LMFDB - Embedded newform 138.2.f.a.11.2

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			11.2
Character	$\chi$	$=$	138.11
Dual form			138.2.f.a.113.2

$q$-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 $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$

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	−0.905138	−	0.425117i	$-0.860233\pi$
$5$	−3.21268	+	0.943327i	−1.43675	+	0.421869i	−0.531615	+	0.846986i	$0.678415\pi$
$6$	1.41801	−	0.994615i	0.578899	−	0.406050i
$7$	−1.80758	+	1.56628i	−0.683202	+	0.591998i	−0.925747	−	0.378142i	$-0.876563\pi$
$7$	−1.80758	+	1.56628i	−0.683202	+	0.591998i	0.242546	+	0.970140i	$0.422018\pi$
$8$	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	0.562577	−	0.826745i	$-0.309810\pi$
$11$	0.146746	+	0.0943077i	0.0442455	+	0.0284348i	−0.518331	+	0.855180i	$0.673447\pi$
$12$	−1.60336	−	0.655173i	−0.462849	−	0.189132i
$13$	0.435504	−	0.502599i	0.120787	−	0.139396i	−0.692135	−	0.721768i	$-0.743330\pi$
$13$	0.435504	−	0.502599i	0.120787	−	0.139396i	0.812922	+	0.582372i	$0.197875\pi$
$14$	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	0.999929	+	0.0119287i	$0.00379712\pi$
$17$	1.46011	+	3.19721i	0.354130	+	0.775436i	−0.645799	+	0.763507i	$0.723476\pi$
$18$	1.82070	+	2.38433i	0.429144	+	0.561993i
$19$	6.08977	+	2.78111i	1.39709	+	0.638029i	0.964626	−	0.263622i	$-0.0849173\pi$
$19$	6.08977	+	2.78111i	1.39709	+	0.638029i	0.432463	+	0.901652i	$0.357645\pi$
$20$	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	−0.857613	−	0.514296i	$-0.828053\pi$
$29$	−5.54968	+	2.53446i	−1.03055	+	0.470636i	−0.172938	+	0.984933i	$0.555326\pi$
$30$	−3.61735	+	4.53302i	−0.660435	+	0.827613i
$31$	−1.22988	−	8.55402i	−0.220893	−	1.53635i	−0.734671	−	0.678423i	$-0.762664\pi$
$31$	−1.22988	−	8.55402i	−0.220893	−	1.53635i	0.513778	−	0.857923i	$-0.328246\pi$
$32$	−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	0.412470	+	0.910971i	$0.364666\pi$
$37$	−2.59752	+	8.84635i	−0.427030	+	1.45433i	−0.839500	+	0.543360i	$0.817152\pi$
$38$	−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	0.874258	−	0.485462i	$-0.161349\pi$
$41$	−0.791908	−	2.69699i	−0.123675	−	0.421199i	−0.997933	+	0.0642628i	$0.979530\pi$
$42$	−1.00532	+	4.01884i	−0.155124	+	0.620121i
$43$	−5.73482	−	0.824543i	−0.874552	−	0.125742i	−0.309601	−	0.950866i	$-0.600196\pi$
$43$	−5.73482	−	0.824543i	−0.874552	−	0.125742i	−0.564950	+	0.825125i	$0.691105\pi$
$44$	−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	$-0.805102\pi$
$47$		−	7.88048i		−	1.14949i	0.818334	−	0.574743i	$-0.194898\pi$
$48$	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	0.972984	+	0.230873i	$0.0741581\pi$
$53$	7.73902	+	8.93131i	1.06304	+	1.22681i	0.0900527	+	0.995937i	$0.471296\pi$
$54$	−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	0.991090	−	0.133193i	$-0.0425231\pi$
$59$	7.68344	+	6.65774i	1.00030	+	0.866764i	0.00920920	+	0.999958i	$0.497069\pi$
$60$	5.76911	+	0.592371i	0.744789	+	0.0764748i
$61$	−0.619733	+	0.0891041i	−0.0793486	+	0.0114086i	−0.181875	−	0.983322i	$-0.558217\pi$
$61$	−0.619733	+	0.0891041i	−0.0793486	+	0.0114086i	0.102526	+	0.994730i	$0.467307\pi$
$62$	−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	0.995330	−	0.0965269i	$-0.0307734\pi$
$67$	4.04398	+	6.29256i	0.494051	+	0.768759i	−0.501279	+	0.865286i	$0.667137\pi$
$68$	−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	0.691681	−	0.722203i	$-0.256870\pi$
$71$	−2.12838	−	3.31183i	−0.252593	−	0.393042i	−0.944274	+	0.329161i	$0.893234\pi$
$72$	−2.92521	+	0.665682i	−0.344740	+	0.0784513i
$73$	−2.52644	+	5.53213i	−0.295697	+	0.647487i	−0.997920	−	0.0644710i	$-0.979464\pi$
$73$	−2.52644	+	5.53213i	−0.295697	+	0.647487i	0.702222	+	0.711958i	$0.252191\pi$
$74$	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	0.404917	−	0.914354i	$-0.367300\pi$
