LMFDB - Embedded newform 273.2.bh.a.131.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.13
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.734739 - 0.424202i) q^{2} +(0.243844 - 1.71480i) q^{3} +(-0.640106 - 1.10870i) q^{4} +(-1.44264 + 2.49872i) q^{5} +(-0.906583 + 1.15649i) q^{6} +(-1.51284 + 2.17056i) q^{7} +2.78294i q^{8} +(-2.88108 - 0.836289i) q^{9} +O(q^{10})$	\(q+(-0.734739 - 0.424202i) q^{2} +(0.243844 - 1.71480i) q^{3} +(-0.640106 - 1.10870i) q^{4} +(-1.44264 + 2.49872i) q^{5} +(-0.906583 + 1.15649i) q^{6} +(-1.51284 + 2.17056i) q^{7} +2.78294i q^{8} +(-2.88108 - 0.836289i) q^{9} +(2.11992 - 1.22394i) q^{10} +(-1.29721 + 0.748942i) q^{11} +(-2.05728 + 0.827304i) q^{12} +1.00000i q^{13} +(2.03230 - 0.953044i) q^{14} +(3.93303 + 3.08313i) q^{15} +(-0.0996816 + 0.172654i) q^{16} +(-0.812718 - 1.40767i) q^{17} +(1.76209 + 1.83661i) q^{18} +(-1.58307 - 0.913984i) q^{19} +3.69376 q^{20} +(3.35317 + 3.12349i) q^{21} +1.27081 q^{22} +(2.10587 + 1.21582i) q^{23} +(4.77219 + 0.678605i) q^{24} +(-1.66240 - 2.87936i) q^{25} +(0.424202 - 0.734739i) q^{26} +(-2.13660 + 4.73655i) q^{27} +(3.37486 + 0.287891i) q^{28} -3.71033i q^{29} +(-1.58188 - 3.93370i) q^{30} +(-8.38619 + 4.84177i) q^{31} +(4.96668 - 2.86751i) q^{32} +(0.967969 + 2.40707i) q^{33} +1.37903i q^{34} +(-3.24114 - 6.91149i) q^{35} +(0.917005 + 3.72955i) q^{36} +(-0.936328 + 1.62177i) q^{37} +(0.775428 + 1.34308i) q^{38} +(1.71480 + 0.243844i) q^{39} +(-6.95380 - 4.01478i) q^{40} -8.73497 q^{41} +(-1.13872 - 3.71738i) q^{42} -6.95036 q^{43} +(1.66070 + 0.958804i) q^{44} +(6.24600 - 5.99255i) q^{45} +(-1.03151 - 1.78663i) q^{46} +(-1.24667 + 2.15929i) q^{47} +(0.271760 + 0.213035i) q^{48} +(-2.42264 - 6.56741i) q^{49} +2.82077i q^{50} +(-2.61205 + 1.05040i) q^{51} +(1.10870 - 0.640106i) q^{52} +(1.76288 - 1.01780i) q^{53} +(3.57910 - 2.57378i) q^{54} -4.32180i q^{55} +(-6.04054 - 4.21014i) q^{56} +(-1.95332 + 2.49177i) q^{57} +(-1.57393 + 2.72612i) q^{58} +(7.41271 + 12.8392i) q^{59} +(0.900703 - 6.33406i) q^{60} +(7.29866 + 4.21389i) q^{61} +8.21555 q^{62} +(6.17382 - 4.98838i) q^{63} -4.46689 q^{64} +(-2.49872 - 1.44264i) q^{65} +(0.309880 - 2.17919i) q^{66} +(-7.19942 - 12.4698i) q^{67} +(-1.04045 + 1.80211i) q^{68} +(2.59840 - 3.31467i) q^{69} +(-0.550474 + 6.45304i) q^{70} -10.1763i q^{71} +(2.32735 - 8.01788i) q^{72} +(13.6322 - 7.87057i) q^{73} +(1.37591 - 0.794384i) q^{74} +(-5.34290 + 2.14857i) q^{75} +2.34019i q^{76} +(0.336841 - 3.94869i) q^{77} +(-1.15649 - 0.906583i) q^{78} +(-4.62175 + 8.00511i) q^{79} +(-0.287609 - 0.498153i) q^{80} +(7.60124 + 4.81883i) q^{81} +(6.41793 + 3.70539i) q^{82} -12.4457 q^{83} +(1.31662 - 5.71702i) q^{84} +4.68982 q^{85} +(5.10670 + 2.94836i) q^{86} +(-6.36248 - 0.904744i) q^{87} +(-2.08426 - 3.61005i) q^{88} +(1.78870 - 3.09812i) q^{89} +(-7.13123 + 1.75339i) q^{90} +(-2.17056 - 1.51284i) q^{91} -3.11302i q^{92} +(6.25774 + 15.5613i) q^{93} +(1.83195 - 1.05768i) q^{94} +(4.56758 - 2.63709i) q^{95} +(-3.70612 - 9.21609i) q^{96} +1.31690i q^{97} +(-1.00590 + 5.85302i) q^{98} +(4.36368 - 1.07292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.734739	−	0.424202i	−0.519539	−	0.299956i	0.217207	−	0.976126i	$-0.430305\pi$
$2$	−0.734739	−	0.424202i	−0.519539	−	0.299956i	−0.736746	+	0.676170i	$0.763639\pi$
$3$	0.243844	−	1.71480i	0.140784	−	0.990040i
$3$	0.243844	−	1.71480i	0.140784	−	0.990040i
$4$	−0.640106	−	1.10870i	−0.320053	−	0.554348i
$5$	−1.44264	+	2.49872i	−0.645167	+	1.11746i	0.339096	+	0.940752i	$0.389879\pi$
$5$	−1.44264	+	2.49872i	−0.645167	+	1.11746i	−0.984263	+	0.176710i	$0.943455\pi$
$6$	−0.906583	+	1.15649i	−0.370111	+	0.472136i
$7$	−1.51284	+	2.17056i	−0.571799	+	0.820394i
$7$	−1.51284	+	2.17056i	−0.571799	+	0.820394i
$8$			2.78294i			0.983919i
$9$	−2.88108	−	0.836289i	−0.960360	−	0.278763i
$10$	2.11992	−	1.22394i	0.670379	−	0.387043i
$11$	−1.29721	+	0.748942i	−0.391122	+	0.225814i	−0.682646	−	0.730749i	$-0.739171\pi$
$11$	−1.29721	+	0.748942i	−0.391122	+	0.225814i	0.291524	+	0.956563i	$0.405838\pi$
$12$	−2.05728	+	0.827304i	−0.593885	+	0.238822i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	2.03230	−	0.953044i	0.543154	−	0.254712i
$15$	3.93303	+	3.08313i	1.01550	+	0.796061i
$16$	−0.0996816	+	0.172654i	−0.0249204	+	0.0431634i
$17$	−0.812718	−	1.40767i	−0.197113	−	0.341410i	0.750478	−	0.660895i	$-0.229823\pi$
$17$	−0.812718	−	1.40767i	−0.197113	−	0.341410i	−0.947591	+	0.319486i	$0.896490\pi$
$18$	1.76209	+	1.83661i	0.415328	+	0.432894i
$19$	−1.58307	−	0.913984i	−0.363180	−	0.209682i	0.307295	−	0.951614i	$-0.400576\pi$
$19$	−1.58307	−	0.913984i	−0.363180	−	0.209682i	−0.670475	+	0.741932i	$0.733910\pi$
$20$	3.69376			0.825950
$21$	3.35317	+	3.12349i	0.731723	+	0.681602i
$22$	1.27081			0.270938
$23$	2.10587	+	1.21582i	0.439104	+	0.253517i	0.703218	−	0.710975i	$-0.251746\pi$
$23$	2.10587	+	1.21582i	0.439104	+	0.253517i	−0.264113	+	0.964492i	$0.585079\pi$
$24$	4.77219	+	0.678605i	0.974120	+	0.138520i
$25$	−1.66240	−	2.87936i	−0.332480	−	0.575873i
$26$	0.424202	−	0.734739i	0.0831928	−	0.144094i
$27$	−2.13660	+	4.73655i	−0.411190	+	0.911550i
$28$	3.37486	+	0.287891i	0.637789	+	0.0544064i
$29$		−	3.71033i		−	0.688991i	−0.938788	−	0.344496i	$-0.888050\pi$
$29$		−	3.71033i		−	0.688991i	0.938788	−	0.344496i	$-0.111950\pi$
$30$	−1.58188	−	3.93370i	−0.288810	−	0.718191i
$31$	−8.38619	+	4.84177i	−1.50620	+	0.869608i	−0.506230	+	0.862398i	$0.668961\pi$
$31$	−8.38619	+	4.84177i	−1.50620	+	0.869608i	−0.999974	+	0.00720922i	$0.997705\pi$
$32$	4.96668	−	2.86751i	0.877993	−	0.506910i
$33$	0.967969	+	2.40707i	0.168502	+	0.419018i
$34$			1.37903i			0.236501i
$35$	−3.24114	−	6.91149i	−0.547852	−	1.16825i
$36$	0.917005	+	3.72955i	0.152834	+	0.621592i
$37$	−0.936328	+	1.62177i	−0.153931	+	0.266617i	−0.932669	−	0.360732i	$-0.882527\pi$
$37$	−0.936328	+	1.62177i	−0.153931	+	0.266617i	0.778738	+	0.627349i	$0.215860\pi$
$38$	0.775428	+	1.34308i	0.125791	+	0.217876i
$39$	1.71480	+	0.243844i	0.274588	+	0.0390464i
$40$	−6.95380	−	4.01478i	−1.09949	−	0.634792i
$41$	−8.73497			−1.36417			−0.682087	−	0.731271i	$-0.738927\pi$
$41$	−8.73497			−1.36417			−0.682087	+	0.731271i	$0.738927\pi$
$42$	−1.13872	−	3.71738i	−0.175708	−	0.573604i
$43$	−6.95036			−1.05992			−0.529960	−	0.848023i	$-0.677793\pi$
$43$	−6.95036			−1.05992			−0.529960	+	0.848023i	$0.677793\pi$
$44$	1.66070	+	0.958804i	0.250359	+	0.144545i
$45$	6.24600	−	5.99255i	0.931099	−	0.893317i
$46$	−1.03151	−	1.78663i	−0.152088	−	0.263424i
$47$	−1.24667	+	2.15929i	−0.181845	+	0.314964i	−0.942509	−	0.334181i	$-0.891540\pi$
$47$	−1.24667	+	2.15929i	−0.181845	+	0.314964i	0.760664	+	0.649146i	$0.224874\pi$
$48$	0.271760	+	0.213035i	0.0392251	+	0.0307489i
$49$	−2.42264	−	6.56741i	−0.346091	−	0.938201i
$50$			2.82077i			0.398918i
$51$	−2.61205	+	1.05040i	−0.365760	+	0.147085i
$52$	1.10870	−	0.640106i	0.153748	−	0.0887667i
$53$	1.76288	−	1.01780i	0.242150	−	0.139805i	−0.374014	−	0.927423i	$-0.622019\pi$
$53$	1.76288	−	1.01780i	0.242150	−	0.139805i	0.616165	+	0.787617i	$0.288686\pi$
$54$	3.57910	−	2.57378i	0.487054	−	0.350247i
$55$		−	4.32180i		−	0.582752i
$56$	−6.04054	−	4.21014i	−0.807201	−	0.562604i
$57$	−1.95332	+	2.49177i	−0.258724	+	0.330043i
$58$	−1.57393	+	2.72612i	−0.206667	+	0.357958i
$59$	7.41271	+	12.8392i	0.965052	+	1.67152i	0.709474	+	0.704731i	$0.248933\pi$
$59$	7.41271	+	12.8392i	0.965052	+	1.67152i	0.255578	+	0.966788i	$0.417734\pi$
$60$	0.900703	−	6.33406i	0.116280	−	0.817724i
$61$	7.29866	+	4.21389i	0.934498	+	0.539533i	0.888231	−	0.459396i	$-0.151934\pi$
$61$	7.29866	+	4.21389i	0.934498	+	0.539533i	0.0462667	+	0.998929i	$0.485268\pi$
$62$	8.21555			1.04338
$63$	6.17382	−	4.98838i	0.777828	−	0.628477i
$64$	−4.46689			−0.558361
$65$	−2.49872	−	1.44264i	−0.309928	−	0.178937i
$66$	0.309880	−	2.17919i	0.0381436	−	0.268239i
$67$	−7.19942	−	12.4698i	−0.879550	−	1.52342i	−0.851836	−	0.523809i	$-0.824511\pi$
$67$	−7.19942	−	12.4698i	−0.879550	−	1.52342i	−0.0277136	−	0.999616i	$-0.508823\pi$
$68$	−1.04045	+	1.80211i	−0.126173	+	0.218538i
$69$	2.59840	−	3.31467i	0.312811	−	0.399040i
$70$	−0.550474	+	6.45304i	−0.0657942	+	0.771285i
$71$		−	10.1763i		−	1.20770i	−0.797098	−	0.603850i	$-0.793633\pi$
$71$		−	10.1763i		−	1.20770i	0.797098	−	0.603850i	$-0.206367\pi$
$72$	2.32735	−	8.01788i	0.274280	−	0.944916i
$73$	13.6322	−	7.87057i	1.59553	−	0.921181i	0.603199	−	0.797591i	$-0.293893\pi$
$73$	13.6322	−	7.87057i	1.59553	−	0.921181i	0.992333	−	0.123590i	$-0.0394408\pi$
$74$	1.37591	−	0.794384i	0.159947	−	0.0923453i
$75$	−5.34290	+	2.14857i	−0.616945	+	0.248095i
$76$			2.34019i			0.268438i
$77$	0.336841	−	3.94869i	0.0383866	−	0.449995i
$78$	−1.15649	−	0.906583i	−0.130947	−	0.102650i
