LMFDB - Embedded newform 138.2.f.a.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			83.3
Character	$\chi$	$=$	138.83
Dual form			138.2.f.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281733 - 0.959493i) q^{2} +(0.583374 + 1.63085i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.140990 + 0.980604i) q^{5} +(1.40043 - 1.01921i) q^{6} +(1.30276 + 0.594948i) q^{7} +(0.755750 + 0.654861i) q^{8} +(-2.31935 + 1.90279i) q^{9} +O(q^{10})$	\(q+(-0.281733 - 0.959493i) q^{2} +(0.583374 + 1.63085i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.140990 + 0.980604i) q^{5} +(1.40043 - 1.01921i) q^{6} +(1.30276 + 0.594948i) q^{7} +(0.755750 + 0.654861i) q^{8} +(-2.31935 + 1.90279i) q^{9} +(0.901161 - 0.411546i) q^{10} +(3.75438 + 1.10239i) q^{11} +(-1.37247 - 1.05656i) q^{12} +(-0.318796 - 0.698067i) q^{13} +(0.203820 - 1.41760i) q^{14} +(-1.51697 + 0.801992i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.408580 + 0.262579i) q^{17} +(2.47915 + 1.68932i) q^{18} +(-4.07796 - 6.34543i) q^{19} +(-0.648762 - 0.748712i) q^{20} +(-0.210278 + 2.47168i) q^{21} -3.91288i q^{22} +(-1.71381 - 4.47916i) q^{23} +(-0.627095 + 1.61454i) q^{24} +(3.85576 - 1.13215i) q^{25} +(-0.579975 + 0.502551i) q^{26} +(-4.45622 - 2.67247i) q^{27} +(-1.41760 + 0.203820i) q^{28} +(-3.13747 + 4.88200i) q^{29} +(1.19689 + 1.22957i) q^{30} +(0.102577 - 0.118380i) q^{31} +(-0.989821 - 0.142315i) q^{32} +(0.392383 + 6.76594i) q^{33} +(0.136832 - 0.466007i) q^{34} +(-0.399734 + 1.36137i) q^{35} +(0.922432 - 2.85467i) q^{36} +(-5.07638 - 0.729874i) q^{37} +(-4.93950 + 5.70049i) q^{38} +(0.952465 - 0.927144i) q^{39} +(-0.535606 + 0.833419i) q^{40} +(3.04414 - 0.437682i) q^{41} +(2.43080 - 0.494592i) q^{42} +(0.209322 - 0.181379i) q^{43} +(-3.75438 + 1.10239i) q^{44} +(-2.19289 - 2.00609i) q^{45} +(-3.81489 + 2.90631i) q^{46} -6.75849i q^{47} +(1.72582 + 0.146824i) q^{48} +(-3.24082 - 3.74010i) q^{49} +(-2.17259 - 3.38061i) q^{50} +(-0.189871 + 0.819515i) q^{51} +(0.645592 + 0.414897i) q^{52} +(-1.44656 + 3.16753i) q^{53} +(-1.30875 + 5.02863i) q^{54} +(-0.551675 + 3.83698i) q^{55} +(0.594948 + 1.30276i) q^{56} +(7.96947 - 10.3523i) q^{57} +(5.56817 + 1.63496i) q^{58} +(11.2477 - 5.13667i) q^{59} +(0.842566 - 1.49481i) q^{60} +(11.4538 + 9.92474i) q^{61} +(-0.142484 - 0.0650700i) q^{62} +(-4.15361 + 1.09898i) q^{63} +(0.142315 + 0.989821i) q^{64} +(0.639580 - 0.411033i) q^{65} +(6.38132 - 2.28267i) q^{66} +(1.96590 + 6.69523i) q^{67} -0.485680 q^{68} +(6.30505 - 5.40799i) q^{69} +1.41884 q^{70} +(-4.19016 - 14.2704i) q^{71} +(-2.99891 - 0.0808151i) q^{72} +(-1.16181 + 0.746652i) q^{73} +(0.729874 + 5.07638i) q^{74} +(4.09572 + 5.62770i) q^{75} +(6.86120 + 3.13340i) q^{76} +(4.23518 + 3.66980i) q^{77} +(-1.15793 - 0.652677i) q^{78} +(-6.31629 + 2.88455i) q^{79} +(0.950558 + 0.279109i) q^{80} +(1.75876 - 8.82648i) q^{81} +(-1.27759 - 2.79752i) q^{82} +(0.592165 - 4.11860i) q^{83} +(-1.15939 - 2.19299i) q^{84} +(-0.199880 + 0.437676i) q^{85} +(-0.233005 - 0.149743i) q^{86} +(-9.79213 - 2.26871i) q^{87} +(2.11546 + 3.29172i) q^{88} +(10.0879 + 11.6421i) q^{89} +(-1.30702 + 2.66924i) q^{90} -1.09908i q^{91} +(3.86336 + 2.84155i) q^{92} +(0.252900 + 0.0982273i) q^{93} +(-6.48472 + 1.90409i) q^{94} +(5.64740 - 4.89350i) q^{95} +(-0.345342 - 1.69727i) q^{96} +(1.80716 - 0.259831i) q^{97} +(-2.67556 + 4.16325i) q^{98} +(-10.8053 + 4.58699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.281733	−	0.959493i	−0.199215	−	0.678464i
$2$	−0.281733	−	0.959493i	−0.199215	−	0.678464i
$3$	0.583374	+	1.63085i	0.336811	+	0.941572i
$3$	0.583374	+	1.63085i	0.336811	+	0.941572i
$4$	−0.841254	+	0.540641i	−0.420627	+	0.270320i
$5$	0.140990	+	0.980604i	0.0630524	+	0.438539i	0.996755	+	0.0804907i	$0.0256487\pi$
$5$	0.140990	+	0.980604i	0.0630524	+	0.438539i	−0.933703	+	0.358049i	$0.883442\pi$
$6$	1.40043	−	1.01921i	0.571725	−	0.416090i
$7$	1.30276	+	0.594948i	0.492395	+	0.224869i	0.646108	−	0.763246i	$-0.276396\pi$
$7$	1.30276	+	0.594948i	0.492395	+	0.224869i	−0.153712	+	0.988116i	$0.549123\pi$
$8$	0.755750	+	0.654861i	0.267198	+	0.231528i
$9$	−2.31935	+	1.90279i	−0.773116	+	0.634264i
$10$	0.901161	−	0.411546i	0.284972	−	0.130142i
$11$	3.75438	+	1.10239i	1.13199	+	0.332382i	0.793489	−	0.608585i	$-0.208262\pi$
$11$	3.75438	+	1.10239i	1.13199	+	0.332382i	0.338500	+	0.940967i	$0.390081\pi$
$12$	−1.37247	−	1.05656i	−0.396198	−	0.305003i
$13$	−0.318796	−	0.698067i	−0.0884182	−	0.193609i	0.860257	−	0.509860i	$-0.170303\pi$
$13$	−0.318796	−	0.698067i	−0.0884182	−	0.193609i	−0.948675	+	0.316251i	$0.897576\pi$
$14$	0.203820	−	1.41760i	0.0544733	−	0.378870i
$15$	−1.51697	+	0.801992i	−0.391680	+	0.207073i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	0.408580	+	0.262579i	0.0990953	+	0.0636847i	0.589250	−	0.807951i	$-0.299423\pi$
$17$	0.408580	+	0.262579i	0.0990953	+	0.0636847i	−0.490155	+	0.871635i	$0.663060\pi$
$18$	2.47915	+	1.68932i	0.584342	+	0.398176i
$19$	−4.07796	−	6.34543i	−0.935548	−	1.45574i	−0.889570	−	0.456799i	$-0.848996\pi$
$19$	−4.07796	−	6.34543i	−0.935548	−	1.45574i	−0.0459785	−	0.998942i	$-0.514641\pi$
$20$	−0.648762	−	0.748712i	−0.145068	−	0.167417i
$21$	−0.210278	+	2.47168i	−0.0458864	+	0.539364i
$22$		−	3.91288i		−	0.834229i
$23$	−1.71381	−	4.47916i	−0.357354	−	0.933969i
$23$	−1.71381	−	4.47916i	−0.357354	−	0.933969i
$24$	−0.627095	+	1.61454i	−0.128005	+	0.329567i
$25$	3.85576	−	1.13215i	0.771152	−	0.226431i
$26$	−0.579975	+	0.502551i	−0.113742	+	0.0985584i
$27$	−4.45622	−	2.67247i	−0.857600	−	0.514317i
$28$	−1.41760	+	0.203820i	−0.267901	+	0.0385184i
$29$	−3.13747	+	4.88200i	−0.582613	+	0.906564i	−0.999998	−	0.00216601i	$-0.999311\pi$
$29$	−3.13747	+	4.88200i	−0.582613	+	0.906564i	0.417384	+	0.908730i	$0.362947\pi$
$30$	1.19689	+	1.22957i	0.218520	+	0.224488i
$31$	0.102577	−	0.118380i	0.0184233	−	0.0212616i	−0.746463	−	0.665427i	$-0.768250\pi$
$31$	0.102577	−	0.118380i	0.0184233	−	0.0212616i	0.764886	+	0.644165i	$0.222795\pi$
$32$	−0.989821	−	0.142315i	−0.174977	−	0.0251579i
$33$	0.392383	+	6.76594i	0.0683052	+	1.17780i
$34$	0.136832	−	0.466007i	0.0234665	−	0.0799195i
$35$	−0.399734	+	1.36137i	−0.0675673	+	0.230113i
$36$	0.922432	−	2.85467i	0.153739	−	0.475778i
$37$	−5.07638	−	0.729874i	−0.834552	−	0.119991i	−0.288226	−	0.957563i	$-0.593065\pi$
$37$	−5.07638	−	0.729874i	−0.834552	−	0.119991i	−0.546327	+	0.837572i	$0.683974\pi$
$38$	−4.93950	+	5.70049i	−0.801293	+	0.924741i
$39$	0.952465	−	0.927144i	0.152516	−	0.148462i
$40$	−0.535606	+	0.833419i	−0.0846868	+	0.131775i
$41$	3.04414	−	0.437682i	0.475415	−	0.0683544i	0.0995576	−	0.995032i	$-0.468257\pi$
$41$	3.04414	−	0.437682i	0.475415	−	0.0683544i	0.375858	+	0.926677i	$0.377348\pi$
$42$	2.43080	−	0.494592i	0.375080	−	0.0763172i
$43$	0.209322	−	0.181379i	0.0319214	−	0.0276600i	−0.638754	−	0.769411i	$-0.720550\pi$
$43$	0.209322	−	0.181379i	0.0319214	−	0.0276600i	0.670675	+	0.741751i	$0.266004\pi$
$44$	−3.75438	+	1.10239i	−0.565994	+	0.166191i
$45$	−2.19289	−	2.00609i	−0.326897	−	0.299050i
$46$	−3.81489	+	2.90631i	−0.562474	+	0.428512i
$47$		−	6.75849i		−	0.985827i	−0.870078	−	0.492913i	$-0.835932\pi$
$47$		−	6.75849i		−	0.985827i	0.870078	−	0.492913i	$-0.164068\pi$
$48$	1.72582	+	0.146824i	0.249100	+	0.0211922i
$49$	−3.24082	−	3.74010i	−0.462974	−	0.534300i
$50$	−2.17259	−	3.38061i	−0.307250	−	0.478090i
$51$	−0.189871	+	0.819515i	−0.0265873	+	0.114755i
$52$	0.645592	+	0.414897i	0.0895275	+	0.0575358i
$53$	−1.44656	+	3.16753i	−0.198700	+	0.435093i	−0.982585	−	0.185813i	$-0.940508\pi$
$53$	−1.44656	+	3.16753i	−0.198700	+	0.435093i	0.783885	+	0.620907i	$0.213235\pi$
$54$	−1.30875	+	5.02863i	−0.178099	+	0.684310i
$55$	−0.551675	+	3.83698i	−0.0743879	+	0.517379i
$56$	0.594948	+	1.30276i	0.0795033	+	0.174088i
$57$	7.96947	−	10.3523i	1.05558	−	1.37120i
$58$	5.56817	+	1.63496i	0.731136	+	0.214681i
$59$	11.2477	−	5.13667i	1.46433	−	0.668737i	0.485655	−	0.874151i	$-0.338581\pi$
$59$	11.2477	−	5.13667i	1.46433	−	0.668737i	0.978675	+	0.205414i	$0.0658540\pi$
$60$	0.842566	−	1.49481i	0.108775	−	0.192980i
$61$	11.4538	+	9.92474i	1.46650	+	1.27073i	0.891847	+	0.452338i	$0.149410\pi$
$61$	11.4538	+	9.92474i	1.46650	+	1.27073i	0.574657	+	0.818395i	$0.305136\pi$
$62$	−0.142484	−	0.0650700i	−0.0180954	−	0.00826390i
$63$	−4.15361	+	1.09898i	−0.523305	+	0.138459i
$64$	0.142315	+	0.989821i	0.0177894	+	0.123728i
$65$	0.639580	−	0.411033i	0.0793301	−	0.0509824i
$66$	6.38132	−	2.28267i	0.785487	−	0.280978i
$67$	1.96590	+	6.69523i	0.240173	+	0.817953i	0.988052	+	0.154118i	$0.0492537\pi$
$67$	1.96590	+	6.69523i	0.240173	+	0.817953i	−0.747880	+	0.663834i	$0.768928\pi$
$68$	−0.485680			−0.0588974
$69$	6.30505	−	5.40799i	0.759039	−	0.651046i
$70$	1.41884			0.169584
$71$	−4.19016	−	14.2704i	−0.497281	−	1.69358i	−0.699829	−	0.714311i	$-0.746740\pi$
$71$	−4.19016	−	14.2704i	−0.497281	−	1.69358i	0.202548	−	0.979272i	$-0.435078\pi$
$72$	−2.99891	−	0.0808151i	−0.353425	−	0.00952415i
$73$	−1.16181	+	0.746652i	−0.135980	+	0.0873890i	−0.606862	−	0.794807i	$-0.707572\pi$
$73$	−1.16181	+	0.746652i	−0.135980	+	0.0873890i	0.470882	+	0.882196i	$0.343936\pi$
$74$	0.729874	+	5.07638i	0.0848461	+	0.590118i
$75$	4.09572	+	5.62770i	0.472933	+	0.649831i
$76$	6.86120	+	3.13340i	0.787033	+	0.359426i
$77$	4.23518	+	3.66980i	0.482643	+	0.418213i
