LMFDB - Embedded newform 930.2.bg.b.391.2

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:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 195x^{12} + 892x^{10} + 2229x^{8} + 2923x^{6} + 1685x^{4} + 213x^{2} + 1 $ x^16 + 22x^14 + 195x^12 + 892x^10 + 2229x^8 + 2923x^6 + 1685x^4 + 213*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			391.2
Root			$-1.18748i$ of defining polynomial
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.b.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0748188 - 0.0830946i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0748188 - 0.0830946i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.913545 - 0.406737i) q^{10} +(-2.81033 - 0.597354i) q^{11} +(0.104528 - 0.994522i) q^{12} +(0.184583 + 1.75619i) q^{13} +(-0.109371 + 0.0232476i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.842426 - 0.179063i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(0.0430249 - 0.409354i) q^{19} +(-0.978148 - 0.207912i) q^{20} +(-0.102148 + 0.0454792i) q^{21} +(1.92249 + 2.13514i) q^{22} +(1.67860 - 5.16619i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.882933 - 1.52929i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.102148 + 0.0454792i) q^{28} +(-4.53405 - 3.29418i) q^{29} -1.00000 q^{30} +(4.45069 + 3.34535i) q^{31} +1.00000 q^{32} +(2.32440 + 1.68877i) q^{33} +(-0.786788 - 0.350301i) q^{34} +(0.0345527 + 0.106342i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.61467 - 4.52874i) q^{37} +(-0.275420 + 0.305885i) q^{38} +(0.545683 - 1.67944i) q^{39} +(0.669131 + 0.743145i) q^{40} +(-4.14533 + 1.84562i) q^{41} +(0.109371 + 0.0232476i) q^{42} +(1.06421 - 10.1253i) q^{43} +(-0.300322 - 2.85738i) q^{44} +(-0.978148 + 0.207912i) q^{45} +(-4.39462 + 3.19288i) q^{46} +(7.91556 - 5.75099i) q^{47} +(0.978148 - 0.207912i) q^{48} +(0.730392 + 6.94922i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-0.842426 - 0.179063i) q^{51} +(-1.61320 + 0.718243i) q^{52} +(-7.76116 - 8.61965i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.92249 - 2.13514i) q^{55} +(-0.0559074 - 0.0968345i) q^{56} +(-0.205805 + 0.356464i) q^{57} +(1.73185 + 5.33010i) q^{58} +(-7.80684 - 3.47583i) q^{59} +(0.809017 + 0.587785i) q^{60} -1.32069 q^{61} +(-1.63433 - 5.32249i) q^{62} +0.111815 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.61320 - 0.718243i) q^{65} +(-0.887841 - 2.73249i) q^{66} +(7.07875 - 12.2608i) q^{67} +(0.430623 + 0.745861i) q^{68} +(-3.63475 + 4.03680i) q^{69} +(0.0345527 - 0.106342i) q^{70} +(-6.74426 - 7.49026i) q^{71} +(0.913545 - 0.406737i) q^{72} +(1.43987 + 0.306055i) q^{73} +(-0.546615 + 5.20069i) q^{74} +(0.104528 + 0.994522i) q^{75} +(0.402614 - 0.0855783i) q^{76} +(-0.259902 + 0.188830i) q^{77} +(-1.42862 + 1.03795i) q^{78} +(-11.5295 + 2.45068i) q^{79} +(-0.104528 - 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.43847 + 0.943427i) q^{82} +(-14.7299 + 6.55816i) q^{83} +(-0.0748188 - 0.0830946i) q^{84} +(-0.266140 + 0.819094i) q^{85} +(-6.81244 + 7.56598i) q^{86} +(2.80220 + 4.85355i) q^{87} +(-1.43656 + 2.48819i) q^{88} +(-1.19541 - 3.67909i) q^{89} +(0.913545 + 0.406737i) q^{90} +(0.159741 + 0.116058i) q^{91} +5.43205 q^{92} +(-2.70523 - 4.86639i) q^{93} -9.78417 q^{94} +(0.332999 + 0.241938i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(0.388073 + 1.19437i) q^{97} +(3.49375 - 6.05135i) q^{98} +(-1.43656 - 2.48819i) 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} + 3 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 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	0.0748188	−	0.0830946i	0.0282788	−	0.0314068i	−0.728839	−	0.684685i	$-0.759940\pi$
$7$	0.0748188	−	0.0830946i	0.0282788	−	0.0314068i	0.757118	+	0.653278i	$0.226607\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	0.913545	−	0.406737i	0.288888	−	0.128621i
$11$	−2.81033	−	0.597354i	−0.847347	−	0.180109i	−0.236277	−	0.971686i	$-0.575927\pi$
$11$	−2.81033	−	0.597354i	−0.847347	−	0.180109i	−0.611070	+	0.791577i	$0.709261\pi$
$12$	0.104528	−	0.994522i	0.0301748	−	0.287094i
$13$	0.184583	+	1.75619i	0.0511942	+	0.487080i	0.989839	+	0.142194i	$0.0454158\pi$
$13$	0.184583	+	1.75619i	0.0511942	+	0.487080i	−0.938645	+	0.344886i	$0.887918\pi$
$14$	−0.109371	+	0.0232476i	−0.0292307	+	0.00621319i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.842426	−	0.179063i	0.204318	−	0.0434292i	−0.104615	−	0.994513i	$-0.533361\pi$
$17$	0.842426	−	0.179063i	0.204318	−	0.0434292i	0.308934	+	0.951084i	$0.400028\pi$
$18$	−0.104528	−	0.994522i	−0.0246376	−	0.234411i
$19$	0.0430249	−	0.409354i	0.00987058	−	0.0939123i	−0.988477	−	0.151368i	$-0.951632\pi$
$19$	0.0430249	−	0.409354i	0.00987058	−	0.0939123i	0.998348	+	0.0574557i	$0.0182988\pi$
$20$	−0.978148	−	0.207912i	−0.218720	−	0.0464905i
$21$	−0.102148	+	0.0454792i	−0.0222905	+	0.00992438i
$22$	1.92249	+	2.13514i	0.409876	+	0.455213i
$23$	1.67860	−	5.16619i	0.350012	−	1.07723i	−0.608834	−	0.793298i	$-0.708363\pi$
$23$	1.67860	−	5.16619i	0.350012	−	1.07723i	0.958846	−	0.283927i	$-0.0916375\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.882933	−	1.52929i	0.173157	−	0.299917i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.102148	+	0.0454792i	0.0193042	+	0.00859476i
$29$	−4.53405	−	3.29418i	−0.841952	−	0.611714i	0.0809630	−	0.996717i	$-0.474200\pi$
$29$	−4.53405	−	3.29418i	−0.841952	−	0.611714i	−0.922915	+	0.385003i	$0.874200\pi$
$30$	−1.00000			−0.182574
$31$	4.45069	+	3.34535i	0.799367	+	0.600843i
$31$	4.45069	+	3.34535i	0.799367	+	0.600843i
$32$	1.00000			0.176777
$33$	2.32440	+	1.68877i	0.404626	+	0.293978i
$34$	−0.786788	−	0.350301i	−0.134933	−	0.0600760i
$35$	0.0345527	+	0.106342i	0.00584047	+	0.0179751i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.61467	−	4.52874i	−0.429849	−	0.744521i	0.567010	−	0.823711i	$-0.308100\pi$
$37$	−2.61467	−	4.52874i	−0.429849	−	0.744521i	−0.996860	+	0.0791900i	$0.974767\pi$
$38$	−0.275420	+	0.305885i	−0.0446791	+	0.0496211i
$39$	0.545683	−	1.67944i	0.0873792	−	0.268925i
$40$	0.669131	+	0.743145i	0.105799	+	0.117502i
$41$	−4.14533	+	1.84562i	−0.647392	+	0.288238i	−0.704044	−	0.710156i	$-0.748624\pi$
$41$	−4.14533	+	1.84562i	−0.647392	+	0.288238i	0.0566517	+	0.998394i	$0.481958\pi$
$42$	0.109371	+	0.0232476i	0.0168764	+	0.00358719i
$43$	1.06421	−	10.1253i	0.162290	−	1.54409i	−0.545770	−	0.837935i	$-0.683763\pi$
$43$	1.06421	−	10.1253i	0.162290	−	1.54409i	0.708060	−	0.706152i	$-0.249571\pi$
$44$	−0.300322	−	2.85738i	−0.0452753	−	0.430766i
$45$	−0.978148	+	0.207912i	−0.145814	+	0.0309936i
$46$	−4.39462	+	3.19288i	−0.647952	+	0.470765i
$47$	7.91556	−	5.75099i	1.15460	−	0.838868i	0.165517	−	0.986207i	$-0.447071\pi$
$47$	7.91556	−	5.75099i	1.15460	−	0.838868i	0.989086	+	0.147339i	$0.0470709\pi$
$48$	0.978148	−	0.207912i	0.141183	−	0.0300095i
$49$	0.730392	+	6.94922i	0.104342	+	0.992746i
$50$	−0.104528	+	0.994522i	−0.0147826	+	0.140647i
$51$	−0.842426	−	0.179063i	−0.117963	−	0.0250739i
$52$	−1.61320	+	0.718243i	−0.223710	+	0.0996023i
$53$	−7.76116	−	8.61965i	−1.06608	−	1.18400i	−0.982261	−	0.187518i	$-0.939956\pi$
$53$	−7.76116	−	8.61965i	−1.06608	−	1.18400i	−0.0838168	−	0.996481i	$-0.526711\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	1.92249	−	2.13514i	0.259228	−	0.287902i
$56$	−0.0559074	−	0.0968345i	−0.00747095	−	0.0129401i
$57$	−0.205805	+	0.356464i	−0.0272595	+	0.0472148i
$58$	1.73185	+	5.33010i	0.227404	+	0.699876i
$59$	−7.80684	−	3.47583i	−1.01636	−	0.452514i	−0.170184	−	0.985412i	$-0.554436\pi$
$59$	−7.80684	−	3.47583i	−1.01636	−	0.452514i	−0.846179	+	0.532898i	$0.821103\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−1.32069			−0.169097			−0.0845485	−	0.996419i	$-0.526945\pi$
$61$	−1.32069			−0.169097			−0.0845485	+	0.996419i	$0.526945\pi$
$62$	−1.63433	−	5.32249i	−0.207561	−	0.675958i
$63$	0.111815			0.0140873
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.61320	−	0.718243i	−0.200093	−	0.0890870i
$66$	−0.887841	−	2.73249i	−0.109286	−	0.336347i
$67$	7.07875	−	12.2608i	0.864807	−	1.49789i	−0.00243094	−	0.999997i	$-0.500774\pi$
$67$	7.07875	−	12.2608i	0.864807	−	1.49789i	0.867238	−	0.497893i	$-0.165893\pi$
$68$	0.430623	+	0.745861i	0.0522207	+	0.0904490i
$69$	−3.63475	+	4.03680i	−0.437573	+	0.485974i
$70$	0.0345527	−	0.106342i	0.00412984	−	0.0127103i
$71$	−6.74426	−	7.49026i	−0.800397	−	0.888930i	0.195381	−	0.980727i	$-0.437406\pi$
$71$	−6.74426	−	7.49026i	−0.800397	−	0.888930i	−0.995778	+	0.0917969i	$0.970739\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	1.43987	+	0.306055i	0.168525	+	0.0358210i	0.291401	−	0.956601i	$-0.405879\pi$
$73$	1.43987	+	0.306055i	0.168525	+	0.0358210i	−0.122877	+	0.992422i	$0.539212\pi$
$74$	−0.546615	+	5.20069i	−0.0635427	+	0.604568i
$75$	0.104528	+	0.994522i	0.0120699	+	0.114837i
$76$	0.402614	−	0.0855783i	0.0461830	−	0.00981651i
$77$	−0.259902	+	0.188830i	−0.0296186	+	0.0215192i
$78$	−1.42862	+	1.03795i	−0.161759	+	0.117525i
$79$	−11.5295	+	2.45068i	−1.29718	+	0.275723i	−0.804220	−	0.594332i	$-0.797417\pi$
$79$	−11.5295	+	2.45068i	−1.29718	+	0.275723i	−0.492955	+	0.870055i	$0.664083\pi$
$80$	−0.104528	−	0.994522i	−0.0116866	−	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	4.43847	+	0.943427i	0.490147	+	0.104184i
$83$	−14.7299	+	6.55816i	−1.61681	+	0.719851i	−0.997848	−	0.0655678i	$-0.979114\pi$
$83$	−14.7299	+	6.55816i	−1.61681	+	0.719851i	−0.618964	+	0.785419i	$0.712447\pi$
$84$	−0.0748188	−	0.0830946i	−0.00816340	−	0.00906637i
$85$	−0.266140	+	0.819094i	−0.0288669	+	0.0888432i