$79$	−3.93306	−	3.40802i	−0.442504	−	0.383432i	−0.847421	+	0.530921i	$0.821846\pi$
$80$	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	0.839547	−	0.543288i	$-0.182821\pi$
$83$	11.4071	+	3.34943i	1.25209	+	0.367648i	0.412548	+	0.910936i	$0.364639\pi$
$84$	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	−0.473398	−	0.880849i	$-0.656973\pi$
$89$	2.16027	−	15.0250i	0.228988	−	1.59265i	0.702386	−	0.711797i	$-0.252118\pi$
$90$	−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	0.884217	−	0.467076i	$-0.154693\pi$
$97$	−1.10459	−	3.76189i	−0.112154	−	0.381962i	−0.996371	+	0.0851145i	$0.972874\pi$
$98$	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	0.527551	+	0.849523i	$0.323110\pi$
$101$	−3.77413	+	12.8535i	−0.375540	+	1.27897i	−0.903091	+	0.429449i	$0.858708\pi$
$102$	5.25044	+	3.08140i	0.519871	+	0.305104i
$103$	−0.709786	+	1.10445i	−0.0699373	+	0.108825i	−0.874461	−	0.485096i	$-0.838784\pi$
$103$	−0.709786	+	1.10445i	−0.0699373	+	0.108825i	0.804523	+	0.593921i	$0.202421\pi$
$104$	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	0.970520	−	0.241020i	$-0.0774818\pi$
$107$	−0.295739	−	2.05691i	−0.0285902	−	0.198849i	−0.999110	+	0.0421705i	$0.986573\pi$
$108$	4.95326	+	1.57010i	0.476628	+	0.151083i
$109$	2.64483	−	1.20785i	0.253328	−	0.115691i	−0.284704	−	0.958616i	$-0.591895\pi$
$109$	2.64483	−	1.20785i	0.253328	−	0.115691i	0.538032	+	0.842924i	$0.319168\pi$
$110$	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	−0.883246	−	0.468911i	$-0.844647\pi$
$113$	−8.75523	+	5.62665i	−0.823623	+	0.529310i	0.0596226	+	0.998221i	$0.481010\pi$
$114$	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	0.959105	+	0.283051i	$0.0913464\pi$
$127$	18.2002	+	11.6965i	1.61500	+	1.03790i	0.655898	+	0.754849i	$0.272290\pi$
$128$	−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	−0.250636	−	0.968081i	$-0.580640\pi$
$131$	7.69051	−	6.66386i	0.671923	−	0.582224i	0.922559	+	0.385857i	$0.126094\pi$
$132$	−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	−0.267875	−	0.963454i	$-0.586321\pi$
$149$	−15.3258	−	9.84932i	−1.25554	−	0.806888i	−0.987668	+	0.156566i	$0.949958\pi$
$150$	4.06939	−	9.95871i	0.332264	−	0.813125i
$151$	4.64937	−	5.36566i	0.378360	−	0.436651i	−0.534347	−	0.845265i	$-0.679442\pi$
$151$	4.64937	−	5.36566i	0.378360	−	0.436651i	0.912707	+	0.408614i	$0.133988\pi$
$152$	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	0.476855	−	0.878982i	$-0.341777\pi$
$157$	1.56422	+	0.714356i	0.124838	+	0.0570118i	−0.352017	+	0.935994i	$0.614504\pi$
$158$	−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	−0.573023	−	0.819539i	$-0.694229\pi$
$163$	−0.837342	+	0.538127i	−0.0655857	+	0.0421494i	0.507437	+	0.861689i	$0.330593\pi$
$164$	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	0.0144375	−	0.999896i	$-0.495404\pi$
$167$	10.0742	−	4.60072i	0.779563	−	0.356014i	0.765125	+	0.643881i	$0.222677\pi$
$168$	−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	−0.787937	−	0.615755i	$-0.788851\pi$
$173$	1.30865	−	2.03629i	0.0994945	−	0.154817i	0.887432	+	0.460939i	$0.152487\pi$
$174$	−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	0.978626	+	0.205647i	$0.0659299\pi$
$179$	3.56599	+	12.1447i	0.266535	+	0.907734i	−0.712092	+	0.702087i	$0.752252\pi$
$180$	−0.620812	+	10.0257i	−0.0462726	+	0.747273i
$181$	−9.15702	−	1.31658i	−0.680636	−	0.0978607i	−0.206679	−	0.978409i	$-0.566266\pi$
$181$	−9.15702	−	1.31658i	−0.680636	−	0.0978607i	−0.473957	+	0.880548i	$0.657175\pi$
$182$	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	0.719831	−	0.694150i	$-0.244219\pi$
$191$	−0.963220	−	1.11162i	−0.0696962	−	0.0804337i	−0.789527	+	0.613716i	$0.789674\pi$
$192$	0.554828	+	1.64078i	0.0400412	+	0.118413i
$193$	5.88402	+	1.72770i	0.423541	+	0.124363i	0.486555	−	0.873650i	$-0.338253\pi$
$193$	5.88402	+	1.72770i	0.423541	+	0.124363i	−0.0630142	+	0.998013i	$0.520071\pi$
