LMFDB - Embedded newform 930.2.bg.f.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.1669788916259765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 16x^{14} + 90x^{12} + 239x^{10} + 329x^{8} + 239x^{6} + 90x^{4} + 16x^{2} + 1 $ x^16 + 16x^14 + 90x^12 + 239x^10 + 329x^8 + 239x^6 + 90x^4 + 16*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.1
Root			$0.559146i$ of defining polynomial
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.f.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.95386 + 0.627863i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.95386 + 0.627863i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(-1.54416 - 1.71496i) q^{11} +(0.913545 + 0.406737i) q^{12} +(-2.44976 + 1.09070i) q^{13} +(-2.02068 + 2.24419i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.33642 - 2.59485i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-3.27351 - 1.45746i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.315661 - 3.00331i) q^{21} +(-2.25728 - 0.479800i) q^{22} +(-1.82522 - 5.61743i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.34080 + 2.32233i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.315661 + 3.00331i) q^{28} +(-8.41017 + 6.11035i) q^{29} -1.00000 q^{30} +(-3.50248 - 4.32812i) q^{31} -1.00000 q^{32} +(1.86698 - 1.35644i) q^{33} +(0.364984 - 3.47259i) q^{34} +(0.933186 - 2.87205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.24027 - 2.14821i) q^{37} +(-3.50500 + 0.745011i) q^{38} +(-0.828658 - 2.55035i) q^{39} +(0.978148 + 0.207912i) q^{40} +(0.895053 + 8.51586i) q^{41} +(-2.02068 - 2.24419i) q^{42} +(10.2121 + 4.54671i) q^{43} +(-2.10820 + 0.938630i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-4.77848 - 3.47177i) q^{46} +(-4.74436 - 3.44698i) q^{47} +(0.669131 - 0.743145i) q^{48} +(1.93627 - 0.862085i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(2.33642 + 2.59485i) q^{51} +(0.280303 + 2.66690i) q^{52} +(2.24489 + 0.477166i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(2.25728 - 0.479800i) q^{55} +(1.50993 + 2.61527i) q^{56} +(1.79165 - 3.10323i) q^{57} +(-3.21240 + 9.88675i) q^{58} +(0.0198689 - 0.189040i) q^{59} +(-0.809017 + 0.587785i) q^{60} -9.54559 q^{61} +(-5.37757 - 1.44281i) q^{62} +3.01985 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.280303 - 2.66690i) q^{65} +(0.713121 - 2.19476i) q^{66} +(8.03661 - 13.9198i) q^{67} +(-1.74586 - 3.02392i) q^{68} +(5.77745 - 1.22803i) q^{69} +(-0.933186 - 2.87205i) q^{70} +(1.58060 + 0.335967i) q^{71} +(0.104528 + 0.994522i) q^{72} +(-4.58769 - 5.09514i) q^{73} +(-2.26609 - 1.00893i) q^{74} +(0.913545 - 0.406737i) q^{75} +(-2.39770 + 2.66292i) q^{76} +(5.63799 + 4.09624i) q^{77} +(-2.16945 - 1.57620i) q^{78} +(-5.41750 + 6.01674i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(5.72961 + 6.36337i) q^{82} +(1.64936 + 15.6926i) q^{83} +(-2.95386 - 0.627863i) q^{84} +(1.07900 + 3.32082i) q^{85} +(10.9342 - 2.32414i) q^{86} +(-5.19777 - 9.00280i) q^{87} +(-1.15385 + 1.99853i) q^{88} +(-3.47841 + 10.7054i) q^{89} +(0.104528 - 0.994522i) q^{90} +(6.55143 - 4.75989i) q^{91} -5.90652 q^{92} +(4.67052 - 3.03089i) q^{93} -5.86435 q^{94} +(2.89896 - 2.10622i) q^{95} +(0.104528 - 0.994522i) q^{96} +(-2.00934 + 6.18410i) q^{97} +(1.05976 - 1.83555i) q^{98} +(1.15385 + 1.99853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−2.95386	+	0.627863i	−1.11646	+	0.237310i	−0.728956	−	0.684560i	$-0.759994\pi$
$7$	−2.95386	+	0.627863i	−1.11646	+	0.237310i	−0.387499	+	0.921870i	$0.626661\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.104528	+	0.994522i	0.0330548	+	0.314495i
$11$	−1.54416	−	1.71496i	−0.465581	−	0.517080i	0.463931	−	0.885871i	$-0.346439\pi$
$11$	−1.54416	−	1.71496i	−0.465581	−	0.517080i	−0.929512	+	0.368791i	$0.879772\pi$
$12$	0.913545	+	0.406737i	0.263718	+	0.117415i
$13$	−2.44976	+	1.09070i	−0.679440	+	0.302506i	−0.717288	−	0.696777i	$-0.754617\pi$
$13$	−2.44976	+	1.09070i	−0.679440	+	0.302506i	0.0378473	+	0.999284i	$0.487950\pi$
$14$	−2.02068	+	2.24419i	−0.540049	+	0.599785i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	2.33642	−	2.59485i	0.566664	−	0.629344i	−0.389903	−	0.920856i	$-0.627491\pi$
$17$	2.33642	−	2.59485i	0.566664	−	0.629344i	0.956567	+	0.291511i	$0.0941582\pi$
$18$	−0.913545	+	0.406737i	−0.215325	+	0.0958687i
$19$	−3.27351	−	1.45746i	−0.750996	−	0.334365i	−0.00470844	−	0.999989i	$-0.501499\pi$
$19$	−3.27351	−	1.45746i	−0.750996	−	0.334365i	−0.746287	+	0.665624i	$0.768165\pi$
$20$	0.669131	+	0.743145i	0.149622	+	0.166172i
$21$	−0.315661	−	3.00331i	−0.0688828	−	0.655376i
$22$	−2.25728	−	0.479800i	−0.481254	−	0.102294i
$23$	−1.82522	−	5.61743i	−0.380584	−	1.17132i	−0.939634	−	0.342182i	$-0.888834\pi$
$23$	−1.82522	−	5.61743i	−0.380584	−	1.17132i	0.559050	−	0.829134i	$-0.311166\pi$
$24$	0.978148	−	0.207912i	0.199664	−	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.34080	+	2.32233i	−0.262952	+	0.455446i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.315661	+	3.00331i	−0.0596543	+	0.567572i
$29$	−8.41017	+	6.11035i	−1.56173	+	1.13466i	−0.627156	+	0.778894i	$0.715781\pi$
$29$	−8.41017	+	6.11035i	−1.56173	+	1.13466i	−0.934574	+	0.355769i	$0.884219\pi$
$30$	−1.00000			−0.182574
$31$	−3.50248	−	4.32812i	−0.629065	−	0.777353i
$31$	−3.50248	−	4.32812i	−0.629065	−	0.777353i
$32$	−1.00000			−0.176777
$33$	1.86698	−	1.35644i	0.324999	−	0.236125i
$34$	0.364984	−	3.47259i	0.0625943	−	0.595545i
$35$	0.933186	−	2.87205i	0.157737	−	0.485465i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.24027	−	2.14821i	−0.203899	−	0.353164i	0.745882	−	0.666078i	$-0.232028\pi$
$37$	−1.24027	−	2.14821i	−0.203899	−	0.353164i	−0.949781	+	0.312914i	$0.898695\pi$
$38$	−3.50500	+	0.745011i	−0.568587	+	0.120857i
$39$	−0.828658	−	2.55035i	−0.132691	−	0.408382i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	0.895053	+	8.51586i	0.139784	+	1.32995i	0.809405	+	0.587251i	$0.199790\pi$
$41$	0.895053	+	8.51586i	0.139784	+	1.32995i	−0.669621	+	0.742703i	$0.733544\pi$
$42$	−2.02068	−	2.24419i	−0.311797	−	0.346286i
$43$	10.2121	+	4.54671i	1.55733	+	0.693366i	0.991373	−	0.131071i	$-0.0418415\pi$
$43$	10.2121	+	4.54671i	1.55733	+	0.693366i	0.565953	+	0.824437i	$0.308508\pi$
$44$	−2.10820	+	0.938630i	−0.317823	+	0.141504i
$45$	0.669131	−	0.743145i	0.0997481	−	0.110781i
$46$	−4.77848	−	3.47177i	−0.704548	−	0.511884i
$47$	−4.74436	−	3.44698i	−0.692036	−	0.502793i	0.185293	−	0.982683i	$-0.440677\pi$
$47$	−4.74436	−	3.44698i	−0.692036	−	0.502793i	−0.877329	+	0.479890i	$0.840677\pi$
$48$	0.669131	−	0.743145i	0.0965807	−	0.107264i
$49$	1.93627	−	0.862085i	0.276611	−	0.123155i
$50$	−0.913545	−	0.406737i	−0.129195	−	0.0575212i
$51$	2.33642	+	2.59485i	0.327164	+	0.363352i
$52$	0.280303	+	2.66690i	0.0388710	+	0.369833i
$53$	2.24489	+	0.477166i	0.308359	+	0.0655437i	0.359492	−	0.933148i	$-0.382950\pi$
$53$	2.24489	+	0.477166i	0.308359	+	0.0655437i	−0.0511331	+	0.998692i	$0.516283\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	2.25728	−	0.479800i	0.304372	−	0.0646962i
$56$	1.50993	+	2.61527i	0.201772	+	0.349480i
$57$	1.79165	−	3.10323i	0.237310	−	0.411034i
$58$	−3.21240	+	9.88675i	−0.421809	+	1.29819i
$59$	0.0198689	−	0.189040i	0.00258671	−	0.0246109i	−0.993152	−	0.116826i	$-0.962728\pi$
$59$	0.0198689	−	0.189040i	0.00258671	−	0.0246109i	0.995739	+	0.0922150i	$0.0293947\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−9.54559			−1.22219			−0.611094	−	0.791558i	$-0.709270\pi$
$61$	−9.54559			−1.22219			−0.611094	+	0.791558i	$0.709270\pi$
$62$	−5.37757	−	1.44281i	−0.682952	−	0.183237i
$63$	3.01985			0.380466
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.280303	−	2.66690i	0.0347673	−	0.330789i
$66$	0.713121	−	2.19476i	0.0877791	−	0.270156i
$67$	8.03661	−	13.9198i	0.981828	−	1.70058i	0.326566	−	0.945174i	$-0.394109\pi$
$67$	8.03661	−	13.9198i	0.981828	−	1.70058i	0.655262	−	0.755402i	$-0.272558\pi$
$68$	−1.74586	−	3.02392i	−0.211717	−	0.366704i
$69$	5.77745	−	1.22803i	0.695523	−	0.147838i
$70$	−0.933186	−	2.87205i	−0.111537	−	0.343276i
$71$	1.58060	+	0.335967i	0.187582	+	0.0398719i	0.300745	−	0.953705i	$-0.402765\pi$
$71$	1.58060	+	0.335967i	0.187582	+	0.0398719i	−0.113162	+	0.993576i	$0.536098\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	−4.58769	−	5.09514i	−0.536948	−	0.596342i	0.412230	−	0.911080i	$-0.364750\pi$
$73$	−4.58769	−	5.09514i	−0.536948	−	0.596342i	−0.949179	+	0.314738i	$0.898083\pi$
$74$	−2.26609	−	1.00893i	−0.263427	−	0.117285i
$75$	0.913545	−	0.406737i	0.105487	−	0.0469659i
$76$	−2.39770	+	2.66292i	−0.275035	+	0.305457i
$77$	5.63799	+	4.09624i	0.642509	+	0.466810i
$78$	−2.16945	−	1.57620i	−0.245642	−	0.178470i
$79$	−5.41750	+	6.01674i	−0.609517	+	0.676937i	−0.966350	−	0.257231i	$-0.917190\pi$
$79$	−5.41750	+	6.01674i	−0.609517	+	0.676937i	0.356833	+	0.934168i	$0.383856\pi$
$80$	0.913545	−	0.406737i	0.102137	−	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	5.72961	+	6.36337i	0.632729	+	0.702717i
$83$	1.64936	+	15.6926i	0.181040	+	1.72248i	0.587850	+	0.808970i	$0.299975\pi$
$83$	1.64936	+	15.6926i	0.181040	+	1.72248i	−0.406810	+	0.913513i	$0.633359\pi$
$84$	−2.95386	−	0.627863i	−0.322293	−	0.0685055i
$85$	1.07900	+	3.32082i	0.117034	+	0.360194i
$86$	10.9342	−	2.32414i	1.17907	−	0.250619i
$87$	−5.19777	−	9.00280i	−0.557260	−	0.965202i
$88$	−1.15385	+	1.99853i	−0.123001	+	0.213044i
