LMFDB - Embedded newform 930.2.bg.h.541.2

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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.2
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.h.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.0963276 - 0.916496i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(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} +(0.0963276 - 0.916496i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(0.338482 - 0.150702i) q^{11} +(0.978148 - 0.207912i) q^{12} +(4.54331 + 0.965710i) q^{13} +(0.841873 + 0.374826i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.57056 + 0.699260i) q^{17} +(0.978148 + 0.207912i) q^{18} +(3.27158 - 0.695397i) q^{19} +(0.913545 - 0.406737i) q^{20} +(0.616633 + 0.684841i) q^{21} +(0.0387294 + 0.368485i) q^{22} +(-0.334745 + 0.243207i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.32241 + 4.02252i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.616633 + 0.684841i) q^{28} +(-2.86638 + 8.82182i) q^{29} +1.00000 q^{30} +(-2.80097 + 4.81192i) q^{31} -1.00000 q^{32} +(-0.114495 + 0.352381i) q^{33} +(-1.15037 + 1.27761i) q^{34} +(0.745545 + 0.541670i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.498251 - 0.862996i) q^{37} +(-0.349614 + 3.32635i) q^{38} +(-3.75773 + 2.73015i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-0.000431126 - 0.000478814i) q^{41} +(-0.841873 + 0.374826i) q^{42} +(7.35038 - 1.56237i) q^{43} +(-0.362418 - 0.0770344i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-0.127861 - 0.393517i) q^{46} +(-1.72796 - 5.31810i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(6.01635 + 1.27881i) q^{49} +(0.978148 - 0.207912i) q^{50} +(-1.57056 + 0.699260i) q^{51} +(-3.10798 - 3.45177i) q^{52} +(1.16705 + 11.1037i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.0387294 + 0.368485i) q^{55} +(-0.460772 - 0.798081i) q^{56} +(-1.67234 + 2.89657i) q^{57} +(-7.50428 - 5.45218i) q^{58} +(-6.81672 + 7.57074i) q^{59} +(-0.309017 + 0.951057i) q^{60} -5.50466 q^{61} +(-3.71086 - 4.15084i) q^{62} -0.921544 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.10798 + 3.45177i) q^{65} +(-0.299753 - 0.217783i) q^{66} +(0.427924 - 0.741186i) q^{67} +(-0.859598 - 1.48887i) q^{68} +(0.0432505 - 0.411501i) q^{69} +(-0.745545 + 0.541670i) q^{70} +(0.00473567 + 0.0450569i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-2.39261 + 1.06526i) q^{73} +(0.974727 - 0.207185i) q^{74} +(0.978148 + 0.207912i) q^{75} +(-3.05551 - 1.36040i) q^{76} +(-0.105513 - 0.324734i) q^{77} +(-1.43533 - 4.41748i) q^{78} +(0.432335 + 0.192488i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.000588605 - 0.000262064i) q^{82} +(5.00232 + 5.55564i) q^{83} +(-0.0963276 - 0.916496i) q^{84} +(-1.39086 + 1.01052i) q^{85} +(-0.785489 + 7.47343i) q^{86} +(-4.63790 - 8.03308i) q^{87} +(0.185257 - 0.320875i) q^{88} +(11.7620 + 8.54563i) q^{89} +(-0.669131 + 0.743145i) q^{90} +(1.32272 - 4.07090i) q^{91} +0.413768 q^{92} +(-1.70174 - 5.30133i) q^{93} +5.59178 q^{94} +(-1.03356 + 3.18097i) q^{95} +(0.669131 - 0.743145i) q^{96} +(-5.40981 - 3.93045i) q^{97} +(-3.07538 + 5.32671i) q^{98} +(-0.185257 - 0.320875i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

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
$7$	0.0963276	−	0.916496i	0.0364084	−	0.346403i	−0.961120	−	0.276133i	$-0.910947\pi$
$7$	0.0963276	−	0.916496i	0.0364084	−	0.346403i	0.997528	−	0.0702704i	$-0.0223862\pi$
$8$	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
$11$	0.338482	−	0.150702i	0.102056	−	0.0454384i	−0.355074	−	0.934838i	$-0.615544\pi$
$11$	0.338482	−	0.150702i	0.102056	−	0.0454384i	0.457130	+	0.889400i	$0.348877\pi$
$12$	0.978148	−	0.207912i	0.282367	−	0.0600189i
$13$	4.54331	+	0.965710i	1.26009	+	0.267840i	0.789081	−	0.614290i	$-0.210557\pi$
$13$	4.54331	+	0.965710i	1.26009	+	0.267840i	0.471007	+	0.882130i	$0.343891\pi$
$14$	0.841873	+	0.374826i	0.225000	+	0.100176i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.57056	+	0.699260i	0.380918	+	0.169596i	0.588258	−	0.808673i	$-0.299814\pi$
$17$	1.57056	+	0.699260i	0.380918	+	0.169596i	−0.207340	+	0.978269i	$0.566481\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	3.27158	−	0.695397i	0.750553	−	0.159535i	0.183275	−	0.983062i	$-0.441330\pi$
$19$	3.27158	−	0.695397i	0.750553	−	0.159535i	0.567277	+	0.823527i	$0.307997\pi$
$20$	0.913545	−	0.406737i	0.204275	−	0.0909491i
$21$	0.616633	+	0.684841i	0.134560	+	0.149445i
$22$	0.0387294	+	0.368485i	0.00825713	+	0.0785613i
$23$	−0.334745	+	0.243207i	−0.0697992	+	0.0507121i	−0.622138	−	0.782908i	$-0.713736\pi$
$23$	−0.334745	+	0.243207i	−0.0697992	+	0.0507121i	0.552338	+	0.833620i	$0.313736\pi$
$24$	−0.104528	+	0.994522i	−0.0213368	+	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.32241	+	4.02252i	−0.455461	+	0.788882i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.616633	+	0.684841i	−0.116533	+	0.129423i
$29$	−2.86638	+	8.82182i	−0.532274	+	1.63817i	0.217194	+	0.976129i	$0.430310\pi$
$29$	−2.86638	+	8.82182i	−0.532274	+	1.63817i	−0.749467	+	0.662041i	$0.769690\pi$
$30$	1.00000			0.182574
$31$	−2.80097	+	4.81192i	−0.503068	+	0.864247i
$31$	−2.80097	+	4.81192i	−0.503068	+	0.864247i
$32$	−1.00000			−0.176777
$33$	−0.114495	+	0.352381i	−0.0199311	+	0.0613416i
$34$	−1.15037	+	1.27761i	−0.197286	+	0.219109i
$35$	0.745545	+	0.541670i	0.126020	+	0.0915590i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.498251	−	0.862996i	−0.0819120	−	0.141876i	0.822159	−	0.569258i	$-0.192769\pi$
$37$	−0.498251	−	0.862996i	−0.0819120	−	0.141876i	−0.904071	+	0.427382i	$0.859436\pi$
$38$	−0.349614	+	3.32635i	−0.0567148	+	0.539605i
$39$	−3.75773	+	2.73015i	−0.601718	+	0.437174i
$40$	0.104528	+	0.994522i	0.0165274	+	0.157248i
$41$	−0.000431126	0	0.000478814i	−6.73306e−5	0	7.47783e-5i	0.743111	−	0.669168i	$-0.233349\pi$
$41$	−0.000431126	0	0.000478814i	−6.73306e−5	0	7.47783e-5i	−0.743178	+	0.669093i	$0.766683\pi$
$42$	−0.841873	+	0.374826i	−0.129904	+	0.0578369i
$43$	7.35038	−	1.56237i	1.12092	−	0.238259i	0.390064	−	0.920788i	$-0.372453\pi$
$43$	7.35038	−	1.56237i	1.12092	−	0.238259i	0.730859	+	0.682528i	$0.239120\pi$
$44$	−0.362418	−	0.0770344i	−0.0546366	−	0.0116134i
$45$	0.913545	+	0.406737i	0.136183	+	0.0606327i
$46$	−0.127861	−	0.393517i	−0.0188521	−	0.0580209i
$47$	−1.72796	−	5.31810i	−0.252048	−	0.775725i	−0.994397	−	0.105711i	$-0.966288\pi$
$47$	−1.72796	−	5.31810i	−0.252048	−	0.775725i	0.742349	−	0.670014i	$-0.233712\pi$
$48$	−0.913545	−	0.406737i	−0.131859	−	0.0587074i
$49$	6.01635	+	1.27881i	0.859478	+	0.182688i
$50$	0.978148	−	0.207912i	0.138331	−	0.0294032i
$51$	−1.57056	+	0.699260i	−0.219923	+	0.0979160i
$52$	−3.10798	−	3.45177i	−0.431000	−	0.478674i
$53$	1.16705	+	11.1037i	0.160306	+	1.52521i	0.718516	+	0.695511i	$0.244822\pi$
$53$	1.16705	+	11.1037i	0.160306	+	1.52521i	−0.558209	+	0.829700i	$0.688511\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−0.0387294	+	0.368485i	−0.00522227	+	0.0496865i
$56$	−0.460772	−	0.798081i	−0.0615733	−	0.106648i
$57$	−1.67234	+	2.89657i	−0.221506	+	0.383660i
$58$	−7.50428	−	5.45218i	−0.985361	−	0.715907i
$59$	−6.81672	+	7.57074i	−0.887462	+	0.985626i	−0.999968	−	0.00802470i	$-0.997446\pi$
$59$	−6.81672	+	7.57074i	−0.887462	+	0.985626i	0.112506	+	0.993651i	$0.464112\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	−5.50466			−0.704800			−0.352400	−	0.935850i	$-0.614634\pi$
$61$	−5.50466			−0.704800			−0.352400	+	0.935850i	$0.614634\pi$
$62$	−3.71086	−	4.15084i	−0.471280	−	0.527158i
$63$	−0.921544			−0.116104
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−3.10798	+	3.45177i	−0.385498	+	0.428139i
$66$	−0.299753	−	0.217783i	−0.0368970	−	0.0268073i
$67$	0.427924	−	0.741186i	0.0522792	−	0.0905502i	−0.838702	−	0.544591i	$-0.816685\pi$
$67$	0.427924	−	0.741186i	0.0522792	−	0.0905502i	0.890981	+	0.454041i	$0.150018\pi$
$68$	−0.859598	−	1.48887i	−0.104242	−	0.180552i
$69$	0.0432505	−	0.411501i	0.00520675	−	0.0495389i
$70$	−0.745545	+	0.541670i	−0.0891097	+	0.0647420i
$71$	0.00473567	+	0.0450569i	0.000562021	+	0.00534727i	0.994799	−	0.101854i	$-0.0324776\pi$
$71$	0.00473567	+	0.0450569i	0.000562021	+	0.00534727i	−0.994237	+	0.107202i	$0.965811\pi$
$72$	−0.669131	−	0.743145i	−0.0788578	−	0.0875805i
$73$	−2.39261	+	1.06526i	−0.280034	+	0.124679i	−0.541948	−	0.840412i	$-0.682313\pi$
$73$	−2.39261	+	1.06526i	−0.280034	+	0.124679i	0.261914	+	0.965091i	$0.415646\pi$
$74$	0.974727	−	0.207185i	0.113310	−	0.0240847i
$75$	0.978148	+	0.207912i	0.112947	+	0.0240076i
$76$	−3.05551	−	1.36040i	−0.350491	−	0.156049i
$77$	−0.105513	−	0.324734i	−0.0120243	−	0.0370069i
$78$	−1.43533	−	4.41748i	−0.162519	−	0.500181i
$79$	0.432335	+	0.192488i	0.0486414	+	0.0216566i	0.430913	−	0.902393i	$-0.358192\pi$
$79$	0.432335	+	0.192488i	0.0486414	+	0.0216566i	−0.382272	+	0.924050i	$0.624858\pi$
$80$	−0.978148	−	0.207912i	−0.109360	−	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	0.000588605	0	0.000262064i	6.50005e−5	0	2.89401e-5i
$83$	5.00232	+	5.55564i	0.549076	+	0.609811i	0.952253	−	0.305312i	$-0.0987606\pi$
$83$	5.00232	+	5.55564i	0.549076	+	0.609811i	−0.403177	+	0.915122i	$0.632094\pi$
$84$	−0.0963276	−	0.916496i	−0.0105102	−	0.0999979i
