LMFDB - Embedded newform 105.2.j.a.8.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,2,Mod(8,105)] 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("105.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.j (of order $4$, degree $2$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.11
Character	$\chi$	$=$	105.8
Dual form			105.2.j.a.92.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.54414 + 1.54414i) q^{2} +(-1.73204 - 0.00622252i) q^{3} +2.76875i q^{4} +(-0.252500 + 2.22177i) q^{5} +(-2.66491 - 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.18705 + 1.18705i) q^{8} +(2.99992 + 0.0215553i) q^{9} +(-3.82062 + 3.04083i) q^{10} -3.38507i q^{11} +(0.0172286 - 4.79558i) q^{12} +(-0.206632 - 0.206632i) q^{13} +2.18375 q^{14} +(0.451165 - 3.84662i) q^{15} +1.87154 q^{16} +(0.167409 + 0.167409i) q^{17} +(4.59902 + 4.66559i) q^{18} -5.31419i q^{19} +(-6.15151 - 0.699108i) q^{20} +(-1.22914 + 1.22034i) q^{21} +(5.22702 - 5.22702i) q^{22} +(-5.07773 + 5.07773i) q^{23} +(2.06341 - 2.04864i) q^{24} +(-4.87249 - 1.12199i) q^{25} -0.638138i q^{26} +(-5.19585 - 0.0560017i) q^{27} +(1.95780 + 1.95780i) q^{28} -2.84268 q^{29} +(6.63638 - 5.24306i) q^{30} +9.11776 q^{31} +(5.26402 + 5.26402i) q^{32} +(-0.0210636 + 5.86307i) q^{33} +0.517005i q^{34} +(1.39248 + 1.74957i) q^{35} +(-0.0596812 + 8.30602i) q^{36} +(-5.27013 + 5.27013i) q^{37} +(8.20586 - 8.20586i) q^{38} +(0.356609 + 0.359180i) q^{39} +(-2.33762 - 2.93708i) q^{40} -0.0314968i q^{41} +(-3.78233 - 0.0135884i) q^{42} +(-3.76875 - 3.76875i) q^{43} +9.37239 q^{44} +(-0.805371 + 6.65968i) q^{45} -15.6815 q^{46} +(-3.56639 - 3.56639i) q^{47} +(-3.24158 - 0.0116457i) q^{48} -1.00000i q^{49} +(-5.79130 - 9.25632i) q^{50} +(-0.288917 - 0.291000i) q^{51} +(0.572111 - 0.572111i) q^{52} +(3.55291 - 3.55291i) q^{53} +(-7.93665 - 8.10960i) q^{54} +(7.52082 + 0.854729i) q^{55} +1.67875i q^{56} +(-0.0330677 + 9.20439i) q^{57} +(-4.38949 - 4.38949i) q^{58} -10.3168 q^{59} +(10.6503 + 1.24916i) q^{60} -6.80634 q^{61} +(14.0791 + 14.0791i) q^{62} +(2.13651 - 2.10602i) q^{63} +12.5137i q^{64} +(0.511262 - 0.406913i) q^{65} +(-9.08593 + 9.02088i) q^{66} +(6.34806 - 6.34806i) q^{67} +(-0.463512 + 0.463512i) q^{68} +(8.82642 - 8.76323i) q^{69} +(-0.551396 + 4.85177i) q^{70} -3.95454i q^{71} +(-3.58665 + 3.53548i) q^{72} +(8.61099 + 8.61099i) q^{73} -16.2757 q^{74} +(8.43236 + 1.97365i) q^{75} +14.7136 q^{76} +(-2.39360 - 2.39360i) q^{77} +(-0.00397083 + 1.10528i) q^{78} +11.4449i q^{79} +(-0.472563 + 4.15812i) q^{80} +(8.99907 + 0.129328i) q^{81} +(0.0486356 - 0.0486356i) q^{82} +(3.88059 - 3.88059i) q^{83} +(-3.37880 - 3.40317i) q^{84} +(-0.414214 + 0.329672i) q^{85} -11.6390i q^{86} +(4.92363 + 0.0176886i) q^{87} +(4.01825 + 4.01825i) q^{88} +2.00190 q^{89} +(-11.5271 + 9.03989i) q^{90} -0.292222 q^{91} +(-14.0589 - 14.0589i) q^{92} +(-15.7923 - 0.0567354i) q^{93} -11.0140i q^{94} +(11.8069 + 1.34183i) q^{95} +(-9.08474 - 9.15025i) q^{96} +(2.26760 - 2.26760i) q^{97} +(1.54414 - 1.54414i) q^{98} +(0.0729661 - 10.1549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.54414	+	1.54414i	1.09187	+	1.09187i	0.995329	+	0.0965442i	$0.0307789\pi$
$2$	1.54414	+	1.54414i	1.09187	+	1.09187i	0.0965442	+	0.995329i	$0.469221\pi$
$3$	−1.73204	−	0.00622252i	−0.999994	−	0.00359257i
$3$	−1.73204	−	0.00622252i	−0.999994	−	0.00359257i
$4$			2.76875i			1.38437i
$5$	−0.252500	+	2.22177i	−0.112921	+	0.993604i
$5$	−0.252500	+	2.22177i	−0.112921	+	0.993604i
$6$	−2.66491	−	2.68412i	−1.08794	−	1.09579i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−1.18705	+	1.18705i	−0.419686	+	0.419686i
$9$	2.99992	+	0.0215553i	0.999974	+	0.00718510i
$10$	−3.82062	+	3.04083i	−1.20819	+	0.961593i
$11$		−	3.38507i		−	1.02064i	−0.859986	−	0.510318i	$-0.829528\pi$
$11$		−	3.38507i		−	1.02064i	0.859986	−	0.510318i	$-0.170472\pi$
$12$	0.0172286	−	4.79558i	0.00497346	−	1.38436i
$13$	−0.206632	−	0.206632i	−0.0573094	−	0.0573094i	0.677871	−	0.735181i	$-0.262903\pi$
$13$	−0.206632	−	0.206632i	−0.0573094	−	0.0573094i	−0.735181	+	0.677871i	$0.762903\pi$
$14$	2.18375			0.583631
$15$	0.451165	−	3.84662i	0.116490	−	0.993192i
$16$	1.87154			0.467884
$17$	0.167409	+	0.167409i	0.0406026	+	0.0406026i	0.727117	−	0.686514i	$-0.240860\pi$
$17$	0.167409	+	0.167409i	0.0406026	+	0.0406026i	−0.686514	+	0.727117i	$0.740860\pi$
$18$	4.59902	+	4.66559i	1.08400	+	1.09969i
$19$		−	5.31419i		−	1.21916i	−0.792725	−	0.609579i	$-0.791338\pi$
$19$		−	5.31419i		−	1.21916i	0.792725	−	0.609579i	$-0.208662\pi$
$20$	−6.15151	−	0.699108i	−1.37552	−	0.156325i
$21$	−1.22914	+	1.22034i	−0.268220	+	0.266299i
$22$	5.22702	−	5.22702i	1.11440	−	1.11440i
$23$	−5.07773	+	5.07773i	−1.05878	+	1.05878i	−0.0606179	+	0.998161i	$0.519307\pi$
$23$	−5.07773	+	5.07773i	−1.05878	+	1.05878i	−0.998161	+	0.0606179i	$0.980693\pi$
$24$	2.06341	−	2.04864i	0.421191	−	0.418176i
$25$	−4.87249	−	1.12199i	−0.974497	−	0.224398i
$26$		−	0.638138i		−	0.125149i
$27$	−5.19585	−	0.0560017i	−0.999942	−	0.0107775i
$28$	1.95780	+	1.95780i	0.369989	+	0.369989i
$29$	−2.84268			−0.527872			−0.263936	−	0.964540i	$-0.585021\pi$
$29$	−2.84268			−0.527872			−0.263936	+	0.964540i	$0.585021\pi$
$30$	6.63638	−	5.24306i	1.21163	−	0.957247i
$31$	9.11776			1.63760			0.818799	−	0.574081i	$-0.194640\pi$
$31$	9.11776			1.63760			0.818799	+	0.574081i	$0.194640\pi$
$32$	5.26402	+	5.26402i	0.930557	+	0.930557i
$33$	−0.0210636	+	5.86307i	−0.00366671	+	1.02063i
$34$			0.517005i			0.0886657i
$35$	1.39248	+	1.74957i	0.235372	+	0.295731i
$36$	−0.0596812	+	8.30602i	−0.00994686	+	1.38434i
$37$	−5.27013	+	5.27013i	−0.866404	+	0.866404i	−0.992072	−	0.125668i	$-0.959893\pi$
$37$	−5.27013	+	5.27013i	−0.866404	+	0.866404i	0.125668	+	0.992072i	$0.459893\pi$
$38$	8.20586	−	8.20586i	1.33117	−	1.33117i
$39$	0.356609	+	0.359180i	0.0571031	+	0.0575149i
$40$	−2.33762	−	2.93708i	−0.369611	−	0.464394i
$41$		−	0.0314968i		−	0.00491898i	−0.999997	−	0.00245949i	$-0.999217\pi$
$41$		−	0.0314968i		−	0.00491898i	0.999997	−	0.00245949i	$-0.000782881\pi$
$42$	−3.78233	−	0.0135884i	−0.583627	−	0.00209674i
$43$	−3.76875	−	3.76875i	−0.574728	−	0.574728i	0.358718	−	0.933446i	$-0.383214\pi$
$43$	−3.76875	−	3.76875i	−0.574728	−	0.574728i	−0.933446	+	0.358718i	$0.883214\pi$
$44$	9.37239			1.41294
$45$	−0.805371	+	6.65968i	−0.120058	+	0.992767i
$46$	−15.6815			−2.31210
$47$	−3.56639	−	3.56639i	−0.520211	−	0.520211i	0.397424	−	0.917635i	$-0.369904\pi$
$47$	−3.56639	−	3.56639i	−0.520211	−	0.520211i	−0.917635	+	0.397424i	$0.869904\pi$
$48$	−3.24158	−	0.0116457i	−0.467881	−	0.00168091i
$49$		−	1.00000i		−	0.142857i
$50$	−5.79130	−	9.25632i	−0.819013	−	1.30904i
$51$	−0.288917	−	0.291000i	−0.0404564	−	0.0407482i
$52$	0.572111	−	0.572111i	0.0793376	−	0.0793376i
$53$	3.55291	−	3.55291i	0.488030	−	0.488030i	−0.419654	−	0.907684i	$-0.637849\pi$
$53$	3.55291	−	3.55291i	0.488030	−	0.488030i	0.907684	+	0.419654i	$0.137849\pi$
$54$	−7.93665	−	8.10960i	−1.08004	−	1.10358i
$55$	7.52082	+	0.854729i	1.01411	+	0.115252i
$56$			1.67875i			0.224332i
$57$	−0.0330677	+	9.20439i	−0.00437992	+	1.21915i
$58$	−4.38949	−	4.38949i	−0.576369	−	0.576369i
$59$	−10.3168			−1.34313			−0.671565	−	0.740946i	$-0.734378\pi$
$59$	−10.3168			−1.34313			−0.671565	+	0.740946i	$0.734378\pi$
$60$	10.6503	+	1.24916i	1.37495	+	0.161266i
$61$	−6.80634			−0.871462			−0.435731	−	0.900077i	$-0.643510\pi$
$61$	−6.80634			−0.871462			−0.435731	+	0.900077i	$0.643510\pi$
$62$	14.0791	+	14.0791i	1.78805	+	1.78805i
$63$	2.13651	−	2.10602i	0.269175	−	0.265334i
$64$			12.5137i			1.56422i
$65$	0.511262	−	0.406913i	0.0634143	−	0.0504714i
$66$	−9.08593	+	9.02088i	−1.11840	+	1.11039i
$67$	6.34806	−	6.34806i	0.775539	−	0.775539i	−0.203530	−	0.979069i	$-0.565241\pi$
$67$	6.34806	−	6.34806i	0.775539	−	0.775539i	0.979069	+	0.203530i	$0.0652413\pi$
$68$	−0.463512	+	0.463512i	−0.0562091	+	0.0562091i
$69$	8.82642	−	8.76323i	1.06258	−	1.05497i
$70$	−0.551396	+	4.85177i	−0.0659044	+	0.579898i
$71$		−	3.95454i		−	0.469318i	−0.972078	−	0.234659i	$-0.924603\pi$
$71$		−	3.95454i		−	0.469318i	0.972078	−	0.234659i	$-0.0753973\pi$
$72$	−3.58665	+	3.53548i	−0.422691	+	0.416660i
$73$	8.61099	+	8.61099i	1.00784	+	1.00784i	0.999969	+	0.00787086i	$0.00250540\pi$
$73$	8.61099	+	8.61099i	1.00784	+	1.00784i	0.00787086	+	0.999969i	$0.497495\pi$
$74$	−16.2757			−1.89201
$75$	8.43236	+	1.97365i	0.973685	+	0.227898i
$76$	14.7136			1.68777
$77$	−2.39360	−	2.39360i	−0.272776	−	0.272776i
$78$	−0.00397083	+	1.10528i	−0.000449608	+	0.125148i
$79$			11.4449i			1.28766i	0.765170	+	0.643828i	$0.222655\pi$
$79$			11.4449i			1.28766i	−0.765170	+	0.643828i	$0.777345\pi$
$80$	−0.472563	+	4.15812i	−0.0528342	+	0.464892i
$81$	8.99907	+	0.129328i	0.999897	+	0.0143698i
$82$	0.0486356	−	0.0486356i	0.00537090	−	0.00537090i