$78$	−1.15793	−	0.652677i	−0.131110	−	0.0739011i
$79$	−6.31629	+	2.88455i	−0.710638	+	0.324537i	−0.737730	−	0.675096i	$-0.764102\pi$
$79$	−6.31629	+	2.88455i	−0.710638	+	0.324537i	0.0270926	+	0.999633i	$0.491375\pi$
$80$	0.950558	+	0.279109i	0.106276	+	0.0312053i
$81$	1.75876	−	8.82648i	0.195417	−	0.980720i
$82$	−1.27759	−	2.79752i	−0.141086	−	0.308935i
$83$	0.592165	−	4.11860i	0.0649986	−	0.452075i	−0.931167	−	0.364592i	$-0.881209\pi$
$83$	0.592165	−	4.11860i	0.0649986	−	0.452075i	0.996166	−	0.0874831i	$-0.0278824\pi$
$84$	−1.15939	−	2.19299i	−0.126500	−	0.239275i
$85$	−0.199880	+	0.437676i	−0.0216800	+	0.0474726i
$86$	−0.233005	−	0.149743i	−0.0251256	−	0.0161472i
$87$	−9.79213	−	2.26871i	−1.04983	−	0.243231i
$88$	2.11546	+	3.29172i	0.225509	+	0.350899i
$89$	10.0879	+	11.6421i	1.06932	+	1.23406i	0.971044	+	0.238902i	$0.0767873\pi$
$89$	10.0879	+	11.6421i	1.06932	+	1.23406i	0.0982759	+	0.995159i	$0.468667\pi$
$90$	−1.30702	+	2.66924i	−0.137772	+	0.281363i
$91$		−	1.09908i		−	0.115215i
$92$	3.86336	+	2.84155i	0.402783	+	0.296252i
$93$	0.252900	+	0.0982273i	0.0262245	+	0.0101857i
$94$	−6.48472	+	1.90409i	−0.668848	+	0.196391i
$95$	5.64740	−	4.89350i	0.579411	−	0.502063i
$96$	−0.345342	−	1.69727i	−0.0352463	−	0.173227i
$97$	1.80716	−	0.259831i	0.183490	−	0.0263818i	−0.0499573	−	0.998751i	$-0.515909\pi$
$97$	1.80716	−	0.259831i	0.183490	−	0.0263818i	0.233447	+	0.972370i	$0.424999\pi$
$98$	−2.67556	+	4.16325i	−0.270272	+	0.420552i
$99$	−10.8053	+	4.58699i	−1.08598	+	0.461010i
$100$	−2.63158	+	3.03701i	−0.263158	+	0.303701i
$101$	−10.3179	−	1.48349i	−1.02667	−	0.147613i	−0.391655	−	0.920112i	$-0.628097\pi$
$101$	−10.3179	−	1.48349i	−1.02667	−	0.147613i	−0.635016	+	0.772499i	$0.719007\pi$
$102$	0.839812	−	0.0487040i	0.0831538	−	0.00482241i
$103$	−0.265994	+	0.905893i	−0.0262092	+	0.0892603i	−0.971559	−	0.236797i	$-0.923902\pi$
$103$	−0.265994	+	0.905893i	−0.0262092	+	0.0892603i	0.945350	+	0.326058i	$0.105720\pi$
$104$	0.216206	−	0.736331i	0.0212008	−	0.0722032i
$105$	−2.45338	+	0.142281i	−0.239426	+	0.0138852i
$106$	3.44676	+	0.495570i	0.334779	+	0.0481340i
$107$	−11.5254	+	13.3011i	−1.11421	+	1.28586i	−0.159867	+	0.987139i	$0.551107\pi$
$107$	−11.5254	+	13.3011i	−1.11421	+	1.28586i	−0.954339	+	0.298724i	$0.903439\pi$
$108$	5.19366	−	0.160990i	0.499760	−	0.0154912i
$109$	−3.94777	+	6.14285i	−0.378128	+	0.588378i	−0.977201	−	0.212316i	$-0.931899\pi$
$109$	−3.94777	+	6.14285i	−0.378128	+	0.588378i	0.599073	+	0.800694i	$0.295536\pi$
$110$	3.83698	−	0.551675i	0.365842	−	0.0526002i
$111$	−1.77112	−	8.70461i	−0.168107	−	0.826205i
$112$	1.08237	−	0.937877i	0.102274	−	0.0886211i
$113$	−16.3239	+	4.79312i	−1.53562	+	0.450899i	−0.936765	−	0.349959i	$-0.886196\pi$
$113$	−16.3239	+	4.79312i	−1.53562	+	0.450899i	−0.598855	+	0.800858i	$0.704377\pi$
$114$	−12.1782	−	4.73007i	−1.14060	−	0.443012i
$115$	4.15065	−	2.31208i	0.387050	−	0.215603i
$116$		−	5.80324i		−	0.538817i
$117$	2.06768	+	1.01246i	0.191157	+	0.0936016i
$118$	−8.09745	−	9.34495i	−0.745431	−	0.860273i
$119$	0.376059	+	0.585160i	0.0344733	+	0.0536415i
$120$	−1.67164	−	0.387298i	−0.152599	−	0.0353553i
$121$	3.62633	+	2.33050i	0.329666	+	0.211864i
$122$	6.29582	−	13.7859i	0.569997	−	1.24812i
$123$	2.48967	+	4.70921i	0.224486	+	0.424615i
$124$	−0.0222920	+	0.155044i	−0.00200188	+	0.0139234i
$125$	3.71155	+	8.12716i	0.331971	+	0.726915i
$126$	2.22467	+	3.67574i	0.198189	+	0.327461i
$127$	−14.5399	−	4.26930i	−1.29021	−	0.378839i	−0.436554	−	0.899678i	$-0.643801\pi$
$127$	−14.5399	−	4.26930i	−1.29021	−	0.378839i	−0.853655	+	0.520839i	$0.825619\pi$
$128$	0.909632	−	0.415415i	0.0804009	−	0.0367178i
$129$	0.417915	+	0.235562i	0.0367954	+	0.0207401i
$130$	−0.574574	−	0.497871i	−0.0503935	−	0.0436662i
$131$	11.3332	+	5.17572i	0.990190	+	0.452205i	0.843588	−	0.536991i	$-0.180439\pi$
$131$	11.3332	+	5.17572i	0.990190	+	0.452205i	0.146602	+	0.989196i	$0.453166\pi$
$132$	−3.98804	−	5.47973i	−0.347114	−	0.476949i
$133$	−1.53738	−	10.6927i	−0.133308	−	0.927176i
$134$	5.87017	−	3.77253i	0.507105	−	0.325897i
$135$	1.99235	−	4.74658i	0.171475	−	0.408520i
$136$	0.136832	+	0.466007i	0.0117332	+	0.0399598i
$137$	0.183210			0.0156527			0.00782633	−	0.999969i	$-0.497509\pi$
$137$	0.183210			0.0156527			0.00782633	+	0.999969i	$0.497509\pi$
$138$	−6.96527	−	4.52604i	−0.592923	−	0.385282i
$139$	17.5005			1.48437			0.742185	−	0.670195i	$-0.233790\pi$
$139$	17.5005			1.48437			0.742185	+	0.670195i	$0.233790\pi$
$140$	−0.399734	−	1.36137i	−0.0337837	−	0.115057i
$141$	11.0221	−	3.94273i	0.928227	−	0.332038i
$142$	−12.5118	+	8.04086i	−1.04997	+	0.674774i
$143$	−0.427344	−	2.97224i	−0.0357363	−	0.248552i
$144$	0.767349	+	2.90020i	0.0639458	+	0.241684i
$145$	−5.22965	−	2.38830i	−0.434299	−	0.198338i
$146$	1.04373	+	0.904395i	0.0863795	+	0.0748483i
$147$	4.20894	−	7.46717i	0.347147	−	0.615882i
$148$	4.66513	−	2.13049i	0.383471	−	0.175125i
$149$	−13.0310	−	3.82624i	−1.06754	−	0.313458i	−0.299656	−	0.954047i	$-0.596872\pi$
$149$	−13.0310	−	3.82624i	−1.06754	−	0.313458i	−0.767884	+	0.640589i	$0.778690\pi$
$150$	4.24584	−	5.51532i	0.346671	−	0.450324i
$151$	5.10763	+	11.1842i	0.415653	+	0.910154i	0.995440	+	0.0953856i	$0.0304084\pi$
$151$	5.10763	+	11.1842i	0.415653	+	0.910154i	−0.579787	+	0.814768i	$0.696864\pi$
$152$	1.07346	−	7.46605i	0.0870688	−	0.605577i
$153$	−1.44727	+	0.168432i	−0.117005	+	0.0136170i
$154$	2.32796	−	5.09752i	0.187592	−	0.410770i
$155$	0.130546	+	0.0838966i	0.0104857	+	0.00673874i
$156$	−0.300013	+	1.29490i	−0.0240203	+	0.103675i
$157$	−6.14901	−	9.56805i	−0.490745	−	0.763613i	0.504248	−	0.863559i	$-0.331770\pi$
$157$	−6.14901	−	9.56805i	−0.490745	−	0.763613i	−0.994993	+	0.0999453i	$0.968133\pi$
$158$	4.54721	+	5.24776i	0.361757	+	0.417489i
$159$	−6.00965	−	0.511271i	−0.476596	−	0.0405464i
$160$		−	0.990687i		−	0.0783207i
$161$	0.432196	−	6.85488i	0.0340618	−	0.540240i
$162$	−8.96445	+	0.799194i	−0.704313	+	0.0627906i
$163$	−14.2895	+	4.19578i	−1.11924	+	0.328639i	−0.788470	−	0.615073i	$-0.789127\pi$
$163$	−14.2895	+	4.19578i	−1.11924	+	0.328639i	−0.330770	+	0.943711i	$0.607308\pi$
$164$	−2.32427	+	2.01399i	−0.181495	+	0.157266i
$165$	−6.57938	+	1.33870i	−0.512204	+	0.104218i
$166$	−4.11860	+	0.592165i	−0.319665	+	0.0459609i
$167$	−12.0382	+	18.7318i	−0.931541	+	1.44951i	−0.0386407	+	0.999253i	$0.512303\pi$
$167$	−12.0382	+	18.7318i	−0.931541	+	1.44951i	−0.892901	+	0.450254i	$0.851334\pi$
$168$	−1.77752	+	1.73027i	−0.137139	+	0.133493i
$169$	8.12752	−	9.37966i	0.625194	−	0.721512i
$170$	0.476260	+	0.0684758i	0.0365275	+	0.00525186i
$171$	21.5323	+	6.95775i	1.64661	+	0.532072i
$172$	−0.0780324	+	0.265754i	−0.00594991	+	0.0202635i
$173$	−0.0580449	+	0.197683i	−0.00441307	+	0.0150295i	−0.961670	−	0.274209i	$-0.911584\pi$
$173$	−0.0580449	+	0.197683i	−0.00441307	+	0.0150295i	0.957257	+	0.289239i	$0.0934021\pi$
$174$	0.581948	+	10.0346i	0.0441174	+	0.760725i
$175$	5.69668	+	0.819059i	0.430629	+	0.0619151i
$176$	2.56239	−	2.95716i	0.193148	−	0.222904i
$177$	14.9388	+	15.3468i	1.12287	+	1.15353i
$178$	8.32842	−	12.9593i	0.624241	−	0.971338i
$179$	9.06212	−	1.30294i	0.677335	−	0.0973860i	0.204942	−	0.978774i	$-0.434299\pi$
$179$	9.06212	−	1.30294i	0.677335	−	0.0973860i	0.472393	+	0.881388i	$0.343390\pi$
$180$	2.92935	+	0.502063i	0.218341	+	0.0374215i
$181$	−4.13527	+	3.58323i	−0.307372	+	0.266339i	−0.794863	−	0.606788i	$-0.792458\pi$
$181$	−4.13527	+	3.58323i	−0.307372	+	0.266339i	0.487491	+	0.873128i	$0.337912\pi$
$182$	−1.05456	+	0.309646i	−0.0781690	+	0.0229525i
$183$	−9.50394	+	24.4692i	−0.702551	+	1.80882i
$184$	1.63802	−	4.50743i	0.120756	−	0.332292i
$185$		−	5.08083i		−	0.373550i
$186$	0.0229983	−	0.270330i	0.00168632	−	0.0198215i
$187$	1.24450	+	1.43623i	0.0910071	+	0.105028i
$188$	3.65391	+	5.68560i	0.266489	+	0.414665i
$189$	−4.21538	−	6.13280i	−0.306624	−	0.446095i
$190$	−6.28634	−	4.03998i	−0.456059	−	0.293091i
$191$	5.03496	−	11.0250i	0.364317	−	0.797743i	−0.635357	−	0.772218i	$-0.719147\pi$
$191$	5.03496	−	11.0250i	0.364317	−	0.797743i	0.999674	−	0.0255246i	$-0.00812562\pi$
$192$	−1.53123	+	0.809531i	−0.110507	+	0.0584229i
$193$	−1.81945	+	12.6545i	−0.130967	+	0.910893i	0.813331	+	0.581801i	$0.197652\pi$
$193$	−1.81945	+	12.6545i	−0.130967	+	0.910893i	−0.944298	+	0.329092i	$0.893257\pi$
$194$	−0.758443	−	1.66076i	−0.0544530	−	0.119236i
$195$	1.04345	+	0.803273i	0.0747229	+	0.0575236i
$196$	4.74840	+	1.39426i	0.339172	+	0.0995897i
$197$	−19.9545	+	9.11293i	−1.42170	+	0.649269i	−0.970045	−	0.242923i	$-0.921894\pi$
$197$	−19.9545	+	9.11293i	−1.42170	+	0.649269i	−0.451655	+	0.892192i	$0.649166\pi$
$198$	7.44540	+	9.07533i	0.529122	+	0.644956i
$199$	−3.00738	−	2.60591i	−0.213188	−	0.184728i	0.541720	−	0.840559i	$-0.317773\pi$
$199$	−3.00738	−	2.60591i	−0.213188	−	0.184728i	−0.754908	+	0.655830i	$0.772319\pi$
$200$	3.65539	+	1.66936i	0.258475	+	0.118042i
$201$	−9.77207	+	7.11191i	−0.689268	+	0.501635i
$202$	1.48349	+	10.3179i	0.104378	+	0.725966i
$203$	−6.99189	+	4.49342i	−0.490735	+	0.315376i
$204$	−0.283333	−	0.792072i	−0.0198373	−	0.0554561i
$205$	0.858385	+	2.92339i	0.0599522	+	0.204178i
$206$	0.944137			0.0657812
$207$	12.4978	+	7.12771i	0.868659	+	0.495410i
$208$	−0.767417			−0.0532108
$209$	−8.31510	−	28.3186i	−0.575168	−	1.95884i
$210$	0.827716	+	2.31392i	0.0571178	+	0.159676i
