LMFDB - Embedded newform 336.3.bv.a.61.23

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)

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);

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")

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			61.23
Character	$\chi$	$=$	336.61
Dual form			336.3.bv.a.325.23

$q$-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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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	0.357021	−	0.934097i	$-0.383793\pi$
$5$	5.66629	−	1.51828i	1.13326	−	0.303656i	0.776237	+	0.630441i	$0.217126\pi$
$6$	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	−0.708896	−	0.705313i	$-0.750807\pi$
$11$	−18.4302	−	4.93836i	−1.67547	−	0.448942i	−0.966579	+	0.256371i	$0.917473\pi$
$12$	3.69340	+	5.86163i	0.307784	+	0.488470i
$13$	12.6887	−	12.6887i	0.976051	−	0.976051i	−0.0236687	−	0.999720i	$-0.507535\pi$
$13$	12.6887	−	12.6887i	0.976051	−	0.976051i	0.999720	+	0.0236687i	$0.00753469\pi$
$14$	−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	0.0576399	−	0.998337i	$-0.481642\pi$
$17$	16.1678	−	9.33447i	0.951045	−	0.549086i	0.893406	+	0.449251i	$0.148309\pi$
$18$	−4.68863	+	3.74389i	−0.260480	+	0.207994i
$19$	−3.59750	−	13.4261i	−0.189342	−	0.706635i	−0.993659	−	0.112434i	$-0.964135\pi$
$19$	−3.59750	−	13.4261i	−0.189342	−	0.706635i	0.804317	−	0.594200i	$-0.202531\pi$
$20$	−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	0.959551	−	0.281533i	$-0.0908430\pi$
$23$	27.4968	+	15.8753i	1.19551	+	0.690229i	0.235961	+	0.971763i	$0.424176\pi$
$24$	−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	0.725670	−	0.688043i	$-0.241530\pi$
$29$	1.09119	+	1.09119i	0.0376272	+	0.0376272i	−0.688043	+	0.725670i	$0.741530\pi$
$30$	7.41220	−	18.9210i	0.247073	−	0.630699i
$31$	52.0589	−	30.0562i	1.67932	−	0.969556i	0.717225	−	0.696842i	$-0.245412\pi$
$31$	52.0589	−	30.0562i	1.67932	−	0.969556i	0.962095	−	0.272714i	$-0.0879213\pi$
$32$	−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	0.999032	−	0.0439928i	$-0.0140079\pi$
$37$	4.13839	+	15.4447i	0.111848	+	0.417424i	−0.887183	+	0.461417i	$0.847341\pi$
$38$	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	−0.493102	−	0.869972i	$-0.664137\pi$
$43$	16.2054	−	16.2054i	0.376870	−	0.376870i	0.869972	+	0.493102i	$0.164137\pi$
$44$	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	0.962145	−	0.272538i	$-0.0878631\pi$
$47$	56.7381	+	32.7577i	1.20719	+	0.696973i	0.245048	+	0.969511i	$0.421196\pi$
$48$	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	0.664170	−	0.747581i	$-0.268785\pi$
$53$	45.8751	+	12.2922i	0.865568	+	0.231928i	0.201398	+	0.979510i	$0.435452\pi$
$54$	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	−0.915080	−	0.403273i	$-0.867873\pi$
$59$	4.66330	−	17.4037i	0.0790389	−	0.294977i	0.994119	+	0.108295i	$0.0345392\pi$
$60$	29.8275	+	27.6061i	0.497125	+	0.460102i
$61$	−10.8844	−	40.6210i	−0.178432	−	0.665918i	−0.995942	−	0.0900024i	$-0.971313\pi$
$61$	−10.8844	−	40.6210i	−0.178432	−	0.665918i	0.817509	−	0.575915i	$-0.195354\pi$
$62$	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	−0.847152	−	0.531350i	$-0.821685\pi$
$67$	10.1959	−	38.0517i	0.152178	−	0.567936i	0.999330	−	0.0365864i	$-0.0116484\pi$
$68$	−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	$0.0669529\pi$
$71$			29.6483i			0.417582i	−0.977960	+	0.208791i	$0.933047\pi$
$72$	23.9362	+	1.74835i	0.332448	+	0.0242826i
$73$	−1.79304	−	3.10563i	−0.0245621	−	0.0425429i	0.853483	−	0.521121i	$-0.174486\pi$
$73$	−1.79304	−	3.10563i	−0.0245621	−	0.0425429i	−0.878045	+	0.478578i	$0.841152\pi$
