LMFDB - Embedded newform 840.2.dj.a.67.16

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			67.16
Character	$\chi$	$=$	840.67
Dual form			840.2.dj.a.163.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20530 - 0.739767i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.905490 + 1.78328i) q^{4} +(0.248009 - 2.22227i) q^{5} +(0.402606 - 1.35569i) q^{6} +(-0.660700 + 2.56193i) q^{7} +(0.227825 - 2.81924i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.94289 + 2.49503i) q^{10} +(-1.25171 + 2.16802i) q^{11} +(-1.48816 + 1.33618i) 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} +(4.48505 - 1.20177i) q^{17} +(1.41370 + 0.0380074i) q^{18} +(-6.80025 + 3.92613i) q^{19} +(4.18750 - 1.56998i) q^{20} +(-2.64563 + 0.0248885i) q^{21} +(3.11251 - 1.68714i) q^{22} +(-1.18151 + 4.40947i) q^{23} +(2.78214 - 0.509610i) q^{24} +(-4.87698 - 1.10229i) q^{25} +(1.35473 + 5.66027i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-5.16689 + 1.14159i) q^{28} -4.44393 q^{29} +(-2.91287 - 1.23092i) q^{30} +(-1.81658 - 1.04880i) q^{31} +(5.23378 - 2.14652i) q^{32} +(-2.41811 - 0.647932i) q^{33} +(-6.29486 - 1.86941i) q^{34} +(5.52944 + 2.10364i) q^{35} +(-1.67582 - 1.09162i) q^{36} +(7.94521 + 2.12891i) q^{37} +(11.1008 + 0.298444i) q^{38} +(2.05773 - 3.56409i) q^{39} +(-6.20861 - 1.20548i) q^{40} +0.898009 q^{41} +(3.20719 + 1.92715i) q^{42} +(0.112372 - 0.112372i) q^{43} +(-4.99960 - 0.269023i) q^{44} +(0.896354 + 2.04855i) q^{45} +(4.68605 - 4.44068i) q^{46} +(-6.46294 - 1.73174i) q^{47} +(-3.73030 - 1.44390i) q^{48} +(-6.12695 - 3.38533i) q^{49} +(5.06279 + 4.93641i) q^{50} +(2.32164 + 4.02119i) q^{51} +(2.55442 - 7.82449i) q^{52} +(-0.970823 + 0.260131i) 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} +(5.35626 + 3.28747i) q^{58} +(-8.96896 - 5.17823i) q^{59} +(2.60029 + 3.63848i) q^{60} +(-6.16163 + 3.55742i) q^{61} +(1.41365 + 2.60797i) q^{62} +(-0.708781 - 2.54904i) q^{63} +(-7.89619 - 1.28458i) q^{64} +(-7.18868 + 5.74523i) q^{65} +(2.43523 + 2.56979i) q^{66} +(-11.7294 + 3.14289i) q^{67} +(6.20426 + 6.90992i) q^{68} -4.56502 q^{69} +(-5.10843 - 6.62601i) q^{70} +12.0186i q^{71} +(1.21232 + 2.55544i) q^{72} +(1.98659 + 7.41406i) q^{73} +(-8.00145 - 8.44358i) q^{74} +(-0.197529 - 4.99610i) q^{75} +(-13.1589 - 8.57168i) q^{76} +(-4.72731 - 4.63920i) q^{77} +(-5.11677 + 2.77355i) q^{78} +(3.56693 + 6.17810i) q^{79} +(6.59145 + 6.04589i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.08237 - 0.664317i) 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} +(-1.15017 - 4.29250i) q^{87} +(5.82700 + 4.02279i) q^{88} +(-2.89589 + 1.67194i) q^{89} +(0.435074 - 3.13221i) q^{90} +(9.37806 - 5.53270i) q^{91} +(-8.93316 + 1.88576i) q^{92} +(0.542901 - 2.02613i) q^{93} +(6.50869 + 6.86833i) q^{94} +(7.03840 + 16.0857i) q^{95} +(3.42798 + 4.49989i) q^{96} +(1.21658 + 1.21658i) q^{97} +(4.88045 + 8.61285i) 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 $

$2$	−1.20530	−	0.739767i	−0.852275	−	0.523094i
$2$	−1.20530	−	0.739767i	−0.852275	−	0.523094i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.905490	+	1.78328i	0.452745	+	0.891640i
$5$	0.248009	−	2.22227i	0.110913	−	0.993830i
$5$	0.248009	−	2.22227i	0.110913	−	0.993830i
$6$	0.402606	−	1.35569i	0.164363	−	0.553460i
$7$	−0.660700	+	2.56193i	−0.249721	+	0.968318i
$7$	−0.660700	+	2.56193i	−0.249721	+	0.968318i
$8$	0.227825	−	2.81924i	0.0805482	−	0.996751i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−1.94289	+	2.49503i	−0.614395	+	0.788999i
$11$	−1.25171	+	2.16802i	−0.377404	+	0.653683i	−0.990684	−	0.136183i	$-0.956517\pi$
$11$	−1.25171	+	2.16802i	−0.377404	+	0.653683i	0.613280	+	0.789866i	$0.289850\pi$
$12$	−1.48816	+	1.33618i	−0.429594	+	0.385723i
$13$	−2.91006	−	2.91006i	−0.807107	−	0.807107i	0.177088	−	0.984195i	$-0.443332\pi$
$13$	−2.91006	−	2.91006i	−0.807107	−	0.807107i	−0.984195	+	0.177088i	$0.943332\pi$
$14$	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
$17$	4.48505	−	1.20177i	1.08779	−	0.291471i	0.330004	−	0.943980i	$-0.392950\pi$
$17$	4.48505	−	1.20177i	1.08779	−	0.291471i	0.757782	+	0.652508i	$0.226283\pi$
$18$	1.41370	+	0.0380074i	0.333213	+	0.00895843i
$19$	−6.80025	+	3.92613i	−1.56009	+	0.900716i	−0.562838	+	0.826567i	$0.690291\pi$
$19$	−6.80025	+	3.92613i	−1.56009	+	0.900716i	−0.997247	+	0.0741484i	$0.976376\pi$
$20$	4.18750	−	1.56998i	0.936354	−	0.351057i
$21$	−2.64563	+	0.0248885i	−0.577325	+	0.00543112i
$22$	3.11251	−	1.68714i	0.663590	−	0.359700i
$23$	−1.18151	+	4.40947i	−0.246363	+	0.919437i	0.726331	+	0.687345i	$0.241224\pi$
$23$	−1.18151	+	4.40947i	−0.246363	+	0.919437i	−0.972694	+	0.232093i	$0.925443\pi$
$24$	2.78214	−	0.509610i	0.567902	−	0.104024i
$25$	−4.87698	−	1.10229i	−0.975397	−	0.220457i
$26$	1.35473	+	5.66027i	0.265684	+	1.11007i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−5.16689	+	1.14159i	−0.976451	+	0.215740i
$29$	−4.44393			−0.825216			−0.412608	−	0.910909i	$-0.635382\pi$
$29$	−4.44393			−0.825216			−0.412608	+	0.910909i	$0.635382\pi$
$30$	−2.91287	−	1.23092i	−0.531815	−	0.224735i
$31$	−1.81658	−	1.04880i	−0.326268	−	0.188371i	0.327915	−	0.944707i	$-0.393654\pi$
$31$	−1.81658	−	1.04880i	−0.326268	−	0.188371i	−0.654183	+	0.756336i	$0.726987\pi$
$32$	5.23378	−	2.14652i	0.925211	−	0.379454i
$33$	−2.41811	−	0.647932i	−0.420940	−	0.112790i
$34$	−6.29486	−	1.86941i	−1.07956	−	0.320601i
$35$	5.52944	+	2.10364i	0.934646	+	0.355579i
$36$	−1.67582	−	1.09162i	−0.279303	−	0.181937i
$37$	7.94521	+	2.12891i	1.30618	+	0.349991i	0.843785	−	0.536681i	$-0.180322\pi$
$37$	7.94521	+	2.12891i	1.30618	+	0.349991i	0.462399	+	0.886672i	$0.346989\pi$
$38$	11.1008	+	0.298444i	1.80078	+	0.0484140i
$39$	2.05773	−	3.56409i	0.329500	−	0.570711i
$40$	−6.20861	−	1.20548i	−0.981667	−	0.190604i
$41$	0.898009			0.140245			0.0701227	−	0.997538i	$-0.477661\pi$
$41$	0.898009			0.140245			0.0701227	+	0.997538i	$0.477661\pi$
$42$	3.20719	+	1.92715i	0.494880	+	0.297366i
$43$	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
$45$	0.896354	+	2.04855i	0.133621	+	0.305380i
$46$	4.68605	−	4.44068i	0.690921	−	0.654743i
$47$	−6.46294	−	1.73174i	−0.942716	−	0.252600i	−0.245448	−	0.969410i	$-0.578935\pi$
$47$	−6.46294	−	1.73174i	−0.942716	−	0.252600i	−0.697269	+	0.716810i	$0.745602\pi$
$48$	−3.73030	−	1.44390i	−0.538423	−	0.208409i
$49$	−6.12695	−	3.38533i	−0.875279	−	0.483619i
$50$	5.06279	+	4.93641i	0.715986	+	0.698114i
$51$	2.32164	+	4.02119i	0.325094	+	0.563079i
$52$	2.55442	−	7.82449i	0.354235	−	1.08506i
$53$	−0.970823	+	0.260131i	−0.133353	+	0.0357318i	−0.324878	−	0.945756i	$-0.605323\pi$
$53$	−0.970823	+	0.260131i	−0.133353	+	0.0357318i	0.191525	+	0.981488i	$0.438657\pi$
$54$	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
$58$	5.35626	+	3.28747i	0.703311	+	0.431666i
$59$	−8.96896	−	5.17823i	−1.16766	−	0.674148i	−0.214531	−	0.976717i	$-0.568822\pi$
$59$	−8.96896	−	5.17823i	−1.16766	−	0.674148i	−0.953127	+	0.302569i	$0.902156\pi$
$60$	2.60029	+	3.63848i	0.335695	+	0.469725i
$61$	−6.16163	+	3.55742i	−0.788916	+	0.455481i	−0.839581	−	0.543235i	$-0.817199\pi$
$61$	−6.16163	+	3.55742i	−0.788916	+	0.455481i	0.0506651	+	0.998716i	$0.483866\pi$
$62$	1.41365	+	2.60797i	0.179534	+	0.331212i
$63$	−0.708781	−	2.54904i	−0.0892980	−	0.321149i
$64$	−7.89619	−	1.28458i	−0.987024	−	0.160573i
$65$	−7.18868	+	5.74523i	−0.891645	+	0.712608i
$66$	2.43523	+	2.56979i	0.299756	+	0.316319i
$67$	−11.7294	+	3.14289i	−1.43298	+	0.383965i	−0.890068	−	0.455828i	$-0.849343\pi$
$67$	−11.7294	+	3.14289i	−1.43298	+	0.383965i	−0.542908	+	0.839792i	$0.682677\pi$
$68$	6.20426	+	6.90992i	0.752377	+	0.837951i
$69$	−4.56502			−0.549563
$70$	−5.10843	−	6.62601i	−0.610574	−	0.791959i
$71$			12.0186i			1.42635i	0.700987	+	0.713174i	$0.252743\pi$
$71$			12.0186i			1.42635i	−0.700987	+	0.713174i	$0.747257\pi$
$72$	1.21232	+	2.55544i	0.142873	+	0.301162i
$73$	1.98659	+	7.41406i	0.232513	+	0.867750i	0.979254	+	0.202636i	$0.0649507\pi$
$73$	1.98659	+	7.41406i	0.232513	+	0.867750i	−0.746741	+	0.665115i	$0.768383\pi$
$74$	−8.00145	−	8.44358i	−0.930150	−	0.981546i
$75$	−0.197529	−	4.99610i	−0.0228087	−	0.576900i
$76$	−13.1589	−	8.57168i	−1.50944	−	0.983240i
$77$	−4.72731	−	4.63920i	−0.538727	−	0.528686i
$78$	−5.11677	+	2.77355i	−0.579360	+	0.314043i
$79$	3.56693	+	6.17810i	0.401311	+	0.695091i	0.993884	−	0.110426i	$-0.0352214\pi$
