LMFDB - Embedded newform 399.2.bq.b.100.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(4,399)] 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("399.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 12, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.bq (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [90] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$15$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.10
Character	$\chi$	$=$	399.100
Dual form			399.2.bq.b.4.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.162768 - 0.923101i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(1.05376 + 0.383539i) q^{4} +(0.955023 - 0.347600i) q^{5} +(0.162768 + 0.923101i) q^{6} +(1.03944 + 2.43301i) q^{7} +(1.46290 - 2.53382i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.165423 - 0.938160i) q^{10} -2.35664 q^{11} -1.12139 q^{12} +(0.223172 + 1.26567i) q^{13} +(2.41510 - 0.563494i) q^{14} +(-0.778542 + 0.653274i) q^{15} +(-0.382790 - 0.321199i) q^{16} +(4.96569 + 4.16671i) q^{17} +(-0.468670 - 0.811761i) q^{18} +(3.60993 + 2.44303i) q^{19} +1.13969 q^{20} +(-1.80890 - 1.93078i) q^{21} +(-0.383585 + 2.17542i) q^{22} +(-1.42427 - 8.07745i) q^{23} +(-0.508061 + 2.88136i) q^{24} +(-3.03898 + 2.55001i) q^{25} +1.20467 q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.162172 + 2.96249i) q^{28} +(1.04660 + 0.380930i) q^{29} +(0.476316 + 0.825004i) q^{30} +(5.11980 - 8.86776i) q^{31} +(4.12379 - 3.46027i) q^{32} +(2.21452 - 0.806019i) q^{33} +(4.65455 - 3.90563i) q^{34} +(1.83841 + 1.96227i) q^{35} +(1.05376 - 0.383539i) q^{36} +(-0.800106 + 1.38583i) q^{37} +(2.84274 - 2.93468i) q^{38} +(-0.642598 - 1.11301i) q^{39} +(0.516350 - 2.92837i) q^{40} +(0.504190 - 2.85941i) q^{41} +(-2.07673 + 1.35553i) q^{42} +(-6.53730 - 5.48544i) q^{43} +(-2.48334 - 0.903863i) q^{44} +(0.508157 - 0.880154i) q^{45} -7.68813 q^{46} +(-5.80832 + 4.87376i) q^{47} +(0.469561 + 0.170906i) q^{48} +(-4.83912 + 5.05796i) q^{49} +(1.85927 + 3.22034i) q^{50} +(-6.09133 - 2.21706i) q^{51} +(-0.250263 + 1.41931i) q^{52} +(7.59535 + 2.76448i) q^{53} +(0.718045 + 0.602511i) q^{54} +(-2.25065 + 0.819168i) q^{55} +(7.68544 + 0.925503i) q^{56} +(-4.22779 - 1.06103i) q^{57} +(0.521989 - 0.904111i) q^{58} +(-4.97391 - 4.17361i) q^{59} +(-1.07095 + 0.389796i) q^{60} +(2.19419 + 12.4439i) q^{61} +(-7.35249 - 6.16948i) q^{62} +(2.36017 + 1.19566i) q^{63} +(-3.02266 - 5.23540i) q^{64} +(0.653081 + 1.13117i) q^{65} +(-0.383585 - 2.17542i) q^{66} +(0.938720 + 5.32375i) q^{67} +(3.63457 + 6.29527i) q^{68} +(4.10103 + 7.10319i) q^{69} +(2.11061 - 1.37764i) q^{70} +(-10.4644 - 8.78070i) q^{71} +(-0.508061 - 2.88136i) q^{72} +(-8.96582 + 3.26329i) q^{73} +(1.14902 + 0.964146i) q^{74} +(1.98355 - 3.43561i) q^{75} +(2.86702 + 3.95893i) q^{76} +(-2.44959 - 5.73375i) q^{77} +(-1.13202 + 0.412020i) q^{78} +(-5.03752 - 4.22698i) q^{79} +(-0.477222 - 0.173694i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-2.55745 - 0.930837i) q^{82} +(3.89275 + 6.74244i) q^{83} +(-1.16562 - 2.72836i) q^{84} +(6.19070 + 2.25323i) q^{85} +(-6.12768 + 5.14173i) q^{86} -1.11376 q^{87} +(-3.44754 + 5.97132i) q^{88} +(-13.1896 - 4.80064i) q^{89} +(-0.729759 - 0.612340i) q^{90} +(-2.84742 + 1.85857i) q^{91} +(1.59717 - 9.05799i) q^{92} +(-1.77809 + 10.0840i) q^{93} +(3.55356 + 6.15495i) q^{94} +(4.29676 + 1.07834i) q^{95} +(-2.69162 + 4.66201i) q^{96} +(-2.21143 + 0.804893i) q^{97} +(3.88135 + 5.29027i) q^{98} +(-1.80529 + 1.51482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 6 q^{7} - 6 q^{10} + 18 q^{11} + 108 q^{12} - 9 q^{13} - 3 q^{14} - 12 q^{17} - 30 q^{19} - 60 q^{20} - 9 q^{21} + 18 q^{23} + 9 q^{24} + 6 q^{25} + 12 q^{26} - 45 q^{27} - 45 q^{28} - 18 q^{29}+ \cdots + 6 q^{99}+O(q^{100}) $ 90 * q + 6 * q^7 - 6 * q^10 + 18 * q^11 + 108 * q^12 - 9 * q^13 - 3 * q^14 - 12 * q^17 - 30 * q^19 - 60 * q^20 - 9 * q^21 + 18 * q^23 + 9 * q^24 + 6 * q^25 + 12 * q^26 - 45 * q^27 - 45 * q^28 - 18 * q^29 - 12 * q^30 - 18 * q^31 - 21 * q^32 - 12 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 + 39 * q^38 - 12 * q^39 + 18 * q^40 + 27 * q^41 - 3 * q^42 - 39 * q^43 - 78 * q^44 + 3 * q^45 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 9 * q^50 + 6 * q^51 - 48 * q^52 + 27 * q^53 - 42 * q^55 + 39 * q^56 - 6 * q^57 - 18 * q^58 - 60 * q^59 - 18 * q^60 - 12 * q^61 + 93 * q^62 - 12 * q^63 - 108 * q^64 - 33 * q^65 - 42 * q^67 + 18 * q^68 - 12 * q^69 + 6 * q^70 - 18 * q^71 + 9 * q^72 + 51 * q^73 + 114 * q^74 - 72 * q^75 + 24 * q^76 - 39 * q^77 + 9 * q^78 + 87 * q^79 + 42 * q^80 + 12 * q^82 + 24 * q^83 + 3 * q^84 + 36 * q^85 - 69 * q^86 - 36 * q^88 - 48 * q^89 + 3 * q^90 + 6 * q^91 - 18 * q^92 - 21 * q^93 - 54 * q^94 + 36 * q^95 + 21 * q^97 - 75 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.162768	−	0.923101i	0.115094	−	0.652731i	−0.871610	−	0.490201i	$-0.836923\pi$
$2$	0.162768	−	0.923101i	0.115094	−	0.652731i	0.986704	−	0.162530i	$-0.0519654\pi$
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i
$4$	1.05376	+	0.383539i	0.526882	+	0.191769i
$5$	0.955023	−	0.347600i	0.427099	−	0.155451i	−0.119522	−	0.992832i	$-0.538136\pi$
$5$	0.955023	−	0.347600i	0.427099	−	0.155451i	0.546621	+	0.837380i	$0.315914\pi$
$6$	0.162768	+	0.923101i	0.0664496	+	0.376854i
$7$	1.03944	+	2.43301i	0.392872	+	0.919593i
$7$	1.03944	+	2.43301i	0.392872	+	0.919593i
$8$	1.46290	−	2.53382i	0.517215	−	0.895842i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−0.165423	−	0.938160i	−0.0523113	−	0.296672i
$11$	−2.35664			−0.710554			−0.355277	−	0.934761i	$-0.615614\pi$
$11$	−2.35664			−0.710554			−0.355277	+	0.934761i	$0.615614\pi$
$12$	−1.12139			−0.323718
$13$	0.223172	+	1.26567i	0.0618967	+	0.351034i	0.999989	+	0.00464888i	$0.00147979\pi$
$13$	0.223172	+	1.26567i	0.0618967	+	0.351034i	−0.938092	+	0.346385i	$0.887409\pi$
$14$	2.41510	−	0.563494i	0.645464	−	0.150600i
$15$	−0.778542	+	0.653274i	−0.201019	+	0.168675i
$16$	−0.382790	−	0.321199i	−0.0956974	−	0.0802997i
$17$	4.96569	+	4.16671i	1.20436	+	1.01058i	0.999495	+	0.0317855i	$0.0101193\pi$
$17$	4.96569	+	4.16671i	1.20436	+	1.01058i	0.204863	+	0.978791i	$0.434325\pi$
$18$	−0.468670	−	0.811761i	−0.110467	−	0.191334i
$19$	3.60993	+	2.44303i	0.828175	+	0.560470i
$19$	3.60993	+	2.44303i	0.828175	+	0.560470i
$20$	1.13969			0.254842
$21$	−1.80890	−	1.93078i	−0.394734	−	0.421330i
$22$	−0.383585	+	2.17542i	−0.0817806	+	0.463801i
$23$	−1.42427	−	8.07745i	−0.296981	−	1.68427i	−0.659039	−	0.752109i	$-0.729037\pi$
$23$	−1.42427	−	8.07745i	−0.296981	−	1.68427i	0.362057	−	0.932156i	$-0.382074\pi$
$24$	−0.508061	+	2.88136i	−0.103708	+	0.588155i
$25$	−3.03898	+	2.55001i	−0.607796	+	0.510001i
$26$	1.20467			0.236255
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	0.162172	+	2.96249i	0.0306476	+	0.559858i
$29$	1.04660	+	0.380930i	0.194348	+	0.0707369i	0.437361	−	0.899286i	$-0.355913\pi$
$29$	1.04660	+	0.380930i	0.194348	+	0.0707369i	−0.243012	+	0.970023i	$0.578136\pi$
$30$	0.476316	+	0.825004i	0.0869631	+	0.150624i
$31$	5.11980	−	8.86776i	0.919543	−	1.59270i	0.119434	−	0.992842i	$-0.461892\pi$
$31$	5.11980	−	8.86776i	0.919543	−	1.59270i	0.800110	−	0.599854i	$-0.204775\pi$
$32$	4.12379	−	3.46027i	0.728991	−	0.611696i
$33$	2.21452	−	0.806019i	0.385498	−	0.140310i
$34$	4.65455	−	3.90563i	0.798249	−	0.669810i
$35$	1.83841	+	1.96227i	0.310747	+	0.331685i
$36$	1.05376	−	0.383539i	0.175627	−	0.0639231i
$37$	−0.800106	+	1.38583i	−0.131537	+	0.227828i	−0.924269	−	0.381742i	$-0.875324\pi$
$37$	−0.800106	+	1.38583i	−0.131537	+	0.227828i	0.792732	+	0.609570i	$0.208658\pi$
$38$	2.84274	−	2.93468i	0.461154	−	0.476068i
$39$	−0.642598	−	1.11301i	−0.102898	−	0.178225i
$40$	0.516350	−	2.92837i	0.0816421	−	0.463015i
$41$	0.504190	−	2.85941i	0.0787413	−	0.446564i	−0.919791	−	0.392408i	$-0.871642\pi$
$41$	0.504190	−	2.85941i	0.0787413	−	0.446564i	0.998532	−	0.0541560i	$-0.0172468\pi$
$42$	−2.07673	+	1.35553i	−0.320446	+	0.209162i
$43$	−6.53730	−	5.48544i	−0.996929	−	0.836522i	−0.0103726	−	0.999946i	$-0.503302\pi$
$43$	−6.53730	−	5.48544i	−0.996929	−	0.836522i	−0.986556	+	0.163424i	$0.947746\pi$
$44$	−2.48334	−	0.903863i	−0.374378	−	0.136263i
$45$	0.508157	−	0.880154i	0.0757516	−	0.131206i
$46$	−7.68813			−1.13355
$47$	−5.80832	+	4.87376i	−0.847231	+	0.710911i	−0.959178	−	0.282803i	$-0.908736\pi$
$47$	−5.80832	+	4.87376i	−0.847231	+	0.710911i	0.111947	+	0.993714i	$0.464291\pi$
$48$	0.469561	+	0.170906i	0.0677753	+	0.0246682i
$49$	−4.83912	+	5.05796i	−0.691303	+	0.722565i
$50$	1.85927	+	3.22034i	0.262940	+	0.455425i
$51$	−6.09133	−	2.21706i	−0.852956	−	0.310451i
$52$	−0.250263	+	1.41931i	−0.0347052	+	0.196823i
$53$	7.59535	+	2.76448i	1.04330	+	0.379731i	0.806131	−	0.591737i	$-0.201558\pi$
$53$	7.59535	+	2.76448i	1.04330	+	0.379731i	0.237170	+	0.971468i	$0.423780\pi$
$54$	0.718045	+	0.602511i	0.0977135	+	0.0819914i
$55$	−2.25065	+	0.819168i	−0.303477	+	0.110457i
$56$	7.68544	+	0.925503i	1.02701	+	0.123675i
$57$	−4.22779	−	1.06103i	−0.559985	−	0.140537i
$58$	0.521989	−	0.904111i	0.0685405	−	0.118716i
$59$	−4.97391	−	4.17361i	−0.647548	−	0.543357i	0.258778	−	0.965937i	$-0.416680\pi$
$59$	−4.97391	−	4.17361i	−0.647548	−	0.543357i	−0.906326	+	0.422579i	$0.861125\pi$
$60$	−1.07095	+	0.389796i	−0.138260	+	0.0503224i
$61$	2.19419	+	12.4439i	0.280938	+	1.59328i	0.719446	+	0.694549i	$0.244396\pi$
$61$	2.19419	+	12.4439i	0.280938	+	1.59328i	−0.438508	+	0.898727i	$0.644493\pi$
