LMFDB - Embedded newform 840.2.dj.a.667.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dj (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			667.32
Character	$\chi$	$=$	840.667
Dual form			840.2.dj.a.403.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.739767 - 1.20530i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.905490 + 1.78328i) q^{4} +(2.04855 - 0.896354i) q^{5} +(0.402606 + 1.35569i) q^{6} +(2.56193 - 0.660700i) q^{7} +(2.81924 - 0.227825i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.59582 - 1.80602i) q^{10} +(-1.25171 - 2.16802i) q^{11} +(1.33618 - 1.48816i) q^{12} +(2.91006 + 2.91006i) q^{13} +(-2.69157 - 2.59912i) q^{14} +(-2.21074 + 0.335608i) q^{15} +(-2.36017 - 3.22949i) q^{16} +(-1.20177 + 4.48505i) q^{17} +(-0.0380074 - 1.41370i) q^{18} +(6.80025 + 3.92613i) q^{19} +(-0.256491 + 4.46477i) q^{20} +(-2.64563 - 0.0248885i) q^{21} +(-1.68714 + 3.11251i) q^{22} +(-4.40947 + 1.18151i) q^{23} +(-2.78214 - 0.509610i) q^{24} +(3.39310 - 3.67245i) q^{25} +(1.35473 - 5.66027i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.14159 + 5.16689i) q^{28} +4.44393 q^{29} +(2.03994 + 2.41633i) q^{30} +(-1.81658 + 1.04880i) q^{31} +(-2.14652 + 5.23378i) q^{32} +(0.647932 + 2.41811i) q^{33} +(6.29486 - 1.86941i) q^{34} +(4.65601 - 3.64987i) q^{35} +(-1.67582 + 1.09162i) q^{36} +(2.12891 + 7.94521i) q^{37} +(-0.298444 - 11.1008i) q^{38} +(-2.05773 - 3.56409i) q^{39} +(5.57113 - 2.99374i) q^{40} +0.898009 q^{41} +(1.92715 + 3.20719i) q^{42} +(0.112372 - 0.112372i) q^{43} +(4.99960 - 0.269023i) q^{44} +(2.22227 + 0.248009i) q^{45} +(4.68605 + 4.44068i) q^{46} +(-1.73174 - 6.46294i) q^{47} +(1.44390 + 3.73030i) q^{48} +(6.12695 - 3.38533i) q^{49} +(-6.93650 - 1.37294i) q^{50} +(2.32164 - 4.02119i) q^{51} +(-7.82449 + 2.55442i) q^{52} +(-0.260131 + 0.970823i) q^{53} +(-0.329181 + 1.37537i) q^{54} +(-4.50750 - 3.31932i) q^{55} +(7.07216 - 2.44634i) q^{56} +(-5.55238 - 5.55238i) q^{57} +(-3.28747 - 5.35626i) q^{58} +(8.96896 - 5.17823i) q^{59} +(1.40332 - 4.24626i) q^{60} +(-6.16163 - 3.55742i) q^{61} +(2.60797 + 1.41365i) q^{62} +(2.54904 + 0.708781i) q^{63} +(7.89619 - 1.28458i) q^{64} +(8.56985 + 3.35296i) q^{65} +(2.43523 - 2.56979i) q^{66} +(3.14289 - 11.7294i) q^{67} +(-6.90992 - 6.20426i) q^{68} +4.56502 q^{69} +(-7.84355 - 2.91183i) q^{70} -12.0186i q^{71} +(2.55544 + 1.21232i) q^{72} +(-7.41406 - 1.98659i) q^{73} +(8.00145 - 8.44358i) q^{74} +(-4.22798 + 2.66911i) q^{75} +(-13.1589 + 8.57168i) q^{76} +(-4.63920 - 4.72731i) q^{77} +(-2.77355 + 5.11677i) q^{78} +(-3.56693 + 6.17810i) q^{79} +(-7.72969 - 4.50021i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.664317 - 1.08237i) q^{82} +(3.10456 - 3.10456i) q^{83} +(2.43998 - 4.69537i) q^{84} +(1.55832 + 10.2651i) q^{85} +(-0.218571 - 0.0523127i) q^{86} +(-4.29250 - 1.15017i) q^{87} +(-4.02279 - 5.82700i) q^{88} +(2.89589 + 1.67194i) q^{89} +(-1.34504 - 2.86197i) q^{90} +(9.37806 + 5.53270i) q^{91} +(1.88576 - 8.93316i) q^{92} +(2.02613 - 0.542901i) q^{93} +(-6.50869 + 6.86833i) q^{94} +(17.4498 + 1.94743i) q^{95} +(3.42798 - 4.49989i) q^{96} +(1.21658 + 1.21658i) q^{97} +(-8.61285 - 4.88045i) q^{98} -2.50342i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−0.739767	−	1.20530i	−0.523094	−	0.852275i
$2$	−0.739767	−	1.20530i	−0.523094	−	0.852275i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−0.905490	+	1.78328i	−0.452745	+	0.891640i
$5$	2.04855	−	0.896354i	0.916139	−	0.400862i
$5$	2.04855	−	0.896354i	0.916139	−	0.400862i
$6$	0.402606	+	1.35569i	0.164363	+	0.553460i
$7$	2.56193	−	0.660700i	0.968318	−	0.249721i
$7$	2.56193	−	0.660700i	0.968318	−	0.249721i
$8$	2.81924	−	0.227825i	0.996751	−	0.0805482i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−2.59582	−	1.80602i	−0.820871	−	0.571114i
$11$	−1.25171	−	2.16802i	−0.377404	−	0.653683i	0.613280	−	0.789866i	$-0.289850\pi$
$11$	−1.25171	−	2.16802i	−0.377404	−	0.653683i	−0.990684	+	0.136183i	$0.956517\pi$
$12$	1.33618	−	1.48816i	0.385723	−	0.429594i
$13$	2.91006	+	2.91006i	0.807107	+	0.807107i	0.984195	−	0.177088i	$-0.0566678\pi$
$13$	2.91006	+	2.91006i	0.807107	+	0.807107i	−0.177088	+	0.984195i	$0.556668\pi$
$14$	−2.69157	−	2.59912i	−0.719352	−	0.694645i
$15$	−2.21074	+	0.335608i	−0.570810	+	0.0866536i
$16$	−2.36017	−	3.22949i	−0.590044	−	0.807371i
$17$	−1.20177	+	4.48505i	−0.291471	+	1.08779i	0.652508	+	0.757782i	$0.273717\pi$
$17$	−1.20177	+	4.48505i	−0.291471	+	1.08779i	−0.943980	+	0.330004i	$0.892950\pi$
$18$	−0.0380074	−	1.41370i	−0.00895843	−	0.333213i
$19$	6.80025	+	3.92613i	1.56009	+	0.900716i	0.997247	+	0.0741484i	$0.0236238\pi$
$19$	6.80025	+	3.92613i	1.56009	+	0.900716i	0.562838	+	0.826567i	$0.309709\pi$
$20$	−0.256491	+	4.46477i	−0.0573531	+	0.998354i
$21$	−2.64563	−	0.0248885i	−0.577325	−	0.00543112i
$22$	−1.68714	+	3.11251i	−0.359700	+	0.663590i
$23$	−4.40947	+	1.18151i	−0.919437	+	0.246363i	−0.687345	−	0.726331i	$-0.741224\pi$
$23$	−4.40947	+	1.18151i	−0.919437	+	0.246363i	−0.232093	+	0.972694i	$0.574557\pi$
$24$	−2.78214	−	0.509610i	−0.567902	−	0.104024i
$25$	3.39310	−	3.67245i	0.678620	−	0.734490i
$26$	1.35473	−	5.66027i	0.265684	−	1.11007i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.14159	+	5.16689i	−0.215740	+	0.976451i
$29$	4.44393			0.825216			0.412608	−	0.910909i	$-0.364618\pi$
$29$	4.44393			0.825216			0.412608	+	0.910909i	$0.364618\pi$
$30$	2.03994	+	2.41633i	0.372440	+	0.441159i
$31$	−1.81658	+	1.04880i	−0.326268	+	0.188371i	−0.654183	−	0.756336i	$-0.726987\pi$
$31$	−1.81658	+	1.04880i	−0.326268	+	0.188371i	0.327915	+	0.944707i	$0.393654\pi$
$32$	−2.14652	+	5.23378i	−0.379454	+	0.925211i
$33$	0.647932	+	2.41811i	0.112790	+	0.420940i
$34$	6.29486	−	1.86941i	1.07956	−	0.320601i
$35$	4.65601	−	3.64987i	0.787010	−	0.616941i
$36$	−1.67582	+	1.09162i	−0.279303	+	0.181937i
$37$	2.12891	+	7.94521i	0.349991	+	1.30618i	0.886672	+	0.462399i	$0.153011\pi$
$37$	2.12891	+	7.94521i	0.349991	+	1.30618i	−0.536681	+	0.843785i	$0.680322\pi$
$38$	−0.298444	−	11.1008i	−0.0484140	−	1.80078i
$39$	−2.05773	−	3.56409i	−0.329500	−	0.570711i
$40$	5.57113	−	2.99374i	0.880873	−	0.473352i
$41$	0.898009			0.140245			0.0701227	−	0.997538i	$-0.477661\pi$
$41$	0.898009			0.140245			0.0701227	+	0.997538i	$0.477661\pi$
$42$	1.92715	+	3.20719i	0.297366	+	0.494880i
$43$	0.112372	−	0.112372i	0.0171365	−	0.0171365i	−0.698487	−	0.715623i	$-0.746143\pi$
$43$	0.112372	−	0.112372i	0.0171365	−	0.0171365i	0.715623	+	0.698487i	$0.246143\pi$
$44$	4.99960	−	0.269023i	0.753718	−	0.0405567i
$45$	2.22227	+	0.248009i	0.331277	+	0.0369710i
$46$	4.68605	+	4.44068i	0.690921	+	0.654743i
$47$	−1.73174	−	6.46294i	−0.252600	−	0.942716i	−0.969410	−	0.245448i	$-0.921065\pi$
$47$	−1.73174	−	6.46294i	−0.252600	−	0.942716i	0.716810	−	0.697269i	$-0.245602\pi$
$48$	1.44390	+	3.73030i	0.208409	+	0.538423i
$49$	6.12695	−	3.38533i	0.875279	−	0.483619i
$50$	−6.93650	−	1.37294i	−0.980969	−	0.194164i
$51$	2.32164	−	4.02119i	0.325094	−	0.563079i
$52$	−7.82449	+	2.55442i	−1.08506	+	0.354235i
$53$	−0.260131	+	0.970823i	−0.0357318	+	0.133353i	−0.981488	−	0.191525i	$-0.938657\pi$
$53$	−0.260131	+	0.970823i	−0.0357318	+	0.133353i	0.945756	+	0.324878i	$0.105323\pi$
$54$	−0.329181	+	1.37537i	−0.0447958	+	0.187164i
$55$	−4.50750	−	3.31932i	−0.607791	−	0.447578i
$56$	7.07216	−	2.44634i	0.945057	−	0.326906i
$57$	−5.55238	−	5.55238i	−0.735431	−	0.735431i
$58$	−3.28747	−	5.35626i	−0.431666	−	0.703311i
$59$	8.96896	−	5.17823i	1.16766	−	0.674148i	0.214531	−	0.976717i	$-0.431178\pi$
$59$	8.96896	−	5.17823i	1.16766	−	0.674148i	0.953127	+	0.302569i	$0.0978443\pi$
$60$	1.40332	−	4.24626i	0.181168	−	0.548189i
$61$	−6.16163	−	3.55742i	−0.788916	−	0.455481i	0.0506651	−	0.998716i	$-0.483866\pi$
$61$	−6.16163	−	3.55742i	−0.788916	−	0.455481i	−0.839581	+	0.543235i	$0.817199\pi$
$62$	2.60797	+	1.41365i	0.331212	+	0.179534i
$63$	2.54904	+	0.708781i	0.321149	+	0.0892980i
$64$	7.89619	−	1.28458i	0.987024	−	0.160573i
$65$	8.56985	+	3.35296i	1.06296	+	0.415883i
$66$	2.43523	−	2.56979i	0.299756	−	0.316319i
$67$	3.14289	−	11.7294i	0.383965	−	1.43298i	−0.455828	−	0.890068i	$-0.650657\pi$
$67$	3.14289	−	11.7294i	0.383965	−	1.43298i	0.839792	−	0.542908i	$-0.182677\pi$
$68$	−6.90992	−	6.20426i	−0.837951	−	0.752377i
$69$	4.56502			0.549563
$70$	−7.84355	−	2.91183i	−0.937483	−	0.348031i
$71$		−	12.0186i		−	1.42635i	−0.700987	−	0.713174i	$-0.747257\pi$
$71$		−	12.0186i		−	1.42635i	0.700987	−	0.713174i	$-0.252743\pi$
$72$	2.55544	+	1.21232i	0.301162	+	0.142873i
$73$	−7.41406	−	1.98659i	−0.867750	−	0.232513i	−0.202636	−	0.979254i	$-0.564951\pi$
$73$	−7.41406	−	1.98659i	−0.867750	−	0.232513i	−0.665115	+	0.746741i	$0.731617\pi$
$74$	8.00145	−	8.44358i	0.930150	−	0.981546i
$75$	−4.22798	+	2.66911i	−0.488205	+	0.308203i
$76$	−13.1589	+	8.57168i	−1.50944	+	0.983240i
$77$	−4.63920	−	4.72731i	−0.528686	−	0.538727i
$78$	−2.77355	+	5.11677i	−0.314043	+	0.579360i
$79$	−3.56693	+	6.17810i	−0.401311	+	0.695091i	−0.993884	−	0.110426i	$-0.964779\pi$
$79$	−3.56693	+	6.17810i	−0.401311	+	0.695091i	0.592574	+	0.805516i	$0.298112\pi$
$80$	−7.72969	−	4.50021i	−0.864206	−	0.503138i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−0.664317	−	1.08237i	−0.0733615	−	0.119528i
