LMFDB - Embedded newform 680.2.co.a.99.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (of order $16$, degree $8$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			99.17
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20473 + 0.740697i) q^{2} +(1.63264 + 0.324753i) q^{3} +(0.902737 - 1.78468i) q^{4} +(2.22079 + 0.260961i) q^{5} +(-2.20744 + 0.818055i) q^{6} +(-0.693159 - 0.463154i) q^{7} +(0.234351 + 2.81870i) q^{8} +(-0.211574 - 0.0876370i) q^{9} +(-2.86874 + 1.33054i) q^{10} +(5.70222 - 1.13424i) q^{11} +(2.05343 - 2.62057i) q^{12} +(-0.791428 - 0.791428i) q^{13} +(1.17812 + 0.0445539i) q^{14} +(3.54101 + 1.14726i) q^{15} +(-2.37013 - 3.22218i) q^{16} +(-1.86239 + 3.67852i) q^{17} +(0.319802 - 0.0511338i) q^{18} +(1.74054 - 0.720955i) q^{19} +(2.47052 - 3.72781i) q^{20} +(-0.981272 - 0.981272i) q^{21} +(-6.02949 + 5.59007i) q^{22} +(0.716030 + 3.59973i) q^{23} +(-0.532770 + 4.67804i) q^{24} +(4.86380 + 1.15908i) q^{25} +(1.53966 + 0.367247i) q^{26} +(-4.46923 - 2.98625i) q^{27} +(-1.45232 + 0.818958i) q^{28} +(7.13568 - 4.76791i) q^{29} +(-5.11573 + 1.24067i) q^{30} +(-0.420894 + 2.11598i) q^{31} +(5.24202 + 2.12631i) q^{32} +9.67805 q^{33} +(-0.480995 - 5.81108i) q^{34} +(-1.41849 - 1.20945i) q^{35} +(-0.347400 + 0.298478i) q^{36} +(0.424529 - 2.13425i) q^{37} +(-1.56287 + 2.15777i) q^{38} +(-1.03510 - 1.54914i) q^{39} +(-0.215126 + 6.32090i) q^{40} +(-3.08795 - 2.06330i) q^{41} +(1.90899 + 0.455340i) q^{42} +(-1.72320 + 4.16017i) q^{43} +(3.12335 - 11.2005i) q^{44} +(-0.446992 - 0.249836i) q^{45} +(-3.52893 - 3.80633i) q^{46} +(-7.04908 - 7.04908i) q^{47} +(-2.82317 - 6.03039i) q^{48} +(-2.41283 - 5.82508i) q^{49} +(-6.71808 + 2.20623i) q^{50} +(-4.23523 + 5.40090i) q^{51} +(-2.12689 + 0.697990i) q^{52} +(8.10860 - 3.35869i) q^{53} +(7.59611 + 0.287267i) q^{54} +(12.9594 - 1.03086i) q^{55} +(1.14305 - 2.06235i) q^{56} +(3.07582 - 0.611818i) q^{57} +(-5.06498 + 11.0294i) q^{58} +(-4.00568 + 9.67056i) q^{59} +(5.24409 - 5.28388i) q^{60} +(8.90360 + 5.94920i) q^{61} +(-1.06023 - 2.86093i) q^{62} +(0.106065 + 0.158738i) q^{63} +(-7.89016 + 1.32113i) q^{64} +(-1.55106 - 1.96412i) q^{65} +(-11.6594 + 7.16850i) q^{66} -9.22896 q^{67} +(4.88372 + 6.64450i) q^{68} +6.10961i q^{69} +(2.60474 + 0.406389i) q^{70} +(2.73634 + 0.544291i) q^{71} +(0.197440 - 0.616903i) q^{72} +(9.15520 + 13.7017i) q^{73} +(1.06939 + 2.88564i) q^{74} +(7.56444 + 3.47189i) q^{75} +(0.284579 - 3.75713i) q^{76} +(-4.47788 - 1.85480i) q^{77} +(2.39446 + 1.09959i) q^{78} +(0.721559 + 3.62752i) q^{79} +(-4.42270 - 7.77430i) q^{80} +(-5.84108 - 5.84108i) q^{81} +(5.24841 + 0.198482i) q^{82} +(1.61962 - 0.670870i) q^{83} +(-2.63708 + 0.865421i) q^{84} +(-5.09592 + 7.68320i) q^{85} +(-1.00544 - 6.28824i) q^{86} +(13.1984 - 5.46697i) q^{87} +(4.53341 + 15.8070i) q^{88} +(-8.32848 + 8.32848i) q^{89} +(0.723556 - 0.0301016i) q^{90} +(0.182032 + 0.915138i) q^{91} +(7.07073 + 1.97173i) q^{92} +(-1.37434 + 3.31795i) q^{93} +(13.7135 + 3.27099i) q^{94} +(4.05351 - 1.14688i) q^{95} +(7.86784 + 5.17387i) q^{96} +(-1.19945 + 0.801448i) q^{97} +(7.22141 + 5.23046i) q^{98} +(-1.30585 - 0.259749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

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 $

$2$	−1.20473	+	0.740697i	−0.851871	+	0.523752i
$2$	−1.20473	+	0.740697i	−0.851871	+	0.523752i
$3$	1.63264	+	0.324753i	0.942608	+	0.187496i	0.642393	−	0.766375i	$-0.277942\pi$
$3$	1.63264	+	0.324753i	0.942608	+	0.187496i	0.300215	+	0.953872i	$0.402942\pi$
$4$	0.902737	−	1.78468i	0.451368	−	0.892338i
$5$	2.22079	+	0.260961i	0.993167	+	0.116705i
$5$	2.22079	+	0.260961i	0.993167	+	0.116705i
$6$	−2.20744	+	0.818055i	−0.901182	+	0.333970i
$7$	−0.693159	−	0.463154i	−0.261990	−	0.175056i	0.417637	−	0.908614i	$-0.362858\pi$
$7$	−0.693159	−	0.463154i	−0.261990	−	0.175056i	−0.679627	+	0.733558i	$0.737858\pi$
$8$	0.234351	+	2.81870i	0.0828556	+	0.996562i
$9$	−0.211574	−	0.0876370i	−0.0705248	−	0.0292123i
$10$	−2.86874	+	1.33054i	−0.907174	+	0.420755i
$11$	5.70222	−	1.13424i	1.71928	−	0.341987i	0.765720	−	0.643175i	$-0.222383\pi$
$11$	5.70222	−	1.13424i	1.71928	−	0.341987i	0.953565	+	0.301188i	$0.0973831\pi$
$12$	2.05343	−	2.62057i	0.592774	−	0.756495i
$13$	−0.791428	−	0.791428i	−0.219503	−	0.219503i	0.588786	−	0.808289i	$-0.299606\pi$
$13$	−0.791428	−	0.791428i	−0.219503	−	0.219503i	−0.808289	+	0.588786i	$0.799606\pi$
$14$	1.17812	+	0.0445539i	0.314867	+	0.0119075i
$15$	3.54101	+	1.14726i	0.914285	+	0.296222i
$16$	−2.37013	−	3.22218i	−0.592533	−	0.805546i
$17$	−1.86239	+	3.67852i	−0.451696	+	0.892172i
$17$	−1.86239	+	3.67852i	−0.451696	+	0.892172i
$18$	0.319802	−	0.0511338i	0.0753780	−	0.0120523i
$19$	1.74054	−	0.720955i	0.399307	−	0.165398i	−0.173987	−	0.984748i	$-0.555665\pi$
$19$	1.74054	−	0.720955i	0.399307	−	0.165398i	0.573294	+	0.819349i	$0.305665\pi$
$20$	2.47052	−	3.72781i	0.552424	−	0.833563i
$21$	−0.981272	−	0.981272i	−0.214131	−	0.214131i
$22$	−6.02949	+	5.59007i	−1.28549	+	1.19181i
$23$	0.716030	+	3.59973i	0.149303	+	0.750595i	0.980792	+	0.195055i	$0.0624885\pi$
$23$	0.716030	+	3.59973i	0.149303	+	0.750595i	−0.831490	+	0.555540i	$0.812512\pi$
$24$	−0.532770	+	4.67804i	−0.108751	+	0.954902i
$25$	4.86380	+	1.15908i	0.972760	+	0.231815i
$26$	1.53966	+	0.367247i	0.301953	+	0.0720230i
$27$	−4.46923	−	2.98625i	−0.860104	−	0.574703i
$28$	−1.45232	+	0.818958i	−0.274463	+	0.154768i
$29$	7.13568	−	4.76791i	1.32506	−	0.885379i	0.326847	−	0.945077i	$-0.394014\pi$
$29$	7.13568	−	4.76791i	1.32506	−	0.885379i	0.998216	+	0.0596986i	$0.0190140\pi$
$30$	−5.11573	+	1.24067i	−0.934000	+	0.226515i
$31$	−0.420894	+	2.11598i	−0.0755947	+	0.380040i	−0.999999	−	0.00137362i	$-0.999563\pi$
$31$	−0.420894	+	2.11598i	−0.0755947	+	0.380040i	0.924404	+	0.381414i	$0.124563\pi$
$32$	5.24202	+	2.12631i	0.926668	+	0.375881i
$33$	9.67805			1.68473
$34$	−0.480995	−	5.81108i	−0.0824900	−	0.996592i
$35$	−1.41849	−	1.20945i	−0.239769	−	0.204435i
$36$	−0.347400	+	0.298478i	−0.0578999	+	0.0497464i
$37$	0.424529	−	2.13425i	0.0697921	−	0.350869i	−0.930072	−	0.367378i	$-0.880255\pi$
$37$	0.424529	−	2.13425i	0.0697921	−	0.350869i	0.999864	+	0.0165096i	$0.00525542\pi$
$38$	−1.56287	+	2.15777i	−0.253531	+	0.350036i
$39$	−1.03510	−	1.54914i	−0.165749	−	0.248061i
$40$	−0.215126	+	6.32090i	−0.0340144	+	0.999421i
$41$	−3.08795	−	2.06330i	−0.482256	−	0.322233i	0.290567	−	0.956855i	$-0.406156\pi$
$41$	−3.08795	−	2.06330i	−0.482256	−	0.322233i	−0.772823	+	0.634621i	$0.781156\pi$
$42$	1.90899	+	0.455340i	0.294564	+	0.0702606i
$43$	−1.72320	+	4.16017i	−0.262785	+	0.634420i	−0.999109	−	0.0422097i	$-0.986560\pi$
$43$	−1.72320	+	4.16017i	−0.262785	+	0.634420i	0.736323	+	0.676630i	$0.236560\pi$
$44$	3.12335	−	11.2005i	0.470863	−	1.68854i
$45$	−0.446992	−	0.249836i	−0.0666336	−	0.0372433i
$46$	−3.52893	−	3.80633i	−0.520312	−	0.561213i
$47$	−7.04908	−	7.04908i	−1.02821	−	1.02821i	−0.999590	−	0.0286244i	$-0.990887\pi$
$47$	−7.04908	−	7.04908i	−1.02821	−	1.02821i	−0.0286244	−	0.999590i	$-0.509113\pi$
$48$	−2.82317	−	6.03039i	−0.407489	−	0.870412i
$49$	−2.41283	−	5.82508i	−0.344689	−	0.832154i
$50$	−6.71808	+	2.20623i	−0.950080	+	0.312008i
$51$	−4.23523	+	5.40090i	−0.593051	+	0.756277i
$52$	−2.12689	+	0.697990i	−0.294947	+	0.0967939i
$53$	8.10860	−	3.35869i	1.11380	−	0.461352i	0.251557	−	0.967843i	$-0.419058\pi$
$53$	8.10860	−	3.35869i	1.11380	−	0.461352i	0.862245	+	0.506491i	$0.169058\pi$
$54$	7.59611	+	0.287267i	1.03370	+	0.0390921i
$55$	12.9594	−	1.03086i	1.74745	−	0.139001i
$56$	1.14305	−	2.06235i	0.152747	−	0.275593i
$57$	3.07582	−	0.611818i	0.407402	−	0.0810373i
$58$	−5.06498	+	11.0294i	−0.665064	+	1.44823i
$59$	−4.00568	+	9.67056i	−0.521494	+	1.25900i	0.415480	+	0.909602i	$0.363614\pi$
$59$	−4.00568	+	9.67056i	−0.521494	+	1.25900i	−0.936975	+	0.349397i	$0.886386\pi$
$60$	5.24409	−	5.28388i	0.677010	−	0.682145i
$61$	8.90360	+	5.94920i	1.13999	+	0.761717i	0.974476	−	0.224491i	$-0.0720719\pi$
$61$	8.90360	+	5.94920i	1.13999	+	0.761717i	0.165513	+	0.986208i	$0.447072\pi$
$62$	−1.06023	−	2.86093i	−0.134650	−	0.363338i
$63$	0.106065	+	0.158738i	0.0133630	+	0.0199991i
$64$	−7.89016	+	1.32113i	−0.986270	+	0.165141i
$65$	−1.55106	−	1.96412i	−0.192385	−	0.243620i
$66$	−11.6594	+	7.16850i	−1.43517	+	0.882381i
$67$	−9.22896			−1.12750			−0.563749	−	0.825946i	$-0.690641\pi$
$67$	−9.22896			−1.12750			−0.563749	+	0.825946i	$0.690641\pi$
$68$	4.88372	+	6.64450i	0.592237	+	0.805763i
$69$			6.10961i			0.735511i
$70$	2.60474	+	0.406389i	0.311326	+	0.0485727i
$71$	2.73634	+	0.544291i	0.324743	+	0.0645954i	0.354770	−	0.934954i	$-0.384559\pi$
$71$	2.73634	+	0.544291i	0.324743	+	0.0645954i	−0.0300266	+	0.999549i	$0.509559\pi$
$72$	0.197440	−	0.616903i	0.0232685	−	0.0727027i
$73$	9.15520	+	13.7017i	1.07154	+	1.60367i	0.755780	+	0.654826i	$0.227258\pi$
$73$	9.15520	+	13.7017i	1.07154	+	1.60367i	0.315756	+	0.948840i	$0.397742\pi$
$74$	1.06939	+	2.88564i	0.124314	+	0.335449i
$75$	7.56444	+	3.47189i	0.873467	+	0.400900i
$76$	0.284579	−	3.75713i	0.0326434	−	0.430973i
$77$	−4.47788	−	1.85480i	−0.510301	−	0.211374i
$78$	2.39446	+	1.09959i	0.271119	+	0.124504i
$79$	0.721559	+	3.62752i	0.0811818	+	0.408128i	0.999912	+	0.0132432i	$0.00421558\pi$
