LMFDB - Embedded newform 336.3.bv.a.325.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(61,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 10])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bv (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:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			325.23
Character	$\chi$	$=$	336.325
Dual form			336.3.bv.a.61.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.729511 - 1.86221i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-2.93563 + 2.71700i) q^{4} +(5.66629 + 1.51828i) q^{5} +(2.05530 + 2.78850i) q^{6} +(-2.28470 - 6.61666i) q^{7} +(7.20119 + 3.48467i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-1.30627 - 11.6594i) q^{10} +(-18.4302 + 4.93836i) q^{11} +(3.69340 - 5.86163i) q^{12} +(12.6887 + 12.6887i) q^{13} +(-10.6549 + 9.08151i) q^{14} -10.1605 q^{15} +(1.23583 - 15.9522i) q^{16} +(16.1678 + 9.33447i) q^{17} +(-4.68863 - 3.74389i) q^{18} +(-3.59750 + 13.4261i) q^{19} +(-20.7593 + 10.9382i) q^{20} +(6.78855 + 10.0457i) q^{21} +(22.6413 + 30.7183i) q^{22} +(27.4968 - 15.8753i) q^{23} +(-13.6100 - 2.60176i) q^{24} +(8.15103 + 4.70600i) q^{25} +(14.3724 - 32.8854i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(24.6845 + 13.2165i) q^{28} +(1.09119 - 1.09119i) q^{29} +(7.41220 + 18.9210i) q^{30} +(52.0589 + 30.0562i) q^{31} +(-30.6078 + 9.33593i) q^{32} +(28.6206 - 16.5241i) q^{33} +(5.58815 - 36.9173i) q^{34} +(-2.89986 - 40.9607i) q^{35} +(-3.55149 + 11.4624i) q^{36} +(4.13839 - 15.4447i) q^{37} +(27.6265 - 3.09516i) q^{38} +(-26.9167 - 15.5404i) q^{39} +(35.5133 + 30.6785i) q^{40} +8.66197 q^{41} +(13.7548 - 19.9701i) q^{42} +(16.2054 + 16.2054i) q^{43} +(40.6868 - 64.5721i) q^{44} +(16.9989 - 4.55483i) q^{45} +(-49.6222 - 39.6235i) q^{46} +(56.7381 - 32.7577i) q^{47} +(5.08359 + 27.2426i) q^{48} +(-38.5603 + 30.2342i) q^{49} +(2.81728 - 18.6120i) q^{50} +(-31.2337 - 8.36906i) q^{51} +(-71.7243 - 2.77411i) q^{52} +(45.8751 - 12.2922i) q^{53} +(9.52258 + 4.16179i) q^{54} -111.929 q^{55} +(6.60428 - 55.6092i) q^{56} -24.0749i q^{57} +(-2.82805 - 1.23598i) q^{58} +(4.66330 + 17.4037i) q^{59} +(29.8275 - 27.6061i) q^{60} +(-10.8844 + 40.6210i) q^{61} +(17.9934 - 118.871i) q^{62} +(-15.8608 - 13.7635i) q^{63} +(39.7142 + 50.1875i) q^{64} +(52.6327 + 91.1626i) q^{65} +(-51.6503 - 41.2429i) q^{66} +(10.1959 + 38.0517i) q^{67} +(-72.8243 + 16.5253i) q^{68} +(-38.8863 + 38.8863i) q^{69} +(-74.1618 + 35.2814i) q^{70} -29.6483i q^{71} +(23.9362 - 1.74835i) q^{72} +(-1.79304 + 3.10563i) q^{73} +(-31.7802 + 3.56052i) q^{74} +(-15.7466 - 4.21928i) q^{75} +(-25.9177 - 49.1883i) q^{76} +(74.7830 + 110.664i) q^{77} +(-9.30336 + 61.4614i) q^{78} +(24.9201 + 43.1629i) q^{79} +(31.2224 - 88.5134i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-6.31900 - 16.1304i) q^{82} +(-4.13095 - 4.13095i) q^{83} +(-47.2228 - 11.0459i) q^{84} +(77.4390 + 77.4390i) q^{85} +(18.3558 - 41.9998i) q^{86} +(-1.33643 + 2.31476i) q^{87} +(-149.928 - 28.6611i) q^{88} +(-30.2420 - 52.3807i) q^{89} +(-20.8829 - 28.3326i) q^{90} +(54.9667 - 112.946i) q^{91} +(-37.5872 + 121.313i) q^{92} +(-100.570 - 26.9477i) q^{93} +(-102.393 - 81.7609i) q^{94} +(-40.7690 + 70.6139i) q^{95} +(47.0227 - 29.3404i) q^{96} +42.9368i q^{97} +(84.4324 + 49.7510i) q^{98} +(-40.4756 + 40.4756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) $ 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.729511	−	1.86221i	−0.364755	−	0.931103i
$2$	−0.729511	−	1.86221i	−0.364755	−	0.931103i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$3$	−1.67303	+	0.448288i	−0.557678	+	0.149429i
$4$	−2.93563	+	2.71700i	−0.733907	+	0.679250i
$5$	5.66629	+	1.51828i	1.13326	+	0.303656i	0.776237	−	0.630441i	$-0.217126\pi$
$5$	5.66629	+	1.51828i	1.13326	+	0.303656i	0.357021	+	0.934097i	$0.383793\pi$
$6$	2.05530	+	2.78850i	0.342550	+	0.464750i
$7$	−2.28470	−	6.61666i	−0.326386	−	0.945237i
$7$	−2.28470	−	6.61666i	−0.326386	−	0.945237i
$8$	7.20119	+	3.48467i	0.900148	+	0.435583i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	−1.30627	−	11.6594i	−0.130627	−	1.16594i
$11$	−18.4302	+	4.93836i	−1.67547	+	0.448942i	−0.966579	−	0.256371i	$-0.917473\pi$
$11$	−18.4302	+	4.93836i	−1.67547	+	0.448942i	−0.708896	+	0.705313i	$0.750807\pi$
$12$	3.69340	−	5.86163i	0.307784	−	0.488470i
$13$	12.6887	+	12.6887i	0.976051	+	0.976051i	0.999720	−	0.0236687i	$-0.00753469\pi$
$13$	12.6887	+	12.6887i	0.976051	+	0.976051i	−0.0236687	+	0.999720i	$0.507535\pi$
$14$	−10.6549	+	9.08151i	−0.761062	+	0.648679i
$15$	−10.1605			−0.677367
$16$	1.23583	−	15.9522i	0.0772393	−	0.997013i
$17$	16.1678	+	9.33447i	0.951045	+	0.549086i	0.893406	−	0.449251i	$-0.148309\pi$
$17$	16.1678	+	9.33447i	0.951045	+	0.549086i	0.0576399	+	0.998337i	$0.481642\pi$
$18$	−4.68863	−	3.74389i	−0.260480	−	0.207994i
$19$	−3.59750	+	13.4261i	−0.189342	+	0.706635i	0.804317	+	0.594200i	$0.202531\pi$
$19$	−3.59750	+	13.4261i	−0.189342	+	0.706635i	−0.993659	+	0.112434i	$0.964135\pi$
$20$	−20.7593	+	10.9382i	−1.03796	+	0.546910i
$21$	6.78855	+	10.0457i	0.323264	+	0.478366i
$22$	22.6413	+	30.7183i	1.02915	+	1.39629i
$23$	27.4968	−	15.8753i	1.19551	−	0.690229i	0.235961	−	0.971763i	$-0.424176\pi$
$23$	27.4968	−	15.8753i	1.19551	−	0.690229i	0.959551	+	0.281533i	$0.0908430\pi$
$24$	−13.6100	−	2.60176i	−0.567081	−	0.108407i
$25$	8.15103	+	4.70600i	0.326041	+	0.188240i
$26$	14.3724	−	32.8854i	0.552785	−	1.26482i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	24.6845	+	13.2165i	0.881589	+	0.472018i
$29$	1.09119	−	1.09119i	0.0376272	−	0.0376272i	−0.688043	−	0.725670i	$-0.741530\pi$
$29$	1.09119	−	1.09119i	0.0376272	−	0.0376272i	0.725670	+	0.688043i	$0.241530\pi$
$30$	7.41220	+	18.9210i	0.247073	+	0.630699i
$31$	52.0589	+	30.0562i	1.67932	+	0.969556i	0.962095	+	0.272714i	$0.0879213\pi$
$31$	52.0589	+	30.0562i	1.67932	+	0.969556i	0.717225	+	0.696842i	$0.245412\pi$
$32$	−30.6078	+	9.33593i	−0.956495	+	0.291748i
$33$	28.6206	−	16.5241i	0.867290	−	0.500730i
$34$	5.58815	−	36.9173i	0.164357	−	1.08580i
$35$	−2.89986	−	40.9607i	−0.0828532	−	1.17031i
$36$	−3.55149	+	11.4624i	−0.0986524	+	0.318400i
$37$	4.13839	−	15.4447i	0.111848	−	0.417424i	−0.887183	−	0.461417i	$-0.847341\pi$
$37$	4.13839	−	15.4447i	0.111848	−	0.417424i	0.999032	+	0.0439928i	$0.0140079\pi$
$38$	27.6265	−	3.09516i	0.727013	−	0.0814516i
$39$	−26.9167	−	15.5404i	−0.690172	−	0.398471i
$40$	35.5133	+	30.6785i	0.887833	+	0.766963i
$41$	8.66197			0.211268			0.105634	−	0.994405i	$-0.466313\pi$
$41$	8.66197			0.211268			0.105634	+	0.994405i	$0.466313\pi$
$42$	13.7548	−	19.9701i	0.327496	−	0.475479i
$43$	16.2054	+	16.2054i	0.376870	+	0.376870i	0.869972	−	0.493102i	$-0.164137\pi$
$43$	16.2054	+	16.2054i	0.376870	+	0.376870i	−0.493102	+	0.869972i	$0.664137\pi$
$44$	40.6868	−	64.5721i	0.924699	−	1.46755i
$45$	16.9989	−	4.55483i	0.377753	−	0.101219i
$46$	−49.6222	−	39.6235i	−1.07874	−	0.861381i
$47$	56.7381	−	32.7577i	1.20719	−	0.696973i	0.245048	−	0.969511i	$-0.421196\pi$
$47$	56.7381	−	32.7577i	1.20719	−	0.696973i	0.962145	+	0.272538i	$0.0878631\pi$
$48$	5.08359	+	27.2426i	0.105908	+	0.567553i
$49$	−38.5603	+	30.2342i	−0.786944	+	0.617024i
$50$	2.81728	−	18.6120i	0.0563456	−	0.372240i
$51$	−31.2337	−	8.36906i	−0.612426	−	0.164099i
$52$	−71.7243	−	2.77411i	−1.37931	−	0.0533483i
$53$	45.8751	−	12.2922i	0.865568	−	0.231928i	0.201398	−	0.979510i	$-0.435452\pi$
$53$	45.8751	−	12.2922i	0.865568	−	0.231928i	0.664170	+	0.747581i	$0.268785\pi$
$54$	9.52258	+	4.16179i	0.176344	+	0.0770702i
$55$	−111.929			−2.03507
$56$	6.60428	−	55.6092i	0.117934	−	0.993021i
$57$		−	24.0749i		−	0.422367i
$58$	−2.82805	−	1.23598i	−0.0487595	−	0.0213101i
$59$	4.66330	+	17.4037i	0.0790389	+	0.294977i	0.994119	−	0.108295i	$-0.0345392\pi$
$59$	4.66330	+	17.4037i	0.0790389	+	0.294977i	−0.915080	+	0.403273i	$0.867873\pi$
$60$	29.8275	−	27.6061i	0.497125	−	0.460102i
$61$	−10.8844	+	40.6210i	−0.178432	+	0.665918i	0.817509	+	0.575915i	$0.195354\pi$
$61$	−10.8844	+	40.6210i	−0.178432	+	0.665918i	−0.995942	+	0.0900024i	$0.971313\pi$
$62$	17.9934	−	118.871i	0.290216	−	1.91727i
$63$	−15.8608	−	13.7635i	−0.251759	−	0.218469i
$64$	39.7142	+	50.1875i	0.620534	+	0.784179i
$65$	52.6327	+	91.1626i	0.809734	+	1.40250i
$66$	−51.6503	−	41.2429i	−0.782580	−	0.624892i
$67$	10.1959	+	38.0517i	0.152178	+	0.567936i	0.999330	+	0.0365864i	$0.0116484\pi$
$67$	10.1959	+	38.0517i	0.152178	+	0.567936i	−0.847152	+	0.531350i	$0.821685\pi$
$68$	−72.8243	+	16.5253i	−1.07095	+	0.243019i
$69$	−38.8863	+	38.8863i	−0.563570	+	0.563570i
$70$	−74.1618	+	35.2814i	−1.05945	+	0.504020i
$71$		−	29.6483i		−	0.417582i	−0.977960	−	0.208791i	$-0.933047\pi$
$71$		−	29.6483i		−	0.417582i	0.977960	−	0.208791i	$-0.0669529\pi$
$72$	23.9362	−	1.74835i	0.332448	−	0.0242826i
$73$	−1.79304	+	3.10563i	−0.0245621	+	0.0425429i	−0.878045	−	0.478578i	$-0.841152\pi$
$73$	−1.79304	+	3.10563i	−0.0245621	+	0.0425429i	0.853483	+	0.521121i	$0.174486\pi$
$74$	−31.7802	+	3.56052i	−0.429462	+	0.0481152i
$75$	−15.7466	−	4.21928i	−0.209954	−	0.0562571i
$76$	−25.9177	−	49.1883i	−0.341022	−	0.647215i
