LMFDB - Embedded newform 138.2.f.a.113.2

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			113.2
Character	$\chi$	$=$	138.113
Dual form			138.2.f.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(0.0700914 - 1.73063i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.21268 - 0.943327i) q^{5} +(1.41801 + 0.994615i) q^{6} +(-1.80758 - 1.56628i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.99017 - 0.242605i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(0.0700914 - 1.73063i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.21268 - 0.943327i) q^{5} +(1.41801 + 0.994615i) q^{6} +(-1.80758 - 1.56628i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.99017 - 0.242605i) q^{9} +(2.53048 - 2.19268i) q^{10} +(0.146746 - 0.0943077i) q^{11} +(-1.60336 + 0.655173i) q^{12} +(0.435504 + 0.502599i) q^{13} +(2.29489 - 0.673841i) q^{14} +(-1.85773 + 5.49384i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.46011 - 3.19721i) q^{17} +(1.82070 - 2.38433i) q^{18} +(6.08977 - 2.78111i) q^{19} +(0.476514 + 3.31423i) q^{20} +(-2.83735 + 3.01848i) q^{21} +0.174437i q^{22} +(2.56678 - 4.05113i) q^{23} +(0.315673 - 1.70304i) q^{24} +(5.22517 + 3.35801i) q^{25} +(-0.658264 + 0.0946441i) q^{26} +(-0.629445 + 5.15789i) q^{27} +(-0.673841 + 2.29489i) q^{28} +(-5.54968 - 2.53446i) q^{29} +(-3.61735 - 4.53302i) q^{30} +(-1.22988 + 8.55402i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-0.152926 - 0.260573i) q^{33} +(1.90026 + 2.95687i) q^{34} +(4.32967 + 6.73709i) q^{35} +(1.02148 + 2.82074i) q^{36} +(-2.59752 - 8.84635i) q^{37} +(-0.952764 + 6.62662i) q^{38} +(0.900339 - 0.718470i) q^{39} +(-3.04573 - 1.39094i) q^{40} +(-0.791908 + 2.69699i) q^{41} +(-1.00532 - 4.01884i) q^{42} +(-5.73482 + 0.824543i) q^{43} +(-0.146746 - 0.0943077i) q^{44} +(9.37761 + 3.60013i) q^{45} +(2.02032 + 4.34952i) q^{46} +7.88048i q^{47} +(1.26202 + 1.18629i) q^{48} +(-0.182080 - 1.26640i) q^{49} +(-5.64988 + 2.58021i) q^{50} +(-5.43084 - 2.75102i) q^{51} +(0.276265 - 0.604936i) q^{52} +(7.73902 - 8.93131i) q^{53} +(-3.99879 - 3.31809i) q^{54} +(-0.560410 + 0.164551i) q^{55} +(-1.56628 - 1.80758i) q^{56} +(-4.38623 - 10.7341i) q^{57} +(5.13250 - 3.29846i) q^{58} +(7.68344 - 6.65774i) q^{59} +(5.76911 - 0.592371i) q^{60} +(-0.619733 - 0.0891041i) q^{61} +(-6.53117 - 5.65929i) q^{62} +(5.02500 + 5.12197i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-0.925020 - 2.02551i) q^{65} +(0.301886 + 0.0122265i) q^{66} +(4.04398 - 6.29256i) q^{67} -3.51483 q^{68} +(-6.83110 - 4.72610i) q^{69} -8.00840 q^{70} +(-2.12838 + 3.31183i) q^{71} +(-2.92521 - 0.665682i) q^{72} +(-2.52644 - 5.53213i) q^{73} +(8.84635 + 2.59752i) q^{74} +(6.17772 - 8.80747i) q^{75} +(-5.05956 - 4.38414i) q^{76} +(-0.412967 - 0.0593757i) q^{77} +(0.117656 + 1.14585i) q^{78} +(-3.93306 + 3.40802i) q^{79} +(2.81678 - 1.81023i) q^{80} +(8.88229 + 1.45086i) q^{81} +(-1.84072 - 2.12430i) q^{82} +(11.4071 - 3.34943i) q^{83} +(3.92438 + 1.32702i) q^{84} +(-7.70689 + 8.89423i) q^{85} +(2.40683 - 5.27022i) q^{86} +(-4.77519 + 9.42681i) q^{87} +(0.158673 - 0.0724637i) q^{88} +(2.16027 + 15.0250i) q^{89} +(-8.09854 + 5.94258i) q^{90} -1.59061i q^{91} +(-4.75131 - 0.651925i) q^{92} +(14.7177 + 2.72804i) q^{93} +(-6.62948 - 4.26051i) q^{94} +(-22.1880 + 3.19015i) q^{95} +(-1.68028 + 0.420323i) q^{96} +(-1.10459 + 3.76189i) q^{97} +(1.16380 + 0.531490i) q^{98} +(-0.461675 + 0.246395i) 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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	0.0700914	−	1.73063i	0.0404673	−	0.999181i
$3$	0.0700914	−	1.73063i	0.0404673	−	0.999181i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−3.21268	−	0.943327i	−1.43675	−	0.421869i	−0.531615	−	0.846986i	$-0.678415\pi$
$5$	−3.21268	−	0.943327i	−1.43675	−	0.421869i	−0.905138	+	0.425117i	$0.860233\pi$
$6$	1.41801	+	0.994615i	0.578899	+	0.406050i
$7$	−1.80758	−	1.56628i	−0.683202	−	0.591998i	0.242546	−	0.970140i	$-0.422018\pi$
$7$	−1.80758	−	1.56628i	−0.683202	−	0.591998i	−0.925747	+	0.378142i	$0.876563\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	−2.99017	−	0.242605i	−0.996725	−	0.0808683i
$10$	2.53048	−	2.19268i	0.800209	−	0.693385i
$11$	0.146746	−	0.0943077i	0.0442455	−	0.0284348i	−0.518331	−	0.855180i	$-0.673447\pi$
$11$	0.146746	−	0.0943077i	0.0442455	−	0.0284348i	0.562577	+	0.826745i	$0.309810\pi$
$12$	−1.60336	+	0.655173i	−0.462849	+	0.189132i
$13$	0.435504	+	0.502599i	0.120787	+	0.139396i	0.812922	−	0.582372i	$-0.197875\pi$
$13$	0.435504	+	0.502599i	0.120787	+	0.139396i	−0.692135	+	0.721768i	$0.743330\pi$
$14$	2.29489	−	0.673841i	0.613335	−	0.180091i
$15$	−1.85773	+	5.49384i	−0.479665	+	1.41850i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.46011	−	3.19721i	0.354130	−	0.775436i	−0.645799	−	0.763507i	$-0.723476\pi$
$17$	1.46011	−	3.19721i	0.354130	−	0.775436i	0.999929	−	0.0119287i	$-0.00379712\pi$
$18$	1.82070	−	2.38433i	0.429144	−	0.561993i
$19$	6.08977	−	2.78111i	1.39709	−	0.638029i	0.432463	−	0.901652i	$-0.357645\pi$
$19$	6.08977	−	2.78111i	1.39709	−	0.638029i	0.964626	+	0.263622i	$0.0849173\pi$
$20$	0.476514	+	3.31423i	0.106552	+	0.741084i
$21$	−2.83735	+	3.01848i	−0.619160	+	0.658686i
$22$			0.174437i			0.0371901i
$23$	2.56678	−	4.05113i	0.535211	−	0.844719i
$23$	2.56678	−	4.05113i	0.535211	−	0.844719i
$24$	0.315673	−	1.70304i	0.0644364	−	0.347632i
$25$	5.22517	+	3.35801i	1.04503	+	0.671602i
$26$	−0.658264	+	0.0946441i	−0.129096	+	0.0185612i
$27$	−0.629445	+	5.15789i	−0.121137	+	0.992636i
$28$	−0.673841	+	2.29489i	−0.127344	+	0.433693i
$29$	−5.54968	−	2.53446i	−1.03055	−	0.470636i	−0.172938	−	0.984933i	$-0.555326\pi$
$29$	−5.54968	−	2.53446i	−1.03055	−	0.470636i	−0.857613	+	0.514296i	$0.828053\pi$
$30$	−3.61735	−	4.53302i	−0.660435	−	0.827613i
$31$	−1.22988	+	8.55402i	−0.220893	+	1.53635i	0.513778	+	0.857923i	$0.328246\pi$
$31$	−1.22988	+	8.55402i	−0.220893	+	1.53635i	−0.734671	+	0.678423i	$0.762664\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	−0.152926	−	0.260573i	−0.0266211	−	0.0453599i
$34$	1.90026	+	2.95687i	0.325892	+	0.507098i
$35$	4.32967	+	6.73709i	0.731847	+	1.13878i
$36$	1.02148	+	2.82074i	0.170247	+	0.470123i
$37$	−2.59752	−	8.84635i	−0.427030	−	1.45433i	−0.839500	−	0.543360i	$-0.817152\pi$
$37$	−2.59752	−	8.84635i	−0.427030	−	1.45433i	0.412470	−	0.910971i	$-0.364666\pi$
$38$	−0.952764	+	6.62662i	−0.154559	+	1.07498i
$39$	0.900339	−	0.718470i	0.144170	−	0.115047i
$40$	−3.04573	−	1.39094i	−0.481572	−	0.219927i
$41$	−0.791908	+	2.69699i	−0.123675	+	0.421199i	−0.997933	−	0.0642628i	$-0.979530\pi$
$41$	−0.791908	+	2.69699i	−0.123675	+	0.421199i	0.874258	+	0.485462i	$0.161349\pi$
$42$	−1.00532	−	4.01884i	−0.155124	−	0.620121i
$43$	−5.73482	+	0.824543i	−0.874552	+	0.125742i	−0.564950	−	0.825125i	$-0.691105\pi$
$43$	−5.73482	+	0.824543i	−0.874552	+	0.125742i	−0.309601	+	0.950866i	$0.600196\pi$
$44$	−0.146746	−	0.0943077i	−0.0221227	−	0.0142174i
$45$	9.37761	+	3.60013i	1.39793	+	0.536675i
$46$	2.02032	+	4.34952i	0.297880	+	0.641301i
$47$			7.88048i			1.14949i	0.818334	+	0.574743i	$0.194898\pi$
$47$			7.88048i			1.14949i	−0.818334	+	0.574743i	$0.805102\pi$
$48$	1.26202	+	1.18629i	0.182158	+	0.171227i
$49$	−0.182080	−	1.26640i	−0.0260115	−	0.180914i
$50$	−5.64988	+	2.58021i	−0.799013	+	0.364897i
$51$	−5.43084	−	2.75102i	−0.760470	−	0.385220i
$52$	0.276265	−	0.604936i	0.0383111	−	0.0838895i
$53$	7.73902	−	8.93131i	1.06304	−	1.22681i	0.0900527	−	0.995937i	$-0.471296\pi$
$53$	7.73902	−	8.93131i	1.06304	−	1.22681i	0.972984	−	0.230873i	$-0.0741581\pi$
$54$	−3.99879	−	3.31809i	−0.544166	−	0.451534i
$55$	−0.560410	+	0.164551i	−0.0755656	+	0.0221881i
$56$	−1.56628	−	1.80758i	−0.209303	−	0.241548i
$57$	−4.38623	−	10.7341i	−0.580970	−	1.42176i
$58$	5.13250	−	3.29846i	0.673931	−	0.433109i
$59$	7.68344	−	6.65774i	1.00030	−	0.866764i	0.00920920	−	0.999958i	$-0.497069\pi$
$59$	7.68344	−	6.65774i	1.00030	−	0.866764i	0.991090	+	0.133193i	$0.0425231\pi$
$60$	5.76911	−	0.592371i	0.744789	−	0.0764748i
$61$	−0.619733	−	0.0891041i	−0.0793486	−	0.0114086i	0.102526	−	0.994730i	$-0.467307\pi$
$61$	−0.619733	−	0.0891041i	−0.0793486	−	0.0114086i	−0.181875	+	0.983322i	$0.558217\pi$
$62$	−6.53117	−	5.65929i	−0.829460	−	0.718731i
$63$	5.02500	+	5.12197i	0.633090	+	0.645308i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−0.925020	−	2.02551i	−0.114735	−	0.251234i
$66$	0.301886	+	0.0122265i	0.0371596	+	0.00150498i
$67$	4.04398	−	6.29256i	0.494051	−	0.768759i	−0.501279	−	0.865286i	$-0.667137\pi$
$67$	4.04398	−	6.29256i	0.494051	−	0.768759i	0.995330	+	0.0965269i	$0.0307734\pi$
$68$	−3.51483			−0.426236
$69$	−6.83110	−	4.72610i	−0.822368	−	0.568956i
$70$	−8.00840			−0.957186
$71$	−2.12838	+	3.31183i	−0.252593	+	0.393042i	−0.944274	−	0.329161i	$-0.893234\pi$
$71$	−2.12838	+	3.31183i	−0.252593	+	0.393042i	0.691681	+	0.722203i	$0.256870\pi$
$72$	−2.92521	−	0.665682i	−0.344740	−	0.0784513i
$73$	−2.52644	−	5.53213i	−0.295697	−	0.647487i	0.702222	−	0.711958i	$-0.252191\pi$
$73$	−2.52644	−	5.53213i	−0.295697	−	0.647487i	−0.997920	+	0.0644710i	$0.979464\pi$
$74$	8.84635	+	2.59752i	1.02837	+	0.301956i
$75$	6.17772	−	8.80747i	0.713342	−	1.01700i
$76$	−5.05956	−	4.38414i	−0.580372	−	0.502895i
$77$	−0.412967	−	0.0593757i	−0.0470619	−	0.00676649i
