LMFDB - Embedded newform 91.2.bb.a.47.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [91,2,Mod(5,91)] 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("91.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(91, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.bb (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.4
Character	$\chi$	$=$	91.47
Dual form			91.2.bb.a.31.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.746505 + 0.200025i) q^{2} +(-0.421869 + 0.243566i) q^{3} +(-1.21479 + 0.701360i) q^{4} +(0.472319 + 1.76272i) q^{5} +(0.266208 - 0.266208i) q^{6} +(-0.210751 + 2.63734i) q^{7} +(1.85952 - 1.85952i) q^{8} +(-1.38135 + 2.39257i) q^{9} +(-0.705177 - 1.22140i) q^{10} +(0.990745 + 0.265469i) q^{11} +(0.341655 - 0.591765i) q^{12} +(-0.266208 - 3.59571i) q^{13} +(-0.370209 - 2.01095i) q^{14} +(-0.628596 - 0.628596i) q^{15} +(0.386531 - 0.669491i) q^{16} +(2.60029 + 4.50383i) q^{17} +(0.552611 - 2.06237i) q^{18} +(-1.36051 - 5.07751i) q^{19} +(-1.81007 - 1.81007i) q^{20} +(-0.553459 - 1.16395i) q^{21} -0.792697 q^{22} +(0.730699 + 0.421869i) q^{23} +(-0.331558 + 1.23739i) q^{24} +(1.44604 - 0.834871i) q^{25} +(0.917960 + 2.63097i) q^{26} -2.80720i q^{27} +(-1.59371 - 3.35163i) q^{28} +10.3454 q^{29} +(0.594985 + 0.343515i) q^{30} +(-5.69625 - 1.52630i) q^{31} +(-1.51589 + 5.65739i) q^{32} +(-0.482625 + 0.129319i) q^{33} +(-2.84201 - 2.84201i) q^{34} +(-4.74843 + 0.874173i) q^{35} -3.87530i q^{36} +(1.61677 + 6.03388i) q^{37} +(2.03126 + 3.51825i) q^{38} +(0.988100 + 1.45208i) q^{39} +(4.15609 + 2.39952i) q^{40} +(-0.0927742 + 0.0927742i) q^{41} +(0.645979 + 0.758186i) q^{42} +7.36681i q^{43} +(-1.38974 + 0.372379i) q^{44} +(-4.86986 - 1.30488i) q^{45} +(-0.629856 - 0.168769i) q^{46} +(2.17913 - 0.583897i) q^{47} +0.376584i q^{48} +(-6.91117 - 1.11164i) q^{49} +(-0.912480 + 0.912480i) q^{50} +(-2.19397 - 1.26669i) q^{51} +(2.84527 + 4.18133i) q^{52} +(3.38590 + 5.86455i) q^{53} +(0.561512 + 2.09559i) q^{54} +1.87179i q^{55} +(4.51229 + 5.29608i) q^{56} +(1.81067 + 1.81067i) q^{57} +(-7.72287 + 2.06934i) q^{58} +(2.60938 - 9.73833i) q^{59} +(1.20448 + 0.322741i) q^{60} +(1.13174 + 0.653409i) q^{61} +4.55758 q^{62} +(-6.01891 - 4.14733i) q^{63} -2.98037i q^{64} +(6.21249 - 2.16757i) q^{65} +(0.334415 - 0.193074i) q^{66} +(1.11471 - 4.16014i) q^{67} +(-6.31762 - 3.64748i) q^{68} -0.411013 q^{69} +(3.36987 - 1.60238i) q^{70} +(-6.02388 - 6.02388i) q^{71} +(1.88038 + 7.01767i) q^{72} +(2.93641 - 10.9588i) q^{73} +(-2.41386 - 4.18093i) q^{74} +(-0.406693 + 0.704413i) q^{75} +(5.21390 + 5.21390i) q^{76} +(-0.908934 + 2.55699i) q^{77} +(-1.02807 - 0.886341i) q^{78} +(5.16240 - 8.94154i) q^{79} +(1.36269 + 0.365132i) q^{80} +(-3.46031 - 5.99344i) q^{81} +(0.0506992 - 0.0878136i) q^{82} +(-4.16974 + 4.16974i) q^{83} +(1.48868 + 1.02578i) q^{84} +(-6.71082 + 6.71082i) q^{85} +(-1.47355 - 5.49936i) q^{86} +(-4.36440 + 2.51978i) q^{87} +(2.33595 - 1.34866i) q^{88} +(-7.49857 + 2.00924i) q^{89} +3.89639 q^{90} +(9.53923 + 0.0557161i) q^{91} -1.18353 q^{92} +(2.77483 - 0.743513i) q^{93} +(-1.50994 + 0.871764i) q^{94} +(8.30761 - 4.79640i) q^{95} +(-0.738442 - 2.75590i) q^{96} +(2.49152 - 2.49152i) q^{97} +(5.38158 - 0.552561i) q^{98} +(-2.00372 + 2.00372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9} - 10 q^{11} + 28 q^{14} - 44 q^{15} + 12 q^{16} - 4 q^{18} + 12 q^{19} - 26 q^{21} - 8 q^{22} - 12 q^{24} + 24 q^{26} - 6 q^{28} + 16 q^{29}+ \cdots - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9 - 10 * q^11 + 28 * q^14 - 44 * q^15 + 12 * q^16 - 4 * q^18 + 12 * q^19 - 26 * q^21 - 8 * q^22 - 12 * q^24 + 24 * q^26 - 6 * q^28 + 16 * q^29 + 24 * q^31 + 4 * q^32 + 48 * q^33 + 28 * q^35 - 8 * q^37 - 6 * q^39 - 132 * q^40 - 16 * q^42 - 42 * q^44 - 24 * q^45 + 12 * q^46 + 30 * q^47 + 88 * q^50 + 36 * q^52 - 12 * q^53 + 78 * q^54 + 40 * q^57 + 26 * q^58 - 54 * q^59 + 16 * q^60 - 48 * q^61 + 24 * q^63 - 8 * q^65 + 12 * q^66 + 16 * q^67 - 48 * q^68 + 50 * q^70 - 36 * q^71 + 22 * q^72 + 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 + 138 * q^80 + 16 * q^81 - 58 * q^84 - 84 * q^85 + 42 * q^86 - 24 * q^87 - 60 * q^89 + 48 * q^92 + 6 * q^93 - 72 * q^94 - 42 * q^96 - 86 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.746505	+	0.200025i	−0.527859	+	0.141439i	−0.512899	−	0.858449i	$-0.671429\pi$
$2$	−0.746505	+	0.200025i	−0.527859	+	0.141439i	−0.0149595	+	0.999888i	$0.504762\pi$
$3$	−0.421869	+	0.243566i	−0.243566	+	0.140623i	−0.616815	−	0.787108i	$-0.711577\pi$
$3$	−0.421869	+	0.243566i	−0.243566	+	0.140623i	0.373248	+	0.927731i	$0.378244\pi$
$4$	−1.21479	+	0.701360i	−0.607395	+	0.350680i
$5$	0.472319	+	1.76272i	0.211227	+	0.788311i	0.987461	+	0.157865i	$0.0504612\pi$
$5$	0.472319	+	1.76272i	0.211227	+	0.788311i	−0.776233	+	0.630446i	$0.782872\pi$
$6$	0.266208	−	0.266208i	0.108679	−	0.108679i
$7$	−0.210751	+	2.63734i	−0.0796563	+	0.996822i
$7$	−0.210751	+	2.63734i	−0.0796563	+	0.996822i
$8$	1.85952	−	1.85952i	0.657439	−	0.657439i
$9$	−1.38135	+	2.39257i	−0.460450	+	0.797523i
$10$	−0.705177	−	1.22140i	−0.222996	−	0.386241i
$11$	0.990745	+	0.265469i	0.298721	+	0.0800420i	0.405067	−	0.914287i	$-0.367248\pi$
$11$	0.990745	+	0.265469i	0.298721	+	0.0800420i	−0.106346	+	0.994329i	$0.533915\pi$
$12$	0.341655	−	0.591765i	0.0986274	−	0.170828i
$13$	−0.266208	−	3.59571i	−0.0738329	−	0.997271i
$13$	−0.266208	−	3.59571i	−0.0738329	−	0.997271i
$14$	−0.370209	−	2.01095i	−0.0989426	−	0.537448i
$15$	−0.628596	−	0.628596i	−0.162303	−	0.162303i
$16$	0.386531	−	0.669491i	0.0966328	−	0.167373i
$17$	2.60029	+	4.50383i	0.630663	+	1.09234i	0.987416	+	0.158142i	$0.0505503\pi$
$17$	2.60029	+	4.50383i	0.630663	+	1.09234i	−0.356753	+	0.934199i	$0.616116\pi$
$18$	0.552611	−	2.06237i	0.130252	−	0.486106i
$19$	−1.36051	−	5.07751i	−0.312123	−	1.16486i	−0.926638	−	0.375954i	$-0.877315\pi$
$19$	−1.36051	−	5.07751i	−0.312123	−	1.16486i	0.614515	−	0.788905i	$-0.289352\pi$
$20$	−1.81007	−	1.81007i	−0.404743	−	0.404743i
$21$	−0.553459	−	1.16395i	−0.120775	−	0.253994i
$22$	−0.792697			−0.169004
$23$	0.730699	+	0.421869i	0.152361	+	0.0879659i	0.574242	−	0.818685i	$-0.305297\pi$
$23$	0.730699	+	0.421869i	0.152361	+	0.0879659i	−0.421881	+	0.906651i	$0.638630\pi$
$24$	−0.331558	+	1.23739i	−0.0676789	+	0.252581i
$25$	1.44604	−	0.834871i	0.289208	−	0.166974i
$26$	0.917960	+	2.63097i	0.180027	+	0.515975i
$27$		−	2.80720i		−	0.540246i
$28$	−1.59371	−	3.35163i	−0.301183	−	0.633399i
$29$	10.3454			1.92109			0.960543	−	0.278130i	$-0.0897147\pi$
$29$	10.3454			1.92109			0.960543	+	0.278130i	$0.0897147\pi$
$30$	0.594985	+	0.343515i	0.108629	+	0.0627169i
$31$	−5.69625	−	1.52630i	−1.02308	−	0.274132i	−0.291993	−	0.956421i	$-0.594318\pi$
$31$	−5.69625	−	1.52630i	−1.02308	−	0.274132i	−0.731083	+	0.682288i	$0.760985\pi$
$32$	−1.51589	+	5.65739i	−0.267975	+	1.00009i
$33$	−0.482625	+	0.129319i	−0.0840142	+	0.0225115i
$34$	−2.84201	−	2.84201i	−0.487401	−	0.487401i
$35$	−4.74843	+	0.874173i	−0.802632	+	0.147762i
$36$		−	3.87530i		−	0.645883i
$37$	1.61677	+	6.03388i	0.265796	+	0.991964i	0.961761	+	0.273889i	$0.0883101\pi$
$37$	1.61677	+	6.03388i	0.265796	+	0.991964i	−0.695965	+	0.718075i	$0.745023\pi$
$38$	2.03126	+	3.51825i	0.329514	+	0.570735i
$39$	0.988100	+	1.45208i	0.158223	+	0.232519i
$40$	4.15609	+	2.39952i	0.657135	+	0.379397i
$41$	−0.0927742	+	0.0927742i	−0.0144889	+	0.0144889i	−0.714314	−	0.699825i	$-0.753261\pi$
$41$	−0.0927742	+	0.0927742i	−0.0144889	+	0.0144889i	0.699825	+	0.714314i	$0.253261\pi$
$42$	0.645979	+	0.758186i	0.0996768	+	0.116991i
$43$			7.36681i			1.12343i	0.827331	+	0.561714i	$0.189858\pi$
$43$			7.36681i			1.12343i	−0.827331	+	0.561714i	$0.810142\pi$
$44$	−1.38974	+	0.372379i	−0.209511	+	0.0561383i
$45$	−4.86986	−	1.30488i	−0.725956	−	0.194519i
$46$	−0.629856	−	0.168769i	−0.0928671	−	0.0248837i
$47$	2.17913	−	0.583897i	0.317859	−	0.0851701i	−0.0963621	−	0.995346i	$-0.530721\pi$
$47$	2.17913	−	0.583897i	0.317859	−	0.0851701i	0.414221	+	0.910176i	$0.364054\pi$
$48$			0.376584i			0.0543552i
$49$	−6.91117	−	1.11164i	−0.987310	−	0.158806i
$50$	−0.912480	+	0.912480i	−0.129044	+	0.129044i
$51$	−2.19397	−	1.26669i	−0.307217	−	0.177372i
$52$	2.84527	+	4.18133i	0.394569	+	0.579846i
$53$	3.38590	+	5.86455i	0.465089	+	0.805558i	0.999206	−	0.0398532i	$-0.0126890\pi$
$53$	3.38590	+	5.86455i	0.465089	+	0.805558i	−0.534117	+	0.845411i	$0.679356\pi$
$54$	0.561512	+	2.09559i	0.0764121	+	0.285174i
$55$			1.87179i			0.252392i
$56$	4.51229	+	5.29608i	0.602980	+	0.707719i
$57$	1.81067	+	1.81067i	0.239829	+	0.239829i
$58$	−7.72287	+	2.06934i	−1.01406	+	0.271717i
$59$	2.60938	−	9.73833i	0.339712	−	1.26782i	−0.558958	−	0.829196i	$-0.688799\pi$
$59$	2.60938	−	9.73833i	0.339712	−	1.26782i	0.898670	−	0.438626i	$-0.144535\pi$
$60$	1.20448	+	0.322741i	0.155498	+	0.0416656i
$61$	1.13174	+	0.653409i	0.144904	+	0.0836604i	0.570699	−	0.821159i	$-0.306672\pi$
$61$	1.13174	+	0.653409i	0.144904	+	0.0836604i	−0.425795	+	0.904820i	$0.640006\pi$
$62$	4.55758			0.578813
$63$	−6.01891	−	4.14733i	−0.758311	−	0.522515i
$64$		−	2.98037i		−	0.372546i
$65$	6.21249	−	2.16757i	0.770564	−	0.268854i
$66$	0.334415	−	0.193074i	0.0411636	−	0.0237658i
$67$	1.11471	−	4.16014i	0.136183	−	0.508242i	−0.863807	−	0.503823i	$-0.831926\pi$
$67$	1.11471	−	4.16014i	0.136183	−	0.508242i	0.999990	−	0.00441973i	$-0.00140685\pi$
$68$	−6.31762	−	3.64748i	−0.766124	−	0.442322i