$79$	3.56693	+	6.17810i	0.401311	+	0.695091i	−0.592574	+	0.805516i	$0.701888\pi$
$80$	6.59145	+	6.04589i	0.736947	+	0.675951i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−1.08237	−	0.664317i	−0.119528	−	0.0733615i
$83$	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
$87$	−1.15017	−	4.29250i	−0.123311	−	0.460205i
$88$	5.82700	+	4.02279i	0.621160	+	0.428831i
$89$	−2.89589	+	1.67194i	−0.306964	+	0.177226i	−0.645567	−	0.763704i	$-0.723379\pi$
$89$	−2.89589	+	1.67194i	−0.306964	+	0.177226i	0.338603	+	0.940929i	$0.390046\pi$
$90$	0.435074	−	3.13221i	0.0458608	−	0.330163i
$91$	9.37806	−	5.53270i	0.983087	−	0.579984i
$92$	−8.93316	+	1.88576i	−0.931347	+	0.196604i
$93$	0.542901	−	2.02613i	0.0562962	−	0.210100i
$94$	6.50869	+	6.86833i	0.671320	+	0.708414i
$95$	7.03840	+	16.0857i	0.722125	+	1.65036i
$96$	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	$0.722162\pi$
$98$	4.88045	+	8.61285i	0.493000	+	0.870029i
$99$		−	2.50342i		−	0.251603i
$100$	−2.45038	−	9.69514i	−0.245038	−	0.969514i
$101$	−0.941621	−	0.543645i	−0.0936948	−	0.0540947i	0.452420	−	0.891805i	$-0.350561\pi$
$101$	−0.941621	−	0.543645i	−0.0936948	−	0.0540947i	−0.546115	+	0.837710i	$0.683894\pi$
$102$	0.176479	−	6.56420i	0.0174740	−	0.649953i
$103$	−1.93754	+	7.23099i	−0.190911	+	0.712491i	0.802376	+	0.596819i	$0.203569\pi$
$103$	−1.93754	+	7.23099i	−0.190911	+	0.712491i	−0.993287	+	0.115672i	$0.963098\pi$
$104$	−8.86715	+	7.54118i	−0.869495	+	0.739473i
$105$	−0.600832	+	5.88549i	−0.0586352	+	0.574365i
$106$	1.36257	+	0.404647i	0.132344	+	0.0393028i
$107$	3.96775	−	14.8079i	0.383577	−	1.43153i	−0.456821	−	0.889559i	$-0.651012\pi$
$107$	3.96775	−	14.8079i	0.383577	−	1.43153i	0.840398	−	0.541970i	$-0.182321\pi$
$108$	0.620691	−	1.90125i	0.0597260	−	0.182948i
$109$	−8.39032	+	14.5325i	−0.803646	+	1.39196i	0.113555	+	0.993532i	$0.463776\pi$
$109$	−8.39032	+	14.5325i	−0.803646	+	1.39196i	−0.917201	+	0.398425i	$0.869557\pi$
$110$	−2.97736	−	7.33527i	−0.283880	−	0.699391i
$111$			8.22549i			0.780729i
$112$	−6.71434	−	8.18032i	−0.634446	−	0.772967i
$113$	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
$115$	9.50601	+	3.71923i	0.886440	+	0.346820i
$116$	−4.02393	−	7.92476i	−0.373613	−	0.735796i
$117$	3.97522	+	1.06516i	0.367509	+	0.0984738i
$118$	6.97959	+	12.8762i	0.642523	+	1.18535i
$119$	0.115564	+	12.2844i	0.0105937	+	1.12611i
$120$	−0.442498	−	6.30906i	−0.0403943	−	0.575935i
$121$	2.36645	+	4.09882i	0.215132	+	0.372620i
$122$	10.0583	+	0.270416i	0.910632	+	0.0244823i
$123$	0.232422	+	0.867410i	0.0209568	+	0.0782117i
$124$	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	−0.353417	−	0.935466i	$-0.614980\pi$
$127$	6.55936	−	6.55936i	0.582049	−	0.582049i	0.935466	+	0.353417i	$0.114980\pi$
$128$	8.56698	+	7.38965i	0.757221	+	0.653159i
$129$	0.137627	+	0.0794589i	0.0121174	+	0.00699596i
$130$	12.9146	−	1.60678i	1.13269	−	0.140924i
$131$	3.85449	+	6.67616i	0.336768	+	0.583299i	0.983823	−	0.179144i	$-0.0573329\pi$
$131$	3.85449	+	6.67616i	0.336768	+	0.583299i	−0.647055	+	0.762443i	$0.724000\pi$
$132$	−1.03414	−	4.89887i	−0.0900099	−	0.426392i
$133$	−5.56553	−	20.0158i	−0.482593	−	1.73559i
$134$	16.4625	+	4.88891i	1.42214	+	0.422338i
$135$	−1.74675	+	1.39601i	−0.150336	+	0.120150i
$136$	−2.36626	−	12.9182i	−0.202905	−	1.10773i
$137$	−4.63067	+	1.24079i	−0.395625	+	0.106007i	−0.451146	−	0.892450i	$-0.648985\pi$
$137$	−4.63067	+	1.24079i	−0.395625	+	0.106007i	0.0555210	+	0.998458i	$0.482318\pi$
$138$	5.50221	+	3.37705i	0.468379	+	0.287473i
$139$		−	20.9415i		−	1.77623i	−0.459617	−	0.888117i	$-0.652013\pi$
$139$		−	20.9415i		−	1.77623i	0.459617	−	0.888117i	$-0.347987\pi$
$140$	1.25548	+	11.7654i	0.106108	+	0.994355i
$141$		−	6.69093i		−	0.563478i
$142$	8.89097	−	14.4860i	0.746114	−	1.21564i
$143$	9.95163	−	2.66653i	0.832197	−	0.222987i
$144$	0.429228	−	3.97690i	0.0357690	−	0.331409i
$145$	−1.10213	+	9.87561i	−0.0915272	+	0.820125i
$146$	3.09024	−	10.4058i	0.255750	−	0.861188i
$147$	1.68421	−	6.79437i	0.138911	−	0.560390i
$148$	3.39786	+	16.0962i	0.279303	+	1.32310i
$149$	1.65802	+	2.87177i	0.135830	+	0.235265i	0.925914	−	0.377734i	$-0.123297\pi$
$149$	1.65802	+	2.87177i	0.135830	+	0.235265i	−0.790084	+	0.612998i	$0.789963\pi$
$150$	−3.45786	+	6.16792i	−0.282333	+	0.503608i
$151$	−4.94725	−	2.85630i	−0.402602	−	0.232442i	0.285004	−	0.958526i	$-0.408005\pi$
$151$	−4.94725	−	2.85630i	−0.402602	−	0.232442i	−0.687606	+	0.726084i	$0.741338\pi$
$152$	9.51942	+	20.0660i	0.772127	+	1.62757i
$153$	−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
$157$	3.64705	+	13.6110i	0.291067	+	1.08628i	0.944291	+	0.329111i	$0.106749\pi$
$157$	3.64705	+	13.6110i	0.291067	+	1.08628i	−0.653225	+	0.757164i	$0.726584\pi$
$158$	0.271139	−	10.0852i	0.0215707	−	0.802331i
$159$	−0.502535	−	0.870416i	−0.0398536	−	0.0690285i
$160$	−3.47212	−	12.1632i	−0.274495	−	0.961589i
$161$	−10.5161	−	5.94029i	−0.828786	−	0.468160i
$162$	−1.24331	+	0.673936i	−0.0976834	+	0.0529494i
$163$	−23.6129	−	6.32707i	−1.84951	−	0.495574i	−0.849996	−	0.526789i	$-0.823396\pi$
$163$	−23.6129	−	6.32707i	−1.84951	−	0.495574i	−0.999513	+	0.0312150i	$0.990062\pi$
$164$	0.813138	+	1.60140i	0.0634954	+	0.125048i
$165$	−2.03959	+	5.21301i	−0.158782	+	0.405833i
$166$	−6.03857	+	1.44527i	−0.468684	+	0.112175i
$167$	8.37606	−	8.37606i	0.648159	−	0.648159i	−0.304389	−	0.952548i	$-0.598452\pi$
$167$	8.37606	−	8.37606i	0.648159	−	0.648159i	0.952548	+	0.304389i	$0.0984522\pi$
$168$	−0.532574	+	7.46434i	−0.0410890	+	0.575886i
$169$			3.93695i			0.302842i
$170$	−5.71551	+	13.5253i	−0.438360	+	1.03734i
$171$	3.92613	−	6.80025i	0.300239	−	0.520028i
$172$	0.302142	+	0.0986388i	0.0230381	+	0.00752114i
$173$	5.32478	−	19.8724i	0.404836	−	1.51087i	−0.399523	−	0.916723i	$-0.630824\pi$
$173$	5.32478	−	19.8724i	0.404836	−	1.51087i	0.804358	−	0.594144i	$-0.202509\pi$
$174$	−1.78915	+	6.02461i	−0.135635	+	0.456724i
$175$	6.04620	−	11.7662i	0.457050	−	0.889441i
$176$	−4.04735	−	9.15928i	−0.305080	−	0.690407i
$177$	2.68045	−	10.0036i	0.201475	−	0.751914i
$178$	4.72726	+	0.127092i	0.354323	+	0.00952597i
$179$	4.73569	+	2.73415i	0.353962	+	0.204360i	0.666429	−	0.745569i	$-0.267822\pi$
$179$	4.73569	+	2.73415i	0.353962	+	0.204360i	−0.312467	+	0.949929i	$0.601155\pi$
$180$	−2.84150	+	3.45339i	−0.211793	+	0.257401i
$181$			1.91630i			0.142438i	0.997461	+	0.0712189i	$0.0226889\pi$
$181$			1.91630i			0.142438i	−0.997461	+	0.0712189i	$0.977311\pi$
$182$	−15.3963	−	0.269022i	−1.14125	−	0.0199412i
$183$	−5.03095	−	5.03095i	−0.371898	−	0.371898i
$184$	12.1622	+	4.33555i	0.896606	+	0.319621i
$185$	6.70150	−	17.1284i	0.492704	−	1.25931i
$186$	−2.15322	+	2.04048i	−0.157882	+	0.149615i
$187$	−3.00852	+	11.2280i	−0.220005	+	0.821070i
$188$	−2.76395	−	13.0933i	−0.201582	−	0.954927i
$189$	2.27874	−	1.34437i	0.165754	−	0.0977886i
$190$	3.41631	−	24.5949i	0.247845	−	1.78430i
$191$	−1.95595	+	1.12927i	−0.141528	+	0.0817110i	−0.569092	−	0.822274i	$-0.692705\pi$
$191$	−1.95595	+	1.12927i	−0.141528	+	0.0817110i	0.427564	+	0.903985i	$0.359372\pi$
$192$	−0.802872	−	7.95961i	−0.0579423	−	0.574435i
$193$	4.31781	+	16.1143i	0.310802	+	1.15993i	0.927834	+	0.372992i	$0.121668\pi$
$193$	4.31781	+	16.1143i	0.310802	+	1.15993i	−0.617032	+	0.786938i	$0.711665\pi$
$194$	−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	$-0.430852\pi$
$197$	16.7309	−	16.7309i	1.19203	−	1.19203i	0.976497	−	0.215530i	$-0.0691479\pi$
$198$	−1.85194	+	3.01736i	−0.131612	+	0.214435i
$199$	8.68665	−	15.0457i	0.615780	−	1.06656i	−0.374467	−	0.927240i	$-0.622174\pi$
$199$	8.68665	−	15.0457i	0.615780	−	1.06656i	0.990247	−	0.139322i	$-0.0444924\pi$
$200$	−4.21870	+	13.4982i	−0.298307	+	0.954470i
$201$	−6.07159	−	10.5163i	−0.428257	−	0.741763i
$202$	0.732764	+	1.35184i	0.0515571	+	0.0951148i
$203$	2.93610	−	11.3850i	0.206074	−	0.799072i
$204$	−5.06869	+	7.78127i	−0.354879	+	0.544798i
$205$	0.222714	−	1.99562i	0.0155550	−	0.139380i
$206$	7.68456	−	7.28218i	0.535409	−	0.507374i
$207$	−1.18151	−	4.40947i	−0.0821208	−	0.306479i
$208$	16.2663	−	2.52975i	1.12786	−	0.175407i
$209$		−	19.6575i		−	1.35974i
$210$	5.07807	−	6.64930i	0.350420	−	0.458845i
$211$	10.9810			0.755960			0.377980	−	0.925814i	$-0.376619\pi$
$211$	10.9810			0.755960			0.377980	+	0.925814i	$0.376619\pi$
$212$	−1.34296	−	1.49570i	−0.0922347	−	0.102725i
$213$	−11.6091	+	3.11065i	−0.795442	+	0.213138i
$214$	−15.7367	+	14.9127i	−1.07574	+	1.01941i