$79$	0.721559	+	3.62752i	0.0811818	+	0.408128i	−0.918731	+	0.394885i	$0.870784\pi$
$80$	−4.42270	−	7.77430i	−0.494473	−	0.869193i
$81$	−5.84108	−	5.84108i	−0.649009	−	0.649009i
$82$	5.24841	+	0.198482i	0.579590	+	0.0219187i
$83$	1.61962	−	0.670870i	0.177777	−	0.0736375i	−0.292020	−	0.956412i	$-0.594327\pi$
$83$	1.61962	−	0.670870i	0.177777	−	0.0736375i	0.469796	+	0.882775i	$0.344327\pi$
$84$	−2.63708	+	0.865421i	−0.287729	+	0.0944252i
$85$	−5.09592	+	7.68320i	−0.552730	+	0.833360i
$86$	−1.00544	−	6.28824i	−0.108419	−	0.678078i
$87$	13.1984	−	5.46697i	1.41502	−	0.586121i
$88$	4.53341	+	15.8070i	0.483263	+	1.68504i
$89$	−8.32848	+	8.32848i	−0.882818	+	0.882818i	−0.993820	−	0.111003i	$-0.964594\pi$
$89$	−8.32848	+	8.32848i	−0.882818	+	0.882818i	0.111003	+	0.993820i	$0.464594\pi$
$90$	0.723556	−	0.0301016i	0.0762695	−	0.00317298i
$91$	0.182032	+	0.915138i	0.0190822	+	0.0959325i
$92$	7.07073	+	1.97173i	0.737175	+	0.205567i
$93$	−1.37434	+	3.31795i	−0.142512	+	0.344055i
$94$	13.7135	+	3.27099i	1.41444	+	0.337377i
$95$	4.05351	−	1.14688i	0.415881	−	0.117667i
$96$	7.86784	+	5.17387i	0.803008	+	0.528055i
$97$	−1.19945	+	0.801448i	−0.121786	+	0.0813747i	−0.614971	−	0.788550i	$-0.710832\pi$
$97$	−1.19945	+	0.801448i	−0.121786	+	0.0813747i	0.493185	+	0.869924i	$0.335832\pi$
$98$	7.22141	+	5.23046i	0.729473	+	0.528356i
$99$	−1.30585	−	0.259749i	−0.131242	−	0.0261057i
$100$	6.45931	−	7.63396i	0.645931	−	0.763396i
$101$	−11.0712			−1.10163			−0.550813	−	0.834628i	$-0.685682\pi$
$101$	−11.0712			−1.10163			−0.550813	+	0.834628i	$0.685682\pi$
$102$	1.10187	−	9.64363i	0.109102	−	0.954862i
$103$	−13.8536			−1.36504			−0.682518	−	0.730869i	$-0.739115\pi$
$103$	−13.8536			−1.36504			−0.682518	+	0.730869i	$0.739115\pi$
$104$	2.04533	−	2.41627i	0.200561	−	0.236935i
$105$	−1.92312	−	2.43527i	−0.187678	−	0.237658i
$106$	−7.28088	+	10.0523i	−0.707182	+	0.976368i
$107$	−0.207920	−	0.311175i	−0.0201004	−	0.0300824i	0.821283	−	0.570521i	$-0.193259\pi$
$107$	−0.207920	−	0.311175i	−0.0201004	−	0.0300824i	−0.841384	+	0.540438i	$0.818259\pi$
$108$	−9.36402	+	5.28034i	−0.901053	+	0.508101i
$109$	−0.544704	+	0.815206i	−0.0521731	+	0.0780826i	−0.856639	−	0.515916i	$-0.827452\pi$
$109$	−0.544704	+	0.815206i	−0.0521731	+	0.0780826i	0.804466	+	0.593999i	$0.202452\pi$
$110$	−14.8490	+	10.8409i	−1.41580	+	1.03364i
$111$	1.38621	−	3.34661i	0.131573	−	0.317646i
$112$	0.150511	+	3.33122i	0.0142219	+	0.314771i
$113$	−2.90842	−	14.6216i	−0.273601	−	1.37549i	−0.836050	−	0.548654i	$-0.815141\pi$
$113$	−2.90842	−	14.6216i	−0.273601	−	1.37549i	0.562449	−	0.826832i	$-0.309859\pi$
$114$	−3.25235	+	3.01532i	−0.304610	+	0.282411i
$115$	0.650765	+	8.18109i	0.0606841	+	0.762890i
$116$	−2.06753	−	17.0390i	−0.191965	−	1.58204i
$117$	0.0980875	+	0.236804i	0.00906819	+	0.0218925i
$118$	−2.33720	−	14.6174i	−0.215157	−	1.34564i
$119$	2.99465	−	1.68723i	0.274519	−	0.154668i
$120$	−2.40396	+	10.2499i	−0.219450	+	0.935685i
$121$	21.0661	−	8.72588i	1.91510	−	0.793262i
$122$	−15.1330	−	0.572293i	−1.37007	−	0.0518129i
$123$	−4.37146	−	4.37146i	−0.394161	−	0.394161i
$124$	3.39637	+	2.66133i	0.305003	+	0.238994i
$125$	10.4990	+	3.84332i	0.939059	+	0.343757i
$126$	−0.245356	−	0.112674i	−0.0218581	−	0.0100378i
$127$	0.133794	−	0.323007i	0.0118723	−	0.0286623i	−0.917832	−	0.396969i	$-0.870062\pi$
$127$	0.133794	−	0.323007i	0.0118723	−	0.0286623i	0.929705	+	0.368306i	$0.120062\pi$
$128$	8.52693	−	7.43582i	0.753682	−	0.657240i
$129$	−4.16440	+	6.23247i	−0.366655	+	0.548738i
$130$	3.32343	+	1.21737i	0.291484	+	0.106770i
$131$	−3.99977	−	5.98607i	−0.349461	−	0.523005i	0.614546	−	0.788881i	$-0.289339\pi$
$131$	−3.99977	−	5.98607i	−0.349461	−	0.523005i	−0.964007	+	0.265875i	$0.914339\pi$
$132$	8.73673	−	17.2722i	0.760435	−	1.50335i
$133$	−1.54038	−	0.306402i	−0.133568	−	0.0265684i
$134$	11.1184	−	6.83586i	0.960482	−	0.590529i
$135$	−9.14593	−	7.79811i	−0.787156	−	0.671155i
$136$	−10.8051	−	4.38746i	−0.926530	−	0.376221i
$137$		−	13.9544i		−	1.19220i	−0.802909	−	0.596102i	$-0.796716\pi$
$137$		−	13.9544i		−	1.19220i	0.802909	−	0.596102i	$-0.203284\pi$
$138$	−4.52537	−	7.36041i	−0.385225	−	0.626560i
$139$	−2.45988	+	12.3666i	−0.208644	+	1.04892i	0.724460	+	0.689317i	$0.242089\pi$
$139$	−2.45988	+	12.3666i	−0.208644	+	1.04892i	−0.933104	+	0.359608i	$0.882911\pi$
$140$	−3.43901	+	1.43973i	−0.290649	+	0.121680i
$141$	−9.21944	−	13.7979i	−0.776417	−	1.16199i
$142$	−3.69969	+	1.37107i	−0.310471	+	0.115058i
$143$	−5.41057	−	3.61522i	−0.452454	−	0.302320i
$144$	0.219077	+	0.889443i	0.0182564	+	0.0741202i
$145$	17.0911	−	8.72639i	1.41934	−	0.724687i
$146$	−21.1784	−	9.72562i	−1.75273	−	0.804898i
$147$	−2.04758	−	10.2939i	−0.168881	−	0.849023i
$148$	−3.42571	−	2.68431i	−0.281591	−	0.220649i
$149$	−7.30705	+	7.30705i	−0.598617	+	0.598617i	−0.939944	−	0.341328i	$-0.889123\pi$
$149$	−7.30705	+	7.30705i	−0.598617	+	0.598617i	0.341328	+	0.939944i	$0.389123\pi$
$150$	−11.6847	+	1.42027i	−0.954053	+	0.115965i
$151$	−20.1723	+	8.35563i	−1.64160	+	0.679972i	−0.996458	−	0.0840929i	$-0.973201\pi$
$151$	−20.1723	+	8.35563i	−1.64160	+	0.679972i	−0.645139	+	0.764065i	$0.723201\pi$
$152$	2.44006	+	4.73711i	0.197915	+	0.384230i
$153$	0.716408	−	0.615066i	0.0579182	−	0.0497252i
$154$	6.76846	−	1.08222i	0.545418	−	0.0872080i
$155$	−1.48690	+	4.58930i	−0.119431	+	0.368621i
$156$	−3.69913	+	0.448855i	−0.296168	+	0.0359372i
$157$	−8.46210	+	8.46210i	−0.675349	+	0.675349i	−0.958944	−	0.283595i	$-0.908473\pi$
$157$	−8.46210	+	8.46210i	−0.675349	+	0.675349i	0.283595	+	0.958944i	$0.408473\pi$
$158$	−3.55618	−	3.83572i	−0.282914	−	0.305154i
$159$	14.3292	−	2.85026i	1.13638	−	0.226040i
$160$	11.0865	+	6.09004i	0.876468	+	0.481460i
$161$	1.17091	−	2.82682i	0.0922803	−	0.222784i
$162$	11.3634	+	2.71044i	0.892792	+	0.212952i
$163$	−3.21159	−	2.14592i	−0.251551	−	0.168081i	0.423401	−	0.905942i	$-0.360836\pi$
$163$	−3.21159	−	2.14592i	−0.251551	−	0.168081i	−0.674953	+	0.737861i	$0.735836\pi$
$164$	−6.46992	+	3.64837i	−0.505216	+	0.284889i
$165$	21.4929	+	2.52559i	1.67322	+	0.196617i
$166$	−1.45429	+	2.00786i	−0.112875	+	0.155841i
$167$	5.24869	+	1.04403i	0.406156	+	0.0807894i	0.393940	−	0.919136i	$-0.371112\pi$
$167$	5.24869	+	1.04403i	0.406156	+	0.0807894i	0.0122153	+	0.999925i	$0.496112\pi$
$168$	2.53595	−	2.99587i	0.195653	−	0.231137i
$169$		−	11.7473i		−	0.903637i
$170$	0.448274	−	13.0307i	0.0343811	−	0.999409i
$171$	−0.431436			−0.0329927
$172$	5.86896	+	6.83089i	0.447504	+	0.520851i
$173$	2.81206	−	14.1372i	0.213797	−	1.07483i	−0.713544	−	0.700610i	$-0.752911\pi$
$173$	2.81206	−	14.1372i	0.213797	−	1.07483i	0.927341	−	0.374218i	$-0.122089\pi$
$174$	−11.8511	+	16.3622i	−0.898433	+	1.24042i
$175$	−2.83456	−	3.05611i	−0.214272	−	0.231020i
$176$	−17.1698	−	15.6853i	−1.29422	−	1.18232i
$177$	−9.68039	+	14.4877i	−0.727623	+	1.08896i
$178$	3.86467	−	16.2024i	0.289670	−	1.21442i
$179$	−18.5114	−	7.66769i	−1.38361	−	0.573110i	−0.438166	−	0.898894i	$-0.644372\pi$
$179$	−18.5114	−	7.66769i	−1.38361	−	0.573110i	−0.945444	+	0.325784i	$0.894372\pi$
$180$	−0.849392	+	0.572200i	−0.0633099	+	0.0426493i
$181$	−0.438918	−	2.20659i	−0.0326245	−	0.164015i	0.961039	−	0.276414i	$-0.0891463\pi$
$181$	−0.438918	−	2.20659i	−0.0326245	−	0.164015i	−0.993663	+	0.112400i	$0.964146\pi$
$182$	−0.897139	−	0.967661i	−0.0665004	−	0.0717278i
$183$	12.6044	+	12.6044i	0.931744	+	0.931744i
$184$	−9.97876	+	2.86188i	−0.735644	+	0.210980i
$185$	1.49974	−	4.62893i	0.110263	−	0.340326i
$186$	−0.801889	−	5.01519i	−0.0587974	−	0.367732i
$187$	−6.44742	+	23.0881i	−0.471482	+	1.68837i
$188$	−18.9438	+	6.21686i	−1.38162	+	0.453411i
$189$	1.71480	+	4.13989i	0.124733	+	0.301133i
$190$	−4.03389	+	4.38410i	−0.292649	+	0.318056i
$191$	−11.3936	−	11.3936i	−0.824410	−	0.824410i	0.162327	−	0.986737i	$-0.448100\pi$
$191$	−11.3936	−	11.3936i	−0.824410	−	0.824410i	−0.986737	+	0.162327i	$0.948100\pi$
$192$	−13.3109	−	0.405416i	−0.960629	−	0.0292584i
$193$	9.84881	−	1.95905i	0.708933	−	0.141015i	0.172563	−	0.984999i	$-0.444795\pi$
$193$	9.84881	−	1.95905i	0.708933	−	0.141015i	0.536370	+	0.843983i	$0.319795\pi$
$194$	0.851382	−	1.85396i	0.0611257	−	0.133106i
$195$	−1.89448	−	3.71043i	−0.135666	−	0.265709i
$196$	−12.5740	−	0.952401i	−0.898144	−	0.0680286i
$197$	9.58271	−	14.3415i	0.682740	−	1.02179i	−0.314623	−	0.949217i	$-0.601878\pi$
$197$	9.58271	−	14.3415i	0.682740	−	1.02179i	0.997363	−	0.0725757i	$-0.0231219\pi$
$198$	1.76558	−	0.654309i	0.125475	−	0.0464997i
$199$	10.4480	−	6.98112i	0.740638	−	0.494878i	−0.127107	−	0.991889i	$-0.540569\pi$
$199$	10.4480	−	6.98112i	0.740638	−	0.494878i	0.867744	+	0.497011i	$0.165569\pi$
$200$	−2.12725	+	13.9812i	−0.150420	+	0.988622i
$201$	−15.0676	−	2.99714i	−1.06279	−	0.211402i
$202$	13.3378	−	8.20041i	0.938444	−	0.576979i
$203$	−7.15444			−0.502143
$204$	5.81555	+	12.4341i	0.407170	+	0.870561i
$205$	−6.31924	−	5.38798i	−0.441355	−	0.376313i
$206$	16.6898	−	10.2613i	1.16283	−	0.714939i
$207$	0.163976	−	0.824361i	0.0113971	−	0.0572970i
$208$	−0.674338	+	4.42591i	−0.0467569	+	0.306882i
$209$	9.10721	−	6.08524i	0.629959	−	0.420925i
$210$	4.12064	+	1.50939i	0.284351	+	0.104158i
$211$	2.18387	+	1.45921i	0.150344	+	0.100456i	0.628467	−	0.777836i	$-0.283683\pi$
$211$	2.18387	+	1.45921i	0.150344	+	0.100456i	−0.478123	+	0.878293i	$0.658683\pi$