$78$	0.117656	+	1.14585i	0.0133219	+	0.129742i
$79$	−3.93306	+	3.40802i	−0.442504	+	0.383432i	−0.847421	−	0.530921i	$-0.821846\pi$
$79$	−3.93306	+	3.40802i	−0.442504	+	0.383432i	0.404917	+	0.914354i	$0.367300\pi$
$80$	2.81678	−	1.81023i	0.314925	−	0.202390i
$81$	8.88229	+	1.45086i	0.986921	+	0.161207i
$82$	−1.84072	−	2.12430i	−0.203273	−	0.234590i
$83$	11.4071	−	3.34943i	1.25209	−	0.367648i	0.412548	−	0.910936i	$-0.364639\pi$
$83$	11.4071	−	3.34943i	1.25209	−	0.367648i	0.839547	+	0.543288i	$0.182821\pi$
$84$	3.92438	+	1.32702i	0.428185	+	0.144790i
$85$	−7.70689	+	8.89423i	−0.835930	+	0.964714i
$86$	2.40683	−	5.27022i	0.259535	−	0.568302i
$87$	−4.77519	+	9.42681i	−0.511955	+	1.01066i
$88$	0.158673	−	0.0724637i	0.0169146	−	0.00772466i
$89$	2.16027	+	15.0250i	0.228988	+	1.59265i	0.702386	+	0.711797i	$0.252118\pi$
$89$	2.16027	+	15.0250i	0.228988	+	1.59265i	−0.473398	+	0.880849i	$0.656973\pi$
$90$	−8.09854	+	5.94258i	−0.853661	+	0.626402i
$91$		−	1.59061i		−	0.166741i
$92$	−4.75131	−	0.651925i	−0.495359	−	0.0679679i
$93$	14.7177	+	2.72804i	1.52615	+	0.282884i
$94$	−6.62948	−	4.26051i	−0.683779	−	0.439438i
$95$	−22.1880	+	3.19015i	−2.27644	+	0.327302i
$96$	−1.68028	+	0.420323i	−0.171492	+	0.0428991i
$97$	−1.10459	+	3.76189i	−0.112154	+	0.381962i	−0.996371	−	0.0851145i	$-0.972874\pi$
$97$	−1.10459	+	3.76189i	−0.112154	+	0.381962i	0.884217	+	0.467076i	$0.154693\pi$
$98$	1.16380	+	0.531490i	0.117562	+	0.0536886i
$99$	−0.461675	+	0.246395i	−0.0464000	+	0.0247637i
$100$	0.883941	−	6.14795i	0.0883941	−	0.614795i
$101$	−3.77413	−	12.8535i	−0.375540	−	1.27897i	−0.903091	−	0.429449i	$-0.858708\pi$
$101$	−3.77413	−	12.8535i	−0.375540	−	1.27897i	0.527551	−	0.849523i	$-0.323110\pi$
$102$	5.25044	−	3.08140i	0.519871	−	0.305104i
$103$	−0.709786	−	1.10445i	−0.0699373	−	0.108825i	0.804523	−	0.593921i	$-0.202421\pi$
$103$	−0.709786	−	1.10445i	−0.0699373	−	0.108825i	−0.874461	+	0.485096i	$0.838784\pi$
$104$	0.359544	+	0.559462i	0.0352562	+	0.0548597i
$105$	11.9629	−	7.02085i	1.16746	−	0.685164i
$106$	3.32946	+	11.3391i	0.323386	+	1.10135i
$107$	−0.295739	+	2.05691i	−0.0285902	+	0.198849i	−0.999110	−	0.0421705i	$-0.986573\pi$
$107$	−0.295739	+	2.05691i	−0.0285902	+	0.198849i	0.970520	+	0.241020i	$0.0774818\pi$
$108$	4.95326	−	1.57010i	0.476628	−	0.151083i
$109$	2.64483	+	1.20785i	0.253328	+	0.115691i	0.538032	−	0.842924i	$-0.319168\pi$
$109$	2.64483	+	1.20785i	0.253328	+	0.115691i	−0.284704	+	0.958616i	$0.591895\pi$
$110$	0.164551	−	0.560410i	0.0156893	−	0.0534330i
$111$	−15.4918	+	3.87530i	−1.47042	+	0.367828i
$112$	2.36743	−	0.340385i	0.223701	−	0.0321633i
$113$	−8.75523	−	5.62665i	−0.823623	−	0.529310i	0.0596226	−	0.998221i	$-0.481010\pi$
$113$	−8.75523	−	5.62665i	−0.823623	−	0.529310i	−0.883246	+	0.468911i	$0.844647\pi$
$114$	11.4015	+	2.11335i	1.06784	+	0.197934i
$115$	−12.0678	+	10.5937i	−1.12533	+	0.987864i
$116$			6.10102i			0.566465i
$117$	−1.18030	−	1.60851i	−0.109119	−	0.148707i
$118$	1.44687	+	10.0632i	0.133195	+	0.926390i
$119$	−7.64699	+	3.49226i	−0.700999	+	0.320135i
$120$	−2.62068	+	5.17354i	−0.239234	+	0.472278i
$121$	−4.55692	+	9.97827i	−0.414266	+	0.907116i
$122$	0.410012	−	0.473179i	0.0371207	−	0.0428396i
$123$	4.61199	+	1.55954i	0.415849	+	0.140619i
$124$	8.29192	−	2.43473i	0.744636	−	0.218645i
$125$	−2.65570	−	3.06484i	−0.237533	−	0.274128i
$126$	−7.02560	+	1.45815i	−0.625890	+	0.129902i
$127$	18.2002	−	11.6965i	1.61500	−	1.03790i	0.655898	−	0.754849i	$-0.272290\pi$
$127$	18.2002	−	11.6965i	1.61500	−	1.03790i	0.959105	−	0.283051i	$-0.0913464\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	1.02502	+	9.98265i	0.0902478	+	0.878924i
$130$	2.20407	+	0.316898i	0.193310	+	0.0277938i
$131$	7.69051	+	6.66386i	0.671923	+	0.582224i	0.922559	−	0.385857i	$-0.126094\pi$
$131$	7.69051	+	6.66386i	0.671923	+	0.582224i	−0.250636	+	0.968081i	$0.580640\pi$
$132$	−0.173498	+	0.247353i	−0.0151010	+	0.0215293i
$133$	−15.3637	−	4.51120i	−1.33221	−	0.391171i
$134$	3.10730	+	6.80403i	0.268430	+	0.587779i
$135$	6.88778	−	15.9769i	0.592806	−	1.37507i
$136$	1.90026	−	2.95687i	0.162946	−	0.253549i
$137$	10.2876			0.878926			0.439463	−	0.898261i	$-0.355169\pi$
$137$	10.2876			0.878926			0.439463	+	0.898261i	$0.355169\pi$
$138$	7.66902	−	3.19157i	0.652830	−	0.271684i
$139$	2.55486			0.216700			0.108350	−	0.994113i	$-0.465443\pi$
$139$	2.55486			0.216700			0.108350	+	0.994113i	$0.465443\pi$
$140$	4.32967	−	6.73709i	0.365924	−	0.569388i
$141$	13.6382	+	0.552354i	1.14855	+	0.0465166i
$142$	−1.63540	−	3.58102i	−0.137240	−	0.300513i
$143$	0.111307	+	0.0326828i	0.00930798	+	0.00273307i
$144$	2.14150	−	2.10095i	0.178458	−	0.175079i
$145$	15.4385	+	13.3776i	1.28210	+	1.11095i
$146$	6.01982	+	0.865519i	0.498204	+	0.0716309i
$147$	−2.20443	+	0.226350i	−0.181818	+	0.0186691i
$148$	−6.96787	+	6.03770i	−0.572756	+	0.496296i
$149$	−15.3258	+	9.84932i	−1.25554	+	0.806888i	−0.987668	−	0.156566i	$-0.949958\pi$
$149$	−15.3258	+	9.84932i	−1.25554	+	0.806888i	−0.267875	+	0.963454i	$0.586321\pi$
$150$	4.06939	+	9.95871i	0.332264	+	0.813125i
$151$	4.64937	+	5.36566i	0.378360	+	0.436651i	0.912707	−	0.408614i	$-0.133988\pi$
$151$	4.64937	+	5.36566i	0.378360	+	0.436651i	−0.534347	+	0.845265i	$0.679442\pi$
$152$	6.42358	−	1.88613i	0.521021	−	0.152986i
$153$	−5.14166	+	9.20597i	−0.415678	+	0.744259i
$154$	0.273217	−	0.315309i	0.0220164	−	0.0254083i
$155$	12.0205	−	26.3211i	0.965506	−	2.11416i
$156$	−1.02756	−	0.520514i	−0.0822704	−	0.0416745i
$157$	1.56422	−	0.714356i	0.124838	−	0.0570118i	−0.352017	−	0.935994i	$-0.614504\pi$
$157$	1.56422	−	0.714356i	0.124838	−	0.0570118i	0.476855	+	0.878982i	$0.341777\pi$
$158$	−0.740633	−	5.15122i	−0.0589216	−	0.409809i
$159$	−14.9144	−	14.0194i	−1.18279	−	1.11181i
$160$			3.34831i			0.264707i
$161$	−10.9849	+	3.30245i	−0.865728	+	0.260270i
$162$	−6.02267	+	6.68786i	−0.473186	+	0.525448i
$163$	−0.837342	−	0.538127i	−0.0655857	−	0.0421494i	0.507437	−	0.861689i	$-0.330593\pi$
$163$	−0.837342	−	0.538127i	−0.0655857	−	0.0421494i	−0.573023	+	0.819539i	$0.694229\pi$
$164$	2.78224	−	0.400026i	0.217256	−	0.0312368i
$165$	0.245498	+	0.981396i	0.0191120	+	0.0764016i
$166$	−3.34943	+	11.4071i	−0.259966	+	0.885365i
$167$	10.0742	+	4.60072i	0.779563	+	0.356014i	0.765125	−	0.643881i	$-0.222677\pi$
$167$	10.0742	+	4.60072i	0.779563	+	0.356014i	0.0144375	+	0.999896i	$0.495404\pi$
$168$	−3.23804	+	2.58396i	−0.249820	+	0.199357i
$169$	1.78715	−	12.4299i	0.137473	−	0.956147i
$170$	−3.31564	−	11.2920i	−0.254298	−	0.866059i
$171$	−18.8842	+	6.83858i	−1.44411	+	0.522959i
$172$	3.13236	+	4.87405i	0.238840	+	0.371643i
$173$	1.30865	+	2.03629i	0.0994945	+	0.154817i	0.887432	−	0.460939i	$-0.152487\pi$
$173$	1.30865	+	2.03629i	0.0994945	+	0.154817i	−0.787937	+	0.615755i	$0.788851\pi$
$174$	−5.34868	−	9.11367i	−0.405482	−	0.690906i
$175$	−4.18534	−	14.2539i	−0.316382	−	1.07750i
$176$	−0.0248250	+	0.172661i	−0.00187125	+	0.0130148i
$177$	−10.9836	−	13.7639i	−0.825575	−	1.03456i
$178$	−13.8078	−	6.30579i	−1.03493	−	0.472639i
$179$	3.56599	−	12.1447i	0.266535	−	0.907734i	−0.712092	−	0.702087i	$-0.752252\pi$
$179$	3.56599	−	12.1447i	0.266535	−	0.907734i	0.978626	−	0.205647i	$-0.0659299\pi$
$180$	−0.620812	−	10.0257i	−0.0462726	−	0.747273i
$181$	−9.15702	+	1.31658i	−0.680636	+	0.0978607i	−0.473957	−	0.880548i	$-0.657175\pi$
$181$	−9.15702	+	1.31658i	−0.680636	+	0.0978607i	−0.206679	+	0.978409i	$0.566266\pi$
$182$	1.33811	+	0.859949i	0.0991870	+	0.0637436i
$183$	−0.197644	+	1.06628i	−0.0146103	+	0.0788220i
$184$	3.11719	−	3.64460i	0.229802	−	0.268684i
$185$			30.8708i			2.26967i
$186$	−10.2519	+	10.9064i	−0.751708	+	0.799695i
$187$	−0.0872556	−	0.606876i	−0.00638076	−	0.0443792i
$188$	7.16834	−	3.27367i	0.522805	−	0.238757i
$189$	9.21646	−	8.33742i	0.670399	−	0.606458i
$190$	9.31200	−	20.3904i	0.675563	−	1.47928i
$191$	−0.963220	+	1.11162i	−0.0696962	+	0.0804337i	−0.789527	−	0.613716i	$-0.789674\pi$
$191$	−0.963220	+	1.11162i	−0.0696962	+	0.0804337i	0.719831	+	0.694150i	$0.244219\pi$
$192$	0.554828	−	1.64078i	0.0400412	−	0.118413i
$193$	5.88402	−	1.72770i	0.423541	−	0.124363i	−0.0630142	−	0.998013i	$-0.520071\pi$
$193$	5.88402	−	1.72770i	0.423541	−	0.124363i	0.486555	+	0.873650i	$0.338253\pi$
$194$	−2.56751	−	2.96307i	−0.184337	−	0.212736i
$195$	−3.57025	+	1.45890i	−0.255671	+	0.104474i
$196$	−1.07632	+	0.691706i	−0.0768797	+	0.0494076i
$197$	−16.4790	+	14.2792i	−1.17408	+	1.01735i	−0.174618	+	0.984636i	$0.555869\pi$
$197$	−16.4790	+	14.2792i	−1.17408	+	1.01735i	−0.999465	+	0.0327122i	$0.989586\pi$
$198$	0.0423192	−	0.521597i	0.00300750	−	0.0370683i
$199$	−0.422569	−	0.0607563i	−0.0299551	−	0.00430690i	0.127321	−	0.991862i	$-0.459362\pi$
$199$	−0.422569	−	0.0607563i	−0.0299551	−	0.00430690i	−0.157276	+	0.987555i	$0.550271\pi$
$200$	4.69409	+	4.06745i	0.331922	+	0.287612i
$201$	−10.6067	−	7.43970i	−0.748136	−	0.524756i
$202$	12.8535	+	3.77413i	0.904370	+	0.265547i
$203$	6.06184	+	13.2736i	0.425458	+	0.931623i
$204$	−0.246360	+	6.08288i	−0.0172486	+	0.425887i
$205$	5.08829	−	7.91754i	0.355382	−	0.552985i
$206$	1.31286			0.0914714
$207$	−8.65794	+	11.4909i	−0.601769	+	0.798671i
$208$	−0.665034			−0.0461118
$209$	0.631368	−	0.982427i	0.0436726	−	0.0679559i
$210$	−0.561320	+	13.8596i	−0.0387347	+	0.956402i
