LMFDB - Embedded newform 138.2.f.a.5.8

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			5.8
Character	$\chi$	$=$	138.5
Dual form			138.2.f.a.83.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.281733 - 0.959493i) q^{2} +(1.53123 - 0.809531i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.140990 + 0.980604i) q^{5} +(-0.345342 - 1.69727i) q^{6} +(1.30276 - 0.594948i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.68932 - 2.47915i) q^{9} +O(q^{10})$	\(q+(0.281733 - 0.959493i) q^{2} +(1.53123 - 0.809531i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.140990 + 0.980604i) q^{5} +(-0.345342 - 1.69727i) q^{6} +(1.30276 - 0.594948i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.68932 - 2.47915i) q^{9} +(0.901161 + 0.411546i) q^{10} +(-3.75438 + 1.10239i) q^{11} +(-1.72582 - 0.146824i) q^{12} +(-0.318796 + 0.698067i) q^{13} +(-0.203820 - 1.41760i) q^{14} +(0.577942 + 1.61566i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.408580 + 0.262579i) q^{17} +(-1.90279 - 2.31935i) q^{18} +(-4.07796 + 6.34543i) q^{19} +(0.648762 - 0.748712i) q^{20} +(1.51319 - 1.96562i) 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} +(0.579784 - 5.16371i) q^{27} +(-1.41760 - 0.203820i) q^{28} +(3.13747 + 4.88200i) q^{29} +(1.71304 - 0.0993461i) q^{30} +(0.102577 + 0.118380i) q^{31} +(0.989821 - 0.142315i) q^{32} +(-4.85640 + 4.72729i) q^{33} +(0.136832 + 0.466007i) q^{34} +(0.399734 + 1.36137i) q^{35} +(-2.76148 + 1.17228i) q^{36} +(-5.07638 + 0.729874i) q^{37} +(4.93950 + 5.70049i) q^{38} +(0.0769565 + 1.32697i) q^{39} +(-0.535606 - 0.833419i) q^{40} +(-3.04414 - 0.437682i) q^{41} +(-1.45969 - 2.00567i) 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} +(1.37247 + 1.05656i) q^{48} +(-3.24082 + 3.74010i) q^{49} +(2.17259 - 3.38061i) q^{50} +(-0.413064 + 0.732826i) q^{51} +(0.645592 - 0.414897i) q^{52} +(1.44656 + 3.16753i) q^{53} +(-4.79119 - 2.01108i) q^{54} +(-0.551675 - 3.83698i) q^{55} +(-0.594948 + 1.30276i) q^{56} +(-1.10747 + 13.0175i) q^{57} +(5.56817 - 1.63496i) q^{58} +(-11.2477 - 5.13667i) q^{59} +(0.387298 - 1.67164i) q^{60} +(11.4538 - 9.92474i) q^{61} +(0.142484 - 0.0650700i) q^{62} +(0.725802 - 4.23479i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.639580 - 0.411033i) q^{65} +(3.16760 + 5.99151i) q^{66} +(1.96590 - 6.69523i) q^{67} +0.485680 q^{68} +(-1.00179 - 8.24599i) q^{69} +1.41884 q^{70} +(4.19016 - 14.2704i) q^{71} +(0.346797 + 2.97989i) q^{72} +(-1.16181 - 0.746652i) q^{73} +(-0.729874 + 5.07638i) q^{74} +(6.82056 - 1.38777i) q^{75} +(6.86120 - 3.13340i) q^{76} +(-4.23518 + 3.66980i) q^{77} +(1.29490 + 0.300013i) q^{78} +(-6.31629 - 2.88455i) q^{79} +(-0.950558 + 0.279109i) q^{80} +(-3.29240 - 8.37616i) q^{81} +(-1.27759 + 2.79752i) q^{82} +(-0.592165 - 4.11860i) q^{83} +(-2.33567 + 0.835496i) q^{84} +(-0.199880 - 0.437676i) q^{85} +(0.233005 - 0.149743i) q^{86} +(8.75631 + 4.93557i) q^{87} +(2.11546 - 3.29172i) q^{88} +(-10.0879 + 11.6421i) q^{89} +(2.54264 - 1.53888i) 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} +(1.40043 - 1.01921i) q^{96} +(1.80716 + 0.259831i) q^{97} +(2.67556 + 4.16325i) q^{98} +(-3.60937 + 11.1700i) 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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

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

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
$3$	1.53123	−	0.809531i	0.884055	−	0.467383i
$3$	1.53123	−	0.809531i	0.884055	−	0.467383i
$4$	−0.841254	−	0.540641i	−0.420627	−	0.270320i
$5$	−0.140990	+	0.980604i	−0.0630524	+	0.438539i	0.933703	+	0.358049i	$0.116558\pi$
$5$	−0.140990	+	0.980604i	−0.0630524	+	0.438539i	−0.996755	+	0.0804907i	$0.974351\pi$
$6$	−0.345342	−	1.69727i	−0.140985	−	0.692909i
$7$	1.30276	−	0.594948i	0.492395	−	0.224869i	−0.153712	−	0.988116i	$-0.549123\pi$
$7$	1.30276	−	0.594948i	0.492395	−	0.224869i	0.646108	+	0.763246i	$0.276396\pi$
$8$	−0.755750	+	0.654861i	−0.267198	+	0.231528i
$9$	1.68932	−	2.47915i	0.563107	−	0.826384i
$10$	0.901161	+	0.411546i	0.284972	+	0.130142i
$11$	−3.75438	+	1.10239i	−1.13199	+	0.332382i	−0.793489	−	0.608585i	$-0.791738\pi$
$11$	−3.75438	+	1.10239i	−1.13199	+	0.332382i	−0.338500	+	0.940967i	$0.609919\pi$
$12$	−1.72582	−	0.146824i	−0.498200	−	0.0423844i
$13$	−0.318796	+	0.698067i	−0.0884182	+	0.193609i	−0.948675	−	0.316251i	$-0.897576\pi$
$13$	−0.318796	+	0.698067i	−0.0884182	+	0.193609i	0.860257	+	0.509860i	$0.170303\pi$
$14$	−0.203820	−	1.41760i	−0.0544733	−	0.378870i
$15$	0.577942	+	1.61566i	0.149224	+	0.417163i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	−0.408580	+	0.262579i	−0.0990953	+	0.0636847i	−0.589250	−	0.807951i	$-0.700577\pi$
$17$	−0.408580	+	0.262579i	−0.0990953	+	0.0636847i	0.490155	+	0.871635i	$0.336940\pi$
$18$	−1.90279	−	2.31935i	−0.448493	−	0.546676i
$19$	−4.07796	+	6.34543i	−0.935548	+	1.45574i	−0.0459785	+	0.998942i	$0.514641\pi$
$19$	−4.07796	+	6.34543i	−0.935548	+	1.45574i	−0.889570	+	0.456799i	$0.848996\pi$
$20$	0.648762	−	0.748712i	0.145068	−	0.167417i
$21$	1.51319	−	1.96562i	0.330204	−	0.428934i
$22$			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
$27$	0.579784	−	5.16371i	0.111579	−	0.993756i
$28$	−1.41760	−	0.203820i	−0.267901	−	0.0385184i
$29$	3.13747	+	4.88200i	0.582613	+	0.906564i	0.999998	−	0.00216601i	$-0.000689464\pi$
$29$	3.13747	+	4.88200i	0.582613	+	0.906564i	−0.417384	+	0.908730i	$0.637053\pi$
$30$	1.71304	−	0.0993461i	0.312757	−	0.0181380i
$31$	0.102577	+	0.118380i	0.0184233	+	0.0212616i	0.764886	−	0.644165i	$-0.222795\pi$
$31$	0.102577	+	0.118380i	0.0184233	+	0.0212616i	−0.746463	+	0.665427i	$0.768250\pi$
$32$	0.989821	−	0.142315i	0.174977	−	0.0251579i
$33$	−4.85640	+	4.72729i	−0.845390	+	0.822916i
$34$	0.136832	+	0.466007i	0.0234665	+	0.0799195i
$35$	0.399734	+	1.36137i	0.0675673	+	0.230113i
$36$	−2.76148	+	1.17228i	−0.460246	+	0.195380i
$37$	−5.07638	+	0.729874i	−0.834552	+	0.119991i	−0.546327	−	0.837572i	$-0.683974\pi$
$37$	−5.07638	+	0.729874i	−0.834552	+	0.119991i	−0.288226	+	0.957563i	$0.593065\pi$
$38$	4.93950	+	5.70049i	0.801293	+	0.924741i
$39$	0.0769565	+	1.32697i	0.0123229	+	0.212486i
$40$	−0.535606	−	0.833419i	−0.0846868	−	0.131775i
$41$	−3.04414	−	0.437682i	−0.475415	−	0.0683544i	−0.0995576	−	0.995032i	$-0.531743\pi$
$41$	−3.04414	−	0.437682i	−0.475415	−	0.0683544i	−0.375858	+	0.926677i	$0.622652\pi$
$42$	−1.45969	−	2.00567i	−0.225235	−	0.309482i
$43$	0.209322	+	0.181379i	0.0319214	+	0.0276600i	0.670675	−	0.741751i	$-0.266004\pi$
$43$	0.209322	+	0.181379i	0.0319214	+	0.0276600i	−0.638754	+	0.769411i	$0.720550\pi$
$44$	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	$-0.164068\pi$
$48$	1.37247	+	1.05656i	0.198099	+	0.152502i
$49$	−3.24082	+	3.74010i	−0.462974	+	0.534300i
$50$	2.17259	−	3.38061i	0.307250	−	0.478090i
$51$	−0.413064	+	0.732826i	−0.0578405	+	0.102616i
$52$	0.645592	−	0.414897i	0.0895275	−	0.0575358i
$53$	1.44656	+	3.16753i	0.198700	+	0.435093i	0.982585	−	0.185813i	$-0.0594919\pi$
$53$	1.44656	+	3.16753i	0.198700	+	0.435093i	−0.783885	+	0.620907i	$0.786765\pi$
$54$	−4.79119	−	2.01108i	−0.651999	−	0.273674i
$55$	−0.551675	−	3.83698i	−0.0743879	−	0.517379i
$56$	−0.594948	+	1.30276i	−0.0795033	+	0.174088i
$57$	−1.10747	+	13.0175i	−0.146688	+	1.72421i
$58$	5.56817	−	1.63496i	0.731136	−	0.214681i
$59$	−11.2477	−	5.13667i	−1.46433	−	0.668737i	−0.485655	−	0.874151i	$-0.661419\pi$
$59$	−11.2477	−	5.13667i	−1.46433	−	0.668737i	−0.978675	+	0.205414i	$0.934146\pi$
$60$	0.387298	−	1.67164i	0.0500000	−	0.215808i
$61$	11.4538	−	9.92474i	1.46650	−	1.27073i	0.574657	−	0.818395i	$-0.305136\pi$
$61$	11.4538	−	9.92474i	1.46650	−	1.27073i	0.891847	−	0.452338i	$-0.149410\pi$
$62$	0.142484	−	0.0650700i	0.0180954	−	0.00826390i
$63$	0.725802	−	4.23479i	0.0914425	−	0.533533i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.639580	−	0.411033i	−0.0793301	−	0.0509824i
$66$	3.16760	+	5.99151i	0.389904	+	0.737504i
$67$	1.96590	−	6.69523i	0.240173	−	0.817953i	−0.747880	−	0.663834i	$-0.768928\pi$
$67$	1.96590	−	6.69523i	0.240173	−	0.817953i	0.988052	−	0.154118i	$-0.0492537\pi$
$68$	0.485680			0.0588974
$69$	−1.00179	−	8.24599i	−0.120601	−	0.992701i
$70$	1.41884			0.169584
$71$	4.19016	−	14.2704i	0.497281	−	1.69358i	−0.202548	−	0.979272i	$-0.564922\pi$
$71$	4.19016	−	14.2704i	0.497281	−	1.69358i	0.699829	−	0.714311i	$-0.253260\pi$
$72$	0.346797	+	2.97989i	0.0408704	+	0.351183i
$73$	−1.16181	−	0.746652i	−0.135980	−	0.0873890i	0.470882	−	0.882196i	$-0.343936\pi$
$73$	−1.16181	−	0.746652i	−0.135980	−	0.0873890i	−0.606862	+	0.794807i	$0.707572\pi$
$74$	−0.729874	+	5.07638i	−0.0848461	+	0.590118i
$75$	6.82056	−	1.38777i	0.787570	−	0.160246i
$76$	6.86120	−	3.13340i	0.787033	−	0.359426i
