LMFDB - Embedded newform 483.2.q.d.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Character	$\chi$	$=$	483.85
Dual form			483.2.q.d.358.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76537 + 2.03734i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.749611 - 5.21366i) q^{4} +(-1.11741 - 2.44678i) q^{5} +(0.383651 - 2.66835i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(7.40965 + 4.76189i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-1.76537 + 2.03734i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.749611 - 5.21366i) q^{4} +(-1.11741 - 2.44678i) q^{5} +(0.383651 - 2.66835i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(7.40965 + 4.76189i) q^{8} +(0.415415 - 0.909632i) q^{9} +(6.95754 + 2.04292i) q^{10} +(3.39796 + 3.92146i) q^{11} +(3.44933 + 3.98074i) q^{12} +(-0.660974 - 0.194079i) q^{13} +(1.11987 - 2.45217i) q^{14} +(2.26285 + 1.45424i) q^{15} +(-12.6745 + 3.72157i) q^{16} +(-0.579656 + 4.03160i) q^{17} +(1.11987 + 2.45217i) q^{18} +(-1.14124 - 7.93751i) q^{19} +(-11.9190 + 7.65990i) q^{20} +(0.654861 - 0.755750i) q^{21} -13.9880 q^{22} +(-4.60886 - 1.32604i) q^{23} -8.80787 q^{24} +(-1.46382 + 1.68933i) q^{25} +(1.56227 - 1.00401i) q^{26} +(0.142315 + 0.989821i) q^{27} +(2.18810 + 4.79128i) q^{28} +(-0.444614 + 3.09236i) q^{29} +(-6.95754 + 2.04292i) q^{30} +(-0.458284 - 0.294521i) q^{31} +(7.47520 - 16.3684i) q^{32} +(-4.97865 - 1.46186i) q^{33} +(-7.19043 - 8.29820i) q^{34} +(1.76148 + 2.03286i) q^{35} +(-5.05391 - 1.48396i) q^{36} +(-4.86957 + 10.6629i) q^{37} +(18.1861 + 11.6875i) q^{38} +(0.660974 - 0.194079i) q^{39} +(3.37170 - 23.4507i) q^{40} +(3.46249 + 7.58180i) q^{41} +(0.383651 + 2.66835i) q^{42} +(-5.71222 + 3.67102i) q^{43} +(17.8980 - 20.6554i) q^{44} -2.68985 q^{45} +(10.8379 - 7.04888i) q^{46} -3.31300 q^{47} +(8.65045 - 9.98315i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.857578 - 5.96458i) q^{50} +(-1.69201 - 3.70498i) q^{51} +(-0.516391 + 3.59158i) q^{52} +(-6.73788 + 1.97842i) q^{53} +(-2.26784 - 1.45745i) q^{54} +(5.79803 - 12.6959i) q^{55} +(-8.45109 - 2.48146i) q^{56} +(5.25142 + 6.06046i) q^{57} +(-5.51528 - 6.36497i) q^{58} +(-10.2607 - 3.01282i) q^{59} +(5.88568 - 12.8878i) q^{60} +(3.52479 + 2.26525i) q^{61} +(1.40908 - 0.413743i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(9.17662 + 20.0940i) q^{64} +(0.263707 + 1.83412i) q^{65} +(11.7674 - 7.56248i) q^{66} +(0.0851697 - 0.0982911i) q^{67} +21.4539 q^{68} +(4.59413 - 1.37621i) q^{69} -7.25127 q^{70} +(-4.83469 + 5.57953i) q^{71} +(7.40965 - 4.76189i) q^{72} +(0.841390 + 5.85199i) q^{73} +(-13.1273 - 28.7448i) q^{74} +(0.318118 - 2.21256i) q^{75} +(-40.5280 + 11.9001i) q^{76} +(-4.36512 - 2.80530i) q^{77} +(-0.771455 + 1.68925i) q^{78} +(7.69147 + 2.25842i) q^{79} +(23.2684 + 26.8532i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-21.5593 - 6.33037i) q^{82} +(0.0788784 - 0.172720i) q^{83} +(-4.43111 - 2.84770i) q^{84} +(10.5121 - 3.08664i) q^{85} +(2.60504 - 18.1184i) q^{86} +(-1.29782 - 2.84183i) q^{87} +(6.50415 + 45.2374i) q^{88} +(-8.58260 + 5.51570i) q^{89} +(4.74857 - 5.48015i) q^{90} +0.688878 q^{91} +(-3.45865 + 25.0230i) q^{92} +0.544763 q^{93} +(5.84865 - 6.74971i) q^{94} +(-18.1461 + 11.6618i) q^{95} +(2.56089 + 17.8114i) q^{96} +(2.84490 + 6.22947i) q^{97} +(-0.383651 + 2.66835i) q^{98} +(4.97865 - 1.46186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−1.76537	+	2.03734i	−1.24830	+	1.44062i	−0.395431	+	0.918496i	$0.629405\pi$
$2$	−1.76537	+	2.03734i	−1.24830	+	1.44062i	−0.852871	+	0.522121i	$0.825141\pi$
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−0.749611	−	5.21366i	−0.374805	−	2.60683i
$5$	−1.11741	−	2.44678i	−0.499719	−	1.09423i	−0.976561	−	0.215243i	$-0.930946\pi$
$5$	−1.11741	−	2.44678i	−0.499719	−	1.09423i	0.476842	−	0.878989i	$-0.341781\pi$
$6$	0.383651	−	2.66835i	0.156625	−	1.08935i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$7$	−0.959493	+	0.281733i	−0.362654	+	0.106485i
$8$	7.40965	+	4.76189i	2.61971	+	1.68358i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	6.95754	+	2.04292i	2.20017	+	0.646028i
$11$	3.39796	+	3.92146i	1.02452	+	1.18236i	0.983071	+	0.183224i	$0.0586533\pi$
$11$	3.39796	+	3.92146i	1.02452	+	1.18236i	0.0414533	+	0.999140i	$0.486801\pi$
$12$	3.44933	+	3.98074i	0.995735	+	1.14914i
$13$	−0.660974	−	0.194079i	−0.183321	−	0.0538280i	0.188783	−	0.982019i	$-0.439546\pi$
$13$	−0.660974	−	0.194079i	−0.183321	−	0.0538280i	−0.372105	+	0.928191i	$0.621364\pi$
$14$	1.11987	−	2.45217i	0.299298	−	0.655371i
$15$	2.26285	+	1.45424i	0.584265	+	0.375484i
$16$	−12.6745	+	3.72157i	−3.16863	+	0.930393i
$17$	−0.579656	+	4.03160i	−0.140587	+	0.977806i	0.790358	+	0.612646i	$0.209895\pi$
$17$	−0.579656	+	4.03160i	−0.140587	+	0.977806i	−0.930945	+	0.365160i	$0.881014\pi$
$18$	1.11987	+	2.45217i	0.263956	+	0.577983i
$19$	−1.14124	−	7.93751i	−0.261819	−	1.82099i	−0.519168	−	0.854672i	$-0.673758\pi$
$19$	−1.14124	−	7.93751i	−0.261819	−	1.82099i	0.257349	−	0.966319i	$-0.417151\pi$
$20$	−11.9190	+	7.65990i	−2.66518	+	1.71281i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	−13.9880			−2.98225
$23$	−4.60886	−	1.32604i	−0.961015	−	0.276498i
$23$	−4.60886	−	1.32604i	−0.961015	−	0.276498i
$24$	−8.80787			−1.79790
$25$	−1.46382	+	1.68933i	−0.292763	+	0.337867i
$26$	1.56227	−	1.00401i	0.306386	−	0.196902i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	2.18810	+	4.79128i	0.413513	+	0.905466i
$29$	−0.444614	+	3.09236i	−0.0825627	+	0.574236i	0.905983	+	0.423314i	$0.139133\pi$
$29$	−0.444614	+	3.09236i	−0.0825627	+	0.574236i	−0.988546	+	0.150922i	$0.951776\pi$
$30$	−6.95754	+	2.04292i	−1.27027	+	0.372984i
$31$	−0.458284	−	0.294521i	−0.0823102	−	0.0528975i	0.498838	−	0.866695i	$-0.333760\pi$
$31$	−0.458284	−	0.294521i	−0.0823102	−	0.0528975i	−0.581149	+	0.813797i	$0.697396\pi$
$32$	7.47520	−	16.3684i	1.32144	−	2.89355i
$33$	−4.97865	−	1.46186i	−0.866672	−	0.254478i
$34$	−7.19043	−	8.29820i	−1.23315	−	1.42313i
$35$	1.76148	+	2.03286i	0.297744	+	0.343615i
$36$	−5.05391	−	1.48396i	−0.842318	−	0.247327i
$37$	−4.86957	+	10.6629i	−0.800552	+	1.75297i	−0.156948	+	0.987607i	$0.550165\pi$
$37$	−4.86957	+	10.6629i	−0.800552	+	1.75297i	−0.643604	+	0.765358i	$0.722562\pi$
$38$	18.1861	+	11.6875i	2.95018	+	1.89597i
$39$	0.660974	−	0.194079i	0.105841	−	0.0310776i
$40$	3.37170	−	23.4507i	0.533113	−	3.70788i
$41$	3.46249	+	7.58180i	0.540751	+	1.18408i	0.960969	+	0.276656i	$0.0892261\pi$
$41$	3.46249	+	7.58180i	0.540751	+	1.18408i	−0.420219	+	0.907423i	$0.638047\pi$
$42$	0.383651	+	2.66835i	0.0591986	+	0.411735i
$43$	−5.71222	+	3.67102i	−0.871105	+	0.559825i	−0.898090	−	0.439811i	$-0.855046\pi$
$43$	−5.71222	+	3.67102i	−0.871105	+	0.559825i	0.0269856	+	0.999636i	$0.491409\pi$
$44$	17.8980	−	20.6554i	2.69822	−	3.11392i
$45$	−2.68985			−0.400980
$46$	10.8379	−	7.04888i	1.59796	−	1.03930i
$47$	−3.31300			−0.483251			−0.241625	−	0.970370i	$-0.577680\pi$
$47$	−3.31300			−0.483251			−0.241625	+	0.970370i	$0.577680\pi$
$48$	8.65045	−	9.98315i	1.24858	−	1.44094i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.857578	−	5.96458i	−0.121280	−	0.843520i
$51$	−1.69201	−	3.70498i	−0.236929	−	0.518801i
$52$	−0.516391	+	3.59158i	−0.0716105	+	0.498062i
$53$	−6.73788	+	1.97842i	−0.925519	+	0.271757i	−0.709559	−	0.704646i	$-0.751106\pi$
$53$	−6.73788	+	1.97842i	−0.925519	+	0.271757i	−0.215959	+	0.976402i	$0.569288\pi$
$54$	−2.26784	−	1.45745i	−0.308614	−	0.198334i
$55$	5.79803	−	12.6959i	0.781806	−	1.71192i
$56$	−8.45109	−	2.48146i	−1.12932	−	0.331599i
$57$	5.25142	+	6.06046i	0.695567	+	0.802728i
$58$	−5.51528	−	6.36497i	−0.724192	−	0.835762i
$59$	−10.2607	−	3.01282i	−1.33583	−	0.392235i	−0.465650	−	0.884969i	$-0.654180\pi$
$59$	−10.2607	−	3.01282i	−1.33583	−	0.392235i	−0.870180	+	0.492733i	$0.835998\pi$
$60$	5.88568	−	12.8878i	0.759837	−	1.66381i
$61$	3.52479	+	2.26525i	0.451303	+	0.290035i	0.746480	−	0.665408i	$-0.231742\pi$
$61$	3.52479	+	2.26525i	0.451303	+	0.290035i	−0.295177	+	0.955443i	$0.595379\pi$
$62$	1.40908	−	0.413743i	0.178953	−	0.0525454i
$63$	−0.142315	+	0.989821i	−0.0179300	+	0.124706i
$64$	9.17662	+	20.0940i	1.14708	+	2.51175i
$65$	0.263707	+	1.83412i	0.0327088	+	0.227495i
$66$	11.7674	−	7.56248i	1.44847	−	0.930877i
$67$	0.0851697	−	0.0982911i	0.0104051	−	0.0120082i	−0.750523	−	0.660844i	$-0.770198\pi$
$67$	0.0851697	−	0.0982911i	0.0104051	−	0.0120082i	0.760928	+	0.648836i	$0.224744\pi$
$68$	21.4539			2.60166
$69$	4.59413	−	1.37621i	0.553069	−	0.165676i
$70$	−7.25127			−0.866693
$71$	−4.83469	+	5.57953i	−0.573772	+	0.662168i	−0.966254	−	0.257591i	$-0.917071\pi$
$71$	−4.83469	+	5.57953i	−0.573772	+	0.662168i	0.392482	+	0.919760i	$0.371617\pi$
$72$	7.40965	−	4.76189i	0.873235	−	0.561194i
$73$	0.841390	+	5.85199i	0.0984772	+	0.684924i	0.977929	+	0.208937i	$0.0670002\pi$
$73$	0.841390	+	5.85199i	0.0984772	+	0.684924i	−0.879452	+	0.475988i	$0.842091\pi$
$74$	−13.1273	−	28.7448i	−1.52602	−	3.34152i
$75$	0.318118	−	2.21256i	0.0367331	−	0.255484i
$76$	−40.5280	+	11.9001i	−4.64888	+	1.36503i
$77$	−4.36512	−	2.80530i	−0.497452	−	0.319693i
$78$	−0.771455	+	1.68925i	−0.0873500	+	0.191270i
$79$	7.69147	+	2.25842i	0.865358	+	0.254092i	0.684140	−	0.729351i	$-0.260178\pi$