$215$	−0.221851	−	0.277590i	−0.0151301	−	0.0189315i
$216$	−2.15460	+	1.83241i	−0.146602	+	0.124679i
$217$	3.88718	−	3.96101i	0.263879	−	0.268891i
$218$	20.8635	−	11.3091i	1.41305	−	0.765947i
$219$	−6.64727	+	3.83780i	−0.449181	+	0.259335i
$220$	−1.83779	+	11.0437i	−0.123904	+	0.744569i
$221$	−16.5490	−	9.55458i	−1.11321	−	0.642711i
$222$	6.08494	−	9.91417i	0.408394	−	0.665395i
$223$	12.2628	+	12.2628i	0.821178	+	0.821178i	0.986277	−	0.165099i	$-0.0527943\pi$
$223$	12.2628	+	12.2628i	0.821178	+	0.821178i	−0.165099	+	0.986277i	$0.552794\pi$
$224$	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
$227$	27.5850	−	7.39138i	1.83088	−	0.490583i	0.832860	−	0.553483i	$-0.186702\pi$
$227$	27.5850	−	7.39138i	1.83088	−	0.490583i	0.998020	+	0.0629007i	$0.0200351\pi$
$228$	4.87382	−	14.9291i	0.322777	−	0.988703i
$229$	4.08294	+	7.07185i	0.269808	+	0.467321i	0.968812	−	0.247796i	$-0.0797064\pi$
$229$	4.08294	+	7.07185i	0.269808	+	0.467321i	−0.699004	+	0.715118i	$0.746373\pi$
$230$	−8.70622	−	11.5150i	−0.574071	−	0.759277i
$231$	3.25760	−	5.76695i	0.214335	−	0.379437i
$232$	−1.01244	+	12.5285i	−0.0664697	+	0.822535i
$233$	1.75405	+	0.469995i	0.114911	+	0.0307904i	0.315816	−	0.948820i	$-0.397722\pi$
$233$	1.75405	+	0.469995i	0.114911	+	0.0307904i	−0.200905	+	0.979611i	$0.564388\pi$
$234$	−4.00336	−	4.22457i	−0.261708	−	0.276169i
$235$	−5.45126	+	13.9329i	−0.355601	+	0.908883i
$236$	1.11293	−	20.6830i	0.0724455	−	1.34635i
$237$	−5.04440	+	5.04440i	−0.327669	+	0.327669i
$238$	8.94830	−	14.8919i	0.580032	−	0.965296i
$239$	7.43701			0.481060			0.240530	−	0.970642i	$-0.422679\pi$
$239$	7.43701			0.481060			0.240530	+	0.970642i	$0.422679\pi$
$240$	−4.13389	+	7.93164i	−0.266841	+	0.511985i
$241$	−8.17415	+	14.1580i	−0.526543	+	0.912000i	0.472978	+	0.881074i	$0.343179\pi$
$241$	−8.17415	+	14.1580i	−0.526543	+	0.912000i	−0.999522	+	0.0309256i	$0.990155\pi$
$242$	0.179886	−	6.69093i	0.0115635	−	0.430109i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−11.9232	−	7.76670i	−0.763302	−	0.497212i
$245$	−9.04267	+	12.7762i	−0.577715	+	0.816239i
$246$	0.361543	−	1.21743i	0.0230512	−	0.0776202i
$247$	31.2145	+	8.36389i	1.98613	+	0.532182i
$248$	−3.37069	+	4.88243i	−0.214039	+	0.310035i
$249$	3.80229	+	2.19525i	0.240960	+	0.139119i
$250$	12.2257	−	10.0266i	0.773219	−	0.634139i
$251$	8.99623			0.567837			0.283918	−	0.958848i	$-0.408366\pi$
$251$	8.99623			0.567837			0.283918	+	0.958848i	$0.408366\pi$
$252$	3.90387	−	3.57209i	0.245920	−	0.225021i
$253$	−8.08091	−	8.08091i	−0.508042	−	0.508042i
$254$	−12.7584	+	3.05359i	−0.800533	+	0.191599i
$255$	9.51196	−	4.16201i	0.595662	−	0.260635i
$256$	−4.85915	−	15.2443i	−0.303697	−	0.952769i
$257$	0.483750	−	1.80538i	0.0301755	−	0.112617i	−0.949195	−	0.314687i	$-0.898100\pi$
$257$	0.483750	−	1.80538i	0.0301755	−	0.112617i	0.979371	+	0.202071i	$0.0647671\pi$
$258$	−0.107100	−	0.197583i	−0.00666778	−	0.0123010i
$259$	−10.7035	+	18.9485i	−0.665084	+	1.17740i
$260$	−16.7546	−	7.61717i	−1.03908	−	0.472397i
$261$	3.84855	−	2.22196i	0.238219	−	0.137536i
$262$	0.292998	−	10.8982i	0.0181015	−	0.673293i
$263$	−22.9662	+	6.15376i	−1.41615	+	0.379457i	−0.884118	−	0.467265i	$-0.845240\pi$
$263$	−22.9662	+	6.15376i	−1.41615	+	0.379457i	−0.532036	+	0.846722i	$0.678573\pi$
$264$	−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
$268$	−16.2255	−	18.0710i	−0.991131	−	1.10386i
$269$	10.7987	−	18.7039i	0.658410	−	1.14040i	−0.322618	−	0.946529i	$-0.604563\pi$
$269$	10.7987	−	18.7039i	0.658410	−	1.14040i	0.981027	−	0.193870i	$-0.0621038\pi$
$270$	3.13808	−	0.390426i	0.190978	−	0.0237605i
$271$	19.0805	−	11.0161i	1.15906	−	0.669182i	0.207980	−	0.978133i	$-0.433311\pi$
$271$	19.0805	−	11.0161i	1.15906	−	0.669182i	0.951078	+	0.308951i	$0.0999778\pi$
$272$	−6.70442	+	17.3208i	−0.406515	+	1.05023i
$273$	7.77139	+	7.62654i	0.470346	+	0.461579i
$274$	6.49924	+	1.93010i	0.392633	+	0.116602i
$275$	8.49434	−	9.19366i	0.512228	−	0.554399i
$276$	−4.13358	−	8.14070i	−0.248812	−	0.490013i
$277$	−6.97992	−	26.0494i	−0.419383	−	1.56516i	−0.775891	−	0.630867i	$-0.782700\pi$
$277$	−6.97992	−	26.0494i	−0.419383	−	1.56516i	0.356508	−	0.934292i	$-0.383967\pi$
$278$	−15.4918	+	25.2408i	−0.929138	+	1.51384i
$279$	2.09761			0.125580
$280$	7.19039	−	15.1095i	0.429708	−	0.902968i
$281$	−9.91189			−0.591294			−0.295647	−	0.955297i	$-0.595535\pi$
$281$	−9.91189			−0.591294			−0.295647	+	0.955297i	$0.595535\pi$
$282$	−4.94972	+	8.06457i	−0.294752	+	0.480238i
$283$	3.94140	+	14.7095i	0.234292	+	0.874390i	0.978467	+	0.206405i	$0.0661764\pi$
$283$	3.94140	+	14.7095i	0.234292	+	0.874390i	−0.744175	+	0.667985i	$0.767157\pi$
$284$	−21.4326	+	10.8827i	−1.27179	+	0.645772i
$285$	−13.7159	+	10.9619i	−0.812463	+	0.649325i
$286$	−13.9673	−	4.14792i	−0.825904	−	0.245272i
$287$	−0.593314	+	2.30063i	−0.0350222	+	0.135802i
$288$	−3.45933	+	4.47583i	−0.203843	+	0.263741i
$289$	3.94904	−	2.27998i	0.232297	−	0.134116i
$290$	8.63405	−	11.0877i	0.507009	−	0.651094i
$291$	−0.860252	+	1.49000i	−0.0504289	+	0.0873454i
$292$	−11.4225	+	10.2560i	−0.668452	+	0.600188i
$293$	8.30117	+	8.30117i	0.484959	+	0.484959i	0.906711	−	0.421752i	$-0.138585\pi$
$293$	8.30117	+	8.30117i	0.484959	+	0.484959i	−0.421752	+	0.906711i	$0.638585\pi$
$294$	−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
$297$	2.41811	−	0.647932i	0.140313	−	0.0375968i
$298$	0.126034	−	4.68789i	0.00730094	−	0.271562i
$299$	16.2701	−	9.39355i	0.940925	−	0.543243i
$300$	8.73058	−	4.87617i	0.504060	−	0.281526i
$301$	0.213644	+	0.362133i	0.0123143	+	0.0208730i
$302$	3.84992	+	7.10250i	0.221538	+	0.408703i
$303$	0.281412	−	1.05024i	0.0161667	−	0.0603348i
$304$	3.37041	−	31.2277i	0.193306	−	1.79103i
$305$	6.37741	+	14.5751i	0.365169	+	0.834567i
$306$	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	$0.820305\pi$
$308$	3.99245	−	12.6309i	0.227491	−	0.719711i
$309$	−7.48608			−0.425868
$310$	6.14621	−	2.49472i	0.349081	−	0.141691i
$311$	−10.4092	−	6.00978i	−0.590254	−	0.340783i	0.174944	−	0.984578i	$-0.444026\pi$
$311$	−10.4092	−	6.00978i	−0.590254	−	0.340783i	−0.765198	+	0.643795i	$0.777359\pi$
$312$	−9.57920	−	6.61320i	−0.542316	−	0.374399i
$313$	−17.5475	−	4.70184i	−0.991845	−	0.265764i	−0.273819	−	0.961781i	$-0.588287\pi$
$313$	−17.5475	−	4.70184i	−0.991845	−	0.265764i	−0.718025	+	0.696017i	$0.754954\pi$
$314$	5.67317	−	19.1033i	0.320155	−	1.07806i
$315$	−5.84045	+	0.942918i	−0.329072	+	0.0531274i
$316$	−7.78746	+	11.9550i	−0.438079	+	0.672524i
$317$	−28.5483	−	7.64949i	−1.60343	−	0.429638i	−0.657354	−	0.753582i	$-0.728324\pi$
$317$	−28.5483	−	7.64949i	−1.60343	−	0.429638i	−0.946076	+	0.323944i	$0.894991\pi$
$318$	−0.0382001	+	1.42087i	−0.00214215	+	0.0796785i
$319$	5.56250	−	9.63453i	0.311440	−	0.539430i
$320$	−4.81302	+	17.2289i	−0.269056	+	0.963125i
$321$	15.3302			0.855649
$322$	8.28063	+	14.9393i	0.461461	+	0.832534i
$323$	−25.7812	+	25.7812i	−1.43451	+	1.43451i
$324$	1.99711	+	0.107462i	0.110951	+	0.00597013i
$325$	10.9846	+	17.4001i	0.609317	+	0.965182i
$326$	23.7801	+	25.0941i	1.31706	+	1.38983i
$327$	−16.2088	−	4.34315i	−0.896351	−	0.240177i
$328$	0.204589	−	2.53170i	0.0112965	−	0.139790i
$329$	8.70666	−	15.4134i	0.480013	−	0.849770i
$330$	6.31473	−	4.77442i	0.347615	−	0.262823i
$331$	10.2623	+	17.7749i	0.564068	+	0.976995i	0.997136	+	0.0756334i	$0.0240979\pi$
$331$	10.2623	+	17.7749i	0.564068	+	0.976995i	−0.433067	+	0.901362i	$0.642569\pi$
$332$	8.34744	+	2.72515i	0.458125	+	0.149562i
$333$	−7.94521	+	2.12891i	−0.435395	+	0.116664i
$334$	−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	$0.409983\pi$
$338$	2.91242	−	4.74520i	0.158415	−	0.258105i
$339$	4.48079	+	2.58699i	0.243363	+	0.140506i
$340$	16.8944	−	12.0738i	0.916229	−	0.654795i
$341$	4.54766	−	2.62559i	0.246270	−	0.142184i
$342$	−9.76276	+	5.29192i	−0.527910	+	0.286154i
$343$	12.7211	−	13.4601i	0.686872	−	0.726778i
$344$	−0.291202	−	0.342404i	−0.0157005	−	0.0184612i
$345$	−1.13216	+	10.1447i	−0.0609537	+	0.546173i
$346$	−21.1189	+	20.0130i	−1.13536	+	1.07591i
$347$	−22.2741	+	5.96833i	−1.19574	+	0.320397i	−0.801151	−	0.598462i	$-0.795779\pi$
$347$	−22.2741	+	5.96833i	−1.19574	+	0.320397i	−0.394586	+	0.918859i	$0.629112\pi$
$348$	6.61326	−	5.93790i	0.354508	−	0.318305i
$349$	14.4900			0.775631			0.387815	−	0.921737i	$-0.373230\pi$
$349$	14.4900			0.775631			0.387815	+	0.921737i	$0.373230\pi$
$350$	−15.9917	+	9.70901i	−0.854793	+	0.518968i