$77$	−4.23518	+	3.66980i	−0.482643	+	0.418213i
$78$	1.29490	+	0.300013i	0.146619	+	0.0339698i
$79$	−6.31629	−	2.88455i	−0.710638	−	0.324537i	0.0270926	−	0.999633i	$-0.491375\pi$
$79$	−6.31629	−	2.88455i	−0.710638	−	0.324537i	−0.737730	+	0.675096i	$0.764102\pi$
$80$	−0.950558	+	0.279109i	−0.106276	+	0.0312053i
$81$	−3.29240	−	8.37616i	−0.365822	−	0.930685i
$82$	−1.27759	+	2.79752i	−0.141086	+	0.308935i
$83$	−0.592165	−	4.11860i	−0.0649986	−	0.452075i	−0.996166	−	0.0874831i	$-0.972118\pi$
$83$	−0.592165	−	4.11860i	−0.0649986	−	0.452075i	0.931167	−	0.364592i	$-0.118791\pi$
$84$	−2.33567	+	0.835496i	−0.254842	+	0.0911601i
$85$	−0.199880	−	0.437676i	−0.0216800	−	0.0474726i
$86$	0.233005	−	0.149743i	0.0251256	−	0.0161472i
$87$	8.75631	+	4.93557i	0.938775	+	0.529149i
$88$	2.11546	−	3.29172i	0.225509	−	0.350899i
$89$	−10.0879	+	11.6421i	−1.06932	+	1.23406i	−0.0982759	+	0.995159i	$0.531333\pi$
$89$	−10.0879	+	11.6421i	−1.06932	+	1.23406i	−0.971044	+	0.238902i	$0.923213\pi$
$90$	2.54264	−	1.53888i	0.268017	−	0.162212i
$91$			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
$96$	1.40043	−	1.01921i	0.142931	−	0.104022i
$97$	1.80716	+	0.259831i	0.183490	+	0.0263818i	0.233447	−	0.972370i	$-0.424999\pi$
$97$	1.80716	+	0.259831i	0.183490	+	0.0263818i	−0.0499573	+	0.998751i	$0.515909\pi$
$98$	2.67556	+	4.16325i	0.270272	+	0.420552i
$99$	−3.60937	+	11.1700i	−0.362755	+	1.12262i
$100$	−2.63158	−	3.03701i	−0.263158	−	0.303701i
$101$	10.3179	−	1.48349i	1.02667	−	0.147613i	0.391655	−	0.920112i	$-0.371903\pi$
$101$	10.3179	−	1.48349i	1.02667	−	0.147613i	0.635016	+	0.772499i	$0.280993\pi$
$102$	0.586768	+	0.602793i	0.0580987	+	0.0596854i
$103$	−0.265994	−	0.905893i	−0.0262092	−	0.0892603i	0.945350	−	0.326058i	$-0.105720\pi$
$103$	−0.265994	−	0.905893i	−0.0262092	−	0.0892603i	−0.971559	+	0.236797i	$0.923902\pi$
$104$	−0.216206	−	0.736331i	−0.0212008	−	0.0722032i
$105$	1.71415	+	1.76097i	0.167284	+	0.171853i
$106$	3.44676	−	0.495570i	0.334779	−	0.0481340i
$107$	11.5254	+	13.3011i	1.11421	+	1.28586i	0.954339	+	0.298724i	$0.0965611\pi$
$107$	11.5254	+	13.3011i	1.11421	+	1.28586i	0.159867	+	0.987139i	$0.448893\pi$
$108$	−3.27945	+	4.03053i	−0.315566	+	0.387838i
$109$	−3.94777	−	6.14285i	−0.378128	−	0.588378i	0.599073	−	0.800694i	$-0.295536\pi$
$109$	−3.94777	−	6.14285i	−0.378128	−	0.588378i	−0.977201	+	0.212316i	$0.931899\pi$
$110$	−3.83698	−	0.551675i	−0.365842	−	0.0526002i
$111$	−7.18225	+	5.22709i	−0.681709	+	0.496134i
$112$	1.08237	+	0.937877i	0.102274	+	0.0886211i
$113$	16.3239	+	4.79312i	1.53562	+	0.450899i	0.936765	−	0.349959i	$-0.113804\pi$
$113$	16.3239	+	4.79312i	1.53562	+	0.450899i	0.598855	+	0.800858i	$0.295623\pi$
$114$	12.1782	+	4.73007i	1.14060	+	0.443012i
$115$	4.15065	+	2.31208i	0.387050	+	0.215603i
$116$		−	5.80324i		−	0.538817i
$117$	1.19206	+	1.96960i	0.110206	+	0.182090i
$118$	−8.09745	+	9.34495i	−0.745431	+	0.860273i
$119$	−0.376059	+	0.585160i	−0.0344733	+	0.0536415i
$120$	−1.49481	−	0.842566i	−0.136457	−	0.0769154i
$121$	3.62633	−	2.33050i	0.329666	−	0.211864i
$122$	−6.29582	−	13.7859i	−0.569997	−	1.24812i
$123$	−5.01559	+	1.79414i	−0.452241	+	0.161772i
$124$	−0.0222920	−	0.155044i	−0.00200188	−	0.0139234i
$125$	−3.71155	+	8.12716i	−0.331971	+	0.726915i
$126$	−3.85877	−	1.88948i	−0.343766	−	0.168328i
$127$	−14.5399	+	4.26930i	−1.29021	+	0.378839i	−0.853655	−	0.520839i	$-0.825619\pi$
$127$	−14.5399	+	4.26930i	−1.29021	+	0.378839i	−0.436554	+	0.899678i	$0.643801\pi$
$128$	−0.909632	−	0.415415i	−0.0804009	−	0.0367178i
$129$	0.467352	+	0.108280i	0.0411481	+	0.00953349i
$130$	−0.574574	+	0.497871i	−0.0503935	+	0.0436662i
$131$	−11.3332	+	5.17572i	−0.990190	+	0.452205i	−0.843588	−	0.536991i	$-0.819561\pi$
$131$	−11.3332	+	5.17572i	−0.990190	+	0.452205i	−0.146602	+	0.989196i	$0.546834\pi$
$132$	6.64123	−	1.35128i	0.578045	−	0.117614i
$133$	−1.53738	+	10.6927i	−0.133308	+	0.927176i
$134$	−5.87017	−	3.77253i	−0.507105	−	0.325897i
$135$	4.98181	+	1.29657i	0.428766	+	0.111591i
$136$	0.136832	−	0.466007i	0.0117332	−	0.0399598i
$137$	−0.183210			−0.0156527			−0.00782633	−	0.999969i	$-0.502491\pi$
$137$	−0.183210			−0.0156527			−0.00782633	+	0.999969i	$0.502491\pi$
$138$	−8.19421	−	1.36196i	−0.697537	−	0.115938i
$139$	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
$141$	−5.47120	−	10.3488i	−0.460758	−	0.871525i
$142$	−12.5118	−	8.04086i	−1.04997	−	0.674774i
$143$	0.427344	−	2.97224i	0.0357363	−	0.248552i
$144$	2.95689	+	0.506782i	0.246407	+	0.0422318i
$145$	−5.22965	+	2.38830i	−0.434299	+	0.198338i
$146$	−1.04373	+	0.904395i	−0.0863795	+	0.0748483i
$147$	−1.93470	+	8.35049i	−0.159572	+	0.688737i
$148$	4.66513	+	2.13049i	0.383471	+	0.175125i
$149$	13.0310	−	3.82624i	1.06754	−	0.313458i	0.299656	−	0.954047i	$-0.403128\pi$
$149$	13.0310	−	3.82624i	1.06754	−	0.313458i	0.767884	+	0.640589i	$0.221310\pi$
$150$	0.590017	−	6.93526i	0.0481747	−	0.566262i
$151$	5.10763	−	11.1842i	0.415653	−	0.910154i	−0.579787	−	0.814768i	$-0.696864\pi$
$151$	5.10763	−	11.1842i	0.415653	−	0.910154i	0.995440	−	0.0953856i	$-0.0304084\pi$
$152$	−1.07346	−	7.46605i	−0.0870688	−	0.605577i
$153$	−0.0392503	+	1.45651i	−0.00317320	+	0.117752i
$154$	2.32796	+	5.09752i	0.187592	+	0.410770i
$155$	−0.130546	+	0.0838966i	−0.0104857	+	0.00673874i
$156$	0.652677	−	1.15793i	0.0522560	−	0.0927084i
$157$	−6.14901	+	9.56805i	−0.490745	+	0.763613i	−0.994993	−	0.0999453i	$-0.968133\pi$
$157$	−6.14901	+	9.56805i	−0.490745	+	0.763613i	0.504248	+	0.863559i	$0.331770\pi$
$158$	−4.54721	+	5.24776i	−0.361757	+	0.417489i
$159$	4.77923	+	3.67917i	0.379017	+	0.291777i
$160$			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	−0.330770	−	0.943711i	$-0.607308\pi$
$163$	−14.2895	−	4.19578i	−1.11924	−	0.328639i	−0.788470	+	0.615073i	$0.789127\pi$
$164$	2.32427	+	2.01399i	0.181495	+	0.157266i
$165$	−3.95090	−	5.42870i	−0.307577	−	0.422624i
$166$	−4.11860	−	0.592165i	−0.319665	−	0.0459609i
$167$	12.0382	+	18.7318i	0.931541	+	1.44951i	0.892901	+	0.450254i	$0.148666\pi$
$167$	12.0382	+	18.7318i	0.931541	+	1.44951i	0.0386407	+	0.999253i	$0.487697\pi$
$168$	0.143619	+	2.47644i	0.0110804	+	0.191062i
$169$	8.12752	+	9.37966i	0.625194	+	0.721512i
$170$	−0.476260	+	0.0684758i	−0.0365275	+	0.00525186i
$171$	8.84231	+	20.8293i	0.676189	+	1.59286i
$172$	−0.0780324	−	0.265754i	−0.00594991	−	0.0202635i
$173$	0.0580449	+	0.197683i	0.00441307	+	0.0150295i	0.961670	−	0.274209i	$-0.0884161\pi$
$173$	0.0580449	+	0.197683i	0.00441307	+	0.0150295i	−0.957257	+	0.289239i	$0.906598\pi$
$174$	7.20259	−	7.01110i	0.546027	−	0.531510i
$175$	5.69668	−	0.819059i	0.430629	−	0.0619151i
$176$	−2.56239	−	2.95716i	−0.193148	−	0.222904i
$177$	−21.3811	+	1.23998i	−1.60710	+	0.0932023i
$178$	8.32842	+	12.9593i	0.624241	+	0.971338i
$179$	−9.06212	−	1.30294i	−0.677335	−	0.0973860i	−0.204942	−	0.978774i	$-0.565701\pi$
$179$	−9.06212	−	1.30294i	−0.677335	−	0.0973860i	−0.472393	+	0.881388i	$0.656610\pi$
$180$	−0.760204	−	2.87319i	−0.0566622	−	0.214155i
$181$	−4.13527	−	3.58323i	−0.307372	−	0.266339i	0.487491	−	0.873128i	$-0.337912\pi$
$181$	−4.13527	−	3.58323i	−0.307372	−	0.266339i	−0.794863	+	0.606788i	$0.792458\pi$
$182$	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
$186$	0.165499	−	0.214982i	0.0121349	−	0.0157632i
$187$	1.24450	−	1.43623i	0.0910071	−	0.105028i
$188$	−3.65391	+	5.68560i	−0.266489	+	0.414665i
$189$	−2.31682	−	7.07199i	−0.168524	−	0.514411i
$190$	−6.28634	+	4.03998i	−0.456059	+	0.293091i
$191$	−5.03496	−	11.0250i	−0.364317	−	0.797743i	−0.999674	−	0.0255246i	$-0.991874\pi$
$191$	−5.03496	−	11.0250i	−0.364317	−	0.797743i	0.635357	−	0.772218i	$-0.280853\pi$
$192$	−0.583374	−	1.63085i	−0.0421014	−	0.117697i
$193$	−1.81945	−	12.6545i	−0.130967	−	0.910893i	−0.944298	−	0.329092i	$-0.893257\pi$
$193$	−1.81945	−	12.6545i	−0.130967	−	0.910893i	0.813331	−	0.581801i	$-0.197652\pi$
$194$	0.758443	−	1.66076i	0.0544530	−	0.119236i
$195$	−1.31209	−	0.111626i	−0.0939605	−	0.00799369i
$196$	4.74840	−	1.39426i	0.339172	−	0.0995897i
$197$	19.9545	+	9.11293i	1.42170	+	0.649269i	0.970045	−	0.242923i	$-0.0781064\pi$
$197$	19.9545	+	9.11293i	1.42170	+	0.649269i	0.451655	+	0.892192i	$0.350834\pi$
$198$	9.70063	+	6.61011i	0.689394	+	0.469760i
$199$	−3.00738	+	2.60591i	−0.213188	+	0.184728i	−0.754908	−	0.655830i	$-0.772319\pi$
$199$	−3.00738	+	2.60591i	−0.213188	+	0.184728i	0.541720	+	0.840559i	$0.317773\pi$
$200$	−3.65539	+	1.66936i	−0.258475	+	0.118042i
$201$	−2.40976	−	11.8434i	−0.169971	−	0.835368i
$202$	1.48349	−	10.3179i	0.104378	−	0.725966i
$203$	6.99189	+	4.49342i	0.490735	+	0.315376i
$204$	0.743687	−	0.393173i	0.0520685	−	0.0275276i
$205$	0.858385	−	2.92339i	0.0599522	−	0.204178i
