LMFDB - Embedded newform 805.2.u.d.36.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(36,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("805.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.u (of order $11$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$130$
Relative dimension:	$13$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			36.5
Character	$\chi$	$=$	805.36
Dual form			805.2.u.d.246.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382224 - 0.441110i) q^{2} +(-1.87858 - 1.20729i) q^{3} +(0.236147 - 1.64244i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.185490 + 1.29011i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-1.79679 + 1.15473i) q^{8} +(0.825261 + 1.80707i) q^{9} +O(q^{10})$	\(q+(-0.382224 - 0.441110i) q^{2} +(-1.87858 - 1.20729i) q^{3} +(0.236147 - 1.64244i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.185490 + 1.29011i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-1.79679 + 1.15473i) q^{8} +(0.825261 + 1.80707i) q^{9} +(-0.560029 + 0.164439i) q^{10} +(3.57807 - 4.12931i) q^{11} +(-2.42652 + 2.80035i) q^{12} +(3.74762 - 1.10040i) q^{13} +(-0.242466 - 0.530926i) q^{14} +(-1.87858 + 1.20729i) q^{15} +(-1.98809 - 0.583756i) q^{16} +(-0.722733 - 5.02672i) q^{17} +(0.481681 - 1.05474i) q^{18} +(0.815110 - 5.66922i) q^{19} +(-1.39591 - 0.897100i) q^{20} +(-1.46235 - 1.68764i) q^{21} -3.18910 q^{22} +(3.66743 + 3.09030i) q^{23} +4.76949 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-1.91782 - 1.23251i) q^{26} +(-0.322059 + 2.23997i) q^{27} +(0.689309 - 1.50938i) q^{28} +(-1.01349 - 7.04901i) q^{29} +(1.25058 + 0.367204i) q^{30} +(-0.537361 + 0.345341i) q^{31} +(2.27692 + 4.98576i) q^{32} +(-11.7070 + 3.43747i) q^{33} +(-1.94109 + 2.24013i) q^{34} +(0.654861 - 0.755750i) q^{35} +(3.16288 - 0.928706i) q^{36} +(4.38280 + 9.59699i) q^{37} +(-2.81230 + 1.80736i) q^{38} +(-8.36868 - 2.45727i) q^{39} +(0.303963 + 2.11411i) q^{40} +(-4.58510 + 10.0400i) q^{41} +(-0.185490 + 1.29011i) q^{42} +(0.732029 + 0.470447i) q^{43} +(-5.93719 - 6.85188i) q^{44} +1.98659 q^{45} +(-0.0386191 - 2.79892i) q^{46} -5.65525 q^{47} +(3.03002 + 3.49683i) q^{48} +(0.841254 + 0.540641i) q^{49} +(-0.0830651 + 0.577731i) q^{50} +(-4.71099 + 10.3156i) q^{51} +(-0.922350 - 6.41508i) q^{52} +(-2.72899 - 0.801303i) q^{53} +(1.11117 - 0.714107i) q^{54} +(-2.26977 - 4.97011i) q^{55} +(-2.04933 + 0.601737i) q^{56} +(-8.37562 + 9.66598i) q^{57} +(-2.72200 + 3.14136i) q^{58} +(10.5542 - 3.09900i) q^{59} +(1.53928 + 3.37054i) q^{60} +(-6.66515 + 4.28343i) q^{61} +(0.357726 + 0.105038i) q^{62} +(0.282722 + 1.96637i) q^{63} +(-0.392524 + 0.859508i) q^{64} +(0.555858 - 3.86607i) q^{65} +(5.99098 + 3.85017i) q^{66} +(5.86034 + 6.76319i) q^{67} -8.42674 q^{68} +(-3.15867 - 10.2330i) q^{69} -0.583672 q^{70} +(6.71366 + 7.74797i) q^{71} +(-3.56949 - 2.29397i) q^{72} +(0.258789 - 1.79992i) q^{73} +(2.55812 - 5.60149i) q^{74} +(0.317799 + 2.21034i) q^{75} +(-9.11885 - 2.67754i) q^{76} +(4.59650 - 2.95399i) q^{77} +(2.11478 + 4.63073i) q^{78} +(-0.350982 + 0.103058i) q^{79} +(-1.35689 + 1.56593i) q^{80} +(7.21213 - 8.32324i) q^{81} +(6.18126 - 1.81498i) q^{82} +(-6.87929 - 15.0635i) q^{83} +(-3.11717 + 2.00329i) q^{84} +(-4.87270 - 1.43075i) q^{85} +(-0.0722804 - 0.502721i) q^{86} +(-6.60626 + 14.4657i) q^{87} +(-1.66081 + 11.5512i) q^{88} +(-14.1044 - 9.06437i) q^{89} +(-0.759323 - 0.876306i) q^{90} +3.90583 q^{91} +(5.94168 - 5.29376i) q^{92} +1.42640 q^{93} +(2.16157 + 2.49458i) q^{94} +(-4.81829 - 3.09653i) q^{95} +(1.74188 - 12.1150i) q^{96} +(-0.737038 + 1.61389i) q^{97} +(-0.0830651 - 0.577731i) q^{98} +(10.4148 + 3.05806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) $ 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	−0.382224	−	0.441110i	−0.270273	−	0.311912i	0.604347	−	0.796722i	$-0.293434\pi$
$2$	−0.382224	−	0.441110i	−0.270273	−	0.311912i	−0.874620	+	0.484810i	$0.838889\pi$
$3$	−1.87858	−	1.20729i	−1.08460	−	0.697028i	−0.128982	−	0.991647i	$-0.541171\pi$
$3$	−1.87858	−	1.20729i	−1.08460	−	0.697028i	−0.955615	+	0.294619i	$0.904807\pi$
$4$	0.236147	−	1.64244i	0.118073	−	0.821219i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$5$	0.415415	−	0.909632i	0.185779	−	0.406800i
$6$	0.185490	+	1.29011i	0.0757260	+	0.526686i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$7$	0.959493	+	0.281733i	0.362654	+	0.106485i
$8$	−1.79679	+	1.15473i	−0.635260	+	0.408257i
$9$	0.825261	+	1.80707i	0.275087	+	0.602356i
$10$	−0.560029	+	0.164439i	−0.177097	+	0.0520003i
$11$	3.57807	−	4.12931i	1.07883	−	1.24504i	0.110895	−	0.993832i	$-0.464628\pi$
$11$	3.57807	−	4.12931i	1.07883	−	1.24504i	0.967934	−	0.251203i	$-0.0808262\pi$
$12$	−2.42652	+	2.80035i	−0.700475	+	0.808391i
$13$	3.74762	−	1.10040i	1.03940	−	0.305196i	0.282874	−	0.959157i	$-0.408712\pi$
$13$	3.74762	−	1.10040i	1.03940	−	0.305196i	0.756528	+	0.653961i	$0.226894\pi$
$14$	−0.242466	−	0.530926i	−0.0648018	−	0.141896i
$15$	−1.87858	+	1.20729i	−0.485046	+	0.311720i
$16$	−1.98809	−	0.583756i	−0.497023	−	0.145939i
$17$	−0.722733	−	5.02672i	−0.175288	−	1.21916i	−0.867490	−	0.497454i	$-0.834268\pi$
$17$	−0.722733	−	5.02672i	−0.175288	−	1.21916i	0.692202	−	0.721704i	$-0.256641\pi$
$18$	0.481681	−	1.05474i	0.113533	−	0.248603i
$19$	0.815110	−	5.66922i	0.186999	−	1.30061i	−0.652725	−	0.757595i	$-0.726374\pi$
$19$	0.815110	−	5.66922i	0.186999	−	1.30061i	0.839724	−	0.543013i	$-0.182716\pi$
$20$	−1.39591	−	0.897100i	−0.312136	−	0.200598i
$21$	−1.46235	−	1.68764i	−0.319111	−	0.368273i
$22$	−3.18910			−0.679919
$23$	3.66743	+	3.09030i	0.764712	+	0.644372i
$23$	3.66743	+	3.09030i	0.764712	+	0.644372i
$24$	4.76949			0.973568
$25$	−0.654861	−	0.755750i	−0.130972	−	0.151150i
$26$	−1.91782	−	1.23251i	−0.376116	−	0.241715i
$27$	−0.322059	+	2.23997i	−0.0619803	+	0.431083i
$28$	0.689309	−	1.50938i	0.130267	−	0.285245i
$29$	−1.01349	−	7.04901i	−0.188201	−	1.30897i	−0.836662	−	0.547720i	$-0.815496\pi$
$29$	−1.01349	−	7.04901i	−0.188201	−	1.30897i	0.648460	−	0.761248i	$-0.275413\pi$
$30$	1.25058	+	0.367204i	0.228324	+	0.0670420i
$31$	−0.537361	+	0.345341i	−0.0965129	+	0.0620251i	−0.588007	−	0.808856i	$-0.700087\pi$
$31$	−0.537361	+	0.345341i	−0.0965129	+	0.0620251i	0.491494	+	0.870881i	$0.336451\pi$
$32$	2.27692	+	4.98576i	0.402506	+	0.881366i
$33$	−11.7070	+	3.43747i	−2.03792	+	0.598387i
$34$	−1.94109	+	2.24013i	−0.332894	+	0.384180i
$35$	0.654861	−	0.755750i	0.110692	−	0.127745i
$36$	3.16288	−	0.928706i	0.527147	−	0.154784i
$37$	4.38280	+	9.59699i	0.720528	+	1.57774i	0.813164	+	0.582035i	$0.197743\pi$
$37$	4.38280	+	9.59699i	0.720528	+	1.57774i	−0.0926359	+	0.995700i	$0.529529\pi$
$38$	−2.81230	+	1.80736i	−0.456215	+	0.293192i
$39$	−8.36868	−	2.45727i	−1.34006	−	0.393478i
$40$	0.303963	+	2.11411i	0.0480607	+	0.334270i
$41$	−4.58510	+	10.0400i	−0.716073	+	1.56798i	0.103255	+	0.994655i	$0.467074\pi$
$41$	−4.58510	+	10.0400i	−0.716073	+	1.56798i	−0.819328	+	0.573325i	$0.805653\pi$
$42$	−0.185490	+	1.29011i	−0.0286217	+	0.199069i
$43$	0.732029	+	0.470447i	0.111633	+	0.0717424i	0.595266	−	0.803529i	$-0.297047\pi$
$43$	0.732029	+	0.470447i	0.111633	+	0.0717424i	−0.483633	+	0.875271i	$0.660683\pi$
$44$	−5.93719	−	6.85188i	−0.895065	−	1.03296i
$45$	1.98659			0.296144
$46$	−0.0386191	−	2.79892i	−0.00569407	−	0.412679i
$47$	−5.65525			−0.824902			−0.412451	−	0.910980i	$-0.635327\pi$
$47$	−5.65525			−0.824902			−0.412451	+	0.910980i	$0.635327\pi$
$48$	3.03002	+	3.49683i	0.437345	+	0.504724i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	−0.0830651	+	0.577731i	−0.0117472	+	0.0817035i
$51$	−4.71099	+	10.3156i	−0.659670	+	1.44448i
$52$	−0.922350	−	6.41508i	−0.127907	−	0.889612i
$53$	−2.72899	−	0.801303i	−0.374855	−	0.110067i	0.0888775	−	0.996043i	$-0.471672\pi$
$53$	−2.72899	−	0.801303i	−0.374855	−	0.110067i	−0.463733	+	0.885975i	$0.653490\pi$
$54$	1.11117	−	0.714107i	0.151211	−	0.0971776i
$55$	−2.26977	−	4.97011i	−0.306056	−	0.670169i
$56$	−2.04933	+	0.601737i	−0.273853	+	0.0804105i
$57$	−8.37562	+	9.66598i	−1.10938	+	1.28029i
$58$	−2.72200	+	3.14136i	−0.357417	+	0.412481i
$59$	10.5542	−	3.09900i	1.37404	−	0.403456i	0.490352	−	0.871525i	$-0.336868\pi$
$59$	10.5542	−	3.09900i	1.37404	−	0.403456i	0.883692	+	0.468069i	$0.155050\pi$
$60$	1.53928	+	3.37054i	0.198720	+	0.435135i
$61$	−6.66515	+	4.28343i	−0.853385	+	0.548437i	−0.892629	−	0.450793i	$-0.851141\pi$
$61$	−6.66515	+	4.28343i	−0.853385	+	0.548437i	0.0392439	+	0.999230i	$0.487505\pi$
$62$	0.357726	+	0.105038i	0.0454312	+	0.0133398i
$63$	0.282722	+	1.96637i	0.0356196	+	0.247740i
$64$	−0.392524	+	0.859508i	−0.0490655	+	0.107439i
$65$	0.555858	−	3.86607i	0.0689456	−	0.479527i
$66$	5.99098	+	3.85017i	0.737438	+	0.473923i
$67$	5.86034	+	6.76319i	0.715954	+	0.826255i	0.990814	−	0.135229i	$-0.0431771\pi$
$67$	5.86034	+	6.76319i	0.715954	+	0.826255i	−0.274860	+	0.961484i	$0.588632\pi$
$68$	−8.42674			−1.02189
$69$	−3.15867	−	10.2330i	−0.380259	−	1.23191i
$70$	−0.583672			−0.0697621
$71$	6.71366	+	7.74797i	0.796764	+	0.919515i	0.998199	−	0.0599868i	$-0.0191059\pi$
$71$	6.71366	+	7.74797i	0.796764	+	0.919515i	−0.201435	+	0.979502i	$0.564560\pi$
$72$	−3.56949	−	2.29397i	−0.420668	−	0.270347i
$73$	0.258789	−	1.79992i	0.0302889	−	0.210664i	−0.969057	−	0.246839i	$-0.920608\pi$
$73$	0.258789	−	1.79992i	0.0302889	−	0.210664i	0.999345	+	0.0361747i	$0.0115173\pi$
$74$	2.55812	−	5.60149i	0.297375	−	0.651160i
$75$	0.317799	+	2.21034i	0.0366962	+	0.255228i
