LMFDB - Embedded newform 138.2.f.a.11.7

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			11.7
Character	$\chi$	$=$	138.11
Dual form			138.2.f.a.113.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 + 0.841254i) q^{2} +(-0.554828 + 1.64078i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(3.21268 - 0.943327i) q^{5} +(-1.68028 + 0.420323i) q^{6} +(-1.80758 + 1.56628i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.38433 - 1.82070i) q^{9} +O(q^{10})$	\(q+(0.540641 + 0.841254i) q^{2} +(-0.554828 + 1.64078i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(3.21268 - 0.943327i) q^{5} +(-1.68028 + 0.420323i) q^{6} +(-1.80758 + 1.56628i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.38433 - 1.82070i) q^{9} +(2.53048 + 2.19268i) q^{10} +(-0.146746 - 0.0943077i) q^{11} +(-1.26202 - 1.18629i) q^{12} +(0.435504 - 0.502599i) q^{13} +(-2.29489 - 0.673841i) q^{14} +(-0.234688 + 5.79469i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.46011 - 3.19721i) q^{17} +(0.242605 - 2.99017i) q^{18} +(6.08977 + 2.78111i) q^{19} +(-0.476514 + 3.31423i) q^{20} +(-1.56703 - 3.83486i) 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} +(4.31027 - 2.90199i) q^{27} +(-0.673841 - 2.29489i) q^{28} +(5.54968 - 2.53446i) q^{29} +(-5.00168 + 2.93541i) q^{30} +(-1.22988 - 8.55402i) q^{31} +(0.281733 - 0.959493i) q^{32} +(0.236157 - 0.188453i) q^{33} +(1.90026 - 2.95687i) q^{34} +(-4.32967 + 6.73709i) q^{35} +(2.64666 - 1.41252i) q^{36} +(-2.59752 + 8.84635i) q^{37} +(0.952764 + 6.62662i) q^{38} +(0.583025 + 0.993424i) q^{39} +(-3.04573 + 1.39094i) q^{40} +(0.791908 + 2.69699i) q^{41} +(2.37889 - 3.39155i) 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} +(1.60336 - 0.655173i) q^{48} +(-0.182080 + 1.26640i) q^{49} +(5.64988 + 2.58021i) q^{50} +(6.05603 - 0.621833i) q^{51} +(0.276265 + 0.604936i) q^{52} +(-7.73902 - 8.93131i) q^{53} +(4.77162 + 2.05709i) q^{54} +(-0.560410 - 0.164551i) q^{55} +(1.56628 - 1.80758i) q^{56} +(-7.94196 + 8.44895i) q^{57} +(5.13250 + 3.29846i) q^{58} +(-7.68344 - 6.65774i) q^{59} +(-5.17354 - 2.62068i) q^{60} +(-0.619733 + 0.0891041i) q^{61} +(6.53117 - 5.65929i) q^{62} +(7.16160 - 0.443460i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.925020 - 2.02551i) q^{65} +(0.286213 + 0.0967824i) q^{66} +(4.04398 + 6.29256i) q^{67} +3.51483 q^{68} +(8.07114 - 1.96385i) q^{69} -8.00840 q^{70} +(2.12838 + 3.31183i) q^{71} +(2.61918 + 1.46284i) q^{72} +(-2.52644 + 5.53213i) q^{73} +(-8.84635 + 2.59752i) q^{74} +(2.61070 + 10.4365i) q^{75} +(-5.05956 + 4.38414i) q^{76} +(0.412967 - 0.0593757i) q^{77} +(-0.520514 + 1.02756i) q^{78} +(-3.93306 - 3.40802i) q^{79} +(-2.81678 - 1.81023i) q^{80} +(2.37008 + 8.68232i) q^{81} +(-1.84072 + 2.12430i) q^{82} +(-11.4071 - 3.34943i) q^{83} +(4.13928 + 0.167643i) q^{84} +(-7.70689 - 8.89423i) q^{85} +(-2.40683 - 5.27022i) q^{86} +(1.07937 + 10.5120i) q^{87} +(0.158673 + 0.0724637i) q^{88} +(-2.16027 + 15.0250i) q^{89} +(-2.04130 - 9.83532i) 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} +(1.41801 + 0.994615i) q^{96} +(-1.10459 - 3.76189i) q^{97} +(-1.16380 + 0.531490i) q^{98} +(0.178184 + 0.492041i) 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
$3$	−0.554828	+	1.64078i	−0.320330	+	0.947306i
$3$	−0.554828	+	1.64078i	−0.320330	+	0.947306i
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	3.21268	−	0.943327i	1.43675	−	0.421869i	0.531615	−	0.846986i	$-0.321585\pi$
$5$	3.21268	−	0.943327i	1.43675	−	0.421869i	0.905138	+	0.425117i	$0.139767\pi$
$6$	−1.68028	+	0.420323i	−0.685970	+	0.171596i
$7$	−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
$9$	−2.38433	−	1.82070i	−0.794778	−	0.606901i
$10$	2.53048	+	2.19268i	0.800209	+	0.693385i
$11$	−0.146746	−	0.0943077i	−0.0442455	−	0.0284348i	0.518331	−	0.855180i	$-0.326553\pi$
$11$	−0.146746	−	0.0943077i	−0.0442455	−	0.0284348i	−0.562577	+	0.826745i	$0.690190\pi$
$12$	−1.26202	−	1.18629i	−0.364315	−	0.342454i
$13$	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
$15$	−0.234688	+	5.79469i	−0.0605961	+	1.49618i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−1.46011	−	3.19721i	−0.354130	−	0.775436i	−0.999929	−	0.0119287i	$-0.996203\pi$
$17$	−1.46011	−	3.19721i	−0.354130	−	0.775436i	0.645799	−	0.763507i	$-0.276524\pi$
$18$	0.242605	−	2.99017i	0.0571825	−	0.704791i
$19$	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
$21$	−1.56703	−	3.83486i	−0.341953	−	0.836836i
$22$		−	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
$27$	4.31027	−	2.90199i	0.829512	−	0.558489i
$28$	−0.673841	−	2.29489i	−0.127344	−	0.433693i
$29$	5.54968	−	2.53446i	1.03055	−	0.470636i	0.172938	−	0.984933i	$-0.444674\pi$
$29$	5.54968	−	2.53446i	1.03055	−	0.470636i	0.857613	+	0.514296i	$0.171947\pi$
$30$	−5.00168	+	2.93541i	−0.913179	+	0.535931i
$31$	−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
$33$	0.236157	−	0.188453i	0.0411096	−	0.0328055i
$34$	1.90026	−	2.95687i	0.325892	−	0.507098i
$35$	−4.32967	+	6.73709i	−0.731847	+	1.13878i
$36$	2.64666	−	1.41252i	0.441109	−	0.235420i
$37$	−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
$39$	0.583025	+	0.993424i	0.0933588	+	0.159075i
$40$	−3.04573	+	1.39094i	−0.481572	+	0.219927i
$41$	0.791908	+	2.69699i	0.123675	+	0.421199i	0.997933	−	0.0642628i	$-0.0204696\pi$
$41$	0.791908	+	2.69699i	0.123675	+	0.421199i	−0.874258	+	0.485462i	$0.838651\pi$
$42$	2.37889	−	3.39155i	0.367071	−	0.523327i
$43$	−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	$0.194898\pi$
$47$			7.88048i			1.14949i	−0.818334	+	0.574743i	$0.805102\pi$
$48$	1.60336	−	0.655173i	0.231424	−	0.0945661i
$49$	−0.182080	+	1.26640i	−0.0260115	+	0.180914i
$50$	5.64988	+	2.58021i	0.799013	+	0.364897i
$51$	6.05603	−	0.621833i	0.848014	−	0.0870740i
$52$	0.276265	+	0.604936i	0.0383111	+	0.0838895i
$53$	−7.73902	−	8.93131i	−1.06304	−	1.22681i	−0.972984	−	0.230873i	$-0.925842\pi$
$53$	−7.73902	−	8.93131i	−1.06304	−	1.22681i	−0.0900527	−	0.995937i	$-0.528704\pi$
$54$	4.77162	+	2.05709i	0.649335	+	0.279935i
$55$	−0.560410	−	0.164551i	−0.0755656	−	0.0221881i
$56$	1.56628	−	1.80758i	0.209303	−	0.241548i
$57$	−7.94196	+	8.44895i	−1.05194	+	1.11909i
$58$	5.13250	+	3.29846i	0.673931	+	0.433109i
$59$	−7.68344	−	6.65774i	−1.00030	−	0.866764i	−0.00920920	−	0.999958i	$-0.502931\pi$
$59$	−7.68344	−	6.65774i	−1.00030	−	0.866764i	−0.991090	+	0.133193i	$0.957477\pi$
$60$	−5.17354	−	2.62068i	−0.667901	−	0.338328i
$61$	−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
$63$	7.16160	−	0.443460i	0.902277	−	0.0558708i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	0.925020	−	2.02551i	0.114735	−	0.251234i
$66$	0.286213	+	0.0967824i	0.0352304	+	0.0119131i
$67$	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
$69$	8.07114	−	1.96385i	0.971651	−	0.236420i
$70$	−8.00840			−0.957186
$71$	2.12838	+	3.31183i	0.252593	+	0.393042i	0.944274	−	0.329161i	$-0.106766\pi$
$71$	2.12838	+	3.31183i	0.252593	+	0.393042i	−0.691681	+	0.722203i	$0.743130\pi$
$72$	2.61918	+	1.46284i	0.308673	+	0.172398i
$73$	−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
$75$	2.61070	+	10.4365i	0.301457	+	1.20510i
$76$	−5.05956	+	4.38414i	−0.580372	+	0.502895i
