LMFDB - Embedded newform 670.2.k.b.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (of order $11$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	670.91
Dual form			670.2.k.b.81.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(2.41302 - 1.55075i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.408210 - 2.83916i) q^{6} +(1.65229 - 3.61802i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.17157 - 4.75508i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(2.41302 - 1.55075i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.408210 - 2.83916i) q^{6} +(1.65229 - 3.61802i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.17157 - 4.75508i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(-0.806005 + 5.60589i) q^{11} +(-2.75217 - 0.808110i) q^{12} +(3.63212 + 1.06649i) q^{13} +(-2.60468 - 3.00596i) q^{14} +(-1.19156 - 2.60915i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.0234027 - 0.0270081i) q^{17} +(-3.42327 - 3.95066i) q^{18} +(2.78326 + 6.09449i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(-1.62364 - 11.2926i) q^{21} +(4.76447 + 3.06194i) q^{22} +(-6.27359 + 4.03179i) q^{23} +(-1.87837 + 2.16776i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(2.47895 - 2.86086i) q^{26} +(-0.909277 - 6.32416i) q^{27} +(-3.81634 + 1.12058i) q^{28} -7.29206 q^{29} -2.86836 q^{30} +(-7.85758 + 2.30719i) q^{31} +(0.841254 + 0.540641i) q^{32} +(6.74844 + 14.7770i) q^{33} +(-0.0148456 - 0.0325074i) q^{34} +(-3.34605 - 2.15037i) q^{35} +(-5.01573 + 1.47275i) q^{36} +5.46548 q^{37} +6.69995 q^{38} +(10.4182 - 3.05906i) q^{39} +(0.142315 + 0.989821i) q^{40} +(-1.23640 + 1.42688i) q^{41} +(-10.9466 - 3.21422i) q^{42} +(4.39083 - 5.06728i) q^{43} +(4.76447 - 3.06194i) q^{44} +(-4.39763 - 2.82619i) q^{45} +(1.06130 + 7.38153i) q^{46} +(7.57578 - 4.86866i) q^{47} +(1.19156 + 2.60915i) q^{48} +(-5.77595 - 6.66581i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(0.0145881 - 0.101463i) q^{51} +(-1.57254 - 3.44337i) q^{52} +(-8.37419 - 9.66433i) q^{53} +(-6.13039 - 1.80004i) q^{54} +(5.43412 + 1.59560i) q^{55} +(-0.566050 + 3.93697i) q^{56} +(16.1671 + 10.3900i) q^{57} +(-3.02923 + 6.63309i) q^{58} +(2.51420 - 0.738235i) q^{59} +(-1.19156 + 2.60915i) q^{60} +(0.821081 + 5.71075i) q^{61} +(-1.16546 + 8.10595i) q^{62} +(-13.6159 - 15.7136i) q^{63} +(0.841254 - 0.540641i) q^{64} +(1.57254 - 3.44337i) q^{65} +16.2450 q^{66} +(7.96550 - 1.88438i) q^{67} -0.0357368 q^{68} +(-8.88597 + 19.4576i) q^{69} +(-3.34605 + 2.15037i) q^{70} +(1.21217 + 1.39892i) q^{71} +(-0.743947 + 5.17427i) q^{72} +(0.773631 + 5.38072i) q^{73} +(2.27044 - 4.97158i) q^{74} +(-2.75217 + 0.808110i) q^{75} +(2.78326 - 6.09449i) q^{76} +(18.9505 + 12.1787i) q^{77} +(1.54526 - 10.7475i) q^{78} +(-11.4834 - 3.37184i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-1.73150 - 1.99826i) q^{81} +(0.784319 + 1.71742i) q^{82} +(-0.298897 + 2.07887i) q^{83} +(-7.47115 + 8.62216i) q^{84} +(-0.0234027 - 0.0270081i) q^{85} +(-2.78535 - 6.09906i) q^{86} +(-17.5958 + 11.3082i) q^{87} +(-0.806005 - 5.60589i) q^{88} +(-8.42384 - 5.41367i) q^{89} +(-4.39763 + 2.82619i) q^{90} +(9.85989 - 11.3789i) q^{91} +(7.15536 + 2.10100i) q^{92} +(-15.3826 + 17.7524i) q^{93} +(-1.28159 - 8.91369i) q^{94} +(6.42856 - 1.88759i) q^{95} +2.86836 q^{96} -12.0888 q^{97} +(-8.46285 + 2.48492i) q^{98} +(24.9062 + 16.0062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} + 5 q^{10} + 30 q^{11} - 9 q^{12} + 20 q^{13} - 21 q^{14} - 2 q^{15} - 5 q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + 5 q^{20} + 23 q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 5 q^{25} - 2 q^{26} + 2 q^{27} - 10 q^{28} + 26 q^{29} - 2 q^{30} + 3 q^{31} - 5 q^{32} + 38 q^{33} + 2 q^{34} - 12 q^{35} - q^{36} + 22 q^{37} - 40 q^{38} - 35 q^{39} + 5 q^{40} - 18 q^{41} - 10 q^{42} + 87 q^{43} - 3 q^{44} + 12 q^{45} + 17 q^{46} + 35 q^{47} + 2 q^{48} + 60 q^{49} - 5 q^{50} + 19 q^{51} - 24 q^{52} - 9 q^{53} + 2 q^{54} + 25 q^{55} + 12 q^{56} + 64 q^{57} + 4 q^{58} - 49 q^{59} - 2 q^{60} - 47 q^{61} - 19 q^{62} - 24 q^{63} - 5 q^{64} + 24 q^{65} - 6 q^{66} - 21 q^{67} + 2 q^{68} - 25 q^{69} - 12 q^{70} + 92 q^{71} - q^{72} + 18 q^{73} - 22 q^{74} - 9 q^{75} + 4 q^{76} - 65 q^{77} + 31 q^{78} - 58 q^{79} + 5 q^{80} - 77 q^{81} - 18 q^{82} - 49 q^{83} - 54 q^{84} - 2 q^{85} - q^{86} - 147 q^{87} + 30 q^{88} - 21 q^{89} + 12 q^{90} + 62 q^{91} + 6 q^{92} - 34 q^{93} - 9 q^{94} + 7 q^{95} + 2 q^{96} + 98 q^{97} - 39 q^{98} - 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 + 5 * q^10 + 30 * q^11 - 9 * q^12 + 20 * q^13 - 21 * q^14 - 2 * q^15 - 5 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 5 * q^20 + 23 * q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 5 * q^25 - 2 * q^26 + 2 * q^27 - 10 * q^28 + 26 * q^29 - 2 * q^30 + 3 * q^31 - 5 * q^32 + 38 * q^33 + 2 * q^34 - 12 * q^35 - q^36 + 22 * q^37 - 40 * q^38 - 35 * q^39 + 5 * q^40 - 18 * q^41 - 10 * q^42 + 87 * q^43 - 3 * q^44 + 12 * q^45 + 17 * q^46 + 35 * q^47 + 2 * q^48 + 60 * q^49 - 5 * q^50 + 19 * q^51 - 24 * q^52 - 9 * q^53 + 2 * q^54 + 25 * q^55 + 12 * q^56 + 64 * q^57 + 4 * q^58 - 49 * q^59 - 2 * q^60 - 47 * q^61 - 19 * q^62 - 24 * q^63 - 5 * q^64 + 24 * q^65 - 6 * q^66 - 21 * q^67 + 2 * q^68 - 25 * q^69 - 12 * q^70 + 92 * q^71 - q^72 + 18 * q^73 - 22 * q^74 - 9 * q^75 + 4 * q^76 - 65 * q^77 + 31 * q^78 - 58 * q^79 + 5 * q^80 - 77 * q^81 - 18 * q^82 - 49 * q^83 - 54 * q^84 - 2 * q^85 - q^86 - 147 * q^87 + 30 * q^88 - 21 * q^89 + 12 * q^90 + 62 * q^91 + 6 * q^92 - 34 * q^93 - 9 * q^94 + 7 * q^95 + 2 * q^96 + 98 * q^97 - 39 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	2.41302	−	1.55075i	1.39316	−	0.895327i	0.393444	−	0.919349i	$-0.371284\pi$
$3$	2.41302	−	1.55075i	1.39316	−	0.895327i	0.999711	+	0.0240220i	$0.00764716\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$5$	0.142315	−	0.989821i	0.0636451	−	0.442662i
$6$	−0.408210	−	2.83916i	−0.166651	−	1.15908i
$7$	1.65229	−	3.61802i	0.624508	−	1.36748i	−0.287686	−	0.957725i	$-0.592886\pi$
$7$	1.65229	−	3.61802i	0.624508	−	1.36748i	0.912194	−	0.409758i	$-0.134387\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	2.17157	−	4.75508i	0.723857	−	1.58503i
$10$	−0.841254	−	0.540641i	−0.266028	−	0.170966i
$11$	−0.806005	+	5.60589i	−0.243020	+	1.69024i	0.393776	+	0.919207i	$0.371169\pi$
$11$	−0.806005	+	5.60589i	−0.243020	+	1.69024i	−0.636795	+	0.771033i	$0.719740\pi$
$12$	−2.75217	−	0.808110i	−0.794483	−	0.233281i
$13$	3.63212	+	1.06649i	1.00737	+	0.295790i	0.743476	−	0.668762i	$-0.233176\pi$
$13$	3.63212	+	1.06649i	1.00737	+	0.295790i	0.263892	+	0.964552i	$0.414994\pi$
$14$	−2.60468	−	3.00596i	−0.696129	−	0.803376i
$15$	−1.19156	−	2.60915i	−0.307659	−	0.673680i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	0.0234027	−	0.0270081i	0.00567598	−	0.00655043i	−0.752904	−	0.658130i	$-0.771348\pi$
$17$	0.0234027	−	0.0270081i	0.00567598	−	0.00655043i	0.758580	+	0.651579i	$0.225893\pi$
$18$	−3.42327	−	3.95066i	−0.806872	−	0.931180i
$19$	2.78326	+	6.09449i	0.638524	+	1.39817i	0.901249	+	0.433301i	$0.142651\pi$
$19$	2.78326	+	6.09449i	0.638524	+	1.39817i	−0.262725	+	0.964871i	$0.584621\pi$
$20$	−0.841254	+	0.540641i	−0.188110	+	0.120891i
$21$	−1.62364	−	11.2926i	−0.354306	−	2.46425i
$22$	4.76447	+	3.06194i	1.01579	+	0.652808i
$23$	−6.27359	+	4.03179i	−1.30813	+	0.840687i	−0.994073	−	0.108715i	$-0.965326\pi$
$23$	−6.27359	+	4.03179i	−1.30813	+	0.840687i	−0.314062	+	0.949403i	$0.601690\pi$
$24$	−1.87837	+	2.16776i	−0.383422	+	0.442492i
$25$	−0.959493	−	0.281733i	−0.191899	−	0.0563465i
$26$	2.47895	−	2.86086i	0.486161	−	0.561060i
$27$	−0.909277	−	6.32416i	−0.174991	−	1.21709i
$28$	−3.81634	+	1.12058i	−0.721220	+	0.211769i
$29$	−7.29206			−1.35410			−0.677050	−	0.735937i	$-0.736742\pi$
$29$	−7.29206			−1.35410			−0.677050	+	0.735937i	$0.736742\pi$
$30$	−2.86836			−0.523688
$31$	−7.85758	+	2.30719i	−1.41126	+	0.414384i	−0.896536	−	0.442970i	$-0.853925\pi$
$31$	−7.85758	+	2.30719i	−1.41126	+	0.414384i	−0.514727	+	0.857354i	$0.672107\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	6.74844	+	14.7770i	1.17475	+	2.57235i
$34$	−0.0148456	−	0.0325074i	−0.00254600	−	0.00557497i
$35$	−3.34605	−	2.15037i	−0.565585	−	0.363479i
$36$	−5.01573	+	1.47275i	−0.835954	+	0.245458i
$37$	5.46548			0.898520			0.449260	−	0.893401i	$-0.351688\pi$
$37$	5.46548			0.898520			0.449260	+	0.893401i	$0.351688\pi$
$38$	6.69995			1.08688
$39$	10.4182	−	3.05906i	1.66825	−	0.489842i
$40$	0.142315	+	0.989821i	0.0225020	+	0.156505i
$41$	−1.23640	+	1.42688i	−0.193094	+	0.222842i	−0.844038	−	0.536284i	$-0.819828\pi$
$41$	−1.23640	+	1.42688i	−0.193094	+	0.222842i	0.650944	+	0.759126i	$0.274373\pi$
$42$	−10.9466	−	3.21422i	−1.68910	−	0.495965i
$43$	4.39083	−	5.06728i	0.669595	−	0.772754i	−0.314718	−	0.949185i	$-0.601910\pi$
$43$	4.39083	−	5.06728i	0.669595	−	0.772754i	0.984313	+	0.176432i	$0.0564554\pi$
$44$	4.76447	−	3.06194i	0.718271	−	0.461605i
$45$	−4.39763	−	2.82619i	−0.655560	−	0.421303i
$46$	1.06130	+	7.38153i	0.156481	+	1.08835i
$47$	7.57578	−	4.86866i	1.10504	−	0.710167i	0.144834	−	0.989456i	$-0.453735\pi$
$47$	7.57578	−	4.86866i	1.10504	−	0.710167i	0.960207	+	0.279289i	$0.0900988\pi$
$48$	1.19156	+	2.60915i	0.171987	+	0.376598i
$49$	−5.77595	−	6.66581i	−0.825136	−	0.952258i
$50$	−0.654861	+	0.755750i	−0.0926113	+	0.106879i
$51$	0.0145881	−	0.101463i	0.00204275	−	0.0142076i
$52$	−1.57254	−	3.44337i	−0.218071	−	0.477510i
$53$	−8.37419	−	9.66433i	−1.15028	−	1.32750i	−0.936521	−	0.350611i	$-0.885974\pi$
$53$	−8.37419	−	9.66433i	−1.15028	−	1.32750i	−0.213762	−	0.976886i	$-0.568572\pi$
$54$	−6.13039	−	1.80004i	−0.834240	−	0.244955i
