LMFDB - Embedded newform 930.2.bg.c.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 40x^{14} + 654x^{12} + 5650x^{10} + 27831x^{8} + 78445x^{6} + 119819x^{4} + 87030x^{2} + 22801 $ x^16 + 40x^14 + 654x^12 + 5650x^10 + 27831x^8 + 78445x^6 + 119819x^4 + 87030*x^2 + 22801
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.1
Root			$2.47367i$ of defining polynomial
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.c.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.01621 + 1.12862i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(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} +(1.01621 + 1.12862i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.913545 - 0.406737i) q^{10} +(4.53907 - 0.964808i) q^{11} +(0.104528 + 0.994522i) q^{12} +(0.403031 - 3.83458i) q^{13} +(-1.48552 - 0.315757i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.709057 - 0.150715i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(-0.291115 - 2.76978i) q^{19} +(0.978148 - 0.207912i) q^{20} +(-1.38741 - 0.617714i) q^{21} +(-3.10508 + 3.44854i) q^{22} +(-0.612577 - 1.88532i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.92785 + 3.33914i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.38741 - 0.617714i) q^{28} +(2.08060 - 1.51165i) q^{29} +1.00000 q^{30} +(-1.36830 - 5.39701i) q^{31} +1.00000 q^{32} +(-3.75422 + 2.72760i) q^{33} +(0.662227 - 0.294842i) q^{34} +(-0.469306 + 1.44438i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.30253 + 2.25605i) q^{37} +(1.86355 + 2.06968i) q^{38} +(1.19148 + 3.66699i) q^{39} +(-0.669131 + 0.743145i) q^{40} +(8.72506 + 3.88464i) q^{41} +(1.48552 - 0.315757i) q^{42} +(0.101378 + 0.964545i) q^{43} +(0.485061 - 4.61505i) q^{44} +(0.978148 + 0.207912i) q^{45} +(1.60375 + 1.16519i) q^{46} +(5.74060 + 4.17079i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.490607 - 4.66782i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(0.709057 - 0.150715i) q^{51} +(-3.52236 - 1.56826i) q^{52} +(-1.95242 + 2.16838i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(3.10508 + 3.44854i) q^{55} +(-0.759354 + 1.31524i) q^{56} +(1.39252 + 2.41191i) q^{57} +(-0.794719 + 2.44589i) q^{58} +(12.9937 - 5.78517i) q^{59} +(-0.809017 + 0.587785i) q^{60} -1.76325 q^{61} +(4.27926 + 3.56201i) q^{62} +1.51871 q^{63} +(-0.809017 + 0.587785i) q^{64} +(3.52236 - 1.56826i) q^{65} +(1.43398 - 4.41335i) q^{66} +(1.27951 + 2.21618i) q^{67} +(-0.362449 + 0.627780i) q^{68} +(1.32645 + 1.47317i) q^{69} +(-0.469306 - 1.44438i) q^{70} +(1.62747 - 1.80749i) q^{71} +(0.913545 + 0.406737i) q^{72} +(1.97939 - 0.420733i) q^{73} +(-0.272304 - 2.59080i) q^{74} +(0.104528 - 0.994522i) q^{75} +(-2.72417 - 0.579041i) q^{76} +(5.70156 + 4.14243i) q^{77} +(-3.11933 - 2.26632i) q^{78} +(1.32956 + 0.282607i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-9.34205 + 1.98572i) q^{82} +(1.31801 + 0.586816i) q^{83} +(-1.01621 + 1.12862i) q^{84} +(-0.224006 - 0.689419i) q^{85} +(-0.648962 - 0.720745i) q^{86} +(-1.28588 + 2.22721i) q^{87} +(2.32024 + 4.01877i) q^{88} +(-3.47781 + 10.7036i) q^{89} +(-0.913545 + 0.406737i) q^{90} +(4.73735 - 3.44188i) q^{91} -1.98234 q^{92} +(3.44517 + 4.37388i) q^{93} -7.09577 q^{94} +(2.25314 - 1.63700i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-2.53434 + 7.79991i) q^{97} +(2.34676 + 4.06472i) q^{98} +(2.32024 - 4.01877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

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
$7$	1.01621	+	1.12862i	0.384093	+	0.426578i	0.903926	−	0.427690i	$-0.140672\pi$
$7$	1.01621	+	1.12862i	0.384093	+	0.426578i	−0.519833	+	0.854268i	$0.674006\pi$
$8$	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
$11$	4.53907	−	0.964808i	1.36858	−	0.290901i	0.535725	−	0.844392i	$-0.320038\pi$
$11$	4.53907	−	0.964808i	1.36858	−	0.290901i	0.832855	+	0.553492i	$0.186705\pi$
$12$	0.104528	+	0.994522i	0.0301748	+	0.287094i
$13$	0.403031	−	3.83458i	0.111781	−	1.06352i	−0.784529	−	0.620092i	$-0.787095\pi$
$13$	0.403031	−	3.83458i	0.111781	−	1.06352i	0.896310	−	0.443429i	$-0.146238\pi$
$14$	−1.48552	−	0.315757i	−0.397022	−	0.0843896i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.709057	−	0.150715i	−0.171972	−	0.0365537i	0.121121	−	0.992638i	$-0.461351\pi$
$17$	−0.709057	−	0.150715i	−0.171972	−	0.0365537i	−0.293093	+	0.956084i	$0.594684\pi$
$18$	−0.104528	+	0.994522i	−0.0246376	+	0.234411i
$19$	−0.291115	−	2.76978i	−0.0667864	−	0.635430i	−0.975800	−	0.218664i	$-0.929830\pi$
$19$	−0.291115	−	2.76978i	−0.0667864	−	0.635430i	0.909014	−	0.416766i	$-0.136837\pi$
$20$	0.978148	−	0.207912i	0.218720	−	0.0464905i
$21$	−1.38741	−	0.617714i	−0.302757	−	0.134796i
$22$	−3.10508	+	3.44854i	−0.662006	+	0.735232i
$23$	−0.612577	−	1.88532i	−0.127731	−	0.393116i	0.866658	−	0.498903i	$-0.166264\pi$
$23$	−0.612577	−	1.88532i	−0.127731	−	0.393116i	−0.994389	+	0.105787i	$0.966264\pi$
$24$	−0.669131	−	0.743145i	−0.136586	−	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.92785	+	3.33914i	0.378083	+	0.654858i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	1.38741	−	0.617714i	0.262195	−	0.116737i
$29$	2.08060	−	1.51165i	0.386358	−	0.280705i	−0.377603	−	0.925967i	$-0.623252\pi$
$29$	2.08060	−	1.51165i	0.386358	−	0.280705i	0.763961	+	0.645262i	$0.223252\pi$
$30$	1.00000			0.182574
$31$	−1.36830	−	5.39701i	−0.245754	−	0.969332i
$31$	−1.36830	−	5.39701i	−0.245754	−	0.969332i
$32$	1.00000			0.176777
$33$	−3.75422	+	2.72760i	−0.653526	+	0.474814i
$34$	0.662227	−	0.294842i	0.113571	−	0.0505651i
$35$	−0.469306	+	1.44438i	−0.0793272	+	0.244144i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.30253	+	2.25605i	−0.214135	+	0.370893i	−0.953005	−	0.302956i	$-0.902027\pi$
$37$	−1.30253	+	2.25605i	−0.214135	+	0.370893i	0.738870	+	0.673848i	$0.235360\pi$
$38$	1.86355	+	2.06968i	0.302308	+	0.335747i
$39$	1.19148	+	3.66699i	0.190789	+	0.587188i
$40$	−0.669131	+	0.743145i	−0.105799	+	0.117502i
$41$	8.72506	+	3.88464i	1.36262	+	0.606680i	0.952273	−	0.305248i	$-0.0987393\pi$
$41$	8.72506	+	3.88464i	1.36262	+	0.606680i	0.410352	+	0.911927i	$0.365406\pi$
$42$	1.48552	−	0.315757i	0.229221	−	0.0487224i
$43$	0.101378	+	0.964545i	0.0154600	+	0.147092i	0.999529	−	0.0306964i	$-0.00977250\pi$
$43$	0.101378	+	0.964545i	0.0154600	+	0.147092i	−0.984069	+	0.177788i	$0.943106\pi$
$44$	0.485061	−	4.61505i	0.0731257	−	0.695745i
$45$	0.978148	+	0.207912i	0.145814	+	0.0309936i
$46$	1.60375	+	1.16519i	0.236460	+	0.171798i
$47$	5.74060	+	4.17079i	0.837352	+	0.608372i	0.921630	−	0.388071i	$-0.126858\pi$
$47$	5.74060	+	4.17079i	0.837352	+	0.608372i	−0.0842777	+	0.996442i	$0.526858\pi$
$48$	0.978148	+	0.207912i	0.141183	+	0.0300095i
$49$	0.490607	−	4.66782i	0.0700868	−	0.666831i
$50$	−0.104528	−	0.994522i	−0.0147826	−	0.140647i
$51$	0.709057	−	0.150715i	0.0992878	−	0.0211043i
$52$	−3.52236	−	1.56826i	−0.488463	−	0.217478i
$53$	−1.95242	+	2.16838i	−0.268186	+	0.297850i	−0.862163	−	0.506632i	$-0.830890\pi$
$53$	−1.95242	+	2.16838i	−0.268186	+	0.297850i	0.593977	+	0.804482i	$0.297557\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	3.10508	+	3.44854i	0.418689	+	0.465001i
$56$	−0.759354	+	1.31524i	−0.101473	+	0.175756i
$57$	1.39252	+	2.41191i	0.184443	+	0.319465i
$58$	−0.794719	+	2.44589i	−0.104352	+	0.321162i
$59$	12.9937	−	5.78517i	1.69164	−	0.753164i	0.692128	−	0.721775i	$-0.256673\pi$
$59$	12.9937	−	5.78517i	1.69164	−	0.753164i	0.999507	−	0.0313896i	$-0.00999325\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−1.76325			−0.225761			−0.112880	−	0.993609i	$-0.536008\pi$
$61$	−1.76325			−0.225761			−0.112880	+	0.993609i	$0.536008\pi$
$62$	4.27926	+	3.56201i	0.543467	+	0.452376i
$63$	1.51871			0.191339
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	3.52236	−	1.56826i	0.436895	−	0.194518i
$66$	1.43398	−	4.41335i	0.176511	−	0.543246i
$67$	1.27951	+	2.21618i	0.156317	+	0.270750i	0.933538	−	0.358479i	$-0.116704\pi$
$67$	1.27951	+	2.21618i	0.156317	+	0.270750i	−0.777221	+	0.629228i	$0.783371\pi$
$68$	−0.362449	+	0.627780i	−0.0439534	+	0.0761295i
$69$	1.32645	+	1.47317i	0.159685	+	0.177348i
$70$	−0.469306	−	1.44438i	−0.0560928	−	0.172636i
$71$	1.62747	−	1.80749i	0.193145	−	0.214510i	−0.638792	−	0.769380i	$-0.720565\pi$
$71$	1.62747	−	1.80749i	0.193145	−	0.214510i	0.831937	+	0.554870i	$0.187232\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	1.97939	−	0.420733i	0.231670	−	0.0492431i	−0.0906134	−	0.995886i	$-0.528883\pi$
$73$	1.97939	−	0.420733i	0.231670	−	0.0492431i	0.322284	+	0.946643i	$0.395549\pi$
$74$	−0.272304	−	2.59080i	−0.0316546	−	0.301174i
$75$	0.104528	−	0.994522i	0.0120699	−	0.114837i
$76$	−2.72417	−	0.579041i	−0.312484	−	0.0664206i
$77$	5.70156	+	4.14243i	0.649753	+	0.472073i
$78$	−3.11933	−	2.26632i	−0.353194	−	0.256611i
$79$	1.32956	+	0.282607i	0.149588	+	0.0317958i	0.282097	−	0.959386i	$-0.408970\pi$
$79$	1.32956	+	0.282607i	0.149588	+	0.0317958i	−0.132509	+	0.991182i	$0.542303\pi$
$80$	0.104528	−	0.994522i	0.0116866	−	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−9.34205	+	1.98572i	−1.03166	+	0.219286i
$83$	1.31801	+	0.586816i	0.144670	+	0.0644114i	0.477795	−	0.878471i	$-0.341436\pi$
$83$	1.31801	+	0.586816i	0.144670	+	0.0644114i	−0.333124	+	0.942883i	$0.608103\pi$
$84$	−1.01621	+	1.12862i	−0.110878	+	0.123142i
$85$	−0.224006	−	0.689419i	−0.0242968	−	0.0747780i