$76$	−9.11885	−	2.67754i	−1.04600	−	0.307134i
$77$	4.59650	−	2.95399i	0.523819	−	0.336638i
$78$	2.11478	+	4.63073i	0.239452	+	0.524327i
$79$	−0.350982	+	0.103058i	−0.0394885	+	0.0115949i	−0.301417	−	0.953492i	$-0.597460\pi$
$79$	−0.350982	+	0.103058i	−0.0394885	+	0.0115949i	0.261929	+	0.965087i	$0.415641\pi$
$80$	−1.35689	+	1.56593i	−0.151704	+	0.175076i
$81$	7.21213	−	8.32324i	0.801348	−	0.924805i
$82$	6.18126	−	1.81498i	0.682606	−	0.200431i
$83$	−6.87929	−	15.0635i	−0.755100	−	1.65344i	−0.756979	−	0.653440i	$-0.773325\pi$
$83$	−6.87929	−	15.0635i	−0.755100	−	1.65344i	0.00187901	−	0.999998i	$-0.499402\pi$
$84$	−3.11717	+	2.00329i	−0.340111	+	0.218576i
$85$	−4.87270	−	1.43075i	−0.528518	−	0.155187i
$86$	−0.0722804	−	0.502721i	−0.00779419	−	0.0542098i
$87$	−6.60626	+	14.4657i	−0.708265	+	1.55088i
$88$	−1.66081	+	11.5512i	−0.177043	+	1.23136i
$89$	−14.1044	−	9.06437i	−1.49507	−	0.960822i	−0.995522	−	0.0945346i	$-0.969864\pi$
$89$	−14.1044	−	9.06437i	−1.49507	−	0.960822i	−0.499546	−	0.866287i	$-0.666500\pi$
$90$	−0.759323	−	0.876306i	−0.0800397	−	0.0923707i
$91$	3.90583			0.409442
$92$	5.94168	−	5.29376i	0.619462	−	0.551913i
$93$	1.42640			0.147911
$94$	2.16157	+	2.49458i	0.222949	+	0.257297i
$95$	−4.81829	−	3.09653i	−0.494346	−	0.317697i
$96$	1.74188	−	12.1150i	0.177780	−	1.23648i
$97$	−0.737038	+	1.61389i	−0.0748349	+	0.163866i	−0.943352	−	0.331794i	$-0.892346\pi$
$97$	−0.737038	+	1.61389i	−0.0748349	+	0.163866i	0.868517	+	0.495659i	$0.165074\pi$
$98$	−0.0830651	−	0.577731i	−0.00839085	−	0.0583596i
$99$	10.4148	+	3.05806i	1.04673	+	0.307347i
$100$	−1.39591	+	0.897100i	−0.139591	+	0.0897100i
$101$	−0.913915	−	2.00119i	−0.0909379	−	0.199126i	0.858698	−	0.512482i	$-0.171274\pi$
$101$	−0.913915	−	2.00119i	−0.0909379	−	0.199126i	−0.949636	+	0.313356i	$0.898547\pi$
$102$	6.35097	−	1.86481i	0.628840	−	0.184644i
$103$	−4.45265	+	5.13864i	−0.438733	+	0.506325i	−0.931452	−	0.363863i	$-0.881458\pi$
$103$	−4.45265	+	5.13864i	−0.438733	+	0.506325i	0.492719	+	0.870188i	$0.336003\pi$
$104$	−5.46301	+	6.30465i	−0.535692	+	0.618222i
$105$	−2.14261	+	0.629128i	−0.209098	+	0.0613966i
$106$	0.689621	+	1.51006i	0.0669819	+	0.146670i
$107$	−2.07120	+	1.33108i	−0.200231	+	0.128680i	−0.636914	−	0.770935i	$-0.719789\pi$
$107$	−2.07120	+	1.33108i	−0.200231	+	0.128680i	0.436683	+	0.899615i	$0.356153\pi$
$108$	3.60296	+	1.05792i	0.346695	+	0.101799i
$109$	2.28277	+	15.8770i	0.218650	+	1.52074i	0.743029	+	0.669260i	$0.233389\pi$
$109$	2.28277	+	15.8770i	0.218650	+	1.52074i	−0.524379	+	0.851485i	$0.675702\pi$
$110$	−1.32480	+	2.90091i	−0.126315	+	0.276591i
$111$	3.35291	−	23.3200i	0.318244	−	2.21343i
$112$	−1.74310	−	1.12022i	−0.164707	−	0.105851i
$113$	1.02319	+	1.18083i	0.0962540	+	0.111083i	0.801833	−	0.597548i	$-0.203858\pi$
$113$	1.02319	+	1.18083i	0.0962540	+	0.111083i	−0.705579	+	0.708631i	$0.749313\pi$
$114$	7.46512			0.699172
$115$	4.33454	−	2.05226i	0.404198	−	0.191374i
$116$	−11.8169			−1.09717
$117$	5.08126	+	5.86408i	0.469763	+	0.542135i
$118$	−5.40108	−	3.47106i	−0.497209	−	0.319537i
$119$	0.722733	−	5.02672i	0.0662528	−	0.460798i
$120$	1.98132	−	4.33848i	0.180869	−	0.396047i
$121$	−2.68318	−	18.6619i	−0.243925	−	1.69654i
$122$	4.43704	+	1.30283i	0.401711	+	0.117953i
$123$	20.7346	−	13.3253i	1.86958	−	1.20150i
$124$	0.440305	+	0.964134i	0.0395406	+	0.0865818i
$125$	−0.959493	+	0.281733i	−0.0858197	+	0.0251989i
$126$	0.759323	−	0.876306i	0.0676459	−	0.0780675i
$127$	6.36836	−	7.34948i	0.565101	−	0.652161i	−0.399233	−	0.916849i	$-0.630724\pi$
$127$	6.36836	−	7.34948i	0.565101	−	0.652161i	0.964334	+	0.264688i	$0.0852690\pi$
$128$	11.0473	−	3.24377i	0.976450	−	0.286712i
$129$	−0.807208	−	1.76754i	−0.0710707	−	0.155623i
$130$	−1.91782	+	1.23251i	−0.168204	+	0.108098i
$131$	10.3055	+	3.02596i	0.900394	+	0.264380i	0.698992	−	0.715129i	$-0.253632\pi$
$131$	10.3055	+	3.02596i	0.900394	+	0.264380i	0.201402	+	0.979509i	$0.435450\pi$
$132$	2.88127	+	20.0397i	0.250783	+	1.74423i
$133$	2.37930	−	5.20993i	0.206311	−	0.451758i
$134$	0.743348	−	5.17010i	0.0642155	−	0.446629i
$135$	1.90376	+	1.22347i	0.163850	+	0.105300i
$136$	7.10308	+	8.19739i	0.609084	+	0.702920i
$137$	−12.2068			−1.04289			−0.521447	−	0.853284i	$-0.674607\pi$
$137$	−12.2068			−1.04289			−0.521447	+	0.853284i	$0.674607\pi$
$138$	−3.30656	+	5.30462i	−0.281473	+	0.451559i
$139$	5.50724			0.467118			0.233559	−	0.972343i	$-0.424963\pi$
$139$	5.50724			0.467118			0.233559	+	0.972343i	$0.424963\pi$
$140$	−1.08663	−	1.25404i	−0.0918369	−	0.105985i
$141$	10.6238	+	6.82751i	0.894686	+	0.574980i
$142$	0.851587	−	5.92292i	0.0714636	−	0.497040i
$143$	8.86534	−	19.4124i	0.741357	−	1.62335i
$144$	−0.585806	−	4.07437i	−0.0488171	−	0.339531i
$145$	−6.83303	−	2.00636i	−0.567452	−	0.166619i
$146$	−0.892875	+	0.573816i	−0.0738949	+	0.0474894i
$147$	−0.927650	−	2.03127i	−0.0765113	−	0.167536i
$148$	16.7974	−	4.93217i	1.38074	−	0.405422i
$149$	7.17049	−	8.27519i	0.587430	−	0.677930i	−0.381756	−	0.924263i	$-0.624680\pi$
$149$	7.17049	−	8.27519i	0.587430	−	0.677930i	0.969185	+	0.246333i	$0.0792258\pi$
$150$	0.853532	−	0.985028i	0.0696906	−	0.0804272i
$151$	3.35978	−	0.986520i	0.273415	−	0.0802819i	−0.142151	−	0.989845i	$-0.545402\pi$
$151$	3.35978	−	0.986520i	0.273415	−	0.0802819i	0.415566	+	0.909563i	$0.363584\pi$
$152$	5.08181	+	11.1276i	0.412189	+	0.902568i
$153$	8.48718	−	5.45438i	0.686148	−	0.440961i
$154$	−3.05992	−	0.898474i	−0.246576	−	0.0724011i
$155$	0.0909054	+	0.632261i	0.00730170	+	0.0507844i
$156$	−6.01215	+	13.1648i	−0.481357	+	1.05402i
$157$	−2.45569	+	17.0797i	−0.195985	+	1.36311i	0.619804	+	0.784756i	$0.287212\pi$
$157$	−2.45569	+	17.0797i	−0.195985	+	1.36311i	−0.815789	+	0.578349i	$0.803697\pi$
$158$	0.179613	+	0.115430i	0.0142893	+	0.00918315i
$159$	4.15921	+	4.79998i	0.329847	+	0.380663i
$160$	5.48107			0.433317
$161$	2.64824	+	3.99835i	0.208710	+	0.315114i
$162$	−6.42811			−0.505040
$163$	1.92154	+	2.21758i	0.150507	+	0.173694i	0.825996	−	0.563675i	$-0.190613\pi$
$163$	1.92154	+	2.21758i	0.150507	+	0.173694i	−0.675490	+	0.737370i	$0.736068\pi$
$164$	15.4073	+	9.90165i	1.20311	+	0.773189i
$165$	−1.73641	+	12.0770i	−0.135179	+	0.940193i
$166$	−4.01524	+	8.79216i	−0.311643	+	0.682404i
$167$	2.03783	+	14.1734i	0.157692	+	1.09677i	0.902873	+	0.429908i	$0.141454\pi$
$167$	2.03783	+	14.1734i	0.157692	+	1.09677i	−0.745181	+	0.666862i	$0.767637\pi$
$168$	4.57629	+	1.34372i	0.353069	+	0.103670i
$169$	1.89745	−	1.21942i	0.145958	−	0.0938015i
$170$	1.23134	+	2.69626i	0.0944396	+	0.206794i
$171$	10.9173	−	3.20562i	0.834870	−	0.245140i
$172$	0.945546	−	1.09122i	0.0720972	−	0.0832046i
$173$	−6.45158	+	7.44552i	−0.490504	+	0.566072i	−0.946000	−	0.324166i	$-0.894916\pi$
$173$	−6.45158	+	7.44552i	−0.490504	+	0.566072i	0.455496	+	0.890238i	$0.349462\pi$
$174$	8.90602	−	2.61504i	0.675164	−	0.198246i
$175$	−0.415415	−	0.909632i	−0.0314024	−	0.0687617i
$176$	−9.52404	+	6.12073i	−0.717902	+	0.461367i
$177$	−23.5683	−	6.92028i	−1.77150	−	0.520160i
$178$	1.39267	+	9.68622i	0.104385	+	0.726013i
$179$	7.86144	−	17.2142i	0.587592	−	1.28665i	−0.349295	−	0.937013i	$-0.613579\pi$
$179$	7.86144	−	17.2142i	0.587592	−	1.28665i	0.936886	−	0.349634i	$-0.113694\pi$
$180$	0.469128	−	3.26286i	0.0349667	−	0.243199i
$181$	−5.18265	−	3.33068i	−0.385223	−	0.247568i	0.333668	−	0.942691i	$-0.391714\pi$
$181$	−5.18265	−	3.33068i	−0.385223	−	0.247568i	−0.718891	+	0.695123i	$0.755350\pi$
$182$	−1.49290	−	1.72290i	−0.110661	−	0.127710i
$183$	17.6923			1.30785
$184$	−10.1580	−	1.31773i	−0.748861	−	0.0971446i
$185$	10.5504			0.775681
$186$	−0.545204	−	0.629199i	−0.0399763	−	0.0461351i
$187$	−23.3429	−	15.0016i	−1.70700	−	1.09702i
$188$	−1.33547	+	9.28839i	−0.0973991	+	0.677425i
$189$	−0.940087	+	2.05850i	−0.0683812	+	0.149734i
$190$	0.475757	+	3.30896i	0.0345150	+	0.240057i
$191$	20.6563	+	6.06525i	1.49464	+	0.438866i	0.924019	−	0.382347i	$-0.124884\pi$
$191$	20.6563	+	6.06525i	1.49464	+	0.438866i	0.570622	+	0.821213i	$0.306702\pi$
$192$	1.77506	−	1.14076i	0.128104	−	0.0823274i
$193$	7.14560	+	15.6467i	0.514351	+	1.12627i	0.971534	+	0.236900i	$0.0761313\pi$
$193$	7.14560	+	15.6467i	0.514351	+	1.12627i	−0.457183	+	0.889373i	$0.651141\pi$
$194$	0.993616	−	0.291752i	0.0713374	−	0.0209466i
$195$	−5.71169	+	6.59164i	−0.409022	+	0.472037i
$196$	1.08663	−	1.25404i	0.0776163	−	0.0895740i
$197$	0.202731	−	0.0595272i	0.0144440	−	0.00424114i	−0.274503	−	0.961586i	$-0.588513\pi$
$197$	0.202731	−	0.0595272i	0.0144440	−	0.00424114i	0.288947	+	0.957345i	$0.406695\pi$
$198$	−2.63184	−	5.76293i	−0.187037	−	0.409554i
$199$	14.5820	−	9.37127i	1.03369	−	0.664312i	0.0902710	−	0.995917i	$-0.471227\pi$
$199$	14.5820	−	9.37127i	1.03369	−	0.664312i	0.943418	+	0.331606i	$0.107590\pi$
$200$	2.04933	+	0.601737i	0.144909	+	0.0425493i
$201$	−2.84397	−	19.7803i	−0.200598	−	1.39519i
$202$	−0.533426	+	1.16804i	−0.0375317	+	0.0821831i
$203$	1.01349	−	7.04901i	0.0711334	−	0.494744i
$204$	15.8303	+	10.1735i	1.10834	+	0.712288i
$205$	7.22796	+	8.34151i	0.504823	+	0.582596i
$206$	3.96861			0.276506
$207$	−2.55779	+	9.17760i	−0.177779	+	0.637888i
$208$	−8.09296			−0.561146
$209$	−20.4935	−	23.6507i	−1.41756	−	1.63595i
$210$	1.09647	+	0.704660i	0.0756638	+	0.0486261i
$211$	0.0225249	−	0.156664i	0.00155068	−	0.0107852i	−0.989031	−	0.147705i	$-0.952811\pi$
$211$	0.0225249	−	0.156664i	0.00155068	−	0.0107852i	0.990582	+	0.136920i	$0.0437204\pi$
$212$	−1.96053	+	4.29297i	−0.134650	+	0.294842i
$213$	−3.25808	−	22.6605i	−0.223240	−	1.55267i