$85$	−1.39086	+	1.01052i	−0.150860	+	0.109606i
$86$	−0.785489	+	7.47343i	−0.0847014	+	0.805880i
$87$	−4.63790	−	8.03308i	−0.497235	−	0.861237i
$88$	0.185257	−	0.320875i	0.0197485	−	0.0342054i
$89$	11.7620	+	8.54563i	1.24677	+	0.905835i	0.998030	−	0.0627343i	$-0.0199821\pi$
$89$	11.7620	+	8.54563i	1.24677	+	0.905835i	0.248744	+	0.968569i	$0.419982\pi$
$90$	−0.669131	+	0.743145i	−0.0705326	+	0.0783343i
$91$	1.32272	−	4.07090i	0.138658	−	0.426746i
$92$	0.413768			0.0431383
$93$	−1.70174	−	5.30133i	−0.176462	−	0.549722i
$94$	5.59178			0.576748
$95$	−1.03356	+	3.18097i	−0.106041	+	0.326361i
$96$	0.669131	−	0.743145i	0.0682929	−	0.0758469i
$97$	−5.40981	−	3.93045i	−0.549283	−	0.399077i	0.278238	−	0.960512i	$-0.410250\pi$
$97$	−5.40981	−	3.93045i	−0.549283	−	0.399077i	−0.827521	+	0.561435i	$0.810250\pi$
$98$	−3.07538	+	5.32671i	−0.310660	+	0.538079i
$99$	−0.185257	−	0.320875i	−0.0186191	−	0.0322492i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−0.956225	+	0.694738i	−0.0951480	+	0.0691291i	−0.634342	−	0.773052i	$-0.718729\pi$
$101$	−0.956225	+	0.694738i	−0.0951480	+	0.0691291i	0.539194	+	0.842182i	$0.318729\pi$
$102$	−0.179705	−	1.70978i	−0.0177934	−	0.169293i
$103$	−1.49980	−	1.66570i	−0.147780	−	0.164126i	0.664710	−	0.747101i	$-0.268555\pi$
$103$	−1.49980	−	1.66570i	−0.147780	−	0.164126i	−0.812490	+	0.582975i	$0.801888\pi$
$104$	4.24325	−	1.88921i	0.416084	−	0.185253i
$105$	−0.901406	+	0.191600i	−0.0879683	+	0.0186982i
$106$	−10.9209	−	2.32131i	−1.06073	−	0.225465i
$107$	2.58911	+	1.15274i	0.250298	+	0.111440i	0.528051	−	0.849213i	$-0.322923\pi$
$107$	2.58911	+	1.15274i	0.250298	+	0.111440i	−0.277753	+	0.960653i	$0.589590\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	3.37551	+	10.3887i	0.323315	+	0.995062i	0.972195	+	0.234171i	$0.0752376\pi$
$109$	3.37551	+	10.3887i	0.323315	+	0.995062i	−0.648880	+	0.760890i	$0.724762\pi$
$110$	−0.338482	−	0.150702i	−0.0322730	−	0.0143689i
$111$	0.974727	+	0.207185i	0.0925169	+	0.0196651i
$112$	0.901406	−	0.191600i	0.0851749	−	0.0181045i
$113$	9.65074	−	4.29679i	0.907865	−	0.404208i	0.100961	−	0.994890i	$-0.467808\pi$
$113$	9.65074	−	4.29679i	0.907865	−	0.404208i	0.806904	+	0.590683i	$0.201142\pi$
$114$	−2.23802	−	2.48558i	−0.209610	−	0.232796i
$115$	−0.0432505	−	0.411501i	−0.00403313	−	0.0383727i
$116$	7.50428	−	5.45218i	0.696755	−	0.506222i
$117$	0.485515	−	4.61937i	0.0448859	−	0.427060i
$118$	−5.09372	−	8.82258i	−0.468915	−	0.812184i
$119$	0.792158	−	1.37206i	0.0726170	−	0.125776i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−7.26858	+	8.07257i	−0.660780	+	0.733870i
$122$	1.70103	−	5.23524i	0.154004	−	0.473977i
$123$	0.000644308	0		5.80953e−5	0
$124$	5.09441	−	2.24656i	0.457491	−	0.201747i
$125$	1.00000			0.0894427
$126$	0.284773	−	0.876441i	0.0253696	−	0.0780795i
$127$	9.02095	−	10.0188i	0.800479	−	0.889022i	−0.195305	−	0.980742i	$-0.562570\pi$
$127$	9.02095	−	10.0188i	0.800479	−	0.889022i	0.995785	+	0.0917200i	$0.0292365\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−3.75730	+	6.50783i	−0.330811	+	0.572982i
$130$	−2.32241	−	4.02252i	−0.203688	−	0.352799i
$131$	−0.682300	+	6.49165i	−0.0596128	+	0.567178i	0.923425	+	0.383778i	$0.125377\pi$
$131$	−0.682300	+	6.49165i	−0.0596128	+	0.567178i	−0.983038	+	0.183400i	$0.941290\pi$
$132$	0.299753	−	0.217783i	0.0260901	−	0.0189556i
$133$	−0.322184	−	3.06538i	−0.0279369	−	0.265802i
$134$	0.572674	+	0.636019i	0.0494715	+	0.0549436i
$135$	−0.913545	+	0.406737i	−0.0786255	+	0.0350063i
$136$	1.68163	−	0.357441i	0.144198	−	0.0306503i
$137$	−15.2063	−	3.23221i	−1.29917	−	0.276146i	−0.494138	−	0.869383i	$-0.664516\pi$
$137$	−15.2063	−	3.23221i	−1.29917	−	0.276146i	−0.805028	+	0.593237i	$0.797850\pi$
$138$	0.377996	+	0.168295i	0.0321772	+	0.0143262i
$139$	−1.60714	−	4.94626i	−0.136316	−	0.419537i	0.859477	−	0.511175i	$-0.170790\pi$
$139$	−1.60714	−	4.94626i	−0.136316	−	0.419537i	−0.995792	+	0.0916384i	$0.970790\pi$
$140$	−0.284773	−	0.876441i	−0.0240677	−	0.0740728i
$141$	5.10835	+	2.27438i	0.430200	+	0.191538i
$142$	−0.0443151	−	0.00941946i	−0.00371884	−	0.000790463i
$143$	1.68336	−	0.357810i	0.140770	−	0.0299216i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	−6.20673	−	6.89327i	−0.515440	−	0.572455i
$146$	−0.273764	−	2.60469i	−0.0226569	−	0.215566i
$147$	−4.97607	+	3.61532i	−0.410419	+	0.298187i
$148$	−0.104163	+	0.991044i	−0.00856214	+	0.0814633i
$149$	3.96634	+	6.86991i	0.324935	+	0.562805i	0.981499	−	0.191466i	$-0.0613241\pi$
$149$	3.96634	+	6.86991i	0.324935	+	0.562805i	−0.656564	+	0.754270i	$0.727991\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	11.6459	+	8.46127i	0.947733	+	0.688569i	0.950270	−	0.311428i	$-0.100807\pi$
$151$	11.6459	+	8.46127i	0.947733	+	0.688569i	−0.00253639	+	0.999997i	$0.500807\pi$
$152$	2.23802	−	2.48558i	0.181528	−	0.201607i
$153$	0.531261	−	1.63505i	0.0429499	−	0.132186i
$154$	0.341446			0.0275145
$155$	−2.76676	−	4.83167i	−0.222232	−	0.388089i
$156$	4.64481			0.371882
$157$	6.15234	−	18.9350i	0.491010	−	1.51117i	−0.332073	−	0.943254i	$-0.607748\pi$
$157$	6.15234	−	18.9350i	0.491010	−	1.51117i	0.823083	−	0.567921i	$-0.192252\pi$
$158$	−0.316665	+	0.351693i	−0.0251925	+	0.0279792i
$159$	−9.03257	−	6.56254i	−0.716329	−	0.520444i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.190653	+	0.330220i	0.0150255	+	0.0260250i
$162$	0.104528	−	0.994522i	0.00821253	−	0.0781370i
$163$	16.5169	−	12.0002i	1.29370	−	0.939928i	0.293827	−	0.955859i	$-0.405071\pi$
$163$	16.5169	−	12.0002i	1.29370	−	0.939928i	0.999873	+	0.0159309i	$0.00507118\pi$
$164$	6.73486e−5	0	0.000640779i	5.25904e−6	0	5.00364e-5i
$165$	−0.247923	−	0.275346i	−0.0193008	−	0.0214357i
$166$	−6.82953	+	3.04070i	−0.530074	+	0.236004i
$167$	1.71143	−	0.363777i	0.132435	−	0.0281499i	−0.141217	−	0.989979i	$-0.545102\pi$
$167$	1.71143	−	0.363777i	0.132435	−	0.0281499i	0.273652	+	0.961829i	$0.411768\pi$
$168$	0.901406	+	0.191600i	0.0695450	+	0.0147822i
$169$	7.83298	+	3.48747i	0.602537	+	0.268267i
$170$	−0.531261	−	1.63505i	−0.0407459	−	0.125403i
$171$	−1.03356	−	3.18097i	−0.0790384	−	0.243255i
$172$	−6.86492	−	3.05646i	−0.523445	−	0.233053i
$173$	18.5883	+	3.95106i	1.41324	+	0.300393i	0.850384	−	0.526162i	$-0.176369\pi$
$173$	18.5883	+	3.95106i	1.41324	+	0.300393i	0.562855	+	0.826555i	$0.309703\pi$
$174$	9.07311	−	1.92855i	0.687830	−	0.146203i
$175$	−0.841873	+	0.374826i	−0.0636396	+	0.0283342i
$176$	0.247923	+	0.275346i	0.0186879	+	0.0207550i
$177$	−1.06488	−	10.1316i	−0.0800411	−	0.761540i
$178$	−11.7620	+	8.54563i	−0.881603	+	0.640522i
$179$	0.698786	−	6.64851i	0.0522297	−	0.496933i	−0.936869	−	0.349680i	$-0.886290\pi$
$179$	0.698786	−	6.64851i	0.0522297	−	0.496933i	0.989099	−	0.147253i	$-0.0470430\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−1.12401	+	1.94684i	−0.0835467	+	0.144707i	−0.904771	−	0.425898i	$-0.859958\pi$
$181$	−1.12401	+	1.94684i	−0.0835467	+	0.144707i	0.821224	+	0.570605i	$0.193291\pi$
$182$	3.46291	+	2.51595i	0.256688	+	0.186495i
$183$	3.68334	−	4.09076i	0.272280	−	0.302398i
$184$	−0.127861	+	0.393517i	−0.00942607	+	0.0290104i
$185$	0.996503			0.0732643
$186$	5.56773	+	0.0197478i	0.408246	+	0.00144798i
$187$	0.636988			0.0465812
$188$	−1.72796	+	5.31810i	−0.126024	+	0.387862i
$189$	0.616633	−	0.684841i	0.0448535	−	0.0498148i
$190$	−2.70590	−	1.96595i	−0.196306	−	0.142625i
$191$	0.853976	−	1.47913i	0.0617916	−	0.107026i	−0.833475	−	0.552558i	$-0.813652\pi$
$191$	0.853976	−	1.47913i	0.0617916	−	0.107026i	0.895266	+	0.445531i	$0.146985\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−1.04443	+	9.93710i	−0.0751798	+	0.715288i	0.890400	+	0.455180i	$0.150425\pi$
$193$	−1.04443	+	9.93710i	−0.0751798	+	0.715288i	−0.965579	+	0.260108i	$0.916242\pi$
$194$	5.40981	−	3.93045i	0.388402	−	0.282190i
$195$	−0.485515	−	4.61937i	−0.0347684	−	0.330800i
$196$	−4.11566	−	4.57090i	−0.293976	−	0.326493i
$197$	−4.58954	+	2.04339i	−0.326991	+	0.145586i	−0.563665	−	0.826003i	$-0.690609\pi$
$197$	−4.58954	+	2.04339i	−0.326991	+	0.145586i	0.236674	+	0.971589i	$0.423943\pi$
$198$	0.362418	−	0.0770344i	0.0257560	−	0.00547460i
$199$	−3.13709	−	0.666809i	−0.222382	−	0.0472688i	0.0953728	−	0.995442i	$-0.469596\pi$
$199$	−3.13709	−	0.666809i	−0.222382	−	0.0472688i	−0.317755	+	0.948173i	$0.602929\pi$
$200$	−0.913545	−	0.406737i	−0.0645974	−	0.0287606i
$201$	0.264471	+	0.813959i	0.0186544	+	0.0574123i
$202$	−0.365246	−	1.12411i	−0.0256986	−	0.0790921i
$203$	7.80905	+	3.47681i	0.548088	+	0.244024i
$204$	1.68163	+	0.357441i	0.117738	+	0.0250259i
$205$	0.000630229	0	0.000133959i	4.40171e−5	0	9.35612e-6i
$206$	2.04764	−	0.911666i	0.142666	−	0.0635188i
$207$	0.276865	+	0.307490i	0.0192434	+	0.0213720i
$208$	0.485515	+	4.61937i	0.0336644	+	0.320295i
$209$	1.00258	−	0.728414i	0.0693496	−	0.0503854i
$210$	0.0963276	−	0.916496i	0.00664724	−	0.0632442i
$211$	−10.1954	−	17.6589i	−0.701877	−	1.21569i	−0.967807	−	0.251695i	$-0.919012\pi$
$211$	−10.1954	−	17.6589i	−0.701877	−	1.21569i	0.265929	−	0.963993i	$-0.414321\pi$
$212$	5.58243	−	9.66906i	0.383403	−	0.664074i
$213$	−0.0366526	−	0.0266297i	−0.00251139	−	0.00182463i
$214$	−1.89640	+	2.10617i	−0.129635	+	0.143975i
$215$	−2.32214	+	7.14680i	−0.158368	+	0.487408i
$216$	1.00000			0.0680414
$217$	4.14030	+	3.03060i	0.281062	+	0.205730i
