LMFDB - Embedded newform 930.2.bg.f.361.2

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			361.2
Root			$2.76635i$ of defining polynomial
Character	$\chi$	$=$	930.361
Dual form			930.2.bg.f.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.318079 + 3.02632i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(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} +(0.318079 + 3.02632i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.16771 - 1.41036i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-3.78551 + 0.804634i) q^{13} +(2.77991 - 1.23769i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.972600 + 0.433029i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-2.29672 - 0.488183i) q^{19} +(0.913545 + 0.406737i) q^{20} +(-2.03616 + 2.26138i) q^{21} +(-0.362452 + 3.44850i) q^{22} +(-1.36200 - 0.989553i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.93504 + 3.35159i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.03616 - 2.26138i) q^{28} +(-2.30648 - 7.09862i) q^{29} -1.00000 q^{30} +(-5.36487 + 1.48935i) q^{31} -1.00000 q^{32} +(-1.07151 - 3.29778i) q^{33} +(0.712385 + 0.791184i) q^{34} +(2.46183 - 1.78862i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.30415 + 2.25886i) q^{37} +(0.245436 + 2.33517i) q^{38} +(-3.13096 - 2.27477i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-0.0605445 + 0.0672414i) q^{41} +(2.77991 + 1.23769i) q^{42} +(-4.05961 - 0.862897i) q^{43} +(3.39172 - 0.720932i) q^{44} +(0.913545 - 0.406737i) q^{45} +(-0.520239 + 1.60113i) q^{46} +(-0.499907 + 1.53855i) q^{47} +(0.913545 - 0.406737i) q^{48} +(-2.21039 + 0.469833i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-0.972600 - 0.433029i) q^{51} +(2.58959 - 2.87603i) q^{52} +(-0.0310146 + 0.295084i) q^{53} +(0.809017 + 0.587785i) q^{54} +(0.362452 + 3.44850i) q^{55} +(-1.52149 + 2.63530i) q^{56} +(-1.17401 - 2.03345i) q^{57} +(-6.03844 + 4.38719i) q^{58} +(0.957186 + 1.06306i) q^{59} +(0.309017 + 0.951057i) q^{60} +1.22227 q^{61} +(3.07429 + 4.64206i) q^{62} -3.04299 q^{63} +(0.309017 + 0.951057i) q^{64} +(2.58959 + 2.87603i) q^{65} +(-2.80526 + 2.03814i) q^{66} +(7.47347 + 12.9444i) q^{67} +(0.532322 - 0.922008i) q^{68} +(-0.175977 - 1.67431i) q^{69} +(-2.46183 - 1.78862i) q^{70} +(-1.44311 + 13.7303i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(-11.6214 - 5.17420i) q^{73} +(2.55131 + 0.542298i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(2.14503 - 0.955030i) q^{76} +(3.26060 - 10.0351i) q^{77} +(-1.19592 + 3.68066i) q^{78} +(-4.61110 + 2.05299i) q^{79} +(-0.978148 + 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.0826597 + 0.0368025i) q^{82} +(2.71330 - 3.01343i) q^{83} +(0.318079 - 3.02632i) q^{84} +(0.861314 + 0.625781i) q^{85} +(0.433825 + 4.12757i) q^{86} +(3.73196 - 6.46395i) q^{87} +(-1.73375 - 3.00294i) q^{88} +(-12.1530 + 8.82969i) q^{89} +(-0.669131 - 0.743145i) q^{90} +(-3.63917 - 11.2002i) q^{91} +1.68353 q^{92} +(-4.69660 - 2.99030i) q^{93} +1.61773 q^{94} +(0.725581 + 2.23311i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(6.45252 - 4.68803i) q^{97} +(1.12989 + 1.95702i) q^{98} +(1.73375 - 3.00294i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{15}\right)$

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
$7$	0.318079	+	3.02632i	0.120222	+	1.14384i	0.873733	+	0.486405i	$0.161692\pi$
$7$	0.318079	+	3.02632i	0.120222	+	1.14384i	−0.753511	+	0.657435i	$0.771641\pi$
$8$	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
$11$	−3.16771	−	1.41036i	−0.955101	−	0.425238i	−0.130812	−	0.991407i	$-0.541758\pi$
$11$	−3.16771	−	1.41036i	−0.955101	−	0.425238i	−0.824289	+	0.566169i	$0.808425\pi$
$12$	−0.978148	−	0.207912i	−0.282367	−	0.0600189i
$13$	−3.78551	+	0.804634i	−1.04991	+	0.223165i	−0.700388	−	0.713762i	$-0.746990\pi$
$13$	−3.78551	+	0.804634i	−1.04991	+	0.223165i	−0.349523	+	0.936928i	$0.613656\pi$
$14$	2.77991	−	1.23769i	0.742961	−	0.330788i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.972600	+	0.433029i	−0.235890	+	0.105025i	−0.521278	−	0.853387i	$-0.674544\pi$
$17$	−0.972600	+	0.433029i	−0.235890	+	0.105025i	0.285387	+	0.958412i	$0.407878\pi$
$18$	0.978148	−	0.207912i	0.230552	−	0.0490053i
$19$	−2.29672	−	0.488183i	−0.526904	−	0.111997i	−0.0632233	−	0.997999i	$-0.520138\pi$
$19$	−2.29672	−	0.488183i	−0.526904	−	0.111997i	−0.463680	+	0.886003i	$0.653471\pi$
$20$	0.913545	+	0.406737i	0.204275	+	0.0909491i
$21$	−2.03616	+	2.26138i	−0.444326	+	0.493474i
$22$	−0.362452	+	3.44850i	−0.0772749	+	0.735222i
$23$	−1.36200	−	0.989553i	−0.283997	−	0.206336i	0.436662	−	0.899626i	$-0.356161\pi$
$23$	−1.36200	−	0.989553i	−0.283997	−	0.206336i	−0.720659	+	0.693290i	$0.756161\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.93504	+	3.35159i	0.379492	+	0.657300i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−2.03616	−	2.26138i	−0.384797	−	0.427361i
$29$	−2.30648	−	7.09862i	−0.428303	−	1.31818i	−0.899796	−	0.436311i	$-0.856285\pi$
$29$	−2.30648	−	7.09862i	−0.428303	−	1.31818i	0.471493	−	0.881870i	$-0.343715\pi$
$30$	−1.00000			−0.182574
$31$	−5.36487	+	1.48935i	−0.963559	+	0.267495i
$31$	−5.36487	+	1.48935i	−0.963559	+	0.267495i
$32$	−1.00000			−0.176777
$33$	−1.07151	−	3.29778i	−0.186527	−	0.574070i
$34$	0.712385	+	0.791184i	0.122173	+	0.135687i
$35$	2.46183	−	1.78862i	0.416125	−	0.302332i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.30415	+	2.25886i	−0.214402	+	0.371354i	−0.953087	−	0.302696i	$-0.902113\pi$
$37$	−1.30415	+	2.25886i	−0.214402	+	0.371354i	0.738686	+	0.674050i	$0.235447\pi$
$38$	0.245436	+	2.33517i	0.0398150	+	0.378814i
$39$	−3.13096	−	2.27477i	−0.501355	−	0.364255i
$40$	0.104528	−	0.994522i	0.0165274	−	0.157248i
$41$	−0.0605445	+	0.0672414i	−0.00945545	+	0.0105013i	−0.747854	−	0.663863i	$-0.768916\pi$
$41$	−0.0605445	+	0.0672414i	−0.00945545	+	0.0105013i	0.738399	+	0.674365i	$0.235582\pi$
$42$	2.77991	+	1.23769i	0.428949	+	0.190980i
$43$	−4.05961	−	0.862897i	−0.619085	−	0.131591i	−0.112316	−	0.993673i	$-0.535827\pi$
$43$	−4.05961	−	0.862897i	−0.619085	−	0.131591i	−0.506769	+	0.862082i	$0.669160\pi$
$44$	3.39172	−	0.720932i	0.511321	−	0.108685i
$45$	0.913545	−	0.406737i	0.136183	−	0.0606327i
$46$	−0.520239	+	1.60113i	−0.0767050	+	0.236074i
$47$	−0.499907	+	1.53855i	−0.0729189	+	0.224421i	−0.980873	−	0.194648i	$-0.937644\pi$
$47$	−0.499907	+	1.53855i	−0.0729189	+	0.224421i	0.907954	+	0.419069i	$0.137644\pi$
$48$	0.913545	−	0.406737i	0.131859	−	0.0587074i
$49$	−2.21039	+	0.469833i	−0.315770	+	0.0671189i
$50$	0.978148	+	0.207912i	0.138331	+	0.0294032i
$51$	−0.972600	−	0.433029i	−0.136191	−	0.0606362i
$52$	2.58959	−	2.87603i	0.359111	−	0.398833i
$53$	−0.0310146	+	0.295084i	−0.00426018	+	0.0405329i	−0.996445	−	0.0842403i	$-0.973154\pi$
$53$	−0.0310146	+	0.295084i	−0.00426018	+	0.0405329i	0.992185	+	0.124773i	$0.0398203\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	0.362452	+	3.44850i	0.0488730	+	0.464995i
$56$	−1.52149	+	2.63530i	−0.203318	+	0.352157i
$57$	−1.17401	−	2.03345i	−0.155502	−	0.269337i
$58$	−6.03844	+	4.38719i	−0.792887	+	0.576066i
$59$	0.957186	+	1.06306i	0.124615	+	0.138399i	0.802223	−	0.597024i	$-0.203650\pi$
$59$	0.957186	+	1.06306i	0.124615	+	0.138399i	−0.677608	+	0.735423i	$0.736984\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	1.22227			0.156496			0.0782478	−	0.996934i	$-0.475067\pi$
$61$	1.22227			0.156496			0.0782478	+	0.996934i	$0.475067\pi$
$62$	3.07429	+	4.64206i	0.390436	+	0.589542i
$63$	−3.04299			−0.383380
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	2.58959	+	2.87603i	0.321199	+	0.356727i
$66$	−2.80526	+	2.03814i	−0.345304	+	0.250878i
$67$	7.47347	+	12.9444i	0.913029	+	1.58141i	0.809761	+	0.586760i	$0.199597\pi$
$67$	7.47347	+	12.9444i	0.913029	+	1.58141i	0.103268	+	0.994654i	$0.467070\pi$
$68$	0.532322	−	0.922008i	0.0645535	−	0.111810i
$69$	−0.175977	−	1.67431i	−0.0211851	−	0.201563i
$70$	−2.46183	−	1.78862i	−0.294245	−	0.213781i
$71$	−1.44311	+	13.7303i	−0.171266	+	1.62948i	0.484691	+	0.874685i	$0.338932\pi$
$71$	−1.44311	+	13.7303i	−0.171266	+	1.62948i	−0.655957	+	0.754799i	$0.727735\pi$
$72$	−0.669131	+	0.743145i	−0.0788578	+	0.0875805i
$73$	−11.6214	−	5.17420i	−1.36019	−	0.605594i	−0.408527	−	0.912746i	$-0.633957\pi$
$73$	−11.6214	−	5.17420i	−1.36019	−	0.605594i	−0.951660	+	0.307152i	$0.900624\pi$
$74$	2.55131	+	0.542298i	0.296584	+	0.0630408i
$75$	−0.978148	+	0.207912i	−0.112947	+	0.0240076i
$76$	2.14503	−	0.955030i	0.246052	−	0.109549i
$77$	3.26060	−	10.0351i	0.371580	−	1.14361i
$78$	−1.19592	+	3.68066i	−0.135411	+	0.416753i
$79$	−4.61110	+	2.05299i	−0.518789	+	0.230980i	−0.649390	−	0.760455i	$-0.724976\pi$
$79$	−4.61110	+	2.05299i	−0.518789	+	0.230980i	0.130601	+	0.991435i	$0.458309\pi$
$80$	−0.978148	+	0.207912i	−0.109360	+	0.0232452i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	0.0826597	+	0.0368025i	0.00912823	+	0.00406415i
$83$	2.71330	−	3.01343i	0.297824	−	0.330767i	−0.575597	−	0.817734i	$-0.695230\pi$
$83$	2.71330	−	3.01343i	0.297824	−	0.330767i	0.873420	+	0.486967i	$0.161897\pi$
$84$	0.318079	−	3.02632i	0.0347052	−	0.330198i
$85$	0.861314	+	0.625781i	0.0934227	+	0.0678755i