$86$	−6.81244	+	7.56598i	−0.734604	+	0.815861i
$87$	2.80220	+	4.85355i	0.300427	+	0.520355i
$88$	−1.43656	+	2.48819i	−0.153138	+	0.265242i
$89$	−1.19541	−	3.67909i	−0.126713	−	0.389982i	0.867496	−	0.497444i	$-0.165728\pi$
$89$	−1.19541	−	3.67909i	−0.126713	−	0.389982i	−0.994209	+	0.107461i	$0.965728\pi$
$90$	0.913545	+	0.406737i	0.0962961	+	0.0428738i
$91$	0.159741	+	0.116058i	0.0167454	+	0.0121662i
$92$	5.43205			0.566331
$93$	−2.70523	−	4.86639i	−0.280519	−	0.504621i
$94$	−9.78417			−1.00916
$95$	0.332999	+	0.241938i	0.0341649	+	0.0248223i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	0.388073	+	1.19437i	0.0394028	+	0.121269i	0.968823	−	0.247754i	$-0.0796923\pi$
$97$	0.388073	+	1.19437i	0.0394028	+	0.121269i	−0.929420	+	0.369023i	$0.879692\pi$
$98$	3.49375	−	6.05135i	0.352922	−	0.611279i
$99$	−1.43656	−	2.48819i	−0.144379	−	0.250073i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	1.38492	−	4.26235i	0.137805	−	0.424119i	−0.858211	−	0.513297i	$-0.828424\pi$
$101$	1.38492	−	4.26235i	0.137805	−	0.424119i	0.996016	+	0.0891777i	$0.0284239\pi$
$102$	0.576286	+	0.640031i	0.0570609	+	0.0633725i
$103$	−7.20476	+	3.20777i	−0.709906	+	0.316071i	−0.729732	−	0.683733i	$-0.760355\pi$
$103$	−7.20476	+	3.20777i	−0.709906	+	0.316071i	0.0198261	+	0.999803i	$0.493689\pi$
$104$	1.72728	+	0.367144i	0.169374	+	0.0360015i
$105$	0.0116878	−	0.111202i	0.00114062	−	0.0108522i
$106$	1.21241	+	11.5353i	0.117760	+	1.12041i
$107$	12.6165	−	2.68172i	1.21968	−	0.259252i	0.447287	−	0.894391i	$-0.352390\pi$
$107$	12.6165	−	2.68172i	1.21968	−	0.259252i	0.772398	+	0.635139i	$0.219057\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	0.923071	−	0.670651i	0.0884142	−	0.0642367i	−0.542700	−	0.839927i	$-0.682598\pi$
$109$	0.923071	−	0.670651i	0.0884142	−	0.0642367i	0.631114	+	0.775690i	$0.282598\pi$
$110$	−2.81033	+	0.597354i	−0.267954	+	0.0569555i
$111$	0.546615	+	5.20069i	0.0518824	+	0.493628i
$112$	−0.0116878	+	0.111202i	−0.00110440	+	0.0105076i
$113$	−6.72383	−	1.42919i	−0.632525	−	0.134447i	−0.119518	−	0.992832i	$-0.538135\pi$
$113$	−6.72383	−	1.42919i	−0.632525	−	0.134447i	−0.513006	+	0.858385i	$0.671468\pi$
$114$	0.376024	−	0.167416i	0.0352178	−	0.0156800i
$115$	3.63475	+	4.03680i	0.338942	+	0.376434i
$116$	1.73185	−	5.33010i	0.160799	−	0.494887i
$117$	−1.18160	+	1.31229i	−0.109239	+	0.121322i
$118$	4.27282	+	7.40075i	0.393345	+	0.681294i
$119$	0.0481501	−	0.0833984i	0.00441391	−	0.00764512i
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	−2.50787	−	1.11658i	−0.227989	−	0.101507i
$122$	1.06846	+	0.776282i	0.0967338	+	0.0702812i
$123$	4.53763			0.409145
$124$	−1.80628	+	5.26663i	−0.162209	+	0.472957i
$125$	1.00000			0.0894427
$126$	−0.0904601	−	0.0657231i	−0.00805883	−	0.00585508i
$127$	6.66565	+	2.96774i	0.591481	+	0.263344i	0.680574	−	0.732679i	$-0.261730\pi$
$127$	6.66565	+	2.96774i	0.591481	+	0.263344i	−0.0890936	+	0.996023i	$0.528397\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−5.09051	+	8.81703i	−0.448195	+	0.776296i
$130$	0.882933	+	1.52929i	0.0774384	+	0.134127i
$131$	3.68900	−	4.09705i	0.322309	−	0.357961i	−0.560115	−	0.828415i	$-0.689243\pi$
$131$	3.68900	−	4.09705i	0.322309	−	0.357961i	0.882425	+	0.470454i	$0.155910\pi$
$132$	−0.887841	+	2.73249i	−0.0772767	+	0.237833i
$133$	−0.0307961	−	0.0342025i	−0.00267036	−	0.00296573i
$134$	−12.9335	+	5.75838i	−1.11729	+	0.497448i
$135$	0.978148	+	0.207912i	0.0841855	+	0.0178942i
$136$	0.0900248	−	0.856529i	0.00771956	−	0.0734467i
$137$	−1.02997	−	9.79955i	−0.0879967	−	0.837232i	−0.946126	−	0.323799i	$-0.895040\pi$
$137$	−1.02997	−	9.79955i	−0.0879967	−	0.837232i	0.858129	−	0.513434i	$-0.171627\pi$
$138$	5.31335	−	1.12939i	0.452302	−	0.0961398i
$139$	10.1587	−	7.38071i	0.861647	−	0.626023i	−0.0666853	−	0.997774i	$-0.521242\pi$
$139$	10.1587	−	7.38071i	0.861647	−	0.626023i	0.928333	+	0.371751i	$0.121242\pi$
$140$	−0.0904601	+	0.0657231i	−0.00764528	+	0.00555462i
$141$	−9.57036	+	2.03424i	−0.805970	+	0.171314i
$142$	1.05356	+	10.0239i	0.0884125	+	0.841189i
$143$	0.530329	−	5.04574i	0.0443483	−	0.421946i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	5.11987	−	2.27951i	0.425182	−	0.189303i
$146$	−0.984989	−	1.09394i	−0.0815182	−	0.0905352i
$147$	2.15926	−	6.64550i	0.178092	−	0.548112i
$148$	3.49911	−	3.88616i	0.287625	−	0.319440i
$149$	3.02024	+	5.23120i	0.247427	+	0.428557i	0.962811	−	0.270175i	$-0.0870815\pi$
$149$	3.02024	+	5.23120i	0.247427	+	0.428557i	−0.715384	+	0.698732i	$0.753748\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	2.64964	+	8.15475i	0.215625	+	0.663624i	0.999109	+	0.0422123i	$0.0134406\pi$
$151$	2.64964	+	8.15475i	0.215625	+	0.663624i	−0.783484	+	0.621412i	$0.786559\pi$
$152$	−0.376024	−	0.167416i	−0.0304995	−	0.0135793i
$153$	0.696763	+	0.506228i	0.0563300	+	0.0409261i
$154$	0.321257			0.0258876
$155$	−5.12250	+	2.18173i	−0.411449	+	0.175241i
$156$	1.76587			0.141382
$157$	−1.33023	−	0.966469i	−0.106164	−	0.0771326i	0.533437	−	0.845840i	$-0.320900\pi$
$157$	−1.33023	−	0.966469i	−0.106164	−	0.0771326i	−0.639601	+	0.768707i	$0.720900\pi$
$158$	10.7681	+	4.79425i	0.856662	+	0.381410i
$159$	3.58425	+	11.0312i	0.284250	+	0.874830i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−0.303692	−	0.526010i	−0.0239343	−	0.0414554i
$162$	0.669131	−	0.743145i	0.0525719	−	0.0583870i
$163$	−0.175871	+	0.541274i	−0.0137753	+	0.0423959i	−0.957708	−	0.287742i	$-0.907095\pi$
$163$	−0.175871	+	0.541274i	−0.0137753	+	0.0423959i	0.943933	+	0.330138i	$0.107095\pi$
$164$	−3.03627	−	3.37212i	−0.237093	−	0.263318i
$165$	−2.62472	+	1.16860i	−0.204334	+	0.0909755i
$166$	15.7715	+	3.35234i	1.22411	+	0.260192i
$167$	0.450030	−	4.28175i	0.0348244	−	0.331332i	−0.963214	−	0.268734i	$-0.913395\pi$
$167$	0.450030	−	4.28175i	0.0348244	−	0.331332i	0.998039	−	0.0625980i	$-0.0199386\pi$
$168$	0.0116878	+	0.111202i	0.000901736	+	0.00857945i
$169$	9.66578	−	2.05452i	0.743521	−	0.158040i
$170$	0.696763	−	0.506228i	0.0534393	−	0.0388259i
$171$	0.332999	−	0.241938i	0.0254650	−	0.0185014i
$172$	9.95855	−	2.11676i	0.759332	−	0.161401i
$173$	0.479771	+	4.56471i	0.0364763	+	0.347049i	0.997505	+	0.0705993i	$0.0224912\pi$
$173$	0.479771	+	4.56471i	0.0364763	+	0.347049i	−0.961028	+	0.276449i	$0.910842\pi$
$174$	0.585819	−	5.57370i	0.0444108	−	0.422541i
$175$	−0.109371	−	0.0232476i	−0.00826770	−	0.00175735i
$176$	2.62472	−	1.16860i	0.197846	−	0.0880866i
$177$	5.71815	+	6.35065i	0.429803	+	0.477344i
$178$	−1.19541	+	3.67909i	−0.0895996	+	0.275759i
$179$	9.83507	−	10.9230i	0.735108	−	0.816420i	−0.253436	−	0.967352i	$-0.581561\pi$
$179$	9.83507	−	10.9230i	0.735108	−	0.816420i	0.988544	+	0.150932i	$0.0482275\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	2.70072	−	4.67779i	0.200743	−	0.347698i	−0.748025	−	0.663671i	$-0.768998\pi$
$181$	2.70072	−	4.67779i	0.200743	−	0.347698i	0.948768	+	0.315973i	$0.102331\pi$
$182$	−0.0610154	−	0.187786i	−0.00452277	−	0.0139196i
$183$	1.20651	+	0.537173i	0.0891878	+	0.0397089i
$184$	−4.39462	−	3.19288i	−0.323976	−	0.235382i
$185$	5.22934			0.384469
$186$	−0.671815	+	5.52708i	−0.0492598	+	0.405266i
$187$	−2.47446			−0.180950
$188$	7.91556	+	5.75099i	0.577301	+	0.419434i
$189$	−0.102148	−	0.0454792i	−0.00743017	−	0.00330813i
$190$	−0.127194	−	0.391463i	−0.00922764	−	0.0283997i
$191$	−3.71059	+	6.42693i	−0.268489	+	0.465036i	−0.968472	−	0.249123i	$-0.919858\pi$
$191$	−3.71059	+	6.42693i	−0.268489	+	0.465036i	0.699983	+	0.714160i	$0.253191\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−5.52851	+	6.14004i	−0.397951	+	0.441969i	−0.908504	−	0.417877i	$-0.862774\pi$
$193$	−5.52851	+	6.14004i	−0.397951	+	0.441969i	0.510552	+	0.859847i	$0.329441\pi$
$194$	0.388073	−	1.19437i	0.0278620	−	0.0857505i
$195$	1.18160	+	1.31229i	0.0846158	+	0.0939754i
$196$	−6.38340	+	2.84207i	−0.455957	+	0.203005i
$197$	15.1283	+	3.21563i	1.07785	+	0.229104i	0.712433	−	0.701740i	$-0.247593\pi$
$197$	15.1283	+	3.21563i	1.07785	+	0.229104i	0.365417	+	0.930844i	$0.380927\pi$
$198$	−0.300322	+	2.85738i	−0.0213430	+	0.203065i
$199$	−2.11877	−	20.1587i	−0.150196	−	1.42901i	−0.766873	−	0.641799i	$-0.778188\pi$
$199$	−2.11877	−	20.1587i	−0.150196	−	1.42901i	0.616677	−	0.787216i	$-0.288478\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	−11.4537	+	8.32157i	−0.807879	+	0.586959i
$202$	−3.62577	+	2.63428i	−0.255108	+	0.185347i
$203$	−0.612961	+	0.130289i	−0.0430214	+	0.00914449i
$204$	−0.0900248	−	0.856529i	−0.00630299	−	0.0599690i
$205$	0.474312	−	4.51277i	0.0331274	−	0.315186i
$206$	7.71425	+	1.63972i	0.537478	+	0.114244i
$207$	4.96243	−	2.20942i	0.344913	−	0.153565i
$208$	−1.18160	−	1.31229i	−0.0819289	−	0.0909913i
$209$	−0.365444	+	1.12472i	−0.0252783	+	0.0777985i
$210$	−0.0748188	+	0.0830946i	−0.00516298	+	0.00573408i
$211$	6.09292	+	10.5532i	0.419454	+	0.726515i	0.995885	−	0.0906309i	$-0.0288883\pi$
$211$	6.09292	+	10.5532i	0.419454	+	0.726515i	−0.576431	+	0.817146i	$0.695555\pi$
$212$	5.79944	−	10.0449i	0.398307	−	0.689888i
$213$	3.11463	+	9.58583i	0.213411	+	0.656810i
$214$	−11.7833	−	5.24624i	−0.805487	−	0.358626i
$215$	8.23663	+	5.98426i	0.561733	+	0.408123i
$216$	−1.00000			−0.0680414
$217$	0.610976	−	0.119533i	0.0414757	−	0.00811446i
$218$	−1.14098			−0.0772769
$219$	−1.19091	−	0.865245i	−0.0804741	−	0.0584678i
$220$	2.62472	+	1.16860i	0.176959	+	0.0787871i
$221$	0.469967	+	1.44641i	0.0316134	+	0.0972961i
$222$	2.61467	−	4.52874i	0.175485	−	0.303949i
$223$	6.00883	+	10.4076i	0.402381	+	0.696944i	0.994013	−	0.109264i	$-0.0348495\pi$
$223$	6.00883	+	10.4076i	0.402381	+	0.696944i	−0.591632	+	0.806208i	$0.701516\pi$