$77$	74.7830	+	110.664i	0.971208	+	1.43719i
$78$	−9.30336	+	61.4614i	−0.119274	+	0.787966i
$79$	24.9201	+	43.1629i	0.315444	+	0.546365i	0.979532	−	0.201289i	$-0.0645132\pi$
$79$	24.9201	+	43.1629i	0.315444	+	0.546365i	−0.664088	+	0.747655i	$0.731180\pi$
$80$	31.2224	−	88.5134i	0.390280	−	1.10642i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	−6.31900	−	16.1304i	−0.0770610	−	0.196712i
$83$	−4.13095	−	4.13095i	−0.0497705	−	0.0497705i	0.681784	−	0.731554i	$-0.261205\pi$
$83$	−4.13095	−	4.13095i	−0.0497705	−	0.0497705i	−0.731554	+	0.681784i	$0.761205\pi$
$84$	−47.2228	−	11.0459i	−0.562176	−	0.131499i
$85$	77.4390	+	77.4390i	0.911047	+	0.911047i
$86$	18.3558	−	41.9998i	0.213439	−	0.488370i
$87$	−1.33643	+	2.31476i	−0.0153612	+	0.0266064i
$88$	−149.928	−	28.6611i	−1.70373	−	0.325695i
$89$	−30.2420	−	52.3807i	−0.339798	−	0.588547i	0.644597	−	0.764523i	$-0.277025\pi$
$89$	−30.2420	−	52.3807i	−0.339798	−	0.588547i	−0.984395	+	0.175976i	$0.943692\pi$
$90$	−20.8829	−	28.3326i	−0.232032	−	0.314807i
$91$	54.9667	−	112.946i	0.604030	−	1.24117i
$92$	−37.5872	+	121.313i	−0.408557	+	1.31862i
$93$	−100.570	−	26.9477i	−1.08140	−	0.289760i
$94$	−102.393	−	81.7609i	−1.08928	−	0.869797i
$95$	−40.7690	+	70.6139i	−0.429147	+	0.743304i
$96$	47.0227	−	29.3404i	0.489820	−	0.305630i
$97$			42.9368i			0.442647i	0.975200	+	0.221324i	$0.0710377\pi$
$97$			42.9368i			0.442647i	−0.975200	+	0.221324i	$0.928962\pi$
$98$	84.4324	+	49.7510i	0.861555	+	0.507664i
$99$	−40.4756	+	40.4756i	−0.408844	+	0.408844i
$100$	−36.7146	+	8.33128i	−0.367146	+	0.0833128i
$101$	−32.6194	−	121.737i	−0.322965	−	1.20532i	−0.916342	−	0.400396i	$-0.868873\pi$
$101$	−32.6194	−	121.737i	−0.322965	−	1.20532i	0.593378	−	0.804924i	$-0.297794\pi$
$102$	7.20043	+	64.2690i	0.0705925	+	0.630088i
$103$	28.1974	+	48.8393i	0.273761	+	0.474168i	0.969822	−	0.243815i	$-0.0783989\pi$
$103$	28.1974	+	48.8393i	0.273761	+	0.474168i	−0.696061	+	0.717983i	$0.745066\pi$
$104$	47.1577	+	135.589i	0.453439	+	1.30374i
$105$	23.2137	+	67.2286i	0.221083	+	0.640272i
$106$	−56.3570	−	76.4616i	−0.531670	−	0.721336i
$107$	−49.1869	+	183.568i	−0.459691	+	1.71559i	0.214226	+	0.976784i	$0.431277\pi$
$107$	−49.1869	+	183.568i	−0.459691	+	1.71559i	−0.673918	+	0.738807i	$0.735390\pi$
$108$	0.803295	−	20.7691i	0.00743791	−	0.192306i
$109$	42.0495	+	156.931i	0.385776	+	1.43973i	0.836941	+	0.547294i	$0.184342\pi$
$109$	42.0495	+	156.931i	0.385776	+	1.43973i	−0.451165	+	0.892441i	$0.648991\pi$
$110$	81.6532	+	208.435i	0.742302	+	1.89486i
$111$			27.6947i			0.249502i
$112$	−108.374	+	28.2690i	−0.967623	+	0.252402i
$113$	−54.1422			−0.479134			−0.239567	−	0.970880i	$-0.577006\pi$
$113$	−54.1422			−0.479134			−0.239567	+	0.970880i	$0.577006\pi$
$114$	−44.8325	+	17.5629i	−0.393268	+	0.154061i
$115$	179.908	−	48.2061i	1.56442	−	0.419184i
$116$	−0.238565	+	6.16808i	−0.00205660	+	0.0531731i
$117$	51.9991	+	13.9331i	0.444437	+	0.119087i
$118$	29.0073	−	21.3802i	0.245825	−	0.181188i
$119$	24.8244	−	128.303i	0.208609	−	1.07818i
$120$	−73.1677	−	35.4060i	−0.609731	−	0.295050i
$121$	210.497	−	121.530i	1.73964	−	1.00438i
$122$	83.5849	−	9.36451i	0.685122	−	0.0767583i
$123$	−14.4918	+	3.88306i	−0.117819	+	0.0315696i
$124$	−234.488	+	53.2101i	−1.89104	+	0.429114i
$125$	−64.6592	−	64.6592i	−0.517274	−	0.517274i
$126$	−14.0599	+	39.5768i	−0.111586	+	0.314101i
$127$	−203.416			−1.60170			−0.800852	−	0.598862i	$-0.795620\pi$
$127$	−203.416			−1.60170			−0.800852	+	0.598862i	$0.795620\pi$
$128$	64.4876	−	110.568i	0.503809	−	0.863815i
$129$	−34.3768	−	19.8475i	−0.266487	−	0.153856i
$130$	131.367	−	164.517i	1.01052	−	1.26552i
$131$	38.4604	−	143.536i	0.293591	−	1.09569i	−0.648740	−	0.761010i	$-0.724704\pi$
$131$	38.4604	−	143.536i	0.293591	−	1.09569i	0.942330	−	0.334684i	$-0.108630\pi$
$132$	−39.1234	+	126.271i	−0.296389	+	0.956596i
$133$	97.0548	−	6.87111i	0.729735	−	0.0516625i
$134$	63.4222	−	46.7461i	0.473300	−	0.348851i
$135$	−26.3978	+	15.2408i	−0.195539	+	0.112895i
$136$	83.8996	+	123.559i	0.616909	+	0.908519i
$137$	−133.640	−	77.1571i	−0.975474	−	0.563190i	−0.0745733	−	0.997216i	$-0.523759\pi$
$137$	−133.640	−	77.1571i	−0.975474	−	0.563190i	−0.900901	+	0.434025i	$0.857093\pi$
$138$	100.782	+	44.0464i	0.730307	+	0.319177i
$139$	−82.0748	+	82.0748i	−0.590466	+	0.590466i	−0.937757	−	0.347291i	$-0.887102\pi$
$139$	−82.0748	+	82.0748i	−0.590466	+	0.590466i	0.347291	+	0.937757i	$0.387102\pi$
$140$	119.803	+	112.366i	0.855736	+	0.802618i
$141$	−80.2397	+	80.2397i	−0.569076	+	0.569076i
$142$	−55.2114	+	21.6288i	−0.388812	+	0.152315i
$143$	−296.516	−	171.194i	−2.07354	−	1.19716i
$144$	−20.7175	−	43.2988i	−0.143872	−	0.300686i
$145$	7.83971	−	4.52626i	0.0540670	−	0.0312156i
$146$	7.09136	+	1.07341i	0.0485710	+	0.00735215i
$147$	50.9590	−	67.8689i	0.346660	−	0.461693i
$148$	29.8144	+	56.5839i	0.201449	+	0.382324i
$149$	−7.60722	+	28.3905i	−0.0510552	+	0.190541i	−0.986744	−	0.162287i	$-0.948113\pi$
$149$	−7.60722	+	28.3905i	−0.0510552	+	0.190541i	0.935688	+	0.352827i	$0.114780\pi$
$150$	3.63012	+	32.4014i	0.0242008	+	0.216009i
$151$	−0.147788	−	0.0853252i	−0.000978726	−	0.000565067i	0.499511	−	0.866308i	$-0.333513\pi$
$151$	−0.147788	−	0.0853252i	−0.000978726	−	0.000565067i	−0.500489	+	0.865743i	$0.666847\pi$
$152$	−72.6916	+	84.1474i	−0.478234	+	0.553602i
$153$	56.0068			0.366058
$154$	151.524	−	219.992i	0.983921	−	1.42852i
$155$	249.347	+	249.347i	1.60869	+	1.60869i
$156$	121.241	−	27.5119i	0.777184	−	0.176359i
$157$	−127.756	+	34.2322i	−0.813734	+	0.218039i	−0.641605	−	0.767035i	$-0.721731\pi$
$157$	−127.756	+	34.2322i	−0.813734	+	0.218039i	−0.172129	+	0.985074i	$0.555065\pi$
$158$	62.1987	−	77.8941i	0.393663	−	0.493001i
$159$	−71.2401	+	41.1305i	−0.448051	+	0.258682i
$160$	−187.607	+	6.42888i	−1.17255	+	0.0401805i
$161$	−167.863	−	145.666i	−1.04263	−	0.904761i
$162$	−17.7973	−	2.69396i	−0.109860	−	0.0166294i
$163$	−179.657	−	48.1388i	−1.10219	−	0.295330i	−0.338532	−	0.940955i	$-0.609930\pi$
$163$	−179.657	−	48.1388i	−1.10219	−	0.295330i	−0.763655	+	0.645625i	$0.776597\pi$
$164$	−25.4283	+	23.5346i	−0.155051	+	0.143503i
$165$	187.261	−	50.1763i	1.13491	−	0.304099i
$166$	−4.67911	+	10.7062i	−0.0281874	+	0.0644955i
$167$	−202.685			−1.21368			−0.606840	−	0.794824i	$-0.707563\pi$
$167$	−202.685			−1.21368			−0.606840	+	0.794824i	$0.707563\pi$
$168$	13.8798	+	95.9966i	0.0826176	+	0.571408i
$169$			153.004i			0.905352i
$170$	87.7148	−	200.700i	0.515969	−	1.18059i
$171$	10.7925	+	40.2782i	0.0631141	+	0.235545i
$172$	−91.6031	−	3.54297i	−0.532576	−	0.0205987i
$173$	41.3307	−	154.248i	0.238906	−	0.891609i	−0.737443	−	0.675409i	$-0.763967\pi$
$173$	41.3307	−	154.248i	0.238906	−	0.891609i	0.976349	−	0.216200i	$-0.0693663\pi$
$174$	5.28550	+	0.800062i	0.0303764	+	0.00459806i
$175$	12.5153	−	64.6844i	0.0715160	−	0.369625i
$176$	56.0012	+	300.106i	0.318188	+	1.70515i
$177$	−15.6037	−	27.0264i	−0.0881565	−	0.152692i
$178$	−75.4818	+	94.5292i	−0.424055	+	0.531063i
$179$	37.8094	+	141.106i	0.211225	+	0.788304i	0.987461	+	0.157861i	$0.0504599\pi$
$179$	37.8094	+	141.106i	0.211225	+	0.788304i	−0.776236	+	0.630443i	$0.782873\pi$
$180$	−37.5269	+	59.5572i	−0.208483	+	0.330873i
$181$	−60.1237	+	60.1237i	−0.332175	+	0.332175i	−0.853412	−	0.521237i	$-0.825471\pi$
$181$	−60.1237	+	60.1237i	−0.332175	+	0.332175i	0.521237	+	0.853412i	$0.325471\pi$
$182$	−250.428	−	19.9638i	−1.37598	−	0.109691i
$183$		−	72.8395i		−	0.398030i
$184$	253.329	−	18.5037i	1.37679	−	0.100563i
$185$	46.8987	−	81.2309i	0.253506	−	0.439086i
$186$	23.1848	+	206.941i	0.124650	+	1.11259i
$187$	−344.073	−	92.1940i	−1.83996	−	0.493016i
$188$	−77.5591	+	250.322i	−0.412548	+	1.33150i
$189$	32.7057	+	15.9166i	0.173046	+	0.0842149i
$190$	161.239	+	24.4066i	0.848627	+	0.128456i
$191$	−180.974	−	313.457i	−0.947509	−	1.64113i	−0.750647	−	0.660703i	$-0.770258\pi$
$191$	−180.974	−	313.457i	−0.947509	−	1.64113i	−0.196862	−	0.980431i	$-0.563075\pi$
$192$	−88.9416	−	66.1619i	−0.463237	−	0.344593i
$193$	128.975	−	223.392i	0.668265	−	1.15747i	−0.310124	−	0.950696i	$-0.600370\pi$
$193$	128.975	−	223.392i	0.668265	−	1.15747i	0.978389	−	0.206773i	$-0.0662962\pi$
$194$	79.9572	−	31.3228i	0.412150	−	0.161458i
$195$	−128.923	−	128.923i	−0.661145	−	0.661145i
$196$	31.0524	−	193.525i	0.158431	−	0.987370i
$197$	200.105	+	200.105i	1.01576	+	1.01576i	0.999874	+	0.0158874i	$0.00505732\pi$
$197$	200.105	+	200.105i	1.01576	+	1.01576i	0.0158874	+	0.999874i	$0.494943\pi$
$198$	104.901	+	45.8465i	0.529804	+	0.231548i
$199$	119.109	−	206.303i	0.598539	−	1.03670i	−0.394498	−	0.918897i	$-0.629081\pi$
$199$	119.109	−	206.303i	0.598539	−	1.03670i	0.993037	−	0.117803i	$-0.0375853\pi$
$200$	42.2982	+	62.2924i	0.211491	+	0.311462i
$201$	−34.1163	−	59.0911i	−0.169733	−	0.293985i
$202$	−202.904	+	149.553i	−1.00447	+	0.740361i
$203$	−9.71305	−	4.72698i	−0.0478476	−	0.0232856i
$204$	114.429	−	60.2936i	0.560928	−	0.295557i
$205$	49.0812	+	13.1513i	0.239421	+	0.0641526i
$206$	70.3786	−	88.1382i	0.341644	−	0.427855i
$207$	47.6258	−	82.4903i	0.230076	−	0.398504i
$208$	218.093	−	186.731i	1.04852	−	0.897746i
$209$		−	265.211i		−	1.26895i
