LMFDB - Embedded newform 930.2.bg.c.541.1

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:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 40x^{14} + 654x^{12} + 5650x^{10} + 27831x^{8} + 78445x^{6} + 119819x^{4} + 87030x^{2} + 22801 $ x^16 + 40x^14 + 654x^12 + 5650x^10 + 27831x^8 + 78445x^6 + 119819x^4 + 87030*x^2 + 22801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.1
Root			$1.63922i$ of defining polynomial
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.426549 + 4.05835i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.426549 + 4.05835i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(0.249078 - 0.110896i) q^{11} +(0.978148 - 0.207912i) q^{12} +(0.982842 + 0.208909i) q^{13} +(3.72791 + 1.65977i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.45630 - 1.09361i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-8.10615 + 1.72301i) q^{19} +(-0.913545 + 0.406737i) q^{20} +(-2.73052 - 3.03255i) q^{21} +(-0.0284996 - 0.271156i) q^{22} +(-4.05657 + 2.94727i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.502399 - 0.870181i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.73052 - 3.03255i) q^{28} +(1.32839 - 4.08837i) q^{29} +1.00000 q^{30} +(-3.82591 + 4.04505i) q^{31} +1.00000 q^{32} +(-0.0842533 + 0.259305i) q^{33} +(-1.79912 + 1.99813i) q^{34} +(3.30136 + 2.39858i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.91272 + 10.2411i) q^{37} +(-0.866253 + 8.24184i) q^{38} +(-0.812899 + 0.590606i) q^{39} +(0.104528 + 0.994522i) q^{40} +(2.53213 + 2.81222i) q^{41} +(-3.72791 + 1.65977i) q^{42} +(-7.92111 + 1.68368i) q^{43} +(-0.266691 - 0.0566870i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(1.54947 + 4.76878i) q^{46} +(1.12587 + 3.46507i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(-9.44120 - 2.00679i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(2.45630 - 1.09361i) q^{51} +(-0.672342 - 0.746711i) q^{52} +(0.479723 + 4.56426i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.0284996 - 0.271156i) q^{55} +(-2.04035 - 3.53399i) q^{56} +(4.14362 - 7.17696i) q^{57} +(-3.47778 - 2.52675i) q^{58} +(-2.45414 + 2.72559i) q^{59} +(0.309017 - 0.951057i) q^{60} +6.54526 q^{61} +(2.66480 + 4.88864i) q^{62} +4.08070 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.672342 - 0.746711i) q^{65} +(0.220578 + 0.160259i) q^{66} +(2.37610 - 4.11552i) q^{67} +(1.34437 + 2.32853i) q^{68} +(0.524126 - 4.98673i) q^{69} +(3.30136 - 2.39858i) q^{70} +(-0.0675796 - 0.642977i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-1.41043 + 0.627966i) q^{73} +(11.5670 - 2.45865i) q^{74} +(0.978148 + 0.207912i) q^{75} +(7.57077 + 3.37073i) q^{76} +(0.343812 + 1.05815i) q^{77} +(0.310500 + 0.955620i) q^{78} +(-1.28088 - 0.570284i) q^{79} +(0.978148 + 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(3.45705 - 1.53918i) q^{82} +(0.748097 + 0.830846i) q^{83} +(0.426549 + 4.05835i) q^{84} +(-2.17524 + 1.58041i) q^{85} +(-0.846479 + 8.05371i) q^{86} +(2.14938 + 3.72284i) q^{87} +(-0.136325 + 0.236121i) q^{88} +(-9.49149 - 6.89597i) q^{89} +(-0.669131 + 0.743145i) q^{90} +(-1.26706 + 3.89960i) q^{91} +5.01420 q^{92} +(-0.446028 - 5.54987i) q^{93} +3.64339 q^{94} +(-2.56090 + 7.88164i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(-4.06080 - 2.95035i) q^{97} +(-4.82606 + 8.35898i) q^{98} +(-0.136325 - 0.236121i) 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} + 11 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 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	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
$7$	−0.426549	+	4.05835i	−0.161221	+	1.53391i	0.552520	+	0.833500i	$0.313666\pi$
$7$	−0.426549	+	4.05835i	−0.161221	+	1.53391i	−0.713740	+	0.700411i	$0.753000\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−0.669131	−	0.743145i	−0.211598	−	0.235003i
$11$	0.249078	−	0.110896i	0.0750997	−	0.0334365i	−0.368843	−	0.929492i	$-0.620246\pi$
$11$	0.249078	−	0.110896i	0.0750997	−	0.0334365i	0.443943	+	0.896055i	$0.353579\pi$
$12$	0.978148	−	0.207912i	0.282367	−	0.0600189i
$13$	0.982842	+	0.208909i	0.272591	+	0.0579410i	0.342179	−	0.939635i	$-0.388835\pi$
$13$	0.982842	+	0.208909i	0.272591	+	0.0579410i	−0.0695878	+	0.997576i	$0.522168\pi$
$14$	3.72791	+	1.65977i	0.996325	+	0.443592i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.45630	−	1.09361i	−0.595739	−	0.265240i	0.0866387	−	0.996240i	$-0.472387\pi$
$17$	−2.45630	−	1.09361i	−0.595739	−	0.265240i	−0.682378	+	0.731000i	$0.739054\pi$
$18$	−0.978148	−	0.207912i	−0.230552	−	0.0490053i
$19$	−8.10615	+	1.72301i	−1.85968	+	0.395287i	−0.994371	−	0.105956i	$-0.966210\pi$
$19$	−8.10615	+	1.72301i	−1.85968	+	0.395287i	−0.865307	+	0.501243i	$0.832876\pi$
$20$	−0.913545	+	0.406737i	−0.204275	+	0.0909491i
$21$	−2.73052	−	3.03255i	−0.595849	−	0.661757i
$22$	−0.0284996	−	0.271156i	−0.00607614	−	0.0578106i
$23$	−4.05657	+	2.94727i	−0.845853	+	0.614548i	−0.924000	−	0.382393i	$-0.875100\pi$
$23$	−4.05657	+	2.94727i	−0.845853	+	0.614548i	0.0781462	+	0.996942i	$0.475100\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.502399	−	0.870181i	0.0985286	−	0.170657i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.73052	−	3.03255i	0.516020	−	0.573098i
$29$	1.32839	−	4.08837i	0.246676	−	0.759192i	−0.748680	−	0.662932i	$-0.769312\pi$
$29$	1.32839	−	4.08837i	0.246676	−	0.759192i	0.995356	−	0.0962599i	$-0.0306880\pi$
$30$	1.00000			0.182574
$31$	−3.82591	+	4.04505i	−0.687153	+	0.726513i
$31$	−3.82591	+	4.04505i	−0.687153	+	0.726513i
$32$	1.00000			0.176777
$33$	−0.0842533	+	0.259305i	−0.0146666	+	0.0451392i
$34$	−1.79912	+	1.99813i	−0.308547	+	0.342677i
$35$	3.30136	+	2.39858i	0.558031	+	0.405433i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.91272	+	10.2411i	0.972045	+	1.68363i	0.689360	+	0.724419i	$0.257892\pi$
$37$	5.91272	+	10.2411i	0.972045	+	1.68363i	0.282686	+	0.959213i	$0.408775\pi$
$38$	−0.866253	+	8.24184i	−0.140525	+	1.33700i
$39$	−0.812899	+	0.590606i	−0.130168	+	0.0945726i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	2.53213	+	2.81222i	0.395453	+	0.439195i	0.907685	−	0.419652i	$-0.137848\pi$
$41$	2.53213	+	2.81222i	0.395453	+	0.439195i	−0.512232	+	0.858847i	$0.671181\pi$
$42$	−3.72791	+	1.65977i	−0.575228	+	0.256108i
$43$	−7.92111	+	1.68368i	−1.20796	+	0.256759i	−0.767521	−	0.641024i	$-0.778510\pi$
$43$	−7.92111	+	1.68368i	−1.20796	+	0.256759i	−0.440437	+	0.897783i	$0.645177\pi$
$44$	−0.266691	−	0.0566870i	−0.0402052	−	0.00854588i
$45$	−0.913545	−	0.406737i	−0.136183	−	0.0606327i
$46$	1.54947	+	4.76878i	0.228457	+	0.703119i
$47$	1.12587	+	3.46507i	0.164225	+	0.505433i	0.998978	−	0.0451913i	$-0.0143897\pi$
$47$	1.12587	+	3.46507i	0.164225	+	0.505433i	−0.834753	+	0.550624i	$0.814390\pi$
$48$	−0.913545	−	0.406737i	−0.131859	−	0.0587074i
$49$	−9.44120	−	2.00679i	−1.34874	−	0.286684i
$50$	−0.978148	+	0.207912i	−0.138331	+	0.0294032i
$51$	2.45630	−	1.09361i	0.343950	−	0.153136i
$52$	−0.672342	−	0.746711i	−0.0932370	−	0.103550i
$53$	0.479723	+	4.56426i	0.0658950	+	0.626949i	0.976773	+	0.214274i	$0.0687387\pi$
$53$	0.479723	+	4.56426i	0.0658950	+	0.626949i	−0.910878	+	0.412675i	$0.864595\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	0.0284996	−	0.271156i	0.00384289	−	0.0365626i
$56$	−2.04035	−	3.53399i	−0.272653	−	0.472249i
$57$	4.14362	−	7.17696i	0.548836	−	0.950612i
$58$	−3.47778	−	2.52675i	−0.456654	−	0.331779i
$59$	−2.45414	+	2.72559i	−0.319501	+	0.354842i	−0.881406	−	0.472360i	$-0.843402\pi$
$59$	−2.45414	+	2.72559i	−0.319501	+	0.354842i	0.561904	+	0.827202i	$0.310069\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	6.54526			0.838035			0.419017	−	0.907978i	$-0.362375\pi$
$61$	6.54526			0.838035			0.419017	+	0.907978i	$0.362375\pi$
$62$	2.66480	+	4.88864i	0.338430	+	0.620858i
$63$	4.08070			0.514120
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.672342	−	0.746711i	0.0833937	−	0.0926181i
$66$	0.220578	+	0.160259i	0.0271513	+	0.0197265i
$67$	2.37610	−	4.11552i	0.290286	−	0.502791i	−0.683591	−	0.729865i	$-0.739583\pi$
$67$	2.37610	−	4.11552i	0.290286	−	0.502791i	0.973877	+	0.227075i	$0.0729161\pi$
$68$	1.34437	+	2.32853i	0.163029	+	0.282375i
$69$	0.524126	−	4.98673i	0.0630974	−	0.600332i
$70$	3.30136	−	2.39858i	0.394588	−	0.286685i
$71$	−0.0675796	−	0.642977i	−0.00802022	−	0.0763073i	0.989780	−	0.142605i	$-0.0455479\pi$
$71$	−0.0675796	−	0.642977i	−0.00802022	−	0.0763073i	−0.997800	+	0.0662979i	$0.978881\pi$
$72$	0.669131	+	0.743145i	0.0788578	+	0.0875805i
$73$	−1.41043	+	0.627966i	−0.165079	+	0.0734978i	−0.487613	−	0.873060i	$-0.662132\pi$
$73$	−1.41043	+	0.627966i	−0.165079	+	0.0734978i	0.322534	+	0.946558i	$0.395465\pi$
$74$	11.5670	−	2.45865i	1.34464	−	0.285812i
$75$	0.978148	+	0.207912i	0.112947	+	0.0240076i
$76$	7.57077	+	3.37073i	0.868427	+	0.386649i
$77$	0.343812	+	1.05815i	0.0391811	+	0.120587i
$78$	0.310500	+	0.955620i	0.0351572	+	0.108203i
$79$	−1.28088	−	0.570284i	−0.144110	−	0.0641620i	0.333414	−	0.942780i	$-0.391799\pi$
$79$	−1.28088	−	0.570284i	−0.144110	−	0.0641620i	−0.477525	+	0.878618i	$0.658466\pi$
$80$	0.978148	+	0.207912i	0.109360	+	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	3.45705	−	1.53918i	0.381768	−	0.169974i