$89$	−3.47841	+	10.7054i	−0.368711	+	1.13477i	0.578914	+	0.815389i	$0.303477\pi$
$89$	−3.47841	+	10.7054i	−0.368711	+	1.13477i	−0.947625	+	0.319386i	$0.896523\pi$
$90$	0.104528	−	0.994522i	0.0110183	−	0.104832i
$91$	6.55143	−	4.75989i	0.686777	−	0.498973i
$92$	−5.90652			−0.615797
$93$	4.67052	−	3.03089i	0.484310	−	0.314288i
$94$	−5.86435			−0.604861
$95$	2.89896	−	2.10622i	0.297427	−	0.216093i
$96$	0.104528	−	0.994522i	0.0106684	−	0.101503i
$97$	−2.00934	+	6.18410i	−0.204017	+	0.627900i	0.795735	+	0.605645i	$0.207085\pi$
$97$	−2.00934	+	6.18410i	−0.204017	+	0.627900i	−0.999752	+	0.0222555i	$0.992915\pi$
$98$	1.05976	−	1.83555i	0.107052	−	0.185419i
$99$	1.15385	+	1.99853i	0.115967	+	0.200860i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	1.28802	+	3.96412i	0.128163	+	0.394445i	0.994464	−	0.105077i	$-0.0335090\pi$
$101$	1.28802	+	3.96412i	0.128163	+	0.394445i	−0.866301	+	0.499522i	$0.833509\pi$
$102$	3.41542	+	0.725969i	0.338177	+	0.0718817i
$103$	0.224588	+	2.13681i	0.0221293	+	0.210546i	0.999999	+	0.00133174i	$0.000423907\pi$
$103$	0.224588	+	2.13681i	0.0221293	+	0.210546i	−0.977870	+	0.209214i	$0.932909\pi$
$104$	1.79434	+	1.99281i	0.175949	+	0.195411i
$105$	2.75877	+	1.22829i	0.269229	+	0.119868i
$106$	2.09662	−	0.933477i	0.203642	−	0.0906673i
$107$	−6.65431	+	7.39036i	−0.643297	+	0.714453i	−0.973303	−	0.229526i	$-0.926283\pi$
$107$	−6.65431	+	7.39036i	−0.643297	+	0.714453i	0.330006	+	0.943979i	$0.392949\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	1.03429	+	0.751456i	0.0990671	+	0.0719765i	0.636216	−	0.771511i	$-0.280499\pi$
$109$	1.03429	+	0.751456i	0.0990671	+	0.0719765i	−0.537149	+	0.843487i	$0.680499\pi$
$110$	1.54416	−	1.71496i	0.147230	−	0.163515i
$111$	2.26609	−	1.00893i	0.215088	−	0.0957632i
$112$	2.75877	+	1.22829i	0.260680	+	0.116062i
$113$	−2.57057	−	2.85491i	−0.241819	−	0.268568i	0.610002	−	0.792400i	$-0.291169\pi$
$113$	−2.57057	−	2.85491i	−0.241819	−	0.268568i	−0.851821	+	0.523832i	$0.824502\pi$
$114$	−0.374558	−	3.56368i	−0.0350805	−	0.333769i
$115$	5.77745	+	1.22803i	0.538750	+	0.114515i
$116$	3.21240	+	9.88675i	0.298264	+	0.917962i
$117$	2.62299	−	0.557534i	0.242496	−	0.0515441i
$118$	−0.0950407	−	0.164615i	−0.00874920	−	0.0151541i
$119$	−5.27224	+	9.13179i	−0.483306	+	0.837110i
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	0.593145	−	5.64340i	0.0539223	−	0.513036i
$122$	−7.72254	+	5.61076i	−0.699166	+	0.507974i
$123$	−8.56276			−0.772078
$124$	−5.19861	+	1.99360i	−0.466849	+	0.179030i
$125$	1.00000			0.0894427
$126$	2.44311	−	1.77503i	0.217650	−	0.158132i
$127$	2.02781	−	19.2933i	0.179939	−	1.71201i	−0.416322	−	0.909217i	$-0.636681\pi$
$127$	2.02781	−	19.2933i	0.179939	−	1.71201i	0.596261	−	0.802791i	$-0.296652\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−5.58925	+	9.68087i	−0.492106	+	0.852353i
$130$	−1.34080	−	2.32233i	−0.117596	−	0.203682i
$131$	11.0484	−	2.34840i	0.965301	−	0.205181i	0.301812	−	0.953367i	$-0.402408\pi$
$131$	11.0484	−	2.34840i	0.965301	−	0.205181i	0.663489	+	0.748186i	$0.269075\pi$
$132$	−0.713121	−	2.19476i	−0.0620692	−	0.191029i
$133$	10.5846	+	2.24983i	0.917801	+	0.195085i
$134$	−1.68011	−	15.9852i	−0.145139	−	1.38091i
$135$	0.669131	+	0.743145i	0.0575896	+	0.0639597i
$136$	−3.18984	−	1.42021i	−0.273527	−	0.121782i
$137$	16.3710	−	7.28883i	1.39867	−	0.622726i	0.437632	−	0.899154i	$-0.355817\pi$
$137$	16.3710	−	7.28883i	1.39867	−	0.622726i	0.961035	+	0.276428i	$0.0891507\pi$
$138$	3.95223	−	4.38940i	0.336436	−	0.373651i
$139$	−6.45443	−	4.68942i	−0.547458	−	0.397751i	0.279390	−	0.960178i	$-0.409868\pi$
$139$	−6.45443	−	4.68942i	−0.547458	−	0.397751i	−0.826847	+	0.562427i	$0.809868\pi$
$140$	−2.44311	−	1.77503i	−0.206481	−	0.150017i
$141$	3.92402	−	4.35806i	0.330462	−	0.367015i
$142$	1.47621	−	0.657250i	0.123881	−	0.0551552i
$143$	5.65332	+	2.51702i	0.472755	+	0.210484i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	−1.08663	−	10.3386i	−0.0902397	−	0.858574i
$146$	−6.70637	−	1.42548i	−0.555023	−	0.117974i
$147$	0.654966	+	2.01578i	0.0540207	+	0.166259i
$148$	−2.42634	+	0.515734i	−0.199444	+	0.0423931i
$149$	2.48682	+	4.30730i	0.203728	+	0.352868i	0.949727	−	0.313080i	$-0.101361\pi$
$149$	2.48682	+	4.30730i	0.203728	+	0.352868i	−0.745998	+	0.665948i	$0.768027\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	2.43793	−	7.50318i	0.198396	−	0.610600i	−0.801524	−	0.597962i	$-0.795977\pi$
$151$	2.43793	−	7.50318i	0.198396	−	0.610600i	0.999920	−	0.0126377i	$-0.00402281\pi$
$152$	−0.374558	+	3.56368i	−0.0303806	+	0.289052i
$153$	−2.82486	+	2.05238i	−0.228376	+	0.165925i
$154$	6.96894			0.561573
$155$	5.49950	−	0.869181i	0.441731	−	0.0698143i
$156$	−2.68159			−0.214699
$157$	−14.6723	+	10.6600i	−1.17097	+	0.850762i	−0.991125	−	0.132932i	$-0.957561\pi$
$157$	−14.6723	+	10.6600i	−1.17097	+	0.850762i	−0.179849	+	0.983694i	$0.557561\pi$
$158$	−0.846297	+	8.05198i	−0.0673278	+	0.640581i
$159$	−0.709206	+	2.18271i	−0.0562437	+	0.173100i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	8.91841	+	15.4471i	0.702869	+	1.21741i
$162$	0.978148	−	0.207912i	0.0768505	−	0.0163351i
$163$	0.787127	+	2.42253i	0.0616526	+	0.189747i	0.977139	−	0.212602i	$-0.0681938\pi$
$163$	0.787127	+	2.42253i	0.0616526	+	0.189747i	−0.915486	+	0.402349i	$0.868194\pi$
$164$	8.37565	+	1.78030i	0.654028	+	0.139018i
$165$	0.241221	+	2.29507i	0.0187790	+	0.178671i
$166$	10.5582	+	11.7261i	0.819476	+	0.910121i
$167$	15.9791	+	7.11433i	1.23650	+	0.550524i	0.917690	−	0.397296i	$-0.130052\pi$
$167$	15.9791	+	7.11433i	1.23650	+	0.550524i	0.318806	+	0.947820i	$0.396718\pi$
$168$	−2.75877	+	1.22829i	−0.212844	+	0.0947643i
$169$	−3.88702	+	4.31697i	−0.299002	+	0.332075i
$170$	2.82486	+	2.05238i	0.216657	+	0.157410i
$171$	2.89896	+	2.10622i	0.221689	+	0.161066i
$172$	7.47988	−	8.30725i	0.570336	−	0.633422i
$173$	−7.30957	+	3.25443i	−0.555736	+	0.247430i	−0.665333	−	0.746546i	$-0.731711\pi$
$173$	−7.30957	+	3.25443i	−0.555736	+	0.247430i	0.109597	+	0.993976i	$0.465044\pi$
$174$	−9.49680	−	4.22825i	−0.719951	−	0.320543i
$175$	2.02068	+	2.24419i	0.152749	+	0.169645i
$176$	0.241221	+	2.29507i	0.0181827	+	0.172997i
$177$	0.185928	+	0.0395201i	0.0139752	+	0.00297052i
$178$	3.47841	+	10.7054i	0.260718	+	0.802407i
$179$	−18.3539	+	3.90123i	−1.37183	+	0.291592i	−0.834142	−	0.551550i	$-0.814036\pi$
$179$	−18.3539	+	3.90123i	−1.37183	+	0.291592i	−0.537690	+	0.843142i	$0.680703\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	12.7158	−	22.0245i	0.945161	−	1.63707i	0.189733	−	0.981836i	$-0.439238\pi$
$181$	12.7158	−	22.0245i	0.945161	−	1.63707i	0.755428	−	0.655231i	$-0.227429\pi$
$182$	2.50242	−	7.70167i	0.185492	−	0.570886i
$183$	0.997786	−	9.49330i	0.0737585	−	0.701765i
$184$	−4.77848	+	3.47177i	−0.352274	+	0.255942i
$185$	2.48054			0.182373
$186$	1.99702	−	5.19730i	0.146429	−	0.381084i
$187$	−8.05787			−0.589250
$188$	−4.74436	+	3.44698i	−0.346018	+	0.251397i
$189$	−0.315661	+	3.00331i	−0.0229609	+	0.218459i
$190$	1.10730	−	3.40793i	0.0803322	−	0.247237i
$191$	7.14555	−	12.3765i	0.517034	−	0.895529i	−0.482770	−	0.875747i	$-0.660369\pi$
$191$	7.14555	−	12.3765i	0.517034	−	0.895529i	0.999804	−	0.0197823i	$-0.00629733\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−10.5893	+	2.25083i	−0.762237	+	0.162019i	−0.572599	−	0.819836i	$-0.694065\pi$
$193$	−10.5893	+	2.25083i	−0.762237	+	0.162019i	−0.189638	+	0.981854i	$0.560731\pi$
$194$	2.00934	+	6.18410i	0.144262	+	0.443993i
$195$	2.62299	+	0.557534i	0.187836	+	0.0399259i
$196$	−0.221550	−	2.10791i	−0.0158250	−	0.150565i
$197$	−1.30612	−	1.45060i	−0.0930575	−	0.103351i	0.694817	−	0.719186i	$-0.255485\pi$
$197$	−1.30612	−	1.45060i	−0.0930575	−	0.103351i	−0.787875	+	0.615836i	$0.788819\pi$
$198$	2.10820	+	0.938630i	0.149823	+	0.0667055i
$199$	11.1485	−	4.96362i	0.790295	−	0.351862i	0.0284282	−	0.999596i	$-0.490950\pi$
$199$	11.1485	−	4.96362i	0.790295	−	0.351862i	0.761867	+	0.647734i	$0.224283\pi$
$200$	−0.669131	+	0.743145i	−0.0473147	+	0.0525483i
$201$	13.0035	+	9.44760i	0.917197	+	0.666382i
$202$	3.37208	+	2.44996i	0.237259	+	0.172379i
$203$	21.0060	−	23.3296i	1.47433	−	1.63741i
$204$	3.18984	−	1.42021i	0.223334	−	0.0994346i
$205$	−7.82247	−	3.48279i	−0.546345	−	0.243249i
$206$	1.43768	+	1.59670i	0.100168	+	0.111248i
$207$	0.617399	+	5.87416i	0.0429122	+	0.408283i
$208$	2.62299	+	0.557534i	0.181872	+	0.0386581i
$209$	2.55533	+	7.86450i	0.176756	+	0.543999i
$210$	2.95386	−	0.627863i	0.203836	−	0.0433267i
$211$	−1.53791	−	2.66375i	−0.105874	−	0.183380i	0.808221	−	0.588880i	$-0.200431\pi$
$211$	−1.53791	−	2.66375i	−0.105874	−	0.183380i	−0.914095	+	0.405500i	$0.867097\pi$
$212$	1.14752	−	1.98756i	0.0788120	−	0.136506i
$213$	−0.499344	+	1.53682i	−0.0342145	+	0.105301i
$214$	−1.03951	+	9.89024i	−0.0710591	+	0.676083i
$215$	−9.04360	+	6.57056i	−0.616768	+	0.448109i
$216$	−1.00000			−0.0680414
$217$	13.0633	+	10.5856i	0.886796	+	0.718596i
$218$	1.27845			0.0865878
$219$	5.54678	−	4.02997i	0.374816	−	0.272320i
$220$	0.241221	−	2.29507i	0.0162631	−	0.154733i
$221$	−2.89344	+	8.90509i	−0.194634	+	0.599021i
$222$	1.24027	−	2.14821i	0.0832415	−	0.144179i
$223$	1.20235	+	2.08252i	0.0805150	+	0.139456i	0.903471	−	0.428649i	$-0.141010\pi$
$223$	1.20235	+	2.08252i	0.0805150	+	0.139456i	−0.822956	+	0.568105i	$0.807677\pi$
$224$	2.95386	−	0.627863i	0.197363	−	0.0419509i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−3.75771	−	0.798727i	−0.249959	−	0.0531305i
