LMFDB - Embedded newform 1000.2.t.b.701.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(101,1000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1000.101"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.t (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [224] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.25
Character	$\chi$	$=$	1000.701
Dual form			1000.2.t.b.301.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.421131 - 1.35006i) q^{2} +(1.30450 - 0.423859i) q^{3} +(-1.64530 + 1.13710i) q^{4} +(-1.12160 - 1.58265i) q^{6} -0.927462 q^{7} +(2.22803 + 1.74238i) q^{8} +(-0.904979 + 0.657506i) q^{9} +(-1.54449 + 2.12581i) q^{11} +(-1.66433 + 2.18072i) q^{12} +(1.51507 + 2.08531i) q^{13} +(0.390583 + 1.25213i) q^{14} +(1.41401 - 3.74173i) q^{16} +(-0.290328 + 0.893539i) q^{17} +(1.26878 + 0.944876i) q^{18} +(0.336558 + 0.109354i) q^{19} +(-1.20988 + 0.393113i) q^{21} +(3.52040 + 1.18991i) q^{22} +(5.80876 + 4.22031i) q^{23} +(3.64500 + 1.32856i) q^{24} +(2.17724 - 2.92361i) q^{26} +(-3.32054 + 4.57033i) q^{27} +(1.52595 - 1.05462i) q^{28} +(1.33062 - 0.432345i) q^{29} +(-1.34398 + 4.13636i) q^{31} +(-5.64703 - 0.333231i) q^{32} +(-1.11375 + 3.42777i) q^{33} +(1.32859 + 0.0156626i) q^{34} +(0.741311 - 2.11084i) q^{36} +(5.42869 + 7.47195i) q^{37} +(0.00589944 - 0.500425i) q^{38} +(2.86029 + 2.07812i) q^{39} +(7.67997 - 5.57982i) q^{41} +(1.04024 + 1.46785i) q^{42} -5.59241i q^{43} +(0.123891 - 5.25383i) q^{44} +(3.25140 - 9.61944i) q^{46} +(2.55210 + 7.85457i) q^{47} +(0.258613 - 5.48044i) q^{48} -6.13981 q^{49} +1.28868i q^{51} +(-4.86395 - 1.70818i) q^{52} +(-9.26543 + 3.01052i) q^{53} +(7.56858 + 2.55821i) q^{54} +(-2.06642 - 1.61599i) q^{56} +0.485392 q^{57} +(-1.14405 - 1.61434i) q^{58} +(-2.55804 - 3.52083i) q^{59} +(2.14775 - 2.95612i) q^{61} +(6.15030 + 0.0725051i) q^{62} +(0.839334 - 0.609812i) q^{63} +(1.92826 + 7.76414i) q^{64} +(5.09672 + 0.0600846i) q^{66} +(-1.00295 - 0.325879i) q^{67} +(-0.538366 - 1.80027i) q^{68} +(9.36636 + 3.04331i) q^{69} +(3.56365 + 10.9678i) q^{71} +(-3.16194 - 0.111869i) q^{72} +(12.7408 + 9.25671i) q^{73} +(7.80136 - 10.4757i) q^{74} +(-0.678086 + 0.202780i) q^{76} +(1.43246 - 1.97161i) q^{77} +(1.60102 - 4.73671i) q^{78} +(1.73030 + 5.32530i) q^{79} +(-1.35747 + 4.17785i) q^{81} +(-10.7673 - 8.01855i) q^{82} +(-6.70408 - 2.17829i) q^{83} +(1.54360 - 2.02254i) q^{84} +(-7.55006 + 2.35514i) q^{86} +(1.55254 - 1.12799i) q^{87} +(-7.14514 + 2.04529i) q^{88} +(-7.12799 - 5.17879i) q^{89} +(-1.40517 - 1.93405i) q^{91} +(-14.3560 - 0.338530i) q^{92} +5.96555i q^{93} +(9.52933 - 6.75328i) q^{94} +(-7.50781 + 1.95884i) q^{96} +(0.496446 + 1.52791i) q^{97} +(2.58566 + 8.28909i) q^{98} -2.93933i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56}+ \cdots + 92 q^{96}+O(q^{100}) $ 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.421131	−	1.35006i	−0.297784	−	0.954633i
$2$	−0.421131	−	1.35006i	−0.297784	−	0.954633i
$3$	1.30450	−	0.423859i	0.753155	−	0.244715i	0.0928169	−	0.995683i	$-0.470413\pi$
$3$	1.30450	−	0.423859i	0.753155	−	0.244715i	0.660338	+	0.750968i	$0.270413\pi$
$4$	−1.64530	+	1.13710i	−0.822649	+	0.568550i
$5$		0			0
$5$		0			0
$6$	−1.12160	−	1.58265i	−0.457891	−	0.646115i
$7$	−0.927462			−0.350548			−0.175274	−	0.984520i	$-0.556081\pi$
$7$	−0.927462			−0.350548			−0.175274	+	0.984520i	$0.556081\pi$
$8$	2.22803	+	1.74238i	0.787728	+	0.616023i
$9$	−0.904979	+	0.657506i	−0.301660	+	0.219169i
$10$		0			0
$11$	−1.54449	+	2.12581i	−0.465682	+	0.640956i	−0.975675	−	0.219222i	$-0.929648\pi$
$11$	−1.54449	+	2.12581i	−0.465682	+	0.640956i	0.509993	+	0.860179i	$0.329648\pi$
$12$	−1.66433	+	2.18072i	−0.480450	+	0.629521i
$13$	1.51507	+	2.08531i	0.420204	+	0.578362i	0.965670	−	0.259771i	$-0.0836472\pi$
$13$	1.51507	+	2.08531i	0.420204	+	0.578362i	−0.545466	+	0.838133i	$0.683647\pi$
$14$	0.390583	+	1.25213i	0.104388	+	0.334645i
$15$		0			0
$16$	1.41401	−	3.74173i	0.353502	−	0.935434i
$17$	−0.290328	+	0.893539i	−0.0704150	+	0.216715i	−0.980071	−	0.198647i	$-0.936345\pi$
$17$	−0.290328	+	0.893539i	−0.0704150	+	0.216715i	0.909656	+	0.415362i	$0.136345\pi$
$18$	1.26878	+	0.944876i	0.299055	+	0.222709i
$19$	0.336558	+	0.109354i	0.0772118	+	0.0250876i	0.347368	−	0.937729i	$-0.387075\pi$
$19$	0.336558	+	0.109354i	0.0772118	+	0.0250876i	−0.270156	+	0.962816i	$0.587075\pi$
$20$		0			0
$21$	−1.20988	+	0.393113i	−0.264017	+	0.0857843i
$22$	3.52040	+	1.18991i	0.750551	+	0.253689i
$23$	5.80876	+	4.22031i	1.21121	+	0.879995i	0.995340	−	0.0964270i	$-0.0307414\pi$
$23$	5.80876	+	4.22031i	1.21121	+	0.879995i	0.215869	+	0.976422i	$0.430741\pi$
$24$	3.64500	+	1.32856i	0.744032	+	0.271192i
$25$		0			0
$26$	2.17724	−	2.92361i	0.426993	−	0.573368i
$27$	−3.32054	+	4.57033i	−0.639038	+	0.879561i
$28$	1.52595	−	1.05462i	0.288378	−	0.199304i
$29$	1.33062	−	0.432345i	0.247090	−	0.0802844i	−0.182854	−	0.983140i	$-0.558533\pi$
$29$	1.33062	−	0.432345i	0.247090	−	0.0802844i	0.429944	+	0.902856i	$0.358533\pi$
$30$		0			0
$31$	−1.34398	+	4.13636i	−0.241387	+	0.742911i	0.754823	+	0.655928i	$0.227723\pi$
$31$	−1.34398	+	4.13636i	−0.241387	+	0.742911i	−0.996210	+	0.0869831i	$0.972277\pi$
$32$	−5.64703	−	0.333231i	−0.998263	−	0.0589075i
$33$	−1.11375	+	3.42777i	−0.193879	+	0.596699i
$34$	1.32859	+	0.0156626i	0.227852	+	0.00268612i
$35$		0			0
$36$	0.741311	−	2.11084i	0.123552	−	0.351807i
$37$	5.42869	+	7.47195i	0.892471	+	1.22838i	0.972808	+	0.231613i	$0.0744004\pi$
$37$	5.42869	+	7.47195i	0.892471	+	1.22838i	−0.0803370	+	0.996768i	$0.525600\pi$
$38$	0.00589944	−	0.500425i	0.000957016	−	0.0811796i
$39$	2.86029	+	2.07812i	0.458013	+	0.332766i
$40$		0			0
$41$	7.67997	−	5.57982i	1.19941	−	0.871422i	0.205183	−	0.978724i	$-0.434221\pi$
$41$	7.67997	−	5.57982i	1.19941	−	0.871422i	0.994227	+	0.107301i	$0.0342210\pi$
$42$	1.04024	+	1.46785i	0.160513	+	0.226494i
$43$		−	5.59241i		−	0.852834i	−0.904527	−	0.426417i	$-0.859776\pi$
$43$		−	5.59241i		−	0.852834i	0.904527	−	0.426417i	$-0.140224\pi$
$44$	0.123891	−	5.25383i	0.0186772	−	0.792045i
$45$		0			0
$46$	3.25140	−	9.61944i	0.479393	−	1.41831i
$47$	2.55210	+	7.85457i	0.372263	+	1.14571i	0.945307	+	0.326182i	$0.105762\pi$
$47$	2.55210	+	7.85457i	0.372263	+	1.14571i	−0.573044	+	0.819524i	$0.694238\pi$
$48$	0.258613	−	5.48044i	0.0373275	−	0.791034i
$49$	−6.13981			−0.877116
$50$		0			0
$51$			1.28868i			0.180452i
$52$	−4.86395	−	1.70818i	−0.674508	−	0.236881i
$53$	−9.26543	+	3.01052i	−1.27270	+	0.413527i	−0.866005	−	0.500035i	$-0.833320\pi$
$53$	−9.26543	+	3.01052i	−1.27270	+	0.413527i	−0.406699	+	0.913562i	$0.633320\pi$
$54$	7.56858	+	2.55821i	1.02995	+	0.348128i
$55$		0			0
$56$	−2.06642	−	1.61599i	−0.276136	−	0.215945i
$57$	0.485392			0.0642918
$58$	−1.14405	−	1.61434i	−0.150222	−	0.211973i
$59$	−2.55804	−	3.52083i	−0.333028	−	0.458374i	0.609361	−	0.792893i	$-0.291426\pi$
$59$	−2.55804	−	3.52083i	−0.333028	−	0.458374i	−0.942389	+	0.334519i	$0.891426\pi$
$60$		0			0
$61$	2.14775	−	2.95612i	0.274991	−	0.378492i	−0.649076	−	0.760724i	$-0.724844\pi$
$61$	2.14775	−	2.95612i	0.274991	−	0.378492i	0.924067	+	0.382231i	$0.124844\pi$
$62$	6.15030	+	0.0725051i	0.781089	+	0.00920816i
$63$	0.839334	−	0.609812i	0.105746	−	0.0768291i
$64$	1.92826	+	7.76414i	0.241032	+	0.970517i
$65$		0			0
$66$	5.09672	+	0.0600846i	0.627363	+	0.00739590i
$67$	−1.00295	−	0.325879i	−0.122530	−	0.0398124i	0.247110	−	0.968987i	$-0.420519\pi$
$67$	−1.00295	−	0.325879i	−0.122530	−	0.0398124i	−0.369640	+	0.929175i	$0.620519\pi$
$68$	−0.538366	−	1.80027i	−0.0652865	−	0.218315i
$69$	9.36636	+	3.04331i	1.12758	+	0.366372i
$70$		0			0
$71$	3.56365	+	10.9678i	0.422927	+	1.30164i	0.904965	+	0.425486i	$0.139897\pi$
$71$	3.56365	+	10.9678i	0.422927	+	1.30164i	−0.482038	+	0.876151i	$0.660103\pi$
$72$	−3.16194	−	0.111869i	−0.372639	−	0.0131839i
$73$	12.7408	+	9.25671i	1.49119	+	1.08342i	0.973729	+	0.227712i	$0.0731245\pi$
$73$	12.7408	+	9.25671i	1.49119	+	1.08342i	0.517466	+	0.855704i	$0.326876\pi$
$74$	7.80136	−	10.4757i	0.906889	−	1.21778i
$75$		0			0
$76$	−0.678086	+	0.202780i	−0.0777817	+	0.0232604i
$77$	1.43246	−	1.97161i	0.163244	−	0.224686i
$78$	1.60102	−	4.73671i	0.181280	−	0.536327i
$79$	1.73030	+	5.32530i	0.194673	+	0.599143i	0.999980	+	0.00628500i	$0.00200059\pi$
$79$	1.73030	+	5.32530i	0.194673	+	0.599143i	−0.805307	+	0.592858i	$0.797999\pi$