$211$	4.16291	+	9.11550i	0.286586	+	0.627537i	0.997096	−	0.0761505i	$-0.0242629\pi$
$211$	4.16291	+	9.11550i	0.286586	+	0.627537i	−0.710510	+	0.703687i	$0.751536\pi$
$212$	−11.3391	−	3.32946i	−0.778773	−	0.228669i
$213$	5.58238	+	3.91558i	0.382498	+	0.268291i
$214$	−1.57050	−	1.36084i	−0.107357	−	0.0930253i
$215$	19.2019	+	2.76082i	1.30956	+	0.188287i
$216$	−1.35708	+	5.01581i	−0.0923378	+	0.341282i
$217$	15.6211	−	13.5357i	1.06043	−	0.918866i
$218$	−2.44601	+	1.57196i	−0.165665	+	0.106466i
$219$	−9.75116	+	3.98458i	−0.658922	+	0.269253i
$220$	0.382484	+	0.441410i	0.0257870	+	0.0297598i
$221$	2.24280	−	0.658545i	0.150867	−	0.0442985i
$222$	5.11541	−	15.1277i	0.343324	−	1.01531i
$223$	3.02207	−	3.48765i	0.202372	−	0.233550i	−0.645487	−	0.763771i	$-0.723346\pi$
$223$	3.02207	−	3.48765i	0.202372	−	0.233550i	0.847860	+	0.530221i	$0.177891\pi$
$224$	−0.993579	+	2.17563i	−0.0663863	+	0.145366i
$225$	−14.8095	−	11.3087i	−0.987300	−	0.753913i
$226$	9.46687	−	4.32338i	0.629727	−	0.287587i
$227$	−0.571788	−	3.97688i	−0.0379509	−	0.263955i	0.962008	−	0.273021i	$-0.0880230\pi$
$227$	−0.571788	−	3.97688i	−0.0379509	−	0.263955i	−0.999959	+	0.00906687i	$0.997114\pi$
$228$	−7.94196	+	8.44895i	−0.525969	+	0.559546i
$229$		−	6.47386i		−	0.427805i	−0.976855	−	0.213902i	$-0.931383\pi$
$229$		−	6.47386i		−	0.427805i	0.976855	−	0.213902i	$-0.0686174\pi$
$230$	−2.38762	−	15.8794i	−0.157435	−	1.04706i
$231$	−0.131703	+	0.710532i	−0.00866541	+	0.0467496i
$232$	−5.13250	−	3.29846i	−0.336965	−	0.216555i
$233$	−20.6304	+	2.96621i	−1.35155	+	0.194323i	−0.779759	−	0.626080i	$-0.784658\pi$
$233$	−20.6304	+	2.96621i	−1.35155	+	0.194323i	−0.571786	+	0.820403i	$0.693749\pi$
$234$	1.99129	−	0.123304i	0.130174	−	0.00806066i
$235$	7.43388	−	25.3175i	0.484933	−	1.65153i
$236$	−9.24791	−	4.22338i	−0.601988	−	0.274919i
$237$	5.62235	+	7.04556i	0.365211	+	0.457658i
$238$	1.19640	−	8.32112i	0.0775509	−	0.539378i
$239$	−2.55094	−	8.68772i	−0.165007	−	0.561962i	−0.999933	−	0.0115993i	$-0.996308\pi$
$239$	−2.55094	−	8.68772i	−0.165007	−	0.561962i	0.834926	−	0.550362i	$-0.185510\pi$
$240$	−2.93541	−	5.00168i	−0.189480	−	0.322857i
$241$	2.19681	+	3.41830i	0.141509	+	0.220192i	0.904773	−	0.425895i	$-0.140041\pi$
$241$	2.19681	+	3.41830i	0.141509	+	0.220192i	−0.763264	+	0.646087i	$0.776404\pi$
$242$	−5.93060	−	9.22819i	−0.381233	−	0.593211i
$243$	3.13348	−	15.2703i	0.201013	−	0.979589i
$244$	0.176394	+	0.600744i	0.0112925	+	0.0384587i
$245$	−0.609661	+	4.24028i	−0.0389498	+	0.270902i
$246$	−3.80540	+	3.03671i	−0.242623	+	0.193613i
$247$	4.04990	+	1.84953i	0.257689	+	0.117683i
$248$	−2.43473	+	8.29192i	−0.154605	+	0.526537i
$249$	−4.99710	−	19.9763i	−0.316678	−	1.26595i
$250$	4.01409	−	0.577139i	0.253873	−	0.0365015i
$251$	4.41926	+	2.84009i	0.278942	+	0.179265i	0.672630	−	0.739979i	$-0.265165\pi$
$251$	4.41926	+	2.84009i	0.278942	+	0.179265i	−0.393688	+	0.919244i	$0.628801\pi$
$252$	2.57165	−	6.69864i	0.161999	−	0.421975i
$253$	−0.00538890	−	0.836553i	−0.000338797	−	0.0525936i
$254$			21.6346i			1.35747i
$255$	14.8524	+	13.9612i	0.930096	+	0.874284i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	16.6280	−	7.59377i	1.03723	−	0.473687i	0.177330	−	0.984151i	$-0.443254\pi$
$257$	16.6280	−	7.59377i	1.03723	−	0.473687i	0.859899	+	0.510465i	$0.170527\pi$
$258$	−8.95211	−	4.53473i	−0.557334	−	0.282320i
$259$	−9.16062	+	20.0589i	−0.569213	+	1.24640i
$260$	−1.45820	+	1.68286i	−0.0904339	+	0.104366i
$261$	15.9796	+	8.92484i	0.989115	+	0.552434i
$262$	−9.76380	+	2.86691i	−0.603209	+	0.177118i
$263$	−15.1908	−	17.5311i	−0.936703	−	1.08101i	−0.996566	−	0.0828062i	$-0.973612\pi$
$263$	−15.1908	−	17.5311i	−0.936703	−	1.08101i	0.0598627	−	0.998207i	$-0.480934\pi$
$264$	−0.114286	−	0.279684i	−0.00703384	−	0.0172134i
$265$	−33.2881	+	21.3930i	−2.04487	+	1.31416i
$266$	12.1013	−	10.4859i	0.741980	−	0.642930i
$267$	26.1541	−	2.68550i	1.60061	−	0.164350i
$268$	−7.40385	−	1.06451i	−0.452262	−	0.0650254i
$269$	6.91584	+	5.99261i	0.421666	+	0.365376i	0.839695	−	0.543058i	$-0.182734\pi$
$269$	6.91584	+	5.99261i	0.421666	+	0.365376i	−0.418029	+	0.908434i	$0.637279\pi$
$270$	9.71677	+	14.4321i	0.591344	+	0.878310i
$271$	25.6521	+	7.53215i	1.55826	+	0.457545i	0.943555	−	0.331215i	$-0.107458\pi$
$271$	25.6521	+	7.53215i	1.55826	+	0.457545i	0.614701	+	0.788760i	$0.289277\pi$
$272$	1.46011	+	3.19721i	0.0885325	+	0.193859i
$273$	−2.75276	−	0.111488i	−0.166605	−	0.00674757i
$274$	−5.56188	+	8.65445i	−0.336005	+	0.522835i
$275$	1.08346			0.0653349
$276$	−1.46127	+	8.17708i	−0.0879580	+	0.492203i
$277$	27.7970			1.67016			0.835078	−	0.550131i	$-0.185422\pi$
$277$	27.7970			1.67016			0.835078	+	0.550131i	$0.185422\pi$
$278$	−1.38126	+	2.14928i	−0.0828424	+	0.128905i
$279$	5.75281	−	25.2796i	0.344412	−	1.51345i
$280$	3.32681	+	7.28469i	0.198815	+	0.435344i
$281$	19.3165	+	5.67184i	1.15233	+	0.338354i	0.801447	−	0.598066i	$-0.204064\pi$
$281$	19.3165	+	5.67184i	1.15233	+	0.338354i	0.350881	+	0.936420i	$0.385882\pi$
$282$	−7.83805	+	11.1746i	−0.466749	+	0.665436i
$283$	−7.96292	−	6.89991i	−0.473347	−	0.410157i	0.385247	−	0.922813i	$-0.374116\pi$
$283$	−7.96292	−	6.89991i	−0.473347	−	0.410157i	−0.858594	+	0.512656i	$0.828662\pi$
$284$	3.89671	+	0.560262i	0.231227	+	0.0332454i
$285$	3.96579	+	38.6228i	0.234913	+	2.28782i
$286$	−0.0876718	+	0.0759680i	−0.00518414	+	0.00449208i
$287$	5.65568	−	3.63468i	0.333844	−	0.214549i
$288$	0.609652	+	2.93740i	0.0359241	+	0.173088i
$289$	3.04245	+	3.51117i	0.178967	+	0.206539i
$290$	−19.6006	+	5.75526i	−1.15099	+	0.337960i
$291$	6.43302	+	2.17531i	0.377110	+	0.127519i
$292$	−3.98268	+	4.59626i	−0.233069	+	0.268976i
$293$	−0.626345	+	1.37150i	−0.0365914	+	0.0801241i	−0.927045	−	0.374950i	$-0.877660\pi$
$293$	−0.626345	+	1.37150i	−0.0365914	+	0.0801241i	0.890454	+	0.455074i	$0.150387\pi$
$294$	1.00139	−	1.97686i	0.0584020	−	0.115293i
$295$	−30.9649	+	14.1412i	−1.80284	+	0.823331i
$296$	−1.31212	−	9.12597i	−0.0762653	−	0.530436i
$297$	0.394060	+	0.816259i	0.0228657	+	0.0473642i
$298$		−	18.2179i		−	1.05533i
$299$	3.15394	−	0.474224i	0.182397	−	0.0274251i
$300$	−10.5779	−	1.96070i	−0.610714	−	0.113201i
$301$	11.6576	+	7.49190i	0.671934	+	0.431826i
$302$	−7.02752	+	1.01040i	−0.404388	+	0.0581423i
$303$	−22.5092	+	5.63071i	−1.29312	+	0.323476i
$304$	−1.88613	+	6.42358i	−0.108177	+	0.368417i
$305$	1.90695	+	0.870874i	0.109192	+	0.0498661i
$306$	−4.96477	−	9.30256i	−0.283817	−	0.531792i
$307$	−2.15733	+	15.0046i	−0.123125	+	0.856356i	0.830856	+	0.556488i	$0.187852\pi$
$307$	−2.15733	+	15.0046i	−0.123125	+	0.856356i	−0.953981	+	0.299867i	$0.903058\pi$
$308$	0.117543	+	0.400313i	0.00669761	+	0.0228100i
$309$	−1.96114	+	1.15097i	−0.111566	+	0.0654762i
$310$	15.6440	+	24.3425i	0.888519	+	1.38256i
$311$	−2.59708	−	4.04114i	−0.147267	−	0.229152i	0.759781	−	0.650179i	$-0.225306\pi$
$311$	−2.59708	−	4.04114i	−0.147267	−	0.229152i	−0.907048	+	0.421027i	$0.861670\pi$
$312$	0.993424	−	0.583025i	0.0562415	−	0.0330073i
$313$	−3.56220	−	12.1317i	−0.201348	−	0.685727i	−0.996816	−	0.0797321i	$-0.974594\pi$
$313$	−3.56220	−	12.1317i	−0.201348	−	0.685727i	0.795469	−	0.605995i	$-0.207225\pi$
$314$	−0.244727	+	1.70212i	−0.0138108	+	0.0960560i
$315$	−11.3120	−	21.1955i	−0.637359	−	1.19423i
$316$	4.73390	+	2.16190i	0.266302	+	0.121616i
$317$	1.40230	−	4.77580i	0.0787610	−	0.268235i	−0.910693	−	0.413084i	$-0.864451\pi$
$317$	1.40230	−	4.77580i	0.0787610	−	0.268235i	0.989454	+	0.144849i	$0.0462696\pi$
$318$	19.8572	−	4.96730i	1.11354	−	0.278552i
$319$	−1.05341	+	0.151458i	−0.0589797	+	0.00847999i
$320$	−2.81678	−	1.81023i	−0.157463	−	0.101195i
$321$	3.53903	+	0.655988i	0.197529	+	0.0366137i
$322$	3.16066	−	11.0265i	0.176137	−	0.614483i
$323$		−	23.5310i		−	1.30930i
$324$	−2.37008	−	8.68232i	−0.131671	−	0.482351i
$325$	0.587851	+	4.08859i	0.0326081	+	0.226794i
$326$	0.905402	−	0.413483i	0.0501456	−	0.0229007i
$327$	2.27573	−	4.49256i	0.125848	−	0.248439i
$328$	−1.16767	+	2.55684i	−0.0644738	+	0.141178i
$329$	12.3430	−	14.2446i	0.680493	−	0.785331i
$330$	−0.958329	−	0.324057i	−0.0527543	−	0.0178388i
$331$	−7.66449	+	2.25050i	−0.421279	+	0.123699i	−0.485499	−	0.874237i	$-0.661362\pi$
$331$	−7.66449	+	2.25050i	−0.421279	+	0.123699i	0.0642205	+	0.997936i	$0.479544\pi$
$332$	−7.78544	−	8.98488i	−0.427282	−	0.493109i
$333$	5.62088	+	27.0823i	0.308022	+	1.48410i
$334$	−9.31688	+	5.98760i	−0.509797	+	0.327627i
$335$	−18.9280	+	16.4012i	−1.03415	+	0.896092i
$336$	−0.423145	−	4.12101i	−0.0230844	−	0.224819i
$337$	−7.97998	−	1.14735i	−0.434697	−	0.0625001i	−0.0785073	−	0.996914i	$-0.525015\pi$
$337$	−7.97998	−	1.14735i	−0.434697	−	0.0625001i	−0.356190	+	0.934413i	$0.615924\pi$
$338$	9.49050	+	8.22356i	0.516215	+	0.447303i
$339$	−10.3513	+	14.7577i	−0.562207	+	0.801529i
$340$	11.2920	+	3.31564i	0.612396	+	0.179816i
$341$	0.626230	+	1.37125i	0.0339122	+	0.0742575i
$342$	4.45658	−	19.5836i	0.240984	−	1.05896i
$343$	−10.7060	+	16.6589i	−0.578072	+	0.899497i
$344$	−5.79379			−0.312380
$345$	17.4879	+	21.6274i	0.941516	+	1.16438i
$346$	−2.42055			−0.130129
$347$	−0.838961	+	1.30545i	−0.0450378	+	0.0700802i	−0.863042	−	0.505132i	$-0.831444\pi$
$347$	−0.838961	+	1.30545i	−0.0450378	+	0.0700802i	0.818005	+	0.575212i	$0.195080\pi$
$348$	10.5586	+	0.427629i	0.566001	+	0.0229233i
