LMFDB - Embedded newform 231.2.be.a.200.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(2,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			200.16
Character	$\chi$	$=$	231.200
Dual form			231.2.be.a.149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.160234 - 0.0340589i) q^{2} +(1.67633 - 0.435777i) q^{3} +(-1.80258 + 0.802558i) q^{4} +(1.00420 + 0.904189i) q^{5} +(0.253764 - 0.126921i) q^{6} +(2.63918 - 0.186311i) q^{7} +(-0.526557 + 0.382566i) q^{8} +(2.62020 - 1.46102i) q^{9} +O(q^{10})$	\(q+(0.160234 - 0.0340589i) q^{2} +(1.67633 - 0.435777i) q^{3} +(-1.80258 + 0.802558i) q^{4} +(1.00420 + 0.904189i) q^{5} +(0.253764 - 0.126921i) q^{6} +(2.63918 - 0.186311i) q^{7} +(-0.526557 + 0.382566i) q^{8} +(2.62020 - 1.46102i) q^{9} +(0.191704 + 0.110680i) q^{10} +(-3.27699 + 0.511202i) q^{11} +(-2.67198 + 2.13088i) q^{12} +(2.86915 + 0.932244i) q^{13} +(0.416542 - 0.119741i) q^{14} +(2.07741 + 1.07811i) q^{15} +(2.56927 - 2.85346i) q^{16} +(0.953678 + 0.202711i) q^{17} +(0.370085 - 0.323346i) q^{18} +(-0.978849 + 2.19853i) q^{19} +(-2.53582 - 0.823937i) q^{20} +(4.34296 - 1.46242i) q^{21} +(-0.507676 + 0.193523i) q^{22} +(-2.70664 + 1.56268i) q^{23} +(-0.715972 + 0.870770i) q^{24} +(-0.331775 - 3.15663i) q^{25} +(0.491488 + 0.0516575i) q^{26} +(3.75565 - 3.59098i) q^{27} +(-4.60780 + 2.45394i) q^{28} +(-6.95634 - 5.05408i) q^{29} +(0.369591 + 0.101997i) q^{30} +(-3.23073 - 3.58809i) q^{31} +(0.965360 - 1.67205i) q^{32} +(-5.27056 + 2.28498i) q^{33} +0.159716 q^{34} +(2.81874 + 2.19923i) q^{35} +(-3.55055 + 4.73646i) q^{36} +(0.355785 - 3.38507i) q^{37} +(-0.0819658 + 0.385619i) q^{38} +(5.21591 + 0.312442i) q^{39} +(-0.874682 - 0.0919328i) q^{40} +(-6.95208 + 5.05098i) q^{41} +(0.646084 - 0.382246i) q^{42} +9.87461i q^{43} +(5.49676 - 3.55146i) q^{44} +(3.95225 + 0.901994i) q^{45} +(-0.380474 + 0.342580i) q^{46} +(-0.619491 + 1.39140i) q^{47} +(3.06348 - 5.90298i) q^{48} +(6.93058 - 0.983420i) q^{49} +(-0.160673 - 0.494501i) q^{50} +(1.68702 - 0.0757805i) q^{51} +(-5.92004 + 0.622222i) q^{52} +(-4.58493 + 4.12829i) q^{53} +(0.479479 - 0.703311i) q^{54} +(-3.75299 - 2.44967i) q^{55} +(-1.31840 + 1.10777i) q^{56} +(-0.682809 + 4.11203i) q^{57} +(-1.28678 - 0.572912i) q^{58} +(-5.72565 - 12.8600i) q^{59} +(-4.60993 - 0.276143i) q^{60} +(-5.28847 - 4.76176i) q^{61} +(-0.639881 - 0.464900i) q^{62} +(6.64297 - 4.34406i) q^{63} +(-2.27534 + 7.00276i) q^{64} +(2.03829 + 3.53042i) q^{65} +(-0.766701 + 0.545642i) q^{66} +(-1.55978 + 2.70162i) q^{67} +(-1.88176 + 0.399981i) q^{68} +(-3.85626 + 3.79907i) q^{69} +(0.526562 + 0.256388i) q^{70} +(8.43794 - 2.74165i) q^{71} +(-0.820747 + 1.77171i) q^{72} +(-2.19828 - 4.93742i) q^{73} +(-0.0582826 - 0.554522i) q^{74} +(-1.93175 - 5.14699i) q^{75} -4.74860i q^{76} +(-8.55334 + 1.95970i) q^{77} +(0.846409 - 0.127584i) q^{78} +(0.556251 + 2.61696i) q^{79} +(5.16013 - 0.542352i) q^{80} +(4.73086 - 7.65630i) q^{81} +(-0.941931 + 1.04612i) q^{82} +(3.83565 + 11.8049i) q^{83} +(-6.65485 + 6.12160i) q^{84} +(0.774398 + 1.06587i) q^{85} +(0.336318 + 1.58225i) q^{86} +(-13.8636 - 5.44091i) q^{87} +(1.52995 - 1.52284i) q^{88} +(9.72722 - 5.61602i) q^{89} +(0.664006 + 0.00992141i) q^{90} +(7.74591 + 1.92581i) q^{91} +(3.62479 - 4.98909i) q^{92} +(-6.97940 - 4.60696i) q^{93} +(-0.0518742 + 0.244049i) q^{94} +(-2.97085 + 1.32271i) q^{95} +(0.889624 - 3.22360i) q^{96} +(4.09209 - 12.5942i) q^{97} +(1.07702 - 0.393625i) q^{98} +(-7.83949 + 6.12719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.160234	−	0.0340589i	0.113303	−	0.0240833i	−0.150911	−	0.988547i	$-0.548221\pi$
$2$	0.160234	−	0.0340589i	0.113303	−	0.0240833i	0.264214	+	0.964464i	$0.414887\pi$
$3$	1.67633	−	0.435777i	0.967832	−	0.251596i
$3$	1.67633	−	0.435777i	0.967832	−	0.251596i
$4$	−1.80258	+	0.802558i	−0.901288	+	0.401279i
$5$	1.00420	+	0.904189i	0.449093	+	0.404366i	0.862401	−	0.506226i	$-0.168960\pi$
$5$	1.00420	+	0.904189i	0.449093	+	0.404366i	−0.413307	+	0.910592i	$0.635627\pi$
$6$	0.253764	−	0.126921i	0.103599	−	0.0518151i
$7$	2.63918	−	0.186311i	0.997517	−	0.0704191i
$7$	2.63918	−	0.186311i	0.997517	−	0.0704191i
$8$	−0.526557	+	0.382566i	−0.186166	+	0.135258i
$9$	2.62020	−	1.46102i	0.873399	−	0.487006i
$10$	0.191704	+	0.110680i	0.0606220	+	0.0350001i
$11$	−3.27699	+	0.511202i	−0.988050	+	0.154133i
$11$	−3.27699	+	0.511202i	−0.988050	+	0.154133i
$12$	−2.67198	+	2.13088i	−0.771335	+	0.615132i
$13$	2.86915	+	0.932244i	0.795760	+	0.258558i	0.678555	−	0.734550i	$-0.262607\pi$
$13$	2.86915	+	0.932244i	0.795760	+	0.258558i	0.117205	+	0.993108i	$0.462607\pi$
$14$	0.416542	−	0.119741i	0.111326	−	0.0320021i
$15$	2.07741	+	1.07811i	0.536384	+	0.278368i
$16$	2.56927	−	2.85346i	0.642317	−	0.713365i
$17$	0.953678	+	0.202711i	0.231301	+	0.0491645i	0.322104	−	0.946704i	$-0.395610\pi$
$17$	0.953678	+	0.202711i	0.231301	+	0.0491645i	−0.0908029	+	0.995869i	$0.528943\pi$
$18$	0.370085	−	0.323346i	0.0872298	−	0.0762134i
$19$	−0.978849	+	2.19853i	−0.224563	+	0.504378i	−0.990328	−	0.138743i	$-0.955694\pi$
$19$	−0.978849	+	2.19853i	−0.224563	+	0.504378i	0.765765	+	0.643120i	$0.222361\pi$
$20$	−2.53582	−	0.823937i	−0.567026	−	0.184238i
$21$	4.34296	−	1.46242i	0.947712	−	0.319125i
$22$	−0.507676	+	0.193523i	−0.108237	+	0.0412592i
$23$	−2.70664	+	1.56268i	−0.564374	+	0.325841i	−0.754899	−	0.655841i	$-0.772314\pi$
$23$	−2.70664	+	1.56268i	−0.564374	+	0.325841i	0.190525	+	0.981682i	$0.438981\pi$
$24$	−0.715972	+	0.870770i	−0.146147	+	0.177745i
$25$	−0.331775	−	3.15663i	−0.0663550	−	0.631326i
$26$	0.491488	+	0.0516575i	0.0963887	+	0.0101309i
$27$	3.75565	−	3.59098i	0.722775	−	0.691084i
$28$	−4.60780	+	2.45394i	−0.870793	+	0.463751i
$29$	−6.95634	−	5.05408i	−1.29176	−	0.938518i	−0.291920	−	0.956443i	$-0.594294\pi$
$29$	−6.95634	−	5.05408i	−1.29176	−	0.938518i	−0.999839	+	0.0179242i	$0.994294\pi$
$30$	0.369591	+	0.101997i	0.0674778	+	0.0186220i
$31$	−3.23073	−	3.58809i	−0.580257	−	0.644440i	0.379527	−	0.925181i	$-0.376087\pi$
$31$	−3.23073	−	3.58809i	−0.580257	−	0.644440i	−0.959784	+	0.280740i	$0.909420\pi$
$32$	0.965360	−	1.67205i	0.170653	−	0.295580i
$33$	−5.27056	+	2.28498i	−0.917487	+	0.397765i
$34$	0.159716			0.0273911
$35$	2.81874	+	2.19923i	0.476454	+	0.371737i
$36$	−3.55055	+	4.73646i	−0.591759	+	0.789409i
$37$	0.355785	−	3.38507i	0.0584907	−	0.556502i	−0.925558	−	0.378605i	$-0.876404\pi$
$37$	0.355785	−	3.38507i	0.0584907	−	0.556502i	0.984049	−	0.177897i	$-0.0569294\pi$
$38$	−0.0819658	+	0.385619i	−0.0132966	+	0.0625556i
$39$	5.21591	+	0.312442i	0.835214	+	0.0500307i
$40$	−0.874682	−	0.0919328i	−0.138299	−	0.0145359i
$41$	−6.95208	+	5.05098i	−1.08573	+	0.788830i	−0.978673	−	0.205422i	$-0.934143\pi$
$41$	−6.95208	+	5.05098i	−1.08573	+	0.788830i	−0.107059	+	0.994253i	$0.534143\pi$
$42$	0.646084	−	0.382246i	0.0996929	−	0.0589818i
$43$			9.87461i			1.50586i	0.658099	+	0.752932i	$0.271361\pi$
$43$			9.87461i			1.50586i	−0.658099	+	0.752932i	$0.728639\pi$
$44$	5.49676	−	3.55146i	0.828667	−	0.535402i
$45$	3.95225	+	0.901994i	0.589166	+	0.134461i
$46$	−0.380474	+	0.342580i	−0.0560978	+	0.0505107i
$47$	−0.619491	+	1.39140i	−0.0903620	+	0.202956i	−0.953073	−	0.302741i	$-0.902098\pi$
$47$	−0.619491	+	1.39140i	−0.0903620	+	0.202956i	0.862711	+	0.505698i	$0.168765\pi$
$48$	3.06348	−	5.90298i	0.442175	−	0.852022i
$49$	6.93058	−	0.983420i	0.990082	−	0.140489i
$50$	−0.160673	−	0.494501i	−0.0227226	−	0.0699330i
$51$	1.68702	−	0.0757805i	0.236230	−	0.0106114i
$52$	−5.92004	+	0.622222i	−0.820962	+	0.0862866i
$53$	−4.58493	+	4.12829i	−0.629788	+	0.567064i	−0.920984	−	0.389599i	$-0.872613\pi$
$53$	−4.58493	+	4.12829i	−0.629788	+	0.567064i	0.291196	+	0.956663i	$0.405947\pi$
$54$	0.479479	−	0.703311i	0.0652489	−	0.0957085i
$55$	−3.75299	−	2.44967i	−0.506053	−	0.330313i
$56$	−1.31840	+	1.10777i	−0.176179	+	0.148031i
$57$	−0.682809	+	4.11203i	−0.0904402	+	0.544652i
$58$	−1.28678	−	0.572912i	−0.168963	−	0.0752270i
$59$	−5.72565	−	12.8600i	−0.745416	−	1.67423i	−0.738498	−	0.674256i	$-0.764464\pi$
$59$	−5.72565	−	12.8600i	−0.745416	−	1.67423i	−0.00691868	−	0.999976i	$-0.502202\pi$
$60$	−4.60993	−	0.276143i	−0.595140	−	0.0356499i
$61$	−5.28847	−	4.76176i	−0.677119	−	0.609681i	0.257098	−	0.966385i	$-0.417234\pi$
$61$	−5.28847	−	4.76176i	−0.677119	−	0.609681i	−0.934217	+	0.356704i	$0.883900\pi$
$62$	−0.639881	−	0.464900i	−0.0812649	−	0.0590424i
$63$	6.64297	−	4.34406i	0.836936	−	0.547301i
$64$	−2.27534	+	7.00276i	−0.284417	+	0.875345i
$65$	2.03829	+	3.53042i	0.252818	+	0.437894i
$66$	−0.766701	+	0.545642i	−0.0943744	+	0.0671639i
$67$	−1.55978	+	2.70162i	−0.190558	+	0.330056i	−0.945435	−	0.325810i	$-0.894363\pi$
$67$	−1.55978	+	2.70162i	−0.190558	+	0.330056i	0.754878	+	0.655866i	$0.227696\pi$
$68$	−1.88176	+	0.399981i	−0.228197	+	0.0485049i
$69$	−3.85626	+	3.79907i	−0.464239	+	0.457354i
$70$	0.526562	+	0.256388i	0.0629362	+	0.0306443i
$71$	8.43794	−	2.74165i	1.00140	−	0.325374i	0.237975	−	0.971271i	$-0.423516\pi$
$71$	8.43794	−	2.74165i	1.00140	−	0.325374i	0.763425	+	0.645897i	$0.223516\pi$
$72$	−0.820747	+	1.77171i	−0.0967260	+	0.208798i
$73$	−2.19828	−	4.93742i	−0.257289	−	0.577881i	0.738003	−	0.674797i	$-0.235769\pi$
$73$	−2.19828	−	4.93742i	−0.257289	−	0.577881i	−0.995293	+	0.0969158i	$0.969102\pi$
$74$	−0.0582826	−	0.554522i	−0.00677521	−	0.0644618i
$75$	−1.93175	−	5.14699i	−0.223060	−	0.594323i
$76$		−	4.74860i		−	0.544702i
$77$	−8.55334	+	1.95970i	−0.974743	+	0.223328i