$211$	20.5417	−	13.2013i	1.41415	−	0.908818i	0.414149	−	0.910209i	$-0.364079\pi$
$211$	20.5417	−	13.2013i	1.41415	−	0.908818i	0.999999	+	0.00139133i	$0.000442876\pi$
$212$	−0.495570	−	3.44676i	−0.0340359	−	0.236725i
$213$	20.8284	−	15.1585i	1.42714	−	1.03864i
$214$	16.0094	+	7.31124i	1.09438	+	0.499786i
$215$	0.207373	+	0.179690i	0.0141427	+	0.0122547i
$216$	−1.61769	−	4.93792i	−0.110070	−	0.335983i
$217$	0.204062	−	0.0931919i	0.0138526	−	0.00632628i
$218$	7.00624	+	2.05722i	0.474522	+	0.139332i
$219$	−1.89545	−	1.45917i	−0.128083	−	0.0986013i
$220$	−1.61033	−	3.52613i	−0.108569	−	0.237732i
$221$	0.0530435	−	0.368925i	0.00356809	−	0.0248166i
$222$	−7.85304	+	4.15175i	−0.527061	+	0.278647i
$223$	12.2322	−	26.7848i	0.819131	−	1.79365i	0.257450	−	0.966292i	$-0.417118\pi$
$223$	12.2322	−	26.7848i	0.819131	−	1.79365i	0.561681	−	0.827354i	$-0.310155\pi$
$224$	−1.20483	−	0.774294i	−0.0805008	−	0.0517347i
$225$	−6.78860	+	9.96257i	−0.452573	+	0.664171i
$226$	9.19793	+	14.3123i	0.611837	+	0.952037i
$227$	12.6932	+	14.6488i	0.842480	+	0.972273i	0.999884	−	0.0152611i	$-0.00485795\pi$
$227$	12.6932	+	14.6488i	0.842480	+	0.972273i	−0.157404	+	0.987534i	$0.550312\pi$
$228$	−1.10747	+	13.0175i	−0.0733438	+	0.862107i
$229$			5.01011i			0.331077i	0.986203	+	0.165539i	$0.0529362\pi$
$229$			5.01011i			0.331077i	−0.986203	+	0.165539i	$0.947064\pi$
$230$	−3.38780	−	3.33113i	−0.223385	−	0.219648i
$231$	−3.51420	+	9.04781i	−0.231218	+	0.595302i
$232$	−5.56817	+	1.63496i	−0.365568	+	0.107341i
$233$	3.51005	−	3.04148i	0.229951	−	0.199254i	−0.532262	−	0.846579i	$-0.678658\pi$
$233$	3.51005	−	3.04148i	0.229951	−	0.199254i	0.762214	+	0.647326i	$0.224113\pi$
$234$	0.388913	−	2.26916i	0.0254240	−	0.148340i
$235$	6.62740	−	0.952876i	0.432324	−	0.0621588i
$236$	−6.68510	+	10.4022i	−0.435163	+	0.677127i
$237$	−8.38903	−	8.61815i	−0.544926	−	0.559809i
$238$	0.455509	−	0.525685i	0.0295262	−	0.0340751i
$239$	−2.60852	−	0.375049i	−0.168731	−	0.0242599i	0.0574313	−	0.998349i	$-0.481709\pi$
$239$	−2.60852	−	0.375049i	−0.168731	−	0.0242599i	−0.226163	+	0.974090i	$0.572618\pi$
$240$	0.0993461	+	1.71304i	0.00641276	+	0.110576i
$241$	−2.87433	+	9.78906i	−0.185152	+	0.630569i	0.813637	+	0.581373i	$0.197484\pi$
$241$	−2.87433	+	9.78906i	−0.185152	+	0.630569i	−0.998789	+	0.0491963i	$0.984334\pi$
$242$	1.21444	−	4.13602i	0.0780674	−	0.265873i
$243$	15.4207	−	2.28088i	0.989238	−	0.146318i
$244$	−15.0012	−	2.15685i	−0.960355	−	0.138078i
$245$	3.21064	−	3.70527i	0.205120	−	0.236721i
$246$	3.81703	−	3.71556i	0.243365	−	0.236895i
$247$	−3.12949	+	4.86959i	−0.199125	+	0.309845i
$248$	0.155044	−	0.0222920i	0.00984532	−	0.00141554i
$249$	7.06227	−	1.43695i	0.447553	−	0.0910631i
$250$	6.75228	−	5.85089i	0.427052	−	0.370043i
$251$	−1.96014	+	0.575550i	−0.123723	+	0.0363284i	−0.343008	−	0.939332i	$-0.611446\pi$
$251$	−1.96014	+	0.575550i	−0.123723	+	0.0363284i	0.219285	+	0.975661i	$0.429628\pi$
$252$	2.90008	−	3.17013i	0.182688	−	0.199700i
$253$	−1.49653	−	18.7057i	−0.0940858	−	1.17602i
$254$			15.1537i			0.950831i
$255$	−0.830389	−	0.0706454i	−0.0520010	−	0.00442398i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	−4.76670	−	7.41713i	−0.297339	−	0.462668i	0.660152	−	0.751132i	$-0.270492\pi$
$257$	−4.76670	−	7.41713i	−0.297339	−	0.462668i	−0.957491	+	0.288464i	$0.906855\pi$
$258$	0.108280	−	0.467352i	0.00674119	−	0.0290961i
$259$	−6.17905	−	3.97103i	−0.383947	−	0.246748i
$260$	−0.315828	+	0.691566i	−0.0195868	+	0.0428891i
$261$	−2.01255	−	17.2930i	−0.124574	−	1.07041i
$262$	1.77312	−	12.3323i	0.109544	−	0.761894i
$263$	−6.87563	−	15.0555i	−0.423969	−	0.928363i	−0.994267	−	0.106925i	$-0.965899\pi$
$263$	−6.87563	−	15.0555i	−0.423969	−	0.928363i	0.570298	−	0.821438i	$-0.306828\pi$
$264$	−4.13420	+	5.37031i	−0.254443	+	0.330520i
$265$	−3.31004	−	0.971915i	−0.203334	−	0.0597043i
$266$	−9.82646	+	4.48759i	−0.602499	+	0.275152i
$267$	−13.1015	+	23.2436i	−0.801798	+	1.42249i
$268$	−5.27353	−	4.56954i	−0.322132	−	0.279129i
$269$	9.85091	+	4.49876i	0.600620	+	0.274294i	0.692433	−	0.721482i	$-0.256539\pi$
$269$	9.85091	+	4.49876i	0.600620	+	0.274294i	−0.0918126	+	0.995776i	$0.529266\pi$
$270$	−5.11562	−	0.574384i	−0.311327	−	0.0349559i
$271$	0.0562958	+	0.391546i	0.00341972	+	0.0237847i	0.991460	−	0.130412i	$-0.0416301\pi$
$271$	0.0562958	+	0.391546i	0.00341972	+	0.0237847i	−0.988040	+	0.154197i	$0.950721\pi$
$272$	0.408580	−	0.262579i	0.0247738	−	0.0159212i
$273$	1.79243	−	0.641174i	0.108483	−	0.0388056i
$274$	−0.0516162	−	0.175788i	−0.00311825	−	0.0106198i
$275$	15.7241			0.948196
$276$	−2.38036	+	7.95826i	−0.143281	+	0.479031i
$277$	−17.2310			−1.03531			−0.517655	−	0.855589i	$-0.673195\pi$
$277$	−17.2310			−1.03531			−0.517655	+	0.855589i	$0.673195\pi$
$278$	−4.93045	−	16.7916i	−0.295709	−	1.00709i
$279$	−0.0126588	+	0.469745i	−0.000757860	+	0.0281229i
$280$	−1.19361	+	0.767084i	−0.0713316	+	0.0458420i
$281$	−1.06794	−	7.42768i	−0.0637079	−	0.443098i	−0.996562	−	0.0828450i	$-0.973599\pi$
$281$	−1.06794	−	7.42768i	−0.0637079	−	0.443098i	0.932855	−	0.360253i	$-0.117310\pi$
$282$	−6.88830	−	9.46482i	−0.410192	−	0.563622i
$283$	−23.3663	−	10.6710i	−1.38898	−	0.634327i	−0.426206	−	0.904626i	$-0.640150\pi$
$283$	−23.3663	−	10.6710i	−1.38898	−	0.634327i	−0.962776	+	0.270299i	$0.912877\pi$
$284$	11.2401	+	9.73964i	0.666980	+	0.577941i
$285$	11.2751	+	6.35533i	0.667881	+	0.376457i
$286$	−2.73145	+	1.24741i	−0.161514	+	0.0737610i
$287$	4.22617	+	1.24092i	0.249463	+	0.0732490i
$288$	2.56654	−	1.55335i	0.151235	−	0.0915319i
$289$	−6.96406	−	15.2492i	−0.409651	−	0.897010i
$290$	−0.818196	+	5.69068i	−0.0480461	+	0.334168i
$291$	1.47800	+	2.79564i	0.0866418	+	0.163883i
$292$	0.573709	−	1.25625i	0.0335738	−	0.0735163i
$293$	20.1565	+	12.9538i	1.17755	+	0.756768i	0.974935	−	0.222490i	$-0.0714185\pi$
$293$	20.1565	+	12.9538i	1.17755	+	0.756768i	0.202619	+	0.979258i	$0.435055\pi$
$294$	−8.35049	−	1.93470i	−0.487011	−	0.112834i
$295$	6.62285	+	10.3054i	0.385597	+	0.600001i
$296$	−3.35851	−	3.87593i	−0.195209	−	0.225284i
$297$	−13.7843	−	14.9459i	−0.799844	−	0.867252i
$298$			13.5811i			0.786733i
$299$	−2.58040	+	2.62429i	−0.149228	+	0.151767i
$300$	−6.48811	−	2.52001i	−0.374591	−	0.145493i
$301$	0.380607	−	0.111756i	0.0219378	−	0.00644153i
$302$	9.29213	−	8.05168i	0.534702	−	0.463322i
$303$	−3.59985	−	17.6924i	−0.206806	−	1.01640i
$304$	−7.46605	+	1.07346i	−0.428207	+	0.0615669i
$305$	−8.11737	+	12.6309i	−0.464800	+	0.723242i
$306$	0.569354	+	1.34119i	0.0325478	+	0.0766710i
$307$	4.57183	−	5.27617i	0.260928	−	0.301127i	−0.610136	−	0.792297i	$-0.708885\pi$
$307$	4.57183	−	5.27617i	0.260928	−	0.301127i	0.871064	+	0.491170i	$0.163431\pi$
$308$	−5.54690	−	0.797524i	−0.316064	−	0.0454432i
$309$	−1.63255	+	0.0946780i	−0.0928726	+	0.00538604i
$310$	0.0437192	−	0.148894i	0.00248309	−	0.00845662i
$311$	−5.38154	+	18.3278i	−0.305159	+	1.03928i	0.654020	+	0.756477i	$0.273081\pi$
$311$	−5.38154	+	18.3278i	−0.305159	+	1.03928i	−0.959179	+	0.282799i	$0.908737\pi$
$312$	1.32697	−	0.0769565i	0.0751252	−	0.00435680i
$313$	6.86238	+	0.986661i	0.387885	+	0.0557694i	0.333499	−	0.942751i	$-0.391771\pi$
$313$	6.86238	+	0.986661i	0.387885	+	0.0557694i	0.0543860	+	0.998520i	$0.482680\pi$
$314$	−7.44810	+	8.59556i	−0.420321	+	0.485076i
$315$	−1.66328	−	3.91810i	−0.0937152	−	0.220760i
$316$	3.75409	−	5.84148i	0.211184	−	0.328609i
$317$	9.15329	−	1.31604i	0.514100	−	0.0739164i	0.119618	−	0.992820i	$-0.461833\pi$
$317$	9.15329	−	1.31604i	0.514100	−	0.0739164i	0.394482	+	0.918904i	$0.370924\pi$
$318$	1.20255	+	5.91026i	0.0674358	+	0.331431i
$319$	−17.1611	+	14.8702i	−0.960837	+	0.832570i
$320$	−0.950558	+	0.279109i	−0.0531378	+	0.0156027i
$321$	−28.4157	−	11.0368i	−1.58601	−	0.616013i
$322$	−6.69897	+	1.51655i	−0.373319	+	0.0845142i
$323$		−	3.66340i		−	0.203837i
$324$	3.29240	+	8.37616i	0.182911	+	0.465342i
$325$	−2.01952	−	2.33065i	−0.112023	−	0.129281i
$326$	8.05163	+	12.5286i	0.445939	+	0.693894i
$327$	−12.3211	−	2.85464i	−0.681359	−	0.157862i
$328$	2.58723	+	1.66271i	0.142856	+	0.0918079i
$329$	4.02095	−	8.80465i	0.221682	−	0.485416i
$330$	3.13810	+	5.93572i	0.172747	+	0.326750i
$331$	−2.38295	+	16.5738i	−0.130979	+	0.910979i	0.813303	+	0.581841i	$0.197667\pi$
$331$	−2.38295	+	16.5738i	−0.130979	+	0.910979i	−0.944282	+	0.329138i	$0.893242\pi$
$332$	1.72852	+	3.78493i	0.0948649	+	0.207725i
$333$	13.1627	−	7.96648i	0.721312	−	0.436560i
$334$	21.3645	+	6.27319i	1.16902	+	0.343254i
$335$	−6.28820	+	2.87172i	−0.343561	+	0.156899i
$336$	2.16096	+	1.21805i	0.117890	+	0.0664499i
$337$	14.2763	+	12.3705i	0.777680	+	0.673864i	0.950373	−	0.311112i	$-0.100701\pi$
$337$	14.2763	+	12.3705i	0.777680	+	0.673864i	−0.172693	+	0.984976i	$0.555247\pi$
$338$	−11.2895	−	5.15575i	−0.614068	−	0.280436i
$339$	−17.3398	−	23.8256i	−0.941768	−	1.29403i
$340$	−0.0684758	−	0.476260i	−0.00371362	−	0.0258288i
$341$	0.515611	−	0.331363i	0.0279219	−	0.0179443i
$342$	0.609574	−	22.6203i	0.0329620	−	1.22316i
$343$	−4.82126	−	16.4197i	−0.260324	−	0.886581i
$344$	0.276973			0.0149334
$345$	6.19204	+	5.42028i	0.333368	+	0.291818i
$346$	0.206028			0.0110761
$347$	4.55189	+	15.5023i	0.244358	+	0.832209i	0.986751	+	0.162243i	$0.0518729\pi$
$347$	4.55189	+	15.5023i	0.244358	+	0.832209i	−0.742392	+	0.669965i	$0.766309\pi$
$348$	9.46422	−	3.38546i	0.507335	−	0.181480i