$349$	0.688116	+	1.50676i	0.0368340	+	0.0806552i	0.927155	−	0.374679i	$-0.122247\pi$
$349$	0.688116	+	1.50676i	0.0368340	+	0.0806552i	−0.890321	+	0.455334i	$0.849520\pi$
$350$	14.2539	+	4.18534i	0.761906	+	0.223716i
$351$	−2.86647	+	1.92992i	−0.153001	+	0.103012i
$352$	−0.131831	−	0.114232i	−0.00702659	−	0.00608858i
$353$	−20.8552	−	2.99853i	−1.11001	−	0.159596i	−0.437168	−	0.899380i	$-0.644019\pi$
$353$	−20.8552	−	2.99853i	−1.11001	−	0.159596i	−0.672844	+	0.739784i	$0.734928\pi$
$354$	17.5171	−	1.79865i	0.931021	−	0.0955972i
$355$	9.96195	−	8.63208i	0.528726	−	0.458143i
$356$	12.7698	−	8.20665i	0.676798	−	0.434952i
$357$	5.50784	+	13.4789i	0.291506	+	0.713379i
$358$	8.28881	+	9.56580i	0.438077	+	0.505568i
$359$	−5.28399	+	1.55152i	−0.278878	+	0.0818860i	−0.418181	−	0.908364i	$-0.637332\pi$
$359$	−5.28399	+	1.55152i	−0.278878	+	0.0818860i	0.139303	+	0.990250i	$0.455514\pi$
$360$	8.76981	+	4.89805i	0.462210	+	0.258150i
$361$	16.9084	−	19.5133i	0.889916	−	1.02702i
$362$	3.84308	−	8.41517i	0.201988	−	0.442292i
$363$	16.9493	+	8.58575i	0.889608	+	0.450635i
$364$	−1.44687	+	0.660763i	−0.0758366	+	0.0346334i
$365$	2.89803	+	20.1562i	0.151690	+	1.05502i
$366$	−0.790161	−	0.742746i	−0.0413024	−	0.0388239i
$367$		−	14.8562i		−	0.775487i	−0.921767	−	0.387744i	$-0.873255\pi$
$367$		−	14.8562i		−	0.775487i	0.921767	−	0.387744i	$-0.126745\pi$
$368$	1.38076	+	4.59277i	0.0719769	+	0.239415i
$369$	3.02225	−	7.87235i	0.157332	−	0.409818i
$370$	−25.9702	−	16.6900i	−1.35012	−	0.867672i
$371$	−27.9778	+	4.02261i	−1.45254	+	0.208843i
$372$	−3.63242	−	14.5209i	−0.188332	−	0.752874i
$373$	1.27986	−	4.35881i	0.0662688	−	0.225691i	−0.919700	−	0.392623i	$-0.871568\pi$
$373$	1.27986	−	4.35881i	0.0662688	−	0.225691i	0.985968	+	0.166932i	$0.0533860\pi$
$374$	0.557711	+	0.254698i	0.0288385	+	0.0131701i
$375$	−5.49025	+	4.38122i	−0.283516	+	0.226245i
$376$	−1.12151	+	7.80027i	−0.0578374	+	0.402268i
$377$	−1.14310	−	3.89303i	−0.0588725	−	0.200501i
$378$	2.03109	+	12.2609i	0.104468	+	0.630634i
$379$	−16.9516	−	26.3772i	−0.870745	−	1.35491i	−0.934136	−	0.356917i	$-0.883828\pi$
$379$	−16.9516	−	26.3772i	−0.870745	−	1.35491i	0.0633915	−	0.997989i	$-0.479808\pi$
$380$	12.1191	+	18.8576i	0.621695	+	0.967377i
$381$	−18.9667	−	32.3176i	−0.971695	−	1.65568i
$382$	−0.414394	−	1.41130i	−0.0212023	−	0.0722083i
$383$	1.57094	−	10.9261i	0.0802712	−	0.558298i	−0.909508	−	0.415687i	$-0.863541\pi$
$383$	1.57094	−	10.9261i	0.0802712	−	0.558298i	0.989779	−	0.142611i	$-0.0455498\pi$
$384$	1.08035	+	1.35382i	0.0551315	+	0.0690871i
$385$	1.27072	+	0.580318i	0.0647618	+	0.0295757i
$386$	−1.72770	+	5.88402i	−0.0879379	+	0.299489i
$387$	17.3481	−	1.07423i	0.881856	−	0.0546062i
$388$	3.88079	−	0.557974i	0.197017	−	0.0283268i
$389$	−7.36837	−	4.73537i	−0.373591	−	0.240093i	0.340349	−	0.940299i	$-0.389455\pi$
$389$	−7.36837	−	4.73537i	−0.373591	−	0.240093i	−0.713940	+	0.700207i	$0.753091\pi$
$390$	0.702920	−	3.79223i	0.0355937	−	0.192027i
$391$	−9.20450	−	14.1216i	−0.465491	−	0.714162i
$392$		−	1.27942i		−	0.0646204i
$393$	12.0717	−	12.8424i	0.608938	−	0.647811i
$394$	−3.10316	−	21.5829i	−0.156335	−	1.08733i
$395$	15.8505	−	7.23870i	0.797527	−	0.364219i
$396$	0.415916	+	0.317598i	0.0209005	+	0.0159599i
$397$	−8.98453	+	19.6734i	−0.450921	+	0.987378i	0.538543	+	0.842598i	$0.318975\pi$
$397$	−8.98453	+	19.6734i	−0.450921	+	0.987378i	−0.989464	+	0.144780i	$0.953752\pi$
$398$	0.279570	−	0.322641i	0.0140136	−	0.0161725i
$399$	−8.88410	+	26.2728i	−0.444761	+	1.31528i
$400$	−5.95957	+	1.74989i	−0.297979	+	0.0874944i
$401$	20.6984	+	23.8872i	1.03363	+	1.19287i	0.980950	+	0.194258i	$0.0622301\pi$
$401$	20.6984	+	23.8872i	1.03363	+	1.19287i	0.0526774	+	0.998612i	$0.483224\pi$
$402$	11.9931	−	4.90068i	0.598160	−	0.244424i
$403$	−4.83486	+	3.10717i	−0.240841	+	0.154779i
$404$	−10.1241	+	8.77261i	−0.503694	+	0.436454i
$405$	−27.1673	−	13.0401i	−1.34995	−	0.647966i
$406$	−14.4437	−	2.07669i	−0.716830	−	0.103065i
$407$	−1.21545	−	1.05320i	−0.0602478	−	0.0522050i
$408$	−4.98406	−	3.49591i	−0.246748	−	0.173073i
$409$	−8.06409	−	2.36783i	−0.398744	−	0.117082i	0.0762116	−	0.997092i	$-0.475718\pi$
$409$	−8.06409	−	2.36783i	−0.398744	−	0.117082i	−0.474955	+	0.880010i	$0.657536\pi$
$410$	3.90972	+	8.56109i	0.193087	+	0.422802i
$411$	0.721070	−	17.8040i	0.0355678	−	0.878206i
$412$	−0.709786	+	1.10445i	−0.0349687	+	0.0544123i
$413$	−24.3163			−1.19653
$414$	−4.98590	−	13.4960i	−0.245043	−	0.663290i
$415$	−39.8070			−1.95405
$416$	0.359544	−	0.559462i	0.0176281	−	0.0274299i
$417$	0.179073	−	4.42151i	0.00876926	−	0.216522i
$418$	0.485127	+	1.06228i	0.0237284	+	0.0519578i
$419$	3.68715	+	1.08265i	0.180129	+	0.0528907i	0.370553	−	0.928811i	$-0.379168\pi$
$419$	3.68715	+	1.08265i	0.180129	+	0.0528907i	−0.190424	+	0.981702i	$0.560986\pi$
$420$	−11.3560	−	7.96527i	−0.554114	−	0.388665i
$421$	7.60912	+	6.59334i	0.370846	+	0.321340i	0.820268	−	0.571980i	$-0.193824\pi$
$421$	7.60912	+	6.59334i	0.370846	+	0.321340i	−0.449422	+	0.893320i	$0.648370\pi$
$422$	−9.91908	−	1.42615i	−0.482853	−	0.0694238i
$423$	1.91184	−	23.5640i	0.0929570	−	1.14572i
$424$	8.93131	−	7.73902i	0.433743	−	0.375840i
$425$	18.3656	−	11.8029i	0.890862	−	0.572522i
$426$	−6.31206	+	2.57927i	−0.305820	+	0.124966i
$427$	0.980656	+	1.13174i	0.0474573	+	0.0547686i
$428$	1.99389	−	0.585458i	0.0963782	−	0.0282992i
$429$	0.0643635	−	0.190341i	0.00310750	−	0.00918976i
$430$	−12.7039	+	14.6611i	−0.612637	+	0.707020i
$431$	−0.368781	+	0.807518i	−0.0177636	+	0.0388968i	−0.918306	−	0.395872i	$-0.870443\pi$
$431$	−0.368781	+	0.807518i	−0.0177636	+	0.0388968i	0.900542	+	0.434768i	$0.143170\pi$
$432$	−3.48587	−	3.85340i	−0.167714	−	0.185397i
$433$	−12.4673	+	5.69362i	−0.599140	+	0.273618i	−0.691811	−	0.722079i	$-0.743187\pi$
$433$	−12.4673	+	5.69362i	−0.599140	+	0.273618i	0.0926709	+	0.995697i	$0.470460\pi$
$434$	2.94160	+	20.4593i	0.141201	+	0.982076i
$435$	24.2337	−	25.7808i	1.16192	−	1.23609i
$436$		−	2.90758i		−	0.139248i
$437$	4.36448	−	31.8089i	0.208782	−	1.52163i
$438$	1.91983	−	10.3574i	0.0917332	−	0.494897i
$439$	22.2826	+	14.3202i	1.06349	+	0.683464i	0.950686	−	0.310154i	$-0.100380\pi$
$439$	22.2826	+	14.3202i	1.06349	+	0.683464i	0.112804	+	0.993617i	$0.464017\pi$
$440$	−0.578124	+	0.0831216i	−0.0275610	+	0.00396267i
$441$	0.237218	+	3.83092i	0.0112961	+	0.182425i
$442$	−0.658545	+	2.24280i	−0.0313238	+	0.106679i
$443$	3.04728	+	1.39165i	0.144781	+	0.0661191i	0.486488	−	0.873687i	$-0.338278\pi$
$443$	3.04728	+	1.39165i	0.144781	+	0.0661191i	−0.341707	+	0.939806i	$0.611005\pi$
$444$	9.96064	+	12.4820i	0.472711	+	0.592370i
$445$	7.23324	−	50.3083i	0.342888	−	2.38484i
$446$	1.30015	+	4.42789i	0.0615637	+	0.209667i
$447$	15.9713	+	27.2137i	0.755419	+	1.28717i
$448$	−1.29309	−	2.01209i	−0.0610928	−	0.0950622i
$449$	−17.7152	−	27.5654i	−0.836031	−	1.30089i	−0.951522	−	0.307581i	$-0.900480\pi$
$449$	−17.7152	−	27.5654i	−0.836031	−	1.30089i	0.115491	−	0.993309i	$-0.463156\pi$
$450$	17.5201	−	6.34460i	0.825905	−	0.299087i
$451$	0.138138	+	0.470455i	0.00650466	+	0.0221528i
$452$	−1.48112	+	10.3014i	−0.0696661	+	0.484539i
$453$	9.61187	−	7.67026i	0.451605	−	0.360380i
$454$	3.65469	+	1.66904i	0.171523	+	0.0783320i
$455$	−1.50047	+	5.11012i	−0.0703429	+	0.239566i
$456$	−2.81396	−	11.2491i	−0.131776	−	0.526785i
$457$	−21.6467	+	3.11233i	−1.01259	+	0.145588i	−0.628584	−	0.777742i	$-0.716365\pi$
$457$	−21.6467	+	3.11233i	−1.01259	+	0.145588i	−0.384006	+	0.923330i	$0.625456\pi$
$458$	5.44616	+	3.50003i	0.254482	+	0.163546i
$459$	15.5718	+	9.54357i	0.726828	+	0.445456i
$460$	14.6495	+	6.57647i	0.683035	+	0.306630i
$461$		−	32.3466i		−	1.50653i	−0.657715	−	0.753267i	$-0.728477\pi$
$461$		−	32.3466i		−	1.50653i	0.657715	−	0.753267i	$-0.271523\pi$
$462$	−0.526534	−	0.494938i	−0.0244966	−	0.0230266i
$463$	1.87739	+	13.0575i	0.0872497	+	0.606835i	0.985795	+	0.167954i	$0.0537160\pi$
$463$	1.87739	+	13.0575i	0.0872497	+	0.606835i	−0.898545	+	0.438881i	$0.855375\pi$
$464$	5.54968	−	2.53446i	0.257638	−	0.117659i
$465$	−44.7096	−	22.6479i	−2.07336	−	1.05027i
$466$	8.65833	−	18.9591i	0.401089	−	0.878263i
$467$	−15.3824	+	17.7523i	−0.711815	+	0.821478i	−0.990298	−	0.138963i	$-0.955623\pi$
$467$	−15.3824	+	17.7523i	−0.711815	+	0.821478i	0.278483	+	0.960441i	$0.410168\pi$
$468$	−0.972841	+	1.74184i	−0.0449696	+	0.0805166i
$469$	−17.1657	+	5.04032i	−0.792640	+	0.232740i
$470$	17.2793	+	19.9414i	0.797037	+	0.919829i
$471$	−1.12665	−	2.75716i	−0.0519132	−	0.127043i
$472$	8.55273	−	5.49651i	0.393671	−	0.252997i
$473$	−0.763799	+	0.661836i	−0.0351195	+	0.0304312i
$474$	−8.96677	+	0.920708i	−0.411858	+	0.0422895i
$475$	41.1591	+	5.91778i	1.88851	+	0.271526i
$476$	6.35335	+	5.50521i	0.291205	+	0.252331i
$477$	−25.3078	+	24.8286i	−1.15877	+	1.13683i
$478$	8.68772	+	2.55094i	0.397367	+	0.116677i
$479$	6.11943	+	13.3997i	0.279604	+	0.612247i	0.996376	−	0.0850605i	$-0.0271084\pi$
$479$	6.11943	+	13.3997i	0.279604	+	0.612247i	−0.716772	+	0.697308i	$0.754381\pi$
$480$	5.79469	+	0.234688i	0.264490	+	0.0107120i
$481$	3.31493	−	5.15814i	0.151148	−	0.235191i
$482$	−4.06334			−0.185080
$483$	4.94539	+	19.2422i	0.225023	+	0.875552i
$484$	10.9696			0.498617
$485$	7.09738	−	11.0437i	0.322275	−	0.501470i
$486$	11.1521	+	10.8918i	0.505869	+	0.494061i
$487$	10.3827	+	22.7350i	0.470486	+	1.03022i	0.984971	+	0.172721i	$0.0552559\pi$