$78$	0.846409	−	0.127584i	0.0958370	−	0.0144460i
$79$	0.556251	+	2.61696i	0.0625831	+	0.294430i	0.998297	−	0.0583282i	$-0.0185770\pi$
$79$	0.556251	+	2.61696i	0.0625831	+	0.294430i	−0.935714	+	0.352759i	$0.885244\pi$
$80$	5.16013	−	0.542352i	0.576921	−	0.0606368i
$81$	4.73086	−	7.65630i	0.525651	−	0.850700i
$82$	−0.941931	+	1.04612i	−0.104019	+	0.115525i
$83$	3.83565	+	11.8049i	0.421017	+	1.29576i	0.906757	+	0.421654i	$0.138550\pi$
$83$	3.83565	+	11.8049i	0.421017	+	1.29576i	−0.485739	+	0.874104i	$0.661450\pi$
$84$	−6.65485	+	6.12160i	−0.726103	+	0.667921i
$85$	0.774398	+	1.06587i	0.0839953	+	0.115610i
$86$	0.336318	+	1.58225i	0.0362661	+	0.170619i
$87$	−13.8636	−	5.44091i	−1.48633	−	0.583327i
$88$	1.52995	−	1.52284i	0.163094	−	0.162336i
$89$	9.72722	−	5.61602i	1.03108	−	0.595296i	0.113789	−	0.993505i	$-0.463701\pi$
$89$	9.72722	−	5.61602i	1.03108	−	0.595296i	0.917295	+	0.398208i	$0.130368\pi$
$90$	0.664006	+	0.00992141i	0.0699924	+	0.00104581i
$91$	7.74591	+	1.92581i	0.811992	+	0.201879i
$92$	3.62479	−	4.98909i	0.377910	−	0.520149i
$93$	−6.97940	−	4.60696i	−0.723730	−	0.477720i
$94$	−0.0518742	+	0.244049i	−0.00535042	+	0.0251717i
$95$	−2.97085	+	1.32271i	−0.304803	+	0.135707i
$96$	0.889624	−	3.22360i	0.0907968	−	0.329007i
$97$	4.09209	−	12.5942i	0.415489	−	1.27874i	−0.496324	−	0.868137i	$-0.665317\pi$
$97$	4.09209	−	12.5942i	0.415489	−	1.27874i	0.911813	−	0.410606i	$-0.134683\pi$
$98$	1.07702	−	0.393625i	0.108796	−	0.0397621i
$99$	−7.83949	+	6.12719i	−0.787898	+	0.615806i
$100$	3.13143	+	5.42380i	0.313143	+	0.542380i
$101$	−1.61053	−	1.78867i	−0.160253	−	0.177979i	0.657671	−	0.753305i	$-0.271542\pi$
$101$	−1.61053	−	1.78867i	−0.160253	−	0.177979i	−0.817924	+	0.575326i	$0.804875\pi$
$102$	0.267738	−	0.0696006i	0.0265100	−	0.00689149i
$103$	−0.989965	+	9.41889i	−0.0975442	+	0.928071i	0.830856	+	0.556488i	$0.187851\pi$
$103$	−0.989965	+	9.41889i	−0.0975442	+	0.928071i	−0.928400	+	0.371583i	$0.878815\pi$
$104$	−1.86742	+	0.606761i	−0.183115	+	0.0594978i
$105$	5.68352	+	2.45830i	0.554655	+	0.239905i
$106$	−0.594058	+	0.817651i	−0.0577000	+	0.0794173i
$107$	6.51418	+	2.90030i	0.629749	+	0.280382i	0.696688	−	0.717375i	$-0.254656\pi$
$107$	6.51418	+	2.90030i	0.629749	+	0.280382i	−0.0669382	+	0.997757i	$0.521323\pi$
$108$	−3.88787	+	9.48713i	−0.374111	+	0.912900i
$109$	10.1281	+	5.84745i	0.970094	+	0.560084i	0.899265	−	0.437404i	$-0.144102\pi$
$109$	10.1281	+	5.84745i	0.970094	+	0.560084i	0.0708293	+	0.997488i	$0.477435\pi$
$110$	−0.684791	−	0.264698i	−0.0652922	−	0.0252380i
$111$	−0.878721	−	5.82955i	−0.0834045	−	0.553316i
$112$	6.24913	−	8.00949i	0.590488	−	0.756826i
$113$	9.90899	+	13.6386i	0.932160	+	1.28301i	0.959011	+	0.283368i	$0.0914519\pi$
$113$	9.90899	+	13.6386i	0.932160	+	1.28301i	−0.0268514	+	0.999639i	$0.508548\pi$
$114$	0.0306418	+	0.682145i	0.00286986	+	0.0638887i
$115$	−4.13098	−	0.878067i	−0.385216	−	0.0818801i
$116$	16.5955	+	3.52749i	1.54086	+	0.327519i
$117$	8.87977	−	1.74922i	0.820935	−	0.161715i
$118$	−1.35544	−	1.86561i	−0.124779	−	0.171743i
$119$	2.55470	+	0.357309i	0.234189	+	0.0327545i
$120$	−1.50632	+	0.227057i	−0.137508	+	0.0207273i
$121$	10.4773	−	3.35041i	0.952486	−	0.304583i
$122$	−1.00957	−	0.582878i	−0.0914026	−	0.0527713i
$123$	−9.45291	+	11.4967i	−0.852340	+	1.03662i
$124$	8.70329	+	3.87496i	0.781579	+	0.347981i
$125$	6.49236	−	8.93597i	0.580694	−	0.799257i
$126$	0.916479	−	0.922320i	0.0816464	−	0.0821668i
$127$	6.70438	−	2.17839i	0.594918	−	0.193300i	0.00394520	−	0.999992i	$-0.498744\pi$
$127$	6.70438	−	2.17839i	0.594918	−	0.193300i	0.590972	+	0.806692i	$0.298744\pi$
$128$	−0.529711	+	5.03986i	−0.0468203	+	0.445465i
$129$	4.30313	+	16.5531i	0.378869	+	1.45742i
$130$	0.446846	+	0.496272i	0.0391910	+	0.0435260i
$131$	−4.16977	−	7.22225i	−0.364314	−	0.631011i	0.624352	−	0.781144i	$-0.285363\pi$
$131$	−4.16977	−	7.22225i	−0.364314	−	0.631011i	−0.988666	+	0.150133i	$0.952030\pi$
$132$	7.66676	−	8.34879i	0.667306	−	0.726669i
$133$	−2.17375	+	5.98470i	−0.188488	+	0.518939i
$134$	−0.157916	+	0.486017i	−0.0136419	+	0.0419855i
$135$	7.01836	−	0.210255i	0.604044	−	0.0180959i
$136$	−0.579716	+	0.258106i	−0.0497102	+	0.0221324i
$137$	2.34859	−	11.0492i	0.200654	−	0.944001i	−0.756404	−	0.654104i	$-0.773046\pi$
$137$	2.34859	−	11.0492i	0.200654	−	0.944001i	0.957058	−	0.289897i	$-0.0936210\pi$
$138$	−0.488513	+	0.740081i	−0.0415850	+	0.0629999i
$139$	−5.66003	+	7.79037i	−0.480078	+	0.660770i	−0.978520	−	0.206153i	$-0.933906\pi$
$139$	−5.66003	+	7.79037i	−0.480078	+	0.660770i	0.498442	+	0.866923i	$0.333906\pi$
$140$	−6.84600	−	1.70207i	−0.578592	−	0.143851i
$141$	−0.432134	+	2.60241i	−0.0363922	+	0.219162i
$142$	1.25867	−	0.726694i	0.105625	−	0.0609828i
$143$	−9.87875	−	1.58824i	−0.826103	−	0.132815i
$144$	2.56303	−	11.2304i	0.213586	−	0.935864i
$145$	−2.41574	−	11.3652i	−0.200616	−	0.943826i
$146$	−0.520403	−	0.716273i	−0.0430689	−	0.0592792i
$147$	11.1894	−	4.66873i	0.922887	−	0.385070i
$148$	2.07539	+	6.38738i	0.170596	+	0.525039i
$149$	−7.77320	+	8.63302i	−0.636806	+	0.707244i	−0.972020	−	0.234897i	$-0.924525\pi$
$149$	−7.77320	+	8.63302i	−0.636806	+	0.707244i	0.335214	+	0.942142i	$0.391191\pi$
$150$	−0.484834	−	0.758931i	−0.0395865	−	0.0619665i
$151$	−5.11522	+	0.537631i	−0.416271	+	0.0437518i	−0.310349	−	0.950623i	$-0.600446\pi$
$151$	−5.11522	+	0.537631i	−0.416271	+	0.0437518i	−0.105922	+	0.994374i	$0.533779\pi$
$152$	−0.325664	−	1.53213i	−0.0264148	−	0.124272i
$153$	2.79499	−	0.862199i	0.225961	−	0.0697046i
$154$	−1.30379	+	0.605328i	−0.105063	+	0.0487787i
$155$		−	6.52437i		−	0.524050i
$156$	−9.65283	+	3.62287i	−0.772845	+	0.290062i
$157$	−0.799686	−	7.60850i	−0.0638219	−	0.607225i	−0.978955	−	0.204074i	$-0.934582\pi$
$157$	−0.799686	−	7.60850i	−0.0638219	−	0.607225i	0.915134	−	0.403151i	$-0.132085\pi$
$158$	0.178261	+	0.400381i	0.0141817	+	0.0318526i
$159$	−5.88686	+	8.91840i	−0.466858	+	0.707275i
$160$	2.48127	−	0.806213i	0.196161	−	0.0637367i
$161$	−6.85218	+	4.62848i	−0.540028	+	0.364775i
$162$	0.497281	−	1.38793i	0.0390701	−	0.109046i
$163$	−1.59053	+	0.338078i	−0.124580	+	0.0264803i	−0.269780	−	0.962922i	$-0.586951\pi$
$163$	−1.59053	+	0.338078i	−0.124580	+	0.0264803i	0.145200	+	0.989402i	$0.453618\pi$
$164$	8.47794	−	14.6842i	0.662016	−	1.14665i
$165$	−7.35878	−	2.47100i	−0.572880	−	0.192367i
$166$	1.01667	+	1.76092i	0.0789085	+	0.136674i
$167$	−4.45847	+	13.7218i	−0.345007	+	1.06182i	0.616573	+	0.787298i	$0.288520\pi$
$167$	−4.45847	+	13.7218i	−0.345007	+	1.06182i	−0.961580	+	0.274524i	$0.911480\pi$
$168$	−1.72735	+	2.43152i	−0.133268	+	0.187596i
$169$	−3.15427	−	2.29171i	−0.242636	−	0.176285i
$170$	0.160387	+	0.144413i	0.0123012	+	0.0110760i
$171$	0.647315	+	7.19070i	0.0495014	+	0.549886i
$172$	−7.92495	−	17.7997i	−0.604272	−	1.35722i
$173$	6.84074	+	3.04569i	0.520092	+	0.231560i	0.649956	−	0.759972i	$-0.274787\pi$
$173$	6.84074	+	3.04569i	0.520092	+	0.231560i	−0.129864	+	0.991532i	$0.541454\pi$
$174$	−2.40674	−	0.399642i	−0.182454	−	0.0302968i
$175$	−1.46373	−	8.26911i	−0.110648	−	0.625086i
$176$	−6.96077	+	10.6642i	−0.524688	+	0.803843i
$177$	−15.2022	−	19.0626i	−1.14267	−	1.43283i
$178$	1.36736	−	1.23118i	0.102488	−	0.0922806i
$179$	0.486025	−	0.0510833i	0.0363272	−	0.00381814i	−0.0863474	−	0.996265i	$-0.527520\pi$
$179$	0.486025	−	0.0510833i	0.0363272	−	0.00381814i	0.122675	+	0.992447i	$0.460853\pi$
$180$	−7.84813	+	1.54600i	−0.584965	+	0.115232i
$181$	5.29269	+	16.2892i	0.393403	+	1.21077i	0.930198	+	0.367057i	$0.119635\pi$
$181$	5.29269	+	16.2892i	0.393403	+	1.21077i	−0.536796	+	0.843712i	$0.680365\pi$
$182$	1.30675	+	0.0447637i	0.0968628	+	0.00331810i
$183$	−10.9403	−	5.67771i	−0.808731	−	0.419708i
$184$	0.827373	−	1.85831i	0.0609948	−	0.136996i
$185$	3.41802	−	3.07760i	0.251298	−	0.226270i
$186$	−1.27525	−	0.500483i	−0.0935057	−	0.0366972i
$187$	−3.22882	−	0.176758i	−0.236115	−	0.0129258i
$188$		−	3.00528i		−	0.219182i
$189$	9.24280	−	10.1770i	0.672315	−	0.740265i
$190$	−0.430982	+	0.313127i	−0.0312668	+	0.0227166i
$191$	13.5489	+	1.42405i	0.980364	+	0.103040i	0.581132	−	0.813810i	$-0.302610\pi$
$191$	13.5489	+	1.42405i	0.980364	+	0.103040i	0.399232	+	0.916850i	$0.369277\pi$
$192$	−0.762579	+	12.7305i	−0.0550344	+	0.918746i
$193$	−1.40253	+	6.59840i	−0.100957	+	0.474964i	0.898403	+	0.439173i	$0.144728\pi$
$193$	−1.40253	+	6.59840i	−0.100957	+	0.474964i	−0.999359	+	0.0357909i	$0.988605\pi$
$194$	0.226751	−	2.15739i	0.0162798	−	0.154892i
$195$	4.95533	+	5.02992i	0.354858	+	0.360200i
$196$	−11.7036	+	7.33488i	−0.835974	+	0.523920i
$197$	13.8265			0.985094			0.492547	−	0.870286i	$-0.336066\pi$
$197$	13.8265			0.985094			0.492547	+	0.870286i	$0.336066\pi$
$198$	−1.04747	+	1.24879i	−0.0744404	+	0.0887477i
$199$	−7.00955	+	12.1409i	−0.496893	+	0.860645i	−0.999994	−	0.00358340i	$-0.998859\pi$
$199$	−7.00955	+	12.1409i	−0.496893	+	0.860645i	0.503100	+	0.864228i	$0.332193\pi$
$200$	1.38232	+	1.53522i	0.0977447	+	0.108556i
$201$	−1.43741	+	5.20854i	−0.101387	+	0.367382i
$202$	−0.318982	−	0.231754i	−0.0224435	−	0.0163061i
$203$	−19.3007	−	12.0426i	−1.35464	−	0.845224i
$204$	−2.98016	+	1.49053i	−0.208653	+	0.104358i
$205$	−11.5483	−	1.21378i	−0.806571	−	0.0847740i
$206$	0.162170	+	1.54295i	0.0112989	+	0.107502i
$207$	−4.80883	+	8.04898i	−0.334237	+	0.559443i
$208$	10.0317	−	5.79183i	0.695576	−	0.401591i
$209$	2.08379	−	7.70496i	0.144138	−	0.532963i
$210$	0.994422	+	0.200329i	0.0686216	+	0.0138240i