$86$	0.433825	+	4.12757i	0.0467805	+	0.445087i
$87$	3.73196	−	6.46395i	0.400109	−	0.693008i
$88$	−1.73375	−	3.00294i	−0.184818	−	0.320114i
$89$	−12.1530	+	8.82969i	−1.28822	+	0.935945i	−0.999768	−	0.0215502i	$-0.993140\pi$
$89$	−12.1530	+	8.82969i	−1.28822	+	0.935945i	−0.288450	+	0.957495i	$0.593140\pi$
$90$	−0.669131	−	0.743145i	−0.0705326	−	0.0783343i
$91$	−3.63917	−	11.2002i	−0.381489	−	1.17410i
$92$	1.68353			0.175520
$93$	−4.69660	−	2.99030i	−0.487015	−	0.310080i
$94$	1.61773			0.166856
$95$	0.725581	+	2.23311i	0.0744430	+	0.229112i
$96$	−0.669131	−	0.743145i	−0.0682929	−	0.0758469i
$97$	6.45252	−	4.68803i	0.655155	−	0.475998i	−0.209869	−	0.977730i	$-0.567304\pi$
$97$	6.45252	−	4.68803i	0.655155	−	0.475998i	0.865023	+	0.501732i	$0.167304\pi$
$98$	1.12989	+	1.95702i	0.114136	+	0.197689i
$99$	1.73375	−	3.00294i	0.174248	−	0.301806i
$100$	−0.104528	−	0.994522i	−0.0104528	−	0.0994522i
$101$	−1.90481	−	1.38392i	−0.189535	−	0.137706i	0.488971	−	0.872300i	$-0.337372\pi$
$101$	−1.90481	−	1.38392i	−0.189535	−	0.137706i	−0.678506	+	0.734595i	$0.737372\pi$
$102$	−0.111286	+	1.05881i	−0.0110189	+	0.104838i
$103$	−5.02716	+	5.58323i	−0.495341	+	0.550132i	−0.938035	−	0.346541i	$-0.887356\pi$
$103$	−5.02716	+	5.58323i	−0.495341	+	0.550132i	0.442694	+	0.896673i	$0.354023\pi$
$104$	−3.53549	−	1.57410i	−0.346684	−	0.154353i
$105$	2.97649	+	0.632673i	0.290476	+	0.0617425i
$106$	0.290226	−	0.0616893i	0.0281892	−	0.00599180i
$107$	15.7576	−	7.01574i	1.52335	−	0.678237i	0.537100	−	0.843519i	$-0.319520\pi$
$107$	15.7576	−	7.01574i	1.52335	−	0.678237i	0.986246	+	0.165282i	$0.0528533\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	−0.992347	+	3.05413i	−0.0950496	+	0.292533i	−0.987267	−	0.159074i	$-0.949149\pi$
$109$	−0.992347	+	3.05413i	−0.0950496	+	0.292533i	0.892217	+	0.451607i	$0.149149\pi$
$110$	3.16771	−	1.41036i	0.302029	−	0.134472i
$111$	−2.55131	+	0.542298i	−0.242160	+	0.0514726i
$112$	2.97649	+	0.632673i	0.281252	+	0.0597819i
$113$	5.93408	+	2.64202i	0.558231	+	0.248541i	0.666403	−	0.745592i	$-0.267833\pi$
$113$	5.93408	+	2.64202i	0.558231	+	0.248541i	−0.108172	+	0.994132i	$0.534500\pi$
$114$	−1.57114	+	1.74493i	−0.147151	+	0.163427i
$115$	−0.175977	+	1.67431i	−0.0164099	+	0.156130i
$116$	6.03844	+	4.38719i	0.560655	+	0.407340i
$117$	−0.404533	−	3.84888i	−0.0373991	−	0.355829i
$118$	0.715246	−	1.23884i	0.0658437	−	0.114045i
$119$	−1.61985	−	2.80566i	−0.148491	−	0.257194i
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	0.684852	+	0.760605i	0.0622592	+	0.0691459i
$122$	−0.377702	−	1.16245i	−0.0341955	−	0.105243i
$123$	−0.0904823			−0.00815851
$124$	3.46485	−	4.35830i	0.311153	−	0.391387i
$125$	1.00000			0.0894427
$126$	0.940335	+	2.89405i	0.0837717	+	0.257823i
$127$	8.26303	+	9.17702i	0.733225	+	0.814329i	0.988289	−	0.152595i	$-0.0487630\pi$
$127$	8.26303	+	9.17702i	0.733225	+	0.814329i	−0.255063	+	0.966924i	$0.582096\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−2.07515	−	3.59427i	−0.182707	−	0.316458i
$130$	1.93504	−	3.35159i	0.169714	−	0.293954i
$131$	0.151468	+	1.44112i	0.0132338	+	0.125912i	0.999144	−	0.0413630i	$-0.0131700\pi$
$131$	0.151468	+	1.44112i	0.0132338	+	0.125912i	−0.985910	+	0.167275i	$0.946503\pi$
$132$	2.80526	+	2.03814i	0.244166	+	0.177397i
$133$	0.746858	−	7.10588i	0.0647608	−	0.616158i
$134$	10.0015	−	11.1077i	0.863994	−	0.959562i
$135$	0.913545	+	0.406737i	0.0786255	+	0.0350063i
$136$	−1.04138	−	0.221352i	−0.0892974	−	0.0189808i
$137$	2.28940	−	0.486626i	0.195596	−	0.0415753i	−0.109072	−	0.994034i	$-0.534788\pi$
$137$	2.28940	−	0.486626i	0.195596	−	0.0415753i	0.304668	+	0.952459i	$0.401454\pi$
$138$	−1.53798	+	0.684753i	−0.130922	+	0.0582900i
$139$	0.239157	−	0.736050i	0.0202850	−	0.0624309i	−0.940402	−	0.340066i	$-0.889551\pi$
$139$	0.239157	−	0.736050i	0.0202850	−	0.0624309i	0.960687	+	0.277635i	$0.0895506\pi$
$140$	−0.940335	+	2.89405i	−0.0794728	+	0.244592i
$141$	−1.47787	+	0.657991i	−0.124459	+	0.0554128i
$142$	13.5042	−	2.87041i	1.13325	−	0.240879i
$143$	13.1262	+	2.79006i	1.09767	+	0.233317i
$144$	0.913545	+	0.406737i	0.0761288	+	0.0338947i
$145$	−4.99434	+	5.54678i	−0.414758	+	0.460635i
$146$	−1.32973	+	12.6516i	−0.110049	+	1.04705i
$147$	−1.82819	−	1.32826i	−0.150787	−	0.109553i
$148$	−0.272642	−	2.59402i	−0.0224111	−	0.213227i
$149$	6.43780	−	11.1506i	0.527405	−	0.913493i	−0.472084	−	0.881553i	$-0.656498\pi$
$149$	6.43780	−	11.1506i	0.527405	−	0.913493i	0.999490	−	0.0319396i	$-0.0101684\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−13.5826	+	9.86835i	−1.10534	+	0.803075i	−0.981923	−	0.189280i	$-0.939385\pi$
$151$	−13.5826	+	9.86835i	−1.10534	+	0.803075i	−0.123415	+	0.992355i	$0.539385\pi$
$152$	−1.57114	−	1.74493i	−0.127436	−	0.141532i
$153$	−0.328993	−	1.01254i	−0.0265975	−	0.0818587i
$154$	−10.5515			−0.850267
$155$	3.97225	+	3.90144i	0.319059	+	0.313371i
$156$	3.87008			0.309854
$157$	−2.58076	−	7.94276i	−0.205967	−	0.633901i	−0.999672	−	0.0255987i	$-0.991851\pi$
$157$	−2.58076	−	7.94276i	−0.205967	−	0.633901i	0.793705	−	0.608302i	$-0.208149\pi$
$158$	3.37742	+	3.75101i	0.268693	+	0.298414i
$159$	−0.240043	+	0.174401i	−0.0190366	+	0.0138309i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	2.56148	−	4.43661i	0.201873	−	0.349654i
$162$	0.104528	+	0.994522i	0.00821253	+	0.0781370i
$163$	−3.43312	−	2.49431i	−0.268903	−	0.195369i	0.445160	−	0.895451i	$-0.353147\pi$
$163$	−3.43312	−	2.49431i	−0.268903	−	0.195369i	−0.714063	+	0.700082i	$0.753147\pi$
$164$	0.00945797	−	0.0899866i	0.000738544	−	0.00702677i
$165$	−2.32020	+	2.57685i	−0.180628	+	0.200607i
$166$	−3.70440	−	1.64930i	−0.287517	−	0.128011i
$167$	15.4201	+	3.27764i	1.19324	+	0.253632i	0.761379	−	0.648307i	$-0.224523\pi$
$167$	15.4201	+	3.27764i	1.19324	+	0.253632i	0.431864	+	0.901939i	$0.357856\pi$
$168$	−2.97649	+	0.632673i	−0.229641	+	0.0488117i
$169$	1.80654	−	0.804323i	0.138965	−	0.0618710i
$170$	0.328993	−	1.01254i	0.0252326	−	0.0776579i
$171$	0.725581	−	2.23311i	0.0554866	−	0.170770i
$172$	3.79149	−	1.68808i	0.289099	−	0.128715i
$173$	−3.30102	+	0.701653i	−0.250972	+	0.0533457i	−0.331680	−	0.943392i	$-0.607615\pi$
$173$	−3.30102	+	0.701653i	−0.250972	+	0.0533457i	0.0807078	+	0.996738i	$0.474282\pi$
$174$	−7.30082	−	1.55184i	−0.553474	−	0.117645i
$175$	−2.77991	−	1.23769i	−0.210141	−	0.0935609i
$176$	−2.32020	+	2.57685i	−0.174892	+	0.194237i
$177$	−0.149527	+	1.42266i	−0.0112391	+	0.106933i
$178$	12.1530	+	8.82969i	0.910907	+	0.661813i
$179$	1.34735	+	12.8192i	0.100706	+	0.958150i	0.921881	+	0.387474i	$0.126652\pi$
$179$	1.34735	+	12.8192i	0.100706	+	0.958150i	−0.821175	+	0.570676i	$0.806681\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−0.380692	−	0.659378i	−0.0282966	−	0.0490112i	0.851530	−	0.524305i	$-0.175675\pi$
$181$	−0.380692	−	0.659378i	−0.0282966	−	0.0490112i	−0.879827	+	0.475294i	$0.842342\pi$
$182$	−9.52747	+	6.92211i	−0.706223	+	0.513101i
$183$	0.817858	+	0.908323i	0.0604578	+	0.0671452i
$184$	−0.520239	−	1.60113i	−0.0383525	−	0.118037i
$185$	2.60831			0.191767
$186$	−1.39262	+	5.39079i	−0.102112	+	0.395272i
$187$	3.69164			0.269959
$188$	−0.499907	−	1.53855i	−0.0364595	−	0.112211i
$189$	−2.03616	−	2.26138i	−0.148109	−	0.164491i
$190$	1.89960	−	1.38014i	0.137811	−	0.100126i
$191$	−8.52715	−	14.7695i	−0.617003	−	1.06868i	−0.990030	−	0.140860i	$-0.955013\pi$
$191$	−8.52715	−	14.7695i	−0.617003	−	1.06868i	0.373027	−	0.927821i	$-0.378320\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	1.74443	+	16.5971i	0.125567	+	1.19469i	0.857928	+	0.513770i	$0.171751\pi$
$193$	1.74443	+	16.5971i	0.125567	+	1.19469i	−0.732362	+	0.680916i	$0.761582\pi$
$194$	−6.45252	−	4.68803i	−0.463264	−	0.336581i
$195$	−0.404533	+	3.84888i	−0.0289692	+	0.275624i
$196$	1.51208	−	1.67934i	0.108006	−	0.119953i
$197$	6.39397	+	2.84678i	0.455552	+	0.202825i	0.621667	−	0.783282i	$-0.286456\pi$
$197$	6.39397	+	2.84678i	0.455552	+	0.202825i	−0.166115	+	0.986106i	$0.553122\pi$
$198$	−3.39172	−	0.720932i	−0.241039	−	0.0512344i
$199$	−4.44238	+	0.944258i	−0.314912	+	0.0669367i	−0.362656	−	0.931923i	$-0.618130\pi$
$199$	−4.44238	+	0.944258i	−0.314912	+	0.0669367i	0.0477441	+	0.998860i	$0.484797\pi$
$200$	−0.913545	+	0.406737i	−0.0645974	+	0.0287606i
$201$	−4.61886	+	14.2154i	−0.325789	+	1.00268i
$202$	−0.727572	+	2.23924i	−0.0511918	+	0.157552i
$203$	20.7490	−	9.23806i	1.45630	−	0.648385i
$204$	1.04138	−	0.221352i	0.0729110	−	0.0154977i
$205$	0.0885050	+	0.0188123i	0.00618146	+	0.00131391i
$206$	6.86344	+	3.05580i	0.478199	+	0.212908i
$207$	1.12650	−	1.25111i	0.0782972	−	0.0869578i
$208$	−0.404533	+	3.84888i	−0.0280493	+	0.266872i
$209$	6.58683	+	4.78561i	0.455621	+	0.331028i
$210$	−0.318079	−	3.02632i	−0.0219495	−	0.208836i
$211$	7.53699	−	13.0545i	0.518868	−	0.898706i	−0.480892	−	0.876780i	$-0.659687\pi$
$211$	7.53699	−	13.0545i	0.518868	−	0.898706i	0.999760	−	0.0219256i	$-0.00697968\pi$
$212$	−0.148355	−	0.256958i	−0.0101890	−	0.0176479i
$213$	−11.1692	+	8.11491i	−0.765302	+	0.556024i
$214$	−11.5417	−	12.8184i	−0.788977	−	0.876248i
$215$	1.28251	+	3.94717i	0.0874668	+	0.269195i
$216$	−1.00000			−0.0680414
$217$	−6.21370	−	15.7621i	−0.421814	−	1.07000i