$224$	0.0748188	−	0.0830946i	0.00499904	−	0.00555199i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	4.59963	+	5.10841i	0.305963	+	0.339806i
$227$	18.7230	−	8.33600i	1.24269	−	0.553280i	0.323174	−	0.946340i	$-0.395250\pi$
$227$	18.7230	−	8.33600i	1.24269	−	0.553280i	0.919513	+	0.393060i	$0.128583\pi$
$228$	−0.402614	−	0.0855783i	−0.0266638	−	0.00566756i
$229$	−0.757712	+	7.20915i	−0.0500710	+	0.476394i	0.940540	+	0.339683i	$0.110320\pi$
$229$	−0.757712	+	7.20915i	−0.0500710	+	0.476394i	−0.990611	+	0.136711i	$0.956347\pi$
$230$	−0.567804	−	5.40230i	−0.0374399	−	0.356217i
$231$	0.314237	−	0.0667931i	0.0206753	−	0.00439466i
$232$	−4.53405	+	3.29418i	−0.297675	+	0.216274i
$233$	−18.8810	+	13.7179i	−1.23694	+	0.898687i	−0.997390	−	0.0721975i	$-0.976999\pi$
$233$	−18.8810	+	13.7179i	−1.23694	+	0.898687i	−0.239547	+	0.970885i	$0.576999\pi$
$234$	1.72728	−	0.367144i	0.112916	−	0.0240010i
$235$	1.02272	+	9.73057i	0.0667151	+	0.634752i
$236$	0.893263	−	8.49883i	0.0581465	−	0.553227i
$237$	11.5295	+	2.45068i	0.748924	+	0.159189i
$238$	−0.0879746	+	0.0391688i	−0.00570255	+	0.00253894i
$239$	17.5473	+	19.4883i	1.13504	+	1.26059i	0.961210	+	0.275816i	$0.0889481\pi$
$239$	17.5473	+	19.4883i	1.13504	+	1.26059i	0.173831	+	0.984775i	$0.444385\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	6.69393	−	7.43436i	0.431194	−	0.478889i	−0.487916	−	0.872891i	$-0.662243\pi$
$241$	6.69393	−	7.43436i	0.431194	−	0.478889i	0.919110	+	0.394001i	$0.128909\pi$
$242$	1.37261	+	2.37742i	0.0882344	+	0.152826i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.408115	−	1.25605i	−0.0261269	−	0.0804104i
$245$	−6.38340	−	2.84207i	−0.407820	−	0.181573i
$246$	−3.67102	−	2.66715i	−0.234056	−	0.170051i
$247$	0.726847			0.0462481
$248$	4.55696	−	3.19909i	0.289367	−	0.203142i
$249$	16.1238			1.02181
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	4.64558	+	2.06835i	0.293227	+	0.130553i	0.548078	−	0.836427i	$-0.315360\pi$
$251$	4.64558	+	2.06835i	0.293227	+	0.130553i	−0.254851	+	0.966980i	$0.582026\pi$
$252$	0.0345527	+	0.106342i	0.00217662	+	0.00669893i
$253$	−7.80346	+	13.5160i	−0.490599	+	0.849743i
$254$	−3.64823	−	6.31892i	−0.228910	−	0.396484i
$255$	0.576286	−	0.640031i	0.0360885	−	0.0400803i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	16.9449	+	18.8192i	1.05699	+	1.17391i	0.984291	+	0.176554i	$0.0564951\pi$
$257$	16.9449	+	18.8192i	1.05699	+	1.17391i	0.0727005	+	0.997354i	$0.476838\pi$
$258$	9.30083	−	4.14100i	0.579045	−	0.257807i
$259$	−0.571941	−	0.121570i	−0.0355387	−	0.00755398i
$260$	0.184583	−	1.75619i	0.0114474	−	0.108914i
$261$	−0.585819	−	5.57370i	−0.0362613	−	0.345003i
$262$	−5.39265	+	1.14624i	−0.333159	+	0.0708151i
$263$	1.60910	−	1.16908i	0.0992213	−	0.0720885i	−0.537068	−	0.843539i	$-0.680468\pi$
$263$	1.60910	−	1.16908i	0.0992213	−	0.0720885i	0.636290	+	0.771450i	$0.280468\pi$
$264$	2.32440	−	1.68877i	0.143057	−	0.103937i
$265$	11.3454	−	2.41154i	0.696943	−	0.148140i
$266$	0.00481082	+	0.0457719i	0.000294970	+	0.00280645i
$267$	−0.404360	+	3.84723i	−0.0247464	+	0.235447i
$268$	13.8481	+	2.94351i	0.845909	+	0.179804i
$269$	−26.8232	+	11.9425i	−1.63544	+	0.728145i	−0.999065	−	0.0432351i	$-0.986234\pi$
$269$	−26.8232	+	11.9425i	−1.63544	+	0.728145i	−0.636375	+	0.771380i	$0.719567\pi$
$270$	−0.669131	−	0.743145i	−0.0407220	−	0.0452264i
$271$	3.18572	−	9.80465i	0.193519	−	0.595590i	−0.806472	−	0.591273i	$-0.798626\pi$
$271$	3.18572	−	9.80465i	0.193519	−	0.595590i	0.999991	−	0.00431738i	$-0.00137427\pi$
$272$	−0.576286	+	0.640031i	−0.0349425	+	0.0388076i
$273$	−0.0987251	−	0.170997i	−0.00597511	−	0.0103492i
$274$	−4.92677	+	8.53341i	−0.297637	+	0.515522i
$275$	0.887841	+	2.73249i	0.0535388	+	0.164776i
$276$	−4.96243	−	2.20942i	−0.298703	−	0.132991i
$277$	−5.06120	−	3.67718i	−0.304098	−	0.220940i	0.425262	−	0.905070i	$-0.360182\pi$
$277$	−5.06120	−	3.67718i	−0.304098	−	0.220940i	−0.729360	+	0.684130i	$0.760182\pi$
$278$	−12.5568			−0.753107
$279$	0.492012	+	5.54598i	0.0294560	+	0.332029i
$280$	0.111815			0.00668222
$281$	3.28004	+	2.38309i	0.195671	+	0.142163i	0.681307	−	0.731998i	$-0.261412\pi$
$281$	3.28004	+	2.38309i	0.195671	+	0.142163i	−0.485636	+	0.874161i	$0.661412\pi$
$282$	8.93828	+	3.97958i	0.532267	+	0.236980i
$283$	−9.59715	−	29.5370i	−0.570491	−	1.75579i	−0.651042	−	0.759042i	$-0.725668\pi$
$283$	−9.59715	−	29.5370i	−0.570491	−	1.75579i	0.0805507	−	0.996751i	$-0.474332\pi$
$284$	5.03957	−	8.72879i	0.299043	−	0.517958i
$285$	−0.205805	−	0.356464i	−0.0121908	−	0.0211151i
$286$	−3.39486	+	3.77037i	−0.200742	+	0.222947i
$287$	−0.156787	+	0.482542i	−0.00925487	+	0.0284836i
$288$	0.669131	+	0.743145i	0.0394289	+	0.0437902i
$289$	−14.8527	+	6.61283i	−0.873686	+	0.388990i
$290$	−5.48193	−	1.16522i	−0.321910	−	0.0684241i
$291$	0.131270	−	1.24895i	0.00769518	−	0.0732148i
$292$	0.153870	+	1.46398i	0.00900458	+	0.0856729i
$293$	−17.1971	+	3.65536i	−1.00467	+	0.213549i	−0.680733	−	0.732531i	$-0.738339\pi$
$293$	−17.1971	+	3.65536i	−1.00467	+	0.213549i	−0.323934	+	0.946080i	$0.605005\pi$
$294$	−5.65300	+	4.10715i	−0.329690	+	0.239534i
$295$	6.91357	−	5.02301i	0.402524	−	0.292451i
$296$	−5.11507	+	1.08724i	−0.297307	+	0.0631946i
$297$	0.300322	+	2.85738i	0.0174265	+	0.165802i
$298$	0.631401	−	6.00738i	0.0365761	−	0.347998i
$299$	9.38267	+	1.99435i	0.542614	+	0.115336i
$300$	−0.913545	+	0.406737i	−0.0527436	+	0.0234830i
$301$	−0.761732	−	0.845989i	−0.0439055	−	0.0487620i
$302$	2.64964	−	8.15475i	0.152470	−	0.469253i
$303$	−2.99884	+	3.33055i	−0.172279	+	0.191335i
$304$	0.205805	+	0.356464i	0.0118037	+	0.0204446i
$305$	0.660345	−	1.14375i	0.0378112	−	0.0654910i
$306$	−0.266140	−	0.819094i	−0.0152142	−	0.0468245i
$307$	−19.2371	−	8.56492i	−1.09792	−	0.488826i	−0.223849	−	0.974624i	$-0.571862\pi$
$307$	−19.2371	−	8.56492i	−1.09792	−	0.488826i	−0.874071	+	0.485798i	$0.838529\pi$
$308$	−0.259902	−	0.188830i	−0.0148093	−	0.0107596i
$309$	7.88659			0.448653
$310$	5.42658	+	1.24587i	0.308209	+	0.0707608i
$311$	23.4502			1.32974			0.664868	−	0.746961i	$-0.268488\pi$
$311$	23.4502			1.32974			0.664868	+	0.746961i	$0.268488\pi$
$312$	−1.42862	−	1.03795i	−0.0808795	−	0.0587624i
$313$	−6.07940	−	2.70672i	−0.343628	−	0.152993i	0.227664	−	0.973740i	$-0.426891\pi$
$313$	−6.07940	−	2.70672i	−0.343628	−	0.152993i	−0.571292	+	0.820747i	$0.693558\pi$
$314$	0.508103	+	1.56378i	0.0286739	+	0.0882492i
$315$	−0.0559074	+	0.0968345i	−0.00315003	+	0.00545601i
$316$	−5.89356	−	10.2079i	−0.331539	−	0.574242i
$317$	−11.3844	+	12.6437i	−0.639414	+	0.710141i	−0.972539	−	0.232742i	$-0.925230\pi$
$317$	−11.3844	+	12.6437i	−0.639414	+	0.710141i	0.333125	+	0.942883i	$0.391897\pi$
$318$	3.58425	−	11.0312i	0.200995	−	0.618598i
$319$	10.7744	+	11.9662i	0.603250	+	0.669977i
$320$	0.913545	−	0.406737i	0.0510687	−	0.0227373i
$321$	−12.6165	−	2.68172i	−0.704185	−	0.149679i
$322$	−0.0634890	+	0.604057i	−0.00353810	+	0.0336628i
$323$	−0.0370550	−	0.352555i	−0.00206180	−	0.0196167i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	1.42862	−	1.03795i	0.0792454	−	0.0575751i
$326$	0.460435	−	0.334526i	0.0255012	−	0.0185277i
$327$	−1.11605	+	0.237223i	−0.0617175	+	0.0131185i
$328$	0.474312	+	4.51277i	0.0261895	+	0.249176i
$329$	0.114356	−	1.08802i	0.00630464	−	0.0599846i
$330$	2.81033	+	0.597354i	0.154704	+	0.0328833i
$331$	−29.5595	+	13.1607i	−1.62474	+	0.723379i	−0.998420	−	0.0561900i	$-0.982105\pi$
$331$	−29.5595	+	13.1607i	−1.62474	+	0.723379i	−0.626316	+	0.779569i	$0.715438\pi$
$332$	−10.7890	−	11.9823i	−0.592121	−	0.657617i
$333$	1.61596	−	4.97340i	0.0885538	−	0.272541i
$334$	−2.88083	+	3.19949i	−0.157632	+	0.175068i
$335$	7.07875	+	12.2608i	0.386754	+	0.669877i
$336$	0.0559074	−	0.0968345i	0.00305000	−	0.00528276i
$337$	−0.334545	−	1.02962i	−0.0182238	−	0.0560871i	0.941531	−	0.336926i	$-0.109387\pi$
$337$	−0.334545	−	1.02962i	−0.0182238	−	0.0560871i	−0.959755	+	0.280839i	$0.909387\pi$
$338$	−9.02740	−	4.01926i	−0.491026	−	0.218619i
$339$	5.56122	+	4.04046i	0.302044	+	0.219448i
$340$	−0.861247			−0.0467076
$341$	−10.5095	−	12.0602i	−0.569124	−	0.653095i
$342$	−0.411609			−0.0222573
$343$	1.26531	+	0.919302i	0.0683204	+	0.0496377i
$344$	−9.30083	−	4.14100i	−0.501467	−	0.223268i
$345$	−1.67860	−	5.16619i	−0.0903726	−	0.278138i
$346$	2.29493	−	3.97493i	0.123376	−	0.213694i
$347$	4.73011	+	8.19279i	0.253926	+	0.439812i	0.964603	−	0.263706i	$-0.0849449\pi$
$347$	4.73011	+	8.19279i	0.253926	+	0.439812i	−0.710678	+	0.703518i	$0.751612\pi$
$348$	−3.75007	+	4.16488i	−0.201025	+	0.223261i
$349$	−4.10851	+	12.6447i	−0.219924	+	0.676855i	0.778844	+	0.627218i	$0.215807\pi$
$349$	−4.10851	+	12.6447i	−0.219924	+	0.676855i	−0.998767	+	0.0496372i	$0.984193\pi$
$350$	0.0748188	+	0.0830946i	0.00399923	+	0.00444160i
$351$	1.61320	−	0.718243i	0.0861062	−	0.0383370i
$352$	−2.81033	−	0.597354i	−0.149791	−	0.0318391i
$353$	−0.0916553	+	0.872042i	−0.00487832	+	0.0464141i	−0.996690	−	0.0812930i	$-0.974095\pi$
$353$	−0.0916553	+	0.872042i	−0.00487832	+	0.0464141i	0.991812	+	0.127707i	$0.0407617\pi$
$354$	−0.893263	−	8.49883i	−0.0474764	−	0.451708i
$355$	9.85889	−	2.09557i	0.523255	−	0.111221i
$356$	3.12962	−	2.27380i	0.165869	−	0.120511i
$357$	−0.0779085	+	0.0566038i	−0.00412335	+	0.00299579i
$358$	−14.3771	+	3.05595i	−0.759853	+	0.161512i
$359$	−0.886062	−	8.43031i	−0.0467645	−	0.444935i	−0.992703	−	0.120588i	$-0.961522\pi$
$359$	−0.886062	−	8.43031i	−0.0467645	−	0.444935i	0.945938	−	0.324347i	$-0.105145\pi$
$360$	−0.104528	+	0.994522i	−0.00550913	+	0.0524159i