$80$		0			0
$81$	−1.35747	+	4.17785i	−0.150830	+	0.464206i
$82$	−10.7673	−	8.01855i	−1.18905	−	0.885500i
$83$	−6.70408	−	2.17829i	−0.735868	−	0.239098i	−0.0829787	−	0.996551i	$-0.526443\pi$
$83$	−6.70408	−	2.17829i	−0.735868	−	0.239098i	−0.652889	+	0.757453i	$0.726443\pi$
$84$	1.54360	−	2.02254i	0.168421	−	0.220677i
$85$		0			0
$86$	−7.55006	+	2.35514i	−0.814144	+	0.253961i
$87$	1.55254	−	1.12799i	0.166450	−	0.120933i
$88$	−7.14514	+	2.04529i	−0.761675	+	0.218029i
$89$	−7.12799	−	5.17879i	−0.755566	−	0.548951i	0.141981	−	0.989869i	$-0.454653\pi$
$89$	−7.12799	−	5.17879i	−0.755566	−	0.548951i	−0.897547	+	0.440919i	$0.854653\pi$
$90$		0			0
$91$	−1.40517	−	1.93405i	−0.147302	−	0.202743i
$92$	−14.3560	−	0.338530i	−1.49672	−	0.0352942i
$93$			5.96555i			0.618598i
$94$	9.52933	−	6.75328i	0.982875	−	0.696548i
$95$		0			0
$96$	−7.50781	+	1.95884i	−0.766263	+	0.199923i
$97$	0.496446	+	1.52791i	0.0504065	+	0.155135i	0.973091	−	0.230420i	$-0.0740100\pi$
$97$	0.496446	+	1.52791i	0.0504065	+	0.155135i	−0.922685	+	0.385555i	$0.874010\pi$
$98$	2.58566	+	8.28909i	0.261192	+	0.837324i
$99$		−	2.93933i		−	0.295414i
$100$		0			0
$101$		−	7.75829i		−	0.771979i	−0.922503	−	0.385989i	$-0.873860\pi$
$101$		−	7.75829i		−	0.771979i	0.922503	−	0.385989i	$-0.126140\pi$
$102$	1.73979	−	0.542704i	0.172265	−	0.0537357i
$103$	−0.436559	−	1.34359i	−0.0430155	−	0.132388i	0.927242	−	0.374462i	$-0.122172\pi$
$103$	−0.436559	−	1.34359i	−0.0430155	−	0.132388i	−0.970258	+	0.242074i	$0.922172\pi$
$104$	−0.257775	+	7.28596i	−0.0252770	+	0.714447i
$105$		0			0
$106$	7.96632	+	11.2410i	0.773758	+	1.09182i
$107$		−	16.9717i		−	1.64071i	−0.571852	−	0.820357i	$-0.693775\pi$
$107$		−	16.9717i		−	1.64071i	0.571852	−	0.820357i	$-0.306225\pi$
$108$	0.266356	−	11.2953i	0.0256301	−	1.08689i
$109$	−6.86530	−	9.44928i	−0.657577	−	0.905077i	0.341822	−	0.939765i	$-0.388956\pi$
$109$	−6.86530	−	9.44928i	−0.657577	−	0.905077i	−0.999398	+	0.0346883i	$0.988956\pi$
$110$		0			0
$111$	10.2488	+	7.44618i	0.972772	+	0.706760i
$112$	−1.31144	+	3.47032i	−0.123919	+	0.327914i
$113$	−0.733494	+	0.532915i	−0.0690013	+	0.0501324i	−0.621751	−	0.783215i	$-0.713578\pi$
$113$	−0.733494	+	0.532915i	−0.0690013	+	0.0501324i	0.552750	+	0.833347i	$0.313578\pi$
$114$	−0.204414	−	0.655306i	−0.0191451	−	0.0613751i
$115$		0			0
$116$	−1.69765	+	2.22438i	−0.157623	+	0.206529i
$117$	−2.74221	−	0.890998i	−0.253517	−	0.0823728i
$118$	−3.67605	+	4.93622i	−0.338408	+	0.454416i
$119$	0.269269	−	0.828724i	0.0246838	−	0.0759690i
$120$		0			0
$121$	1.26557	+	3.89502i	0.115052	+	0.354093i
$122$	−4.89541	−	1.65466i	−0.443209	−	0.149806i
$123$	7.65349	−	10.5341i	0.690092	−	0.949830i
$124$	−2.49219	−	8.33378i	−0.223806	−	0.748395i
$125$		0			0
$126$	−1.17675	−	0.876337i	−0.104833	−	0.0780703i
$127$	13.1690	+	9.56787i	1.16856	+	0.849012i	0.990836	−	0.135068i	$-0.0431253\pi$
$127$	13.1690	+	9.56787i	1.16856	+	0.849012i	0.177728	+	0.984080i	$0.443125\pi$
$128$	9.66996	−	5.87297i	0.854712	−	0.519102i
$129$	−2.37039	−	7.29531i	−0.208701	−	0.642317i
$130$		0			0
$131$	−15.6123	−	5.07274i	−1.36405	−	0.443207i	−0.466657	−	0.884438i	$-0.654542\pi$
$131$	−15.6123	−	5.07274i	−1.36405	−	0.443207i	−0.897393	+	0.441231i	$0.854542\pi$
$132$	−2.06527	−	6.90616i	−0.179758	−	0.601104i
$133$	−0.312145	−	0.101422i	−0.0270664	−	0.00879441i
$134$	−0.0175805	+	1.49128i	−0.00151872	+	0.128827i
$135$		0			0
$136$	−2.20374	+	1.48497i	−0.188969	+	0.127335i
$137$	18.1256	−	13.1690i	1.54857	−	1.12510i	0.603913	−	0.797051i	$-0.293608\pi$
$137$	18.1256	−	13.1690i	1.54857	−	1.12510i	0.944659	−	0.328053i	$-0.106392\pi$
$138$	0.164180	−	13.9267i	0.0139760	−	1.18552i
$139$	−6.92525	+	9.53178i	−0.587392	+	0.808475i	−0.994481	−	0.104913i	$-0.966544\pi$
$139$	−6.92525	+	9.53178i	−0.587392	+	0.808475i	0.407090	+	0.913388i	$0.366544\pi$
$140$		0			0
$141$	6.65845	+	9.16457i	0.560743	+	0.771796i
$142$	13.3064	−	9.42999i	1.11664	−	0.791348i
$143$	−6.77299			−0.566386
$144$	1.18056	+	4.31591i	0.0983803	+	0.359659i
$145$		0			0
$146$	7.13154	−	21.0990i	0.590210	−	1.74617i
$147$	−8.00941	+	2.60241i	−0.660605	+	0.214643i
$148$	−17.4282	−	6.12062i	−1.43259	−	0.503112i
$149$		−	13.3102i		−	1.09041i	−0.838302	−	0.545207i	$-0.816451\pi$
$149$		−	13.3102i		−	1.09041i	0.838302	−	0.545207i	$-0.183549\pi$
$150$		0			0
$151$	−21.1864			−1.72412			−0.862062	−	0.506802i	$-0.830827\pi$
$151$	−21.1864			−1.72412			−0.862062	+	0.506802i	$0.830827\pi$
$152$	0.559326	+	0.830056i	0.0453674	+	0.0673264i
$153$	−0.324766	−	0.999527i	−0.0262558	−	0.0808069i
$154$	−3.26503	−	1.10359i	−0.263104	−	0.0889300i
$155$		0			0
$156$	−7.06906	−	0.166696i	−0.565978	−	0.0133463i
$157$			3.41079i			0.272211i	0.990694	+	0.136105i	$0.0434586\pi$
$157$			3.41079i			0.272211i	−0.990694	+	0.136105i	$0.956541\pi$
$158$	6.46077	−	4.57864i	0.513991	−	0.364257i
$159$	−10.8107	+	7.85446i	−0.857348	+	0.622900i
$160$		0			0
$161$	−5.38740	−	3.91418i	−0.424587	−	0.308480i
$162$	6.21200	+	0.0732325i	0.488061	+	0.00575369i
$163$	11.4146	+	15.7109i	0.894062	+	1.23057i	0.972324	+	0.233639i	$0.0750632\pi$
$163$	11.4146	+	15.7109i	0.894062	+	1.23057i	−0.0782611	+	0.996933i	$0.524937\pi$
$164$	−6.29102	+	17.9134i	−0.491246	+	1.39880i
$165$		0			0
$166$	−0.117514	+	9.96822i	−0.00912086	+	0.773684i
$167$	0.874029	−	2.68999i	0.0676344	−	0.208157i	−0.911527	−	0.411240i	$-0.865096\pi$
$167$	0.874029	−	2.68999i	0.0676344	−	0.208157i	0.979162	+	0.203082i	$0.0650959\pi$
$168$	−3.38060	−	1.23219i	−0.260819	−	0.0950657i
$169$	1.96412	−	6.04495i	0.151087	−	0.464997i
$170$		0			0
$171$	−0.376479	+	0.122326i	−0.0287901	+	0.00935447i
$172$	6.35913	+	9.20118i	0.484879	+	0.701583i
$173$	0.504895	−	0.694928i	0.0383864	−	0.0528344i	−0.789392	−	0.613889i	$-0.789604\pi$
$173$	0.504895	−	0.694928i	0.0383864	−	0.0528344i	0.827779	+	0.561055i	$0.189604\pi$
$174$	−2.17667	−	1.62099i	−0.165013	−	0.122887i
$175$		0			0
$176$	5.77030	+	8.78500i	0.434952	+	0.662194i
$177$	−4.82930	−	3.50869i	−0.362993	−	0.263730i
$178$	−3.98983	+	11.8041i	−0.299051	+	0.884757i
$179$	−21.7579	+	7.06957i	−1.62626	+	0.528404i	−0.973408	−	0.229079i	$-0.926428\pi$
$179$	−21.7579	+	7.06957i	−1.62626	+	0.528404i	−0.652854	+	0.757484i	$0.726428\pi$
$180$		0			0
$181$	18.5330	+	6.02173i	1.37754	+	0.447591i	0.901862	−	0.432025i	$-0.142201\pi$
$181$	18.5330	+	6.02173i	1.37754	+	0.447591i	0.475683	+	0.879617i	$0.342201\pi$
$182$	−2.01931	+	2.71154i	−0.149681	+	0.200993i
$183$	1.54876	−	4.76661i	0.114488	−	0.352358i
$184$	5.58874	+	19.5240i	0.412007	+	1.43933i
$185$		0			0
$186$	8.05382	−	2.51228i	0.590535	−	0.184209i
$187$	−1.45109	−	1.99725i	−0.106114	−	0.146053i
$188$	−13.1304	−	10.0211i	−0.957632	−	0.730864i
$189$	3.07968	−	4.23881i	0.224013	−	0.308328i
$190$		0			0
$191$	10.2038	−	7.41347i	0.738318	−	0.536420i	−0.153866	−	0.988092i	$-0.549172\pi$
$191$	10.2038	−	7.41347i	0.738318	−	0.536420i	0.892184	+	0.451672i	$0.149172\pi$
$192$	5.80632	+	9.31103i	0.419035	+	0.671966i
$193$	8.48402			0.610693			0.305347	−	0.952241i	$-0.401228\pi$
$193$	8.48402			0.610693			0.305347	+	0.952241i	$0.401228\pi$
$194$	1.85369	−	1.31368i	0.133087	−	0.0943166i
$195$		0			0
$196$	10.1018	−	6.98158i	0.721559	−	0.498684i
$197$	14.0122	−	4.55285i	0.998331	−	0.324377i	0.236132	−	0.971721i	$-0.424120\pi$
$197$	14.0122	−	4.55285i	0.998331	−	0.324377i	0.762198	+	0.647344i	$0.224120\pi$
$198$	−3.96825	+	1.23784i	−0.282012	+	0.0879695i
$199$	−5.70622			−0.404503			−0.202252	−	0.979334i	$-0.564826\pi$
$199$	−5.70622			−0.404503			−0.202252	+	0.979334i	$0.564826\pi$
$200$		0			0
$201$	−1.44648			−0.102027
$202$	−10.4741	+	3.26725i	−0.736956	+	0.229883i
$203$	−1.23410	+	0.400983i	−0.0866168	+	0.0281435i
$204$	−1.46536	−	2.12027i	−0.102596	−	0.148448i
$205$		0			0
$206$	−1.63007	+	1.15521i	−0.113573	+	0.0804871i
$207$	−8.03168			−0.558240
$208$	9.94501	−	2.72033i	0.689562	−	0.188621i
$209$	−0.752279	+	0.546562i	−0.0520362	+	0.0378065i
$210$		0			0
$211$	−7.99954	+	11.0104i	−0.550711	+	0.757989i	−0.990108	−	0.140304i	$-0.955192\pi$
$211$	−7.99954	+	11.0104i	−0.550711	+	0.757989i	0.439398	+	0.898293i	$0.355192\pi$
$212$	11.8211	−	15.4889i	0.811878	−	1.06378i
$213$	9.29758	+	12.7970i	0.637060	+	0.876838i
$214$	−22.9127	+	7.14729i	−1.56628	+	0.488579i
$215$		0			0
$216$	−15.3615	+	4.39722i	−1.04522	+	0.299193i
$217$	1.24649	−	3.83631i	0.0846175	−	0.260426i
