LMFDB - Embedded newform 368.2.i.b.91.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [368,2,Mod(91,368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(368, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("368.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 368 = 2^{4} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	368.i (of order $4$, 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:	$2.93849479438$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.13
Character	$\chi$	$=$	368.91
Dual form			368.2.i.b.275.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.786933 + 1.17505i) q^{2} +(1.81358 + 1.81358i) q^{3} +(-0.761472 - 1.84937i) q^{4} +(-1.82931 + 1.82931i) q^{5} +(-3.55821 + 0.703875i) q^{6} +3.62156i q^{7} +(2.77232 + 0.560564i) q^{8} +3.57815i q^{9} +(-0.709980 - 3.58907i) q^{10} +(-0.269052 - 0.269052i) q^{11} +(1.97299 - 4.73497i) q^{12} +(2.55855 - 2.55855i) q^{13} +(-4.25550 - 2.84993i) q^{14} -6.63520 q^{15} +(-2.84032 + 2.81648i) q^{16} -6.31617i q^{17} +(-4.20449 - 2.81576i) q^{18} +(-1.10308 + 1.10308i) q^{19} +(4.77603 + 1.99010i) q^{20} +(-6.56799 + 6.56799i) q^{21} +(0.527875 - 0.104423i) q^{22} +(-2.12539 + 4.29915i) q^{23} +(4.01120 + 6.04446i) q^{24} -1.69274i q^{25} +(0.993009 + 5.01983i) q^{26} +(-1.04852 + 1.04852i) q^{27} +(6.69759 - 2.75771i) q^{28} +(-5.25282 + 5.25282i) q^{29} +(5.22146 - 7.79667i) q^{30} -1.15984i q^{31} +(-1.07435 - 5.55390i) q^{32} -0.975895i q^{33} +(7.42180 + 4.97040i) q^{34} +(-6.62495 - 6.62495i) q^{35} +(6.61731 - 2.72466i) q^{36} +(8.02716 - 8.02716i) q^{37} +(-0.428121 - 2.16422i) q^{38} +9.28028 q^{39} +(-6.09688 + 4.04599i) q^{40} +4.40957i q^{41} +(-2.54913 - 12.8863i) q^{42} +(4.91652 + 4.91652i) q^{43} +(-0.292701 + 0.702451i) q^{44} +(-6.54554 - 6.54554i) q^{45} +(-3.37917 - 5.88058i) q^{46} +10.2762i q^{47} +(-10.2591 - 0.0432366i) q^{48} -6.11569 q^{49} +(1.98905 + 1.33208i) q^{50} +(11.4549 - 11.4549i) q^{51} +(-6.67997 - 2.78344i) q^{52} +(-4.81276 + 4.81276i) q^{53} +(-0.406944 - 2.05717i) q^{54} +0.984358 q^{55} +(-2.03012 + 10.0401i) q^{56} -4.00105 q^{57} +(-2.03869 - 10.3059i) q^{58} +(8.66803 - 8.66803i) q^{59} +(5.05251 + 12.2709i) q^{60} +(-2.24389 - 2.24389i) q^{61} +(1.36287 + 0.912720i) q^{62} -12.9585 q^{63} +(7.37154 + 3.10813i) q^{64} +9.36077i q^{65} +(1.14672 + 0.767964i) q^{66} +(7.78083 - 7.78083i) q^{67} +(-11.6809 + 4.80958i) q^{68} +(-11.6514 + 3.94229i) q^{69} +(12.9980 - 2.57123i) q^{70} +1.20079 q^{71} +(-2.00578 + 9.91978i) q^{72} +4.91373i q^{73} +(3.11545 + 15.7491i) q^{74} +(3.06993 - 3.06993i) q^{75} +(2.87997 + 1.20004i) q^{76} +(0.974388 - 0.974388i) q^{77} +(-7.30296 + 10.9048i) q^{78} +8.60340 q^{79} +(0.0436116 - 10.3480i) q^{80} +6.93130 q^{81} +(-5.18145 - 3.47004i) q^{82} +(4.76079 - 4.76079i) q^{83} +(17.1480 + 7.14529i) q^{84} +(11.5542 + 11.5542i) q^{85} +(-9.64611 + 1.90817i) q^{86} -19.0528 q^{87} +(-0.595078 - 0.896720i) q^{88} -1.19209 q^{89} +(12.8422 - 2.54041i) q^{90} +(9.26595 + 9.26595i) q^{91} +(9.56914 + 0.656946i) q^{92} +(2.10347 - 2.10347i) q^{93} +(-12.0750 - 8.08670i) q^{94} -4.03575i q^{95} +(8.12401 - 12.0209i) q^{96} -0.0586996i q^{97} +(4.81264 - 7.18622i) q^{98} +(0.962708 - 0.962708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) $ 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/368\mathbb{Z}\right)^\times$.

$n$	$47$	$97$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.786933	+	1.17505i	−0.556446	+	0.830884i
$2$	−0.786933	+	1.17505i	−0.556446	+	0.830884i
$3$	1.81358	+	1.81358i	1.04707	+	1.04707i	0.998836	+	0.0482351i	$0.0153597\pi$
$3$	1.81358	+	1.81358i	1.04707	+	1.04707i	0.0482351	+	0.998836i	$0.484640\pi$
$4$	−0.761472	−	1.84937i	−0.380736	−	0.924684i
$5$	−1.82931	+	1.82931i	−0.818092	+	0.818092i	−0.985831	−	0.167739i	$-0.946353\pi$
$5$	−1.82931	+	1.82931i	−0.818092	+	0.818092i	0.167739	+	0.985831i	$0.446353\pi$
$6$	−3.55821	+	0.703875i	−1.45263	+	0.287356i
$7$			3.62156i			1.36882i	0.729097	+	0.684410i	$0.239940\pi$
$7$			3.62156i			1.36882i	−0.729097	+	0.684410i	$0.760060\pi$
$8$	2.77232	+	0.560564i	0.980164	+	0.198189i
$9$			3.57815i			1.19272i
$10$	−0.709980	−	3.58907i	−0.224515	−	1.13496i
$11$	−0.269052	−	0.269052i	−0.0811222	−	0.0811222i	0.665381	−	0.746504i	$-0.268269\pi$
$11$	−0.269052	−	0.269052i	−0.0811222	−	0.0811222i	−0.746504	+	0.665381i	$0.768269\pi$
$12$	1.97299	−	4.73497i	0.569552	−	1.36687i
$13$	2.55855	−	2.55855i	0.709615	−	0.709615i	−0.256839	−	0.966454i	$-0.582681\pi$
$13$	2.55855	−	2.55855i	0.709615	−	0.709615i	0.966454	+	0.256839i	$0.0826811\pi$
$14$	−4.25550	−	2.84993i	−1.13733	−	0.761675i
$15$	−6.63520			−1.71320
$16$	−2.84032	+	2.81648i	−0.710081	+	0.704120i
$17$		−	6.31617i		−	1.53190i	−0.642903	−	0.765948i	$-0.722270\pi$
$17$		−	6.31617i		−	1.53190i	0.642903	−	0.765948i	$-0.277730\pi$
$18$	−4.20449	−	2.81576i	−0.991008	−	0.663682i
$19$	−1.10308	+	1.10308i	−0.253064	+	0.253064i	−0.822226	−	0.569161i	$-0.807268\pi$
$19$	−1.10308	+	1.10308i	−0.253064	+	0.253064i	0.569161	+	0.822226i	$0.307268\pi$
$20$	4.77603	+	1.99010i	1.06795	+	0.445000i
$21$	−6.56799	+	6.56799i	−1.43325	+	1.43325i
$22$	0.527875	−	0.104423i	0.112543	−	0.0222630i
$23$	−2.12539	+	4.29915i	−0.443175	+	0.896435i
$23$	−2.12539	+	4.29915i	−0.443175	+	0.896435i
$24$	4.01120	+	6.04446i	0.818783	+	1.23382i
$25$		−	1.69274i		−	0.338549i
$26$	0.993009	+	5.01983i	0.194745	+	0.984470i
$27$	−1.04852	+	1.04852i	−0.201787	+	0.201787i
$28$	6.69759	−	2.75771i	1.26573	−	0.521159i
$29$	−5.25282	+	5.25282i	−0.975425	+	0.975425i	−0.999705	−	0.0242801i	$-0.992271\pi$
$29$	−5.25282	+	5.25282i	−0.975425	+	0.975425i	0.0242801	+	0.999705i	$0.492271\pi$
$30$	5.22146	−	7.79667i	0.953304	−	1.42347i
$31$		−	1.15984i		−	0.208314i	−0.994561	−	0.104157i	$-0.966786\pi$
$31$		−	1.15984i		−	0.208314i	0.994561	−	0.104157i	$-0.0332145\pi$
$32$	−1.07435	−	5.55390i	−0.189921	−	0.981799i
$33$		−	0.975895i		−	0.169881i
$34$	7.42180	+	4.97040i	1.27283	+	0.852417i
$35$	−6.62495	−	6.62495i	−1.11982	−	1.11982i
$36$	6.61731	−	2.72466i	1.10289	−	0.454110i
$37$	8.02716	−	8.02716i	1.31966	−	1.31966i	0.405613	−	0.914045i	$-0.367058\pi$
$37$	8.02716	−	8.02716i	1.31966	−	1.31966i	0.914045	−	0.405613i	$-0.132942\pi$
$38$	−0.428121	−	2.16422i	−0.0694504	−	0.351084i
$39$	9.28028			1.48603
$40$	−6.09688	+	4.04599i	−0.964001	+	0.639727i
$41$			4.40957i			0.688659i	0.938849	+	0.344330i	$0.111894\pi$
$41$			4.40957i			0.688659i	−0.938849	+	0.344330i	$0.888106\pi$
$42$	−2.54913	−	12.8863i	−0.393339	−	1.98839i
$43$	4.91652	+	4.91652i	0.749762	+	0.749762i	0.974434	−	0.224673i	$-0.0721313\pi$
$43$	4.91652	+	4.91652i	0.749762	+	0.749762i	−0.224673	+	0.974434i	$0.572131\pi$
$44$	−0.292701	+	0.702451i	−0.0441263	+	0.105899i
$45$	−6.54554	−	6.54554i	−0.975751	−	0.975751i
$46$	−3.37917	−	5.88058i	−0.498231	−	0.867044i
$47$			10.2762i			1.49894i	0.662038	+	0.749470i	$0.269692\pi$
$47$			10.2762i			1.49894i	−0.662038	+	0.749470i	$0.730308\pi$
$48$	−10.2591	−	0.0432366i	−1.48077	−	0.00624067i
$49$	−6.11569			−0.873670
$50$	1.98905	+	1.33208i	0.281295	+	0.188384i
$51$	11.4549	−	11.4549i	1.60400	−	1.60400i
$52$	−6.67997	−	2.78344i	−0.926345	−	0.385994i
$53$	−4.81276	+	4.81276i	−0.661083	+	0.661083i	−0.955635	−	0.294552i	$-0.904829\pi$
$53$	−4.81276	+	4.81276i	−0.661083	+	0.661083i	0.294552	+	0.955635i	$0.404829\pi$
$54$	−0.406944	−	2.05717i	−0.0553781	−	0.279946i
$55$	0.984358			0.132731
$56$	−2.03012	+	10.0401i	−0.271286	+	1.34167i
$57$	−4.00105			−0.529953
$58$	−2.03869	−	10.3059i	−0.267694	−	1.35324i
$59$	8.66803	−	8.66803i	1.12848	−	1.12848i	0.138057	−	0.990424i	$-0.455914\pi$
$59$	8.66803	−	8.66803i	1.12848	−	1.12848i	0.990424	−	0.138057i	$-0.0440857\pi$
$60$	5.05251	+	12.2709i	0.652277	+	1.58417i
$61$	−2.24389	−	2.24389i	−0.287301	−	0.287301i	0.548711	−	0.836012i	$-0.315119\pi$
$61$	−2.24389	−	2.24389i	−0.287301	−	0.287301i	−0.836012	+	0.548711i	$0.815119\pi$
$62$	1.36287	+	0.912720i	0.173085	+	0.115916i
$63$	−12.9585			−1.63261
$64$	7.37154	+	3.10813i	0.921442	+	0.388516i
$65$			9.36077i			1.16106i
$66$	1.14672	+	0.767964i	0.141152	+	0.0945299i
$67$	7.78083	−	7.78083i	0.950580	−	0.950580i	−0.0482552	−	0.998835i	$-0.515366\pi$
$67$	7.78083	−	7.78083i	0.950580	−	0.950580i	0.998835	+	0.0482552i	$0.0153661\pi$
$68$	−11.6809	+	4.80958i	−1.41652	+	0.583248i
$69$	−11.6514	+	3.94229i	−1.40267	+	0.474596i
$70$	12.9980	−	2.57123i	1.55356	−	0.307321i
$71$	1.20079			0.142507			0.0712537	−	0.997458i	$-0.477300\pi$
$71$	1.20079			0.142507			0.0712537	+	0.997458i	$0.477300\pi$
$72$	−2.00578	+	9.91978i	−0.236384	+	1.16906i
$73$			4.91373i			0.575109i	0.957764	+	0.287554i	$0.0928422\pi$