$206$	−0.944137			−0.0657812
$207$	−8.20935	−	11.8155i	−0.570589	−	0.821236i
$208$	−0.767417			−0.0532108
$209$	8.31510	−	28.3186i	0.575168	−	1.95884i
$210$	2.17257	−	1.14860i	0.149922	−	0.0792606i
$211$	20.5417	+	13.2013i	1.41415	+	0.908818i	0.999999	−	0.00139133i	$-0.000442876\pi$
$211$	20.5417	+	13.2013i	1.41415	+	0.908818i	0.414149	+	0.910209i	$0.364079\pi$
$212$	0.495570	−	3.44676i	0.0340359	−	0.236725i
$213$	−5.13622	−	25.2433i	−0.351928	−	1.72964i
$214$	16.0094	−	7.31124i	1.09438	−	0.499786i
$215$	−0.207373	+	0.179690i	−0.0141427	+	0.0122547i
$216$	2.94334	+	4.28215i	0.200269	+	0.291363i
$217$	0.204062	+	0.0931919i	0.0138526	+	0.00632628i
$218$	−7.00624	+	2.05722i	−0.474522	+	0.139332i
$219$	−2.38344	−	0.202771i	−0.161058	−	0.0137020i
$220$	−1.61033	+	3.52613i	−0.108569	+	0.237732i
$221$	−0.0530435	−	0.368925i	−0.00356809	−	0.0248166i
$222$	2.99189	+	8.36396i	0.200802	+	0.561352i
$223$	12.2322	+	26.7848i	0.819131	+	1.79365i	0.561681	+	0.827354i	$0.310155\pi$
$223$	12.2322	+	26.7848i	0.819131	+	1.79365i	0.257450	+	0.966292i	$0.417118\pi$
$224$	1.20483	−	0.774294i	0.0805008	−	0.0517347i
$225$	9.32039	−	7.64645i	0.621359	−	0.509763i
$226$	9.19793	−	14.3123i	0.611837	−	0.952037i
$227$	−12.6932	+	14.6488i	−0.842480	+	0.972273i	−0.999884	−	0.0152611i	$-0.995142\pi$
$227$	−12.6932	+	14.6488i	−0.842480	+	0.972273i	0.157404	+	0.987534i	$0.449688\pi$
$228$	7.96947	−	10.3523i	0.527791	−	0.685598i
$229$		−	5.01011i		−	0.331077i	−0.986203	−	0.165539i	$-0.947064\pi$
$229$		−	5.01011i		−	0.331077i	0.986203	−	0.165539i	$-0.0529362\pi$
$230$	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	$-0.321342\pi$
$233$	−3.51005	−	3.04148i	−0.229951	−	0.199254i	−0.762214	+	0.647326i	$0.775887\pi$
$234$	2.22566	−	0.588877i	0.145496	−	0.0384961i
$235$	6.62740	+	0.952876i	0.432324	+	0.0621588i
$236$	6.68510	+	10.4022i	0.435163	+	0.677127i
$237$	−12.0068	+	0.696322i	−0.779926	+	0.0452310i
$238$	0.455509	+	0.525685i	0.0295262	+	0.0340751i
$239$	2.60852	−	0.375049i	0.168731	−	0.0242599i	−0.0574313	−	0.998349i	$-0.518291\pi$
$239$	2.60852	−	0.375049i	0.168731	−	0.0242599i	0.226163	+	0.974090i	$0.427382\pi$
$240$	−1.22957	+	1.19689i	−0.0793686	+	0.0772586i
$241$	−2.87433	−	9.78906i	−0.185152	−	0.630569i	−0.998789	−	0.0491963i	$-0.984334\pi$
$241$	−2.87433	−	9.78906i	−0.185152	−	0.630569i	0.813637	−	0.581373i	$-0.197484\pi$
$242$	−1.21444	−	4.13602i	−0.0780674	−	0.265873i
$243$	−11.8222	−	10.1605i	−0.758393	−	0.651798i
$244$	−15.0012	+	2.15685i	−0.960355	+	0.138078i
$245$	−3.21064	−	3.70527i	−0.205120	−	0.236721i
$246$	0.308406	+	5.31789i	0.0196632	+	0.339057i
$247$	−3.12949	−	4.86959i	−0.199125	−	0.309845i
$248$	−0.155044	−	0.0222920i	−0.00984532	−	0.00141554i
$249$	−4.24087	−	5.82714i	−0.268754	−	0.369280i
$250$	6.75228	+	5.85089i	0.427052	+	0.370043i
$251$	1.96014	+	0.575550i	0.123723	+	0.0363284i	0.343008	−	0.939332i	$-0.388554\pi$
$251$	1.96014	+	0.575550i	0.123723	+	0.0363284i	−0.219285	+	0.975661i	$0.570372\pi$
$252$	−2.90008	+	3.17013i	−0.182688	+	0.199700i
$253$	−1.49653	+	18.7057i	−0.0940858	+	1.17602i
$254$			15.1537i			0.950831i
$255$	−0.660374	−	0.508373i	−0.0413542	−	0.0318356i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	4.76670	−	7.41713i	0.297339	−	0.462668i	−0.660152	−	0.751132i	$-0.729508\pi$
$257$	4.76670	−	7.41713i	0.297339	−	0.462668i	0.957491	+	0.288464i	$0.0931446\pi$
$258$	0.235562	−	0.417915i	0.0146654	−	0.0260183i
$259$	−6.17905	+	3.97103i	−0.383947	+	0.246748i
$260$	0.315828	+	0.691566i	0.0195868	+	0.0428891i
$261$	17.4034	+	0.468989i	1.07724	+	0.0290297i
$262$	1.77312	+	12.3323i	0.109544	+	0.761894i
$263$	6.87563	−	15.0555i	0.423969	−	0.928363i	−0.570298	−	0.821438i	$-0.693172\pi$
$263$	6.87563	−	15.0555i	0.423969	−	0.928363i	0.994267	−	0.106925i	$-0.0341005\pi$
$264$	0.574504	−	6.75291i	0.0353583	−	0.415613i
$265$	−3.31004	+	0.971915i	−0.203334	+	0.0597043i
$266$	9.82646	+	4.48759i	0.602499	+	0.275152i
$267$	−6.02230	+	25.9932i	−0.368559	+	1.59076i
$268$	−5.27353	+	4.56954i	−0.322132	+	0.279129i
$269$	−9.85091	+	4.49876i	−0.600620	+	0.274294i	−0.692433	−	0.721482i	$-0.743461\pi$
$269$	−9.85091	+	4.49876i	−0.600620	+	0.274294i	0.0918126	+	0.995776i	$0.470734\pi$
$270$	2.64758	−	4.41472i	0.161127	−	0.268671i
$271$	0.0562958	−	0.391546i	0.00341972	−	0.0237847i	−0.988040	−	0.154197i	$-0.950721\pi$
$271$	0.0562958	−	0.391546i	0.00341972	−	0.0237847i	0.991460	+	0.130412i	$0.0416301\pi$
$272$	−0.408580	−	0.262579i	−0.0247738	−	0.0159212i
$273$	0.889737	+	1.68294i	0.0538493	+	0.101856i
$274$	−0.0516162	+	0.175788i	−0.00311825	+	0.0106198i
$275$	−15.7241			−0.948196
$276$	−3.61537	+	7.47858i	−0.217619	+	0.450158i
$277$	−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
$279$	0.466766	−	0.0543218i	0.0279445	−	0.00325216i
$280$	−1.19361	−	0.767084i	−0.0713316	−	0.0458420i
$281$	1.06794	−	7.42768i	0.0637079	−	0.443098i	−0.932855	−	0.360253i	$-0.882690\pi$
$281$	1.06794	−	7.42768i	0.0637079	−	0.443098i	0.996562	−	0.0828450i	$-0.0264006\pi$
$282$	−11.4710	+	2.33399i	−0.683088	+	0.138987i
$283$	−23.3663	+	10.6710i	−1.38898	+	0.634327i	−0.962776	−	0.270299i	$-0.912877\pi$
$283$	−23.3663	+	10.6710i	−1.38898	+	0.634327i	−0.426206	+	0.904626i	$0.640150\pi$
$284$	−11.2401	+	9.73964i	−0.666980	+	0.577941i
$285$	−12.6089	−	2.92132i	−0.746887	−	0.173044i
$286$	−2.73145	−	1.24741i	−0.161514	−	0.0737610i
$287$	−4.22617	+	1.24092i	−0.249463	+	0.0732490i
$288$	1.31930	−	2.69433i	0.0777408	−	0.158765i
$289$	−6.96406	+	15.2492i	−0.409651	+	0.897010i
$290$	0.818196	+	5.69068i	0.0480461	+	0.334168i
$291$	2.97752	−	1.06509i	0.174545	−	0.0624370i
$292$	0.573709	+	1.25625i	0.0335738	+	0.0735163i
$293$	−20.1565	+	12.9538i	−1.17755	+	0.756768i	−0.974935	−	0.222490i	$-0.928582\pi$
$293$	−20.1565	+	12.9538i	−1.17755	+	0.756768i	−0.202619	+	0.979258i	$0.564945\pi$
$294$	7.46717	+	4.20894i	0.435494	+	0.245470i
$295$	6.62285	−	10.3054i	0.385597	−	0.600001i
$296$	3.35851	−	3.87593i	0.195209	−	0.225284i
$297$	3.51567	+	20.0257i	0.204000	+	1.16201i
$298$		−	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
$303$	14.5982	−	10.6242i	0.838642	−	0.610347i
$304$	−7.46605	−	1.07346i	−0.428207	−	0.0615669i
$305$	8.11737	+	12.6309i	0.464800	+	0.723242i
$306$	1.38645	+	0.448007i	0.0792583	+	0.0256109i
$307$	4.57183	+	5.27617i	0.260928	+	0.301127i	0.871064	−	0.491170i	$-0.163431\pi$
$307$	4.57183	+	5.27617i	0.260928	+	0.301127i	−0.610136	+	0.792297i	$0.708885\pi$
$308$	5.54690	−	0.797524i	0.316064	−	0.0454432i
$309$	−1.14065	−	1.17180i	−0.0648891	−	0.0666613i
$310$	0.0437192	+	0.148894i	0.00248309	+	0.00845662i
$311$	5.38154	+	18.3278i	0.305159	+	1.03928i	0.959179	+	0.282799i	$0.0912628\pi$
$311$	5.38154	+	18.3278i	0.305159	+	1.03928i	−0.654020	+	0.756477i	$0.726919\pi$
$312$	−0.927144	−	0.952465i	−0.0524892	−	0.0539227i
$313$	6.86238	−	0.986661i	0.387885	−	0.0557694i	0.0543860	−	0.998520i	$-0.482680\pi$
$313$	6.86238	−	0.986661i	0.387885	−	0.0557694i	0.333499	+	0.942751i	$0.391771\pi$
$314$	7.44810	+	8.59556i	0.420321	+	0.485076i
$315$	4.05032	+	1.30879i	0.228210	+	0.0737417i
$316$	3.75409	+	5.84148i	0.211184	+	0.328609i
$317$	−9.15329	−	1.31604i	−0.514100	−	0.0739164i	−0.119618	−	0.992820i	$-0.538167\pi$
$317$	−9.15329	−	1.31604i	−0.514100	−	0.0739164i	−0.394482	+	0.918904i	$0.629076\pi$
$318$	4.87660	−	3.54909i	0.273466	−	0.199023i
$319$	−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
$324$	−1.75876	+	8.82648i	−0.0977086	+	0.490360i
$325$	−2.01952	+	2.33065i	−0.112023	+	0.129281i
$326$	−8.05163	+	12.5286i	−0.445939	+	0.693894i
$327$	−11.0178	−	6.21027i	−0.609284	−	0.343428i
$328$	2.58723	−	1.66271i	0.142856	−	0.0918079i
$329$	−4.02095	−	8.80465i	−0.221682	−	0.485416i
$330$	−6.32190	+	2.26142i	−0.348009	+	0.124487i
$331$	−2.38295	−	16.5738i	−0.130979	−	0.910979i	−0.944282	−	0.329138i	$-0.893242\pi$
$331$	−2.38295	−	16.5738i	−0.130979	−	0.910979i	0.813303	−	0.581841i	$-0.197667\pi$
$332$	−1.72852	+	3.78493i	−0.0948649	+	0.207725i
$333$	−6.76617	+	13.8181i	−0.370784	+	0.757228i
$334$	21.3645	−	6.27319i	1.16902	−	0.343254i
$335$	6.28820	+	2.87172i	0.343561	+	0.156899i
$336$	2.41659	+	0.559894i	0.131836	+	0.0305447i
$337$	14.2763	−	12.3705i	0.777680	−	0.673864i	−0.172693	−	0.984976i	$-0.555247\pi$
$337$	14.2763	−	12.3705i	0.777680	−	0.673864i	0.950373	+	0.311112i	$0.100701\pi$
$338$	11.2895	−	5.15575i	0.614068	−	0.280436i
$339$	28.8757	−	5.87531i	1.56831	−	0.319103i
$340$	−0.0684758	+	0.476260i	−0.00371362	+	0.0258288i
$341$	−0.515611	−	0.331363i	−0.0279219	−	0.0179443i
$342$	22.4768	−	2.61583i	1.21541	−	0.141448i
$343$	−4.82126	+	16.4197i	−0.260324	+	0.886581i
$344$	−0.276973			−0.0149334
$345$	8.22729	+	0.180244i	0.442943	+	0.00970400i