$211$	−19.1265	−	6.21459i	−1.31672	−	0.427830i	−0.435356	−	0.900259i	$-0.643377\pi$
$211$	−19.1265	−	6.21459i	−1.31672	−	0.427830i	−0.881369	+	0.472429i	$0.843377\pi$
$212$	4.95149	−	11.1212i	0.340070	−	0.763809i
$213$	12.9501	−	8.27299i	0.887324	−	0.566856i
$214$	1.14258	+	0.242862i	0.0781049	+	0.0166017i
$215$	−8.92851	+	9.91612i	−0.608919	+	0.676273i
$216$	−0.603777	+	3.32764i	−0.0410819	+	0.226417i
$217$	−9.19500	−	8.86771i	−0.624197	−	0.601979i
$218$	1.82202	+	0.592011i	0.123403	+	0.0400961i
$219$	−5.83667	−	7.31881i	−0.394406	−	0.494559i
$220$	8.73105	+	1.40372i	0.588647	+	0.0946387i
$221$	2.54727	+	1.47067i	0.171348	+	0.0989278i
$222$	−0.339349	−	0.904166i	−0.0227756	−	0.0606836i
$223$	−15.2366	+	11.0700i	−1.02032	+	0.741305i	−0.966348	−	0.257238i	$-0.917188\pi$
$223$	−15.2366	+	11.0700i	−1.02032	+	0.741305i	−0.0539702	+	0.998543i	$0.517188\pi$
$224$	2.23624	−	4.59271i	0.149415	−	0.306863i
$225$	−5.48121	−	7.78626i	−0.365414	−	0.519084i
$226$	2.05228	+	1.84788i	0.136515	+	0.122919i
$227$	12.5370	−	5.58182i	0.832108	−	0.370478i	0.0539476	−	0.998544i	$-0.482820\pi$
$227$	12.5370	−	5.58182i	0.832108	−	0.370478i	0.778161	+	0.628065i	$0.216153\pi$
$228$	−2.06933	−	7.96025i	−0.137045	−	0.527180i
$229$	−16.9945	+	3.61230i	−1.12303	+	0.238707i	−0.731756	−	0.681567i	$-0.761299\pi$
$229$	−16.9945	+	3.61230i	−1.12303	+	0.238707i	−0.391274	+	0.920274i	$0.627965\pi$
$230$	−0.691831			−0.0456180
$231$	−13.4843	+	7.01246i	−0.887200	+	0.461386i
$232$	5.59643			0.367424
$233$	19.7728	−	4.20285i	1.29536	−	0.275338i	0.491878	−	0.870664i	$-0.336311\pi$
$233$	19.7728	−	4.20285i	1.29536	−	0.275338i	0.803484	+	0.595326i	$0.202977\pi$
$234$	1.36327	−	0.582719i	0.0891196	−	0.0380936i
$235$	−1.88018	+	0.837111i	−0.122650	+	0.0546071i
$236$	20.6418	+	18.5860i	1.34367	+	1.20985i
$237$	2.07287	+	4.14449i	0.134648	+	0.269214i
$238$	0.421520	−	0.0297569i	0.0273231	−	0.00192886i
$239$	−0.755444	+	0.548862i	−0.0488656	+	0.0355029i	−0.611950	−	0.790896i	$-0.709615\pi$
$239$	−0.755444	+	0.548862i	−0.0488656	+	0.0355029i	0.563084	+	0.826399i	$0.309615\pi$
$240$	8.41377	−	3.15783i	0.543106	−	0.203837i
$241$	22.1368	+	12.7807i	1.42596	+	0.823278i	0.996799	−	0.0799509i	$-0.0254764\pi$
$241$	22.1368	+	12.7807i	1.42596	+	0.823278i	0.429160	+	0.903229i	$0.358810\pi$
$242$	1.56472	−	0.893697i	0.100584	−	0.0574490i
$243$	4.59406	−	14.8961i	0.294709	−	0.955587i
$244$	13.3545	+	4.33913i	0.854932	+	0.277784i
$245$	7.84891	+	5.27900i	0.501448	+	0.337263i
$246$	−1.12312	+	2.16412i	−0.0716073	+	0.137979i
$247$	−4.85803	+	5.39539i	−0.309109	+	0.343301i
$248$	3.07385	+	0.653366i	0.195189	+	0.0414888i
$249$	11.5742	+	18.1175i	0.733482	+	1.14815i
$250$	0.735950	−	1.65297i	0.0465456	−	0.104543i
$251$	−10.8409	−	3.52241i	−0.684270	−	0.222333i	−0.0538062	−	0.998551i	$-0.517135\pi$
$251$	−10.8409	−	3.52241i	−0.684270	−	0.222333i	−0.630464	+	0.776219i	$0.717135\pi$
$252$	−8.48810	+	13.1619i	−0.534700	+	0.829121i
$253$	8.07080	−	6.50453i	0.507407	−	0.408937i
$254$	1.00008	−	0.577396i	0.0627505	−	0.0362290i
$255$	1.76263	+	1.44929i	0.110380	+	0.0907578i
$256$	−1.45254	−	13.8200i	−0.0907838	−	0.863751i
$257$	−19.3157	−	2.03016i	−1.20488	−	0.126638i	−0.519272	−	0.854609i	$-0.673797\pi$
$257$	−19.3157	−	2.03016i	−1.20488	−	0.126638i	−0.685608	+	0.727971i	$0.740464\pi$
$258$	1.25329	+	2.50582i	0.0780265	+	0.156006i
$259$	0.308305	−	9.00010i	0.0191571	−	0.559239i
$260$	−6.50753	−	4.72800i	−0.403580	−	0.293218i
$261$	−25.6111	−	3.07934i	−1.58529	−	0.190606i
$262$	−0.914122	−	1.01524i	−0.0564746	−	0.0627214i
$263$	−13.4597	+	23.3128i	−0.829958	+	1.43753i	0.0681120	+	0.997678i	$0.478302\pi$
$263$	−13.4597	+	23.3128i	−0.829958	+	1.43753i	−0.898070	+	0.439852i	$0.855031\pi$
$264$	1.90110	−	3.21951i	0.117004	−	0.198147i
$265$	−8.33695			−0.512135
$266$	−0.144478	+	1.03299i	−0.00885849	+	0.0633366i
$267$	13.8588	−	13.6532i	0.848142	−	0.835564i
$268$	0.643416	−	6.12169i	0.0393029	−	0.373942i
$269$	0.603022	−	2.83699i	0.0367669	−	0.172975i	−0.955933	−	0.293585i	$-0.905152\pi$
$269$	0.603022	−	2.83699i	0.0367669	−	0.172975i	0.992700	+	0.120610i	$0.0384851\pi$
$270$	1.11742	−	0.272727i	0.0680040	−	0.0165977i
$271$	−9.17696	−	0.964538i	−0.557461	−	0.0585915i	−0.178391	−	0.983960i	$-0.557089\pi$
$271$	−9.17696	−	0.964538i	−0.557461	−	0.0585915i	−0.379070	+	0.925368i	$0.623756\pi$
$272$	3.02868	−	2.20047i	0.183641	−	0.133423i
$273$	13.8240	−	0.147193i	0.836664	−	0.00890850i
$274$		−	1.85046i		−	0.111790i
$275$	2.70090	+	10.1746i	0.162870	+	0.613554i
$276$	3.90222	−	9.94298i	0.234886	−	0.598497i
$277$	−6.75772	+	6.08468i	−0.406032	+	0.365593i	−0.846694	−	0.532080i	$-0.821410\pi$
$277$	−6.75772	+	6.08468i	−0.406032	+	0.365593i	0.440662	+	0.897673i	$0.354744\pi$
$278$	−0.641601	+	1.44106i	−0.0384806	+	0.0864289i
$279$	−13.7074	−	4.68135i	−0.820642	−	0.280265i
$280$	−2.32558	−	0.0796642i	−0.138980	−	0.00476085i
$281$	−8.36422	−	25.7424i	−0.498967	−	1.53566i	−0.810681	−	0.585488i	$-0.800903\pi$
$281$	−8.36422	−	25.7424i	−0.498967	−	1.53566i	0.311714	−	0.950176i	$-0.399097\pi$
$282$	0.0193925	+	0.431713i	0.00115480	+	0.0257082i
$283$	3.18290	−	0.334536i	0.189204	−	0.0198861i	−0.00945262	−	0.999955i	$-0.503009\pi$
$283$	3.18290	−	0.334536i	0.189204	−	0.0198861i	0.198656	+	0.980069i	$0.436342\pi$
$284$	−13.0097	+	11.7140i	−0.771983	+	0.695097i
$285$	−4.40373	+	3.51193i	−0.260855	+	0.208029i
$286$	−1.63701	+	0.0819687i	−0.0967984	+	0.00484691i
$287$	−17.4067	+	14.6257i	−1.02749	+	0.863328i
$288$	0.0865352	−	5.79151i	0.00509914	−	0.341268i
$289$	−14.6619	−	6.52788i	−0.862462	−	0.383993i
$290$	−0.774169	−	1.73881i	−0.0454608	−	0.102107i
$291$	1.37147	−	22.8953i	0.0803967	−	1.34214i
$292$	7.92514	+	7.13583i	0.463784	+	0.417593i
$293$	−5.19871	−	3.77708i	−0.303712	−	0.220660i	0.425482	−	0.904967i	$-0.360105\pi$
$293$	−5.19871	−	3.77708i	−0.303712	−	0.220660i	−0.729194	+	0.684307i	$0.760105\pi$
$294$	1.63392	−	1.12919i	0.0952920	−	0.0658557i
$295$	5.87817	−	18.0911i	0.342240	−	1.05331i
$296$	1.10767	+	1.91854i	0.0643821	+	0.111513i
$297$	−10.4715	+	13.6875i	−0.607619	+	0.794229i
$298$	−0.951504	+	1.64805i	−0.0551191	+	0.0954691i
$299$	−9.22257	+	1.96032i	−0.533355	+	0.113368i
$300$	7.61289	+	7.72749i	0.439531	+	0.446147i
$301$	1.83975	+	26.0609i	0.106042	+	1.50213i
$302$	−0.801323	+	0.260366i	−0.0461110	+	0.0149824i
$303$	−3.47924	−	2.29658i	−0.199877	−	0.131935i
$304$	3.75850	+	8.44172i	0.215565	+	0.484166i
$305$	−1.00517	−	9.56355i	−0.0575559	−	0.547608i
$306$	0.418487	−	0.233348i	0.0239233	−	0.0133396i
$307$		−	14.1560i		−	0.807925i	−0.914776	−	0.403962i	$-0.867633\pi$
$307$		−	14.1560i		−	0.807925i	0.914776	−	0.403962i	$-0.132367\pi$
$308$	13.8453	−	10.3971i	0.788907	−	0.592427i
$309$	2.44502	+	16.2206i	0.139093	+	0.922758i
$310$	−0.222212	−	1.04543i	−0.0126208	−	0.0593763i
$311$	−20.7109	+	2.17681i	−1.17441	+	0.123435i	−0.671568	−	0.740943i	$-0.734379\pi$
$311$	−20.7109	+	2.17681i	−1.17441	+	0.123435i	−0.502841	+	0.864379i	$0.667712\pi$
$312$	−2.86600	+	1.83091i	−0.162256	+	0.103655i
$313$	21.4171	−	23.7861i	1.21057	−	1.34447i	0.288483	−	0.957485i	$-0.406849\pi$
$313$	21.4171	−	23.7861i	1.21057	−	1.34447i	0.922085	−	0.386987i	$-0.126484\pi$
$314$	−0.387274	−	1.19191i	−0.0218551	−	0.0672632i
$315$	10.5988	+	1.64418i	0.597172	+	0.0926390i
$316$	−3.10294	−	4.27084i	−0.174554	−	0.240253i
$317$	−2.36711	−	11.1364i	−0.132950	−	0.625481i	−0.993279	−	0.115742i	$-0.963075\pi$
$317$	−2.36711	−	11.1364i	−0.132950	−	0.625481i	0.860329	−	0.509739i	$-0.170258\pi$
$318$	−0.639527	+	1.62953i	−0.0358629	+	0.0913797i
$319$	25.3795	+	13.0061i	1.42098	+	0.728200i
$320$	−8.61672	+	4.97487i	−0.481689	+	0.278103i
$321$	12.1838	+	2.02314i	0.680035	+	0.112921i
$322$	−0.940314	+	0.975019i	−0.0524016	+	0.0543357i
$323$	−1.37917	+	1.89827i	−0.0767392	+	0.105622i
$324$	−2.38310	+	17.5979i	−0.132394	+	0.977659i
$325$	1.99084	−	9.36615i	0.110432	−	0.519540i
$326$	−0.243344	+	0.108344i	−0.0134776	+	0.00600059i
$327$	19.5262	+	5.38870i	1.07980	+	0.297996i
$328$	1.72833	−	5.31926i	0.0954311	−	0.293707i
$329$	−1.37572	+	3.78757i	−0.0758457	+	0.208816i
$330$	−1.26329	−	0.145307i	−0.0695417	−	0.00799888i
$331$	16.4520	+	28.4957i	0.904284	+	1.56627i	0.821876	+	0.569667i	$0.192928\pi$
$331$	16.4520	+	28.4957i	0.904284	+	1.56627i	0.0824081	+	0.996599i	$0.473739\pi$
$332$	−16.3882	−	18.2009i	−0.899419	−	0.998906i
$333$	−4.01341	−	9.38935i	−0.219934	−	0.514533i
$334$	−0.247053	+	2.35055i	−0.0135181	+	0.128616i
$335$	−4.00911	+	1.30264i	−0.219041	+	0.0711708i
$336$	6.98529	−	16.1498i	0.381079	−	0.881045i
$337$	16.7364	−	23.0356i	0.911688	−	1.25483i	−0.0548993	−	0.998492i	$-0.517484\pi$
$337$	16.7364	−	23.0356i	0.911688	−	1.25483i	0.966587	−	0.256339i	$-0.0825162\pi$
$338$	−0.583475	−	0.259780i	−0.0317369	−	0.0141302i
$339$	22.5542	+	18.5447i	1.22497	+	1.00721i
$340$	−2.25133	−	1.29981i	−0.122096	−	0.0704920i
$341$	12.4213	+	10.1066i	0.672652	+	0.547302i
$342$	0.348629	+	1.13015i	0.0188517	+	0.0611115i
$343$	18.1078	−	3.88667i	0.977731	−	0.209861i
$344$	−3.77769	−	5.19954i	−0.203679	−	0.280341i
$345$	−7.30754	+	0.328253i	−0.393425	+	0.0176725i
$346$	1.19985	+	0.255037i	0.0645046	+	0.0137109i
$347$	20.0575	+	4.26335i	1.07674	+	0.228869i	0.711957	−	0.702223i	$-0.247809\pi$
$347$	20.0575	+	4.26335i	1.07674	+	0.228869i	0.364785	+	0.931092i	$0.381142\pi$
$348$	29.3568	−	1.31870i	1.57369	−	0.0706898i
$349$	11.3148	+	15.5735i	0.605668	+	0.833630i	0.996212	−	0.0869539i	$-0.0277133\pi$