$487$	10.3827	+	22.7350i	0.470486	+	1.03022i	−0.514485	+	0.857499i	$0.672017\pi$
$488$	−0.600744	−	0.176394i	−0.0271944	−	0.00798500i
$489$	−0.989990	+	1.41141i	−0.0447689	+	0.0638263i
$490$	−3.23755	−	2.80535i	−0.146257	−	0.126733i
$491$	−9.28010	−	1.33428i	−0.418805	−	0.0602151i	−0.0703089	−	0.997525i	$-0.522398\pi$
$491$	−9.28010	−	1.33428i	−0.418805	−	0.0602151i	−0.348496	+	0.937310i	$0.613308\pi$
$492$	−0.497286	−	4.84307i	−0.0224194	−	0.218343i
$493$	−16.2063	+	14.0429i	−0.729897	+	0.632459i
$494$	−3.74546	+	2.40706i	−0.168516	+	0.108299i
$495$	1.71564	−	0.356078i	0.0771124	−	0.0160045i
$496$	−5.65929	−	6.53117i	−0.254110	−	0.293258i
$497$	9.03448	−	2.65276i	0.405252	−	0.118993i
$498$	19.5068	+	6.59618i	0.874119	+	0.295582i
$499$	6.20722	−	7.16351i	0.277873	−	0.320683i	−0.599608	−	0.800294i	$-0.704677\pi$
$499$	6.20722	−	7.16351i	0.277873	−	0.320683i	0.877481	+	0.479611i	$0.159222\pi$
$500$	−1.68466	+	3.68889i	−0.0753403	+	0.164972i
$501$	8.66827	−	17.1122i	0.387270	−	0.764517i
$502$	−4.77847	+	2.18225i	−0.213274	+	0.0973988i
$503$	3.97959	+	27.6786i	0.177441	+	1.23413i	0.862657	+	0.505789i	$0.168799\pi$
$503$	3.97959	+	27.6786i	0.177441	+	1.23413i	−0.685216	+	0.728340i	$0.740292\pi$
$504$	4.24492	+	5.78497i	0.189084	+	0.257683i
$505$			44.8544i			1.99600i
$506$	0.706666	+	0.447741i	0.0314151	+	0.0199045i
$507$	−21.3863	−	3.96413i	−0.949801	−	0.176053i
$508$	−18.2002	−	11.6965i	−0.807502	−	0.518950i
$509$	34.8720	−	5.01384i	1.54568	−	0.222235i	0.683920	−	0.729557i	$-0.260274\pi$
$509$	34.8720	−	5.01384i	1.54568	−	0.222235i	0.861756	+	0.507323i	$0.169365\pi$
$510$	−19.7747	+	4.94668i	−0.875641	+	0.219043i
$511$	−4.09811	+	13.9569i	−0.181290	+	0.617416i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	10.5114	+	33.1609i	0.464092	+	1.46409i
$514$	−2.60151	+	18.0939i	−0.114748	+	0.798088i
$515$	1.23846	+	4.21780i	0.0545730	+	0.185858i
$516$	8.65473	−	5.07933i	0.381003	−	0.223605i
$517$	0.743190	+	1.15643i	0.0326855	+	0.0508596i
$518$	−11.9221	−	18.5511i	−0.523825	−	0.815088i
$519$	3.61580	−	2.12206i	0.158716	−	0.0931480i
$520$	−0.627344	−	2.13654i	−0.0275109	−	0.0936934i
$521$	−0.0294211	+	0.204628i	−0.00128896	+	0.00896492i	−0.990456	−	0.137831i	$-0.955987\pi$
$521$	−0.0294211	+	0.204628i	−0.00128896	+	0.00896492i	0.989167	+	0.146796i	$0.0468960\pi$
$522$	−16.1473	+	8.61780i	−0.706748	+	0.377191i
$523$	13.7188	+	6.26517i	0.599882	+	0.273957i	0.692123	−	0.721780i	$-0.256676\pi$
$523$	13.7188	+	6.26517i	0.599882	+	0.273957i	−0.0922407	+	0.995737i	$0.529403\pi$
$524$	2.86691	−	9.76380i	0.125242	−	0.426533i
$525$	−24.9617	+	6.24420i	−1.08942	+	0.272519i
$526$	22.9608	−	3.30127i	1.00114	−	0.143942i
$527$	25.5532	+	16.4220i	1.11311	+	0.715355i
$528$	0.297073	+	0.0550649i	0.0129285	+	0.00239639i
$529$	−9.82329	−	20.7967i	−0.427099	−	0.904205i
$530$		−	39.5697i		−	1.71880i
$531$	−24.5900	+	18.0438i	−1.06712	+	0.783033i
$532$	2.27880	+	15.8494i	0.0987983	+	0.687158i
$533$	−1.70038	+	0.776539i	−0.0736518	+	0.0336357i
$534$	−11.8808	+	23.4542i	−0.514133	+	1.01496i
$535$	2.89046	−	6.32922i	0.124965	−	0.273636i
$536$	4.89835	−	5.65299i	0.211576	−	0.244172i
$537$	−20.7680	−	7.02265i	−0.896204	−	0.303050i
$538$	−8.78029	+	2.57813i	−0.378545	+	0.111151i
$539$	−0.146150	−	0.168667i	−0.00629514	−	0.00726498i
$540$	−17.3943	+	0.371680i	−0.748534	+	0.0159946i
$541$	33.1433	−	21.2999i	1.42494	−	0.915754i	0.424997	−	0.905195i	$-0.360275\pi$
$541$	33.1433	−	21.2999i	1.42494	−	0.915754i	0.999944	−	0.0105589i	$-0.00336105\pi$
$542$	−20.2050	+	17.5078i	−0.867881	+	0.752023i
$543$	1.63669	+	15.9397i	0.0702370	+	0.684038i
$544$	−3.47906	−	0.500213i	−0.149163	−	0.0214465i
$545$	−7.35758	−	6.37538i	−0.315164	−	0.273091i
$546$	1.58204	−	2.25549i	0.0677052	−	0.0965262i
$547$	−13.5569	−	3.98068i	−0.579653	−	0.170201i	−0.0212542	−	0.999774i	$-0.506766\pi$
$547$	−13.5569	−	3.98068i	−0.579653	−	0.170201i	−0.558399	+	0.829573i	$0.688584\pi$
$548$	−4.27361	−	9.35790i	−0.182560	−	0.399750i
$549$	1.83149	+	0.416787i	0.0781662	+	0.0177880i
$550$	−0.585761	+	0.911462i	−0.0249769	+	0.0388649i
$551$	−40.8449			−1.74005
$552$	−6.08898	−	5.65016i	−0.259164	−	0.240487i
$553$	12.4472			0.529311
$554$	−15.0282	+	23.3843i	−0.638486	+	0.993503i
$555$	53.4260	+	2.16378i	2.26781	+	0.0918472i
$556$	−1.06133	−	2.32398i	−0.0450102	−	0.0985586i
$557$	13.5725	+	3.98526i	0.575087	+	0.168861i	0.556327	−	0.830963i	$-0.312210\pi$
$557$	13.5725	+	3.98526i	0.575087	+	0.168861i	0.0187599	+	0.999824i	$0.494028\pi$
$558$	18.1564	+	18.5068i	0.768621	+	0.783454i
$559$	−2.91195	−	2.52322i	−0.123162	−	0.106721i
$560$	−7.92688	−	1.13971i	−0.334972	−	0.0481617i
$561$	−1.05639	+	0.108471i	−0.0446010	+	0.00457963i
$562$	−15.2148	+	13.1837i	−0.641796	+	0.556119i
$563$	7.24324	−	4.65495i	0.305266	−	0.196183i	−0.379035	−	0.925382i	$-0.623744\pi$
$563$	7.24324	−	4.65495i	0.305266	−	0.196183i	0.684301	+	0.729200i	$0.260108\pi$
$564$	−5.16308	−	12.6352i	−0.217405	−	0.532039i
$565$	22.8200	+	26.3357i	0.960044	+	1.10795i
$566$	10.1097	−	2.96846i	0.424941	−	0.124774i
$567$	−13.7830	−	16.5347i	−0.578832	−	0.694392i
$568$	−2.57804	+	2.97522i	−0.108172	+	0.124837i
$569$	3.20388	−	7.01552i	0.134314	−	0.294106i	−0.830510	−	0.557004i	$-0.811951\pi$
$569$	3.20388	−	7.01552i	0.134314	−	0.294106i	0.964824	+	0.262898i	$0.0846782\pi$
$570$	−34.6356	−	17.5448i	−1.45073	−	0.734872i
$571$	−15.9160	+	7.26859i	−0.666064	+	0.304181i	−0.719604	−	0.694385i	$-0.755677\pi$
$571$	−15.9160	+	7.26859i	−0.666064	+	0.304181i	0.0535404	+	0.998566i	$0.482949\pi$
$572$	−0.0165094	−	0.114826i	−0.000690294	−	0.00480110i
$573$	1.85628	+	1.74489i	0.0775474	+	0.0728940i
$574$			6.72292i			0.280609i
$575$	27.0156	−	12.5486i	1.12663	−	0.523311i
$576$	−2.80070	−	1.07521i	−0.116696	−	0.0448003i
$577$	−17.9450	−	11.5325i	−0.747058	−	0.480105i	0.110896	−	0.993832i	$-0.464628\pi$
$577$	−17.9450	−	11.5325i	−0.747058	−	0.480105i	−0.857954	+	0.513727i	$0.828264\pi$
$578$	−4.59865	+	0.661187i	−0.191279	+	0.0275017i
$579$	−2.57760	−	10.3042i	−0.107121	−	0.428227i
$580$	5.75526	−	19.6006i	0.238974	−	0.813871i
$581$	−25.8655	−	11.8124i	−1.07308	−	0.490059i
$582$	−5.30794	+	4.23574i	−0.220021	+	0.175577i
$583$	0.293377	−	2.04048i	0.0121504	−	0.0845081i
$584$	−1.71342	−	5.83537i	−0.0709018	−	0.241469i
$585$	2.27457	+	6.28105i	0.0940420	+	0.259689i
$586$	−0.815155	−	1.26841i	−0.0336737	−	0.0523973i
$587$	8.61402	+	13.4037i	0.355539	+	0.553229i	0.972245	−	0.233964i	$-0.0751698\pi$
$587$	8.61402	+	13.4037i	0.355539	+	0.553229i	−0.616706	+	0.787193i	$0.711533\pi$
$588$	1.12165	+	1.91119i	0.0462560	+	0.0788161i
$589$	16.2999	+	55.5124i	0.671626	+	2.28735i
$590$	4.84455	−	33.6946i	0.199447	−	1.38718i
$591$	23.5569	+	29.5200i	0.969003	+	1.21429i
$592$	8.38664	+	3.83005i	0.344689	+	0.157414i
$593$	−12.4444	+	42.3816i	−0.511029	+	1.74041i	0.148681	+	0.988885i	$0.452497\pi$
$593$	−12.4444	+	42.3816i	−0.511029	+	1.74041i	−0.659710	+	0.751520i	$0.729321\pi$
$594$	−0.899726	−	0.109798i	−0.0369162	−	0.00450509i
$595$	27.8617	−	4.00590i	1.14222	−	0.164226i
$596$	15.3258	+	9.84932i	0.627771	+	0.403444i
$597$	−0.134765	+	0.727053i	−0.00551557	+	0.0297563i
$598$	−1.30620	+	2.90964i	−0.0534147	+	0.118984i
$599$			17.2927i			0.706560i	0.935518	+	0.353280i	$0.114934\pi$
$599$			17.2927i			0.706560i	−0.935518	+	0.353280i	$0.885066\pi$
$600$	7.36828	−	7.83865i	0.300809	−	0.320011i
$601$	−3.18966	−	22.1846i	−0.130109	−	0.904928i	−0.945408	−	0.325888i	$-0.894337\pi$
$601$	−3.18966	−	22.1846i	−0.130109	−	0.904928i	0.815299	−	0.579040i	$-0.196572\pi$
$602$	−12.6052	+	5.75659i	−0.513748	+	0.234621i
$603$	−13.6188	+	17.8348i	−0.554601	+	0.726288i
$604$	2.94936	−	6.45819i	0.120008	−	0.262780i
$605$	24.0527	−	27.7583i	0.977882	−	1.12854i
$606$	7.43255	−	21.9802i	0.301927	−	0.892883i
$607$	28.7490	−	8.44146i	1.16688	−	0.342628i	0.359780	−	0.933037i	$-0.382852\pi$
$607$	28.7490	−	8.44146i	1.16688	−	0.342628i	0.807104	+	0.590409i	$0.201034\pi$
$608$	−4.38414	−	5.05956i	−0.177800	−	0.205192i
$609$	23.3966	−	9.56046i	0.948077	−	0.387409i
$610$	−1.76360	+	1.13340i	−0.0714061	+	0.0458899i
$611$	−3.96072	+	3.43198i	−0.160234	+	0.138843i
$612$	10.5100	+	0.852716i	0.424840	+	0.0344690i
$613$	−19.0654	−	2.74119i	−0.770043	−	0.110715i	−0.253914	−	0.967227i	$-0.581718\pi$
$613$	−19.0654	−	2.74119i	−0.770043	−	0.110715i	−0.516128	+	0.856511i	$0.672627\pi$
$614$	−11.4563	−	9.92694i	−0.462339	−	0.400619i
$615$	−13.3457	−	9.36091i	−0.538150	−	0.377468i
$616$	−0.400313	−	0.117543i	−0.0161291	−	0.00473593i
$617$	17.4628	+	38.2382i	0.703026	+	1.53941i	0.836264	+	0.548328i	$0.184735\pi$
$617$	17.4628	+	38.2382i	0.703026	+	1.53941i	−0.133238	+	0.991084i	$0.542537\pi$
$618$	0.0920203	−	2.27208i	0.00370160	−	0.0913964i
$619$	22.5746	−	35.1268i	0.907352	−	1.41187i	−0.00388892	−	0.999992i	$-0.501238\pi$
$619$	22.5746	−	35.1268i	0.907352	−	1.41187i	0.911241	−	0.411874i	$-0.135126\pi$
$620$	−28.9360			−1.16210
$621$	19.2796	+	15.7891i	0.773664	+	0.633596i
$622$	4.80371			0.192611
$623$	19.6285	−	30.5425i	0.786398	−	1.22366i
$624$	−0.0466131	+	1.15093i	−0.00186602	+	0.0460740i
$625$	−7.26030	−	15.8978i	−0.290412	−	0.635914i
$626$	12.1317	+	3.56220i	0.484882	+	0.142374i
$627$	−1.65597	−	1.16152i	−0.0661329	−	0.0463868i