$346$	0.206028			0.0110761
$347$	−4.55189	+	15.5023i	−0.244358	+	0.832209i	0.742392	+	0.669965i	$0.233691\pi$
$347$	−4.55189	+	15.5023i	−0.244358	+	0.832209i	−0.986751	+	0.162243i	$0.948127\pi$
$348$	−4.69790	−	8.88609i	−0.251834	−	0.476344i
$349$	11.3922	+	7.32134i	0.609812	+	0.391902i	0.808786	−	0.588102i	$-0.200125\pi$
$349$	11.3922	+	7.32134i	0.609812	+	0.391902i	−0.198975	+	0.980005i	$0.563761\pi$
$350$	0.819059	−	5.69668i	0.0437806	−	0.304501i
$351$	3.41978	+	2.05090i	0.182534	+	0.109469i
$352$	−3.55928	+	1.62547i	−0.189710	+	0.0866378i
$353$	9.20121	−	7.97289i	0.489731	−	0.424354i	−0.374669	−	0.927158i	$-0.622244\pi$
$353$	9.20121	−	7.97289i	0.489731	−	0.424354i	0.864400	+	0.502804i	$0.167698\pi$
$354$	−4.83401	+	20.8644i	−0.256925	+	1.10893i
$355$	13.4028	+	6.12086i	0.711348	+	0.324862i
$356$	14.7807	−	4.34001i	0.783376	−	0.230020i
$357$	−0.102128	+	1.20044i	−0.00540518	+	0.0635343i
$358$	−3.80325	+	8.32796i	−0.201008	+	0.440146i
$359$	−3.84519	−	26.7439i	−0.202941	−	1.41149i	−0.795496	−	0.605959i	$-0.792790\pi$
$359$	−3.84519	−	26.7439i	−0.202941	−	1.41149i	0.592555	−	0.805530i	$-0.298119\pi$
$360$	−2.97098	−	0.0800625i	−0.156585	−	0.00421966i
$361$	−15.7418	−	34.4698i	−0.828518	−	1.81420i
$362$	−4.60312	+	2.95825i	−0.241935	+	0.155482i
$363$	3.66613	−	6.50416i	0.192422	−	0.341380i
$364$	0.594206	−	0.924603i	0.0311449	−	0.0484624i
$365$	0.895973	−	1.03401i	0.0468974	−	0.0541225i
$366$	−20.8005	−	16.0127i	−1.08726	−	0.836999i
$367$		−	19.0718i		−	0.995540i	−0.867309	−	0.497770i	$-0.834152\pi$
$367$		−	19.0718i		−	0.995540i	0.867309	−	0.497770i	$-0.165848\pi$
$368$	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
$372$	−0.159647	−	0.219362i	−0.00827733	−	0.0113734i
$373$	19.5863	+	2.81609i	1.01414	+	0.145811i	0.629292	−	0.777169i	$-0.283345\pi$
$373$	19.5863	+	2.81609i	1.01414	+	0.145811i	0.384848	+	0.922980i	$0.374254\pi$
$374$	−1.02744	−	1.59873i	−0.0531276	−	0.0826681i
$375$	0.895956	+	15.4491i	0.0462670	+	0.797790i
$376$	4.42587	+	5.10772i	0.228247	+	0.263411i
$377$	−4.40817	+	0.633800i	−0.227032	+	0.0326423i
$378$	−7.43824	+	0.230566i	−0.382582	+	0.0118590i
$379$	−8.21058	−	27.9627i	−0.421749	−	1.43635i	−0.847156	−	0.531344i	$-0.821687\pi$
$379$	−8.21058	−	27.9627i	−0.421749	−	1.43635i	0.425407	−	0.905002i	$-0.360131\pi$
$380$	2.10527	+	7.16989i	0.107998	+	0.367808i
$381$	−18.8078	+	18.3078i	−0.963553	+	0.937936i
$382$	−11.9969	+	1.72490i	−0.613817	+	0.0882536i
$383$	−1.56512	−	1.80624i	−0.0799739	−	0.0922948i	0.714352	−	0.699786i	$-0.246721\pi$
$383$	−1.56512	−	1.80624i	−0.0799739	−	0.0922948i	−0.794326	+	0.607491i	$0.792176\pi$
$384$	−1.72915	+	0.100280i	−0.0882401	+	0.00511739i
$385$	−3.00151	−	4.67043i	−0.152971	−	0.238027i
$386$	−12.6545	−	1.81945i	−0.644099	−	0.0926074i
$387$	0.803279	−	0.212535i	0.0408330	−	0.0108038i
$388$	−1.37981	−	1.19561i	−0.0700492	−	0.0606979i
$389$	−11.8783	−	3.48779i	−0.602255	−	0.176838i	−0.0336295	−	0.999434i	$-0.510707\pi$
$389$	−11.8783	−	3.48779i	−0.602255	−	0.176838i	−0.568626	+	0.822596i	$0.692525\pi$
$390$	−0.476762	+	1.22749i	−0.0241418	+	0.0621563i
$391$	0.475903	+	2.28010i	0.0240675	+	0.115310i
$392$		−	4.94886i		−	0.249955i
$393$	−13.1639	+	17.0998i	−0.664030	+	0.862572i
$394$	14.3656	−	16.5788i	0.723730	−	0.835229i
$395$	3.71913	−	5.78708i	0.187130	−	0.291180i
$396$	9.07533	−	7.44540i	0.456053	−	0.374145i
$397$	14.8999	−	9.57558i	0.747804	−	0.480584i	−0.110404	−	0.993887i	$-0.535214\pi$
$397$	14.8999	−	9.57558i	0.747804	−	0.480584i	0.858208	+	0.513302i	$0.171578\pi$
$398$	1.65308	+	3.61973i	0.0828613	+	0.181441i
$399$	6.30200	+	17.6176i	0.315495	+	0.881981i
$400$	0.571898	+	3.97764i	0.0285949	+	0.198882i
$401$	−2.33475	+	5.11239i	−0.116592	+	0.255300i	−0.958927	−	0.283654i	$-0.908453\pi$
$401$	−2.33475	+	5.11239i	−0.116592	+	0.255300i	0.842335	+	0.538955i	$0.181181\pi$
$402$	−12.0425	−	1.02452i	−0.600628	−	0.0510984i
$403$	−0.115338	+	0.0338663i	−0.00574539	+	0.00168700i
$404$	−9.48202	−	4.33029i	−0.471748	−	0.215440i
$405$	8.67789	−	2.04759i	0.431208	−	0.101745i
$406$	6.28124	−	5.44273i	0.311733	−	0.270118i
$407$	18.2541	−	8.33636i	0.904821	−	0.413218i
$408$	−0.167726	−	0.824332i	−0.00830367	−	0.0408105i
$409$	−2.37432	+	16.5137i	−0.117402	+	0.816552i	0.842996	+	0.537920i	$0.180790\pi$
$409$	−2.37432	+	16.5137i	−0.117402	+	0.816552i	−0.960398	+	0.278632i	$0.910119\pi$
$410$	−2.56314	−	1.64723i	−0.126584	−	0.0813508i
$411$	−0.280536	+	0.148314i	−0.0138378	+	0.00731579i
$412$	−0.265994	+	0.905893i	−0.0131046	+	0.0446302i
$413$	−17.7091			−0.871408
$414$	−13.6498	+	4.54800i	−0.670849	+	0.223522i
$415$	4.12220			0.202351
$416$	−0.216206	+	0.736331i	−0.0106004	+	0.0361016i
$417$	26.7972	−	14.1672i	1.31226	−	0.693769i
$418$	−24.8289	−	15.9566i	−1.21442	−	0.780461i
$419$	−2.39837	+	16.6811i	−0.117168	+	0.814923i	0.843481	+	0.537159i	$0.180502\pi$
$419$	−2.39837	+	16.6811i	−0.117168	+	0.814923i	−0.960649	+	0.277764i	$0.910407\pi$
$420$	−0.489986	−	2.40816i	−0.0239089	−	0.117506i
$421$	21.5533	−	9.84305i	1.05044	−	0.479721i	0.186051	−	0.982540i	$-0.440431\pi$
$421$	21.5533	−	9.84305i	1.05044	−	0.479721i	0.864392	+	0.502819i	$0.167704\pi$
$422$	18.4539	−	15.9904i	0.898320	−	0.778398i
$423$	−16.7553	−	11.4172i	−0.814672	−	0.555125i
$424$	−3.16753	−	1.44656i	−0.153829	−	0.0702512i
$425$	−1.87267	+	0.549864i	−0.0908376	+	0.0266723i
$426$	−25.6678	−	2.18369i	−1.24361	−	0.105800i
$427$	9.01674	−	19.7439i	0.436350	−	0.955474i
$428$	−2.50472	−	17.4207i	−0.121070	−	0.842061i
$429$	−1.75176	−	4.89713i	−0.0845759	−	0.236436i
$430$	0.113987	+	0.249598i	0.00549696	+	0.0120367i
$431$	−13.4649	+	8.65334i	−0.648579	+	0.416817i	−0.823147	−	0.567829i	$-0.807784\pi$
$431$	−13.4649	+	8.65334i	−0.648579	+	0.416817i	0.174567	+	0.984645i	$0.444147\pi$
$432$	4.93792	−	1.61769i	0.237576	−	0.0778312i
$433$	−7.75522	+	12.0674i	−0.372692	+	0.579920i	−0.976049	−	0.217551i	$-0.930193\pi$
$433$	−7.75522	+	12.0674i	−0.372692	+	0.579920i	0.603357	+	0.797471i	$0.293829\pi$
$434$	0.146908	−	0.169541i	0.00705180	−	0.00813821i
$435$	−6.07439	+	7.89060i	−0.291245	+	0.378325i
$436$			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	0.448271	−	0.893898i	$-0.352040\pi$
$439$	7.16787	+	2.10468i	0.342104	+	0.100451i	−0.106168	+	0.994348i	$0.533858\pi$
$440$	2.92962	+	2.53853i	0.139664	+	0.121020i
$441$	3.79751	+	14.3527i	0.180834	+	0.683462i
$442$	−0.368925	−	0.0530435i	−0.0175480	−	0.00252302i
$443$	−12.3954	−	19.2876i	−0.588923	−	0.916383i	−0.999989	−	0.00477675i	$-0.998480\pi$
$443$	−12.3954	−	19.2876i	−0.588923	−	0.916383i	0.411065	−	0.911606i	$-0.365157\pi$
$444$	8.86807	−	0.514294i	0.420860	−	0.0244073i
$445$	−9.99400	−	11.5337i	−0.473761	−	0.546749i
$446$	29.1461	−	4.19057i	1.38011	−	0.198429i
$447$	16.8559	−	16.4078i	0.797259	−	0.776064i
$448$	−0.403491	−	1.37417i	−0.0190632	−	0.0649232i
$449$	0.217998	+	0.742433i	0.0102880	+	0.0350376i	0.964477	−	0.264167i	$-0.0850969\pi$
$449$	0.217998	+	0.742433i	0.0102880	+	0.0350376i	−0.954189	+	0.299204i	$0.903279\pi$
$450$	−4.71086	−	11.0971i	−0.222072	−	0.523122i
$451$	11.9114	−	1.71260i	0.560884	−	0.0806430i
$452$	−11.1412	−	12.8576i	−0.524036	−	0.604769i
$453$	−1.23297	−	21.2603i	−0.0579298	−	0.998895i
$454$	10.4793	+	16.3061i	0.491818	+	0.765283i
$455$	−1.07776	−	0.154958i	−0.0505261	−	0.00726456i
$456$	−7.68771	−	10.5632i	−0.360010	−	0.494669i
$457$	2.76305	+	2.39420i	0.129250	+	0.111996i	0.717087	−	0.696983i	$-0.245475\pi$
$457$	2.76305	+	2.39420i	0.129250	+	0.111996i	−0.587837	+	0.808979i	$0.700020\pi$
$458$	−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	$0.977175\pi$
$462$	7.69124	+	5.92092i	0.357829	+	0.275466i
$463$	−5.05378	+	5.83237i	−0.234869	+	0.271053i	−0.860933	−	0.508718i	$-0.830119\pi$
$463$	−5.05378	+	5.83237i	−0.234869	+	0.271053i	0.626064	+	0.779772i	$0.284665\pi$
$464$	−3.13747	+	4.88200i	−0.145653	+	0.226641i
$465$	−0.131978	+	0.234146i	−0.00612035	+	0.0108582i
$466$	−3.90718	+	2.51099i	−0.180996	+	0.116319i
$467$	−2.39118	−	5.23595i	−0.110651	−	0.242291i	0.846204	−	0.532860i	$-0.178883\pi$
$467$	−2.39118	−	5.23595i	−0.110651	−	0.242291i	−0.956854	+	0.290569i	$0.906155\pi$
$468$	0.0620188	−	2.30141i	0.00286682	−	0.106383i
$469$	−1.42223	−	9.89185i	−0.0656727	−	0.456763i
$470$	2.78143	−	6.09048i	0.128298	−	0.280933i
$471$	−1.66991	+	19.6287i	−0.0769454	+	0.904442i
$472$	11.8643	−	3.48366i	0.546097	−	0.160349i
$473$	−0.985826	−	0.450212i	−0.0453283	−	0.0207007i
$474$	−2.71459	+	11.7166i	−0.124685	+	0.538162i
$475$	−22.9076	+	19.8496i	−1.05107	+	0.910761i
$476$	0.632723	−	0.288955i	0.0290008	−	0.0132442i
$477$	10.2965	+	1.76472i	0.471444	+	0.0808010i
$478$	0.375049	−	2.60852i	0.0171543	−	0.119311i