$349$	11.3148	+	15.5735i	0.605668	+	0.833630i	−0.390545	+	0.920584i	$0.627713\pi$
$350$	−0.516177	−	1.27514i	−0.0275908	−	0.0681592i
$351$	14.1232	−	6.80187i	0.753840	−	0.363057i
$352$	−2.30872	+	5.97279i	−0.123055	+	0.318351i
$353$	17.4589	+	10.0799i	0.929245	+	0.536500i	0.886573	−	0.462590i	$-0.153080\pi$
$353$	17.4589	+	10.0799i	0.929245	+	0.536500i	0.0426720	+	0.999089i	$0.486413\pi$
$354$	−3.08517	−	2.53671i	−0.163975	−	0.134825i
$355$	10.9524	+	4.87632i	0.581292	+	0.258808i
$356$	−13.0269	+	17.9300i	−0.690423	+	0.950286i
$357$	4.43824	−	0.514310i	0.234896	−	0.0272202i
$358$	0.0761381	−	0.0247388i	0.00402402	−	0.00130748i
$359$	−0.553638	+	5.26751i	−0.0292199	+	0.278009i	0.970150	+	0.242507i	$0.0779696\pi$
$359$	−0.553638	+	5.26751i	−0.0292199	+	0.278009i	−0.999370	+	0.0355019i	$0.988697\pi$
$360$	−2.42616	+	1.03704i	−0.127870	+	0.0546570i
$361$	8.83809	+	9.81569i	0.465163	+	0.516615i
$362$	1.40286	+	2.42983i	0.0737329	+	0.127709i
$363$	16.1035	−	10.1822i	0.845215	−	0.534427i
$364$	−15.5082	+	2.74513i	−0.812848	+	0.143884i
$365$	2.25684	−	6.94584i	0.118128	−	0.363562i
$366$	−1.94639	−	0.537149i	−0.101739	−	0.0280773i
$367$	−1.92787	+	0.858343i	−0.100634	+	0.0448052i	−0.456436	−	0.889756i	$-0.650874\pi$
$367$	−1.92787	+	0.858343i	−0.100634	+	0.0448052i	0.355802	+	0.934561i	$0.384208\pi$
$368$	−2.49504	+	11.7382i	−0.130063	+	0.611898i
$369$	−10.8362	+	23.3917i	−0.564112	+	1.21772i
$370$	0.442865	−	0.609551i	0.0230234	−	0.0316890i
$371$	−11.3313	+	11.7495i	−0.588293	+	0.610005i
$372$	16.2783	+	2.70303i	0.843988	+	0.140145i
$373$	−7.32708	+	4.23029i	−0.379382	+	0.219036i	−0.677549	−	0.735477i	$-0.736958\pi$
$373$	−7.32708	+	4.23029i	−0.379382	+	0.219036i	0.298167	+	0.954514i	$0.403625\pi$
$374$	−0.523388	+	0.0816472i	−0.0270638	+	0.00422188i
$375$	6.98928	−	17.8089i	0.360925	−	0.919647i
$376$	−0.206105	−	0.969647i	−0.0106290	−	0.0500057i
$377$	−15.2472	−	20.9859i	−0.785269	−	1.08083i
$378$	1.13440	−	1.94550i	0.0583472	−	0.100066i
$379$	−5.24240	−	16.1344i	−0.269284	−	0.828770i	−0.990675	−	0.136243i	$-0.956497\pi$
$379$	−5.24240	−	16.1344i	−0.269284	−	0.828770i	0.721392	−	0.692527i	$-0.243503\pi$
$380$	4.29363	−	4.76856i	0.220259	−	0.244622i
$381$	10.2895	−	6.57332i	0.527147	−	0.336761i
$382$	2.21950	−	0.233279i	0.113559	−	0.0119356i
$383$	−6.53552	−	30.7472i	−0.333949	−	1.57111i	−0.749793	−	0.661672i	$-0.769847\pi$
$383$	−6.53552	−	30.7472i	−0.333949	−	1.57111i	0.415844	−	0.909436i	$-0.363486\pi$
$384$	1.30828	+	8.67933i	0.0667631	+	0.442915i
$385$	−10.3612	−	5.76590i	−0.528057	−	0.293857i
$386$			1.10506i			0.0562461i
$387$	14.4270	+	25.8734i	0.733364	+	1.31522i
$388$	2.73125	+	25.9861i	0.138658	+	1.31924i
$389$	10.2776	+	23.0840i	0.521097	+	1.17040i	0.962050	+	0.272873i	$0.0879738\pi$
$389$	10.2776	+	23.0840i	0.521097	+	1.17040i	−0.440953	+	0.897530i	$0.645360\pi$
$390$	0.965327	+	0.637194i	0.0488812	+	0.0322655i
$391$	−2.89804	+	0.941630i	−0.146560	+	0.0476203i
$392$	−3.27312	+	3.16923i	−0.165318	+	0.160070i
$393$	−10.1372	−	10.2898i	−0.511355	−	0.519053i
$394$	2.21547	−	0.470913i	0.111614	−	0.0237243i
$395$	−1.80763	+	3.13091i	−0.0909519	+	0.157533i
$396$	9.21384	−	17.3364i	0.463013	−	0.871185i
$397$	6.79368	+	11.7670i	0.340965	+	0.590569i	0.984612	−	0.174753i	$-0.0559128\pi$
$397$	6.79368	+	11.7670i	0.340965	+	0.590569i	−0.643647	+	0.765322i	$0.722580\pi$
$398$	−0.709665	+	2.18412i	−0.0355723	+	0.109480i
$399$	−1.03594	+	10.9796i	−0.0518618	+	0.549669i
$400$	−9.85974	−	7.16352i	−0.492987	−	0.358176i
$401$	1.54895	+	1.39468i	0.0773506	+	0.0696468i	0.706899	−	0.707314i	$-0.250093\pi$
$401$	1.54895	+	1.39468i	0.0773506	+	0.0696468i	−0.629549	+	0.776961i	$0.716760\pi$
$402$	−0.0529257	+	0.883543i	−0.00263970	+	0.0440671i
$403$	−5.92448	−	13.3066i	−0.295120	−	0.662849i
$404$	4.33861	+	1.93167i	0.215854	+	0.0961043i
$405$	11.6735	−	3.41090i	0.580060	−	0.169489i
$406$	−3.50279	−	1.27228i	−0.173841	−	0.0631420i
$407$	0.564550	+	11.2747i	0.0279837	+	0.558867i
$408$	−0.859321	+	0.685300i	−0.0425428	+	0.0339274i
$409$	−1.64892	+	1.48469i	−0.0815338	+	0.0734133i	−0.708890	−	0.705319i	$-0.750804\pi$
$409$	−1.64892	+	1.48469i	−0.0815338	+	0.0734133i	0.627356	+	0.778732i	$0.284137\pi$
$410$	−1.89178	+	0.198834i	−0.0934284	+	0.00981972i
$411$	−0.877988	−	19.5457i	−0.0433080	−	0.964118i
$412$	−5.77472	−	17.7728i	−0.284500	−	0.875601i
$413$	−17.5070	−	32.8732i	−0.861464	−	1.61758i
$414$	−0.496401	+	1.45351i	−0.0243968	+	0.0714360i
$415$	−6.82210	+	15.3227i	−0.334884	+	0.752161i
$416$	4.32852	−	3.89742i	0.212223	−	0.191087i
$417$	−6.09324	+	15.5258i	−0.298387	+	0.760300i
$418$	0.0714720	−	1.30557i	0.00349581	−	0.0638575i
$419$			9.49763i			0.463990i	0.972717	+	0.231995i	$0.0745253\pi$
$419$			9.49763i			0.463990i	−0.972717	+	0.231995i	$0.925475\pi$
$420$	−12.2179	+	0.130092i	−0.596173	+	0.00634783i
$421$	−6.64198	+	4.82568i	−0.323710	+	0.235189i	−0.737757	−	0.675066i	$-0.764115\pi$
$421$	−6.64198	+	4.82568i	−0.323710	+	0.235189i	0.414047	+	0.910256i	$0.364115\pi$
$422$	−3.27639	−	0.344362i	−0.159492	−	0.0167633i
$423$	0.409670	+	4.55082i	0.0199188	+	0.221269i
$424$	0.834883	−	3.92782i	0.0405455	−	0.190752i
$425$	0.323475	−	3.07766i	0.0156909	−	0.149289i
$426$	1.79328	−	1.76668i	0.0868845	−	0.0855960i
$427$	−14.8444	−	11.5819i	−0.718372	−	0.560485i
$428$	−14.0700			−0.680097
$429$	−17.2522	+	1.64252i	−0.832945	+	0.0793014i
$430$	−1.09292	+	1.89300i	−0.0527054	+	0.0912884i
$431$	6.54561	+	7.26963i	0.315291	+	0.350166i	0.879871	−	0.475212i	$-0.157629\pi$
$431$	6.54561	+	7.26963i	0.315291	+	0.350166i	−0.564580	+	0.825378i	$0.690962\pi$
$432$	−0.597443	−	19.9428i	−0.0287445	−	0.959497i
$433$	2.99010	+	2.17244i	0.143695	+	0.104401i	0.657310	−	0.753620i	$-0.271694\pi$
$433$	2.99010	+	2.17244i	0.143695	+	0.104401i	−0.513615	+	0.858021i	$0.671694\pi$
$434$	−1.77538	−	1.10774i	−0.0852209	−	0.0531732i
$435$	−9.00227	−	17.9991i	−0.431626	−	0.862991i
$436$	−22.9496	−	2.41210i	−1.09908	−	0.115518i
$437$	−0.786208	−	7.48027i	−0.0376094	−	0.357830i
$438$	−1.18451	−	0.973934i	−0.0565979	−	0.0465364i
$439$	−9.17272	+	5.29587i	−0.437790	+	0.252758i	−0.702660	−	0.711526i	$-0.748004\pi$
$439$	−9.17272	+	5.29587i	−0.437790	+	0.252758i	0.264870	+	0.964284i	$0.414671\pi$
$440$	2.91332	−	0.145877i	0.138887	−	0.00695439i
$441$	16.7227	−	12.7024i	0.796318	−	0.604878i
$442$	0.458250	+	0.148894i	0.0217967	+	0.00708218i
$443$	−1.72502	+	3.87447i	−0.0819584	+	0.184082i	−0.949876	−	0.312626i	$-0.898791\pi$
$443$	−1.72502	+	3.87447i	−0.0819584	+	0.184082i	0.867918	+	0.496708i	$0.165458\pi$
$444$	6.26251	+	9.80298i	0.297206	+	0.465229i
$445$	14.8461	+	3.15563i	0.703770	+	0.149591i
$446$	−2.06439	+	2.29274i	−0.0977519	+	0.108564i
$447$	−9.26842	+	17.8592i	−0.438381	+	0.844712i
$448$	−4.70033	+	18.9055i	−0.222070	+	0.893201i
$449$	34.2600	+	11.1318i	1.61683	+	0.525340i	0.971191	−	0.238302i	$-0.0765910\pi$
$449$	34.2600	+	11.1318i	1.61683	+	0.525340i	0.645639	+	0.763643i	$0.276591\pi$
$450$	−1.14347	−	1.06094i	−0.0539036	−	0.0500133i
$451$	20.1998	−	20.1059i	0.951172	−	0.946751i
$452$	−28.8075	−	16.6320i	−1.35499	−	0.782303i
$453$	−8.34053	+	3.13035i	−0.391873	+	0.147077i
$454$	1.81874	−	1.32139i	0.0853579	−	0.0620161i
$455$	6.03717	+	8.93766i	0.283027	+	0.419004i
$456$	−1.21359	−	2.42644i	−0.0568314	−	0.113628i
$457$	−15.3315	−	13.8046i	−0.717179	−	0.645751i	0.227489	−	0.973781i	$-0.426949\pi$
$457$	−15.3315	−	13.8046i	−0.717179	−	0.645751i	−0.944667	+	0.328030i	$0.893615\pi$
$458$	−2.60007	+	1.15763i	−0.121493	+	0.0540924i
$459$	4.30961	−	2.66333i	0.201155	−	0.124313i
$460$	8.15110	−	1.73257i	0.380047	−	0.0807815i
$461$	−14.5194			−0.676235			−0.338118	−	0.941104i	$-0.609790\pi$
$461$	−14.5194			−0.676235			−0.338118	+	0.941104i	$0.609790\pi$
$462$	−1.92181	+	1.58290i	−0.0894105	+	0.0736430i
$463$	3.95940			0.184009			0.0920044	−	0.995759i	$-0.470673\pi$
$463$	3.95940			0.184009			0.0920044	+	0.995759i	$0.470673\pi$
$464$	−32.2943	+	6.86437i	−1.49923	+	0.318670i
$465$	−2.84317	−	10.9370i	−0.131849	−	0.507192i
$466$	3.02514	−	1.34688i	0.140137	−	0.0623931i
$467$	3.31741	+	2.98701i	0.153511	+	0.138222i	0.742308	−	0.670059i	$-0.233731\pi$
$467$	3.31741	+	2.98701i	0.153511	+	0.138222i	−0.588796	+	0.808281i	$0.700398\pi$
$468$	−14.6026	+	10.2796i	−0.675006	+	0.475176i
$469$	−3.61321	+	7.42068i	−0.166842	+	0.342655i
$470$	−0.272759	+	0.198171i	−0.0125814	+	0.00914093i
$471$	−4.65615	−	12.4059i	−0.214544	−	0.571634i
$472$	7.93469	+	4.58110i	0.365224	+	0.210862i
$473$	−5.04792	−	32.3590i	−0.232104	−	1.48787i
$474$	0.473302	+	0.593490i	0.0217395	+	0.0272599i
$475$	7.26471	+	2.36045i	0.333328	+	0.108305i
$476$	−4.89180	+	1.40622i	−0.224215	+	0.0644539i
$477$	−5.98191	+	17.5156i	−0.273893	+	0.801983i
$478$	−0.102354	+	0.113676i	−0.00468158	+	0.00519943i
$479$	−29.0401	−	6.17266i	−1.32687	−	0.282036i	−0.510659	−	0.859783i	$-0.670599\pi$
$479$	−29.0401	−	6.17266i	−1.32687	−	0.282036i	−0.816216	+	0.577747i	$0.803932\pi$
$480$	3.80811	−	2.43276i	0.173815	−	0.111040i
$481$	4.17651	−	9.38059i	0.190432	−	0.427718i
$482$	3.98238	+	1.29395i	0.181392	+	0.0589379i
$483$	−9.46956	+	10.7449i	−0.430880	+	0.488910i
$484$	−16.1973	+	14.4481i	−0.736241	+	0.656730i
$485$	15.4968	−	8.94708i	0.703673	−	0.406266i
$486$	0.228781	−	2.54334i	0.0103777	−	0.115368i
$487$	1.26722	+	12.0568i	0.0574231	+	0.546345i	0.984981	+	0.172664i	$0.0552376\pi$