$83$	3.88059	−	3.88059i	0.425951	−	0.425951i	−0.461296	−	0.887246i	$-0.652615\pi$
$83$	3.88059	−	3.88059i	0.425951	−	0.425951i	0.887246	+	0.461296i	$0.152615\pi$
$84$	−3.37880	−	3.40317i	−0.368658	−	0.371316i
$85$	−0.414214	+	0.329672i	−0.0449278	+	0.0357580i
$86$		−	11.6390i		−	1.25506i
$87$	4.92363	+	0.0176886i	0.527868	+	0.00189642i
$88$	4.01825	+	4.01825i	0.428347	+	0.428347i
$89$	2.00190			0.212201			0.106100	−	0.994355i	$-0.466164\pi$
$89$	2.00190			0.212201			0.106100	+	0.994355i	$0.466164\pi$
$90$	−11.5271	+	9.03989i	−1.21506	+	0.952888i
$91$	−0.292222			−0.0306332
$92$	−14.0589	−	14.0589i	−1.46574	−	1.46574i
$93$	−15.7923	−	0.0567354i	−1.63759	−	0.00588319i
$94$		−	11.0140i		−	1.13601i
$95$	11.8069	+	1.34183i	1.21136	+	0.137669i
$96$	−9.08474	−	9.15025i	−0.927208	−	0.933894i
$97$	2.26760	−	2.26760i	0.230240	−	0.230240i	−0.582553	−	0.812793i	$-0.697946\pi$
$97$	2.26760	−	2.26760i	0.230240	−	0.230240i	0.812793	+	0.582553i	$0.197946\pi$
$98$	1.54414	−	1.54414i	0.155982	−	0.155982i
$99$	0.0729661	−	10.1549i	0.00733337	−	1.02061i
$100$	3.10651	−	13.4907i	0.310651	−	1.34907i
$101$			8.63630i			0.859344i	0.902985	+	0.429672i	$0.141371\pi$
$101$			8.63630i			0.859344i	−0.902985	+	0.429672i	$0.858629\pi$
$102$	0.00321708	−	0.895474i	0.000318538	−	0.0886651i
$103$	0.964332	+	0.964332i	0.0950185	+	0.0950185i	0.753018	−	0.658000i	$-0.228597\pi$
$103$	0.964332	+	0.964332i	0.0950185	+	0.0950185i	−0.658000	+	0.753018i	$0.728597\pi$
$104$	0.490566			0.0481039
$105$	−2.40095	−	3.03899i	−0.234308	−	0.296575i
$106$	10.9724			1.06573
$107$	−2.95847	−	2.95847i	−0.286007	−	0.286007i	0.549492	−	0.835499i	$-0.314821\pi$
$107$	−2.95847	−	2.95847i	−0.286007	−	0.286007i	−0.835499	+	0.549492i	$0.814821\pi$
$108$	0.155055	−	14.3860i	0.0149201	−	1.38429i
$109$			2.82182i			0.270281i	0.990826	+	0.135141i	$0.0431486\pi$
$109$			2.82182i			0.270281i	−0.990826	+	0.135141i	$0.956851\pi$
$110$	10.2934	+	12.9330i	0.981436	+	1.23312i
$111$	9.16087	−	9.09528i	0.869511	−	0.863286i
$112$	1.32338	−	1.32338i	0.125047	−	0.125047i
$113$	2.01798	−	2.01798i	0.189835	−	0.189835i	−0.605790	−	0.795625i	$-0.707143\pi$
$113$	2.01798	−	2.01798i	0.189835	−	0.189835i	0.795625	+	0.605790i	$0.207143\pi$
$114$	−14.2639	+	14.1618i	−1.33594	+	1.32638i
$115$	−9.99939	−	12.5636i	−0.932448	−	1.17157i
$116$		−	7.87065i		−	0.730771i
$117$	−0.615426	−	0.624334i	−0.0568961	−	0.0577197i
$118$	−15.9306	−	15.9306i	−1.46653	−	1.46653i
$119$	0.236752			0.0217030
$120$	4.03058	+	5.10169i	0.367940	+	0.465719i
$121$	−0.458667			−0.0416970
$122$	−10.5099	−	10.5099i	−0.951526	−	0.951526i
$123$	−0.000195990		0.0545538i	−1.76718e−5		0.00491895i
$124$			25.2448i			2.26705i
$125$	3.72311	−	10.5422i	0.333005	−	0.942925i
$126$	6.55107	+	0.0470713i	0.583616	+	0.00419345i
$127$	−11.6271	+	11.6271i	−1.03174	+	1.03174i	−0.0322583	+	0.999480i	$0.510270\pi$
$127$	−11.6271	+	11.6271i	−1.03174	+	1.03174i	−0.999480	+	0.0322583i	$0.989730\pi$
$128$	−8.79491	+	8.79491i	−0.777367	+	0.777367i
$129$	6.50417	+	6.55107i	0.572660	+	0.576789i
$130$	1.41779	+	0.161130i	0.124349	+	0.0141320i
$131$			12.7013i			1.10972i	0.831943	+	0.554861i	$0.187228\pi$
$131$			12.7013i			1.10972i	−0.831943	+	0.554861i	$0.812772\pi$
$132$	−16.2333	−	0.0583199i	−1.41293	−	0.00507609i
$133$	−3.75770	−	3.75770i	−0.325834	−	0.325834i
$134$	19.6046			1.69358
$135$	1.43638	−	11.5298i	0.123623	−	0.992329i
$136$	−0.397446			−0.0340807
$137$	−5.19451	−	5.19451i	−0.443797	−	0.443797i	0.449489	−	0.893286i	$-0.351606\pi$
$137$	−5.19451	−	5.19451i	−0.443797	−	0.443797i	−0.893286	+	0.449489i	$0.851606\pi$
$138$	27.1609	+	0.0975782i	2.31209	+	0.00830641i
$139$			12.3138i			1.04444i	0.852810	+	0.522221i	$0.174897\pi$
$139$			12.3138i			1.04444i	−0.852810	+	0.522221i	$0.825103\pi$
$140$	−4.84412	+	3.85543i	−0.409402	+	0.325843i
$141$	6.15493	+	6.19932i	0.518339	+	0.522077i
$142$	6.10637	−	6.10637i	0.512435	−	0.512435i
$143$	−0.699463	+	0.699463i	−0.0584920	+	0.0584920i
$144$	5.61447	+	0.0403416i	0.467872	+	0.00336180i
$145$	0.717776	−	6.31576i	0.0596080	−	0.524495i
$146$			26.5932i			2.20087i
$147$	−0.00622252	+	1.73204i	−0.000513225	+	0.142856i
$148$	−14.5917	−	14.5917i	−1.19943	−	1.19943i
$149$	18.9350			1.55121			0.775607	−	0.631216i	$-0.217444\pi$
$149$	18.9350			1.55121			0.775607	+	0.631216i	$0.217444\pi$
$150$	9.97316	+	16.0684i	0.814305	+	1.31198i
$151$	−1.90527			−0.155049			−0.0775243	−	0.996990i	$-0.524702\pi$
$151$	−1.90527			−0.155049			−0.0775243	+	0.996990i	$0.524702\pi$
$152$	6.30822	+	6.30822i	0.511665	+	0.511665i
$153$	0.498604	+	0.505822i	0.0403098	+	0.0408933i
$154$		−	7.39212i		−	0.595674i
$155$	−2.30223	+	20.2575i	−0.184920	+	1.62712i
$156$	−0.994479	+	0.987359i	−0.0796221	+	0.0790520i
$157$	−4.31728	+	4.31728i	−0.344557	+	0.344557i	−0.858077	−	0.513521i	$-0.828341\pi$
$157$	−4.31728	+	4.31728i	−0.344557	+	0.344557i	0.513521	+	0.858077i	$0.328341\pi$
$158$	−17.6726	+	17.6726i	−1.40596	+	1.40596i
$159$	−6.17589	+	6.13167i	−0.489780	+	0.486273i
$160$	−13.0246	+	10.3663i	−1.02968	+	0.819525i
$161$			7.18099i			0.565941i
$162$	13.6961	+	14.0955i	1.07607	+	1.10745i
$163$	3.57655	+	3.57655i	0.280137	+	0.280137i	0.833164	−	0.553027i	$-0.186527\pi$
$163$	3.57655	+	3.57655i	0.280137	+	0.280137i	−0.553027	+	0.833164i	$0.686527\pi$
$164$	0.0872068			0.00680970
$165$	−13.0210	−	1.52722i	−1.01369	−	0.118894i
$166$	11.9844			0.930168
$167$	−6.39241	−	6.39241i	−0.494659	−	0.494659i	0.415111	−	0.909771i	$-0.363743\pi$
$167$	−6.39241	−	6.39241i	−0.494659	−	0.494659i	−0.909771	+	0.415111i	$0.863743\pi$
$168$	0.0104460	−	2.90765i	0.000805929	−	0.224330i
$169$		−	12.9146i		−	0.993431i
$170$	−1.14866	−	0.130544i	−0.0880986	−	0.0100123i
$171$	0.114549	−	15.9422i	0.00875978	−	1.21913i
$172$	10.4347	−	10.4347i	0.795638	−	0.795638i
$173$	3.88791	−	3.88791i	0.295592	−	0.295592i	−0.543692	−	0.839285i	$-0.682974\pi$
$173$	3.88791	−	3.88791i	0.295592	−	0.295592i	0.839285	+	0.543692i	$0.182974\pi$
$174$	7.57546	+	7.63009i	0.574294	+	0.578436i
$175$	−4.23874	+	2.65200i	−0.320418	+	0.200472i
$176$		−	6.33528i		−	0.477540i
$177$	17.8691	+	0.0641964i	1.34312	+	0.00482529i
$178$	3.09121	+	3.09121i	0.231696	+	0.231696i
$179$	−14.6322			−1.09366			−0.546832	−	0.837242i	$-0.684166\pi$
$179$	−14.6322			−1.09366			−0.546832	+	0.837242i	$0.684166\pi$
$180$	−18.4390	−	2.22987i	−1.37436	−	0.166205i
$181$	−9.83718			−0.731192			−0.365596	−	0.930774i	$-0.619135\pi$
$181$	−9.83718			−0.731192			−0.365596	+	0.930774i	$0.619135\pi$
$182$	−0.451232	−	0.451232i	−0.0334475	−	0.0334475i
$183$	11.7888	+	0.0423526i	0.871456	+	0.00313079i
$184$		−	12.0551i		−	0.888710i
$185$	−10.3783	−	13.0397i	−0.763027	−	0.958698i
$186$	−24.2980	−	24.4732i	−1.78161	−	1.79446i
$187$	0.566689	−	0.566689i	0.0414404	−	0.0414404i
$188$	9.87442	−	9.87442i	0.720166	−	0.720166i
$189$	−3.71362	+	3.63442i	−0.270126	+	0.264365i
$190$	16.1595	+	20.3035i	1.17234	+	1.47297i
$191$			6.37886i			0.461558i	0.973006	+	0.230779i	$0.0741275\pi$
$191$			6.37886i			0.461558i	−0.973006	+	0.230779i	$0.925873\pi$
$192$	0.0778669	−	21.6743i	0.00561956	−	1.56421i
$193$	7.56336	+	7.56336i	0.544422	+	0.544422i	0.924822	−	0.380400i	$-0.124214\pi$
$193$	7.56336	+	7.56336i	0.544422	+	0.544422i	−0.380400	+	0.924822i	$0.624214\pi$
$194$	7.00299			0.502785
$195$	−0.888059	+	0.701608i	−0.0635952	+	0.0502432i
$196$	2.76875			0.197768
$197$	−1.01490	−	1.01490i	−0.0723090	−	0.0723090i	0.670027	−	0.742336i	$-0.266282\pi$
$197$	−1.01490	−	1.01490i	−0.0723090	−	0.0723090i	−0.742336	+	0.670027i	$0.766282\pi$
$198$	15.7933	−	15.5680i	1.12238	−	1.10637i
$199$		−	9.40041i		−	0.666378i	−0.942860	−	0.333189i	$-0.891875\pi$
$199$		−	9.40041i		−	0.666378i	0.942860	−	0.333189i	$-0.108125\pi$
$200$	7.11576	−	4.45204i	0.503160	−	0.314806i
$201$	−11.0346	+	10.9556i	−0.778320	+	0.772748i
$202$	−13.3357	+	13.3357i	−0.938295	+	0.938295i
$203$	−2.01007	+	2.01007i	−0.141080	+	0.141080i
$204$	0.805705	−	0.799937i	0.0564107	−	0.0560068i
$205$	0.0699786	+	0.00795295i	0.00488752	+	0.000555458i
$206$			2.97813i			0.207496i
$207$	−15.3422	+	15.1233i	−1.06636	+	1.05114i
$208$	−0.386719	−	0.386719i	−0.0268142	−	0.0268142i
$209$	−17.9889			−1.24432
$210$	0.985230	−	8.40003i	0.0679873	−	0.579657i
$211$	−8.29157			−0.570815			−0.285407	−	0.958406i	$-0.592129\pi$
$211$	−8.29157			−0.570815			−0.285407	+	0.958406i	$0.592129\pi$
$212$	9.83710	+	9.83710i	0.675615	+	0.675615i
$213$	−0.0246072	+	6.84942i	−0.00168606	+	0.469315i
$214$		−	9.13661i		−	0.624566i
$215$	9.32488	−	7.42166i	0.635952	−	0.506153i
$216$	6.23422	−	6.10127i	0.424185	−	0.415139i
$217$	6.44723	−	6.44723i	0.437666	−	0.437666i
$218$	−4.35729	+	4.35729i	−0.295113	+	0.295113i
$219$	−14.8610	−	14.9682i	−1.00421	−	1.01145i
$220$	−2.36653	+	20.8232i	−0.159551	+	1.40390i