$62$	−7.35249	−	6.16948i	−0.933768	−	0.783524i
$63$	2.36017	+	1.19566i	0.297354	+	0.150639i
$64$	−3.02266	−	5.23540i	−0.377832	−	0.654425i
$65$	0.653081	+	1.13117i	0.0810047	+	0.140304i
$66$	−0.383585	−	2.17542i	−0.0472160	−	0.267775i
$67$	0.938720	+	5.32375i	0.114683	+	0.650399i	0.986907	+	0.161292i	$0.0515662\pi$
$67$	0.938720	+	5.32375i	0.114683	+	0.650399i	−0.872224	+	0.489107i	$0.837323\pi$
$68$	3.63457	+	6.29527i	0.440757	+	0.763413i
$69$	4.10103	+	7.10319i	0.493706	+	0.855124i
$70$	2.11061	−	1.37764i	0.252266	−	0.164659i
$71$	−10.4644	−	8.78070i	−1.24190	−	1.04208i	−0.997373	−	0.0724355i	$-0.976923\pi$
$71$	−10.4644	−	8.78070i	−1.24190	−	1.04208i	−0.244527	−	0.969642i	$-0.578633\pi$
$72$	−0.508061	−	2.88136i	−0.0598756	−	0.339571i
$73$	−8.96582	+	3.26329i	−1.04937	+	0.381939i	−0.808425	−	0.588599i	$-0.799680\pi$
$73$	−8.96582	+	3.26329i	−1.04937	+	0.381939i	−0.240945	+	0.970539i	$0.577457\pi$
$74$	1.14902	+	0.964146i	0.133571	+	0.112080i
$75$	1.98355	−	3.43561i	0.229041	−	0.396711i
$76$	2.86702	+	3.95893i	0.328869	+	0.454120i
$77$	−2.44959	−	5.73375i	−0.279157	−	0.653421i
$78$	−1.13202	+	0.412020i	−0.128176	+	0.0466521i
$79$	−5.03752	−	4.22698i	−0.566765	−	0.475572i	0.313806	−	0.949487i	$-0.398396\pi$
$79$	−5.03752	−	4.22698i	−0.566765	−	0.475572i	−0.880571	+	0.473915i	$0.842840\pi$
$80$	−0.477222	−	0.173694i	−0.0533550	−	0.0194196i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	−2.55745	−	0.930837i	−0.282424	−	0.102794i
$83$	3.89275	+	6.74244i	0.427285	+	0.740079i	0.996631	−	0.0820191i	$-0.0261369\pi$
$83$	3.89275	+	6.74244i	0.427285	+	0.740079i	−0.569346	+	0.822098i	$0.692804\pi$
$84$	−1.16562	−	2.72836i	−0.127180	−	0.297689i
$85$	6.19070	+	2.25323i	0.671476	+	0.244397i
$86$	−6.12768	+	5.14173i	−0.660764	+	0.554447i
$87$	−1.11376			−0.119408
$88$	−3.44754	+	5.97132i	−0.367509	+	0.636545i
$89$	−13.1896	−	4.80064i	−1.39810	−	0.508866i	−0.470485	−	0.882408i	$-0.655921\pi$
$89$	−13.1896	−	4.80064i	−1.39810	−	0.508866i	−0.927613	+	0.373542i	$0.878143\pi$
$90$	−0.729759	−	0.612340i	−0.0769233	−	0.0645464i
$91$	−2.84742	+	1.85857i	−0.298491	+	0.194831i
$92$	1.59717	−	9.05799i	0.166516	−	0.944361i
$93$	−1.77809	+	10.0840i	−0.184379	+	1.04567i
$94$	3.55356	+	6.15495i	0.366522	+	0.634835i
$95$	4.29676	+	1.07834i	0.440839	+	0.110635i
$96$	−2.69162	+	4.66201i	−0.274712	+	0.475815i
$97$	−2.21143	+	0.804893i	−0.224536	+	0.0817245i	−0.451839	−	0.892100i	$-0.649232\pi$
$97$	−2.21143	+	0.804893i	−0.224536	+	0.0817245i	0.227302	+	0.973824i	$0.427009\pi$
$98$	3.88135	+	5.29027i	0.392076	+	0.534397i
$99$	−1.80529	+	1.51482i	−0.181439	+	0.152245i
$100$	−4.18039	+	1.52154i	−0.418039	+	0.152154i
$101$	4.87840	−	4.09346i	0.485419	−	0.407315i	−0.366962	−	0.930236i	$-0.619602\pi$
$101$	4.87840	−	4.09346i	0.485419	−	0.407315i	0.852381	+	0.522921i	$0.175158\pi$
$102$	−3.03804	+	5.26204i	−0.300811	+	0.521020i
$103$	−5.66249	−	9.80771i	−0.557941	−	0.966383i	−0.997668	−	0.0682511i	$-0.978258\pi$
$103$	−5.66249	−	9.80771i	−0.557941	−	0.966383i	0.439727	−	0.898132i	$-0.355075\pi$
$104$	3.53347	+	1.28608i	0.346485	+	0.126110i
$105$	−2.39867	−	1.21516i	−0.234087	−	0.118588i
$106$	3.78817	−	6.56130i	0.367940	−	0.637290i
$107$	−1.40400			−0.135729			−0.0678647	−	0.997695i	$-0.521619\pi$
$107$	−1.40400			−0.135729			−0.0678647	+	0.997695i	$0.521619\pi$
$108$	−0.859036	+	0.720817i	−0.0826608	+	0.0693606i
$109$	2.60310	−	14.7629i	0.249332	−	1.41403i	−0.560881	−	0.827896i	$-0.689537\pi$
$109$	2.60310	−	14.7629i	0.249332	−	1.41403i	0.810213	−	0.586136i	$-0.199351\pi$
$110$	0.389843	+	2.21091i	0.0371700	+	0.210802i
$111$	0.277874	−	1.57590i	0.0263746	−	0.149578i
$112$	0.383593	−	1.26520i	0.0362462	−	0.119550i
$113$	−5.07516			−0.477431			−0.238716	−	0.971090i	$-0.576726\pi$
$113$	−5.07516			−0.477431			−0.238716	+	0.971090i	$0.576726\pi$
$114$	−1.66758	+	3.72998i	−0.156184	+	0.349344i
$115$	−4.16793	−	7.21907i	−0.388662	−	0.673182i
$116$	0.956764	+	0.802820i	0.0888333	+	0.0745400i
$117$	0.984517	+	0.826108i	0.0910186	+	0.0763737i
$118$	−4.66225	+	3.91209i	−0.429195	+	0.360137i
$119$	−4.97612	+	16.4127i	−0.456160	+	1.50455i
$120$	0.516350	+	2.92837i	0.0471361	+	0.267322i
$121$	−5.44624			−0.495112
$122$	11.8441			1.07231
$123$	0.504190	+	2.85941i	0.0454613	+	0.257824i
$124$	8.79619	−	7.38088i	0.789921	−	0.662822i
$125$	−4.55670	+	7.89243i	−0.407563	+	0.705920i
$126$	1.48787	−	1.98406i	0.132550	−	0.176754i
$127$	2.74060	+	15.5427i	0.243189	+	1.37919i	0.824662	+	0.565626i	$0.191366\pi$
$127$	2.74060	+	15.5427i	0.243189	+	1.37919i	−0.581473	+	0.813566i	$0.697523\pi$
$128$	4.79238	−	1.74428i	0.423590	−	0.154174i
$129$	8.01918	+	2.91874i	0.706050	+	0.256981i
$130$	1.15048	−	0.418742i	0.100904	−	0.0367261i
$131$	−0.326701	+	1.85281i	−0.0285440	+	0.161881i	−0.995748	−	0.0921202i	$-0.970636\pi$
$131$	−0.326701	+	1.85281i	−0.0285440	+	0.161881i	0.967204	+	0.254001i	$0.0817467\pi$
$132$	2.64272			0.230019
$133$	−2.19162	+	11.3224i	−0.190037	+	0.981777i
$134$	5.06715			0.437735
$135$	−0.176481	+	1.00087i	−0.0151891	+	0.0861415i
$136$	17.8221	−	6.48670i	1.52823	−	0.556230i
$137$	3.45262	+	1.25665i	0.294977	+	0.107363i	0.485270	−	0.874365i	$-0.338721\pi$
$137$	3.45262	+	1.25665i	0.294977	+	0.107363i	−0.190293	+	0.981727i	$0.560944\pi$
$138$	7.22448	−	2.62949i	0.614988	−	0.223837i
$139$	0.722647	+	4.09833i	0.0612941	+	0.347616i	0.999996	+	0.00288574i	$0.000918560\pi$
$139$	0.722647	+	4.09833i	0.0612941	+	0.347616i	−0.938702	+	0.344730i	$0.887970\pi$
$140$	1.18464	+	2.77287i	0.100120	+	0.234351i
$141$	3.79111	−	6.56640i	0.319269	−	0.552990i
$142$	−9.80875	+	8.23051i	−0.823132	+	0.690689i
$143$	−0.525936	−	2.98273i	−0.0439810	−	0.249429i
$144$	−0.499697			−0.0416414
$145$	1.13193			0.0940020
$146$	1.55300	+	8.80751i	0.128527	+	0.728915i
$147$	2.81736	−	6.40800i	0.232372	−	0.528523i
$148$	−1.37464	+	1.15346i	−0.112995	+	0.0948139i
$149$	−14.3480	−	12.0394i	−1.17544	−	0.986308i	−0.999998	−	0.00181769i	$-0.999421\pi$
$149$	−14.3480	−	12.0394i	−1.17544	−	0.986308i	−0.175438	−	0.984490i	$-0.556134\pi$
$150$	−2.84856	−	2.39023i	−0.232584	−	0.195161i
$151$	−2.83930	−	4.91781i	−0.231059	−	0.400206i	0.727061	−	0.686573i	$-0.240886\pi$
$151$	−2.83930	−	4.91781i	−0.231059	−	0.400206i	−0.958120	+	0.286367i	$0.907552\pi$
$152$	11.4712	−	5.57301i	0.930437	−	0.452031i
$153$	6.48225			0.524059
$154$	−5.69154	+	1.32795i	−0.458637	+	0.107010i
$155$	1.80710	−	10.2485i	0.145149	−	0.823183i
$156$	−0.250263	−	1.41931i	−0.0200371	−	0.113636i
$157$	3.17291	−	17.9944i	0.253226	−	1.43611i	−0.547361	−	0.836896i	$-0.684368\pi$
$157$	3.17291	−	17.9944i	0.253226	−	1.43611i	0.800587	−	0.599217i	$-0.204521\pi$
$158$	−4.72187	+	3.96212i	−0.375652	+	0.315210i
$159$	−8.08280			−0.641008
$160$	2.73553	−	4.73807i	0.216262	−	0.374577i
$161$	18.1721	−	11.8613i	1.43216	−	0.934803i
$162$	−0.880812	−	0.320590i	−0.0692032	−	0.0251879i
$163$	4.68558	+	8.11566i	0.367003	+	0.635668i	0.989095	−	0.147276i	$-0.0470506\pi$
$163$	4.68558	+	8.11566i	0.367003	+	0.635668i	−0.622093	+	0.782944i	$0.713717\pi$
$164$	1.62799	−	2.81976i	0.127125	−	0.220186i
$165$	1.83474	−	1.53953i	0.142835	−	0.119852i
$166$	6.85756	−	2.49595i	0.532250	−	0.193723i
$167$	−13.5321	+	11.3547i	−1.04714	+	0.878656i	−0.992790	−	0.119866i	$-0.961754\pi$
$167$	−13.5321	+	11.3547i	−1.04714	+	0.878656i	−0.0543516	+	0.998522i	$0.517309\pi$
$168$	−7.53849	+	1.75889i	−0.581607	+	0.135701i
$169$	10.6639	−	3.88134i	0.820299	−	0.298564i
$170$	3.08760	−	5.34789i	0.236808	−	0.410164i
$171$	4.33572	−	0.448948i	0.331561	−	0.0343319i
$172$	−4.78489	−	8.28767i	−0.364844	−	0.631929i
$173$	−0.819459	+	4.64738i	−0.0623023	+	0.353334i	0.937681	+	0.347498i	$0.112969\pi$
$173$	−0.819459	+	4.64738i	−0.0623023	+	0.353334i	−0.999983	+	0.00583580i	$0.998142\pi$
$174$	−0.181285	+	1.02812i	−0.0137432	+	0.0779413i
$175$	−9.36305	−	4.74330i	−0.707780	−	0.358560i
$176$	0.902099	+	0.756951i	0.0679982	+	0.0570573i
$177$	6.10141	+	2.22073i	0.458610	+	0.166920i
$178$	−6.57831	+	11.3940i	−0.493066	+	0.854015i
$179$	−6.47395			−0.483886			−0.241943	−	0.970290i	$-0.577785\pi$
$179$	−6.47395			−0.483886			−0.241943	+	0.970290i	$0.577785\pi$
$180$	0.873050	−	0.732576i	0.0650733	−	0.0546030i
$181$	5.52708	+	2.01169i	0.410825	+	0.149528i	0.539161	−	0.842203i	$-0.318741\pi$
$181$	5.52708	+	2.01169i	0.410825	+	0.149528i	−0.128336	+	0.991731i	$0.540964\pi$
$182$	1.25218	+	2.93097i	0.0928179	+	0.217258i
$183$	−6.31792	−	10.9430i	−0.467034	−	0.808927i
$184$	−22.5504	−	8.20768i	−1.66244	−	0.605078i
$185$	−0.282407	+	1.60161i	−0.0207630	+	0.117753i
$186$	9.01917	+	3.28271i	0.661318	+	0.240700i
$187$	−11.7024	−	9.81945i	−0.855762	−	0.718069i
$188$	−7.98987	+	2.90808i	−0.582721	+	0.212093i
$189$	−2.62677	−	0.316324i	−0.191070	−	0.0230092i
$190$	1.69479	−	3.79083i	0.122953	−	0.275015i
$191$	13.5366	−	23.4460i	0.979472	−	1.69650i	0.315163	−	0.949037i	$-0.397941\pi$
$191$	13.5366	−	23.4460i	0.979472	−	1.69650i	0.664309	−	0.747458i	$-0.268726\pi$
$192$	4.63098	+	3.88585i	0.334212	+	0.280437i
$193$	7.27199	−	2.64679i	0.523450	−	0.190520i	−0.0667616	−	0.997769i	$-0.521267\pi$
$193$	7.27199	−	2.64679i	0.523450	−	0.190520i	0.590211	+	0.807249i	$0.299044\pi$
$194$	0.383049	+	2.17238i	0.0275013	+	0.155968i
$195$	−1.00058	−	0.839585i	−0.0716529	−	0.0601239i
$196$	−7.03921	+	3.47390i	−0.502801	+	0.248136i
$197$	6.66712	+	11.5478i	0.475013	+	0.822747i	0.999590	−	0.0286161i	$-0.00911003\pi$
$197$	6.66712	+	11.5478i	0.475013	+	0.822747i	−0.524577	+	0.851363i	$0.675777\pi$