$487$	1.26722	+	12.0568i	0.0574231	+	0.546345i	−0.927558	+	0.373680i	$0.878096\pi$
$488$	4.60637	+	0.484149i	0.208521	+	0.0219164i
$489$	−2.51894	+	1.25985i	−0.113910	+	0.0569724i
$490$	1.43746	+	0.578552i	0.0649379	+	0.0261363i
$491$	28.5539	+	20.7456i	1.28862	+	0.936236i	0.999777	−	0.0211411i	$-0.00672993\pi$
$491$	28.5539	+	20.7456i	1.28862	+	0.936236i	0.288842	+	0.957377i	$0.406730\pi$
$492$	7.81281	−	28.3102i	0.352229	−	1.27632i
$493$	−5.60959	−	6.23009i	−0.252643	−	0.280589i
$494$	−0.594663	+	1.02999i	−0.0267552	+	0.0463413i
$495$	−13.4126	−	0.935429i	−0.602850	−	0.0420444i
$496$	−18.5391			−0.832430
$497$	21.7585	−	8.80781i	0.976001	−	0.395084i
$498$	2.47164	+	2.50884i	0.110757	+	0.112424i
$499$	1.05753	−	10.0617i	0.0473417	−	0.450426i	−0.945015	−	0.327026i	$-0.893954\pi$
$499$	1.05753	−	10.0617i	0.0473417	−	0.450426i	0.992357	−	0.123400i	$-0.0393798\pi$
$500$	−4.53133	+	21.3183i	−0.202647	+	0.953381i
$501$	−1.49426	+	24.9452i	−0.0667585	+	1.11447i
$502$	−1.85705	−	0.195184i	−0.0828842	−	0.00871148i
$503$	29.9992	−	21.7957i	1.33760	−	0.971822i	0.338069	−	0.941121i	$-0.390226\pi$
$503$	29.9992	−	21.7957i	1.33760	−	0.971822i	0.999529	−	0.0307003i	$-0.00977376\pi$
$504$	−1.83601	+	4.82877i	−0.0817825	+	0.215091i
$505$		−	3.25241i		−	0.144730i
$506$	1.07168	−	1.31713i	0.0476421	−	0.0585537i
$507$	−6.28628	−	2.46711i	−0.279184	−	0.109568i
$508$	−10.3369	+	9.30736i	−0.458625	+	0.412947i
$509$	7.86797	−	17.6718i	0.348742	−	0.783287i	−0.650966	−	0.759107i	$-0.725636\pi$
$509$	7.86797	−	17.6718i	0.348742	−	0.783287i	0.999708	−	0.0241797i	$-0.00769739\pi$
$510$	0.331795	+	0.172192i	0.0146921	+	0.00762480i
$511$	−6.72157	−	12.6212i	−0.297345	−	0.558329i
$512$	−3.83540	−	11.8042i	−0.169503	−	0.521675i
$513$	4.21866	+	11.7719i	0.186258	+	0.519744i
$514$	−3.16418	+	0.332569i	−0.139566	+	0.0146690i
$515$	−9.51058	+	8.56336i	−0.419086	+	0.377347i
$516$	−21.0416	−	26.3848i	−0.926304	−	1.16153i
$517$	1.31878	−	4.87629i	0.0579998	−	0.214459i
$518$	−0.257132	−	1.45263i	−0.0112977	−	0.0638247i
$519$	12.7946	+	2.12456i	0.561621	+	0.0932580i
$520$	−2.42389	−	1.07919i	−0.106295	−	0.0473255i
$521$	7.78791	+	17.4919i	0.341194	+	0.766335i	0.999903	+	0.0139370i	$0.00443642\pi$
$521$	7.78791	+	17.4919i	0.341194	+	0.766335i	−0.658708	+	0.752398i	$0.728897\pi$
$522$	−4.20865	+	0.378868i	−0.184208	+	0.0165826i
$523$	−24.4811	−	22.0429i	−1.07048	−	0.963867i	−0.0710472	−	0.997473i	$-0.522634\pi$
$523$	−24.4811	−	22.0429i	−1.07048	−	0.963867i	−0.999435	+	0.0336063i	$0.989301\pi$
$524$	13.3126	+	9.67217i	0.581564	+	0.422531i
$525$	−6.05720	−	13.2239i	−0.264358	−	0.577140i
$526$	−1.36269	+	4.19393i	−0.0594162	+	0.182864i
$527$	−2.35373	−	4.07679i	−0.102530	−	0.177588i
$528$	−7.02138	+	20.9101i	−0.305566	+	0.909995i
$529$	−6.61606	+	11.4593i	−0.287655	+	0.498232i
$530$	−1.33587	+	0.283947i	−0.0580263	+	0.0123339i
$531$	−33.7910	−	25.3305i	−1.46641	−	1.09925i
$532$	−0.884719	−	12.5324i	−0.0383574	−	0.543350i
$533$	−24.6553	+	8.01100i	−1.06794	+	0.346995i
$534$	1.75563	−	2.65973i	0.0759738	−	0.115098i
$535$	3.91914	+	8.80254i	0.169439	+	0.380567i
$536$	−0.212235	−	2.01928i	−0.00916714	−	0.0872195i
$537$	0.792480	−	0.297431i	0.0341980	−	0.0128351i
$538$		−	0.475122i		−	0.0204840i
$539$	−22.2087	+	6.76559i	−0.956597	+	0.291414i
$540$	−12.4824	+	6.01164i	−0.537156	+	0.258700i
$541$	−3.58791	−	16.8798i	−0.154256	−	0.725719i	−0.985481	−	0.169783i	$-0.945693\pi$
$541$	−3.58791	−	16.8798i	−0.154256	−	0.725719i	0.831225	−	0.555936i	$-0.187640\pi$
$542$	−1.50332	+	0.158005i	−0.0645729	+	0.00678689i
$543$	15.9708	+	24.9998i	0.685373	+	1.07284i
$544$	1.25958	−	1.39891i	0.0540043	−	0.0599778i
$545$	4.88345	+	15.0297i	0.209184	+	0.643803i
$546$	2.21006	−	0.494413i	0.0945818	−	0.0211589i
$547$	12.8467	+	17.6820i	0.549287	+	0.756029i	0.989915	−	0.141661i	$-0.0452442\pi$
$547$	12.8467	+	17.6820i	0.549287	+	0.756029i	−0.440628	+	0.897690i	$0.645244\pi$
$548$	4.63416	+	21.8020i	0.197961	+	0.931335i
$549$	−20.8138	−	4.75020i	−0.888313	−	0.202734i
$550$	0.779314	+	1.53834i	0.0332301	+	0.0655950i
$551$	17.9208	−	10.3466i	0.763450	−	0.440778i
$552$	0.577145	−	3.47570i	0.0245649	−	0.147936i
$553$	1.95562	+	6.80299i	0.0831613	+	0.289292i
$554$	−0.875581	+	1.20513i	−0.0371999	+	0.0512013i
$555$	4.38860	−	6.64858i	0.186286	−	0.282217i
$556$	3.95041	−	18.5852i	0.167535	−	0.788189i
$557$	39.8620	−	17.7477i	1.68901	−	0.751995i	0.689390	−	0.724391i	$-0.257879\pi$
$557$	39.8620	−	17.7477i	1.68901	−	0.751995i	0.999619	−	0.0276042i	$-0.00878781\pi$
$558$	−2.35584	−	0.283254i	−0.0997307	−	0.0119911i
$559$	−9.20554	+	28.3318i	−0.389353	+	1.19831i
$560$	13.5175	−	2.39276i	0.571218	−	0.101112i
$561$	−5.48961	+	1.11074i	−0.231772	+	0.0468955i
$562$	−2.21699	−	3.83994i	−0.0935182	−	0.161978i
$563$	7.03643	+	7.81474i	0.296550	+	0.329352i	0.872945	−	0.487819i	$-0.162208\pi$
$563$	7.03643	+	7.81474i	0.296550	+	0.329352i	−0.576395	+	0.817172i	$0.695541\pi$
$564$	−1.30963	−	5.03785i	−0.0551455	−	0.212132i
$565$	−2.38119	+	22.6555i	−0.100177	+	0.953124i
$566$	0.498616	−	0.162010i	0.0209584	−	0.00680979i
$567$	11.0591	−	21.0878i	0.464440	−	0.885604i
$568$	−3.39419	+	4.67171i	−0.142417	+	0.196021i
$569$	7.07546	+	3.15020i	0.296619	+	0.132063i	0.549650	−	0.835395i	$-0.314761\pi$
$569$	7.07546	+	3.15020i	0.296619	+	0.132063i	−0.253031	+	0.967458i	$0.581428\pi$
$570$	−0.586017	+	0.712718i	−0.0245456	+	0.0298525i
$571$	−7.97168	−	4.60245i	−0.333605	−	0.192607i	0.323836	−	0.946113i	$-0.395027\pi$
$571$	−7.97168	−	4.60245i	−0.333605	−	0.192607i	−0.657440	+	0.753507i	$0.728361\pi$
$572$	19.0819	−	5.06536i	0.797852	−	0.211793i
$573$	23.3331	−	3.51712i	0.974752	−	0.146930i
$574$	−2.29102	+	2.93640i	−0.0956255	+	0.122563i
$575$	5.83080	+	8.02541i	0.243161	+	0.334683i
$576$	4.26933	+	21.6729i	0.177889	+	0.903038i
$577$	−10.6514	−	2.26403i	−0.443424	−	0.0942526i	−0.0192116	−	0.999815i	$-0.506116\pi$
$577$	−10.6514	−	2.26403i	−0.443424	−	0.0942526i	−0.424212	+	0.905563i	$0.639449\pi$
$578$	−2.57167	−	0.546625i	−0.106967	−	0.0227366i
$579$	0.524318	+	11.6723i	0.0217899	+	0.485085i
$580$	13.4758	+	18.5478i	0.559551	+	0.770155i
$581$	12.3224	+	30.4407i	0.511218	+	1.26289i
$582$	−0.560031	−	3.71532i	−0.0232140	−	0.154005i
$583$	12.9144	−	15.8722i	0.534859	−	0.657359i
$584$	3.04641	+	1.75885i	0.126061	+	0.0727816i
$585$	10.4987	+	6.27241i	0.434068	+	0.259332i
$586$	−0.961655	−	0.428156i	−0.0397256	−	0.0176870i
$587$	−15.1422	+	20.8415i	−0.624986	+	0.860220i	−0.997704	−	0.0677247i	$-0.978426\pi$
$587$	−15.1422	+	20.8415i	−0.624986	+	0.860220i	0.372718	+	0.927945i	$0.378426\pi$
$588$	−16.4228	+	17.3959i	−0.677266	+	0.717395i
$589$	11.0509	−	3.59066i	0.455346	−	0.147951i
$590$	0.325721	−	3.09903i	0.0134097	−	0.127585i
$591$	23.1778	−	6.02525i	0.953406	−	0.247846i
$592$	−8.74505	−	9.71236i	−0.359419	−	0.399176i
$593$	−16.7107	−	28.9438i	−0.686226	−	1.18858i	−0.973050	−	0.230595i	$-0.925933\pi$
$593$	−16.7107	−	28.9438i	−0.686226	−	1.18858i	0.286824	−	0.957983i	$-0.407400\pi$
$594$	−1.21172	+	2.54985i	−0.0497173	+	0.104622i
$595$	2.24236	+	2.66874i	0.0919279	+	0.109408i
$596$	7.08329	−	21.8001i	0.290143	−	0.892968i
$597$	−6.45962	+	23.4068i	−0.264375	+	0.957976i
$598$	−1.41101	+	0.628220i	−0.0577003	+	0.0256898i
$599$	9.16695	−	43.1271i	0.374551	−	1.76213i	−0.237578	−	0.971368i	$-0.576354\pi$
$599$	9.16695	−	43.1271i	0.374551	−	1.76213i	0.612129	−	0.790758i	$-0.290313\pi$
$600$	2.98624	+	1.97116i	0.121913	+	0.0804723i
$601$	18.1828	−	25.0265i	0.741692	−	1.02085i	−0.256827	−	0.966457i	$-0.582677\pi$
$601$	18.1828	−	25.0265i	0.741692	−	1.02085i	0.998520	−	0.0543947i	$-0.0173229\pi$
$602$	1.18240	+	4.11319i	0.0481909	+	0.167641i
$603$	−0.139819	+	9.35765i	−0.00569389	+	0.381073i
$604$	8.78909	−	5.07439i	0.357623	−	0.206474i
$605$	13.5508	+	6.10900i	0.550918	+	0.248366i
$606$	−0.635713	−	0.249492i	−0.0258241	−	0.0101349i
$607$	−1.77680	−	8.35916i	−0.0721179	−	0.339288i	0.927265	−	0.374405i	$-0.122153\pi$
$607$	−1.77680	−	8.35916i	−0.0721179	−	0.339288i	−0.999383	+	0.0351169i	$0.988820\pi$
$608$	2.73112	+	3.75906i	0.110761	+	0.152450i
$609$	−37.6023	−	11.7766i	−1.52372	−	0.477212i
$610$	−0.486787	−	1.49817i	−0.0197094	−	0.0606593i
$611$	−3.07454	+	3.41462i	−0.124382	+	0.138141i
$612$	−4.34621	+	3.79732i	−0.175685	+	0.153498i
$613$	−29.8938	+	3.14197i	−1.20740	+	0.126903i	−0.686767	−	0.726878i	$-0.740971\pi$
$613$	−29.8938	+	3.14197i	−1.20740	+	0.126903i	−0.520633	+	0.853781i	$0.674304\pi$
$614$	−0.482137	−	2.26827i	−0.0194575	−	0.0915401i
$615$	−19.8878	+	2.99780i	−0.801954	+	0.120883i
$616$	3.75411	−	4.30411i	0.151257	−	0.173418i
$617$		−	2.20330i		−	0.0887014i	−0.999016	−	0.0443507i	$-0.985878\pi$
$617$		−	2.20330i		−	0.0887014i	0.999016	−	0.0443507i	$-0.0141219\pi$
$618$	0.944233	+	2.51582i	0.0379826	+	0.101201i
$619$	−1.74605	−	16.6125i	−0.0701795	−	0.667713i	−0.971900	−	0.235394i	$-0.924362\pi$
$619$	−1.74605	−	16.6125i	−0.0701795	−	0.667713i	0.901721	−	0.432319i	$-0.142305\pi$
$620$	5.23619	+	11.7607i	0.210290	+	0.472320i
$621$	−4.55365	+	15.5884i	−0.182732	+	0.625540i
$622$	−3.24446	+	1.05419i	−0.130091	+	0.0422692i
$623$	24.6256	−	16.6340i	0.986604	−	0.666427i
$624$	14.2926	−	14.0806i	0.572162	−	0.563677i
$625$	−0.923841	+	0.196368i	−0.0369536	+	0.00785473i
$626$	2.62163	−	4.54080i	0.104781	−	0.181487i
$627$	0.135477	−	13.8242i	0.00541045	−	0.552084i
$628$	7.54776	+	13.0731i	0.301189	+	0.521674i
$629$	1.02549	−	3.15614i	0.0408891	−	0.125844i