$73$			4.91373i			0.575109i	−0.957764	+	0.287554i	$0.907158\pi$
$74$	3.11545	+	15.7491i	0.362164	+	1.83080i
$75$	3.06993	−	3.06993i	0.354485	−	0.354485i
$76$	2.87997	+	1.20004i	0.330355	+	0.137654i
$77$	0.974388	−	0.974388i	0.111042	−	0.111042i
$78$	−7.30296	+	10.9048i	−0.826898	+	1.23472i
$79$	8.60340			0.967958			0.483979	−	0.875080i	$-0.339191\pi$
$79$	8.60340			0.967958			0.483979	+	0.875080i	$0.339191\pi$
$80$	0.0436116	−	10.3480i	0.00487593	−	1.15695i
$81$	6.93130			0.770145
$82$	−5.18145	−	3.47004i	−0.572196	−	0.383202i
$83$	4.76079	−	4.76079i	0.522564	−	0.522564i	−0.395781	−	0.918345i	$-0.629526\pi$
$83$	4.76079	−	4.76079i	0.522564	−	0.522564i	0.918345	+	0.395781i	$0.129526\pi$
$84$	17.1480	+	7.14529i	1.87100	+	0.779615i
$85$	11.5542	+	11.5542i	1.25323	+	1.25323i
$86$	−9.64611	+	1.90817i	−1.04017	+	0.205763i
$87$	−19.0528			−2.04268
$88$	−0.595078	−	0.896720i	−0.0634355	−	0.0955906i
$89$	−1.19209			−0.126361			−0.0631807	−	0.998002i	$-0.520124\pi$
$89$	−1.19209			−0.126361			−0.0631807	+	0.998002i	$0.520124\pi$
$90$	12.8422	−	2.54041i	1.35369	−	0.267783i
$91$	9.26595	+	9.26595i	0.971335	+	0.971335i
$92$	9.56914	+	0.656946i	0.997652	+	0.0684914i
$93$	2.10347	−	2.10347i	0.218120	−	0.218120i
$94$	−12.0750	−	8.08670i	−1.24545	−	0.834079i
$95$		−	4.03575i		−	0.414060i
$96$	8.12401	−	12.0209i	0.829153	−	1.22687i
$97$		−	0.0586996i		−	0.00596004i	−0.999996	−	0.00298002i	$-0.999051\pi$
$97$		−	0.0586996i		−	0.00596004i	0.999996	−	0.00298002i	$-0.000948572\pi$
$98$	4.81264	−	7.18622i	0.486150	−	0.725918i
$99$	0.962708	−	0.962708i	0.0967558	−	0.0967558i
$100$	−3.13051	+	1.28898i	−0.313051	+	0.128898i
$101$	1.67390	+	1.67390i	0.166559	+	0.166559i	0.785465	−	0.618906i	$-0.212424\pi$
$101$	1.67390	+	1.67390i	0.166559	+	0.166559i	−0.618906	+	0.785465i	$0.712424\pi$
$102$	4.44580	+	22.4743i	0.440199	+	2.22528i
$103$			10.3304i			1.01789i	0.860800	+	0.508943i	$0.169964\pi$
$103$			10.3304i			1.01789i	−0.860800	+	0.508943i	$0.830036\pi$
$104$	8.52736	−	5.65890i	0.836177	−	0.554900i
$105$		−	24.0298i		−	2.34506i
$106$	−1.86790	−	9.44253i	−0.181426	−	0.917140i
$107$	−6.74147	−	6.74147i	−0.651723	−	0.651723i	0.301685	−	0.953408i	$-0.402451\pi$
$107$	−6.74147	−	6.74147i	−0.651723	−	0.651723i	−0.953408	+	0.301685i	$0.902451\pi$
$108$	2.73751	+	1.14068i	0.263417	+	0.109762i
$109$	6.47373	+	6.47373i	0.620071	+	0.620071i	0.945549	−	0.325479i	$-0.105525\pi$
$109$	6.47373	+	6.47373i	0.620071	+	0.620071i	−0.325479	+	0.945549i	$0.605525\pi$
$110$	−0.774625	+	1.15667i	−0.0738576	+	0.110284i
$111$	29.1158			2.76355
$112$	−10.2001	−	10.2864i	−0.963815	−	0.971973i
$113$			16.4848i			1.55076i	0.631497	+	0.775378i	$0.282441\pi$
$113$			16.4848i			1.55076i	−0.631497	+	0.775378i	$0.717559\pi$
$114$	3.14856	−	4.70143i	0.294890	−	0.440329i
$115$	−3.97648	−	11.7525i	−0.370809	−	1.09592i
$116$	13.7143	+	5.71453i	1.27334	+	0.530581i
$117$	9.15488	+	9.15488i	0.846369	+	0.846369i
$118$	3.36418	+	17.0065i	0.309698	+	1.56558i
$119$	22.8744			2.09689
$120$	−18.3949	−	3.71946i	−1.67922	−	0.339538i
$121$		−	10.8552i		−	0.986838i
$122$	4.40247	−	0.870884i	0.398581	−	0.0788462i
$123$	−7.99711	+	7.99711i	−0.721075	+	0.721075i
$124$	−2.14498	+	0.883189i	−0.192625	+	0.0793127i
$125$	−6.04999	−	6.04999i	−0.541128	−	0.541128i
$126$	10.1975	−	15.2268i	0.908462	−	1.35651i
$127$		−	8.43988i		−	0.748918i	−0.927244	−	0.374459i	$-0.877828\pi$
$127$		−	8.43988i		−	0.748918i	0.927244	−	0.374459i	$-0.122172\pi$
$128$	−9.45311	+	6.21601i	−0.835544	+	0.549423i
$129$			17.8330i			1.57011i
$130$	−10.9993	−	7.36630i	−0.964706	−	0.646067i
$131$	−1.31950	−	1.31950i	−0.115285	−	0.115285i	0.647111	−	0.762396i	$-0.275977\pi$
$131$	−1.31950	−	1.31950i	−0.115285	−	0.115285i	−0.762396	+	0.647111i	$0.775977\pi$
$132$	−1.80479	+	0.743116i	−0.157087	+	0.0646799i
$133$	−3.99488	−	3.99488i	−0.346400	−	0.346400i
$134$	3.01985	+	15.2658i	0.260875	+	1.31877i
$135$		−	3.83613i		−	0.330161i
$136$	3.54062	−	17.5104i	0.303606	−	1.50151i
$137$	−9.54260			−0.815279			−0.407640	−	0.913143i	$-0.633648\pi$
$137$	−9.54260			−0.815279			−0.407640	+	0.913143i	$0.633648\pi$
$138$	4.53652	−	16.7933i	0.386174	−	1.42954i
$139$	−7.75982	+	7.75982i	−0.658179	+	0.658179i	−0.954949	−	0.296770i	$-0.904091\pi$
$139$	−7.75982	+	7.75982i	−0.658179	+	0.658179i	0.296770	+	0.954949i	$0.404091\pi$
$140$	−7.20726	+	17.2967i	−0.609125	+	1.46184i
$141$	−18.6367	+	18.6367i	−1.56950	+	1.56950i
$142$	−0.944941	+	1.41098i	−0.0792977	+	0.118407i
$143$	−1.37677			−0.115131
$144$	−10.0778	−	10.1631i	−0.839816	−	0.846924i
$145$		−	19.2181i		−	1.59597i
$146$	−5.77387	−	3.86678i	−0.477849	−	0.320017i
$147$	−11.0913	−	11.0913i	−0.914795	−	0.914795i
$148$	−20.9576	−	8.73272i	−1.72271	−	0.717825i
$149$	6.97103	−	6.97103i	0.571089	−	0.571089i	−0.361343	−	0.932433i	$-0.617682\pi$
$149$	6.97103	−	6.97103i	0.571089	−	0.571089i	0.932433	+	0.361343i	$0.117682\pi$
$150$	1.19148	+	6.02314i	0.0972840	+	0.491787i
$151$	−7.39871			−0.602099			−0.301049	−	0.953609i	$-0.597337\pi$
$151$	−7.39871			−0.602099			−0.301049	+	0.953609i	$0.597337\pi$
$152$	−3.67645	+	2.43975i	−0.298199	+	0.197890i
$153$	22.6002			1.82712
$154$	0.378173	+	1.91173i	0.0304741	+	0.154052i
$155$	2.12171	+	2.12171i	0.170420	+	0.170420i
$156$	−7.06667	−	17.1627i	−0.565786	−	1.37411i
$157$	−15.9324	−	15.9324i	−1.27154	−	1.27154i	−0.945278	−	0.326267i	$-0.894209\pi$
$157$	−15.9324	−	15.9324i	−1.27154	−	1.27154i	−0.326267	−	0.945278i	$-0.605791\pi$
$158$	−6.77030	+	10.1094i	−0.538616	+	0.804260i
$159$	−17.4566			−1.38440
$160$	12.1251	+	8.19447i	0.958575	+	0.647830i
$161$	−15.5696	−	7.69723i	−1.22706	−	0.606626i
$162$	−5.45447	+	8.14461i	−0.428544	+	0.639901i
$163$	9.18369	+	9.18369i	0.719322	+	0.719322i	0.968466	−	0.249144i	$-0.0801493\pi$
$163$	9.18369	+	9.18369i	0.719322	+	0.719322i	−0.249144	+	0.968466i	$0.580149\pi$
$164$	8.15492	−	3.35776i	0.636792	−	0.262197i
$165$	1.78521	+	1.78521i	0.138979	+	0.138979i
$166$	1.84773	+	9.34057i	0.143411	+	0.724969i
$167$	20.7370			1.60468			0.802338	−	0.596869i	$-0.203589\pi$
$167$	20.7370			1.60468			0.802338	+	0.596869i	$0.203589\pi$
$168$	−21.8904	+	14.5268i	−1.68888	+	1.12077i
$169$		−	0.0923780i		−	0.00710600i
$170$	−22.6692	+	4.48435i	−1.73865	+	0.343934i
$171$	−3.94699	−	3.94699i	−0.301834	−	0.301834i
$172$	5.34866	−	12.8362i	0.407831	−	0.978754i
$173$	−3.19814	+	3.19814i	−0.243150	+	0.243150i	−0.818152	−	0.575002i	$-0.805001\pi$
$173$	−3.19814	+	3.19814i	−0.243150	+	0.243150i	0.575002	+	0.818152i	$0.305001\pi$
$174$	14.9933	−	22.3880i	1.13664	−	1.69723i
$175$	6.13037			0.463413
$176$	1.52197	+	0.00641433i	0.114723	+	0.000483498i
$177$	31.4403			2.36320
$178$	0.938096	−	1.40076i	0.0703133	−	0.104992i
$179$	−7.17303	−	7.17303i	−0.536138	−	0.536138i	0.386255	−	0.922392i	$-0.373769\pi$
$179$	−7.17303	−	7.17303i	−0.536138	−	0.536138i	−0.922392	+	0.386255i	$0.873769\pi$
$180$	−7.12087	+	17.0894i	−0.530758	+	1.27376i
$181$	0.541249	−	0.541249i	0.0402307	−	0.0402307i	−0.686705	−	0.726936i	$-0.740944\pi$
$181$	0.541249	−	0.541249i	0.0402307	−	0.0402307i	0.726936	+	0.686705i	$0.240944\pi$
$182$	−18.1796	+	3.59624i	−1.34756	+	0.266571i
$183$		−	8.13895i		−	0.601649i
$184$	−8.30222	+	10.7272i	−0.612048	+	0.790821i
$185$			29.3683i			2.15920i
$186$	0.816386	+	4.12697i	0.0598603	+	0.302604i
$187$	−1.69938	+	1.69938i	−0.124271	+	0.124271i
$188$	19.0045	−	7.82505i	1.38605	−	0.570700i
$189$	−3.79727	−	3.79727i	−0.276211	−	0.276211i
$190$	4.74220	+	3.17587i	0.344036	+	0.230402i
$191$	5.02779			0.363798			0.181899	−	0.983317i	$-0.441776\pi$
$191$	5.02779			0.363798			0.181899	+	0.983317i	$0.441776\pi$
$192$	7.73203	+	19.0057i	0.558011	+	1.37162i
$193$	−2.40024			−0.172773			−0.0863865	−	0.996262i	$-0.527532\pi$
$193$	−2.40024			−0.172773			−0.0863865	+	0.996262i	$0.527532\pi$
$194$	0.0689748	+	0.0461927i	0.00495210	+	0.00331644i
$195$	−16.9765	+	16.9765i	−1.21571	+	1.21571i
$196$	4.65692	+	11.3102i	0.332637	+	0.807869i
$197$	−16.3275	−	16.3275i	−1.16329	−	1.16329i	−0.983751	−	0.179537i	$-0.942540\pi$
$197$	−16.3275	−	16.3275i	−1.16329	−	1.16329i	−0.179537	−	0.983751i	$-0.557460\pi$
$198$	0.373640	+	1.88881i	0.0265534	+	0.134232i
$199$			10.8769i			0.771046i	0.922698	+	0.385523i	$0.125979\pi$
$199$			10.8769i			0.771046i	−0.922698	+	0.385523i	$0.874021\pi$
$200$	0.948892	−	4.69283i	0.0670968	−	0.331833i
$201$	28.2223			1.99065
$202$	−3.28416	+	0.649663i	−0.231072	+	0.0457101i
$203$	−19.0234	−	19.0234i	−1.33518	−	1.33518i
$204$	−29.9068	−	12.4617i	−2.09390	−	0.872495i
$205$	−8.06647	−	8.06647i	−0.563387	−	0.563387i
$206$	−12.1387	−	8.12935i	−0.845745	−	0.566398i