$77$	0.412967	−	0.0593757i	0.0470619	−	0.00676649i
$78$	−0.520514	+	1.02756i	−0.0589366	+	0.116348i
$79$	−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
$81$	2.37008	+	8.68232i	0.263343	+	0.964702i
$82$	−1.84072	+	2.12430i	−0.203273	+	0.234590i
$83$	−11.4071	−	3.34943i	−1.25209	−	0.367648i	−0.412548	−	0.910936i	$-0.635361\pi$
$83$	−11.4071	−	3.34943i	−1.25209	−	0.367648i	−0.839547	+	0.543288i	$0.817179\pi$
$84$	4.13928	+	0.167643i	0.451632	+	0.0182913i
$85$	−7.70689	−	8.89423i	−0.835930	−	0.964714i
$86$	−2.40683	−	5.27022i	−0.259535	−	0.568302i
$87$	1.07937	+	10.5120i	0.115721	+	1.12701i
$88$	0.158673	+	0.0724637i	0.0169146	+	0.00772466i
$89$	−2.16027	+	15.0250i	−0.228988	+	1.59265i	0.473398	+	0.880849i	$0.343027\pi$
$89$	−2.16027	+	15.0250i	−0.228988	+	1.59265i	−0.702386	+	0.711797i	$0.747882\pi$
$90$	−2.04130	−	9.83532i	−0.215172	−	1.03673i
$91$			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
$96$	1.41801	+	0.994615i	0.144725	+	0.101512i
$97$	−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
$99$	0.178184	+	0.492041i	0.0179082	+	0.0494520i
$100$	0.883941	+	6.14795i	0.0883941	+	0.614795i
$101$	3.77413	−	12.8535i	0.375540	−	1.27897i	−0.527551	−	0.849523i	$-0.676890\pi$
$101$	3.77413	−	12.8535i	0.375540	−	1.27897i	0.903091	−	0.429449i	$-0.141292\pi$
$102$	3.79726	+	4.75847i	0.375984	+	0.471159i
$103$	−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
$105$	−8.65188	−	10.8420i	−0.844337	−	1.05807i
$106$	3.32946	−	11.3391i	0.323386	−	1.10135i
$107$	0.295739	+	2.05691i	0.0285902	+	0.198849i	0.999110	−	0.0421705i	$-0.0134273\pi$
$107$	0.295739	+	2.05691i	0.0285902	+	0.198849i	−0.970520	+	0.241020i	$0.922518\pi$
$108$	0.849196	+	5.12629i	0.0817140	+	0.493278i
$109$	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
$111$	−13.0738	−	9.17017i	−1.24091	−	0.870394i
$112$	2.36743	+	0.340385i	0.223701	+	0.0321633i
$113$	8.75523	−	5.62665i	0.823623	−	0.529310i	−0.0596226	−	0.998221i	$-0.518990\pi$
$113$	8.75523	−	5.62665i	0.823623	−	0.529310i	0.883246	+	0.468911i	$0.155353\pi$
$114$	−11.4015	−	2.11335i	−1.06784	−	0.197934i
$115$	−12.0678	−	10.5937i	−1.12533	−	0.987864i
$116$			6.10102i			0.566465i
$117$	−1.95347	+	0.405439i	−0.180598	+	0.0374828i
$118$	1.44687	−	10.0632i	0.133195	−	0.926390i
$119$	7.64699	+	3.49226i	0.700999	+	0.320135i
$120$	−0.592371	−	5.76911i	−0.0540759	−	0.526645i
$121$	−4.55692	−	9.97827i	−0.414266	−	0.907116i
$122$	−0.410012	−	0.473179i	−0.0371207	−	0.0428396i
$123$	−4.86455	−	0.197016i	−0.438621	−	0.0177644i
$124$	8.29192	+	2.43473i	0.744636	+	0.218645i
$125$	2.65570	−	3.06484i	0.237533	−	0.274128i
$126$	4.24492	+	5.78497i	0.378167	+	0.515366i
$127$	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
$129$	4.53473	−	8.95211i	0.399261	−	0.788189i
$130$	2.20407	−	0.316898i	0.193310	−	0.0277938i
$131$	−7.69051	+	6.66386i	−0.671923	+	0.582224i	−0.922559	−	0.385857i	$-0.873906\pi$
$131$	−7.69051	+	6.66386i	−0.671923	+	0.582224i	0.250636	+	0.968081i	$0.419360\pi$
$132$	0.0733199	+	0.293102i	0.00638168	+	0.0255113i
$133$	−15.3637	+	4.51120i	−1.33221	+	0.391171i
$134$	−3.10730	+	6.80403i	−0.268430	+	0.587779i
$135$	11.1100	−	13.3892i	0.956195	−	1.15236i
$136$	1.90026	+	2.95687i	0.162946	+	0.253549i
$137$	−10.2876			−0.878926			−0.439463	−	0.898261i	$-0.644831\pi$
$137$	−10.2876			−0.878926			−0.439463	+	0.898261i	$0.644831\pi$
$138$	6.01568	+	5.72814i	0.512089	+	0.487612i
$139$	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
$141$	−12.9302	−	4.37231i	−1.08892	−	0.368215i
$142$	−1.63540	+	3.58102i	−0.137240	+	0.300513i
$143$	−0.111307	+	0.0326828i	−0.00930798	+	0.00273307i
$144$	0.185411	+	2.99426i	0.0154509	+	0.249522i
$145$	15.4385	−	13.3776i	1.28210	−	1.11095i
$146$	−6.01982	+	0.865519i	−0.498204	+	0.0716309i
$147$	−1.97686	−	1.00139i	−0.163048	−	0.0825929i
$148$	−6.96787	−	6.03770i	−0.572756	−	0.496296i
$149$	15.3258	+	9.84932i	1.25554	+	0.806888i	0.987668	−	0.156566i	$-0.0500424\pi$
$149$	15.3258	+	9.84932i	1.25554	+	0.806888i	0.267875	+	0.963454i	$0.413679\pi$
$150$	−7.36828	+	7.83865i	−0.601617	+	0.640023i
$151$	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
$153$	−2.33976	+	10.2816i	−0.189158	+	0.831221i
$154$	0.273217	+	0.315309i	0.0220164	+	0.0254083i
$155$	−12.0205	−	26.3211i	−0.965506	−	2.11416i
$156$	−1.14585	+	0.117656i	−0.0917412	+	0.00941998i
$157$	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
$159$	18.9482	−	7.74272i	1.50269	−	0.614037i
$160$		−	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
$165$	0.580923	−	0.828213i	0.0452248	−	0.0644763i
$166$	−3.34943	−	11.4071i	−0.259966	−	0.885365i
$167$	−10.0742	+	4.60072i	−0.779563	+	0.356014i	−0.765125	−	0.643881i	$-0.777323\pi$
$167$	−10.0742	+	4.60072i	−0.779563	+	0.356014i	−0.0144375	+	0.999896i	$0.504596\pi$
$168$	2.09683	+	3.57282i	0.161774	+	0.275649i
$169$	1.78715	+	12.4299i	0.137473	+	0.956147i
$170$	3.31564	−	11.2920i	0.254298	−	0.866059i
$171$	−9.45647	−	17.7187i	−0.723155	−	1.35499i
$172$	3.13236	−	4.87405i	0.238840	−	0.371643i
$173$	−1.30865	+	2.03629i	−0.0994945	+	0.154817i	−0.887432	−	0.460939i	$-0.847513\pi$
$173$	−1.30865	+	2.03629i	−0.0994945	+	0.154817i	0.787937	+	0.615755i	$0.211149\pi$
$174$	−8.25971	+	6.59124i	−0.626167	+	0.499681i
$175$	−4.18534	+	14.2539i	−0.316382	+	1.07750i
$176$	0.0248250	+	0.172661i	0.00187125	+	0.0130148i
$177$	15.1869	−	8.91296i	1.14152	−	0.669939i
$178$	−13.8078	+	6.30579i	−1.03493	+	0.472639i
$179$	−3.56599	−	12.1447i	−0.266535	−	0.907734i	−0.978626	−	0.205647i	$-0.934070\pi$
$179$	−3.56599	−	12.1447i	−0.266535	−	0.907734i	0.712092	−	0.702087i	$-0.247748\pi$
$180$	7.17039	−	7.03463i	0.534449	−	0.524330i
$181$	−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
$186$	5.66199	+	13.8562i	0.415157	+	1.01598i
$187$	−0.0872556	+	0.606876i	−0.00638076	+	0.0443792i
$188$	−7.16834	−	3.27367i	−0.522805	−	0.238757i
$189$	−3.24583	+	11.9967i	−0.236100	+	0.872630i
$190$	9.31200	+	20.3904i	0.675563	+	1.47928i
$191$	0.963220	+	1.11162i	0.0696962	+	0.0804337i	0.789527	−	0.613716i	$-0.210326\pi$
$191$	0.963220	+	1.11162i	0.0696962	+	0.0804337i	−0.719831	+	0.694150i	$0.755781\pi$
$192$	−0.0700914	+	1.73063i	−0.00505841	+	0.124898i
$193$	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
$195$	2.81020	+	2.64157i	0.201242	+	0.189166i
$196$	−1.07632	−	0.691706i	−0.0768797	−	0.0494076i
$197$	16.4790	+	14.2792i	1.17408	+	1.01735i	0.999465	+	0.0327122i	$0.0104145\pi$
$197$	16.4790	+	14.2792i	1.17408	+	1.01735i	0.174618	+	0.984636i	$0.444131\pi$
$198$	−0.317598	+	0.415916i	−0.0225707	+	0.0295578i
$199$	−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
$201$	−12.5684	+	3.14401i	−0.886509	+	0.221761i
$202$	12.8535	−	3.77413i	0.904370	−	0.265547i
$203$	−6.06184	+	13.2736i	−0.425458	+	0.931623i
$204$	−1.95013	+	5.76708i	−0.136536	+	0.403776i
$205$	5.08829	+	7.91754i	0.355382	+	0.552985i
$206$	−1.31286			−0.0914714
$207$	−1.25584	+	14.3326i	−0.0872872	+	0.996183i
$208$	−0.665034			−0.0461118
$209$	−0.631368	−	0.982427i	−0.0436726	−	0.0679559i
$210$	4.44328	−	13.1400i	0.306615	−	0.906748i
$211$	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
$213$	−6.61488	+	1.65472i	−0.453244	+	0.113380i