$79$	−4.62175	+	8.00511i	−0.519988	+	0.900645i	0.479742	+	0.877410i	$0.340730\pi$
$79$	−4.62175	+	8.00511i	−0.519988	+	0.900645i	−0.999730	+	0.0232359i	$0.992603\pi$
$80$	−0.287609	−	0.498153i	−0.0321556	−	0.0556952i
$81$	7.60124	+	4.81883i	0.844582	+	0.535426i
$82$	6.41793	+	3.70539i	0.708741	+	0.409192i
$83$	−12.4457			−1.36609			−0.683047	−	0.730375i	$-0.739345\pi$
$83$	−12.4457			−1.36609			−0.683047	+	0.730375i	$0.739345\pi$
$84$	1.31662	−	5.71702i	0.143655	−	0.623778i
$85$	4.68982			0.508683
$86$	5.10670	+	2.94836i	0.550670	+	0.317929i
$87$	−6.36248	−	0.904744i	−0.682129	−	0.0969987i
$88$	−2.08426	−	3.61005i	−0.222183	−	0.384832i
$89$	1.78870	−	3.09812i	0.189602	−	0.328400i	−0.755516	−	0.655131i	$-0.772614\pi$
$89$	1.78870	−	3.09812i	0.189602	−	0.328400i	0.945118	+	0.326731i	$0.105947\pi$
$90$	−7.13123	+	1.75339i	−0.751698	+	0.184824i
$91$	−2.17056	−	1.51284i	−0.227536	−	0.158589i
$92$		−	3.11302i		−	0.324555i
$93$	6.25774	+	15.5613i	0.648898	+	1.61363i
$94$	1.83195	−	1.05768i	0.188951	−	0.109091i
$95$	4.56758	−	2.63709i	0.468624	−	0.270560i
$96$	−3.70612	−	9.21609i	−0.378254	−	0.940613i
$97$			1.31690i			0.133711i	0.997763	+	0.0668554i	$0.0212966\pi$
$97$			1.31690i			0.133711i	−0.997763	+	0.0668554i	$0.978703\pi$
$98$	−1.00590	+	5.85302i	−0.101611	+	0.591244i
$99$	4.36368	−	1.07292i	0.438567	−	0.107833i
$100$	−2.12822	+	3.68619i	−0.212822	+	0.368619i
$101$	5.63250	+	9.75577i	0.560454	+	0.970735i	0.997457	+	0.0712749i	$0.0227068\pi$
$101$	5.63250	+	9.75577i	0.560454	+	0.970735i	−0.437002	+	0.899460i	$0.643960\pi$
$102$	2.36475	+	0.336268i	0.234145	+	0.0332955i
$103$	6.04261	+	3.48870i	0.595396	+	0.343752i	0.767228	−	0.641374i	$-0.221635\pi$
$103$	6.04261	+	3.48870i	0.595396	+	0.343752i	−0.171832	+	0.985126i	$0.554969\pi$
$104$	−2.78294			−0.272890
$105$	−12.6422	+	3.87258i	−1.23375	+	0.377925i
$106$	−1.72701			−0.167742
$107$	1.30816	+	0.755267i	0.126465	+	0.0730145i	0.561898	−	0.827207i	$-0.310071\pi$
$107$	1.30816	+	0.755267i	0.126465	+	0.0730145i	−0.435433	+	0.900221i	$0.643405\pi$
$108$	6.61905	−	0.663050i	0.636918	−	0.0638020i
$109$	−6.30615	−	10.9226i	−0.604020	−	1.04619i	−0.992206	−	0.124612i	$-0.960231\pi$
$109$	−6.30615	−	10.9226i	−0.604020	−	1.04619i	0.388186	−	0.921581i	$-0.373102\pi$
$110$	−1.83332	+	3.17540i	−0.174800	+	0.302762i
$111$	2.55269	+	2.00108i	0.242291	+	0.189934i
$112$	−0.223952	−	0.477562i	−0.0211615	−	0.0451254i
$113$		−	4.59986i		−	0.432719i	−0.976314	−	0.216359i	$-0.930582\pi$
$113$		−	4.59986i		−	0.432719i	0.976314	−	0.216359i	$-0.0694183\pi$
$114$	2.49220	−	1.00220i	0.233416	−	0.0938647i
$115$	−6.07601	+	3.50799i	−0.566591	+	0.327121i
$116$	−4.11363	+	2.37500i	−0.381941	+	0.220514i
$117$	0.836289	−	2.88108i	0.0773150	−	0.266356i
$118$		−	12.5779i		−	1.15789i
$119$	4.28493	+	0.365525i	0.392799	+	0.0335076i
$120$	−8.58018	+	10.9454i	−0.783260	+	0.999173i
$121$	−4.37817	+	7.58322i	−0.398016	+	0.689383i
$122$	−3.57508	−	6.19221i	−0.323672	−	0.560617i
$123$	−2.12997	+	14.9787i	−0.192053	+	1.35059i
$124$	10.7361	+	6.19849i	0.964130	+	0.556641i
$125$	−4.83340			−0.432313
$126$	−6.65223	+	1.04621i	−0.592628	+	0.0932038i
$127$	13.9505			1.23790			0.618952	−	0.785429i	$-0.287557\pi$
$127$	13.9505			1.23790			0.618952	+	0.785429i	$0.287557\pi$
$128$	−6.65136	−	3.84016i	−0.587903	−	0.339426i
$129$	−1.69481	+	11.9185i	−0.149219	+	1.04936i
$130$	1.22394	+	2.11992i	0.107346	+	0.185930i
$131$	−10.7990	+	18.7044i	−0.943514	+	1.63421i	−0.184815	+	0.982773i	$0.559169\pi$
$131$	−10.7990	+	18.7044i	−0.943514	+	1.63421i	−0.758699	+	0.651441i	$0.774165\pi$
$132$	2.04911	−	2.61396i	0.178352	−	0.227516i
$133$	4.37878	−	2.05343i	0.379688	−	0.178055i
$134$			12.2160i			1.05530i
$135$	−8.75297	−	12.1719i	−0.753336	−	1.04759i
$136$	3.91746	−	2.26175i	0.335919	−	0.193943i
$137$	−3.11243	+	1.79696i	−0.265913	+	0.153525i	−0.627029	−	0.778996i	$-0.715729\pi$
$137$	−3.11243	+	1.79696i	−0.265913	+	0.153525i	0.361116	+	0.932521i	$0.382396\pi$
$138$	−3.31524	+	1.33317i	−0.282212	+	0.113487i
$139$			8.14169i			0.690569i	0.938498	+	0.345285i	$0.112218\pi$
$139$			8.14169i			0.690569i	−0.938498	+	0.345285i	$0.887782\pi$
$140$	−5.58806	+	8.01752i	−0.472277	+	0.677604i
$141$	3.39875	+	2.66431i	0.286227	+	0.224376i
$142$	−4.31679	+	7.47690i	−0.362257	+	0.627447i
$143$	−0.748942	−	1.29721i	−0.0626297	−	0.108478i
$144$	0.431579	−	0.414066i	0.0359649	−	0.0345055i
$145$	9.27108	+	5.35266i	0.769921	+	0.444514i
$146$	−13.3548			−1.10526
$147$	−11.8525	+	2.55292i	−0.977581	+	0.210561i
$148$	2.39740			0.197065
$149$	11.4668	+	6.62035i	0.939395	+	0.542360i	0.889771	−	0.456408i	$-0.150864\pi$
$149$	11.4668	+	6.62035i	0.939395	+	0.542360i	0.0496245	+	0.998768i	$0.484198\pi$
$150$	4.83707	+	0.687830i	0.394945	+	0.0561611i
$151$	−0.793909	−	1.37509i	−0.0646074	−	0.111903i	0.831912	−	0.554907i	$-0.187246\pi$
$151$	−0.793909	−	1.37509i	−0.0646074	−	0.111903i	−0.896520	+	0.443004i	$0.853913\pi$
$152$	2.54357	−	4.40559i	0.206310	−	0.357340i
$153$	1.16429	+	4.73527i	0.0941270	+	0.382824i
$154$	−1.92253	+	2.75837i	−0.154922	+	0.222275i
$155$		−	27.9397i		−	2.24417i
$156$	−0.827304	−	2.05728i	−0.0662373	−	0.164714i
$157$	11.5452	−	6.66563i	0.921408	−	0.531975i	0.0373240	−	0.999303i	$-0.488117\pi$
$157$	11.5452	−	6.66563i	0.921408	−	0.531975i	0.884084	+	0.467328i	$0.154783\pi$
$158$	6.79157	−	3.92111i	0.540308	−	0.311947i
$159$	−1.31545	−	3.27117i	−0.104322	−	0.259421i
$160$			16.5471i			1.30816i
$161$	−5.82486	+	2.73157i	−0.459063	+	0.215277i
$162$	−3.54077	−	6.76504i	−0.278189	−	0.531512i
$163$	7.66710	−	13.2798i	0.600534	−	1.04016i	−0.392206	−	0.919877i	$-0.628288\pi$
$163$	7.66710	−	13.2798i	0.600534	−	1.04016i	0.992740	−	0.120278i	$-0.0383786\pi$
$164$	5.59130	+	9.68442i	0.436608	+	0.756226i
$165$	−7.41103	−	1.05385i	−0.576948	−	0.0820419i
$166$	9.14434	+	5.27949i	0.709739	+	0.409768i
$167$	−7.98750			−0.618091			−0.309046	−	0.951047i	$-0.600010\pi$
$167$	−7.98750			−0.618091			−0.309046	+	0.951047i	$0.600010\pi$
$168$	−8.69251	+	9.33170i	−0.670642	+	0.719956i
$169$	−1.00000			−0.0769231
$170$	−3.44580	−	1.98943i	−0.264281	−	0.152582i
$171$	3.79659	+	3.95716i	0.290332	+	0.302612i
$172$	4.44897	+	7.70583i	0.339230	+	0.587564i
$173$	3.79516	−	6.57341i	0.288541	−	0.499767i	−0.684921	−	0.728617i	$-0.740163\pi$
$173$	3.79516	−	6.57341i	0.288541	−	0.499767i	0.973462	+	0.228850i	$0.0734967\pi$
$174$	4.29097	+	3.36372i	0.325297	+	0.255003i
$175$	8.76477	+	0.747675i	0.662554	+	0.0565189i
$176$		−	0.298623i		−	0.0225096i
$177$	23.8242	−	9.58055i	1.79074	−	0.720118i
$178$	−2.62846	+	1.51754i	−0.197011	+	0.113744i
$179$	14.8321	−	8.56329i	1.10860	−	0.640050i	0.170134	−	0.985421i	$-0.445580\pi$
$179$	14.8321	−	8.56329i	1.10860	−	0.640050i	0.938466	+	0.345371i	$0.112247\pi$
$180$	−10.6420	−	3.08905i	−0.793209	−	0.230244i
$181$			15.1108i			1.12318i	0.827416	+	0.561589i	$0.189810\pi$
$181$			15.1108i			1.12318i	−0.827416	+	0.561589i	$0.810190\pi$
$182$	0.953044	+	2.03230i	0.0706444	+	0.150644i
$183$	9.00571	−	11.4882i	0.665721	−	0.849233i
$184$	−3.38357	+	5.86052i	−0.249440	+	0.432043i
$185$	−2.70156	−	4.67924i	−0.198623	−	0.344025i
$186$	2.00332	−	14.0880i	0.146890	−	1.03298i
$187$	2.10852	+	1.21736i	0.154190	+	0.0890219i
$188$	3.19199			0.232800
$189$	−7.04862	−	11.8033i	−0.512712	−	0.858561i
$190$	−4.47464			−0.324625
$191$	−7.47297	−	4.31452i	−0.540725	−	0.312188i	0.204648	−	0.978836i	$-0.434395\pi$
$191$	−7.47297	−	4.31452i	−0.540725	−	0.312188i	−0.745373	+	0.666648i	$0.767729\pi$
$192$	−1.08923	+	7.65983i	−0.0786082	+	0.552800i
$193$	5.19264	+	8.99391i	0.373774	+	0.647396i	0.990143	−	0.140062i	$-0.0447301\pi$
$193$	5.19264	+	8.99391i	0.373774	+	0.647396i	−0.616369	+	0.787458i	$0.711397\pi$
$194$	0.558630	−	0.967576i	0.0401073	−	0.0694679i
$195$	−3.08313	+	3.93303i	−0.220788	+	0.281650i
$196$	−5.73051	+	6.88980i	−0.409322	+	0.492129i
$197$			13.7325i			0.978403i	0.872171	+	0.489202i	$0.162712\pi$
$197$			13.7325i			0.978403i	−0.872171	+	0.489202i	$0.837288\pi$
$198$	−3.66130	−	1.06276i	−0.260198	−	0.0755274i
$199$	−15.5817	+	8.99608i	−1.10455	+	0.637715i	−0.937414	−	0.348218i	$-0.886787\pi$
$199$	−15.5817	+	8.99608i	−1.10455	+	0.637715i	−0.167141	+	0.985933i	$0.553454\pi$
$200$	8.01311	−	4.62637i	0.566612	−	0.327134i
$201$	−23.1387	+	9.30489i	−1.63208	+	0.656316i
$202$		−	9.55726i		−	0.672446i
$203$	8.05348	+	5.61313i	0.565244	+	0.393965i
$204$	2.83656	+	2.22360i	0.198599	+	0.155683i
$205$	12.6014	−	21.8262i	0.880119	−	1.52441i
$206$	−2.95983	−	5.12657i	−0.206221	−	0.357185i
$207$	−5.05040	−	5.26400i	−0.351027	−	0.365874i
$208$	−0.172654	−	0.0996816i	−0.0119714	−	0.00691168i
$209$	2.73808			0.189397
$210$	10.9314	+	2.51749i	0.754341	+	0.173723i
$211$	−9.05229			−0.623185			−0.311593	−	0.950216i	$-0.600862\pi$