$83$	3.10456	−	3.10456i	0.340769	−	0.340769i	−0.515887	−	0.856657i	$-0.672538\pi$
$83$	3.10456	−	3.10456i	0.340769	−	0.340769i	0.856657	+	0.515887i	$0.172538\pi$
$84$	2.43998	−	4.69537i	0.266224	−	0.512307i
$85$	1.55832	+	10.2651i	0.169023	+	1.11340i
$86$	−0.218571	−	0.0523127i	−0.0235691	−	0.00564102i
$87$	−4.29250	−	1.15017i	−0.460205	−	0.123311i
$88$	−4.02279	−	5.82700i	−0.428831	−	0.621160i
$89$	2.89589	+	1.67194i	0.306964	+	0.177226i	0.645567	−	0.763704i	$-0.276621\pi$
$89$	2.89589	+	1.67194i	0.306964	+	0.177226i	−0.338603	+	0.940929i	$0.609954\pi$
$90$	−1.34504	−	2.86197i	−0.141779	−	0.301678i
$91$	9.37806	+	5.53270i	0.983087	+	0.579984i
$92$	1.88576	−	8.93316i	0.196604	−	0.931347i
$93$	2.02613	−	0.542901i	0.210100	−	0.0562962i
$94$	−6.50869	+	6.86833i	−0.671320	+	0.708414i
$95$	17.4498	+	1.94743i	1.79032	+	0.199802i
$96$	3.42798	−	4.49989i	0.349867	−	0.459268i
$97$	1.21658	+	1.21658i	0.123525	+	0.123525i	0.766167	−	0.642642i	$-0.222162\pi$
$97$	1.21658	+	1.21658i	0.123525	+	0.123525i	−0.642642	+	0.766167i	$0.722162\pi$
$98$	−8.61285	−	4.88045i	−0.870029	−	0.493000i
$99$		−	2.50342i		−	0.251603i
$100$	3.47658	+	9.37621i	0.347658	+	0.937621i
$101$	−0.941621	+	0.543645i	−0.0936948	+	0.0540947i	−0.546115	−	0.837710i	$-0.683894\pi$
$101$	−0.941621	+	0.543645i	−0.0936948	+	0.0540947i	0.452420	+	0.891805i	$0.350561\pi$
$102$	−6.56420	+	0.176479i	−0.649953	+	0.0174740i
$103$	−7.23099	+	1.93754i	−0.712491	+	0.190911i	−0.596819	−	0.802376i	$-0.703569\pi$
$103$	−7.23099	+	1.93754i	−0.712491	+	0.190911i	−0.115672	+	0.993287i	$0.536902\pi$
$104$	8.86715	+	7.54118i	0.869495	+	0.739473i
$105$	−5.44202	+	2.32044i	−0.531087	+	0.226452i
$106$	1.36257	−	0.404647i	0.132344	−	0.0393028i
$107$	−14.8079	+	3.96775i	−1.43153	+	0.383577i	−0.889559	−	0.456821i	$-0.848988\pi$
$107$	−14.8079	+	3.96775i	−1.43153	+	0.383577i	−0.541970	+	0.840398i	$0.682321\pi$
$108$	1.90125	−	0.620691i	0.182948	−	0.0597260i
$109$	8.39032	+	14.5325i	0.803646	+	1.39196i	0.917201	+	0.398425i	$0.130443\pi$
$109$	8.39032	+	14.5325i	0.803646	+	1.39196i	−0.113555	+	0.993532i	$0.536224\pi$
$110$	−0.666279	+	7.88841i	−0.0635272	+	0.752130i
$111$		−	8.22549i		−	0.780729i
$112$	−8.18032	−	6.71434i	−0.772967	−	0.634446i
$113$	3.65855	−	3.65855i	0.344168	−	0.344168i	−0.513764	−	0.857932i	$-0.671749\pi$
$113$	3.65855	−	3.65855i	0.344168	−	0.344168i	0.857932	+	0.513764i	$0.171749\pi$
$114$	−2.58481	+	10.7998i	−0.242090	+	1.01149i
$115$	−7.97395	+	6.37283i	−0.743575	+	0.594269i
$116$	−4.02393	+	7.92476i	−0.373613	+	0.735796i
$117$	1.06516	+	3.97522i	0.0984738	+	0.367509i
$118$	−12.8762	−	6.97959i	−1.18535	−	0.642523i
$119$	−0.115564	+	12.2844i	−0.0105937	+	1.12611i
$120$	−6.15614	+	1.44982i	−0.561976	+	0.132350i
$121$	2.36645	−	4.09882i	0.215132	−	0.372620i
$122$	0.270416	+	10.0583i	0.0244823	+	0.910632i
$123$	−0.867410	−	0.232422i	−0.0782117	−	0.0209568i
$124$	−0.225414	−	4.18916i	−0.0202428	−	0.376197i
$125$	3.65911	−	10.5646i	0.327281	−	0.944927i
$126$	−1.03141	−	3.59669i	−0.0918849	−	0.320419i
$127$	−6.55936	+	6.55936i	−0.582049	+	0.582049i	−0.935466	−	0.353417i	$-0.885020\pi$
$127$	−6.55936	+	6.55936i	−0.582049	+	0.582049i	0.353417	+	0.935466i	$0.385020\pi$
$128$	−7.38965	−	8.56698i	−0.653159	−	0.757221i
$129$	−0.137627	+	0.0794589i	−0.0121174	+	0.00699596i
$130$	−2.29838	−	12.8096i	−0.201581	−	1.12348i
$131$	3.85449	−	6.67616i	0.336768	−	0.583299i	−0.647055	−	0.762443i	$-0.724000\pi$
$131$	3.85449	−	6.67616i	0.336768	−	0.583299i	0.983823	+	0.179144i	$0.0573329\pi$
$132$	−4.89887	−	1.03414i	−0.426392	−	0.0900099i
$133$	20.0158	+	5.56553i	1.73559	+	0.482593i
$134$	−16.4625	+	4.88891i	−1.42214	+	0.422338i
$135$	−2.08236	−	0.814724i	−0.179221	−	0.0701203i
$136$	−2.36626	+	12.9182i	−0.202905	+	1.10773i
$137$	1.24079	−	4.63067i	0.106007	−	0.395625i	−0.892450	−	0.451146i	$-0.851015\pi$
$137$	1.24079	−	4.63067i	0.106007	−	0.395625i	0.998458	+	0.0555210i	$0.0176820\pi$
$138$	−3.37705	−	5.50221i	−0.287473	−	0.468379i
$139$		−	20.9415i		−	1.77623i	−0.459617	−	0.888117i	$-0.652013\pi$
$139$		−	20.9415i		−	1.77623i	0.459617	−	0.888117i	$-0.347987\pi$
$140$	2.29277	+	11.6079i	0.193774	+	0.981046i
$141$			6.69093i			0.563478i
$142$	−14.4860	+	8.89097i	−1.21564	+	0.746114i
$143$	2.66653	−	9.95163i	0.222987	−	0.832197i
$144$	−0.429228	−	3.97690i	−0.0357690	−	0.331409i
$145$	9.10359	−	3.98333i	0.756012	−	0.330798i
$146$	3.09024	+	10.4058i	0.255750	+	0.861188i
$147$	−6.79437	+	1.68421i	−0.560390	+	0.138911i
$148$	−16.0962	−	3.39786i	−1.32310	−	0.279303i
$149$	−1.65802	+	2.87177i	−0.135830	+	0.235265i	−0.925914	−	0.377734i	$-0.876703\pi$
$149$	−1.65802	+	2.87177i	−0.135830	+	0.235265i	0.790084	+	0.612998i	$0.210037\pi$
$150$	6.34480	+	3.12146i	0.518051	+	0.254866i
$151$	−4.94725	+	2.85630i	−0.402602	+	0.232442i	−0.687606	−	0.726084i	$-0.741338\pi$
$151$	−4.94725	+	2.85630i	−0.402602	+	0.232442i	0.285004	+	0.958526i	$0.408005\pi$
$152$	20.0660	+	9.51942i	1.62757	+	0.772127i
$153$	−3.28329	+	3.28329i	−0.265438	+	0.265438i
$154$	−2.26590	+	9.08873i	−0.182591	+	0.732391i
$155$	−2.78126	+	3.77683i	−0.223396	+	0.303362i
$156$	8.21902	−	0.442256i	0.658048	−	0.0354088i
$157$	13.6110	+	3.64705i	1.08628	+	0.291067i	0.757164	−	0.653225i	$-0.226584\pi$
$157$	13.6110	+	3.64705i	1.08628	+	0.291067i	0.329111	+	0.944291i	$0.393251\pi$
$158$	10.0852	−	0.271139i	0.802331	−	0.0215707i
$159$	0.502535	−	0.870416i	0.0398536	−	0.0690285i
$160$	0.294078	+	12.6457i	0.0232489	+	0.999730i
$161$	−10.5161	+	5.94029i	−0.828786	+	0.468160i
$162$	0.673936	−	1.24331i	0.0529494	−	0.0976834i
$163$	6.32707	+	23.6129i	0.495574	+	1.84951i	0.526789	+	0.849996i	$0.323396\pi$
$163$	6.32707	+	23.6129i	0.495574	+	1.84951i	−0.0312150	+	0.999513i	$0.509938\pi$
$164$	−0.813138	+	1.60140i	−0.0634954	+	0.125048i
$165$	3.49481	+	4.37285i	0.272070	+	0.340426i
$166$	−6.03857	−	1.44527i	−0.468684	−	0.112175i
$167$	−8.37606	+	8.37606i	−0.648159	+	0.648159i	−0.952548	−	0.304389i	$-0.901548\pi$
$167$	−8.37606	+	8.37606i	−0.648159	+	0.648159i	0.304389	+	0.952548i	$0.401548\pi$
$168$	−7.46434	+	0.532574i	−0.575886	+	0.0410890i
$169$			3.93695i			0.302842i
$170$	11.2197	−	9.47199i	0.860509	−	0.726468i
$171$	3.92613	+	6.80025i	0.300239	+	0.520028i
$172$	0.0986388	+	0.302142i	0.00752114	+	0.0230381i
$173$	19.8724	−	5.32478i	1.51087	−	0.404836i	0.594144	−	0.804358i	$-0.297491\pi$
$173$	19.8724	−	5.32478i	1.51087	−	0.404836i	0.916723	+	0.399523i	$0.130824\pi$
$174$	1.78915	+	6.02461i	0.135635	+	0.456724i
$175$	6.26649	−	11.6504i	0.473702	−	0.880685i
$176$	−4.04735	+	9.15928i	−0.305080	+	0.690407i
$177$	−10.0036	+	2.68045i	−0.751914	+	0.201475i
$178$	−0.127092	−	4.72726i	−0.00952597	−	0.354323i
$179$	−4.73569	+	2.73415i	−0.353962	+	0.204360i	−0.666429	−	0.745569i	$-0.732178\pi$
$179$	−4.73569	+	2.73415i	−0.353962	+	0.204360i	0.312467	+	0.949929i	$0.398845\pi$
$180$	−2.45451	+	3.73836i	−0.182949	+	0.278641i
$181$		−	1.91630i		−	0.142438i	−0.997461	−	0.0712189i	$-0.977311\pi$
$181$		−	1.91630i		−	0.142438i	0.997461	−	0.0712189i	$-0.0226889\pi$
$182$	−0.269022	−	15.3963i	−0.0199412	−	1.14125i
$183$	5.03095	+	5.03095i	0.371898	+	0.371898i
$184$	−12.1622	+	4.33555i	−0.896606	+	0.319621i
$185$	11.4829	+	14.3679i	0.844239	+	1.05635i
$186$	−2.15322	−	2.04048i	−0.157882	−	0.149615i
$187$	11.2280	−	3.00852i	0.821070	−	0.220005i
$188$	13.0933	+	2.76395i	0.954927	+	0.201582i
$189$	−2.27874	−	1.34437i	−0.165754	−	0.0977886i
$190$	−10.5616	−	22.4729i	−0.766218	−	1.63036i
$191$	−1.95595	−	1.12927i	−0.141528	−	0.0817110i	0.427564	−	0.903985i	$-0.359372\pi$
$191$	−1.95595	−	1.12927i	−0.141528	−	0.0817110i	−0.569092	+	0.822274i	$0.692705\pi$
$192$	−7.95961	−	0.802872i	−0.574435	−	0.0579423i
$193$	−16.1143	−	4.31781i	−1.15993	−	0.310802i	−0.372992	−	0.927834i	$-0.621668\pi$
$193$	−16.1143	−	4.31781i	−1.15993	−	0.310802i	−0.786938	+	0.617032i	$0.788335\pi$
$194$	0.566357	−	2.36633i	0.0406621	−	0.169893i
$195$	−7.41003	−	5.45675i	−0.530644	−	0.390766i
$196$	0.489100	+	13.9915i	0.0349357	+	0.999390i
$197$	−16.7309	+	16.7309i	−1.19203	+	1.19203i	−0.215530	+	0.976497i	$0.569148\pi$
$197$	−16.7309	+	16.7309i	−1.19203	+	1.19203i	−0.976497	+	0.215530i	$0.930852\pi$
$198$	−3.01736	+	1.85194i	−0.214435	+	0.131612i
$199$	−8.68665	−	15.0457i	−0.615780	−	1.06656i	−0.990247	−	0.139322i	$-0.955508\pi$
$199$	−8.68665	−	15.0457i	−0.615780	−	1.06656i	0.374467	−	0.927240i	$-0.377826\pi$
$200$	8.72928	−	11.1265i	0.617253	−	0.786765i
$201$	−6.07159	+	10.5163i	−0.428257	+	0.741763i
$202$	1.35184	+	0.732764i	0.0951148	+	0.0515571i
$203$	11.3850	−	2.93610i	0.799072	−	0.206074i
$204$	5.06869	+	7.78127i	0.354879	+	0.544798i
$205$	1.83961	−	0.804933i	0.128484	−	0.0562190i
$206$	7.68456	+	7.28218i	0.535409	+	0.507374i
$207$	−4.40947	−	1.18151i	−0.306479	−	0.0821208i
$208$	2.52975	−	16.2663i	0.175407	−	1.12786i
$209$		−	19.6575i		−	1.35974i
$210$	6.82265	+	4.84267i	0.470807	+	0.334176i
$211$	10.9810			0.755960			0.377980	−	0.925814i	$-0.376619\pi$
$211$	10.9810			0.755960			0.377980	+	0.925814i	$0.376619\pi$
$212$	−1.49570	−	1.34296i	−0.102725	−	0.0922347i
$213$	−3.11065	+	11.6091i	−0.213138	+	0.795442i