$55$	5.43412	+	1.59560i	0.732737	+	0.215151i
$56$	−0.566050	+	3.93697i	−0.0756417	+	0.526099i
$57$	16.1671	+	10.3900i	2.14138	+	1.37618i
$58$	−3.02923	+	6.63309i	−0.397757	+	0.870967i
$59$	2.51420	−	0.738235i	0.327321	−	0.0961100i	−0.113944	−	0.993487i	$-0.536348\pi$
$59$	2.51420	−	0.738235i	0.327321	−	0.0961100i	0.441264	+	0.897377i	$0.354530\pi$
$60$	−1.19156	+	2.60915i	−0.153830	+	0.336840i
$61$	0.821081	+	5.71075i	0.105129	+	0.731186i	0.972395	+	0.233341i	$0.0749660\pi$
$61$	0.821081	+	5.71075i	0.105129	+	0.731186i	−0.867266	+	0.497845i	$0.834125\pi$
$62$	−1.16546	+	8.10595i	−0.148014	+	1.02946i
$63$	−13.6159	−	15.7136i	−1.71544	−	1.97972i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	1.57254	−	3.44337i	0.195049	−	0.427098i
$66$	16.2450			1.99963
$67$	7.96550	−	1.88438i	0.973140	−	0.230213i
$67$	7.96550	−	1.88438i	0.973140	−	0.230213i
$68$	−0.0357368			−0.00433373
$69$	−8.88597	+	19.4576i	−1.06975	+	2.34242i
$70$	−3.34605	+	2.15037i	−0.399929	+	0.257019i
$71$	1.21217	+	1.39892i	0.143858	+	0.166021i	0.823106	−	0.567888i	$-0.192239\pi$
$71$	1.21217	+	1.39892i	0.143858	+	0.166021i	−0.679248	+	0.733909i	$0.737694\pi$
$72$	−0.743947	+	5.17427i	−0.0876750	+	0.609793i
$73$	0.773631	+	5.38072i	0.0905466	+	0.629766i	0.983674	+	0.179961i	$0.0575972\pi$
$73$	0.773631	+	5.38072i	0.0905466	+	0.629766i	−0.893127	+	0.449804i	$0.851494\pi$
$74$	2.27044	−	4.97158i	0.263934	−	0.577934i
$75$	−2.75217	+	0.808110i	−0.317793	+	0.0933125i
$76$	2.78326	−	6.09449i	0.319262	−	0.699086i
$77$	18.9505	+	12.1787i	2.15960	+	1.38789i
$78$	1.54526	−	10.7475i	0.174966	−	1.21692i
$79$	−11.4834	−	3.37184i	−1.29199	−	0.379361i	−0.437680	−	0.899131i	$-0.644200\pi$
$79$	−11.4834	−	3.37184i	−1.29199	−	0.379361i	−0.854307	+	0.519770i	$0.826018\pi$
$80$	0.959493	+	0.281733i	0.107275	+	0.0314987i
$81$	−1.73150	−	1.99826i	−0.192389	−	0.222029i
$82$	0.784319	+	1.71742i	0.0866136	+	0.189657i
$83$	−0.298897	+	2.07887i	−0.0328082	+	0.228186i	−0.999628	−	0.0272733i	$-0.991318\pi$
$83$	−0.298897	+	2.07887i	−0.0328082	+	0.228186i	0.966820	+	0.255459i	$0.0822267\pi$
$84$	−7.47115	+	8.62216i	−0.815169	+	0.940755i
$85$	−0.0234027	−	0.0270081i	−0.00253837	−	0.00292944i
$86$	−2.78535	−	6.09906i	−0.300352	−	0.657679i
$87$	−17.5958	+	11.3082i	−1.88647	+	1.21236i
$88$	−0.806005	−	5.60589i	−0.0859205	−	0.597590i
$89$	−8.42384	−	5.41367i	−0.892925	−	0.573848i	0.0117589	−	0.999931i	$-0.496257\pi$
$89$	−8.42384	−	5.41367i	−0.892925	−	0.573848i	−0.904684	+	0.426083i	$0.859893\pi$
$90$	−4.39763	+	2.82619i	−0.463551	+	0.297906i
$91$	9.85989	−	11.3789i	1.03360	−	1.19283i
$92$	7.15536	+	2.10100i	0.745997	+	0.219045i
$93$	−15.3826	+	17.7524i	−1.59510	+	1.84084i
$94$	−1.28159	−	8.91369i	−0.132186	−	0.919376i
$95$	6.42856	−	1.88759i	0.659556	−	0.193663i
$96$	2.86836			0.292751
$97$	−12.0888			−1.22743			−0.613715	−	0.789527i	$-0.710326\pi$
$97$	−12.0888			−1.22743			−0.613715	+	0.789527i	$0.710326\pi$
$98$	−8.46285	+	2.48492i	−0.854877	+	0.251015i
$99$	24.9062	+	16.0062i	2.50316	+	1.60868i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	−2.74098	−	6.00191i	−0.272738	−	0.597212i	0.722854	−	0.691000i	$-0.242830\pi$
$101$	−2.74098	−	6.00191i	−0.272738	−	0.597212i	−0.995592	+	0.0937880i	$0.970102\pi$
$102$	−0.0862336	−	0.0554189i	−0.00853840	−	0.00548729i
$103$	−0.176546	+	0.0518385i	−0.0173956	+	0.00510780i	−0.290419	−	0.956900i	$-0.593795\pi$
$103$	−0.176546	+	0.0518385i	−0.0173956	+	0.00510780i	0.273023	+	0.962007i	$0.411976\pi$
$104$	−3.78546			−0.371194
$105$	−11.4088			−1.11338
$106$	−12.2697	+	3.60272i	−1.19174	+	0.349927i
$107$	−0.0293866	−	0.204388i	−0.00284091	−	0.0197590i	0.988352	−	0.152187i	$-0.0486317\pi$
$107$	−0.0293866	−	0.204388i	−0.00284091	−	0.0197590i	−0.991193	+	0.132428i	$0.957723\pi$
$108$	−4.18403	+	4.82863i	−0.402609	+	0.464635i
$109$	8.82720	+	2.59190i	0.845492	+	0.248259i	0.675659	−	0.737214i	$-0.263859\pi$
$109$	8.82720	+	2.59190i	0.845492	+	0.248259i	0.169833	+	0.985473i	$0.445677\pi$
$110$	3.70883	−	4.28022i	0.353623	−	0.408103i
$111$	13.1883	−	8.47560i	1.25178	−	0.804469i
$112$	3.34605	+	2.15037i	0.316172	+	0.203191i
$113$	0.445612	+	3.09930i	0.0419196	+	0.291557i	0.999987	+	0.00501571i	$0.00159656\pi$
$113$	0.445612	+	3.09930i	0.0419196	+	0.291557i	−0.958068	+	0.286542i	$0.907494\pi$
$114$	16.1671	−	10.3900i	1.51419	−	0.973109i
$115$	3.09793	+	6.78352i	0.288884	+	0.632567i
$116$	4.77528	+	5.51097i	0.443374	+	0.511681i
$117$	12.9586	−	14.9551i	1.19803	−	1.38260i
$118$	0.372913	−	2.59367i	0.0343294	−	0.238767i
$119$	−0.0590477	−	0.129297i	−0.00541290	−	0.0118526i
$120$	1.87837	+	2.16776i	0.171471	+	0.197889i
$121$	−20.2219	−	5.93770i	−1.83836	−	0.539791i
$122$	5.53577	+	1.62545i	0.501185	+	0.147161i
$123$	−0.770716	+	5.36045i	−0.0694931	+	0.483335i
$124$	6.88928	+	4.42747i	0.618676	+	0.397599i
$125$	−0.415415	+	0.909632i	−0.0371558	+	0.0813600i
$126$	−19.9498	+	5.85779i	−1.77727	+	0.521854i
$127$	8.93671	−	19.5687i	0.793004	−	1.73644i	0.125160	−	0.992137i	$-0.460056\pi$
$127$	8.93671	−	19.5687i	0.793004	−	1.73644i	0.667845	−	0.744301i	$-0.267217\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	2.73704	−	19.0365i	0.240983	−	1.67607i
$130$	−2.47895	−	2.86086i	−0.217418	−	0.250914i
$131$	−4.00605	+	2.57453i	−0.350010	+	0.224938i	−0.703818	−	0.710380i	$-0.748523\pi$
$131$	−4.00605	+	2.57453i	−0.350010	+	0.224938i	0.353808	+	0.935318i	$0.384887\pi$
$132$	6.74844	−	14.7770i	0.587376	−	1.28617i
$133$	26.6487			2.31074
$134$	1.59490	−	8.02847i	0.137778	−	0.693554i
$135$	−6.38920			−0.549894
$136$	−0.0148456	+	0.0325074i	−0.00127300	+	0.00278748i
$137$	−1.69018	+	1.08621i	−0.144402	+	0.0928014i	−0.610847	−	0.791749i	$-0.709171\pi$
$137$	−1.69018	+	1.08621i	−0.144402	+	0.0928014i	0.466445	+	0.884550i	$0.345535\pi$
$138$	14.0079	+	16.1659i	1.19243	+	1.37614i
$139$	−0.602395	+	4.18975i	−0.0510945	+	0.355370i	0.948195	+	0.317688i	$0.102906\pi$
$139$	−0.602395	+	4.18975i	−0.0510945	+	0.355370i	−0.999290	+	0.0376819i	$0.988003\pi$
$140$	0.566050	+	3.93697i	0.0478400	+	0.332734i
$141$	10.7304	−	23.4963i	0.903663	−	1.97875i
$142$	1.77605	−	0.521496i	0.149043	−	0.0437629i
$143$	−8.90611	+	19.5017i	−0.744766	+	1.63081i
$144$	4.39763	+	2.82619i	0.366469	+	0.235516i
$145$	−1.03777	+	7.21783i	−0.0861819	+	0.599408i
$146$	5.21585	+	1.53151i	0.431667	+	0.126749i
$147$	−24.2745	−	7.12763i	−2.00213	−	0.587877i
$148$	−3.57913	−	4.13054i	−0.294203	−	0.339528i
$149$	6.23072	+	13.6434i	0.510440	+	1.11771i	0.972933	+	0.231085i	$0.0742277\pi$
$149$	6.23072	+	13.6434i	0.510440	+	1.11771i	−0.462493	+	0.886623i	$0.653045\pi$
$150$	−0.408210	+	2.83916i	−0.0333302	+	0.231817i
$151$	10.5160	−	12.1361i	0.855781	−	0.987623i	−0.144218	−	0.989546i	$-0.546067\pi$
$151$	10.5160	−	12.1361i	0.855781	−	0.987623i	0.999998	+	0.00192262i	$0.000611990\pi$
$152$	−4.38754	−	5.06349i	−0.355876	−	0.410703i
$153$	−0.0776051	−	0.169931i	−0.00627400	−	0.0137381i
$154$	18.9505	−	12.1787i	1.52707	−	0.981389i
$155$	1.16546	+	8.10595i	0.0936120	+	0.651085i
$156$	−9.13436	−	5.87030i	−0.731334	−	0.470000i
$157$	1.20463	−	0.774166i	0.0961395	−	0.0617851i	−0.491688	−	0.870772i	$-0.663620\pi$
$157$	1.20463	−	0.774166i	0.0961395	−	0.0617851i	0.587827	+	0.808986i	$0.299983\pi$
$158$	−7.83752	+	9.04498i	−0.623520	+	0.719580i
$159$	−35.1940	−	10.3339i	−2.79107	−	0.819531i
$160$	0.654861	−	0.755750i	0.0517713	−	0.0597472i
$161$	4.22128	+	29.3597i	0.332684	+	2.31387i
$162$	−2.53697	+	0.744922i	−0.199323	+	0.0585266i
$163$	−9.11066			−0.713602			−0.356801	−	0.934180i	$-0.616133\pi$
$163$	−9.11066			−0.713602			−0.356801	+	0.934180i	$0.616133\pi$
$164$	1.88804			0.147431
$165$	15.5870	−	4.57676i	1.21345	−	0.356300i
$166$	1.76684	+	1.13548i	0.137134	+	0.0881304i
$167$	1.51319	+	3.31342i	0.117094	+	0.256400i	0.959100	−	0.283069i	$-0.0913524\pi$
$167$	1.51319	+	3.31342i	0.117094	+	0.256400i	−0.842006	+	0.539469i	$0.818625\pi$
$168$	4.73937	+	10.3778i	0.365650	+	0.800662i
$169$	1.11859	+	0.718876i	0.0860456	+	0.0552982i
$170$	−0.0342892	+	0.0100682i	−0.00262987	+	0.000772198i
$171$	35.0238			2.67834
$172$	−6.70498			−0.511250
$173$	−3.80628	+	1.11763i	−0.289386	+	0.0849715i	−0.423204	−	0.906035i	$-0.639095\pi$
$173$	−3.80628	+	1.11763i	−0.289386	+	0.0849715i	0.133818	+	0.991006i	$0.457276\pi$
$174$	2.97669	+	20.7033i	0.225662	+	1.56952i
$175$	−2.60468	+	3.00596i	−0.196895	+	0.227229i
$176$	−5.43412	−	1.59560i	−0.409613	−	0.120273i
$177$	4.92198	−	5.68027i	0.369959	−	0.426955i
$178$	−8.42384	+	5.41367i	−0.631394	+	0.405772i
$179$	9.02443	+	5.79965i	0.674517	+	0.433486i	0.832551	−	0.553948i	$-0.186879\pi$
$179$	9.02443	+	5.79965i	0.674517	+	0.433486i	−0.158034	+	0.987434i	$0.550516\pi$
$180$	0.743947	+	5.17427i	0.0554506	+	0.385667i
$181$	8.13308	−	5.22681i	0.604527	−	0.388506i	−0.202274	−	0.979329i	$-0.564833\pi$
$181$	8.13308	−	5.22681i	0.604527	−	0.388506i	0.806801	+	0.590823i	$0.201197\pi$
$182$	−6.25468	−	13.6958i	−0.463628	−	1.01520i
$183$	10.8372	+	12.5068i	0.801111	+	0.924532i
$184$	4.88358	−	5.63595i	0.360022	−	0.415488i
$185$	0.777819	−	5.40985i	0.0571864	−	0.397740i
$186$	9.75804	+	21.3671i	0.715494	+	1.56671i
$187$	0.132542	+	0.152961i	0.00969242	+	0.0111856i
$188$	−8.64057	−	2.53710i	−0.630178	−	0.185037i
$189$	−24.3833	−	7.15959i	−1.77363	−	0.520784i
$190$	0.953502	−	6.63176i	0.0691743	−	0.481118i
$191$	6.08990	+	3.91374i	0.440650	+	0.283188i	0.742095	−	0.670295i	$-0.233833\pi$
$191$	6.08990	+	3.91374i	0.440650	+	0.283188i	−0.301445	+	0.953484i	$0.597469\pi$
$192$	1.19156	−	2.60915i	0.0859934	−	0.188299i
$193$	−8.09845	+	2.37792i	−0.582939	+	0.171166i	−0.559889	−	0.828568i	$-0.689156\pi$
$193$	−8.09845	+	2.37792i	−0.582939	+	0.171166i	−0.0230507	+	0.999734i	$0.507338\pi$