$211$	−9.05229			−0.623185			−0.311593	+	0.950216i	$0.600862\pi$
$212$	−2.25686	−	1.30300i	−0.155002	−	0.0894902i
$213$	−17.4503	−	2.48143i	−1.19567	−	0.170024i
$214$	−0.640772	−	1.10985i	−0.0438022	−	0.0758677i
$215$	10.0268	−	17.3670i	0.683825	−	1.18442i
$216$	−13.1816	−	5.94605i	−0.896891	−	0.404577i
$217$	2.17762	−	25.5275i	0.147826	−	1.73292i
$218$			10.7003i			0.724717i
$219$	−10.1723	−	25.2958i	−0.687381	−	1.70933i
$220$	−4.79156	+	2.76641i	−0.323047	+	0.186511i
$221$	1.40767	−	0.812718i	0.0946900	−	0.0546693i
$222$	−1.02670	−	2.55312i	−0.0689077	−	0.171354i
$223$		−	20.1273i		−	1.34783i	−0.738811	−	0.673913i	$-0.764612\pi$
$223$		−	20.1273i		−	1.34783i	0.738811	−	0.673913i	$-0.235388\pi$
$224$	−1.28968	+	15.1185i	−0.0861705	+	1.01015i
$225$	2.38153	+	9.68592i	0.158769	+	0.645728i
$226$	−1.95127	+	3.37970i	−0.129797	+	0.224814i
$227$	8.57904	+	14.8593i	0.569411	+	0.986248i	0.996624	+	0.0820975i	$0.0261619\pi$
$227$	8.57904	+	14.8593i	0.569411	+	0.986248i	−0.427214	+	0.904151i	$0.640505\pi$
$228$	4.01295	+	0.570641i	0.265764	+	0.0377916i
$229$	−1.65212	−	0.953853i	−0.109175	−	0.0630324i	0.444418	−	0.895819i	$-0.353410\pi$
$229$	−1.65212	−	0.953853i	−0.109175	−	0.0630324i	−0.553593	+	0.832787i	$0.686744\pi$
$230$	5.95238			0.392488
$231$	−6.68907	−	1.54048i	−0.440109	−	0.101356i
$232$	10.3256			0.677911
$233$	−4.88191	−	2.81857i	−0.319825	−	0.184651i	0.331490	−	0.943459i	$-0.392449\pi$
$233$	−4.88191	−	2.81857i	−0.319825	−	0.184651i	−0.651314	+	0.758808i	$0.725782\pi$
$234$	−1.83661	+	1.76209i	−0.120063	+	0.115191i
$235$	−3.59697	−	6.23013i	−0.234640	−	0.406409i
$236$	9.48983	−	16.4369i	0.617735	−	1.06995i
$237$	12.6002	+	9.87739i	0.818470	+	0.641605i
$238$	−2.99325	−	2.08624i	−0.194024	−	0.135231i
$239$		−	3.84106i		−	0.248457i	−0.992254	−	0.124229i	$-0.960354\pi$
$239$		−	3.84106i		−	0.248457i	0.992254	−	0.124229i	$-0.0396456\pi$
$240$	−0.924365	+	0.371720i	−0.0596675	+	0.0239944i
$241$	−12.2622	+	7.07960i	−0.789879	+	0.456037i	−0.839920	−	0.542710i	$-0.817398\pi$
$241$	−12.2622	+	7.07960i	−0.789879	+	0.456037i	0.0500409	+	0.998747i	$0.484065\pi$
$242$	6.43363	−	3.71446i	0.413569	−	0.238774i
$243$	10.1169	−	11.8596i	0.648996	−	0.760791i
$244$		−	10.7893i		−	0.690716i
$245$	19.9051	+	3.42089i	1.27169	+	0.218552i
$246$	7.91898	−	10.1019i	0.504896	−	0.644075i
$247$	0.913984	−	1.58307i	0.0581554	−	0.100728i
$248$	−13.4744	−	23.3383i	−0.855623	−	1.48198i
$249$	−3.03482	+	21.3419i	−0.192324	+	1.35249i
$250$	3.55129	+	2.05034i	0.224603	+	0.129675i
$251$	0.186249			0.0117559			0.00587795	−	0.999983i	$-0.498129\pi$
$251$	0.186249			0.0117559			0.00587795	+	0.999983i	$0.498129\pi$
$252$	−9.48249	−	3.65180i	−0.597341	−	0.230042i
$253$	−3.64233			−0.228991
$254$	−10.2500	−	5.91782i	−0.643140	−	0.371317i
$255$	1.14359	−	8.04211i	0.0716142	−	0.503617i
$256$	7.72490	+	13.3799i	0.482806	+	0.836245i
$257$	−8.14195	+	14.1023i	−0.507881	+	0.879676i	0.492077	+	0.870552i	$0.336238\pi$
$257$	−8.14195	+	14.1023i	−0.507881	+	0.879676i	−0.999958	+	0.00912445i	$0.997096\pi$
$258$	6.30108	−	8.03803i	0.392288	−	0.500426i
$259$	−2.10363	−	4.48583i	−0.130713	−	0.278736i
$260$			3.69376i			0.229077i
$261$	−3.10291	+	10.6898i	−0.192065	+	0.661679i
$262$	15.8689	−	9.16192i	0.980385	−	0.566025i
$263$	11.1183	−	6.41917i	0.685585	−	0.395823i	−0.116371	−	0.993206i	$-0.537126\pi$
$263$	11.1183	−	6.41917i	0.685585	−	0.395823i	0.801956	+	0.597383i	$0.203793\pi$
$264$	−6.69875	+	2.69380i	−0.412279	+	0.165792i
$265$			5.87326i			0.360791i
$266$	−4.08833	−	0.348753i	−0.250672	−	0.0213834i
$267$	−4.87649	−	3.82272i	−0.298436	−	0.233947i
$268$	−9.21678	+	15.9639i	−0.563005	+	0.975153i
$269$	9.16739	+	15.8784i	0.558945	+	0.968122i	0.997585	+	0.0694587i	$0.0221272\pi$
$269$	9.16739	+	15.8784i	0.558945	+	0.968122i	−0.438639	+	0.898663i	$0.644539\pi$
$270$	1.26781	+	12.6562i	0.0771565	+	0.770232i
$271$	2.12427	+	1.22645i	0.129040	+	0.0745013i	0.563130	−	0.826368i	$-0.309597\pi$
$271$	2.12427	+	1.22645i	0.129040	+	0.0745013i	−0.434090	+	0.900869i	$0.642930\pi$
$272$	0.324052			0.0196485
$273$	−3.12349	+	3.35317i	−0.189042	+	0.202943i
$274$	3.04910			0.184203
$275$	4.31295	+	2.49008i	0.260081	+	0.150158i
$276$	−5.33822	−	0.759094i	−0.321323	−	0.0456921i
$277$	0.892124	+	1.54520i	0.0536026	+	0.0928424i	0.891582	−	0.452860i	$-0.149596\pi$
$277$	0.892124	+	1.54520i	0.0536026	+	0.0928424i	−0.837979	+	0.545702i	$0.816263\pi$
$278$	3.45372	−	5.98202i	0.207140	−	0.358778i
$279$	28.2104	−	6.93624i	1.68891	−	0.415262i
$280$	19.2343	−	9.01990i	1.14947	−	0.539042i
$281$			25.5292i			1.52294i	0.648198	+	0.761472i	$0.275523\pi$
$281$			25.5292i			1.52294i	−0.648198	+	0.761472i	$0.724477\pi$
$282$	−1.36699	−	3.39933i	−0.0814032	−	0.202427i
$283$	−1.85950	+	1.07358i	−0.110536	+	0.0638179i	−0.554249	−	0.832351i	$-0.686994\pi$
$283$	−1.85950	+	1.07358i	−0.110536	+	0.0638179i	0.443713	+	0.896169i	$0.353661\pi$
$284$	−11.2824	+	6.51388i	−0.669486	+	0.386528i
$285$	−3.40831	−	8.47553i	−0.201891	−	0.502047i
$286$			1.27081i			0.0751446i
$287$	13.2146	−	18.9598i	0.780033	−	1.11916i
$288$	−16.7075	+	4.10796i	−0.984497	+	0.242064i
$289$	7.17898	−	12.4344i	0.422293	−	0.731433i
$290$	−4.54122	−	7.86562i	−0.266669	−	0.461885i
$291$	2.25822	+	0.321118i	0.132379	+	0.0188243i
$292$	−17.4521	−	10.0760i	−1.02131	−	0.589653i
$293$	2.79728			0.163419			0.0817095	−	0.996656i	$-0.473962\pi$
$293$	2.79728			0.163419			0.0817095	+	0.996656i	$0.473962\pi$
$294$	9.79147	+	3.15214i	0.571050	+	0.183837i
$295$	−42.7754			−2.49048
$296$	−4.51329	−	2.60575i	−0.262330	−	0.151456i
$297$	−0.775787	−	7.74447i	−0.0450158	−	0.449380i
$298$	−5.61673	−	9.72846i	−0.325368	−	0.563554i
$299$	−1.21582	+	2.10587i	−0.0703130	+	0.121786i
$300$	5.80213	+	4.54834i	0.334986	+	0.262598i
$301$	10.5148	−	15.0862i	0.606062	−	0.869552i
$302$			1.34711i			0.0775175i
$303$	18.1026	−	7.27971i	1.03997	−	0.418209i
$304$	0.315605	−	0.182215i	0.0181012	−	0.0104507i
$305$	−21.0586	+	12.1582i	−1.20581	+	0.696177i
$306$	1.15326	−	3.97308i	0.0659277	−	0.227126i
$307$			15.3541i			0.876304i	0.898901	+	0.438152i	$0.144367\pi$
$307$			15.3541i			0.876304i	−0.898901	+	0.438152i	$0.855633\pi$
$308$	−4.59350	+	2.15412i	−0.261739	+	0.122742i
$309$	7.45589	−	9.51117i	0.424151	−	0.541072i
$310$	−11.8521	+	20.5284i	−0.673151	+	1.16593i
$311$	−16.4732	−	28.5325i	−0.934111	−	1.61793i	−0.776212	−	0.630472i	$-0.782861\pi$
$311$	−16.4732	−	28.5325i	−0.934111	−	1.61793i	−0.157899	−	0.987455i	$-0.550472\pi$
$312$	−0.678605	+	4.77219i	−0.0384185	+	0.270172i
$313$	−4.29781	−	2.48134i	−0.242927	−	0.140254i	0.373594	−	0.927592i	$-0.378125\pi$
$313$	−4.29781	−	2.48134i	−0.242927	−	0.140254i	−0.616521	+	0.787338i	$0.711459\pi$
$314$	−11.3103			−0.638277
$315$	3.55798	+	22.6231i	0.200469	+	1.27467i
$316$	11.8336			0.665694
$317$	26.0415	+	15.0351i	1.46264	+	0.844455i	0.999133	−	0.0416395i	$-0.0132581\pi$
$317$	26.0415	+	15.0351i	1.46264	+	0.844455i	0.463505	+	0.886094i	$0.346591\pi$
$318$	−0.421121	+	2.96147i	−0.0236153	+	0.166071i
$319$	2.77882	+	4.81306i	0.155584	+	0.269480i
$320$	6.44410	−	11.1615i	0.360236	−	0.623947i
$321$	1.61412	−	2.05907i	0.0900914	−	0.114926i
$322$	5.43849	+	0.463928i	0.303075	+	0.0258537i
$323$			2.97124i			0.165324i
$324$	0.477019	−	11.5120i	0.0265011	−	0.639557i
$325$	2.87936	−	1.66240i	0.159718	−	0.0922134i
$326$	−11.2666	+	6.50480i	−0.624002	+	0.360268i
$327$	−20.2678	+	8.15038i	−1.12081	+	0.450717i
$328$		−	24.3089i		−	1.34224i
$329$	−2.80085	−	5.97261i	−0.154416	−	0.329281i
$330$	4.99813	+	3.91808i	0.275138	+	0.215683i
$331$	−12.2231	+	21.1709i	−0.671840	+	1.16366i	0.305542	+	0.952179i	$0.401162\pi$
$331$	−12.2231	+	21.1709i	−0.671840	+	1.16366i	−0.977382	+	0.211482i	$0.932171\pi$
$332$	7.96656	+	13.7985i	0.437222	+	0.757291i
$333$	4.05390	−	3.88940i	0.222153	−	0.213138i
$334$	5.86873	+	3.38831i	0.321122	+	0.185400i
$335$	41.5446			2.26982
$336$	−0.873533	+	0.267583i	−0.0476551	+	0.0145978i
$337$	−1.50589			−0.0820310			−0.0410155	−	0.999159i	$-0.513059\pi$
$337$	−1.50589			−0.0820310			−0.0410155	+	0.999159i	$0.513059\pi$
$338$	0.734739	+	0.424202i	0.0399645	+	0.0230735i
$339$	−7.88784	−	1.12165i	−0.428409	−	0.0609197i
$340$	−3.00198	−	5.19959i	−0.162805	−	0.281987i
$341$	7.25241	−	12.5615i	0.392740	−	0.680245i
$342$	−1.11087	−	4.51800i	−0.0600687	−	0.244306i
$343$	17.9200	+	4.67695i	0.967589	+	0.252532i
$344$		−	19.3425i		−	1.04288i
$345$	4.53389	+	11.2745i	0.244097	+	0.607001i
$346$	−5.57690	+	3.21983i	−0.299816	+	0.173099i
$347$	−28.0438	+	16.1911i	−1.50547	+	0.869184i	−0.505491	+	0.862832i	$0.668689\pi$
$347$	−28.0438	+	16.1911i	−1.50547	+	0.869184i	−0.999980	+	0.00635188i	$0.997978\pi$
$348$	3.06957	+	7.63318i	0.164546	+	0.409181i