$210$	108.259	−	92.2728i	0.515519	−	0.439394i
$211$	262.933	−	262.933i	1.24613	−	1.24613i	0.288714	−	0.957415i	$-0.406772\pi$
$211$	262.933	−	262.933i	1.24613	−	1.24613i	0.957415	−	0.288714i	$-0.0932278\pi$
$212$	−101.274	+	160.728i	−0.477709	+	0.758150i
$213$	13.2910	+	49.6027i	0.0623990	+	0.232876i
$214$	377.724	−	42.3187i	1.76507	−	0.197751i
$215$	67.2202	+	116.429i	0.312652	+	0.541529i
$216$	−39.2623	+	13.6554i	−0.181770	+	0.0632193i
$217$	79.9326	−	413.125i	0.368353	−	1.90380i
$218$	261.562	−	192.788i	1.19983	−	0.884348i
$219$	1.60759	−	5.99961i	0.00734060	−	0.0273955i
$220$	328.581	−	304.110i	1.49355	−	1.38232i
$221$	86.7055	+	323.589i	0.392333	+	1.46421i
$222$	51.5732	−	20.2036i	0.232312	−	0.0910070i
$223$			385.806i			1.73007i	0.501709	+	0.865036i	$0.332705\pi$
$223$			385.806i			1.73007i	−0.501709	+	0.865036i	$0.667295\pi$
$224$	131.702	+	181.192i	0.587957	+	0.808892i
$225$	28.2360			0.125493
$226$	39.4973	+	100.824i	0.174767	+	0.446123i
$227$	243.229	−	65.1729i	1.07149	−	0.287105i	0.320386	−	0.947287i	$-0.396187\pi$
$227$	243.229	−	65.1729i	1.07149	−	0.287105i	0.751106	+	0.660182i	$0.229521\pi$
$228$	65.4116	+	70.6751i	0.286893	+	0.309978i
$229$	39.2335	+	10.5126i	0.171325	+	0.0459065i	0.343462	−	0.939167i	$-0.388400\pi$
$229$	39.2335	+	10.5126i	0.171325	+	0.0459065i	−0.172137	+	0.985073i	$0.555067\pi$
$230$	−221.014	−	299.859i	−0.960932	−	1.30373i
$231$	−174.724	−	151.620i	−0.756379	−	0.656363i
$232$	11.6603	−	4.05542i	0.0502598	−	0.0174803i
$233$	−80.7208	+	46.6042i	−0.346441	+	0.200018i	−0.663117	−	0.748516i	$-0.730767\pi$
$233$	−80.7208	+	46.6042i	−0.346441	+	0.200018i	0.316676	+	0.948534i	$0.397433\pi$
$234$	−11.9876	−	106.997i	−0.0512289	−	0.457254i
$235$	371.230	−	99.4707i	1.57970	−	0.423279i
$236$	−60.9755	−	38.4205i	−0.258371	−	0.162799i
$237$	−61.0415	−	61.0415i	−0.257559	−	0.257559i
$238$	−257.037	+	47.3703i	−1.07999	+	0.199035i
$239$	210.868			0.882292			0.441146	−	0.897435i	$-0.354572\pi$
$239$	210.868			0.882292			0.441146	+	0.897435i	$0.354572\pi$
$240$	−12.5567	+	162.083i	−0.0523194	+	0.675344i
$241$	380.541	+	219.705i	1.57901	+	0.911641i	0.994998	+	0.0998950i	$0.0318507\pi$
$241$	380.541	+	219.705i	1.57901	+	0.911641i	0.584011	+	0.811746i	$0.301483\pi$
$242$	−379.874	−	303.331i	−1.56973	−	1.25343i
$243$	−4.03459	+	15.0573i	−0.0166032	+	0.0619642i
$244$	−78.4147	−	148.821i	−0.321372	−	0.609922i
$245$	−264.398	+	112.770i	−1.07917	+	0.460287i
$246$	17.8029	+	24.1539i	0.0723697	+	0.0981867i
$247$	−216.006	+	124.711i	−0.874519	+	0.504904i
$248$	270.150	+	397.849i	1.08931	+	1.60423i
$249$	8.76306	+	5.05936i	0.0351930	+	0.0203187i
$250$	−73.2392	+	167.578i	−0.292957	+	0.670314i
$251$	308.202	−	308.202i	1.22790	−	1.22790i	0.263138	−	0.964758i	$-0.415243\pi$
$251$	308.202	−	308.202i	1.22790	−	1.22790i	0.964758	−	0.263138i	$-0.0847574\pi$
$252$	83.9569	−	2.68923i	0.333162	−	0.0106716i
$253$	−428.374	+	428.374i	−1.69318	+	1.69318i
$254$	148.394	+	378.803i	0.584230	+	1.49135i
$255$	−164.273	−	94.8430i	−0.644207	−	0.371933i
$256$	−252.945	−	39.4284i	−0.988068	−	0.154017i
$257$	−98.6973	+	56.9829i	−0.384036	+	0.221723i	−0.679573	−	0.733608i	$-0.737835\pi$
$257$	−98.6973	+	56.9829i	−0.384036	+	0.221723i	0.295537	+	0.955331i	$0.404502\pi$
$258$	−11.8818	+	78.4957i	−0.0460536	+	0.304247i
$259$	−111.647	+	7.90420i	−0.431070	+	0.0305182i
$260$	−402.199	−	124.616i	−1.54692	−	0.479293i
$261$	1.19821	−	4.47177i	0.00459083	−	0.0171332i
$262$	−295.351	+	33.0899i	−1.12729	+	0.126297i
$263$	119.986	+	69.2737i	0.456219	+	0.263398i	0.710453	−	0.703745i	$-0.248490\pi$
$263$	119.986	+	69.2737i	0.456219	+	0.263398i	−0.254234	+	0.967143i	$0.581823\pi$
$264$	263.683	−	19.2599i	0.998799	−	0.0729542i
$265$	278.604			1.05134
$266$	−83.5980	−	175.724i	−0.314278	−	0.660615i
$267$	74.0775	+	74.0775i	0.277444	+	0.277444i
$268$	−133.318	−	84.0034i	−0.497455	−	0.313446i
$269$	−213.118	+	57.1047i	−0.792259	+	0.212285i	−0.632183	−	0.774819i	$-0.717841\pi$
$269$	−213.118	+	57.1047i	−0.792259	+	0.212285i	−0.160076	+	0.987105i	$0.551174\pi$
$270$	47.6389	+	38.0398i	0.176440	+	0.140888i
$271$	−226.954	+	131.032i	−0.837468	+	0.483512i	−0.856403	−	0.516308i	$-0.827306\pi$
$271$	−226.954	+	131.032i	−0.837468	+	0.483512i	0.0189346	+	0.999821i	$0.493973\pi$
$272$	168.886	−	246.376i	0.620904	−	0.905793i
$273$	−41.3286	+	213.604i	−0.151387	+	0.782432i
$274$	−46.1906	+	305.152i	−0.168579	+	1.11369i
$275$	−173.465	−	46.4799i	−0.630783	−	0.169018i
$276$	8.50168	−	219.810i	0.0308032	−	0.796413i
$277$	212.120	−	56.8374i	0.765776	−	0.205189i	0.145271	−	0.989392i	$-0.453594\pi$
$277$	212.120	−	56.8374i	0.765776	−	0.205189i	0.620505	+	0.784203i	$0.286928\pi$
$278$	212.715	+	92.9658i	0.765161	+	0.334409i
$279$	180.337			0.646371
$280$	121.852	−	305.071i	0.435186	−	1.08954i
$281$		−	145.122i		−	0.516449i	−0.966085	−	0.258224i	$-0.916863\pi$
$281$		−	145.122i		−	0.516449i	0.966085	−	0.258224i	$-0.0831373\pi$
$282$	207.959	+	90.8872i	0.737442	+	0.322295i
$283$	29.5712	+	110.361i	0.104492	+	0.389969i	0.998287	−	0.0585064i	$-0.0186338\pi$
$283$	29.5712	+	110.361i	0.104492	+	0.389969i	−0.893795	+	0.448475i	$0.851967\pi$
$284$	80.5545	+	87.0365i	0.283643	+	0.306467i
$285$	36.5524	−	136.416i	0.128254	−	0.478651i
$286$	−102.486	+	677.062i	−0.358344	+	2.36735i
$287$	−19.7900	−	57.3133i	−0.0689548	−	0.199698i
$288$	−65.5176	+	70.1672i	−0.227492	+	0.243636i
$289$	29.7646	+	51.5538i	0.102992	+	0.178387i
$290$	−14.1480	−	11.2972i	−0.0487862	−	0.0389559i
$291$	−19.2480	−	71.8346i	−0.0661444	−	0.246854i
$292$	−3.17431	−	13.9886i	−0.0108709	−	0.0479063i
$293$	111.884	−	111.884i	0.381855	−	0.381855i	−0.489915	−	0.871770i	$-0.662972\pi$
$293$	111.884	−	111.884i	0.381855	−	0.381855i	0.871770	+	0.489915i	$0.162972\pi$
$294$	−163.561	−	45.3851i	−0.556330	−	0.154371i
$295$			105.694i			0.358286i
$296$	83.6210	−	96.7992i	0.282503	−	0.327024i
$297$	49.5723	−	85.8617i	0.166910	−	0.289097i
$298$	58.4186	−	6.54498i	0.196036	−	0.0219630i
$299$	550.333	+	147.461i	1.84058	+	0.493182i
$300$	57.6899	−	30.3972i	0.192300	−	0.101324i
$301$	70.2010	−	144.250i	0.233226	−	0.479236i
$302$	−0.0510805	+	0.337457i	−0.000169141	+	0.00111741i
$303$	109.147	+	189.048i	0.360220	+	0.623920i
$304$	209.729	+	73.9804i	0.689899	+	0.243356i
$305$	−123.348	+	213.645i	−0.404419	+	0.700474i
$306$	−40.8576	−	104.296i	−0.133521	−	0.340837i
$307$	−14.5675	−	14.5675i	−0.0474511	−	0.0474511i	0.682983	−	0.730434i	$-0.260682\pi$
$307$	−14.5675	−	14.5675i	−0.0474511	−	0.0474511i	−0.730434	+	0.682983i	$0.760682\pi$
$308$	−520.209	−	121.682i	−1.68899	−	0.395072i
$309$	−69.0692	−	69.0692i	−0.223525	−	0.223525i
$310$	282.435	−	646.237i	0.911079	−	2.08464i
$311$	−309.745	+	536.494i	−0.995964	+	1.72506i	−0.420249	+	0.907409i	$0.638057\pi$
$311$	−309.745	+	536.494i	−0.995964	+	1.72506i	−0.575715	+	0.817651i	$0.695276\pi$
$312$	−139.679	−	205.705i	−0.447690	−	0.659311i
$313$	−169.422	−	293.448i	−0.541285	−	0.937533i	−0.998831	−	0.0483472i	$-0.984605\pi$
$313$	−169.422	−	293.448i	−0.541285	−	0.937533i	0.457545	−	0.889186i	$-0.348729\pi$
$314$	156.947	+	212.936i	0.499831	+	0.678139i
$315$	−68.9751	−	102.069i	−0.218969	−	0.324029i
$316$	−190.430	−	59.0023i	−0.602625	−	0.186716i
$317$	−189.838	−	50.8671i	−0.598860	−	0.160464i	−0.0533604	−	0.998575i	$-0.516993\pi$
$317$	−189.838	−	50.8671i	−0.598860	−	0.160464i	−0.545499	+	0.838111i	$0.683660\pi$
$318$	128.564	+	102.659i	0.404289	+	0.322826i
$319$	−14.7222	+	25.4995i	−0.0461510	+	0.0799358i
$320$	148.834	+	344.674i	0.465105	+	1.07711i
$321$		−	329.165i		−	1.02544i
$322$	−148.803	+	418.861i	−0.462121	+	1.30081i
$323$	−183.489	+	183.489i	−0.568076	+	0.568076i
$324$	7.96659	+	35.1075i	0.0245882	+	0.108356i
$325$	43.7128	+	163.138i	0.134501	+	0.501965i
$326$	41.4169	+	369.675i	0.127046	+	1.13397i
$327$	−140.701	−	243.700i	−0.430277	−	0.745261i
$328$	62.3765	+	30.1841i	0.190172	+	0.0920247i
$329$	−346.376	−	300.575i	−1.05282	−	0.913600i
$330$	−230.047	−	312.114i	−0.697113	−	0.945799i
$331$	−7.11030	+	26.5360i	−0.0214813	+	0.0801692i	−0.975834	−	0.218512i	$-0.929880\pi$
$331$	−7.11030	+	26.5360i	−0.0214813	+	0.0801692i	0.954353	+	0.298681i	$0.0965465\pi$
$332$	23.3507	+	0.903145i	0.0703335	+	0.00272032i
$333$	−12.4152	−	46.3341i	−0.0372828	−	0.139141i
$334$	147.861	+	377.441i	0.442696	+	1.13006i
$335$			231.092i			0.689828i
$336$	168.640	−	95.8775i	0.501905	−	0.285350i
$337$	234.321			0.695314			0.347657	−	0.937622i	$-0.386977\pi$
$337$	234.321			0.695314			0.347657	+	0.937622i	$0.386977\pi$
$338$	284.926	−	111.618i	0.842976	−	0.330232i
$339$	90.5816	−	24.2713i	0.267202	−	0.0715967i
$340$	−437.734	−	16.9304i	−1.28745	−	0.0497953i
$341$	−1107.89	−	296.857i	−3.24893	−	0.870549i
$342$	67.1330	−	49.4812i	0.196295	−	0.144682i
$343$	288.148	+	186.064i	0.840081	+	0.542461i
$344$	60.2277	+	173.169i	0.175080	+	0.503397i
$345$	−279.381	+	161.301i	−0.809801	+	0.467539i
$346$	−317.394	+	35.5595i	−0.917322	+	0.102773i
$347$	−110.332	+	29.5634i	−0.317959	+	0.0851970i	−0.414269	−	0.910154i	$-0.635963\pi$
$347$	−110.332	+	29.5634i	−0.317959	+	0.0851970i	0.0963096	+	0.995351i	$0.469296\pi$