$69$	−0.411013			−0.0494802
$70$	3.36987	−	1.60238i	0.402777	−	0.191521i
$71$	−6.02388	−	6.02388i	−0.714903	−	0.714903i	0.252654	−	0.967557i	$-0.418697\pi$
$71$	−6.02388	−	6.02388i	−0.714903	−	0.714903i	−0.967557	+	0.252654i	$0.918697\pi$
$72$	1.88038	+	7.01767i	0.221605	+	0.827040i
$73$	2.93641	−	10.9588i	0.343681	−	1.28264i	−0.550464	−	0.834859i	$-0.685549\pi$
$73$	2.93641	−	10.9588i	0.343681	−	1.28264i	0.894146	−	0.447776i	$-0.147784\pi$
$74$	−2.41386	−	4.18093i	−0.280606	−	0.486023i
$75$	−0.406693	+	0.704413i	−0.0469609	+	0.0813386i
$76$	5.21390	+	5.21390i	0.598075	+	0.598075i
$77$	−0.908934	+	2.55699i	−0.103583	+	0.291396i
$78$	−1.02807	−	0.886341i	−0.116407	−	0.100358i
$79$	5.16240	−	8.94154i	0.580816	−	1.00600i	−0.414567	−	0.910019i	$-0.636067\pi$
$79$	5.16240	−	8.94154i	0.580816	−	1.00600i	0.995383	−	0.0959836i	$-0.0305996\pi$
$80$	1.36269	+	0.365132i	0.152353	+	0.0408230i
$81$	−3.46031	−	5.99344i	−0.384479	−	0.665937i
$82$	0.0506992	−	0.0878136i	0.00559879	−	0.00969739i
$83$	−4.16974	+	4.16974i	−0.457689	+	0.457689i	−0.897896	−	0.440207i	$-0.854905\pi$
$83$	−4.16974	+	4.16974i	−0.457689	+	0.457689i	0.440207	+	0.897896i	$0.354905\pi$
$84$	1.48868	+	1.02578i	0.162429	+	0.111922i
$85$	−6.71082	+	6.71082i	−0.727891	+	0.727891i
$86$	−1.47355	−	5.49936i	−0.158897	−	0.593011i
$87$	−4.36440	+	2.51978i	−0.467912	+	0.270149i
$88$	2.33595	−	1.34866i	0.249013	−	0.143768i
$89$	−7.49857	+	2.00924i	−0.794847	+	0.212979i	−0.633320	−	0.773890i	$-0.718308\pi$
$89$	−7.49857	+	2.00924i	−0.794847	+	0.212979i	−0.161526	+	0.986868i	$0.551642\pi$
$90$	3.89639			0.410715
$91$	9.53923	+	0.0557161i	0.999983	+	0.00584064i
$92$	−1.18353			−0.123391
$93$	2.77483	−	0.743513i	0.287736	−	0.0770987i
$94$	−1.50994	+	0.871764i	−0.155738	+	0.0899156i
$95$	8.30761	−	4.79640i	0.852343	−	0.492100i
$96$	−0.738442	−	2.75590i	−0.0753669	−	0.281273i
$97$	2.49152	−	2.49152i	0.252976	−	0.252976i	−0.569214	−	0.822189i	$-0.692752\pi$
$97$	2.49152	−	2.49152i	0.252976	−	0.252976i	0.822189	+	0.569214i	$0.192752\pi$
$98$	5.38158	−	0.552561i	0.543622	−	0.0558171i
$99$	−2.00372	+	2.00372i	−0.201381	+	0.201381i
$100$	−1.17109	+	2.02839i	−0.117109	+	0.202839i
$101$	1.21686	+	2.10766i	0.121082	+	0.209720i	0.920195	−	0.391461i	$-0.128030\pi$
$101$	1.21686	+	2.10766i	0.121082	+	0.209720i	−0.799113	+	0.601181i	$0.794697\pi$
$102$	1.89118	+	0.506739i	0.187254	+	0.0501747i
$103$	−1.36817	+	2.36974i	−0.134810	+	0.233498i	−0.925525	−	0.378687i	$-0.876376\pi$
$103$	−1.36817	+	2.36974i	−0.134810	+	0.233498i	0.790715	+	0.612185i	$0.209709\pi$
$104$	−7.18131	−	6.19127i	−0.704185	−	0.607104i
$105$	1.79030	−	1.52535i	0.174715	−	0.148859i
$106$	−3.70065	−	3.70065i	−0.359439	−	0.359439i
$107$	−1.12814	+	1.95399i	−0.109061	+	0.188899i	−0.915390	−	0.402568i	$-0.868118\pi$
$107$	−1.12814	+	1.95399i	−0.109061	+	0.188899i	0.806329	+	0.591467i	$0.201451\pi$
$108$	1.96886	+	3.41016i	0.189454	+	0.328143i
$109$	0.421507	−	1.57309i	0.0403730	−	0.150674i	−0.942797	−	0.333368i	$-0.891815\pi$
$109$	0.421507	−	1.57309i	0.0403730	−	0.150674i	0.983170	+	0.182693i	$0.0584816\pi$
$110$	−0.374406	−	1.39730i	−0.0356982	−	0.133227i
$111$	−2.15172	−	2.15172i	−0.204232	−	0.204232i
$112$	1.68422	+	1.16051i	0.159144	+	0.109658i
$113$	2.63227			0.247623			0.123812	−	0.992306i	$-0.460488\pi$
$113$	2.63227			0.247623			0.123812	+	0.992306i	$0.460488\pi$
$114$	−1.71385	−	0.989494i	−0.160517	−	0.0926746i
$115$	−0.398514	+	1.48727i	−0.0371616	+	0.138689i
$116$	−12.5675	+	7.25583i	−1.16686	+	0.673687i
$117$	8.97071	+	4.33002i	0.829343	+	0.400310i
$118$			7.79165i			0.717280i
$119$	−12.4262	+	5.90867i	−1.13911	+	0.541647i
$120$	−2.33777			−0.213408
$121$	−8.61518	−	4.97398i	−0.783198	−	0.452180i
$122$	−0.975546	−	0.261397i	−0.0883218	−	0.0236658i
$123$	0.0165419	−	0.0617353i	0.00149153	−	0.00556648i
$124$	7.99024	−	2.14098i	0.717544	−	0.192265i
$125$	8.60663	+	8.60663i	0.769800	+	0.769800i
$126$	5.32272	+	1.89207i	0.474186	+	0.168559i
$127$			11.8104i			1.04801i	0.851716	+	0.524004i	$0.175562\pi$
$127$			11.8104i			1.04801i	−0.851716	+	0.524004i	$0.824438\pi$
$128$	−2.43564	−	9.08992i	−0.215282	−	0.803443i
$129$	−1.79431	−	3.10783i	−0.157980	−	0.273629i
$130$	−4.20408	+	2.86076i	−0.368723	+	0.250905i
$131$	−13.3773	−	7.72337i	−1.16878	−	0.674794i	−0.215386	−	0.976529i	$-0.569101\pi$
$131$	−13.3773	−	7.72337i	−1.16878	−	0.674794i	−0.953392	+	0.301735i	$0.902434\pi$
$132$	0.495589	−	0.495589i	0.0431355	−	0.0431355i
$133$	13.6779	−	2.51805i	1.18602	−	0.218343i
$134$			3.32854i			0.287542i
$135$	4.94830	−	1.32589i	0.425882	−	0.114115i
$136$	13.2102	+	3.53967i	1.13277	+	0.303525i
$137$	0.990138	+	0.265307i	0.0845932	+	0.0226667i	0.300867	−	0.953666i	$-0.402724\pi$
$137$	0.990138	+	0.265307i	0.0845932	+	0.0226667i	−0.216274	+	0.976333i	$0.569391\pi$
$138$	0.306823	−	0.0822131i	0.0261185	−	0.00699844i
$139$			11.4028i			0.967171i	0.875297	+	0.483585i	$0.160666\pi$
$139$			11.4028i			0.967171i	−0.875297	+	0.483585i	$0.839334\pi$
$140$	5.15525	−	4.39230i	0.435698	−	0.371217i
$141$	−0.777092	+	0.777092i	−0.0654429	+	0.0654429i
$142$	5.70178	+	3.29193i	0.478483	+	0.276252i
$143$	0.690806	−	3.63310i	0.0577681	−	0.303815i
$144$	1.06787	+	1.84961i	0.0889892	+	0.154134i
$145$	4.88631	+	18.2360i	0.405786	+	1.51441i
$146$			8.76819i			0.725660i
$147$	3.18637	−	1.21436i	0.262807	−	0.100159i
$148$	−6.19597	−	6.19597i	−0.509305	−	0.509305i
$149$	7.37799	−	1.97693i	0.604428	−	0.161956i	0.0563893	−	0.998409i	$-0.482041\pi$
$149$	7.37799	−	1.97693i	0.604428	−	0.161956i	0.548039	+	0.836453i	$0.315375\pi$
$150$	0.162698	−	0.607197i	0.0132842	−	0.0495774i
$151$	−6.61717	−	1.77307i	−0.538498	−	0.144290i	−0.0206882	−	0.999786i	$-0.506586\pi$
$151$	−6.61717	−	1.77307i	−0.538498	−	0.144290i	−0.517810	+	0.855496i	$0.673252\pi$
$152$	−11.9716	−	6.91181i	−0.971026	−	0.560622i
$153$	−14.3677			−1.16156
$154$	0.167062	−	2.09062i	0.0134622	−	0.168467i
$155$		−	10.7618i		−	0.864406i
$156$	−2.21877	−	1.07096i	−0.177643	−	0.0857455i
$157$	−11.1262	+	6.42373i	−0.887970	+	0.512670i	−0.873278	−	0.487222i	$-0.838010\pi$
$157$	−11.1262	+	6.42373i	−0.887970	+	0.512670i	−0.0146919	+	0.999892i	$0.504677\pi$
$158$	−2.06522	+	7.70752i	−0.164300	+	0.613177i
$159$	−2.85681	−	1.64938i	−0.226560	−	0.130805i
$160$	−10.6884			−0.844990
$161$	−1.26661	+	1.83820i	−0.0998229	+	0.144870i
$162$	3.78198	+	3.78198i	0.297140	+	0.297140i
$163$	−0.254057	−	0.948153i	−0.0198993	−	0.0742651i	0.955262	−	0.295760i	$-0.0955730\pi$
$163$	−0.254057	−	0.948153i	−0.0198993	−	0.0742651i	−0.975161	+	0.221495i	$0.928906\pi$
$164$	0.0476332	−	0.177769i	0.00371952	−	0.0138815i
$165$	−0.455905	−	0.789651i	−0.0354922	−	0.0614743i
$166$	2.27868	−	3.94679i	0.176860	−	0.306330i
$167$	9.25126	+	9.25126i	0.715884	+	0.715884i	0.967760	−	0.251876i	$-0.0810474\pi$
$167$	9.25126	+	9.25126i	0.715884	+	0.715884i	−0.251876	+	0.967760i	$0.581047\pi$
$168$	−3.19355	−	1.13521i	−0.246387	−	0.0875835i
$169$	−12.8583	+	1.91442i	−0.989097	+	0.147263i
$170$	3.66733	−	6.35200i	0.281271	−	0.487176i
$171$	14.0276	+	3.75869i	1.07272	+	0.287434i
$172$	−5.16678	−	8.94913i	−0.393964	−	0.682365i
$173$	11.0561	−	19.1496i	0.840576	−	1.45592i	−0.0488321	−	0.998807i	$-0.515550\pi$
$173$	11.0561	−	19.1496i	0.840576	−	1.45592i	0.889408	−	0.457114i	$-0.151117\pi$
$174$	2.75402	−	2.75402i	0.208782	−	0.208782i
$175$	1.89709	+	3.98965i	0.143406	+	0.301589i
$176$	0.560683	−	0.560683i	0.0422631	−	0.0422631i
$177$	1.27111	+	4.74386i	0.0955427	+	0.356570i
$178$	5.19582	−	2.99981i	0.389443	−	0.224845i
$179$	6.98924	−	4.03524i	0.522400	−	0.301608i	−0.215516	−	0.976500i	$-0.569143\pi$
$179$	6.98924	−	4.03524i	0.522400	−	0.301608i	0.737916	+	0.674893i	$0.235810\pi$
$180$	6.83105	−	1.83037i	0.509157	−	0.136428i
$181$	20.5622			1.52838			0.764189	−	0.644993i	$-0.223140\pi$
$181$	20.5622			1.52838			0.764189	+	0.644993i	$0.223140\pi$
$182$	−7.13223	+	1.86650i	−0.528676	+	0.138354i
$183$	−0.636594			−0.0470584
$184$	2.14322	−	0.574275i	0.158000	−	0.0423361i
$185$	−9.87240	+	5.69983i	−0.725833	+	0.419060i
$186$	−1.92270	+	1.11007i	−0.140979	+	0.0813945i
$187$	1.38059	+	5.15245i	0.100959	+	0.376784i
$188$	−2.23767	+	2.23767i	−0.163199	+	0.163199i
$189$	7.40356	+	0.591620i	0.538530	+	0.0430340i
$190$	−5.24227	+	5.24227i	−0.380314	+	0.380314i
$191$	6.91909	−	11.9842i	0.500647	−	0.867147i	−0.499352	−	0.866399i	$-0.666429\pi$
$191$	6.91909	−	11.9842i	0.500647	−	0.867147i	1.00000		0.000747762i	$-0.000238020\pi$
$192$	0.725917	+	1.25733i	0.0523885	+	0.0907396i
$193$	−23.5751	−	6.31692i	−1.69697	−	0.454702i	−0.724797	−	0.688962i	$-0.758067\pi$
$193$	−23.5751	−	6.31692i	−1.69697	−	0.454702i	−0.972174	+	0.234260i	$0.924733\pi$
$194$	−1.36157	+	2.35830i	−0.0977547	+	0.169316i
$195$	−2.09291	+	2.42759i	−0.149876	+	0.173843i
$196$	9.17529	−	3.49680i	0.655378	−	0.249771i
$197$	−14.3424	−	14.3424i	−1.02185	−	1.02185i	−0.999756	−	0.0220979i	$-0.992965\pi$
$197$	−14.3424	−	14.3424i	−1.02185	−	1.02185i	−0.0220979	−	0.999756i	$-0.507035\pi$
$198$	1.09499	−	1.89658i	0.0778177	−	0.134784i
$199$	−7.40801	−	12.8310i	−0.525140	−	0.909569i	−0.999571	−	0.0292766i	$-0.990680\pi$
$199$	−7.40801	−	12.8310i	−0.525140	−	0.909569i	0.474431	−	0.880292i	$-0.342654\pi$
$200$	1.13648	−	4.24139i	0.0803611	−	0.299912i
$201$	0.543011	+	2.02654i	0.0383010	+	0.142941i
$202$	−1.32998	−	1.32998i	−0.0935770	−	0.0935770i