$218$	−10.9234			−0.739824
$219$	0.809327	−	2.49085i	0.0546892	−	0.168316i
$220$	0.247923	−	0.275346i	0.0167150	−	0.0185638i
$221$	6.46028	+	4.69367i	0.434565	+	0.315730i
$222$	−0.498251	+	0.862996i	−0.0334404	+	0.0579205i
$223$	−3.92153	−	6.79229i	−0.262605	−	0.454846i	0.704328	−	0.709874i	$-0.251248\pi$
$223$	−3.92153	−	6.79229i	−0.262605	−	0.454846i	−0.966933	+	0.255029i	$0.917915\pi$
$224$	−0.0963276	+	0.916496i	−0.00643616	+	0.0612360i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	1.10424	+	10.5062i	0.0734532	+	0.698860i
$227$	−12.7013	−	14.1062i	−0.843014	−	0.936262i	0.155656	−	0.987811i	$-0.450251\pi$
$227$	−12.7013	−	14.1062i	−0.843014	−	0.936262i	−0.998670	+	0.0515492i	$0.983584\pi$
$228$	3.05551	−	1.36040i	0.202356	−	0.0900948i
$229$	22.4387	−	4.76949i	1.48279	−	0.315177i	0.605774	−	0.795636i	$-0.292863\pi$
$229$	22.4387	−	4.76949i	1.48279	−	0.315177i	0.877017	+	0.480459i	$0.159530\pi$
$230$	0.404726	+	0.0860272i	0.0266869	+	0.00567247i
$231$	0.311926	+	0.138879i	0.0205233	+	0.00913754i
$232$	2.86638	+	8.82182i	0.188187	+	0.579181i
$233$	7.21828	+	22.2156i	0.472886	+	1.45539i	0.848788	+	0.528733i	$0.177333\pi$
$233$	7.21828	+	22.2156i	0.472886	+	1.45539i	−0.375903	+	0.926659i	$0.622667\pi$
$234$	4.24325	+	1.88921i	0.277390	+	0.123502i
$235$	5.46959	+	1.16260i	0.356797	+	0.0758394i
$236$	9.96482	−	2.11809i	0.648654	−	0.137876i
$237$	−0.432335	+	0.192488i	−0.0280831	+	0.0125034i
$238$	1.06011	+	1.17738i	0.0687170	+	0.0763180i
$239$	0.230061	+	2.18888i	0.0148814	+	0.141587i	0.999440	−	0.0334697i	$-0.0106557\pi$
$239$	0.230061	+	2.18888i	0.0148814	+	0.141587i	−0.984558	+	0.175057i	$0.943989\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	−0.585214	+	5.56794i	−0.0376970	+	0.358663i	0.959371	+	0.282146i	$0.0910464\pi$
$241$	−0.585214	+	5.56794i	−0.0376970	+	0.358663i	−0.997068	+	0.0765163i	$0.975620\pi$
$242$	−5.43136	−	9.40739i	−0.349141	−	0.604730i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	4.45336	+	3.23556i	0.285097	+	0.207135i
$245$	−4.11566	+	4.57090i	−0.262940	+	0.292024i
$246$	−0.000199102	0	0.000612774i	−1.26943e−5	0	3.90690e-5i
$247$	15.5354			0.988492
$248$	0.562347	+	5.53929i	0.0357090	+	0.351745i
$249$	−7.47585			−0.473763
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	19.2053	−	21.3296i	1.21222	−	1.34631i	0.291271	−	0.956641i	$-0.405922\pi$
$251$	19.2053	−	21.3296i	1.21222	−	1.34631i	0.920954	−	0.389671i	$-0.127411\pi$
$252$	0.745545	+	0.541670i	0.0469649	+	0.0341220i
$253$	−0.0766536	+	0.132768i	−0.00481917	+	0.00834705i
$254$	6.74080	+	11.6754i	0.422955	+	0.732580i
$255$	0.179705	−	1.70978i	0.0112536	−	0.107071i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.830738	−	7.90394i	−0.0518200	−	0.493035i	−0.989395	−	0.145251i	$-0.953601\pi$
$257$	−0.830738	−	7.90394i	−0.0518200	−	0.493035i	0.937575	−	0.347784i	$-0.113066\pi$
$258$	−5.02824	−	5.58443i	−0.313045	−	0.347671i
$259$	−0.838928	+	0.373515i	−0.0521285	+	0.0232091i
$260$	4.54331	−	0.965710i	0.281764	−	0.0598908i
$261$	9.07311	+	1.92855i	0.561611	+	0.119374i
$262$	−5.96308	−	2.65494i	−0.368401	−	0.164022i
$263$	−8.59011	−	26.4377i	−0.529689	−	1.63022i	−0.754853	−	0.655894i	$-0.772292\pi$
$263$	−8.59011	−	26.4377i	−0.529689	−	1.63022i	0.225164	−	0.974321i	$-0.427708\pi$
$264$	0.114495	+	0.352381i	0.00704671	+	0.0216875i
$265$	−10.1996	−	4.54116i	−0.626557	−	0.278961i
$266$	3.01491	+	0.640839i	0.184856	+	0.0392923i
$267$	−14.2210	+	3.02276i	−0.870310	+	0.184990i
$268$	−0.781855	+	0.348104i	−0.0477594	+	0.0212639i
$269$	−3.48849	−	3.87436i	−0.212697	−	0.236224i	0.627350	−	0.778737i	$-0.284139\pi$
$269$	−3.48849	−	3.87436i	−0.212697	−	0.236224i	−0.840047	+	0.542514i	$0.817473\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	−1.88801	+	1.37172i	−0.114688	+	0.0833259i	−0.643651	−	0.765319i	$-0.722581\pi$
$271$	−1.88801	+	1.37172i	−0.114688	+	0.0833259i	0.528963	+	0.848645i	$0.322581\pi$
$272$	−0.179705	+	1.70978i	−0.0108962	+	0.103671i
$273$	2.14020	+	3.70693i	0.129531	+	0.224354i
$274$	7.77303	−	13.4633i	0.469586	−	0.813347i
$275$	−0.299753	−	0.217783i	−0.0180758	−	0.0131328i
$276$	−0.276865	+	0.307490i	−0.0166653	+	0.0185087i
$277$	0.575583	−	1.77146i	0.0345834	−	0.106437i	−0.932275	−	0.361751i	$-0.882179\pi$
$277$	0.575583	−	1.77146i	0.0345834	−	0.106437i	0.966858	+	0.255314i	$0.0821790\pi$
$278$	5.20081			0.311924
$279$	5.07834	+	2.28264i	0.304032	+	0.136658i
$280$	0.921544			0.0550728
$281$	−0.431720	+	1.32870i	−0.0257543	+	0.0792635i	−0.963108	−	0.269117i	$-0.913268\pi$
$281$	−0.431720	+	1.32870i	−0.0257543	+	0.0792635i	0.937353	+	0.348380i	$0.113268\pi$
$282$	−3.74163	+	4.15550i	−0.222811	+	0.247457i
$283$	0.448215	+	0.325647i	0.0266436	+	0.0193577i	0.601027	−	0.799228i	$-0.294758\pi$
$283$	0.448215	+	0.325647i	0.0266436	+	0.0193577i	−0.574384	+	0.818586i	$0.694758\pi$
$284$	0.0226525	−	0.0392354i	0.00134418	−	0.00232819i
$285$	−1.67234	−	2.89657i	−0.0990607	−	0.171578i
$286$	−0.179891	+	1.71154i	−0.0106372	+	0.101206i
$287$	−0.000480361	0	0.000349003i	−2.83548e−5	0	2.06010e-5i
$288$	0.104528	+	0.994522i	0.00615940	+	0.0586028i
$289$	−9.39751	−	10.4370i	−0.552795	−	0.613941i
$290$	8.47387	−	3.77281i	0.497603	−	0.221547i
$291$	6.54076	−	1.39028i	0.383426	−	0.0814998i
$292$	2.56180	+	0.544528i	0.149918	+	0.0318661i
$293$	9.02088	+	4.01635i	0.527005	+	0.234638i	0.652952	−	0.757399i	$-0.273530\pi$
$293$	9.02088	+	4.01635i	0.527005	+	0.234638i	−0.125947	+	0.992037i	$0.540197\pi$
$294$	−1.90069	−	5.84972i	−0.110850	−	0.341162i
$295$	−3.14809	−	9.68883i	−0.183289	−	0.564105i
$296$	−0.910350	−	0.405314i	−0.0529130	−	0.0235584i
$297$	0.362418	+	0.0770344i	0.0210296	+	0.00446999i
$298$	−7.75934	+	1.64930i	−0.449486	+	0.0955413i
$299$	−1.75572	+	0.781697i	−0.101536	+	0.0452067i
$300$	−0.669131	−	0.743145i	−0.0386323	−	0.0429055i
$301$	−0.723863	−	6.88709i	−0.0417228	−	0.396965i
$302$	−11.6459	+	8.46127i	−0.670149	+	0.486891i
$303$	0.123548	−	1.17548i	0.00709767	−	0.0675298i
$304$	1.67234	+	2.89657i	0.0959151	+	0.166130i
$305$	2.75233	−	4.76718i	0.157598	−	0.272968i
$306$	1.39086	+	1.01052i	0.0795101	+	0.0577675i
$307$	12.0228	−	13.3527i	0.686179	−	0.762079i	−0.294933	−	0.955518i	$-0.595297\pi$
$307$	12.0228	−	13.3527i	0.686179	−	0.762079i	0.981112	+	0.193439i	$0.0619641\pi$
$308$	−0.105513	+	0.324734i	−0.00601214	+	0.0185035i
$309$	2.24142			0.127510
$310$	5.45017	−	1.13828i	0.309549	−	0.0646499i
$311$	−16.2575			−0.921876			−0.460938	−	0.887432i	$-0.652487\pi$
$311$	−16.2575			−0.921876			−0.460938	+	0.887432i	$0.652487\pi$
$312$	−1.43533	+	4.41748i	−0.0812593	+	0.250090i
$313$	−14.3041	+	15.8863i	−0.808513	+	0.897945i	−0.996446	−	0.0842370i	$-0.973155\pi$
$313$	−14.3041	+	15.8863i	−0.808513	+	0.897945i	0.187932	+	0.982182i	$0.439821\pi$
$314$	16.1070	+	11.7025i	0.908973	+	0.660408i
$315$	0.460772	−	0.798081i	0.0259616	−	0.0449668i
$316$	−0.236625	−	0.409846i	−0.0133112	−	0.0230556i
$317$	−0.512512	+	4.87622i	−0.0287855	+	0.273876i	0.970656	+	0.240471i	$0.0773018\pi$
$317$	−0.512512	+	4.87622i	−0.0287855	+	0.273876i	−0.999442	+	0.0334052i	$0.989365\pi$
$318$	9.03257	−	6.56254i	0.506521	−	0.368009i
$319$	0.359246	+	3.41800i	0.0201139	+	0.191371i
$320$	0.669131	+	0.743145i	0.0374055	+	0.0415431i
$321$	−2.58911	+	1.15274i	−0.144510	+	0.0643399i
$322$	−0.372973	+	0.0792779i	−0.0207850	+	0.00441798i
$323$	5.62450	+	1.19552i	0.312955	+	0.0665207i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−1.43533	−	4.41748i	−0.0796175	−	0.245038i
$326$	6.30888	+	19.4167i	0.349416	+	1.07539i
$327$	−9.97900	−	4.44294i	−0.551840	−	0.245695i
$328$	−0.000630229	0	0.000133959i	−3.47986e−5	0	7.39666e-6i
$329$	−5.04047	+	1.07138i	−0.277890	+	0.0590673i
$330$	0.338482	−	0.150702i	0.0186328	−	0.00829587i
$331$	−2.96686	−	3.29503i	−0.163073	−	0.181111i	0.656070	−	0.754700i	$-0.272218\pi$
$331$	−2.96686	−	3.29503i	−0.163073	−	0.181111i	−0.819144	+	0.573589i	$0.805551\pi$
$332$	−0.781439	−	7.43490i	−0.0428870	−	0.408043i
$333$	−0.806187	+	0.585729i	−0.0441788	+	0.0320978i
$334$	−0.182890	+	1.74008i	−0.0100073	+	0.0952131i
$335$	0.427924	+	0.741186i	0.0233800	+	0.0404953i
$336$	−0.460772	+	0.798081i	−0.0251372	+	0.0435389i
$337$	13.4262	+	9.75472i	0.731373	+	0.531374i	0.889998	−	0.455965i	$-0.150706\pi$
$337$	13.4262	+	9.75472i	0.731373	+	0.531374i	−0.158625	+	0.987339i	$0.550706\pi$
$338$	−5.73730	+	6.37192i	−0.312068	+	0.346587i
$339$	−3.26447	+	10.0470i	−0.177302	+	0.545678i
$340$	1.71920			0.0932365
$341$	−0.222911	+	2.05086i	−0.0120713	+	0.111060i
$342$	3.34467			0.180859
$343$	3.74498	−	11.5259i	0.202210	−	0.622338i
$344$	5.02824	−	5.58443i	0.271105	−	0.301092i
$345$	0.334745	+	0.243207i	0.0180221	+	0.0130938i
$346$	−9.50177	+	16.4575i	−0.510818	+	0.884763i
$347$	−15.7122	−	27.2144i	−0.843477	−	1.46095i	−0.886937	−	0.461890i	$-0.847171\pi$
$347$	−15.7122	−	27.2144i	−0.843477	−	1.46095i	0.0434600	−	0.999055i	$-0.486162\pi$
$348$	−0.969586	+	9.22499i	−0.0519752	+	0.494511i
$349$	−19.9585	+	14.5007i	−1.06835	+	0.776204i	−0.975615	−	0.219487i	$-0.929562\pi$
$349$	−19.9585	+	14.5007i	−1.06835	+	0.776204i	−0.0927371	+	0.995691i	$0.529562\pi$
$350$	−0.0963276	−	0.916496i	−0.00514893	−	0.0489888i
$351$	3.10798	+	3.45177i	0.165892	+	0.184242i