$198$	1.10449	+	1.91303i	0.0784926	+	0.135953i
$199$	−0.805391	−	4.56760i	−0.0570927	−	0.323789i	0.942863	−	0.333180i	$-0.108122\pi$
$199$	−0.805391	−	4.56760i	−0.0570927	−	0.323789i	−0.999956	+	0.00939145i	$0.997011\pi$
$200$	2.01553	+	11.4307i	0.142520	+	0.808269i
$201$	−2.70294	−	4.68163i	−0.190651	−	0.330216i
$202$	−2.98463	−	5.16954i	−0.209998	−	0.363727i
$203$	0.161069	+	2.94234i	0.0113048	+	0.206512i
$204$	−5.56849	−	4.67252i	−0.389872	−	0.327142i
$205$	−0.512416	−	2.90605i	−0.0357887	−	0.202968i
$206$	−9.97518	+	3.63067i	−0.695003	+	0.252961i
$207$	−6.28314	−	5.27218i	−0.436709	−	0.366442i
$208$	0.321104	−	0.556168i	0.0222646	−	0.0385633i
$209$	−8.50732	−	5.75735i	−0.588463	−	0.398244i
$210$	−1.51214	+	2.01643i	−0.104348	+	0.139147i
$211$	24.5738	−	8.94413i	1.69173	−	0.615739i	0.696888	−	0.717180i	$-0.254568\pi$
$211$	24.5738	−	8.94413i	1.69173	−	0.615739i	0.994842	+	0.101441i	$0.0323454\pi$
$212$	6.94342	+	5.82622i	0.476876	+	0.400146i
$213$	12.8365	+	4.67212i	0.879545	+	0.320128i
$214$	−0.228525	+	1.29603i	−0.0156217	+	0.0885948i
$215$	−8.15001	−	2.96636i	−0.555826	−	0.202304i
$216$	1.46290	+	2.53382i	0.0995380	+	0.172405i
$217$	26.8971	+	3.23903i	1.82590	+	0.219880i
$218$	−13.2040	−	4.80585i	−0.894286	−	0.325493i
$219$	7.30900	−	6.13298i	0.493897	−	0.414428i
$220$	−2.68583			−0.181079
$221$	−4.16548	+	7.21483i	−0.280201	+	0.485322i
$222$	−1.40949	−	0.513011i	−0.0945986	−	0.0344311i
$223$	16.1439	+	13.5463i	1.08107	+	0.907129i	0.996010	−	0.0892461i	$-0.0284458\pi$
$223$	16.1439	+	13.5463i	1.08107	+	0.907129i	0.0850650	+	0.996375i	$0.472890\pi$
$224$	12.7053	+	6.43650i	0.848911	+	0.430056i
$225$	−0.688881	+	3.90684i	−0.0459254	+	0.260456i
$226$	−0.826072	+	4.68489i	−0.0549495	+	0.311634i
$227$	−3.33026	−	5.76818i	−0.221037	−	0.382848i	0.734086	−	0.679057i	$-0.237611\pi$
$227$	−3.33026	−	5.76818i	−0.221037	−	0.382848i	−0.955123	+	0.296209i	$0.904278\pi$
$228$	−4.04815	−	2.73960i	−0.268095	−	0.181434i
$229$	8.37594	−	14.5075i	0.553497	−	0.958686i	−0.444521	−	0.895768i	$-0.646626\pi$
$229$	8.37594	−	14.5075i	0.553497	−	0.958686i	0.998019	−	0.0629174i	$-0.0200405\pi$
$230$	−7.34233	+	2.67239i	−0.484139	+	0.176212i
$231$	4.26292	+	4.55015i	0.280480	+	0.299378i
$232$	2.49628	−	2.09463i	0.163889	−	0.137519i
$233$	3.32231	−	1.20922i	0.217652	−	0.0792187i	−0.230893	−	0.972979i	$-0.574165\pi$
$233$	3.32231	−	1.20922i	0.217652	−	0.0792187i	0.448545	+	0.893760i	$0.351943\pi$
$234$	0.922828	−	0.774345i	0.0603272	−	0.0506205i
$235$	−3.85296	+	6.67352i	−0.251339	+	0.435333i
$236$	−3.64059	−	6.30568i	−0.236982	−	0.410465i
$237$	6.17943	+	2.24913i	0.401397	+	0.146097i
$238$	14.3406	+	7.26491i	0.929562	+	0.470914i
$239$	−8.73672	+	15.1324i	−0.565132	+	0.978837i	0.431906	+	0.901919i	$0.357841\pi$
$239$	−8.73672	+	15.1324i	−0.565132	+	0.978837i	−0.997037	+	0.0769179i	$0.975492\pi$
$240$	0.507849			0.0327815
$241$	15.7874	−	13.2472i	1.01695	−	0.853326i	0.0277128	−	0.999616i	$-0.491178\pi$
$241$	15.7874	−	13.2472i	1.01695	−	0.853326i	0.989242	+	0.146290i	$0.0467332\pi$
$242$	−0.886471	+	5.02742i	−0.0569845	+	0.323175i
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$	−2.46055	+	13.9545i	−0.157521	+	0.893343i
$245$	−2.86332	+	6.51254i	−0.182931	+	0.416071i
$246$	2.72159			0.173522
$247$	−2.28644	+	5.11420i	−0.145483	+	0.325409i
$248$	−14.9796	−	25.9454i	−0.951203	−	1.64753i
$249$	−5.96404	−	5.00442i	−0.377956	−	0.317142i
$250$	6.54383	+	5.49092i	0.413868	+	0.347276i
$251$	12.4388	−	10.4374i	0.785131	−	0.658804i	−0.159404	−	0.987213i	$-0.550957\pi$
$251$	12.4388	−	10.4374i	0.785131	−	0.658804i	0.944535	+	0.328410i	$0.106513\pi$
$252$	2.02848	+	2.16516i	0.127782	+	0.136392i
$253$	3.35650	+	19.0357i	0.211021	+	1.19676i
$254$	14.7936			0.928231
$255$	−6.58800			−0.412557
$256$	−2.92962	−	16.6147i	−0.183101	−	1.03842i
$257$	−16.9369	+	14.2117i	−1.05649	+	0.886503i	−0.993761	−	0.111527i	$-0.964426\pi$
$257$	−16.9369	+	14.2117i	−1.05649	+	0.886503i	−0.0627323	+	0.998030i	$0.519981\pi$
$258$	3.99956	−	6.92744i	0.249002	−	0.431283i
$259$	−4.20340	−	0.506185i	−0.261186	−	0.0314528i
$260$	0.254346	+	1.44247i	0.0157739	+	0.0894580i
$261$	1.04660	−	0.380930i	0.0647827	−	0.0235790i
$262$	1.65716	+	0.603155i	0.102379	+	0.0372631i
$263$	−23.7473	+	8.64332i	−1.46432	+	0.532970i	−0.946552	−	0.322550i	$-0.895460\pi$
$263$	−23.7473	+	8.64332i	−1.46432	+	0.532970i	−0.517770	+	0.855520i	$0.673238\pi$
$264$	1.19732	−	6.79033i	0.0736899	−	0.417916i
$265$	8.21466			0.504623
$266$	10.0950	+	3.86600i	0.618964	+	0.237040i
$267$	14.0361			0.858996
$268$	−1.05267	+	5.97001i	−0.0643023	+	0.364676i
$269$	−4.55755	+	1.65881i	−0.277879	+	0.101140i	−0.477200	−	0.878795i	$-0.658348\pi$
$269$	−4.55755	+	1.65881i	−0.277879	+	0.101140i	0.199322	+	0.979934i	$0.436126\pi$
$270$	0.895182	+	0.325820i	0.0544790	+	0.0198287i
$271$	−19.8564	+	7.22715i	−1.20619	+	0.439018i	−0.865381	−	0.501114i	$-0.832924\pi$
$271$	−19.8564	+	7.22715i	−1.20619	+	0.439018i	−0.340811	+	0.940132i	$0.610702\pi$
$272$	−0.562474	−	3.18995i	−0.0341050	−	0.193419i
$273$	2.04003	−	2.72036i	0.123468	−	0.164644i
$274$	1.72199	−	2.98257i	0.104029	−	0.180184i
$275$	7.16179	−	6.00945i	0.431872	−	0.362384i
$276$	1.59717	+	9.05799i	0.0961382	+	0.545227i
$277$	21.5534			1.29502			0.647509	−	0.762058i	$-0.275811\pi$
$277$	21.5534			1.29502			0.647509	+	0.762058i	$0.275811\pi$
$278$	3.90080			0.233954
$279$	−1.77809	−	10.0840i	−0.106451	−	0.603716i
$280$	7.66147	−	1.78758i	0.457860	−	0.106828i
$281$	−0.168253	+	0.141181i	−0.0100371	+	0.00842214i	−0.647792	−	0.761817i	$-0.724308\pi$
$281$	−0.168253	+	0.141181i	−0.0100371	+	0.00842214i	0.637755	+	0.770239i	$0.279863\pi$
$282$	−5.44438	−	4.56837i	−0.324208	−	0.272043i
$283$	11.8443	+	9.93852i	0.704068	+	0.590784i	0.922928	−	0.384973i	$-0.125789\pi$
$283$	11.8443	+	9.93852i	0.704068	+	0.590784i	−0.218859	+	0.975756i	$0.570234\pi$
$284$	−7.65930	−	13.2663i	−0.454496	−	0.787210i
$285$	−4.40645	+	0.456272i	−0.261016	+	0.0270272i
$286$	−2.83897			−0.167872
$287$	7.48105	−	1.74549i	0.441593	−	0.103033i
$288$	0.934788	−	5.30145i	0.0550829	−	0.312391i
$289$	4.34461	+	24.6395i	0.255565	+	1.44938i
$290$	0.184242	−	1.04489i	0.0108191	−	0.0613580i
$291$	1.80277	−	1.51270i	0.105680	−	0.0886763i
$292$	−10.6995			−0.626138
$293$	−4.84932	+	8.39928i	−0.283301	+	0.490691i	−0.972196	−	0.234170i	$-0.924763\pi$
$293$	−4.84932	+	8.39928i	−0.283301	+	0.490691i	0.688895	+	0.724861i	$0.258096\pi$
$294$	−5.45665	−	3.64372i	−0.318239	−	0.212506i
$295$	−6.20094	−	2.25696i	−0.361033	−	0.131405i
$296$	2.34096	+	4.05466i	0.136065	+	0.235672i
$297$	1.17832	−	2.04091i	0.0683731	−	0.118426i
$298$	−13.4490	+	11.2850i	−0.779079	+	0.653725i
$299$	9.90553	−	3.60532i	0.572852	−	0.208501i
$300$	3.40789	−	2.85956i	0.196754	−	0.165097i
$301$	6.55102	−	21.6071i	0.377595	−	1.24541i
$302$	−5.00178	+	1.82050i	−0.287820	+	0.104758i
$303$	−3.18415	+	5.51511i	−0.182925	+	0.316835i
$304$	−0.597146	−	2.09467i	−0.0342487	−	0.120138i
$305$	6.42099	+	11.1215i	0.367665	+	0.636815i
$306$	1.05510	−	5.98377i	0.0603161	−	0.342070i
$307$	0.885934	−	5.02438i	0.0505630	−	0.286757i	−0.949033	−	0.315176i	$-0.897936\pi$
$307$	0.885934	−	5.02438i	0.0505630	−	0.286757i	0.999596	+	0.0284196i	$0.00904745\pi$
$308$	−0.382181	−	6.98153i	−0.0217768	−	0.397809i
$309$	8.67543	+	7.27955i	0.493528	+	0.414119i
$310$	−9.16631	−	3.33626i	−0.520611	−	0.189487i
$311$	−2.99979	+	5.19580i	−0.170103	+	0.294627i	−0.938456	−	0.345400i	$-0.887743\pi$
$311$	−2.99979	+	5.19580i	−0.170103	+	0.294627i	0.768353	+	0.640026i	$0.221077\pi$
$312$	−3.76024			−0.212881
$313$	19.0529	−	15.9873i	1.07693	−	0.903653i	0.0812698	−	0.996692i	$-0.474102\pi$
$313$	19.0529	−	15.9873i	1.07693	−	0.903653i	0.995662	+	0.0930387i	$0.0296580\pi$
$314$	−16.0942	−	5.85782i	−0.908251	−	0.330576i
$315$	2.66963	+	0.321484i	0.150416	+	0.0181136i
$316$	−3.68714	−	6.38632i	−0.207418	−	0.359259i
$317$	4.41409	+	1.60660i	0.247920	+	0.0902356i	0.462991	−	0.886363i	$-0.346776\pi$
$317$	4.41409	+	1.60660i	0.247920	+	0.0902356i	−0.215071	+	0.976598i	$0.568998\pi$
$318$	−1.31562	+	7.46124i	−0.0737762	+	0.418405i
$319$	−2.46645	−	0.897716i	−0.138095	−	0.0502624i
$320$	−4.70653	−	3.94925i	−0.263103	−	0.220770i
$321$	1.31933	−	0.480195i	0.0736375	−	0.0268019i
$322$	−7.99136	−	18.7053i	−0.445341	−	1.04241i
$323$	7.74640	+	27.1729i	0.431021	+	1.51194i
$324$	0.560696	−	0.971154i	0.0311498	−	0.0539530i
$325$	−3.90568	−	3.27726i	−0.216648	−	0.181790i
$326$	8.25423	−	3.00429i	0.457160	−	0.166392i
$327$	2.60310	+	14.7629i	0.143952	+	0.816392i
$328$	−6.50765	−	5.46057i	−0.359325	−	0.301509i
$329$	−17.8953	−	9.06573i	−0.986602	−	0.499810i
$330$	−1.12251	−	1.94424i	−0.0617920	−	0.107027i
$331$	8.69585	+	15.0617i	0.477967	+	0.827863i	0.999681	−	0.0252571i	$-0.00804045\pi$
$331$	8.69585	+	15.0617i	0.477967	+	0.827863i	−0.521714	+	0.853121i	$0.674707\pi$
$332$	1.51605	+	8.59796i	0.0832042	+	0.471874i
$333$	0.277874	+	1.57590i	0.0152274	+	0.0863589i
$334$	8.27899	+	14.3396i	0.453006	+	0.784630i
$335$	2.74703	+	4.75800i	0.150086	+	0.259957i
$336$	0.0722643	+	1.32010i	0.00394234	+	0.0720172i
$337$	−11.0616	−	9.28181i	−0.602566	−	0.505613i	0.289704	−	0.957116i	$-0.406443\pi$
$337$	−11.0616	−	9.28181i	−0.602566	−	0.505613i	−0.892269	+	0.451504i	$0.850888\pi$
$338$	−1.84713	−	10.4756i	−0.100471	−	0.569797i
$339$	4.76909	−	1.73581i	0.259022	−	0.0942762i
$340$	5.65933	+	4.74874i	0.306920	+	0.257537i