$203$	−2.18030	+	27.2843i	−0.153027	+	1.91498i
$204$	3.55361			0.248803
$205$	−0.207354	−	0.119716i	−0.0144822	−	0.00836131i
$206$	0.547339	−	2.04270i	0.0381349	−	0.142321i
$207$	−2.01870	+	1.16550i	−0.140310	+	0.0810078i
$208$	−2.51020	−	1.21163i	−0.174051	−	0.0840114i
$209$		−	5.39169i		−	0.372951i
$210$	−1.03136	+	1.49678i	−0.0711706	+	0.103288i
$211$	6.98585			0.480925			0.240463	−	0.970658i	$-0.422701\pi$
$211$	6.98585			0.480925			0.240463	+	0.970658i	$0.422701\pi$
$212$	−8.22632	−	4.74947i	−0.564986	−	0.326195i
$213$	4.00850	+	1.07408i	0.274658	+	0.0735944i
$214$	0.451312	−	1.68432i	0.0308510	−	0.115138i
$215$	−12.9856	+	3.47948i	−0.885611	+	0.237299i
$216$	−5.22004	−	5.22004i	−0.355179	−	0.355179i
$217$	5.22588	−	14.7013i	0.354756	−	0.997988i
$218$			1.25863i			0.0852451i
$219$	1.43042	+	5.33841i	0.0966590	+	0.360736i
$220$	−1.31280	−	2.27383i	−0.0885088	−	0.153302i
$221$	15.5023	−	10.5488i	1.04280	−	0.709592i
$222$	2.03667	+	1.17587i	0.136692	+	0.0789193i
$223$	19.4291	−	19.4291i	1.30107	−	1.30107i	0.373403	−	0.927669i	$-0.378191\pi$
$223$	19.4291	−	19.4291i	1.30107	−	1.30107i	0.927669	−	0.373403i	$-0.121809\pi$
$224$	−14.6010	−	5.19023i	−0.975571	−	0.346787i
$225$			4.61300i			0.307533i
$226$	−1.96500	+	0.526521i	−0.130710	+	0.0350237i
$227$	−0.0680123	−	0.0182238i	−0.00451413	−	0.00120956i	0.256561	−	0.966528i	$-0.417410\pi$
$227$	−0.0680123	−	0.0182238i	−0.00451413	−	0.00120956i	−0.261075	+	0.965318i	$0.584077\pi$
$228$	−3.46952	−	0.929654i	−0.229774	−	0.0615678i
$229$	5.28034	−	1.41486i	0.348935	−	0.0934968i	−0.0800948	−	0.996787i	$-0.525522\pi$
$229$	5.28034	−	1.41486i	0.348935	−	0.0934968i	0.429030	+	0.903290i	$0.358856\pi$
$230$		−	1.18997i		−	0.0784643i
$231$	−0.239345	−	1.30010i	−0.0157477	−	0.0855404i
$232$	19.2374	−	19.2374i	1.26300	−	1.26300i
$233$	0.913139	+	0.527201i	0.0598217	+	0.0345381i	0.529613	−	0.848240i	$-0.322337\pi$
$233$	0.913139	+	0.527201i	0.0598217	+	0.0345381i	−0.469791	+	0.882778i	$0.655671\pi$
$234$	−7.56280	−	1.43801i	−0.494396	−	0.0940055i
$235$	2.05849	+	3.56541i	0.134281	+	0.232582i
$236$	3.66022	+	13.6601i	0.238260	+	0.889200i
$237$			5.02955i			0.326705i
$238$	8.09432	−	6.89641i	0.524677	−	0.447028i
$239$	18.6963	+	18.6963i	1.20936	+	1.20936i	0.971234	+	0.238127i	$0.0765333\pi$
$239$	18.6963	+	18.6963i	1.20936	+	1.20936i	0.238127	+	0.971234i	$0.423467\pi$
$240$	−0.663811	+	0.177868i	−0.0428488	+	0.0114813i
$241$	−2.53663	+	9.46683i	−0.163399	+	0.609812i	0.834840	+	0.550492i	$0.185560\pi$
$241$	−2.53663	+	9.46683i	−0.163399	+	0.609812i	−0.998239	+	0.0593200i	$0.981107\pi$
$242$	7.42620	+	1.98984i	0.477374	+	0.127912i
$243$	10.2129	+	5.89643i	0.655159	+	0.378256i
$244$	−1.83310			−0.117352
$245$	−1.30476	−	12.7075i	−0.0833579	−	0.811852i
$246$			0.0493945i			0.00314928i
$247$	−17.8951	+	6.24369i	−1.13864	+	0.397276i
$248$	−13.4305	+	7.75408i	−0.852835	+	0.492384i
$249$	0.743478	−	2.77470i	0.0471160	−	0.175839i
$250$	−8.14644	−	4.70335i	−0.515226	−	0.297466i
$251$	−24.9249			−1.57325			−0.786623	−	0.617434i	$-0.788172\pi$
$251$	−24.9249			−1.57325			−0.786623	+	0.617434i	$0.788172\pi$
$252$	10.2205	+	0.816722i	0.643830	+	0.0514486i
$253$	0.611943	+	0.611943i	0.0384726	+	0.0384726i
$254$	−2.36239	−	8.81656i	−0.148230	−	0.553200i
$255$	1.19656	−	4.46562i	0.0749315	−	0.279648i
$256$	6.61680	+	11.4606i	0.413550	+	0.716289i
$257$	−1.98118	+	3.43150i	−0.123583	+	0.214051i	−0.921178	−	0.389142i	$-0.872772\pi$
$257$	−1.98118	+	3.43150i	−0.123583	+	0.214051i	0.797595	+	0.603193i	$0.206105\pi$
$258$	1.96111	+	1.96111i	0.122093	+	0.122093i
$259$	−16.2542	+	2.99234i	−1.00998	+	0.185935i
$260$	−6.02662	+	6.99033i	−0.373755	+	0.433522i
$261$	−14.2906	+	24.7520i	−0.884565	+	1.53211i
$262$	11.5311	+	3.08974i	0.712392	+	0.190885i
$263$	15.4634	+	26.7834i	0.953516	+	1.65154i	0.737729	+	0.675097i	$0.235898\pi$
$263$	15.4634	+	26.7834i	0.953516	+	1.65154i	0.215787	+	0.976440i	$0.430768\pi$
$264$	−0.656978	+	1.13792i	−0.0404342	+	0.0700341i
$265$	−8.73832	+	8.73832i	−0.536791	+	0.536791i
$266$	−9.70692	+	4.61566i	−0.595169	+	0.283004i
$267$	2.67403	−	2.67403i	0.163648	−	0.163648i
$268$	1.56362	+	5.83552i	0.0955134	+	0.356461i
$269$	9.53617	−	5.50571i	0.581430	−	0.335689i	−0.180271	−	0.983617i	$-0.557698\pi$
$269$	9.53617	−	5.50571i	0.581430	−	0.335689i	0.761702	+	0.647928i	$0.224364\pi$
$270$	−3.42872	+	1.97957i	−0.208665	+	0.120473i
$271$	−4.83826	+	1.29641i	−0.293903	+	0.0787511i	−0.402758	−	0.915307i	$-0.631948\pi$
$271$	−4.83826	+	1.29641i	−0.293903	+	0.0787511i	0.108855	+	0.994058i	$0.465282\pi$
$272$	4.02037			0.243771
$273$	−4.03788	+	2.29993i	−0.244384	+	0.139198i
$274$	−0.792211			−0.0478592
$275$	1.65429	−	0.443265i	0.0997574	−	0.0267299i
$276$	0.499295	−	0.288268i	0.0300540	−	0.0173517i
$277$	10.5720	−	6.10374i	0.635209	−	0.366738i	−0.147558	−	0.989053i	$-0.547141\pi$
$277$	10.5720	−	6.10374i	0.635209	−	0.366738i	0.782767	+	0.622315i	$0.213808\pi$
$278$	−2.28085	−	8.51223i	−0.136796	−	0.510530i
$279$	11.5203	−	11.5203i	0.689702	−	0.689702i
$280$	−7.20426	+	10.4553i	−0.430537	+	0.624826i
$281$	−12.8351	+	12.8351i	−0.765677	+	0.765677i	−0.977342	−	0.211665i	$-0.932111\pi$
$281$	−12.8351	+	12.8351i	−0.765677	+	0.765677i	0.211665	+	0.977342i	$0.432111\pi$
$282$	0.424665	−	0.735541i	0.0252884	−	0.0438008i
$283$	8.44961	+	14.6351i	0.502277	+	0.869969i	0.999997	+	0.00263116i	$0.000837525\pi$
$283$	8.44961	+	14.6351i	0.502277	+	0.869969i	−0.497720	+	0.867338i	$0.665829\pi$
$284$	11.5427	+	3.09285i	0.684931	+	0.183527i
$285$	−2.33649	+	4.04691i	−0.138401	+	0.239718i
$286$	0.211023	+	2.85031i	0.0124780	+	0.168542i
$287$	−0.225125	−	0.264230i	−0.0132887	−	0.0155970i
$288$	−11.4417	−	11.4417i	−0.674210	−	0.674210i
$289$	−5.02302	+	8.70012i	−0.295472	+	0.511772i
$290$	−7.29531	−	12.6359i	−0.428396	−	0.742003i
$291$	−0.444246	+	1.65795i	−0.0260421	+	0.0971906i
$292$	4.11896	+	15.3722i	0.241044	+	0.899589i
$293$	−11.1183	−	11.1183i	−0.649536	−	0.649536i	0.303345	−	0.952881i	$-0.401897\pi$
$293$	−11.1183	−	11.1183i	−0.649536	−	0.649536i	−0.952881	+	0.303345i	$0.901897\pi$
$294$	−2.13574	+	1.54388i	−0.124559	+	0.0900410i
$295$	18.3984			1.07120
$296$	14.2265	+	8.21369i	0.826900	+	0.477411i
$297$	0.745226	−	2.78122i	0.0432424	−	0.161383i
$298$	−5.11227	+	2.95157i	−0.296146	+	0.170980i
$299$	1.32240	−	2.73969i	0.0764765	−	0.158440i
$300$		−	1.14095i		−	0.0658730i
$301$	−19.4288	−	1.55256i	−1.11986	−	0.0894882i
$302$	5.29441			0.304659
$303$	−1.02671	−	0.592773i	−0.0589831	−	0.0340539i
$304$	−3.92523	−	1.05176i	−0.225127	−	0.0603227i
$305$	−0.617234	+	2.30355i	−0.0353427	+	0.131901i
$306$	10.7255	−	2.87390i	0.613138	−	0.164290i
$307$	−14.6604	−	14.6604i	−0.836715	−	0.836715i	0.151710	−	0.988425i	$-0.451522\pi$
$307$	−14.6604	−	14.6604i	−0.836715	−	0.836715i	−0.988425	+	0.151710i	$0.951522\pi$
$308$	−0.689203	−	3.74370i	−0.0392710	−	0.213317i
$309$		−	1.33296i		−	0.0758296i
$310$	2.15263	+	8.03372i	0.122261	+	0.456285i
$311$	−5.35317	−	9.27196i	−0.303550	−	0.525765i	0.673387	−	0.739290i	$-0.264839\pi$
$311$	−5.35317	−	9.27196i	−0.303550	−	0.525765i	−0.976938	+	0.213525i	$0.931505\pi$
$312$	4.53756	+	0.862782i	0.256889	+	0.0488454i
$313$	−9.30922	−	5.37468i	−0.526188	−	0.303795i	0.213275	−	0.976992i	$-0.431587\pi$
$313$	−9.30922	−	5.37468i	−0.526188	−	0.303795i	−0.739463	+	0.673197i	$0.764920\pi$
$314$	7.02088	−	7.02088i	0.396211	−	0.396211i
$315$	4.46773	−	12.5685i	0.251728	−	0.708155i
$316$			14.4828i			0.814722i
$317$	−11.3244	+	3.03435i	−0.636040	+	0.170426i	−0.562409	−	0.826859i	$-0.690125\pi$
$317$	−11.3244	+	3.03435i	−0.636040	+	0.170426i	−0.0736308	+	0.997286i	$0.523459\pi$
$318$	2.46255	+	0.659837i	0.138093	+	0.0370018i
$319$	10.2496	+	2.74638i	0.573869	+	0.153768i
$320$	5.25354	−	1.40768i	0.293682	−	0.0786918i
$321$		−	1.09910i		−	0.0613460i
$322$	0.577845	−	1.62558i	0.0322021	−	0.0905899i
$323$	19.3305	−	19.3305i	1.07558	−	1.07558i
$324$	8.40711	+	4.85385i	0.467062	+	0.269658i
$325$	−3.38690	−	4.97729i	−0.187872	−	0.276090i
$326$	0.379310	+	0.656983i	0.0210080	+	0.0363869i
$327$	0.205330	+	0.766302i	0.0113548	+	0.0423766i
$328$			0.345031i			0.0190511i
$329$	1.08068	+	5.87018i	0.0595799	+	0.323633i
$330$	0.498286	+	0.498286i	0.0274297	+	0.0274297i
$331$	26.1893	−	7.01741i	1.43950	−	0.385712i	0.547138	−	0.837042i	$-0.315717\pi$
$331$	26.1893	−	7.01741i	1.43950	−	0.385712i	0.892357	+	0.451331i	$0.149050\pi$
$332$	2.14088	−	7.98986i	0.117496	−	0.438500i
$333$	−16.6698	−	4.46667i	−0.913501	−	0.244772i
$334$	−8.75660	−	5.05563i	−0.479140	−	0.276632i
$335$	7.85966			0.429419
$336$	−0.993182	−	0.0793654i	−0.0541825	−	0.00432974i
$337$		−	20.5911i		−	1.12167i	−0.827927	−	0.560835i	$-0.810480\pi$
$337$		−	20.5911i		−	1.12167i	0.827927	−	0.560835i	$-0.189520\pi$
$338$	9.21583	−	4.00110i	0.501275	−	0.217631i
$339$	−1.11047	+	0.641133i	−0.0603127	+	0.0348216i
$340$	3.44554	−	12.8589i	0.186861	−	0.697374i
$341$	−5.23834	−	3.02436i	−0.283672	−	0.163778i
$342$	−11.2235			−0.606899
$343$	4.38832	−	17.9928i	0.236947	−	0.971523i
$344$	13.6987	+	13.6987i	0.738585	+	0.738585i
$345$	−0.194129	−	0.724500i	−0.0104516	−	0.0390058i
$346$	−4.42298	+	16.5068i	−0.237781	+	0.887411i
$347$	−7.48956	−	12.9723i	−0.402061	−	0.696390i	0.591914	−	0.806001i	$-0.298373\pi$
$347$	−7.48956	−	12.9723i	−0.402061	−	0.696390i	−0.993974	+	0.109612i	$0.965039\pi$
$348$	3.53455	−	6.12202i	0.189472	−	0.328175i