$218$	−9.86586	+	13.2479i	−0.668200	+	0.897262i
$219$	20.5439	+	6.67512i	1.38823	+	0.451063i
$220$		0			0
$221$	−2.30318	+	0.748347i	−0.154928	+	0.0503393i
$222$	5.73668	−	16.9723i	0.385021	−	1.13910i
$223$	−18.3612	−	13.3402i	−1.22956	−	0.893328i	−0.232703	−	0.972548i	$-0.574757\pi$
$223$	−18.3612	−	13.3402i	−1.22956	−	0.893328i	−0.996857	+	0.0792204i	$0.974757\pi$
$224$	5.23741	+	0.309059i	0.349939	+	0.0206499i
$225$		0			0
$226$	1.02836	+	0.765831i	0.0684056	+	0.0509423i
$227$	−8.07830	+	11.1188i	−0.536176	+	0.737983i	−0.988056	−	0.154096i	$-0.950753\pi$
$227$	−8.07830	+	11.1188i	−0.536176	+	0.737983i	0.451880	+	0.892079i	$0.350753\pi$
$228$	−0.798615	+	0.551939i	−0.0528895	+	0.0365531i
$229$	−6.28758	+	2.04296i	−0.415495	+	0.135002i	−0.509302	−	0.860588i	$-0.670096\pi$
$229$	−6.28758	+	2.04296i	−0.415495	+	0.135002i	0.0938071	+	0.995590i	$0.470096\pi$
$230$		0			0
$231$	1.03296	−	3.17913i	0.0679639	−	0.209171i
$232$	3.71797	+	1.35516i	0.244097	+	0.0889707i
$233$	−4.44945	+	13.6940i	−0.291493	+	0.897123i	0.692884	+	0.721049i	$0.256340\pi$
$233$	−4.44945	+	13.6940i	−0.291493	+	0.897123i	−0.984377	+	0.176074i	$0.943660\pi$
$234$	−0.0480675	+	4.07736i	−0.00314227	+	0.266545i
$235$		0			0
$236$	8.21227	+	2.88408i	0.534573	+	0.187738i
$237$	4.51435	+	6.21347i	0.293239	+	0.403608i
$238$	−1.23222	−	0.0145265i	−0.0798730	−	0.000941612i
$239$	0.520809	+	0.378390i	0.0336883	+	0.0244760i	0.604502	−	0.796604i	$-0.293372\pi$
$239$	0.520809	+	0.378390i	0.0336883	+	0.0244760i	−0.570814	+	0.821080i	$0.693372\pi$
$240$		0			0
$241$	−18.0169	+	13.0900i	−1.16057	+	0.843202i	−0.989850	−	0.142118i	$-0.954609\pi$
$241$	−18.0169	+	13.0900i	−1.16057	+	0.843202i	−0.170719	+	0.985320i	$0.554609\pi$
$242$	4.72552	−	3.34890i	0.303768	−	0.215276i
$243$		−	10.9223i		−	0.700668i
$244$	−0.172281	+	7.30590i	−0.0110291	+	0.467712i
$245$		0			0
$246$	−17.4448	−	5.89639i	−1.11224	−	0.375940i
$247$	0.281871	+	0.867509i	0.0179350	+	0.0551983i
$248$	−10.2015	+	6.87421i	−0.647797	+	0.436513i
$249$	−9.66877			−0.612734
$250$		0			0
$251$		−	5.01412i		−	0.316488i	−0.987400	−	0.158244i	$-0.949417\pi$
$251$		−	5.01412i		−	0.316488i	0.987400	−	0.158244i	$-0.0505833\pi$
$252$	−0.687538	+	1.95773i	−0.0433108	+	0.123325i
$253$	−17.9432	+	5.83009i	−1.12808	+	0.366534i
$254$	7.37127	−	21.8083i	0.462514	−	1.36837i
$255$		0			0
$256$	−12.0012	−	10.5817i	−0.750072	−	0.661356i
$257$	4.08455			0.254787			0.127394	−	0.991852i	$-0.459339\pi$
$257$	4.08455			0.254787			0.127394	+	0.991852i	$0.459339\pi$
$258$	−8.85083	+	6.27244i	−0.551029	+	0.390505i
$259$	−5.03490	−	6.92995i	−0.312854	−	0.430606i
$260$		0			0
$261$	−0.919914	+	1.26615i	−0.0569412	+	0.0783729i
$262$	−0.273664	+	23.2137i	−0.0169070	+	1.43415i
$263$	−19.3404	+	14.0516i	−1.19258	+	0.866458i	−0.993534	−	0.113532i	$-0.963783\pi$
$263$	−19.3404	+	14.0516i	−1.19258	+	0.866458i	−0.199043	+	0.979991i	$0.563783\pi$
$264$	−8.45394	+	5.69662i	−0.520304	+	0.350603i
$265$		0			0
$266$	−0.00547151	+	0.464125i	−0.000335480	+	0.0284573i
$267$	−11.4936	−	3.73448i	−0.703395	−	0.228547i
$268$	2.02071	−	0.604288i	0.123435	−	0.0369128i
$269$	28.5572	+	9.27879i	1.74116	+	0.565738i	0.994986	−	0.100011i	$-0.0318876\pi$
$269$	28.5572	+	9.27879i	1.74116	+	0.565738i	0.746176	+	0.665749i	$0.231888\pi$
$270$		0			0
$271$	1.45987	+	4.49301i	0.0886807	+	0.272931i	0.985555	−	0.169354i	$-0.0541680\pi$
$271$	1.45987	+	4.49301i	0.0886807	+	0.272931i	−0.896875	+	0.442285i	$0.854168\pi$
$272$	2.93286	+	2.34980i	0.177831	+	0.142478i
$273$	−2.65281	−	1.92738i	−0.160555	−	0.116650i
$274$	−25.4121	−	18.9246i	−1.53520	−	1.14328i
$275$		0			0
$276$	−18.8710	+	5.64332i	−1.13590	+	0.339688i
$277$	2.18376	−	3.00568i	0.131209	−	0.180594i	−0.738357	−	0.674410i	$-0.764398\pi$
$277$	2.18376	−	3.00568i	0.131209	−	0.180594i	0.869567	+	0.493816i	$0.164398\pi$
$278$	15.7849	+	5.33534i	0.946713	+	0.319992i
$279$	−1.50340	−	4.62699i	−0.0900062	−	0.277011i
$280$		0			0
$281$	4.25051	−	13.0817i	0.253564	−	0.780389i	−0.740545	−	0.672006i	$-0.765433\pi$
$281$	4.25051	−	13.0817i	0.253564	−	0.780389i	0.994109	−	0.108383i	$-0.0345673\pi$
$282$	9.56860	−	12.8488i	0.569802	−	0.765133i
$283$	1.41763	+	0.460617i	0.0842695	+	0.0273808i	0.350848	−	0.936432i	$-0.385893\pi$
$283$	1.41763	+	0.460617i	0.0842695	+	0.0273808i	−0.266579	+	0.963813i	$0.585893\pi$
$284$	−18.3347	−	13.9930i	−1.08797	−	0.830335i
$285$		0			0
$286$	2.85232	+	9.14391i	0.168661	+	0.540691i
$287$	−7.12288	+	5.17508i	−0.420450	+	0.305475i
$288$	5.32955	−	3.41139i	0.314047	−	0.201018i
$289$	13.0392	+	9.47351i	0.767010	+	0.557265i
$290$		0			0
$291$	1.29523	+	1.78273i	0.0759278	+	0.104506i
$292$	−31.4882	−	0.742523i	−1.84271	−	0.0434529i
$293$		−	7.33412i		−	0.428464i	−0.976783	−	0.214232i	$-0.931275\pi$
$293$		−	7.33412i		−	0.428464i	0.976783	−	0.214232i	$-0.0687248\pi$
$294$	6.88641	+	9.71718i	0.401624	+	0.566718i
$295$		0			0
$296$	−0.923643	+	26.1066i	−0.0536857	+	1.51741i
$297$	−4.58711	−	14.1177i	−0.266171	−	0.819191i
$298$	−17.9695	+	5.60533i	−1.04094	+	0.324708i
$299$			18.5071i			1.07029i
$300$		0			0
$301$			5.18675i			0.298959i
$302$	8.92224	+	28.6028i	0.513417	+	1.64591i
$303$	−3.28842	−	10.1207i	−0.188915	−	0.581420i
$304$	0.885072	−	1.10468i	0.0507624	−	0.0633580i
$305$		0			0
$306$	−1.21265	+	0.859383i	−0.0693224	+	0.0491277i
$307$			3.91344i			0.223352i	0.993745	+	0.111676i	$0.0356218\pi$
$307$			3.91344i			0.223352i	−0.993745	+	0.111676i	$0.964378\pi$
$308$	−0.114904	+	4.87273i	−0.00654727	+	0.277650i
$309$	−1.13899	−	1.56768i	−0.0647947	−	0.0891822i
$310$		0			0
$311$	5.35582	+	3.89123i	0.303701	+	0.220652i	0.729189	−	0.684312i	$-0.239898\pi$
$311$	5.35582	+	3.89123i	0.303701	+	0.220652i	−0.425488	+	0.904964i	$0.639898\pi$
$312$	2.75195	+	9.61382i	0.155798	+	0.544275i
$313$	16.5981	−	12.0592i	0.938180	−	0.681628i	−0.00980162	−	0.999952i	$-0.503120\pi$
$313$	16.5981	−	12.0592i	0.938180	−	0.681628i	0.947982	+	0.318324i	$0.103120\pi$
$314$	4.60476	−	1.43639i	0.259861	−	0.0810601i
$315$		0			0
$316$	−8.90225	−	6.79419i	−0.500791	−	0.382203i
$317$	−4.73712	−	1.53918i	−0.266063	−	0.0864492i	0.172947	−	0.984931i	$-0.444671\pi$
$317$	−4.73712	−	1.53918i	−0.266063	−	0.0864492i	−0.439011	+	0.898482i	$0.644671\pi$
$318$	15.1567	+	11.2873i	0.849945	+	0.632963i
$319$	−1.13605	+	3.49640i	−0.0636065	+	0.195761i
$320$		0			0
$321$	−7.19359	−	22.1396i	−0.401507	−	1.23571i
$322$	−3.01555	+	8.92167i	−0.168050	+	0.497185i
$323$	−0.195425	+	0.268979i	−0.0108737	+	0.0149664i
$324$	−2.51720	−	8.41738i	−0.139844	−	0.467632i
$325$		0			0
$326$	16.4035	−	22.0267i	0.908506	−	1.21995i
$327$	−12.9610	−	9.41669i	−0.716743	−	0.520744i
$328$	26.8334	+	0.949358i	1.48163	+	0.0524195i
$329$	−2.36698	−	7.28481i	−0.130496	−	0.401625i
$330$		0			0
$331$	−18.8854	−	6.13623i	−1.03803	−	0.337278i	−0.260072	−	0.965589i	$-0.583746\pi$
$331$	−18.8854	−	6.13623i	−1.03803	−	0.337278i	−0.777962	+	0.628311i	$0.783746\pi$
$332$	13.5071	−	4.03927i	0.741300	−	0.221684i
$333$	−9.82570	−	3.19256i	−0.538445	−	0.174951i
$334$	−3.99971	−	0.0471521i	−0.218854	−	0.00258005i
$335$		0			0
$336$	−0.239854	+	5.08291i	−0.0130851	+	0.277295i
$337$	−11.2693	+	8.18761i	−0.613876	+	0.446007i	−0.850777	−	0.525527i	$-0.823868\pi$
$337$	−11.2693	+	8.18761i	−0.613876	+	0.446007i	0.236901	+	0.971534i	$0.423868\pi$
$338$	−8.98818	−	0.105960i	−0.488892	−	0.00576349i
$339$	−0.730965	+	1.00609i	−0.0397005	+	0.0546431i
$340$		0			0
$341$	−6.71734	−	9.24562i	−0.363764	−	0.500679i
$342$	0.323693	+	0.456753i	0.0175033	+	0.0246984i
$343$	12.1867			0.658019
$344$	9.74407	−	12.4601i	0.525365	−	0.671802i
$345$		0			0
$346$	−1.15082	−	0.388980i	−0.0618684	−	0.0209117i
$347$	3.02554	−	0.983057i	0.162419	−	0.0527733i	−0.226679	−	0.973970i	$-0.572787\pi$
$347$	3.02554	−	0.983057i	0.162419	−	0.0527733i	0.389098	+	0.921196i	$0.372787\pi$
$348$	−1.27176	+	3.62128i	−0.0681736	+	0.194121i
$349$			17.7286i			0.948990i	0.880258	+	0.474495i	$0.157369\pi$
$349$			17.7286i			0.948990i	−0.880258	+	0.474495i	$0.842631\pi$
$350$		0			0
$351$	−14.5614			−0.777231
$352$	9.43018	−	11.4898i	0.502630	−	0.612411i
$353$	−7.77568	−	23.9311i	−0.413858	−	1.27372i	−0.913269	−	0.407358i	$-0.866450\pi$
$353$	−7.77568	−	23.9311i	−0.413858	−	1.27372i	0.499411	−	0.866365i	$-0.333550\pi$
$354$	−2.70316	+	7.99744i	−0.143671	+	0.425059i
$355$		0			0