$628$	−1.29960	−	1.12611i	−0.0518597	−	0.0449367i
$629$	−32.0763	−	4.61187i	−1.27897	−	0.183887i
$630$	23.9465	+	1.94288i	0.954051	+	0.0774060i
$631$	29.5322	−	25.5898i	1.17566	−	1.01871i	0.176247	−	0.984346i	$-0.443604\pi$
$631$	29.5322	−	25.5898i	1.17566	−	1.01871i	0.999409	−	0.0343665i	$-0.0109414\pi$
$632$	−4.37804	+	2.81360i	−0.174149	+	0.111919i
$633$	16.0674	−	6.56554i	0.638620	−	0.260957i
$634$	3.25951	+	3.76168i	0.129452	+	0.149395i
$635$	−69.5049	+	20.4085i	−2.75822	+	0.809886i
$636$	−6.55685	+	19.3905i	−0.259996	+	0.768882i
$637$	0.557192	−	0.643034i	0.0220768	−	0.0254779i
$638$	0.442102	−	0.968069i	0.0175030	−	0.0383262i
$639$	7.16770	−	9.38659i	0.283550	−	0.371328i
$640$	3.04573	−	1.39094i	0.120393	−	0.0549816i
$641$	−4.47358	−	31.1145i	−0.176696	−	1.22895i	−0.864343	−	0.502902i	$-0.832266\pi$
$641$	−4.47358	−	31.1145i	−0.176696	−	1.22895i	0.687647	−	0.726045i	$-0.258644\pi$
$642$	−2.46520	+	2.62257i	−0.0972935	+	0.103504i
$643$		−	15.5189i		−	0.612005i	−0.952031	−	0.306003i	$-0.901008\pi$
$643$		−	15.5189i		−	0.612005i	0.952031	−	0.306003i	$-0.0989916\pi$
$644$	7.56729	+	8.62029i	0.298193	+	0.339687i
$645$	6.12386	−	33.0380i	0.241127	−	1.30087i
$646$	19.7955	+	12.7218i	0.778844	+	0.500533i
$647$	18.9730	−	2.72790i	0.745904	−	0.107245i	0.241126	−	0.970494i	$-0.422483\pi$
$647$	18.9730	−	2.72790i	0.745904	−	0.107245i	0.504778	+	0.863249i	$0.331574\pi$
$648$	8.58540	+	2.70018i	0.337266	+	0.106073i
$649$	0.499636	−	1.70160i	0.0196124	−	0.0667937i
$650$	−3.75736	−	1.71593i	−0.147376	−	0.0673042i
$651$	−22.3305	−	27.9831i	−0.875201	−	1.09674i
$652$	−0.141653	+	0.985219i	−0.00554756	+	0.0385842i
$653$	−0.503391	−	1.71439i	−0.0196992	−	0.0670894i	0.949057	−	0.315105i	$-0.102040\pi$
$653$	−0.503391	−	1.71439i	−0.0196992	−	0.0670894i	−0.968756	+	0.248016i	$0.920222\pi$
$654$	2.54903	+	4.34333i	0.0996751	+	0.169837i
$655$	−18.4209	−	28.6635i	−0.719765	−	1.11998i
$656$	−1.51966	−	2.36464i	−0.0593328	−	0.0923236i
$657$	6.21237	+	17.1550i	0.242368	+	0.669279i
$658$	5.31019	+	18.0848i	0.207013	+	0.705021i
$659$	0.757007	−	5.26510i	0.0294888	−	0.205099i	−0.969750	−	0.244099i	$-0.921508\pi$
$659$	0.757007	−	5.26510i	0.0294888	−	0.205099i	0.999239	+	0.0389994i	$0.0124170\pi$
$660$	0.790726	−	0.630999i	0.0307790	−	0.0245616i
$661$	−10.3085	−	4.70775i	−0.400956	−	0.183110i	0.204722	−	0.978820i	$-0.434371\pi$
$661$	−10.3085	−	4.70775i	−0.400956	−	0.183110i	−0.605678	+	0.795710i	$0.707098\pi$
$662$	2.25050	−	7.66449i	0.0874681	−	0.297889i
$663$	−0.982498	−	3.92762i	−0.0381571	−	0.152536i
$664$	11.7677	−	1.69194i	0.456675	−	0.0656599i
$665$	45.1032	+	28.9861i	1.74903	+	1.12403i
$666$	−25.8220	−	9.91321i	−1.00058	−	0.384129i
$667$	−24.5122	+	15.9771i	−0.949117	+	0.618635i
$668$		−	11.0750i		−	0.428505i
$669$	−5.82402	−	5.47454i	−0.225169	−	0.211658i
$670$	−3.56432	−	24.7904i	−0.137702	−	0.957735i
$671$	−0.0993463	+	0.0453699i	−0.00383522	+	0.00175149i
$672$	3.69558	+	1.87201i	0.142560	+	0.0722144i
$673$	2.75706	−	6.03712i	0.106277	−	0.232714i	−0.849021	−	0.528359i	$-0.822807\pi$
$673$	2.75706	−	6.03712i	0.106277	−	0.232714i	0.955298	+	0.295645i	$0.0955347\pi$
$674$	5.27952	−	6.09289i	0.203359	−	0.234689i
$675$	−20.6092	+	24.8371i	−0.793248	+	0.955982i
$676$	−12.0491	+	3.53792i	−0.463425	+	0.136074i
$677$	−21.5893	−	24.9153i	−0.829743	−	0.957575i	0.169868	−	0.985467i	$-0.445666\pi$
$677$	−21.5893	−	24.9153i	−0.829743	−	0.957575i	−0.999611	+	0.0278922i	$0.991120\pi$
$678$	−6.81863	−	16.6867i	−0.261868	−	0.640849i
$679$	7.88880	−	5.06982i	0.302744	−	0.194562i
$680$	−8.89423	+	7.70689i	−0.341078	+	0.295546i
$681$	−6.92259	+	0.710810i	−0.265274	+	0.0272383i
$682$	−1.49214	−	0.214537i	−0.0571368	−	0.00821504i
$683$	4.45133	+	3.85710i	0.170325	+	0.147588i	0.735852	−	0.677142i	$-0.236782\pi$
$683$	4.45133	+	3.85710i	0.170325	+	0.147588i	−0.565527	+	0.824730i	$0.691327\pi$
$684$	14.0654	+	14.3368i	0.537803	+	0.548182i
$685$	−33.0506	−	9.70455i	−1.26280	−	0.370792i
$686$	−8.22625	−	18.0130i	−0.314080	−	0.687739i
$687$	−11.2039	−	0.453762i	−0.427454	−	0.0173121i
$688$	3.13236	−	4.87405i	0.119420	−	0.185821i
$689$	7.85924			0.299413
$690$	−27.6488	+	3.01908i	−1.05257	+	0.114934i
$691$	14.0488			0.534442			0.267221	−	0.963635i	$-0.413895\pi$
$691$	14.0488			0.534442			0.267221	+	0.963635i	$0.413895\pi$
$692$	1.30865	−	2.03629i	0.0497473	−	0.0774083i
$693$	1.22044	+	0.277731i	0.0463606	+	0.0105501i
$694$	−0.644637	−	1.41156i	−0.0244701	−	0.0535820i
$695$	−8.20793	−	2.41007i	−0.311344	−	0.0914190i
$696$	−6.06817	+	8.65128i	−0.230013	+	0.327926i
$697$	7.46656	+	6.46981i	0.282816	+	0.245061i
$698$	−1.63959	−	0.235738i	−0.0620595	−	0.00892281i
$699$	3.68740	+	35.9116i	0.139470	+	1.35830i
$700$	−11.2272	+	9.72842i	−0.424348	+	0.367700i
$701$	7.79469	−	5.00934i	0.294401	−	0.189200i	−0.385099	−	0.922875i	$-0.625833\pi$
$701$	7.79469	−	5.00934i	0.294401	−	0.189200i	0.679501	+	0.733675i	$0.262196\pi$
$702$	−0.0738223	−	3.45483i	−0.00278624	−	0.130394i
$703$	−40.4210	−	46.6483i	−1.52451	−	1.75937i
$704$	0.167371	−	0.0491445i	0.00630803	−	0.00185220i
$705$	−43.2942	−	14.6398i	−1.63055	−	0.551368i
$706$	13.7977	−	15.9234i	0.519284	−	0.599286i
$707$	−13.3101	+	29.1451i	−0.500579	+	1.09611i
$708$	−7.95732	+	15.7087i	−0.299054	+	0.590370i
$709$	37.3484	−	17.0564i	1.40265	−	0.640568i	0.436772	−	0.899572i	$-0.356122\pi$
$709$	37.3484	−	17.0564i	1.40265	−	0.640568i	0.965876	+	0.259004i	$0.0833944\pi$
$710$	1.87593	+	13.0474i	0.0704024	+	0.489660i
$711$	12.5873	−	9.23639i	0.472062	−	0.346392i
$712$			15.1795i			0.568875i
$713$	31.4966	+	26.9387i	1.17956	+	1.00886i
$714$	−14.3169	−	2.65376i	−0.535798	−	0.0993145i
$715$	−0.326764	−	0.209998i	−0.0122203	−	0.00785350i
$716$	−12.5285	+	1.80133i	−0.468213	+	0.0673189i
$717$	−15.2140	+	3.80581i	−0.568179	+	0.142131i
$718$	1.55152	−	5.28399i	0.0579022	−	0.197197i
$719$	−13.1320	−	5.99720i	−0.489742	−	0.223658i	0.155209	−	0.987882i	$-0.450395\pi$
$719$	−13.1320	−	5.99720i	−0.489742	−	0.223658i	−0.644951	+	0.764224i	$0.723122\pi$
$720$	−8.86182	+	4.72955i	−0.330261	+	0.176260i
$721$	−0.446878	+	3.10811i	−0.0166426	+	0.115752i
$722$	7.27429	+	24.7740i	0.270721	+	0.921991i
$723$	6.06979	−	3.56227i	0.225738	−	0.132482i
$724$	5.00157	+	7.78259i	0.185882	+	0.289238i
$725$	−20.4873	−	31.8788i	−0.760879	−	1.18395i
$726$	−16.3863	+	9.61687i	−0.608152	+	0.356915i
$727$	−3.71466	−	12.6510i	−0.137769	−	0.469199i	0.861486	−	0.507781i	$-0.169534\pi$
$727$	−3.71466	−	12.6510i	−0.137769	−	0.469199i	−0.999255	+	0.0385823i	$0.987716\pi$
$728$	0.226367	−	1.57442i	0.00838973	−	0.0583519i
$729$	−26.2076	−	6.49322i	−0.970652	−	0.240489i
$730$	−18.5233	−	8.45930i	−0.685577	−	0.313093i
$731$	−5.73726	+	19.5393i	−0.212200	+	0.722688i
$732$	1.05203	−	0.263167i	0.0388842	−	0.00972692i
$733$	−32.6830	+	4.69910i	−1.20717	+	0.173565i	−0.716380	−	0.697711i	$-0.754202\pi$
$733$	−32.6830	+	4.69910i	−1.20717	+	0.173565i	−0.490794	+	0.871276i	$0.663293\pi$
$734$	12.4978	+	8.03187i	0.461303	+	0.296462i
$735$	7.29564	+	1.35231i	0.269104	+	0.0498806i
$736$	−4.61017	−	1.32147i	−0.169933	−	0.0487101i
$737$		−	1.30478i		−	0.0480624i
$738$	4.98869	+	6.79859i	0.183636	+	0.250260i
$739$	6.07636	+	42.2620i	0.223522	+	1.55463i	0.724563	+	0.689209i	$0.242042\pi$
$739$	6.07636	+	42.2620i	0.223522	+	1.55463i	−0.501040	+	0.865424i	$0.667049\pi$
$740$	28.0811	−	12.8242i	1.03228	−	0.471427i
$741$	3.48472	−	6.87925i	0.128014	−	0.252716i
$742$	11.7419	−	25.7112i	0.431060	−	0.943889i
$743$	4.25720	−	4.91307i	0.156181	−	0.180243i	−0.672266	−	0.740309i	$-0.734679\pi$
$743$	4.25720	−	4.91307i	0.156181	−	0.180243i	0.828448	+	0.560067i	$0.189224\pi$
$744$	14.1796	+	4.79481i	0.519850	+	0.175786i
$745$	58.5281	−	17.1854i	2.14431	−	0.629625i
$746$	2.97492	+	3.43324i	0.108920	+	0.125700i
$747$	−34.9219	+	7.24797i	−1.27772	+	0.265189i
$748$	−0.515787	+	0.331476i	−0.0188590	+	0.0121200i
$749$	3.75627	−	3.25483i	0.137251	−	0.118929i
$750$	−0.717462	−	6.98736i	−0.0261980	−	0.255142i
$751$	40.7209	+	5.85478i	1.48593	+	0.213644i	0.836998	−	0.547206i	$-0.184308\pi$
$751$	40.7209	+	5.85478i	1.48593	+	0.213644i	0.648928	+	0.760850i	$0.275217\pi$
$752$	−5.95567	−	5.16062i	−0.217181	−	0.188188i
$753$	5.22490	−	7.44906i	0.190406	−	0.271459i
$754$	3.89303	+	1.14310i	0.141776	+	0.0416291i
$755$	−9.87536	−	21.6240i	−0.359401	−	0.786979i
$756$	−11.4126	−	4.92010i	−0.415074	−	0.178942i
$757$	−23.4969	+	36.5618i	−0.854008	+	1.32886i	0.0889786	+	0.996034i	$0.471640\pi$
$757$	−23.4969	+	36.5618i	−0.854008	+	1.32886i	−0.942987	+	0.332829i	$0.891997\pi$
$758$	31.3546			1.13885
$759$	−1.44814	−	0.0493089i	−0.0525642	−	0.00178980i
$760$	−22.4161			−0.813119
$761$	−18.9836	+	29.5390i	−0.688154	+	1.07079i	0.304815	+	0.952412i	$0.401405\pi$
$761$	−18.9836	+	29.5390i	−0.688154	+	1.07079i	−0.992969	+	0.118377i	$0.962231\pi$
$762$	37.4415	+	1.51640i	1.35636	+	0.0549333i
$763$	−2.88891	−	6.32583i	−0.104586	−	0.229010i
$764$	1.41130	+	0.414394i	0.0510589	+	0.0149923i
$765$	25.2027	−	24.7256i	0.911207	−	0.893954i
$766$	8.34232	+	7.22866i	0.301420	+	0.261182i
$767$	6.69235	+	0.962214i	0.241647	+	0.0347435i
$768$	−1.72299	+	0.176917i	−0.0621731	+	0.00638393i
$769$	−7.25051	+	6.28260i	−0.261460	+	0.226556i	−0.775719	−	0.631079i	$-0.782613\pi$