$79$	7.69147	+	2.25842i	0.865358	+	0.254092i	0.181218	+	0.983443i	$0.441996\pi$
$80$	23.2684	+	26.8532i	2.60149	+	3.00228i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−21.5593	−	6.33037i	−2.38082	−	0.699073i
$83$	0.0788784	−	0.172720i	0.00865803	−	0.0189584i	−0.905254	−	0.424872i	$-0.860319\pi$
$83$	0.0788784	−	0.172720i	0.00865803	−	0.0189584i	0.913912	+	0.405913i	$0.133046\pi$
$84$	−4.43111	−	2.84770i	−0.483474	−	0.310710i
$85$	10.5121	−	3.08664i	1.14020	−	0.334793i
$86$	2.60504	−	18.1184i	0.280908	−	1.95376i
$87$	−1.29782	−	2.84183i	−0.139141	−	0.304676i
$88$	6.50415	+	45.2374i	0.693345	+	4.82232i
$89$	−8.58260	+	5.51570i	−0.909754	+	0.584663i	−0.909668	−	0.415337i	$-0.863664\pi$
$89$	−8.58260	+	5.51570i	−0.909754	+	0.584663i	−8.61435e−5		1.00000i	$0.500027\pi$
$90$	4.74857	−	5.48015i	0.500544	−	0.577658i
$91$	0.688878			0.0722141
$92$	−3.45865	+	25.0230i	−0.360589	+	2.60883i
$93$	0.544763			0.0564893
$94$	5.84865	−	6.74971i	0.603243	−	0.696179i
$95$	−18.1461	+	11.6618i	−1.86175	+	1.19647i
$96$	2.56089	+	17.8114i	0.261370	+	1.81787i
$97$	2.84490	+	6.22947i	0.288856	+	0.632507i	0.997314	−	0.0732463i	$-0.0233359\pi$
$97$	2.84490	+	6.22947i	0.288856	+	0.632507i	−0.708458	+	0.705753i	$0.750609\pi$
$98$	−0.383651	+	2.66835i	−0.0387546	+	0.269544i
$99$	4.97865	−	1.46186i	0.500373	−	0.146923i
$100$	9.90490	+	6.36549i	0.990490	+	0.636549i
$101$	2.14507	−	4.69704i	0.213442	−	0.467373i	−0.772381	−	0.635159i	$-0.780934\pi$
$101$	2.14507	−	4.69704i	0.213442	−	0.467373i	0.985823	+	0.167786i	$0.0536618\pi$
$102$	10.5353	+	3.09345i	1.04315	+	0.306297i
$103$	−2.54326	−	2.93508i	−0.250595	−	0.289202i	0.616490	−	0.787363i	$-0.288554\pi$
$103$	−2.54326	−	2.93508i	−0.250595	−	0.289202i	−0.867084	+	0.498161i	$0.834009\pi$
$104$	−3.97340	−	4.58555i	−0.389624	−	0.449650i
$105$	−2.58090	−	0.757819i	−0.251870	−	0.0739556i
$106$	7.86410	−	17.2200i	0.763829	−	1.67255i
$107$	6.36391	+	4.08984i	0.615222	+	0.395379i	0.810812	−	0.585306i	$-0.199026\pi$
$107$	6.36391	+	4.08984i	0.615222	+	0.395379i	−0.195590	+	0.980686i	$0.562662\pi$
$108$	5.05391	−	1.48396i	0.486313	−	0.142794i
$109$	−1.82658	+	12.7042i	−0.174955	+	1.21684i	0.693274	+	0.720674i	$0.256168\pi$
$109$	−1.82658	+	12.7042i	−0.174955	+	1.21684i	−0.868229	+	0.496164i	$0.834741\pi$
$110$	15.6303	+	34.2255i	1.49029	+	3.26327i
$111$	−1.66824	−	11.6029i	−0.158342	−	1.10130i
$112$	11.1126	−	7.14165i	1.05004	−	0.674822i
$113$	5.73142	−	6.61441i	0.539167	−	0.622231i	−0.419158	−	0.907913i	$-0.637675\pi$
$113$	5.73142	−	6.61441i	0.539167	−	0.622231i	0.958325	+	0.285682i	$0.0922201\pi$
$114$	−21.6179			−2.02470
$115$	1.90545	+	12.7586i	0.177684	+	1.18974i
$116$	16.4558			1.52788
$117$	−0.451119	+	0.520620i	−0.0417060	+	0.0481313i
$118$	24.2520	−	15.5858i	2.23258	−	1.43479i
$119$	−0.579656	−	4.03160i	−0.0531370	−	0.369576i
$120$	9.84196	+	21.5509i	0.898444	+	1.96732i
$121$	−2.26622	+	15.7619i	−0.206020	+	1.43290i
$122$	−10.8376	+	3.18221i	−0.981192	+	0.288104i
$123$	−7.01187	−	4.50625i	−0.632239	−	0.406315i
$124$	−1.19200	+	2.61011i	−0.107045	+	0.234395i
$125$	−7.13538	−	2.09514i	−0.638207	−	0.187395i
$126$	−1.76537	−	2.03734i	−0.157271	−	0.181501i
$127$	−4.12905	−	4.76517i	−0.366394	−	0.422841i	0.542378	−	0.840135i	$-0.317524\pi$
$127$	−4.12905	−	4.76517i	−0.366394	−	0.422841i	−0.908772	+	0.417294i	$0.862979\pi$
$128$	−22.6071	−	6.63805i	−1.99821	−	0.586726i
$129$	2.82072	−	6.17651i	0.248351	−	0.543812i
$130$	−4.20227	−	2.70063i	−0.368563	−	0.236861i
$131$	−18.3120	+	5.37688i	−1.59992	+	0.469780i	−0.955525	−	0.294910i	$-0.904710\pi$
$131$	−18.3120	+	5.37688i	−1.59992	+	0.469780i	−0.644399	+	0.764690i	$0.722892\pi$
$132$	−3.88961	+	27.0528i	−0.338547	+	2.35464i
$133$	3.33127	+	7.29446i	0.288858	+	0.632510i
$134$	0.0498967	+	0.347039i	0.00431042	+	0.0299796i
$135$	2.26285	−	1.45424i	0.194755	−	0.125161i
$136$	−23.4931	+	27.1125i	−2.01451	+	2.32487i
$137$	17.6528			1.50818			0.754088	−	0.656773i	$-0.228079\pi$
$137$	17.6528			1.50818			0.754088	+	0.656773i	$0.228079\pi$
$138$	−5.30652	+	11.7893i	−0.451721	+	1.00357i
$139$	15.4316			1.30889			0.654446	−	0.756109i	$-0.272902\pi$
$139$	15.4316			1.30889			0.654446	+	0.756109i	$0.272902\pi$
$140$	9.27819	−	10.7076i	0.784150	−	0.904957i
$141$	2.78707	−	1.79114i	0.234714	−	0.150841i
$142$	−2.83241	−	19.6998i	−0.237690	−	1.65317i
$143$	−1.48489	−	3.25146i	−0.124173	−	0.271900i
$144$	−1.87992	+	13.0751i	−0.156660	+	1.08960i
$145$	8.06312	−	2.36755i	0.669606	−	0.196614i
$146$	−13.4079	−	8.61671i	−1.10964	−	0.713124i
$147$	−0.415415	+	0.909632i	−0.0342629	+	0.0750252i
$148$	59.2428	+	17.3953i	4.86973	+	1.42988i
$149$	−10.4761	−	12.0901i	−0.858237	−	0.990458i	−1.00000		0.000557360i	$-0.999823\pi$
$149$	−10.4761	−	12.0901i	−0.858237	−	0.990458i	0.141763	−	0.989901i	$-0.454723\pi$
$150$	3.94614	+	4.55409i	0.322201	+	0.371840i
$151$	−0.168263	−	0.0494064i	−0.0136930	−	0.00402064i	0.274879	−	0.961479i	$-0.411362\pi$
$151$	−0.168263	−	0.0494064i	−0.0136930	−	0.00402064i	−0.288572	+	0.957458i	$0.593180\pi$
$152$	29.3414	−	64.2487i	2.37990	−	5.21126i
$153$	3.42647	+	2.20206i	0.277014	+	0.178026i
$154$	13.4214	−	3.94087i	1.08153	−	0.317565i
$155$	−0.208539	+	1.45042i	−0.0167502	+	0.116500i
$156$	−1.50734	−	3.30061i	−0.120684	−	0.264260i
$157$	−1.15254	−	8.01606i	−0.0919823	−	0.639751i	−0.982701	−	0.185197i	$-0.940708\pi$
$157$	−1.15254	−	8.01606i	−0.0919823	−	0.639751i	0.890719	−	0.454554i	$-0.150201\pi$
$158$	−18.1794	+	11.6832i	−1.44628	+	0.929466i
$159$	4.59865	−	5.30712i	0.364697	−	0.420882i
$160$	−48.4026			−3.82656
$161$	4.79576	−	0.0261438i	0.377959	−	0.00206042i
$162$	2.69579			0.211801
$163$	−4.18765	+	4.83281i	−0.328002	+	0.378535i	−0.895667	−	0.444725i	$-0.853301\pi$
$163$	−4.18765	+	4.83281i	−0.328002	+	0.378535i	0.567665	+	0.823260i	$0.307847\pi$
$164$	36.9334	−	23.7357i	2.88401	−	1.85344i
$165$	1.98632	+	13.8151i	0.154635	+	1.07551i
$166$	0.212639	+	0.465615i	0.0165040	+	0.0361388i
$167$	−0.668527	+	4.64971i	−0.0517322	+	0.359805i	0.947469	+	0.319847i	$0.103632\pi$
$167$	−0.668527	+	4.64971i	−0.0517322	+	0.359805i	−0.999201	+	0.0399582i	$0.987278\pi$
$168$	8.45109	−	2.48146i	0.652015	−	0.191449i
$169$	−10.5371	−	6.77177i	−0.810544	−	0.520905i
$170$	−12.2692	+	26.8658i	−0.941006	+	2.06051i
$171$	−7.69431	−	2.25925i	−0.588398	−	0.172769i
$172$	23.4214	+	27.0297i	1.78586	+	2.06100i
$173$	−2.44350	−	2.81995i	−0.185776	−	0.214397i	0.655220	−	0.755438i	$-0.272576\pi$
$173$	−2.44350	−	2.81995i	−0.185776	−	0.214397i	−0.840996	+	0.541041i	$0.818030\pi$
$174$	8.08091	+	2.37277i	0.612612	+	0.179879i
$175$	0.928581	−	2.03331i	0.0701941	−	0.153704i
$176$	−57.6615	−	37.0568i	−4.34640	−	2.79326i
$177$	10.2607	−	3.01282i	0.771242	−	0.226457i
$178$	3.91406	−	27.2229i	0.293371	−	2.04044i
$179$	4.88128	+	10.6885i	0.364844	+	0.798896i	0.999656	+	0.0262298i	$0.00835017\pi$
$179$	4.88128	+	10.6885i	0.364844	+	0.798896i	−0.634812	+	0.772666i	$0.718923\pi$
$180$	2.01634	+	14.0240i	0.150289	+	1.04529i
$181$	−0.495780	+	0.318618i	−0.0368510	+	0.0236827i	−0.558937	−	0.829210i	$-0.688791\pi$
$181$	−0.495780	+	0.318618i	−0.0368510	+	0.0236827i	0.522086	+	0.852893i	$0.325154\pi$
$182$	−1.21612	+	1.40348i	−0.0901450	+	0.104033i
$183$	−4.18993			−0.309728
$184$	−27.8356	−	31.7724i	−2.05207	−	2.34229i
$185$	31.5309			2.31820
$186$	−0.961706	+	1.10987i	−0.0705157	+	0.0813794i
$187$	−17.7794	+	11.4261i	−1.30016	+	0.835561i
$188$	2.48346	+	17.2728i	0.181125	+	1.25975i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	8.27546	−	57.5571i	0.600365	−	4.17563i
$191$	−13.6420	+	4.00566i	−0.987103	+	0.289840i	−0.735154	−	0.677901i	$-0.762890\pi$
$191$	−13.6420	+	4.00566i	−0.987103	+	0.289840i	−0.251950	+	0.967740i	$0.581072\pi$
$192$	−18.5835	−	11.9429i	−1.34115	−	0.861903i
$193$	−0.254691	+	0.557696i	−0.0183331	+	0.0401439i	−0.918577	−	0.395242i	$-0.870661\pi$
$193$	−0.254691	+	0.557696i	−0.0183331	+	0.0401439i	0.900244	+	0.435386i	$0.143388\pi$
$194$	−17.7139	−	5.20126i	−1.27178	−	0.373428i
$195$	−1.21344	−	1.40039i	−0.0868966	−	0.100284i
$196$	−3.44933	−	3.98074i	−0.246381	−	0.284338i
$197$	9.49451	+	2.78784i	0.676456	+	0.198625i	0.601876	−	0.798590i	$-0.294420\pi$
$197$	9.49451	+	2.78784i	0.676456	+	0.198625i	0.0745800	+	0.997215i	$0.476238\pi$
$198$	−5.81082	+	12.7239i	−0.412957	+	0.904250i
$199$	4.09310e−5	0	2.63047e-5i	2.90152e−6	0	1.86469e-6i	0.540642	−	0.841253i	$-0.318181\pi$
$199$	4.09310e−5	0	2.63047e-5i	2.90152e−6	0	1.86469e-6i	−0.540639	+	0.841254i	$0.681818\pi$
$200$	−18.8908	+	5.54684i	−1.33578	+	0.392221i
$201$	−0.0185091	+	0.128734i	−0.00130553	+	0.00908019i
$202$	5.78265	+	12.6622i	0.406866	+	0.890911i
$203$	−0.444614	−	3.09236i	−0.0312058	−	0.217041i
$204$	−18.0482	+	11.5988i	−1.26362	+	0.812081i
$205$	14.6820	−	16.9439i	1.02543	−	1.18341i
$206$	10.4695			0.729447
$207$	−3.12080	+	3.64151i	−0.216910	+	0.253103i
$208$	9.09980			0.630958
$209$	27.2487	−	31.4467i	1.88483	−	2.17522i
$210$	6.10016	−	3.92033i	0.420951	−	0.270529i
$211$	−1.30294	−	9.06217i	−0.0896984	−	0.623866i	−0.984234	−	0.176870i	$-0.943403\pi$
$211$	−1.30294	−	9.06217i	−0.0896984	−	0.623866i	0.894536	−	0.446996i	$-0.147506\pi$
$212$	15.3656	+	33.6459i	1.05531	+	2.31081i
