88930i	0.422825	−	0.449979i
$484$	−16.8986	−	2.76586i	−0.768117	−	0.125721i
$485$	35.7678	−	22.9866i	1.62413	−	1.04377i
$486$	−5.02786	+	22.0775i	−0.228069	+	1.00146i
$487$	19.5944	+	8.94848i	0.887908	+	0.405494i	0.806533	−	0.591189i	$-0.201341\pi$
$487$	19.5944	+	8.94848i	0.887908	+	0.405494i	0.0813755	+	0.996684i	$0.474069\pi$
$488$	7.24850	−	0.306399i	0.328124	−	0.0138701i
$489$	−1.54382	−	3.38049i	−0.0698138	−	0.152871i
$490$	−10.7877	−	14.7065i	−0.487341	−	0.664372i
$491$	23.1213	−	3.32434i	1.04345	−	0.150025i	0.400785	−	0.916172i	$-0.368738\pi$
$491$	23.1213	−	3.32434i	1.04345	−	0.150025i	0.642666	+	0.766147i	$0.277828\pi$
$492$	−3.25666	+	6.77922i	−0.146821	+	0.305631i
$493$	11.1231	+	9.63820i	0.500958	+	0.434083i
$494$	0.0482053	−	0.0631070i	0.00216886	−	0.00283932i
$495$	−16.8624	+	26.2384i	−0.757907	+	1.17933i
$496$	−2.19998	−	3.73482i	−0.0987821	−	0.167698i
$497$	7.56188	−	25.7534i	0.339197	−	1.15520i
$498$	0.874701	+	14.1629i	0.0391963	+	0.634654i
$499$	−20.6574	+	17.8997i	−0.924751	+	0.801301i	−0.980373	−	0.197151i	$-0.936831\pi$
$499$	−20.6574	+	17.8997i	−0.924751	+	0.801301i	0.0556221	+	0.998452i	$0.482286\pi$
$500$	2.76508	−	0.753850i	0.123658	−	0.0337132i
$501$	18.8087	−	5.52273i	0.840311	−	0.246737i
$502$	−9.46843	−	5.29024i	−0.422597	−	0.236115i
$503$	0.999263	−	6.95003i	0.0445549	−	0.309886i	−0.955342	−	0.295504i	$-0.904513\pi$
$503$	0.999263	−	6.95003i	0.0445549	−	0.309886i	0.999897	−	0.0143828i	$-0.00457835\pi$
$504$	6.95314	+	20.4433i	0.309717	+	0.910615i
$505$		−	25.6266i		−	1.14037i
$506$	−29.5939	+	4.90293i	−1.31561	+	0.217962i
$507$		−	10.6299i		−	0.472090i
$508$	7.67181	+	17.7015i	0.340381	+	0.785377i
$509$	−3.89263	+	27.0739i	−0.172538	+	1.20003i	0.700960	+	0.713201i	$0.252755\pi$
$509$	−3.89263	+	27.0739i	−0.172538	+	1.20003i	−0.873498	+	0.486828i	$0.838154\pi$
$510$	12.6971	−	22.7252i	0.562239	−	1.00629i
$511$	−23.0768	+	6.77595i	−1.02086	+	0.299750i
$512$	21.6057	+	6.72278i	0.954844	+	0.297108i
$513$	0.285809	−	0.247655i	0.0126188	−	0.0109342i
$514$	16.1101	−	0.994964i	0.710588	−	0.0438860i
$515$	8.57352	−	29.1987i	0.377794	−	1.28665i
$516$	−0.781666	−	0.938336i	−0.0344109	−	0.0413079i
$517$	23.8789	−	37.1563i	1.05019	−	1.63413i
$518$	−21.8805	−	16.7138i	−0.961375	−	0.734362i
$519$	−1.22414	−	1.06072i	−0.0537338	−	0.0465606i
$520$	5.00706	+	2.92668i	0.219574	+	0.128344i
$521$	−5.62811	+	0.809200i	−0.246572	+	0.0354517i	−0.264493	−	0.964388i	$-0.585204\pi$
$521$	−5.62811	+	0.809200i	−0.246572	+	0.0354517i	0.0179206	+	0.999839i	$0.494295\pi$
$522$	−5.44204	+	3.99193i	−0.238192	+	0.174722i
$523$	−0.247609	−	0.542188i	−0.0108272	−	0.0237082i	0.904141	−	0.427234i	$-0.140512\pi$
$523$	−0.247609	−	0.542188i	−0.0108272	−	0.0237082i	−0.914968	+	0.403526i	$0.867785\pi$
$524$	3.96791	+	32.0011i	0.173339	+	1.39797i
$525$	−11.6750	−	5.33178i	−0.509537	−	0.232698i
$526$	18.8733	+	4.29813i	0.822914	+	0.187408i
$527$	6.42026	−	4.12605i	0.279671	−	0.179734i
$528$	−4.77379	+	14.1925i	−0.207753	+	0.617650i
$529$	−20.2872	+	10.8366i	−0.882050	+	0.471156i
$530$	−2.19155	+	26.9575i	−0.0951946	+	1.17096i
$531$	3.99073	+	6.20970i	0.173183	+	0.269478i
$532$	0.169813	−	0.539323i	0.00736231	−	0.0233826i
$533$	1.22554	−	2.68355i	0.0530839	−	0.116238i
$534$	0.480168	+	2.31540i	0.0207789	+	0.100197i
$535$	35.9325	−	16.4098i	1.55350	−	0.709459i
$536$	−22.5757	+	11.4860i	−0.975123	+	0.496120i
$537$	0.506618	+	3.52361i	0.0218622	+	0.152055i
$538$	9.99586	−	26.0247i	0.430952	−	1.12200i
$539$	−12.0963	+	13.9599i	−0.521026	+	0.601296i
$540$	20.5179	+	18.4891i	0.882950	+	0.795646i
$541$	13.8600	+	8.90729i	0.595889	+	0.382954i	0.803542	−	0.595248i	$-0.202946\pi$
$541$	13.8600	+	8.90729i	0.595889	+	0.382954i	−0.207653	+	0.978202i	$0.566583\pi$
$542$	−0.747826	+	0.733431i	−0.0321219	+	0.0315035i
$543$	−4.64653	−	1.36434i	−0.199402	−	0.0585496i
$544$	−10.3493	+	38.4715i	−0.443721	+	1.64945i
$545$	1.29789	+	1.49784i	0.0555953	+	0.0641605i
$546$	0.904334	+	2.49850i	0.0387019	+	0.106926i
$547$	8.10787	+	27.6129i	0.346668	+	1.18064i	0.929739	+	0.368220i	$0.120033\pi$
$547$	8.10787	+	27.6129i	0.346668	+	1.18064i	−0.583071	+	0.812421i	$0.698149\pi$
$548$	1.20409	+	0.807316i	0.0514364	+	0.0344868i
$549$	−5.79792	−	0.833615i	−0.247449	−	0.0355778i
$550$	13.3545	+	25.0323i	0.569439	+	1.06738i
$551$	0.176728			0.00752887
$552$	0.0223476	+	11.4810i	0.000951176	+	0.488663i
$553$	16.4271			0.698551
$554$	13.0526	+	24.4663i	0.554551	+	1.03947i
$555$	−15.0664	−	2.16622i	−0.639533	−	0.0919510i
$556$	−22.9781	−	15.4062i	−0.974487	−	0.653369i
$557$	−9.07075	−	30.8921i	−0.384340	−	1.30894i	−0.893807	−	0.448451i	$-0.851976\pi$
$557$	−9.07075	−	30.8921i	−0.384340	−	1.30894i	0.509467	−	0.860490i	$-0.329842\pi$
$558$	1.19109	+	3.29076i	0.0504229	+	0.139309i
$559$	0.313713	+	0.362044i	0.0132686	+	0.0153128i
$560$	40.6150	+	7.46086i	1.71630	+	0.315279i
$561$	−25.2960	−	7.42758i	−1.06800	−	0.313593i