$214$	15.7367	+	14.9127i	1.07574	+	1.01941i
$215$	0.129474	−	0.330924i	0.00883006	−	0.0225688i
$216$	−2.15460	−	1.83241i	−0.146602	−	0.124679i
$217$	−3.96101	+	3.88718i	−0.268891	+	0.263879i
$218$	11.3091	−	20.8635i	0.765947	−	1.41305i
$219$	6.64727	+	3.83780i	0.449181	+	0.259335i
$220$	10.0008	−	5.03252i	0.674252	−	0.339292i
$221$	−16.5490	+	9.55458i	−1.11321	+	0.642711i
$222$	−9.91417	+	6.08494i	−0.665395	+	0.408394i
$223$	−12.2628	−	12.2628i	−0.821178	−	0.821178i	0.165099	−	0.986277i	$-0.447206\pi$
$223$	−12.2628	−	12.2628i	−0.821178	−	0.821178i	−0.986277	+	0.165099i	$0.947206\pi$
$224$	−2.04126	+	14.8268i	−0.136387	+	0.990656i
$225$	4.77473	−	1.48388i	0.318316	−	0.0989256i
$226$	−7.11613	−	1.70317i	−0.473358	−	0.113293i
$227$	−7.39138	+	27.5850i	−0.490583	+	1.83088i	0.0629007	+	0.998020i	$0.479965\pi$
$227$	−7.39138	+	27.5850i	−0.490583	+	1.83088i	−0.553483	+	0.832860i	$0.686702\pi$
$228$	14.9291	−	4.87382i	0.988703	−	0.322777i
$229$	−4.08294	+	7.07185i	−0.269808	+	0.467321i	−0.968812	−	0.247796i	$-0.920294\pi$
$229$	−4.08294	+	7.07185i	−0.269808	+	0.467321i	0.699004	+	0.715118i	$0.253627\pi$
$230$	13.5800	+	4.89659i	0.895441	+	0.322871i
$231$	3.25760	+	5.76695i	0.214335	+	0.379437i
$232$	12.5285	−	1.01244i	0.822535	−	0.0664697i
$233$	−0.469995	−	1.75405i	−0.0307904	−	0.114911i	0.948820	−	0.315816i	$-0.102278\pi$
$233$	−0.469995	−	1.75405i	−0.0307904	−	0.114911i	−0.979611	+	0.200905i	$0.935612\pi$
$234$	4.00336	−	4.22457i	0.261708	−	0.276169i
$235$	−9.34063	−	11.6874i	−0.609316	−	0.762401i
$236$	1.11293	+	20.6830i	0.0724455	+	1.34635i
$237$	5.04440	−	5.04440i	0.327669	−	0.327669i
$238$	14.8919	−	8.94830i	0.965296	−	0.580032i
$239$	−7.43701			−0.481060			−0.240530	−	0.970642i	$-0.577321\pi$
$239$	−7.43701			−0.481060			−0.240530	+	0.970642i	$0.577321\pi$
$240$	6.30157	+	6.34746i	0.406765	+	0.409727i
$241$	−8.17415	−	14.1580i	−0.526543	−	0.912000i	−0.999522	−	0.0309256i	$-0.990155\pi$
$241$	−8.17415	−	14.1580i	−0.526543	−	0.912000i	0.472978	−	0.881074i	$-0.343179\pi$
$242$	−6.69093	+	0.179886i	−0.430109	+	0.0115635i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	11.9232	−	7.76670i	0.763302	−	0.497212i
$245$	9.51690	−	12.4269i	0.608012	−	0.793928i
$246$	0.361543	+	1.21743i	0.0230512	+	0.0776202i
$247$	8.36389	+	31.2145i	0.532182	+	1.98613i
$248$	−4.88243	+	3.37069i	−0.310035	+	0.214039i
$249$	−3.80229	+	2.19525i	−0.240960	+	0.139119i
$250$	−15.4404	+	3.40502i	−0.976536	+	0.215352i
$251$	8.99623			0.567837			0.283918	−	0.958848i	$-0.408366\pi$
$251$	8.99623			0.567837			0.283918	+	0.958848i	$0.408366\pi$
$252$	−3.57209	+	3.90387i	−0.225021	+	0.245920i
$253$	8.08091	+	8.08091i	0.508042	+	0.508042i
$254$	12.7584	+	3.05359i	0.800533	+	0.191599i
$255$	1.15157	−	10.3186i	0.0721143	−	0.646176i
$256$	−4.85915	+	15.2443i	−0.303697	+	0.952769i
$257$	−1.80538	+	0.483750i	−0.112617	+	0.0301755i	−0.314687	−	0.949195i	$-0.601900\pi$
$257$	−1.80538	+	0.483750i	−0.112617	+	0.0301755i	0.202071	+	0.979371i	$0.435233\pi$
$258$	0.197583	+	0.107100i	0.0123010	+	0.00666778i
$259$	10.7035	+	18.9485i	0.665084	+	1.17740i
$260$	−13.7392	+	12.2464i	−0.852068	+	0.759488i
$261$	3.84855	+	2.22196i	0.238219	+	0.137536i
$262$	−10.8982	+	0.292998i	−0.673293	+	0.0181015i
$263$	−6.15376	+	22.9662i	−0.379457	+	1.41615i	0.467265	+	0.884118i	$0.345240\pi$
$263$	−6.15376	+	22.9662i	−0.379457	+	1.41615i	−0.846722	+	0.532036i	$0.821427\pi$
$264$	2.37758	+	6.66962i	0.146330	+	0.410487i
$265$	0.337310	+	2.22195i	0.0207208	+	0.136493i
$266$	−8.09886	−	28.2422i	−0.496573	−	1.73164i
$267$	−2.36448	−	2.36448i	−0.144704	−	0.144704i
$268$	18.0710	+	16.2255i	1.10386	+	0.991131i
$269$	−10.7987	−	18.7039i	−0.658410	−	1.14040i	−0.981027	−	0.193870i	$-0.937896\pi$
$269$	−10.7987	−	18.7039i	−0.658410	−	1.14040i	0.322618	−	0.946529i	$-0.395437\pi$
$270$	0.558474	+	3.11257i	0.0339877	+	0.189425i
$271$	19.0805	+	11.0161i	1.15906	+	0.669182i	0.951078	−	0.308951i	$-0.0999778\pi$
$271$	19.0805	+	11.0161i	1.15906	+	0.669182i	0.207980	+	0.978133i	$0.433311\pi$
$272$	17.3208	−	6.70442i	1.05023	−	0.406515i
$273$	−7.62654	−	7.77139i	−0.461579	−	0.470346i
$274$	−6.49924	+	1.93010i	−0.392633	+	0.116602i
$275$	−12.2091	−	2.75948i	−0.736237	−	0.166403i
$276$	−4.13358	+	8.14070i	−0.248812	+	0.490013i
$277$	−26.0494	−	6.97992i	−1.56516	−	0.419383i	−0.630867	−	0.775891i	$-0.717300\pi$
$277$	−26.0494	−	6.97992i	−1.56516	−	0.419383i	−0.934292	+	0.356508i	$0.883967\pi$
$278$	−25.2408	+	15.4918i	−1.51384	+	0.929138i
$279$	−2.09761			−0.125580
$280$	12.2949	−	11.3506i	0.734759	−	0.678328i
$281$	−9.91189			−0.591294			−0.295647	−	0.955297i	$-0.595535\pi$
$281$	−9.91189			−0.591294			−0.295647	+	0.955297i	$0.595535\pi$
$282$	8.06457	−	4.94972i	0.480238	−	0.294752i
$283$	−14.7095	−	3.94140i	−0.874390	−	0.234292i	−0.206405	−	0.978467i	$-0.566176\pi$
$283$	−14.7095	−	3.94140i	−0.874390	−	0.234292i	−0.667985	+	0.744175i	$0.732843\pi$
$284$	21.4326	+	10.8827i	1.27179	+	0.645772i
$285$	−16.3512	−	6.39743i	−0.968563	−	0.378951i
$286$	−13.9673	+	4.14792i	−0.825904	+	0.245272i
$287$	2.30063	−	0.593314i	0.135802	−	0.0350222i
$288$	−4.47583	+	3.45933i	−0.263741	+	0.203843i
$289$	−3.94904	−	2.27998i	−0.232297	−	0.134116i
$290$	−11.5356	−	8.02582i	−0.677396	−	0.471292i
$291$	−0.860252	−	1.49000i	−0.0504289	−	0.0873454i
$292$	10.2560	−	11.4225i	0.600188	−	0.668452i
$293$	−8.30117	−	8.30117i	−0.484959	−	0.484959i	0.421752	−	0.906711i	$-0.361415\pi$
$293$	−8.30117	−	8.30117i	−0.484959	−	0.484959i	−0.906711	+	0.421752i	$0.861415\pi$
$294$	7.05622	+	6.94332i	0.411527	+	0.404943i
$295$	13.7318	−	18.6472i	0.799497	−	1.08568i
$296$	7.81202	+	21.9144i	0.454065	+	1.27375i
$297$	−0.647932	+	2.41811i	−0.0375968	+	0.140313i
$298$	4.68789	−	0.126034i	0.271562	−	0.00730094i
$299$	−16.2701	−	9.39355i	−0.940925	−	0.543243i
$300$	−0.931380	−	9.95653i	−0.0537733	−	0.574841i
$301$	0.213644	−	0.362133i	0.0123143	−	0.0208730i
$302$	7.10250	+	3.84992i	0.408703	+	0.221538i
$303$	1.05024	−	0.281412i	0.0603348	−	0.0161667i
$304$	−3.37041	−	31.2277i	−0.193306	−	1.79103i
$305$	−15.8111	−	1.76454i	−0.905341	−	0.101037i
$306$	6.38621	+	1.52848i	0.365075	+	0.0873771i
$307$	−5.42854	−	5.42854i	−0.309823	−	0.309823i	0.535018	−	0.844841i	$-0.320305\pi$
$307$	−5.42854	−	5.42854i	−0.309823	−	0.309823i	−0.844841	+	0.535018i	$0.820305\pi$
$308$	12.6309	−	3.99245i	0.719711	−	0.227491i
$309$	7.48608			0.425868
$310$	6.60968	+	0.558274i	0.375405	+	0.0317078i
$311$	−10.4092	+	6.00978i	−0.590254	+	0.340783i	−0.765198	−	0.643795i	$-0.777359\pi$
$311$	−10.4092	+	6.00978i	−0.590254	+	0.340783i	0.174944	+	0.984578i	$0.444026\pi$
$312$	−6.61320	−	9.57920i	−0.374399	−	0.542316i
$313$	4.70184	+	17.5475i	0.265764	+	0.991845i	0.961781	+	0.273819i	$0.0882871\pi$
$313$	4.70184	+	17.5475i	0.265764	+	0.991845i	−0.696017	+	0.718025i	$0.745046\pi$
$314$	−5.67317	−	19.1033i	−0.320155	−	1.07806i
$315$	5.85716	−	0.832874i	0.330014	−	0.0469271i
$316$	−7.78746	−	11.9550i	−0.438079	−	0.672524i
$317$	−7.64949	−	28.5483i	−0.429638	−	1.60343i	−0.753582	−	0.657354i	$-0.771676\pi$
$317$	−7.64949	−	28.5483i	−0.429638	−	1.60343i	0.323944	−	0.946076i	$-0.394991\pi$
$318$	−1.42087	+	0.0382001i	−0.0796785	+	0.00214215i
$319$	−5.56250	−	9.63453i	−0.311440	−	0.539430i
$320$	15.0243	−	9.70931i	0.839883	−	0.542767i
$321$	15.3302			0.855649
$322$	14.9393	+	8.28063i	0.832534	+	0.461461i
$323$	−25.7812	+	25.7812i	−1.43451	+	1.43451i
$324$	−1.99711	+	0.107462i	−0.110951	+	0.00597013i
$325$	20.5612	−	0.812923i	1.14053	−	0.0450929i
$326$	23.7801	−	25.0941i	1.31706	−	1.38983i
$327$	−4.34315	−	16.2088i	−0.240177	−	0.896351i
$328$	2.53170	−	0.204589i	0.139790	−	0.0112965i
$329$	−8.70666	−	15.4134i	−0.480013	−	0.849770i
$330$	2.68525	−	7.44717i	0.147818	−	0.409953i
$331$	10.2623	−	17.7749i	0.564068	−	0.976995i	−0.433067	−	0.901362i	$-0.642569\pi$
$331$	10.2623	−	17.7749i	0.564068	−	0.976995i	0.997136	−	0.0756334i	$-0.0240979\pi$
$332$	2.72515	+	8.34744i	0.149562	+	0.458125i
$333$	−2.12891	+	7.94521i	−0.116664	+	0.435395i
$334$	16.2920	+	3.89932i	0.891458	+	0.213362i
$335$	−4.07535	−	26.8454i	−0.222660	−	1.46672i
$336$	6.16378	+	8.60278i	0.336262	+	0.469320i
$337$	22.7509	+	22.7509i	1.23932	+	1.23932i	0.960279	+	0.279041i	$0.0900165\pi$
$337$	22.7509	+	22.7509i	1.23932	+	1.23932i	0.279041	+	0.960279i	$0.409983\pi$
$338$	4.74520	−	2.91242i	0.258105	−	0.158415i
$339$	−4.48079	+	2.58699i	−0.243363	+	0.140506i
$340$	−19.7165	−	6.51599i	−1.06928	−	0.353379i
$341$	4.54766	+	2.62559i	0.246270	+	0.142184i
$342$	5.29192	−	9.76276i	0.286154	−	0.527910i
$343$	13.4601	−	12.7211i	0.726778	−	0.686872i
$344$	0.291202	−	0.342404i	0.0157005	−	0.0184612i
$345$	9.35166	−	4.09187i	0.503476	−	0.220299i
$346$	−21.1189	−	20.0130i	−1.13536	−	1.07591i
$347$	5.96833	−	22.2741i	0.320397	−	1.19574i	−0.598462	−	0.801151i	$-0.704221\pi$
$347$	5.96833	−	22.2741i	0.320397	−	1.19574i	0.918859	−	0.394586i	$-0.129112\pi$
$348$	5.93790	−	6.61326i	0.318305	−	0.354508i
$349$	−14.4900			−0.775631			−0.387815	−	0.921737i	$-0.626770\pi$
$349$	−14.4900			−0.775631			−0.387815	+	0.921737i	$0.626770\pi$
$350$	−18.6779	+	1.06556i	−0.998377	+	0.0569567i
$351$		−	4.11545i		−	0.219667i