$213$	1.05068	−	7.30763i	0.0719913	−	0.500711i
$214$	−19.5670	+	5.74539i	−1.33757	+	0.392747i
$215$	15.3650	+	9.87450i	1.04789	+	0.673435i
$216$	−3.65892	+	8.01192i	−0.248958	+	0.545142i
$217$	0.522696	+	0.153477i	0.0354829	+	0.0104187i
$218$	−22.6581	−	26.1489i	−1.53460	−	1.77103i
$219$	−3.87165	−	4.46812i	−0.261622	−	0.301928i
$220$	−70.5384	−	20.7119i	−4.75570	−	1.39640i
$221$	1.16559	−	2.55228i	0.0784059	−	0.171685i
$222$	26.5840	+	17.0845i	1.78420	+	1.14664i
$223$	13.2020	−	3.87645i	0.884069	−	0.259586i	0.191980	−	0.981399i	$-0.438509\pi$
$223$	13.2020	−	3.87645i	0.884069	−	0.259586i	0.692088	+	0.721813i	$0.256691\pi$
$224$	−2.56089	+	17.8114i	−0.171107	+	1.19007i
$225$	0.928581	+	2.03331i	0.0619054	+	0.135554i
$226$	3.35776	+	23.3537i	0.223355	+	1.55347i
$227$	14.5294	−	9.33751i	0.964353	−	0.619752i	0.0391538	−	0.999233i	$-0.487534\pi$
$227$	14.5294	−	9.33751i	0.964353	−	0.619752i	0.925200	+	0.379481i	$0.123897\pi$
$228$	27.6606	−	31.9221i	1.83187	−	2.11409i
$229$	21.8896			1.44651			0.723254	−	0.690582i	$-0.242646\pi$
$229$	21.8896			1.44651			0.723254	+	0.690582i	$0.242646\pi$
$230$	−29.3574	−	18.6415i	−1.93577	−	1.22918i
$231$	5.18883			0.341400
$232$	−18.0199	+	20.7961i	−1.18306	+	1.36533i
$233$	−12.7499	+	8.19384i	−0.835271	+	0.536796i	−0.886949	−	0.461868i	$-0.847179\pi$
$233$	−12.7499	+	8.19384i	−0.835271	+	0.536796i	0.0516779	+	0.998664i	$0.483543\pi$
$234$	−0.264289	−	1.83817i	−0.0172771	−	0.120165i
$235$	3.70196	+	8.10617i	0.241489	+	0.528788i
$236$	−8.01625	+	55.7543i	−0.521814	+	3.62929i
$237$	−7.69147	+	2.25842i	−0.499615	+	0.146700i
$238$	9.23704	+	5.93628i	0.598748	+	0.384792i
$239$	−8.74135	+	19.1409i	−0.565431	+	1.23812i	0.383764	+	0.923431i	$0.374628\pi$
$239$	−8.74135	+	19.1409i	−0.565431	+	1.23812i	−0.949195	+	0.314689i	$0.898100\pi$
$240$	−34.0926	−	10.0105i	−2.20067	−	0.646174i
$241$	−6.57768	−	7.59105i	−0.423706	−	0.488983i	0.503257	−	0.864137i	$-0.332135\pi$
$241$	−6.57768	−	7.59105i	−0.423706	−	0.488983i	−0.926962	+	0.375155i	$0.877590\pi$
$242$	−28.1117	−	32.4426i	−1.80709	−	2.08549i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	9.16800	−	20.0751i	0.586921	−	1.28518i
$245$	−2.26285	−	1.45424i	−0.144568	−	0.0929083i
$246$	21.5593	−	6.33037i	1.37457	−	0.403610i
$247$	−0.786177	+	5.46798i	−0.0500233	+	0.347919i
$248$	−1.99324	−	4.36460i	−0.126571	−	0.277152i
$249$	0.0270225	+	0.187946i	0.00171248	+	0.0119106i
$250$	16.8651	−	10.8385i	1.06664	−	0.685488i
$251$	−0.981798	+	1.13306i	−0.0619705	+	0.0715178i	−0.785888	−	0.618368i	$-0.787794\pi$
$251$	−0.981798	+	1.13306i	−0.0619705	+	0.0715178i	0.723918	+	0.689886i	$0.242339\pi$
$252$	5.26727			0.331807
$253$	−10.4608	−	22.5793i	−0.657662	−	1.41955i
$254$	16.9976			1.06652
$255$	−7.17460	+	8.27993i	−0.449291	+	0.518509i
$256$	16.2668	−	10.4540i	1.01668	−	0.653378i
$257$	1.32107	+	9.18825i	0.0824062	+	0.573147i	0.988632	+	0.150354i	$0.0480413\pi$
$257$	1.32107	+	9.18825i	0.0824062	+	0.573147i	−0.906226	+	0.422793i	$0.861050\pi$
$258$	7.60406	+	16.6506i	0.473408	+	1.03662i
$259$	1.66824	−	11.6029i	0.103659	−	0.720967i
$260$	9.36480	−	2.74975i	0.580780	−	0.170532i
$261$	2.62821	+	1.68905i	0.162682	+	0.104549i
$262$	21.3728	−	46.7999i	1.32041	−	2.89130i
$263$	−10.7370	−	3.15268i	−0.662074	−	0.194402i	−0.0666031	−	0.997780i	$-0.521216\pi$
$263$	−10.7370	−	3.15268i	−0.662074	−	0.194402i	−0.595470	+	0.803377i	$0.703034\pi$
$264$	−29.9288	−	34.5397i	−1.84199	−	2.12577i
$265$	12.3697	+	14.2754i	0.759864	+	0.876930i
$266$	−20.7422	−	6.09046i	−1.27179	−	0.373430i
$267$	4.23813	−	9.28021i	0.259369	−	0.567940i
$268$	−0.576300	−	0.370366i	−0.0352031	−	0.0226237i
$269$	−6.06383	+	1.78050i	−0.369718	+	0.108559i	−0.461313	−	0.887237i	$-0.652622\pi$
$269$	−6.06383	+	1.78050i	−0.369718	+	0.108559i	0.0915951	+	0.995796i	$0.470803\pi$
$270$	−1.03196	+	7.17746i	−0.0628033	+	0.436807i
$271$	−9.19325	−	20.1304i	−0.558450	−	1.22284i	−0.952723	−	0.303842i	$-0.901731\pi$
$271$	−9.19325	−	20.1304i	−0.558450	−	1.22284i	0.394272	−	0.918994i	$-0.370997\pi$
$272$	−7.65702	−	53.2558i	−0.464275	−	3.22910i
$273$	−0.579521	+	0.372436i	−0.0350742	+	0.0225408i
$274$	−31.1636	+	35.9647i	−1.88266	+	2.17270i
$275$	−11.5986			−0.699425
$276$	−10.6189	−	22.9206i	−0.639181	−	1.37966i
$277$	−23.1548			−1.39124			−0.695618	−	0.718412i	$-0.744869\pi$
$277$	−23.1548			−1.39124			−0.695618	+	0.718412i	$0.744869\pi$
$278$	−27.2424	+	31.4394i	−1.63389	+	1.88561i
$279$	−0.458284	+	0.294521i	−0.0274367	+	0.0176325i
$280$	3.37170	+	23.4507i	0.201498	+	1.40145i
$281$	10.6006	+	23.2120i	0.632376	+	1.38471i	0.906167	+	0.422921i	$0.138995\pi$
$281$	10.6006	+	23.2120i	0.632376	+	1.38471i	−0.273791	+	0.961789i	$0.588278\pi$
$282$	−1.27103	+	8.84023i	−0.0756890	+	0.526428i
$283$	16.8141	−	4.93705i	0.999492	−	0.293477i	0.259245	−	0.965812i	$-0.416526\pi$
$283$	16.8141	−	4.93705i	0.999492	−	0.293477i	0.740248	+	0.672334i	$0.234708\pi$
$284$	32.7139	+	21.0239i	1.94121	+	1.24754i
$285$	8.96063	−	19.6210i	0.530782	−	1.16225i
$286$	9.24570	+	2.71478i	0.546710	+	0.160528i
$287$	−5.45828	−	6.29919i	−0.322192	−	0.371829i
$288$	−11.7839	−	13.5994i	−0.694374	−	0.801350i
$289$	0.393610	+	0.115574i	0.0231535	+	0.00679848i
$290$	−9.41086	+	20.6069i	−0.552625	+	1.21008i
$291$	−5.76119	−	3.70249i	−0.337727	−	0.217044i
$292$	29.8796	−	8.77344i	1.74857	−	0.513426i
$293$	1.37314	−	9.55041i	0.0802198	−	0.557941i	−0.909586	−	0.415516i	$-0.863601\pi$
$293$	1.37314	−	9.55041i	0.0802198	−	0.557941i	0.989806	−	0.142425i	$-0.0454900\pi$
$294$	−1.11987	−	2.45217i	−0.0653122	−	0.143014i
$295$	4.09368	+	28.4722i	0.238344	+	1.65772i
$296$	−86.8572	+	55.8198i	−5.04847	+	3.24446i
$297$	−3.39796	+	3.92146i	−0.197170	+	0.227546i
$298$	43.1258			2.49821
$299$	2.78898	+	1.77096i	0.161291	+	0.102417i
$300$	−11.7740			−0.679771
$301$	4.44659	−	5.13163i	0.256297	−	0.295782i
$302$	0.397703	−	0.255588i	0.0228852	−	0.0147074i
$303$	0.734867	+	5.11111i	0.0422170	+	0.293626i
$304$	44.0047	+	96.3569i	2.52384	+	5.52645i
$305$	1.60393	−	11.1556i	0.0918408	−	0.638767i
$306$	−10.5353	+	3.09345i	−0.602264	+	0.176841i
$307$	−17.1400	−	11.0152i	−0.978232	−	0.628672i	−0.0492463	−	0.998787i	$-0.515682\pi$
$307$	−17.1400	−	11.0152i	−0.978232	−	0.628672i	−0.928986	+	0.370115i	$0.879318\pi$
$308$	−11.3537	+	24.8611i	−0.646937	+	1.41660i
$309$	3.72635	+	1.09415i	0.211984	+	0.0622443i
$310$	−2.58685	−	2.98538i	−0.146923	−	0.169558i
$311$	−0.986479	−	1.13846i	−0.0559381	−	0.0645560i	0.727091	−	0.686541i	$-0.240872\pi$
$311$	−0.986479	−	1.13846i	−0.0559381	−	0.0645560i	−0.783029	+	0.621985i	$0.786326\pi$
$312$	5.82177	+	1.70943i	0.329593	+	0.0967772i
$313$	−12.4520	+	27.2661i	−0.703829	+	1.54117i	0.131438	+	0.991324i	$0.458041\pi$
$313$	−12.4520	+	27.2661i	−0.703829	+	1.54117i	−0.835266	+	0.549845i	$0.814687\pi$
$314$	18.3661	+	11.8032i	1.03646	+	0.666091i
$315$	2.58090	−	0.757819i	0.145417	−	0.0426983i
$316$	6.00902	−	41.7936i	0.338034	−	2.35108i
$317$	−11.4475	−	25.0665i	−0.642955	−	1.40787i	−0.897587	−	0.440837i	$-0.854682\pi$
$317$	−11.4475	−	25.0665i	−0.642955	−	1.40787i	0.254632	−	0.967038i	$-0.418046\pi$
$318$	2.69412	+	18.7380i	0.151079	+	1.05078i
$319$	−13.6373	+	8.76418i	−0.763544	+	0.490700i
$320$	38.9115	−	44.9063i	2.17522	−	2.51034i
$321$	−7.56479			−0.422226
$322$	−8.41301	+	9.81675i	−0.468838	+	0.547066i
$323$	32.6624			1.81738
$324$	−3.44933	+	3.98074i	−0.191629	+	0.221152i
$325$	1.29541	−	0.832509i	0.0718564	−	0.0461793i
$326$	−2.45334	−	17.0633i	−0.135878	−	0.945051i
$327$	−5.33177	−	11.6750i	−0.294848	−	0.645626i
$328$	−10.4479	+	72.6665i	−0.576887	+	4.01234i
$329$	3.17880	−	0.933380i	0.175253	−	0.0514589i
$330$	−31.6527	−	20.3420i	−1.74242	−	1.11979i
$331$	12.0010	−	26.2784i	0.659633	−	1.44439i	−0.223232	−	0.974765i	$-0.571661\pi$
$331$	12.0010	−	26.2784i	0.659633	−	1.44439i	0.882864	−	0.469628i	$-0.155612\pi$
$332$	−0.959629	−	0.281773i	−0.0526665	−	0.0154643i
$333$	7.67640	+	8.85903i	0.420664	+	0.485472i
$334$	−8.29285	−	9.57046i	−0.453764	−	0.523672i
$335$	−0.335665	−	0.0985602i	−0.0183394	−	0.00538492i
$336$	−5.48746	+	12.0159i	−0.299366	+	0.655519i
$337$	14.6820	+	9.43554i	0.799779	+	0.513987i	0.875544	−	0.483139i	$-0.160503\pi$
$337$	14.6820	+	9.43554i	0.799779	+	0.513987i	−0.0757647	+	0.997126i	$0.524140\pi$
$338$	32.3982	−	9.51297i	1.76223	−	0.517437i
$339$	−1.24556	+	8.66304i	−0.0676493	+	0.470512i
$340$	−23.9727	−	52.4928i	−1.30010	−	2.84682i
$341$	−0.402279	−	2.79791i	−0.0217846	−	0.151515i
$342$	18.1861	−	11.6875i	0.983393	−	0.631988i
$343$	−0.654861	+	0.755750i	−0.0353592	+	0.0408066i
$344$	−59.8065			−3.22455
$345$	−8.50078	−	9.70303i	−0.457667	−	0.522394i
$346$	10.0589			0.540768
$347$	10.3711	−	11.9689i	0.556752	−	0.642526i	−0.405691	−	0.914010i	$-0.632969\pi$
$347$	10.3711	−	11.9689i	0.556752	−	0.642526i	0.962443	+	0.271484i	$0.0875144\pi$
$348$	−13.8435	+	8.89667i	−0.742089	+	0.476911i
$349$	−3.02521	−	21.0408i	−0.161936	−	1.12629i	−0.894980	−	0.446106i	$-0.852810\pi$
$349$	−3.02521	−	21.0408i	−0.161936	−	1.12629i	0.733044	−	0.680181i	$-0.238099\pi$
$350$	2.50326	+	5.48137i	0.133805	+	0.292991i
$351$	0.0980376	−	0.681867i	0.00523286	−	0.0363953i
$352$	89.5885	−	26.3055i	4.77508	−	1.40209i
$353$	12.7636	+	8.20264i	0.679335	+	0.436582i	0.834280	−	0.551341i	$-0.185884\pi$