$74$	−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	−0.664088	−	0.747655i	$-0.731180\pi$
$79$	24.9201	−	43.1629i	0.315444	−	0.546365i	0.979532	+	0.201289i	$0.0645132\pi$
$80$	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	−0.731554	−	0.681784i	$-0.761205\pi$
$83$	−4.13095	+	4.13095i	−0.0497705	+	0.0497705i	0.681784	+	0.731554i	$0.261205\pi$
$84$	−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	−0.984395	−	0.175976i	$-0.943692\pi$
$89$	−30.2420	+	52.3807i	−0.339798	+	0.588547i	0.644597	+	0.764523i	$0.277025\pi$
$90$	−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	$-0.928962\pi$
$97$		−	42.9368i		−	0.442647i	0.975200	−	0.221324i	$-0.0710377\pi$
$98$	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	0.593378	+	0.804924i	$0.297794\pi$
$101$	−32.6194	+	121.737i	−0.322965	+	1.20532i	−0.916342	+	0.400396i	$0.868873\pi$
$102$	7.20043	−	64.2690i	0.0705925	−	0.630088i
$103$	28.1974	−	48.8393i	0.273761	−	0.474168i	−0.696061	−	0.717983i	$-0.745066\pi$
$103$	28.1974	−	48.8393i	0.273761	−	0.474168i	0.969822	+	0.243815i	$0.0783989\pi$
$104$	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	−0.673918	−	0.738807i	$-0.735390\pi$
$107$	−49.1869	−	183.568i	−0.459691	−	1.71559i	0.214226	−	0.976784i	$-0.431277\pi$
$108$	0.803295	+	20.7691i	0.00743791	+	0.192306i
$109$	42.0495	−	156.931i	0.385776	−	1.43973i	−0.451165	−	0.892441i	$-0.648991\pi$
$109$	42.0495	−	156.931i	0.385776	−	1.43973i	0.836941	−	0.547294i	$-0.184342\pi$
$110$	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	0.942330	+	0.334684i	$0.108630\pi$
$131$	38.4604	+	143.536i	0.293591	+	1.09569i	−0.648740	+	0.761010i	$0.724704\pi$
$132$	−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	−0.900901	−	0.434025i	$-0.857093\pi$
$137$	−133.640	+	77.1571i	−0.975474	+	0.563190i	−0.0745733	+	0.997216i	$0.523759\pi$
$138$	100.782	−	44.0464i	0.730307	−	0.319177i
$139$	−82.0748	−	82.0748i	−0.590466	−	0.590466i	0.347291	−	0.937757i	$-0.387102\pi$
$139$	−82.0748	−	82.0748i	−0.590466	−	0.590466i	−0.937757	+	0.347291i	$0.887102\pi$
$140$	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	0.935688	−	0.352827i	$-0.114780\pi$
$149$	−7.60722	−	28.3905i	−0.0510552	−	0.190541i	−0.986744	+	0.162287i	$0.948113\pi$
$150$	3.63012	−	32.4014i	0.0242008	−	0.216009i
$151$	−0.147788	+	0.0853252i	−0.000978726	+	0.000565067i	−0.500489	−	0.865743i	$-0.666847\pi$
$151$	−0.147788	+	0.0853252i	−0.000978726	+	0.000565067i	0.499511	+	0.866308i	$0.333513\pi$
$152$	−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	−0.172129	−	0.985074i	$-0.555065\pi$
$157$	−127.756	−	34.2322i	−0.813734	−	0.218039i	−0.641605	+	0.767035i	$0.721731\pi$
$158$	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	−0.763655	−	0.645625i	$-0.776597\pi$
$163$	−179.657	+	48.1388i	−1.10219	+	0.295330i	−0.338532	+	0.940955i	$0.609930\pi$
$164$	−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	0.976349	+	0.216200i	$0.0693663\pi$
$173$	41.3307	+	154.248i	0.238906	+	0.891609i	−0.737443	+	0.675409i	$0.763967\pi$
$174$	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	−0.776236	−	0.630443i	$-0.782873\pi$
$179$	37.8094	−	141.106i	0.211225	−	0.788304i	0.987461	−	0.157861i	$-0.0504599\pi$
$180$	−37.5269	−	59.5572i	−0.208483	−	0.330873i
$181$	−60.1237	−	60.1237i	−0.332175	−	0.332175i	0.521237	−	0.853412i	$-0.325471\pi$
$181$	−60.1237	−	60.1237i	−0.332175	−	0.332175i	−0.853412	+	0.521237i	$0.825471\pi$
$182$	−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	−0.196862	+	0.980431i	$0.563075\pi$
$191$	−180.974	+	313.457i	−0.947509	+	1.64113i	−0.750647	+	0.660703i	$0.770258\pi$