$83$	0.748097	+	0.830846i	0.0821143	+	0.0911972i	0.782802	−	0.622271i	$-0.213790\pi$
$83$	0.748097	+	0.830846i	0.0821143	+	0.0911972i	−0.700687	+	0.713468i	$0.747123\pi$
$84$	0.426549	+	4.05835i	0.0465404	+	0.442802i
$85$	−2.17524	+	1.58041i	−0.235938	+	0.171419i
$86$	−0.846479	+	8.05371i	−0.0912782	+	0.868454i
$87$	2.14938	+	3.72284i	0.230438	+	0.399131i
$88$	−0.136325	+	0.236121i	−0.0145323	+	0.0251706i
$89$	−9.49149	−	6.89597i	−1.00610	−	0.730972i	−0.0427094	−	0.999088i	$-0.513599\pi$
$89$	−9.49149	−	6.89597i	−1.00610	−	0.730972i	−0.963387	+	0.268116i	$0.913599\pi$
$90$	−0.669131	+	0.743145i	−0.0705326	+	0.0783343i
$91$	−1.26706	+	3.89960i	−0.132824	+	0.408789i
$92$	5.01420			0.522766
$93$	−0.446028	−	5.54987i	−0.0462509	−	0.575495i
$94$	3.64339			0.375787
$95$	−2.56090	+	7.88164i	−0.262743	+	0.808639i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	−4.06080	−	2.95035i	−0.412312	−	0.299562i	0.362225	−	0.932091i	$-0.382017\pi$
$97$	−4.06080	−	2.95035i	−0.412312	−	0.299562i	−0.774537	+	0.632528i	$0.782017\pi$
$98$	−4.82606	+	8.35898i	−0.487506	+	0.844384i
$99$	−0.136325	−	0.236121i	−0.0137011	−	0.0237311i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−6.10742	+	4.43730i	−0.607711	+	0.441528i	−0.848607	−	0.529023i	$-0.822559\pi$
$101$	−6.10742	+	4.43730i	−0.607711	+	0.441528i	0.240897	+	0.970551i	$0.422559\pi$
$102$	−0.281051	−	2.67402i	−0.0278282	−	0.264767i
$103$	−5.44354	−	6.04566i	−0.536368	−	0.595697i	0.412662	−	0.910884i	$-0.364599\pi$
$103$	−5.44354	−	6.04566i	−0.536368	−	0.595697i	−0.949029	+	0.315188i	$0.897932\pi$
$104$	−0.917929	+	0.408688i	−0.0900104	+	0.0400752i
$105$	−3.99153	+	0.848425i	−0.389533	+	0.0827978i
$106$	4.48911	+	0.954190i	0.436021	+	0.0926791i
$107$	14.3598	+	6.39338i	1.38821	+	0.618072i	0.958552	−	0.284919i	$-0.0919667\pi$
$107$	14.3598	+	6.39338i	1.38821	+	0.618072i	0.429660	+	0.902991i	$0.358633\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	1.72706	+	5.31533i	0.165422	+	0.509117i	0.999067	−	0.0431839i	$-0.0137501\pi$
$109$	1.72706	+	5.31533i	0.165422	+	0.509117i	−0.833645	+	0.552300i	$0.813750\pi$
$110$	−0.249078	−	0.110896i	−0.0237486	−	0.0105736i
$111$	−11.5670	−	2.45865i	−1.09789	−	0.233365i
$112$	−3.99153	+	0.848425i	−0.377164	+	0.0801687i
$113$	12.5787	−	5.60040i	1.18330	−	0.526841i	0.281742	−	0.959490i	$-0.409088\pi$
$113$	12.5787	−	5.60040i	1.18330	−	0.526841i	0.901562	+	0.432649i	$0.142421\pi$
$114$	−5.54525	−	6.15862i	−0.519360	−	0.576808i
$115$	0.524126	+	4.98673i	0.0488750	+	0.465015i
$116$	−3.47778	+	2.52675i	−0.322903	+	0.234603i
$117$	0.105030	−	0.999294i	0.00971003	−	0.0923848i
$118$	1.83382	+	3.17628i	0.168817	+	0.292400i
$119$	5.48599	−	9.50202i	0.502900	−	0.871048i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−7.31070	+	8.11935i	−0.664609	+	0.738123i
$122$	2.02260	−	6.22491i	0.183117	−	0.563577i
$123$	−3.78422			−0.341211
$124$	5.47284	−	1.02370i	0.491476	−	0.0919313i
$125$	−1.00000			−0.0894427
$126$	1.26101	−	3.88098i	0.112339	−	0.345745i
$127$	−0.0605950	+	0.0672976i	−0.00537694	+	0.00597170i	−0.745827	−	0.666139i	$-0.767946\pi$
$127$	−0.0605950	+	0.0672976i	−0.00537694	+	0.00597170i	0.740450	+	0.672111i	$0.234612\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	4.04904	−	7.01314i	0.356498	−	0.617472i
$130$	−0.502399	−	0.870181i	−0.0440633	−	0.0763199i
$131$	−1.72379	+	16.4008i	−0.150609	+	1.43295i	0.614435	+	0.788967i	$0.289384\pi$
$131$	−1.72379	+	16.4008i	−0.150609	+	1.43295i	−0.765044	+	0.643978i	$0.777283\pi$
$132$	0.220578	−	0.160259i	0.0191988	−	0.0139488i
$133$	−3.53492	−	33.6325i	−0.306516	−	2.91631i
$134$	−3.17984	−	3.53157i	−0.274696	−	0.305081i
$135$	0.913545	−	0.406737i	0.0786255	−	0.0350063i
$136$	2.62999	−	0.559023i	0.225520	−	0.0479358i
$137$	8.15277	+	1.73292i	0.696538	+	0.148054i	0.542556	−	0.840020i	$-0.317457\pi$
$137$	8.15277	+	1.73292i	0.696538	+	0.148054i	0.153982	+	0.988074i	$0.450790\pi$
$138$	−4.58070	−	2.03946i	−0.389935	−	0.173610i
$139$	−6.69326	−	20.5997i	−0.567715	−	1.74725i	−0.659744	−	0.751491i	$-0.729335\pi$
$139$	−6.69326	−	20.5997i	−0.567715	−	1.74725i	0.0920288	−	0.995756i	$-0.470665\pi$
$140$	−1.26101	−	3.88098i	−0.106574	−	0.328002i
$141$	−3.32841	−	1.48190i	−0.280302	−	0.124799i
$142$	−0.632390	−	0.134419i	−0.0530690	−	0.0112802i
$143$	0.267971	−	0.0569590i	0.0224089	−	0.00476315i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	−2.87644	−	3.19461i	−0.238875	−	0.265298i
$146$	0.161383	+	1.53545i	0.0133561	+	0.127075i
$147$	7.80873	−	5.67337i	0.644053	−	0.467932i
$148$	1.23610	−	11.7607i	0.101606	−	0.966720i
$149$	−3.18642	−	5.51904i	−0.261042	−	0.452138i	0.705477	−	0.708733i	$-0.250733\pi$
$149$	−3.18642	−	5.51904i	−0.261042	−	0.452138i	−0.966519	+	0.256595i	$0.917399\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−3.67371	−	2.66910i	−0.298962	−	0.217209i	0.428184	−	0.903692i	$-0.359154\pi$
$151$	−3.67371	−	2.66910i	−0.298962	−	0.217209i	−0.727146	+	0.686483i	$0.759154\pi$
$152$	5.54525	−	6.15862i	0.449779	−	0.499530i
$153$	−0.830869	+	2.55715i	−0.0671718	+	0.206734i
$154$	1.11260			0.0896559
$155$	1.59016	+	5.33586i	0.127725	+	0.428586i
$156$	1.00480			0.0804483
$157$	1.10210	−	3.39193i	0.0879576	−	0.270706i	−0.897397	−	0.441224i	$-0.854544\pi$
$157$	1.10210	−	3.39193i	0.0879576	−	0.270706i	0.985354	+	0.170519i	$0.0545443\pi$
$158$	−0.938186	+	1.04196i	−0.0746380	+	0.0828939i
$159$	−3.71290	−	2.69758i	−0.294452	−	0.213932i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−10.2307	−	17.7201i	−0.806294	−	1.39654i
$162$	−0.104528	+	0.994522i	−0.00821253	+	0.0781370i
$163$	2.80625	−	2.03886i	0.219802	−	0.159696i	−0.472435	−	0.881365i	$-0.656625\pi$
$163$	2.80625	−	2.03886i	0.219802	−	0.159696i	0.692238	+	0.721670i	$0.256625\pi$
$164$	−0.395558	−	3.76349i	−0.0308879	−	0.293879i
$165$	0.182438	+	0.202618i	0.0142028	+	0.0157738i
$166$	1.02136	−	0.454737i	0.0792726	−	0.0352944i
$167$	5.12666	−	1.08971i	0.396713	−	0.0843240i	−0.00523533	−	0.999986i	$-0.501666\pi$
$167$	5.12666	−	1.08971i	0.396713	−	0.0843240i	0.401948	+	0.915662i	$0.368333\pi$
$168$	3.99153	+	0.848425i	0.307953	+	0.0654574i
$169$	−10.9538	−	4.87693i	−0.842597	−	0.375148i
$170$	0.830869	+	2.55715i	0.0637248	+	0.196125i
$171$	2.56090	+	7.88164i	0.195837	+	0.602724i
$172$	7.39796	+	3.29378i	0.564089	+	0.251149i
$173$	22.7322	+	4.83188i	1.72830	+	0.367361i	0.961559	−	0.274598i	$-0.0885449\pi$
$173$	22.7322	+	4.83188i	1.72830	+	0.367361i	0.766739	+	0.641959i	$0.221878\pi$
$174$	4.20483	−	0.893764i	0.318767	−	0.0677561i
$175$	3.72791	−	1.65977i	0.281803	−	0.125467i
$176$	0.182438	+	0.202618i	0.0137518	+	0.0152729i
$177$	−0.383374	−	3.64756i	−0.0288161	−	0.274167i
$178$	−9.49149	+	6.89597i	−0.711417	+	0.516875i
$179$	−1.27720	+	12.1518i	−0.0954625	+	0.908265i	0.837050	+	0.547127i	$0.184278\pi$
$179$	−1.27720	+	12.1518i	−0.0954625	+	0.908265i	−0.932512	+	0.361138i	$0.882388\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−2.24815	+	3.89392i	−0.167104	+	0.289432i	−0.937400	−	0.348253i	$-0.886775\pi$
$181$	−2.24815	+	3.89392i	−0.167104	+	0.289432i	0.770297	+	0.637686i	$0.220108\pi$
$182$	3.31720	+	2.41009i	0.245887	+	0.178647i
$183$	−4.37963	+	4.86408i	−0.323752	+	0.359563i
$184$	1.54947	−	4.76878i	0.114229	−	0.351559i
$185$	11.8254			0.869424
$186$	−5.41607	−	1.29081i	−0.397126	−	0.0946465i
$187$	−0.733086			−0.0536085
$188$	1.12587	−	3.46507i	0.0821126	−	0.252717i
$189$	−2.73052	+	3.03255i	−0.198616	+	0.220586i
$190$	6.70452	+	4.87112i	0.486397	+	0.353388i
$191$	7.77641	−	13.4691i	0.562682	−	0.974593i	−0.434580	−	0.900633i	$-0.643103\pi$
$191$	7.77641	−	13.4691i	0.562682	−	0.974593i	0.997261	−	0.0739597i	$-0.0235636\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	0.952375	−	9.06125i	0.0685535	−	0.652243i	−0.905254	−	0.424870i	$-0.860320\pi$
$193$	0.952375	−	9.06125i	0.0685535	−	0.652243i	0.973808	−	0.227373i	$-0.0730136\pi$
$194$	−4.06080	+	2.95035i	−0.291549	+	0.211822i
$195$	0.105030	+	0.999294i	0.00752136	+	0.0715610i
$196$	6.45853	+	7.17292i	0.461323	+	0.512352i
$197$	6.08717	−	2.71018i	0.433693	−	0.193092i	−0.178266	−	0.983982i	$-0.557049\pi$
$197$	6.08717	−	2.71018i	0.433693	−	0.193092i	0.611958	+	0.790890i	$0.290382\pi$
$198$	−0.266691	+	0.0566870i	−0.0189529	+	0.00402857i
$199$	22.0026	+	4.67680i	1.55972	+	0.331530i	0.905358	−	0.424648i	$-0.139602\pi$
$199$	22.0026	+	4.67680i	1.55972	+	0.331530i	0.654366	+	0.756178i	$0.272936\pi$
$200$	0.913545	+	0.406737i	0.0645974	+	0.0287606i
$201$	1.46851	+	4.51960i	0.103581	+	0.318788i
$202$	2.33283	+	7.17970i	0.164137	+	0.505162i
$203$	16.0254	+	7.13497i	1.12476	+	0.500777i
$204$	−2.62999	−	0.559023i	−0.184136	−	0.0391394i
$205$	3.70152	−	0.786783i	0.258525	−	0.0549513i
$206$	−7.43191	+	3.30890i	−0.517806	+	0.230542i
$207$	3.35515	+	3.72627i	0.233199	+	0.258994i
$208$	0.105030	+	0.999294i	0.00728253	+	0.0692886i
$209$	−1.82798	+	1.32811i	−0.126444	+	0.0918671i
$210$	−0.426549	+	4.05835i	−0.0294347	+	0.280052i
$211$	−9.44656	−	16.3619i	−0.650328	−	1.12640i	−0.983043	−	0.183374i	$-0.941298\pi$
$211$	−9.44656	−	16.3619i	−0.650328	−	1.12640i	0.332716	−	0.943027i	$-0.392035\pi$