$218$	3.21130			0.217497
$219$	−3.93108	−	12.0986i	−0.265638	−	0.817550i
$220$	−2.32020	−	2.57685i	−0.156428	−	0.173731i
$221$	3.33335	−	2.42182i	0.224226	−	0.162909i
$222$	1.30415	+	2.25886i	0.0875291	+	0.151605i
$223$	12.3578	−	21.4043i	0.827539	−	1.43334i	−0.0724239	−	0.997374i	$-0.523073\pi$
$223$	12.3578	−	21.4043i	0.827539	−	1.43334i	0.899963	−	0.435966i	$-0.143593\pi$
$224$	−0.318079	−	3.02632i	−0.0212525	−	0.202204i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	0.678981	−	6.46008i	0.0451652	−	0.429718i
$227$	9.31986	−	10.3508i	0.618581	−	0.687004i	−0.349702	−	0.936861i	$-0.613717\pi$
$227$	9.31986	−	10.3508i	0.618581	−	0.687004i	0.968283	+	0.249857i	$0.0803837\pi$
$228$	2.14503	+	0.955030i	0.142058	+	0.0632484i
$229$	9.52408	+	2.02441i	0.629369	+	0.133776i	0.511543	−	0.859258i	$-0.329074\pi$
$229$	9.52408	+	2.02441i	0.629369	+	0.133776i	0.117826	+	0.993034i	$0.462407\pi$
$230$	1.64674	−	0.350025i	0.108583	−	0.0230800i
$231$	9.63930	−	4.29169i	0.634220	−	0.282373i
$232$	2.30648	−	7.09862i	0.151428	−	0.466047i
$233$	2.37979	−	7.32425i	0.155905	−	0.479828i	−0.842346	−	0.538937i	$-0.818826\pi$
$233$	2.37979	−	7.32425i	0.155905	−	0.479828i	0.998252	+	0.0591093i	$0.0188261\pi$
$234$	−3.53549	+	1.57410i	−0.231122	+	0.102902i
$235$	1.58238	−	0.336345i	0.103223	−	0.0219408i
$236$	−1.39923	−	0.297416i	−0.0910823	−	0.0193601i
$237$	−4.61110	−	2.05299i	−0.299523	−	0.133356i
$238$	−2.16778	+	2.40756i	−0.140516	+	0.156059i
$239$	0.722156	−	6.87085i	0.0467124	−	0.444439i	−0.946021	−	0.324105i	$-0.894937\pi$
$239$	0.722156	−	6.87085i	0.0467124	−	0.444439i	0.992734	−	0.120334i	$-0.0383964\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	−1.12914	−	10.7431i	−0.0727344	−	0.692021i	−0.968757	−	0.248012i	$-0.920223\pi$
$241$	−1.12914	−	10.7431i	−0.0727344	−	0.692021i	0.896022	−	0.444009i	$-0.146444\pi$
$242$	0.511747	−	0.886372i	0.0328964	−	0.0569782i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.988836	+	0.718432i	−0.0633038	+	0.0459929i
$245$	1.51208	+	1.67934i	0.0966033	+	0.107289i
$246$	0.0279606	+	0.0860537i	0.00178270	+	0.00548659i
$247$	9.08706			0.578196
$248$	−5.21569	−	1.94848i	−0.331197	−	0.123729i
$249$	4.05497			0.256973
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−19.5253	−	21.6851i	−1.23243	−	1.36875i	−0.905860	−	0.423577i	$-0.860774\pi$
$251$	−19.5253	−	21.6851i	−1.23243	−	1.36875i	−0.326569	−	0.945173i	$-0.605893\pi$
$252$	2.46183	−	1.78862i	0.155081	−	0.112673i
$253$	2.91881	+	5.05553i	0.183504	+	0.317838i
$254$	6.17445	−	10.6945i	0.387420	−	0.671030i
$255$	0.111286	+	1.05881i	0.00696897	+	0.0663053i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.741045	+	7.05057i	−0.0462251	+	0.439803i	0.946793	+	0.321843i	$0.104302\pi$
$257$	−0.741045	+	7.05057i	−0.0462251	+	0.439803i	−0.993018	+	0.117960i	$0.962365\pi$
$258$	−2.77710	+	3.08428i	−0.172894	+	0.192019i
$259$	−7.25085	−	3.22829i	−0.450546	−	0.200596i
$260$	−3.78551	−	0.804634i	−0.234767	−	0.0499013i
$261$	7.30082	−	1.55184i	0.451910	−	0.0960563i
$262$	1.32378	−	0.589387i	0.0817837	−	0.0364124i
$263$	6.87013	−	21.1441i	0.423630	−	1.30380i	−0.480669	−	0.876902i	$-0.659606\pi$
$263$	6.87013	−	21.1441i	0.423630	−	1.30380i	0.904300	−	0.426898i	$-0.140394\pi$
$264$	1.07151	−	3.29778i	0.0659471	−	0.202964i
$265$	0.271057	−	0.120683i	0.0166509	−	0.00741347i
$266$	−6.98889	+	1.48553i	−0.428516	+	0.0910839i
$267$	−14.6937	−	3.12324i	−0.899239	−	0.191139i
$268$	−13.6547	−	6.07947i	−0.834094	−	0.371362i
$269$	−13.4731	+	14.9634i	−0.821472	+	0.912337i	−0.997400	−	0.0720656i	$-0.977041\pi$
$269$	−13.4731	+	14.9634i	−0.821472	+	0.912337i	0.175928	+	0.984403i	$0.443708\pi$
$270$	0.104528	−	0.994522i	0.00636140	−	0.0605247i
$271$	15.6240	+	11.3515i	0.949091	+	0.689555i	0.950592	−	0.310444i	$-0.100478\pi$
$271$	15.6240	+	11.3515i	0.949091	+	0.689555i	−0.00150071	+	0.999999i	$0.500478\pi$
$272$	0.111286	+	1.05881i	0.00674767	+	0.0641998i
$273$	5.88830	−	10.1988i	0.356376	−	0.617261i
$274$	−1.17027	−	2.02697i	−0.0706987	−	0.122454i
$275$	2.80526	−	2.03814i	0.169163	−	0.122904i
$276$	1.12650	+	1.25111i	0.0678074	+	0.0753077i
$277$	−0.451105	−	1.38836i	−0.0271042	−	0.0834183i	0.936589	−	0.350429i	$-0.113964\pi$
$277$	−0.451105	−	1.38836i	−0.0271042	−	0.0834183i	−0.963694	+	0.267011i	$0.913964\pi$
$278$	−0.773929			−0.0464172
$279$	−0.920411	−	5.49116i	−0.0551036	−	0.328747i
$280$	3.04299			0.181853
$281$	−0.307584	−	0.946645i	−0.0183489	−	0.0564721i	0.941463	−	0.337117i	$-0.109452\pi$
$281$	−0.307584	−	0.946645i	−0.0183489	−	0.0564721i	−0.959812	+	0.280645i	$0.909452\pi$
$282$	1.08247	+	1.20221i	0.0644604	+	0.0715905i
$283$	10.4267	−	7.57542i	0.619801	−	0.450312i	−0.233051	−	0.972465i	$-0.574871\pi$
$283$	10.4267	−	7.57542i	0.619801	−	0.450312i	0.852852	+	0.522153i	$0.174871\pi$
$284$	−6.90295	−	11.9563i	−0.409615	−	0.709474i
$285$	−1.17401	+	2.03345i	−0.0695426	+	0.120451i
$286$	−1.40272	−	13.3459i	−0.0829443	−	0.789162i
$287$	−0.222752	−	0.161839i	−0.0131486	−	0.00955303i
$288$	0.104528	−	0.994522i	0.00615940	−	0.0586028i
$289$	−10.6168	+	11.7911i	−0.624517	+	0.693596i
$290$	6.81864	+	3.03585i	0.400404	+	0.178271i
$291$	7.80147	+	1.65825i	0.457330	+	0.0972085i
$292$	12.4433	−	2.64490i	0.728187	−	0.154781i
$293$	−17.6212	+	7.84549i	−1.02944	+	0.458338i	−0.850752	−	0.525567i	$-0.823853\pi$
$293$	−17.6212	+	7.84549i	−1.02944	+	0.458338i	−0.178692	+	0.983905i	$0.557187\pi$
$294$	−0.698307	+	2.14917i	−0.0407261	+	0.125342i
$295$	0.442046	−	1.36048i	0.0257369	−	0.0792101i
$296$	−2.38281	+	1.06089i	−0.138498	+	0.0616632i
$297$	3.39172	−	0.720932i	0.196807	−	0.0418327i
$298$	−12.5942	−	2.67699i	−0.729565	−	0.155074i
$299$	5.95210	+	2.65005i	0.344219	+	0.153256i
$300$	0.669131	−	0.743145i	0.0386323	−	0.0429055i
$301$	1.32012	−	12.5601i	0.0760907	−	0.723954i
$302$	13.5826	+	9.86835i	0.781592	+	0.567860i
$303$	−0.246109	−	2.34157i	−0.0141386	−	0.134520i
$304$	−1.17401	+	2.03345i	−0.0673344	+	0.116627i
$305$	−0.611135	−	1.05852i	−0.0349935	−	0.0606105i
$306$	−0.861314	+	0.625781i	−0.0492381	+	0.0357735i
$307$	15.7605	+	17.5038i	0.899501	+	0.998997i	0.999992	+	0.00405934i	$0.00129213\pi$
$307$	15.7605	+	17.5038i	0.899501	+	0.998997i	−0.100490	+	0.994938i	$0.532041\pi$
$308$	3.26060	+	10.0351i	0.185790	+	0.571803i
$309$	−7.51297			−0.427398
$310$	2.48299	−	4.98345i	0.141025	−	0.283041i
$311$	−24.8408			−1.40859			−0.704295	−	0.709907i	$-0.748737\pi$
$311$	−24.8408			−1.40859			−0.704295	+	0.709907i	$0.748737\pi$
$312$	−1.19592	−	3.68066i	−0.0677056	−	0.208377i
$313$	−11.1491	−	12.3823i	−0.630184	−	0.699890i	0.340501	−	0.940244i	$-0.389403\pi$
$313$	−11.1491	−	12.3823i	−0.630184	−	0.699890i	−0.970685	+	0.240354i	$0.922737\pi$
$314$	−6.75651	+	4.90889i	−0.381292	+	0.277025i
$315$	1.52149	+	2.63530i	0.0857264	+	0.148483i
$316$	2.52374	−	4.37124i	0.141971	−	0.245902i
$317$	−1.93338	−	18.3949i	−0.108589	−	1.03316i	−0.904130	−	0.427258i	$-0.859479\pi$
$317$	−1.93338	−	18.3949i	−0.108589	−	1.03316i	0.795540	−	0.605901i	$-0.207187\pi$
$318$	0.240043	+	0.174401i	0.0134609	+	0.00977994i
$319$	−2.70531	+	25.7393i	−0.151468	+	1.44113i
$320$	0.669131	−	0.743145i	0.0374055	−	0.0415431i
$321$	15.7576	+	7.01574i	0.879504	+	0.391580i
$322$	−5.01101	−	1.06512i	−0.279252	−	0.0593569i
$323$	2.44519	−	0.519740i	0.136054	−	0.0289191i
$324$	0.913545	−	0.406737i	0.0507525	−	0.0225965i
$325$	1.19592	−	3.68066i	0.0663377	−	0.204166i
$326$	−1.31134	+	4.03588i	−0.0726282	+	0.223527i
$327$	−2.93367	+	1.30615i	−0.162232	+	0.0722305i
$328$	−0.0885050	+	0.0188123i	−0.00488687	+	0.00103874i
$329$	−4.81517	−	1.02349i	−0.265469	−	0.0564271i
$330$	3.16771	+	1.41036i	0.174377	+	0.0776375i
$331$	23.0530	−	25.6030i	1.26711	−	1.40727i	0.394465	−	0.918911i	$-0.370930\pi$
$331$	23.0530	−	25.6030i	1.26711	−	1.40727i	0.872644	−	0.488356i	$-0.162403\pi$
$332$	−0.423859	+	4.03275i	−0.0232623	+	0.221326i
$333$	−2.11016	−	1.53312i	−0.115636	−	0.0840147i
$334$	−1.64785	−	15.6782i	−0.0901663	−	0.857875i
$335$	7.47347	−	12.9444i	0.408319	−	0.707229i
$336$	1.52149	+	2.63530i	0.0830043	+	0.143768i
$337$	−25.7907	+	18.7380i	−1.40491	+	1.02073i	−0.410870	+	0.911694i	$0.634775\pi$
$337$	−25.7907	+	18.7380i	−1.40491	+	1.02073i	−0.994038	+	0.109032i	$0.965225\pi$
$338$	−1.32321	−	1.46957i	−0.0719730	−	0.0799341i
$339$	2.00727	+	6.17774i	0.109020	+	0.335529i
$340$	−1.06464			−0.0577384
$341$	19.0949	+	2.84854i	1.03405	+	0.154257i
$342$	−2.34803			−0.126967
$343$	4.45740	+	13.7185i	0.240677	+	0.740728i
$344$	−2.77710	−	3.08428i	−0.149731	−	0.166293i
$345$	−1.36200	+	0.989553i	−0.0733278	+	0.0532757i
$346$	1.68738	+	2.92263i	0.0907142	+	0.157122i
$347$	−15.1310	+	26.2076i	−0.812273	+	1.40690i	0.0989973	+	0.995088i	$0.468436\pi$
$347$	−15.1310	+	26.2076i	−0.812273	+	1.40690i	−0.911270	+	0.411810i	$0.864897\pi$
$348$	0.780193	+	7.42304i	0.0418227	+	0.397917i
$349$	7.38817	+	5.36782i	0.395480	+	0.287333i	0.767697	−	0.640813i	$-0.221402\pi$
$349$	7.38817	+	5.36782i	0.395480	+	0.287333i	−0.372218	+	0.928145i	$0.621402\pi$
$350$	−0.318079	+	3.02632i	−0.0170020	+	0.161763i
$351$	2.58959	−	2.87603i	0.138222	−	0.153511i
$352$	3.16771	+	1.41036i	0.168840	+	0.0751722i