$349$	−3.25693	−	3.25693i	−0.174340	−	0.174340i	0.614543	−	0.788883i	$-0.289340\pi$
$349$	−3.25693	−	3.25693i	−0.174340	−	0.174340i	−0.788883	+	0.614543i	$0.789340\pi$
$350$	−2.21422	−	2.59883i	−0.118355	−	0.138913i
$351$	−10.0939	+	0.747300i	−0.538772	+	0.0398879i
$352$	−3.00373	+	5.20261i	−0.160099	+	0.277300i
$353$	5.38517	+	1.44295i	0.286624	+	0.0768006i	0.399266	−	0.916835i	$-0.369265\pi$
$353$	5.38517	+	1.44295i	0.286624	+	0.0768006i	−0.112643	+	0.993636i	$0.535932\pi$
$354$	−1.89779	−	3.28706i	−0.100866	−	0.174705i
$355$	7.77320	−	13.4636i	0.412559	−	0.714573i
$356$	7.70000	−	7.70000i	0.408099	−	0.408099i
$357$	3.80307	−	5.51929i	0.201280	−	0.292112i
$358$	−4.41035	+	4.41035i	−0.233094	+	0.233094i
$359$	1.29947	+	4.84968i	0.0685833	+	0.255956i	0.991702	−	0.128559i	$-0.0410352\pi$
$359$	1.29947	+	4.84968i	0.0685833	+	0.255956i	−0.923119	+	0.384515i	$0.874369\pi$
$360$	−11.4820	+	6.62915i	−0.605156	+	0.349387i
$361$	−7.47558	+	4.31603i	−0.393452	+	0.227159i
$362$	−15.3498	+	4.11297i	−0.806768	+	0.216173i
$363$	4.84597			0.254348
$364$	−11.6272	+	6.62275i	−0.609433	+	0.347126i
$365$	20.7043			1.08371
$366$	0.475221	−	0.127335i	0.0248402	−	0.00665591i
$367$	2.66201	−	1.53691i	0.138956	−	0.0802262i	−0.428910	−	0.903347i	$-0.641102\pi$
$367$	2.66201	−	1.53691i	0.138956	−	0.0802262i	0.567866	+	0.823121i	$0.307769\pi$
$368$	0.564876	−	0.326131i	0.0294462	−	0.0170008i
$369$	−0.0938150	−	0.350122i	−0.00488382	−	0.0182266i
$370$	6.22969	−	6.22969i	0.323866	−	0.323866i
$371$	−16.1804	+	7.69382i	−0.840045	+	0.399443i
$372$	−2.84937	+	2.84937i	−0.147733	+	0.147733i
$373$	−11.6754	+	20.2225i	−0.604532	+	1.04708i	0.387594	+	0.921830i	$0.373306\pi$
$373$	−11.6754	+	20.2225i	−0.604532	+	1.04708i	−0.992125	+	0.125249i	$0.960027\pi$
$374$	−2.06124	−	3.57018i	−0.106584	−	0.184609i
$375$	−5.72716	−	1.53459i	−0.295749	−	0.0792458i
$376$	2.96637	−	5.13790i	0.152979	−	0.264967i
$377$	−2.75402	−	37.1989i	−0.141839	−	1.91584i
$378$	−5.64513	+	1.03925i	−0.290354	+	0.0534534i
$379$	−1.97284	−	1.97284i	−0.101338	−	0.101338i	0.654620	−	0.755958i	$-0.272829\pi$
$379$	−1.97284	−	1.97284i	−0.101338	−	0.101338i	−0.755958	+	0.654620i	$0.772829\pi$
$380$	−6.72801	+	11.6533i	−0.345140	+	0.597799i
$381$	−2.87663	−	4.98247i	−0.147374	−	0.255260i
$382$	−2.76799	+	10.3303i	−0.141623	+	0.528542i
$383$	0.801419	+	2.99094i	0.0409506	+	0.152830i	0.983374	−	0.181593i	$-0.0581253\pi$
$383$	0.801419	+	2.99094i	0.0409506	+	0.152830i	−0.942423	+	0.334423i	$0.891459\pi$
$384$	3.24152	+	3.24152i	0.165418	+	0.165418i
$385$	−4.93655	−	0.394481i	−0.251590	−	0.0201046i
$386$	18.8625			0.960074
$387$	−17.6256	−	10.1761i	−0.895960	−	0.517283i
$388$	−1.27922	+	4.77413i	−0.0649427	+	0.242370i
$389$	9.53607	−	5.50565i	0.483498	−	0.279148i	−0.238375	−	0.971173i	$-0.576615\pi$
$389$	9.53607	−	5.50565i	0.483498	−	0.279148i	0.721873	+	0.692026i	$0.243281\pi$
$390$	1.07679	−	2.23084i	0.0545254	−	0.112963i
$391$			4.38793i			0.221907i
$392$	−14.9186	+	10.7843i	−0.753501	+	0.544690i
$393$	7.52462			0.379567
$394$	13.5755	+	7.83783i	0.683925	+	0.394864i
$395$	18.1997	+	4.87660i	0.915727	+	0.245368i
$396$	1.02877	−	3.83943i	0.0516978	−	0.192939i
$397$	36.9941	−	9.91254i	1.85668	−	0.497496i	0.856845	−	0.515575i	$-0.172422\pi$
$397$	36.9941	−	9.91254i	1.85668	−	0.497496i	0.999837	+	0.0180784i	$0.00575485\pi$
$398$	8.09666	+	8.09666i	0.405849	+	0.405849i
$399$	−5.15696	+	4.39376i	−0.258171	+	0.219963i
$400$		−	1.29081i		−	0.0645407i
$401$	−1.74089	−	6.49711i	−0.0869361	−	0.324450i	0.908738	−	0.417368i	$-0.137047\pi$
$401$	−1.74089	−	6.49711i	−0.0869361	−	0.324450i	−0.995674	+	0.0929177i	$0.970381\pi$
$402$	−0.810720	−	1.40421i	−0.0404351	−	0.0700356i
$403$	−3.97176	+	20.8884i	−0.197847	+	1.04052i
$404$	−2.95646	−	1.70691i	−0.147089	−	0.0849222i
$405$	8.93036	−	8.93036i	0.443753	−	0.443753i
$406$	−3.82995	−	20.8040i	−0.190077	−	1.03248i
$407$			6.40725i			0.317595i
$408$	−6.43515	+	1.72429i	−0.318587	+	0.0853652i
$409$	−32.8797	−	8.81009i	−1.62580	−	0.435631i	−0.673100	−	0.739552i	$-0.735038\pi$
$409$	−32.8797	−	8.81009i	−1.62580	−	0.435631i	−0.952697	+	0.303920i	$0.901704\pi$
$410$	0.178737	+	0.0478924i	0.00882718	+	0.00236524i
$411$	−0.482329	+	0.129240i	−0.0237915	+	0.00637492i
$412$		−	3.83832i		−	0.189101i
$413$	25.1334	+	8.93419i	1.23673	+	0.439623i
$414$	1.27384	−	1.27384i	0.0626060	−	0.0626060i
$415$	−9.31953	−	5.38063i	−0.457478	−	0.264125i
$416$	20.7459	+	3.94467i	1.01715	+	0.193403i
$417$	−2.77733	−	4.81048i	−0.136007	−	0.235570i
$418$	1.07848	+	4.02492i	0.0527499	+	0.196865i
$419$			35.5515i			1.73680i	0.495862	+	0.868401i	$0.334852\pi$
$419$			35.5515i			1.73680i	−0.495862	+	0.868401i	$0.665148\pi$
$420$	−1.10502	+	3.10862i	−0.0539197	+	0.151685i
$421$	−10.3166	−	10.3166i	−0.502802	−	0.502802i	0.409505	−	0.912308i	$-0.365701\pi$
$421$	−10.3166	−	10.3166i	−0.502802	−	0.502802i	−0.912308	+	0.409505i	$0.865701\pi$
$422$	−5.21497	+	1.39735i	−0.253861	+	0.0680218i
$423$	−1.61313	+	6.02029i	−0.0784332	+	0.292717i
$424$	17.2014	+	4.60909i	0.835372	+	0.223837i
$425$	7.52024	+	4.34181i	0.364785	+	0.210609i
$426$	−3.20721			−0.155390
$427$	−1.96178	+	2.84707i	−0.0949371	+	0.137780i
$428$		−	3.16492i		−	0.152982i
$429$	0.593472	+	1.70095i	0.0286531	+	0.0821228i
$430$	8.99784	−	5.19490i	0.433914	−	0.250520i
$431$	−9.24210	+	34.4920i	−0.445176	+	1.66142i	0.270294	+	0.962778i	$0.412879\pi$
$431$	−9.24210	+	34.4920i	−0.445176	+	1.66142i	−0.715471	+	0.698643i	$0.753788\pi$
$432$	−1.87940	−	1.08507i	−0.0904226	−	0.0522055i
$433$	−18.6845			−0.897919			−0.448959	−	0.893552i	$-0.648205\pi$
$433$	−18.6845			−0.897919			−0.448959	+	0.893552i	$0.648205\pi$
$434$	−0.960513	+	12.0199i	−0.0461061	+	0.576974i
$435$	−6.50305	−	6.50305i	−0.311798	−	0.311798i
$436$	0.591256	+	2.20660i	0.0283160	+	0.105677i
$437$	1.14792	−	4.28409i	0.0549124	−	0.204936i
$438$	−2.13564	−	3.69903i	−0.102045	−	0.176747i
$439$	−11.9158	+	20.6388i	−0.568712	+	0.985038i	0.427982	+	0.903787i	$0.359225\pi$
$439$	−11.9158	+	20.6388i	−0.568712	+	0.985038i	−0.996694	+	0.0812508i	$0.974109\pi$
$440$	3.48063	+	3.48063i	0.165932	+	0.165932i
$441$	12.2064	−	14.9999i	0.581259	−	0.714280i
$442$	−9.46248	+	10.9756i	−0.450084	+	0.522057i
$443$	11.6908	−	20.2490i	0.555445	−	0.962059i	−0.442424	−	0.896806i	$-0.645881\pi$
$443$	11.6908	−	20.2490i	0.555445	−	0.962059i	0.997869	−	0.0652531i	$-0.0207855\pi$
$444$	4.12302	+	1.10476i	0.195670	+	0.0524296i
$445$	−7.08343	−	12.2689i	−0.335787	−	0.581600i
$446$	−10.6176	+	18.3903i	−0.502760	+	0.870805i
$447$	−2.63104	+	2.63104i	−0.124444	+	0.124444i
$448$	7.86025	+	0.628114i	0.371362	+	0.0296756i
$449$	−17.6188	+	17.6188i	−0.831482	+	0.831482i	−0.987720	−	0.156237i	$-0.950063\pi$
$449$	−17.6188	+	17.6188i	−0.831482	+	0.831482i	0.156237	+	0.987720i	$0.450063\pi$
$450$	−0.922717	−	3.44363i	−0.0434973	−	0.162334i
$451$	−0.116544	+	0.0672869i	−0.00548786	+	0.00316842i
$452$	−3.19766	+	1.84617i	−0.150405	+	0.0868365i
$453$	3.22344	−	0.863719i	0.151451	−	0.0405810i
$454$	0.0544168			0.00255391
$455$	4.40734	+	16.8413i	0.206620	+	0.789531i
$456$	6.73394			0.315346
$457$	−3.91842	+	1.04994i	−0.183296	+	0.0491140i	−0.349299	−	0.937011i	$-0.613580\pi$
$457$	−3.91842	+	1.04994i	−0.183296	+	0.0491140i	0.166003	+	0.986125i	$0.446914\pi$
$458$	−3.65879	+	2.11241i	−0.170964	+	0.0987062i
$459$	12.6432	−	7.29954i	0.590133	−	0.340713i
$460$	−0.559003	−	2.08623i	−0.0260637	−	0.0972709i
$461$	−7.54874	+	7.54874i	−0.351580	+	0.351580i	−0.860697	−	0.509117i	$-0.829972\pi$
$461$	−7.54874	+	7.54874i	−0.351580	+	0.351580i	0.509117	+	0.860697i	$0.329972\pi$
$462$	0.438726	+	0.922657i	0.0204114	+	0.0429259i
$463$	13.5419	−	13.5419i	0.629344	−	0.629344i	−0.318559	−	0.947903i	$-0.603199\pi$
$463$	13.5419	−	13.5419i	0.629344	−	0.629344i	0.947903	+	0.318559i	$0.103199\pi$
$464$	3.99881	−	6.92614i	0.185640	−	0.321538i
$465$	2.62121	+	4.54006i	0.121556	+	0.210540i
$466$	−0.787117	−	0.210907i	−0.0364625	−	0.00977009i
$467$	−18.0634	+	31.2867i	−0.835873	+	1.44777i	0.0574445	+	0.998349i	$0.481705\pi$
$467$	−18.0634	+	31.2867i	−0.835873	+	1.44777i	−0.893318	+	0.449426i	$0.851629\pi$
$468$	−13.9344	+	1.03164i	−0.644120	+	0.0476874i
$469$	10.7368	+	3.81662i	0.495780	+	0.176235i
$470$	−2.24985	−	2.24985i	−0.103778	−	0.103778i
$471$	3.12921	−	5.41995i	0.144186	−	0.249738i
$472$	−13.2564	−	22.9608i	−0.610176	−	1.05686i
$473$	−1.95566	+	7.29863i	−0.0899215	+	0.335591i
$474$	−1.00604	−	3.75459i	−0.0462089	−	0.172454i
$475$	−6.20642	−	6.20642i	−0.284770	−	0.284770i
$476$	10.9511	−	15.8930i	0.501943	−	0.728456i
$477$	−18.7085			−0.856601
$478$	−17.6966	−	10.2171i	−0.809423	−	0.467321i
$479$	−8.54403	+	31.8868i	−0.390387	+	1.45694i	0.439111	+	0.898433i	$0.355293\pi$
$479$	−8.54403	+	31.8868i	−0.390387	+	1.45694i	−0.829498	+	0.558510i	$0.811373\pi$
$480$	4.50910	−	2.60333i	0.205811	−	0.118825i
$481$	21.2657	−	7.41972i	0.969633	−	0.338310i
$482$		−	7.57443i		−	0.345006i
$483$	0.0866213	−	1.08398i	0.00394141	−	0.0493229i
$484$	13.9542			0.634281
$485$	5.56864	+	3.21505i	0.252859	+	0.145988i
$486$	−8.80344	−	2.35887i	−0.399332	−	0.107001i
$487$	−1.60059	+	5.97348i	−0.0725297	+	0.270684i	−0.992662	−	0.120924i	$-0.961414\pi$
$487$	−1.60059	+	5.97348i	−0.0725297	+	0.270684i	0.920132	+	0.391608i	$0.128081\pi$
$488$	3.31951	−	0.889460i	0.150267	−	0.0402640i
$489$	0.338117	+	0.338117i	0.0152902	+	0.0152902i