$212$	2.29470	−	3.97454i	0.157601	−	0.272972i
$213$	0.523044	+	0.380014i	0.0358384	+	0.0260381i
$214$	10.5179	−	11.6813i	0.718988	−	0.798517i
$215$	−2.50244	+	7.70172i	−0.170665	+	0.525253i
$216$	−1.00000			−0.0680414
$217$	−14.7843	−	17.2523i	−1.00362	−	1.17116i
$218$	5.58887			0.378526
$219$	0.477095	−	1.46835i	0.0322391	−	0.0992217i
$220$	−0.182438	+	0.202618i	−0.0123000	+	0.0136605i
$221$	−2.18568	−	1.58799i	−0.147025	−	0.106820i
$222$	−5.91272	+	10.2411i	−0.396836	+	0.687340i
$223$	1.61932	+	2.80475i	0.108438	+	0.187820i	0.915138	−	0.403142i	$-0.132082\pi$
$223$	1.61932	+	2.80475i	0.108438	+	0.187820i	−0.806700	+	0.590962i	$0.798748\pi$
$224$	−0.426549	+	4.05835i	−0.0285000	+	0.271160i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−1.43926	−	13.6937i	−0.0957384	−	0.910890i
$227$	−9.77178	−	10.8527i	−0.648576	−	0.720316i	0.325751	−	0.945456i	$-0.394383\pi$
$227$	−9.77178	−	10.8527i	−0.648576	−	0.720316i	−0.974327	+	0.225139i	$0.927716\pi$
$228$	−7.57077	+	3.37073i	−0.501387	+	0.223232i
$229$	−13.4373	+	2.85619i	−0.887963	+	0.188742i	−0.629242	−	0.777210i	$-0.716634\pi$
$229$	−13.4373	+	2.85619i	−0.887963	+	0.188742i	−0.258721	+	0.965952i	$0.583301\pi$
$230$	4.90462	+	1.04251i	0.323401	+	0.0687411i
$231$	−1.01641	−	0.452535i	−0.0668749	−	0.0297746i
$232$	1.32839	+	4.08837i	0.0872132	+	0.268415i
$233$	−5.30260	−	16.3197i	−0.347385	−	1.06914i	−0.960295	−	0.278987i	$-0.910001\pi$
$233$	−5.30260	−	16.3197i	−0.347385	−	1.06914i	0.612910	−	0.790153i	$-0.289999\pi$
$234$	−0.917929	−	0.408688i	−0.0600069	−	0.0267168i
$235$	3.56378	+	0.757504i	0.232475	+	0.0494141i
$236$	3.58750	−	0.762547i	0.233526	−	0.0496376i
$237$	1.28088	−	0.570284i	0.0832020	−	0.0370439i
$238$	−7.34169	−	8.15377i	−0.475891	−	0.528531i
$239$	−0.913078	−	8.68736i	−0.0590621	−	0.561938i	−0.983538	−	0.180699i	$-0.942164\pi$
$239$	−0.913078	−	8.68736i	−0.0590621	−	0.561938i	0.924476	−	0.381239i	$-0.124503\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	−2.49833	+	23.7700i	−0.160931	+	1.53116i	0.554326	+	0.832300i	$0.312976\pi$
$241$	−2.49833	+	23.7700i	−0.160931	+	1.53116i	−0.715257	+	0.698861i	$0.753691\pi$
$242$	5.46283	+	9.46190i	0.351164	+	0.608234i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.29523	−	3.84721i	−0.338992	−	0.246292i
$245$	−6.45853	+	7.17292i	−0.412620	+	0.458261i
$246$	−1.16939	+	3.59900i	−0.0745574	+	0.229464i
$247$	−8.32701			−0.529835
$248$	0.717602	−	5.52133i	0.0455678	−	0.350605i
$249$	−1.11801			−0.0708512
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	20.5316	−	22.8026i	1.29594	−	1.43929i	0.462564	−	0.886586i	$-0.346930\pi$
$251$	20.5316	−	22.8026i	1.29594	−	1.43929i	0.833378	−	0.552703i	$-0.186404\pi$
$252$	−3.30136	−	2.39858i	−0.207966	−	0.151096i
$253$	−0.683559	+	1.18396i	−0.0429750	+	0.0744348i
$254$	0.0452789	+	0.0784254i	0.00284105	+	0.00492085i
$255$	0.281051	−	2.67402i	0.0176001	−	0.167454i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.25090	−	11.9015i	−0.0780291	−	0.742398i	−0.961666	−	0.274224i	$-0.911579\pi$
$257$	−1.25090	−	11.9015i	−0.0780291	−	0.742398i	0.883637	−	0.468173i	$-0.155088\pi$
$258$	−5.41867	−	6.01804i	−0.337352	−	0.374667i
$259$	−44.0841	+	19.6275i	−2.73925	+	1.21959i
$260$	−0.982842	+	0.208909i	−0.0609532	+	0.0129560i
$261$	−4.20483	−	0.893764i	−0.260272	−	0.0553226i
$262$	15.0654	+	6.70755i	0.930744	+	0.414394i
$263$	5.54452	+	17.0643i	0.341889	+	1.05223i	0.963228	+	0.268685i	$0.0865892\pi$
$263$	5.54452	+	17.0643i	0.341889	+	1.05223i	−0.621339	+	0.783542i	$0.713411\pi$
$264$	−0.0842533	−	0.259305i	−0.00518543	−	0.0159591i
$265$	4.19263	+	1.86668i	0.257551	+	0.114669i
$266$	−33.0788	−	7.03111i	−2.02819	−	0.431105i
$267$	11.4758	−	2.43925i	0.702305	−	0.149279i
$268$	−4.34134	+	1.93289i	−0.265190	+	0.118070i
$269$	2.76135	+	3.06679i	0.168362	+	0.186985i	0.821422	−	0.570322i	$-0.193181\pi$
$269$	2.76135	+	3.06679i	0.168362	+	0.186985i	−0.653059	+	0.757307i	$0.726515\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	24.3181	−	17.6681i	1.47722	−	1.07326i	0.498780	−	0.866729i	$-0.333782\pi$
$271$	24.3181	−	17.6681i	1.47722	−	1.07326i	0.978440	−	0.206534i	$-0.0662183\pi$
$272$	0.281051	−	2.67402i	0.0170412	−	0.162136i
$273$	−2.05014	−	3.55095i	−0.124080	−	0.214913i
$274$	4.16745	−	7.21824i	0.251765	−	0.436070i
$275$	−0.220578	−	0.160259i	−0.0133013	−	0.00966400i
$276$	−3.35515	+	3.72627i	−0.201956	+	0.224295i
$277$	−6.62595	+	20.3926i	−0.398115	+	1.22527i	0.528395	+	0.848999i	$0.322794\pi$
$277$	−6.62595	+	20.3926i	−0.398115	+	1.22527i	−0.926509	+	0.376272i	$0.877206\pi$
$278$	−21.6598			−1.29907
$279$	4.42281	+	3.38212i	0.264787	+	0.202483i
$280$	−4.08070			−0.243869
$281$	−3.60646	+	11.0996i	−0.215144	+	0.662144i	0.784000	+	0.620761i	$0.213176\pi$
$281$	−3.60646	+	11.0996i	−0.215144	+	0.662144i	−0.999143	+	0.0413829i	$0.986824\pi$
$282$	−2.43791	+	2.70757i	−0.145175	+	0.161233i
$283$	13.4986	+	9.80732i	0.802409	+	0.582985i	0.911620	−	0.411034i	$-0.134832\pi$
$283$	13.4986	+	9.80732i	0.802409	+	0.582985i	−0.109211	+	0.994019i	$0.534832\pi$
$284$	−0.323259	+	0.559901i	−0.0191819	+	0.0332240i
$285$	−4.14362	−	7.17696i	−0.245447	−	0.425127i
$286$	0.0286364	−	0.272457i	0.00169330	−	0.0161107i
$287$	−12.4930	+	9.07673i	−0.737441	+	0.535782i
$288$	−0.104528	−	0.994522i	−0.00615940	−	0.0586028i
$289$	−6.53782	−	7.26099i	−0.384578	−	0.427117i
$290$	−3.92712	+	1.74847i	−0.230608	+	0.102673i
$291$	4.90974	−	1.04360i	0.287814	−	0.0611768i
$292$	1.51017	+	0.320997i	0.0883763	+	0.0187850i
$293$	−23.5433	−	10.4822i	−1.37542	−	0.612375i	−0.419969	−	0.907538i	$-0.637959\pi$
$293$	−23.5433	−	10.4822i	−1.37542	−	0.612375i	−0.955447	+	0.295164i	$0.904626\pi$
$294$	−2.98267	−	9.17971i	−0.173953	−	0.535372i
$295$	1.13337	+	3.48814i	0.0659871	+	0.203087i
$296$	−10.8031	−	4.80984i	−0.627916	−	0.279566i
$297$	0.266691	+	0.0566870i	0.0154750	+	0.00328931i
$298$	−6.23358	+	1.32499i	−0.361102	+	0.0767545i
$299$	−4.60268	+	2.04924i	−0.266180	+	0.118511i
$300$	−0.669131	−	0.743145i	−0.0386323	−	0.0429055i
$301$	−3.45423	−	32.8648i	−0.199098	−	1.89429i
$302$	−3.67371	+	2.66910i	−0.211398	+	0.153590i
$303$	0.789105	−	7.50783i	0.0453329	−	0.431313i
$304$	−4.14362	−	7.17696i	−0.237653	−	0.411627i
$305$	3.27263	−	5.66836i	0.187390	−	0.324570i
$306$	2.17524	+	1.58041i	0.124350	+	0.0903459i
$307$	1.88689	−	2.09561i	0.107691	−	0.119603i	−0.686889	−	0.726762i	$-0.741024\pi$
$307$	1.88689	−	2.09561i	0.107691	−	0.119603i	0.794580	+	0.607159i	$0.207691\pi$
$308$	0.343812	−	1.05815i	0.0195905	−	0.0602934i
$309$	8.13524			0.462797
$310$	5.56609	+	0.136535i	0.316133	+	0.00775467i
$311$	14.3032			0.811058			0.405529	−	0.914082i	$-0.367087\pi$
$311$	14.3032			0.811058			0.405529	+	0.914082i	$0.367087\pi$
$312$	0.310500	−	0.955620i	0.0175786	−	0.0541014i
$313$	−11.4806	+	12.7505i	−0.648920	+	0.720699i	−0.974393	−	0.224852i	$-0.927810\pi$
$313$	−11.4806	+	12.7505i	−0.648920	+	0.720699i	0.325472	+	0.945552i	$0.394477\pi$
$314$	−2.88535	−	2.09633i	−0.162830	−	0.118303i
$315$	2.04035	−	3.53399i	0.114961	−	0.199118i
$316$	0.701048	+	1.21425i	0.0394370	+	0.0683070i
$317$	−3.51287	+	33.4227i	−0.197302	+	1.87721i	0.230133	+	0.973159i	$0.426084\pi$
$317$	−3.51287	+	33.4227i	−0.197302	+	1.87721i	−0.427435	+	0.904046i	$0.640583\pi$
$318$	−3.71290	+	2.69758i	−0.208209	+	0.151273i
$319$	−0.122513	−	1.16564i	−0.00685942	−	0.0652631i
$320$	−0.669131	−	0.743145i	−0.0374055	−	0.0415431i
$321$	−14.3598	+	6.39338i	−0.801484	+	0.356844i
$322$	−20.0143	+	4.25417i	−1.11535	+	0.237076i
$323$	21.7954	+	4.63276i	1.21273	+	0.257773i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−0.310500	−	0.955620i	−0.0172234	−	0.0530083i
$326$	−1.07189	−	3.29894i	−0.0593665	−	0.182711i
$327$	−5.10569	−	2.27320i	−0.282345	−	0.125708i
$328$	−3.70152	−	0.786783i	−0.204382	−	0.0434428i
$329$	−14.5427	+	3.09115i	−0.801766	+	0.170421i
$330$	0.249078	−	0.110896i	0.0137113	−	0.00610465i
$331$	15.9412	+	17.7044i	0.876205	+	0.973125i	0.999816	−	0.0192063i	$-0.00611394\pi$
$331$	15.9412	+	17.7044i	0.876205	+	0.973125i	−0.123610	+	0.992331i	$0.539447\pi$
$332$	−0.116864	−	1.11189i	−0.00641376	−	0.0610228i
$333$	9.56698	−	6.95082i	0.524267	−	0.380903i
$334$	0.547854	−	5.21248i	0.0299772	−	0.285214i
$335$	−2.37610	−	4.11552i	−0.129820	−	0.224855i
$336$	2.04035	−	3.53399i	0.111310	−	0.192795i
$337$	18.7757	+	13.6414i	1.02278	+	0.743093i	0.966851	−	0.255342i	$-0.0821880\pi$
$337$	18.7757	+	13.6414i	1.02278	+	0.743093i	0.0559287	+	0.998435i	$0.482188\pi$
$338$	−8.02313	+	8.91059i	−0.436401	+	0.484672i
$339$	−4.25489	+	13.0952i	−0.231094	+	0.711233i
$340$	2.68875			0.145818
$341$	−0.504366	+	1.43181i	−0.0273129	+	0.0775369i
$342$	8.28724			0.448123
$343$	3.34434	−	10.2928i	0.180577	−	0.555759i
$344$	5.41867	−	6.01804i	0.292155	−	0.324471i
$345$	−4.05657	−	2.94727i	−0.218398	−	0.158676i
$346$	11.6200	−	20.1265i	0.624697	−	1.08201i
$347$	13.7128	+	23.7512i	0.736140	+	1.27503i	0.954221	+	0.299102i	$0.0966870\pi$
$347$	13.7128	+	23.7512i	0.736140	+	1.27503i	−0.218081	+	0.975931i	$0.569980\pi$
$348$	0.449344	−	4.27522i	0.0240873	−	0.229176i
$349$	−14.6324	+	10.6311i	−0.783257	+	0.569070i	−0.905955	−	0.423375i	$-0.860845\pi$