$341$	−12.0655	+	20.8981i	−0.653386	+	1.13170i
$342$	0.291290	−	4.07538i	0.0157511	−	0.220371i
$343$	−17.3361	−	6.51619i	−0.936060	−	0.351841i
$344$	−23.4626	+	8.53969i	−1.26502	+	0.460429i
$345$	6.38564	+	5.35819i	0.343792	+	0.288475i
$346$	4.15662	+	1.51289i	0.223461	+	0.0813333i
$347$	−0.458275	+	2.59900i	−0.0246015	+	0.139522i	−0.994635	−	0.103451i	$-0.967012\pi$
$347$	−0.458275	+	2.59900i	−0.0246015	+	0.139522i	0.970033	+	0.242973i	$0.0781226\pi$
$348$	−1.17364	−	0.427172i	−0.0629140	−	0.0228988i
$349$	1.65085	+	2.85936i	0.0883679	+	0.153058i	0.906821	−	0.421515i	$-0.138502\pi$
$349$	1.65085	+	2.85936i	0.0883679	+	0.153058i	−0.818453	+	0.574573i	$0.805168\pi$
$350$	−5.90254	+	7.87098i	−0.315504	+	0.420722i
$351$	−1.20769	−	0.439563i	−0.0644617	−	0.0234621i
$352$	−9.71831	+	8.15463i	−0.517988	+	0.434643i
$353$	5.91878			0.315025			0.157512	−	0.987517i	$-0.449653\pi$
$353$	5.91878			0.315025			0.157512	+	0.987517i	$0.449653\pi$
$354$	3.04307	−	5.27075i	0.161737	−	0.280137i
$355$	−13.0459	−	4.74834i	−0.692407	−	0.252015i
$356$	−12.0575	−	10.1175i	−0.639048	−	0.536225i
$357$	−0.937440	−	17.1248i	−0.0496146	−	0.906340i
$358$	−1.05375	+	5.97611i	−0.0556924	+	0.315847i
$359$	0.750898	−	4.25855i	0.0396309	−	0.224758i	−0.958559	−	0.284893i	$-0.908042\pi$
$359$	0.750898	−	4.25855i	0.0396309	−	0.224758i	0.998190	+	0.0601349i	$0.0191531\pi$
$360$	−1.48677	−	2.57516i	−0.0783597	−	0.135723i
$361$	7.06320	+	17.6383i	0.371747	+	0.928334i
$362$	2.75663	−	4.77462i	0.144885	−	0.250948i
$363$	5.11779	−	1.86272i	0.268614	−	0.0977676i
$364$	−3.71334	+	0.866400i	−0.194632	+	0.0454117i
$365$	−7.42824	+	6.23303i	−0.388812	+	0.326252i
$366$	−11.1298	+	4.05092i	−0.581765	+	0.211745i
$367$	−7.84688	+	6.58431i	−0.409604	+	0.343698i	−0.824192	−	0.566311i	$-0.808370\pi$
$367$	−7.84688	+	6.58431i	−0.409604	+	0.343698i	0.414588	+	0.910009i	$0.363926\pi$
$368$	−2.04927	+	3.54944i	−0.106826	+	0.185027i
$369$	−1.45176	−	2.51452i	−0.0755755	−	0.130901i
$370$	1.43248	+	0.521381i	0.0744712	+	0.0271053i
$371$	1.16891	+	21.3531i	0.0606865	+	1.10860i
$372$	−5.74130	+	9.94423i	−0.297673	+	0.515584i
$373$	−4.01188			−0.207727			−0.103864	−	0.994592i	$-0.533121\pi$
$373$	−4.01188			−0.207727			−0.103864	+	0.994592i	$0.533121\pi$
$374$	−10.9691	+	9.20417i	−0.567199	+	0.475936i
$375$	1.58252	−	8.97494i	0.0817212	−	0.463464i
$376$	3.85223	+	21.8471i	0.198664	+	1.12668i
$377$	−0.248561	+	1.40966i	−0.0128015	+	0.0726011i
$378$	−0.719552	+	2.37329i	−0.0370098	+	0.122069i
$379$	−10.3857			−0.533477			−0.266739	−	0.963769i	$-0.585946\pi$
$379$	−10.3857			−0.533477			−0.266739	+	0.963769i	$0.585946\pi$
$380$	4.11419	+	2.78429i	0.211053	+	0.142831i
$381$	−7.89124	−	13.6680i	−0.404280	−	0.700234i
$382$	−19.4397	−	16.3119i	−0.994623	−	0.834588i
$383$	−6.46015	−	5.42071i	−0.330098	−	0.276985i	0.462642	−	0.886545i	$-0.346902\pi$
$383$	−6.46015	−	5.42071i	−0.330098	−	0.276985i	−0.792740	+	0.609560i	$0.791346\pi$
$384$	−3.90678	+	3.27818i	−0.199367	+	0.167289i
$385$	−4.33247	−	4.62438i	−0.220803	−	0.235680i
$386$	−1.25961	−	7.14359i	−0.0641124	−	0.363599i
$387$	−8.53384			−0.433799
$388$	−2.63903			−0.133976
$389$	4.05792	+	23.0136i	0.205745	+	1.16684i	0.896264	+	0.443521i	$0.146271\pi$
$389$	4.05792	+	23.0136i	0.205745	+	1.16684i	−0.690519	+	0.723314i	$0.742618\pi$
$390$	−0.937883	+	0.786977i	−0.0474915	+	0.0398501i
$391$	26.5839	−	46.0447i	1.34441	−	2.32858i
$392$	5.73681	+	19.6608i	0.289753	+	0.993020i
$393$	−0.326701	−	1.85281i	−0.0164799	−	0.0934620i
$394$	11.7450	−	4.27482i	0.591703	−	0.215362i
$395$	−6.28024	−	2.28582i	−0.315993	−	0.115012i
$396$	−2.48334	+	0.903863i	−0.124793	+	0.0454208i
$397$	−2.04602	+	11.6035i	−0.102687	+	0.582365i	0.889432	+	0.457067i	$0.151100\pi$
$397$	−2.04602	+	11.6035i	−0.102687	+	0.582365i	−0.992119	+	0.125298i	$0.960011\pi$
$398$	−4.34745			−0.217918
$399$	−1.81305	−	11.3892i	−0.0907658	−	0.570171i
$400$	1.98235			0.0991175
$401$	0.597544	−	3.38884i	0.0298399	−	0.169231i	−0.966246	−	0.257621i	$-0.917061\pi$
$401$	0.597544	−	3.38884i	0.0298399	−	0.169231i	0.996086	+	0.0883906i	$0.0281724\pi$
$402$	−4.76156	+	1.73307i	−0.237485	+	0.0864375i
$403$	12.3663	+	4.50095i	0.616007	+	0.224208i
$404$	6.71068	−	2.44249i	0.333869	−	0.121518i
$405$	−0.176481	−	1.00087i	−0.00876941	−	0.0497338i
$406$	2.74229	+	0.330235i	0.136098	+	0.0163893i
$407$	1.88556	−	3.26589i	0.0934640	−	0.161884i
$408$	−14.5287	+	12.1910i	−0.719276	+	0.603545i
$409$	1.91102	+	10.8379i	0.0944938	+	0.535901i	0.994901	+	0.100853i	$0.0321573\pi$
$409$	1.91102	+	10.8379i	0.0944938	+	0.535901i	−0.900408	+	0.435047i	$0.856732\pi$
$410$	−2.76599			−0.136602
$411$	−3.67420			−0.181235
$412$	−2.20529	−	12.5068i	−0.108647	−	0.616165i
$413$	4.98435	−	16.4398i	0.245264	−	0.808951i
$414$	−5.88945	+	4.94183i	−0.289450	+	0.242878i
$415$	6.06133	+	5.08606i	0.297539	+	0.249665i
$416$	5.29988	+	4.44713i	0.259848	+	0.218038i
$417$	−2.08078	−	3.60401i	−0.101896	−	0.176489i
$418$	−6.69933	+	6.91600i	−0.327675	+	0.338273i
$419$	−18.6703			−0.912102			−0.456051	−	0.889954i	$-0.650737\pi$
$419$	−18.6703			−0.912102			−0.456051	+	0.889954i	$0.650737\pi$
$420$	−2.06157	−	2.20048i	−0.100595	−	0.107372i
$421$	−3.10706	+	17.6210i	−0.151429	+	0.858796i	0.810549	+	0.585670i	$0.199169\pi$
$421$	−3.10706	+	17.6210i	−0.151429	+	0.858796i	−0.961978	+	0.273126i	$0.911942\pi$
$422$	−4.25651	−	24.1399i	−0.207204	−	1.17511i
$423$	−1.31664	+	7.46703i	−0.0640172	+	0.363060i
$424$	18.1160	−	15.2011i	0.879789	−	0.738231i
$425$	−25.7158			−1.24740
$426$	6.40220	−	11.0889i	0.310188	−	0.537261i
$427$	−27.9954	+	18.2732i	−1.35479	+	0.884302i
$428$	−1.47948	−	0.538487i	−0.0715134	−	0.0260287i
$429$	1.51437	+	2.62297i	0.0731146	+	0.126638i
$430$	−4.06481	+	7.04045i	−0.196022	+	0.339521i
$431$	17.1172	−	14.3630i	0.824505	−	0.691842i	−0.129518	−	0.991577i	$-0.541343\pi$
$431$	17.1172	−	14.3630i	0.824505	−	0.691842i	0.954022	+	0.299736i	$0.0968984\pi$
$432$	0.469561	−	0.170906i	0.0225918	−	0.00822273i
$433$	−25.6089	+	21.4884i	−1.23068	+	1.03267i	−0.232489	+	0.972599i	$0.574687\pi$
$433$	−25.6089	+	21.4884i	−1.23068	+	1.03267i	−0.998194	+	0.0600671i	$0.980869\pi$
$434$	7.36793	−	24.3015i	0.353672	−	1.16651i
$435$	−1.06367	+	0.387144i	−0.0509991	+	0.0185622i
$436$	8.40521	−	14.5582i	0.402536	−	0.697214i
$437$	14.5919	−	32.6386i	0.698027	−	1.56132i
$438$	−4.47169	−	7.74520i	−0.213666	−	0.370080i
$439$	5.15706	−	29.2471i	0.246133	−	1.39589i	−0.571714	−	0.820453i	$-0.693721\pi$
$439$	5.15706	−	29.2471i	0.246133	−	1.39589i	0.817847	−	0.575436i	$-0.195168\pi$
$440$	−1.21685	+	6.90111i	−0.0580111	+	0.328997i
$441$	−0.455788	+	6.98515i	−0.0217042	+	0.332626i
$442$	5.98201	+	5.01950i	0.284535	+	0.238753i
$443$	−19.1166	−	6.95786i	−0.908256	−	0.330578i	−0.154699	−	0.987962i	$-0.549441\pi$
$443$	−19.1166	−	6.95786i	−0.908256	−	0.330578i	−0.753556	+	0.657384i	$0.771663\pi$
$444$	0.897233	−	1.55405i	0.0425808	−	0.0737521i
$445$	−14.2651			−0.676231
$446$	15.1323	−	12.6975i	0.716536	−	0.601245i
$447$	17.6005	+	6.40604i	0.832473	+	0.302996i
$448$	9.59592	−	12.7961i	0.453365	−	0.604557i
$449$	−15.2479	−	26.4102i	−0.719593	−	1.24637i	−0.961161	−	0.275988i	$-0.910995\pi$
$449$	−15.2479	−	26.4102i	−0.719593	−	1.24637i	0.241568	−	0.970384i	$-0.422338\pi$
$450$	3.49428	+	1.27181i	0.164722	+	0.0599538i
$451$	−1.18820	+	6.73860i	−0.0559500	+	0.317308i
$452$	−5.34802	−	1.94652i	−0.251550	−	0.0915566i
$453$	4.35006	+	3.65013i	0.204383	+	0.171498i
$454$	−5.86667	+	2.13529i	−0.275337	+	0.100214i
$455$	−2.07331	+	2.76474i	−0.0971984	+	0.129613i
$456$	−8.87332	+	9.16030i	−0.415531	+	0.428970i
$457$	3.88102	−	6.72213i	0.181547	−	0.314448i	−0.760861	−	0.648915i	$-0.775223\pi$
$457$	3.88102	−	6.72213i	0.181547	−	0.314448i	0.942407	+	0.334467i	$0.108556\pi$
$458$	−12.0286	−	10.0932i	−0.562059	−	0.471624i
$459$	−6.09133	+	2.21706i	−0.284319	+	0.103484i
$460$	−1.62322	−	9.20576i	−0.0756832	−	0.429221i
$461$	10.0497	+	8.43274i	0.468063	+	0.392752i	0.846088	−	0.533044i	$-0.178952\pi$
$461$	10.0497	+	8.43274i	0.468063	+	0.392752i	−0.378024	+	0.925796i	$0.623396\pi$
$462$	4.89411	−	3.19449i	0.227695	−	0.148621i
$463$	6.25193	+	10.8287i	0.290552	+	0.503251i	0.973940	−	0.226804i	$-0.0728277\pi$
$463$	6.25193	+	10.8287i	0.290552	+	0.503251i	−0.683388	+	0.730055i	$0.739494\pi$
$464$	−0.278272	−	0.481982i	−0.0129185	−	0.0223754i
$465$	1.80710	+	10.2485i	0.0838021	+	0.475265i
$466$	−0.575469	−	3.26365i	−0.0266581	−	0.151186i
$467$	−1.11865	−	1.93756i	−0.0517649	−	0.0896594i	0.838982	−	0.544159i	$-0.183151\pi$
$467$	−1.11865	−	1.93756i	−0.0517649	−	0.0896594i	−0.890747	+	0.454500i	$0.849818\pi$
$468$	0.720604	+	1.24812i	0.0333099	+	0.0576945i
$469$	−11.9770	+	7.81765i	−0.553047	+	0.360986i
$470$	5.53320	+	4.64290i	0.255227	+	0.214161i
$471$	3.17291	+	17.9944i	0.146200	+	0.829140i
$472$	−17.8515	+	6.49743i	−0.821684	+	0.299069i
$473$	15.4061	+	12.9272i	0.708372	+	0.594395i
$474$	3.08198	−	5.33815i	0.141560	−	0.245189i
$475$	−17.2003	+	1.78103i	−0.789202	+	0.0817190i
$476$	−11.5385	+	15.3865i	−0.528868	+	0.705241i
$477$	7.59535	−	2.76448i	0.347767	−	0.126577i
$478$	12.5467	+	10.5279i	0.573873	+	0.481537i
$479$	21.7197	+	7.90533i	0.992399	+	0.361204i	0.786649	−	0.617401i	$-0.211814\pi$
$479$	21.7197	+	7.90533i	0.992399	+	0.361204i	0.205751	+	0.978604i	$0.434036\pi$
$480$	−0.950038	+	5.38793i	−0.0433631	+	0.245924i
$481$	−1.93256	−	0.703394i	−0.0881171	−	0.0320720i