$348$	−2.36595	−	10.4263i	−0.00679870	−	0.0299608i
$349$	−261.232	−	261.232i	−0.748514	−	0.748514i	0.225686	−	0.974200i	$-0.427538\pi$
$349$	−261.232	−	261.232i	−0.748514	−	0.748514i	−0.974200	+	0.225686i	$0.927538\pi$
$350$	−129.586	+	23.8818i	−0.370245	+	0.0682338i
$351$	−93.2423			−0.265647
$352$	518.005	−	323.216i	1.47161	−	0.918227i
$353$	101.712	+	58.7237i	0.288137	+	0.166356i	0.637101	−	0.770780i	$-0.280133\pi$
$353$	101.712	+	58.7237i	0.288137	+	0.166356i	−0.348964	+	0.937136i	$0.613467\pi$
$354$	−38.9457	+	48.7734i	−0.110016	+	0.137778i
$355$	45.0144	−	167.996i	0.126801	−	0.473228i
$356$	231.098	+	71.6028i	0.649151	+	0.201131i
$357$	15.9846	+	225.784i	0.0447749	+	0.632447i
$358$	235.187	−	173.347i	0.656947	−	0.484211i
$359$	497.641	−	287.313i	1.38619	−	0.800315i	0.393303	−	0.919409i	$-0.371332\pi$
$359$	497.641	−	287.313i	1.38619	−	0.800315i	0.992883	+	0.119094i	$0.0379989\pi$
$360$	138.284	+	26.4352i	0.384122	+	0.0734311i
$361$	145.318	+	83.8995i	0.402543	+	0.232409i
$362$	155.824	+	68.1019i	0.430452	+	0.188127i
$363$	−297.687	+	297.687i	−0.820075	+	0.820075i
$364$	145.513	+	480.913i	0.399762	+	1.32119i
$365$	−14.8751	+	14.8751i	−0.0407536	+	0.0407536i
$366$	−135.642	+	53.1372i	−0.370607	+	0.145184i
$367$	−450.930	−	260.345i	−1.22869	−	0.709386i	−0.261936	−	0.965085i	$-0.584361\pi$
$367$	−450.930	−	260.345i	−1.22869	−	0.709386i	−0.966756	+	0.255699i	$0.917694\pi$
$368$	−219.264	−	458.253i	−0.595827	−	1.24525i
$369$	22.5045	−	12.9930i	0.0609877	−	0.0352113i
$370$	−185.482	−	28.0762i	−0.501302	−	0.0758817i
$371$	−186.144	−	275.456i	−0.501736	−	0.742468i
$372$	368.453	−	194.141i	0.990466	−	0.521883i
$373$	110.846	−	413.683i	0.297174	−	1.10907i	−0.642301	−	0.766452i	$-0.722020\pi$
$373$	110.846	−	413.683i	0.297174	−	1.10907i	0.939475	−	0.342616i	$-0.111313\pi$
$374$	79.3204	+	707.991i	0.212087	+	1.89302i
$375$	137.163	+	79.1910i	0.365768	+	0.211176i
$376$	522.731	−	38.1813i	1.39024	−	0.101546i
$377$	27.6914			0.0734521
$378$	5.78089	−	72.5161i	0.0152934	−	0.191841i
$379$	−429.423	−	429.423i	−1.13304	−	1.13304i	−0.989669	−	0.143374i	$-0.954205\pi$
$379$	−429.423	−	429.423i	−1.13304	−	1.13304i	−0.143374	−	0.989669i	$-0.545795\pi$
$380$	−72.1754	−	318.065i	−0.189935	−	0.837014i
$381$	340.322	−	91.1891i	0.893234	−	0.239341i
$382$	−451.698	+	565.682i	−1.18246	+	1.48084i
$383$	132.161	−	76.3029i	0.345067	−	0.199224i	−0.317444	−	0.948277i	$-0.602824\pi$
$383$	132.161	−	76.3029i	0.345067	−	0.199224i	0.662510	+	0.749053i	$0.269491\pi$
$384$	−58.3233	+	213.893i	−0.151884	+	0.557014i
$385$	255.724	+	740.594i	0.664218	+	1.92362i
$386$	−510.090	−	77.2119i	−1.32148	−	0.200031i
$387$	66.4110	+	17.7948i	0.171605	+	0.0459813i
$388$	−116.659	−	126.046i	−0.300668	−	0.324862i
$389$	127.939	−	34.2812i	0.328893	−	0.0881265i	−0.0905943	−	0.995888i	$-0.528877\pi$
$389$	127.939	−	34.2812i	0.328893	−	0.0881265i	0.419487	+	0.907761i	$0.362210\pi$
$390$	−146.031	+	334.133i	−0.374438	+	0.856751i
$391$	592.749			1.51598
$392$	−383.036	+	83.3522i	−0.977132	+	0.212633i
$393$			257.382i			0.654915i
$394$	226.658	−	518.615i	0.575274	−	1.31628i
$395$	75.6712	+	282.409i	0.191573	+	0.714959i
$396$	8.84914	−	228.793i	0.0223463	−	0.577761i
$397$	−62.0466	+	231.561i	−0.156289	+	0.583277i	0.842703	+	0.538379i	$0.180963\pi$
$397$	−62.0466	+	231.561i	−0.156289	+	0.583277i	−0.998992	+	0.0448984i	$0.985704\pi$
$398$	−471.071	−	71.3057i	−1.18360	−	0.179160i
$399$	−159.296	+	55.0041i	−0.399237	+	0.137855i
$400$	85.1443	−	124.211i	0.212861	−	0.310528i
$401$	−151.128	−	261.762i	−0.376879	−	0.652773i	0.613728	−	0.789518i	$-0.289669\pi$
$401$	−151.128	−	261.762i	−0.376879	−	0.652773i	−0.990606	+	0.136745i	$0.956336\pi$
$402$	−85.1516	+	106.639i	−0.211820	+	0.265271i
$403$	279.185	+	1041.93i	0.692766	+	2.58544i
$404$	426.519	+	268.749i	1.05574	+	0.665220i
$405$	37.3321	−	37.3321i	0.0921780	−	0.0921780i
$406$	−1.71683	+	21.5361i	−0.00422864	+	0.0530446i
$407$			305.086i			0.749597i
$408$	−195.757	−	169.106i	−0.479796	−	0.414476i
$409$	−112.297	+	194.505i	−0.274566	+	0.475562i	−0.970025	−	0.243003i	$-0.921867\pi$
$409$	−112.297	+	194.505i	−0.274566	+	0.475562i	0.695460	+	0.718565i	$0.255201\pi$
$410$	−11.3149	−	100.993i	−0.0275973	−	0.246325i
$411$	258.173	+	69.1771i	0.628157	+	0.168314i
$412$	−215.473	−	66.7618i	−0.522994	−	0.162043i
$413$	104.500	−	70.6176i	0.253026	−	0.170987i
$414$	−188.358	−	28.5115i	−0.454970	−	0.0688685i
$415$	−17.1352	−	29.6791i	−0.0412897	−	0.0715158i
$416$	−506.833	−	269.912i	−1.21835	−	0.648827i
$417$	100.521	−	174.107i	0.241057	−	0.417523i
$418$	−493.878	+	193.474i	−1.18153	+	0.462857i
$419$	−9.73289	−	9.73289i	−0.0232288	−	0.0232288i	0.695397	−	0.718626i	$-0.255229\pi$
$419$	−9.73289	−	9.73289i	−0.0232288	−	0.0232288i	−0.718626	+	0.695397i	$0.755229\pi$
$420$	−250.807	−	134.286i	−0.597160	−	0.319730i
$421$	−91.3599	−	91.3599i	−0.217007	−	0.217007i	0.590229	−	0.807236i	$-0.299037\pi$
$421$	−91.3599	−	91.3599i	−0.217007	−	0.217007i	−0.807236	+	0.590229i	$0.799037\pi$
$422$	−681.449	−	297.824i	−1.61481	−	0.705743i
$423$	98.2732	−	170.214i	0.232324	−	0.402398i
$424$	373.189	+	71.3410i	0.880163	+	0.168257i
$425$	87.8560	+	152.171i	0.206720	+	0.358049i
$426$	82.6745	−	60.9362i	0.194072	−	0.143043i
$427$	293.643	−	20.7888i	0.687687	−	0.0486857i
$428$	−354.360	−	672.529i	−0.827944	−	1.57133i
$429$	572.825	+	153.488i	1.33526	+	0.357781i
$430$	167.777	−	210.114i	0.390178	−	0.488637i
$431$	−89.0329	+	154.210i	−0.206573	+	0.357795i	−0.950633	−	0.310318i	$-0.899564\pi$
$431$	−89.0329	+	154.210i	−0.206573	+	0.357795i	0.744060	+	0.668113i	$0.232898\pi$
$432$	54.0714	+	63.1529i	0.125165	+	0.146187i
$433$		−	66.6693i		−	0.153971i	−0.997032	−	0.0769853i	$-0.975471\pi$
$433$		−	66.6693i		−	0.153971i	0.997032	−	0.0769853i	$-0.0245295\pi$
$434$	−827.637	+	152.528i	−1.90700	+	0.351448i
$435$	−11.0870	+	11.0870i	−0.0254874	+	0.0254874i
$436$	−549.823	−	346.443i	−1.26106	−	0.794593i
$437$	114.223	+	426.285i	0.261379	+	0.975480i
$438$	−12.3453	+	1.38311i	−0.0281856	+	0.00315779i
$439$	−330.517	−	572.472i	−0.752885	−	1.30404i	−0.946419	−	0.322942i	$-0.895328\pi$
$439$	−330.517	−	572.472i	−0.752885	−	1.30404i	0.193533	−	0.981094i	$-0.438005\pi$
$440$	−806.020	−	390.035i	−1.83186	−	0.886442i
$441$	−54.8313	+	136.391i	−0.124334	+	0.309277i
$442$	539.338	−	397.525i	1.22022	−	0.899379i
$443$	−113.269	+	422.727i	−0.255687	+	0.954236i	0.712020	+	0.702159i	$0.247780\pi$
$443$	−113.269	+	422.727i	−0.255687	+	0.954236i	−0.967707	+	0.252077i	$0.918886\pi$
$444$	−75.2464	−	81.3013i	−0.169474	−	0.183111i
$445$	−91.8315	−	342.720i	−0.206363	−	0.770157i
$446$	718.451	−	281.450i	1.61088	−	0.631053i
$447$		−	50.9085i		−	0.113889i
$448$	241.338	−	377.439i	0.538701	−	0.842497i
$449$	−332.053			−0.739539			−0.369769	−	0.929124i	$-0.620563\pi$
$449$	−332.053			−0.739539			−0.369769	+	0.929124i	$0.620563\pi$
$450$	−20.5985	−	52.5813i	−0.0457743	−	0.116847i
$451$	−159.642	+	42.7760i	−0.353974	+	0.0948469i
$452$	158.941	−	147.104i	0.351640	−	0.325452i
$453$	0.285504	+	0.0765005i	0.000630251	+	0.000168875i
$454$	−298.803	−	405.398i	−0.658157	−	0.892946i
$455$	482.941	−	556.532i	1.06141	−	1.22315i
$456$	83.8932	−	173.368i	0.183976	−	0.380193i
$457$	−658.735	+	380.321i	−1.44143	+	0.832211i	−0.997945	−	0.0640694i	$-0.979592\pi$
$457$	−658.735	+	380.321i	−1.44143	+	0.832211i	−0.443487	+	0.896281i	$0.646259\pi$
$458$	−9.04466	−	80.7300i	−0.0197482	−	0.176266i
$459$	−93.7012	+	25.1072i	−0.204142	+	0.0546997i
$460$	−397.166	+	630.325i	−0.863405	+	1.37027i
$461$	64.7608	+	64.7608i	0.140479	+	0.140479i	0.773849	−	0.633370i	$-0.218329\pi$
$461$	64.7608	+	64.7608i	0.140479	+	0.140479i	−0.633370	+	0.773849i	$0.718329\pi$
$462$	−154.885	+	435.980i	−0.335248	+	0.943679i
$463$	547.220			1.18190			0.590950	−	0.806708i	$-0.298753\pi$
$463$	547.220			1.18190			0.590950	+	0.806708i	$0.298753\pi$
$464$	−16.0583	−	18.7554i	−0.0346085	−	0.0404211i
$465$	−528.945	−	305.387i	−1.13752	−	0.656746i
$466$	145.673	+	116.321i	0.312604	+	0.249615i
$467$	26.4765	−	98.8116i	0.0566948	−	0.211588i	−0.931767	−	0.363056i	$-0.881733\pi$
$467$	26.4765	−	98.8116i	0.0566948	−	0.211588i	0.988462	+	0.151468i	$0.0484000\pi$
$468$	−190.506	+	100.379i	−0.407065	+	0.214485i
$469$	228.481	−	154.400i	0.487165	−	0.329211i
$470$	−456.051	−	618.741i	−0.970321	−	1.31647i
$471$	198.394	−	114.543i	0.421220	−	0.243191i
$472$	−27.0647	+	141.577i	−0.0573405	+	0.299951i
$473$	−378.697	−	218.641i	−0.800629	−	0.462243i
$474$	−69.1415	+	158.202i	−0.145868	+	0.333760i
$475$	−92.5063	+	92.5063i	−0.194750	+	0.194750i
$476$	275.724	+	444.098i	0.579252	+	0.932979i
$477$	100.749	−	100.749i	0.211213	−	0.211213i
$478$	−153.830	−	392.679i	−0.321821	−	0.821505i
$479$	−196.476	−	113.436i	−0.410180	−	0.236818i	0.280687	−	0.959799i	$-0.409438\pi$
$479$	−196.476	−	113.436i	−0.410180	−	0.236818i	−0.690867	+	0.722982i	$0.742771\pi$
$480$	310.991	−	94.8578i	0.647899	−	0.197620i
$481$	248.483	−	143.462i	0.516597	−	0.298258i
$482$	131.528	−	868.924i	0.272880	−	1.80275i
$483$	346.141	+	168.454i	0.716648	+	0.348765i
$484$	−287.742	+	928.687i	−0.594509	+	1.91878i
