LMFDB - Embedded newform 189.2.ba.a.101.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(5,189)] 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("189.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	189.101
Dual form			189.2.ba.a.131.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.582560 + 0.694268i) q^{2} +(-1.06977 - 1.36221i) q^{3} +(0.204665 + 1.16071i) q^{4} +(-0.931176 + 0.781349i) q^{5} +(1.56894 + 0.0508626i) q^{6} +(-2.06750 - 1.65089i) q^{7} +(-2.49483 - 1.44039i) q^{8} +(-0.711206 + 2.91448i) q^{9} -1.10167i q^{10} +(-2.30628 + 2.74851i) q^{11} +(1.36218 - 1.52048i) q^{12} +(0.206055 - 0.566132i) q^{13} +(2.35060 - 0.473658i) q^{14} +(2.06050 + 0.432592i) q^{15} +(0.238336 - 0.0867472i) q^{16} -7.94939 q^{17} +(-1.60911 - 2.19163i) q^{18} -1.41477i q^{19} +(-1.09750 - 0.920911i) q^{20} +(-0.0371098 + 4.58243i) q^{21} +(-0.564660 - 3.20235i) q^{22} +(-0.349041 + 0.958983i) q^{23} +(0.706775 + 4.93936i) q^{24} +(-0.611659 + 3.46889i) q^{25} +(0.273008 + 0.472864i) q^{26} +(4.73094 - 2.14900i) q^{27} +(1.49306 - 2.73765i) q^{28} +(-0.413325 - 1.13560i) q^{29} +(-1.50070 + 1.17853i) q^{30} +(8.17053 - 1.44069i) q^{31} +(1.89196 - 5.19810i) q^{32} +(6.21122 + 0.201358i) q^{33} +(4.63100 - 5.51901i) q^{34} +(3.21513 - 0.0781722i) q^{35} +(-3.52842 - 0.229013i) q^{36} +(-4.22521 + 7.31828i) q^{37} +(0.982231 + 0.824190i) q^{38} +(-0.991619 + 0.324939i) q^{39} +(3.44858 - 0.608078i) q^{40} +(6.73814 + 2.45248i) q^{41} +(-3.15981 - 2.69530i) q^{42} +(1.41438 - 8.02135i) q^{43} +(-3.66224 - 2.11440i) q^{44} +(-1.61497 - 3.26959i) q^{45} +(-0.462454 - 0.800993i) q^{46} +(-0.0548081 + 0.310832i) q^{47} +(-0.373131 - 0.231863i) q^{48} +(1.54913 + 6.82643i) q^{49} +(-2.05201 - 2.44549i) q^{50} +(8.50398 + 10.8287i) q^{51} +(0.699288 + 0.123303i) q^{52} +(5.74259 + 3.31549i) q^{53} +(-1.26408 + 4.53646i) q^{54} -4.36136i q^{55} +(2.78014 + 7.09671i) q^{56} +(-1.92721 + 1.51347i) q^{57} +(1.02920 + 0.374598i) q^{58} +(-0.936973 - 0.341030i) q^{59} +(-0.0804037 + 2.48018i) q^{60} +(-12.0683 - 2.12796i) q^{61} +(-3.75960 + 6.51182i) q^{62} +(6.28190 - 4.85157i) q^{63} +(2.76033 + 4.78103i) q^{64} +(0.250473 + 0.688170i) q^{65} +(-3.75820 + 4.19494i) q^{66} +(-7.90859 + 6.63609i) q^{67} +(-1.62696 - 9.22694i) q^{68} +(1.67972 - 0.550421i) q^{69} +(-1.81873 + 2.27770i) q^{70} +(-0.952881 + 0.550146i) q^{71} +(5.97234 - 6.24673i) q^{72} +(-0.808112 + 0.466563i) q^{73} +(-2.61941 - 7.19676i) q^{74} +(5.37967 - 2.87769i) q^{75} +(1.64214 - 0.289554i) q^{76} +(9.30573 - 1.87515i) q^{77} +(0.352083 - 0.877746i) q^{78} +(-10.3048 - 8.64674i) q^{79} +(-0.154153 + 0.267000i) q^{80} +(-7.98837 - 4.14559i) q^{81} +(-5.62805 + 3.24936i) q^{82} +(-5.66119 + 2.06050i) q^{83} +(-5.32646 + 0.894786i) q^{84} +(7.40228 - 6.21125i) q^{85} +(4.74500 + 5.65488i) q^{86} +(-1.10476 + 1.77786i) q^{87} +(9.71272 - 3.53514i) q^{88} -5.92334 q^{89} +(3.21079 + 0.783513i) q^{90} +(-1.36064 + 0.830305i) q^{91} +(-1.18454 - 0.208866i) q^{92} +(-10.7031 - 9.58875i) q^{93} +(-0.183872 - 0.219130i) q^{94} +(1.10543 + 1.31740i) q^{95} +(-9.10483 + 2.98352i) q^{96} +(-8.29293 - 1.46227i) q^{97} +(-5.64183 - 2.90130i) q^{98} +(-6.37025 - 8.67636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.582560	+	0.694268i	−0.411932	+	0.490922i	−0.931620	−	0.363435i	$-0.881604\pi$
$2$	−0.582560	+	0.694268i	−0.411932	+	0.490922i	0.519688	+	0.854356i	$0.326048\pi$
$3$	−1.06977	−	1.36221i	−0.617629	−	0.786470i
$3$	−1.06977	−	1.36221i	−0.617629	−	0.786470i
$4$	0.204665	+	1.16071i	0.102332	+	0.580355i
$5$	−0.931176	+	0.781349i	−0.416434	+	0.349430i	−0.826805	−	0.562489i	$-0.809844\pi$
$5$	−0.931176	+	0.781349i	−0.416434	+	0.349430i	0.410370	+	0.911919i	$0.365399\pi$
$6$	1.56894	+	0.0508626i	0.640516	+	0.0207646i
$7$	−2.06750	−	1.65089i	−0.781442	−	0.623978i
$7$	−2.06750	−	1.65089i	−0.781442	−	0.623978i
$8$	−2.49483	−	1.44039i	−0.882057	−	0.509256i
$9$	−0.711206	+	2.91448i	−0.237069	+	0.971493i
$10$		−	1.10167i		−	0.348378i
$11$	−2.30628	+	2.74851i	−0.695369	+	0.828708i	−0.991994	−	0.126286i	$-0.959694\pi$
$11$	−2.30628	+	2.74851i	−0.695369	+	0.828708i	0.296625	+	0.954994i	$0.404139\pi$
$12$	1.36218	−	1.52048i	0.393228	−	0.438925i
$13$	0.206055	−	0.566132i	0.0571495	−	0.157017i	−0.907833	−	0.419333i	$-0.862264\pi$
$13$	0.206055	−	0.566132i	0.0571495	−	0.157017i	0.964982	+	0.262316i	$0.0844863\pi$
$14$	2.35060	−	0.473658i	0.628225	−	0.126590i
$15$	2.06050	+	0.432592i	0.532018	+	0.111695i
$16$	0.238336	−	0.0867472i	0.0595840	−	0.0216868i
$17$	−7.94939			−1.92801			−0.964005	−	0.265883i	$-0.914336\pi$
$17$	−7.94939			−1.92801			−0.964005	+	0.265883i	$0.914336\pi$
$18$	−1.60911	−	2.19163i	−0.379271	−	0.516571i
$19$		−	1.41477i		−	0.324571i	−0.986744	−	0.162286i	$-0.948113\pi$
$19$		−	1.41477i		−	0.324571i	0.986744	−	0.162286i	$-0.0518866\pi$
$20$	−1.09750	−	0.920911i	−0.245408	−	0.205922i
$21$	−0.0371098	+	4.58243i	−0.00809802	+	0.999967i
$22$	−0.564660	−	3.20235i	−0.120386	−	0.682743i
$23$	−0.349041	+	0.958983i	−0.0727802	+	0.199962i	−0.970749	−	0.240098i	$-0.922820\pi$
$23$	−0.349041	+	0.958983i	−0.0727802	+	0.199962i	0.897969	+	0.440060i	$0.145043\pi$
$24$	0.706775	+	4.93936i	0.144270	+	1.00824i
$25$	−0.611659	+	3.46889i	−0.122332	+	0.693778i
$26$	0.273008	+	0.472864i	0.0535413	+	0.0927362i
$27$	4.73094	−	2.14900i	0.910470	−	0.413575i
$28$	1.49306	−	2.73765i	0.282162	−	0.517367i
$29$	−0.413325	−	1.13560i	−0.0767526	−	0.210876i	0.895382	−	0.445298i	$-0.146902\pi$
$29$	−0.413325	−	1.13560i	−0.0767526	−	0.210876i	−0.972135	+	0.234422i	$0.924680\pi$
$30$	−1.50070	+	1.17853i	−0.273989	+	0.215168i
$31$	8.17053	−	1.44069i	1.46747	−	0.258755i	0.617912	−	0.786247i	$-0.287979\pi$
$31$	8.17053	−	1.44069i	1.46747	−	0.258755i	0.849560	+	0.527493i	$0.176868\pi$
$32$	1.89196	−	5.19810i	0.334454	−	0.918904i
$33$	6.21122	+	0.201358i	1.08123	+	0.0350520i
$34$	4.63100	−	5.51901i	0.794209	−	0.946502i
$35$	3.21513	−	0.0781722i	0.543456	−	0.0132135i
$36$	−3.52842	−	0.229013i	−0.588071	−	0.0381689i
$37$	−4.22521	+	7.31828i	−0.694620	+	1.20312i	0.275689	+	0.961247i	$0.411094\pi$
$37$	−4.22521	+	7.31828i	−0.694620	+	1.20312i	−0.970309	+	0.241870i	$0.922239\pi$
$38$	0.982231	+	0.824190i	0.159339	+	0.133701i
$39$	−0.991619	+	0.324939i	−0.158786	+	0.0520319i
$40$	3.44858	−	0.608078i	0.545268	−	0.0961455i
$41$	6.73814	+	2.45248i	1.05232	+	0.383013i	0.809538	−	0.587067i	$-0.199718\pi$
$41$	6.73814	+	2.45248i	1.05232	+	0.383013i	0.242782	+	0.970081i	$0.421940\pi$
$42$	−3.15981	−	2.69530i	−0.487570	−	0.415894i
$43$	1.41438	−	8.02135i	0.215691	−	1.22324i	−0.664012	−	0.747722i	$-0.731148\pi$
$43$	1.41438	−	8.02135i	0.215691	−	1.22324i	0.879703	−	0.475523i	$-0.157741\pi$
$44$	−3.66224	−	2.11440i	−0.552104	−	0.318757i
$45$	−1.61497	−	3.26959i	−0.240745	−	0.487402i
$46$	−0.462454	−	0.800993i	−0.0681851	−	0.118100i
$47$	−0.0548081	+	0.310832i	−0.00799458	+	0.0453395i	−0.988544	−	0.150932i	$-0.951772\pi$
$47$	−0.0548081	+	0.310832i	−0.00799458	+	0.0453395i	0.980550	+	0.196272i	$0.0628835\pi$
$48$	−0.373131	−	0.231863i	−0.0538568	−	0.0334666i
$49$	1.54913	+	6.82643i	0.221304	+	0.975205i
$50$	−2.05201	−	2.44549i	−0.290198	−	0.345845i
$51$	8.50398	+	10.8287i	1.19080	+	1.51632i
$52$	0.699288	+	0.123303i	0.0969738	+	0.0170991i
$53$	5.74259	+	3.31549i	0.788806	+	0.455417i	0.839542	−	0.543295i	$-0.182823\pi$
$53$	5.74259	+	3.31549i	0.788806	+	0.455417i	−0.0507361	+	0.998712i	$0.516157\pi$
$54$	−1.26408	+	4.53646i	−0.172019	+	0.617334i
$55$		−	4.36136i		−	0.588085i
$56$	2.78014	+	7.09671i	0.371512	+	0.948338i
$57$	−1.92721	+	1.51347i	−0.255265	+	0.200465i
$58$	1.02920	+	0.374598i	0.135140	+	0.0491871i
$59$	−0.936973	−	0.341030i	−0.121983	−	0.0443983i	0.280307	−	0.959910i	$-0.409564\pi$
$59$	−0.936973	−	0.341030i	−0.121983	−	0.0443983i	−0.402291	+	0.915512i	$0.631786\pi$
$60$	−0.0804037	+	2.48018i	−0.0103801	+	0.320189i
$61$	−12.0683	−	2.12796i	−1.54518	−	0.272458i	−0.664911	−	0.746923i	$-0.731530\pi$
$61$	−12.0683	−	2.12796i	−1.54518	−	0.272458i	−0.880274	+	0.474465i	$0.842641\pi$
$62$	−3.75960	+	6.51182i	−0.477470	+	0.827003i
$63$	6.28190	−	4.85157i	0.791445	−	0.611240i
$64$	2.76033	+	4.78103i	0.345041	+	0.597629i
$65$	0.250473	+	0.688170i	0.0310674	+	0.0853570i
$66$	−3.75820	+	4.19494i	−0.462603	+	0.516362i
$67$	−7.90859	+	6.63609i	−0.966188	+	0.810728i	−0.981949	−	0.189148i	$-0.939427\pi$
$67$	−7.90859	+	6.63609i	−0.966188	+	0.810728i	0.0157609	+	0.999876i	$0.494983\pi$
$68$	−1.62696	−	9.22694i	−0.197298	−	1.11893i
$69$	1.67972	−	0.550421i	0.202215	−	0.0662629i
$70$	−1.81873	+	2.27770i	−0.217380	+	0.272237i
$71$	−0.952881	+	0.550146i	−0.113086	+	0.0652904i	−0.555476	−	0.831532i	$-0.687464\pi$
$71$	−0.952881	+	0.550146i	−0.113086	+	0.0652904i	0.442390	+	0.896823i	$0.354131\pi$
$72$	5.97234	−	6.24673i	0.703847	−	0.736184i
$73$	−0.808112	+	0.466563i	−0.0945823	+	0.0546071i	−0.546545	−	0.837430i	$-0.684057\pi$
$73$	−0.808112	+	0.466563i	−0.0945823	+	0.0546071i	0.451963	+	0.892037i	$0.350724\pi$
$74$	−2.61941	−	7.19676i	−0.304500	−	0.836606i
$75$	5.37967	−	2.87769i	0.621191	−	0.332287i
$76$	1.64214	−	0.289554i	0.188366	−	0.0332141i
$77$	9.30573	−	1.87515i	1.06049	−	0.213693i
$78$	0.352083	−	0.877746i	0.0398655	−	0.0993851i