$482$	−9.65881	−	16.7296i	−0.439947	−	0.762010i
$483$	−13.0194	+	17.3612i	−0.592402	+	0.789963i
$484$	−5.73905	−	2.08884i	−0.260866	−	0.0949474i
$485$	−1.83218	+	1.53738i	−0.0831950	+	0.0698089i
$486$	0.937341			0.0425187
$487$	13.2246	−	22.9057i	0.599265	−	1.03796i	−0.393665	−	0.919254i	$-0.628793\pi$
$487$	13.2246	−	22.9057i	0.599265	−	1.03796i	0.992930	−	0.118703i	$-0.0378736\pi$
$488$	34.7405	+	12.6445i	1.57263	+	0.572390i
$489$	−7.17872	−	6.02366i	−0.324633	−	0.272399i
$490$	5.54567	+	3.70317i	0.250528	+	0.167292i
$491$	2.30774	−	13.0878i	0.104147	−	0.590646i	−0.887411	−	0.460979i	$-0.847498\pi$
$491$	2.30774	−	13.0878i	0.104147	−	0.590646i	0.991558	−	0.129666i	$-0.0413906\pi$
$492$	−0.565395	+	3.20652i	−0.0254900	+	0.144561i
$493$	3.60985	+	6.25245i	0.162580	+	0.281596i
$494$	4.34876	+	2.94304i	0.195660	+	0.132414i
$495$	−1.19754	+	2.07421i	−0.0538256	+	0.0932287i
$496$	−4.80812	+	1.75001i	−0.215891	+	0.0785779i
$497$	10.4864	−	34.5872i	0.470379	−	1.55145i
$498$	−5.59034	+	4.69085i	−0.250509	+	0.210202i
$499$	24.9044	−	9.06446i	1.11487	−	0.405781i	0.282095	−	0.959386i	$-0.408971\pi$
$499$	24.9044	−	9.06446i	1.11487	−	0.405781i	0.832779	+	0.553606i	$0.186748\pi$
$500$	−7.82873	+	6.56909i	−0.350112	+	0.293779i
$501$	8.83242	−	15.2982i	0.394603	−	0.683473i
$502$	−7.61014	−	13.1812i	−0.339657	−	0.588304i
$503$	17.3840	+	6.32728i	0.775116	+	0.282119i	0.699135	−	0.714990i	$-0.253569\pi$
$503$	17.3840	+	6.32728i	0.775116	+	0.282119i	0.0759816	+	0.997109i	$0.475791\pi$
$504$	6.48229	−	4.23113i	0.288744	−	0.188469i
$505$	3.23609	−	5.60508i	0.144004	−	0.249423i
$506$	18.1182			0.805451
$507$	−8.69328	+	7.29453i	−0.386082	+	0.323961i
$508$	−3.07328	+	17.4295i	−0.136355	+	0.773307i
$509$	4.37485	+	24.8110i	0.193912	+	1.09973i	0.913960	+	0.405805i	$0.133009\pi$
$509$	4.37485	+	24.8110i	0.193912	+	1.09973i	−0.720048	+	0.693925i	$0.755880\pi$
$510$	−1.07231	+	6.08139i	−0.0474828	+	0.269289i
$511$	−17.2591	−	18.4220i	−0.763497	−	0.814940i
$512$	−5.61402			−0.248107
$513$	−3.92069	+	1.90478i	−0.173103	+	0.0840979i
$514$	10.3621	+	17.9477i	0.457052	+	0.791637i
$515$	−8.81696	−	7.39831i	−0.388522	−	0.326008i
$516$	7.33087	+	6.15133i	0.322724	+	0.270797i
$517$	13.6881	−	11.4857i	0.602003	−	0.505141i
$518$	−1.15144	+	3.79777i	−0.0505912	+	0.166864i
$519$	−0.819459	−	4.64738i	−0.0359703	−	0.203997i
$520$	3.82158			0.167587
$521$	−7.83951			−0.343455			−0.171728	−	0.985144i	$-0.554935\pi$
$521$	−7.83951			−0.343455			−0.171728	+	0.985144i	$0.554935\pi$
$522$	−0.181285	−	1.02812i	−0.00793462	−	0.0449994i
$523$	−2.17260	+	1.82303i	−0.0950014	+	0.0797156i	−0.689051	−	0.724713i	$-0.741973\pi$
$523$	−2.17260	+	1.82303i	−0.0950014	+	0.0797156i	0.594050	+	0.804428i	$0.297528\pi$
$524$	−1.05489	+	1.82712i	−0.0460831	+	0.0798183i
$525$	10.4207	+	1.25489i	0.454796	+	0.0547679i
$526$	4.11336	+	23.3280i	0.179351	+	1.01715i
$527$	62.3728	−	22.7018i	2.71700	−	0.988907i
$528$	−1.10659	−	0.402765i	−0.0481581	−	0.0175281i
$529$	−41.6037	+	15.1425i	−1.80886	+	0.658370i
$530$	1.33708	−	7.58296i	0.0580791	−	0.329383i
$531$	−6.49298			−0.281771
$532$	−6.65202	+	11.0906i	−0.288402	+	0.480837i
$533$	3.73159			0.161633
$534$	2.28462	−	12.9568i	0.0988654	−	0.560693i
$535$	−1.34085	+	0.488029i	−0.0579699	+	0.0210993i
$536$	14.8627	+	5.40958i	0.641971	+	0.233658i
$537$	6.08353	−	2.21422i	0.262523	−	0.0955507i
$538$	0.789429	+	4.47708i	0.0340347	+	0.193020i
$539$	11.4041	−	11.9198i	0.491208	−	0.513422i
$540$	−0.569843	+	0.986997i	−0.0245221	+	0.0424736i
$541$	−10.2367	+	8.58958i	−0.440109	+	0.369295i	−0.835750	−	0.549110i	$-0.814967\pi$
$541$	−10.2367	+	8.58958i	−0.440109	+	0.369295i	0.395641	+	0.918405i	$0.370522\pi$
$542$	3.43940	+	19.5058i	0.147735	+	0.837847i
$543$	−5.88180			−0.252412
$544$	34.8955			1.49613
$545$	−2.64557	−	15.0038i	−0.113324	−	0.642691i
$546$	−2.17912	−	2.32594i	−0.0932576	−	0.0995411i
$547$	9.39497	−	7.88331i	0.401700	−	0.337066i	−0.419450	−	0.907778i	$-0.637777\pi$
$547$	9.39497	−	7.88331i	0.401700	−	0.337066i	0.821150	+	0.570712i	$0.193333\pi$
$548$	3.15627	+	2.64842i	0.134829	+	0.113135i
$549$	9.67962	+	8.12217i	0.413116	+	0.346646i
$550$	−4.38162	−	7.58920i	−0.186833	−	0.323604i
$551$	2.84752	+	3.93200i	0.121308	+	0.167509i
$552$	23.9977			1.02141
$553$	5.04809	−	16.6501i	0.214667	−	0.708033i
$554$	3.50819	−	19.8960i	0.149049	−	0.845298i
$555$	−0.282407	−	1.60161i	−0.0119875	−	0.0679846i
$556$	−0.810370	+	4.59584i	−0.0343674	+	0.194907i
$557$	12.6205	−	10.5899i	0.534749	−	0.448707i	−0.334989	−	0.942222i	$-0.608733\pi$
$557$	12.6205	−	10.5899i	0.534749	−	0.448707i	0.869737	+	0.493515i	$0.164288\pi$
$558$	−9.59800			−0.406316
$559$	5.48382	−	9.49826i	0.231941	−	0.401734i
$560$	−0.0734432	−	1.34163i	−0.00310354	−	0.0566943i
$561$	14.3551	+	5.22482i	0.606072	+	0.220592i
$562$	0.102938	+	0.178294i	0.00434218	+	0.00752087i
$563$	−6.39813	+	11.0819i	−0.269649	+	0.467046i	−0.968771	−	0.247956i	$-0.920241\pi$
$563$	−6.39813	+	11.0819i	−0.269649	+	0.467046i	0.699122	+	0.715002i	$0.253574\pi$
$564$	6.51340	−	5.46539i	0.274264	−	0.230135i
$565$	−4.84690	+	1.76413i	−0.203910	+	0.0742173i
$566$	11.1021	−	9.31578i	0.466657	−	0.391571i
$567$	2.57655	−	0.601162i	0.108205	−	0.0252464i
$568$	−37.5572	+	13.6697i	−1.57587	+	0.573569i
$569$	−4.21337	+	7.29777i	−0.176634	+	0.305938i	−0.940725	−	0.339169i	$-0.889854\pi$
$569$	−4.21337	+	7.29777i	−0.176634	+	0.305938i	0.764092	+	0.645108i	$0.223187\pi$
$570$	−0.296042	+	4.14186i	−0.0123998	+	0.173484i
$571$	−4.58175	−	7.93583i	−0.191740	−	0.332104i	0.754087	−	0.656775i	$-0.228080\pi$
$571$	−4.58175	−	7.93583i	−0.191740	−	0.332104i	−0.945827	+	0.324671i	$0.894746\pi$
$572$	0.589781	−	3.34481i	0.0246600	−	0.139854i
$573$	−4.70120	+	26.6618i	−0.196396	+	1.11381i
$574$	−0.393586	−	7.18987i	−0.0164280	−	0.300100i
$575$	24.9259	+	20.9153i	1.03948	+	0.872229i
$576$	−5.68074	−	2.06762i	−0.236697	−	0.0861508i
$577$	−7.15342	+	12.3901i	−0.297801	+	0.515806i	−0.975633	−	0.219411i	$-0.929586\pi$
$577$	−7.15342	+	12.3901i	−0.297801	+	0.515806i	0.677832	+	0.735217i	$0.262920\pi$
$578$	23.4519			0.975471
$579$	−5.92818	+	4.97434i	−0.246367	+	0.206726i
$580$	1.19279	+	0.434141i	0.0495280	+	0.0180267i
$581$	−12.3582	+	16.4795i	−0.512703	+	0.683685i
$582$	−1.10295	−	1.91036i	−0.0457186	−	0.0791869i
$583$	−17.8995	−	6.51489i	−0.741322	−	0.269819i
$584$	−4.84753	+	27.4917i	−0.200592	+	1.13761i
$585$	1.22739	+	0.446734i	0.0507464	+	0.0184702i
$586$	6.96406	+	5.84354i	0.287683	+	0.241395i
$587$	30.4146	−	11.0700i	1.25535	−	0.456908i	0.373141	−	0.927775i	$-0.378281\pi$
$587$	30.4146	−	11.0700i	1.25535	−	0.456908i	0.882205	+	0.470866i	$0.156059\pi$
$588$	5.42655	−	5.67195i	0.223787	−	0.233907i
$589$	40.1463	−	19.5041i	1.65420	−	0.803654i
$590$	−3.09271	+	5.35674i	−0.127325	+	0.220533i
$591$	−10.2146	−	8.57109i	−0.420174	−	0.352568i
$592$	0.751398	−	0.273486i	0.0308823	−	0.0112402i
$593$	1.17295	+	6.65213i	0.0481673	+	0.273170i	0.999374	−	0.0353848i	$-0.0112657\pi$
$593$	1.17295	+	6.65213i	0.0481673	+	0.273170i	−0.951206	+	0.308555i	$0.900155\pi$
$594$	−1.69217	−	1.41990i	−0.0694308	−	0.0582593i
$595$	0.952733	+	17.4042i	0.0390583	+	0.713501i
$596$	−10.5018	−	18.1897i	−0.430172	−	0.745080i
$597$	2.31903	+	4.01668i	0.0949116	+	0.164392i
$598$	−1.71577	−	9.73063i	−0.0701632	−	0.397915i
$599$	6.99840	+	39.6899i	0.285947	+	1.62169i	0.701883	+	0.712292i	$0.252343\pi$
$599$	6.99840	+	39.6899i	0.285947	+	1.62169i	−0.415936	+	0.909394i	$0.636546\pi$
$600$	−5.80350	−	10.0520i	−0.236927	−	0.410369i
$601$	−5.40849	−	9.36779i	−0.220617	−	0.382120i	0.734378	−	0.678740i	$-0.237474\pi$
$601$	−5.40849	−	9.36779i	−0.220617	−	0.382120i	−0.954996	+	0.296620i	$0.904140\pi$
$602$	−18.8793	−	9.56419i	−0.769462	−	0.389807i
$603$	4.14114	+	3.47483i	0.168640	+	0.141506i
$604$	−1.10578	−	6.27119i	−0.0449935	−	0.255171i
$605$	−5.20128	+	1.89311i	−0.211462	+	0.0769659i
$606$	4.57272	+	3.83697i	0.185754	+	0.155866i
$607$	−2.04280	+	3.53823i	−0.0829145	+	0.143612i	−0.904501	−	0.426472i	$-0.859756\pi$
$607$	−2.04280	+	3.53823i	−0.0829145	+	0.143612i	0.821586	+	0.570084i	$0.193090\pi$
$608$	23.3402	−	2.41679i	0.946569	−	0.0980139i
$609$	−1.15769	−	2.70981i	−0.0469121	−	0.109807i
$610$	11.3114	−	4.11701i	0.457985	−	0.166693i
$611$	−7.46483	−	6.26373i	−0.301995	−	0.253404i
$612$	6.83076	+	2.48619i	0.276117	+	0.100498i
$613$	2.38888	−	13.5480i	0.0964858	−	0.547198i	−0.897796	−	0.440411i	$-0.854833\pi$
$613$	2.38888	−	13.5480i	0.0964858	−	0.547198i	0.994282	−	0.106787i	$-0.0340563\pi$
$614$	−4.49381	−	1.63561i	−0.181355	−	0.0660080i
$615$	1.47544	+	2.55554i	0.0594956	+	0.103049i
$616$	−18.1118	−	2.18108i	−0.729746	−	0.0878782i
$617$	20.7261	+	7.54367i	0.834400	+	0.303697i	0.723664	−	0.690153i	$-0.242457\pi$
$617$	20.7261	+	7.54367i	0.834400	+	0.303697i	0.110737	+	0.993850i	$0.464679\pi$
$618$	8.13184	−	6.82342i	0.327110	−	0.274478i
$619$	−30.8505			−1.23999			−0.619993	−	0.784607i	$-0.712865\pi$
$619$	−30.8505			−1.23999			−0.619993	+	0.784607i	$0.712865\pi$
$620$	5.83497	−	10.1065i	0.234338	−	0.405885i
$621$	7.70741	+	2.80527i	0.309288	+	0.112572i
$622$	4.30797	+	3.61482i	0.172734	+	0.144941i
$623$	−2.02985	−	37.0806i	−0.0813243	−	1.48560i
$624$	−0.111518	+	0.632451i	−0.00446430	+	0.0253183i
$625$	1.83606	−	10.4128i	0.0734425	−	0.416513i
$626$	−11.6567	−	20.1899i	−0.465894	−	0.806952i
$627$	9.96339	+	2.50047i	0.397900	+	0.0998590i
$628$	10.2451	−	17.7450i	0.408822	−	0.708101i
$629$	−9.74742	+	3.54777i	−0.388655	+	0.141459i