$194$	−5.02186	+	10.9963i	−0.360549	+	0.789492i
$195$	−1.54526	−	10.7475i	−0.110658	−	0.769646i
$196$	−1.25523	+	8.73035i	−0.0896596	+	0.623596i
$197$	−15.6342	−	18.0428i	−1.11389	−	1.28549i	−0.954478	−	0.298282i	$-0.903586\pi$
$197$	−15.6342	−	18.0428i	−1.11389	−	1.28549i	−0.159410	−	0.987213i	$-0.550959\pi$
$198$	24.9062	−	16.0062i	1.77000	−	1.13751i
$199$	−0.0454276	+	0.0994725i	−0.00322028	+	0.00705142i	−0.911235	−	0.411886i	$-0.864870\pi$
$199$	−0.0454276	+	0.0994725i	−0.00322028	+	0.00705142i	0.908015	+	0.418938i	$0.137597\pi$
$200$	1.00000			0.0707107
$201$	16.2987	−	16.8995i	1.14962	−	1.19200i
$202$	−6.59817			−0.464246
$203$	−12.0486	+	26.3828i	−0.845647	+	1.85171i
$204$	−0.0862336	+	0.0554189i	−0.00603756	+	0.00388010i
$205$	1.23640	+	1.42688i	0.0863541	+	0.0996579i
$206$	−0.0261858	+	0.182126i	−0.00182445	+	0.0126893i
$207$	5.54794	+	38.5868i	0.385608	+	2.68197i
$208$	−1.57254	+	3.44337i	−0.109036	+	0.238755i
$209$	−36.4084	+	10.6905i	−2.51842	+	0.739475i
$210$	−4.73937	+	10.3778i	−0.327047	+	0.716134i
$211$	5.29908	+	3.40551i	0.364804	+	0.234445i	0.710181	−	0.704019i	$-0.248613\pi$
$211$	5.29908	+	3.40551i	0.364804	+	0.234445i	−0.345378	+	0.938464i	$0.612249\pi$
$212$	−1.81988	+	12.6576i	−0.124990	+	0.869326i
$213$	5.09435	+	1.49584i	0.349059	+	0.102493i
$214$	−0.198126	−	0.0581750i	−0.0135436	−	0.00397676i
$215$	−4.39083	−	5.06728i	−0.299452	−	0.345586i
$216$	2.65417	+	5.81182i	0.180593	+	0.395444i
$217$	−4.63556	+	32.2410i	−0.314682	+	2.18866i
$218$	6.02462	−	6.95279i	0.408039	−	0.470902i
$219$	10.2109	+	11.7841i	0.689991	+	0.796293i
$220$	−2.35272	−	5.15173i	−0.158620	−	0.347330i
$221$	0.113805	−	0.0731380i	0.00765535	−	0.00491979i
$222$	−2.23106	−	15.5174i	−0.149739	−	1.04146i
$223$	−23.1436	−	14.8735i	−1.54981	−	0.996003i	−0.985350	−	0.170542i	$-0.945448\pi$
$223$	−23.1436	−	14.8735i	−1.54981	−	0.996003i	−0.564460	−	0.825460i	$-0.690916\pi$
$224$	3.34605	−	2.15037i	0.223567	−	0.143678i
$225$	−3.42327	+	3.95066i	−0.228218	+	0.263377i
$226$	3.00433	+	0.882152i	0.199845	+	0.0586799i
$227$	12.8541	−	14.8344i	0.853153	−	0.984592i	−0.146836	−	0.989161i	$-0.546909\pi$
$227$	12.8541	−	14.8344i	0.853153	−	0.984592i	0.999990	+	0.00456928i	$0.00145445\pi$
$228$	−2.73499	−	19.0222i	−0.181129	−	1.25978i
$229$	22.6588	−	6.65323i	1.49734	−	0.439658i	0.572462	−	0.819931i	$-0.305988\pi$
$229$	22.6588	−	6.65323i	1.49734	−	0.439658i	0.924874	+	0.380273i	$0.124170\pi$
$230$	7.45743			0.491729
$231$	64.6139			4.25128
$232$	6.99668	−	2.05441i	0.459354	−	0.134879i
$233$	−2.60074	−	1.67140i	−0.170380	−	0.109497i	0.452671	−	0.891677i	$-0.350471\pi$
$233$	−2.60074	−	1.67140i	−0.170380	−	0.109497i	−0.623052	+	0.782181i	$0.714107\pi$
$234$	−8.22039	−	18.0001i	−0.537384	−	1.17671i
$235$	−3.74096	−	8.19155i	−0.244033	−	0.534358i
$236$	−2.20437	−	1.41666i	−0.143492	−	0.0922169i
$237$	−32.9386	+	9.67164i	−2.13959	+	0.628240i
$238$	−0.142142			−0.00921367
$239$	25.7677			1.66677			0.833387	−	0.552690i	$-0.186399\pi$
$239$	25.7677			1.66677			0.833387	+	0.552690i	$0.186399\pi$
$240$	2.75217	−	0.808110i	0.177652	−	0.0521633i
$241$	0.419796	+	2.91974i	0.0270414	+	0.188077i	0.998865	−	0.0476325i	$-0.0151676\pi$
$241$	0.419796	+	2.91974i	0.0270414	+	0.188077i	−0.971824	+	0.235710i	$0.924259\pi$
$242$	−13.8016	+	15.9279i	−0.887202	+	1.02389i
$243$	11.1142	+	3.26343i	0.712978	+	0.209349i
$244$	3.77820	−	4.36028i	0.241875	−	0.279138i
$245$	−7.41996	+	4.76852i	−0.474044	+	0.304650i
$246$	4.55587	+	2.92788i	0.290471	+	0.186675i
$247$	3.60944	+	25.1042i	0.229663	+	1.59734i
$248$	6.88928	−	4.42747i	0.437470	−	0.281145i
$249$	2.50257	+	5.47987i	0.158594	+	0.347273i
$250$	0.654861	+	0.755750i	0.0414170	+	0.0477978i
$251$	8.12153	−	9.37275i	0.512626	−	0.591603i	−0.439143	−	0.898417i	$-0.644718\pi$
$251$	8.12153	−	9.37275i	0.512626	−	0.591603i	0.951769	+	0.306815i	$0.0992632\pi$
$252$	−2.95902	+	20.5804i	−0.186400	+	1.29644i
$253$	−17.5452	−	38.4187i	−1.10306	−	2.41536i
$254$	−14.0878	−	16.2582i	−0.883949	−	1.02013i
$255$	−0.0983538	−	0.0288793i	−0.00615916	−	0.00180849i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	2.05334	−	14.2813i	0.128084	−	0.890842i	−0.819896	−	0.572512i	$-0.805969\pi$
$257$	2.05334	−	14.2813i	0.128084	−	0.890842i	0.947980	−	0.318330i	$-0.103122\pi$
$258$	−16.1792	−	10.3978i	−1.00727	−	0.647336i
$259$	9.03058	−	19.7742i	0.561133	−	1.22871i
$260$	−3.63212	+	1.06649i	−0.225254	+	0.0661407i
$261$	−15.8352	+	34.6743i	−0.980176	+	2.14629i
$262$	0.677704	+	4.71353i	0.0418687	+	0.291203i
$263$	−3.74505	+	26.0474i	−0.230930	+	1.60615i	0.463169	+	0.886270i	$0.346712\pi$
$263$	−3.74505	+	26.0474i	−0.230930	+	1.60615i	−0.694098	+	0.719880i	$0.744197\pi$
$264$	−10.6382	−	12.2772i	−0.654739	−	0.755609i
$265$	−10.7577	+	6.91357i	−0.660842	+	0.424697i
$266$	11.0703	−	24.2405i	0.678763	−	1.48628i
$267$	−28.7221			−1.75777
$268$	−6.64041	−	4.78592i	−0.405627	−	0.292346i
$269$	−13.0864			−0.797890			−0.398945	−	0.916975i	$-0.630624\pi$
$269$	−13.0864			−0.797890			−0.398945	+	0.916975i	$0.630624\pi$
$270$	−2.65417	+	5.81182i	−0.161528	+	0.353696i
$271$	1.76241	−	1.13263i	0.107059	−	0.0688024i	−0.486016	−	0.873950i	$-0.661550\pi$
$271$	1.76241	−	1.13263i	0.107059	−	0.0688024i	0.593075	+	0.805148i	$0.297914\pi$
$272$	0.0234027	+	0.0270081i	0.00141899	+	0.00163761i
$273$	6.14620	−	42.7478i	0.371985	−	2.58721i
$274$	0.285928	+	1.98867i	0.0172735	+	0.120140i
$275$	2.35272	−	5.15173i	0.141874	−	0.310661i
$276$	20.5241	−	6.02643i	1.23541	−	0.362748i
$277$	−5.14841	+	11.2734i	−0.309338	+	0.677355i	−0.998901	−	0.0468704i	$-0.985075\pi$
$277$	−5.14841	+	11.2734i	−0.309338	+	0.677355i	0.689563	+	0.724225i	$0.257802\pi$
$278$	3.56089	+	2.28844i	0.213568	+	0.137252i
$279$	−6.09241	+	42.3736i	−0.364743	+	2.53684i
$280$	3.81634	+	1.12058i	0.228070	+	0.0669673i
$281$	−14.9407	−	4.38698i	−0.891287	−	0.261705i	−0.196142	−	0.980575i	$-0.562841\pi$
$281$	−14.9407	−	4.38698i	−0.891287	−	0.261705i	−0.695144	+	0.718870i	$0.744660\pi$
$282$	−16.9154	−	19.5214i	−1.00730	−	1.16248i
$283$	3.34729	+	7.32954i	0.198976	+	0.435696i	0.982648	−	0.185478i	$-0.0593834\pi$
$283$	3.34729	+	7.32954i	0.198976	+	0.435696i	−0.783673	+	0.621174i	$0.786656\pi$
$284$	0.263429	−	1.83219i	0.0156316	−	0.108720i
$285$	12.5850	−	14.5239i	0.745472	−	0.860321i
$286$	14.0396	+	16.2026i	0.830179	+	0.958078i
$287$	3.11959	+	6.83096i	0.184144	+	0.403219i
$288$	4.39763	−	2.82619i	0.259133	−	0.166535i
$289$	2.41917	+	16.8257i	0.142304	+	0.989747i
$290$	6.13447	+	3.94238i	0.360228	+	0.231505i
$291$	−29.1704	+	18.7467i	−1.71000	+	1.09895i
$292$	3.55986	−	4.10829i	0.208325	−	0.240420i
$293$	−2.10809	−	0.618991i	−0.123156	−	0.0361619i	0.219574	−	0.975596i	$-0.429533\pi$
$293$	−2.10809	−	0.618991i	−0.123156	−	0.0361619i	−0.342730	+	0.939434i	$0.611352\pi$
$294$	−16.5675	+	19.1199i	−0.966236	+	1.11510i
$295$	−0.372913	−	2.59367i	−0.0217118	−	0.151009i
$296$	−5.24409	+	1.53980i	−0.304807	+	0.0894993i
$297$	36.1854			2.09969
$298$	14.9988			0.868856
$299$	−27.0863	+	7.95325i	−1.56644	+	0.459948i
$300$	2.41302	+	1.55075i	0.139316	+	0.0895327i
$301$	−11.0786	−	24.2587i	−0.638559	−	1.39825i
$302$	−6.67090	−	14.6072i	−0.383867	−	0.840551i
$303$	−15.9215	−	10.2321i	−0.914666	−	0.587820i
$304$	−6.42856	+	1.88759i	−0.368703	+	0.108261i
$305$	5.76947			0.330359
$306$	−0.186813			−0.0106794
$307$	−9.58204	+	2.81354i	−0.546876	+	0.160577i	−0.543488	−	0.839417i	$-0.682897\pi$
$307$	−9.58204	+	2.81354i	−0.546876	+	0.160577i	−0.00338806	+	0.999994i	$0.501078\pi$
$308$	−3.20585	−	22.2972i	−0.182670	−	1.27050i
$309$	−0.345619	+	0.398865i	−0.0196616	+	0.0226907i
$310$	7.85758	+	2.30719i	0.446281	+	0.131040i
$311$	−5.56401	+	6.42121i	−0.315506	+	0.364114i	−0.891247	−	0.453519i	$-0.850168\pi$
$311$	−5.56401	+	6.42121i	−0.315506	+	0.364114i	0.575740	+	0.817633i	$0.304714\pi$
$312$	−9.13436	+	5.87030i	−0.517132	+	0.332340i
$313$	−7.06335	−	4.53934i	−0.399244	−	0.256579i	0.325577	−	0.945515i	$-0.394441\pi$
$313$	−7.06335	−	4.53934i	−0.399244	−	0.256579i	−0.724821	+	0.688937i	$0.758078\pi$
$314$	−0.203786	−	1.41737i	−0.0115003	−	0.0799866i
$315$	−17.4914	+	11.2410i	−0.985527	+	0.633360i
$316$	4.97178	+	10.8867i	0.279684	+	0.612423i
$317$	−14.8605	−	17.1500i	−0.834650	−	0.963238i	0.165084	−	0.986279i	$-0.447210\pi$
$317$	−14.8605	−	17.1500i	−0.834650	−	0.963238i	−0.999735	+	0.0230419i	$0.992665\pi$
$318$	−24.0202	+	27.7207i	−1.34698	+	1.55450i
$319$	5.87744	−	40.8785i	0.329073	−	2.28875i
$320$	−0.415415	−	0.909632i	−0.0232224	−	0.0508500i
$321$	−0.387866	−	0.447621i	−0.0216486	−	0.0249838i
$322$	28.4601	+	8.35664i	1.58602	+	0.465697i
$323$	0.229736	+	0.0674567i	0.0127829	+	0.00375339i
$324$	−0.376291	+	2.61716i	−0.0209050	+	0.145398i
$325$	−3.18453	−	2.04657i	−0.176646	−	0.113523i
$326$	−3.78470	+	8.28734i	−0.209615	+	0.458994i
$327$	25.3196	−	7.43449i	1.40017	−	0.411128i
$328$	0.784319	−	1.71742i	0.0433068	−	0.0948287i
$329$	−5.09748	−	35.4538i	−0.281033	−	1.95463i
$330$	2.31191	−	16.0797i	0.127267	−	0.885158i
$331$	5.79158	+	6.68384i	0.318334	+	0.367377i	0.892254	−	0.451535i	$-0.149123\pi$
$331$	5.79158	+	6.68384i	0.318334	+	0.367377i	−0.573920	+	0.818912i	$0.694578\pi$
$332$	1.76684	−	1.13548i	0.0969681	−	0.0623176i
$333$	11.8687	−	25.9888i	0.650400	−	1.42418i
$334$	3.64259			0.199314
$335$	−0.731588	−	8.15259i	−0.0399709	−	0.445424i
$336$	11.4088			0.622399
$337$	13.8045	−	30.2277i	0.751981	−	1.64661i	−0.0107904	−	0.999942i	$-0.503435\pi$
$337$	13.8045	−	30.2277i	0.751981	−	1.64661i	0.762772	−	0.646668i	$-0.223838\pi$
$338$	1.11859	−	0.718876i	0.0608434	−	0.0391017i
$339$	5.88150	+	6.78762i	0.319439	+	0.368653i
$340$	−0.00508588	+	0.0353731i	−0.000275821	+	0.00191838i