$86$	−0.648962	−	0.720745i	−0.0699793	−	0.0777199i
$87$	−1.28588	+	2.22721i	−0.137861	+	0.238782i
$88$	2.32024	+	4.01877i	0.247338	+	0.428402i
$89$	−3.47781	+	10.7036i	−0.368647	+	1.13458i	0.579019	+	0.815314i	$0.303436\pi$
$89$	−3.47781	+	10.7036i	−0.368647	+	1.13458i	−0.947666	+	0.319264i	$0.896564\pi$
$90$	−0.913545	+	0.406737i	−0.0962961	+	0.0428738i
$91$	4.73735	−	3.44188i	0.496609	−	0.360807i
$92$	−1.98234			−0.206673
$93$	3.44517	+	4.37388i	0.357247	+	0.453550i
$94$	−7.09577			−0.731872
$95$	2.25314	−	1.63700i	0.231167	−	0.167953i
$96$	−0.913545	+	0.406737i	−0.0932383	+	0.0415124i
$97$	−2.53434	+	7.79991i	−0.257324	+	0.791960i	0.736039	+	0.676939i	$0.236694\pi$
$97$	−2.53434	+	7.79991i	−0.257324	+	0.791960i	−0.993363	+	0.115022i	$0.963306\pi$
$98$	2.34676	+	4.06472i	0.237059	+	0.410598i
$99$	2.32024	−	4.01877i	0.233192	−	0.403901i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	3.61091	+	11.1132i	0.359299	+	1.10581i	0.953475	+	0.301473i	$0.0974782\pi$
$101$	3.61091	+	11.1132i	0.359299	+	1.10581i	−0.594176	+	0.804335i	$0.702522\pi$
$102$	−0.485051	+	0.538704i	−0.0480272	+	0.0533396i
$103$	−5.78003	−	2.57344i	−0.569524	−	0.253568i	0.101710	−	0.994814i	$-0.467569\pi$
$103$	−5.78003	−	2.57344i	−0.569524	−	0.253568i	−0.671234	+	0.741246i	$0.734235\pi$
$104$	3.77145	−	0.801646i	0.369821	−	0.0786078i
$105$	−0.158748	−	1.51039i	−0.0154922	−	0.147399i
$106$	0.304998	−	2.90186i	0.0296240	−	0.281854i
$107$	10.3907	+	2.20860i	1.00450	+	0.213514i	0.680662	−	0.732598i	$-0.261692\pi$
$107$	10.3907	+	2.20860i	1.00450	+	0.213514i	0.323841	+	0.946112i	$0.395026\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	6.61739	+	4.80782i	0.633831	+	0.460505i	0.857725	−	0.514108i	$-0.171877\pi$
$109$	6.61739	+	4.80782i	0.633831	+	0.460505i	−0.223894	+	0.974613i	$0.571877\pi$
$110$	−4.53907	−	0.964808i	−0.432783	−	0.0919909i
$111$	0.272304	−	2.59080i	0.0258459	−	0.245907i
$112$	−0.158748	−	1.51039i	−0.0150003	−	0.142718i
$113$	3.30886	−	0.703320i	0.311271	−	0.0661628i	−0.0496273	−	0.998768i	$-0.515803\pi$
$113$	3.30886	−	0.703320i	0.311271	−	0.0661628i	0.360899	+	0.932605i	$0.382470\pi$
$114$	−2.54426	−	1.13278i	−0.238291	−	0.106094i
$115$	1.32645	−	1.47317i	0.123692	−	0.137374i
$116$	−0.794719	−	2.44589i	−0.0737878	−	0.227096i
$117$	−2.57997	−	2.86534i	−0.238518	−	0.264901i
$118$	−7.11169	+	12.3178i	−0.654684	+	1.13395i
$119$	−0.550454	−	0.953414i	−0.0504600	−	0.0873993i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	9.62326	−	4.28455i	0.874842	−	0.389505i
$122$	1.42650	−	1.03641i	0.129149	−	0.0938323i
$123$	−9.55076			−0.861163
$124$	−5.55569	−	0.366439i	−0.498916	−	0.0329072i
$125$	−1.00000			−0.0894427
$126$	−1.22866	+	0.892674i	−0.109458	+	0.0795257i
$127$	2.43435	−	1.08384i	0.216014	−	0.0961756i	−0.295877	−	0.955226i	$-0.595612\pi$
$127$	2.43435	−	1.08384i	0.216014	−	0.0961756i	0.511891	+	0.859050i	$0.328945\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.484929	−	0.839922i	−0.0426956	−	0.0739510i
$130$	−1.92785	+	3.33914i	−0.169084	+	0.292862i
$131$	−8.08091	−	8.97476i	−0.706032	−	0.784128i	0.278292	−	0.960497i	$-0.410232\pi$
$131$	−8.08091	−	8.97476i	−0.706032	−	0.784128i	−0.984324	+	0.176368i	$0.943565\pi$
$132$	1.43398	+	4.41335i	0.124812	+	0.384133i
$133$	2.83019	−	3.14324i	0.245408	−	0.272554i
$134$	−2.33779	−	1.04085i	−0.201954	−	0.0899157i
$135$	−0.978148	+	0.207912i	−0.0841855	+	0.0178942i
$136$	−0.0757724	−	0.720927i	−0.00649743	−	0.0618189i
$137$	−2.14207	+	20.3805i	−0.183010	+	1.74122i	0.389236	+	0.921138i	$0.372739\pi$
$137$	−2.14207	+	20.3805i	−0.183010	+	1.74122i	−0.572246	+	0.820082i	$0.693928\pi$
$138$	−1.93902	−	0.412152i	−0.165061	−	0.0350847i
$139$	−13.6477	−	9.91563i	−1.15758	−	0.841033i	−0.168112	−	0.985768i	$-0.553767\pi$
$139$	−13.6477	−	9.91563i	−1.15758	−	0.841033i	−0.989470	+	0.144735i	$0.953767\pi$
$140$	1.22866	+	0.892674i	0.103841	+	0.0754447i
$141$	−6.94071	−	1.47529i	−0.584513	−	0.124242i
$142$	−0.254236	+	2.41889i	−0.0213350	+	0.202989i
$143$	−1.87025	−	17.7943i	−0.156398	−	1.48803i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	2.34942	+	1.04603i	0.195109	+	0.0868681i
$146$	−1.35406	+	1.50384i	−0.112063	+	0.124459i
$147$	1.45038	+	4.46381i	0.119625	+	0.368169i
$148$	1.74313	+	1.93594i	0.143284	+	0.159133i
$149$	−4.68492	+	8.11452i	−0.383803	+	0.664767i	−0.991602	−	0.129324i	$-0.958719\pi$
$149$	−4.68492	+	8.11452i	−0.383803	+	0.664767i	0.607799	+	0.794091i	$0.292053\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	−1.89270	+	5.82512i	−0.154026	+	0.474042i	−0.998061	−	0.0622457i	$-0.980174\pi$
$151$	−1.89270	+	5.82512i	−0.154026	+	0.474042i	0.844035	+	0.536288i	$0.180174\pi$
$152$	2.54426	−	1.13278i	0.206366	−	0.0918802i
$153$	−0.586455	+	0.426084i	−0.0474120	+	0.0344469i
$154$	−7.04752			−0.567905
$155$	3.98980	−	3.88349i	0.320469	−	0.311929i
$156$	3.85570			0.308703
$157$	−1.56229	+	1.13507i	−0.124684	+	0.0905882i	−0.648379	−	0.761317i	$-0.724553\pi$
$157$	−1.56229	+	1.13507i	−0.124684	+	0.0905882i	0.523695	+	0.851906i	$0.324553\pi$
$158$	−1.24175	+	0.552863i	−0.0987885	+	0.0439835i
$159$	0.901664	−	2.77504i	0.0715066	−	0.220075i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	1.50530	−	2.60725i	0.118634	−	0.205480i
$162$	0.669131	+	0.743145i	0.0525719	+	0.0583870i
$163$	−1.54668	−	4.76018i	−0.121145	−	0.372846i	0.872034	−	0.489445i	$-0.162801\pi$
$163$	−1.54668	−	4.76018i	−0.121145	−	0.372846i	−0.993179	+	0.116599i	$0.962801\pi$
$164$	6.39071	−	7.09760i	0.499030	−	0.554229i
$165$	−4.23928	−	1.88745i	−0.330028	−	0.146938i
$166$	−1.41121	+	0.299963i	−0.109532	+	0.0232816i
$167$	0.0175170	+	0.166663i	0.00135550	+	0.0128967i	0.995179	−	0.0980779i	$-0.0312694\pi$
$167$	0.0175170	+	0.166663i	0.00135550	+	0.0128967i	−0.993823	+	0.110975i	$0.964603\pi$
$168$	0.158748	−	1.51039i	0.0122477	−	0.116529i
$169$	−1.82565	−	0.388054i	−0.140435	−	0.0298503i
$170$	0.586455	+	0.426084i	0.0449790	+	0.0326792i
$171$	−2.25314	−	1.63700i	−0.172302	−	0.125185i
$172$	0.948664	+	0.201645i	0.0723350	+	0.0153753i
$173$	2.37839	−	22.6288i	0.180825	−	1.72044i	−0.408683	−	0.912676i	$-0.634012\pi$
$173$	2.37839	−	22.6288i	0.180825	−	1.72044i	0.589508	−	0.807762i	$-0.299321\pi$
$174$	−0.268823	−	2.55768i	−0.0203794	−	0.193897i
$175$	−1.48552	+	0.315757i	−0.112295	+	0.0238690i
$176$	−4.23928	−	1.88745i	−0.319548	−	0.142272i
$177$	−9.51729	+	10.5700i	−0.715364	+	0.794492i
$178$	−3.47781	−	10.7036i	−0.260673	−	0.802268i
$179$	−12.0519	−	13.3849i	−0.900798	−	1.00044i	−0.999986	−	0.00536923i	$-0.998291\pi$
$179$	−12.0519	−	13.3849i	−0.900798	−	1.00044i	0.0991871	−	0.995069i	$-0.468376\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−1.70568	−	2.95433i	−0.126782	−	0.219594i	0.795646	−	0.605762i	$-0.207132\pi$
$181$	−1.70568	−	2.95433i	−0.126782	−	0.219594i	−0.922428	+	0.386168i	$0.873798\pi$
$182$	−1.80951	+	5.56908i	−0.134129	+	0.412808i
$183$	1.61081	−	0.717178i	0.119074	−	0.0530153i
$184$	1.60375	−	1.16519i	0.118230	−	0.0858990i
$185$	−2.60507			−0.191528
$186$	−5.35810	−	1.51352i	−0.392875	−	0.110977i
$187$	−3.36387			−0.245990
$188$	5.74060	−	4.17079i	0.418676	−	0.304186i
$189$	−1.38741	+	0.617714i	−0.100919	+	0.0449321i
$190$	−0.860623	+	2.64872i	−0.0624361	+	0.192159i
$191$	−9.79321	−	16.9623i	−0.708612	−	1.22735i	−0.965372	−	0.260876i	$-0.915988\pi$
$191$	−9.79321	−	16.9623i	−0.708612	−	1.22735i	0.256761	−	0.966475i	$-0.417345\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	0.587707	+	0.652715i	0.0423041	+	0.0469834i	0.763925	−	0.645304i	$-0.223269\pi$
$193$	0.587707	+	0.652715i	0.0423041	+	0.0469834i	−0.721621	+	0.692288i	$0.756603\pi$
$194$	−2.53434	−	7.79991i	−0.181955	−	0.560001i
$195$	−2.57997	+	2.86534i	−0.184755	+	0.205192i
$196$	−4.28775	−	1.90903i	−0.306268	−	0.136359i
$197$	−16.2341	+	3.45068i	−1.15664	+	0.245850i	−0.745998	−	0.665948i	$-0.768027\pi$
$197$	−16.2341	+	3.45068i	−1.15664	+	0.245850i	−0.410637	+	0.911799i	$0.634694\pi$
$198$	0.485061	+	4.61505i	0.0344718	+	0.327977i
$199$	1.64691	−	15.6693i	0.116746	−	1.11077i	−0.766625	−	0.642095i	$-0.778065\pi$
$199$	1.64691	−	15.6693i	0.116746	−	1.11077i	0.883371	−	0.468673i	$-0.155268\pi$
$200$	−0.978148	−	0.207912i	−0.0691655	−	0.0147016i
$201$	−2.07029	−	1.50416i	−0.146027	−	0.106095i
$202$	−9.45348	−	6.86835i	−0.665144	−	0.483256i
$203$	3.82041	+	0.812053i	0.268140	+	0.0569949i
$204$	0.0757724	−	0.720927i	0.00530513	−	0.0504750i
$205$	0.998326	+	9.49844i	0.0697261	+	0.663400i
$206$	6.18877	−	1.31546i	0.431192	−	0.0916527i
$207$	−1.81096	−	0.806291i	−0.125870	−	0.0560411i
$208$	−2.57997	+	2.86534i	−0.178889	+	0.198676i
$209$	−3.99370	−	12.2913i	−0.276250	−	0.850209i
$210$	1.01621	+	1.12862i	0.0701254	+	0.0778821i
$211$	−8.62319	+	14.9358i	−0.593645	+	1.02822i	0.400091	+	0.916475i	$0.368978\pi$
$211$	−8.62319	+	14.9358i	−0.593645	+	1.02822i	−0.993737	+	0.111748i	$0.964355\pi$
$212$	1.45892	+	2.52693i	0.100199	+	0.173550i
$213$	−0.751596	+	2.31318i	−0.0514985	+	0.158496i
$214$	−9.70440	+	4.32068i	−0.663379	+	0.295355i
$215$	−0.784632	+	0.570068i	−0.0535114	+	0.0388783i
$216$	−1.00000			−0.0680414
$217$	4.70069	−	7.02881i	0.319104	−	0.477146i
$218$	−8.17955			−0.553989
$219$	−1.63714	+	1.18945i	−0.110628	+	0.0803756i
$220$	4.23928	−	1.88745i	0.285812	−	0.127252i
$221$	−0.863699	+	2.65819i	−0.0580987	+	0.178809i