$630$	0.731291	−	2.41201i	0.0291353	−	0.0960966i
$631$	−15.0777	+	12.6517i	−0.600235	+	0.503657i	−0.891521	−	0.452979i	$-0.850361\pi$
$631$	−15.0777	+	12.6517i	−0.600235	+	0.503657i	0.291286	+	0.956636i	$0.405917\pi$
$632$	−18.0798	+	6.58052i	−0.719177	+	0.261759i
$633$	−20.0327	+	16.8095i	−0.796230	+	0.668116i
$634$	2.20152	−	3.81315i	0.0874337	−	0.151440i
$635$	8.01998	+	13.8910i	0.318263	+	0.551248i
$636$	−8.51736	−	3.10007i	−0.337735	−	0.122926i
$637$	−7.48166	−	4.99594i	−0.296434	−	0.197946i
$638$	−1.23014	+	2.13067i	−0.0487017	+	0.0843539i
$639$	−13.6604			−0.540395
$640$	3.97051	−	3.33166i	0.156948	−	0.131695i
$641$	2.26145	−	12.8253i	0.0893218	−	0.506569i	−0.907018	−	0.421091i	$-0.861647\pi$
$641$	2.26145	−	12.8253i	0.0893218	−	0.506569i	0.996340	−	0.0854779i	$-0.0272417\pi$
$642$	−0.228525	−	1.29603i	−0.00901917	−	0.0511502i
$643$	−2.07943	+	11.7930i	−0.0820047	+	0.465072i	0.915958	+	0.401274i	$0.131432\pi$
$643$	−2.07943	+	11.7930i	−0.0820047	+	0.465072i	−0.997963	+	0.0637978i	$0.979679\pi$
$644$	23.6984	−	5.52932i	0.933847	−	0.217886i
$645$	8.67306			0.341501
$646$	26.3442	−	2.72785i	1.03650	−	0.107326i
$647$	7.91956	+	13.7171i	0.311350	+	0.539274i	0.978655	−	0.205511i	$-0.0658855\pi$
$647$	7.91956	+	13.7171i	0.311350	+	0.539274i	−0.667305	+	0.744785i	$0.732552\pi$
$648$	−2.24130	−	1.88067i	−0.0880466	−	0.0738798i
$649$	11.7217	+	9.83570i	0.460118	+	0.386085i
$650$	−3.66096	+	3.07191i	−0.143595	+	0.120490i
$651$	−26.3828	+	6.15566i	−1.03402	+	0.241260i
$652$	1.82482	+	10.3491i	0.0714656	+	0.405302i
$653$	25.4908			0.997533			0.498766	−	0.866736i	$-0.333787\pi$
$653$	25.4908			0.997533			0.498766	+	0.866736i	$0.333787\pi$
$654$	14.0514			0.549452
$655$	0.332030	+	1.88304i	0.0129735	+	0.0735764i
$656$	−1.11144	+	0.932606i	−0.0433943	+	0.0364122i
$657$	−4.77061	+	8.26294i	−0.186119	+	0.322368i
$658$	−11.2814	+	15.0436i	−0.439793	+	0.586460i
$659$	6.51227	+	36.9329i	0.253682	+	1.43870i	0.799434	+	0.600754i	$0.205133\pi$
$659$	6.51227	+	36.9329i	0.253682	+	1.43870i	−0.545752	+	0.837947i	$0.683756\pi$
$660$	2.52386	−	0.918609i	0.0982410	−	0.0357568i
$661$	−17.0157	−	6.19320i	−0.661833	−	0.240887i	−0.0108054	−	0.999942i	$-0.503440\pi$
$661$	−17.0157	−	6.19320i	−0.661833	−	0.240887i	−0.651027	+	0.759054i	$0.725662\pi$
$662$	15.3188	−	5.57560i	0.595383	−	0.216702i
$663$	1.44666	−	8.20440i	0.0561835	−	0.318632i
$664$	22.7789			0.883992
$665$	1.84262	+	11.5750i	0.0714539	+	0.448858i
$666$	1.49995			0.0581217
$667$	1.58630	−	8.99638i	0.0614219	−	0.348341i
$668$	−18.6146	+	6.77515i	−0.720219	+	0.262138i
$669$	−19.8034	−	7.20785i	−0.765644	−	0.278672i
$670$	4.83924	−	1.76134i	0.186956	−	0.0680465i
$671$	−5.17093	−	29.3258i	−0.199621	−	1.13211i
$672$	−14.1405	−	1.70284i	−0.545483	−	0.0656886i
$673$	1.34564	−	2.33071i	0.0518706	−	0.0898425i	−0.838924	−	0.544248i	$-0.816815\pi$
$673$	1.34564	−	2.33071i	0.0518706	−	0.0898425i	0.890795	+	0.454406i	$0.150148\pi$
$674$	−10.3685	+	8.70022i	−0.399381	+	0.335120i
$675$	−0.688881	−	3.90684i	−0.0265150	−	0.150374i
$676$	12.7259			0.489456
$677$	32.9601			1.26676			0.633379	−	0.773841i	$-0.281667\pi$
$677$	32.9601			1.26676			0.633379	+	0.773841i	$0.281667\pi$
$678$	−0.826072	−	4.68489i	−0.0317251	−	0.179922i
$679$	−4.25697	−	4.54379i	−0.163367	−	0.174375i
$680$	14.7657	−	12.3899i	0.566238	−	0.475130i
$681$	5.10226	+	4.28130i	0.195519	+	0.164060i
$682$	17.3272	+	14.5392i	0.663493	+	0.556737i
$683$	−13.5367	−	23.4463i	−0.517968	−	0.897147i	−0.999782	−	0.0208738i	$-0.993355\pi$
$683$	−13.5367	−	23.4463i	−0.517968	−	0.897147i	0.481814	−	0.876274i	$-0.339978\pi$
$684$	4.74101	+	1.18983i	0.181277	+	0.0454943i
$685$	3.73414			0.142674
$686$	−8.83685	+	14.9423i	−0.337393	+	0.570500i
$687$	−2.90893	+	16.4974i	−0.110983	+	0.629414i
$688$	0.740493	+	4.19954i	0.0282310	+	0.160106i
$689$	−1.80385	+	10.2302i	−0.0687213	+	0.389738i
$690$	5.98553	−	5.02245i	0.227865	−	0.191202i
$691$	−30.9042			−1.17565			−0.587826	−	0.808987i	$-0.700016\pi$
$691$	−30.9042			−1.17565			−0.587826	+	0.808987i	$0.700016\pi$
$692$	−2.64597	+	4.58295i	−0.100585	+	0.174218i
$693$	−5.56208	−	2.81773i	−0.211286	−	0.107037i
$694$	2.32455	+	0.846067i	0.0882387	+	0.0321163i
$695$	2.11472	+	3.66281i	0.0802161	+	0.138938i
$696$	−1.62933	+	2.82208i	−0.0617596	+	0.106971i
$697$	14.4180	−	12.0981i	0.546120	−	0.458249i
$698$	2.90818	−	1.05849i	0.110076	−	0.0400644i
$699$	−2.70837	+	2.27259i	−0.102440	+	0.0859574i
$700$	−8.04720	−	8.58940i	−0.304156	−	0.324649i
$701$	−26.0425	+	9.47869i	−0.983611	+	0.358005i	−0.783243	−	0.621716i	$-0.786436\pi$
$701$	−26.0425	+	9.47869i	−0.983611	+	0.358005i	−0.200368	+	0.979721i	$0.564214\pi$
$702$	−0.602333	+	1.04327i	−0.0227336	+	0.0393758i
$703$	−6.27394	+	3.04805i	−0.236626	+	0.114959i
$704$	7.12332	+	12.3380i	0.268470	+	0.465004i
$705$	1.33812	−	7.58885i	0.0503965	−	0.285813i
$706$	0.963385	−	5.46363i	0.0362575	−	0.205626i
$707$	15.0303	+	7.61429i	0.565271	+	0.286365i
$708$	5.57770	+	4.68025i	0.209623	+	0.175895i
$709$	48.2951	+	17.5780i	1.81376	+	0.660155i	0.996472	+	0.0839282i	$0.0267466\pi$
$709$	48.2951	+	17.5780i	1.81376	+	0.660155i	0.817290	+	0.576227i	$0.195476\pi$
$710$	−6.50665	+	11.2698i	−0.244190	+	0.422950i
$711$	−6.57601			−0.246620
$712$	−31.4591	+	26.3974i	−1.17898	+	0.989283i
$713$	−78.9209	−	28.7248i	−2.95561	−	1.07575i
$714$	−15.9605	−	1.92201i	−0.597306	−	0.0719294i
$715$	−1.53908	−	2.66576i	−0.0575583	−	0.0996938i
$716$	−6.82202	−	2.48301i	−0.254951	−	0.0927945i
$717$	3.03423	−	17.2080i	0.113315	−	0.642644i
$718$	−3.80885	−	1.38631i	−0.142145	−	0.0517366i
$719$	8.81950	+	7.40044i	0.328912	+	0.275990i	0.792256	−	0.610188i	$-0.208906\pi$
$719$	8.81950	+	7.40044i	0.328912	+	0.275990i	−0.463344	+	0.886178i	$0.653351\pi$
$720$	−0.477222	+	0.173694i	−0.0177850	+	0.00647321i
$721$	17.9765	−	23.9715i	0.669479	−	0.892744i
$722$	17.4316	−	3.64909i	0.648738	−	0.135805i
$723$	−10.3045	+	17.8479i	−0.383228	+	0.663770i
$724$	5.05268	+	4.23970i	0.187781	+	0.157567i
$725$	−4.15196	+	1.51119i	−0.154200	+	0.0561242i
$726$	−0.886471	−	5.02742i	−0.0329000	−	0.186585i
$727$	15.3470	+	12.8776i	0.569187	+	0.477605i	0.881376	−	0.472415i	$-0.156618\pi$
$727$	15.3470	+	12.8776i	0.569187	+	0.477605i	−0.312189	+	0.950020i	$0.601062\pi$
$728$	0.543792	+	9.93378i	0.0201543	+	0.368170i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	4.54464	+	7.87155i	0.168205	+	0.291339i
$731$	−9.60595	−	54.4781i	−0.355289	−	2.01494i
$732$	−2.46055	−	13.9545i	−0.0909445	−	0.515772i
$733$	−9.04835	−	15.6722i	−0.334208	−	0.578866i	0.649124	−	0.760682i	$-0.275136\pi$
$733$	−9.04835	−	15.6722i	−0.334208	−	0.578866i	−0.983332	+	0.181817i	$0.941802\pi$
$734$	4.80077	+	8.31517i	0.177200	+	0.306919i
$735$	0.463224	−	7.09910i	0.0170863	−	0.261854i
$736$	−33.8236	−	28.3814i	−1.24675	−	1.04615i
$737$	−2.21223	−	12.5462i	−0.0814885	−	0.462144i
$738$	−2.55745	+	0.930837i	−0.0941412	+	0.0342646i
$739$	−12.6701	−	10.6315i	−0.466078	−	0.391086i	0.379283	−	0.925281i	$-0.376171\pi$
$739$	−12.6701	−	10.6315i	−0.466078	−	0.391086i	−0.845362	+	0.534194i	$0.820615\pi$
$740$	−0.911870	+	1.57941i	−0.0335210	+	0.0580601i
$741$	0.399390	−	5.58778i	0.0146719	−	0.205272i
$742$	19.9013	+	2.39658i	0.730601	+	0.0879811i
$743$	6.37573	−	2.32058i	0.233903	−	0.0851337i	−0.222409	−	0.974953i	$-0.571392\pi$
$743$	6.37573	−	2.32058i	0.233903	−	0.0851337i	0.456312	+	0.889820i	$0.349170\pi$
$744$	22.9500	+	19.2573i	0.841388	+	0.706009i
$745$	−17.8876	−	6.51055i	−0.655351	−	0.238528i
$746$	−0.653004	+	3.70337i	−0.0239082	+	0.135590i
$747$	7.31598	+	2.66280i	0.267678	+	0.0974267i
$748$	−8.56539	−	14.8357i	−0.313182	−	0.542447i
$749$	−1.45937	−	3.41594i	−0.0533243	−	0.124816i
$750$	−8.02719	−	2.92166i	−0.293112	−	0.106684i
$751$	−21.1312	+	17.7312i	−0.771090	+	0.647021i	−0.940988	−	0.338440i	$-0.890101\pi$
$751$	−21.1312	+	17.7312i	−0.771090	+	0.647021i	0.169898	+	0.985462i	$0.445656\pi$
$752$	3.78881			0.138164
$753$	−8.11886	+	14.0623i	−0.295868	+	0.512458i
$754$	1.26080	+	0.458893i	0.0459156	+	0.0167119i
$755$	−4.42102	−	3.70968i	−0.160897	−	0.135009i
$756$	−2.64668	−	1.34080i	−0.0962587	−	0.0487644i
$757$	−2.05693	+	11.6654i	−0.0747605	+	0.423988i	0.924339	+	0.381571i	$0.124617\pi$
$757$	−2.05693	+	11.6654i	−0.0747605	+	0.423988i	−0.999100	+	0.0424168i	$0.986494\pi$
$758$	−1.69045	+	9.58704i	−0.0614000	+	0.348217i
$759$	−9.66466	−	16.7397i	−0.350805	−	0.607612i
$760$	9.01807	−	9.30974i	0.327120	−	0.337700i
$761$	2.31049	−	4.00188i	0.0837551	−	0.145068i	−0.821105	−	0.570777i	$-0.806642\pi$
$761$	2.31049	−	4.00188i	0.0837551	−	0.145068i	0.904860	+	0.425709i	$0.139975\pi$
$762$	−13.9014	+	5.05970i	−0.503595	+	0.183293i
$763$	38.6242	−	9.01183i	1.39829	−	0.326250i
$764$	23.2568	−	19.5148i	0.841402	−	0.706020i
$765$	6.19070	−	2.25323i	0.223825	−	0.0814657i
$766$	−6.05536	+	5.08105i	−0.218789	+	0.183586i
$767$	4.17238	−	7.22677i	0.150656	−	0.260943i
$768$	8.43551	+	14.6107i	0.304390	+	0.527219i
$769$	−0.593576	−	0.216044i	−0.0214049	−	0.00779074i	0.331296	−	0.943527i	$-0.392514\pi$
$769$	−0.593576	−	0.216044i	−0.0214049	−	0.00779074i	−0.352700	+	0.935736i	$0.614737\pi$
$770$	−4.97395	+	3.24660i	−0.179249	+	0.116999i
$771$	11.0548	−	19.1474i	0.398128	−	0.689577i
$772$	8.67811			0.312332
$773$	2.49189	−	2.09095i	0.0896272	−	0.0752061i	−0.596873	−	0.802336i	$-0.703590\pi$
$773$	2.49189	−	2.09095i	0.0896272	−	0.0752061i	0.686500	+	0.727129i	$0.259146\pi$