$341$	−6.60062	−	45.9083i	−0.357444	−	2.48608i
$342$	14.5494	−	31.8588i	0.786743	−	1.72273i
$343$	−6.94622	+	2.03959i	−0.375061	+	0.110128i
$344$	−2.78535	+	6.09906i	−0.150176	+	0.328839i
$345$	17.9949	+	11.5646i	0.968813	+	0.622619i
$346$	−0.564559	+	3.92659i	−0.0303509	+	0.211095i
$347$	10.5727	+	3.10442i	0.567571	+	0.166654i	0.552913	−	0.833239i	$-0.313516\pi$
$347$	10.5727	+	3.10442i	0.567571	+	0.166654i	0.0146575	+	0.999893i	$0.495334\pi$
$348$	20.0690	+	5.89278i	1.07581	+	0.315886i
$349$	−0.769436	−	0.887977i	−0.0411870	−	0.0475323i	0.734782	−	0.678303i	$-0.237284\pi$
$349$	−0.769436	−	0.887977i	−0.0411870	−	0.0475323i	−0.775969	+	0.630771i	$0.782739\pi$
$350$	1.65229	+	3.61802i	0.0883188	+	0.193391i
$351$	3.44203	−	23.9398i	0.183722	−	1.27781i
$352$	−3.70883	+	4.28022i	−0.197681	+	0.228136i
$353$	10.2221	+	11.7969i	0.544067	+	0.627887i	0.959490	−	0.281741i	$-0.0909119\pi$
$353$	10.2221	+	11.7969i	0.544067	+	0.627887i	−0.415423	+	0.909628i	$0.636366\pi$
$354$	−3.12229	−	6.83686i	−0.165948	−	0.363375i
$355$	1.55719	−	1.00074i	0.0826469	−	0.0531139i
$356$	1.42506	+	9.91152i	0.0755281	+	0.525309i
$357$	−0.342990	−	0.220426i	−0.0181530	−	0.0116662i
$358$	9.02443	−	5.79965i	0.476956	−	0.306521i
$359$	22.6148	−	26.0988i	1.19356	−	1.37744i	0.285621	−	0.958343i	$-0.407800\pi$
$359$	22.6148	−	26.0988i	1.19356	−	1.37744i	0.907940	−	0.419100i	$-0.137654\pi$
$360$	5.01573	+	1.47275i	0.264352	+	0.0776207i
$361$	−16.9539	+	19.5659i	−0.892311	+	1.02978i
$362$	−1.37587	−	9.56940i	−0.0723143	−	0.502957i
$363$	−58.0038	+	17.0314i	−3.04441	+	0.893919i
$364$	−15.0565			−0.789173
$365$	5.43605			0.284536
$366$	15.8786	−	4.66237i	0.829986	−	0.243706i
$367$	−5.39473	−	3.46699i	−0.281603	−	0.180975i	0.392213	−	0.919874i	$-0.371710\pi$
$367$	−5.39473	−	3.46699i	−0.281603	−	0.180975i	−0.673816	+	0.738899i	$0.735346\pi$
$368$	−3.09793	−	6.78352i	−0.161491	−	0.353615i
$369$	4.10001	+	8.97777i	0.213438	+	0.467364i
$370$	−4.59786	−	2.95486i	−0.239031	−	0.153616i
$371$	−48.8023	+	14.3297i	−2.53369	+	0.743958i
$372$	23.4899			1.21789
$373$	−9.77090			−0.505918			−0.252959	−	0.967477i	$-0.581404\pi$
$373$	−9.77090			−0.505918			−0.252959	+	0.967477i	$0.581404\pi$
$374$	0.194198	−	0.0570218i	0.0100418	−	0.00294853i
$375$	0.408210	+	2.83916i	0.0210799	+	0.146614i
$376$	−5.89725	+	6.80579i	−0.304127	+	0.350982i
$377$	−26.4856	−	7.77688i	−1.36408	−	0.400529i
$378$	−16.6418	+	19.2057i	−0.855962	+	0.987832i
$379$	−15.7616	+	10.1294i	−0.809620	+	0.520311i	−0.878742	−	0.477297i	$-0.841617\pi$
$379$	−15.7616	+	10.1294i	−0.809620	+	0.520311i	0.0691222	+	0.997608i	$0.477980\pi$
$380$	−5.63636	−	3.62227i	−0.289139	−	0.185818i
$381$	−8.78170	−	61.0781i	−0.449900	−	3.12912i
$382$	6.08990	−	3.91374i	0.311586	−	0.200244i
$383$	−4.46073	−	9.76764i	−0.227933	−	0.499103i	0.760765	−	0.649028i	$-0.224824\pi$
$383$	−4.46073	−	9.76764i	−0.227933	−	0.499103i	−0.988697	+	0.149925i	$0.952097\pi$
$384$	−1.87837	−	2.16776i	−0.0958554	−	0.110623i
$385$	14.7517	−	17.0244i	0.751816	−	0.867641i
$386$	−1.20119	+	8.35443i	−0.0611388	+	0.425230i
$387$	−14.5603	−	31.8827i	−0.740144	−	1.62069i
$388$	7.91647	+	9.13610i	0.401898	+	0.463815i
$389$	12.9772	+	3.81045i	0.657970	+	0.193197i	0.593639	−	0.804731i	$-0.297691\pi$
$389$	12.9772	+	3.81045i	0.657970	+	0.193197i	0.0643306	+	0.997929i	$0.479509\pi$
$390$	−10.4182	−	3.05906i	−0.527547	−	0.154902i
$391$	−0.0379276	+	0.263793i	−0.00191808	+	0.0133406i
$392$	7.41996	+	4.76852i	0.374765	+	0.240847i
$393$	−5.67421	+	12.4248i	−0.286226	+	0.626747i
$394$	−22.9070	+	6.72609i	−1.15404	+	0.338855i
$395$	−4.97178	+	10.8867i	−0.250157	+	0.547768i
$396$	−4.21337	−	29.3047i	−0.211730	−	1.47261i
$397$	−5.29297	+	36.8134i	−0.265646	+	1.84761i	0.222605	+	0.974909i	$0.428544\pi$
$397$	−5.29297	+	36.8134i	−0.265646	+	1.84761i	−0.488252	+	0.872703i	$0.662365\pi$
$398$	0.0716121	+	0.0826448i	0.00358959	+	0.00414261i
$399$	64.3038	−	41.3256i	3.21922	−	2.06887i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	−11.1879			−0.558695			−0.279347	−	0.960190i	$-0.590118\pi$
$401$	−11.1879			−0.558695			−0.279347	+	0.960190i	$0.590118\pi$
$402$	−8.60164	−	21.8461i	−0.429011	−	1.08959i
$403$	−31.0002			−1.54423
$404$	−2.74098	+	6.00191i	−0.136369	+	0.298606i
$405$	−2.22434	+	1.42949i	−0.110528	+	0.0710321i
$406$	18.9935	+	21.9196i	0.942629	+	1.08785i
$407$	−4.40521	+	30.6389i	−0.218358	+	1.51871i
$408$	0.0145881	+	0.101463i	0.000722220	+	0.00502315i
$409$	−1.45238	+	3.18026i	−0.0718154	+	0.157254i	−0.942135	−	0.335233i	$-0.891185\pi$
$409$	−1.45238	+	3.18026i	−0.0718154	+	0.157254i	0.870320	+	0.492487i	$0.163912\pi$
$410$	1.81156	−	0.531922i	0.0894665	−	0.0262697i
$411$	−2.39399	+	5.24210i	−0.118087	+	0.258574i
$412$	0.154790	+	0.0994773i	0.00762594	+	0.00490090i
$413$	1.48324	−	10.3162i	0.0729857	−	0.507627i
$414$	37.4045	+	10.9829i	1.83833	+	0.539782i
$415$	2.01518	+	0.591709i	0.0989211	+	0.0290458i
$416$	2.47895	+	2.86086i	0.121540	+	0.140265i
$417$	5.04367	+	11.0441i	0.246990	+	0.540832i
$418$	−5.40020	+	37.5592i	−0.264132	+	1.83708i
$419$	−23.5185	+	27.1418i	−1.14895	+	1.32596i	−0.211693	+	0.977336i	$0.567898\pi$
$419$	−23.5185	+	27.1418i	−1.14895	+	1.32596i	−0.937261	+	0.348628i	$0.886648\pi$
$420$	7.47115	+	8.62216i	0.364555	+	0.420718i
$421$	2.69665	+	5.90483i	0.131426	+	0.287784i	0.963892	−	0.266293i	$-0.0857988\pi$
$421$	2.69665	+	5.90483i	0.131426	+	0.287784i	−0.832466	+	0.554077i	$0.813071\pi$
$422$	5.29908	−	3.40551i	0.257955	−	0.165778i
$423$	−6.69950	−	46.5961i	−0.325741	−	2.26558i
$424$	10.7577	+	6.91357i	0.522441	+	0.335753i
$425$	−0.0300637	+	0.0193208i	−0.00145831	+	0.000937196i
$426$	3.47693	−	4.01259i	0.168458	−	0.194411i
$427$	22.0183	+	6.46514i	1.06554	+	0.312870i
$428$	−0.135222	+	0.156055i	−0.00653622	+	0.00754319i
$429$	8.75164	+	60.8690i	0.422533	+	2.93878i
$430$	−6.43338	+	1.88901i	−0.310245	+	0.0910962i
$431$	−9.43984			−0.454701			−0.227350	−	0.973813i	$-0.573006\pi$
$431$	−9.43984			−0.454701			−0.227350	+	0.973813i	$0.573006\pi$
$432$	6.38920			0.307400
$433$	36.5505	−	10.7322i	1.75650	−	0.515756i	0.764797	−	0.644271i	$-0.222839\pi$
$433$	36.5505	−	10.7322i	1.75650	−	0.515756i	0.991708	+	0.128515i	$0.0410210\pi$
$434$	27.4018	+	17.6101i	1.31533	+	0.845310i
$435$	8.68891	+	19.0261i	0.416602	+	0.912230i
$436$	−3.82176	−	8.36848i	−0.183029	−	0.400778i
$437$	−42.0328	−	27.0128i	−2.01070	−	1.29220i
$438$	14.9609	−	4.39293i	0.714861	−	0.209902i
$439$	0.110271			0.00526293			0.00263147	−	0.999997i	$-0.499162\pi$
$439$	0.110271			0.00526293			0.00263147	+	0.999997i	$0.499162\pi$
$440$	−5.66354			−0.269999
$441$	−44.2393	+	12.9898i	−2.10664	+	0.618564i
$442$	−0.0192524	−	0.133903i	−0.000915742	−	0.00636913i
$443$	3.33268	−	3.84612i	0.158341	−	0.182735i	−0.671036	−	0.741425i	$-0.734150\pi$
$443$	3.33268	−	3.84612i	0.158341	−	0.182735i	0.829377	+	0.558690i	$0.188696\pi$
$444$	−15.0419	−	4.41671i	−0.713858	−	0.209608i
$445$	−6.55741	+	7.56765i	−0.310851	+	0.358741i
$446$	−23.1436	+	14.8735i	−1.09588	+	0.704280i
$447$	36.1923	+	23.2594i	1.71184	+	1.10013i
$448$	−0.566050	−	3.93697i	−0.0267434	−	0.186004i
$449$	−14.0249	+	9.01325i	−0.661875	+	0.425361i	−0.827988	−	0.560745i	$-0.810515\pi$
$449$	−14.0249	+	9.01325i	−0.661875	+	0.425361i	0.166113	+	0.986107i	$0.446878\pi$
$450$	2.17157	+	4.75508i	0.102369	+	0.224157i
$451$	−7.00241	−	8.08121i	−0.329731	−	0.380529i
$452$	2.05048	−	2.36638i	0.0964464	−	0.111305i
$453$	6.55519	−	45.5924i	0.307990	−	2.14212i
$454$	−8.15405	−	17.8549i	−0.382688	−	0.837971i
$455$	−9.85989	−	11.3789i	−0.462239	−	0.533452i
$456$	−18.4394	−	5.41430i	−0.863504	−	0.253548i
$457$	−27.3884	−	8.04195i	−1.28117	−	0.376187i	−0.430840	−	0.902429i	$-0.641783\pi$
$457$	−27.3884	−	8.04195i	−1.28117	−	0.376187i	−0.850335	+	0.526242i	$0.823601\pi$
$458$	3.36082	−	23.3750i	0.157041	−	1.09224i
$459$	−0.192083	−	0.123444i	−0.00896567	−	0.00576189i
$460$	3.09793	−	6.78352i	0.144442	−	0.316283i
$461$	−24.0553	+	7.06326i	−1.12037	+	0.328969i	−0.788914	−	0.614503i	$-0.789356\pi$
$461$	−24.0553	+	7.06326i	−1.12037	+	0.328969i	−0.331451	+	0.943472i	$0.607538\pi$
$462$	26.8416	−	58.7749i	1.24878	−	2.73445i
$463$	2.33162	+	16.2168i	0.108359	+	0.753656i	0.969465	+	0.245230i	$0.0788635\pi$
$463$	2.33162	+	16.2168i	0.108359	+	0.753656i	−0.861106	+	0.508426i	$0.830227\pi$
$464$	1.03777	−	7.21783i	0.0481772	−	0.335079i
$465$	15.3826	+	17.7524i	0.713350	+	0.823250i
$466$	−2.60074	+	1.67140i	−0.120477	+	0.0774259i
$467$	−6.96240	+	15.2455i	−0.322182	+	0.705479i	−0.999545	−	0.0301695i	$-0.990395\pi$
$467$	−6.96240	+	15.2455i	−0.322182	+	0.705479i	0.677363	+	0.735649i	$0.263123\pi$
$468$	−19.7884			−0.914718
$469$	6.34363	−	31.9328i	0.292922	−	1.47452i
$470$	−9.00535			−0.415386
$471$	1.70624	−	3.73615i	0.0786195	−	0.172153i
$472$	−2.20437	+	1.41666i	−0.101464	+	0.0652072i
$473$	24.8676	+	28.6988i	1.14341	+	1.31957i
$474$	−4.88555	+	33.9797i	−0.224401	+	1.56074i
$475$	−0.953502	−	6.63176i	−0.0437497	−	0.304286i
$476$	−0.0590477	+	0.129297i	−0.00270645	+	0.00592630i
$477$	−64.1398	+	18.8331i	−2.93676	+	0.862310i
$478$	10.7043	−	23.4391i	0.489603	−	1.07208i
$479$	1.26652	+	0.813942i	0.0578687	+	0.0371899i	0.569255	−	0.822161i	$-0.307232\pi$
$479$	1.26652	+	0.813942i	0.0578687	+	0.0371899i	−0.511387	+	0.859351i	$0.670868\pi$
$480$	0.408210	−	2.83916i	0.0186321	−	0.129589i
$481$	19.8513	+	5.82886i	0.905140	+	0.265773i
$482$	2.83028	+	0.831046i	0.128916	+	0.0378531i
$483$	55.7156	+	64.2992i	2.53515	+	2.92572i
$484$	8.75514	+	19.1711i	0.397961	+	0.871413i
$485$	−1.72041	+	11.9657i	−0.0781200	+	0.543336i
$486$	7.58554	−	8.75418i	0.344087	−	0.397098i