$490$	3.51583	+	9.22522i	0.158829	+	0.416753i
$491$		−	33.4149i		−	1.50799i	−0.656879	−	0.753996i	$-0.728124\pi$
$491$		−	33.4149i		−	1.50799i	0.656879	−	0.753996i	$-0.271876\pi$
$492$	0.0232037	+	0.0865973i	0.00104610	+	0.00390411i
$493$	26.9010	+	46.5938i	1.21156	+	2.09848i
$494$	12.1099	−	8.24041i	0.544848	−	0.370754i
$495$	−4.47839	−	2.58560i	−0.201289	−	0.116214i
$496$	−3.22362	+	3.22362i	−0.144745	+	0.144745i
$497$	17.1566	−	14.6175i	0.769577	−	0.655684i
$498$			2.22004i			0.0994824i
$499$	14.3549	−	3.84639i	0.642615	−	0.172188i	0.0772276	−	0.997013i	$-0.475393\pi$
$499$	14.3549	−	3.84639i	0.642615	−	0.172188i	0.565388	+	0.824825i	$0.308727\pi$
$500$	−16.4916	−	4.41891i	−0.737527	−	0.197620i
$501$	−6.15612	−	1.64953i	−0.275035	−	0.0736955i
$502$	18.6066	−	4.98561i	0.830452	−	0.222519i
$503$			24.9299i			1.11157i	0.831327	+	0.555784i	$0.187582\pi$
$503$			24.9299i			1.11157i	−0.831327	+	0.555784i	$0.812418\pi$
$504$	−18.9043	+	3.48023i	−0.842065	+	0.155022i
$505$	−3.14047	+	3.14047i	−0.139749	+	0.139749i
$506$	−0.579223	−	0.334415i	−0.0257496	−	0.0148665i
$507$	4.95822	−	3.93948i	0.220202	−	0.174958i
$508$	−8.28337	−	14.3472i	−0.367515	−	0.636555i
$509$	0.493093	+	1.84025i	0.0218560	+	0.0815676i	0.975992	−	0.217804i	$-0.0698895\pi$
$509$	0.493093	+	1.84025i	0.0218560	+	0.0815676i	−0.954136	+	0.299372i	$0.903223\pi$
$510$			3.57295i			0.158213i
$511$	28.2834	+	10.0539i	1.25118	+	0.444759i
$512$	6.07668	+	6.07668i	0.268554	+	0.268554i
$513$	−14.2536	+	3.81924i	−0.629311	+	0.168623i
$514$	0.792573	−	2.95792i	0.0349589	−	0.130468i
$515$	−4.82340	−	1.29243i	−0.212545	−	0.0569511i
$516$	4.35942	+	2.51691i	0.191913	+	0.110801i
$517$	2.31397			0.101768
$518$	11.5353	−	5.48505i	0.506831	−	0.240999i
$519$			10.7715i			0.472818i
$520$	7.52159	−	15.5829i	0.329844	−	0.683354i
$521$	9.41368	−	5.43499i	0.412421	−	0.238111i	−0.279409	−	0.960172i	$-0.590138\pi$
$521$	9.41368	−	5.43499i	0.412421	−	0.238111i	0.691829	+	0.722061i	$0.256805\pi$
$522$	5.71696	−	21.3360i	0.250225	−	0.933851i
$523$	−20.2470	−	11.6896i	−0.885339	−	0.511151i	−0.0129241	−	0.999916i	$-0.504114\pi$
$523$	−20.2470	−	11.6896i	−0.885339	−	0.511151i	−0.872415	+	0.488766i	$0.837447\pi$
$524$	21.6675			0.946547
$525$	−1.77207	−	1.22105i	−0.0773394	−	0.0532908i
$526$	−16.9009	−	16.9009i	−0.736914	−	0.736914i
$527$	−7.93767	−	29.6238i	−0.345770	−	1.29043i
$528$	−0.0999715	+	0.373099i	−0.00435070	+	0.0162370i
$529$	−11.1441	−	19.3021i	−0.484524	−	0.839220i
$530$	4.77531	−	8.27109i	0.207426	−	0.359273i
$531$	19.6952	+	19.6952i	0.854697	+	0.854697i
$532$	−14.8497	+	12.6520i	−0.643815	+	0.548534i
$533$	0.358286	+	0.308892i	0.0155191	+	0.0133796i
$534$	−1.46131	+	2.53106i	−0.0632369	+	0.109530i
$535$	−3.97717	−	1.06568i	−0.171948	−	0.0460733i
$536$	−5.66304	−	9.80868i	−0.244606	−	0.423670i
$537$	−1.96570	+	3.40469i	−0.0848261	+	0.146923i
$538$	−6.01752	+	6.01752i	−0.259434	+	0.259434i
$539$	−6.55210	−	2.93606i	−0.282219	−	0.126465i
$540$	−5.08123	+	5.08123i	−0.218661	+	0.218661i
$541$	−1.75979	−	6.56763i	−0.0756593	−	0.282364i	0.917723	−	0.397222i	$-0.130026\pi$
$541$	−1.75979	−	6.56763i	−0.0756593	−	0.282364i	−0.993382	+	0.114857i	$0.963359\pi$
$542$	3.35247	−	1.93555i	0.144001	−	0.0831390i
$543$	−8.67457	+	5.00827i	−0.372261	+	0.214925i
$544$	−29.4217	+	7.88353i	−1.26145	+	0.338003i
$545$	2.97199			0.127306
$546$	2.55425	−	2.52459i	0.109312	−	0.108042i
$547$	−14.2303			−0.608446			−0.304223	−	0.952601i	$-0.598397\pi$
$547$	−14.2303			−0.608446			−0.304223	+	0.952601i	$0.598397\pi$
$548$	−1.38889	+	0.372151i	−0.0593303	+	0.0158975i
$549$	−3.12665	+	1.80517i	−0.133442	+	0.0770429i
$550$	−1.14627	+	0.661800i	−0.0488772	+	0.0282192i
$551$	−14.0750	−	52.5287i	−0.599616	−	2.23780i
$552$	−0.764286	+	0.764286i	−0.0325302	+	0.0325302i
$553$	22.4939	+	15.4995i	0.956540	+	0.659104i
$554$	−6.67114	+	6.67114i	−0.283429	+	0.283429i
$555$	2.77658	−	4.80917i	0.117859	−	0.204138i
$556$	−7.99745	−	13.8520i	−0.339167	−	0.587455i
$557$	−7.83328	−	2.09892i	−0.331907	−	0.0889342i	0.0890171	−	0.996030i	$-0.471627\pi$
$557$	−7.83328	−	2.09892i	−0.331907	−	0.0889342i	−0.420924	+	0.907096i	$0.638294\pi$
$558$	−6.29561	+	10.9043i	−0.266514	+	0.461617i
$559$	26.4889	−	1.96111i	1.12036	−	0.0829459i
$560$	−1.25017	+	3.51693i	−0.0528292	+	0.148617i
$561$	−1.83739	−	1.83739i	−0.0775749	−	0.0775749i
$562$	7.01412	−	12.1488i	0.295873	−	0.512467i
$563$	17.7523	+	30.7479i	0.748170	+	1.29587i	0.948699	+	0.316181i	$0.102401\pi$
$563$	17.7523	+	30.7479i	0.748170	+	1.29587i	−0.200529	+	0.979688i	$0.564266\pi$
$564$	0.398983	−	1.48902i	0.0168002	−	0.0626992i
$565$	1.24327	+	4.63995i	0.0523048	+	0.195204i
$566$	−9.23508	−	9.23508i	−0.388179	−	0.388179i
$567$	16.5360	−	7.86291i	0.694447	−	0.330211i
$568$	−22.4030			−0.940009
$569$	27.4931	+	15.8731i	1.15257	+	0.665437i	0.949512	−	0.313730i	$-0.101579\pi$
$569$	27.4931	+	15.8731i	1.15257	+	0.665437i	0.203058	+	0.979167i	$0.434912\pi$
$570$	0.934713	−	3.48840i	0.0391508	−	0.146113i
$571$	7.15860	−	4.13302i	0.299578	−	0.172961i	−0.342675	−	0.939454i	$-0.611333\pi$
$571$	7.15860	−	4.13302i	0.299578	−	0.172961i	0.642253	+	0.766492i	$0.278000\pi$
$572$	1.70893	+	4.89796i	0.0714538	+	0.204794i
$573$			6.74103i			0.281611i
$574$	0.220910	+	0.152218i	0.00922060	+	0.00635346i
$575$	1.40883			0.0587521
$576$	7.13073	+	4.11693i	0.297114	+	0.171539i
$577$	−3.25238	−	0.871473i	−0.135398	−	0.0362799i	0.190483	−	0.981690i	$-0.438994\pi$
$577$	−3.25238	−	0.871473i	−0.135398	−	0.0362799i	−0.325882	+	0.945411i	$0.605661\pi$
$578$	2.00946	−	7.49942i	0.0835826	−	0.311935i
$579$	11.4842	−	3.07718i	0.477267	−	0.127883i
$580$	−18.7258	−	18.7258i	−0.777547	−	0.777547i
$581$	−10.1183	−	11.8758i	−0.419777	−	0.492692i
$582$		−	1.32653i		−	0.0549863i
$583$	1.79770	+	6.70912i	0.0744533	+	0.277864i
$584$	−14.9178	−	25.8385i	−0.617305	−	1.06920i
$585$	−3.39556	+	17.8580i	−0.140389	+	0.738337i
$586$	10.5238	+	6.07591i	0.434734	+	0.250994i
$587$	−3.33097	+	3.33097i	−0.137484	+	0.137484i	−0.772499	−	0.635016i	$-0.780994\pi$
$587$	−3.33097	+	3.33097i	−0.137484	+	0.137484i	0.635016	+	0.772499i	$0.280994\pi$
$588$	−3.01907	+	3.70999i	−0.124504	+	0.152997i
$589$			30.9993i			1.27730i
$590$	−13.7345	+	3.68014i	−0.565440	+	0.151509i
$591$	9.54395	+	2.55729i	0.392586	+	0.105193i
$592$	4.66457	+	1.24987i	0.191713	+	0.0513692i
$593$	14.5195	−	3.89048i	0.596243	−	0.159763i	0.0519381	−	0.998650i	$-0.483460\pi$
$593$	14.5195	−	3.89048i	0.596243	−	0.159763i	0.544305	+	0.838888i	$0.316793\pi$
$594$			2.22526i			0.0913035i
$595$	−16.2844	−	19.1131i	−0.667597	−	0.783559i
$596$	−7.57618	+	7.57618i	−0.310332	+	0.310332i
$597$	6.25043	+	3.60869i	0.255813	+	0.147694i
$598$	−0.439173	+	2.30971i	−0.0179591	+	0.0944509i
$599$	−3.63773	−	6.30073i	−0.148633	−	0.257441i	0.782089	−	0.623167i	$-0.214154\pi$
$599$	−3.63773	−	6.30073i	−0.148633	−	0.257441i	−0.930723	+	0.365726i	$0.880821\pi$
$600$	0.553616	+	2.06612i	0.0226013	+	0.0843491i
$601$		−	2.83288i		−	0.115555i	−0.998329	−	0.0577777i	$-0.981599\pi$
$601$		−	2.83288i		−	0.115555i	0.998329	−	0.0577777i	$-0.0184015\pi$
$602$	14.8143	−	2.72726i	0.603784	−	0.111155i
$603$	8.41363	+	8.41363i	0.342630	+	0.342630i
$604$	9.28204	−	2.48711i	0.377681	−	0.101199i
$605$	4.69860	−	17.5354i	0.191025	−	0.712916i
$606$	0.885016	+	0.237139i	0.0359513	+	0.00963313i
$607$	−23.8592	−	13.7751i	−0.968414	−	0.559114i	−0.0696619	−	0.997571i	$-0.522192\pi$
$607$	−23.8592	−	13.7751i	−0.968414	−	0.559114i	−0.898752	+	0.438456i	$0.855525\pi$
$608$	30.7878			1.24861
$609$	−5.72574	−	12.0415i	−0.232019	−	0.487945i
$610$		−	1.84308i		−	0.0746239i
$611$	−2.67963	−	7.68009i	−0.108406	−	0.310703i
$612$	17.4537	−	10.0769i	0.705524	−	0.407334i
$613$	−6.36125	+	23.7405i	−0.256928	+	0.958870i	0.710079	+	0.704122i	$0.248659\pi$
$613$	−6.36125	+	23.7405i	−0.256928	+	0.958870i	−0.967008	+	0.254748i	$0.918008\pi$
$614$	13.8765	+	8.01163i	0.560012	+	0.323323i
$615$	0.116635			0.00470318
$616$	3.06458	+	6.44494i	0.123476	+	0.259674i
$617$	−10.3106	−	10.3106i	−0.415090	−	0.415090i	0.468417	−	0.883507i	$-0.344824\pi$
$617$	−10.3106	−	10.3106i	−0.415090	−	0.415090i	−0.883507	+	0.468417i	$0.844824\pi$
$618$	0.266627	+	0.995064i	0.0107253	+	0.0400274i
$619$	7.84564	−	29.2803i	0.315343	−	1.17688i	−0.608327	−	0.793686i	$-0.708159\pi$
$619$	7.84564	−	29.2803i	0.315343	−	1.17688i	0.923670	−	0.383189i	$-0.125174\pi$
$620$	7.54788	+	13.0733i	0.303130	+	0.525037i
$621$	1.18427	−	2.05122i	0.0475232	−	0.0823126i
$622$	5.85080	+	5.85080i	0.234596	+	0.234596i
$623$	−3.71872	−	20.1998i	−0.148987	−	0.809286i
$624$	1.35409	−	0.100250i	0.0542069	−	0.00401320i
$625$	−6.93163	+	12.0059i	−0.277265	+	0.480237i
$626$	8.02445	+	2.15015i	0.320722	+	0.0859371i
$627$	1.31323	+	2.27459i	0.0524455	+	0.0908383i
$628$	9.01070	−	15.6070i	0.359566	−	0.622786i
$629$	−22.9715	+	22.9715i	−0.915935	+	0.915935i
$630$	−0.821167	+	10.2761i	−0.0327161	+	0.409410i
$631$	−9.56348	+	9.56348i	−0.380716	+	0.380716i	−0.871360	−	0.490644i	$-0.836762\pi$
$631$	−9.56348	+	9.56348i	−0.380716	+	0.380716i	0.490644	+	0.871360i	$0.336762\pi$
$632$	−7.02738	−	26.2265i	−0.279534	−	1.04324i
$633$	−2.94712	+	1.70152i	−0.117137	+	0.0676293i
$634$	7.84675	−	4.53032i	0.311634	−	0.179922i
$635$	−20.8185	+	5.57829i	−0.826156	+	0.221368i
$636$	4.62724			0.183482
$637$	−2.15734	+	25.1465i	−0.0854770	+	0.996340i