$774$	−1.38903	+	7.87759i	−0.0499277	+	0.283154i
$775$	7.05387	+	40.0045i	0.253382	+	1.43700i
$776$	−1.19565	+	6.78085i	−0.0429212	+	0.243418i
$777$	4.12303	−	0.961988i	0.147913	−	0.0345111i
$778$	21.9044			0.785309
$779$	8.80571	−	9.09051i	0.315497	−	0.325701i
$780$	−0.732360	−	1.26848i	−0.0262227	−	0.0454190i
$781$	24.6609	+	20.6930i	0.882438	+	0.740453i
$782$	−38.1769	−	32.0342i	−1.36520	−	1.14554i
$783$	−0.853193	+	0.715914i	−0.0304906	+	0.0255847i
$784$	3.47697	−	0.381815i	0.124178	−	0.0136363i
$785$	−3.22467	−	18.2880i	−0.115093	−	0.652727i
$786$	−1.76351			−0.0629022
$787$	−6.20296			−0.221112			−0.110556	−	0.993870i	$-0.535263\pi$
$787$	−6.20296			−0.221112			−0.110556	+	0.993870i	$0.535263\pi$
$788$	2.59655	+	14.7258i	0.0924982	+	0.524583i
$789$	19.3590	−	16.2441i	0.689198	−	0.578306i
$790$	−3.13226	+	5.42524i	−0.111441	+	0.193021i
$791$	−5.27534	−	12.3479i	−0.187569	−	0.439042i
$792$	1.19732	+	6.79033i	0.0425449	+	0.241284i
$793$	−15.2602	+	5.55425i	−0.541905	+	0.197237i
$794$	10.3782	+	3.77736i	0.368309	+	0.134054i
$795$	−7.71926	+	2.80958i	−0.273774	+	0.0996455i
$796$	0.903159	−	5.12207i	0.0320116	−	0.181547i
$797$	−27.5095			−0.974437			−0.487218	−	0.873280i	$-0.661988\pi$
$797$	−27.5095			−0.974437			−0.487218	+	0.873280i	$0.661988\pi$
$798$	−10.8084	−	0.180162i	−0.382615	−	0.00637765i
$799$	−49.1499			−1.73880
$800$	−3.70840	+	21.0314i	−0.131112	+	0.743572i
$801$	−13.1896	+	4.80064i	−0.466033	+	0.169622i
$802$	−3.03098	−	1.10319i	−0.107028	−	0.0389549i
$803$	21.1292	−	7.69041i	0.745634	−	0.271389i
$804$	−1.05267	−	5.97001i	−0.0371249	−	0.210546i
$805$	13.2318	−	17.6445i	0.466359	−	0.621885i
$806$	6.16765	−	10.6827i	0.217246	−	0.376282i
$807$	3.71535	−	3.11755i	0.130786	−	0.109743i
$808$	−3.23548	−	18.3493i	−0.113824	−	0.645528i
$809$	50.1893			1.76456			0.882281	−	0.470724i	$-0.156007\pi$
$809$	50.1893			1.76456			0.882281	+	0.470724i	$0.156007\pi$
$810$	−0.952633			−0.0334721
$811$	0.772337	+	4.38014i	0.0271204	+	0.153807i	0.995361	−	0.0962142i	$-0.0306734\pi$
$811$	0.772337	+	4.38014i	0.0271204	+	0.153807i	−0.968240	+	0.250022i	$0.919562\pi$
$812$	−0.958772	+	3.16231i	−0.0336463	+	0.110975i
$813$	16.1871	−	13.5826i	0.567707	−	0.476362i
$814$	−2.70784	−	2.27215i	−0.0949098	−	0.0796387i
$815$	7.29584	+	6.12193i	0.255562	+	0.214442i
$816$	1.61958	+	2.80519i	0.0566966	+	0.0982015i
$817$	−10.1981	−	35.7729i	−0.356786	−	1.25154i
$818$	10.3155			0.360675
$819$	−0.986584	+	3.25404i	−0.0344740	+	0.113705i
$820$	0.574619	−	3.25883i	0.0200666	−	0.113803i
$821$	−3.44116	−	19.5158i	−0.120097	−	0.681106i	−0.984100	−	0.177618i	$-0.943161\pi$
$821$	−3.44116	−	19.5158i	−0.120097	−	0.681106i	0.864002	−	0.503488i	$-0.167950\pi$
$822$	−0.598040	+	3.39166i	−0.0208591	+	0.118298i
$823$	−0.159568	+	0.133893i	−0.00556219	+	0.00466723i	−0.645564	−	0.763706i	$-0.723378\pi$
$823$	−0.159568	+	0.133893i	−0.00556219	+	0.00466723i	0.640002	+	0.768373i	$0.278933\pi$
$824$	−33.1347			−1.15430
$825$	−4.67453	+	8.09652i	−0.162746	+	0.281884i
$826$	−14.3643	−	7.27693i	−0.499799	−	0.253197i
$827$	−42.3610	−	15.4182i	−1.47304	−	0.536142i	−0.524114	−	0.851648i	$-0.675603\pi$
$827$	−42.3610	−	15.4182i	−1.47304	−	0.536142i	−0.948923	+	0.315507i	$0.897826\pi$
$828$	−4.59886	−	7.96546i	−0.159821	−	0.276819i
$829$	−26.0687	+	45.1523i	−0.905403	+	1.56820i	−0.0850272	+	0.996379i	$0.527098\pi$
$829$	−26.0687	+	45.1523i	−0.905403	+	1.56820i	−0.820376	+	0.571825i	$0.806236\pi$
$830$	5.68154	−	4.76738i	0.197209	−	0.165478i
$831$	−20.2536	+	7.37169i	−0.702588	+	0.255721i
$832$	5.95172	−	4.99408i	0.206339	−	0.173139i
$833$	−45.1046	+	4.95305i	−1.56278	+	0.171613i
$834$	−3.66555	+	1.33415i	−0.126928	+	0.0461979i
$835$	−8.97651	+	15.5478i	−0.310645	+	0.538053i
$836$	−6.75653	−	9.32977i	−0.233680	−	0.322677i
$837$	5.11980	+	8.86776i	0.176966	+	0.306514i
$838$	−3.03891	+	17.2345i	−0.104977	+	0.595357i
$839$	0.348504	−	1.97647i	0.0120317	−	0.0682352i	−0.978201	−	0.207662i	$-0.933415\pi$
$839$	0.348504	−	1.97647i	0.0120317	−	0.0682352i	0.990232	+	0.139426i	$0.0445258\pi$
$840$	−6.58804	+	4.30015i	−0.227309	+	0.148369i
$841$	−21.2650	−	17.8435i	−0.733277	−	0.615292i
$842$	15.7603	+	5.73626i	0.543134	+	0.197685i
$843$	0.109819	−	0.190212i	0.00378237	−	0.00655126i
$844$	29.3254			1.00942
$845$	8.83510	−	7.41353i	0.303937	−	0.255033i
$846$	6.67852	+	2.43078i	0.229612	+	0.0835720i
$847$	−5.66105	−	13.2508i	−0.194516	−	0.455302i
$848$	−2.01947	−	3.49783i	−0.0693490	−	0.120116i
$849$	−14.5291	−	5.28818i	−0.498639	−	0.181490i
$850$	−4.18570	+	23.7383i	−0.143568	+	0.814216i
$851$	12.3335	+	4.48903i	0.422787	+	0.153882i
$852$	11.7347	+	9.84661i	0.402025	+	0.337339i
$853$	−7.50911	+	2.73309i	−0.257107	+	0.0935793i	−0.467358	−	0.884068i	$-0.654794\pi$
$853$	−7.50911	+	2.73309i	−0.257107	+	0.0935793i	0.210251	+	0.977647i	$0.432572\pi$
$854$	12.3113	+	28.8169i	0.421283	+	0.986093i
$855$	3.98465	−	1.93585i	0.136272	−	0.0662047i
$856$	−2.05391	+	3.55748i	−0.0702013	+	0.121592i
$857$	−2.96400	−	2.48709i	−0.101248	−	0.0849573i	0.590758	−	0.806849i	$-0.298829\pi$
$857$	−2.96400	−	2.48709i	−0.101248	−	0.0849573i	−0.692007	+	0.721891i	$0.743273\pi$
$858$	2.66776	−	0.970984i	0.0910757	−	0.0331489i
$859$	6.14954	+	34.8758i	0.209820	+	1.18995i	0.889673	+	0.456598i	$0.150932\pi$
$859$	6.14954	+	34.8758i	0.209820	+	1.18995i	−0.679854	+	0.733348i	$0.737957\pi$
$860$	−7.45047	−	6.25168i	−0.254059	−	0.213181i
$861$	−6.43290	+	4.19889i	−0.219233	+	0.143098i
$862$	−10.4724	−	18.1387i	−0.356691	−	0.617806i
$863$	14.0127	+	24.2707i	0.476997	+	0.826183i	0.999652	−	0.0263608i	$-0.00839187\pi$
$863$	14.0127	+	24.2707i	0.476997	+	0.826183i	−0.522655	+	0.852544i	$0.675059\pi$
$864$	0.934788	+	5.30145i	0.0318021	+	0.180359i
$865$	0.832828	+	4.72320i	0.0283170	+	0.160594i
$866$	15.6677	+	27.1372i	0.532409	+	0.922159i
$867$	−12.5098	−	21.6676i	−0.424855	−	0.735871i
$868$	27.1009	+	13.7293i	0.919865	+	0.466001i
$869$	11.8716	+	9.96148i	0.402717	+	0.337920i
$870$	0.184242	+	1.04489i	0.00624640	+	0.0354251i
$871$	−6.52862	+	2.37622i	−0.221214	+	0.0805152i
$872$	−33.5986	−	28.1926i	−1.13779	−	0.954720i
$873$	−1.17668	+	2.03806i	−0.0398244	+	0.0689779i
$874$	−27.7536	−	18.7823i	−0.938780	−	0.635322i
$875$	−23.9388	−	2.88278i	−0.809280	−	0.0974558i
$876$	10.0542	−	3.65943i	0.339700	−	0.123641i
$877$	23.4631	+	19.6879i	0.792292	+	0.664812i	0.946311	−	0.323256i	$-0.104778\pi$
$877$	23.4631	+	19.6879i	0.792292	+	0.664812i	−0.154020	+	0.988068i	$0.549222\pi$
$878$	−26.1586	−	9.52096i	−0.882811	−	0.321317i
$879$	1.68415	−	9.55130i	0.0568051	−	0.322157i
$880$	1.12464	+	0.409336i	0.0379116	+	0.0137987i
$881$	2.70704	+	4.68873i	0.0912026	+	0.157967i	0.908017	−	0.418932i	$-0.137596\pi$
$881$	2.70704	+	4.68873i	0.0912026	+	0.157967i	−0.816815	+	0.576900i	$0.804262\pi$
$882$	6.37380	+	1.55769i	0.214617	+	0.0524503i
$883$	20.5805	+	7.49069i	0.692589	+	0.252082i	0.664243	−	0.747516i	$-0.268754\pi$
$883$	20.5805	+	7.49069i	0.692589	+	0.252082i	0.0283458	+	0.999598i	$0.490976\pi$
$884$	−7.15660	+	6.00510i	−0.240702	+	0.201973i
$885$	6.59891			0.221820
$886$	−9.53436	+	16.5140i	−0.320313	+	0.554799i
$887$	−3.70927	−	1.35006i	−0.124545	−	0.0453307i	0.278996	−	0.960292i	$-0.409998\pi$
$887$	−3.70927	−	1.35006i	−0.124545	−	0.0453307i	−0.403541	+	0.914962i	$0.632221\pi$
$888$	−3.58656	−	3.00948i	−0.120357	−	0.100991i
$889$	−34.9669	+	22.8237i	−1.17275	+	0.765481i
$890$	−2.32190	+	13.1681i	−0.0778301	+	0.441397i
$891$	−0.409227	+	2.32084i	−0.0137096	+	0.0777511i
$892$	11.8163	+	20.4664i	0.395639	+	0.685267i
$893$	−32.8744	+	3.40403i	−1.10010	+	0.113911i
$894$	8.77821	−	15.2043i	0.293587	−	0.508508i
$895$	−6.18277	+	2.25034i	−0.206667	+	0.0752207i
$896$	9.22526	+	9.84684i	0.308194	+	0.328960i
$897$	−8.07507	+	6.77578i	−0.269619	+	0.226237i
$898$	−26.8611	+	9.77664i	−0.896366	+	0.326251i
$899$	8.73636	−	7.33068i	0.291374	−	0.244492i
$900$	−2.22434	+	3.85267i	−0.0741447	+	0.128422i
$901$	26.1974	+	45.3752i	0.872761	+	1.51167i
$902$	6.02700	+	2.19365i	0.200677	+	0.0730406i
$903$	1.23413	+	22.5447i	0.0410694	+	0.750239i
$904$	−7.42448	+	12.8596i	−0.246934	+	0.427703i
$905$	5.97775			0.198707
$906$	4.07749	−	3.42142i	0.135465	−	0.113669i
$907$	−1.35444	+	7.68139i	−0.0449733	+	0.255056i	−0.999002	−	0.0446578i	$-0.985780\pi$
$907$	−1.35444	+	7.68139i	−0.0449733	+	0.255056i	0.954029	+	0.299714i	$0.0968914\pi$
$908$	−1.29699	−	7.35559i	−0.0430421	−	0.244104i
$909$	1.10584	−	6.27155i	0.0366785	−	0.208014i
$910$	2.21467	+	2.36389i	0.0734155	+	0.0783620i
$911$	41.6435			1.37971			0.689856	−	0.723947i	$-0.257674\pi$
$911$	41.6435			1.37971			0.689856	+	0.723947i	$0.257674\pi$
$912$	1.27755	+	1.76411i	0.0423040	+	0.0584156i
$913$	−9.17382	−	15.8895i	−0.303609	−	0.525866i
$914$	−5.57350	−	4.67672i	−0.184355	−	0.154692i
$915$	−9.83753	−	8.25467i	−0.325219	−	0.272891i
$916$	14.3905	−	12.0750i	0.475474	−	0.398970i
$917$	−4.84750	+	1.13102i	−0.160079	+	0.0373497i
$918$	1.05510	+	5.98377i	0.0348235	+	0.197494i
$919$	18.5640			0.612369			0.306185	−	0.951972i	$-0.400948\pi$
$919$	18.5640			0.612369			0.306185	+	0.951972i	$0.400948\pi$
$920$	−24.3891			−0.804086
$921$	0.885934	+	5.02438i	0.0291925	+	0.165559i
$922$	9.42004	−	7.90435i	0.310233	−	0.260316i
$923$	8.77811	−	15.2041i	0.288935	−	0.500450i
$924$	2.74695	+	6.42977i	0.0903682	+	0.211524i
$925$	−1.10236	−	6.25177i	−0.0362452	−	0.205557i
$926$	11.0136	−	4.00861i	0.361928	−	0.131731i
$927$	−10.6420	−	3.87337i	−0.349529	−	0.127218i