$479$	15.7608	+	10.1288i	0.720129	+	0.462799i	0.848682	−	0.528904i	$-0.177397\pi$
$479$	15.7608	+	10.1288i	0.720129	+	0.462799i	−0.128553	+	0.991703i	$0.541033\pi$
$480$	0.801992	+	1.51697i	0.0366058	+	0.0692398i
$481$	1.10883	−	3.77634i	0.0505584	−	0.172186i
$482$	−10.2023			−0.464703
$483$	−6.21102	−	10.1465i	−0.282611	−	0.461682i
$484$	−4.31063			−0.195938
$485$	−0.509583	+	1.73548i	−0.0231390	+	0.0788040i
$486$	−13.0796	+	8.48074i	−0.593305	+	0.384694i
$487$	10.0131	+	6.43504i	0.453737	+	0.291599i	0.747479	−	0.664286i	$-0.231264\pi$
$487$	10.0131	+	6.43504i	0.453737	+	0.291599i	−0.293741	+	0.955885i	$0.594900\pi$
$488$	−2.15685	+	15.0012i	−0.0976361	+	0.679074i
$489$	−25.2771	+	5.14310i	−1.14307	+	0.232579i
$490$	−4.45972	+	2.03669i	−0.201470	+	0.0920082i
$491$	3.89586	−	3.37578i	0.175818	−	0.152347i	−0.562507	−	0.826793i	$-0.690163\pi$
$491$	3.89586	−	3.37578i	0.175818	−	0.152347i	0.738324	+	0.674446i	$0.235617\pi$
$492$	5.18937	+	1.20231i	0.233955	+	0.0542044i
$493$	−2.56382	−	1.17086i	−0.115468	−	0.0527327i
$494$	−5.55402	+	1.63081i	−0.249887	+	0.0733735i
$495$	−10.4444	−	5.11421i	−0.469442	−	0.229867i
$496$	−0.0650700	+	0.142484i	−0.00292173	+	0.00639770i
$497$	−3.03139	−	21.0837i	−0.135976	−	0.945735i
$498$	−6.78589	+	2.42739i	−0.304083	+	0.108774i
$499$	−6.44830	−	14.1198i	−0.288666	−	0.632090i	0.708630	−	0.705580i	$-0.249313\pi$
$499$	−6.44830	−	14.1198i	−0.288666	−	0.632090i	−0.997296	+	0.0734905i	$0.976586\pi$
$500$	7.51622	−	4.83038i	0.336136	−	0.216021i
$501$	33.5971	+	18.9373i	1.50101	+	0.846057i
$502$	1.10447	−	1.71859i	0.0492950	−	0.0767045i
$503$	0.00837455	−	0.00966474i	0.000373403	−	0.000430930i	−0.755563	−	0.655076i	$-0.772637\pi$
$503$	0.00837455	−	0.00966474i	0.000373403	−	0.000430930i	0.755936	+	0.654645i	$0.227182\pi$
$504$	2.22467	+	3.67574i	0.0990947	+	0.163730i
$505$			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	$-0.0603844\pi$
$509$	21.0985	+	18.2819i	0.935174	+	0.810333i	−0.0468863	+	0.998900i	$0.514930\pi$
$510$	−0.673829	+	0.490399i	−0.0298377	+	0.0217152i
$511$	−1.95778	−	0.281486i	−0.0866070	−	0.0124522i
$512$	0.540641	+	0.841254i	0.0238932	+	0.0371785i
$513$	30.4016	+	24.7364i	1.34226	+	1.09214i
$514$	−5.77375	−	6.66326i	−0.254669	−	0.293904i
$515$	0.925825	−	0.133113i	0.0407967	−	0.00586568i
$516$	−0.334621	−	0.343760i	−0.0147309	−	0.0151332i
$517$	7.45046	+	25.3739i	0.327671	+	1.11594i
$518$	2.06934	+	7.04752i	0.0909216	+	0.309650i
$519$	0.248910	+	0.255708i	0.0109259	+	0.0112243i
$520$	0.752532	−	0.108198i	0.0330007	−	0.00474478i
$521$	−8.85887	−	10.2237i	−0.388114	−	0.447907i	0.527748	−	0.849401i	$-0.323037\pi$
$521$	−8.85887	−	10.2237i	−0.388114	−	0.447907i	−0.915862	+	0.401494i	$0.868491\pi$
$522$	5.35310	−	16.5663i	0.234299	−	0.725088i
$523$	6.32151	+	9.83647i	0.276421	+	0.430119i	0.951510	−	0.307617i	$-0.0995315\pi$
$523$	6.32151	+	9.83647i	0.276421	+	0.430119i	−0.675090	+	0.737736i	$0.735895\pi$
$524$	12.3323	+	1.77312i	0.538741	+	0.0774592i
$525$	8.05987	−	5.86581i	0.351762	−	0.256005i
$526$	−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
$531$	−31.7356	+	19.2074i	−1.37721	+	0.833529i
$532$	7.07425	−	8.16412i	0.306708	−	0.353959i
$533$	1.27599	−	1.98548i	0.0552694	−	0.0860008i
$534$	23.2436	+	13.1015i	1.00585	+	0.566957i
$535$	−14.6680	+	9.42658i	−0.634155	+	0.407547i
$536$	2.89872	+	6.34731i	0.125206	+	0.274162i
$537$	−14.9309	+	5.34097i	−0.644318	+	0.230480i
$538$	1.54121	+	10.7193i	0.0664461	+	0.462143i
$539$	8.04423	−	17.6144i	0.346489	−	0.758706i
$540$	−3.48998	−	3.78411i	−0.150185	−	0.162842i
$541$	−28.4755	+	8.36116i	−1.22426	+	0.359474i	−0.829080	−	0.559130i	$-0.811135\pi$
$541$	−28.4755	+	8.36116i	−1.22426	+	0.359474i	−0.395177	+	0.918605i	$0.629317\pi$
$542$	−0.359825	−	0.164327i	−0.0154558	−	0.00705843i
$543$	−9.23277	−	2.13912i	−0.396216	−	0.0917982i
$544$	−0.367053	+	0.318053i	−0.0157373	+	0.0136364i
$545$	6.58030	−	3.00512i	0.281869	−	0.128725i
$546$	1.86544	−	0.379558i	0.0798333	−	0.0162436i
$547$	−1.34391	+	9.34710i	−0.0574615	+	0.399653i	0.940710	+	0.339211i	$0.110160\pi$
$547$	−1.34391	+	9.34710i	−0.0574615	+	0.399653i	−0.998172	+	0.0604420i	$0.980749\pi$
$548$	0.154126	+	0.0990507i	0.00658393	+	0.00423124i
$549$	−5.25588	−	45.1617i	−0.224316	−	1.92745i
$550$	−4.42998	+	15.0871i	−0.188895	+	0.643317i
$551$	−43.7728			−1.86479
$552$	6.15708	+	5.57588i	0.262063	+	0.237325i
$553$	−9.94473			−0.422893
$554$	−4.85453	+	16.5330i	−0.206249	+	0.702421i
$555$	−4.11308	−	7.77990i	−0.174591	−	0.330239i
$556$	−14.7223	−	9.46147i	−0.624366	−	0.401256i
$557$	−3.06304	+	21.3039i	−0.129785	+	0.902677i	0.816039	+	0.577997i	$0.196166\pi$
$557$	−3.06304	+	21.3039i	−0.129785	+	0.902677i	−0.945824	+	0.324680i	$0.894744\pi$
$558$	0.0793817	−	0.463163i	0.00336049	−	0.0196072i
$559$	−0.193346	+	0.0882981i	−0.00817766	+	0.00373461i
$560$	−1.07229	+	0.929143i	−0.0453125	+	0.0392635i
$561$	0.742943	−	3.20666i	0.0313671	−	0.135385i
$562$	−6.82593	−	3.11730i	−0.287935	−	0.131495i
$563$	26.8949	−	7.89705i	1.13348	−	0.332821i	0.339408	−	0.940639i	$-0.389773\pi$
$563$	26.8949	−	7.89705i	1.13348	−	0.332821i	0.794076	+	0.607819i	$0.207955\pi$
$564$	−0.992307	+	11.6639i	−0.0417837	+	0.491139i
$565$	−7.00164	+	15.3315i	−0.294561	+	0.644999i
$566$	3.65573	+	25.4262i	0.153662	+	1.06874i
$567$	−9.27257	−	8.95329i	−0.389411	−	0.376003i
$568$	6.17840	+	13.5288i	0.259240	+	0.567656i
$569$	−33.4384	+	21.4895i	−1.40181	+	0.900888i	−0.999891	−	0.0147870i	$-0.995293\pi$
$569$	−33.4384	+	21.4895i	−1.40181	+	0.900888i	−0.401919	+	0.915675i	$0.631657\pi$
$570$	−6.35533	+	11.2751i	−0.266195	+	0.472263i
$571$	−7.45842	+	11.6055i	−0.312125	+	0.485676i	−0.961505	−	0.274788i	$-0.911392\pi$
$571$	−7.45842	+	11.6055i	−0.312125	+	0.485676i	0.649380	+	0.760464i	$0.275029\pi$
$572$	−1.96642	+	2.26937i	−0.0822202	+	0.0948872i
$573$	−16.6348	−	12.8059i	−0.694928	−	0.534973i
$574$			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	0.920211	−	0.391424i	$-0.128017\pi$
$577$	35.6162	+	10.4579i	1.48272	+	0.435366i	0.562511	+	0.826790i	$0.309836\pi$
$578$	12.6695	+	10.9782i	0.526981	+	0.456631i
$579$	−13.0302	−	17.9041i	−0.541517	−	0.744068i
$580$	5.69068	+	0.818196i	0.236293	+	0.0339737i
$581$	−3.22180	−	5.01322i	−0.133663	−	0.207983i
$582$	−0.183086	−	3.15698i	−0.00758915	−	0.130861i
$583$	−8.92278	−	10.2974i	−0.369544	−	0.426476i
$584$	1.36699	−	0.196544i	0.0565666	−	0.00813304i
$585$	−2.09947	+	0.891250i	−0.0868023	+	0.0368487i
$586$	6.75032	+	22.9895i	0.278853	+	0.949687i
$587$	0.357155	+	1.21636i	0.0147414	+	0.0502045i	0.966535	−	0.256534i	$-0.0825805\pi$
$587$	0.357155	+	1.21636i	0.0147414	+	0.0502045i	−0.951794	+	0.306738i	$0.900762\pi$
$588$	6.14219	−	5.97890i	0.253300	−	0.246566i
$589$	−1.16947	+	0.168145i	−0.0481873	+	0.00692828i
$590$	−8.02204	−	9.25793i	−0.330262	−	0.381143i
$591$	37.9321	−	2.19983i	1.56032	−	0.0904890i
$592$	−2.77272	−	4.31444i	−0.113958	−	0.177322i
$593$	−19.7497	−	2.83958i	−0.811023	−	0.116608i	−0.275688	−	0.961247i	$-0.588906\pi$
$593$	−19.7497	−	2.83958i	−0.811023	−	0.116608i	−0.535335	+	0.844640i	$0.679815\pi$
$594$	20.2050	+	2.26862i	0.829019	+	0.0930828i
$595$	−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	$-0.179683\pi$
$600$	−4.24584	+	5.51532i	−0.173336	+	0.225162i
$601$	−14.9635	+	17.2688i	−0.610375	+	0.704410i	−0.973849	−	0.227194i	$-0.927045\pi$
$601$	−14.9635	+	17.2688i	−0.610375	+	0.704410i	0.363475	+	0.931604i	$0.381590\pi$
$602$	0.214459	−	0.333704i	0.00874069	−	0.0136008i
$603$	−13.2775	−	16.1841i	−0.540700	−	0.659069i
$604$	−10.3434	+	6.64731i	−0.420868	+	0.270475i
$605$	1.77402	+	3.88457i	0.0721243	+	0.157930i
$606$	−6.08111	−	17.0000i	−0.247028	−	0.690579i
$607$	2.88275	+	20.0500i	0.117007	+	0.813804i	0.960821	+	0.277168i	$0.0893959\pi$
$607$	2.88275	+	20.0500i	0.117007	+	0.813804i	−0.843814	+	0.536636i	$0.819695\pi$
$608$	−3.13340	+	6.86120i	−0.127076	+	0.278258i
$609$	14.3437	+	1.22029i	0.581238	+	0.0494488i
$610$	14.4062	−	4.23003i	0.583289	−	0.171269i
$611$	4.71787	+	2.15458i	0.190865	+	0.0871650i
$612$	0.820469	−	1.20408i	0.0331655	−	0.0486719i
$613$	7.49497	−	6.49443i	0.302719	−	0.262308i	−0.490233	−	0.871591i	$-0.663088\pi$
$613$	7.49497	−	6.49443i	0.302719	−	0.262308i	0.792952	+	0.609284i	$0.208543\pi$
$614$	6.35048	−	2.90017i	0.256284	−	0.117041i
$615$	−1.05219	−	5.17127i	−0.0424284	−	0.208526i
$616$	0.797524	−	5.54690i	0.0321332	−	0.223491i
$617$	−21.7944	−	14.0064i	−0.877410	−	0.563877i	0.0226007	−	0.999745i	$-0.492805\pi$
$617$	−21.7944	−	14.0064i	−0.877410	−	0.563877i	−0.900011	+	0.435867i	$0.856442\pi$
$618$	−1.44569	+	0.764308i	−0.0581542	+	0.0307450i
$619$	−4.36353	+	14.8608i	−0.175385	+	0.597307i	0.824137	+	0.566391i	$0.191661\pi$