$222$	1.30253	+	2.25605i	0.0874203	+	0.151416i
$223$	6.38966	−	11.0672i	0.427883	−	0.741115i	−0.568802	−	0.822475i	$-0.692593\pi$
$223$	6.38966	−	11.0672i	0.427883	−	0.741115i	0.996685	+	0.0813593i	$0.0259261\pi$
$224$	1.01621	+	1.12862i	0.0678986	+	0.0754090i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−2.26352	+	2.51390i	−0.150567	+	0.167222i
$227$	17.6783	+	7.87088i	1.17335	+	0.522408i	0.898455	−	0.439066i	$-0.144691\pi$
$227$	17.6783	+	7.87088i	1.17335	+	0.522408i	0.274894	+	0.961475i	$0.411357\pi$
$228$	2.72417	−	0.579041i	0.180413	−	0.0383479i
$229$	−0.224356	−	2.13461i	−0.0148259	−	0.141059i	0.984605	−	0.174795i	$-0.0559262\pi$
$229$	−0.224356	−	2.13461i	−0.0148259	−	0.141059i	−0.999431	+	0.0337358i	$0.989260\pi$
$230$	−0.207211	+	1.97148i	−0.0136631	+	0.129996i
$231$	−6.89351	−	1.46526i	−0.453560	−	0.0964071i
$232$	2.08060	+	1.51165i	0.136598	+	0.0992444i
$233$	0.0770148	+	0.0559545i	0.00504541	+	0.00366570i	0.590305	−	0.807180i	$-0.299007\pi$
$233$	0.0770148	+	0.0559545i	0.00504541	+	0.00366570i	−0.585260	+	0.810846i	$0.699007\pi$
$234$	3.77145	+	0.801646i	0.246547	+	0.0524052i
$235$	−0.741710	+	7.05690i	−0.0483838	+	0.460341i
$236$	−1.48675	−	14.1455i	−0.0967790	−	0.920791i
$237$	−1.32956	+	0.282607i	−0.0863644	+	0.0183573i
$238$	1.00573	+	0.447779i	0.0651917	+	0.0290252i
$239$	2.62072	−	2.91061i	0.169520	−	0.188272i	−0.652398	−	0.757876i	$-0.726237\pi$
$239$	2.62072	−	2.91061i	0.169520	−	0.188272i	0.821919	+	0.569605i	$0.192904\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	1.68460	+	1.87094i	0.108515	+	0.120518i	0.794955	−	0.606668i	$-0.207494\pi$
$241$	1.68460	+	1.87094i	0.108515	+	0.120518i	−0.686440	+	0.727186i	$0.740828\pi$
$242$	−5.26699	+	9.12269i	−0.338575	+	0.586429i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.544874	+	1.67695i	−0.0348820	+	0.107356i
$245$	4.28775	−	1.90903i	0.273934	−	0.121963i
$246$	7.72673	−	5.61380i	0.492638	−	0.357923i
$247$	−10.7383			−0.683259
$248$	4.71004	−	2.96910i	0.299088	−	0.188538i
$249$	−1.44274			−0.0914301
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	18.6219	−	8.29101i	1.17540	−	0.523324i	0.276306	−	0.961070i	$-0.410890\pi$
$251$	18.6219	−	8.29101i	1.17540	−	0.523324i	0.899099	+	0.437746i	$0.144223\pi$
$252$	0.469306	−	1.44438i	0.0295635	−	0.0909872i
$253$	−4.59950	−	7.96657i	−0.289168	−	0.500854i
$254$	−1.33237	+	2.30773i	−0.0836001	+	0.144800i
$255$	0.485051	+	0.538704i	0.0303751	+	0.0337350i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−14.3048	+	15.8871i	−0.892312	+	0.991013i	−0.999995	−	0.00317254i	$-0.998990\pi$
$257$	−14.3048	+	15.8871i	−0.892312	+	0.991013i	0.107683	+	0.994185i	$0.465657\pi$
$258$	0.886009	+	0.394477i	0.0551605	+	0.0245591i
$259$	−3.86988	+	0.822568i	−0.240462	+	0.0511119i
$260$	−0.403031	−	3.83458i	−0.0249949	−	0.237811i
$261$	0.268823	−	2.55768i	0.0166397	−	0.158316i
$262$	11.8128	+	2.51089i	0.729799	+	0.155124i
$263$	−11.8687	−	8.62310i	−0.731854	−	0.531723i	0.158295	−	0.987392i	$-0.449400\pi$
$263$	−11.8687	−	8.62310i	−0.731854	−	0.531723i	−0.890150	+	0.455668i	$0.849400\pi$
$264$	−3.75422	−	2.72760i	−0.231056	−	0.167872i
$265$	−2.85409	−	0.606655i	−0.175325	−	0.0372665i
$266$	−0.442119	+	4.20648i	−0.0271080	+	0.257916i
$267$	−1.17641	−	11.1928i	−0.0719949	−	0.684986i
$268$	2.50310	−	0.532051i	0.152901	−	0.0325002i
$269$	29.1300	+	12.9695i	1.77609	+	0.790765i	0.983476	+	0.181037i	$0.0579454\pi$
$269$	29.1300	+	12.9695i	1.77609	+	0.790765i	0.792611	+	0.609728i	$0.208721\pi$
$270$	0.669131	−	0.743145i	0.0407220	−	0.0452264i
$271$	−2.70123	−	8.31352i	−0.164088	−	0.505010i	0.834880	−	0.550432i	$-0.185537\pi$
$271$	−2.70123	−	8.31352i	−0.164088	−	0.505010i	−0.998968	+	0.0454216i	$0.985537\pi$
$272$	0.485051	+	0.538704i	0.0294106	+	0.0326637i
$273$	−2.92784	+	5.07117i	−0.177201	+	0.306921i
$274$	−10.2464	−	17.7472i	−0.619005	−	1.07215i
$275$	−1.43398	+	4.41335i	−0.0864725	+	0.266135i
$276$	1.81096	−	0.806291i	0.109007	−	0.0485330i
$277$	−1.52093	+	1.10502i	−0.0913841	+	0.0663944i	−0.632539	−	0.774528i	$-0.717987\pi$
$277$	−1.52093	+	1.10502i	−0.0913841	+	0.0663944i	0.541155	+	0.840923i	$0.317987\pi$
$278$	16.8695			1.01176
$279$	−4.92633	−	2.59446i	−0.294932	−	0.155326i
$280$	−1.51871			−0.0907601
$281$	−14.8228	+	10.7694i	−0.884255	+	0.642449i	−0.934374	−	0.356294i	$-0.884040\pi$
$281$	−14.8228	+	10.7694i	−0.884255	+	0.642449i	0.0501186	+	0.998743i	$0.484040\pi$
$282$	6.48231	−	2.88611i	0.386016	−	0.171865i
$283$	1.98342	−	6.10435i	0.117902	−	0.362866i	−0.874639	−	0.484775i	$-0.838902\pi$
$283$	1.98342	−	6.10435i	0.117902	−	0.362866i	0.992541	+	0.121909i	$0.0389016\pi$
$284$	−1.21611	−	2.10636i	−0.0721628	−	0.124990i
$285$	−1.39252	+	2.41191i	−0.0824856	+	0.142869i
$286$	11.9723	+	13.2966i	0.707935	+	0.786242i
$287$	4.48223	+	13.7949i	0.264578	+	0.814287i
$288$	0.669131	−	0.743145i	0.0394289	−	0.0437902i
$289$	−15.0502	−	6.70079i	−0.885307	−	0.394164i
$290$	−2.51557	+	0.534700i	−0.147719	+	0.0313987i
$291$	−0.857270	−	8.15638i	−0.0502541	−	0.478135i
$292$	0.211525	−	2.01253i	0.0123786	−	0.117774i
$293$	−13.2593	−	2.81834i	−0.774614	−	0.164649i	−0.196389	−	0.980526i	$-0.562921\pi$
$293$	−13.2593	−	2.81834i	−0.774614	−	0.164649i	−0.578226	+	0.815877i	$0.696255\pi$
$294$	−3.79714	−	2.75879i	−0.221454	−	0.160896i
$295$	11.5069	+	8.36029i	0.669960	+	0.486755i
$296$	−2.54814	−	0.541624i	−0.148108	−	0.0314812i
$297$	−0.485061	+	4.61505i	−0.0281461	+	0.267792i
$298$	−0.979415	−	9.31851i	−0.0567360	−	0.539807i
$299$	−7.47629	+	1.58914i	−0.432365	+	0.0919021i
$300$	−0.913545	−	0.406737i	−0.0527436	−	0.0234830i
$301$	−0.985583	+	1.09460i	−0.0568080	+	0.0630917i
$302$	−1.89270	−	5.82512i	−0.108913	−	0.335198i
$303$	−7.81889	−	8.68375i	−0.449183	−	0.498869i
$304$	−1.39252	+	2.41191i	−0.0798663	+	0.138333i
$305$	−0.881624	−	1.52702i	−0.0504817	−	0.0874368i
$306$	0.224006	−	0.689419i	0.0128056	−	0.0394114i
$307$	8.23504	−	3.66648i	0.469999	−	0.209257i	−0.158050	−	0.987431i	$-0.550521\pi$
$307$	8.23504	−	3.66648i	0.469999	−	0.209257i	0.628048	+	0.778174i	$0.283854\pi$
$308$	5.70156	−	4.14243i	0.324877	−	0.236037i
$309$	6.32703			0.359932
$310$	−0.945159	+	5.48695i	−0.0536814	+	0.311638i
$311$	−21.9840			−1.24660			−0.623299	−	0.781984i	$-0.714208\pi$
$311$	−21.9840			−1.24660			−0.623299	+	0.781984i	$0.714208\pi$
$312$	−3.11933	+	2.26632i	−0.176597	+	0.128305i
$313$	−24.0248	+	10.6965i	−1.35796	+	0.604604i	−0.951099	−	0.308886i	$-0.900044\pi$
$313$	−24.0248	+	10.6965i	−1.35796	+	0.604604i	−0.406863	+	0.913489i	$0.633377\pi$
$314$	0.596740	−	1.83658i	0.0336760	−	0.103644i
$315$	0.759354	+	1.31524i	0.0427847	+	0.0741053i
$316$	0.679633	−	1.17716i	0.0382324	−	0.0662204i
$317$	4.71042	+	5.23145i	0.264563	+	0.293827i	0.860760	−	0.509011i	$-0.169989\pi$
$317$	4.71042	+	5.23145i	0.264563	+	0.293827i	−0.596197	+	0.802838i	$0.703322\pi$
$318$	0.901664	+	2.77504i	0.0505628	+	0.155616i
$319$	7.98554	−	8.86884i	0.447104	−	0.496560i
$320$	−0.913545	−	0.406737i	−0.0510687	−	0.0227373i
$321$	−10.3907	+	2.20860i	−0.579950	+	0.123272i
$322$	0.314693	+	2.99410i	0.0175372	+	0.166855i
$323$	−0.211029	+	2.00781i	−0.0117420	+	0.111717i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	3.11933	+	2.26632i	0.173029	+	0.125713i
$326$	4.04925	+	2.94196i	0.224267	+	0.162940i
$327$	−8.00080	−	1.70062i	−0.442445	−	0.0940447i
$328$	−0.998326	+	9.49844i	−0.0551234	+	0.524464i
$329$	1.12644	+	10.7174i	0.0621026	+	0.590867i
$330$	4.53907	−	0.964808i	0.249867	−	0.0531109i
$331$	26.2870	+	11.7037i	1.44487	+	0.643296i	0.971386	−	0.237508i	$-0.0763307\pi$
$331$	26.2870	+	11.7037i	1.44487	+	0.643296i	0.473481	+	0.880804i	$0.342997\pi$
$332$	0.965383	−	1.07217i	0.0529823	−	0.0588428i
$333$	0.805010	+	2.47757i	0.0441143	+	0.135770i
$334$	−0.112133	−	0.124537i	−0.00613567	−	0.00681435i
$335$	−1.27951	+	2.21618i	−0.0699072	+	0.121083i
$336$	0.759354	+	1.31524i	0.0414261	+	0.0717522i
$337$	3.39809	−	10.4582i	0.185106	−	0.569697i	−0.814844	−	0.579680i	$-0.803178\pi$
$337$	3.39809	−	10.4582i	0.185106	−	0.569697i	0.999950	+	0.00998283i	$0.00317769\pi$
$338$	1.70508	−	0.759149i	0.0927439	−	0.0412922i
$339$	−2.73673	+	1.98835i	−0.148639	+	0.107992i
$340$	−0.724898			−0.0393131
$341$	−11.4179	−	23.1773i	−0.618313	−	1.25512i
$342$	2.78503			0.150597
$343$	14.3674	−	10.4385i	0.775765	−	0.563626i
$344$	−0.886009	+	0.394477i	−0.0477704	+	0.0212688i
$345$	−0.612577	+	1.88532i	−0.0329801	+	0.101502i
$346$	11.3767	+	19.7051i	0.611617	+	1.05935i
$347$	−13.5783	+	23.5182i	−0.728919	+	1.26253i	0.228421	+	0.973562i	$0.426644\pi$
$347$	−13.5783	+	23.5182i	−0.728919	+	1.26253i	−0.957340	+	0.288963i	$0.906690\pi$
$348$	1.72085	+	1.91119i	0.0922471	+	0.102451i
$349$	7.07598	+	21.7776i	0.378768	+	1.16573i	0.940901	+	0.338682i	$0.109981\pi$
$349$	7.07598	+	21.7776i	0.378768	+	1.16573i	−0.562132	+	0.827047i	$0.690019\pi$
$350$	1.01621	−	1.12862i	0.0543189	−	0.0603272i
$351$	3.52236	+	1.56826i	0.188010	+	0.0837073i
$352$	4.53907	−	0.964808i	0.241933	−	0.0514245i
$353$	−2.44694	−	23.2811i	−0.130237	−	1.23913i	−0.843075	−	0.537796i	$-0.819257\pi$
$353$	−2.44694	−	23.2811i	−0.130237	−	1.23913i	0.712838	−	0.701329i	$-0.247410\pi$
$354$	1.48675	−	14.1455i	0.0790197	−	0.751822i
$355$	2.37907	+	0.505686i	0.126268	+	0.0268390i