$192$	−88.9416	+	66.1619i	−0.463237	+	0.344593i
$193$	128.975	+	223.392i	0.668265	+	1.15747i	0.978389	+	0.206773i	$0.0662962\pi$
$193$	128.975	+	223.392i	0.668265	+	1.15747i	−0.310124	+	0.950696i	$0.600370\pi$
$194$	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	0.0158874	−	0.999874i	$-0.494943\pi$
$197$	200.105	−	200.105i	1.01576	−	1.01576i	0.999874	−	0.0158874i	$-0.00505732\pi$
$198$	104.901	−	45.8465i	0.529804	−	0.231548i
$199$	119.109	+	206.303i	0.598539	+	1.03670i	0.993037	+	0.117803i	$0.0375853\pi$
$199$	119.109	+	206.303i	0.598539	+	1.03670i	−0.394498	+	0.918897i	$0.629081\pi$
$200$	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	0.957415	+	0.288714i	$0.0932278\pi$
$211$	262.933	+	262.933i	1.24613	+	1.24613i	0.288714	+	0.957415i	$0.406772\pi$
$212$	−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	$-0.667295\pi$
$223$		−	385.806i		−	1.73007i	0.501709	−	0.865036i	$-0.332705\pi$
$224$	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	0.751106	−	0.660182i	$-0.229521\pi$
$227$	243.229	+	65.1729i	1.07149	+	0.287105i	0.320386	+	0.947287i	$0.396187\pi$
$228$	65.4116	−	70.6751i	0.286893	−	0.309978i
$229$	39.2335	−	10.5126i	0.171325	−	0.0459065i	−0.172137	−	0.985073i	$-0.555067\pi$
$229$	39.2335	−	10.5126i	0.171325	−	0.0459065i	0.343462	+	0.939167i	$0.388400\pi$
$230$	−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	0.316676	−	0.948534i	$-0.397433\pi$
$233$	−80.7208	−	46.6042i	−0.346441	−	0.200018i	−0.663117	+	0.748516i	$0.730767\pi$
$234$	−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	0.584011	−	0.811746i	$-0.301483\pi$
$241$	380.541	−	219.705i	1.57901	−	0.911641i	0.994998	−	0.0998950i	$-0.0318507\pi$
$242$	−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	0.964758	+	0.263138i	$0.0847574\pi$
$251$	308.202	+	308.202i	1.22790	+	1.22790i	0.263138	+	0.964758i	$0.415243\pi$
$252$	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	0.295537	−	0.955331i	$-0.404502\pi$
$257$	−98.6973	−	56.9829i	−0.384036	−	0.221723i	−0.679573	+	0.733608i	$0.737835\pi$
$258$	−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	−0.254234	−	0.967143i	$-0.581823\pi$
$263$	119.986	−	69.2737i	0.456219	−	0.263398i	0.710453	+	0.703745i	$0.248490\pi$
$264$	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	−0.160076	−	0.987105i	$-0.551174\pi$
$269$	−213.118	−	57.1047i	−0.792259	−	0.212285i	−0.632183	+	0.774819i	$0.717841\pi$
$270$	47.6389	−	38.0398i	0.176440	−	0.140888i
$271$	−226.954	−	131.032i	−0.837468	−	0.483512i	0.0189346	−	0.999821i	$-0.493973\pi$
$271$	−226.954	−	131.032i	−0.837468	−	0.483512i	−0.856403	+	0.516308i	$0.827306\pi$
$272$	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	0.620505	−	0.784203i	$-0.286928\pi$
$277$	212.120	+	56.8374i	0.765776	+	0.205189i	0.145271	+	0.989392i	$0.453594\pi$
$278$	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	$0.0831373\pi$
$281$			145.122i			0.516449i	−0.966085	+	0.258224i	$0.916863\pi$
$282$	207.959	−	90.8872i	0.737442	−	0.322295i
$283$	29.5712	−	110.361i	0.104492	−	0.389969i	−0.893795	−	0.448475i	$-0.851967\pi$
$283$	29.5712	−	110.361i	0.104492	−	0.389969i	0.998287	+	0.0585064i	$0.0186338\pi$
$284$	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	0.871770	−	0.489915i	$-0.162972\pi$
$293$	111.884	+	111.884i	0.381855	+	0.381855i	−0.489915	+	0.871770i	$0.662972\pi$
$294$	−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	−0.730434	−	0.682983i	$-0.760682\pi$
$307$	−14.5675	+	14.5675i	−0.0474511	+	0.0474511i	0.682983	+	0.730434i	$0.260682\pi$
$308$	−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	−0.575715	−	0.817651i	$-0.695276\pi$