$207$	−15.3830	−	7.60496i	−1.06919	−	0.528581i
$208$	−0.0609971	+	14.4732i	−0.00422939	+	1.00354i
$209$	0.593573			0.0410583
$210$	28.2361	+	18.9098i	1.94848	+	1.30490i
$211$	−8.71787	−	8.71787i	−0.600163	−	0.600163i	0.340193	−	0.940356i	$-0.389508\pi$
$211$	−8.71787	−	8.71787i	−0.600163	−	0.600163i	−0.940356	+	0.340193i	$0.889508\pi$
$212$	12.5653	+	5.23578i	0.862991	+	0.359595i
$213$	2.17773	+	2.17773i	0.149215	+	0.149215i
$214$	13.2266	−	2.61646i	0.904155	−	0.178857i
$215$	−17.9877			−1.22675
$216$	−3.49459	+	2.31907i	−0.237777	+	0.157793i
$217$	4.20045			0.285145
$218$	−12.7013	+	2.51254i	−0.860243	+	0.170171i
$219$	−8.91145	+	8.91145i	−0.602180	+	0.602180i
$220$	−0.749561	−	1.82044i	−0.0505354	−	0.122734i
$221$	−16.1602	−	16.1602i	−1.08706	−	1.08706i
$222$	−22.9122	+	34.2125i	−1.53777	+	2.29619i
$223$		−	13.6151i		−	0.911737i	−0.890047	−	0.455868i	$-0.849329\pi$
$223$		−	13.6151i		−	0.911737i	0.890047	−	0.455868i	$-0.150671\pi$
$224$	20.1138	−	3.89084i	1.34391	−	0.259968i
$225$	6.05689			0.403793
$226$	−19.3704	−	12.9724i	−1.28850	−	0.862912i
$227$	5.70418	−	5.70418i	0.378600	−	0.378600i	−0.491997	−	0.870597i	$-0.663733\pi$
$227$	5.70418	−	5.70418i	0.378600	−	0.378600i	0.870597	+	0.491997i	$0.163733\pi$
$228$	3.04669	+	7.39942i	0.201772	+	0.490039i
$229$	14.1391	−	14.1391i	0.934340	−	0.934340i	−0.0636330	−	0.997973i	$-0.520269\pi$
$229$	14.1391	−	14.1391i	0.934340	−	0.934340i	0.997973	+	0.0636330i	$0.0202687\pi$
$230$	16.9389	+	4.57586i	1.11692	+	0.301723i
$231$	3.53426			0.232537
$232$	−17.5071	+	11.6180i	−1.14940	+	0.762757i
$233$		−	15.6726i		−	1.02675i	−0.858165	−	0.513374i	$-0.828395\pi$
$233$		−	15.6726i		−	1.02675i	0.858165	−	0.513374i	$-0.171605\pi$
$234$	−17.9617	+	3.55313i	−1.17419	+	0.232276i
$235$	−18.7984	−	18.7984i	−1.22627	−	1.22627i
$236$	−22.6308	−	9.42992i	−1.47314	−	0.613835i
$237$	15.6030	+	15.6030i	1.01352	+	1.01352i
$238$	−18.0006	+	26.8785i	−1.16681	+	1.74227i
$239$		−	3.15550i		−	0.204112i	−0.994779	−	0.102056i	$-0.967458\pi$
$239$		−	3.15550i		−	0.204112i	0.994779	−	0.102056i	$-0.0325421\pi$
$240$	18.8461	−	18.6879i	1.21651	−	1.20630i
$241$			4.79423i			0.308824i	0.988007	+	0.154412i	$0.0493483\pi$
$241$			4.79423i			0.308824i	−0.988007	+	0.154412i	$0.950652\pi$
$242$	12.7554	+	8.54234i	0.819948	+	0.549122i
$243$	15.7160	+	15.7160i	1.00818	+	1.00818i
$244$	−2.44112	+	5.85844i	−0.156277	+	0.375048i
$245$	11.1875	−	11.1875i	0.714742	−	0.714742i
$246$	−3.10379	−	15.6902i	−0.197890	−	1.00037i
$247$			5.64458i			0.359156i
$248$	0.650168	−	3.21546i	0.0412857	−	0.204182i
$249$	17.2681			1.09432
$250$	11.8700	−	2.34809i	0.750723	−	0.148506i
$251$	11.2466	+	11.2466i	0.709880	+	0.709880i	0.966510	−	0.256629i	$-0.0826120\pi$
$251$	11.2466	+	11.2466i	0.709880	+	0.709880i	−0.256629	+	0.966510i	$0.582612\pi$
$252$	9.86751	+	23.9650i	0.621595	+	1.50965i
$253$	1.72854	−	0.584855i	0.108672	−	0.0367695i
$254$	9.91725	+	6.64162i	0.622264	+	0.416732i
$255$			41.9090i			2.62445i
$256$	0.134861	−	15.9994i	0.00842881	−	0.999964i
$257$	2.57936			0.160896			0.0804480	−	0.996759i	$-0.474365\pi$
$257$	2.57936			0.160896			0.0804480	+	0.996759i	$0.474365\pi$
$258$	−20.9546	−	14.0334i	−1.30458	−	0.873680i
$259$	29.0708	+	29.0708i	1.80637	+	1.80637i
$260$	17.3115	−	7.12796i	1.07361	−	0.442057i
$261$	−18.7954	−	18.7954i	−1.16341	−	1.16341i
$262$	2.58884	−	0.512117i	0.159939	−	0.0316387i
$263$		−	26.2487i		−	1.61856i	−0.587422	−	0.809281i	$-0.699857\pi$
$263$		−	26.2487i		−	1.61856i	0.587422	−	0.809281i	$-0.300143\pi$
$264$	0.547052	−	2.70549i	0.0336687	−	0.166512i
$265$		−	17.6080i		−	1.08165i
$266$	7.83787	−	1.55047i	0.480571	−	0.0950652i
$267$	−2.16195	−	2.16195i	−0.132309	−	0.132309i
$268$	−20.3145	−	8.46474i	−1.24091	−	0.517066i
$269$	17.4945	−	17.4945i	1.06666	−	1.06666i	0.0690446	−	0.997614i	$-0.478005\pi$
$269$	17.4945	−	17.4945i	1.06666	−	1.06666i	0.997614	−	0.0690446i	$-0.0219951\pi$
$270$	4.50763	+	3.01878i	0.274326	+	0.183717i
$271$		−	18.5245i		−	1.12528i	−0.826701	−	0.562641i	$-0.809785\pi$
$271$		−	18.5245i		−	1.12528i	0.826701	−	0.562641i	$-0.190215\pi$
$272$	17.7894	+	17.9400i	1.07864	+	1.08777i
$273$			33.6091i			2.03411i
$274$	7.50939	−	11.2130i	0.453659	−	0.677402i
$275$	−0.455436	+	0.455436i	−0.0274638	+	0.0274638i
$276$	16.1630	+	18.5458i	0.972897	+	1.11633i
$277$	−21.1888	−	21.1888i	−1.27311	−	1.27311i	−0.944446	−	0.328667i	$-0.893401\pi$
$277$	−21.1888	−	21.1888i	−1.27311	−	1.27311i	−0.328667	−	0.944446i	$-0.606599\pi$
$278$	−3.01169	−	15.2246i	−0.180629	−	0.913111i
$279$	4.15010			0.248460
$280$	−14.6528	−	22.0802i	−0.875671	−	1.31954i
$281$	20.5488			1.22584			0.612920	−	0.790145i	$-0.289995\pi$
$281$	20.5488			1.22584			0.612920	+	0.790145i	$0.289995\pi$
$282$	−7.23318	−	36.5649i	−0.430729	−	2.17741i
$283$	1.22470	+	1.22470i	0.0728009	+	0.0728009i	0.742570	−	0.669769i	$-0.233607\pi$
$283$	1.22470	+	1.22470i	0.0728009	+	0.0728009i	−0.669769	+	0.742570i	$0.733607\pi$
$284$	−0.914367	−	2.22070i	−0.0542577	−	0.131774i
$285$	7.31917	−	7.31917i	0.433550	−	0.433550i
$286$	1.08342	−	1.61777i	0.0640642	−	0.0956605i
$287$	−15.9695			−0.942651
$288$	19.8727	−	3.84420i	1.17101	−	0.226522i
$289$	−22.8940			−1.34670
$290$	22.5822	+	15.1234i	1.32607	+	0.888074i
$291$	0.106456	−	0.106456i	0.00624059	−	0.00624059i
$292$	9.08730	−	3.74167i	0.531794	−	0.218965i
$293$	14.7388	−	14.7388i	0.861047	−	0.861047i	−0.130413	−	0.991460i	$-0.541630\pi$
$293$	14.7388	−	14.7388i	0.861047	−	0.861047i	0.991460	+	0.130413i	$0.0416302\pi$
$294$	21.7609	−	4.30468i	1.26912	−	0.251054i
$295$			31.7130i			1.84640i
$296$	26.7536	−	17.7541i	1.55502	−	1.03194i
$297$	0.564212			0.0327389
$298$	2.70555	+	13.6770i	0.156729	+	0.792289i
$299$	5.56168	+	16.4375i	0.321641	+	0.950607i
$300$	−8.01509	−	3.33976i	−0.462751	−	0.192821i
$301$	−17.8055	+	17.8055i	−1.02629	+	1.02629i
$302$	5.82229	−	8.69384i	0.335035	−	0.500274i
$303$			6.07150i			0.348798i
$304$	0.0262980	−	6.23992i	0.00150829	−	0.357884i
$305$	8.20954			0.470077
$306$	−17.7848	+	26.5563i	−1.01669	+	1.51812i
$307$	7.92903	+	7.92903i	0.452534	+	0.452534i	0.896195	−	0.443661i	$-0.146321\pi$
$307$	7.92903	+	7.92903i	0.452534	+	0.452534i	−0.443661	+	0.896195i	$0.646321\pi$
$308$	−2.54397	−	1.06003i	−0.144956	−	0.0604010i
$309$	−18.7350	+	18.7350i	−1.06580	+	1.06580i
$310$	−4.16276	+	0.823466i	−0.236429	+	0.0467697i
$311$	−17.0177			−0.964986			−0.482493	−	0.875900i	$-0.660269\pi$
$311$	−17.0177			−0.964986			−0.482493	+	0.875900i	$0.660269\pi$
$312$	25.7279	+	5.20219i	1.45656	+	0.294516i
$313$	−14.4861			−0.818802			−0.409401	−	0.912354i	$-0.634262\pi$
$313$	−14.4861			−0.818802			−0.409401	+	0.912354i	$0.634262\pi$
$314$	31.2591	−	6.18359i	1.76405	−	0.348960i
$315$	23.7051	−	23.7051i	1.33563	−	1.33563i
$316$	−6.55124	−	15.9108i	−0.368536	−	0.895055i
$317$	−15.6355	+	15.6355i	−0.878179	+	0.878179i	−0.993346	−	0.115167i	$-0.963260\pi$
$317$	−15.6355	+	15.6355i	−0.878179	+	0.878179i	0.115167	+	0.993346i	$0.463260\pi$
$318$	13.7372	−	20.5124i	0.770345	−	1.15028i
$319$	2.82657			0.158257
$320$	−19.1705	+	7.79909i	−1.07167	+	0.435982i
$321$		−	24.4524i		−	1.36480i
$322$	21.2969	−	12.2379i	1.18683	−	0.681989i
$323$	6.96725	+	6.96725i	0.387668	+	0.387668i
$324$	−5.27799	−	12.8185i	−0.293222	−	0.712140i
$325$	−4.33097	−	4.33097i	−0.240239	−	0.240239i
$326$	−18.0182	+	3.56432i	−0.997937	+	0.197409i
$327$			23.4813i			1.29852i
$328$	−2.47185	+	12.2248i	−0.136485	+	0.674999i
$329$	−37.2159			−2.05178
$330$	−3.50255	+	0.692866i	−0.192809	+	0.0381410i
$331$	8.19088	−	8.19088i	0.450211	−	0.450211i	−0.445213	−	0.895425i	$-0.646872\pi$
$331$	8.19088	−	8.19088i	0.450211	−	0.450211i	0.895425	+	0.445213i	$0.146872\pi$
$332$	−12.4297	−	5.17924i	−0.682166	−	0.284248i
$333$	28.7224	+	28.7224i	1.57398	+	1.57398i
$334$	−16.3186	+	24.3669i	−0.892916	+	1.33330i
$335$			28.4671i			1.55532i
$336$	0.156584	−	37.1538i	0.00854236	−	2.02691i
$337$			7.93831i			0.432427i	0.976346	+	0.216214i	$0.0693708\pi$
$337$			7.93831i			0.432427i	−0.976346	+	0.216214i	$0.930629\pi$
$338$	0.108548	+	0.0726953i	0.00590426	+	0.00395410i
$339$	−29.8964	+	29.8964i	−1.62375	+	1.62375i
$340$	12.5698	−	30.1662i	0.681693	−	1.63599i
$341$	−0.312058	+	0.312058i	−0.0168989	+	0.0168989i
$342$	7.74392	−	1.53188i	0.418743	−	0.0828346i
$343$			3.20258i			0.172923i
$344$	10.8741	+	16.3862i	0.586294	+	0.883484i
$345$	14.1024	−	28.5257i	0.759247	−	1.53577i
$346$	−1.24124	−	6.27469i	−0.0667296	−	0.337329i
$347$	−22.2968	+	22.2968i	−1.19695	+	1.19695i	−0.221881	+	0.975074i	$0.571220\pi$
$347$	−22.2968	+	22.2968i	−1.19695	+	1.19695i	−0.975074	+	0.221881i	$0.928780\pi$