$630$	1.75428	−	0.0975276i	0.0698923	−	0.00388559i
$631$	−5.50651	−	4.00072i	−0.219211	−	0.159266i	0.472761	−	0.881191i	$-0.343258\pi$
$631$	−5.50651	−	4.00072i	−0.219211	−	0.159266i	−0.691971	+	0.721925i	$0.743258\pi$
$632$	−1.29406	−	1.16517i	−0.0514748	−	0.0463481i
$633$	−34.7706	−	2.08282i	−1.38201	−	0.0827847i
$634$	−0.758584	−	1.70381i	−0.0301272	−	0.0676669i
$635$	8.70223	+	3.87448i	0.345338	+	0.153754i
$636$	3.45397	−	20.8006i	0.136959	−	0.824799i
$637$	20.8017	+	3.63941i	0.824192	+	0.144199i
$638$	4.50964	+	1.21962i	0.178538	+	0.0482853i
$639$	18.1035	−	19.5116i	0.716162	−	0.771869i
$640$	−5.08893	+	4.58209i	−0.201157	+	0.181123i
$641$	−34.2498	+	3.59980i	−1.35279	+	0.142183i	−0.753023	−	0.657994i	$-0.771405\pi$
$641$	−34.2498	+	3.59980i	−1.35279	+	0.142183i	−0.599763	+	0.800178i	$0.704738\pi$
$642$	2.02117	−	0.0907906i	0.0797694	−	0.00358322i
$643$	6.56159	+	20.1945i	0.258764	+	0.796393i	0.993065	+	0.117569i	$0.0375102\pi$
$643$	6.56159	+	20.1945i	0.258764	+	0.796393i	−0.734301	+	0.678824i	$0.762490\pi$
$644$	8.63695	−	13.8425i	0.340344	−	0.545469i
$645$	−10.6460	+	20.5136i	−0.419184	+	0.807721i
$646$	−0.156338	+	0.351141i	−0.00615103	+	0.0138154i
$647$	25.7986	−	23.2292i	1.01425	−	0.913233i	0.0180049	−	0.999838i	$-0.494269\pi$
$647$	25.7986	−	23.2292i	1.01425	−	0.913233i	0.996243	+	0.0866053i	$0.0276019\pi$
$648$	0.437976	+	5.84135i	0.0172053	+	0.229470i
$649$	25.3370	+	39.2152i	0.994563	+	1.53933i
$650$		−	1.56858i		−	0.0615249i
$651$	−19.2782	−	10.8583i	−0.755574	−	0.425569i
$652$	2.59573	−	1.88591i	0.101657	−	0.0738579i
$653$	−21.5137	−	2.26118i	−0.841895	−	0.0884868i	−0.326244	−	0.945285i	$-0.605783\pi$
$653$	−21.5137	−	2.26118i	−0.841895	−	0.0884868i	−0.515651	+	0.856799i	$0.672450\pi$
$654$	3.31231	+	0.198413i	0.129521	+	0.00775855i
$655$	2.34298	−	11.0229i	0.0915479	−	0.430699i
$656$	−3.44897	+	32.8148i	−0.134660	+	1.28120i
$657$	−12.9736	−	9.72529i	−0.506148	−	0.379420i
$658$	−0.0914364	+	0.653755i	−0.00356456	+	0.0254860i
$659$	13.0694			0.509113			0.254557	−	0.967058i	$-0.418070\pi$
$659$	13.0694			0.509113			0.254557	+	0.967058i	$0.418070\pi$
$660$	15.2479	−	1.45169i	0.593523	−	0.0565070i
$661$	0.301430	−	0.522093i	0.0117243	−	0.0203071i	−0.860104	−	0.510119i	$-0.829601\pi$
$661$	0.301430	−	0.522093i	0.0117243	−	0.0203071i	0.871828	+	0.489812i	$0.162935\pi$
$662$	3.60671	+	4.00565i	0.140179	+	0.155684i
$663$	4.91096	+	1.35529i	0.190726	+	0.0526351i
$664$	−6.53585	−	4.74857i	−0.253640	−	0.184280i
$665$	−7.59418	+	4.04437i	−0.294490	+	0.156834i
$666$	−0.962877	−	1.36780i	−0.0373107	−	0.0530013i
$667$	26.7262	+	2.80904i	1.03484	+	0.108766i
$668$	−2.97579	−	28.3127i	−0.115137	−	1.09545i
$669$	−20.7176	+	25.1969i	−0.800988	+	0.974167i
$670$	−0.598031	+	0.345274i	−0.0231040	+	0.0133391i
$671$	19.7645	+	12.9008i	0.763000	+	0.498029i
$672$	1.74729	−	8.67342i	0.0674030	−	0.334584i
$673$	12.2164	+	3.96934i	0.470907	+	0.153007i	0.534851	−	0.844947i	$-0.320368\pi$
$673$	12.2164	+	3.96934i	0.470907	+	0.153007i	−0.0639439	+	0.997953i	$0.520368\pi$
$674$	1.89717	−	4.26112i	0.0730764	−	0.164132i
$675$	−12.5814	−	10.6638i	−0.484259	−	0.410450i
$676$	7.52504	+	1.59950i	0.289424	+	0.0615191i
$677$	−27.0628	+	30.0563i	−1.04011	+	1.15516i	−0.0524359	+	0.998624i	$0.516699\pi$
$677$	−27.0628	+	30.0563i	−1.04011	+	1.15516i	−0.987673	+	0.156533i	$0.949968\pi$
$678$	4.24556	+	2.20333i	0.163050	+	0.0846182i
$679$	8.45334	−	34.0007i	0.324409	−	1.30483i
$680$	−0.815530	−	0.264982i	−0.0312741	−	0.0101616i
$681$	18.5837	−	14.8203i	0.712130	−	0.567916i
$682$	2.33454	+	1.19637i	0.0893942	+	0.0458112i
$683$	4.46231	+	2.57632i	0.170746	+	0.0985801i	0.582937	−	0.812517i	$-0.301903\pi$
$683$	4.46231	+	2.57632i	0.170746	+	0.0985801i	−0.412192	+	0.911097i	$0.635237\pi$
$684$	−6.93779	−	12.4423i	−0.265273	−	0.475742i
$685$	12.3491	−	8.97213i	0.471834	−	0.342807i
$686$	2.76912	−	1.23951i	0.105726	−	0.0473247i
$687$	−26.9143	+	13.4612i	−1.02685	+	0.513578i
$688$	28.1768	+	25.3705i	1.07423	+	0.967242i
$689$	−17.0034	+	7.57041i	−0.647779	+	0.288410i
$690$	−1.15974	+	0.301484i	−0.0441505	+	0.0114773i
$691$	21.9406	−	4.66361i	0.834659	−	0.177412i	0.229291	−	0.973358i	$-0.426359\pi$
$691$	21.9406	−	4.66361i	0.834659	−	0.177412i	0.605368	+	0.795946i	$0.293026\pi$
$692$	−14.7753			−0.561673
$693$	−19.5483	+	17.6314i	−0.742577	+	0.669760i
$694$	3.35910			0.127510
$695$	−12.7278	+	2.70537i	−0.482792	+	0.102621i
$696$	9.38149	−	2.43880i	0.355604	−	0.0924423i
$697$	−7.65393	+	3.40775i	−0.289913	+	0.129078i
$698$	2.34344	+	2.11004i	0.0887004	+	0.0798662i
$699$	31.3144	−	15.6619i	1.18442	−	0.592389i
$700$	9.27493	+	13.7310i	0.350560	+	0.518982i
$701$	−20.3692	+	14.7991i	−0.769333	+	0.558953i	−0.901759	−	0.432240i	$-0.857723\pi$
$701$	−20.3692	+	14.7991i	−0.769333	+	0.558953i	0.132426	+	0.991193i	$0.457723\pi$
$702$	2.03136	−	1.57091i	0.0766686	−	0.0592903i
$703$	7.09392	+	4.09567i	0.267552	+	0.154471i
$704$	3.87643	−	24.1112i	0.146098	−	0.908723i
$705$	−2.78702	+	2.22262i	−0.104965	+	0.0837086i
$706$	3.14083	+	1.02052i	0.118207	+	0.0384077i
$707$	−4.58372	−	4.42057i	−0.172389	−	0.166253i
$708$	42.7020	+	22.1611i	1.60484	+	0.832865i
$709$	3.96449	−	4.40302i	0.148890	−	0.165359i	−0.664086	−	0.747656i	$-0.731179\pi$
$709$	3.96449	−	4.40302i	0.148890	−	0.165359i	0.812976	+	0.582297i	$0.197846\pi$
$710$	1.92103	+	0.408327i	0.0720950	+	0.0153243i
$711$	5.28090	+	6.04424i	0.198049	+	0.226677i
$712$	−2.97344	+	6.67846i	−0.111434	+	0.250286i
$713$	14.3515	+	4.66308i	0.537467	+	0.174634i
$714$	0.693641	−	0.233571i	0.0259589	−	0.00874119i
$715$	−8.48421	−	10.5272i	−0.317291	−	0.393694i
$716$	−0.835100	+	0.482145i	−0.0312091	+	0.0180186i
$717$	−1.02720	+	1.24928i	−0.0383613	+	0.0466553i
$718$	0.0906937	+	0.862892i	0.00338466	+	0.0322029i
$719$	−6.58510	−	0.692122i	−0.245583	−	0.0258118i	−0.0190627	−	0.999818i	$-0.506068\pi$
$719$	−6.58510	−	0.692122i	−0.245583	−	0.0258118i	−0.226520	+	0.974007i	$0.572735\pi$
$720$	12.7282	−	8.96011i	0.474351	−	0.333924i
$721$	−0.857853	+	25.0426i	−0.0319481	+	0.932636i
$722$	1.75048	+	1.27180i	0.0651460	+	0.0473313i
$723$	42.6783	+	11.7780i	1.58722	+	0.438029i
$724$	−22.6135	−	25.1149i	−0.840426	−	0.933387i
$725$	−13.6459	+	23.6354i	−0.506796	+	0.877797i
$726$	2.23354	−	2.18000i	0.0828945	−	0.0809076i
$727$	0.0198007			0.000734366			0.000367183	−	1.00000i	$-0.499883\pi$
$727$	0.0198007			0.000734366			0.000367183		1.00000i	$0.499883\pi$
$728$	−4.81541	+	1.94927i	−0.178471	+	0.0722449i
$729$	1.20979	−	26.9729i	0.0448069	−	0.998996i
$730$	0.125056	−	1.18983i	0.00462852	−	0.0440375i
$731$	−2.00169	+	9.41720i	−0.0740351	+	0.348308i
$732$	24.2774	+	1.45426i	0.897320	+	0.0537510i
$733$	−39.9606	−	4.20003i	−1.47598	−	0.155132i	−0.667920	−	0.744233i	$-0.732815\pi$
$733$	−39.9606	−	4.20003i	−1.47598	−	0.155132i	−0.808059	+	0.589101i	$0.799482\pi$
$734$	−0.279677	+	0.203197i	−0.0103231	+	0.00750014i
$735$	15.4579	+	5.42899i	0.570172	+	0.200251i
$736$			6.03420i			0.222423i
$737$	3.73032	−	9.65055i	0.137408	−	0.355483i
$738$	−0.939644	+	4.11722i	−0.0345888	+	0.151557i
$739$	28.1646	−	25.3596i	1.03605	−	0.932867i	0.0382603	−	0.999268i	$-0.487818\pi$
$739$	28.1646	−	25.3596i	1.03605	−	0.932867i	0.997793	+	0.0664012i	$0.0211517\pi$
$740$	−3.69129	+	8.29077i	−0.135694	+	0.304775i
$741$	−5.79250	+	11.1615i	−0.212793	+	0.410028i
$742$	−1.41549	+	2.26861i	−0.0519643	+	0.0832833i
$743$	−11.4046	−	35.0999i	−0.418396	−	1.28769i	−0.909178	−	0.416407i	$-0.863289\pi$
$743$	−11.4046	−	35.0999i	−0.418396	−	1.28769i	0.490782	−	0.871282i	$-0.336711\pi$
$744$	5.43752	−	0.244252i	0.199349	−	0.00895471i
$745$	−15.6118	+	1.64086i	−0.571971	+	0.0601165i
$746$	−1.02997	+	0.927390i	−0.0377099	+	0.0339542i
$747$	27.2973	+	25.3273i	0.998758	+	0.926676i
$748$	5.96205	−	2.27270i	0.217994	−	0.0830981i
$749$	17.7325	+	6.44075i	0.647930	+	0.235340i
$750$	0.513372	−	3.09164i	0.0187457	−	0.112891i
$751$	25.5477	+	11.3746i	0.932247	+	0.415063i	0.815931	−	0.578149i	$-0.196225\pi$
$751$	25.5477	+	11.3746i	0.932247	+	0.415063i	0.116316	+	0.993212i	$0.462891\pi$
$752$	2.37866	+	5.34257i	0.0867409	+	0.194823i
$753$	−19.7079	−	1.18054i	−0.718197	−	0.0430212i
$754$	−3.15788	−	2.84336i	−0.115003	−	0.103549i
$755$	−5.62284	−	4.08523i	−0.204636	−	0.148677i
$756$	−8.49325	+	25.7626i	−0.308896	+	0.936978i
$757$	−15.8523	+	48.7884i	−0.576162	+	1.77324i	0.0560274	+	0.998429i	$0.482157\pi$
$757$	−15.8523	+	48.7884i	−0.576162	+	1.77324i	−0.632189	+	0.774814i	$0.717843\pi$
$758$	−1.38953	−	2.40674i	−0.0504701	−	0.0874168i
$759$	10.6948	−	14.4208i	0.388198	−	0.523444i
$760$	1.05830	−	1.83303i	0.0383886	−	0.0664909i
$761$	11.6955	−	2.48596i	0.423962	−	0.0901159i	0.00901050	−	0.999959i	$-0.497132\pi$
$761$	11.6955	−	2.48596i	0.423962	−	0.0901159i	0.414952	+	0.909843i	$0.363798\pi$
$762$	1.42485	−	1.40372i	0.0516169	−	0.0508514i
$763$	27.8193	+	13.5455i	1.00713	+	0.490381i
$764$	−25.5658	+	8.30683i	−0.924938	+	0.300531i
$765$	3.58633	+	1.66137i	0.129664	+	0.0600671i
$766$	−2.09443	−	4.70416i	−0.0756748	−	0.169968i
$767$	−4.43908	−	42.2351i	−0.160286	−	1.52502i
$768$	−8.45739	−	22.5340i	−0.305180	−	0.813125i
$769$		−	30.4338i		−	1.09747i	−0.835996	−	0.548735i	$-0.815110\pi$
$769$		−	30.4338i		−	1.09747i	0.835996	−	0.548735i	$-0.184890\pi$
$770$	−1.85660	−	0.571003i	−0.0669074	−	0.0205775i
$771$	−33.2643	+	5.01411i	−1.19798	+	0.180579i
$772$	−2.76743	−	13.0197i	−0.0996020	−	0.468591i