$562$	3.40996	−	3.34432i	0.143840	−	0.141071i
$563$	−19.7258	−	12.6770i	−0.831343	−	0.534271i	0.0543617	−	0.998521i	$-0.482688\pi$
$563$	−19.7258	−	12.6770i	−0.831343	−	0.534271i	−0.885704	+	0.464250i	$0.846324\pi$
$564$	−12.5580	−	11.3163i	−0.528788	−	0.476502i
$565$	−34.7953	+	40.1559i	−1.46385	+	1.68937i
$566$	−7.02852	+	18.2991i	−0.295431	+	0.769168i
$567$	−1.45863	−	10.1450i	−0.0612567	−	0.426050i
$568$	10.2974	+	20.2395i	0.432068	+	0.849229i
$569$	1.26223	−	0.576443i	0.0529156	−	0.0241657i	−0.388781	−	0.921330i	$-0.627104\pi$
$569$	1.26223	−	0.576443i	0.0529156	−	0.0241657i	0.441697	+	0.897164i	$0.354377\pi$
$570$	−0.0634725	−	0.306069i	−0.00265857	−	0.0128198i
$571$	3.54564	−	7.76388i	0.148381	−	0.324908i	−0.820818	−	0.571190i	$-0.806482\pi$
$571$	3.54564	−	7.76388i	0.148381	−	0.324908i	0.969198	+	0.246282i	$0.0792090\pi$
$572$	1.76402	−	5.60252i	0.0737574	−	0.234253i
$573$	−9.86374	−	15.3483i	−0.412064	−	0.641184i
$574$	1.70206	−	20.9365i	0.0710425	−	0.873871i
$575$	15.8530	+	14.8964i	0.661117	+	0.621223i
$576$	−16.1475	−	8.54474i	−0.672814	−	0.356031i
$577$	26.1245	−	16.7892i	1.08758	−	0.698943i	0.131281	−	0.991345i	$-0.458091\pi$
$577$	26.1245	−	16.7892i	1.08758	−	0.698943i	0.956295	+	0.292403i	$0.0944547\pi$
$578$	−44.9509	−	10.2370i	−1.86971	−	0.425801i
$579$	13.4917	+	6.16144i	0.560695	+	0.256061i
$580$	1.58821	+	12.8088i	0.0659468	+	0.531858i
$581$	−16.4636	−	36.0503i	−0.683026	−	1.49562i
$582$	−13.2886	+	9.74769i	−0.550832	+	0.404055i
$583$	27.1127	−	3.89822i	1.12289	−	0.161448i
$584$	10.2683	−	17.5674i	0.424907	−	0.726943i
$585$	−3.53884	−	3.06642i	−0.146313	−	0.126781i
$586$	−5.87224	−	4.48561i	−0.242580	−	0.185299i
$587$	2.23271	−	3.47416i	0.0921538	−	0.143394i	−0.792116	−	0.610371i	$-0.791020\pi$
$587$	2.23271	−	3.47416i	0.0921538	−	0.143394i	0.884270	+	0.466977i	$0.154657\pi$
$588$	4.52496	+	5.43190i	0.186606	+	0.224008i
$589$	0.0258179	−	0.0879278i	0.00106381	−	0.00362300i
$590$	14.0893	−	0.870157i	0.580048	−	0.0358238i
$591$	14.4721	−	12.5402i	0.595304	−	0.515834i
$592$	23.1692	−	2.41662i	0.952247	−	0.0993223i
$593$	17.0812	−	5.01549i	0.701440	−	0.205961i	0.0884831	−	0.996078i	$-0.471798\pi$
$593$	17.0812	−	5.01549i	0.701440	−	0.205961i	0.612957	+	0.790116i	$0.289980\pi$
$594$	13.6434	−	24.4189i	0.559796	−	1.00192i
$595$	−10.3471	+	71.9657i	−0.424190	+	2.95031i
$596$	0.829429	+	1.91378i	0.0339747	+	0.0783914i
$597$		−	6.68370i		−	0.273546i
$598$	−0.0962905	−	4.50252i	−0.00393761	−	0.184122i
$599$			5.53940i			0.226334i	0.993576	+	0.113167i	$0.0360995\pi$
$599$			5.53940i			0.226334i	−0.993576	+	0.113167i	$0.963901\pi$
$600$	10.2805	−	3.49659i	0.419699	−	0.142748i
$601$	1.18541	−	8.24468i	0.0483537	−	0.336308i	−0.951257	−	0.308400i	$-0.900206\pi$
$601$	1.18541	−	8.24468i	0.0483537	−	0.336308i	0.999611	−	0.0279077i	$-0.00888444\pi$
$602$	2.97768	+	1.66370i	0.121361	+	0.0678074i
$603$	19.6223	−	5.76164i	0.799083	−	0.234632i
$604$	17.2365	−	4.69921i	0.701341	−	0.191208i
$605$	19.9811	−	17.3138i	0.812349	−	0.703905i
$606$	0.612317	+	9.91444i	0.0248737	+	0.402747i
$607$	−5.51262	+	18.7743i	−0.223751	+	0.762024i	0.768725	+	0.639580i	$0.220892\pi$
$607$	−5.51262	+	18.7743i	−0.223751	+	0.762024i	−0.992475	+	0.122445i	$0.960927\pi$
$608$	0.208598	+	0.430501i	0.00845975	+	0.0174591i
$609$	−3.19699	+	4.97461i	−0.129549	+	0.201582i
$610$	−6.79982	+	8.90184i	−0.275317	+	0.360425i
$611$	5.01136	+	4.34237i	0.202738	+	0.175673i
$612$	13.9282	−	28.9936i	0.563012	−	1.17200i
$613$	−40.7154	+	5.85399i	−1.64448	+	0.236440i	−0.901470	−	0.432842i	$-0.857511\pi$
$613$	−40.7154	+	5.85399i	−1.64448	+	0.236440i	−0.743008	+	0.669282i	$0.766602\pi$
$614$	13.3091	+	18.1438i	0.537113	+	0.732225i
$615$	−4.82395	−	10.5630i	−0.194521	−	0.425941i
$616$	−1.76625	−	41.7841i	−0.0711641	−	1.68353i
$617$	24.9382	+	11.3889i	1.00397	+	0.458500i	0.848418	−	0.529327i	$-0.177556\pi$
$617$	24.9382	+	11.3889i	1.00397	+	0.458500i	0.155557	+	0.987827i	$0.450283\pi$
$618$	−2.61926	+	11.5013i	−0.105362	+	0.462649i
$619$	−1.27298	+	0.818096i	−0.0511655	+	0.0328821i	−0.565974	−	0.824423i	$-0.691500\pi$
$619$	−1.27298	+	0.818096i	−0.0511655	+	0.0328821i	0.514808	+	0.857305i	$0.327863\pi$
$620$	6.60482	+	1.08104i	0.265256	+	0.0434156i
$621$	3.90501	−	21.0885i	0.156703	−	0.846252i
$622$	8.36997	+	0.680448i	0.335605	+	0.0272835i
$623$	−3.57062	−	5.55600i	−0.143054	−	0.222596i
$624$	−2.00706	−	1.01264i	−0.0803469	−	0.0405380i
$625$	−11.2598	+	24.6555i	−0.450391	+	0.986220i
$626$	−19.6015	+	4.06495i	−0.783432	+	0.162468i
$627$	−0.287962	+	0.131508i	−0.0115001	+	0.00525191i
$628$	−17.2424	+	10.6133i	−0.688046	+	0.423515i
$629$	5.83695	+	40.5969i	0.232735	+	1.61870i
$630$	−31.1237	−	11.9543i	−1.24000	−	0.476272i
$631$	13.7222	−	15.8362i	0.546271	−	0.630430i	−0.413739	−	0.910395i	$-0.635777\pi$
$631$	13.7222	−	15.8362i	0.546271	−	0.630430i	0.960010	+	0.279965i	$0.0903229\pi$
$632$	−10.1097	+	9.53679i	−0.402143	+	0.379353i