$212$	1.32576	−	17.5032i	0.0910534	−	1.20213i
$213$	4.29070	+	1.77727i	0.293994	+	0.121776i
$214$	0.480973	+	0.220875i	0.0328787	+	0.0150987i
$215$	−4.91250	+	8.78917i	−0.335030	+	0.599417i
$216$	7.36997	−	13.2973i	0.501463	−	0.904764i
$217$	1.27177	−	1.27177i	0.0863333	−	0.0863333i
$218$	0.0523986	−	1.38556i	0.00354888	−	0.0938421i
$219$	10.4975	+	25.3432i	0.709356	+	1.71254i
$220$	9.85920	−	24.0589i	0.664707	−	1.62205i
$221$	4.38523	−	1.43734i	0.294982	−	0.0966856i
$222$	0.808815	+	5.05851i	0.0542841	+	0.339505i
$223$	0.651353	−	0.269799i	0.0436178	−	0.0180671i	−0.360768	−	0.932656i	$-0.617485\pi$
$223$	0.651353	−	0.269799i	0.0436178	−	0.0180671i	0.404386	+	0.914589i	$0.367485\pi$
$224$	−2.64875	−	3.90173i	−0.176977	−	0.260696i
$225$	−0.927477	−	0.671479i	−0.0618318	−	0.0447653i
$226$	14.3340	+	15.4608i	0.953486	+	1.02844i
$227$	−19.3475	+	3.84845i	−1.28414	+	0.255431i	−0.789544	−	0.613694i	$-0.789683\pi$
$227$	−19.3475	+	3.84845i	−1.28414	+	0.255431i	−0.494592	+	0.869125i	$0.664683\pi$
$228$	1.68476	−	6.04164i	0.111576	−	0.400118i
$229$	−21.3164	−	8.82955i	−1.40863	−	0.583473i	−0.456652	−	0.889645i	$-0.650951\pi$
$229$	−21.3164	−	8.82955i	−1.40863	−	0.583473i	−0.951976	+	0.306173i	$0.900951\pi$
$230$	−6.84370	−	9.37396i	−0.451260	−	0.618101i
$231$	−6.70843	−	4.48243i	−0.441382	−	0.294922i
$232$	15.1116	+	18.9960i	0.992123	+	1.24715i
$233$	0.420693	−	0.281098i	0.0275605	−	0.0184153i	−0.541714	−	0.840563i	$-0.682224\pi$
$233$	0.420693	−	0.281098i	0.0275605	−	0.0184153i	0.569274	+	0.822148i	$0.307224\pi$
$234$	−0.293569	−	0.212631i	−0.0191912	−	0.0139001i
$235$	−13.8150	−	17.4941i	−0.901191	−	1.14119i
$236$	13.6427	+	15.8788i	0.888066	+	1.03362i
$237$			6.15679i			0.399926i
$238$	−2.35802	+	4.25078i	−0.152848	+	0.275537i
$239$		−	15.1718i		−	0.981381i	−0.871334	−	0.490690i	$-0.836745\pi$
$239$		−	15.1718i		−	0.981381i	0.871334	−	0.490690i	$-0.163255\pi$
$240$	−4.69597	−	14.1290i	−0.303123	−	0.912020i
$241$	0.733977	−	3.68995i	0.0472796	−	0.237691i	−0.949918	−	0.312498i	$-0.898834\pi$
$241$	0.733977	−	3.68995i	0.0472796	−	0.237691i	0.997198	+	0.0748074i	$0.0238342\pi$
$242$	−18.9157	+	26.1159i	−1.21595	+	1.67880i
$243$	1.31924	+	1.97438i	0.0846292	+	0.126657i
$244$	18.6550	−	10.5195i	1.19426	−	0.673441i
$245$	−3.83826	−	13.5659i	−0.245217	−	0.866695i
$246$	8.50434	+	2.02849i	0.542217	+	0.129332i
$247$	−1.94810	−	0.806927i	−0.123954	−	0.0513436i
$248$	−6.06294	−	0.690492i	−0.384997	−	0.0438463i
$249$	2.86214	−	0.569314i	0.181381	−	0.0360788i
$250$	−15.4952	+	3.14641i	−0.980000	+	0.198997i
$251$	7.68901	+	7.68901i	0.485326	+	0.485326i	0.906828	−	0.421501i	$-0.138497\pi$
$251$	7.68901	+	7.68901i	0.485326	+	0.485326i	−0.421501	+	0.906828i	$0.638497\pi$
$252$	0.379045	−	0.0459935i	0.0238776	−	0.00289732i
$253$	8.16593	+	19.7143i	0.513387	+	1.23943i
$254$	0.0780651	+	0.488237i	0.00489824	+	0.0306347i
$255$	−10.8150	+	10.8890i	−0.677260	+	0.681897i
$256$	−4.76495	+	15.2740i	−0.297809	+	0.954625i
$257$	1.07291	+	2.59024i	0.0669264	+	0.161575i	0.953804	−	0.300430i	$-0.0971303\pi$
$257$	1.07291	+	2.59024i	0.0669264	+	0.161575i	−0.886877	+	0.462005i	$0.847130\pi$
$258$	0.400601	−	10.5930i	0.0249404	−	0.659490i
$259$	−1.28275	+	1.28275i	−0.0797064	+	0.0797064i
$260$	−4.90552	+	0.995054i	−0.304228	+	0.0617106i
$261$	−1.92757	+	0.383418i	−0.119314	+	0.0237330i
$262$	9.25249	+	4.24897i	0.571621	+	0.262502i
$263$	−8.89242	+	21.4682i	−0.548330	+	1.32379i	0.370390	+	0.928876i	$0.379224\pi$
$263$	−8.89242	+	21.4682i	−0.548330	+	1.32379i	−0.918720	+	0.394909i	$0.870776\pi$
$264$	2.26806	+	27.2795i	0.139590	+	1.67894i
$265$	18.8840	−	5.34292i	1.16003	−	0.328213i
$266$	2.08269	−	0.771827i	0.127698	−	0.0473238i
$267$	−16.3022	+	10.8928i	−0.997676	+	0.666626i
$268$	−8.33132	+	16.4707i	−0.508917	+	1.00611i
$269$	−3.10609	+	15.6154i	−0.189382	+	0.952087i	0.762818	+	0.646613i	$0.223815\pi$
$269$	−3.10609	+	15.6154i	−0.189382	+	0.952087i	−0.952200	+	0.305474i	$0.901185\pi$
$270$	16.7944	+	2.62024i	1.02207	+	0.159463i
$271$	−25.3129			−1.53765			−0.768826	−	0.639458i	$-0.779159\pi$
$271$	−25.3129			−1.53765			−0.768826	+	0.639458i	$0.779159\pi$
$272$	16.2670	−	2.71761i	0.986330	−	0.164780i
$273$			1.55321i			0.0940046i
$274$	10.3360	+	16.8112i	0.624418	+	1.01560i
$275$	29.0491	+	1.09258i	1.75173	+	0.0658852i
$276$	10.9037	+	5.51537i	0.656324	+	0.331986i
$277$	−11.1341	+	7.43956i	−0.668983	+	0.447000i	−0.843123	−	0.537721i	$-0.819285\pi$
$277$	−11.1341	+	7.43956i	−0.668983	+	0.447000i	0.174140	+	0.984721i	$0.444285\pi$
$278$	−6.19645	−	16.7205i	−0.371638	−	1.00283i
$279$	0.274488	−	0.410800i	0.0164332	−	0.0245940i
$280$	3.07667	−	4.28175i	0.183866	−	0.255884i
$281$	16.8511	+	6.97996i	1.00525	+	0.416389i	0.823721	−	0.566996i	$-0.191894\pi$
$281$	16.8511	+	6.97996i	1.00525	+	0.416389i	0.181532	+	0.983385i	$0.441894\pi$
$282$	21.3269	+	9.79386i	1.27000	+	0.583216i
$283$	−1.44073	−	7.24303i	−0.0856424	−	0.430554i	−0.999689	−	0.0249440i	$-0.992059\pi$
$283$	−1.44073	−	7.24303i	−0.0856424	−	0.430554i	0.914046	−	0.405610i	$-0.132941\pi$
$284$	3.44157	−	4.39212i	0.204220	−	0.260624i
$285$	6.99040	−	0.556051i	0.414075	−	0.0329376i
$286$	9.19604	+	0.347772i	0.543773	+	0.0205642i
$287$	1.18481	+	2.86039i	0.0699373	+	0.168844i
$288$	−0.922735	−	0.909267i	−0.0543727	−	0.0535791i
$289$	−10.0630	−	13.7017i	−0.591942	−	0.805981i
$290$	−14.1265	+	23.1722i	−0.829536	+	1.36072i
$291$	−2.21855	+	0.918954i	−0.130054	+	0.0538700i
$292$	32.7179	−	3.97001i	1.91467	−	0.232327i
$293$	10.5333	−	10.5333i	0.615365	−	0.615365i	−0.328974	−	0.944339i	$-0.606703\pi$
$293$	10.5333	−	10.5333i	0.615365	−	0.615365i	0.944339	+	0.328974i	$0.106703\pi$
$294$	10.0914	+	10.8847i	0.588542	+	0.634806i
$295$	−11.4194	+	20.4309i	−0.664863	+	1.18953i
$296$	6.11531	+	0.696456i	0.355445	+	0.0404807i
$297$	−28.8717	−	11.9590i	−1.67531	−	0.693934i
$298$	3.39070	−	14.2153i	0.196418	−	0.823471i
$299$	2.28224	−	3.41561i	0.131985	−	0.197530i
$300$	13.0249	−	10.3659i	0.751993	−	0.598474i
$301$	3.12125	−	2.08555i	0.179906	−	0.120209i
$302$	18.1131	−	25.0078i	1.04229	−	1.43904i
$303$	−18.0754	−	3.59541i	−1.03840	−	0.206551i
$304$	−6.44836	−	3.89958i	−0.369839	−	0.223656i
$305$	18.2205	+	15.5354i	1.04330	+	0.889554i
$306$	−0.407499	+	1.27163i	−0.0232952	+	0.0726942i
$307$			3.32653i			0.189855i	0.995484	+	0.0949274i	$0.0302619\pi$
$307$			3.32653i			0.189855i	−0.995484	+	0.0949274i	$0.969738\pi$
$308$	−7.35255	+	6.31716i	−0.418951	+	0.359954i
$309$	−22.6180	−	4.49900i	−1.28669	−	0.255939i
$310$	−1.60796	−	6.63019i	−0.0913263	−	0.376570i
$311$	16.9690	+	25.3959i	0.962225	+	1.44007i	0.896913	+	0.442206i	$0.145804\pi$
$311$	16.9690	+	25.3959i	0.962225	+	1.44007i	0.0653113	+	0.997865i	$0.479196\pi$
$312$	4.12398	−	3.28068i	0.233475	−	0.185732i
$313$	1.75723	−	2.62988i	0.0993246	−	0.148650i	−0.778479	−	0.627671i	$-0.784008\pi$
$313$	1.75723	−	2.62988i	0.0993246	−	0.148650i	0.877803	+	0.479021i	$0.159008\pi$
$314$	3.92667	−	16.4624i	0.221595	−	0.929025i
$315$	0.194124	+	0.380202i	0.0109377	+	0.0214220i
$316$	7.12533	+	1.98695i	0.400831	+	0.111775i
$317$	6.68042	−	1.32882i	0.375210	−	0.0746339i	−0.00388305	−	0.999992i	$-0.501236\pi$
$317$	6.68042	−	1.32882i	0.375210	−	0.0746339i	0.379093	+	0.925359i	$0.376236\pi$
$318$	−15.1516	+	14.0474i	−0.849661	+	0.787738i
$319$	35.2813	−	35.2813i	1.97537	−	1.97537i
$320$	−17.8671	+	0.874934i	−0.998803	+	0.0489103i
$321$	−0.238405	−	0.575560i	−0.0133065	−	0.0321247i
$322$	0.683191	+	4.27283i	0.0380728	+	0.238115i
$323$	−0.589516	+	7.74531i	−0.0328015	+	0.430961i
$324$	−15.6974	+	5.15147i	−0.872077	+	0.286193i
$325$	−2.93202	−	4.76667i	−0.162639	−	0.264407i
$326$	5.45857	+	0.206430i	0.302322	+	0.0114331i
$327$	−1.15405	+	1.15405i	−0.0638190	+	0.0638190i
$328$	5.09216	−	9.18754i	0.281168	−	0.507297i
$329$	1.62132	+	8.15095i	0.0893865	+	0.449376i
$330$	−27.7638	+	12.8771i	−1.52835	+	0.708859i
$331$	6.62845	−	16.0025i	0.364332	−	0.879576i	−0.630324	−	0.776332i	$-0.717078\pi$
$331$	6.62845	−	16.0025i	0.364332	−	0.879576i	0.994656	−	0.103244i	$-0.0329222\pi$
$332$	0.264809	−	3.49612i	0.0145333	−	0.191875i
$333$	−0.276859	+	0.414348i	−0.0151718	+	0.0227062i
$334$	−7.09655	+	2.62992i	−0.388306	+	0.143903i
$335$	−20.4956	−	2.40840i	−1.11979	−	0.131585i
$336$	−0.836095	+	5.48758i	−0.0456127	+	0.299372i
$337$	−3.69834	+	18.5928i	−0.201461	+	1.01282i	0.739204	+	0.673481i	$0.235202\pi$
$337$	−3.69834	+	18.5928i	−0.201461	+	1.01282i	−0.940666	+	0.339334i	$0.889798\pi$
$338$	8.70117	+	14.1523i	0.473282	+	0.769782i
$339$		−	24.8164i		−	1.34784i
$340$	9.11175	+	16.0305i	0.494154	+	0.869375i
$341$			12.5432i			0.679250i
$342$	0.519763	−	0.319563i	0.0281056	−	0.0172800i
$343$	−2.16390	+	10.8787i	−0.116840	+	0.587393i
$344$	−12.1301	−	3.88224i	−0.654012	−	0.209317i
$345$	−1.59437	+	13.5681i	−0.0858378	+	0.730484i
$346$	7.08359	+	19.1143i	0.380816	+	1.02759i
$347$	3.35404	−	5.01968i	0.180054	−	0.269470i	−0.730453	−	0.682963i	$-0.760691\pi$
$347$	3.35404	−	5.01968i	0.180054	−	0.269470i	0.910508	+	0.413492i	$0.135691\pi$
$348$	2.15794	−	28.4901i	0.115678	−	1.52723i
$349$	−11.8464	+	28.5999i	−0.634126	+	1.53092i	0.200265	+	0.979742i	$0.435820\pi$
$349$	−11.8464	+	28.5999i	−0.634126	+	1.53092i	−0.834391	+	0.551173i	$0.814180\pi$