$356$	9.10501	+	6.61518i	0.482565	+	0.350604i
$357$	0.890653	+	0.647097i	0.0471383	+	0.0342480i
$358$	17.6176	+	3.74474i	0.931121	+	0.197916i
$359$	−1.69218	+	16.1000i	−0.0893097	+	0.849725i	0.854548	+	0.519373i	$0.173834\pi$
$359$	−1.69218	+	16.1000i	−0.0893097	+	0.849725i	−0.943858	+	0.330353i	$0.892832\pi$
$360$	0.104528	+	0.994522i	0.00550913	+	0.0524159i
$361$	10.9979	−	2.33767i	0.578836	−	0.123035i
$362$	3.11644	+	1.38753i	0.163796	+	0.0729269i
$363$	−7.04860	+	7.82827i	−0.369956	+	0.410878i
$364$	−1.80951	−	5.56908i	−0.0948438	−	0.291899i
$365$	1.35406	+	1.50384i	0.0708749	+	0.0787145i
$366$	−0.881624	+	1.52702i	−0.0460832	+	0.0798185i
$367$	−16.5405	−	28.6489i	−0.863405	−	1.49546i	−0.868622	−	0.495476i	$-0.834994\pi$
$367$	−16.5405	−	28.6489i	−0.863405	−	1.49546i	0.00521645	−	0.999986i	$-0.498340\pi$
$368$	−0.612577	+	1.88532i	−0.0319328	+	0.0982791i
$369$	8.72506	−	3.88464i	0.454208	−	0.202227i
$370$	2.10754	−	1.53122i	0.109566	−	0.0796043i
$371$	−4.43136			−0.230065
$372$	5.22442	−	1.92495i	0.270874	−	0.0998038i
$373$	4.02234			0.208269			0.104134	−	0.994563i	$-0.466793\pi$
$373$	4.02234			0.208269			0.104134	+	0.994563i	$0.466793\pi$
$374$	2.72143	−	1.97723i	0.140722	−	0.102240i
$375$	0.913545	−	0.406737i	0.0471753	−	0.0210038i
$376$	−2.19271	+	6.74847i	−0.113081	+	0.348026i
$377$	−4.95798	−	8.58747i	−0.255349	−	0.442277i
$378$	0.759354	−	1.31524i	0.0390569	−	0.0676486i
$379$	23.1541	+	25.7152i	1.18934	+	1.32090i	0.935362	+	0.353692i	$0.115074\pi$
$379$	23.1541	+	25.7152i	1.18934	+	1.32090i	0.253983	+	0.967209i	$0.418259\pi$
$380$	−0.860623	−	2.64872i	−0.0441490	−	0.135877i
$381$	−1.78305	+	1.98028i	−0.0913486	+	0.101453i
$382$	17.8931	+	7.96651i	0.915490	+	0.407602i
$383$	−19.2822	+	4.09856i	−0.985274	+	0.209426i	−0.672254	−	0.740320i	$-0.734674\pi$
$383$	−19.2822	+	4.09856i	−0.985274	+	0.209426i	−0.313020	+	0.949747i	$0.601341\pi$
$384$	0.104528	+	0.994522i	0.00533420	+	0.0507515i
$385$	−0.736666	+	7.00891i	−0.0375440	+	0.357207i
$386$	−0.859121	−	0.182612i	−0.0437281	−	0.00929470i
$387$	0.784632	+	0.570068i	0.0398851	+	0.0289782i
$388$	6.63500	+	4.82061i	0.336841	+	0.244729i
$389$	6.70059	+	1.42425i	0.339733	+	0.0722126i	0.374619	−	0.927179i	$-0.377773\pi$
$389$	6.70059	+	1.42425i	0.339733	+	0.0722126i	−0.0348859	+	0.999391i	$0.511107\pi$
$390$	0.403031	−	3.83458i	0.0204082	−	0.194172i
$391$	0.150207	+	1.42912i	0.00759629	+	0.0722739i
$392$	4.59096	−	0.975840i	0.231879	−	0.0492873i
$393$	11.0326	+	4.91205i	0.556523	+	0.247780i
$394$	11.1054	−	12.3338i	0.559484	−	0.621370i
$395$	0.420036	+	1.29274i	0.0211343	+	0.0650448i
$396$	−3.10508	−	3.44854i	−0.156036	−	0.173296i
$397$	1.50675	−	2.60976i	0.0756214	−	0.130980i	−0.825735	−	0.564058i	$-0.809239\pi$
$397$	1.50675	−	2.60976i	0.0756214	−	0.130980i	0.901356	+	0.433078i	$0.142573\pi$
$398$	7.87781	+	13.6448i	0.394879	+	0.683951i
$399$	−1.30703	+	4.02264i	−0.0654335	+	0.201384i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	−23.1985	+	16.8547i	−1.15848	+	0.841683i	−0.989585	−	0.143951i	$-0.954019\pi$
$401$	−23.1985	+	16.8547i	−1.15848	+	0.841683i	−0.168893	+	0.985634i	$0.554019\pi$
$402$	2.55902			0.127633
$403$	−21.2467	+	3.07169i	−1.05838	+	0.153012i
$404$	11.6851			0.581357
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	−3.56809	+	1.58861i	−0.177081	+	0.0788416i
$407$	−3.73562	+	11.4971i	−0.185168	+	0.569889i
$408$	0.362449	+	0.627780i	0.0179439	+	0.0310797i
$409$	15.0109	−	25.9997i	0.742242	−	1.28560i	−0.209230	−	0.977866i	$-0.567096\pi$
$409$	15.0109	−	25.9997i	0.742242	−	1.28560i	0.951472	−	0.307735i	$-0.0995710\pi$
$410$	−6.39071	−	7.09760i	−0.315615	−	0.350525i
$411$	−6.33260	−	19.4897i	−0.312364	−	0.961358i
$412$	−4.23361	+	4.70190i	−0.208575	+	0.231646i
$413$	19.7336	+	8.78597i	0.971028	+	0.432329i
$414$	1.93902	−	0.412152i	0.0952978	−	0.0202562i
$415$	0.150808	+	1.43484i	0.00740286	+	0.0704335i
$416$	0.403031	−	3.83458i	0.0197602	−	0.188006i
$417$	16.5008	+	3.50736i	0.808050	+	0.171756i
$418$	10.4556	+	7.59646i	0.511402	+	0.371555i
$419$	15.4557	+	11.2293i	0.755063	+	0.548585i	0.897392	−	0.441234i	$-0.145459\pi$
$419$	15.4557	+	11.2293i	0.755063	+	0.548585i	−0.142329	+	0.989819i	$0.545459\pi$
$420$	−1.48552	−	0.315757i	−0.0724859	−	0.0154074i
$421$	−2.87473	+	27.3512i	−0.140106	+	1.33302i	0.668080	+	0.744090i	$0.267116\pi$
$421$	−2.87473	+	27.3512i	−0.140106	+	1.33302i	−0.808186	+	0.588928i	$0.799550\pi$
$422$	−1.80274	−	17.1519i	−0.0877559	−	0.834942i
$423$	6.94071	−	1.47529i	0.337469	−	0.0717312i
$424$	−2.66559	−	1.18680i	−0.129452	−	0.0576359i
$425$	0.485051	−	0.538704i	0.0235284	−	0.0261310i
$426$	−0.751596	−	2.31318i	−0.0364150	−	0.112074i
$427$	−1.79184	−	1.99004i	−0.0867131	−	0.0963046i
$428$	5.31139	−	9.19960i	0.256736	−	0.444680i
$429$	8.94614	+	15.4952i	0.431924	+	0.748114i
$430$	0.299703	−	0.922390i	0.0144529	−	0.0444816i
$431$	8.92149	−	3.97210i	0.429733	−	0.191329i	−0.180460	−	0.983582i	$-0.557759\pi$
$431$	8.92149	−	3.97210i	0.429733	−	0.191329i	0.610193	+	0.792253i	$0.291092\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	−2.39073			−0.114891			−0.0574455	−	0.998349i	$-0.518296\pi$
$433$	−2.39073			−0.114891			−0.0574455	+	0.998349i	$0.518296\pi$
$434$	0.328491	+	8.44942i	0.0157681	+	0.405585i
$435$	−2.57176			−0.123307
$436$	6.61739	−	4.80782i	0.316916	−	0.230253i
$437$	−5.04358	+	2.24555i	−0.241267	+	0.107419i
$438$	0.625331	−	1.92457i	0.0298795	−	0.0919596i
$439$	14.9552	+	25.9032i	0.713772	+	1.23629i	0.963431	+	0.267956i	$0.0863482\pi$
$439$	14.9552	+	25.9032i	0.713772	+	1.23629i	−0.249659	+	0.968334i	$0.580318\pi$
$440$	−2.32024	+	4.01877i	−0.110613	+	0.191587i
$441$	−3.14058	−	3.48797i	−0.149552	−	0.166094i
$442$	−0.863699	−	2.65819i	−0.0410820	−	0.126437i
$443$	−13.9195	+	15.4592i	−0.661336	+	0.734488i	−0.976730	−	0.214473i	$-0.931197\pi$
$443$	−13.9195	+	15.4592i	−0.661336	+	0.734488i	0.315394	+	0.948961i	$0.397863\pi$
$444$	−2.37985	−	1.05958i	−0.112943	−	0.0502853i
$445$	−11.0085	+	2.33992i	−0.521852	+	0.110923i
$446$	1.33580	+	12.7093i	0.0632521	+	0.601803i
$447$	0.979415	−	9.31851i	0.0463247	−	0.440750i
$448$	−1.48552	−	0.315757i	−0.0701842	−	0.0149181i
$449$	−18.5603	−	13.4849i	−0.875915	−	0.636390i	0.0562522	−	0.998417i	$-0.482085\pi$
$449$	−18.5603	−	13.4849i	−0.875915	−	0.636390i	−0.932168	+	0.362027i	$0.882085\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	43.3515	+	9.21465i	2.04134	+	0.433901i
$452$	0.353597	−	3.36425i	0.0166318	−	0.158241i
$453$	−0.640226	−	6.09134i	−0.0300804	−	0.286196i
$454$	−18.9284	+	4.02336i	−0.888354	+	0.188826i
$455$	5.34943	+	2.38172i	0.250785	+	0.111657i
$456$	−1.86355	+	2.06968i	−0.0872688	+	0.0969218i
$457$	−10.4595	−	32.1912i	−0.489277	−	1.50584i	−0.825690	−	0.564124i	$-0.809214\pi$
$457$	−10.4595	−	32.1912i	−0.489277	−	1.50584i	0.336413	−	0.941715i	$-0.390786\pi$
$458$	1.43620	+	1.59506i	0.0671092	+	0.0745323i
$459$	0.362449	−	0.627780i	0.0169177	−	0.0293023i
$460$	−0.991171	−	1.71676i	−0.0462136	−	0.0800443i
$461$	−10.0423	+	30.9072i	−0.467719	+	1.43949i	0.387812	+	0.921738i	$0.373231\pi$
$461$	−10.0423	+	30.9072i	−0.467719	+	1.43949i	−0.855531	+	0.517752i	$0.826769\pi$
$462$	6.43823	−	2.86648i	0.299533	−	0.133361i
$463$	26.2651	−	19.0827i	1.22064	−	0.886850i	0.224491	−	0.974476i	$-0.427928\pi$
$463$	26.2651	−	19.0827i	1.22064	−	0.886850i	0.996153	+	0.0876262i	$0.0279281\pi$
$464$	−2.57176			−0.119391
$465$	−2.06531	+	5.17054i	−0.0957763	+	0.239778i
$466$	−0.0951955			−0.00440985
$467$	16.5985	−	12.0595i	0.768086	−	0.558047i	−0.133294	−	0.991077i	$-0.542555\pi$
$467$	16.5985	−	12.0595i	0.768086	−	0.558047i	0.901380	+	0.433030i	$0.142555\pi$
$468$	−3.52236	+	1.56826i	−0.162821	+	0.0724926i
$469$	−1.20097	+	3.69619i	−0.0554555	+	0.170674i
$470$	−3.54788	−	6.14511i	−0.163652	−	0.283453i
$471$	0.965546	−	1.67237i	0.0444900	−	0.0770589i
$472$	9.51729	+	10.5700i	0.438069	+	0.486525i
$473$	1.39076	+	4.28032i	0.0639473	+	0.196809i
$474$	0.909527	−	1.01013i	0.0417759	−	0.0463969i
$475$	2.54426	+	1.13278i	0.116738	+	0.0519753i
$476$	−1.07685	+	0.228891i	−0.0493573	+	0.0104912i
$477$	0.304998	+	2.90186i	0.0139649	+	0.132867i
$478$	−0.409397	+	3.89515i	−0.0187254	+	0.178160i
$479$	−21.6601	−	4.60399i	−0.989674	−	0.210362i	−0.315493	−	0.948928i	$-0.602170\pi$
$479$	−21.6601	−	4.60399i	−0.989674	−	0.210362i	−0.674181	+	0.738566i	$0.735503\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	8.12606	+	5.90393i	0.370516	+	0.269196i
$482$	−2.46258	−	0.523438i	−0.112168	−	0.0238420i
$483$	−0.314693	+	2.99410i	−0.0143190	+	0.136236i
$484$	−1.10110	−	10.4763i	−0.0500500	−	0.476194i
$485$	−8.02209	+	1.70515i	−0.364264	+	0.0774268i
$486$	−0.913545	−	0.406737i	−0.0414393	−	0.0184499i
$487$	6.06762	−	6.73877i	0.274950	−	0.305363i	−0.589816	−	0.807537i	$-0.700800\pi$
$487$	6.06762	−	6.73877i	0.274950	−	0.305363i	0.864766	+	0.502175i	$0.167467\pi$
$488$	−0.544874	−	1.67695i	−0.0246653	−	0.0759119i
$489$	3.34910	+	3.71955i	0.151452	+	0.168204i
$490$	−2.34676	+	4.06472i	−0.106016	+	0.183625i
$491$	−2.42135	−	4.19390i	−0.109274	−	0.189268i	0.806202	−	0.591640i	$-0.201519\pi$
$491$	−2.42135	−	4.19390i	−0.109274	−	0.189268i	−0.915476	+	0.402372i	$0.868186\pi$
$492$	−2.95135	+	9.08331i	−0.133057	+	0.409507i
$493$	−1.70309	+	0.758265i	−0.0767034	+	0.0341506i
$494$	8.68744	−	6.31179i	0.390866	−	0.283981i