$348$	14.5082	+	35.2357i	0.777721	+	1.88883i
$349$	18.2616	−	18.2616i	0.977522	−	0.977522i	−0.0222312	−	0.999753i	$-0.507077\pi$
$349$	18.2616	−	18.2616i	0.977522	−	0.977522i	0.999753	+	0.0222312i	$0.00707699\pi$
$350$	−4.82420	+	7.20348i	−0.257864	+	0.385042i
$351$			5.36538i			0.286383i
$352$	−1.20523	+	1.78334i	−0.0642389	+	0.0950525i
$353$	32.3066			1.71951			0.859754	−	0.510708i	$-0.170617\pi$
$353$	32.3066			1.71951			0.859754	+	0.510708i	$0.170617\pi$
$354$	−24.7414	+	36.9439i	−1.31499	+	1.96354i
$355$	−2.19661	+	2.19661i	−0.116584	+	0.116584i
$356$	0.907743	+	2.20461i	0.0481103	+	0.116844i
$357$	41.4845	+	41.4845i	2.19559	+	2.19559i
$358$	14.0733	−	2.78395i	0.743800	−	0.147136i
$359$		−	2.45445i		−	0.129541i	−0.997900	−	0.0647706i	$-0.979368\pi$
$359$		−	2.45445i		−	0.129541i	0.997900	−	0.0647706i	$-0.0206316\pi$
$360$	−14.4771	−	21.8155i	−0.763012	−	1.14978i
$361$			16.5664i			0.871917i
$362$	0.210066	+	1.06192i	0.0110408	+	0.0558132i
$363$	19.6868	−	19.6868i	1.03329	−	1.03329i
$364$	10.0804	−	24.1919i	0.528356	−	1.26800i
$365$	−8.98874	−	8.98874i	−0.470492	−	0.470492i
$366$	9.56365	+	6.40481i	0.499900	+	0.334785i
$367$	−17.1727			−0.896408			−0.448204	−	0.893931i	$-0.647936\pi$
$367$	−17.1727			−0.896408			−0.448204	+	0.893931i	$0.647936\pi$
$368$	−6.07169	−	18.1971i	−0.316509	−	0.948590i
$369$	−15.7781			−0.821375
$370$	−34.5092	−	23.1109i	−1.79405	−	1.20148i
$371$	−17.4297	−	17.4297i	−0.904904	−	0.904904i
$372$	−5.49183	−	2.28836i	−0.284738	−	0.118646i
$373$	7.25484	−	7.25484i	0.375641	−	0.375641i	−0.493886	−	0.869527i	$-0.664424\pi$
$373$	7.25484	−	7.25484i	0.375641	−	0.375641i	0.869527	+	0.493886i	$0.164424\pi$
$374$	−0.659552	−	3.33415i	−0.0341046	−	0.172405i
$375$		−	21.9443i		−	1.13320i
$376$	−5.76048	+	28.4890i	−0.297074	+	1.46921i
$377$			26.8793i			1.38435i
$378$	7.45017	−	1.47377i	0.383195	−	0.0758027i
$379$	2.78196	+	2.78196i	0.142900	+	0.142900i	0.774938	−	0.632038i	$-0.217781\pi$
$379$	2.78196	+	2.78196i	0.142900	+	0.142900i	−0.632038	+	0.774938i	$0.717781\pi$
$380$	−7.46360	+	3.07311i	−0.382874	+	0.157647i
$381$	15.3064	−	15.3064i	0.784170	−	0.784170i
$382$	−3.95654	+	5.90789i	−0.202434	+	0.302274i
$383$	−11.8815			−0.607118			−0.303559	−	0.952813i	$-0.598175\pi$
$383$	−11.8815			−0.607118			−0.303559	+	0.952813i	$0.598175\pi$
$384$	−28.4172	−	5.87073i	−1.45016	−	0.299590i
$385$			3.56491i			0.181685i
$386$	1.88883	−	2.82040i	0.0961389	−	0.143554i
$387$	−17.5920	+	17.5920i	−0.894253	+	0.894253i
$388$	−0.108557	+	0.0446981i	−0.00551116	+	0.00226920i
$389$	−1.71369	+	1.71369i	−0.0868875	+	0.0868875i	−0.749215	−	0.662327i	$-0.769569\pi$
$389$	−1.71369	+	1.71369i	−0.0868875	+	0.0868875i	0.662327	+	0.749215i	$0.269569\pi$
$390$	−6.58881	−	33.3076i	−0.333638	−	1.68659i
$391$	27.1542	+	13.4243i	1.37325	+	0.678897i
$392$	−16.9547	−	3.42824i	−0.856340	−	0.173152i
$393$		−	4.78604i		−	0.241424i
$394$	32.0343	−	6.33694i	1.61386	−	0.319250i
$395$	−15.7383	+	15.7383i	−0.791878	+	0.791878i
$396$	−2.51348	−	1.04733i	−0.126307	−	0.0526301i
$397$	7.56504	−	7.56504i	0.379678	−	0.379678i	−0.491308	−	0.870986i	$-0.663481\pi$
$397$	7.56504	−	7.56504i	0.379678	−	0.379678i	0.870986	+	0.491308i	$0.163481\pi$
$398$	−12.7809	−	8.55943i	−0.640649	−	0.429045i
$399$		−	14.4901i		−	0.725410i
$400$	4.76758	+	4.80794i	0.238379	+	0.240397i
$401$		−	3.05609i		−	0.152614i	−0.997084	−	0.0763070i	$-0.975687\pi$
$401$		−	3.05609i		−	0.152614i	0.997084	−	0.0763070i	$-0.0243129\pi$
$402$	−22.2091	+	33.1626i	−1.10769	+	1.65400i
$403$	−2.96752	−	2.96752i	−0.147823	−	0.147823i
$404$	1.82103	−	4.37028i	0.0905995	−	0.217429i
$405$	−12.6795	+	12.6795i	−0.630049	+	0.630049i
$406$	37.3236	−	7.38325i	1.85234	−	0.366424i
$407$	−4.31945			−0.214107
$408$	38.1778	−	25.3354i	1.89008	−	1.25429i
$409$			33.0835i			1.63588i	0.575307	+	0.817938i	$0.304883\pi$
$409$			33.0835i			1.63588i	−0.575307	+	0.817938i	$0.695117\pi$
$410$	15.8263	−	3.13071i	0.781603	−	0.154615i
$411$	−17.3063	−	17.3063i	−0.853655	−	0.853655i
$412$	19.1047	−	7.86631i	0.941222	−	0.387545i
$413$	31.3918	+	31.3918i	1.54469	+	1.54469i
$414$	21.0416	−	12.0912i	1.03414	−	0.594248i
$415$			17.4179i			0.855011i
$416$	−16.9587	−	11.4611i	−0.831470	−	0.561929i
$417$	−28.1461			−1.37832
$418$	−0.467102	+	0.697476i	−0.0228467	+	0.0341147i
$419$	−22.6177	+	22.6177i	−1.10494	+	1.10494i	−0.111140	+	0.993805i	$0.535450\pi$
$419$	−22.6177	+	22.6177i	−1.10494	+	1.10494i	−0.993805	+	0.111140i	$0.964550\pi$
$420$	−44.4399	+	18.2980i	−2.16844	+	0.892850i
$421$	−22.8799	+	22.8799i	−1.11510	+	1.11510i	−0.122647	+	0.992450i	$0.539138\pi$
$421$	−22.8799	+	22.8799i	−1.11510	+	1.11510i	−0.992450	+	0.122647i	$0.960862\pi$
$422$	17.1043	−	3.38352i	0.832624	−	0.164707i
$423$	−36.7698			−1.78781
$424$	−16.0404	+	10.6446i	−0.778989	+	0.516950i
$425$	−10.6917			−0.518622
$426$	−4.27266	+	0.845206i	−0.207011	+	0.0409504i
$427$	8.12638	−	8.12638i	0.393263	−	0.393263i
$428$	−7.33402	+	17.6009i	−0.354503	+	0.850772i
$429$	−2.49688	−	2.49688i	−0.120550	−	0.120550i
$430$	14.1551	−	21.1363i	0.682619	−	1.01928i
$431$	17.8629			0.860428			0.430214	−	0.902727i	$-0.358438\pi$
$431$	17.8629			0.860428			0.430214	+	0.902727i	$0.358438\pi$
$432$	0.0249972	−	5.93126i	0.00120268	−	0.285368i
$433$		−	2.86324i		−	0.137598i	−0.997631	−	0.0687992i	$-0.978083\pi$
$433$		−	2.86324i		−	0.137598i	0.997631	−	0.0687992i	$-0.0219168\pi$
$434$	−3.30547	+	4.93572i	−0.158668	+	0.236922i
$435$	34.8535	−	34.8535i	1.67110	−	1.67110i
$436$	7.04275	−	16.9019i	0.337286	−	0.809453i
$437$	−2.39784	−	7.08680i	−0.114704	−	0.339007i
$438$	−3.45866	−	17.4841i	−0.165261	−	0.835422i
$439$	25.3589			1.21031			0.605157	−	0.796106i	$-0.293110\pi$
$439$	25.3589			1.21031			0.605157	+	0.796106i	$0.293110\pi$
$440$	2.72896	+	0.551796i	0.130098	+	0.0263059i
$441$		−	21.8828i		−	1.04204i
$442$	31.7061	−	6.27201i	1.50810	−	0.298329i
$443$	11.7406	−	11.7406i	0.557811	−	0.557811i	−0.370873	−	0.928684i	$-0.620941\pi$
$443$	11.7406	−	11.7406i	0.557811	−	0.557811i	0.928684	+	0.370873i	$0.120941\pi$
$444$	−22.1709	−	53.8459i	−1.05218	−	2.55541i
$445$	2.18070	−	2.18070i	0.103375	−	0.103375i
$446$	15.9984	+	10.7142i	0.757547	+	0.507332i
$447$	25.2851			1.19594
$448$	−11.2563	+	26.6965i	−0.531809	+	1.26129i
$449$	2.50438			0.118189			0.0590946	−	0.998252i	$-0.481179\pi$
$449$	2.50438			0.118189			0.0590946	+	0.998252i	$0.481179\pi$
$450$	−4.76637	+	7.11713i	−0.224689	+	0.335505i
$451$	1.18640	−	1.18640i	0.0558656	−	0.0558656i
$452$	30.4864	−	12.5527i	1.43396	−	0.590428i
$453$	−13.4182	−	13.4182i	−0.630440	−	0.630440i
$454$	2.21387	+	11.1915i	0.103902	+	0.525243i
$455$	−33.9006			−1.58928
$456$	−11.0922	−	2.24285i	−0.519440	−	0.105031i
$457$	−3.91619			−0.183192			−0.0915959	−	0.995796i	$-0.529197\pi$
$457$	−3.91619			−0.183192			−0.0915959	+	0.995796i	$0.529197\pi$
$458$	5.48759	+	27.7407i	0.256418	+	1.29624i
$459$	6.62262	+	6.62262i	0.309117	+	0.309117i
$460$	−18.7067	+	16.3032i	−0.872203	+	0.760139i
$461$	18.3420	−	18.3420i	0.854272	−	0.854272i	−0.136384	−	0.990656i	$-0.543548\pi$
$461$	18.3420	−	18.3420i	0.854272	−	0.854272i	0.990656	+	0.136384i	$0.0435482\pi$
$462$	−2.78123	+	4.15292i	−0.129394	+	0.193211i
$463$		−	17.5418i		−	0.815236i	−0.913153	−	0.407618i	$-0.866360\pi$
$463$		−	17.5418i		−	0.815236i	0.913153	−	0.407618i	$-0.133640\pi$
$464$	0.125230	−	29.7142i	0.00581365	−	1.37945i
$465$			7.69580i			0.356884i
$466$	18.4161	+	12.3333i	0.853109	+	0.571330i
$467$	11.3199	−	11.3199i	0.523820	−	0.523820i	−0.394903	−	0.918723i	$-0.629222\pi$
$467$	11.3199	−	11.3199i	0.523820	−	0.523820i	0.918723	+	0.394903i	$0.129222\pi$
$468$	9.95956	−	23.9019i	0.460381	−	1.10487i
$469$	28.1787	+	28.1787i	1.30117	+	1.30117i
$470$	36.8821	−	7.29591i	1.70124	−	0.336535i
$471$		−	57.7894i		−	2.66280i
$472$	28.8896	−	19.1716i	1.32975	−	0.882443i
$473$		−	2.64560i		−	0.121645i
$474$	−30.6127	+	6.05572i	−1.40609	+	0.278148i
$475$	1.86724	+	1.86724i	0.0856746	+	0.0856746i
$476$	−17.4182	−	42.3031i	−0.798361	−	1.93896i
$477$	−17.2208	−	17.2208i	−0.788484	−	0.788484i
$478$	3.70786	+	2.48317i	0.169593	+	0.113577i
$479$	−37.7331			−1.72407			−0.862034	−	0.506851i	$-0.830810\pi$
$479$	−37.7331			−1.72407			−0.862034	+	0.506851i	$0.830810\pi$
$480$	7.12855	+	36.8512i	0.325372	+	1.68202i
$481$		−	41.0758i		−	1.87290i
$482$	−5.63345	−	3.77274i	−0.256597	−	0.171844i
$483$	−14.2772	−	42.1963i	−0.649637	−	1.92000i
$484$	−20.0753	+	8.26594i	−0.912514	+	0.375725i
$485$	0.107380	+	0.107380i	0.00487586	+	0.00487586i
$486$	−30.8345	+	6.09960i	−1.39868	+	0.276684i
$487$	8.34618			0.378201			0.189101	−	0.981958i	$-0.439443\pi$