$353$	1.55839	+	0.331246i	0.0829447	+	0.0176304i	0.249197	−	0.968453i	$-0.419833\pi$
$353$	1.55839	+	0.331246i	0.0829447	+	0.0176304i	−0.166252	+	0.986083i	$0.553167\pi$
$354$	1.39923	−	0.297416i	0.0743684	−	0.0158075i
$355$	12.6123	−	5.61537i	0.669393	−	0.298033i
$356$	4.64204	−	14.2867i	0.246028	−	0.757195i
$357$	1.00112	−	3.08113i	0.0529849	−	0.163071i
$358$	11.7754	−	5.24275i	0.622349	−	0.277088i
$359$	−17.5870	+	3.73823i	−0.928207	+	0.197296i	−0.647122	−	0.762386i	$-0.724028\pi$
$359$	−17.5870	+	3.73823i	−0.928207	+	0.197296i	−0.281085	+	0.959683i	$0.590694\pi$
$360$	0.978148	+	0.207912i	0.0515529	+	0.0109579i
$361$	−12.3208	−	5.48556i	−0.648461	−	0.288714i
$362$	−0.509465	+	0.565818i	−0.0267769	+	0.0297388i
$363$	−0.106984	+	1.01789i	−0.00561522	+	0.0534253i
$364$	9.52747	+	6.92211i	0.499375	+	0.362817i
$365$	1.32973	+	12.6516i	0.0696014	+	0.662213i
$366$	0.611135	−	1.05852i	0.0319445	−	0.0553295i
$367$	18.1820	+	31.4921i	0.949092	+	1.64388i	0.747344	+	0.664438i	$0.231329\pi$
$367$	18.1820	+	31.4921i	0.949092	+	1.64388i	0.201748	+	0.979437i	$0.435338\pi$
$368$	−1.36200	+	0.989553i	−0.0709993	+	0.0515840i
$369$	−0.0605445	−	0.0672414i	−0.00315182	−	0.00350045i
$370$	−0.806011	−	2.48065i	−0.0419025	−	0.128963i
$371$	−0.902883			−0.0468753
$372$	5.55729	−	0.341387i	0.288132	−	0.0177001i
$373$	−13.2384			−0.685456			−0.342728	−	0.939435i	$-0.611351\pi$
$373$	−13.2384			−0.685456			−0.342728	+	0.939435i	$0.611351\pi$
$374$	−1.14078	−	3.51096i	−0.0589883	−	0.181547i
$375$	0.669131	+	0.743145i	0.0345538	+	0.0383758i
$376$	−1.30877	+	0.950879i	−0.0674948	+	0.0490379i
$377$	14.4430	+	25.0160i	0.743852	+	1.28839i
$378$	−1.52149	+	2.63530i	−0.0782572	+	0.135545i
$379$	2.64464	+	25.1621i	0.135846	+	1.29249i	0.823861	+	0.566792i	$0.191816\pi$
$379$	2.64464	+	25.1621i	0.135846	+	1.29249i	−0.688015	+	0.725696i	$0.741518\pi$
$380$	−1.89960	−	1.38014i	−0.0974472	−	0.0707995i
$381$	−1.29081	+	12.2813i	−0.0661303	+	0.629188i
$382$	−11.4116	+	12.6738i	−0.583866	+	0.648449i
$383$	−23.9823	−	10.6776i	−1.22544	−	0.545601i	−0.311034	−	0.950399i	$-0.600675\pi$
$383$	−23.9823	−	10.6776i	−1.22544	−	0.545601i	−0.914406	+	0.404798i	$0.867342\pi$
$384$	0.978148	+	0.207912i	0.0499159	+	0.0106099i
$385$	−10.3210	+	2.19379i	−0.526005	+	0.111806i
$386$	15.2457	−	6.78783i	0.775987	−	0.345492i
$387$	1.28251	−	3.94717i	0.0651939	−	0.200646i
$388$	−2.46464	+	7.58540i	−0.125123	+	0.385090i
$389$	−25.9242	+	11.5422i	−1.31441	+	0.585214i	−0.939723	−	0.341937i	$-0.888917\pi$
$389$	−25.9242	+	11.5422i	−1.31441	+	0.585214i	−0.374688	+	0.927151i	$0.622250\pi$
$390$	3.78551	−	0.804634i	0.191687	−	0.0407442i
$391$	1.75319	+	0.372652i	0.0886626	+	0.0188458i
$392$	−2.06440	−	0.919131i	−0.104268	−	0.0464231i
$393$	−0.969612	+	1.07686i	−0.0489104	+	0.0543206i
$394$	0.731603	−	6.96073i	0.0368576	−	0.350677i
$395$	4.08349	+	2.96683i	0.205463	+	0.149278i
$396$	0.362452	+	3.44850i	0.0182139	+	0.173293i
$397$	−11.2163	+	19.4273i	−0.562932	+	0.975026i	0.434307	+	0.900765i	$0.356993\pi$
$397$	−11.2163	+	19.4273i	−0.562932	+	0.975026i	−0.997239	+	0.0742616i	$0.976340\pi$
$398$	2.27081	+	3.93317i	0.113826	+	0.197152i
$399$	5.78045	−	4.19974i	0.289384	−	0.210250i
$400$	0.669131	+	0.743145i	0.0334565	+	0.0371572i
$401$	5.25121	+	16.1616i	0.262233	+	0.807070i	0.992318	+	0.123713i	$0.0394804\pi$
$401$	5.25121	+	16.1616i	0.262233	+	0.807070i	−0.730085	+	0.683356i	$0.760520\pi$
$402$	14.9469			0.745485
$403$	19.1104	−	9.95471i	0.951955	−	0.495879i
$404$	2.35447			0.117139
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	−15.1977	−	16.8788i	−0.754250	−	0.837680i
$407$	7.31698	−	5.31610i	0.362689	−	0.263509i
$408$	−0.532322	−	0.922008i	−0.0263538	−	0.0456462i
$409$	10.5152	−	18.2129i	0.519944	−	0.900570i	−0.479787	−	0.877385i	$-0.659286\pi$
$409$	10.5152	−	18.2129i	0.519944	−	0.900570i	0.999731	−	0.0231848i	$-0.00738062\pi$
$410$	−0.00945797	−	0.0899866i	−0.000467096	−	0.00444412i
$411$	1.89354	+	1.37574i	0.0934014	+	0.0678601i
$412$	0.785319	−	7.47181i	0.0386899	−	0.368110i
$413$	−2.91270	+	3.23489i	−0.143325	+	0.159178i
$414$	−1.53798	−	0.684753i	−0.0755876	−	0.0336538i
$415$	−3.96636	−	0.843075i	−0.194701	−	0.0413849i
$416$	3.78551	−	0.804634i	0.185600	−	0.0394504i
$417$	0.707019	−	0.314785i	0.0346229	−	0.0154151i
$418$	2.51595	−	7.74328i	0.123059	−	0.378736i
$419$	0.516867	−	1.59075i	0.0252506	−	0.0777134i	−0.937637	−	0.347616i	$-0.886991\pi$
$419$	0.516867	−	1.59075i	0.0252506	−	0.0777134i	0.962888	+	0.269902i	$0.0869914\pi$
$420$	−2.77991	+	1.23769i	−0.135646	+	0.0603933i
$421$	−24.1302	+	5.12902i	−1.17603	+	0.249973i	−0.754165	−	0.656685i	$-0.771958\pi$
$421$	−24.1302	+	5.12902i	−1.17603	+	0.249973i	−0.421867	+	0.906658i	$0.638625\pi$
$422$	−14.7446	−	3.13406i	−0.717755	−	0.152564i
$423$	−1.47787	−	0.657991i	−0.0718566	−	0.0319926i
$424$	−0.198537	+	0.220498i	−0.00964182	+	0.0107083i
$425$	0.111286	−	1.05881i	0.00539814	−	0.0513599i
$426$	11.1692	+	8.11491i	0.541150	+	0.393169i
$427$	0.388778	+	3.69897i	0.0188143	+	0.179006i
$428$	−8.62443	+	14.9379i	−0.416877	+	0.722053i
$429$	6.70973	+	11.6216i	0.323949	+	0.561096i
$430$	3.35767	−	2.43949i	0.161921	−	0.117643i
$431$	18.3987	+	20.4338i	0.886233	+	0.984261i	0.999957	−	0.00925090i	$-0.00294469\pi$
$431$	18.3987	+	20.4338i	0.886233	+	0.984261i	−0.113724	+	0.993512i	$0.536278\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	6.28233			0.301910			0.150955	−	0.988541i	$-0.451765\pi$
$433$	6.28233			0.301910			0.150955	+	0.988541i	$0.451765\pi$
$434$	−13.0705	+	10.7803i	−0.627403	+	0.517472i
$435$	−7.46393			−0.357868
$436$	−0.992347	−	3.05413i	−0.0475248	−	0.146266i
$437$	2.64506	+	2.93763i	0.126530	+	0.140526i
$438$	−10.2917	+	7.47736i	−0.491757	+	0.357282i
$439$	10.7167	+	18.5619i	0.511480	+	0.885910i	0.999911	+	0.0133074i	$0.00423602\pi$
$439$	10.7167	+	18.5619i	0.511480	+	0.885910i	−0.488431	+	0.872602i	$0.662431\pi$
$440$	−1.73375	+	3.00294i	−0.0826531	+	0.143159i
$441$	−0.236210	−	2.24739i	−0.0112481	−	0.107019i
$442$	−3.33335	−	2.42182i	−0.158551	−	0.115194i
$443$	−1.31429	+	12.5046i	−0.0624438	+	0.594113i	0.917899	+	0.396813i	$0.129884\pi$
$443$	−1.31429	+	12.5046i	−0.0624438	+	0.594113i	−0.980343	+	0.197300i	$0.936783\pi$
$444$	1.74530	−	1.93835i	0.0828282	−	0.0919900i
$445$	13.7232	+	6.10998i	0.650544	+	0.289641i
$446$	−24.1755	−	5.13866i	−1.14474	−	0.243323i
$447$	12.5942	−	2.67699i	0.595687	−	0.126617i
$448$	−2.77991	+	1.23769i	−0.131338	+	0.0584756i
$449$	7.64070	−	23.5157i	0.360587	−	1.10977i	−0.592112	−	0.805856i	$-0.701706\pi$
$449$	7.64070	−	23.5157i	0.360587	−	1.10977i	0.952699	−	0.303917i	$-0.0982944\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	0.286622	−	0.127612i	0.0134965	−	0.00600902i
$452$	−6.35371	+	1.35052i	−0.298854	+	0.0635233i
$453$	−16.4222	−	3.49064i	−0.771580	−	0.164004i
$454$	−12.7242	−	5.66516i	−0.597174	−	0.265879i
$455$	−7.88008	+	8.75172i	−0.369424	+	0.410287i
$456$	0.245436	−	2.33517i	0.0114936	−	0.109354i
$457$	11.1854	+	8.12668i	0.523232	+	0.380150i	0.817820	−	0.575474i	$-0.195182\pi$
$457$	11.1854	+	8.12668i	0.523232	+	0.380150i	−0.294588	+	0.955624i	$0.595182\pi$
$458$	−1.01778	−	9.68351i	−0.0475577	−	0.452481i
$459$	0.532322	−	0.922008i	0.0248466	−	0.0430356i
$460$	−0.841764	−	1.45798i	−0.0392475	−	0.0679786i
$461$	−15.1489	+	11.0063i	−0.705554	+	0.512615i	−0.881736	−	0.471743i	$-0.843625\pi$
$461$	−15.1489	+	11.0063i	−0.705554	+	0.512615i	0.176183	+	0.984358i	$0.443625\pi$
$462$	−7.06035	−	7.84132i	−0.328477	−	0.364811i
$463$	6.76883	+	20.8323i	0.314574	+	0.968159i	0.975929	+	0.218087i	$0.0699816\pi$
$463$	6.76883	+	20.8323i	0.314574	+	0.968159i	−0.661355	+	0.750073i	$0.730018\pi$
$464$	−7.46393			−0.346504
$465$	−0.241378	+	5.56253i	−0.0111937	+	0.257956i
$466$	−7.70117			−0.356750
$467$	−5.41678	−	16.6711i	−0.250659	−	0.771448i	−0.994654	−	0.103263i	$-0.967072\pi$
$467$	−5.41678	−	16.6711i	−0.250659	−	0.771448i	0.743995	−	0.668185i	$-0.232928\pi$
$468$	2.58959	+	2.87603i	0.119704	+	0.132944i
$469$	−36.7968	+	26.7344i	−1.69912	+	1.23448i
$470$	−0.808866	−	1.40100i	−0.0373102	−	0.0646232i
$471$	4.17576	−	7.23262i	0.192409	−	0.333262i
$472$	0.149527	+	1.42266i	0.00688254	+	0.0654830i
$473$	11.6427	+	8.45890i	0.535331	+	0.388941i
$474$	−0.527605	+	5.01983i	−0.0242337	+	0.230568i
$475$	1.57114	−	1.74493i	0.0720888	−	0.0800627i
$476$	2.95961	+	1.31770i	0.135653	+	0.0603968i
$477$	−0.290226	−	0.0616893i	−0.0132885	−	0.00282456i
$478$	−6.75773	+	1.43640i	−0.309091	+	0.0656994i
$479$	−32.7957	+	14.6016i	−1.49847	+	0.667164i	−0.981955	−	0.189112i	$-0.939439\pi$
$479$	−32.7957	+	14.6016i	−1.49847	+	0.667164i	−0.516519	+	0.856276i	$0.672772\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	3.11933	−	9.60030i	0.142229	−	0.437736i
$482$	−9.86833	+	4.39366i	−0.449490	+	0.200126i
$483$	5.01101	−	1.06512i	0.228009	−	0.0484647i
$484$	−1.00113	−	0.212797i	−0.0455059	−	0.00967257i
$485$	−7.28622	−	3.24403i	−0.330850	−	0.147304i
$486$	−0.669131	+	0.743145i	−0.0303524	+	0.0337097i
$487$	−1.33762	+	12.7266i	−0.0606135	+	0.576699i	0.921496	+	0.388388i	$0.126968\pi$