$769$	−7.25051	+	6.28260i	−0.261460	+	0.226556i	0.514259	+	0.857635i	$0.328067\pi$
$770$	−1.17520	+	0.755253i	−0.0423512	+	0.0272174i
$771$	−11.9765	−	29.3093i	−0.431325	−	1.05555i
$772$	−4.01589	−	4.63458i	−0.144535	−	0.166802i
$773$	−11.4452	+	3.36061i	−0.411655	+	0.120873i	−0.481001	−	0.876720i	$-0.659727\pi$
$773$	−11.4452	+	3.36061i	−0.411655	+	0.120873i	0.0693464	+	0.997593i	$0.477909\pi$
$774$	−8.47542	+	15.1750i	−0.304643	+	0.545453i
$775$	−35.1508	+	40.5662i	−1.26265	+	1.45718i
$776$	−1.62872	+	3.56640i	−0.0584676	+	0.128026i
$777$	34.0726	+	17.2596i	1.22235	+	0.619185i
$778$	7.96729	−	3.63854i	0.285641	−	0.130448i
$779$	2.67808	+	18.6264i	0.0959521	+	0.667361i
$780$	2.81020	+	2.64157i	0.100621	+	0.0945832i
$781$			0.686720i			0.0245728i
$782$	16.8562	−	0.108584i	0.602777	−	0.00388297i
$783$	16.5657	−	27.0293i	0.592008	−	0.965950i
$784$	1.07632	+	0.691706i	0.0384398	+	0.0247038i
$785$	−5.69921	+	0.819423i	−0.203414	+	0.0292464i
$786$	4.27721	+	17.0985i	0.152563	+	0.609883i
$787$	−13.0008	+	44.2766i	−0.463428	+	1.57829i	0.314068	+	0.949401i	$0.398308\pi$
$787$	−13.0008	+	44.2766i	−0.463428	+	1.57829i	−0.777495	+	0.628889i	$0.783510\pi$
$788$	19.8344	+	9.05808i	0.706572	+	0.322681i
$789$	−31.4046	+	25.0609i	−1.11803	+	0.892190i
$790$	−2.47987	+	17.2479i	−0.0882298	+	0.613651i
$791$	7.01290	+	23.8838i	0.249350	+	0.849209i
$792$	−0.492041	+	0.178184i	−0.0174839	+	0.00633150i
$793$	−0.225113	−	0.350282i	−0.00799399	−	0.0124389i
$794$	−11.6929	−	18.1945i	−0.414965	−	0.645698i
$795$	34.6902	+	59.1090i	1.23033	+	2.09638i
$796$	0.120276	+	0.409622i	0.00426306	+	0.0145187i
$797$	6.37259	−	44.3223i	0.225729	−	1.56998i	−0.490078	−	0.871678i	$-0.663032\pi$
$797$	6.37259	−	44.3223i	0.225729	−	1.56998i	0.715807	−	0.698298i	$-0.246059\pi$
$798$	−17.2990	−	21.6779i	−0.612377	−	0.767390i
$799$	25.1955	+	11.5064i	0.891354	+	0.407068i
$800$	1.74989	−	5.95957i	0.0618679	−	0.210703i
$801$	−2.81444	−	45.4514i	−0.0994434	−	1.60595i
$802$	−31.2856	+	4.49819i	−1.10473	+	0.158837i
$803$	−0.892466	−	0.573553i	−0.0314945	−	0.0202403i
$804$	−2.36123	+	12.7387i	−0.0832740	+	0.449260i
$805$	38.4061	−	0.247405i	1.35364	−	0.00871986i
$806$		−	5.74721i		−	0.202437i
$807$	10.8557	−	11.5487i	0.382140	−	0.406535i
$808$	−1.90647	−	13.2598i	−0.0670694	−	0.466478i
$809$	32.3825	−	14.7886i	1.13851	−	0.519939i	0.245239	−	0.969463i	$-0.421133\pi$
$809$	32.3825	−	14.7886i	1.13851	−	0.519939i	0.893269	+	0.449523i	$0.148406\pi$
$810$	25.6577	−	15.8046i	0.901521	−	0.555317i
$811$	−3.11653	+	6.82424i	−0.109436	+	0.239631i	−0.956424	−	0.291980i	$-0.905686\pi$
$811$	−3.11653	+	6.82424i	−0.109436	+	0.239631i	0.846988	+	0.531611i	$0.178413\pi$
$812$	9.55590	−	11.0281i	0.335346	−	0.387010i
$813$	14.8334	−	43.8665i	0.520229	−	1.53846i
$814$	1.54313	−	0.453104i	0.0540867	−	0.0158813i
$815$	2.18248	+	2.51872i	0.0764489	+	0.0882268i
$816$	5.63553	−	2.30282i	0.197283	−	0.0806150i
$817$	−32.6306	+	20.9704i	−1.14160	+	0.733662i
$818$	6.35172	−	5.50380i	0.222083	−	0.192436i
$819$	−0.385890	+	4.75620i	−0.0134841	+	0.166195i
$820$	−9.31580	−	1.33941i	−0.325322	−	0.0467742i
$821$	40.4292	+	35.0321i	1.41099	+	1.22263i	0.940307	+	0.340328i	$0.110538\pi$
$821$	40.4292	+	35.0321i	1.41099	+	1.22263i	0.470684	+	0.882302i	$0.344007\pi$
$822$	14.5878	+	10.2322i	0.508809	+	0.356888i
$823$	7.35580	+	2.15986i	0.256407	+	0.0752879i	0.407410	−	0.913245i	$-0.366432\pi$
$823$	7.35580	+	2.15986i	0.256407	+	0.0752879i	−0.151003	+	0.988533i	$0.548250\pi$
$824$	−0.545382	−	1.19422i	−0.0189993	−	0.0416026i
$825$	0.0759410	−	1.87507i	0.00264393	−	0.0652814i
$826$	13.1464	−	20.4562i	0.457422	−	0.711762i
$827$	−43.2407			−1.50363			−0.751813	−	0.659377i	$-0.770820\pi$
$827$	−43.2407			−1.50363			−0.751813	+	0.659377i	$0.770820\pi$
$828$	14.0491	+	3.10206i	0.488240	+	0.107804i
$829$	−44.6571			−1.55100			−0.775502	−	0.631345i	$-0.782503\pi$
$829$	−44.6571			−1.55100			−0.775502	+	0.631345i	$0.782503\pi$
$830$	21.5213	−	33.4878i	0.747015	−	1.16238i
$831$	1.94833	−	48.1063i	0.0675867	−	1.66879i
$832$	0.276265	+	0.604936i	0.00957776	+	0.0209724i
$833$	−4.31479	−	1.26694i	−0.149498	−	0.0438967i
$834$	3.62280	+	2.54110i	0.125447	+	0.0879910i
$835$	−28.0251	−	24.2839i	−0.969848	−	0.840378i
$836$	−1.15593	−	0.166197i	−0.0399786	−	0.00574805i
$837$	−43.3465	−	11.7279i	−1.49827	−	0.405375i
$838$	−2.90421	+	2.51651i	−0.100324	+	0.0869314i
$839$	−3.24484	+	2.08533i	−0.112024	+	0.0719936i	−0.595453	−	0.803390i	$-0.703027\pi$
$839$	−3.24484	+	2.08533i	−0.112024	+	0.0719936i	0.483429	+	0.875384i	$0.339391\pi$
$840$	12.8403	−	5.24689i	0.443033	−	0.181035i
$841$	5.38455	+	6.21410i	0.185674	+	0.214279i
$842$	−9.66048	+	2.83657i	−0.332922	+	0.0977547i
$843$	11.1698	−	33.0322i	0.384708	−	1.13769i
$844$	6.56241	−	7.57343i	0.225888	−	0.260688i
$845$	−17.4670	+	38.2474i	−0.600884	+	1.31575i
$846$	18.7897	+	14.3480i	0.646003	+	0.493295i
$847$	23.8658	−	10.8991i	0.820038	−	0.374499i
$848$	1.68185	+	11.6975i	0.0577550	+	0.401695i
$849$	−12.4993	+	13.2973i	−0.428976	+	0.456361i
$850$			21.8312i			0.748805i
$851$	−42.5050	−	12.1837i	−1.45705	−	0.417653i
$852$	1.24273	−	6.70450i	0.0425753	−	0.229692i
$853$	37.7963	+	24.2902i	1.29412	+	0.831681i	0.992559	−	0.121766i	$-0.0388557\pi$
$853$	37.7963	+	24.2902i	1.29412	+	0.831681i	0.301562	+	0.953447i	$0.402492\pi$
$854$	−1.48226	+	0.213117i	−0.0507219	+	0.00729271i
$855$	67.1198	−	4.15619i	2.29545	−	0.142139i
$856$	−0.585458	+	1.99389i	−0.0200106	+	0.0681497i
$857$	11.3382	+	5.17799i	0.387306	+	0.176877i	0.599545	−	0.800341i	$-0.295348\pi$
$857$	11.3382	+	5.17799i	0.387306	+	0.176877i	−0.212239	+	0.977218i	$0.568075\pi$
$858$	0.125328	+	0.157052i	0.00427862	+	0.00536168i
$859$	−7.66120	+	53.2848i	−0.261397	+	1.81806i	0.260984	+	0.965343i	$0.415953\pi$
$859$	−7.66120	+	53.2848i	−0.261397	+	1.81806i	−0.522381	+	0.852712i	$0.674956\pi$
$860$	−5.46544	−	18.6136i	−0.186370	−	0.634718i
$861$	−5.89389	−	10.0427i	−0.200863	−	0.342253i
$862$	−0.479949	−	0.746816i	−0.0163471	−	0.0254366i
$863$	−15.1208	−	23.5285i	−0.514719	−	0.800919i	0.482465	−	0.875915i	$-0.339742\pi$
$863$	−15.1208	−	23.5285i	−0.514719	−	0.800919i	−0.997184	+	0.0749969i	$0.976105\pi$
$864$	5.12629	−	0.849196i	0.174400	−	0.0288902i
$865$	−2.28337	−	7.77644i	−0.0776368	−	0.264407i
$866$	1.95055	−	13.5664i	0.0662823	−	0.461004i
$867$	6.28979	−	5.01925i	0.213613	−	0.170463i
$868$	−18.8018	−	8.58649i	−0.638174	−	0.291444i
$869$	−0.255757	+	0.871030i	−0.00867598	+	0.0295477i
$870$	8.58640	+	34.3248i	0.291106	+	1.16372i
$871$	4.92381	−	0.707937i	0.166837	−	0.0239875i
$872$	2.44601	+	1.57196i	0.0828324	+	0.0532331i
$873$	4.21557	−	10.9807i	0.142675	−	0.371641i
$874$	24.3998	+	20.8688i	0.825334	+	0.705899i
$875$			9.69952i			0.327904i
$876$	7.67528	+	7.21471i	0.259324	+	0.243763i
$877$	0.183098	+	1.27348i	0.00618280	+	0.0430023i	0.992679	−	0.120780i	$-0.0385396\pi$
$877$	0.183098	+	1.27348i	0.00618280	+	0.0430023i	−0.986496	+	0.163782i	$0.947631\pi$
$878$	−24.0938	+	11.0033i	−0.813125	+	0.371342i
$879$	2.32967	+	1.18010i	0.0785777	+	0.0398039i
$880$	0.242631	−	0.531287i	0.00817908	−	0.0179097i
$881$	−27.3633	+	31.5789i	−0.921892	+	1.06392i	0.0758739	+	0.997117i	$0.475825\pi$
$881$	−27.3633	+	31.5789i	−0.921892	+	1.06392i	−0.997766	+	0.0668030i	$0.978720\pi$
$882$	−3.35102	−	1.87159i	−0.112835	−	0.0630197i
$883$	−44.5467	+	13.0801i	−1.49912	+	0.440180i	−0.925437	−	0.378901i	$-0.876302\pi$
$883$	−44.5467	+	13.0801i	−1.49912	+	0.440180i	−0.573678	+	0.819081i	$0.694484\pi$
$884$	−1.53073	−	1.76655i	−0.0514839	−	0.0594156i
$885$	22.3028	+	54.5800i	0.749701	+	1.83469i
$886$	−2.81821	+	1.81115i	−0.0946796	+	0.0608469i
$887$	−2.25405	+	1.95314i	−0.0756835	+	0.0655801i	−0.691881	−	0.722012i	$-0.743218\pi$
$887$	−2.25405	+	1.95314i	−0.0756835	+	0.0655801i	0.616198	+	0.787592i	$0.288672\pi$
$888$	−15.8857	+	1.63114i	−0.533088	+	0.0547375i
$889$	−51.2183	−	7.36408i	−1.71781	−	0.246983i
$890$	38.4114	+	33.2837i	1.28755	+	1.11567i
$891$	1.44026	−	0.624760i	0.0482507	−	0.0209303i
$892$	−4.42789	−	1.30015i	−0.148257	−	0.0435321i
$893$	21.9165	+	47.9903i	0.733406	+	1.60594i
$894$	−31.5284	−	1.27692i	−1.05447	−	0.0427065i
$895$	−22.9128	+	35.6530i	−0.765889	+	1.19175i
$896$	2.39177			0.0799036
$897$	−0.599643	−	5.49154i	−0.0200215	−	0.183357i
$898$	32.7670			1.09345
$899$	28.5052	−	44.3550i	0.950702	−	1.47932i
$900$	−4.13466	+	18.1690i	−0.137822	+	0.605633i
$901$	−17.2554	−	37.7840i	−0.574860	−	1.25877i
$902$	−0.470455	−	0.138138i	−0.0156644	−	0.00459949i
$903$	13.7828	−	19.6499i	0.458663	−	0.653909i
$904$	−7.86536	−	6.81537i	−0.261598	−	0.226676i
$905$	30.6605	+	4.40832i	1.01919	+	0.146537i
$906$	1.25607	+	12.2329i	0.0417301	+	0.406410i
$907$	−3.54906	+	3.07528i	−0.117845	+	0.102113i	−0.711790	−	0.702393i	$-0.752115\pi$
$907$	−3.54906	+	3.07528i	−0.117845	+	0.102113i	0.593945	+	0.804506i	$0.297570\pi$
$908$	−3.37996	+	2.17217i	−0.112168	+	0.0720860i
$909$	8.16698	+	39.3498i	0.270882	+	1.30515i
$910$	−3.48769	−	4.02501i	−0.115616	−	0.133428i
$911$	−21.8033	+	6.40202i	−0.722375	+	0.212108i	−0.622196	−	0.782861i	$-0.713760\pi$
$911$	−21.8033	+	6.40202i	−0.722375	+	0.212108i	−0.100178	+	0.994970i	$0.531941\pi$
$912$	10.9846	+	3.71444i	0.363738	+	0.122997i
$913$	1.35807	−	1.56729i	0.0449455	−	0.0518699i
$914$	9.08484	−	19.8930i	0.300500	−	0.658002i