$638$	−8.20074			−0.324671
$639$	22.7336	−	6.09146i	0.899329	−	0.240974i
$640$	14.8726	−	8.58668i	0.587890	−	0.339418i
$641$	−23.6472	+	13.6527i	−0.934010	+	0.539251i	−0.888077	−	0.459694i	$-0.847959\pi$
$641$	−23.6472	+	13.6527i	−0.934010	+	0.539251i	−0.0459322	+	0.998945i	$0.514626\pi$
$642$	0.219849	+	0.820487i	0.00867674	+	0.0323820i
$643$	−17.4331	+	17.4331i	−0.687495	+	0.687495i	−0.961678	−	0.274183i	$-0.911593\pi$
$643$	−17.4331	+	17.4331i	−0.687495	+	0.687495i	0.274183	+	0.961678i	$0.411593\pi$
$644$	0.249430	−	3.12137i	0.00982891	−	0.122999i
$645$	4.63075	−	4.63075i	0.182335	−	0.182335i
$646$	−10.5637	+	18.2969i	−0.415625	+	0.719883i
$647$	−9.60708	−	16.6399i	−0.377693	−	0.654184i	0.613033	−	0.790057i	$-0.289949\pi$
$647$	−9.60708	−	16.6399i	−0.377693	−	0.654184i	−0.990726	+	0.135874i	$0.956616\pi$
$648$	−17.5794	−	4.71039i	−0.690584	−	0.185042i
$649$	5.17046	−	8.95549i	0.202958	−	0.351534i
$650$	3.52392	+	3.03810i	0.138220	+	0.119164i
$651$	1.37610	+	7.47487i	0.0539337	+	0.292963i
$652$	0.973622	+	0.973622i	0.0381300	+	0.0381300i
$653$	9.08140	−	15.7294i	0.355383	−	0.615541i	−0.631801	−	0.775131i	$-0.717684\pi$
$653$	9.08140	−	15.7294i	0.355383	−	0.615541i	0.987183	+	0.159590i	$0.0510173\pi$
$654$	−0.306560	−	0.530977i	−0.0119874	−	0.0207628i
$655$	7.29579	−	27.2283i	0.285070	−	1.06390i
$656$	0.0262514	+	0.0979717i	0.00102495	+	0.00382515i
$657$	22.1636	+	22.1636i	0.864683	+	0.864683i
$658$	−1.98092	−	4.16595i	−0.0772243	−	0.162406i
$659$	−36.6851			−1.42905			−0.714525	−	0.699610i	$-0.753357\pi$
$659$	−36.6851			−1.42905			−0.714525	+	0.699610i	$0.753357\pi$
$660$	1.10766	+	0.639507i	0.0431156	+	0.0248928i
$661$	−0.651913	+	2.43297i	−0.0253565	+	0.0946316i	−0.977444	−	0.211193i	$-0.932265\pi$
$661$	−0.651913	+	2.43297i	−0.0253565	+	0.0946316i	0.952088	+	0.305824i	$0.0989320\pi$
$662$	−18.1468	+	10.4771i	−0.705296	+	0.407203i
$663$	−3.97059	+	8.22607i	−0.154205	+	0.319474i
$664$			15.5074i			0.601805i
$665$	10.8989	+	22.9209i	0.422642	+	0.888834i
$666$	13.3376			0.516820
$667$	7.55935	+	4.36440i	0.292699	+	0.168990i
$668$	−17.7268	−	4.74988i	−0.685871	−	0.183779i
$669$	−3.46428	+	12.9289i	−0.133937	+	0.499858i
$670$	−5.86727	+	1.57213i	−0.226673	+	0.0607367i
$671$	0.947803	+	0.947803i	0.0365895	+	0.0365895i
$672$	7.42389	−	1.36672i	0.286383	−	0.0527222i
$673$		−	3.52257i		−	0.135785i	−0.997693	−	0.0678925i	$-0.978373\pi$
$673$		−	3.52257i		−	0.135785i	0.997693	−	0.0678925i	$-0.0216275\pi$
$674$	4.11875	+	15.3714i	0.158648	+	0.592084i
$675$	−2.34365	−	4.05932i	−0.0902072	−	0.156243i
$676$	14.2774	−	11.3439i	0.549131	−	0.436303i
$677$	18.4439	+	10.6486i	0.708857	+	0.409259i	0.810638	−	0.585548i	$-0.199121\pi$
$677$	18.4439	+	10.6486i	0.708857	+	0.409259i	−0.101781	+	0.994807i	$0.532454\pi$
$678$	0.700732	−	0.700732i	0.0269115	−	0.0269115i
$679$	6.04591	+	7.09609i	0.232021	+	0.272323i
$680$			24.9578i			0.957087i
$681$	0.0331310	−	0.00887743i	0.00126958	−	0.000340184i
$682$	4.51540	+	1.20990i	0.172903	+	0.0463293i
$683$	−1.95301	−	0.523307i	−0.0747298	−	0.0200238i	0.221260	−	0.975215i	$-0.428983\pi$
$683$	−1.95301	−	0.523307i	−0.0747298	−	0.0200238i	−0.295990	+	0.955191i	$0.595650\pi$
$684$	−19.6768	+	5.27239i	−0.752363	+	0.201595i
$685$			1.87064i			0.0714736i
$686$	0.323121	+	14.3095i	0.0123368	+	0.546340i
$687$	−1.88300	+	1.88300i	−0.0718410	+	0.0718410i
$688$	4.93202	+	2.84750i	0.188031	+	0.108560i
$689$	20.1859	−	13.7359i	0.769020	−	0.523296i
$690$	0.289837	+	0.502012i	0.0110339	+	0.0191113i
$691$	−0.329271	−	1.22886i	−0.0125261	−	0.0467479i	0.959380	−	0.282117i	$-0.0910367\pi$
$691$	−0.329271	−	1.22886i	−0.0125261	−	0.0467479i	−0.971906	+	0.235369i	$0.924370\pi$
$692$			31.0171i			1.17909i
$693$	−4.86221	−	5.70679i	−0.184700	−	0.216783i
$694$	8.18579	+	8.18579i	0.310728	+	0.310728i
$695$	−20.0999	+	5.38575i	−0.762432	+	0.204293i
$696$	−3.43009	+	12.8013i	−0.130017	+	0.485230i
$697$	−0.659080	−	0.176600i	−0.0249644	−	0.00668920i
$698$	3.08279	+	1.77985i	0.116685	+	0.0673683i
$699$	−0.513634			−0.0194274
$700$	−5.10275	−	3.51605i	−0.192866	−	0.132894i
$701$		−	2.12113i		−	0.0801138i	−0.999197	−	0.0400569i	$-0.987246\pi$
$701$		−	2.12113i		−	0.0801138i	0.999197	−	0.0400569i	$-0.0127539\pi$
$702$	7.38566	−	2.57690i	0.278754	−	0.0972587i
$703$	28.4374	−	16.4184i	1.07254	−	0.619230i
$704$	0.791196	−	2.95278i	0.0298193	−	0.111287i
$705$	−1.73683	−	1.00276i	−0.0654127	−	0.0377660i
$706$	−4.30869			−0.162160
$707$	−5.81509	+	2.76509i	−0.218699	+	0.103992i
$708$	−4.87129	−	4.87129i	−0.183074	−	0.183074i
$709$	−0.362596	−	1.35323i	−0.0136176	−	0.0508214i	0.958783	−	0.284140i	$-0.0917081\pi$
$709$	−0.362596	−	1.35323i	−0.0136176	−	0.0508214i	−0.972400	+	0.233319i	$0.925041\pi$
$710$	−3.10968	+	11.6055i	−0.116704	+	0.435546i
$711$	14.2622	+	24.7028i	0.534873	+	0.926428i
$712$	−10.2075	+	17.6799i	−0.382543	+	0.662583i
$713$	−3.51834	−	3.51834i	−0.131763	−	0.131763i
$714$	−1.73501	+	4.88089i	−0.0649312	+	0.182663i
$715$	6.73041	−	0.498286i	0.251703	−	0.0186348i
$716$	−5.66031	+	9.80394i	−0.211536	+	0.366390i
$717$	−12.4412	−	3.33360i	−0.464624	−	0.124496i
$718$	−1.94012	−	3.36038i	−0.0724046	−	0.125408i
$719$	16.5251	−	28.6223i	0.616281	−	1.06743i	−0.373877	−	0.927478i	$-0.621972\pi$
$719$	16.5251	−	28.6223i	0.616281	−	1.06743i	0.990158	−	0.139952i	$-0.0446949\pi$
$720$	−2.75596	+	2.75596i	−0.102708	+	0.102708i
$721$	−5.96149	−	4.10777i	−0.222017	−	0.152981i
$722$	4.71725	−	4.71725i	0.175558	−	0.175558i
$723$	−1.23568	−	4.61161i	−0.0459553	−	0.171507i
$724$	−24.9788	+	14.4215i	−0.928329	+	0.535971i
$725$	14.9598	−	8.63705i	0.555593	−	0.320772i
$726$	−3.61755	+	0.969318i	−0.134260	+	0.0359748i
$727$	−33.8896			−1.25689			−0.628447	−	0.777852i	$-0.716309\pi$
$727$	−33.8896			−1.25689			−0.628447	+	0.777852i	$0.716309\pi$
$728$	17.8420	−	17.6348i	0.661267	−	0.653588i
$729$	15.0172			0.556192
$730$	−15.4558	+	4.14138i	−0.572046	+	0.153279i
$731$	−33.1789	+	19.1558i	−1.22717	+	0.708504i
$732$	0.773329	−	0.446481i	0.0285830	−	0.0165024i
$733$	10.1931	+	38.0411i	0.376490	+	1.40508i	0.851156	+	0.524913i	$0.175902\pi$
$733$	10.1931	+	38.0411i	0.376490	+	1.40508i	−0.474666	+	0.880166i	$0.657431\pi$
$734$	−1.67978	+	1.67978i	−0.0620020	+	0.0620020i
$735$	3.64556	+	5.04311i	0.134468	+	0.186018i
$736$	−3.49434	+	3.49434i	−0.128803	+	0.128803i
$737$	2.20878	−	3.82572i	0.0813615	−	0.140922i
$738$	0.140067	+	0.242603i	0.00515593	+	0.00893034i
$739$	36.4024	+	9.75398i	1.33908	+	0.358806i	0.856094	−	0.516820i	$-0.172885\pi$
$739$	36.4024	+	9.75398i	1.33908	+	0.358806i	0.482989	+	0.875627i	$0.339551\pi$
$740$	7.99527	−	13.8482i	0.293912	−	0.509070i
$741$	6.02863	−	6.99266i	0.221467	−	0.256882i
$742$	10.5398	−	8.97997i	0.386928	−	0.329665i
$743$	−31.2340	−	31.2340i	−1.14587	−	1.14587i	−0.987358	−	0.158508i	$-0.949332\pi$
$743$	−31.2340	−	31.2340i	−1.14587	−	1.14587i	−0.158508	−	0.987358i	$-0.550668\pi$
$744$	3.77727	−	6.54242i	0.138481	−	0.239857i
$745$	6.96952	+	12.0716i	0.255344	+	0.442268i
$746$	4.67077	−	17.4316i	0.171009	−	0.638215i
$747$	−4.21652	−	15.7363i	−0.154275	−	0.575760i
$748$	−5.29086	−	5.29086i	−0.193453	−	0.193453i
$749$	−4.91559	−	3.38709i	−0.179612	−	0.123762i
$750$	4.58231			0.167322
$751$	−15.6656	−	9.04454i	−0.571646	−	0.330040i	0.186161	−	0.982519i	$-0.440396\pi$
$751$	−15.6656	−	9.04454i	−0.571646	−	0.330040i	−0.757806	+	0.652479i	$0.773729\pi$
$752$	0.451388	−	1.68460i	0.0164604	−	0.0614312i
$753$	10.5151	−	6.07087i	0.383190	−	0.221235i
$754$	9.49663	+	27.2183i	0.345847	+	0.991233i
$755$		−	12.5017i		−	0.454982i
$756$	−9.40871	+	4.47386i	−0.342192	+	0.162713i
$757$	4.04733			0.147103			0.0735514	−	0.997291i	$-0.476567\pi$
$757$	4.04733			0.147103			0.0735514	+	0.997291i	$0.476567\pi$
$758$	1.86735	+	1.07812i	0.0678254	+	0.0391590i
$759$	−0.407209	−	0.109111i	−0.0147808	−	0.00396049i
$760$	6.52916	−	24.3671i	0.236837	−	0.883889i
$761$	−37.0456	+	9.92634i	−1.34290	+	0.359830i	−0.857510	−	0.514467i	$-0.827990\pi$
$761$	−37.0456	+	9.92634i	−1.34290	+	0.359830i	−0.485392	+	0.874296i	$0.661323\pi$
$762$	3.14404	+	3.14404i	0.113897	+	0.113897i
$763$	4.05993	+	1.44319i	0.146979	+	0.0522469i
$764$			19.4111i			0.702268i
$765$	−6.78611	−	25.3261i	−0.245352	−	0.915667i
$766$	−1.19653	−	2.07245i	−0.0432323	−	0.0748805i
$767$	−35.7108	−	6.79014i	−1.28944	−	0.245178i
$768$	−5.58285	−	3.22326i	−0.201454	−	0.116309i
$769$	24.8051	−	24.8051i	0.894496	−	0.894496i	−0.100446	−	0.994942i	$-0.532027\pi$
$769$	24.8051	−	24.8051i	0.894496	−	0.894496i	0.994942	+	0.100446i	$0.0320271\pi$
$770$	3.76407	−	0.692954i	0.135648	−	0.0249723i
$771$		−	1.93020i		−	0.0695143i
$772$	33.0692	−	8.86087i	1.19019	−	0.318910i
$773$	29.1030	+	7.79813i	1.04676	+	0.280479i	0.740914	−	0.671600i	$-0.234393\pi$
$773$	29.1030	+	7.79813i	1.04676	+	0.280479i	0.305850	+	0.952080i	$0.401059\pi$
$774$	15.1931	+	4.07098i	0.546105	+	0.146328i
$775$	−9.51126	+	2.54853i	−0.341655	+	0.0915461i
$776$		−	9.26605i		−	0.332632i
$777$	6.12830	−	5.22135i	0.219852	−	0.187315i
$778$	−6.01745	+	6.01745i	−0.215736	+	0.215736i
$779$	0.597282	+	0.344841i	0.0213999	+	0.0123552i
$780$	0.839838	−	4.41689i	0.0300710	−	0.158150i
$781$	−4.36897	−	7.56728i	−0.156334	−	0.270779i
$782$	−0.877698	−	3.27561i	−0.0313864	−	0.117136i
$783$		−	29.0415i		−	1.03786i
$784$	−3.41562	+	4.19728i	−0.121986	+	0.149903i
$785$	−16.5784	−	16.5784i	−0.591707	−	0.591707i