$487$	−1.33762	+	12.7266i	−0.0606135	+	0.576699i	−0.982109	+	0.188311i	$0.939699\pi$
$488$	0.988836	+	0.718432i	0.0447625	+	0.0325219i
$489$	−0.443574	−	4.22033i	−0.0200591	−	0.190850i
$490$	1.12989	−	1.95702i	0.0510430	−	0.0884091i
$491$	0.449531	+	0.778610i	0.0202870	+	0.0351382i	0.875991	−	0.482328i	$-0.160209\pi$
$491$	0.449531	+	0.778610i	0.0202870	+	0.0351382i	−0.855704	+	0.517466i	$0.826875\pi$
$492$	0.0732017	−	0.0531841i	0.00330019	−	0.00239773i
$493$	5.31719	+	5.90534i	0.239474	+	0.265963i
$494$	−2.80806	−	8.64231i	−0.126340	−	0.388836i
$495$	−3.46749			−0.155852
$496$	−0.241378	+	5.56253i	−0.0108382	+	0.249765i
$497$	−42.0112			−1.88446
$498$	−1.25305	−	3.85650i	−0.0561507	−	0.172814i
$499$	2.19939	+	2.44267i	0.0984584	+	0.109349i	0.790360	−	0.612643i	$-0.209893\pi$
$499$	2.19939	+	2.44267i	0.0984584	+	0.109349i	−0.691902	+	0.721992i	$0.743227\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	7.88230	+	13.6525i	0.352155	+	0.609951i
$502$	−14.5901	+	25.2708i	−0.651187	+	1.12789i
$503$	3.67169	+	34.9338i	0.163713	+	1.55762i	0.700345	+	0.713805i	$0.253030\pi$
$503$	3.67169	+	34.9338i	0.163713	+	1.55762i	−0.536632	+	0.843816i	$0.680304\pi$
$504$	−2.46183	−	1.78862i	−0.109659	−	0.0796716i
$505$	−0.246109	+	2.34157i	−0.0109517	+	0.104199i
$506$	3.90613	−	4.33820i	0.173649	−	0.192856i
$507$	1.80654	+	0.804323i	0.0802312	+	0.0357212i
$508$	−12.0791	−	2.56748i	−0.535921	−	0.113914i
$509$	−24.9362	+	5.30036i	−1.10528	+	0.234934i	−0.724188	−	0.689603i	$-0.757785\pi$
$509$	−24.9362	+	5.30036i	−1.10528	+	0.234934i	−0.381091	+	0.924537i	$0.624452\pi$
$510$	0.972600	−	0.433029i	0.0430674	−	0.0191749i
$511$	11.9622	−	36.8160i	0.529178	−	1.62864i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	2.14503	−	0.955030i	0.0947055	−	0.0421656i
$514$	6.93449	−	1.47397i	0.305867	−	0.0650141i
$515$	7.34879	+	1.56203i	0.323827	+	0.0688315i
$516$	3.79149	+	1.68808i	0.166911	+	0.0743136i
$517$	3.75347	−	4.16865i	0.165077	−	0.183337i
$518$	−0.829647	+	7.89356i	−0.0364526	+	0.346823i
$519$	−2.73024	−	1.98364i	−0.119844	−	0.0870720i
$520$	0.404533	+	3.84888i	0.0177400	+	0.168784i
$521$	5.18861	−	8.98693i	0.227317	−	0.393724i	−0.729695	−	0.683773i	$-0.760338\pi$
$521$	5.18861	−	8.98693i	0.227317	−	0.393724i	0.957012	+	0.290048i	$0.0936713\pi$
$522$	−3.73196	−	6.46395i	−0.163344	−	0.282919i
$523$	15.9778	−	11.6085i	0.698660	−	0.507606i	−0.180836	−	0.983513i	$-0.557880\pi$
$523$	15.9778	−	11.6085i	0.698660	−	0.507606i	0.879496	+	0.475907i	$0.157880\pi$
$524$	−0.969612	−	1.07686i	−0.0423577	−	0.0470430i
$525$	−0.940335	−	2.89405i	−0.0410396	−	0.126307i
$526$	−22.2322			−0.969370
$527$	4.57294	−	3.77169i	0.199200	−	0.164297i
$528$	−3.46749			−0.150903
$529$	−6.23155	−	19.1788i	−0.270937	−	0.833859i
$530$	−0.198537	−	0.220498i	−0.00862391	−	0.00957782i
$531$	−1.15729	+	0.840822i	−0.0502222	+	0.0364886i
$532$	3.57251	+	6.18777i	0.154888	+	0.268274i
$533$	0.175087	−	0.303259i	0.00758385	−	0.0131356i
$534$	1.57022	+	14.9397i	0.0679502	+	0.646503i
$535$	−13.9546	−	10.1386i	−0.603311	−	0.438331i
$536$	−1.56238	+	14.8651i	−0.0674845	+	0.642072i
$537$	−8.62495	+	9.57898i	−0.372194	+	0.413363i
$538$	18.3945	+	8.18977i	0.793044	+	0.353086i
$539$	7.66450	+	1.62914i	0.330134	+	0.0701720i
$540$	−0.978148	+	0.207912i	−0.0420928	+	0.00894709i
$541$	26.8568	−	11.9574i	1.15466	−	0.514090i	0.262114	−	0.965037i	$-0.415580\pi$
$541$	26.8568	−	11.9574i	1.15466	−	0.514090i	0.892551	+	0.450947i	$0.148914\pi$
$542$	5.96784	−	18.3671i	0.256341	−	0.788936i
$543$	0.235281	−	0.724119i	0.0100969	−	0.0310749i
$544$	0.972600	−	0.433029i	0.0416999	−	0.0185660i
$545$	3.14113	−	0.667668i	0.134551	−	0.0285997i
$546$	−11.5193	−	2.44849i	−0.492978	−	0.104786i
$547$	32.9668	+	14.6778i	1.40956	+	0.627577i	0.963569	−	0.267461i	$-0.0861846\pi$
$547$	32.9668	+	14.6778i	1.40956	+	0.627577i	0.445991	+	0.895037i	$0.352851\pi$
$548$	−1.56613	+	1.73936i	−0.0669017	+	0.0743019i
$549$	−0.127762	+	1.21557i	−0.00545275	+	0.0518794i
$550$	−2.80526	−	2.03814i	−0.119617	−	0.0869066i
$551$	1.83192	+	17.4295i	0.0780422	+	0.742522i
$552$	0.841764	−	1.45798i	0.0358279	−	0.0620557i
$553$	−7.67970	−	13.3016i	−0.326574	−	0.565643i
$554$	−1.18101	+	0.858052i	−0.0501762	+	0.0364551i
$555$	1.74530	+	1.93835i	0.0740838	+	0.0822784i
$556$	0.239157	+	0.736050i	0.0101425	+	0.0312155i
$557$	−7.03852			−0.298232			−0.149116	−	0.988820i	$-0.547643\pi$
$557$	−7.03852			−0.298232			−0.149116	+	0.988820i	$0.547643\pi$
$558$	−4.93798	+	2.57222i	−0.209041	+	0.108891i
$559$	16.0620			0.679350
$560$	−0.940335	−	2.89405i	−0.0397364	−	0.122296i
$561$	2.47019	+	2.74342i	0.104291	+	0.115827i
$562$	−0.805264	+	0.585059i	−0.0339680	+	0.0246792i
$563$	−14.6683	−	25.4063i	−0.618196	−	1.07075i	−0.989815	−	0.142361i	$-0.954531\pi$
$563$	−14.6683	−	25.4063i	−0.618196	−	1.07075i	0.371619	−	0.928385i	$-0.378803\pi$
$564$	0.808866	−	1.40100i	0.0340594	−	0.0589926i
$565$	−0.678981	−	6.46008i	−0.0285650	−	0.271777i
$566$	−10.4267	−	7.57542i	−0.438266	−	0.318419i
$567$	0.318079	−	3.02632i	0.0133581	−	0.127093i
$568$	−9.23795	+	10.2598i	−0.387616	+	0.430491i
$569$	−8.78629	−	3.91191i	−0.368340	−	0.163996i	0.214215	−	0.976786i	$-0.431281\pi$
$569$	−8.78629	−	3.91191i	−0.368340	−	0.163996i	−0.582556	+	0.812791i	$0.697947\pi$
$570$	2.29672	+	0.488183i	0.0961990	+	0.0204477i
$571$	−26.4172	+	5.61515i	−1.10552	+	0.234987i	−0.724293	−	0.689493i	$-0.757834\pi$
$571$	−26.4172	+	5.61515i	−1.10552	+	0.234987i	−0.381232	+	0.924479i	$0.624500\pi$
$572$	−12.2593	+	5.45819i	−0.512587	+	0.228218i
$573$	5.27007	−	16.2196i	0.220160	−	0.677584i
$574$	−0.0850836	+	0.261860i	−0.00355132	+	0.0109298i
$575$	1.53798	−	0.684753i	0.0641382	−	0.0285562i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−13.1670	−	2.79874i	−0.548151	−	0.116513i	−0.0744925	−	0.997222i	$-0.523734\pi$
$577$	−13.1670	−	2.79874i	−0.548151	−	0.116513i	−0.473659	+	0.880708i	$0.657067\pi$
$578$	14.4948	+	6.45350i	0.602904	+	0.268430i
$579$	−11.1668	+	12.4020i	−0.464076	+	0.515409i
$580$	0.780193	−	7.42304i	0.0323957	−	0.308225i
$581$	9.98263	+	7.25281i	0.414149	+	0.300897i
$582$	−0.833694	−	7.93207i	−0.0345577	−	0.328795i
$583$	0.514418	−	0.890999i	0.0213050	−	0.0369014i
$584$	−6.36063	−	11.0169i	−0.263205	−	0.455884i
$585$	−3.13096	+	2.27477i	−0.129449	+	0.0940504i
$586$	12.9068	+	14.3344i	0.533174	+	0.592149i
$587$	−12.6215	−	38.8448i	−0.520943	−	1.60330i	−0.772202	−	0.635378i	$-0.780844\pi$
$587$	−12.6215	−	38.8448i	−0.520943	−	1.60330i	0.251258	−	0.967920i	$-0.419156\pi$
$588$	2.25977			0.0931913
$589$	13.0487	−	0.801586i	0.537661	−	0.0330288i
$590$	−1.43049			−0.0588924
$591$	2.16283	+	6.65652i	0.0889671	+	0.273813i
$592$	1.74530	+	1.93835i	0.0717313	+	0.0796657i
$593$	15.3505	−	11.1528i	0.630370	−	0.457991i	−0.226158	−	0.974091i	$-0.572617\pi$
$593$	15.3505	−	11.1528i	0.630370	−	0.457991i	0.856528	+	0.516100i	$0.172617\pi$
$594$	−1.73375	−	3.00294i	−0.0711364	−	0.123212i
$595$	−1.61985	+	2.80566i	−0.0664073	+	0.115021i
$596$	1.34587	+	12.8051i	0.0551289	+	0.524516i
$597$	−3.67425	−	2.66950i	−0.150377	−	0.109255i
$598$	0.681043	−	6.47969i	0.0278499	−	0.264974i
$599$	21.3170	−	23.6749i	0.870989	−	0.967331i	−0.128715	−	0.991682i	$-0.541085\pi$
$599$	21.3170	−	23.6749i	0.870989	−	0.967331i	0.999703	+	0.0243506i	$0.00775179\pi$
$600$	−0.913545	−	0.406737i	−0.0372953	−	0.0166050i
$601$	−11.1873	−	2.37793i	−0.456339	−	0.0969978i	−0.0259934	−	0.999662i	$-0.508275\pi$
$601$	−11.1873	−	2.37793i	−0.456339	−	0.0969978i	−0.430345	+	0.902664i	$0.641608\pi$
$602$	−12.3533	+	2.62578i	−0.503485	+	0.107019i
$603$	−13.6547	+	6.07947i	−0.556063	+	0.247575i
$604$	5.18810	−	15.9673i	0.211101	−	0.649701i
$605$	0.316277	−	0.973401i	0.0128585	−	0.0395744i
$606$	−2.15092	+	0.957650i	−0.0873750	+	0.0389019i
$607$	−9.23855	+	1.96372i	−0.374981	+	0.0797047i	−0.391547	−	0.920158i	$-0.628060\pi$
$607$	−9.23855	+	1.96372i	−0.374981	+	0.0797047i	0.0165659	+	0.999863i	$0.494727\pi$
$608$	2.29672	+	0.488183i	0.0931443	+	0.0197984i
$609$	20.7490	+	9.23806i	0.840793	+	0.374345i
$610$	−0.817858	+	0.908323i	−0.0331141	+	0.0367769i
$611$	0.654427	−	6.22645i	0.0264753	−	0.251895i
$612$	0.861314	+	0.625781i	0.0348166	+	0.0252957i
$613$	4.18424	+	39.8104i	0.169000	+	1.60793i	0.669920	+	0.742433i	$0.266328\pi$
$613$	4.18424	+	39.8104i	0.169000	+	1.60793i	−0.500920	+	0.865493i	$0.667005\pi$
$614$	11.7769	−	20.3981i	0.475276	−	0.823202i
$615$	0.0452411	+	0.0783599i	0.00182430	+	0.00315978i
$616$	8.53637	−	6.20203i	0.343940	−	0.249887i
$617$	−4.00451	−	4.44746i	−0.161216	−	0.179048i	0.657125	−	0.753782i	$-0.271772\pi$
$617$	−4.00451	−	4.44746i	−0.161216	−	0.179048i	−0.818341	+	0.574734i	$0.805106\pi$
$618$	2.32164	+	7.14526i	0.0933899	+	0.287425i
$619$	6.79755			0.273217			0.136608	−	0.990625i	$-0.456380\pi$
$619$	6.79755			0.273217			0.136608	+	0.990625i	$0.456380\pi$
$620$	−5.50683	−	0.821499i	−0.221159	−	0.0329922i
$621$	1.68353			0.0675577
$622$	7.67622	+	23.6250i	0.307788	+	0.947275i
$623$	−30.5870	−	33.9704i	−1.22544	−	1.36099i
$624$	−3.13096	+	2.27477i	−0.125339	+	0.0910639i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.33103	+	14.4298i	−0.332975	+	0.576729i