$633$	9.89551	+	6.35946i	0.393311	+	0.252766i
$634$	23.5823	+	24.0452i	0.936574	+	0.954956i
$635$	−28.5813	−	8.39222i	−1.13421	−	0.333035i
$636$	0.203750	−	10.4817i	0.00807920	−	0.415626i
$637$	−1.81604	−	2.09583i	−0.0719542	−	0.0830396i
$638$	12.2913	−	4.44883i	0.486616	−	0.176131i
$639$	−5.16539	−	17.5917i	−0.204340	−	0.695917i
$640$	−29.3271	+	18.9875i	−1.15925	+	0.750545i
$641$	23.3242	+	3.35352i	0.921251	+	0.132456i	0.586591	−	0.809883i	$-0.300470\pi$
$641$	23.3242	+	3.35352i	0.921251	+	0.132456i	0.334660	+	0.942339i	$0.391379\pi$
$642$	−13.5095	+	7.20721i	−0.533178	+	0.284446i
$643$	−29.1525			−1.14966			−0.574831	−	0.818272i	$-0.694932\pi$
$643$	−29.1525			−1.14966			−0.574831	+	0.818272i	$0.694932\pi$
$644$	−11.5556	−	29.9115i	−0.455354	−	1.17868i
$645$	1.88565			0.0742472
$646$	−0.743121	+	0.396449i	−0.0292377	+	0.0155981i
$647$	−19.8454	−	2.85334i	−0.780204	−	0.112176i	−0.259306	−	0.965795i	$-0.583494\pi$
$647$	−19.8454	−	2.85334i	−0.780204	−	0.112176i	−0.520898	+	0.853619i	$0.674403\pi$
$648$	6.78739	+	5.39673i	0.266634	+	0.212003i
$649$	−4.02773	−	13.7172i	−0.158102	−	0.538446i
$650$	−4.00522	+	1.44969i	−0.157098	+	0.0568616i
$651$	2.00798	+	2.31734i	0.0786991	+	0.0908236i
$652$	−8.77992	−	0.170669i	−0.343848	−	0.00668393i
$653$	25.6134	+	7.52079i	1.00233	+	0.294311i	0.741413	−	0.671049i	$-0.234156\pi$
$653$	25.6134	+	7.52079i	1.00233	+	0.294311i	0.260919	+	0.965361i	$0.415974\pi$
$654$	−0.537916	−	0.548474i	−0.0210342	−	0.0214470i
$655$	−41.8848	−	26.9177i	−1.63657	−	1.05176i
$656$	11.1072	+	13.8731i	0.433664	+	0.541652i
$657$	−10.7586	+	12.4161i	−0.419733	+	0.484397i
$658$	44.0744	+	16.9286i	1.71820	+	0.659945i
$659$	1.04175	+	7.24553i	0.0405808	+	0.282246i	1.00000		0.000261894i	$8.33635e-5\pi$
$659$	1.04175	+	7.24553i	0.0405808	+	0.282246i	−0.959419	+	0.281984i	$0.909008\pi$
$660$	−12.1192	−	19.6890i	−0.471739	−	0.766392i
$661$	23.7076	−	10.8269i	0.922117	−	0.421117i	0.102960	−	0.994686i	$-0.467169\pi$
$661$	23.7076	−	10.8269i	0.922117	−	0.421117i	0.819157	+	0.573569i	$0.194441\pi$
$662$	−2.42922	+	0.503770i	−0.0944141	+	0.0195796i
$663$	1.64424	−	3.60038i	0.0638570	−	0.139827i
$664$	31.0613	+	12.6284i	1.20541	+	0.490079i
$665$	0.471994	+	0.734437i	0.0183031	+	0.0284802i
$666$	−18.7460	−	1.52398i	−0.726393	−	0.0590531i
$667$	7.83275	−	6.25283i	0.303285	−	0.242111i
$668$	7.48197	−	45.7126i	0.289486	−	1.76867i
$669$	−6.04763	+	3.88657i	−0.233815	+	0.150264i
$670$	8.68429	−	38.1331i	0.335503	−	1.47321i
$671$	10.3195	+	4.71277i	0.398381	+	0.181935i
$672$	−15.8914	−	1.91602i	−0.613025	−	0.0739120i
$673$	12.9656	+	28.3907i	0.499787	+	1.09438i	0.976539	+	0.215342i	$0.0690867\pi$
$673$	12.9656	+	28.3907i	0.499787	+	1.09438i	−0.476752	+	0.879038i	$0.658186\pi$
$674$	−11.8758	−	16.1899i	−0.457440	−	0.623610i
$675$	−20.0783	+	2.88683i	−0.772816	+	0.111114i
$676$	−22.6412	−	10.8766i	−0.870815	−	0.418329i
$677$	5.58351	+	4.83814i	0.214592	+	0.185945i	0.755523	−	0.655122i	$-0.227383\pi$
$677$	5.58351	+	4.83814i	0.214592	+	0.185945i	−0.540931	+	0.841067i	$0.681928\pi$
$678$	12.5021	−	16.3669i	0.480142	−	0.628568i
$679$	24.8853	−	38.7223i	0.955011	−	1.48603i
$680$	−35.4119	−	50.2969i	−1.35799	−	1.92880i
$681$	−6.25745	+	21.3109i	−0.239786	+	0.816637i
$682$	−0.417820	−	6.76521i	−0.0159992	−	0.259053i
$683$	−4.13553	+	3.58346i	−0.158242	+	0.137117i	−0.730383	−	0.683038i	$-0.760658\pi$
$683$	−4.13553	+	3.58346i	−0.158242	+	0.137117i	0.572141	+	0.820155i	$0.306113\pi$
$684$	−0.101591	−	0.372632i	−0.00388445	−	0.0142480i
$685$	−2.14768	+	0.630615i	−0.0820585	+	0.0240946i
$686$	11.6540	+	6.51137i	0.444952	+	0.248605i
$687$	−0.387357	+	2.69413i	−0.0147786	+	0.102787i
$688$	−2.79842	+	0.704805i	−0.106689	+	0.0268704i
$689$			4.11234i			0.156668i
$690$	−13.6422	−	11.3195i	−0.519350	−	0.430927i
$691$			35.1026i			1.33537i	0.744445	+	0.667684i	$0.232714\pi$
$691$			35.1026i			1.33537i	−0.744445	+	0.667684i	$0.767286\pi$
$692$	−3.51184	+	1.52203i	−0.133500	+	0.0578588i
$693$	−4.80539	+	33.4222i	−0.182542	+	1.26961i
$694$	−2.28947	+	4.09767i	−0.0869071	+	0.155546i
$695$	40.9847	−	12.0342i	1.55464	−	0.456483i
$696$	−0.920499	−	4.91755i	−0.0348914	−	0.186399i
$697$	−23.6473	+	20.4905i	−0.895707	+	0.776134i
$698$	−19.8915	+	1.22850i	−0.752903	+	0.0464994i
$699$	−5.49463	+	18.7130i	−0.207826	+	0.707791i
$700$	−23.3023	+	19.4116i	−0.880745	+	0.733691i
$701$	−16.1509	+	25.1313i	−0.610012	+	0.949197i	0.389590	+	0.920988i	$0.372617\pi$
$701$	−16.1509	+	25.1313i	−0.610012	+	0.949197i	−0.999602	+	0.0282090i	$0.991020\pi$
$702$	3.33723	+	2.54920i	0.125956	+	0.0962132i
$703$	0.372197	+	0.322510i	0.0140377	+	0.0121637i
$704$	25.3449	+	24.6898i	0.955221	+	0.930532i
$705$	25.8352	−	3.71454i	0.973009	−	0.139898i
$706$	21.8468	−	16.0254i	0.822214	−	0.603123i
$707$	−11.5250	−	25.2363i	−0.433443	−	0.949109i
$708$	−5.43009	+	0.673294i	−0.204075	+	0.0253039i
$709$	−44.0947	−	20.1374i	−1.65601	−	0.756275i	−0.999999	−	0.00152411i	$-0.999515\pi$