$786$	−5.61717	+	1.50512i	−0.200358	+	0.0536857i
$787$	−2.51144	+	9.37281i	−0.0895230	+	0.334105i	−0.996132	−	0.0878668i	$-0.971995\pi$
$787$	−2.51144	+	9.37281i	−0.0895230	+	0.334105i	0.906609	+	0.421971i	$0.138662\pi$
$788$	27.4822	+	7.36383i	0.979013	+	0.262326i
$789$	−13.0471	−	7.53275i	−0.464489	−	0.268173i
$790$	−14.5616			−0.518079
$791$	−0.554753	+	6.94220i	−0.0197248	+	0.246836i
$792$			7.45191i			0.264792i
$793$	2.04819	−	4.24334i	0.0727334	−	0.150686i
$794$	−25.6335	+	14.7995i	−0.909700	+	0.525216i
$795$	1.55807	−	5.81479i	0.0552590	−	0.206229i
$796$	17.9984	+	10.3914i	0.637935	+	0.368312i
$797$	9.46979			0.335437			0.167719	−	0.985835i	$-0.446360\pi$
$797$	9.46979			0.335437			0.167719	+	0.985835i	$0.446360\pi$
$798$	2.97083	−	4.31149i	0.105166	−	0.152625i
$799$	8.29615	+	8.29615i	0.293497	+	0.293497i
$800$	2.53115	+	9.44638i	0.0894897	+	0.333980i
$801$	5.55092	−	20.7163i	0.196132	−	0.731975i
$802$	2.59917	+	4.50190i	0.0917800	+	0.158968i
$803$	5.81847	−	10.0779i	0.205329	−	0.355641i
$804$	−2.08098	−	2.08098i	−0.0733905	−	0.0733905i
$805$	−3.83846	−	1.36446i	−0.135288	−	0.0480910i
$806$	−1.21326	−	16.3877i	−0.0427354	−	0.577233i
$807$	−2.68201	+	4.64538i	−0.0944113	+	0.163525i
$808$	6.18201	+	1.65647i	0.217482	+	0.0582742i
$809$	−11.8530	−	20.5300i	−0.416729	−	0.721796i	0.578879	−	0.815413i	$-0.303490\pi$
$809$	−11.8530	−	20.5300i	−0.416729	−	0.721796i	−0.995608	+	0.0936173i	$0.970157\pi$
$810$	−4.88026	+	8.45286i	−0.171475	+	0.297003i
$811$	29.4470	−	29.4470i	1.03403	−	1.03403i	0.0346248	−	0.999400i	$-0.488976\pi$
$811$	29.4470	−	29.4470i	1.03403	−	1.03403i	0.999400	−	0.0346248i	$-0.0110236\pi$
$812$	−16.4875	−	34.6739i	−0.578598	−	1.21681i
$813$	1.72535	−	1.72535i	0.0605108	−	0.0605108i
$814$	−1.28161	−	4.78304i	−0.0449205	−	0.167646i
$815$	1.55133	−	0.895661i	0.0543407	−	0.0313736i
$816$	−1.69607	+	0.979228i	−0.0593744	+	0.0342798i
$817$	37.4050	−	10.0226i	1.30864	−	0.350648i
$818$	26.3071			0.919807
$819$	−13.3103	+	22.7463i	−0.465100	+	0.794820i
$820$	0.335855			0.0117286
$821$	−20.7328	+	5.55533i	−0.723578	+	0.193882i	−0.601768	−	0.798671i	$-0.705537\pi$
$821$	−20.7328	+	5.55533i	−0.723578	+	0.193882i	−0.121811	+	0.992553i	$0.538870\pi$
$822$	0.334210	−	0.192956i	0.0116569	−	0.00673011i
$823$	−16.4018	+	9.46958i	−0.571731	+	0.330089i	−0.757840	−	0.652440i	$-0.773745\pi$
$823$	−16.4018	+	9.46958i	−0.571731	+	0.330089i	0.186109	+	0.982529i	$0.440412\pi$
$824$	1.86244	+	6.95072i	0.0648812	+	0.242140i
$825$	−0.589929	+	0.589929i	−0.0205387	+	0.0205387i
$826$	−20.5493	−	1.64210i	−0.715001	−	0.0571359i
$827$	0.174463	−	0.174463i	0.00606667	−	0.00606667i	−0.704067	−	0.710134i	$-0.748635\pi$
$827$	0.174463	−	0.174463i	0.00606667	−	0.00606667i	0.710134	+	0.704067i	$0.248635\pi$
$828$	1.63487	−	2.83168i	0.0568156	−	0.0984076i
$829$	−8.54219	−	14.7955i	−0.296682	−	0.513869i	0.678692	−	0.734423i	$-0.262547\pi$
$829$	−8.54219	−	14.7955i	−0.296682	−	0.513869i	−0.975375	+	0.220554i	$0.929214\pi$
$830$	8.03334	+	2.15253i	0.278841	+	0.0747153i
$831$	−2.97333	+	5.14996i	−0.103144	+	0.178650i
$832$	−10.7165	+	0.793398i	−0.371529	+	0.0275061i
$833$	−12.9644	−	34.0174i	−0.449189	−	1.17863i
$834$	3.03551	+	3.03551i	0.105111	+	0.105111i
$835$	−11.9378	+	20.6769i	−0.413125	+	0.715554i
$836$	3.78151	+	6.54977i	0.130786	+	0.226529i
$837$	−4.28464	+	15.9905i	−0.148099	+	0.552713i
$838$	−7.11120	−	26.5394i	−0.245652	−	0.916787i
$839$	−22.4787	−	22.4787i	−0.776052	−	0.776052i	0.203105	−	0.979157i	$-0.434897\pi$
$839$	−22.4787	−	22.4787i	−0.776052	−	0.776052i	−0.979157	+	0.203105i	$0.934897\pi$
$840$	0.492687	−	6.16550i	0.0169993	−	0.212730i
$841$	78.0266			2.69057
$842$	9.76502	+	5.63784i	0.336525	+	0.194293i
$843$	2.28854	−	8.54093i	0.0788214	−	0.294165i
$844$	−8.48634	+	4.89959i	−0.292112	+	0.168651i
$845$	−9.44777	−	21.7613i	−0.325013	−	0.748611i
$846$		−	4.81685i		−	0.165607i
$847$	14.9337	−	21.6729i	0.513129	−	0.744690i
$848$	5.23502			0.179771
$849$	−7.12926	−	4.11608i	−0.244676	−	0.141264i
$850$	−6.48237	−	1.73695i	−0.222344	−	0.0595768i
$851$	−1.36414	+	5.09102i	−0.0467620	+	0.174518i
$852$	−5.62281	+	1.50663i	−0.192634	+	0.0516162i
$853$	−3.63231	−	3.63231i	−0.124368	−	0.124368i	0.642183	−	0.766551i	$-0.278029\pi$
$853$	−3.63231	−	3.63231i	−0.124368	−	0.124368i	−0.766551	+	0.642183i	$0.778029\pi$
$854$	0.894991	−	2.51776i	0.0306259	−	0.0861560i
$855$			26.5021i			0.906351i
$856$	1.53569	+	5.73127i	0.0524887	+	0.195891i
$857$	24.0900	+	41.7250i	0.822897	+	1.42530i	0.903516	+	0.428555i	$0.140977\pi$
$857$	24.0900	+	41.7250i	0.822897	+	1.42530i	−0.0806185	+	0.996745i	$0.525690\pi$
$858$	−0.783264	−	1.15106i	−0.0267402	−	0.0392966i
$859$	−2.67516	−	1.54450i	−0.0912752	−	0.0526978i	0.453668	−	0.891171i	$-0.350115\pi$
$859$	−2.67516	−	1.54450i	−0.0912752	−	0.0526978i	−0.544943	+	0.838473i	$0.683449\pi$
$860$	13.3344	−	13.3344i	0.454700	−	0.454700i
$861$	0.159331	+	0.0566375i	0.00542999	+	0.00193020i
$862$		−	27.5971i		−	0.939961i
$863$	−24.8574	+	6.66053i	−0.846157	+	0.226727i	−0.655750	−	0.754978i	$-0.727647\pi$
$863$	−24.8574	+	6.66053i	−0.846157	+	0.226727i	−0.190407	+	0.981705i	$0.560981\pi$
$864$	15.8814	+	4.25542i	0.540297	+	0.144772i
$865$	38.9774	+	10.4440i	1.32527	+	0.355105i
$866$	13.9481	−	3.73737i	0.473975	−	0.127001i
$867$		−	4.89375i		−	0.166201i
$868$	3.96254	+	21.5242i	0.134498	+	0.730579i
$869$	7.48833	−	7.48833i	0.254024	−	0.254024i
$870$	6.15534	+	3.55379i	0.208686	+	0.120485i
$871$	−15.2554	−	2.90070i	−0.516910	−	0.0982864i
$872$	−2.14138	−	3.70898i	−0.0725163	−	0.125602i
$873$	2.51947	+	9.40280i	0.0852712	+	0.318236i
$874$			3.42771i			0.115944i
$875$	−24.5125	+	20.8848i	−0.828673	+	0.706035i
$876$	−5.48181	−	5.48181i	−0.185213	−	0.185213i
$877$	−1.15484	+	0.309439i	−0.0389962	+	0.0104490i	−0.278264	−	0.960505i	$-0.589759\pi$
$877$	−1.15484	+	0.309439i	−0.0389962	+	0.0104490i	0.239268	+	0.970954i	$0.423092\pi$
$878$	4.76694	−	17.7905i	0.160877	−	0.600400i
$879$	7.39850	+	1.98242i	0.249545	+	0.0668654i
$880$	1.25315	+	0.723505i	0.0422436	+	0.0243893i
$881$	−20.3067			−0.684151			−0.342075	−	0.939672i	$-0.611130\pi$
$881$	−20.3067			−0.684151			−0.342075	+	0.939672i	$0.611130\pi$
$882$	−6.11181	+	13.6391i	−0.205795	+	0.459252i
$883$		−	28.8309i		−	0.970238i	−0.874448	−	0.485119i	$-0.838776\pi$
$883$		−	28.8309i		−	0.970238i	0.874448	−	0.485119i	$-0.161224\pi$
$884$	−11.4335	+	23.6873i	−0.384549	+	0.796691i
$885$	−7.76171	+	4.48123i	−0.260907	+	0.150635i
$886$	−4.67690	+	17.4544i	−0.157124	+	0.586393i
$887$	1.37828	+	0.795749i	0.0462781	+	0.0267186i	0.522961	−	0.852357i	$-0.324828\pi$
$887$	1.37828	+	0.795749i	0.0462781	+	0.0267186i	−0.476682	+	0.879076i	$0.658161\pi$
$888$	−8.00232			−0.268540
$889$	−31.1482	−	2.48906i	−1.04468	−	0.0834804i
$890$	7.74190	+	7.74190i	0.259509	+	0.259509i
$891$	−1.83721	−	6.85657i	−0.0615490	−	0.229704i
$892$	−9.97553	+	37.2292i	−0.334005	+	1.24653i
$893$	−5.92948	−	10.2702i	−0.198422	−	0.343678i
$894$	1.43781	−	2.49036i	0.0480875	−	0.0832900i
$895$	10.4141	+	10.4141i	0.348106	+	0.348106i
$896$	24.4866	−	4.50791i	0.818039	−	0.150599i
$897$	0.109415	+	1.47788i	0.00365326	+	0.0493451i
$898$	9.62831	−	16.6767i	0.321301	−	0.556510i
$899$	−58.9298	−	15.7902i	−1.96542	−	0.526632i
$900$	−3.23537	−	5.60383i	−0.107846	−	0.186794i
$901$	−17.6086	+	30.4990i	−0.586629	+	1.01607i
$902$	0.0735418	−	0.0735418i	0.00244868	−	0.00244868i
$903$	8.57458	−	4.07723i	0.285344	−	0.135682i
$904$	4.89475	−	4.89475i	0.162797	−	0.162797i
$905$	9.71192	+	36.2454i	0.322835	+	1.20484i
$906$	−2.23355	+	1.28954i	−0.0742047	+	0.0428421i
$907$	0.101102	−	0.0583711i	0.00335703	−	0.00193818i	−0.498321	−	0.866993i	$-0.666050\pi$
$907$	0.101102	−	0.0583711i	0.00335703	−	0.00193818i	0.501678	+	0.865055i	$0.332716\pi$
$908$	0.0954022	−	0.0255629i	0.00316603	−	0.000848336i
$909$	−6.72364			−0.223009
$910$	−6.65879	−	11.6905i	−0.220737	−	0.387537i
$911$	19.0003			0.629507			0.314753	−	0.949173i	$-0.398078\pi$
$911$	19.0003			0.629507			0.314753	+	0.949173i	$0.398078\pi$
$912$	1.91211	−	0.512348i	0.0633162	−	0.0169655i
$913$	−5.23809	+	3.02421i	−0.173356	+	0.100087i
$914$	2.71511	−	1.56757i	0.0898077	−	0.0518505i
$915$	−0.300675	−	1.12214i	−0.00994002	−	0.0370966i
$916$	−5.42218	+	5.42218i	−0.179154	+	0.179154i
$917$	23.1885	−	33.6528i	0.765751	−	1.11131i
$918$	−7.97810	+	7.97810i	−0.263317	+	0.263317i
$919$	5.82183	−	10.0837i	0.192045	−	0.332631i	−0.753883	−	0.657009i	$-0.771822\pi$
$919$	5.82183	−	10.0837i	0.192045	−	0.332631i	0.945928	+	0.324378i	$0.105155\pi$
$920$	2.02457	+	3.50665i	0.0667480	+	0.115611i
$921$	9.75558	+	2.61400i	0.321457	+	0.0861342i
$922$	4.12523	−	7.14512i	0.135857	−	0.235312i
$923$	−20.0565	+	23.2637i	−0.660168	+	0.765735i
$924$	1.20259	+	1.41148i	0.0395624	+	0.0464344i
$925$	7.37543	+	7.37543i	0.242503	+	0.242503i
$926$	−7.40036	+	12.8178i	−0.243191	+	0.421219i
$927$	−3.77985	−	6.54689i	−0.124147	−	0.215028i
$928$	−15.6825	+	58.5278i	−0.514802	+	1.92127i
$929$	13.3958	+	49.9939i	0.439502	+	1.64025i	0.730056	+	0.683387i	$0.239494\pi$
$929$	13.3958	+	49.9939i	0.439502	+	1.64025i	−0.290554	+	0.956859i	$0.593840\pi$
$930$	−2.86487	−	2.86487i	−0.0939429	−	0.0939429i
$931$	3.75835	+	36.6039i	0.123175	+	1.19964i
$932$	−1.47903			−0.0484473
$933$	4.51668	+	2.60771i	0.147869	+	0.0853724i
$934$	7.22627	−	26.9688i	0.236451	−	0.882446i
$935$	−8.43023	+	4.86720i	−0.275698	+	0.159174i