$349$	−14.6324	+	10.6311i	−0.783257	+	0.569070i	0.122698	+	0.992444i	$0.460845\pi$
$350$	−0.426549	−	4.05835i	−0.0228000	−	0.216928i
$351$	0.672342	+	0.746711i	0.0358869	+	0.0398565i
$352$	0.249078	−	0.110896i	0.0132759	−	0.00591080i
$353$	−21.8459	+	4.64349i	−1.16274	+	0.247148i	−0.748573	−	0.663053i	$-0.769261\pi$
$353$	−21.8459	+	4.64349i	−1.16274	+	0.247148i	−0.414168	+	0.910201i	$0.635927\pi$
$354$	−3.58750	−	0.762547i	−0.190674	−	0.0405289i
$355$	−0.590624	−	0.262963i	−0.0313471	−	0.0139566i
$356$	3.62543	+	11.1579i	0.192147	+	0.591368i
$357$	3.39053	+	10.4350i	0.179446	+	0.552278i
$358$	11.1623	+	4.96979i	0.589947	+	0.262662i
$359$	−18.3619	−	3.90294i	−0.969104	−	0.205989i	−0.303944	−	0.952690i	$-0.598303\pi$
$359$	−18.3619	−	3.90294i	−0.969104	−	0.205989i	−0.665160	+	0.746701i	$0.731637\pi$
$360$	0.978148	−	0.207912i	0.0515529	−	0.0109579i
$361$	45.3835	−	20.2060i	2.38860	−	1.06347i
$362$	3.00862	+	3.34141i	0.158129	+	0.175620i
$363$	−1.14204	−	10.8658i	−0.0599417	−	0.570307i
$364$	3.31720	−	2.41009i	0.173868	−	0.126323i
$365$	−0.161383	+	1.53545i	−0.00844716	+	0.0803694i
$366$	3.27263	+	5.66836i	0.171063	+	0.296290i
$367$	−0.125460	+	0.217303i	−0.00654895	+	0.0113431i	−0.869281	−	0.494318i	$-0.835418\pi$
$367$	−0.125460	+	0.217303i	−0.00654895	+	0.0113431i	0.862732	+	0.505661i	$0.168751\pi$
$368$	−4.05657	−	2.94727i	−0.211463	−	0.153637i
$369$	2.53213	−	2.81222i	0.131818	−	0.146398i
$370$	3.65426	−	11.2467i	0.189976	−	0.584686i
$371$	−18.7280			−0.972308
$372$	−2.90129	+	4.75211i	−0.150425	+	0.246385i
$373$	14.2997			0.740410			0.370205	−	0.928950i	$-0.379288\pi$
$373$	14.2997			0.740410			0.370205	+	0.928950i	$0.379288\pi$
$374$	−0.226536	+	0.697206i	−0.0117139	+	0.0360517i
$375$	0.669131	−	0.743145i	0.0345538	−	0.0383758i
$376$	−2.94757	−	2.14153i	−0.152009	−	0.110441i
$377$	2.15970	−	3.74071i	0.111230	−	0.192656i
$378$	2.04035	+	3.53399i	0.104944	+	0.181769i
$379$	−0.871762	+	8.29426i	−0.0447794	+	0.426048i	0.949050	+	0.315126i	$0.102047\pi$
$379$	−0.871762	+	8.29426i	−0.0447794	+	0.426048i	−0.993829	+	0.110921i	$0.964620\pi$
$380$	6.70452	−	4.87112i	0.343935	−	0.249883i
$381$	−0.00946587	−	0.0900618i	−0.000484951	−	0.00461400i
$382$	−10.4069	−	11.5580i	−0.532462	−	0.591359i
$383$	1.49282	−	0.664644i	0.0762793	−	0.0339617i	−0.368242	−	0.929730i	$-0.620040\pi$
$383$	1.49282	−	0.664644i	0.0762793	−	0.0339617i	0.444522	+	0.895768i	$0.353374\pi$
$384$	0.978148	−	0.207912i	0.0499159	−	0.0106099i
$385$	1.08829	+	0.231323i	0.0554643	+	0.0117893i
$386$	−8.32346	−	3.70584i	−0.423653	−	0.188622i
$387$	2.50244	+	7.70172i	0.127206	+	0.391501i
$388$	1.55109	+	4.77376i	0.0787446	+	0.242351i
$389$	29.0405	+	12.9297i	1.47241	+	0.655561i	0.977028	−	0.213112i	$-0.0683599\pi$
$389$	29.0405	+	12.9297i	1.47241	+	0.655561i	0.495386	+	0.868673i	$0.335027\pi$
$390$	0.982842	+	0.208909i	0.0497681	+	0.0105785i
$391$	13.1873	−	2.80305i	0.666911	−	0.141756i
$392$	8.81765	−	3.92587i	0.445359	−	0.198286i
$393$	−11.0347	−	12.2553i	−0.556629	−	0.618199i
$394$	−0.696498	−	6.62673i	−0.0350890	−	0.333850i
$395$	−1.13432	+	0.824132i	−0.0570738	+	0.0414666i
$396$	−0.0284996	+	0.271156i	−0.00143216	+	0.0136261i
$397$	−6.18440	−	10.7117i	−0.310386	−	0.537605i	0.668060	−	0.744108i	$-0.267125\pi$
$397$	−6.18440	−	10.7117i	−0.310386	−	0.537605i	−0.978446	+	0.206503i	$0.933792\pi$
$398$	11.2471	−	19.4805i	0.563766	−	0.976471i
$399$	27.3591	+	19.8776i	1.36967	+	0.995124i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	−5.61961	+	17.2954i	−0.280630	+	0.863691i	0.707044	+	0.707169i	$0.250028\pi$
$401$	−5.61961	+	17.2954i	−0.280630	+	0.863691i	−0.987675	+	0.156522i	$0.949972\pi$
$402$	4.75219			0.237018
$403$	−4.60531	+	3.17638i	−0.229407	+	0.158227i
$404$	7.54918			0.375586
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	11.7379	−	13.0362i	0.582541	−	0.646978i
$407$	2.60843	+	1.89514i	0.129295	+	0.0939384i
$408$	−1.34437	+	2.32853i	−0.0665565	+	0.115279i
$409$	13.8539	+	23.9957i	0.685032	+	1.18651i	0.973427	+	0.228999i	$0.0735451\pi$
$409$	13.8539	+	23.9957i	0.685032	+	1.18651i	−0.288395	+	0.957512i	$0.593122\pi$
$410$	0.395558	−	3.76349i	0.0195352	−	0.185865i
$411$	−6.74308	+	4.89913i	−0.332612	+	0.241656i
$412$	0.850364	+	8.09067i	0.0418944	+	0.398599i
$413$	−10.0146	−	11.1223i	−0.492786	−	0.547294i
$414$	4.58070	−	2.03946i	0.225129	−	0.100234i
$415$	1.09358	−	0.232448i	0.0536818	−	0.0114104i
$416$	0.982842	+	0.208909i	0.0481878	+	0.0102426i
$417$	19.7873	+	8.80985i	0.968986	+	0.431420i
$418$	0.698227	+	2.14892i	0.0341514	+	0.105107i
$419$	−8.37333	−	25.7705i	−0.409064	−	1.25897i	−0.917454	−	0.397842i	$-0.869759\pi$
$419$	−8.37333	−	25.7705i	−0.409064	−	1.25897i	0.508390	−	0.861127i	$-0.330241\pi$
$420$	3.72791	+	1.65977i	0.181903	+	0.0809885i
$421$	14.7688	+	3.13921i	0.719788	+	0.152996i	0.553221	−	0.833035i	$-0.313399\pi$
$421$	14.7688	+	3.13921i	0.719788	+	0.152996i	0.166567	+	0.986030i	$0.446732\pi$
$422$	−18.4803	+	3.92810i	−0.899605	+	0.191217i
$423$	3.32841	−	1.48190i	0.161833	−	0.0720525i
$424$	−3.07091	−	3.41059i	−0.149136	−	0.165633i
$425$	0.281051	+	2.67402i	0.0136330	+	0.129709i
$426$	0.523044	−	0.380014i	0.0253416	−	0.0184117i
$427$	−2.79188	+	26.5629i	−0.135108	+	1.28547i
$428$	−7.85936	−	13.6128i	−0.379897	−	0.658000i
$429$	−0.136979	+	0.237254i	−0.00661340	+	0.0114547i
$430$	6.55148	+	4.75993i	0.315940	+	0.229544i
$431$	10.9639	−	12.1766i	0.528111	−	0.586527i	−0.418777	−	0.908089i	$-0.637541\pi$
$431$	10.9639	−	12.1766i	0.528111	−	0.586527i	0.946888	+	0.321562i	$0.104208\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	35.1706			1.69019			0.845096	−	0.534614i	$-0.179543\pi$
$433$	35.1706			1.69019			0.845096	+	0.534614i	$0.179543\pi$
$434$	−20.9765	+	8.72944i	−1.00690	+	0.419027i
$435$	4.29877			0.206110
$436$	1.72706	−	5.31533i	0.0827110	−	0.254558i
$437$	27.8050	−	30.8805i	1.33009	−	1.47722i
$438$	−1.24905	−	0.907489i	−0.0596820	−	0.0433615i
$439$	−16.8763	+	29.2306i	−0.805461	+	1.39510i	0.110519	+	0.993874i	$0.464749\pi$
$439$	−16.8763	+	29.2306i	−0.805461	+	1.39510i	−0.915980	+	0.401225i	$0.868585\pi$
$440$	0.136325	+	0.236121i	0.00649902	+	0.0112566i
$441$	−1.00892	+	9.59924i	−0.0480439	+	0.457107i
$442$	−2.18568	+	1.58799i	−0.103962	+	0.0755331i
$443$	1.78312	+	16.9653i	0.0847186	+	0.806044i	0.951561	+	0.307461i	$0.0994794\pi$
$443$	1.78312	+	16.9653i	0.0847186	+	0.806044i	−0.866842	+	0.498583i	$0.833854\pi$
$444$	7.91277	+	8.78802i	0.375523	+	0.417061i
$445$	−10.7178	+	4.77189i	−0.508074	+	0.226209i
$446$	3.16788	−	0.673353i	0.150003	−	0.0318842i
$447$	6.23358	+	1.32499i	0.294838	+	0.0626698i
$448$	3.72791	+	1.65977i	0.176127	+	0.0784168i
$449$	9.97590	+	30.7027i	0.470792	+	1.44895i	0.851550	+	0.524274i	$0.175663\pi$
$449$	9.97590	+	30.7027i	0.470792	+	1.44895i	−0.380758	+	0.924675i	$0.624337\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	0.942563	+	0.419656i	0.0443836	+	0.0197608i
$452$	−13.4682	−	2.86276i	−0.633492	−	0.134653i
$453$	4.44172	−	0.944117i	0.208690	−	0.0443585i
$454$	−13.3411	+	5.93986i	−0.626131	+	0.278771i
$455$	2.74362	+	3.04710i	0.128623	+	0.142850i
$456$	0.866253	+	8.24184i	0.0405660	+	0.385960i
$457$	3.51772	−	2.55577i	0.164552	−	0.119554i	−0.502462	−	0.864599i	$-0.667572\pi$
$457$	3.51772	−	2.55577i	0.164552	−	0.119554i	0.667014	+	0.745045i	$0.267572\pi$
$458$	−1.43596	+	13.6623i	−0.0670980	+	0.638395i
$459$	−1.34437	−	2.32853i	−0.0627500	−	0.108686i
$460$	2.50710	−	4.34242i	0.116894	−	0.202466i
$461$	−28.7005	−	20.8521i	−1.33672	−	0.971181i	−0.999558	−	0.0297327i	$-0.990534\pi$
$461$	−28.7005	−	20.8521i	−1.33672	−	0.971181i	−0.337158	−	0.941448i	$-0.609466\pi$
$462$	−0.744475	+	0.826823i	−0.0346361	+	0.0384673i
$463$	−4.62250	+	14.2266i	−0.214826	+	0.661166i	0.784340	+	0.620331i	$0.213002\pi$
$463$	−4.62250	+	14.2266i	−0.214826	+	0.661166i	−0.999166	+	0.0408349i	$0.986998\pi$
$464$	4.29877			0.199565
$465$	−5.02934	−	2.38866i	−0.233230	−	0.110772i
$466$	−17.1596			−0.794902
$467$	−8.08506	+	24.8833i	−0.374132	+	1.15146i	0.569930	+	0.821693i	$0.306970\pi$
$467$	−8.08506	+	24.8833i	−0.374132	+	1.15146i	−0.944062	+	0.329767i	$0.893030\pi$
$468$	−0.672342	+	0.746711i	−0.0310790	+	0.0345167i
$469$	15.6887	+	11.3985i	0.724436	+	0.526333i
$470$	1.82170	−	3.15527i	0.0840286	−	0.145542i
$471$	1.78324	+	3.08867i	0.0821675	+	0.142318i
$472$	0.383374	−	3.64756i	0.0176462	−	0.167892i
$473$	−1.78626	+	1.29779i	−0.0821321	+	0.0596725i
$474$	−0.146559	−	1.39442i	−0.00673168	−	0.0640476i
$475$	5.54525	+	6.15862i	0.254433	+	0.282577i
$476$	−10.0234	+	4.46271i	−0.459422	+	0.204548i
$477$	4.48911	−	0.954190i	0.205542	−	0.0436894i
$478$	−8.54432	−	1.81615i	−0.390808	−	0.0830689i
$479$	−12.7818	−	5.69082i	−0.584015	−	0.260020i	0.0933908	−	0.995630i	$-0.470229\pi$
$479$	−12.7818	−	5.69082i	−0.584015	−	0.260020i	−0.677406	+	0.735609i	$0.736896\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	3.67180	+	11.3006i	0.167420	+	0.515265i
$482$	21.8346	+	9.72139i	0.994539	+	0.442797i
$483$	20.0143	+	4.25417i	0.910682	+	0.193572i
$484$	10.6869	−	2.27157i	0.485769	−	0.103253i
$485$	−4.58547	+	2.04158i	−0.208216	+	0.0927036i