$353$	12.7636	+	8.20264i	0.679335	+	0.436582i	−0.154945	+	0.987923i	$0.549520\pi$
$354$	−11.9758	+	26.2233i	−0.636505	+	1.39375i
$355$	19.0542	+	5.59481i	1.01129	+	0.296942i
$356$	35.1906	+	40.6121i	1.86510	+	2.15244i
$357$	2.66728	+	3.07821i	0.141168	+	0.162916i
$358$	−30.3934	−	8.92429i	−1.60634	−	0.471664i
$359$	5.90558	−	12.9314i	0.311685	−	0.682494i	−0.687354	−	0.726322i	$-0.741228\pi$
$359$	5.90558	−	12.9314i	0.311685	−	0.682494i	0.999039	+	0.0438279i	$0.0139553\pi$
$360$	−19.9309	−	12.8088i	−1.05045	−	0.675083i
$361$	−43.4713	+	12.7643i	−2.28797	+	0.671807i
$362$	0.226098	−	1.57255i	0.0118835	−	0.0826514i
$363$	−6.61507	−	14.4850i	−0.347201	−	0.760264i
$364$	−0.516391	−	3.59158i	−0.0270662	−	0.188250i
$365$	13.3783	−	8.59774i	0.700255	−	0.450026i
$366$	7.39676	−	8.53631i	0.386635	−	0.446200i
$367$	−16.0272			−0.836613			−0.418307	−	0.908306i	$-0.637376\pi$
$367$	−16.0272			−0.836613			−0.418307	+	0.908306i	$0.637376\pi$
$368$	63.3501	−	0.345349i	3.30235	−	0.0180026i
$369$	8.33502			0.433904
$370$	−55.6636	+	64.2393i	−2.89381	+	3.33964i
$371$	5.90756	−	3.79656i	0.306705	−	0.197107i
$372$	−0.408360	−	2.84021i	−0.0211725	−	0.147258i
$373$	−1.57519	−	3.44919i	−0.0815605	−	0.178592i	0.864458	−	0.502705i	$-0.167662\pi$
$373$	−1.57519	−	3.44919i	−0.0815605	−	0.178592i	−0.946019	+	0.324112i	$0.894934\pi$
$374$	8.10823	−	56.3939i	0.419266	−	2.91606i
$375$	7.13538	−	2.09514i	0.368469	−	0.108192i
$376$	−24.5482	−	15.7761i	−1.26597	−	0.813592i
$377$	0.894041	−	1.95768i	0.0460455	−	0.100826i
$378$	2.58659	+	0.759491i	0.133040	+	0.0390640i
$379$	13.2495	+	15.2907i	0.680581	+	0.785432i	0.985993	−	0.166788i	$-0.0533397\pi$
$379$	13.2495	+	15.2907i	0.680581	+	0.785432i	−0.305412	+	0.952220i	$0.598794\pi$
$380$	74.4031	+	85.8657i	3.81680	+	4.40482i
$381$	6.04982	+	1.77639i	0.309942	+	0.0910071i
$382$	15.9223	−	34.8649i	0.814655	−	1.78385i
$383$	19.1924	+	12.3342i	0.980685	+	0.630248i	0.929648	−	0.368449i	$-0.120111\pi$
$383$	19.1924	+	12.3342i	0.980685	+	0.630248i	0.0510372	+	0.998697i	$0.483747\pi$
$384$	22.6071	−	6.63805i	1.15366	−	0.338747i
$385$	−1.98632	+	13.8151i	−0.101232	+	0.704085i
$386$	−0.686594	−	1.50343i	−0.0349467	−	0.0765226i
$387$	0.966336	+	6.72101i	0.0491216	+	0.341648i
$388$	30.3458	−	19.5020i	1.54057	−	0.990066i
$389$	−2.42949	+	2.80378i	−0.123180	+	0.142157i	−0.813990	−	0.580879i	$-0.802709\pi$
$389$	−2.42949	+	2.80378i	−0.123180	+	0.142157i	0.690810	+	0.723037i	$0.257254\pi$
$390$	4.99524			0.252944
$391$	8.01760	−	17.8124i	0.405468	−	0.900814i
$392$	8.80787			0.444864
$393$	12.4980	−	14.4235i	0.630443	−	0.727570i
$394$	−22.4411	+	14.4220i	−1.13056	+	0.726569i
$395$	−3.06864	−	21.3429i	−0.154400	−	1.07388i
$396$	−11.3537	−	24.8611i	−0.570545	−	1.24932i
$397$	1.86063	−	12.9410i	0.0933824	−	0.649489i	−0.888342	−	0.459182i	$-0.848143\pi$
$397$	1.86063	−	12.9410i	0.0933824	−	0.649489i	0.981725	−	0.190307i	$-0.0609483\pi$
$398$	−0.000125850	0	3.69528e-5i	−6.30828e−6	0	1.85228e-6i
$399$	−6.74613	−	4.33547i	−0.337729	−	0.217045i
$400$	12.2662	−	26.8592i	0.613309	−	1.34296i
$401$	24.3531	+	7.15070i	1.21613	+	0.357089i	0.826001	−	0.563669i	$-0.190611\pi$
$401$	24.3531	+	7.15070i	1.21613	+	0.357089i	0.390133	+	0.920758i	$0.372429\pi$
$402$	−0.229599	−	0.264972i	−0.0114514	−	0.0132156i
$403$	0.245753	+	0.283614i	0.0122418	+	0.0141278i
$404$	−26.0967	−	7.66269i	−1.29836	−	0.381233i
$405$	−1.11741	+	2.44678i	−0.0555243	+	0.121581i
$406$	7.08509	+	4.55331i	0.351627	+	0.225977i
$407$	−58.3606	+	17.1362i	−2.89283	+	0.849411i
$408$	5.10553	−	35.5098i	0.252762	−	1.75800i
$409$	3.05575	+	6.69117i	0.151097	+	0.330857i	0.970012	−	0.243059i	$-0.0781509\pi$
$409$	3.05575	+	6.69117i	0.151097	+	0.330857i	−0.818914	+	0.573916i	$0.805424\pi$
$410$	8.60144	+	59.8243i	0.424795	+	2.95451i
$411$	−14.8504	+	9.54380i	−0.732518	+	0.470761i
$412$	−13.3960	+	15.4598i	−0.659975	+	0.761652i
$413$	10.6939			0.526212
$414$	−1.90966	−	12.7867i	−0.0938545	−	0.628433i
$415$	−0.510745			−0.0250715
$416$	−8.11768	+	9.36830i	−0.398002	+	0.459319i
$417$	−12.9819	+	8.34296i	−0.635726	+	0.408556i
$418$	15.9637	+	111.030i	0.780810	+	5.43065i
$419$	3.21500	+	7.03986i	0.157063	+	0.343920i	0.971762	−	0.235965i	$-0.0758250\pi$
$419$	3.21500	+	7.03986i	0.157063	+	0.343920i	−0.814699	+	0.579884i	$0.803098\pi$
$420$	−2.01634	+	14.0240i	−0.0983874	+	0.684300i
$421$	23.7168	−	6.96387i	1.15588	−	0.339398i	0.353052	−	0.935604i	$-0.385144\pi$
$421$	23.7168	−	6.96387i	1.15588	−	0.339398i	0.802832	+	0.596205i	$0.203326\pi$
$422$	20.7629	+	13.3435i	1.01072	+	0.649552i
$423$	−1.37627	+	3.01361i	−0.0669165	+	0.146527i
$424$	−59.3463	−	17.4257i	−2.88211	−	0.846264i
$425$	−5.96220	−	6.88075i	−0.289209	−	0.333765i
$426$	13.0333	+	15.0412i	0.631465	+	0.728750i
$427$	−4.02021	−	1.18044i	−0.194551	−	0.0571255i
$428$	16.5525	−	36.2450i	0.800098	−	1.75197i
$429$	3.00704	+	1.93251i	0.145181	+	0.0933023i
$430$	−47.2426	+	13.8717i	−2.27824	+	0.668952i
$431$	3.46425	−	24.0944i	0.166867	−	1.16059i	−0.718443	−	0.695586i	$-0.755145\pi$
$431$	3.46425	−	24.0944i	0.166867	−	1.16059i	0.885310	−	0.465001i	$-0.153946\pi$
$432$	−5.48746	−	12.0159i	−0.264016	−	0.578114i
$433$	2.81114	+	19.5519i	0.135095	+	0.939604i	0.938772	+	0.344539i	$0.111965\pi$
$433$	2.81114	+	19.5519i	0.135095	+	0.939604i	−0.803678	+	0.595065i	$0.797126\pi$
$434$	−1.23544	+	0.793966i	−0.0593028	+	0.0381116i
$435$	−5.50314	+	6.35096i	−0.263855	+	0.304505i
$436$	67.6044			3.23766
$437$	−5.26561	+	38.0963i	−0.251888	+	1.82239i
$438$	15.9380			0.761545
$439$	−10.3173	+	11.9068i	−0.492418	+	0.568280i	−0.946510	−	0.322674i	$-0.895418\pi$
$439$	−10.3173	+	11.9068i	−0.492418	+	0.568280i	0.454092	+	0.890955i	$0.349964\pi$
$440$	103.418	−	66.4627i	4.93026	−	3.16848i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	3.14218	+	6.88041i	0.149458	+	0.327268i
$443$	2.88620	−	20.0740i	0.137128	−	0.953743i	−0.798812	−	0.601581i	$-0.794538\pi$
$443$	2.88620	−	20.0740i	0.137128	−	0.953743i	0.935939	−	0.352162i	$-0.114553\pi$
$444$	−59.2428	+	17.3953i	−2.81154	+	0.825543i
$445$	23.0859	+	14.8364i	1.09438	+	0.703314i
$446$	−15.4086	+	33.7402i	−0.729621	+	1.59765i
$447$	15.3495	+	4.50701i	0.726004	+	0.213174i
$448$	−14.4660	−	16.6947i	−0.683456	−	0.788750i
$449$	−6.39735	−	7.38294i	−0.301910	−	0.348422i	0.584442	−	0.811436i	$-0.301314\pi$
$449$	−6.39735	−	7.38294i	−0.301910	−	0.348422i	−0.886351	+	0.463013i	$0.846768\pi$
$450$	−5.78183	−	1.69770i	−0.272558	−	0.0800302i
$451$	−17.9663	+	39.3407i	−0.846000	+	1.85248i
$452$	−38.7816	−	24.9234i	−1.82413	−	1.17230i
$453$	0.168263	−	0.0494064i	0.00790568	−	0.00232132i
$454$	−6.62610	+	46.0855i	−0.310978	+	2.16290i
$455$	−0.769756	−	1.68553i	−0.0360867	−	0.0790189i
$456$	10.0519	+	69.9126i	0.470724	+	3.27396i
$457$	−14.3229	+	9.20474i	−0.669995	+	0.430580i	−0.830924	−	0.556386i	$-0.812187\pi$
$457$	−14.3229	+	9.20474i	−0.669995	+	0.430580i	0.160929	+	0.986966i	$0.448551\pi$
$458$	−38.6432	+	44.5966i	−1.80568	+	2.08386i
$459$	−4.07305			−0.190114
$460$	65.0905	−	19.4983i	3.03486	−	0.909115i
$461$	−35.4780			−1.65238			−0.826188	−	0.563395i	$-0.809495\pi$
$461$	−35.4780			−1.65238			−0.826188	+	0.563395i	$0.809495\pi$
$462$	−9.16019	+	10.5714i	−0.426170	+	0.491827i
$463$	−8.50561	+	5.46622i	−0.395289	+	0.254037i	−0.723153	−	0.690688i	$-0.757308\pi$
$463$	−8.50561	+	5.46622i	−0.395289	+	0.254037i	0.327864	+	0.944725i	$0.393671\pi$
$464$	−5.87317	−	40.8488i	−0.272655	−	1.89636i
$465$	−0.608721	−	1.33291i	−0.0282288	−	0.0618124i
$466$	5.81452	−	40.4409i	0.269353	−	1.87339i
$467$	−5.59838	+	1.64383i	−0.259062	+	0.0760675i	−0.408685	−	0.912676i	$-0.634012\pi$
$467$	−5.59838	+	1.64383i	−0.259062	+	0.0760675i	0.149622	+	0.988743i	$0.452194\pi$
$468$	3.05250	+	1.96172i	0.141102	+	0.0906805i
$469$	−0.0540279	+	0.118305i	−0.00249478	+	0.00546280i
$470$	−23.0503	−	6.76819i	−1.06323	−	0.312193i
$471$	5.30338	+	6.12043i	0.244367	+	0.282015i
$472$	−61.6816	−	71.1843i	−2.83912	−	3.27652i
$473$	−33.8057	−	9.92623i	−1.55439	−	0.456409i
$474$	8.97709	−	19.6571i	0.412331	−	0.902880i
$475$	15.0797	+	9.69112i	0.691903	+	0.444659i
$476$	−20.5848	+	6.04426i	−0.943505	+	0.277038i
$477$	−0.999382	+	6.95085i	−0.0457585	+	0.318258i
$478$	−23.5648	−	51.5997i	−1.07783	−	2.36012i
$479$	−2.30812	−	16.0533i	−0.105460	−	0.733494i	−0.972101	−	0.234561i	$-0.924635\pi$
$479$	−2.30812	−	16.0533i	−0.105460	−	0.733494i	0.866641	−	0.498933i	$-0.166274\pi$
$480$	40.7189	−	26.1684i	1.85855	−	1.19442i
$481$	5.28810	−	6.10280i	0.241117	−	0.278264i
$482$	27.0776			1.23335
$483$	−4.02032	+	2.61478i	−0.182931	+	0.118976i
$484$	83.8760			3.81254
$485$	12.0632	−	13.9217i	0.547762	−	0.632151i
$486$	−2.26784	+	1.45745i	−0.102871	+	0.0661114i
$487$	−2.32543	−	16.1737i	−0.105375	−	0.732902i	−0.972177	−	0.234249i	$-0.924737\pi$
$487$	−2.32543	−	16.1737i	−0.105375	−	0.732902i	0.866801	−	0.498654i	$-0.166172\pi$
$488$	15.3306	+	33.5694i	0.693984	+	1.51961i
$489$	0.910064	−	6.32963i	0.0411545	−	0.286236i
$490$	6.95754	−	2.04292i	0.314310	−	0.0922897i
$491$	−30.6557	−	19.7012i	−1.38347	−	0.889105i	−0.384059	−	0.923309i	$-0.625474\pi$
$491$	−30.6557	−	19.7012i	−1.38347	−	0.889105i	−0.999415	+	0.0342042i	$0.989110\pi$