$619$	−4.36353	+	14.8608i	−0.175385	+	0.597307i	−0.999522	+	0.0309160i	$0.990158\pi$
$620$	0.155180			0.00623218
$621$	−22.1354	−	11.4465i	−0.888264	−	0.459334i
$622$	19.1016			0.765903
$623$	−6.21567	+	21.1686i	−0.249025	+	0.848103i
$624$	−1.17509	+	0.621247i	−0.0470412	+	0.0248698i
$625$	9.45682	+	6.07753i	0.378273	+	0.243101i
$626$	0.986661	−	6.86238i	0.0394349	−	0.274276i
$627$	−10.1925	−	50.0936i	−0.407049	−	2.00055i
$628$	10.3458	−	4.72475i	0.412841	−	0.188538i
$629$	1.88246	−	1.63116i	0.0750586	−	0.0650387i
$630$	2.39688	−	3.51752i	0.0954939	−	0.140142i
$631$	8.26279	+	3.77349i	0.328936	+	0.150220i	0.573037	−	0.819530i	$-0.305765\pi$
$631$	8.26279	+	3.77349i	0.328936	+	0.150220i	−0.244100	+	0.969750i	$0.578493\pi$
$632$	6.66251	−	1.95629i	0.265020	−	0.0778170i
$633$	42.1409	+	3.58514i	1.67495	+	0.142496i
$634$	−3.84151	+	8.41174i	−0.152566	+	0.334073i
$635$	−2.13652	−	14.8598i	−0.0847852	−	0.589694i
$636$	−2.03143	−	5.67896i	−0.0805515	−	0.225185i
$637$	−1.57768	−	3.45464i	−0.0625100	−	0.136878i
$638$	−19.1027	+	12.2765i	−0.756282	+	0.486033i
$639$	−28.2999	−	34.4953i	−1.11953	−	1.36461i
$640$	0.535606	−	0.833419i	0.0211717	−	0.0329438i
$641$	28.9540	−	33.4147i	1.14361	−	1.31980i	0.203447	−	0.979086i	$-0.434786\pi$
$641$	28.9540	−	33.4147i	1.14361	−	1.31980i	0.940167	−	0.340715i	$-0.110669\pi$
$642$	18.5953	−	24.1553i	0.733899	−	0.953332i
$643$			19.9105i			0.785192i	0.919711	+	0.392596i	$0.128423\pi$
$643$			19.9105i			0.785192i	−0.919711	+	0.392596i	$0.871577\pi$
$644$	−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	$-0.167261\pi$
$647$	12.5068	+	10.8372i	0.491694	+	0.426055i	−0.373396	+	0.927672i	$0.621807\pi$
$648$	7.97345	+	4.17422i	0.313227	+	0.163979i
$649$	47.8909	+	6.88567i	1.87988	+	0.270286i
$650$	1.66728	+	2.59434i	0.0653960	+	0.101758i
$651$	0.387907	−	0.0224962i	0.0152033	−	0.000881697i
$652$	9.75268	+	11.2552i	0.381945	+	0.440788i
$653$	−27.5008	+	3.95401i	−1.07619	+	0.154732i	−0.657542	−	0.753417i	$-0.728404\pi$
$653$	−27.5008	+	3.95401i	−1.07619	+	0.154732i	−0.418645	+	0.908150i	$0.637495\pi$
$654$	−9.06277	+	8.82183i	−0.354382	+	0.344961i
$655$	−3.47746	−	11.8431i	−0.135876	−	0.462750i
$656$	−0.866453	−	2.95087i	−0.0338293	−	0.115212i
$657$	−3.81374	+	1.61898i	−0.148788	+	0.0631623i
$658$	−9.58084	+	1.37752i	−0.373500	+	0.0537012i
$659$	−4.23361	−	4.88584i	−0.164918	−	0.190325i	0.667275	−	0.744811i	$-0.267460\pi$
$659$	−4.23361	−	4.88584i	−0.164918	−	0.190325i	−0.832193	+	0.554486i	$0.812915\pi$
$660$	0.388729	+	6.70293i	0.0151313	+	0.260911i
$661$	−22.8371	−	35.5351i	−0.888258	−	1.38216i	−0.923835	−	0.382790i	$-0.874963\pi$
$661$	−22.8371	−	35.5351i	−0.888258	−	1.38216i	0.0355770	−	0.999367i	$-0.488673\pi$
$662$	−16.5738	−	2.38295i	−0.644159	−	0.0926161i
$663$	−0.379878	−	0.521969i	−0.0147532	−	0.0202716i
$664$	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
$669$	40.4135	+	31.1113i	1.56248	+	1.20283i
$670$	4.52699	−	5.22442i	0.174893	−	0.201837i
$671$	−32.0609	+	49.8877i	−1.23770	+	1.92589i
$672$	1.21805	−	2.16096i	0.0469872	−	0.0833610i
$673$	−8.60902	+	5.53268i	−0.331853	+	0.213269i	−0.695947	−	0.718093i	$-0.745015\pi$
$673$	−8.60902	+	5.53268i	−0.331853	+	0.213269i	0.364094	+	0.931362i	$0.381379\pi$
$674$	−7.84730	−	17.1832i	−0.302267	−	0.661872i
$675$	8.08161	−	19.2536i	0.311061	−	0.741071i
$676$	−1.76628	−	12.2847i	−0.0679338	−	0.472490i
$677$	16.0588	−	35.1640i	0.617192	−	1.35146i	−0.300353	−	0.953828i	$-0.597104\pi$
$677$	16.0588	−	35.1640i	0.617192	−	1.35146i	0.917545	−	0.397633i	$-0.130168\pi$
$678$	2.49792	−	29.3613i	0.0959319	−	1.12762i
$679$	2.50888	−	0.736673i	0.0962819	−	0.0282709i
$680$	0.437676	+	0.199880i	0.0167841	+	0.00766505i
$681$	−7.57761	+	32.7062i	−0.290374	+	1.25330i
$682$	−0.463205	+	0.401370i	−0.0177370	+	0.0153692i
$683$	31.8935	−	14.5653i	1.22037	−	0.557325i	0.302100	−	0.953276i	$-0.402312\pi$
$683$	31.8935	−	14.5653i	1.22037	−	0.557325i	0.918272	+	0.395951i	$0.129585\pi$
$684$	3.82257	−	22.3033i	0.146160	−	0.852787i
$685$	0.0258307	−	0.179656i	0.000986939	−	0.00686431i
$686$	14.3963	+	9.25194i	0.549653	+	0.353241i
$687$	−4.05583	−	7.67161i	−0.154740	−	0.292690i
$688$	−0.0780324	+	0.265754i	−0.00297496	+	0.0101318i
$689$	−2.67230			−0.101807
$690$	2.49084	−	7.84325i	0.0948246	−	0.298587i
$691$	−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
$693$	1.94343	+	16.6991i	0.0738248	+	0.634347i
$694$	13.5920	+	8.73502i	0.515944	+	0.331577i
$695$	−2.46738	+	17.1610i	−0.0935932	+	0.650955i
$696$	−9.84969	+	2.00410i	−0.373352	+	0.0759654i
$697$	1.35870	−	0.620499i	0.0514645	−	0.0235031i
$698$	10.2343	−	8.86810i	0.387375	−	0.335663i
$699$	−7.83687	−	1.81570i	−0.296418	−	0.0686762i
$700$	−5.23517	−	2.39082i	−0.197871	−	0.0903646i
$701$	3.40079	−	0.998563i	0.128446	−	0.0377152i	−0.216878	−	0.976199i	$-0.569587\pi$
$701$	3.40079	−	0.998563i	0.128446	−	0.0377152i	0.345324	+	0.938484i	$0.387769\pi$
$702$	2.93129	−	2.70345i	0.110634	−	0.102035i
$703$	16.0699	−	35.1882i	0.606089	−	1.32715i
$704$	0.556861	+	3.87305i	0.0209875	+	0.145971i
$705$	10.9194	−	3.90601i	0.411250	−	0.147109i
$706$	−5.05765	−	11.0747i	−0.190347	−	0.416802i
$707$	12.5591	−	8.07126i	0.472334	−	0.303551i
$708$	18.6573	+	10.5164i	0.701186	+	0.395230i
$709$	11.1532	−	17.3547i	0.418867	−	0.651770i	−0.566135	−	0.824313i	$-0.691562\pi$
$709$	11.1532	−	17.3547i	0.418867	−	0.651770i	0.985002	+	0.172543i	$0.0551982\pi$
$710$	9.64894	−	11.1355i	0.362118	−	0.417907i
$711$	−17.8215	+	10.7861i	−0.668357	+	0.404511i
$712$		−	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
$717$	3.69063	−	2.68596i	0.137829	−	0.100309i
$718$	−26.7439	−	3.84519i	−0.998073	−	0.143501i
$719$	8.91727	+	13.8755i	0.332558	+	0.517470i	0.966756	−	0.255700i	$-0.0823060\pi$
$719$	8.91727	+	13.8755i	0.332558	+	0.517470i	−0.634198	+	0.773171i	$0.718670\pi$
$720$	−0.913842	+	2.82808i	−0.0340569	+	0.105396i
$721$	−0.885485	−	1.02190i	−0.0329772	−	0.0380577i
$722$	−37.5085	+	5.39291i	−1.39592	+	0.200703i
$723$	−12.3258	−	12.6624i	−0.458401	−	0.470921i
$724$	1.54157	+	5.25010i	0.0572919	+	0.195118i
$725$	6.57016	+	22.3759i	0.244010	+	0.831020i
$726$	−5.20782	−	5.35006i	−0.193280	−	0.198559i
$727$	26.2884	−	3.77971i	0.974984	−	0.140182i	0.363634	−	0.931542i	$-0.381536\pi$
$727$	26.2884	−	3.77971i	0.974984	−	0.140182i	0.611350	+	0.791360i	$0.290627\pi$
$728$	−0.719743	−	0.830627i	−0.0266754	−	0.0307851i
$729$	−26.3277	−	5.98766i	−0.975100	−	0.221765i
$730$	−0.739699	−	1.15099i	−0.0273775	−	0.0426002i
$731$	−0.133151	−	0.0191443i	−0.00492478	−	0.000708076i
$732$	−21.2243	+	15.4466i	−0.784472	+	0.570922i
$733$	21.9088	+	18.9841i	0.809221	+	0.701194i	0.957715	−	0.287720i	$-0.0928971\pi$
$733$	21.9088	+	18.9841i	0.809221	+	0.701194i	−0.148494	+	0.988913i	$0.547443\pi$
$734$	−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
$738$	4.77724	+	7.89325i	0.175853	+	0.290554i
$739$	8.89595	−	10.2665i	0.327243	−	0.377659i	−0.568158	−	0.822920i	$-0.692344\pi$
$739$	8.89595	−	10.2665i	0.327243	−	0.377659i	0.895401	+	0.445261i	$0.146889\pi$
$740$	−2.74690	+	4.27426i	−0.100978	+	0.157125i
$741$	−8.73405	−	4.92303i	−0.320853	−	0.180852i
$742$	4.19545	−	2.69625i	0.154020	−	0.0989826i
$743$	11.0460	+	24.1874i	0.405239	+	0.887350i	0.996712	+	0.0810253i	$0.0258195\pi$
$743$	11.0460	+	24.1874i	0.405239	+	0.887350i	−0.591473	+	0.806325i	$0.701453\pi$
$744$	−0.255454	+	0.0913790i	−0.00936541	+	0.00335012i
$745$	1.91479	+	13.3177i	0.0701527	+	0.487922i
$746$	8.22011	−	17.9995i	0.300960	−	0.659010i
$747$	−11.2110	−	5.48956i	−0.410189	−	0.200853i
$748$	−1.82343	+	0.535407i	−0.0666711	+	0.0195764i
$749$	22.9283	+	10.4710i	0.837781	+	0.382602i
$750$	15.0758	+	3.49286i	0.550489	+	0.127541i
$751$	−28.8881	+	25.0316i	−1.05414	+	0.913418i	−0.996388	−	0.0849132i	$-0.972939\pi$
$751$	−28.8881	+	25.0316i	−1.05414	+	0.913418i	−0.0577519	+	0.998331i	$0.518393\pi$
$752$	6.14774	−	2.80758i	0.224185	−	0.102382i
$753$	3.46735	−	0.705498i	0.126357	−	0.0257098i
$754$	−0.633800	+	4.40817i	−0.0230816	+	0.160536i
$755$	10.2471	+	6.58541i	0.372930	+	0.239668i
$756$	−1.87437	+	7.20190i	−0.0681702	+	0.261931i
$757$	12.6565	−	43.1040i	0.460008	−	1.56664i	−0.324103	−	0.946022i	$-0.605062\pi$
$757$	12.6565	−	43.1040i	0.460008	−	1.56664i	0.784111	−	0.620621i	$-0.213119\pi$
$758$	−29.1432			−1.05853
$759$	12.8514	+	29.8542i	0.466474	+	1.08364i
$760$	7.47259			0.271059
$761$	5.34989	−	18.2201i	0.193933	−	0.660476i	−0.803905	−	0.594758i	$-0.797248\pi$
$761$	5.34989	−	18.2201i	0.193933	−	0.660476i	0.997838	−	0.0657185i	$-0.0209339\pi$
$762$	12.2674	+	23.2038i	0.444402	+	0.840587i
$763$	−8.79766	−	5.65391i	−0.318497	−	0.204685i
$764$	−1.72490	+	11.9969i	−0.0624047	+	0.434034i