$351$			4.11545i			0.219667i
$352$	−1.89747	+	14.0338i	−0.101136	+	0.748002i
$353$	7.16622	+	26.7447i	0.381420	+	1.42348i	0.843734	+	0.536761i	$0.180352\pi$
$353$	7.16622	+	26.7447i	0.381420	+	1.42348i	−0.462315	+	0.886716i	$0.652981\pi$
$354$	−10.6310	+	10.0744i	−0.565034	+	0.535447i
$355$	26.7086	+	2.98072i	1.41755	+	0.158200i
$356$	−5.60374	−	3.65025i	−0.296998	−	0.193463i
$357$	−11.8359	+	3.29106i	−0.626422	+	0.174181i
$358$	−3.68528	−	6.79877i	−0.194773	−	0.359326i
$359$	10.9619	+	18.9866i	0.578548	+	1.00207i	0.995646	+	0.0932126i	$0.0297136\pi$
$359$	10.9619	+	18.9866i	0.578548	+	1.00207i	−0.417099	+	0.908861i	$0.636953\pi$
$360$	5.97955	−	2.06032i	0.315150	−	0.108589i
$361$	21.3290	−	36.9429i	1.12258	−	1.94436i
$362$	1.41762	−	2.30972i	0.0745083	−	0.121396i
$363$	−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
$367$	−4.32024	−	16.1234i	−0.225515	−	0.841633i	−0.982198	−	0.187851i	$-0.939848\pi$
$367$	−4.32024	−	16.1234i	−0.225515	−	0.841633i	0.756683	−	0.653782i	$-0.226819\pi$
$368$	−11.4517	−	14.2228i	−0.596963	−	0.741414i
$369$	−0.777698	+	0.449004i	−0.0404854	+	0.0233742i
$370$	−20.7484	+	15.6873i	−1.07866	+	0.815545i
$371$	−0.0250147	−	2.65905i	−0.00129870	−	0.138051i
$372$	4.10475	−	0.866500i	0.212822	−	0.0449259i
$373$	−4.62726	+	17.2692i	−0.239590	+	0.894164i	0.736435	+	0.676508i	$0.236508\pi$
$373$	−4.62726	+	17.2692i	−0.239590	+	0.894164i	−0.976026	+	0.217656i	$0.930159\pi$
$374$	11.9322	−	11.3074i	0.617001	−	0.584694i
$375$	−11.1517	−	0.800112i	−0.575870	−	0.0413176i
$376$	−6.35460	+	17.8260i	−0.327713	+	0.919307i
$377$	12.9321	+	12.9321i	0.666037	+	0.666037i
$378$	−3.74109	−	0.0653687i	−0.192421	−	0.00336220i
$379$			6.18127i			0.317511i	0.987318	+	0.158755i	$0.0507481\pi$
$379$			6.18127i			0.317511i	−0.987318	+	0.158755i	$0.949252\pi$
$380$	−22.3121	+	27.1169i	−1.14459	+	1.39107i
$381$	8.03355	+	4.63817i	0.411571	+	0.237621i
$382$	3.19290	+	0.0858411i	0.163363	+	0.00439201i
$383$	2.03011	−	7.57648i	0.103734	−	0.387140i	−0.894465	−	0.447139i	$-0.852443\pi$
$383$	2.03011	−	7.57648i	0.103734	−	0.387140i	0.998198	+	0.0599988i	$0.0191097\pi$
$384$	−4.92055	+	10.1876i	−0.251101	+	0.519886i
$385$	−11.4820	+	9.35481i	−0.585176	+	0.476765i
$386$	6.71656	−	22.6167i	0.341864	−	1.15116i
$387$	−0.0411309	+	0.153503i	−0.00209080	+	0.00780298i
$388$	−1.06790	+	3.27111i	−0.0542145	+	0.166065i
$389$	−7.60813	+	13.1777i	−0.385748	+	0.668135i	−0.991873	−	0.127235i	$-0.959390\pi$
$389$	−7.60813	+	13.1777i	−0.385748	+	0.668135i	0.606125	+	0.795369i	$0.292723\pi$
$390$	4.89458	+	12.0587i	0.247847	+	0.610617i
$391$			21.1966i			1.07196i
$392$	−10.9399	+	16.5021i	−0.552550	+	0.833480i
$393$	−5.45107	+	5.45107i	−0.274970	+	0.274970i
$394$	−32.5427	+	7.78877i	−1.63948	+	0.392393i
$395$	14.6140	−	6.39446i	0.735312	−	0.321740i
$396$	4.46429	−	2.26682i	0.224339	−	0.113912i
$397$	24.7344	+	6.62755i	1.24138	+	0.332627i	0.819002	−	0.573791i	$-0.194528\pi$
$397$	24.7344	+	6.62755i	1.24138	+	0.332627i	0.422381	+	0.906418i	$0.361195\pi$
$398$	−21.6003	+	11.7085i	−1.08273	+	0.586893i
$399$	17.8933	−	10.5563i	0.895784	−	0.528478i
$400$	15.0703	−	13.1486i	0.753517	−	0.657428i
$401$	−3.65413	−	6.32914i	−0.182479	−	0.316062i	0.760245	−	0.649636i	$-0.225079\pi$
$401$	−3.65413	−	6.32914i	−0.182479	−	0.316062i	−0.942724	+	0.333574i	$0.891745\pi$
$402$	−0.461531	+	17.1669i	−0.0230191	+	0.856205i
$403$	2.23428	+	8.33846i	0.111298	+	0.415368i
$404$	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
$408$	11.8656	−	5.62911i	0.587435	−	0.278683i
$409$	10.5869	+	6.11237i	0.523490	+	0.302237i	0.738362	−	0.674405i	$-0.235600\pi$
$409$	10.5869	+	6.11237i	0.523490	+	0.302237i	−0.214871	+	0.976642i	$0.568933\pi$
$410$	−1.74473	+	2.24056i	−0.0861661	+	0.110653i
$411$	−2.39701	−	4.15175i	−0.118236	−	0.204791i
$412$	−14.6493	+	3.09242i	−0.721720	+	0.152353i
$413$	19.1920	−	19.5566i	0.944379	−	0.962316i
$414$	−1.83790	+	6.18877i	−0.0903279	+	0.304161i
$415$	−6.12921	−	7.66913i	−0.300871	−	0.376463i
$416$	−21.4771	−	8.98414i	−1.05300	−	0.440484i
$417$	20.2279	−	5.42006i	0.990566	−	0.265421i
$418$	−14.5419	+	23.6931i	−0.711269	+	1.15887i
$419$			18.1365i			0.886025i	0.896515	+	0.443013i	$0.146090\pi$
$419$			18.1365i			0.886025i	−0.896515	+	0.443013i	$0.853910\pi$
$420$	−11.0395	+	4.25780i	−0.538674	+	0.207760i
$421$			35.1440i			1.71282i	0.516300	+	0.856408i	$0.327309\pi$
$421$			35.1440i			1.71282i	−0.516300	+	0.856408i	$0.672691\pi$
$422$	−13.2353	−	8.12335i	−0.644286	−	0.395438i
$423$	6.46294	−	1.73174i	0.314239	−	0.0842000i
$424$	0.512194	+	2.79624i	0.0248743	+	0.135798i
$425$	−23.1982	+	0.917182i	−1.12528	+	0.0444899i
$426$	16.2936	+	4.83876i	0.789426	+	0.234439i
$427$	−5.04286	−	18.1360i	−0.244041	−	0.877664i
$428$	29.9993	−	6.33275i	1.45007	−	0.306105i
$429$	5.15134	+	8.92239i	0.248709	+	0.430777i
$430$	0.0620456	+	0.498697i	0.00299210	+	0.0240493i
$431$	−8.59615	−	4.96299i	−0.414062	−	0.239059i	0.278472	−	0.960444i	$-0.410172\pi$
$431$	−8.59615	−	4.96299i	−0.414062	−	0.239059i	−0.692533	+	0.721386i	$0.743506\pi$
$432$	3.95249	−	0.614696i	0.190164	−	0.0295746i
$433$	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
$437$	−9.27754	−	34.6243i	−0.443805	−	1.65630i
$438$	10.8510	+	0.291730i	0.518482	+	0.0139394i
$439$	−8.92288	−	15.4549i	−0.425866	−	0.737621i	0.570635	−	0.821204i	$-0.306697\pi$
$439$	−8.92288	−	15.4549i	−0.425866	−	0.737621i	−0.996501	+	0.0835826i	$0.973364\pi$
$440$	10.3849	−	11.9515i	0.495080	−	0.569765i
$441$	6.99876	−	0.131692i	0.333274	−	0.00627103i
$442$	12.8784	+	23.7585i	0.612561	+	1.13008i
$443$	−4.45800	−	1.19452i	−0.211806	−	0.0567533i	0.151356	−	0.988479i	$-0.451636\pi$
$443$	−4.45800	−	1.19452i	−0.211806	−	0.0567533i	−0.363162	+	0.931726i	$0.618303\pi$
$444$	−14.6683	+	7.44810i	−0.696129	+	0.353471i
$445$	2.99730	+	6.85011i	0.142086	+	0.324726i
$446$	−5.70873	−	23.8520i	−0.270316	−	1.12942i
$447$	−2.34479	+	2.34479i	−0.110905	+	0.110905i
$448$	8.50803	−	19.3808i	0.401966	−	0.915654i
$449$		−	5.02676i		−	0.237228i	−0.992940	−	0.118614i	$-0.962155\pi$
$449$		−	5.02676i		−	0.237228i	0.992940	−	0.118614i	$-0.0378450\pi$
$450$	−6.85271	−	1.74367i	−0.323040	−	0.0821972i
$451$	−1.12404	+	1.94690i	−0.0529292	+	0.0916760i
$452$	9.83701	+	3.21144i	0.462694	+	0.151053i
$453$	1.47853	−	5.51794i	0.0694673	−	0.259256i
$454$	−38.7160	−	11.4976i	−1.81703	−	0.539611i
$455$	−9.96931	−	22.2127i	−0.467369	−	1.04135i
$456$	−16.9185	+	14.3885i	−0.792279	+	0.673804i
$457$	−8.69348	+	32.4445i	−0.406664	+	1.51769i	0.394303	+	0.918980i	$0.370986\pi$
$457$	−8.69348	+	32.4445i	−0.406664	+	1.51769i	−0.800967	+	0.598709i	$0.795681\pi$
$458$	0.310364	−	11.5441i	0.0145023	−	0.539421i
$459$	−4.02119	−	2.32164i	−0.187693	−	0.108365i
$460$	1.97517	+	20.3196i	0.0920928	+	0.947406i
$461$			0.392085i			0.0182612i	0.999958	+	0.00913062i	$0.00290641\pi$
$461$			0.392085i			0.0182612i	−0.999958	+	0.00913062i	$0.997094\pi$
$462$	−8.19258	+	4.54103i	−0.381153	+	0.211268i
$463$	−8.76491	−	8.76491i	−0.407340	−	0.407340i	0.473470	−	0.880810i	$-0.343001\pi$
$463$	−8.76491	−	8.76491i	−0.407340	−	0.407340i	−0.880810	+	0.473470i	$0.843001\pi$
$464$	10.4884	−	14.3516i	0.486914	−	0.666256i
$465$	−4.36797	−	1.70897i	−0.202560	−	0.0792517i
$466$	−1.76646	−	1.86407i	−0.0818298	−	0.0863513i
$467$	−6.99059	+	26.0892i	−0.323486	+	1.20727i	0.592339	+	0.805689i	$0.298204\pi$
$467$	−6.99059	+	26.0892i	−0.323486	+	1.20727i	−0.915825	+	0.401577i	$0.868462\pi$
$468$	1.70005	+	8.05342i	0.0785849	+	0.372270i
$469$	−0.302226	−	32.1264i	−0.0139555	−	1.48346i
$470$	16.8775	−	12.7607i	0.778501	−	0.588606i
$471$	−12.2033	+	7.04557i	−0.562297	+	0.324643i
$472$	−16.6420	+	24.1059i	−0.766010	+	1.10956i
$473$	0.102968	+	0.384281i	0.00473447	+	0.0176693i
$474$	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
$478$	−8.96382	−	5.50165i	−0.409996	−	0.251640i
$479$	−16.2572	+	28.1583i	−0.742812	+	1.28659i	0.208398	+	0.978044i	$0.433175\pi$
$479$	−16.2572	+	28.1583i	−0.742812	+	1.28659i	−0.951210	+	0.308544i	$0.900158\pi$
$480$	10.8501	−	6.50189i	0.495239	−	0.296769i
$481$	−16.9258	−	29.3163i	−0.771750	−	1.33671i
$482$	20.3259	−	11.0177i	0.925821	−	0.501843i
$483$	3.01611	−	11.6952i	0.137238	−	0.532152i
$484$	−5.16654	+	7.93149i	−0.234843	+	0.360522i
$485$	3.00530	−	2.40185i	0.136463	−	0.109062i
$486$	−0.972764	−	1.02651i	−0.0441254	−	0.0465636i