$486$	−0.669131	−	0.743145i	−0.0303524	−	0.0337097i
$487$	−0.898203	−	8.54583i	−0.0407014	−	0.387248i	−0.995842	−	0.0910959i	$-0.970963\pi$
$487$	−0.898203	−	8.54583i	−0.0407014	−	0.387248i	0.955141	−	0.296152i	$-0.0957037\pi$
$488$	−5.29523	+	3.84721i	−0.239704	+	0.174155i
$489$	−0.362579	+	3.44971i	−0.0163964	+	0.156001i
$490$	4.82606	+	8.35898i	0.218019	+	0.377620i
$491$	14.4816	−	25.0829i	0.653548	−	1.13198i	−0.328708	−	0.944432i	$-0.606613\pi$
$491$	14.4816	−	25.0829i	0.653548	−	1.13198i	0.982256	−	0.187546i	$-0.0600534\pi$
$492$	3.06149	+	2.22431i	0.138023	+	0.100279i
$493$	−7.73402	+	8.58950i	−0.348323	+	0.386852i
$494$	−2.57319	+	7.91946i	−0.115773	+	0.356313i
$495$	−0.272649			−0.0122547
$496$	−5.02934	−	2.38866i	−0.225824	−	0.107254i
$497$	2.63825			0.118342
$498$	−0.345485	+	1.06329i	−0.0154816	+	0.0476473i
$499$	−9.80932	+	10.8943i	−0.439125	+	0.487698i	−0.921561	−	0.388233i	$-0.873085\pi$
$499$	−9.80932	+	10.8943i	−0.439125	+	0.487698i	0.482436	+	0.875931i	$0.339752\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−2.62060	+	4.53901i	−0.117080	+	0.202788i
$502$	−15.3420	−	26.5731i	−0.684746	−	1.18602i
$503$	1.85169	−	17.6176i	0.0825626	−	0.785531i	−0.872398	−	0.488797i	$-0.837436\pi$
$503$	1.85169	−	17.6176i	0.0825626	−	0.785531i	0.954960	−	0.296734i	$-0.0958975\pi$
$504$	−3.30136	+	2.39858i	−0.147054	+	0.106841i
$505$	0.789105	+	7.50783i	0.0351147	+	0.334094i
$506$	0.914780	+	1.01597i	0.0406669	+	0.0451652i
$507$	10.9538	−	4.87693i	0.486473	−	0.216592i
$508$	0.0885790	−	0.0188280i	0.00393006	−	0.000835359i
$509$	1.60865	+	0.341930i	0.0713024	+	0.0151558i	0.243425	−	0.969920i	$-0.421729\pi$
$509$	1.60865	+	0.341930i	0.0713024	+	0.0151558i	−0.172122	+	0.985076i	$0.555062\pi$
$510$	−2.45630	−	1.09361i	−0.108767	−	0.0484260i
$511$	−1.94688	−	5.99189i	−0.0861250	−	0.265066i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−7.57077	−	3.37073i	−0.334258	−	0.148821i
$514$	−11.7056	−	2.48810i	−0.516311	−	0.109745i
$515$	−7.95746	+	1.69141i	−0.350648	+	0.0745325i
$516$	−7.39796	+	3.29378i	−0.325677	+	0.145001i
$517$	0.664694	+	0.738217i	0.0292332	+	0.0324667i
$518$	5.04413	+	47.9917i	0.221627	+	2.10864i
$519$	−18.8016	+	13.6602i	−0.825299	+	0.599615i
$520$	−0.105030	+	0.999294i	−0.00460587	+	0.0438220i
$521$	−20.1912	−	34.9722i	−0.884592	−	1.53216i	−0.846180	−	0.532897i	$-0.821103\pi$
$521$	−20.1912	−	34.9722i	−0.884592	−	1.53216i	−0.0384120	−	0.999262i	$-0.512230\pi$
$522$	−2.14938	+	3.72284i	−0.0940760	+	0.162944i
$523$	9.89601	+	7.18987i	0.432722	+	0.314391i	0.782737	−	0.622353i	$-0.213823\pi$
$523$	9.89601	+	7.18987i	0.432722	+	0.314391i	−0.350014	+	0.936744i	$0.613823\pi$
$524$	11.0347	−	12.2553i	0.482054	−	0.535376i
$525$	−1.26101	+	3.88098i	−0.0550348	+	0.169380i
$526$	17.9424			0.782327
$527$	13.8213	−	5.75178i	0.602064	−	0.250551i
$528$	−0.272649			−0.0118655
$529$	0.661966	−	2.03732i	0.0287811	−	0.0885792i
$530$	3.07091	−	3.41059i	0.133392	−	0.148147i
$531$	2.96719	+	2.15579i	0.128765	+	0.0935533i
$532$	−16.9089	+	29.2870i	−0.733093	+	1.26975i
$533$	1.90119	+	3.29295i	0.0823496	+	0.142634i
$534$	1.22634	−	11.6679i	0.0530690	−	0.504918i
$535$	12.7167	−	9.23924i	0.549792	−	0.399447i
$536$	0.496739	+	4.72616i	0.0214559	+	0.204139i
$537$	−8.17590	−	9.08026i	−0.352816	−	0.391842i
$538$	3.76999	−	1.67851i	0.162536	−	0.0723656i
$539$	−2.57414	+	0.547149i	−0.110876	+	0.0235674i
$540$	−0.978148	−	0.207912i	−0.0420928	−	0.00894709i
$541$	−28.8165	−	12.8299i	−1.23892	−	0.551602i	−0.320514	−	0.947244i	$-0.603856\pi$
$541$	−28.8165	−	12.8299i	−1.23892	−	0.551602i	−0.918405	+	0.395642i	$0.870522\pi$
$542$	−9.28869	−	28.5876i	−0.398983	−	1.22794i
$543$	−1.38943	−	4.27624i	−0.0596264	−	0.183511i
$544$	−2.45630	−	1.09361i	−0.105313	−	0.0468883i
$545$	5.46674	+	1.16199i	0.234169	+	0.0497743i
$546$	−4.01068	+	0.852497i	−0.171641	+	0.0364835i
$547$	−12.8964	+	5.74183i	−0.551409	+	0.245503i	−0.663476	−	0.748198i	$-0.730920\pi$
$547$	−12.8964	+	5.74183i	−0.551409	+	0.245503i	0.112067	+	0.993701i	$0.464253\pi$
$548$	−5.57714	−	6.19404i	−0.238244	−	0.264596i
$549$	−0.684166	−	6.50941i	−0.0291995	−	0.277815i
$550$	−0.220578	+	0.160259i	−0.00940547	+	0.00683348i
$551$	−3.72382	+	35.4298i	−0.158640	+	1.50936i
$552$	2.50710	+	4.34242i	0.106709	+	0.184826i
$553$	2.86077	−	4.95500i	0.121652	−	0.210708i
$554$	17.3470	+	12.6033i	0.737001	+	0.535463i
$555$	−7.91277	+	8.78802i	−0.335878	+	0.373030i
$556$	−6.69326	+	20.5997i	−0.283857	+	0.873623i
$557$	8.75326			0.370887			0.185444	−	0.982655i	$-0.440628\pi$
$557$	8.75326			0.370887			0.185444	+	0.982655i	$0.440628\pi$
$558$	4.58331	−	3.16121i	0.194027	−	0.133825i
$559$	−8.13693			−0.344156
$560$	−1.26101	+	3.88098i	−0.0532872	+	0.164001i
$561$	0.490530	−	0.544789i	0.0207102	−	0.0230010i
$562$	9.44185	+	6.85990i	0.398280	+	0.289368i
$563$	−6.24183	+	10.8112i	−0.263062	+	0.455636i	−0.967054	−	0.254571i	$-0.918066\pi$
$563$	−6.24183	+	10.8112i	−0.263062	+	0.455636i	0.703992	+	0.710208i	$0.251399\pi$
$564$	1.82170	+	3.15527i	0.0767073	+	0.132861i
$565$	1.43926	−	13.6937i	0.0605503	−	0.576097i
$566$	13.4986	−	9.80732i	0.567389	−	0.412232i
$567$	−0.426549	−	4.05835i	−0.0179134	−	0.170435i
$568$	0.432605	+	0.480457i	0.0181517	+	0.0201595i
$569$	12.0321	−	5.35704i	0.504412	−	0.224579i	−0.138723	−	0.990331i	$-0.544300\pi$
$569$	12.0321	−	5.35704i	0.504412	−	0.224579i	0.643136	+	0.765752i	$0.277633\pi$
$570$	−8.10615	+	1.72301i	−0.339529	+	0.0721691i
$571$	29.2769	+	6.22299i	1.22520	+	0.260424i	0.774686	−	0.632346i	$-0.217908\pi$
$571$	29.2769	+	6.22299i	1.22520	+	0.260424i	0.450513	+	0.892770i	$0.351241\pi$
$572$	−0.250273	−	0.111429i	−0.0104644	−	0.00465907i
$573$	4.80609	+	14.7916i	0.200777	+	0.617929i
$574$	4.77192	+	14.6865i	0.199176	+	0.613001i
$575$	4.58070	+	2.03946i	0.191028	+	0.0850513i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	−22.7206	+	4.82941i	−0.945871	+	0.201051i	−0.654930	−	0.755690i	$-0.727302\pi$
$577$	−22.7206	+	4.82941i	−0.945871	+	0.201051i	−0.290941	+	0.956741i	$0.593968\pi$
$578$	−8.92591	+	3.97407i	−0.371269	+	0.165300i
$579$	6.09656	+	6.77091i	0.253364	+	0.281389i
$580$	0.449344	+	4.27522i	0.0186580	+	0.177519i
$581$	−3.69096	+	2.68164i	−0.153127	+	0.111253i
$582$	0.524673	−	4.99193i	0.0217484	−	0.206922i
$583$	0.625648	+	1.08365i	0.0259117	+	0.0448804i
$584$	0.771956	−	1.33707i	0.0319438	−	0.0553282i
$585$	−0.812899	−	0.590606i	−0.0336092	−	0.0244185i
$586$	−17.2444	+	19.1519i	−0.712360	+	0.791156i
$587$	−9.71361	+	29.8954i	−0.400924	+	1.23392i	0.523328	+	0.852132i	$0.324690\pi$
$587$	−9.71361	+	29.8954i	−0.400924	+	1.23392i	−0.924251	+	0.381785i	$0.875310\pi$
$588$	−9.65212			−0.398047
$589$	24.0437	−	39.3819i	0.990702	−	1.62270i
$590$	3.66765			0.150995
$591$	−2.05905	+	6.33711i	−0.0846981	+	0.260674i
$592$	−7.91277	+	8.78802i	−0.325213	+	0.361185i
$593$	−16.5917	−	12.0546i	−0.681339	−	0.495022i	0.192463	−	0.981304i	$-0.438353\pi$
$593$	−16.5917	−	12.0546i	−0.681339	−	0.495022i	−0.873802	+	0.486282i	$0.838353\pi$
$594$	0.136325	−	0.236121i	0.00559347	−	0.00968817i
$595$	−5.48599	−	9.50202i	−0.224904	−	0.389545i
$596$	−0.666144	+	6.33793i	−0.0272863	+	0.259612i
$597$	−18.1982	+	13.2217i	−0.744802	+	0.541130i
$598$	0.526641	+	5.01066i	0.0215360	+	0.204901i
$599$	−26.2198	−	29.1200i	−1.07131	−	1.18981i	−0.981022	−	0.193897i	$-0.937887\pi$
$599$	−26.2198	−	29.1200i	−1.07131	−	1.18981i	−0.0902904	−	0.995915i	$-0.528780\pi$
$600$	−0.913545	+	0.406737i	−0.0372953	+	0.0166050i
$601$	27.5628	−	5.85866i	1.12431	−	0.238980i	0.392010	−	0.919961i	$-0.371780\pi$
$601$	27.5628	−	5.85866i	1.12431	−	0.238980i	0.732301	+	0.680981i	$0.238447\pi$
$602$	−32.3237	−	6.87061i	−1.31741	−	0.280025i
$603$	−4.34134	−	1.93289i	−0.176793	−	0.0787134i
$604$	1.40323	+	4.31870i	0.0570967	+	0.175725i
$605$	3.37622	+	10.3909i	0.137263	+	0.422451i
$606$	−6.89652	−	3.07053i	−0.280152	−	0.124732i
$607$	−27.4091	−	5.82599i	−1.11250	−	0.236470i	−0.385231	−	0.922820i	$-0.625878\pi$
$607$	−27.4091	−	5.82599i	−1.11250	−	0.236470i	−0.727271	+	0.686350i	$0.759212\pi$
$608$	−8.10615	+	1.72301i	−0.328748	+	0.0698775i
$609$	−16.0254	+	7.13497i	−0.649382	+	0.289124i
$610$	−4.37963	−	4.86408i	−0.177326	−	0.196941i
$611$	0.382666	+	3.64082i	0.0154810	+	0.147292i
$612$	2.17524	−	1.58041i	0.0879290	−	0.0638842i
$613$	−1.06180	+	10.1023i	−0.0428855	+	0.408028i	0.951929	+	0.306320i	$0.0990976\pi$
$613$	−1.06180	+	10.1023i	−0.0428855	+	0.408028i	−0.994814	+	0.101709i	$0.967569\pi$
$614$	−1.40996	−	2.44212i	−0.0569013	−	0.0985560i
$615$	−1.89211	+	3.27723i	−0.0762972	+	0.132151i
$616$	−0.900113	−	0.653970i	−0.0362666	−	0.0263492i
$617$	23.3142	−	25.8930i	0.938594	−	1.04241i	−0.0604269	−	0.998173i	$-0.519246\pi$
$617$	23.3142	−	25.8930i	0.938594	−	1.04241i	0.999021	−	0.0442416i	$-0.0140871\pi$
$618$	2.51393	−	7.73707i	0.101125	−	0.311231i
$619$	−10.0995			−0.405935			−0.202968	−	0.979185i	$-0.565059\pi$
$619$	−10.0995			−0.405935			−0.202968	+	0.979185i	$0.565059\pi$
$620$	1.84987	−	5.25147i	0.0742925	−	0.210904i
$621$	−5.01420			−0.201213
$622$	4.41992	−	13.6031i	0.177223	−	0.545435i
$623$	32.0348	−	35.5783i	1.28345	−	1.42541i