$495$	4.64047			0.208574
$496$	−2.06531	+	5.17054i	−0.0927350	+	0.232164i
$497$	3.69382			0.165691
$498$	1.16720	−	0.848023i	0.0523036	−	0.0380008i
$499$	−20.7870	+	9.25499i	−0.930556	+	0.414310i	−0.815309	−	0.579027i	$-0.803433\pi$
$499$	−20.7870	+	9.25499i	−0.930556	+	0.414310i	−0.115247	+	0.993337i	$0.536766\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−0.0837904	−	0.145129i	−0.00374348	−	0.00648389i
$502$	−10.1921	+	17.6533i	−0.454896	+	0.787903i
$503$	−8.31590	−	9.23574i	−0.370788	−	0.411801i	0.528657	−	0.848835i	$-0.322696\pi$
$503$	−8.31590	−	9.23574i	−0.370788	−	0.411801i	−0.899445	+	0.437034i	$0.856029\pi$
$504$	0.469306	+	1.44438i	0.0209046	+	0.0643376i
$505$	−7.81889	+	8.68375i	−0.347936	+	0.386422i
$506$	8.40370	+	3.74157i	0.373590	+	0.166333i
$507$	1.82565	−	0.388054i	0.0810800	−	0.0172341i
$508$	−0.278540	−	2.65013i	−0.0123582	−	0.117581i
$509$	0.195435	−	1.85944i	0.00866252	−	0.0824184i	−0.989336	−	0.145648i	$-0.953473\pi$
$509$	0.195435	−	1.85944i	0.00866252	−	0.0824184i	0.997999	+	0.0632295i	$0.0201400\pi$
$510$	−0.709057	−	0.150715i	−0.0313976	−	0.00667376i
$511$	2.48633	+	1.80643i	0.109989	+	0.0799116i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	2.72417	+	0.579041i	0.120275	+	0.0255653i
$514$	2.23464	−	21.2611i	0.0985656	−	0.937789i
$515$	−0.661355	−	6.29237i	−0.0291428	−	0.277275i
$516$	−0.948664	+	0.201645i	−0.0417626	+	0.00887692i
$517$	30.0810	+	13.3929i	1.32296	+	0.589019i
$518$	2.64730	−	2.94013i	0.116316	−	0.129182i
$519$	7.03121	+	21.6398i	0.308636	+	0.949884i
$520$	2.57997	+	2.86534i	0.113139	+	0.125654i
$521$	−11.5027	+	19.9233i	−0.503944	+	0.872857i	0.496046	+	0.868297i	$0.334785\pi$
$521$	−11.5027	+	19.9233i	−0.503944	+	0.872857i	−0.999990	+	0.00456023i	$0.998548\pi$
$522$	1.28588	+	2.22721i	0.0562815	+	0.0974825i
$523$	4.30627	−	13.2533i	0.188300	−	0.579528i	−0.811689	−	0.584089i	$-0.801452\pi$
$523$	4.30627	−	13.2533i	0.188300	−	0.579528i	0.999990	+	0.00456090i	$0.00145178\pi$
$524$	−11.0326	+	4.91205i	−0.481963	+	0.214584i
$525$	1.22866	−	0.892674i	0.0536231	−	0.0389595i
$526$	14.6705			0.639664
$527$	0.156793	+	4.03301i	0.00683001	+	0.175681i
$528$	4.64047			0.201951
$529$	15.4282	−	11.2093i	0.670792	−	0.487359i
$530$	2.66559	−	1.18680i	0.115786	−	0.0515511i
$531$	4.39526	−	13.5272i	0.190738	−	0.587032i
$532$	−2.11483	−	3.66298i	−0.0916893	−	0.158811i
$533$	18.4124	−	31.8913i	0.797532	−	1.38137i
$534$	7.53067	+	8.36366i	0.325884	+	0.361931i
$535$	3.28262	+	10.1029i	0.141920	+	0.436785i
$536$	−1.71232	+	1.90173i	−0.0739610	+	0.0821420i
$537$	16.4541	+	7.32583i	0.710046	+	0.316133i
$538$	−31.1899	+	6.62963i	−1.34469	+	0.285824i
$539$	−2.27665	−	21.6609i	−0.0980622	−	0.933000i
$540$	−0.104528	+	0.994522i	−0.00449819	+	0.0427974i
$541$	−22.8201	−	4.85057i	−0.981114	−	0.208542i	−0.310683	−	0.950514i	$-0.600558\pi$
$541$	−22.8201	−	4.85057i	−0.981114	−	0.208542i	−0.670431	+	0.741971i	$0.733891\pi$
$542$	7.07190	+	5.13804i	0.303764	+	0.220698i
$543$	2.75985	+	2.00515i	0.118437	+	0.0860493i
$544$	−0.709057	−	0.150715i	−0.0304006	−	0.00646184i
$545$	−0.854995	+	8.13474i	−0.0366240	+	0.348454i
$546$	−0.612085	−	5.82360i	−0.0261948	−	0.249227i
$547$	−38.9470	+	8.27843i	−1.66525	+	0.353960i	−0.941737	−	0.336349i	$-0.890808\pi$
$547$	−38.9470	+	8.27843i	−1.66525	+	0.353960i	−0.723514	+	0.690309i	$0.757474\pi$
$548$	18.7210	+	8.33514i	0.799723	+	0.356060i
$549$	−1.17984	+	1.31035i	−0.0503545	+	0.0559243i
$550$	−1.43398	−	4.41335i	−0.0611453	−	0.188186i
$551$	−4.79262	−	5.32274i	−0.204172	−	0.226756i
$552$	−0.991171	+	1.71676i	−0.0421870	+	0.0730701i
$553$	1.03216	+	1.78776i	0.0438921	+	0.0760233i
$554$	0.580945	−	1.78796i	0.0246820	−	0.0759633i
$555$	2.37985	−	1.05958i	0.101019	−	0.0449765i
$556$	−13.6477	+	9.91563i	−0.578791	+	0.420517i
$557$	40.9169			1.73370			0.866852	−	0.498565i	$-0.166139\pi$
$557$	40.9169			1.73370			0.866852	+	0.498565i	$0.166139\pi$
$558$	5.51047	−	0.796662i	0.233277	−	0.0337254i
$559$	3.73948			0.158163
$560$	1.22866	−	0.892674i	0.0519204	−	0.0377223i
$561$	3.07305	−	1.36821i	0.129744	−	0.0577658i
$562$	5.66181	−	17.4253i	0.238829	−	0.735041i
$563$	−3.06131	−	5.30235i	−0.129019	−	0.223467i	0.794278	−	0.607555i	$-0.207849\pi$
$563$	−3.06131	−	5.30235i	−0.129019	−	0.223467i	−0.923297	+	0.384087i	$0.874516\pi$
$564$	−3.54788	+	6.14511i	−0.149393	+	0.258756i
$565$	2.26352	+	2.51390i	0.0952271	+	0.105760i
$566$	1.98342	+	6.10435i	0.0833694	+	0.256585i
$567$	1.01621	−	1.12862i	0.0426769	−	0.0473976i
$568$	2.22194	+	0.989272i	0.0932306	+	0.0415089i
$569$	−11.5069	+	2.44587i	−0.482395	+	0.102536i	−0.442689	−	0.896675i	$-0.645975\pi$
$569$	−11.5069	+	2.44587i	−0.482395	+	0.102536i	−0.0397060	+	0.999211i	$0.512642\pi$
$570$	−0.291115	−	2.76978i	−0.0121935	−	0.116013i
$571$	1.20285	−	11.4443i	0.0503375	−	0.478930i	−0.940093	−	0.340918i	$-0.889262\pi$
$571$	1.20285	−	11.4443i	0.0503375	−	0.478930i	0.990431	−	0.138012i	$-0.0440711\pi$
$572$	−17.5013	−	3.72001i	−0.731765	−	0.155542i
$573$	15.8457	+	11.5126i	0.661965	+	0.480946i
$574$	−11.7346	−	8.52571i	−0.489794	−	0.355856i
$575$	1.93902	+	0.412152i	0.0808628	+	0.0171879i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−3.00663	−	28.6061i	−0.125167	−	1.19089i	−0.859151	−	0.511722i	$-0.829008\pi$
$577$	−3.00663	−	28.6061i	−0.125167	−	1.19089i	0.733984	−	0.679167i	$-0.237659\pi$
$578$	16.1145	−	3.42525i	0.670275	−	0.142471i
$579$	−0.802380	−	0.357243i	−0.0333458	−	0.0148465i
$580$	1.72085	−	1.91119i	0.0714543	−	0.0793580i
$581$	0.677088	+	2.08386i	0.0280903	+	0.0864532i
$582$	5.48775	+	6.09476i	0.227474	+	0.252636i
$583$	−6.77009	+	11.7261i	−0.280389	+	0.485647i
$584$	1.01181	+	1.75250i	0.0418689	+	0.0725190i
$585$	1.19148	−	3.66699i	0.0492615	−	0.151611i
$586$	12.3835	−	5.51351i	0.511560	−	0.227761i
$587$	6.12089	−	4.44709i	0.252636	−	0.183551i	−0.454258	−	0.890870i	$-0.650096\pi$
$587$	6.12089	−	4.44709i	0.252636	−	0.183551i	0.706894	+	0.707319i	$0.250096\pi$
$588$	4.69353			0.193558
$589$	−14.5502	+	5.36104i	−0.599530	+	0.220898i
$590$	−14.2234			−0.585567
$591$	13.4271	−	9.75537i	0.552318	−	0.401282i
$592$	2.37985	−	1.05958i	0.0978111	−	0.0435483i
$593$	0.896611	−	2.75948i	0.0368194	−	0.113318i	−0.930958	−	0.365127i	$-0.881025\pi$
$593$	0.896611	−	2.75948i	0.0368194	−	0.113318i	0.967777	+	0.251809i	$0.0810254\pi$
$594$	−2.32024	−	4.01877i	−0.0952004	−	0.164892i
$595$	0.550454	−	0.953414i	0.0225664	−	0.0390861i
$596$	6.26964	+	6.96315i	0.256815	+	0.285222i
$597$	4.86876	+	14.9845i	0.199265	+	0.613275i
$598$	5.11438	−	5.68009i	0.209143	−	0.232276i
$599$	−39.9526	−	17.7880i	−1.63242	−	0.726799i	−0.633519	−	0.773727i	$-0.718390\pi$
$599$	−39.9526	−	17.7880i	−1.63242	−	0.726799i	−0.998898	+	0.0469280i	$0.985057\pi$
$600$	0.978148	−	0.207912i	0.0399327	−	0.00848796i
$601$	−1.03088	−	9.80817i	−0.0420505	−	0.400084i	−0.995221	−	0.0976498i	$-0.968867\pi$
$601$	−1.03088	−	9.80817i	−0.0420505	−	0.400084i	0.953170	−	0.302434i	$-0.0977992\pi$
$602$	0.153963	−	1.46486i	0.00627507	−	0.0597033i
$603$	2.50310	+	0.532051i	0.101934	+	0.0216668i
$604$	4.95515	+	3.60012i	0.201622	+	0.146487i
$605$	8.52216	+	6.19171i	0.346475	+	0.251729i
$606$	11.4298	+	2.42948i	0.464304	+	0.0986908i
$607$	−2.31648	+	22.0398i	−0.0940229	+	0.894568i	0.841251	+	0.540644i	$0.181819\pi$
$607$	−2.31648	+	22.0398i	−0.0940229	+	0.894568i	−0.935274	+	0.353924i	$0.884847\pi$
$608$	−0.291115	−	2.76978i	−0.0118063	−	0.112329i
$609$	−3.82041	+	0.812053i	−0.154811	+	0.0329060i
$610$	1.61081	+	0.717178i	0.0652197	+	0.0290377i
$611$	18.3069	−	20.3318i	0.740616	−	0.822537i
$612$	0.224006	+	0.689419i	0.00905489	+	0.0278681i
$613$	7.82465	+	8.69015i	0.316035	+	0.350992i	0.880143	−	0.474709i	$-0.157447\pi$
$613$	7.82465	+	8.69015i	0.316035	+	0.350992i	−0.564108	+	0.825701i	$0.690780\pi$
$614$	−4.50719	+	7.80668i	−0.181895	+	0.315052i
$615$	−4.77538	−	8.27120i	−0.192562	−	0.333527i
$616$	−2.17780	+	6.70259i	−0.0877462	+	0.270055i
$617$	19.2154	−	8.55523i	0.773581	−	0.344421i	0.0183095	−	0.999832i	$-0.494172\pi$
$617$	19.2154	−	8.55523i	0.773581	−	0.344421i	0.755272	+	0.655412i	$0.227505\pi$
$618$	−5.11868	+	3.71894i	−0.205903	+	0.149598i
$619$	38.1564			1.53364			0.766818	−	0.641865i	$-0.221839\pi$
$619$	38.1564			1.53364			0.766818	+	0.641865i	$0.221839\pi$
$620$	−2.46050	−	4.99459i	−0.0988161	−	0.200588i
$621$	1.98234			0.0795486
$622$	17.7854	−	12.9219i	0.713131	−	0.518120i
$623$	−15.6145	+	6.95201i	−0.625580	+	0.278526i
$624$	1.19148	−	3.66699i	0.0476973	−	0.146797i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.1492	−	22.7751i	0.525548	−	0.910276i
$627$	8.64776	+	9.60431i	0.345358	+	0.383559i
$628$	0.596740	+	1.83658i	0.0238125	+	0.0732874i
$629$	1.26359	−	1.40336i	0.0503827	−	0.0559556i
$630$	−1.38741	−	0.617714i	−0.0552757	−	0.0246103i
$631$	−9.07873	+	1.92974i	−0.361418	+	0.0768219i	−0.385042	−	0.922899i	$-0.625813\pi$
$631$	−9.07873	+	1.92974i	−0.361418	+	0.0768219i	0.0236235	+	0.999721i	$0.492480\pi$
$632$	0.142082	+	1.35182i	0.00565172	+	0.0537725i
$633$	1.80274	−	17.1519i	0.0716524	−	0.681727i
$634$	−6.88577	−	1.46362i	−0.273469	−	0.0581276i
$635$	2.15581	+	1.56629i	0.0855508	+	0.0621563i
$636$	−2.36059	−	1.71507i	−0.0936034	−	0.0680069i
$637$	−17.7014	−	3.76255i	−0.701355	−	0.149078i
$638$	−1.24746	+	11.8688i	−0.0493876	+	0.469891i