$361$	18.4191	+	3.91510i	0.969426	+	0.206058i
$362$	−4.93447	+	2.19697i	−0.259350	+	0.115470i
$363$	1.83690	+	2.04009i	0.0964125	+	0.107077i
$364$	−0.0610154	+	0.187786i	−0.00319808	+	0.00984267i
$365$	−0.984989	+	1.09394i	−0.0515567	+	0.0572595i
$366$	−0.660345	−	1.14375i	−0.0345168	−	0.0597848i
$367$	4.22765	−	7.32250i	0.220681	−	0.382231i	−0.734334	−	0.678789i	$-0.762505\pi$
$367$	4.22765	−	7.32250i	0.220681	−	0.382231i	0.955015	+	0.296557i	$0.0958385\pi$
$368$	1.67860	+	5.16619i	0.0875029	+	0.269306i
$369$	−4.14533	−	1.84562i	−0.215797	−	0.0960792i
$370$	−4.23063	−	3.07373i	−0.219940	−	0.159796i
$371$	−1.29693			−0.0673331
$372$	3.79225	−	4.07662i	0.196619	−	0.211363i
$373$	−2.09235			−0.108338			−0.0541689	−	0.998532i	$-0.517251\pi$
$373$	−2.09235			−0.108338			−0.0541689	+	0.998532i	$0.517251\pi$
$374$	2.00188	+	1.45445i	0.103515	+	0.0752079i
$375$	−0.913545	−	0.406737i	−0.0471753	−	0.0210038i
$376$	−3.02347	−	9.30529i	−0.155924	−	0.479884i
$377$	4.94831	−	8.57072i	0.254851	−	0.441415i
$378$	0.0559074	+	0.0968345i	0.00287557	+	0.00498063i
$379$	4.37348	−	4.85724i	0.224651	−	0.249500i	−0.620274	−	0.784385i	$-0.712979\pi$
$379$	4.37348	−	4.85724i	0.224651	−	0.249500i	0.844925	+	0.534886i	$0.179645\pi$
$380$	−0.127194	+	0.391463i	−0.00652492	+	0.0200817i
$381$	−4.88229	−	5.42233i	−0.250127	−	0.277794i
$382$	6.77959	−	3.01847i	0.346874	−	0.154438i
$383$	−1.86424	−	0.396257i	−0.0952584	−	0.0202478i	0.160036	−	0.987111i	$-0.448839\pi$
$383$	−1.86424	−	0.396257i	−0.0952584	−	0.0202478i	−0.255294	+	0.966863i	$0.582172\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−0.0335805	−	0.319497i	−0.00171142	−	0.0162831i
$386$	8.08168	−	1.71781i	0.411347	−	0.0874345i
$387$	8.23663	−	5.98426i	0.418691	−	0.304197i
$388$	−1.01599	+	0.738159i	−0.0515790	+	0.0374743i
$389$	−8.05228	+	1.71156i	−0.408267	+	0.0867797i	−0.407467	−	0.913220i	$-0.633588\pi$
$389$	−8.05228	+	1.71156i	−0.408267	+	0.0867797i	−0.000799603		1.00000i	$0.500255\pi$
$390$	−0.184583	−	1.75619i	−0.00934674	−	0.0889283i
$391$	0.489019	−	4.65271i	0.0247308	−	0.235298i
$392$	6.83480	+	1.45278i	0.345210	+	0.0733766i
$393$	−5.03649	+	2.24239i	−0.254057	+	0.113114i
$394$	−10.3490	−	11.4937i	−0.521374	−	0.579045i
$395$	3.64242	−	11.2102i	0.183270	−	0.564047i
$396$	1.92249	−	2.13514i	0.0966087	−	0.107295i
$397$	−7.14879	−	12.3821i	−0.358788	−	0.621438i	0.628971	−	0.777429i	$-0.283476\pi$
$397$	−7.14879	−	12.3821i	−0.358788	−	0.621438i	−0.987759	+	0.155990i	$0.950143\pi$
$398$	−10.1349	+	17.5541i	−0.508016	+	0.879910i
$399$	0.0142222	+	0.0437714i	0.000712001	+	0.00219131i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	−21.3859	−	15.5378i	−1.06796	−	0.775919i	−0.0924163	−	0.995720i	$-0.529459\pi$
$401$	−21.3859	−	15.5378i	−1.06796	−	0.775919i	−0.975545	+	0.219801i	$0.929459\pi$
$402$	14.1575			0.706112
$403$	−5.05356	+	8.43376i	−0.251736	+	0.420116i
$404$	4.48170			0.222973
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	0.572478	+	0.254884i	0.0284116	+	0.0126497i
$407$	4.64283	+	14.2891i	0.230136	+	0.708287i
$408$	−0.430623	+	0.745861i	−0.0213190	+	0.0369256i
$409$	−6.13688	−	10.6294i	−0.303449	−	0.525590i	0.673465	−	0.739219i	$-0.264805\pi$
$409$	−6.13688	−	10.6294i	−0.303449	−	0.525590i	−0.976915	+	0.213629i	$0.931472\pi$
$410$	−3.03627	+	3.37212i	−0.149951	+	0.166537i
$411$	−3.04491	+	9.37127i	−0.150194	+	0.462250i
$412$	−5.27716	−	5.86088i	−0.259987	−	0.288745i
$413$	−0.872920	+	0.388649i	−0.0429536	+	0.0191242i
$414$	−5.31335	−	1.12939i	−0.261137	−	0.0555064i
$415$	1.68540	−	16.0355i	0.0827331	−	0.787152i
$416$	0.184583	+	1.75619i	0.00904994	+	0.0861044i
$417$	−12.2824	+	2.61071i	−0.601472	+	0.127847i
$418$	0.956744	−	0.695115i	0.0467959	−	0.0339992i
$419$	−20.3098	+	14.7559i	−0.992197	+	0.720874i	−0.960401	−	0.278621i	$-0.910123\pi$
$419$	−20.3098	+	14.7559i	−0.992197	+	0.720874i	−0.0317962	+	0.999494i	$0.510123\pi$
$420$	0.109371	−	0.0232476i	0.00533678	−	0.00113437i
$421$	1.12957	+	10.7471i	0.0550518	+	0.523783i	0.986946	+	0.161052i	$0.0514888\pi$
$421$	1.12957	+	10.7471i	0.0550518	+	0.523783i	−0.931894	+	0.362730i	$0.881845\pi$
$422$	1.27377	−	12.1191i	0.0620060	−	0.589947i
$423$	9.57036	+	2.03424i	0.465327	+	0.0989083i
$424$	−10.5961	+	4.71769i	−0.514592	+	0.229111i
$425$	−0.576286	−	0.640031i	−0.0279540	−	0.0310461i
$426$	3.11463	−	9.58583i	0.150904	−	0.464435i
$427$	−0.0988123	+	0.109742i	−0.00478186	+	0.00531080i
$428$	6.44919	+	11.1703i	0.311733	+	0.539938i
$429$	−2.53677	+	4.39381i	−0.122476	+	0.212135i
$430$	−3.14611	−	9.68273i	−0.151719	−	0.466943i
$431$	−5.62792	−	2.50571i	−0.271087	−	0.120696i	0.266691	−	0.963782i	$-0.414070\pi$
$431$	−5.62792	−	2.50571i	−0.271087	−	0.120696i	−0.537779	+	0.843086i	$0.680736\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	9.20805			0.442511			0.221255	−	0.975216i	$-0.428985\pi$
$433$	9.20805			0.442511			0.221255	+	0.975216i	$0.428985\pi$
$434$	−0.564550	−	0.262418i	−0.0270993	−	0.0125965i
$435$	−5.60440			−0.268710
$436$	0.923071	+	0.670651i	0.0442071	+	0.0321183i
$437$	−2.04258	−	0.909415i	−0.0977099	−	0.0435032i
$438$	0.454886	+	1.40000i	0.0217353	+	0.0668944i
$439$	0.439519	−	0.761269i	0.0209771	−	0.0363334i	−0.855346	−	0.518057i	$-0.826656\pi$
$439$	0.439519	−	0.761269i	0.0209771	−	0.0363334i	0.876323	+	0.481723i	$0.159989\pi$
$440$	−1.43656	−	2.48819i	−0.0684852	−	0.118620i
$441$	−4.67555	+	5.19272i	−0.222645	+	0.247273i
$442$	0.469967	−	1.44641i	0.0223541	−	0.0687987i
$443$	−4.36248	−	4.84502i	−0.207268	−	0.230194i	0.630544	−	0.776154i	$-0.282832\pi$
$443$	−4.36248	−	4.84502i	−0.207268	−	0.230194i	−0.837811	+	0.545960i	$0.816165\pi$
$444$	−4.77724	+	2.12696i	−0.226718	+	0.100941i
$445$	3.78388	+	0.804290i	0.179373	+	0.0381270i
$446$	1.25619	−	11.9518i	0.0594822	−	0.565935i
$447$	−0.631401	−	6.00738i	−0.0298642	−	0.284139i
$448$	−0.109371	+	0.0232476i	−0.00516732	+	0.00109835i
$449$	5.30955	−	3.85762i	0.250573	−	0.182052i	−0.455408	−	0.890283i	$-0.650506\pi$
$449$	5.30955	−	3.85762i	0.250573	−	0.182052i	0.705981	+	0.708231i	$0.250506\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	12.7522	−	2.71057i	0.600480	−	0.127636i
$452$	−0.718533	−	6.83639i	−0.0337970	−	0.321557i
$453$	0.896270	−	8.52744i	0.0421104	−	0.400654i
$454$	−20.0470	−	4.26112i	−0.940851	−	0.199984i
$455$	−0.180380	+	0.0803102i	−0.00845633	+	0.00376500i
$456$	0.275420	+	0.305885i	0.0128977	+	0.0143244i
$457$	−4.87738	+	15.0110i	−0.228154	+	0.702187i	0.769802	+	0.638283i	$0.220355\pi$
$457$	−4.87738	+	15.0110i	−0.228154	+	0.702187i	−0.997956	+	0.0639036i	$0.979645\pi$
$458$	4.85043	−	5.38695i	0.226646	−	0.251716i
$459$	−0.430623	−	0.745861i	−0.0200998	−	0.0348138i
$460$	−2.71603	+	4.70430i	−0.126635	+	0.219339i
$461$	−0.988249	−	3.04152i	−0.0460273	−	0.141658i	0.925402	−	0.378988i	$-0.123728\pi$
$461$	−0.988249	−	3.04152i	−0.0460273	−	0.141658i	−0.971429	+	0.237330i	$0.923728\pi$
$462$	−0.293483	−	0.130667i	−0.0136541	−	0.00607918i
$463$	−21.4660	−	15.5960i	−0.997610	−	0.724806i	−0.0360357	−	0.999351i	$-0.511473\pi$
$463$	−21.4660	−	15.5960i	−0.997610	−	0.724806i	−0.961574	+	0.274544i	$0.911473\pi$
$464$	5.60440			0.260178
$465$	5.56703	+	0.0903967i	0.258165	+	0.00419205i
$466$	23.3382			1.08112
$467$	1.18838	+	0.863409i	0.0549917	+	0.0399538i	0.614942	−	0.788573i	$-0.289180\pi$
$467$	1.18838	+	0.863409i	0.0549917	+	0.0399538i	−0.559950	+	0.828527i	$0.689180\pi$
$468$	−1.61320	−	0.718243i	−0.0745702	−	0.0332008i
$469$	−0.489180	−	1.50554i	−0.0225882	−	0.0695194i
$470$	4.89208	−	8.47334i	0.225655	−	0.390846i
$471$	0.822127	+	1.42397i	0.0378816	+	0.0656129i
$472$	−5.71815	+	6.35065i	−0.263199	+	0.292313i
$473$	−9.03914	+	27.8196i	−0.415620	+	1.27915i
$474$	−7.88712	−	8.75954i	−0.362268	−	0.402339i
$475$	−0.376024	+	0.167416i	−0.0172531	+	0.00768159i
$476$	0.0941958	+	0.0200219i	0.00431746	+	0.000917704i
$477$	1.21241	−	11.5353i	0.0555126	−	0.528167i
$478$	−2.74116	−	26.0804i	−0.125378	−	1.19289i
$479$	20.1285	−	4.27844i	0.919693	−	0.195487i	0.276343	−	0.961059i	$-0.410877\pi$
$479$	20.1285	−	4.27844i	0.919693	−	0.195487i	0.643350	+	0.765572i	$0.277544\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	7.47072	−	5.42780i	0.340636	−	0.247486i
$482$	−9.78531	+	2.07993i	−0.445709	+	0.0947383i
$483$	0.0634890	+	0.604057i	0.00288885	+	0.0274855i
$484$	0.286953	−	2.73017i	0.0130433	−	0.124099i
$485$	−1.22839	−	0.261102i	−0.0557782	−	0.0118560i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	2.94733	+	3.27334i	0.133556	+	0.148329i	0.806213	−	0.591625i	$-0.201514\pi$
$487$	2.94733	+	3.27334i	0.133556	+	0.148329i	−0.672657	+	0.739955i	$0.734847\pi$
$488$	−0.408115	+	1.25605i	−0.0184745	+	0.0568587i
$489$	0.380822	−	0.422946i	0.0172214	−	0.0191263i
$490$	3.49375	+	6.05135i	0.157831	+	0.273372i
$491$	−10.8570	+	18.8049i	−0.489970	+	0.848653i	−0.999933	−	0.0115433i	$-0.996326\pi$
$491$	−10.8570	+	18.8049i	−0.489970	+	0.848653i	0.509963	+	0.860196i	$0.329659\pi$
$492$	1.40221	+	4.31554i	0.0632163	+	0.194560i
$493$	−4.40947	−	1.96322i	−0.198593	−	0.0884191i
$494$	−0.588031	−	0.427230i	−0.0264568	−	0.0192220i
$495$	2.87311			0.129137
$496$	−5.56703	−	0.0903967i	−0.249967	−	0.00405893i
$497$	−1.12700			−0.0505528
$498$	−13.0445	−	9.47736i	−0.584536	−	0.424691i
$499$	−18.9093	−	8.41898i	−0.846499	−	0.376885i	−0.0627995	−	0.998026i	$-0.520003\pi$
$499$	−18.9093	−	8.41898i	−0.846499	−	0.376885i	−0.783699	+	0.621141i	$0.786670\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−2.15267	+	3.72853i	−0.0961742	+	0.166579i