$485$	−65.1899	+	243.292i	−0.134412	+	0.501633i
$486$	30.9831	−	3.47122i	0.0637512	−	0.00714242i
$487$	−392.327	−	226.510i	−0.805599	−	0.465113i	0.0398260	−	0.999207i	$-0.487320\pi$
$487$	−392.327	−	226.510i	−0.805599	−	0.465113i	−0.845425	+	0.534094i	$0.820653\pi$
$488$	−219.931	+	254.591i	−0.450678	+	0.521703i
$489$	322.151			0.658796
$490$	402.883	+	410.096i	0.822209	+	0.836930i
$491$	391.606	+	391.606i	0.797567	+	0.797567i	0.982711	−	0.185144i	$-0.0592752\pi$
$491$	391.606	+	391.606i	0.797567	+	0.797567i	−0.185144	+	0.982711i	$0.559275\pi$
$492$	31.9922	−	50.7733i	0.0650247	−	0.103198i
$493$	27.8277	−	7.45642i	0.0564457	−	0.0151246i
$494$	389.817	+	311.270i	0.789103	+	0.630101i
$495$	−290.800	+	167.893i	−0.587474	+	0.339178i
$496$	543.799	−	793.310i	1.09637	−	1.59942i
$497$	−196.173	+	67.7376i	−0.394714	+	0.136293i
$498$	3.02882	−	20.0095i	0.00608197	−	0.0401797i
$499$	248.802	+	66.6664i	0.498602	+	0.133600i	0.499351	−	0.866400i	$-0.333572\pi$
$499$	248.802	+	66.6664i	0.498602	+	0.133600i	−0.000749103		1.00000i	$0.500238\pi$
$500$	365.494	+	14.1364i	0.730989	+	0.0282728i
$501$	339.098	−	90.8610i	0.676842	−	0.181359i
$502$	−798.772	−	349.099i	−1.59118	−	0.695417i
$503$	231.615			0.460468			0.230234	−	0.973135i	$-0.426051\pi$
$503$	231.615			0.460468			0.230234	+	0.973135i	$0.426051\pi$
$504$	−66.2554	−	154.383i	−0.131459	−	0.306316i
$505$		−	739.324i		−	1.46401i
$506$	1110.22	+	485.217i	2.19412	+	0.958928i
$507$	−68.5900	−	255.981i	−0.135286	−	0.504894i
$508$	597.155	−	552.682i	1.17550	−	1.08796i
$509$	40.4522	−	150.970i	0.0794739	−	0.296601i	−0.914737	−	0.404051i	$-0.867602\pi$
$509$	40.4522	−	150.970i	0.0794739	−	0.296601i	0.994210	+	0.107450i	$0.0342686\pi$
$510$	−56.7784	+	375.099i	−0.111330	+	0.735488i
$511$	24.6454	+	4.76846i	0.0482298	+	0.00933163i
$512$	111.103	+	499.800i	0.216997	+	0.976172i
$513$	−36.1124	−	62.5485i	−0.0703946	−	0.121927i
$514$	178.115	+	142.225i	0.346527	+	0.276703i
$515$	85.6229	+	319.549i	0.166258	+	0.620484i
$516$	154.843	−	35.1370i	0.300084	−	0.0680950i
$517$	−883.925	+	883.925i	−1.70972	+	1.70972i
$518$	96.1671	+	202.144i	0.185651	+	0.390239i
$519$			276.591i			0.532930i
$520$	61.3469	+	839.886i	0.117975	+	1.61517i
$521$	−74.5036	+	129.044i	−0.143001	+	0.247685i	−0.928625	−	0.371019i	$-0.879009\pi$
$521$	−74.5036	+	129.044i	−0.143001	+	0.247685i	0.785624	+	0.618704i	$0.212342\pi$
$522$	−9.20147	+	1.03089i	−0.0176273	+	0.00197489i
$523$	658.412	+	176.421i	1.25891	+	0.337325i	0.825774	−	0.564001i	$-0.190739\pi$
$523$	658.412	+	176.421i	1.25891	+	0.337325i	0.433140	+	0.901326i	$0.357405\pi$
$524$	277.082	+	525.865i	0.528782	+	1.00356i
$525$	8.05870	+	113.829i	0.0153499	+	0.216818i
$526$	41.4712	−	273.974i	0.0788426	−	0.520863i
$527$	561.118	+	971.885i	1.06474	+	1.84418i
$528$	−228.225	−	476.982i	−0.432245	−	0.903375i
$529$	239.548	−	414.910i	0.452833	−	0.784329i
$530$	−203.245	−	518.819i	−0.383481	−	0.978904i
$531$	38.2211	+	38.2211i	0.0719795	+	0.0719795i
$532$	−266.248	+	283.869i	−0.500466	+	0.533588i
$533$	109.909	+	109.909i	0.206208	+	0.206208i
$534$	83.9073	−	191.988i	0.157130	−	0.359528i
$535$	−557.415	+	965.471i	−1.04190	+	1.80462i
$536$	−59.1748	+	309.547i	−0.110401	+	0.577513i
$537$	−126.513	−	219.126i	−0.235591	−	0.408056i
$538$	261.812	+	355.211i	0.486640	+	0.660243i
$539$	561.367	−	747.647i	1.04150	−	1.38710i
$540$	36.0849	−	116.464i	0.0668239	−	0.215674i
$541$	−128.916	−	34.5430i	−0.238292	−	0.0638502i	0.137696	−	0.990474i	$-0.456030\pi$
$541$	−128.916	−	34.5430i	−0.238292	−	0.0638502i	−0.375989	+	0.926624i	$0.622697\pi$
$542$	409.574	+	327.046i	0.755671	+	0.603406i
$543$	73.6362	−	127.542i	0.135610	−	0.234883i
$544$	−582.007	−	134.767i	−1.06987	−	0.247733i
$545$			953.059i			1.74873i
$546$	427.924	−	78.8638i	0.783744	−	0.144439i
$547$	335.643	−	335.643i	0.613608	−	0.613608i	−0.330277	−	0.943884i	$-0.607142\pi$
$547$	335.643	−	335.643i	0.613608	−	0.613608i	0.943884	+	0.330277i	$0.107142\pi$
$548$	601.953	−	136.595i	1.09845	−	0.249261i
$549$	32.6531	+	121.863i	0.0594774	+	0.221973i
$550$	39.9896	+	356.936i	0.0727084	+	0.648974i
$551$	10.7248	+	18.5759i	0.0194642	+	0.0337131i
$552$	−415.533	+	144.522i	−0.752778	+	0.261815i
$553$	228.659	−	263.502i	0.413488	−	0.476495i
$554$	−260.587	−	353.548i	−0.470373	−	0.638173i
$555$	−42.0482	+	156.926i	−0.0757625	+	0.282750i
$556$	17.9439	−	463.938i	0.0322733	−	0.834422i
$557$	−182.661	−	681.701i	−0.327938	−	1.22388i	−0.911326	−	0.411686i	$-0.864940\pi$
$557$	−182.661	−	681.701i	−0.327938	−	1.22388i	0.583388	−	0.812194i	$-0.301727\pi$
$558$	−131.558	−	335.826i	−0.235767	−	0.601838i
$559$			411.250i			0.735688i
$560$	−656.997	−	4.36122i	−1.17321	−	0.00778789i
$561$	616.974			1.09978
$562$	−270.247	+	105.868i	−0.480867	+	0.188377i
$563$	−324.900	+	87.0566i	−0.577086	+	0.154630i	−0.535545	−	0.844507i	$-0.679894\pi$
$563$	−324.900	+	87.0566i	−0.577086	+	0.154630i	−0.0415417	+	0.999137i	$0.513227\pi$
$564$	17.5427	−	453.565i	0.0311041	−	0.804194i
$565$	−306.785	−	82.2028i	−0.542982	−	0.145492i
$566$	183.943	−	135.577i	0.324987	−	0.239536i
$567$	−61.8529	−	11.9675i	−0.109088	−	0.0211066i
$568$	103.315	−	213.503i	0.181892	−	0.375886i
$569$	−447.540	+	258.387i	−0.786538	+	0.454108i	−0.838742	−	0.544529i	$-0.816709\pi$
$569$	−447.540	+	258.387i	−0.786538	+	0.454108i	0.0522046	+	0.998636i	$0.483375\pi$
$570$	−280.699	+	31.4484i	−0.492455	+	0.0551726i
$571$	−866.821	+	232.264i	−1.51808	+	0.406767i	−0.919108	−	0.394006i	$-0.871089\pi$
$571$	−866.821	+	232.264i	−1.51808	+	0.406767i	−0.598968	+	0.800773i	$0.704422\pi$
$572$	1335.59	−	303.073i	2.33496	−	0.529848i
$573$	443.295	+	443.295i	0.773638	+	0.773638i
$574$	−92.2922	+	78.6638i	−0.160788	+	0.137045i
$575$	298.836			0.519715
$576$	178.462	+	70.8196i	0.309829	+	0.122951i
$577$	423.487	+	244.500i	0.733947	+	0.423744i	0.819864	−	0.572558i	$-0.194049\pi$
$577$	423.487	+	244.500i	0.733947	+	0.423744i	−0.0859176	+	0.996302i	$0.527382\pi$
$578$	74.2902	−	93.0368i	0.128530	−	0.160963i
$579$	−115.636	+	431.559i	−0.199717	+	0.745353i
$580$	−10.7166	+	34.5879i	−0.0184770	+	0.0596343i
$581$	−17.8951	+	36.7710i	−0.0308005	+	0.0632892i
$582$	−119.729	+	88.2479i	−0.205720	+	0.151629i
$583$	−784.785	+	453.096i	−1.34611	+	0.777180i
$584$	−23.7341	+	16.1161i	−0.0406405	+	0.0275960i
$585$	273.488	+	157.898i	0.467500	+	0.269911i
$586$	−289.971	−	126.730i	−0.494830	−	0.216263i
$587$	445.770	−	445.770i	0.759404	−	0.759404i	−0.216810	−	0.976214i	$-0.569565\pi$
$587$	445.770	−	445.770i	0.759404	−	0.759404i	0.976214	+	0.216810i	$0.0695653\pi$
$588$	34.8030	+	337.693i	0.0591888	+	0.574308i
$589$	−590.819	+	590.819i	−1.00309	+	1.00309i
$590$	196.825	−	77.1052i	0.333601	−	0.130687i
$591$	−424.487	−	245.078i	−0.718252	−	0.414683i
$592$	−241.263	−	85.1035i	−0.407538	−	0.143756i
$593$	124.431	−	71.8405i	0.209834	−	0.121148i	−0.391400	−	0.920220i	$-0.628009\pi$
$593$	124.431	−	71.8405i	0.209834	−	0.121148i	0.601234	+	0.799073i	$0.294676\pi$
$594$	−196.056	−	29.6768i	−0.330060	−	0.0499609i
$595$	335.462	−	689.312i	0.563802	−	1.15851i
$596$	−54.8051	−	104.013i	−0.0919549	−	0.174518i
$597$	−106.790	+	398.548i	−0.178879	+	0.667584i
$598$	−126.870	−	1132.41i	−0.212158	−	1.89366i
$599$	715.438	+	413.058i	1.19439	+	0.689580i	0.959299	−	0.282394i	$-0.0911285\pi$
$599$	715.438	+	413.058i	1.19439	+	0.689580i	0.235089	+	0.971974i	$0.424462\pi$
$600$	−98.6912	−	85.2554i	−0.164485	−	0.142092i
$601$	−45.1057			−0.0750510			−0.0375255	−	0.999296i	$-0.511948\pi$
$601$	−45.1057			−0.0750510			−0.0375255	+	0.999296i	$0.511948\pi$
$602$	−319.836	−	25.4969i	−0.531289	−	0.0423537i
$603$	83.5674	+	83.5674i	0.138586	+	0.138586i
$604$	0.665678	−	0.151056i	0.00110212	−	0.000250092i
$605$	1377.25	−	369.033i	2.27645	−	0.609973i
$606$	272.422	−	341.166i	0.449542	−	0.562980i
$607$	817.055	−	471.727i	1.34605	−	0.777145i	0.358366	−	0.933581i	$-0.383334\pi$
$607$	817.055	−	471.727i	1.34605	−	0.777145i	0.987688	+	0.156437i	$0.0500007\pi$
$608$	−15.2330	−	444.529i	−0.0250542	−	0.731133i
$609$	18.3693	+	3.55414i	0.0301631	+	0.00583603i
$610$	487.834	+	73.8431i	0.799728	+	0.121054i
$611$	1135.58	+	304.278i	1.85856	+	0.498000i
$612$	−164.415	+	152.170i	−0.268652	+	0.248645i
$613$	1057.40	−	283.331i	1.72497	−	0.462203i	0.745953	−	0.665999i	$-0.231995\pi$
$613$	1057.40	−	283.331i	1.72497	−	0.462203i	0.979013	+	0.203796i	$0.0653279\pi$
$614$	−16.5005	+	37.7548i	−0.0268738	+	0.0614899i
$615$	−88.0101			−0.143106
$616$	152.900	+	1057.50i	0.248215	+	1.71673i
$617$		−	1151.98i		−	1.86706i	−0.358493	−	0.933532i	$-0.616709\pi$
$617$		−	1151.98i		−	1.86706i	0.358493	−	0.933532i	$-0.383291\pi$
$618$	−78.2344	+	179.008i	−0.126593	+	0.289657i
$619$	−185.161	−	691.030i	−0.299129	−	1.11636i	−0.937882	−	0.346953i	$-0.887216\pi$
$619$	−185.161	−	691.030i	−0.299129	−	1.11636i	0.638753	−	0.769411i	$-0.279450\pi$
$620$	−1409.47	−	54.5145i	−2.27333	−	0.0879267i
$621$	−42.7001	+	159.359i	−0.0687603	+	0.256617i
$622$	1225.02	+	185.431i	1.96949	+	0.298120i
$623$	−277.491	+	319.775i	−0.445411	+	0.513283i
$624$	−281.168	+	410.176i	−0.450589	+	0.657333i