$79$	−10.3048	−	8.64674i	−1.15938	−	0.972834i	−0.159482	−	0.987201i	$-0.550982\pi$
$79$	−10.3048	−	8.64674i	−1.15938	−	0.972834i	−0.999897	+	0.0143668i	$0.995427\pi$
$80$	−0.154153	+	0.267000i	−0.0172348	+	0.0298516i
$81$	−7.98837	−	4.14559i	−0.887597	−	0.460621i
$82$	−5.62805	+	3.24936i	−0.621514	+	0.358831i
$83$	−5.66119	+	2.06050i	−0.621396	+	0.226170i	−0.633482	−	0.773757i	$-0.718375\pi$
$83$	−5.66119	+	2.06050i	−0.621396	+	0.226170i	0.0120862	+	0.999927i	$0.496153\pi$
$84$	−5.32646	+	0.894786i	−0.581165	+	0.0976292i
$85$	7.40228	−	6.21125i	0.802890	−	0.673705i
$86$	4.74500	+	5.65488i	0.511667	+	0.609781i
$87$	−1.10476	+	1.77786i	−0.118443	+	0.190607i
$88$	9.71272	−	3.53514i	1.03538	−	0.376847i
$89$	−5.92334			−0.627873			−0.313937	−	0.949444i	$-0.601648\pi$
$89$	−5.92334			−0.627873			−0.313937	+	0.949444i	$0.601648\pi$
$90$	3.21079	+	0.783513i	0.338447	+	0.0825895i
$91$	−1.36064	+	0.830305i	−0.142634	+	0.0870396i
$92$	−1.18454	−	0.208866i	−0.123497	−	0.0217758i
$93$	−10.7031	−	9.58875i	−1.10986	−	0.994307i
$94$	−0.183872	−	0.219130i	−0.0189649	−	0.0226015i
$95$	1.10543	+	1.31740i	0.113415	+	0.135163i
$96$	−9.10483	+	2.98352i	−0.929258	+	0.304504i
$97$	−8.29293	−	1.46227i	−0.842019	−	0.148471i	−0.264029	−	0.964515i	$-0.585052\pi$
$97$	−8.29293	−	1.46227i	−0.842019	−	0.148471i	−0.577990	+	0.816044i	$0.696163\pi$
$98$	−5.64183	−	2.90130i	−0.569911	−	0.293075i
$99$	−6.37025	−	8.67636i	−0.640234	−	0.872007i
$100$	−4.15156			−0.415156
$101$	2.32994	−	0.848029i	0.231838	−	0.0843821i	−0.223489	−	0.974706i	$-0.571745\pi$
$101$	2.32994	−	0.848029i	0.231838	−	0.0843821i	0.455327	+	0.890324i	$0.349522\pi$
$102$	−12.4721	−	0.404327i	−1.23492	−	0.0400343i
$103$	6.14176	+	7.31947i	0.605166	+	0.721208i	0.978444	−	0.206511i	$-0.0662109\pi$
$103$	6.14176	+	7.31947i	0.605166	+	0.721208i	−0.373279	+	0.927719i	$0.621766\pi$
$104$	−1.32953	+	1.11561i	−0.130371	+	0.109394i
$105$	−3.54592	−	4.29604i	−0.346046	−	0.419250i
$106$	−5.64724	+	2.05543i	−0.548509	+	0.199641i
$107$	10.6429	−	6.14467i	1.02889	−	0.594028i	0.112221	−	0.993683i	$-0.464203\pi$
$107$	10.6429	−	6.14467i	1.02889	−	0.594028i	0.916666	+	0.399655i	$0.130870\pi$
$108$	3.46262	+	5.05143i	0.333191	+	0.486074i
$109$	−4.67103	+	8.09046i	−0.447404	+	0.774926i	−0.998216	−	0.0597033i	$-0.980985\pi$
$109$	−4.67103	+	8.09046i	−0.447404	+	0.774926i	0.550813	+	0.834629i	$0.314318\pi$
$110$	3.02795	+	2.54075i	0.288704	+	0.242251i
$111$	14.4890	−	2.07323i	1.37523	−	0.196783i
$112$	−0.635970	−	0.214116i	−0.0600935	−	0.0202321i
$113$	3.90833	−	0.689145i	0.367665	−	0.0648293i	0.0132365	−	0.999912i	$-0.495787\pi$
$113$	3.90833	−	0.689145i	0.367665	−	0.0648293i	0.354428	+	0.935083i	$0.384675\pi$
$114$	0.0719591	−	2.21969i	0.00673958	−	0.207893i
$115$	−0.424282	−	1.16571i	−0.0395645	−	0.108703i
$116$	1.23351	−	0.712168i	0.114529	−	0.0661232i
$117$	1.50343	+	1.00318i	0.138992	+	0.0927441i
$118$	0.782609	−	0.451839i	0.0720450	−	0.0415952i
$119$	16.4354	+	13.1236i	1.50663	+	1.20304i
$120$	−4.51750	−	4.04717i	−0.412389	−	0.369455i
$121$	−0.325286	−	1.84479i	−0.0295714	−	0.167708i
$122$	8.50787	−	7.13895i	0.770267	−	0.646330i
$123$	−3.86744	−	11.8023i	−0.348715	−	1.06418i
$124$	3.34444	+	9.18877i	0.300339	+	0.825176i
$125$	−5.17976	−	8.97161i	−0.463292	−	0.802445i
$126$	−0.291297	+	7.18765i	−0.0259508	+	0.640327i
$127$	−7.34765	+	12.7265i	−0.651998	+	1.12929i	0.330639	+	0.943757i	$0.392736\pi$
$127$	−7.34765	+	12.7265i	−0.651998	+	1.12929i	−0.982637	+	0.185537i	$0.940598\pi$
$128$	5.96796	+	1.05231i	0.527498	+	0.0930121i
$129$	−12.4398	+	6.65428i	−1.09526	+	0.585877i
$130$	−0.623690	−	0.227005i	−0.0547012	−	0.0199096i
$131$	−16.6664	−	6.06609i	−1.45615	−	0.529996i	−0.511850	−	0.859075i	$-0.671040\pi$
$131$	−16.6664	−	6.06609i	−1.45615	−	0.529996i	−0.944303	+	0.329078i	$0.893262\pi$
$132$	1.03750	+	7.25063i	0.0903025	+	0.631087i
$133$	−2.33563	+	2.92504i	−0.202525	+	0.253634i
$134$		−	9.35660i		−	0.808287i
$135$	−2.72622	+	5.69761i	−0.234636	+	0.490372i
$136$	19.8324	+	11.4503i	1.70062	+	0.981851i
$137$	3.29168	+	0.580412i	0.281227	+	0.0495879i	0.312483	−	0.949923i	$-0.398839\pi$
$137$	3.29168	+	0.580412i	0.281227	+	0.0495879i	−0.0312554	+	0.999511i	$0.509951\pi$
$138$	−0.596400	+	1.48683i	−0.0507690	+	0.126568i
$139$	2.56143	+	3.05259i	0.217257	+	0.258917i	0.863655	−	0.504084i	$-0.168170\pi$
$139$	2.56143	+	3.05259i	0.217257	+	0.258917i	−0.646397	+	0.763001i	$0.723725\pi$
$140$	0.748758	+	3.71583i	0.0632816	+	0.314045i
$141$	0.482049	−	0.257857i	0.0405958	−	0.0217155i
$142$	0.173162	−	0.982048i	0.0145314	−	0.0824117i
$143$	1.08080	+	1.87200i	0.0903812	+	0.156545i
$144$	0.0833170	+	0.756320i	0.00694308	+	0.0630267i
$145$	1.27218	+	0.734493i	0.105649	+	0.0609964i
$146$	0.146853	−	0.832847i	0.0121537	−	0.0689269i
$147$	7.64180	−	9.41291i	0.630285	−	0.776364i
$148$	−9.35915	−	3.40645i	−0.769317	−	0.280009i
$149$	−13.8612	+	2.44410i	−1.13555	+	0.200228i	−0.709659	−	0.704546i	$-0.751151\pi$
$149$	−13.8612	+	2.44410i	−1.13555	+	0.200228i	−0.425892	+	0.904774i	$0.640040\pi$
$150$	−1.13609	+	5.41136i	−0.0927615	+	0.441836i
$151$	10.1132	+	8.48596i	0.822998	+	0.690577i	0.953672	−	0.300848i	$-0.0972697\pi$
$151$	10.1132	+	8.48596i	0.822998	+	0.690577i	−0.130674	+	0.991425i	$0.541714\pi$
$152$	−2.03783	+	3.52962i	−0.165290	+	0.286290i
$153$	5.65365	−	23.1683i	0.457071	−	1.87305i
$154$	−4.11929	+	7.55305i	−0.331942	+	0.608642i
$155$	−6.48252	+	7.72557i	−0.520689	+	0.620533i
$156$	−0.580109	−	1.08448i	−0.0464459	−	0.0868278i
$157$	−1.70932	+	4.69633i	−0.136419	+	0.374808i	−0.989025	−	0.147746i	$-0.952798\pi$
$157$	−1.70932	+	4.69633i	−0.136419	+	0.374808i	0.852606	+	0.522554i	$0.175021\pi$
$158$	12.0063	−	2.11704i	0.955170	−	0.168422i
$159$	−1.62685	−	11.3694i	−0.129018	−	0.901651i
$160$	2.29979	+	6.31863i	0.181815	+	0.499531i
$161$	2.30482	−	1.40647i	0.181645	−	0.110845i
$162$	7.53185	−	3.13102i	0.591758	−	0.245996i
$163$	−1.07224	−	1.85718i	−0.0839847	−	0.145466i	0.820973	−	0.570966i	$-0.193431\pi$
$163$	−1.07224	−	1.85718i	−0.0839847	−	0.145466i	−0.904958	+	0.425501i	$0.860098\pi$
$164$	−1.46756	+	8.32296i	−0.114597	+	0.649914i
$165$	−5.94106	+	4.66563i	−0.462511	+	0.363219i
$166$	1.86744	−	5.13075i	0.144941	−	0.398223i
$167$	2.40447	+	13.6365i	0.186064	+	1.05522i	0.924581	+	0.380986i	$0.124415\pi$
$167$	2.40447	+	13.6365i	0.186064	+	1.05522i	−0.738517	+	0.674235i	$0.764474\pi$
$168$	6.69308	−	11.3789i	0.516382	−	0.877904i
$169$	9.68053	+	8.12293i	0.744656	+	0.624841i
$170$			8.75759i			0.671677i
$171$	4.12332	+	1.00619i	0.315318	+	0.0769456i
$172$	9.59994			0.731988
$173$	−3.40013	+	1.23754i	−0.258507	+	0.0940888i	−0.468023	−	0.883716i	$-0.655033\pi$
$173$	−3.40013	+	1.23754i	−0.258507	+	0.0940888i	0.209516	+	0.977805i	$0.432811\pi$
$174$	−0.590722	−	1.80271i	−0.0447825	−	0.136663i
$175$	6.99136	−	6.16216i	0.528498	−	0.465815i
$176$	−0.311243	+	0.855133i	−0.0234608	+	0.0644581i
$177$	0.537787	+	1.64117i	0.0404226	+	0.123358i
$178$	3.45070	−	4.11239i	0.258641	−	0.308236i
$179$		−	24.4587i		−	1.82813i	−0.405573	−	0.914063i	$-0.632928\pi$
$179$		−	24.4587i		−	1.82813i	0.405573	−	0.914063i	$-0.367072\pi$
$180$	3.46452	−	2.54368i	0.258230	−	0.189595i
$181$	−13.8640	−	8.00438i	−1.03050	−	0.594961i	−0.113374	−	0.993552i	$-0.536166\pi$
$181$	−13.8640	−	8.00438i	−1.03050	−	0.594961i	−0.917129	+	0.398591i	$0.869499\pi$
$182$	0.216201	−	1.42835i	0.0160259	−	0.105877i
$183$	10.0115	+	18.7159i	0.740071	+	1.38352i
$184$	2.25211	−	1.88975i	0.166028	−	0.139314i
$185$	−1.78372	−	10.1160i	−0.131142	−	0.743740i
$186$	12.8923	−	1.84477i	0.945312	−	0.135265i
$187$	18.3335	−	21.8490i	1.34068	−	1.59776i
$188$	−0.372003			−0.0271311
$189$	−13.3290	−	3.36720i	−0.969541	−	0.244928i
$190$	−1.55861			−0.113073
$191$	4.13129	−	4.92349i	0.298930	−	0.356251i	−0.595582	−	0.803294i	$-0.703079\pi$
$191$	4.13129	−	4.92349i	0.298930	−	0.356251i	0.894512	+	0.447043i	$0.147523\pi$
$192$	3.55984	−	8.87472i	0.256910	−	0.640478i
$193$	−0.237958	−	1.34953i	−0.0171286	−	0.0971411i	0.975045	−	0.222007i	$-0.0712609\pi$
$193$	−0.237958	−	1.34953i	−0.0171286	−	0.0971411i	−0.992174	+	0.124866i	$0.960150\pi$
$194$	5.84633	−	4.90566i	0.419742	−	0.352206i
$195$	0.669481	−	1.07738i	0.0479425	−	0.0771525i
$196$	−7.60646	+	3.19522i	−0.543319	+	0.228230i
$197$	19.2475	+	11.1125i	1.37132	+	0.791734i	0.991095	−	0.133158i	$-0.0425118\pi$
$197$	19.2475	+	11.1125i	1.37132	+	0.791734i	0.380229	+	0.924892i	$0.375845\pi$
$198$	9.73477	+	0.631838i	0.691820	+	0.0449027i
$199$		−	13.3056i		−	0.943207i	−0.881811	−	0.471603i	$-0.843675\pi$
$199$		−	13.3056i		−	0.943207i	0.881811	−	0.471603i	$-0.156325\pi$
$200$	6.52256	−	7.77328i	0.461215	−	0.549654i
$201$	17.5000	+	3.67406i	1.23436	+	0.259148i
$202$	−0.768571	+	2.11163i	−0.0540765	+	0.148574i
$203$	−1.02020	+	3.03021i	−0.0716042	+	0.212679i
$204$	−10.8285	+	12.0869i	−0.758148	+	0.846253i
$205$	−8.19064	+	2.98115i	−0.572059	+	0.208212i
$206$	−8.65961			−0.603344
$207$	−2.54670	−	1.69931i	−0.177008	−	0.118110i
$208$		−	0.152804i		−	0.0105951i
$209$	3.88852	+	3.26286i	0.268975	+	0.225697i
$210$	5.04831	+	0.0408826i	0.348367	+	0.00282117i
$211$	−2.63818	−	14.9619i	−0.181620	−	1.03002i	−0.930222	−	0.366997i	$-0.880386\pi$