$487$	18.3119	+	21.1331i	0.829793	+	0.957632i	0.999612	−	0.0278428i	$-0.00886378\pi$
$487$	18.3119	+	21.1331i	0.829793	+	0.957632i	−0.169819	+	0.985475i	$0.554318\pi$
$488$	−2.39673	−	5.24810i	−0.108495	−	0.237570i
$489$	−21.9842	+	14.1284i	−0.994158	+	0.638907i
$490$	1.25523	+	8.73035i	0.0567057	+	0.394397i
$491$	15.0567	+	9.67633i	0.679498	+	0.436687i	0.834338	−	0.551253i	$-0.185850\pi$
$491$	15.0567	+	9.67633i	0.679498	+	0.436687i	−0.154840	+	0.987939i	$0.549486\pi$
$492$	4.55587	−	2.92788i	0.205394	−	0.131999i
$493$	−0.170653	+	0.196945i	−0.00768584	+	0.00886994i
$494$	24.3350	+	7.14540i	1.09488	+	0.321487i
$495$	19.3878	−	22.3747i	0.871417	−	1.00567i
$496$	−1.16546	−	8.10595i	−0.0523307	−	0.363968i
$497$	7.06416	−	2.07422i	0.316871	−	0.0930417i
$498$	6.02427			0.269954
$499$	15.0072			0.671813			0.335906	−	0.941895i	$-0.390957\pi$
$499$	15.0072			0.671813			0.335906	+	0.941895i	$0.390957\pi$
$500$	0.959493	−	0.281733i	0.0429098	−	0.0125995i
$501$	8.78963	+	5.64875i	0.392692	+	0.252368i
$502$	−5.15194	−	11.2812i	−0.229943	−	0.503504i
$503$	−2.06636	−	4.52471i	−0.0921346	−	0.201747i	0.857954	−	0.513726i	$-0.171735\pi$
$503$	−2.06636	−	4.52471i	−0.0921346	−	0.201747i	−0.950089	+	0.311979i	$0.899008\pi$
$504$	17.4914	+	11.2410i	0.779128	+	0.500715i
$505$	−6.33090	+	1.85892i	−0.281721	+	0.0827209i
$506$	−42.2355			−1.87760
$507$	3.81398			0.169385
$508$	−20.6413	+	6.06083i	−0.915810	+	0.268906i
$509$	−3.02278	−	21.0239i	−0.133982	−	0.931868i	−0.940291	−	0.340372i	$-0.889447\pi$
$509$	−3.02278	−	21.0239i	−0.133982	−	0.931868i	0.806308	−	0.591495i	$-0.201462\pi$
$510$	−0.0671272	+	0.0774689i	−0.00297244	+	0.00343038i
$511$	20.7458	+	6.09152i	0.917740	+	0.269473i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	36.0118	−	23.1434i	1.58996	−	1.02180i
$514$	−12.1377	−	7.80044i	−0.535372	−	0.344063i
$515$	0.0261858	+	0.182126i	0.00115388	+	0.00802543i
$516$	−16.1792	+	10.3978i	−0.712250	+	0.457736i
$517$	21.1870	+	46.3932i	0.931805	+	2.04037i
$518$	−14.2358	−	16.4290i	−0.625486	−	0.721849i
$519$	−7.45146	+	8.59944i	−0.327083	+	0.377474i
$520$	−0.538726	+	3.74693i	−0.0236247	+	0.164314i
$521$	7.46095	+	16.3372i	0.326870	+	0.715746i	0.999711	−	0.0240415i	$-0.00765337\pi$
$521$	7.46095	+	16.3372i	0.326870	+	0.715746i	−0.672841	+	0.739787i	$0.734926\pi$
$522$	24.9627	+	28.8084i	1.09259	+	1.26091i
$523$	4.61601	+	1.35538i	0.201844	+	0.0592667i	0.381092	−	0.924537i	$-0.375548\pi$
$523$	4.61601	+	1.35538i	0.201844	+	0.0592667i	−0.179248	+	0.983804i	$0.557366\pi$
$524$	4.56911	+	1.34161i	0.199602	+	0.0586086i
$525$	−1.62364	+	11.2926i	−0.0708613	+	0.492851i
$526$	22.1378	+	14.2271i	0.965253	+	0.620331i
$527$	−0.121575	+	0.266213i	−0.00529590	+	0.0115964i
$528$	−15.5870	+	4.57676i	−0.678338	+	0.199178i
$529$	13.5481	−	29.6661i	0.589046	−	1.28983i
$530$	1.81988	+	12.6576i	0.0790507	+	0.549810i
$531$	1.94939	−	13.5583i	0.0845965	−	0.588382i
$532$	−17.4512	−	20.1398i	−0.756606	−	0.873170i
$533$	−6.01251	+	3.86401i	−0.260431	+	0.167369i
$534$	−11.9316	+	26.1266i	−0.516331	+	1.13061i
$535$	−0.206490			−0.00892735
$536$	−7.11195	+	4.05219i	−0.307189	+	0.175028i
$537$	30.7699			1.32782
$538$	−5.43628	+	11.9038i	−0.234375	+	0.513209i
$539$	42.0232	−	27.0067i	1.81007	−	1.16326i
$540$	4.18403	+	4.82863i	0.180052	+	0.207791i
$541$	5.35620	−	37.2532i	0.230281	−	1.60164i	−0.466610	−	0.884463i	$-0.654525\pi$
$541$	5.35620	−	37.2532i	0.230281	−	1.60164i	0.696891	−	0.717177i	$-0.254566\pi$
$542$	−0.298146	−	2.07365i	−0.0128065	−	0.0890711i
$543$	11.5198	−	25.2248i	0.494360	−	1.08250i
$544$	0.0342892	−	0.0100682i	0.00147014	−	0.000431672i
$545$	3.82176	−	8.36848i	0.163706	−	0.358466i
$546$	−36.3315	−	23.3488i	−1.55484	−	0.999238i
$547$	5.26157	−	36.5950i	0.224968	−	1.56469i	−0.493884	−	0.869528i	$-0.664423\pi$
$547$	5.26157	−	36.5950i	0.224968	−	1.56469i	0.718853	−	0.695163i	$-0.244668\pi$
$548$	1.92774	+	0.566035i	0.0823489	+	0.0241798i
$549$	28.9381	+	8.49699i	1.23505	+	0.362643i
$550$	−3.70883	−	4.28022i	−0.158145	−	0.182509i
$551$	−20.2957	−	44.4414i	−0.864625	−	1.89327i
$552$	3.04420	−	21.1729i	0.129570	−	0.901177i
$553$	−31.1734	+	35.9760i	−1.32563	+	1.52985i
$554$	8.11595	+	9.36631i	0.344814	+	0.397936i
$555$	−6.51244	−	14.2603i	−0.276438	−	0.605314i
$556$	3.56089	−	2.28844i	0.151015	−	0.0970516i
$557$	−2.25436	−	15.6794i	−0.0955205	−	0.664359i	−0.980178	−	0.198118i	$-0.936517\pi$
$557$	−2.25436	−	15.6794i	−0.0955205	−	0.664359i	0.884658	−	0.466241i	$-0.154392\pi$
$558$	36.0135	+	23.1445i	1.52458	+	0.979785i
$559$	21.3522	−	13.7222i	0.903101	−	0.580388i
$560$	2.60468	−	3.00596i	0.110068	−	0.127025i
$561$	0.557031	+	0.163559i	0.0235178	+	0.00690546i
$562$	−10.1971	+	11.7681i	−0.430140	+	0.496408i
$563$	4.24056	+	29.4937i	0.178718	+	1.24301i	0.859733	+	0.510744i	$0.170630\pi$
$563$	4.24056	+	29.4937i	0.178718	+	1.24301i	−0.681015	+	0.732270i	$0.738461\pi$
$564$	−24.7842	+	7.27731i	−1.04360	+	0.306430i
$565$	3.13117			0.131729
$566$	8.05769			0.338690
$567$	−10.0907	+	2.96289i	−0.423769	+	0.124430i
$568$	−1.55719	−	1.00074i	−0.0653381	−	0.0419902i
$569$	6.09830	+	13.3534i	0.255654	+	0.559804i	0.993324	−	0.115357i	$-0.0368013\pi$
$569$	6.09830	+	13.3534i	0.255654	+	0.559804i	−0.737670	+	0.675161i	$0.764074\pi$
$570$	−7.98339	−	17.4812i	−0.334387	−	0.732206i
$571$	−28.8111	−	18.5158i	−1.20571	−	0.774861i	−0.225772	−	0.974180i	$-0.572490\pi$
$571$	−28.8111	−	18.5158i	−1.20571	−	0.774861i	−0.979935	+	0.199319i	$0.936127\pi$
$572$	20.5706	−	6.04008i	0.860101	−	0.252549i
$573$	20.7643			0.867440
$574$	7.50958			0.313444
$575$	7.15536	−	2.10100i	0.298399	−	0.0876178i
$576$	−0.743947	−	5.17427i	−0.0309978	−	0.215594i
$577$	−20.9833	+	24.2161i	−0.873548	+	1.00813i	0.126322	+	0.991989i	$0.459683\pi$
$577$	−20.9833	+	24.2161i	−0.873548	+	1.00813i	−0.999870	+	0.0161387i	$0.994863\pi$
$578$	16.3102	+	4.78909i	0.678413	+	0.199200i
$579$	−15.8541	+	18.2966i	−0.658875	+	0.760383i
$580$	6.13447	−	3.94238i	0.254720	−	0.163699i
$581$	7.02753	+	4.51632i	0.291551	+	0.187369i
$582$	4.93476	+	34.3220i	0.204553	+	1.42269i
$583$	60.9268	−	39.1553i	2.52333	−	1.62165i
$584$	−2.25822	−	4.94481i	−0.0934457	−	0.204618i
$585$	−12.9586	−	14.9551i	−0.535773	−	0.618316i
$586$	−1.43879	+	1.66045i	−0.0594357	+	0.0685925i
$587$	−0.143973	+	1.00136i	−0.00594242	+	0.0413305i	−0.992577	−	0.121619i	$-0.961192\pi$
$587$	−0.143973	+	1.00136i	−0.00594242	+	0.0413305i	0.986634	+	0.162949i	$0.0521006\pi$
$588$	10.5097	+	23.0130i	0.433413	+	0.949041i
$589$	−35.9309	−	41.4664i	−1.48051	−	1.70859i
$590$	−2.51420	−	0.738235i	−0.103508	−	0.0303927i
$591$	−65.7053	−	19.2928i	−2.70276	−	0.793601i
$592$	−0.777819	+	5.40985i	−0.0319682	+	0.222344i
$593$	32.6142	+	20.9598i	1.33930	+	0.860718i	0.996888	−	0.0788313i	$-0.0251189\pi$
$593$	32.6142	+	20.9598i	1.33930	+	0.860718i	0.342415	+	0.939549i	$0.388755\pi$
$594$	15.0320	−	32.9154i	0.616770	−	1.35054i
$595$	−0.136384	+	0.0400459i	−0.00559119	+	0.00164172i
$596$	6.23072	−	13.6434i	0.255220	−	0.558854i
$597$	0.0446397	+	0.310476i	0.00182698	+	0.0127069i
$598$	−4.01752	+	27.9425i	−0.164289	+	1.14265i
$599$	23.5706	+	27.2019i	0.963069	+	1.11144i	0.993718	+	0.111910i	$0.0356970\pi$
$599$	23.5706	+	27.2019i	0.963069	+	1.11144i	−0.0306495	+	0.999530i	$0.509758\pi$
$600$	2.41302	−	1.55075i	0.0985110	−	0.0633092i
$601$	−0.925556	+	2.02669i	−0.0377542	+	0.0826702i	−0.927569	−	0.373651i	$-0.878106\pi$
$601$	−0.925556	+	2.02669i	−0.0377542	+	0.0826702i	0.889815	+	0.456321i	$0.150833\pi$
$602$	−26.6687			−1.08694
$603$	8.33729	−	41.9686i	0.339521	−	1.70909i
$604$	−16.0584			−0.653407
$605$	−8.75514	+	19.1711i	−0.355947	+	0.779416i
$606$	−15.9215	+	10.2321i	−0.646767	+	0.415652i
$607$	7.47143	+	8.62249i	0.303256	+	0.349976i	0.886840	−	0.462077i	$-0.152896\pi$
$607$	7.47143	+	8.62249i	0.303256	+	0.349976i	−0.583584	+	0.812053i	$0.698350\pi$
$608$	−0.953502	+	6.63176i	−0.0386696	+	0.268953i
$609$	11.8396	+	82.3465i	0.479766	+	3.33685i
$610$	2.39673	−	5.24810i	0.0970406	−	0.212489i
$611$	32.7085	−	9.60408i	1.32324	−	0.388539i
$612$	−0.0776051	+	0.169931i	−0.00313700	+	0.00686907i
$613$	7.74163	+	4.97524i	0.312681	+	0.200948i	0.687563	−	0.726124i	$-0.258680\pi$
$613$	7.74163	+	4.97524i	0.312681	+	0.200948i	−0.374882	+	0.927073i	$0.622317\pi$
$614$	−1.42124	+	9.88492i	−0.0573564	+	0.398923i
$615$	5.19620	+	1.52574i	0.209531	+	0.0615239i
$616$	−21.6140	−	6.34643i	−0.870852	−	0.255705i
$617$	0.613759	+	0.708315i	0.0247090	+	0.0285157i	0.767970	−	0.640486i	$-0.221267\pi$
$617$	0.613759	+	0.708315i	0.0247090	+	0.0285157i	−0.743261	+	0.669002i	$0.766722\pi$
$618$	0.219245	+	0.480081i	0.00881935	+	0.0193117i
$619$	3.33471	−	23.1934i	0.134033	−	0.932222i	−0.806188	−	0.591659i	$-0.798473\pi$
$619$	3.33471	−	23.1934i	0.134033	−	0.932222i	0.940222	−	0.340563i	$-0.110618\pi$
$620$	5.36285	−	6.18906i	0.215377	−	0.248559i
$621$	31.2022	+	36.0092i	1.25210	+	1.44500i
$622$	3.52957	+	7.72867i	0.141523	+	0.309892i
$623$	−33.5054	+	21.5326i	−1.34237	+	0.862687i
$624$	1.54526	+	10.7475i	0.0618599	+	0.430245i
$625$	0.841254	+	0.540641i	0.0336501	+	0.0216256i
$626$	−7.06335	+	4.53934i	−0.282308	+	0.181428i
$627$	−71.2757	+	82.2566i	−2.84648	+	3.28501i
$628$	−1.37394	−	0.403424i	−0.0548261	−	0.0160984i
$629$	0.127907	−	0.147612i	0.00509998	−	0.00588569i
$630$	2.95902	+	20.5804i	0.117890	+	0.819943i
$631$	−5.03556	+	1.47857i	−0.200463	+	0.0588611i	−0.380422	−	0.924813i	$-0.624221\pi$
$631$	−5.03556	+	1.47857i	−0.200463	+	0.0588611i	0.179960	+	0.983674i	$0.442403\pi$
$632$	11.9682			0.476070
$633$	18.0679			0.718133
$634$	−21.7734	+	6.39326i	−0.864734	+	0.253909i
$635$	−18.0976	−	11.6307i	−0.718183	−	0.461548i
$636$	15.2373	+	33.3651i	0.604200	+	1.32301i