$625$	−385.857	−	668.324i	−0.617371	−	1.06932i
$626$	−422.865	+	529.573i	−0.675504	+	0.845963i
$627$	118.891	+	443.707i	0.189619	+	0.707666i
$628$	282.036	−	447.607i	0.449102	−	0.712749i
$629$	211.077	−	211.077i	0.335575	−	0.335575i
$630$	−139.756	+	202.906i	−0.221835	+	0.322074i
$631$			689.162i			1.09217i	0.837728	+	0.546087i	$0.183883\pi$
$631$			689.162i			1.09217i	−0.837728	+	0.546087i	$0.816117\pi$
$632$	29.0460	+	397.662i	0.0459589	+	0.629212i
$633$	−322.026	+	557.766i	−0.508730	+	0.881147i
$634$	43.7642	+	390.627i	0.0690287	+	0.616130i
$635$	−1152.62	−	308.843i	−1.81514	−	0.486366i
$636$	97.3829	−	314.303i	0.153118	−	0.494187i
$637$	−872.910	−	105.647i	−1.37034	−	0.165851i
$638$	58.2253	+	8.81353i	0.0912623	+	0.0138143i
$639$	−44.4725	−	77.0287i	−0.0695971	−	0.120546i
$640$	533.279	−	528.602i	0.833248	−	0.825941i
$641$	−65.0888	+	112.737i	−0.101543	+	0.175877i	−0.912320	−	0.409477i	$-0.865711\pi$
$641$	−65.0888	+	112.737i	−0.101543	+	0.175877i	0.810778	+	0.585354i	$0.199044\pi$
$642$	−612.974	+	240.130i	−0.954788	+	0.374034i
$643$	−93.8911	−	93.8911i	−0.146020	−	0.146020i	0.630317	−	0.776338i	$-0.282925\pi$
$643$	−93.8911	−	93.8911i	−0.146020	−	0.146020i	−0.776338	+	0.630317i	$0.782925\pi$
$644$	888.559	−	28.4615i	1.37975	−	0.0441949i
$645$	−164.655	−	164.655i	−0.255279	−	0.255279i
$646$	475.551	+	207.837i	0.736147	+	0.321729i
$647$	305.543	−	529.216i	0.472245	−	0.817953i	−0.527250	−	0.849710i	$-0.676777\pi$
$647$	305.543	−	529.216i	0.472245	−	0.817953i	0.999496	+	0.0317570i	$0.0101103\pi$
$648$	59.5656	−	40.4467i	0.0919223	−	0.0624177i
$649$	−171.891	−	297.724i	−0.264856	−	0.458743i
$650$	271.909	−	200.414i	0.418321	−	0.308329i
$651$	51.4692	+	727.005i	0.0790618	+	1.11675i
$652$	658.198	−	346.809i	1.00951	−	0.531916i
$653$	−1051.42	−	281.727i	−1.61014	−	0.431435i	−0.662053	−	0.749457i	$-0.730315\pi$
$653$	−1051.42	−	281.727i	−1.61014	−	0.431435i	−0.948083	+	0.318022i	$0.896981\pi$
$654$	−351.178	+	439.795i	−0.536970	+	0.672470i
$655$	435.855	−	754.923i	0.665428	−	1.15255i
$656$	10.7047	−	138.178i	0.0163182	−	0.210636i
$657$			10.7582i			0.0163748i
$658$	−307.047	+	864.296i	−0.466636	+	1.31352i
$659$	−485.902	+	485.902i	−0.737332	+	0.737332i	−0.972061	−	0.234729i	$-0.924580\pi$
$659$	−485.902	+	485.902i	−0.737332	+	0.737332i	0.234729	+	0.972061i	$0.424580\pi$
$660$	−413.398	+	656.086i	−0.626361	+	0.994069i
$661$	−129.226	−	482.276i	−0.195500	−	0.729616i	−0.992137	−	0.125158i	$-0.960056\pi$
$661$	−129.226	−	482.276i	−0.195500	−	0.729616i	0.796637	−	0.604458i	$-0.206610\pi$
$662$	54.6025	−	6.11744i	0.0824812	−	0.00924085i
$663$	−290.122	−	502.507i	−0.437590	−	0.757928i
$664$	−15.3527	−	44.1427i	−0.0231216	−	0.0664800i
$665$	560.373	+	108.422i	0.842666	+	0.163041i
$666$	−77.2266	+	56.9208i	−0.115956	+	0.0854667i
$667$	12.6812	−	47.3271i	0.0190124	−	0.0709551i
$668$	595.007	−	550.694i	0.890729	−	0.824392i
$669$	−172.952	−	645.466i	−0.258523	−	0.964823i
$670$	430.342	−	168.584i	0.642301	−	0.251618i
$671$		−	802.405i		−	1.19583i
$672$	−301.569	−	244.099i	−0.448763	−	0.363243i
$673$	−951.394			−1.41366			−0.706831	−	0.707383i	$-0.749876\pi$
$673$	−951.394			−1.41366			−0.706831	+	0.707383i	$0.749876\pi$
$674$	−170.940	−	436.354i	−0.253620	−	0.647410i
$675$	−47.2397	+	12.6578i	−0.0699848	+	0.0187524i
$676$	−415.713	−	449.164i	−0.614960	−	0.664444i
$677$	89.6976	+	24.0344i	0.132493	+	0.0355013i	0.324456	−	0.945901i	$-0.394819\pi$
$677$	89.6976	+	24.0344i	0.132493	+	0.0355013i	−0.191963	+	0.981402i	$0.561485\pi$
$678$	−111.278	−	150.976i	−0.164127	−	0.222678i
$679$	284.098	−	98.0978i	0.418406	−	0.144474i
$680$	287.803	+	827.501i	0.423240	+	1.21691i
$681$	−377.713	+	218.073i	−0.554645	+	0.320224i
$682$	255.405	+	2279.67i	0.374494	+	3.34263i
$683$	−301.350	+	80.7465i	−0.441215	+	0.118223i	−0.472586	−	0.881285i	$-0.656679\pi$
$683$	−301.350	+	80.7465i	−0.441215	+	0.118223i	0.0313707	+	0.999508i	$0.490013\pi$
$684$	−141.119	−	88.9185i	−0.206314	−	0.129998i
$685$	−640.097	−	640.097i	−0.934448	−	0.934448i
$686$	136.283	−	672.327i	0.198663	−	0.980068i
$687$	−70.3516			−0.102404
$688$	278.539	−	238.485i	0.404853	−	0.346635i
$689$	738.065	+	426.122i	1.07121	+	0.618465i
$690$	504.187	+	402.595i	0.730706	+	0.583471i
$691$	50.4144	−	188.149i	0.0729586	−	0.272285i	−0.919804	−	0.392378i	$-0.871653\pi$
$691$	50.4144	−	188.149i	0.0729586	−	0.272285i	0.992763	+	0.120093i	$0.0383192\pi$
$692$	297.761	+	565.111i	0.430291	+	0.816635i
$693$	360.288	+	175.338i	0.519896	+	0.253013i
$694$	135.541	+	183.894i	0.195305	+	0.264977i
$695$	−589.672	+	340.447i	−0.848449	+	0.489852i
$696$	−17.6900	+	12.0120i	−0.0254167	+	0.0172586i
$697$	140.045	+	80.8549i	0.200925	+	0.116004i
$698$	−295.896	+	677.038i	−0.423920	+	0.969969i
$699$	114.156	−	114.156i	0.163314	−	0.163314i
$700$	139.007	+	223.893i	0.198582	+	0.319848i
$701$	152.677	−	152.677i	0.217798	−	0.217798i	−0.589772	−	0.807570i	$-0.700782\pi$
$701$	152.677	−	152.677i	0.217798	−	0.217798i	0.807570	+	0.589772i	$0.200782\pi$
$702$	68.0212	+	173.636i	0.0968963	+	0.247345i
$703$	192.473	+	111.125i	0.273789	+	0.158072i
$704$	−979.785	−	728.843i	−1.39174	−	1.03529i
$705$	−576.488	+	332.835i	−0.817713	+	0.472107i
$706$	35.1554	−	232.249i	0.0497951	−	0.328965i
$707$	−730.969	+	493.965i	−1.03390	+	0.698678i
$708$	119.237	+	36.9442i	0.168414	+	0.0521811i
$709$	−70.4076	+	262.765i	−0.0993054	+	0.370613i	−0.997637	−	0.0687052i	$-0.978113\pi$
$709$	−70.4076	+	262.765i	−0.0993054	+	0.370613i	0.898332	+	0.439318i	$0.144780\pi$
$710$	−345.682	+	38.7288i	−0.486876	+	0.0545476i
$711$	129.489	+	74.7603i	0.182122	+	0.105148i
$712$	−35.2491	−	482.587i	−0.0495071	−	0.677790i
$713$	1908.60			2.67686
$714$	408.795	−	194.478i	0.572542	−	0.272379i
$715$	−1420.23	−	1420.23i	−1.98633	−	1.98633i
$716$	−494.380	−	311.508i	−0.690475	−	0.435067i
$717$	−352.789	+	94.5294i	−0.492034	+	0.131840i
$718$	−898.071	−	717.112i	−1.25079	−	0.998764i
$719$	1105.86	−	638.470i	1.53806	−	0.887997i	0.539103	−	0.842240i	$-0.318763\pi$
$719$	1105.86	−	638.470i	1.53806	−	0.887997i	0.998953	−	0.0457573i	$-0.0145701\pi$
$720$	−51.6519	−	276.798i	−0.0717388	−	0.384442i
$721$	258.730	−	298.156i	0.358849	−	0.413531i
$722$	50.2271	−	331.818i	0.0695666	−	0.459582i
$723$	−735.149	−	196.983i	−1.01680	−	0.272452i
$724$	13.1448	−	339.857i	0.0181558	−	0.469416i
$725$	14.0294	−	3.75917i	0.0193509	−	0.00518507i
$726$	771.521	+	337.189i	1.06270	+	0.464448i
$727$	−541.136			−0.744341			−0.372170	−	0.928164i	$-0.621386\pi$
$727$	−541.136			−0.744341			−0.372170	+	0.928164i	$0.621386\pi$
$728$	789.406	−	621.807i	1.08435	−	0.854131i
$729$		−	27.0000i		−	0.0370370i
$730$	38.5520	+	16.8489i	0.0528109	+	0.0230807i
$731$	110.736	+	413.274i	0.151486	+	0.565354i
$732$	197.905	+	213.830i	0.270362	+	0.292117i
$733$	−16.5812	+	61.8820i	−0.0226211	+	0.0844230i	−0.976314	−	0.216360i	$-0.930581\pi$
$733$	−16.5812	+	61.8820i	−0.0226211	+	0.0844230i	0.953693	+	0.300783i	$0.0972481\pi$
$734$	−155.857	+	1029.65i	−0.212340	+	1.40279i
$735$	391.792	−	307.195i	0.533050	−	0.417952i
$736$	−693.407	+	742.616i	−0.942129	+	1.00899i
$737$	−375.827	−	650.951i	−0.509941	−	0.883244i
$738$	−40.6128	−	32.4295i	−0.0550309	−	0.0439424i
$739$	−173.441	−	647.289i	−0.234696	−	0.875898i	−0.978286	−	0.207262i	$-0.933545\pi$
$739$	−173.441	−	647.289i	−0.234696	−	0.875898i	0.743589	−	0.668637i	$-0.233122\pi$
$740$	83.0272	+	365.887i	0.112199	+	0.494442i
$741$	305.479	−	305.479i	0.412252	−	0.412252i
$742$	−377.161	+	547.587i	−0.508304	+	0.737988i
$743$		−	473.322i		−	0.637041i	−0.947916	−	0.318521i	$-0.896814\pi$
$743$		−	473.322i		−	0.637041i	0.947916	−	0.318521i	$-0.103186\pi$
$744$	−630.320	−	544.509i	−0.847205	−	0.731866i
$745$	−86.2094	+	149.319i	−0.115717	+	0.200428i
$746$	−851.226	+	95.3678i	−1.14105	+	0.127839i
$747$	−16.9289	−	4.53610i	−0.0226626	−	0.00607242i
$748$	1260.56	−	664.198i	1.68524	−	0.887965i
$749$	1326.99	−	93.9455i	1.77168	−	0.125428i
$750$	47.4083	−	313.196i	0.0632111	−	0.417595i
$751$	315.084	+	545.742i	0.419553	+	0.726687i	0.995894	−	0.0905220i	$-0.0288535\pi$
$751$	315.084	+	545.742i	0.419553	+	0.726687i	−0.576342	+	0.817209i	$0.695520\pi$
$752$	−452.439	−	945.580i	−0.601648	−	1.25742i
$753$	−377.469	+	653.795i	−0.501286	+	0.868254i
$754$	−20.2012	−	51.5672i	−0.0267920	−	0.0683915i
$755$	−0.707860	−	0.707860i	−0.000937562	−	0.000937562i
$756$	−139.257	+	42.1360i	−0.184203	+	0.0557355i
$757$	−206.486	−	206.486i	−0.272769	−	0.272769i	0.557445	−	0.830214i	$-0.311782\pi$
$757$	−206.486	−	206.486i	−0.272769	−	0.272769i	−0.830214	+	0.557445i	$0.811782\pi$
$758$	−486.406	+	1112.94i	−0.641697	+	1.46826i
$759$	524.649	−	908.718i	0.691237	−	1.19726i
$760$	−539.651	+	366.438i	−0.710067	+	0.482155i
$761$	348.244	+	603.176i	0.457614	+	0.792610i	0.998834	−	0.0482705i	$-0.0153710\pi$
$761$	348.244	+	603.176i	0.457614	+	0.792610i	−0.541221	+	0.840881i	$0.682038\pi$
$762$	−418.082	−	567.227i	−0.548664	−	0.744393i
$763$	942.288	−	636.768i	1.23498	−	0.834558i
$764$	1382.93	+	428.485i	1.81012	+	0.560845i
$765$	317.351	+	85.0339i	0.414838	+	0.111155i
$766$	−238.504	−	190.446i	−0.311363	−	0.248625i