$502$	−2.54261	−	4.40393i	−0.113482	−	0.196557i
$503$	−14.8271	+	16.4672i	−0.661109	+	0.734236i	−0.976688	−	0.214663i	$-0.931135\pi$
$503$	−14.8271	+	16.4672i	−0.661109	+	0.734236i	0.315579	+	0.948899i	$0.397801\pi$
$504$	0.0345527	−	0.106342i	0.00153910	−	0.00473686i
$505$	2.99884	+	3.33055i	0.133447	+	0.148208i
$506$	14.2576	−	6.34790i	0.633829	−	0.282199i
$507$	−9.66578	−	2.05452i	−0.429272	−	0.0912446i
$508$	−0.762688	+	7.25649i	−0.0338388	+	0.321955i
$509$	3.76687	+	35.8394i	0.166964	+	1.58855i	0.681980	+	0.731371i	$0.261119\pi$
$509$	3.76687	+	35.8394i	0.166964	+	1.58855i	−0.515016	+	0.857181i	$0.672214\pi$
$510$	−0.842426	+	0.179063i	−0.0373033	+	0.00792905i
$511$	0.133161	−	0.0967472i	0.00589070	−	0.00427985i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−0.402614	+	0.0855783i	−0.0177759	+	0.00377838i
$514$	−2.64705	−	25.1850i	−0.116756	−	1.11086i
$515$	0.824374	−	7.84339i	0.0363262	−	0.345621i
$516$	−9.95855	−	2.11676i	−0.438401	−	0.0931849i
$517$	−25.6807	+	11.4338i	−1.12944	+	0.502857i
$518$	0.391253	+	0.434530i	0.0171907	+	0.0190922i
$519$	1.41834	−	4.36521i	0.0622584	−	0.191612i
$520$	−1.18160	+	1.31229i	−0.0518164	+	0.0575479i
$521$	−0.987814	−	1.71094i	−0.0432769	−	0.0749578i	0.843576	−	0.537010i	$-0.180446\pi$
$521$	−0.987814	−	1.71094i	−0.0432769	−	0.0749578i	−0.886852	+	0.462053i	$0.847113\pi$
$522$	−2.80220	+	4.85355i	−0.122649	+	0.212434i
$523$	−9.09826	−	28.0016i	−0.397839	−	1.22442i	−0.926728	−	0.375732i	$-0.877391\pi$
$523$	−9.09826	−	28.0016i	−0.397839	−	1.22442i	0.528889	−	0.848691i	$-0.322609\pi$
$524$	5.03649	+	2.24239i	0.220020	+	0.0979592i
$525$	0.0904601	+	0.0657231i	0.00394800	+	0.00286839i
$526$	−1.98896			−0.0867226
$527$	4.34841	+	2.02126i	0.189420	+	0.0880473i
$528$	−2.87311			−0.125036
$529$	−5.26444	−	3.82484i	−0.228889	−	0.166297i
$530$	−10.5961	−	4.71769i	−0.460265	−	0.204923i
$531$	−2.64075	−	8.12739i	−0.114599	−	0.352699i
$532$	0.0230120	−	0.0398580i	0.000997697	−	0.00172806i
$533$	−4.00643	−	6.93933i	−0.173538	−	0.300576i
$534$	2.58848	−	2.87480i	0.112014	−	0.124405i
$535$	−3.98582	+	12.2671i	−0.172322	+	0.530352i
$536$	−9.47322	−	10.5211i	−0.409181	−	0.454441i
$537$	−13.4276	+	5.97833i	−0.579442	+	0.257984i
$538$	28.7200	+	6.10463i	1.23821	+	0.263189i
$539$	2.09850	−	19.9659i	0.0903888	−	0.859992i
$540$	0.104528	+	0.994522i	0.00449819	+	0.0427974i
$541$	22.8253	−	4.85166i	0.981336	−	0.208589i	0.310807	−	0.950473i	$-0.399401\pi$
$541$	22.8253	−	4.85166i	0.981336	−	0.208589i	0.670529	+	0.741884i	$0.266067\pi$
$542$	−8.34033	+	6.05961i	−0.358248	+	0.260282i
$543$	−4.36986	+	3.17489i	−0.187529	+	0.136248i
$544$	0.842426	−	0.179063i	0.0361187	−	0.00767727i
$545$	0.119265	+	1.13473i	0.00510874	+	0.0486064i
$546$	−0.0206392	+	0.196368i	−0.000883274	+	0.00840380i
$547$	−41.3075	−	8.78018i	−1.76618	−	0.375413i	−0.793684	−	0.608330i	$-0.791840\pi$
$547$	−41.3075	−	8.78018i	−1.76618	−	0.375413i	−0.972497	+	0.232917i	$0.925173\pi$
$548$	9.00165	−	4.00779i	0.384531	−	0.171204i
$549$	−0.883714	−	0.981463i	−0.0377160	−	0.0418878i
$550$	0.887841	−	2.73249i	0.0378577	−	0.116514i
$551$	−1.54356	+	1.71430i	−0.0657580	+	0.0730317i
$552$	2.71603	+	4.70430i	0.115602	+	0.200228i
$553$	−0.658988	+	1.14140i	−0.0280230	+	0.0485373i
$554$	1.93321	+	5.94980i	0.0821341	+	0.252783i
$555$	−4.77724	−	2.12696i	−0.202783	−	0.0902846i
$556$	10.1587	+	7.38071i	0.430824	+	0.313012i
$557$	10.2519			0.434388			0.217194	−	0.976128i	$-0.430310\pi$
$557$	10.2519			0.434388			0.217194	+	0.976128i	$0.430310\pi$
$558$	2.86180	−	4.77599i	0.121150	−	0.202184i
$559$	17.9783			0.760403
$560$	−0.0904601	−	0.0657231i	−0.00382264	−	0.00277731i
$561$	2.26053	+	1.00645i	0.0954397	+	0.0424925i
$562$	−1.25286	−	3.85592i	−0.0528489	−	0.162652i
$563$	5.75528	−	9.96844i	0.242556	−	0.420120i	−0.718885	−	0.695129i	$-0.755347\pi$
$563$	5.75528	−	9.96844i	0.242556	−	0.420120i	0.961442	+	0.275009i	$0.0886808\pi$
$564$	−4.89208	−	8.47334i	−0.205994	−	0.356792i
$565$	4.59963	−	5.10841i	0.193508	−	0.214912i
$566$	−9.59715	+	29.5370i	−0.403398	+	1.24153i
$567$	0.0748188	+	0.0830946i	0.00314209	+	0.00348965i
$568$	−9.20775	+	4.09956i	−0.386349	+	0.172014i
$569$	23.7087	+	5.03945i	0.993922	+	0.211265i	0.676039	−	0.736866i	$-0.263695\pi$
$569$	23.7087	+	5.03945i	0.993922	+	0.211265i	0.317882	+	0.948130i	$0.397028\pi$
$570$	−0.0430249	+	0.409354i	−0.00180211	+	0.0171460i
$571$	−4.64422	−	44.1868i	−0.194355	−	1.84916i	−0.463544	−	0.886074i	$-0.653422\pi$
$571$	−4.64422	−	44.1868i	−0.194355	−	1.84916i	0.269189	−	0.963087i	$-0.413244\pi$
$572$	4.96267	−	1.05485i	0.207500	−	0.0441054i
$573$	6.00386	−	4.36206i	0.250815	−	0.182228i
$574$	0.410475	−	0.298227i	0.0171329	−	0.0124478i
$575$	−5.31335	+	1.12939i	−0.221582	+	0.0470987i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	3.62823	−	34.5203i	0.151045	−	1.43710i	−0.612053	−	0.790816i	$-0.709656\pi$
$577$	3.62823	−	34.5203i	0.151045	−	1.43710i	0.763099	−	0.646282i	$-0.223677\pi$
$578$	15.9030	+	3.38028i	0.661476	+	0.140601i
$579$	7.54793	−	3.36055i	0.313681	−	0.139660i
$580$	3.75007	+	4.16488i	0.155713	+	0.172937i
$581$	−0.557122	+	1.71465i	−0.0231133	+	0.0711355i
$582$	−0.840315	+	0.933264i	−0.0348322	+	0.0386850i
$583$	16.6625	+	28.8602i	0.690088	+	1.19527i
$584$	0.736021	−	1.27483i	0.0304568	−	0.0527527i
$585$	−0.545683	−	1.67944i	−0.0225612	−	0.0694362i
$586$	16.0613	+	7.15097i	0.663488	+	0.295404i
$587$	29.1841	+	21.2035i	1.20456	+	0.875162i	0.994725	−	0.102575i	$-0.0327081\pi$
$587$	29.1841	+	21.2035i	1.20456	+	0.875162i	0.209833	+	0.977737i	$0.432708\pi$
$588$	6.98750			0.288160
$589$	1.56092	−	1.67797i	0.0643167	−	0.0691397i
$590$	−8.54565			−0.351819
$591$	−12.5125	−	9.09087i	−0.514696	−	0.373949i
$592$	4.77724	+	2.12696i	0.196343	+	0.0874177i
$593$	6.39029	+	19.6673i	0.262418	+	0.807639i	0.992277	+	0.124041i	$0.0395855\pi$
$593$	6.39029	+	19.6673i	0.262418	+	0.807639i	−0.729859	+	0.683597i	$0.760414\pi$
$594$	1.43656	−	2.48819i	0.0589427	−	0.102092i
$595$	0.0481501	+	0.0833984i	0.00197396	+	0.00341900i
$596$	−4.04186	+	4.48894i	−0.165561	+	0.183874i
$597$	−6.26371	+	19.2777i	−0.256356	+	0.788984i
$598$	−6.41849	−	7.12845i	−0.262472	−	0.291504i
$599$	−10.7176	+	4.77180i	−0.437911	+	0.194971i	−0.613837	−	0.789433i	$-0.710375\pi$
$599$	−10.7176	+	4.77180i	−0.437911	+	0.194971i	0.175926	+	0.984403i	$0.443708\pi$
$600$	0.978148	+	0.207912i	0.0399327	+	0.00848796i
$601$	3.75080	−	35.6864i	0.152998	−	1.45568i	−0.601234	−	0.799073i	$-0.705324\pi$
$601$	3.75080	−	35.6864i	0.152998	−	1.45568i	0.754233	−	0.656607i	$-0.228009\pi$
$602$	0.118994	+	1.13215i	0.00484984	+	0.0461432i
$603$	13.8481	−	2.94351i	0.563940	−	0.119869i
$604$	−6.93684	+	5.03991i	−0.282256	+	0.205071i
$605$	2.22092	−	1.61359i	0.0902933	−	0.0656019i
$606$	4.38376	−	0.931797i	0.178078	−	0.0378517i
$607$	3.27274	+	31.1380i	0.132836	+	1.26385i	0.834365	+	0.551212i	$0.185834\pi$
$607$	3.27274	+	31.1380i	0.132836	+	1.26385i	−0.701529	+	0.712641i	$0.747499\pi$
$608$	0.0430249	−	0.409354i	0.00174489	−	0.0166015i
$609$	0.612961	+	0.130289i	0.0248384	+	0.00527957i
$610$	−1.20651	+	0.537173i	−0.0488501	+	0.0217495i
$611$	11.5609	+	12.8397i	0.467705	+	0.519439i
$612$	−0.266140	+	0.819094i	−0.0107581	+	0.0331099i
$613$	19.4837	−	21.6389i	0.786940	−	0.873985i	−0.207614	−	0.978211i	$-0.566570\pi$
$613$	19.4837	−	21.6389i	0.786940	−	0.873985i	0.994554	+	0.104226i	$0.0332364\pi$
$614$	10.5288	+	18.2365i	0.424909	+	0.735964i
$615$	−2.26882	+	3.92970i	−0.0914875	+	0.158461i
$616$	0.0992739	+	0.305534i	0.00399986	+	0.0123103i
$617$	−25.5087	−	11.3572i	−1.02694	−	0.457224i	−0.177061	−	0.984200i	$-0.556659\pi$
$617$	−25.5087	−	11.3572i	−1.02694	−	0.457224i	−0.849880	+	0.526976i	$0.823326\pi$
$618$	−6.38039	−	4.63562i	−0.256657	−	0.186472i
$619$	−31.5587			−1.26845			−0.634225	−	0.773149i	$-0.718681\pi$
$619$	−31.5587			−1.26845			−0.634225	+	0.773149i	$0.718681\pi$
$620$	−3.65789	−	4.19760i	−0.146905	−	0.168580i
$621$	−5.43205			−0.217981
$622$	−18.9716	−	13.7837i	−0.760691	−	0.552674i
$623$	−0.395151	−	0.175933i	−0.0158314	−	0.00704859i
$624$	0.545683	+	1.67944i	0.0218448	+	0.0672314i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.32736	+	5.76316i	0.132988	+	0.230342i
$627$	0.791314	−	0.878843i	0.0316020	−	0.0350976i
$628$	0.508103	−	1.56378i	0.0202755	−	0.0624016i
$629$	−3.01360	−	3.34694i	−0.120160	−	0.133451i
$630$	0.102148	−	0.0454792i	0.00406967	−	0.00181193i
$631$	21.4097	+	4.55077i	0.852306	+	0.181163i	0.613295	−	0.789854i	$-0.289843\pi$
$631$	21.4097	+	4.55077i	0.852306	+	0.181163i	0.239011	+	0.971017i	$0.423177\pi$
$632$	−1.23209	+	11.7225i	−0.0490099	+	0.466298i
$633$	−1.27377	−	12.1191i	−0.0506277	−	0.481690i
$634$	16.6420	−	3.53736i	0.660938	−	0.140487i
$635$	−5.90296	+	4.28875i	−0.234252	+	0.170194i
$636$	−9.38369	+	6.81765i	−0.372087	+	0.270337i
$637$	−12.0694	+	2.56542i	−0.478205	+	0.101646i
$638$	−1.68313	−	16.0139i	−0.0666356	−	0.633995i
$639$	1.05356	−	10.0239i	0.0416781	−	0.396540i
$640$	−0.978148	−	0.207912i	−0.0386647	−	0.00821843i
$641$	−39.3530	+	17.5211i	−1.55435	+	0.692041i	−0.990961	−	0.134151i	$-0.957169\pi$
$641$	−39.3530	+	17.5211i	−1.55435	+	0.692041i	−0.563388	+	0.826192i	$0.690502\pi$
$642$	8.63070	+	9.58536i	0.340627	+	0.378304i
$643$	4.47527	−	13.7735i	0.176487	−	0.543172i	−0.823211	−	0.567736i	$-0.807820\pi$
$643$	4.47527	−	13.7735i	0.176487	−	0.543172i	0.999698	+	0.0245636i	$0.00781963\pi$
$644$	0.406419	−	0.451375i	0.0160152	−	0.0177866i
$645$	−5.09051	−	8.81703i	−0.200439	−	0.347170i