$487$	−1.47724	−	5.51312i	−0.0669399	−	0.249823i	0.924345	−	0.381557i	$-0.124612\pi$
$487$	−1.47724	−	5.51312i	−0.0669399	−	0.249823i	−0.991285	+	0.131734i	$0.957945\pi$
$488$	8.62543	+	18.1816i	0.390455	+	0.823040i
$489$		−	24.4459i		−	1.10548i
$490$	20.3505	−	8.70962i	0.919341	−	0.393461i
$491$	−24.8485			−1.12140			−0.560699	−	0.828020i	$-0.689467\pi$
$491$	−24.8485			−1.12140			−0.560699	+	0.828020i	$0.689467\pi$
$492$	−1.33638	+	1.19990i	−0.0602486	+	0.0540959i
$493$	−19.9312	+	5.34056i	−0.897658	+	0.240527i
$494$	−31.4354	−	33.1724i	−1.41435	−	1.49250i
$495$	−5.56327	−	0.620869i	−0.250050	−	0.0279060i
$496$	7.67455	−	3.39126i	0.344597	−	0.152272i
$497$	−30.7908	−	7.94070i	−1.38116	−	0.356189i
$498$	−2.95892	−	5.45874i	−0.132592	−	0.244612i
$499$	5.26914	−	3.04214i	0.235879	−	0.136185i	−0.377402	−	0.926049i	$-0.623183\pi$
$499$	5.26914	−	3.04214i	0.235879	−	0.136185i	0.613281	+	0.789865i	$0.289849\pi$
$500$	−22.1529	+	3.04092i	−0.990710	+	0.135994i
$501$	10.2585	+	5.92277i	0.458318	+	0.264610i
$502$	−10.8431	−	6.65511i	−0.483953	−	0.297032i
$503$	−27.8070	−	27.8070i	−1.23985	−	1.23985i	−0.960061	−	0.279790i	$-0.909735\pi$
$503$	−27.8070	−	27.8070i	−1.23985	−	1.23985i	−0.279790	−	0.960061i	$-0.590265\pi$
$504$	−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
$507$	−3.80280	+	1.01896i	−0.168888	+	0.0452535i
$508$	17.6366	+	5.75774i	0.782498	+	0.255458i
$509$	−16.5276	−	28.6266i	−0.732571	−	1.26885i	−0.955781	−	0.294080i	$-0.904987\pi$
$509$	−16.5276	−	28.6266i	−0.732571	−	1.26885i	0.223210	−	0.974770i	$-0.428346\pi$
$510$	−14.5437	−	2.02016i	−0.644005	−	0.0894544i
$511$	−20.3068	+	0.191034i	−0.898321	+	0.00845085i
$512$	−5.42049	+	21.9686i	−0.239554	+	0.970883i
$513$	7.58470	+	2.03231i	0.334873	+	0.0897288i
$514$	−1.91862	+	1.81816i	−0.0846269	+	0.0801956i
$515$	15.5887	+	6.09909i	0.686920	+	0.268758i
$516$	−0.0170777	+	0.317376i	−0.000751802	+	0.0139717i
$517$	11.8442	−	11.8442i	0.520906	−	0.520906i
$518$	26.9184	−	14.9205i	1.18273	−	0.655568i
$519$	20.5734			0.903071
$520$	14.5594	+	21.5755i	0.638472	+	0.946148i
$521$	−18.5173	+	32.0729i	−0.811258	+	1.40514i	0.100725	+	0.994914i	$0.467884\pi$
$521$	−18.5173	+	32.0729i	−0.811258	+	1.40514i	−0.911984	+	0.410227i	$0.865450\pi$
$522$	−6.28239	−	0.168902i	−0.274973	−	0.00739264i
$523$	−5.22057	−	1.39885i	−0.228280	−	0.0611673i	0.142866	−	0.989742i	$-0.454368\pi$
$523$	−5.22057	−	1.39885i	−0.228280	−	0.0611673i	−0.371145	+	0.928575i	$0.621035\pi$
$524$	−8.41527	+	12.9188i	−0.367623	+	0.564362i
$525$	12.9301	+	2.79487i	0.564318	+	0.121978i
$526$	32.2334	+	9.57247i	1.40544	+	0.417380i
$527$	−9.40789	−	2.52084i	−0.409814	−	0.109809i
$528$	7.79966	−	6.28003i	0.339436	−	0.273303i
$529$	1.87116	+	1.08031i	0.0813547	+	0.0469702i
$530$	1.23716	−	2.92764i	0.0537390	−	0.127169i
$531$	10.3565			0.449432
$532$	30.6542	−	28.0490i	1.32903	−	1.21608i
$533$	−2.61326	−	2.61326i	−0.113193	−	0.113193i
$534$	1.10074	+	4.59908i	0.0476338	+	0.199021i
$535$	−31.9230	−	12.4899i	−1.38015	−	0.539985i
$536$	6.18829	+	33.7840i	0.267294	+	1.45925i
$537$	−1.41530	+	5.28197i	−0.0610747	+	0.227934i
$538$	−26.8522	+	14.5553i	−1.15768	+	0.627523i
$539$	15.0086	−	9.04591i	0.646467	−	0.389635i
$540$	−4.07115	−	1.85087i	−0.175194	−	0.0796488i
$541$	−5.14830	+	2.97237i	−0.221343	+	0.127792i	−0.606572	−	0.795029i	$-0.707456\pi$
$541$	−5.14830	+	2.97237i	−0.221343	+	0.127792i	0.385229	+	0.922821i	$0.374122\pi$
$542$	−31.1471	−	0.837389i	−1.33788	−	0.0359689i
$543$	−1.85101	+	0.495976i	−0.0794343	+	0.0212844i
$544$	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	$0.658625\pi$
$548$	−6.40570	−	7.13427i	−0.273638	−	0.304761i
$549$	3.55742	−	6.16163i	0.151827	−	0.262972i
$550$	−17.0394	+	4.79728i	−0.726562	+	0.204557i
$551$	30.2198	−	17.4474i	1.28741	−	0.743285i
$552$	−1.04002	+	12.8699i	−0.0442663	+	0.547778i
$553$	−18.1845	+	5.05634i	−0.773284	+	0.215017i
$554$	−10.8576	+	36.5609i	−0.461296	+	1.55332i
$555$	18.2793	+	2.03999i	0.775912	+	0.0865929i
$556$	37.3446	−	18.9623i	1.58376	−	0.804182i
$557$	0.258379	+	0.964283i	0.0109479	+	0.0408580i	0.971184	−	0.238332i	$-0.0766007\pi$
$557$	0.258379	+	0.964283i	0.0109479	+	0.0408580i	−0.960236	+	0.279190i	$0.909934\pi$
$558$	−2.52824	−	1.55174i	−0.107029	−	0.0656904i
$559$	−0.654018			−0.0276620
$560$	−19.8441	+	12.8923i	−0.838567	+	0.544799i
$561$	−11.6240			−0.490767
$562$	11.9468	+	7.33249i	0.503945	+	0.309302i
$563$	−9.73850	−	36.3446i	−0.410429	−	1.53174i	−0.793819	−	0.608154i	$-0.791910\pi$
$563$	−9.73850	−	36.3446i	−0.410429	−	1.53174i	0.383390	−	0.923587i	$-0.374756\pi$
$564$	11.9318	−	6.05857i	0.502419	−	0.255112i
$565$	−7.22295	−	9.03765i	−0.303872	−	0.380217i
$566$	6.13104	−	20.6451i	0.257707	−	0.867777i
$567$	1.88834	+	1.85315i	0.0793030	+	0.0778249i
$568$	33.8833	+	2.73814i	1.42171	+	0.114890i
$569$	−2.34364	+	1.35310i	−0.0982505	+	0.0567249i	−0.548320	−	0.836268i	$-0.684732\pi$
$569$	−2.34364	+	1.35310i	−0.0982505	+	0.0567249i	0.450070	+	0.892993i	$0.351399\pi$
$570$	24.6410	−	3.06572i	1.03210	−	0.128409i
$571$	3.58498	−	6.20936i	0.150027	−	0.259854i	−0.781210	−	0.624268i	$-0.785397\pi$
$571$	3.58498	−	6.20936i	0.150027	−	0.259854i	0.931237	+	0.364414i	$0.118731\pi$
$572$	13.7663	+	15.3320i	0.575597	+	0.641064i
$573$	−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
$577$	−26.2319	+	7.02881i	−1.09205	+	0.292613i	−0.759522	−	0.650481i	$-0.774567\pi$
$577$	−26.2319	+	7.02881i	−1.09205	+	0.292613i	−0.332525	+	0.943094i	$0.607901\pi$
$578$	−6.44643	−	0.173312i	−0.268136	−	0.00720884i
$579$	−14.4477	+	8.34136i	−0.600424	+	0.346655i
$580$	−18.6089	+	6.97686i	−0.772694	+	0.289698i
$581$	5.90247	+	10.0048i	0.244876	+	0.415070i
$582$	2.13911	−	1.15951i	0.0886691	−	0.0480632i
$583$	0.651217	−	2.43037i	0.0269706	−	0.100656i
$584$	21.3546	−	3.91157i	0.883659	−	0.161862i
$585$	3.35296	−	8.56985i	0.138628	−	0.354320i
$586$	−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	$-0.505872\pi$
$588$	13.6413	−	3.14882i	0.562558	−	0.129855i
$589$	16.4710			0.678674
$590$	30.3455	−	12.3171i	1.24931	−	0.507088i
$591$	20.4911	+	11.8305i	0.842891	+	0.486643i
$592$	−25.6274	+	20.6343i	−1.05328	+	0.848066i
$593$	18.2308	+	4.88492i	0.748648	+	0.200600i	0.612918	−	0.790146i	$-0.289995\pi$
$593$	18.2308	+	4.88492i	0.748648	+	0.200600i	0.135730	+	0.990746i	$0.456662\pi$
$594$	−3.39387	−	1.00789i	−0.139252	−	0.0413542i
$595$	27.3279	+	2.78982i	1.12034	+	0.114372i
$596$	−3.61985	+	5.55707i	−0.148275	+	0.227626i
$597$	16.7813	+	4.49654i	0.686813	+	0.184031i
$598$	−26.5594	−	0.714049i	−1.08609	−	0.0291996i
$599$	−20.8175	+	36.0569i	−0.850579	+	1.47325i	0.0301067	+	0.999547i	$0.490415\pi$
$599$	−20.8175	+	36.0569i	−0.850579	+	1.47325i	−0.880686	+	0.473700i	$0.842918\pi$
$600$	−14.1302	−	0.581352i	−0.576862	−	0.0237336i
$601$	−21.5895			−0.880654			−0.440327	−	0.897837i	$-0.645137\pi$
$601$	−21.5895			−0.880654			−0.440327	+	0.897837i	$0.645137\pi$
$602$	0.0103882	−	0.594525i	0.000423393	−	0.0242310i
$603$	8.58653	−	8.58653i	0.349670	−	0.349670i
$604$	0.613889	−	11.4087i	0.0249788	−	0.464213i
$605$	9.69559	−	4.24236i	0.394182	−	0.172477i
$606$	−1.11612	+	1.05768i	−0.0453392	+	0.0429652i
$607$	5.67556	+	1.52076i	0.230364	+	0.0617258i	0.372154	−	0.928171i	$-0.378619\pi$
$607$	5.67556	+	1.52076i	0.230364	+	0.0617258i	−0.141790	+	0.989897i	$0.545286\pi$
$608$	−27.1635	+	35.1454i	−1.10163	+	1.42533i
$609$	11.7570	−	0.110603i	0.476418	−	0.00448184i
$610$	3.09548	−	22.2851i	0.125332	−	0.902298i
$611$	13.7681	+	23.8470i	0.556997	+	0.964748i
$612$	−8.82801	−	2.88204i	−0.356851	−	0.116499i
$613$	−11.4187	+	3.05963i	−0.461197	+	0.123577i	−0.481934	−	0.876208i	$-0.660065\pi$
$613$	−11.4187	+	3.05963i	−0.461197	+	0.123577i	0.0207368	+	0.999785i	$0.493399\pi$
$614$	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	$0.788391\pi$
$618$	9.02296	+	5.53795i	0.362957	+	0.222769i
$619$	−33.6158	−	19.4081i	−1.35113	−	0.780078i	−0.362726	−	0.931896i	$-0.618154\pi$
$619$	−33.6158	−	19.4081i	−1.35113	−	0.780078i	−0.988408	+	0.151818i	$0.951487\pi$
$620$	−9.25354	−	1.53988i	−0.371631	−	0.0618430i
$621$	3.95342	−	2.28251i	0.158645	−	0.0915939i
$622$	8.10041	+	14.9440i	0.324797	+	0.599199i
$623$	−2.37008	−	8.52371i	−0.0949553	−	0.341495i
$624$	6.65357	+	15.0573i	0.266356	+	0.602773i
$625$	22.5699	+	10.7517i	0.902797	+	0.430067i
$626$	17.6717	+	18.6482i	0.706305	+	0.745332i
$627$	18.9877	−	5.08773i	0.758294	−	0.203184i