$214$	−1.57050	+	1.36084i	−0.107357	+	0.0930253i
$215$	−19.2019	+	2.76082i	−1.30956	+	0.188287i
$216$	−3.85340	+	3.48587i	−0.262191	+	0.237184i
$217$	15.6211	+	13.5357i	1.06043	+	0.918866i
$218$	2.44601	+	1.57196i	0.165665	+	0.106466i
$219$	−7.67528	−	7.21471i	−0.518647	−	0.487525i
$220$	0.382484	−	0.441410i	0.0257870	−	0.0297598i
$221$	−2.24280	−	0.658545i	−0.150867	−	0.0442985i
$222$	0.646230	−	15.9561i	0.0433721	−	1.07090i
$223$	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
$225$	−18.5725	−	1.50686i	−1.23817	−	0.100457i
$226$	9.46687	+	4.32338i	0.629727	+	0.287587i
$227$	0.571788	−	3.97688i	0.0379509	−	0.263955i	−0.962008	−	0.273021i	$-0.911977\pi$
$227$	0.571788	−	3.97688i	0.0379509	−	0.263955i	0.999959	+	0.00906687i	$0.00288611\pi$
$228$	−4.38623	−	10.7341i	−0.290485	−	0.710882i
$229$			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	0.779759	−	0.626080i	$-0.215342\pi$
$233$	20.6304	+	2.96621i	1.35155	+	0.194323i	0.571786	+	0.820403i	$0.306251\pi$
$234$	−1.39720	−	1.42417i	−0.0913380	−	0.0931007i
$235$	7.43388	+	25.3175i	0.484933	+	1.65153i
$236$	9.24791	−	4.22338i	0.601988	−	0.274919i
$237$	7.77399	−	4.56244i	0.504975	−	0.296362i
$238$	1.19640	+	8.32112i	0.0775509	+	0.539378i
$239$	2.55094	−	8.68772i	0.165007	−	0.561962i	−0.834926	−	0.550362i	$-0.814490\pi$
$239$	2.55094	−	8.68772i	0.165007	−	0.561962i	0.999933	−	0.0115993i	$-0.00369226\pi$
$240$	4.53302	−	3.61735i	0.292605	−	0.233499i
$241$	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
$243$	−15.5608	−	0.928398i	−0.998225	−	0.0595568i
$244$	0.176394	−	0.600744i	0.0112925	−	0.0384587i
$245$	0.609661	+	4.24028i	0.0389498	+	0.270902i
$246$	−2.46423	−	4.19883i	−0.157114	−	0.267708i
$247$	4.04990	−	1.84953i	0.257689	−	0.117683i
$248$	2.43473	+	8.29192i	0.154605	+	0.526537i
$249$	11.8247	−	16.8582i	0.749359	−	1.06835i
$250$	4.01409	+	0.577139i	0.253873	+	0.0365015i
$251$	−4.41926	+	2.84009i	−0.278942	+	0.179265i	−0.672630	−	0.739979i	$-0.734835\pi$
$251$	−4.41926	+	2.84009i	−0.278942	+	0.179265i	0.393688	+	0.919244i	$0.371199\pi$
$252$	−2.57165	+	6.69864i	−0.161999	+	0.421975i
$253$	−0.00538890	+	0.836553i	−0.000338797	+	0.0525936i
$254$			21.6346i			1.35747i
$255$	18.8695	−	7.71057i	1.18165	−	0.482854i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−16.6280	−	7.59377i	−1.03723	−	0.473687i	−0.177330	−	0.984151i	$-0.556746\pi$
$257$	−16.6280	−	7.59377i	−1.03723	−	0.473687i	−0.859899	+	0.510465i	$0.829473\pi$
$258$	9.98265	−	1.02502i	0.621493	−	0.0638148i
$259$	−9.16062	−	20.0589i	−0.569213	−	1.24640i
$260$	1.45820	+	1.68286i	0.0904339	+	0.104366i
$261$	−17.8468	−	4.06134i	−1.10469	−	0.251390i
$262$	−9.76380	−	2.86691i	−0.603209	−	0.177118i
$263$	15.1908	−	17.5311i	0.936703	−	1.08101i	−0.0598627	−	0.998207i	$-0.519066\pi$
$263$	15.1908	−	17.5311i	0.936703	−	1.08101i	0.996566	−	0.0828062i	$-0.0263883\pi$
$264$	−0.206934	+	0.220144i	−0.0127359	+	0.0135489i
$265$	−33.2881	−	21.3930i	−2.04487	−	1.31416i
$266$	−12.1013	−	10.4859i	−0.741980	−	0.642930i
$267$	−23.4542	−	11.8808i	−1.43537	−	0.727093i
$268$	−7.40385	+	1.06451i	−0.452262	+	0.0650254i
$269$	−6.91584	+	5.99261i	−0.421666	+	0.365376i	−0.839695	−	0.543058i	$-0.817266\pi$
$269$	−6.91584	+	5.99261i	−0.421666	+	0.365376i	0.418029	+	0.908434i	$0.362721\pi$
$270$	17.2702	+	2.10758i	1.05103	+	0.128263i
$271$	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
$273$	−2.60984	−	0.882514i	−0.157955	−	0.0534122i
$274$	−5.56188	−	8.65445i	−0.336005	−	0.522835i
$275$	−1.08346			−0.0653349
$276$	−1.56649	+	8.15758i	−0.0942918	+	0.491029i
$277$	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
$279$	−12.6419	+	22.6349i	−0.756849	+	1.35511i
$280$	3.32681	−	7.28469i	0.198815	−	0.435344i
$281$	−19.3165	+	5.67184i	−1.15233	+	0.338354i	−0.801447	−	0.598066i	$-0.795936\pi$
$281$	−19.3165	+	5.67184i	−1.15233	+	0.338354i	−0.350881	+	0.936420i	$0.614118\pi$
$282$	−3.31235	−	13.2414i	−0.197248	−	0.788513i
$283$	−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
$285$	−17.5448	+	34.6356i	−1.03927	+	2.05164i
$286$	−0.0876718	−	0.0759680i	−0.00518414	−	0.00449208i
$287$	−5.65568	−	3.63468i	−0.333844	−	0.214549i
$288$	−2.41870	+	1.77480i	−0.142523	+	0.104581i
$289$	3.04245	−	3.51117i	0.178967	−	0.206539i
$290$	19.6006	+	5.75526i	1.15099	+	0.337960i
$291$	6.78529	+	0.274807i	0.397761	+	0.0161095i
$292$	−3.98268	−	4.59626i	−0.233069	−	0.268976i
$293$	0.626345	+	1.37150i	0.0365914	+	0.0801241i	0.927045	−	0.374950i	$-0.122340\pi$
$293$	0.626345	+	1.37150i	0.0365914	+	0.0801241i	−0.890454	+	0.455074i	$0.849613\pi$
$294$	−0.226350	−	2.20443i	−0.0132010	−	0.128565i
$295$	−30.9649	−	14.1412i	−1.80284	−	0.823331i
$296$	1.31212	−	9.12597i	0.0762653	−	0.530436i
$297$	−0.906194	+	0.0193634i	−0.0525827	+	0.00112358i
$298$			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
$303$	18.9958	+	13.3240i	1.09128	+	0.765444i
$304$	−1.88613	−	6.42358i	−0.108177	−	0.368417i
$305$	−1.90695	+	0.870874i	−0.109192	+	0.0498661i
$306$	−9.91443	+	3.59034i	−0.566770	+	0.205246i
$307$	−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
$309$	−1.41835	−	1.77738i	−0.0806872	−	0.101112i
$310$	15.6440	−	24.3425i	0.888519	−	1.38256i
$311$	2.59708	−	4.04114i	0.147267	−	0.229152i	−0.759781	−	0.650179i	$-0.774694\pi$
$311$	2.59708	−	4.04114i	0.147267	−	0.229152i	0.907048	+	0.421027i	$0.138330\pi$
$312$	−0.718470	−	0.900339i	−0.0406754	−	0.0509716i
$313$	−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
$315$	22.5896	−	8.18043i	1.27278	−	0.460915i
$316$	4.73390	−	2.16190i	0.266302	−	0.121616i
$317$	−1.40230	−	4.77580i	−0.0787610	−	0.268235i	0.910693	−	0.413084i	$-0.135549\pi$
$317$	−1.40230	−	4.77580i	−0.0787610	−	0.268235i	−0.989454	+	0.144849i	$0.953730\pi$
$318$	16.7577	+	11.7542i	0.939727	+	0.659142i
$319$	−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
$324$	−8.88229	−	1.45086i	−0.493460	−	0.0806034i
$325$	0.587851	−	4.08859i	0.0326081	−	0.226794i
$326$	−0.905402	−	0.413483i	−0.0501456	−	0.0229007i
$327$	0.514399	+	5.00973i	0.0284463	+	0.277039i
$328$	−1.16767	−	2.55684i	−0.0644738	−	0.141178i
$329$	−12.3430	−	14.2446i	−0.680493	−	0.785331i
$330$	1.01081	+	0.0409382i	0.0556431	+	0.00225357i
$331$	−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
$333$	22.2999	−	16.3633i	1.22203	−	0.896705i
$334$	−9.31688	−	5.98760i	−0.509797	−	0.327627i
$335$	18.9280	+	16.4012i	1.03415	+	0.896092i
$336$	−1.87201	+	3.69558i	−0.102127	+	0.201610i
$337$	−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
$339$	4.37446	+	17.4872i	0.237588	+	0.949777i
$340$	11.2920	−	3.31564i	0.612396	−	0.179816i
$341$	−0.626230	+	1.37125i	−0.0339122	+	0.0742575i
$342$	9.79340	−	17.5348i	0.529566	−	0.948172i
$343$	−10.7060	−	16.6589i	−0.578072	−	0.899497i
$344$	5.79379			0.312380
$345$	24.0774	−	13.9229i	1.29628	−	0.749586i
$346$	−2.42055			−0.130129
$347$	0.838961	+	1.30545i	0.0450378	+	0.0700802i	0.863042	−	0.505132i	$-0.168556\pi$
$347$	0.838961	+	1.30545i	0.0450378	+	0.0700802i	−0.818005	+	0.575212i	$0.804920\pi$
$348$	−10.0104	−	3.38501i	−0.536616	−	0.181456i
$349$	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
$351$	0.418602	−	3.43017i	0.0223433	−	0.183089i