$221$		−	0.0691839i		−	0.00465382i
$222$	28.1901	+	0.101276i	1.89199	+	0.00679717i
$223$	3.86020	+	3.86020i	0.258498	+	0.258498i	0.824443	−	0.565945i	$-0.191489\pi$
$223$	3.86020	+	3.86020i	0.258498	+	0.258498i	−0.565945	+	0.824443i	$0.691489\pi$
$224$	7.44445			0.497404
$225$	−14.5929	−	3.47092i	−0.972860	−	0.231394i
$226$	6.23208			0.414552
$227$	1.50739	+	1.50739i	0.100049	+	0.100049i	0.755360	−	0.655310i	$-0.227462\pi$
$227$	1.50739	+	1.50739i	0.100049	+	0.100049i	−0.655310	+	0.755360i	$0.727462\pi$
$228$	−25.4846	−	0.0915560i	−1.68776	−	0.00606344i
$229$			6.26009i			0.413678i	0.978375	+	0.206839i	$0.0663177\pi$
$229$			6.26009i			0.413678i	−0.978375	+	0.206839i	$0.933682\pi$
$230$	3.95957	−	34.8405i	0.261086	−	2.29732i
$231$	4.13092	+	4.16071i	0.271795	+	0.273755i
$232$	3.37440	−	3.37440i	0.221541	−	0.221541i
$233$	−2.67422	+	2.67422i	−0.175194	+	0.175194i	−0.789257	−	0.614063i	$-0.789534\pi$
$233$	−2.67422	+	2.67422i	−0.175194	+	0.175194i	0.614063	+	0.789257i	$0.289534\pi$
$234$	0.0137553	−	1.91436i	0.000899209	−	0.125146i
$235$	8.82419	−	7.02317i	0.575627	−	0.458141i
$236$		−	28.5645i		−	1.85939i
$237$	0.0712164	−	19.8231i	0.00462600	−	1.28765i
$238$	0.365578	+	0.365578i	0.0236969	+	0.0236969i
$239$	2.08521			0.134881			0.0674406	−	0.997723i	$-0.478517\pi$
$239$	2.08521			0.134881			0.0674406	+	0.997723i	$0.478517\pi$
$240$	0.844372	−	7.19909i	0.0545040	−	0.464699i
$241$	−5.43686			−0.350219			−0.175110	−	0.984549i	$-0.556028\pi$
$241$	−5.43686			−0.350219			−0.175110	+	0.984549i	$0.556028\pi$
$242$	−0.708247	−	0.708247i	−0.0455279	−	0.0455279i
$243$	−15.5859	−	0.279999i	−0.999839	−	0.0179619i
$244$		−	18.8450i		−	1.20643i
$245$	2.22177	+	0.252500i	0.141943	+	0.0161316i
$246$	−0.0845414	+	0.0839361i	−0.00539016	+	0.00535157i
$247$	−1.09808	+	1.09808i	−0.0698692	+	0.0698692i
$248$	−10.8233	+	10.8233i	−0.687278	+	0.687278i
$249$	−6.74549	+	6.69720i	−0.427478	+	0.424418i
$250$	22.0277	−	10.5297i	1.39315	−	0.665956i
$251$			23.3428i			1.47339i	0.676227	+	0.736693i	$0.263614\pi$
$251$			23.3428i			1.47339i	−0.676227	+	0.736693i	$0.736386\pi$
$252$	5.83104	+	5.91545i	0.367321	+	0.372638i
$253$	17.1884	+	17.1884i	1.08063	+	1.08063i
$254$	−35.9078			−2.25305
$255$	0.719486	−	0.568428i	0.0450559	−	0.0355963i
$256$	−2.13372			−0.133358
$257$	10.9273	+	10.9273i	0.681627	+	0.681627i	0.960367	−	0.278740i	$-0.0899167\pi$
$257$	10.9273	+	10.9273i	0.681627	+	0.681627i	−0.278740	+	0.960367i	$0.589917\pi$
$258$	−0.0724236	+	20.1591i	−0.00450890	+	1.25505i
$259$			7.45309i			0.463112i
$260$	1.12664	+	1.41556i	0.0698712	+	0.0877890i
$261$	−8.52781	−	0.0612747i	−0.527858	−	0.00379281i
$262$	−19.6127	+	19.6127i	−1.21167	+	1.21167i
$263$	18.1808	−	18.1808i	1.12108	−	1.12108i	0.129497	−	0.991580i	$-0.458664\pi$
$263$	18.1808	−	18.1808i	1.12108	−	1.12108i	0.991580	−	0.129497i	$-0.0413364\pi$
$264$	−6.93477	−	6.98477i	−0.426805	−	0.429883i
$265$	6.99662	+	8.79084i	0.429799	+	0.540017i
$266$		−	11.6048i		−	0.711539i
$267$	−3.46737	−	0.0124569i	−0.212199	−	0.000762347i
$268$	17.5762	+	17.5762i	1.07364	+	1.07364i
$269$	28.5125			1.73844			0.869219	−	0.494428i	$-0.164622\pi$
$269$	28.5125			1.73844			0.869219	+	0.494428i	$0.164622\pi$
$270$	20.0216	−	15.5857i	1.21848	−	0.948516i
$271$	3.12214			0.189656			0.0948282	−	0.995494i	$-0.469770\pi$
$271$	3.12214			0.189656			0.0948282	+	0.995494i	$0.469770\pi$
$272$	0.313312	+	0.313312i	0.0189973	+	0.0189973i
$273$	0.506139	+	0.00181836i	0.0306330	+	0.000110052i
$274$		−	16.0421i		−	0.969139i
$275$	−3.79802	+	16.4937i	−0.229029	+	0.994607i
$276$	24.2631	+	24.4381i	1.46047	+	1.47100i
$277$	12.2472	−	12.2472i	0.735861	−	0.735861i	−0.235913	−	0.971774i	$-0.575808\pi$
$277$	12.2472	−	12.2472i	0.735861	−	0.735861i	0.971774	+	0.235913i	$0.0758081\pi$
$278$	−19.0142	+	19.0142i	−1.14040	+	1.14040i
$279$	27.3526	+	0.196536i	1.63756	+	0.0117663i
$280$	−3.72978	−	0.423883i	−0.222897	−	0.0253319i
$281$		−	12.7181i		−	0.758698i	−0.925254	−	0.379349i	$-0.876148\pi$
$281$		−	12.7181i		−	0.758698i	0.925254	−	0.379349i	$-0.123852\pi$
$282$	−0.0685349	+	19.0767i	−0.00408120	+	1.13600i
$283$	−19.8271	−	19.8271i	−1.17860	−	1.17860i	−0.980102	−	0.198495i	$-0.936395\pi$
$283$	−19.8271	−	19.8271i	−1.17860	−	1.17860i	−0.198495	−	0.980102i	$-0.563605\pi$
$284$	10.9491			0.649711
$285$	−20.4416	−	2.39758i	−1.21086	−	0.142020i
$286$	−2.16014			−0.127732
$287$	−0.0222716	−	0.0222716i	−0.00131465	−	0.00131465i
$288$	15.6782	+	15.9051i	0.923847	+	0.937219i
$289$		−	16.9439i		−	0.996703i
$290$	10.8608	−	8.64408i	0.637767	−	0.507598i
$291$	−3.94168	+	3.91346i	−0.231066	+	0.229411i
$292$	−23.8416	+	23.8416i	−1.39523	+	1.39523i
$293$	−6.72836	+	6.72836i	−0.393075	+	0.393075i	−0.875782	−	0.482707i	$-0.839654\pi$
$293$	−6.72836	+	6.72836i	−0.393075	+	0.393075i	0.482707	+	0.875782i	$0.339654\pi$
$294$	−2.68412	+	2.66491i	−0.156541	+	0.155420i
$295$	2.60499	−	22.9215i	0.151668	−	1.33454i
$296$		−	12.5118i		−	0.727236i
$297$	−0.189570	+	17.5883i	−0.0109999	+	1.02058i
$298$	29.2383	+	29.2383i	1.69373	+	1.69373i
$299$	2.09844			0.121356
$300$	−5.46455	+	23.3471i	−0.315496	+	1.34794i
$301$	−5.32981			−0.307205
$302$	−2.94201	−	2.94201i	−0.169293	−	0.169293i
$303$	0.0537396	−	14.9584i	0.00308726	−	0.859339i
$304$		−	9.94571i		−	0.570426i
$305$	1.71860	−	15.1221i	0.0984068	−	0.865888i
$306$	−0.0111442	+	1.55098i	−0.000637072	+	0.0886634i
$307$	10.1105	−	10.1105i	0.577034	−	0.577034i	−0.357051	−	0.934085i	$-0.616218\pi$
$307$	10.1105	−	10.1105i	0.577034	−	0.577034i	0.934085	+	0.357051i	$0.116218\pi$
$308$	6.62728	−	6.62728i	0.377624	−	0.377624i
$309$	−1.66426	−	1.67626i	−0.0946765	−	0.0953592i
$310$	−34.8355	+	27.7255i	−1.97852	+	1.57470i
$311$			0.394155i			0.0223505i	0.999938	+	0.0111752i	$0.00355726\pi$
$311$			0.394155i			0.0223505i	−0.999938	+	0.0111752i	$0.996443\pi$
$312$	−0.849680	−	0.00305256i	−0.0481036	−	0.000172817i
$313$	−10.3810	−	10.3810i	−0.586767	−	0.586767i	0.349987	−	0.936754i	$-0.386186\pi$
$313$	−10.3810	−	10.3810i	−0.586767	−	0.586767i	−0.936754	+	0.349987i	$0.886186\pi$
$314$	−13.3330			−0.752424
$315$	4.13962	+	5.27859i	0.233241	+	0.297415i
$316$	−31.6881			−1.78260
$317$	−19.8075	−	19.8075i	−1.11250	−	1.11250i	−0.992812	−	0.119688i	$-0.961810\pi$
$317$	−19.8075	−	19.8075i	−1.11250	−	1.11250i	−0.119688	−	0.992812i	$-0.538190\pi$
$318$	−19.0046	−	0.0682759i	−1.06573	−	0.00382872i
$319$			9.62264i			0.538764i
$320$	−27.8026	−	3.15971i	−1.55421	−	0.176633i
$321$	5.10579	+	5.14260i	0.284977	+	0.287032i
$322$	−11.0885	+	11.0885i	−0.617936	+	0.617936i
$323$	0.889642	−	0.889642i	0.0495010	−	0.0495010i
$324$	−0.358078	+	24.9161i	−0.0198932	+	1.38423i
$325$	0.774972	+	1.23865i	0.0429877	+	0.0687080i
$326$			11.0454i			0.611748i
$327$	0.0175588	−	4.88750i	0.000971005	−	0.270279i
$328$	0.0373884	+	0.0373884i	0.00206443	+	0.00206443i
$329$	−5.04363			−0.278065
$330$	−17.7481	−	22.4646i	−0.977000	−	1.23663i
$331$	−24.7348			−1.35955			−0.679774	−	0.733422i	$-0.737922\pi$
$331$	−24.7348			−1.35955			−0.679774	+	0.733422i	$0.737922\pi$
$332$	10.7444	+	10.7444i	0.589674	+	0.589674i
$333$	−15.9236	+	15.6964i	−0.872607	+	0.860157i
$334$		−	19.7416i		−	1.08021i
$335$	12.5010	+	15.7068i	0.683004	+	0.858154i
$336$	−2.30038	+	2.28391i	−0.125496	+	0.124597i
$337$	−3.40139	+	3.40139i	−0.185286	+	0.185286i	−0.793655	−	0.608369i	$-0.791824\pi$
$337$	−3.40139	+	3.40139i	−0.185286	+	0.185286i	0.608369	+	0.793655i	$0.291824\pi$
$338$	19.9420	−	19.9420i	1.08470	−	1.08470i
$339$	−3.50777	+	3.48266i	−0.190516	+	0.189152i
$340$	−0.912779	−	1.14685i	−0.0495024	−	0.0621968i
$341$		−	30.8642i		−	1.67139i
$342$	24.7938	−	24.4401i	1.34070	−	1.32157i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	8.94740			0.482411
$345$	17.2412	+	21.8229i	0.928233	+	1.17491i
$346$	12.0070			0.645498
$347$	24.0324	+	24.0324i	1.29013	+	1.29013i	0.934706	+	0.355421i	$0.115663\pi$
$347$	24.0324	+	24.0324i	1.29013	+	1.29013i	0.355421	+	0.934706i	$0.384337\pi$
$348$	−0.0489753	+	13.6323i	−0.00262535	+	0.730766i
$349$		−	9.37078i		−	0.501607i	−0.968038	−	0.250803i	$-0.919305\pi$
$349$		−	9.37078i		−	0.501607i	0.968038	−	0.250803i	$-0.0806947\pi$
$350$	−10.6403	−	2.45015i	−0.568747	−	0.130966i
$351$	1.06206	+	1.08520i	0.0566884	+	0.0579237i
$352$	17.8191	−	17.8191i	0.949759	−	0.949759i
$353$	14.5888	−	14.5888i	0.776481	−	0.776481i	−0.202750	−	0.979231i	$-0.564988\pi$
$353$	14.5888	−	14.5888i	0.776481	−	0.776481i	0.979231	+	0.202750i	$0.0649878\pi$
$354$	27.4932	+	27.6915i	1.46125	+	1.47179i
$355$	8.78606	+	0.998522i	0.466316	+	0.0529960i
$356$			5.54275i			0.293765i
$357$	−0.410063	−	0.00147319i	−0.0217028	−	7.79696e-5i
$358$	−22.5942	−	22.5942i	−1.19414	−	1.19414i
$359$	27.2654			1.43901			0.719506	−	0.694486i	$-0.244368\pi$
$359$	27.2654			1.43901			0.719506	+	0.694486i	$0.244368\pi$