$639$	−0.254236	−	2.41889i	−0.0100574	−	0.0956899i
$640$	0.978148	−	0.207912i	0.0386647	−	0.00821843i
$641$	−3.37960	−	1.50470i	−0.133486	−	0.0594319i	0.338907	−	0.940820i	$-0.389943\pi$
$641$	−3.37960	−	1.50470i	−0.133486	−	0.0594319i	−0.472393	+	0.881388i	$0.656610\pi$
$642$	7.10803	−	7.89427i	0.280532	−	0.311562i
$643$	8.86702	+	27.2899i	0.349681	+	1.07621i	0.959030	+	0.283306i	$0.0914311\pi$
$643$	8.86702	+	27.2899i	0.349681	+	1.07621i	−0.609348	+	0.792903i	$0.708569\pi$
$644$	−2.01448	−	2.23731i	−0.0793817	−	0.0881623i
$645$	0.484929	−	0.839922i	0.0190941	−	0.0330719i
$646$	−1.00943	−	1.74839i	−0.0397156	−	0.0687894i
$647$	8.58199	−	26.4127i	0.337393	−	1.03839i	−0.628138	−	0.778102i	$-0.716183\pi$
$647$	8.58199	−	26.4127i	0.337393	−	1.03839i	0.965531	−	0.260287i	$-0.0838172\pi$
$648$	0.913545	−	0.406737i	0.0358875	−	0.0159781i
$649$	53.3977	−	38.7957i	2.09604	−	1.52286i
$650$	−3.85570			−0.151233
$651$	−1.43542	+	8.33308i	−0.0562586	+	0.326599i
$652$	−5.00515			−0.196017
$653$	−15.9400	+	11.5811i	−0.623781	+	0.453204i	−0.854240	−	0.519878i	$-0.825977\pi$
$653$	−15.9400	+	11.5811i	−0.623781	+	0.453204i	0.230459	+	0.973082i	$0.425977\pi$
$654$	7.47239	−	3.32692i	0.292193	−	0.130093i
$655$	3.73191	−	11.4857i	0.145818	−	0.448782i
$656$	−4.77538	−	8.27120i	−0.186447	−	0.322936i
$657$	1.01181	−	1.75250i	0.0394744	−	0.0683716i
$658$	−7.21081	−	8.00842i	−0.281107	−	0.312201i
$659$	8.89295	+	27.3697i	0.346420	+	1.06617i	0.960819	+	0.277176i	$0.0893984\pi$
$659$	8.89295	+	27.3697i	0.346420	+	1.06617i	−0.614399	+	0.788995i	$0.710602\pi$
$660$	−3.10508	+	3.44854i	−0.120865	+	0.134234i
$661$	9.18893	+	4.09117i	0.357408	+	0.159128i	0.577583	−	0.816332i	$-0.303996\pi$
$661$	9.18893	+	4.09117i	0.357408	+	0.159128i	−0.220175	+	0.975460i	$0.570663\pi$
$662$	−28.1459	+	5.98261i	−1.09392	+	0.232521i
$663$	−0.292156	−	2.77968i	−0.0113464	−	0.107954i
$664$	−0.150808	+	1.43484i	−0.00585247	+	0.0556825i
$665$	4.13722	+	0.879394i	0.160435	+	0.0341014i
$666$	−2.10754	−	1.53122i	−0.0816656	−	0.0593336i
$667$	−4.12446	−	2.99660i	−0.159700	−	0.116029i
$668$	0.163919	+	0.0348420i	0.00634221	+	0.00134808i
$669$	−1.33580	+	12.7093i	−0.0516451	+	0.491370i
$670$	−0.267491	−	2.54501i	−0.0103341	−	0.0983222i
$671$	−8.00350	+	1.70120i	−0.308972	+	0.0656740i
$672$	−1.38741	−	0.617714i	−0.0535204	−	0.0238288i
$673$	−33.2482	+	36.9259i	−1.28163	+	1.42339i	−0.426909	+	0.904294i	$0.640398\pi$
$673$	−33.2482	+	36.9259i	−1.28163	+	1.42339i	−0.854716	+	0.519095i	$0.826269\pi$
$674$	3.39809	+	10.4582i	0.130890	+	0.402837i
$675$	−0.669131	−	0.743145i	−0.0257548	−	0.0286037i
$676$	−0.933219	+	1.61638i	−0.0358930	+	0.0621686i
$677$	−2.96357	−	5.13305i	−0.113899	−	0.197279i	0.803440	−	0.595386i	$-0.203001\pi$
$677$	−2.96357	−	5.13305i	−0.113899	−	0.197279i	−0.917339	+	0.398107i	$0.869667\pi$
$678$	1.04534	−	3.21722i	0.0401459	−	0.123556i
$679$	−11.3786	+	5.06606i	−0.436669	+	0.194418i
$680$	0.586455	−	0.426084i	0.0224895	−	0.0163396i
$681$	−19.3513			−0.741543
$682$	22.8605	+	12.0395i	0.875374	+	0.461017i
$683$	−9.91294			−0.379308			−0.189654	−	0.981851i	$-0.560737\pi$
$683$	−9.91294			−0.379308			−0.189654	+	0.981851i	$0.560737\pi$
$684$	−2.25314	+	1.63700i	−0.0861510	+	0.0625923i
$685$	−18.7210	+	8.33514i	−0.715294	+	0.318469i
$686$	−5.48785	+	16.8899i	−0.209527	+	0.644858i
$687$	1.07318	+	1.85881i	0.0409445	+	0.0709179i
$688$	0.484929	−	0.839922i	0.0184877	−	0.0320217i
$689$	7.52795	+	8.36064i	0.286792	+	0.318515i
$690$	−0.612577	−	1.88532i	−0.0233204	−	0.0717729i
$691$	−29.5996	+	32.8737i	−1.12602	+	1.25057i	−0.161414	+	0.986887i	$0.551605\pi$
$691$	−29.5996	+	32.8737i	−1.12602	+	1.25057i	−0.964608	+	0.263687i	$0.915061\pi$
$692$	−20.7863	−	9.25468i	−0.790178	−	0.351810i
$693$	6.89351	−	1.46526i	0.261863	−	0.0556607i
$694$	−2.83863	−	27.0078i	−0.107753	−	1.02520i
$695$	1.76334	−	16.7771i	0.0668873	−	0.636391i
$696$	−2.51557	−	0.534700i	−0.0953523	−	0.0202677i
$697$	−5.60109	−	4.06943i	−0.212156	−	0.154141i
$698$	−18.5252	−	13.4593i	−0.701187	−	0.509442i
$699$	−0.0931153	−	0.0197923i	−0.00352194	−	0.000748612i
$700$	−0.158748	+	1.51039i	−0.00600011	+	0.0570873i
$701$	1.02448	+	9.74729i	0.0386941	+	0.368150i	0.996685	+	0.0813527i	$0.0259240\pi$
$701$	1.02448	+	9.74729i	0.0386941	+	0.368150i	−0.957991	+	0.286798i	$0.907409\pi$
$702$	−3.77145	+	0.801646i	−0.142344	+	0.0302562i
$703$	6.62795	+	2.95096i	0.249978	+	0.111297i
$704$	−3.10508	+	3.44854i	−0.117027	+	0.129972i
$705$	−2.19271	−	6.74847i	−0.0825823	−	0.254162i
$706$	15.6639	+	17.3965i	0.589518	+	0.654726i
$707$	−8.87315	+	15.3688i	−0.333709	+	0.578001i
$708$	7.11169	+	12.3178i	0.267274	+	0.462931i
$709$	−0.795799	+	2.44922i	−0.0298869	+	0.0919824i	−0.964887	−	0.262664i	$-0.915399\pi$
$709$	−0.795799	+	2.44922i	−0.0298869	+	0.0919824i	0.935000	+	0.354647i	$0.115399\pi$
$710$	−2.22194	+	0.989272i	−0.0833879	+	0.0371267i
$711$	1.09967	−	0.798957i	0.0412408	−	0.0299632i
$712$	−11.2544			−0.421777
$713$	−9.33690	+	5.88577i	−0.349670	+	0.220424i
$714$	−1.10091			−0.0412004
$715$	14.4752	−	10.5168i	0.541340	−	0.393307i
$716$	−16.4541	+	7.32583i	−0.614918	+	0.273779i
$717$	−1.21030	+	3.72492i	−0.0451994	+	0.139110i
$718$	−8.09434	−	14.0198i	−0.302078	−	0.523214i
$719$	1.44429	−	2.50158i	0.0538629	−	0.0932933i	−0.837837	−	0.545921i	$-0.816180\pi$
$719$	1.44429	−	2.50158i	0.0538629	−	0.0932933i	0.891700	+	0.452628i	$0.149513\pi$
$720$	−0.669131	−	0.743145i	−0.0249370	−	0.0276954i
$721$	−2.96932	−	9.13862i	−0.110583	−	0.340340i
$722$	−7.52343	+	8.35561i	−0.279993	+	0.310964i
$723$	−2.29994	−	1.02400i	−0.0855357	−	0.0380829i
$724$	−3.33682	+	0.709263i	−0.124012	+	0.0263596i
$725$	0.268823	+	2.55768i	0.00998382	+	0.0949897i
$726$	1.10110	−	10.4763i	0.0408657	−	0.388811i
$727$	−25.7470	−	5.47269i	−0.954903	−	0.202971i	−0.295991	−	0.955191i	$-0.595650\pi$
$727$	−25.7470	−	5.47269i	−0.954903	−	0.202971i	−0.658912	+	0.752220i	$0.728983\pi$
$728$	4.73735	+	3.44188i	0.175578	+	0.127565i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−1.97939	−	0.420733i	−0.0732606	−	0.0155720i
$731$	0.0734885	−	0.699196i	0.00271807	−	0.0258607i
$732$	−0.184310	−	1.75359i	−0.00681228	−	0.0648145i
$733$	4.64665	−	0.987676i	0.171628	−	0.0364806i	−0.121296	−	0.992616i	$-0.538705\pi$
$733$	4.64665	−	0.987676i	0.171628	−	0.0364806i	0.292924	+	0.956136i	$0.405372\pi$
$734$	30.2209	+	13.4552i	1.11548	+	0.496642i
$735$	−3.14058	+	3.48797i	−0.115842	+	0.128656i
$736$	−0.612577	−	1.88532i	−0.0225799	−	0.0694938i
$737$	7.94598	+	8.82490i	0.292694	+	0.325070i
$738$	−4.77538	+	8.27120i	−0.175784	+	0.304467i
$739$	−2.58393	−	4.47551i	−0.0950516	−	0.164634i	0.814579	−	0.580053i	$-0.196968\pi$
$739$	−2.58393	−	4.47551i	−0.0950516	−	0.164634i	−0.909630	+	0.415419i	$0.863635\pi$
$740$	−0.805010	+	2.47757i	−0.0295927	+	0.0910771i
$741$	9.80989	−	4.36764i	0.360375	−	0.160449i
$742$	3.58504	−	2.60469i	0.131611	−	0.0956210i
$743$	−18.1631			−0.666341			−0.333171	−	0.942867i	$-0.608118\pi$
$743$	−18.1631			−0.666341			−0.333171	+	0.942867i	$0.608118\pi$
$744$	−3.09519	+	4.62815i	−0.113475	+	0.169676i
$745$	−9.36984			−0.343284
$746$	−3.25414	+	2.36427i	−0.119143	+	0.0865621i
$747$	1.31801	−	0.586816i	0.0482235	−	0.0214705i
$748$	−1.03949	+	3.19923i	−0.0380076	+	0.116975i
$749$	8.06645	+	13.9715i	0.294742	+	0.510508i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	3.95327	+	4.39055i	0.144257	+	0.160214i	0.810943	−	0.585125i	$-0.198955\pi$
$751$	3.95327	+	4.39055i	0.144257	+	0.160214i	−0.666686	+	0.745339i	$0.732288\pi$
$752$	−2.19271	−	6.74847i	−0.0799600	−	0.246092i
$753$	−13.6397	+	15.1484i	−0.497058	+	0.552039i
$754$	9.05868	+	4.03318i	0.329898	+	0.146880i
$755$	−5.99105	+	1.27344i	−0.218037	+	0.0463451i
$756$	0.158748	+	1.51039i	0.00577361	+	0.0549323i
$757$	4.54067	−	43.2016i	0.165033	−	1.57019i	−0.527976	−	0.849259i	$-0.677049\pi$
$757$	4.54067	−	43.2016i	0.165033	−	1.57019i	0.693009	−	0.720929i	$-0.256285\pi$
$758$	−33.8471	−	7.19441i	−1.22938	−	0.261313i
$759$	7.44215	+	5.40704i	0.270133	+	0.196263i
$760$	2.25314	+	1.63700i	0.0817300	+	0.0593803i
$761$	−31.9462	−	6.79037i	−1.15805	−	0.246151i	−0.411454	−	0.911431i	$-0.634979\pi$
$761$	−31.9462	−	6.79037i	−1.15805	−	0.246151i	−0.746594	+	0.665280i	$0.768312\pi$
$762$	0.278540	−	2.65013i	0.0100905	−	0.0960042i
$763$	1.29849	+	12.3543i	0.0470084	+	0.447255i
$764$	−19.1584	+	4.07225i	−0.693127	+	0.147329i
$765$	−0.662227	−	0.294842i	−0.0239429	−	0.0106601i
$766$	13.1906	−	14.6496i	0.476594	−	0.529311i
$767$	−16.9468	−	52.1570i	−0.611914	−	1.88328i
$768$	−0.669131	−	0.743145i	−0.0241452	−	0.0268159i
$769$	2.39565	−	4.14939i	0.0863893	−	0.149631i	−0.819593	−	0.572946i	$-0.805800\pi$
$769$	2.39565	−	4.14939i	0.0863893	−	0.149631i	0.905982	+	0.423315i	$0.139134\pi$
$770$	−3.52376	−	6.10333i	−0.126987	−	0.219949i
$771$	6.60625	−	20.3319i	0.237918	−	0.732237i
$772$	0.802380	−	0.357243i	0.0288783	−	0.0128574i
$773$	−15.6535	+	11.3729i	−0.563018	+	0.409056i	−0.832562	−	0.553932i	$-0.813127\pi$
$773$	−15.6535	+	11.3729i	−0.563018	+	0.409056i	0.269545	+	0.962988i	$0.413127\pi$
$774$	−0.969858			−0.0348608
$775$	5.35810	+	1.51352i	0.192469	+	0.0543674i
$776$	−8.20131			−0.294410
$777$	3.20074	−	2.32547i	0.114826	−	0.0834259i
$778$	−6.25805	+	2.78626i	−0.224362	+	0.0998923i