$227$	0.693130	+	6.59469i	0.0460046	+	0.437705i	0.993145	+	0.116886i	$0.0372913\pi$
$227$	0.693130	+	6.59469i	0.0460046	+	0.437705i	−0.947141	+	0.320819i	$0.896042\pi$
$228$	−2.39770	−	2.66292i	−0.158792	−	0.176356i
$229$	5.54304	+	2.46792i	0.366294	+	0.163085i	0.581626	−	0.813456i	$-0.302417\pi$
$229$	5.54304	+	2.46792i	0.366294	+	0.163085i	−0.215332	+	0.976541i	$0.569083\pi$
$230$	5.39587	−	2.40240i	0.355793	−	0.158409i
$231$	−4.66313	+	5.17893i	−0.306812	+	0.340749i
$232$	8.41017	+	6.11035i	0.552155	+	0.401164i
$233$	−15.7936	−	11.4747i	−1.03467	−	0.751733i	−0.0654331	−	0.997857i	$-0.520843\pi$
$233$	−15.7936	−	11.4747i	−1.03467	−	0.751733i	−0.969238	+	0.246124i	$0.920843\pi$
$234$	1.79434	−	1.99281i	0.117299	−	0.130274i
$235$	5.35735	−	2.38525i	0.349475	−	0.155596i
$236$	−0.173648	−	0.0773131i	−0.0113035	−	0.00503265i
$237$	−5.41750	−	6.01674i	−0.351905	−	0.390830i
$238$	1.10220	+	10.4867i	0.0714449	+	0.679753i
$239$	0.921755	+	0.195925i	0.0596234	+	0.0126733i	0.237627	−	0.971357i	$-0.423630\pi$
$239$	0.921755	+	0.195925i	0.0596234	+	0.0126733i	−0.178003	+	0.984030i	$0.556964\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−8.26116	+	1.75596i	−0.532148	+	0.113112i	−0.466146	−	0.884708i	$-0.654358\pi$
$241$	−8.26116	+	1.75596i	−0.532148	+	0.113112i	−0.0660022	+	0.997819i	$0.521024\pi$
$242$	−2.83724	−	4.91424i	−0.182385	−	0.315900i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.94975	+	9.07840i	−0.188838	+	0.581185i
$245$	−0.221550	+	2.10791i	−0.0141543	+	0.134669i
$246$	−6.92742	+	5.03307i	−0.441676	+	0.320897i
$247$	9.60897			0.611404
$248$	−3.03396	+	4.66852i	−0.192657	+	0.296451i
$249$	−15.7790			−0.999954
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−0.529694	+	5.03970i	−0.0334340	+	0.318103i	0.965004	+	0.262235i	$0.0844595\pi$
$251$	−0.529694	+	5.03970i	−0.0334340	+	0.318103i	−0.998438	+	0.0558686i	$0.982207\pi$
$252$	0.933186	−	2.87205i	0.0587852	−	0.180922i
$253$	−6.81526	+	11.8044i	−0.428472	+	0.742135i
$254$	−9.69981	−	16.8006i	−0.608620	−	1.05416i
$255$	−3.41542	+	0.725969i	−0.213882	+	0.0454620i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	25.1110	+	5.33751i	1.56638	+	0.332945i	0.907747	−	0.419517i	$-0.137801\pi$
$257$	25.1110	+	5.33751i	1.56638	+	0.332945i	0.658635	+	0.752462i	$0.271134\pi$
$258$	1.16847	+	11.1173i	0.0727459	+	0.692131i
$259$	5.01237	+	5.56680i	0.311454	+	0.345904i
$260$	−2.44976	−	1.09070i	−0.151927	−	0.0676425i
$261$	9.49680	−	4.22825i	0.587837	−	0.261722i
$262$	7.55797	−	8.39397i	0.466933	−	0.518581i
$263$	−24.6641	−	17.9195i	−1.52085	−	1.10497i	−0.961062	−	0.276332i	$-0.910881\pi$
$263$	−24.6641	−	17.9195i	−1.52085	−	1.10497i	−0.559792	−	0.828633i	$-0.689119\pi$
$264$	−1.86698	−	1.35644i	−0.114904	−	0.0834829i
$265$	−1.53568	+	1.70555i	−0.0943361	+	0.104771i
$266$	9.88553	−	4.40132i	0.606121	−	0.269862i
$267$	−10.2832	−	4.57838i	−0.629322	−	0.280192i
$268$	−10.7551	−	11.9447i	−0.656971	−	0.729640i
$269$	0.716844	+	6.82031i	0.0437067	+	0.415842i	0.994398	+	0.105702i	$0.0337091\pi$
$269$	0.716844	+	6.82031i	0.0437067	+	0.415842i	−0.950691	+	0.310140i	$0.899624\pi$
$270$	0.978148	+	0.207912i	0.0595282	+	0.0126531i
$271$	−3.00041	−	9.23430i	−0.182262	−	0.560944i	0.817629	−	0.575746i	$-0.195288\pi$
$271$	−3.00041	−	9.23430i	−0.182262	−	0.560944i	−0.999890	+	0.0148019i	$0.995288\pi$
$272$	−3.41542	+	0.725969i	−0.207090	+	0.0440184i
$273$	4.04901	+	7.01309i	0.245057	+	0.424451i
$274$	8.96013	−	15.5194i	0.541301	−	0.937561i
$275$	−0.713121	+	2.19476i	−0.0430028	+	0.132349i
$276$	0.617399	−	5.87416i	0.0371631	−	0.353583i
$277$	25.1581	−	18.2785i	1.51161	−	1.09825i	0.546147	−	0.837689i	$-0.316094\pi$
$277$	25.1581	−	18.2785i	1.51161	−	1.09825i	0.965459	−	0.260556i	$-0.0839059\pi$
$278$	−7.97812			−0.478496
$279$	2.52608	+	4.96175i	0.151232	+	0.297052i
$280$	−3.01985			−0.180471
$281$	−15.4380	+	11.2164i	−0.920953	+	0.669111i	−0.943761	−	0.330628i	$-0.892739\pi$
$281$	−15.4380	+	11.2164i	−0.920953	+	0.669111i	0.0228081	+	0.999740i	$0.492739\pi$
$282$	0.612991	−	5.83222i	0.0365031	−	0.347304i
$283$	5.42368	−	16.6924i	0.322405	−	0.992259i	−0.650194	−	0.759768i	$-0.725312\pi$
$283$	5.42368	−	16.6924i	0.322405	−	0.992259i	0.972599	−	0.232491i	$-0.0746876\pi$
$284$	0.807955	−	1.39942i	0.0479433	−	0.0830402i
$285$	1.79165	+	3.10323i	0.106128	+	0.183820i
$286$	6.05310	−	1.28663i	0.357928	−	0.0760798i
$287$	−7.99065	−	24.5927i	−0.471673	−	1.45166i
$288$	0.978148	+	0.207912i	0.0576379	+	0.0122513i
$289$	0.502562	+	4.78155i	0.0295624	+	0.281268i
$290$	−6.95598	−	7.72539i	−0.408469	−	0.453651i
$291$	−5.94019	−	2.64474i	−0.348220	−	0.155038i
$292$	−6.26344	+	2.78866i	−0.366540	+	0.163194i
$293$	−5.25180	+	5.83272i	−0.306814	+	0.340751i	−0.876758	−	0.480932i	$-0.840298\pi$
$293$	−5.25180	+	5.83272i	−0.306814	+	0.340751i	0.569944	+	0.821684i	$0.306965\pi$
$294$	1.71472	+	1.24582i	0.100005	+	0.0726577i
$295$	0.153779	+	0.111727i	0.00895336	+	0.00650500i
$296$	−1.65981	+	1.84340i	−0.0964743	+	0.107146i
$297$	−2.10820	+	0.938630i	−0.122330	+	0.0544648i
$298$	4.54365	+	2.02296i	0.263206	+	0.117187i
$299$	10.5983	+	11.7706i	0.612914	+	0.680710i
$300$	−0.104528	−	0.994522i	−0.00603495	−	0.0574187i
$301$	−33.0198	−	7.01857i	−1.90323	−	0.404544i
$302$	−2.43793	−	7.50318i	−0.140287	−	0.431759i
$303$	−4.07704	+	0.866602i	−0.234220	+	0.0497850i
$304$	1.79165	+	3.10323i	0.102758	+	0.177983i
$305$	4.77279	−	8.26672i	0.273289	−	0.473351i
$306$	−1.07900	+	3.32082i	−0.0616824	+	0.189839i
$307$	1.24544	−	11.8495i	0.0710808	−	0.676289i	−0.899731	−	0.436445i	$-0.856237\pi$
$307$	1.24544	−	11.8495i	0.0710808	−	0.676289i	0.970812	−	0.239843i	$-0.0770961\pi$
$308$	5.63799	−	4.09624i	0.321254	−	0.233405i
$309$	−2.14858			−0.122228
$310$	3.93830	−	3.93571i	0.223680	−	0.223533i
$311$	−28.3944			−1.61010			−0.805048	−	0.593209i	$-0.797861\pi$
$311$	−28.3944			−1.61010			−0.805048	+	0.593209i	$0.797861\pi$
$312$	−2.16945	+	1.57620i	−0.122821	+	0.0892348i
$313$	3.01903	−	28.7241i	0.170646	−	1.62358i	−0.489192	−	0.872176i	$-0.662708\pi$
$313$	3.01903	−	28.7241i	0.170646	−	1.62358i	0.659838	−	0.751408i	$-0.270625\pi$
$314$	−5.60431	+	17.2483i	−0.316269	+	0.973377i
$315$	−1.50993	+	2.61527i	−0.0850747	+	0.147354i
$316$	4.04816	+	7.01163i	0.227727	+	0.394435i
$317$	−11.7879	+	2.50560i	−0.662075	+	0.140728i	−0.526681	−	0.850063i	$-0.676564\pi$
$317$	−11.7879	+	2.50560i	−0.662075	+	0.140728i	−0.135395	+	0.990792i	$0.543230\pi$
$318$	0.709206	+	2.18271i	0.0397703	+	0.122400i
$319$	23.4656	+	4.98778i	1.31382	+	0.279262i
$320$	−0.104528	−	0.994522i	−0.00584332	−	0.0555955i
$321$	−6.65431	−	7.39036i	−0.371407	−	0.412490i
$322$	16.2948	+	7.25489i	0.908071	+	0.404299i
$323$	−11.4302	+	5.08905i	−0.635993	+	0.283162i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	2.16945	+	1.57620i	0.120340	+	0.0874319i
$326$	2.06073	+	1.49721i	0.114133	+	0.0829225i
$327$	−0.855453	+	0.950076i	−0.0473066	+	0.0525393i
$328$	7.82247	−	3.48279i	0.431924	−	0.192305i
$329$	16.1784	+	7.20309i	0.891945	+	0.397119i
$330$	1.54416	+	1.71496i	0.0850031	+	0.0944055i
$331$	0.534346	+	5.08396i	0.0293703	+	0.279440i	0.999344	+	0.0362281i	$0.0115343\pi$
$331$	0.534346	+	5.08396i	0.0293703	+	0.279440i	−0.969973	+	0.243212i	$0.921799\pi$
$332$	15.4342	+	3.28064i	0.847062	+	0.180048i
$333$	0.766530	+	2.35914i	0.0420056	+	0.129280i
$334$	17.1090	−	3.63664i	0.936164	−	0.198988i
$335$	8.03661	+	13.9198i	0.439087	+	0.760521i
$336$	−1.50993	+	2.61527i	−0.0823733	+	0.142675i
$337$	6.63884	−	20.4322i	0.361641	−	1.11302i	−0.590417	−	0.807098i	$-0.701037\pi$
$337$	6.63884	−	20.4322i	0.361641	−	1.11302i	0.952058	−	0.305917i	$-0.0989632\pi$
$338$	−0.607212	+	5.77724i	−0.0330280	+	0.314240i
$339$	3.10797	−	2.25807i	0.168802	−	0.122642i
$340$	3.49172			0.189365
$341$	−2.01417	+	12.6899i	−0.109073	+	0.687198i
$342$	3.58331			0.193763
$343$	11.9236	−	8.66298i	0.643812	−	0.467757i
$344$	1.16847	−	11.1173i	0.0629998	−	0.599403i
$345$	−1.82522	+	5.61743i	−0.0982663	+	0.302433i
$346$	−4.00066	+	6.92935i	−0.215077	+	0.372524i
$347$	−3.80828	−	6.59613i	−0.204439	−	0.354099i	0.745515	−	0.666489i	$-0.232204\pi$
$347$	−3.80828	−	6.59613i	−0.204439	−	0.354099i	−0.949954	+	0.312390i	$0.898870\pi$
$348$	−10.1684	+	2.16135i	−0.545082	+	0.115861i
$349$	0.763199	+	2.34889i	0.0408531	+	0.125733i	0.969403	−	0.245475i	$-0.0789438\pi$
$349$	0.763199	+	2.34889i	0.0408531	+	0.125733i	−0.928550	+	0.371208i	$0.878944\pi$
$350$	2.95386	+	0.627863i	0.157891	+	0.0335607i
$351$	0.280303	+	2.66690i	0.0149615	+	0.142349i
$352$	1.54416	+	1.71496i	0.0823039	+	0.0914078i
$353$	31.9913	+	14.2435i	1.70273	+	0.758103i	0.998858	+	0.0477740i	$0.0152127\pi$
$353$	31.9913	+	14.2435i	1.70273	+	0.758103i	0.703870	+	0.710329i	$0.251454\pi$
$354$	0.173648	−	0.0773131i	0.00922929	−	0.00410914i
$355$	−1.08125	+	1.20085i	−0.0573870	+	0.0637348i
$356$	9.10659	+	6.61633i	0.482649	+	0.350665i
$357$	−8.53067	−	6.19789i	−0.451491	−	0.328027i
$358$	−12.5555	+	13.9443i	−0.663579	+	0.736979i
$359$	−12.2881	+	5.47099i	−0.648539	+	0.288748i	−0.704520	−	0.709684i	$-0.748838\pi$
$359$	−12.2881	+	5.47099i	−0.648539	+	0.288748i	0.0559817	+	0.998432i	$0.482171\pi$
$360$	−0.913545	−	0.406737i	−0.0481481	−	0.0214369i
$361$	−4.12178	−	4.57771i	−0.216936	−	0.240932i
$362$	−2.65834	−	25.2924i	−0.139719	−	1.32934i
$363$	5.55048	+	1.17979i	0.291325	+	0.0619230i