$356$	17.6165	+	0.415414i	0.933671	+	0.0220169i
$357$		−	1.19520i		−	0.0632569i
$358$	18.7072	+	26.3971i	0.988708	+	1.39513i
$359$	24.3831	−	17.7154i	1.28689	−	0.934983i	0.287156	−	0.957884i	$-0.407290\pi$
$359$	24.3831	−	17.7154i	1.28689	−	0.934983i	0.999738	+	0.0229013i	$0.00729034\pi$
$360$		0			0
$361$	−15.2700	−	11.0943i	−0.803685	−	0.583911i
$362$	0.324860	−	27.5565i	0.0170742	−	1.44834i
$363$	3.30188	+	4.54465i	0.173304	+	0.238532i
$364$	4.51113	+	1.58427i	0.236447	+	0.0830383i
$365$		0			0
$366$	−7.08741	−	0.0835526i	−0.370465	−	0.00436737i
$367$	−2.07559	+	6.38802i	−0.108345	+	0.333452i	−0.990501	−	0.137506i	$-0.956091\pi$
$367$	−2.07559	+	6.38802i	−0.108345	+	0.333452i	0.882156	+	0.470957i	$0.156091\pi$
$368$	24.0049	−	15.7673i	1.25134	−	0.821926i
$369$	−3.28144	+	10.0992i	−0.170825	+	0.525746i
$370$		0			0
$371$	8.59333	−	2.79214i	0.446144	−	0.144961i
$372$	−6.78342	−	9.81510i	−0.351704	−	0.508889i
$373$	14.2472	−	19.6096i	0.737692	−	1.01535i	−0.261056	−	0.965324i	$-0.584071\pi$
$373$	14.2472	−	19.6096i	0.737692	−	1.01535i	0.998748	−	0.0500223i	$-0.0159292\pi$
$374$	−2.08530	+	2.80015i	−0.107828	+	0.144792i
$375$		0			0
$376$	−7.99943	+	21.9470i	−0.412539	+	1.13183i
$377$	2.91755	+	2.11973i	0.150262	+	0.109171i
$378$	−7.01957	−	2.37264i	−0.361048	−	0.122035i
$379$	−7.74403	+	2.51619i	−0.397784	+	0.129248i	−0.501076	−	0.865403i	$-0.667062\pi$
$379$	−7.74403	+	2.51619i	−0.397784	+	0.129248i	0.103292	+	0.994651i	$0.467062\pi$
$380$		0			0
$381$	21.2345	+	6.89950i	1.08788	+	0.353472i
$382$	−14.3057	−	10.6536i	−0.731944	−	0.545086i
$383$	2.79177	−	8.59217i	0.142653	−	0.439040i	−0.854049	−	0.520192i	$-0.825860\pi$
$383$	2.79177	−	8.59217i	0.142653	−	0.439040i	0.996702	+	0.0811529i	$0.0258602\pi$
$384$	10.1252	−	11.7600i	0.516699	−	0.600125i
$385$		0			0
$386$	−3.57288	−	11.4539i	−0.181855	−	0.582988i
$387$	3.67704	+	5.06101i	0.186914	+	0.257266i
$388$	−2.55418	−	1.94935i	−0.129669	−	0.0989632i
$389$	7.45733	−	10.2641i	0.378102	−	0.520412i	−0.576979	−	0.816759i	$-0.695768\pi$
$389$	7.45733	−	10.2641i	0.378102	−	0.520412i	0.955080	+	0.296347i	$0.0957685\pi$
$390$		0			0
$391$	−5.45746	+	3.96507i	−0.275995	+	0.200522i
$392$	−13.6797	−	10.6979i	−0.690929	−	0.540323i
$393$	−22.5164			−1.13580
$394$	−12.0476	−	16.9999i	−0.606949	−	0.856445i
$395$		0			0
$396$	3.34231	+	4.83607i	0.167957	+	0.243022i
$397$	13.0071	−	4.22625i	0.652805	−	0.212109i	0.0361546	−	0.999346i	$-0.488489\pi$
$397$	13.0071	−	4.22625i	0.652805	−	0.212109i	0.616651	+	0.787237i	$0.288489\pi$
$398$	2.40307	+	7.70372i	0.120455	+	0.386152i
$399$	−0.450183			−0.0225373
$400$		0			0
$401$	34.7894			1.73730			0.868649	−	0.495428i	$-0.164989\pi$
$401$	34.7894			1.73730			0.868649	+	0.495428i	$0.164989\pi$
$402$	0.609157	+	1.95283i	0.0303820	+	0.0973982i
$403$	−10.6618	+	3.46424i	−0.531103	+	0.172566i
$404$	8.82195	+	12.7647i	0.438908	+	0.635067i
$405$		0			0
$406$	1.06107	+	1.49724i	0.0526599	+	0.0743066i
$407$	−24.2685			−1.20295
$408$	−2.24537	+	2.87123i	−0.111162	+	0.142147i
$409$	13.3846	−	9.72446i	0.661824	−	0.480843i	−0.205454	−	0.978667i	$-0.565867\pi$
$409$	13.3846	−	9.72446i	0.661824	−	0.480843i	0.867278	+	0.497823i	$0.165867\pi$
$410$		0			0
$411$	18.0631	−	24.8617i	0.890985	−	1.22634i
$412$	2.24607	+	1.71420i	0.110656	+	0.0844524i
$413$	2.37248	+	3.26544i	0.116742	+	0.160682i
$414$	3.38239	+	10.8432i	0.166235	+	0.532915i
$415$		0			0
$416$	−7.86074	−	12.2807i	−0.385405	−	0.602110i
$417$	−4.99387	+	15.3696i	−0.244551	+	0.752651i
$418$	1.05470	+	0.785443i	0.0515869	+	0.0384173i
$419$	−2.26155	−	0.734822i	−0.110484	−	0.0358984i	0.253253	−	0.967400i	$-0.418499\pi$
$419$	−2.26155	−	0.734822i	−0.110484	−	0.0358984i	−0.363737	+	0.931502i	$0.618499\pi$
$420$		0			0
$421$	−5.82497	+	1.89265i	−0.283892	+	0.0922420i	−0.447502	−	0.894283i	$-0.647686\pi$
$421$	−5.82497	+	1.89265i	−0.283892	+	0.0922420i	0.163610	+	0.986525i	$0.447686\pi$
$422$	18.2335	+	6.16299i	0.887594	+	0.300010i
$423$	−7.47402	−	5.43020i	−0.363399	−	0.264025i
$424$	−25.8891	−	9.43631i	−1.25729	−	0.458268i
$425$		0			0
$426$	13.3612	−	17.9415i	0.647352	−	0.869267i
$427$	−1.99195	+	2.74169i	−0.0963974	+	0.132680i
$428$	19.2985	+	27.9235i	0.932827	+	1.34973i
$429$	−8.83539	+	2.87079i	−0.426577	+	0.138603i
$430$		0			0
$431$	9.67194	−	29.7672i	0.465881	−	1.43383i	−0.391990	−	0.919970i	$-0.628213\pi$
$431$	9.67194	−	29.7672i	0.465881	−	1.43383i	0.857871	−	0.513865i	$-0.171787\pi$
$432$	12.4057	+	18.8871i	0.596869	+	0.908705i
$433$	4.60823	−	14.1827i	0.221457	−	0.681575i	−0.777175	−	0.629285i	$-0.783348\pi$
$433$	4.60823	−	14.1827i	0.221457	−	0.681575i	0.998632	−	0.0522905i	$-0.0166522\pi$
$434$	−5.70417	−	0.0672458i	−0.273809	−	0.00322790i
$435$		0			0
$436$	22.0402	+	7.74034i	1.05554	+	0.370695i
$437$	1.49348	+	2.05559i	0.0714426	+	0.0983324i
$438$	0.360109	−	30.5465i	0.0172067	−	1.45957i
$439$	26.3874	+	19.1715i	1.25940	+	0.915008i	0.998728	−	0.0504195i	$-0.0160558\pi$
$439$	26.3874	+	19.1715i	1.25940	+	0.915008i	0.260672	+	0.965427i	$0.416056\pi$
$440$		0			0
$441$	5.55640	−	4.03696i	0.264591	−	0.192236i
$442$	1.98025	+	2.79426i	0.0941908	+	0.132909i
$443$		−	24.4310i		−	1.16075i	−0.814349	−	0.580375i	$-0.802906\pi$
$443$		−	24.4310i		−	1.16075i	0.814349	−	0.580375i	$-0.197094\pi$
$444$	−25.3294	−	0.597292i	−1.20208	−	0.0283462i
$445$		0			0
$446$	−10.2776	+	30.4067i	−0.486656	+	1.43980i
$447$	−5.64164	−	17.3632i	−0.266841	−	0.821251i
$448$	−1.78839	−	7.20094i	−0.0844933	−	0.340213i
$449$	11.0987			0.523780			0.261890	−	0.965098i	$-0.415654\pi$
$449$	11.0987			0.523780			0.261890	+	0.965098i	$0.415654\pi$
$450$		0			0
$451$			24.9442i			1.17457i
$452$	0.600839	−	1.71086i	0.0282611	−	0.0804720i
$453$	−27.6377	+	8.98004i	−1.29853	+	0.421919i
$454$	18.4131	+	6.22367i	0.864168	+	0.292091i
$455$		0			0
$456$	1.08147	+	0.845735i	0.0506445	+	0.0396052i
$457$	10.7162			0.501281			0.250641	−	0.968080i	$-0.419359\pi$
$457$	10.7162			0.501281			0.250641	+	0.968080i	$0.419359\pi$
$458$	5.40600	+	7.62822i	0.252606	+	0.356443i
$459$	−3.11972	−	4.29393i	−0.145616	−	0.200423i
$460$		0			0
$461$	9.05653	−	12.4652i	0.421804	−	0.580564i	−0.544243	−	0.838927i	$-0.683183\pi$
$461$	9.05653	−	12.4652i	0.421804	−	0.580564i	0.966048	+	0.258363i	$0.0831832\pi$
$462$	−4.72701	−	0.0557262i	−0.219921	−	0.00259262i
$463$	−1.49042	+	1.08285i	−0.0692657	+	0.0503245i	−0.621879	−	0.783113i	$-0.713631\pi$
$463$	−1.49042	+	1.08285i	−0.0692657	+	0.0503245i	0.552614	+	0.833438i	$0.313631\pi$
$464$	0.263790	−	5.59016i	0.0122462	−	0.259517i
$465$		0			0
$466$	20.3614	+	0.240039i	0.943226	+	0.0111196i
$467$	20.0087	+	6.50123i	0.925894	+	0.300841i	0.732883	−	0.680355i	$-0.238174\pi$
$467$	20.0087	+	6.50123i	0.925894	+	0.300841i	0.193012	+	0.981196i	$0.438174\pi$
$468$	5.52490	−	1.65221i	0.255389	−	0.0763734i
$469$	0.930200	+	0.302240i	0.0429527	+	0.0139562i
$470$		0			0
$471$	1.44569	+	4.44939i	0.0666140	+	0.205017i
$472$	0.435227	−	12.3016i	0.0200329	−	0.566227i
$473$	11.8884	+	8.63743i	0.546630	+	0.397150i
$474$	6.48740	−	8.71131i	0.297976	−	0.400124i
$475$		0			0
$476$	0.499314	+	1.66968i	0.0228860	+	0.0765298i
$477$	6.40558	−	8.81653i	0.293292	−	0.403681i
$478$	0.291518	−	0.862472i	0.0133337	−	0.0394485i
$479$	−0.641151	−	1.97326i	−0.0292949	−	0.0901606i	0.935340	−	0.353750i	$-0.115094\pi$
$479$	−0.641151	−	1.97326i	−0.0292949	−	0.0901606i	−0.964635	+	0.263589i	$0.915094\pi$
$480$		0			0
$481$	−7.35651	+	22.6410i	−0.335428	+	1.03234i
$482$	25.2597	+	18.8112i	1.15055	+	0.856824i
$483$	−8.68694	−	2.82256i	−0.395270	−	0.128431i
$484$	−6.51127	−	4.96939i	−0.295967	−	0.225882i
$485$		0			0
$486$	−14.7457	+	4.59973i	−0.668881	+	0.208648i
$487$	−3.94704	+	2.86770i	−0.178858	+	0.129948i	−0.673612	−	0.739085i	$-0.735258\pi$
$487$	−3.94704	+	2.86770i	−0.178858	+	0.129948i	0.494754	+	0.869033i	$0.335258\pi$
$488$	9.93592	−	2.84415i	0.449778	−	0.128749i
$489$	21.5496	+	15.6567i	0.974507	+	0.708021i
$490$		0			0
$491$	11.2000	+	15.4154i	0.505447	+	0.695688i	0.983143	−	0.182837i	$-0.0585280\pi$
$491$	11.2000	+	15.4154i	0.505447	+	0.695688i	−0.477696	+	0.878525i	$0.658528\pi$
$492$	−0.613921	+	26.0345i	−0.0276777	+	1.17373i
$493$			1.31448i			0.0592013i
$494$	1.05248	−	0.745875i	0.0473533	−	0.0335585i
$495$		0			0
$496$	13.5767	+	10.8777i	0.609614	+	0.488422i
$497$	−3.30515	−	10.1722i	−0.148256	−	0.456286i