$349$	11.3922	−	7.32134i	0.609812	−	0.391902i	−0.198975	−	0.980005i	$-0.563761\pi$
$349$	11.3922	−	7.32134i	0.609812	−	0.391902i	0.808786	+	0.588102i	$0.200125\pi$
$350$	−0.819059	−	5.69668i	−0.0437806	−	0.304501i
$351$	−0.444936	+	3.96271i	−0.0237489	+	0.211514i
$352$	−3.55928	−	1.62547i	−0.189710	−	0.0866378i
$353$	−9.20121	−	7.97289i	−0.489731	−	0.424354i	0.374669	−	0.927158i	$-0.377756\pi$
$353$	−9.20121	−	7.97289i	−0.489731	−	0.424354i	−0.864400	+	0.502804i	$0.832302\pi$
$354$	10.5164	−	18.6573i	0.558939	−	0.991626i
$355$	13.4028	−	6.12086i	0.711348	−	0.324862i
$356$	−14.7807	−	4.34001i	−0.783376	−	0.230020i
$357$	−0.734925	+	0.954664i	−0.0388963	+	0.0505262i
$358$	−3.80325	−	8.32796i	−0.201008	−	0.440146i
$359$	3.84519	−	26.7439i	0.202941	−	1.41149i	−0.592555	−	0.805530i	$-0.701881\pi$
$359$	3.84519	−	26.7439i	0.202941	−	1.41149i	0.795496	−	0.605959i	$-0.207210\pi$
$360$	−0.343568	−	2.95214i	−0.0181076	−	0.155591i
$361$	−15.7418	+	34.4698i	−0.828518	+	1.81420i
$362$	4.60312	+	2.95825i	0.241935	+	0.155482i
$363$	−1.68519	+	7.27356i	−0.0884496	+	0.381763i
$364$	0.594206	+	0.924603i	0.0311449	+	0.0484624i
$365$	−0.895973	−	1.03401i	−0.0468974	−	0.0541225i
$366$	26.1556	+	2.22519i	1.36718	+	0.116312i
$367$			19.0718i			0.995540i	0.867309	+	0.497770i	$0.165848\pi$
$367$			19.0718i			0.995540i	−0.867309	+	0.497770i	$0.834152\pi$
$368$	−4.78633	−	0.301775i	−0.249505	−	0.0157311i
$369$	−6.22761	+	6.80751i	−0.324196	+	0.354385i
$370$	−4.87502	+	1.43143i	−0.253440	+	0.0744167i
$371$	−3.76903	+	3.26588i	−0.195678	+	0.169556i
$372$	−0.265859	+	0.0540939i	−0.0137841	+	0.00280464i
$373$	19.5863	−	2.81609i	1.01414	−	0.145811i	0.384848	−	0.922980i	$-0.374254\pi$
$373$	19.5863	−	2.81609i	1.01414	−	0.145811i	0.629292	+	0.777169i	$0.283345\pi$
$374$	1.02744	−	1.59873i	0.0531276	−	0.0826681i
$375$	−11.0890	+	10.7942i	−0.572631	+	0.557408i
$376$	4.42587	−	5.10772i	0.228247	−	0.263411i
$377$	4.40817	+	0.633800i	0.227032	+	0.0326423i
$378$	−4.69676	+	5.77244i	−0.241575	+	0.296902i
$379$	−8.21058	+	27.9627i	−0.421749	+	1.43635i	0.425407	+	0.905002i	$0.360131\pi$
$379$	−8.21058	+	27.9627i	−0.421749	+	1.43635i	−0.847156	+	0.531344i	$0.821687\pi$
$380$	−2.10527	+	7.16989i	−0.107998	+	0.367808i
$381$	−1.51962	−	26.2030i	−0.0778523	−	1.34242i
$382$	−11.9969	−	1.72490i	−0.613817	−	0.0882536i
$383$	1.56512	−	1.80624i	0.0799739	−	0.0922948i	−0.714352	−	0.699786i	$-0.753279\pi$
$383$	1.56512	−	1.80624i	0.0799739	−	0.0922948i	0.794326	+	0.607491i	$0.207824\pi$
$384$	1.20814	+	1.24113i	0.0616524	+	0.0633362i
$385$	−3.00151	+	4.67043i	−0.152971	+	0.238027i
$386$	12.6545	−	1.81945i	0.644099	−	0.0926074i
$387$	−0.140365	+	0.818978i	−0.00713516	+	0.0416310i
$388$	−1.37981	+	1.19561i	−0.0700492	+	0.0606979i
$389$	11.8783	−	3.48779i	0.602255	−	0.176838i	0.0336295	−	0.999434i	$-0.489293\pi$
$389$	11.8783	−	3.48779i	0.602255	−	0.176838i	0.568626	+	0.822596i	$0.307475\pi$
$390$	0.476762	−	1.22749i	0.0241418	−	0.0621563i
$391$	0.475903	−	2.28010i	0.0240675	−	0.115310i
$392$		−	4.94886i		−	0.249955i
$393$	−1.82930	+	21.5022i	−0.0922760	+	1.08464i
$394$	14.3656	+	16.5788i	0.723730	+	0.835229i
$395$	−3.71913	−	5.78708i	−0.187130	−	0.291180i
$396$	6.61011	−	9.70063i	0.332170	−	0.487475i
$397$	14.8999	+	9.57558i	0.747804	+	0.480584i	0.858208	−	0.513302i	$-0.171578\pi$
$397$	14.8999	+	9.57558i	0.747804	+	0.480584i	−0.110404	+	0.993887i	$0.535214\pi$
$398$	−1.65308	+	3.61973i	−0.0828613	+	0.181441i
$399$	16.5414	−	8.74510i	0.828104	−	0.437803i
$400$	0.571898	−	3.97764i	0.0285949	−	0.198882i
$401$	2.33475	+	5.11239i	0.116592	+	0.255300i	0.958927	−	0.283654i	$-0.0915467\pi$
$401$	2.33475	+	5.11239i	0.116592	+	0.255300i	−0.842335	+	0.538955i	$0.818819\pi$
$402$	9.57694	+	7.37257i	0.477654	+	0.367711i
$403$	−0.115338	−	0.0338663i	−0.00574539	−	0.00168700i
$404$	9.48202	−	4.33029i	0.471748	−	0.215440i
$405$	8.90325	+	0.480200i	0.442406	+	0.0238614i
$406$	6.28124	+	5.44273i	0.311733	+	0.270118i
$407$	−18.2541	−	8.33636i	−0.904821	−	0.413218i
$408$	−0.680163	+	0.495009i	−0.0336731	+	0.0245066i
$409$	−2.37432	−	16.5137i	−0.117402	−	0.816552i	−0.960398	−	0.278632i	$-0.910119\pi$
$409$	−2.37432	−	16.5137i	−0.117402	−	0.816552i	0.842996	−	0.537920i	$-0.180790\pi$
$410$	2.56314	−	1.64723i	0.126584	−	0.0813508i
$411$	0.106880	+	0.298788i	0.00527200	+	0.0147381i
$412$	−0.265994	−	0.905893i	−0.0131046	−	0.0446302i
$413$	17.7091			0.871408
$414$	3.31794	−	13.9997i	0.163068	−	0.688047i
$415$	4.12220			0.202351
$416$	0.216206	+	0.736331i	0.0106004	+	0.0361016i
$417$	10.2093	+	28.5406i	0.499953	+	1.39764i
$418$	−24.8289	+	15.9566i	−1.21442	+	0.780461i
$419$	2.39837	+	16.6811i	0.117168	+	0.814923i	0.960649	+	0.277764i	$0.0895933\pi$
$419$	2.39837	+	16.6811i	0.117168	+	0.814923i	−0.843481	+	0.537159i	$0.819498\pi$
$420$	1.98699	−	1.44609i	0.0969554	−	0.0705621i
$421$	21.5533	+	9.84305i	1.05044	+	0.479721i	0.864392	−	0.502819i	$-0.167704\pi$
$421$	21.5533	+	9.84305i	1.05044	+	0.479721i	0.186051	+	0.982540i	$0.440431\pi$
$422$	−18.4539	−	15.9904i	−0.898320	−	0.778398i
$423$	12.8600	+	15.6753i	0.625275	+	0.762158i
$424$	−3.16753	+	1.44656i	−0.153829	+	0.0702512i
$425$	1.87267	+	0.549864i	0.0908376	+	0.0266723i
$426$	−20.4125	−	15.7141i	−0.988990	−	0.761350i
$427$	9.01674	+	19.7439i	0.436350	+	0.955474i
$428$	2.50472	−	17.4207i	0.121070	−	0.842061i
$429$	4.59799	−	2.43087i	0.221993	−	0.117363i
$430$	0.113987	−	0.249598i	0.00549696	−	0.0120367i
$431$	13.4649	+	8.65334i	0.648579	+	0.416817i	0.823147	−	0.567829i	$-0.192216\pi$
$431$	13.4649	+	8.65334i	0.648579	+	0.416817i	−0.174567	+	0.984645i	$0.555853\pi$
$432$	−4.28215	+	2.94334i	−0.206025	+	0.141611i
$433$	−7.75522	−	12.0674i	−0.372692	−	0.579920i	0.603357	−	0.797471i	$-0.293829\pi$
$433$	−7.75522	−	12.0674i	−0.372692	−	0.579920i	−0.976049	+	0.217551i	$0.930193\pi$
$434$	−0.146908	−	0.169541i	−0.00705180	−	0.00813821i
$435$	0.844119	−	9.92206i	0.0404724	−	0.475726i
$436$		−	7.30202i		−	0.349703i
$437$	−21.4333	+	29.1407i	−1.02530	+	1.39399i
$438$	−0.866050	+	2.22977i	−0.0413814	+	0.106542i
$439$	7.16787	−	2.10468i	0.342104	−	0.100451i	−0.106168	−	0.994348i	$-0.533858\pi$
$439$	7.16787	−	2.10468i	0.342104	−	0.100451i	0.448271	+	0.893898i	$0.352040\pi$
$440$	−2.92962	+	2.53853i	−0.139664	+	0.121020i
$441$	14.6332	+	2.50800i	0.696820	+	0.119428i
$442$	−0.368925	+	0.0530435i	−0.0175480	+	0.00252302i
$443$	12.3954	−	19.2876i	0.588923	−	0.916383i	−0.411065	−	0.911606i	$-0.634843\pi$
$443$	12.3954	−	19.2876i	0.588923	−	0.916383i	0.999989	−	0.00477675i	$-0.00152049\pi$
$444$	6.19603	+	6.36525i	0.294051	+	0.302081i
$445$	−9.99400	+	11.5337i	−0.473761	+	0.546749i
$446$	−29.1461	−	4.19057i	−1.38011	−	0.198429i
$447$	−1.36191	−	23.4837i	−0.0644163	−	1.11074i
$448$	−0.403491	+	1.37417i	−0.0190632	+	0.0649232i
$449$	−0.217998	+	0.742433i	−0.0102880	+	0.0350376i	−0.964477	−	0.264167i	$-0.914903\pi$
$449$	−0.217998	+	0.742433i	−0.0102880	+	0.0350376i	0.954189	+	0.299204i	$0.0967212\pi$
$450$	11.4716	+	3.70683i	0.540776	+	0.174742i
$451$	11.9114	+	1.71260i	0.560884	+	0.0806430i
$452$	11.1412	−	12.8576i	0.524036	−	0.604769i
$453$	−15.2600	+	14.8543i	−0.716979	+	0.697918i
$454$	10.4793	−	16.3061i	0.491818	−	0.765283i
$455$	1.07776	−	0.154958i	0.0505261	−	0.00726456i
$456$	12.8022	−	2.60486i	0.599520	−	0.121984i
$457$	2.76305	−	2.39420i	0.129250	−	0.111996i	−0.587837	−	0.808979i	$-0.700020\pi$
$457$	2.76305	−	2.39420i	0.129250	−	0.111996i	0.717087	+	0.696983i	$0.245475\pi$
$458$	4.80716	−	1.41151i	0.224624	−	0.0659555i
$459$	−1.11899	−	2.26203i	−0.0522300	−	0.105582i
$460$	−2.24174	+	4.18906i	−0.104522	+	0.195316i
$461$			3.07655i			0.143289i	0.997430	+	0.0716446i	$0.0228247\pi$
$461$			3.07655i			0.143289i	−0.997430	+	0.0716446i	$0.977175\pi$
$462$	9.67138	+	0.822792i	0.449953	+	0.0382798i
$463$	−5.05378	−	5.83237i	−0.234869	−	0.271053i	0.626064	−	0.779772i	$-0.284665\pi$
$463$	−5.05378	−	5.83237i	−0.234869	−	0.271053i	−0.860933	+	0.508718i	$0.830119\pi$
$464$	3.13747	+	4.88200i	0.145653	+	0.226641i
$465$	−0.0606658	+	0.261844i	−0.00281331	+	0.0121427i
$466$	−3.90718	−	2.51099i	−0.180996	−	0.116319i
$467$	2.39118	−	5.23595i	0.110651	−	0.242291i	−0.846204	−	0.532860i	$-0.821117\pi$
$467$	2.39118	−	5.23595i	0.110651	−	0.242291i	0.956854	+	0.290569i	$0.0938446\pi$
$468$	−2.28682	+	0.266138i	−0.105708	+	0.0123022i
$469$	−1.42223	+	9.89185i	−0.0656727	+	0.456763i
$470$	−2.78143	−	6.09048i	−0.128298	−	0.280933i
$471$	12.0169	−	15.6099i	0.553709	−	0.719265i
$472$	11.8643	+	3.48366i	0.546097	+	0.160349i
$473$	0.985826	−	0.450212i	0.0453283	−	0.0207007i
$474$	−5.90559	+	10.4772i	−0.271253	+	0.481235i
$475$	−22.9076	−	19.8496i	−1.05107	−	0.910761i
$476$	−0.632723	−	0.288955i	−0.0290008	−	0.0132442i
$477$	−2.67207	−	10.0991i	−0.122346	−	0.462406i
$478$	0.375049	+	2.60852i	0.0171543	+	0.119311i
$479$	−15.7608	+	10.1288i	−0.720129	+	0.462799i	−0.848682	−	0.528904i	$-0.822603\pi$
$479$	−15.7608	+	10.1288i	−0.720129	+	0.462799i	0.128553	+	0.991703i	$0.458967\pi$
$480$	1.61566	−	0.577942i	0.0737446	−	0.0263793i
$481$	1.10883	+	3.77634i	0.0505584	+	0.172186i
$482$	10.2023			0.464703
$483$	11.4314	−	3.29411i	0.520147	−	0.149887i
$484$	−4.31063			−0.195938
$485$	0.509583	+	1.73548i	0.0231390	+	0.0788040i
$486$	−6.53299	−	14.1534i	−0.296343	−	0.642013i