$194$	−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	−0.999465	−	0.0327122i	$-0.989586\pi$
$197$	−16.4790	−	14.2792i	−1.17408	−	1.01735i	−0.174618	−	0.984636i	$-0.555869\pi$
$198$	0.0423192	+	0.521597i	0.00300750	+	0.0370683i
$199$	−0.422569	+	0.0607563i	−0.0299551	+	0.00430690i	−0.157276	−	0.987555i	$-0.550271\pi$
$199$	−0.422569	+	0.0607563i	−0.0299551	+	0.00430690i	0.127321	+	0.991862i	$0.459362\pi$
$200$	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	−0.710510	−	0.703687i	$-0.751536\pi$
$211$	4.16291	−	9.11550i	0.286586	−	0.627537i	0.997096	+	0.0761505i	$0.0242629\pi$
$212$	−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	0.847860	−	0.530221i	$-0.177891\pi$
$223$	3.02207	+	3.48765i	0.202372	+	0.233550i	−0.645487	+	0.763771i	$0.723346\pi$
$224$	−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	−0.999959	−	0.00906687i	$-0.997114\pi$
$227$	−0.571788	+	3.97688i	−0.0379509	+	0.263955i	0.962008	+	0.273021i	$0.0880230\pi$
$228$	−7.94196	−	8.44895i	−0.525969	−	0.559546i
$229$			6.47386i			0.427805i	0.976855	+	0.213902i	$0.0686174\pi$
$229$			6.47386i			0.427805i	−0.976855	+	0.213902i	$0.931383\pi$
$230$	−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	−0.571786	−	0.820403i	$-0.693749\pi$
$233$	−20.6304	−	2.96621i	−1.35155	−	0.194323i	−0.779759	+	0.626080i	$0.784658\pi$
$234$	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	0.834926	+	0.550362i	$0.185510\pi$
$239$	−2.55094	+	8.68772i	−0.165007	+	0.561962i	−0.999933	+	0.0115993i	$0.996308\pi$
$240$	−2.93541	+	5.00168i	−0.189480	+	0.322857i
$241$	2.19681	−	3.41830i	0.141509	−	0.220192i	−0.763264	−	0.646087i	$-0.776404\pi$
$241$	2.19681	−	3.41830i	0.141509	−	0.220192i	0.904773	+	0.425895i	$0.140041\pi$
$242$	−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	−0.393688	−	0.919244i	$-0.628801\pi$
$251$	4.41926	−	2.84009i	0.278942	−	0.179265i	0.672630	+	0.739979i	$0.265165\pi$
$252$	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	0.859899	−	0.510465i	$-0.170527\pi$
$257$	16.6280	+	7.59377i	1.03723	+	0.473687i	0.177330	+	0.984151i	$0.443254\pi$
$258$	−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	0.0598627	+	0.998207i	$0.480934\pi$
$263$	−15.1908	+	17.5311i	−0.936703	+	1.08101i	−0.996566	+	0.0828062i	$0.973612\pi$
$264$	−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	−0.418029	−	0.908434i	$-0.637279\pi$
$269$	6.91584	−	5.99261i	0.421666	−	0.365376i	0.839695	+	0.543058i	$0.182734\pi$
$270$	9.71677	−	14.4321i	0.591344	−	0.878310i
$271$	25.6521	−	7.53215i	1.55826	−	0.457545i	0.614701	−	0.788760i	$-0.289277\pi$
$271$	25.6521	−	7.53215i	1.55826	−	0.457545i	0.943555	+	0.331215i	$0.107458\pi$
$272$	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	0.350881	−	0.936420i	$-0.385882\pi$
$281$	19.3165	−	5.67184i	1.15233	−	0.338354i	0.801447	+	0.598066i	$0.204064\pi$
$282$	−7.83805	−	11.1746i	−0.466749	−	0.665436i
$283$	−7.96292	+	6.89991i	−0.473347	+	0.410157i	−0.858594	−	0.512656i	$-0.828662\pi$
$283$	−7.96292	+	6.89991i	−0.473347	+	0.410157i	0.385247	+	0.922813i	$0.374116\pi$
$284$	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	0.890454	−	0.455074i	$-0.150387\pi$
$293$	−0.626345	−	1.37150i	−0.0365914	−	0.0801241i	−0.927045	+	0.374950i	$0.877660\pi$
$294$	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	−0.953981	−	0.299867i	$-0.903058\pi$
$307$	−2.15733	−	15.0046i	−0.123125	−	0.856356i	0.830856	−	0.556488i	$-0.187852\pi$
$308$	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	−0.907048	−	0.421027i	$-0.861670\pi$
$311$	−2.59708	+	4.04114i	−0.147267	+	0.229152i	0.759781	+	0.650179i	$0.225306\pi$
$312$	0.993424	+	0.583025i	0.0562415	+	0.0330073i
$313$	−3.56220	+	12.1317i	−0.201348	+	0.685727i	0.795469	+	0.605995i	$0.207225\pi$
$313$	−3.56220	+	12.1317i	−0.201348	+	0.685727i	−0.996816	+	0.0797321i	$0.974594\pi$