$627$	0.851047	+	8.09717i	0.0339875	+	0.323370i
$628$	6.75651	+	4.90889i	0.269614	+	0.195886i
$629$	0.290267	−	2.76170i	0.0115737	−	0.110116i
$630$	2.03616	−	2.26138i	0.0811224	−	0.0900955i
$631$	25.4058	+	11.3114i	1.01139	+	0.450299i	0.844431	−	0.535665i	$-0.179939\pi$
$631$	25.4058	+	11.3114i	1.01139	+	0.450299i	0.166958	+	0.985964i	$0.446606\pi$
$632$	−4.93718	−	1.04943i	−0.196390	−	0.0417441i
$633$	14.7446	−	3.13406i	0.586044	−	0.124568i
$634$	−16.8971	+	7.52308i	−0.671070	+	0.298780i
$635$	3.81602	−	11.7445i	0.151434	−	0.466067i
$636$	0.0916882	−	0.282187i	0.00363567	−	0.0111895i
$637$	7.98940	−	3.55711i	0.316552	−	0.140938i
$638$	25.3155	−	5.38098i	1.00225	−	0.213035i
$639$	−13.5042	−	2.87041i	−0.534218	−	0.113552i
$640$	−0.913545	−	0.406737i	−0.0361111	−	0.0160777i
$641$	−9.70945	+	10.7834i	−0.383500	+	0.425920i	−0.903728	−	0.428107i	$-0.859180\pi$
$641$	−9.70945	+	10.7834i	−0.383500	+	0.425920i	0.520228	+	0.854028i	$0.325847\pi$
$642$	1.80300	−	17.1544i	0.0711586	−	0.677029i
$643$	15.4326	+	11.2124i	0.608601	+	0.442175i	0.848921	−	0.528519i	$-0.177252\pi$
$643$	15.4326	+	11.2124i	0.608601	+	0.442175i	−0.240320	+	0.970694i	$0.577252\pi$
$644$	0.535495	+	5.09489i	0.0211014	+	0.200767i
$645$	−2.07515	+	3.59427i	−0.0817090	+	0.141524i
$646$	−1.24991	−	2.16490i	−0.0491769	−	0.0851769i
$647$	3.45645	−	2.51126i	0.135887	−	0.0987278i	−0.517765	−	0.855523i	$-0.673236\pi$
$647$	3.45645	−	2.51126i	0.135887	−	0.0987278i	0.653652	+	0.756795i	$0.273236\pi$
$648$	−0.669131	−	0.743145i	−0.0262859	−	0.0291935i
$649$	−1.53279	−	4.71745i	−0.0601673	−	0.185176i
$650$	−3.87008			−0.151797
$651$	7.55572	−	15.1646i	0.296132	−	0.594346i
$652$	4.24357			0.166191
$653$	−4.98630	−	15.3462i	−0.195129	−	0.600545i	−0.999975	−	0.00706139i	$-0.997752\pi$
$653$	−4.98630	−	15.3462i	−0.195129	−	0.600545i	0.804846	−	0.593483i	$-0.202248\pi$
$654$	2.14878	+	2.38646i	0.0840240	+	0.0933181i
$655$	1.17232	−	0.851737i	0.0458062	−	0.0332801i
$656$	0.0452411	+	0.0783599i	0.00176637	+	0.00305944i
$657$	6.36063	−	11.0169i	0.248152	−	0.429811i
$658$	0.514566	+	4.89577i	0.0200599	+	0.190857i
$659$	31.4301	+	22.8353i	1.22434	+	0.889536i	0.996453	−	0.0841514i	$-0.0268180\pi$
$659$	31.4301	+	22.8353i	1.22434	+	0.889536i	0.227888	+	0.973687i	$0.426818\pi$
$660$	0.362452	−	3.44850i	0.0141084	−	0.134233i
$661$	−26.8409	+	29.8098i	−1.04399	+	1.15947i	−0.0570515	+	0.998371i	$0.518170\pi$
$661$	−26.8409	+	29.8098i	−1.04399	+	1.15947i	−0.986939	+	0.161097i	$0.948497\pi$
$662$	−31.4737	−	14.0130i	−1.22326	−	0.544630i
$663$	4.03021	+	0.856648i	0.156521	+	0.0332695i
$664$	3.96636	−	0.843075i	0.153924	−	0.0327177i
$665$	−6.52730	+	2.90614i	−0.253118	+	0.112695i
$666$	−0.806011	+	2.48065i	−0.0312323	+	0.0961231i
$667$	−3.88303	+	11.9507i	−0.150351	+	0.462734i
$668$	−14.4017	+	6.41204i	−0.557218	+	0.248089i
$669$	24.1755	−	5.13866i	0.934679	−	0.198672i
$670$	−14.6203	−	3.10764i	−0.564832	−	0.120059i
$671$	−3.87179	−	1.72383i	−0.149469	−	0.0665479i
$672$	2.03616	−	2.26138i	0.0785464	−	0.0872346i
$673$	4.97248	−	47.3100i	0.191675	−	1.82367i	−0.301195	−	0.953562i	$-0.597386\pi$
$673$	4.97248	−	47.3100i	0.191675	−	1.82367i	0.492870	−	0.870103i	$-0.335948\pi$
$674$	25.7907	+	18.7380i	0.993420	+	0.721762i
$675$	−0.104528	−	0.994522i	−0.00402330	−	0.0382792i
$676$	−0.988752	+	1.71257i	−0.0380289	+	0.0658680i
$677$	−12.9058	−	22.3535i	−0.496009	−	0.859113i	0.503980	−	0.863715i	$-0.331868\pi$
$677$	−12.9058	−	22.3535i	−0.496009	−	0.859113i	−0.999989	+	0.00460200i	$0.998535\pi$
$678$	5.25510	−	3.81805i	0.201821	−	0.146631i
$679$	16.2399	+	18.0362i	0.623230	+	0.692167i
$680$	0.328993	+	1.01254i	0.0126163	+	0.0388290i
$681$	13.9283			0.533734
$682$	−3.19152	−	19.0406i	−0.122210	−	0.729100i
$683$	−42.5314			−1.62742			−0.813710	−	0.581271i	$-0.802556\pi$
$683$	−42.5314			−1.62742			−0.813710	+	0.581271i	$0.802556\pi$
$684$	0.725581	+	2.23311i	0.0277433	+	0.0853850i
$685$	−1.56613	−	1.73936i	−0.0598387	−	0.0664576i
$686$	11.6696	−	8.47848i	0.445549	−	0.323710i
$687$	4.86843	+	8.43236i	0.185742	+	0.321715i
$688$	−2.07515	+	3.59427i	−0.0791144	+	0.137030i
$689$	−0.120029	−	1.14200i	−0.00457273	−	0.0435066i
$690$	1.36200	+	0.989553i	0.0518506	+	0.0376716i
$691$	1.43819	−	13.6834i	0.0547112	−	0.520543i	−0.932505	−	0.361157i	$-0.882382\pi$
$691$	1.43819	−	13.6834i	0.0547112	−	0.520543i	0.987216	−	0.159386i	$-0.0509514\pi$
$692$	2.25816	−	2.50794i	0.0858423	−	0.0953375i
$693$	9.63930	+	4.29169i	0.366167	+	0.163028i
$694$	29.6006	+	6.29181i	1.12362	+	0.238834i
$695$	−0.757016	+	0.160909i	−0.0287153	+	0.00610362i
$696$	6.81864	−	3.03585i	0.258460	−	0.115074i
$697$	0.0297680	−	0.0916165i	0.00112754	−	0.00347022i
$698$	2.82203	−	8.68531i	0.106815	−	0.328744i
$699$	7.03537	−	3.13235i	0.266102	−	0.118476i
$700$	2.97649	−	0.632673i	0.112501	−	0.0239128i
$701$	11.4665	+	2.43728i	0.433084	+	0.0920549i	0.419295	−	0.907850i	$-0.362277\pi$
$701$	11.4665	+	2.43728i	0.433084	+	0.0920549i	0.0137892	+	0.999905i	$0.495611\pi$
$702$	−3.53549	−	1.57410i	−0.133439	−	0.0594107i
$703$	4.09801	−	4.55130i	0.154559	−	0.171656i
$704$	0.362452	−	3.44850i	0.0136604	−	0.129970i
$705$	1.30877	+	0.950879i	0.0492912	+	0.0358122i
$706$	−0.166535	−	1.58448i	−0.00626763	−	0.0596325i
$707$	3.58231	−	6.20475i	0.134727	−	0.233354i
$708$	−0.715246	−	1.23884i	−0.0268806	−	0.0465585i
$709$	3.29843	−	2.39645i	0.123875	−	0.0900007i	−0.524122	−	0.851643i	$-0.675607\pi$
$709$	3.29843	−	2.39645i	0.123875	−	0.0900007i	0.647998	+	0.761642i	$0.275607\pi$
$710$	−9.23795	−	10.2598i	−0.346694	−	0.385043i
$711$	−1.55976	−	4.80044i	−0.0584954	−	0.180030i
$712$	−15.0220			−0.562972
$713$	8.78076	+	3.28032i	0.328842	+	0.122849i
$714$	−3.23970			−0.121243
$715$	−4.14684	−	12.7627i	−0.155083	−	0.477297i
$716$	−8.62495	−	9.57898i	−0.322329	−	0.357983i
$717$	5.58926	−	4.06083i	0.208735	−	0.151655i
$718$	8.98996	+	15.5711i	0.335502	+	0.581107i
$719$	−11.1299	+	19.2775i	−0.415075	+	0.718931i	−0.995436	−	0.0954280i	$-0.969578\pi$
$719$	−11.1299	+	19.2775i	−0.415075	+	0.718931i	0.580361	+	0.814359i	$0.302911\pi$
$720$	−0.104528	−	0.994522i	−0.00389555	−	0.0370636i
$721$	−18.4956	−	13.4379i	−0.688814	−	0.500452i
$722$	−1.40975	+	13.4129i	−0.0524655	+	0.499176i
$723$	7.22810	−	8.02762i	0.268816	−	0.298551i
$724$	0.695559	+	0.309683i	0.0258502	+	0.0115093i
$725$	7.30082	+	1.55184i	0.271146	+	0.0576338i
$726$	1.00113	−	0.212797i	0.0371554	−	0.00789762i
$727$	−34.0475	+	15.1589i	−1.26275	+	0.562213i	−0.925338	−	0.379144i	$-0.876219\pi$
$727$	−34.0475	+	15.1589i	−1.26275	+	0.562213i	−0.337413	+	0.941357i	$0.609552\pi$
$728$	3.63917	−	11.2002i	0.134877	−	0.415107i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	11.6214	−	5.17420i	0.430129	−	0.191506i
$731$	4.32204	−	0.918677i	0.159856	−	0.0339785i
$732$	−1.19556	−	0.254124i	−0.0441892	−	0.00939269i
$733$	−41.0885	−	18.2938i	−1.51764	−	0.675696i	−0.532338	−	0.846532i	$-0.678686\pi$
$733$	−41.0885	−	18.2938i	−1.51764	−	0.675696i	−0.985299	+	0.170836i	$0.945353\pi$
$734$	24.3322	−	27.0237i	0.898119	−	0.997463i
$735$	−0.236210	+	2.24739i	−0.00871275	+	0.0828963i
$736$	1.36200	+	0.989553i	0.0502041	+	0.0364754i
$737$	−5.41754	−	51.5444i	−0.199558	−	1.89866i
$738$	−0.0452411	+	0.0783599i	−0.00166535	+	0.00288447i
$739$	7.72042	+	13.3722i	0.284000	+	0.491903i	0.972366	−	0.233461i	$-0.0750050\pi$
$739$	7.72042	+	13.3722i	0.284000	+	0.491903i	−0.688366	+	0.725363i	$0.741672\pi$
$740$	−2.11016	+	1.53312i	−0.0775712	+	0.0563588i
$741$	6.08043	+	6.75300i	0.223370	+	0.248078i
$742$	0.279006	+	0.858692i	0.0102426	+	0.0315236i
$743$	−40.7161			−1.49373			−0.746864	−	0.664977i	$-0.768441\pi$
$743$	−40.7161			−1.49373			−0.746864	+	0.664977i	$0.768441\pi$
$744$	−2.04197	−	5.17980i	−0.0748624	−	0.189901i
$745$	−12.8756			−0.471726
$746$	4.09088	+	12.5904i	0.149778	+	0.460968i
$747$	2.71330	+	3.01343i	0.0992745	+	0.110256i
$748$	−2.98660	+	2.16989i	−0.109201	+	0.0793391i
$749$	26.2440	+	45.4560i	0.958936	+	1.66093i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	1.27364	+	12.1179i	0.0464759	+	0.442188i	0.992872	+	0.119181i	$0.0380270\pi$
$751$	1.27364	+	12.1179i	0.0464759	+	0.442188i	−0.946397	+	0.323007i	$0.895306\pi$
$752$	1.30877	+	0.950879i	0.0477260	+	0.0346750i
$753$	3.05016	−	29.0203i	0.111154	−	1.05756i
$754$	19.3285	−	21.4665i	0.703902	−	0.781763i
$755$	15.3375	+	6.82872i	0.558191	+	0.248522i
$756$	2.97649	+	0.632673i	0.108254	+	0.0230101i
$757$	−16.1681	+	3.43664i	−0.587641	+	0.124907i	−0.492130	−	0.870521i	$-0.663782\pi$
$757$	−16.1681	+	3.43664i	−0.587641	+	0.124907i	−0.0955106	+	0.995428i	$0.530448\pi$
$758$	23.1133	−	10.2907i	0.839513	−	0.373775i
$759$	−1.80392	+	5.55191i	−0.0654783	+	0.201521i
$760$	−0.725581	+	2.23311i	−0.0263196	+	0.0810034i
$761$	43.4847	−	19.3606i	1.57632	−	0.701822i	0.582499	−	0.812831i	$-0.302075\pi$
$761$	43.4847	−	19.3606i	1.57632	−	0.701822i	0.993819	+	0.111009i	$0.0354082\pi$
$762$	12.0791	−	2.56748i	0.437578	−	0.0930100i
$763$	−9.55841	−	2.03170i	−0.346038	−	0.0735526i
$764$	15.5799	+	6.93661i	0.563660	+	0.250958i
$765$	−0.712385	+	0.791184i	−0.0257563	+	0.0286053i