$628$	−20.9698	+	18.8283i	−0.836787	+	0.751332i
$629$	38.1932			1.52286
$630$	7.73703	+	3.18408i	0.308251	+	0.126857i
$631$		−	12.3972i		−	0.493524i	−0.969076	−	0.246762i	$-0.920633\pi$
$631$		−	12.3972i		−	0.493524i	0.969076	−	0.246762i	$-0.0793666\pi$
$632$	18.2302	−	8.64849i	0.725157	−	0.344018i
$633$	2.84208	+	10.6068i	0.112963	+	0.421582i
$634$	28.7504	+	30.3390i	1.14182	+	1.20491i
$635$	−12.9499	−	16.2035i	−0.513901	−	0.643015i
$636$	1.09716	−	1.68431i	0.0435050	−	0.0667874i
$637$	7.97829	+	27.6814i	0.316111	+	1.09678i
$638$	−13.8318	+	7.49753i	−0.547605	+	0.296830i
$639$	−6.00931	−	10.4084i	−0.237725	−	0.411751i
$640$	18.5465	−	17.2055i	0.733114	−	0.680105i
$641$	19.7202	−	34.1565i	0.778903	−	1.34910i	−0.153671	−	0.988122i	$-0.549110\pi$
$641$	19.7202	−	34.1565i	0.778903	−	1.34910i	0.932574	−	0.360978i	$-0.117557\pi$
$642$	−18.4775	−	11.3408i	−0.729248	−	0.447585i
$643$	−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
$647$	−6.83790	−	25.5194i	−0.268826	−	1.00327i	−0.959867	−	0.280456i	$-0.909514\pi$
$647$	−6.83790	−	25.5194i	−0.268826	−	1.00327i	0.691041	−	0.722815i	$-0.257152\pi$
$648$	−2.32762	−	1.60692i	−0.0914375	−	0.0631258i
$649$	22.4530	−	12.9633i	0.881358	−	0.508852i
$650$	−0.367754	−	29.0983i	−0.0144245	−	1.14133i
$651$	4.83211	+	2.72954i	0.189385	+	0.106979i
$652$	−10.0984	−	47.8376i	−0.395482	−	1.87346i
$653$	−0.836253	+	3.12094i	−0.0327251	+	0.122132i	−0.980356	−	0.197235i	$-0.936804\pi$
$653$	−0.836253	+	3.12094i	−0.0327251	+	0.122132i	0.947631	+	0.319367i	$0.103470\pi$
$654$	16.3236	+	17.2256i	0.638303	+	0.673572i
$655$	15.7922	−	6.90997i	0.617052	−	0.269995i
$656$	−2.11946	+	2.90011i	−0.0827509	+	0.113230i
$657$	−5.42747	−	5.42747i	−0.211746	−	0.211746i
$658$	−21.8965	+	12.1369i	−0.853613	+	0.473145i
$659$			39.2336i			1.52832i	0.645025	+	0.764161i	$0.276847\pi$
$659$			39.2336i			1.52832i	−0.645025	+	0.764161i	$0.723153\pi$
$660$	−11.1431	+	1.08317i	−0.433744	+	0.0421622i
$661$	20.4849	+	11.8269i	0.796769	+	0.460015i	0.842340	−	0.538946i	$-0.181177\pi$
$661$	20.4849	+	11.8269i	0.796769	+	0.460015i	−0.0455709	+	0.998961i	$0.514511\pi$
$662$	0.780088	−	29.0157i	0.0303190	−	1.12773i
$663$	4.94581	−	18.4580i	0.192080	−	0.716851i
$664$	−8.04519	−	9.45978i	−0.312214	−	0.367110i
$665$	−45.8607	+	7.40404i	−1.77840	+	0.287116i
$666$	11.1512	+	3.31163i	0.432102	+	0.128323i
$667$	5.25056	−	19.5953i	0.203302	−	0.758735i
$668$	22.5213	+	7.35242i	0.871375	+	0.284474i
$669$	−8.67111	+	15.0188i	−0.335245	+	0.580661i
$670$	14.9473	−	35.3715i	0.577466	−	1.36652i
$671$		−	17.8114i		−	0.687601i
$672$	−13.7932	+	5.80916i	−0.532086	+	0.224093i
$673$	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
$675$	2.66911	+	4.22798i	0.102734	+	0.162735i
$676$	−7.02068	+	3.56487i	−0.270026	+	0.137110i
$677$	16.0692	+	4.30573i	0.617590	+	0.165483i	0.554032	−	0.832496i	$-0.313089\pi$
$677$	16.0692	+	4.30573i	0.617590	+	0.165483i	0.0635578	+	0.997978i	$0.479755\pi$
$678$	−3.48693	−	6.43284i	−0.133915	−	0.247052i
$679$	−3.92059	+	2.31300i	−0.150458	+	0.0887647i
$680$	−29.2947	+	2.05464i	−1.12340	+	0.0787917i
$681$	14.2790	+	24.7320i	0.547174	+	0.947733i
$682$	−7.42361	−	0.199584i	−0.284265	−	0.00764246i
$683$	7.14976	+	26.6833i	0.273578	+	1.02101i	0.956788	+	0.290785i	$0.0939165\pi$
$683$	7.14976	+	26.6833i	0.273578	+	1.02101i	−0.683210	+	0.730222i	$0.739417\pi$
$684$	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
$688$	0.0976861	+	0.628120i	0.00372425	+	0.0239469i
$689$	3.58216	+	2.06816i	0.136469	+	0.0787906i
$690$	8.86931	−	11.3899i	0.337649	−	0.433605i
$691$	11.5239	+	19.9599i	0.438389	+	0.759311i	0.997565	−	0.0697372i	$-0.0222161\pi$
$691$	11.5239	+	19.9599i	0.438389	+	0.759311i	−0.559177	+	0.829048i	$0.688883\pi$
$692$	40.2595	−	8.49865i	1.53044	−	0.323070i
$693$	6.41357	+	1.65401i	0.243631	+	0.0628305i
$694$	31.2621	+	9.28403i	1.18669	+	0.352417i
$695$	−46.5377	−	5.19368i	−1.76528	−	0.197007i
$696$	−12.3636	+	2.26467i	−0.468642	+	0.0858421i
$697$	4.02762	−	1.07920i	0.152557	−	0.0408775i
$698$	−17.4648	−	10.7192i	−0.661051	−	0.405728i
$699$			1.81592i			0.0686845i
$700$	26.4572	+	0.127889i	0.999988	+	0.00483374i
$701$		−	19.9955i		−	0.755219i	−0.925965	−	0.377610i	$-0.876746\pi$
$701$		−	19.9955i		−	0.755219i	0.925965	−	0.377610i	$-0.123254\pi$
$702$	3.04447	−	4.96035i	0.114906	−	0.187216i
$703$	−62.3878	+	16.7168i	−2.35300	+	0.630485i
$704$	12.6687	−	15.5112i	0.477471	−	0.584600i
$705$	−14.8691	−	1.65941i	−0.560001	−	0.0624970i
$706$	11.1474	−	37.5367i	0.419538	−	1.41271i
$707$	2.01491	−	2.05318i	0.0757785	−	0.0772178i
$708$	20.2663	−	4.27815i	0.761654	−	0.160783i
$709$	9.81393	+	16.9982i	0.368570	+	0.638381i	0.989342	−	0.145609i	$-0.0465143\pi$
$709$	9.81393	+	16.9982i	0.368570	+	0.638381i	−0.620772	+	0.783991i	$0.713181\pi$
$710$	−29.9868	−	23.3508i	−1.12539	−	0.876341i
$711$	−6.17810	−	3.56693i	−0.231697	−	0.133770i
$712$	4.05385	+	8.54511i	0.151924	+	0.320241i
$713$	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
$717$	1.92484	+	7.18360i	0.0718845	+	0.268277i
$718$	0.833267	−	30.9938i	0.0310973	−	1.15668i
$719$	7.81531	+	13.5365i	0.291462	+	0.504827i	0.974156	−	0.225878i	$-0.0725250\pi$
$719$	7.81531	+	13.5365i	0.291462	+	0.504827i	−0.682694	+	0.730705i	$0.739192\pi$
$720$	−8.73131	−	1.94017i	−0.325397	−	0.0723058i
$721$	−17.2452	−	9.74135i	−0.642243	−	0.362787i
$722$	−53.0369	+	28.7487i	−1.97383	+	1.06992i
$723$	−15.7912	−	4.23125i	−0.587283	−	0.157362i
$724$	−3.41731	+	1.73519i	−0.127003	+	0.0644880i
$725$	21.6729	+	4.89848i	0.804913	+	0.181925i
$726$	6.50950	−	1.55798i	0.241590	−	0.0578222i
$727$	−0.213513	+	0.213513i	−0.00791876	+	0.00791876i	−0.711055	−	0.703136i	$-0.751782\pi$
$727$	−0.213513	+	0.213513i	−0.00791876	+	0.00791876i	0.703136	+	0.711055i	$0.251782\pi$
$728$	−13.4614	−	27.6994i	−0.498914	−	1.02661i
$729$			1.00000i			0.0370370i
$730$	−22.3580	−	9.44808i	−0.827509	−	0.349689i
$731$	0.368949	−	0.639038i	0.0136461	−	0.0236357i
$732$	4.41611	−	13.5271i	0.163224	−	0.499975i
$733$	−10.4380	+	38.9553i	−0.385537	+	1.43885i	0.451781	+	0.892129i	$0.350789\pi$
$733$	−10.4380	+	38.9553i	−0.385537	+	1.43885i	−0.837318	+	0.546716i	$0.815878\pi$
$734$	−6.72035	+	22.6295i	−0.248053	+	0.835268i
$735$	−14.6812	−	5.42783i	−0.541525	−	0.200209i
$736$	3.28121	+	25.6143i	0.120947	+	0.944156i
$737$	7.86795	−	29.3636i	0.289820	−	1.08162i
$738$	1.26952	+	0.0341310i	0.0467316	+	0.00125638i
$739$	−14.0619	−	8.11863i	−0.517275	−	0.298649i	0.218544	−	0.975827i	$-0.429869\pi$
$739$	−14.0619	−	8.11863i	−0.517275	−	0.298649i	−0.735819	+	0.677178i	$0.763203\pi$
$740$	36.6129	−	3.55897i	1.34592	−	0.130830i
$741$			32.3156i			1.18714i
$742$	−1.93693	+	3.22345i	−0.0711068	+	0.118337i
$743$	4.93484	+	4.93484i	0.181042	+	0.181042i	0.791810	−	0.610768i	$-0.209139\pi$
$743$	4.93484	+	4.93484i	0.181042	+	0.181042i	−0.610768	+	0.791810i	$0.709139\pi$
$744$	−5.58846	−	1.99217i	−0.204883	−	0.0730365i
$745$	6.79306	−	2.97234i	0.248878	−	0.108898i
$746$	18.3524	−	17.3914i	0.671929	−	0.636745i
$747$	−1.13635	+	4.24090i	−0.0415768	+	0.155167i
$748$	−22.7468	+	4.80177i	−0.831705	+	0.175570i
$749$	35.3152	+	19.9486i	1.29039	+	0.728908i
$750$	12.8492	+	9.21401i	0.469187	+	0.336448i
$751$	7.57077	−	4.37098i	0.276261	−	0.159499i	−0.355468	−	0.934688i	$-0.615679\pi$
$751$	7.57077	−	4.37098i	0.276261	−	0.159499i	0.631730	+	0.775189i	$0.282345\pi$
$752$	20.8463	−	16.7848i	0.760186	−	0.612077i
$753$	2.32840	+	8.68969i	0.0848514	+	0.316670i
$754$	−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	$0.571096\pi$
$757$	−32.9245	+	32.9245i	−1.19666	+	1.19666i	−0.975160	+	0.221502i	$0.928904\pi$
$758$	4.57270	−	7.45028i	0.166088	−	0.270606i
$759$	5.71407	−	9.89705i	0.207407	−	0.359240i
$760$	46.9530	−	16.1782i	1.70316	−	0.586845i
$761$	−25.3417	−	43.8932i	−0.918637	−	1.59113i	−0.801487	−	0.598013i	$-0.795957\pi$
$761$	−25.3417	−	43.8932i	−0.918637	−	1.59113i	−0.117151	−	0.993114i	$-0.537376\pi$
$762$	−6.25166	−	11.5333i	−0.226474	−	0.417808i
$763$	−31.6876	−	31.0970i	−1.14717	−	1.12579i
$764$	−3.78490	−	2.46547i	−0.136933	−	0.0891974i
$765$	6.48207	+	8.11064i	0.234360	+	0.293241i
$766$	−8.05172	+	7.63011i	−0.290920	+	0.275687i
$767$	11.0313	+	41.1692i	0.398316	+	1.48653i
$768$	13.4672	−	8.63910i	0.485956	−	0.311737i
$769$		−	31.8160i		−	1.14731i	−0.819095	−	0.573657i	$-0.805524\pi$
$769$		−	31.8160i		−	1.14731i	0.819095	−	0.573657i	$-0.194476\pi$