$352$	−0.131831	+	0.114232i	−0.00702659	+	0.00608858i
$353$	20.8552	−	2.99853i	1.11001	−	0.159596i	0.437168	−	0.899380i	$-0.355981\pi$
$353$	20.8552	−	2.99853i	1.11001	−	0.159596i	0.672844	+	0.739784i	$0.265072\pi$
$354$	15.7087	+	7.95732i	0.834909	+	0.422927i
$355$	9.96195	+	8.63208i	0.528726	+	0.458143i
$356$	−12.7698	−	8.20665i	−0.676798	−	0.434952i
$357$	−9.97281	+	10.6094i	−0.527817	+	0.561511i
$358$	8.28881	−	9.56580i	0.438077	−	0.505568i
$359$	5.28399	+	1.55152i	0.278878	+	0.0818860i	0.418181	−	0.908364i	$-0.362668\pi$
$359$	5.28399	+	1.55152i	0.278878	+	0.0818860i	−0.139303	+	0.990250i	$0.544486\pi$
$360$	9.79451	+	2.22891i	0.516216	+	0.117474i
$361$	16.9084	+	19.5133i	0.889916	+	1.02702i
$362$	−3.84308	−	8.41517i	−0.201988	−	0.442292i
$363$	18.9005	−	1.94070i	0.992018	−	0.101860i
$364$	−1.44687	−	0.660763i	−0.0758366	−	0.0346334i
$365$	−2.89803	+	20.1562i	−0.151690	+	1.05502i
$366$	1.00387	−	0.410208i	0.0524731	−	0.0214419i
$367$			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
$372$	−8.59544	+	12.2544i	−0.445653	+	0.635360i
$373$	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
$375$	3.55528	+	6.05788i	0.183594	+	0.312828i
$376$	−1.12151	−	7.80027i	−0.0578374	−	0.402268i
$377$	1.14310	−	3.89303i	0.0588725	−	0.200501i
$378$	−11.8471	+	3.75532i	−0.609348	+	0.193153i
$379$	−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
$381$	−29.2894	+	23.3729i	−1.50054	+	1.19743i
$382$	−0.414394	+	1.41130i	−0.0212023	+	0.0722083i
$383$	−1.57094	−	10.9261i	−0.0802712	−	0.558298i	−0.989779	−	0.142611i	$-0.954450\pi$
$383$	−1.57094	−	10.9261i	−0.0802712	−	0.558298i	0.909508	−	0.415687i	$-0.136459\pi$
$384$	−1.49379	+	0.876686i	−0.0762299	+	0.0447382i
$385$	1.27072	−	0.580318i	0.0647618	−	0.0295757i
$386$	1.72770	+	5.88402i	0.0879379	+	0.299489i
$387$	12.1725	+	12.4074i	0.618761	+	0.630703i
$388$	3.88079	+	0.557974i	0.197017	+	0.0283268i
$389$	7.36837	−	4.73537i	0.373591	−	0.240093i	−0.340349	−	0.940299i	$-0.610545\pi$
$389$	7.36837	−	4.73537i	0.373591	−	0.240093i	0.713940	+	0.700207i	$0.246909\pi$
$390$	−0.702920	+	3.79223i	−0.0355937	+	0.192027i
$391$	−9.20450	+	14.1216i	−0.465491	+	0.714162i
$392$		−	1.27942i		−	0.0646204i
$393$	−6.66704	−	16.3157i	−0.336308	−	0.823020i
$394$	−3.10316	+	21.5829i	−0.156335	+	1.08733i
$395$	−15.8505	−	7.23870i	−0.797527	−	0.364219i
$396$	−0.521597	−	0.0423192i	−0.0262112	−	0.00212662i
$397$	−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
$399$	1.12233	−	27.7115i	0.0561867	−	1.38731i
$400$	−5.95957	−	1.74989i	−0.297979	−	0.0874944i
$401$	−20.6984	+	23.8872i	−1.03363	+	1.19287i	−0.0526774	+	0.998612i	$0.516776\pi$
$401$	−20.6984	+	23.8872i	−1.03363	+	1.19287i	−0.980950	+	0.194258i	$0.937770\pi$
$402$	−9.43992	−	8.87346i	−0.470820	−	0.442568i
$403$	−4.83486	−	3.10717i	−0.240841	−	0.154779i
$404$	10.1241	+	8.77261i	0.503694	+	0.436454i
$405$	15.8046	+	25.6577i	0.785336	+	1.27494i
$406$	−14.4437	+	2.07669i	−0.716830	+	0.103065i
$407$	1.21545	−	1.05320i	0.0602478	−	0.0522050i
$408$	−5.90589	+	1.47737i	−0.292385	+	0.0731405i
$409$	−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
$411$	5.70783	−	16.8797i	0.281546	−	0.832612i
$412$	−0.709786	−	1.10445i	−0.0349687	−	0.0544123i
$413$	24.3163			1.19653
$414$	−12.7363	+	6.69229i	−0.625955	+	0.328908i
$415$	−39.8070			−1.95405
$416$	−0.359544	−	0.559462i	−0.0176281	−	0.0274299i
$417$	−1.41750	+	4.19196i	−0.0694155	+	0.205281i
$418$	0.485127	−	1.06228i	0.0237284	−	0.0519578i
$419$	−3.68715	+	1.08265i	−0.180129	+	0.0528907i	−0.370553	−	0.928811i	$-0.620832\pi$
$419$	−3.68715	+	1.08265i	−0.180129	+	0.0528907i	0.190424	+	0.981702i	$0.439014\pi$
$420$	13.4563	−	3.36611i	0.656601	−	0.164250i
$421$	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
$423$	14.3480	−	18.7897i	0.697624	−	0.913586i
$424$	8.93131	+	7.73902i	0.433743	+	0.375840i
$425$	−18.3656	−	11.8029i	−0.890862	−	0.572522i
$426$	−4.96831	−	4.67018i	−0.240715	−	0.226271i
$427$	0.980656	−	1.13174i	0.0474573	−	0.0547686i
$428$	−1.99389	−	0.585458i	−0.0963782	−	0.0282992i
$429$	0.00813105	−	0.200764i	0.000392571	−	0.00969299i
$430$	−12.7039	−	14.6611i	−0.612637	−	0.707020i
$431$	0.368781	+	0.807518i	0.0177636	+	0.0388968i	0.918306	−	0.395872i	$-0.129557\pi$
$431$	0.368781	+	0.807518i	0.0177636	+	0.0388968i	−0.900542	+	0.434768i	$0.856830\pi$
$432$	−5.01581	−	1.35708i	−0.241323	−	0.0652927i
$433$	−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
$435$	13.3839	+	32.7535i	0.641711	+	1.57041i
$436$			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
$441$	2.73987	−	2.68799i	0.130470	−	0.128000i
$442$	−0.658545	−	2.24280i	−0.0313238	−	0.106679i
$443$	−3.04728	+	1.39165i	−0.144781	+	0.0661191i	−0.486488	−	0.873687i	$-0.661722\pi$
$443$	−3.04728	+	1.39165i	−0.144781	+	0.0661191i	0.341707	+	0.939806i	$0.388995\pi$
$444$	13.7725	−	8.08288i	0.653615	−	0.383597i
$445$	7.23324	+	50.3083i	0.342888	+	2.38484i
$446$	−1.30015	+	4.42789i	−0.0615637	+	0.209667i
$447$	−24.6638	+	19.6817i	−1.16656	+	0.930912i
$448$	−1.29309	+	2.01209i	−0.0610928	+	0.0950622i
$449$	17.7152	−	27.5654i	0.836031	−	1.30089i	−0.115491	−	0.993309i	$-0.536844\pi$
$449$	17.7152	−	27.5654i	0.836031	−	1.30089i	0.951522	−	0.307581i	$-0.0995196\pi$
$450$	−8.77339	−	16.4388i	−0.413582	−	0.774934i
$451$	0.138138	−	0.470455i	0.00650466	−	0.0221528i
$452$	1.48112	+	10.3014i	0.0696661	+	0.484539i
$453$	6.22428	+	10.6056i	0.292442	+	0.498296i
$454$	3.65469	−	1.66904i	0.171523	−	0.0783320i
$455$	1.50047	+	5.11012i	0.0703429	+	0.239566i
$456$	6.65871	−	9.49321i	0.311823	−	0.444560i
$457$	−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	$-0.728477\pi$
$461$		−	32.3466i		−	1.50653i	0.657715	−	0.753267i	$-0.271523\pi$
$462$	−0.668942	+	0.273347i	−0.0311220	+	0.0127173i
$463$	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
$465$	49.8565	−	5.11926i	2.31204	−	0.237400i
$466$	8.65833	+	18.9591i	0.401089	+	0.878263i
$467$	15.3824	+	17.7523i	0.711815	+	0.821478i	0.990298	−	0.138963i	$-0.0443770\pi$
$467$	15.3824	+	17.7523i	0.711815	+	0.821478i	−0.278483	+	0.960441i	$0.589832\pi$
$468$	0.442701	−	1.94536i	0.0204638	−	0.0899245i
$469$	−17.1657	−	5.04032i	−0.792640	−	0.232740i
$470$	−17.2793	+	19.9414i	−0.797037	+	0.919829i
$471$	−2.03997	+	2.17020i	−0.0939971	+	0.0999976i
$472$	8.55273	+	5.49651i	0.393671	+	0.252997i
$473$	0.763799	+	0.661836i	0.0351195	+	0.0304312i
$474$	8.04110	+	4.07326i	0.369340	+	0.187091i
$475$	41.1591	−	5.91778i	1.88851	−	0.271526i
$476$	−6.35335	+	5.50521i	−0.291205	+	0.252331i
$477$	2.19115	+	35.3857i	0.100326	+	1.62020i
$478$	8.68772	−	2.55094i	0.397367	−	0.116677i
$479$	−6.11943	+	13.3997i	−0.279604	+	0.612247i	−0.996376	−	0.0850605i	$-0.972892\pi$
$479$	−6.11943	+	13.3997i	−0.279604	+	0.612247i	0.716772	+	0.697308i	$0.245619\pi$
$480$	5.49384	+	1.85773i	0.250759	+	0.0847936i
$481$	3.31493	+	5.15814i	0.151148	+	0.235191i
$482$	4.06334			0.185080
$483$	−11.5133	+	16.1915i	−0.523874	+	0.736737i
$484$	10.9696			0.498617
$485$	−7.09738	−	11.0437i	−0.322275	−	0.501470i
$486$	−7.63178	−	13.5925i	−0.346184	−	0.616568i
$487$	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
$489$	−0.418369	−	1.67246i	−0.0189193	−	0.0756314i