$311$	−309.745	−	536.494i	−0.995964	−	1.72506i	−0.420249	−	0.907409i	$-0.638057\pi$
$312$	−139.679	+	205.705i	−0.447690	+	0.659311i
$313$	−169.422	+	293.448i	−0.541285	+	0.937533i	0.457545	+	0.889186i	$0.348729\pi$
$313$	−169.422	+	293.448i	−0.541285	+	0.937533i	−0.998831	+	0.0483472i	$0.984605\pi$
$314$	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	−0.545499	−	0.838111i	$-0.683660\pi$
$317$	−189.838	+	50.8671i	−0.598860	+	0.160464i	−0.0533604	+	0.998575i	$0.516993\pi$
$318$	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	0.954353	−	0.298681i	$-0.0965465\pi$
$331$	−7.11030	−	26.5360i	−0.0214813	−	0.0801692i	−0.975834	+	0.218512i	$0.929880\pi$
$332$	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	0.0963096	−	0.995351i	$-0.469296\pi$
$347$	−110.332	−	29.5634i	−0.317959	−	0.0851970i	−0.414269	+	0.910154i	$0.635963\pi$
$348$	−2.36595	+	10.4263i	−0.00679870	+	0.0299608i
$349$	−261.232	+	261.232i	−0.748514	+	0.748514i	−0.974200	−	0.225686i	$-0.927538\pi$
$349$	−261.232	+	261.232i	−0.748514	+	0.748514i	0.225686	+	0.974200i	$0.427538\pi$
$350$	−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	−0.348964	−	0.937136i	$-0.613467\pi$
$353$	101.712	−	58.7237i	0.288137	−	0.166356i	0.637101	+	0.770780i	$0.280133\pi$
$354$	−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	0.992883	−	0.119094i	$-0.0379989\pi$
$359$	497.641	+	287.313i	1.38619	+	0.800315i	0.393303	+	0.919409i	$0.371332\pi$
$360$	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	−0.966756	−	0.255699i	$-0.917694\pi$
$367$	−450.930	+	260.345i	−1.22869	+	0.709386i	−0.261936	+	0.965085i	$0.584361\pi$
$368$	−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	0.939475	+	0.342616i	$0.111313\pi$
$373$	110.846	+	413.683i	0.297174	+	1.10907i	−0.642301	+	0.766452i	$0.722020\pi$
$374$	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	−0.143374	+	0.989669i	$0.545795\pi$
$379$	−429.423	+	429.423i	−1.13304	+	1.13304i	−0.989669	+	0.143374i	$0.954205\pi$
$380$	−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	0.662510	−	0.749053i	$-0.269491\pi$
$383$	132.161	+	76.3029i	0.345067	+	0.199224i	−0.317444	+	0.948277i	$0.602824\pi$
$384$	−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	0.419487	−	0.907761i	$-0.362210\pi$
$389$	127.939	+	34.2812i	0.328893	+	0.0881265i	−0.0905943	+	0.995888i	$0.528877\pi$
$390$	−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	−0.998992	−	0.0448984i	$-0.985704\pi$
$397$	−62.0466	−	231.561i	−0.156289	−	0.583277i	0.842703	−	0.538379i	$-0.180963\pi$
$398$	−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	−0.990606	−	0.136745i	$-0.956336\pi$
$401$	−151.128	+	261.762i	−0.376879	+	0.652773i	0.613728	+	0.789518i	$0.289669\pi$
$402$	−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	0.695460	−	0.718565i	$-0.255201\pi$
$409$	−112.297	−	194.505i	−0.274566	−	0.475562i	−0.970025	+	0.243003i	$0.921867\pi$
$410$	−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	−0.718626	−	0.695397i	$-0.755229\pi$
$419$	−9.73289	+	9.73289i	−0.0232288	+	0.0232288i	0.695397	+	0.718626i	$0.255229\pi$
$420$	−250.807	+	134.286i	−0.597160	+	0.319730i
$421$	−91.3599	+	91.3599i	−0.217007	+	0.217007i	−0.807236	−	0.590229i	$-0.799037\pi$
$421$	−91.3599	+	91.3599i	−0.217007	+	0.217007i	0.590229	+	0.807236i	$0.299037\pi$
$422$	−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	0.744060	−	0.668113i	$-0.232898\pi$
$431$	−89.0329	−	154.210i	−0.206573	−	0.357795i	−0.950633	+	0.310318i	$0.899564\pi$
$432$	54.0714	−	63.1529i	0.125165	−	0.146187i
$433$			66.6693i			0.153971i	0.997032	+	0.0769853i	$0.0245295\pi$