$349$		−	4.22849i		−	0.226346i	−0.993575	−	0.113173i	$-0.963899\pi$
$349$		−	4.22849i		−	0.226346i	0.993575	−	0.113173i	$-0.0361014\pi$
$350$	−6.12265	−	4.26738i	−0.327270	−	0.228101i
$351$	−4.73655	−	2.13660i	−0.252818	−	0.114043i
$352$	−4.29520	+	7.43951i	−0.228935	+	0.396527i
$353$	−10.2792	−	17.8041i	−0.547107	−	0.947617i	−0.998471	−	0.0552773i	$-0.982396\pi$
$353$	−10.2792	−	17.8041i	−0.547107	−	0.947617i	0.451364	−	0.892340i	$-0.350938\pi$
$354$	−21.5687	−	3.06706i	−1.14636	−	0.163012i
$355$	25.4276	+	14.6806i	1.34956	+	0.779168i
$356$	−4.57983			−0.242730
$357$	1.67166	−	7.25868i	0.0884736	−	0.384170i
$358$	−14.5303			−0.767948
$359$	−8.53293	−	4.92649i	−0.450351	−	0.260010i	0.257627	−	0.966244i	$-0.417059\pi$
$359$	−8.53293	−	4.92649i	−0.450351	−	0.260010i	−0.707978	+	0.706234i	$0.750393\pi$
$360$	16.6769	+	17.3823i	0.878951	+	0.916126i
$361$	−7.82927	−	13.5607i	−0.412067	−	0.713720i
$362$	6.41004	−	11.1025i	0.336904	−	0.583535i
$363$	11.9361	+	9.35682i	0.626483	+	0.491106i
$364$	−0.287891	+	3.37486i	−0.0150896	+	0.176891i
$365$			45.4175i			2.37726i
$366$	−11.4902	+	4.62060i	−0.600601	+	0.241523i
$367$	−15.4397	+	8.91413i	−0.805947	+	0.465314i	−0.845547	−	0.533902i	$-0.820725\pi$
$367$	−15.4397	+	8.91413i	−0.805947	+	0.465314i	0.0395991	+	0.999216i	$0.487392\pi$
$368$	−0.419833	+	0.242391i	−0.0218853	+	0.0126355i
$369$	25.1661	+	7.30496i	1.31010	+	0.380281i
$370$			4.58403i			0.238312i
$371$	−0.457761	+	5.36620i	−0.0237658	+	0.278599i
$372$	13.2471	−	16.8988i	0.686830	−	0.876162i
$373$	−11.2001	+	19.3991i	−0.579917	+	1.00445i	0.415572	+	0.909560i	$0.363582\pi$
$373$	−11.2001	+	19.3991i	−0.579917	+	1.00445i	−0.995488	+	0.0948847i	$0.969752\pi$
$374$	−1.03281	−	1.78888i	−0.0534053	−	0.0925007i
$375$	−1.17860	+	8.28832i	−0.0608626	+	0.428007i
$376$	−6.00917	−	3.46940i	−0.309899	−	0.178921i
$377$	3.71033			0.191092
$378$	0.171932	+	11.6624i	0.00884324	+	0.599847i
$379$	1.91843			0.0985431			0.0492716	−	0.998785i	$-0.484310\pi$
$379$	1.91843			0.0985431			0.0492716	+	0.998785i	$0.484310\pi$
$380$	−5.84747	−	3.37604i	−0.299969	−	0.173187i
$381$	3.40175	−	23.9223i	0.174277	−	1.22558i
$382$	3.66046	+	6.34010i	0.187285	+	0.324388i
$383$	−7.94693	+	13.7645i	−0.406069	+	0.703332i	−0.994445	−	0.105255i	$-0.966434\pi$
$383$	−7.94693	+	13.7645i	−0.406069	+	0.703332i	0.588376	+	0.808587i	$0.299767\pi$
$384$	−8.20701	+	10.4693i	−0.418812	+	0.534262i
$385$	9.38072	+	6.53819i	0.478086	+	0.333217i
$386$		−	8.81091i		−	0.448463i
$387$	20.0245	+	5.81251i	1.01790	+	0.295467i
$388$	1.46004	−	0.842954i	0.0741222	−	0.0427945i
$389$	−9.74647	+	5.62713i	−0.494166	+	0.285307i	−0.726301	−	0.687377i	$-0.758762\pi$
$389$	−9.74647	+	5.62713i	−0.494166	+	0.285307i	0.232135	+	0.972684i	$0.425429\pi$
$390$	3.93370	−	1.58188i	0.199190	−	0.0801015i
$391$		−	3.95249i		−	0.199886i
$392$	18.2767	−	6.74207i	0.923114	−	0.340526i
$393$	29.4411	+	23.0791i	1.48511	+	1.16419i
$394$	5.82537	−	10.0898i	0.293478	−	0.508319i
$395$	−13.3350	−	23.0969i	−0.670958	−	1.16213i
$396$	−3.98276	−	4.15121i	−0.200141	−	0.208606i
$397$	−2.13361	−	1.23184i	−0.107083	−	0.0618243i	0.445502	−	0.895281i	$-0.353025\pi$
$397$	−2.13361	−	1.23184i	−0.107083	−	0.0618243i	−0.552585	+	0.833457i	$0.686359\pi$
$398$	15.2646			0.765146
$399$	−2.45348	−	8.00945i	−0.122827	−	0.400974i
$400$	0.662844			0.0331422
$401$	2.58757	+	1.49394i	0.129217	+	0.0746036i	0.563215	−	0.826310i	$-0.309564\pi$
$401$	2.58757	+	1.49394i	0.129217	+	0.0746036i	−0.433998	+	0.900914i	$0.642898\pi$
$402$	20.9481	+	2.97881i	1.04479	+	0.148570i
$403$	−4.84177	−	8.38619i	−0.241186	−	0.417746i
$404$	7.21078	−	12.4894i	0.358750	−	0.621373i
$405$	−23.0067	+	12.0416i	−1.14321	+	0.598349i
$406$	−3.53611	−	7.54049i	−0.175494	−	0.374228i
$407$		−	2.80502i		−	0.139040i
$408$	−2.92319	−	7.26918i	−0.144720	−	0.359878i
$409$	8.02337	−	4.63229i	0.396730	−	0.229052i	−0.288342	−	0.957527i	$-0.593104\pi$
$409$	8.02337	−	4.63229i	0.396730	−	0.229052i	0.685072	+	0.728475i	$0.259771\pi$
$410$	−18.5175	+	10.6911i	−0.914513	+	0.527994i
$411$	2.32248	+	5.77537i	0.114560	+	0.284878i
$412$		−	8.93255i		−	0.440075i
$413$	−39.0824	−	3.33391i	−1.92312	−	0.164051i
$414$	1.47773	+	6.01006i	0.0726262	+	0.295378i
$415$	17.9546	−	31.0983i	0.881358	−	1.52656i
$416$	2.86751	+	4.96668i	0.140591	+	0.243511i
$417$	13.9614	+	1.98531i	0.683691	+	0.0972209i
$418$	−2.01178	−	1.16150i	−0.0983992	−	0.0568108i
$419$	−17.3067			−0.845489			−0.422745	−	0.906249i	$-0.638933\pi$
$419$	−17.3067			−0.845489			−0.422745	+	0.906249i	$0.638933\pi$
$420$	12.3858	+	11.5374i	0.604366	+	0.562969i
$421$	−11.0648			−0.539264			−0.269632	−	0.962963i	$-0.586902\pi$
$421$	−11.0648			−0.539264			−0.269632	+	0.962963i	$0.586902\pi$
$422$	6.65107	+	3.84000i	0.323769	+	0.186928i
$423$	5.39753	−	5.17851i	0.262437	−	0.251788i
$424$	2.83248	+	4.90599i	0.137557	+	0.238256i
$425$	−2.70213	+	4.68022i	−0.131072	+	0.227024i
$426$	11.7688	+	9.22563i	0.570198	+	0.446983i
$427$	−20.1882	+	9.46724i	−0.976974	+	0.458152i
$428$		−	1.93380i		−	0.0934739i
$429$	−2.40707	+	0.967969i	−0.116215	+	0.0467340i
$430$	−14.7342	+	8.50681i	−0.710548	+	0.410235i
$431$	−18.7270	+	10.8120i	−0.902048	+	0.520798i	−0.877864	−	0.478910i	$-0.841032\pi$
$431$	−18.7270	+	10.8120i	−0.902048	+	0.520798i	−0.0241841	+	0.999708i	$0.507699\pi$
$432$	−0.604803	−	0.841040i	−0.0290986	−	0.0404645i
$433$		−	14.4547i		−	0.694649i	−0.937745	−	0.347325i	$-0.887090\pi$
$433$		−	14.4547i		−	0.694649i	0.937745	−	0.347325i	$-0.112910\pi$
$434$	−12.4288	+	17.8323i	−0.596602	+	0.855979i
$435$	11.4394	−	14.5928i	0.548479	−	0.699673i
$436$	−8.07320	+	13.9832i	−0.386636	+	0.669674i
$437$	−2.22249	−	3.84946i	−0.106316	−	0.184145i
$438$	−3.25651	+	22.9009i	−0.155602	+	1.09425i
$439$	−12.6049	−	7.27745i	−0.601600	−	0.347334i	0.168071	−	0.985775i	$-0.446246\pi$
$439$	−12.6049	−	7.27745i	−0.601600	−	0.347334i	−0.769671	+	0.638441i	$0.779580\pi$
$440$	12.0273			0.573381
$441$	1.48756	+	20.9472i	0.0708364	+	0.997488i
$442$	−1.37903			−0.0655935
$443$	12.7360	+	7.35313i	0.605106	+	0.349358i	0.771048	−	0.636778i	$-0.219733\pi$
$443$	12.7360	+	7.35313i	0.605106	+	0.349358i	−0.165942	+	0.986136i	$0.553066\pi$
$444$	0.584592	−	4.11105i	0.0277435	−	0.195102i
$445$	5.16089	+	8.93892i	0.244650	+	0.423745i
$446$	−8.53805	+	14.7883i	−0.404289	+	0.700248i
$447$	14.1487	−	18.0489i	0.669210	−	0.853684i
$448$	6.75769	−	9.69564i	0.319271	−	0.458076i
$449$		−	14.2365i		−	0.671862i	−0.941887	−	0.335931i	$-0.890949\pi$
$449$		−	14.2365i		−	0.671862i	0.941887	−	0.335931i	$-0.109051\pi$
$450$	2.35898	−	8.12688i	0.111204	−	0.383105i
$451$	11.3310	−	6.54198i	0.533558	−	0.308050i
$452$	−5.09985	+	2.94440i	−0.239877	+	0.138493i
$453$	−2.55160	+	1.02609i	−0.119884	+	0.0482098i
$454$		−	14.5570i		−	0.683193i
$455$	6.91149	−	3.24114i	0.324015	−	0.151947i
$456$	−6.93446	−	5.43599i	−0.324736	−	0.254563i
$457$	4.10055	−	7.10235i	0.191815	−	0.332234i	−0.754036	−	0.656833i	$-0.771896\pi$
$457$	4.10055	−	7.10235i	0.191815	−	0.332234i	0.945852	+	0.324598i	$0.105229\pi$
$458$	0.809252	+	1.40167i	0.0378139	+	0.0654955i
$459$	8.40395	−	0.841849i	0.392263	−	0.0392942i
$460$	7.77858	+	4.49096i	0.362678	+	0.209392i
$461$	−33.7358			−1.57124			−0.785618	−	0.618712i	$-0.787655\pi$
$461$	−33.7358			−1.57124			−0.785618	+	0.618712i	$0.787655\pi$
$462$	4.26125	+	3.96937i	0.198251	+	0.184672i
$463$	−25.2866			−1.17517			−0.587583	−	0.809164i	$-0.699920\pi$
$463$	−25.2866			−1.17517			−0.587583	+	0.809164i	$0.699920\pi$
$464$	0.640602	+	0.369852i	0.0297392	+	0.0171699i
$465$	−47.9109	−	6.81293i	−2.22182	−	0.315942i
$466$	2.39129	+	4.14183i	0.110774	+	0.191867i
$467$	−20.1614	+	34.9205i	−0.932957	+	1.61593i	−0.154721	+	0.987958i	$0.549448\pi$
$467$	−20.1614	+	34.9205i	−0.932957	+	1.61593i	−0.778236	+	0.627971i	$0.783885\pi$
$468$	−3.72955	+	0.917005i	−0.172399	+	0.0423886i
$469$	37.9579	+	3.23798i	1.75273	+	0.149516i
$470$			6.10336i			0.281527i
$471$	−8.61499	−	21.4231i	−0.396958	−	0.987125i
$472$	−35.7307	+	20.6291i	−1.64464	+	0.949533i
$473$	9.01604	−	5.20542i	0.414558	−	0.239345i
$474$	−5.06784	−	12.6023i	−0.232774	−	0.578844i
$475$			6.07763i			0.278861i
$476$	−2.33756	−	4.98466i	−0.107142	−	0.228472i
$477$	−5.93017	+	1.45808i	−0.271524	+	0.0667610i
$478$	−1.62938	+	2.82218i	−0.0745263	+	0.129083i
$479$	7.11025	+	12.3153i	0.324876	+	0.562701i	0.981487	−	0.191528i	$-0.0613442\pi$
$479$	7.11025	+	12.3153i	0.324876	+	0.562701i	−0.656612	+	0.754229i	$0.728011\pi$
$480$	28.3750	+	4.03492i	1.29514	+	0.184168i
$481$	−1.62177	−	0.936328i	−0.0739463	−	0.0426929i
$482$	12.0127			0.547164
$483$	3.26373	+	10.6545i	0.148505	+	0.484799i
$484$	11.2100			0.509544
$485$	−3.29056	−	1.89980i	−0.149417	−	0.0862657i
$486$	−12.4641	+	4.42210i	−0.565383	+	0.200590i