$766$	−2.74407	+	26.1081i	−0.0991474	+	0.943324i
$767$	−4.47881	−	3.25405i	−0.161721	−	0.117497i
$768$	−0.104528	−	0.994522i	−0.00377185	−	0.0358867i
$769$	3.54587	−	6.14163i	0.127867	−	0.221473i	−0.794983	−	0.606632i	$-0.792520\pi$
$769$	3.54587	−	6.14163i	0.127867	−	0.221473i	0.922850	+	0.385159i	$0.125853\pi$
$770$	5.27577	+	9.13789i	0.190125	+	0.329307i
$771$	−5.73545	+	4.16705i	−0.206557	+	0.150073i
$772$	−11.1668	−	12.4020i	−0.401902	−	0.446357i
$773$	−3.45986	−	10.6483i	−0.124442	−	0.382994i	0.869357	−	0.494185i	$-0.164533\pi$
$773$	−3.45986	−	10.6483i	−0.124442	−	0.382994i	−0.993799	+	0.111191i	$0.964533\pi$
$774$	−4.15030			−0.149180
$775$	1.39262	−	5.39079i	0.0500243	−	0.193643i
$776$	7.97576			0.286313
$777$	−2.45268	−	7.54858i	−0.0879895	−	0.270804i
$778$	18.9883	+	21.0887i	0.680765	+	0.756066i
$779$	0.171880	−	0.124878i	0.00615823	−	0.00447422i
$780$	−1.93504	−	3.35159i	−0.0692855	−	0.120006i
$781$	23.9359	−	41.4582i	0.856495	−	1.48349i
$782$	−0.187352	−	1.78254i	−0.00669970	−	0.0637434i
$783$	6.03844	+	4.38719i	0.215796	+	0.156785i
$784$	−0.236210	+	2.24739i	−0.00843608	+	0.0802640i
$785$	−5.58825	+	6.20638i	−0.199453	+	0.221515i
$786$	1.32378	+	0.589387i	0.0472178	+	0.0210227i
$787$	13.3952	+	2.84723i	0.477486	+	0.101493i	0.440367	−	0.897818i	$-0.354848\pi$
$787$	13.3952	+	2.84723i	0.477486	+	0.101493i	0.0371196	+	0.999311i	$0.488182\pi$
$788$	−6.84613	+	1.45519i	−0.243883	+	0.0518390i
$789$	20.3101	−	9.04266i	0.723060	−	0.321927i
$790$	1.55976	−	4.80044i	0.0554936	−	0.170792i
$791$	−6.10809	+	18.7988i	−0.217179	+	0.668408i
$792$	3.16771	−	1.41036i	0.112560	−	0.0501148i
$793$	−4.62691	+	0.983480i	−0.164306	+	0.0349244i
$794$	21.9425	+	4.66402i	0.778709	+	0.165520i
$795$	0.271057	+	0.120683i	0.00961342	+	0.00428017i
$796$	3.03894	−	3.37509i	0.107712	−	0.119627i
$797$	−0.686111	+	6.52791i	−0.0243033	+	0.231230i	0.975627	+	0.219435i	$0.0704214\pi$
$797$	−0.686111	+	6.52791i	−0.0243033	+	0.231230i	−0.999930	+	0.0117955i	$0.996245\pi$
$798$	−5.78045	−	4.19974i	−0.204626	−	0.148669i
$799$	−0.180030	−	1.71287i	−0.00636901	−	0.0605971i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−7.51098	−	13.0094i	−0.265387	−	0.459664i
$802$	13.7478	−	9.98839i	0.485453	−	0.352702i
$803$	29.5159	+	32.7807i	1.04159	+	1.15681i
$804$	−4.61886	−	14.2154i	−0.162895	−	0.501338i
$805$	−5.12295			−0.180560
$806$	−15.3729	−	15.0989i	−0.541488	−	0.531835i
$807$	−20.1353			−0.708796
$808$	−0.727572	−	2.23924i	−0.0255959	−	0.0787760i
$809$	−21.1694	−	23.5110i	−0.744277	−	0.826603i	0.245475	−	0.969403i	$-0.421056\pi$
$809$	−21.1694	−	23.5110i	−0.744277	−	0.826603i	−0.989752	+	0.142800i	$0.954390\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	−8.16289	−	14.1385i	−0.286638	−	0.496471i	0.686367	−	0.727255i	$-0.259204\pi$
$811$	−8.16289	−	14.1385i	−0.286638	−	0.496471i	−0.973005	+	0.230784i	$0.925871\pi$
$812$	−11.3563	+	19.6697i	−0.398529	+	0.690272i
$813$	2.01869	+	19.2065i	0.0707985	+	0.673603i
$814$	−7.31698	−	5.31610i	−0.256460	−	0.186329i
$815$	−0.443574	+	4.22033i	−0.0155377	+	0.147832i
$816$	−0.712385	+	0.791184i	−0.0249385	+	0.0276970i
$817$	8.90253	+	3.96366i	0.311460	+	0.138671i
$818$	−20.5709	−	4.37248i	−0.719244	−	0.152880i
$819$	11.5193	−	2.44849i	0.402515	−	0.0855572i
$820$	−0.0826597	+	0.0368025i	−0.00288660	+	0.00128520i
$821$	−5.26544	+	16.2054i	−0.183765	+	0.565571i	−0.999925	−	0.0122554i	$-0.996099\pi$
$821$	−5.26544	+	16.2054i	−0.183765	+	0.565571i	0.816160	+	0.577826i	$0.196099\pi$
$822$	0.723267	−	2.22599i	0.0252268	−	0.0776402i
$823$	−29.1216	+	12.9658i	−1.01511	+	0.451958i	−0.845741	−	0.533594i	$-0.820841\pi$
$823$	−29.1216	+	12.9658i	−1.01511	+	0.451958i	−0.169374	+	0.985552i	$0.554174\pi$
$824$	−7.34879	+	1.56203i	−0.256007	+	0.0544160i
$825$	3.39172	+	0.720932i	0.118084	+	0.0250996i
$826$	3.97663	+	1.77051i	0.138365	+	0.0616040i
$827$	25.8962	−	28.7606i	0.900499	−	1.00011i	−0.0994882	−	0.995039i	$-0.531721\pi$
$827$	25.8962	−	28.7606i	0.900499	−	1.00011i	0.999987	−	0.00506663i	$-0.00161277\pi$
$828$	−0.175977	+	1.67431i	−0.00611561	+	0.0581861i
$829$	17.7718	+	12.9120i	0.617242	+	0.448452i	0.851957	−	0.523612i	$-0.175416\pi$
$829$	17.7718	+	12.9120i	0.617242	+	0.448452i	−0.234715	+	0.972064i	$0.575416\pi$
$830$	0.423859	+	4.03275i	0.0147124	+	0.139979i
$831$	0.729903	−	1.26423i	0.0253200	−	0.0438556i
$832$	−1.93504	−	3.35159i	−0.0670854	−	0.116195i
$833$	1.94637	−	1.41412i	0.0674378	−	0.0489964i
$834$	−0.517859	−	0.575141i	−0.0179320	−	0.0199155i
$835$	−4.87153	−	14.9930i	−0.168586	−	0.518855i
$836$	−8.14177			−0.281589
$837$	3.46485	−	4.35830i	0.119763	−	0.150645i
$838$	−1.67262			−0.0577796
$839$	−10.6819	−	32.8756i	−0.368781	−	1.13499i	−0.947579	−	0.319520i	$-0.896478\pi$
$839$	−10.6819	−	32.8756i	−0.368781	−	1.13499i	0.578799	−	0.815471i	$-0.303522\pi$
$840$	2.03616	+	2.26138i	0.0702540	+	0.0780250i
$841$	−21.6090	+	15.6999i	−0.745139	+	0.541375i
$842$	12.3346	+	21.3642i	0.425079	+	0.736259i
$843$	0.497681	−	0.862008i	0.0171410	−	0.0296891i
$844$	1.57566	+	14.9914i	0.0542365	+	0.516025i
$845$	−1.59983	−	1.16235i	−0.0550360	−	0.0399860i
$846$	−0.169099	+	1.60887i	−0.00581375	+	0.0553141i
$847$	−2.08399	+	2.31451i	−0.0716069	+	0.0795275i
$848$	0.271057	+	0.120683i	0.00930815	+	0.00414426i
$849$	12.6064	+	2.67958i	0.432652	+	0.0919630i
$850$	−1.04138	+	0.221352i	−0.0357190	+	0.00759230i
$851$	4.01152	−	1.78605i	0.137513	−	0.0612248i
$852$	4.26626	−	13.1302i	0.146160	−	0.449833i
$853$	−3.51771	+	10.8264i	−0.120444	+	0.370689i	−0.993044	−	0.117747i	$-0.962433\pi$
$853$	−3.51771	+	10.8264i	−0.120444	+	0.370689i	0.872599	+	0.488437i	$0.162433\pi$
$854$	3.39779	−	1.51280i	0.116270	−	0.0517668i
$855$	−2.29672	+	0.488183i	−0.0785461	+	0.0166955i
$856$	16.8719	+	3.58624i	0.576671	+	0.122575i
$857$	−13.0585	−	5.81403i	−0.446071	−	0.198604i	0.171393	−	0.985203i	$-0.445173\pi$
$857$	−13.0585	−	5.81403i	−0.446071	−	0.198604i	−0.617464	+	0.786599i	$0.711840\pi$
$858$	8.97937	−	9.97260i	0.306551	−	0.340459i
$859$	4.89344	−	46.5580i	0.166962	−	1.58854i	−0.515025	−	0.857175i	$-0.672217\pi$
$859$	4.89344	−	46.5580i	0.166962	−	1.58854i	0.681987	−	0.731364i	$-0.261116\pi$
$860$	−3.35767	−	2.43949i	−0.114495	−	0.0831858i
$861$	−0.0287805	−	0.273828i	−0.000980836	−	0.00933203i
$862$	13.7482	−	23.8126i	0.468265	−	0.811059i
$863$	−4.69711	−	8.13564i	−0.159892	−	0.276940i	0.774938	−	0.632038i	$-0.217781\pi$
$863$	−4.69711	−	8.13564i	−0.159892	−	0.276940i	−0.934829	+	0.355097i	$0.884448\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	2.25816	+	2.50794i	0.0767797	+	0.0852724i
$866$	−1.94135	−	5.97485i	−0.0659697	−	0.203034i
$867$	−15.8665			−0.538856
$868$	14.2917	+	9.09946i	0.485092	+	0.308856i
$869$	17.5021			0.593717
$870$	2.30648	+	7.09862i	0.0781970	+	0.240666i
$871$	−38.7064	−	42.9878i	−1.31152	−	1.45659i
$872$	−2.59800	+	1.88756i	−0.0879794	+	0.0639207i
$873$	3.98788	+	6.90721i	0.134969	+	0.233774i
$874$	1.97649	−	3.42338i	0.0668557	−	0.115797i
$875$	0.318079	+	3.02632i	0.0107530	+	0.102308i
$876$	10.2917	+	7.47736i	0.347725	+	0.252637i
$877$	5.17244	−	49.2125i	0.174661	−	1.66179i	−0.459195	−	0.888336i	$-0.651862\pi$
$877$	5.17244	−	49.2125i	0.174661	−	1.66179i	0.633856	−	0.773451i	$-0.281471\pi$
$878$	14.3417	−	15.9281i	0.484011	−	0.537548i
$879$	−17.6212	−	7.84549i	−0.594350	−	0.264622i
$880$	3.39172	+	0.720932i	0.114335	+	0.0243026i
$881$	−35.3699	+	7.51811i	−1.19164	+	0.253291i	−0.760709	−	0.649093i	$-0.775149\pi$
$881$	−35.3699	+	7.51811i	−1.19164	+	0.253291i	−0.430933	+	0.902384i	$0.641815\pi$
$882$	−2.06440	+	0.919131i	−0.0695121	+	0.0309488i
$883$	−3.35118	+	10.3139i	−0.112776	+	0.347089i	−0.991477	−	0.130284i	$-0.958411\pi$
$883$	−3.35118	+	10.3139i	−0.112776	+	0.347089i	0.878701	+	0.477373i	$0.158411\pi$
$884$	−1.27323	+	3.91859i	−0.0428233	+	0.131797i
$885$	1.30682	−	0.581834i	0.0439283	−	0.0195581i
$886$	12.2988	−	2.61418i	0.413185	−	0.0878251i
$887$	−5.98014	−	1.27112i	−0.200793	−	0.0426800i	0.106417	−	0.994322i	$-0.466062\pi$
$887$	−5.98014	−	1.27112i	−0.200793	−	0.0426800i	−0.307210	+	0.951642i	$0.599396\pi$
$888$	−2.38281	−	1.06089i	−0.0799618	−	0.0356013i
$889$	−25.1443	+	27.9256i	−0.843313	+	0.936593i
$890$	1.57022	−	14.9397i	0.0526340	−	0.500779i
$891$	2.80526	+	2.03814i	0.0939797	+	0.0682803i
$892$	2.58348	+	24.5802i	0.0865014	+	0.823006i
$893$	1.89924	−	3.28958i	0.0635557	−	0.110082i
$894$	−6.43780	−	11.1506i	−0.215312	−	0.372932i
$895$	10.4281	−	7.57642i	0.348571	−	0.253252i
$896$	2.03616	+	2.26138i	0.0680232	+	0.0755474i
$897$	2.01336	+	6.19650i	0.0672243	+	0.206895i
$898$	−24.7258			−0.825111
$899$	22.9463	+	34.6480i	0.765302	+	1.15558i
$900$	1.00000			0.0333333
$901$	−0.0976152	−	0.300429i	−0.00325203	−	0.0100087i
$902$	−0.209937	−	0.233159i	−0.00699015	−	0.00776335i
$903$	10.2173	−	7.42333i	0.340012	−	0.247033i
$904$	3.24783	+	5.62541i	0.108021	+	0.187098i
$905$	−0.380692	+	0.659378i	−0.0126546	+	0.0219185i
$906$	1.75493	+	16.6971i	0.0583037	+	0.554723i
$907$	−13.4058	−	9.73989i	−0.445133	−	0.323408i	0.342538	−	0.939504i	$-0.388713\pi$
$907$	−13.4058	−	9.73989i	−0.445133	−	0.323408i	−0.787671	+	0.616096i	$0.788713\pi$