$490$	−3.23755	+	2.80535i	−0.146257	+	0.126733i
$491$	9.28010	−	1.33428i	0.418805	−	0.0602151i	0.0703089	−	0.997525i	$-0.477602\pi$
$491$	9.28010	−	1.33428i	0.418805	−	0.0602151i	0.348496	+	0.937310i	$0.386692\pi$
$492$	2.20002	−	4.34310i	0.0991845	−	0.195802i
$493$	−16.2063	−	14.0429i	−0.729897	−	0.632459i
$494$	3.74546	+	2.40706i	0.168516	+	0.108299i
$495$	1.03660	+	1.41268i	0.0465919	+	0.0634954i
$496$	−5.65929	+	6.53117i	−0.254110	+	0.293258i
$497$	−9.03448	−	2.65276i	−0.405252	−	0.118993i
$498$	20.5750	+	0.833296i	0.921986	+	0.0373409i
$499$	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
$501$	−1.95935	−	19.0821i	−0.0875374	−	0.852527i
$502$	−4.77847	−	2.18225i	−0.213274	−	0.0973988i
$503$	−3.97959	+	27.6786i	−0.177441	+	1.23413i	0.685216	+	0.728340i	$0.259708\pi$
$503$	−3.97959	+	27.6786i	−0.177441	+	1.23413i	−0.862657	+	0.505789i	$0.831201\pi$
$504$	−7.02560	+	1.45815i	−0.312945	+	0.0649511i
$505$		−	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	$-0.739726\pi$
$509$	−34.8720	−	5.01384i	−1.54568	−	0.222235i	−0.861756	+	0.507323i	$0.830635\pi$
$510$	16.6882	+	11.7054i	0.738964	+	0.518323i
$511$	−4.09811	−	13.9569i	−0.181290	−	0.617416i
$512$	−0.909632	+	0.415415i	−0.0402004	+	0.0183589i
$513$	34.3193	−	5.68517i	1.51523	−	0.251006i
$514$	−2.60151	−	18.0939i	−0.114748	−	0.798088i
$515$	−1.23846	+	4.21780i	−0.0545730	+	0.185858i
$516$	6.25933	+	7.84378i	0.275552	+	0.345303i
$517$	0.743190	−	1.15643i	0.0326855	−	0.0508596i
$518$	11.9221	−	18.5511i	0.523825	−	0.815088i
$519$	−2.61504	−	3.27700i	−0.114788	−	0.143844i
$520$	−0.627344	+	2.13654i	−0.0275109	+	0.0936934i
$521$	0.0294211	+	0.204628i	0.00128896	+	0.00896492i	0.990456	−	0.137831i	$-0.0440131\pi$
$521$	0.0294211	+	0.204628i	0.00128896	+	0.00896492i	−0.989167	+	0.146796i	$0.953104\pi$
$522$	−6.23208	−	17.2094i	−0.272771	−	0.753235i
$523$	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
$525$	−21.0655	−	14.7757i	−0.919373	−	0.644865i
$526$	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
$531$	6.19812	+	29.8635i	0.268975	+	1.29597i
$532$	2.27880	−	15.8494i	0.0987983	−	0.687158i
$533$	1.70038	+	0.776539i	0.0736518	+	0.0336357i
$534$	−2.68550	−	26.1541i	−0.116213	−	1.13180i
$535$	2.89046	+	6.32922i	0.124965	+	0.273636i
$536$	−4.89835	−	5.65299i	−0.211576	−	0.244172i
$537$	21.9052	+	0.887172i	0.945281	+	0.0382843i
$538$	−8.78029	−	2.57813i	−0.378545	−	0.111151i
$539$	0.146150	−	0.168667i	0.00629514	−	0.00726498i
$540$	7.56397	+	15.6681i	0.325501	+	0.674246i
$541$	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
$543$	7.24079	−	14.2942i	0.310732	−	0.613423i
$544$	−3.47906	+	0.500213i	−0.149163	+	0.0214465i
$545$	7.35758	−	6.37538i	0.315164	−	0.273091i
$546$	−0.668570	−	2.67266i	−0.0286122	−	0.114379i
$547$	−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
$549$	1.63988	+	0.915895i	0.0699884	+	0.0390895i
$550$	−0.585761	−	0.911462i	−0.0249769	−	0.0388649i
$551$	40.8449			1.74005
$552$	−7.70950	+	3.09250i	−0.328138	+	0.131626i
$553$	12.4472			0.529311
$554$	15.0282	+	23.3843i	0.638486	+	0.993503i
$555$	−50.6523	−	17.1280i	−2.15007	−	0.727042i
$556$	−1.06133	+	2.32398i	−0.0450102	+	0.0985586i
$557$	−13.5725	+	3.98526i	−0.575087	+	0.168861i	−0.556327	−	0.830963i	$-0.687790\pi$
$557$	−13.5725	+	3.98526i	−0.575087	+	0.168861i	−0.0187599	+	0.999824i	$0.505972\pi$
$558$	−25.8764	+	1.60232i	−1.09543	+	0.0678314i
$559$	−2.91195	+	2.52322i	−0.123162	+	0.106721i
$560$	7.92688	−	1.13971i	0.334972	−	0.0481617i
$561$	−0.947340	−	0.479879i	−0.0399967	−	0.0202605i
$562$	−15.2148	−	13.1837i	−0.641796	−	0.556119i
$563$	−7.24324	−	4.65495i	−0.305266	−	0.196183i	0.379035	−	0.925382i	$-0.376256\pi$
$563$	−7.24324	−	4.65495i	−0.305266	−	0.196183i	−0.684301	+	0.729200i	$0.739892\pi$
$564$	9.34857	−	9.94536i	0.393646	−	0.418775i
$565$	22.8200	−	26.3357i	0.960044	−	1.10795i
$566$	−10.1097	−	2.96846i	−0.424941	−	0.124774i
$567$	−17.8831	−	11.9818i	−0.751018	−	0.503188i
$568$	−2.57804	−	2.97522i	−0.108172	−	0.124837i
$569$	−3.20388	−	7.01552i	−0.134314	−	0.294106i	0.830510	−	0.557004i	$-0.188049\pi$
$569$	−3.20388	−	7.01552i	−0.134314	−	0.294106i	−0.964824	+	0.262898i	$0.915322\pi$
$570$	−38.6228	+	3.96579i	−1.61773	+	0.166109i
$571$	−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
$573$	−2.35834	+	0.963680i	−0.0985211	+	0.0402583i
$574$		−	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
$579$	−6.09941	+	8.69582i	−0.253483	+	0.361386i
$580$	5.75526	+	19.6006i	0.238974	+	0.813871i
$581$	25.8655	−	11.8124i	1.07308	−	0.490059i
$582$	3.43722	+	5.85672i	0.142477	+	0.242769i
$583$	0.293377	+	2.04048i	0.0121504	+	0.0845081i
$584$	1.71342	−	5.83537i	0.0709018	−	0.241469i
$585$	−5.89341	+	3.14531i	−0.243663	+	0.130042i
$586$	−0.815155	+	1.26841i	−0.0336737	+	0.0523973i
$587$	−8.61402	+	13.4037i	−0.355539	+	0.553229i	−0.972245	−	0.233964i	$-0.924830\pi$
$587$	−8.61402	+	13.4037i	−0.355539	+	0.553229i	0.616706	+	0.787193i	$0.288467\pi$
$588$	1.73211	−	1.38222i	0.0714309	−	0.0570019i
$589$	16.2999	−	55.5124i	0.671626	−	2.28735i
$590$	−4.84455	−	33.6946i	−0.199447	−	1.38718i
$591$	−32.5720	+	19.1160i	−1.33983	+	0.786329i
$592$	8.38664	−	3.83005i	0.344689	−	0.157414i
$593$	12.4444	+	42.3816i	0.511029	+	1.74041i	0.659710	+	0.751520i	$0.270679\pi$
$593$	12.4444	+	42.3816i	0.511029	+	1.74041i	−0.148681	+	0.988885i	$0.547503\pi$
$594$	−0.506215	−	0.751870i	−0.0207702	−	0.0308496i
$595$	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	$0.885066\pi$
$600$	−4.06939	−	9.95871i	−0.166132	−	0.406563i
$601$	−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
$603$	1.81468	−	22.3665i	0.0738995	−	0.910832i
$604$	2.94936	+	6.45819i	0.120008	+	0.262780i
$605$	−24.0527	−	27.7583i	−0.977882	−	1.12854i
$606$	−0.938955	+	23.1838i	−0.0381424	+	0.941777i
$607$	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
$609$	−18.4158	−	17.3107i	−0.746245	−	0.701466i
$610$	−1.76360	−	1.13340i	−0.0714061	−	0.0458899i
$611$	3.96072	+	3.43198i	0.160234	+	0.138843i
$612$	−8.38053	−	6.39947i	−0.338763	−	0.258683i
$613$	−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
$615$	−15.8141	+	3.95591i	−0.637685	+	0.159518i
$616$	−0.400313	+	0.117543i	−0.0161291	+	0.00473593i
$617$	−17.4628	+	38.2382i	−0.703026	+	1.53941i	0.133238	+	0.991084i	$0.457463\pi$
$617$	−17.4628	+	38.2382i	−0.703026	+	1.53941i	−0.836264	+	0.548328i	$0.815265\pi$
$618$	0.728411	−	2.15412i	0.0293010	−	0.0866514i
$619$	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
$621$	−22.8199	−	10.0127i	−0.915730	−	0.401795i
$622$	4.80371			0.192611
$623$	−19.6285	−	30.5425i	−0.786398	−	1.22366i
$624$	0.368979	−	1.09118i	0.0147710	−	0.0436820i
$625$	−7.26030	+	15.8978i	−0.290412	+	0.635914i
$626$	−12.1317	+	3.56220i	−0.484882	+	0.142374i
$627$	1.96225	−	0.490859i	0.0783647	−	0.0196030i
$628$	−1.29960	+	1.12611i	−0.0518597	+	0.0449367i
$629$	32.0763	−	4.61187i	1.27897	−	0.183887i
$630$	19.0947	+	14.5809i	0.760750	+	0.580917i
$631$	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
$633$	12.6468	+	11.8880i	0.502667	+	0.472504i
$634$	3.25951	−	3.76168i	0.129452	−	0.149395i
$635$	69.5049	+	20.4085i	2.75822	+	0.809886i