$433$			66.6693i			0.153971i	−0.997032	+	0.0769853i	$0.975471\pi$
$434$	−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	0.193533	+	0.981094i	$0.438005\pi$
$439$	−330.517	+	572.472i	−0.752885	+	1.30404i	−0.946419	+	0.322942i	$0.895328\pi$
$440$	−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	−0.967707	−	0.252077i	$-0.918886\pi$
$443$	−113.269	−	422.727i	−0.255687	−	0.954236i	0.712020	−	0.702159i	$-0.247780\pi$
$444$	−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	−0.443487	−	0.896281i	$-0.646259\pi$
$457$	−658.735	−	380.321i	−1.44143	−	0.832211i	−0.997945	+	0.0640694i	$0.979592\pi$
$458$	−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	−0.633370	−	0.773849i	$-0.718329\pi$
$461$	64.7608	−	64.7608i	0.140479	−	0.140479i	0.773849	+	0.633370i	$0.218329\pi$
$462$	−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	0.988462	−	0.151468i	$-0.0484000\pi$
$467$	26.4765	+	98.8116i	0.0566948	+	0.211588i	−0.931767	+	0.363056i	$0.881733\pi$
$468$	−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	−0.690867	−	0.722982i	$-0.742771\pi$
$479$	−196.476	+	113.436i	−0.410180	+	0.236818i	0.280687	+	0.959799i	$0.409438\pi$
$480$	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	−0.845425	−	0.534094i	$-0.820653\pi$
$487$	−392.327	+	226.510i	−0.805599	+	0.465113i	0.0398260	+	0.999207i	$0.487320\pi$
$488$	−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	−0.185144	−	0.982711i	$-0.559275\pi$
$491$	391.606	−	391.606i	0.797567	−	0.797567i	0.982711	+	0.185144i	$0.0592752\pi$
$492$	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	−0.000749103	−	1.00000i	$-0.500238\pi$
$499$	248.802	−	66.6664i	0.498602	−	0.133600i	0.499351	+	0.866400i	$0.333572\pi$
$500$	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	0.994210	−	0.107450i	$-0.0342686\pi$
$509$	40.4522	+	150.970i	0.0794739	+	0.296601i	−0.914737	+	0.404051i	$0.867602\pi$
$510$	−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	0.785624	−	0.618704i	$-0.212342\pi$
$521$	−74.5036	−	129.044i	−0.143001	−	0.247685i	−0.928625	+	0.371019i	$0.879009\pi$
$522$	−9.20147	−	1.03089i	−0.0176273	−	0.00197489i
$523$	658.412	−	176.421i	1.25891	−	0.337325i	0.433140	−	0.901326i	$-0.357405\pi$
$523$	658.412	−	176.421i	1.25891	−	0.337325i	0.825774	+	0.564001i	$0.190739\pi$
$524$	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	−0.375989	−	0.926624i	$-0.622697\pi$
$541$	−128.916	+	34.5430i	−0.238292	+	0.0638502i	0.137696	+	0.990474i	$0.456030\pi$
$542$	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	0.943884	−	0.330277i	$-0.107142\pi$
$547$	335.643	+	335.643i	0.613608	+	0.613608i	−0.330277	+	0.943884i	$0.607142\pi$
$548$	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	0.583388	+	0.812194i	$0.301727\pi$
$557$	−182.661	+	681.701i	−0.327938	+	1.22388i	−0.911326	+	0.411686i	$0.864940\pi$
$558$	−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	−0.0415417	−	0.999137i	$-0.513227\pi$
$563$	−324.900	−	87.0566i	−0.577086	−	0.154630i	−0.535545	+	0.844507i	$0.679894\pi$
$564$	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	0.0522046	−	0.998636i	$-0.483375\pi$
$569$	−447.540	−	258.387i	−0.786538	−	0.454108i	−0.838742	+	0.544529i	$0.816709\pi$
$570$	−280.699	−	31.4484i	−0.492455	−	0.0551726i
$571$	−866.821	−	232.264i	−1.51808	−	0.406767i	−0.598968	−	0.800773i	$-0.704422\pi$
$571$	−866.821	−	232.264i	−1.51808	−	0.406767i	−0.919108	+	0.394006i	$0.871089\pi$
$572$	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	−0.0859176	−	0.996302i	$-0.527382\pi$
$577$	423.487	−	244.500i	0.733947	−	0.423744i	0.819864	+	0.572558i	$0.194049\pi$