$646$	−0.177248	+	0.307003i	−0.00697375	+	0.0120789i
$647$	7.82722	+	24.0897i	0.307720	+	0.947064i	0.978648	+	0.205542i	$0.0658956\pi$
$647$	7.82722	+	24.0897i	0.307720	+	0.947064i	−0.670929	+	0.741522i	$0.734104\pi$
$648$	0.913545	+	0.406737i	0.0358875	+	0.0159781i
$649$	19.8635	+	14.4317i	0.779710	+	0.566493i
$650$	−1.76587			−0.0692630
$651$	−0.606773	−	0.139307i	−0.0237813	−	0.00545987i
$652$	−0.569130			−0.0222888
$653$	−31.5855	−	22.9482i	−1.23604	−	0.898034i	−0.238709	−	0.971091i	$-0.576724\pi$
$653$	−31.5855	−	22.9482i	−1.23604	−	0.898034i	−0.997328	+	0.0730575i	$0.976724\pi$
$654$	1.04234	+	0.464078i	0.0407586	+	0.0181469i
$655$	1.70365	+	5.24329i	0.0665670	+	0.204872i
$656$	2.26882	−	3.92970i	0.0885824	−	0.153429i
$657$	0.736021	+	1.27483i	0.0287149	+	0.0497357i
$658$	−0.732039	+	0.813012i	−0.0285379	+	0.0316945i
$659$	4.34083	−	13.3597i	0.169095	−	0.520420i	−0.830220	−	0.557436i	$-0.811785\pi$
$659$	4.34083	−	13.3597i	0.169095	−	0.520420i	0.999315	+	0.0370158i	$0.0117852\pi$
$660$	−1.92249	−	2.13514i	−0.0748328	−	0.0831102i
$661$	29.2704	−	13.0320i	1.13849	−	0.506887i	0.251123	−	0.967955i	$-0.419200\pi$
$661$	29.2704	−	13.0320i	1.13849	−	0.506887i	0.887365	+	0.461068i	$0.152534\pi$
$662$	31.6498	+	6.72737i	1.23010	+	0.261467i
$663$	0.158972	−	1.51251i	0.00617395	−	0.0587412i
$664$	1.68540	+	16.0355i	0.0654062	+	0.622299i
$665$	0.0450183	−	0.00956893i	0.00174573	−	0.000371067i
$666$	−4.23063	+	3.07373i	−0.163933	+	0.119105i
$667$	−24.6292	+	17.8942i	−0.953647	+	0.692865i
$668$	4.21126	−	0.895130i	0.162938	−	0.0346336i
$669$	−1.25619	−	11.9518i	−0.0485670	−	0.462084i
$670$	1.47986	−	14.0800i	0.0571721	−	0.543956i
$671$	3.71157	+	0.788919i	0.143284	+	0.0304559i
$672$	−0.102148	+	0.0454792i	−0.00394044	+	0.00175440i
$673$	−11.5091	−	12.7822i	−0.443643	−	0.492716i	0.479300	−	0.877651i	$-0.340890\pi$
$673$	−11.5091	−	12.7822i	−0.443643	−	0.492716i	−0.922944	+	0.384935i	$0.874224\pi$
$674$	−0.334545	+	1.02962i	−0.0128862	+	0.0396596i
$675$	−0.669131	+	0.743145i	−0.0257548	+	0.0286037i
$676$	4.94086	+	8.55782i	0.190033	+	0.329147i
$677$	−5.04565	+	8.73933i	−0.193920	+	0.335880i	−0.946546	−	0.322569i	$-0.895454\pi$
$677$	−5.04565	+	8.73933i	−0.193920	+	0.335880i	0.752626	+	0.658449i	$0.228787\pi$
$678$	−2.12420	−	6.53760i	−0.0815793	−	0.251075i
$679$	0.128281	+	0.0571142i	0.00492295	+	0.00219184i
$680$	0.696763	+	0.506228i	0.0267196	+	0.0194130i
$681$	−20.4948			−0.785364
$682$	1.41361	+	15.9342i	0.0541298	+	0.610154i
$683$	31.8487			1.21866			0.609328	−	0.792918i	$-0.291439\pi$
$683$	31.8487			1.21866			0.609328	+	0.792918i	$0.291439\pi$
$684$	0.332999	+	0.241938i	0.0127325	+	0.00925072i
$685$	9.00165	+	4.00779i	0.343935	+	0.153130i
$686$	−0.483306	−	1.48746i	−0.0184527	−	0.0567916i
$687$	3.62443	−	6.27770i	0.138281	−	0.239509i
$688$	5.09051	+	8.81703i	0.194074	+	0.336146i
$689$	13.7052	−	15.2211i	0.522126	−	0.579879i
$690$	−1.67860	+	5.16619i	−0.0639031	+	0.196673i
$691$	30.3522	+	33.7095i	1.15465	+	1.28237i	0.953020	+	0.302908i	$0.0979574\pi$
$691$	30.3522	+	33.7095i	1.15465	+	1.28237i	0.201631	+	0.979462i	$0.435376\pi$
$692$	−4.19304	+	1.86686i	−0.159396	+	0.0709675i
$693$	−0.314237	−	0.0667931i	−0.0119369	−	0.00253726i
$694$	0.988862	−	9.40839i	0.0375367	−	0.357138i
$695$	1.31254	+	12.4880i	0.0497876	+	0.473698i
$696$	5.48193	−	1.16522i	0.207792	−	0.0441675i
$697$	−3.16165	+	2.29708i	−0.119756	+	0.0870080i
$698$	10.7562	−	7.81485i	0.407129	−	0.295797i
$699$	22.8282	−	4.85229i	0.863443	−	0.183530i
$700$	−0.0116878	−	0.111202i	−0.000441759	−	0.00420305i
$701$	2.18027	−	20.7439i	0.0823476	−	0.783485i	−0.872944	−	0.487820i	$-0.837792\pi$
$701$	2.18027	−	20.7439i	0.0823476	−	0.783485i	0.955292	−	0.295665i	$-0.0955411\pi$
$702$	−1.72728	−	0.367144i	−0.0651919	−	0.0138570i
$703$	−1.96636	+	0.875478i	−0.0741625	+	0.0330193i
$704$	1.92249	+	2.13514i	0.0724565	+	0.0804711i
$705$	3.02347	−	9.30529i	0.113871	−	0.350458i
$706$	0.586724	−	0.651623i	0.0220816	−	0.0245242i
$707$	−0.250560	−	0.433983i	−0.00942329	−	0.0163216i
$708$	−4.27282	+	7.40075i	−0.160583	+	0.278137i
$709$	12.9565	+	39.8759i	0.486590	+	1.49757i	0.829664	+	0.558262i	$0.188532\pi$
$709$	12.9565	+	39.8759i	0.486590	+	1.49757i	−0.343074	+	0.939308i	$0.611468\pi$
$710$	−9.20775	−	4.09956i	−0.345561	−	0.153854i
$711$	−9.53598	−	6.92830i	−0.357627	−	0.259831i
$712$	−3.86842			−0.144975
$713$	24.7536	−	17.3776i	0.927031	−	0.650796i
$714$	0.0963002			0.00360394
$715$	4.10458	+	2.98215i	0.153503	+	0.111526i
$716$	13.4276	+	5.97833i	0.501811	+	0.223421i
$717$	−8.10368	−	24.9406i	−0.302637	−	0.931422i
$718$	−4.23838	+	7.34108i	−0.158175	+	0.273967i
$719$	−15.8780	−	27.5016i	−0.592151	−	1.02564i	−0.993942	−	0.109905i	$-0.964945\pi$
$719$	−15.8780	−	27.5016i	−0.592151	−	1.02564i	0.401791	−	0.915731i	$-0.368388\pi$
$720$	0.669131	−	0.743145i	0.0249370	−	0.0276954i
$721$	−0.272503	+	0.838678i	−0.0101485	+	0.0312340i
$722$	−12.6001	−	13.9938i	−0.468928	−	0.520797i
$723$	−9.13903	+	4.06896i	−0.339884	+	0.151326i
$724$	5.28341	+	1.12302i	0.196357	+	0.0417369i
$725$	−0.585819	+	5.57370i	−0.0217568	+	0.207002i
$726$	−0.286953	−	2.73017i	−0.0106498	−	0.101326i
$727$	−40.2166	+	8.54831i	−1.49155	+	0.317039i	−0.880308	−	0.474403i	$-0.842664\pi$
$727$	−40.2166	+	8.54831i	−1.49155	+	0.317039i	−0.611244	+	0.791442i	$0.709331\pi$
$728$	0.159741	−	0.116058i	0.00592038	−	0.00430141i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	1.43987	−	0.306055i	0.0532922	−	0.0113276i
$731$	−0.916545	−	8.72034i	−0.0338996	−	0.322533i
$732$	−0.138050	+	1.31345i	−0.00510246	+	0.0485467i
$733$	18.7677	+	3.98920i	0.693201	+	0.147344i	0.541022	−	0.841009i	$-0.318038\pi$
$733$	18.7677	+	3.98920i	0.693201	+	0.147344i	0.152179	+	0.988353i	$0.451371\pi$
$734$	−7.72430	+	3.43908i	−0.285109	+	0.126939i
$735$	4.67555	+	5.19272i	0.172460	+	0.191536i
$736$	1.67860	−	5.16619i	0.0618739	−	0.190428i
$737$	−27.2177	+	30.2283i	−1.00258	+	1.11347i
$738$	2.26882	+	3.92970i	0.0835163	+	0.144654i
$739$	−20.4252	+	35.3774i	−0.751351	+	1.30138i	0.195817	+	0.980641i	$0.437264\pi$
$739$	−20.4252	+	35.3774i	−0.751351	+	1.30138i	−0.947168	+	0.320738i	$0.896069\pi$
$740$	1.61596	+	4.97340i	0.0594037	+	0.182826i
$741$	−0.664007	−	0.295635i	−0.0243929	−	0.0108604i
$742$	1.04924	+	0.762315i	0.0385187	+	0.0279855i
$743$	11.9491			0.438371			0.219185	−	0.975683i	$-0.429660\pi$
$743$	11.9491			0.438371			0.219185	+	0.975683i	$0.429660\pi$
$744$	−5.46417	+	1.06903i	−0.200326	+	0.0391925i
$745$	−6.04047			−0.221306
$746$	1.69275	+	1.22985i	0.0619758	+	0.0450281i
$747$	−14.7299	−	6.55816i	−0.538938	−	0.239950i
$748$	−0.764650	−	2.35335i	−0.0279584	−	0.0860471i
$749$	0.721115	−	1.24901i	0.0263490	−	0.0456378i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	−21.3488	+	23.7103i	−0.779029	+	0.865200i	−0.993768	−	0.111472i	$-0.964443\pi$
$751$	−21.3488	+	23.7103i	−0.779029	+	0.865200i	0.214738	+	0.976672i	$0.431110\pi$
$752$	−3.02347	+	9.30529i	−0.110255	+	0.339329i
$753$	−3.40268	−	3.77906i	−0.124001	−	0.137717i
$754$	−9.04101	+	4.02532i	−0.329254	+	0.146593i
$755$	−8.38704	−	1.78272i	−0.305236	−	0.0648798i
$756$	0.0116878	−	0.111202i	0.000425083	−	0.00404439i
$757$	−3.04017	−	28.9253i	−0.110497	−	1.05131i	−0.899501	−	0.436919i	$-0.856070\pi$
$757$	−3.04017	−	28.9253i	−0.110497	−	1.05131i	0.789004	−	0.614388i	$-0.210597\pi$
$758$	−6.39323	+	1.35892i	−0.232213	+	0.0493583i
$759$	12.6263	−	9.17351i	0.458304	−	0.332977i
$760$	0.332999	−	0.241938i	0.0120791	−	0.00877600i
$761$	23.5680	−	5.00953i	0.854339	−	0.181595i	0.240132	−	0.970740i	$-0.422809\pi$
$761$	23.5680	−	5.00953i	0.854339	−	0.181595i	0.614207	+	0.789145i	$0.289476\pi$
$762$	0.762688	+	7.25649i	0.0276293	+	0.262875i
$763$	0.0133356	−	0.126880i	0.000482780	−	0.00459335i
$764$	−7.25901	−	1.54295i	−0.262622	−	0.0558220i
$765$	−0.786788	+	0.350301i	−0.0284464	+	0.0126651i
$766$	1.27529	+	1.41635i	0.0460781	+	0.0511750i
$767$	4.66321	−	14.3519i	0.168379	−	0.518217i
$768$	−0.669131	+	0.743145i	−0.0241452	+	0.0268159i
$769$	9.11032	+	15.7795i	0.328527	+	0.569025i	0.982220	−	0.187735i	$-0.0601146\pi$
$769$	9.11032	+	15.7795i	0.328527	+	0.569025i	−0.653693	+	0.756760i	$0.726781\pi$
$770$	−0.160628	+	0.278217i	−0.00578865	+	0.0100262i
$771$	−7.82545	−	24.0843i	−0.281827	−	0.867374i
$772$	−7.54793	−	3.36055i	−0.271656	−	0.120949i
$773$	18.0296	+	13.0993i	0.648481	+	0.471149i	0.862753	−	0.505625i	$-0.168738\pi$
$773$	18.0296	+	13.0993i	0.648481	+	0.471149i	−0.214272	+	0.976774i	$0.568738\pi$
$774$	−10.1810			−0.365950
$775$	0.671815	−	5.52708i	0.0241323	−	0.198539i
$776$	1.25583			0.0450817
$777$	0.473047	+	0.343689i	0.0169705	+	0.0123298i
$778$	7.52046	+	3.34832i	0.269622	+	0.120043i
$779$	0.577160	+	1.77632i	0.0206789	+	0.0636432i
$780$	−0.882933	+	1.52929i	−0.0316141	+	0.0547572i
$781$	14.4793	+	25.0788i	0.518109	+	0.897391i
$782$	−3.13042	+	3.47668i	−0.111944	+	0.124326i
$783$	−1.73185	+	5.33010i	−0.0618914	+	0.190482i
$784$	−4.67555	−	5.19272i	−0.166984	−	0.185454i
$785$	1.50210	−	0.668779i	0.0536123	−	0.0238697i
$786$	5.39265	+	1.14624i	0.192349	+	0.0408851i
$787$	3.84274	−	36.5612i	0.136979	−	1.30327i	−0.682808	−	0.730598i	$-0.739242\pi$
$787$	3.84274	−	36.5612i	0.136979	−	1.30327i	0.819787	−	0.572669i	$-0.194092\pi$
$788$	1.61667	+	15.3816i	0.0575915	+	0.547947i
$789$	−1.94549	+	0.413527i	−0.0692614	+	0.0147220i
$790$	−9.53598	+	6.92830i	−0.339275	+	0.246498i
$791$	−0.621827	+	0.451784i	−0.0221096	+	0.0160636i
$792$	−2.81033	+	0.597354i	−0.0998607	+	0.0212261i