$624$	−0.812899	−	0.590606i	−0.0325420	−	0.0236432i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.57872	+	14.8588i	0.342875	+	0.593876i
$627$	0.236183	−	2.24713i	0.00943225	−	0.0897419i
$628$	−2.88535	+	2.09633i	−0.115138	+	0.0836526i
$629$	−3.32355	−	31.6215i	−0.132519	−	1.26083i
$630$	−2.73052	−	3.03255i	−0.108787	−	0.120820i
$631$	−29.1876	+	12.9952i	−1.16194	+	0.517330i	−0.894861	−	0.446344i	$-0.852726\pi$
$631$	−29.1876	+	12.9952i	−1.16194	+	0.517330i	−0.267080	+	0.963674i	$0.586059\pi$
$632$	1.37146	−	0.291512i	0.0545536	−	0.0115957i
$633$	18.4803	+	3.92810i	0.734524	+	0.156128i
$634$	30.7013	+	13.6691i	1.21931	+	0.542870i
$635$	0.0279839	+	0.0861256i	0.00111051	+	0.00341779i
$636$	1.41820	+	4.36478i	0.0562354	+	0.173075i
$637$	−8.85996	−	3.94471i	−0.351045	−	0.156295i
$638$	−1.14644	−	0.243684i	−0.0453882	−	0.00964755i
$639$	−0.632390	+	0.134419i	−0.0250170	+	0.00531752i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	−3.71868	−	4.13001i	−0.146879	−	0.163126i	0.665216	−	0.746651i	$-0.268339\pi$
$641$	−3.71868	−	4.13001i	−0.146879	−	0.163126i	−0.812095	+	0.583526i	$0.801673\pi$
$642$	1.64305	+	15.6326i	0.0648462	+	0.616970i
$643$	−34.8547	+	25.3234i	−1.37453	+	0.998657i	−0.377166	+	0.926146i	$0.623101\pi$
$643$	−34.8547	+	25.3234i	−1.37453	+	0.998657i	−0.997368	+	0.0725116i	$0.976899\pi$
$644$	−2.13880	+	20.3493i	−0.0842806	+	0.801877i
$645$	−4.04904	−	7.01314i	−0.159431	−	0.276142i
$646$	11.1412	−	19.2971i	0.438343	−	0.759233i
$647$	−9.00795	−	6.54466i	−0.354139	−	0.257297i	0.396464	−	0.918050i	$-0.370237\pi$
$647$	−9.00795	−	6.54466i	−0.354139	−	0.257297i	−0.750603	+	0.660753i	$0.770237\pi$
$648$	0.669131	−	0.743145i	0.0262859	−	0.0291935i
$649$	−0.309011	+	0.951039i	−0.0121298	+	0.0373315i
$650$	−1.00480			−0.0394115
$651$	22.7135	+	0.557159i	0.890214	+	0.0218368i
$652$	−3.46871			−0.135845
$653$	3.77444	−	11.6165i	0.147705	−	0.454590i	−0.849644	−	0.527357i	$-0.823183\pi$
$653$	3.77444	−	11.6165i	0.147705	−	0.454590i	0.997349	+	0.0727673i	$0.0231830\pi$
$654$	−3.73969	+	4.15334i	−0.146233	+	0.162408i
$655$	13.3416	+	9.69325i	0.521300	+	0.378747i
$656$	−1.89211	+	3.27723i	−0.0738744	+	0.127954i
$657$	0.771956	+	1.33707i	0.0301169	+	0.0521640i
$658$	−1.55409	+	14.7862i	−0.0605846	+	0.576424i
$659$	34.8308	−	25.3061i	1.35682	−	0.985785i	0.358177	−	0.933654i	$-0.383399\pi$
$659$	34.8308	−	25.3061i	1.35682	−	0.985785i	0.998640	−	0.0521313i	$-0.0166014\pi$
$660$	−0.0284996	−	0.271156i	−0.00110935	−	0.0105547i
$661$	21.7316	+	24.1354i	0.845262	+	0.938758i	0.998780	−	0.0493875i	$-0.0157269\pi$
$661$	21.7316	+	24.1354i	0.845262	+	0.938758i	−0.153518	+	0.988146i	$0.549060\pi$
$662$	21.7640	−	9.68997i	0.845883	−	0.376611i
$663$	2.64261	−	0.561705i	0.102631	−	0.0218148i
$664$	−1.09358	−	0.232448i	−0.0424392	−	0.00902073i
$665$	−30.8941	−	13.7549i	−1.19802	−	0.533393i
$666$	−3.65426	−	11.2467i	−0.141600	−	0.435799i
$667$	6.66082	+	20.4999i	0.257908	+	0.793759i
$668$	−4.78807	−	2.13179i	−0.185256	−	0.0824813i
$669$	−3.16788	−	0.673353i	−0.122477	−	0.0260333i
$670$	−4.64835	+	0.988036i	−0.179581	+	0.0381712i
$671$	1.63028	−	0.725846i	0.0629362	−	0.0280210i
$672$	−2.73052	−	3.03255i	−0.105332	−	0.116983i
$673$	3.85796	+	36.7061i	0.148713	+	1.41491i	0.773340	+	0.633991i	$0.218584\pi$
$673$	3.85796	+	36.7061i	0.148713	+	1.41491i	−0.624627	+	0.780923i	$0.714749\pi$
$674$	18.7757	−	13.6414i	0.723214	−	0.525446i
$675$	0.104528	−	0.994522i	0.00402330	−	0.0382792i
$676$	5.99519	+	10.3840i	0.230584	+	0.399384i
$677$	−12.0195	+	20.8184i	−0.461946	+	0.800115i	−0.999058	−	0.0433967i	$-0.986182\pi$
$677$	−12.0195	+	20.8184i	−0.461946	+	0.800115i	0.537112	+	0.843511i	$0.319515\pi$
$678$	11.1394	+	8.09328i	0.427808	+	0.310820i
$679$	13.7057	−	15.2217i	0.525975	−	0.584154i
$680$	0.830869	−	2.55715i	0.0318624	−	0.0980623i
$681$	14.6037			0.559615
$682$	1.20588	+	0.922134i	0.0461754	+	0.0353103i
$683$	32.8457			1.25680			0.628402	−	0.777889i	$-0.283709\pi$
$683$	32.8457			1.25680			0.628402	+	0.777889i	$0.283709\pi$
$684$	2.56090	−	7.88164i	0.0979184	−	0.301362i
$685$	5.57714	−	6.19404i	0.213092	−	0.236662i
$686$	−8.75559	−	6.36131i	−0.334290	−	0.242876i
$687$	6.86875	−	11.8970i	0.262059	−	0.453900i
$688$	−4.04904	−	7.01314i	−0.154368	−	0.267373i
$689$	−0.482025	+	4.58616i	−0.0183637	+	0.174719i
$690$	−4.05657	+	2.94727i	−0.154431	+	0.112201i
$691$	4.35396	+	41.4252i	0.165632	+	1.57589i	0.689626	+	0.724166i	$0.257775\pi$
$691$	4.35396	+	41.4252i	0.165632	+	1.57589i	−0.523994	+	0.851722i	$0.675558\pi$
$692$	−15.5506	−	17.2707i	−0.591146	−	0.656535i
$693$	1.01641	−	0.452535i	0.0386103	−	0.0171904i
$694$	26.8262	−	5.70209i	1.01831	−	0.216448i
$695$	−21.1865	−	4.50334i	−0.803651	−	0.170821i
$696$	−3.92712	−	1.74847i	−0.148857	−	0.0662755i
$697$	−3.14419	−	9.67682i	−0.119095	−	0.366536i
$698$	5.58910	+	17.2015i	0.211550	+	0.651085i
$699$	15.6760	+	6.97942i	0.592922	+	0.263986i
$700$	−3.99153	−	0.848425i	−0.150866	−	0.0320675i
$701$	−26.0860	+	5.54476i	−0.985256	+	0.209423i	−0.672247	−	0.740327i	$-0.734671\pi$
$701$	−26.0860	+	5.54476i	−0.985256	+	0.209423i	−0.313010	+	0.949750i	$0.601337\pi$
$702$	0.917929	−	0.408688i	0.0346450	−	0.0154250i
$703$	−65.5750	−	72.8284i	−2.47321	−	2.74678i
$704$	−0.0284996	−	0.271156i	−0.00107412	−	0.0102196i
$705$	−2.94757	+	2.14153i	−0.111012	+	0.0806548i
$706$	−2.33453	+	22.2116i	−0.0878614	+	0.835945i
$707$	−15.4030	−	26.6787i	−0.579289	−	1.00336i
$708$	−1.83382	+	3.17628i	−0.0689193	+	0.119372i
$709$	−9.09520	−	6.60805i	−0.341577	−	0.248170i	0.403750	−	0.914869i	$-0.367707\pi$
$709$	−9.09520	−	6.60805i	−0.341577	−	0.248170i	−0.745327	+	0.666699i	$0.767707\pi$
$710$	−0.432605	+	0.480457i	−0.0162354	+	0.0180312i
$711$	−0.433272	+	1.33347i	−0.0162490	+	0.0500091i
$712$	11.7321			0.439680
$713$	3.59820	−	27.6850i	0.134754	−	1.03681i
$714$	10.9720			0.410616
$715$	0.0846576	−	0.260549i	0.00316601	−	0.00974399i
$716$	8.17590	−	9.08026i	0.305548	−	0.339345i
$717$	7.06693	+	5.13443i	0.263919	+	0.191749i
$718$	−9.38606	+	16.2571i	−0.350285	+	0.606711i
$719$	10.4005	+	18.0142i	0.387874	+	0.671818i	0.992163	−	0.124947i	$-0.0398762\pi$
$719$	10.4005	+	18.0142i	0.387874	+	0.671818i	−0.604289	+	0.796765i	$0.706543\pi$
$720$	0.104528	−	0.994522i	0.00389555	−	0.0370636i
$721$	26.8573	−	19.5130i	1.00022	−	0.726701i
$722$	−5.19281	−	49.4062i	−0.193256	−	1.83871i
$723$	−15.9929	−	17.7619i	−0.594781	−	0.660571i
$724$	4.10758	−	1.82881i	0.152657	−	0.0679673i
$725$	−4.20483	+	0.893764i	−0.156163	+	0.0331936i
$726$	−10.6869	−	2.27157i	−0.396628	−	0.0843060i
$727$	−1.60141	−	0.712992i	−0.0593929	−	0.0264434i	0.376825	−	0.926284i	$-0.377016\pi$
$727$	−1.60141	−	0.712992i	−0.0593929	−	0.0264434i	−0.436218	+	0.899841i	$0.643682\pi$
$728$	−1.26706	−	3.89960i	−0.0469603	−	0.144529i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	1.41043	+	0.627966i	0.0522025	+	0.0232421i
$731$	21.2979	+	4.52701i	0.787731	+	0.167437i
$732$	6.40223	−	1.36084i	0.236633	−	0.0502980i
$733$	−40.4598	+	18.0139i	−1.49442	+	0.665357i	−0.981216	−	0.192912i	$-0.938207\pi$
$733$	−40.4598	+	18.0139i	−1.49442	+	0.665357i	−0.513200	+	0.858269i	$0.671540\pi$
$734$	0.167898	+	0.186470i	0.00619723	+	0.00688272i
$735$	−1.00892	−	9.59924i	−0.0372146	−	0.354073i
$736$	−4.05657	+	2.94727i	−0.149527	+	0.108638i
$737$	0.135436	−	1.28858i	0.00498884	−	0.0474656i
$738$	−1.89211	−	3.27723i	−0.0696495	−	0.120636i
$739$	−16.8681	+	29.2164i	−0.620502	+	1.07474i	0.368890	+	0.929473i	$0.379738\pi$
$739$	−16.8681	+	29.2164i	−0.620502	+	1.07474i	−0.989392	+	0.145268i	$0.953595\pi$
$740$	−9.56698	−	6.95082i	−0.351689	−	0.255517i
$741$	5.57186	−	6.18818i	0.204687	−	0.227328i
$742$	−5.78726	+	17.8114i	−0.212457	+	0.653875i
$743$	−29.5049			−1.08243			−0.541216	−	0.840884i	$-0.682036\pi$
$743$	−29.5049			−1.08243			−0.541216	+	0.840884i	$0.682036\pi$
$744$	3.62298	+	4.22777i	0.132825	+	0.154998i
$745$	−6.37284			−0.233483
$746$	4.41885	−	13.5998i	0.161785	−	0.497924i
$747$	0.748097	−	0.830846i	0.0273714	−	0.0303991i
$748$	0.593079	+	0.430897i	0.0216851	+	0.0157552i
$749$	−32.0717	+	55.5498i	−1.17187	+	2.02975i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	3.63431	−	34.5781i	0.132618	−	1.26177i	−0.702493	−	0.711691i	$-0.747930\pi$
$751$	3.63431	−	34.5781i	0.132618	−	1.26177i	0.835111	−	0.550082i	$-0.185404\pi$
$752$	−2.94757	+	2.14153i	−0.107487	+	0.0780937i
$753$	3.20735	+	30.5159i	0.116882	+	1.11206i
$754$	−2.89024	−	3.20994i	−0.105256	−	0.116899i
$755$	−4.14837	+	1.84697i	−0.150974	+	0.0672182i
$756$	3.99153	−	0.848425i	0.145170	−	0.0308569i
$757$	5.53416	+	1.17632i	0.201143	+	0.0427542i	0.307381	−	0.951587i	$-0.400547\pi$
$757$	5.53416	+	1.17632i	0.201143	+	0.0427542i	−0.106239	+	0.994341i	$0.533881\pi$
$758$	7.61892	+	3.39216i	0.276732	+	0.123209i
$759$	−0.422462	−	1.30021i	−0.0153344	−	0.0471945i
$760$	−2.56090	−	7.88164i	−0.0928936	−	0.285897i
$761$	−11.5959	−	5.16284i	−0.420352	−	0.187153i	0.185650	−	0.982616i	$-0.440561\pi$
$761$	−11.5959	−	5.16284i	−0.420352	−	0.187153i	−0.606002	+	0.795463i	$0.707228\pi$
$762$	−0.0885790	−	0.0188280i	−0.00320888	−	0.000682068i
$763$	−22.3081	+	4.74174i	−0.807609	+	0.171663i
$764$	−14.2082	+	6.32591i	−0.514035	+	0.228863i