$498$	4.07182	+	13.0534i	0.182463	+	0.584936i
$499$		−	12.8562i		−	0.575522i	−0.957702	−	0.287761i	$-0.907089\pi$
$499$		−	12.8562i		−	0.575522i	0.957702	−	0.287761i	$-0.0929108\pi$
$500$		0			0
$501$		−	3.87956i		−	0.173326i
$502$	−6.76934	+	2.11160i	−0.302130	+	0.0942453i
$503$	7.75639	+	23.8717i	0.345840	+	1.06439i	0.961132	+	0.276088i	$0.0890381\pi$
$503$	7.75639	+	23.8717i	0.345840	+	1.06439i	−0.615292	+	0.788299i	$0.710962\pi$
$504$	2.93258	+	0.103754i	0.130628	+	0.00462157i
$505$		0			0
$506$	15.4274	+	21.7690i	0.685830	+	0.967751i
$507$		−	8.71817i		−	0.387188i
$508$	−32.5466	−	0.767483i	−1.44402	−	0.0340515i
$509$	−7.89183	−	10.8622i	−0.349799	−	0.481457i	0.597472	−	0.801890i	$-0.296172\pi$
$509$	−7.89183	−	10.8622i	−0.349799	−	0.481457i	−0.947271	+	0.320432i	$0.896172\pi$
$510$		0			0
$511$	−11.8166	−	8.58525i	−0.522735	−	0.379789i
$512$	−9.23182	+	20.6585i	−0.407993	+	0.912985i
$513$	−1.61734	+	1.17507i	−0.0714074	+	0.0518805i
$514$	−1.72013	−	5.51436i	−0.0758716	−	0.243228i
$515$		0			0
$516$	12.1955	+	9.30759i	0.536877	+	0.409744i
$517$	−20.6390	−	6.70603i	−0.907704	−	0.294931i
$518$	−7.23546	+	9.71581i	−0.317908	+	0.426888i
$519$	0.364086	−	1.12054i	0.0159816	−	0.0491862i
$520$		0			0
$521$	−7.91688	−	24.3656i	−0.346845	−	1.06748i	−0.960589	−	0.277973i	$-0.910337\pi$
$521$	−7.91688	−	24.3656i	−0.346845	−	1.06748i	0.613744	−	0.789505i	$-0.289663\pi$
$522$	2.09678	+	0.708719i	0.0917736	+	0.0310198i
$523$	15.7926	−	21.7366i	0.690562	−	0.950476i	−0.309438	−	0.950919i	$-0.600141\pi$
$523$	15.7926	−	21.7366i	0.690562	−	0.950476i	1.00000		0.000443114i	$0.000141047\pi$
$524$	31.4550	−	9.40655i	1.37412	−	0.410927i
$525$		0			0
$526$	27.1152	+	20.1930i	1.18228	+	0.880456i
$527$	−3.30580	−	2.40180i	−0.144003	−	0.104624i
$528$	11.2510	+	9.01427i	0.489635	+	0.392296i
$529$	8.82326	+	27.1552i	0.383620	+	1.18066i
$530$		0			0
$531$	4.62994	+	1.50436i	0.200922	+	0.0652836i
$532$	0.628899	−	0.188071i	0.0272662	−	0.00815389i
$533$	23.2714	+	7.56132i	1.00799	+	0.327517i
$534$	−0.201468	+	17.0896i	−0.00871836	+	0.739541i
$535$		0			0
$536$	−1.66681	−	2.47359i	−0.0719951	−	0.106843i
$537$	−25.3867	+	18.4446i	−1.09552	+	0.795941i
$538$	0.500572	−	42.4614i	0.0215812	−	1.83064i
$539$	9.48290	−	13.0521i	0.408457	−	0.562193i
$540$		0			0
$541$	−11.1415	−	15.3350i	−0.479011	−	0.659302i	0.499304	−	0.866427i	$-0.333589\pi$
$541$	−11.1415	−	15.3350i	−0.479011	−	0.659302i	−0.978314	+	0.207125i	$0.933589\pi$
$542$	5.45102	−	3.86305i	0.234141	−	0.165932i
$543$	26.7287			1.14704
$544$	1.93725	−	4.94910i	0.0830588	−	0.212191i
$545$		0			0
$546$	−1.48489	+	4.39312i	−0.0635474	+	0.188008i
$547$	14.4470	−	4.69413i	0.617711	−	0.200706i	0.0165870	−	0.999862i	$-0.494720\pi$
$547$	14.4470	−	4.69413i	0.617711	−	0.200706i	0.601124	+	0.799156i	$0.294720\pi$
$548$	−14.8475	+	42.2775i	−0.634254	+	1.80601i
$549$			4.08738i			0.174445i
$550$		0			0
$551$	0.495110			0.0210924
$552$	15.5660	+	23.1003i	0.662531	+	0.983214i
$553$	−1.60478	−	4.93902i	−0.0682424	−	0.210028i
$554$	−4.97748	−	1.68241i	−0.211473	−	0.0714786i
$555$		0			0
$556$	0.555506	−	23.5573i	0.0235587	−	0.999053i
$557$			1.85471i			0.0785867i	0.999228	+	0.0392933i	$0.0125107\pi$
$557$			1.85471i			0.0785867i	−0.999228	+	0.0392933i	$0.987489\pi$
$558$	−5.61357	+	3.97824i	−0.237641	+	0.168412i
$559$	11.6619	−	8.47288i	0.493247	−	0.358365i
$560$		0			0
$561$	−2.73950	−	1.99036i	−0.115662	−	0.0840331i
$562$	−19.4510	−	0.229306i	−0.820493	−	0.00967269i
$563$	22.0332	+	30.3261i	0.928587	+	1.27809i	0.960408	+	0.278597i	$0.0898694\pi$
$563$	22.0332	+	30.3261i	0.928587	+	1.27809i	−0.0318207	+	0.999494i	$0.510131\pi$
$564$	−21.3762	−	7.50713i	−0.900099	−	0.316107i
$565$		0			0
$566$	0.0248493	−	2.10786i	0.00104449	−	0.0886000i
$567$	1.25900	−	3.87480i	0.0528730	−	0.162726i
$568$	−11.1701	+	30.6458i	−0.468686	+	1.28587i
$569$	8.05065	−	24.7774i	0.337501	−	1.03872i	−0.627976	−	0.778233i	$-0.716116\pi$
$569$	8.05065	−	24.7774i	0.337501	−	1.03872i	0.965477	−	0.260488i	$-0.0838835\pi$
$570$		0			0
$571$	31.4963	−	10.2338i	1.31808	−	0.428270i	0.436244	−	0.899828i	$-0.356308\pi$
$571$	31.4963	−	10.2338i	1.31808	−	0.428270i	0.881835	+	0.471558i	$0.156308\pi$
$572$	11.1436	−	7.70157i	0.465937	−	0.322019i
$573$	10.1686	−	13.9958i	0.424798	−	0.584685i
$574$	9.98630	+	7.43690i	0.416820	+	0.310410i
$575$		0			0
$576$	−6.85000	−	5.75854i	−0.285417	−	0.239939i
$577$	−14.0705	−	10.2228i	−0.585761	−	0.425580i	0.255035	−	0.966932i	$-0.417913\pi$
$577$	−14.0705	−	10.2228i	−0.585761	−	0.425580i	−0.840796	+	0.541351i	$0.817913\pi$
$578$	7.29857	−	21.5932i	0.303580	−	0.898158i
$579$	11.0674	−	3.59603i	0.459947	−	0.149446i
$580$		0			0
$581$	6.21778	+	2.02028i	0.257957	+	0.0838153i
$582$	1.86133	−	2.49940i	0.0771545	−	0.103603i
$583$	7.91058	−	24.3463i	0.327623	−	1.00832i
$584$	12.2582	+	42.8234i	0.507247	+	1.77205i
$585$		0			0
$586$	−9.90146	+	3.08862i	−0.409026	+	0.127590i
$587$	−19.7090	−	27.1271i	−0.813476	−	1.11965i	−0.990778	−	0.135497i	$-0.956737\pi$
$587$	−19.7090	−	27.1271i	−0.813476	−	1.11965i	0.177301	−	0.984157i	$-0.443263\pi$
$588$	10.2187	−	13.3892i	0.421410	−	0.552163i
$589$	−0.904658	+	1.24515i	−0.0372758	+	0.0513057i
$590$		0			0
$591$	16.3492	−	11.8784i	0.672518	−	0.488613i
$592$	35.6343	−	9.74731i	1.46456	−	0.400612i
$593$	−19.5523			−0.802917			−0.401458	−	0.915877i	$-0.631497\pi$
$593$	−19.5523			−0.802917			−0.401458	+	0.915877i	$0.631497\pi$
$594$	−17.1279	+	12.1382i	−0.702765	+	0.498038i
$595$		0			0
$596$	15.1350	+	21.8992i	0.619954	+	0.897027i
$597$	−7.44379	+	2.41863i	−0.304654	+	0.0989880i
$598$	24.9856	−	7.79392i	1.02174	−	0.318717i
$599$	15.7131			0.642018			0.321009	−	0.947076i	$-0.395978\pi$
$599$	15.7131			0.642018			0.321009	+	0.947076i	$0.395978\pi$
$600$		0			0
$601$	44.4894			1.81476			0.907380	−	0.420310i	$-0.138079\pi$
$601$	44.4894			1.81476			0.907380	+	0.420310i	$0.138079\pi$
$602$	7.00240	−	2.18430i	0.285396	−	0.0890254i
$603$	1.12192	−	0.364533i	0.0456880	−	0.0148449i
$604$	34.8579	−	24.0910i	1.41835	−	0.980251i
$605$		0			0
$606$	−12.2787	+	8.70169i	−0.498787	+	0.353482i
$607$	21.4173			0.869301			0.434651	−	0.900599i	$-0.356872\pi$
$607$	21.4173			0.869301			0.434651	+	0.900599i	$0.356872\pi$
$608$	−1.86411	−	0.729680i	−0.0755998	−	0.0295924i
$609$	−1.43993	+	1.04617i	−0.0583488	+	0.0423929i
$610$		0			0
$611$	−12.5126	+	17.2221i	−0.506206	+	0.696733i
$612$	1.67090	+	1.27523i	0.0675420	+	0.0515480i
$613$	1.40405	+	1.93251i	0.0567090	+	0.0780532i	0.836430	−	0.548074i	$-0.184639\pi$
$613$	1.40405	+	1.93251i	0.0567090	+	0.0780532i	−0.779721	+	0.626128i	$0.784639\pi$
$614$	5.28336	−	1.64807i	0.213219	−	0.0665106i
$615$		0			0
$616$	6.62685	−	1.89693i	0.267003	−	0.0764295i
$617$	−3.17299	+	9.76545i	−0.127740	+	0.393142i	−0.994390	−	0.105773i	$-0.966268\pi$
$617$	−3.17299	+	9.76545i	−0.127740	+	0.393142i	0.866651	+	0.498915i	$0.166268\pi$
$618$	−1.63679	+	2.19789i	−0.0658414	+	0.0884122i
$619$	22.9711	+	7.46375i	0.923285	+	0.299994i	0.731814	−	0.681505i	$-0.238674\pi$
$619$	22.9711	+	7.46375i	0.923285	+	0.299994i	0.191471	+	0.981498i	$0.438674\pi$
$620$		0			0
$621$	−38.5764	+	12.5342i	−1.54802	+	0.502982i
$622$	2.99788	−	8.86938i	0.120204	−	0.355630i
$623$	6.61094	+	4.80313i	0.264862	+	0.192433i
$624$	11.8203	−	7.76396i	0.473189	−	0.310807i
$625$		0			0
$626$	−23.2706	−	17.3298i	−0.930080	−	0.692640i
$627$	−0.749685	+	1.03185i	−0.0299395	+	0.0412082i
$628$	−3.87841	−	5.61177i	−0.154765	−	0.223934i
$629$	−8.25258	+	2.68143i	−0.329052	+	0.106915i
$630$		0			0
$631$	5.14314	−	15.8289i	0.204745	−	0.630140i	−0.794979	−	0.606637i	$-0.792518\pi$
$631$	5.14314	−	15.8289i	0.204745	−	0.630140i	0.999724	−	0.0235031i	$-0.00748197\pi$
$632$	−5.42352	+	14.8798i	−0.215736	+	0.591885i
$633$	−5.76856	+	17.7538i	−0.229280	+	0.705650i
$634$	−0.0830358	+	7.04357i	−0.00329777	+	0.279736i
$635$		0			0
$636$	8.85558	−	25.2158i	0.351147	−	0.999872i
$637$	−9.30224	−	12.8034i	−0.368568	−	0.507290i
$638$	5.19876	+	0.0612875i	0.205821	+	0.00242639i
$639$	−10.4364	−	7.58250i	−0.412858	−	0.299959i
$640$		0			0
$641$	−11.9869	+	8.70898i	−0.473454	+	0.343984i	−0.798786	−	0.601616i	$-0.794524\pi$
$641$	−11.9869	+	8.70898i	−0.473454	+	0.343984i	0.325332	+	0.945600i	$0.394524\pi$
$642$	−26.8602	+	19.0354i	−1.06009	+	0.751268i
$643$			17.1919i			0.677981i	0.940790	+	0.338990i	$0.110085\pi$