$352$	14.0338	−	1.89747i	0.748002	−	0.101136i
$353$	−26.7447	−	7.16622i	−1.42348	−	0.381420i	−0.536761	−	0.843734i	$-0.680352\pi$
$353$	−26.7447	−	7.16622i	−1.42348	−	0.381420i	−0.886716	+	0.462315i	$0.847019\pi$
$354$	10.6310	+	10.0744i	0.565034	+	0.535447i
$355$	−10.7729	−	24.6207i	−0.571768	−	1.30673i
$356$	−5.60374	+	3.65025i	−0.296998	+	0.193463i
$357$	3.29106	−	11.8359i	0.174181	−	0.626422i
$358$	6.79877	+	3.68528i	0.359326	+	0.194773i
$359$	−10.9619	+	18.9866i	−0.578548	+	1.00207i	0.417099	+	0.908861i	$0.363047\pi$
$359$	−10.9619	+	18.9866i	−0.578548	+	1.00207i	−0.995646	+	0.0932126i	$0.970286\pi$
$360$	6.32161	+	0.192907i	0.333178	+	0.0101671i
$361$	21.3290	+	36.9429i	1.12258	+	1.94436i
$362$	−2.30972	+	1.41762i	−0.121396	+	0.0745083i
$363$	−3.34667	+	3.34667i	−0.175655	+	0.175655i
$364$	−18.3581	+	11.7139i	−0.962225	+	0.613975i
$365$	−16.9688	+	2.57599i	−0.888185	+	0.134834i
$366$	2.34207	−	9.78552i	0.122422	−	0.511497i
$367$	−16.1234	−	4.32024i	−0.841633	−	0.225515i	−0.187851	−	0.982198i	$-0.560152\pi$
$367$	−16.1234	−	4.32024i	−0.841633	−	0.225515i	−0.653782	+	0.756683i	$0.726819\pi$
$368$	14.2228	+	11.4517i	0.741414	+	0.596963i
$369$	0.777698	+	0.449004i	0.0404854	+	0.0233742i
$370$	8.82293	−	24.4692i	0.458682	−	1.27209i
$371$	−0.0250147	+	2.65905i	−0.00129870	+	0.138051i
$372$	−0.866500	+	4.10475i	−0.0449259	+	0.212822i
$373$	−17.2692	+	4.62726i	−0.894164	+	0.239590i	−0.676508	−	0.736435i	$-0.736508\pi$
$373$	−17.2692	+	4.62726i	−0.894164	+	0.239590i	−0.217656	+	0.976026i	$0.569841\pi$
$374$	−11.9322	−	11.3074i	−0.617001	−	0.584694i
$375$	−6.26875	+	9.25758i	−0.323717	+	0.478059i
$376$	−6.35460	−	17.8260i	−0.327713	−	0.919307i
$377$	12.9321	+	12.9321i	0.666037	+	0.666037i
$378$	0.0653687	+	3.74109i	0.00336220	+	0.192421i
$379$			6.18127i			0.317511i	0.987318	+	0.158755i	$0.0507481\pi$
$379$			6.18127i			0.317511i	−0.987318	+	0.158755i	$0.949252\pi$
$380$	−19.2735	+	29.3546i	−0.988709	+	1.50586i
$381$	8.03355	−	4.63817i	0.411571	−	0.237621i
$382$	0.0858411	+	3.19290i	0.00439201	+	0.163363i
$383$	7.57648	−	2.03011i	0.387140	−	0.103734i	−0.0599988	−	0.998198i	$-0.519110\pi$
$383$	7.57648	−	2.03011i	0.387140	−	0.103734i	0.447139	+	0.894465i	$0.352443\pi$
$384$	4.92055	+	10.1876i	0.251101	+	0.519886i
$385$	−13.7410	−	5.52576i	−0.700304	−	0.281619i
$386$	6.71656	+	22.6167i	0.341864	+	1.15116i
$387$	0.153503	−	0.0411309i	0.00780298	−	0.00209080i
$388$	−3.27111	+	1.06790i	−0.166065	+	0.0542145i
$389$	7.60813	+	13.1777i	0.385748	+	0.668135i	0.991873	−	0.127235i	$-0.0406102\pi$
$389$	7.60813	+	13.1777i	0.385748	+	0.668135i	−0.606125	+	0.795369i	$0.707277\pi$
$390$	−1.09532	+	12.9680i	−0.0554637	+	0.656662i
$391$		−	21.1966i		−	1.07196i
$392$	16.5021	−	10.9399i	0.833480	−	0.552550i
$393$	−5.45107	+	5.45107i	−0.274970	+	0.274970i
$394$	32.5427	+	7.78877i	1.63948	+	0.392393i
$395$	−1.76926	+	15.8534i	−0.0890211	+	0.797669i
$396$	4.46429	+	2.26682i	0.224339	+	0.113912i
$397$	6.62755	+	24.7344i	0.332627	+	1.24138i	0.906418	+	0.422381i	$0.138805\pi$
$397$	6.62755	+	24.7344i	0.332627	+	1.24138i	−0.573791	+	0.819002i	$0.694528\pi$
$398$	−11.7085	+	21.6003i	−0.586893	+	1.08273i
$399$	−17.8933	−	10.5563i	−0.895784	−	0.528478i
$400$	−19.8684	−	2.29035i	−0.993421	−	0.114517i
$401$	−3.65413	+	6.32914i	−0.182479	+	0.316062i	−0.942724	−	0.333574i	$-0.891745\pi$
$401$	−3.65413	+	6.32914i	−0.182479	+	0.316062i	0.760245	+	0.649636i	$0.225079\pi$
$402$	17.1669	−	0.461531i	0.856205	−	0.0230191i
$403$	−8.33846	−	2.23428i	−0.415368	−	0.111298i
$404$	−0.116843	−	2.17144i	−0.00581314	−	0.108033i
$405$	1.80054	+	1.32592i	0.0894695	+	0.0658854i
$406$	−11.9611	−	11.5503i	−0.593621	−	0.573233i
$407$	14.5606	−	14.5606i	0.721743	−	0.721743i
$408$	5.62911	−	11.8656i	0.278683	−	0.587435i
$409$	−10.5869	+	6.11237i	−0.523490	+	0.302237i	−0.738362	−	0.674405i	$-0.764400\pi$
$409$	−10.5869	+	6.11237i	−0.523490	+	0.302237i	0.214871	+	0.976642i	$0.431067\pi$
$410$	−2.33107	−	1.62182i	−0.115123	−	0.0800960i
$411$	−2.39701	+	4.15175i	−0.118236	+	0.204791i
$412$	3.09242	−	14.6493i	0.152353	−	0.721720i
$413$	19.5566	−	19.1920i	0.962316	−	0.944379i
$414$	1.83790	+	6.18877i	0.0903279	+	0.304161i
$415$	3.57705	−	9.14262i	0.175591	−	0.448793i
$416$	−21.4771	+	8.98414i	−1.05300	+	0.440484i
$417$	−5.42006	+	20.2279i	−0.265421	+	0.990566i
$418$	−23.6931	+	14.5419i	−1.15887	+	0.711269i
$419$			18.1365i			0.886025i	0.896515	+	0.443013i	$0.146090\pi$
$419$			18.1365i			0.886025i	−0.896515	+	0.443013i	$0.853910\pi$
$420$	0.789702	−	11.8058i	0.0385335	−	0.576063i
$421$		−	35.1440i		−	1.71282i	−0.516300	−	0.856408i	$-0.672691\pi$
$421$		−	35.1440i		−	1.71282i	0.516300	−	0.856408i	$-0.327309\pi$
$422$	−8.12335	−	13.2353i	−0.395438	−	0.644286i
$423$	1.73174	−	6.46294i	0.0842000	−	0.314239i
$424$	−0.512194	+	2.79624i	−0.0248743	+	0.135798i
$425$	12.3934	+	19.6317i	0.601169	+	0.952276i
$426$	16.2936	−	4.83876i	0.789426	−	0.234439i
$427$	−18.1360	−	5.04286i	−0.877664	−	0.244041i
$428$	6.33275	−	29.9993i	0.306105	−	1.45007i
$429$	−5.15134	+	8.92239i	−0.248709	+	0.430777i
$430$	−0.494643	+	0.0887515i	−0.0238538	+	0.00427998i
$431$	−8.59615	+	4.96299i	−0.414062	+	0.239059i	−0.692533	−	0.721386i	$-0.743506\pi$
$431$	−8.59615	+	4.96299i	−0.414062	+	0.239059i	0.278472	+	0.960444i	$0.410172\pi$
$432$	−0.614696	+	3.95249i	−0.0295746	+	0.190164i
$433$	17.6891	−	17.6891i	0.850083	−	0.850083i	−0.140060	−	0.990143i	$-0.544729\pi$
$433$	17.6891	−	17.6891i	0.850083	−	0.850083i	0.990143	+	0.140060i	$0.0447294\pi$
$434$	7.61543	+	1.89859i	0.365552	+	0.0911354i
$435$	−9.82436	+	1.49142i	−0.471042	+	0.0715080i
$436$	−33.5128	+	1.80329i	−1.60497	+	0.0863617i
$437$	−34.6243	−	9.27754i	−1.65630	−	0.443805i
$438$	−0.291730	−	10.8510i	−0.0139394	−	0.518482i
$439$	8.92288	−	15.4549i	0.425866	−	0.737621i	−0.570635	−	0.821204i	$-0.693303\pi$
$439$	8.92288	−	15.4549i	0.425866	−	0.737621i	0.996501	+	0.0835826i	$0.0266362\pi$
$440$	−13.4639	−	8.33104i	−0.641868	−	0.397167i
$441$	6.99876	+	0.131692i	0.333274	+	0.00627103i
$442$	23.7585	+	12.8784i	1.13008	+	0.612561i
$443$	1.19452	+	4.45800i	0.0567533	+	0.211806i	0.988479	−	0.151356i	$-0.0483639\pi$
$443$	1.19452	+	4.45800i	0.0567533	+	0.211806i	−0.931726	+	0.363162i	$0.881697\pi$
$444$	14.6683	+	7.44810i	0.696129	+	0.353471i
$445$	7.43102	+	0.829313i	0.352264	+	0.0393132i
$446$	−5.70873	+	23.8520i	−0.270316	+	1.12942i
$447$	2.34479	−	2.34479i	0.110905	−	0.110905i
$448$	19.3808	−	8.50803i	0.915654	−	0.401966i
$449$		−	5.02676i		−	0.237228i	−0.992940	−	0.118614i	$-0.962155\pi$
$449$		−	5.02676i		−	0.237228i	0.992940	−	0.118614i	$-0.0378450\pi$
$450$	−5.32071	−	4.65725i	−0.250821	−	0.219545i
$451$	−1.12404	−	1.94690i	−0.0529292	−	0.0916760i
$452$	3.21144	+	9.83701i	0.151053	+	0.462694i
$453$	5.51794	−	1.47853i	0.259256	−	0.0694673i
$454$	38.7160	−	11.4976i	1.81703	−	0.539611i
$455$	24.1707	+	2.92794i	1.13314	+	0.137264i
$456$	−16.9185	−	14.3885i	−0.792279	−	0.673804i
$457$	32.4445	−	8.69348i	1.51769	−	0.406664i	0.598709	−	0.800967i	$-0.295681\pi$
$457$	32.4445	−	8.69348i	1.51769	−	0.406664i	0.918980	+	0.394303i	$0.129014\pi$
$458$	11.5441	−	0.310364i	0.539421	−	0.0145023i
$459$	4.02119	−	2.32164i	0.187693	−	0.108365i
$460$	−4.14420	−	19.9903i	−0.193224	−	0.932054i
$461$		−	0.392085i		−	0.0182612i	−0.999958	−	0.00913062i	$-0.997094\pi$
$461$		−	0.392085i		−	0.0182612i	0.999958	−	0.00913062i	$-0.00290641\pi$
$462$	4.54103	−	8.19258i	0.211268	−	0.381153i
$463$	8.76491	+	8.76491i	0.407340	+	0.407340i	0.880810	−	0.473470i	$-0.156999\pi$
$463$	8.76491	+	8.76491i	0.407340	+	0.407340i	−0.473470	+	0.880810i	$0.656999\pi$
$464$	−10.4884	−	14.3516i	−0.486914	−	0.666256i
$465$	3.66400	−	2.92829i	0.169914	−	0.135796i
$466$	−1.76646	+	1.86407i	−0.0818298	+	0.0863513i
$467$	26.0892	−	6.99059i	1.20727	−	0.323486i	0.401577	−	0.915825i	$-0.368462\pi$
$467$	26.0892	−	6.99059i	1.20727	−	0.323486i	0.805689	+	0.592339i	$0.201796\pi$
$468$	−8.05342	−	1.70005i	−0.372270	−	0.0785849i
$469$	0.302226	−	32.1264i	0.0139555	−	1.48346i
$470$	−7.17691	+	19.9042i	−0.331046	+	0.918112i
$471$	−12.2033	−	7.04557i	−0.562297	−	0.324643i
$472$	24.1059	−	16.6420i	1.10956	−	0.766010i
$473$	−0.384281	−	0.102968i	−0.0176693	−	0.00473447i
$474$	−9.81168	−	2.34833i	−0.450666	−	0.107862i
$475$	37.4924	−	11.6518i	1.72027	−	0.534623i
$476$	−21.8019	−	11.3295i	−0.999287	−	0.519286i
$477$	−0.710692	+	0.710692i	−0.0325403	+	0.0325403i
$478$	5.50165	+	8.96382i	0.251640	+	0.409996i
$479$	16.2572	+	28.1583i	0.742812	+	1.28659i	0.951210	+	0.308544i	$0.0998416\pi$
$479$	16.2572	+	28.1583i	0.742812	+	1.28659i	−0.208398	+	0.978044i	$0.566825\pi$
$480$	2.98889	−	12.2909i	0.136423	−	0.561001i
$481$	−16.9258	+	29.3163i	−0.771750	+	1.33671i
$482$	−11.0177	+	20.3259i	−0.501843	+	0.925821i
$483$	11.6952	−	3.01611i	0.532152	−	0.137238i
$484$	5.16654	+	7.93149i	0.234843	+	0.360522i
$485$	3.58271	+	1.40174i	0.162683	+	0.0636496i
$486$	−0.972764	+	1.02651i	−0.0441254	+	0.0465636i
$487$	−5.51312	−	1.47724i	−0.249823	−	0.0669399i	0.131734	−	0.991285i	$-0.457945\pi$
$487$	−5.51312	−	1.47724i	−0.249823	−	0.0669399i	−0.381557	+	0.924345i	$0.624612\pi$
$488$	−18.1816	−	8.62543i	−0.823040	−	0.390455i