$765$	1.79912	+	1.99813i	0.0650475	+	0.0722426i
$766$	−0.170809	−	1.62514i	−0.00617158	−	0.0587186i
$767$	−2.98143	+	2.16613i	−0.107653	+	0.0782146i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	8.43102	+	14.6030i	0.304030	+	0.526596i	0.977045	−	0.213033i	$-0.0683342\pi$
$769$	8.43102	+	14.6030i	0.304030	+	0.526596i	−0.673015	+	0.739629i	$0.735001\pi$
$770$	0.556300	−	0.963540i	0.0200477	−	0.0347236i
$771$	9.68158	+	7.03408i	0.348674	+	0.253326i
$772$	−6.09656	+	6.77091i	−0.219420	+	0.243690i
$773$	12.6973	−	39.0783i	0.456691	−	1.40555i	−0.412447	−	0.910981i	$-0.635326\pi$
$773$	12.6973	−	39.0783i	0.456691	−	1.40555i	0.869138	−	0.494569i	$-0.164674\pi$
$774$	8.09807			0.291079
$775$	5.41607	+	1.29081i	0.194551	+	0.0463671i
$776$	5.01943			0.180187
$777$	14.9120	−	45.8943i	0.534963	−	1.64645i
$778$	21.2709	−	23.6237i	0.762598	−	0.846951i
$779$	−25.3714	−	18.4334i	−0.909023	−	0.660444i
$780$	0.502399	−	0.870181i	0.0179888	−	0.0311575i
$781$	−0.0881364	−	0.152657i	−0.00315377	−	0.00546249i
$782$	1.40924	−	13.4081i	0.0503945	−	0.479471i
$783$	3.47778	−	2.52675i	0.124286	−	0.0902988i
$784$	−1.00892	−	9.59924i	−0.0360329	−	0.342830i
$785$	−2.38645	−	2.65042i	−0.0851759	−	0.0945974i
$786$	−15.0654	+	6.70755i	−0.537365	+	0.239251i
$787$	−52.9092	+	11.2462i	−1.88601	+	0.400884i	−0.998235	−	0.0593924i	$-0.981084\pi$
$787$	−52.9092	+	11.2462i	−1.88601	+	0.400884i	−0.887776	+	0.460276i	$0.847750\pi$
$788$	−6.51763	−	1.38536i	−0.232181	−	0.0493516i
$789$	−16.3912	−	7.29784i	−0.583543	−	0.259810i
$790$	0.433272	+	1.33347i	0.0154151	+	0.0474428i
$791$	17.3629	+	53.4376i	0.617354	+	1.90002i
$792$	0.249078	+	0.110896i	0.00885059	+	0.00394053i
$793$	6.43295	+	1.36737i	0.228441	+	0.0485566i
$794$	−12.0985	+	2.57162i	−0.429360	+	0.0912634i
$795$	−4.19263	+	1.86668i	−0.148697	+	0.0662042i
$796$	−15.0515	−	16.7164i	−0.533488	−	0.592498i
$797$	4.44649	+	42.3056i	0.157503	+	1.49854i	0.732715	+	0.680535i	$0.238253\pi$
$797$	4.44649	+	42.3056i	0.157503	+	1.49854i	−0.575212	+	0.818004i	$0.695081\pi$
$798$	27.3591	−	19.8776i	0.968503	−	0.703659i
$799$	1.02398	−	9.74251i	0.0362258	−	0.344665i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−5.86606	+	10.1603i	−0.207267	+	0.358997i
$802$	14.7123	+	10.6891i	0.519511	+	0.377447i
$803$	−0.281668	+	0.312824i	−0.00993986	+	0.0110393i
$804$	1.46851	−	4.51960i	0.0517903	−	0.159394i
$805$	−20.4614			−0.721171
$806$	1.59779	+	5.36146i	0.0562799	+	0.188849i
$807$	−4.12677			−0.145269
$808$	2.33283	−	7.17970i	0.0820685	−	0.252581i
$809$	9.63928	−	10.7055i	0.338899	−	0.376385i	−0.549472	−	0.835512i	$-0.685171\pi$
$809$	9.63928	−	10.7055i	0.338899	−	0.376385i	0.888371	+	0.459127i	$0.151838\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	5.22714	−	9.05367i	0.183550	−	0.317917i	−0.759537	−	0.650464i	$-0.774575\pi$
$811$	5.22714	−	9.05367i	0.183550	−	0.317917i	0.943087	+	0.332547i	$0.107908\pi$
$812$	−8.77099	−	15.1918i	−0.307802	−	0.533128i
$813$	−3.14200	+	29.8942i	−0.110195	+	1.04843i
$814$	2.60843	−	1.89514i	0.0914255	−	0.0664245i
$815$	−0.362579	−	3.44971i	−0.0127006	−	0.120838i
$816$	1.79912	+	1.99813i	0.0629820	+	0.0699486i
$817$	61.3087	−	27.2964i	2.14492	−	0.954979i
$818$	27.1023	−	5.76078i	0.947611	−	0.201421i
$819$	4.01068	+	0.852497i	0.140145	+	0.0297886i
$820$	−3.45705	−	1.53918i	−0.120726	−	0.0537505i
$821$	−10.9816	−	33.7978i	−0.383260	−	1.17955i	−0.937735	−	0.347352i	$-0.887081\pi$
$821$	−10.9816	−	33.7978i	−0.383260	−	1.17955i	0.554475	−	0.832200i	$-0.312919\pi$
$822$	2.57563	+	7.92697i	0.0898353	+	0.276485i
$823$	48.0468	+	21.3918i	1.67481	+	0.745672i	0.999970	+	0.00770534i	$0.00245271\pi$
$823$	48.0468	+	21.3918i	1.67481	+	0.745672i	0.674837	+	0.737967i	$0.264214\pi$
$824$	7.95746	+	1.69141i	0.277211	+	0.0589231i
$825$	0.266691	−	0.0566870i	0.00928500	−	0.00197359i
$826$	−13.6726	+	6.08745i	−0.475732	+	0.211810i
$827$	0.993321	+	1.10319i	0.0345412	+	0.0383618i	0.760168	−	0.649727i	$-0.225117\pi$
$827$	0.993321	+	1.10319i	0.0345412	+	0.0383618i	−0.725627	+	0.688089i	$0.758450\pi$
$828$	−0.524126	−	4.98673i	−0.0182146	−	0.173301i
$829$	−1.99841	+	1.45193i	−0.0694078	+	0.0504277i	−0.621948	−	0.783058i	$-0.713659\pi$
$829$	−1.99841	+	1.45193i	−0.0694078	+	0.0504277i	0.552540	+	0.833486i	$0.313659\pi$
$830$	0.116864	−	1.11189i	0.00405642	−	0.0385942i
$831$	−10.7210	−	18.5693i	−0.371908	−	0.644163i
$832$	0.502399	−	0.870181i	0.0174176	−	0.0301681i
$833$	20.9957	+	15.2543i	0.727458	+	0.528529i
$834$	14.4933	−	16.0964i	0.501861	−	0.557373i
$835$	1.61962	−	4.98467i	0.0560492	−	0.172502i
$836$	2.25951			0.0781468
$837$	−5.47284	+	1.02370i	−0.189169	+	0.0353844i
$838$	−27.0967			−0.936039
$839$	16.3194	−	50.2259i	0.563408	−	1.73399i	−0.109226	−	0.994017i	$-0.534837\pi$
$839$	16.3194	−	50.2259i	0.563408	−	1.73399i	0.672634	−	0.739975i	$-0.265163\pi$
$840$	2.73052	−	3.03255i	0.0942120	−	0.104633i
$841$	8.51134	+	6.18385i	0.293494	+	0.213236i
$842$	7.54938	−	13.0759i	0.260169	−	0.450625i
$843$	−5.83538	−	10.1072i	−0.200981	−	0.348110i
$844$	−1.97487	+	18.7896i	−0.0679778	+	0.646765i
$845$	−9.70042	+	7.04777i	−0.333705	+	0.242451i
$846$	−0.380838	−	3.62344i	−0.0130935	−	0.124576i
$847$	−29.8328	−	33.1326i	−1.02507	−	1.13845i
$848$	−4.19263	+	1.86668i	−0.143975	+	0.0641020i
$849$	−16.3206	+	3.46905i	−0.560121	+	0.119057i
$850$	2.62999	+	0.559023i	0.0902081	+	0.0191743i
$851$	−54.1688	−	24.1175i	−1.85688	−	0.826737i
$852$	−0.199785	−	0.614875i	−0.00684453	−	0.0210653i
$853$	8.77615	+	27.0102i	0.300490	+	0.924812i	0.981322	+	0.192373i	$0.0616183\pi$
$853$	8.77615	+	27.0102i	0.300490	+	0.924812i	−0.680832	+	0.732439i	$0.738382\pi$
$854$	24.4001	+	10.8636i	0.834955	+	0.371746i
$855$	8.10615	+	1.72301i	0.277224	+	0.0589259i
$856$	−15.3752	+	3.26811i	−0.525515	+	0.111702i
$857$	−26.8264	+	11.9439i	−0.916372	+	0.407995i	−0.810066	−	0.586338i	$-0.800569\pi$
$857$	−26.8264	+	11.9439i	−0.916372	+	0.407995i	−0.106306	+	0.994333i	$0.533902\pi$
$858$	0.183313	+	0.203590i	0.00625822	+	0.00695046i
$859$	−0.813703	−	7.74186i	−0.0277632	−	0.264149i	−0.999595	−	0.0284719i	$-0.990936\pi$
$859$	−0.813703	−	7.74186i	−0.0277632	−	0.264149i	0.971831	−	0.235677i	$-0.0757308\pi$
$860$	6.55148	−	4.75993i	0.223404	−	0.162312i
$861$	1.61415	−	15.3577i	0.0550103	−	0.523388i
$862$	−8.19262	−	14.1900i	−0.279042	−	0.483315i
$863$	−19.2325	+	33.3117i	−0.654683	+	1.13394i	0.327290	+	0.944924i	$0.393864\pi$
$863$	−19.2325	+	33.3117i	−0.654683	+	1.13394i	−0.981973	+	0.189020i	$0.939469\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	15.5506	−	17.2707i	0.528737	−	0.587222i
$866$	10.8683	−	33.4493i	0.369321	−	1.13665i
$867$	9.77062			0.331828
$868$	1.82011	+	22.6474i	0.0617784	+	0.768701i
$869$	−0.382281			−0.0129680
$870$	1.32839	−	4.08837i	0.0450367	−	0.138609i
$871$	3.19510	−	3.54851i	0.108262	−	0.120237i
$872$	−4.52149	−	3.28506i	−0.153117	−	0.111246i
$873$	−2.50971	+	4.34695i	−0.0849409	+	0.147122i
$874$	−20.7769	−	35.9867i	−0.702790	−	1.21727i
$875$	0.426549	−	4.05835i	0.0144200	−	0.137197i
$876$	−1.24905	+	0.907489i	−0.0422015	+	0.0306612i
$877$	−2.13621	−	20.3247i	−0.0721348	−	0.686317i	−0.969511	−	0.245050i	$-0.921196\pi$
$877$	−2.13621	−	20.3247i	−0.0721348	−	0.686317i	0.897376	−	0.441267i	$-0.145471\pi$
$878$	22.5849	+	25.0830i	0.762202	+	0.846511i
$879$	23.5433	−	10.4822i	0.794097	−	0.353555i
$880$	0.266691	−	0.0566870i	0.00899016	−	0.00191092i
$881$	−22.7681	−	4.83950i	−0.767076	−	0.163047i	−0.192276	−	0.981341i	$-0.561587\pi$
$881$	−22.7681	−	4.83950i	−0.767076	−	0.163047i	−0.574800	+	0.818294i	$0.694920\pi$
$882$	8.81765	+	3.92587i	0.296906	+	0.132191i
$883$	−4.18627	−	12.8840i	−0.140879	−	0.433582i	0.855579	−	0.517673i	$-0.173201\pi$
$883$	−4.18627	−	12.8840i	−0.140879	−	0.433582i	−0.996458	+	0.0840906i	$0.973201\pi$
$884$	0.834857	+	2.56942i	0.0280793	+	0.0864191i
$885$	−3.35056	−	1.49177i	−0.112628	−	0.0501452i
$886$	16.6859	+	3.54670i	0.560575	+	0.119154i
$887$	41.6950	−	8.86255i	1.39998	−	0.297575i	0.554769	−	0.832004i	$-0.312807\pi$
$887$	41.6950	−	8.86255i	1.39998	−	0.297575i	0.845213	+	0.534429i	$0.179473\pi$
$888$	10.8031	−	4.80984i	0.362528	−	0.161408i
$889$	−0.247270	−	0.274621i	−0.00829318	−	0.00921051i
$890$	1.22634	+	11.6679i	0.0411071	+	0.391107i
$891$	−0.220578	+	0.160259i	−0.00738964	+	0.00536889i
$892$	0.338531	−	3.22091i	0.0113349	−	0.107844i
$893$	−15.0968	−	26.1485i	−0.505197	−	0.875026i
$894$	3.18642	−	5.51904i	0.106570	−	0.184584i
$895$	9.88513	+	7.18197i	0.330423	+	0.240067i
$896$	2.73052	−	3.03255i	0.0912203	−	0.101310i
$897$	1.55691	−	4.79167i	0.0519836	−	0.159989i
$898$	32.2827			1.07729
$899$	11.4554	+	21.0151i	0.382058	+	0.700894i
$900$	1.00000			0.0333333
$901$	3.81319	−	11.7358i	0.127036	−	0.390976i
$902$	0.690385	−	0.766750i	0.0229873	−	0.0255300i
$903$	26.7346	+	19.4238i	0.889673	+	0.646385i
$904$	−6.88455	+	11.9244i	−0.228977	+	0.396599i
$905$	2.24815	+	3.89392i	0.0747311	+	0.129438i
$906$	0.474659	−	4.51608i	0.0157695	−	0.150037i
$907$	−27.2114	+	19.7702i	−0.903540	+	0.656460i	−0.939373	−	0.342898i	$-0.888592\pi$
$907$	−27.2114	+	19.7702i	−0.903540	+	0.656460i	0.0358331	+	0.999358i	$0.488592\pi$