$350$	5.67852	+	1.58224i	0.303530	+	0.0845741i
$351$	1.17368	+	5.90047i	0.0626462	+	0.314944i
$352$	32.3029	+	6.17894i	1.72175	+	0.329338i
$353$	−2.09608	+	2.09608i	−0.111563	+	0.111563i	−0.760685	−	0.649122i	$-0.775137\pi$
$353$	−2.09608	+	2.09608i	−0.111563	+	0.111563i	0.649122	+	0.760685i	$0.275137\pi$
$354$	0.931221	−	24.6240i	0.0494938	−	1.30875i
$355$	5.93478	+	1.92283i	0.314986	+	0.102053i
$356$	7.34521	+	22.3821i	0.389295	+	1.18625i
$357$	5.43714	−	1.78212i	0.287764	−	0.0943196i
$358$	27.9807	−	4.47388i	1.47882	−	0.236452i
$359$	4.72206	+	11.4001i	0.249221	+	0.601673i	0.998138	−	0.0609908i	$-0.0194260\pi$
$359$	4.72206	+	11.4001i	0.249221	+	0.601673i	−0.748917	+	0.662663i	$0.769426\pi$
$360$	0.599459	−	1.31849i	0.0315943	−	0.0694903i
$361$	−10.9253	+	10.9253i	−0.575017	+	0.575017i
$362$	2.16319	+	2.33324i	0.113695	+	0.122632i
$363$	37.2273	−	7.40497i	1.95393	−	0.388660i
$364$	1.79755	+	0.501260i	0.0942173	+	0.0262732i
$365$	16.7562	+	32.8178i	0.877057	+	1.71776i
$366$	−24.5209	−	5.84883i	−1.28173	−	0.305723i
$367$	4.02147	−	6.01856i	0.209919	−	0.314166i	−0.711537	−	0.702649i	$-0.752001\pi$
$367$	4.02147	−	6.01856i	0.209919	−	0.314166i	0.921456	+	0.388482i	$0.127001\pi$
$368$	9.90190	−	10.8390i	0.516172	−	0.565023i
$369$	0.472509	+	0.707160i	0.0245978	+	0.0368133i
$370$	1.62185	+	6.68746i	0.0843161	+	0.347664i
$371$	−7.17614	−	1.42742i	−0.372567	−	0.0741081i
$372$	4.68080	+	5.44799i	0.242688	+	0.282465i
$373$		−	31.5176i		−	1.63192i	−0.578108	−	0.815960i	$-0.696209\pi$
$373$		−	31.5176i		−	1.63192i	0.578108	−	0.815960i	$-0.303791\pi$
$374$	−9.33391	−	32.5905i	−0.482645	−	1.68521i
$375$	15.8930	+	9.68436i	0.820711	+	0.500098i
$376$	18.2173	−	21.5212i	0.939486	−	1.10987i
$377$	−9.42083	−	1.87392i	−0.485198	−	0.0965118i
$378$	−5.13227	−	3.71729i	−0.263975	−	0.191197i
$379$	17.5749	−	11.7432i	0.902763	−	0.603207i	−0.0151950	−	0.999885i	$-0.504837\pi$
$379$	17.5749	−	11.7432i	0.902763	−	0.603207i	0.917958	+	0.396678i	$0.129837\pi$
$380$	1.61245	−	8.26953i	0.0827170	−	0.424218i
$381$	0.323336	−	0.483906i	0.0165650	−	0.0247913i
$382$	22.1653	+	5.28697i	1.13408	+	0.270505i
$383$	1.91773	+	0.794351i	0.0979916	+	0.0405895i	0.431141	−	0.902285i	$-0.358111\pi$
$383$	1.91773	+	0.794351i	0.0979916	+	0.0405895i	−0.333149	+	0.942874i	$0.608111\pi$
$384$	16.3363	−	9.37090i	0.833656	−	0.478207i
$385$	−9.46038	−	5.28766i	−0.482146	−	0.269484i
$386$	−10.4141	+	9.65510i	−0.530062	+	0.491432i
$387$	0.729170	−	0.729170i	0.0370658	−	0.0370658i
$388$	0.347535	+	2.86413i	0.0176434	+	0.145404i
$389$	−20.3375	+	8.42405i	−1.03115	+	0.427117i	−0.833128	−	0.553081i	$-0.813452\pi$
$389$	−20.3375	+	8.42405i	−1.03115	+	0.427117i	−0.198023	+	0.980197i	$0.563452\pi$
$390$	5.03063	+	3.06682i	0.254736	+	0.155295i
$391$	−14.5752	−	4.07016i	−0.737099	−	0.205837i
$392$	15.8537	−	8.16615i	0.800733	−	0.412453i
$393$	−4.58620	−	11.0721i	−0.231343	−	0.558512i
$394$	−0.921824	+	24.3755i	−0.0464408	+	1.22802i
$395$	0.655790	+	8.24426i	0.0329964	+	0.414814i
$396$	−1.64240	+	2.09603i	−0.0825338	+	0.105329i
$397$	1.97679	+	9.93798i	0.0992121	+	0.498773i	0.998156	+	0.0607083i	$0.0193359\pi$
$397$	1.97679	+	9.93798i	0.0992121	+	0.498773i	−0.898943	+	0.438065i	$0.855664\pi$
$398$	−7.41608	+	16.1491i	−0.371735	+	0.809483i
$399$	−2.41540	−	1.00049i	−0.120921	−	0.0500871i
$400$	−7.79309	−	18.4192i	−0.389655	−	0.920961i
$401$	3.25735	−	4.87497i	0.162664	−	0.243444i	−0.741179	−	0.671307i	$-0.765733\pi$
$401$	3.25735	−	4.87497i	0.162664	−	0.243444i	0.903844	+	0.427863i	$0.140733\pi$
$402$	20.3723	−	7.54980i	1.01608	−	0.376550i
$403$	2.00775	−	1.34153i	0.100013	−	0.0668266i
$404$	−9.99439	+	19.7585i	−0.497240	+	0.983023i
$405$	−11.4475	−	14.4961i	−0.568831	−	0.720317i
$406$	8.61915	−	5.29927i	0.427761	−	0.262998i
$407$		−	12.6515i		−	0.627111i
$408$	−16.2161	−	10.6721i	−0.802814	−	0.528350i
$409$	27.3786			1.35378			0.676891	−	0.736083i	$-0.263327\pi$
$409$	27.3786			1.35378			0.676891	+	0.736083i	$0.263327\pi$
$410$	11.6038	+	1.81042i	0.573072	+	0.0894101i
$411$	4.53173	−	22.7826i	0.223534	−	1.12378i
$412$	−12.5062	+	24.7242i	−0.616134	+	1.21807i
$413$	7.25553	−	4.84799i	0.357021	−	0.238554i
$414$	0.413055	+	1.11459i	0.0203006	+	0.0547789i
$415$	3.77191	−	1.06720i	0.185156	−	0.0523869i
$416$	−2.46587	−	5.83150i	−0.120899	−	0.285913i
$417$	−8.03221	+	19.3915i	−0.393339	+	0.949605i
$418$	−6.46438	+	14.0767i	−0.316183	+	0.688516i
$419$	29.1455	−	5.79740i	1.42385	−	0.283221i	0.577736	−	0.816223i	$-0.303936\pi$
$419$	29.1455	−	5.79740i	1.42385	−	0.283221i	0.846114	+	0.533002i	$0.178936\pi$
$420$	−6.08224	+	1.23374i	−0.296783	+	0.0602005i
$421$	25.4046	−	25.4046i	1.23814	−	1.23814i	0.277385	−	0.960759i	$-0.410532\pi$
$421$	25.4046	−	25.4046i	1.23814	−	1.23814i	0.960759	−	0.277385i	$-0.0894678\pi$
$422$	−3.71180	−	0.140371i	−0.180687	−	0.00683317i
$423$	0.873645	+	2.10917i	0.0424781	+	0.102551i
$424$	11.3674	+	22.0686i	0.552050	+	1.07175i
$425$	−13.3220	+	15.7329i	−0.646211	+	0.763159i
$426$	−6.48554	+	1.03699i	−0.314226	+	0.0502422i
$427$	−3.41622	−	8.24748i	−0.165322	−	0.399124i
$428$	−0.743043	+	0.0901613i	−0.0359163	+	0.00435811i
$429$	−7.65948	−	7.65948i	−0.369803	−	0.369803i
$430$	−0.591885	−	14.2272i	−0.0285432	−	0.686098i
$431$	18.7201	−	3.72365i	0.901713	−	0.179362i	0.277601	−	0.960696i	$-0.410461\pi$
$431$	18.7201	−	3.72365i	0.901713	−	0.179362i	0.624112	+	0.781335i	$0.285461\pi$
$432$	0.970438	+	21.4785i	0.0466902	+	1.03338i
$433$	−8.72685	−	3.61478i	−0.419386	−	0.173715i	0.163003	−	0.986626i	$-0.447882\pi$
$433$	−8.72685	−	3.61478i	−0.419386	−	0.173715i	−0.582389	+	0.812910i	$0.697882\pi$
$434$	−0.590140	+	2.47413i	−0.0283276	+	0.118762i
$435$	30.7376	−	8.69671i	1.47375	−	0.416975i
$436$	0.963155	+	1.70804i	0.0461268	+	0.0818001i
$437$	3.84152	+	5.74924i	0.183765	+	0.275024i
$438$	−31.4183	−	22.7562i	−1.50122	−	1.08733i
$439$	−5.40393	+	27.1674i	−0.257916	+	1.29663i	0.606996	+	0.794705i	$0.292374\pi$
$439$	−5.40393	+	27.1674i	−0.257916	+	1.29663i	−0.864912	+	0.501924i	$0.832626\pi$
$440$	5.94273	+	36.2871i	0.283309	+	1.72992i
$441$			1.44389i			0.0687567i
$442$	−4.21838	+	4.97972i	−0.200648	+	0.236861i
$443$		−	22.1171i		−	1.05081i	−0.850851	−	0.525407i	$-0.823913\pi$
$443$		−	22.1171i		−	1.05081i	0.850851	−	0.525407i	$-0.176087\pi$
$444$	−4.72122	−	5.49504i	−0.224059	−	0.260783i
$445$	−20.6692	+	16.3224i	−0.979814	+	0.773756i
$446$	−0.584864	+	0.807490i	−0.0276941	+	0.0382358i
$447$	−14.3028	+	9.55683i	−0.676499	+	0.452022i
$448$	6.08102	+	2.73861i	0.287301	+	0.129387i
$449$	−4.73128	−	3.16134i	−0.223283	−	0.149193i	0.438898	−	0.898537i	$-0.355369\pi$
$449$	−4.73128	−	3.16134i	−0.223283	−	0.149193i	−0.662181	+	0.749344i	$0.730369\pi$
$450$	1.61472	+	0.121970i	0.0761186	+	0.00574974i
$451$	−19.9484	−	8.26291i	−0.939335	−	0.389085i
$452$	−28.7204	−	8.00889i	−1.35089	−	0.376706i
$453$	−35.6477	+	7.09077i	−1.67487	+	0.333153i
$454$	20.4579	−	18.9669i	0.960136	−	0.890162i
$455$	0.165440	+	2.07983i	0.00775596	+	0.0975040i
$456$	2.44535	+	8.52643i	0.114514	+	0.399287i
$457$	6.25534	−	2.59105i	0.292612	−	0.121204i	−0.231548	−	0.972823i	$-0.574379\pi$
$457$	6.25534	−	2.59105i	0.292612	−	0.121204i	0.524161	+	0.851619i	$0.324379\pi$
$458$	32.2205	−	5.15180i	1.50556	−	0.240728i
$459$	19.3084	−	10.8786i	0.901240	−	0.507770i
$460$	15.1881	+	6.22397i	0.708147	+	0.290194i
$461$	−5.47495	−	13.2177i	−0.254994	−	0.615610i	0.743600	−	0.668625i	$-0.233117\pi$
$461$	−5.47495	−	13.2177i	−0.254994	−	0.615610i	−0.998594	+	0.0530153i	$0.983117\pi$
$462$	11.4019	+	0.431195i	0.530467	+	0.0200610i
$463$	−10.7407	+	10.7407i	−0.499164	+	0.499164i	−0.911178	−	0.412014i	$-0.864825\pi$
$463$	−10.7407	+	10.7407i	−0.499164	+	0.499164i	0.412014	+	0.911178i	$0.364825\pi$
$464$	−32.2756	−	11.6919i	−1.49836	−	0.542783i
$465$	−3.91797	+	7.00981i	−0.181692	+	0.325072i
$466$	−0.298612	+	0.650252i	−0.0138329	+	0.0301223i
$467$	8.36974	+	3.46686i	0.387305	+	0.160427i	0.567835	−	0.823142i	$-0.307781\pi$
$467$	8.36974	+	3.46686i	0.387305	+	0.160427i	−0.180530	+	0.983570i	$0.557781\pi$
$468$	0.511166	+	0.0387175i	0.0236286	+	0.00178972i
$469$	6.39714	+	4.27443i	0.295392	+	0.197375i
$470$	29.6011	+	10.8429i	1.36540	+	0.500144i
$471$	−16.5637	+	11.0675i	−0.763215	+	0.509964i
$472$	−28.1971	−	9.02450i	−1.29788	−	0.415386i
$473$	−5.10742	+	25.6767i	−0.234839	+	1.18062i
$474$	−4.56031	−	7.41725i	−0.209462	−	0.340686i
$475$	9.30128	−	1.48916i	0.426772	−	0.0683275i
$476$	−0.307766	−	6.86761i	−0.0141064	−	0.314776i
$477$	−2.00992			−0.0920278
$478$	11.2377	+	18.2779i	0.514000	+	0.836010i
$479$	5.04342	+	1.00320i	0.230440	+	0.0458374i	0.308959	−	0.951075i	$-0.400019\pi$
$479$	5.04342	+	1.00320i	0.230440	+	0.0458374i	−0.0785195	+	0.996913i	$0.525019\pi$
$480$	16.1226	+	13.5433i	0.735894	+	0.618162i
$481$	−2.02509	+	1.35312i	−0.0923361	+	0.0616970i
$482$	1.84889	+	4.98904i	0.0842148	+	0.227245i
$483$	2.82969	−	4.23493i	0.128755	−	0.192696i
$484$	3.44432	−	45.4734i	0.156560	−	2.06697i
$485$	−2.87287	+	1.46684i	−0.130450	+	0.0666056i
$486$	−3.05174	−	1.40143i	−0.138430	−	0.0635703i
$487$	−21.5019	+	4.27700i	−0.974345	+	0.193809i	−0.656494	−	0.754331i	$-0.727961\pi$
$487$	−21.5019	+	4.27700i	−0.974345	+	0.193809i	−0.317851	+	0.948141i	$0.602961\pi$