$211$	−2.63818	−	14.9619i	−0.181620	−	1.03002i	0.748602	−	0.663019i	$-0.230725\pi$
$212$	−2.67302	+	7.34405i	−0.183583	+	0.504391i
$213$	1.76877	+	0.709493i	0.121194	+	0.0486136i
$214$	−1.93407	+	10.9687i	−0.132210	+	0.749802i
$215$	4.95044	+	8.57441i	0.337617	+	0.584770i
$216$	−14.8983	−	1.45302i	−1.01370	−	0.0988654i
$217$	−19.2710	−	10.5100i	−1.30820	−	0.713467i
$218$	−2.89579	−	7.95612i	−0.196128	−	0.538857i
$219$	1.50004	+	0.601701i	0.101364	+	0.0406592i
$220$	5.06227	−	0.892615i	0.341298	−	0.0601801i
$221$	−1.63801	+	4.50041i	−0.110185	+	0.302730i
$222$	−7.00131	+	11.2670i	−0.469897	+	0.756192i
$223$	−4.53645	+	5.40633i	−0.303783	+	0.362035i	−0.896242	−	0.443566i	$-0.853713\pi$
$223$	−4.53645	+	5.40633i	−0.303783	+	0.362035i	0.592458	+	0.805601i	$0.298158\pi$
$224$	−12.4931	+	7.62368i	−0.834732	+	0.509379i
$225$	−9.67500	−	4.24976i	−0.645000	−	0.283318i
$226$	−1.79839	+	3.11490i	−0.119627	+	0.207200i
$227$	−13.1451	−	11.0301i	−0.872471	−	0.732090i	0.0921457	−	0.995746i	$-0.470627\pi$
$227$	−13.1451	−	11.0301i	−0.872471	−	0.732090i	−0.964617	+	0.263655i	$0.915072\pi$
$228$	−2.15114	−	1.92718i	−0.142462	−	0.127631i
$229$	8.79697	−	1.55114i	0.581320	−	0.102502i	0.124748	−	0.992189i	$-0.460188\pi$
$229$	8.79697	−	1.55114i	0.581320	−	0.102502i	0.456573	+	0.889686i	$0.349077\pi$
$230$	1.05648	+	0.384528i	0.0696623	+	0.0253550i
$231$	−12.5093	−	10.6703i	−0.823050	−	0.702057i
$232$	−0.604535	+	3.42849i	−0.0396897	+	0.225091i
$233$	7.40115	+	4.27306i	0.484866	+	0.279937i	0.722442	−	0.691432i	$-0.243020\pi$
$233$	7.40115	+	4.27306i	0.484866	+	0.279937i	−0.237576	+	0.971369i	$0.576353\pi$
$234$	−1.57232	+	0.459373i	−0.102785	+	0.0300301i
$235$	−0.191832	−	0.332264i	−0.0125138	−	0.0216745i
$236$	0.204072	−	1.15735i	0.0132840	−	0.0753371i
$237$	−0.754937	+	23.2872i	−0.0490384	+	1.51267i
$238$	−18.6859	+	3.76529i	−1.21122	+	0.244068i
$239$	8.54791	+	10.1870i	0.552919	+	0.658943i	0.968032	−	0.250827i	$-0.0807025\pi$
$239$	8.54791	+	10.1870i	0.552919	+	0.658943i	−0.415113	+	0.909770i	$0.636258\pi$
$240$	0.528617	−	0.0756400i	0.0341221	−	0.00488254i
$241$	13.7623	+	2.42667i	0.886510	+	0.156316i	0.598320	−	0.801257i	$-0.295835\pi$
$241$	13.7623	+	2.42667i	0.886510	+	0.156316i	0.288191	+	0.957573i	$0.406946\pi$
$242$	1.47027	+	0.848864i	0.0945128	+	0.0545670i
$243$	2.89854	+	15.3166i	0.185941	+	0.982561i
$244$		−	14.4433i		−	0.924637i
$245$	−6.77634	−	5.14620i	−0.432924	−	0.328779i
$246$	10.4470	+	4.19051i	0.666075	+	0.267177i
$247$	−0.800948	−	0.291521i	−0.0509631	−	0.0185491i
$248$	−22.4593	−	8.17451i	−1.42617	−	0.519082i
$249$	8.86297	+	5.50744i	0.561668	+	0.349020i
$250$	9.24622	+	1.63036i	0.584783	+	0.103113i
$251$	−12.8062	+	22.1810i	−0.808322	+	1.40005i	0.105704	+	0.994398i	$0.466291\pi$
$251$	−12.8062	+	22.1810i	−0.808322	+	1.40005i	−0.914025	+	0.405657i	$0.867043\pi$
$252$	6.91695	+	6.29852i	0.435727	+	0.396770i
$253$	−1.83079	−	3.17103i	−0.115101	−	0.199361i
$254$	−4.55515	−	12.5152i	−0.285816	−	0.785272i
$255$	−16.3797	−	3.43885i	−1.02574	−	0.215349i
$256$	−12.6654	+	10.6276i	−0.791589	+	0.664222i
$257$	2.07412	+	11.7629i	0.129380	+	0.733751i	0.978609	+	0.205727i	$0.0659559\pi$
$257$	2.07412	+	11.7629i	0.129380	+	0.733751i	−0.849229	+	0.528024i	$0.822933\pi$
$258$	2.62706	−	12.5131i	0.163554	−	0.779029i
$259$	20.8173	−	8.15519i	1.29352	−	0.506739i
$260$	−0.747503	+	0.431571i	−0.0463582	+	0.0267649i
$261$	3.60365	−	0.396981i	0.223060	−	0.0245725i
$262$	13.9207	−	8.03711i	0.860023	−	0.496534i
$263$	4.86540	+	13.3676i	0.300013	+	0.824280i	0.994496	+	0.104771i	$0.0334109\pi$
$263$	4.86540	+	13.3676i	0.300013	+	0.824280i	−0.694483	+	0.719509i	$0.744367\pi$
$264$	−15.2059	−	9.44895i	−0.935860	−	0.581543i
$265$	−7.93792	+	1.39967i	−0.487622	+	0.0859810i
$266$	−0.670118	−	3.32557i	−0.0410876	−	0.203904i
$267$	6.33659	+	8.06881i	0.387793	+	0.493803i
$268$	−9.32119	−	7.82141i	−0.569382	−	0.477768i
$269$	15.2108	−	26.3459i	0.927421	−	1.60634i	0.139801	−	0.990180i	$-0.455354\pi$
$269$	15.2108	−	26.3459i	0.927421	−	1.60634i	0.787620	−	0.616161i	$-0.211313\pi$
$270$	−2.36748	−	5.21193i	−0.144080	−	0.317188i
$271$	−11.2849	+	6.51534i	−0.685509	+	0.395779i	−0.801927	−	0.597421i	$-0.796192\pi$
$271$	−11.2849	+	6.51534i	−0.685509	+	0.395779i	0.116418	+	0.993200i	$0.462859\pi$
$272$	−1.89463	+	0.689587i	−0.114879	+	0.0418124i
$273$	2.58661	+	0.965242i	0.156549	+	0.0584191i
$274$	−2.32056	+	1.94718i	−0.140190	+	0.117634i
$275$	−8.12364	−	9.68138i	−0.489874	−	0.583809i
$276$	0.982659	+	1.83702i	0.0591491	+	0.110576i
$277$	−16.8545	+	6.13455i	−1.01269	+	0.368589i	−0.794465	−	0.607309i	$-0.792249\pi$
$277$	−16.8545	+	6.13455i	−1.01269	+	0.368589i	−0.218225	+	0.975899i	$0.570027\pi$
$278$	−3.61150			−0.216603
$279$	−1.61208	+	24.8375i	−0.0965129	+	1.48698i
$280$	−8.13381	−	4.43602i	−0.486088	−	0.265103i
$281$	−9.46609	−	1.66913i	−0.564700	−	0.0995718i	−0.115992	−	0.993250i	$-0.537005\pi$
$281$	−9.46609	−	1.66913i	−0.564700	−	0.0995718i	−0.448708	+	0.893678i	$0.648116\pi$
$282$	−0.101800	+	0.484888i	−0.00606211	+	0.0288747i
$283$	−8.57485	−	10.2191i	−0.509722	−	0.607463i	0.448397	−	0.893835i	$-0.351995\pi$
$283$	−8.57485	−	10.2191i	−0.509722	−	0.607463i	−0.958119	+	0.286372i	$0.907551\pi$
$284$	−0.833582	−	0.993424i	−0.0494640	−	0.0589489i
$285$	0.612020	−	2.91513i	0.0362529	−	0.172678i
$286$	−1.92930	−	0.340188i	−0.114082	−	0.0201158i
$287$	−9.88233	−	16.1944i	−0.583336	−	0.955927i
$288$	13.8042	+	9.21098i	0.813420	+	0.542762i
$289$	46.1928			2.71722
$290$	−1.25106	+	0.455347i	−0.0734645	+	0.0267389i
$291$	6.87958	+	12.8610i	0.403288	+	0.753922i
$292$	−0.706937	−	0.842495i	−0.0413704	−	0.0493033i
$293$	1.25235	−	1.05085i	0.0731631	−	0.0613911i	−0.605473	−	0.795866i	$-0.707016\pi$
$293$	1.25235	−	1.05085i	0.0731631	−	0.0613911i	0.678636	+	0.734475i	$0.262571\pi$
$294$	2.08327	+	10.7890i	0.121499	+	0.629230i
$295$	1.13895	−	0.414544i	0.0663122	−	0.0241357i
$296$	21.0824	−	12.1719i	1.22539	−	0.707479i
$297$	−5.00431	+	17.9592i	−0.290379	+	1.04210i
$298$	6.37810	−	11.0472i	0.369473	−	0.639947i
$299$	0.470990	+	0.395207i	0.0272380	+	0.0228554i
$300$	4.44120	+	5.65528i	0.256413	+	0.326508i
$301$	−16.1666	+	14.2492i	−0.931827	+	0.821308i
$302$	−11.7831	+	2.07767i	−0.678039	+	0.119556i
$303$	−3.64768	−	2.26667i	−0.209554	−	0.130217i
$304$	−0.122728	−	0.337191i	−0.00703891	−	0.0193392i
$305$	12.9004	−	7.44803i	0.738673	−	0.426473i
$306$	12.7914	+	17.4221i	0.731238	+	0.995955i
$307$	−9.99990	+	5.77344i	−0.570724	+	0.329508i	−0.757439	−	0.652906i	$-0.773549\pi$
$307$	−9.99990	+	5.77344i	−0.570724	+	0.329508i	0.186714	+	0.982414i	$0.440216\pi$
$308$	4.08106	+	10.4175i	0.232540	+	0.593591i
$309$	3.40037	−	16.1964i	0.193440	−	0.921384i
$310$	−1.58716	−	9.00122i	−0.0901445	−	0.511235i
$311$	−18.4307	+	15.4652i	−1.04511	+	0.876953i	−0.992571	−	0.121666i	$-0.961176\pi$
$311$	−18.4307	+	15.4652i	−1.04511	+	0.876953i	−0.0525406	+	0.998619i	$0.516732\pi$
$312$	2.94197	+	0.617653i	0.166556	+	0.0349677i
$313$	−11.1193	−	30.5501i	−0.628501	−	1.72679i	−0.685153	−	0.728400i	$-0.740264\pi$
$313$	−11.1193	−	30.5501i	−0.628501	−	1.72679i	0.0566510	−	0.998394i	$-0.481958\pi$
$314$	−2.26473	−	3.92262i	−0.127806	−	0.221366i
$315$	−2.05879	+	9.42602i	−0.115999	+	0.531096i
$316$	7.92734	−	13.7305i	0.445947	−	0.772404i
$317$	−4.97342	−	0.876947i	−0.279335	−	0.0492543i	0.0322255	−	0.999481i	$-0.489741\pi$
$317$	−4.97342	−	0.876947i	−0.279335	−	0.0492543i	−0.311560	+	0.950226i	$0.600852\pi$
$318$	8.84114	+	5.49388i	0.495786	+	0.308081i
$319$	4.07446	+	1.48298i	0.228126	+	0.0830311i
$320$	−6.30601	−	2.29520i	−0.352517	−	0.128306i
$321$	−19.7557	−	7.92444i	−1.10266	−	0.442299i
$322$	−0.366228	+	2.41952i	−0.0204091	+	0.134834i
$323$			11.2466i			0.625776i
$324$	3.17689	−	10.1206i	0.176494	−	0.562258i
$325$	1.83782	+	1.06106i	0.101944	+	0.0588572i
$326$	1.91403	+	0.337495i	0.106008	+	0.0186921i
$327$	16.0178	−	2.29199i	0.885785	−	0.126747i
$328$	−13.2780	−	15.8241i	−0.733155	−	0.873740i
$329$	0.626465	−	0.552164i	0.0345381	−	0.0304418i
$330$	0.221830	−	6.84270i	0.0122113	−	0.376678i
$331$	2.12634	−	12.0591i	0.116874	−	0.662828i	−0.868931	−	0.494934i	$-0.835192\pi$
$331$	2.12634	−	12.0591i	0.116874	−	0.662828i	0.985805	−	0.167894i	$-0.0536966\pi$
$332$	−3.55029	−	6.14928i	−0.194848	−	0.337486i
$333$	−18.3240	−	17.5191i	−1.00415	−	0.960040i
$334$	−10.8681	−	6.27470i	−0.594676	−	0.343336i
$335$	2.17918	−	12.3587i	0.119061	−	0.675230i
$336$	0.388668	+	1.09538i	0.0212036	+	0.0597576i
$337$	16.9278	+	6.16122i	0.922116	+	0.335623i	0.759080	−	0.650997i	$-0.225649\pi$
$337$	16.9278	+	6.16122i	0.922116	+	0.335623i	0.163036	+	0.986620i	$0.447871\pi$
$338$	−11.2790	+	1.98879i	−0.613496	+	0.108176i
$339$	−5.11975	−	4.58673i	−0.278067	−	0.249117i
$340$	8.72445	+	7.32068i	0.473150	+	0.397020i
$341$	−14.8838	+	25.7795i	−0.806001	+	1.39604i
$342$	−3.10065	+	2.27652i	−0.167664	+	0.123100i
$343$	8.06687	−	16.6711i	0.435570	−	0.900155i
$344$	−15.0825	+	17.9747i	−0.813196	+	0.969130i
$345$	−1.13405	+	1.82499i	−0.0610551	+	0.0982541i
$346$	1.12159	−	3.08154i	0.0602970	−	0.165665i
$347$	−11.2670	+	1.98668i	−0.604846	+	0.106651i	−0.467681	−	0.883898i	$-0.654910\pi$
$347$	−11.2670	+	1.98668i	−0.604846	+	0.106651i	−0.137165	+	0.990548i	$0.543799\pi$