$364$	−2.50242	−	7.70167i	−0.131163	−	0.403677i
$365$	6.70637	−	1.42548i	0.351027	−	0.0746132i
$366$	−4.77279	−	8.26672i	−0.249478	−	0.432109i
$367$	−13.7298	+	23.7807i	−0.716691	+	1.24134i	0.245613	+	0.969368i	$0.421011\pi$
$367$	−13.7298	+	23.7807i	−0.716691	+	1.24134i	−0.962304	+	0.271977i	$0.912323\pi$
$368$	−1.82522	+	5.61743i	−0.0951459	+	0.292829i
$369$	0.895053	−	8.51586i	0.0465946	−	0.443318i
$370$	2.00680	−	1.45803i	0.104329	−	0.0757992i
$371$	−6.93068			−0.359823
$372$	−1.43927	−	5.37852i	−0.0746229	−	0.278863i
$373$	−30.6430			−1.58663			−0.793316	−	0.608810i	$-0.791647\pi$
$373$	−30.6430			−1.58663			−0.793316	+	0.608810i	$0.791647\pi$
$374$	−6.51896	+	4.73630i	−0.337087	+	0.244908i
$375$	−0.104528	+	0.994522i	−0.00539783	+	0.0513569i
$376$	−1.81218	+	5.57733i	−0.0934562	+	0.287629i
$377$	13.9383	−	24.1419i	0.717859	−	1.24337i
$378$	1.50993	+	2.61527i	0.0776623	+	0.134515i
$379$	−15.8426	+	3.36745i	−0.813779	+	0.172974i	−0.595959	−	0.803015i	$-0.703228\pi$
$379$	−15.8426	+	3.36745i	−0.813779	+	0.172974i	−0.217820	+	0.975989i	$0.569895\pi$
$380$	−1.10730	−	3.40793i	−0.0568034	−	0.174823i
$381$	18.9757	+	4.03341i	0.972154	+	0.206638i
$382$	−1.49383	−	14.2128i	−0.0764309	−	0.727191i
$383$	−19.8346	−	22.0286i	−1.01350	−	1.12561i	−0.992051	−	0.125839i	$-0.959838\pi$
$383$	−19.8346	−	22.0286i	−1.01350	−	1.12561i	−0.0214522	−	0.999770i	$-0.506829\pi$
$384$	−0.913545	−	0.406737i	−0.0466192	−	0.0207562i
$385$	−6.36645	+	2.83452i	−0.324464	+	0.144461i
$386$	−7.24395	+	8.04522i	−0.368707	+	0.409491i
$387$	−9.04360	−	6.57056i	−0.459712	−	0.334000i
$388$	5.26051	+	3.82198i	0.267062	+	0.194032i
$389$	−1.49292	+	1.65806i	−0.0756942	+	0.0840670i	−0.779802	−	0.626026i	$-0.784680\pi$
$389$	−1.49292	+	1.65806i	−0.0756942	+	0.0840670i	0.704108	+	0.710093i	$0.251347\pi$
$390$	2.44976	−	1.09070i	0.124048	−	0.0552298i
$391$	−18.8409	−	8.38850i	−0.952824	−	0.424225i
$392$	−1.41823	−	1.57511i	−0.0716316	−	0.0795549i
$393$	1.18067	+	11.2333i	0.0595569	+	0.566646i
$394$	−1.90932	−	0.405838i	−0.0961900	−	0.0204458i
$395$	−2.50190	−	7.70007i	−0.125884	−	0.387432i
$396$	2.25728	−	0.479800i	0.113433	−	0.0241108i
$397$	2.88679	+	5.00006i	0.144884	+	0.250946i	0.929330	−	0.369251i	$-0.120386\pi$
$397$	2.88679	+	5.00006i	0.144884	+	0.250946i	−0.784446	+	0.620197i	$0.787053\pi$
$398$	6.10177	−	10.5686i	0.305854	−	0.529755i
$399$	−3.34389	+	10.2914i	−0.167404	+	0.515217i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	−12.7029	+	9.22917i	−0.634351	+	0.460883i	−0.857905	−	0.513809i	$-0.828234\pi$
$401$	−12.7029	+	9.22917i	−0.634351	+	0.460883i	0.223554	+	0.974692i	$0.428234\pi$
$402$	16.0732			0.801659
$403$	13.3009	+	6.78267i	0.662566	+	0.337869i
$404$	4.16812			0.207372
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	3.28146	−	31.2210i	0.162856	−	1.54947i
$407$	−1.76893	+	5.44420i	−0.0876825	+	0.269859i
$408$	1.74586	−	3.02392i	0.0864329	−	0.149706i
$409$	11.7523	+	20.3555i	0.581111	+	1.00651i	0.995348	+	0.0963452i	$0.0307153\pi$
$409$	11.7523	+	20.3555i	0.581111	+	1.00651i	−0.414237	+	0.910169i	$0.635951\pi$
$410$	−8.37565	+	1.78030i	−0.413644	+	0.0879227i
$411$	5.53766	+	17.0432i	0.273153	+	0.840678i
$412$	2.10163	+	0.446714i	0.103540	+	0.0220080i
$413$	0.0600012	+	0.570873i	0.00295247	+	0.0280908i
$414$	3.95223	+	4.38940i	0.194242	+	0.215727i
$415$	−14.4148	−	6.41790i	−0.707597	−	0.315042i
$416$	2.44976	−	1.09070i	0.120109	−	0.0534761i
$417$	5.33840	−	5.92890i	0.261423	−	0.290339i
$418$	6.68995	+	4.86053i	0.327216	+	0.237736i
$419$	−32.7116	−	23.7664i	−1.59807	−	1.16106i	−0.891091	−	0.453825i	$-0.850059\pi$
$419$	−32.7116	−	23.7664i	−1.59807	−	1.16106i	−0.706976	−	0.707238i	$-0.749941\pi$
$420$	2.02068	−	2.24419i	0.0985989	−	0.109505i
$421$	−14.9967	+	6.67698i	−0.730897	+	0.325416i	−0.738223	−	0.674557i	$-0.764335\pi$
$421$	−14.9967	+	6.67698i	−0.730897	+	0.325416i	0.00732602	+	0.999973i	$0.497668\pi$
$422$	−2.80991	−	1.25105i	−0.136784	−	0.0609003i
$423$	3.92402	+	4.35806i	0.190792	+	0.211896i
$424$	−0.239897	−	2.28247i	−0.0116504	−	0.110846i
$425$	−3.41542	−	0.725969i	−0.165672	−	0.0352147i
$426$	0.499344	+	1.53682i	0.0241933	+	0.0744592i
$427$	28.1964	−	5.99332i	1.36452	−	0.290037i
$428$	4.97236	+	8.61237i	0.240348	+	0.416295i
$429$	−3.09417	+	5.35925i	−0.149388	+	0.258747i
$430$	−3.45435	+	10.6314i	−0.166583	+	0.512691i
$431$	−0.221789	+	2.11018i	−0.0106832	+	0.101644i	−0.998564	−	0.0535699i	$-0.982940\pi$
$431$	−0.221789	+	2.11018i	−0.0106832	+	0.101644i	0.987881	+	0.155214i	$0.0496067\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−22.0066			−1.05757			−0.528784	−	0.848756i	$-0.677352\pi$
$433$	−22.0066			−1.05757			−0.528784	+	0.848756i	$0.677352\pi$
$434$	16.7905	+	0.885493i	0.805970	+	0.0425050i
$435$	10.3955			0.498428
$436$	1.03429	−	0.751456i	0.0495336	−	0.0359882i
$437$	−2.21233	+	21.0489i	−0.105830	+	1.00691i
$438$	2.11868	−	6.52063i	0.101234	−	0.311568i
$439$	5.48673	−	9.50329i	0.261867	−	0.453567i	−0.704871	−	0.709336i	$-0.748995\pi$
$439$	5.48673	−	9.50329i	0.261867	−	0.453567i	0.966738	+	0.255768i	$0.0823284\pi$
$440$	−1.15385	−	1.99853i	−0.0550078	−	0.0952764i
$441$	−2.07320	+	0.440672i	−0.0987238	+	0.0209844i
$442$	2.89344	+	8.90509i	0.137627	+	0.423572i
$443$	5.13713	+	1.09193i	0.244072	+	0.0518792i	0.328323	−	0.944565i	$-0.393516\pi$
$443$	5.13713	+	1.09193i	0.244072	+	0.0518792i	−0.0842511	+	0.996445i	$0.526850\pi$
$444$	−0.259287	−	2.46695i	−0.0123052	−	0.117076i
$445$	−7.53198	−	8.36511i	−0.357050	−	0.396544i
$446$	2.19679	+	0.978076i	0.104021	+	0.0463132i
$447$	−4.54365	+	2.02296i	−0.214907	+	0.0956829i
$448$	2.02068	−	2.24419i	0.0954680	−	0.106028i
$449$	−4.76780	−	3.46401i	−0.225006	−	0.163477i	0.469571	−	0.882895i	$-0.344409\pi$
$449$	−4.76780	−	3.46401i	−0.225006	−	0.163477i	−0.694577	+	0.719418i	$0.744409\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	13.2223	−	14.6848i	0.622612	−	0.691481i
$452$	−3.50953	+	1.56254i	−0.165075	+	0.0734959i
$453$	7.20724	+	3.20887i	0.338626	+	0.150766i
$454$	4.43702	+	4.92780i	0.208239	+	0.231273i
$455$	0.846473	+	8.05365i	0.0396833	+	0.377561i
$456$	−3.50500	−	0.745011i	−0.164137	−	0.0348884i
$457$	5.46139	+	16.8084i	0.255473	+	0.786265i	0.993736	+	0.111752i	$0.0356463\pi$
$457$	5.46139	+	16.8084i	0.255473	+	0.786265i	−0.738263	+	0.674513i	$0.764354\pi$
$458$	5.93502	−	1.26153i	0.277325	−	0.0589473i
$459$	−1.74586	−	3.02392i	−0.0814898	−	0.141144i
$460$	2.95326	−	5.11520i	0.137696	−	0.238497i
$461$	−0.337634	+	1.03913i	−0.0157252	+	0.0483972i	−0.958611	−	0.284718i	$-0.908100\pi$
$461$	−0.337634	+	1.03913i	−0.0157252	+	0.0483972i	0.942886	+	0.333116i	$0.108100\pi$
$462$	−0.728453	+	6.93077i	−0.0338907	+	0.322448i
$463$	−27.3754	+	19.8894i	−1.27224	+	0.924337i	−0.999289	−	0.0376905i	$-0.988000\pi$
$463$	−27.3754	+	19.8894i	−1.27224	+	0.924337i	−0.272952	+	0.962028i	$0.588000\pi$
$464$	10.3955			0.482601
$465$	0.289565	+	5.56023i	0.0134282	+	0.257849i
$466$	−19.5219			−0.904336
$467$	−14.8595	+	10.7961i	−0.687616	+	0.499582i	−0.875876	−	0.482537i	$-0.839715\pi$
$467$	−14.8595	+	10.7961i	−0.687616	+	0.499582i	0.188260	+	0.982119i	$0.439715\pi$
$468$	0.280303	−	2.66690i	0.0129570	−	0.123278i
$469$	−14.9993	+	46.1631i	−0.692603	+	2.13161i
$470$	2.93217	−	5.07868i	0.135251	−	0.234262i
$471$	−9.06796	−	15.7062i	−0.417829	−	0.723702i
$472$	−0.185928	+	0.0395201i	−0.00855801	+	0.00181906i
$473$	−7.97163	−	24.5342i	−0.366536	−	1.12808i
$474$	−7.91940	−	1.68332i	−0.363750	−	0.0773175i
$475$	0.374558	+	3.56368i	0.0171859	+	0.163513i
$476$	7.05564	+	7.83608i	0.323395	+	0.359166i
$477$	−2.09662	−	0.933477i	−0.0959978	−	0.0427410i
$478$	0.860877	−	0.383287i	0.0393756	−	0.0175311i
$479$	−4.87156	+	5.41041i	−0.222587	+	0.247208i	−0.844087	−	0.536206i	$-0.819857\pi$
$479$	−4.87156	+	5.41041i	−0.222587	+	0.247208i	0.621500	+	0.783414i	$0.286524\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	5.38142	+	3.90983i	0.245372	+	0.178273i
$482$	−5.65129	+	6.27639i	−0.257409	+	0.285882i
$483$	−16.2948	+	7.25489i	−0.741437	+	0.330109i
$484$	−5.18390	−	2.30802i	−0.235632	−	0.104910i
$485$	−4.35092	−	4.83219i	−0.197565	−	0.219418i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	−17.3936	−	3.69713i	−0.788180	−	0.167533i	−0.203800	−	0.979013i	$-0.565329\pi$
$487$	−17.3936	−	3.69713i	−0.788180	−	0.167533i	−0.584381	+	0.811480i	$0.698663\pi$
$488$	2.94975	+	9.07840i	0.133529	+	0.410960i
$489$	−2.49154	+	0.529592i	−0.112671	+	0.0239490i
$490$	1.05976	+	1.83555i	0.0478750	+	0.0829219i
$491$	2.09910	−	3.63574i	0.0947309	−	0.164079i	−0.814765	−	0.579791i	$-0.803134\pi$
$491$	2.09910	−	3.63574i	0.0947309	−	0.164079i	0.909496	+	0.415712i	$0.136468\pi$
$492$	−2.64604	+	8.14367i	−0.119293	+	0.367145i
$493$	−3.79421	+	36.0995i	−0.170883	+	1.62584i
$494$	7.77382	−	5.64801i	0.349761	−	0.254116i
$495$	−2.30771			−0.103724
$496$	0.289565	+	5.56023i	0.0130018	+	0.249662i
$497$	−4.87981			−0.218889
$498$	−12.7655	+	9.27467i	−0.572035	+	0.415608i
$499$	−0.977545	+	9.30072i	−0.0437609	+	0.416357i	0.950609	+	0.310391i	$0.100460\pi$
$499$	−0.977545	+	9.30072i	−0.0437609	+	0.416357i	−0.994370	+	0.105966i	$0.966207\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−8.74563	+	15.1479i	−0.390726	+	0.676757i
$502$	2.53373	+	4.38855i	0.113086	+	0.195871i
$503$	5.16036	−	1.09687i	0.230089	−	0.0489069i	−0.0914242	−	0.995812i	$-0.529142\pi$