$637$	−13.8700	−	30.3710i	−0.549548	−	1.20334i
$638$	−34.7428	−	22.3278i	−1.37548	−	0.883967i
$639$	9.28426	−	2.72611i	0.367280	−	0.107843i
$640$	−1.00000			−0.0395285
$641$	6.37951			0.251975			0.125988	−	0.992032i	$-0.459790\pi$
$641$	6.37951			0.251975			0.125988	+	0.992032i	$0.459790\pi$
$642$	−0.568296	+	0.166867i	−0.0224288	+	0.00658570i
$643$	3.35884	+	23.3612i	0.132460	+	0.921277i	0.942334	+	0.334674i	$0.108626\pi$
$643$	3.35884	+	23.3612i	0.132460	+	0.921277i	−0.809875	+	0.586603i	$0.800465\pi$
$644$	19.4242	−	22.4167i	0.765421	−	0.883343i
$645$	−18.4532	−	5.41836i	−0.726595	−	0.213348i
$646$	0.156797	−	0.180953i	0.00616908	−	0.00711950i
$647$	16.4199	−	10.5524i	0.645532	−	0.414858i	−0.176499	−	0.984301i	$-0.556477\pi$
$647$	16.4199	−	10.5524i	0.645532	−	0.414858i	0.822031	+	0.569442i	$0.192841\pi$
$648$	2.22434	+	1.42949i	0.0873802	+	0.0561558i
$649$	2.11201	+	14.6893i	0.0829036	+	0.576607i
$650$	−3.18453	+	2.04657i	−0.124907	+	0.0802732i
$651$	38.8121	+	84.9867i	1.52117	+	3.33089i
$652$	5.96621	+	6.88537i	0.233655	+	0.269652i
$653$	−20.4290	+	23.5763i	−0.799449	+	0.922614i	−0.998351	−	0.0574057i	$-0.981717\pi$
$653$	−20.4290	+	23.5763i	−0.799449	+	0.922614i	0.198902	+	0.980019i	$0.436263\pi$
$654$	3.75547	−	26.1199i	0.146851	−	1.02137i
$655$	1.97821	+	4.33167i	0.0772950	+	0.169252i
$656$	−1.23640	−	1.42688i	−0.0482734	−	0.0557105i
$657$	27.2657	+	8.00594i	1.06374	+	0.312342i
$658$	−34.3674	−	10.0912i	−1.33978	−	0.393396i
$659$	−1.73764	+	12.0855i	−0.0676887	+	0.470785i	0.927580	+	0.373625i	$0.121885\pi$
$659$	−1.73764	+	12.0855i	−0.0676887	+	0.470785i	−0.995269	+	0.0971607i	$0.969024\pi$
$660$	−13.6662	−	8.78274i	−0.531956	−	0.341868i
$661$	−8.76638	+	19.1957i	−0.340973	+	0.746626i	−0.999985	−	0.00550606i	$-0.998247\pi$
$661$	−8.76638	+	19.1957i	−0.340973	+	0.746626i	0.659012	+	0.752132i	$0.270975\pi$
$662$	8.48575	−	2.49164i	0.329808	−	0.0968403i
$663$	0.161194	−	0.352966i	0.00626027	−	0.0137081i
$664$	−0.298897	−	2.07887i	−0.0115994	−	0.0806759i
$665$	3.79251	−	26.3775i	0.147067	−	1.02288i
$666$	−18.7098	−	21.5923i	−0.724990	−	0.836684i
$667$	45.7474	−	29.4001i	1.77135	−	1.13838i
$668$	1.51319	−	3.31342i	0.0585470	−	0.128200i
$669$	−78.9110			−3.05087
$670$	−7.71977	−	2.72123i	−0.298241	−	0.105130i
$671$	−32.6756			−1.26143
$672$	4.73937	−	10.3778i	0.182825	−	0.400331i
$673$	−22.6104	+	14.5308i	−0.871566	+	0.560122i	−0.898231	−	0.439523i	$-0.855148\pi$
$673$	−22.6104	+	14.5308i	−0.871566	+	0.560122i	0.0266652	+	0.999644i	$0.491511\pi$
$674$	−21.7615	−	25.1141i	−0.838222	−	0.967359i
$675$	−0.909277	+	6.32416i	−0.0349981	+	0.243417i
$676$	−0.189232	−	1.31614i	−0.00727817	−	0.0506208i
$677$	−1.25552	+	2.74921i	−0.0482536	+	0.105661i	−0.932223	−	0.361884i	$-0.882134\pi$
$677$	−1.25552	+	2.74921i	−0.0482536	+	0.105661i	0.883970	+	0.467544i	$0.154861\pi$
$678$	8.61750	−	2.53033i	0.330953	−	0.0971766i
$679$	−19.9742	+	43.7375i	−0.766540	+	1.67849i
$680$	0.0300637	+	0.0193208i	0.00115289	+	0.000740919i
$681$	8.01262	−	55.7290i	0.307044	−	2.13554i
$682$	−44.5017	−	13.0669i	−1.70406	−	0.500357i
$683$	9.23987	+	2.71307i	0.353554	+	0.103813i	0.453687	−	0.891161i	$-0.350109\pi$
$683$	9.23987	+	2.71307i	0.353554	+	0.103813i	−0.100133	+	0.994974i	$0.531927\pi$
$684$	−22.9357	−	26.4692i	−0.876970	−	1.01208i
$685$	0.834619	+	1.82756i	0.0318892	+	0.0698275i
$686$	−1.03028	+	7.16578i	−0.0393364	+	0.273591i
$687$	44.3586	−	51.1925i	1.69239	−	1.95312i
$688$	4.39083	+	5.06728i	0.167399	+	0.193188i
$689$	−20.1092	−	44.0329i	−0.766098	−	1.67752i
$690$	17.9949	−	11.5646i	0.685055	−	0.440258i
$691$	−0.948022	−	6.59364i	−0.0360645	−	0.250834i	0.963811	−	0.266585i	$-0.0858952\pi$
$691$	−0.948022	−	6.59364i	−0.0360645	−	0.250834i	−0.999876	+	0.0157509i	$0.994986\pi$
$692$	3.33723	+	2.14471i	0.126862	+	0.0815295i
$693$	99.0630	−	63.6639i	3.76309	−	2.41839i
$694$	7.21592	−	8.32762i	0.273913	−	0.316112i
$695$	4.06137	+	1.19253i	0.154057	+	0.0452351i
$696$	13.6972	−	15.8074i	0.519192	−	0.599179i
$697$	0.00960234	+	0.0667857i	0.000363715	+	0.00252969i
$698$	−1.12737	+	0.331025i	−0.0426715	+	0.0125295i
$699$	−8.86756			−0.335402
$700$	3.97745			0.150334
$701$	−18.1060	+	5.31640i	−0.683854	+	0.200798i	−0.605163	−	0.796101i	$-0.706892\pi$
$701$	−18.1060	+	5.31640i	−0.683854	+	0.200798i	−0.0786910	+	0.996899i	$0.525074\pi$
$702$	−20.3466	−	13.0759i	−0.767932	−	0.493520i
$703$	15.2119	+	33.3093i	0.573726	+	1.25628i
$704$	2.35272	+	5.15173i	0.0886714	+	0.194163i
$705$	−21.7300	−	13.9651i	−0.818401	−	0.525954i
$706$	14.9773	−	4.39773i	0.563677	−	0.165511i
$707$	−26.2439			−0.987004
$708$	−7.51607			−0.282471
$709$	30.7299	−	9.02311i	1.15409	−	0.338870i	0.351954	−	0.936017i	$-0.385517\pi$
$709$	30.7299	−	9.02311i	1.15409	−	0.338870i	0.802132	+	0.597147i	$0.203699\pi$
$710$	−0.263429	−	1.83219i	−0.00988632	−	0.0687609i
$711$	−40.9704	+	47.2824i	−1.53651	+	1.77323i
$712$	9.60782	+	2.82111i	0.360068	+	0.105726i
$713$	39.9931	−	46.1545i	1.49775	−	1.72850i
$714$	−0.342990	+	0.220426i	−0.0128361	+	0.00824924i
$715$	18.0357	+	11.5908i	0.674497	+	0.433473i
$716$	−1.52666	−	10.6182i	−0.0570540	−	0.396820i
$717$	62.1778	−	39.9593i	2.32207	−	1.49231i
$718$	−14.3458	−	31.4129i	−0.535381	−	1.17232i
$719$	19.2057	+	22.1645i	0.716251	+	0.826598i	0.990851	−	0.134961i	$-0.0430909\pi$
$719$	19.2057	+	22.1645i	0.716251	+	0.826598i	−0.274600	+	0.961559i	$0.588545\pi$
$720$	3.42327	−	3.95066i	0.127578	−	0.147232i
$721$	−0.104153	+	0.724398i	−0.00387885	+	0.0269780i
$722$	10.7548	+	23.5498i	0.400253	+	0.876432i
$723$	5.54077	+	6.39439i	0.206063	+	0.237810i
$724$	−9.27619	−	2.72374i	−0.344747	−	0.101227i
$725$	6.99668	+	2.05441i	0.259850	+	0.0762989i
$726$	−8.60329	+	59.8372i	−0.319298	+	2.22077i
$727$	26.1046	+	16.7764i	0.968166	+	0.622202i	0.926246	−	0.376919i	$-0.123016\pi$
$727$	26.1046	+	16.7764i	0.968166	+	0.622202i	0.0419194	+	0.999121i	$0.486653\pi$
$728$	−6.25468	+	13.6958i	−0.231814	+	0.507602i
$729$	39.4905	−	11.5955i	1.46261	−	0.429461i
$730$	2.25822	−	4.94481i	0.0835804	−	0.183015i
$731$	−0.0341007	−	0.237176i	−0.00126126	−	0.00877226i
$732$	2.35516	−	16.3805i	0.0870490	−	0.605439i
$733$	−15.1336	−	17.4651i	−0.558972	−	0.645088i	0.403978	−	0.914769i	$-0.367627\pi$
$733$	−15.1336	−	17.4651i	−0.558972	−	0.645088i	−0.962950	+	0.269681i	$0.913082\pi$
$734$	−5.39473	+	3.46699i	−0.199123	+	0.127969i
$735$	−10.5097	+	23.0130i	−0.387656	+	0.848849i
$736$	−7.45743			−0.274885
$737$	4.14338	+	46.1725i	0.152623	+	1.70079i
$738$	9.86967			0.363308
$739$	6.32465	−	13.8490i	0.232656	−	0.509445i	−0.756911	−	0.653518i	$-0.773293\pi$
$739$	6.32465	−	13.8490i	0.232656	−	0.509445i	0.989567	+	0.144072i	$0.0460198\pi$
$740$	−4.59786	+	2.95486i	−0.169021	+	0.108623i
$741$	47.6400	+	54.9795i	1.75010	+	2.01972i
$742$	−7.23850	+	50.3449i	−0.265734	+	1.84822i
$743$	−3.66168	−	25.4676i	−0.134334	−	0.934314i	−0.939813	−	0.341689i	$-0.889001\pi$
$743$	−3.66168	−	25.4676i	−0.134334	−	0.934314i	0.805479	−	0.592624i	$-0.201908\pi$
$744$	9.75804	−	21.3671i	0.357747	−	0.783357i
$745$	14.3912	−	4.22564i	0.527254	−	0.154816i
$746$	−4.05898	+	8.88793i	−0.148610	+	0.325410i
$747$	9.23613	+	5.93570i	0.337932	+	0.217176i
$748$	0.0288041	−	0.200337i	0.00105318	−	0.00732504i
$749$	−0.788036	−	0.231388i	−0.0287942	−	0.00845474i
$750$	2.75217	+	0.808110i	0.100495	+	0.0295080i
$751$	7.21913	+	8.33132i	0.263430	+	0.304014i	0.872020	−	0.489471i	$-0.162810\pi$
$751$	7.21913	+	8.33132i	0.263430	+	0.304014i	−0.608590	+	0.793485i	$0.708265\pi$
$752$	3.74096	+	8.19155i	0.136419	+	0.298715i
$753$	5.06259	−	35.2111i	0.184491	−	1.28316i
$754$	−18.0766	+	20.8615i	−0.658311	+	0.759732i
$755$	−10.5160	−	12.1361i	−0.382717	−	0.441679i
$756$	10.5568	+	23.1162i	0.383948	+	0.840729i
$757$	−22.0841	+	14.1926i	−0.802660	+	0.515838i	−0.876483	−	0.481433i	$-0.840116\pi$
$757$	−22.0841	+	14.1926i	−0.802660	+	0.515838i	0.0738228	+	0.997271i	$0.476480\pi$
$758$	2.66639	+	18.5452i	0.0968477	+	0.673591i
$759$	−101.915	−	65.4967i	−3.69927	−	2.37738i
$760$	−5.63636	+	3.62227i	−0.204452	+	0.131393i
$761$	−4.43780	+	5.12150i	−0.160870	+	0.185654i	−0.830462	−	0.557075i	$-0.811924\pi$
$761$	−4.43780	+	5.12150i	−0.160870	+	0.185654i	0.669592	+	0.742729i	$0.266469\pi$
$762$	−59.2066	−	17.3846i	−2.14483	−	0.629779i
$763$	23.9627	−	27.6544i	0.867506	−	1.00116i
$764$	−1.03023	−	7.16540i	−0.0372724	−	0.259235i
$765$	−0.179246	+	0.0526314i	−0.00648066	+	0.00190289i
$766$	−10.7380			−0.387980
$767$	9.91918			0.358161
$768$	−2.75217	+	0.808110i	−0.0993103	+	0.0291601i
$769$	3.46423	+	2.22632i	0.124923	+	0.0802833i	0.601610	−	0.798790i	$-0.294526\pi$
$769$	3.46423	+	2.22632i	0.124923	+	0.0802833i	−0.476687	+	0.879073i	$0.658162\pi$
$770$	−9.35782	−	20.4908i	−0.337233	−	0.738436i
$771$	−17.1920	−	37.6452i	−0.619154	−	1.35576i
$772$	7.10047	+	4.56319i	0.255552	+	0.164233i
$773$	43.2798	−	12.7081i	1.55667	−	0.457079i	0.613582	−	0.789631i	$-0.289728\pi$
$773$	43.2798	−	12.7081i	1.55667	−	0.457079i	0.943085	+	0.332552i	$0.107910\pi$
$774$	−35.0501			−1.25985
$775$	8.18930			0.294168
$776$	11.5991	−	3.40581i	0.416384	−	0.122261i
$777$	−8.87395	−	61.7197i	−0.318351	−	2.21418i
$778$	8.85703	−	10.2216i	0.317540	−	0.366460i
$779$	−12.1374	−	3.56385i	−0.434866	−	0.127688i
$780$	−7.11050	+	8.20596i	−0.254597	+	0.293820i
$781$	−8.81918	+	5.66774i	−0.315575	+	0.202808i
$782$	0.224198	+	0.144084i	0.00801732	+	0.00515242i
$783$	6.63050	+	46.1162i	0.236955	+	1.64806i
$784$	7.41996	−	4.76852i	0.264999	−	0.170304i
$785$	−0.594850	−	1.30254i	−0.0212311	−	0.0464896i
$786$	8.94483	+	10.3229i	0.319051	+	0.368205i
$787$	−3.68449	+	4.25213i	−0.131338	+	0.151572i	−0.817609	−	0.575774i	$-0.804701\pi$