$578$	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	0.976214	−	0.216810i	$-0.0695653\pi$
$587$	445.770	+	445.770i	0.759404	+	0.759404i	−0.216810	+	0.976214i	$0.569565\pi$
$588$	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	0.601234	−	0.799073i	$-0.294676\pi$
$593$	124.431	+	71.8405i	0.209834	+	0.121148i	−0.391400	+	0.920220i	$0.628009\pi$
$594$	−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	0.235089	−	0.971974i	$-0.424462\pi$
$599$	715.438	−	413.058i	1.19439	−	0.689580i	0.959299	+	0.282394i	$0.0911285\pi$
$600$	−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	0.987688	−	0.156437i	$-0.0500007\pi$
$607$	817.055	+	471.727i	1.34605	+	0.777145i	0.358366	+	0.933581i	$0.383334\pi$
$608$	−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	0.979013	−	0.203796i	$-0.0653279\pi$
$613$	1057.40	+	283.331i	1.72497	+	0.462203i	0.745953	+	0.665999i	$0.231995\pi$
$614$	−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	$0.383291\pi$
$617$			1151.98i			1.86706i	−0.358493	+	0.933532i	$0.616709\pi$
$618$	−78.2344	−	179.008i	−0.126593	−	0.289657i
$619$	−185.161	+	691.030i	−0.299129	+	1.11636i	0.638753	+	0.769411i	$0.279450\pi$
$619$	−185.161	+	691.030i	−0.299129	+	1.11636i	−0.937882	+	0.346953i	$0.887216\pi$
$620$	−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	$-0.816117\pi$
$631$		−	689.162i		−	1.09217i	0.837728	−	0.546087i	$-0.183883\pi$
$632$	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	0.810778	−	0.585354i	$-0.199044\pi$
$641$	−65.0888	−	112.737i	−0.101543	−	0.175877i	−0.912320	+	0.409477i	$0.865711\pi$
$642$	−612.974	−	240.130i	−0.954788	−	0.374034i
$643$	−93.8911	+	93.8911i	−0.146020	+	0.146020i	−0.776338	−	0.630317i	$-0.782925\pi$
$643$	−93.8911	+	93.8911i	−0.146020	+	0.146020i	0.630317	+	0.776338i	$0.282925\pi$
$644$	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	0.999496	−	0.0317570i	$-0.0101103\pi$
$647$	305.543	+	529.216i	0.472245	+	0.817953i	−0.527250	+	0.849710i	$0.676777\pi$
$648$	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	−0.948083	−	0.318022i	$-0.896981\pi$
$653$	−1051.42	+	281.727i	−1.61014	+	0.431435i	−0.662053	+	0.749457i	$0.730315\pi$
$654$	−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	0.234729	−	0.972061i	$-0.424580\pi$
$659$	−485.902	−	485.902i	−0.737332	−	0.737332i	−0.972061	+	0.234729i	$0.924580\pi$
$660$	−413.398	−	656.086i	−0.626361	−	0.994069i
$661$	−129.226	+	482.276i	−0.195500	+	0.729616i	0.796637	+	0.604458i	$0.206610\pi$
$661$	−129.226	+	482.276i	−0.195500	+	0.729616i	−0.992137	+	0.125158i	$0.960056\pi$
$662$	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	−0.191963	−	0.981402i	$-0.561485\pi$
$677$	89.6976	−	24.0344i	0.132493	−	0.0355013i	0.324456	+	0.945901i	$0.394819\pi$
$678$	−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	0.0313707	−	0.999508i	$-0.490013\pi$
$683$	−301.350	−	80.7465i	−0.441215	−	0.118223i	−0.472586	+	0.881285i	$0.656679\pi$
$684$	−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	0.992763	−	0.120093i	$-0.0383192\pi$
$691$	50.4144	+	188.149i	0.0729586	+	0.272285i	−0.919804	+	0.392378i	$0.871653\pi$
$692$	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	0.807570	−	0.589772i	$-0.200782\pi$
$701$	152.677	+	152.677i	0.217798	+	0.217798i	−0.589772	+	0.807570i	$0.700782\pi$
$702$	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	0.898332	−	0.439318i	$-0.144780\pi$
$709$	−70.4076	−	262.765i	−0.0993054	−	0.370613i	−0.997637	+	0.0687052i	$0.978113\pi$
$710$	−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	0.998953	+	0.0457573i	$0.0145701\pi$