$503$	5.16036	−	1.09687i	0.230089	−	0.0489069i	0.321513	+	0.946905i	$0.395809\pi$
$504$	−0.933186	−	2.87205i	−0.0415674	−	0.127931i
$505$	−4.07704	−	0.866602i	−0.181426	−	0.0385633i
$506$	1.42478	+	13.5559i	0.0633391	+	0.602631i
$507$	−3.88702	−	4.31697i	−0.172629	−	0.191724i
$508$	−17.7224	−	7.89054i	−0.786306	−	0.350086i
$509$	8.48891	−	3.77950i	0.376264	−	0.167524i	−0.209886	−	0.977726i	$-0.567309\pi$
$509$	8.48891	−	3.77950i	0.376264	−	0.167524i	0.586150	+	0.810202i	$0.300643\pi$
$510$	−2.33642	+	2.59485i	−0.103458	+	0.114902i
$511$	16.7505	+	12.1699i	0.740996	+	0.538365i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−2.39770	+	2.66292i	−0.105861	+	0.117571i
$514$	23.4526	−	10.4418i	1.03445	−	0.460566i
$515$	−1.96282	−	0.873905i	−0.0864923	−	0.0385089i
$516$	7.47988	+	8.30725i	0.329283	+	0.365706i
$517$	1.41461	+	13.4591i	0.0622143	+	0.591929i
$518$	7.32718	+	1.55744i	0.321938	+	0.0684300i
$519$	−2.47254	−	7.60971i	−0.108533	−	0.334029i
$520$	−2.62299	+	0.557534i	−0.115026	+	0.0244495i
$521$	10.3711	+	17.9633i	0.454368	+	0.786988i	0.998652	−	0.0519133i	$-0.0165319\pi$
$521$	10.3711	+	17.9633i	0.454368	+	0.786988i	−0.544284	+	0.838901i	$0.683199\pi$
$522$	5.19777	−	9.00280i	0.227500	−	0.394042i
$523$	8.55659	−	26.3345i	0.374153	−	1.15153i	−0.569895	−	0.821718i	$-0.693016\pi$
$523$	8.55659	−	26.3345i	0.374153	−	1.15153i	0.944048	−	0.329808i	$-0.106984\pi$
$524$	1.18067	−	11.2333i	0.0515778	−	0.490730i
$525$	−2.44311	+	1.77503i	−0.106626	+	0.0774685i
$526$	−30.4865			−1.32928
$527$	−19.4141	−	1.02386i	−0.845691	−	0.0445998i
$528$	−2.30771			−0.100430
$529$	−9.61677	+	6.98699i	−0.418120	+	0.303782i
$530$	−0.239897	+	2.28247i	−0.0104205	+	0.0991440i
$531$	−0.0587384	+	0.180778i	−0.00254903	+	0.00784510i
$532$	5.41053	−	9.37132i	0.234576	−	0.406298i
$533$	−11.4809	−	19.8855i	−0.497294	−	0.861338i
$534$	−11.0104	+	2.34033i	−0.476466	+	0.101276i
$535$	−3.07309	−	9.45798i	−0.132861	−	0.408904i
$536$	−15.7220	−	3.34181i	−0.679086	−	0.144344i
$537$	−1.96136	−	18.6611i	−0.0846390	−	0.805286i
$538$	4.58882	+	5.09640i	0.197838	+	0.219721i
$539$	−4.46836	−	1.98944i	−0.192466	−	0.0856913i
$540$	0.913545	−	0.406737i	0.0393127	−	0.0175032i
$541$	−18.4749	+	20.5185i	−0.794299	+	0.882158i	−0.995241	−	0.0974451i	$-0.968933\pi$
$541$	−18.4749	+	20.5185i	−0.794299	+	0.882158i	0.200942	+	0.979603i	$0.435600\pi$
$542$	−7.85517	−	5.70711i	−0.337408	−	0.245142i
$543$	20.5747	+	14.9484i	0.882943	+	0.641496i
$544$	−2.33642	+	2.59485i	−0.100173	+	0.111253i
$545$	−1.16793	+	0.519994i	−0.0500284	+	0.0222741i
$546$	7.39791	+	3.29376i	0.316601	+	0.140960i
$547$	13.8656	+	15.3993i	0.592849	+	0.658425i	0.962670	−	0.270677i	$-0.0872477\pi$
$547$	13.8656	+	15.3993i	0.592849	+	0.658425i	−0.369821	+	0.929103i	$0.620581\pi$
$548$	−1.87318	−	17.8221i	−0.0800182	−	0.761322i
$549$	9.33700	+	1.98464i	0.398493	+	0.0847024i
$550$	0.713121	+	2.19476i	0.0304076	+	0.0935849i
$551$	36.4364	−	7.74480i	1.55224	−	0.329940i
$552$	−2.95326	−	5.11520i	−0.125699	−	0.217717i
$553$	12.2249	−	21.1741i	0.519854	−	0.900414i
$554$	9.60955	−	29.5752i	0.408271	−	1.25653i
$555$	−0.259287	+	2.46695i	−0.0110061	+	0.104716i
$556$	−6.45443	+	4.68942i	−0.273729	+	0.198876i
$557$	22.3223			0.945826			0.472913	−	0.881109i	$-0.343202\pi$
$557$	22.3223			0.945826			0.472913	+	0.881109i	$0.343202\pi$
$558$	4.96008	+	2.52934i	0.209977	+	0.107076i
$559$	−29.9762			−1.26786
$560$	−2.44311	+	1.77503i	−0.103240	+	0.0750085i
$561$	0.842277	−	8.01373i	0.0355610	−	0.338340i
$562$	−5.89679	+	18.1484i	−0.248741	+	0.765546i
$563$	7.44952	−	12.9029i	0.313960	−	0.543794i	−0.665256	−	0.746615i	$-0.731678\pi$
$563$	7.44952	−	12.9029i	0.313960	−	0.543794i	0.979216	+	0.202821i	$0.0650109\pi$
$564$	−2.93217	−	5.07868i	−0.123467	−	0.213851i
$565$	3.75771	−	0.798727i	0.158088	−	0.0336027i
$566$	−5.42368	−	16.6924i	−0.227974	−	0.701633i
$567$	−2.95386	−	0.627863i	−0.124051	−	0.0263678i
$568$	−0.168909	−	1.60706i	−0.00708725	−	0.0674306i
$569$	13.1833	+	14.6415i	0.552672	+	0.613804i	0.953149	−	0.302503i	$-0.0978221\pi$
$569$	13.1833	+	14.6415i	0.552672	+	0.613804i	−0.400477	+	0.916307i	$0.631155\pi$
$570$	3.27351	+	1.45746i	0.137112	+	0.0610464i
$571$	2.74192	−	1.22078i	0.114746	−	0.0510881i	−0.348561	−	0.937286i	$-0.613330\pi$
$571$	2.74192	−	1.22078i	0.114746	−	0.0510881i	0.463307	+	0.886198i	$0.346663\pi$
$572$	4.14080	−	4.59883i	0.173136	−	0.192287i
$573$	11.5617	+	8.40010i	0.482999	+	0.350919i
$574$	−20.9198	−	15.1991i	−0.873176	−	0.634399i
$575$	−3.95223	+	4.38940i	−0.164820	+	0.183051i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−1.31626	−	0.586035i	−0.0547965	−	0.0243970i	0.379155	−	0.925333i	$-0.376215\pi$
$577$	−1.31626	−	0.586035i	−0.0547965	−	0.0243970i	−0.433952	+	0.900936i	$0.642881\pi$
$578$	3.21711	+	3.57296i	0.133814	+	0.148616i
$579$	−1.13162	−	10.7666i	−0.0470283	−	0.447445i
$580$	−10.1684	−	2.16135i	−0.422219	−	0.0897454i
$581$	−14.7247	−	45.3181i	−0.610886	−	1.88011i
$582$	−6.36026	+	1.35191i	−0.263641	+	0.0560386i
$583$	−2.64814	−	4.58672i	−0.109675	−	0.189962i
$584$	−3.42810	+	5.93764i	−0.141856	+	0.245701i
$585$	−0.828658	+	2.55035i	−0.0342608	+	0.105444i
$586$	−0.820412	+	7.80570i	−0.0338909	+	0.322451i
$587$	−2.66736	+	1.93795i	−0.110094	+	0.0799878i	−0.641470	−	0.767148i	$-0.721675\pi$
$587$	−2.66736	+	1.93795i	−0.110094	+	0.0799878i	0.531376	+	0.847136i	$0.321675\pi$
$588$	2.11952			0.0874074
$589$	5.15736	+	19.2729i	0.212505	+	0.794126i
$590$	0.190081			0.00782553
$591$	1.57918	−	1.14734i	0.0649587	−	0.0471953i
$592$	−0.259287	+	2.46695i	−0.0106566	+	0.101391i
$593$	−10.7836	+	33.1885i	−0.442829	+	1.36289i	0.442018	+	0.897006i	$0.354263\pi$
$593$	−10.7836	+	33.1885i	−0.442829	+	1.36289i	−0.884847	+	0.465882i	$0.845737\pi$
$594$	−1.15385	+	1.99853i	−0.0473432	+	0.0820009i
$595$	−5.27224	−	9.13179i	−0.216141	−	0.374367i
$596$	4.86496	−	1.03408i	0.199276	−	0.0423575i
$597$	3.77110	+	11.6062i	0.154341	+	0.475012i
$598$	15.4928	+	3.29309i	0.633546	+	0.134664i
$599$	−4.00155	−	38.0722i	−0.163499	−	1.55559i	−0.701515	−	0.712654i	$-0.747493\pi$
$599$	−4.00155	−	38.0722i	−0.163499	−	1.55559i	0.538016	−	0.842934i	$-0.319174\pi$
$600$	−0.669131	−	0.743145i	−0.0273171	−	0.0303388i
$601$	−28.6146	−	12.7400i	−1.16721	−	0.519677i	−0.270687	−	0.962668i	$-0.587251\pi$
$601$	−28.6146	−	12.7400i	−1.16721	−	0.519677i	−0.896526	+	0.442991i	$0.853917\pi$
$602$	−30.8390	+	13.7304i	−1.25690	+	0.559609i
$603$	−10.7551	+	11.9447i	−0.437981	+	0.486427i
$604$	−6.38259	−	4.63722i	−0.259704	−	0.188686i
$605$	4.59075	+	3.33538i	0.186641	+	0.135602i
$606$	−2.78902	+	3.09752i	−0.113296	+	0.125828i
$607$	−22.7751	+	10.1401i	−0.924413	+	0.411575i	−0.813043	−	0.582204i	$-0.802190\pi$
$607$	−22.7751	+	10.1401i	−0.924413	+	0.411575i	−0.111370	+	0.993779i	$0.535524\pi$
$608$	3.27351	+	1.45746i	0.132759	+	0.0591079i
$609$	21.0060	+	23.3296i	0.851207	+	0.945361i
$610$	−0.997786	−	9.49330i	−0.0403992	−	0.384372i
$611$	15.3821	+	3.26958i	0.622295	+	0.132273i
$612$	1.07900	+	3.32082i	0.0436160	+	0.134236i
$613$	30.0332	−	6.38376i	1.21303	−	0.257838i	0.443398	−	0.896325i	$-0.353773\pi$
$613$	30.0332	−	6.38376i	1.21303	−	0.257838i	0.769633	+	0.638487i	$0.220439\pi$
$614$	−5.95740	−	10.3185i	−0.240421	−	0.416422i
$615$	4.28138	−	7.41557i	0.172642	−	0.299025i
$616$	2.15352	−	6.62786i	0.0867679	−	0.267044i
$617$	4.30033	−	40.9149i	0.173125	−	1.64717i	−0.470914	−	0.882179i	$-0.656076\pi$
$617$	4.30033	−	40.9149i	0.173125	−	1.64717i	0.644039	−	0.764993i	$-0.277258\pi$
$618$	−1.73824	+	1.26290i	−0.0699221	+	0.0508014i
$619$	4.68895			0.188465			0.0942325	−	0.995550i	$-0.469960\pi$
$619$	4.68895			0.188465			0.0942325	+	0.995550i	$0.469960\pi$
$620$	0.872800	−	5.49893i	0.0350525	−	0.220842i
$621$	−5.90652			−0.237020
$622$	−22.9715	+	16.6898i	−0.921074	+	0.669200i
$623$	3.55319	−	33.8064i	0.142356	−	1.35442i
$624$	−0.828658	+	2.55035i	−0.0331729	+	0.102096i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−14.4412	−	25.0129i	−0.577186	−	0.999715i
$627$	−8.08853	+	1.71927i	−0.323025	+	0.0686610i
$628$	5.60431	+	17.2483i	0.223636	+	0.688281i
$629$	−8.47209	−	1.80080i	−0.337804	−	0.0718025i
$630$	0.315661	+	3.00331i	0.0125762	+	0.119655i
$631$	−32.7939	−	36.4214i	−1.30551	−	1.44991i	−0.816165	−	0.577819i	$-0.803904\pi$
$631$	−32.7939	−	36.4214i	−1.30551	−	1.44991i	−0.489341	−	0.872092i	$-0.662763\pi$
$632$	7.39636	+	3.29307i	0.294212	+	0.130991i
$633$	2.80991	−	1.25105i	0.111684	−	0.0497249i
$634$	−8.06387	+	8.95583i	−0.320257	+	0.355682i
$635$	15.6946	+	11.4028i	0.622822	+	0.452507i
$636$	1.85673	+	1.34899i	0.0736240	+	0.0534909i
$637$	−3.80312	+	4.22380i	−0.150685	+	0.167353i
$638$	21.9158	−	9.75756i	0.867657	−	0.386306i
$639$	−1.47621	−	0.657250i	−0.0583978	−	0.0260004i
$640$	−0.669131	−	0.743145i	−0.0264497	−	0.0293754i
$641$	−1.67506	−	15.9371i	−0.0661609	−	0.629479i	−0.976485	−	0.215584i	$-0.930835\pi$
$641$	−1.67506	−	15.9371i	−0.0661609	−	0.629479i	0.910324	−	0.413895i	$-0.135832\pi$
$642$	−9.72740	−	2.06762i	−0.383910	−	0.0816025i
$643$	−7.29959	−	22.4658i	−0.287868	−	0.885965i	−0.985524	−	0.169533i	$-0.945774\pi$
$643$	−7.29959	−	22.4658i	−0.287868	−	0.885965i	0.697657	−	0.716432i	$-0.254226\pi$
$644$	17.4470	−	3.70848i	0.687510	−	0.146135i
$645$	−5.58925	−	9.68087i	−0.220077	−	0.381184i
$646$	−6.25595	+	10.8356i	−0.246137	+	0.426322i