$352$	−0.338482	+	0.150702i	−0.0180412	+	0.00803244i
$353$	−21.8452	+	4.64334i	−1.16270	+	0.247140i	−0.748556	−	0.663071i	$-0.769253\pi$
$353$	−21.8452	+	4.64334i	−1.16270	+	0.247140i	−0.414145	+	0.910211i	$0.635919\pi$
$354$	9.96482	+	2.11809i	0.529624	+	0.112575i
$355$	−0.0413883	−	0.0184272i	−0.00219666	−	0.000978016i
$356$	−4.49270	−	13.8271i	−0.238113	−	0.732836i
$357$	0.489581	+	1.50677i	0.0259114	+	0.0797469i
$358$	6.10717	+	2.71909i	0.322774	+	0.143708i
$359$	−2.27240	−	0.483013i	−0.119933	−	0.0254925i	0.147554	−	0.989054i	$-0.452860\pi$
$359$	−2.27240	−	0.483013i	−0.119933	−	0.0254925i	−0.267487	+	0.963561i	$0.586193\pi$
$360$	0.978148	−	0.207912i	0.0515529	−	0.0109579i
$361$	−7.13768	+	3.17790i	−0.375667	+	0.167258i
$362$	−1.50421	−	1.67060i	−0.0790597	−	0.0878047i
$363$	−1.13546	−	10.8032i	−0.0595964	−	0.567022i
$364$	−3.46291	+	2.51595i	−0.181506	+	0.131872i
$365$	0.273764	−	2.60469i	0.0143295	−	0.136336i
$366$	2.75233	+	4.76718i	0.143867	+	0.249184i
$367$	−11.0794	+	19.1901i	−0.578340	+	1.00171i	0.417330	+	0.908755i	$0.362966\pi$
$367$	−11.0794	+	19.1901i	−0.578340	+	1.00171i	−0.995670	+	0.0929594i	$0.970367\pi$
$368$	−0.334745	−	0.243207i	−0.0174498	−	0.0126780i
$369$	−0.000431126	0	0.000478814i	−2.24435e−5	0	2.49261e-5i
$370$	−0.307936	+	0.947730i	−0.0160088	+	0.0492701i
$371$	10.2889			0.534174
$372$	−1.73930	+	5.28912i	−0.0901787	+	0.274228i
$373$	8.27322			0.428371			0.214185	−	0.976793i	$-0.431290\pi$
$373$	8.27322			0.428371			0.214185	+	0.976793i	$0.431290\pi$
$374$	−0.196840	+	0.605812i	−0.0101784	+	0.0313258i
$375$	−0.669131	+	0.743145i	−0.0345538	+	0.0383758i
$376$	−4.52385	−	3.28677i	−0.233300	−	0.169502i
$377$	−21.5422	+	37.3121i	−1.10948	+	1.92167i
$378$	0.460772	+	0.798081i	0.0236996	+	0.0410488i
$379$	−1.50198	+	14.2904i	−0.0771514	+	0.734046i	0.885745	+	0.464173i	$0.153648\pi$
$379$	−1.50198	+	14.2904i	−0.0771514	+	0.734046i	−0.962896	+	0.269873i	$0.913018\pi$
$380$	2.70590	−	1.96595i	0.138810	−	0.100851i
$381$	1.40921	+	13.4077i	0.0721960	+	0.686899i
$382$	1.14284	+	1.26926i	0.0584730	+	0.0649408i
$383$	−28.7128	+	12.7838i	−1.46716	+	0.653220i	−0.975984	−	0.217842i	$-0.930098\pi$
$383$	−28.7128	+	12.7838i	−1.46716	+	0.653220i	−0.491173	+	0.871062i	$0.663432\pi$
$384$	−0.978148	+	0.207912i	−0.0499159	+	0.0106099i
$385$	0.333985	+	0.0709906i	0.0170214	+	0.00361802i
$386$	−9.12800	−	4.06405i	−0.464603	−	0.206854i
$387$	−2.32214	−	7.14680i	−0.118041	−	0.363292i
$388$	2.06636	+	6.35961i	0.104904	+	0.322860i
$389$	−7.97142	−	3.54911i	−0.404167	−	0.179947i	0.194577	−	0.980887i	$-0.437667\pi$
$389$	−7.97142	−	3.54911i	−0.404167	−	0.179947i	−0.598744	+	0.800940i	$0.704333\pi$
$390$	4.54331	+	0.965710i	0.230059	+	0.0489006i
$391$	−0.695804	+	0.147898i	−0.0351883	+	0.00747951i
$392$	5.61900	−	2.50174i	0.283802	−	0.126357i
$393$	−4.36769	−	4.85081i	−0.220321	−	0.244691i
$394$	−0.525138	−	4.99635i	−0.0264561	−	0.251713i
$395$	−0.382867	+	0.278169i	−0.0192641	+	0.0139962i
$396$	−0.0387294	+	0.368485i	−0.00194622	+	0.0185171i
$397$	−8.36582	−	14.4900i	−0.419868	−	0.727233i	0.576058	−	0.817409i	$-0.304590\pi$
$397$	−8.36582	−	14.4900i	−0.419868	−	0.727233i	−0.995926	+	0.0901759i	$0.971257\pi$
$398$	1.60359	−	2.77749i	0.0803805	−	0.139223i
$399$	2.49360	+	1.81171i	0.124836	+	0.0906989i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	8.53878	−	26.2797i	0.426406	−	1.31234i	−0.475235	−	0.879859i	$-0.657637\pi$
$401$	8.53878	−	26.2797i	0.426406	−	1.31234i	0.901641	−	0.432485i	$-0.142363\pi$
$402$	−0.855847			−0.0426858
$403$	−17.3726	+	19.1571i	−0.865390	+	0.954284i
$404$	1.18196			0.0588047
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	−5.71977	+	6.35245i	−0.283868	+	0.315267i
$407$	−0.298705	−	0.217022i	−0.0148062	−	0.0107574i
$408$	−0.859598	+	1.48887i	−0.0425565	+	0.0737100i
$409$	4.42506	+	7.66443i	0.218805	+	0.378981i	0.954443	−	0.298394i	$-0.0964508\pi$
$409$	4.42506	+	7.66443i	0.218805	+	0.378981i	−0.735638	+	0.677375i	$0.763117\pi$
$410$	−6.73486e−5	0	0.000640779i	−3.32611e−6	0	3.16458e-5i
$411$	12.5770	−	9.13775i	0.620379	−	0.450732i
$412$	0.234292	+	2.22914i	0.0115427	+	0.109822i
$413$	6.28191	+	6.97677i	0.309113	+	0.343305i
$414$	−0.377996	+	0.168295i	−0.0185775	+	0.00827123i
$415$	−7.31249	+	1.55432i	−0.358956	+	0.0762984i
$416$	−4.54331	−	0.965710i	−0.222754	−	0.0473478i
$417$	4.75118	+	2.11536i	0.232666	+	0.103590i
$418$	0.382950	+	1.17860i	0.0187307	+	0.0576471i
$419$	−8.40334	−	25.8628i	−0.410530	−	1.26348i	−0.916188	−	0.400748i	$-0.868750\pi$
$419$	−8.40334	−	25.8628i	−0.410530	−	1.26348i	0.505658	−	0.862734i	$-0.331250\pi$
$420$	0.841873	+	0.374826i	0.0410792	+	0.0182896i
$421$	−7.12837	−	1.51518i	−0.347416	−	0.0738455i	0.0308991	−	0.999523i	$-0.490163\pi$
$421$	−7.12837	−	1.51518i	−0.347416	−	0.0738455i	−0.378315	+	0.925677i	$0.623496\pi$
$422$	19.9451	−	4.23947i	0.970914	−	0.206374i
$423$	−5.10835	+	2.27438i	−0.248376	+	0.110584i
$424$	7.47075	+	8.29711i	0.362812	+	0.402943i
$425$	−0.179705	−	1.70978i	−0.00871697	−	0.0829365i
$426$	0.0366526	−	0.0266297i	0.00177582	−	0.00129021i
$427$	−0.530251	+	5.04500i	−0.0256606	+	0.244145i
$428$	−1.41707	−	2.45443i	−0.0684964	−	0.118639i
$429$	−0.860486	+	1.49041i	−0.0415447	+	0.0719574i
$430$	−6.07943	−	4.41697i	−0.293176	−	0.213005i
$431$	2.89536	−	3.21562i	0.139465	−	0.154891i	−0.669366	−	0.742933i	$-0.733434\pi$
$431$	2.89536	−	3.21562i	0.139465	−	0.154891i	0.808831	+	0.588042i	$0.200101\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	35.8255			1.72166			0.860831	−	0.508891i	$-0.169945\pi$
$433$	35.8255			1.72166			0.860831	+	0.508891i	$0.169945\pi$
$434$	−4.16169	+	3.00115i	−0.199767	+	0.144060i
$435$	9.27581			0.444741
$436$	3.37551	−	10.3887i	0.161658	−	0.497531i
$437$	−0.926022	+	1.02845i	−0.0442977	+	0.0491975i
$438$	2.11884	+	1.53943i	0.101242	+	0.0735568i
$439$	−16.8055	+	29.1081i	−0.802085	+	1.38925i	0.116157	+	0.993231i	$0.462942\pi$
$439$	−16.8055	+	29.1081i	−0.802085	+	1.38925i	−0.918242	+	0.396021i	$0.870391\pi$
$440$	0.185257	+	0.320875i	0.00883180	+	0.0152971i
$441$	0.642929	−	6.11706i	0.0306157	−	0.291289i
$442$	−6.46028	+	4.69367i	−0.307284	+	0.223255i
$443$	−4.09689	−	38.9793i	−0.194649	−	1.85196i	−0.460139	−	0.887847i	$-0.652200\pi$
$443$	−4.09689	−	38.9793i	−0.194649	−	1.85196i	0.265490	−	0.964114i	$-0.414466\pi$
$444$	−0.666790	−	0.740546i	−0.0316445	−	0.0351447i
$445$	−13.2818	+	5.91342i	−0.629616	+	0.280323i
$446$	7.67168	−	1.63066i	0.363264	−	0.0772142i
$447$	−7.75934	−	1.64930i	−0.367004	−	0.0780091i
$448$	−0.841873	−	0.374826i	−0.0397747	−	0.0177089i
$449$	−5.92737	−	18.2426i	−0.279730	−	0.860921i	−0.987929	−	0.154908i	$-0.950492\pi$
$449$	−5.92737	−	18.2426i	−0.279730	−	0.860921i	0.708199	−	0.706013i	$-0.249508\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−0.000218087	0	9.70986e-5i	−1.02693e−5	0	4.57219e-6i
$452$	−10.3332	−	2.19639i	−0.486033	−	0.103309i
$453$	−14.0806	+	2.99293i	−0.661565	+	0.140620i
$454$	17.3407	−	7.72058i	0.813840	−	0.362345i
$455$	2.86415	+	3.18096i	0.134273	+	0.149126i
$456$	0.349614	+	3.32635i	0.0163722	+	0.155771i
$457$	5.00943	−	3.63957i	0.234331	−	0.170252i	−0.464423	−	0.885614i	$-0.653738\pi$
$457$	5.00943	−	3.63957i	0.234331	−	0.170252i	0.698754	+	0.715362i	$0.253738\pi$
$458$	−2.39788	+	22.8143i	−0.112046	+	1.06604i
$459$	0.859598	+	1.48887i	0.0401226	+	0.0694944i
$460$	−0.206884	+	0.358334i	−0.00964602	+	0.0167074i
$461$	16.9355	+	12.3044i	0.788765	+	0.573071i	0.907597	−	0.419843i	$-0.137915\pi$
$461$	16.9355	+	12.3044i	0.788765	+	0.573071i	−0.118832	+	0.992914i	$0.537915\pi$
$462$	−0.228472	+	0.253744i	−0.0106295	+	0.0118052i
$463$	2.32014	−	7.14067i	0.107826	−	0.331855i	−0.882557	−	0.470205i	$-0.844180\pi$
$463$	2.32014	−	7.14067i	0.107826	−	0.331855i	0.990383	+	0.138350i	$0.0441799\pi$
$464$	−9.27581			−0.430618
$465$	5.44196	+	1.17691i	0.252365	+	0.0545780i
$466$	−23.3589			−1.08208
$467$	−4.22847	+	13.0139i	−0.195670	+	0.602211i	0.804298	+	0.594226i	$0.202542\pi$
$467$	−4.22847	+	13.0139i	−0.195670	+	0.602211i	−0.999968	+	0.00798479i	$0.997458\pi$
$468$	−3.10798	+	3.45177i	−0.143667	+	0.159558i
$469$	−0.638073	−	0.463587i	−0.0294635	−	0.0214065i
$470$	−2.79589	+	4.84262i	−0.128965	+	0.223374i
$471$	9.95470	+	17.2420i	0.458688	+	0.794472i
$472$	−1.06488	+	10.1316i	−0.0490149	+	0.466346i
$473$	2.25252	−	1.63655i	0.103571	−	0.0752488i
$474$	−0.0494680	−	0.470657i	−0.00227214	−	0.0216180i
$475$	−2.23802	−	2.48558i	−0.102688	−	0.114046i
$476$	−1.44734	+	0.644399i	−0.0663389	+	0.0295360i
$477$	10.9209	−	2.32131i	0.500033	−	0.106285i
$478$	−2.15284	−	0.457601i	−0.0984688	−	0.0209302i
$479$	−29.2300	−	13.0140i	−1.33555	−	0.594626i	−0.390216	−	0.920724i	$-0.627600\pi$
$479$	−29.2300	−	13.0140i	−1.33555	−	0.594626i	−0.945336	+	0.326098i	$0.894266\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−1.43031	−	4.40203i	−0.0652163	−	0.200715i
$482$	−5.11459	−	2.27716i	−0.232963	−	0.103722i
$483$	−0.372973	−	0.0792779i	−0.0169709	−	0.00360727i
$484$	10.6253	−	2.25849i	0.482970	−	0.102658i
$485$	6.10878	−	2.71980i	0.277385	−	0.123500i
$486$	0.669131	+	0.743145i	0.0303524	+	0.0337097i
$487$	1.65397	+	15.7365i	0.0749485	+	0.713087i	0.965887	+	0.258964i	$0.0833809\pi$
$487$	1.65397	+	15.7365i	0.0749485	+	0.713087i	−0.890939	+	0.454124i	$0.849952\pi$