$487$	9.64867	+	16.7120i	0.437223	+	0.757292i	0.997474	−	0.0710304i	$-0.0226287\pi$
$487$	9.64867	+	16.7120i	0.437223	+	0.757292i	−0.560251	+	0.828323i	$0.689295\pi$
$488$	−11.7270	+	20.3118i	−0.530856	+	0.919470i
$489$	−20.9026	−	16.3858i	−0.945250	−	0.740990i
$490$	−13.1739	−	10.9572i	−0.595136	−	0.494998i
$491$		−	29.6404i		−	1.33765i	−0.743420	−	0.668825i	$-0.766797\pi$
$491$		−	29.6404i		−	1.33765i	0.743420	−	0.668825i	$-0.233203\pi$
$492$	17.9703	−	7.22648i	0.810162	−	0.325795i
$493$	−5.22291	+	3.01545i	−0.235228	+	0.135809i
$494$	−1.34308	+	0.775428i	−0.0604280	+	0.0348881i
$495$	−3.61428	+	12.4515i	−0.162450	+	0.559652i
$496$		−	1.93054i		−	0.0866839i
$497$	22.0882	+	15.3950i	0.990789	+	0.690562i
$498$	11.2831	−	14.3934i	0.505606	−	0.644981i
$499$	−12.5372	+	21.7151i	−0.561243	+	0.972101i	0.436146	+	0.899876i	$0.356343\pi$
$499$	−12.5372	+	21.7151i	−0.561243	+	0.972101i	−0.997388	+	0.0722250i	$0.976990\pi$
$500$	3.09389	+	5.35877i	0.138363	+	0.239652i
$501$	−1.94771	+	13.6970i	−0.0870171	+	0.611935i
$502$	−0.136844	−	0.0790070i	−0.00610765	−	0.00352626i
$503$	15.9328			0.710409			0.355205	−	0.934789i	$-0.384411\pi$
$503$	15.9328			0.710409			0.355205	+	0.934789i	$0.384411\pi$
$504$	13.8824	+	17.1814i	0.618370	+	0.765320i
$505$	−32.5026			−1.44635
$506$	2.67616	+	1.54508i	0.118970	+	0.0686873i
$507$	−0.243844	+	1.71480i	−0.0108295	+	0.0761570i
$508$	−8.92978	−	15.4668i	−0.396195	−	0.686230i
$509$	9.92936	−	17.1981i	0.440111	−	0.762294i	−0.557586	−	0.830119i	$-0.688272\pi$
$509$	9.92936	−	17.1981i	0.440111	−	0.762294i	0.997697	+	0.0678245i	$0.0216058\pi$
$510$	−4.25172	+	5.42374i	−0.188269	+	0.240167i
$511$	−3.53984	+	41.4965i	−0.156593	+	1.83569i
$512$			2.25299i			0.0995689i
$513$	7.71152	−	5.54546i	0.340472	−	0.244838i
$514$	11.9644	−	6.90766i	0.527728	−	0.304684i
$515$	−17.4346	+	10.0659i	−0.768260	+	0.443555i
$516$	14.2988	−	5.75006i	0.629470	−	0.253132i
$517$		−	3.73472i		−	0.164253i
$518$	−0.357279	+	4.18828i	−0.0156979	+	0.184022i
$519$	−10.3467	−	8.11083i	−0.454168	−	0.356026i
$520$	4.01478	−	6.95380i	0.176060	−	0.304944i
$521$	0.996831	+	1.72656i	0.0436719	+	0.0756420i	0.887035	−	0.461702i	$-0.152761\pi$
$521$	0.996831	+	1.72656i	0.0436719	+	0.0756420i	−0.843363	+	0.537344i	$0.819428\pi$
$522$	6.81444	−	6.53792i	0.298260	−	0.286157i
$523$	−26.9491	−	15.5591i	−1.17840	−	0.680351i	−0.222758	−	0.974874i	$-0.571506\pi$
$523$	−26.9491	−	15.5591i	−1.17840	−	0.680351i	−0.955644	+	0.294523i	$0.904839\pi$
$524$	27.6500			1.20790
$525$	3.41935	−	14.8475i	0.149233	−	0.647999i
$526$	−10.8921			−0.474918
$527$	13.6312	+	7.86998i	0.593785	+	0.342822i
$528$	−0.512079	−	0.0728176i	−0.0222854	−	0.00316898i
$529$	−8.54354	−	14.7978i	−0.371458	−	0.643385i
$530$	2.49145	−	4.31531i	0.108221	−	0.187445i
$531$	−10.6193	−	43.1899i	−0.460840	−	1.87428i
$532$	−5.07951	−	3.54032i	−0.220225	−	0.153492i
$533$		−	8.73497i		−	0.378354i
$534$	1.96134	+	4.87732i	0.0848756	+	0.211062i
$535$	−3.77440	+	2.17915i	−0.163182	+	0.0942130i
$536$	34.7027	−	20.0356i	1.49893	−	0.865406i
$537$	−11.0676	−	27.5221i	−0.477603	−	1.18767i
$538$		−	15.5553i		−	0.670636i
$539$	8.06126	+	6.70486i	0.347223	+	0.288799i
$540$	−7.89210	+	17.4957i	−0.339622	+	0.752894i
$541$	−9.91521	+	17.1736i	−0.426288	+	0.738353i	−0.996540	−	0.0831173i	$-0.973512\pi$
$541$	−9.91521	+	17.1736i	−0.426288	+	0.738353i	0.570252	+	0.821470i	$0.306846\pi$
$542$	−1.04052	−	1.80224i	−0.0446942	−	0.0774127i
$543$	25.9120	+	3.68469i	1.11199	+	0.158125i
$544$	−8.07301	−	4.66096i	−0.346128	−	0.199837i
$545$	36.3899			1.55877
$546$	3.71738	−	1.13872i	0.159089	−	0.0487326i
$547$	43.9288			1.87826			0.939130	−	0.343562i	$-0.111634\pi$
$547$	43.9288			1.87826			0.939130	+	0.343562i	$0.111634\pi$
$548$	3.98457	+	2.30049i	0.170212	+	0.0982721i
$549$	−17.5040	−	18.2443i	−0.747053	−	0.778649i
$550$	−2.11260	−	3.65912i	−0.0900814	−	0.156026i
$551$	−3.39118	+	5.87370i	−0.144469	+	0.250228i
$552$	9.22455	+	7.23120i	0.392623	+	0.307780i
$553$	−10.3836	−	22.1422i	−0.441555	−	0.941583i
$554$		−	1.51376i		−	0.0643136i
$555$	−8.68273	+	3.49163i	−0.368561	+	0.148212i
$556$	9.02665	−	5.21154i	0.382815	−	0.221019i
$557$	23.9317	−	13.8170i	1.01402	−	0.585445i	0.101654	−	0.994820i	$-0.467587\pi$
$557$	23.9317	−	13.8170i	1.01402	−	0.585445i	0.912366	+	0.409375i	$0.134253\pi$
$558$	−23.6697	−	6.87058i	−1.00202	−	0.290855i
$559$		−	6.95036i		−	0.293969i
$560$	1.51638	+	0.129354i	0.0640786	+	0.00546619i
$561$	2.60167	−	3.31885i	0.109843	−	0.140122i
$562$	10.8295	−	18.7573i	0.456816	−	0.791228i
$563$	−15.0582	−	26.0816i	−0.634629	−	1.09921i	−0.986594	−	0.163196i	$-0.947820\pi$
$563$	−15.0582	−	26.0816i	−0.634629	−	1.09921i	0.351965	−	0.936013i	$-0.385514\pi$
$564$	0.778349	−	5.47362i	0.0327744	−	0.230481i
$565$	11.4938	+	6.63593i	0.483546	+	0.279176i
$566$	1.82166			0.0765702
$567$	−21.9590	+	9.20882i	−0.922191	+	0.386734i
$568$	28.3200			1.18828
$569$	−32.0864	−	18.5251i	−1.34513	−	0.776613i	−0.357578	−	0.933883i	$-0.616397\pi$
$569$	−32.0864	−	18.5251i	−1.34513	−	0.776613i	−0.987556	+	0.157270i	$0.949731\pi$
$570$	−1.09112	+	7.67312i	−0.0457018	+	0.321391i
$571$	22.3494	+	38.7102i	0.935292	+	1.61997i	0.774113	+	0.633048i	$0.218196\pi$
$571$	22.3494	+	38.7102i	0.935292	+	1.61997i	0.161179	+	0.986925i	$0.448470\pi$
$572$	−0.958804	+	1.66070i	−0.0400896	+	0.0694372i
$573$	−9.22079	+	11.7626i	−0.385204	+	0.491389i
$574$	−17.7520	+	8.32482i	−0.740956	+	0.347471i
$575$		−	8.08475i		−	0.337158i
$576$	12.8695	+	3.73561i	0.536228	+	0.155651i
$577$	2.93489	−	1.69446i	0.122181	−	0.0705412i	−0.437664	−	0.899139i	$-0.644194\pi$
$577$	2.93489	−	1.69446i	0.122181	−	0.0705412i	0.559845	+	0.828597i	$0.310861\pi$
$578$	−10.5494	+	6.09067i	−0.438795	+	0.253339i
$579$	16.6890	−	6.71122i	0.693569	−	0.278909i
$580$		−	13.7051i		−	0.569072i
$581$	18.8283	−	27.0141i	0.781131	−	1.12073i
$582$	−1.52298	−	1.19388i	−0.0631296	−	0.0494878i
$583$	−1.52454	+	2.64059i	−0.0631402	+	0.109362i
$584$	21.9034	+	37.9377i	0.906367	+	1.56987i
$585$	5.99255	+	6.24600i	0.247761	+	0.258240i
$586$	−2.05527	−	1.18661i	−0.0849026	−	0.0490185i
$587$	11.5337			0.476049			0.238024	−	0.971259i	$-0.423500\pi$
$587$	11.5337			0.476049			0.238024	+	0.971259i	$0.423500\pi$
$588$	10.4173	+	11.5067i	0.429601	+	0.474529i
$589$	17.7012			0.729365
$590$	31.4287	+	18.1454i	1.29390	+	0.747034i
$591$	23.5486	+	3.34860i	0.968659	+	0.137743i
$592$	−0.186669	−	0.323321i	−0.00767207	−	0.0132884i
$593$	17.7402	−	30.7269i	0.728503	−	1.26180i	−0.229013	−	0.973423i	$-0.573550\pi$
$593$	17.7402	−	30.7269i	0.728503	−	1.26180i	0.957516	−	0.288380i	$-0.0931167\pi$
$594$	−2.71522	+	6.01926i	−0.111407	+	0.246973i
$595$	−7.09495	+	10.1795i	−0.290865	+	0.417320i
$596$		−	16.9509i		−	0.694335i
$597$	11.6270	+	28.9131i	0.475860	+	1.18333i
$598$	1.78663	−	1.03151i	0.0730606	−	0.0421816i
$599$	1.86232	−	1.07521i	0.0760923	−	0.0439319i	−0.461471	−	0.887155i	$-0.652678\pi$
$599$	1.86232	−	1.07521i	0.0760923	−	0.0439319i	0.537563	+	0.843223i	$0.319345\pi$
$600$	−5.97935	−	14.8690i	−0.244106	−	0.607024i
$601$			27.0283i			1.10251i	0.834338	+	0.551254i	$0.185850\pi$
$601$			27.0283i			1.10251i	−0.834338	+	0.551254i	$0.814150\pi$
$602$	−14.1252	+	6.62400i	−0.575700	+	0.269974i
$603$	10.3138	+	41.9472i	0.420010	+	1.70822i
$604$	−1.01637	+	1.76041i	−0.0413556	+	0.0716299i
$605$	−12.6322	−	21.8797i	−0.513573	−	0.889534i
$606$	−16.3888	−	2.33048i	−0.665749	−	0.0946695i
$607$	1.76214	+	1.01737i	0.0715230	+	0.0412938i	0.535335	−	0.844640i	$-0.320185\pi$
$607$	1.76214	+	1.01737i	0.0715230	+	0.0412938i	−0.463812	+	0.885934i	$0.653519\pi$
$608$	−10.4834			−0.425160
$609$	11.5892	−	12.4414i	0.469618	−	0.504150i
$610$	20.6301			0.835290
$611$	−2.15929	−	1.24667i	−0.0873554	−	0.0504347i
$612$	4.50471	−	4.32191i	0.182092	−	0.174703i
$613$	3.25339	+	5.63503i	0.131403	+	0.227597i	0.924218	−	0.381866i	$-0.124718\pi$
$613$	3.25339	+	5.63503i	0.131403	+	0.227597i	−0.792815	+	0.609463i	$0.791385\pi$
$614$	6.51323	−	11.2813i	0.262853	−	0.455274i
$615$	−34.3549	−	26.9311i	−1.38532	−	1.08597i
$616$	10.9890	+	0.937410i	0.442758	+	0.0377693i
$617$		−	49.1555i		−	1.97893i	−0.144781	−	0.989464i	$-0.546248\pi$
$617$		−	49.1555i		−	1.97893i	0.144781	−	0.989464i	$-0.453752\pi$
$618$	−9.51279	+	3.82543i	−0.382660	+	0.153881i
$619$	−9.98666	+	5.76580i	−0.401398	+	0.231747i	−0.687087	−	0.726575i	$-0.741111\pi$
$619$	−9.98666	+	5.76580i	−0.401398	+	0.231747i	0.285689	+	0.958322i	$0.407778\pi$
$620$	−30.9766	+	17.8843i	−1.24405	+	0.718252i
$621$	−10.2582	+	7.37683i	−0.411648	+	0.296022i
$622$			27.9519i			1.12077i
$623$	4.01863	+	8.56943i	0.161003	+	0.343327i
$624$	−0.213035	+	0.271760i	−0.00852821	+	0.0108791i
$625$	15.2849	−	26.4741i	0.611394	−	1.05897i