$647$	14.2740	−	43.9307i	0.561167	−	1.72709i	−0.117907	−	0.993025i	$-0.537618\pi$
$647$	14.2740	−	43.9307i	0.561167	−	1.72709i	0.679074	−	0.734070i	$-0.262382\pi$
$648$	0.104528	−	0.994522i	0.00410627	−	0.0390685i
$649$	−0.354877	+	0.257833i	−0.0139302	+	0.0101208i
$650$	2.68159			0.105181
$651$	−11.8931	+	11.8853i	−0.466127	+	0.465820i
$652$	2.54720			0.0997560
$653$	28.8212	−	20.9398i	1.12786	−	0.819439i	0.142479	−	0.989798i	$-0.454493\pi$
$653$	28.8212	−	20.9398i	1.12786	−	0.819439i	0.985382	+	0.170358i	$0.0544925\pi$
$654$	−0.133635	+	1.27145i	−0.00522554	+	0.0497176i
$655$	−3.49041	+	10.7424i	−0.136382	+	0.419739i
$656$	4.28138	−	7.41557i	0.167160	−	0.289529i
$657$	3.42810	+	5.93764i	0.133743	+	0.231649i
$658$	17.3225	−	3.68201i	0.675301	−	0.143540i
$659$	10.8972	+	33.5382i	0.424495	+	1.30646i	0.903477	+	0.428637i	$0.141006\pi$
$659$	10.8972	+	33.5382i	0.424495	+	1.30646i	−0.478982	+	0.877825i	$0.658994\pi$
$660$	2.25728	+	0.479800i	0.0878645	+	0.0186762i
$661$	−0.937619	−	8.92085i	−0.0364692	−	0.346981i	−0.997507	−	0.0705647i	$-0.977520\pi$
$661$	−0.937619	−	8.92085i	−0.0364692	−	0.346981i	0.961038	−	0.276416i	$-0.0891468\pi$
$662$	3.42057	+	3.79893i	0.132944	+	0.147650i
$663$	−8.55386	−	3.80843i	−0.332205	−	0.147907i
$664$	14.4148	−	6.41790i	0.559404	−	0.249063i
$665$	−7.24070	+	8.04162i	−0.280782	+	0.311841i
$666$	2.00680	+	1.45803i	0.0777620	+	0.0564974i
$667$	49.6748	+	36.0909i	1.92342	+	1.39744i
$668$	11.7039	−	12.9985i	0.452839	−	0.502928i
$669$	−2.19679	+	0.978076i	−0.0849330	+	0.0378146i
$670$	14.6836	+	6.53757i	0.567278	+	0.252568i
$671$	14.7399	+	16.3703i	0.569028	+	0.631969i
$672$	0.315661	+	3.00331i	0.0121769	+	0.115855i
$673$	−31.1069	−	6.61197i	−1.19908	−	0.254873i	−0.435263	−	0.900303i	$-0.643345\pi$
$673$	−31.1069	−	6.61197i	−1.19908	−	0.254873i	−0.763819	+	0.645431i	$0.776678\pi$
$674$	−6.63884	−	20.4322i	−0.255719	−	0.787021i
$675$	−0.978148	+	0.207912i	−0.0376489	+	0.00800252i
$676$	2.90453	+	5.03080i	0.111713	+	0.193492i
$677$	−4.09788	+	7.09773i	−0.157494	+	0.272788i	−0.933964	−	0.357366i	$-0.883675\pi$
$677$	−4.09788	+	7.09773i	−0.157494	+	0.272788i	0.776470	+	0.630154i	$0.217008\pi$
$678$	1.18714	−	3.65364i	0.0455918	−	0.140317i
$679$	2.05254	−	19.5286i	0.0787691	−	0.749438i
$680$	2.82486	−	2.05238i	0.108328	−	0.0787052i
$681$	−6.63102			−0.254101
$682$	5.82946	+	11.4503i	0.223221	+	0.438453i
$683$	7.27008			0.278182			0.139091	−	0.990280i	$-0.455582\pi$
$683$	7.27008			0.278182			0.139091	+	0.990280i	$0.455582\pi$
$684$	2.89896	−	2.10622i	0.110844	−	0.0805331i
$685$	−1.87318	+	17.8221i	−0.0715704	+	0.680947i
$686$	4.55440	−	14.0170i	0.173888	−	0.535172i
$687$	−3.03381	+	5.25471i	−0.115747	+	0.200480i
$688$	−5.58925	−	9.68087i	−0.213088	−	0.369080i
$689$	−6.01987	+	1.27956i	−0.229339	+	0.0487475i
$690$	1.82522	+	5.61743i	0.0694848	+	0.213852i
$691$	−19.5109	−	4.14717i	−0.742229	−	0.157766i	−0.178748	−	0.983895i	$-0.557205\pi$
$691$	−19.5109	−	4.14717i	−0.742229	−	0.157766i	−0.563481	+	0.826129i	$0.690538\pi$
$692$	0.836366	+	7.95749i	0.0317938	+	0.302498i
$693$	−4.66313	−	5.17893i	−0.177138	−	0.196731i
$694$	−6.95807	−	3.09793i	−0.264125	−	0.117596i
$695$	7.28837	−	3.24499i	0.276464	−	0.123090i
$696$	−6.95598	+	7.72539i	−0.263666	+	0.292830i
$697$	24.1886	+	17.5741i	0.916209	+	0.665665i
$698$	1.99808	+	1.45169i	0.0756285	+	0.0549473i
$699$	13.0627	−	14.5076i	0.494078	−	0.548729i
$700$	2.75877	−	1.22829i	0.104272	−	0.0464248i
$701$	−15.3274	−	6.82418i	−0.578906	−	0.257746i	0.0963272	−	0.995350i	$-0.469290\pi$
$701$	−15.3274	−	6.82418i	−0.578906	−	0.257746i	−0.675234	+	0.737604i	$0.735957\pi$
$702$	1.79434	+	1.99281i	0.0677228	+	0.0752138i
$703$	0.929106	+	8.83985i	0.0350419	+	0.333401i
$704$	2.25728	+	0.479800i	0.0850744	+	0.0180831i
$705$	1.81218	+	5.57733i	0.0682508	+	0.210054i
$706$	34.2536	−	7.28084i	1.28915	−	0.274018i
$707$	−6.29356	−	10.9008i	−0.236694	−	0.409966i
$708$	0.0950407	−	0.164615i	0.00357185	−	0.00618662i
$709$	6.02309	−	18.5372i	0.226202	−	0.696178i	−0.771966	−	0.635664i	$-0.780726\pi$
$709$	6.02309	−	18.5372i	0.226202	−	0.696178i	0.998167	−	0.0605133i	$-0.0192738\pi$
$710$	−0.168909	+	1.60706i	−0.00633902	+	0.0603118i
$711$	6.55007	−	4.75890i	0.245647	−	0.178473i
$712$	11.2564			0.421850
$713$	−17.9201	+	27.5747i	−0.671114	+	1.03268i
$714$	−10.5445			−0.394617
$715$	−5.00647	+	3.63741i	−0.187231	+	0.136031i
$716$	−1.96136	+	18.6611i	−0.0732995	+	0.697398i
$717$	−0.291201	+	0.896225i	−0.0108751	+	0.0334702i
$718$	−6.72547	+	11.6489i	−0.250992	+	0.434732i
$719$	−10.8022	−	18.7099i	−0.402853	−	0.697761i	0.591216	−	0.806513i	$-0.298648\pi$
$719$	−10.8022	−	18.7099i	−0.402853	−	0.697761i	−0.994069	+	0.108752i	$0.965315\pi$
$720$	−0.978148	+	0.207912i	−0.0364534	+	0.00774841i
$721$	−2.00502	−	6.17083i	−0.0746709	−	0.229814i
$722$	−6.02530	−	1.28072i	−0.224239	−	0.0476634i
$723$	−0.882818	−	8.39945i	−0.0328324	−	0.312379i
$724$	−17.0171	−	18.8994i	−0.632436	−	0.702392i
$725$	9.49680	+	4.22825i	0.352702	+	0.157033i
$726$	5.18390	−	2.30802i	0.192392	−	0.0856586i
$727$	−22.0069	+	24.4411i	−0.816190	+	0.906471i	−0.997028	−	0.0770419i	$-0.975452\pi$
$727$	−22.0069	+	24.4411i	−0.816190	+	0.906471i	0.180838	+	0.983513i	$0.442119\pi$
$728$	−6.55143	−	4.75989i	−0.242812	−	0.176413i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	4.58769	−	5.09514i	0.169798	−	0.188580i
$731$	35.6577	−	15.8758i	1.31885	−	0.587189i
$732$	−8.72033	−	3.88254i	−0.322313	−	0.143503i
$733$	28.9247	+	32.1242i	1.06836	+	1.18653i	0.981727	+	0.190293i	$0.0609438\pi$
$733$	28.9247	+	32.1242i	1.06836	+	1.18653i	0.0866322	+	0.996240i	$0.472390\pi$
$734$	2.87031	+	27.3092i	0.105945	+	1.00800i
$735$	−2.07320	−	0.440672i	−0.0764711	−	0.0162544i
$736$	1.82522	+	5.61743i	0.0672783	+	0.207061i
$737$	−36.2817	+	7.71192i	−1.33646	+	0.284072i
$738$	−4.28138	−	7.41557i	−0.157600	−	0.272971i
$739$	14.4109	−	24.9604i	0.530114	−	0.918185i	−0.469268	−	0.883056i	$-0.655482\pi$
$739$	14.4109	−	24.9604i	0.530114	−	0.918185i	0.999383	−	0.0351293i	$-0.0111843\pi$
$740$	0.766530	−	2.35914i	0.0281782	−	0.0867236i
$741$	−1.00441	+	9.55633i	−0.0368980	+	0.351061i
$742$	−5.60704	+	4.07375i	−0.205841	+	0.149552i
$743$	−22.8035			−0.836580			−0.418290	−	0.908314i	$-0.637370\pi$
$743$	−22.8035			−0.836580			−0.418290	+	0.908314i	$0.637370\pi$
$744$	−4.32581	−	3.50533i	−0.158592	−	0.128512i
$745$	−4.97364			−0.182220
$746$	−24.7907	+	18.0115i	−0.907651	+	0.659447i
$747$	1.64936	−	15.6926i	0.0603468	−	0.574161i
$748$	−2.49002	+	7.66349i	−0.0910441	+	0.280205i
$749$	15.0158	−	26.0081i	0.548665	−	0.950316i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	28.9386	−	6.15110i	1.05599	−	0.224457i	0.352973	−	0.935634i	$-0.385171\pi$
$751$	28.9386	−	6.15110i	1.05599	−	0.224457i	0.703013	+	0.711177i	$0.251837\pi$
$752$	1.81218	+	5.57733i	0.0660835	+	0.203384i
$753$	−4.95673	−	1.05359i	−0.180633	−	0.0383948i
$754$	−2.91390	−	27.7239i	−0.106118	−	1.00964i
$755$	5.27898	+	5.86290i	0.192122	+	0.213373i
$756$	2.75877	+	1.22829i	0.100336	+	0.0446723i
$757$	−13.4680	+	5.99634i	−0.489503	+	0.217941i	−0.636619	−	0.771179i	$-0.719668\pi$
$757$	−13.4680	+	5.99634i	−0.489503	+	0.217941i	0.147116	+	0.989119i	$0.453001\pi$
$758$	−10.8376	+	12.0364i	−0.393639	+	0.437180i
$759$	−11.0273	−	8.01182i	−0.400267	−	0.290811i
$760$	−2.89896	−	2.10622i	−0.105156	−	0.0764005i
$761$	26.3733	−	29.2906i	0.956033	−	1.06178i	−0.0420019	−	0.999118i	$-0.513374\pi$
$761$	26.3733	−	29.2906i	0.956033	−	1.06178i	0.998035	−	0.0626644i	$-0.0199598\pi$
$762$	17.7224	−	7.89054i	0.642016	−	0.285844i
$763$	−3.52696	−	1.57031i	−0.127685	−	0.0568489i
$764$	−9.56262	−	10.6204i	−0.345963	−	0.384231i
$765$	−0.364984	−	3.47259i	−0.0131960	−	0.125552i
$766$	−28.9946	−	6.16300i	−1.04762	−	0.222678i
$767$	0.157512	+	0.484773i	0.00568744	+	0.0175041i
$768$	−0.978148	+	0.207912i	−0.0352959	+	0.00750237i
$769$	5.94211	+	10.2920i	0.214278	+	0.371140i	0.953049	−	0.302816i	$-0.0979269\pi$
$769$	5.94211	+	10.2920i	0.214278	+	0.371140i	−0.738771	+	0.673956i	$0.764594\pi$
$770$	−3.48447	+	6.03528i	−0.125572	+	0.217496i
$771$	−7.93309	+	24.4155i	−0.285703	+	0.879304i
$772$	−1.13162	+	10.7666i	−0.0407277	+	0.387499i
$773$	15.2065	−	11.0482i	0.546941	−	0.397376i	−0.279715	−	0.960083i	$-0.590240\pi$
$773$	15.2065	−	11.0482i	0.546941	−	0.397376i	0.826656	+	0.562707i	$0.190240\pi$
$774$	−11.1785			−0.401803
$775$	−1.99702	+	5.19730i	−0.0717350	+	0.186692i
$776$	6.50235			0.233421
$777$	−6.06024	+	4.40303i	−0.217410	+	0.157958i
$778$	−0.233218	+	2.21892i	−0.00836125	+	0.0795520i
$779$	9.48157	−	29.1813i	0.339713	−	1.04553i
$780$	1.34080	−	2.32233i	0.0480082	−	0.0831527i
$781$	−1.86452	−	3.22945i	−0.0667179	−	0.115559i
$782$	−20.1732	+	4.28795i	−0.721393	+	0.153337i
$783$	3.21240	+	9.88675i	0.114802	+	0.353324i
$784$	−2.07320	−	0.440672i	−0.0740428	−	0.0157383i
$785$	−1.89572	−	18.0366i	−0.0676611	−	0.643753i
$786$	7.55797	+	8.39397i	0.269584	+	0.299403i
$787$	−6.00807	−	2.67497i	−0.214165	−	0.0953522i	0.296850	−	0.954924i	$-0.404064\pi$
$787$	−6.00807	−	2.67497i	−0.214165	−	0.0953522i	−0.511015	+	0.859572i	$0.670730\pi$
$788$	−1.78321	+	0.793938i	−0.0635244	+	0.0282829i
$789$	20.3995	−	22.6559i	0.726240	−	0.806571i
$790$	−6.55007	−	4.75890i	−0.233041	−	0.169314i
$791$	9.38562	+	6.81905i	0.333714	+	0.242457i
$792$	1.54416	−	1.71496i	0.0548693	−	0.0609385i
$793$	23.3844	−	10.4114i	0.830403	−	0.369719i