$348$	−2.28969	−	0.918443i	−0.122740	−	0.0492337i
$349$	2.98735	+	8.20768i	0.159909	+	0.439347i	0.993610	−	0.112870i	$-0.0360043\pi$
$349$	2.98735	+	8.20768i	0.159909	+	0.439347i	−0.833701	+	0.552217i	$0.813782\pi$
$350$	0.205299	+	8.44371i	0.0109737	+	0.451335i
$351$	−0.241782	−	3.12115i	−0.0129054	−	0.166595i
$352$	9.92369	+	17.1883i	0.528934	+	0.916141i
$353$	3.86470	−	21.9178i	0.205697	−	1.16657i	−0.690642	−	0.723197i	$-0.742672\pi$
$353$	3.86470	−	21.9178i	0.205697	−	1.16657i	0.896339	−	0.443370i	$-0.146217\pi$
$354$	−1.45271	−	0.582712i	−0.0772104	−	0.0309708i
$355$	0.457444	−	1.25682i	0.0242786	−	0.0667049i
$356$	−1.21230	−	6.87529i	−0.0642517	−	0.364389i
$357$	0.295000	−	36.4275i	0.0156131	−	1.92795i
$358$	16.9809	+	14.2486i	0.897466	+	0.753063i
$359$			26.2189i			1.38378i	0.722002	+	0.691891i	$0.243222\pi$
$359$			26.2189i			1.38378i	−0.722002	+	0.691891i	$0.756778\pi$
$360$	−0.680420	+	10.4833i	−0.0358613	+	0.552517i
$361$	16.9984			0.894654
$362$	13.6338	−	4.96229i	0.716576	−	0.260812i
$363$	−2.16500	+	2.41659i	−0.113633	+	0.126838i
$364$	−1.24222	−	1.40938i	−0.0651099	−	0.0738714i
$365$	0.387945	−	1.06587i	0.0203060	−	0.0557902i
$366$	−18.8261	−	3.95247i	−0.984058	−	0.206599i
$367$	−11.4902	+	13.6935i	−0.599785	+	0.714796i	−0.977455	−	0.211144i	$-0.932281\pi$
$367$	−11.4902	+	13.6935i	−0.599785	+	0.714796i	0.377670	+	0.925940i	$0.376725\pi$
$368$			0.258839i			0.0134929i
$369$	−11.9399	+	17.8939i	−0.621567	+	0.931521i
$370$	8.06231	+	4.65478i	0.419140	+	0.241990i
$371$	−6.39932	−	16.3352i	−0.332236	−	0.848080i
$372$	8.93922	−	14.3856i	0.463477	−	0.745860i
$373$	8.20499	−	6.88480i	0.424838	−	0.356482i	−0.405162	−	0.914245i	$-0.632785\pi$
$373$	8.20499	−	6.88480i	0.424838	−	0.356482i	0.830000	+	0.557763i	$0.188340\pi$
$374$	4.48871	+	25.4567i	0.232105	+	1.31634i
$375$	−6.68005	+	16.6534i	−0.344956	+	0.859979i
$376$	0.584458	−	0.696529i	0.0301411	−	0.0359208i
$377$	−0.728069			−0.0374974
$378$	10.1027	−	7.29229i	0.519626	−	0.375075i
$379$	13.1823			0.677127			0.338564	−	0.940944i	$-0.390059\pi$
$379$	13.1823			0.677127			0.338564	+	0.940944i	$0.390059\pi$
$380$	−1.30288	+	1.55271i	−0.0668363	+	0.0796524i
$381$	25.1964	−	3.60536i	1.29085	−	0.184708i
$382$	1.01149	+	5.73645i	0.0517524	+	0.293502i
$383$	12.1923	−	10.2305i	0.622997	−	0.522757i	−0.275747	−	0.961230i	$-0.588925\pi$
$383$	12.1923	−	10.2305i	0.622997	−	0.522757i	0.898744	+	0.438474i	$0.144481\pi$
$384$	−4.95085	−	9.25531i	−0.252647	−	0.472308i
$385$	−7.20012	+	9.01711i	−0.366952	+	0.459555i
$386$	1.07556	+	0.620974i	0.0547445	+	0.0316067i
$387$	22.3721	+	9.82701i	1.13724	+	0.499535i
$388$		−	9.92496i		−	0.503864i
$389$	−16.0481	+	19.1254i	−0.813671	+	0.969696i	−0.999918	−	0.0128074i	$-0.995923\pi$
$389$	−16.0481	+	19.1254i	−0.813671	+	0.969696i	0.186247	+	0.982503i	$0.440368\pi$
$390$	0.357975	+	1.09244i	0.0181268	+	0.0553176i
$391$	2.77467	−	7.62333i	0.140321	−	0.385529i
$392$	5.96794	−	19.2622i	0.301426	−	0.972887i
$393$	9.56591	+	29.1924i	0.482537	+	1.47256i
$394$	−18.9279	+	6.88918i	−0.953572	+	0.347072i
$395$	16.3517			0.822743
$396$	8.76697	−	9.16976i	0.440557	−	0.460798i
$397$			21.5681i			1.08247i	0.840871	+	0.541235i	$0.182043\pi$
$397$			21.5681i			1.08247i	−0.840871	+	0.541235i	$0.817957\pi$
$398$	9.23763	+	7.75129i	0.463041	+	0.388537i
$399$	6.48309	+	0.0525019i	0.324560	+	0.00262838i
$400$	0.155136	+	0.879821i	0.00775681	+	0.0439911i
$401$	−3.23776	+	8.89569i	−0.161686	+	0.444229i	−0.993908	−	0.110214i	$-0.964846\pi$
$401$	−3.23776	+	8.89569i	−0.161686	+	0.444229i	0.832222	+	0.554443i	$0.187069\pi$
$402$	−12.7456	+	10.0094i	−0.635693	+	0.499222i
$403$	0.867963	−	4.92246i	0.0432363	−	0.245205i
$404$	1.46117	+	2.53083i	0.0726961	+	0.125913i
$405$	10.6777	−	2.38144i	0.530581	−	0.118335i
$406$	−1.50945	−	2.47357i	−0.0749128	−	0.122761i
$407$	−10.3699	−	28.4910i	−0.514016	−	1.41225i
$408$	−5.61843	−	39.2649i	−0.278154	−	1.94390i
$409$	−12.8196	+	2.26043i	−0.633886	+	0.111771i	−0.481353	−	0.876527i	$-0.659854\pi$
$409$	−12.8196	+	2.26043i	−0.633886	+	0.111771i	−0.152534	+	0.988298i	$0.548743\pi$
$410$	2.70182	−	7.42319i	0.133433	−	0.366605i
$411$	−2.73068	−	5.10485i	−0.134695	−	0.251804i
$412$	−7.23878	+	8.62684i	−0.356629	+	0.425014i
$413$	1.37419	+	2.25192i	0.0676194	+	0.110810i
$414$	2.66338	−	0.778141i	0.130898	−	0.0382435i
$415$	3.66159	−	6.34205i	0.179740	−	0.311319i
$416$	−2.55297	−	2.14219i	−0.125170	−	0.105030i
$417$	1.41813	−	6.75474i	0.0694461	−	0.330781i
$418$	−4.53059	+	0.798866i	−0.221599	+	0.0390738i
$419$	11.0177	+	4.01012i	0.538251	+	0.195907i	0.596819	−	0.802376i	$-0.296431\pi$
$419$	11.0177	+	4.01012i	0.538251	+	0.195907i	−0.0585680	+	0.998283i	$0.518653\pi$
$420$	4.26073	−	4.99503i	0.207902	−	0.243733i
$421$	−2.93922	+	16.6692i	−0.143249	+	0.812405i	0.825508	+	0.564391i	$0.190889\pi$
$421$	−2.93922	+	16.6692i	−0.143249	+	0.812405i	−0.968756	+	0.248014i	$0.920222\pi$
$422$	11.9244	+	6.88457i	0.580472	+	0.335136i
$423$	−0.866934	−	0.380802i	−0.0421518	−	0.0185153i
$424$	−9.55121	−	16.5432i	−0.463848	−	0.803408i
$425$	4.86232	−	27.5756i	0.235857	−	1.33761i
$426$	−1.52299	+	0.814679i	−0.0737893	+	0.0394713i
$427$	21.4382	+	24.3230i	1.03747	+	1.17707i
$428$	9.31041	+	11.0957i	0.450036	+	0.536332i
$429$	1.39385	−	3.47488i	0.0672957	−	0.167769i
$430$	−8.83687	−	1.55818i	−0.426152	−	0.0751420i
$431$	1.64280	+	0.948469i	0.0791307	+	0.0456861i	0.539043	−	0.842278i	$-0.318786\pi$
$431$	1.64280	+	0.948469i	0.0791307	+	0.0456861i	−0.459913	+	0.887964i	$0.652119\pi$
$432$	0.941133	−	0.922579i	0.0452803	−	0.0443876i
$433$		−	8.59518i		−	0.413058i	−0.978440	−	0.206529i	$-0.933783\pi$
$433$		−	8.59518i		−	0.413058i	0.978440	−	0.206529i	$-0.0662168\pi$
$434$	18.5233	−	7.25652i	0.889146	−	0.348324i
$435$	−0.360403	−	2.51871i	−0.0172800	−	0.120763i
$436$	−10.3467	−	3.76588i	−0.495516	−	0.180353i
$437$	1.35674	+	0.493814i	0.0649018	+	0.0236223i
$438$	−1.29161	+	0.690906i	−0.0617154	+	0.0330128i
$439$	17.1328	+	3.02098i	0.817706	+	0.144184i	0.566829	−	0.823835i	$-0.308170\pi$
$439$	17.1328	+	3.02098i	0.817706	+	0.144184i	0.250877	+	0.968019i	$0.419281\pi$
$440$	−6.28207	+	10.8809i	−0.299486	+	0.518725i
$441$	−20.9972	−	0.340105i	−0.999869	−	0.0161955i
$442$	−2.17025	−	3.75898i	−0.103228	−	0.178796i
$443$	−10.4701	−	28.7664i	−0.497451	−	1.36673i	−0.893730	−	0.448604i	$-0.851921\pi$
$443$	−10.4701	−	28.7664i	−0.497451	−	1.36673i	0.396280	−	0.918130i	$-0.370301\pi$
$444$	5.37180	+	16.3932i	0.254935	+	0.777986i
$445$	5.51567	−	4.62820i	0.261468	−	0.219398i
$446$	−1.11069	−	6.29903i	−0.0525926	−	0.298268i
$447$	18.1575	+	16.2671i	0.858823	+	0.769409i
$448$	2.18597	−	14.4418i	0.103277	−	0.682311i
$449$	23.7529	−	13.7137i	1.12097	−	0.647191i	0.179320	−	0.983791i	$-0.442610\pi$
$449$	23.7529	−	13.7137i	1.12097	−	0.647191i	0.941648	+	0.336600i	$0.109277\pi$
$450$	8.58674	−	4.24130i	0.404783	−	0.199937i
$451$	−22.2807	+	12.8638i	−1.04916	+	0.605731i
$452$	1.59979	+	4.39540i	0.0752480	+	0.206742i
$453$	0.740899	−	22.8542i	0.0348105	−	1.07378i
$454$	15.3156	−	2.70056i	0.718798	−	0.126743i
$455$	0.618239	−	1.83630i	0.0289835	−	0.0860869i
$456$	6.98807	−	0.999926i	0.327246	−	0.0468258i
$457$	17.5654	+	14.7391i	0.821675	+	0.689467i	0.953364	−	0.301824i	$-0.0975955\pi$
$457$	17.5654	+	14.7391i	0.821675	+	0.689467i	−0.131689	+	0.991291i	$0.542040\pi$
$458$	−4.04785	+	7.01109i	−0.189144	+	0.327607i
$459$	−37.6081	+	17.0832i	−1.75540	+	0.797377i
$460$	1.26621	−	0.731047i	0.0590374	−	0.0340852i
$461$	−28.3324	+	10.3121i	−1.31957	+	0.480284i	−0.903321	−	0.428966i	$-0.858878\pi$
$461$	−28.3324	+	10.3121i	−1.31957	+	0.480284i	−0.416250	+	0.909250i	$0.636656\pi$
$462$	14.6955	−	2.46868i	0.683695	−	0.114853i
$463$	−22.9581	+	19.2641i	−1.06695	+	0.895279i	−0.994773	−	0.102113i	$-0.967440\pi$
$463$	−22.9581	+	19.2641i	−1.06695	+	0.895279i	−0.0721787	+	0.997392i	$0.522995\pi$
$464$	−0.197020	−	0.234800i	−0.00914645	−	0.0109003i
$465$	17.4586	+	0.565982i	0.809623	+	0.0262468i
$466$	−7.27826	+	2.64907i	−0.337159	+	0.122716i
$467$	−2.35105			−0.108793			−0.0543967	−	0.998519i	$-0.517324\pi$
$467$	−2.35105			−0.108793			−0.0543967	+	0.998519i	$0.517324\pi$
$468$	−0.856702	+	1.95037i	−0.0396011	+	0.0901557i
$469$	27.3065	−	0.663926i	1.26090	−	0.0306572i
$470$	0.342434	+	0.0603803i	0.0157953	+	0.00278514i
$471$	8.22594	−	2.69552i	0.379031	−	0.124203i
$472$	1.84637	+	2.20042i	0.0849863	+	0.101283i
$473$	18.7848	+	22.3869i	0.863728	+	1.02935i
$474$	−15.7278	−	14.0903i	−0.722400	−	0.647190i
$475$	4.90769	+	0.865359i	0.225180	+	0.0397054i
$476$	−11.8689	+	21.7626i	−0.544011	+	0.997489i
$477$	−13.7471	+	14.3787i	−0.629436	+	0.658354i
$478$	−12.0522			−0.551254
$479$	17.6002	−	6.40596i	0.804175	−	0.292696i	0.0929597	−	0.995670i	$-0.470367\pi$
$479$	17.6002	−	6.40596i	0.804175	−	0.292696i	0.711216	+	0.702974i	$0.248145\pi$
$480$	6.14703	−	9.89223i	0.280572	−	0.451517i
$481$	3.27249	+	3.90000i	0.149213	+	0.177825i
$482$	−9.70215	+	8.14107i	−0.441921	+	0.370816i
$483$	−4.38152	−	1.63504i	−0.199366	−	0.0743971i
$484$	2.07469	−	0.755125i	0.0943040	−	0.0343239i
$485$	8.86472	−	5.11805i	0.402526	−	0.232398i
$486$	−12.3224	−	6.91048i	−0.558955	−	0.313466i
$487$	0.370050	−	0.640946i	0.0167686	−	0.0290440i	−0.857519	−	0.514452i	$-0.827995\pi$