$626$	2.10518	+	3.64628i	0.0841400	+	0.145735i
$627$	0.667667	−	4.69527i	0.0266640	−	0.187511i
$628$	−14.7803	−	8.53341i	−0.589798	−	0.340520i
$629$	3.04388			0.121368
$630$	6.98256	−	18.1314i	0.278192	−	0.722371i
$631$	−19.2682			−0.767055			−0.383527	−	0.923530i	$-0.625291\pi$
$631$	−19.2682			−0.767055			−0.383527	+	0.923530i	$0.625291\pi$
$632$	−22.2778	−	12.8621i	−0.886162	−	0.511626i
$633$	−2.20735	+	15.5229i	−0.0877343	+	0.616978i
$634$	−12.7558	−	22.0937i	−0.506598	−	0.877454i
$635$	−20.1255	+	34.8583i	−0.798655	+	1.38331i
$636$	−2.78470	+	3.55233i	−0.110421	+	0.140859i
$637$	6.56741	−	2.42264i	0.260210	−	0.0959884i
$638$		−	4.71512i		−	0.186674i
$639$	−8.51030	+	29.3186i	−0.336662	+	1.15983i
$640$	19.1910	−	11.0799i	0.758590	−	0.437972i
$641$	39.1882	−	22.6253i	1.54784	−	0.893647i	0.549536	−	0.835470i	$-0.314805\pi$
$641$	39.1882	−	22.6253i	1.54784	−	0.893647i	0.998306	−	0.0581766i	$-0.0185286\pi$
$642$	−2.05942	+	0.828165i	−0.0812787	+	0.0326851i
$643$			15.0422i			0.593208i	0.955001	+	0.296604i	$0.0958541\pi$
$643$			15.0422i			0.593208i	−0.955001	+	0.296604i	$0.904146\pi$
$644$	6.75700	+	4.70950i	0.266263	+	0.185580i
$645$	−27.3360	−	21.4289i	−1.07635	−	0.843762i
$646$	1.26041	−	2.18309i	0.0495901	−	0.0858925i
$647$	−9.47075	−	16.4038i	−0.372334	−	0.644901i	0.617590	−	0.786500i	$-0.288109\pi$
$647$	−9.47075	−	16.4038i	−0.372334	−	0.644901i	−0.989924	+	0.141599i	$0.954776\pi$
$648$	−13.4105	+	21.1538i	−0.526816	+	0.831001i
$649$	−19.2316	−	11.1034i	−0.754907	−	0.435846i
$650$	−2.82077			−0.110640
$651$	−43.2436	−	9.95892i	−1.69485	−	0.390321i
$652$	−19.6310			−0.768810
$653$	7.90001	+	4.56107i	0.309151	+	0.178489i	0.646547	−	0.762874i	$-0.276213\pi$
$653$	7.90001	+	4.56107i	0.309151	+	0.178489i	−0.337395	+	0.941363i	$0.609546\pi$
$654$	18.3489	+	2.60921i	0.717499	+	0.102028i
$655$	−31.1581	−	53.9674i	−1.21745	−	2.10868i
$656$	0.870716	−	1.50812i	0.0339958	−	0.0588824i
$657$	−45.8576	+	11.2753i	−1.78908	+	0.439890i
$658$	−0.475696	+	5.57644i	−0.0185446	+	0.217392i
$659$		−	20.5588i		−	0.800859i	−0.916328	−	0.400429i	$-0.868861\pi$
$659$		−	20.5588i		−	0.800859i	0.916328	−	0.400429i	$-0.131139\pi$
$660$	3.57545	+	8.89115i	0.139174	+	0.346087i
$661$	29.1451	−	16.8269i	1.13361	−	0.654491i	0.188771	−	0.982021i	$-0.439550\pi$
$661$	29.1451	−	16.8269i	1.13361	−	0.654491i	0.944841	+	0.327530i	$0.106216\pi$
$662$	17.9615	−	10.3701i	0.698094	−	0.403045i
$663$	−1.05040	−	2.61205i	−0.0407940	−	0.101443i
$664$		−	34.6357i		−	1.34413i
$665$	−1.18605	+	13.9037i	−0.0459930	+	0.539162i
$666$	−4.62845	+	1.13802i	−0.179349	+	0.0440975i
$667$	4.51111	−	7.81347i	0.174671	−	0.302539i
$668$	5.11284	+	8.85570i	0.197822	+	0.342637i
$669$	−34.5144	−	4.90794i	−1.33440	−	0.189752i
$670$	−30.5245	−	17.6233i	−1.17926	−	0.680847i
$671$	−12.6238			−0.487337
$672$	25.6108	+	5.89812i	0.987958	+	0.227525i
$673$	20.2455			0.780405			0.390202	−	0.920729i	$-0.372405\pi$
$673$	20.2455			0.780405			0.390202	+	0.920729i	$0.372405\pi$
$674$	1.10644	+	0.638801i	0.0426183	+	0.0246057i
$675$	17.1901	−	1.72199i	0.661649	−	0.0662794i
$676$	0.640106	+	1.10870i	0.0246194	+	0.0426421i
$677$	−1.49996	+	2.59801i	−0.0576482	+	0.0998497i	−0.893409	−	0.449244i	$-0.851694\pi$
$677$	−1.49996	+	2.59801i	−0.0576482	+	0.0998497i	0.835761	+	0.549093i	$0.185027\pi$
$678$	5.31970	+	4.17016i	0.204302	+	0.160154i
$679$	−2.85840	−	1.99225i	−0.109695	−	0.0764557i
$680$			13.0515i			0.500503i
$681$	27.5727	−	11.0880i	1.05659	−	0.424892i
$682$	−10.6573	+	6.15297i	−0.408087	+	0.235609i
$683$	2.36000	−	1.36255i	0.0903029	−	0.0521364i	−0.454169	−	0.890916i	$-0.650064\pi$
$683$	2.36000	−	1.36255i	0.0903029	−	0.0521364i	0.544471	+	0.838779i	$0.316730\pi$
$684$	1.95707	−	6.74226i	0.0748305	−	0.257797i
$685$		−	10.3695i		−	0.396196i
$686$	−11.1825	−	11.0380i	−0.426952	−	0.421434i
$687$	−2.03853	+	2.60047i	−0.0777747	+	0.0992140i
$688$	0.692823	−	1.20001i	0.0264136	−	0.0457498i
$689$	1.01780	+	1.76288i	0.0387750	+	0.0671604i
$690$	1.45145	−	10.2071i	0.0552559	−	0.388579i
$691$	32.9210	+	19.0070i	1.25238	+	0.723059i	0.971581	−	0.236709i	$-0.0760687\pi$
$691$	32.9210	+	19.0070i	1.25238	+	0.723059i	0.280794	+	0.959768i	$0.409402\pi$
$692$	−9.71721			−0.369393
$693$	−4.27271	+	11.0948i	−0.162307	+	0.421456i
$694$	27.4732			1.04287
$695$	−20.3438	−	11.7455i	−0.771684	−	0.445532i
$696$	2.51785	−	17.7064i	0.0954389	−	0.671160i
$697$	7.09906	+	12.2959i	0.268896	+	0.465742i
$698$	−1.79373	+	3.10684i	−0.0678938	+	0.117595i
$699$	−6.02372	+	7.68421i	−0.227838	+	0.290644i
$700$	−4.78143	−	10.1961i	−0.180721	−	0.385374i
$701$			51.5487i			1.94697i	0.228757	+	0.973484i	$0.426534\pi$
$701$			51.5487i			1.94697i	−0.228757	+	0.973484i	$0.573466\pi$
$702$	2.57378	+	3.57910i	0.0971410	+	0.135084i
$703$	2.96454	−	1.71158i	0.111810	−	0.0645534i
$704$	5.79447	−	3.34544i	0.218387	−	0.126086i
$705$	−11.5605	+	4.64890i	−0.435395	+	0.175088i
$706$			17.4418i			0.656432i
$707$	−29.6965	−	2.53325i	−1.11685	−	0.0952726i
$708$	−25.8719	−	20.2812i	−0.972326	−	0.762214i
$709$	−20.1154	+	34.8409i	−0.755450	+	1.30848i	0.189700	+	0.981842i	$0.439249\pi$
$709$	−20.1154	+	34.8409i	−0.755450	+	1.30848i	−0.945150	+	0.326636i	$0.894085\pi$
$710$	−12.4551	−	21.5729i	−0.467432	−	0.809616i
$711$	20.0102	−	19.1982i	0.750442	−	0.719990i
$712$	8.62189	+	4.97785i	0.323119	+	0.186553i
$713$	−23.5470			−0.881841
$714$	−4.30738	+	4.62411i	−0.161200	+	0.173053i
$715$	4.32180			0.161626
$716$	−18.9882	−	10.9628i	−0.709621	−	0.409700i
$717$	−6.58665	−	0.936621i	−0.245983	−	0.0349787i
$718$	4.17965	+	7.23937i	0.155983	+	0.270171i
$719$	−4.89105	+	8.47154i	−0.182405	+	0.315935i	−0.942699	−	0.333644i	$-0.891722\pi$
$719$	−4.89105	+	8.47154i	−0.182405	+	0.315935i	0.760294	+	0.649579i	$0.225055\pi$
$720$	0.412024	+	1.67574i	0.0153552	+	0.0624512i
$721$	−16.7139	+	7.83799i	−0.622459	+	0.291902i
$722$			13.2848i			0.494407i
$723$	9.15002	+	22.7536i	0.340293	+	0.846215i
$724$	16.7533	−	9.67253i	0.622632	−	0.359477i
$725$	−10.6834	+	6.16806i	−0.396771	+	0.229076i
$726$	−4.80075	−	11.9381i	−0.178172	−	0.443066i
$727$			15.3676i			0.569953i	0.958535	+	0.284976i	$0.0919857\pi$
$727$			15.3676i			0.569953i	−0.958535	+	0.284976i	$0.908014\pi$
$728$	4.21014	−	6.04054i	0.156038	−	0.223877i
$729$	−17.8698	−	20.2403i	−0.661846	−	0.749640i
$730$	19.2662	−	33.3700i	0.713074	−	1.23508i
$731$	5.64868	+	9.78380i	0.208924	+	0.361867i
$732$	−18.5015	−	2.63092i	−0.683837	−	0.0972415i
$733$	24.1277	+	13.9301i	0.891176	+	0.514521i	0.874327	−	0.485337i	$-0.161303\pi$
$733$	24.1277	+	13.9301i	0.891176	+	0.514521i	0.0168493	+	0.999858i	$0.494636\pi$
$734$	15.1256			0.558295
$735$	10.7199	−	33.2991i	0.395409	−	1.22826i
$736$	13.9456			0.514041
$737$	18.6783	+	10.7839i	0.688023	+	0.397230i
$738$	−15.3918	−	16.0428i	−0.566579	−	0.590542i
$739$	18.7019	+	32.3926i	0.687959	+	1.19158i	0.972497	+	0.232915i	$0.0748264\pi$
$739$	18.7019	+	32.3926i	0.687959	+	1.19158i	−0.284538	+	0.958665i	$0.591840\pi$
$740$	−3.45857	+	5.99042i	−0.127140	+	0.220212i
$741$	−2.49177	−	1.95332i	−0.0915376	−	0.0717571i
$742$	2.61269	−	3.74857i	0.0959147	−	0.137614i
$743$		−	6.06181i		−	0.222386i	−0.993799	−	0.111193i	$-0.964533\pi$
$743$		−	6.06181i		−	0.222386i	0.993799	−	0.111193i	$-0.0354672\pi$
$744$	−43.3062	+	17.4149i	−1.58768	+	0.638463i
$745$	−33.0848	+	19.1015i	−1.21213	+	0.699825i
$746$	16.4582	−	9.50216i	0.602579	−	0.347899i
$747$	35.8571	+	10.4082i	1.31194	+	0.380816i
$748$		−	3.11695i		−	0.113967i
$749$	−3.61839	+	1.69684i	−0.132213	+	0.0620012i
$750$	4.38188	−	5.58979i	0.160004	−	0.204110i
$751$	−6.83221	+	11.8337i	−0.249311	+	0.431819i	−0.963335	−	0.268302i	$-0.913537\pi$
$751$	−6.83221	+	11.8337i	−0.249311	+	0.431819i	0.714024	+	0.700121i	$0.246871\pi$
$752$	−0.248539	−	0.430483i	−0.00906329	−	0.0156981i
$753$	0.0454157	−	0.319379i	0.00165504	−	0.0116388i
$754$	−2.72612	−	1.57393i	−0.0992796	−	0.0573191i
$755$	4.58129			0.166730
$756$	−8.57436	+	15.3701i	−0.311846	+	0.559005i
$757$	−10.9383			−0.397560			−0.198780	−	0.980044i	$-0.563698\pi$
$757$	−10.9383			−0.397560			−0.198780	+	0.980044i	$0.563698\pi$
$758$	−1.40955	−	0.813802i	−0.0511970	−	0.0295586i
$759$	−0.888161	+	6.24586i	−0.0322382	+	0.226710i
$760$	7.33888	+	12.7113i	0.266209	+	0.461088i
$761$	16.9321	−	29.3272i	0.613786	−	1.06311i	−0.376810	−	0.926291i	$-0.622979\pi$
$761$	16.9321	−	29.3272i	0.613786	−	1.06311i	0.990596	−	0.136819i	$-0.0436878\pi$
$762$	−12.6473	+	16.1336i	−0.458162	+	0.584459i
$763$	33.2483	+	2.83623i	1.20367	+	0.102678i
$764$			11.0470i			0.399666i
$765$	−13.5118	−	3.92205i	−0.488519	−	0.141802i
$766$	11.6778	−	6.74220i	0.421937	−	0.243606i
$767$	−12.8392	+	7.41271i	−0.463596	+	0.267657i