$770$	20.7596	−	2.78136i	0.748124	−	0.100233i
$771$	1.86907			0.0673128
$772$	−24.8265	+	22.2912i	−0.893526	+	0.802277i
$773$	1.01572	−	0.272161i	0.0365329	−	0.00978897i	−0.240506	−	0.970648i	$-0.577313\pi$
$773$	1.01572	−	0.272161i	0.0365329	−	0.00978897i	0.277039	+	0.960859i	$0.410647\pi$
$774$	0.163131	−	0.154589i	0.00586363	−	0.00555660i
$775$	7.70336	+	7.11739i	0.276713	+	0.255664i
$776$	3.70700	−	3.15266i	0.133073	−	0.113174i
$777$	−21.0731	−	5.43458i	−0.755993	−	0.194964i
$778$	18.9185	−	10.2548i	0.678260	−	0.367652i
$779$	−6.10669	+	3.52570i	−0.218795	+	0.126321i
$780$	3.02120	−	18.1552i	0.108176	−	0.650060i
$781$	−26.0566	−	15.0438i	−0.932379	−	0.538309i
$782$	15.6805	−	25.5482i	0.560735	−	0.913603i
$783$	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
$787$	8.55647	−	2.29270i	0.305005	−	0.0817259i	−0.103070	−	0.994674i	$-0.532867\pi$
$787$	8.55647	−	2.29270i	0.305005	−	0.0817259i	0.408076	+	0.912948i	$0.366200\pi$
$788$	44.9855	+	14.6862i	1.60254	+	0.523174i
$789$	−11.8882	−	20.5909i	−0.423229	−	0.733055i
$790$	−22.3447	−	3.10375i	−0.794989	−	0.110427i
$791$	6.95574	+	11.7902i	0.247318	+	0.419210i
$792$	−7.05772	−	0.570340i	−0.250785	−	0.0202661i
$793$	28.2830	+	7.57842i	1.00436	+	0.269118i
$794$	−24.9095	−	26.2858i	−0.884004	−	0.932850i
$795$	−2.05893	+	0.900899i	−0.0730229	+	0.0319516i
$796$	34.6964	+	1.86697i	1.22978	+	0.0661731i
$797$	15.8496	−	15.8496i	0.561423	−	0.561423i	−0.368289	−	0.929711i	$-0.620056\pi$
$797$	15.8496	−	15.8496i	0.561423	−	0.561423i	0.929711	+	0.368289i	$0.120056\pi$
$798$	−29.3760	−	0.513292i	−1.03990	−	0.0181703i
$799$	−31.0678			−1.09910
$800$	−27.8911	+	4.69940i	−0.986101	+	0.166149i
$801$	1.67194	−	2.89589i	0.0590752	−	0.102321i
$802$	−0.277768	+	10.3317i	−0.00980833	+	0.364825i
$803$	−18.5605	−	4.97326i	−0.654985	−	0.175503i
$804$	13.2557	−	20.3498i	0.467494	−	0.717681i
$805$	−15.8090	+	21.8964i	−0.557195	+	0.771747i
$806$	3.47553	−	11.7032i	0.122420	−	0.412227i
$807$	20.8615	+	5.58983i	0.734360	+	0.196771i
$808$	−1.74719	+	2.53080i	−0.0614659	+	0.0890332i
$809$	25.4348	+	14.6848i	0.894241	+	0.516290i	0.875327	−	0.483531i	$-0.160646\pi$
$809$	25.4348	+	14.6848i	0.894241	+	0.516290i	0.0189137	+	0.999821i	$0.493979\pi$
$810$	1.18932	+	2.93011i	0.0417884	+	0.102953i
$811$	−32.8020			−1.15184			−0.575918	−	0.817508i	$-0.695355\pi$
$811$	−32.8020			−1.15184			−0.575918	+	0.817508i	$0.695355\pi$
$812$	22.9613	−	5.07313i	0.805783	−	0.178032i
$813$	15.5792	+	15.5792i	0.546385	+	0.546385i
$814$	28.3213	−	6.77843i	0.992662	−	0.237584i
$815$	−19.9167	+	50.9052i	−0.697651	+	1.78313i
$816$	−18.4658	−	1.99302i	−0.646434	−	0.0697698i
$817$	−0.322971	+	1.20534i	−0.0112993	+	0.0421696i
$818$	−8.23869	−	15.1991i	−0.288059	−	0.531424i
$819$	−5.35529	+	9.48048i	−0.187129	+	0.331275i
$820$	3.76041	−	1.40985i	0.131319	−	0.0492342i
$821$	−18.7866	+	10.8465i	−0.655657	+	0.378544i	−0.790620	−	0.612307i	$-0.790242\pi$
$821$	−18.7866	+	10.8465i	−0.655657	+	0.378544i	0.134963	+	0.990851i	$0.456908\pi$
$822$	−0.182208	+	6.77733i	−0.00635525	+	0.236386i
$823$	−1.13033	+	0.302870i	−0.0394007	+	0.0105574i	−0.278466	−	0.960446i	$-0.589826\pi$
$823$	−1.13033	+	0.302870i	−0.0394007	+	0.0105574i	0.239065	+	0.971004i	$0.423159\pi$
$824$	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	$0.823518\pi$
$828$	6.79347	−	6.09970i	0.236089	−	0.211979i
$829$	12.3629	−	21.4132i	0.429382	−	0.743711i	−0.567437	−	0.823417i	$-0.692065\pi$
$829$	12.3629	−	21.4132i	0.429382	−	0.743711i	0.996818	+	0.0797060i	$0.0253982\pi$
$830$	1.71417	+	13.7778i	0.0594996	+	0.478234i
$831$	23.3553	−	13.4842i	0.810186	−	0.467761i
$832$	19.2402	+	26.7166i	0.667034	+	0.926233i
$833$	−31.5481	−	7.82023i	−1.09308	−	0.270955i
$834$	−28.3903	−	8.43116i	−0.983075	−	0.291947i
$835$	−16.5365	−	20.6912i	−0.572271	−	0.716049i
$836$	35.0548	−	17.7996i	1.21239	−	0.615614i
$837$	0.542901	+	2.02613i	0.0187654	+	0.0700334i
$838$	13.4168	−	21.8599i	0.463475	−	0.755137i
$839$	10.4974			0.362411			0.181206	−	0.983445i	$-0.442000\pi$
$839$	10.4974			0.362411			0.181206	+	0.983445i	$0.442000\pi$
$840$	16.4557	+	3.03475i	0.567776	+	0.104709i
$841$	−9.25153			−0.319018
$842$	25.9984	−	42.3591i	0.895964	−	1.45979i
$843$	−2.56539	−	9.57415i	−0.0883566	−	0.329751i
$844$	9.94315	+	19.5821i	0.342257	+	0.674044i
$845$	8.74897	+	0.976399i	0.300974	+	0.0335891i
$846$	−9.07085	−	2.69380i	−0.311862	−	0.0926149i
$847$	−12.0644	+	3.35460i	−0.414538	+	0.115265i
$848$	1.45122	−	3.74921i	0.0498352	−	0.128749i
$849$	−13.1882	+	7.61421i	−0.452618	+	0.261319i
$850$	28.6393	+	16.0558i	0.982320	+	0.550709i
$851$	−18.7747	+	32.5188i	−0.643590	+	1.11473i
$852$	−16.0591	−	17.8856i	−0.550175	−	0.612751i
$853$	−15.0268	−	15.0268i	−0.514506	−	0.514506i	0.401398	−	0.915904i	$-0.368525\pi$
$853$	−15.0268	−	15.0268i	−0.514506	−	0.514506i	−0.915904	+	0.401398i	$0.868525\pi$
$854$	−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
$857$	−49.2244	+	13.1896i	−1.68147	+	0.450549i	−0.968167	−	0.250304i	$-0.919470\pi$
$857$	−49.2244	+	13.1896i	−1.68147	+	0.450549i	−0.713306	+	0.700853i	$0.752803\pi$
$858$	0.391578	−	14.5649i	0.0133683	−	0.497239i
$859$	43.0456	−	24.8524i	1.46870	−	0.847953i	0.469314	−	0.883031i	$-0.344501\pi$
$859$	43.0456	−	24.8524i	1.46870	−	0.847953i	0.999385	+	0.0350780i	$0.0111680\pi$
$860$	0.294136	−	0.646978i	0.0100300	−	0.0220618i
$861$	−2.37580	+	0.0223501i	−0.0809671	+	0.000761689i
$862$	6.68947	+	12.3410i	0.227844	+	0.420337i
$863$	−4.08534	+	15.2467i	−0.139067	+	0.519004i	0.860881	+	0.508806i	$0.169913\pi$
$863$	−4.08534	+	15.2467i	−0.139067	+	0.519004i	−0.999948	+	0.0101982i	$0.996754\pi$
$864$	−5.21866	−	2.18303i	−0.177542	−	0.0742680i
$865$	−42.8412	−	16.7616i	−1.45664	−	0.569913i
$866$	−34.4064	+	8.23484i	−1.16918	+	0.279831i
$867$	3.22438	+	3.22438i	0.109506	+	0.109506i
$868$	10.5834	+	3.34527i	0.359223	+	0.113546i
$869$	−17.8590			−0.605825
$870$	12.9446	+	5.47013i	0.438863	+	0.185455i
$871$	43.2794	+	24.9873i	1.46646	+	0.846664i
$872$	39.0589	+	26.9651i	1.32270	+	0.913155i
$873$	−1.66188	−	0.445299i	−0.0562461	−	0.0150711i
$874$	−14.4317	+	48.5958i	−0.488158	+	1.64378i
$875$	−24.6482	−	16.3544i	−0.833261	−	0.552880i
$876$	−12.8629	−	8.37884i	−0.434597	−	0.283095i
$877$	36.4571	+	9.76865i	1.23107	+	0.329864i	0.814996	−	0.579467i	$-0.196739\pi$
$877$	36.4571	+	9.76865i	1.23107	+	0.329864i	0.416073	+	0.909331i	$0.363406\pi$
$878$	−0.678271	+	25.2286i	−0.0228905	+	0.851424i
$879$	−5.86981	+	10.1668i	−0.197984	+	0.342918i
$880$	−21.3582	+	6.72272i	−0.719984	+	0.226623i
$881$	4.63113			0.156027			0.0780134	−	0.996952i	$-0.475142\pi$
$881$	4.63113			0.156027			0.0780134	+	0.996952i	$0.475142\pi$
$882$	−8.53302	−	5.01872i	−0.287322	−	0.168989i
$883$	−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
$885$	−21.5659	−	8.43766i	−0.724929	−	0.283629i
$886$	4.48956	+	4.73763i	0.150830	+	0.159164i
$887$	19.3624	+	5.18814i	0.650126	+	0.174201i	0.568786	−	0.822486i	$-0.307413\pi$
$887$	19.3624	+	5.18814i	0.650126	+	0.174201i	0.0813404	+	0.996686i	$0.474080\pi$
$888$	23.1896	+	1.87397i	0.778192	+	0.0628863i
$889$	12.4708	+	21.1384i	0.418259	+	0.708959i
$890$	1.45484	−	10.4737i	0.0487662	−	0.351080i
$891$	1.25171	+	2.16802i	0.0419338	+	0.0726315i
$892$	−10.7642	+	32.9719i	−0.360411	+	1.10398i
$893$	50.7487	−	13.5981i	1.69824	−	0.455042i
$894$	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
$898$	−3.71863	+	6.05875i	−0.124092	+	0.202183i
$899$	8.07275	+	4.66081i	0.269241	+	0.155447i
$900$	6.96966	+	7.17105i	0.232322	+	0.239035i
$901$	−4.04158	+	2.33341i	−0.134644	+	0.0777370i
$902$	2.79506	−	1.51507i	0.0930654	−	0.0504462i
$903$	−0.294498	+	0.300091i	−0.00980028	+	0.00998642i
$904$	−9.48082	−	11.1478i	−0.315327	−	0.370772i
$905$	4.25855	+	0.475260i	0.141559	+	0.0157982i
$906$	−5.86406	+	5.55700i	−0.194820	+	0.184619i
$907$	−6.15054	+	1.64803i	−0.204225	+	0.0547220i	−0.359481	−	0.933152i	$-0.617046\pi$
$907$	−6.15054	+	1.64803i	−0.204225	+	0.0547220i	0.155256	+	0.987874i	$0.450380\pi$
$908$	38.1588	+	42.4989i	1.26635	+	1.41038i
$909$	1.08729			0.0360632
$910$	−4.41625	+	34.1480i	−0.146397	+	1.13199i
$911$		−	30.7362i		−	1.01833i	−0.860668	−	0.509167i	$-0.829953\pi$
$911$		−	30.7362i		−	1.01833i	0.860668	−	0.509167i	$-0.170047\pi$
$912$	31.0359	−	4.82675i	1.02770	−	0.159830i
$913$	2.84475	+	10.6167i	0.0941474	+	0.351363i