$636$	−0.828327	+	20.4523i	−0.0328453	+	0.810986i
$637$	0.557192	+	0.643034i	0.0220768	+	0.0254779i
$638$	−0.442102	−	0.968069i	−0.0175030	−	0.0383262i
$639$	0.955082	−	11.7717i	0.0377825	−	0.465680i
$640$	3.04573	+	1.39094i	0.120393	+	0.0549816i
$641$	4.47358	−	31.1145i	0.176696	−	1.22895i	−0.687647	−	0.726045i	$-0.741356\pi$
$641$	4.47358	−	31.1145i	0.176696	−	1.22895i	0.864343	−	0.502902i	$-0.167734\pi$
$642$	−1.36149	−	3.33187i	−0.0537338	−	0.131499i
$643$			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	−0.241126	−	0.970494i	$-0.577517\pi$
$647$	−18.9730	−	2.72790i	−0.745904	−	0.107245i	−0.504778	+	0.863249i	$0.668426\pi$
$648$	−3.58158	−	8.25665i	−0.140698	−	0.324352i
$649$	0.499636	+	1.70160i	0.0196124	+	0.0667937i
$650$	3.75736	−	1.71593i	0.147376	−	0.0673042i
$651$	−30.8762	+	18.1208i	−1.21013	+	0.710210i
$652$	−0.141653	−	0.985219i	−0.00554756	−	0.0385842i
$653$	0.503391	−	1.71439i	0.0196992	−	0.0670894i	−0.949057	−	0.315105i	$-0.897960\pi$
$653$	0.503391	−	1.71439i	0.0196992	−	0.0670894i	0.968756	+	0.248016i	$0.0797784\pi$
$654$	−3.93635	+	3.14121i	−0.153924	+	0.122831i
$655$	−18.4209	+	28.6635i	−0.719765	+	1.11998i
$656$	1.51966	−	2.36464i	0.0593328	−	0.0923236i
$657$	16.0962	−	8.59054i	0.627974	−	0.335149i
$658$	5.31019	−	18.0848i	0.207013	−	0.705021i
$659$	−0.757007	−	5.26510i	−0.0294888	−	0.205099i	0.969750	−	0.244099i	$-0.0784921\pi$
$659$	−0.757007	−	5.26510i	−0.0294888	−	0.205099i	−0.999239	+	0.0389994i	$0.987583\pi$
$660$	0.512044	+	0.872478i	0.0199313	+	0.0339612i
$661$	−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
$663$	2.32489	−	3.31456i	0.0902914	−	0.128727i
$664$	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
$669$	−7.39920	+	3.02351i	−0.286070	+	0.116896i
$670$	−3.56432	+	24.7904i	−0.137702	+	0.957735i
$671$	0.0993463	+	0.0453699i	0.00383522	+	0.00175149i
$672$	−4.12101	+	0.423145i	−0.158971	+	0.0163232i
$673$	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
$675$	12.7770	−	29.6373i	0.491785	−	1.14074i
$676$	−12.0491	−	3.53792i	−0.463425	−	0.136074i
$677$	21.5893	−	24.9153i	0.829743	−	0.957575i	−0.169868	−	0.985467i	$-0.554334\pi$
$677$	21.5893	−	24.9153i	0.829743	−	0.957575i	0.999611	+	0.0278922i	$0.00887951\pi$
$678$	−12.3462	+	13.1343i	−0.474153	+	0.504422i
$679$	7.88880	+	5.06982i	0.302744	+	0.194562i
$680$	8.89423	+	7.70689i	0.341078	+	0.295546i
$681$	6.20794	+	3.14466i	0.237889	+	0.120504i
$682$	−1.49214	+	0.214537i	−0.0571368	+	0.00821504i
$683$	−4.45133	+	3.85710i	−0.170325	+	0.147588i	−0.735852	−	0.677142i	$-0.763218\pi$
$683$	−4.45133	+	3.85710i	−0.170325	+	0.147588i	0.565527	+	0.824730i	$0.308673\pi$
$684$	20.0459	−	1.24128i	0.766474	−	0.0474616i
$685$	−33.0506	+	9.70455i	−1.26280	+	0.370792i
$686$	8.22625	−	18.0130i	0.314080	−	0.687739i
$687$	−10.6222	−	3.59188i	−0.405262	−	0.137039i
$688$	3.13236	+	4.87405i	0.119420	+	0.185821i
$689$	−7.85924			−0.299413
$690$	24.7300	+	12.7279i	0.941454	+	0.484543i
$691$	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
$693$	−1.09276	−	0.610319i	−0.0415104	−	0.0231841i
$694$	−0.644637	+	1.41156i	−0.0244701	+	0.0535820i
$695$	8.20793	−	2.41007i	0.311344	−	0.0914190i
$696$	−2.56440	−	10.2514i	−0.0972033	−	0.388578i
$697$	7.46656	−	6.46981i	0.282816	−	0.245061i
$698$	1.63959	−	0.235738i	0.0620595	−	0.00892281i
$699$	−16.3132	+	32.2043i	−0.617024	+	1.21808i
$700$	−11.2272	−	9.72842i	−0.424348	−	0.367700i
$701$	−7.79469	−	5.00934i	−0.294401	−	0.189200i	0.385099	−	0.922875i	$-0.374167\pi$
$701$	−7.79469	−	5.00934i	−0.294401	−	0.189200i	−0.679501	+	0.733675i	$0.737804\pi$
$702$	3.11195	−	1.50234i	0.117453	−	0.0567021i
$703$	−40.4210	+	46.6483i	−1.52451	+	1.75937i
$704$	−0.167371	−	0.0491445i	−0.00630803	−	0.00185220i
$705$	−45.6650	−	1.84945i	−1.71984	−	0.0696544i
$706$	13.7977	+	15.9234i	0.519284	+	0.599286i
$707$	13.3101	+	29.1451i	0.500579	+	1.09611i
$708$	1.79865	+	17.5171i	0.0675974	+	0.658331i
$709$	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
$711$	3.17274	+	15.2868i	0.118987	+	0.573299i
$712$		−	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
$717$	12.8393	+	9.00573i	0.479493	+	0.336325i
$718$	1.55152	+	5.28399i	0.0579022	+	0.197197i
$719$	13.1320	−	5.99720i	0.489742	−	0.223658i	−0.155209	−	0.987882i	$-0.549605\pi$
$719$	13.1320	−	5.99720i	0.489742	−	0.223658i	0.644951	+	0.764224i	$0.276878\pi$
$720$	3.42024	+	9.44471i	0.127465	+	0.351983i
$721$	−0.446878	−	3.10811i	−0.0166426	−	0.115752i
$722$	−7.27429	+	24.7740i	−0.270721	+	0.921991i
$723$	4.38983	+	5.50104i	0.163260	+	0.204586i
$724$	5.00157	−	7.78259i	0.185882	−	0.289238i
$725$	20.4873	−	31.8788i	0.760879	−	1.18395i
$726$	11.8510	+	14.8509i	0.439832	+	0.551168i
$727$	−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
$729$	10.1569	−	25.0168i	0.376180	−	0.926547i
$730$	−18.5233	+	8.45930i	−0.685577	+	0.313093i
$731$	5.73726	+	19.5393i	0.212200	+	0.722688i
$732$	0.887822	+	0.622734i	0.0328148	+	0.0230169i
$733$	−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
$738$	8.25659	−	1.71364i	0.303929	−	0.0630800i
$739$	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
$741$	0.787676	+	7.67118i	0.0289360	+	0.281808i
$742$	11.7419	+	25.7112i	0.431060	+	0.943889i
$743$	−4.25720	−	4.91307i	−0.156181	−	0.180243i	0.672266	−	0.740309i	$-0.265321\pi$
$743$	−4.25720	−	4.91307i	−0.156181	−	0.180243i	−0.828448	+	0.560067i	$0.810776\pi$
$744$	−14.9561	−	0.605728i	−0.548317	−	0.0222071i
$745$	58.5281	+	17.1854i	2.14431	+	0.629625i
$746$	−2.97492	+	3.43324i	−0.108920	+	0.125700i
$747$	21.1001	+	28.7551i	0.772011	+	1.05210i
$748$	−0.515787	−	0.331476i	−0.0188590	−	0.0121200i
$749$	−3.75627	−	3.25483i	−0.137251	−	0.118929i
$750$	−3.17409	+	6.26603i	−0.115901	+	0.228803i
$751$	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
$753$	−2.20804	−	8.82681i	−0.0804654	−	0.321667i
$754$	3.89303	−	1.14310i	0.141776	−	0.0416291i
$755$	9.87536	−	21.6240i	0.359401	−	0.786979i
$756$	−9.56419	−	7.93611i	−0.347846	−	0.288634i
$757$	−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
$759$	−1.36961	−	0.472984i	−0.0497137	−	0.0171682i
$760$	−22.4161			−0.813119
$761$	18.9836	+	29.5390i	0.688154	+	1.07079i	0.992969	+	0.118377i	$0.0377691\pi$
$761$	18.9836	+	29.5390i	0.688154	+	1.07079i	−0.304815	+	0.952412i	$0.598595\pi$
$762$	−35.4976	−	12.0035i	−1.28594	−	0.434839i
$763$	−2.88891	+	6.32583i	−0.104586	+	0.229010i
$764$	−1.41130	+	0.414394i	−0.0510589	+	0.0149923i
$765$	2.18205	+	35.2387i	0.0788922	+	1.27406i
$766$	8.34232	−	7.22866i	0.301420	−	0.261182i
$767$	−6.69235	+	0.962214i	−0.241647	+	0.0347435i
$768$	−1.54512	−	0.782688i	−0.0557548	−	0.0282428i
$769$	−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
$771$	21.6854	−	23.0698i	0.780982	−	0.830837i
$772$	−4.01589	+	4.63458i	−0.144535	+	0.166802i
$773$	11.4452	+	3.36061i	0.411655	+	0.120873i	0.481001	−	0.876720i	$-0.340273\pi$
$773$	11.4452	+	3.36061i	0.411655	+	0.120873i	−0.0693464	+	0.997593i	$0.522091\pi$
$774$	−3.85682	+	16.9481i	−0.138631	+	0.609186i
$775$	−35.1508	−	40.5662i	−1.26265	−	1.45718i
$776$	1.62872	+	3.56640i	0.0584676	+	0.128026i
$777$	37.9949	−	3.90132i	1.36306	−	0.139959i
$778$	7.96729	+	3.63854i	0.285641	+	0.130448i