$314$	−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	0.989454	−	0.144849i	$-0.0462696\pi$
$317$	1.40230	+	4.77580i	0.0787610	+	0.268235i	−0.910693	+	0.413084i	$0.864451\pi$
$318$	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	0.0642205	−	0.997936i	$-0.479544\pi$
$331$	−7.66449	−	2.25050i	−0.421279	−	0.123699i	−0.485499	+	0.874237i	$0.661362\pi$
$332$	−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	−0.356190	−	0.934413i	$-0.615924\pi$
$337$	−7.97998	+	1.14735i	−0.434697	+	0.0625001i	−0.0785073	+	0.996914i	$0.525015\pi$
$338$	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	0.818005	−	0.575212i	$-0.195080\pi$
$347$	−0.838961	−	1.30545i	−0.0450378	−	0.0700802i	−0.863042	+	0.505132i	$0.831444\pi$
$348$	10.5586	−	0.427629i	0.566001	−	0.0229233i
$349$	0.688116	−	1.50676i	0.0368340	−	0.0806552i	−0.890321	−	0.455334i	$-0.849520\pi$
$349$	0.688116	−	1.50676i	0.0368340	−	0.0806552i	0.927155	+	0.374679i	$0.122247\pi$
$350$	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	−0.672844	−	0.739784i	$-0.734928\pi$
$353$	−20.8552	+	2.99853i	−1.11001	+	0.159596i	−0.437168	+	0.899380i	$0.644019\pi$
$354$	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	0.139303	−	0.990250i	$-0.455514\pi$
$359$	−5.28399	−	1.55152i	−0.278878	−	0.0818860i	−0.418181	+	0.908364i	$0.637332\pi$
$360$	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	$0.126745\pi$
$367$			14.8562i			0.775487i	−0.921767	+	0.387744i	$0.873255\pi$
$368$	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	0.985968	−	0.166932i	$-0.0533860\pi$
$373$	1.27986	+	4.35881i	0.0662688	+	0.225691i	−0.919700	+	0.392623i	$0.871568\pi$
$374$	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	0.0633915	+	0.997989i	$0.479808\pi$
$379$	−16.9516	+	26.3772i	−0.870745	+	1.35491i	−0.934136	+	0.356917i	$0.883828\pi$
$380$	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	0.989779	+	0.142611i	$0.0455498\pi$
$383$	1.57094	+	10.9261i	0.0802712	+	0.558298i	−0.909508	+	0.415687i	$0.863541\pi$
$384$	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	−0.713940	−	0.700207i	$-0.753091\pi$
$389$	−7.36837	+	4.73537i	−0.373591	+	0.240093i	0.340349	+	0.940299i	$0.389455\pi$
$390$	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	−0.989464	−	0.144780i	$-0.953752\pi$
$397$	−8.98453	−	19.6734i	−0.450921	−	0.987378i	0.538543	−	0.842598i	$-0.318975\pi$
$398$	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	0.0526774	−	0.998612i	$-0.483224\pi$
$401$	20.6984	−	23.8872i	1.03363	−	1.19287i	0.980950	−	0.194258i	$-0.0622301\pi$
$402$	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	−0.474955	−	0.880010i	$-0.657536\pi$
$409$	−8.06409	+	2.36783i	−0.398744	+	0.117082i	0.0762116	+	0.997092i	$0.475718\pi$
$410$	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	−0.190424	−	0.981702i	$-0.560986\pi$
$419$	3.68715	−	1.08265i	0.180129	−	0.0528907i	0.370553	+	0.928811i	$0.379168\pi$
$420$	−11.3560	+	7.96527i	−0.554114	+	0.388665i
$421$	7.60912	−	6.59334i	0.370846	−	0.321340i	−0.449422	−	0.893320i	$-0.648370\pi$
$421$	7.60912	−	6.59334i	0.370846	−	0.321340i	0.820268	+	0.571980i	$0.193824\pi$
$422$	−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	0.900542	−	0.434768i	$-0.143170\pi$
$431$	−0.368781	−	0.807518i	−0.0177636	−	0.0388968i	−0.918306	+	0.395872i	$0.870443\pi$
$432$	−3.48587	+	3.85340i	−0.167714	+	0.185397i
$433$	−12.4673	−	5.69362i	−0.599140	−	0.273618i	0.0926709	−	0.995697i	$-0.470460\pi$
$433$	−12.4673	−	5.69362i	−0.599140	−	0.273618i	−0.691811	+	0.722079i	$0.743187\pi$
$434$	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	0.112804	−	0.993617i	$-0.464017\pi$
$439$	22.2826	−	14.3202i	1.06349	−	0.683464i	0.950686	+	0.310154i	$0.100380\pi$
$440$	−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	−0.341707	−	0.939806i	$-0.611005\pi$
$443$	3.04728	−	1.39165i	0.144781	−	0.0661191i	0.486488	+	0.873687i	$0.338278\pi$