$488$	−4.45336	+	3.23556i	−0.201594	+	0.146467i
$489$	−2.13405	+	20.3041i	−0.0965050	+	0.918184i
$490$	−3.07538	−	5.32671i	−0.138931	−	0.240636i
$491$	7.79822	−	13.5069i	0.351929	−	0.609558i	−0.634659	−	0.772793i	$-0.718859\pi$
$491$	7.79822	−	13.5069i	0.351929	−	0.609558i	0.986587	+	0.163234i	$0.0521926\pi$
$492$	−0.000521256	0	0.000378715i	−2.35001e−5	0	1.70738e-5i
$493$	−10.6706	+	11.8509i	−0.480579	+	0.533737i
$494$	−4.80069	+	14.7750i	−0.215993	+	0.664759i
$495$	0.370515			0.0166534
$496$	−5.44196	−	1.17691i	−0.244351	−	0.0528449i
$497$	0.0417507			0.00187277
$498$	2.31016	−	7.10996i	0.103521	−	0.318605i
$499$	19.1298	−	21.2457i	0.856365	−	0.951090i	−0.142887	−	0.989739i	$-0.545639\pi$
$499$	19.1298	−	21.2457i	0.856365	−	0.951090i	0.999253	+	0.0386489i	$0.0123054\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−0.874834	+	1.51526i	−0.0390847	+	0.0676967i
$502$	14.3509	+	24.8565i	0.640512	+	1.10940i
$503$	−2.84444	+	27.0631i	−0.126827	+	1.20668i	0.727189	+	0.686437i	$0.240826\pi$
$503$	−2.84444	+	27.0631i	−0.126827	+	1.20668i	−0.854017	+	0.520246i	$0.825840\pi$
$504$	−0.745545	+	0.541670i	−0.0332092	+	0.0241279i
$505$	−0.123548	−	1.17548i	−0.00549783	−	0.0523084i
$506$	−0.102583	−	0.113930i	−0.00456035	−	0.00506478i
$507$	−7.83298	+	3.48747i	−0.347875	+	0.154884i
$508$	−13.1870	+	2.80298i	−0.585078	+	0.124362i
$509$	−25.3145	−	5.38076i	−1.12204	−	0.238498i	−0.390708	−	0.920515i	$-0.627770\pi$
$509$	−25.3145	−	5.38076i	−1.12204	−	0.238498i	−0.731336	+	0.682017i	$0.761103\pi$
$510$	1.57056	+	0.699260i	0.0695458	+	0.0309638i
$511$	0.745830	+	2.29543i	0.0329936	+	0.101544i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	3.05551	+	1.36040i	0.134904	+	0.0600632i
$514$	7.77381	+	1.65237i	0.342888	+	0.0728831i
$515$	2.19244	−	0.466017i	0.0966103	−	0.0205351i
$516$	6.86492	−	3.05646i	0.302211	−	0.134553i
$517$	−1.38633	−	1.53968i	−0.0609708	−	0.0677149i
$518$	−0.0959907	−	0.913291i	−0.00421759	−	0.0401277i
$519$	−15.3742	+	11.1700i	−0.674852	+	0.490309i
$520$	−0.485515	+	4.61937i	−0.0212912	+	0.202573i
$521$	−17.1136	−	29.6416i	−0.749759	−	1.29862i	−0.947938	−	0.318455i	$-0.896836\pi$
$521$	−17.1136	−	29.6416i	−0.749759	−	1.29862i	0.198179	−	0.980166i	$-0.436497\pi$
$522$	−4.63790	+	8.03308i	−0.202995	+	0.351599i
$523$	31.3818	+	22.8002i	1.37223	+	0.996983i	0.997559	+	0.0698241i	$0.0222438\pi$
$523$	31.3818	+	22.8002i	1.37223	+	0.996983i	0.374669	+	0.927158i	$0.377756\pi$
$524$	4.36769	−	4.85081i	0.190803	−	0.211909i
$525$	0.284773	−	0.876441i	0.0124285	−	0.0382510i
$526$	27.7982			1.21206
$527$	−7.76388	+	5.59883i	−0.338200	+	0.243889i
$528$	−0.370515			−0.0161246
$529$	−7.05449	+	21.7115i	−0.306717	+	0.943977i
$530$	7.47075	−	8.29711i	0.324509	−	0.360404i
$531$	8.24181	+	5.98802i	0.357664	+	0.259858i
$532$	−1.54113	+	2.66932i	−0.0668166	+	0.115730i
$533$	−0.00149635	−	0.00259175i	−6.48139e−5	−	0.000112261i
$534$	1.51971	−	14.4590i	0.0657642	−	0.625704i
$535$	−2.29286	+	1.66586i	−0.0991290	+	0.0720214i
$536$	−0.0894604	−	0.851159i	−0.00386410	−	0.0367645i
$537$	4.47322	+	4.96802i	0.193034	+	0.214386i
$538$	4.76273	−	2.12050i	0.205336	−	0.0914215i
$539$	2.22915	−	0.473820i	0.0960162	−	0.0204089i
$540$	0.978148	+	0.207912i	0.0420928	+	0.00894709i
$541$	−16.2101	−	7.21721i	−0.696928	−	0.310292i	0.0275208	−	0.999621i	$-0.491239\pi$
$541$	−16.2101	−	7.21721i	−0.696928	−	0.310292i	−0.724448	+	0.689329i	$0.757905\pi$
$542$	−0.721154	−	2.21948i	−0.0309762	−	0.0953350i
$543$	−0.694674	−	2.13799i	−0.0298113	−	0.0917498i
$544$	−1.57056	−	0.699260i	−0.0673374	−	0.0299805i
$545$	−10.6847	−	2.27110i	−0.457681	−	0.0972831i
$546$	−4.18686	+	0.889945i	−0.179181	+	0.0380861i
$547$	−24.7705	+	11.0286i	−1.05911	+	0.471547i	−0.860986	−	0.508629i	$-0.830152\pi$
$547$	−24.7705	+	11.0286i	−1.05911	+	0.471547i	−0.198126	+	0.980176i	$0.563486\pi$
$548$	10.4023	+	11.5530i	0.444366	+	0.493519i
$549$	0.575394	+	5.47451i	0.0245572	+	0.233646i
$550$	0.299753	−	0.217783i	0.0127815	−	0.00928631i
$551$	−3.24295	+	30.8546i	−0.138154	+	1.31445i
$552$	−0.206884	−	0.358334i	−0.00880557	−	0.0152517i
$553$	0.218060	−	0.377691i	0.00927285	−	0.0160611i
$554$	1.50690	+	1.09482i	0.0640219	+	0.0465146i
$555$	−0.666790	+	0.740546i	−0.0283037	+	0.0314344i
$556$	−1.60714	+	4.94626i	−0.0681579	+	0.209768i
$557$	13.2100			0.559727			0.279863	−	0.960040i	$-0.409711\pi$
$557$	13.2100			0.559727			0.279863	+	0.960040i	$0.409711\pi$
$558$	−3.74021	+	4.12442i	−0.158336	+	0.174600i
$559$	34.9039			1.47628
$560$	−0.284773	+	0.876441i	−0.0120338	+	0.0370364i
$561$	−0.426228	+	0.473374i	−0.0179954	+	0.0199859i
$562$	−1.13026	−	0.821180i	−0.0476771	−	0.0346394i
$563$	−10.4904	+	18.1698i	−0.442116	+	0.765767i	−0.997846	−	0.0655957i	$-0.979105\pi$
$563$	−10.4904	+	18.1698i	−0.442116	+	0.765767i	0.555731	+	0.831362i	$0.312439\pi$
$564$	−2.79589	−	4.84262i	−0.117728	−	0.203911i
$565$	−1.10424	+	10.5062i	−0.0464559	+	0.441998i
$566$	−0.448215	+	0.325647i	−0.0188399	+	0.0136880i
$567$	0.0963276	+	0.916496i	0.00404538	+	0.0384892i
$568$	0.0303150	+	0.0336682i	0.00127199	+	0.00141269i
$569$	−5.14819	+	2.29212i	−0.215823	+	0.0960907i	−0.511801	−	0.859104i	$-0.671021\pi$
$569$	−5.14819	+	2.29212i	−0.215823	+	0.0960907i	0.295977	+	0.955195i	$0.404355\pi$
$570$	3.27158	−	0.695397i	0.137032	−	0.0291270i
$571$	14.3860	+	3.05784i	0.602035	+	0.127966i	0.498839	−	0.866695i	$-0.333760\pi$
$571$	14.3860	+	3.05784i	0.602035	+	0.127966i	0.103196	+	0.994661i	$0.467093\pi$
$572$	−1.57219	−	0.699982i	−0.0657364	−	0.0292677i
$573$	0.527786	+	1.62436i	0.0220486	+	0.0678586i
$574$	−0.000183482	0	0.000564698i	−7.65837e−6	0	2.35700e-5i
$575$	0.377996	+	0.168295i	0.0157635	+	0.00701837i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	30.0162	−	6.38014i	1.24959	−	0.265609i	0.464826	−	0.885402i	$-0.346117\pi$
$577$	30.0162	−	6.38014i	1.24959	−	0.265609i	0.784765	+	0.619793i	$0.212784\pi$
$578$	12.8302	−	5.71236i	0.533664	−	0.237603i
$579$	−6.68584	−	7.42538i	−0.277854	−	0.308588i
$580$	0.969586	+	9.22499i	0.0402599	+	0.383047i
$581$	5.57358	−	4.04944i	0.231231	−	0.167999i
$582$	−0.698970	+	6.65026i	−0.0289732	+	0.275662i
$583$	2.06838	+	3.58253i	0.0856633	+	0.148373i
$584$	−1.30952	+	2.26815i	−0.0541882	+	0.0938568i
$585$	3.75773	+	2.73015i	0.155363	+	0.112878i
$586$	−6.60738	+	7.33824i	−0.272949	+	0.303140i
$587$	1.17613	−	3.61975i	0.0485440	−	0.149403i	−0.923846	−	0.382764i	$-0.874972\pi$
$587$	1.17613	−	3.61975i	0.0485440	−	0.149403i	0.972390	+	0.233361i	$0.0749723\pi$
$588$	6.15076			0.253653
$589$	−5.81740	+	17.6904i	−0.239702	+	0.728920i
$590$	10.1874			0.419410
$591$	1.55246	−	4.77799i	0.0638598	−	0.196540i
$592$	0.666790	−	0.740546i	0.0274049	−	0.0304362i
$593$	10.2631	+	7.45661i	0.421457	+	0.306206i	0.778224	−	0.627987i	$-0.216121\pi$
$593$	10.2631	+	7.45661i	0.421457	+	0.306206i	−0.356767	+	0.934193i	$0.616121\pi$
$594$	−0.185257	+	0.320875i	−0.00760121	+	0.0131657i
$595$	0.792158	+	1.37206i	0.0324753	+	0.0562489i
$596$	0.829191	−	7.88923i	0.0339650	−	0.323155i
$597$	2.59466	−	1.88513i	0.106192	−	0.0771532i
$598$	−0.200891	−	1.91135i	−0.00821503	−	0.0781607i
$599$	1.07720	+	1.19635i	0.0440133	+	0.0488817i	0.764749	−	0.644328i	$-0.222863\pi$
$599$	1.07720	+	1.19635i	0.0440133	+	0.0488817i	−0.720736	+	0.693209i	$0.756196\pi$
$600$	0.913545	−	0.406737i	0.0372953	−	0.0166050i
$601$	−27.4057	+	5.82526i	−1.11790	+	0.237617i	−0.729572	−	0.683904i	$-0.760281\pi$
$601$	−27.4057	+	5.82526i	−1.11790	+	0.237617i	−0.388329	+	0.921521i	$0.626948\pi$
$602$	6.77370	+	1.43979i	0.276075	+	0.0586816i
$603$	−0.781855	−	0.348104i	−0.0318396	−	0.0141759i
$604$	−4.44835	−	13.6906i	−0.181001	−	0.557064i
$605$	−3.35676	−	10.3311i	−0.136472	−	0.420017i
$606$	1.07977	+	0.480746i	0.0438628	+	0.0195290i
$607$	−9.41360	−	2.00092i	−0.382086	−	0.0812149i	0.0128645	−	0.999917i	$-0.495905\pi$
$607$	−9.41360	−	2.00092i	−0.382086	−	0.0812149i	−0.394951	+	0.918702i	$0.629238\pi$
$608$	−3.27158	+	0.695397i	−0.132680	+	0.0282021i
$609$	−7.80905	+	3.47681i	−0.316439	+	0.140888i
$610$	3.68334	+	4.09076i	0.149134	+	0.165630i
$611$	−2.71489	−	25.8305i	−0.109833	−	1.04499i
$612$	−1.39086	+	1.01052i	−0.0562222	+	0.0408478i
$613$	2.18186	−	20.7590i	0.0881246	−	0.838449i	−0.857783	−	0.514012i	$-0.828159\pi$
$613$	2.18186	−	20.7590i	0.0881246	−	0.838449i	0.945907	−	0.324437i	$-0.105175\pi$
$614$	8.98392	+	15.5606i	0.362561	+	0.627975i
$615$	−0.000322154	0	0.000557987i	−1.29905e−5	0	2.25002e-5i
$616$	−0.276236	−	0.200697i	−0.0111298	−	0.00808631i
$617$	−6.90546	+	7.66929i	−0.278003	+	0.308754i	−0.865935	−	0.500157i	$-0.833276\pi$
$617$	−6.90546	+	7.66929i	−0.278003	+	0.308754i	0.587932	+	0.808911i	$0.299942\pi$
$618$	−0.692636	+	2.13171i	−0.0278619	+	0.0857501i
$619$	−43.0614			−1.73079			−0.865393	−	0.501094i	$-0.832931\pi$
$619$	−43.0614			−1.73079			−0.865393	+	0.501094i	$0.832931\pi$
$620$	−0.601626	+	5.53516i	−0.0241619	+	0.222298i
$621$	−0.413768			−0.0166039
$622$	5.02383	−	15.4618i	0.201437	−	0.619961i
$623$	8.96504	−	9.95669i	0.359177	−	0.398906i
$624$	−3.75773	−	2.73015i	−0.150430	−	0.109294i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−10.6885	−	18.5131i	−0.427200	−	0.739932i
$627$	−0.129537	+	1.23246i	−0.00517321	+	0.0492198i