$214$	1.37882	+	0.404857i	0.0942539	+	0.0276754i
$215$	0.732029	−	0.470447i	0.0499240	−	0.0320842i
$216$	−2.00788	−	4.39664i	−0.136619	−	0.299154i
$217$	−0.612888	+	0.179960i	−0.0416056	+	0.0122165i
$218$	6.13099	−	7.07554i	0.415243	−	0.479216i
$219$	−2.65917	+	3.06885i	−0.179690	+	0.207373i
$220$	−8.69909	+	2.55428i	−0.586493	+	0.172210i
$221$	−8.23992	−	18.0429i	−0.554277	−	1.21370i
$222$	−11.5682	+	7.43445i	−0.776409	+	0.498968i
$223$	6.05871	+	1.77900i	0.405721	+	0.119131i	0.478224	−	0.878238i	$-0.341281\pi$
$223$	6.05871	+	1.77900i	0.405721	+	0.119131i	−0.0725031	+	0.997368i	$0.523099\pi$
$224$	0.780038	+	5.42528i	0.0521185	+	0.362492i
$225$	0.825261	−	1.80707i	0.0550174	−	0.120471i
$226$	0.129786	−	0.902681i	0.00863323	−	0.0600455i
$227$	−15.1257	−	9.72067i	−1.00393	−	0.645184i	−0.0681113	−	0.997678i	$-0.521697\pi$
$227$	−15.1257	−	9.72067i	−1.00393	−	0.645184i	−0.935814	+	0.352494i	$0.885334\pi$
$228$	13.8979	+	16.0390i	0.920411	+	1.06221i
$229$	9.08977			0.600669			0.300335	−	0.953834i	$-0.402902\pi$
$229$	9.08977			0.600669			0.300335	+	0.953834i	$0.402902\pi$
$230$	−2.56203	−	1.12759i	−0.168936	−	0.0743508i
$231$	−12.2012			−0.802779
$232$	9.96071	+	11.4953i	0.653952	+	0.754701i
$233$	−15.3272	−	9.85021i	−1.00412	−	0.645308i	−0.0682548	−	0.997668i	$-0.521743\pi$
$233$	−15.3272	−	9.85021i	−1.00412	−	0.645308i	−0.935865	+	0.352359i	$0.885379\pi$
$234$	0.644527	−	4.48278i	0.0421341	−	0.293049i
$235$	−2.34927	+	5.14419i	−0.153250	+	0.335570i
$236$	−2.59757	−	18.0665i	−0.169087	−	1.17603i
$237$	0.783766	+	0.230135i	0.0509111	+	0.0149488i
$238$	−2.49358	+	1.60253i	−0.161635	+	0.103876i
$239$	2.19377	+	4.80369i	0.141903	+	0.310725i	0.967218	−	0.253948i	$-0.0817294\pi$
$239$	2.19377	+	4.80369i	0.141903	+	0.310725i	−0.825314	+	0.564674i	$0.809002\pi$
$240$	4.43954	−	1.30357i	0.286571	−	0.0841449i
$241$	4.48735	−	5.17868i	0.289056	−	0.333588i	−0.592586	−	0.805507i	$-0.701893\pi$
$241$	4.48735	−	5.17868i	0.289056	−	0.333588i	0.881642	+	0.471919i	$0.156438\pi$
$242$	−7.20638	+	8.31661i	−0.463244	+	0.534612i
$243$	−17.0831	+	5.01604i	−1.09588	+	0.321779i
$244$	5.46131	+	11.9586i	0.349625	+	0.765572i
$245$	0.841254	−	0.540641i	0.0537457	−	0.0345403i
$246$	−13.8032	−	4.05298i	−0.880059	−	0.258409i
$247$	−3.18368	−	22.1430i	−0.202573	−	1.40892i
$248$	0.566750	−	1.24101i	0.0359887	−	0.0788042i
$249$	−5.26276	+	36.6033i	−0.333514	+	2.31964i
$250$	0.491016	+	0.315557i	0.0310546	+	0.0199576i
$251$	16.9329	+	19.5417i	1.06880	+	1.23346i	0.971208	+	0.238232i	$0.0765678\pi$
$251$	16.9329	+	19.5417i	1.06880	+	1.23346i	0.0975895	+	0.995227i	$0.468887\pi$
$252$	3.29641			0.207654
$253$	25.8831	−	4.08667i	1.62726	−	0.256927i
$254$	−5.67607			−0.356148
$255$	7.42640	+	8.57053i	0.465059	+	0.536707i
$256$	−4.06359	−	2.61151i	−0.253974	−	0.163219i
$257$	3.26730	−	22.7246i	0.203808	−	1.41752i	−0.589042	−	0.808102i	$-0.700495\pi$
$257$	3.26730	−	22.7246i	0.203808	−	1.41752i	0.792850	−	0.609416i	$-0.208596\pi$
$258$	−0.471145	+	1.03166i	−0.0293322	+	0.0642285i
$259$	1.50148	+	10.4430i	0.0932974	+	0.648898i
$260$	−6.21852	−	1.82592i	−0.385656	−	0.113239i
$261$	11.9017	−	7.64873i	0.736694	−	0.473444i
$262$	−2.60422	−	5.70244i	−0.160889	−	0.352298i
$263$	−5.07764	+	1.49093i	−0.313101	+	0.0919347i	−0.434508	−	0.900668i	$-0.643078\pi$
$263$	−5.07764	+	1.49093i	−0.313101	+	0.0919347i	0.121407	+	0.992603i	$0.461259\pi$
$264$	17.0656	−	19.6947i	1.05031	−	1.21213i
$265$	−1.86255	+	2.14950i	−0.114416	+	0.132043i
$266$	−3.20757	+	0.941828i	−0.196669	+	0.0577472i
$267$	15.5530	+	34.0562i	0.951826	+	2.08421i
$268$	12.4920	−	8.02813i	0.763071	−	0.490396i
$269$	−28.2963	−	8.30853i	−1.72525	−	0.506580i	−0.739268	−	0.673411i	$-0.764828\pi$
$269$	−28.2963	−	8.30853i	−1.72525	−	0.506580i	−0.985985	+	0.166831i	$0.946646\pi$
$270$	−0.187977	−	1.30741i	−0.0114399	−	0.0795663i
$271$	−8.80379	+	19.2776i	−0.534792	+	1.17103i	0.428738	+	0.903429i	$0.358958\pi$
$271$	−8.80379	+	19.2776i	−0.534792	+	1.17103i	−0.963530	+	0.267602i	$0.913769\pi$
$272$	−1.49752	+	10.4155i	−0.0908004	+	0.631531i
$273$	−7.33740	−	4.71546i	−0.444080	−	0.285393i
$274$	4.66571	+	5.38452i	0.281866	+	0.325291i
$275$	−5.46387			−0.329484
$276$	−17.5530	+	2.77143i	−1.05657	+	0.166820i
$277$	16.8719			1.01373			0.506867	−	0.862024i	$-0.330803\pi$
$277$	16.8719			1.01373			0.506867	+	0.862024i	$0.330803\pi$
$278$	−2.10500	−	2.42930i	−0.126249	−	0.145700i
$279$	−1.06752	−	0.686052i	−0.0639107	−	0.0410729i
$280$	−0.303963	+	2.11411i	−0.0181652	+	0.126342i
$281$	3.86987	−	8.47384i	0.230857	−	0.505507i	−0.758383	−	0.651810i	$-0.774010\pi$
$281$	3.86987	−	8.47384i	0.230857	−	0.505507i	0.989240	+	0.146303i	$0.0467374\pi$
$282$	−1.04899	−	7.29590i	−0.0624666	−	0.434465i
$283$	−5.87308	−	1.72449i	−0.349118	−	0.102510i	0.102472	−	0.994736i	$-0.467325\pi$
$283$	−5.87308	−	1.72449i	−0.349118	−	0.102510i	−0.451590	+	0.892226i	$0.649143\pi$
$284$	14.3110	−	9.19710i	0.849200	−	0.545748i
$285$	5.31313	+	11.6341i	0.314723	+	0.689146i
$286$	−11.9515	+	3.50929i	−0.706709	+	0.207509i
$287$	−7.22796	+	8.34151i	−0.426653	+	0.492384i
$288$	−7.13056	+	8.22910i	−0.420172	+	0.484904i
$289$	−8.43416	+	2.47649i	−0.496127	+	0.145676i
$290$	1.72672	+	3.78099i	0.101397	+	0.222027i
$291$	3.33301	−	2.14200i	0.195385	−	0.125566i
$292$	−2.89514	−	0.850089i	−0.169425	−	0.0497477i
$293$	−2.27661	−	15.8342i	−0.133001	−	0.925043i	−0.941612	−	0.336700i	$-0.890689\pi$
$293$	−2.27661	−	15.8342i	−0.133001	−	0.925043i	0.808611	−	0.588344i	$-0.200220\pi$
$294$	−0.541443	+	1.18559i	−0.0315776	+	0.0691453i
$295$	1.56543	−	10.8878i	0.0911431	−	0.633914i
$296$	−18.9568	−	12.1828i	−1.10184	−	0.708112i
$297$	8.09720	+	9.34466i	0.469847	+	0.542232i
$298$	−6.39100			−0.370221
$299$	17.1447	+	7.54561i	0.991503	+	0.436374i
$300$	3.70539			0.213931
$301$	0.569837	+	0.657627i	0.0328448	+	0.0379050i
$302$	−1.71935	−	1.10496i	−0.0989375	−	0.0635833i
$303$	−0.699159	+	4.86276i	−0.0401656	+	0.279358i
$304$	−4.92995	+	10.7951i	−0.282752	+	0.619141i
$305$	1.12754	+	7.84223i	0.0645629	+	0.449045i
$306$	−5.64998	−	1.65898i	−0.322988	−	0.0948378i
$307$	3.13374	−	2.01393i	0.178852	−	0.114941i	−0.448151	−	0.893958i	$-0.647917\pi$
$307$	3.13374	−	2.01393i	0.178852	−	0.114941i	0.627004	+	0.779016i	$0.284281\pi$
$308$	−3.76629	−	8.24703i	−0.214605	−	0.469918i
$309$	14.5685	−	4.27769i	0.828771	−	0.243349i
$310$	0.244150	−	0.281764i	0.0138668	−	0.0160031i
$311$	−6.99728	+	8.07529i	−0.396780	+	0.457908i	−0.918624	−	0.395133i	$-0.870699\pi$
$311$	−6.99728	+	8.07529i	−0.396780	+	0.457908i	0.521845	+	0.853041i	$0.325244\pi$
$312$	17.8742	−	5.24834i	1.01193	−	0.297129i
$313$	−6.42353	−	14.0656i	−0.363080	−	0.795033i	−0.999715	−	0.0238685i	$-0.992402\pi$
$313$	−6.42353	−	14.0656i	−0.363080	−	0.795033i	0.636636	−	0.771165i	$-0.280326\pi$
$314$	8.47263	−	5.44503i	0.478138	−	0.307281i
$315$	1.90612	+	0.559688i	0.107398	+	0.0315349i
$316$	0.0863824	+	0.600803i	0.00485939	+	0.0337978i
$317$	−6.88893	+	15.0847i	−0.386921	+	0.847239i	0.611510	+	0.791237i	$0.290563\pi$
$317$	−6.88893	+	15.0847i	−0.386921	+	0.847239i	−0.998431	+	0.0560017i	$0.982165\pi$
$318$	0.527571	−	3.66933i	0.0295847	−	0.205766i
$319$	−32.7339	−	21.0368i	−1.83275	−	1.17784i
$320$	0.618776	+	0.714105i	0.0345906	+	0.0399197i
$321$	5.49791			0.306863
$322$	0.751494	−	2.69643i	0.0418791	−	0.150266i
$323$	−29.0867			−1.61842
$324$	−11.9673	−	13.8110i	−0.664849	−	0.767277i
$325$	−3.28579	−	2.11165i	−0.182263	−	0.117133i
$326$	0.243736	−	1.69522i	0.0134993	−	0.0938896i
$327$	14.8798	−	32.5822i	0.822855	−	1.80180i
$328$	−3.35496	−	23.3342i	−0.185246	−	1.28842i
$329$	−5.42617	−	1.59327i	−0.299154	−	0.0878397i
$330$	5.99098	−	3.85017i	0.329792	−	0.211945i
$331$	11.9458	+	26.1577i	0.656601	+	1.43776i	0.885656	+	0.464342i	$0.153709\pi$
$331$	11.9458	+	26.1577i	0.656601	+	1.43776i	−0.229055	+	0.973413i	$0.573564\pi$
$332$	−26.3654	+	7.74159i	−1.44699	+	0.424875i
$333$	−13.7255	+	15.8400i	−0.752151	+	0.868029i
$334$	5.47311	−	6.31631i	0.299475	−	0.345613i
$335$	8.58648	−	2.52122i	0.469130	−	0.137749i
$336$	1.92211	+	4.20884i	0.104860	+	0.229611i
$337$	5.78179	−	3.71573i	0.314954	−	0.202409i	−0.373607	−	0.927587i	$-0.621879\pi$
$337$	5.78179	−	3.71573i	0.314954	−	0.202409i	0.688561	+	0.725178i	$0.258243\pi$
$338$	−1.26315	−	0.370894i	−0.0687063	−	0.0201740i
$339$	−0.496548	−	3.45357i	−0.0269688	−	0.187572i
$340$	−3.50059	+	7.66523i	−0.189846	+	0.415706i
$341$	−0.496695	+	3.45459i	−0.0268975	+	0.187076i
$342$	−5.58690	−	3.59048i	−0.302105	−	0.194151i
$343$	0.654861	+	0.755750i	0.0353592	+	0.0408066i
$344$	−1.85854			−0.100206
$345$	−10.6204	−	1.37772i	−0.571785	−	0.0741737i
$346$	5.75023			0.309134
$347$	−16.1655	−	18.6560i	−0.867810	−	1.00151i	−0.999947	−	0.0102746i	$-0.996729\pi$
$347$	−16.1655	−	18.6560i	−0.867810	−	1.00151i	0.132137	−	0.991231i	$-0.457816\pi$
$348$	22.1989	+	14.2664i	1.18999	+	0.764759i
$349$	−0.787303	+	5.47581i	−0.0421434	+	0.293114i	0.957840	+	0.287303i	$0.0927587\pi$
$349$	−0.787303	+	5.47581i	−0.0421434	+	0.293114i	−0.999983	+	0.00581059i	$0.998150\pi$
$350$	−0.242466	+	0.530926i	−0.0129604	+	0.0283792i
$351$	1.25791	+	8.74895i	0.0671422	+	0.466984i
$352$	28.7347	+	8.43728i	1.53157	+	0.449709i
$353$	25.1135	−	16.1395i	1.33666	−	0.859018i	0.339979	−	0.940433i	$-0.389580\pi$
$353$	25.1135	−	16.1395i	1.33666	−	0.859018i	0.996680	+	0.0814147i	$0.0259438\pi$
$354$	5.95577	+	13.0413i	0.316545	+	0.693138i
$355$	9.83676	−	2.88833i	0.522081	−	0.153297i