$444$	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	0.115491	+	0.993309i	$0.463156\pi$
$449$	−17.7152	+	27.5654i	−0.836031	+	1.30089i	−0.951522	+	0.307581i	$0.900480\pi$
$450$	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	−0.384006	−	0.923330i	$-0.625456\pi$
$457$	−21.6467	−	3.11233i	−1.01259	−	0.145588i	−0.628584	+	0.777742i	$0.716365\pi$
$458$	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	$0.271523\pi$
$461$			32.3466i			1.50653i	−0.657715	+	0.753267i	$0.728477\pi$
$462$	−0.526534	+	0.494938i	−0.0244966	+	0.0230266i
$463$	1.87739	−	13.0575i	0.0872497	−	0.606835i	−0.898545	−	0.438881i	$-0.855375\pi$
$463$	1.87739	−	13.0575i	0.0872497	−	0.606835i	0.985795	−	0.167954i	$-0.0537160\pi$
$464$	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	0.278483	−	0.960441i	$-0.410168\pi$
$467$	−15.3824	−	17.7523i	−0.711815	−	0.821478i	−0.990298	+	0.138963i	$0.955623\pi$
$468$	−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	−0.716772	−	0.697308i	$-0.754381\pi$
$479$	6.11943	−	13.3997i	0.279604	−	0.612247i	0.996376	+	0.0850605i	$0.0271084\pi$
$480$	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	−0.514485	−	0.857499i	$-0.672017\pi$
$487$	10.3827	−	22.7350i	0.470486	−	1.03022i	0.984971	−	0.172721i	$-0.0552559\pi$
$488$	−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	−0.348496	−	0.937310i	$-0.613308\pi$
$491$	−9.28010	+	1.33428i	−0.418805	+	0.0602151i	−0.0703089	+	0.997525i	$0.522398\pi$
$492$	−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	0.877481	−	0.479611i	$-0.159222\pi$
$499$	6.20722	+	7.16351i	0.277873	+	0.320683i	−0.599608	+	0.800294i	$0.704677\pi$
$500$	−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	−0.685216	−	0.728340i	$-0.740292\pi$
$503$	3.97959	−	27.6786i	0.177441	−	1.23413i	0.862657	−	0.505789i	$-0.168799\pi$
$504$	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	0.861756	−	0.507323i	$-0.169365\pi$
$509$	34.8720	+	5.01384i	1.54568	+	0.222235i	0.683920	+	0.729557i	$0.260274\pi$
$510$	−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	0.989167	−	0.146796i	$-0.0468960\pi$
$521$	−0.0294211	−	0.204628i	−0.00128896	−	0.00896492i	−0.990456	+	0.137831i	$0.955987\pi$
$522$	−16.1473	−	8.61780i	−0.706748	−	0.377191i
$523$	13.7188	−	6.26517i	0.599882	−	0.273957i	−0.0922407	−	0.995737i	$-0.529403\pi$
$523$	13.7188	−	6.26517i	0.599882	−	0.273957i	0.692123	+	0.721780i	$0.256676\pi$
$524$	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	0.999944	+	0.0105589i	$0.00336105\pi$
$541$	33.1433	+	21.2999i	1.42494	+	0.915754i	0.424997	+	0.905195i	$0.360275\pi$
$542$	−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	−0.558399	−	0.829573i	$-0.688584\pi$
$547$	−13.5569	+	3.98068i	−0.579653	+	0.170201i	−0.0212542	+	0.999774i	$0.506766\pi$
$548$	−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	0.0187599	−	0.999824i	$-0.494028\pi$
$557$	13.5725	−	3.98526i	0.575087	−	0.168861i	0.556327	+	0.830963i	$0.312210\pi$
$558$	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	0.684301	−	0.729200i	$-0.260108\pi$
$563$	7.24324	+	4.65495i	0.305266	+	0.196183i	−0.379035	+	0.925382i	$0.623744\pi$
$564$	−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	0.964824	−	0.262898i	$-0.0846782\pi$
$569$	3.20388	+	7.01552i	0.134314	+	0.294106i	−0.830510	+	0.557004i	$0.811951\pi$
$570$	−34.6356	+	17.5448i	−1.45073	+	0.734872i
$571$	−15.9160	−	7.26859i	−0.666064	−	0.304181i	0.0535404	−	0.998566i	$-0.482949\pi$
$571$	−15.9160	−	7.26859i	−0.666064	−	0.304181i	−0.719604	+	0.694385i	$0.755677\pi$
$572$	−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	−0.857954	−	0.513727i	$-0.828264\pi$
$577$	−17.9450	+	11.5325i	−0.747058	+	0.480105i	0.110896	+	0.993832i	$0.464628\pi$
$578$	−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	−0.616706	−	0.787193i	$-0.711533\pi$