$765$	−1.42273	−	0.243842i	−0.0514388	−	0.00881612i
$766$	−2.17402	+	0.992843i	−0.0785507	+	0.0358729i
$767$	7.17147	−	6.21412i	0.258947	−	0.224379i
$768$	−0.390939	+	1.68736i	−0.0141068	+	0.0608872i
$769$	−48.7532	−	22.2648i	−1.75808	−	0.802890i	−0.985867	−	0.167532i	$-0.946420\pi$
$769$	−48.7532	−	22.2648i	−1.75808	−	0.802890i	−0.772218	−	0.635358i	$-0.780853\pi$
$770$	−5.32687	+	1.56411i	−0.191967	+	0.0563666i
$771$	1.29451	−	15.2161i	0.0466207	−	0.547995i
$772$	−5.31094	+	11.6293i	−0.191145	+	0.418549i
$773$	4.53689	+	31.5548i	0.163181	+	1.13495i	0.892590	+	0.450869i	$0.148886\pi$
$773$	4.53689	+	31.5548i	0.163181	+	1.13495i	−0.729410	+	0.684077i	$0.760205\pi$
$774$	0.0223836	−	0.830618i	0.000804562	−	0.0298560i
$775$	0.261486	+	0.572576i	0.00939287	+	0.0205675i
$776$	−1.53592	+	0.987074i	−0.0551362	+	0.0354339i
$777$	−6.24686	+	11.0827i	−0.224105	+	0.397589i
$778$	−6.69303	+	10.4146i	−0.239957	+	0.373380i
$779$	15.1912	−	17.5315i	0.544280	−	0.628133i
$780$	1.04345	+	0.803273i	0.0373614	+	0.0287618i
$781$			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
$786$	12.6985	+	17.4482i	0.452939	+	0.622358i
$787$	−34.7521	−	4.99659i	−1.23878	−	0.178109i	−0.508381	−	0.861132i	$-0.669756\pi$
$787$	−34.7521	−	4.99659i	−1.23878	−	0.178109i	−0.730397	+	0.683023i	$0.760665\pi$
$788$	−11.8600	−	18.4545i	−0.422495	−	0.657415i
$789$	−1.65975	−	28.6195i	−0.0590888	−	1.01888i
$790$	−4.50486	−	5.19889i	−0.160276	−	0.184968i
$791$	24.1177	−	3.46760i	0.857525	−	0.123294i
$792$	−4.58699	−	10.8053i	−0.162992	−	0.383951i
$793$	3.27671	+	11.1595i	0.116359	+	0.396284i
$794$	−4.98992	−	16.9941i	−0.177085	−	0.603098i
$795$	−4.28163	+	4.16780i	−0.151854	+	0.147817i
$796$	3.93883	−	0.566319i	0.139608	−	0.0200726i
$797$	−26.7852	−	30.9118i	−0.948782	−	1.09495i	−0.995378	−	0.0960386i	$-0.969383\pi$
$797$	−26.7852	−	30.9118i	−0.948782	−	1.09495i	0.0465960	−	0.998914i	$-0.485163\pi$
$798$	18.6794	−	1.08329i	0.661243	−	0.0383481i
$799$	1.77463	+	2.76138i	0.0627820	+	0.0976907i
$800$	3.97764	+	0.571898i	0.140631	+	0.0202196i
$801$	11.8208	+	44.6768i	0.417667	+	1.57858i
$802$	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
$807$	−11.4421	+	14.8632i	−0.402781	+	0.523211i
$808$	−6.82628	+	7.87795i	−0.240148	+	0.277145i
$809$	−9.68844	+	15.0755i	−0.340627	+	0.530026i	−0.968734	−	0.248101i	$-0.920194\pi$
$809$	−9.68844	+	15.0755i	−0.340627	+	0.530026i	0.628107	+	0.778127i	$0.283830\pi$
$810$	0.480200	−	8.90325i	0.0168725	−	0.312828i
$811$	21.0744	−	13.5437i	0.740021	−	0.475582i	−0.115528	−	0.993304i	$-0.536856\pi$
$811$	21.0744	−	13.5437i	0.740021	−	0.475582i	0.855549	+	0.517722i	$0.173220\pi$
$812$	−3.45263	−	7.56020i	−0.121164	−	0.265311i
$813$	−0.230767	−	0.645119i	−0.00809334	−	0.0226253i
$814$	−2.85591	−	19.8633i	−0.100100	−	0.696208i
$815$	6.12906	−	13.4208i	0.214692	−	0.470109i
$816$	−0.838195	−	0.0713094i	−0.0293427	−	0.00249633i
$817$	−2.00454	+	0.588585i	−0.0701298	+	0.0205920i
$818$	15.1759	+	6.93060i	0.530613	+	0.242323i
$819$	2.72478	+	1.85669i	0.0952116	+	0.0648781i
$820$	−2.30262	+	1.99523i	−0.0804111	+	0.0696766i
$821$	24.2624	−	11.0803i	0.846765	−	0.386704i	0.0557077	−	0.998447i	$-0.482258\pi$
$821$	24.2624	−	11.0803i	0.846765	−	0.386704i	0.791057	+	0.611743i	$0.209531\pi$
$822$	0.0632701	+	0.310957i	0.00220680	+	0.0108459i
$823$	3.92743	−	27.3159i	0.136902	−	0.952173i	−0.799356	−	0.600858i	$-0.794826\pi$
$823$	3.92743	−	27.3159i	0.136902	−	0.952173i	0.936258	−	0.351315i	$-0.114265\pi$
$824$	0.794259	+	0.510439i	0.0276693	+	0.0177820i
$825$	−24.0771	+	12.7291i	−0.838258	+	0.443171i
$826$	−4.98923	+	16.9918i	−0.173597	+	0.591219i
$827$	33.9438			1.18034			0.590171	−	0.807278i	$-0.299060\pi$
$827$	33.9438			1.18034			0.590171	+	0.807278i	$0.299060\pi$
$828$	0.518190	+	14.3782i	0.0180084	+	0.499676i
$829$	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
$831$	−26.3846	+	13.9490i	−0.915272	+	0.483886i
$832$	0.645592	+	0.414897i	0.0223819	+	0.0143840i
$833$	0.342063	−	2.37910i	0.0118518	−	0.0824310i
$834$	−6.04365	−	29.7031i	−0.209275	−	1.02853i
$835$	−20.0657	+	9.16369i	−0.694402	+	0.317123i
$836$	−22.3053	+	19.3277i	−0.771446	+	0.668462i
$837$	0.670749	−	0.461040i	0.0231845	−	0.0159359i
$838$	15.3297	+	7.00082i	0.529554	+	0.241839i
$839$	4.61660	−	1.35556i	0.159383	−	0.0467990i	−0.201068	−	0.979577i	$-0.564441\pi$
$839$	4.61660	−	1.35556i	0.159383	−	0.0467990i	0.360450	+	0.932778i	$0.382623\pi$
$840$	−2.44866	−	0.208320i	−0.0844868	−	0.00718771i
$841$	−1.94315	+	4.25490i	−0.0670051	+	0.146721i
$842$	−3.37208	−	23.4533i	−0.116209	−	0.808255i
$843$	−4.37768	−	12.2380i	−0.150775	−	0.421499i
$844$	−10.1436	−	22.2113i	−0.349157	−	0.764546i
$845$	−10.3436	+	6.64745i	−0.355832	+	0.228679i
$846$	−15.6753	+	12.8600i	−0.538927	+	0.442136i
$847$	3.33769	−	5.19355i	0.114685	−	0.178453i
$848$	−2.28036	+	2.63168i	−0.0783079	+	0.0903722i
$849$	−27.1406	+	35.2555i	−0.931463	+	1.20997i
$850$			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	−0.0849762	−	0.996383i	$-0.527081\pi$
$853$	−20.3026	−	5.96138i	−0.695148	−	0.204114i	−0.610172	+	0.792269i	$0.708900\pi$
$854$	−16.4038	−	14.2140i	−0.561327	−	0.486393i
$855$	−21.6720	+	5.73408i	−0.741167	+	0.196102i
$856$	−17.4207	−	2.50472i	−0.595427	−	0.0856095i
$857$	−11.2878	−	17.5642i	−0.385584	−	0.599980i	0.593156	−	0.805088i	$-0.297882\pi$
$857$	−11.2878	−	17.5642i	−0.385584	−	0.599980i	−0.978739	+	0.205108i	$0.934246\pi$
$858$	−5.19229	+	0.301121i	−0.177262	+	0.0102801i
$859$	−2.96243	−	3.41883i	−0.101077	−	0.116649i	0.702957	−	0.711232i	$-0.251863\pi$
$859$	−2.96243	−	3.41883i	−0.101077	−	0.116649i	−0.804034	+	0.594583i	$0.797317\pi$
$860$	0.271601	−	0.0390503i	0.00926152	−	0.00133161i
$861$	−5.46667	+	5.32134i	−0.186304	+	0.181351i
$862$	4.50933	+	15.3574i	0.153588	+	0.523074i
$863$	3.08047	+	10.4911i	0.104861	+	0.357122i	0.995162	−	0.0982499i	$-0.0313244\pi$
$863$	3.08047	+	10.4911i	0.104861	+	0.357122i	−0.890301	+	0.455372i	$0.849506\pi$
$864$	−0.160990	−	5.19366i	−0.00547698	−	0.176692i
$865$	−0.202032	+	0.0290478i	−0.00686930	+	0.000987656i
$866$	9.39364	+	10.8408i	0.319209	+	0.368387i
$867$	1.68110	+	28.9876i	0.0570933	+	0.984470i
$868$	−0.121284	−	0.188722i	−0.00411666	−	0.00640565i
$869$	26.8936	+	3.86672i	0.912304	+	0.131169i
$870$	5.85963	+	8.05137i	0.198660	+	0.272967i
$871$	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
$876$	1.89545	+	1.45917i	0.0640413	+	0.0493006i
$877$	21.8053	−	25.1647i	0.736314	−	0.849751i	−0.256854	−	0.966450i	$-0.582686\pi$
$877$	21.8053	−	25.1647i	0.736314	−	0.849751i	0.993167	+	0.116699i	$0.0372312\pi$
$878$	4.03884	−	6.28456i	0.136304	−	0.212094i
$879$	−20.3777	+	36.1525i	−0.687322	+	1.21939i
$880$	3.26107	−	2.09576i	0.109931	−	0.0706481i
$881$	−19.8109	−	43.3798i	−0.667446	−	1.46150i	−0.875417	−	0.483368i	$-0.839413\pi$
$881$	−19.8109	−	43.3798i	−0.667446	−	1.46150i	0.207971	−	0.978135i	$-0.433314\pi$
$882$	14.8412	+	0.399943i	0.499729	+	0.0134668i
$883$	5.27020	+	36.6550i	0.177356	+	1.23354i	0.862849	+	0.505461i	$0.168678\pi$
$883$	5.27020	+	36.6550i	0.177356	+	1.23354i	−0.685493	+	0.728079i	$0.740413\pi$
$884$	−0.154833	+	0.339037i	−0.00520760	+	0.0114031i
$885$	1.79859	−	21.1412i	0.0604590	−	0.710655i
$886$	−21.9985	+	6.45935i	−0.739055	+	0.217006i
$887$	−3.20851	−	1.46528i	−0.107731	−	0.0491992i	0.360820	−	0.932635i	$-0.382497\pi$
$887$	−3.20851	−	1.46528i	−0.107731	−	0.0491992i	−0.468552	+	0.883436i	$0.655224\pi$
$888$	2.00496	−	8.65374i	0.0672821	−	0.290401i
$889$	−16.4019	+	14.2124i	−0.550103	+	0.476667i
$890$	−13.8821	+	6.33976i	−0.465330	+	0.212509i
$891$	21.5947	+	27.8178i	0.723449	+	0.931932i
$892$	4.19057	−	29.1461i	0.140311	−	0.975883i
$893$	42.8855	+	27.5608i	1.43511	+	0.922288i
$894$	−10.9943	−	20.7958i	−0.367705	−	0.695515i
$895$	2.55533	−	8.70265i	0.0854152	−	0.290897i
$896$	−1.43218			−0.0478457
$897$	6.07562	+	1.92948i	0.202859	+	0.0644235i
$898$	0.773776			0.0258212
$899$	−0.256098	+	0.872190i	−0.00854135	+	0.0290892i
$900$	−11.9748	+	1.39362i	−0.399160	+	0.0464539i
$901$	−1.42276	−	0.914353i	−0.0473990	−	0.0304615i
$902$	1.71260	−	11.9114i	0.0570232	−	0.396605i
$903$	0.673266	−	0.136989i	0.0224049	−	0.00455870i
$904$	−15.4756	+	7.06746i	−0.514710	+	0.235060i
$905$	4.09676	−	3.54986i	0.136181	−	0.118001i
$906$	−20.7465	−	4.80669i	−0.689255	−	0.159692i
$907$	−28.4290	−	12.9831i	−0.943971	−	0.431097i	−0.116868	−	0.993147i	$-0.537285\pi$
$907$	−28.4290	−	12.9831i	−0.943971	−	0.431097i	−0.827103	+	0.562050i	$0.810013\pi$
$908$	18.5980	−	5.46085i	0.617195	−	0.181225i
$909$	13.7525	−	28.0858i	0.456140	−	0.931547i
$910$	−0.452321	+	0.990446i	−0.0149943	+	0.0328330i
$911$	6.53428	+	45.4469i	0.216490	+	1.50572i	0.750853	+	0.660469i	$0.229643\pi$