$643$			17.1919i			0.677981i	−0.940790	+	0.338990i	$0.889915\pi$
$644$	13.3147	+	0.313974i	0.524672	+	0.0123723i
$645$		0			0
$646$	0.445436	+	0.150559i	0.0175255	+	0.00592366i
$647$	−2.43430	−	7.49201i	−0.0957023	−	0.294541i	0.891734	−	0.452560i	$-0.149489\pi$
$647$	−2.43430	−	7.49201i	−0.0957023	−	0.294541i	−0.987436	+	0.158019i	$0.949489\pi$
$648$	−10.3039	+	6.94317i	−0.404774	+	0.272754i
$649$	11.4355			0.448882
$650$		0			0
$651$		−	5.53282i		−	0.216848i
$652$	−36.6453	−	12.8695i	−1.43514	−	0.504009i
$653$	36.6029	−	11.8930i	1.43238	−	0.465409i	0.512869	−	0.858467i	$-0.328583\pi$
$653$	36.6029	−	11.8930i	1.43238	−	0.465409i	0.919514	+	0.393057i	$0.128583\pi$
$654$	−7.25479	+	21.4637i	−0.283685	+	0.839296i
$655$		0			0
$656$	−10.0187	−	36.6263i	−0.391163	−	1.43002i
$657$	−17.6165			−0.687284
$658$	−8.83809	+	6.26341i	−0.344545	+	0.244173i
$659$	−20.8965	−	28.7616i	−0.814013	−	1.12039i	−0.990692	−	0.136124i	$-0.956535\pi$
$659$	−20.8965	−	28.7616i	−0.814013	−	1.12039i	0.176679	−	0.984269i	$-0.443465\pi$
$660$		0			0
$661$	−17.1104	+	23.5504i	−0.665516	+	0.916005i	−0.999648	−	0.0265217i	$-0.991557\pi$
$661$	−17.1104	+	23.5504i	−0.665516	+	0.916005i	0.334132	+	0.942526i	$0.391557\pi$
$662$	−0.331037	+	28.0805i	−0.0128661	+	1.09138i
$663$	−2.68731	+	1.95244i	−0.104366	+	0.0758266i
$664$	−11.1415	−	16.5343i	−0.432374	−	0.641656i
$665$		0			0
$666$	−0.172232	+	14.6097i	−0.00667386	+	0.566115i
$667$	9.55387	+	3.10424i	0.369927	+	0.120197i
$668$	1.62074	+	5.41969i	0.0627084	+	0.209694i
$669$	−29.6067	−	9.61979i	−1.14466	−	0.371923i
$670$		0			0
$671$	2.96697	+	9.13141i	0.114539	+	0.352514i
$672$	6.96321	−	1.81675i	0.268612	−	0.0700827i
$673$	2.67251	+	1.94169i	0.103018	+	0.0748467i	0.638102	−	0.769952i	$-0.279720\pi$
$673$	2.67251	+	1.94169i	0.103018	+	0.0748467i	−0.535084	+	0.844799i	$0.679720\pi$
$674$	15.7996	+	11.7661i	0.608576	+	0.453213i
$675$		0			0
$676$	3.64214	+	12.1792i	0.140082	+	0.468429i
$677$	−12.5043	+	17.2107i	−0.480579	+	0.661460i	−0.978616	−	0.205696i	$-0.934054\pi$
$677$	−12.5043	+	17.2107i	−0.480579	+	0.661460i	0.498037	+	0.867156i	$0.334054\pi$
$678$	1.66610	+	0.563149i	0.0639863	+	0.0216276i
$679$	−0.460435	−	1.41707i	−0.0176699	−	0.0543823i
$680$		0			0
$681$	−5.82536	+	17.9286i	−0.223228	+	0.687026i
$682$	−9.65322	+	12.9624i	−0.369641	+	0.496356i
$683$	−12.0784	−	3.92453i	−0.462169	−	0.150168i	0.0686719	−	0.997639i	$-0.478124\pi$
$683$	−12.0784	−	3.92453i	−0.462169	−	0.150168i	−0.530841	+	0.847471i	$0.678124\pi$
$684$	0.480324	−	0.629357i	0.0183657	−	0.0240640i
$685$		0			0
$686$	−5.13219	−	16.4527i	−0.195948	−	0.628167i
$687$	−7.33624	+	5.33009i	−0.279895	+	0.203356i
$688$	−20.9253	−	7.90772i	−0.797770	−	0.301479i
$689$	−20.3156	−	14.7602i	−0.773964	−	0.562318i
$690$		0			0
$691$	−22.6417	−	31.1636i	−0.861329	−	1.18552i	−0.981251	−	0.192734i	$-0.938264\pi$
$691$	−22.6417	−	31.1636i	−0.861329	−	1.18552i	0.119922	−	0.992783i	$-0.461736\pi$
$692$	−0.0404999	+	1.71748i	−0.00153958	+	0.0652888i
$693$			2.72612i			0.103557i
$694$	−2.60133	−	3.67065i	−0.0987451	−	0.139336i
$695$		0			0
$696$	5.42450	+	0.191917i	0.205615	+	0.00727461i
$697$	2.75608	+	8.48233i	0.104394	+	0.321291i
$698$	23.9346	−	7.46606i	0.905937	−	0.282594i
$699$			19.7498i			0.747006i
$700$		0			0
$701$		−	39.6154i		−	1.49625i	−0.663555	−	0.748127i	$-0.730953\pi$
$701$		−	39.6154i		−	1.49625i	0.663555	−	0.748127i	$-0.269047\pi$
$702$	6.13226	+	19.6587i	0.231447	+	0.741970i
$703$	1.00998	+	3.10840i	0.0380921	+	0.117235i
$704$	−19.4833	−	7.89254i	−0.734303	−	0.297461i
$705$		0			0
$706$	−29.0337	+	20.5757i	−1.09270	+	0.774377i
$707$			7.19552i			0.270615i
$708$	11.9354	+	0.281448i	0.448559	+	0.0105775i
$709$	5.04361	+	6.94194i	0.189417	+	0.260710i	0.893154	−	0.449750i	$-0.148487\pi$
$709$	5.04361	+	6.94194i	0.189417	+	0.260710i	−0.703738	+	0.710460i	$0.748487\pi$
$710$		0			0
$711$	−5.06730	−	3.68161i	−0.190039	−	0.138071i
$712$	−6.85800	−	23.9581i	−0.257015	−	0.897870i
$713$	−25.2636	+	18.3551i	−0.946128	+	0.687402i
$714$	−1.61359	+	0.503337i	−0.0603872	+	0.0188369i
$715$		0			0
$716$	27.7594	−	36.3724i	1.03742	−	1.35930i
$717$	0.839780	+	0.272861i	0.0313622	+	0.0101902i
$718$	−34.1853	−	25.4581i	−1.27578	−	0.950088i
$719$	−2.74075	+	8.43517i	−0.102213	+	0.314579i	−0.989066	−	0.147472i	$-0.952886\pi$
$719$	−2.74075	+	8.43517i	−0.102213	+	0.314579i	0.886853	+	0.462051i	$0.152886\pi$
$720$		0			0
$721$	0.404892	+	1.24613i	0.0150790	+	0.0464083i
$722$	−8.54726	+	25.2875i	−0.318096	+	0.941104i
$723$	−17.9547	+	24.7126i	−0.667744	+	0.919071i
$724$	−37.3396	+	11.1663i	−1.38771	+	0.414992i
$725$		0			0
$726$	4.74500	−	6.37161i	0.176103	−	0.236473i
$727$	26.8677	+	19.5205i	0.996468	+	0.723976i	0.961328	−	0.275406i	$-0.0888124\pi$
$727$	26.8677	+	19.5205i	0.996468	+	0.723976i	0.0351397	+	0.999382i	$0.488812\pi$
$728$	0.239077	−	6.75745i	0.00886078	−	0.250448i
$729$	−8.70192	−	26.7818i	−0.322293	−	0.991917i
$730$		0			0
$731$	4.99703	+	1.62364i	0.184822	+	0.0600523i
$732$	2.87193	+	9.60359i	0.106149	+	0.354959i
$733$	−0.572607	−	0.186051i	−0.0211497	−	0.00687196i	0.298423	−	0.954434i	$-0.403539\pi$
$733$	−0.572607	−	0.186051i	−0.0211497	−	0.00687196i	−0.319573	+	0.947562i	$0.603539\pi$
$734$	9.49827	+	0.111974i	0.350588	+	0.00413303i
$735$		0			0
$736$	−31.3959	−	25.7679i	−1.15727	−	0.949816i
$737$	2.24181	−	1.62877i	0.0825781	−	0.0599965i
$738$	15.0165	+	0.177027i	0.552764	+	0.00651646i
$739$	21.4919	−	29.5811i	0.790594	−	1.08816i	−0.203440	−	0.979087i	$-0.565212\pi$
$739$	21.4919	−	29.5811i	0.790594	−	1.08816i	0.994034	−	0.109072i	$-0.0347878\pi$
$740$		0			0
$741$	0.735402	+	1.01219i	0.0270157	+	0.0371839i
$742$	−7.38847	−	10.4256i	−0.271239	−	0.382736i
$743$	−0.112858			−0.00414038			−0.00207019	−	0.999998i	$-0.500659\pi$
$743$	−0.112858			−0.00414038			−0.00207019	+	0.999998i	$0.500659\pi$
$744$	−10.3942	+	13.2914i	−0.381071	+	0.487288i
$745$		0			0
$746$	−32.4740	−	10.9763i	−1.18896	−	0.401871i
$747$	7.49929	−	2.43667i	0.274385	−	0.0891529i
$748$	4.65854	+	1.63604i	0.170333	+	0.0598195i
$749$			15.7406i			0.575149i
$750$		0			0
$751$	−21.9164			−0.799742			−0.399871	−	0.916571i	$-0.630945\pi$
$751$	−21.9164			−0.799742			−0.399871	+	0.916571i	$0.630945\pi$
$752$	32.9984	+	1.55714i	1.20333	+	0.0567830i
$753$	−2.12528	−	6.54093i	−0.0774495	−	0.238365i
$754$	1.63308	−	4.83154i	0.0594731	−	0.175954i
$755$		0			0
$756$	−0.247035	+	10.4760i	−0.00898457	+	0.381008i
$757$			16.3710i			0.595014i	0.954720	+	0.297507i	$0.0961551\pi$
$757$			16.3710i			0.595014i	−0.954720	+	0.297507i	$0.903845\pi$
$758$	6.65824	+	9.39523i	0.241838	+	0.341250i
$759$	−20.9358	+	15.2107i	−0.759921	+	0.552115i
$760$		0			0
$761$	−5.84229	−	4.24467i	−0.211783	−	0.153869i	0.476837	−	0.878992i	$-0.341783\pi$
$761$	−5.84229	−	4.24467i	−0.211783	−	0.153869i	−0.688620	+	0.725122i	$0.741783\pi$
$762$	0.372214	−	31.5733i	0.0134839	−	1.14378i
$763$	6.36731	+	8.76385i	0.230512	+	0.317273i
$764$	−8.35838	+	23.8001i	−0.302395	+	0.861056i
$765$		0			0
$766$	−12.7756	−	0.150610i	−0.461601	−	0.00544176i
$767$	3.46644	−	10.6686i	0.125166	−	0.385221i
$768$	−20.1407	−	8.71706i	−0.726764	−	0.314550i
$769$	−12.3133	+	37.8964i	−0.444028	+	1.36658i	0.439518	+	0.898234i	$0.355149\pi$
$769$	−12.3133	+	37.8964i	−0.444028	+	1.36658i	−0.883546	+	0.468344i	$0.844851\pi$
$770$		0			0
$771$	5.32830	−	1.73127i	0.191894	−	0.0623502i
$772$	−13.9587	+	9.64718i	−0.502386	+	0.347210i
$773$	29.5054	−	40.6107i	1.06123	−	1.46066i	0.182590	−	0.983189i	$-0.441552\pi$
$773$	29.5054	−	40.6107i	1.06123	−	1.46066i	0.878645	−	0.477475i	$-0.158448\pi$
$774$	5.28413	−	7.09556i	0.189934	−	0.255044i
$775$		0			0
$776$	−1.55609	+	4.26922i	−0.0558602	+	0.153256i
$777$	−9.50537	−	6.90605i	−0.341003	−	0.247753i
$778$	−16.9977	−	5.74526i	−0.609395	−	0.205978i
$779$	3.19494	−	1.03810i	0.114470	−	0.0371937i
$780$		0			0
$781$	−28.8195	−	9.36401i	−1.03124	−	0.335071i
$782$	7.65137	+	5.69805i	0.273613	+	0.203762i
$783$	−2.44242	+	7.51699i	−0.0872849	+	0.268635i
$784$	−8.68175	+	22.9736i	−0.310063	+	0.820484i
$785$		0			0
$786$	9.48234	+	30.3984i	0.338224	+	1.08427i
$787$	24.4497	+	33.6522i	0.871539	+	1.19957i	0.978693	+	0.205329i	$0.0658263\pi$
$787$	24.4497	+	33.6522i	0.871539	+	1.19957i	−0.107154	+	0.994242i	$0.534174\pi$
$788$	−17.8773	+	23.4241i	−0.636851	+	0.834449i