$587$	8.61402	−	13.4037i	0.355539	−	0.553229i	0.972245	+	0.233964i	$0.0751698\pi$
$588$	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	−0.659710	−	0.751520i	$-0.729321\pi$
$593$	−12.4444	−	42.3816i	−0.511029	−	1.74041i	0.148681	−	0.988885i	$-0.452497\pi$
$594$	−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	$-0.885066\pi$
$599$		−	17.2927i		−	0.706560i	0.935518	−	0.353280i	$-0.114934\pi$
$600$	7.36828	+	7.83865i	0.300809	+	0.320011i
$601$	−3.18966	+	22.1846i	−0.130109	+	0.904928i	0.815299	+	0.579040i	$0.196572\pi$
$601$	−3.18966	+	22.1846i	−0.130109	+	0.904928i	−0.945408	+	0.325888i	$0.894337\pi$
$602$	−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	0.807104	−	0.590409i	$-0.201034\pi$
$607$	28.7490	+	8.44146i	1.16688	+	0.342628i	0.359780	+	0.933037i	$0.382852\pi$
$608$	−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	−0.516128	−	0.856511i	$-0.672627\pi$
$613$	−19.0654	+	2.74119i	−0.770043	+	0.110715i	−0.253914	+	0.967227i	$0.581718\pi$
$614$	−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	−0.133238	−	0.991084i	$-0.542537\pi$
$617$	17.4628	−	38.2382i	0.703026	−	1.53941i	0.836264	−	0.548328i	$-0.184735\pi$
$618$	0.0920203	+	2.27208i	0.00370160	+	0.0913964i
$619$	22.5746	+	35.1268i	0.907352	+	1.41187i	0.911241	+	0.411874i	$0.135126\pi$
$619$	22.5746	+	35.1268i	0.907352	+	1.41187i	−0.00388892	+	0.999992i	$0.501238\pi$
$620$	−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	0.999409	+	0.0343665i	$0.0109414\pi$
$631$	29.5322	+	25.5898i	1.17566	+	1.01871i	0.176247	+	0.984346i	$0.443604\pi$
$632$	−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	0.687647	+	0.726045i	$0.258644\pi$
$641$	−4.47358	+	31.1145i	−0.176696	+	1.22895i	−0.864343	+	0.502902i	$0.832266\pi$
$642$	−2.46520	−	2.62257i	−0.0972935	−	0.103504i
$643$			15.5189i			0.612005i	0.952031	+	0.306003i	$0.0989916\pi$
$643$			15.5189i			0.612005i	−0.952031	+	0.306003i	$0.901008\pi$
$644$	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	0.504778	−	0.863249i	$-0.331574\pi$
$647$	18.9730	+	2.72790i	0.745904	+	0.107245i	0.241126	+	0.970494i	$0.422483\pi$
$648$	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	−0.968756	−	0.248016i	$-0.920222\pi$
$653$	−0.503391	+	1.71439i	−0.0196992	+	0.0670894i	0.949057	+	0.315105i	$0.102040\pi$
$654$	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	0.999239	−	0.0389994i	$-0.0124170\pi$
$659$	0.757007	+	5.26510i	0.0294888	+	0.205099i	−0.969750	+	0.244099i	$0.921508\pi$
$660$	0.790726	+	0.630999i	0.0307790	+	0.0245616i
$661$	−10.3085	+	4.70775i	−0.400956	+	0.183110i	−0.605678	−	0.795710i	$-0.707098\pi$
$661$	−10.3085	+	4.70775i	−0.400956	+	0.183110i	0.204722	+	0.978820i	$0.434371\pi$
$662$	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	0.955298	−	0.295645i	$-0.0955347\pi$
$673$	2.75706	+	6.03712i	0.106277	+	0.232714i	−0.849021	+	0.528359i	$0.822807\pi$
$674$	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	−0.999611	−	0.0278922i	$-0.991120\pi$
$677$	−21.5893	+	24.9153i	−0.829743	+	0.957575i	0.169868	+	0.985467i	$0.445666\pi$
$678$	−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	−0.565527	−	0.824730i	$-0.691327\pi$
$683$	4.45133	−	3.85710i	0.170325	−	0.147588i	0.735852	+	0.677142i	$0.236782\pi$
$684$	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	0.679501	−	0.733675i	$-0.262196\pi$
$701$	7.79469	+	5.00934i	0.294401	+	0.189200i	−0.385099	+	0.922875i	$0.625833\pi$
$702$	−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	0.965876	−	0.259004i	$-0.0833944\pi$
$709$	37.3484	+	17.0564i	1.40265	+	0.640568i	0.436772	+	0.899572i	$0.356122\pi$
$710$	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	−0.644951	−	0.764224i	$-0.723122\pi$
$719$	−13.1320	+	5.99720i	−0.489742	+	0.223658i	0.155209	+	0.987882i	$0.450395\pi$
$720$	−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	−0.999255	−	0.0385823i	$-0.987716\pi$