$488$	−14.6824	+	26.4908i	−0.664643	+	1.19918i
$489$	−4.54649	−	4.54649i	−0.205600	−	0.205600i
$490$	14.6723	+	13.5002i	0.662826	+	0.609879i
$491$	4.12613	+	9.96135i	0.186210	+	0.449550i	0.989224	−	0.146410i	$-0.0467719\pi$
$491$	4.12613	+	9.96135i	0.186210	+	0.449550i	−0.803014	+	0.595960i	$0.796772\pi$
$492$	−11.7479	+	3.85536i	−0.529637	+	0.173813i
$493$	4.24943	+	35.1285i	0.191385	+	1.58211i
$494$	2.94461	−	0.470820i	0.132484	−	0.0211832i
$495$	−2.83222	−	0.917621i	−0.127299	−	0.0412440i
$496$	7.81564	−	3.65894i	0.350932	−	0.164291i
$497$	−1.64463	−	1.64463i	−0.0737715	−	0.0737715i
$498$	−3.02641	+	2.80584i	−0.135616	+	0.125733i
$499$	6.07923	+	30.5623i	0.272144	+	1.36816i	0.838906	+	0.544277i	$0.183196\pi$
$499$	6.07923	+	30.5623i	0.272144	+	1.36816i	−0.566762	+	0.823881i	$0.691804\pi$
$500$	16.3369	−	15.2678i	0.730609	−	0.682796i
$501$	8.23019	+	3.40906i	0.367698	+	0.152305i
$502$	−14.9584	−	3.56794i	−0.667626	−	0.159245i
$503$	22.4258	−	33.5626i	0.999917	−	1.49648i	0.137359	−	0.990521i	$-0.456139\pi$
$503$	22.4258	−	33.5626i	0.999917	−	1.49648i	0.862557	−	0.505960i	$-0.168861\pi$
$504$	−0.422578	+	0.336167i	−0.0188231	+	0.0149741i
$505$	−24.5868	−	2.88915i	−1.09410	−	0.128565i
$506$	−24.4400	−	17.7019i	−1.08649	−	0.786944i
$507$	3.81497	−	19.1791i	0.169429	−	0.851776i
$508$	−0.455683	−	0.530370i	−0.0202176	−	0.0235313i
$509$	−3.05215			−0.135284			−0.0676420	−	0.997710i	$-0.521548\pi$
$509$	−3.05215			−0.135284			−0.0676420	+	0.997710i	$0.521548\pi$
$510$	4.96363	−	21.1289i	0.219793	−	0.935604i
$511$		−	13.7378i		−	0.607722i
$512$	−5.57294	−	21.9304i	−0.246292	−	0.969196i
$513$	−9.93183	−	1.97556i	−0.438501	−	0.0872233i
$514$	−3.21115	−	2.32583i	−0.141638	−	0.102588i
$515$	−30.7659	−	3.61524i	−1.35571	−	0.159307i
$516$	7.36357	+	13.0584i	0.324163	+	0.574863i
$517$	−48.1908	−	32.2001i	−2.11943	−	1.41616i
$518$	0.595237	−	2.49550i	0.0261532	−	0.109646i
$519$	9.18218	−	22.1677i	0.403053	−	0.973056i
$520$	5.17279	−	4.83227i	0.226842	−	0.211909i
$521$	−17.7129	+	3.52331i	−0.776014	+	0.154359i	−0.567182	−	0.823593i	$-0.691966\pi$
$521$	−17.7129	+	3.52331i	−0.776014	+	0.154359i	−0.208832	+	0.977951i	$0.566966\pi$
$522$	2.03820	−	1.88966i	0.0892097	−	0.0827082i
$523$	−29.3743	+	29.3743i	−1.28445	+	1.28445i	−0.346338	+	0.938110i	$0.612575\pi$
$523$	−29.3743	+	29.3743i	−1.28445	+	1.28445i	−0.938110	+	0.346338i	$0.887425\pi$
$524$	−14.2939	+	1.73443i	−0.624433	+	0.0757691i
$525$	−3.63534	−	5.91008i	−0.158659	−	0.257937i
$526$	−5.18848	−	32.4499i	−0.226229	−	1.41488i
$527$	−6.99979	−	5.48904i	−0.304916	−	0.239106i
$528$	−22.9383	−	31.1845i	−0.998260	−	1.35713i
$529$	8.80389	−	3.64669i	0.382778	−	0.158552i
$530$	−18.7926	+	20.4241i	−0.816296	+	0.887164i
$531$	1.69500	−	1.69500i	0.0735566	−	0.0735566i
$532$	−1.93739	+	2.47249i	−0.0839965	+	0.107196i
$533$	0.810934	+	4.07684i	0.0351254	+	0.176587i
$534$	11.5714	−	25.1978i	0.500745	−	1.09041i
$535$	−0.380543	−	0.745312i	−0.0164523	−	0.0322226i
$536$	−2.16282	−	26.0137i	−0.0934195	−	1.12362i
$537$	−27.7325	−	18.5303i	−1.19675	−	0.799640i
$538$	−7.82427	−	21.1130i	−0.337328	−	0.910244i
$539$	−20.3655	−	30.4792i	−0.877205	−	1.31283i
$540$	−22.1735	+	9.28287i	−0.954194	+	0.399471i
$541$	−5.37119	+	27.0028i	−0.230926	+	1.16094i	0.675102	+	0.737724i	$0.264099\pi$
$541$	−5.37119	+	27.0028i	−0.230926	+	1.16094i	−0.906028	+	0.423218i	$0.860901\pi$
$542$	30.4952	−	18.7492i	1.30988	−	0.805348i
$543$		−	3.74512i		−	0.160719i
$544$	−17.5843	+	15.3229i	−0.753923	+	0.656963i
$545$	−1.42241	+	1.66825i	−0.0609293	+	0.0714602i
$546$	−1.15046	−	1.87120i	−0.0492351	−	0.0800798i
$547$	7.27286	+	1.44666i	0.310965	+	0.0618548i	0.348106	−	0.937455i	$-0.386825\pi$
$547$	7.27286	+	1.44666i	0.310965	+	0.0618548i	−0.0371408	+	0.999310i	$0.511825\pi$
$548$	−24.9040	−	12.5971i	−1.06385	−	0.538123i
$549$	−1.36240	−	2.03898i	−0.0581460	−	0.0870216i
$550$	−35.8056	+	20.2003i	−1.52675	+	0.861345i
$551$	8.98249	−	13.4432i	0.382667	−	0.572702i
$552$	−17.2212	+	1.43179i	−0.732982	+	0.0609412i
$553$	1.17995	−	2.84864i	0.0501765	−	0.121137i
$554$	7.90309	−	17.2096i	0.335770	−	0.731167i
$555$	3.95181	−	7.07036i	0.167745	−	0.300120i
$556$	19.8498	+	15.5539i	0.841820	+	0.659633i
$557$	10.0735	+	10.0735i	0.426827	+	0.426827i	0.887546	−	0.460719i	$-0.152408\pi$
$557$	10.0735	+	10.0735i	0.426827	+	0.426827i	−0.460719	+	0.887546i	$0.652408\pi$
$558$	−0.0264048	+	0.698215i	−0.00111781	+	0.0295578i
$559$	4.65626	−	1.92869i	0.196939	−	0.0815748i
$560$	−0.535065	+	7.43722i	−0.0226106	+	0.314280i
$561$	−18.0243	+	35.6009i	−0.760987	+	1.50307i
$562$	−25.4710	+	4.07261i	−1.07443	+	0.171793i
$563$	−4.99118	−	12.0498i	−0.210353	−	0.507837i	0.783125	−	0.621865i	$-0.213625\pi$
$563$	−4.99118	−	12.0498i	−0.210353	−	0.507837i	−0.993478	+	0.114028i	$0.963625\pi$
$564$	−32.9474	+	3.99786i	−1.38734	+	0.168340i
$565$	−2.64332	−	33.2305i	−0.111205	−	1.39802i
$566$	7.10058	+	7.65874i	0.298459	+	0.321921i
$567$	1.34348	+	6.75412i	0.0564208	+	0.283646i
$568$	−0.892930	+	7.84047i	−0.0374665	+	0.328979i
$569$	0.930557	−	2.24656i	0.0390110	−	0.0941808i	−0.903173	−	0.429276i	$-0.858769\pi$
$569$	0.930557	−	2.24656i	0.0390110	−	0.0941808i	0.942184	+	0.335096i	$0.108769\pi$
$570$	−8.00966	+	5.84765i	−0.335488	+	0.244931i
$571$	−18.9840	+	28.4116i	−0.794457	+	1.18899i	0.184079	+	0.982911i	$0.441070\pi$
$571$	−18.9840	+	28.4116i	−0.794457	+	1.18899i	−0.978536	+	0.206077i	$0.933930\pi$
$572$	−11.3363	+	6.39251i	−0.473995	+	0.267284i
$573$	−14.9016	−	22.3017i	−0.622521	−	0.931669i
$574$	−3.54606	−	2.56840i	−0.148010	−	0.107203i
$575$	−0.689731	+	18.3383i	−0.0287638	+	0.764759i
$576$	1.78514	+	0.411952i	0.0743806	+	0.0171647i
$577$	23.8173			0.991525			0.495763	−	0.868458i	$-0.334889\pi$
$577$	23.8173			0.991525			0.495763	+	0.868458i	$0.334889\pi$
$578$	22.2720	+	9.05314i	0.926392	+	0.376561i
$579$	16.7158			0.694685
$580$	−0.145025	−	38.3797i	−0.00602182	−	1.59363i
$581$	−1.43337	−	0.285116i	−0.0594663	−	0.0118286i
$582$	1.99208	−	2.75036i	0.0825745	−	0.114006i
$583$	42.4275	−	28.3491i	1.75717	−	1.17410i
$584$	−36.4756	+	29.0168i	−1.50937	+	1.20072i
$585$	0.156035	+	0.551489i	0.00645125	+	0.0228013i
$586$	−4.88780	+	20.4918i	−0.201913	+	0.846509i
$587$	−3.23779	+	7.81671i	−0.133638	+	0.322630i	−0.976506	−	0.215490i	$-0.930865\pi$
$587$	−3.23779	+	7.81671i	−0.133638	+	0.322630i	0.842868	+	0.538120i	$0.180865\pi$
$588$	−20.2196	−	5.63839i	−0.833843	−	0.232523i
$589$	0.792941	+	3.98639i	0.0326726	+	0.164256i
$590$	−1.37587	−	33.0720i	−0.0566437	−	1.36155i
$591$	20.3026	−	20.3026i	0.835138	−	0.835138i
$592$	−7.88314	+	3.69055i	−0.323995	+	0.151681i
$593$	−4.27413	+	1.77040i	−0.175518	+	0.0727018i	−0.468712	−	0.883351i	$-0.655282\pi$
$593$	−4.27413	+	1.77040i	−0.175518	+	0.0727018i	0.293194	+	0.956053i	$0.405282\pi$
$594$	43.6405	−	6.97777i	1.79059	−	0.286301i
$595$	7.09079	−	2.96548i	0.290694	−	0.121573i
$596$	6.44437	+	19.6370i	0.263972	+	0.804365i
$597$	19.3250	−	8.00467i	0.790919	−	0.327609i
$598$	−0.219544	+	5.80532i	−0.00897780	+	0.237397i
$599$	−11.0817	−	11.0817i	−0.452784	−	0.452784i	0.443493	−	0.896278i	$-0.353739\pi$
$599$	−11.0817	−	11.0817i	−0.452784	−	0.452784i	−0.896278	+	0.443493i	$0.853739\pi$
$600$	−8.01350	+	22.1355i	−0.327150	+	0.903680i
$601$	1.82261	+	9.16287i	0.0743457	+	0.373761i	0.999989	−	0.00463542i	$-0.00147551\pi$
$601$	1.82261	+	9.16287i	0.0743457	+	0.373761i	−0.925644	+	0.378397i	$0.876476\pi$
$602$	−2.21550	+	4.82443i	−0.0902968	+	0.196629i
$603$	1.95261	+	0.808798i	0.0795165	+	0.0329368i
$604$	−3.29817	+	43.5439i	−0.134201	+	1.77178i
$605$	49.0606	−	13.8809i	1.99460	−	0.564339i
$606$	24.4390	−	9.05687i	0.992766	−	0.367910i
$607$	−5.89991	−	8.82984i	−0.239470	−	0.358392i	0.692195	−	0.721710i	$-0.256644\pi$
$607$	−5.89991	−	8.82984i	−0.239470	−	0.358392i	−0.931665	+	0.363318i	$0.881644\pi$
$608$	10.6569	−	0.0783461i	0.432195	−	0.00317735i
$609$	−11.6807	−	2.32343i	−0.473324	−	0.0941501i
$610$	−33.4578	−	5.22005i	−1.35467	−	0.211354i
$611$			11.1577i			0.451391i
$612$	−0.450965	−	1.83380i	−0.0182292	−	0.0741269i
$613$	16.7399			0.676117			0.338058	−	0.941125i	$-0.390230\pi$
$613$	16.7399			0.676117			0.338058	+	0.941125i	$0.390230\pi$
$614$	−2.46395	−	4.00756i	−0.0994368	−	0.161732i
$615$	−8.56730	−	10.8489i	−0.345467	−	0.437468i
$616$	4.17872	−	13.0565i	0.168366	−	0.526060i
$617$	−3.40826	−	5.10083i	−0.137211	−	0.205351i	0.756500	−	0.653994i	$-0.226908\pi$
$617$	−3.40826	−	5.10083i	−0.137211	−	0.205351i	−0.893711	+	0.448642i	$0.851908\pi$
$618$	30.5809	−	11.3330i	1.23015	−	0.455880i
$619$	−28.5423	−	19.0713i	−1.14721	−	0.766542i	−0.171409	−	0.985200i	$-0.554832\pi$
$619$	−28.5423	−	19.0713i	−1.14721	−	0.766542i	−0.975801	+	0.218658i	$0.929832\pi$
$620$	6.84812	+	6.79656i	0.275027	+	0.272957i
$621$	7.54957	−	18.2263i	0.302954	−	0.731395i
$622$	−39.2537	−	18.0263i	−1.57393	−	0.722788i
$623$	9.63034	−	1.91559i	0.385831	−	0.0767466i
$624$	−2.53828	+	7.00695i	−0.101613	+	0.280503i
$625$	22.3131	+	11.2750i	0.892523	+	0.451001i
$626$	−0.169040	+	4.46987i	−0.00675619	+	0.178652i
$627$	16.8450	−	6.97744i	0.672726	−	0.278652i
$628$	7.46305	+	22.7411i	0.297808	+	0.907470i
$629$	7.06025	+	5.53644i	0.281510	+	0.220753i
$630$	−0.515481	−	0.314253i	−0.0205373	−	0.0125201i