$911$	6.53428	+	45.4469i	0.216490	+	1.50572i	−0.534363	+	0.845255i	$0.679448\pi$
$912$	−12.3012	+	4.40029i	−0.407334	+	0.145708i
$913$	6.76350	+	14.8100i	0.223839	+	0.490139i
$914$	3.07566	−	1.97661i	0.101734	−	0.0653803i
$915$	22.6546	+	12.7695i	0.748939	+	0.422147i
$916$	−2.70867	+	4.21477i	−0.0894969	+	0.139260i
$917$	−11.6852	+	13.4854i	−0.385878	+	0.445327i
$918$	2.48565	−	0.436377i	0.0820388	−	0.0144026i
$919$		−	12.9563i		−	0.427389i	−0.976901	−	0.213694i	$-0.931450\pi$
$919$		−	12.9563i		−	0.427389i	0.976901	−	0.213694i	$-0.0685496\pi$
$920$	−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
$924$	7.84795	−	5.71158i	0.258179	−	0.187897i
$925$	−20.3996	−	2.93303i	−0.670736	−	0.0964373i
$926$	4.17230	+	6.49223i	0.137110	+	0.213348i
$927$	−2.69520	−	0.870903i	−0.0885219	−	0.0286042i
$928$	3.80031	+	4.38580i	0.124751	+	0.143971i
$929$	−4.85973	+	0.698724i	−0.159443	+	0.0229244i	−0.221574	−	0.975144i	$-0.571119\pi$
$929$	−4.85973	+	0.698724i	−0.159443	+	0.0229244i	0.0621312	+	0.998068i	$0.480210\pi$
$930$	0.187478	+	0.192599i	0.00614766	+	0.00631556i
$931$	−10.5166	−	35.8164i	−0.344669	−	1.17383i
$932$	1.30850	+	4.45633i	0.0428613	+	0.145972i
$933$	23.0773	+	23.7076i	0.755517	+	0.776151i
$934$	−5.69753	+	0.819181i	−0.186429	+	0.0268044i
$935$	1.23291	+	1.42286i	0.0403206	+	0.0465324i
$936$	−2.19072	−	0.707890i	−0.0716059	−	0.0231381i
$937$	0.670883	+	1.04391i	0.0219168	+	0.0341032i	0.852039	−	0.523478i	$-0.175366\pi$
$937$	0.670883	+	1.04391i	0.0219168	+	0.0341032i	−0.830122	+	0.557581i	$0.811729\pi$
$938$	−9.89185	−	1.42223i	−0.322980	−	0.0464376i
$939$	9.70913	−	7.06611i	0.316846	−	0.230594i
$940$	−5.06016	−	4.38465i	−0.165044	−	0.143012i
$941$	−52.4042	−	15.3873i	−1.70833	−	0.501611i	−0.725829	−	0.687875i	$-0.758544\pi$
$941$	−52.4042	−	15.3873i	−1.70833	−	0.501611i	−0.982500	+	0.186264i	$0.940362\pi$
$942$	18.3631	+	7.13231i	0.598303	+	0.232383i
$943$	−7.17752	+	12.8851i	−0.233732	+	0.419596i
$944$		−	12.3651i		−	0.402451i
$945$	7.26146	−	1.27481i	0.236215	−	0.0414695i
$946$	−0.709714	+	0.819054i	−0.0230748	+	0.0266297i
$947$	−6.11395	+	9.51350i	−0.198677	+	0.309147i	−0.926269	−	0.376863i	$-0.877003\pi$
$947$	−6.11395	+	9.51350i	−0.198677	+	0.309147i	0.727592	+	0.686010i	$0.240639\pi$
$948$	10.4772	+	5.90559i	0.340285	+	0.191805i
$949$	0.891595	−	0.572993i	0.0289424	−	0.0186001i
$950$	12.5917	+	27.5720i	0.408529	+	0.894553i
$951$	−15.0811	+	5.39470i	−0.489040	+	0.174935i
$952$	−0.0989915	−	0.688501i	−0.00320833	−	0.0223144i
$953$	−11.1369	+	24.3865i	−0.360760	+	0.789955i	0.639024	+	0.769187i	$0.279338\pi$
$953$	−11.1369	+	24.3865i	−0.360760	+	0.789955i	−0.999784	+	0.0207679i	$0.993389\pi$
$954$	4.59409	−	9.38223i	0.148739	−	0.303761i
$955$	11.5211	−	3.38289i	0.372813	−	0.109468i
$956$	−2.39720	−	1.09476i	−0.0775308	−	0.0354071i
$957$	−38.3154	−	8.87719i	−1.23856	−	0.286959i
$958$	14.1589	−	12.2687i	0.457453	−	0.396385i
$959$	−0.238678	+	0.109000i	−0.00770730	+	0.00351981i
$960$	1.68147	−	0.342126i	0.0542691	−	0.0110421i
$961$	4.40827	−	30.6602i	0.142202	−	0.989038i
$962$	−3.31097	−	2.12783i	−0.106750	−	0.0686041i
$963$	52.4455	−	6.10357i	1.69003	−	0.196685i
$964$	−2.87433	+	9.78906i	−0.0925759	+	0.315284i
$965$	12.6656			0.407720
$966$	−11.4853	+	3.10083i	−0.369535	+	0.0997677i
$967$	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
$969$	−2.96564	−	5.60951i	−0.0952700	−	0.180203i
$970$	1.52161	+	0.977882i	0.0488561	+	0.0313979i
$971$	3.51908	−	24.4757i	0.112933	−	0.785463i	−0.852109	−	0.523365i	$-0.824676\pi$
$971$	3.51908	−	24.4757i	0.112933	−	0.785463i	0.965041	−	0.262098i	$-0.0844145\pi$
$972$	4.45225	+	14.9391i	0.142806	+	0.479173i
$973$	22.7988	−	10.4119i	0.730897	−	0.333789i
$974$	8.99539	−	7.79455i	0.288231	−	0.249754i
$975$	−1.20561	+	5.20362i	−0.0386105	+	0.166649i
$976$	13.7859	+	6.29582i	0.441277	+	0.201524i
$977$	31.7281	−	9.31620i	1.01507	−	0.298052i	0.268445	−	0.963295i	$-0.413490\pi$
$977$	31.7281	−	9.31620i	1.01507	−	0.298052i	0.746627	+	0.665243i	$0.231672\pi$
$978$	−2.18661	+	25.7022i	−0.0699202	+	0.821865i
$979$	25.0399	−	54.8297i	0.800278	−	1.75236i
$980$	0.697738	+	4.85288i	0.0222884	+	0.155019i
$981$	−21.8981	−	0.590113i	−0.699153	−	0.0188409i
$982$	−2.14145	−	4.68911i	−0.0683363	−	0.149636i
$983$	−26.5409	+	17.0568i	−0.846522	+	0.544026i	−0.890488	−	0.455007i	$-0.849637\pi$
$983$	−26.5409	+	17.0568i	−0.846522	+	0.544026i	0.0439664	+	0.999033i	$0.486001\pi$
$984$	2.61562	−	4.64043i	0.0833830	−	0.147932i
$985$	−11.7495	+	18.2827i	−0.374372	+	0.582534i
$986$	−1.84574	+	2.13009i	−0.0587803	+	0.0678360i
$987$	−13.2846	−	10.2269i	−0.422855	−	0.325524i
$988$			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	0.690963	−	0.722890i	$-0.257187\pi$
$991$	27.7470	+	8.14726i	0.881413	+	0.258806i	0.190451	+	0.981697i	$0.439005\pi$
$992$	0.118380	+	0.102577i	0.00375856	+	0.00325681i
$993$	−17.0658	−	23.4492i	−0.541568	−	0.744138i
$994$	−21.0837	−	3.03139i	−0.668736	−	0.0961497i
$995$	−2.13136	−	3.31646i	−0.0675686	−	0.105139i
$996$	0.417260	+	7.19489i	0.0132214	+	0.227979i
$997$	−25.3426	−	29.2469i	−0.802607	−	0.926258i	0.195914	−	0.980621i	$-0.437233\pi$
$997$	−25.3426	−	29.2469i	−0.802607	−	0.926258i	−0.998521	+	0.0543629i	$0.982687\pi$
$998$	−15.3646	+	2.20909i	−0.486356	+	0.0699275i
$999$	0.825649	+	26.6361i	0.0261224	+	0.842730i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.5.3	✓	80	3.2	odd	2	inner
138.2.f.a.5.8	yes	80	1.1	even	1	trivial
138.2.f.a.83.3	yes	80	23.14	odd	22	inner
138.2.f.a.83.8	yes	80	69.14	even	22	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)

\(f(q)\)	\(=\)	\(q+(0.281733 - 0.959493i) q^{2} +(1.53123 - 0.809531i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.140990 + 0.980604i) q^{5} +(-0.345342 - 1.69727i) q^{6} +(1.30276 - 0.594948i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.68932 - 2.47915i) q^{9} +O(q^{10})\)	\(q+(0.281733 - 0.959493i) q^{2} +(1.53123 - 0.809531i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.140990 + 0.980604i) q^{5} +(-0.345342 - 1.69727i) q^{6} +(1.30276 - 0.594948i) q^{7} +(-0.755750 + 0.654861i) q^{8} +(1.68932 - 2.47915i) q^{9} +(0.901161 + 0.411546i) q^{10} +(-3.75438 + 1.10239i) q^{11} +(-1.72582 - 0.146824i) q^{12} +(-0.318796 + 0.698067i) q^{13} +(-0.203820 - 1.41760i) q^{14} +(0.577942 + 1.61566i) q^{15} +(0.415415 + 0.909632i) q^{16} +(-0.408580 + 0.262579i) q^{17} +(-1.90279 - 2.31935i) q^{18} +(-4.07796 + 6.34543i) q^{19} +(0.648762 - 0.748712i) q^{20} +(1.51319 - 1.96562i) 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} +(0.579784 - 5.16371i) q^{27} +(-1.41760 - 0.203820i) q^{28} +(3.13747 + 4.88200i) q^{29} +(1.71304 - 0.0993461i) q^{30} +(0.102577 + 0.118380i) q^{31} +(0.989821 - 0.142315i) q^{32} +(-4.85640 + 4.72729i) q^{33} +(0.136832 + 0.466007i) q^{34} +(0.399734 + 1.36137i) q^{35} +(-2.76148 + 1.17228i) q^{36} +(-5.07638 + 0.729874i) q^{37} +(4.93950 + 5.70049i) q^{38} +(0.0769565 + 1.32697i) q^{39} +(-0.535606 - 0.833419i) q^{40} +(-3.04414 - 0.437682i) q^{41} +(-1.45969 - 2.00567i) 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} +(1.37247 + 1.05656i) q^{48} +(-3.24082 + 3.74010i) q^{49} +(2.17259 - 3.38061i) q^{50} +(-0.413064 + 0.732826i) q^{51} +(0.645592 - 0.414897i) q^{52} +(1.44656 + 3.16753i) q^{53} +(-4.79119 - 2.01108i) q^{54} +(-0.551675 - 3.83698i) q^{55} +(-0.594948 + 1.30276i) q^{56} +(-1.10747 + 13.0175i) q^{57} +(5.56817 - 1.63496i) q^{58} +(-11.2477 - 5.13667i) q^{59} +(0.387298 - 1.67164i) q^{60} +(11.4538 - 9.92474i) q^{61} +(0.142484 - 0.0650700i) q^{62} +(0.725802 - 4.23479i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.639580 - 0.411033i) q^{65} +(3.16760 + 5.99151i) q^{66} +(1.96590 - 6.69523i) q^{67} +0.485680 q^{68} +(-1.00179 - 8.24599i) q^{69} +1.41884 q^{70} +(4.19016 - 14.2704i) q^{71} +(0.346797 + 2.97989i) q^{72} +(-1.16181 - 0.746652i) q^{73} +(-0.729874 + 5.07638i) q^{74} +(6.82056 - 1.38777i) q^{75} +(6.86120 - 3.13340i) q^{76} +(-4.23518 + 3.66980i) q^{77} +(1.29490 + 0.300013i) q^{78} +(-6.31629 - 2.88455i) q^{79} +(-0.950558 + 0.279109i) q^{80} +(-3.29240 - 8.37616i) q^{81} +(-1.27759 + 2.79752i) q^{82} +(-0.592165 - 4.11860i) q^{83} +(-2.33567 + 0.835496i) q^{84} +(-0.199880 - 0.437676i) q^{85} +(0.233005 - 0.149743i) q^{86} +(8.75631 + 4.93557i) q^{87} +(2.11546 - 3.29172i) q^{88} +(-10.0879 + 11.6421i) q^{89} +(2.54264 - 1.53888i) 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} +(1.40043 - 1.01921i) q^{96} +(1.80716 + 0.259831i) q^{97} +(2.67556 + 4.16325i) q^{98} +(-3.60937 + 11.1700i) 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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