$360$	−6.94938	−	8.86141i	−0.366264	−	0.467037i
$361$	−9.24062			−0.486349
$362$	−15.1900	−	15.1900i	−0.798369	−	0.798369i
$363$	0.794430	+	0.00285407i	0.0416968	+	0.000149800i
$364$		−	0.809088i		−	0.0424077i
$365$	−21.3059	+	16.9573i	−1.11520	+	0.887587i
$366$	18.1382	+	18.2690i	0.948101	+	0.954938i
$367$	15.9239	−	15.9239i	0.831218	−	0.831218i	−0.156465	−	0.987683i	$-0.550010\pi$
$367$	15.9239	−	15.9239i	0.831218	−	0.831218i	0.987683	+	0.156465i	$0.0500099\pi$
$368$	−9.50315	+	9.50315i	−0.495386	+	0.495386i
$369$	0.000678924	−	0.0944881i	3.53434e−5	−	0.00491885i
$370$	4.10960	−	36.1607i	0.213648	−	1.87990i
$371$		−	5.02457i		−	0.260863i
$372$	0.157086	−	43.7249i	0.00814453	−	2.26703i
$373$	23.3283	+	23.3283i	1.20790	+	1.20790i	0.971707	+	0.236189i	$0.0758984\pi$
$373$	23.3283	+	23.3283i	1.20790	+	1.20790i	0.236189	+	0.971707i	$0.424102\pi$
$374$	1.75010			0.0904954
$375$	−6.51417	+	18.2364i	−0.336390	+	0.941723i
$376$	8.46698			0.436651
$377$	0.587387	+	0.587387i	0.0302520	+	0.0302520i
$378$	−11.3464	−	0.122294i	−0.583597	−	0.00629010i
$379$			37.4477i			1.92356i	0.273828	+	0.961779i	$0.411710\pi$
$379$			37.4477i			1.92356i	−0.273828	+	0.961779i	$0.588290\pi$
$380$	−3.71520	+	32.6903i	−0.190586	+	1.67698i
$381$	20.2109	−	20.0662i	1.03544	−	1.02802i
$382$	−9.84986	+	9.84986i	−0.503963	+	0.503963i
$383$	−4.95443	+	4.95443i	−0.253159	+	0.253159i	−0.822265	−	0.569105i	$-0.807290\pi$
$383$	−4.95443	+	4.95443i	−0.253159	+	0.253159i	0.569105	+	0.822265i	$0.307290\pi$
$384$	15.2879	−	15.1784i	0.780155	−	0.774570i
$385$	5.92241	−	4.71364i	0.301834	−	0.240229i
$386$			23.3578i			1.18888i
$387$	−11.2247	−	11.3872i	−0.570584	−	0.578843i
$388$	6.27841	+	6.27841i	0.318738	+	0.318738i
$389$	9.20279			0.466600			0.233300	−	0.972405i	$-0.425048\pi$
$389$	9.20279			0.466600			0.233300	+	0.972405i	$0.425048\pi$
$390$	−2.45467	−	0.287905i	−0.124297	−	0.0145787i
$391$	−1.70011			−0.0859783
$392$	1.18705	+	1.18705i	0.0599552	+	0.0599552i
$393$	0.0790344	−	21.9992i	0.00398676	−	1.10971i
$394$		−	3.13431i		−	0.157904i
$395$	−25.4280	−	2.88985i	−1.27942	−	0.145404i
$396$	28.1164	+	0.202025i	1.41290	+	0.0101521i
$397$	21.9242	−	21.9242i	1.10034	−	1.10034i	0.105976	−	0.994369i	$-0.466203\pi$
$397$	21.9242	−	21.9242i	1.10034	−	1.10034i	0.994369	−	0.105976i	$-0.0337966\pi$
$398$	14.5156	−	14.5156i	0.727600	−	0.727600i
$399$	6.48510	+	6.53187i	0.324661	+	0.327002i
$400$	−9.11904	−	2.09985i	−0.455952	−	0.104993i
$401$		−	25.7514i		−	1.28596i	−0.765882	−	0.642982i	$-0.777697\pi$
$401$		−	25.7514i		−	1.28596i	0.765882	−	0.642982i	$-0.222303\pi$
$402$	−33.9560	−	0.121990i	−1.69357	−	0.00608431i
$403$	−1.88402	−	1.88402i	−0.0938497	−	0.0938497i
$404$	−23.9117			−1.18965
$405$	−2.55960	+	19.9612i	−0.127188	+	0.991879i
$406$	−6.20768			−0.308082
$407$	17.8397	+	17.8397i	0.884283	+	0.884283i
$408$	0.688392	+	0.00247311i	0.0340805	+	0.000122437i
$409$			10.9496i			0.541425i	0.962660	+	0.270712i	$0.0872592\pi$
$409$			10.9496i			0.541425i	−0.962660	+	0.270712i	$0.912741\pi$
$410$	0.0957764	+	0.120337i	0.00473006	+	0.00594304i
$411$	8.96477	+	9.02942i	0.442200	+	0.445388i
$412$	−2.66999	+	2.66999i	−0.131541	+	0.131541i
$413$	−7.29506	+	7.29506i	−0.358967	+	0.358967i
$414$	−47.0431	−	0.338019i	−2.31204	−	0.0166127i
$415$	7.64192	+	9.60162i	0.375127	+	0.471325i
$416$		−	2.17543i		−	0.106659i
$417$	0.0766229	−	21.3280i	0.00375224	−	1.04444i
$418$	−27.7774	−	27.7774i	−1.35864	−	1.35864i
$419$	−5.86958			−0.286748			−0.143374	−	0.989669i	$-0.545795\pi$
$419$	−5.86958			−0.286748			−0.143374	+	0.989669i	$0.545795\pi$
$420$	8.41419	−	6.64761i	0.410570	−	0.324370i
$421$	26.8842			1.31026			0.655129	−	0.755517i	$-0.272614\pi$
$421$	26.8842			1.31026			0.655129	+	0.755517i	$0.272614\pi$
$422$	−12.8034	−	12.8034i	−0.623257	−	0.623257i
$423$	−10.6220	−	10.7758i	−0.516460	−	0.523936i
$424$			8.43498i			0.409639i
$425$	−0.627865	−	1.00353i	−0.0304559	−	0.0486782i
$426$	−10.6145	+	10.5385i	−0.514273	+	0.510591i
$427$	−4.81281	+	4.81281i	−0.232908	+	0.232908i
$428$	8.19126	−	8.19126i	0.395940	−	0.395940i
$429$	1.21585	−	1.20714i	0.0587018	−	0.0582815i
$430$	25.8590	+	2.93884i	1.24703	+	0.141723i
$431$		−	4.18118i		−	0.201400i	−0.994917	−	0.100700i	$-0.967892\pi$
$431$		−	4.18118i		−	0.201400i	0.994917	−	0.100700i	$-0.0321083\pi$
$432$	−9.72423	−	0.104809i	−0.467857	−	0.00504264i
$433$	−2.20877	−	2.20877i	−0.106146	−	0.106146i	0.652039	−	0.758185i	$-0.273914\pi$
$433$	−2.20877	−	2.20877i	−0.106146	−	0.106146i	−0.758185	+	0.652039i	$0.773914\pi$
$434$	19.9109			0.955752
$435$	−1.28252	+	10.9347i	−0.0614919	+	0.524278i
$436$	−7.81290			−0.374170
$437$	26.9840	+	26.9840i	1.29082	+	1.29082i
$438$	0.165477	−	46.0604i	0.00790678	−	2.20085i
$439$			27.6028i			1.31741i	0.752401	+	0.658706i	$0.228896\pi$
$439$			27.6028i			1.31741i	−0.752401	+	0.658706i	$0.771104\pi$
$440$	−9.94222	+	7.91300i	−0.473977	+	0.377238i
$441$	0.0215553	−	2.99992i	0.00102644	−	0.142853i
$442$	0.106830	−	0.106830i	0.00508138	−	0.00508138i
$443$	12.3040	−	12.3040i	0.584582	−	0.584582i	−0.351577	−	0.936159i	$-0.614354\pi$
$443$	12.3040	−	12.3040i	0.584582	−	0.584582i	0.936159	+	0.351577i	$0.114354\pi$
$444$	25.1825	+	25.3641i	1.19511	+	1.20373i
$445$	−0.505479	+	4.44775i	−0.0239620	+	0.210843i
$446$			11.9214i			0.564494i
$447$	−32.7961	−	0.117823i	−1.55120	−	0.00557285i
$448$	8.84854	+	8.84854i	0.418054	+	0.418054i
$449$	−34.1859			−1.61333			−0.806666	−	0.591008i	$-0.798730\pi$
$449$	−34.1859			−1.61333			−0.806666	+	0.591008i	$0.798730\pi$
$450$	−17.1739	−	27.8931i	−0.809586	−	1.31489i
$451$	−0.106619			−0.00502049
$452$	5.58726	+	5.58726i	0.262803	+	0.262803i
$453$	3.30000	+	0.0118556i	0.155048	+	0.000557024i
$454$			4.65526i			0.218482i
$455$	0.0737860	−	0.649248i	0.00345914	−	0.0304372i
$456$	−10.8868	−	10.9653i	−0.509823	−	0.513499i
$457$	−9.31021	+	9.31021i	−0.435513	+	0.435513i	−0.890499	−	0.454986i	$-0.849644\pi$
$457$	−9.31021	+	9.31021i	−0.435513	+	0.435513i	0.454986	+	0.890499i	$0.349644\pi$
$458$	−9.66646	+	9.66646i	−0.451684	+	0.451684i
$459$	−0.860455	−	0.879206i	−0.0401626	−	0.0410378i
$460$	34.7855	−	27.6858i	1.62188	−	1.29086i
$461$		−	25.6579i		−	1.19501i	−0.801865	−	0.597505i	$-0.796159\pi$
$461$		−	25.6579i		−	1.19501i	0.801865	−	0.597505i	$-0.203841\pi$
$462$	−0.0459976	+	12.8034i	−0.00214000	+	0.595670i
$463$	13.2170	+	13.2170i	0.614248	+	0.614248i	0.944050	−	0.329802i	$-0.106982\pi$
$463$	13.2170	+	13.2170i	0.614248	+	0.614248i	−0.329802	+	0.944050i	$0.606982\pi$
$464$	−5.32017			−0.246983
$465$	4.11361	−	35.0725i	0.190764	−	1.62645i
$466$	−8.25874			−0.382579
$467$	−19.6659	−	19.6659i	−0.910031	−	0.910031i	0.0862431	−	0.996274i	$-0.472514\pi$
$467$	−19.6659	−	19.6659i	−0.910031	−	0.910031i	−0.996274	+	0.0862431i	$0.972514\pi$
$468$	1.72862	−	1.70396i	0.0799056	−	0.0787655i
$469$		−	8.97752i		−	0.414543i
$470$	24.4706	+	2.78104i	1.12874	+	0.128280i
$471$	7.50457	−	7.45084i	0.345792	−	0.343317i
$472$	12.2466	−	12.2466i	0.563693	−	0.563693i
$473$	−12.7575	+	12.7575i	−0.586588	+	0.586588i
$474$	30.7196	−	30.4997i	1.41100	−	1.40090i
$475$	−5.96248	+	25.8933i	−0.273577	+	1.18807i
$476$			0.655505i			0.0300450i
$477$	10.7350	−	10.5819i	0.491524	−	0.484510i
$478$	3.21986	+	3.21986i	0.147273	+	0.147273i
$479$	−26.9725			−1.23240			−0.616202	−	0.787588i	$-0.711330\pi$
$479$	−26.9725			−1.23240			−0.616202	+	0.787588i	$0.711330\pi$
$480$	22.6236	−	17.8737i	1.03262	−	0.815821i
$481$	2.17795			0.0993062
$482$	−8.39528	−	8.39528i	−0.382395	−	0.382395i
$483$	0.0446838	−	12.4378i	0.00203319	−	0.565937i
$484$		−	1.26993i		−	0.0577242i
$485$	4.46551	+	5.61064i	0.202768	+	0.254766i
$486$	−23.6345	−	24.4993i	−1.07208	−	1.11131i
$487$	−28.6505	+	28.6505i	−1.29828	+	1.29828i	−0.368749	+	0.929529i	$0.620214\pi$
$487$	−28.6505	+	28.6505i	−1.29828	+	1.29828i	−0.929529	+	0.368749i	$0.879786\pi$
$488$	8.07948	−	8.07948i	0.365741	−	0.365741i
$489$	−6.17247	−	6.21698i	−0.279129	−	0.281141i
$490$	3.04083	+	3.82062i	0.137370	+	0.172598i
$491$		−	2.74522i		−	0.123890i	−0.998080	−	0.0619450i	$-0.980270\pi$
$491$		−	2.74522i		−	0.123890i	0.998080	−	0.0619450i	$-0.0197303\pi$
$492$	−0.151046		0.000542646i	−0.00680966		2.44644e-5i
$493$	−0.475888	−	0.475888i	−0.0214329	−	0.0214329i
$494$	−3.39119			−0.152577
$495$	22.5435	+	2.72623i	1.01325	+	0.122535i
$496$	17.0642			0.766206
$497$	−2.79628	−	2.79628i	−0.125430	−	0.125430i
$498$	−20.7574	−	0.0745730i	−0.930162	−	0.00334170i
$499$		−	30.3151i		−	1.35709i	−0.734558	−	0.678546i	$-0.762611\pi$
$499$		−	30.3151i		−	1.35709i	0.734558	−	0.678546i	$-0.237389\pi$
$500$	29.1887	+	10.3083i	1.30536	+	0.461003i
$501$	11.0321	+	11.1117i	0.492879	+	0.496433i
$502$	−36.0446	+	36.0446i	−1.60875	+	1.60875i