$356$	−18.2184	+	21.0251i	−0.965573	+	1.11433i
$357$	−7.42640	+	8.57053i	−0.393047	+	0.453600i
$358$	−10.5982	+	3.11190i	−0.560130	+	0.164469i
$359$	1.10614	+	2.42211i	0.0583798	+	0.127834i	0.936573	−	0.350471i	$-0.113979\pi$
$359$	1.10614	+	2.42211i	0.0583798	+	0.127834i	−0.878194	+	0.478305i	$0.841251\pi$
$360$	−3.56949	+	2.29397i	−0.188128	+	0.120903i
$361$	−13.2452	−	3.88915i	−0.697118	−	0.204692i
$362$	0.511733	+	3.55918i	0.0268961	+	0.187066i
$363$	−17.4898	+	38.2972i	−0.917974	+	2.01008i
$364$	0.922350	−	6.41508i	0.0483443	−	0.336242i
$365$	−1.52976	−	0.983114i	−0.0800711	−	0.0514586i
$366$	−6.76243	−	7.80426i	−0.353478	−	0.407935i
$367$	25.3207			1.32173			0.660864	−	0.750506i	$-0.270190\pi$
$367$	25.3207			1.32173			0.660864	+	0.750506i	$0.270190\pi$
$368$	−5.48721	−	8.28468i	−0.286040	−	0.431869i
$369$	−21.9268			−1.14147
$370$	−4.03262	−	4.65389i	−0.209646	−	0.241944i
$371$	−2.39269	−	1.53769i	−0.124222	−	0.0798328i
$372$	0.336840	−	2.34277i	0.0174643	−	0.121467i
$373$	−0.349518	+	0.765337i	−0.0180973	+	0.0396276i	−0.918465	−	0.395503i	$-0.870570\pi$
$373$	−0.349518	+	0.765337i	−0.0180973	+	0.0396276i	0.900368	+	0.435130i	$0.143298\pi$
$374$	2.30487	+	16.0307i	0.119182	+	0.828929i
$375$	2.14261	+	0.629128i	0.110644	+	0.0324880i
$376$	10.1613	−	6.53026i	0.524028	−	0.336772i
$377$	−11.5549	−	25.3017i	−0.595108	−	1.30311i
$378$	1.26735	−	0.372127i	0.0651854	−	0.0191402i
$379$	16.0513	−	18.5242i	0.824502	−	0.951526i	−0.174952	−	0.984577i	$-0.555977\pi$
$379$	16.0513	−	18.5242i	0.824502	−	0.951526i	0.999454	+	0.0330510i	$0.0105224\pi$
$380$	−6.22368	+	7.18251i	−0.319268	+	0.368455i
$381$	−20.8364	+	6.11812i	−1.06748	+	0.313441i
$382$	−5.21990	−	11.4300i	−0.267074	−	0.584810i
$383$	5.01422	−	3.22244i	0.256215	−	0.164659i	−0.406228	−	0.913772i	$-0.633156\pi$
$383$	5.01422	−	3.22244i	0.256215	−	0.164659i	0.662443	+	0.749113i	$0.269520\pi$
$384$	−24.6693	−	7.24356i	−1.25890	−	0.369646i
$385$	−0.777589	−	5.40825i	−0.0396296	−	0.275630i
$386$	4.17068	−	9.13252i	0.212282	−	0.464833i
$387$	−0.246014	+	1.71107i	−0.0125056	+	0.0869785i
$388$	2.47666	+	1.59165i	0.125734	+	0.0808040i
$389$	16.6662	+	19.2338i	0.845011	+	0.975194i	0.999919	−	0.0127347i	$-0.00405369\pi$
$389$	16.6662	+	19.2338i	0.845011	+	0.975194i	−0.154908	+	0.987929i	$0.549508\pi$
$390$	5.09078			0.257781
$391$	12.8835	−	20.6686i	0.651546	−	1.04526i
$392$	−2.13585			−0.107877
$393$	−15.7064	−	18.1262i	−0.792285	−	0.914345i
$394$	−0.103747	−	0.0666740i	−0.00522668	−	0.00335899i
$395$	−0.0520587	+	0.362076i	−0.00261936	+	0.0182180i
$396$	7.48210	−	16.3835i	0.375989	−	0.823302i
$397$	4.02904	+	28.0226i	0.202212	+	1.40641i	0.797702	+	0.603052i	$0.206049\pi$
$397$	4.02904	+	28.0226i	0.202212	+	1.40641i	−0.595490	+	0.803362i	$0.703042\pi$
$398$	−9.70734	−	2.85033i	−0.486585	−	0.142874i
$399$	−10.7596	+	6.91476i	−0.538652	+	0.346171i
$400$	0.860749	+	1.88478i	0.0430374	+	0.0942389i
$401$	−17.4471	+	5.12294i	−0.871267	+	0.255827i	−0.686654	−	0.726984i	$-0.740921\pi$
$401$	−17.4471	+	5.12294i	−0.871267	+	0.255827i	−0.184613	+	0.982811i	$0.559103\pi$
$402$	−7.63824	+	8.81499i	−0.380961	+	0.439652i
$403$	−1.63381	+	1.88552i	−0.0813859	+	0.0939244i
$404$	−3.50266	+	1.02847i	−0.174264	+	0.0511684i
$405$	−4.57506	−	10.0180i	−0.227337	−	0.497798i
$406$	−3.49677	+	2.24724i	−0.173542	+	0.111528i
$407$	55.3110	+	16.2408i	2.74166	+	0.805025i
$408$	−3.44707	−	23.9749i	−0.170655	−	1.18693i
$409$	−8.03142	+	17.5864i	−0.397128	+	0.869589i	0.600425	+	0.799681i	$0.294998\pi$
$409$	−8.03142	+	17.5864i	−0.397128	+	0.869589i	−0.997553	+	0.0699086i	$0.977729\pi$
$410$	0.916823	−	6.37665i	0.0452787	−	0.314920i
$411$	22.9313	+	14.7371i	1.13112	+	0.726926i
$412$	7.38841	+	8.52668i	0.364001	+	0.420079i
$413$	10.9998			0.541265
$414$	5.02598	−	2.37963i	0.247013	−	0.116952i
$415$	−16.5600			−0.812900
$416$	14.0193	+	16.1792i	0.687355	+	0.793250i
$417$	−10.3458	−	6.64883i	−0.506635	−	0.325594i
$418$	−2.59947	+	18.0797i	−0.127144	+	0.884308i
$419$	14.2110	−	31.1177i	0.694252	−	1.52020i	−0.152553	−	0.988295i	$-0.548750\pi$
$419$	14.2110	−	31.1177i	0.694252	−	1.52020i	0.846805	−	0.531904i	$-0.178523\pi$
$420$	0.527332	+	3.66768i	0.0257312	+	0.178964i
$421$	−9.56312	−	2.80798i	−0.466078	−	0.136853i	0.0402577	−	0.999189i	$-0.487182\pi$
$421$	−9.56312	−	2.80798i	−0.466078	−	0.136853i	−0.506336	+	0.862337i	$0.669000\pi$
$422$	−0.0777157	+	0.0499449i	−0.00378314	+	0.00243128i
$423$	−4.66705	−	10.2194i	−0.226920	−	0.496885i
$424$	5.82870	−	1.71146i	0.283067	−	0.0831158i
$425$	−3.32565	+	3.83800i	−0.161318	+	0.186171i
$426$	−8.75044	+	10.0985i	−0.423960	+	0.489276i
$427$	−7.60195	+	2.23213i	−0.367884	+	0.108020i
$428$	1.69711	+	3.71615i	0.0820329	+	0.179627i
$429$	−40.0906	+	25.7646i	−1.93559	+	1.24393i
$430$	−0.487317	−	0.143089i	−0.0235005	−	0.00690038i
$431$	−1.80983	−	12.5876i	−0.0871762	−	0.606324i	−0.985840	−	0.167687i	$-0.946370\pi$
$431$	−1.80983	−	12.5876i	−0.0871762	−	0.606324i	0.898664	−	0.438637i	$-0.144539\pi$
$432$	1.94788	−	4.26526i	0.0937174	−	0.205213i
$433$	5.34933	−	37.2054i	0.257072	−	1.78798i	−0.296353	−	0.955078i	$-0.595771\pi$
$433$	5.34933	−	37.2054i	0.257072	−	1.78798i	0.553426	−	0.832899i	$-0.313320\pi$
$434$	0.313643	+	0.201566i	0.0150553	+	0.00967547i
$435$	10.4141	+	12.0185i	0.499318	+	0.576244i
$436$	26.6161			1.27468
$437$	20.5089	−	18.2725i	0.981075	−	0.874094i
$438$	2.37010			0.113248
$439$	13.8770	+	16.0149i	0.662313	+	0.764350i	0.983153	−	0.182783i	$-0.0585107\pi$
$439$	13.8770	+	16.0149i	0.662313	+	0.764350i	−0.320840	+	0.947133i	$0.603965\pi$
$440$	9.81741	+	6.30926i	0.468027	+	0.300782i
$441$	−0.282722	+	1.96637i	−0.0134629	+	0.0936368i
$442$	−4.80941	+	10.5311i	−0.228760	+	0.500915i
$443$	4.24964	+	29.5569i	0.201906	+	1.40429i	0.798620	+	0.601836i	$0.205564\pi$
$443$	4.24964	+	29.5569i	0.201906	+	1.40429i	−0.596713	+	0.802455i	$0.703527\pi$
$444$	−37.5098	−	11.0139i	−1.78014	−	0.522696i
$445$	−14.1044	+	9.06437i	−0.668615	+	0.429693i
$446$	−1.53105	−	3.35253i	−0.0724973	−	0.158747i
$447$	−23.4609	+	6.88873i	−1.10966	+	0.325826i
$448$	−0.618776	+	0.714105i	−0.0292344	+	0.0337383i
$449$	−12.2689	+	14.1590i	−0.579003	+	0.668206i	−0.967390	−	0.253291i	$-0.918487\pi$
$449$	−12.2689	+	14.1590i	−0.579003	+	0.668206i	0.388387	+	0.921496i	$0.373032\pi$
$450$	−1.11255	+	0.326674i	−0.0524461	+	0.0153996i
$451$	25.0524	+	54.8571i	1.17967	+	2.58312i
$452$	2.18106	−	1.40168i	0.102588	−	0.0659296i
$453$	−7.50261	−	2.20297i	−0.352504	−	0.103504i
$454$	1.49350	+	10.3875i	0.0700936	+	0.487512i
$455$	1.62254	−	3.55287i	0.0760659	−	0.166561i
$456$	3.88766	−	27.0393i	0.182056	−	1.26623i
$457$	−15.7878	−	10.1462i	−0.738524	−	0.474621i	0.116512	−	0.993189i	$-0.462829\pi$
$457$	−15.7878	−	10.1462i	−0.738524	−	0.474621i	−0.855036	+	0.518569i	$0.826465\pi$
$458$	−3.47433	−	4.00959i	−0.162345	−	0.187356i
$459$	11.4925			0.536422
$460$	−2.34712	−	7.60385i	−0.109435	−	0.354531i
$461$	−21.9837			−1.02388			−0.511942	−	0.859020i	$-0.671074\pi$
$461$	−21.9837			−1.02388			−0.511942	+	0.859020i	$0.671074\pi$
$462$	4.66358	+	5.38206i	0.216969	+	0.250396i
$463$	−20.6875	−	13.2951i	−0.961430	−	0.617874i	−0.0370368	−	0.999314i	$-0.511792\pi$
$463$	−20.6875	−	13.2951i	−0.961430	−	0.617874i	−0.924394	+	0.381440i	$0.875428\pi$
$464$	−2.09998	+	14.6057i	−0.0974893	+	0.678053i
$465$	0.592548	−	1.29750i	0.0274788	−	0.0601701i
$466$	1.51341	+	10.5260i	0.0701072	+	0.487606i
$467$	−20.2872	−	5.95687i	−0.938782	−	0.275651i	−0.223673	−	0.974664i	$-0.571805\pi$
$467$	−20.2872	−	5.95687i	−0.938782	−	0.275651i	−0.715109	+	0.699013i	$0.753623\pi$
$468$	10.8313	−	6.96087i	0.500678	−	0.321766i
$469$	3.71754	+	8.14028i	0.171660	+	0.375883i
$470$	3.16710	−	0.929945i	0.146087	−	0.0428952i
$471$	25.2333	−	29.1207i	1.16269	−	1.34181i
$472$	−15.3852	+	17.7555i	−0.708162	+	0.817263i
$473$	4.56187	−	1.33949i	0.209755	−	0.0615897i
$474$	−0.198059	−	0.433690i	−0.00909717	−	0.0199200i
$475$	−4.81829	+	3.09653i	−0.221078	+	0.142078i
$476$	−8.08540	−	2.37409i	−0.370594	−	0.108816i
$477$	−0.804116	−	5.59275i	−0.0368180	−	0.256075i
$478$	1.28044	−	2.80378i	0.0585661	−	0.128242i
$479$	−0.898299	+	6.24781i	−0.0410443	+	0.285470i	0.958954	+	0.283562i	$0.0915163\pi$
$479$	−0.898299	+	6.24781i	−0.0410443	+	0.285470i	−0.999998	+	0.00190746i	$0.999393\pi$
$480$	−10.2966	−	6.61723i	−0.469974	−	0.302034i
$481$	26.9856	+	31.1430i	1.23044	+	1.42000i
$482$	−3.99954			−0.182174
$483$	−0.147753	−	10.7084i	−0.00672297	−	0.487249i
$484$	−31.2847			−1.42203
$485$	1.16187	+	1.34087i	0.0527577	+	0.0608857i
$486$	8.74218	+	5.61826i	0.396553	+	0.254849i
$487$	0.0412273	−	0.286742i	0.00186819	−	0.0129935i	−0.988866	−	0.148809i	$-0.952456\pi$
$487$	0.0412273	−	0.286742i	0.00186819	−	0.0129935i	0.990734	+	0.135815i	$0.0433653\pi$
$488$	7.02967	−	15.3928i	0.318218	−	0.696801i
$489$	−0.932509	−	6.48574i	−0.0421695	−	0.293295i
$490$	−0.560029	−	0.164439i	−0.0252995	−	0.00742861i
$491$	−4.32675	+	2.78064i	−0.195264	+	0.125488i	−0.634619	−	0.772825i	$-0.718843\pi$
$491$	−4.32675	+	2.78064i	−0.195264	+	0.125488i	0.439356	+	0.898313i	$0.355207\pi$
$492$	−16.9896	−	37.2020i	−0.765950	−	1.67720i
$493$	−34.7009	+	10.1891i	−1.56285	+	0.458894i
$494$	−8.55061	+	9.86793i	−0.384710	+	0.443979i
$495$	7.10817	−	8.20327i	0.319489	−	0.368710i
$496$	1.26992	−	0.372882i	0.0570210	−	0.0167429i
$497$	4.25885	+	9.32558i	0.191036	+	0.418309i
$498$	18.1576	−	11.6692i	0.813662	−	0.522909i
$499$	1.37353	+	0.403306i	0.0614878	+	0.0180545i	0.312332	−	0.949973i	$-0.398890\pi$