$794$	5.27442	+	2.34832i	0.187182	+	0.0833389i
$795$	−1.53568	−	1.70555i	−0.0544650	−	0.0604895i
$796$	−1.27562	−	12.1367i	−0.0452130	−	0.430173i
$797$	46.0350	+	9.78504i	1.63064	+	0.346604i	0.930185	−	0.367090i	$-0.119646\pi$
$797$	46.0350	+	9.78504i	1.63064	+	0.346604i	0.700457	+	0.713694i	$0.252979\pi$
$798$	3.34389	+	10.2914i	0.118373	+	0.364313i
$799$	−20.0292	+	4.25734i	−0.708582	+	0.150614i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	5.62818	−	9.74830i	0.198862	−	0.344439i
$802$	−4.85206	+	14.9331i	−0.171332	+	0.527307i
$803$	−1.65386	+	15.7354i	−0.0583634	+	0.555291i
$804$	13.0035	−	9.44760i	0.458598	−	0.333191i
$805$	−17.8368			−0.628666
$806$	14.7474	−	2.33079i	0.519456	−	0.0820985i
$807$	−6.85788			−0.241409
$808$	3.37208	−	2.44996i	0.118629	−	0.0861894i
$809$	3.32501	−	31.6354i	0.116901	−	1.11224i	−0.766052	−	0.642779i	$-0.777781\pi$
$809$	3.32501	−	31.6354i	0.116901	−	1.11224i	0.882953	−	0.469462i	$-0.155552\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	−8.90999	+	15.4325i	−0.312872	+	0.541910i	−0.978983	−	0.203943i	$-0.934624\pi$
$811$	−8.90999	+	15.4325i	−0.312872	+	0.541910i	0.666111	+	0.745853i	$0.267958\pi$
$812$	−15.6965	−	27.1872i	−0.550839	−	0.954082i
$813$	9.49734	−	2.01872i	0.333086	−	0.0707997i
$814$	1.76893	+	5.44420i	0.0620009	+	0.190819i
$815$	−2.49154	−	0.529592i	−0.0872747	−	0.0185508i
$816$	−0.364984	−	3.47259i	−0.0127770	−	0.121565i
$817$	−26.8027	−	29.7674i	−0.937708	−	1.04143i
$818$	21.4724	+	9.56014i	0.750766	+	0.334263i
$819$	−7.39791	+	3.29376i	−0.258504	+	0.115093i
$820$	−5.72961	+	6.36337i	−0.200087	+	0.222219i
$821$	22.9683	+	16.6874i	0.801599	+	0.582396i	0.911383	−	0.411560i	$-0.135016\pi$
$821$	22.9683	+	16.6874i	0.801599	+	0.582396i	−0.109784	+	0.993955i	$0.535016\pi$
$822$	14.4978	+	10.5333i	0.505669	+	0.367390i
$823$	−14.0773	+	15.6344i	−0.490703	+	0.544981i	−0.936736	−	0.350036i	$-0.886170\pi$
$823$	−14.0773	+	15.6344i	−0.490703	+	0.544981i	0.446034	+	0.895016i	$0.352836\pi$
$824$	1.96282	−	0.873905i	0.0683782	−	0.0304439i
$825$	−2.10820	−	0.938630i	−0.0733980	−	0.0326789i
$826$	0.384093	+	0.426578i	0.0133643	+	0.0148426i
$827$	4.40934	+	41.9520i	0.153328	+	1.45882i	0.752710	+	0.658352i	$0.228746\pi$
$827$	4.40934	+	41.9520i	0.153328	+	1.45882i	−0.599382	+	0.800463i	$0.704587\pi$
$828$	5.77745	+	1.22803i	0.200780	+	0.0426772i
$829$	−3.71832	−	11.4438i	−0.129143	−	0.397460i	0.865490	−	0.500925i	$-0.167007\pi$
$829$	−3.71832	−	11.4438i	−0.129143	−	0.397460i	−0.994633	+	0.103465i	$0.967007\pi$
$830$	−15.4342	+	3.28064i	−0.535729	+	0.113873i
$831$	15.5486	+	26.9309i	0.539374	+	0.934224i
$832$	1.34080	−	2.32233i	0.0464837	−	0.0805122i
$833$	2.28696	−	7.03854i	0.0792384	−	0.243871i
$834$	0.833940	−	7.93441i	0.0288770	−	0.274746i
$835$	−14.1507	+	10.2811i	−0.489706	+	0.355792i
$836$	8.26923			0.285997
$837$	−5.19861	+	1.99360i	−0.179690	+	0.0689088i
$838$	−40.4338			−1.39676
$839$	−43.9599	+	31.9388i	−1.51767	+	1.10265i	−0.555036	+	0.831826i	$0.687296\pi$
$839$	−43.9599	+	31.9388i	−1.51767	+	1.10265i	−0.962629	+	0.270822i	$0.912704\pi$
$840$	0.315661	−	3.00331i	0.0108913	−	0.103624i
$841$	24.4331	−	75.1975i	0.842522	−	2.59302i
$842$	−8.20799	+	14.2167i	−0.282866	+	0.489938i
$843$	−9.54120	−	16.5258i	−0.328616	−	0.569180i
$844$	−3.00862	+	0.639501i	−0.103561	+	0.0220125i
$845$	−1.79510	−	5.52475i	−0.0617533	−	0.190057i
$846$	5.73620	+	1.21927i	0.197215	+	0.0419193i
$847$	1.79121	+	17.0422i	0.0615467	+	0.585578i
$848$	−1.53568	−	1.70555i	−0.0527355	−	0.0585687i
$849$	16.0340	+	7.13880i	0.550286	+	0.245003i
$850$	−3.18984	+	1.42021i	−0.109411	+	0.0487128i
$851$	−9.80368	+	10.8881i	−0.336066	+	0.373239i
$852$	1.30730	+	0.949808i	0.0447873	+	0.0325399i
$853$	23.9236	+	17.3815i	0.819128	+	0.595132i	0.916463	−	0.400120i	$-0.131032\pi$
$853$	23.9236	+	17.3815i	0.819128	+	0.595132i	−0.0973343	+	0.995252i	$0.531032\pi$
$854$	19.2885	−	21.4221i	0.660041	−	0.733049i
$855$	−3.27351	+	1.45746i	−0.111952	+	0.0498442i
$856$	9.08495	+	4.04488i	0.310517	+	0.138251i
$857$	−16.8507	−	18.7146i	−0.575610	−	0.639280i	0.383086	−	0.923713i	$-0.374861\pi$
$857$	−16.8507	−	18.7146i	−0.575610	−	0.639280i	−0.958696	+	0.284433i	$0.908195\pi$
$858$	0.646857	+	6.15443i	0.0220833	+	0.210109i
$859$	46.5031	+	9.88453i	1.58666	+	0.337256i	0.914954	−	0.403558i	$-0.132227\pi$
$859$	46.5031	+	9.88453i	1.58666	+	0.337256i	0.671710	+	0.740814i	$0.265560\pi$
$860$	3.45435	+	10.6314i	0.117792	+	0.362527i
$861$	25.2932	−	5.37624i	0.861991	−	0.183222i
$862$	1.06090	+	1.83754i	0.0361345	+	0.0625868i
$863$	−11.3553	+	19.6680i	−0.386541	+	0.669508i	−0.991982	−	0.126382i	$-0.959663\pi$
$863$	−11.3553	+	19.6680i	−0.386541	+	0.669508i	0.605441	+	0.795890i	$0.292997\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	0.836366	−	7.95749i	0.0284373	−	0.270563i
$866$	−17.8037	+	12.9351i	−0.604994	+	0.439554i
$867$	−4.80789			−0.163285
$868$	14.1043	−	9.15283i	0.478730	−	0.310667i
$869$	18.6840			0.633810
$870$	8.41017	−	6.11035i	0.285132	−	0.207160i
$871$	−4.50537	+	42.8657i	−0.152659	+	1.45245i
$872$	0.395064	−	1.21588i	0.0133786	−	0.0411750i
$873$	3.25117	−	5.63120i	0.110036	−	0.190587i
$874$	10.5824	+	18.3293i	0.357956	+	0.619999i
$875$	−2.95386	+	0.627863i	−0.0998588	+	0.0212256i
$876$	−2.11868	−	6.52063i	−0.0715836	−	0.220312i
$877$	12.3985	+	2.63538i	0.418667	+	0.0889903i	0.412428	−	0.910990i	$-0.364681\pi$
$877$	12.3985	+	2.63538i	0.418667	+	0.0889903i	0.00623857	+	0.999981i	$0.498014\pi$
$878$	−1.14704	−	10.9133i	−0.0387107	−	0.368307i
$879$	−5.25180	−	5.83272i	−0.177139	−	0.196733i
$880$	−2.10820	−	0.938630i	−0.0710673	−	0.0316412i
$881$	0.327437	−	0.145784i	0.0110316	−	0.00491160i	−0.401213	−	0.915985i	$-0.631411\pi$
$881$	0.327437	−	0.145784i	0.0110316	−	0.00491160i	0.412245	+	0.911073i	$0.364745\pi$
$882$	−1.41823	+	1.57511i	−0.0477544	+	0.0530366i
$883$	32.7119	+	23.7666i	1.10084	+	0.799810i	0.981197	−	0.193007i	$-0.0618239\pi$
$883$	32.7119	+	23.7666i	1.10084	+	0.799810i	0.119646	+	0.992817i	$0.461824\pi$
$884$	7.57513	+	5.50365i	0.254779	+	0.185108i
$885$	−0.127189	+	0.141258i	−0.00427542	+	0.00474834i
$886$	4.79784	−	2.13614i	0.161187	−	0.0717649i
$887$	24.7593	+	11.0236i	0.831336	+	0.370135i	0.777862	−	0.628435i	$-0.216304\pi$
$887$	24.7593	+	11.0236i	0.831336	+	0.370135i	0.0534736	+	0.998569i	$0.482971\pi$
$888$	−1.65981	−	1.84340i	−0.0556995	−	0.0618605i
$889$	6.12370	+	58.2631i	0.205382	+	1.95408i
$890$	−11.0104	−	2.34033i	−0.369069	−	0.0784481i
$891$	−0.713121	−	2.19476i	−0.0238905	−	0.0735273i
$892$	2.35214	−	0.499963i	0.0787555	−	0.0167400i
$893$	10.5069	+	18.1985i	0.351599	+	0.608988i
$894$	−2.48682	+	4.30730i	−0.0831717	+	0.144058i
$895$	5.79836	−	17.8455i	0.193818	−	0.596510i
$896$	0.315661	−	3.00331i	0.0105455	−	0.100334i
$897$	−12.8139	+	9.30986i	−0.427844	+	0.310847i
$898$	−5.89332			−0.196663
$899$	55.9028	+	14.9988i	1.86446	+	0.500239i
$900$	1.00000			0.0333333
$901$	6.48317	−	4.71030i	0.215986	−	0.156923i
$902$	2.06552	−	19.6521i	0.0687743	−	0.654344i
$903$	10.4316	−	32.1052i	0.347143	−	1.06840i
$904$	−1.92083	+	3.32698i	−0.0638859	+	0.110654i
$905$	12.7158	+	22.0245i	0.422689	+	0.732119i
$906$	7.71691	−	1.64028i	0.256377	−	0.0544946i
$907$	−11.1399	−	34.2851i	−0.369894	−	1.13842i	−0.946859	−	0.321648i	$-0.895763\pi$
$907$	−11.1399	−	34.2851i	−0.369894	−	1.13842i	0.576965	−	0.816769i	$-0.304237\pi$
$908$	6.48611	+	1.37867i	0.215249	+	0.0457526i
$909$	−0.435688	−	4.14529i	−0.0144508	−	0.137491i
$910$	5.41863	+	6.01800i	0.179626	+	0.199495i
$911$	31.4313	+	13.9941i	1.04137	+	0.463646i	0.854888	−	0.518813i	$-0.173626\pi$
$911$	31.4313	+	13.9941i	1.04137	+	0.463646i	0.186479	+	0.982459i	$0.440292\pi$
$912$	−3.27351	+	1.45746i	−0.108397	+	0.0482614i
$913$	24.3653	−	27.0604i	0.806373	−	0.895568i
$914$	14.2981	+	10.3882i	0.472939	+	0.343610i
$915$	7.72254	+	5.61076i	0.255299	+	0.185486i
$916$	4.06003	−	4.50912i	0.134147	−	0.148985i
$917$	−31.1609	+	13.8737i	−1.02902	+	0.458151i
$918$	−3.18984	−	1.42021i	−0.105281	−	0.0468739i
$919$	19.4187	+	21.5667i	0.640564	+	0.711418i	0.972766	−	0.231790i	$-0.0744582\pi$
$919$	19.4187	+	21.5667i	0.640564	+	0.711418i	−0.332202	+	0.943208i	$0.607792\pi$
$920$	−0.617399	−	5.87416i	−0.0203551	−	0.193665i
$921$	11.6544	+	2.47723i	0.384027	+	0.0816274i
$922$	0.337634	+	1.03913i	0.0111194	+	0.0342220i
$923$	−4.23852	+	0.900925i	−0.139513	+	0.0296543i
$924$	3.48447	+	6.03528i	0.114631	+	0.198546i
$925$	−1.24027	+	2.14821i	−0.0407799	+	0.0706328i
$926$	−10.4565	+	32.1817i	−0.343621	+	1.05756i
$927$	0.224588	−	2.13681i	0.00737642	−	0.0701820i
$928$	8.41017	−	6.11035i	0.276077	−	0.200582i
$929$	−42.0756			−1.38046			−0.690228	−	0.723591i	$-0.742490\pi$
$929$	−42.0756			−1.38046			−0.690228	+	0.723591i	$0.742490\pi$
$930$	3.50248	+	4.32812i	0.114851	+	0.141925i
$931$	−7.59488			−0.248912
$932$	−15.7936	+	11.4747i	−0.517336	+	0.375866i
$933$	2.96802	−	28.2388i	0.0971686	−	0.924497i
$934$	−5.67583	+	17.4684i	−0.185719	+	0.571583i
$935$	4.02894	−	6.97832i	0.131760	−	0.228216i
$936$	−1.34080	−	2.32233i	−0.0438253	−	0.0759076i
$937$	19.6333	−	4.17318i	0.641391	−	0.136332i	0.124276	−	0.992248i	$-0.460339\pi$
$937$	19.6333	−	4.17318i	0.641391	−	0.136332i	0.517115	+	0.855916i	$0.327006\pi$
$938$	14.9993	+	46.1631i	0.489745	+	1.50728i
$939$	28.2512	+	6.00498i	0.921943	+	0.195965i
$940$	−0.612991	−	5.83222i	−0.0199936	−	0.190226i