$492$	−18.2379	+	39.9354i	−0.822227	+	1.80043i
$493$	−12.2094	−	3.58501i	−0.549884	−	0.161461i
$494$	−9.75225	−	11.2547i	−0.438774	−	0.506373i
$495$	−9.14002	−	10.5481i	−0.410813	−	0.474104i
$496$	6.90461	+	2.02738i	0.310026	+	0.0910318i
$497$	3.06692	−	6.71561i	0.137570	−	0.301236i
$498$	−0.430614	−	0.276739i	−0.0192963	−	0.0124010i
$499$	−15.4214	+	4.52814i	−0.690358	+	0.202707i	−0.608049	−	0.793899i	$-0.708048\pi$
$499$	−15.4214	+	4.52814i	−0.690358	+	0.202707i	−0.0823089	+	0.996607i	$0.526229\pi$
$500$	−5.57456	+	38.7719i	−0.249302	+	1.73393i
$501$	−1.95142	−	4.27302i	−0.0871831	−	0.190904i
$502$	−0.575187	−	4.00051i	−0.0256719	−	0.178552i
$503$	−37.2809	+	23.9590i	−1.66228	+	1.06828i	−0.747547	+	0.664209i	$0.768769\pi$
$503$	−37.2809	+	23.9590i	−1.66228	+	1.06828i	−0.914728	+	0.404071i	$0.867595\pi$
$504$	−5.76793	+	6.65654i	−0.256924	+	0.296506i
$505$	−13.8895			−0.618076
$506$	64.4688	+	18.5486i	2.86599	+	0.824586i
$507$	12.5254			0.556275
$508$	−21.7488	+	25.0995i	−0.964947	+	1.11361i
$509$	13.6565	−	8.77650i	0.605313	−	0.389011i	−0.201784	−	0.979430i	$-0.564674\pi$
$509$	13.6565	−	8.77650i	0.605313	−	0.389011i	0.807097	+	0.590419i	$0.201037\pi$
$510$	−4.20324	−	29.2342i	−0.186123	−	1.29451i
$511$	−2.45600	−	5.37790i	−0.108647	−	0.237904i
$512$	−0.712109	+	4.95283i	−0.0314711	+	0.218886i
$513$	7.69431	−	2.25925i	0.339712	−	0.0997484i
$514$	−21.0518	−	13.5292i	−0.928554	−	0.596745i
$515$	−4.33963	+	9.50246i	−0.191227	+	0.418728i
$516$	−34.3167	−	10.0763i	−1.51071	−	0.443584i
$517$	−11.2574	−	12.9918i	−0.495102	−	0.571378i
$518$	20.6939	+	23.8821i	0.909239	+	1.04932i
$519$	3.58018	+	1.05124i	0.157153	+	0.0461442i
$520$	−6.77991	+	14.8459i	−0.297319	+	0.651037i
$521$	6.71097	+	4.31288i	0.294013	+	0.188951i	0.679329	−	0.733834i	$-0.262271\pi$
$521$	6.71097	+	4.31288i	0.294013	+	0.188951i	−0.385316	+	0.922785i	$0.625907\pi$
$522$	−8.08091	+	2.37277i	−0.353692	+	0.103853i
$523$	3.96749	−	27.5945i	0.173486	−	1.20662i	−0.697961	−	0.716135i	$-0.745909\pi$
$523$	3.96749	−	27.5945i	0.173486	−	1.20662i	0.871448	−	0.490488i	$-0.163182\pi$
$524$	41.7600	+	91.4417i	1.82430	+	3.99465i
$525$	0.318118	+	2.21256i	0.0138838	+	0.0965639i
$526$	25.3779	−	16.3094i	1.10653	−	0.711122i
$527$	1.45304	−	1.67689i	0.0632953	−	0.0730467i
$528$	68.5424			2.98292
$529$	19.4833	+	12.2230i	0.847098	+	0.531437i
$530$	−50.9208			−2.21186
$531$	−7.00301	+	8.08190i	−0.303905	+	0.350725i
$532$	35.5337	−	22.8361i	1.54058	−	0.990071i
$533$	−0.817146	−	5.68337i	−0.0353945	−	0.246174i
$534$	11.4251	+	25.0175i	0.494412	+	1.08261i
$535$	2.89585	−	20.1411i	0.125198	−	0.870774i
$536$	1.09913	−	0.322733i	0.0474751	−	0.0139400i
$537$	−9.88503	−	6.35272i	−0.426571	−	0.274140i
$538$	7.07739	−	15.4973i	0.305128	−	0.668137i
$539$	4.97865	+	1.46186i	0.214446	+	0.0629669i
$540$	−9.27819	−	10.7076i	−0.399270	−	0.460782i
$541$	22.9131	+	26.4431i	0.985111	+	1.13688i	0.990586	+	0.136893i	$0.0437117\pi$
$541$	22.9131	+	26.4431i	0.985111	+	1.13688i	−0.00547516	+	0.999985i	$0.501743\pi$
$542$	57.2419	+	16.8078i	2.45875	+	0.721955i
$543$	0.244818	−	0.536077i	0.0105062	−	0.0230053i
$544$	61.6577	+	39.6250i	2.64355	+	1.69891i
$545$	33.1253	−	9.72647i	1.41893	−	0.416636i
$546$	0.264289	−	1.83817i	0.0113105	−	0.0786663i
$547$	3.65906	+	8.01221i	0.156450	+	0.342578i	0.971584	−	0.236695i	$-0.0760641\pi$
$547$	3.65906	+	8.01221i	0.156450	+	0.342578i	−0.815134	+	0.579272i	$0.803337\pi$
$548$	−13.2327	−	92.0354i	−0.565273	−	3.93156i
$549$	3.52479	−	2.26525i	0.150434	−	0.0966784i
$550$	20.4759	−	23.6304i	0.873093	−	1.00760i
$551$	25.0530			1.06730
$552$	40.5943	+	11.6796i	1.72781	+	0.497115i
$553$	−8.01618			−0.340883
$554$	40.8766	−	47.1741i	1.73668	−	2.00424i
$555$	−26.5255	+	17.0469i	−1.12595	+	0.723601i
$556$	−11.5677	−	80.4551i	−0.490580	−	3.41206i
$557$	−5.76519	−	12.6240i	−0.244279	−	0.534897i	0.747287	−	0.664502i	$-0.231356\pi$
$557$	−5.76519	−	12.6240i	−0.244279	−	0.534897i	−0.991566	+	0.129605i	$0.958629\pi$
$558$	0.208999	−	1.45362i	0.00884762	−	0.0615365i
$559$	4.48810	−	1.31782i	0.189826	−	0.0557380i
$560$	−29.8913	−	19.2100i	−1.26314	−	0.811770i
$561$	8.77955	−	19.2245i	0.370673	−	0.811660i
$562$	−66.0045	−	19.3807i	−2.78423	−	0.817525i
$563$	−24.5700	−	28.3553i	−1.03550	−	1.19503i	−0.980494	−	0.196547i	$-0.937027\pi$
$563$	−24.5700	−	28.3553i	−1.03550	−	1.19503i	−0.0550070	−	0.998486i	$-0.517518\pi$
$564$	−11.4276	−	13.1882i	−0.481190	−	0.555322i
$565$	−22.5883	−	6.63252i	−0.950297	−	0.279032i
$566$	−19.6245	+	42.9717i	−0.824879	+	1.80623i
$567$	0.841254	+	0.540641i	0.0353293	+	0.0227048i
$568$	−62.3925	+	18.3201i	−2.61793	+	0.768694i
$569$	−6.17631	+	42.9572i	−0.258924	+	1.80086i	0.281602	+	0.959531i	$0.409134\pi$
$569$	−6.17631	+	42.9572i	−0.258924	+	1.80086i	−0.540527	+	0.841327i	$0.681775\pi$
$570$	24.1559	+	52.8941i	1.01178	+	2.21549i
$571$	−1.93928	−	13.4880i	−0.0811564	−	0.564455i	−0.989311	−	0.145821i	$-0.953418\pi$
$571$	−1.93928	−	13.4880i	−0.0811564	−	0.564455i	0.908155	−	0.418635i	$-0.137491\pi$
$572$	−15.8389	+	10.1790i	−0.662257	+	0.425607i
$573$	9.31079	−	10.7452i	0.388964	−	0.448888i
$574$	22.4694			0.937857
$575$	8.98665	−	5.84484i	0.374769	−	0.243747i
$576$	22.0902			0.920427
$577$	25.8480	−	29.8302i	1.07607	−	1.24185i	0.107208	−	0.994237i	$-0.465809\pi$
$577$	25.8480	−	29.8302i	1.07607	−	1.24185i	0.968859	−	0.247612i	$-0.0796457\pi$
$578$	−0.930329	+	0.597886i	−0.0386966	+	0.0248688i
$579$	−0.0872534	−	0.606861i	−0.00362613	−	0.0252203i
$580$	−18.3878	−	40.2636i	−0.763511	−	1.67186i
$581$	−0.0270225	+	0.187946i	−0.00112108	+	0.00779731i
$582$	17.7139	−	5.20126i	0.734263	−	0.215599i
$583$	−30.6533	−	19.6997i	−1.26953	−	0.815879i
$584$	−21.6322	+	47.3678i	−0.895145	+	1.96009i
$585$	1.77792	+	0.522045i	0.0735081	+	0.0215839i
$586$	17.0333	+	19.6575i	0.703641	+	0.812045i
$587$	−6.82395	−	7.87526i	−0.281654	−	0.325047i	0.597240	−	0.802062i	$-0.296264\pi$
$587$	−6.82395	−	7.87526i	−0.281654	−	0.325047i	−0.878895	+	0.477016i	$0.841718\pi$
$588$	5.05391	+	1.48396i	0.208420	+	0.0611975i
$589$	−1.81475	+	3.97375i	−0.0747756	+	0.163736i
$590$	−65.2344	−	41.9236i	−2.68566	−	1.72597i
$591$	−9.49451	+	2.78784i	−0.390552	+	0.114676i
$592$	22.0368	−	153.269i	0.905706	−	6.29932i
$593$	−11.6512	−	25.5127i	−0.478459	−	1.04768i	−0.982884	−	0.184224i	$-0.941023\pi$
$593$	−11.6512	−	25.5127i	−0.478459	−	1.04768i	0.504425	−	0.863455i	$-0.331704\pi$
$594$	−1.99070	−	13.8456i	−0.0816794	−	0.568092i
$595$	−9.21670	+	5.92322i	−0.377848	+	0.242828i
$596$	−55.1805	+	63.6817i	−2.26028	+	2.60850i
$597$	−4.86547e−5	0		−1.99131e−6	0
$598$	−8.53162	+	2.55571i	−0.348884	+	0.104511i
$599$	26.3871			1.07815			0.539075	−	0.842258i	$-0.318774\pi$
$599$	26.3871			1.07815			0.539075	+	0.842258i	$0.318774\pi$
$600$	12.8931	−	14.8794i	0.526359	−	0.607450i
$601$	29.0557	−	18.6730i	1.18521	−	0.761687i	0.208871	−	0.977943i	$-0.433021\pi$
$601$	29.0557	−	18.6730i	1.18521	−	0.761687i	0.976337	+	0.216257i	$0.0693848\pi$
$602$	2.60504	+	18.1184i	0.106173	+	0.738452i
$603$	−0.0540279	−	0.118305i	−0.00220019	−	0.00481774i
$604$	−0.131457	+	0.914300i	−0.00534889	+	0.0372023i
$605$	41.0982	−	12.0675i	1.67088	−	0.490614i
$606$	−11.7104	−	7.52581i	−0.475702	−	0.305715i
$607$	−18.4488	+	40.3973i	−0.748815	+	1.63968i	0.0196676	+	0.999807i	$0.493739\pi$
$607$	−18.4488	+	40.3973i	−0.748815	+	1.63968i	−0.768483	+	0.639870i	$0.778988\pi$
$608$	−138.455	−	40.6542i	−5.61511	−	1.64874i
$609$	2.04589	+	2.36108i	0.0829036	+	0.0956758i
$610$	19.8962	+	22.9614i	0.805573	+	0.929681i
$611$	2.18981	+	0.642985i	0.0885901	+	0.0260124i
$612$	8.91226	−	19.5151i	0.360257	−	0.788853i
$613$	−0.0933975	−	0.0600229i	−0.00377229	−	0.00242430i	0.538753	−	0.842464i	$-0.318895\pi$
$613$	−0.0933975	−	0.0600229i	−0.00377229	−	0.00242430i	−0.542526	+	0.840039i	$0.682532\pi$
$614$	52.7001	−	15.4742i	2.12680	−	0.624486i
$615$	−3.19070	+	22.1918i	−0.128661	+	0.894859i
$616$	−18.9855	−	41.5725i	−0.764949	−	1.67500i
$617$	0.840986	+	5.84919i	0.0338568	+	0.235479i	0.999722	−	0.0235647i	$-0.00750159\pi$
$617$	0.840986	+	5.84919i	0.0338568	+	0.235479i	−0.965865	+	0.259044i	$0.916592\pi$
$618$	−8.80753	+	5.66026i	−0.354291	+	0.227689i
$619$	1.68410	−	1.94355i	0.0676895	−	0.0781179i	−0.720895	−	0.693044i	$-0.756269\pi$
$619$	1.68410	−	1.94355i	0.0676895	−	0.0781179i	0.788584	+	0.614927i	$0.210814\pi$
$620$	7.71830			0.309974
$621$	0.656630	−	4.75067i	0.0263497	−	0.190638i
$622$	4.06092			0.162828
$623$	6.68099	−	7.71028i	0.267668	−	0.308906i
$624$	−7.65524	+	4.91973i	−0.306455	+	0.196947i
$625$	4.43737	+	30.8626i	0.177495	+	1.23450i
$626$	−33.5679	−	73.5036i	−1.34165	−	2.93779i
$627$	−5.92172	+	41.1864i	−0.236491	+	1.64483i
$628$	−40.9290	+	12.0178i	−1.63325	+	0.479564i
$629$	−40.1657	−	25.8129i	−1.60151	−	1.02923i
$630$	−3.01229	+	6.59599i	−0.120012	+	0.262791i
$631$	−3.49808	−	1.02713i	−0.139257	−	0.0408894i	0.211361	−	0.977408i	$-0.432210\pi$
$631$	−3.49808	−	1.02713i	−0.139257	−	0.0408894i	−0.350618	+	0.936519i	$0.614028\pi$
$632$	46.2368	+	53.3601i	1.83920	+	2.12255i
$633$	5.99549	+	6.91916i	0.238299	+	0.275012i
$634$	71.2780	+	20.9291i	2.83081	+	0.831201i
$635$	−7.04549	+	15.4275i	−0.279592	+	0.612221i
$636$	−31.1167	−	19.9975i	−1.23386	−	0.792952i