$489$		−	24.4459i		−	1.10548i
$490$	−22.0185	−	2.27768i	−0.994692	−	0.102895i
$491$	−24.8485			−1.12140			−0.560699	−	0.828020i	$-0.689467\pi$
$491$	−24.8485			−1.12140			−0.560699	+	0.828020i	$0.689467\pi$
$492$	1.19990	−	1.33638i	0.0540959	−	0.0602486i
$493$	−5.34056	+	19.9312i	−0.240527	+	0.897658i
$494$	31.4354	−	33.1724i	1.41435	−	1.49250i
$495$	−2.24395	−	5.12837i	−0.100858	−	0.230503i
$496$	7.67455	+	3.39126i	0.344597	+	0.152272i
$497$	−7.94070	−	30.7908i	−0.356189	−	1.38116i
$498$	5.45874	+	2.95892i	0.244612	+	0.132592i
$499$	−5.26914	−	3.04214i	−0.235879	−	0.136185i	0.377402	−	0.926049i	$-0.376817\pi$
$499$	−5.26914	−	3.04214i	−0.235879	−	0.136185i	−0.613281	+	0.789865i	$0.710151\pi$
$500$	15.5264	+	16.0914i	0.694360	+	0.719628i
$501$	10.2585	−	5.92277i	0.458318	−	0.264610i
$502$	−6.65511	−	10.8431i	−0.297032	−	0.483953i
$503$	27.8070	+	27.8070i	1.23985	+	1.23985i	0.960061	+	0.279790i	$0.0902650\pi$
$503$	27.8070	+	27.8070i	1.23985	+	1.23985i	0.279790	+	0.960061i	$0.409735\pi$
$504$	7.34784	+	1.41749i	0.327299	+	0.0631398i
$505$	−1.44166	+	1.95771i	−0.0641529	+	0.0871169i
$506$	3.76192	−	15.7179i	0.167238	−	0.698746i
$507$	1.01896	−	3.80280i	0.0452535	−	0.168888i
$508$	−5.75774	−	17.6366i	−0.255458	−	0.782498i
$509$	16.5276	−	28.6266i	0.732571	−	1.26885i	−0.223210	−	0.974770i	$-0.571654\pi$
$509$	16.5276	−	28.6266i	0.732571	−	1.26885i	0.955781	−	0.294080i	$-0.0950131\pi$
$510$	−13.2889	+	6.24537i	−0.588442	+	0.276550i
$511$	−20.3068	−	0.191034i	−0.898321	−	0.00845085i
$512$	21.9686	−	5.42049i	0.970883	−	0.239554i
$513$	−2.03231	−	7.58470i	−0.0897288	−	0.334873i
$514$	1.91862	+	1.81816i	0.0846269	+	0.0801956i
$515$	−13.0763	+	10.4507i	−0.576211	+	0.460512i
$516$	−0.0170777	−	0.317376i	−0.000751802	−	0.0139717i
$517$	−11.8442	+	11.8442i	−0.520906	+	0.520906i
$518$	14.9205	−	26.9184i	0.655568	−	1.18273i
$519$	−20.5734			−0.903071
$520$	24.9243	+	7.50036i	1.09300	+	0.328913i
$521$	−18.5173	−	32.0729i	−0.811258	−	1.40514i	−0.911984	−	0.410227i	$-0.865450\pi$
$521$	−18.5173	−	32.0729i	−0.811258	−	1.40514i	0.100725	−	0.994914i	$-0.467884\pi$
$522$	−0.168902	−	6.28239i	−0.00739264	−	0.274973i
$523$	1.39885	+	5.22057i	0.0611673	+	0.228280i	0.989742	−	0.142866i	$-0.0456318\pi$
$523$	1.39885	+	5.22057i	0.0611673	+	0.228280i	−0.928575	+	0.371145i	$0.878965\pi$
$524$	8.41527	+	12.9188i	0.367623	+	0.564362i
$525$	−9.06830	+	9.63151i	−0.395773	+	0.420353i
$526$	32.2334	−	9.57247i	1.40544	−	0.417380i
$527$	−2.52084	−	9.40789i	−0.109809	−	0.409814i
$528$	6.28003	−	7.79966i	0.273303	−	0.339436i
$529$	−1.87116	+	1.08031i	−0.0813547	+	0.0469702i
$530$	2.42858	−	2.05028i	0.105491	−	0.0890586i
$531$	10.3565			0.449432
$532$	−28.0490	+	30.6542i	−1.21608	+	1.32903i
$533$	2.61326	+	2.61326i	0.113193	+	0.113193i
$534$	−1.10074	+	4.59908i	−0.0476338	+	0.199021i
$535$	−26.7781	+	21.4012i	−1.15772	+	0.925255i
$536$	6.18829	−	33.7840i	0.267294	−	1.45925i
$537$	5.28197	−	1.41530i	0.227934	−	0.0610747i
$538$	−14.5553	+	26.8522i	−0.627523	+	1.15768i
$539$	−15.0086	−	9.04591i	−0.646467	−	0.389635i
$540$	3.33844	−	2.97571i	0.143664	−	0.128054i
$541$	−5.14830	−	2.97237i	−0.221343	−	0.127792i	0.385229	−	0.922821i	$-0.374122\pi$
$541$	−5.14830	−	2.97237i	−0.221343	−	0.127792i	−0.606572	+	0.795029i	$0.707456\pi$
$542$	−0.837389	−	31.1471i	−0.0359689	−	1.33788i
$543$	−0.495976	+	1.85101i	−0.0212844	+	0.0794343i
$544$	−20.8942	−	15.9170i	−0.895831	−	0.682437i
$545$	30.2142	+	22.2497i	1.29423	+	0.953074i
$546$	−3.72499	+	14.9413i	−0.159415	+	0.639428i
$547$	9.36495	+	9.36495i	0.400416	+	0.400416i	0.878380	−	0.477963i	$-0.158625\pi$
$547$	9.36495	+	9.36495i	0.400416	+	0.400416i	−0.477963	+	0.878380i	$0.658625\pi$
$548$	7.13427	+	6.40570i	0.304761	+	0.273638i
$549$	−3.55742	−	6.16163i	−0.151827	−	0.262972i
$550$	5.70590	+	16.7570i	0.243300	+	0.714521i
$551$	30.2198	+	17.4474i	1.28741	+	0.743285i
$552$	12.8699	−	1.04002i	0.547778	−	0.0442663i
$553$	−5.05634	+	18.1845i	−0.215017	+	0.773284i
$554$	10.8576	+	36.5609i	0.461296	+	1.55332i
$555$	−7.37295	−	16.8503i	−0.312964	−	0.715256i
$556$	37.3446	+	18.9623i	1.58376	+	0.804182i
$557$	0.964283	+	0.258379i	0.0408580	+	0.0109479i	0.279190	−	0.960236i	$-0.409934\pi$
$557$	0.964283	+	0.258379i	0.0408580	+	0.0109479i	−0.238332	+	0.971184i	$0.576601\pi$
$558$	1.55174	+	2.52824i	0.0656904	+	0.107029i
$559$	0.654018			0.0276620
$560$	−22.7762	−	6.42219i	−0.962470	−	0.271387i
$561$	−11.6240			−0.490767
$562$	7.33249	+	11.9468i	0.309302	+	0.503945i
$563$	36.3446	+	9.73850i	1.53174	+	0.410429i	0.923587	−	0.383390i	$-0.125244\pi$
$563$	36.3446	+	9.73850i	1.53174	+	0.410429i	0.608154	+	0.793819i	$0.291910\pi$
$564$	−11.9318	−	6.05857i	−0.502419	−	0.255112i
$565$	4.21536	−	10.7741i	0.177342	−	0.453269i
$566$	6.13104	+	20.6451i	0.257707	+	0.867777i
$567$	1.85315	+	1.88834i	0.0778249	+	0.0793030i
$568$	−2.73814	−	33.8833i	−0.114890	−	1.42171i
$569$	2.34364	+	1.35310i	0.0982505	+	0.0567249i	0.548320	−	0.836268i	$-0.315268\pi$
$569$	2.34364	+	1.35310i	0.0982505	+	0.0567249i	−0.450070	+	0.892993i	$0.648601\pi$
$570$	4.38528	+	24.4407i	0.183679	+	1.02371i
$571$	3.58498	+	6.20936i	0.150027	+	0.259854i	0.931237	−	0.364414i	$-0.118731\pi$
$571$	3.58498	+	6.20936i	0.150027	+	0.259854i	−0.781210	+	0.624268i	$0.785397\pi$
$572$	15.3320	+	13.7663i	0.641064	+	0.575597i
$573$	1.59703	+	1.59703i	0.0667168	+	0.0667168i
$574$	−2.41705	−	2.33404i	−0.100886	−	0.0974208i
$575$	−10.6227	+	20.2025i	−0.442998	+	0.842504i
$576$	7.48059	+	2.83561i	0.311691	+	0.118151i
$577$	7.02881	−	26.2319i	0.292613	−	1.09205i	−0.650481	−	0.759522i	$-0.725433\pi$
$577$	7.02881	−	26.2319i	0.292613	−	1.09205i	0.943094	−	0.332525i	$-0.107901\pi$
$578$	0.173312	+	6.44643i	0.00720884	+	0.268136i
$579$	14.4477	+	8.34136i	0.600424	+	0.346655i
$580$	−1.13983	+	19.8411i	−0.0473287	+	0.823858i
$581$	5.90247	−	10.0048i	0.244876	−	0.415070i
$582$	−1.15951	+	2.13911i	−0.0480632	+	0.0886691i
$583$	2.43037	−	0.651217i	0.100656	−	0.0269706i
$584$	−21.3546	−	3.91157i	−0.883659	−	0.161862i
$585$	5.74523	+	7.18868i	0.237536	+	0.297215i
$586$	−3.86446	+	16.1463i	−0.159639	+	0.666998i
$587$	−24.6708	−	24.6708i	−1.01827	−	1.01827i	−0.999830	−	0.0184450i	$-0.994128\pi$
$587$	−24.6708	−	24.6708i	−1.01827	−	1.01827i	−0.0184450	−	0.999830i	$-0.505872\pi$
$588$	3.14882	−	13.6413i	0.129855	−	0.562558i
$589$	−16.4710			−0.678674
$590$	−32.6338	−	2.75635i	−1.34351	−	0.113477i
$591$	20.4911	−	11.8305i	0.842891	−	0.486643i
$592$	20.6343	−	25.6274i	0.848066	−	1.05328i
$593$	−4.88492	−	18.2308i	−0.200600	−	0.748648i	−0.990746	−	0.135730i	$-0.956662\pi$
$593$	−4.88492	−	18.2308i	−0.200600	−	0.748648i	0.790146	−	0.612918i	$-0.210005\pi$
$594$	3.39387	−	1.00789i	0.139252	−	0.0413542i
$595$	10.7744	+	25.2688i	0.441708	+	1.03592i
$596$	−3.61985	−	5.55707i	−0.148275	−	0.227626i
$597$	4.49654	+	16.7813i	0.184031	+	0.686813i
$598$	0.714049	+	26.5594i	0.0291996	+	1.08609i
$599$	20.8175	+	36.0569i	0.850579	+	1.47325i	0.880686	+	0.473700i	$0.157082\pi$
$599$	20.8175	+	36.0569i	0.850579	+	1.47325i	−0.0301067	+	0.999547i	$0.509585\pi$
$600$	−11.3116	+	8.48810i	−0.461794	+	0.346525i
$601$	−21.5895			−0.880654			−0.440327	−	0.897837i	$-0.645137\pi$
$601$	−21.5895			−0.880654			−0.440327	+	0.897837i	$0.645137\pi$
$602$	−0.594525	+	0.0103882i	−0.0242310	+	0.000423393i
$603$	8.58653	−	8.58653i	0.349670	−	0.349670i
$604$	−0.613889	−	11.4087i	−0.0249788	−	0.464213i
$605$	1.17380	−	10.5178i	0.0477219	−	0.427610i
$606$	−1.11612	−	1.05768i	−0.0453392	−	0.0429652i
$607$	1.52076	+	5.67556i	0.0617258	+	0.230364i	0.989897	−	0.141790i	$-0.0452859\pi$
$607$	1.52076	+	5.67556i	0.0617258	+	0.230364i	−0.928171	+	0.372154i	$0.878619\pi$
$608$	−35.1454	+	27.1635i	−1.42533	+	1.10163i
$609$	−11.7570	−	0.110603i	−0.476418	−	0.00448184i
$610$	9.56972	+	20.3624i	0.387467	+	0.824451i
$611$	13.7681	−	23.8470i	0.556997	−	0.964748i
$612$	−2.88204	−	8.82801i	−0.116499	−	0.356851i
$613$	−3.05963	+	11.4187i	−0.123577	+	0.461197i	−0.999785	−	0.0207368i	$-0.993399\pi$
$613$	−3.05963	+	11.4187i	−0.123577	+	0.461197i	0.876208	+	0.481934i	$0.160065\pi$
$614$	−2.52716	+	10.5589i	−0.101988	+	0.426121i
$615$	−1.98526	+	0.301379i	−0.0800535	+	0.0121528i
$616$	−14.1560	−	12.2705i	−0.570361	−	0.494392i
$617$	−4.22652	−	4.22652i	−0.170153	−	0.170153i	0.616893	−	0.787047i	$-0.288391\pi$
$617$	−4.22652	−	4.22652i	−0.170153	−	0.170153i	−0.787047	+	0.616893i	$0.788391\pi$
$618$	−5.53795	−	9.02296i	−0.222769	−	0.362957i
$619$	33.6158	−	19.4081i	1.35113	−	0.780078i	0.362726	−	0.931896i	$-0.381846\pi$
$619$	33.6158	−	19.4081i	1.35113	−	0.780078i	0.988408	+	0.151818i	$0.0485128\pi$
$620$	−4.21674	−	8.37964i	−0.169348	−	0.336534i
$621$	3.95342	+	2.28251i	0.158645	+	0.0915939i
$622$	14.9440	+	8.10041i	0.599199	+	0.324797i
$623$	8.52371	+	2.37008i	0.341495	+	0.0949553i
$624$	−6.65357	+	15.0573i	−0.266356	+	0.602773i
$625$	−1.97375	−	24.9220i	−0.0789501	−	0.996879i
$626$	17.6717	−	18.6482i	0.706305	−	0.745332i
$627$	−5.08773	+	18.9877i	−0.203184	+	0.758294i
$628$	−18.8283	+	20.9698i	−0.751332	+	0.836787i
$629$	−38.1932			−1.52286
$630$	−5.33679	−	6.44349i	−0.212623	−	0.256715i
$631$			12.3972i			0.493524i	0.969076	+	0.246762i	$0.0793666\pi$