$787$	−3.68449	+	4.25213i	−0.131338	+	0.151572i	0.686271	+	0.727346i	$0.259246\pi$
$788$	−3.39763	+	23.6310i	−0.121035	+	0.841820i
$789$	31.3562	+	68.6604i	1.11631	+	2.44437i
$790$	7.83752	+	9.04498i	0.278846	+	0.321806i
$791$	11.9496	+	3.50872i	0.424878	+	0.124756i
$792$	−28.4067	−	8.34097i	−1.00939	−	0.296384i
$793$	−3.10817	+	21.6178i	−0.110374	+	0.767670i
$794$	31.2879	+	20.1075i	1.11036	+	0.713588i
$795$	−15.2373	+	33.3651i	−0.540413	+	1.18334i
$796$	0.104925	−	0.0308088i	0.00371897	−	0.00109199i
$797$	1.35923	−	2.97629i	0.0481463	−	0.105426i	−0.884030	−	0.467430i	$-0.845180\pi$
$797$	1.35923	−	2.97629i	0.0481463	−	0.105426i	0.932177	+	0.362004i	$0.117907\pi$
$798$	−10.8783	−	75.6601i	−0.385087	−	2.67834i
$799$	0.0458001	−	0.318547i	0.00162029	−	0.0112694i
$800$	−0.654861	−	0.755750i	−0.0231528	−	0.0267198i
$801$	−44.0354	+	28.2998i	−1.55592	+	0.999926i
$802$	−4.64760	+	10.1768i	−0.164113	+	0.359356i
$803$	−30.7873			−1.08646
$804$	−23.4452	−	1.25087i	−0.826848	−	0.0441149i
$805$	29.6616			1.04543
$806$	−12.8780	+	28.1988i	−0.453607	+	0.993261i
$807$	−31.5776	+	20.2937i	−1.11159	+	0.714372i
$808$	4.32088	+	4.98657i	0.152008	+	0.175427i
$809$	−2.91356	+	20.2642i	−0.102435	+	0.712452i	0.872281	+	0.489005i	$0.162640\pi$
$809$	−2.91356	+	20.2642i	−0.102435	+	0.712452i	−0.974716	+	0.223447i	$0.928269\pi$
$810$	0.376291	+	2.61716i	0.0132215	+	0.0919576i
$811$	−4.23458	+	9.27244i	−0.148696	+	0.325599i	−0.969293	−	0.245908i	$-0.920914\pi$
$811$	−4.23458	+	9.27244i	−0.148696	+	0.325599i	0.820597	+	0.571507i	$0.193641\pi$
$812$	27.8289	−	8.17132i	0.976605	−	0.286757i
$813$	2.49629	−	5.46611i	0.0875487	−	0.191705i
$814$	26.0401	+	16.7350i	0.912706	+	0.586561i
$815$	−1.29658	+	9.01792i	−0.0454173	+	0.315884i
$816$	0.0983538	+	0.0288793i	0.00344307	+	0.00101098i
$817$	43.1033	+	12.6563i	1.50799	+	0.442787i
$818$	2.28953	+	2.64226i	0.0800515	+	0.0923843i
$819$	−32.6962	−	71.5947i	−1.14250	−	2.50172i
$820$	0.268696	−	1.86882i	0.00938327	−	0.0652621i
$821$	−8.75335	+	10.1019i	−0.305494	+	0.352559i	−0.887650	−	0.460518i	$-0.847664\pi$
$821$	−8.75335	+	10.1019i	−0.305494	+	0.352559i	0.582156	+	0.813077i	$0.302209\pi$
$822$	3.77388	+	4.35529i	0.131629	+	0.151908i
$823$	4.55731	+	9.97911i	0.158858	+	0.347850i	0.972279	−	0.233826i	$-0.0751245\pi$
$823$	4.55731	+	9.97911i	0.158858	+	0.347850i	−0.813421	+	0.581676i	$0.802397\pi$
$824$	0.154790	−	0.0994773i	0.00539236	−	0.00346546i
$825$	−2.31191	−	16.0797i	−0.0804904	−	0.559823i
$826$	−8.76778	−	5.63471i	−0.305070	−	0.196057i
$827$	27.5620	−	17.7130i	0.958423	−	0.615941i	0.0348619	−	0.999392i	$-0.488901\pi$
$827$	27.5620	−	17.7130i	0.958423	−	0.615941i	0.923561	+	0.383451i	$0.125265\pi$
$828$	25.5288	−	29.4618i	0.887187	−	1.02387i
$829$	24.8917	+	7.30886i	0.864524	+	0.253847i	0.683785	−	0.729684i	$-0.260333\pi$
$829$	24.8917	+	7.30886i	0.864524	+	0.253847i	0.180739	+	0.983531i	$0.442151\pi$
$830$	1.37537	−	1.58726i	0.0477398	−	0.0550947i
$831$	5.05911	+	35.1869i	0.175499	+	1.22062i
$832$	3.63212	−	1.06649i	0.125921	−	0.0369738i
$833$	−0.315203			−0.0109212
$834$	12.1413			0.420418
$835$	3.49504	−	1.02624i	0.120951	−	0.0355144i
$836$	31.9217	+	20.5148i	1.10404	+	0.709521i
$837$	21.7358	+	47.5947i	0.751299	+	1.64511i
$838$	14.9191	+	32.6683i	0.515372	+	1.12851i
$839$	−6.96872	−	4.47852i	−0.240587	−	0.154616i	0.414792	−	0.909916i	$-0.363854\pi$
$839$	−6.96872	−	4.47852i	−0.240587	−	0.154616i	−0.655378	+	0.755301i	$0.727491\pi$
$840$	10.9466	−	3.21422i	0.377694	−	0.110901i
$841$	24.1741			0.833589
$842$	6.49145			0.223710
$843$	−42.8552	+	12.5834i	−1.47601	+	0.433396i
$844$	−0.896445	−	6.23491i	−0.0308569	−	0.214615i
$845$	0.870751	−	1.00490i	0.0299548	−	0.0345696i
$846$	−45.1684	−	13.2626i	−1.55292	−	0.455978i
$847$	−54.8953	+	63.3525i	−1.88622	+	2.17682i
$848$	10.7577	−	6.91357i	0.369422	−	0.237413i
$849$	19.4433	+	12.4955i	0.667294	+	0.428844i
$850$	0.00508588	+	0.0353731i	0.000174444	+	0.00121329i
$851$	−34.2882	+	22.0357i	−1.17538	+	0.755374i
$852$	−2.20561	−	4.82962i	−0.0755630	−	0.165460i
$853$	−22.6617	−	26.1530i	−0.775921	−	0.895461i	0.220887	−	0.975299i	$-0.429105\pi$
$853$	−22.6617	−	26.1530i	−0.775921	−	0.895461i	−0.996808	+	0.0798389i	$0.974559\pi$
$854$	15.0276	−	17.3428i	0.514234	−	0.593458i
$855$	4.98441	−	34.6673i	0.170463	−	1.18560i
$856$	0.0857791	+	0.187830i	0.00293187	+	0.00641990i
$857$	9.02607	+	10.4166i	0.308325	+	0.355826i	0.888672	−	0.458543i	$-0.151629\pi$
$857$	9.02607	+	10.4166i	0.308325	+	0.355826i	−0.580347	+	0.814369i	$0.697083\pi$
$858$	59.0039	+	17.3251i	2.01436	+	0.591470i
$859$	−6.69584	−	1.96608i	−0.228459	−	0.0670817i	0.165499	−	0.986210i	$-0.447076\pi$
$859$	−6.69584	−	1.96608i	−0.228459	−	0.0670817i	−0.393958	+	0.919128i	$0.628895\pi$
$860$	−0.954218	+	6.63673i	−0.0325386	+	0.226311i
$861$	18.1207	+	11.6455i	0.617553	+	0.396877i
$862$	−3.92145	+	8.58678i	−0.133565	+	0.292467i
$863$	−12.9793	+	3.81107i	−0.441821	+	0.129730i	−0.495074	−	0.868851i	$-0.664859\pi$
$863$	−12.9793	+	3.81107i	−0.441821	+	0.129730i	0.0532532	+	0.998581i	$0.483041\pi$
$864$	2.65417	−	5.81182i	0.0902966	−	0.197722i
$865$	0.564559	+	3.92659i	0.0191956	+	0.133508i
$866$	5.42128	−	37.7058i	0.184223	−	1.28130i
$867$	31.9300	+	36.8492i	1.08440	+	1.25146i
$868$	27.4018	−	17.6101i	0.930077	−	0.597724i
$869$	28.1579	−	61.6571i	0.955190	−	2.09157i
$870$	20.9162			0.709126
$871$	30.9413	+	1.65081i	1.04841	+	0.0559357i
$872$	−9.19986			−0.311546
$873$	−26.2517	+	57.4831i	−0.888485	+	1.94551i
$874$	−42.0328	+	27.0128i	−1.42178	+	0.913722i
$875$	2.60468	+	3.00596i	0.0880542	+	0.101620i
$876$	2.21905	−	15.4338i	0.0749747	−	0.521461i
$877$	2.08696	+	14.5151i	0.0704717	+	0.490141i	0.994239	+	0.107187i	$0.0341843\pi$
$877$	2.08696	+	14.5151i	0.0704717	+	0.490141i	−0.923767	+	0.382955i	$0.874907\pi$
$878$	0.0458081	−	0.100306i	0.00154595	−	0.00338516i
$879$	−6.04676	+	1.77549i	−0.203952	+	0.0598857i
$880$	−2.35272	+	5.15173i	−0.0793101	+	0.173665i
$881$	−23.7415	−	15.2577i	−0.799870	−	0.514045i	0.0757035	−	0.997130i	$-0.475880\pi$
$881$	−23.7415	−	15.2577i	−0.799870	−	0.514045i	−0.875573	+	0.483085i	$0.839516\pi$
$882$	−6.56171	+	45.6377i	−0.220944	+	1.53670i
$883$	−17.2410	−	5.06242i	−0.580207	−	0.170364i	−0.0215568	−	0.999768i	$-0.506862\pi$
$883$	−17.2410	−	5.06242i	−0.580207	−	0.170364i	−0.558650	+	0.829404i	$0.688680\pi$
$884$	−0.129800	−	0.0381128i	−0.00436566	−	0.00128187i
$885$	−4.92198	−	5.68027i	−0.165451	−	0.190940i
$886$	−2.11411	−	4.62925i	−0.0710249	−	0.155523i
$887$	2.44632	−	17.0145i	0.0821394	−	0.571292i	−0.906640	−	0.421906i	$-0.861361\pi$
$887$	2.44632	−	17.0145i	0.0821394	−	0.571292i	0.988779	−	0.149386i	$-0.0477297\pi$
$888$	−10.2662	+	11.8479i	−0.344512	+	0.397588i
$889$	−56.0337	−	64.6663i	−1.87931	−	2.16884i
$890$	4.15973	+	9.10854i	0.139435	+	0.305319i
$891$	12.5976	−	8.09599i	0.422036	−	0.271226i
$892$	3.91520	+	27.2308i	0.131091	+	0.911756i
$893$	50.7574	+	32.6198i	1.69853	+	1.09158i
$894$	36.1923	−	23.2594i	1.21045	−	0.777910i
$895$	7.02492	−	8.10720i	0.234817	−	0.270994i
$896$	−3.81634	−	1.12058i	−0.127495	−	0.0374359i
$897$	−53.0261	+	61.1954i	−1.77049	+	2.04326i
$898$	2.37259	+	16.5017i	0.0791743	+	0.550670i
$899$	57.2979	−	16.8242i	1.91099	−	0.561118i
$900$	5.22748			0.174249
$901$	−0.456993			−0.0152247
$902$	−10.2598	+	3.01256i	−0.341615	+	0.100307i
$903$	−64.3521	−	41.3566i	−2.14150	−	1.37626i
$904$	−1.30073	−	2.84821i	−0.0432618	−	0.0947300i
$905$	−4.01615	−	8.79415i	−0.133501	−	0.292327i
$906$	−38.7491	−	24.9026i	−1.28735	−	0.827332i
$907$	−7.79391	+	2.28850i	−0.258792	+	0.0759883i	−0.408555	−	0.912734i	$-0.633967\pi$
$907$	−7.79391	+	2.28850i	−0.258792	+	0.0759883i	0.149763	+	0.988722i	$0.452149\pi$
$908$	−19.6287			−0.651401
$909$	−34.4918			−1.14402
$910$	−14.4466	+	4.24190i	−0.478899	+	0.140618i
$911$	−5.78373	−	40.2267i	−0.191624	−	1.33277i	−0.827711	−	0.561154i	$-0.810357\pi$
$911$	−5.78373	−	40.2267i	−0.191624	−	1.33277i	0.636088	−	0.771617i	$-0.280552\pi$
$912$	−12.5850	+	14.5239i	−0.416732	+	0.480934i
$913$	−11.4130	−	3.35117i	−0.377716	−	0.110907i
$914$	−18.6928	+	21.5726i	−0.618302	+	0.713558i
$915$	13.9218	−	8.94702i	0.460241	−	0.295779i
$916$	−19.8665	−	12.7675i	−0.656409	−	0.421848i
$917$	2.69553	+	18.7479i	0.0890144	+	0.619109i
$918$	−0.192083	+	0.123444i	−0.00633969	+	0.00407427i
$919$	−9.05333	−	19.8240i	−0.298642	−	0.653934i	0.699515	−	0.714618i	$-0.253399\pi$
$919$	−9.05333	−	19.8240i	−0.298642	−	0.653934i	−0.998157	+	0.0606835i	$0.980672\pi$
$920$	−4.88358	−	5.63595i	−0.161007	−	0.185812i
$921$	−18.7585	+	21.6485i	−0.618114	+	0.713342i
$922$	−3.56795	+	24.8156i	−0.117504	+	0.817259i
$923$	2.91081	+	6.37379i	0.0958105	+	0.209796i
$924$	−42.3131	−	48.8319i	−1.39200	−	1.60645i
$925$	−5.24409	−	1.53980i	−0.172425	−	0.0506284i
$926$	15.7199	+	4.61577i	0.516587	+	0.151684i
$927$	−0.136885	+	0.952059i	−0.00449591	+	0.0312697i
$928$	−6.13447	−	3.94238i	−0.201374	−	0.129415i
$929$	−14.5232	+	31.8015i	−0.476492	+	1.04337i	0.506921	+	0.861993i	$0.330784\pi$
$929$	−14.5232	+	31.8015i	−0.476492	+	1.04337i	−0.983413	+	0.181380i	$0.941944\pi$
$930$	22.5383	−	6.61786i	0.739062	−	0.217008i
$931$	24.5487	−	53.7542i	0.804551	−	1.76172i
$932$	0.439968	+	3.06004i	0.0144116	+	0.100235i
$933$	−3.46835	+	24.1229i	−0.113549	+	0.789748i
$934$	10.9755	+	12.6664i	0.359131	+	0.414459i
$935$	0.170267	−	0.109424i	0.00556833	−	0.00357855i
$936$	−8.22039	+	18.0001i	−0.268692	+	0.588353i
$937$	−21.0326			−0.687105			−0.343553	−	0.939133i	$-0.611630\pi$
$937$	−21.0326			−0.687105			−0.343553	+	0.939133i	$0.611630\pi$
$938$	−26.4119	−	19.0358i	−0.862379	−	0.621539i
$939$	−24.0834			−0.785931
$940$	−3.74096	+	8.19155i	−0.122017	+	0.267179i