$487$	0.370050	−	0.640946i	0.0167686	−	0.0290440i	0.874288	+	0.485408i	$0.161329\pi$
$488$	27.0433	+	22.6920i	1.22419	+	1.02722i
$489$	−1.38281	+	3.44737i	−0.0625330	+	0.155895i
$490$	7.52047	−	1.70662i	0.339740	−	0.0770973i
$491$	13.6257	−	2.40259i	0.614921	−	0.108427i	0.142492	−	0.989796i	$-0.454488\pi$
$491$	13.6257	−	2.40259i	0.614921	−	0.108427i	0.472429	+	0.881369i	$0.343377\pi$
$492$	12.9075	−	6.90449i	0.581916	−	0.311279i
$493$	3.28568	+	9.02734i	0.147980	+	0.406571i
$494$	0.668994	−	0.386244i	0.0300995	−	0.0173779i
$495$	12.7111	+	3.10182i	0.571321	+	0.139417i
$496$	1.82236	−	1.05214i	0.0818262	−	0.0472424i
$497$	2.87832	+	0.435674i	0.129110	+	0.0195426i
$498$	−8.98685	+	2.94486i	−0.402710	+	0.131962i
$499$	0.415762	+	2.35790i	0.0186121	+	0.105554i	0.992699	−	0.120622i	$-0.0384887\pi$
$499$	0.415762	+	2.35790i	0.0186121	+	0.105554i	−0.974087	+	0.226176i	$0.927378\pi$
$500$	9.35333	−	7.84837i	0.418294	−	0.350990i
$501$	16.0034	−	17.8632i	0.714980	−	0.798068i
$502$	−7.93919	−	21.8127i	−0.354343	−	0.973550i
$503$	0.926534	+	1.60480i	0.0413121	+	0.0715547i	0.885942	−	0.463796i	$-0.153513\pi$
$503$	0.926534	+	1.60480i	0.0413121	+	0.0715547i	−0.844630	+	0.535350i	$0.820180\pi$
$504$	−22.6605	+	3.05545i	−1.00938	+	0.136100i
$505$	−1.50698	+	2.61016i	−0.0670596	+	0.116151i
$506$	3.26809	+	0.576252i	0.145284	+	0.0256175i
$507$	0.709204	−	21.8765i	0.0314968	−	0.971569i
$508$	−16.2756	−	5.92383i	−0.722112	−	0.262827i
$509$	−4.99958	−	1.81970i	−0.221602	−	0.0806567i	0.228833	−	0.973466i	$-0.426509\pi$
$509$	−4.99958	−	1.81970i	−0.221602	−	0.0806567i	−0.450435	+	0.892809i	$0.648731\pi$
$510$	11.9296	−	9.36856i	0.528253	−	0.414847i
$511$	2.44102	+	0.369483i	0.107984	+	0.0163449i
$512$		−	2.86433i		−	0.126587i
$513$	−3.04035	−	6.69320i	−0.134235	−	0.295512i
$514$	−9.37492	−	5.41261i	−0.413510	−	0.238740i
$515$	−11.4381	−	2.01685i	−0.504024	−	0.0888730i
$516$	−10.2697	−	13.0771i	−0.452097	−	0.575687i
$517$	−0.727924	−	0.867506i	−0.0320140	−	0.0381529i
$518$	−6.46543	+	19.2037i	−0.284075	+	0.843761i
$519$	5.32313	+	3.30779i	0.233659	+	0.145196i
$520$	0.366346	−	2.07765i	0.0160653	−	0.0911110i
$521$	12.2120	+	21.1518i	0.535018	+	0.926679i	0.999162	+	0.0409190i	$0.0130286\pi$
$521$	12.2120	+	21.1518i	0.535018	+	0.926679i	−0.464144	+	0.885760i	$0.653638\pi$
$522$	−1.82373	+	2.73316i	−0.0798224	+	0.119627i
$523$	−26.6209	−	15.3696i	−1.16405	−	0.672065i	−0.211780	−	0.977317i	$-0.567926\pi$
$523$	−26.6209	−	15.3696i	−1.16405	−	0.672065i	−0.952272	+	0.305252i	$0.901259\pi$
$524$	3.62994	−	20.5864i	0.158575	−	0.899322i
$525$	−15.8732	−	2.93161i	−0.692765	−	0.127946i
$526$	−12.1151	−	4.40952i	−0.528242	−	0.192264i
$527$	−64.9508	+	11.4526i	−2.82930	+	0.498882i
$528$	1.49782	−	0.490814i	0.0651844	−	0.0213600i
$529$	16.8212	+	14.1147i	0.731357	+	0.613681i
$530$	3.65257	−	6.32643i	0.158657	−	0.274803i
$531$	1.66031	−	2.48824i	0.0720511	−	0.107981i
$532$	−3.87315	−	2.11234i	−0.167922	−	0.0915816i
$533$	2.77686	−	3.30933i	0.120279	−	0.143343i
$534$	−9.29336	−	0.301277i	−0.402163	−	0.0130375i
$535$	−5.10926	+	14.0376i	−0.220893	+	0.606898i
$536$	29.2892	−	5.16448i	1.26510	−	0.223071i
$537$	−33.3177	+	26.1650i	−1.43776	+	1.12910i
$538$	9.42992	+	25.9085i	0.406553	+	1.11699i
$539$	−22.3353	−	11.4859i	−0.962048	−	0.494731i
$540$	−7.17124	−	1.99825i	−0.308601	−	0.0859910i
$541$	14.3316	+	24.8231i	0.616166	+	1.06723i	0.990179	+	0.139807i	$0.0446481\pi$
$541$	14.3316	+	24.8231i	0.616166	+	1.06723i	−0.374013	+	0.927423i	$0.622019\pi$
$542$	2.05074	−	11.6303i	0.0880868	−	0.499565i
$543$	3.92761	+	27.4484i	0.168550	+	1.17792i
$544$	−15.0399	+	41.3218i	−0.644830	+	1.77166i
$545$	−1.97193	−	11.1833i	−0.0844680	−	0.479042i
$546$	−2.17699	+	1.23349i	−0.0931667	+	0.0527885i
$547$	−28.4534	−	23.8752i	−1.21658	−	1.02083i	−0.998996	−	0.0447884i	$-0.985739\pi$
$547$	−28.4534	−	23.8752i	−1.21658	−	1.02083i	−0.217582	−	0.976042i	$-0.569817\pi$
$548$			3.93948i			0.168286i
$549$	14.7849	−	33.6593i	0.631006	−	1.43655i
$550$	11.4540			0.488399
$551$	−1.60662	+	0.584761i	−0.0684442	+	0.0249117i
$552$	−4.98346	−	1.04625i	−0.212110	−	0.0445316i
$553$	7.03034	+	34.8892i	0.298960	+	1.48364i
$554$	5.55975	−	15.2753i	0.236211	−	0.648985i
$555$	−11.8719	+	13.2515i	−0.503932	+	0.562495i
$556$	−3.01894	+	3.59783i	−0.128032	+	0.152582i
$557$		−	24.0793i		−	1.02027i	−0.860094	−	0.510136i	$-0.829595\pi$
$557$		−	24.0793i		−	1.02027i	0.860094	−	0.510136i	$-0.170405\pi$
$558$	−16.3047	−	15.5885i	−0.690234	−	0.659915i
$559$	−4.24971	−	2.45357i	−0.179743	−	0.103775i
$560$	0.759499	−	0.297535i	0.0320947	−	0.0125731i
$561$	−49.3754	−	1.60068i	−2.08463	−	0.0675806i
$562$	6.67339	−	5.59964i	0.281500	−	0.236206i
$563$	1.01488	+	5.75568i	0.0427721	+	0.242573i	0.998697	−	0.0510398i	$-0.0162535\pi$
$563$	1.01488	+	5.75568i	0.0427721	+	0.242573i	−0.955924	+	0.293613i	$0.905142\pi$
$564$	0.397956	+	0.506745i	0.0167570	+	0.0213378i
$565$	−3.10088	+	3.69549i	−0.130455	+	0.155470i
$566$	12.0902			0.508187
$567$	9.67207	+	21.7589i	0.406189	+	0.913789i
$568$	3.16971			0.132998
$569$	9.33442	−	11.1243i	0.391319	−	0.466356i	−0.534033	−	0.845463i	$-0.679324\pi$
$569$	9.33442	−	11.1243i	0.391319	−	0.466356i	0.925353	+	0.379107i	$0.123769\pi$
$570$	1.66735	+	2.12315i	0.0698374	+	0.0889288i
$571$	−6.94818	−	39.4051i	−0.290772	−	1.64905i	−0.683906	−	0.729571i	$-0.739720\pi$
$571$	−6.94818	−	39.4051i	−0.290772	−	1.64905i	0.393133	−	0.919482i	$-0.371391\pi$
$572$	−1.95165	+	1.63763i	−0.0816027	+	0.0684728i
$573$	−11.1263	−	0.360699i	−0.464808	−	0.0150684i
$574$	17.0003	+	2.57324i	0.709580	+	0.107405i
$575$	−3.11312	−	1.79736i	−0.129826	−	0.0749550i
$576$	−15.8974	+	4.64463i	−0.662391	+	0.193526i
$577$			12.0256i			0.500634i	0.968164	+	0.250317i	$0.0805348\pi$
$577$			12.0256i			0.500634i	−0.968164	+	0.250317i	$0.919465\pi$
$578$	−26.9101	+	32.0702i	−1.11931	+	1.33394i
$579$	−1.58377	+	1.76782i	−0.0658194	+	0.0734683i
$580$	−0.592164	+	1.62696i	−0.0245883	+	0.0675557i
$581$	15.1062	+	5.08590i	0.626710	+	0.210999i
$582$	−12.9367	−	2.71601i	−0.536244	−	0.112582i
$583$	−22.3567	+	8.13717i	−0.925919	+	0.337007i
$584$	2.68814			0.111236
$585$	−2.18379	+	0.240569i	−0.0902888	+	0.00994630i
$586$			1.48165i			0.0612063i
$587$	13.0785	+	10.9742i	0.539807	+	0.452952i	0.871472	−	0.490445i	$-0.163166\pi$
$587$	13.0785	+	10.9742i	0.539807	+	0.452952i	−0.331665	+	0.943397i	$0.607610\pi$
$588$	12.4897	+	6.94343i	0.515065	+	0.286342i
$589$	−2.03824	−	11.5594i	−0.0839843	−	0.476299i
$590$	−0.375702	+	1.03223i	−0.0154674	+	0.0424963i
$591$	−5.45272	−	38.1068i	−0.224295	−	1.56750i
$592$	−0.372179	+	2.11073i	−0.0152965	+	0.0867506i
$593$	8.82192	+	15.2800i	0.362273	+	0.627475i	0.988335	−	0.152299i	$-0.0486675\pi$
$593$	8.82192	+	15.2800i	0.362273	+	0.627475i	−0.626062	+	0.779774i	$0.715334\pi$
$594$	−9.55322	−	13.9367i	−0.391973	−	0.571828i
$595$	−25.5583	+	0.621421i	−1.04779	+	0.0254758i
$596$	−5.67378	−	15.5886i	−0.232407	−	0.638533i
$597$	−18.1249	+	14.2338i	−0.741804	+	0.582552i
$598$	−0.548759	+	0.0967611i	−0.0224404	+	0.00395685i
$599$	5.13784	−	14.1161i	0.209927	−	0.576768i	−0.789384	−	0.613900i	$-0.789600\pi$
$599$	5.13784	−	14.1161i	0.209927	−	0.576768i	0.999310	+	0.0371316i	$0.0118221\pi$
$600$	−17.5664	−	0.569477i	−0.717146	−	0.0232488i
$601$	4.19281	−	4.99680i	0.171028	−	0.203824i	−0.673721	−	0.738986i	$-0.735305\pi$
$601$	4.19281	−	4.99680i	0.171028	−	0.203824i	0.844749	+	0.535162i	$0.179749\pi$
$602$	−0.474727	−	19.5249i	−0.0193484	−	0.795777i
$603$	−13.7161	−	27.7690i	−0.558564	−	1.13084i
$604$	−7.77993	+	13.4752i	−0.316561	+	0.548299i
$605$	1.74432	+	1.46366i	0.0709167	+	0.0595062i
$606$	3.69866	−	1.21200i	0.150248	−	0.0492340i
$607$	31.9011	−	5.62502i	1.29482	−	0.228312i	0.516561	−	0.856251i	$-0.327212\pi$
$607$	31.9011	−	5.62502i	1.29482	−	0.228312i	0.778263	+	0.627938i	$0.216101\pi$
$608$	−7.35413	−	2.67669i	−0.298250	−	0.108554i
$609$	5.21915	−	1.85189i	0.211491	−	0.0750424i
$610$	−2.34431	+	13.2952i	−0.0949183	+	0.538308i
$611$	0.164679	+	0.0950772i	0.00666218	+	0.00384641i
$612$	28.0488	+	1.82052i	1.13381	+	0.0735900i
$613$	−1.92702	−	3.33770i	−0.0778317	−	0.134809i	0.824482	−	0.565888i	$-0.191466\pi$
$613$	−1.92702	−	3.33770i	−0.0778317	−	0.134809i	−0.902314	+	0.431079i	$0.858133\pi$
$614$	1.81722	−	10.3060i	0.0733372	−	0.415916i
$615$	12.8230	+	7.96820i	0.517073	+	0.321309i
$616$	−25.9172	−	8.72572i	−1.04423	−	0.351569i
$617$	−20.8477	−	24.8453i	−0.839295	−	1.00023i	−0.999913	−	0.0132165i	$-0.995793\pi$
$617$	−20.8477	−	24.8453i	−0.839295	−	1.00023i	0.160617	−	0.987017i	$-0.448652\pi$
$618$	9.26375	+	11.7962i	0.372643	+	0.474512i
$619$	−18.5003	−	3.26210i	−0.743589	−	0.131115i	−0.210997	−	0.977487i	$-0.567671\pi$
$619$	−18.5003	−	3.26210i	−0.743589	−	0.131115i	−0.532592	+	0.846372i	$0.678782\pi$
$620$	−10.2939	−	5.94318i	−0.413413	−	0.238684i
$621$	0.409560	+	5.28698i	0.0164351	+	0.212159i
$622$		−	21.8053i		−	0.874313i
$623$	12.2465	+	9.77879i	0.490647	+	0.391779i
$624$	−0.208151	+	0.163465i	−0.00833271	+	0.00654383i
$625$	−4.71666	−	1.71672i	−0.188666	−	0.0686689i
$626$	27.6876	+	10.0775i	1.10662	+	0.402777i
$627$	0.284876	−	8.78746i	0.0113769	−	0.350937i
$628$	−5.80092	−	1.02286i	−0.231482	−	0.0408165i