$499$	1.37353	+	0.403306i	0.0614878	+	0.0180545i	−0.250844	+	0.968028i	$0.580708\pi$
$500$	0.236147	+	1.64244i	0.0105608	+	0.0734521i
$501$	13.2831	−	29.0860i	0.593447	−	1.29947i
$502$	2.14784	−	14.9386i	0.0958629	−	0.666741i
$503$	−0.0422225	−	0.0271348i	−0.00188261	−	0.00120988i	0.539699	−	0.841858i	$-0.318538\pi$
$503$	−0.0422225	−	0.0271348i	−0.00188261	−	0.00120988i	−0.541582	+	0.840648i	$0.682174\pi$
$504$	−2.77861	−	3.20669i	−0.123769	−	0.142837i
$505$	−2.20000			−0.0978989
$506$	−11.6958	−	9.85528i	−0.519943	−	0.438121i
$507$	−5.03670			−0.223688
$508$	−10.5672	−	12.1952i	−0.468844	−	0.541075i
$509$	−3.75068	−	2.41041i	−0.166246	−	0.106840i	0.454872	−	0.890557i	$-0.349685\pi$
$509$	−3.75068	−	2.41041i	−0.166246	−	0.106840i	−0.621118	+	0.783717i	$0.713321\pi$
$510$	0.941995	−	6.55172i	0.0417122	−	0.290115i
$511$	0.755401	−	1.65410i	0.0334170	−	0.0731729i
$512$	−2.87589	−	20.0023i	−0.127098	−	0.883983i
$513$	12.4364	+	3.65165i	0.549079	+	0.161224i
$514$	−11.2729	+	7.24463i	−0.497224	+	0.319547i
$515$	2.82457	+	6.18494i	0.124465	+	0.272541i
$516$	−3.09369	+	0.908390i	−0.136192	+	0.0399897i
$517$	−20.2349	+	23.3523i	−0.889929	+	1.02703i
$518$	4.03262	−	4.65389i	0.177183	−	0.204480i
$519$	21.1087	−	6.19806i	0.926567	−	0.272065i
$520$	3.46550	+	7.58838i	0.151972	+	0.332772i
$521$	24.1909	−	15.5465i	1.05982	−	0.681106i	0.110010	−	0.993930i	$-0.464912\pi$
$521$	24.1909	−	15.5465i	1.05982	−	0.681106i	0.949811	+	0.312825i	$0.101275\pi$
$522$	−7.92302	−	2.32641i	−0.346781	−	0.101824i
$523$	4.85543	+	33.7702i	0.212313	+	1.47667i	0.765405	+	0.643549i	$0.222539\pi$
$523$	4.85543	+	33.7702i	0.212313	+	1.47667i	−0.553092	+	0.833120i	$0.686552\pi$
$524$	7.40356	−	16.2115i	0.323426	−	0.708205i
$525$	−0.317799	+	2.21034i	−0.0138699	+	0.0964671i
$526$	2.59846	+	1.66993i	0.113298	+	0.0728123i
$527$	2.12430	+	2.45157i	0.0925360	+	0.106792i
$528$	25.2811			1.10022
$529$	3.90011	+	22.6669i	0.169570	+	0.985518i
$530$	1.66008			0.0721092
$531$	14.3101	+	16.5147i	0.621006	+	0.716679i
$532$	−7.99512	−	5.13815i	−0.346633	−	0.222767i
$533$	−6.13522	+	42.6714i	−0.265746	+	1.84830i
$534$	9.07783	−	19.8777i	0.392836	−	0.860191i
$535$	0.350385	+	2.43698i	0.0151485	+	0.105360i
$536$	−18.3394	−	5.38493i	−0.792142	−	0.232594i
$537$	−35.5508	+	22.8471i	−1.53413	+	0.985925i
$538$	7.15053	+	15.6575i	0.308281	+	0.675041i
$539$	5.24254	−	1.53935i	0.225812	−	0.0663045i
$540$	2.45905	−	2.83789i	0.105820	−	0.122123i
$541$	24.2406	−	27.9751i	1.04218	−	1.20275i	0.0633714	−	0.997990i	$-0.479815\pi$
$541$	24.2406	−	27.9751i	1.04218	−	1.20275i	0.978813	−	0.204755i	$-0.0656398\pi$
$542$	11.8686	−	3.48492i	0.509798	−	0.149690i
$543$	5.71490	+	12.5139i	0.245250	+	0.537022i
$544$	23.4164	−	15.0488i	1.00397	−	0.645212i
$545$	15.3906	+	4.51908i	0.659259	+	0.193576i
$546$	0.724493	+	5.03896i	0.0310054	+	0.215648i
$547$	12.9774	−	28.4166i	0.554876	−	1.21501i	−0.399592	−	0.916693i	$-0.630848\pi$
$547$	12.9774	−	28.4166i	0.554876	−	1.21501i	0.954467	−	0.298315i	$-0.0964246\pi$
$548$	−2.88259	+	20.0488i	−0.123138	+	0.856444i
$549$	−13.2409	−	8.50944i	−0.565110	−	0.363174i
$550$	2.08842	+	2.41016i	0.0890505	+	0.102770i
$551$	−40.7885			−1.73765
$552$	17.4918	+	14.7391i	0.744500	+	0.627340i
$553$	−0.365799			−0.0155554
$554$	−6.44884	−	7.44236i	−0.273985	−	0.316196i
$555$	−19.8198	−	12.7374i	−0.841302	−	0.540672i
$556$	1.30052	−	9.04530i	0.0551543	−	0.383606i
$557$	1.31987	−	2.89011i	0.0559246	−	0.122458i	−0.879607	−	0.475702i	$-0.842194\pi$
$557$	1.31987	−	2.89011i	0.0559246	−	0.122458i	0.935531	+	0.353244i	$0.114921\pi$
$558$	0.105406	+	0.733118i	0.00446221	+	0.0310354i
$559$	3.26104	+	0.957529i	0.137927	+	0.0404992i
$560$	−1.74310	+	1.12022i	−0.0736592	+	0.0473379i
$561$	25.7402	+	56.3632i	1.08675	+	2.37965i
$562$	−5.21705	+	1.53186i	−0.220068	+	0.0646178i
$563$	12.8075	−	14.7806i	0.539771	−	0.622928i	−0.418698	−	0.908125i	$-0.637514\pi$
$563$	12.8075	−	14.7806i	0.539771	−	0.622928i	0.958469	+	0.285197i	$0.0920590\pi$
$564$	13.7225	−	15.8367i	0.577823	−	0.666844i
$565$	1.49917	−	0.440196i	0.0630705	−	0.0185192i
$566$	1.48414	+	3.24981i	0.0623831	+	0.136600i
$567$	9.26492	−	5.95420i	0.389090	−	0.250053i
$568$	−21.0098	−	6.16903i	−0.881551	−	0.258847i
$569$	4.18066	+	29.0771i	0.175262	+	1.21898i	0.867548	+	0.497353i	$0.165695\pi$
$569$	4.18066	+	29.0771i	0.175262	+	1.21898i	−0.692286	+	0.721624i	$0.743396\pi$
$570$	3.10112	−	6.79051i	0.129892	−	0.284423i
$571$	2.82936	−	19.6786i	0.118405	−	0.823524i	−0.840908	−	0.541178i	$-0.817978\pi$
$571$	2.82936	−	19.6786i	0.118405	−	0.823524i	0.959313	−	0.282346i	$-0.0911125\pi$
$572$	−29.7901	−	19.1450i	−1.24559	−	0.800491i
$573$	−31.4820	−	36.3322i	−1.31518	−	1.51780i
$574$	6.44222			0.268893
$575$	−0.0661657	−	4.79538i	−0.00275930	−	0.199981i
$576$	−1.87713			−0.0782136
$577$	1.81413	+	2.09361i	0.0755231	+	0.0871583i	0.792254	−	0.610192i	$-0.208908\pi$
$577$	1.81413	+	2.09361i	0.0755231	+	0.0871583i	−0.716731	+	0.697350i	$0.754362\pi$
$578$	4.31614	+	2.77382i	0.179528	+	0.115376i
$579$	5.46649	−	38.0203i	0.227180	−	1.58007i
$580$	−4.90892	+	10.7490i	−0.203832	+	0.446329i
$581$	−2.35674	−	16.3915i	−0.0977740	−	0.680033i
$582$	−2.21881	−	0.651502i	−0.0919727	−	0.0270056i
$583$	−13.0733	+	8.40173i	−0.541443	+	0.347964i
$584$	1.61342	+	3.53290i	0.0667638	+	0.146192i
$585$	7.44499	−	2.18605i	0.307812	−	0.0903819i
$586$	−6.11444	+	7.05644i	−0.252585	+	0.291499i
$587$	12.3873	−	14.2957i	0.511279	−	0.590048i	−0.440147	−	0.897926i	$-0.645074\pi$
$587$	12.3873	−	14.2957i	0.511279	−	0.590048i	0.951426	+	0.307878i	$0.0996190\pi$
$588$	−3.55530	+	1.04393i	−0.146618	+	0.0430509i
$589$	1.51980	+	3.32791i	0.0626225	+	0.137124i
$590$	−5.40108	+	3.47106i	−0.222359	+	0.142901i
$591$	−0.452713	−	0.132928i	−0.0186221	−	0.00546794i
$592$	−3.11110	−	21.6382i	−0.127865	−	0.889323i
$593$	−4.30450	+	9.42554i	−0.176765	+	0.387060i	−0.977188	−	0.212374i	$-0.931881\pi$
$593$	−4.30450	+	9.42554i	−0.176765	+	0.387060i	0.800424	+	0.599434i	$0.204608\pi$
$594$	1.02708	−	7.14350i	0.0421416	−	0.293101i
$595$	−4.27223	−	2.74559i	−0.175144	−	0.112558i
$596$	−11.8982	−	13.7312i	−0.487369	−	0.562454i
$597$	−38.7072			−1.58418
$598$	−3.22466	−	10.4468i	−0.131866	−	0.427201i
$599$	−47.7257			−1.95002			−0.975009	−	0.222166i	$-0.928687\pi$
$599$	−47.7257			−1.95002			−0.975009	+	0.222166i	$0.928687\pi$
$600$	−3.12335	−	3.60454i	−0.127510	−	0.147155i
$601$	1.87142	+	1.20269i	0.0763370	+	0.0490588i	0.578253	−	0.815858i	$-0.303735\pi$
$601$	1.87142	+	1.20269i	0.0763370	+	0.0490588i	−0.501916	+	0.864917i	$0.667371\pi$
$602$	0.0722804	−	0.502721i	0.00294593	−	0.0204894i
$603$	−7.38524	+	16.1714i	−0.300750	+	0.658551i
$604$	−0.826896	−	5.75119i	−0.0336459	−	0.234013i
$605$	−18.0901	−	5.31174i	−0.735468	−	0.215953i
$606$	2.41224	−	1.55025i	0.0979907	−	0.0629748i
$607$	5.86050	+	12.8327i	0.237870	+	0.520863i	0.990489	−	0.137594i	$-0.0439368\pi$
$607$	5.86050	+	12.8327i	0.237870	+	0.520863i	−0.752619	+	0.658457i	$0.771210\pi$
$608$	30.1213	−	8.84441i	1.22158	−	0.358688i
$609$	−10.4141	+	12.0185i	−0.422001	+	0.487015i
$610$	3.02831	−	3.49486i	0.122613	−	0.141503i
$611$	−21.1937	+	6.22303i	−0.857405	+	0.251757i
$612$	−6.95426	−	15.2277i	−0.281109	−	0.615543i
$613$	−31.0958	+	19.9840i	−1.25595	+	0.807147i	−0.987724	−	0.156210i	$-0.950072\pi$
$613$	−31.0958	+	19.9840i	−1.25595	+	0.807147i	−0.268222	+	0.963357i	$0.586436\pi$
$614$	−2.08616	−	0.612551i	−0.0841904	−	0.0247205i
$615$	−3.50767	−	24.3964i	−0.141443	−	0.983758i
$616$	−4.84788	+	10.6154i	−0.195327	+	0.427706i
$617$	−0.892941	+	6.21054i	−0.0359485	+	0.250027i	−0.999869	−	0.0161617i	$-0.994855\pi$
$617$	−0.892941	+	6.21054i	−0.0359485	+	0.250027i	0.963921	+	0.266189i	$0.0857644\pi$
$618$	−7.45534	−	4.79126i	−0.299898	−	0.192733i
$619$	−1.86669	−	2.15428i	−0.0750287	−	0.0865877i	0.716994	−	0.697079i	$-0.245517\pi$
$619$	−1.86669	−	2.15428i	−0.0750287	−	0.0865877i	−0.792023	+	0.610491i	$0.790972\pi$
$620$	1.05992			0.0425673
$621$	−8.10331	+	7.21968i	−0.325175	+	0.289716i
$622$	6.23662			0.250066
$623$	−10.9794	−	12.6709i	−0.439880	−	0.507648i
$624$	15.2033	+	9.77054i	0.608617	+	0.391135i
$625$	−0.142315	+	0.989821i	−0.00569259	+	0.0395929i
$626$	−3.74923	+	8.20968i	−0.149850	+	0.328125i
$627$	9.94531	+	69.1712i	0.397177	+	2.76243i
$628$	27.4724	+	8.06662i	1.09627	+	0.321893i
$629$	45.0738	−	28.9671i	1.79721	−	1.15500i
$630$	−0.481681	−	1.05474i	−0.0191906	−	0.0420217i
$631$	−33.6835	+	9.89038i	−1.34092	+	0.393730i	−0.871998	−	0.489510i	$-0.837176\pi$
$631$	−33.6835	+	9.89038i	−1.34092	+	0.393730i	−0.468922	+	0.883239i	$0.655358\pi$
$632$	0.511637	−	0.590460i	0.0203518	−	0.0234872i
$633$	−0.231454	+	0.267112i	−0.00919947	+	0.0106167i
$634$	9.28710	−	2.72694i	0.368838	−	0.108301i
$635$	−4.03981	−	8.84595i	−0.160315	−	0.351041i
$636$	8.86586	−	5.69774i	0.351554	−	0.225930i
$637$	3.74762	+	1.10040i	0.148486	+	0.0435994i
$638$	3.23214	+	22.4800i	0.127962	+	0.889993i
$639$	−8.46060	+	18.5261i	−0.334696	+	0.732883i
$640$	1.63856	−	11.3965i	0.0647699	−	0.450485i
$641$	22.7568	+	14.6249i	0.898841	+	0.577650i	0.906446	−	0.422321i	$-0.138784\pi$
$641$	22.7568	+	14.6249i	0.898841	+	0.577650i	−0.00760527	+	0.999971i	$0.502421\pi$
$642$	−2.10143	−	2.42518i	−0.0829369	−	0.0957143i
$643$	−40.3242			−1.59023			−0.795116	−	0.606457i	$-0.792590\pi$
$643$	−40.3242			−1.59023			−0.795116	+	0.606457i	$0.792590\pi$
$644$	7.19242	−	3.40537i	0.283421	−	0.134190i