$793$	−0.243777	−	2.31938i	−0.00865678	−	0.0823638i
$794$	−1.49450	+	14.2193i	−0.0530380	+	0.504623i
$795$	−11.3454	−	2.41154i	−0.402380	−	0.0855286i
$796$	18.5174	−	8.24446i	0.656330	−	0.292217i
$797$	24.4982	+	27.2080i	0.867770	+	0.963756i	0.999621	−	0.0275137i	$-0.00875899\pi$
$797$	24.4982	+	27.2080i	0.867770	+	0.963756i	−0.131852	+	0.991269i	$0.542092\pi$
$798$	0.0142222	−	0.0437714i	0.000503460	−	0.00154949i
$799$	5.63848	−	6.26217i	0.199475	−	0.221540i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	1.93421	−	3.35015i	0.0683419	−	0.118372i
$802$	8.16869	+	25.1406i	0.288446	+	0.887747i
$803$	−3.86370	−	1.72023i	−0.136347	−	0.0607056i
$804$	−11.4537	−	8.32157i	−0.403940	−	0.293479i
$805$	0.607384			0.0214075
$806$	9.04566	−	3.85265i	0.318620	−	0.135704i
$807$	29.3617			1.03358
$808$	−3.62577	−	2.63428i	−0.127554	−	0.0926735i
$809$	49.3193	+	21.9584i	1.73397	+	0.772015i	0.995178	+	0.0980842i	$0.0312714\pi$
$809$	49.3193	+	21.9584i	1.73397	+	0.772015i	0.738795	+	0.673930i	$0.235395\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	−4.60051	+	7.96831i	−0.161546	+	0.279805i	−0.935423	−	0.353530i	$-0.884981\pi$
$811$	−4.60051	+	7.96831i	−0.161546	+	0.279805i	0.773878	+	0.633335i	$0.218315\pi$
$812$	−0.313327	−	0.542699i	−0.0109956	−	0.0190450i
$813$	−6.89821	+	7.66124i	−0.241931	+	0.268691i
$814$	4.64283	−	14.2891i	0.162731	−	0.500834i
$815$	−0.380822	−	0.422946i	−0.0133396	−	0.0148151i
$816$	0.786788	−	0.350301i	0.0275431	−	0.0122630i
$817$	−4.09903	−	0.871275i	−0.143407	−	0.0304821i
$818$	−1.28296	+	12.2065i	−0.0448576	+	0.426791i
$819$	0.0206392	+	0.196368i	0.000721191	+	0.00686167i
$820$	4.43847	−	0.943427i	0.154998	−	0.0329459i
$821$	5.87779	−	4.27046i	0.205136	−	0.149040i	−0.480474	−	0.877009i	$-0.659535\pi$
$821$	5.87779	−	4.27046i	0.205136	−	0.149040i	0.685610	+	0.727969i	$0.259535\pi$
$822$	7.97167	−	5.79176i	0.278044	−	0.202011i
$823$	−13.3576	+	2.83924i	−0.465616	+	0.0989698i	−0.434745	−	0.900554i	$-0.643162\pi$
$823$	−13.3576	+	2.83924i	−0.465616	+	0.0989698i	−0.0308712	+	0.999523i	$0.509828\pi$
$824$	0.824374	+	7.84339i	0.0287184	+	0.273237i
$825$	0.300322	−	2.85738i	0.0104559	−	0.0994811i
$826$	0.934650	+	0.198666i	0.0325206	+	0.00691247i
$827$	−32.8833	+	14.6406i	−1.14346	+	0.509103i	−0.888967	−	0.457970i	$-0.848577\pi$
$827$	−32.8833	+	14.6406i	−1.14346	+	0.509103i	−0.254497	+	0.967074i	$0.581910\pi$
$828$	3.63475	+	4.03680i	0.126316	+	0.140289i
$829$	11.9903	−	36.9024i	0.416441	−	1.28167i	−0.494515	−	0.869169i	$-0.664654\pi$
$829$	11.9903	−	36.9024i	0.416441	−	1.28167i	0.910956	−	0.412504i	$-0.135346\pi$
$830$	−10.7890	+	11.9823i	−0.374490	+	0.415913i
$831$	3.12800	+	5.41785i	0.108509	+	0.187943i
$832$	0.882933	−	1.52929i	0.0306102	−	0.0530184i
$833$	1.85965	+	5.72342i	0.0644331	+	0.198305i
$834$	11.4712	+	5.10731i	0.397216	+	0.176852i
$835$	3.48309	+	2.53061i	0.120537	+	0.0875755i
$836$	−1.18260			−0.0409011
$837$	1.80628	−	5.26663i	0.0624341	−	0.182041i
$838$	25.1043			0.867212
$839$	34.5032	+	25.0680i	1.19118	+	0.865444i	0.993389	−	0.114799i	$-0.0366225\pi$
$839$	34.5032	+	25.0680i	1.19118	+	0.865444i	0.197793	+	0.980244i	$0.436622\pi$
$840$	−0.102148	−	0.0454792i	−0.00352444	−	0.00156918i
$841$	0.744505	+	2.29135i	0.0256726	+	0.0790120i
$842$	5.40316	−	9.35855i	0.186205	−	0.322517i
$843$	−2.02718	−	3.51117i	−0.0698197	−	0.120931i
$844$	−8.15391	+	9.05584i	−0.280669	+	0.311715i
$845$	−3.05362	+	9.39807i	−0.105048	+	0.323303i
$846$	−6.54688	−	7.27105i	−0.225087	−	0.249984i
$847$	−0.280418	+	0.124850i	−0.00963527	+	0.00428990i
$848$	11.3454	+	2.41154i	0.389603	+	0.0828127i
$849$	−3.24634	+	30.8869i	−0.111414	+	1.06004i
$850$	0.0900248	+	0.856529i	0.00308782	+	0.0293787i
$851$	−27.7853	+	5.90595i	−0.952469	+	0.202453i
$852$	−8.15420	+	5.92437i	−0.279358	+	0.202966i
$853$	8.47406	−	6.15676i	0.290146	−	0.210804i	−0.433185	−	0.901305i	$-0.642610\pi$
$853$	8.47406	−	6.15676i	0.290146	−	0.210804i	0.723331	+	0.690502i	$0.242610\pi$
$854$	0.144446	−	0.0307029i	0.00494283	−	0.00105063i
$855$	0.0430249	+	0.409354i	0.00147142	+	0.0139996i
$856$	1.34825	−	12.8277i	0.0460822	−	0.438442i
$857$	37.9608	+	8.06882i	1.29672	+	0.275626i	0.804034	−	0.594584i	$-0.202683\pi$
$857$	37.9608	+	8.06882i	1.29672	+	0.275626i	0.492682	+	0.870209i	$0.336016\pi$
$858$	4.63491	−	2.06359i	0.158233	−	0.0704499i
$859$	−2.13017	−	2.36579i	−0.0726805	−	0.0807199i	0.705708	−	0.708503i	$-0.250629\pi$
$859$	−2.13017	−	2.36579i	−0.0726805	−	0.0807199i	−0.778388	+	0.627783i	$0.783962\pi$
$860$	−3.14611	+	9.68273i	−0.107281	+	0.330178i
$861$	0.339500	−	0.377053i	0.0115701	−	0.0128499i
$862$	3.08026	+	5.33517i	0.104914	+	0.181717i
$863$	15.3157	−	26.5276i	0.521352	−	0.903009i	−0.478339	−	0.878175i	$-0.658761\pi$
$863$	15.3157	−	26.5276i	0.521352	−	0.903009i	0.999692	−	0.0248336i	$-0.00790559\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−4.19304	−	1.86686i	−0.142568	−	0.0634753i
$866$	−7.44947	−	5.41236i	−0.253143	−	0.183919i
$867$	16.2583			0.552159
$868$	0.302485	+	0.544135i	0.0102670	+	0.0184691i
$869$	33.8658			1.14882
$870$	4.53405	+	3.29418i	0.153719	+	0.111683i
$871$	22.8389	+	10.1685i	0.773866	+	0.344547i
$872$	−0.352582	−	1.08514i	−0.0119399	−	0.0367473i
$873$	−0.627915	+	1.08758i	−0.0212517	+	0.0368090i
$874$	1.11794	+	1.93633i	0.0378149	+	0.0654974i
$875$	0.0748188	−	0.0830946i	0.00252934	−	0.00280911i
$876$	0.454886	−	1.40000i	0.0153692	−	0.0473015i
$877$	38.8084	+	43.1011i	1.31047	+	1.45542i	0.805901	+	0.592050i	$0.201681\pi$
$877$	38.8084	+	43.1011i	1.31047	+	1.45542i	0.504567	+	0.863373i	$0.331652\pi$
$878$	−0.803041	+	0.357537i	−0.0271013	+	0.0120663i
$879$	17.1971	+	3.65536i	0.580045	+	0.123292i
$880$	−0.300322	+	2.85738i	−0.0101239	+	0.0963221i
$881$	−2.20778	−	21.0057i	−0.0743821	−	0.707699i	−0.966634	−	0.256161i	$-0.917542\pi$
$881$	−2.20778	−	21.0057i	−0.0743821	−	0.707699i	0.892252	−	0.451538i	$-0.149124\pi$
$882$	6.83480	−	1.45278i	0.230140	−	0.0489177i
$883$	22.2996	−	16.2016i	0.750442	−	0.545228i	−0.145522	−	0.989355i	$-0.546486\pi$
$883$	22.2996	−	16.2016i	0.750442	−	0.545228i	0.895964	+	0.444127i	$0.146486\pi$
$884$	−1.23039	+	0.893931i	−0.0413825	+	0.0300662i
$885$	−8.35890	+	1.77674i	−0.280981	+	0.0597245i
$886$	0.681486	+	6.48390i	0.0228950	+	0.217831i
$887$	0.587223	−	5.58706i	0.0197170	−	0.187595i	−0.980230	−	0.197860i	$-0.936601\pi$
$887$	0.587223	−	5.58706i	0.0197170	−	0.187595i	0.999947	+	0.0102650i	$0.00326752\pi$
$888$	5.11507	+	1.08724i	0.171650	+	0.0364854i
$889$	0.745319	−	0.331837i	0.0249972	−	0.0111295i
$890$	−2.58848	−	2.87480i	−0.0867660	−	0.0963634i
$891$	0.887841	−	2.73249i	0.0297438	−	0.0915420i
$892$	−8.04138	+	8.93086i	−0.269245	+	0.299027i
$893$	−2.01363	−	3.48770i	−0.0673834	−	0.116711i
$894$	−3.02024	+	5.23120i	−0.101012	+	0.174958i
$895$	4.54202	+	13.9789i	0.151823	+	0.467263i
$896$	0.102148	+	0.0454792i	0.00341252	+	0.00151935i
$897$	−7.76032	−	5.63820i	−0.259109	−	0.188254i
$898$	−6.56297			−0.219009
$899$	−9.15946	−	29.8294i	−0.305485	−	0.994865i
$900$	1.00000			0.0333333
$901$	−8.08167	−	5.87168i	−0.269239	−	0.195614i
$902$	−11.9100	−	5.30268i	−0.396560	−	0.176560i
$903$	0.351782	+	1.08267i	0.0117066	+	0.0360291i
$904$	−3.43702	+	5.95310i	−0.114314	+	0.197997i
$905$	2.70072	+	4.67779i	0.0897751	+	0.155495i
$906$	−5.73740	+	6.37203i	−0.190612	+	0.211696i
$907$	−3.00597	+	9.25142i	−0.0998116	+	0.307188i	−0.988478	−	0.151366i	$-0.951633\pi$
$907$	−3.00597	+	9.25142i	−0.0998116	+	0.307188i	0.888666	+	0.458555i	$0.151633\pi$
$908$	13.7137	+	15.2306i	0.455106	+	0.505446i
$909$	4.09423	−	1.82287i	0.135797	−	0.0604608i
$910$	0.193135	+	0.0410522i	0.00640238	+	0.00136087i
$911$	−0.999526	+	9.50986i	−0.0331158	+	0.315076i	0.965407	+	0.260747i	$0.0839687\pi$
$911$	−0.999526	+	9.50986i	−0.0331158	+	0.315076i	−0.998523	+	0.0543291i	$0.982698\pi$
$912$	−0.0430249	−	0.409354i	−0.00142470	−	0.0135551i
$913$	45.3133	−	9.63164i	1.49965	−	0.318761i
$914$	12.7691	−	9.27733i	0.422366	−	0.306867i
$915$	−1.06846	+	0.776282i	−0.0353222	+	0.0256631i
$916$	−7.09045	+	1.50712i	−0.234275	+	0.0497967i
$917$	−0.0644365	−	0.613072i	−0.00212788	−	0.0202454i
$918$	−0.0900248	+	0.856529i	−0.00297126	+	0.0282697i
$919$	29.7076	+	6.31455i	0.979964	+	0.208298i	0.669927	−	0.742427i	$-0.266325\pi$
$919$	29.7076	+	6.31455i	0.979964	+	0.208298i	0.310037	+	0.950725i	$0.399659\pi$
$920$	4.96243	−	2.20942i	0.163606	−	0.0728423i
$921$	14.0903	+	15.6489i	0.464292	+	0.515648i
$922$	−0.988249	+	3.04152i	−0.0325462	+	0.100167i
$923$	11.9095	−	13.2268i	0.392005	−	0.435365i
$924$	0.160628	+	0.278217i	0.00528429	+	0.00915266i
$925$	−2.61467	+	4.52874i	−0.0859698	+	0.148904i
$926$	8.19929	+	25.2348i	0.269445	+	0.829267i
$927$	−7.20476	−	3.20777i	−0.236635	−	0.105357i
$928$	−4.53405	−	3.29418i	−0.148838	−	0.108137i
$929$	−15.5004			−0.508553			−0.254277	−	0.967132i	$-0.581837\pi$
$929$	−15.5004			−0.508553			−0.254277	+	0.967132i	$0.581837\pi$
$930$	−4.45069	−	3.34535i	−0.145944	−	0.109698i
$931$	2.87612			0.0942609
$932$	−18.8810	−	13.7179i	−0.618469	−	0.449344i
$933$	−21.4228	−	9.53804i	−0.701351	−	0.312261i
$934$	−0.453921	−	1.39703i	−0.0148528	−	0.0457121i
$935$	1.23723	−	2.14295i	0.0404618	−	0.0700818i
$936$	0.882933	+	1.52929i	0.0288596	+	0.0499862i
$937$	−19.5779	+	21.7434i	−0.639581	+	0.710326i	−0.972572	−	0.232604i	$-0.925275\pi$
$937$	−19.5779	+	21.7434i	−0.639581	+	0.710326i	0.332991	+	0.942930i	$0.391942\pi$
$938$	−0.489180	+	1.50554i	−0.0159723	+	0.0491577i
$939$	4.45288	+	4.94543i	0.145314	+	0.161388i