$789$	−19.2737	+	26.5279i	−0.686161	+	0.944419i
$790$		0			0
$791$	0.680288	−	0.494258i	0.0241883	−	0.0175738i
$792$	5.12141	−	6.54892i	0.181981	−	0.232706i
$793$	9.41841			0.334458
$794$	−11.1833	−	15.7804i	−0.396882	−	0.560027i
$795$		0			0
$796$	9.38844	−	6.48854i	0.332764	−	0.229980i
$797$	−33.7472	+	10.9651i	−1.19539	+	0.388404i	−0.838061	−	0.545576i	$-0.816311\pi$
$797$	−33.7472	+	10.9651i	−1.19539	+	0.388404i	−0.357324	+	0.933980i	$0.616311\pi$
$798$	0.189586	+	0.607772i	0.00671127	+	0.0215149i
$799$	−7.75931			−0.274505
$800$		0			0
$801$	9.85577			0.348236
$802$	−14.6509	−	46.9676i	−0.517340	−	1.65848i
$803$	−39.3560	+	12.7876i	−1.38884	+	0.451263i
$804$	2.37989	−	1.64479i	0.0839323	−	0.0580074i
$805$		0			0
$806$	9.16693	+	12.9351i	0.322891	+	0.455621i
$807$	41.1858			1.44981
$808$	13.5179	−	17.2857i	0.475556	−	0.608110i
$809$	−15.2356	+	11.0693i	−0.535656	+	0.389177i	−0.822469	−	0.568810i	$-0.807404\pi$
$809$	−15.2356	+	11.0693i	−0.535656	+	0.389177i	0.286813	+	0.957986i	$0.407404\pi$
$810$		0			0
$811$	30.8789	−	42.5012i	1.08431	−	1.49242i	0.229616	−	0.973281i	$-0.426253\pi$
$811$	30.8789	−	42.5012i	1.08431	−	1.49242i	0.854690	−	0.519138i	$-0.173747\pi$
$812$	1.57450	−	2.06303i	0.0552542	−	0.0723982i
$813$	3.80881	+	5.24237i	0.133581	+	0.183858i
$814$	10.2202	+	32.7638i	0.358219	+	1.14837i
$815$		0			0
$816$	4.82191	+	1.82221i	0.168801	+	0.0637901i
$817$	0.611555	−	1.88217i	0.0213956	−	0.0658489i
$818$	−18.7652	−	13.9746i	−0.656110	−	0.488612i
$819$	2.54330	+	0.826367i	0.0888700	+	0.0288756i
$820$		0			0
$821$	−4.70172	+	1.52768i	−0.164091	+	0.0533164i	−0.389910	−	0.920853i	$-0.627494\pi$
$821$	−4.70172	+	1.52768i	−0.164091	+	0.0533164i	0.225819	+	0.974169i	$0.427494\pi$
$822$	−41.1715	−	13.9161i	−1.43602	−	0.485380i
$823$	4.38694	+	3.18730i	0.152919	+	0.111102i	0.661614	−	0.749845i	$-0.269872\pi$
$823$	4.38694	+	3.18730i	0.152919	+	0.111102i	−0.508695	+	0.860947i	$0.669872\pi$
$824$	1.36837	−	3.75422i	0.0476695	−	0.130784i
$825$		0			0
$826$	3.40940	−	4.57816i	0.118628	−	0.159295i
$827$	24.4852	−	33.7010i	0.851435	−	1.17190i	−0.132110	−	0.991235i	$-0.542175\pi$
$827$	24.4852	−	33.7010i	0.851435	−	1.17190i	0.983545	−	0.180664i	$-0.0578248\pi$
$828$	13.2145	−	9.13282i	0.459236	−	0.317387i
$829$	−27.3761	+	8.89503i	−0.950811	+	0.308937i	−0.743045	−	0.669241i	$-0.766619\pi$
$829$	−27.3761	+	8.89503i	−0.950811	+	0.308937i	−0.207766	+	0.978179i	$0.566619\pi$
$830$		0			0
$831$	1.57473	−	4.84653i	0.0546268	−	0.168124i
$832$	−13.2692	+	15.7842i	−0.460027	+	0.547219i
$833$	1.78256	−	5.48616i	0.0617621	−	0.190084i
$834$	22.8528	+	0.269409i	0.791329	+	0.00932888i
$835$		0			0
$836$	0.616227	−	1.75467i	0.0213126	−	0.0606867i
$837$	−14.4418	−	19.8774i	−0.499180	−	0.687063i
$838$	−0.0396421	+	3.36267i	−0.00136942	+	0.116162i
$839$	−43.0983	−	31.3128i	−1.48792	−	1.08104i	−0.974895	−	0.222663i	$-0.928525\pi$
$839$	−43.0983	−	31.3128i	−1.48792	−	1.08104i	−0.513024	−	0.858374i	$-0.671475\pi$
$840$		0			0
$841$	−21.8779	+	15.8952i	−0.754409	+	0.548110i
$842$	5.00825	+	7.06698i	0.172596	+	0.243544i
$843$		−	18.8667i		−	0.649805i
$844$	0.641680	−	27.2117i	0.0220875	−	0.936665i
$845$		0			0
$846$	−4.18352	+	12.3772i	−0.143832	+	0.425536i
$847$	−1.17377	−	3.61249i	−0.0403311	−	0.124126i
$848$	−1.83684	+	38.9257i	−0.0630772	+	1.33671i
$849$	2.04454			0.0701685
$850$		0			0
$851$			66.3135i			2.27320i
$852$	−29.8488	−	10.4826i	−1.02260	−	0.359129i
$853$	−49.7048	+	16.1501i	−1.70186	+	0.552968i	−0.988945	−	0.148283i	$-0.952625\pi$
$853$	−49.7048	+	16.1501i	−1.70186	+	0.552968i	−0.712915	+	0.701250i	$0.752625\pi$
$854$	4.54030	+	1.53464i	0.155366	+	0.0525142i
$855$		0			0
$856$	29.5710	−	37.8134i	1.01072	−	1.29244i
$857$	6.32615			0.216097			0.108049	−	0.994146i	$-0.465540\pi$
$857$	6.32615			0.216097			0.108049	+	0.994146i	$0.465540\pi$
$858$	7.59658	+	10.7193i	0.259343	+	0.365950i
$859$	31.4567	+	43.2964i	1.07329	+	1.47726i	0.866701	+	0.498827i	$0.166236\pi$
$859$	31.4567	+	43.2964i	1.07329	+	1.47726i	0.206588	+	0.978428i	$0.433764\pi$
$860$		0			0
$861$	−7.09832	+	9.77000i	−0.241910	+	0.332961i
$862$	−44.2605	−	0.521781i	−1.50752	−	0.0177719i
$863$	−35.2585	+	25.6168i	−1.20021	+	0.872007i	−0.994306	−	0.106564i	$-0.966015\pi$
$863$	−35.2585	+	25.6168i	−1.20021	+	0.872007i	−0.205909	+	0.978571i	$0.566015\pi$
$864$	20.2742	−	24.7023i	0.689741	−	0.840389i
$865$		0			0
$866$	−21.0880	−	0.248604i	−0.716601	−	0.00844792i
$867$	21.0251	+	6.83146i	0.714049	+	0.232008i
$868$	2.31142	+	7.72927i	0.0784546	+	0.262348i
$869$	−13.9930	−	4.54661i	−0.474681	−	0.154233i
$870$		0			0
$871$	−0.839981	−	2.58520i	−0.0284617	−	0.0875961i
$872$	1.16807	−	33.0152i	0.0395558	−	1.11804i
$873$	−1.45388	−	1.05631i	−0.0492064	−	0.0357505i
$874$	2.14622	−	2.88195i	0.0725968	−	0.0974834i
$875$		0			0
$876$	−41.3911	+	12.3779i	−1.39848	+	0.418211i
$877$	−2.19672	+	3.02353i	−0.0741781	+	0.102097i	−0.844494	−	0.535565i	$-0.820099\pi$
$877$	−2.19672	+	3.02353i	−0.0741781	+	0.102097i	0.770316	+	0.637663i	$0.220099\pi$
$878$	14.7701	−	43.6981i	0.498467	−	1.47474i
$879$	−3.10863	−	9.56738i	−0.104851	−	0.322700i
$880$		0			0
$881$	−13.5548	+	41.7174i	−0.456673	+	1.40549i	0.412487	+	0.910963i	$0.364660\pi$
$881$	−13.5548	+	41.7174i	−0.456673	+	1.40549i	−0.869160	+	0.494531i	$0.835340\pi$
$882$	−7.79009	−	5.80136i	−0.262306	−	0.195342i
$883$	−18.4883	−	6.00720i	−0.622179	−	0.202158i	−0.0190716	−	0.999818i	$-0.506071\pi$
$883$	−18.4883	−	6.00720i	−0.622179	−	0.202158i	−0.603108	+	0.797660i	$0.706071\pi$
$884$	2.93846	−	3.85019i	0.0988312	−	0.129496i
$885$		0			0
$886$	−32.9832	+	10.2886i	−1.10809	+	0.345654i
$887$	14.5304	−	10.5570i	0.487883	−	0.354468i	−0.316486	−	0.948597i	$-0.602503\pi$
$887$	14.5304	−	10.5570i	0.487883	−	0.354468i	0.804370	+	0.594129i	$0.202503\pi$
$888$	9.86060	+	34.4476i	0.330900	+	1.15599i
$889$	−12.2138	−	8.87384i	−0.409638	−	0.297619i
$890$		0			0
$891$	−6.78473	−	9.33838i	−0.227297	−	0.312847i
$892$	45.3789	+	1.07008i	1.51940	+	0.0358289i
$893$			2.92260i			0.0978012i
$894$	−21.0654	+	14.9287i	−0.704532	+	0.499290i
$895$		0			0
$896$	−8.96853	+	5.44696i	−0.299617	+	0.181970i
$897$	7.84441	+	24.1426i	0.261917	+	0.806098i
$898$	−4.67401	−	14.9839i	−0.155974	−	0.500018i
$899$			6.08498i			0.202945i
$900$		0			0
$901$		−	9.15306i		−	0.304933i
$902$	33.6760	−	10.5048i	1.12129	−	0.349770i
$903$	2.19845	+	6.76613i	0.0731598	+	0.225163i
$904$	−2.56279	−	0.0906707i	−0.0852370	−	0.00301566i
$905$		0			0
$906$	23.7626	+	33.5307i	0.789461	+	1.11398i
$907$			14.9961i			0.497938i	0.968511	+	0.248969i	$0.0800917\pi$
$907$			14.9961i			0.497938i	−0.968511	+	0.248969i	$0.919908\pi$
$908$	0.647998	−	27.4796i	0.0215046	−	0.911943i
$909$	5.10112	+	7.02109i	0.169193	+	0.232875i
$910$		0			0
$911$	28.4325	+	20.6574i	0.942011	+	0.684411i	0.948904	−	0.315565i	$-0.102194\pi$
$911$	28.4325	+	20.6574i	0.942011	+	0.684411i	−0.00689309	+	0.999976i	$0.502194\pi$
$912$	0.686349	−	1.81621i	0.0227273	−	0.0601407i
$913$	14.9850	−	10.8873i	0.495932	−	0.360316i
$914$	−4.51291	−	14.4674i	−0.149274	−	0.478540i
$915$		0			0
$916$	8.02189	−	10.5109i	0.265051	−	0.347289i
$917$	14.4798	+	4.70477i	0.478165	+	0.155365i
$918$	−4.48323	+	6.02010i	−0.147969	+	0.198693i
$919$	−1.49412	+	4.59844i	−0.0492866	+	0.151689i	−0.972671	−	0.232188i	$-0.925411\pi$
$919$	−1.49412	+	4.59844i	−0.0492866	+	0.151689i	0.923384	+	0.383877i	$0.125411\pi$
$920$		0			0
$921$	1.65874	+	5.10509i	0.0546575	+	0.168218i
$922$	−20.6427	−	6.97731i	−0.679833	−	0.229786i
$923$	−17.4721	+	24.0483i	−0.575101	+	0.791558i
$924$	1.91546	+	6.40520i	0.0630139	+	0.210716i
$925$		0			0
$926$	2.08957	+	1.55613i	0.0686677	+	0.0511375i
$927$	1.27850	+	0.928882i	0.0419913	+	0.0305085i
$928$	−7.65812	+	1.99806i	−0.251390	+	0.0655895i
$929$	1.73466	+	5.33873i	0.0569124	+	0.175158i	0.975472	−	0.220125i	$-0.0706465\pi$
$929$	1.73466	+	5.33873i	0.0569124	+	0.175158i	−0.918559	+	0.395283i	$0.870646\pi$
$930$		0			0
$931$	−2.06641	−	0.671416i	−0.0677237	−	0.0220048i
$932$	−8.25077	−	27.5902i	−0.270263	−	0.903746i
$933$	8.63602	+	2.80601i	0.282731	+	0.0918648i
$934$	0.350728	−	29.7508i	0.0114762	−	0.973475i
$935$		0			0
$936$	−4.55728	−	6.76313i	−0.148959	−	0.221060i
$937$	28.0687	−	20.3931i	0.916964	−	0.666213i	−0.0258024	−	0.999667i	$-0.508214\pi$