$503$	−0.331820	+	0.331820i	−0.0147951	+	0.0147951i	−0.714466	−	0.699671i	$-0.753330\pi$
$503$	−0.331820	+	0.331820i	−0.0147951	+	0.0147951i	0.699671	+	0.714466i	$0.253330\pi$
$504$	−0.0361859	+	5.03611i	−0.00161185	+	0.224326i
$505$	−19.1878	−	2.18067i	−0.853848	−	0.0970384i
$506$			53.0827i			2.35982i
$507$	−0.0803614	+	22.3686i	−0.00356898	+	0.993425i
$508$	−32.1925	−	32.1925i	−1.42831	−	1.42831i
$509$	14.6491			0.649311			0.324656	−	0.945832i	$-0.394752\pi$
$509$	14.6491			0.649311			0.324656	+	0.945832i	$0.394752\pi$
$510$	1.98872	+	0.233255i	0.0880620	+	0.0103287i
$511$	12.1778			0.538713
$512$	14.2950	+	14.2950i	0.631758	+	0.631758i
$513$	−0.297604	+	27.6117i	−0.0131395	+	1.21909i
$514$			33.7466i			1.48850i
$515$	−2.38601	+	1.89903i	−0.105140	+	0.0836811i
$516$	−18.1382	+	18.0084i	−0.798492	+	0.792775i
$517$	−12.0725	+	12.0725i	−0.530946	+	0.530946i
$518$	−11.5086	+	11.5086i	−0.505660	+	0.505660i
$519$	−6.75820	+	6.70982i	−0.296652	+	0.294528i
$520$	−0.123868	+	1.08992i	−0.00543197	+	0.0477963i
$521$			24.6501i			1.07994i	0.841683	+	0.539971i	$0.181565\pi$
$521$			24.6501i			1.07994i	−0.841683	+	0.539971i	$0.818435\pi$
$522$	−13.0735	−	13.2628i	−0.572212	−	0.580495i
$523$	−23.4069	−	23.4069i	−1.02351	−	1.02351i	−0.999717	−	0.0237950i	$-0.992425\pi$
$523$	−23.4069	−	23.4069i	−1.02351	−	1.02351i	−0.0237950	−	0.999717i	$-0.507575\pi$
$524$	−35.1668			−1.53627
$525$	7.35816	−	4.56699i	0.321137	−	0.199320i
$526$	56.1475			2.44815
$527$	1.52639	+	1.52639i	0.0664907	+	0.0664907i
$528$	−0.0394214	+	10.9730i	−0.00171560	+	0.477536i
$529$		−	28.5666i		−	1.24203i
$530$	−2.77053	+	24.3781i	−0.120344	+	1.05892i
$531$	−30.9495	−	0.222381i	−1.34310	−	0.00965053i
$532$	10.4041	−	10.4041i	0.451076	−	0.451076i
$533$	−0.00650825	+	0.00650825i	−0.000281904	+	0.000281904i
$534$	−5.33487	−	5.37334i	−0.230862	−	0.232527i
$535$	7.32005	−	5.82602i	0.316473	−	0.251881i
$536$			15.0710i			0.650967i
$537$	25.3436	+	0.0910493i	1.09366	+	0.00392907i
$538$	44.0273	+	44.0273i	1.89815	+	1.89815i
$539$	−3.38507			−0.145805
$540$	31.9232	+	3.97696i	1.37375	+	0.171141i
$541$	−27.2143			−1.17003			−0.585017	−	0.811021i	$-0.698912\pi$
$541$	−27.2143			−1.17003			−0.585017	+	0.811021i	$0.698912\pi$
$542$	4.82102	+	4.82102i	0.207081	+	0.207081i
$543$	17.0384	+	0.0612121i	0.731187	+	0.00262686i
$544$			1.76249i			0.0755660i
$545$	−6.26942	−	0.712509i	−0.268552	−	0.0305205i
$546$	0.778743	+	0.784359i	0.0333271	+	0.0335675i
$547$	−3.63475	+	3.63475i	−0.155411	+	0.155411i	−0.780530	−	0.625119i	$-0.785051\pi$
$547$	−3.63475	+	3.63475i	−0.155411	+	0.155411i	0.625119	+	0.780530i	$0.285051\pi$
$548$	14.3823	−	14.3823i	0.614380	−	0.614380i
$549$	−20.4185	−	0.146713i	−0.871440	−	0.00626154i
$550$	−31.3333	+	19.6039i	−1.33605	+	0.835914i
$551$			15.1065i			0.643559i
$552$	−0.0750128	+	20.8798i	−0.00319276	+	0.888705i
$553$	8.09279	+	8.09279i	0.344141	+	0.344141i
$554$	37.8227			1.60693
$555$	17.8945	+	22.6499i	0.759578	+	0.961433i
$556$	−34.0938			−1.44590
$557$	5.91751	+	5.91751i	0.250733	+	0.250733i	0.821271	−	0.570538i	$-0.193265\pi$
$557$	5.91751	+	5.91751i	0.250733	+	0.250733i	−0.570538	+	0.821271i	$0.693265\pi$
$558$	41.9328	+	42.5397i	1.77516	+	1.80085i
$559$			1.55749i			0.0658747i
$560$	2.60608	+	3.27439i	0.110127	+	0.138368i
$561$	−0.985055	+	0.978002i	−0.0415890	+	0.0412913i
$562$	19.6385	−	19.6385i	0.828402	−	0.828402i
$563$	−13.8267	+	13.8267i	−0.582728	+	0.582728i	−0.935652	−	0.352924i	$-0.885187\pi$
$563$	−13.8267	+	13.8267i	−0.582728	+	0.582728i	0.352924	+	0.935652i	$0.385187\pi$
$564$	−17.1643	+	17.0414i	−0.722749	+	0.717574i
$565$	3.97393	+	4.99301i	0.167185	+	0.210058i
$566$		−	61.2316i		−	2.57376i
$567$	6.45475	−	6.27185i	0.271074	−	0.263393i
$568$	4.69425	+	4.69425i	0.196966	+	0.196966i
$569$	−6.82232			−0.286007			−0.143003	−	0.989722i	$-0.545676\pi$
$569$	−6.82232			−0.286007			−0.143003	+	0.989722i	$0.545676\pi$
$570$	−27.8626	−	35.2670i	−1.16704	−	1.47717i
$571$	19.7545			0.826701			0.413351	−	0.910572i	$-0.364358\pi$
$571$	19.7545			0.826701			0.413351	+	0.910572i	$0.364358\pi$
$572$	−1.93663	−	1.93663i	−0.0809747	−	0.0809747i
$573$	0.0396926	−	11.0484i	0.00165818	−	0.461555i
$574$		−	0.0687811i		−	0.00287087i
$575$	30.4383	−	19.0440i	1.26937	−	0.794189i
$576$	−0.269737	+	37.5402i	−0.0112390	+	1.56417i
$577$	1.10727	−	1.10727i	0.0460964	−	0.0460964i	−0.683683	−	0.729779i	$-0.739623\pi$
$577$	1.10727	−	1.10727i	0.0460964	−	0.0460964i	0.729779	+	0.683683i	$0.239623\pi$
$578$	26.1639	−	26.1639i	1.08827	−	1.08827i
$579$	−13.0530	−	13.1471i	−0.542463	−	0.546375i
$580$	17.4867	+	1.98734i	0.726097	+	0.0825197i
$581$		−	5.48799i		−	0.227680i
$582$	−12.1295	−	0.0435762i	−0.502782	−	0.00180629i
$583$	−12.0268	−	12.0268i	−0.498100	−	0.498100i
$584$	−20.4434			−0.845953
$585$	1.54252	−	1.20969i	0.0637753	−	0.0500144i
$586$	−20.7791			−0.858376
$587$	7.76708	+	7.76708i	0.320582	+	0.320582i	0.848990	−	0.528408i	$-0.177211\pi$
$587$	7.76708	+	7.76708i	0.320582	+	0.320582i	−0.528408	+	0.848990i	$0.677211\pi$
$588$	−4.79558	−	0.0172286i	−0.197766	−	0.000710495i
$589$		−	48.4535i		−	1.99649i
$590$	39.4165	−	31.3715i	1.62275	−	1.29154i
$591$	1.75154	+	1.76417i	0.0720487	+	0.0725683i
$592$	−9.86325	+	9.86325i	−0.405377	+	0.405377i
$593$	−8.01301	+	8.01301i	−0.329055	+	0.329055i	−0.852227	−	0.523172i	$-0.824748\pi$
$593$	−8.01301	+	8.01301i	−0.329055	+	0.329055i	0.523172	+	0.852227i	$0.324748\pi$
$594$	−27.4515	+	26.8661i	−1.12635	+	1.10233i
$595$	−0.0597798	+	0.526007i	−0.00245073	+	0.0215642i
$596$			52.4261i			2.14746i
$597$	−0.0584943	+	16.2819i	−0.00239401	+	0.666373i
$598$	3.24029	+	3.24029i	0.132505	+	0.132505i
$599$	−20.3742			−0.832467			−0.416233	−	0.909258i	$-0.636650\pi$
$599$	−20.3742			−0.832467			−0.416233	+	0.909258i	$0.636650\pi$
$600$	−12.3525	+	7.66682i	−0.504288	+	0.312997i
$601$	−32.4833			−1.32502			−0.662511	−	0.749052i	$-0.730509\pi$
$601$	−32.4833			−1.32502			−0.662511	+	0.749052i	$0.730509\pi$
$602$	−8.22998	−	8.22998i	−0.335429	−	0.335429i
$603$	19.1805	−	18.9069i	0.781092	−	0.769947i
$604$		−	5.27521i		−	0.214645i
$605$	0.115814	−	1.01905i	0.00470849	−	0.0414303i
$606$	23.1809	−	23.0149i	0.941660	−	0.934918i
$607$	−0.0701607	+	0.0701607i	−0.00284774	+	0.00284774i	−0.708529	−	0.705681i	$-0.750641\pi$
$607$	−0.0701607	+	0.0701607i	−0.00284774	+	0.00284774i	0.705681	+	0.708529i	$0.250641\pi$
$608$	27.9740	−	27.9740i	1.13450	−	1.13450i
$609$	3.49404	−	3.46902i	0.141586	−	0.140572i
$610$	26.0044	−	20.6969i	1.05289	−	0.837992i
$611$			1.47386i			0.0596260i
$612$	−1.40049	+	1.38051i	−0.0566115	+	0.0558038i
$613$	−26.6840	−	26.6840i	−1.07776	−	1.07776i	−0.996710	−	0.0810445i	$-0.974174\pi$
$613$	−26.6840	−	26.6840i	−1.07776	−	1.07776i	−0.0810445	−	0.996710i	$-0.525826\pi$
$614$	31.2239			1.26010
$615$	−0.121156	−	0.0142103i	−0.00488549	−	0.000573014i
$616$	5.68266			0.228961
$617$	6.37294	+	6.37294i	0.256565	+	0.256565i	0.823656	−	0.567090i	$-0.191931\pi$
$617$	6.37294	+	6.37294i	0.256565	+	0.256565i	−0.567090	+	0.823656i	$0.691931\pi$
$618$	0.0185315	−	5.15824i	0.000745446	−	0.207495i
$619$			17.7676i			0.714139i	0.934078	+	0.357070i	$0.116224\pi$
$619$			17.7676i			0.714139i	−0.934078	+	0.357070i	$0.883776\pi$
$620$	−56.0879	−	6.37430i	−2.25255	−	0.255998i
$621$	26.6675	−	26.0987i	1.07013	−	1.04731i
$622$	−0.608631	+	0.608631i	−0.0244039	+	0.0244039i
$623$	1.41556	−	1.41556i	0.0567130	−	0.0567130i
$624$	0.667407	+	0.672220i	0.0267177	+	0.0269103i
$625$	22.4823	+	10.9338i	0.899291	+	0.437351i
$626$		−	32.0594i		−	1.28135i
$627$	31.1575	+	0.111936i	1.24431	+	0.00447030i
$628$	−11.9535	−	11.9535i	−0.476995	−	0.476995i
$629$	−1.76453			−0.0703565
$630$	−1.75873	+	14.5431i	−0.0700693	+	0.579409i
$631$	17.8248			0.709592			0.354796	−	0.934944i	$-0.384550\pi$
$631$	17.8248			0.709592			0.354796	+	0.934944i	$0.384550\pi$
$632$	−13.5857	−	13.5857i	−0.540412	−	0.540412i
$633$	14.3613	+	0.0515944i	0.570811	+	0.00205070i
$634$		−	61.1712i		−	2.42942i
$635$	−22.8968	−	28.7685i	−0.908633	−	1.14164i
$636$	−16.9770	−	17.0995i	−0.673183	−	0.678038i
$637$	−0.206632	+	0.206632i	−0.00818705	+	0.00818705i
$638$	−14.8587	+	14.8587i	−0.588262	+	0.588262i
$639$	0.0852413	−	11.8633i	0.00337210	−	0.469306i
$640$	−17.3195	−	21.7609i	−0.684614	−	0.860177i
$641$		−	14.8270i		−	0.585630i	−0.956169	−	0.292815i	$-0.905408\pi$
$641$		−	14.8270i		−	0.585630i	0.956169	−	0.292815i	$-0.0945920\pi$
$642$	−0.0568527	+	15.8250i	−0.00224380	+	0.624562i
$643$	−32.7229	−	32.7229i	−1.29047	−	1.29047i	−0.934498	−	0.355968i	$-0.884151\pi$
$643$	−32.7229	−	32.7229i	−1.29047	−	1.29047i	−0.355968	−	0.934498i	$-0.615849\pi$
$644$	−19.8823			−0.783474
$645$	−16.1972	+	12.7966i	−0.637766	+	0.503865i
$646$	2.74747			0.108098
$647$	−27.0564	−	27.0564i	−1.06370	−	1.06370i	−0.997828	−	0.0658674i	$-0.979019\pi$