$487$	10.0131	−	6.43504i	0.453737	−	0.291599i	−0.293741	−	0.955885i	$-0.594900\pi$
$487$	10.0131	−	6.43504i	0.453737	−	0.291599i	0.747479	+	0.664286i	$0.231264\pi$
$488$	2.15685	+	15.0012i	0.0976361	+	0.679074i
$489$	−15.1788	−	20.8563i	−0.686410	−	0.943156i
$490$	−4.45972	−	2.03669i	−0.201470	−	0.0920082i
$491$	−3.89586	−	3.37578i	−0.175818	−	0.152347i	0.562507	−	0.826793i	$-0.309837\pi$
$491$	−3.89586	−	3.37578i	−0.175818	−	0.152347i	−0.738324	+	0.674446i	$0.764383\pi$
$492$	−4.64043	−	2.61562i	−0.209207	−	0.117921i
$493$	−2.56382	+	1.17086i	−0.115468	+	0.0527327i
$494$	5.55402	+	1.63081i	0.249887	+	0.0733735i
$495$	−6.02146	−	9.94903i	−0.270645	−	0.447176i
$496$	−0.0650700	−	0.142484i	−0.00292173	−	0.00639770i
$497$	3.03139	−	21.0837i	0.135976	−	0.945735i
$498$	−3.36842	−	6.37137i	−0.150942	−	0.285508i
$499$	−6.44830	+	14.1198i	−0.288666	+	0.632090i	−0.997296	−	0.0734905i	$-0.976586\pi$
$499$	−6.44830	+	14.1198i	−0.288666	+	0.632090i	0.708630	+	0.705580i	$0.249313\pi$
$500$	−7.51622	−	4.83038i	−0.336136	−	0.216021i
$501$	−37.5715	−	8.70483i	−1.67857	−	0.388903i
$502$	1.10447	+	1.71859i	0.0492950	+	0.0767045i
$503$	−0.00837455	−	0.00966474i	−0.000373403	−	0.000430930i	0.755563	−	0.655076i	$-0.227363\pi$
$503$	−0.00837455	−	0.00966474i	−0.000373403	−	0.000430930i	−0.755936	+	0.654645i	$0.772818\pi$
$504$	−3.85877	−	1.88948i	−0.171883	−	0.0841641i
$505$		−	10.3269i		−	0.459543i
$506$	−17.5264	+	6.70592i	−0.779144	+	0.298115i
$507$	20.0382	+	7.78292i	0.889929	+	0.345652i
$508$	14.5399	−	4.26930i	0.645104	−	0.189420i
$509$	−21.0985	+	18.2819i	−0.935174	+	0.810333i	−0.982060	−	0.188567i	$-0.939616\pi$
$509$	−21.0985	+	18.2819i	−0.935174	+	0.810333i	0.0468863	+	0.998900i	$0.485070\pi$
$510$	0.166164	+	0.816656i	0.00735786	+	0.0361621i
$511$	−1.95778	+	0.281486i	−0.0866070	+	0.0124522i
$512$	−0.540641	+	0.841254i	−0.0238932	+	0.0371785i
$513$	1.21432	+	39.1749i	0.0536134	+	1.72961i
$514$	−5.77375	+	6.66326i	−0.254669	+	0.293904i
$515$	−0.925825	−	0.133113i	−0.0407967	−	0.00586568i
$516$	−0.478927	+	0.0277749i	−0.0210836	+	0.00122272i
$517$	7.45046	−	25.3739i	0.327671	−	1.11594i
$518$	−2.06934	+	7.04752i	−0.0909216	+	0.309650i
$519$	−0.356253	+	0.0206605i	−0.0156378	+	0.000906895i
$520$	0.752532	+	0.108198i	0.0330007	+	0.00474478i
$521$	8.85887	−	10.2237i	0.388114	−	0.447907i	−0.527748	−	0.849401i	$-0.676963\pi$
$521$	8.85887	−	10.2237i	0.388114	−	0.447907i	0.915862	+	0.401494i	$0.131509\pi$
$522$	−16.0255	+	6.80303i	−0.701418	+	0.297760i
$523$	6.32151	−	9.83647i	0.276421	−	0.430119i	−0.675090	−	0.737736i	$-0.735895\pi$
$523$	6.32151	−	9.83647i	0.276421	−	0.430119i	0.951510	+	0.307617i	$0.0995315\pi$
$524$	−12.3323	+	1.77312i	−0.538741	+	0.0774592i
$525$	1.98754	+	9.76826i	0.0867432	+	0.426322i
$526$	−12.5086	+	10.8387i	−0.545400	+	0.472592i
$527$	0.0729947	−	0.0214332i	0.00317970	−	0.000933644i
$528$	6.31752	+	2.45375i	0.274935	+	0.106786i
$529$	−17.1257	+	15.3528i	−0.744597	+	0.667515i
$530$			3.44978i			0.149849i
$531$	−16.3134	+	33.3158i	−0.707941	+	1.44578i
$532$	7.07425	+	8.16412i	0.306708	+	0.353959i
$533$	−1.27599	−	1.98548i	−0.0552694	−	0.0860008i
$534$	25.9932	+	6.02230i	1.12484	+	0.260610i
$535$	−14.6680	−	9.42658i	−0.634155	−	0.407547i
$536$	−2.89872	+	6.34731i	−0.125206	+	0.274162i
$537$	7.41150	+	14.0189i	0.319830	+	0.604959i
$538$	1.54121	−	10.7193i	0.0664461	−	0.462143i
$539$	−8.04423	−	17.6144i	−0.346489	−	0.758706i
$540$	0.890118	+	5.07022i	0.0383046	+	0.218188i
$541$	−28.4755	−	8.36116i	−1.22426	−	0.359474i	−0.395177	−	0.918605i	$-0.629317\pi$
$541$	−28.4755	−	8.36116i	−1.22426	−	0.359474i	−0.829080	+	0.559130i	$0.811135\pi$
$542$	0.359825	−	0.164327i	0.0154558	−	0.00705843i
$543$	−8.25612	−	4.65364i	−0.354304	−	0.199707i
$544$	−0.367053	−	0.318053i	−0.0157373	−	0.0136364i
$545$	−6.58030	−	3.00512i	−0.281869	−	0.128725i
$546$	−1.12019	−	1.53919i	−0.0479396	−	0.0658711i
$547$	−1.34391	−	9.34710i	−0.0574615	−	0.399653i	−0.998172	−	0.0604420i	$-0.980749\pi$
$547$	−1.34391	−	9.34710i	−0.0574615	−	0.399653i	0.940710	−	0.339211i	$-0.110160\pi$
$548$	−0.154126	+	0.0990507i	−0.00658393	+	0.00423124i
$549$	−45.4500	−	1.22479i	−1.93976	−	0.0522729i
$550$	−4.42998	−	15.0871i	−0.188895	−	0.643317i
$551$	43.7728			1.86479
$552$	8.30652	+	0.0418409i	0.353549	+	0.00178087i
$553$	−9.94473			−0.422893
$554$	4.85453	+	16.5330i	0.206249	+	0.702421i
$555$	8.28607	−	2.96402i	0.351724	−	0.125816i
$556$	−14.7223	+	9.46147i	−0.624366	+	0.401256i
$557$	3.06304	+	21.3039i	0.129785	+	0.902677i	0.945824	+	0.324680i	$0.105256\pi$
$557$	3.06304	+	21.3039i	0.129785	+	0.902677i	−0.816039	+	0.577997i	$0.803834\pi$
$558$	0.454284	−	0.120197i	0.0192314	−	0.00508833i
$559$	−0.193346	−	0.0882981i	−0.00817766	−	0.00373461i
$560$	1.07229	+	0.929143i	0.0453125	+	0.0392635i
$561$	−1.61627	+	2.86746i	−0.0682390	+	0.121064i
$562$	−6.82593	+	3.11730i	−0.287935	+	0.131495i
$563$	−26.8949	−	7.89705i	−1.13348	−	0.332821i	−0.339408	−	0.940639i	$-0.610227\pi$
$563$	−26.8949	−	7.89705i	−1.13348	−	0.332821i	−0.794076	+	0.607819i	$0.792045\pi$
$564$	−7.14077	+	9.27582i	−0.300681	+	0.390583i
$565$	−7.00164	−	15.3315i	−0.294561	−	0.644999i
$566$	−3.65573	+	25.4262i	−0.153662	+	1.06874i
$567$	7.54253	−	10.4524i	0.316756	−	0.438959i
$568$	6.17840	−	13.5288i	0.259240	−	0.567656i
$569$	33.4384	+	21.4895i	1.40181	+	0.900888i	0.999891	−	0.0147870i	$-0.00470703\pi$
$569$	33.4384	+	21.4895i	1.40181	+	0.900888i	0.401919	+	0.915675i	$0.368343\pi$
$570$	2.92132	−	12.6089i	0.122361	−	0.528129i
$571$	−7.45842	−	11.6055i	−0.312125	−	0.485676i	0.649380	−	0.760464i	$-0.275029\pi$
$571$	−7.45842	−	11.6055i	−0.312125	−	0.485676i	−0.961505	+	0.274788i	$0.911392\pi$
$572$	1.96642	+	2.26937i	0.0822202	+	0.0948872i
$573$	20.9174	+	1.77955i	0.873839	+	0.0743418i
$574$		−	4.40459i		−	0.183844i
$575$	−11.6791	−	15.3303i	−0.487053	−	0.639316i
$576$	−2.21350	−	2.02495i	−0.0922293	−	0.0843727i
$577$	35.6162	−	10.4579i	1.48272	−	0.435366i	0.562511	−	0.826790i	$-0.309836\pi$
$577$	35.6162	−	10.4579i	1.48272	−	0.435366i	0.920211	+	0.391424i	$0.128017\pi$
$578$	−12.6695	+	10.9782i	−0.526981	+	0.456631i
$579$	−21.6991	+	4.41508i	−0.901783	+	0.183485i
$580$	5.69068	−	0.818196i	0.236293	−	0.0339737i
$581$	3.22180	−	5.01322i	0.133663	−	0.207983i
$582$	2.26599	−	2.20575i	0.0939285	−	0.0914314i
$583$	−8.92278	+	10.2974i	−0.369544	+	0.426476i
$584$	−1.36699	−	0.196544i	−0.0565666	−	0.00813304i
$585$	−0.701298	+	2.17032i	−0.0289951	+	0.0897316i
$586$	6.75032	−	22.9895i	0.278853	−	0.949687i
$587$	−0.357155	+	1.21636i	−0.0147414	+	0.0502045i	−0.966535	−	0.256534i	$-0.917419\pi$
$587$	−0.357155	+	1.21636i	−0.0147414	+	0.0502045i	0.951794	+	0.306738i	$0.0992377\pi$
$588$	0.496272	+	8.55731i	0.0204659	+	0.352897i
$589$	−1.16947	−	0.168145i	−0.0481873	−	0.00692828i
$590$	8.02204	−	9.25793i	0.330262	−	0.381143i
$591$	−26.5028	−	27.2266i	−1.09018	−	1.11995i
$592$	−2.77272	+	4.31444i	−0.113958	+	0.177322i
$593$	19.7497	−	2.83958i	0.811023	−	0.116608i	0.275688	−	0.961247i	$-0.411094\pi$
$593$	19.7497	−	2.83958i	0.811023	−	0.116608i	0.535335	+	0.844640i	$0.320185\pi$
$594$	−10.4571	+	17.4367i	−0.429058	+	0.715435i
$595$	−0.520789	+	0.451267i	−0.0213503	+	0.0185001i
$596$	13.0310	−	3.82624i	0.533770	−	0.156729i
$597$	2.49542	−	6.42482i	0.102131	−	0.262950i
$598$	3.24497	+	1.73652i	0.132697	+	0.0710117i
$599$		−	26.1869i		−	1.06997i	−0.844862	−	0.534985i	$-0.820317\pi$
$599$		−	26.1869i		−	1.06997i	0.844862	−	0.534985i	$-0.179683\pi$
$600$	−0.590017	+	6.93526i	−0.0240874	+	0.283131i
$601$	−14.9635	−	17.2688i	−0.610375	−	0.704410i	0.363475	−	0.931604i	$-0.381590\pi$
$601$	−14.9635	−	17.2688i	−0.610375	−	0.704410i	−0.973849	+	0.227194i	$0.927045\pi$
$602$	−0.214459	−	0.333704i	−0.00874069	−	0.0136008i
$603$	−17.2992	−	11.7879i	−0.704479	−	0.480039i
$604$	−10.3434	−	6.64731i	−0.420868	−	0.270475i
$605$	−1.77402	+	3.88457i	−0.0721243	+	0.157930i
$606$	−15.9616	+	8.43857i	−0.648394	+	0.342793i
$607$	2.88275	−	20.0500i	0.117007	−	0.813804i	−0.843814	−	0.536636i	$-0.819695\pi$
$607$	2.88275	−	20.0500i	0.117007	−	0.813804i	0.960821	−	0.277168i	$-0.0893959\pi$
$608$	3.13340	+	6.86120i	0.127076	+	0.278258i
$609$	−11.4070	−	8.78139i	−0.462234	−	0.355840i
$610$	14.4062	+	4.23003i	0.583289	+	0.171269i
$611$	−4.71787	+	2.15458i	−0.190865	+	0.0871650i
$612$	1.12646	−	0.924149i	0.0455345	−	0.0373565i
$613$	7.49497	+	6.49443i	0.302719	+	0.262308i	0.792952	−	0.609284i	$-0.208543\pi$
$613$	7.49497	+	6.49443i	0.302719	+	0.262308i	−0.490233	+	0.871591i	$0.663088\pi$
$614$	−6.35048	−	2.90017i	−0.256284	−	0.117041i
$615$	−4.26685	+	3.10533i	−0.172056	+	0.125219i
$616$	0.797524	+	5.54690i	0.0321332	+	0.223491i
$617$	21.7944	−	14.0064i	0.877410	−	0.563877i	−0.0226007	−	0.999745i	$-0.507195\pi$
$617$	21.7944	−	14.0064i	0.877410	−	0.563877i	0.900011	+	0.435867i	$0.143558\pi$
$618$	0.550786	+	1.53975i	0.0221558	+	0.0619377i
$619$	−4.36353	−	14.8608i	−0.175385	−	0.597307i	−0.999522	−	0.0309160i	$-0.990158\pi$
$619$	−4.36353	−	14.8608i	−0.175385	−	0.597307i	0.824137	−	0.566391i	$-0.191661\pi$
$620$	−0.155180			−0.00623218
$621$	−4.33331	+	24.5402i	−0.173890	+	0.984765i
$622$	19.1016			0.765903
$623$	6.21567	+	21.1686i	0.249025	+	0.848103i
$624$	−0.447691	−	1.25154i	−0.0179220	−	0.0501018i
$625$	9.45682	−	6.07753i	0.378273	−	0.243101i