$631$	12.2226	+	29.5081i	0.486576	+	1.17470i	0.956432	+	0.291955i	$0.0943058\pi$
$631$	12.2226	+	29.5081i	0.486576	+	1.17470i	−0.469856	+	0.882743i	$0.655694\pi$
$632$	−10.0558	+	2.88397i	−0.399999	+	0.114718i
$633$	3.09159	+	3.09159i	0.122880	+	0.122880i
$634$	−7.06384	+	6.54903i	−0.280541	+	0.260095i
$635$	0.381420	−	0.682416i	0.0151362	−	0.0270809i
$636$	7.84872	−	28.1460i	0.311222	−	1.11606i
$637$	−2.70055	+	6.51970i	−0.107000	+	0.258320i
$638$	−16.3716	+	68.6370i	−0.648158	+	2.71737i
$639$	−0.531238	−	0.354962i	−0.0210155	−	0.0140421i
$640$	20.8770	−	14.2882i	0.825235	−	0.564790i
$641$	23.6681	+	35.4218i	0.934835	+	1.39908i	0.916846	+	0.399241i	$0.130726\pi$
$641$	23.6681	+	35.4218i	0.934835	+	1.39908i	0.0179883	+	0.999838i	$0.494274\pi$
$642$	0.713529	+	0.516808i	0.0281607	+	0.0203968i
$643$	4.35047	−	21.8713i	0.171566	−	0.862519i	−0.795100	−	0.606478i	$-0.792582\pi$
$643$	4.35047	−	21.8713i	0.171566	−	0.862519i	0.966666	−	0.256041i	$-0.0824181\pi$
$644$	−3.98793	−	4.64156i	−0.157146	−	0.182903i
$645$	−10.8747	+	12.7542i	−0.428190	+	0.502198i
$646$	−5.02672	−	9.76764i	−0.197774	−	0.384303i
$647$	47.1213			1.85253			0.926265	−	0.376873i	$-0.123001\pi$
$647$	47.1213			1.85253			0.926265	+	0.376873i	$0.123001\pi$
$648$	15.0954	−	17.8331i	0.593003	−	0.700552i
$649$	−11.8725	+	59.6871i	−0.466036	+	2.34292i
$650$	7.06294	+	3.57080i	0.277031	+	0.140058i
$651$	2.48936	−	1.66334i	0.0975656	−	0.0651913i
$652$	−6.72899	+	3.79445i	−0.263527	+	0.148602i
$653$	21.1895	+	14.1584i	0.829208	+	0.554059i	0.896178	−	0.443696i	$-0.146333\pi$
$653$	21.1895	+	14.1584i	0.829208	+	0.554059i	−0.0669691	+	0.997755i	$0.521333\pi$
$654$	0.535514	−	2.24511i	0.0209403	−	0.0877909i
$655$	−7.32050	−	14.3376i	−0.286036	−	0.560215i
$656$	0.670509	+	14.8402i	0.0261790	+	0.579414i
$657$	−0.736228	−	3.70127i	−0.0287230	−	0.144400i
$658$	−7.99064	−	8.61876i	−0.311507	−	0.335994i
$659$	6.54117	+	6.54117i	0.254808	+	0.254808i	0.822938	−	0.568130i	$-0.192333\pi$
$659$	6.54117	+	6.54117i	0.254808	+	0.254808i	−0.568130	+	0.822938i	$0.692333\pi$
$660$	23.9098	−	36.0779i	0.930687	−	1.40433i
$661$	33.4301	−	13.8472i	1.30028	−	0.538594i	0.378248	−	0.925704i	$-0.376527\pi$
$661$	33.4301	−	13.8472i	1.30028	−	0.538594i	0.922034	+	0.387110i	$0.126527\pi$
$662$	3.86752	+	24.1883i	0.150315	+	0.940105i
$663$	7.62630	−	0.922541i	0.296181	−	0.0358285i
$664$	2.27054	+	4.40802i	0.0881141	+	0.171064i
$665$	−3.34091	−	1.08243i	−0.129555	−	0.0419749i
$666$	0.0266329	−	0.704245i	0.00103200	−	0.0272889i
$667$	22.2725	+	22.2725i	0.862396	+	0.862396i
$668$	6.60144	−	8.42472i	0.255417	−	0.325962i
$669$	1.15105	−	0.228957i	0.0445020	−	0.00885201i
$670$	26.4755	−	12.2795i	1.02284	−	0.474400i
$671$	57.5181	+	23.8248i	2.22046	+	0.919746i
$672$	−3.05737	−	7.23034i	−0.117941	−	0.278916i
$673$	−28.9785	−	19.3628i	−1.11704	−	0.746382i	−0.146953	−	0.989143i	$-0.546947\pi$
$673$	−28.9785	−	19.3628i	−1.11704	−	0.746382i	−0.970086	+	0.242762i	$0.921947\pi$
$674$	−9.31614	−	25.1386i	−0.358844	−	0.968304i
$675$	−18.2762	−	19.7047i	−0.703450	−	0.758434i
$676$	−20.9651	−	10.6047i	−0.806350	−	0.407873i
$677$	1.66393	+	0.330977i	0.0639501	+	0.0127205i	0.226962	−	0.973904i	$-0.427121\pi$
$677$	1.66393	+	0.330977i	0.0639501	+	0.0127205i	−0.163012	+	0.986624i	$0.552121\pi$
$678$	18.3814	+	29.8970i	0.705935	+	1.14819i
$679$	1.20260			0.0461517
$680$	−22.8509	−	12.5633i	−0.876292	−	0.481781i
$681$	−32.8373			−1.25833
$682$	−9.29067	−	15.1111i	−0.355758	−	0.578633i
$683$	42.2258	+	8.39924i	1.61573	+	0.321388i	0.918487	−	0.395450i	$-0.129412\pi$
$683$	42.2258	+	8.39924i	1.61573	+	0.321388i	0.697239	+	0.716838i	$0.254412\pi$
$684$	−0.389473	+	0.769973i	−0.0148919	+	0.0294407i
$685$	3.64154	−	30.9897i	0.139136	−	1.18406i
$686$	−5.45088	−	14.7086i	−0.208116	−	0.561578i
$687$	−31.9347	−	21.3381i	−1.21838	−	0.814099i
$688$	17.4890	−	4.30769i	0.666764	−	0.164229i
$689$	−9.07553	−	3.75921i	−0.345750	−	0.143214i
$690$	−8.12910	−	17.5269i	−0.309470	−	0.667236i
$691$	25.6422	−	5.10054i	0.975474	−	0.194034i	0.318480	−	0.947930i	$-0.396828\pi$
$691$	25.6422	−	5.10054i	0.975474	−	0.194034i	0.656994	+	0.753896i	$0.271828\pi$
$692$	−22.6917	−	17.7807i	−0.862609	−	0.675923i
$693$	0.784855	+	0.784855i	0.0298142	+	0.0298142i
$694$	−0.322647	+	8.53167i	−0.0122475	+	0.323858i
$695$	−8.69007	+	26.8218i	−0.329633	+	1.01741i
$696$	18.5028	+	35.9212i	0.701348	+	1.36159i
$697$	13.3408	−	7.51640i	0.505321	−	0.284704i
$698$	−6.91208	−	43.2297i	−0.261626	−	1.63627i
$699$	0.778129	−	0.322312i	0.0294315	−	0.0121909i
$700$	−8.01303	+	2.29990i	−0.302864	+	0.0869279i
$701$	12.2153	+	12.2153i	0.461367	+	0.461367i	0.899103	−	0.437736i	$-0.144220\pi$
$701$	12.2153	+	12.2153i	0.461367	+	0.461367i	−0.437736	+	0.899103i	$0.644220\pi$
$702$	−5.78442	−	6.23912i	−0.218319	−	0.235481i
$703$	−0.799790	−	4.02082i	−0.0301646	−	0.151648i
$704$	−43.4929	+	16.4827i	−1.63920	+	0.621217i
$705$	−16.8737	−	33.0480i	−0.635501	−	1.24466i
$706$	0.972644	−	4.07776i	0.0366059	−	0.153468i
$707$	7.67411	+	5.12768i	0.288615	+	0.192846i
$708$	17.1170	+	30.3550i	0.643298	+	1.14081i
$709$	10.7630	−	7.19160i	0.404213	−	0.270086i	−0.336802	−	0.941576i	$-0.609345\pi$
$709$	10.7630	−	7.19160i	0.404213	−	0.270086i	0.741014	+	0.671489i	$0.234345\pi$
$710$	−8.57403	+	2.07939i	−0.321778	+	0.0780380i
$711$	0.165242	−	0.830726i	0.00619705	−	0.0311547i
$712$	−25.4273	−	21.5237i	−0.952928	−	0.806636i
$713$	−7.91831			−0.296543
$714$	−5.23026	+	6.17424i	−0.195738	+	0.231065i
$715$	−11.0723	−	9.44059i	−0.414080	−	0.353058i
$716$	−30.3953	+	26.1150i	−1.13593	+	0.975963i
$717$	4.92708	−	24.7701i	0.184005	−	0.925057i
$718$	−14.1328	−	10.2364i	−0.527431	−	0.382018i
$719$	−9.50829	−	14.2302i	−0.354599	−	0.530695i	0.610693	−	0.791868i	$-0.290891\pi$
$719$	−9.50829	−	14.2302i	−0.354599	−	0.530695i	−0.965292	+	0.261172i	$0.915891\pi$
$720$	0.254414	+	2.03243i	0.00948143	+	0.0757444i
$721$	9.60275	+	6.41635i	0.357625	+	0.238957i
$722$	5.06969	−	21.2544i	0.188674	−	0.791007i
$723$	2.39665	−	5.78602i	0.0891323	−	0.215184i
$724$	−4.33428	−	1.20864i	−0.161082	−	0.0449189i
$725$	40.2329	−	14.9194i	1.49421	−	0.554091i
$726$	−39.3639	+	36.4951i	−1.46093	+	1.35446i
$727$	29.4063	+	29.4063i	1.09062	+	1.09062i	0.995462	+	0.0951573i	$0.0303354\pi$
$727$	29.4063	+	29.4063i	1.09062	+	1.09062i	0.0951573	+	0.995462i	$0.469665\pi$
$728$	−2.53684	+	0.727558i	−0.0940216	+	0.0269651i
$729$	10.9962	+	26.5471i	0.407266	+	0.983226i
$730$	−44.4946	−	27.1253i	−1.64682	−	1.00395i
$731$	−12.0940	−	14.0867i	−0.447313	−	0.521015i
$732$	33.8732	−	11.1163i	1.25199	−	0.410870i
$733$	6.92433	−	2.86815i	0.255756	−	0.105938i	−0.251122	−	0.967955i	$-0.580799\pi$
$733$	6.92433	−	2.86815i	0.255756	−	0.105938i	0.506878	+	0.862018i	$0.330799\pi$
$734$	−0.386852	+	10.2294i	−0.0142790	+	0.377575i
$735$	−1.86094	−	23.3948i	−0.0686418	−	0.862930i
$736$	−3.90067	+	20.3924i	−0.143781	+	0.751672i
$737$	−52.6256	+	10.4679i	−1.93849	+	0.385589i
$738$	−1.09304	−	0.501949i	−0.0402352	−	0.0184770i
$739$	−3.22954	+	7.79680i	−0.118801	+	0.286810i	−0.972082	−	0.234640i	$-0.924609\pi$
$739$	−3.22954	+	7.79680i	−0.118801	+	0.286810i	0.853282	+	0.521450i	$0.174609\pi$
$740$	−6.90727	−	6.85527i	−0.253916	−	0.252005i
$741$	−2.91850	−	1.95008i	−0.107214	−	0.0716378i
$742$	9.70259	−	3.59569i	0.356193	−	0.132002i
$743$	18.5833	+	27.8119i	0.681755	+	1.02032i	0.997444	+	0.0714560i	$0.0227645\pi$
$743$	18.5833	+	27.8119i	0.681755	+	1.02032i	−0.315688	+	0.948863i	$0.602235\pi$
$744$	−9.67439	−	3.09629i	−0.354680	−	0.113515i
$745$	−18.1343	+	14.3206i	−0.664388	+	0.524664i
$746$	23.3450	+	37.9702i	0.854721	+	1.39019i
$747$	−0.401464			−0.0146888
$748$	35.3845	+	32.3491i	1.29379	+	1.18280i
$749$			0.311993i			0.0114000i
$750$	−26.3199	+	0.104871i	−0.961067	+	0.00382936i
$751$	−9.20356	−	1.83070i	−0.335843	−	0.0668033i	0.0242883	−	0.999705i	$-0.492268\pi$
$751$	−9.20356	−	1.83070i	−0.335843	−	0.0668033i	−0.360131	+	0.932902i	$0.617268\pi$
$752$	−6.00619	+	39.4207i	−0.219023	+	1.43753i
$753$	10.0564	+	15.0505i	0.366475	+	0.548469i
$754$	12.7375	−	4.72042i	0.463874	−	0.171907i
$755$	−46.9789	+	13.2919i	−1.70974	+	0.483743i
$756$	8.93637	+	0.676872i	0.325013	+	0.0246176i
$757$	19.9150	+	8.24908i	0.723825	+	0.299818i	0.714012	−	0.700134i	$-0.246876\pi$
$757$	19.9150	+	8.24908i	0.723825	+	0.299818i	0.00981312	+	0.999952i	$0.496876\pi$
$758$	−12.4749	+	27.1650i	−0.453107	+	0.986678i
$759$	6.92978	+	34.8383i	0.251535	+	1.26455i
$760$	4.18265	+	11.1569i	0.151721	+	0.404702i
$761$	−0.0488229	−	0.0488229i	−0.00176983	−	0.00176983i	0.706221	−	0.707991i	$-0.250398\pi$
$761$	−0.0488229	−	0.0488229i	−0.00176983	−	0.00176983i	−0.707991	+	0.706221i	$0.750398\pi$
$762$	−0.0311038	+	0.822469i	−0.00112677	+	0.0297949i
$763$	0.755132	−	0.312786i	0.0273376	−	0.0113236i
$764$	−30.6192	+	10.0484i	−1.10776	+	0.363539i
$765$	1.75150	−	1.17898i	0.0633256	−	0.0426260i
$766$	−2.89872	+	0.463482i	−0.104735	+	0.0167463i
$767$	10.8237	−	4.48334i	0.390823	−	0.161884i
$768$	−12.7397	+	23.3896i	−0.459706	+	0.843999i
$769$	15.4153	−	15.4153i	0.555889	−	0.555889i	−0.372245	−	0.928134i	$-0.621412\pi$
$769$	15.4153	−	15.4153i	0.555889	−	0.555889i	0.928134	+	0.372245i	$0.121412\pi$
$770$	15.3137	−	0.637086i	0.551869	−	0.0229590i