$629$	33.5878	−	58.1758i	1.33923	−	2.31962i
$630$	−5.34482	−	6.92057i	−0.212943	−	0.275722i
$631$	3.17557	+	5.50025i	0.126417	+	0.218961i	0.922286	−	0.386508i	$-0.126319\pi$
$631$	3.17557	+	5.50025i	0.126417	+	0.218961i	−0.795869	+	0.605469i	$0.792985\pi$
$632$	13.2540	+	36.4151i	0.527217	+	1.44852i
$633$	−17.5589	+	19.5994i	−0.697903	+	0.779007i
$634$	3.50615	−	2.94201i	0.139247	−	0.116842i
$635$	−3.10189	−	17.5917i	−0.123095	−	0.698105i
$636$	12.8636	−	4.21521i	0.510075	−	0.167144i
$637$	4.18387	+	0.529613i	0.165771	+	0.0209840i
$638$	−3.40320	+	1.96484i	−0.134734	+	0.0777888i
$639$	−0.925695	−	3.16842i	−0.0366199	−	0.125341i
$640$	−6.37944	+	3.68317i	−0.252170	+	0.145590i
$641$	−10.3834	−	28.5283i	−0.410122	−	1.12680i	−0.957126	−	0.289670i	$-0.906454\pi$
$641$	−10.3834	−	28.5283i	−0.410122	−	1.12680i	0.547005	−	0.837129i	$-0.315768\pi$
$642$	17.0106	−	9.09928i	0.671353	−	0.359120i
$643$	−3.55310	+	0.626507i	−0.140121	+	0.0247070i	−0.243268	−	0.969959i	$-0.578220\pi$
$643$	−3.55310	+	0.626507i	−0.140121	+	0.0247070i	0.103148	+	0.994666i	$0.467108\pi$
$644$	2.10422	+	2.38737i	0.0829179	+	0.0940757i
$645$	6.38430	−	15.9161i	0.251382	−	0.626697i
$646$	−7.80814	−	6.55181i	−0.307207	−	0.257777i
$647$	−4.12557	+	7.14569i	−0.162193	+	0.280926i	−0.935655	−	0.352917i	$-0.885190\pi$
$647$	−4.12557	+	7.14569i	−0.162193	+	0.280926i	0.773462	+	0.633843i	$0.218523\pi$
$648$	13.9584	+	21.8490i	0.548337	+	0.858308i
$649$	3.09824	−	1.78877i	0.121617	−	0.0702155i
$650$	−1.80730	+	0.657804i	−0.0708882	+	0.0258012i
$651$	6.29863	+	37.4943i	0.246863	+	1.46952i
$652$	1.93620	−	1.62466i	0.0758274	−	0.0636268i
$653$	25.5407	+	30.4382i	0.999483	+	1.19114i	0.981532	+	0.191299i	$0.0612700\pi$
$653$	25.5407	+	30.4382i	0.999483	+	1.19114i	0.0179514	+	0.999839i	$0.494286\pi$
$654$	−7.74006	+	12.4558i	−0.302660	+	0.487062i
$655$	20.2591	−	7.37371i	0.791589	−	0.288115i
$656$	1.81869			0.0710078
$657$	−0.785056	−	2.68705i	−0.0306279	−	0.104832i
$658$	0.0183959	+	0.756603i	0.000717148	+	0.0294955i
$659$	28.1991	+	4.97227i	1.09848	+	0.193692i	0.693375	−	0.720577i	$-0.256123\pi$
$659$	28.1991	+	4.97227i	1.09848	+	0.193692i	0.405107	+	0.914269i	$0.367234\pi$
$660$	−6.63137	−	5.94097i	−0.258126	−	0.231252i
$661$	−0.182595	−	0.217608i	−0.00710211	−	0.00846396i	0.762482	−	0.647010i	$-0.223981\pi$
$661$	−0.182595	−	0.217608i	−0.00710211	−	0.00846396i	−0.769584	+	0.638546i	$0.779536\pi$
$662$	7.13352	+	8.50139i	0.277252	+	0.330416i
$663$	7.88277	−	2.58307i	0.306141	−	0.100318i
$664$	17.0917	+	3.01372i	0.663285	+	0.116955i
$665$	−0.110596	−	4.54868i	−0.00428872	−	0.176390i
$666$	22.8377	−	2.51583i	0.884944	−	0.0974863i
$667$	1.23329			0.0477532
$668$	−15.3359	+	5.58180i	−0.593362	+	0.215966i
$669$	12.2175	+	0.396072i	0.472355	+	0.0153130i
$670$	7.31077	+	8.71264i	0.282440	+	0.336599i
$671$	33.6815	−	28.2622i	1.30026	−	1.09105i
$672$	23.7497	+	8.86264i	0.916165	+	0.341884i
$673$	−4.12151	+	1.50011i	−0.158873	+	0.0578249i	−0.420232	−	0.907417i	$-0.638051\pi$
$673$	−4.12151	+	1.50011i	−0.158873	+	0.0578249i	0.261360	+	0.965241i	$0.415829\pi$
$674$	−14.1390	+	8.16315i	−0.544614	+	0.314433i
$675$	4.56092	+	17.7256i	0.175550	+	0.682258i
$676$	−7.44711	+	12.8988i	−0.286427	+	0.496106i
$677$	38.8843	+	32.6278i	1.49445	+	1.25399i	0.888835	+	0.458227i	$0.151515\pi$
$677$	38.8843	+	32.6278i	1.49445	+	1.25399i	0.605610	+	0.795762i	$0.292929\pi$
$678$	6.16698	−	0.882437i	0.236841	−	0.0338898i
$679$	14.7316	+	16.7140i	0.565347	+	0.641423i
$680$	−27.4141	+	4.83385i	−1.05128	+	0.185370i
$681$	−0.963021	+	29.7059i	−0.0369031	+	1.13833i
$682$	−9.22715	−	25.3514i	−0.353326	−	0.970755i
$683$	−35.1328	+	20.2839i	−1.34432	+	0.776143i	−0.987438	−	0.158007i	$-0.949493\pi$
$683$	−35.1328	+	20.2839i	−1.34432	+	0.776143i	−0.356880	+	0.934150i	$0.616160\pi$
$684$	−0.324002	+	4.99192i	−0.0123885	+	0.190871i
$685$	−3.51864	+	2.03149i	−0.134440	+	0.0776191i
$686$	6.87477	+	15.3125i	0.262480	+	0.584633i
$687$	−11.5237	−	10.3239i	−0.439655	−	0.393882i
$688$	−0.358732	−	2.03447i	−0.0136765	−	0.0775634i
$689$	3.06030	−	2.56789i	0.116588	−	0.0978290i
$690$	−0.606381	−	1.85050i	−0.0230845	−	0.0704473i
$691$	−1.10466	−	3.03503i	−0.0420233	−	0.115458i	0.916906	−	0.399103i	$-0.130678\pi$
$691$	−1.10466	−	3.03503i	−0.0420233	−	0.115458i	−0.958929	+	0.283645i	$0.908456\pi$
$692$	−2.13232	−	3.69328i	−0.0810585	−	0.140397i
$693$	−1.15321	+	28.4550i	−0.0438067	+	1.08091i
$694$	5.18443	−	8.97970i	0.196798	−	0.340865i
$695$	−4.77028	−	0.841129i	−0.180947	−	0.0319058i
$696$	5.31702	−	2.84418i	0.201541	−	0.107808i
$697$	−53.5641	−	19.4957i	−2.02888	−	0.738454i
$698$	−7.43864	−	2.70744i	−0.281557	−	0.102478i
$699$	−2.09671	−	14.6531i	−0.0793050	−	0.554230i
$700$	8.58336	+	6.85377i	0.324421	+	0.259048i
$701$		−	6.55534i		−	0.247592i	−0.992308	−	0.123796i	$-0.960493\pi$
$701$		−	6.55534i		−	0.247592i	0.992308	−	0.123796i	$-0.0395068\pi$
$702$	2.30777	+	1.65040i	0.0871011	+	0.0622902i
$703$	10.3537	+	5.97771i	0.390497	+	0.225454i
$704$	−19.5068	−	3.43958i	−0.735191	−	0.129634i
$705$	−0.247395	+	0.616759i	−0.00931745	+	0.0232285i
$706$	12.9654	+	15.4516i	0.487959	+	0.581527i
$707$	−6.21716	−	2.09317i	−0.233820	−	0.0787219i
$708$	−1.79486	+	0.960105i	−0.0674549	+	0.0360830i
$709$	−1.70465	+	9.66753i	−0.0640194	+	0.363072i	0.935922	+	0.352208i	$0.114569\pi$
$709$	−1.70465	+	9.66753i	−0.0640194	+	0.363072i	−0.999941	+	0.0108635i	$0.996542\pi$
$710$	0.606079	+	1.04976i	0.0227457	+	0.0393968i
$711$	32.5296	−	23.8835i	1.21995	−	0.895700i
$712$	14.7778	+	8.53195i	0.553820	+	0.319748i
$713$	−1.47026	+	8.33826i	−0.0550617	+	0.312270i
$714$	25.1186	+	21.4260i	0.940039	+	0.801848i
$715$	−2.46911	−	0.898681i	−0.0923393	−	0.0336088i
$716$	28.3894	−	5.00582i	1.06096	−	0.187076i
$717$	4.73253	−	22.5417i	0.176740	−	0.841836i
$718$	−18.2030	−	15.2741i	−0.679329	−	0.570025i
$719$	−5.92304	+	10.2590i	−0.220892	+	0.382596i	−0.955079	−	0.296351i	$-0.904230\pi$
$719$	−5.92304	+	10.2590i	−0.220892	+	0.382596i	0.734187	+	0.678947i	$0.237563\pi$
$720$	−0.668533	−	0.639167i	−0.0249147	−	0.0238204i
$721$	−0.614469	−	25.2724i	−0.0228840	−	0.941192i
$722$	−9.90260	+	11.8015i	−0.368537	+	0.439205i
$723$	−11.4168	−	21.3431i	−0.424597	−	0.793758i
$724$	6.45330	−	17.7303i	0.239835	−	0.658941i
$725$	4.19209	−	0.739179i	0.155690	−	0.0274524i
$726$	−0.416522	−	2.91090i	−0.0154586	−	0.108034i
$727$	−15.4099	−	42.3383i	−0.571521	−	1.57024i	−0.802101	−	0.597188i	$-0.796284\pi$
$727$	−15.4099	−	42.3383i	−0.571521	−	1.57024i	0.230580	−	0.973053i	$-0.425938\pi$
$728$	4.59054	−	0.111614i	0.170137	−	0.00413668i
$729$	17.7636	−	20.3336i	0.657911	−	0.753095i
$730$	0.513998	+	0.890271i	0.0190239	+	0.0329504i
$731$	−11.2435	+	63.7649i	−0.415855	+	2.35843i
$732$	−19.6747	+	15.4509i	−0.727199	+	0.571083i
$733$	1.46593	−	4.02762i	0.0541454	−	0.148763i	−0.909671	−	0.415329i	$-0.863667\pi$
$733$	1.46593	−	4.02762i	0.0541454	−	0.148763i	0.963817	+	0.266565i	$0.0858888\pi$
$734$	−2.81322	−	15.9546i	−0.103838	−	0.588895i
$735$	0.238906	+	14.7360i	0.00881216	+	0.543545i
$736$	4.32452	+	3.62871i	0.159404	+	0.133756i
$737$		−	37.0415i		−	1.36444i
$738$	−5.46748	−	18.7138i	−0.201261	−	0.688864i
$739$	12.5282			0.460857			0.230429	−	0.973089i	$-0.425987\pi$
$739$	12.5282			0.460857			0.230429	+	0.973089i	$0.425987\pi$
$740$	11.3766	−	4.14076i	0.418214	−	0.152217i
$741$	0.459715	+	1.40292i	0.0168880	+	0.0515374i
$742$	15.0690	+	5.07337i	0.553199	+	0.186249i
$743$	−5.70379	+	15.6710i	−0.209252	+	0.574914i	−0.999271	−	0.0381673i	$-0.987848\pi$
$743$	−5.70379	+	15.6710i	−0.209252	+	0.574914i	0.790020	+	0.613081i	$0.210070\pi$
$744$	12.8908	+	39.3390i	0.472600	+	1.44224i
$745$	10.9975	−	13.1063i	0.402917	−	0.480177i
$746$			9.70727i			0.355408i
$747$	−1.97902	−	17.9648i	−0.0724087	−	0.657299i
$748$	29.1126	+	16.8082i	1.06446	+	0.614567i
$749$	−32.1484	−	4.86611i	−1.17468	−	0.177804i
$750$	−7.67040	−	14.3394i	−0.280084	−	0.523599i
$751$	38.5102	−	32.3139i	1.40526	−	1.17915i	0.446548	−	0.894760i	$-0.352653\pi$
$751$	38.5102	−	32.3139i	1.40526	−	1.17915i	0.958709	−	0.284390i	$-0.0917911\pi$
$752$	0.0139011	+	0.0788369i	0.000506920	+	0.00287489i
$753$	43.9148	−	6.28379i	1.60034	−	0.228994i
$754$	0.424144	−	0.505475i	0.0154464	−	0.0184083i
$755$	−16.0476			−0.584033
$756$	1.18038	−	16.1602i	0.0429298	−	0.587742i
$757$	8.96036			0.325670			0.162835	−	0.986653i	$-0.447936\pi$
$757$	8.96036			0.325670			0.162835	+	0.986653i	$0.447936\pi$
$758$	−7.67946	+	9.15202i	−0.278930	+	0.332416i
$759$	−2.36107	+	5.88617i	−0.0857014	+	0.213654i
$760$	−0.860292	−	4.87896i	−0.0312061	−	0.176978i
$761$	−21.8623	+	18.3447i	−0.792509	+	0.664994i	−0.946365	−	0.323099i	$-0.895275\pi$
$761$	−21.8623	+	18.3447i	−0.792509	+	0.664994i	0.153856	+	0.988093i	$0.450831\pi$
$762$	−12.1753	+	19.5934i	−0.441065	+	0.709792i
$763$	23.0138	−	9.01569i	0.833156	−	0.326390i
$764$	6.56027	+	3.78757i	0.237342	+	0.137030i
$765$	12.8380	+	25.9913i	0.464159	+	0.939716i
$766$			14.4246i			0.521183i
$767$	−0.386136	+	0.460179i	−0.0139426	+	0.0166161i
$768$	28.0259	+	5.88392i	1.01130	+	0.212318i
$769$	−0.460020	+	1.26389i	−0.0165887	+	0.0455772i	−0.947711	−	0.319131i	$-0.896609\pi$
$769$	−0.460020	+	1.26389i	−0.0165887	+	0.0455772i	0.931122	+	0.364708i	$0.118831\pi$