$645$	−1.94314			−0.0765109
$646$	11.1176	+	12.8304i	0.437416	+	0.504805i
$647$	8.41508	+	5.40804i	0.330831	+	0.212612i	0.695502	−	0.718524i	$-0.255182\pi$
$647$	8.41508	+	5.40804i	0.330831	+	0.212612i	−0.364671	+	0.931136i	$0.618819\pi$
$648$	−3.34761	+	23.2831i	−0.131506	+	0.914648i
$649$	24.9670	−	54.6702i	0.980042	−	2.14599i
$650$	0.324438	+	2.25652i	0.0127255	+	0.0885079i
$651$	1.36862	+	0.401863i	0.0536405	+	0.0157503i
$652$	4.09600	−	2.63234i	0.160412	−	0.103090i
$653$	12.2970	+	26.9267i	0.481219	+	1.05372i	0.982127	+	0.188222i	$0.0602724\pi$
$653$	12.2970	+	26.9267i	0.481219	+	1.05372i	−0.500908	+	0.865501i	$0.667000\pi$
$654$	−20.0597	+	5.89007i	−0.784398	+	0.230320i
$655$	7.03357	−	8.11717i	0.274824	−	0.317164i
$656$	14.9765	−	17.2838i	0.584734	−	0.674819i
$657$	3.46614	−	1.01775i	0.135227	−	0.0397062i
$658$	1.37120	+	3.00252i	0.0534551	+	0.117050i
$659$	18.3055	−	11.7642i	0.713081	−	0.458269i	−0.133143	−	0.991097i	$-0.542507\pi$
$659$	18.3055	−	11.7642i	0.713081	−	0.458269i	0.846224	+	0.532828i	$0.178871\pi$
$660$	19.4257	+	5.70389i	0.756143	+	0.222024i
$661$	2.02379	+	14.0758i	0.0787163	+	0.547484i	0.990574	+	0.136978i	$0.0437389\pi$
$661$	2.02379	+	14.0758i	0.0787163	+	0.547484i	−0.911858	+	0.410506i	$0.865352\pi$
$662$	6.97243	−	15.2675i	0.270991	−	0.593388i
$663$	−6.30366	+	43.8429i	−0.244814	+	1.70272i
$664$	29.7549	+	19.1223i	1.15471	+	0.742089i
$665$	−3.75072	−	4.32857i	−0.145447	−	0.167855i
$666$	12.2334			0.474034
$667$	18.0666	−	28.9838i	0.699542	−	1.12226i
$668$	23.7601			0.919307
$669$	−9.23399	−	10.6566i	−0.357007	−	0.412008i
$670$	−4.39409	−	2.82391i	−0.169759	−	0.109097i
$671$	−6.16074	+	42.8489i	−0.237833	+	1.65416i
$672$	5.08452	−	11.1335i	0.196139	−	0.429486i
$673$	−3.10446	−	21.5920i	−0.119668	−	0.832310i	−0.957922	−	0.287030i	$-0.907332\pi$
$673$	−3.10446	−	21.5920i	−0.119668	−	0.832310i	0.838254	−	0.545281i	$-0.183577\pi$
$674$	−3.84898	−	1.13016i	−0.148257	−	0.0435322i
$675$	1.90376	−	1.22347i	0.0732758	−	0.0470915i
$676$	−1.55474	−	3.40441i	−0.0597978	−	0.130939i
$677$	21.7262	−	6.37939i	0.835006	−	0.245180i	0.163840	−	0.986487i	$-0.447612\pi$
$677$	21.7262	−	6.37939i	0.835006	−	0.245180i	0.671166	+	0.741307i	$0.265794\pi$
$678$	−1.33361	+	1.53907i	−0.0512169	+	0.0591075i
$679$	−1.16187	+	1.34087i	−0.0445884	+	0.0514578i
$680$	10.4073	−	3.05587i	0.399103	−	0.117187i
$681$	16.6791	+	36.5221i	0.639143	+	1.39953i
$682$	1.71370	−	1.10133i	0.0656210	−	0.0421721i
$683$	20.5883	+	6.04527i	0.787790	+	0.231316i	0.650793	−	0.759256i	$-0.274437\pi$
$683$	20.5883	+	6.04527i	0.787790	+	0.231316i	0.136997	+	0.990571i	$0.456255\pi$
$684$	−2.68694	−	18.6881i	−0.102738	−	0.714556i
$685$	−5.07087	+	11.1037i	−0.193748	+	0.424249i
$686$	0.0830651	−	0.577731i	0.00317144	−	0.0220579i
$687$	−17.0758	−	10.9740i	−0.651484	−	0.418683i
$688$	−1.18071	−	1.36262i	−0.0450143	−	0.0519493i
$689$	−11.1090			−0.423217
$690$	3.45166	+	5.21137i	0.131402	+	0.198393i
$691$	−1.58832			−0.0604225			−0.0302112	−	0.999544i	$-0.509618\pi$
$691$	−1.58832			−0.0604225			−0.0302112	+	0.999544i	$0.509618\pi$
$692$	10.7053	+	12.3545i	0.406954	+	0.469649i
$693$	9.13137	+	5.86838i	0.346872	+	0.222921i
$694$	−2.05050	+	14.2615i	−0.0778358	+	0.541360i
$695$	2.28779	−	5.00956i	0.0867809	−	0.190024i
$696$	−4.83385	−	33.6202i	−0.183227	−	1.27437i
$697$	53.7819	+	15.7918i	2.03714	+	0.598157i
$698$	2.71636	−	1.74570i	0.102816	−	0.0660757i
$699$	16.9013	+	37.0087i	0.639267	+	1.39980i
$700$	−1.59211	+	0.467487i	−0.0601762	+	0.0176693i
$701$	10.2786	−	11.8621i	0.388216	−	0.448025i	−0.527679	−	0.849444i	$-0.676938\pi$
$701$	10.2786	−	11.8621i	0.388216	−	0.448025i	0.915894	+	0.401419i	$0.131483\pi$
$702$	3.37844	−	3.89893i	0.127511	−	0.147156i
$703$	57.9799	−	17.0244i	2.18675	−	0.642088i
$704$	2.14470	+	4.69624i	0.0808314	+	0.176996i
$705$	10.6238	−	6.82751i	0.400116	−	0.257139i
$706$	−16.7183	−	4.90893i	−0.629201	−	0.184750i
$707$	−0.313093	−	2.17761i	−0.0117751	−	0.0818975i
$708$	−16.9317	+	37.0753i	−0.636333	+	1.39337i
$709$	−5.71286	+	39.7338i	−0.214551	+	1.49224i	0.543151	+	0.839635i	$0.317231\pi$
$709$	−5.71286	+	39.7338i	−0.214551	+	1.49224i	−0.757702	+	0.652600i	$0.773678\pi$
$710$	−5.03391	−	3.23510i	−0.188919	−	0.121411i
$711$	−0.475884	−	0.549199i	−0.0178470	−	0.0205966i
$712$	35.8096			1.34202
$713$	−3.03794	−	0.394091i	−0.113772	−	0.0147588i
$714$	6.61909			0.247713
$715$	−13.9753	−	16.1284i	−0.522648	−	0.603168i
$716$	−26.4167	−	16.9770i	−0.987240	−	0.634460i
$717$	1.67827	−	11.6726i	0.0626761	−	0.435922i
$718$	0.645622	−	1.41372i	0.0240944	−	0.0527594i
$719$	2.03558	+	14.1577i	0.0759142	+	0.527995i	0.991923	+	0.126838i	$0.0404827\pi$
$719$	2.03558	+	14.1577i	0.0759142	+	0.527995i	−0.916009	+	0.401157i	$0.868608\pi$
$720$	−3.94953	−	1.15969i	−0.147190	−	0.0432189i
$721$	−5.72001	+	3.67603i	−0.213024	+	0.136902i
$722$	3.34710	+	7.32913i	0.124566	+	0.272762i
$723$	−14.6820	+	4.31102i	−0.546029	+	0.160329i
$724$	−6.69431	+	7.72564i	−0.248792	+	0.287121i
$725$	−4.66359	+	5.38207i	−0.173201	+	0.199885i
$726$	23.5783	−	6.92321i	0.875072	−	0.256944i
$727$	−3.59031	−	7.86169i	−0.133157	−	0.291574i	0.831295	−	0.555832i	$-0.187600\pi$
$727$	−3.59031	−	7.86169i	−0.133157	−	0.291574i	−0.964452	+	0.264258i	$0.914873\pi$
$728$	−7.01795	+	4.51016i	−0.260102	+	0.167158i
$729$	6.44632	+	1.89281i	0.238753	+	0.0701041i
$730$	0.151048	+	1.05056i	0.00559053	+	0.0388830i
$731$	1.83574	−	4.01971i	0.0678973	−	0.148674i
$732$	4.17799	−	29.0585i	0.154423	−	1.07403i
$733$	18.6646	+	11.9950i	0.689394	+	0.443047i	0.837870	−	0.545869i	$-0.183800\pi$
$733$	18.6646	+	11.9950i	0.689394	+	0.443047i	−0.148476	+	0.988916i	$0.547437\pi$
$734$	−9.67815	−	11.1692i	−0.357227	−	0.412262i
$735$	−2.23307			−0.0823680
$736$	−7.05703	+	25.3213i	−0.260126	+	0.933355i
$737$	48.8960			1.80111
$738$	8.38095	+	9.67214i	0.308507	+	0.356036i
$739$	−30.3661	−	19.5151i	−1.11704	−	0.717876i	−0.154221	−	0.988036i	$-0.549287\pi$
$739$	−30.3661	−	19.5151i	−1.11704	−	0.717876i	−0.962815	+	0.270161i	$0.912923\pi$
$740$	2.49145	−	17.3284i	0.0915874	−	0.637004i
$741$	−20.7522	+	45.4409i	−0.762350	+	1.66931i
$742$	0.236254	+	1.64318i	0.00867315	+	0.0603230i
$743$	6.03669	+	1.77253i	0.221465	+	0.0650279i	0.390582	−	0.920568i	$-0.372274\pi$
$743$	6.03669	+	1.77253i	0.221465	+	0.0650279i	−0.169118	+	0.985596i	$0.554092\pi$
$744$	−2.56294	+	1.64710i	−0.0939619	+	0.0603856i
$745$	−4.54865	−	9.96015i	−0.166650	−	0.364912i
$746$	0.471191	−	0.138354i	0.0172515	−	0.00506551i
$747$	21.5436	−	24.8627i	0.788241	−	0.909678i
$748$	−30.1515	+	34.7967i	−1.10245	+	1.27229i
$749$	−2.36231	+	0.693638i	−0.0863170	+	0.0253450i
$750$	−0.541443	−	1.18559i	−0.0197707	−	0.0432918i
$751$	36.0335	−	23.1573i	1.31488	−	0.845023i	0.320133	−	0.947373i	$-0.396273\pi$
$751$	36.0335	−	23.1573i	1.31488	−	0.845023i	0.994748	+	0.102350i	$0.0326362\pi$
$752$	11.2431	+	3.30128i	0.409995	+	0.120385i
$753$	−8.21742	−	57.1534i	−0.299460	−	2.08279i
$754$	−6.74428	+	14.7679i	−0.245612	+	0.537816i
$755$	0.498332	−	3.46598i	0.0181362	−	0.126140i
$756$	3.15896	+	2.03014i	0.114890	+	0.0738356i
$757$	−31.8932	−	36.8067i	−1.15918	−	1.33776i	−0.931377	−	0.364055i	$-0.881392\pi$
$757$	−31.8932	−	36.8067i	−1.15918	−	1.33776i	−0.227801	−	0.973708i	$-0.573153\pi$
$758$	−14.3064			−0.519633
$759$	−53.5573	−	23.5713i	−1.94401	−	0.855583i
$760$	12.2331			0.443741
$761$	−28.0798	−	32.4059i	−1.01789	−	1.17471i	−0.984521	−	0.175269i	$-0.943921\pi$
$761$	−28.0798	−	32.4059i	−1.01789	−	1.17471i	−0.0333727	−	0.999443i	$-0.510625\pi$
$762$	10.6629	+	6.85265i	0.386277	+	0.248245i
$763$	−2.28277	+	15.8770i	−0.0826420	+	0.574788i
$764$	14.8397	−	32.4945i	0.536883	−	1.17561i
$765$	−1.43578	−	9.98604i	−0.0519106	−	0.361046i
$766$	−3.33800	−	0.980126i	−0.120607	−	0.0354134i
$767$	36.1431	−	23.2277i	1.30505	−	0.838705i
$768$	4.48092	+	9.81185i	0.161691	+	0.354055i
$769$	17.8580	−	5.24357i	0.643974	−	0.189088i	0.0565918	−	0.998397i	$-0.481977\pi$
$769$	17.8580	−	5.24357i	0.643974	−	0.189088i	0.587382	+	0.809310i	$0.300158\pi$
$770$	−2.08842	+	2.41016i	−0.0752614	+	0.0868563i
$771$	−33.5729	+	38.7452i	−1.20910	+	1.39538i
$772$	27.3861	−	8.04129i	0.985648	−	0.289412i
$773$	14.7405	+	32.2773i	0.530181	+	1.16093i	0.965439	+	0.260628i	$0.0839296\pi$
$773$	14.7405	+	32.2773i	0.530181	+	1.16093i	−0.435259	+	0.900305i	$0.643343\pi$
$774$	0.848801	−	0.545491i	0.0305095	−	0.0196073i
$775$	0.612888	+	0.179960i	0.0220156	+	0.00646436i
$776$	−0.539297	−	3.75089i	−0.0193596	−	0.134649i
$777$	9.78709	−	21.4307i	0.351110	−	0.768823i
$778$	2.11401	−	14.7033i	0.0757909	−	0.527137i
$779$	53.1814	+	34.1776i	1.90542	+	1.22454i
$780$	9.47756	+	10.9377i	0.339351	+	0.391632i
$781$	56.0158			2.00440
$782$	−14.0415	+	2.21700i	−0.502123	+	0.0792798i
$783$	16.1160			0.575938
$784$	−1.35689	−	1.56593i	−0.0484602	−	0.0559261i
$785$	14.5161	+	9.32892i	0.518101	+	0.332963i
$786$	−1.99227	+	13.8565i	−0.0710618	+	0.494246i
$787$	6.78102	−	14.8484i	0.241717	−	0.529287i	−0.749425	−	0.662089i	$-0.769670\pi$
$787$	6.78102	−	14.8484i	0.241717	−	0.529287i	0.991143	+	0.132802i	$0.0423973\pi$
$788$	−0.0498955	−	0.347031i	−0.00177745	−	0.0123624i
$789$	11.3387	+	3.32935i	0.403669	+	0.118528i
$790$	0.179613	−	0.115430i	0.00639035	−	0.00410683i
$791$	0.649069	+	1.42126i	0.0230782	+	0.0505343i
$792$	−22.2444	+	6.53155i	−0.790420	+	0.232088i
$793$	−20.2649	+	23.3870i	−0.719629	+	0.830496i
$794$	10.8210	−	12.4881i	0.384024	−	0.443188i
$795$	6.09401	−	1.78936i	0.216132	−	0.0634622i