$771$	0.910495	+	4.57737i	0.0327907	+	0.164850i
$772$	5.39461	−	19.3454i	0.194156	−	0.696257i
$773$	4.95940	−	11.9730i	0.178377	−	0.430640i	−0.809249	−	0.587465i	$-0.800126\pi$
$773$	4.95940	−	11.9730i	0.178377	−	0.430640i	0.987626	+	0.156825i	$0.0501258\pi$
$774$	−0.338357	+	1.41854i	−0.0121620	+	0.0509885i
$775$	−4.49972	+	9.80383i	−0.161635	+	0.352164i
$776$	−2.54014	−	3.19308i	−0.0911855	−	0.114625i
$777$	−2.51086	+	1.67770i	−0.0900766	+	0.0601872i
$778$	18.2614	−	25.2126i	0.654704	−	0.903915i
$779$	−6.86224	−	1.36498i	−0.245865	−	0.0489057i
$780$	−8.33213	+	0.0314845i	−0.298338	+	0.00112732i
$781$	16.2205			0.580417
$782$	20.5739	−	5.89236i	0.735721	−	0.210710i
$783$	−46.1292			−1.64852
$784$	−13.0508	+	21.5808i	−0.466098	+	0.770742i
$785$	−21.0008	+	16.5842i	−0.749550	+	0.591917i
$786$	13.7262	+	9.94184i	0.489596	+	0.354614i
$787$	−24.1128	−	36.0874i	−0.859529	−	1.28638i	−0.956690	−	0.291108i	$-0.905976\pi$
$787$	−24.1128	−	36.0874i	−0.859529	−	1.28638i	0.0971613	−	0.995269i	$-0.469024\pi$
$788$	−16.9443	−	30.0487i	−0.603617	−	1.07044i
$789$	−21.4900	+	32.1621i	−0.765065	+	1.14500i
$790$	−6.89654	−	9.44634i	−0.245368	−	0.336086i
$791$	−4.75606	+	11.4822i	−0.169106	+	0.408258i
$792$	0.426128	−	3.74166i	0.0151418	−	0.132954i
$793$	−2.33820	−	11.7549i	−0.0830318	−	0.417429i
$794$	−9.74252	−	10.5084i	−0.345749	−	0.372928i
$795$	32.5659	−	2.59046i	1.15500	−	0.0918741i
$796$	−3.02725	−	24.9484i	−0.107298	−	0.884272i
$797$	−17.1467	−	41.3959i	−0.607368	−	1.46632i	−0.865852	−	0.500301i	$-0.833223\pi$
$797$	−17.1467	−	41.3959i	−0.607368	−	1.46632i	0.258483	−	0.966016i	$-0.416777\pi$
$798$	3.65095	−	0.583758i	0.129242	−	0.0206648i
$799$	39.0583	−	12.8021i	1.38178	−	0.452904i
$800$	23.0316	+	16.4178i	0.814290	+	0.580458i
$801$	2.49198	−	1.03221i	0.0880497	−	0.0364714i
$802$	−0.313346	+	8.28572i	−0.0110646	+	0.292579i
$803$	67.7461	+	67.7461i	2.39071	+	2.39071i
$804$	−18.9510	+	24.1852i	−0.668350	+	0.852946i
$805$	3.33802	−	5.97220i	0.117650	−	0.210492i
$806$	−1.42512	+	3.10332i	−0.0501977	+	0.109310i
$807$	−10.1423	+	24.4857i	−0.357026	+	0.861936i
$808$	−2.59455	−	31.2064i	−0.0912760	−	1.09784i
$809$	17.6459	−	26.4089i	0.620395	−	0.928487i	−0.379599	−	0.925151i	$-0.623938\pi$
$809$	17.6459	−	26.4089i	0.620395	−	0.928487i	0.999994	−	0.00333595i	$-0.00106187\pi$
$810$	24.5283	+	8.98471i	0.861838	+	0.315691i
$811$	9.57167	+	14.3250i	0.336107	+	0.503019i	0.960571	−	0.278034i	$-0.0896828\pi$
$811$	9.57167	+	14.3250i	0.336107	+	0.503019i	−0.624465	+	0.781053i	$0.714683\pi$
$812$	−6.45858	+	12.7684i	−0.226652	+	0.448081i
$813$	−41.3271	−	8.22046i	−1.44940	−	0.288304i
$814$	9.37092	+	15.2416i	0.328450	+	0.534218i
$815$	−6.57226	−	5.60372i	−0.230216	−	0.196290i
$816$	27.4408	+	0.845854i	0.960618	+	0.0296108i
$817$			8.48329i			0.296793i
$818$	−32.9837	+	20.2792i	−1.15325	+	0.709046i
$819$	0.0416866	−	0.209573i	0.00145665	−	0.00732306i
$820$	−15.3204	+	6.41385i	−0.535012	+	0.223981i
$821$	6.48511	+	9.70566i	0.226332	+	0.338730i	0.927204	−	0.374558i	$-0.122205\pi$
$821$	6.48511	+	9.70566i	0.226332	+	0.338730i	−0.700872	+	0.713287i	$0.747205\pi$
$822$	11.4155	+	30.8034i	0.398160	+	1.07439i
$823$	−36.6784	−	24.5077i	−1.27853	−	0.854286i	−0.284008	−	0.958822i	$-0.591664\pi$
$823$	−36.6784	−	24.5077i	−1.27853	−	0.854286i	−0.994521	+	0.104536i	$0.966664\pi$
$824$	−3.24661	−	39.0492i	−0.113101	−	1.36034i
$825$	47.0721	+	11.2176i	1.63884	+	0.390547i
$826$	−5.15005	+	11.2147i	−0.179193	+	0.390208i
$827$	5.60228	+	28.1646i	0.194810	+	0.979377i	0.947196	+	0.320655i	$0.103903\pi$
$827$	5.60228	+	28.1646i	0.194810	+	0.979377i	−0.752386	+	0.658723i	$0.771097\pi$
$828$	−1.32319	−	1.03682i	−0.0459840	−	0.0360321i
$829$	−15.8570	+	15.8570i	−0.550735	+	0.550735i	−0.926653	−	0.375918i	$-0.877327\pi$
$829$	−15.8570	+	15.8570i	−0.550735	+	0.550735i	0.375918	+	0.926653i	$0.377327\pi$
$830$	−3.75365	+	4.07953i	−0.130291	+	0.141603i
$831$	−20.5940	+	8.53033i	−0.714399	+	0.295914i
$832$	7.29007	+	5.19891i	0.252738	+	0.180240i
$833$	25.9213	+	1.97294i	0.898119	+	0.0683582i
$834$	−4.68658	−	29.3109i	−0.162283	−	1.01495i
$835$	11.3838	+	3.68827i	0.393952	+	0.127638i
$836$	−2.63877	−	21.7468i	−0.0912637	−	0.752128i
$837$	8.19990	−	8.19990i	0.283430	−	0.283430i
$838$	−30.8183	+	28.5723i	−1.06460	+	0.987012i
$839$	24.2657	−	4.82675i	0.837746	−	0.166638i	0.242469	−	0.970159i	$-0.422043\pi$
$839$	24.2657	−	4.82675i	0.837746	−	0.166638i	0.595276	+	0.803521i	$0.297043\pi$
$840$	6.41361	−	5.99142i	0.221291	−	0.206724i
$841$	17.0872	−	41.2521i	0.589213	−	1.42249i
$842$	−11.7885	+	49.4227i	−0.406259	+	1.70322i
$843$	25.2451	+	16.8682i	0.869488	+	0.580973i
$844$	4.57568	−	2.58021i	0.157501	−	0.0888144i
$845$	3.06558	−	26.0882i	0.105459	−	0.897462i
$846$	−2.61476	−	1.89386i	−0.0898972	−	0.0651124i
$847$	−18.6436	−	3.70845i	−0.640602	−	0.127424i
$848$	−30.0408	−	18.1669i	−1.03160	−	0.623853i
$849$		−	12.2932i		−	0.421901i
$850$	4.39602	−	28.8214i	0.150782	−	0.988567i
$851$	7.98670			0.273780
$852$	7.04522	−	6.05311i	0.241365	−	0.207376i
$853$	0.290228	−	1.45907i	0.00993722	−	0.0499578i	−0.975499	−	0.220006i	$-0.929392\pi$
$853$	0.290228	−	1.45907i	0.00993722	−	0.0499578i	0.985436	+	0.170048i	$0.0543923\pi$
$854$	10.2245	+	7.40559i	0.349875	+	0.253414i
$855$	−0.958128	−	0.112588i	−0.0327673	−	0.00385042i
$856$	0.828382	−	0.658989i	0.0283135	−	0.0225238i
$857$	18.2073	−	27.2491i	0.621948	−	0.930811i	−0.378040	−	0.925789i	$-0.623402\pi$
$857$	18.2073	−	27.2491i	0.621948	−	0.930811i	0.999987	−	0.00502126i	$-0.00159832\pi$
$858$	14.9009	+	3.55423i	0.508709	+	0.121340i
$859$	−26.0345	−	10.7838i	−0.888285	−	0.367940i	−0.108581	−	0.994088i	$-0.534631\pi$
$859$	−26.0345	−	10.7838i	−0.888285	−	0.367940i	−0.779704	+	0.626148i	$0.784631\pi$
$860$	11.2511	+	16.7015i	0.383660	+	0.569517i
$861$	1.00546	+	5.05477i	0.0342659	+	0.172266i
$862$	−19.7945	+	18.3519i	−0.674202	+	0.625067i
$863$	13.8563	+	13.8563i	0.471675	+	0.471675i	0.902456	−	0.430782i	$-0.141762\pi$
$863$	13.8563	+	13.8563i	0.471675	+	0.471675i	−0.430782	+	0.902456i	$0.641762\pi$
$864$	−17.0782	−	25.1569i	−0.581011	−	0.855856i
$865$	9.93422	−	30.6618i	0.337774	−	1.04253i
$866$	13.1909	−	2.10913i	0.448246	−	0.0716710i
$867$	−11.9797	−	25.6380i	−0.406851	−	0.870711i
$868$	−1.12162	−	3.41777i	−0.0380703	−	0.116007i
$869$	8.22898	+	19.8665i	0.279149	+	0.673925i
$870$	−30.5888	+	33.2444i	−1.03706	+	1.12709i
$871$	7.30405	+	7.30405i	0.247488	+	0.247488i
$872$	−2.42548	−	1.34431i	−0.0821370	−	0.0455242i
$873$	0.324010	−	0.0644495i	0.0109661	−	0.00218129i
$874$	−8.88643	−	4.08087i	−0.300588	−	0.138037i
$875$	−5.49742	−	7.52669i	−0.185847	−	0.254448i
$876$	54.7060	+	4.14362i	1.84834	+	0.140000i
$877$	−18.1713	+	27.1952i	−0.613600	+	0.918318i	−0.999992	−	0.00401720i	$-0.998721\pi$
$877$	−18.1713	+	27.1952i	−0.613600	+	0.918318i	0.386392	+	0.922335i	$0.373721\pi$
$878$	−13.6125	−	36.7320i	−0.459401	−	1.23964i
$879$	20.6179	−	13.7765i	0.695426	−	0.464669i
$880$	−34.0371	−	39.3144i	−1.14739	−	1.32529i
$881$	11.5198	+	2.29144i	0.388113	+	0.0772004i	0.385290	−	0.922796i	$-0.374101\pi$
$881$	11.5198	+	2.29144i	0.388113	+	0.0772004i	0.00282289	+	0.999996i	$0.499101\pi$
$882$	−1.06948	−	1.73949i	−0.0360114	−	0.0585718i
$883$	−58.1126			−1.95564			−0.977822	−	0.209437i	$-0.932837\pi$
$883$	−58.1126			−1.95564			−0.977822	+	0.209437i	$0.932837\pi$
$884$	1.39353	−	9.12374i	0.0468695	−	0.306865i
$885$	−25.2788	+	29.6480i	−0.849738	+	0.996606i
$886$	16.3820	+	26.6450i	0.550365	+	0.895158i
$887$	7.28884	−	36.6435i	0.244735	−	1.23037i	−0.641496	−	0.767126i	$-0.721686\pi$
$887$	7.28884	−	36.6435i	0.244735	−	1.23037i	0.886232	−	0.463242i	$-0.153314\pi$
$888$	9.75795	+	3.12303i	0.327455	+	0.104802i
$889$	−0.242343	+	0.161928i	−0.00812792	+	0.00543090i
$890$	12.8108	−	34.9736i	0.429420	−	1.17232i
$891$	−39.9323	−	26.6819i	−1.33778	−	0.893879i
$892$	0.106496	−	1.40601i	0.00356576	−	0.0470768i
$893$	−17.3513	−	7.18714i	−0.580639	−	0.240508i
$894$	10.1523	−	22.1074i	0.339543	−	0.739382i
$895$	−39.1090	−	21.8591i	−1.30727	−	0.730668i
$896$	−9.35445	+	1.20492i	−0.312510	+	0.0402536i
$897$	4.83531	−	4.83531i	0.161446	−	0.161446i
$898$	8.04150	+	0.304110i	0.268348	+	0.0101483i
$899$	7.08542	+	17.1057i	0.236312	+	0.570507i
$900$	−2.03564	+	1.04908i	−0.0678547	+	0.0349692i
$901$	−2.74636	+	36.0828i	−0.0914944	+	1.20209i
$902$	30.1527	−	4.82118i	1.00398	−	0.160528i
$903$	5.77319	−	2.39133i	0.192120	−	0.0795785i
$904$	40.5324	−	11.6246i	1.34809	−	0.386627i
$905$	−0.398911	−	5.01491i	−0.0132603	−	0.166701i
$906$	37.6937	−	34.9466i	1.25229	−	1.16102i
$907$	2.92881	−	0.582577i	0.0972496	−	0.0193442i	−0.146226	−	0.989251i	$-0.546713\pi$
$907$	2.92881	−	0.582577i	0.0972496	−	0.0193442i	0.243475	+	0.969907i	$0.421713\pi$
$908$	−10.5974	+	38.0031i	−0.351688	+	1.26118i
$909$	2.34238	+	0.970248i	0.0776920	+	0.0321811i
$910$	−1.73983	−	2.38309i	−0.0576749	−	0.0789986i
$911$	−3.19147	−	2.13247i	−0.105738	−	0.0706520i	0.501577	−	0.865113i	$-0.332753\pi$
$911$	−3.19147	−	2.13247i	−0.105738	−	0.0706520i	−0.607315	+	0.794461i	$0.707753\pi$
$912$	−9.26148	−	8.46076i	−0.306678	−	0.280164i
$913$	8.47452	−	5.66249i	0.280466	−	0.187401i
$914$	−5.61680	+	7.75481i	−0.185787	+	0.256506i