$719$	1105.86	+	638.470i	1.53806	+	0.887997i	0.539103	+	0.842240i	$0.318763\pi$
$720$	−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	0.953693	−	0.300783i	$-0.0972481\pi$
$733$	−16.5812	−	61.8820i	−0.0226211	−	0.0844230i	−0.976314	+	0.216360i	$0.930581\pi$
$734$	−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	0.743589	+	0.668637i	$0.233122\pi$
$739$	−173.441	+	647.289i	−0.234696	+	0.875898i	−0.978286	+	0.207262i	$0.933545\pi$
$740$	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	$0.103186\pi$
$743$			473.322i			0.637041i	−0.947916	+	0.318521i	$0.896814\pi$
$744$	−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	−0.576342	−	0.817209i	$-0.695520\pi$
$751$	315.084	−	545.742i	0.419553	−	0.726687i	0.995894	+	0.0905220i	$0.0288535\pi$
$752$	−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	−0.830214	−	0.557445i	$-0.811782\pi$
$757$	−206.486	+	206.486i	−0.272769	+	0.272769i	0.557445	+	0.830214i	$0.311782\pi$
$758$	−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	−0.541221	−	0.840881i	$-0.682038\pi$
$761$	348.244	−	603.176i	0.457614	−	0.792610i	0.998834	+	0.0482705i	$0.0153710\pi$
$762$	−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	$-0.988355\pi$
$769$		−	56.2543i		−	0.0731525i	0.999331	−	0.0365762i	$-0.0116452\pi$
$770$	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	−0.616190	−	0.787597i	$-0.711325\pi$
$773$	240.592	−	897.902i	0.311245	−	1.16158i	0.927435	−	0.373984i	$-0.122009\pi$
$774$	−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	−0.743310	−	0.668947i	$-0.766745\pi$
$787$	−1354.83	−	363.025i	−1.72151	−	0.461277i	−0.978199	+	0.207671i	$0.933412\pi$
$788$	−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	−0.445947	−	0.895059i	$-0.647133\pi$
$797$	357.942	−	357.942i	0.449112	−	0.449112i	0.895059	+	0.445947i	$0.147133\pi$
$798$	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	−0.654838	−	0.755769i	$-0.727263\pi$
$809$	−265.144	+	153.081i	−0.327743	+	0.189222i	0.327096	+	0.944991i	$0.393930\pi$
$810$	−96.7543	+	42.2859i	−0.119450	+	0.0522049i
$811$	279.770	+	279.770i	0.344969	+	0.344969i	0.858232	−	0.513263i	$-0.171563\pi$
$811$	279.770	+	279.770i	0.344969	+	0.344969i	−0.513263	+	0.858232i	$0.671563\pi$
$812$	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	0.877615	+	0.479366i	$0.159133\pi$
$821$	293.311	+	1094.65i	0.357261	+	1.33332i	−0.520354	+	0.853950i	$0.674200\pi$
$822$	−59.5175	+	531.236i	−0.0724057	+	0.646273i
$823$	104.659	−	60.4250i	0.127168	−	0.0734204i	−0.435067	−	0.900398i	$-0.643275\pi$
$823$	104.659	−	60.4250i	0.127168	−	0.0734204i	0.562234	+	0.826978i	$0.309942\pi$
$824$	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	−0.712675	−	0.701494i	$-0.752517\pi$
$827$	−9.24705	+	9.24705i	−0.0111814	+	0.0111814i	0.701494	+	0.712675i	$0.252517\pi$
$828$	84.3145	−	371.560i	0.101829	−	0.448744i
$829$	668.905	+	179.232i	0.806881	+	0.216203i	0.638603	−	0.769536i	$-0.279513\pi$
$829$	668.905	+	179.232i	0.806881	+	0.216203i	0.168278	+	0.985740i	$0.446179\pi$
$830$	−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	0.633960	−	0.773366i	$-0.281428\pi$
$853$	−118.913	−	118.913i	−0.139405	−	0.139405i	−0.773366	+	0.633960i	$0.781428\pi$
$854$	−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	0.601131	−	0.799150i	$-0.294717\pi$
$857$	−335.532	−	581.158i	−0.391519	−	0.678131i	−0.992650	+	0.121020i	$0.961384\pi$
$858$	−132.056	+	1178.69i	−0.153911	+	1.37376i
$859$	−1015.41	+	272.078i	−1.18208	+	0.316738i	−0.795752	−	0.605623i	$-0.792924\pi$
$859$	−1015.41	+	272.078i	−1.18208	+	0.316738i	−0.386330	+	0.922361i	$0.626257\pi$