$487$	8.34618			0.378201			0.189101	+	0.981958i	$0.439443\pi$
$488$	−4.96294	−	7.47863i	−0.224662	−	0.338542i
$489$			33.3107i			1.50636i
$490$	4.34202	+	21.9496i	0.196152	+	0.991583i
$491$	15.7248	−	15.7248i	0.709648	−	0.709648i	−0.256813	−	0.966461i	$-0.582672\pi$
$491$	15.7248	−	15.7248i	0.709648	−	0.709648i	0.966461	+	0.256813i	$0.0826724\pi$
$492$	20.8792	+	8.70003i	0.941306	+	0.392228i
$493$	33.1777	+	33.1777i	1.49425	+	1.49425i
$494$	−6.63265	−	4.44191i	−0.298417	−	0.199851i
$495$			3.52218i			0.158310i
$496$	3.26668	+	3.29433i	0.146678	+	0.147920i
$497$			4.34873i			0.195067i
$498$	−13.5889	+	20.2909i	−0.608932	+	0.909256i
$499$	−12.1067	−	12.1067i	−0.541970	−	0.541970i	0.382136	−	0.924106i	$-0.375189\pi$
$499$	−12.1067	−	12.1067i	−0.541970	−	0.541970i	−0.924106	+	0.382136i	$0.875189\pi$
$500$	−6.58177	+	15.7956i	−0.294345	+	0.706399i
$501$	37.6082	+	37.6082i	1.68021	+	1.68021i
$502$	−22.0657	+	4.36497i	−0.984838	+	0.194818i
$503$		−	9.70841i		−	0.432876i	−0.976296	−	0.216438i	$-0.930556\pi$
$503$		−	9.70841i		−	0.432876i	0.976296	−	0.216438i	$-0.0694440\pi$
$504$	−35.9251	−	7.26406i	−1.60023	−	0.323567i
$505$	−6.12415			−0.272521
$506$	−0.673011	+	2.49135i	−0.0299190	+	0.110754i
$507$	0.167535	−	0.167535i	0.00744049	−	0.00744049i
$508$	−15.6084	+	6.42672i	−0.692512	+	0.285140i
$509$	−12.6583	+	12.6583i	−0.561070	+	0.561070i	−0.929611	−	0.368541i	$-0.879857\pi$
$509$	−12.6583	+	12.6583i	−0.561070	+	0.561070i	0.368541	+	0.929611i	$0.379857\pi$
$510$	−49.2451	−	32.9796i	−2.18061	−	1.46036i
$511$	−17.7954			−0.787221
$512$	18.6940	+	12.7490i	0.826164	+	0.563430i
$513$		−	2.31320i		−	0.102130i
$514$	−2.02978	+	3.03087i	−0.0895299	+	0.133686i
$515$	−18.8975	−	18.8975i	−0.832724	−	0.832724i
$516$	32.9798	−	13.5793i	1.45185	−	0.597796i
$517$	2.76484	−	2.76484i	0.121597	−	0.121597i
$518$	−57.0364	+	11.2828i	−2.50604	+	0.495738i
$519$	−11.6002			−0.509191
$520$	−5.24731	+	25.9511i	−0.230110	+	1.13803i
$521$	−14.4708			−0.633976			−0.316988	−	0.948430i	$-0.602672\pi$
$521$	−14.4708			−0.633976			−0.316988	+	0.948430i	$0.602672\pi$
$522$	36.8762	−	7.29475i	1.61403	−	0.319282i
$523$	−19.9077	−	19.9077i	−0.870505	−	0.870505i	0.122023	−	0.992527i	$-0.461062\pi$
$523$	−19.9077	−	19.9077i	−0.870505	−	0.870505i	−0.992527	+	0.122023i	$0.961062\pi$
$524$	−1.43548	+	3.44501i	−0.0627093	+	0.150496i
$525$	11.1179	+	11.1179i	0.485226	+	0.485226i
$526$	30.8434	+	20.6560i	1.34484	+	0.900642i
$527$	−7.32577			−0.319116
$528$	2.74859	+	2.77186i	0.119617	+	0.120630i
$529$	−13.9654	−	18.2748i	−0.607193	−	0.794555i
$530$	20.6903	+	13.8564i	0.898728	+	0.601882i
$531$	31.0155	+	31.0155i	1.34596	+	1.34596i
$532$	−4.34601	+	10.4300i	−0.188423	+	0.452197i
$533$	11.2821	+	11.2821i	0.488683	+	0.488683i
$534$	4.24171	−	0.839083i	0.183557	−	0.0363107i
$535$	24.6645			1.06634
$536$	25.9326	−	17.2093i	1.12012	−	0.743329i
$537$		−	26.0177i		−	1.12275i
$538$	6.78985	+	34.3239i	0.292731	+	1.47981i
$539$	1.64544	+	1.64544i	0.0708741	+	0.0708741i
$540$	−7.09441	+	2.92110i	−0.305295	+	0.125704i
$541$	−15.8009	+	15.8009i	−0.679335	+	0.679335i	−0.959850	−	0.280515i	$-0.909495\pi$
$541$	−15.8009	+	15.8009i	−0.679335	+	0.679335i	0.280515	+	0.959850i	$0.409495\pi$
$542$	21.7671	+	14.5775i	0.934979	+	0.626159i
$543$	1.96320			0.0842488
$544$	−35.0793	+	6.78580i	−1.50401	+	0.290939i
$545$	−23.6849			−1.01455
$546$	−39.4923	−	26.4481i	−1.69011	−	1.13187i
$547$	13.8316	+	13.8316i	0.591398	+	0.591398i	0.938009	−	0.346611i	$-0.112668\pi$
$547$	13.8316	+	13.8316i	0.591398	+	0.591398i	−0.346611	+	0.938009i	$0.612668\pi$
$548$	7.26642	+	17.6478i	0.310406	+	0.753876i
$549$	8.02897	−	8.02897i	0.342668	−	0.342668i
$550$	−0.176761	−	0.893557i	−0.00753711	−	0.0381014i
$551$		−	11.5886i		−	0.493691i
$552$	−34.5114	+	4.39793i	−1.46890	+	0.187188i
$553$			31.1577i			1.32496i
$554$	41.5720	−	8.22367i	1.76623	−	0.349390i
$555$	−53.2618	+	53.2618i	−2.26084	+	2.26084i
$556$	20.2596	+	8.44188i	0.859200	+	0.358015i
$557$	−8.54938	−	8.54938i	−0.362249	−	0.362249i	0.502392	−	0.864640i	$-0.332454\pi$
$557$	−8.54938	−	8.54938i	−0.362249	−	0.362249i	−0.864640	+	0.502392i	$0.832454\pi$
$558$	−3.26585	+	4.87656i	−0.138254	+	0.206441i
$559$	25.1583			1.06408
$560$	37.4761	+	0.157942i	1.58365	+	0.00667427i
$561$	−6.16392			−0.260241
$562$	−16.1706	+	24.1458i	−0.682114	+	1.01853i
$563$	28.8921	−	28.8921i	1.21766	−	1.21766i	0.249207	−	0.968450i	$-0.419830\pi$
$563$	28.8921	−	28.8921i	1.21766	−	1.21766i	0.968450	−	0.249207i	$-0.0801699\pi$
$564$	48.6576	+	20.2748i	2.04885	+	0.853725i
$565$	−30.1557	−	30.1557i	−1.26866	−	1.26866i
$566$	−2.40284	+	0.475323i	−0.100999	+	0.0199793i
$567$			25.1021i			1.05419i
$568$	3.32897	+	0.673120i	0.139681	+	0.0282435i
$569$	−40.3352			−1.69094			−0.845469	−	0.534025i	$-0.820679\pi$
$569$	−40.3352			−1.69094			−0.845469	+	0.534025i	$0.820679\pi$
$570$	2.84067	+	14.3601i	0.118983	+	0.601477i
$571$	32.0516	+	32.0516i	1.34132	+	1.34132i	0.894751	+	0.446566i	$0.147353\pi$
$571$	32.0516	+	32.0516i	1.34132	+	1.34132i	0.446566	+	0.894751i	$0.352647\pi$
$572$	1.04837	+	2.54615i	0.0438345	+	0.106460i
$573$	9.11831	+	9.11831i	0.380923	+	0.380923i
$574$	12.5670	−	18.7649i	0.524535	−	0.783234i
$575$	7.27737	+	3.59774i	0.303487	+	0.150036i
$576$	−11.1213	+	26.3764i	−0.463390	+	1.09902i
$577$	−17.0251			−0.708764			−0.354382	−	0.935101i	$-0.615309\pi$
$577$	−17.0251			−0.708764			−0.354382	+	0.935101i	$0.615309\pi$
$578$	18.0160	−	26.9015i	0.749368	−	1.11896i
$579$	−4.35303	−	4.35303i	−0.180906	−	0.180906i
$580$	−35.5413	+	14.6340i	−1.47577	+	0.607645i
$581$	17.2415	+	17.2415i	0.715297	+	0.715297i
$582$	0.0413172	+	0.208866i	0.00171265	+	0.00865775i
$583$	2.58976			0.107257
$584$	−2.75446	+	13.6224i	−0.113981	+	0.563701i
$585$	−33.4942			−1.38481
$586$	5.72031	+	28.9171i	0.236304	+	1.19456i
$587$	−13.1179	+	13.1179i	−0.541436	+	0.541436i	−0.923950	−	0.382514i	$-0.875058\pi$
$587$	−13.1179	+	13.1179i	−0.541436	+	0.541436i	0.382514	+	0.923950i	$0.375058\pi$
$588$	−12.0662	+	28.9576i	−0.497601	+	1.19419i
$589$	1.27940	+	1.27940i	0.0527169	+	0.0527169i
$590$	−37.2643	−	24.9560i	−1.53415	−	1.02742i
$591$		−	59.2226i		−	2.43609i
$592$	−0.191372	+	45.4081i	−0.00786532	+	1.86626i
$593$	24.3249			0.998903			0.499452	−	0.866342i	$-0.333535\pi$
$593$	24.3249			0.998903			0.499452	+	0.866342i	$0.333535\pi$
$594$	−0.443997	+	0.662975i	−0.0182174	+	0.0272022i
$595$	−41.8443	+	41.8443i	−1.71545	+	1.71545i
$596$	−18.2003	−	7.58376i	−0.745511	−	0.310643i
$597$	−19.7262	+	19.7262i	−0.807340	+	0.807340i
$598$	−23.6915	−	6.40000i	−0.968819	−	0.261715i
$599$	−2.73279			−0.111659			−0.0558294	−	0.998440i	$-0.517780\pi$
$599$	−2.73279			−0.111659			−0.0558294	+	0.998440i	$0.517780\pi$
$600$	10.2317	−	6.78993i	0.417708	−	0.277198i
$601$		−	37.7173i		−	1.53852i	−0.638934	−	0.769261i	$-0.720624\pi$
$601$		−	37.7173i		−	1.53852i	0.638934	−	0.769261i	$-0.279376\pi$
$602$	−6.91054	−	34.9340i	−0.281653	−	1.42380i
$603$	27.8410	+	27.8410i	1.13377	+	1.13377i
$604$	5.63391	+	13.6829i	0.229240	+	0.556751i
$605$	19.8576	+	19.8576i	0.807325	+	0.807325i
$606$	−7.13429	−	4.77786i	−0.289811	−	0.194087i
$607$			11.3587i			0.461034i	0.973068	+	0.230517i	$0.0740417\pi$
$607$			11.3587i			0.461034i	−0.973068	+	0.230517i	$0.925958\pi$
$608$	7.31150	+	4.94130i	0.296521	+	0.200396i
$609$		−	69.0010i		−	2.79606i
$610$	−6.46036	+	9.64659i	−0.261572	+	0.390579i
$611$	26.2922	+	26.2922i	1.06367	+	1.06367i
$612$	−17.2094	−	41.7961i	−0.695649	−	1.68951i
$613$	−17.7923	+	17.7923i	−0.718623	+	0.718623i	−0.968323	−	0.249700i	$-0.919668\pi$
$613$	−17.7923	+	17.7923i	−0.718623	+	0.718623i	0.249700	+	0.968323i	$0.419668\pi$
$614$	−15.5566	+	3.07737i	−0.627814	+	0.124192i
$615$		−	29.2584i		−	1.17981i
$616$	3.24752	−	2.15511i	0.130846	−	0.0868318i
$617$	−44.1833			−1.77875			−0.889375	−	0.457177i	$-0.848860\pi$
$617$	−44.1833			−1.77875			−0.889375	+	0.457177i	$0.848860\pi$
$618$	−7.27132	−	36.7578i	−0.292495	−	1.47861i
$619$	12.9187	+	12.9187i	0.519247	+	0.519247i	0.917343	−	0.398097i	$-0.130329\pi$
$619$	12.9187	+	12.9187i	0.519247	+	0.519247i	−0.398097	+	0.917343i	$0.630329\pi$
$620$	2.30820	−	5.53945i	0.0926997	−	0.222470i
$621$	−2.27923	−	6.73625i	−0.0914623	−	0.270316i
$622$	13.3918	−	19.9966i	0.536963	−	0.801791i
$623$		−	4.31723i		−	0.172966i
$624$	−26.3590	+	26.1377i	−1.05520	+	1.04635i
$625$	30.5983			1.22393
$626$	11.3996	−	17.0218i	0.455619	−	0.680330i
$627$	1.07649	+	1.07649i	0.0429909	+	0.0429909i
$628$	−17.3328	+	41.5970i	−0.691654	+	1.65990i
$629$	−50.7009	−	50.7009i	−2.02158	−	2.02158i
$630$	9.20026	+	46.5089i	0.366547	+	1.85296i
$631$			11.8121i			0.470232i	0.971967	+	0.235116i	$0.0755471\pi$