$767$	−161.658	+	280.000i	−0.210767	+	0.365059i
$768$	440.861	−	47.4274i	0.574038	−	0.0617544i
$769$			56.2543i			0.0731525i	0.999331	+	0.0365762i	$0.0116452\pi$
$769$			56.2543i			0.0731525i	−0.999331	+	0.0365762i	$0.988355\pi$
$770$	1192.59	−	1016.48i	1.54881	−	1.32011i
$771$	139.579	−	139.579i	0.181036	−	0.181036i
$772$	228.332	+	1006.22i	0.295766	+	1.30339i
$773$	240.592	+	897.902i	0.311245	+	1.16158i	0.927435	+	0.373984i	$0.122009\pi$
$773$	240.592	+	897.902i	0.311245	+	1.16158i	−0.616190	+	0.787597i	$0.711325\pi$
$774$	−15.3100	−	136.652i	−0.0197803	−	0.176553i
$775$	282.889	+	489.978i	0.365018	+	0.632230i
$776$	−149.620	+	309.196i	−0.192810	+	0.398448i
$777$	183.246	−	63.2741i	0.235838	−	0.0814338i
$778$	−157.172	−	213.241i	−0.202020	−	0.274088i
$779$	−31.1615	+	116.296i	−0.0400019	+	0.149289i
$780$	728.756	+	28.1864i	0.934302	+	0.0361364i
$781$	146.414	+	546.426i	0.187470	+	0.699649i
$782$	−432.417	−	1103.82i	−0.552962	−	1.41154i
$783$			8.01856i			0.0102408i
$784$	434.648	+	652.485i	0.554398	+	0.832252i
$785$	−775.878			−0.988379
$786$	479.298	−	187.763i	0.609794	−	0.238884i
$787$	−1354.83	+	363.025i	−1.72151	+	0.461277i	−0.978199	−	0.207671i	$-0.933412\pi$
$787$	−1354.83	+	363.025i	−1.72151	+	0.461277i	−0.743310	+	0.668947i	$0.766745\pi$
$788$	−1131.12	−	43.7488i	−1.43543	−	0.0555187i
$789$	−231.794	−	62.1091i	−0.293782	−	0.0787188i
$790$	470.701	−	346.936i	0.595824	−	0.439159i
$791$	123.699	+	358.240i	0.156383	+	0.452895i
$792$	−432.516	+	150.428i	−0.546106	+	0.189935i
$793$	−653.534	+	377.318i	−0.824128	+	0.475811i
$794$	476.478	−	53.3827i	0.600099	−	0.0672326i
$795$	−466.114	+	124.895i	−0.586307	+	0.157101i
$796$	210.865	+	929.250i	0.264906	+	1.16740i
$797$	357.942	+	357.942i	0.449112	+	0.449112i	0.895059	−	0.445947i	$-0.147133\pi$
$797$	357.942	+	357.942i	0.449112	+	0.449112i	−0.445947	+	0.895059i	$0.647133\pi$
$798$	218.637	+	256.515i	0.273981	+	0.321448i
$799$	1223.10			1.53079
$800$	−293.420	−	67.9430i	−0.366775	−	0.0849288i
$801$	−157.142	−	90.7260i	−0.196182	−	0.113266i
$802$	−377.205	+	472.390i	−0.470330	+	0.589015i
$803$	17.7093	−	66.0921i	0.0220540	−	0.0823065i
$804$	260.703	+	80.7756i	0.324258	+	0.100467i
$805$	−729.999	−	1080.25i	−0.906831	−	1.34193i
$806$	1736.62	−	1280.00i	2.15462	−	1.58809i
$807$	330.953	−	191.076i	0.410103	−	0.236773i
$808$	189.316	−	990.321i	0.234302	−	1.22565i
$809$	−265.144	−	153.081i	−0.327743	−	0.189222i	0.327096	−	0.944991i	$-0.393930\pi$
$809$	−265.144	−	153.081i	−0.327743	−	0.189222i	−0.654838	+	0.755769i	$0.727263\pi$
$810$	−96.7543	−	42.2859i	−0.119450	−	0.0522049i
$811$	279.770	−	279.770i	0.344969	−	0.344969i	−0.513263	−	0.858232i	$-0.671563\pi$
$811$	279.770	−	279.770i	0.344969	−	0.344969i	0.858232	+	0.513263i	$0.171563\pi$
$812$	41.3571	−	12.5137i	0.0509324	−	0.0154110i
$813$	320.961	−	320.961i	0.394786	−	0.394786i
$814$	568.133	−	222.564i	0.697953	−	0.273420i
$815$	−944.898	−	545.537i	−1.15938	−	0.669371i
$816$	−172.104	+	487.904i	−0.210912	+	0.597922i
$817$	−275.874	+	159.276i	−0.337666	+	0.194952i
$818$	444.130	+	67.2277i	0.542947	+	0.0821854i
$819$	−26.6118	−	375.893i	−0.0324931	−	0.458966i
$820$	−179.816	+	94.7464i	−0.219288	+	0.115544i
$821$	293.311	−	1094.65i	0.357261	−	1.33332i	−0.520354	−	0.853950i	$-0.674200\pi$
$821$	293.311	−	1094.65i	0.357261	−	1.33332i	0.877615	−	0.479366i	$-0.159133\pi$
$822$	−59.5175	−	531.236i	−0.0724057	−	0.646273i
$823$	104.659	+	60.4250i	0.127168	+	0.0734204i	0.562234	−	0.826978i	$-0.309942\pi$
$823$	104.659	+	60.4250i	0.127168	+	0.0734204i	−0.435067	+	0.900398i	$0.643275\pi$
$824$	32.8659	+	449.959i	0.0398858	+	0.546067i
$825$	311.049			0.377029
$826$	−207.738	−	143.084i	−0.251499	−	0.173225i
$827$	−9.24705	−	9.24705i	−0.0111814	−	0.0111814i	0.701494	−	0.712675i	$-0.252517\pi$
$827$	−9.24705	−	9.24705i	−0.0111814	−	0.0111814i	−0.712675	+	0.701494i	$0.752517\pi$
$828$	84.3145	+	371.560i	0.101829	+	0.448744i
$829$	668.905	−	179.232i	0.806881	−	0.216203i	0.168278	−	0.985740i	$-0.446179\pi$
$829$	668.905	−	179.232i	0.806881	−	0.216203i	0.638603	+	0.769536i	$0.279513\pi$
$830$	−42.7682	+	53.5605i	−0.0515280	+	0.0645307i
$831$	−329.404	+	190.182i	−0.396395	+	0.228859i
$832$	−132.892	+	1140.73i	−0.159726	+	1.37107i
$833$	−905.654	+	128.880i	−1.08722	+	0.154718i
$834$	−397.554	−	60.1775i	−0.476684	−	0.0721552i
$835$	−1148.47	−	307.732i	−1.37541	−	0.368541i
$836$	720.578	+	778.561i	0.861936	+	0.931293i
$837$	−301.710	+	80.8430i	−0.360466	+	0.0965867i
$838$	−11.0244	+	25.2249i	−0.0131556	+	0.0301013i
$839$	−652.560			−0.777783			−0.388891	−	0.921284i	$-0.627142\pi$
$839$	−652.560			−0.777783			−0.388891	+	0.921284i	$0.627142\pi$
$840$	−67.1028	+	565.018i	−0.0798843	+	0.672640i
$841$			838.619i			0.997168i
$842$	−103.483	+	236.779i	−0.122901	+	0.281210i
$843$	65.0564	+	242.794i	0.0771725	+	0.288012i
$844$	−57.4849	+	1486.26i	−0.0681100	+	1.76098i
$845$	−232.303	+	866.967i	−0.274915	+	1.02600i
$846$	−388.665	−	58.8320i	−0.459415	−	0.0695413i
$847$	−1285.05	−	1115.12i	−1.51717	−	1.31656i
$848$	−139.394	−	747.000i	−0.164379	−	0.880896i
$849$	−98.9472	−	171.382i	−0.116546	−	0.201863i
$850$	219.282	−	274.616i	0.257979	−	0.323078i
$851$	−131.396	−	490.377i	−0.154402	−	0.576237i
$852$	−173.788	−	109.503i	−0.203976	−	0.128525i
$853$	−118.913	+	118.913i	−0.139405	+	0.139405i	−0.773366	−	0.633960i	$-0.781428\pi$
$853$	−118.913	+	118.913i	−0.139405	+	0.139405i	0.633960	+	0.773366i	$0.281428\pi$
$854$	−252.928	−	531.657i	−0.296169	−	0.622550i
$855$			244.614i			0.286098i
$856$	−993.879	+	1150.51i	−1.16107	+	1.34405i
$857$	−335.532	+	581.158i	−0.391519	+	0.678131i	−0.992650	−	0.121020i	$-0.961384\pi$
$857$	−335.532	+	581.158i	−0.391519	+	0.678131i	0.601131	+	0.799150i	$0.294717\pi$
$858$	−132.056	−	1178.69i	−0.153911	−	1.37376i
$859$	−1015.41	−	272.078i	−1.18208	−	0.316738i	−0.386330	−	0.922361i	$-0.626257\pi$
$859$	−1015.41	−	272.078i	−1.18208	−	0.316738i	−0.795752	+	0.605623i	$0.792924\pi$
$860$	−513.670	−	159.154i	−0.597291	−	0.185063i
$861$	58.8022	+	87.0154i	0.0682952	+	0.101063i
$862$	352.121	+	53.3002i	0.408493	+	0.0618332i
$863$	−459.474	−	795.832i	−0.532415	−	0.922170i	−0.999284	−	0.0378431i	$-0.987951\pi$
$863$	−459.474	−	795.832i	−0.532415	−	0.922170i	0.466869	−	0.884327i	$-0.345382\pi$
$864$	78.1580	−	146.763i	0.0904607	−	0.169864i
$865$	468.384	−	811.264i	0.541484	−	0.937878i
$866$	−124.152	+	48.6359i	−0.143363	+	0.0561616i
$867$	−72.9081	−	72.9081i	−0.0840923	−	0.0840923i
$868$	887.809	+	1429.96i	1.02282	+	1.64742i
$869$	−672.437	−	672.437i	−0.773805	−	0.773805i
$870$	28.7344	+	12.5582i	0.0330281	+	0.0144347i
$871$	−353.453	+	612.198i	−0.405801	+	0.702868i
$872$	−244.046	+	1276.62i	−0.279869	+	1.46401i
$873$	64.4052	+	111.553i	0.0737745	+	0.127781i
$874$	710.503	−	523.685i	0.812933	−	0.599182i
$875$	−280.101	+	575.555i	−0.320115	+	0.657777i
$876$	11.5817	+	21.9805i	0.0132211	+	0.0250919i
$877$	621.464	+	166.521i	0.708625	+	0.189875i	0.595091	−	0.803659i	$-0.297116\pi$
$877$	621.464	+	166.521i	0.708625	+	0.189875i	0.113534	+	0.993534i	$0.463783\pi$
$878$	−824.945	+	1033.11i	−0.939573	+	1.17667i
$879$	−137.029	+	237.341i	−0.155892	+	0.270012i
$880$	−138.325	+	1785.51i	−0.157187	+	2.02899i
$881$		−	1426.45i		−	1.61912i	−0.587035	−	0.809562i	$-0.699705\pi$
$881$		−	1426.45i		−	1.61912i	0.587035	−	0.809562i	$-0.300295\pi$
$882$	293.988	+	2.60839i	0.333320	+	0.00295735i
$883$	−713.380	+	713.380i	−0.807905	+	0.807905i	−0.984316	−	0.176412i	$-0.943551\pi$
$883$	−713.380	+	713.380i	−0.807905	+	0.807905i	0.176412	+	0.984316i	$0.443551\pi$
$884$	−1133.73	−	714.359i	−1.28250	−	0.808099i
$885$	−47.3815	−	176.830i	−0.0535384	−	0.199808i
$886$	869.835	−	97.4528i	0.981755	−	0.109992i
$887$	−581.488	−	1007.17i	−0.655567	−	1.13548i	−0.981751	−	0.190170i	$-0.939096\pi$
$887$	−581.488	−	1007.17i	−0.655567	−	1.13548i	0.326184	−	0.945306i	$-0.394237\pi$
$888$	−96.5067	+	199.434i	−0.108679	+	0.224588i
$889$	464.746	+	1345.94i	0.522774	+	1.51399i
$890$	−571.223	+	421.027i	−0.641824	+	0.473064i
$891$	−44.4453	+	165.872i	−0.0498825	+	0.186164i
$892$	−1048.24	−	1132.58i	−1.17515	−	1.26971i
$893$	235.692	+	879.614i	0.263933	+	0.985010i
$894$	−94.8022	+	37.1383i	−0.106043	+	0.0415417i
$895$			856.955i			0.957492i
$896$	−878.927	−	174.076i	−0.980946	−	0.194282i
$897$	−986.831			−1.10015
$898$	242.236	+	618.351i	0.269751	+	0.688587i
$899$	89.6031	−	24.0091i	0.0996697	−	0.0267064i
$900$	−82.8904	+	76.7172i	−0.0921004	+	0.0852413i
$901$	856.439	+	229.482i	0.950543	+	0.254697i
$902$	196.118	+	266.081i	0.217426	+	0.294990i
$903$	−52.7831	+	272.805i	−0.0584530	+	0.302110i
$904$	−389.888	−	188.667i	−0.431292	−	0.208703i
$905$	−431.963	+	249.394i	−0.477307	+	0.275573i
$906$	−0.0658182	−	0.587475i	−7.26471e−5	−	0.000648427i
$907$	−992.484	+	265.935i	−1.09425	+	0.293203i	−0.760421	−	0.649431i	$-0.775007\pi$
$907$	−992.484	+	265.935i	−1.09425	+	0.293203i	−0.333828	+	0.942634i	$0.608341\pi$
$908$	−536.954	+	852.175i	−0.591359	+	0.938519i
$909$	−267.354	−	267.354i	−0.294119	−	0.294119i
$910$	−1388.69	−	493.340i	−1.52603	−	0.542132i
$911$	853.765			0.937174			0.468587	−	0.883417i	$-0.344763\pi$