$928$	5.63407	−	2.05063i	0.184947	−	0.0673153i
$929$	0.486808	−	2.76082i	0.0159716	−	0.0905797i	−0.975780	−	0.218754i	$-0.929801\pi$
$929$	0.486808	−	2.76082i	0.0159716	−	0.0905797i	0.991752	+	0.128175i	$0.0409118\pi$
$930$	9.75458			0.319865
$931$	−29.8256	+	6.43675i	−0.977496	+	0.210956i
$932$	3.96471			0.129868
$933$	1.04182	−	5.90844i	0.0341076	−	0.193434i
$934$	−1.97064	+	0.717254i	−0.0644813	+	0.0234693i
$935$	−14.5893	−	5.31006i	−0.477120	−	0.173657i
$936$	3.53347	−	1.28608i	0.115495	−	0.0420367i
$937$	−5.01315	−	28.4310i	−0.163773	−	0.928801i	−0.950321	−	0.311272i	$-0.899245\pi$
$937$	−5.01315	−	28.4310i	−0.163773	−	0.928801i	0.786548	−	0.617529i	$-0.211866\pi$
$938$	5.26701	+	12.3284i	0.171974	+	0.402538i
$939$	−12.4359	+	21.5396i	−0.405830	+	0.702918i
$940$	−6.61966	+	5.55456i	−0.215910	+	0.181170i
$941$	−1.11830	−	6.34222i	−0.0364557	−	0.206750i	0.961139	−	0.276064i	$-0.0890302\pi$
$941$	−1.11830	−	6.34222i	−0.0364557	−	0.206750i	−0.997595	+	0.0693136i	$0.977919\pi$
$942$	17.1271			0.558032
$943$	−23.8148			−0.775517
$944$	0.563405	+	3.19523i	0.0183373	+	0.103996i
$945$	−2.61858	+	0.610970i	−0.0851825	+	0.0198748i
$946$	14.4407	−	12.1172i	0.469509	−	0.393965i
$947$	−24.4468	−	20.5133i	−0.794415	−	0.666593i	0.152419	−	0.988316i	$-0.451294\pi$
$947$	−24.4468	−	20.5133i	−0.794415	−	0.666593i	−0.946834	+	0.321723i	$0.895738\pi$
$948$	5.64903	+	4.74010i	0.183472	+	0.153951i
$949$	−6.13117	−	10.6195i	−0.199026	−	0.344724i
$950$	−1.15558	+	16.1675i	−0.0374919	+	0.524542i
$951$	−4.69738			−0.152323
$952$	34.3072	+	36.6188i	1.11190	+	1.18682i
$953$	−0.277832	+	1.57567i	−0.00899988	+	0.0510408i	−0.988977	−	0.148069i	$-0.952694\pi$
$953$	−0.277832	+	1.57567i	−0.00899988	+	0.0510408i	0.979977	+	0.199110i	$0.0638052\pi$
$954$	−1.31562	−	7.46124i	−0.0425947	−	0.241566i
$955$	4.77790	−	27.0968i	0.154609	−	0.876832i
$956$	−15.0103	+	12.5952i	−0.485468	+	0.407356i
$957$	2.62474			0.0848459
$958$	10.8327	−	18.7628i	0.349988	−	0.606197i
$959$	0.531349	+	9.70648i	0.0171582	+	0.313439i
$960$	5.77341	+	2.10135i	0.186336	+	0.0678208i
$961$	−36.9247	−	63.9555i	−1.19112	−	2.06308i
$962$	−0.963861	+	1.66946i	−0.0310761	+	0.0538255i
$963$	−1.07552	+	0.902472i	−0.0346583	+	0.0290817i
$964$	21.7170	−	7.90433i	0.699457	−	0.254581i
$965$	6.02490	−	5.05549i	0.193948	−	0.162742i
$966$	13.9070	+	14.8440i	0.447451	+	0.477599i
$967$	−22.5896	+	8.22193i	−0.726432	+	0.264400i	−0.678654	−	0.734458i	$-0.737436\pi$
$967$	−22.5896	+	8.22193i	−0.726432	+	0.264400i	−0.0477782	+	0.998858i	$0.515214\pi$
$968$	−7.96732	+	13.7998i	−0.256079	+	0.443543i
$969$	−16.5729	−	22.8847i	−0.532399	−	0.735164i
$970$	1.12094	+	1.94152i	0.0359912	+	0.0623386i
$971$	−9.83309	+	55.7662i	−0.315559	+	1.78962i	0.253510	+	0.967333i	$0.418415\pi$
$971$	−9.83309	+	55.7662i	−0.315559	+	1.78962i	−0.569068	+	0.822290i	$0.692696\pi$
$972$	−0.194728	+	1.10436i	−0.00624589	+	0.0354222i
$973$	−9.22016	+	6.01819i	−0.295585	+	0.192934i
$974$	−18.9917	−	15.9360i	−0.608535	−	0.510621i
$975$	4.79103	+	1.74379i	0.153436	+	0.0558460i
$976$	3.15705	−	5.46816i	0.101055	−	0.175032i
$977$	−37.3230			−1.19407			−0.597035	−	0.802215i	$-0.703655\pi$
$977$	−37.3230			−1.19407			−0.597035	+	0.802215i	$0.703655\pi$
$978$	−6.72891	+	5.64623i	−0.215167	+	0.180546i
$979$	31.0833	+	11.3134i	0.993425	+	0.361577i
$980$	−5.51508	+	5.76448i	−0.176173	+	0.184140i
$981$	−7.49533	−	12.9823i	−0.239308	−	0.414493i
$982$	−11.7058	−	4.26055i	−0.373546	−	0.135960i
$983$	−0.0454037	+	0.257497i	−0.00144815	+	0.00821289i	−0.985523	−	0.169540i	$-0.945772\pi$
$983$	−0.0454037	+	0.257497i	−0.00144815	+	0.00821289i	0.984075	+	0.177753i	$0.0568828\pi$
$984$	7.98282	+	2.90551i	0.254483	+	0.0926242i
$985$	10.3813	+	8.71092i	0.330775	+	0.277553i
$986$	6.35920	−	2.31456i	0.202518	−	0.0737106i
$987$	19.9168	+	2.39844i	0.633958	+	0.0763431i
$988$	−4.37086	+	4.51222i	−0.139056	+	0.143553i
$989$	−34.9975	+	60.6175i	−1.11286	+	1.92752i
$990$	1.71978	+	1.44307i	0.0546582	+	0.0458637i
$991$	−33.1649	+	12.0711i	−1.05352	+	0.383450i	−0.809990	−	0.586444i	$-0.800527\pi$
$991$	−33.1649	+	12.0711i	−1.05352	+	0.383450i	−0.243529	+	0.969894i	$0.578305\pi$
$992$	−9.57186	−	54.2847i	−0.303907	−	1.72354i
$993$	−13.3228	−	11.1792i	−0.422787	−	0.354760i
$994$	−30.2206	−	15.3097i	−0.958539	−	0.485593i
$995$	−2.35686	−	4.08221i	−0.0747176	−	0.129415i
$996$	−4.36530	−	7.56092i	−0.138320	−	0.239577i
$997$	3.33753	+	18.9281i	0.105701	+	0.599459i	0.990938	+	0.134319i	$0.0428848\pi$
$997$	3.33753	+	18.9281i	0.105701	+	0.599459i	−0.885237	+	0.465140i	$0.846004\pi$
$998$	−4.31378	−	24.4647i	−0.136550	−	0.774415i
$999$	−0.800106	−	1.38583i	−0.0253142	−	0.0438456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.bq.b.100.10	yes	90
7.4	even	3		399.2.bp.b.214.10	✓	90
19.4	even	9		399.2.bp.b.289.10	yes	90
133.4	even	9	inner	399.2.bq.b.4.10	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.bp.b.214.10	✓	90	7.4	even	3
399.2.bp.b.289.10	yes	90	19.4	even	9
399.2.bq.b.4.10	yes	90	133.4	even	9	inner
399.2.bq.b.100.10	yes	90	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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.162768 - 0.923101i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(1.05376 + 0.383539i) q^{4} +(0.955023 - 0.347600i) q^{5} +(0.162768 + 0.923101i) q^{6} +(1.03944 + 2.43301i) q^{7} +(1.46290 - 2.53382i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-0.165423 - 0.938160i) q^{10} -2.35664 q^{11} -1.12139 q^{12} +(0.223172 + 1.26567i) q^{13} +(2.41510 - 0.563494i) q^{14} +(-0.778542 + 0.653274i) q^{15} +(-0.382790 - 0.321199i) q^{16} +(4.96569 + 4.16671i) q^{17} +(-0.468670 - 0.811761i) q^{18} +(3.60993 + 2.44303i) q^{19} +1.13969 q^{20} +(-1.80890 - 1.93078i) q^{21} +(-0.383585 + 2.17542i) q^{22} +(-1.42427 - 8.07745i) q^{23} +(-0.508061 + 2.88136i) q^{24} +(-3.03898 + 2.55001i) q^{25} +1.20467 q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.162172 + 2.96249i) q^{28} +(1.04660 + 0.380930i) q^{29} +(0.476316 + 0.825004i) q^{30} +(5.11980 - 8.86776i) q^{31} +(4.12379 - 3.46027i) q^{32} +(2.21452 - 0.806019i) q^{33} +(4.65455 - 3.90563i) q^{34} +(1.83841 + 1.96227i) q^{35} +(1.05376 - 0.383539i) q^{36} +(-0.800106 + 1.38583i) q^{37} +(2.84274 - 2.93468i) q^{38} +(-0.642598 - 1.11301i) q^{39} +(0.516350 - 2.92837i) q^{40} +(0.504190 - 2.85941i) q^{41} +(-2.07673 + 1.35553i) q^{42} +(-6.53730 - 5.48544i) q^{43} +(-2.48334 - 0.903863i) q^{44} +(0.508157 - 0.880154i) q^{45} -7.68813 q^{46} +(-5.80832 + 4.87376i) q^{47} +(0.469561 + 0.170906i) q^{48} +(-4.83912 + 5.05796i) q^{49} +(1.85927 + 3.22034i) q^{50} +(-6.09133 - 2.21706i) q^{51} +(-0.250263 + 1.41931i) q^{52} +(7.59535 + 2.76448i) q^{53} +(0.718045 + 0.602511i) q^{54} +(-2.25065 + 0.819168i) q^{55} +(7.68544 + 0.925503i) q^{56} +(-4.22779 - 1.06103i) q^{57} +(0.521989 - 0.904111i) q^{58} +(-4.97391 - 4.17361i) q^{59} +(-1.07095 + 0.389796i) q^{60} +(2.19419 + 12.4439i) q^{61} +(-7.35249 - 6.16948i) q^{62} +(2.36017 + 1.19566i) q^{63} +(-3.02266 - 5.23540i) q^{64} +(0.653081 + 1.13117i) q^{65} +(-0.383585 - 2.17542i) q^{66} +(0.938720 + 5.32375i) q^{67} +(3.63457 + 6.29527i) q^{68} +(4.10103 + 7.10319i) q^{69} +(2.11061 - 1.37764i) q^{70} +(-10.4644 - 8.78070i) q^{71} +(-0.508061 - 2.88136i) q^{72} +(-8.96582 + 3.26329i) q^{73} +(1.14902 + 0.964146i) q^{74} +(1.98355 - 3.43561i) q^{75} +(2.86702 + 3.95893i) q^{76} +(-2.44959 - 5.73375i) q^{77} +(-1.13202 + 0.412020i) q^{78} +(-5.03752 - 4.22698i) q^{79} +(-0.477222 - 0.173694i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-2.55745 - 0.930837i) q^{82} +(3.89275 + 6.74244i) q^{83} +(-1.16562 - 2.72836i) q^{84} +(6.19070 + 2.25323i) q^{85} +(-6.12768 + 5.14173i) q^{86} -1.11376 q^{87} +(-3.44754 + 5.97132i) q^{88} +(-13.1896 - 4.80064i) q^{89} +(-0.729759 - 0.612340i) q^{90} +(-2.84742 + 1.85857i) q^{91} +(1.59717 - 9.05799i) q^{92} +(-1.77809 + 10.0840i) q^{93} +(3.55356 + 6.15495i) q^{94} +(4.29676 + 1.07834i) q^{95} +(-2.69162 + 4.66201i) q^{96} +(-2.21143 + 0.804893i) q^{97} +(3.88135 + 5.29027i) q^{98} +(-1.80529 + 1.51482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 6 q^{7} - 6 q^{10} + 18 q^{11} + 108 q^{12} - 9 q^{13} - 3 q^{14} - 12 q^{17} - 30 q^{19} - 60 q^{20} - 9 q^{21} + 18 q^{23} + 9 q^{24} + 6 q^{25} + 12 q^{26} - 45 q^{27} - 45 q^{28} - 18 q^{29}+ \cdots + 6 q^{99}+O(q^{100}) \) 90 * q + 6 * q^7 - 6 * q^10 + 18 * q^11 + 108 * q^12 - 9 * q^13 - 3 * q^14 - 12 * q^17 - 30 * q^19 - 60 * q^20 - 9 * q^21 + 18 * q^23 + 9 * q^24 + 6 * q^25 + 12 * q^26 - 45 * q^27 - 45 * q^28 - 18 * q^29 - 12 * q^30 - 18 * q^31 - 21 * q^32 - 12 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 + 39 * q^38 - 12 * q^39 + 18 * q^40 + 27 * q^41 - 3 * q^42 - 39 * q^43 - 78 * q^44 + 3 * q^45 + 18 * q^46 + 24 * q^47 - 6 * q^49 - 9 * q^50 + 6 * q^51 - 48 * q^52 + 27 * q^53 - 42 * q^55 + 39 * q^56 - 6 * q^57 - 18 * q^58 - 60 * q^59 - 18 * q^60 - 12 * q^61 + 93 * q^62 - 12 * q^63 - 108 * q^64 - 33 * q^65 - 42 * q^67 + 18 * q^68 - 12 * q^69 + 6 * q^70 - 18 * q^71 + 9 * q^72 + 51 * q^73 + 114 * q^74 - 72 * q^75 + 24 * q^76 - 39 * q^77 + 9 * q^78 + 87 * q^79 + 42 * q^80 + 12 * q^82 + 24 * q^83 + 3 * q^84 + 36 * q^85 - 69 * q^86 - 36 * q^88 - 48 * q^89 + 3 * q^90 + 6 * q^91 - 18 * q^92 - 21 * q^93 - 54 * q^94 + 36 * q^95 + 21 * q^97 - 75 * q^98 + 6 * q^99

Introduction

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