$936$	24.7329	−	8.62946i	0.808421	−	0.282063i
$937$			47.9005i			1.56484i	0.622751	+	0.782420i	$0.286015\pi$
$937$			47.9005i			1.56484i	−0.622751	+	0.782420i	$0.713985\pi$
$938$	−8.77850	−	0.701492i	−0.286628	−	0.0229045i
$939$	5.23637			0.170882
$940$	−5.00127	−	2.88748i	−0.163123	−	0.0941793i
$941$	30.4567	+	8.16086i	0.992861	+	0.266036i	0.718452	−	0.695577i	$-0.244851\pi$
$941$	30.4567	+	8.16086i	0.992861	+	0.266036i	0.274409	+	0.961613i	$0.411518\pi$
$942$	−1.25184	+	4.67195i	−0.0407873	+	0.152220i
$943$	−0.106929	+	0.0286515i	−0.00348208	+	0.000933020i
$944$	−5.51112	−	5.51112i	−0.179372	−	0.179372i
$945$	2.45398	+	13.3298i	0.0798280	+	0.433619i
$946$		−	5.83965i		−	0.189863i
$947$	7.12168	+	26.5785i	0.231424	+	0.863684i	0.979729	+	0.200330i	$0.0642013\pi$
$947$	7.12168	+	26.5785i	0.231424	+	0.863684i	−0.748305	+	0.663355i	$0.769132\pi$
$948$	−3.52753	−	6.10985i	−0.114569	−	0.198439i
$949$	−40.1865	−	7.64115i	−1.30451	−	0.248042i
$950$	5.87456	+	3.39168i	0.190596	+	0.110041i
$951$	4.03834	−	4.03834i	0.130952	−	0.130952i
$952$	−12.1194	+	34.0940i	−0.392792	+	1.10499i
$953$		−	16.2238i		−	0.525541i	−0.964858	−	0.262771i	$-0.915364\pi$
$953$		−	16.2238i		−	0.525541i	0.964858	−	0.262771i	$-0.0846362\pi$
$954$	13.9660	−	3.74217i	0.452165	−	0.121157i
$955$	24.3928	+	6.53603i	0.789332	+	0.211501i
$956$	−35.8249	−	9.59924i	−1.15866	−	0.310462i
$957$	−4.99293	+	1.33785i	−0.161398	+	0.0432466i
$958$		−	25.5127i		−	0.824276i
$959$	−0.908377	+	2.55542i	−0.0293330	+	0.0825188i
$960$	−1.87344	+	1.87344i	−0.0604652	+	0.0604652i
$961$	3.27081	+	1.88841i	0.105510	+	0.0609163i
$962$	−14.3908	+	9.79254i	−0.463979	+	0.315724i
$963$	−3.11670	−	5.39829i	−0.100434	−	0.173957i
$964$	−3.55818	−	13.2793i	−0.114601	−	0.427698i
$965$		−	44.5398i		−	1.43379i
$966$	0.152161	+	0.826525i	0.00489570	+	0.0265930i
$967$	18.2029	+	18.2029i	0.585366	+	0.585366i	0.936373	−	0.351007i	$-0.114161\pi$
$967$	18.2029	+	18.2029i	0.585366	+	0.585366i	−0.351007	+	0.936373i	$0.614161\pi$
$968$	−25.2693	+	6.77088i	−0.812185	+	0.217624i
$969$	−3.44669	+	12.8632i	−0.110724	+	0.413226i
$970$	−4.80011	−	1.28619i	−0.154122	−	0.0412969i
$971$	36.2770	+	20.9445i	1.16418	+	0.672142i	0.952303	−	0.305153i	$-0.0987077\pi$
$971$	36.2770	+	20.9445i	1.16418	+	0.672142i	0.211881	+	0.977295i	$0.432041\pi$
$972$	−16.5421			−0.530588
$973$	−30.0730	−	2.40314i	−0.964098	−	0.0770413i
$974$		−	4.77939i		−	0.153142i
$975$	2.64113	+	1.27483i	0.0845839	+	0.0408272i
$976$	0.874903	−	0.505126i	0.0280050	−	0.0161687i
$977$	−3.81461	+	14.2363i	−0.122040	+	0.455460i	−0.999717	−	0.0237930i	$-0.992426\pi$
$977$	−3.81461	+	14.2363i	−0.122040	+	0.455460i	0.877677	+	0.479253i	$0.159092\pi$
$978$	−0.320038	−	0.184774i	−0.0102337	−	0.00590843i
$979$	−7.96256			−0.254485
$980$	10.4975	+	14.5218i	0.335331	+	0.463883i
$981$	3.18147	+	3.18147i	0.101576	+	0.101576i
$982$	6.68382	+	24.9444i	0.213289	+	0.796007i
$983$	−5.20218	+	19.4148i	−0.165924	+	0.619236i	0.831997	+	0.554780i	$0.187198\pi$
$983$	−5.20218	+	19.4148i	−0.165924	+	0.619236i	−0.997921	+	0.0644554i	$0.979469\pi$
$984$	−0.0840379	−	0.145558i	−0.00267903	−	0.00464021i
$985$	18.5074	−	32.0558i	0.589695	−	1.02138i
$986$	−29.4017	−	29.4017i	−0.936340	−	0.936340i
$987$	−1.88569	−	2.21323i	−0.0600220	−	0.0704479i
$988$	17.3597	−	20.1357i	0.552285	−	0.640600i
$989$	−3.10783	+	5.38292i	−0.0988233	+	0.171167i
$990$	3.86033	+	1.03437i	0.122689	+	0.0328745i
$991$	13.5325	+	23.4389i	0.429873	+	0.744562i	0.996862	−	0.0791634i	$-0.0252249\pi$
$991$	13.5325	+	23.4389i	0.429873	+	0.744562i	−0.566988	+	0.823726i	$0.691892\pi$
$992$	17.2698	−	29.9122i	0.548317	−	0.949712i
$993$	−9.33927	+	9.33927i	−0.296373	+	0.296373i
$994$	−9.88360	+	14.3438i	−0.313489	+	0.454957i
$995$	19.1186	−	19.1186i	0.606100	−	0.606100i
$996$	1.04289	+	3.89212i	0.0330453	+	0.123327i
$997$	−24.5408	+	14.1686i	−0.777214	+	0.448725i	−0.835442	−	0.549579i	$-0.814788\pi$
$997$	−24.5408	+	14.1686i	−0.777214	+	0.448725i	0.0582281	+	0.998303i	$0.481455\pi$
$998$	−9.94666	+	5.74271i	−0.314856	+	0.181782i
$999$	16.9383	−	4.53861i	0.535905	−	0.143595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.bb.a.47.4	yes	32
3.2	odd	2		819.2.fn.e.775.5		32
7.2	even	3		637.2.i.a.489.9		32
7.3	odd	6	inner	91.2.bb.a.73.5	yes	32
7.4	even	3		637.2.bc.b.619.5		32
7.5	odd	6		637.2.i.a.489.10		32
7.6	odd	2		637.2.bc.b.411.4		32
13.5	odd	4	inner	91.2.bb.a.5.5	✓	32
21.17	even	6		819.2.fn.e.73.4		32
39.5	even	4		819.2.fn.e.460.4		32
91.5	even	12		637.2.i.a.538.10		32
91.18	odd	12		637.2.bc.b.31.4		32
91.31	even	12	inner	91.2.bb.a.31.4	yes	32
91.44	odd	12		637.2.i.a.538.9		32
91.83	even	4		637.2.bc.b.460.5		32
273.122	odd	12		819.2.fn.e.577.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.5	✓	32	13.5	odd	4	inner
91.2.bb.a.31.4	yes	32	91.31	even	12	inner
91.2.bb.a.47.4	yes	32	1.1	even	1	trivial
91.2.bb.a.73.5	yes	32	7.3	odd	6	inner
637.2.i.a.489.9		32	7.2	even	3
637.2.i.a.489.10		32	7.5	odd	6
637.2.i.a.538.9		32	91.44	odd	12
637.2.i.a.538.10		32	91.5	even	12
637.2.bc.b.31.4		32	91.18	odd	12
637.2.bc.b.411.4		32	7.6	odd	2
637.2.bc.b.460.5		32	91.83	even	4
637.2.bc.b.619.5		32	7.4	even	3
819.2.fn.e.73.4		32	21.17	even	6
819.2.fn.e.460.4		32	39.5	even	4
819.2.fn.e.577.5		32	273.122	odd	12
819.2.fn.e.775.5		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.bb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.746505 + 0.200025i) q^{2} +(-0.421869 + 0.243566i) q^{3} +(-1.21479 + 0.701360i) q^{4} +(0.472319 + 1.76272i) q^{5} +(0.266208 - 0.266208i) q^{6} +(-0.210751 + 2.63734i) q^{7} +(1.85952 - 1.85952i) q^{8} +(-1.38135 + 2.39257i) q^{9} +(-0.705177 - 1.22140i) q^{10} +(0.990745 + 0.265469i) q^{11} +(0.341655 - 0.591765i) q^{12} +(-0.266208 - 3.59571i) q^{13} +(-0.370209 - 2.01095i) q^{14} +(-0.628596 - 0.628596i) q^{15} +(0.386531 - 0.669491i) q^{16} +(2.60029 + 4.50383i) q^{17} +(0.552611 - 2.06237i) q^{18} +(-1.36051 - 5.07751i) q^{19} +(-1.81007 - 1.81007i) q^{20} +(-0.553459 - 1.16395i) q^{21} -0.792697 q^{22} +(0.730699 + 0.421869i) q^{23} +(-0.331558 + 1.23739i) q^{24} +(1.44604 - 0.834871i) q^{25} +(0.917960 + 2.63097i) q^{26} -2.80720i q^{27} +(-1.59371 - 3.35163i) q^{28} +10.3454 q^{29} +(0.594985 + 0.343515i) q^{30} +(-5.69625 - 1.52630i) q^{31} +(-1.51589 + 5.65739i) q^{32} +(-0.482625 + 0.129319i) q^{33} +(-2.84201 - 2.84201i) q^{34} +(-4.74843 + 0.874173i) q^{35} -3.87530i q^{36} +(1.61677 + 6.03388i) q^{37} +(2.03126 + 3.51825i) q^{38} +(0.988100 + 1.45208i) q^{39} +(4.15609 + 2.39952i) q^{40} +(-0.0927742 + 0.0927742i) q^{41} +(0.645979 + 0.758186i) q^{42} +7.36681i q^{43} +(-1.38974 + 0.372379i) q^{44} +(-4.86986 - 1.30488i) q^{45} +(-0.629856 - 0.168769i) q^{46} +(2.17913 - 0.583897i) q^{47} +0.376584i q^{48} +(-6.91117 - 1.11164i) q^{49} +(-0.912480 + 0.912480i) q^{50} +(-2.19397 - 1.26669i) q^{51} +(2.84527 + 4.18133i) q^{52} +(3.38590 + 5.86455i) q^{53} +(0.561512 + 2.09559i) q^{54} +1.87179i q^{55} +(4.51229 + 5.29608i) q^{56} +(1.81067 + 1.81067i) q^{57} +(-7.72287 + 2.06934i) q^{58} +(2.60938 - 9.73833i) q^{59} +(1.20448 + 0.322741i) q^{60} +(1.13174 + 0.653409i) q^{61} +4.55758 q^{62} +(-6.01891 - 4.14733i) q^{63} -2.98037i q^{64} +(6.21249 - 2.16757i) q^{65} +(0.334415 - 0.193074i) q^{66} +(1.11471 - 4.16014i) q^{67} +(-6.31762 - 3.64748i) q^{68} -0.411013 q^{69} +(3.36987 - 1.60238i) q^{70} +(-6.02388 - 6.02388i) q^{71} +(1.88038 + 7.01767i) q^{72} +(2.93641 - 10.9588i) q^{73} +(-2.41386 - 4.18093i) q^{74} +(-0.406693 + 0.704413i) q^{75} +(5.21390 + 5.21390i) q^{76} +(-0.908934 + 2.55699i) q^{77} +(-1.02807 - 0.886341i) q^{78} +(5.16240 - 8.94154i) q^{79} +(1.36269 + 0.365132i) q^{80} +(-3.46031 - 5.99344i) q^{81} +(0.0506992 - 0.0878136i) q^{82} +(-4.16974 + 4.16974i) q^{83} +(1.48868 + 1.02578i) q^{84} +(-6.71082 + 6.71082i) q^{85} +(-1.47355 - 5.49936i) q^{86} +(-4.36440 + 2.51978i) q^{87} +(2.33595 - 1.34866i) q^{88} +(-7.49857 + 2.00924i) q^{89} +3.89639 q^{90} +(9.53923 + 0.0557161i) q^{91} -1.18353 q^{92} +(2.77483 - 0.743513i) q^{93} +(-1.50994 + 0.871764i) q^{94} +(8.30761 - 4.79640i) q^{95} +(-0.738442 - 2.75590i) q^{96} +(2.49152 - 2.49152i) q^{97} +(5.38158 - 0.552561i) q^{98} +(-2.00372 + 2.00372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 12 q^{3} - 6 q^{5} - 6 q^{7} - 16 q^{8} + 8 q^{9} - 10 q^{11} + 28 q^{14} - 44 q^{15} + 12 q^{16} - 4 q^{18} + 12 q^{19} - 26 q^{21} - 8 q^{22} - 12 q^{24} + 24 q^{26} - 6 q^{28} + 16 q^{29}+ \cdots - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 12 * q^3 - 6 * q^5 - 6 * q^7 - 16 * q^8 + 8 * q^9 - 10 * q^11 + 28 * q^14 - 44 * q^15 + 12 * q^16 - 4 * q^18 + 12 * q^19 - 26 * q^21 - 8 * q^22 - 12 * q^24 + 24 * q^26 - 6 * q^28 + 16 * q^29 + 24 * q^31 + 4 * q^32 + 48 * q^33 + 28 * q^35 - 8 * q^37 - 6 * q^39 - 132 * q^40 - 16 * q^42 - 42 * q^44 - 24 * q^45 + 12 * q^46 + 30 * q^47 + 88 * q^50 + 36 * q^52 - 12 * q^53 + 78 * q^54 + 40 * q^57 + 26 * q^58 - 54 * q^59 + 16 * q^60 - 48 * q^61 + 24 * q^63 - 8 * q^65 + 12 * q^66 + 16 * q^67 - 48 * q^68 + 50 * q^70 - 36 * q^71 + 22 * q^72 + 66 * q^73 + 12 * q^74 - 176 * q^78 - 32 * q^79 + 138 * q^80 + 16 * q^81 - 58 * q^84 - 84 * q^85 + 42 * q^86 - 24 * q^87 - 60 * q^89 + 48 * q^92 + 6 * q^93 - 72 * q^94 - 42 * q^96 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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