$937$	28.0687	−	20.3931i	0.916964	−	0.666213i	0.942767	+	0.333454i	$0.108214\pi$
$938$	0.0163052	−	1.38310i	0.000532385	−	0.0451600i
$939$	16.5409	−	22.7666i	0.539791	−	0.742958i
$940$		0			0
$941$	27.7263	+	38.1620i	0.903853	+	1.24405i	0.969223	+	0.246185i	$0.0791771\pi$
$941$	27.7263	+	38.1620i	0.903853	+	1.24405i	−0.0653703	+	0.997861i	$0.520823\pi$
$942$	5.39809	−	3.82554i	0.175879	−	0.124643i
$943$	68.1597			2.21958
$944$	−16.7911	+	4.59300i	−0.546504	+	0.149489i
$945$		0			0
$946$	6.65444	−	19.6875i	0.216354	−	0.640096i
$947$	3.39273	−	1.10237i	0.110249	−	0.0358221i	−0.253373	−	0.967369i	$-0.581540\pi$
$947$	3.39273	−	1.10237i	0.110249	−	0.0358221i	0.363622	+	0.931547i	$0.381540\pi$
$948$	−14.4928	−	5.08974i	−0.470704	−	0.165307i
$949$			40.5930i			1.31771i
$950$		0			0
$951$	−6.83199			−0.221542
$952$	2.04389	−	1.37726i	0.0662427	−	0.0446371i
$953$	−8.58834	−	26.4322i	−0.278204	−	0.856222i	−0.988354	−	0.152172i	$-0.951373\pi$
$953$	−8.58834	−	26.4322i	−0.278204	−	0.856222i	0.710150	−	0.704050i	$-0.248627\pi$
$954$	−14.6004	−	4.93498i	−0.472705	−	0.159776i
$955$		0			0
$956$	−1.28715	−	0.0303524i	−0.0416295	−	0.000981665i
$957$			5.04259i			0.163004i
$958$	−2.39400	+	1.69659i	−0.0773467	+	0.0548143i
$959$	−16.8108	+	12.2137i	−0.542848	+	0.394402i
$960$		0			0
$961$	9.77638	+	7.10296i	0.315367	+	0.229128i
$962$	33.6647	+	0.396869i	1.08539	+	0.0127956i
$963$	11.1590	+	15.3590i	0.359593	+	0.494937i
$964$	14.7585	−	42.0239i	0.475338	−	1.35350i
$965$		0			0
$966$	−0.152271	+	12.9165i	−0.00489924	+	0.415582i
$967$	7.73379	−	23.8022i	0.248702	−	0.765426i	−0.746304	−	0.665606i	$-0.768173\pi$
$967$	7.73379	−	23.8022i	0.248702	−	0.765426i	0.995006	−	0.0998201i	$-0.0318267\pi$
$968$	−3.96686	+	10.8833i	−0.127500	+	0.349804i
$969$	−0.140923	+	0.433717i	−0.00452710	+	0.0139330i
$970$		0			0
$971$	23.8687	−	7.75540i	0.765982	−	0.248883i	0.100138	−	0.994974i	$-0.468072\pi$
$971$	23.8687	−	7.75540i	0.765982	−	0.248883i	0.665844	+	0.746091i	$0.268072\pi$
$972$	12.4198	+	17.9705i	0.398364	+	0.576403i
$973$	6.42290	−	8.84037i	0.205909	−	0.283409i
$974$	5.53377	+	4.12105i	0.177313	+	0.132047i
$975$		0			0
$976$	−8.02408	−	12.2163i	−0.256844	−	0.391033i
$977$	27.9703	+	20.3216i	0.894850	+	0.650146i	0.937138	−	0.348959i	$-0.113465\pi$
$977$	27.9703	+	20.3216i	0.894850	+	0.650146i	−0.0422882	+	0.999105i	$0.513465\pi$
$978$	12.0622	−	35.6867i	0.385707	−	1.14113i
$979$	22.0183	−	7.15417i	0.703707	−	0.228648i
$980$		0			0
$981$	12.4259	+	4.03742i	0.396729	+	0.128905i
$982$	16.0950	−	21.6125i	0.513613	−	0.689682i
$983$	5.35074	−	16.4679i	0.170662	−	0.525244i	−0.828747	−	0.559624i	$-0.810946\pi$
$983$	5.35074	−	16.4679i	0.170662	−	0.525244i	0.999409	+	0.0343798i	$0.0109456\pi$
$984$	35.4066	−	10.1351i	1.12872	−	0.323096i
$985$		0			0
$986$	1.77462	−	0.553569i	0.0565155	−	0.0176292i
$987$	−6.17546	−	8.49980i	−0.196567	−	0.270552i
$988$	−1.45020	−	1.10680i	−0.0461372	−	0.0352118i
$989$	23.6017	−	32.4849i	0.750490	−	1.03296i
$990$		0			0
$991$	−45.0802	+	32.7527i	−1.43202	+	1.04042i	−0.442385	+	0.896825i	$0.645868\pi$
$991$	−45.0802	+	32.7527i	−1.43202	+	1.04042i	−0.989636	+	0.143599i	$0.954132\pi$
$992$	8.96788	−	22.9103i	0.284730	−	0.727402i
$993$	−27.2369			−0.864338
$994$	−12.3411	+	8.74596i	−0.391437	+	0.277405i
$995$		0			0
$996$	15.9080	−	10.9944i	0.504065	−	0.348370i
$997$	−18.3906	+	5.97548i	−0.582438	+	0.189245i	−0.585392	−	0.810750i	$-0.699060\pi$
$997$	−18.3906	+	5.97548i	−0.582438	+	0.189245i	0.00295465	+	0.999996i	$0.499060\pi$
$998$	−17.3566	+	5.41413i	−0.549412	+	0.171381i
$999$	−52.1755			−1.65076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.t.b.701.25		224
5.2	odd	4		1000.2.o.a.549.27		112
5.3	odd	4		200.2.o.a.109.2	✓	112
5.4	even	2	inner	1000.2.t.b.701.32		224
8.5	even	2	inner	1000.2.t.b.701.2		224
20.3	even	4		800.2.be.a.209.9		112
25.2	odd	20		200.2.o.a.189.15	yes	112
25.11	even	5	inner	1000.2.t.b.301.2		224
25.14	even	10	inner	1000.2.t.b.301.55		224
25.23	odd	20		1000.2.o.a.949.14		112
40.3	even	4		800.2.be.a.209.20		112
40.13	odd	4		200.2.o.a.109.15	yes	112
40.29	even	2	inner	1000.2.t.b.701.55		224
40.37	odd	4		1000.2.o.a.549.14		112
100.27	even	20		800.2.be.a.689.20		112
200.27	even	20		800.2.be.a.689.9		112
200.61	even	10	inner	1000.2.t.b.301.25		224
200.77	odd	20		200.2.o.a.189.2	yes	112
200.173	odd	20		1000.2.o.a.949.27		112
200.189	even	10	inner	1000.2.t.b.301.32		224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.2	✓	112	5.3	odd	4
200.2.o.a.109.15	yes	112	40.13	odd	4
200.2.o.a.189.2	yes	112	200.77	odd	20
200.2.o.a.189.15	yes	112	25.2	odd	20
800.2.be.a.209.9		112	20.3	even	4
800.2.be.a.209.20		112	40.3	even	4
800.2.be.a.689.9		112	200.27	even	20
800.2.be.a.689.20		112	100.27	even	20
1000.2.o.a.549.14		112	40.37	odd	4
1000.2.o.a.549.27		112	5.2	odd	4
1000.2.o.a.949.14		112	25.23	odd	20
1000.2.o.a.949.27		112	200.173	odd	20
1000.2.t.b.301.2		224	25.11	even	5	inner
1000.2.t.b.301.25		224	200.61	even	10	inner
1000.2.t.b.301.32		224	200.189	even	10	inner
1000.2.t.b.301.55		224	25.14	even	10	inner
1000.2.t.b.701.2		224	8.5	even	2	inner
1000.2.t.b.701.25		224	1.1	even	1	trivial
1000.2.t.b.701.32		224	5.4	even	2	inner
1000.2.t.b.701.55		224	40.29	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.t (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.421131 - 1.35006i) q^{2} +(1.30450 - 0.423859i) q^{3} +(-1.64530 + 1.13710i) q^{4} +(-1.12160 - 1.58265i) q^{6} -0.927462 q^{7} +(2.22803 + 1.74238i) q^{8} +(-0.904979 + 0.657506i) q^{9} +(-1.54449 + 2.12581i) q^{11} +(-1.66433 + 2.18072i) q^{12} +(1.51507 + 2.08531i) q^{13} +(0.390583 + 1.25213i) q^{14} +(1.41401 - 3.74173i) q^{16} +(-0.290328 + 0.893539i) q^{17} +(1.26878 + 0.944876i) q^{18} +(0.336558 + 0.109354i) q^{19} +(-1.20988 + 0.393113i) q^{21} +(3.52040 + 1.18991i) q^{22} +(5.80876 + 4.22031i) q^{23} +(3.64500 + 1.32856i) q^{24} +(2.17724 - 2.92361i) q^{26} +(-3.32054 + 4.57033i) q^{27} +(1.52595 - 1.05462i) q^{28} +(1.33062 - 0.432345i) q^{29} +(-1.34398 + 4.13636i) q^{31} +(-5.64703 - 0.333231i) q^{32} +(-1.11375 + 3.42777i) q^{33} +(1.32859 + 0.0156626i) q^{34} +(0.741311 - 2.11084i) q^{36} +(5.42869 + 7.47195i) q^{37} +(0.00589944 - 0.500425i) q^{38} +(2.86029 + 2.07812i) q^{39} +(7.67997 - 5.57982i) q^{41} +(1.04024 + 1.46785i) q^{42} -5.59241i q^{43} +(0.123891 - 5.25383i) q^{44} +(3.25140 - 9.61944i) q^{46} +(2.55210 + 7.85457i) q^{47} +(0.258613 - 5.48044i) q^{48} -6.13981 q^{49} +1.28868i q^{51} +(-4.86395 - 1.70818i) q^{52} +(-9.26543 + 3.01052i) q^{53} +(7.56858 + 2.55821i) q^{54} +(-2.06642 - 1.61599i) q^{56} +0.485392 q^{57} +(-1.14405 - 1.61434i) q^{58} +(-2.55804 - 3.52083i) q^{59} +(2.14775 - 2.95612i) q^{61} +(6.15030 + 0.0725051i) q^{62} +(0.839334 - 0.609812i) q^{63} +(1.92826 + 7.76414i) q^{64} +(5.09672 + 0.0600846i) q^{66} +(-1.00295 - 0.325879i) q^{67} +(-0.538366 - 1.80027i) q^{68} +(9.36636 + 3.04331i) q^{69} +(3.56365 + 10.9678i) q^{71} +(-3.16194 - 0.111869i) q^{72} +(12.7408 + 9.25671i) q^{73} +(7.80136 - 10.4757i) q^{74} +(-0.678086 + 0.202780i) q^{76} +(1.43246 - 1.97161i) q^{77} +(1.60102 - 4.73671i) q^{78} +(1.73030 + 5.32530i) q^{79} +(-1.35747 + 4.17785i) q^{81} +(-10.7673 - 8.01855i) q^{82} +(-6.70408 - 2.17829i) q^{83} +(1.54360 - 2.02254i) q^{84} +(-7.55006 + 2.35514i) q^{86} +(1.55254 - 1.12799i) q^{87} +(-7.14514 + 2.04529i) q^{88} +(-7.12799 - 5.17879i) q^{89} +(-1.40517 - 1.93405i) q^{91} +(-14.3560 - 0.338530i) q^{92} +5.96555i q^{93} +(9.52933 - 6.75328i) q^{94} +(-7.50781 + 1.95884i) q^{96} +(0.496446 + 1.52791i) q^{97} +(2.58566 + 8.28909i) q^{98} -2.93933i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 6 q^{4} + 2 q^{6} + 60 q^{9} + 6 q^{14} - 30 q^{16} + 32 q^{24} - 28 q^{26} - 36 q^{31} - 18 q^{34} + 82 q^{36} + 20 q^{39} - 20 q^{41} + 64 q^{44} + 26 q^{46} + 160 q^{49} - 86 q^{54} + 72 q^{56}+ \cdots + 92 q^{96}+O(q^{100}) \) 224 * q + 6 * q^4 + 2 * q^6 + 60 * q^9 + 6 * q^14 - 30 * q^16 + 32 * q^24 - 28 * q^26 - 36 * q^31 - 18 * q^34 + 82 * q^36 + 20 * q^39 - 20 * q^41 + 64 * q^44 + 26 * q^46 + 160 * q^49 - 86 * q^54 + 72 * q^56 + 72 * q^64 + 80 * q^66 + 44 * q^71 - 8 * q^74 - 72 * q^76 - 28 * q^79 - 12 * q^81 - 156 * q^84 - 118 * q^86 - 48 * q^89 - 90 * q^94 + 92 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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