$709$	−44.0947	−	20.1374i	−1.65601	−	0.756275i	−0.656012	−	0.754751i	$-0.727758\pi$
$710$	−34.1868	−	7.78559i	−1.28301	−	0.292188i
$711$	9.43977	−	6.06657i	0.354019	−	0.227514i
$712$	5.42301	+	1.34639i	0.203236	+	0.0504582i
$713$	−1.96671	−	4.81051i	−0.0736537	−	0.180155i
$714$	2.28356	−	28.0894i	0.0854602	−	1.05122i
$715$	4.90309	+	7.62936i	0.183365	+	0.285322i
$716$	8.02350	+	2.52630i	0.299852	+	0.0944121i
$717$	−8.52947	+	18.6769i	−0.318539	+	0.697503i
$718$	−3.95030	−	19.0486i	−0.147424	−	0.710889i
$719$	−6.01042	+	2.74487i	−0.224151	+	0.102366i	−0.524325	−	0.851518i	$-0.675682\pi$
$719$	−6.01042	+	2.74487i	−0.224151	+	0.102366i	0.300174	+	0.953884i	$0.402955\pi$
$720$	26.0946	−	10.7119i	0.972487	−	0.399207i
$721$	−4.68858	−	32.6098i	−0.174612	−	1.21445i
$722$	9.63071	−	25.0740i	0.358418	−	0.933158i
$723$	1.23502	−	1.42529i	0.0459309	−	0.0530071i
$724$	−7.66034	+	8.50090i	−0.284694	+	0.315933i
$725$	−7.97455	−	5.12493i	−0.296167	−	0.190335i
$726$	−7.31663	+	7.17579i	−0.271546	+	0.266318i
$727$	7.49170	+	2.19976i	0.277852	+	0.0815847i	0.417690	−	0.908590i	$-0.362840\pi$
$727$	7.49170	+	2.19976i	0.277852	+	0.0815847i	−0.139838	+	0.990174i	$0.544658\pi$
$728$	6.24701	+	0.630289i	0.231530	+	0.0233600i
$729$	2.85130	+	3.29057i	0.105604	+	0.121873i
$730$	10.6929	+	29.5424i	0.395762	+	1.09341i
$731$	−1.43146	−	4.87512i	−0.0529446	−	0.180313i
$732$	2.41802	−	3.60642i	0.0893726	−	0.133297i
$733$	−21.1996	−	3.04804i	−0.783024	−	0.112582i	−0.260803	−	0.965392i	$-0.583987\pi$
$733$	−21.1996	−	3.04804i	−0.783024	−	0.112582i	−0.522221	+	0.852810i	$0.674896\pi$
$734$	−3.57209	−	6.69568i	−0.131848	−	0.247142i
$735$	−10.9158			−0.402634
$736$	24.4768	+	11.6998i	0.902228	+	0.431260i
$737$	−39.6085			−1.45900
$738$	−6.75381	−	12.6596i	−0.248611	−	0.466008i
$739$	30.3336	+	4.36131i	1.11584	+	0.160433i	0.675473	−	0.737385i	$-0.263940\pi$
$739$	30.3336	+	4.36131i	1.11584	+	0.160433i	0.440366	+	0.897818i	$0.354849\pi$
$740$	−20.0300	+	29.8743i	−0.736316	+	1.09820i
$741$	−0.0133899	−	0.0456019i	−0.000491892	−	0.00167523i
$742$	9.96541	+	27.5325i	0.365842	+	1.01075i
$743$	−8.16266	−	9.42021i	−0.299459	−	0.345594i	0.586000	−	0.810311i	$-0.300702\pi$
$743$	−8.16266	−	9.42021i	−0.299459	−	0.345594i	−0.885459	+	0.464717i	$0.846156\pi$
$744$	−2.58111	−	0.260419i	−0.0946280	−	0.00954743i
$745$	−3.09004	−	0.907316i	−0.113210	−	0.0332415i
$746$	17.9914	−	17.6450i	0.658710	−	0.646030i
$747$	−22.7742	−	14.6361i	−0.833266	−	0.535507i
$748$	−41.7034	+	46.2794i	−1.52483	+	1.69214i
$749$	28.0053	−	32.3198i	1.02329	−	1.18094i
$750$	0.615015	−	1.60122i	0.0224572	−	0.0584683i
$751$	−0.323766	−	2.25184i	−0.0118144	−	0.0821708i	0.983061	−	0.183278i	$-0.0586707\pi$
$751$	−0.323766	−	2.25184i	−0.0118144	−	0.0821708i	−0.994876	+	0.101107i	$0.967762\pi$
$752$	−36.9526	+	15.1691i	−1.34752	+	0.553161i
$753$	−5.90466	+	2.69657i	−0.215178	+	0.0982684i
$754$	0.398497	+	1.92158i	0.0145124	+	0.0699798i
$755$	−11.4591	+	25.0919i	−0.417039	+	0.913189i
$756$	28.5205	+	8.98003i	1.03728	+	0.326601i
$757$	7.18139	+	11.1745i	0.261012	+	0.406143i	0.946882	−	0.321581i	$-0.104214\pi$
$757$	7.18139	+	11.1745i	0.261012	+	0.406143i	−0.685870	+	0.727724i	$0.740578\pi$
$758$	3.80515	−	46.8060i	0.138209	−	1.70007i
$759$	−8.10984	+	16.0169i	−0.294369	+	0.581378i
$760$	−0.716858	−	0.177977i	−0.0260032	−	0.00645592i
$761$	−12.9134	+	8.29895i	−0.468111	+	0.300837i	−0.753350	−	0.657620i	$-0.771563\pi$
$761$	−12.9134	+	8.29895i	−0.468111	+	0.300837i	0.285239	+	0.958456i	$0.407927\pi$
$762$	11.2581	+	2.56387i	0.407837	+	0.0928794i
$763$	1.95174	+	0.891330i	0.0706578	+	0.0322683i
$764$	−42.7838	+	5.30489i	−1.54786	+	0.191924i
$765$	20.6312	+	45.1760i	0.745923	+	1.63334i
$766$	10.7390	−	7.87744i	0.388016	−	0.284624i
$767$	2.12448	−	0.305454i	0.0767105	−	0.0110293i
$768$	10.8924	−	8.04662i	0.393046	−	0.290357i
$769$	−16.6153	−	14.3972i	−0.599162	−	0.519177i	0.301631	−	0.953425i	$-0.402469\pi$
$769$	−16.6153	−	14.3972i	−0.599162	−	0.519177i	−0.900794	+	0.434247i	$0.857014\pi$
$770$	51.3149	+	39.1977i	1.84926	+	1.41259i
$771$	5.22265	−	8.12660i	0.188089	−	0.292672i
$772$	26.9283	−	22.4322i	0.969172	−	0.807354i
$773$	−8.18357	+	27.8707i	−0.294343	+	1.00244i	0.671001	+	0.741456i	$0.265865\pi$
$773$	−8.18357	+	27.8707i	−0.294343	+	1.00244i	−0.965344	+	0.260982i	$0.915954\pi$
$774$	2.32552	−	0.143624i	0.0835891	−	0.00516247i
$775$	−3.71480	+	3.21890i	−0.133440	+	0.115626i
$776$	7.16515	+	38.2781i	0.257214	+	1.37410i
$777$	−15.8111	+	4.64257i	−0.567222	+	0.166551i
$778$	−5.33235	+	9.54380i	−0.191174	+	0.342162i
$779$	−0.0534703	+	0.371894i	−0.00191577	+	0.0133245i
$780$	3.18479	−	1.38028i	0.114034	−	0.0494221i
$781$			35.5096i			1.27063i
$782$	−18.9090	+	43.8634i	−0.676185	+	1.56855i
$783$			9.34574i			0.333989i
$784$	16.1997	−	4.08002i	0.578560	−	0.145715i
$785$	4.44901	−	30.9435i	0.158792	−	1.10442i
$786$	16.8476	+	9.41316i	0.600933	+	0.335756i