$637$	−0.660974	+	0.194079i	−0.0261887	+	0.00768971i
$638$	6.21926	−	43.2559i	0.246223	−	1.71252i
$639$	3.06692	+	6.71561i	0.121325	+	0.265665i
$640$	9.01949	+	62.7320i	0.356527	+	2.47970i
$641$	−28.2662	+	18.1656i	−1.11645	+	0.717498i	−0.962689	−	0.270610i	$-0.912775\pi$
$641$	−28.2662	+	18.1656i	−1.11645	+	0.717498i	−0.153760	+	0.988108i	$0.549138\pi$
$642$	13.3546	−	15.4121i	0.527065	−	0.608265i
$643$	−42.4681			−1.67478			−0.837390	−	0.546606i	$-0.815920\pi$
$643$	−42.4681			−1.67478			−0.837390	+	0.546606i	$0.815920\pi$
$644$	−3.73126	−	24.9839i	−0.147032	−	0.984502i
$645$	−18.2644			−0.719162
$646$	−57.6610	+	66.5444i	−2.26864	+	2.61815i
$647$	−10.1496	+	6.52273i	−0.399020	+	0.256435i	−0.724727	−	0.689036i	$-0.758034\pi$
$647$	−10.1496	+	6.52273i	−0.399020	+	0.256435i	0.325707	+	0.945471i	$0.394398\pi$
$648$	−1.25349	−	8.71822i	−0.0492417	−	0.342484i
$649$	−23.0509	−	50.4744i	−0.904826	−	1.98129i
$650$	−0.590767	+	4.10887i	−0.0231718	+	0.161163i
$651$	−0.522696	+	0.153477i	−0.0204861	+	0.00601526i
$652$	28.3357	+	18.2103i	1.10971	+	0.713169i
$653$	2.09691	−	4.59159i	0.0820584	−	0.179683i	−0.864155	−	0.503225i	$-0.832147\pi$
$653$	2.09691	−	4.59159i	0.0820584	−	0.179683i	0.946214	+	0.323542i	$0.104874\pi$
$654$	33.1984	+	9.74792i	1.29816	+	0.381174i
$655$	33.6179	+	38.7971i	1.31356	+	1.51593i
$656$	−72.1017	−	83.2097i	−2.81510	−	3.24879i
$657$	5.67269	+	1.66565i	0.221313	+	0.0649832i
$658$	−3.71013	+	8.12405i	−0.144636	+	0.316709i
$659$	4.59154	+	2.95080i	0.178861	+	0.114947i	0.627008	−	0.779013i	$-0.284279\pi$
$659$	4.59154	+	2.95080i	0.178861	+	0.114947i	−0.448147	+	0.893960i	$0.647916\pi$
$660$	70.5384	−	20.7119i	2.74570	−	0.806211i
$661$	−5.66376	+	39.3923i	−0.220295	+	1.53218i	0.516630	+	0.856209i	$0.327186\pi$
$661$	−5.66376	+	39.3923i	−0.220295	+	1.53218i	−0.736925	+	0.675975i	$0.763723\pi$
$662$	32.3520	+	70.8411i	1.25740	+	2.75332i
$663$	0.399313	+	2.77728i	0.0155080	+	0.107861i
$664$	1.40693	−	0.904181i	0.0545996	−	0.0350890i
$665$	14.1255	−	16.3017i	0.547765	−	0.632155i
$666$	−31.6005			−1.22449
$667$	6.14975	−	13.6627i	0.238119	−	0.529021i
$668$	24.7431			0.957340
$669$	−9.01043	+	10.3986i	−0.348363	+	0.402033i
$670$	0.793373	−	0.509870i	0.0306507	−	0.0196980i
$671$	3.09404	+	21.5196i	0.119444	+	0.830753i
$672$	−7.47520	−	16.3684i	−0.288362	−	0.631425i
$673$	1.83941	−	12.7933i	0.0709039	−	0.493147i	−0.923166	−	0.384402i	$-0.874408\pi$
$673$	1.83941	−	12.7933i	0.0709039	−	0.493147i	0.994070	−	0.108745i	$-0.0346833\pi$
$674$	−45.1425	+	13.2550i	−1.73882	+	0.510565i
$675$	−1.88046	−	1.20850i	−0.0723790	−	0.0465152i
$676$	−27.4070	+	60.0129i	−1.05411	+	2.30819i
$677$	−7.73038	−	2.26984i	−0.297103	−	0.0872372i	0.129784	−	0.991542i	$-0.458572\pi$
$677$	−7.73038	−	2.26984i	−0.297103	−	0.0872372i	−0.426887	+	0.904305i	$0.640390\pi$
$678$	−15.4507	−	17.8310i	−0.593380	−	0.684797i
$679$	−4.48471	−	5.17563i	−0.172107	−	0.198623i
$680$	92.5894	+	27.1867i	3.55064	+	1.04256i
$681$	−7.17471	+	15.7104i	−0.274936	+	0.602025i
$682$	6.41047	+	4.11976i	0.245470	+	0.157754i
$683$	−18.2981	+	5.37279i	−0.700156	+	0.205584i	−0.612389	−	0.790557i	$-0.709791\pi$
$683$	−18.2981	+	5.37279i	−0.700156	+	0.205584i	−0.0877669	+	0.996141i	$0.527973\pi$
$684$	−6.01123	+	41.8090i	−0.229845	+	1.59861i
$685$	−19.7253	−	43.1923i	−0.753664	−	1.65029i
$686$	−0.383651	−	2.66835i	−0.0146478	−	0.101878i
$687$	−18.4147	+	11.8344i	−0.702566	+	0.451512i
$688$	58.7376	−	67.7868i	2.23935	−	2.58435i
$689$	4.83753			0.184295
$690$	34.7754	−	0.189576i	1.32388	−	0.00721704i
$691$	20.5627			0.782240			0.391120	−	0.920340i	$-0.372088\pi$
$691$	20.5627			0.782240			0.391120	+	0.920340i	$0.372088\pi$
$692$	−12.8706	+	14.8534i	−0.489266	+	0.564643i
$693$	−4.36512	+	2.80530i	−0.165817	+	0.106564i
$694$	6.07594	+	42.2591i	0.230640	+	1.60413i
$695$	−17.2434	−	37.7577i	−0.654078	−	1.43223i
$696$	3.91610	−	27.2371i	0.148439	−	1.03242i
$697$	−32.5738	+	9.56454i	−1.23382	+	0.362283i
$698$	48.2078	+	30.9813i	1.82469	+	1.17266i
$699$	6.29594	−	13.7862i	0.238134	−	0.521441i
$700$	−11.2971	−	3.31711i	−0.426988	−	0.125375i
$701$	15.9568	+	18.4152i	0.602681	+	0.695531i	0.972322	−	0.233643i	$-0.0750649\pi$
$701$	15.9568	+	18.4152i	0.602681	+	0.695531i	−0.369641	+	0.929175i	$0.620519\pi$
$702$	1.21612	+	1.40348i	0.0458996	+	0.0529709i
$703$	90.1941	+	26.4834i	3.40173	+	0.998839i
$704$	−47.6159	+	104.264i	−1.79459	+	3.92961i
$705$	−7.49681	−	4.81791i	−0.282346	−	0.181453i
$706$	−39.2439	+	11.5230i	−1.47696	+	0.433676i
$707$	−0.734867	+	5.11111i	−0.0276375	+	0.192223i
$708$	−23.3993	−	51.2374i	−0.879401	−	1.92562i
$709$	6.07126	+	42.2266i	0.228011	+	1.58585i	0.706471	+	0.707742i	$0.250286\pi$
$709$	6.07126	+	42.2266i	0.228011	+	1.58585i	−0.478460	+	0.878110i	$0.658805\pi$
$710$	−45.0361	+	28.9430i	−1.69018	+	1.08621i
$711$	5.24948	−	6.05823i	0.196871	−	0.227201i
$712$	−89.8592			−3.36762
$713$	1.72162	+	1.96511i	0.0644752	+	0.0735939i
$714$	−10.9801			−0.410920
$715$	−6.29636	+	7.26639i	−0.235471	+	0.271748i
$716$	52.0671	−	33.4615i	1.94584	−	1.25052i
$717$	−2.99465	−	20.8283i	−0.111837	−	0.777846i
$718$	15.9202	+	34.8604i	0.594136	+	1.30098i
$719$	−0.894131	+	6.21882i	−0.0333455	+	0.231923i	−0.999678	−	0.0253735i	$-0.991923\pi$
$719$	−0.894131	+	6.21882i	−0.0333455	+	0.231923i	0.966333	+	0.257296i	$0.0828316\pi$
$720$	34.0926	−	10.0105i	1.27056	−	0.373069i
$721$	3.26715	+	2.09967i	0.121675	+	0.0781957i
$722$	50.7375	−	111.100i	1.88825	−	4.13470i
$723$	9.63753	+	2.82983i	0.358424	+	0.105243i
$724$	2.03281	+	2.34599i	0.0755487	+	0.0871879i
$725$	−4.57319	−	5.27774i	−0.169844	−	0.196011i
$726$	41.1888	+	12.0941i	1.52866	+	0.448855i
$727$	−11.7749	+	25.7834i	−0.436706	+	0.956252i	0.555485	+	0.831526i	$0.312532\pi$
$727$	−11.7749	+	25.7834i	−0.436706	+	0.956252i	−0.992191	+	0.124726i	$0.960195\pi$
$728$	5.10435	+	3.28036i	0.189180	+	0.121578i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−6.10115	+	42.4344i	−0.225814	+	1.57057i
$731$	−11.4889	−	25.1573i	−0.424934	−	0.930476i
$732$	3.14082	+	21.8449i	0.116088	+	0.807409i
$733$	3.56447	−	2.29075i	0.131657	−	0.0846106i	−0.473155	−	0.880979i	$-0.656885\pi$
$733$	3.56447	−	2.29075i	0.131657	−	0.0846106i	0.604811	+	0.796369i	$0.293248\pi$
$734$	28.2939	−	32.6529i	1.04435	−	1.20524i
$735$	2.68985			0.0992167
$736$	−56.1573	+	65.5273i	−2.06998	+	2.41537i
$737$	0.674848			0.0248583
$738$	−14.7144	+	16.9813i	−0.541643	+	0.625089i
$739$	29.8504	−	19.1837i	1.09806	−	0.705683i	0.139403	−	0.990236i	$-0.455481\pi$
$739$	29.8504	−	19.1837i	1.09806	−	0.705683i	0.958660	+	0.284553i	$0.0918451\pi$
$740$	−23.6359	−	164.392i	−0.868874	−	6.04315i
$741$	−2.29484	−	5.02500i	−0.0843031	−	0.184598i
$742$	−2.69412	+	18.7380i	−0.0989043	+	0.687894i
$743$	−5.66628	+	1.66377i	−0.207876	+	0.0610378i	−0.384012	−	0.923328i	$-0.625458\pi$
$743$	−5.66628	+	1.66377i	−0.207876	+	0.0610378i	0.176137	+	0.984366i	$0.443640\pi$
$744$	4.03650	+	2.59410i	0.147985	+	0.0951044i
$745$	−17.8757	+	39.1422i	−0.654913	+	1.43406i
$746$	9.80797	+	2.87988i	0.359095	+	0.105440i
$747$	−0.124344	−	0.143501i	−0.00454951	−	0.00525041i
$748$	72.8995	+	84.1305i	2.66547	+	3.07612i
$749$	−7.25837	−	2.13125i	−0.265215	−	0.0778741i
$750$	−8.32804	+	18.2359i	−0.304097	+	0.665880i
$751$	19.9899	+	12.8467i	0.729441	+	0.468783i	0.851910	−	0.523689i	$-0.175445\pi$
$751$	19.9899	+	12.8467i	0.729441	+	0.468783i	−0.122468	+	0.992472i	$0.539081\pi$
$752$	41.9907	−	12.3296i	1.53124	−	0.449613i
$753$	0.213365	−	1.48399i	0.00777546	−	0.0540795i
$754$	2.41015	+	5.27748i	0.0877723	+	0.192195i
$755$	0.0671313	+	0.466908i	0.00244316	+	0.0169925i
$756$	−4.43111	+	2.84770i	−0.161158	+	0.103570i
$757$	−18.7996	+	21.6959i	−0.683283	+	0.788551i	−0.986393	−	0.164405i	$-0.947430\pi$
$757$	−18.7996	+	21.6959i	−0.683283	+	0.788551i	0.303110	+	0.952956i	$0.401975\pi$
$758$	−54.5426			−1.98108
$759$	21.0074	+	13.3394i	0.762521	+	0.484190i
$760$	−189.988			−6.89160
$761$	6.39567	−	7.38100i	0.231843	−	0.267561i	−0.627893	−	0.778300i	$-0.716083\pi$
$761$	6.39567	−	7.38100i	0.231843	−	0.267561i	0.859736	+	0.510739i	$0.170628\pi$
$762$	−14.2993	+	9.18957i	−0.518007	+	0.332903i
$763$	−1.82658	−	12.7042i	−0.0661268	−	0.459922i
$764$	31.1104	+	68.1222i	1.12553	+	2.46458i
$765$	1.55919	−	10.8444i	0.0563726	−	0.392080i
$766$	−59.0105	+	17.3271i	−2.13214	+	0.626052i
$767$	6.19734	+	3.98279i	0.223773	+	0.143810i
$768$	−8.03263	+	17.5890i	−0.289853	+	0.634689i
$769$	12.7375	+	3.74006i	0.459325	+	0.134870i	0.503206	−	0.864167i	$-0.332154\pi$
$769$	12.7375	+	3.74006i	0.459325	+	0.134870i	−0.0438802	+	0.999037i	$0.513972\pi$
$770$	−24.6396	−	28.4356i	−0.887948	−	1.02475i
$771$	−6.07890	−	7.01543i	−0.218926	−	0.252654i
$772$	3.09856	+	0.909818i	0.111519	+	0.0327451i
$773$	17.5794	−	38.4934i	0.632286	−	1.38451i	−0.273952	−	0.961743i	$-0.588331\pi$
$773$	17.5794	−	38.4934i	0.632286	−	1.38451i	0.906237	−	0.422769i	$-0.138942\pi$
$774$	−15.3989	−	9.89629i	−0.553503	−	0.355715i
$775$	1.16839	−	0.343070i	0.0419697	−	0.0123234i
$776$	−8.58433	+	59.7053i	−0.308160	+	2.14330i
$777$	4.86957	+	10.6629i	0.174695	+	0.382528i
$778$	−1.42332	−	9.89941i	−0.0510285	−	0.354911i
$779$	56.2291	−	36.1363i	2.01462	−	1.29472i