$779$	−2.67808	+	18.6264i	−0.0959521	+	0.667361i
$780$	−3.57025	+	1.45890i	−0.127835	+	0.0522369i
$781$		−	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
$786$	10.1212	−	14.4296i	0.361011	−	0.514688i
$787$	−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
$789$	20.3364	+	34.6515i	0.723996	+	1.23363i
$790$	−2.47987	−	17.2479i	−0.0882298	−	0.613651i
$791$	−7.01290	+	23.8838i	−0.249350	+	0.849209i
$792$	−0.246395	−	0.461675i	−0.00875527	−	0.0164049i
$793$	−0.225113	+	0.350282i	−0.00799399	+	0.0124389i
$794$	11.6929	−	18.1945i	0.414965	−	0.645698i
$795$	53.5704	−	42.7492i	1.89995	−	1.51616i
$796$	0.120276	−	0.409622i	0.00426306	−	0.0145187i
$797$	−6.37259	−	44.3223i	−0.225729	−	1.56998i	−0.715807	−	0.698298i	$-0.753941\pi$
$797$	−6.37259	−	44.3223i	−0.225729	−	1.56998i	0.490078	−	0.871678i	$-0.336968\pi$
$798$	23.9192	−	14.0378i	0.846730	−	0.496933i
$799$	25.1955	−	11.5064i	0.891354	−	0.407068i
$800$	−1.74989	−	5.95957i	−0.0618679	−	0.210703i
$801$	32.5068	−	31.8914i	1.14857	−	1.12683i
$802$	−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
$807$	−5.99547	−	14.6723i	−0.211051	−	0.516488i
$808$	−1.90647	+	13.2598i	−0.0670694	+	0.466478i
$809$	−32.3825	−	14.7886i	−1.13851	−	0.519939i	−0.245239	−	0.969463i	$-0.578867\pi$
$809$	−32.3825	−	14.7886i	−1.13851	−	0.519939i	−0.893269	+	0.449523i	$0.851594\pi$
$810$	−13.0401	+	27.1673i	−0.458181	+	0.954561i
$811$	−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
$813$	−1.87390	+	46.2686i	−0.0657206	+	1.62271i
$814$	1.54313	+	0.453104i	0.0540867	+	0.0158813i
$815$	−2.18248	+	2.51872i	−0.0764489	+	0.0882268i
$816$	−4.43581	−	4.16963i	−0.155284	−	0.145966i
$817$	−32.6306	−	20.9704i	−1.14160	−	0.733662i
$818$	−6.35172	−	5.50380i	−0.222083	−	0.192436i
$819$	2.89603	−	3.79254i	0.101195	−	0.132522i
$820$	−9.31580	+	1.33941i	−0.325322	+	0.0467742i
$821$	−40.4292	+	35.0321i	−1.41099	+	1.22263i	−0.470684	+	0.882302i	$0.655993\pi$
$821$	−40.4292	+	35.0321i	−1.41099	+	1.22263i	−0.940307	+	0.340328i	$0.889462\pi$
$822$	17.2860	−	4.32410i	0.602917	−	0.150820i
$823$	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
$825$	0.601132	−	1.77772i	0.0209287	−	0.0618922i
$826$	13.1464	+	20.4562i	0.457422	+	0.711762i
$827$	43.2407			1.50363			0.751813	−	0.659377i	$-0.229180\pi$
$827$	43.2407			1.50363			0.751813	+	0.659377i	$0.229180\pi$
$828$	−12.5157	−	7.09632i	−0.434950	−	0.246614i
$829$	−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
$831$	−15.4225	+	45.6087i	−0.535001	+	1.58215i
$832$	0.276265	−	0.604936i	0.00957776	−	0.0209724i
$833$	4.31479	−	1.26694i	0.149498	−	0.0438967i
$834$	−4.29286	+	1.07386i	−0.148650	+	0.0371849i
$835$	−28.0251	+	24.2839i	−0.969848	+	0.840378i
$836$	1.15593	−	0.166197i	0.0399786	−	0.00574805i
$837$	−30.1248	−	33.3010i	−1.04127	−	1.15105i
$838$	−2.90421	−	2.51651i	−0.100324	−	0.0869314i
$839$	3.24484	+	2.08533i	0.112024	+	0.0719936i	0.595453	−	0.803390i	$-0.296973\pi$
$839$	3.24484	+	2.08533i	0.112024	+	0.0719936i	−0.483429	+	0.875384i	$0.660609\pi$
$840$	10.1068	+	9.50032i	0.348717	+	0.327792i
$841$	5.38455	−	6.21410i	0.185674	−	0.214279i
$842$	9.66048	+	2.83657i	0.332922	+	0.0977547i
$843$	1.41108	−	34.8411i	0.0486002	−	1.19999i
$844$	6.56241	+	7.57343i	0.225888	+	0.260688i
$845$	17.4670	+	38.2474i	0.600884	+	1.31575i
$846$	23.5640	+	1.91184i	0.810148	+	0.0657305i
$847$	23.8658	+	10.8991i	0.820038	+	0.374499i
$848$	−1.68185	+	11.6975i	−0.0577550	+	0.401695i
$849$	−6.90320	−	16.8937i	−0.236917	−	0.579790i
$850$		−	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
$855$	−47.0952	−	48.0041i	−1.61062	−	1.64170i
$856$	−0.585458	−	1.99389i	−0.0200106	−	0.0681497i
$857$	−11.3382	+	5.17799i	−0.387306	+	0.176877i	−0.599545	−	0.800341i	$-0.704652\pi$
$857$	−11.3382	+	5.17799i	−0.387306	+	0.176877i	0.212239	+	0.977218i	$0.431925\pi$
$858$	0.173290	−	0.101701i	0.00591601	−	0.00347202i
$859$	−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
$861$	9.10165	−	7.26311i	0.310183	−	0.247526i
$862$	−0.479949	+	0.746816i	−0.0163471	+	0.0254366i
$863$	15.1208	−	23.5285i	0.514719	−	0.800919i	−0.482465	−	0.875915i	$-0.660258\pi$
$863$	15.1208	−	23.5285i	0.514719	−	0.800919i	0.997184	+	0.0749969i	$0.0238947\pi$
$864$	−1.57010	−	4.95326i	−0.0534159	−	0.168513i
$865$	−2.28337	+	7.77644i	−0.0776368	+	0.264407i
$866$	−1.95055	−	13.5664i	−0.0662823	−	0.461004i
$867$	4.07303	+	6.94009i	0.138327	+	0.235698i
$868$	−18.8018	+	8.58649i	−0.638174	+	0.291444i
$869$	0.255757	+	0.871030i	0.00867598	+	0.0295477i
$870$	−20.3181	+	28.9672i	−0.688848	+	0.982079i
$871$	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
$876$	9.75116	−	3.98458i	0.329461	−	0.134627i
$877$	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
$879$	−2.59785	+	0.266747i	−0.0876234	+	0.00899716i
$880$	0.242631	+	0.531287i	0.00817908	+	0.0179097i
$881$	27.3633	+	31.5789i	0.921892	+	1.06392i	0.997766	+	0.0668030i	$0.0212799\pi$
$881$	27.3633	+	31.5789i	0.921892	+	1.06392i	−0.0758739	+	0.997117i	$0.524175\pi$
$882$	3.74257	+	0.851685i	0.126019	+	0.0286777i
$883$	−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
$885$	40.3828	−	42.9607i	1.35745	−	1.44411i
$886$	−2.81821	−	1.81115i	−0.0946796	−	0.0608469i
$887$	2.25405	+	1.95314i	0.0756835	+	0.0655801i	0.691881	−	0.722012i	$-0.256782\pi$
$887$	2.25405	+	1.95314i	0.0756835	+	0.0655801i	−0.616198	+	0.787592i	$0.711328\pi$
$888$	14.2457	+	7.21624i	0.478056	+	0.242161i
$889$	−51.2183	+	7.36408i	−1.71781	+	0.246983i
$890$	−38.4114	+	33.2837i	−1.28755	+	1.11567i
$891$	0.471010	−	1.49761i	0.0157794	−	0.0501718i
$892$	−4.42789	+	1.30015i	−0.148257	+	0.0435321i
$893$	−21.9165	+	47.9903i	−0.733406	+	1.60594i
$894$	−29.8916	−	10.1078i	−0.999723	−	0.338055i
$895$	−22.9128	−	35.6530i	−0.765889	−	1.19175i
$896$	−2.39177			−0.0799036
$897$	2.52799	−	4.91181i	0.0844071	−	0.164001i
$898$	32.7670			1.09345
$899$	−28.5052	−	44.3550i	−0.950702	−	1.47932i
$900$	9.08597	−	16.2681i	0.302866	−	0.542272i
$901$	−17.2554	+	37.7840i	−0.574860	+	1.25877i
$902$	0.470455	−	0.138138i	0.0156644	−	0.00459949i
$903$	5.82460	+	23.2843i	0.193831	+	0.774854i
$904$	−7.86536	+	6.81537i	−0.261598	+	0.226676i
$905$	−30.6605	+	4.40832i	−1.01919	+	0.146537i
$906$	−5.55692	+	10.9700i	−0.184616	+	0.364455i
$907$	−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
$909$	−32.4012	+	23.7755i	−1.07468	+	0.788582i
$910$	−3.48769	+	4.02501i	−0.115616	+	0.133428i
$911$	21.8033	+	6.40202i	0.722375	+	0.212108i	0.622196	−	0.782861i	$-0.286240\pi$
$911$	21.8033	+	6.40202i	0.722375	+	0.212108i	0.100178	+	0.994970i	$0.468059\pi$
$912$	11.5862	+	0.469245i	0.383656	+	0.0155383i
$913$	1.35807	+	1.56729i	0.0449455	+	0.0518699i
$914$	−9.08484	−	19.8930i	−0.300500	−	0.658002i
$915$	−0.370887	−	3.61207i	−0.0122611	−	0.119411i
$916$	−5.88883	−	2.68934i	−0.194572	−	0.0888582i
$917$	3.46376	−	24.0909i	0.114383	−	0.795553i
$918$	−0.390166	−	18.2594i	−0.0128774	−	0.602651i
$919$		−	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
$924$	−0.591611	−	0.414967i	−0.0194626	−	0.0136514i
$925$	16.1337	+	54.9462i	0.530471	+	1.80662i
$926$	11.9997	−	5.48008i	0.394334	−	0.180087i
$927$	3.70324	−	1.34106i	0.121630	−	0.0440463i