$773$	23.2637	−	2.44512i	0.836739	−	0.0879448i	0.323540	−	0.946215i	$-0.395127\pi$
$773$	23.2637	−	2.44512i	0.836739	−	0.0879448i	0.513199	+	0.858270i	$0.328460\pi$
$774$	3.19292	+	3.65444i	0.114767	+	0.131356i
$775$	−10.2544	+	11.3887i	−0.368349	+	0.409093i
$776$	2.66338	+	8.19704i	0.0956098	+	0.294257i
$777$	−3.40522	−	15.2215i	−0.122161	−	0.546069i
$778$	2.43304	+	3.34880i	0.0872288	+	0.120060i
$779$	−4.29970	−	20.2285i	−0.154053	−	0.724761i
$780$	−12.9692	−	5.08988i	−0.464370	−	0.182247i
$781$	−26.2495	+	13.2979i	−0.939282	+	0.475835i
$782$	−0.432294	+	0.249585i	−0.0154588	+	0.00892515i
$783$	−44.2746	+	5.99871i	−1.58225	+	0.214377i
$784$	15.0004	−	22.3028i	0.535727	−	0.796528i
$785$	6.07648	−	8.36355i	0.216879	−	0.298508i
$786$	−1.97479	−	1.30352i	−0.0704384	−	0.0464950i
$787$	−4.97140	+	23.3886i	−0.177211	+	0.833713i	0.796269	+	0.604942i	$0.206804\pi$
$787$	−4.97140	+	23.3886i	−0.177211	+	0.833713i	−0.973480	+	0.228770i	$0.926529\pi$
$788$	−24.9232	+	11.0965i	−0.887853	+	0.395298i
$789$	−12.4037	+	44.9455i	−0.441583	+	1.60010i
$790$	−0.183010	+	0.563245i	−0.00651119	+	0.0200394i
$791$	28.6927	+	34.1485i	1.02019	+	1.21418i
$792$	1.78388	−	6.22544i	0.0633874	−	0.221211i
$793$	−10.7343	−	18.5924i	−0.381186	−	0.660234i
$794$	1.48935	+	1.65409i	0.0528551	+	0.0587016i
$795$	−13.9755	+	3.63305i	−0.495661	+	0.128851i
$796$	2.89146	−	27.5104i	0.102485	−	0.975082i
$797$	22.3127	−	7.24983i	0.790355	−	0.256802i	0.114100	−	0.993469i	$-0.463602\pi$
$797$	22.3127	−	7.24983i	0.790355	−	0.256802i	0.676255	+	0.736667i	$0.263602\pi$
$798$	0.207961	+	1.79460i	0.00736173	+	0.0635280i
$799$	−0.872846	+	1.20137i	−0.0308791	+	0.0425014i
$800$	−5.59833	−	2.49254i	−0.197931	−	0.0881245i
$801$	17.2821	−	28.9267i	0.610635	−	1.02207i
$802$	0.295695	+	0.170720i	0.0104414	+	0.00602832i
$803$	9.72777	+	15.0561i	0.343286	+	0.531319i
$804$	−1.58911	−	10.5424i	−0.0560437	−	0.371802i
$805$	−11.0660	−	1.54773i	−0.390025	−	0.0545503i
$806$	−1.40251	−	1.93039i	−0.0494014	−	0.0679953i
$807$	−0.225431	−	5.01853i	−0.00793555	−	0.176661i
$808$	1.53232	+	0.325704i	0.0539068	+	0.0114582i
$809$	50.1366	+	10.6569i	1.76271	+	0.374675i	0.971531	−	0.236912i	$-0.0761353\pi$
$809$	50.1366	+	10.6569i	1.76271	+	0.374675i	0.791177	+	0.611587i	$0.209469\pi$
$810$	1.75432	−	0.944129i	0.0616406	−	0.0331733i
$811$	−28.9257	−	39.8128i	−1.01572	−	1.39802i	−0.915162	−	0.403087i	$-0.867937\pi$
$811$	−28.9257	−	39.8128i	−1.01572	−	1.39802i	−0.100558	−	0.994931i	$-0.532063\pi$
$812$	44.4558	+	6.21775i	1.56009	+	0.218200i
$813$	−15.8040	+	2.38222i	−0.554270	+	0.0835482i
$814$	0.474464	+	1.78737i	0.0166300	+	0.0626472i
$815$	−1.90291	−	1.09864i	−0.0666559	−	0.0384838i
$816$	4.11817	−	5.00855i	0.144165	−	0.175334i
$817$	−21.7096	−	9.66575i	−0.759524	−	0.338162i
$818$	−0.213646	+	0.294059i	−0.00746997	+	0.0102815i
$819$	23.1094	−	6.27091i	0.807509	−	0.219123i
$820$	21.7909	−	7.08029i	0.760971	−	0.247254i
$821$	2.11180	−	20.0924i	0.0737022	−	0.701230i	−0.893817	−	0.448432i	$-0.851983\pi$
$821$	2.11180	−	20.0924i	0.0737022	−	0.701230i	0.967519	−	0.252798i	$-0.0813508\pi$
$822$	−0.806388	−	3.10199i	−0.0281260	−	0.108194i
$823$	−11.6025	−	12.8859i	−0.404438	−	0.449173i	0.506177	−	0.862429i	$-0.331058\pi$
$823$	−11.6025	−	12.8859i	−0.404438	−	0.449173i	−0.910615	+	0.413256i	$0.864391\pi$
$824$	−3.08207	−	5.33831i	−0.107369	−	0.185969i
$825$	8.96149	+	15.8791i	0.311999	+	0.552840i
$826$	−3.92485	−	4.67115i	−0.136563	−	0.162530i
$827$	1.60322	−	4.93421i	0.0557495	−	0.171579i	−0.919305	−	0.393547i	$-0.871248\pi$
$827$	1.60322	−	4.93421i	0.0557495	−	0.171579i	0.975054	+	0.221968i	$0.0712479\pi$
$828$	2.20851	−	18.3683i	0.0767509	−	0.638342i
$829$	−38.8884	+	17.3142i	−1.35065	+	0.601349i	−0.949241	−	0.314550i	$-0.898146\pi$
$829$	−38.8884	+	17.3142i	−1.35065	+	0.601349i	−0.401410	+	0.915898i	$0.631480\pi$
$830$	−0.571262	+	2.68757i	−0.0198288	+	0.0932871i
$831$	−8.67663	+	13.1448i	−0.300989	+	0.455989i
$832$	−13.0566	+	17.9708i	−0.452655	+	0.623026i
$833$	6.80889	+	0.467035i	0.235914	+	0.0161818i
$834$	−0.447557	+	2.69529i	−0.0154976	+	0.0933303i
$835$	−16.8843	+	9.74814i	−0.584305	+	0.337348i
$836$	2.42750	+	15.5611i	0.0839567	+	0.538193i
$837$	−25.0182	−	1.87413i	−0.864757	−	0.0647793i
$838$	0.323479	+	1.52185i	0.0111744	+	0.0525713i
$839$	4.18902	+	5.76569i	0.144621	+	0.199054i	0.875182	−	0.483793i	$-0.160741\pi$
$839$	4.18902	+	5.76569i	0.144621	+	0.199054i	−0.730561	+	0.682847i	$0.760741\pi$
$840$	−3.93316	+	0.879889i	−0.135707	+	0.0303591i
$841$	13.8855	+	42.7351i	0.478810	+	1.47362i
$842$	−0.899916	+	0.999458i	−0.0310132	+	0.0344436i
$843$	−25.2392	−	39.5080i	−0.869284	−	1.36073i
$844$	39.4646	−	4.14790i	1.35843	−	0.142776i
$845$	−1.09539	−	5.15340i	−0.0376825	−	0.177282i
$846$	0.220639	+	0.715245i	0.00758573	+	0.0245906i
$847$	27.0274	−	10.7944i	0.928673	−	0.370900i
$848$			23.6896i			0.813504i
$849$	5.18982	−	1.94783i	0.178114	−	0.0668493i
$850$	−0.0529898	−	0.504165i	−0.00181754	−	0.0172927i
$851$	4.32680	+	9.71815i	0.148321	+	0.333134i
$852$	−16.7039	+	25.3059i	−0.572267	+	0.866965i
$853$	−20.1863	+	6.55893i	−0.691166	+	0.224574i	−0.633478	−	0.773761i	$-0.718373\pi$
$853$	−20.1863	+	6.55893i	−0.691166	+	0.224574i	−0.0576888	+	0.998335i	$0.518373\pi$
$854$	−2.77305	−	1.35023i	−0.0948918	−	0.0462038i
$855$	−5.85171	+	7.80622i	−0.200124	+	0.266967i
$856$	−4.53964	+	0.964931i	−0.155162	+	0.0329807i
$857$	−9.60331	+	16.6334i	−0.328043	+	0.568187i	−0.982123	−	0.188238i	$-0.939722\pi$
$857$	−9.60331	+	16.6334i	−0.328043	+	0.568187i	0.654081	+	0.756425i	$0.273056\pi$
$858$	−2.70845	+	0.850778i	−0.0924651	+	0.0290451i
$859$	−6.66076	−	11.5368i	−0.227262	−	0.393630i	0.729733	−	0.683732i	$-0.239644\pi$
$859$	−6.66076	−	11.5368i	−0.227262	−	0.393630i	−0.956996	+	0.290102i	$0.906311\pi$
$860$	8.13605	−	25.0402i	0.277437	−	0.853864i
$861$	−22.8060	+	32.1031i	−0.777226	+	1.09407i
$862$	1.29643	+	0.941909i	0.0441565	+	0.0320815i
$863$	2.75960	+	2.48476i	0.0939380	+	0.0845822i	0.714762	−	0.699368i	$-0.246535\pi$
$863$	2.75960	+	2.48476i	0.0939380	+	0.0845822i	−0.620824	+	0.783950i	$0.713202\pi$
$864$	−2.37875	−	9.74622i	−0.0809266	−	0.331573i
$865$	4.11561	+	9.24382i	0.139935	+	0.314299i
$866$	0.553108	+	0.246260i	0.0187954	+	0.00836824i
$867$	−27.4229	−	4.55361i	−0.931330	−	0.154649i
$868$	23.6915	+	8.60520i	0.804143	+	0.292079i
$869$	−3.16062	−	8.29138i	−0.107217	−	0.281266i
$870$	−2.05550	−	2.57747i	−0.0696880	−	0.0873843i
$871$	−6.99382	+	6.29726i	−0.236977	+	0.213375i
$872$	−7.57005	+	0.795644i	−0.256354	+	0.0269439i
$873$	−7.67820	−	38.9778i	−0.259868	−	1.31920i
$874$	−0.380747	−	1.17182i	−0.0128790	−	0.0396373i
$875$	15.4697	−	24.7933i	0.522970	−	0.838165i
$876$	16.3948	+	8.50844i	0.553929	+	0.287474i
$877$	−4.78105	+	10.7384i	−0.161445	+	0.362611i	−0.976096	−	0.217341i	$-0.930262\pi$
$877$	−4.78105	+	10.7384i	−0.161445	+	0.362611i	0.814651	+	0.579951i	$0.196928\pi$
$878$	−1.28941	+	1.16099i	−0.0435156	+	0.0391816i
$879$	−10.3607	−	4.06618i	−0.349459	−	0.137149i
$880$	−16.6325	+	4.41516i	−0.560680	+	0.148835i
$881$		−	32.2617i		−	1.08693i	−0.839433	−	0.543463i	$-0.817113\pi$
$881$		−	32.2617i		−	1.08693i	0.839433	−	0.543463i	$-0.182887\pi$
$882$	2.24692	−	2.60492i	0.0756576	−	0.0877123i
$883$	−29.4373	+	21.3874i	−0.990643	+	0.719745i	−0.960062	−	0.279788i	$-0.909736\pi$
$883$	−29.4373	+	21.3874i	−0.990643	+	0.719745i	−0.0305816	+	0.999532i	$0.509736\pi$
$884$	−5.77195	−	0.606656i	−0.194132	−	0.0204041i
$885$	1.97007	−	32.8884i	0.0662232	−	1.10553i
$886$	−0.144448	+	0.679575i	−0.00485283	+	0.0228308i
$887$	2.48588	−	23.6515i	0.0834676	−	0.794141i	−0.870082	−	0.492906i	$-0.835935\pi$
$887$	2.48588	−	23.6515i	0.0834676	−	0.794141i	0.953550	−	0.301235i	$-0.0973988\pi$
$888$	2.69288	+	2.73342i	0.0903673	+	0.0917276i
$889$	17.2882	−	6.99826i	0.579829	−	0.234714i
$890$	2.48632			0.0833418
$891$	−11.5891	+	27.5081i	−0.388248	+	0.921555i
$892$	18.5808	−	32.1828i	0.622130	−	1.07756i
$893$	−2.45265	−	2.72394i	−0.0820746	−	0.0911531i
$894$	−0.876855	+	3.17733i	−0.0293264	+	0.106266i
$895$	0.534257	+	0.388160i	0.0178582	+	0.0129748i
$896$	−0.459020	+	13.3998i	−0.0153348	+	0.447656i
$897$	−14.6059	+	7.30513i	−0.487675	+	0.243911i
$898$	5.86877	+	0.616832i	0.195843	+	0.0205840i
$899$	4.33958	+	41.2884i	0.144733	+	1.37704i
$900$	16.1292	+	9.63634i	0.537641	+	0.321211i
$901$	−5.20939	+	3.00764i	−0.173550	+	0.100199i
$902$	2.55192	−	3.90964i	0.0849696	−	0.130177i
$903$	14.4408	+	42.8851i	0.480559	+	1.42713i
$904$	−10.4353	−	3.39064i	−0.347073	−	0.112771i
$905$	−9.41360	+	21.1433i	−0.312919	+	0.702827i
$906$	−1.22982	+	0.785658i	−0.0408582	+	0.0261017i
$907$	18.9933	+	4.03715i	0.630663	+	0.134051i	0.512143	−	0.858900i	$-0.328852\pi$
$907$	18.9933	+	4.03715i	0.630663	+	0.134051i	0.118520	+	0.992952i	$0.462185\pi$
$908$	−18.1191	+	20.1233i	−0.601304	+	0.667816i
$909$	−6.83317	−	2.33366i	−0.226642	−	0.0774026i
$910$	1.27177	+	1.22650i	0.0421587	+	0.0406581i
$911$	−24.5027	−	7.96140i	−0.811809	−	0.263773i	−0.126445	−	0.991974i	$-0.540357\pi$
$911$	−24.5027	−	7.96140i	−0.811809	−	0.263773i	−0.685364	+	0.728201i	$0.740357\pi$
$912$	9.97921	+	12.5133i	0.330445	+	0.414356i
$913$	−18.6041	−	36.7238i	−0.615706	−	1.21538i
$914$	−2.92681	−	1.68979i	−0.0968101	−	0.0558934i
$915$	−5.85258	−	15.5937i	−0.193480	−	0.515511i
$916$	27.7348	−	20.1505i	0.916384	−	0.665792i
$917$	−12.3504	−	18.2840i	−0.407845	−	0.603790i
$918$	0.599837	−	0.573537i	0.0197976	−	0.0189295i