$631$			11.8121i			0.470232i	−0.971967	+	0.235116i	$0.924453\pi$
$632$	23.8514	+	4.82276i	0.948757	+	0.191839i
$633$		−	31.6211i		−	1.25683i
$634$	−6.06837	−	30.6766i	−0.241006	−	1.21832i
$635$	15.4391	+	15.4391i	0.612684	+	0.612684i
$636$	13.2927	+	32.2837i	0.527091	+	1.28013i
$637$	−15.6473	+	15.6473i	−0.619969	+	0.619969i
$638$	−2.22432	+	3.32135i	−0.0880616	+	0.131493i
$639$			4.29660i			0.169971i
$640$	5.92165	−	28.6637i	0.234074	−	1.13303i
$641$		−	2.80644i		−	0.110848i	−0.998463	−	0.0554239i	$-0.982349\pi$
$641$		−	2.80644i		−	0.110848i	0.998463	−	0.0554239i	$-0.0176510\pi$
$642$	28.7327	+	19.2424i	1.13399	+	0.759438i
$643$	−26.0085	+	26.0085i	−1.02568	+	1.02568i	−0.0260150	+	0.999662i	$0.508282\pi$
$643$	−26.0085	+	26.0085i	−1.02568	+	1.02568i	−0.999662	+	0.0260150i	$0.991718\pi$
$644$	−2.37917	+	34.6552i	−0.0937524	+	1.36561i
$645$	−32.6221	−	32.6221i	−1.28449	−	1.28449i
$646$	−13.6696	+	2.70408i	−0.537824	+	0.106391i
$647$	11.2848			0.443649			0.221825	−	0.975087i	$-0.428799\pi$
$647$	11.2848			0.443649			0.221825	+	0.975087i	$0.428799\pi$
$648$	19.2158	+	3.88544i	0.754868	+	0.152635i
$649$	−4.66430			−0.183090
$650$	8.49729	−	1.68091i	0.333291	−	0.0659307i
$651$	7.61785	+	7.61785i	0.298567	+	0.298567i
$652$	9.99090	−	23.9771i	0.391274	−	0.939017i
$653$	−7.11987	+	7.11987i	−0.278622	+	0.278622i	−0.832559	−	0.553937i	$-0.813125\pi$
$653$	−7.11987	+	7.11987i	−0.278622	+	0.278622i	0.553937	+	0.832559i	$0.313125\pi$
$654$	−27.5916	−	18.4782i	−1.07892	−	0.722554i
$655$	4.82755			0.188628
$656$	−12.4195	−	12.5246i	−0.484899	−	0.489004i
$657$	−17.5821			−0.685942
$658$	29.2865	−	43.7305i	1.14171	−	1.70479i
$659$	20.3612	−	20.3612i	0.793161	−	0.793161i	−0.188846	−	0.982007i	$-0.560475\pi$
$659$	20.3612	−	20.3612i	0.793161	−	0.793161i	0.982007	+	0.188846i	$0.0604746\pi$
$660$	1.94213	−	4.66090i	0.0755972	−	0.181425i
$661$	6.63554	−	6.63554i	0.258092	−	0.258092i	−0.566185	−	0.824278i	$-0.691581\pi$
$661$	6.63554	−	6.63554i	0.258092	−	0.258092i	0.824278	+	0.566185i	$0.191581\pi$
$662$	3.17899	+	16.0703i	0.123555	+	0.624592i
$663$		−	58.6158i		−	2.27645i
$664$	15.8672	−	10.5297i	0.615765	−	0.408632i
$665$	14.6157			0.566774
$666$	−56.3528	+	11.1475i	−2.18362	+	0.431959i
$667$	−11.4184	−	33.7470i	−0.442122	−	1.30669i
$668$	−15.7906	−	38.3503i	−0.610958	−	1.48382i
$669$	24.6921	−	24.6921i	0.954653	−	0.954653i
$670$	−33.4502	−	22.4017i	−1.29229	−	0.865453i
$671$			1.20745i			0.0466129i
$672$	43.5343	+	29.4216i	1.67937	+	1.13496i
$673$	2.07658			0.0800463			0.0400231	−	0.999199i	$-0.487257\pi$
$673$	2.07658			0.0800463			0.0400231	+	0.999199i	$0.487257\pi$
$674$	−9.32789	−	6.24692i	−0.359297	−	0.240622i
$675$	1.77487	+	1.77487i	0.0683149	+	0.0683149i
$676$	−0.170841	+	0.0703432i	−0.00657080	+	0.00270551i
$677$	26.5625	−	26.5625i	1.02088	−	1.02088i	0.0211017	−	0.999777i	$-0.493283\pi$
$677$	26.5625	−	26.5625i	1.02088	−	1.02088i	0.999777	−	0.0211017i	$-0.00671738\pi$
$678$	−11.6032	−	58.6562i	−0.445619	−	2.25268i
$679$	0.212584			0.00815823
$680$	25.5551	+	38.5089i	0.979995	+	1.47675i
$681$	20.6900			0.792842
$682$	−0.121114	−	0.612253i	−0.00463770	−	0.0234444i
$683$	−5.37857	+	5.37857i	−0.205805	+	0.205805i	−0.802482	−	0.596677i	$-0.796488\pi$
$683$	−5.37857	+	5.37857i	−0.205805	+	0.205805i	0.596677	+	0.802482i	$0.296488\pi$
$684$	−4.29392	+	10.3050i	−0.164182	+	0.394020i
$685$	17.4564	−	17.4564i	0.666973	−	0.666973i
$686$	−3.76318	−	2.52022i	−0.143679	−	0.0962223i
$687$	51.2849			1.95664
$688$	−27.8118	−	0.117212i	−1.06031	−	0.00446867i
$689$			24.6274i			0.938228i
$690$	22.4214	+	39.0188i	0.853570	+	1.48542i
$691$	10.9391	+	10.9391i	0.416144	+	0.416144i	0.883872	−	0.467729i	$-0.154928\pi$
$691$	10.9391	+	10.9391i	0.416144	+	0.416144i	−0.467729	+	0.883872i	$0.654928\pi$
$692$	8.34983	+	3.47925i	0.317413	+	0.132261i
$693$	3.48650	+	3.48650i	0.132441	+	0.132441i
$694$	−8.65369	−	43.7459i	−0.328490	−	1.66057i
$695$		−	28.3902i		−	1.07690i
$696$	−52.8206	−	10.6803i	−2.00216	−	0.404837i
$697$	27.8516			1.05495
$698$	7.08758	+	35.8289i	0.268269	+	1.35614i
$699$	28.4236	−	28.4236i	1.07508	−	1.07508i
$700$	−4.66810	−	11.3373i	−0.176438	−	0.428510i
$701$	10.8750	+	10.8750i	0.410744	+	0.410744i	0.881998	−	0.471253i	$-0.156198\pi$
$701$	10.8750	+	10.8750i	0.410744	+	0.410744i	−0.471253	+	0.881998i	$0.656198\pi$
$702$	−6.30457	−	4.22219i	−0.237951	−	0.159356i
$703$			17.7092i			0.667916i
$704$	−1.14708	−	2.81957i	−0.0432321	−	0.106267i
$705$		−	68.1847i		−	2.56799i
$706$	−25.4232	+	37.9618i	−0.956814	+	1.42871i
$707$	−6.06212	+	6.06212i	−0.227989	+	0.227989i
$708$	−23.9409	−	58.1447i	−0.899755	−	2.18521i
$709$	14.6083	−	14.6083i	0.548626	−	0.548626i	−0.377417	−	0.926043i	$-0.623188\pi$
$709$	14.6083	−	14.6083i	0.548626	−	0.548626i	0.926043	+	0.377417i	$0.123188\pi$
$710$	−0.852536	−	4.30971i	−0.0319951	−	0.161741i
$711$			30.7842i			1.15450i
$712$	−3.30486	−	0.668244i	−0.123855	−	0.0250435i
$713$	4.98635	+	2.46512i	0.186740	+	0.0923196i
$714$	−81.3918	+	16.1007i	−3.04601	+	0.602554i
$715$	2.51853	−	2.51853i	0.0941878	−	0.0941878i
$716$	−7.80351	+	18.7276i	−0.291631	+	0.699884i
$717$	5.72275	−	5.72275i	0.213720	−	0.213720i
$718$	2.88410	+	1.93149i	0.107634	+	0.0720826i
$719$			27.6279i			1.03035i	0.857086	+	0.515173i	$0.172272\pi$
$719$			27.6279i			1.03035i	−0.857086	+	0.515173i	$0.827728\pi$
$720$	37.0268	+	0.156049i	1.37991	+	0.00581560i
$721$	−37.4122			−1.39330
$722$	−19.4663	−	13.0367i	−0.724462	−	0.485175i
$723$	−8.69473	+	8.69473i	−0.323360	+	0.323360i
$724$	−1.41311	−	0.588822i	−0.0525179	−	0.0218834i
$725$	8.89169	+	8.89169i	0.330229	+	0.330229i
$726$	7.64072	+	38.6252i	0.283574	+	1.43351i
$727$			27.3088i			1.01283i	0.862290	+	0.506414i	$0.169029\pi$
$727$			27.3088i			1.01283i	−0.862290	+	0.506414i	$0.830971\pi$
$728$	20.4940	+	30.8823i	0.759559	+	1.14458i
$729$			36.2106i			1.34114i
$730$	17.6357	−	3.48865i	0.652727	−	0.129121i
$731$	31.0535	−	31.0535i	1.14856	−	1.14856i
$732$	−15.0519	+	6.19758i	−0.556335	+	0.229069i
$733$	−7.12573	−	7.12573i	−0.263195	−	0.263195i	0.563156	−	0.826351i	$-0.309587\pi$
$733$	−7.12573	−	7.12573i	−0.263195	−	0.263195i	−0.826351	+	0.563156i	$0.809587\pi$
$734$	13.5138	−	20.1787i	0.498803	−	0.744811i
$735$	40.5788			1.49677
$736$	26.1605	+	7.18538i	0.964288	+	0.264857i
$737$	−4.18690			−0.154226
$738$	12.4163	−	18.5400i	0.457051	−	0.682467i
$739$	−25.3504	−	25.3504i	−0.932530	−	0.932530i	0.0653333	−	0.997864i	$-0.479189\pi$
$739$	−25.3504	−	25.3504i	−0.932530	−	0.932530i	−0.997864	+	0.0653333i	$0.979189\pi$
$740$	54.3128	−	22.3631i	1.99658	−	0.822086i
$741$	−10.2369	+	10.2369i	−0.376062	+	0.376062i
$742$	34.1967	−	6.76470i	1.25540	−	0.248340i
$743$		−	21.9573i		−	0.805533i	−0.915303	−	0.402767i	$-0.868049\pi$
$743$		−	21.9573i		−	0.805533i	0.915303	−	0.402767i	$-0.131951\pi$
$744$	7.01063	−	4.65237i	0.257022	−	0.170564i
$745$			25.5044i			0.934407i
$746$	2.81570	+	14.2339i	0.103090	+	0.521138i
$747$	17.0348	+	17.0348i	0.623271	+	0.623271i
$748$	4.43680	+	1.84875i	0.162226	+	0.0675969i
$749$	24.4146	−	24.4146i	0.892092	−	0.892092i
$750$	25.7856	+	17.2687i	0.941556	+	0.630564i
$751$	−36.4936			−1.33167			−0.665836	−	0.746098i	$-0.731925\pi$
$751$	−36.4936			−1.33167			−0.665836	+	0.746098i	$0.731925\pi$
$752$	−28.9428	−	29.1878i	−1.05543	−	1.06437i
$753$			40.7933i			1.48659i
$754$	−31.5844	−	21.1522i	−1.15024	−	0.770317i
$755$	13.5345	−	13.5345i	0.492572	−	0.492572i
$756$	−4.13104	+	9.91406i	−0.150244	+	0.360571i
$757$	−19.4110	+	19.4110i	−0.705507	+	0.705507i	−0.965587	−	0.260080i	$-0.916251\pi$
$757$	−19.4110	+	19.4110i	−0.705507	+	0.705507i	0.260080	+	0.965587i	$0.416251\pi$
$758$	−5.45815	+	1.07972i	−0.198249	+	0.0392171i
$759$	4.19552	+	2.07416i	0.152288	+	0.0752871i
$760$	2.26230	−	11.1884i	0.0820623	−	0.405846i
$761$			6.97306i			0.252773i	0.991981	+	0.126387i	$0.0403380\pi$
$761$			6.97306i			0.252773i	−0.991981	+	0.126387i	$0.959662\pi$
$762$	5.94062	+	30.0308i	0.215206	+	1.08790i
$763$	−23.4450	+	23.4450i	−0.848766	+	0.848766i
$764$	−3.82852	−	9.29824i	−0.138511	−	0.336398i
$765$	−41.3427	+	41.3427i	−1.49475	+	1.49475i
$766$	9.34997	−	13.9614i	0.337828	−	0.504444i
$767$		−	44.3552i		−	1.60157i
$768$	29.2608	−	28.7717i	1.05586	−	1.03821i
$769$			28.8756i			1.04128i	0.853776	+	0.520640i	$0.174307\pi$
$769$			28.8756i			1.04128i	−0.853776	+	0.520640i	$0.825693\pi$
$770$	−4.18894	−	2.80535i	−0.150959	−	0.101098i
$771$	4.67787	+	4.67787i	0.168470	+	0.168470i
$772$	1.82771	+	4.43893i	0.0657809	+	0.159760i
$773$	15.8352	−	15.8352i	0.569551	−	0.569551i	−0.362452	−	0.932003i	$-0.618060\pi$