$796$	−11.9482	−	26.1630i	−0.423494	−	0.927323i
$797$	−17.1958	+	11.0511i	−0.609107	+	0.391450i	−0.808522	−	0.588466i	$-0.799732\pi$
$797$	−17.1958	+	11.0511i	−0.609107	+	0.391450i	0.199415	+	0.979915i	$0.436096\pi$
$798$	7.16273	+	2.10317i	0.253558	+	0.0744513i
$799$	4.08723	+	28.4273i	0.144596	+	1.00569i
$800$	2.27692	−	4.98576i	0.0805013	−	0.176273i
$801$	4.74011	−	32.9682i	0.167483	−	1.16487i
$802$	8.92848	+	5.73798i	0.315276	+	0.202615i
$803$	−6.50645	−	7.50885i	−0.229608	−	0.264981i
$804$	−33.1595			−1.16944
$805$	4.73715	−	0.747945i	0.166963	−	0.0263616i
$806$	1.45620			0.0512925
$807$	43.1259	+	49.7699i	1.51810	+	1.75198i
$808$	3.95294	+	2.54040i	0.139064	+	0.0893710i
$809$	5.76793	−	40.1168i	0.202790	−	1.41043i	−0.593167	−	0.805079i	$-0.702123\pi$
$809$	5.76793	−	40.1168i	0.202790	−	1.41043i	0.795957	−	0.605353i	$-0.206968\pi$
$810$	−2.67033	+	5.84721i	−0.0938259	+	0.205450i
$811$	−0.415536	−	2.89011i	−0.0145914	−	0.101486i	0.981224	−	0.192871i	$-0.0617797\pi$
$811$	−0.415536	−	2.89011i	−0.0145914	−	0.101486i	−0.995816	+	0.0913849i	$0.970871\pi$
$812$	−11.3382	−	3.32920i	−0.397894	−	0.116832i
$813$	39.8122	−	25.5857i	1.39627	−	0.897331i
$814$	−13.9772	−	30.6058i	−0.489901	−	1.07273i
$815$	2.81542	−	0.826681i	0.0986197	−	0.0289574i
$816$	15.3877	−	17.7583i	0.538676	−	0.621665i
$817$	3.26375	−	3.76657i	0.114184	−	0.131775i
$818$	10.8273	−	3.17919i	0.378568	−	0.111158i
$819$	3.22333	+	7.05810i	0.112632	+	0.246630i
$820$	15.4073	−	9.90165i	0.538045	−	0.345781i
$821$	−13.4649	−	3.95366i	−0.469929	−	0.137984i	0.0381898	−	0.999271i	$-0.487841\pi$
$821$	−13.4649	−	3.95366i	−0.469929	−	0.137984i	−0.508119	+	0.861287i	$0.669659\pi$
$822$	−2.26423	−	15.7481i	−0.0789742	−	0.549277i
$823$	4.15919	−	9.10734i	0.144980	−	0.317462i	−0.823186	−	0.567772i	$-0.807805\pi$
$823$	4.15919	−	9.10734i	0.144980	−	0.317462i	0.968166	+	0.250310i	$0.0805326\pi$
$824$	2.06676	−	14.3746i	0.0719990	−	0.500764i
$825$	10.2643	+	6.59646i	0.357357	+	0.229659i
$826$	−4.20438	−	4.85212i	−0.146289	−	0.168827i
$827$	−0.101130			−0.00351665			−0.00175833	−	0.999998i	$-0.500560\pi$
$827$	−0.101130			−0.00351665			−0.00175833	+	0.999998i	$0.500560\pi$
$828$	14.4696	+	6.36828i	0.502854	+	0.221313i
$829$	−10.7231			−0.372429			−0.186215	−	0.982509i	$-0.559622\pi$
$829$	−10.7231			−0.372429			−0.186215	+	0.982509i	$0.559622\pi$
$830$	6.32964	+	7.30479i	0.219705	+	0.253553i
$831$	−31.6952	−	20.3692i	−1.09949	−	0.706601i
$832$	−0.525228	+	3.65304i	−0.0182090	+	0.126646i
$833$	2.10965	−	4.61948i	0.0730949	−	0.160056i
$834$	1.02154	+	7.10496i	0.0353730	+	0.246025i
$835$	13.7391	+	4.03417i	0.475462	+	0.139608i
$836$	−43.6843	+	28.0742i	−1.51085	+	0.970966i
$837$	−0.600492	−	1.31489i	−0.0207560	−	0.0454494i
$838$	−19.1581	+	5.62532i	−0.661805	+	0.194324i
$839$	−9.85720	+	11.3758i	−0.340308	+	0.392737i	−0.899946	−	0.436000i	$-0.856395\pi$
$839$	−9.85720	+	11.3758i	−0.340308	+	0.392737i	0.559638	+	0.828737i	$0.310940\pi$
$840$	3.12335	−	3.60454i	0.107766	−	0.124368i
$841$	−20.8361	+	6.11803i	−0.718486	+	0.210966i
$842$	2.41662	+	5.29166i	0.0832823	+	0.182363i
$843$	−17.5002	+	11.2467i	−0.602739	+	0.387357i
$844$	−0.251992	−	0.0739916i	−0.00867393	−	0.00254690i
$845$	−0.320992	−	2.23255i	−0.0110425	−	0.0768020i
$846$	−2.72403	+	5.96479i	−0.0936540	+	0.205074i
$847$	2.68318	−	18.6619i	0.0921952	−	0.641231i
$848$	4.95771	+	3.18613i	0.170248	+	0.109412i
$849$	8.95107	+	10.3301i	0.307200	+	0.354528i
$850$	2.96412			0.101669
$851$	−13.5839	+	48.7405i	−0.465652	+	1.67080i
$852$	−37.9878			−1.30144
$853$	1.97299	+	2.27695i	0.0675539	+	0.0779614i	0.788521	−	0.615008i	$-0.210847\pi$
$853$	1.97299	+	2.27695i	0.0675539	+	0.0779614i	−0.720967	+	0.692970i	$0.756302\pi$
$854$	3.89026	+	2.50012i	0.133122	+	0.0855523i
$855$	1.61929	−	11.2624i	0.0553786	−	0.385167i
$856$	2.18448	−	4.78334i	0.0746639	−	0.163491i
$857$	0.832521	+	5.79031i	0.0284384	+	0.197793i	0.999088	−	0.0427061i	$-0.0135979\pi$
$857$	0.832521	+	5.79031i	0.0284384	+	0.197793i	−0.970649	+	0.240499i	$0.922689\pi$
$858$	26.6886	+	7.83648i	0.911134	+	0.267533i
$859$	7.03641	−	4.52202i	0.240079	−	0.154289i	−0.415069	−	0.909790i	$-0.636243\pi$
$859$	7.03641	−	4.52202i	0.240079	−	0.154289i	0.655148	+	0.755500i	$0.272606\pi$
$860$	−0.599813	−	1.31341i	−0.0204534	−	0.0447868i
$861$	23.6489	−	6.94394i	0.805952	−	0.236649i
$862$	−4.86076	+	5.60961i	−0.165558	+	0.191064i
$863$	32.2450	−	37.2127i	1.09763	−	1.26674i	0.136502	−	0.990640i	$-0.456414\pi$
$863$	32.2450	−	37.2127i	1.09763	−	1.26674i	0.961130	−	0.276096i	$-0.0890407\pi$
$864$	−11.9013	+	3.49453i	−0.404889	+	0.118886i
$865$	4.09260	+	8.96154i	0.139152	+	0.304701i
$866$	−18.4563	+	11.8611i	−0.627170	+	0.403058i
$867$	18.8341	+	5.53018i	0.639638	+	0.187815i
$868$	0.150842	+	1.04913i	0.00511990	+	0.0356097i
$869$	−0.830281	+	1.81806i	−0.0281654	+	0.0616735i
$870$	1.32097	−	9.18753i	0.0447850	−	0.311486i
$871$	29.4045	+	18.8971i	0.996333	+	0.640305i
$872$	−22.4353	−	25.8917i	−0.759755	−	0.876804i
$873$	−3.52466			−0.119292
$874$	−15.8992	−	2.06249i	−0.537798	−	0.0697648i
$875$	−1.00000			−0.0338062
$876$	4.41243	+	5.09222i	0.149082	+	0.172050i
$877$	−16.1468	−	10.3769i	−0.545238	−	0.350403i	0.238846	−	0.971057i	$-0.423231\pi$
$877$	−16.1468	−	10.3769i	−0.545238	−	0.350403i	−0.784085	+	0.620654i	$0.786867\pi$
$878$	1.76021	−	12.2426i	0.0594043	−	0.413166i
$879$	−14.8396	+	32.4943i	−0.500529	+	1.09600i
$880$	1.61118	+	11.2060i	0.0543129	+	0.377755i
$881$	19.9296	+	5.85187i	0.671447	+	0.197155i	0.599647	−	0.800265i	$-0.295308\pi$
$881$	19.9296	+	5.85187i	0.671447	+	0.197155i	0.0717996	+	0.997419i	$0.477126\pi$
$882$	0.975449	−	0.626883i	0.0328451	−	0.0211082i
$883$	6.99208	+	15.3105i	0.235302	+	0.515240i	0.990040	−	0.140787i	$-0.0449632\pi$
$883$	6.99208	+	15.3105i	0.235302	+	0.515240i	−0.754738	+	0.656027i	$0.772236\pi$
$884$	−31.5802	+	9.27278i	−1.06216	+	0.311877i
$885$	−16.0855	+	18.5637i	−0.540710	+	0.624012i
$886$	11.4135	−	13.1719i	0.383445	−	0.442519i
$887$	23.3165	−	6.84633i	0.782890	−	0.229877i	0.134225	−	0.990951i	$-0.457146\pi$
$887$	23.3165	−	6.84633i	0.782890	−	0.229877i	0.648666	+	0.761074i	$0.275327\pi$
$888$	20.9037	+	45.7727i	0.701483	+	1.53603i
$889$	8.18099	−	5.25760i	0.274382	−	0.176334i
$890$	9.38943	+	2.75699i	0.314735	+	0.0924144i
$891$	−8.56377	−	59.5623i	−0.286897	−	1.99541i
$892$	4.35264	−	9.53095i	0.145737	−	0.319120i
$893$	−4.60965	+	32.0608i	−0.154256	+	1.07287i
$894$	12.0060	+	7.71577i	0.401540	+	0.258054i
$895$	−12.3928	−	14.3020i	−0.414245	−	0.478064i
$896$	11.5137			0.384644
$897$	−23.0979	−	34.8736i	−0.771216	−	1.16440i
$898$	10.9351			0.364910
$899$	2.97893	+	3.43786i	0.0993528	+	0.114659i
$900$	−2.77312	−	1.78217i	−0.0924372	−	0.0594058i
$901$	−2.05559	+	14.2970i	−0.0684818	+	0.476301i
$902$	14.6224	−	32.0185i	0.486872	−	1.06610i
$903$	−0.276537	−	1.92336i	−0.00920258	−	0.0640054i
$904$	−3.20199	−	0.940190i	−0.106497	−	0.0312703i
$905$	−5.18265	+	3.33068i	−0.172277	+	0.110716i
$906$	1.89593	+	4.15150i	0.0629880	+	0.137924i
$907$	−18.0201	+	5.29119i	−0.598349	+	0.175691i	−0.566862	−	0.823813i	$-0.691843\pi$
$907$	−18.0201	+	5.29119i	−0.598349	+	0.175691i	−0.0314875	+	0.999504i	$0.510024\pi$
$908$	−19.5375	+	22.5474i	−0.648374	+	0.748263i
$909$	2.86208	−	3.30301i	0.0949292	−	0.109554i
$910$	−2.18738	+	0.642272i	−0.0725109	+	0.0212911i
$911$	−19.5673	−	42.8464i	−0.648293	−	1.41956i	−0.893040	−	0.449977i	$-0.851432\pi$
$911$	−19.5673	−	42.8464i	−0.648293	−	1.41956i	0.244747	−	0.969587i	$-0.421295\pi$
$912$	22.2941	−	14.3275i	0.738230	−	0.474432i
$913$	−86.8166	−	25.4917i	−2.87321	−	0.843651i
$914$	1.55889	+	10.8423i	0.0515634	+	0.358631i
$915$	7.34966	−	16.0935i	0.242972	−	0.532035i
$916$	2.14652	−	14.9294i	0.0709231	−	0.493281i
$917$	9.03553	+	5.80678i	0.298379	+	0.191757i
$918$	−4.39269	−	5.06944i	−0.144980	−	0.167316i
$919$	44.1692			1.45701			0.728504	−	0.685041i	$-0.240216\pi$
$919$	44.1692			1.45701			0.728504	+	0.685041i	$0.240216\pi$
$920$	−5.41846	+	8.69267i	−0.178641	+	0.286589i
$921$	−8.31837			−0.274100
$922$	8.40269	+	9.69723i	0.276728	+	0.319361i
$923$	33.6861	+	21.6487i	1.10879	+	0.712576i
$924$	−2.88127	+	20.0397i	−0.0947869	+	0.659257i
$925$	4.38280	−	9.59699i	0.144106	−	0.315547i
$926$	2.04268	+	14.2071i	0.0671266	+	0.466876i
$927$	−12.9605	−	3.80554i	−0.425678	−	0.124990i
$928$	32.8370	−	21.1031i	1.07793	−	0.692742i
$929$	8.60731	+	18.8474i	0.282397	+	0.618362i	0.996673	−	0.0815011i	$-0.0259714\pi$
$929$	8.60731	+	18.8474i	0.282397	+	0.618362i	−0.714277	+	0.699864i	$0.753244\pi$
$930$	−0.798825	+	0.234556i	−0.0261945	+	0.00769141i
$931$	3.75072	−	4.32857i	0.122925	−	0.141863i
$932$	−19.7978	+	22.8479i	−0.648499	+	0.748408i
$933$	22.8941	−	6.72232i	0.749520	−	0.220079i
$934$	5.12663	+	11.2258i	0.167749	+	0.367318i
$935$	−23.3429	+	15.0016i	−0.763394	+	0.490604i
$936$	−15.9014	−	4.66906i	−0.519752	−	0.152613i
$937$	−7.31939	−	50.9075i	−0.239114	−	1.66308i	−0.656485	−	0.754339i	$-0.727957\pi$
$937$	−7.31939	−	50.9075i	−0.239114	−	1.66308i	0.417371	−	0.908736i	$-0.362952\pi$
$938$	2.16982	−	4.75125i	0.0708472	−	0.155134i
$939$	−4.91410	+	34.1783i	−0.160366	+	1.11537i
$940$	7.89424	+	5.07332i	0.257482	+	0.165474i
$941$	15.8559	+	18.2986i	0.516886	+	0.596519i	0.952849	−	0.303446i	$-0.0981373\pi$
$941$	15.8559	+	18.2986i	0.516886	+	0.596519i	−0.435962	+	0.899965i	$0.643592\pi$
$942$	−22.4902			−0.732770
$943$	−47.8421	+	22.6516i	−1.55795	+	0.737637i