$919$	4.00599	+	3.60701i	0.132145	+	0.118984i	0.732553	−	0.680710i	$-0.238328\pi$
$919$	4.00599	+	3.60701i	0.132145	+	0.118984i	−0.600408	+	0.799694i	$0.704995\pi$
$920$	2.51111	−	1.11802i	0.0827890	−	0.0368600i
$921$	−6.16886	−	23.7302i	−0.203271	−	0.781936i
$922$	−2.32650	+	0.494514i	−0.0766193	+	0.0162859i
$923$	26.7656			0.881001
$924$	18.6785	−	23.4624i	0.614478	−	0.771856i
$925$	−10.8034			−0.355215
$926$	0.634432	−	0.134853i	0.0208487	−	0.00443153i
$927$	11.1673	+	26.1257i	0.366781	+	0.858080i
$928$	−15.1660	+	6.75236i	−0.497850	+	0.221657i
$929$	−5.15803	−	4.64431i	−0.169230	−	0.152375i	0.580164	−	0.814499i	$-0.302988\pi$
$929$	−5.15803	−	4.64431i	−0.169230	−	0.152375i	−0.749394	+	0.662125i	$0.769655\pi$
$930$	−0.828076	−	1.65565i	−0.0271537	−	0.0542909i
$931$	−4.62191	+	16.1997i	−0.151477	+	0.530924i
$932$	−32.2690	+	23.4448i	−1.05701	+	0.767960i
$933$	−33.7698	+	12.6744i	−1.10558	+	0.414941i
$934$	0.633297	+	0.365634i	0.0207221	+	0.0119639i
$935$	−3.08257	−	3.09697i	−0.100811	−	0.101282i
$936$	−4.00651	+	4.31816i	−0.130957	+	0.141143i
$937$	−16.9324	−	5.50168i	−0.553158	−	0.179732i	0.0190821	−	0.999818i	$-0.493926\pi$
$937$	−16.9324	−	5.50168i	−0.553158	−	0.179732i	−0.572241	+	0.820086i	$0.693926\pi$
$938$	−0.326220	+	1.31211i	−0.0106515	+	0.0428419i
$939$	25.5368	−	49.2066i	0.833363	−	1.60580i
$940$	2.71734	−	3.01791i	0.0886298	−	0.0984334i
$941$	−20.5783	−	4.37404i	−0.670832	−	0.142590i	−0.140110	−	0.990136i	$-0.544746\pi$
$941$	−20.5783	−	4.37404i	−0.670832	−	0.142590i	−0.530722	+	0.847546i	$0.678079\pi$
$942$	−1.16861	−	1.82927i	−0.0380753	−	0.0596008i
$943$	10.9237	−	24.5351i	0.355725	−	0.798972i
$944$	−51.4063	−	16.7029i	−1.67313	−	0.543634i
$945$	18.4836	−	1.86250i	0.601270	−	0.0605872i
$946$	−1.91096	−	5.01310i	−0.0621307	−	0.162990i
$947$	−41.0002	+	23.6715i	−1.33233	+	0.769219i	−0.985656	−	0.168767i	$-0.946021\pi$
$947$	−41.0002	+	23.6715i	−1.33233	+	0.769219i	−0.346671	+	0.937987i	$0.612688\pi$
$948$	−7.06271	−	5.80716i	−0.229386	−	0.188608i
$949$	−1.70432	−	16.2155i	−0.0553246	−	0.526379i
$950$	1.24445	+	0.130797i	0.0403753	+	0.00424361i
$951$	−8.82104	−	17.6368i	−0.286042	−	0.571911i
$952$	−1.48189	+	0.789197i	−0.0480283	+	0.0255780i
$953$	0.940173	+	0.683076i	0.0304552	+	0.0221270i	0.602909	−	0.797810i	$-0.294008\pi$
$953$	0.940173	+	0.683076i	0.0304552	+	0.0221270i	−0.572454	+	0.819937i	$0.694008\pi$
$954$	−0.361947	+	3.01033i	−0.0117185	+	0.0974632i
$955$	12.3182	+	13.6808i	0.398609	+	0.442700i
$956$	0.921251	−	1.59565i	0.0297954	−	0.0516071i
$957$	48.2123	+	10.7427i	1.55848	+	0.347262i
$958$	−4.86345			−0.157131
$959$	4.13976	−	29.5986i	0.133680	−	0.955787i
$960$	−12.2766	+	12.0945i	−0.396225	+	0.390349i
$961$	0.803612	−	7.64585i	0.0259230	−	0.246640i
$962$	0.349728	−	1.64534i	0.0112757	−	0.0530479i
$963$	21.3058	−	1.91797i	0.686570	−	0.0618058i
$964$	−50.1606	−	5.27209i	−1.61556	−	0.169803i
$965$	−7.37463	+	5.35798i	−0.237398	+	0.172480i
$966$	−1.15139	+	2.04423i	−0.0370454	+	0.0657719i
$967$			28.2516i			0.908512i	0.890871	+	0.454256i	$0.150095\pi$
$967$			28.2516i			0.908512i	−0.890871	+	0.454256i	$0.849905\pi$
$968$	−4.23517	+	5.77246i	−0.136123	+	0.185534i
$969$	−1.48473	+	3.78314i	−0.0476965	+	0.121532i
$970$	2.17839	−	1.96143i	0.0699439	−	0.0629778i
$971$	3.13695	−	7.04570i	0.100669	−	0.226107i	−0.856188	−	0.516664i	$-0.827174\pi$
$971$	3.13695	−	7.04570i	0.100669	−	0.226107i	0.956858	+	0.290556i	$0.0938404\pi$
$972$	3.67388	+	30.5384i	0.117840	+	0.979520i
$973$	−13.4864	+	21.6147i	−0.432355	+	0.692936i
$974$	0.613692	+	1.88875i	0.0196640	+	0.0605194i
$975$	−0.744246	−	16.5684i	−0.0238350	−	0.530612i
$976$	−27.1750	+	2.85621i	−0.869850	+	0.0914250i
$977$	−17.1256	+	15.4199i	−0.547895	+	0.493327i	−0.895955	−	0.444146i	$-0.853507\pi$
$977$	−17.1256	+	15.4199i	−0.547895	+	0.493327i	0.348060	+	0.937472i	$0.386841\pi$
$978$	−0.360712	+	0.287664i	−0.0115343	+	0.00919847i
$979$	−29.0051	+	23.3762i	−0.927007	+	0.747107i
$980$	−18.3850	−	3.21658i	−0.587286	−	0.102750i
$981$	35.0808	+	0.524168i	1.12004	+	0.0167354i
$982$	5.28188	+	2.35165i	0.168552	+	0.0750440i
$983$	3.88496	+	8.72576i	0.123911	+	0.278308i	0.964841	−	0.262836i	$-0.0846578\pi$
$983$	3.88496	+	8.72576i	0.123911	+	0.278308i	−0.840930	+	0.541145i	$0.817991\pi$
$984$	0.579251	−	9.67002i	0.0184658	−	0.308269i
$985$	13.8846	+	12.5017i	0.442399	+	0.398338i
$986$	−1.11104	−	0.807217i	−0.0353827	−	0.0257070i
$987$	−0.655621	+	6.94875i	−0.0208687	+	0.221181i
$988$	4.42686	−	13.6245i	0.140837	−	0.433452i
$989$	−15.4309	−	26.7270i	−0.490673	−	0.849870i
$990$	−2.18101	+	0.306929i	−0.0693172	+	0.00975485i
$991$	9.51472	−	16.4800i	0.302245	−	0.523504i	−0.674399	−	0.738367i	$-0.735597\pi$
$991$	9.51472	−	16.4800i	0.302245	−	0.523504i	0.976644	+	0.214863i	$0.0689305\pi$
$992$	−9.11829	+	1.93815i	−0.289506	+	0.0615364i
$993$	39.9968	+	40.5989i	1.26926	+	1.28837i
$994$	3.18647	−	2.15238i	0.101069	−	0.0682694i
$995$	−18.0167	+	5.85397i	−0.571167	+	0.185583i
$996$	−35.4036	−	23.3692i	−1.12181	−	0.740483i
$997$	13.7121	+	30.7978i	0.434266	+	0.975378i	0.989613	+	0.143759i	$0.0459189\pi$
$997$	13.7121	+	30.7978i	0.434266	+	0.975378i	−0.555347	+	0.831619i	$0.687414\pi$
$998$	−0.173239	−	1.64826i	−0.00548378	−	0.0521746i
$999$	−10.8195	−	13.9907i	−0.342314	−	0.442647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.200.16	yes	224
3.2	odd	2	inner	231.2.be.a.200.13	yes	224
7.2	even	3	inner	231.2.be.a.2.13	✓	224
11.6	odd	10	inner	231.2.be.a.116.16	yes	224
21.2	odd	6	inner	231.2.be.a.2.16	yes	224
33.17	even	10	inner	231.2.be.a.116.13	yes	224
77.72	odd	30	inner	231.2.be.a.149.13	yes	224
231.149	even	30	inner	231.2.be.a.149.16	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.13	✓	224	7.2	even	3	inner
231.2.be.a.2.16	yes	224	21.2	odd	6	inner
231.2.be.a.116.13	yes	224	33.17	even	10	inner
231.2.be.a.116.16	yes	224	11.6	odd	10	inner
231.2.be.a.149.13	yes	224	77.72	odd	30	inner
231.2.be.a.149.16	yes	224	231.149	even	30	inner
231.2.be.a.200.13	yes	224	3.2	odd	2	inner
231.2.be.a.200.16	yes	224	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160234 - 0.0340589i) q^{2} +(1.67633 - 0.435777i) q^{3} +(-1.80258 + 0.802558i) q^{4} +(1.00420 + 0.904189i) q^{5} +(0.253764 - 0.126921i) q^{6} +(2.63918 - 0.186311i) q^{7} +(-0.526557 + 0.382566i) q^{8} +(2.62020 - 1.46102i) q^{9} +O(q^{10})\)	\(q+(0.160234 - 0.0340589i) q^{2} +(1.67633 - 0.435777i) q^{3} +(-1.80258 + 0.802558i) q^{4} +(1.00420 + 0.904189i) q^{5} +(0.253764 - 0.126921i) q^{6} +(2.63918 - 0.186311i) q^{7} +(-0.526557 + 0.382566i) q^{8} +(2.62020 - 1.46102i) q^{9} +(0.191704 + 0.110680i) q^{10} +(-3.27699 + 0.511202i) q^{11} +(-2.67198 + 2.13088i) q^{12} +(2.86915 + 0.932244i) q^{13} +(0.416542 - 0.119741i) q^{14} +(2.07741 + 1.07811i) q^{15} +(2.56927 - 2.85346i) q^{16} +(0.953678 + 0.202711i) q^{17} +(0.370085 - 0.323346i) q^{18} +(-0.978849 + 2.19853i) q^{19} +(-2.53582 - 0.823937i) q^{20} +(4.34296 - 1.46242i) q^{21} +(-0.507676 + 0.193523i) q^{22} +(-2.70664 + 1.56268i) q^{23} +(-0.715972 + 0.870770i) q^{24} +(-0.331775 - 3.15663i) q^{25} +(0.491488 + 0.0516575i) q^{26} +(3.75565 - 3.59098i) q^{27} +(-4.60780 + 2.45394i) q^{28} +(-6.95634 - 5.05408i) q^{29} +(0.369591 + 0.101997i) q^{30} +(-3.23073 - 3.58809i) q^{31} +(0.965360 - 1.67205i) q^{32} +(-5.27056 + 2.28498i) q^{33} +0.159716 q^{34} +(2.81874 + 2.19923i) q^{35} +(-3.55055 + 4.73646i) q^{36} +(0.355785 - 3.38507i) q^{37} +(-0.0819658 + 0.385619i) q^{38} +(5.21591 + 0.312442i) q^{39} +(-0.874682 - 0.0919328i) q^{40} +(-6.95208 + 5.05098i) q^{41} +(0.646084 - 0.382246i) q^{42} +9.87461i q^{43} +(5.49676 - 3.55146i) q^{44} +(3.95225 + 0.901994i) q^{45} +(-0.380474 + 0.342580i) q^{46} +(-0.619491 + 1.39140i) q^{47} +(3.06348 - 5.90298i) q^{48} +(6.93058 - 0.983420i) q^{49} +(-0.160673 - 0.494501i) q^{50} +(1.68702 - 0.0757805i) q^{51} +(-5.92004 + 0.622222i) q^{52} +(-4.58493 + 4.12829i) q^{53} +(0.479479 - 0.703311i) q^{54} +(-3.75299 - 2.44967i) q^{55} +(-1.31840 + 1.10777i) q^{56} +(-0.682809 + 4.11203i) q^{57} +(-1.28678 - 0.572912i) q^{58} +(-5.72565 - 12.8600i) q^{59} +(-4.60993 - 0.276143i) q^{60} +(-5.28847 - 4.76176i) q^{61} +(-0.639881 - 0.464900i) q^{62} +(6.64297 - 4.34406i) q^{63} +(-2.27534 + 7.00276i) q^{64} +(2.03829 + 3.53042i) q^{65} +(-0.766701 + 0.545642i) q^{66} +(-1.55978 + 2.70162i) q^{67} +(-1.88176 + 0.399981i) q^{68} +(-3.85626 + 3.79907i) q^{69} +(0.526562 + 0.256388i) q^{70} +(8.43794 - 2.74165i) q^{71} +(-0.820747 + 1.77171i) q^{72} +(-2.19828 - 4.93742i) q^{73} +(-0.0582826 - 0.554522i) q^{74} +(-1.93175 - 5.14699i) q^{75} -4.74860i q^{76} +(-8.55334 + 1.95970i) q^{77} +(0.846409 - 0.127584i) q^{78} +(0.556251 + 2.61696i) q^{79} +(5.16013 - 0.542352i) q^{80} +(4.73086 - 7.65630i) q^{81} +(-0.941931 + 1.04612i) q^{82} +(3.83565 + 11.8049i) q^{83} +(-6.65485 + 6.12160i) q^{84} +(0.774398 + 1.06587i) q^{85} +(0.336318 + 1.58225i) q^{86} +(-13.8636 - 5.44091i) q^{87} +(1.52995 - 1.52284i) q^{88} +(9.72722 - 5.61602i) q^{89} +(0.664006 + 0.00992141i) q^{90} +(7.74591 + 1.92581i) q^{91} +(3.62479 - 4.98909i) q^{92} +(-6.97940 - 4.60696i) q^{93} +(-0.0518742 + 0.244049i) q^{94} +(-2.97085 + 1.32271i) q^{95} +(0.889624 - 3.22360i) q^{96} +(4.09209 - 12.5942i) q^{97} +(1.07702 - 0.393625i) q^{98} +(-7.83949 + 6.12719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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