$647$	−27.0564	−	27.0564i	−1.06370	−	1.06370i	−0.0658674	−	0.997828i	$-0.520981\pi$
$648$	−10.8359	+	10.5289i	−0.425674	+	0.413612i
$649$			34.9230i			1.37085i
$650$	−0.715985	+	3.10932i	−0.0280833	+	0.121958i
$651$	−11.2070	+	11.1267i	−0.439236	+	0.436091i
$652$	−9.90255	+	9.90255i	−0.387814	+	0.387814i
$653$	−4.04918	+	4.04918i	−0.158457	+	0.158457i	−0.781883	−	0.623426i	$-0.785740\pi$
$653$	−4.04918	+	4.04918i	−0.158457	+	0.158457i	0.623426	+	0.781883i	$0.285740\pi$
$654$	7.57410	−	7.51988i	0.296171	−	0.294050i
$655$	−28.2194	−	3.20709i	−1.10262	−	0.125311i
$656$		−	0.0589475i		−	0.00230151i
$657$	25.6467	+	26.0179i	1.00057	+	1.01506i
$658$	−7.78809	−	7.78809i	−0.303611	−	0.303611i
$659$	11.5870			0.451366			0.225683	−	0.974201i	$-0.427539\pi$
$659$	11.5870			0.451366			0.225683	+	0.974201i	$0.427539\pi$
$660$	4.22849	−	36.0520i	0.164594	−	1.40332i
$661$	−15.1550			−0.589462			−0.294731	−	0.955580i	$-0.595230\pi$
$661$	−15.1550			−0.589462			−0.294731	+	0.955580i	$0.595230\pi$
$662$	−38.1940	−	38.1940i	−1.48445	−	1.48445i
$663$	−0.000430499		0.119829i	−1.67192e−5		0.00465379i
$664$			9.21294i			0.357531i
$665$	9.29755	−	7.39991i	0.360544	−	0.286956i
$666$	−48.8257	−	0.350827i	−1.89196	−	0.0135943i
$667$	14.4343	−	14.4343i	0.558899	−	0.558899i
$668$	17.6990	−	17.6990i	0.684793	−	0.684793i
$669$	−6.66199	−	6.71003i	−0.257568	−	0.259425i
$670$	−4.95017	+	43.5569i	−0.191242	+	1.68275i
$671$			23.0399i			0.889445i
$672$	−12.8941	−	0.0463233i	−0.497400	−	0.00178696i
$673$	−13.7667	−	13.7667i	−0.530666	−	0.530666i	0.390105	−	0.920770i	$-0.372439\pi$
$673$	−13.7667	−	13.7667i	−0.530666	−	0.530666i	−0.920770	+	0.390105i	$0.872439\pi$
$674$	−10.5045			−0.404617
$675$	25.2539	+	6.10257i	0.972022	+	0.234888i
$676$	35.7573			1.37528
$677$	16.3594	+	16.3594i	0.628742	+	0.628742i	0.947752	−	0.319009i	$-0.103350\pi$
$677$	16.3594	+	16.3594i	0.628742	+	0.628742i	−0.319009	+	0.947752i	$0.603350\pi$
$678$	−10.7942	−	0.0387793i	−0.414549	−	0.00148931i
$679$		−	3.20687i		−	0.123068i
$680$	0.100355	−	0.883031i	0.00384844	−	0.0338627i
$681$	−2.60148	−	2.62024i	−0.0996891	−	0.100408i
$682$	47.6587	−	47.6587i	1.82495	−	1.82495i
$683$	5.85622	−	5.85622i	0.224082	−	0.224082i	−0.586133	−	0.810215i	$-0.699350\pi$
$683$	5.85622	−	5.85622i	0.224082	−	0.224082i	0.810215	+	0.586133i	$0.199350\pi$
$684$	44.1398	+	0.317157i	1.68773	+	0.0121268i
$685$	12.8526	−	10.2294i	0.491072	−	0.390844i
$686$		−	2.18375i		−	0.0833758i
$687$	0.0389535	−	10.8427i	0.00148617	−	0.413676i
$688$	−7.05335	−	7.05335i	−0.268906	−	0.268906i
$689$	−1.46829			−0.0559373
$690$	−7.07492	+	60.3205i	−0.269338	+	2.29636i
$691$	25.9095			0.985642			0.492821	−	0.870131i	$-0.335966\pi$
$691$	25.9095			0.985642			0.492821	+	0.870131i	$0.335966\pi$
$692$	10.7646	+	10.7646i	0.409210	+	0.409210i
$693$	−7.12903	−	7.23222i	−0.270809	−	0.274729i
$694$			74.2189i			2.81731i
$695$	−27.3584	−	3.10923i	−1.03776	−	0.117940i
$696$	−5.86560	+	5.82361i	−0.222335	+	0.220743i
$697$	0.00527284	−	0.00527284i	0.000199723	−	0.000199723i
$698$	14.4698	−	14.4698i	0.547691	−	0.547691i
$699$	4.64849	−	4.61521i	0.175822	−	0.174563i
$700$	−7.34272	−	11.7360i	−0.277529	−	0.443579i
$701$		−	37.9089i		−	1.43180i	−0.698204	−	0.715899i	$-0.746017\pi$
$701$		−	37.9089i		−	1.43180i	0.698204	−	0.715899i	$-0.253983\pi$
$702$	−0.0357368	+	3.31567i	−0.00134880	+	0.125142i
$703$	28.0065	+	28.0065i	1.05628	+	1.05628i
$704$	42.3598			1.59649
$705$	−15.3276	+	12.1095i	−0.577269	+	0.456070i
$706$	45.0542			1.69564
$707$	6.10679	+	6.10679i	0.229669	+	0.229669i
$708$	−0.177743	+	49.4749i	−0.00668001	+	1.85938i
$709$			16.6841i			0.626586i	0.949656	+	0.313293i	$0.101432\pi$
$709$			16.6841i			0.626586i	−0.949656	+	0.313293i	$0.898568\pi$
$710$	12.0251	+	15.1088i	0.451293	+	0.567023i
$711$	−0.246699	+	34.3339i	−0.00925194	+	1.28762i
$712$	−2.37636	+	2.37636i	−0.0890578	+	0.0890578i
$713$	−46.2975	+	46.2975i	−1.73385	+	1.73385i
$714$	−0.630921	−	0.635470i	−0.0236116	−	0.0237819i
$715$	−1.37743	−	1.73066i	−0.0515129	−	0.0647229i
$716$		−	40.5129i		−	1.51404i
$717$	−3.61167	−	0.0129753i	−0.134880	−	0.000484570i
$718$	42.1016	+	42.1016i	1.57122	+	1.57122i
$719$	13.0709			0.487464			0.243732	−	0.969843i	$-0.421628\pi$
$719$	13.0709			0.487464			0.243732	+	0.969843i	$0.421628\pi$
$720$	−1.50728	+	12.4638i	−0.0561731	+	0.464500i
$721$	1.36377			0.0507895
$722$	−14.2688	−	14.2688i	−0.531031	−	0.531031i
$723$	9.41686	+	0.0338310i	0.350217	+	0.00125819i
$724$		−	27.2367i		−	1.01224i
$725$	13.8509	+	3.18946i	0.514409	+	0.118454i
$726$	1.22231	+	1.23112i	0.0453640	+	0.0456911i
$727$	19.4878	−	19.4878i	0.722761	−	0.722761i	−0.246406	−	0.969167i	$-0.579250\pi$
$727$	19.4878	−	19.4878i	0.722761	−	0.722761i	0.969167	+	0.246406i	$0.0792495\pi$
$728$	0.346882	−	0.346882i	0.0128563	−	0.0128563i
$729$	26.9937	+	0.581953i	0.999768	+	0.0215538i
$730$	−59.0838	−	6.71478i	−2.18679	−	0.248525i
$731$		−	1.26184i		−	0.0466709i
$732$	−0.117264	+	32.6403i	−0.00433418	+	1.20642i
$733$	24.5624	+	24.5624i	0.907232	+	0.907232i	0.996048	−	0.0888162i	$-0.0283084\pi$
$733$	24.5624	+	24.5624i	0.907232	+	0.907232i	−0.0888162	+	0.996048i	$0.528308\pi$
$734$	49.1774			1.81517
$735$	−3.84662	−	0.451165i	−0.141885	−	0.0166415i
$736$	−53.4585			−1.97051
$737$	−21.4886	−	21.4886i	−0.791543	−	0.791543i
$738$	0.146951	−	0.144855i	0.00540935	−	0.00533217i
$739$			25.3925i			0.934079i	0.884236	+	0.467040i	$0.154679\pi$
$739$			25.3925i			0.934079i	−0.884236	+	0.467040i	$0.845321\pi$
$740$	36.1036	−	28.7348i	1.32720	−	1.05631i
$741$	1.90875	−	1.89509i	0.0701198	−	0.0696178i
$742$	7.75865	−	7.75865i	0.284829	−	0.284829i
$743$	−14.4447	+	14.4447i	−0.529923	+	0.529923i	−0.920549	−	0.390626i	$-0.872258\pi$
$743$	−14.4447	+	14.4447i	−0.529923	+	0.529923i	0.390626	+	0.920549i	$0.372258\pi$
$744$	18.8137	−	18.6790i	0.689742	−	0.684804i
$745$	−4.78108	+	42.0691i	−0.175165	+	1.54129i
$746$			72.0445i			2.63774i
$747$	11.7251	−	11.5578i	0.429000	−	0.422879i
$748$	1.56902	+	1.56902i	0.0573690	+	0.0573690i
$749$	−4.18391			−0.152877
$750$	−38.2184	+	18.1008i	−1.39554	+	0.660946i
$751$	27.4358			1.00115			0.500573	−	0.865694i	$-0.333123\pi$
$751$	27.4358			1.00115			0.500573	+	0.865694i	$0.333123\pi$
$752$	−6.67463	−	6.67463i	−0.243399	−	0.243399i
$753$	0.145251	−	40.4307i	0.00529325	−	1.47338i
$754$			1.81402i			0.0660627i
$755$	0.481081	−	4.23306i	0.0175083	−	0.154057i
$756$	−10.0628	−	10.2821i	−0.365980	−	0.373955i
$757$	−11.9760	+	11.9760i	−0.435274	+	0.435274i	−0.890418	−	0.455144i	$-0.849588\pi$
$757$	−11.9760	+	11.9760i	−0.435274	+	0.435274i	0.455144	+	0.890418i	$0.349588\pi$
$758$	−57.8245	+	57.8245i	−2.10028	+	2.10028i
$759$	−29.6641	−	29.8780i	−1.07674	−	1.08450i
$760$	−15.6082	+	12.4226i	−0.566170	+	0.450614i
$761$			41.1635i			1.49217i	0.665848	+	0.746087i	$0.268070\pi$
$761$			41.1635i			1.49217i	−0.665848	+	0.746087i	$0.731930\pi$
$762$	62.1937	+	0.223437i	2.25304	+	0.00809426i
$763$	1.99533	+	1.99533i	0.0722357	+	0.0722357i
$764$	−17.6614			−0.638969
$765$	−1.24971	+	0.980062i	−0.0451835	+	0.0354342i
$766$	−15.3007			−0.552836
$767$	2.13178	+	2.13178i	0.0769740	+	0.0769740i
$768$	3.69569	+	0.0132771i	0.133357	+	0.000479097i
$769$		−	3.96520i		−	0.142989i	−0.997441	−	0.0714944i	$-0.977223\pi$
$769$		−	3.96520i		−	0.142989i	0.997441	−	0.0714944i	$-0.0227768\pi$
$770$	16.4236	+	1.86651i	0.591864	+	0.0672644i
$771$	−18.8585	−	18.9945i	−0.679174	−	0.684071i
$772$	−20.9410	+	20.9410i	−0.753684	+	0.753684i
$773$	−5.99943	+	5.99943i	−0.215785	+	0.215785i	−0.806719	−	0.590935i	$-0.798759\pi$
$773$	−5.99943	+	5.99943i	−0.215785	+	0.215785i	0.590935	+	0.806719i	$0.298759\pi$
$774$	0.250881	−	34.9160i	0.00901774	−	1.25503i
$775$	−44.4262	−	10.2301i	−1.59583	−	0.367474i
$776$			5.38352i			0.193257i
$777$	0.0463770	−	12.9090i	0.00166377	−	0.463109i
$778$	14.2104	+	14.2104i	0.509468	+	0.509468i
$779$	−0.167380			−0.00599702
$780$	−1.94258	−	2.45881i	−0.0695554	−	0.0880395i
$781$	−13.3864			−0.479002
$782$	−2.62521	−	2.62521i	−0.0938774	−	0.0938774i
$783$	14.7701	+	0.159195i	0.527841	+	0.00568916i
$784$		−	1.87154i		−	0.0668406i
$785$	−8.50188	−	10.6821i	−0.303445	−	0.381261i
$786$	34.0920	−	33.8479i	1.21602	−	1.20731i
$787$	15.8108	−	15.8108i	0.563593	−	0.563593i	−0.366733	−	0.930326i	$-0.619524\pi$
$787$	15.8108	−	15.8108i	0.563593	−	0.563593i	0.930326	+	0.366733i	$0.119524\pi$
$788$	2.81001	−	2.81001i	0.100103	−	0.100103i
$789$	−31.6030	+	31.3768i	−1.12510	+	1.11704i
$790$	−34.8021	−	43.7267i	−1.23820	−	1.55573i
$791$		−	2.85385i		−	0.101471i
$792$	11.9678	+	12.1411i	0.425258	+	0.431414i
$793$	1.40641	+	1.40641i	0.0499429	+	0.0499429i
$794$	67.7082			2.40287
$795$	−12.0637	−	15.2696i	−0.427856	−	0.541558i
$796$	26.0274			0.922515
$797$	8.46554	+	8.46554i	0.299865	+	0.299865i	0.840961	−	0.541096i	$-0.181990\pi$