$787$	41.4535	−	12.1718i	1.47766	−	0.433879i	0.559078	−	0.829115i	$-0.311155\pi$
$787$	41.4535	−	12.1718i	1.47766	−	0.433879i	0.918580	+	0.395236i	$0.129337\pi$
$788$	−11.9021	−	43.6562i	−0.423993	−	1.55519i
$789$	8.75509	−	7.58633i	0.311690	−	0.270080i
$790$	−1.32278	−	21.4181i	−0.0470625	−	0.762021i
$791$	−16.2060	+	55.1927i	−0.576220	+	1.96243i
$792$	−16.4460	−	23.3588i	−0.584382	−	0.830020i
$793$	−0.920822	+	1.43283i	−0.0326993	+	0.0508812i
$794$	1.68303	−	2.20331i	0.0597286	−	0.0781925i
$795$	12.2333	+	10.6002i	0.433871	+	0.375951i
$796$	−14.2360	−	6.83879i	−0.504581	−	0.242394i
$797$	53.9281	−	7.75369i	1.91023	−	0.274650i	0.917761	−	0.397132i	$-0.129995\pi$
$797$	53.9281	−	7.75369i	1.91023	−	0.274650i	0.992471	+	0.122482i	$0.0390855\pi$
$798$	−0.200154	−	0.272862i	−0.00708537	−	0.00965920i
$799$	−29.2160	−	63.9740i	−1.03359	−	2.26324i
$800$	3.07147	−	25.4747i	0.108593	−	0.900667i
$801$	−4.10369	−	1.87409i	−0.144997	−	0.0662178i
$802$	10.5045	−	46.1258i	0.370928	−	1.62876i
$803$	26.7678	−	17.2026i	0.944615	−	0.607067i
$804$	−2.44864	+	14.9604i	−0.0863569	+	0.527614i
$805$	46.9044	+	15.8513i	1.65316	+	0.558684i
$806$	1.01426	+	0.0824558i	0.0357259	+	0.00290438i
$807$	−9.02052	−	14.0362i	−0.317537	−	0.494098i
$808$	21.7438	+	8.84029i	0.764945	+	0.311000i
$809$	14.6056	−	31.9819i	0.513507	−	1.12442i	−0.458333	−	0.888780i	$-0.651553\pi$
$809$	14.6056	−	31.9819i	0.513507	−	1.12442i	0.971840	−	0.235642i	$-0.0757194\pi$
$810$	−13.1099	+	2.71872i	−0.460633	+	0.0955261i
$811$	−25.1569	+	11.4888i	−0.883378	+	0.403425i	−0.804844	−	0.593486i	$-0.797751\pi$
$811$	−25.1569	+	11.4888i	−0.883378	+	0.403425i	−0.0785338	+	0.996911i	$0.525024\pi$
$812$	7.32453	+	11.8995i	0.257041	+	0.417590i
$813$	0.0892158	+	0.620510i	0.00312894	+	0.0217622i
$814$	34.0046	+	13.0609i	1.19186	+	0.457783i
$815$	8.87920	−	10.2471i	0.311025	−	0.358942i
$816$	14.9020	+	18.6128i	0.521674	+	0.651577i
$817$	−0.0513250	−	0.0329846i	−0.00179563	−	0.00115398i
$818$	−14.9866	−	15.2807i	−0.523993	−	0.534278i
$819$	−4.86399	−	1.42820i	−0.169962	−	0.0499053i
$820$	−27.4346	−	0.533290i	−0.958057	−	0.0186233i
$821$	−34.7252	−	40.0750i	−1.21192	−	1.39863i	−0.892521	−	0.451006i	$-0.851065\pi$
$821$	−34.7252	−	40.0750i	−1.21192	−	1.39863i	−0.319397	−	0.947621i	$-0.603480\pi$
$822$	0.815827	−	0.295289i	0.0284552	−	0.0102994i
$823$	13.2868	+	45.2507i	0.463148	+	1.57734i	0.778042	+	0.628212i	$0.216213\pi$
$823$	13.2868	+	45.2507i	0.463148	+	1.57734i	−0.314894	+	0.949127i	$0.601969\pi$
$824$	21.8172	+	17.3471i	0.760037	+	0.604314i
$825$	16.8074	+	2.41653i	0.585157	+	0.0841329i
$826$	13.4834	−	7.19328i	0.469147	−	0.250286i
$827$	19.5657			0.680367			0.340183	−	0.940359i	$-0.389511\pi$
$827$	19.5657			0.680367			0.340183	+	0.940359i	$0.389511\pi$
$828$	−17.6868	−	12.9210i	−0.614658	−	0.449036i
$829$	28.6991			0.996760			0.498380	−	0.866959i	$-0.333928\pi$
$829$	28.6991			0.996760			0.498380	+	0.866959i	$0.333928\pi$
$830$	−45.6776	+	24.3686i	−1.58549	+	0.845847i
$831$	16.4274	+	2.36190i	0.569859	+	0.0819333i
$832$	−4.21051	+	3.23882i	−0.145973	+	0.112286i
$833$	8.28656	+	28.2214i	0.287112	+	0.977815i
$834$	−15.5686	+	5.63508i	−0.539098	+	0.195127i
$835$	46.8357	+	54.0513i	1.62082	+	1.87052i
$836$	−0.0145382	+	0.747904i	−0.000502815	+	0.0258668i
$837$	4.64980	+	1.36530i	0.160721	+	0.0471918i
$838$	−22.4153	−	22.8553i	−0.774324	−	0.789522i
$839$	−16.3919	−	10.5344i	−0.565911	−	0.363689i	0.226186	−	0.974084i	$-0.427374\pi$
$839$	−16.3919	−	10.5344i	−0.565911	−	0.363689i	−0.792097	+	0.610395i	$0.791011\pi$
$840$	17.9776	−	16.9588i	0.620288	−	0.585135i
$841$	16.1309	−	18.6161i	0.556239	−	0.641934i
$842$	16.6690	+	6.40241i	0.574451	+	0.220642i
$843$	−0.406809	−	2.82942i	−0.0140112	−	0.0974503i
$844$	23.6705	−	14.5700i	0.814772	−	0.501519i
$845$	35.2782	−	16.1110i	1.21361	−	0.554235i
$846$	31.5790	−	6.54884i	1.08571	−	0.225154i
$847$	11.8903	−	26.0362i	0.408556	−	0.894613i
$848$	−22.1171	−	11.1589i	−0.759503	−	0.383198i
$849$	6.34271	+	9.86945i	0.217681	+	0.338719i
$850$	45.0287	+	3.66066i	1.54447	+	0.125560i
$851$	27.9069	+	1.12523i	0.956635	+	0.0385724i
$852$	13.4123	+	2.19524i	0.459496	+	0.0752078i
$853$	−40.2843	+	25.8891i	−1.37931	+	0.886428i	−0.999257	−	0.0385379i	$-0.987730\pi$
$853$	−40.2843	+	25.8891i	−1.37931	+	0.886428i	−0.380051	+	0.924965i	$0.624094\pi$
$854$	−2.69283	+	11.8243i	−0.0921469	+	0.404620i
$855$	0.542459	+	0.247733i	0.0185517	+	0.00847228i
$856$	1.52805	+	36.1491i	0.0522276	+	1.23555i
$857$	−20.7683	−	45.4763i	−0.709433	−	1.55344i	−0.828146	−	0.560513i	$-0.810604\pi$
$857$	−20.7683	−	45.4763i	−0.709433	−	1.55344i	0.118713	−	0.992929i	$-0.462123\pi$
$858$	−2.07921	−	2.83450i	−0.0709830	−	0.0967682i
$859$	−27.3056	+	3.92596i	−0.931656	+	0.133952i	−0.591397	−	0.806380i	$-0.701424\pi$
$859$	−27.3056	+	3.92596i	−0.931656	+	0.133952i	−0.340258	+	0.940332i	$0.610514\pi$
$860$	1.92940	−	4.01634i	0.0657920	−	0.136956i