$628$	−16.1070	+	11.7025i	−0.642741	+	0.466979i
$629$	−0.179076	−	1.70380i	−0.00714025	−	0.0679349i
$630$	0.616633	+	0.684841i	0.0245673	+	0.0272847i
$631$	4.84395	−	2.15667i	0.192835	−	0.0858556i	−0.308048	−	0.951371i	$-0.599676\pi$
$631$	4.84395	−	2.15667i	0.192835	−	0.0858556i	0.500882	+	0.865515i	$0.333009\pi$
$632$	0.462907	−	0.0983940i	0.0184135	−	0.00391390i
$633$	19.9451	+	4.23947i	0.792748	+	0.168504i
$634$	−4.47919	−	1.99426i	−0.177891	−	0.0792023i
$635$	4.16604	+	12.8218i	0.165324	+	0.508816i
$636$	3.45013	+	10.6184i	0.136807	+	0.421048i
$637$	26.0992	+	11.6201i	1.03409	+	0.460405i
$638$	−3.36172	−	0.714556i	−0.133092	−	0.0282895i
$639$	0.0443151	−	0.00941946i	0.00175308	−	0.000372628i
$640$	−0.913545	+	0.406737i	−0.0361111	+	0.0160777i
$641$	1.20972	+	1.34354i	0.0477813	+	0.0530665i	0.766562	−	0.642171i	$-0.221966\pi$
$641$	1.20972	+	1.34354i	0.0477813	+	0.0530665i	−0.718780	+	0.695237i	$0.755299\pi$
$642$	−0.296247	−	2.81861i	−0.0116920	−	0.111241i
$643$	28.8913	−	20.9908i	1.13936	−	0.827795i	0.152332	−	0.988329i	$-0.451322\pi$
$643$	28.8913	−	20.9908i	1.13936	−	0.827795i	0.987030	+	0.160534i	$0.0513217\pi$
$644$	0.0398573	−	0.379217i	0.00157060	−	0.0149432i
$645$	−3.75730	−	6.50783i	−0.147943	−	0.256245i
$646$	−2.87508	+	4.97978i	−0.113118	+	0.195927i
$647$	−0.689027	−	0.500607i	−0.0270885	−	0.0196809i	0.574159	−	0.818744i	$-0.305329\pi$
$647$	−0.689027	−	0.500607i	−0.0270885	−	0.0196809i	−0.601247	+	0.799063i	$0.705329\pi$
$648$	−0.669131	+	0.743145i	−0.0262859	+	0.0291935i
$649$	−1.16641	+	3.58986i	−0.0457858	+	0.140914i
$650$	4.64481			0.182184
$651$	−5.02257	+	1.04898i	−0.196850	+	0.0411126i
$652$	−20.4160			−0.799550
$653$	14.8621	−	45.7409i	0.581600	−	1.78998i	−0.0309166	−	0.999522i	$-0.509843\pi$
$653$	14.8621	−	45.7409i	0.581600	−	1.78998i	0.612516	−	0.790458i	$-0.290157\pi$
$654$	7.30916	−	8.11765i	0.285811	−	0.317425i
$655$	−5.28078	−	3.83671i	−0.206337	−	0.149913i
$656$	0.000322154	0	0.000557987i	1.25780e−5	0	2.17857e-5i
$657$	1.30952	+	2.26815i	0.0510892	+	0.0884890i
$658$	0.538643	−	5.12484i	0.0209985	−	0.199787i
$659$	16.5939	−	12.0562i	0.646407	−	0.469642i	−0.215638	−	0.976473i	$-0.569183\pi$
$659$	16.5939	−	12.0562i	0.646407	−	0.469642i	0.862045	+	0.506831i	$0.169183\pi$
$660$	0.0387294	+	0.368485i	0.00150754	+	0.0143433i
$661$	−9.86954	−	10.9612i	−0.383880	−	0.426342i	0.519974	−	0.854182i	$-0.325942\pi$
$661$	−9.86954	−	10.9612i	−0.383880	−	0.426342i	−0.903855	+	0.427839i	$0.859275\pi$
$662$	4.05057	−	1.80343i	0.157430	−	0.0700923i
$663$	−7.81084	+	1.66025i	−0.303348	+	0.0644786i
$664$	7.31249	+	1.55432i	0.283779	+	0.0603192i
$665$	2.81579	+	1.25367i	0.109192	+	0.0486152i
$666$	−0.307936	−	0.947730i	−0.0119323	−	0.0367238i
$667$	−1.18602	−	3.65019i	−0.0459228	−	0.141336i
$668$	−1.59840	−	0.711654i	−0.0618440	−	0.0275347i
$669$	7.67168	+	1.63066i	0.296604	+	0.0630451i
$670$	−0.837145	+	0.177941i	−0.0323417	+	0.00687445i
$671$	−1.86323	+	0.829564i	−0.0719292	+	0.0320249i
$672$	−0.616633	−	0.684841i	−0.0237872	−	0.0264183i
$673$	−4.36539	−	41.5339i	−0.168273	−	1.60101i	−0.674275	−	0.738480i	$-0.735544\pi$
$673$	−4.36539	−	41.5339i	−0.168273	−	1.60101i	0.506002	−	0.862532i	$-0.331123\pi$
$674$	−13.4262	+	9.75472i	−0.517159	+	0.375738i
$675$	0.104528	−	0.994522i	0.00402330	−	0.0382792i
$676$	−4.28713	−	7.42553i	−0.164890	−	0.285597i
$677$	−6.92863	+	12.0007i	−0.266289	+	0.461226i	−0.967900	−	0.251334i	$-0.919131\pi$
$677$	−6.92863	+	12.0007i	−0.266289	+	0.461226i	0.701612	+	0.712560i	$0.252464\pi$
$678$	−8.54649	−	6.20939i	−0.328226	−	0.238470i
$679$	−4.12336	+	4.57946i	−0.158240	+	0.175743i
$680$	−0.531261	+	1.63505i	−0.0203729	+	0.0627014i
$681$	18.9818			0.727383
$682$	−1.88160	−	0.845752i	−0.0720503	−	0.0323855i
$683$	−15.9442			−0.610087			−0.305044	−	0.952338i	$-0.598671\pi$
$683$	−15.9442			−0.610087			−0.305044	+	0.952338i	$0.598671\pi$
$684$	−1.03356	+	3.18097i	−0.0395192	+	0.121628i
$685$	10.4023	−	11.5530i	0.397453	−	0.441417i
$686$	9.80448	+	7.12337i	0.374337	+	0.271972i
$687$	−11.4700	+	19.8666i	−0.437608	+	0.757959i
$688$	3.75730	+	6.50783i	0.143246	+	0.248109i
$689$	−5.42071	+	51.5746i	−0.206513	+	1.96484i
$690$	−0.334745	+	0.243207i	−0.0127435	+	0.00925872i
$691$	0.979492	+	9.31924i	0.0372616	+	0.354521i	0.997228	+	0.0744056i	$0.0237059\pi$
$691$	0.979492	+	9.31924i	0.0372616	+	0.354521i	−0.959966	+	0.280115i	$0.909627\pi$
$692$	−12.7159	−	14.1224i	−0.483384	−	0.536852i
$693$	−0.311926	+	0.138879i	−0.0118491	+	0.00527556i
$694$	30.7378	−	6.53352i	1.16679	−	0.248009i
$695$	5.08716	+	1.08131i	0.192967	+	0.0410164i
$696$	−8.47387	−	3.77281i	−0.321201	−	0.143008i
$697$	−0.000342296	−	0.00105348i	−1.29654e−5	−	3.99033e-5i
$698$	−7.62346	−	23.4626i	−0.288552	−	0.888072i
$699$	−21.3394	−	9.50090i	−0.807129	−	0.359357i
$700$	0.901406	+	0.191600i	0.0340700	+	0.00724179i
$701$	1.19876	−	0.254804i	0.0452766	−	0.00962383i	−0.185218	−	0.982698i	$-0.559299\pi$
$701$	1.19876	−	0.254804i	0.0452766	−	0.00962383i	0.230494	+	0.973074i	$0.425966\pi$
$702$	−4.24325	+	1.88921i	−0.160151	+	0.0713038i
$703$	−2.23020	−	2.47688i	−0.0841134	−	0.0934174i
$704$	−0.0387294	−	0.368485i	−0.00145967	−	0.0138878i
$705$	−4.52385	+	3.28677i	−0.170378	+	0.123787i
$706$	2.33446	−	22.2109i	0.0878584	−	0.835917i
$707$	0.544614	+	0.943299i	0.0204823	+	0.0354764i
$708$	−5.09372	+	8.82258i	−0.191434	+	0.331573i
$709$	27.3254	+	19.8531i	1.02623	+	0.745598i	0.967550	−	0.252679i	$-0.0813116\pi$
$709$	27.3254	+	19.8531i	1.02623	+	0.745598i	0.0586775	+	0.998277i	$0.481312\pi$
$710$	0.0303150	−	0.0336682i	0.00113770	−	0.00126355i
$711$	0.146242	−	0.450087i	0.00548450	−	0.0168796i
$712$	14.5387			0.544861
$713$	−0.232681	−	2.29198i	−0.00871397	−	0.0858354i
$714$	−1.58432			−0.0592915
$715$	−0.531810	+	1.63674i	−0.0198885	+	0.0612107i
$716$	−4.47322	+	4.96802i	−0.167172	+	0.185664i
$717$	−1.78060	−	1.29368i	−0.0664977	−	0.0483134i
$718$	1.16158	−	2.01192i	0.0433499	−	0.0750842i
$719$	−7.18753	−	12.4492i	−0.268049	−	0.464275i	0.700309	−	0.713840i	$-0.253046\pi$
$719$	−7.18753	−	12.4492i	−0.268049	−	0.464275i	−0.968358	+	0.249565i	$0.919712\pi$
$720$	−0.104528	+	0.994522i	−0.00389555	+	0.0370636i
$721$	−1.67108	+	1.21411i	−0.0622341	+	0.0452158i
$722$	−0.816698	−	7.77036i	−0.0303944	−	0.289183i
$723$	−3.74620	−	4.16058i	−0.139323	−	0.154734i
$724$	2.05366	−	0.914349i	0.0763237	−	0.0339815i
$725$	9.07311	−	1.92855i	0.336967	−	0.0716245i
$726$	10.6253	+	2.25849i	0.394343	+	0.0838203i
$727$	15.9117	+	7.08434i	0.590132	+	0.262744i	0.680003	−	0.733210i	$-0.261979\pi$
$727$	15.9117	+	7.08434i	0.590132	+	0.262744i	−0.0898705	+	0.995953i	$0.528645\pi$
$728$	−1.32272	−	4.07090i	−0.0490231	−	0.150878i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	2.39261	+	1.06526i	0.0885544	+	0.0394270i
$731$	12.6368	+	2.68602i	0.467387	+	0.0993462i
$732$	−5.38437	+	1.14448i	−0.199012	+	0.0423013i
$733$	1.86350	−	0.829683i	0.0688299	−	0.0306450i	−0.372033	−	0.928220i	$-0.621339\pi$
$733$	1.86350	−	0.829683i	0.0688299	−	0.0306450i	0.440863	+	0.897574i	$0.354673\pi$
$734$	−14.8271	−	16.4672i	−0.547280	−	0.607816i
$735$	−0.642929	−	6.11706i	−0.0237148	−	0.225631i
$736$	0.334745	−	0.243207i	0.0123389	−	0.00896472i
$737$	0.0331464	−	0.315367i	0.00122096	−	0.0116167i
$738$	−0.000322154	0	0.000557987i	−1.18587e−5	0	2.05398e-5i
$739$	16.1164	−	27.9145i	0.592853	−	1.02685i	−0.400993	−	0.916081i	$-0.631335\pi$
$739$	16.1164	−	27.9145i	0.592853	−	1.02685i	0.993846	−	0.110770i	$-0.0353317\pi$
$740$	−0.806187	−	0.585729i	−0.0296360	−	0.0215318i
$741$	−10.3952	+	11.5450i	−0.381877	+	0.424117i
$742$	−3.17945	+	9.78534i	−0.116721	+	0.359231i
$743$	−0.552198			−0.0202582			−0.0101291	−	0.999949i	$-0.503224\pi$
$743$	−0.552198			−0.0202582			−0.0101291	+	0.999949i	$0.503224\pi$
$744$	−4.49278	−	3.28861i	−0.164713	−	0.120566i
$745$	−7.93269			−0.290631
$746$	−2.55656	+	7.86830i	−0.0936025	+	0.288079i
$747$	5.00232	−	5.55564i	0.183025	−	0.203270i
$748$	−0.515334	−	0.374412i	−0.0188425	−	0.0136899i
$749$	1.30589	−	2.26187i	0.0477161	−	0.0826468i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−1.89055	+	17.9874i	−0.0689870	+	0.656368i	0.904319	+	0.426857i	$0.140379\pi$
$751$	−1.89055	+	17.9874i	−0.0689870	+	0.656368i	−0.973306	+	0.229511i	$0.926287\pi$
$752$	4.52385	−	3.28677i	0.164968	−	0.119856i
$753$	3.00015	+	28.5446i	0.109332	+	1.04022i
$754$	−28.8291	−	32.0179i	−1.04989	−	1.16602i
$755$	−13.1506	+	5.85505i	−0.478601	+	0.213087i
$756$	−0.901406	+	0.191600i	−0.0327838	+	0.00696842i
$757$	52.5005	+	11.1593i	1.90816	+	0.405592i	0.999917	−	0.0128469i	$-0.00408939\pi$
$757$	52.5005	+	11.1593i	1.90816	+	0.405592i	0.908245	+	0.418439i	$0.137423\pi$
$758$	−13.1268	−	5.84443i	−0.476787	−	0.212279i
$759$	−0.0473746	−	0.145804i	−0.00171959	−	0.00529235i
$760$	1.03356	+	3.18097i	0.0374912	+	0.115386i
$761$	13.3968	+	5.96464i	0.485634	+	0.216218i	0.634923	−	0.772576i	$-0.281032\pi$
$761$	13.3968	+	5.96464i	0.485634	+	0.216218i	−0.149289	+	0.988794i	$0.547699\pi$
$762$	−13.1870	−	2.80298i	−0.477714	−	0.101541i
$763$	9.84640	−	2.09292i	0.356464	−	0.0757687i
$764$	−1.56029	+	0.694687i	−0.0564494	+	0.0251329i
$765$	1.15037	+	1.27761i	0.0415916	+	0.0461922i