$626$	−0.986661	−	6.86238i	−0.0394349	−	0.274276i
$627$	41.3327	−	30.0811i	1.65067	−	1.20132i
$628$	10.3458	+	4.72475i	0.412841	+	0.188538i
$629$	−1.88246	−	1.63116i	−0.0750586	−	0.0650387i
$630$	−3.29079	+	2.69976i	−0.131108	+	0.107561i
$631$	8.26279	−	3.77349i	0.328936	−	0.150220i	−0.244100	−	0.969750i	$-0.578493\pi$
$631$	8.26279	−	3.77349i	0.328936	−	0.150220i	0.573037	+	0.819530i	$0.305765\pi$
$632$	−6.66251	−	1.95629i	−0.265020	−	0.0778170i
$633$	33.5129	+	25.7991i	1.33202	+	1.02542i
$634$	−3.84151	−	8.41174i	−0.152566	−	0.334073i
$635$	2.13652	−	14.8598i	0.0847852	−	0.589694i
$636$	5.33205	−	2.81895i	0.211430	−	0.111779i
$637$	−1.57768	+	3.45464i	−0.0625100	+	0.136878i
$638$	19.1027	+	12.2765i	0.756282	+	0.486033i
$639$	36.8720	+	25.1250i	1.45864	+	0.993929i
$640$	0.535606	+	0.833419i	0.0211717	+	0.0329438i
$641$	−28.9540	−	33.4147i	−1.14361	−	1.31980i	−0.940167	−	0.340715i	$-0.889331\pi$
$641$	−28.9540	−	33.4147i	−1.14361	−	1.31980i	−0.203447	−	0.979086i	$-0.565214\pi$
$642$	−2.58408	+	30.3741i	−0.101985	+	1.19877i
$643$		−	19.9105i		−	0.785192i	−0.919711	−	0.392596i	$-0.871577\pi$
$643$		−	19.9105i		−	0.785192i	0.919711	−	0.392596i	$-0.128423\pi$
$644$	3.34244	+	6.00035i	0.131711	+	0.236447i
$645$	−0.172071	+	0.443021i	−0.00677529	+	0.0174439i
$646$	−3.51501	+	1.03210i	−0.138296	+	0.0406074i
$647$	−12.5068	+	10.8372i	−0.491694	+	0.426055i	−0.865090	−	0.501617i	$-0.832739\pi$
$647$	−12.5068	+	10.8372i	−0.491694	+	0.426055i	0.373396	+	0.927672i	$0.378193\pi$
$648$	7.10929	−	5.51887i	0.279279	−	0.216802i
$649$	47.8909	−	6.88567i	1.87988	−	0.270286i
$650$	−1.66728	+	2.59434i	−0.0653960	+	0.101758i
$651$	0.271027	+	0.278429i	0.0106224	+	0.0109125i
$652$	9.75268	−	11.2552i	0.381945	−	0.440788i
$653$	27.5008	+	3.95401i	1.07619	+	0.154732i	0.657542	−	0.753417i	$-0.271596\pi$
$653$	27.5008	+	3.95401i	1.07619	+	0.154732i	0.418645	+	0.908150i	$0.362505\pi$
$654$	0.732246	+	12.6263i	0.0286331	+	0.493726i
$655$	−3.47746	+	11.8431i	−0.135876	+	0.462750i
$656$	0.866453	−	2.95087i	0.0338293	−	0.115212i
$657$	1.27393	−	3.94244i	0.0497005	−	0.153809i
$658$	−9.58084	−	1.37752i	−0.373500	−	0.0537012i
$659$	4.23361	−	4.88584i	0.164918	−	0.190325i	−0.667275	−	0.744811i	$-0.732540\pi$
$659$	4.23361	−	4.88584i	0.164918	−	0.190325i	0.832193	+	0.554486i	$0.187085\pi$
$660$	4.81117	−	4.68327i	0.187275	−	0.182296i
$661$	−22.8371	+	35.5351i	−0.888258	+	1.38216i	0.0355770	+	0.999367i	$0.488673\pi$
$661$	−22.8371	+	35.5351i	−0.888258	+	1.38216i	−0.923835	+	0.382790i	$0.874963\pi$
$662$	16.5738	−	2.38295i	0.644159	−	0.0926161i
$663$	0.632606	−	0.128716i	0.0245684	−	0.00499890i
$664$	3.14464	−	2.72484i	0.122036	−	0.105744i
$665$	10.2686	−	3.01512i	0.398198	−	0.116921i
$666$	−11.3521	−	10.3851i	−0.439887	−	0.402415i
$667$	27.2443	+	5.68642i	1.05490	+	0.220179i
$668$		−	22.2665i		−	0.861516i
$669$	50.8181	+	4.32335i	1.96474	+	0.167150i
$670$	4.52699	+	5.22442i	0.174893	+	0.201837i
$671$	32.0609	+	49.8877i	1.23770	+	1.92589i
$672$	0.559894	−	2.41659i	0.0215984	−	0.0932221i
$673$	−8.60902	−	5.53268i	−0.331853	−	0.213269i	0.364094	−	0.931362i	$-0.381379\pi$
$673$	−8.60902	−	5.53268i	−0.331853	−	0.213269i	−0.695947	+	0.718093i	$0.745015\pi$
$674$	7.84730	−	17.1832i	0.302267	−	0.661872i
$675$	−20.2078	−	5.25928i	−0.777797	−	0.202430i
$676$	−1.76628	+	12.2847i	−0.0679338	+	0.472490i
$677$	−16.0588	−	35.1640i	−0.617192	−	1.35146i	−0.917545	−	0.397633i	$-0.869832\pi$
$677$	−16.0588	−	35.1640i	−0.617192	−	1.35146i	0.300353	−	0.953828i	$-0.402896\pi$
$678$	−17.9753	+	23.3498i	−0.690338	+	0.896746i
$679$	2.50888	+	0.736673i	0.0962819	+	0.0282709i
$680$	−0.437676	+	0.199880i	−0.0167841	+	0.00766505i
$681$	−16.4851	+	29.2465i	−0.631709	+	1.12073i
$682$	−0.463205	−	0.401370i	−0.0177370	−	0.0153692i
$683$	−31.8935	−	14.5653i	−1.22037	−	0.557325i	−0.302100	−	0.953276i	$-0.597688\pi$
$683$	−31.8935	−	14.5653i	−1.22037	−	0.557325i	−0.918272	+	0.395951i	$0.870415\pi$
$684$	−21.8757	+	5.78798i	−0.836439	+	0.221309i
$685$	0.0258307	+	0.179656i	0.000986939	+	0.00686431i
$686$	−14.3963	+	9.25194i	−0.549653	+	0.353241i
$687$	−8.17073	+	2.92277i	−0.311733	+	0.111511i
$688$	−0.0780324	−	0.265754i	−0.00297496	−	0.0101318i
$689$	2.67230			0.101807
$690$	3.45622	−	7.46829i	0.131576	−	0.284313i
$691$	−22.4532			−0.854161			−0.427081	−	0.904214i	$-0.640458\pi$
$691$	−22.4532			−0.854161			−0.427081	+	0.904214i	$0.640458\pi$
$692$	−0.0580449	−	0.197683i	−0.00220654	−	0.00751477i
$693$	−16.8057	−	0.452883i	−0.638397	−	0.0172036i
$694$	13.5920	−	8.73502i	0.515944	−	0.331577i
$695$	2.46738	+	17.1610i	0.0935932	+	0.650955i
$696$	−5.91471	−	8.12706i	−0.224196	−	0.308055i
$697$	1.35870	+	0.620499i	0.0514645	+	0.0235031i
$698$	−10.2343	−	8.86810i	−0.387375	−	0.335663i
$699$	7.00788	+	3.95005i	0.265062	+	0.149405i
$700$	−5.23517	+	2.39082i	−0.197871	+	0.0903646i
$701$	−3.40079	−	0.998563i	−0.128446	−	0.0377152i	0.216878	−	0.976199i	$-0.430413\pi$
$701$	−3.40079	−	0.998563i	−0.128446	−	0.0377152i	−0.345324	+	0.938484i	$0.612231\pi$
$702$	3.92755	−	0.689513i	0.148236	−	0.0260240i
$703$	16.0699	+	35.1882i	0.606089	+	1.32715i
$704$	−0.556861	+	3.87305i	−0.0209875	+	0.145971i
$705$	5.42025	+	10.2524i	0.204139	+	0.386128i
$706$	−5.05765	+	11.0747i	−0.190347	+	0.416802i
$707$	−12.5591	−	8.07126i	−0.472334	−	0.303551i
$708$	−20.8644	−	4.83401i	−0.784132	−	0.181673i
$709$	11.1532	+	17.3547i	0.418867	+	0.651770i	0.985002	−	0.172543i	$-0.0551982\pi$
$709$	11.1532	+	17.3547i	0.418867	+	0.651770i	−0.566135	+	0.824313i	$0.691562\pi$
$710$	−9.64894	−	11.1355i	−0.362118	−	0.417907i
$711$	9.16096	−	18.7089i	0.343563	−	0.701637i
$712$			15.4047i			0.577316i
$713$	−0.706037	−	0.256577i	−0.0264413	−	0.00960887i
$714$	1.12305	+	0.436195i	0.0420289	+	0.0163242i
$715$	2.85434	−	0.838111i	0.106746	−	0.0313436i
$716$	−6.91912	+	5.99545i	−0.258580	+	0.224061i
$717$	−0.910096	−	4.47290i	−0.0339882	−	0.167044i
$718$	−26.7439	+	3.84519i	−0.998073	+	0.143501i
$719$	−8.91727	+	13.8755i	−0.332558	+	0.517470i	−0.966756	−	0.255700i	$-0.917694\pi$
$719$	−8.91727	+	13.8755i	−0.332558	+	0.517470i	0.634198	+	0.773171i	$0.281330\pi$
$720$	−2.73576	+	1.16136i	−0.101956	+	0.0432815i
$721$	−0.885485	+	1.02190i	−0.0329772	+	0.0380577i
$722$	37.5085	+	5.39291i	1.39592	+	0.200703i
$723$	−17.6413	+	1.02309i	−0.656087	+	0.0380491i
$724$	1.54157	−	5.25010i	0.0572919	−	0.195118i
$725$	−6.57016	+	22.3759i	−0.244010	+	0.831020i
$726$	7.45370	−	0.432269i	0.276633	−	0.0160430i
$727$	26.2884	+	3.77971i	0.974984	+	0.140182i	0.611350	−	0.791360i	$-0.290627\pi$
$727$	26.2884	+	3.77971i	0.974984	+	0.140182i	0.363634	+	0.931542i	$0.381536\pi$
$728$	0.719743	−	0.830627i	0.0266754	−	0.0307851i
$729$	12.7158	+	23.8182i	0.470956	+	0.882157i
$730$	−0.739699	+	1.15099i	−0.0273775	+	0.0426002i
$731$	0.133151	−	0.0191443i	0.00492478	−	0.000708076i
$732$	−5.23383	−	25.7230i	−0.193448	−	0.950750i
$733$	21.9088	−	18.9841i	0.809221	−	0.701194i	−0.148494	−	0.988913i	$-0.547443\pi$
$733$	21.9088	−	18.9841i	0.809221	−	0.701194i	0.957715	+	0.287720i	$0.0928971\pi$
$734$	18.2993	−	5.37315i	0.675438	−	0.198327i
$735$	7.91575	+	3.07451i	0.291977	+	0.113405i
$736$	1.05891	+	4.67747i	0.0390321	+	0.172414i
$737$			27.3036i			1.00574i
$738$	8.28628	+	4.05745i	0.305022	+	0.149357i
$739$	8.89595	+	10.2665i	0.327243	+	0.377659i	0.895401	−	0.445261i	$-0.146889\pi$
$739$	8.89595	+	10.2665i	0.327243	+	0.377659i	−0.568158	+	0.822920i	$0.692344\pi$
$740$	2.74690	+	4.27426i	0.100978	+	0.157125i
$741$	−9.76724	−	2.26295i	−0.358809	−	0.0831314i
$742$	4.19545	+	2.69625i	0.154020	+	0.0989826i
$743$	−11.0460	+	24.1874i	−0.405239	+	0.887350i	0.591473	+	0.806325i	$0.298547\pi$
$743$	−11.0460	+	24.1874i	−0.405239	+	0.887350i	−0.996712	+	0.0810253i	$0.974181\pi$
$744$	0.126804	+	0.239850i	0.00464885	+	0.00879331i
$745$	1.91479	−	13.3177i	0.0701527	−	0.487922i
$746$	−8.22011	−	17.9995i	−0.300960	−	0.659010i
$747$	6.46340	+	10.6792i	0.236484	+	0.390733i
$748$	−1.82343	−	0.535407i	−0.0666711	−	0.0195764i
$749$	−22.9283	+	10.4710i	−0.837781	+	0.382602i
$750$	13.4810	+	7.59871i	0.492258	+	0.277466i
$751$	−28.8881	−	25.0316i	−1.05414	−	0.913418i	−0.0577519	−	0.998331i	$-0.518393\pi$
$751$	−28.8881	−	25.0316i	−1.05414	−	0.913418i	−0.996388	+	0.0849132i	$0.972939\pi$
$752$	−6.14774	−	2.80758i	−0.224185	−	0.102382i
$753$	−2.08213	−	2.86094i	−0.0758772	−	0.104258i
$754$	−0.633800	−	4.40817i	−0.0230816	−	0.160536i
$755$	−10.2471	+	6.58541i	−0.372930	+	0.239668i
$756$	6.86185	+	2.88023i	0.249563	+	0.104753i
$757$	12.6565	+	43.1040i	0.460008	+	1.56664i	0.784111	+	0.620621i	$0.213119\pi$
$757$	12.6565	+	43.1040i	0.460008	+	1.56664i	−0.324103	+	0.946022i	$0.605062\pi$
$758$	29.1432			1.05853
$759$	29.6332	−	13.3531i	1.07562	−	0.484686i
$760$	7.47259			0.271059
$761$	−5.34989	−	18.2201i	−0.193933	−	0.660476i	−0.997838	−	0.0657185i	$-0.979066\pi$
$761$	−5.34989	−	18.2201i	−0.193933	−	0.660476i	0.803905	−	0.594758i	$-0.202752\pi$
$762$	−24.7135	+	8.84031i	−0.895276	+	0.320251i
$763$	−8.79766	+	5.65391i	−0.318497	+	0.204685i
$764$	1.72490	+	11.9969i	0.0624047	+	0.434034i
$765$	−0.369216	−	1.39545i	−0.0133490	−	0.0504527i
$766$	−2.17402	−	0.992843i	−0.0785507	−	0.0358729i
$767$	−7.17147	−	6.21412i	−0.258947	−	0.224379i
$768$	0.850486	−	1.50887i	0.0306893	−	0.0544465i