$908$	1.52650	+	14.5237i	0.0506587	+	0.481986i
$909$	5.05139	+	5.61014i	0.167544	+	0.186077i
$910$	3.74580	−	1.66774i	0.124172	−	0.0552849i
$911$	32.7506	−	6.96135i	1.08508	−	0.230640i	0.369539	−	0.929215i	$-0.379516\pi$
$911$	32.7506	−	6.96135i	1.08508	−	0.230640i	0.715537	+	0.698575i	$0.246182\pi$
$912$	8.10615	+	1.72301i	0.268421	+	0.0570547i
$913$	0.278472	+	0.123984i	0.00921608	+	0.00410326i
$914$	−1.34365	−	4.13533i	−0.0444440	−	0.136785i
$915$	2.02260	+	6.22491i	0.0668650	+	0.205789i
$916$	12.5498	+	5.58755i	0.414658	+	0.184618i
$917$	−65.8249	−	13.9915i	−2.17373	−	0.462040i
$918$	−2.62999	+	0.559023i	−0.0868027	+	0.0184505i
$919$	39.7087	−	17.6795i	1.30987	−	0.583192i	0.371375	−	0.928483i	$-0.378887\pi$
$919$	39.7087	−	17.6795i	1.30987	−	0.583192i	0.938496	+	0.345291i	$0.112220\pi$
$920$	−3.35515	−	3.72627i	−0.110616	−	0.122852i
$921$	0.294762	+	2.80447i	0.00971273	+	0.0924105i
$922$	−28.7005	+	20.8521i	−0.945201	+	0.686729i
$923$	0.0679039	−	0.646062i	0.00223508	−	0.0212654i
$924$	0.556300	+	0.963540i	0.0183009	+	0.0316981i
$925$	5.91272	−	10.2411i	0.194409	−	0.336726i
$926$	12.1019	+	8.79252i	0.397692	+	0.288940i
$927$	−5.44354	+	6.04566i	−0.178789	+	0.198566i
$928$	1.32839	−	4.08837i	0.0436066	−	0.134207i
$929$	30.5848			1.00345			0.501727	−	0.865026i	$-0.332698\pi$
$929$	30.5848			1.00345			0.501727	+	0.865026i	$0.332698\pi$
$930$	−3.82591	+	4.04505i	−0.125456	+	0.132642i
$931$	79.9894			2.62155
$932$	−5.30260	+	16.3197i	−0.173692	+	0.534570i
$933$	−9.57069	+	10.6293i	−0.313330	+	0.347988i
$934$	21.1670	+	15.3787i	0.692604	+	0.503206i
$935$	−0.366543	+	0.634871i	−0.0119872	+	0.0207625i
$936$	0.502399	+	0.870181i	0.0164214	+	0.0284428i
$937$	2.46812	−	23.4826i	0.0806299	−	0.767142i	−0.877262	−	0.480012i	$-0.840632\pi$
$937$	2.46812	−	23.4826i	0.0806299	−	0.767142i	0.957892	−	0.287130i	$-0.0927012\pi$
$938$	15.6887	−	11.3985i	0.512254	−	0.372174i
$939$	−1.79344	−	17.0635i	−0.0585268	−	0.556845i
$940$	−2.43791	−	2.70757i	−0.0795158	−	0.0883112i
$941$	−35.8083	+	15.9429i	−1.16732	+	0.519724i	−0.896559	−	0.442923i	$-0.853941\pi$
$941$	−35.8083	+	15.9429i	−1.16732	+	0.519724i	−0.270759	+	0.962647i	$0.587275\pi$
$942$	3.48855	−	0.741514i	0.113663	−	0.0241598i
$943$	−18.5602	−	3.94508i	−0.604402	−	0.128470i
$944$	−3.35056	−	1.49177i	−0.109052	−	0.0485529i
$945$	1.26101	+	3.88098i	0.0410205	+	0.126248i
$946$	0.682289	+	2.09987i	0.0221831	+	0.0682727i
$947$	10.6280	+	4.73188i	0.345363	+	0.153766i	0.572086	−	0.820194i	$-0.306134\pi$
$947$	10.6280	+	4.73188i	0.345363	+	0.153766i	−0.226723	+	0.973959i	$0.572801\pi$
$948$	−1.37146	−	0.291512i	−0.0445429	−	0.00946788i
$949$	−1.51742	+	0.322538i	−0.0492576	+	0.0104700i
$950$	7.57077	−	3.37073i	0.245628	−	0.109361i
$951$	−22.4873	−	24.9747i	−0.729202	−	0.809860i
$952$	1.14688	+	10.9119i	0.0371707	+	0.353656i
$953$	−1.66441	+	1.20927i	−0.0539157	+	0.0391720i	−0.614417	−	0.788982i	$-0.710609\pi$
$953$	−1.66441	+	1.20927i	−0.0539157	+	0.0391720i	0.560501	+	0.828154i	$0.310609\pi$
$954$	0.479723	−	4.56426i	0.0155316	−	0.147773i
$955$	−7.77641	−	13.4691i	−0.251639	−	0.435851i
$956$	−4.36761	+	7.56491i	−0.141258	+	0.244667i
$957$	0.948213	+	0.688917i	0.0306514	+	0.0222695i
$958$	−9.36209	+	10.3977i	−0.302475	+	0.335933i
$959$	−10.5104	+	32.3476i	−0.339397	+	1.04456i
$960$	1.00000			0.0322749
$961$	−1.72488	−	30.9520i	−0.0556413	−	0.998451i
$962$	11.8822			0.383097
$963$	4.85735	−	14.9494i	0.156526	−	0.481738i
$964$	15.9929	−	17.7619i	0.515095	−	0.572071i
$965$	−7.37108	−	5.35541i	−0.237284	−	0.172397i
$966$	10.2307	−	17.7201i	0.329168	−	0.570136i
$967$	−5.38020	−	9.31878i	−0.173015	−	0.299672i	0.766457	−	0.642295i	$-0.222018\pi$
$967$	−5.38020	−	9.31878i	−0.173015	−	0.299672i	−0.939473	+	0.342624i	$0.888684\pi$
$968$	1.14204	−	10.8658i	0.0367066	−	0.349240i
$969$	−18.0268	+	13.0972i	−0.579103	+	0.420743i
$970$	0.524673	+	4.99193i	0.0168462	+	0.160281i
$971$	−0.373649	−	0.414979i	−0.0119910	−	0.0133173i	0.737120	−	0.675762i	$-0.236185\pi$
$971$	−0.373649	−	0.414979i	−0.0119910	−	0.0133173i	−0.749110	+	0.662445i	$0.769519\pi$
$972$	−0.913545	+	0.406737i	−0.0293020	+	0.0130461i
$973$	86.4559	−	18.3768i	2.77165	−	0.589132i
$974$	−8.40512	−	1.78656i	−0.269318	−	0.0572452i
$975$	0.917929	+	0.408688i	0.0293973	+	0.0130885i
$976$	2.02260	+	6.22491i	0.0647418	+	0.199255i
$977$	−5.17838	−	15.9374i	−0.165671	−	0.509883i	0.833414	−	0.552649i	$-0.186383\pi$
$977$	−5.17838	−	15.9374i	−0.165671	−	0.509883i	−0.999085	+	0.0427662i	$0.986383\pi$
$978$	3.16883	+	1.41085i	0.101328	+	0.0451141i
$979$	−3.12886	−	0.665059i	−0.0999987	−	0.0212554i
$980$	9.44120	−	2.00679i	0.301588	−	0.0641045i
$981$	5.10569	−	2.27320i	0.163012	−	0.0725777i
$982$	−19.3802	−	21.5239i	−0.618448	−	0.686856i
$983$	0.802396	+	7.63428i	0.0255924	+	0.243496i	0.999838	+	0.0180057i	$0.00573169\pi$
$983$	0.802396	+	7.63428i	0.0255924	+	0.243496i	−0.974245	+	0.225490i	$0.927602\pi$
$984$	3.06149	−	2.22431i	0.0975969	−	0.0709083i
$985$	0.696498	−	6.62673i	0.0221923	−	0.211145i
$986$	5.77916	+	10.0098i	0.184046	+	0.318777i
$987$	7.43380	−	12.8757i	0.236621	−	0.409839i
$988$	6.73669	+	4.89449i	0.214323	+	0.155715i
$989$	27.1703	−	30.1756i	0.863964	−	0.959530i
$990$	−0.0842533	+	0.259305i	−0.00267774	+	0.00824125i
$991$	11.7414			0.372977			0.186489	−	0.982457i	$-0.440289\pi$
$991$	11.7414			0.372977			0.186489	+	0.982457i	$0.440289\pi$
$992$	−3.82591	+	4.04505i	−0.121473	+	0.128431i
$993$	−23.8237			−0.756022
$994$	0.815263	−	2.50912i	0.0258586	−	0.0795845i
$995$	15.0515	−	16.7164i	0.477166	−	0.529946i
$996$	0.904492	+	0.657152i	0.0286599	+	0.0208226i
$997$	−16.8386	+	29.1653i	−0.533284	+	0.923676i	0.465960	+	0.884806i	$0.345709\pi$
$997$	−16.8386	+	29.1653i	−0.533284	+	0.923676i	−0.999244	+	0.0388699i	$0.987624\pi$
$998$	7.32990	+	12.6958i	0.232024	+	0.401877i
$999$	−1.23610	+	11.7607i	−0.0391083	+	0.372091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.c.541.1	yes	16
31.20	even	15	inner	930.2.bg.c.361.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.c.361.1	✓	16	31.20	even	15	inner
930.2.bg.c.541.1	yes	16	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.426549 + 4.05835i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.426549 + 4.05835i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(0.249078 - 0.110896i) q^{11} +(0.978148 - 0.207912i) q^{12} +(0.982842 + 0.208909i) q^{13} +(3.72791 + 1.65977i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.45630 - 1.09361i) q^{17} +(-0.978148 - 0.207912i) q^{18} +(-8.10615 + 1.72301i) q^{19} +(-0.913545 + 0.406737i) q^{20} +(-2.73052 - 3.03255i) q^{21} +(-0.0284996 - 0.271156i) q^{22} +(-4.05657 + 2.94727i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.502399 - 0.870181i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.73052 - 3.03255i) q^{28} +(1.32839 - 4.08837i) q^{29} +1.00000 q^{30} +(-3.82591 + 4.04505i) q^{31} +1.00000 q^{32} +(-0.0842533 + 0.259305i) q^{33} +(-1.79912 + 1.99813i) q^{34} +(3.30136 + 2.39858i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(5.91272 + 10.2411i) q^{37} +(-0.866253 + 8.24184i) q^{38} +(-0.812899 + 0.590606i) q^{39} +(0.104528 + 0.994522i) q^{40} +(2.53213 + 2.81222i) q^{41} +(-3.72791 + 1.65977i) q^{42} +(-7.92111 + 1.68368i) q^{43} +(-0.266691 - 0.0566870i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(1.54947 + 4.76878i) q^{46} +(1.12587 + 3.46507i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(-9.44120 - 2.00679i) q^{49} +(-0.978148 + 0.207912i) q^{50} +(2.45630 - 1.09361i) q^{51} +(-0.672342 - 0.746711i) q^{52} +(0.479723 + 4.56426i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.0284996 - 0.271156i) q^{55} +(-2.04035 - 3.53399i) q^{56} +(4.14362 - 7.17696i) q^{57} +(-3.47778 - 2.52675i) q^{58} +(-2.45414 + 2.72559i) q^{59} +(0.309017 - 0.951057i) q^{60} +6.54526 q^{61} +(2.66480 + 4.88864i) q^{62} +4.08070 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.672342 - 0.746711i) q^{65} +(0.220578 + 0.160259i) q^{66} +(2.37610 - 4.11552i) q^{67} +(1.34437 + 2.32853i) q^{68} +(0.524126 - 4.98673i) q^{69} +(3.30136 - 2.39858i) q^{70} +(-0.0675796 - 0.642977i) q^{71} +(0.669131 + 0.743145i) q^{72} +(-1.41043 + 0.627966i) q^{73} +(11.5670 - 2.45865i) q^{74} +(0.978148 + 0.207912i) q^{75} +(7.57077 + 3.37073i) q^{76} +(0.343812 + 1.05815i) q^{77} +(0.310500 + 0.955620i) q^{78} +(-1.28088 - 0.570284i) q^{79} +(0.978148 + 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(3.45705 - 1.53918i) q^{82} +(0.748097 + 0.830846i) q^{83} +(0.426549 + 4.05835i) q^{84} +(-2.17524 + 1.58041i) q^{85} +(-0.846479 + 8.05371i) q^{86} +(2.14938 + 3.72284i) q^{87} +(-0.136325 + 0.236121i) q^{88} +(-9.49149 - 6.89597i) q^{89} +(-0.669131 + 0.743145i) q^{90} +(-1.26706 + 3.89960i) q^{91} +5.01420 q^{92} +(-0.446028 - 5.54987i) q^{93} +3.64339 q^{94} +(-2.56090 + 7.88164i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(-4.06080 - 2.95035i) q^{97} +(-4.82606 + 8.35898i) q^{98} +(-0.136325 - 0.236121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

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Database

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