$768$	24.8276	−	9.98404i	0.895888	−	0.360268i
$769$			26.8561i			0.968456i	0.874942	+	0.484228i	$0.160900\pi$
$769$			26.8561i			0.968456i	−0.874942	+	0.484228i	$0.839100\pi$
$770$	−4.11887	−	8.78318i	−0.148434	−	0.316524i
$771$	22.1972	+	17.4006i	0.799413	+	0.626667i
$772$	6.64767	−	11.5141i	0.239255	−	0.414402i
$773$	16.5898	+	28.7344i	0.596694	+	1.03350i	0.993305	+	0.115518i	$0.0368527\pi$
$773$	16.5898	+	28.7344i	0.596694	+	1.03350i	−0.396611	+	0.917987i	$0.629814\pi$
$774$	−12.2471	−	12.7651i	−0.440214	−	0.458833i
$775$	27.8824	+	16.0979i	1.00157	+	0.578255i
$776$	−3.66485			−0.131561
$777$	−8.20526	+	2.51346i	−0.294362	+	0.0901697i
$778$	9.54815			0.342318
$779$	13.8280	+	7.98363i	0.495441	+	0.286043i
$780$	6.33406	+	0.900703i	0.226796	+	0.0322503i
$781$	7.62143	+	13.2007i	0.272716	+	0.472358i
$782$	−1.67665	+	2.90405i	−0.0599570	+	0.103849i
$783$	17.5742	+	7.92751i	0.628050	+	0.283306i
$784$	1.37538	+	0.236372i	0.0491207	+	0.00844187i
$785$			38.4643i			1.37285i
$786$	−11.8413	−	29.4461i	−0.422366	−	1.05031i
$787$	1.14981	−	0.663846i	0.0409865	−	0.0236636i	−0.479367	−	0.877615i	$-0.659134\pi$
$787$	1.14981	−	0.663846i	0.0409865	−	0.0236636i	0.520353	+	0.853951i	$0.325800\pi$
$788$	15.2252	−	8.79028i	0.542376	−	0.313141i
$789$	−8.29645	−	20.6310i	−0.295361	−	0.734483i
$790$			22.6270i			0.805031i
$791$	9.98426	+	6.95885i	0.355000	+	0.247428i
$792$	2.98588	+	12.1439i	0.106099	+	0.431514i
$793$	−4.21389	+	7.29866i	−0.149639	+	0.259183i
$794$	1.04510	+	1.81016i	0.0370892	+	0.0642403i
$795$	10.0715	+	1.43216i	0.357198	+	0.0507935i
$796$	19.9478	+	11.5169i	0.707032	+	0.408205i
$797$	13.4281			0.475648			0.237824	−	0.971308i	$-0.423566\pi$
$797$	13.4281			0.475648			0.237824	+	0.971308i	$0.423566\pi$
$798$	−1.59496	+	6.92563i	−0.0564609	+	0.245164i
$799$	4.05275			0.143376
$800$	−16.5132	−	9.53392i	−0.583831	−	0.337075i
$801$	−7.74431	+	7.43006i	−0.273632	+	0.262528i
$802$	−1.26746	−	2.19531i	−0.0447556	−	0.0775189i
$803$	−11.7892	+	20.4195i	−0.416032	+	0.720588i
$804$	25.1275	+	19.6977i	0.886179	+	0.694683i
$805$	1.57774	−	18.4953i	0.0556080	−	0.651875i
$806$			8.21555i			0.289380i
$807$	29.4637	−	11.8484i	1.03717	−	0.417083i
$808$	−27.1497	+	15.6749i	−0.955125	+	0.551442i
$809$	−30.5878	+	17.6599i	−1.07541	+	0.620889i	−0.929655	−	0.368432i	$-0.879895\pi$
$809$	−30.5878	+	17.6599i	−1.07541	+	0.620889i	−0.145756	+	0.989321i	$0.546561\pi$
$810$	22.0120	+	0.912103i	0.773423	+	0.0320480i
$811$		−	19.2063i		−	0.674426i	−0.941428	−	0.337213i	$-0.890516\pi$
$811$		−	19.2063i		−	0.674426i	0.941428	−	0.337213i	$-0.109484\pi$
$812$	1.06817	−	12.5219i	0.0374855	−	0.439431i
$813$	2.62110	−	3.34363i	0.0919260	−	0.117266i
$814$	−1.18990	+	2.06096i	−0.0417058	+	0.0722366i
$815$	22.1217	+	38.3159i	0.774889	+	1.34215i
$816$	0.0790183	−	0.555685i	0.00276619	−	0.0194529i
$817$	11.0029	+	6.35252i	0.384942	+	0.222247i
$818$	−7.86011			−0.274822
$819$	4.98838	+	6.17382i	0.174308	+	0.215731i
$820$	−32.2649			−1.12674
$821$	−17.7528	−	10.2496i	−0.619578	−	0.357714i	0.157126	−	0.987578i	$-0.449777\pi$
$821$	−17.7528	−	10.2496i	−0.619578	−	0.357714i	−0.776705	+	0.629865i	$0.783110\pi$
$822$	0.743506	−	5.22859i	0.0259327	−	0.182368i
$823$	−8.05191	−	13.9463i	−0.280672	−	0.486138i	0.690879	−	0.722971i	$-0.257224\pi$
$823$	−8.05191	−	13.9463i	−0.280672	−	0.486138i	−0.971550	+	0.236833i	$0.923891\pi$
$824$	−9.70886	+	16.8162i	−0.338224	+	0.585822i
$825$	5.32169	−	6.78866i	0.185277	−	0.236351i
$826$	27.3011	+	19.0284i	0.949928	+	0.662082i
$827$			19.0344i			0.661890i	0.943650	+	0.330945i	$0.107367\pi$
$827$			19.0344i			0.661890i	−0.943650	+	0.330945i	$0.892633\pi$
$828$	−2.60339	+	8.96887i	−0.0904740	+	0.311690i
$829$	−18.6186	+	10.7494i	−0.646649	+	0.373343i	−0.787171	−	0.616734i	$-0.788455\pi$
$829$	−18.6186	+	10.7494i	−0.646649	+	0.373343i	0.140522	+	0.990078i	$0.455122\pi$
$830$	−26.3839	+	15.2328i	−0.915800	+	0.528737i
$831$	2.86726	−	1.15303i	0.0994641	−	0.0399980i
$832$		−	4.46689i		−	0.154862i
$833$	−7.27581	+	8.74772i	−0.252092	+	0.303090i
$834$	−9.41580	−	7.38112i	−0.326042	−	0.255587i
$835$	11.5231	−	19.9585i	0.398772	−	0.690693i
$836$	−1.75266	−	3.03570i	−0.0606171	−	0.104992i
$837$	−5.01532	−	50.0666i	−0.173355	−	1.73055i
$838$	12.7159	+	7.34155i	0.439265	+	0.253610i
$839$	3.47585			0.120000			0.0599999	−	0.998198i	$-0.480890\pi$
$839$	3.47585			0.120000			0.0599999	+	0.998198i	$0.480890\pi$
$840$	−10.7772	−	35.1824i	−0.371847	−	1.21391i
$841$	15.2334			0.525291
$842$	8.12973	+	4.69370i	0.280169	+	0.161756i
$843$	43.7774	+	6.22515i	1.50778	+	0.214406i
$844$	5.79442	+	10.0362i	0.199452	+	0.345461i
$845$	1.44264	−	2.49872i	0.0496282	−	0.0859586i
$846$	−6.16251	+	1.51521i	−0.211871	+	0.0520940i
$847$	−9.83634	−	20.9753i	−0.337981	−	0.720718i
$848$			0.405823i			0.0139360i
$849$	1.38755	+	3.45046i	0.0476207	+	0.118419i
$850$	3.97071	−	2.29249i	0.136194	−	0.0786319i
$851$	−3.94357	+	2.27682i	−0.135184	+	0.0780484i
$852$	8.41886	+	20.9354i	0.288425	+	0.717235i
$853$			9.52321i			0.326068i	0.986620	+	0.163034i	$0.0521281\pi$
$853$			9.52321i			0.326068i	−0.986620	+	0.163034i	$0.947872\pi$
$854$	18.8491	+	1.60791i	0.645002	+	0.0550216i
$855$	−15.3649	+	3.77786i	−0.525470	+	0.129200i
$856$	−2.10187	+	3.64054i	−0.0718403	+	0.124431i
$857$	−5.59152	−	9.68480i	−0.191003	−	0.330827i	0.754580	−	0.656208i	$-0.227841\pi$
$857$	−5.59152	−	9.68480i	−0.191003	−	0.330827i	−0.945583	+	0.325381i	$0.894507\pi$
$858$	2.17919	+	0.309880i	0.0743962	+	0.0105791i
$859$	6.47584	+	3.73883i	0.220953	+	0.127567i	0.606391	−	0.795166i	$-0.292616\pi$
$859$	6.47584	+	3.73883i	0.220953	+	0.127567i	−0.385438	+	0.922734i	$0.625950\pi$
$860$	−25.6730			−0.875441
$861$	−29.2899	−	27.2836i	−0.998197	−	0.929824i
$862$	18.3460			0.624866
$863$	17.0099	+	9.82068i	0.579025	+	0.334300i	0.760746	−	0.649050i	$-0.224833\pi$
$863$	17.0099	+	9.82068i	0.579025	+	0.334300i	−0.181721	+	0.983350i	$0.558167\pi$
$864$	2.97030	+	29.6517i	0.101052	+	1.00877i
$865$	10.9501	+	18.9661i	0.372314	+	0.644866i
$866$	−6.13172	+	10.6204i	−0.208364	+	0.360897i
$867$	−19.5719	−	15.3426i	−0.664696	−	0.521061i
$868$	−29.6962	+	13.9260i	−1.00795	+	0.472679i
$869$		−	13.8457i		−	0.469683i
$870$	−14.5953	+	5.86929i	−0.494827	+	0.198988i
$871$	12.4698	−	7.19942i	0.422522	−	0.243943i
$872$	30.3969	−	17.5497i	1.02937	−	0.594306i
$873$	1.10131	−	3.79409i	0.0372736	−	0.128410i
$874$			3.77114i			0.127561i
$875$	7.31216	−	10.4912i	0.247196	−	0.354667i
$876$	−21.5339	+	27.4700i	−0.727564	+	0.928124i
$877$	8.77258	−	15.1946i	0.296229	−	0.513084i	−0.679041	−	0.734100i	$-0.737604\pi$
$877$	8.77258	−	15.1946i	0.296229	−	0.513084i	0.975270	+	0.221017i	$0.0709375\pi$
$878$	6.17422	+	10.6941i	0.208370	+	0.360907i
$879$	0.682102	−	4.79678i	0.0230067	−	0.161791i
$880$	0.746175	+	0.430804i	0.0251536	+	0.0145224i
$881$	−14.2848			−0.481266			−0.240633	−	0.970616i	$-0.577355\pi$
$881$	−14.2848			−0.481266			−0.240633	+	0.970616i	$0.577355\pi$
$882$	7.79289	−	16.0218i	0.262400	−	0.539482i
$883$	−24.7462			−0.832776			−0.416388	−	0.909187i	$-0.636704\pi$
$883$	−24.7462			−0.832776			−0.416388	+	0.909187i	$0.636704\pi$
$884$	−1.80211	−	1.04045i	−0.0606116	−	0.0349941i
$885$	−10.4305	+	73.3512i	−0.350619	+	2.46567i
$886$	−6.23843	−	10.8053i	−0.209584	−	0.363010i
$887$	−13.7291	+	23.7795i	−0.460979	+	0.798439i	−0.999010	−	0.0444860i	$-0.985835\pi$
$887$	−13.7291	+	23.7795i	−0.460979	+	0.798439i	0.538031	+	0.842925i	$0.319168\pi$
$888$	−5.56888	+	7.10399i	−0.186879	+	0.238394i
$889$	−21.1048	+	30.2803i	−0.707833	+	1.01557i
$890$		−	8.75703i		−	0.293536i
$891$	−13.4694	−	0.558126i	−0.451242	−	0.0186979i
$892$	−22.3151	+	12.8836i	−0.747164	+	0.431376i
$893$	3.94711	−	2.27886i	0.132085	−	0.0762593i
$894$	−18.0520	+	7.25934i	−0.603748	+	0.242789i
$895$			49.4149i			1.65176i
$896$	18.3977	−	8.62761i	0.614625	−	0.288228i
$897$	3.31467	+	2.59840i	0.110674	+	0.0867581i
$898$	−6.03915	+	10.4601i	−0.201529	+	0.349059i
$899$	17.9646	+	31.1155i	0.599152	+	1.03776i
$900$	9.21431	−	8.84041i	0.307144	−	0.294680i
$901$	−2.86545	−	1.65437i	−0.0954618	−	0.0551149i
$902$	−11.1005			−0.369606
$903$	−23.3058	−	21.7094i	−0.775568	−	0.722444i
$904$	12.8012			0.425760
$905$	−37.7577	−	21.7994i	−1.25511	−	0.724638i
$906$	2.31003	+	0.328486i	0.0767455	+	0.0109132i
$907$	−18.5137	−	32.0668i	−0.614739	−	1.06476i	−0.990430	−	0.138014i	$-0.955928\pi$
$907$	−18.5137	−	32.0668i	−0.614739	−	1.06476i	0.375691	−	0.926745i	$-0.377405\pi$
$908$	10.9830	−	19.0231i	0.364483	−	0.631303i
$909$	−8.06903	−	32.8175i	−0.267633	−	1.08849i
$910$	−6.45304	−	0.550474i	−0.213916	−	0.0182480i
$911$			50.4270i			1.67072i	0.549701	+	0.835361i	$0.314742\pi$
$911$			50.4270i			1.67072i	−0.549701	+	0.835361i	$0.685258\pi$