$941$	6.45818	+	7.17253i	0.210531	+	0.233818i	0.839157	−	0.543890i	$-0.183049\pi$
$941$	6.45818	+	7.17253i	0.210531	+	0.233818i	−0.628626	+	0.777708i	$0.716382\pi$
$942$	−16.5680	−	7.37654i	−0.539814	−	0.240341i
$943$	46.2036	−	20.5712i	1.50460	−	0.669889i
$944$	−0.127189	+	0.141258i	−0.00413966	+	0.00459756i
$945$	−2.44311	−	1.77503i	−0.0794745	−	0.0577416i
$946$	−20.8700	−	15.1629i	−0.678542	−	0.492990i
$947$	34.3791	−	38.1818i	1.11717	−	1.24074i	0.149436	−	0.988771i	$-0.452254\pi$
$947$	34.3791	−	38.1818i	1.11717	−	1.24074i	0.967735	−	0.251972i	$-0.0810790\pi$
$948$	−7.39636	+	3.29307i	−0.240223	+	0.106954i
$949$	16.7960	+	7.47806i	0.545221	+	0.242748i
$950$	2.39770	+	2.66292i	0.0777917	+	0.0863964i
$951$	−1.25970	−	11.9852i	−0.0408486	−	0.388648i
$952$	10.3141	+	2.19232i	0.334281	+	0.0710535i
$953$	−5.19352	−	15.9840i	−0.168235	−	0.517773i	0.831026	−	0.556234i	$-0.187754\pi$
$953$	−5.19352	−	15.9840i	−0.168235	−	0.517773i	−0.999260	+	0.0384616i	$0.987754\pi$
$954$	−2.24489	+	0.477166i	−0.0726809	+	0.0154488i
$955$	7.14555	+	12.3765i	0.231225	+	0.400493i
$956$	0.471174	−	0.816097i	0.0152388	−	0.0263945i
$957$	−7.41328	+	22.8157i	−0.239637	+	0.737528i
$958$	−0.761012	+	7.24054i	−0.0245872	+	0.233931i
$959$	−43.7812	+	31.8089i	−1.41377	+	1.02716i
$960$	1.00000			0.0322749
$961$	−6.46522	+	30.3183i	−0.208555	+	0.978011i
$962$	6.65180			0.214463
$963$	8.04544	−	5.84536i	0.259261	−	0.188364i
$964$	−0.882818	+	8.39945i	−0.0284337	+	0.270528i
$965$	3.34539	−	10.2961i	0.107692	−	0.331442i
$966$	−8.91841	+	15.4471i	−0.286945	+	0.497004i
$967$	−2.13836	−	3.70374i	−0.0687649	−	0.119104i	0.829593	−	0.558369i	$-0.188573\pi$
$967$	−2.13836	−	3.70374i	−0.0687649	−	0.119104i	−0.898358	+	0.439264i	$0.855239\pi$
$968$	−5.55048	+	1.17979i	−0.178399	+	0.0379199i
$969$	−3.86639	−	11.8995i	−0.124206	−	0.382268i
$970$	−6.36026	−	1.35191i	−0.204216	−	0.0434073i
$971$	3.80931	+	36.2432i	0.122247	+	1.16310i	0.867891	+	0.496755i	$0.165475\pi$
$971$	3.80931	+	36.2432i	0.122247	+	1.16310i	−0.745644	+	0.666344i	$0.767858\pi$
$972$	0.669131	+	0.743145i	0.0214624	+	0.0238364i
$973$	22.0098	+	9.79940i	0.705602	+	0.314154i
$974$	−16.2449	+	7.23268i	−0.520519	+	0.231750i
$975$	−1.79434	+	1.99281i	−0.0574647	+	0.0638210i
$976$	7.72254	+	5.61076i	0.247193	+	0.179596i
$977$	41.8499	+	30.4057i	1.33890	+	0.972766i	0.999484	+	0.0321284i	$0.0102285\pi$
$977$	41.8499	+	30.4057i	1.33890	+	0.972766i	0.339413	+	0.940637i	$0.389771\pi$
$978$	−1.70441	+	1.89294i	−0.0545010	+	0.0605294i
$979$	23.7306	−	10.5656i	0.758435	−	0.337677i
$980$	1.93627	+	0.862085i	0.0618520	+	0.0275383i
$981$	−0.855453	−	0.950076i	−0.0273125	−	0.0303336i
$982$	−0.438831	−	4.17520i	−0.0140037	−	0.133236i
$983$	−34.1619	−	7.26133i	−1.08959	−	0.231601i	−0.372120	−	0.928185i	$-0.621369\pi$
$983$	−34.1619	−	7.26133i	−1.08959	−	0.231601i	−0.717475	+	0.696584i	$0.754702\pi$
$984$	2.64604	+	8.14367i	0.0843527	+	0.259611i
$985$	1.90932	−	0.405838i	0.0608359	−	0.0129311i
$986$	18.1492	+	31.4353i	0.577987	+	1.00110i
$987$	−8.85474	+	15.3369i	−0.281849	+	0.488178i
$988$	2.96933	−	9.13867i	0.0944671	−	0.290740i
$989$	6.90160	−	65.6644i	0.219458	−	2.08801i
$990$	−1.86698	+	1.35644i	−0.0593364	+	0.0431104i
$991$	−0.237376			−0.00754050			−0.00377025	−	0.999993i	$-0.501200\pi$
$991$	−0.237376			−0.00754050			−0.00377025	+	0.999993i	$0.501200\pi$
$992$	3.50248	+	4.32812i	0.111204	+	0.137418i
$993$	−5.11197			−0.162223
$994$	−3.94785	+	2.86828i	−0.125218	+	0.0909763i
$995$	−1.27562	+	12.1367i	−0.0404398	+	0.384759i
$996$	−4.87598	+	15.0067i	−0.154501	+	0.475506i
$997$	−15.2736	+	26.4546i	−0.483720	+	0.837827i	−0.999825	−	0.0186979i	$-0.994048\pi$
$997$	−15.2736	+	26.4546i	−0.483720	+	0.837827i	0.516105	+	0.856525i	$0.327381\pi$
$998$	4.67598	+	8.09903i	0.148015	+	0.256370i
$999$	−2.42634	+	0.515734i	−0.0767659	+	0.0163171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.f.121.1	✓	16
31.10	even	15	inner	930.2.bg.f.661.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.f.121.1	✓	16	1.1	even	1	trivial
930.2.bg.f.661.1	yes	16	31.10	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.95386 + 0.627863i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.95386 + 0.627863i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(-1.54416 - 1.71496i) q^{11} +(0.913545 + 0.406737i) q^{12} +(-2.44976 + 1.09070i) q^{13} +(-2.02068 + 2.24419i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(2.33642 - 2.59485i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(-3.27351 - 1.45746i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.315661 - 3.00331i) q^{21} +(-2.25728 - 0.479800i) q^{22} +(-1.82522 - 5.61743i) q^{23} +(0.978148 - 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.34080 + 2.32233i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.315661 + 3.00331i) q^{28} +(-8.41017 + 6.11035i) q^{29} -1.00000 q^{30} +(-3.50248 - 4.32812i) q^{31} -1.00000 q^{32} +(1.86698 - 1.35644i) q^{33} +(0.364984 - 3.47259i) q^{34} +(0.933186 - 2.87205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.24027 - 2.14821i) q^{37} +(-3.50500 + 0.745011i) q^{38} +(-0.828658 - 2.55035i) q^{39} +(0.978148 + 0.207912i) q^{40} +(0.895053 + 8.51586i) q^{41} +(-2.02068 - 2.24419i) q^{42} +(10.2121 + 4.54671i) q^{43} +(-2.10820 + 0.938630i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-4.77848 - 3.47177i) q^{46} +(-4.74436 - 3.44698i) q^{47} +(0.669131 - 0.743145i) q^{48} +(1.93627 - 0.862085i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(2.33642 + 2.59485i) q^{51} +(0.280303 + 2.66690i) q^{52} +(2.24489 + 0.477166i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(2.25728 - 0.479800i) q^{55} +(1.50993 + 2.61527i) q^{56} +(1.79165 - 3.10323i) q^{57} +(-3.21240 + 9.88675i) q^{58} +(0.0198689 - 0.189040i) q^{59} +(-0.809017 + 0.587785i) q^{60} -9.54559 q^{61} +(-5.37757 - 1.44281i) q^{62} +3.01985 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.280303 - 2.66690i) q^{65} +(0.713121 - 2.19476i) q^{66} +(8.03661 - 13.9198i) q^{67} +(-1.74586 - 3.02392i) q^{68} +(5.77745 - 1.22803i) q^{69} +(-0.933186 - 2.87205i) q^{70} +(1.58060 + 0.335967i) q^{71} +(0.104528 + 0.994522i) q^{72} +(-4.58769 - 5.09514i) q^{73} +(-2.26609 - 1.00893i) q^{74} +(0.913545 - 0.406737i) q^{75} +(-2.39770 + 2.66292i) q^{76} +(5.63799 + 4.09624i) q^{77} +(-2.16945 - 1.57620i) q^{78} +(-5.41750 + 6.01674i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(5.72961 + 6.36337i) q^{82} +(1.64936 + 15.6926i) q^{83} +(-2.95386 - 0.627863i) q^{84} +(1.07900 + 3.32082i) q^{85} +(10.9342 - 2.32414i) q^{86} +(-5.19777 - 9.00280i) q^{87} +(-1.15385 + 1.99853i) q^{88} +(-3.47841 + 10.7054i) q^{89} +(0.104528 - 0.994522i) q^{90} +(6.55143 - 4.75989i) q^{91} -5.90652 q^{92} +(4.67052 - 3.03089i) q^{93} -5.86435 q^{94} +(2.89896 - 2.10622i) q^{95} +(0.104528 - 0.994522i) q^{96} +(-2.00934 + 6.18410i) q^{97} +(1.05976 - 1.83555i) q^{98} +(1.15385 + 1.99853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9	\( 16 q + 4 q^{2} + 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} - 13 q^{7} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{12} - 6 q^{13} - 2 q^{14} - 4 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{18} + 9 q^{19} + 2 q^{20} + 2 q^{21} - 13 q^{22} - 3 q^{23} - 2 q^{24} - 8 q^{25} + q^{26} - 4 q^{27} + 2 q^{28} - q^{29} - 16 q^{30} - 19 q^{31} - 16 q^{32} + 14 q^{33} + 4 q^{34} + 11 q^{35} - 8 q^{36} - 3 q^{37} + 6 q^{38} - 13 q^{39} - 2 q^{40} - 2 q^{42} + 2 q^{43} - 7 q^{44} + 2 q^{45} - 7 q^{46} - q^{47} + 2 q^{48} + 3 q^{49} - 2 q^{50} + 6 q^{51} - 6 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} - 7 q^{56} - 6 q^{57} - 4 q^{58} + 16 q^{59} - 4 q^{60} - 28 q^{61} - 21 q^{62} - 14 q^{63} - 4 q^{64} - 6 q^{65} + 11 q^{66} + 47 q^{67} - 4 q^{68} + 9 q^{69} - 11 q^{70} + 3 q^{71} - 2 q^{72} - 27 q^{73} + 8 q^{74} + 2 q^{75} - 6 q^{76} + 14 q^{77} - 12 q^{78} + 4 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} + 66 q^{83} - 13 q^{84} + 18 q^{85} + 13 q^{86} + 3 q^{87} - 3 q^{88} - 45 q^{89} - 2 q^{90} + 12 q^{91} - 8 q^{92} - 26 q^{93} + 36 q^{94} - 18 q^{95} - 2 q^{96} + 5 q^{97} - 13 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 - 13 * q^7 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^12 - 6 * q^13 - 2 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^18 + 9 * q^19 + 2 * q^20 + 2 * q^21 - 13 * q^22 - 3 * q^23 - 2 * q^24 - 8 * q^25 + q^26 - 4 * q^27 + 2 * q^28 - q^29 - 16 * q^30 - 19 * q^31 - 16 * q^32 + 14 * q^33 + 4 * q^34 + 11 * q^35 - 8 * q^36 - 3 * q^37 + 6 * q^38 - 13 * q^39 - 2 * q^40 - 2 * q^42 + 2 * q^43 - 7 * q^44 + 2 * q^45 - 7 * q^46 - q^47 + 2 * q^48 + 3 * q^49 - 2 * q^50 + 6 * q^51 - 6 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 - 7 * q^56 - 6 * q^57 - 4 * q^58 + 16 * q^59 - 4 * q^60 - 28 * q^61 - 21 * q^62 - 14 * q^63 - 4 * q^64 - 6 * q^65 + 11 * q^66 + 47 * q^67 - 4 * q^68 + 9 * q^69 - 11 * q^70 + 3 * q^71 - 2 * q^72 - 27 * q^73 + 8 * q^74 + 2 * q^75 - 6 * q^76 + 14 * q^77 - 12 * q^78 + 4 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 + 66 * q^83 - 13 * q^84 + 18 * q^85 + 13 * q^86 + 3 * q^87 - 3 * q^88 - 45 * q^89 - 2 * q^90 + 12 * q^91 - 8 * q^92 - 26 * q^93 + 36 * q^94 - 18 * q^95 - 2 * q^96 + 5 * q^97 - 13 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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