$773$	15.8352	−	15.8352i	0.569551	−	0.569551i	0.932003	+	0.362452i	$0.118060\pi$
$774$	−6.82770	−	34.5152i	−0.245417	−	1.24062i
$775$	−1.96332			−0.0705245
$776$	0.0329049	−	0.162734i	0.00118122	−	0.00584182i
$777$			105.445i			3.78281i
$778$	−0.665107	−	3.36223i	−0.0238452	−	0.120542i
$779$	−4.86412	−	4.86412i	−0.174275	−	0.174275i
$780$	44.3229	+	18.4687i	1.58702	+	0.661285i
$781$	−0.323075	−	0.323075i	−0.0115605	−	0.0115605i
$782$	−37.1427	+	21.3434i	−1.32822	+	0.763238i
$783$		−	11.0154i		−	0.393657i
$784$	17.3705	−	17.2247i	0.620376	−	0.615169i
$785$	58.2906			2.08048
$786$	5.62383	+	3.76630i	0.200595	+	0.134339i
$787$	30.5600	−	30.5600i	1.08935	−	1.08935i	0.0937510	−	0.995596i	$-0.470114\pi$
$787$	30.5600	−	30.5600i	1.08935	−	1.08935i	0.995596	−	0.0937510i	$-0.0298858\pi$
$788$	−17.7627	+	42.6286i	−0.632768	+	1.51858i
$789$	47.6041	−	47.6041i	1.69475	−	1.69475i
$790$	−6.10824	−	30.8782i	−0.217321	−	1.09860i
$791$	−59.7005			−2.12271
$792$	3.20860	−	2.12928i	0.114012	−	0.0756605i
$793$	−11.4822			−0.407746
$794$	2.93610	+	14.8425i	0.104198	+	0.526739i
$795$	31.9336	−	31.9336i	1.13257	−	1.13257i
$796$	20.1155	−	8.28248i	0.712973	−	0.293565i
$797$	−0.527263	−	0.527263i	−0.0186766	−	0.0186766i	0.697707	−	0.716383i	$-0.254204\pi$
$797$	−0.527263	−	0.527263i	−0.0186766	−	0.0186766i	−0.716383	+	0.697707i	$0.754204\pi$
$798$	17.0265	+	11.4027i	0.602732	+	0.403652i
$799$	64.9063			2.29622
$800$	−9.40133	+	1.81861i	−0.332387	+	0.0642975i
$801$		−	4.26548i		−	0.150713i
$802$	3.59105	+	2.40494i	0.126804	+	0.0849214i
$803$	1.32205	−	1.32205i	0.0466541	−	0.0466541i
$804$	−21.4905	−	52.1935i	−0.757911	−	1.84072i
$805$	42.5623	−	14.4011i	1.50012	−	0.507571i
$806$	5.82222	−	1.15174i	0.205079	−	0.0405682i
$807$	63.4553			2.23373
$808$	3.70226	+	5.57891i	0.130245	+	0.196265i
$809$		−	36.7312i		−	1.29140i	−0.763590	−	0.645701i	$-0.776565\pi$
$809$		−	36.7312i		−	1.29140i	0.763590	−	0.645701i	$-0.223435\pi$
$810$	−4.92108	−	24.8769i	−0.172909	−	0.874086i
$811$	−13.9161	+	13.9161i	−0.488661	+	0.488661i	−0.907884	−	0.419223i	$-0.862303\pi$
$811$	−13.9161	+	13.9161i	−0.488661	+	0.488661i	0.419223	+	0.907884i	$0.362303\pi$
$812$	−20.6955	+	49.6671i	−0.726270	+	1.74297i
$813$	33.5957	−	33.5957i	1.17825	−	1.17825i
$814$	3.39912	−	5.07556i	0.119139	−	0.177898i
$815$	−33.5996			−1.17694
$816$	−0.273090	+	64.7980i	−0.00956006	+	2.26838i
$817$	−10.8466			−0.379476
$818$	−38.8747	−	26.0345i	−1.35922	−	0.910276i
$819$	−33.1549	+	33.1549i	−1.15853	+	1.15853i
$820$	−8.77548	+	21.0603i	−0.306453	+	0.735456i
$821$	−3.09909	−	3.09909i	−0.108159	−	0.108159i	0.650956	−	0.759115i	$-0.274368\pi$
$821$	−3.09909	−	3.09909i	−0.108159	−	0.108159i	−0.759115	+	0.650956i	$0.774368\pi$
$822$	33.9546	−	6.71680i	1.18430	−	0.234275i
$823$	−18.8122			−0.655751			−0.327876	−	0.944721i	$-0.606333\pi$
$823$	−18.8122			−0.655751			−0.327876	+	0.944721i	$0.606333\pi$
$824$	−5.79086	+	28.6392i	−0.201734	+	0.997694i
$825$	−1.65194			−0.0575132
$826$	−61.5901	+	12.1836i	−2.14299	+	0.423921i
$827$	−32.6370	−	32.6370i	−1.13490	−	1.13490i	−0.989351	−	0.145549i	$-0.953505\pi$
$827$	−32.6370	−	32.6370i	−1.13490	−	1.13490i	−0.145549	−	0.989351i	$-0.546495\pi$
$828$	−2.35065	+	34.2398i	−0.0816908	+	1.18992i
$829$	−22.7084	+	22.7084i	−0.788695	+	0.788695i	−0.981280	−	0.192586i	$-0.938313\pi$
$829$	−22.7084	+	22.7084i	−0.788695	+	0.788695i	0.192586	+	0.981280i	$0.438313\pi$
$830$	−20.4669	−	13.7067i	−0.710415	−	0.475768i
$831$		−	76.8552i		−	2.66608i
$832$	26.8128	−	10.9081i	0.929566	−	0.378172i
$833$			38.6277i			1.33837i
$834$	22.1491	−	33.0730i	0.766961	−	1.14522i
$835$	−37.9344	+	37.9344i	−1.31277	+	1.31277i
$836$	−0.451989	−	1.09773i	−0.0156324	−	0.0379659i
$837$	1.21612	+	1.21612i	0.0420352	+	0.0420352i
$838$	−8.77822	−	44.3754i	−0.303239	−	1.53292i
$839$			43.5406i			1.50319i	0.659626	+	0.751594i	$0.270715\pi$
$839$			43.5406i			1.50319i	−0.659626	+	0.751594i	$0.729285\pi$
$840$	13.4702	−	66.6182i	0.464767	−	2.29855i
$841$		−	26.1843i		−	0.902908i
$842$	−8.88000	−	44.8899i	−0.306025	−	1.54701i
$843$	37.2669	+	37.2669i	1.28354	+	1.28354i
$844$	−9.48414	+	22.7610i	−0.326457	+	0.783464i
$845$	0.168988	+	0.168988i	0.00581336	+	0.00581336i
$846$	28.9354	−	43.2063i	0.994820	−	1.48546i
$847$	39.3128			1.35080
$848$	0.114738	−	27.2248i	0.00394013	−	0.934904i
$849$			4.44219i			0.152455i
$850$	8.41362	−	12.5632i	0.288585	−	0.430914i
$851$	17.4491	+	51.5709i	0.598149	+	1.76783i
$852$	2.36914	−	5.68570i	0.0811655	−	0.194789i
$853$	6.37782	+	6.37782i	0.218372	+	0.218372i	0.807812	−	0.589440i	$-0.200652\pi$
$853$	6.37782	+	6.37782i	0.218372	+	0.218372i	−0.589440	+	0.807812i	$0.700652\pi$
$854$	3.15396	+	15.9438i	0.107926	+	0.545586i
$855$	14.4405			0.493856
$856$	−14.9105	−	22.4686i	−0.509631	−	0.767960i
$857$		−	47.9956i		−	1.63950i	−0.572723	−	0.819749i	$-0.694113\pi$
$857$		−	47.9956i		−	1.63950i	0.572723	−	0.819749i	$-0.305887\pi$
$858$	4.89883	−	0.969072i	0.167243	−	0.0330836i
$859$	−1.67924	+	1.67924i	−0.0572948	+	0.0572948i	−0.735174	−	0.677879i	$-0.762899\pi$
$859$	−1.67924	+	1.67924i	−0.0572948	+	0.0572948i	0.677879	+	0.735174i	$0.262899\pi$
$860$	13.6971	+	33.2658i	0.467067	+	1.13435i
$861$	−28.9620	−	28.9620i	−0.987023	−	0.987023i
$862$	−14.0569	+	20.9898i	−0.478781	+	0.714915i
$863$			47.2239i			1.60752i	0.594954	+	0.803760i	$0.297170\pi$
$863$			47.2239i			1.60752i	−0.594954	+	0.803760i	$0.702830\pi$
$864$	6.94984	+	4.69688i	0.236438	+	0.159791i
$865$		−	11.7008i		−	0.397838i
$866$	3.36444	+	2.25318i	0.114328	+	0.0765661i
$867$	−41.5201	−	41.5201i	−1.41010	−	1.41010i
$868$	−3.19852	−	7.76817i	−0.108565	−	0.263669i
$869$	−2.31476	−	2.31476i	−0.0785229	−	0.0785229i
$870$	13.5271	+	68.3820i	0.458613	+	2.31837i
$871$		−	39.8153i		−	1.34909i
$872$	14.3183	+	21.5762i	0.484879	+	0.730663i
$873$	0.210036			0.00710864
$874$	10.2143	+	2.75926i	0.345502	+	0.0933335i
$875$	21.9104	−	21.9104i	0.740707	−	0.740707i
$876$	23.2664	+	9.69473i	0.786097	+	0.327555i
$877$	16.6262	−	16.6262i	0.561426	−	0.561426i	−0.368286	−	0.929712i	$-0.620055\pi$
$877$	16.6262	−	16.6262i	0.561426	−	0.561426i	0.929712	+	0.368286i	$0.120055\pi$
$878$	−19.9558	+	29.7979i	−0.673475	+	1.00563i
$879$	53.4598			1.80316
$880$	−2.79590	+	2.77243i	−0.0942496	+	0.0934585i
$881$			18.2592i			0.615170i	0.951521	+	0.307585i	$0.0995208\pi$
$881$			18.2592i			0.615170i	−0.951521	+	0.307585i	$0.900479\pi$
$882$	25.7134	+	17.2203i	0.865814	+	0.579839i
$883$	−12.9343	−	12.9343i	−0.435275	−	0.435275i	0.455143	−	0.890418i	$-0.349588\pi$
$883$	−12.9343	−	12.9343i	−0.435275	−	0.435275i	−0.890418	+	0.455143i	$0.849588\pi$
$884$	−17.5807	+	42.1918i	−0.591302	+	1.41906i
$885$	−57.5141	+	57.5141i	−1.93331	+	1.93331i
$886$	4.55667	+	23.0348i	0.153084	+	0.773868i
$887$	−25.1920			−0.845866			−0.422933	−	0.906161i	$-0.638999\pi$
$887$	−25.1920			−0.845866			−0.422933	+	0.906161i	$0.638999\pi$
$888$	80.7184	+	16.3213i	2.70873	+	0.547707i
$889$	30.5655			1.02513
$890$	0.846360	+	4.27850i	0.0283701	+	0.143415i
$891$	−1.86488	−	1.86488i	−0.0624758	−	0.0624758i
$892$	−25.1794	+	10.3675i	−0.843068	+	0.347131i
$893$	−11.3355	−	11.3355i	−0.379328	−	0.379328i
$894$	−19.8977	+	29.7111i	−0.665477	+	0.993689i
$895$	26.2434			0.877220
$896$	−22.5116	−	34.2350i	−0.752061	−	1.14371i
$897$	−19.7242	+	39.8973i	−0.658573	+	1.33213i
$898$	−1.97078	+	2.94277i	−0.0657659	+	0.0982015i
$899$	6.09246	+	6.09246i	0.203195	+	0.203195i
$900$	−4.61215	−	11.2014i	−0.153738	−	0.373381i
$901$	30.3982	+	30.3982i	1.01271	+	1.01271i
$902$	0.460460	+	2.32770i	0.0153316	+	0.0775040i
$903$	−64.5832			−2.14920
$904$	−9.24077	+	45.7011i	−0.307344	+	1.51999i
$905$			1.98022i			0.0658248i
$906$	26.3262	−	5.20777i	0.874628	−	0.173017i
$907$	14.0482	+	14.0482i	0.466464	+	0.466464i	0.900767	−	0.434303i	$-0.143005\pi$
$907$	14.0482	+	14.0482i	0.466464	+	0.466464i	−0.434303	+	0.900767i	$0.643005\pi$
$908$	−14.8927	−	6.20556i	−0.494232	−	0.205939i
$909$	−5.98945	+	5.98945i	−0.198658	+	0.198658i
$910$	26.6775	−	39.8348i	0.884350	−	1.32051i
$911$	15.3452			0.508409			0.254204	−	0.967151i	$-0.418186\pi$
$911$	15.3452			0.508409			0.254204	+	0.967151i	$0.418186\pi$
$912$	11.3643	−	11.2689i	0.376309	−	0.373150i
$913$	−2.56180			−0.0847832
$914$	3.08178	−	4.60171i	0.101936	−	0.152211i
$915$	14.8887	+	14.8887i	0.492204	+	0.492204i
$916$	−36.9150	−	15.3819i	−1.21971	−	0.508233i
$917$	4.77865	−	4.77865i	0.157805	−	0.157805i
$918$	−12.9934	+	2.57033i	−0.428848	+	0.0848335i
$919$			33.0339i			1.08969i	0.838538	+	0.544843i	$0.183411\pi$
$919$			33.0339i			1.08969i	−0.838538	+	0.544843i	$0.816589\pi$
$920$	−4.43607	−	34.8107i	−0.146253	−	1.14768i