$779$	8.21960	−	25.2973i	0.294498	−	0.906371i
$780$	1.92785	+	3.33914i	0.0690281	+	0.119560i
$781$	5.64332	−	9.77451i	0.201934	−	0.349759i
$782$	−0.961537	−	1.06790i	−0.0343845	−	0.0381879i
$783$	0.794719	+	2.44589i	0.0284009	+	0.0874091i
$784$	−3.14058	+	3.48797i	−0.112164	+	0.124570i
$785$	−1.76414	−	0.785446i	−0.0629649	−	0.0280338i
$786$	−11.8128	+	2.51089i	−0.421349	+	0.0895606i
$787$	−5.43311	−	51.6926i	−0.193669	−	1.84264i	−0.471324	−	0.881960i	$-0.656224\pi$
$787$	−5.43311	−	51.6926i	−0.193669	−	1.84264i	0.277654	−	0.960681i	$-0.410443\pi$
$788$	−1.73484	+	16.5059i	−0.0618012	+	0.587999i
$789$	14.3499	+	3.05017i	0.510870	+	0.108589i
$790$	−1.09967	−	0.798957i	−0.0391245	−	0.0284256i
$791$	4.15629	+	3.01972i	0.147781	+	0.107369i
$792$	4.53907	+	0.964808i	0.161289	+	0.0342830i
$793$	−0.710643	+	6.76132i	−0.0252357	+	0.240101i
$794$	0.314996	+	2.99698i	0.0111788	+	0.106359i
$795$	2.85409	−	0.606655i	0.101224	−	0.0215158i
$796$	−14.3935	−	6.40839i	−0.510164	−	0.227139i
$797$	−7.55999	+	8.39622i	−0.267789	+	0.297409i	−0.862009	−	0.506893i	$-0.830794\pi$
$797$	−7.55999	+	8.39622i	−0.267789	+	0.297409i	0.594220	+	0.804302i	$0.297461\pi$
$798$	−1.30703	−	4.02264i	−0.0462685	−	0.142400i
$799$	−3.44181	−	3.82252i	−0.121762	−	0.135231i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	5.62721	+	9.74661i	0.198828	+	0.344379i
$802$	8.86104	−	27.2715i	0.312894	−	0.962989i
$803$	8.57867	−	3.81947i	0.302735	−	0.134786i
$804$	−2.07029	+	1.50416i	−0.0730137	+	0.0530475i
$805$	3.01060			0.106110
$806$	15.3835	−	14.9736i	0.541860	−	0.527422i
$807$	−31.8867			−1.12247
$808$	−9.45348	+	6.86835i	−0.332572	+	0.241628i
$809$	−17.7161	+	7.88773i	−0.622866	+	0.277318i	−0.693805	−	0.720163i	$-0.744067\pi$
$809$	−17.7161	+	7.88773i	−0.622866	+	0.277318i	0.0709388	+	0.997481i	$0.477400\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	23.3148	+	40.3824i	0.818692	+	1.41802i	0.906646	+	0.421892i	$0.138634\pi$
$811$	23.3148	+	40.3824i	0.818692	+	1.41802i	−0.0879535	+	0.996125i	$0.528033\pi$
$812$	1.95288	−	3.38248i	0.0685326	−	0.118702i
$813$	5.84910	+	6.49609i	0.205137	+	0.227828i
$814$	−3.73562	−	11.4971i	−0.130934	−	0.402972i
$815$	3.34910	−	3.71955i	0.117314	−	0.130290i
$816$	−0.662227	−	0.294842i	−0.0231826	−	0.0103216i
$817$	2.64206	−	0.561588i	0.0924341	−	0.0196475i
$818$	3.13814	+	29.8574i	0.109722	+	1.04394i
$819$	0.612085	−	5.82360i	0.0213880	−	0.203493i
$820$	9.34205	+	1.98572i	0.326239	+	0.0693442i
$821$	−35.3501	−	25.6833i	−1.23373	−	0.896354i	−0.236562	−	0.971616i	$-0.576021\pi$
$821$	−35.3501	−	25.6833i	−1.23373	−	0.896354i	−0.997164	+	0.0752620i	$0.976021\pi$
$822$	16.5790	+	12.0453i	0.578258	+	0.420129i
$823$	−10.4351	−	2.21805i	−0.363744	−	0.0773162i	0.0224140	−	0.999749i	$-0.492865\pi$
$823$	−10.4351	−	2.21805i	−0.363744	−	0.0773162i	−0.386158	+	0.922433i	$0.626198\pi$
$824$	0.661355	−	6.29237i	0.0230394	−	0.219205i
$825$	−0.485061	−	4.61505i	−0.0168877	−	0.160675i
$826$	−21.1291	+	4.49113i	−0.735175	+	0.156266i
$827$	15.6691	+	6.97633i	0.544868	+	0.242591i	0.660663	−	0.750682i	$-0.270275\pi$
$827$	15.6691	+	6.97633i	0.544868	+	0.242591i	−0.115796	+	0.993273i	$0.536942\pi$
$828$	−1.32645	+	1.47317i	−0.0460972	+	0.0511961i
$829$	−3.43218	−	10.5632i	−0.119205	−	0.366874i	0.873596	−	0.486652i	$-0.161782\pi$
$829$	−3.43218	−	10.5632i	−0.119205	−	0.366874i	−0.992801	+	0.119777i	$0.961782\pi$
$830$	−0.965383	−	1.07217i	−0.0335089	−	0.0372154i
$831$	0.939989	−	1.62811i	0.0326078	−	0.0564784i
$832$	1.92785	+	3.33914i	0.0668362	+	0.115764i
$833$	−1.05138	+	3.23581i	−0.0364281	+	0.112114i
$834$	−15.4110	+	6.86144i	−0.533641	+	0.237592i
$835$	−0.135576	+	0.0985015i	−0.00469179	+	0.00340878i
$836$	−12.9239			−0.446981
$837$	5.55569	+	0.366439i	0.192033	+	0.0126660i
$838$	−19.1044			−0.659949
$839$	−19.7074	+	14.3183i	−0.680376	+	0.494322i	−0.873482	−	0.486856i	$-0.838144\pi$
$839$	−19.7074	+	14.3183i	−0.680376	+	0.494322i	0.193106	+	0.981178i	$0.438144\pi$
$840$	1.38741	−	0.617714i	0.0478701	−	0.0213132i
$841$	−6.91766	+	21.2904i	−0.238540	+	0.734151i
$842$	−13.7509	−	23.8173i	−0.473889	−	0.820800i
$843$	9.16101	−	15.8673i	0.315522	−	0.546500i
$844$	11.5401	+	12.8166i	0.397226	+	0.441164i
$845$	−0.576761	−	1.77509i	−0.0198412	−	0.0610649i
$846$	−4.74799	+	5.27318i	−0.163239	+	0.181296i
$847$	14.6149	+	6.50698i	0.502175	+	0.223583i
$848$	2.85409	−	0.606655i	0.0980097	−	0.0208326i
$849$	0.670915	+	6.38333i	0.0230257	+	0.219075i
$850$	−0.0757724	+	0.720927i	−0.00259897	+	0.0247276i
$851$	5.05128	+	1.07368i	0.173156	+	0.0368054i
$852$	1.96770	+	1.42962i	0.0674125	+	0.0489780i
$853$	−40.2243	−	29.2247i	−1.37725	−	1.00063i	−0.997131	−	0.0756967i	$-0.975882\pi$
$853$	−40.2243	−	29.2247i	−1.37725	−	1.00063i	−0.380122	−	0.924936i	$-0.624118\pi$
$854$	2.61934	+	0.556758i	0.0896320	+	0.0190519i
$855$	0.291115	−	2.76978i	0.00995593	−	0.0947244i
$856$	1.11038	+	10.5646i	0.0379521	+	0.361090i
$857$	43.9895	−	9.35025i	1.50265	−	0.319399i	0.618197	−	0.786023i	$-0.287864\pi$
$857$	43.9895	−	9.35025i	1.50265	−	0.319399i	0.884455	+	0.466625i	$0.154530\pi$
$858$	−16.3454	−	7.27744i	−0.558023	−	0.248448i
$859$	−14.5549	+	16.1648i	−0.496606	+	0.551537i	−0.938387	−	0.345586i	$-0.887680\pi$
$859$	−14.5549	+	16.1648i	−0.496606	+	0.551537i	0.441781	+	0.897123i	$0.354347\pi$
$860$	0.299703	+	0.922390i	0.0102198	+	0.0314532i
$861$	−9.70561	−	10.7792i	−0.330766	−	0.367353i
$862$	−4.88289	+	8.45742i	−0.166312	+	0.288061i
$863$	23.4347	+	40.5901i	0.797726	+	1.38170i	0.921094	+	0.389341i	$0.127297\pi$
$863$	23.4347	+	40.5901i	0.797726	+	1.38170i	−0.123368	+	0.992361i	$0.539369\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	20.7863	−	9.25468i	0.706757	−	0.314668i
$866$	1.93414	−	1.40523i	0.0657247	−	0.0477518i
$867$	16.4745			0.559504
$868$	−5.23220	−	6.64264i	−0.177592	−	0.225466i
$869$	6.30764			0.213972
$870$	2.08060	−	1.51165i	0.0705390	−	0.0512496i
$871$	9.01380	−	4.01320i	0.305421	−	0.135982i
$872$	−2.52762	+	7.77921i	−0.0855960	+	0.263437i
$873$	4.10065	+	7.10254i	0.138786	+	0.240385i
$874$	2.76044	−	4.78123i	0.0933734	−	0.161728i
$875$	−1.01621	−	1.12862i	−0.0343543	−	0.0381543i
$876$	0.625331	+	1.92457i	0.0211280	+	0.0650252i
$877$	−1.34497	+	1.49374i	−0.0454165	+	0.0504402i	−0.765425	−	0.643525i	$-0.777471\pi$
$877$	−1.34497	+	1.49374i	−0.0454165	+	0.0504402i	0.720008	+	0.693965i	$0.244138\pi$
$878$	−27.3245	−	12.1656i	−0.922157	−	0.410571i
$879$	13.2593	−	2.81834i	0.447224	−	0.0950603i
$880$	−0.485061	−	4.61505i	−0.0163514	−	0.155573i
$881$	1.47970	−	14.0784i	0.0498523	−	0.474313i	−0.940905	−	0.338669i	$-0.890023\pi$
$881$	1.47970	−	14.0784i	0.0498523	−	0.474313i	0.990758	−	0.135643i	$-0.0433102\pi$
$882$	4.59096	+	0.975840i	0.154586	+	0.0328582i
$883$	12.6037	+	9.15711i	0.424148	+	0.308161i	0.779305	−	0.626645i	$-0.215573\pi$
$883$	12.6037	+	9.15711i	0.424148	+	0.308161i	−0.355157	+	0.934807i	$0.615573\pi$
$884$	2.26119	+	1.64285i	0.0760522	+	0.0552551i
$885$	−13.9126	−	2.95721i	−0.467665	−	0.0994054i
$886$	2.17444	−	20.6884i	0.0730518	−	0.695041i
$887$	−3.56442	−	33.9132i	−0.119682	−	1.13869i	−0.875266	−	0.483642i	$-0.839314\pi$
$887$	−3.56442	−	33.9132i	−0.119682	−	1.13869i	0.755584	−	0.655052i	$-0.227353\pi$
$888$	2.54814	−	0.541624i	0.0855100	−	0.0181757i
$889$	3.69707	+	1.64604i	0.123996	+	0.0552065i
$890$	7.53067	−	8.36366i	0.252429	−	0.280351i
$891$	−1.43398	−	4.41335i	−0.0480403	−	0.147853i
$892$	−8.55103	−	9.49688i	−0.286310	−	0.317979i
$893$	9.88098	−	17.1144i	0.330654	−	0.572710i
$894$	4.68492	+	8.11452i	0.156687	+	0.271390i
$895$	5.56577	−	17.1297i	0.186043	−	0.572582i
$896$	1.38741	−	0.617714i	0.0463500	−	0.0206364i
$897$	6.18358	−	4.49263i	0.206464	−	0.150005i
$898$	22.9418			0.765578
$899$	−11.0053	−	9.16065i	−0.367046	−	0.305525i
$900$	1.00000			0.0333333
$901$	1.71118	−	1.24325i	0.0570078	−	0.0414186i
$902$	−40.4884	+	18.0266i	−1.34812	+	0.600220i
$903$	0.455160	−	1.40084i	0.0151468	−	0.0466170i
$904$	1.69139	+	2.92958i	0.0562548	+	0.0974362i
$905$	1.70568	−	2.95433i	0.0566988	−	0.0982053i
$906$	4.09836	+	4.55169i	0.136159	+	0.151220i
$907$	−0.254370	−	0.782871i	−0.00844622	−	0.0259948i	0.946745	−	0.321986i	$-0.104350\pi$
$907$	−0.254370	−	0.782871i	−0.00844622	−	0.0259948i	−0.955191	+	0.295991i	$0.904350\pi$
$908$	12.9485	−	14.3808i	0.429712	−	0.477244i
$909$	10.6749	+	4.75277i	0.354064	+	0.157640i
$910$	−5.72772	+	1.21746i	−0.189872	+	0.0403586i
$911$	−4.45134	−	42.3517i	−0.147479	−	1.40317i	−0.778615	−	0.627501i	$-0.784078\pi$
$911$	−4.45134	−	42.3517i	−0.147479	−	1.40317i	0.631136	−	0.775672i	$-0.282589\pi$
$912$	0.291115	−	2.76978i	0.00963979	−	0.0917165i
$913$	6.54870	+	1.39197i	0.216730	+	0.0460675i
$914$	27.3834	+	19.8952i	0.905764	+	0.658076i
$915$	1.42650	+	1.03641i	0.0471586	+	0.0342627i
$916$	−2.09946	−	0.446255i	−0.0693682	−	0.0147447i
$917$	1.91716	−	18.2405i	0.0633101	−	0.602356i
$918$	0.0757724	+	0.720927i	0.00250086	+	0.0237941i
$919$	−48.8911	+	10.3921i	−1.61277	+	0.342804i	−0.924064	−	0.382239i	$-0.875153\pi$
$919$	−48.8911	+	10.3921i	−1.61277	+	0.342804i	−0.688704	+	0.725043i	$0.741820\pi$
$920$	1.81096	+	0.806291i	0.0597056	+	0.0265826i
$921$	−6.03180	+	6.69899i	−0.198754	+	0.220739i
$922$	−10.0423	−	30.9072i	−0.330727	−	1.01787i
$923$	−6.27504	−	6.96914i	−0.206546	−	0.229392i