$727$	−3.71466	+	12.6510i	−0.137769	+	0.469199i	0.861486	+	0.507781i	$0.169534\pi$
$728$	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	−0.490794	−	0.871276i	$-0.663293\pi$
$733$	−32.6830	−	4.69910i	−1.20717	−	0.173565i	−0.716380	+	0.697711i	$0.754202\pi$
$734$	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	−0.501040	−	0.865424i	$-0.667049\pi$
$739$	6.07636	−	42.2620i	0.223522	−	1.55463i	0.724563	−	0.689209i	$-0.242042\pi$
$740$	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	0.828448	−	0.560067i	$-0.189224\pi$
$743$	4.25720	+	4.91307i	0.156181	+	0.180243i	−0.672266	+	0.740309i	$0.734679\pi$
$744$	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	0.648928	−	0.760850i	$-0.275217\pi$
$751$	40.7209	−	5.85478i	1.48593	−	0.213644i	0.836998	+	0.547206i	$0.184308\pi$
$752$	−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	−0.942987	−	0.332829i	$-0.891997\pi$
$757$	−23.4969	−	36.5618i	−0.854008	−	1.32886i	0.0889786	−	0.996034i	$-0.471640\pi$
$758$	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	−0.992969	−	0.118377i	$-0.962231\pi$
$761$	−18.9836	−	29.5390i	−0.688154	−	1.07079i	0.304815	−	0.952412i	$-0.401405\pi$
$762$	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	0.514259	−	0.857635i	$-0.328067\pi$
$769$	−7.25051	−	6.28260i	−0.261460	−	0.226556i	−0.775719	+	0.631079i	$0.782613\pi$
$770$	−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	0.0693464	−	0.997593i	$-0.477909\pi$
$773$	−11.4452	−	3.36061i	−0.411655	−	0.120873i	−0.481001	+	0.876720i	$0.659727\pi$
$774$	−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	−0.777495	−	0.628889i	$-0.783510\pi$
$787$	−13.0008	−	44.2766i	−0.463428	−	1.57829i	0.314068	−	0.949401i	$-0.398308\pi$
$788$	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	0.715807	+	0.698298i	$0.246059\pi$
$797$	6.37259	+	44.3223i	0.225729	+	1.56998i	−0.490078	+	0.871678i	$0.663032\pi$
$798$	−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	0.893269	−	0.449523i	$-0.148406\pi$
$809$	32.3825	+	14.7886i	1.13851	+	0.519939i	0.245239	+	0.969463i	$0.421133\pi$
$810$	25.6577	+	15.8046i	0.901521	+	0.555317i
$811$	−3.11653	−	6.82424i	−0.109436	−	0.239631i	0.846988	−	0.531611i	$-0.178413\pi$
$811$	−3.11653	−	6.82424i	−0.109436	−	0.239631i	−0.956424	+	0.291980i	$0.905686\pi$
$812$	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	0.470684	−	0.882302i	$-0.344007\pi$
$821$	40.4292	−	35.0321i	1.41099	−	1.22263i	0.940307	−	0.340328i	$-0.110538\pi$
$822$	14.5878	−	10.2322i	0.508809	−	0.356888i
$823$	7.35580	−	2.15986i	0.256407	−	0.0752879i	−0.151003	−	0.988533i	$-0.548250\pi$
$823$	7.35580	−	2.15986i	0.256407	−	0.0752879i	0.407410	+	0.913245i	$0.366432\pi$
$824$	−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	0.483429	−	0.875384i	$-0.339391\pi$
$839$	−3.24484	−	2.08533i	−0.112024	−	0.0719936i	−0.595453	+	0.803390i	$0.703027\pi$
$840$	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	0.301562	−	0.953447i	$-0.402492\pi$
$853$	37.7963	−	24.2902i	1.29412	−	0.831681i	0.992559	+	0.121766i	$0.0388557\pi$
$854$	−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	−0.212239	−	0.977218i	$-0.568075\pi$
$857$	11.3382	−	5.17799i	0.387306	−	0.176877i	0.599545	+	0.800341i	$0.295348\pi$
$858$	0.125328	−	0.157052i	0.00427862	−	0.00536168i
$859$	−7.66120	−	53.2848i	−0.261397	−	1.81806i	−0.522381	−	0.852712i	$-0.674956\pi$
$859$	−7.66120	−	53.2848i	−0.261397	−	1.81806i	0.260984	−	0.965343i	$-0.415953\pi$
$860$	−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	−0.997184	−	0.0749969i	$-0.976105\pi$
$863$	−15.1208	+	23.5285i	−0.514719	+	0.800919i	0.482465	+	0.875915i	$0.339742\pi$
$864$	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	−0.986496	−	0.163782i	$-0.947631\pi$
$877$	0.183098	−	1.27348i	0.00618280	−	0.0430023i	0.992679	+	0.120780i	$0.0385396\pi$