$908$	−1.45591	+	13.8520i	−0.0483159	+	0.459695i
$909$	1.57545	−	1.74971i	0.0522543	−	0.0580343i
$910$	10.7585	+	4.78997i	0.356639	+	0.158786i
$911$	−10.8021	−	2.29605i	−0.357889	−	0.0760717i	0.0254584	−	0.999676i	$-0.491895\pi$
$911$	−10.8021	−	2.29605i	−0.357889	−	0.0760717i	−0.383347	+	0.923604i	$0.625229\pi$
$912$	−2.29672	+	0.488183i	−0.0760520	+	0.0161653i
$913$	−12.8450	+	5.71895i	−0.425106	+	0.189269i
$914$	4.27245	−	13.1493i	0.141320	−	0.434939i
$915$	0.377702	−	1.16245i	0.0124864	−	0.0384293i
$916$	−8.89506	+	3.96034i	−0.293901	+	0.130853i
$917$	−4.31312	+	0.916782i	−0.142432	+	0.0302748i
$918$	−1.04138	−	0.221352i	−0.0343706	−	0.00730570i
$919$	6.26718	+	2.79033i	0.206735	+	0.0920444i	0.507492	−	0.861656i	$-0.330573\pi$
$919$	6.26718	+	2.79033i	0.206735	+	0.0920444i	−0.300757	+	0.953701i	$0.597239\pi$
$920$	−1.12650	+	1.25111i	−0.0371396	+	0.0412477i
$921$	−2.46204	+	23.4247i	−0.0811269	+	0.771871i
$922$	15.1489	+	11.0063i	0.498902	+	0.362473i
$923$	−5.58495	−	53.1372i	−0.183831	−	1.74903i
$924$	−5.27577	+	9.13789i	−0.173560	+	0.300615i
$925$	−1.30415	−	2.25886i	−0.0428803	−	0.0742709i
$926$	17.7210	−	12.8751i	0.582349	−	0.423101i
$927$	−5.02716	−	5.58323i	−0.165114	−	0.183377i
$928$	2.30648	+	7.09862i	0.0757139	+	0.233024i
$929$	−39.0396			−1.28085			−0.640424	−	0.768022i	$-0.721241\pi$
$929$	−39.0396			−1.28085			−0.640424	+	0.768022i	$0.721241\pi$
$930$	5.36487	−	1.48935i	0.175921	−	0.0488378i
$931$	5.30601			0.173897
$932$	2.37979	+	7.32425i	0.0779527	+	0.239914i
$933$	−16.6217	−	18.4603i	−0.544171	−	0.604363i
$934$	−14.1813	+	10.3033i	−0.464027	+	0.337135i
$935$	−1.84582	−	3.19705i	−0.0603648	−	0.104555i
$936$	1.93504	−	3.35159i	0.0632487	−	0.109550i
$937$	5.59275	+	53.2115i	0.182707	+	1.73834i	0.574691	+	0.818370i	$0.305122\pi$
$937$	5.59275	+	53.2115i	0.182707	+	1.73834i	−0.391984	+	0.919972i	$0.628211\pi$
$938$	36.7968	+	26.7344i	1.20146	+	0.872910i
$939$	1.74166	−	16.5708i	0.0568369	−	0.540767i
$940$	−1.08247	+	1.20221i	−0.0353064	+	0.0392117i
$941$	18.7555	+	8.35048i	0.611411	+	0.272218i	0.688993	−	0.724768i	$-0.258053\pi$
$941$	18.7555	+	8.35048i	0.611411	+	0.272218i	−0.0775815	+	0.996986i	$0.524720\pi$
$942$	−8.16901	−	1.73638i	−0.266161	−	0.0565742i
$943$	0.149001	−	0.0316711i	0.00485213	−	0.00103135i
$944$	1.30682	−	0.581834i	0.0425334	−	0.0189371i
$945$	−0.940335	+	2.89405i	−0.0305891	+	0.0941435i
$946$	4.44711	−	13.6868i	0.144588	−	0.444996i
$947$	−2.01368	+	0.896546i	−0.0654357	+	0.0291338i	−0.439194	−	0.898392i	$-0.644736\pi$
$947$	−2.01368	+	0.896546i	−0.0654357	+	0.0291338i	0.373758	+	0.927526i	$0.378069\pi$
$948$	4.93718	−	1.04943i	0.160352	−	0.0340839i
$949$	48.1564	+	10.2360i	1.56322	+	0.332273i
$950$	−2.14503	−	0.955030i	−0.0695940	−	0.0309853i
$951$	12.3764	−	13.7454i	0.401331	−	0.445724i
$952$	0.338640	−	3.22195i	0.0109754	−	0.104424i
$953$	41.2303	+	29.9556i	1.33558	+	0.970356i	0.999594	+	0.0284895i	$0.00906971\pi$
$953$	41.2303	+	29.9556i	1.33558	+	0.970356i	0.335987	+	0.941867i	$0.390930\pi$
$954$	0.0310146	+	0.295084i	0.00100413	+	0.00955369i
$955$	−8.52715	+	14.7695i	−0.275932	+	0.477928i
$956$	3.45435	+	5.98311i	0.111722	+	0.193508i
$957$	−20.9383	+	15.2125i	−0.676838	+	0.491751i
$958$	24.0214	+	26.6784i	0.776095	+	0.861941i
$959$	2.20089	+	6.77365i	0.0710705	+	0.218733i
$960$	1.00000			0.0322749
$961$	26.5637	−	15.9804i	0.856892	−	0.515495i
$962$	−10.0944			−0.325455
$963$	5.33019	+	16.4046i	0.171763	+	0.528632i
$964$	7.22810	+	8.02762i	0.232802	+	0.258552i
$965$	13.5013	−	9.80927i	0.434622	−	0.315772i
$966$	−2.56148	−	4.43661i	−0.0824142	−	0.142746i
$967$	−2.58116	+	4.47070i	−0.0830046	+	0.143768i	−0.904539	−	0.426390i	$-0.859785\pi$
$967$	−2.58116	+	4.47070i	−0.0830046	+	0.143768i	0.821535	+	0.570159i	$0.193118\pi$
$968$	0.106984	+	1.01789i	0.00343861	+	0.0327162i
$969$	2.02239	+	1.46935i	0.0649686	+	0.0472024i
$970$	−0.833694	+	7.93207i	−0.0267683	+	0.254683i
$971$	−6.44732	+	7.16047i	−0.206904	+	0.229791i	−0.837661	−	0.546190i	$-0.816078\pi$
$971$	−6.44732	+	7.16047i	−0.206904	+	0.229791i	0.630757	+	0.775980i	$0.282744\pi$
$972$	0.913545	+	0.406737i	0.0293020	+	0.0130461i
$973$	2.30359	+	0.489643i	0.0738497	+	0.0156972i
$974$	12.5171	−	2.66059i	0.401074	−	0.0852508i
$975$	3.53549	−	1.57410i	0.113226	−	0.0504116i
$976$	0.377702	−	1.16245i	0.0120899	−	0.0372090i
$977$	3.57957	−	11.0168i	0.114520	−	0.352458i	−0.877326	−	0.479894i	$-0.840675\pi$
$977$	3.57957	−	11.0168i	0.114520	−	0.352458i	0.991847	+	0.127437i	$0.0406750\pi$
$978$	−3.87670	+	1.72602i	−0.123963	+	0.0551919i
$979$	50.9503	−	10.8298i	1.62838	−	0.346122i
$980$	−2.21039	−	0.469833i	−0.0706083	−	0.0150083i
$981$	−2.93367	−	1.30615i	−0.0936649	−	0.0417023i
$982$	0.601589	−	0.668133i	0.0191975	−	0.0213210i
$983$	0.125161	−	1.19083i	0.00399201	−	0.0379815i	−0.992345	−	0.123500i	$-0.960588\pi$
$983$	0.125161	−	1.19083i	0.00399201	−	0.0379815i	0.996337	+	0.0855187i	$0.0272547\pi$
$984$	−0.0732017	−	0.0531841i	−0.00233358	−	0.00169545i
$985$	−0.731603	−	6.96073i	−0.0233108	−	0.221787i
$986$	3.97321	−	6.88180i	0.126533	−	0.219161i
$987$	−2.46137	−	4.26322i	−0.0783462	−	0.135700i
$988$	−7.35158	+	5.34124i	−0.233885	+	0.169927i
$989$	4.67532	+	5.19247i	0.148667	+	0.165111i
$990$	1.07151	+	3.29778i	0.0340549	+	0.104810i
$991$	6.89760			0.219110			0.109555	−	0.993981i	$-0.465057\pi$
$991$	6.89760			0.219110			0.109555	+	0.993981i	$0.465057\pi$
$992$	5.36487	−	1.48935i	0.170335	−	0.0472870i
$993$	34.4522			1.09331
$994$	12.9822	+	39.9550i	0.411770	+	1.26730i
$995$	3.03894	+	3.37509i	0.0963410	+	0.106997i
$996$	−3.28054	+	2.38345i	−0.103948	+	0.0755225i
$997$	29.8881	+	51.7676i	0.946564	+	1.63950i	0.752589	+	0.658491i	$0.228805\pi$
$997$	29.8881	+	51.7676i	0.946564	+	1.63950i	0.193976	+	0.981006i	$0.437862\pi$
$998$	1.64347	−	2.84658i	0.0520232	−	0.0901068i
$999$	−0.272642	−	2.59402i	−0.00862602	−	0.0820711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.f.361.2	✓	16
31.14	even	15	inner	930.2.bg.f.541.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.f.361.2	✓	16	1.1	even	1	trivial
930.2.bg.f.541.2	yes	16	31.14	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.318079 + 3.02632i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(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} +(0.318079 + 3.02632i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(-0.669131 + 0.743145i) q^{10} +(-3.16771 - 1.41036i) q^{11} +(-0.978148 - 0.207912i) q^{12} +(-3.78551 + 0.804634i) q^{13} +(2.77991 - 1.23769i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.972600 + 0.433029i) q^{17} +(0.978148 - 0.207912i) q^{18} +(-2.29672 - 0.488183i) q^{19} +(0.913545 + 0.406737i) q^{20} +(-2.03616 + 2.26138i) q^{21} +(-0.362452 + 3.44850i) q^{22} +(-1.36200 - 0.989553i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.93504 + 3.35159i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.03616 - 2.26138i) q^{28} +(-2.30648 - 7.09862i) q^{29} -1.00000 q^{30} +(-5.36487 + 1.48935i) q^{31} -1.00000 q^{32} +(-1.07151 - 3.29778i) q^{33} +(0.712385 + 0.791184i) q^{34} +(2.46183 - 1.78862i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.30415 + 2.25886i) q^{37} +(0.245436 + 2.33517i) q^{38} +(-3.13096 - 2.27477i) q^{39} +(0.104528 - 0.994522i) q^{40} +(-0.0605445 + 0.0672414i) q^{41} +(2.77991 + 1.23769i) q^{42} +(-4.05961 - 0.862897i) q^{43} +(3.39172 - 0.720932i) q^{44} +(0.913545 - 0.406737i) q^{45} +(-0.520239 + 1.60113i) q^{46} +(-0.499907 + 1.53855i) q^{47} +(0.913545 - 0.406737i) q^{48} +(-2.21039 + 0.469833i) q^{49} +(0.978148 + 0.207912i) q^{50} +(-0.972600 - 0.433029i) q^{51} +(2.58959 - 2.87603i) q^{52} +(-0.0310146 + 0.295084i) q^{53} +(0.809017 + 0.587785i) q^{54} +(0.362452 + 3.44850i) q^{55} +(-1.52149 + 2.63530i) q^{56} +(-1.17401 - 2.03345i) q^{57} +(-6.03844 + 4.38719i) q^{58} +(0.957186 + 1.06306i) q^{59} +(0.309017 + 0.951057i) q^{60} +1.22227 q^{61} +(3.07429 + 4.64206i) q^{62} -3.04299 q^{63} +(0.309017 + 0.951057i) q^{64} +(2.58959 + 2.87603i) q^{65} +(-2.80526 + 2.03814i) q^{66} +(7.47347 + 12.9444i) q^{67} +(0.532322 - 0.922008i) q^{68} +(-0.175977 - 1.67431i) q^{69} +(-2.46183 - 1.78862i) q^{70} +(-1.44311 + 13.7303i) q^{71} +(-0.669131 + 0.743145i) q^{72} +(-11.6214 - 5.17420i) q^{73} +(2.55131 + 0.542298i) q^{74} +(-0.978148 + 0.207912i) q^{75} +(2.14503 - 0.955030i) q^{76} +(3.26060 - 10.0351i) q^{77} +(-1.19592 + 3.68066i) q^{78} +(-4.61110 + 2.05299i) q^{79} +(-0.978148 + 0.207912i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.0826597 + 0.0368025i) q^{82} +(2.71330 - 3.01343i) q^{83} +(0.318079 - 3.02632i) q^{84} +(0.861314 + 0.625781i) q^{85} +(0.433825 + 4.12757i) q^{86} +(3.73196 - 6.46395i) q^{87} +(-1.73375 - 3.00294i) q^{88} +(-12.1530 + 8.82969i) q^{89} +(-0.669131 - 0.743145i) q^{90} +(-3.63917 - 11.2002i) q^{91} +1.68353 q^{92} +(-4.69660 - 2.99030i) q^{93} +1.61773 q^{94} +(0.725581 + 2.23311i) q^{95} +(-0.669131 - 0.743145i) q^{96} +(6.45252 - 4.68803i) q^{97} +(1.12989 + 1.95702i) q^{98} +(1.73375 - 3.00294i) 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

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