$797$	8.46554	+	8.46554i	0.299865	+	0.299865i	−0.541096	+	0.840961i	$0.681990\pi$
$798$	−0.0722114	+	20.1000i	−0.00255625	+	0.711534i
$799$		−	1.19409i		−	0.0422438i
$800$	−19.7427	−	31.5551i	−0.698010	−	1.11564i
$801$	6.00554	+	0.0431515i	0.212195	+	0.00152468i
$802$	39.7638	−	39.7638i	1.40411	−	1.40411i
$803$	29.1488	−	29.1488i	1.02864	−	1.02864i
$804$	−30.3333	−	30.5520i	−1.06977	−	1.07749i
$805$	−15.9545	−	1.81320i	−0.562321	−	0.0639069i
$806$		−	5.81839i		−	0.204944i
$807$	−49.3848	−	0.177420i	−1.73843	−	0.00624547i
$808$	−10.2517	−	10.2517i	−0.360655	−	0.360655i
$809$	25.5350			0.897764			0.448882	−	0.893591i	$-0.351822\pi$
$809$	25.5350			0.897764			0.448882	+	0.893591i	$0.351822\pi$
$810$	−34.7753	+	26.8705i	−1.22188	+	0.944133i
$811$	−1.94760			−0.0683895			−0.0341947	−	0.999415i	$-0.510887\pi$
$811$	−1.94760			−0.0683895			−0.0341947	+	0.999415i	$0.510887\pi$
$812$	−5.56539	−	5.56539i	−0.195307	−	0.195307i
$813$	−5.40767	−	0.0194276i	−0.189655	−	0.000681355i
$814$			55.0942i			1.93105i
$815$	−8.84933	+	7.04317i	−0.309978	+	0.246712i
$816$	−0.540719	−	0.544618i	−0.0189289	−	0.0190654i
$817$	−20.0278	+	20.0278i	−0.700685	+	0.700685i
$818$	−16.9078	+	16.9078i	−0.591167	+	0.591167i
$819$	−0.876642	−	0.00629893i	−0.0306324	−	0.000220102i
$820$	−0.0220197	+	0.193753i	−0.000768962	+	0.00676615i
$821$			21.6742i			0.756434i	0.925717	+	0.378217i	$0.123463\pi$
$821$			21.6742i			0.756434i	−0.925717	+	0.378217i	$0.876537\pi$
$822$	−0.0998224	+	27.7856i	−0.00348171	+	0.969133i
$823$	8.35207	+	8.35207i	0.291135	+	0.291135i	0.837528	−	0.546394i	$-0.184000\pi$
$823$	8.35207	+	8.35207i	0.291135	+	0.291135i	−0.546394	+	0.837528i	$0.684000\pi$
$824$	−2.28943			−0.0797559
$825$	6.68095	−	28.5441i	0.232601	−	0.993778i
$826$	−22.5292			−0.783892
$827$	−14.1747	−	14.1747i	−0.492902	−	0.492902i	0.416318	−	0.909219i	$-0.363320\pi$
$827$	−14.1747	−	14.1747i	−0.492902	−	0.492902i	−0.909219	+	0.416318i	$0.863320\pi$
$828$	−41.8727	−	42.4788i	−1.45518	−	1.47624i
$829$			19.3836i			0.673219i	0.941644	+	0.336610i	$0.109280\pi$
$829$			19.3836i			0.673219i	−0.941644	+	0.336610i	$0.890720\pi$
$830$	−3.02605	+	26.6265i	−0.105036	+	0.924218i
$831$	−21.2888	+	21.1364i	−0.738500	+	0.733213i
$832$	2.58573	−	2.58573i	0.0896442	−	0.0896442i
$833$	0.167409	−	0.167409i	0.00580037	−	0.00580037i
$834$	33.0517	−	32.8151i	1.14449	−	1.13629i
$835$	15.8165	−	12.5884i	0.547353	−	0.435638i
$836$		−	49.8066i		−	1.72260i
$837$	−47.3745	−	0.510610i	−1.63750	−	0.0176493i
$838$	−9.06346	−	9.06346i	−0.313092	−	0.313092i
$839$	26.2528			0.906346			0.453173	−	0.891423i	$-0.350292\pi$
$839$	26.2528			0.906346			0.453173	+	0.891423i	$0.350292\pi$
$840$	6.45749	+	0.757391i	0.222805	+	0.0261325i
$841$	−20.9192			−0.721352
$842$	41.5131	+	41.5131i	1.43063	+	1.43063i
$843$	−0.0791386	+	22.0282i	−0.00272568	+	0.758693i
$844$		−	22.9572i		−	0.790221i
$845$	28.6932	+	3.26094i	0.987077	+	0.112180i
$846$	0.237410	−	33.0412i	0.00816234	−	1.13598i
$847$	−0.324327	+	0.324327i	−0.0111440	+	0.0111440i
$848$	6.64940	−	6.64940i	0.228341	−	0.228341i
$849$	34.2179	+	34.4646i	1.17435	+	1.18282i
$850$	0.580076	−	2.51910i	0.0198964	−	0.0864045i
$851$		−	53.5206i		−	1.83466i
$852$	−18.9643	−	0.0681311i	−0.649707	−	0.00233413i
$853$	29.8920	+	29.8920i	1.02348	+	1.02348i	0.999718	+	0.0237636i	$0.00756489\pi$
$853$	29.8920	+	29.8920i	1.02348	+	1.02348i	0.0237636	+	0.999718i	$0.492435\pi$
$854$	−14.8633			−0.508612
$855$	35.3908	+	4.27990i	1.21034	+	0.146369i
$856$	7.02373			0.240066
$857$	5.92367	+	5.92367i	0.202349	+	0.202349i	0.801006	−	0.598657i	$-0.204299\pi$
$857$	5.92367	+	5.92367i	0.202349	+	0.202349i	−0.598657	+	0.801006i	$0.704299\pi$
$858$	3.74145	+	0.0134415i	0.127731	+	0.000458885i
$859$		−	10.3620i		−	0.353548i	−0.984252	−	0.176774i	$-0.943434\pi$
$859$		−	10.3620i		−	0.353548i	0.984252	−	0.176774i	$-0.0565661\pi$
$860$	20.5487	+	25.8182i	0.700705	+	0.880394i
$861$	0.0384368	+	0.0387139i	0.00130992	+	0.00131937i
$862$	6.45633	−	6.45633i	0.219904	−	0.219904i
$863$	−13.2818	+	13.2818i	−0.452118	+	0.452118i	−0.896057	−	0.443939i	$-0.853581\pi$
$863$	−13.2818	+	13.2818i	−0.452118	+	0.452118i	0.443939	+	0.896057i	$0.353581\pi$
$864$	−27.0563	−	27.6459i	−0.920474	−	0.940532i
$865$	7.65632	+	9.61971i	0.260323	+	0.327080i
$866$		−	6.82129i		−	0.231797i
$867$	−0.105434	+	29.3476i	−0.00358073	+	0.996696i
$868$	17.8507	+	17.8507i	0.605894	+	0.605894i
$869$	38.7419			1.31423
$870$	−18.8651	+	14.9043i	−0.639586	+	0.505303i
$871$	−2.62342			−0.0888913
$872$	−3.34965	−	3.34965i	−0.113433	−	0.113433i
$873$	6.85150	−	6.75374i	0.231888	−	0.228580i
$874$			83.3342i			2.81882i
$875$	−4.82184	−	10.0871i	−0.163008	−	0.341007i
$876$	41.4430	−	41.1463i	1.40023	−	1.39020i
$877$	4.84197	−	4.84197i	0.163502	−	0.163502i	−0.620614	−	0.784116i	$-0.713117\pi$
$877$	4.84197	−	4.84197i	0.163502	−	0.163502i	0.784116	+	0.620614i	$0.213117\pi$
$878$	−42.6227	+	42.6227i	−1.43845	+	1.43845i
$879$	11.6957	−	11.6119i	0.394485	−	0.391660i
$880$	14.0755	+	1.59966i	0.474485	+	0.0539245i
$881$		−	17.0394i		−	0.574073i	−0.957920	−	0.287036i	$-0.907330\pi$
$881$		−	17.0394i		−	0.574073i	0.957920	−	0.287036i	$-0.0926701\pi$
$882$	4.66559	−	4.59902i	0.157099	−	0.154857i
$883$	12.2389	+	12.2389i	0.411871	+	0.411871i	0.882390	−	0.470519i	$-0.155933\pi$
$883$	12.2389	+	12.2389i	0.411871	+	0.411871i	−0.470519	+	0.882390i	$0.655933\pi$
$884$	0.191553			0.00644262
$885$	−4.65457	+	39.6847i	−0.156462	+	1.33399i
$886$	37.9983			1.27658
$887$	−41.0767	−	41.0767i	−1.37922	−	1.37922i	−0.845934	−	0.533287i	$-0.820957\pi$
$887$	−41.0767	−	41.0767i	−1.37922	−	1.37922i	−0.533287	−	0.845934i	$-0.679043\pi$
$888$	−0.0778552	+	21.6710i	−0.00261265	+	0.727231i
$889$			16.4432i			0.551487i
$890$	−7.64848	+	6.08742i	−0.256378	+	0.204051i
$891$	0.437785	−	30.4624i	0.0146664	−	1.02053i
$892$	−10.6879	+	10.6879i	−0.357858	+	0.357858i
$893$	−18.9525	+	18.9525i	−0.634220	+	0.634220i
$894$	−50.4599	−	50.8238i	−1.68763	−	1.69980i
$895$	3.69464	−	32.5094i	0.123498	−	1.08667i
$896$			12.4379i			0.415520i
$897$	−3.63458	−	0.0130576i	−0.121355	−	0.000435980i
$898$	−52.7879	−	52.7879i	−1.76155	−	1.76155i
$899$	−25.9188			−0.864441
$900$	9.61009	−	40.4040i	0.320336	−	1.34680i
$901$	1.18958			0.0396305
$902$	−0.164635	−	0.164635i	−0.00548173	−	0.00548173i
$903$	9.23144	+	0.0331649i	0.307203	+	0.00110366i
$904$			4.79089i			0.159343i
$905$	2.48389	−	21.8559i	0.0825673	−	0.726515i
$906$	5.07736	+	5.11398i	0.168684	+	0.169901i
$907$	24.8992	−	24.8992i	0.826765	−	0.826765i	−0.160303	−	0.987068i	$-0.551247\pi$
$907$	24.8992	−	24.8992i	0.826765	−	0.826765i	0.987068	+	0.160303i	$0.0512470\pi$
$908$	−4.17359	+	4.17359i	−0.138505	+	0.138505i
$909$	−0.186158	+	25.9082i	−0.00617448	+	0.859322i
$910$	1.11647	−	0.888595i	0.0370105	−	0.0294566i
$911$		−	23.4322i		−	0.776342i	−0.921587	−	0.388171i	$-0.873107\pi$
$911$		−	23.4322i		−	0.776342i	0.921587	−	0.388171i	$-0.126893\pi$
$912$	−0.0618874	+	17.2264i	−0.00204930	+	0.570422i
$913$	−13.1361	−	13.1361i	−0.434740	−	0.434740i
$914$	−28.7526			−0.951050
$915$	−3.07078	+	26.1814i	−0.101517	+	0.865529i
$916$	−17.3326			−0.572685
$917$	8.98121	+	8.98121i	0.296586	+	0.296586i
$918$	0.0289532	−	2.68628i	0.000955598	−	0.0886605i
$919$		−	31.9950i		−	1.05542i	−0.849425	−	0.527710i	$-0.823051\pi$
$919$		−	31.9950i		−	1.05542i	0.849425	−	0.527710i	$-0.176949\pi$
$920$	26.7835	+	3.04390i	0.883026	+	0.100354i
$921$	−17.5746	+	17.4488i	−0.579103	+	0.574957i
$922$	39.6195	−	39.6195i	1.30480	−	1.30480i
$923$	−0.817134	+	0.817134i	−0.0268963	+	0.0268963i
$924$	−11.5199	+	11.4375i	−0.378978	+	0.376265i
$925$	31.5917	−	19.7656i	1.03873	−	0.649889i
$926$			40.8180i			1.34136i
$927$	2.87214	+	2.91371i	0.0943333	+	0.0956987i
$928$	−14.9639	−	14.9639i	−0.491214	−	0.491214i
$929$	−49.7858			−1.63342			−0.816709	−	0.577050i	$-0.804204\pi$
$929$	−49.7858			−1.63342			−0.816709	+	0.577050i	$0.804204\pi$
$930$	60.5089	−	47.8049i	1.98417	−	1.56758i
$931$	−5.31419			−0.174166
$932$	−7.40423	−	7.40423i	−0.242534	−	0.242534i
$933$	0.00245264	−	0.682692i	8.02958e−5	−	0.0223503i
$934$		−	60.7340i		−	1.98728i
$935$	1.11596	+	1.40214i	0.0364959	+	0.0458549i
$936$	1.47166	+	0.0105743i	0.0481027	+	0.000345632i
$937$	18.0919	−	18.0919i	0.591035	−	0.591035i	−0.346876	−	0.937911i	$-0.612757\pi$
$937$	18.0919	−	18.0919i	0.591035	−	0.591035i	0.937911	+	0.346876i	$0.112757\pi$
$938$	13.8626	−	13.8626i	0.452628	−	0.452628i
$939$	17.9157	+	18.0449i	0.584656	+	0.588872i
$940$	19.4454	+	24.4319i	0.634238	+	0.796882i
$941$			61.0502i			1.99018i	0.0989766	+	0.995090i	$0.468443\pi$
$941$			61.0502i			1.99018i	−0.0989766	+	0.995090i	$0.531557\pi$
$942$	23.0933	+	0.0829648i	0.752419	+	0.00270314i