$924$	−3.52376	+	6.10333i	−0.115923	+	0.200785i
$925$	−1.30253	−	2.25605i	−0.0428270	−	0.0741786i
$926$	−10.0324	+	30.8765i	−0.329685	+	1.01467i
$927$	−5.78003	+	2.57344i	−0.189841	+	0.0845227i
$928$	2.08060	−	1.51165i	0.0682991	−	0.0496222i
$929$	3.51671			0.115379			0.0576897	−	0.998335i	$-0.481627\pi$
$929$	3.51671			0.115379			0.0576897	+	0.998335i	$0.481627\pi$
$930$	−1.36830	−	5.39701i	−0.0448683	−	0.176975i
$931$	−13.0716			−0.428406
$932$	0.0770148	−	0.0559545i	0.00252270	−	0.00183285i
$933$	20.0834	−	8.94170i	0.657500	−	0.292738i
$934$	−6.34005	+	19.5127i	−0.207453	+	0.638474i
$935$	−1.68193	−	2.91319i	−0.0550051	−	0.0952716i
$936$	1.92785	−	3.33914i	0.0630138	−	0.109143i
$937$	−34.1555	−	37.9336i	−1.11581	−	1.23924i	−0.968196	−	0.250191i	$-0.919506\pi$
$937$	−34.1555	−	37.9336i	−1.11581	−	1.23924i	−0.147617	−	0.989045i	$-0.547160\pi$
$938$	−1.20097	−	3.69619i	−0.0392129	−	0.120685i
$939$	17.5971	−	19.5435i	0.574259	−	0.637779i
$940$	6.48231	+	2.88611i	0.211429	+	0.0941345i
$941$	−9.07793	+	1.92957i	−0.295932	+	0.0629023i	−0.353485	−	0.935440i	$-0.615004\pi$
$941$	−9.07793	+	1.92957i	−0.295932	+	0.0629023i	0.0575530	+	0.998342i	$0.481670\pi$
$942$	0.201854	+	1.92051i	0.00657676	+	0.0625737i
$943$	1.97902	−	18.8292i	0.0644459	−	0.613162i
$944$	−13.9126	−	2.95721i	−0.452815	−	0.0962488i
$945$	−1.22866	−	0.892674i	−0.0399683	−	0.0290387i
$946$	−3.64106	−	2.64539i	−0.118381	−	0.0860089i
$947$	−15.3308	−	3.25865i	−0.498183	−	0.105892i	−0.0480341	−	0.998846i	$-0.515296\pi$
$947$	−15.3308	−	3.25865i	−0.498183	−	0.105892i	−0.450148	+	0.892954i	$0.648629\pi$
$948$	−0.142082	+	1.35182i	−0.00461461	+	0.0439051i
$949$	−0.815578	−	7.75971i	−0.0264748	−	0.251891i
$950$	−2.72417	+	0.579041i	−0.0883839	+	0.0187866i
$951$	−6.43100	−	2.86327i	−0.208539	−	0.0928477i
$952$	0.736651	−	0.818133i	0.0238750	−	0.0265159i
$953$	3.25175	+	10.0079i	0.105335	+	0.324187i	0.989809	−	0.142402i	$-0.0454827\pi$
$953$	3.25175	+	10.0079i	0.105335	+	0.324187i	−0.884474	+	0.466589i	$0.845483\pi$
$954$	−1.95242	−	2.16838i	−0.0632120	−	0.0702040i
$955$	9.79321	−	16.9623i	0.316901	−	0.548888i
$956$	−1.95830	−	3.39188i	−0.0633361	−	0.109701i
$957$	−3.68787	+	11.3501i	−0.119212	+	0.366897i
$958$	20.2295	−	9.00677i	0.653586	−	0.290995i
$959$	−25.1786	+	18.2933i	−0.813059	+	0.590722i
$960$	1.00000			0.0322749
$961$	−27.2555	+	14.7695i	−0.879210	+	0.476434i
$962$	−10.0444			−0.323843
$963$	8.59401	−	6.24392i	0.276938	−	0.201207i
$964$	2.29994	−	1.02400i	0.0740761	−	0.0329808i
$965$	−0.271414	+	0.835327i	−0.00873713	+	0.0268901i
$966$	−1.50530	−	2.60725i	−0.0484322	−	0.0838870i
$967$	−16.2278	+	28.1074i	−0.521852	+	0.903874i	0.477825	+	0.878455i	$0.341425\pi$
$967$	−16.2278	+	28.1074i	−0.521852	+	0.903874i	−0.999677	+	0.0254188i	$0.991908\pi$
$968$	7.04860	+	7.82827i	0.226551	+	0.251610i
$969$	−0.623863	−	1.92005i	−0.0200414	−	0.0616810i
$970$	5.48775	−	6.09476i	0.176201	−	0.195691i
$971$	30.7976	+	13.7120i	0.988342	+	0.440038i	0.836262	−	0.548330i	$-0.184736\pi$
$971$	30.7976	+	13.7120i	0.988342	+	0.440038i	0.152080	+	0.988368i	$0.451403\pi$
$972$	0.978148	−	0.207912i	0.0313741	−	0.00666877i
$973$	−2.67800	−	25.4795i	−0.0858527	−	0.816834i
$974$	−0.947855	+	9.01824i	−0.0303712	+	0.288963i
$975$	−3.77145	−	0.801646i	−0.120783	−	0.0256732i
$976$	1.42650	+	1.03641i	0.0456611	+	0.0331747i
$977$	3.25158	+	2.36241i	0.104027	+	0.0755801i	0.638583	−	0.769553i	$-0.279521\pi$
$977$	3.25158	+	2.36241i	0.104027	+	0.0755801i	−0.534556	+	0.845133i	$0.679521\pi$
$978$	−4.89578	−	1.04063i	−0.156550	−	0.0332757i
$979$	−5.45908	+	51.9397i	−0.174473	+	1.66000i
$980$	−0.490607	−	4.66782i	−0.0156719	−	0.149108i
$981$	8.00080	−	1.70062i	0.255446	−	0.0542967i
$982$	4.42402	+	1.96970i	0.141176	+	0.0628557i
$983$	−24.3767	+	27.0731i	−0.777497	+	0.863498i	−0.993610	−	0.112871i	$-0.963995\pi$
$983$	−24.3767	+	27.0731i	−0.777497	+	0.863498i	0.216113	+	0.976368i	$0.430662\pi$
$984$	−2.95135	−	9.08331i	−0.0940855	−	0.289565i
$985$	−11.1054	−	12.3338i	−0.353849	−	0.392989i
$986$	0.932133	−	1.61450i	0.0296852	−	0.0514162i
$987$	−5.38820	−	9.33263i	−0.171508	−	0.297061i
$988$	−3.31831	+	10.2127i	−0.105569	+	0.324909i
$989$	1.75637	−	0.781988i	0.0558494	−	0.0248658i
$990$	−3.75422	+	2.72760i	−0.119317	+	0.0866888i
$991$	9.09013			0.288758			0.144379	−	0.989522i	$-0.453882\pi$
$991$	9.09013			0.288758			0.144379	+	0.989522i	$0.453882\pi$
$992$	−1.36830	−	5.39701i	−0.0434436	−	0.171355i
$993$	−28.7747			−0.913139
$994$	−2.98837	+	2.17118i	−0.0947852	+	0.0688655i
$995$	14.3935	−	6.40839i	0.456304	−	0.203160i
$996$	−0.445832	+	1.37213i	−0.0141267	+	0.0434776i
$997$	−24.5331	−	42.4926i	−0.776971	−	1.34575i	−0.933680	−	0.358109i	$-0.883422\pi$
$997$	−24.5331	−	42.4926i	−0.776971	−	1.34575i	0.156708	−	0.987645i	$-0.449912\pi$
$998$	11.3771	−	19.7058i	0.360137	−	0.623775i
$999$	−1.74313	−	1.93594i	−0.0551502	−	0.0612505i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.c.421.1	yes	16
31.19	even	15	inner	930.2.bg.c.391.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.c.391.1	✓	16	31.19	even	15	inner
930.2.bg.c.421.1	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.913545 + 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(1.01621 + 1.12862i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(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} +(1.01621 + 1.12862i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(-0.913545 - 0.406737i) q^{10} +(4.53907 - 0.964808i) q^{11} +(0.104528 + 0.994522i) q^{12} +(0.403031 - 3.83458i) q^{13} +(-1.48552 - 0.315757i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.709057 - 0.150715i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(-0.291115 - 2.76978i) q^{19} +(0.978148 - 0.207912i) q^{20} +(-1.38741 - 0.617714i) q^{21} +(-3.10508 + 3.44854i) q^{22} +(-0.612577 - 1.88532i) q^{23} +(-0.669131 - 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.92785 + 3.33914i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.38741 - 0.617714i) q^{28} +(2.08060 - 1.51165i) q^{29} +1.00000 q^{30} +(-1.36830 - 5.39701i) q^{31} +1.00000 q^{32} +(-3.75422 + 2.72760i) q^{33} +(0.662227 - 0.294842i) q^{34} +(-0.469306 + 1.44438i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.30253 + 2.25605i) q^{37} +(1.86355 + 2.06968i) q^{38} +(1.19148 + 3.66699i) q^{39} +(-0.669131 + 0.743145i) q^{40} +(8.72506 + 3.88464i) q^{41} +(1.48552 - 0.315757i) q^{42} +(0.101378 + 0.964545i) q^{43} +(0.485061 - 4.61505i) q^{44} +(0.978148 + 0.207912i) q^{45} +(1.60375 + 1.16519i) q^{46} +(5.74060 + 4.17079i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.490607 - 4.66782i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(0.709057 - 0.150715i) q^{51} +(-3.52236 - 1.56826i) q^{52} +(-1.95242 + 2.16838i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(3.10508 + 3.44854i) q^{55} +(-0.759354 + 1.31524i) q^{56} +(1.39252 + 2.41191i) q^{57} +(-0.794719 + 2.44589i) q^{58} +(12.9937 - 5.78517i) q^{59} +(-0.809017 + 0.587785i) q^{60} -1.76325 q^{61} +(4.27926 + 3.56201i) q^{62} +1.51871 q^{63} +(-0.809017 + 0.587785i) q^{64} +(3.52236 - 1.56826i) q^{65} +(1.43398 - 4.41335i) q^{66} +(1.27951 + 2.21618i) q^{67} +(-0.362449 + 0.627780i) q^{68} +(1.32645 + 1.47317i) q^{69} +(-0.469306 - 1.44438i) q^{70} +(1.62747 - 1.80749i) q^{71} +(0.913545 + 0.406737i) q^{72} +(1.97939 - 0.420733i) q^{73} +(-0.272304 - 2.59080i) q^{74} +(0.104528 - 0.994522i) q^{75} +(-2.72417 - 0.579041i) q^{76} +(5.70156 + 4.14243i) q^{77} +(-3.11933 - 2.26632i) q^{78} +(1.32956 + 0.282607i) q^{79} +(0.104528 - 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-9.34205 + 1.98572i) q^{82} +(1.31801 + 0.586816i) q^{83} +(-1.01621 + 1.12862i) q^{84} +(-0.224006 - 0.689419i) q^{85} +(-0.648962 - 0.720745i) q^{86} +(-1.28588 + 2.22721i) q^{87} +(2.32024 + 4.01877i) q^{88} +(-3.47781 + 10.7036i) q^{89} +(-0.913545 + 0.406737i) q^{90} +(4.73735 - 3.44188i) q^{91} -1.98234 q^{92} +(3.44517 + 4.37388i) q^{93} -7.09577 q^{94} +(2.25314 - 1.63700i) q^{95} +(-0.913545 + 0.406737i) q^{96} +(-2.53434 + 7.79991i) q^{97} +(2.34676 + 4.06472i) q^{98} +(2.32024 - 4.01877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 + 14 * q^13 - 4 * q^14 - 4 * q^15 - 4 * q^16 - 4 * q^17 + 2 * q^18 + q^19 - 2 * q^20 - 16 * q^21 - 13 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 9 * q^26 + 4 * q^27 + 16 * q^28 + 13 * q^29 + 16 * q^30 + 9 * q^31 + 16 * q^32 + 14 * q^33 + 26 * q^34 + 7 * q^35 - 8 * q^36 - 11 * q^37 - 14 * q^38 - 7 * q^39 - 2 * q^40 + 42 * q^41 + 4 * q^42 - 18 * q^43 + 7 * q^44 - 2 * q^45 - 7 * q^46 - 37 * q^47 - 2 * q^48 + 11 * q^49 + 2 * q^50 + 4 * q^51 - 16 * q^52 + 14 * q^53 + 4 * q^54 + 13 * q^55 - 9 * q^56 + 4 * q^57 - 12 * q^58 + 2 * q^59 - 4 * q^60 - 16 * q^61 + 9 * q^62 + 18 * q^63 - 4 * q^64 + 16 * q^65 - 11 * q^66 + 41 * q^67 + 16 * q^68 + 9 * q^69 + 7 * q^70 + q^71 + 2 * q^72 - 53 * q^73 + 44 * q^74 - 2 * q^75 + 16 * q^76 - 16 * q^77 - 2 * q^78 + 30 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^82 - 11 * q^84 - 38 * q^85 + 7 * q^86 - q^87 - 3 * q^88 - 49 * q^89 - 2 * q^90 + 2 * q^91 + 8 * q^92 + 6 * q^93 + 48 * q^94 + 2 * q^95 - 2 * q^96 + 21 * q^97 - 19 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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