$766$	−3.28534	−	31.2579i	−0.118704	−	1.12939i
$767$	−38.2816	+	27.8132i	−1.38227	+	1.00428i
$768$	0.104528	−	0.994522i	0.00377185	−	0.0358867i
$769$	−14.1758	−	24.5533i	−0.511194	−	0.885414i	−0.999916	−	0.0129742i	$-0.995870\pi$
$769$	−14.1758	−	24.5533i	−0.511194	−	0.885414i	0.488722	−	0.872440i	$-0.337463\pi$
$770$	−0.170723	+	0.295701i	−0.00615243	+	0.0106563i
$771$	6.42965	+	4.67141i	0.231558	+	0.168237i
$772$	6.68584	−	7.42538i	0.240629	−	0.267245i
$773$	11.2028	−	34.4788i	0.402938	−	1.24012i	−0.519666	−	0.854370i	$-0.673944\pi$
$773$	11.2028	−	34.4788i	0.402938	−	1.24012i	0.922604	−	0.385747i	$-0.126056\pi$
$774$	7.51459			0.270106
$775$	5.56773	+	0.0197478i	0.199999	+	0.000709362i
$776$	−6.68689			−0.240045
$777$	0.283777	−	0.873375i	0.0101804	−	0.0313322i
$778$	5.83871	−	6.48454i	0.209328	−	0.232482i
$779$	−0.00174343	−	0.00126668i	−6.24649e−5	−	4.53834e-5i
$780$	−2.32241	+	4.02252i	−0.0831554	+	0.144029i
$781$	0.00839311	+	0.0145373i	0.000300329	+	0.000520185i
$782$	0.0743562	−	0.707452i	0.00265897	−	0.0252984i
$783$	−7.50428	+	5.45218i	−0.268181	+	0.194845i
$784$	0.642929	+	6.11706i	0.0229618	+	0.218466i
$785$	13.3220	+	14.7956i	0.475482	+	0.528077i
$786$	5.96308	−	2.65494i	0.212696	−	0.0946984i
$787$	2.04631	−	0.434956i	0.0729430	−	0.0155045i	−0.171296	−	0.985220i	$-0.554795\pi$
$787$	2.04631	−	0.434956i	0.0729430	−	0.0155045i	0.244239	+	0.969715i	$0.421462\pi$
$788$	4.91409	+	1.04452i	0.175057	+	0.0372096i
$789$	25.3949	+	11.3065i	0.904083	+	0.402524i
$790$	−0.146242	−	0.450087i	−0.00520306	−	0.0160134i
$791$	−3.00835	−	9.25876i	−0.106965	−	0.329204i
$792$	−0.338482	−	0.150702i	−0.0120274	−	0.00535496i
$793$	−25.0094	−	5.31591i	−0.888109	−	0.188773i
$794$	16.3660	−	3.47870i	0.580808	−	0.123455i
$795$	10.1996	−	4.54116i	0.361743	−	0.161058i
$796$	2.14602	+	2.38339i	0.0760636	+	0.0844772i
$797$	0.683167	+	6.49990i	0.0241990	+	0.230238i	0.999936	+	0.0112933i	$0.00359486\pi$
$797$	0.683167	+	6.49990i	0.0241990	+	0.230238i	−0.975737	+	0.218945i	$0.929738\pi$
$798$	−2.49360	+	1.81171i	−0.0882726	+	0.0641338i
$799$	1.00487	−	9.56071i	0.0355498	−	0.338234i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	7.26935	−	12.5909i	0.256850	−	0.444877i
$802$	22.3548	+	16.2417i	0.789376	+	0.573515i
$803$	−0.649319	+	0.721142i	−0.0229140	+	0.0254485i
$804$	0.264471	−	0.813959i	0.00932719	−	0.0287061i
$805$	−0.381306			−0.0134393
$806$	−12.8511	−	22.4422i	−0.452660	−	0.790492i
$807$	5.21346			0.183522
$808$	−0.365246	+	1.12411i	−0.0128493	+	0.0395461i
$809$	34.9681	−	38.8360i	1.22941	−	1.36540i	0.321137	−	0.947033i	$-0.395935\pi$
$809$	34.9681	−	38.8360i	1.22941	−	1.36540i	0.908277	−	0.418370i	$-0.137398\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	10.0698	−	17.4414i	0.353598	−	0.612450i	−0.633279	−	0.773924i	$-0.718291\pi$
$811$	10.0698	−	17.4414i	0.353598	−	0.612450i	0.986877	+	0.161474i	$0.0516248\pi$
$812$	−4.27403	−	7.40284i	−0.149989	−	0.259789i
$813$	0.243939	−	2.32092i	0.00855530	−	0.0813982i
$814$	0.298705	−	0.217022i	0.0104696	−	0.00760660i
$815$	2.13405	+	20.3041i	0.0747524	+	0.711222i
$816$	−1.15037	−	1.27761i	−0.0402709	−	0.0447254i
$817$	22.9609	−	10.2229i	0.803301	−	0.357653i
$818$	−8.65672	+	1.84004i	−0.302675	+	0.0643356i
$819$	−4.18686	−	0.889945i	−0.146301	−	0.0310972i
$820$	−0.000588605	0	0.000262064i	−2.05550e−5	0	9.15167e-6i
$821$	−7.96654	−	24.5185i	−0.278034	−	0.855701i	−0.988401	−	0.151869i	$-0.951471\pi$
$821$	−7.96654	−	24.5185i	−0.278034	−	0.855701i	0.710367	−	0.703832i	$-0.248529\pi$
$822$	4.80400	+	14.7852i	0.167559	+	0.515693i
$823$	4.20432	+	1.87189i	0.146554	+	0.0652498i	0.478703	−	0.877977i	$-0.341107\pi$
$823$	4.20432	+	1.87189i	0.146554	+	0.0652498i	−0.332149	+	0.943227i	$0.607774\pi$
$824$	−2.19244	−	0.466017i	−0.0763771	−	0.0162345i
$825$	0.362418	−	0.0770344i	0.0126178	−	0.00268199i
$826$	−8.57652	+	3.81851i	−0.298415	+	0.132863i
$827$	−12.6688	−	14.0701i	−0.440537	−	0.489266i	0.481457	−	0.876469i	$-0.340108\pi$
$827$	−12.6688	−	14.0701i	−0.440537	−	0.489266i	−0.921994	+	0.387204i	$0.873441\pi$
$828$	−0.0432505	−	0.411501i	−0.00150306	−	0.0143007i
$829$	−0.900432	+	0.654202i	−0.0312733	+	0.0227214i	−0.603312	−	0.797505i	$-0.706153\pi$
$829$	−0.900432	+	0.654202i	−0.0312733	+	0.0227214i	0.572039	+	0.820227i	$0.306153\pi$
$830$	0.781439	−	7.43490i	0.0271241	−	0.258069i
$831$	0.931313	+	1.61308i	0.0323069	+	0.0559572i
$832$	2.32241	−	4.02252i	0.0805149	−	0.139456i
$833$	8.55484	+	6.21545i	0.296408	+	0.215353i
$834$	−3.48002	+	3.86495i	−0.120503	+	0.133832i
$835$	−0.540677	+	1.66403i	−0.0187109	+	0.0575863i
$836$	−1.23925			−0.0428604
$837$	−5.09441	+	2.24656i	−0.176088	+	0.0776524i
$838$	27.1938			0.939394
$839$	4.75092	−	14.6218i	0.164020	−	0.504801i	−0.834943	−	0.550337i	$-0.814499\pi$
$839$	4.75092	−	14.6218i	0.164020	−	0.504801i	0.998963	+	0.0455353i	$0.0144994\pi$
$840$	−0.616633	+	0.684841i	−0.0212759	+	0.0236293i
$841$	−46.1468	−	33.5276i	−1.59127	−	1.15612i
$842$	3.64381	−	6.31127i	0.125574	−	0.217501i
$843$	−0.698538	−	1.20990i	−0.0240589	−	0.0416713i
$844$	−2.13141	+	20.2790i	−0.0733662	+	0.698032i
$845$	−6.93672	+	5.03982i	−0.238631	+	0.173375i
$846$	−0.584500	−	5.56115i	−0.0200955	−	0.191196i
$847$	6.69832	+	7.43923i	0.230157	+	0.255615i
$848$	−10.1996	+	4.54116i	−0.350256	+	0.155944i
$849$	−0.541917	+	0.115188i	−0.0185985	+	0.00395324i
$850$	1.68163	+	0.357441i	0.0576794	+	0.0122601i
$851$	0.376674	+	0.167706i	0.0129122	+	0.00574889i
$852$	0.0140000	+	0.0430877i	0.000479634	+	0.00147616i
$853$	3.44648	+	10.6072i	0.118005	+	0.363183i	0.992562	−	0.121740i	$-0.0388475\pi$
$853$	3.44648	+	10.6072i	0.118005	+	0.363183i	−0.874557	+	0.484923i	$0.838848\pi$
$854$	−4.63422	−	2.06329i	−0.158580	−	0.0706043i
$855$	3.27158	+	0.695397i	0.111886	+	0.0237821i
$856$	2.77220	−	0.589249i	0.0947518	−	0.0201401i
$857$	14.9036	−	6.63551i	0.509097	−	0.226665i	−0.136080	−	0.990698i	$-0.543450\pi$
$857$	14.9036	−	6.63551i	0.509097	−	0.226665i	0.645177	+	0.764033i	$0.276784\pi$
$858$	−1.15155	−	1.27893i	−0.0393134	−	0.0436620i
$859$	3.18463	+	30.2997i	0.108658	+	1.03381i	0.903965	+	0.427606i	$0.140643\pi$
$859$	3.18463	+	30.2997i	0.108658	+	1.03381i	−0.795307	+	0.606206i	$0.792690\pi$
$860$	6.07943	−	4.41697i	0.207307	−	0.150617i
$861$	6.20647e−5	0	0.000590506i	2.11516e−6	0	2.01244e-5i
$862$	2.16352	+	3.74733i	0.0736899	+	0.127635i
$863$	15.0736	−	26.1082i	0.513111	−	0.888735i	−0.486773	−	0.873528i	$-0.661826\pi$
$863$	15.0736	−	26.1082i	0.513111	−	0.888735i	0.999884	−	0.0152064i	$-0.00484054\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−12.7159	+	14.1224i	−0.432352	+	0.480175i
$866$	−11.0707	+	34.0720i	−0.376197	+	1.15781i
$867$	14.0444			0.476972
$868$	−1.56823	−	4.88541i	−0.0532292	−	0.165822i
$869$	0.175346			0.00594820
$870$	−2.86638	+	8.82182i	−0.0971794	+	0.299088i
$871$	2.65996	−	2.95419i	0.0901293	−	0.100099i
$872$	8.83720	+	6.42060i	0.299265	+	0.217429i
$873$	−3.34344	+	5.79102i	−0.113158	+	0.195996i
$874$	−0.691959	−	1.19851i	−0.0234059	−	0.0405402i
$875$	0.0963276	−	0.916496i	0.00325647	−	0.0309832i
$876$	−2.11884	+	1.53943i	−0.0715891	+	0.0520125i
$877$	−1.25697	−	11.9593i	−0.0424449	−	0.403837i	−0.995031	−	0.0995669i	$-0.968254\pi$
$877$	−1.25697	−	11.9593i	−0.0424449	−	0.403837i	0.952586	−	0.304270i	$-0.0984124\pi$
$878$	−22.4902	−	24.9779i	−0.759008	−	0.842963i
$879$	−9.02088	+	4.01635i	−0.304267	+	0.135468i
$880$	−0.362418	+	0.0770344i	−0.0122171	+	0.00259683i
$881$	22.2635	+	4.73225i	0.750076	+	0.159434i	0.567060	−	0.823676i	$-0.308081\pi$
$881$	22.2635	+	4.73225i	0.750076	+	0.159434i	0.183016	+	0.983110i	$0.441414\pi$
$882$	5.61900	+	2.50174i	0.189201	+	0.0842379i
$883$	−8.79477	−	27.0675i	−0.295968	−	0.910895i	−0.982895	−	0.184169i	$-0.941041\pi$
$883$	−8.79477	−	27.0675i	−0.295968	−	0.910895i	0.686927	−	0.726726i	$-0.258959\pi$
$884$	−2.46761	−	7.59451i	−0.0829946	−	0.255431i
$885$	9.30669	+	4.14360i	0.312841	+	0.139286i
$886$	38.3375	+	8.14888i	1.28797	+	0.273767i
$887$	−5.01444	+	1.06585i	−0.168369	+	0.0357878i	−0.291325	−	0.956624i	$-0.594096\pi$
$887$	−5.01444	+	1.06585i	−0.168369	+	0.0357878i	0.122956	+	0.992412i	$0.460763\pi$
$888$	0.910350	−	0.405314i	0.0305494	−	0.0136015i
$889$	−8.31320	−	9.23274i	−0.278816	−	0.309656i
$890$	−1.51971	−	14.4590i	−0.0509407	−	0.484668i
$891$	−0.299753	+	0.217783i	−0.0100421	+	0.00729601i
$892$	−0.819824	+	7.80010i	−0.0274497	+	0.261167i
$893$	−9.35134	−	16.1970i	−0.312931	−	0.542012i
$894$	3.96634	−	6.86991i	0.132654	−	0.229764i
$895$	5.40838	+	3.92942i	0.180782	+	0.131346i
$896$	0.616633	−	0.684841i	0.0206003	−	0.0228789i
$897$	0.593892	−	1.82781i	0.0198295	−	0.0610288i
$898$	19.1814			0.640091
$899$	−34.4212	−	38.5024i	−1.14801	−	1.28413i
$900$	1.00000			0.0333333
$901$	−5.93146	+	18.2552i	−0.197606	+	0.608167i
$902$	0.000159739	0	0.000177408i	5.31872e−6	0	5.90704e-6i
$903$	5.60247	+	4.07043i	0.186438	+	0.135455i
$904$	5.28202	−	9.14873i	0.175677	−	0.304282i
$905$	−1.12401	−	1.94684i	−0.0373632	−	0.0647150i
$906$	1.50471	−	14.3163i	0.0499905	−	0.475628i
$907$	44.7118	−	32.4850i	1.48463	−	1.07865i	0.508605	−	0.861000i	$-0.330161\pi$
$907$	44.7118	−	32.4850i	1.48463	−	1.07865i	0.976027	−	0.217648i	$-0.0698385\pi$
$908$	1.98414	+	18.8778i	0.0658459	+	0.626482i