$914$	34.4796	−	32.6742i	1.14048	−	1.08077i
$915$	−12.4279	+	9.93241i	−0.410852	+	0.328355i
$916$	−8.91404	+	13.6845i	−0.294528	+	0.452149i
$917$	−19.6505	+	5.46397i	−0.648917	+	0.180436i
$918$	3.12927	+	5.77301i	0.103281	+	0.190538i
$919$	3.29202	+	5.70195i	0.108594	+	0.188090i	0.915201	−	0.402998i	$-0.132032\pi$
$919$	3.29202	+	5.70195i	0.108594	+	0.188090i	−0.806607	+	0.591088i	$0.798699\pi$
$920$	12.6511	−	25.9524i	0.417094	−	0.855624i
$921$	3.83856	−	6.64858i	0.126485	−	0.219078i
$922$	0.290052	−	0.472580i	0.00955235	−	0.0155636i
$923$	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
$927$	−1.93754	−	7.23099i	−0.0636371	−	0.237497i
$928$	−23.2585	+	9.53896i	−0.763499	+	0.313132i
$929$	7.49183	−	4.32541i	0.245799	−	0.141912i	−0.372040	−	0.928217i	$-0.621342\pi$
$929$	7.49183	−	4.32541i	0.245799	−	0.141912i	0.617839	+	0.786305i	$0.288008\pi$
$930$	4.00047	+	5.29110i	0.131181	+	0.173502i
$931$	54.9561	−	1.03408i	1.80111	−	0.0338905i
$932$	0.750139	+	3.55353i	0.0245716	+	0.116400i
$933$	3.11089	−	11.6100i	0.101846	−	0.380094i
$934$	27.7257	−	26.2739i	0.907212	−	0.859709i
$935$	24.2054	+	9.47039i	0.791602	+	0.309715i
$936$	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	$0.774945\pi$
$938$	−23.4018	+	38.9455i	−0.764095	+	1.27162i
$939$		−	18.1665i		−	0.592842i
$940$	−29.7824	+	2.89500i	−0.971393	+	0.0944245i
$941$	10.1441	+	5.85669i	0.330688	+	0.190923i	0.656146	−	0.754634i	$-0.272185\pi$
$941$	10.1441	+	5.85669i	0.330688	+	0.190923i	−0.325459	+	0.945556i	$0.605519\pi$
$942$	19.9207	+	0.535567i	0.649051	+	0.0174497i
$943$	−1.06101	+	3.95974i	−0.0345512	+	0.128947i
$944$	37.8913	−	16.7436i	1.23326	−	0.544957i
$945$	−2.42241	−	5.39740i	−0.0788010	−	0.175577i
$946$	0.160171	−	0.539346i	0.00520762	−	0.0175356i
$947$	−0.594235	+	2.21772i	−0.0193101	+	0.0720661i	−0.974909	−	0.222606i	$-0.928544\pi$
$947$	−0.594235	+	2.21772i	−0.0193101	+	0.0720661i	0.955598	+	0.294672i	$0.0952104\pi$
$948$	−13.5632	−	4.42792i	−0.440513	−	0.143812i
$949$	15.7943	−	27.3565i	0.512704	−	0.888030i
$950$	−53.8092	−	13.6917i	−1.74580	−	0.444218i
$951$		−	29.5553i		−	0.958398i
$952$	34.6589	+	2.47289i	1.12330	+	0.0801467i
$953$	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
$955$	2.02445	+	4.62672i	0.0655096	+	0.149717i
$956$	6.73414	+	13.2623i	0.217798	+	0.428933i
$957$	10.7459	+	2.87936i	0.347366	+	0.0930765i
$958$	40.4254	−	21.9127i	1.30609	−	0.707966i
$959$	−0.119316	−	12.6832i	−0.00385292	−	0.409563i
$960$	−17.8875	−	0.189853i	−0.577318	−	0.00612749i
$961$	−13.3000	−	23.0363i	−0.429033	−	0.743107i
$962$	−1.28661	+	47.8561i	−0.0414820	+	1.54294i
$963$	3.96775	+	14.8079i	0.127859	+	0.477176i
$964$	−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	−0.740401	−	0.672166i	$-0.765364\pi$
$967$	−2.12188	+	2.12188i	−0.0682349	+	0.0682349i	0.672166	+	0.740401i	$0.265364\pi$
$968$	12.0947	−	5.73778i	0.388738	−	0.184419i
$969$	−31.5754	−	18.2301i	−1.01435	−	0.585634i
$970$	−5.39909	+	0.671729i	−0.173354	+	0.0215679i
$971$	25.3451	+	43.8989i	0.813362	+	1.40878i	0.910498	+	0.413513i	$0.135698\pi$
$971$	25.3451	+	43.8989i	0.813362	+	1.40878i	−0.0971368	+	0.995271i	$0.530968\pi$
$972$	0.413090	+	1.95687i	0.0132499	+	0.0627668i
$973$	53.6506	+	13.8361i	1.71996	+	0.443563i
$974$	−2.29791	+	7.73776i	−0.0736298	+	0.247934i
$975$	−13.9641	+	15.1138i	−0.447210	+	0.484029i
$976$	3.05389	−	28.2950i	0.0977526	−	0.905701i
$977$	−42.8061	+	11.4699i	−1.36949	+	0.366954i	−0.867292	−	0.497799i	$-0.834142\pi$
$977$	−42.8061	+	11.4699i	−1.36949	+	0.366954i	−0.502197	+	0.864753i	$0.667475\pi$
$978$	−18.0843	+	29.4646i	−0.578271	+	0.942175i
$979$		−	8.37113i		−	0.267543i
$980$	−30.9715	−	4.55692i	−0.989349	−	0.145565i
$981$		−	16.7806i		−	0.535764i
$982$	29.9499	+	18.3821i	0.955739	+	0.586596i
$983$	11.6732	−	3.12783i	0.372318	−	0.0997622i	−0.0678081	−	0.997698i	$-0.521601\pi$
$983$	11.6732	−	3.12783i	0.372318	−	0.0997622i	0.440126	+	0.897936i	$0.354934\pi$
$984$	2.49838	−	0.457634i	0.0796456	−	0.0145889i
$985$	−33.0312	−	41.3300i	−1.05246	−	1.31688i
$986$	27.9739	+	8.30750i	0.890870	+	0.264565i
$987$	17.1417	+	4.42070i	0.545625	+	0.140712i
$988$	13.3492	+	63.2375i	0.424696	+	2.01185i
$989$	0.362731	+	0.628268i	0.0115342	+	0.0199778i
$990$	6.24610	+	4.86386i	0.198514	+	0.154583i
$991$	−3.47494	−	2.00626i	−0.110385	−	0.0637309i	0.443791	−	0.896130i	$-0.353633\pi$
$991$	−3.47494	−	2.00626i	−0.110385	−	0.0637309i	−0.554176	+	0.832399i	$0.686967\pi$
$992$	−11.7589	−	1.58989i	−0.373344	−	0.0504790i
$993$	−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
$997$	6.49294	+	24.2320i	0.205633	+	0.767435i	0.989256	+	0.146197i	$0.0467032\pi$
$997$	6.49294	+	24.2320i	0.205633	+	0.767435i	−0.783622	+	0.621238i	$0.786630\pi$
$998$	−8.60135	−	0.231247i	−0.272271	−	0.00732001i
$999$	−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.67.16	✓	384
5.3	odd	4	inner	840.2.dj.a.403.32	yes	384
7.2	even	3	inner	840.2.dj.a.667.49	yes	384
8.3	odd	2	inner	840.2.dj.a.67.95	yes	384
35.23	odd	12	inner	840.2.dj.a.163.95	yes	384
40.3	even	4	inner	840.2.dj.a.403.49	yes	384
56.51	odd	6	inner	840.2.dj.a.667.32	yes	384
280.163	even	12	inner	840.2.dj.a.163.16	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.16	✓	384	1.1	even	1	trivial
840.2.dj.a.67.95	yes	384	8.3	odd	2	inner
840.2.dj.a.163.16	yes	384	280.163	even	12	inner
840.2.dj.a.163.95	yes	384	35.23	odd	12	inner
840.2.dj.a.403.32	yes	384	5.3	odd	4	inner
840.2.dj.a.403.49	yes	384	40.3	even	4	inner
840.2.dj.a.667.32	yes	384	56.51	odd	6	inner
840.2.dj.a.667.49	yes	384	7.2	even	3	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+(-1.20530 - 0.739767i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.905490 + 1.78328i) q^{4} +(0.248009 - 2.22227i) q^{5} +(0.402606 - 1.35569i) q^{6} +(-0.660700 + 2.56193i) q^{7} +(0.227825 - 2.81924i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.94289 + 2.49503i) q^{10} +(-1.25171 + 2.16802i) q^{11} +(-1.48816 + 1.33618i) 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} +(4.48505 - 1.20177i) q^{17} +(1.41370 + 0.0380074i) q^{18} +(-6.80025 + 3.92613i) q^{19} +(4.18750 - 1.56998i) q^{20} +(-2.64563 + 0.0248885i) q^{21} +(3.11251 - 1.68714i) q^{22} +(-1.18151 + 4.40947i) q^{23} +(2.78214 - 0.509610i) q^{24} +(-4.87698 - 1.10229i) q^{25} +(1.35473 + 5.66027i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-5.16689 + 1.14159i) q^{28} -4.44393 q^{29} +(-2.91287 - 1.23092i) q^{30} +(-1.81658 - 1.04880i) q^{31} +(5.23378 - 2.14652i) q^{32} +(-2.41811 - 0.647932i) q^{33} +(-6.29486 - 1.86941i) q^{34} +(5.52944 + 2.10364i) q^{35} +(-1.67582 - 1.09162i) q^{36} +(7.94521 + 2.12891i) q^{37} +(11.1008 + 0.298444i) q^{38} +(2.05773 - 3.56409i) q^{39} +(-6.20861 - 1.20548i) q^{40} +0.898009 q^{41} +(3.20719 + 1.92715i) q^{42} +(0.112372 - 0.112372i) q^{43} +(-4.99960 - 0.269023i) q^{44} +(0.896354 + 2.04855i) q^{45} +(4.68605 - 4.44068i) q^{46} +(-6.46294 - 1.73174i) q^{47} +(-3.73030 - 1.44390i) q^{48} +(-6.12695 - 3.38533i) q^{49} +(5.06279 + 4.93641i) q^{50} +(2.32164 + 4.02119i) q^{51} +(2.55442 - 7.82449i) q^{52} +(-0.970823 + 0.260131i) 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} +(5.35626 + 3.28747i) q^{58} +(-8.96896 - 5.17823i) q^{59} +(2.60029 + 3.63848i) q^{60} +(-6.16163 + 3.55742i) q^{61} +(1.41365 + 2.60797i) q^{62} +(-0.708781 - 2.54904i) q^{63} +(-7.89619 - 1.28458i) q^{64} +(-7.18868 + 5.74523i) q^{65} +(2.43523 + 2.56979i) q^{66} +(-11.7294 + 3.14289i) q^{67} +(6.20426 + 6.90992i) q^{68} -4.56502 q^{69} +(-5.10843 - 6.62601i) q^{70} +12.0186i q^{71} +(1.21232 + 2.55544i) q^{72} +(1.98659 + 7.41406i) q^{73} +(-8.00145 - 8.44358i) q^{74} +(-0.197529 - 4.99610i) q^{75} +(-13.1589 - 8.57168i) q^{76} +(-4.72731 - 4.63920i) q^{77} +(-5.11677 + 2.77355i) q^{78} +(3.56693 + 6.17810i) q^{79} +(6.59145 + 6.04589i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-1.08237 - 0.664317i) 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} +(-1.15017 - 4.29250i) q^{87} +(5.82700 + 4.02279i) q^{88} +(-2.89589 + 1.67194i) q^{89} +(0.435074 - 3.13221i) q^{90} +(9.37806 - 5.53270i) q^{91} +(-8.93316 + 1.88576i) q^{92} +(0.542901 - 2.02613i) q^{93} +(6.50869 + 6.86833i) q^{94} +(7.03840 + 16.0857i) q^{95} +(3.42798 + 4.49989i) q^{96} +(1.21658 + 1.21658i) q^{97} +(4.88045 + 8.61285i) 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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