$631$			12.3972i			0.493524i	−0.969076	+	0.246762i	$0.920633\pi$
$632$	−8.64849	+	18.2302i	−0.344018	+	0.725157i
$633$	−10.6068	−	2.84208i	−0.421582	−	0.112963i
$634$	−28.7504	+	30.3390i	−1.14182	+	1.20491i
$635$	−7.55766	+	19.3167i	−0.299917	+	0.766559i
$636$	1.09716	+	1.68431i	0.0435050	+	0.0667874i
$637$	27.6814	+	7.97829i	1.09678	+	0.316111i
$638$	−7.49753	+	13.8318i	−0.296830	+	0.547605i
$639$	6.00931	−	10.4084i	0.237725	−	0.411751i
$640$	−22.8171	−	10.9261i	−0.901925	−	0.431893i
$641$	19.7202	+	34.1565i	0.778903	+	1.34910i	0.932574	+	0.360978i	$0.117557\pi$
$641$	19.7202	+	34.1565i	0.778903	+	1.34910i	−0.153671	+	0.988122i	$0.549110\pi$
$642$	−11.3408	−	18.4775i	−0.447585	−	0.729248i
$643$	−27.8250	+	27.8250i	−1.09731	+	1.09731i	−0.102589	+	0.994724i	$0.532713\pi$
$643$	−27.8250	+	27.8250i	−1.09731	+	1.09731i	−0.994724	+	0.102589i	$0.967287\pi$
$644$	−1.07096	−	24.1320i	−0.0422016	−	0.950936i
$645$	−0.210712	+	0.286138i	−0.00829677	+	0.0112667i
$646$	50.1462	+	12.0020i	1.97297	+	0.472212i
$647$	−25.5194	−	6.83790i	−1.00327	−	0.268826i	−0.280456	−	0.959867i	$-0.590486\pi$
$647$	−25.5194	−	6.83790i	−1.00327	−	0.268826i	−0.722815	+	0.691041i	$0.757152\pi$
$648$	1.60692	+	2.32762i	0.0631258	+	0.0914375i
$649$	−22.4530	−	12.9633i	−0.881358	−	0.508852i
$650$	−16.1903	−	24.1810i	−0.635036	−	0.948457i
$651$	4.83211	−	2.72954i	0.189385	−	0.106979i
$652$	−47.8376	−	10.0984i	−1.87346	−	0.395482i
$653$	−3.12094	+	0.836253i	−0.122132	+	0.0327251i	−0.319367	−	0.947631i	$-0.603470\pi$
$653$	−3.12094	+	0.836253i	−0.122132	+	0.0327251i	0.197235	+	0.980356i	$0.436804\pi$
$654$	−16.3236	+	17.2256i	−0.638303	+	0.673572i
$655$	1.91189	−	17.1314i	0.0747038	−	0.669380i
$656$	−2.11946	−	2.90011i	−0.0827509	−	0.113230i
$657$	−5.42747	−	5.42747i	−0.211746	−	0.211746i
$658$	−12.1369	+	21.8965i	−0.473145	+	0.853613i
$659$			39.2336i			1.52832i	0.645025	+	0.764161i	$0.276847\pi$
$659$			39.2336i			1.52832i	−0.645025	+	0.764161i	$0.723153\pi$
$660$	−10.9625	+	2.27264i	−0.426716	+	0.0884626i
$661$	20.4849	−	11.8269i	0.796769	−	0.460015i	−0.0455709	−	0.998961i	$-0.514511\pi$
$661$	20.4849	−	11.8269i	0.796769	−	0.460015i	0.842340	+	0.538946i	$0.181177\pi$
$662$	−29.0157	+	0.780088i	−1.12773	+	0.0303190i
$663$	18.4580	−	4.94581i	0.716851	−	0.192080i
$664$	8.04519	−	9.45978i	0.312214	−	0.367110i
$665$	45.9919	−	6.53994i	1.78349	−	0.253608i
$666$	11.1512	−	3.31163i	0.432102	−	0.128323i
$667$	−19.5953	+	5.25056i	−0.758735	+	0.203302i
$668$	−7.35242	−	22.5213i	−0.284474	−	0.871375i
$669$	8.67111	+	15.0188i	0.335245	+	0.580661i
$670$	−29.3419	+	24.7714i	−1.13358	+	0.957001i
$671$			17.8114i			0.687601i
$672$	5.80916	−	13.7932i	0.224093	−	0.532086i
$673$	34.4348	−	34.4348i	1.32737	−	1.32737i	0.419704	−	0.907661i	$-0.362134\pi$
$673$	34.4348	−	34.4348i	1.32737	−	1.32737i	0.907661	−	0.419704i	$-0.137866\pi$
$674$	10.5913	−	44.2520i	0.407961	−	1.70452i
$675$	−4.99610	+	0.197529i	−0.192300	+	0.00760291i
$676$	−7.02068	−	3.56487i	−0.270026	−	0.137110i
$677$	4.30573	+	16.0692i	0.165483	+	0.617590i	0.997978	+	0.0635578i	$0.0202447\pi$
$677$	4.30573	+	16.0692i	0.165483	+	0.617590i	−0.832496	+	0.554032i	$0.813089\pi$
$678$	6.43284	+	3.48693i	0.247052	+	0.133915i
$679$	3.92059	+	2.31300i	0.150458	+	0.0887647i
$680$	6.73190	+	28.5846i	0.258157	+	1.09617i
$681$	14.2790	−	24.7320i	0.547174	−	0.947733i
$682$	−0.199584	−	7.42361i	−0.00764246	−	0.284265i
$683$	−26.6833	−	7.14976i	−1.02101	−	0.273578i	−0.290785	−	0.956788i	$-0.593917\pi$
$683$	−26.6833	−	7.14976i	−1.02101	−	0.273578i	−0.730222	+	0.683210i	$0.760583\pi$
$684$	−15.6818	+	0.843822i	−0.599610	+	0.0322643i
$685$	−1.60891	−	10.5983i	−0.0614734	−	0.404942i
$686$	−25.2900	−	6.81285i	−0.965577	−	0.260116i
$687$	5.77415	−	5.77415i	0.220297	−	0.220297i
$688$	−0.628120	−	0.0976861i	−0.0239469	−	0.00372425i
$689$	−3.58216	+	2.06816i	−0.136469	+	0.0787906i
$690$	−11.8500	−	8.24451i	−0.451121	−	0.313863i
$691$	11.5239	−	19.9599i	0.438389	−	0.759311i	−0.559177	−	0.829048i	$-0.688883\pi$
$691$	11.5239	−	19.9599i	0.438389	−	0.759311i	0.997565	+	0.0697372i	$0.0222161\pi$
$692$	−8.49865	+	40.2595i	−0.323070	+	1.53044i
$693$	−1.65401	−	6.41357i	−0.0628305	−	0.243631i
$694$	−31.2621	+	9.28403i	−1.18669	+	0.352417i
$695$	−18.7710	−	42.8997i	−0.712024	−	1.62728i
$696$	−12.3636	−	2.26467i	−0.468642	−	0.0858421i
$697$	−1.07920	+	4.02762i	−0.0408775	+	0.152557i
$698$	10.7192	+	17.4648i	0.405728	+	0.661051i
$699$			1.81592i			0.0686845i
$700$	15.1016	+	21.7242i	0.570788	+	0.821098i
$701$			19.9955i			0.755219i	0.925965	+	0.377610i	$0.123254\pi$
$701$			19.9955i			0.755219i	−0.925965	+	0.377610i	$0.876746\pi$
$702$	−4.96035	+	3.04447i	−0.187216	+	0.114906i
$703$	−16.7168	+	62.3878i	−0.630485	+	2.35300i
$704$	−12.6687	−	15.5112i	−0.477471	−	0.584600i
$705$	5.99744	+	13.7067i	0.225877	+	0.516224i
$706$	11.1474	+	37.5367i	0.419538	+	1.41271i
$707$	−2.05318	+	2.01491i	−0.0772178	+	0.0757785i
$708$	4.27815	−	20.2663i	0.160783	−	0.761654i
$709$	−9.81393	+	16.9982i	−0.368570	+	0.638381i	−0.989342	−	0.145609i	$-0.953486\pi$
$709$	−9.81393	+	16.9982i	−0.368570	+	0.638381i	0.620772	+	0.783991i	$0.286819\pi$
$710$	−21.7059	+	31.1982i	−0.814606	+	1.17085i
$711$	−6.17810	+	3.56693i	−0.231697	+	0.133770i
$712$	8.54511	+	4.05385i	0.320241	+	0.151924i
$713$	6.77098	−	6.77098i	0.253575	−	0.253575i
$714$	−16.7004	+	4.78910i	−0.624997	+	0.179227i
$715$	−3.45767	−	22.7766i	−0.129309	−	0.851795i
$716$	−0.587636	−	10.9208i	−0.0219610	−	0.408130i
$717$	7.18360	+	1.92484i	0.268277	+	0.0718845i
$718$	30.9938	−	0.833267i	1.15668	−	0.0310973i
$719$	−7.81531	+	13.5365i	−0.291462	+	0.504827i	−0.974156	−	0.225878i	$-0.927475\pi$
$719$	−7.81531	+	13.5365i	−0.291462	+	0.504827i	0.682694	+	0.730705i	$0.260808\pi$
$720$	−4.44401	−	7.76214i	−0.165618	−	0.289278i
$721$	−17.2452	+	9.74135i	−0.642243	+	0.362787i
$722$	28.7487	−	53.0369i	1.06992	−	1.97383i
$723$	4.23125	+	15.7912i	0.157362	+	0.587283i
$724$	3.41731	+	1.73519i	0.127003	+	0.0644880i
$725$	15.0787	−	16.3201i	0.560008	−	0.606113i
$726$	6.50950	+	1.55798i	0.241590	+	0.0578222i
$727$	0.213513	−	0.213513i	0.00791876	−	0.00791876i	−0.703136	−	0.711055i	$-0.748218\pi$
$727$	0.213513	−	0.213513i	0.00791876	−	0.00791876i	0.711055	+	0.703136i	$0.248218\pi$
$728$	27.6994	+	13.4614i	1.02661	+	0.498914i
$729$			1.00000i			0.0370370i
$730$	15.6578	+	18.5468i	0.579520	+	0.686447i
$731$	0.368949	+	0.639038i	0.0136461	+	0.0236357i
$732$	−13.5271	+	4.41611i	−0.499975	+	0.163224i
$733$	−38.9553	+	10.4380i	−1.43885	+	0.385537i	−0.892129	−	0.451781i	$-0.850789\pi$
$733$	−38.9553	+	10.4380i	−1.43885	+	0.385537i	−0.546716	+	0.837318i	$0.684122\pi$
$734$	6.72035	+	22.6295i	0.248053	+	0.835268i
$735$	−12.4089	+	9.54034i	−0.457711	+	0.351901i
$736$	3.28121	−	25.6143i	0.120947	−	0.944156i
$737$	−29.3636	+	7.86795i	−1.08162	+	0.289820i
$738$	−0.0341310	−	1.26952i	−0.00125638	−	0.0467316i
$739$	14.0619	−	8.11863i	0.517275	−	0.298649i	−0.218544	−	0.975827i	$-0.570131\pi$
$739$	14.0619	−	8.11863i	0.517275	−	0.298649i	0.735819	+	0.677178i	$0.236797\pi$
$740$	−36.0196	+	7.46724i	−1.32411	+	0.274501i
$741$		−	32.3156i		−	1.18714i
$742$	3.22345	−	1.93693i	0.118337	−	0.0711068i
$743$	−4.93484	−	4.93484i	−0.181042	−	0.181042i	0.610768	−	0.791810i	$-0.290861\pi$
$743$	−4.93484	−	4.93484i	−0.181042	−	0.181042i	−0.791810	+	0.610768i	$0.790861\pi$
$744$	5.58846	−	1.99217i	0.204883	−	0.0730365i
$745$	−0.822406	+	7.36913i	−0.0301306	+	0.269984i
$746$	18.3524	+	17.3914i	0.671929	+	0.636745i
$747$	4.24090	−	1.13635i	0.155167	−	0.0415768i
$748$	−4.80177	+	22.7468i	−0.175570	+	0.831705i
$749$	−35.3152	+	19.9486i	−1.29039	+	0.728908i
$750$	15.7956	+	0.707275i	0.576772	+	0.0258260i
$751$	7.57077	+	4.37098i	0.276261	+	0.159499i	0.631730	−	0.775189i	$-0.282345\pi$
$751$	7.57077	+	4.37098i	0.276261	+	0.159499i	−0.355468	+	0.934688i	$0.615679\pi$
$752$	−16.7848	+	20.8463i	−0.612077	+	0.760186i
$753$	−8.68969	−	2.32840i	−0.316670	−	0.0848514i
$754$	6.02031	−	25.1538i	0.219247	−	0.916047i
$755$	−7.57443	+	10.2858i	−0.275662	+	0.374337i
$756$	4.46077	−	2.84632i	0.162237	−	0.103520i
$757$	32.9245	−	32.9245i	1.19666	−	1.19666i	0.221502	−	0.975160i	$-0.428904\pi$
$757$	32.9245	−	32.9245i	1.19666	−	1.19666i	0.975160	−	0.221502i	$-0.0710958\pi$
$758$	7.45028	−	4.57270i	0.270606	−	0.166088i
$759$	−5.71407	−	9.89705i	−0.207407	−	0.359240i
$760$	49.6389	+	1.51476i	1.80059	+	0.0549460i
$761$	−25.3417	+	43.8932i	−0.918637	+	1.59113i	−0.117151	+	0.993114i	$0.537376\pi$
$761$	−25.3417	+	43.8932i	−0.918637	+	1.59113i	−0.801487	+	0.598013i	$0.795957\pi$
$762$	−11.5333	−	6.25166i	−0.417808	−	0.226474i
$763$	31.0970	+	31.6876i	1.12579	+	1.14717i
$764$	3.78490	−	2.46547i	0.136933	−	0.0891974i
$765$	−3.78299	+	9.66896i	−0.136774	+	0.349582i
$766$	−8.05172	−	7.63011i	−0.290920	−	0.275687i
$767$	41.1692	+	11.0313i	1.48653	+	0.398316i
$768$	8.63910	−	13.4672i	0.311737	−	0.485956i
$769$		−	31.8160i		−	1.14731i	−0.819095	−	0.573657i	$-0.805524\pi$
$769$		−	31.8160i		−	1.14731i	0.819095	−	0.573657i	$-0.194476\pi$
$770$	3.50491	+	20.6497i	0.126308	+	0.744165i
$771$	1.86907			0.0673128
$772$	22.2912	−	24.8265i	0.802277	−	0.893526i