$909$	0.790885	+	0.878367i	0.0262320	+	0.0291336i
$910$	−3.91034	+	1.74099i	−0.129626	+	0.0577134i
$911$	25.6130	−	5.44421i	0.848597	−	0.180375i	0.236966	−	0.971518i	$-0.423847\pi$
$911$	25.6130	−	5.44421i	0.848597	−	0.180375i	0.611631	+	0.791143i	$0.290514\pi$
$912$	−3.27158	−	0.695397i	−0.108333	−	0.0230269i
$913$	2.53044	+	1.12663i	0.0837454	+	0.0372859i
$914$	1.91343	+	5.88894i	0.0632908	+	0.194789i
$915$	1.70103	+	5.23524i	0.0562344	+	0.173072i
$916$	−20.9567	−	9.33054i	−0.692430	−	0.308290i
$917$	5.88385	+	1.25065i	0.194302	+	0.0413001i
$918$	−1.68163	+	0.357441i	−0.0555020	+	0.0117973i
$919$	−6.12660	+	2.72774i	−0.202098	+	0.0899797i	−0.505290	−	0.862950i	$-0.668614\pi$
$919$	−6.12660	+	2.72774i	−0.202098	+	0.0899797i	0.303192	+	0.952930i	$0.401948\pi$
$920$	−0.276865	−	0.307490i	−0.00912797	−	0.0101376i
$921$	1.87815	+	17.8694i	0.0618871	+	0.588817i
$922$	−16.9355	+	12.3044i	−0.557741	+	0.405223i
$923$	−0.0219963	+	0.209281i	−0.000724017	+	0.00688856i
$924$	−0.170723	−	0.295701i	−0.00561637	−	0.00972784i
$925$	−0.498251	+	0.862996i	−0.0163824	+	0.0283751i
$926$	6.07421	+	4.41318i	0.199611	+	0.145026i
$927$	−1.49980	+	1.66570i	−0.0492599	+	0.0547087i
$928$	2.86638	−	8.82182i	0.0940936	−	0.289590i
$929$	44.4049			1.45688			0.728439	−	0.685111i	$-0.240246\pi$
$929$	44.4049			1.45688			0.728439	+	0.685111i	$0.240246\pi$
$930$	−2.80097	+	4.81192i	−0.0918473	+	0.157789i
$931$	20.5723			0.674229
$932$	7.21828	−	22.2156i	0.236443	−	0.727696i
$933$	10.8784	−	12.0817i	0.356142	−	0.395536i
$934$	−11.0703	−	8.04303i	−0.362231	−	0.263176i
$935$	−0.318494	+	0.551648i	−0.0104159	+	0.0180408i
$936$	−2.32241	−	4.02252i	−0.0759102	−	0.131480i
$937$	−1.34051	+	12.7541i	−0.0437926	+	0.416659i	0.950561	+	0.310539i	$0.100510\pi$
$937$	−1.34051	+	12.7541i	−0.0437926	+	0.416659i	−0.994353	+	0.106120i	$0.966157\pi$
$938$	0.638073	−	0.463587i	0.0208338	−	0.0151367i
$939$	−2.23451	−	21.2600i	−0.0729206	−	0.693793i
$940$	−3.74163	−	4.15550i	−0.122039	−	0.135538i
$941$	−18.1224	+	8.06863i	−0.590774	+	0.263030i	−0.680275	−	0.732957i	$-0.738140\pi$
$941$	−18.1224	+	8.06863i	−0.590774	+	0.263030i	0.0895005	+	0.995987i	$0.471473\pi$
$942$	−19.4743	+	4.13940i	−0.634508	+	0.134869i
$943$	0.000260769	0	5.54281e-5i	8.49179e−6	0	1.80499e-6i
$944$	−9.30669	−	4.14360i	−0.302907	−	0.134863i
$945$	0.284773	+	0.876441i	0.00926366	+	0.0285106i
$946$	0.860386	+	2.64800i	0.0279736	+	0.0860938i
$947$	12.0821	+	5.37930i	0.392616	+	0.174804i	0.593543	−	0.804802i	$-0.297729\pi$
$947$	12.0821	+	5.37930i	0.392616	+	0.174804i	−0.200927	+	0.979606i	$0.564395\pi$
$948$	0.462907	+	0.0983940i	0.0150345	+	0.00319569i
$949$	−11.8991	+	2.52923i	−0.386261	+	0.0821023i
$950$	3.05551	−	1.36040i	0.0991339	−	0.0441372i
$951$	−3.28080	−	3.64370i	−0.106387	−	0.118155i
$952$	−0.165606	−	1.57564i	−0.00536733	−	0.0510667i
$953$	−4.27676	+	3.10725i	−0.138538	+	0.100654i	−0.654896	−	0.755719i	$-0.727287\pi$
$953$	−4.27676	+	3.10725i	−0.138538	+	0.100654i	0.516358	+	0.856373i	$0.327287\pi$
$954$	−1.16705	+	11.1037i	−0.0377845	+	0.359496i
$955$	0.853976	+	1.47913i	0.0276340	+	0.0478635i
$956$	1.10047	−	1.90607i	0.0355918	−	0.0616467i
$957$	−2.78045	−	2.02012i	−0.0898792	−	0.0653010i
$958$	21.4096	−	23.7778i	0.691714	−	0.768226i
$959$	−4.42710	+	13.6252i	−0.142958	+	0.439981i
$960$	−1.00000			−0.0322749
$961$	−15.3092	−	26.9561i	−0.493844	−	0.869550i
$962$	4.62857			0.149231
$963$	0.875795	−	2.69542i	0.0282221	−	0.0868587i
$964$	3.74620	−	4.16058i	0.120657	−	0.134003i
$965$	−8.08356	−	5.87305i	−0.260219	−	0.189060i
$966$	0.190653	−	0.330220i	0.00613415	−	0.0106247i
$967$	22.1257	+	38.3228i	0.711515	+	1.23238i	0.964288	+	0.264854i	$0.0853238\pi$
$967$	22.1257	+	38.3228i	0.711515	+	1.23238i	−0.252774	+	0.967525i	$0.581343\pi$
$968$	−1.13546	+	10.8032i	−0.0364952	+	0.347228i
$969$	−4.65197	+	3.37985i	−0.149443	+	0.108577i
$970$	0.698970	+	6.65026i	0.0224426	+	0.213527i
$971$	34.7810	+	38.6282i	1.11617	+	1.23964i	0.968074	+	0.250664i	$0.0806490\pi$
$971$	34.7810	+	38.6282i	1.11617	+	1.23964i	0.148100	+	0.988972i	$0.452684\pi$
$972$	−0.913545	+	0.406737i	−0.0293020	+	0.0130461i
$973$	−4.68804	+	0.996474i	−0.150292	+	0.0319455i
$974$	−15.4774	−	3.28982i	−0.495927	−	0.105413i
$975$	4.24325	+	1.88921i	0.135893	+	0.0605033i
$976$	−1.70103	−	5.23524i	−0.0544488	−	0.167576i
$977$	1.70460	+	5.24621i	0.0545349	+	0.167841i	0.974614	−	0.223891i	$-0.0718760\pi$
$977$	1.70460	+	5.24621i	0.0545349	+	0.167841i	−0.920079	+	0.391732i	$0.871876\pi$
$978$	−18.6509	−	8.30392i	−0.596390	−	0.265530i
$979$	5.26909	+	1.11998i	0.168401	+	0.0357947i
$980$	6.01635	−	1.27881i	0.192185	−	0.0408502i
$981$	9.97900	−	4.44294i	0.318605	−	0.141852i
$982$	10.4361	+	11.5904i	0.333028	+	0.369865i
$983$	−1.19187	−	11.3399i	−0.0380149	−	0.361687i	−0.996949	−	0.0780579i	$-0.975128\pi$
$983$	−1.19187	−	11.3399i	−0.0380149	−	0.361687i	0.958934	−	0.283629i	$-0.0915386\pi$
$984$	0.000521256	0	0.000378715i	1.66170e−5	0	1.20730e-5i
$985$	0.525138	−	4.99635i	0.0167323	−	0.159197i
$986$	−7.97347	−	13.8105i	−0.253927	−	0.439814i
$987$	2.57654	−	4.46269i	0.0820121	−	0.142049i
$988$	−12.5684	−	9.13146i	−0.399853	−	0.290510i
$989$	−2.08053	+	2.31066i	−0.0661569	+	0.0734747i
$990$	−0.114495	+	0.352381i	−0.00363890	+	0.0111994i
$991$	25.3305			0.804650			0.402325	−	0.915497i	$-0.368202\pi$
$991$	25.3305			0.804650			0.402325	+	0.915497i	$0.368202\pi$
$992$	2.80097	−	4.81192i	0.0889308	−	0.152779i
$993$	4.43390			0.140706
$994$	−0.0129017	+	0.0397072i	−0.000409216	+	0.00125944i
$995$	2.14602	−	2.38339i	0.0680334	−	0.0755587i
$996$	6.04809	+	4.39419i	0.191641	+	0.139235i
$997$	−14.1489	+	24.5066i	−0.448099	+	0.776130i	−0.998262	−	0.0589267i	$-0.981232\pi$
$997$	−14.1489	+	24.5066i	−0.448099	+	0.776130i	0.550163	+	0.835057i	$0.314566\pi$
$998$	14.2945	+	24.7588i	0.452484	+	0.783725i
$999$	0.104163	−	0.991044i	0.00329557	−	0.0313552i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.541.2	yes	24
31.20	even	15	inner	930.2.bg.h.361.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.361.2	✓	24	31.20	even	15	inner
930.2.bg.h.541.2	yes	24	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.0963276 - 0.916496i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(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} +(0.0963276 - 0.916496i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-0.669131 - 0.743145i) q^{10} +(0.338482 - 0.150702i) q^{11} +(0.978148 - 0.207912i) q^{12} +(4.54331 + 0.965710i) q^{13} +(0.841873 + 0.374826i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.57056 + 0.699260i) q^{17} +(0.978148 + 0.207912i) q^{18} +(3.27158 - 0.695397i) q^{19} +(0.913545 - 0.406737i) q^{20} +(0.616633 + 0.684841i) q^{21} +(0.0387294 + 0.368485i) q^{22} +(-0.334745 + 0.243207i) q^{23} +(-0.104528 + 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.32241 + 4.02252i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.616633 + 0.684841i) q^{28} +(-2.86638 + 8.82182i) q^{29} +1.00000 q^{30} +(-2.80097 + 4.81192i) q^{31} -1.00000 q^{32} +(-0.114495 + 0.352381i) q^{33} +(-1.15037 + 1.27761i) q^{34} +(0.745545 + 0.541670i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.498251 - 0.862996i) q^{37} +(-0.349614 + 3.32635i) q^{38} +(-3.75773 + 2.73015i) q^{39} +(0.104528 + 0.994522i) q^{40} +(-0.000431126 - 0.000478814i) q^{41} +(-0.841873 + 0.374826i) q^{42} +(7.35038 - 1.56237i) q^{43} +(-0.362418 - 0.0770344i) q^{44} +(0.913545 + 0.406737i) q^{45} +(-0.127861 - 0.393517i) q^{46} +(-1.72796 - 5.31810i) q^{47} +(-0.913545 - 0.406737i) q^{48} +(6.01635 + 1.27881i) q^{49} +(0.978148 - 0.207912i) q^{50} +(-1.57056 + 0.699260i) q^{51} +(-3.10798 - 3.45177i) q^{52} +(1.16705 + 11.1037i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-0.0387294 + 0.368485i) q^{55} +(-0.460772 - 0.798081i) q^{56} +(-1.67234 + 2.89657i) q^{57} +(-7.50428 - 5.45218i) q^{58} +(-6.81672 + 7.57074i) q^{59} +(-0.309017 + 0.951057i) q^{60} -5.50466 q^{61} +(-3.71086 - 4.15084i) q^{62} -0.921544 q^{63} +(0.309017 - 0.951057i) q^{64} +(-3.10798 + 3.45177i) q^{65} +(-0.299753 - 0.217783i) q^{66} +(0.427924 - 0.741186i) q^{67} +(-0.859598 - 1.48887i) q^{68} +(0.0432505 - 0.411501i) q^{69} +(-0.745545 + 0.541670i) q^{70} +(0.00473567 + 0.0450569i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(-2.39261 + 1.06526i) q^{73} +(0.974727 - 0.207185i) q^{74} +(0.978148 + 0.207912i) q^{75} +(-3.05551 - 1.36040i) q^{76} +(-0.105513 - 0.324734i) q^{77} +(-1.43533 - 4.41748i) q^{78} +(0.432335 + 0.192488i) q^{79} +(-0.978148 - 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(0.000588605 - 0.000262064i) q^{82} +(5.00232 + 5.55564i) q^{83} +(-0.0963276 - 0.916496i) q^{84} +(-1.39086 + 1.01052i) q^{85} +(-0.785489 + 7.47343i) q^{86} +(-4.63790 - 8.03308i) q^{87} +(0.185257 - 0.320875i) q^{88} +(11.7620 + 8.54563i) q^{89} +(-0.669131 + 0.743145i) q^{90} +(1.32272 - 4.07090i) q^{91} +0.413768 q^{92} +(-1.70174 - 5.30133i) q^{93} +5.59178 q^{94} +(-1.03356 + 3.18097i) q^{95} +(0.669131 - 0.743145i) q^{96} +(-5.40981 - 3.93045i) q^{97} +(-3.07538 + 5.32671i) q^{98} +(-0.185257 - 0.320875i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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