$861$	−9.50096	−	8.23263i	−0.323792	−	0.280567i
$862$	16.3271	−	21.3743i	0.556103	−	0.728011i
$863$	7.89680	−	12.2877i	0.268810	−	0.418277i	−0.680437	−	0.732806i	$-0.738210\pi$
$863$	7.89680	−	12.2877i	0.268810	−	0.418277i	0.949248	+	0.314529i	$0.101847\pi$
$864$	−22.7657	+	11.0311i	−0.774506	+	0.375284i
$865$	1.66495	−	5.67031i	0.0566101	−	0.192796i
$866$	1.38186	+	22.3747i	0.0469576	+	0.760323i
$867$	−20.8522	+	18.0685i	−0.708178	+	0.613640i
$868$	6.99040	−	1.90581i	0.237270	−	0.0646873i
$869$	−20.8524	+	6.12281i	−0.707368	+	0.207702i
$870$	6.74347	+	3.76774i	0.228625	+	0.127738i
$871$	0.846274	−	5.88596i	0.0286749	−	0.199438i
$872$	−1.71862	+	0.584536i	−0.0581999	+	0.0197949i
$873$		−	31.4418i		−	1.06415i
$874$	0.173318	+	0.546739i	0.00586257	+	0.0184937i
$875$			4.79068i			0.161955i
$876$	−4.84275	−	11.1739i	−0.163622	−	0.377531i
$877$	−1.93750	+	13.4756i	−0.0654246	+	0.455038i	0.930606	+	0.366023i	$0.119281\pi$
$877$	−1.93750	+	13.4756i	−0.0654246	+	0.455038i	−0.996030	+	0.0890147i	$0.971628\pi$
$878$	−20.4117	+	36.5327i	−0.688863	+	1.23292i
$879$	−4.24336	+	1.24596i	−0.143125	+	0.0420253i
$880$	−54.3370	+	5.66752i	−1.83170	+	0.191052i
$881$	15.9084	−	13.7847i	0.535969	−	0.464419i	−0.344324	−	0.938851i	$-0.611892\pi$
$881$	15.9084	−	13.7847i	0.535969	−	0.464419i	0.880292	+	0.474432i	$0.157346\pi$
$882$	−13.4621	+	0.831423i	−0.453294	+	0.0279955i
$883$	−6.09164	+	20.7462i	−0.205000	+	0.698166i	0.791238	+	0.611508i	$0.209437\pi$
$883$	−6.09164	+	20.7462i	−0.205000	+	0.698166i	−0.996238	+	0.0866580i	$0.972381\pi$
$884$	−5.98626	−	7.18608i	−0.201340	−	0.241694i
$885$	4.56753	−	7.10721i	0.153536	−	0.238906i
$886$	27.7753	+	21.2166i	0.933129	+	0.712786i
$887$	−12.0750	−	10.4631i	−0.405440	−	0.351316i	0.428142	−	0.903711i	$-0.359168\pi$
$887$	−12.0750	−	10.4631i	−0.405440	−	0.351316i	−0.833582	+	0.552396i	$0.813714\pi$
$888$	7.03540	−	12.0364i	0.236092	−	0.403914i
$889$	−31.9202	+	4.58943i	−1.07057	+	0.153925i
$890$	−6.95653	+	5.10286i	−0.233183	+	0.171048i
$891$	5.63287	+	12.3343i	0.188708	+	0.413214i
$892$	2.09027	+	16.8579i	0.0699874	+	0.564445i
$893$	−0.768179	−	0.350815i	−0.0257061	−	0.0117396i
$894$	1.21715	+	0.277191i	0.0407077	+	0.00927064i
$895$	−10.9262	+	7.02184i	−0.365222	+	0.234714i
$896$	−20.3412	+	31.8875i	−0.679552	+	1.06529i
$897$	−2.20690	−	1.54737i	−0.0736863	−	0.0516652i
$898$	−1.83102	+	22.5228i	−0.0611018	+	0.751594i
$899$	1.22436	+	1.90514i	0.0408347	+	0.0635401i
$900$	−6.22182	+	19.7604i	−0.207394	+	0.658681i
$901$	18.1189	−	39.6748i	0.603627	−	1.32176i
$902$	5.64299	+	27.2109i	0.187891	+	0.906024i
$903$	1.85693	−	0.848030i	0.0617946	−	0.0282207i
$904$	−22.0686	−	43.3757i	−0.733989	−	1.44265i
$905$	−2.51448	−	17.4886i	−0.0835842	−	0.581341i
$906$	3.83376	−	9.98139i	0.127368	−	0.331609i
$907$	−30.4890	+	35.1862i	−1.01237	+	1.16834i	−0.0267031	+	0.999643i	$0.508501\pi$
$907$	−30.4890	+	35.1862i	−1.01237	+	1.16834i	−0.985668	+	0.168695i	$0.946045\pi$
$908$	38.9887	+	35.1335i	1.29388	+	1.16595i
$909$	−15.9426	−	10.2457i	−0.528784	−	0.339829i
$910$	−6.92131	+	6.78808i	−0.229439	+	0.225023i
$911$	−43.4590	−	12.7607i	−1.43986	−	0.422781i	−0.533685	−	0.845683i	$-0.679193\pi$
$911$	−43.4590	−	12.7607i	−1.43986	−	0.422781i	−0.906175	+	0.422902i	$0.861011\pi$
$912$	0.281591	+	0.0517275i	0.00932441	+	0.00171287i
$913$	34.3356	+	39.6254i	1.13634	+	1.31141i
$914$	−3.67882	−	10.1639i	−0.121684	−	0.336191i
$915$	1.88878	+	6.43258i	0.0624410	+	0.212655i
$916$	5.34203	+	3.58170i	0.176505	+	0.118343i
$917$	−53.3525	−	7.67094i	−1.76186	−	0.253317i
$918$	−20.9650	−	39.2977i	−0.691949	−	1.29702i
$919$	24.1537			0.796757			0.398379	−	0.917221i	$-0.369573\pi$
$919$	24.1537			0.796757			0.398379	+	0.917221i	$0.369573\pi$
$920$	−38.0688	+	17.4751i	−1.25509	+	0.576137i
$921$	13.4671			0.443755
$922$	24.0117	+	45.0086i	0.790783	+	1.48228i
$923$	−5.27685	−	0.758696i	−0.173690	−	0.0249728i
$924$	−20.7893	−	13.9387i	−0.683918	−	0.458550i
$925$	−7.44227	−	25.3460i	−0.244700	−	0.833372i
$926$	1.52938	+	4.22539i	0.0502586	+	0.138855i
$927$	−14.7371	−	17.0076i	−0.484031	−	0.558602i
$928$	−11.4160	−	3.07103i	−0.374749	−	0.100812i
$929$	−12.1727	−	3.57422i	−0.399372	−	0.117266i	0.0758777	−	0.997117i	$-0.475824\pi$
$929$	−12.1727	−	3.57422i	−0.399372	−	0.117266i	−0.475250	+	0.879851i	$0.657642\pi$
$930$	2.85971	−	2.80466i	0.0937736	−	0.0919685i
$931$	0.297114	+	0.190943i	0.00973751	+	0.00625792i
$932$	34.2357	+	30.8505i	1.12143	+	1.01054i
$933$	3.29124	−	3.79829i	0.107750	−	0.124350i
$934$	−6.76490	+	17.6127i	−0.221354	+	0.576306i
$935$	−13.6890	−	95.2091i	−0.447678	−	3.11367i
$936$	3.82259	−	1.94485i	0.124945	−	0.0635693i
$937$	−3.63101	+	1.65823i	−0.118620	+	0.0541719i	−0.473841	−	0.880610i	$-0.657133\pi$
$937$	−3.63101	+	1.65823i	−0.118620	+	0.0541719i	0.355221	+	0.934782i	$0.384406\pi$
$938$	−8.59752	−	41.4579i	−0.280719	−	1.35365i
$939$	−4.97703	+	10.8982i	−0.162419	+	0.355648i