$928$	−0.868266	−	6.03892i	−0.0285022	−	0.198237i
$929$	4.60284	−	15.6758i	0.151014	−	0.514307i	−0.848884	−	0.528579i	$-0.822725\pi$
$929$	4.60284	−	15.6758i	0.151014	−	0.514307i	0.999898	+	0.0142720i	$0.00454308\pi$
$930$	31.2611	+	39.1743i	1.02509	+	1.28458i
$931$	−4.63081	+	7.20568i	−0.151769	+	0.236156i
$932$	−11.2684	+	17.5339i	−0.369107	+	0.574342i
$933$	5.18970	+	6.50338i	0.169903	+	0.212911i
$934$	−6.61780	+	22.5381i	−0.216541	+	0.737471i
$935$	0.292159	+	2.03201i	0.00955461	+	0.0664538i
$936$	1.87589	−	0.679320i	0.0613153	−	0.0222043i
$937$	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
$939$	−17.9291	−	12.5758i	−0.585095	−	0.410396i
$940$	−26.1177	−	3.75516i	−0.851866	−	0.122480i
$941$	−2.89516	+	1.86061i	−0.0943795	+	0.0606540i	−0.586979	−	0.809602i	$-0.699683\pi$
$941$	−2.89516	+	1.86061i	−0.0943795	+	0.0606540i	0.492600	+	0.870256i	$0.336047\pi$
$942$	−2.92858	−	0.542837i	−0.0954184	−	0.0176866i
$943$	8.89320	−	10.1307i	0.289603	−	0.329901i
$944$			10.1667i			0.330896i
$945$	0.888976	+	41.6033i	0.0289184	+	1.35336i
$946$	−0.143831	+	1.00036i	−0.00467634	+	0.0325246i
$947$	5.48974	+	2.50708i	0.178393	+	0.0814692i	0.502609	−	0.864514i	$-0.332373\pi$
$947$	5.48974	+	2.50708i	0.178393	+	0.0814692i	−0.324217	+	0.945983i	$0.605101\pi$
$948$	0.920708	+	8.96677i	0.0299032	+	0.291227i
$949$	1.68017	+	3.67905i	0.0545405	+	0.119427i
$950$	27.2306	+	31.4258i	0.883478	+	1.01959i
$951$	8.61408	+	0.348874i	0.279331	+	0.0113130i
$952$	−8.06616	−	2.36844i	−0.261426	−	0.0767615i
$953$	−13.7021	+	15.8131i	−0.443855	+	0.512236i	−0.932956	−	0.359991i	$-0.882780\pi$
$953$	−13.7021	+	15.8131i	−0.443855	+	0.512236i	0.489101	+	0.872227i	$0.337325\pi$
$954$	−28.5837	+	20.9743i	−0.925431	+	0.679066i
$955$	4.14313	+	2.66263i	0.134069	+	0.0861607i
$956$	6.84293	+	5.92943i	0.221316	+	0.191771i
$957$	0.832970	−	1.64438i	0.0269261	−	0.0531554i
$958$	−14.5809	+	2.09642i	−0.471089	+	0.0677324i
$959$	18.5956	−	16.1132i	0.600484	−	0.520322i
$960$	1.40737	+	5.62608i	0.0454227	+	0.181581i
$961$	−41.9143	+	12.3072i	−1.35207	+	0.397005i
$962$	−2.54711	+	5.57740i	−0.0821222	+	0.179823i
$963$	3.03988	−	5.44282i	0.0979589	−	0.175392i
$964$	2.19681	+	3.41830i	0.0707543	+	0.110096i
$965$	20.5333			0.660989
$966$	−19.8457	−	0.931845i	−0.638525	−	0.0299816i
$967$	−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
$969$	38.6092	+	13.0556i	1.24031	+	0.419407i
$970$	5.45345	−	11.9414i	0.175100	−	0.383415i
$971$	−29.4740	+	8.65436i	−0.945867	+	0.277731i	−0.718065	−	0.695976i	$-0.754972\pi$
$971$	−29.4740	+	8.65436i	−0.945867	+	0.277731i	−0.227802	+	0.973708i	$0.573154\pi$
$972$	7.30869	−	13.7689i	0.234426	−	0.441638i
$973$	−4.61811	+	4.00162i	−0.148050	+	0.128286i
$974$	24.7392	−	3.55696i	0.792695	−	0.113972i
$975$	6.38233	+	3.23300i	0.204398	+	0.103539i
$976$	0.473179	+	0.410012i	0.0151461	+	0.0131242i
$977$	−17.3948	−	11.1790i	−0.556509	−	0.357646i	0.231956	−	0.972726i	$-0.425487\pi$
$977$	−17.3948	−	11.1790i	−0.556509	−	0.357646i	−0.788465	+	0.615080i	$0.789124\pi$
$978$	1.18078	−	1.25616i	0.0377571	−	0.0401674i
$979$	1.73398	−	2.00112i	0.0554183	−	0.0639561i
$980$	−4.11036	−	1.20691i	−0.131301	−	0.0385533i
$981$	−8.50529	−	1.93552i	−0.271553	−	0.0617965i
$982$	6.13967	+	7.08555i	0.195925	+	0.226109i
$983$	−8.30399	−	18.1832i	−0.264856	−	0.579954i	0.729746	−	0.683719i	$-0.239638\pi$
$983$	−8.30399	−	18.1832i	−0.264856	−	0.579954i	−0.994602	+	0.103764i	$0.966911\pi$
$984$	4.84307	−	0.497286i	0.154391	−	0.0158529i
$985$	66.4118	+	30.3292i	2.11605	+	0.966370i
$986$	3.05181	−	21.2258i	0.0971894	−	0.675967i
$987$	30.2206	−	12.3489i	0.961931	−	0.393071i
$988$			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
$993$	7.94505	−	11.3271i	0.252129	−	0.359455i
$994$	−2.65276	−	9.03448i	−0.0841405	−	0.286556i
$995$	−1.30027	+	0.593812i	−0.0412212	+	0.0188251i
$996$	10.4227	+	17.7593i	0.330254	+	0.562724i
$997$	−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
$999$	14.4760	+	45.6682i	0.458002	+	1.44488i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.540641 + 0.841254i) q^{2} +(-0.554828 + 1.64078i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(3.21268 - 0.943327i) q^{5} +(-1.68028 + 0.420323i) q^{6} +(-1.80758 + 1.56628i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.38433 - 1.82070i) q^{9} +O(q^{10})\)	\(q+(0.540641 + 0.841254i) q^{2} +(-0.554828 + 1.64078i) q^{3} +(-0.415415 + 0.909632i) q^{4} +(3.21268 - 0.943327i) q^{5} +(-1.68028 + 0.420323i) q^{6} +(-1.80758 + 1.56628i) q^{7} +(-0.989821 + 0.142315i) q^{8} +(-2.38433 - 1.82070i) q^{9} +(2.53048 + 2.19268i) q^{10} +(-0.146746 - 0.0943077i) q^{11} +(-1.26202 - 1.18629i) q^{12} +(0.435504 - 0.502599i) q^{13} +(-2.29489 - 0.673841i) q^{14} +(-0.234688 + 5.79469i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-1.46011 - 3.19721i) q^{17} +(0.242605 - 2.99017i) q^{18} +(6.08977 + 2.78111i) q^{19} +(-0.476514 + 3.31423i) q^{20} +(-1.56703 - 3.83486i) 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} +(4.31027 - 2.90199i) q^{27} +(-0.673841 - 2.29489i) q^{28} +(5.54968 - 2.53446i) q^{29} +(-5.00168 + 2.93541i) q^{30} +(-1.22988 - 8.55402i) q^{31} +(0.281733 - 0.959493i) q^{32} +(0.236157 - 0.188453i) q^{33} +(1.90026 - 2.95687i) q^{34} +(-4.32967 + 6.73709i) q^{35} +(2.64666 - 1.41252i) q^{36} +(-2.59752 + 8.84635i) q^{37} +(0.952764 + 6.62662i) q^{38} +(0.583025 + 0.993424i) q^{39} +(-3.04573 + 1.39094i) q^{40} +(0.791908 + 2.69699i) q^{41} +(2.37889 - 3.39155i) 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} +(1.60336 - 0.655173i) q^{48} +(-0.182080 + 1.26640i) q^{49} +(5.64988 + 2.58021i) q^{50} +(6.05603 - 0.621833i) q^{51} +(0.276265 + 0.604936i) q^{52} +(-7.73902 - 8.93131i) q^{53} +(4.77162 + 2.05709i) q^{54} +(-0.560410 - 0.164551i) q^{55} +(1.56628 - 1.80758i) q^{56} +(-7.94196 + 8.44895i) q^{57} +(5.13250 + 3.29846i) q^{58} +(-7.68344 - 6.65774i) q^{59} +(-5.17354 - 2.62068i) q^{60} +(-0.619733 + 0.0891041i) q^{61} +(6.53117 - 5.65929i) q^{62} +(7.16160 - 0.443460i) q^{63} +(0.959493 - 0.281733i) q^{64} +(0.925020 - 2.02551i) q^{65} +(0.286213 + 0.0967824i) q^{66} +(4.04398 + 6.29256i) q^{67} +3.51483 q^{68} +(8.07114 - 1.96385i) q^{69} -8.00840 q^{70} +(2.12838 + 3.31183i) q^{71} +(2.61918 + 1.46284i) q^{72} +(-2.52644 + 5.53213i) q^{73} +(-8.84635 + 2.59752i) q^{74} +(2.61070 + 10.4365i) q^{75} +(-5.05956 + 4.38414i) q^{76} +(0.412967 - 0.0593757i) q^{77} +(-0.520514 + 1.02756i) q^{78} +(-3.93306 - 3.40802i) q^{79} +(-2.81678 - 1.81023i) q^{80} +(2.37008 + 8.68232i) q^{81} +(-1.84072 + 2.12430i) q^{82} +(-11.4071 - 3.34943i) q^{83} +(4.13928 + 0.167643i) q^{84} +(-7.70689 - 8.89423i) q^{85} +(-2.40683 - 5.27022i) q^{86} +(1.07937 + 10.5120i) q^{87} +(0.158673 + 0.0724637i) q^{88} +(-2.16027 + 15.0250i) q^{89} +(-2.04130 - 9.83532i) 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} +(1.41801 + 0.994615i) q^{96} +(-1.10459 - 3.76189i) q^{97} +(-1.16380 + 0.531490i) q^{98} +(0.178184 + 0.492041i) 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

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Database

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