$773$	0.272161	−	1.01572i	0.00978897	−	0.0365329i	−0.960859	−	0.277039i	$-0.910647\pi$
$773$	0.272161	−	1.01572i	0.00978897	−	0.0365329i	0.970648	+	0.240506i	$0.0773135\pi$
$774$	−0.163131	−	0.154589i	−0.00586363	−	0.00555660i
$775$	−2.31216	+	10.2300i	−0.0830554	+	0.367472i
$776$	3.70700	+	3.15266i	0.133073	+	0.113174i
$777$	−5.43458	−	21.0731i	−0.194964	−	0.755993i
$778$	10.2548	−	18.9185i	0.367652	−	0.678260i
$779$	6.10669	+	3.52570i	0.218795	+	0.126321i
$780$	16.4406	−	8.27313i	0.588669	−	0.296226i
$781$	−26.0566	+	15.0438i	−0.932379	+	0.538309i
$782$	−25.5482	+	15.6805i	−0.913603	+	0.560735i
$783$	−3.14233	−	3.14233i	−0.112298	−	0.112298i
$784$	−25.3936	−	11.7969i	−0.906913	−	0.421319i
$785$	31.1518	−	4.72910i	1.11186	−	0.168789i
$786$	10.6027	+	2.53765i	0.378185	+	0.0905148i
$787$	−2.29270	+	8.55647i	−0.0817259	+	0.305005i	−0.994674	−	0.103070i	$-0.967133\pi$
$787$	−2.29270	+	8.55647i	−0.0817259	+	0.305005i	0.912948	+	0.408076i	$0.133800\pi$
$788$	−14.6862	−	44.9855i	−0.523174	−	1.60254i
$789$	11.8882	−	20.5909i	0.423229	−	0.733055i
$790$	20.4169	−	9.59531i	0.726400	−	0.341386i
$791$	6.95574	−	11.7902i	0.247318	−	0.419210i
$792$	−0.570340	−	7.05772i	−0.0202661	−	0.250785i
$793$	−7.57842	−	28.2830i	−0.269118	−	1.00436i
$794$	24.9095	−	26.2858i	0.884004	−	0.932850i
$795$	0.249266	−	2.23354i	0.00884056	−	0.0792155i
$796$	34.6964	−	1.86697i	1.22978	−	0.0661731i
$797$	−15.8496	+	15.8496i	−0.561423	+	0.561423i	−0.929711	−	0.368289i	$-0.879944\pi$
$797$	−15.8496	+	15.8496i	−0.561423	+	0.561423i	0.368289	+	0.929711i	$0.379944\pi$
$798$	0.513292	+	29.3760i	0.0181703	+	1.03990i
$799$	31.0678			1.09910
$800$	11.9374	+	25.6417i	0.422052	+	0.906571i
$801$	1.67194	+	2.89589i	0.0590752	+	0.102321i
$802$	10.3317	−	0.277768i	0.364825	−	0.00980833i
$803$	4.97326	+	18.5605i	0.175503	+	0.654985i
$804$	−13.2557	−	20.3498i	−0.467494	−	0.717681i
$805$	−16.2182	+	21.5951i	−0.571615	+	0.761128i
$806$	3.47553	+	11.7032i	0.122420	+	0.412227i
$807$	5.58983	+	20.8615i	0.196771	+	0.734360i
$808$	−2.53080	+	1.74719i	−0.0890332	+	0.0614659i
$809$	−25.4348	+	14.6848i	−0.894241	+	0.516290i	−0.875327	−	0.483531i	$-0.839354\pi$
$809$	−25.4348	+	14.6848i	−0.894241	+	0.516290i	−0.0189137	+	0.999821i	$0.506021\pi$
$810$	0.266148	−	3.15106i	0.00935149	−	0.110717i
$811$	−32.8020			−1.15184			−0.575918	−	0.817508i	$-0.695355\pi$
$811$	−32.8020			−1.15184			−0.575918	+	0.817508i	$0.695355\pi$
$812$	−5.07313	+	22.9613i	−0.178032	+	0.805783i
$813$	−15.5792	−	15.5792i	−0.546385	−	0.546385i
$814$	−28.3213	−	6.77843i	−0.992662	−	0.237584i
$815$	34.1269	+	42.7010i	1.19541	+	1.49575i
$816$	−18.4658	+	1.99302i	−0.646434	+	0.0697698i
$817$	1.20534	−	0.322971i	0.0421696	−	0.0112993i
$818$	15.1991	+	8.23869i	0.531424	+	0.288059i
$819$	5.35529	+	9.48048i	0.187129	+	0.331275i
$820$	−0.230331	+	4.00941i	−0.00804351	+	0.140015i
$821$	−18.7866	−	10.8465i	−0.655657	−	0.378544i	0.134963	−	0.990851i	$-0.456908\pi$
$821$	−18.7866	−	10.8465i	−0.655657	−	0.378544i	−0.790620	+	0.612307i	$0.790242\pi$
$822$	6.77733	−	0.182208i	0.236386	−	0.00635525i
$823$	−0.302870	+	1.13033i	−0.0105574	+	0.0394007i	−0.971004	−	0.239065i	$-0.923159\pi$
$823$	−0.302870	+	1.13033i	−0.0105574	+	0.0394007i	0.960446	+	0.278466i	$0.0898258\pi$
$824$	−19.9445	+	7.10978i	−0.694798	+	0.247681i
$825$	11.0789	+	5.82541i	0.385718	+	0.202815i
$826$	−37.5994	−	9.37387i	−1.30825	−	0.326159i
$827$	−9.30990	−	9.30990i	−0.323737	−	0.323737i	0.526462	−	0.850199i	$-0.323518\pi$
$827$	−9.30990	−	9.30990i	−0.323737	−	0.323737i	−0.850199	+	0.526462i	$0.823518\pi$
$828$	6.09970	−	6.79347i	0.211979	−	0.236089i
$829$	−12.3629	−	21.4132i	−0.429382	−	0.743711i	0.567437	−	0.823417i	$-0.307935\pi$
$829$	−12.3629	−	21.4132i	−0.429382	−	0.743711i	−0.996818	+	0.0797060i	$0.974602\pi$
$830$	−13.6658	+	2.45199i	−0.474346	+	0.0851097i
$831$	23.3553	+	13.4842i	0.810186	+	0.467761i
$832$	26.7166	+	19.2402i	0.926233	+	0.667034i
$833$	7.82023	+	31.5481i	0.270955	+	1.09308i
$834$	28.3903	−	8.43116i	0.983075	−	0.291947i
$835$	−9.65085	+	24.6667i	−0.333981	+	0.853626i
$836$	35.0548	+	17.7996i	1.21239	+	0.615614i
$837$	2.02613	+	0.542901i	0.0700334	+	0.0187654i
$838$	21.8599	−	13.4168i	0.755137	−	0.463475i
$839$	−10.4974			−0.362411			−0.181206	−	0.983445i	$-0.558000\pi$
$839$	−10.4974			−0.362411			−0.181206	+	0.983445i	$0.558000\pi$
$840$	−14.8137	+	7.78169i	−0.511121	+	0.268494i
$841$	−9.25153			−0.319018
$842$	−42.3591	+	25.9984i	−1.45979	+	0.895964i
$843$	9.57415	+	2.56539i	0.329751	+	0.0883566i
$844$	−9.94315	+	19.5821i	−0.342257	+	0.674044i
$845$	3.52890	+	8.06503i	0.121398	+	0.277446i
$846$	−9.07085	+	2.69380i	−0.311862	+	0.0926149i
$847$	3.35460	−	12.0644i	0.115265	−	0.414538i
$848$	3.74921	−	1.45122i	0.128749	−	0.0498352i
$849$	13.1882	+	7.61421i	0.452618	+	0.261319i
$850$	14.4938	−	29.4606i	0.497133	−	1.01049i
$851$	−18.7747	−	32.5188i	−0.643590	−	1.11473i
$852$	−17.8856	−	16.0591i	−0.612751	−	0.550175i
$853$	15.0268	+	15.0268i	0.514506	+	0.514506i	0.915904	−	0.401398i	$-0.131475\pi$
$853$	15.0268	+	15.0268i	0.514506	+	0.514506i	−0.401398	+	0.915904i	$0.631475\pi$
$854$	7.33828	+	25.5899i	0.251111	+	0.875668i
$855$	14.1383	+	10.4114i	0.483520	+	0.356064i
$856$	−40.8429	+	14.5596i	−1.39598	+	0.497638i
$857$	13.1896	−	49.2244i	0.450549	−	1.68147i	−0.250304	−	0.968167i	$-0.580530\pi$
$857$	13.1896	−	49.2244i	0.450549	−	1.68147i	0.700853	−	0.713306i	$-0.252803\pi$
$858$	14.5649	−	0.391578i	0.497239	−	0.0133683i
$859$	−43.0456	−	24.8524i	−1.46870	−	0.847953i	−0.469314	−	0.883031i	$-0.655499\pi$
$859$	−43.0456	−	24.8524i	−1.46870	−	0.847953i	−0.999385	+	0.0350780i	$0.988832\pi$
$860$	0.472892	+	0.530537i	0.0161255	+	0.0180912i
$861$	−2.37580	−	0.0223501i	−0.0809671	−	0.000761689i
$862$	12.3410	+	6.68947i	0.420337	+	0.227844i
$863$	−15.2467	+	4.08534i	−0.519004	+	0.139067i	−0.508806	−	0.860881i	$-0.669913\pi$
$863$	−15.2467	+	4.08534i	−0.519004	+	0.139067i	−0.0101982	+	0.999948i	$0.503246\pi$
$864$	5.21866	−	2.18303i	0.177542	−	0.0742680i
$865$	35.9366	−	28.7207i	1.22188	−	0.976535i
$866$	−34.4064	−	8.23484i	−1.16918	−	0.279831i
$867$	3.22438	+	3.22438i	0.109506	+	0.109506i
$868$	−3.34527	−	10.5834i	−0.113546	−	0.359223i
$869$	17.8590			0.605825
$870$	9.06534	+	10.7380i	0.307344	+	0.364052i
$871$	43.2794	−	24.9873i	1.46646	−	0.846664i
$872$	26.9651	+	39.0589i	0.913155	+	1.32270i
$873$	0.445299	+	1.66188i	0.0150711	+	0.0562461i
$874$	14.4317	+	48.5958i	0.488158	+	1.64378i
$875$	2.39435	−	29.4833i	0.0809439	−	0.996719i
$876$	−12.8629	+	8.37884i	−0.434597	+	0.283095i
$877$	9.76865	+	36.4571i	0.329864	+	1.23107i	0.909331	+	0.416073i	$0.136594\pi$
$877$	9.76865	+	36.4571i	0.329864	+	1.23107i	−0.579467	+	0.814996i	$0.696739\pi$
$878$	−25.2286	+	0.678271i	−0.851424	+	0.0228905i
$879$	5.86981	+	10.1668i	0.197984	+	0.342918i
$880$	−0.0812249	+	22.3911i	−0.00273809	+	0.754803i
$881$	4.63113			0.156027			0.0780134	−	0.996952i	$-0.475142\pi$
$881$	4.63113			0.156027			0.0780134	+	0.996952i	$0.475142\pi$
$882$	−5.01872	−	8.53302i	−0.168989	−	0.287322i
$883$	−29.9909	+	29.9909i	−1.00927	+	1.00927i	−0.00931616	+	0.999957i	$0.502965\pi$
$883$	−29.9909	+	29.9909i	−1.00927	+	1.00927i	−0.999957	+	0.00931616i	$0.997035\pi$
$884$	−2.05351	−	38.1631i	−0.0690672	−	1.28356i
$885$	−18.0902	+	14.4578i	−0.608094	+	0.485993i
$886$	4.48956	−	4.73763i	0.150830	−	0.159164i
$887$	5.18814	+	19.3624i	0.174201	+	0.650126i	0.996686	+	0.0813404i	$0.0259201\pi$
$887$	5.18814	+	19.3624i	0.174201	+	0.650126i	−0.822486	+	0.568786i	$0.807413\pi$
$888$	−1.87397	−	23.1896i	−0.0628863	−	0.778192i
$889$	−12.4708	+	21.1384i	−0.418259	+	0.708959i
$890$	−4.49765	−	9.57010i	−0.150762	−	0.320790i
$891$	1.25171	−	2.16802i	0.0419338	−	0.0726315i
$892$	32.9719	−	10.7642i	1.10398	−	0.360411i
$893$	13.5981	−	50.7487i	0.455042	−	1.69824i
$894$	−4.56077	−	1.09158i	−0.152535	−	0.0365077i
$895$	−7.25052	+	9.84589i	−0.242358	+	0.329112i
$896$	−24.5919	−	17.0656i	−0.821559	−	0.570123i
$897$	13.2845	+	13.2845i	0.443556	+	0.443556i
$898$	−6.05875	+	3.71863i	−0.202183	+	0.124092i
$899$	−8.07275	+	4.66081i	−0.269241	+	0.155447i
$900$	−1.67730	+	9.85833i	−0.0559099	+	0.328611i
$901$	−4.04158	−	2.33341i	−0.134644	−	0.0777370i
$902$	−1.51507	+	2.79506i	−0.0504462	+	0.0930654i
$903$	−0.300091	+	0.294498i	−0.00998642	+	0.00980028i
$904$	9.48082	−	11.1478i	0.315327	−	0.370772i
$905$	−1.71769	−	3.92564i	−0.0570978	−	0.130493i
$906$	−5.86406	−	5.55700i	−0.194820	−	0.184619i
$907$	1.64803	−	6.15054i	0.0547220	−	0.204225i	−0.933152	−	0.359481i	$-0.882954\pi$
$907$	1.64803	−	6.15054i	0.0547220	−	0.204225i	0.987874	+	0.155256i	$0.0496203\pi$
$908$	−42.4989	−	38.1588i	−1.41038	−	1.26635i
$909$	−1.08729			−0.0360632
$910$	−14.3516	−	31.2988i	−0.475751	−	1.03755i
$911$			30.7362i			1.01833i	0.860668	+	0.509167i	$0.170047\pi$
$911$			30.7362i			1.01833i	−0.860668	+	0.509167i	$0.829953\pi$
$912$	−4.82675	+	31.0359i	−0.159830	+	1.02770i
$913$	−10.6167	−	2.84475i	−0.351363	−	0.0941474i
$914$	−34.4796	−	32.6742i	−1.14048	−	1.08077i
$915$	14.8156	+	5.79663i	0.489790	+	0.191631i
$916$	−8.91404	−	13.6845i	−0.294528	−	0.452149i
$917$	5.46397	−	19.6505i	0.180436	−	0.648917i