$769$	−48.7532	+	22.2648i	−1.75808	+	0.802890i	−0.772218	+	0.635358i	$0.780853\pi$
$769$	−48.7532	+	22.2648i	−1.75808	+	0.802890i	−0.985867	+	0.167532i	$0.946420\pi$
$770$	5.32687	+	1.56411i	0.191967	+	0.0563666i
$771$	9.31546	−	12.1007i	0.335488	−	0.435797i
$772$	−5.31094	−	11.6293i	−0.191145	−	0.418549i
$773$	−4.53689	+	31.5548i	−0.163181	+	1.13495i	0.729410	+	0.684077i	$0.239795\pi$
$773$	−4.53689	+	31.5548i	−0.163181	+	1.13495i	−0.892590	+	0.450869i	$0.851114\pi$
$774$	0.825349	−	0.0960535i	0.0296666	−	0.00345257i
$775$	0.261486	−	0.572576i	0.00939287	−	0.0205675i
$776$	1.53592	+	0.987074i	0.0551362	+	0.0354339i
$777$	2.87146	−	12.3937i	0.103013	−	0.444622i
$778$	−6.69303	−	10.4146i	−0.239957	−	0.373380i
$779$	−15.1912	−	17.5315i	−0.544280	−	0.628133i
$780$	−1.31209	−	0.111626i	−0.0469802	−	0.00399684i
$781$		−	58.1956i		−	2.08240i
$782$	−2.32182	+	0.185754i	−0.0830282	+	0.00664255i
$783$	27.0282	−	13.3705i	0.965911	−	0.477821i
$784$	−4.74840	+	1.39426i	−0.169586	+	0.0497949i
$785$	8.51552	−	7.37874i	0.303932	−	0.263358i
$786$	21.1466	−	4.30267i	0.754274	−	0.153471i
$787$	−34.7521	+	4.99659i	−1.23878	+	0.178109i	−0.730397	−	0.683023i	$-0.760665\pi$
$787$	−34.7521	+	4.99659i	−1.23878	+	0.178109i	−0.508381	+	0.861132i	$0.669756\pi$
$788$	11.8600	−	18.4545i	0.422495	−	0.657415i
$789$	20.5422	−	19.9961i	0.731323	−	0.711881i
$790$	−4.50486	+	5.19889i	−0.160276	+	0.184968i
$791$	−24.1177	−	3.46760i	−0.857525	−	0.123294i
$792$	−11.1700	−	3.60937i	−0.396907	−	0.128253i
$793$	3.27671	−	11.1595i	0.116359	−	0.396284i
$794$	4.98992	−	16.9941i	0.177085	−	0.603098i
$795$	−0.345944	−	5.96517i	−0.0122694	−	0.211563i
$796$	3.93883	+	0.566319i	0.139608	+	0.0200726i
$797$	26.7852	−	30.9118i	0.948782	−	1.09495i	−0.0465960	−	0.998914i	$-0.514837\pi$
$797$	26.7852	−	30.9118i	0.948782	−	1.09495i	0.995378	−	0.0960386i	$-0.0306172\pi$
$798$	−13.0511	−	13.4075i	−0.462004	−	0.474622i
$799$	1.77463	−	2.76138i	0.0627820	−	0.0976907i
$800$	−3.97764	+	0.571898i	−0.140631	+	0.0202196i
$801$	−45.5500	−	7.80683i	−1.60943	−	0.275841i
$802$	4.24753	−	3.68050i	0.149985	−	0.129963i
$803$	−5.18499	+	1.52245i	−0.182974	+	0.0537261i
$804$	4.37580	−	11.2661i	0.154322	−	0.397325i
$805$	6.78285	−	0.542653i	0.239064	−	0.0191260i
$806$			0.120207i			0.00423411i
$807$	−1.59004	+	18.6898i	−0.0559719	+	0.657913i
$808$	−6.82628	−	7.87795i	−0.240148	−	0.277145i
$809$	9.68844	+	15.0755i	0.340627	+	0.530026i	0.968734	−	0.248101i	$-0.0798063\pi$
$809$	9.68844	+	15.0755i	0.340627	+	0.530026i	−0.628107	+	0.778127i	$0.716170\pi$
$810$	−2.04759	−	8.67789i	−0.0719448	−	0.304910i
$811$	21.0744	+	13.5437i	0.740021	+	0.475582i	0.855549	−	0.517722i	$-0.173220\pi$
$811$	21.0744	+	13.5437i	0.740021	+	0.475582i	−0.115528	+	0.993304i	$0.536856\pi$
$812$	3.45263	−	7.56020i	0.121164	−	0.265311i
$813$	−0.605711	+	0.320228i	−0.0212432	+	0.0112309i
$814$	−2.85591	+	19.8633i	−0.100100	+	0.696208i
$815$	−6.12906	−	13.4208i	−0.214692	−	0.470109i
$816$	0.666582	+	0.513152i	0.0233350	+	0.0179639i
$817$	−2.00454	−	0.588585i	−0.0701298	−	0.0205920i
$818$	−15.1759	+	6.93060i	−0.530613	+	0.242323i
$819$	2.09132	+	2.54914i	0.0730765	+	0.0890743i
$820$	−2.30262	−	1.99523i	−0.0804111	−	0.0696766i
$821$	−24.2624	−	11.0803i	−0.846765	−	0.386704i	−0.0557077	−	0.998447i	$-0.517742\pi$
$821$	−24.2624	−	11.0803i	−0.846765	−	0.386704i	−0.791057	+	0.611743i	$0.790469\pi$
$822$	0.256573	−	0.186729i	0.00894902	−	0.00651291i
$823$	3.92743	+	27.3159i	0.136902	+	0.952173i	0.936258	+	0.351315i	$0.114265\pi$
$823$	3.92743	+	27.3159i	0.136902	+	0.952173i	−0.799356	+	0.600858i	$0.794826\pi$
$824$	−0.794259	+	0.510439i	−0.0276693	+	0.0177820i
$825$	9.17301	+	25.6436i	0.319363	+	0.892795i
$826$	−4.98923	−	16.9918i	−0.173597	−	0.591219i
$827$	−33.9438			−1.18034			−0.590171	−	0.807278i	$-0.700940\pi$
$827$	−33.9438			−1.18034			−0.590171	+	0.807278i	$0.700940\pi$
$828$	−14.3674	+	0.760628i	−0.499301	+	0.0264336i
$829$	3.36268			0.116791			0.0583954	−	0.998294i	$-0.481402\pi$
$829$	3.36268			0.116791			0.0583954	+	0.998294i	$0.481402\pi$
$830$	−1.16136	−	3.95522i	−0.0403113	−	0.137288i
$831$	−10.0521	−	28.1012i	−0.348704	−	0.974820i
$832$	0.645592	−	0.414897i	0.0223819	−	0.0143840i
$833$	−0.342063	−	2.37910i	−0.0118518	−	0.0824310i
$834$	24.5083	−	17.8366i	0.848651	−	0.617631i
$835$	−20.0657	−	9.16369i	−0.694402	−	0.317123i
$836$	22.3053	+	19.3277i	0.771446	+	0.668462i
$837$	−0.773469	+	0.253393i	−0.0267350	+	0.00875854i
$838$	15.3297	−	7.00082i	0.529554	−	0.241839i
$839$	−4.61660	−	1.35556i	−0.159383	−	0.0467990i	0.201068	−	0.979577i	$-0.435559\pi$
$839$	−4.61660	−	1.35556i	−0.159383	−	0.0467990i	−0.360450	+	0.932778i	$0.617377\pi$
$840$	−1.94732	−	1.49910i	−0.0671888	−	0.0517237i
$841$	−1.94315	−	4.25490i	−0.0670051	−	0.146721i
$842$	3.37208	−	23.4533i	0.116209	−	0.808255i
$843$	11.4904	−	6.07477i	0.395751	−	0.209226i
$844$	−10.1436	+	22.2113i	−0.349157	+	0.764546i
$845$	10.3436	+	6.64745i	0.355832	+	0.228679i
$846$	11.4172	−	16.7553i	0.392533	−	0.576060i
$847$	3.33769	+	5.19355i	0.114685	+	0.178453i
$848$	2.28036	+	2.63168i	0.0783079	+	0.0903722i
$849$	3.77156	−	44.3321i	0.129440	−	1.52148i
$850$		−	1.95172i		−	0.0669436i
$851$	5.43073	+	23.9888i	0.186163	+	0.822325i
$852$	−9.32668	+	24.0128i	−0.319527	+	0.822667i
$853$	−20.3026	+	5.96138i	−0.695148	+	0.204114i	−0.610172	−	0.792269i	$-0.708900\pi$
$853$	−20.3026	+	5.96138i	−0.695148	+	0.204114i	−0.0849762	+	0.996383i	$0.527081\pi$
$854$	16.4038	−	14.2140i	0.561327	−	0.486393i
$855$	−3.78697	+	22.0956i	−0.129512	+	0.755653i
$856$	−17.4207	+	2.50472i	−0.595427	+	0.0856095i
$857$	11.2878	−	17.5642i	0.385584	−	0.599980i	−0.593156	−	0.805088i	$-0.702118\pi$
$857$	11.2878	−	17.5642i	0.385584	−	0.599980i	0.978739	+	0.205108i	$0.0657545\pi$
$858$	−3.62780	−	3.72688i	−0.123851	−	0.127234i
$859$	−2.96243	+	3.41883i	−0.101077	+	0.116649i	−0.804034	−	0.594583i	$-0.797317\pi$
$859$	−2.96243	+	3.41883i	−0.101077	+	0.116649i	0.702957	+	0.711232i	$0.251863\pi$
$860$	−0.271601	−	0.0390503i	−0.00926152	−	0.00133161i
$861$	0.441692	+	7.61617i	0.0150528	+	0.259559i
$862$	4.50933	−	15.3574i	0.153588	−	0.523074i
$863$	−3.08047	+	10.4911i	−0.104861	+	0.357122i	−0.995162	−	0.0982499i	$-0.968676\pi$
$863$	−3.08047	+	10.4911i	−0.104861	+	0.357122i	0.890301	+	0.455372i	$0.150494\pi$
$864$	4.03053	+	3.27945i	0.137121	+	0.111569i
$865$	−0.202032	−	0.0290478i	−0.00686930	−	0.000987656i
$866$	−9.39364	+	10.8408i	−0.319209	+	0.368387i
$867$	20.8065	−	20.2533i	0.706625	−	0.687839i
$868$	−0.121284	+	0.188722i	−0.00411666	+	0.00640565i
$869$	−26.8936	+	3.86672i	−0.912304	+	0.131169i
$870$	−9.75796	+	1.98544i	−0.330826	+	0.0673128i
$871$	4.04700	−	3.50674i	0.137127	−	0.118821i
$872$	−7.00624	+	2.05722i	−0.237261	+	0.0696662i
$873$	−3.69704	+	4.04130i	−0.125126	+	0.136777i
$874$	33.9988	+	12.3553i	1.15002	+	0.417923i
$875$			12.7959i			0.432580i
$876$	2.38344	+	0.202771i	0.0805289	+	0.00685100i
$877$	21.8053	+	25.1647i	0.736314	+	0.849751i	0.993167	−	0.116699i	$-0.0372312\pi$
$877$	21.8053	+	25.1647i	0.736314	+	0.849751i	−0.256854	+	0.966450i	$0.582686\pi$
$878$	−4.03884	−	6.28456i	−0.136304	−	0.212094i
$879$	−9.36691	+	40.4291i	−0.315938	+	1.36364i
$880$	3.26107	+	2.09576i	0.109931	+	0.0706481i
$881$	19.8109	−	43.3798i	0.667446	−	1.46150i	−0.207971	−	0.978135i	$-0.566686\pi$
$881$	19.8109	−	43.3798i	0.667446	−	1.46150i	0.875417	−	0.483368i	$-0.160587\pi$
$882$	−1.71625	−	14.7471i	−0.0577892	−	0.496559i
$883$	5.27020	−	36.6550i	0.177356	−	1.23354i	−0.685493	−	0.728079i	$-0.740413\pi$
$883$	5.27020	−	36.6550i	0.177356	−	1.23354i	0.862849	−	0.505461i	$-0.168678\pi$
$884$	0.154833	+	0.339037i	0.00520760	+	0.0114031i
$885$	−12.9429	+	16.8128i	−0.435071	+	0.565155i
$886$	−21.9985	−	6.45935i	−0.739055	−	0.217006i
$887$	3.20851	−	1.46528i	0.107731	−	0.0491992i	−0.360820	−	0.932635i	$-0.617503\pi$
$887$	3.20851	−	1.46528i	0.107731	−	0.0491992i	0.468552	+	0.883436i	$0.344776\pi$
$888$	4.36179	−	7.73834i	0.146372	−	0.259682i
$889$	−16.4019	−	14.2124i	−0.550103	−	0.476667i
$890$	13.8821	+	6.33976i	0.465330	+	0.212509i
$891$	16.3332	−	31.1991i	0.547184	−	1.04521i
$892$	4.19057	+	29.1461i	0.140311	+	0.975883i
$893$	−42.8855	+	27.5608i	−1.43511	+	0.922288i
$894$	−22.1488	+	7.92287i	−0.740766	+	0.264981i
$895$	2.55533	+	8.70265i	0.0854152	+	0.290897i
$896$	1.43218			0.0478457
$897$	−5.78517	−	2.67730i	−0.193161	−	0.0893923i
$898$	0.773776			0.0258212
$899$	0.256098	+	0.872190i	0.00854135	+	0.0290892i
$900$	0.324758	−	12.0512i	0.0108253	−	0.401708i
$901$	−1.42276	+	0.914353i	−0.0473990	+	0.0304615i
$902$	−1.71260	−	11.9114i	−0.0570232	−	0.396605i
$903$	0.404294	+	0.555518i	0.0134541	+	0.0184865i
$904$	−15.4756	−	7.06746i	−0.514710	−	0.235060i
$905$	−4.09676	−	3.54986i	−0.136181	−	0.118001i
$906$	18.5519	+	10.4569i	0.616345	+	0.347408i
$907$	−28.4290	+	12.9831i	−0.943971	+	0.431097i	−0.827103	−	0.562050i	$-0.810013\pi$
$907$	−28.4290	+	12.9831i	−0.943971	+	0.431097i	−0.116868	+	0.993147i	$0.537285\pi$
$908$	−18.5980	−	5.46085i	−0.617195	−	0.181225i
$909$	26.7536	−	16.1921i	0.887362	−	0.537059i
$910$	−0.452321	−	0.990446i	−0.0149943	−	0.0328330i
$911$	−6.53428	+	45.4469i	−0.216490	+	1.50572i	0.534363	+	0.845255i	$0.320552\pi$
$911$	−6.53428	+	45.4469i	−0.216490	+	1.50572i	−0.750853	+	0.660469i	$0.770357\pi$