$941$	12.6668	−	8.14044i	0.412925	−	0.265371i	−0.317644	−	0.948210i	$-0.602892\pi$
$941$	12.6668	−	8.14044i	0.412925	−	0.265371i	0.730568	+	0.682840i	$0.239255\pi$
$942$	−2.68972	−	3.10410i	−0.0876358	−	0.101137i
$943$	2.00378	−	13.9366i	0.0652521	−	0.453838i
$944$	0.372913	+	2.59367i	0.0121373	+	0.0844167i
$945$	−10.5568	+	23.1162i	−0.343414	+	0.751971i
$946$	36.4357	−	10.6985i	1.18463	−	0.347838i
$947$	24.7866	−	54.2751i	0.805457	−	1.76370i	0.179642	−	0.983732i	$-0.442506\pi$
$947$	24.7866	−	54.2751i	0.805457	−	1.76370i	0.625815	−	0.779972i	$-0.284767\pi$
$948$	28.8795	+	18.5597i	0.937963	+	0.602792i
$949$	−2.92854	+	20.3685i	−0.0950646	+	0.661189i
$950$	−6.42856	−	1.88759i	−0.208570	−	0.0612416i
$951$	−62.4540	−	18.3381i	−2.02521	−	0.594655i
$952$	0.0930829	+	0.107423i	0.00301684	+	0.00348161i
$953$	6.71469	+	14.7031i	0.217510	+	0.476281i	0.986661	−	0.162786i	$-0.0520480\pi$
$953$	6.71469	+	14.7031i	0.217510	+	0.476281i	−0.769151	+	0.639067i	$0.779321\pi$
$954$	−9.51340	+	66.1672i	−0.308008	+	2.14224i
$955$	4.74059	−	5.47093i	0.153402	−	0.177035i
$956$	−16.8742	−	19.4739i	−0.545752	−	0.629832i
$957$	−49.2100	−	107.755i	−1.59073	−	3.48322i
$958$	1.26652	−	0.813942i	0.0409193	−	0.0262973i
$959$	1.13726	+	7.90984i	0.0367242	+	0.255422i
$960$	−2.41302	−	1.55075i	−0.0778798	−	0.0500503i
$961$	30.3396	−	19.4981i	0.978695	−	0.628969i
$962$	13.5486	−	15.6360i	0.436826	−	0.504124i
$963$	−1.03570	−	0.304108i	−0.0333749	−	0.00979975i
$964$	1.93169	−	2.22929i	0.0622155	−	0.0718005i
$965$	1.20119	+	8.35443i	0.0386676	+	0.268939i
$966$	81.6337	−	23.9698i	2.62652	−	0.771216i
$967$	−47.4199			−1.52492			−0.762461	−	0.647035i	$-0.776009\pi$
$967$	−47.4199			−1.52492			−0.762461	+	0.647035i	$0.776009\pi$
$968$	21.0757			0.677397
$969$	0.658966	−	0.193490i	0.0211690	−	0.00621579i
$970$	10.1697	+	6.53569i	0.326531	+	0.209848i
$971$	17.8527	+	39.0920i	0.572921	+	1.25452i	0.945227	+	0.326413i	$0.105840\pi$
$971$	17.8527	+	39.0920i	0.572921	+	1.25452i	−0.372306	+	0.928110i	$0.621433\pi$
$972$	−4.81194	−	10.5367i	−0.154343	−	0.337964i
$973$	14.1633	+	9.10217i	0.454053	+	0.291802i
$974$	26.8304	−	7.87812i	0.859702	−	0.252431i
$975$	−10.8580			−0.347736
$976$	−5.76947			−0.184676
$977$	3.58988	−	1.05408i	0.114850	−	0.0337231i	−0.223802	−	0.974635i	$-0.571847\pi$
$977$	3.58988	−	1.05408i	0.114850	−	0.0337231i	0.338653	+	0.940911i	$0.390029\pi$
$978$	3.71906	+	25.8666i	0.118922	+	0.827124i
$979$	37.1381	−	42.8597i	1.18694	−	1.36980i
$980$	8.46285	+	2.48492i	0.270336	+	0.0793778i
$981$	31.4936	−	36.3455i	1.00551	−	1.16042i
$982$	15.0567	−	9.67633i	0.480478	−	0.308784i
$983$	16.9488	+	10.8924i	0.540584	+	0.347412i	0.782267	−	0.622943i	$-0.214063\pi$
$983$	16.9488	+	10.8924i	0.540584	+	0.347412i	−0.241683	+	0.970355i	$0.577700\pi$
$984$	−0.770716	−	5.36045i	−0.0245695	−	0.170885i
$985$	−20.0841	+	12.9073i	−0.639933	+	0.411260i
$986$	0.108255	+	0.237046i	0.00344754	+	0.00754907i
$987$	−67.2803	−	77.6456i	−2.14155	−	2.47149i
$988$	16.6088	−	19.1676i	0.528397	−	0.609803i
$989$	−7.11602	+	49.4930i	−0.226276	+	1.57379i
$990$	−12.2988	−	26.9306i	−0.390881	−	0.855910i
$991$	20.8405	+	24.0512i	0.662021	+	0.764013i	0.983106	−	0.183038i	$-0.0585930\pi$
$991$	20.8405	+	24.0512i	0.662021	+	0.764013i	−0.321085	+	0.947050i	$0.604048\pi$
$992$	−7.85758	−	2.30719i	−0.249478	−	0.0732535i
$993$	24.3402	+	7.14691i	0.772412	+	0.226800i
$994$	1.04778	−	7.28745i	0.0332335	−	0.231144i
$995$	0.0919950	+	0.0591216i	0.00291644	+	0.00187428i
$996$	2.50257	−	5.47987i	0.0792970	−	0.173636i
$997$	−56.8372	+	16.6889i	−1.80005	+	0.528543i	−0.997667	−	0.0682627i	$-0.978254\pi$
$997$	−56.8372	+	16.6889i	−1.80005	+	0.528543i	−0.802386	+	0.596806i	$0.796436\pi$
$998$	6.23420	−	13.6510i	0.197340	−	0.432115i
$999$	−4.96964	−	34.5646i	−0.157232	−	1.09358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.b.91.5	yes	50
67.14	even	11	inner	670.2.k.b.81.5	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.b.81.5	✓	50	67.14	even	11	inner
670.2.k.b.91.5	yes	50	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(2.41302 - 1.55075i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.408210 - 2.83916i) q^{6} +(1.65229 - 3.61802i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.17157 - 4.75508i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(2.41302 - 1.55075i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.142315 - 0.989821i) q^{5} +(-0.408210 - 2.83916i) q^{6} +(1.65229 - 3.61802i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(2.17157 - 4.75508i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(-0.806005 + 5.60589i) q^{11} +(-2.75217 - 0.808110i) q^{12} +(3.63212 + 1.06649i) q^{13} +(-2.60468 - 3.00596i) q^{14} +(-1.19156 - 2.60915i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(0.0234027 - 0.0270081i) q^{17} +(-3.42327 - 3.95066i) q^{18} +(2.78326 + 6.09449i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(-1.62364 - 11.2926i) q^{21} +(4.76447 + 3.06194i) q^{22} +(-6.27359 + 4.03179i) q^{23} +(-1.87837 + 2.16776i) q^{24} +(-0.959493 - 0.281733i) q^{25} +(2.47895 - 2.86086i) q^{26} +(-0.909277 - 6.32416i) q^{27} +(-3.81634 + 1.12058i) q^{28} -7.29206 q^{29} -2.86836 q^{30} +(-7.85758 + 2.30719i) q^{31} +(0.841254 + 0.540641i) q^{32} +(6.74844 + 14.7770i) q^{33} +(-0.0148456 - 0.0325074i) q^{34} +(-3.34605 - 2.15037i) q^{35} +(-5.01573 + 1.47275i) q^{36} +5.46548 q^{37} +6.69995 q^{38} +(10.4182 - 3.05906i) q^{39} +(0.142315 + 0.989821i) q^{40} +(-1.23640 + 1.42688i) q^{41} +(-10.9466 - 3.21422i) q^{42} +(4.39083 - 5.06728i) q^{43} +(4.76447 - 3.06194i) q^{44} +(-4.39763 - 2.82619i) q^{45} +(1.06130 + 7.38153i) q^{46} +(7.57578 - 4.86866i) q^{47} +(1.19156 + 2.60915i) q^{48} +(-5.77595 - 6.66581i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(0.0145881 - 0.101463i) q^{51} +(-1.57254 - 3.44337i) q^{52} +(-8.37419 - 9.66433i) q^{53} +(-6.13039 - 1.80004i) q^{54} +(5.43412 + 1.59560i) q^{55} +(-0.566050 + 3.93697i) q^{56} +(16.1671 + 10.3900i) q^{57} +(-3.02923 + 6.63309i) q^{58} +(2.51420 - 0.738235i) q^{59} +(-1.19156 + 2.60915i) q^{60} +(0.821081 + 5.71075i) q^{61} +(-1.16546 + 8.10595i) q^{62} +(-13.6159 - 15.7136i) q^{63} +(0.841254 - 0.540641i) q^{64} +(1.57254 - 3.44337i) q^{65} +16.2450 q^{66} +(7.96550 - 1.88438i) q^{67} -0.0357368 q^{68} +(-8.88597 + 19.4576i) q^{69} +(-3.34605 + 2.15037i) q^{70} +(1.21217 + 1.39892i) q^{71} +(-0.743947 + 5.17427i) q^{72} +(0.773631 + 5.38072i) q^{73} +(2.27044 - 4.97158i) q^{74} +(-2.75217 + 0.808110i) q^{75} +(2.78326 - 6.09449i) q^{76} +(18.9505 + 12.1787i) q^{77} +(1.54526 - 10.7475i) q^{78} +(-11.4834 - 3.37184i) q^{79} +(0.959493 + 0.281733i) q^{80} +(-1.73150 - 1.99826i) q^{81} +(0.784319 + 1.71742i) q^{82} +(-0.298897 + 2.07887i) q^{83} +(-7.47115 + 8.62216i) q^{84} +(-0.0234027 - 0.0270081i) q^{85} +(-2.78535 - 6.09906i) q^{86} +(-17.5958 + 11.3082i) q^{87} +(-0.806005 - 5.60589i) q^{88} +(-8.42384 - 5.41367i) q^{89} +(-4.39763 + 2.82619i) q^{90} +(9.85989 - 11.3789i) q^{91} +(7.15536 + 2.10100i) q^{92} +(-15.3826 + 17.7524i) q^{93} +(-1.28159 - 8.91369i) q^{94} +(6.42856 - 1.88759i) q^{95} +2.86836 q^{96} -12.0888 q^{97} +(-8.46285 + 2.48492i) q^{98} +(24.9062 + 16.0062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9	\( 50 q - 5 q^{2} + 2 q^{3} - 5 q^{4} + 5 q^{5} + 2 q^{6} + q^{7} - 5 q^{8} - q^{9} + 5 q^{10} + 30 q^{11} - 9 q^{12} + 20 q^{13} - 21 q^{14} - 2 q^{15} - 5 q^{16} + 2 q^{17} - q^{18} + 4 q^{19} + 5 q^{20} + 23 q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 5 q^{25} - 2 q^{26} + 2 q^{27} - 10 q^{28} + 26 q^{29} - 2 q^{30} + 3 q^{31} - 5 q^{32} + 38 q^{33} + 2 q^{34} - 12 q^{35} - q^{36} + 22 q^{37} - 40 q^{38} - 35 q^{39} + 5 q^{40} - 18 q^{41} - 10 q^{42} + 87 q^{43} - 3 q^{44} + 12 q^{45} + 17 q^{46} + 35 q^{47} + 2 q^{48} + 60 q^{49} - 5 q^{50} + 19 q^{51} - 24 q^{52} - 9 q^{53} + 2 q^{54} + 25 q^{55} + 12 q^{56} + 64 q^{57} + 4 q^{58} - 49 q^{59} - 2 q^{60} - 47 q^{61} - 19 q^{62} - 24 q^{63} - 5 q^{64} + 24 q^{65} - 6 q^{66} - 21 q^{67} + 2 q^{68} - 25 q^{69} - 12 q^{70} + 92 q^{71} - q^{72} + 18 q^{73} - 22 q^{74} - 9 q^{75} + 4 q^{76} - 65 q^{77} + 31 q^{78} - 58 q^{79} + 5 q^{80} - 77 q^{81} - 18 q^{82} - 49 q^{83} - 54 q^{84} - 2 q^{85} - q^{86} - 147 q^{87} + 30 q^{88} - 21 q^{89} + 12 q^{90} + 62 q^{91} + 6 q^{92} - 34 q^{93} - 9 q^{94} + 7 q^{95} + 2 q^{96} + 98 q^{97} - 39 q^{98} - 4 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 + 2 * q^3 - 5 * q^4 + 5 * q^5 + 2 * q^6 + q^7 - 5 * q^8 - q^9 + 5 * q^10 + 30 * q^11 - 9 * q^12 + 20 * q^13 - 21 * q^14 - 2 * q^15 - 5 * q^16 + 2 * q^17 - q^18 + 4 * q^19 + 5 * q^20 + 23 * q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 5 * q^25 - 2 * q^26 + 2 * q^27 - 10 * q^28 + 26 * q^29 - 2 * q^30 + 3 * q^31 - 5 * q^32 + 38 * q^33 + 2 * q^34 - 12 * q^35 - q^36 + 22 * q^37 - 40 * q^38 - 35 * q^39 + 5 * q^40 - 18 * q^41 - 10 * q^42 + 87 * q^43 - 3 * q^44 + 12 * q^45 + 17 * q^46 + 35 * q^47 + 2 * q^48 + 60 * q^49 - 5 * q^50 + 19 * q^51 - 24 * q^52 - 9 * q^53 + 2 * q^54 + 25 * q^55 + 12 * q^56 + 64 * q^57 + 4 * q^58 - 49 * q^59 - 2 * q^60 - 47 * q^61 - 19 * q^62 - 24 * q^63 - 5 * q^64 + 24 * q^65 - 6 * q^66 - 21 * q^67 + 2 * q^68 - 25 * q^69 - 12 * q^70 + 92 * q^71 - q^72 + 18 * q^73 - 22 * q^74 - 9 * q^75 + 4 * q^76 - 65 * q^77 + 31 * q^78 - 58 * q^79 + 5 * q^80 - 77 * q^81 - 18 * q^82 - 49 * q^83 - 54 * q^84 - 2 * q^85 - q^86 - 147 * q^87 + 30 * q^88 - 21 * q^89 + 12 * q^90 + 62 * q^91 + 6 * q^92 - 34 * q^93 - 9 * q^94 + 7 * q^95 + 2 * q^96 + 98 * q^97 - 39 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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