$918$	−5.77301	−	3.12927i	−0.190538	−	0.103281i
$919$	−3.29202	+	5.70195i	−0.108594	+	0.188090i	−0.915201	−	0.402998i	$-0.867968\pi$
$919$	−3.29202	+	5.70195i	−0.108594	+	0.188090i	0.806607	+	0.591088i	$0.201301\pi$
$920$	−21.0286	+	19.7832i	−0.693291	+	0.652232i
$921$	3.83856	+	6.64858i	0.126485	+	0.219078i
$922$	−0.472580	+	0.290052i	−0.0155636	+	0.00955235i
$923$	34.9749	−	34.9749i	1.15121	−	1.15121i
$924$	−13.2338	+	0.587303i	−0.435360	+	0.0193209i
$925$	36.4020	+	19.1406i	1.19689	+	0.629338i
$926$	4.08035	−	17.0483i	0.134088	−	0.560243i
$927$	−7.23099	−	1.93754i	−0.237497	−	0.0636371i
$928$	−9.53896	+	23.2585i	−0.313132	+	0.763499i
$929$	−7.49183	−	4.32541i	−0.245799	−	0.141912i	0.372040	−	0.928217i	$-0.378658\pi$
$929$	−7.49183	−	4.32541i	−0.245799	−	0.141912i	−0.617839	+	0.786305i	$0.711992\pi$
$930$	−6.23997	−	2.24996i	−0.204617	−	0.0737792i
$931$	54.9561	+	1.03408i	1.80111	+	0.0338905i
$932$	3.55353	+	0.750139i	0.116400	+	0.0245716i
$933$	11.6100	−	3.11089i	0.380094	−	0.101846i
$934$	−27.7257	−	26.2739i	−0.907212	−	0.859709i
$935$	20.3043	−	16.2273i	0.664022	−	0.530690i
$936$	3.90858	+	10.9644i	0.127756	+	0.358383i
$937$	−3.38898	−	3.38898i	−0.110713	−	0.110713i	0.649580	−	0.760293i	$-0.274945\pi$
$937$	−3.38898	−	3.38898i	−0.110713	−	0.110713i	−0.760293	+	0.649580i	$0.774945\pi$
$938$	−38.9455	+	23.4018i	−1.27162	+	0.764095i
$939$		−	18.1665i		−	0.592842i
$940$	29.2997	−	6.07414i	0.955652	−	0.198117i
$941$	10.1441	−	5.85669i	0.330688	−	0.190923i	−0.325459	−	0.945556i	$-0.605519\pi$
$941$	10.1441	−	5.85669i	0.330688	−	0.190923i	0.656146	+	0.754634i	$0.272185\pi$
$942$	0.535567	+	19.9207i	0.0174497	+	0.649051i
$943$	−3.95974	+	1.06101i	−0.128947	+	0.0345512i
$944$	−37.8913	−	16.7436i	−1.23326	−	0.544957i
$945$	−5.87315	−	0.711450i	−0.191053	−	0.0231435i
$946$	0.160171	+	0.539346i	0.00520762	+	0.0175356i
$947$	2.21772	−	0.594235i	0.0720661	−	0.0193101i	−0.222606	−	0.974909i	$-0.571456\pi$
$947$	2.21772	−	0.594235i	0.0720661	−	0.0193101i	0.294672	+	0.955598i	$0.404790\pi$
$948$	4.42792	+	13.5632i	0.143812	+	0.440513i
$949$	−15.7943	−	27.3565i	−0.512704	−	0.888030i
$950$	−41.7796	−	36.5700i	−1.35551	−	1.18649i
$951$			29.5553i			0.958398i
$952$	2.47289	+	34.6589i	0.0801467	+	1.12330i
$953$	29.5710	−	29.5710i	0.957898	−	0.957898i	−0.0412511	−	0.999149i	$-0.513134\pi$
$953$	29.5710	−	29.5710i	0.957898	−	0.957898i	0.999149	+	0.0412511i	$0.0131344\pi$
$954$	1.38234	+	0.330850i	0.0447550	+	0.0107117i
$955$	−5.01908	−	0.560137i	−0.162414	−	0.0181256i
$956$	6.73414	−	13.2623i	0.217798	−	0.428933i
$957$	2.87936	+	10.7459i	0.0930765	+	0.347366i
$958$	21.9127	−	40.4254i	0.707966	−	1.30609i
$959$	0.119316	−	12.6832i	0.00385292	−	0.409563i
$960$	−17.0253	+	5.48990i	−0.549489	+	0.177186i
$961$	−13.3000	+	23.0363i	−0.429033	+	0.743107i
$962$	47.8561	−	1.28661i	1.54294	−	0.0414820i
$963$	−14.8079	−	3.96775i	−0.477176	−	0.127859i
$964$	32.6494	−	1.75683i	1.05157	−	0.0565835i
$965$	−36.8811	+	5.59886i	−1.18725	+	0.180234i
$966$	−12.2871	−	11.8650i	−0.395330	−	0.381752i
$967$	2.12188	−	2.12188i	0.0682349	−	0.0682349i	−0.672166	−	0.740401i	$-0.734636\pi$
$967$	2.12188	−	2.12188i	0.0682349	−	0.0682349i	0.740401	+	0.672166i	$0.234636\pi$
$968$	5.73778	−	12.0947i	0.184419	−	0.388738i
$969$	31.5754	−	18.2301i	1.01435	−	0.585634i
$970$	−0.960858	−	5.35520i	−0.0308513	−	0.171945i
$971$	25.3451	−	43.8989i	0.813362	−	1.40878i	−0.0971368	−	0.995271i	$-0.530968\pi$
$971$	25.3451	−	43.8989i	0.813362	−	1.40878i	0.910498	−	0.413513i	$-0.135698\pi$
$972$	1.95687	+	0.413090i	0.0627668	+	0.0132499i
$973$	−13.8361	−	53.6506i	−0.443563	−	1.71996i
$974$	2.29791	+	7.73776i	0.0736298	+	0.247934i
$975$	−20.0710	−	4.53641i	−0.642786	−	0.145281i
$976$	3.05389	+	28.2950i	0.0977526	+	0.905701i
$977$	11.4699	−	42.8061i	0.366954	−	1.36949i	−0.497799	−	0.867292i	$-0.665858\pi$
$977$	11.4699	−	42.8061i	0.366954	−	1.36949i	0.864753	−	0.502197i	$-0.167475\pi$
$978$	−29.4646	+	18.0843i	−0.942175	+	0.578271i
$979$		−	8.37113i		−	0.267543i
$980$	13.5432	+	28.2238i	0.432623	+	0.901575i
$981$			16.7806i			0.535764i
$982$	18.3821	+	29.9499i	0.586596	+	0.955739i
$983$	3.12783	−	11.6732i	0.0997622	−	0.372318i	−0.897936	−	0.440126i	$-0.854934\pi$
$983$	3.12783	−	11.6732i	0.0997622	−	0.372318i	0.997698	+	0.0678081i	$0.0216006\pi$
$984$	−2.49838	−	0.457634i	−0.0796456	−	0.0145889i
$985$	−19.2772	+	49.2709i	−0.614224	+	1.56990i
$986$	27.9739	−	8.30750i	0.890870	−	0.264565i
$987$	4.42070	+	17.1417i	0.140712	+	0.545625i
$988$	−63.2375	−	13.3492i	−2.01185	−	0.424696i
$989$	−0.362731	+	0.628268i	−0.0115342	+	0.0199778i
$990$	−4.52122	+	6.49842i	−0.143694	+	0.206533i
$991$	−3.47494	+	2.00626i	−0.110385	+	0.0637309i	−0.554176	−	0.832399i	$-0.686967\pi$
$991$	−3.47494	+	2.00626i	−0.110385	+	0.0637309i	0.443791	+	0.896130i	$0.353633\pi$
$992$	−1.58989	−	11.7589i	−0.0504790	−	0.373344i
$993$	−14.5131	+	14.5131i	−0.460560	+	0.460560i
$994$	−31.2379	+	32.3489i	−0.990806	+	1.02605i
$995$	−31.2813	−	23.0356i	−0.991684	−	0.730276i
$996$	−0.471814	−	8.76833i	−0.0149500	−	0.277835i
$997$	24.2320	+	6.49294i	0.767435	+	0.205633i	0.621238	−	0.783622i	$-0.286630\pi$
$997$	24.2320	+	6.49294i	0.767435	+	0.205633i	0.146197	+	0.989256i	$0.453297\pi$
$998$	0.231247	+	8.60135i	0.00732001	+	0.272271i
$999$	4.11274	−	7.12348i	0.130121	−	0.225377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.667.32	yes	384
5.3	odd	4	inner	840.2.dj.a.163.16	yes	384
7.4	even	3	inner	840.2.dj.a.67.95	yes	384
8.3	odd	2	inner	840.2.dj.a.667.49	yes	384
35.18	odd	12	inner	840.2.dj.a.403.49	yes	384
40.3	even	4	inner	840.2.dj.a.163.95	yes	384
56.11	odd	6	inner	840.2.dj.a.67.16	✓	384
280.123	even	12	inner	840.2.dj.a.403.32	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.16	✓	384	56.11	odd	6	inner
840.2.dj.a.67.95	yes	384	7.4	even	3	inner
840.2.dj.a.163.16	yes	384	5.3	odd	4	inner
840.2.dj.a.163.95	yes	384	40.3	even	4	inner
840.2.dj.a.403.32	yes	384	280.123	even	12	inner
840.2.dj.a.403.49	yes	384	35.18	odd	12	inner
840.2.dj.a.667.32	yes	384	1.1	even	1	trivial
840.2.dj.a.667.49	yes	384	8.3	odd	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.739767 - 1.20530i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-0.905490 + 1.78328i) q^{4} +(2.04855 - 0.896354i) q^{5} +(0.402606 + 1.35569i) q^{6} +(2.56193 - 0.660700i) q^{7} +(2.81924 - 0.227825i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.59582 - 1.80602i) q^{10} +(-1.25171 - 2.16802i) q^{11} +(1.33618 - 1.48816i) q^{12} +(2.91006 + 2.91006i) q^{13} +(-2.69157 - 2.59912i) q^{14} +(-2.21074 + 0.335608i) q^{15} +(-2.36017 - 3.22949i) q^{16} +(-1.20177 + 4.48505i) q^{17} +(-0.0380074 - 1.41370i) q^{18} +(6.80025 + 3.92613i) q^{19} +(-0.256491 + 4.46477i) q^{20} +(-2.64563 - 0.0248885i) q^{21} +(-1.68714 + 3.11251i) q^{22} +(-4.40947 + 1.18151i) q^{23} +(-2.78214 - 0.509610i) q^{24} +(3.39310 - 3.67245i) q^{25} +(1.35473 - 5.66027i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.14159 + 5.16689i) q^{28} +4.44393 q^{29} +(2.03994 + 2.41633i) q^{30} +(-1.81658 + 1.04880i) q^{31} +(-2.14652 + 5.23378i) q^{32} +(0.647932 + 2.41811i) q^{33} +(6.29486 - 1.86941i) q^{34} +(4.65601 - 3.64987i) q^{35} +(-1.67582 + 1.09162i) q^{36} +(2.12891 + 7.94521i) q^{37} +(-0.298444 - 11.1008i) q^{38} +(-2.05773 - 3.56409i) q^{39} +(5.57113 - 2.99374i) q^{40} +0.898009 q^{41} +(1.92715 + 3.20719i) q^{42} +(0.112372 - 0.112372i) q^{43} +(4.99960 - 0.269023i) q^{44} +(2.22227 + 0.248009i) q^{45} +(4.68605 + 4.44068i) q^{46} +(-1.73174 - 6.46294i) q^{47} +(1.44390 + 3.73030i) q^{48} +(6.12695 - 3.38533i) q^{49} +(-6.93650 - 1.37294i) q^{50} +(2.32164 - 4.02119i) q^{51} +(-7.82449 + 2.55442i) q^{52} +(-0.260131 + 0.970823i) q^{53} +(-0.329181 + 1.37537i) q^{54} +(-4.50750 - 3.31932i) q^{55} +(7.07216 - 2.44634i) q^{56} +(-5.55238 - 5.55238i) q^{57} +(-3.28747 - 5.35626i) q^{58} +(8.96896 - 5.17823i) q^{59} +(1.40332 - 4.24626i) q^{60} +(-6.16163 - 3.55742i) q^{61} +(2.60797 + 1.41365i) q^{62} +(2.54904 + 0.708781i) q^{63} +(7.89619 - 1.28458i) q^{64} +(8.56985 + 3.35296i) q^{65} +(2.43523 - 2.56979i) q^{66} +(3.14289 - 11.7294i) q^{67} +(-6.90992 - 6.20426i) q^{68} +4.56502 q^{69} +(-7.84355 - 2.91183i) q^{70} -12.0186i q^{71} +(2.55544 + 1.21232i) q^{72} +(-7.41406 - 1.98659i) q^{73} +(8.00145 - 8.44358i) q^{74} +(-4.22798 + 2.66911i) q^{75} +(-13.1589 + 8.57168i) q^{76} +(-4.63920 - 4.72731i) q^{77} +(-2.77355 + 5.11677i) q^{78} +(-3.56693 + 6.17810i) q^{79} +(-7.72969 - 4.50021i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.664317 - 1.08237i) q^{82} +(3.10456 - 3.10456i) q^{83} +(2.43998 - 4.69537i) q^{84} +(1.55832 + 10.2651i) q^{85} +(-0.218571 - 0.0523127i) q^{86} +(-4.29250 - 1.15017i) q^{87} +(-4.02279 - 5.82700i) q^{88} +(2.89589 + 1.67194i) q^{89} +(-1.34504 - 2.86197i) q^{90} +(9.37806 + 5.53270i) q^{91} +(1.88576 - 8.93316i) q^{92} +(2.02613 - 0.542901i) q^{93} +(-6.50869 + 6.86833i) q^{94} +(17.4498 + 1.94743i) q^{95} +(3.42798 - 4.49989i) q^{96} +(1.21658 + 1.21658i) q^{97} +(-8.61285 - 4.88045i) q^{98} -2.50342i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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