$911$	853.765			0.937174			0.468587	+	0.883417i	$0.344763\pi$
$912$	−384.048	−	29.7525i	−0.421106	−	0.0326234i
$913$	96.5344	+	55.7342i	0.105733	+	0.0610451i
$914$	1188.79	+	949.252i	1.30065	+	1.03857i
$915$	110.591	−	412.730i	0.120864	−	0.451071i
$916$	−143.738	+	75.7364i	−0.156919	+	0.0826817i
$917$	−1037.60	+	73.4581i	−1.13151	+	0.0801070i
$918$	115.111	+	156.175i	0.125393	+	0.170125i
$919$	−743.997	+	429.547i	−0.809572	+	0.467407i	−0.846807	−	0.531900i	$-0.821478\pi$
$919$	−743.997	+	429.547i	−0.809572	+	0.467407i	0.0372352	+	0.999307i	$0.488145\pi$
$920$	1463.53	+	279.777i	1.59080	+	0.304106i
$921$	30.9023	+	17.8414i	0.0335530	+	0.0193718i
$922$	73.3544	−	167.842i	0.0795600	−	0.182041i
$923$	376.198	−	376.198i	0.407582	−	0.407582i
$924$	924.875	−	29.6247i	1.00095	−	0.0320614i
$925$	106.415	−	106.415i	0.115043	−	0.115043i
$926$	−399.203	−	1019.04i	−0.431104	−	1.10047i
$927$	146.518	+	84.5922i	0.158056	+	0.0912537i
$928$	−23.2117	+	43.5862i	−0.0250126	+	0.0469679i
$929$	510.575	−	294.781i	0.549596	−	0.317310i	−0.199363	−	0.979926i	$-0.563887\pi$
$929$	510.575	−	294.781i	0.549596	−	0.317310i	0.748959	+	0.662616i	$0.230554\pi$
$930$	−182.822	+	1207.79i	−0.196583	+	1.29870i
$931$	−267.205	−	626.480i	−0.287009	−	0.672911i
$932$	110.343	−	356.131i	0.118393	−	0.382115i
$933$	277.709	−	1036.43i	0.297652	−	1.11085i
$934$	−203.323	+	22.7794i	−0.217690	+	0.0243891i
$935$	−1809.64	−	1044.80i	−1.93544	−	1.11743i
$936$	325.903	+	281.535i	0.348187	+	0.300785i
$937$	330.256			0.352461			0.176230	−	0.984349i	$-0.443610\pi$
$937$	330.256			0.352461			0.176230	+	0.984349i	$0.443610\pi$
$938$	−454.203	−	312.842i	−0.484225	−	0.333520i
$939$	414.998	+	414.998i	0.441957	+	0.441957i
$940$	−819.530	+	1300.64i	−0.871841	+	1.38366i
$941$	444.260	−	119.039i	0.472115	−	0.126503i	−0.0149136	−	0.999889i	$-0.504747\pi$
$941$	444.260	−	119.039i	0.472115	−	0.126503i	0.487029	+	0.873386i	$0.338081\pi$
$942$	−358.034	−	285.891i	−0.380078	−	0.303494i
$943$	238.176	−	137.511i	0.252573	−	0.145823i
$944$	283.390	−	52.8819i	0.300201	−	0.0560190i
$945$	161.154	+	139.844i	0.170533	+	0.147984i
$946$	−130.891	+	864.714i	−0.138363	+	0.914074i
$947$	−103.154	−	27.6401i	−0.108927	−	0.0291870i	0.203944	−	0.978983i	$-0.434624\pi$
$947$	−103.154	−	27.6401i	−0.108927	−	0.0291870i	−0.312871	+	0.949796i	$0.601291\pi$
$948$	345.045	+	13.3454i	0.363971	+	0.0140775i
$949$	−62.1575	+	16.6551i	−0.0654979	+	0.0175501i
$950$	239.750	+	104.782i	0.252369	+	0.110296i
$951$	340.409			0.357949
$952$	625.859	−	837.430i	0.657415	−	0.879653i
$953$			1472.41i			1.54503i	0.634997	+	0.772515i	$0.281002\pi$
$953$			1472.41i			1.54503i	−0.634997	+	0.772515i	$0.718998\pi$
$954$	−261.112	−	114.118i	−0.273702	−	0.119620i
$955$	−549.538	−	2050.91i	−0.575433	−	2.14754i
$956$	−619.029	+	572.928i	−0.647520	+	0.599297i
$957$	13.1995	−	49.2613i	0.0137926	−	0.0514747i
$958$	−67.9091	+	448.632i	−0.0708863	+	0.468301i
$959$	−205.194	+	1060.53i	−0.213967	+	1.10587i
$960$	−403.516	−	509.930i	−0.420330	−	0.531178i
$961$	1326.25	+	2297.14i	1.38008	+	2.39036i
$962$	−448.427	−	358.070i	−0.466140	−	0.372214i
$963$	147.561	+	550.705i	0.153230	+	0.571864i
$964$	−1714.07	+	388.956i	−1.77808	+	0.403481i
$965$	1069.98	−	1069.98i	1.10879	−	1.10879i
$966$	61.1821	−	767.475i	0.0633355	−	0.794488i
$967$		−	556.184i		−	0.575164i	−0.957756	−	0.287582i	$-0.907149\pi$
$967$		−	556.184i		−	0.575164i	0.957756	−	0.287582i	$-0.0928514\pi$
$968$	1939.32	−	141.652i	2.00343	−	0.146334i
$969$	224.727	−	389.238i	0.231916	−	0.401691i
$970$	500.617	−	56.0871i	0.516100	−	0.0578217i
$971$	−1561.66	−	418.446i	−1.60830	−	0.430943i	−0.660765	−	0.750593i	$-0.729768\pi$
$971$	−1561.66	−	418.446i	−1.60830	−	0.430943i	−0.947536	+	0.319650i	$0.896435\pi$
$972$	−29.0666	−	55.1646i	−0.0299039	−	0.0567537i
$973$	730.577	+	355.544i	0.750850	+	0.365410i
$974$	−135.602	+	895.835i	−0.139222	+	0.919749i
$975$	−146.266	−	253.340i	−0.150016	−	0.259836i
$976$	634.543	+	223.830i	0.650146	+	0.229334i
$977$	483.732	−	837.848i	0.495120	−	0.857572i	−0.504865	−	0.863199i	$-0.668458\pi$
$977$	483.732	−	837.848i	0.495120	−	0.857572i	0.999984	+	0.00562637i	$0.00179094\pi$
$978$	−235.013	−	599.912i	−0.240299	−	0.613407i
$979$	816.042	+	816.042i	0.833547	+	0.833547i
$980$	469.776	−	1049.42i	0.479363	−	1.07084i
$981$	344.644	+	344.644i	0.351320	+	0.351320i
$982$	443.570	−	1014.93i	0.451701	−	1.03353i
$983$	216.378	−	374.778i	0.220120	−	0.381259i	−0.734724	−	0.678366i	$-0.762688\pi$
$983$	216.378	−	374.778i	0.220120	−	0.381259i	0.954844	+	0.297107i	$0.0960217\pi$
$984$	−117.889	−	22.5364i	−0.119806	−	0.0229028i
$985$	830.038	+	1437.67i	0.842678	+	1.45956i
$986$	−34.1860	−	46.3815i	−0.0346714	−	0.0470400i
$987$	714.243	+	347.595i	0.723650	+	0.352173i
$988$	295.274	−	952.995i	0.298860	−	0.964569i
$989$	702.861	+	188.331i	0.710679	+	0.190426i
$990$	524.793	+	419.049i	0.530094	+	0.423282i
$991$	−443.865	+	768.796i	−0.447896	+	0.775778i	−0.998249	−	0.0591536i	$-0.981160\pi$
$991$	−443.865	+	768.796i	−0.447896	+	0.775778i	0.550353	+	0.834932i	$0.314493\pi$
$992$	−1874.01	−	433.938i	−1.88913	−	0.437438i
$993$		−	47.5830i		−	0.0479185i
$994$	269.252	+	315.899i	0.270877	+	0.317806i
$995$	988.134	−	988.134i	0.993099	−	0.993099i
$996$	−39.4714	+	8.95685i	−0.0396299	+	0.00899282i
$997$	201.415	+	751.689i	0.202021	+	0.753951i	0.990337	+	0.138681i	$0.0442864\pi$
$997$	201.415	+	751.689i	0.202021	+	0.753951i	−0.788316	+	0.615270i	$0.789047\pi$
$998$	−57.3574	−	511.955i	−0.0574723	−	0.512981i
$999$	41.5420	+	71.9529i	0.0415836	+	0.0720249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bv.a.325.23	yes	256
7.5	odd	6	inner	336.3.bv.a.229.20	yes	256
16.13	even	4	inner	336.3.bv.a.157.20	yes	256
112.61	odd	12	inner	336.3.bv.a.61.23	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.bv.a.61.23	✓	256	112.61	odd	12	inner
336.3.bv.a.157.20	yes	256	16.13	even	4	inner
336.3.bv.a.229.20	yes	256	7.5	odd	6	inner
336.3.bv.a.325.23	yes	256	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.729511 - 1.86221i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-2.93563 + 2.71700i) q^{4} +(5.66629 + 1.51828i) q^{5} +(2.05530 + 2.78850i) q^{6} +(-2.28470 - 6.61666i) q^{7} +(7.20119 + 3.48467i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-1.30627 - 11.6594i) q^{10} +(-18.4302 + 4.93836i) q^{11} +(3.69340 - 5.86163i) q^{12} +(12.6887 + 12.6887i) q^{13} +(-10.6549 + 9.08151i) q^{14} -10.1605 q^{15} +(1.23583 - 15.9522i) q^{16} +(16.1678 + 9.33447i) q^{17} +(-4.68863 - 3.74389i) q^{18} +(-3.59750 + 13.4261i) q^{19} +(-20.7593 + 10.9382i) q^{20} +(6.78855 + 10.0457i) q^{21} +(22.6413 + 30.7183i) q^{22} +(27.4968 - 15.8753i) q^{23} +(-13.6100 - 2.60176i) q^{24} +(8.15103 + 4.70600i) q^{25} +(14.3724 - 32.8854i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(24.6845 + 13.2165i) q^{28} +(1.09119 - 1.09119i) q^{29} +(7.41220 + 18.9210i) q^{30} +(52.0589 + 30.0562i) q^{31} +(-30.6078 + 9.33593i) q^{32} +(28.6206 - 16.5241i) q^{33} +(5.58815 - 36.9173i) q^{34} +(-2.89986 - 40.9607i) q^{35} +(-3.55149 + 11.4624i) q^{36} +(4.13839 - 15.4447i) q^{37} +(27.6265 - 3.09516i) q^{38} +(-26.9167 - 15.5404i) q^{39} +(35.5133 + 30.6785i) q^{40} +8.66197 q^{41} +(13.7548 - 19.9701i) q^{42} +(16.2054 + 16.2054i) q^{43} +(40.6868 - 64.5721i) q^{44} +(16.9989 - 4.55483i) q^{45} +(-49.6222 - 39.6235i) q^{46} +(56.7381 - 32.7577i) q^{47} +(5.08359 + 27.2426i) q^{48} +(-38.5603 + 30.2342i) q^{49} +(2.81728 - 18.6120i) q^{50} +(-31.2337 - 8.36906i) q^{51} +(-71.7243 - 2.77411i) q^{52} +(45.8751 - 12.2922i) q^{53} +(9.52258 + 4.16179i) q^{54} -111.929 q^{55} +(6.60428 - 55.6092i) q^{56} -24.0749i q^{57} +(-2.82805 - 1.23598i) q^{58} +(4.66330 + 17.4037i) q^{59} +(29.8275 - 27.6061i) q^{60} +(-10.8844 + 40.6210i) q^{61} +(17.9934 - 118.871i) q^{62} +(-15.8608 - 13.7635i) q^{63} +(39.7142 + 50.1875i) q^{64} +(52.6327 + 91.1626i) q^{65} +(-51.6503 - 41.2429i) q^{66} +(10.1959 + 38.0517i) q^{67} +(-72.8243 + 16.5253i) q^{68} +(-38.8863 + 38.8863i) q^{69} +(-74.1618 + 35.2814i) q^{70} -29.6483i q^{71} +(23.9362 - 1.74835i) q^{72} +(-1.79304 + 3.10563i) q^{73} +(-31.7802 + 3.56052i) q^{74} +(-15.7466 - 4.21928i) q^{75} +(-25.9177 - 49.1883i) q^{76} +(74.7830 + 110.664i) q^{77} +(-9.30336 + 61.4614i) q^{78} +(24.9201 + 43.1629i) q^{79} +(31.2224 - 88.5134i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-6.31900 - 16.1304i) q^{82} +(-4.13095 - 4.13095i) q^{83} +(-47.2228 - 11.0459i) q^{84} +(77.4390 + 77.4390i) q^{85} +(18.3558 - 41.9998i) q^{86} +(-1.33643 + 2.31476i) q^{87} +(-149.928 - 28.6611i) q^{88} +(-30.2420 - 52.3807i) q^{89} +(-20.8829 - 28.3326i) q^{90} +(54.9667 - 112.946i) q^{91} +(-37.5872 + 121.313i) q^{92} +(-100.570 - 26.9477i) q^{93} +(-102.393 - 81.7609i) q^{94} +(-40.7690 + 70.6139i) q^{95} +(47.0227 - 29.3404i) q^{96} +42.9368i q^{97} +(84.4324 + 49.7510i) q^{98} +(-40.4756 + 40.4756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) \) 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Introduction

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