$780$	−6.39154	+	7.37623i	−0.228854	+	0.264112i
$781$	−38.3080			−1.37077
$782$	22.1360	+	47.7800i	0.791581	+	1.70861i
$783$	−3.12416			−0.111648
$784$	−8.65045	+	9.98315i	−0.308944	+	0.356541i
$785$	−18.3257	+	11.7772i	−0.654071	+	0.420346i
$786$	7.32199	+	50.9255i	0.261167	+	1.81645i
$787$	9.59939	+	21.0197i	0.342181	+	0.749273i	0.999992	−	0.00391031i	$-0.00124469\pi$
$787$	9.59939	+	21.0197i	0.342181	+	0.749273i	−0.657811	+	0.753183i	$0.728517\pi$
$788$	7.41765	−	51.5909i	0.264243	−	1.83785i
$789$	10.7370	−	3.15268i	0.382248	−	0.112238i
$790$	48.9000	+	31.4261i	1.73978	+	1.11809i
$791$	−3.63576	+	7.96121i	−0.129273	+	0.283068i
$792$	43.8513	+	12.8759i	1.55819	+	0.457525i
$793$	−1.89016	−	2.18136i	−0.0671215	−	0.0774623i
$794$	23.0805	+	26.6363i	0.819096	+	0.945287i
$795$	−18.1239	−	5.32166i	−0.642788	−	0.188740i
$796$	0.000106462	0	0.000233118i	3.77343e−6	0	8.26266e-6i
$797$	11.9274	+	7.66527i	0.422490	+	0.271518i	0.734563	−	0.678540i	$-0.237387\pi$
$797$	11.9274	+	7.66527i	0.422490	+	0.271518i	−0.312073	+	0.950058i	$0.601023\pi$
$798$	20.7422	−	6.09046i	0.734266	−	0.215600i
$799$	1.92040	−	13.3567i	0.0679389	−	0.472525i
$800$	16.7094	+	36.5884i	0.590766	+	1.29360i
$801$	1.45192	+	10.0983i	0.0513010	+	0.356806i
$802$	−57.5605	+	36.9919i	−2.03253	+	1.30623i
$803$	−20.0893	+	23.1843i	−0.708938	+	0.818158i
$804$	0.685049			0.0241598
$805$	−5.42278	−	11.7049i	−0.191128	−	0.412545i
$806$	−1.01166			−0.0356343
$807$	4.13861	−	4.77621i	0.145686	−	0.168131i
$808$	38.2610	−	24.5889i	1.34602	−	0.865033i
$809$	3.50650	+	24.3883i	0.123282	+	0.857446i	0.953797	+	0.300450i	$0.0971370\pi$
$809$	3.50650	+	24.3883i	0.123282	+	0.857446i	−0.830515	+	0.556996i	$0.811954\pi$
$810$	−3.01229	−	6.59599i	−0.105841	−	0.231759i
$811$	2.60416	−	18.1123i	0.0914443	−	0.636009i	−0.891625	−	0.452775i	$-0.850434\pi$
$811$	2.60416	−	18.1123i	0.0914443	−	0.636009i	0.983069	−	0.183234i	$-0.0586567\pi$
$812$	−15.7892	+	4.63613i	−0.554092	+	0.162696i
$813$	18.6172	+	11.9645i	0.652933	+	0.419614i
$814$	68.1155	−	149.152i	2.38745	−	5.22778i
$815$	16.5041	+	4.84604i	0.578114	+	0.169750i
$816$	35.2337	+	40.6619i	1.23343	+	1.42345i
$817$	35.6578	+	41.1513i	1.24751	+	1.43970i
$818$	−19.0267	−	5.58675i	−0.665253	−	0.195336i
$819$	0.286170	−	0.626626i	0.00999960	−	0.0218961i
$820$	−99.3454	−	63.8454i	−3.46929	−	2.22958i
$821$	24.6471	−	7.23703i	0.860189	−	0.252574i	0.178252	−	0.983985i	$-0.442956\pi$
$821$	24.6471	−	7.23703i	0.860189	−	0.252574i	0.681937	+	0.731411i	$0.261138\pi$
$822$	6.77249	−	47.1037i	0.236218	−	1.64293i
$823$	−15.0803	−	33.0213i	−0.525667	−	1.15105i	−0.967249	−	0.253830i	$-0.918310\pi$
$823$	−15.0803	−	33.0213i	−0.525667	−	1.15105i	0.441582	−	0.897221i	$-0.354418\pi$
$824$	−4.86813	−	33.8586i	−0.169589	−	1.17952i
$825$	9.75740	−	6.27070i	0.339709	−	0.218318i
$826$	−18.8786	+	21.7871i	−0.656871	+	0.758070i
$827$	17.9441			0.623978			0.311989	−	0.950086i	$-0.399005\pi$
$827$	17.9441			0.623978			0.311989	+	0.950086i	$0.399005\pi$
$828$	21.3250	+	13.5410i	0.741095	+	0.470584i
$829$	−31.0414			−1.07811			−0.539056	−	0.842270i	$-0.681219\pi$
$829$	−31.0414			−1.07811			−0.539056	+	0.842270i	$0.681219\pi$
$830$	0.901652	−	1.04056i	0.0312968	−	0.0361184i
$831$	19.4790	−	12.5184i	0.675720	−	0.434259i
$832$	−2.16567	−	15.0626i	−0.0750812	−	0.522202i
$833$	1.69201	+	3.70498i	0.0586246	+	0.128370i
$834$	5.92034	−	41.1769i	0.205005	−	1.42584i
$835$	12.1238	−	3.55987i	0.419562	−	0.123195i
$836$	−184.378	−	118.493i	−6.37686	−	4.09816i
$837$	0.226303	−	0.495534i	0.00782217	−	0.0171282i
$838$	−20.0182	−	5.87788i	−0.691518	−	0.203048i
$839$	3.61312	+	4.16976i	0.124739	+	0.143956i	0.814684	−	0.579906i	$-0.196911\pi$
$839$	3.61312	+	4.16976i	0.124739	+	0.143956i	−0.689945	+	0.723862i	$0.742365\pi$
$840$	−15.5149	−	17.9051i	−0.535314	−	0.617785i
$841$	18.4603	+	5.42043i	0.636562	+	0.186912i
$842$	−27.6810	+	60.6129i	−0.953949	+	2.08886i
$843$	−21.4671	−	13.7961i	−0.739366	−	0.475162i
$844$	−46.2704	+	13.5862i	−1.59269	+	0.467656i
$845$	−4.79482	+	33.3487i	−0.164947	+	1.14723i
$846$	−3.71013	−	8.12405i	−0.127557	−	0.279311i
$847$	−2.26622	−	15.7619i	−0.0778683	−	0.541586i
$848$	78.0365	−	50.1510i	2.67978	−	1.72219i
$849$	−11.4757	+	13.2437i	−0.393846	+	0.454522i
$850$	24.5439			0.841849
$851$	36.5825	−	42.6865i	1.25403	−	1.46327i
$852$	−38.8871			−1.33225
$853$	18.4066	−	21.2423i	0.630230	−	0.727324i	−0.347386	−	0.937722i	$-0.612931\pi$
$853$	18.4066	−	21.2423i	0.630230	−	0.727324i	0.977616	+	0.210398i	$0.0674760\pi$
$854$	9.50209	−	6.10662i	0.325155	−	0.208964i
$855$	3.06977	+	21.3507i	0.104984	+	0.730180i
$856$	27.6790	+	60.6085i	0.946048	+	2.07156i
$857$	−5.65681	+	39.3440i	−0.193233	+	1.34397i	0.630147	+	0.776476i	$0.282995\pi$
$857$	−5.65681	+	39.3440i	−0.193233	+	1.34397i	−0.823380	+	0.567490i	$0.807915\pi$
$858$	−9.24570	+	2.71478i	−0.315643	+	0.0926811i
$859$	1.29466	+	0.832029i	0.0441733	+	0.0283885i	0.562541	−	0.826769i	$-0.309824\pi$
$859$	1.29466	+	0.832029i	0.0441733	+	0.0283885i	−0.518368	+	0.855158i	$0.673460\pi$
$860$	39.9645	−	87.5100i	1.36278	−	2.98407i
$861$	7.99739	+	2.34825i	0.272550	+	0.0800280i
$862$	42.9729	+	49.5933i	1.46366	+	1.68916i
$863$	−20.9961	−	24.2308i	−0.714717	−	0.824828i	0.275944	−	0.961174i	$-0.411010\pi$
$863$	−20.9961	−	24.2308i	−0.714717	−	0.824828i	−0.990661	+	0.136346i	$0.956464\pi$
$864$	17.2656	+	5.06964i	0.587388	+	0.172473i
$865$	−4.16941	+	9.12973i	−0.141764	+	0.310420i
$866$	−44.7965	−	28.7890i	−1.52225	−	0.978289i
$867$	−0.393610	+	0.115574i	−0.0133677	+	0.00392511i
$868$	0.408360	−	2.84021i	0.0138606	−	0.0964029i
$869$	17.2790	+	37.8358i	0.586151	+	1.28349i
$870$	−3.22402	−	22.4235i	−0.109304	−	0.760229i
$871$	−0.0753712	+	0.0484382i	−0.00255386	+	0.00164126i
$872$	−74.0302	+	85.4354i	−2.50698	+	2.89321i
$873$	6.84834			0.231781
$874$	−68.3193	−	77.9816i	−2.31094	−	2.63777i
$875$	7.43661			0.251403
$876$	−20.3930	+	23.5348i	−0.689016	+	0.795167i
$877$	1.46213	−	0.939654i	0.0493726	−	0.0317299i	−0.515722	−	0.856756i	$-0.672476\pi$
$877$	1.46213	−	0.939654i	0.0493726	−	0.0317299i	0.565094	+	0.825026i	$0.308840\pi$
$878$	−6.04440	−	42.0397i	−0.203988	−	1.41877i
$879$	4.00818	+	8.77670i	0.135193	+	0.296031i
$880$	−26.2384	+	182.492i	−0.884498	+	6.15182i
$881$	18.0005	−	5.28543i	0.606453	−	0.178071i	0.0359325	−	0.999354i	$-0.488560\pi$
$881$	18.0005	−	5.28543i	0.606453	−	0.178071i	0.570520	+	0.821284i	$0.306742\pi$
$882$	2.26784	+	1.45745i	0.0763622	+	0.0490750i
$883$	−2.57541	+	5.63937i	−0.0866696	+	0.189780i	−0.948004	−	0.318259i	$-0.896902\pi$
$883$	−2.57541	+	5.63937i	−0.0866696	+	0.189780i	0.861334	+	0.508038i	$0.169629\pi$
$884$	−14.1805	−	4.16376i	−0.476940	−	0.140042i
$885$	−18.8371	−	21.7391i	−0.633201	−	0.730753i
$886$	35.8023	+	41.3181i	1.20280	+	1.38811i
$887$	−28.8850	−	8.48141i	−0.969864	−	0.284778i	−0.241830	−	0.970319i	$-0.577748\pi$
$887$	−28.8850	−	8.48141i	−0.969864	−	0.284778i	−0.728034	+	0.685541i	$0.759566\pi$
$888$	42.8905	−	93.9171i	1.43931	−	3.15165i
$889$	5.30429	+	3.40886i	0.177900	+	0.114330i
$890$	−70.9820	+	20.8422i	−2.37932	+	0.698632i
$891$	0.738448	−	5.13602i	0.0247389	−	0.172063i
$892$	−30.1068	−	65.9247i	−1.00805	−	2.20732i
$893$	3.78093	+	26.2970i	0.126524	+	0.879995i
$894$	−36.2797	+	23.3156i	−1.21338	+	0.779789i
$895$	20.6980	−	23.8868i	0.691858	−	0.798447i
$896$	23.5615			0.787135
$897$	−3.30370	+	0.0180099i	−0.110307	+	0.000601334i
$898$	26.3352			0.878817
$899$	1.11452	−	1.28623i	0.0371715	−	0.0428981i
$900$	9.90490	−	6.36549i	0.330163	−	0.212183i
$901$	−4.07054	−	28.3112i	−0.135609	−	0.943183i
$902$	−48.4333	−	106.054i	−1.61265	−	3.53122i
$903$	−0.966336	+	6.72101i	−0.0321576	+	0.223661i
$904$	73.9649	−	21.7181i	2.46004	−	0.722332i
$905$	1.33357	+	0.857036i	0.0443295	+	0.0284888i
$906$	−0.196388	+	0.430029i	−0.00652454	+	0.0142868i
$907$	7.13571	+	2.09523i	0.236937	+	0.0695711i	0.398045	−	0.917366i	$-0.369689\pi$
$907$	7.13571	+	2.09523i	0.236937	+	0.0695711i	−0.161108	+	0.986937i	$0.551507\pi$
$908$	−59.5740	−	68.7521i	−1.97703	−	2.28162i
$909$	−3.38149	−	3.90244i	−0.112157	−	0.129436i
$910$	4.79290	+	1.40732i	0.158883	+	0.0466523i
$911$	−2.53924	+	5.56017i	−0.0841289	+	0.184217i	−0.947021	−	0.321172i	$-0.895923\pi$
$911$	−2.53924	+	5.56017i	−0.0841289	+	0.184217i	0.862892	+	0.505388i	$0.168651\pi$
$912$	−89.1136	−	57.2698i	−2.95085	−	1.89639i
$913$	0.945339	−	0.277577i	0.0312862	−	0.00918644i
$914$	6.53189	−	45.4303i	0.216056	−	1.50270i
$915$	4.68185	+	10.2518i	0.154777	+	0.338915i
$916$	−16.4087	−	114.125i	−0.542159	−	3.77080i
$917$	16.0554	−	10.3182i	0.530195	−	0.340735i
$918$	7.19043	−	8.29820i	0.237320	−	0.273881i
$919$	16.2241			0.535183			0.267592	−	0.963532i	$-0.413772\pi$
$919$	16.2241			0.535183			0.267592	+	0.963532i	$0.413772\pi$
$920$	−46.6362	+	103.610i	−1.53755	+	3.41593i
$921$	20.3744			0.671358
$922$	62.6317	−	72.2808i	2.06266	−	2.38044i
$923$	4.27848	−	2.74961i	0.140828	−	0.0905045i
$924$	−3.88961	−	27.0528i	−0.127959	−	0.889972i
$925$	−10.8850	−	23.8348i	−0.357896	−	0.783684i
$926$	3.87895	−	26.9787i	0.127470	−	0.886575i
$927$	−3.72635	+	1.09415i	−0.122389	+	0.0359367i
$928$	47.2934	+	30.3936i	1.55248	+	0.997719i
$929$	6.81624	−	14.9255i	0.223633	−	0.489689i	−0.764244	−	0.644928i	$-0.776887\pi$