$943$	0.159932	+	0.159932i	0.00520811	+	0.00520811i
$944$	−19.3082			−0.628430
$945$	−7.13715	−	9.16849i	−0.232171	−	0.298251i
$946$	−39.3986			−1.28096
$947$	28.1297	+	28.1297i	0.914093	+	0.914093i	0.996591	−	0.0824986i	$-0.0262900\pi$
$947$	28.1297	+	28.1297i	0.914093	+	0.914093i	−0.0824986	+	0.996591i	$0.526290\pi$
$948$	54.8851	+	0.197180i	1.78259	+	0.00640411i
$949$		−	3.55861i		−	0.115517i
$950$	−49.1899	+	30.7761i	−1.59593	+	0.998507i
$951$	34.1841	+	34.4306i	1.10850	+	1.11649i
$952$	−0.281037	+	0.281037i	−0.00910845	+	0.00910845i
$953$	−16.4406	+	16.4406i	−0.532564	+	0.532564i	−0.921335	−	0.388771i	$-0.872900\pi$
$953$	−16.4406	+	16.4406i	−0.532564	+	0.532564i	0.388771	+	0.921335i	$0.372900\pi$
$954$	32.9163	+	0.236513i	1.06571	+	0.00765740i
$955$	−14.1723	−	1.61066i	−0.458606	−	0.0521198i
$956$			5.77342i			0.186726i
$957$	0.0598771	−	16.6668i	0.00193555	−	0.538761i
$958$	−41.6493	−	41.6493i	−1.34563	−	1.34563i
$959$	−7.34614			−0.237219
$960$	48.1355	+	5.64575i	1.55357	+	0.182216i
$961$	52.1335			1.68173
$962$	3.36307	+	3.36307i	0.108430	+	0.108430i
$963$	−8.81142	−	8.93897i	−0.283944	−	0.288054i
$964$		−	15.0533i		−	0.484834i
$965$	−18.7138	+	14.8943i	−0.602417	+	0.479463i
$966$	19.2747	−	19.1367i	0.620152	−	0.615712i
$967$	−3.29391	+	3.29391i	−0.105925	+	0.105925i	−0.758083	−	0.652158i	$-0.773864\pi$
$967$	−3.29391	+	3.29391i	−0.105925	+	0.105925i	0.652158	+	0.758083i	$0.273864\pi$
$968$	0.544462	−	0.544462i	0.0174997	−	0.0174997i
$969$	−1.54643	+	1.53536i	−0.0496785	+	0.0493228i
$970$	−1.76825	+	15.5590i	−0.0567752	+	0.499569i
$971$			32.3161i			1.03707i	0.855056	+	0.518536i	$0.173523\pi$
$971$			32.3161i			1.03707i	−0.855056	+	0.518536i	$0.826477\pi$
$972$	0.775246	−	43.1535i	0.0248660	−	1.38415i
$973$	8.70717	+	8.70717i	0.279139	+	0.279139i
$974$	−88.4809			−2.83511
$975$	−1.33457	−	2.15021i	−0.0427406	−	0.0688620i
$976$	−12.7383			−0.407744
$977$	−8.42742	−	8.42742i	−0.269617	−	0.269617i	0.559329	−	0.828946i	$-0.311059\pi$
$977$	−8.42742	−	8.42742i	−0.269617	−	0.269617i	−0.828946	+	0.559329i	$0.811059\pi$
$978$	0.0687302	−	19.1311i	0.00219775	−	0.611744i
$979$		−	6.77655i		−	0.216580i
$980$	−0.699108	+	6.15151i	−0.0223322	+	0.196503i
$981$	−0.0608251	+	8.46523i	−0.00194200	+	0.270274i
$982$	4.23900	−	4.23900i	0.135272	−	0.135272i
$983$	43.2280	−	43.2280i	1.37876	−	1.37876i	0.532042	−	0.846718i	$-0.321425\pi$
$983$	43.2280	−	43.2280i	1.37876	−	1.37876i	0.846718	−	0.532042i	$-0.178575\pi$
$984$	−0.0645255	−	0.0649908i	−0.00205700	−	0.00207183i
$985$	2.51114	−	1.99862i	0.0800117	−	0.0636812i
$986$		−	1.46968i		−	0.0468041i
$987$	8.73578	+	0.0313841i	0.278063	+	0.000998968i
$988$	−3.04031	−	3.04031i	−0.0967251	−	0.0967251i
$989$	38.2733			1.21702
$990$	30.6006	+	39.0200i	0.972551	+	1.24014i
$991$	−25.2971			−0.803590			−0.401795	−	0.915730i	$-0.631614\pi$
$991$	−25.2971			−0.803590			−0.401795	+	0.915730i	$0.631614\pi$
$992$	47.9961	+	47.9961i	1.52388	+	1.52388i
$993$	42.8417	+	0.153913i	1.35954	+	0.00488428i
$994$		−	8.63571i		−	0.273908i
$995$	20.8855	+	2.37360i	0.662115	+	0.0752483i
$996$	−18.5428	−	18.6765i	−0.587552	−	0.591789i
$997$	−23.3279	+	23.3279i	−0.738803	+	0.738803i	−0.972346	−	0.233543i	$-0.924968\pi$
$997$	−23.3279	+	23.3279i	−0.738803	+	0.738803i	0.233543	+	0.972346i	$0.424968\pi$
$998$	46.8108	−	46.8108i	1.48177	−	1.48177i
$999$	27.6779	−	27.0877i	0.875691	−	0.857016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.j.a.8.11	yes	24
3.2	odd	2	inner	105.2.j.a.8.2	✓	24
5.2	odd	4	inner	105.2.j.a.92.2	yes	24
5.3	odd	4		525.2.j.b.407.11		24
5.4	even	2		525.2.j.b.218.2		24
7.2	even	3		735.2.y.j.263.11		48
7.3	odd	6		735.2.y.g.128.2		48
7.4	even	3		735.2.y.j.128.2		48
7.5	odd	6		735.2.y.g.263.11		48
7.6	odd	2		735.2.j.h.638.11		24
15.2	even	4	inner	105.2.j.a.92.11	yes	24
15.8	even	4		525.2.j.b.407.2		24
15.14	odd	2		525.2.j.b.218.11		24
21.2	odd	6		735.2.y.j.263.2		48
21.5	even	6		735.2.y.g.263.2		48
21.11	odd	6		735.2.y.j.128.11		48
21.17	even	6		735.2.y.g.128.11		48
21.20	even	2		735.2.j.h.638.2		24
35.2	odd	12		735.2.y.j.557.11		48
35.12	even	12		735.2.y.g.557.11		48
35.17	even	12		735.2.y.g.422.2		48
35.27	even	4		735.2.j.h.197.2		24
35.32	odd	12		735.2.y.j.422.2		48
105.2	even	12		735.2.y.j.557.2		48
105.17	odd	12		735.2.y.g.422.11		48
105.32	even	12		735.2.y.j.422.11		48
105.47	odd	12		735.2.y.g.557.2		48
105.62	odd	4		735.2.j.h.197.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.2	✓	24	3.2	odd	2	inner
105.2.j.a.8.11	yes	24	1.1	even	1	trivial
105.2.j.a.92.2	yes	24	5.2	odd	4	inner
105.2.j.a.92.11	yes	24	15.2	even	4	inner
525.2.j.b.218.2		24	5.4	even	2
525.2.j.b.218.11		24	15.14	odd	2
525.2.j.b.407.2		24	15.8	even	4
525.2.j.b.407.11		24	5.3	odd	4
735.2.j.h.197.2		24	35.27	even	4
735.2.j.h.197.11		24	105.62	odd	4
735.2.j.h.638.2		24	21.20	even	2
735.2.j.h.638.11		24	7.6	odd	2
735.2.y.g.128.2		48	7.3	odd	6
735.2.y.g.128.11		48	21.17	even	6
735.2.y.g.263.2		48	21.5	even	6
735.2.y.g.263.11		48	7.5	odd	6
735.2.y.g.422.2		48	35.17	even	12
735.2.y.g.422.11		48	105.17	odd	12
735.2.y.g.557.2		48	105.47	odd	12
735.2.y.g.557.11		48	35.12	even	12
735.2.y.j.128.2		48	7.4	even	3
735.2.y.j.128.11		48	21.11	odd	6
735.2.y.j.263.2		48	21.2	odd	6
735.2.y.j.263.11		48	7.2	even	3
735.2.y.j.422.2		48	35.32	odd	12
735.2.y.j.422.11		48	105.32	even	12
735.2.y.j.557.2		48	105.2	even	12
735.2.y.j.557.11		48	35.2	odd	12

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.54414 + 1.54414i) q^{2} +(-1.73204 - 0.00622252i) q^{3} +2.76875i q^{4} +(-0.252500 + 2.22177i) q^{5} +(-2.66491 - 2.68412i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.18705 + 1.18705i) q^{8} +(2.99992 + 0.0215553i) q^{9} +(-3.82062 + 3.04083i) q^{10} -3.38507i q^{11} +(0.0172286 - 4.79558i) q^{12} +(-0.206632 - 0.206632i) q^{13} +2.18375 q^{14} +(0.451165 - 3.84662i) q^{15} +1.87154 q^{16} +(0.167409 + 0.167409i) q^{17} +(4.59902 + 4.66559i) q^{18} -5.31419i q^{19} +(-6.15151 - 0.699108i) q^{20} +(-1.22914 + 1.22034i) q^{21} +(5.22702 - 5.22702i) q^{22} +(-5.07773 + 5.07773i) q^{23} +(2.06341 - 2.04864i) q^{24} +(-4.87249 - 1.12199i) q^{25} -0.638138i q^{26} +(-5.19585 - 0.0560017i) q^{27} +(1.95780 + 1.95780i) q^{28} -2.84268 q^{29} +(6.63638 - 5.24306i) q^{30} +9.11776 q^{31} +(5.26402 + 5.26402i) q^{32} +(-0.0210636 + 5.86307i) q^{33} +0.517005i q^{34} +(1.39248 + 1.74957i) q^{35} +(-0.0596812 + 8.30602i) q^{36} +(-5.27013 + 5.27013i) q^{37} +(8.20586 - 8.20586i) q^{38} +(0.356609 + 0.359180i) q^{39} +(-2.33762 - 2.93708i) q^{40} -0.0314968i q^{41} +(-3.78233 - 0.0135884i) q^{42} +(-3.76875 - 3.76875i) q^{43} +9.37239 q^{44} +(-0.805371 + 6.65968i) q^{45} -15.6815 q^{46} +(-3.56639 - 3.56639i) q^{47} +(-3.24158 - 0.0116457i) q^{48} -1.00000i q^{49} +(-5.79130 - 9.25632i) q^{50} +(-0.288917 - 0.291000i) q^{51} +(0.572111 - 0.572111i) q^{52} +(3.55291 - 3.55291i) q^{53} +(-7.93665 - 8.10960i) q^{54} +(7.52082 + 0.854729i) q^{55} +1.67875i q^{56} +(-0.0330677 + 9.20439i) q^{57} +(-4.38949 - 4.38949i) q^{58} -10.3168 q^{59} +(10.6503 + 1.24916i) q^{60} -6.80634 q^{61} +(14.0791 + 14.0791i) q^{62} +(2.13651 - 2.10602i) q^{63} +12.5137i q^{64} +(0.511262 - 0.406913i) q^{65} +(-9.08593 + 9.02088i) q^{66} +(6.34806 - 6.34806i) q^{67} +(-0.463512 + 0.463512i) q^{68} +(8.82642 - 8.76323i) q^{69} +(-0.551396 + 4.85177i) q^{70} -3.95454i q^{71} +(-3.58665 + 3.53548i) q^{72} +(8.61099 + 8.61099i) q^{73} -16.2757 q^{74} +(8.43236 + 1.97365i) q^{75} +14.7136 q^{76} +(-2.39360 - 2.39360i) q^{77} +(-0.00397083 + 1.10528i) q^{78} +11.4449i q^{79} +(-0.472563 + 4.15812i) q^{80} +(8.99907 + 0.129328i) q^{81} +(0.0486356 - 0.0486356i) q^{82} +(3.88059 - 3.88059i) q^{83} +(-3.37880 - 3.40317i) q^{84} +(-0.414214 + 0.329672i) q^{85} -11.6390i q^{86} +(4.92363 + 0.0176886i) q^{87} +(4.01825 + 4.01825i) q^{88} +2.00190 q^{89} +(-11.5271 + 9.03989i) q^{90} -0.292222 q^{91} +(-14.0589 - 14.0589i) q^{92} +(-15.7923 - 0.0567354i) q^{93} -11.0140i q^{94} +(11.8069 + 1.34183i) q^{95} +(-9.08474 - 9.15025i) q^{96} +(2.26760 - 2.26760i) q^{97} +(1.54414 - 1.54414i) q^{98} +(0.0729661 - 10.1549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 24 * q - 4 * q^3 - 16 * q^10 + 16 * q^12 - 8 * q^13 - 16 * q^15 - 16 * q^16 - 20 * q^18 + 4 * q^21 + 8 * q^22 - 16 * q^25 - 16 * q^27 + 20 * q^30 + 28 * q^33 + 16 * q^36 - 16 * q^37 + 64 * q^40 - 20 * q^42 - 40 * q^43 + 20 * q^45 - 64 * q^46 + 16 * q^48 - 20 * q^51 + 40 * q^55 + 4 * q^57 + 40 * q^58 + 32 * q^60 + 32 * q^61 - 8 * q^63 - 16 * q^66 + 24 * q^67 - 8 * q^70 - 8 * q^72 + 32 * q^73 - 60 * q^75 + 32 * q^76 + 60 * q^78 + 52 * q^81 - 80 * q^82 + 24 * q^85 + 4 * q^87 + 96 * q^88 - 24 * q^90 - 24 * q^91 - 76 * q^93 - 96 * q^96 + 24 * q^97

Introduction

L-functions

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