$770$	−2.06579	−	10.2518i	−0.0744459	−	0.369450i
$771$	13.8047	−	15.4089i	0.497164	−	0.554940i
$772$	1.51771	−	0.552401i	0.0546235	−	0.0198813i
$773$	16.7109			0.601048			0.300524	−	0.953774i	$-0.402838\pi$
$773$	16.7109			0.601048			0.300524	+	0.953774i	$0.402838\pi$
$774$	−19.8557	+	9.80743i	−0.713698	+	0.352521i
$775$			29.2239i			1.04975i
$776$	18.5832	+	15.5932i	0.667100	+	0.559763i
$777$	−33.3787	−	19.6333i	−1.19745	−	0.704340i
$778$	−3.92916	−	22.2834i	−0.140867	−	0.798897i
$779$	3.46970	−	9.53293i	0.124315	−	0.341553i
$780$	1.38754	+	0.556573i	0.0496819	+	0.0199285i
$781$	0.685524	−	3.88780i	0.0245300	−	0.139116i
$782$	3.67623	+	6.36741i	0.131462	+	0.227698i
$783$	−4.39582	−	4.48423i	−0.157094	−	0.160253i
$784$	0.961386	+	1.49260i	0.0343352	+	0.0533072i
$785$	−2.07779	−	5.70869i	−0.0741596	−	0.203752i
$786$	−25.8401	−	10.3650i	−0.921684	−	0.369708i
$787$	12.8919	−	2.27319i	0.459547	−	0.0810305i	0.0609179	−	0.998143i	$-0.480597\pi$
$787$	12.8919	−	2.27319i	0.459547	−	0.0810305i	0.398629	+	0.917112i	$0.369486\pi$
$788$	−8.95915	+	24.6151i	−0.319156	+	0.876875i
$789$	13.0045	−	20.9278i	0.462974	−	0.745051i
$790$	−9.52584	+	11.3524i	−0.338914	+	0.403902i
$791$	−9.21819	−	5.02742i	−0.327761	−	0.178754i
$792$	3.39535	+	30.8217i	0.120649	+	1.09520i
$793$	−3.69144	+	6.39377i	−0.131087	+	0.227049i
$794$	−14.9740	−	12.5647i	−0.531408	−	0.445904i
$795$	10.3983	+	9.31576i	0.368791	+	0.330396i
$796$	15.4439	−	2.72318i	0.547395	−	0.0965205i
$797$	28.9247	+	10.5277i	1.02457	+	0.372912i	0.799010	−	0.601318i	$-0.205358\pi$
$797$	28.9247	+	10.5277i	1.02457	+	0.372912i	0.225557	+	0.974230i	$0.427580\pi$
$798$	−3.81324	+	4.47041i	−0.134987	+	0.158251i
$799$	0.435691	−	2.47093i	0.0154136	−	0.0874151i
$800$	16.8744	+	9.74246i	0.596601	+	0.344448i
$801$	4.21272	−	17.2635i	0.148849	−	0.609974i
$802$	−4.28980	−	7.43015i	−0.151478	−	0.262368i
$803$	0.581373	−	3.29713i	0.0205162	−	0.116353i
$804$	−0.682878	+	21.0644i	−0.0240832	+	0.742885i
$805$	−1.04725	+	3.11054i	−0.0369106	+	0.109632i
$806$	2.91187	+	3.47023i	0.102566	+	0.122234i
$807$	−52.1606	+	7.46369i	−1.83614	+	0.262734i
$808$	−7.03431	−	1.24034i	−0.247466	−	0.0436350i
$809$	−48.9190	−	28.2434i	−1.71990	−	0.992985i	−0.919069	−	0.394097i	$-0.871058\pi$
$809$	−48.9190	−	28.2434i	−1.71990	−	0.992985i	−0.800832	−	0.598889i	$-0.795609\pi$
$810$	−4.56706	+	8.80054i	−0.160470	+	0.309219i
$811$			0.658409i			0.0231199i	0.999933	+	0.0115599i	$0.00367972\pi$
$811$			0.658409i			0.0231199i	−0.999933	+	0.0115599i	$0.996320\pi$
$812$	−3.72600	−	0.563983i	−0.130757	−	0.0197919i
$813$	20.9474	+	8.40247i	0.734658	+	0.294687i
$814$	25.8215	+	9.39825i	0.905042	+	0.329408i
$815$	2.44956	+	0.891565i	0.0858042	+	0.0312302i
$816$	2.96616	+	1.84317i	0.103836	+	0.0645239i
$817$	−11.3484	−	2.00103i	−0.397030	−	0.0700071i
$818$	5.89881	−	10.2170i	0.206247	−	0.357231i
$819$	−1.45221	−	4.55608i	−0.0507443	−	0.159202i
$820$	−5.13658	−	8.89682i	−0.179377	−	0.310690i
$821$	−14.2202	−	39.0697i	−0.496289	−	1.36354i	−0.894836	−	0.446394i	$-0.852708\pi$
$821$	−14.2202	−	39.0697i	−0.496289	−	1.36354i	0.398548	−	0.917148i	$-0.369514\pi$
$822$	5.13492	+	1.07805i	0.179101	+	0.0376014i
$823$	−23.3533	+	19.5958i	−0.814045	+	0.683065i	−0.951570	−	0.307433i	$-0.900530\pi$
$823$	−23.3533	+	19.5958i	−0.814045	+	0.683065i	0.137524	+	0.990498i	$0.456085\pi$
$824$	−4.77977	−	27.1074i	−0.166511	−	0.944331i
$825$	−4.49764	+	21.4229i	−0.156588	+	0.745849i
$826$	−2.36398	−	0.357822i	−0.0822535	−	0.0124502i
$827$	−36.1773	+	20.8870i	−1.25801	+	0.726311i	−0.972687	−	0.232121i	$-0.925433\pi$
$827$	−36.1773	+	20.8870i	−1.25801	+	0.726311i	−0.285321	+	0.958432i	$0.592100\pi$
$828$	1.45119	−	3.30376i	0.0504322	−	0.114814i
$829$	−37.7752	+	21.8095i	−1.31199	+	0.757475i	−0.982425	−	0.186659i	$-0.940234\pi$
$829$	−37.7752	+	21.8095i	−1.31199	+	0.757475i	−0.329561	+	0.944134i	$0.606901\pi$
$830$	2.26999	+	6.23675i	0.0787925	+	0.216481i
$831$	26.3869	+	16.3968i	0.915351	+	0.568799i
$832$	3.27548	−	0.577555i	0.113557	−	0.0200231i
$833$	−12.3146	−	54.2660i	−0.426676	−	1.88021i
$834$	3.86346	+	4.91960i	0.133781	+	0.170352i
$835$	−12.8938	−	10.8192i	−0.446209	−	0.374414i
$836$	−2.99139	+	5.18124i	−0.103459	+	0.179197i
$837$	35.5583	−	24.3743i	1.22907	−	0.842498i
$838$	−9.20258	+	5.31311i	−0.317898	+	0.183538i
$839$	−8.50951	+	3.09721i	−0.293781	+	0.106928i	−0.484706	−	0.874677i	$-0.661073\pi$
$839$	−8.50951	+	3.09721i	−0.293781	+	0.106928i	0.190925	+	0.981605i	$0.438851\pi$
$840$	2.65849	+	15.8254i	0.0917268	+	0.546029i
$841$	21.0965	−	17.7021i	0.727467	−	0.610417i
$842$	−9.86059	−	11.7514i	−0.339818	−	0.404980i
$843$	7.85280	+	14.6803i	0.270465	+	0.505618i
$844$	16.8264	−	6.12432i	0.579190	−	0.210808i
$845$	−15.3611			−0.528439
$846$	0.769420	−	0.380044i	0.0264532	−	0.0130662i
$847$	−2.37301	+	4.35111i	−0.0815376	+	0.149506i
$848$	1.65628	+	0.292046i	0.0568767	+	0.0100289i
$849$	−4.74745	+	22.6127i	−0.162932	+	0.776067i
$850$	16.3122	+	19.4402i	0.559505	+	0.666793i
$851$	−5.54333	−	6.60628i	−0.190023	−	0.226461i
$852$	−0.461511	+	2.19824i	−0.0158111	+	0.0753104i
$853$	49.6962	+	8.76279i	1.70157	+	0.300032i	0.938241	−	0.345982i	$-0.112454\pi$
$853$	49.6962	+	8.76279i	1.70157	+	0.300032i	0.763325	+	0.646014i	$0.223565\pi$
$854$	−29.3757	+	0.714236i	−1.00521	+	0.0244406i
$855$	−4.62573	+	2.28481i	−0.158197	+	0.0781389i
$856$	−35.4030			−1.21005
$857$	14.4978	−	5.27677i	0.495235	−	0.180251i	−0.0823144	−	0.996606i	$-0.526231\pi$
$857$	14.4978	−	5.27677i	0.495235	−	0.180251i	0.577550	+	0.816355i	$0.304009\pi$
$858$	1.60050	+	2.99203i	0.0546400	+	0.102146i
$859$	2.96510	+	3.53366i	0.101168	+	0.120567i	0.814253	−	0.580511i	$-0.197147\pi$
$859$	2.96510	+	3.53366i	0.101168	+	0.120567i	−0.713085	+	0.701078i	$0.752703\pi$
$860$	−8.93923	+	7.50090i	−0.304825	+	0.255779i
$861$	−11.4884	+	30.7860i	−0.391522	+	1.04918i
$862$	−1.61552	+	0.588001i	−0.0550248	+	0.0200274i
$863$	−27.5293	+	15.8941i	−0.937108	+	0.541040i	−0.889053	−	0.457805i	$-0.848636\pi$
$863$	−27.5293	+	15.8941i	−0.937108	+	0.541040i	−0.0480557	+	0.998845i	$0.515302\pi$
$864$	−2.21999	−	28.6577i	−0.0755257	−	0.974956i
$865$	2.19916	−	3.80906i	0.0747737	−	0.129512i
$866$	5.96736	+	5.00721i	0.202779	+	0.170152i
$867$	−49.4155	−	62.9241i	−1.67824	−	2.13701i
$868$	8.25501	−	24.5191i	0.280193	−	0.832232i
$869$	47.5314	−	8.38106i	1.61239	−	0.284308i
$870$	1.95861	+	1.21708i	0.0664032	+	0.0412629i
$871$	2.12730	+	5.84471i	0.0720808	+	0.198040i
$872$	23.3069	−	13.4562i	0.789271	−	0.455686i
$873$	10.1597	−	23.1296i	0.343855	−	0.782818i
$874$	−1.13322	+	0.654267i	−0.0383319	+	0.0221309i
$875$	−4.10198	+	27.1000i	−0.138672	+	0.916149i
$876$	−0.391394	+	1.86426i	−0.0132240	+	0.0629877i
$877$	−3.35762	−	19.0420i	−0.113379	−	0.643003i	−0.987540	−	0.157367i	$-0.949699\pi$
$877$	−3.35762	−	19.0420i	−0.113379	−	0.643003i	0.874161	−	0.485636i	$-0.161412\pi$
$878$	−12.0783	+	10.1349i	−0.407622	+	0.342035i
$879$	−2.77119	−	0.581799i	−0.0934699	−	0.0196236i
$880$	−0.378335	−	1.03947i	−0.0127537	−	0.0350405i
$881$	0.310834	+	0.538380i	0.0104723	+	0.0181385i	0.871214	−	0.490903i	$-0.163333\pi$
$881$	0.310834	+	0.538380i	0.0104723	+	0.0181385i	−0.860742	+	0.509042i	$0.830000\pi$
$882$	12.4683	−	14.3796i	0.419829	−	0.484186i
$883$	−1.97025	+	3.41257i	−0.0663041	+	0.114842i	−0.897272	−	0.441479i	$-0.854454\pi$
$883$	−1.97025	+	3.41257i	−0.0663041	+	0.114842i	0.830968	+	0.556321i	$0.187787\pi$
$884$	−5.55891	−	0.980186i	−0.186966	−	0.0329672i
$885$	−1.78310	−	1.10802i	−0.0599383	−	0.0372456i
$886$	26.0711	+	9.48910i	0.875875	+	0.318792i
$887$	−47.0455	−	17.1232i	−1.57963	−	0.574940i	−0.604510	−	0.796597i	$-0.706631\pi$
$887$	−47.0455	−	17.1232i	−1.57963	−	0.574940i	−0.975125	+	0.221657i	$0.928853\pi$
$888$	−39.1339	−	15.6974i	−1.31325	−	0.526772i
$889$	36.2013	−	14.1819i	1.21415	−	0.475646i
$890$			6.52556i			0.218737i
$891$	29.8176	−	12.3953i	0.998928	−	0.415258i
$892$	−7.20364	−	4.15902i	−0.241196	−	0.139254i
$893$	0.439757	+	0.0775410i	0.0147159	+	0.00259481i
$894$	−21.8716	+	3.12962i	−0.731496	+	0.104670i
$895$	19.1107	+	22.7753i	0.638802	+	0.761294i
$896$	−10.6015	−	12.0281i	−0.354172	−	0.401831i
$897$	0.0345051	−	1.06436i	0.00115209	−	0.0355381i
$898$	−4.31647	+	24.4799i	−0.144043	+	0.816906i
$899$	−5.01313	−	8.68300i	−0.167197	−	0.289594i
$900$	2.95262	−	12.0996i	0.0984205	−	0.403321i
$901$	−45.6501	−	26.3561i	−1.52083	−	0.878049i
$902$	4.04894	−	22.9627i	0.134815	−	0.764574i
$903$	36.7048	+	6.77896i	1.22146	+	0.225590i
$904$	−10.7433	−	3.91024i	−0.357316	−	0.130053i
$905$	19.1640	−	3.37914i	0.637034	−	0.112326i
$906$	15.4353	+	13.8283i	0.512804	+	0.459415i
$907$	−17.1617	−	14.4003i	−0.569843	−	0.478155i	0.311751	−	0.950164i	$-0.399085\pi$
$907$	−17.1617	−	14.4003i	−0.569843	−	0.478155i	−0.881594	+	0.472009i	$0.843529\pi$
$908$	10.1124	−	17.5151i	0.335590	−	0.581260i
$909$	0.814496	+	7.39369i	0.0270151	+	0.245233i
$910$	0.914720	+	1.49898i	0.0303227	+	0.0496906i
$911$	−24.0775	+	28.6944i	−0.797723	+	0.950689i	−0.999587	−	0.0287243i	$-0.990855\pi$
$911$	−24.0775	+	28.6944i	−0.797723	+	0.950689i	0.201864	+	0.979413i	$0.435300\pi$
$912$	−0.328034	+	0.527895i	−0.0108623	+	0.0174804i