$929$	6.81624	−	14.9255i	0.223633	−	0.489689i	0.987877	+	0.155239i	$0.0496147\pi$
$930$	3.79021	+	1.11291i	0.124286	+	0.0364937i
$931$	−5.25142	−	6.06046i	−0.172108	−	0.198624i
$932$	52.2773	+	60.3312i	1.71240	+	1.97621i
$933$	1.44538	+	0.424401i	0.0473195	+	0.0138943i
$934$	6.53414	−	14.3078i	0.213804	−	0.468165i
$935$	47.8239	+	30.7346i	1.56401	+	1.00513i
$936$	−5.82177	+	1.70943i	−0.190291	+	0.0558743i
$937$	−1.29039	+	8.97485i	−0.0421552	+	0.293196i	0.957828	+	0.287343i	$0.0927720\pi$
$937$	−1.29039	+	8.97485i	−0.0421552	+	0.293196i	−0.999983	+	0.00585250i	$0.998137\pi$
$938$	−0.145648	−	0.318924i	−0.00475557	−	0.0104132i
$939$	−4.26587	−	29.6697i	−0.139211	−	0.968236i
$940$	39.4877	−	25.3772i	1.28795	−	0.827714i
$941$	−16.2330	+	18.7338i	−0.529180	+	0.610706i	−0.955905	−	0.293675i	$-0.905122\pi$
$941$	−16.2330	+	18.7338i	−0.529180	+	0.610706i	0.426726	+	0.904381i	$0.359667\pi$
$942$	−21.8318			−0.711319
$943$	−5.90441	−	39.5349i	−0.192274	−	1.28743i
$944$	141.262			4.59768
$945$	−1.76148	+	2.03286i	−0.0573009	+	0.0661288i
$946$	79.9024	−	51.3502i	2.59785	−	1.66954i
$947$	4.52800	+	31.4929i	0.147140	+	1.02338i	0.920871	+	0.389868i	$0.127479\pi$
$947$	4.52800	+	31.4929i	0.147140	+	1.02338i	−0.773731	+	0.633515i	$0.781612\pi$
$948$	17.5402	+	38.4078i	0.569680	+	1.24743i
$949$	0.579615	−	4.03131i	0.0188151	−	0.130862i
$950$	−46.3653	+	13.6141i	−1.50429	+	0.441699i
$951$	23.1822	+	14.8983i	0.751735	+	0.483111i
$952$	14.9030	−	32.6330i	0.483008	−	1.05764i
$953$	46.8908	+	13.7684i	1.51894	+	0.446002i	0.931645	−	0.363369i	$-0.118374\pi$
$953$	46.8908	+	13.7684i	1.51894	+	0.446002i	0.587297	+	0.809371i	$0.300192\pi$
$954$	−12.3970	−	14.3069i	−0.401367	−	0.463202i
$955$	25.0447	+	28.9031i	0.810426	+	0.935281i
$956$	106.347	+	31.2262i	3.43949	+	1.00993i
$957$	6.73418	−	14.7458i	0.217685	−	0.476664i
$958$	36.7807	+	23.6375i	1.18833	+	0.763694i
$959$	−16.9377	+	4.97335i	−0.546947	+	0.160598i
$960$	−8.45628	+	58.8147i	−0.272925	+	1.89824i
$961$	−12.7546	−	27.9286i	−0.411438	−	0.900924i
$962$	3.09804	+	21.5473i	0.0998848	+	0.694714i
$963$	6.36391	−	4.08984i	0.205074	−	0.131793i
$964$	−34.6464	+	39.9841i	−1.11589	+	1.28780i
$965$	1.64915			0.0530881
$966$	1.77014	−	12.8068i	0.0569532	−	0.412052i
$967$	37.1964			1.19616			0.598078	−	0.801438i	$-0.295931\pi$
$967$	37.1964			1.19616			0.598078	+	0.801438i	$0.295931\pi$
$968$	−91.8484	+	105.999i	−2.95212	+	3.40693i
$969$	−27.4773	+	17.6586i	−0.882700	+	0.567277i
$970$	7.06724	+	49.1537i	0.226915	+	1.57823i
$971$	5.08927	+	11.1440i	0.163323	+	0.357627i	0.973545	−	0.228496i	$-0.0733809\pi$
$971$	5.08927	+	11.1440i	0.163323	+	0.357627i	−0.810222	+	0.586123i	$0.800654\pi$
$972$	0.749611	−	5.21366i	0.0240438	−	0.167228i
$973$	−14.8065	+	4.34759i	−0.474675	+	0.139377i
$974$	37.0567	+	23.8149i	1.18737	+	0.763078i
$975$	−0.639679	+	1.40070i	−0.0204861	+	0.0448584i
$976$	−53.1053	−	15.5931i	−1.69986	−	0.499124i
$977$	−12.1928	−	14.0712i	−0.390082	−	0.450178i	0.526411	−	0.850230i	$-0.323537\pi$
$977$	−12.1928	−	14.0712i	−0.390082	−	0.450178i	−0.916492	+	0.400052i	$0.868992\pi$
$978$	11.2890	+	13.0282i	0.360983	+	0.416597i
$979$	−50.7930	−	14.9142i	−1.62335	−	0.476659i
$980$	−5.88568	+	12.8878i	−0.188011	+	0.411687i
$981$	10.7973	+	6.93902i	0.344732	+	0.221546i
$982$	94.2567	−	27.6763i	3.00785	−	0.883185i
$983$	4.57707	−	31.8343i	0.145986	−	1.01535i	−0.776719	−	0.629848i	$-0.783117\pi$
$983$	4.57707	−	31.8343i	0.145986	−	1.01535i	0.922705	−	0.385507i	$-0.125974\pi$
$984$	−30.4972	−	66.7795i	−0.972215	−	2.12885i
$985$	−3.78800	−	26.3461i	−0.120696	−	0.839456i
$986$	28.8580	−	18.5459i	0.919025	−	0.590621i
$987$	−2.16955	+	2.50380i	−0.0690576	+	0.0796968i
$988$	29.0975			0.925715
$989$	31.1947	−	9.34461i	0.991935	−	0.297141i
$990$	37.6256			1.19582
$991$	29.2563	−	33.7636i	0.929357	−	1.07253i	−0.0678388	−	0.997696i	$-0.521610\pi$
$991$	29.2563	−	33.7636i	0.929357	−	1.07253i	0.997196	−	0.0748386i	$-0.0238442\pi$
$992$	−8.24660	+	5.29977i	−0.261830	+	0.168268i
$993$	4.11135	+	28.5950i	0.130470	+	0.907436i
$994$	8.26776	+	18.1039i	0.262237	+	0.574220i
$995$	1.86253e−5	0	0.000129542i	5.90463e−7	0	4.10676e-6i
$996$	0.959629	−	0.281773i	0.0304070	−	0.00892830i
$997$	43.1851	+	27.7534i	1.36768	+	0.878957i	0.998725	−	0.0504879i	$-0.0160776\pi$
$997$	43.1851	+	27.7534i	1.36768	+	0.878957i	0.368960	+	0.929445i	$0.379714\pi$
$998$	17.9991	−	39.4125i	0.569751	−	1.24758i
$999$	−11.2474	−	3.30252i	−0.355850	−	0.104487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.d.85.1	✓	60
23.13	even	11	inner	483.2.q.d.358.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.d.85.1	✓	60	1.1	even	1	trivial
483.2.q.d.358.1	yes	60	23.13	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76537 + 2.03734i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.749611 - 5.21366i) q^{4} +(-1.11741 - 2.44678i) q^{5} +(0.383651 - 2.66835i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(7.40965 + 4.76189i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-1.76537 + 2.03734i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.749611 - 5.21366i) q^{4} +(-1.11741 - 2.44678i) q^{5} +(0.383651 - 2.66835i) q^{6} +(-0.959493 + 0.281733i) q^{7} +(7.40965 + 4.76189i) q^{8} +(0.415415 - 0.909632i) q^{9} +(6.95754 + 2.04292i) q^{10} +(3.39796 + 3.92146i) q^{11} +(3.44933 + 3.98074i) q^{12} +(-0.660974 - 0.194079i) q^{13} +(1.11987 - 2.45217i) q^{14} +(2.26285 + 1.45424i) q^{15} +(-12.6745 + 3.72157i) q^{16} +(-0.579656 + 4.03160i) q^{17} +(1.11987 + 2.45217i) q^{18} +(-1.14124 - 7.93751i) q^{19} +(-11.9190 + 7.65990i) q^{20} +(0.654861 - 0.755750i) q^{21} -13.9880 q^{22} +(-4.60886 - 1.32604i) q^{23} -8.80787 q^{24} +(-1.46382 + 1.68933i) q^{25} +(1.56227 - 1.00401i) q^{26} +(0.142315 + 0.989821i) q^{27} +(2.18810 + 4.79128i) q^{28} +(-0.444614 + 3.09236i) q^{29} +(-6.95754 + 2.04292i) q^{30} +(-0.458284 - 0.294521i) q^{31} +(7.47520 - 16.3684i) q^{32} +(-4.97865 - 1.46186i) q^{33} +(-7.19043 - 8.29820i) q^{34} +(1.76148 + 2.03286i) q^{35} +(-5.05391 - 1.48396i) q^{36} +(-4.86957 + 10.6629i) q^{37} +(18.1861 + 11.6875i) q^{38} +(0.660974 - 0.194079i) q^{39} +(3.37170 - 23.4507i) q^{40} +(3.46249 + 7.58180i) q^{41} +(0.383651 + 2.66835i) q^{42} +(-5.71222 + 3.67102i) q^{43} +(17.8980 - 20.6554i) q^{44} -2.68985 q^{45} +(10.8379 - 7.04888i) q^{46} -3.31300 q^{47} +(8.65045 - 9.98315i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.857578 - 5.96458i) q^{50} +(-1.69201 - 3.70498i) q^{51} +(-0.516391 + 3.59158i) q^{52} +(-6.73788 + 1.97842i) q^{53} +(-2.26784 - 1.45745i) q^{54} +(5.79803 - 12.6959i) q^{55} +(-8.45109 - 2.48146i) q^{56} +(5.25142 + 6.06046i) q^{57} +(-5.51528 - 6.36497i) q^{58} +(-10.2607 - 3.01282i) q^{59} +(5.88568 - 12.8878i) q^{60} +(3.52479 + 2.26525i) q^{61} +(1.40908 - 0.413743i) q^{62} +(-0.142315 + 0.989821i) q^{63} +(9.17662 + 20.0940i) q^{64} +(0.263707 + 1.83412i) q^{65} +(11.7674 - 7.56248i) q^{66} +(0.0851697 - 0.0982911i) q^{67} +21.4539 q^{68} +(4.59413 - 1.37621i) q^{69} -7.25127 q^{70} +(-4.83469 + 5.57953i) q^{71} +(7.40965 - 4.76189i) q^{72} +(0.841390 + 5.85199i) q^{73} +(-13.1273 - 28.7448i) q^{74} +(0.318118 - 2.21256i) q^{75} +(-40.5280 + 11.9001i) q^{76} +(-4.36512 - 2.80530i) q^{77} +(-0.771455 + 1.68925i) q^{78} +(7.69147 + 2.25842i) q^{79} +(23.2684 + 26.8532i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-21.5593 - 6.33037i) q^{82} +(0.0788784 - 0.172720i) q^{83} +(-4.43111 - 2.84770i) q^{84} +(10.5121 - 3.08664i) q^{85} +(2.60504 - 18.1184i) q^{86} +(-1.29782 - 2.84183i) q^{87} +(6.50415 + 45.2374i) q^{88} +(-8.58260 + 5.51570i) q^{89} +(4.74857 - 5.48015i) q^{90} +0.688878 q^{91} +(-3.45865 + 25.0230i) q^{92} +0.544763 q^{93} +(5.84865 - 6.74971i) q^{94} +(-18.1461 + 11.6618i) q^{95} +(2.56089 + 17.8114i) q^{96} +(2.84490 + 6.22947i) q^{97} +(-0.383651 + 2.66835i) q^{98} +(4.97865 - 1.46186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9	\( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 60 * q - q^2 + 6 * q^3 - 3 * q^4 - 13 * q^5 + 12 * q^6 - 6 * q^7 + 25 * q^8 - 6 * q^9 + 5 * q^11 + 3 * q^12 + 22 * q^13 - q^14 + 2 * q^15 - 27 * q^16 + q^17 - q^18 + 20 * q^19 - 75 * q^20 + 6 * q^21 - 16 * q^22 - 9 * q^23 - 36 * q^24 - 15 * q^25 - 16 * q^26 + 6 * q^27 - 14 * q^28 - 3 * q^29 + 17 * q^31 - 73 * q^32 - 5 * q^33 + 55 * q^34 - 2 * q^35 - 14 * q^36 + 56 * q^37 - 22 * q^38 - 22 * q^39 - 37 * q^40 - 18 * q^41 + 12 * q^42 - 19 * q^43 - 12 * q^44 + 20 * q^45 - 45 * q^46 + 42 * q^47 - 28 * q^48 - 6 * q^49 - 42 * q^50 - q^51 + 76 * q^52 - 11 * q^53 - 10 * q^54 - 61 * q^55 + 3 * q^56 + 24 * q^57 - 78 * q^58 + 38 * q^59 + 31 * q^60 + 5 * q^61 + 69 * q^62 - 6 * q^63 - 27 * q^64 + 51 * q^65 + 49 * q^66 - 27 * q^67 + 112 * q^68 - 13 * q^69 + 22 * q^70 - 4 * q^71 + 25 * q^72 + 48 * q^73 - 62 * q^74 + 26 * q^75 - 85 * q^76 - 28 * q^77 - 6 * q^78 - 6 * q^79 + 169 * q^80 - 6 * q^81 - 200 * q^82 - 6 * q^83 + 3 * q^84 - 21 * q^85 - 180 * q^86 + 14 * q^87 + 211 * q^88 - 57 * q^89 - 22 * q^91 + 49 * q^92 - 50 * q^93 + 16 * q^94 + 56 * q^95 + 7 * q^96 - 52 * q^97 - 12 * q^98 + 5 * q^99

Introduction

L-functions

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