$944$	−22.7918			−0.741811
$945$	1.48195	+	1.71027i	0.0482080	+	0.0556349i
$946$	−2.33452	−	1.50030i	−0.0759017	−	0.0487791i
$947$	−4.70434	+	32.7194i	−0.152870	+	1.06324i	0.758507	+	0.651665i	$0.225929\pi$
$947$	−4.70434	+	32.7194i	−0.152870	+	1.06324i	−0.911377	+	0.411572i	$0.864980\pi$
$948$	0.563066	−	1.23294i	0.0182875	−	0.0400441i
$949$	−1.01078	−	7.03016i	−0.0328115	−	0.228209i
$950$	3.20757	+	0.941828i	0.104067	+	0.0305570i
$951$	31.1529	−	20.0208i	1.01020	−	0.649217i
$952$	4.50588	+	9.86650i	0.146036	+	0.319775i
$953$	−23.4049	+	6.87229i	−0.758158	+	0.222615i	−0.637892	−	0.770126i	$-0.720193\pi$
$953$	−23.4049	+	6.87229i	−0.758158	+	0.222615i	−0.120267	+	0.992742i	$0.538375\pi$
$954$	−2.15966	+	2.49239i	−0.0699217	+	0.0806940i
$955$	14.0981	−	16.2701i	0.456204	−	0.526487i
$956$	8.40782	−	2.46876i	0.271928	−	0.0798453i
$957$	36.0957	+	79.0386i	1.16681	+	2.55495i
$958$	3.09932	−	1.99181i	0.100134	−	0.0643525i
$959$	−11.7123	−	3.43904i	−0.378210	−	0.111052i
$960$	−0.300287	−	2.08854i	−0.00969172	−	0.0674074i
$961$	−12.7084	+	27.8274i	−0.409947	+	0.897660i
$962$	3.42296	−	23.8072i	0.110361	−	0.767575i
$963$	−4.11464	−	2.64432i	−0.132592	−	0.0852119i
$964$	−7.44599	−	8.59313i	−0.239819	−	0.276766i
$965$	17.2011			0.553723
$966$	−4.66710	+	4.15818i	−0.150162	+	0.133787i
$967$	−28.2051			−0.907014			−0.453507	−	0.891253i	$-0.649827\pi$
$967$	−28.2051			−0.907014			−0.453507	+	0.891253i	$0.649827\pi$
$968$	26.3705	+	30.4332i	0.847580	+	0.978160i
$969$	54.6415	+	35.1160i	1.75534	+	1.12809i
$970$	0.147376	−	1.02502i	0.00473196	−	0.0329115i
$971$	7.68777	−	16.8339i	0.246712	−	0.540224i	−0.745246	−	0.666789i	$-0.767668\pi$
$971$	7.68777	−	16.8339i	0.246712	−	0.540224i	0.991958	+	0.126565i	$0.0403953\pi$
$972$	4.20442	+	29.2424i	0.134857	+	0.937951i
$973$	5.28416	+	1.55157i	0.169402	+	0.0497410i
$974$	−0.142243	+	0.0914139i	−0.00455775	+	0.00292909i
$975$	3.62324	+	7.93380i	0.116037	+	0.254085i
$976$	15.7514	−	4.62503i	0.504190	−	0.148044i
$977$	5.23581	−	6.04244i	0.167508	−	0.193315i	−0.665789	−	0.746140i	$-0.731905\pi$
$977$	5.23581	−	6.04244i	0.167508	−	0.193315i	0.833297	+	0.552825i	$0.186450\pi$
$978$	−2.50450	+	2.89034i	−0.0800850	+	0.0924230i
$979$	−87.8964	+	25.8087i	−2.80918	+	0.824850i
$980$	−0.689309	−	1.50938i	−0.0220192	−	0.0482153i
$981$	−26.8070	+	17.2278i	−0.855883	+	0.550042i
$982$	2.88035	+	0.845748i	0.0919157	+	0.0269889i
$983$	−0.165452	−	1.15074i	−0.00527710	−	0.0367030i	0.987013	−	0.160642i	$-0.0513564\pi$
$983$	−0.165452	−	1.15074i	−0.00527710	−	0.0367030i	−0.992290	+	0.123939i	$0.960447\pi$
$984$	−21.8686	+	47.8855i	−0.697145	+	1.52654i
$985$	0.0300697	−	0.209139i	0.000958100	−	0.00666373i
$986$	17.7580	+	11.4124i	0.565530	+	0.363444i
$987$	8.26994	+	9.54402i	0.263235	+	0.303790i
$988$	−37.1203			−1.18095
$989$	1.23085	+	3.98752i	0.0391387	+	0.126796i
$990$	−6.33545			−0.201354
$991$	−15.9428	−	18.3990i	−0.506440	−	0.584463i	0.443743	−	0.896154i	$-0.353650\pi$
$991$	−15.9428	−	18.3990i	−0.506440	−	0.584463i	−0.950184	+	0.311691i	$0.899105\pi$
$992$	−2.94532	−	1.89284i	−0.0935139	−	0.0600977i
$993$	9.13872	−	63.5612i	0.290009	−	2.01705i
$994$	2.48577	−	5.44308i	0.0788438	−	0.172644i
$995$	−2.46683	−	17.1572i	−0.0782039	−	0.543920i
$996$	58.8758	+	17.2875i	1.86555	+	0.547775i
$997$	−25.5228	+	16.4025i	−0.808315	+	0.519472i	−0.878319	−	0.478074i	$-0.841335\pi$
$997$	−25.5228	+	16.4025i	−0.808315	+	0.519472i	0.0700045	+	0.997547i	$0.477699\pi$
$998$	−0.347095	−	0.760032i	−0.0109871	−	0.0240584i
$999$	−22.9085	+	6.72654i	−0.724793	+	0.212818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.u.d.36.5	✓	130
23.16	even	11	inner	805.2.u.d.246.5	yes	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.u.d.36.5	✓	130	1.1	even	1	trivial
805.2.u.d.246.5	yes	130	23.16	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382224 - 0.441110i) q^{2} +(-1.87858 - 1.20729i) q^{3} +(0.236147 - 1.64244i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.185490 + 1.29011i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-1.79679 + 1.15473i) q^{8} +(0.825261 + 1.80707i) q^{9} +O(q^{10})\)	\(q+(-0.382224 - 0.441110i) q^{2} +(-1.87858 - 1.20729i) q^{3} +(0.236147 - 1.64244i) q^{4} +(0.415415 - 0.909632i) q^{5} +(0.185490 + 1.29011i) q^{6} +(0.959493 + 0.281733i) q^{7} +(-1.79679 + 1.15473i) q^{8} +(0.825261 + 1.80707i) q^{9} +(-0.560029 + 0.164439i) q^{10} +(3.57807 - 4.12931i) q^{11} +(-2.42652 + 2.80035i) q^{12} +(3.74762 - 1.10040i) q^{13} +(-0.242466 - 0.530926i) q^{14} +(-1.87858 + 1.20729i) q^{15} +(-1.98809 - 0.583756i) q^{16} +(-0.722733 - 5.02672i) q^{17} +(0.481681 - 1.05474i) q^{18} +(0.815110 - 5.66922i) q^{19} +(-1.39591 - 0.897100i) q^{20} +(-1.46235 - 1.68764i) q^{21} -3.18910 q^{22} +(3.66743 + 3.09030i) q^{23} +4.76949 q^{24} +(-0.654861 - 0.755750i) q^{25} +(-1.91782 - 1.23251i) q^{26} +(-0.322059 + 2.23997i) q^{27} +(0.689309 - 1.50938i) q^{28} +(-1.01349 - 7.04901i) q^{29} +(1.25058 + 0.367204i) q^{30} +(-0.537361 + 0.345341i) q^{31} +(2.27692 + 4.98576i) q^{32} +(-11.7070 + 3.43747i) q^{33} +(-1.94109 + 2.24013i) q^{34} +(0.654861 - 0.755750i) q^{35} +(3.16288 - 0.928706i) q^{36} +(4.38280 + 9.59699i) q^{37} +(-2.81230 + 1.80736i) q^{38} +(-8.36868 - 2.45727i) q^{39} +(0.303963 + 2.11411i) q^{40} +(-4.58510 + 10.0400i) q^{41} +(-0.185490 + 1.29011i) q^{42} +(0.732029 + 0.470447i) q^{43} +(-5.93719 - 6.85188i) q^{44} +1.98659 q^{45} +(-0.0386191 - 2.79892i) q^{46} -5.65525 q^{47} +(3.03002 + 3.49683i) q^{48} +(0.841254 + 0.540641i) q^{49} +(-0.0830651 + 0.577731i) q^{50} +(-4.71099 + 10.3156i) q^{51} +(-0.922350 - 6.41508i) q^{52} +(-2.72899 - 0.801303i) q^{53} +(1.11117 - 0.714107i) q^{54} +(-2.26977 - 4.97011i) q^{55} +(-2.04933 + 0.601737i) q^{56} +(-8.37562 + 9.66598i) q^{57} +(-2.72200 + 3.14136i) q^{58} +(10.5542 - 3.09900i) q^{59} +(1.53928 + 3.37054i) q^{60} +(-6.66515 + 4.28343i) q^{61} +(0.357726 + 0.105038i) q^{62} +(0.282722 + 1.96637i) q^{63} +(-0.392524 + 0.859508i) q^{64} +(0.555858 - 3.86607i) q^{65} +(5.99098 + 3.85017i) q^{66} +(5.86034 + 6.76319i) q^{67} -8.42674 q^{68} +(-3.15867 - 10.2330i) q^{69} -0.583672 q^{70} +(6.71366 + 7.74797i) q^{71} +(-3.56949 - 2.29397i) q^{72} +(0.258789 - 1.79992i) q^{73} +(2.55812 - 5.60149i) q^{74} +(0.317799 + 2.21034i) q^{75} +(-9.11885 - 2.67754i) q^{76} +(4.59650 - 2.95399i) q^{77} +(2.11478 + 4.63073i) q^{78} +(-0.350982 + 0.103058i) q^{79} +(-1.35689 + 1.56593i) q^{80} +(7.21213 - 8.32324i) q^{81} +(6.18126 - 1.81498i) q^{82} +(-6.87929 - 15.0635i) q^{83} +(-3.11717 + 2.00329i) q^{84} +(-4.87270 - 1.43075i) q^{85} +(-0.0722804 - 0.502721i) q^{86} +(-6.60626 + 14.4657i) q^{87} +(-1.66081 + 11.5512i) q^{88} +(-14.1044 - 9.06437i) q^{89} +(-0.759323 - 0.876306i) q^{90} +3.90583 q^{91} +(5.94168 - 5.29376i) q^{92} +1.42640 q^{93} +(2.16157 + 2.49458i) q^{94} +(-4.81829 - 3.09653i) q^{95} +(1.74188 - 12.1150i) q^{96} +(-0.737038 + 1.61389i) q^{97} +(-0.0830651 - 0.577731i) q^{98} +(10.4148 + 3.05806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9}+O(q^{10}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9	\( 130 q + 2 q^{2} + 2 q^{3} - 16 q^{4} - 13 q^{5} + 5 q^{6} + 13 q^{7} - 7 q^{8} - 39 q^{9} + 2 q^{10} + 2 q^{11} - 5 q^{12} + 13 q^{13} - 2 q^{14} + 2 q^{15} - 6 q^{16} - 51 q^{17} + q^{18} - 9 q^{19} - 16 q^{20} - 2 q^{21} + 34 q^{22} - 10 q^{23} - 76 q^{24} - 13 q^{25} - 31 q^{26} + 14 q^{27} + 27 q^{28} + 3 q^{29} + 5 q^{30} + 6 q^{31} + 22 q^{32} - 58 q^{33} + q^{34} + 13 q^{35} + 193 q^{36} - 36 q^{37} + 4 q^{38} - 2 q^{39} - 29 q^{40} - 34 q^{41} - 5 q^{42} - 22 q^{43} + 8 q^{44} + 170 q^{45} - 198 q^{46} - 14 q^{47} - 120 q^{48} - 13 q^{49} + 2 q^{50} - 6 q^{51} + 33 q^{52} - 18 q^{53} + 188 q^{54} - 31 q^{55} - 15 q^{56} - 9 q^{57} + 114 q^{58} + 46 q^{59} - 16 q^{60} - 56 q^{61} - 146 q^{62} + 17 q^{63} - 109 q^{64} + 2 q^{65} - 14 q^{66} - 10 q^{67} + 86 q^{68} - 6 q^{69} - 2 q^{70} - 25 q^{72} + 64 q^{73} + 79 q^{74} + 2 q^{75} + 32 q^{76} - 13 q^{77} - 64 q^{78} - 118 q^{79} - 17 q^{80} + 23 q^{81} + 129 q^{82} - 117 q^{83} - 72 q^{84} - 7 q^{85} + 74 q^{86} - 51 q^{87} - 40 q^{88} - 35 q^{89} + 100 q^{90} + 42 q^{91} + 76 q^{92} - 90 q^{93} - 7 q^{94} + 2 q^{95} + 393 q^{96} - 4 q^{97} + 2 q^{98} - 40 q^{99}+O(q^{100}) \) 130 * q + 2 * q^2 + 2 * q^3 - 16 * q^4 - 13 * q^5 + 5 * q^6 + 13 * q^7 - 7 * q^8 - 39 * q^9 + 2 * q^10 + 2 * q^11 - 5 * q^12 + 13 * q^13 - 2 * q^14 + 2 * q^15 - 6 * q^16 - 51 * q^17 + q^18 - 9 * q^19 - 16 * q^20 - 2 * q^21 + 34 * q^22 - 10 * q^23 - 76 * q^24 - 13 * q^25 - 31 * q^26 + 14 * q^27 + 27 * q^28 + 3 * q^29 + 5 * q^30 + 6 * q^31 + 22 * q^32 - 58 * q^33 + q^34 + 13 * q^35 + 193 * q^36 - 36 * q^37 + 4 * q^38 - 2 * q^39 - 29 * q^40 - 34 * q^41 - 5 * q^42 - 22 * q^43 + 8 * q^44 + 170 * q^45 - 198 * q^46 - 14 * q^47 - 120 * q^48 - 13 * q^49 + 2 * q^50 - 6 * q^51 + 33 * q^52 - 18 * q^53 + 188 * q^54 - 31 * q^55 - 15 * q^56 - 9 * q^57 + 114 * q^58 + 46 * q^59 - 16 * q^60 - 56 * q^61 - 146 * q^62 + 17 * q^63 - 109 * q^64 + 2 * q^65 - 14 * q^66 - 10 * q^67 + 86 * q^68 - 6 * q^69 - 2 * q^70 - 25 * q^72 + 64 * q^73 + 79 * q^74 + 2 * q^75 + 32 * q^76 - 13 * q^77 - 64 * q^78 - 118 * q^79 - 17 * q^80 + 23 * q^81 + 129 * q^82 - 117 * q^83 - 72 * q^84 - 7 * q^85 + 74 * q^86 - 51 * q^87 - 40 * q^88 - 35 * q^89 + 100 * q^90 + 42 * q^91 + 76 * q^92 - 90 * q^93 - 7 * q^94 + 2 * q^95 + 393 * q^96 - 4 * q^97 + 2 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more