$913$	7.39294	−	20.3119i	0.244671	−	0.672227i
$914$	−20.4658	+	3.60867i	−0.676948	+	0.119364i
$915$	−23.9461	−	9.60531i	−0.791634	−	0.317542i
$916$	3.60086	+	9.89327i	0.118976	+	0.326883i
$917$	24.4434	+	40.0561i	0.807193	+	1.32277i
$918$	10.0486	−	36.0621i	0.331654	−	1.19023i
$919$	6.76771	+	11.7220i	0.223246	+	0.386674i	0.955792	−	0.294044i	$-0.0950012\pi$
$919$	6.76771	+	11.7220i	0.223246	+	0.386674i	−0.732546	+	0.680718i	$0.761668\pi$
$920$	−0.620561	+	3.51937i	−0.0204593	+	0.116030i
$921$	18.5622	+	7.44568i	0.611644	+	0.245344i
$922$	9.34592	−	25.6777i	0.307791	−	0.845650i
$923$	0.115109	+	0.652818i	0.00378887	+	0.0214878i
$924$	9.82497	−	16.7035i	0.323218	−	0.549504i
$925$	−22.8019	−	19.1331i	−0.749722	−	0.629092i
$926$		−	27.1615i		−	0.892583i
$927$	−25.7005	+	12.6944i	−0.844115	+	0.416938i
$928$	−6.68497			−0.219445
$929$	−34.9579	+	12.7236i	−1.14693	+	0.417449i	−0.844412	−	0.535695i	$-0.820050\pi$
$929$	−34.9579	+	12.7236i	−1.14693	+	0.417449i	−0.302519	+	0.953143i	$0.597828\pi$
$930$	−10.5636	+	11.7912i	−0.346395	+	0.386649i
$931$	9.65785	−	2.19166i	0.316523	−	0.0718288i
$932$	−3.44503	+	9.46514i	−0.112846	+	0.310041i
$933$	40.7834	+	8.56229i	1.33519	+	0.280317i
$934$	1.36962	−	1.63226i	0.0448155	−	0.0534090i
$935$			34.6701i			1.13383i
$936$	−2.30584	−	4.66830i	−0.0753688	−	0.152588i
$937$	42.3336	+	24.4413i	1.38298	+	0.798463i	0.992511	−	0.122153i	$-0.0389800\pi$
$937$	42.3336	+	24.4413i	1.38298	+	0.798463i	0.390468	+	0.920617i	$0.372313\pi$
$938$	−15.4467	+	19.3448i	−0.504353	+	0.631630i
$939$	−29.7204	+	47.8282i	−0.969890	+	1.56082i
$940$	0.346400	−	0.290664i	0.0112983	−	0.00948043i
$941$	5.55445	+	31.5009i	0.181070	+	1.02690i	0.930901	+	0.365270i	$0.119023\pi$
$941$	5.55445	+	31.5009i	0.181070	+	1.02690i	−0.749831	+	0.661629i	$0.769865\pi$
$942$	−2.92069	+	7.28131i	−0.0951613	+	0.237238i
$943$	−4.70378	+	5.60574i	−0.153176	+	0.182548i
$944$	−0.252898			−0.00823112
$945$	15.0426	−	7.27914i	0.489336	−	0.236790i
$946$	−26.4858			−0.861128
$947$	22.2598	−	26.5282i	0.723347	−	0.862052i	−0.271604	−	0.962409i	$-0.587554\pi$
$947$	22.2598	−	26.5282i	0.723347	−	0.862052i	0.994951	+	0.100357i	$0.0319986\pi$
$948$	−27.1842	+	3.88980i	−0.882902	+	0.126335i
$949$	0.0976210	+	0.553636i	0.00316891	+	0.0179718i
$950$	−3.45982	+	2.90313i	−0.112251	+	0.0941900i
$951$	4.12580	+	7.71294i	0.133788	+	0.250109i
$952$	−22.1005	−	56.4145i	−0.716280	−	1.82841i
$953$	−43.1385	−	24.9060i	−1.39739	−	0.806786i	−0.403275	−	0.915079i	$-0.632128\pi$
$953$	−43.1385	−	24.9060i	−1.39739	−	0.806786i	−0.994119	+	0.108293i	$0.965461\pi$
$954$	−1.97415	−	17.9206i	−0.0639155	−	0.580201i
$955$			7.81261i			0.252810i
$956$	−10.0747	+	12.0066i	−0.325839	+	0.388320i
$957$	−2.33859	−	7.13669i	−0.0755958	−	0.230697i
$958$	−5.80574	+	15.9511i	−0.187575	+	0.515358i
$959$	−5.84736	−	6.63420i	−0.188821	−	0.214230i
$960$	3.61942	+	11.0454i	0.116816	+	0.356489i
$961$	35.5516	−	12.9397i	1.14683	−	0.417410i
$962$	−4.61406			−0.148763
$963$	10.3392	+	35.3886i	0.333177	+	1.14038i
$964$			16.4707i			0.530487i
$965$	1.27603	+	1.07072i	0.0410770	+	0.0344677i
$966$	3.68765	−	2.08944i	0.118648	−	0.0672265i
$967$	−0.0919287	−	0.521354i	−0.00295623	−	0.0167656i	0.983294	−	0.182025i	$-0.0582651\pi$
$967$	−0.0919287	−	0.521354i	−0.00295623	−	0.0167656i	−0.986250	+	0.165259i	$0.947154\pi$
$968$	−1.84569	+	5.07098i	−0.0593226	+	0.162987i
$969$	15.3201	−	12.0312i	0.492154	−	0.386498i
$970$	−1.61093	+	9.13605i	−0.0517239	+	0.293341i
$971$	−9.94776	−	17.2300i	−0.319239	−	0.552938i	0.661091	−	0.750306i	$-0.270094\pi$
$971$	−9.94776	−	17.2300i	−0.319239	−	0.552938i	−0.980329	+	0.197368i	$0.936761\pi$
$972$	−17.1849	+	6.49913i	−0.551206	+	0.208460i
$973$	−0.256265	−	10.5399i	−0.00821547	−	0.337893i
$974$	0.229412	+	0.630304i	0.00735083	+	0.0201962i
$975$	−0.520645	−	3.63857i	−0.0166740	−	0.116528i
$976$	−3.06090	+	0.539719i	−0.0979770	+	0.0172760i
$977$	−16.8301	+	46.2403i	−0.538442	+	1.47936i	0.310345	+	0.950624i	$0.399555\pi$
$977$	−16.8301	+	46.2403i	−0.538442	+	1.47936i	−0.848788	+	0.528734i	$0.822667\pi$
$978$	−1.58782	−	2.96834i	−0.0507730	−	0.0949170i
$979$	13.6609	−	16.2804i	0.436603	−	0.520324i
$980$	4.58637	−	8.91861i	0.146506	−	0.284895i
$981$	−20.2574	−	19.3676i	−0.646769	−	0.618360i
$982$	−6.26977	+	10.8596i	−0.200076	+	0.346543i
$983$	20.9420	+	17.5724i	0.667945	+	0.560473i	0.912456	−	0.409174i	$-0.134183\pi$
$983$	20.9420	+	17.5724i	0.667945	+	0.560473i	−0.244511	+	0.969646i	$0.578628\pi$
$984$	−7.35134	+	35.0154i	−0.234352	+	1.11625i
$985$	−26.6055	+	4.69127i	−0.847722	+	0.149476i
$986$	−8.18150	−	2.97782i	−0.260552	−	0.0948332i
$987$	−1.42233	−	0.262689i	−0.0452733	−	0.00836148i
$988$	0.174446	−	0.989333i	0.00554987	−	0.0314749i
$989$	7.19866	+	4.15615i	0.228904	+	0.132158i
$990$	−9.55846	+	7.01790i	−0.303788	+	0.223044i
$991$	−22.1860	−	38.4273i	−0.704761	−	1.22068i	−0.966778	−	0.255619i	$-0.917721\pi$
$991$	−22.1860	−	38.4273i	−0.704761	−	1.22068i	0.262017	−	0.965063i	$-0.415612\pi$
$992$	7.96945	−	45.1970i	0.253030	−	1.43501i
$993$	−18.7016	+	10.0039i	−0.593479	+	0.317463i
$994$	−1.97927	+	1.74452i	−0.0627785	+	0.0553327i
$995$	10.3963	+	12.3898i	0.329585	+	0.392784i
$996$	−4.57861	+	11.4145i	−0.145079	+	0.361683i
$997$	−25.9214	−	4.57064i	−0.820939	−	0.144754i	−0.252624	−	0.967565i	$-0.581293\pi$
$997$	−25.9214	−	4.57064i	−0.820939	−	0.144754i	−0.568315	+	0.822811i	$0.692405\pi$
$998$	−1.87922	−	1.08497i	−0.0594857	−	0.0343441i
$999$	−4.26224	+	43.7023i	−0.134851	+	1.38268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.101.8	✓	132
3.2	odd	2		567.2.ba.a.143.15		132
7.5	odd	6		189.2.bd.a.47.15	yes	132
21.5	even	6		567.2.bd.a.467.8		132
27.4	even	9		567.2.bd.a.17.8		132
27.23	odd	18		189.2.bd.a.185.15	yes	132
189.131	even	18	inner	189.2.ba.a.131.8	yes	132
189.166	odd	18		567.2.ba.a.341.15		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.8	✓	132	1.1	even	1	trivial
189.2.ba.a.131.8	yes	132	189.131	even	18	inner
189.2.bd.a.47.15	yes	132	7.5	odd	6
189.2.bd.a.185.15	yes	132	27.23	odd	18
567.2.ba.a.143.15		132	3.2	odd	2
567.2.ba.a.341.15		132	189.166	odd	18
567.2.bd.a.17.8		132	27.4	even	9
567.2.bd.a.467.8		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.582560 + 0.694268i) q^{2} +(-1.06977 - 1.36221i) q^{3} +(0.204665 + 1.16071i) q^{4} +(-0.931176 + 0.781349i) q^{5} +(1.56894 + 0.0508626i) q^{6} +(-2.06750 - 1.65089i) q^{7} +(-2.49483 - 1.44039i) q^{8} +(-0.711206 + 2.91448i) q^{9} -1.10167i q^{10} +(-2.30628 + 2.74851i) q^{11} +(1.36218 - 1.52048i) q^{12} +(0.206055 - 0.566132i) q^{13} +(2.35060 - 0.473658i) q^{14} +(2.06050 + 0.432592i) q^{15} +(0.238336 - 0.0867472i) q^{16} -7.94939 q^{17} +(-1.60911 - 2.19163i) q^{18} -1.41477i q^{19} +(-1.09750 - 0.920911i) q^{20} +(-0.0371098 + 4.58243i) q^{21} +(-0.564660 - 3.20235i) q^{22} +(-0.349041 + 0.958983i) q^{23} +(0.706775 + 4.93936i) q^{24} +(-0.611659 + 3.46889i) q^{25} +(0.273008 + 0.472864i) q^{26} +(4.73094 - 2.14900i) q^{27} +(1.49306 - 2.73765i) q^{28} +(-0.413325 - 1.13560i) q^{29} +(-1.50070 + 1.17853i) q^{30} +(8.17053 - 1.44069i) q^{31} +(1.89196 - 5.19810i) q^{32} +(6.21122 + 0.201358i) q^{33} +(4.63100 - 5.51901i) q^{34} +(3.21513 - 0.0781722i) q^{35} +(-3.52842 - 0.229013i) q^{36} +(-4.22521 + 7.31828i) q^{37} +(0.982231 + 0.824190i) q^{38} +(-0.991619 + 0.324939i) q^{39} +(3.44858 - 0.608078i) q^{40} +(6.73814 + 2.45248i) q^{41} +(-3.15981 - 2.69530i) q^{42} +(1.41438 - 8.02135i) q^{43} +(-3.66224 - 2.11440i) q^{44} +(-1.61497 - 3.26959i) q^{45} +(-0.462454 - 0.800993i) q^{46} +(-0.0548081 + 0.310832i) q^{47} +(-0.373131 - 0.231863i) q^{48} +(1.54913 + 6.82643i) q^{49} +(-2.05201 - 2.44549i) q^{50} +(8.50398 + 10.8287i) q^{51} +(0.699288 + 0.123303i) q^{52} +(5.74259 + 3.31549i) q^{53} +(-1.26408 + 4.53646i) q^{54} -4.36136i q^{55} +(2.78014 + 7.09671i) q^{56} +(-1.92721 + 1.51347i) q^{57} +(1.02920 + 0.374598i) q^{58} +(-0.936973 - 0.341030i) q^{59} +(-0.0804037 + 2.48018i) q^{60} +(-12.0683 - 2.12796i) q^{61} +(-3.75960 + 6.51182i) q^{62} +(6.28190 - 4.85157i) q^{63} +(2.76033 + 4.78103i) q^{64} +(0.250473 + 0.688170i) q^{65} +(-3.75820 + 4.19494i) q^{66} +(-7.90859 + 6.63609i) q^{67} +(-1.62696 - 9.22694i) q^{68} +(1.67972 - 0.550421i) q^{69} +(-1.81873 + 2.27770i) q^{70} +(-0.952881 + 0.550146i) q^{71} +(5.97234 - 6.24673i) q^{72} +(-0.808112 + 0.466563i) q^{73} +(-2.61941 - 7.19676i) q^{74} +(5.37967 - 2.87769i) q^{75} +(1.64214 - 0.289554i) q^{76} +(9.30573 - 1.87515i) q^{77} +(0.352083 - 0.877746i) q^{78} +(-10.3048 - 8.64674i) q^{79} +(-0.154153 + 0.267000i) q^{80} +(-7.98837 - 4.14559i) q^{81} +(-5.62805 + 3.24936i) q^{82} +(-5.66119 + 2.06050i) q^{83} +(-5.32646 + 0.894786i) q^{84} +(7.40228 - 6.21125i) q^{85} +(4.74500 + 5.65488i) q^{86} +(-1.10476 + 1.77786i) q^{87} +(9.71272 - 3.53514i) q^{88} -5.92334 q^{89} +(3.21079 + 0.783513i) q^{90} +(-1.36064 + 0.830305i) q^{91} +(-1.18454 - 0.208866i) q^{92} +(-10.7031 - 9.58875i) q^{93} +(-0.183872 - 0.219130i) q^{94} +(1.10543 + 1.31740i) q^{95} +(-9.10483 + 2.98352i) q^{96} +(-8.29293 - 1.46227i) q^{97} +(-5.64183 - 2.90130i) q^{98} +(-6.37025 - 8.67636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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