$915$	1.64082	−	3.23918i	0.0542439	−	0.107084i
$916$	−5.88883	+	2.68934i	−0.194572	+	0.0888582i
$917$	−3.46376	−	24.0909i	−0.114383	−	0.795553i
$918$	−16.4473	+	7.94015i	−0.542842	+	0.262064i
$919$			6.89830i			0.227554i	0.993506	+	0.113777i	$0.0362949\pi$
$919$			6.89830i			0.227554i	−0.993506	+	0.113777i	$0.963705\pi$
$920$	−13.4526	+	8.76841i	−0.443518	+	0.289086i
$921$	25.8162	+	4.78524i	0.850672	+	0.157679i
$922$	27.2117	+	17.4879i	0.896170	+	0.575934i
$923$	−2.59144	+	0.372593i	−0.0852984	+	0.0122641i
$924$	0.701034	−	0.175365i	0.0230623	−	0.00576907i
$925$	16.1337	−	54.9462i	0.530471	−	1.80662i
$926$	−11.9997	−	5.48008i	−0.394334	−	0.180087i
$927$	1.85444	+	3.47469i	0.0609078	+	0.114124i
$928$	−0.868266	+	6.03892i	−0.0285022	+	0.198237i
$929$	−4.60284	−	15.6758i	−0.151014	−	0.514307i	0.848884	−	0.528579i	$-0.177275\pi$
$929$	−4.60284	−	15.6758i	−0.151014	−	0.514307i	−0.999898	+	0.0142720i	$0.995457\pi$
$930$	43.2245	−	25.3678i	1.41739	−	0.831843i
$931$	−4.63081	−	7.20568i	−0.151769	−	0.236156i
$932$	11.2684	+	17.5339i	0.369107	+	0.574342i
$933$	−7.17576	+	4.21135i	−0.234924	+	0.137873i
$934$	−6.61780	−	22.5381i	−0.216541	−	0.737471i
$935$	−0.292159	+	2.03201i	−0.00955461	+	0.0664538i
$936$	−0.939372	−	1.76012i	−0.0307043	−	0.0575312i
$937$	36.9123	+	16.8573i	1.20587	+	0.550703i	0.913984	−	0.405749i	$-0.132989\pi$
$937$	36.9123	+	16.8573i	1.20587	+	0.550703i	0.291888	+	0.956453i	$0.405717\pi$
$938$	5.04032	−	17.1657i	0.164572	−	0.560481i
$939$	−21.2453	+	5.31453i	−0.693313	+	0.173433i
$940$	−26.1177	+	3.75516i	−0.851866	+	0.122480i
$941$	2.89516	+	1.86061i	0.0943795	+	0.0606540i	0.586979	−	0.809602i	$-0.300317\pi$
$941$	2.89516	+	1.86061i	0.0943795	+	0.0606540i	−0.492600	+	0.870256i	$0.663953\pi$
$942$	2.92858	+	0.542837i	0.0954184	+	0.0176866i
$943$	8.89320	+	10.1307i	0.289603	+	0.329901i
$944$			10.1667i			0.330896i
$945$	−37.4744	+	18.0913i	−1.21904	+	0.588510i
$946$	−0.143831	−	1.00036i	−0.00467634	−	0.0325246i
$947$	−5.48974	+	2.50708i	−0.178393	+	0.0814692i	−0.502609	−	0.864514i	$-0.667627\pi$
$947$	−5.48974	+	2.50708i	−0.178393	+	0.0814692i	0.324217	+	0.945983i	$0.394899\pi$
$948$	4.07326	−	8.04110i	0.132293	−	0.261163i
$949$	1.68017	−	3.67905i	0.0545405	−	0.119427i
$950$	−27.2306	+	31.4258i	−0.883478	+	1.01959i
$951$	−8.16686	−	2.76161i	−0.264828	−	0.0895513i
$952$	−8.06616	+	2.36844i	−0.261426	+	0.0767615i
$953$	13.7021	+	15.8131i	0.443855	+	0.512236i	0.932956	−	0.359991i	$-0.117220\pi$
$953$	13.7021	+	15.8131i	0.443855	+	0.512236i	−0.489101	+	0.872227i	$0.662675\pi$
$954$	−7.20475	−	34.7137i	−0.233263	−	1.12390i
$955$	4.14313	−	2.66263i	0.134069	−	0.0861607i
$956$	−6.84293	+	5.92943i	−0.221316	+	0.191771i
$957$	0.188282	+	1.83368i	0.00608630	+	0.0592745i
$958$	−14.5809	−	2.09642i	−0.471089	−	0.0677324i
$959$	−18.5956	−	16.1132i	−0.600484	−	0.520322i
$960$	−3.33028	+	4.74792i	−0.107484	+	0.153239i
$961$	−41.9143	−	12.3072i	−1.35207	−	0.397005i
$962$	2.54711	+	5.57740i	0.0821222	+	0.179823i
$963$	1.38333	−	6.07878i	0.0445772	−	0.195886i
$964$	2.19681	−	3.41830i	0.0707543	−	0.110096i
$965$	−20.5333			−0.660989
$966$	−18.8613	−	6.24281i	−0.606851	−	0.200859i
$967$	−6.16693			−0.198315			−0.0991575	−	0.995072i	$-0.531615\pi$
$967$	−6.16693			−0.198315			−0.0991575	+	0.995072i	$0.531615\pi$
$968$	−5.93060	+	9.22819i	−0.190617	+	0.296605i
$969$	−40.7235	−	1.64932i	−1.30823	−	0.0529838i
$970$	5.45345	+	11.9414i	0.175100	+	0.383415i
$971$	29.4740	+	8.65436i	0.945867	+	0.277731i	0.718065	−	0.695976i	$-0.245028\pi$
$971$	29.4740	+	8.65436i	0.945867	+	0.277731i	0.227802	+	0.973708i	$0.426846\pi$
$972$	−15.1920	+	3.49319i	−0.487284	+	0.112044i
$973$	−4.61811	−	4.00162i	−0.148050	−	0.128286i
$974$	−24.7392	−	3.55696i	−0.792695	−	0.113972i
$975$	7.11705	−	0.730778i	0.227928	−	0.0234036i
$976$	0.473179	−	0.410012i	0.0151461	−	0.0131242i
$977$	17.3948	−	11.1790i	0.556509	−	0.357646i	−0.231956	−	0.972726i	$-0.574513\pi$
$977$	17.3948	−	11.1790i	0.556509	−	0.357646i	0.788465	+	0.615080i	$0.210876\pi$
$978$	−0.652127	−	1.59590i	−0.0208527	−	0.0510313i
$979$	1.73398	+	2.00112i	0.0554183	+	0.0639561i
$980$	4.11036	−	1.20691i	0.131301	−	0.0385533i
$981$	−7.61546	−	4.25334i	−0.243143	−	0.135799i
$982$	6.13967	−	7.08555i	0.195925	−	0.226109i
$983$	8.30399	−	18.1832i	0.264856	−	0.579954i	−0.729746	−	0.683719i	$-0.760362\pi$
$983$	8.30399	−	18.1832i	0.264856	−	0.579954i	0.994602	+	0.103764i	$0.0330888\pi$
$984$	4.34310	+	2.20002i	0.138453	+	0.0701340i
$985$	66.4118	−	30.3292i	2.11605	−	0.966370i
$986$	−3.05181	−	21.2258i	−0.0971894	−	0.675967i
$987$	−23.7871	−	22.3597i	−0.757150	−	0.711716i
$988$		−	4.45224i		−	0.141645i
$989$	−11.3797	+	25.3489i	−0.361853	+	0.806048i
$990$	−0.627995	+	1.63580i	−0.0199590	+	0.0519892i
$991$	−23.2232	−	14.9246i	−0.737709	−	0.474097i	0.117047	−	0.993126i	$-0.462657\pi$
$991$	−23.2232	−	14.9246i	−0.737709	−	0.474097i	−0.854756	+	0.519030i	$0.826293\pi$
$992$	8.55402	−	1.22988i	0.271590	−	0.0390488i
$993$	3.35757	+	13.4222i	0.106549	+	0.425939i
$994$	−2.65276	+	9.03448i	−0.0841405	+	0.286556i
$995$	1.30027	+	0.593812i	0.0412212	+	0.0188251i
$996$	−16.0952	+	12.8440i	−0.509996	+	0.406977i
$997$	−2.53038	+	17.5992i	−0.0801380	+	0.557372i	0.909710	+	0.415244i	$0.136304\pi$
$997$	−2.53038	+	17.5992i	−0.0801380	+	0.557372i	−0.989848	+	0.142128i	$0.954605\pi$
$998$	2.67045	+	9.09473i	0.0845318	+	0.287889i
$999$	47.2635	−	7.82944i	1.49535	−	0.247712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.113.2	yes	80
3.2	odd	2	inner	138.2.f.a.113.7	yes	80
23.11	odd	22	inner	138.2.f.a.11.7	yes	80
69.11	even	22	inner	138.2.f.a.11.2	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.2	✓	80	69.11	even	22	inner
138.2.f.a.11.7	yes	80	23.11	odd	22	inner
138.2.f.a.113.2	yes	80	1.1	even	1	trivial
138.2.f.a.113.7	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)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(0.0700914 - 1.73063i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.21268 - 0.943327i) q^{5} +(1.41801 + 0.994615i) q^{6} +(-1.80758 - 1.56628i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.99017 - 0.242605i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(0.0700914 - 1.73063i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-3.21268 - 0.943327i) q^{5} +(1.41801 + 0.994615i) q^{6} +(-1.80758 - 1.56628i) q^{7} +(0.989821 + 0.142315i) q^{8} +(-2.99017 - 0.242605i) q^{9} +(2.53048 - 2.19268i) q^{10} +(0.146746 - 0.0943077i) q^{11} +(-1.60336 + 0.655173i) q^{12} +(0.435504 + 0.502599i) q^{13} +(2.29489 - 0.673841i) q^{14} +(-1.85773 + 5.49384i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.46011 - 3.19721i) q^{17} +(1.82070 - 2.38433i) q^{18} +(6.08977 - 2.78111i) q^{19} +(0.476514 + 3.31423i) q^{20} +(-2.83735 + 3.01848i) q^{21} +0.174437i q^{22} +(2.56678 - 4.05113i) q^{23} +(0.315673 - 1.70304i) q^{24} +(5.22517 + 3.35801i) q^{25} +(-0.658264 + 0.0946441i) q^{26} +(-0.629445 + 5.15789i) q^{27} +(-0.673841 + 2.29489i) q^{28} +(-5.54968 - 2.53446i) q^{29} +(-3.61735 - 4.53302i) q^{30} +(-1.22988 + 8.55402i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-0.152926 - 0.260573i) q^{33} +(1.90026 + 2.95687i) q^{34} +(4.32967 + 6.73709i) q^{35} +(1.02148 + 2.82074i) q^{36} +(-2.59752 - 8.84635i) q^{37} +(-0.952764 + 6.62662i) q^{38} +(0.900339 - 0.718470i) q^{39} +(-3.04573 - 1.39094i) q^{40} +(-0.791908 + 2.69699i) q^{41} +(-1.00532 - 4.01884i) q^{42} +(-5.73482 + 0.824543i) q^{43} +(-0.146746 - 0.0943077i) q^{44} +(9.37761 + 3.60013i) q^{45} +(2.02032 + 4.34952i) q^{46} +7.88048i q^{47} +(1.26202 + 1.18629i) q^{48} +(-0.182080 - 1.26640i) q^{49} +(-5.64988 + 2.58021i) q^{50} +(-5.43084 - 2.75102i) q^{51} +(0.276265 - 0.604936i) q^{52} +(7.73902 - 8.93131i) q^{53} +(-3.99879 - 3.31809i) q^{54} +(-0.560410 + 0.164551i) q^{55} +(-1.56628 - 1.80758i) q^{56} +(-4.38623 - 10.7341i) q^{57} +(5.13250 - 3.29846i) q^{58} +(7.68344 - 6.65774i) q^{59} +(5.76911 - 0.592371i) q^{60} +(-0.619733 - 0.0891041i) q^{61} +(-6.53117 - 5.65929i) q^{62} +(5.02500 + 5.12197i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-0.925020 - 2.02551i) q^{65} +(0.301886 + 0.0122265i) q^{66} +(4.04398 - 6.29256i) q^{67} -3.51483 q^{68} +(-6.83110 - 4.72610i) q^{69} -8.00840 q^{70} +(-2.12838 + 3.31183i) q^{71} +(-2.92521 - 0.665682i) q^{72} +(-2.52644 - 5.53213i) q^{73} +(8.84635 + 2.59752i) q^{74} +(6.17772 - 8.80747i) q^{75} +(-5.05956 - 4.38414i) q^{76} +(-0.412967 - 0.0593757i) q^{77} +(0.117656 + 1.14585i) q^{78} +(-3.93306 + 3.40802i) q^{79} +(2.81678 - 1.81023i) q^{80} +(8.88229 + 1.45086i) q^{81} +(-1.84072 - 2.12430i) q^{82} +(11.4071 - 3.34943i) q^{83} +(3.92438 + 1.32702i) q^{84} +(-7.70689 + 8.89423i) q^{85} +(2.40683 - 5.27022i) q^{86} +(-4.77519 + 9.42681i) q^{87} +(0.158673 - 0.0724637i) q^{88} +(2.16027 + 15.0250i) q^{89} +(-8.09854 + 5.94258i) q^{90} -1.59061i q^{91} +(-4.75131 - 0.651925i) q^{92} +(14.7177 + 2.72804i) q^{93} +(-6.62948 - 4.26051i) q^{94} +(-22.1880 + 3.19015i) q^{95} +(-1.68028 + 0.420323i) q^{96} +(-1.10459 + 3.76189i) q^{97} +(1.16380 + 0.531490i) q^{98} +(-0.461675 + 0.246395i) 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

Fields

Representations

Groups

Database

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