$878$	−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	−0.997766	−	0.0668030i	$-0.978720\pi$
$881$	−27.3633	−	31.5789i	−0.921892	−	1.06392i	0.0758739	−	0.997117i	$-0.475825\pi$
$882$	−3.35102	+	1.87159i	−0.112835	+	0.0630197i
$883$	−44.5467	−	13.0801i	−1.49912	−	0.440180i	−0.573678	−	0.819081i	$-0.694484\pi$
$883$	−44.5467	−	13.0801i	−1.49912	−	0.440180i	−0.925437	+	0.378901i	$0.876302\pi$
$884$	−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	0.616198	−	0.787592i	$-0.288672\pi$
$887$	−2.25405	−	1.95314i	−0.0756835	−	0.0655801i	−0.691881	+	0.722012i	$0.743218\pi$
$888$	−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	0.593945	−	0.804506i	$-0.297570\pi$
$907$	−3.54906	−	3.07528i	−0.117845	−	0.102113i	−0.711790	+	0.702393i	$0.752115\pi$
$908$	−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	−0.100178	−	0.994970i	$-0.531941\pi$
$911$	−21.8033	−	6.40202i	−0.722375	−	0.212108i	−0.622196	+	0.782861i	$0.713760\pi$
$912$	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	$-0.963705\pi$
$919$		−	6.89830i		−	0.227554i	0.993506	−	0.113777i	$-0.0362949\pi$
$920$	−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	−0.999898	−	0.0142720i	$-0.995457\pi$
$929$	−4.60284	+	15.6758i	−0.151014	+	0.514307i	0.848884	+	0.528579i	$0.177275\pi$
$930$	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	0.291888	−	0.956453i	$-0.405717\pi$
$937$	36.9123	−	16.8573i	1.20587	−	0.550703i	0.913984	+	0.405749i	$0.132989\pi$
$938$	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	−0.492600	−	0.870256i	$-0.663953\pi$
$941$	2.89516	−	1.86061i	0.0943795	−	0.0606540i	0.586979	+	0.809602i	$0.300317\pi$
$942$	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	0.324217	−	0.945983i	$-0.394899\pi$
$947$	−5.48974	−	2.50708i	−0.178393	−	0.0814692i	−0.502609	+	0.864514i	$0.667627\pi$
$948$	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	−0.489101	−	0.872227i	$-0.662675\pi$
$953$	13.7021	−	15.8131i	0.443855	−	0.512236i	0.932956	+	0.359991i	$0.117220\pi$
$954$	−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	0.227802	−	0.973708i	$-0.426846\pi$
$971$	29.4740	−	8.65436i	0.945867	−	0.277731i	0.718065	+	0.695976i	$0.245028\pi$
$972$	−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	0.788465	−	0.615080i	$-0.210876\pi$
$977$	17.3948	+	11.1790i	0.556509	+	0.357646i	−0.231956	+	0.972726i	$0.574513\pi$
$978$	−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	0.994602	−	0.103764i	$-0.0330888\pi$
$983$	8.30399	+	18.1832i	0.264856	+	0.579954i	−0.729746	+	0.683719i	$0.760362\pi$
$984$	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	−0.854756	−	0.519030i	$-0.826293\pi$
$991$	−23.2232	+	14.9246i	−0.737709	+	0.474097i	0.117047	+	0.993126i	$0.462657\pi$
$992$	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	−0.989848	−	0.142128i	$-0.954605\pi$
$997$	−2.53038	−	17.5992i	−0.0801380	−	0.557372i	0.909710	−	0.415244i	$-0.136304\pi$
$998$	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.11.2	✓	80
3.2	odd	2	inner	138.2.f.a.11.7	yes	80
23.21	odd	22	inner	138.2.f.a.113.7	yes	80
69.44	even	22	inner	138.2.f.a.113.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.2	✓	80	1.1	even	1	trivial
138.2.f.a.11.7	yes	80	3.2	odd	2	inner
138.2.f.a.113.2	yes	80	69.44	even	22	inner
138.2.f.a.113.7	yes	80	23.21	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.540641 - 0.841254i) q^{2} +(0.0700914 + 1.73063i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(-3.21268 + 0.943327i) q^{5} +(1.41801 - 0.994615i) q^{6} +(-1.80758 + 1.56628i) q^{7} +(0.989821 - 0.142315i) q^{8} +(-2.99017 + 0.242605i) q^{9} +O(q^{10})\)	\(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

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Representations

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Database

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