$940$	18.5229	−	58.8285i	0.604149	−	1.91877i
$941$	−20.2037	−	31.4376i	−0.658622	−	1.02484i	−0.996496	−	0.0836445i	$-0.973344\pi$
$941$	−20.2037	−	31.4376i	−0.658622	−	1.02484i	0.337874	−	0.941192i	$-0.390292\pi$
$942$	−0.981877	+	12.0778i	−0.0319913	+	0.393515i
$943$	10.7882	+	18.3745i	0.351311	+	0.598358i
$944$	−4.12201	+	12.2548i	−0.134160	+	0.398859i
$945$	−38.8385	+	24.9600i	−1.26342	+	0.811948i
$946$	−4.39993	−	1.00203i	−0.143054	−	0.0325787i
$947$	−34.5381	−	15.7730i	−1.12234	−	0.512555i	−0.234227	−	0.972182i	$-0.575256\pi$
$947$	−34.5381	−	15.7730i	−1.12234	−	0.512555i	−0.888112	+	0.459627i	$0.847983\pi$
$948$	1.02352	+	8.25463i	0.0332423	+	0.268098i
$949$	1.98445	+	4.34534i	0.0644180	+	0.141056i
$950$	0.437411	−	0.320856i	0.0141915	−	0.0104100i
$951$	19.9515	−	2.86860i	0.646972	−	0.0930206i
$952$	−57.4926	−	33.6051i	−1.86334	−	1.08915i
$953$	−8.77180	−	7.60081i	−0.284146	−	0.246214i	0.501112	−	0.865382i	$-0.332924\pi$
$953$	−8.77180	−	7.60081i	−0.284146	−	0.246214i	−0.785258	+	0.619168i	$0.787470\pi$
$954$	15.8944	+	12.1412i	0.514601	+	0.393086i
$955$	35.9876	−	55.9978i	1.16453	−	1.81205i
$956$	31.0536	+	37.2777i	1.00435	+	1.20565i
$957$	2.20405	−	7.50632i	0.0712469	−	0.242645i
$958$	6.55694	−	0.404957i	0.211845	−	0.0130836i
$959$	−1.83136	+	1.58688i	−0.0591377	+	0.0512431i
$960$	−1.21851	+	20.8739i	−0.0393272	+	0.673703i
$961$	−28.6175	+	8.40287i	−0.923147	+	0.271060i
$962$	−2.66743	+	4.77414i	−0.0860014	+	0.153925i
$963$	4.15733	−	28.9149i	0.133968	−	0.931769i
$964$	−1.77212	−	4.08890i	−0.0570763	−	0.131695i
$965$			54.1142i			1.74200i
$966$	−18.5251	−	5.01182i	−0.596037	−	0.161253i
$967$			22.8979i			0.736346i	0.929757	+	0.368173i	$0.120017\pi$
$967$			22.8979i			0.736346i	−0.929757	+	0.368173i	$0.879983\pi$
$968$	7.79769	+	22.9264i	0.250627	+	0.736882i
$969$	−0.0717384	+	0.498952i	−0.00230457	+	0.0160286i
$970$	−52.4910	−	29.3280i	−1.68538	−	0.941666i
$971$	−18.3648	+	5.39240i	−0.589356	+	0.173051i	−0.562795	−	0.826597i	$-0.690274\pi$
$971$	−18.3648	+	5.39240i	−0.589356	+	0.173051i	−0.0265611	+	0.999647i	$0.508456\pi$
$972$	30.8942	−	8.42274i	0.990932	−	0.270160i
$973$	34.9483	−	30.2829i	1.12039	−	0.970826i
$974$	−1.87786	−	30.4057i	−0.0601705	−	0.974262i
$975$	−0.718211	+	2.44600i	−0.0230012	+	0.0783348i
$976$	−5.20739	−	8.84038i	−0.166685	−	0.282974i
$977$	16.3050	−	25.3711i	0.521644	−	0.811694i	−0.476061	−	0.879413i	$-0.657936\pi$
$977$	16.3050	−	25.3711i	0.521644	−	0.811694i	0.997704	+	0.0677188i	$0.0215721\pi$
$978$	−3.19035	+	4.17658i	−0.102016	+	0.133552i
$979$	6.60337	+	5.72185i	0.211045	+	0.182871i
$980$	−11.1691	+	23.2501i	−0.356782	+	0.742696i
$981$	1.45073	−	0.208584i	0.0463183	−	0.00665957i
$982$	−19.5390	−	26.6368i	−0.623516	−	0.850014i
$983$	11.2837	+	24.7078i	0.359893	+	0.788055i	0.999808	+	0.0196095i	$0.00624230\pi$
$983$	11.2837	+	24.7078i	0.359893	+	0.788055i	−0.639915	+	0.768446i	$0.721030\pi$
$984$	10.6266	−	0.449196i	0.338765	−	0.0143199i
$985$	63.5524	+	29.0234i	2.02495	+	0.924762i
$986$	4.62184	−	20.2947i	0.147189	−	0.646314i
$987$	23.7712	−	15.2768i	0.756644	−	0.486266i
$988$	−0.110831	−	0.0181401i	−0.00352599	−	0.000577115i
$989$	−3.44180	+	0.354027i	−0.109443	+	0.0112574i
$990$	43.9637	+	3.57409i	1.39726	+	0.113592i
$991$	−30.5121	−	47.4777i	−0.969248	−	1.50818i	−0.857526	−	0.514441i	$-0.828000\pi$
$991$	−30.5121	−	47.4777i	−0.969248	−	1.50818i	−0.111722	−	0.993739i	$-0.535637\pi$
$992$	−3.19568	+	5.23118i	−0.101463	+	0.166090i
$993$	−0.616804	+	1.35061i	−0.0195737	+	0.0428604i
$994$	−37.1676	+	7.70781i	−1.17888	+	0.244477i
$995$	22.1816	−	10.1300i	0.703206	−	0.321143i
$996$	17.0895	−	10.5192i	0.541502	−	0.333312i
$997$	−4.47722	−	31.1397i	−0.141795	−	0.986205i	−0.929149	−	0.369704i	$-0.879459\pi$
$997$	−4.47722	−	31.1397i	−0.141795	−	0.986205i	0.787355	−	0.616500i	$-0.211450\pi$
$998$	36.0853	+	13.8601i	1.14226	+	0.438733i
$999$	−17.0550	+	19.6825i	−0.539596	+	0.622727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	92.2.h.a.11.5	✓	100
3.2	odd	2		828.2.u.a.379.6		100
4.3	odd	2	inner	92.2.h.a.11.9	yes	100
12.11	even	2		828.2.u.a.379.2		100
23.21	odd	22	inner	92.2.h.a.67.9	yes	100
69.44	even	22		828.2.u.a.343.2		100
92.67	even	22	inner	92.2.h.a.67.5	yes	100
276.251	odd	22		828.2.u.a.343.6		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
92.2.h.a.11.5	✓	100	1.1	even	1	trivial
92.2.h.a.11.9	yes	100	4.3	odd	2	inner
92.2.h.a.67.5	yes	100	92.67	even	22	inner
92.2.h.a.67.9	yes	100	23.21	odd	22	inner
828.2.u.a.343.2		100	69.44	even	22
828.2.u.a.343.6		100	276.251	odd	22
828.2.u.a.379.2		100	12.11	even	2
828.2.u.a.379.6		100	3.2	odd	2