$921$			28.7599i			0.947670i
$922$	7.11878	+	35.9866i	0.234444	+	1.18516i
$923$	3.07228	−	3.07228i	0.101125	−	0.101125i
$924$	−2.69124	−	6.53615i	−0.0885353	−	0.215023i
$925$	−13.5879	−	13.5879i	−0.446769	−	0.446769i
$926$	20.6124	+	13.8042i	0.677366	+	0.453635i
$927$	−36.9637			−1.21405
$928$	34.8170	+	23.5302i	1.14293	+	0.772418i
$929$	−12.2627			−0.402325			−0.201162	−	0.979558i	$-0.564472\pi$
$929$	−12.2627			−0.402325			−0.201162	+	0.979558i	$0.564472\pi$
$930$	−9.04293	−	6.05608i	−0.296529	−	0.198587i
$931$	6.74611	−	6.74611i	0.221095	−	0.221095i
$932$	−28.9845	+	11.9343i	−0.949418	+	0.390920i
$933$	−30.8630	−	30.8630i	−1.01041	−	1.01041i
$934$	4.39339	+	22.2093i	0.143756	+	0.726711i
$935$		−	6.21737i		−	0.203330i
$936$	20.2484	+	30.5122i	0.661839	+	0.997321i
$937$	−40.3310			−1.31756			−0.658778	−	0.752337i	$-0.728926\pi$
$937$	−40.3310			−1.31756			−0.658778	+	0.752337i	$0.728926\pi$
$938$	−55.2861	+	10.9366i	−1.80516	+	0.357091i
$939$	−26.2717	−	26.2717i	−0.857344	−	0.857344i
$940$	−20.4507	+	49.0795i	−0.667028	+	1.60080i
$941$	10.7068	+	10.7068i	0.349032	+	0.349032i	0.859749	−	0.510717i	$-0.170620\pi$
$941$	10.7068	+	10.7068i	0.349032	+	0.349032i	−0.510717	+	0.859749i	$0.670620\pi$
$942$	67.9053	+	45.4764i	2.21247	+	1.48170i
$943$	−18.9574	−	9.37206i	−0.617339	−	0.305196i
$944$	−0.206650	+	49.0333i	−0.00672589	+	1.59590i
$945$	13.8928			0.451932
$946$	3.10870	+	2.08191i	0.101073	+	0.0676887i
$947$	17.6384	+	17.6384i	0.573171	+	0.573171i	0.933013	−	0.359842i	$-0.117169\pi$
$947$	17.6384	+	17.6384i	0.573171	+	0.573171i	−0.359842	+	0.933013i	$0.617169\pi$
$948$	16.9744	−	40.7368i	0.551303	−	1.32307i
$949$	12.5720	+	12.5720i	0.408106	+	0.408106i
$950$	−3.66348	+	0.724699i	−0.118859	+	0.0235124i
$951$	−56.7126			−1.83903
$952$	63.4151	+	12.8226i	2.05530	+	0.415582i
$953$	−33.4218			−1.08264			−0.541319	−	0.840817i	$-0.682075\pi$
$953$	−33.4218			−1.08264			−0.541319	+	0.840817i	$0.682075\pi$
$954$	33.7868	−	6.68361i	1.09389	−	0.216390i
$955$	−9.19739	+	9.19739i	−0.297620	+	0.297620i
$956$	−5.83568	+	2.40282i	−0.188739	+	0.0777128i
$957$	5.12620	+	5.12620i	0.165707	+	0.165707i
$958$	29.6934	−	44.3381i	0.959351	−	1.43250i
$959$		−	34.5591i		−	1.11597i
$960$	−48.9116	−	20.6231i	−1.57862	−	0.665606i
$961$	29.6548			0.956605
$962$	48.2660	+	32.3239i	1.55616	+	1.04217i
$963$	24.1220	−	24.1220i	0.777320	−	0.777320i
$964$	8.86630	−	3.65067i	0.285564	−	0.117580i
$965$	4.39078	−	4.39078i	0.141344	−	0.141344i
$966$	60.8179	+	16.4293i	1.95678	+	0.528603i
$967$	−59.9286			−1.92717			−0.963587	−	0.267394i	$-0.913838\pi$
$967$	−59.9286			−1.92717			−0.963587	+	0.267394i	$0.913838\pi$
$968$	6.08505	−	30.0942i	0.195581	−	0.967263i
$969$			25.2713i			0.811832i
$970$	−0.210677	+	0.0416755i	−0.00676443	+	0.00133812i
$971$	6.60301	+	6.60301i	0.211901	+	0.211901i	0.805074	−	0.593174i	$-0.202125\pi$
$971$	6.60301	+	6.60301i	0.211901	+	0.211901i	−0.593174	+	0.805074i	$0.702125\pi$
$972$	17.0974	−	41.0320i	0.548400	−	1.31610i
$973$	−28.1026	−	28.1026i	−0.900929	−	0.900929i
$974$	−6.56789	+	9.80715i	−0.210449	+	0.314241i
$975$		−	15.7091i		−	0.503095i
$976$	12.6932	+	0.0534954i	0.406301	+	0.00171235i
$977$		−	55.0487i		−	1.76116i	−0.473895	−	0.880582i	$-0.657152\pi$
$977$		−	55.0487i		−	1.76116i	0.473895	−	0.880582i	$-0.342848\pi$
$978$	−39.1417	−	26.2133i	−1.25161	−	0.838210i
$979$	0.320734	+	0.320734i	0.0102507	+	0.0102507i
$980$	−29.2087	−	12.1708i	−0.933039	−	0.388783i
$981$	−23.1640	+	23.1640i	−0.739568	+	0.739568i
$982$	6.10299	+	30.8517i	0.194754	+	0.984516i
$983$			24.2884i			0.774681i	0.921937	+	0.387340i	$0.126606\pi$
$983$			24.2884i			0.774681i	−0.921937	+	0.387340i	$0.873394\pi$
$984$	−26.6535	+	17.6877i	−0.849682	+	0.563862i
$985$	59.7362			1.90335
$986$	−65.0941	+	12.8767i	−2.07302	+	0.410079i
$987$	−67.4941	−	67.4941i	−2.14836	−	2.14836i
$988$	10.4389	−	4.29819i	0.332106	−	0.136744i
$989$	−31.5864	+	10.6873i	−1.00439	+	0.339838i
$990$	−4.13873	−	2.77172i	−0.131537	−	0.0880911i
$991$			35.3565i			1.12314i	0.827430	+	0.561569i	$0.189802\pi$
$991$			35.3565i			1.12314i	−0.827430	+	0.561569i	$0.810198\pi$
$992$	−6.44166	+	1.24608i	−0.204523	+	0.0395632i
$993$	29.7096			0.942807
$994$	−5.10996	−	3.42216i	−0.162078	−	0.108544i
$995$	−19.8973	−	19.8973i	−0.630786	−	0.630786i
$996$	−13.1492	−	31.9351i	−0.416648	−	1.01190i
$997$	−21.5355	−	21.5355i	−0.682037	−	0.682037i	0.278422	−	0.960459i	$-0.410189\pi$
$997$	−21.5355	−	21.5355i	−0.682037	−	0.682037i	−0.960459	+	0.278422i	$0.910189\pi$
$998$	23.7531	−	4.69878i	0.751892	−	0.148737i
$999$			16.8333i			0.532580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	368.2.i.b.91.13	✓	80
4.3	odd	2		1472.2.i.b.1103.4		80
16.3	odd	4	inner	368.2.i.b.275.14	yes	80
16.13	even	4		1472.2.i.b.367.3		80
23.22	odd	2	inner	368.2.i.b.91.14	yes	80
92.91	even	2		1472.2.i.b.1103.3		80
368.45	odd	4		1472.2.i.b.367.4		80
368.275	even	4	inner	368.2.i.b.275.13	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.i.b.91.13	✓	80	1.1	even	1	trivial
368.2.i.b.91.14	yes	80	23.22	odd	2	inner
368.2.i.b.275.13	yes	80	368.275	even	4	inner
368.2.i.b.275.14	yes	80	16.3	odd	4	inner
1472.2.i.b.367.3		80	16.13	even	4
1472.2.i.b.367.4		80	368.45	odd	4
1472.2.i.b.1103.3		80	92.91	even	2
1472.2.i.b.1103.4		80	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.786933 + 1.17505i) q^{2} +(1.81358 + 1.81358i) q^{3} +(-0.761472 - 1.84937i) q^{4} +(-1.82931 + 1.82931i) q^{5} +(-3.55821 + 0.703875i) q^{6} +3.62156i q^{7} +(2.77232 + 0.560564i) q^{8} +3.57815i q^{9} +(-0.709980 - 3.58907i) q^{10} +(-0.269052 - 0.269052i) q^{11} +(1.97299 - 4.73497i) q^{12} +(2.55855 - 2.55855i) q^{13} +(-4.25550 - 2.84993i) q^{14} -6.63520 q^{15} +(-2.84032 + 2.81648i) q^{16} -6.31617i q^{17} +(-4.20449 - 2.81576i) q^{18} +(-1.10308 + 1.10308i) q^{19} +(4.77603 + 1.99010i) q^{20} +(-6.56799 + 6.56799i) q^{21} +(0.527875 - 0.104423i) q^{22} +(-2.12539 + 4.29915i) q^{23} +(4.01120 + 6.04446i) q^{24} -1.69274i q^{25} +(0.993009 + 5.01983i) q^{26} +(-1.04852 + 1.04852i) q^{27} +(6.69759 - 2.75771i) q^{28} +(-5.25282 + 5.25282i) q^{29} +(5.22146 - 7.79667i) q^{30} -1.15984i q^{31} +(-1.07435 - 5.55390i) q^{32} -0.975895i q^{33} +(7.42180 + 4.97040i) q^{34} +(-6.62495 - 6.62495i) q^{35} +(6.61731 - 2.72466i) q^{36} +(8.02716 - 8.02716i) q^{37} +(-0.428121 - 2.16422i) q^{38} +9.28028 q^{39} +(-6.09688 + 4.04599i) q^{40} +4.40957i q^{41} +(-2.54913 - 12.8863i) q^{42} +(4.91652 + 4.91652i) q^{43} +(-0.292701 + 0.702451i) q^{44} +(-6.54554 - 6.54554i) q^{45} +(-3.37917 - 5.88058i) q^{46} +10.2762i q^{47} +(-10.2591 - 0.0432366i) q^{48} -6.11569 q^{49} +(1.98905 + 1.33208i) q^{50} +(11.4549 - 11.4549i) q^{51} +(-6.67997 - 2.78344i) q^{52} +(-4.81276 + 4.81276i) q^{53} +(-0.406944 - 2.05717i) q^{54} +0.984358 q^{55} +(-2.03012 + 10.0401i) q^{56} -4.00105 q^{57} +(-2.03869 - 10.3059i) q^{58} +(8.66803 - 8.66803i) q^{59} +(5.05251 + 12.2709i) q^{60} +(-2.24389 - 2.24389i) q^{61} +(1.36287 + 0.912720i) q^{62} -12.9585 q^{63} +(7.37154 + 3.10813i) q^{64} +9.36077i q^{65} +(1.14672 + 0.767964i) q^{66} +(7.78083 - 7.78083i) q^{67} +(-11.6809 + 4.80958i) q^{68} +(-11.6514 + 3.94229i) q^{69} +(12.9980 - 2.57123i) q^{70} +1.20079 q^{71} +(-2.00578 + 9.91978i) q^{72} +4.91373i q^{73} +(3.11545 + 15.7491i) q^{74} +(3.06993 - 3.06993i) q^{75} +(2.87997 + 1.20004i) q^{76} +(0.974388 - 0.974388i) q^{77} +(-7.30296 + 10.9048i) q^{78} +8.60340 q^{79} +(0.0436116 - 10.3480i) q^{80} +6.93130 q^{81} +(-5.18145 - 3.47004i) q^{82} +(4.76079 - 4.76079i) q^{83} +(17.1480 + 7.14529i) q^{84} +(11.5542 + 11.5542i) q^{85} +(-9.64611 + 1.90817i) q^{86} -19.0528 q^{87} +(-0.595078 - 0.896720i) q^{88} -1.19209 q^{89} +(12.8422 - 2.54041i) q^{90} +(9.26595 + 9.26595i) q^{91} +(9.56914 + 0.656946i) q^{92} +(2.10347 - 2.10347i) q^{93} +(-12.0750 - 8.08670i) q^{94} -4.03575i q^{95} +(8.12401 - 12.0209i) q^{96} -0.0586996i q^{97} +(4.81264 - 7.18622i) q^{98} +(0.962708 - 0.962708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) \) 80 * q - 4 * q^2 - 4 * q^3 - 16 * q^6 - 4 * q^8 + 20 * q^12 - 4 * q^13 - 16 * q^16 + 24 * q^18 + 4 * q^23 + 4 * q^24 - 24 * q^26 + 44 * q^27 - 20 * q^29 - 24 * q^32 + 16 * q^35 + 104 * q^36 - 128 * q^39 - 16 * q^46 + 56 * q^48 - 160 * q^49 + 8 * q^50 - 72 * q^52 + 52 * q^54 - 8 * q^55 - 44 * q^58 + 80 * q^59 - 92 * q^62 - 24 * q^69 - 12 * q^70 - 8 * q^71 - 120 * q^72 - 12 * q^75 + 40 * q^77 + 136 * q^78 + 40 * q^81 + 132 * q^82 - 16 * q^85 - 8 * q^87 + 4 * q^92 - 28 * q^93 - 60 * q^94 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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