$912$	−6.10615	−	11.5498i	−0.202195	−	0.382452i
$913$	6.76350	−	14.8100i	0.223839	−	0.490139i
$914$	−3.07566	−	1.97661i	−0.101734	−	0.0653803i
$915$	−25.3346	−	5.86969i	−0.837534	−	0.194046i
$916$	−2.70867	−	4.21477i	−0.0894969	−	0.139260i
$917$	11.6852	+	13.4854i	0.385878	+	0.445327i
$918$	−1.85514	+	1.71095i	−0.0612288	+	0.0564698i
$919$			12.9563i			0.427389i	0.976901	+	0.213694i	$0.0685496\pi$
$919$			12.9563i			0.427389i	−0.976901	+	0.213694i	$0.931450\pi$
$920$	4.65094	+	0.970744i	0.153337	+	0.0320045i
$921$	11.2717	+	4.37798i	0.371416	+	0.144259i
$922$	2.95193	−	0.866764i	0.0972165	−	0.0285453i
$923$	−8.62587	+	7.47436i	−0.283924	+	0.246022i
$924$	−1.93528	−	9.51142i	−0.0636660	−	0.312903i
$925$	−20.3996	+	2.93303i	−0.670736	+	0.0964373i
$926$	−4.17230	+	6.49223i	−0.137110	+	0.213348i
$927$	−1.10679	−	2.60721i	−0.0363519	−	0.0856322i
$928$	3.80031	−	4.38580i	0.124751	−	0.143971i
$929$	4.85973	+	0.698724i	0.159443	+	0.0229244i	0.221574	−	0.975144i	$-0.428881\pi$
$929$	4.85973	+	0.698724i	0.159443	+	0.0229244i	−0.0621312	+	0.998068i	$0.519790\pi$
$930$	0.268329	−	0.0155614i	0.00879884	−	0.000510279i
$931$	−10.5166	+	35.8164i	−0.344669	+	1.17383i
$932$	−1.30850	+	4.45633i	−0.0428613	+	0.145972i
$933$	−33.0294	+	1.91550i	−1.08133	+	0.0627108i
$934$	−5.69753	−	0.819181i	−0.186429	−	0.0268044i
$935$	−1.23291	+	1.42286i	−0.0403206	+	0.0465324i
$936$	0.899628	+	2.11920i	0.0294053	+	0.0692683i
$937$	0.670883	−	1.04391i	0.0219168	−	0.0341032i	−0.830122	−	0.557581i	$-0.811729\pi$
$937$	0.670883	−	1.04391i	0.0219168	−	0.0341032i	0.852039	+	0.523478i	$0.175366\pi$
$938$	9.89185	−	1.42223i	0.322980	−	0.0464376i
$939$	2.39424	+	11.7671i	0.0781330	+	0.384005i
$940$	−5.06016	+	4.38465i	−0.165044	+	0.143012i
$941$	52.4042	−	15.3873i	1.70833	−	0.501611i	0.725829	−	0.687875i	$-0.241456\pi$
$941$	52.4042	−	15.3873i	1.70833	−	0.501611i	0.982500	+	0.186264i	$0.0596381\pi$
$942$	−18.3631	−	7.13231i	−0.598303	−	0.232383i
$943$	−7.17752	−	12.8851i	−0.233732	−	0.419596i
$944$		−	12.3651i		−	0.402451i
$945$	5.41952	−	4.99828i	0.176297	−	0.162594i
$946$	−0.709714	−	0.819054i	−0.0230748	−	0.0266297i
$947$	6.11395	+	9.51350i	0.198677	+	0.309147i	0.926269	−	0.376863i	$-0.122997\pi$
$947$	6.11395	+	9.51350i	0.198677	+	0.309147i	−0.727592	+	0.686010i	$0.759361\pi$
$948$	11.7166	+	2.71459i	0.380538	+	0.0881659i
$949$	0.891595	+	0.572993i	0.0289424	+	0.0186001i
$950$	−12.5917	+	27.5720i	−0.408529	+	0.894553i
$951$	7.48606	+	14.1599i	0.242752	+	0.459166i
$952$	−0.0989915	+	0.688501i	−0.00320833	+	0.0223144i
$953$	11.1369	+	24.3865i	0.360760	+	0.789955i	0.999784	+	0.0207679i	$0.00661111\pi$
$953$	11.1369	+	24.3865i	0.360760	+	0.789955i	−0.639024	+	0.769187i	$0.720662\pi$
$954$	−8.93721	+	5.40908i	−0.289353	+	0.175125i
$955$	11.5211	+	3.38289i	0.372813	+	0.109468i
$956$	2.39720	−	1.09476i	0.0775308	−	0.0354071i
$957$	−34.2624	−	19.3123i	−1.10755	−	0.624278i
$958$	14.1589	+	12.2687i	0.457453	+	0.396385i
$959$	0.238678	+	0.109000i	0.00770730	+	0.00351981i
$960$	−1.00972	−	1.38739i	−0.0325884	−	0.0447779i
$961$	4.40827	+	30.6602i	0.142202	+	0.989038i
$962$	3.31097	−	2.12783i	0.106750	−	0.0686041i
$963$	1.42233	−	52.7804i	0.0458340	−	1.70082i
$964$	−2.87433	−	9.78906i	−0.0925759	−	0.315284i
$965$	−12.6656			−0.407720
$966$	−6.38128	−	10.0403i	−0.205314	−	0.323041i
$967$	31.5311			1.01397			0.506986	−	0.861954i	$-0.330759\pi$
$967$	31.5311			1.01397			0.506986	+	0.861954i	$0.330759\pi$
$968$	1.21444	+	4.13602i	0.0390337	+	0.132937i
$969$	5.97446	−	2.13714i	0.191927	−	0.0686547i
$970$	1.52161	−	0.977882i	0.0488561	−	0.0313979i
$971$	−3.51908	−	24.4757i	−0.112933	−	0.785463i	−0.965041	−	0.262098i	$-0.915586\pi$
$971$	−3.51908	−	24.4757i	−0.112933	−	0.785463i	0.852109	−	0.523365i	$-0.175324\pi$
$972$	−11.7396	+	10.2558i	−0.376547	+	0.328956i
$973$	22.7988	+	10.4119i	0.730897	+	0.333789i
$974$	−8.99539	−	7.79455i	−0.288231	−	0.249754i
$975$	2.62281	−	4.65318i	0.0839971	−	0.149021i
$976$	13.7859	−	6.29582i	0.441277	−	0.201524i
$977$	−31.7281	−	9.31620i	−1.01507	−	0.298052i	−0.268445	−	0.963295i	$-0.586510\pi$
$977$	−31.7281	−	9.31620i	−1.01507	−	0.298052i	−0.746627	+	0.665243i	$0.768328\pi$
$978$	−15.7351	+	20.4399i	−0.503154	+	0.653595i
$979$	25.0399	+	54.8297i	0.800278	+	1.75236i
$980$	−0.697738	+	4.85288i	−0.0222884	+	0.155019i
$981$	−2.53232	−	21.7592i	−0.0808508	−	0.694718i
$982$	−2.14145	+	4.68911i	−0.0683363	+	0.149636i
$983$	26.5409	+	17.0568i	0.846522	+	0.544026i	0.890488	−	0.455007i	$-0.150363\pi$
$983$	26.5409	+	17.0568i	0.846522	+	0.544026i	−0.0439664	+	0.999033i	$0.513999\pi$
$984$	−1.20231	+	5.18937i	−0.0383283	+	0.165431i
$985$	−11.7495	−	18.2827i	−0.374372	−	0.582534i
$986$	1.84574	+	2.13009i	0.0587803	+	0.0678360i
$987$	16.7048	+	1.42116i	0.531720	+	0.0452360i
$988$		−	5.78849i		−	0.184156i
$989$	−1.17116	−	0.626740i	−0.0372408	−	0.0199292i
$990$	−7.84958	+	8.58052i	−0.249476	+	0.272707i
$991$	27.7470	−	8.14726i	0.881413	−	0.258806i	0.190451	−	0.981697i	$-0.439005\pi$
$991$	27.7470	−	8.14726i	0.881413	−	0.258806i	0.690963	+	0.722890i	$0.257187\pi$
$992$	−0.118380	+	0.102577i	−0.00375856	+	0.00325681i
$993$	−28.4196	+	5.78249i	−0.901867	+	0.183502i
$994$	−21.0837	+	3.03139i	−0.668736	+	0.0961497i
$995$	2.13136	−	3.31646i	0.0675686	−	0.105139i
$996$	−5.16429	+	5.02699i	−0.163637	+	0.159286i
$997$	−25.3426	+	29.2469i	−0.802607	+	0.926258i	−0.998521	−	0.0543629i	$-0.982687\pi$
$997$	−25.3426	+	29.2469i	−0.802607	+	0.926258i	0.195914	+	0.980621i	$0.437233\pi$
$998$	15.3646	+	2.20909i	0.486356	+	0.0699275i
$999$	20.6709	+	16.8190i	0.653999	+	0.532129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.83.3	yes	80
3.2	odd	2	inner	138.2.f.a.83.8	yes	80
23.5	odd	22	inner	138.2.f.a.5.8	yes	80
69.5	even	22	inner	138.2.f.a.5.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.5.3	✓	80	69.5	even	22	inner
138.2.f.a.5.8	yes	80	23.5	odd	22	inner
138.2.f.a.83.3	yes	80	1.1	even	1	trivial
138.2.f.a.83.8	yes	80	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281733 - 0.959493i) q^{2} +(0.583374 + 1.63085i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.140990 + 0.980604i) q^{5} +(1.40043 - 1.01921i) q^{6} +(1.30276 + 0.594948i) q^{7} +(0.755750 + 0.654861i) q^{8} +(-2.31935 + 1.90279i) q^{9} +O(q^{10})\)	\(q+(-0.281733 - 0.959493i) q^{2} +(0.583374 + 1.63085i) q^{3} +(-0.841254 + 0.540641i) q^{4} +(0.140990 + 0.980604i) q^{5} +(1.40043 - 1.01921i) q^{6} +(1.30276 + 0.594948i) q^{7} +(0.755750 + 0.654861i) q^{8} +(-2.31935 + 1.90279i) q^{9} +(0.901161 - 0.411546i) q^{10} +(3.75438 + 1.10239i) q^{11} +(-1.37247 - 1.05656i) q^{12} +(-0.318796 - 0.698067i) q^{13} +(0.203820 - 1.41760i) q^{14} +(-1.51697 + 0.801992i) q^{15} +(0.415415 - 0.909632i) q^{16} +(0.408580 + 0.262579i) q^{17} +(2.47915 + 1.68932i) q^{18} +(-4.07796 - 6.34543i) q^{19} +(-0.648762 - 0.748712i) q^{20} +(-0.210278 + 2.47168i) q^{21} -3.91288i q^{22} +(-1.71381 - 4.47916i) q^{23} +(-0.627095 + 1.61454i) q^{24} +(3.85576 - 1.13215i) q^{25} +(-0.579975 + 0.502551i) q^{26} +(-4.45622 - 2.67247i) q^{27} +(-1.41760 + 0.203820i) q^{28} +(-3.13747 + 4.88200i) q^{29} +(1.19689 + 1.22957i) q^{30} +(0.102577 - 0.118380i) q^{31} +(-0.989821 - 0.142315i) q^{32} +(0.392383 + 6.76594i) q^{33} +(0.136832 - 0.466007i) q^{34} +(-0.399734 + 1.36137i) q^{35} +(0.922432 - 2.85467i) q^{36} +(-5.07638 - 0.729874i) q^{37} +(-4.93950 + 5.70049i) q^{38} +(0.952465 - 0.927144i) q^{39} +(-0.535606 + 0.833419i) q^{40} +(3.04414 - 0.437682i) q^{41} +(2.43080 - 0.494592i) q^{42} +(0.209322 - 0.181379i) q^{43} +(-3.75438 + 1.10239i) q^{44} +(-2.19289 - 2.00609i) q^{45} +(-3.81489 + 2.90631i) q^{46} -6.75849i q^{47} +(1.72582 + 0.146824i) q^{48} +(-3.24082 - 3.74010i) q^{49} +(-2.17259 - 3.38061i) q^{50} +(-0.189871 + 0.819515i) q^{51} +(0.645592 + 0.414897i) q^{52} +(-1.44656 + 3.16753i) q^{53} +(-1.30875 + 5.02863i) q^{54} +(-0.551675 + 3.83698i) q^{55} +(0.594948 + 1.30276i) q^{56} +(7.96947 - 10.3523i) q^{57} +(5.56817 + 1.63496i) q^{58} +(11.2477 - 5.13667i) q^{59} +(0.842566 - 1.49481i) q^{60} +(11.4538 + 9.92474i) q^{61} +(-0.142484 - 0.0650700i) q^{62} +(-4.15361 + 1.09898i) q^{63} +(0.142315 + 0.989821i) q^{64} +(0.639580 - 0.411033i) q^{65} +(6.38132 - 2.28267i) q^{66} +(1.96590 + 6.69523i) q^{67} -0.485680 q^{68} +(6.30505 - 5.40799i) q^{69} +1.41884 q^{70} +(-4.19016 - 14.2704i) q^{71} +(-2.99891 - 0.0808151i) q^{72} +(-1.16181 + 0.746652i) q^{73} +(0.729874 + 5.07638i) q^{74} +(4.09572 + 5.62770i) q^{75} +(6.86120 + 3.13340i) q^{76} +(4.23518 + 3.66980i) q^{77} +(-1.15793 - 0.652677i) q^{78} +(-6.31629 + 2.88455i) q^{79} +(0.950558 + 0.279109i) q^{80} +(1.75876 - 8.82648i) q^{81} +(-1.27759 - 2.79752i) q^{82} +(0.592165 - 4.11860i) q^{83} +(-1.15939 - 2.19299i) q^{84} +(-0.199880 + 0.437676i) q^{85} +(-0.233005 - 0.149743i) q^{86} +(-9.79213 - 2.26871i) q^{87} +(2.11546 + 3.29172i) q^{88} +(10.0879 + 11.6421i) q^{89} +(-1.30702 + 2.66924i) q^{90} -1.09908i q^{91} +(3.86336 + 2.84155i) q^{92} +(0.252900 + 0.0982273i) q^{93} +(-6.48472 + 1.90409i) q^{94} +(5.64740 - 4.89350i) q^{95} +(-0.345342 - 1.69727i) q^{96} +(1.80716 - 0.259831i) q^{97} +(-2.67556 + 4.16325i) q^{98} +(-10.8053 + 4.58699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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