$940$	−8.93828	+	3.97958i	−0.291535	+	0.129800i
$941$	−10.6367	−	2.26091i	−0.346748	−	0.0737035i	0.0312458	−	0.999512i	$-0.490053\pi$
$941$	−10.6367	−	2.26091i	−0.346748	−	0.0737035i	−0.377994	+	0.925808i	$0.623386\pi$
$942$	0.171871	−	1.63525i	0.00559987	−	0.0532792i
$943$	2.57649	+	24.5136i	0.0839019	+	0.798274i
$944$	8.35890	−	1.77674i	0.272059	−	0.0578280i
$945$	0.0904601	−	0.0657231i	0.00294267	−	0.00213797i
$946$	23.6648	−	17.1935i	0.769408	−	0.559008i
$947$	29.0304	−	6.17061i	0.943362	−	0.200518i	0.289540	−	0.957166i	$-0.406498\pi$
$947$	29.0304	−	6.17061i	0.943362	−	0.200518i	0.653822	+	0.756648i	$0.273164\pi$
$948$	1.23209	+	11.7225i	0.0400164	+	0.380731i
$949$	−0.271714	+	2.58519i	−0.00882022	+	0.0839188i
$950$	0.402614	+	0.0855783i	0.0130625	+	0.00277653i
$951$	15.5429	−	6.92013i	0.504012	−	0.224400i
$952$	−0.0644374	−	0.0715650i	−0.00208843	−	0.00231943i
$953$	9.30019	−	28.6230i	0.301263	−	0.927191i	−0.679783	−	0.733413i	$-0.737926\pi$
$953$	9.30019	−	28.6230i	0.301263	−	0.927191i	0.981045	−	0.193778i	$-0.0620740\pi$
$954$	−7.76116	+	8.61965i	−0.251277	+	0.279071i
$955$	−3.71059	−	6.42693i	−0.120072	−	0.207971i
$956$	−13.1120	+	22.7107i	−0.424073	+	0.734517i
$957$	−4.97582	−	15.3140i	−0.160845	−	0.495031i
$958$	−18.7991	−	8.36989i	−0.607371	−	0.270419i
$959$	−0.891352	−	0.647605i	−0.0287833	−	0.0209123i
$960$	−1.00000			−0.0322749
$961$	8.61726	+	29.7782i	0.277976	+	0.960588i
$962$	−9.23432			−0.297726
$963$	10.4350	+	7.58148i	0.336263	+	0.244310i
$964$	9.13903	+	4.06896i	0.294348	+	0.131052i
$965$	−2.55317	−	7.85785i	−0.0821895	−	0.252953i
$966$	0.303692	−	0.526010i	0.00977114	−	0.0169241i
$967$	−28.1482	−	48.7541i	−0.905185	−	1.56783i	−0.820669	−	0.571404i	$-0.806399\pi$
$967$	−28.1482	−	48.7541i	−0.905185	−	1.56783i	−0.0845155	−	0.996422i	$-0.526934\pi$
$968$	−1.83690	+	2.04009i	−0.0590403	+	0.0655709i
$969$	−0.109546	+	0.337147i	−0.00351911	+	0.0108307i
$970$	0.840315	+	0.933264i	0.0269809	+	0.0299653i
$971$	−29.5795	+	13.1696i	−0.949250	+	0.422633i	−0.822159	−	0.569258i	$-0.807231\pi$
$971$	−29.5795	+	13.1696i	−0.949250	+	0.422633i	−0.127091	+	0.991891i	$0.540564\pi$
$972$	0.978148	+	0.207912i	0.0313741	+	0.00666877i
$973$	0.146762	−	1.39635i	0.00470497	−	0.0447648i
$974$	−0.460418	−	4.38059i	−0.0147528	−	0.140363i
$975$	−1.72728	+	0.367144i	−0.0553172	+	0.0117580i
$976$	1.06846	−	0.776282i	0.0342006	−	0.0248482i
$977$	−25.8418	+	18.7751i	−0.826751	+	0.600670i	−0.918638	−	0.395100i	$-0.870710\pi$
$977$	−25.8418	+	18.7751i	−0.826751	+	0.600670i	0.0918871	+	0.995769i	$0.470710\pi$
$978$	−0.556693	+	0.118329i	−0.0178011	+	0.00378373i
$979$	1.16177	+	11.0535i	0.0371304	+	0.353272i
$980$	0.730392	−	6.94922i	0.0233315	−	0.221985i
$981$	1.11605	+	0.237223i	0.0356326	+	0.00757394i
$982$	19.8367	−	8.83189i	0.633016	−	0.281837i
$983$	−13.8855	−	15.4214i	−0.442878	−	0.491866i	0.479832	−	0.877360i	$-0.340697\pi$
$983$	−13.8855	−	15.4214i	−0.442878	−	0.491866i	−0.922710	+	0.385495i	$0.874031\pi$
$984$	1.40221	−	4.31554i	0.0447007	−	0.137575i
$985$	−10.3490	+	11.4937i	−0.329746	+	0.366220i
$986$	2.41338	+	4.18010i	0.0768578	+	0.133122i
$987$	−0.547008	+	0.947445i	−0.0174114	+	0.0301575i
$988$	0.224608	+	0.691272i	0.00714573	+	0.0219923i
$989$	−50.5226	−	22.4941i	−1.60653	−	0.715271i
$990$	−2.32440	−	1.68877i	−0.0738742	−	0.0536728i
$991$	−16.0170			−0.508797			−0.254398	−	0.967100i	$-0.581877\pi$
$991$	−16.0170			−0.508797			−0.254398	+	0.967100i	$0.581877\pi$
$992$	4.45069	+	3.34535i	0.141309	+	0.106215i
$993$	32.3569			1.02681
$994$	0.911760	+	0.662433i	0.0289193	+	0.0210111i
$995$	18.5174	+	8.24446i	0.587040	+	0.261367i
$996$	4.98254	+	15.3347i	0.157878	+	0.485898i
$997$	−18.4463	+	31.9500i	−0.584201	+	1.01187i	0.410773	+	0.911737i	$0.365259\pi$
$997$	−18.4463	+	31.9500i	−0.584201	+	1.01187i	−0.994975	+	0.100128i	$0.968075\pi$
$998$	10.3494	+	17.9257i	0.327605	+	0.567429i
$999$	−3.49911	+	3.88616i	−0.110707	+	0.122953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.b.391.2	✓	16
31.18	even	15	inner	930.2.bg.b.421.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.b.391.2	✓	16	1.1	even	1	trivial
930.2.bg.b.421.2	yes	16	31.18	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0748188 - 0.0830946i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0748188 - 0.0830946i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.913545 - 0.406737i) q^{10} +(-2.81033 - 0.597354i) q^{11} +(0.104528 - 0.994522i) q^{12} +(0.184583 + 1.75619i) q^{13} +(-0.109371 + 0.0232476i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.842426 - 0.179063i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(0.0430249 - 0.409354i) q^{19} +(-0.978148 - 0.207912i) q^{20} +(-0.102148 + 0.0454792i) q^{21} +(1.92249 + 2.13514i) q^{22} +(1.67860 - 5.16619i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.882933 - 1.52929i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.102148 + 0.0454792i) q^{28} +(-4.53405 - 3.29418i) q^{29} -1.00000 q^{30} +(4.45069 + 3.34535i) q^{31} +1.00000 q^{32} +(2.32440 + 1.68877i) q^{33} +(-0.786788 - 0.350301i) q^{34} +(0.0345527 + 0.106342i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.61467 - 4.52874i) q^{37} +(-0.275420 + 0.305885i) q^{38} +(0.545683 - 1.67944i) q^{39} +(0.669131 + 0.743145i) q^{40} +(-4.14533 + 1.84562i) q^{41} +(0.109371 + 0.0232476i) q^{42} +(1.06421 - 10.1253i) q^{43} +(-0.300322 - 2.85738i) q^{44} +(-0.978148 + 0.207912i) q^{45} +(-4.39462 + 3.19288i) q^{46} +(7.91556 - 5.75099i) q^{47} +(0.978148 - 0.207912i) q^{48} +(0.730392 + 6.94922i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-0.842426 - 0.179063i) q^{51} +(-1.61320 + 0.718243i) q^{52} +(-7.76116 - 8.61965i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.92249 - 2.13514i) q^{55} +(-0.0559074 - 0.0968345i) q^{56} +(-0.205805 + 0.356464i) q^{57} +(1.73185 + 5.33010i) q^{58} +(-7.80684 - 3.47583i) q^{59} +(0.809017 + 0.587785i) q^{60} -1.32069 q^{61} +(-1.63433 - 5.32249i) q^{62} +0.111815 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.61320 - 0.718243i) q^{65} +(-0.887841 - 2.73249i) q^{66} +(7.07875 - 12.2608i) q^{67} +(0.430623 + 0.745861i) q^{68} +(-3.63475 + 4.03680i) q^{69} +(0.0345527 - 0.106342i) q^{70} +(-6.74426 - 7.49026i) q^{71} +(0.913545 - 0.406737i) q^{72} +(1.43987 + 0.306055i) q^{73} +(-0.546615 + 5.20069i) q^{74} +(0.104528 + 0.994522i) q^{75} +(0.402614 - 0.0855783i) q^{76} +(-0.259902 + 0.188830i) q^{77} +(-1.42862 + 1.03795i) q^{78} +(-11.5295 + 2.45068i) q^{79} +(-0.104528 - 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.43847 + 0.943427i) q^{82} +(-14.7299 + 6.55816i) q^{83} +(-0.0748188 - 0.0830946i) q^{84} +(-0.266140 + 0.819094i) q^{85} +(-6.81244 + 7.56598i) q^{86} +(2.80220 + 4.85355i) q^{87} +(-1.43656 + 2.48819i) q^{88} +(-1.19541 - 3.67909i) q^{89} +(0.913545 + 0.406737i) q^{90} +(0.159741 + 0.116058i) q^{91} +5.43205 q^{92} +(-2.70523 - 4.86639i) q^{93} -9.78417 q^{94} +(0.332999 + 0.241938i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(0.388073 + 1.19437i) q^{97} +(3.49375 - 6.05135i) q^{98} +(-1.43656 - 2.48819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} + 8 q^{6} + 3 q^{7} - 4 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} - 2 q^{12} + 14 q^{13} - 12 q^{14} + 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} - 7 q^{19} + 2 q^{20} + 2 q^{21} + 13 q^{22} + 7 q^{23} - 2 q^{24} - 8 q^{25} - q^{26} + 4 q^{27} - 2 q^{28} + 13 q^{29} - 16 q^{30} - 21 q^{31} + 16 q^{32} - 4 q^{33} + 6 q^{34} + 9 q^{35} - 8 q^{36} - 17 q^{37} - 2 q^{38} + 3 q^{39} + 2 q^{40} - 20 q^{41} + 12 q^{42} - 2 q^{43} + 13 q^{44} + 2 q^{45} - 3 q^{46} + 23 q^{47} - 2 q^{48} - q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} - 14 q^{53} + 4 q^{54} + 13 q^{55} + 13 q^{56} - 18 q^{57} - 22 q^{58} - 26 q^{59} + 4 q^{60} + 24 q^{61} + 9 q^{62} - 26 q^{63} - 4 q^{64} - 16 q^{65} + 11 q^{66} + 45 q^{67} - 4 q^{68} + 11 q^{69} + 9 q^{70} - 39 q^{71} + 2 q^{72} - 19 q^{73} - 2 q^{74} - 2 q^{75} - 2 q^{76} - 6 q^{77} - 2 q^{78} - 20 q^{79} + 2 q^{80} + 2 q^{81} + 30 q^{82} - 86 q^{83} - 3 q^{84} + 8 q^{85} + 3 q^{86} + 9 q^{87} - 7 q^{88} - 13 q^{89} + 2 q^{90} + 48 q^{91} - 8 q^{92} + 12 q^{93} - 72 q^{94} + 14 q^{95} - 2 q^{96} + 67 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 + 8 * q^6 + 3 * q^7 - 4 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^11 - 2 * q^12 + 14 * q^13 - 12 * q^14 + 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 - 7 * q^19 + 2 * q^20 + 2 * q^21 + 13 * q^22 + 7 * q^23 - 2 * q^24 - 8 * q^25 - q^26 + 4 * q^27 - 2 * q^28 + 13 * q^29 - 16 * q^30 - 21 * q^31 + 16 * q^32 - 4 * q^33 + 6 * q^34 + 9 * q^35 - 8 * q^36 - 17 * q^37 - 2 * q^38 + 3 * q^39 + 2 * q^40 - 20 * q^41 + 12 * q^42 - 2 * q^43 + 13 * q^44 + 2 * q^45 - 3 * q^46 + 23 * q^47 - 2 * q^48 - q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 - 14 * q^53 + 4 * q^54 + 13 * q^55 + 13 * q^56 - 18 * q^57 - 22 * q^58 - 26 * q^59 + 4 * q^60 + 24 * q^61 + 9 * q^62 - 26 * q^63 - 4 * q^64 - 16 * q^65 + 11 * q^66 + 45 * q^67 - 4 * q^68 + 11 * q^69 + 9 * q^70 - 39 * q^71 + 2 * q^72 - 19 * q^73 - 2 * q^74 - 2 * q^75 - 2 * q^76 - 6 * q^77 - 2 * q^78 - 20 * q^79 + 2 * q^80 + 2 * q^81 + 30 * q^82 - 86 * q^83 - 3 * q^84 + 8 * q^85 + 3 * q^86 + 9 * q^87 - 7 * q^88 - 13 * q^89 + 2 * q^90 + 48 * q^91 - 8 * q^92 + 12 * q^93 - 72 * q^94 + 14 * q^95 - 2 * q^96 + 67 * q^97 + 9 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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