$860$	−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	0.466869	+	0.884327i	$0.345382\pi$
$863$	−459.474	+	795.832i	−0.532415	+	0.922170i	−0.999284	+	0.0378431i	$0.987951\pi$
$864$	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	0.113534	−	0.993534i	$-0.463783\pi$
$877$	621.464	−	166.521i	0.708625	−	0.189875i	0.595091	+	0.803659i	$0.297116\pi$
$878$	−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	$0.300295\pi$
$881$			1426.45i			1.61912i	−0.587035	+	0.809562i	$0.699705\pi$
$882$	293.988	−	2.60839i	0.333320	−	0.00295735i
$883$	−713.380	−	713.380i	−0.807905	−	0.807905i	0.176412	−	0.984316i	$-0.443551\pi$
$883$	−713.380	−	713.380i	−0.807905	−	0.807905i	−0.984316	+	0.176412i	$0.943551\pi$
$884$	−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	0.326184	+	0.945306i	$0.394237\pi$
$887$	−581.488	+	1007.17i	−0.655567	+	1.13548i	−0.981751	+	0.190170i	$0.939096\pi$
$888$	−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	−0.333828	−	0.942634i	$-0.608341\pi$
$907$	−992.484	−	265.935i	−1.09425	−	0.293203i	−0.760421	+	0.649431i	$0.775007\pi$
$908$	−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	0.0372352	−	0.999307i	$-0.488145\pi$
$919$	−743.997	−	429.547i	−0.809572	−	0.467407i	−0.846807	+	0.531900i	$0.821478\pi$
$920$	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	0.748959	−	0.662616i	$-0.230554\pi$
$929$	510.575	+	294.781i	0.549596	+	0.317310i	−0.199363	+	0.979926i	$0.563887\pi$
$930$	−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	0.487029	−	0.873386i	$-0.338081\pi$
$941$	444.260	+	119.039i	0.472115	+	0.126503i	−0.0149136	+	0.999889i	$0.504747\pi$
$942$	−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	−0.312871	−	0.949796i	$-0.601291\pi$
$947$	−103.154	+	27.6401i	−0.108927	+	0.0291870i	0.203944	+	0.978983i	$0.434624\pi$
$948$	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	$-0.718998\pi$
$953$		−	1472.41i		−	1.54503i	0.634997	−	0.772515i	$-0.281002\pi$
$954$	−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	$0.0928514\pi$
$967$			556.184i			0.575164i	−0.957756	+	0.287582i	$0.907149\pi$
$968$	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	−0.947536	−	0.319650i	$-0.896435\pi$
$971$	−1561.66	+	418.446i	−1.60830	+	0.430943i	−0.660765	+	0.750593i	$0.729768\pi$
$972$	−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	0.999984	−	0.00562637i	$-0.00179094\pi$
$977$	483.732	+	837.848i	0.495120	+	0.857572i	−0.504865	+	0.863199i	$0.668458\pi$
$978$	−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	0.954844	−	0.297107i	$-0.0960217\pi$
$983$	216.378	+	374.778i	0.220120	+	0.381259i	−0.734724	+	0.678366i	$0.762688\pi$
$984$	−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	0.550353	−	0.834932i	$-0.314493\pi$
$991$	−443.865	−	768.796i	−0.447896	−	0.775778i	−0.998249	+	0.0591536i	$0.981160\pi$
$992$	−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	−0.788316	−	0.615270i	$-0.789047\pi$
$997$	201.415	−	751.689i	0.202021	−	0.753951i	0.990337	−	0.138681i	$-0.0442864\pi$
$998$	−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.61.23	✓	256
7.3	odd	6	inner	336.3.bv.a.157.20	yes	256
16.5	even	4	inner	336.3.bv.a.229.20	yes	256
112.101	odd	12	inner	336.3.bv.a.325.23	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.bv.a.61.23	✓	256	1.1	even	1	trivial
336.3.bv.a.157.20	yes	256	7.3	odd	6	inner
336.3.bv.a.229.20	yes	256	16.5	even	4	inner
336.3.bv.a.325.23	yes	256	112.101	odd	12	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
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

L-functions

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