$912$	−0.235503	−	0.585632i	−0.00779830	−	0.0193922i
$913$	16.1446	−	9.32111i	0.534309	−	0.308484i
$914$	−6.02566	+	3.47892i	−0.199311	+	0.115072i
$915$	15.7139	+	39.0761i	0.519485	+	1.29182i
$916$			2.44227i			0.0806947i
$917$	−24.2619	−	51.7367i	−0.801198	−	1.70850i
$918$	−6.53182	−	2.94643i	−0.215582	−	0.0972467i
$919$	3.94768	−	6.83758i	0.130222	−	0.225551i	−0.793540	−	0.608518i	$-0.791764\pi$
$919$	3.94768	−	6.83758i	0.130222	−	0.225551i	0.923762	+	0.382967i	$0.125098\pi$
$920$	−9.76253	−	16.9092i	−0.321861	−	0.557480i
$921$	26.3292	+	3.74401i	0.867577	+	0.123369i
$922$	24.7870	+	14.3108i	0.816318	+	0.471301i
$923$	10.1763			0.334956
$924$	2.57379	+	8.40221i	0.0846714	+	0.276413i
$925$	6.22621			0.204717
$926$	18.5790	+	10.7266i	0.610544	+	0.352498i
$927$	−14.4917	−	15.1046i	−0.475969	−	0.496100i
$928$	−10.6394	−	18.4280i	−0.349256	−	0.604929i
$929$	29.3792	−	50.8862i	0.963899	−	1.66952i	0.251354	−	0.967895i	$-0.419124\pi$
$929$	29.3792	−	50.8862i	0.963899	−	1.66952i	0.712545	−	0.701626i	$-0.247542\pi$
$930$	32.3120	+	25.3296i	1.05955	+	0.830591i
$931$	−2.16731	+	12.6109i	−0.0710306	+	0.413305i
$932$			7.21674i			0.236392i
$933$	−52.9444	+	21.2908i	−1.73332	+	0.697030i
$934$	29.6267	−	17.1050i	0.969416	−	0.559692i
$935$	−6.08367	+	3.51241i	−0.198957	+	0.114868i
$936$	8.01788	+	2.32735i	0.262073	+	0.0760717i
$937$			15.8154i			0.516666i	0.966056	+	0.258333i	$0.0831732\pi$
$937$			15.8154i			0.516666i	−0.966056	+	0.258333i	$0.916827\pi$
$938$	−26.5156	−	18.4809i	−0.865765	−	0.603422i
$939$	−5.30301	+	6.76483i	−0.173057	+	0.220762i
$940$	−4.60488	+	7.97589i	−0.150195	+	0.260145i
$941$	−11.2513	−	19.4878i	−0.366782	−	0.635285i	0.622279	−	0.782796i	$-0.286207\pi$
$941$	−11.2513	−	19.4878i	−0.366782	−	0.635285i	−0.989060	+	0.147511i	$0.952874\pi$
$942$	−2.75795	+	19.3949i	−0.0898589	+	0.631920i
$943$	−18.3947	−	10.6202i	−0.599014	−	0.345841i
$944$	−2.95564			−0.0961980
$945$	39.6616	−	0.584712i	1.29019	−	0.0190207i
$946$	−8.83259			−0.287172
$947$	−44.9801	−	25.9693i	−1.46166	−	0.843888i	−0.462568	−	0.886584i	$-0.653072\pi$
$947$	−44.9801	−	25.9693i	−1.46166	−	0.843888i	−0.999088	+	0.0426957i	$0.986405\pi$
$948$	2.88557	−	20.2923i	0.0937189	−	0.659064i
$949$	7.87057	+	13.6322i	0.255490	+	0.442521i
$950$	2.57814	−	4.46548i	0.0836460	−	0.144879i
$951$	32.1323	−	40.9898i	1.04196	−	1.32919i
$952$	−1.01723	+	11.9247i	−0.0329688	+	0.386483i
$953$			54.7090i			1.77220i	0.463495	+	0.886100i	$0.346595\pi$
$953$			54.7090i			1.77220i	−0.463495	+	0.886100i	$0.653405\pi$
$954$	4.97565	+	1.44428i	0.161093	+	0.0467602i
$955$	21.5616	−	12.4486i	0.697716	−	0.402826i
$956$	−4.25856	+	2.45868i	−0.137732	+	0.0795195i
$957$	8.93104	−	3.59149i	0.288699	−	0.116096i
$958$		−	12.0647i		−	0.389793i
$959$	0.808194	−	9.47422i	0.0260980	−	0.305938i
$960$	−17.5684	−	13.7720i	−0.567018	−	0.444490i
$961$	31.3855	−	54.3612i	1.01243	−	1.75359i
$962$	0.794384	+	1.37591i	0.0256120	+	0.0443612i
$963$	−3.13730	−	3.26999i	−0.101098	−	0.105374i
$964$	15.6982	+	9.06338i	0.505606	+	0.291912i
$965$	−29.9644			−0.964587
$966$	2.12169	−	9.21279i	0.0682642	−	0.296417i
$967$	24.3185			0.782030			0.391015	−	0.920384i	$-0.372124\pi$
$967$	24.3185			0.782030			0.391015	+	0.920384i	$0.372124\pi$
$968$	−21.1037	−	12.1842i	−0.678297	−	0.391615i
$969$	5.09509	+	0.724521i	0.163678	+	0.0232750i
$970$	1.61180	+	2.79172i	0.0517518	+	0.0896368i
$971$	9.83663	−	17.0375i	0.315672	−	0.546761i	−0.663908	−	0.747814i	$-0.731103\pi$
$971$	9.83663	−	17.0375i	0.315672	−	0.546761i	0.979580	+	0.201054i	$0.0644366\pi$
$972$	−19.6245	−	3.62514i	−0.629456	−	0.116276i
$973$	−17.6720	−	12.3171i	−0.566538	−	0.394867i
$974$		−	16.3719i		−	0.524591i
$975$	−2.14857	−	5.34290i	−0.0688093	−	0.171110i
$976$	−1.45509	+	0.840094i	−0.0465761	+	0.0268908i
$977$	3.61130	−	2.08498i	0.115536	−	0.0667046i	−0.441119	−	0.897449i	$-0.645418\pi$
$977$	3.61130	−	2.08498i	0.115536	−	0.0667046i	0.556654	+	0.830744i	$0.312085\pi$
$978$	8.40712	+	20.9062i	0.268830	+	0.668507i
$979$			5.35853i			0.171259i
$980$	−8.94864	−	24.2584i	−0.285854	−	0.774907i
$981$	9.03409	+	36.7426i	0.288436	+	1.17310i
$982$	−12.5735	+	21.7779i	−0.401236	+	0.694962i
$983$	−11.9756	−	20.7424i	−0.381963	−	0.661579i	0.609380	−	0.792878i	$-0.291418\pi$
$983$	−11.9756	−	20.7424i	−0.381963	−	0.661579i	−0.991343	+	0.131299i	$0.958085\pi$
$984$	−41.6850	−	5.92760i	−1.32887	−	0.188965i
$985$	−34.3138	−	19.8111i	−1.09333	−	0.631233i
$986$	5.11664			0.162947
$987$	−10.9248	+	3.34652i	−0.347740	+	0.106521i
$988$	−2.34019			−0.0744512
$989$	−14.6366	−	8.45042i	−0.465415	−	0.268708i
$990$	7.93748	−	7.61539i	0.252270	−	0.242033i
$991$	−11.1365	−	19.2889i	−0.353762	−	0.612733i	0.633143	−	0.774034i	$-0.281764\pi$
$991$	−11.1365	−	19.2889i	−0.353762	−	0.612733i	−0.986905	+	0.161301i	$0.948431\pi$
$992$	−27.7677	+	48.0950i	−0.881625	+	1.52702i
$993$	33.3234	+	26.1225i	1.05749	+	0.828973i
$994$	−9.69843	−	20.6812i	−0.307616	−	0.655967i
$995$		−	51.9123i		−	1.64573i
$996$	25.6043	−	10.2964i	0.811302	−	0.326253i
$997$	11.2451	−	6.49237i	0.356136	−	0.205615i	−0.311248	−	0.950329i	$-0.600747\pi$
$997$	11.2451	−	6.49237i	0.356136	−	0.205615i	0.667385	+	0.744713i	$0.267414\pi$
$998$	18.4232	−	10.6366i	0.583175	−	0.336696i
$999$	−5.68103	−	7.90004i	−0.179740	−	0.249946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.131.13	✓	64
3.2	odd	2	inner	273.2.bh.a.131.20	yes	64
7.3	odd	6	inner	273.2.bh.a.248.20	yes	64
21.17	even	6	inner	273.2.bh.a.248.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.13	✓	64	1.1	even	1	trivial
273.2.bh.a.131.20	yes	64	3.2	odd	2	inner
273.2.bh.a.248.13	yes	64	21.17	even	6	inner
273.2.bh.a.248.20	yes	64	7.3	odd	6	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.734739 - 0.424202i) q^{2} +(0.243844 - 1.71480i) q^{3} +(-0.640106 - 1.10870i) q^{4} +(-1.44264 + 2.49872i) q^{5} +(-0.906583 + 1.15649i) q^{6} +(-1.51284 + 2.17056i) q^{7} +2.78294i q^{8} +(-2.88108 - 0.836289i) q^{9} +O(q^{10})\)	\(q+(-0.734739 - 0.424202i) q^{2} +(0.243844 - 1.71480i) q^{3} +(-0.640106 - 1.10870i) q^{4} +(-1.44264 + 2.49872i) q^{5} +(-0.906583 + 1.15649i) q^{6} +(-1.51284 + 2.17056i) q^{7} +2.78294i q^{8} +(-2.88108 - 0.836289i) q^{9} +(2.11992 - 1.22394i) q^{10} +(-1.29721 + 0.748942i) q^{11} +(-2.05728 + 0.827304i) q^{12} +1.00000i q^{13} +(2.03230 - 0.953044i) q^{14} +(3.93303 + 3.08313i) q^{15} +(-0.0996816 + 0.172654i) q^{16} +(-0.812718 - 1.40767i) q^{17} +(1.76209 + 1.83661i) q^{18} +(-1.58307 - 0.913984i) q^{19} +3.69376 q^{20} +(3.35317 + 3.12349i) q^{21} +1.27081 q^{22} +(2.10587 + 1.21582i) q^{23} +(4.77219 + 0.678605i) q^{24} +(-1.66240 - 2.87936i) q^{25} +(0.424202 - 0.734739i) q^{26} +(-2.13660 + 4.73655i) q^{27} +(3.37486 + 0.287891i) q^{28} -3.71033i q^{29} +(-1.58188 - 3.93370i) q^{30} +(-8.38619 + 4.84177i) q^{31} +(4.96668 - 2.86751i) q^{32} +(0.967969 + 2.40707i) q^{33} +1.37903i q^{34} +(-3.24114 - 6.91149i) q^{35} +(0.917005 + 3.72955i) q^{36} +(-0.936328 + 1.62177i) q^{37} +(0.775428 + 1.34308i) q^{38} +(1.71480 + 0.243844i) q^{39} +(-6.95380 - 4.01478i) q^{40} -8.73497 q^{41} +(-1.13872 - 3.71738i) q^{42} -6.95036 q^{43} +(1.66070 + 0.958804i) q^{44} +(6.24600 - 5.99255i) q^{45} +(-1.03151 - 1.78663i) q^{46} +(-1.24667 + 2.15929i) q^{47} +(0.271760 + 0.213035i) q^{48} +(-2.42264 - 6.56741i) q^{49} +2.82077i q^{50} +(-2.61205 + 1.05040i) q^{51} +(1.10870 - 0.640106i) q^{52} +(1.76288 - 1.01780i) q^{53} +(3.57910 - 2.57378i) q^{54} -4.32180i q^{55} +(-6.04054 - 4.21014i) q^{56} +(-1.95332 + 2.49177i) q^{57} +(-1.57393 + 2.72612i) q^{58} +(7.41271 + 12.8392i) q^{59} +(0.900703 - 6.33406i) q^{60} +(7.29866 + 4.21389i) q^{61} +8.21555 q^{62} +(6.17382 - 4.98838i) q^{63} -4.46689 q^{64} +(-2.49872 - 1.44264i) q^{65} +(0.309880 - 2.17919i) q^{66} +(-7.19942 - 12.4698i) q^{67} +(-1.04045 + 1.80211i) q^{68} +(2.59840 - 3.31467i) q^{69} +(-0.550474 + 6.45304i) q^{70} -10.1763i q^{71} +(2.32735 - 8.01788i) q^{72} +(13.6322 - 7.87057i) q^{73} +(1.37591 - 0.794384i) q^{74} +(-5.34290 + 2.14857i) q^{75} +2.34019i q^{76} +(0.336841 - 3.94869i) q^{77} +(-1.15649 - 0.906583i) q^{78} +(-4.62175 + 8.00511i) q^{79} +(-0.287609 - 0.498153i) q^{80} +(7.60124 + 4.81883i) q^{81} +(6.41793 + 3.70539i) q^{82} -12.4457 q^{83} +(1.31662 - 5.71702i) q^{84} +4.68982 q^{85} +(5.10670 + 2.94836i) q^{86} +(-6.36248 - 0.904744i) q^{87} +(-2.08426 - 3.61005i) q^{88} +(1.78870 - 3.09812i) q^{89} +(-7.13123 + 1.75339i) q^{90} +(-2.17056 - 1.51284i) q^{91} -3.11302i q^{92} +(6.25774 + 15.5613i) q^{93} +(1.83195 - 1.05768i) q^{94} +(4.56758 - 2.63709i) q^{95} +(-3.70612 - 9.21609i) q^{96} +1.31690i q^{97} +(-1.00590 + 5.85302i) q^{98} +(4.36368 - 1.07292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more