$915$	24.7024	+	31.2809i	0.816638	+	1.03412i
$916$	−35.0010	+	30.0721i	−1.15646	+	0.993611i
$917$			6.00181i			0.198197i
$918$	−15.2036	+	27.4074i	−0.501795	+	0.904580i
$919$		−	16.3150i		−	0.538183i	−0.963115	−	0.269091i	$-0.913277\pi$
$919$		−	16.3150i		−	0.538183i	0.963115	−	0.269091i	$-0.0867234\pi$
$920$	−22.9075	+	3.75156i	−0.755239	+	0.123685i
$921$	−1.08030	+	5.43104i	−0.0355971	+	0.178959i
$922$	16.3861	+	11.8684i	0.539648	+	0.390866i
$923$	−1.73484	−	2.59638i	−0.0571031	−	0.0854608i
$924$	−14.0556	+	7.92591i	−0.462396	+	0.260743i
$925$	4.53858	−	9.88851i	0.149228	−	0.325132i
$926$	4.98403	−	20.8953i	0.163785	−	0.686661i
$927$	2.93107	+	1.21409i	0.0962688	+	0.0398759i
$928$	47.5435	−	9.82087i	1.56069	−	0.322386i
$929$	−36.9267	+	7.34518i	−1.21153	+	0.240987i	−0.759195	−	0.650863i	$-0.774407\pi$
$929$	−36.9267	+	7.34518i	−1.21153	+	0.240987i	−0.452331	+	0.891850i	$0.649407\pi$
$930$	−0.472058	−	11.3469i	−0.0154794	−	0.372081i
$931$	−8.39924	−	8.39924i	−0.275274	−	0.275274i
$932$	−0.121894	−	1.00456i	−0.00399276	−	0.0329054i
$933$	19.4570	+	46.9733i	0.636993	+	1.53784i
$934$	−12.6511	+	2.02282i	−0.413958	+	0.0661886i
$935$	−20.3435	+	49.5913i	−0.665302	+	1.62181i
$936$	−0.644493	+	0.331975i	−0.0210659	+	0.0108509i
$937$	18.9469	+	45.7418i	0.618967	+	1.49432i	0.852905	+	0.522067i	$0.174839\pi$
$937$	18.9469	+	45.7418i	0.618967	+	1.49432i	−0.233938	+	0.972252i	$0.575161\pi$
$938$	−10.8729	−	0.411186i	−0.355012	−	0.0134257i
$939$	3.72300	−	3.72300i	0.121495	−	0.121495i
$940$	−43.6925	+	8.86274i	−1.42509	+	0.289071i
$941$	13.6880	−	2.72272i	0.446216	−	0.0887580i	0.0331326	−	0.999451i	$-0.489452\pi$
$941$	13.6880	−	2.72272i	0.446216	−	0.0887580i	0.413084	+	0.910693i	$0.364452\pi$
$942$	11.7571	−	25.6020i	0.383066	−	0.834158i
$943$	5.21625	−	12.5932i	0.169865	−	0.410089i
$944$	40.6543	−	10.0135i	1.32318	−	0.325911i
$945$	2.72785	+	9.64131i	0.0887371	+	0.313632i
$946$	−12.8656	−	34.7165i	−0.418298	−	1.12873i
$947$	5.29279	−	3.53653i	0.171992	−	0.114922i	−0.466595	−	0.884471i	$-0.654519\pi$
$947$	5.29279	−	3.53653i	0.171992	−	0.114922i	0.638587	+	0.769550i	$0.279519\pi$
$948$	10.9879	+	5.55796i	0.356869	+	0.180514i
$949$	3.59825	−	18.0896i	0.116804	−	0.587214i
$950$	−10.1025	+	8.68346i	−0.327768	+	0.281729i
$951$	11.3383			0.367670
$952$	5.45759	+	8.04563i	0.176881	+	0.260760i
$953$			32.3758i			1.04876i	0.851486	+	0.524378i	$0.175702\pi$
$953$			32.3758i			1.04876i	−0.851486	+	0.524378i	$0.824298\pi$
$954$	2.42140	−	1.48874i	0.0783958	−	0.0481997i
$955$	−22.3294	−	28.2760i	−0.722563	−	0.914989i
$956$	−27.0767	−	13.6961i	−0.875723	−	0.442964i
$957$	69.0595	−	46.1441i	2.23238	−	1.49163i
$958$	−6.81902	+	2.52707i	−0.220313	+	0.0816458i
$959$	−6.46303	+	9.67261i	−0.208702	+	0.312345i
$960$	−29.4548	−	4.37395i	−0.950650	−	0.141169i
$961$	24.3401	+	10.0820i	0.785163	+	0.325225i
$962$	1.43743	−	3.13012i	0.0463445	−	0.100919i
$963$	0.0167202	+	0.0840581i	0.000538801	+	0.00270873i
$964$	−5.92278	−	4.64097i	−0.190760	−	0.149475i
$965$	22.3833	−	1.78048i	0.720545	−	0.0573158i
$966$	−0.272207	+	7.19788i	−0.00875811	+	0.231588i
$967$	5.62174	+	13.5721i	0.180783	+	0.436448i	0.988128	−	0.153631i	$-0.0490966\pi$
$967$	5.62174	+	13.5721i	0.180783	+	0.436448i	−0.807345	+	0.590079i	$0.799097\pi$
$968$	29.5325	+	57.3343i	0.949212	+	1.84279i
$969$	−3.47778	+	12.4539i	−0.111723	+	0.400077i
$970$	2.37455	−	3.89507i	0.0762422	−	0.125063i
$971$	3.01986	−	1.25087i	0.0969118	−	0.0401422i	−0.333701	−	0.942679i	$-0.608298\pi$
$971$	3.01986	−	1.25087i	0.0969118	−	0.0401422i	0.430613	+	0.902537i	$0.358298\pi$
$972$	4.71455	−	0.572067i	0.151219	−	0.0183490i
$973$	7.43275	−	7.43275i	0.238283	−	0.238283i
$974$	22.7360	−	21.0790i	0.728508	−	0.675415i
$975$	−3.23896	−	8.73446i	−0.103730	−	0.279727i
$976$	−1.93331	−	42.7894i	−0.0618836	−	1.36966i
$977$	−18.0342	−	7.47000i	−0.576964	−	0.238986i	0.0750671	−	0.997178i	$-0.476083\pi$
$977$	−18.0342	−	7.47000i	−0.576964	−	0.238986i	−0.652031	+	0.758192i	$0.726083\pi$
$978$	8.84486	+	2.10971i	0.282827	+	0.0674612i
$979$	−38.0443	+	56.9374i	−1.21590	+	1.81973i
$980$	−27.6757	−	5.39640i	−0.884068	−	0.172382i
$981$	0.186688	−	0.124741i	0.00596047	−	0.00398266i
$982$	−12.3492	−	8.94451i	−0.394079	−	0.285431i
$983$	8.06269	+	1.60377i	0.257160	+	0.0511523i	0.321986	−	0.946744i	$-0.395649\pi$
$983$	8.06269	+	1.60377i	0.257160	+	0.0511523i	−0.0648267	+	0.997897i	$0.520649\pi$
$984$	11.2974	−	13.3463i	0.360147	−	0.425464i
$985$	25.0237	−	29.3488i	0.797323	−	0.935131i
$986$	−31.1389	−	39.1727i	−0.991666	−	1.24751i
$987$			13.8341i			0.440345i
$988$	−3.19872	+	2.74827i	−0.101765	+	0.0874343i
$989$	−16.2093	−	3.22424i	−0.515427	−	0.102525i
$990$	4.09173	−	0.992334i	0.130044	−	0.0315384i
$991$	−31.0051	−	46.4024i	−0.984910	−	1.47402i	−0.877366	−	0.479822i	$-0.840701\pi$
$991$	−31.0051	−	46.4024i	−0.984910	−	1.47402i	−0.107544	−	0.994200i	$-0.534299\pi$
$992$	−6.70554	+	10.1970i	−0.212901	+	0.323757i
$993$	16.0188	−	23.9738i	0.508340	−	0.760785i
$994$	3.19949	+	0.763157i	0.101482	+	0.0242059i
$995$	25.0246	−	12.7771i	0.793332	−	0.405060i
$996$	1.56771	−	5.62193i	0.0496749	−	0.178138i
$997$	−8.05985	+	1.60320i	−0.255258	+	0.0507740i	−0.321060	−	0.947059i	$-0.604039\pi$
$997$	−8.05985	+	1.60320i	−0.255258	+	0.0507740i	0.0658025	+	0.997833i	$0.479039\pi$
$998$	−29.9612	−	32.3164i	−0.948406	−	1.02296i
$999$	−8.27072	+	8.27072i	−0.261674	+	0.261674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.99.17	yes	832
5.4	even	2	inner	680.2.co.a.99.88	yes	832
8.3	odd	2	inner	680.2.co.a.99.96	yes	832
17.11	odd	16	inner	680.2.co.a.419.9	yes	832
40.19	odd	2	inner	680.2.co.a.99.9	✓	832
85.79	odd	16	inner	680.2.co.a.419.96	yes	832
136.11	even	16	inner	680.2.co.a.419.88	yes	832
680.419	even	16	inner	680.2.co.a.419.17	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.9	✓	832	40.19	odd	2	inner
680.2.co.a.99.17	yes	832	1.1	even	1	trivial
680.2.co.a.99.88	yes	832	5.4	even	2	inner
680.2.co.a.99.96	yes	832	8.3	odd	2	inner
680.2.co.a.419.9	yes	832	17.11	odd	16	inner
680.2.co.a.419.17	yes	832	680.419	even	16	inner
680.2.co.a.419.88	yes	832	136.11	even	16	inner
680.2.co.a.419.96	yes	832	85.79	odd	16	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20473 + 0.740697i) q^{2} +(1.63264 + 0.324753i) q^{3} +(0.902737 - 1.78468i) q^{4} +(2.22079 + 0.260961i) q^{5} +(-2.20744 + 0.818055i) q^{6} +(-0.693159 - 0.463154i) q^{7} +(0.234351 + 2.81870i) q^{8} +(-0.211574 - 0.0876370i) q^{9} +(-2.86874 + 1.33054i) q^{10} +(5.70222 - 1.13424i) q^{11} +(2.05343 - 2.62057i) q^{12} +(-0.791428 - 0.791428i) q^{13} +(1.17812 + 0.0445539i) q^{14} +(3.54101 + 1.14726i) q^{15} +(-2.37013 - 3.22218i) q^{16} +(-1.86239 + 3.67852i) q^{17} +(0.319802 - 0.0511338i) q^{18} +(1.74054 - 0.720955i) q^{19} +(2.47052 - 3.72781i) q^{20} +(-0.981272 - 0.981272i) q^{21} +(-6.02949 + 5.59007i) q^{22} +(0.716030 + 3.59973i) q^{23} +(-0.532770 + 4.67804i) q^{24} +(4.86380 + 1.15908i) q^{25} +(1.53966 + 0.367247i) q^{26} +(-4.46923 - 2.98625i) q^{27} +(-1.45232 + 0.818958i) q^{28} +(7.13568 - 4.76791i) q^{29} +(-5.11573 + 1.24067i) q^{30} +(-0.420894 + 2.11598i) q^{31} +(5.24202 + 2.12631i) q^{32} +9.67805 q^{33} +(-0.480995 - 5.81108i) q^{34} +(-1.41849 - 1.20945i) q^{35} +(-0.347400 + 0.298478i) q^{36} +(0.424529 - 2.13425i) q^{37} +(-1.56287 + 2.15777i) q^{38} +(-1.03510 - 1.54914i) q^{39} +(-0.215126 + 6.32090i) q^{40} +(-3.08795 - 2.06330i) q^{41} +(1.90899 + 0.455340i) q^{42} +(-1.72320 + 4.16017i) q^{43} +(3.12335 - 11.2005i) q^{44} +(-0.446992 - 0.249836i) q^{45} +(-3.52893 - 3.80633i) q^{46} +(-7.04908 - 7.04908i) q^{47} +(-2.82317 - 6.03039i) q^{48} +(-2.41283 - 5.82508i) q^{49} +(-6.71808 + 2.20623i) q^{50} +(-4.23523 + 5.40090i) q^{51} +(-2.12689 + 0.697990i) q^{52} +(8.10860 - 3.35869i) q^{53} +(7.59611 + 0.287267i) q^{54} +(12.9594 - 1.03086i) q^{55} +(1.14305 - 2.06235i) q^{56} +(3.07582 - 0.611818i) q^{57} +(-5.06498 + 11.0294i) q^{58} +(-4.00568 + 9.67056i) q^{59} +(5.24409 - 5.28388i) q^{60} +(8.90360 + 5.94920i) q^{61} +(-1.06023 - 2.86093i) q^{62} +(0.106065 + 0.158738i) q^{63} +(-7.89016 + 1.32113i) q^{64} +(-1.55106 - 1.96412i) q^{65} +(-11.6594 + 7.16850i) q^{66} -9.22896 q^{67} +(4.88372 + 6.64450i) q^{68} +6.10961i q^{69} +(2.60474 + 0.406389i) q^{70} +(2.73634 + 0.544291i) q^{71} +(0.197440 - 0.616903i) q^{72} +(9.15520 + 13.7017i) q^{73} +(1.06939 + 2.88564i) q^{74} +(7.56444 + 3.47189i) q^{75} +(0.284579 - 3.75713i) q^{76} +(-4.47788 - 1.85480i) q^{77} +(2.39446 + 1.09959i) q^{78} +(0.721559 + 3.62752i) q^{79} +(-4.42270 - 7.77430i) q^{80} +(-5.84108 - 5.84108i) q^{81} +(5.24841 + 0.198482i) q^{82} +(1.61962 - 0.670870i) q^{83} +(-2.63708 + 0.865421i) q^{84} +(-5.09592 + 7.68320i) q^{85} +(-1.00544 - 6.28824i) q^{86} +(13.1984 - 5.46697i) q^{87} +(4.53341 + 15.8070i) q^{88} +(-8.32848 + 8.32848i) q^{89} +(0.723556 - 0.0301016i) q^{90} +(0.182032 + 0.915138i) q^{91} +(7.07073 + 1.97173i) q^{92} +(-1.37434 + 3.31795i) q^{93} +(13.7135 + 3.27099i) q^{94} +(4.05351 - 1.14688i) q^{95} +(7.86784 + 5.17387i) q^{96} +(-1.19945 + 0.801448i) q^{97} +(7.22141 + 5.23046i) q^{98} +(-1.30585 - 0.259749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

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