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:	\( N \)	\(=\)	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	92.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.665666 - 1.24775i) q^{2} +(-0.837775 - 0.120454i) q^{3} +(-1.11378 + 1.66117i) q^{4} +(-0.870000 - 2.96295i) q^{5} +(0.407382 + 1.12552i) q^{6} +(-2.18927 - 2.52655i) q^{7} +(2.81414 + 0.283931i) q^{8} +(-2.19112 - 0.643371i) q^{9} +O(q^{10})\)	\(q+(-0.665666 - 1.24775i) q^{2} +(-0.837775 - 0.120454i) q^{3} +(-1.11378 + 1.66117i) q^{4} +(-0.870000 - 2.96295i) q^{5} +(0.407382 + 1.12552i) q^{6} +(-2.18927 - 2.52655i) q^{7} +(2.81414 + 0.283931i) q^{8} +(-2.19112 - 0.643371i) q^{9} +(-3.11790 + 3.05788i) q^{10} +(3.72075 + 2.39118i) q^{11} +(1.13319 - 1.25753i) q^{12} +(-0.434836 + 0.501827i) q^{13} +(-1.69519 + 4.41351i) q^{14} +(0.371966 + 2.58708i) q^{15} +(-1.51900 - 3.70036i) q^{16} +(6.40622 - 2.92562i) q^{17} +(0.655787 + 3.16225i) q^{18} +(0.0351299 - 0.0769237i) q^{19} +(5.89096 + 1.85484i) q^{20} +(1.52978 + 2.38039i) q^{21} +(0.506826 - 6.23430i) q^{22} +(-1.16466 - 4.65227i) q^{23} +(-2.32342 - 0.576844i) q^{24} +(-3.81588 + 2.45232i) q^{25} +(0.915612 + 0.208518i) q^{26} +(4.06788 + 1.85774i) q^{27} +(6.63541 - 0.822745i) q^{28} +(0.868147 + 1.90098i) q^{29} +(2.98043 - 2.18625i) q^{30} +(1.07262 - 0.154220i) q^{31} +(-3.60598 + 4.35854i) q^{32} +(-2.82912 - 2.45145i) q^{33} +(-7.91486 - 6.04589i) q^{34} +(-5.58138 + 8.68480i) q^{35} +(3.50917 - 2.92326i) q^{36} +(-1.64073 + 5.58781i) q^{37} +(-0.119367 + 0.00737210i) q^{38} +(0.424742 - 0.368041i) q^{39} +(-1.60703 - 8.58517i) q^{40} +(-4.26295 + 1.25171i) q^{41} +(1.95182 - 3.49334i) q^{42} +(0.102673 - 0.714109i) q^{43} +(-8.11625 + 3.51757i) q^{44} +7.05190i q^{45} +(-5.02961 + 4.55006i) q^{46} -9.98624i q^{47} +(0.826861 + 3.28304i) q^{48} +(-0.594362 + 4.13388i) q^{49} +(5.60000 + 3.12886i) q^{50} +(-5.71938 + 1.67936i) q^{51} +(-0.349312 - 1.28126i) q^{52} +(4.68049 - 4.05566i) q^{53} +(-0.389851 - 6.31235i) q^{54} +(3.84789 - 13.1047i) q^{55} +(-5.44355 - 7.73168i) q^{56} +(-0.0386967 + 0.0602133i) q^{57} +(1.79405 - 2.34865i) q^{58} +(-2.44285 - 2.11674i) q^{59} +(-4.71188 - 2.26353i) q^{60} +(2.53891 - 0.365040i) q^{61} +(-0.906436 - 1.23571i) q^{62} +(3.17145 + 6.94450i) q^{63} +(7.83877 + 1.59804i) q^{64} +(1.86519 + 0.851805i) q^{65} +(-1.17555 + 5.16190i) q^{66} +(-7.53375 + 4.84165i) q^{67} +(-2.27513 + 13.9003i) q^{68} +(0.415337 + 4.03784i) q^{69} +(14.5518 + 1.18301i) q^{70} +(4.34061 + 6.75412i) q^{71} +(-5.98345 - 2.43266i) q^{72} +(2.98858 - 6.54407i) q^{73} +(8.06439 - 1.67239i) q^{74} +(3.49225 - 1.59486i) q^{75} +(0.0886569 + 0.144033i) q^{76} +(-2.10428 - 14.6356i) q^{77} +(-0.741960 - 0.284980i) q^{78} +(-3.21780 + 3.71354i) q^{79} +(-9.64242 + 7.72003i) q^{80} +(2.57912 + 1.65750i) q^{81} +(4.39953 + 4.48588i) q^{82} +(11.3746 + 3.33987i) q^{83} +(-5.65809 - 0.109985i) q^{84} +(-14.2419 - 16.4360i) q^{85} +(-0.959377 + 0.347247i) q^{86} +(-0.498332 - 1.69716i) q^{87} +(9.79178 + 7.78555i) q^{88} +(1.95542 + 0.281148i) q^{89} +(8.79904 - 4.69422i) q^{90} +2.21987 q^{91} +(9.02539 + 3.24689i) q^{92} -0.917193 q^{93} +(-12.4604 + 6.64750i) q^{94} +(-0.258484 - 0.0371644i) q^{95} +(3.54601 - 3.21712i) q^{96} +(3.87901 + 13.2107i) q^{97} +(5.55371 - 2.01017i) q^{98} +(-6.61419 - 7.63318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9}+O(q^{10}) \) 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9	\( 100 q - 7 q^{2} - 11 q^{4} - 22 q^{5} - 12 q^{6} - 10 q^{8} - 12 q^{9} - 11 q^{10} - 18 q^{12} - 18 q^{13} - 11 q^{14} + 5 q^{16} - 22 q^{17} - 24 q^{18} - 11 q^{20} - 22 q^{21} - 30 q^{24} - 16 q^{25} + 12 q^{26} - 11 q^{28} - 42 q^{29} - 11 q^{30} - 27 q^{32} - 22 q^{33} + 11 q^{34} + 77 q^{36} - 22 q^{37} + 44 q^{38} + 77 q^{40} - 10 q^{41} + 99 q^{42} + 66 q^{44} + 65 q^{46} + 38 q^{48} - 8 q^{49} + 30 q^{50} + 96 q^{52} - 22 q^{53} + 48 q^{54} + 44 q^{56} - 22 q^{57} + 79 q^{58} + 11 q^{60} - 22 q^{61} - 36 q^{62} + 10 q^{64} - 22 q^{65} - 44 q^{66} - 10 q^{69} + 34 q^{70} - 21 q^{72} - 18 q^{73} - 22 q^{74} - 66 q^{76} + 122 q^{77} - 66 q^{78} - 110 q^{80} + 8 q^{81} - 122 q^{82} - 165 q^{84} + 54 q^{85} - 121 q^{86} - 99 q^{88} + 22 q^{89} - 198 q^{90} - 86 q^{92} + 212 q^{93} - 61 q^{94} - 147 q^{96} + 22 q^{97} - 71 q^{98}+O(q^{100}) \) 100 * q - 7 * q^2 - 11 * q^4 - 22 * q^5 - 12 * q^6 - 10 * q^8 - 12 * q^9 - 11 * q^10 - 18 * q^12 - 18 * q^13 - 11 * q^14 + 5 * q^16 - 22 * q^17 - 24 * q^18 - 11 * q^20 - 22 * q^21 - 30 * q^24 - 16 * q^25 + 12 * q^26 - 11 * q^28 - 42 * q^29 - 11 * q^30 - 27 * q^32 - 22 * q^33 + 11 * q^34 + 77 * q^36 - 22 * q^37 + 44 * q^38 + 77 * q^40 - 10 * q^41 + 99 * q^42 + 66 * q^44 + 65 * q^46 + 38 * q^48 - 8 * q^49 + 30 * q^50 + 96 * q^52 - 22 * q^53 + 48 * q^54 + 44 * q^56 - 22 * q^57 + 79 * q^58 + 11 * q^60 - 22 * q^61 - 36 * q^62 + 10 * q^64 - 22 * q^65 - 44 * q^66 - 10 * q^69 + 34 * q^70 - 21 * q^72 - 18 * q^73 - 22 * q^74 - 66 * q^76 + 122 * q^77 - 66 * q^78 - 110 * q^80 + 8 * q^81 - 122 * q^82 - 165 * q^84 + 54 * q^85 - 121 * q^86 - 99 * q^88 + 22 * q^89 - 198 * q^90 - 86 * q^92 + 212 * q^93 - 61 * q^94 - 147 * q^96 + 22 * q^97 - 71 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more