LMFDB - Embedded newform 520.2.ca.b.101.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.18
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.449378 + 1.34092i) q^{2} +(-0.700368 + 0.404358i) q^{3} +(-1.59612 + 1.20516i) q^{4} +1.00000 q^{5} +(-0.856940 - 0.757426i) q^{6} +(3.38125 + 1.95217i) q^{7} +(-2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +O(q^{10})$	\(q+(0.449378 + 1.34092i) q^{2} +(-0.700368 + 0.404358i) q^{3} +(-1.59612 + 1.20516i) q^{4} +1.00000 q^{5} +(-0.856940 - 0.757426i) q^{6} +(3.38125 + 1.95217i) q^{7} +(-2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +(0.449378 + 1.34092i) q^{10} +(0.223776 + 0.387591i) q^{11} +(0.630555 - 1.48946i) q^{12} +(3.01089 - 1.98356i) q^{13} +(-1.09823 + 5.41124i) q^{14} +(-0.700368 + 0.404358i) q^{15} +(1.09519 - 3.84715i) q^{16} +(-4.00797 + 6.94201i) q^{17} +(-3.25143 - 0.659890i) q^{18} +(0.861493 - 1.49215i) q^{19} +(-1.59612 + 1.20516i) q^{20} -3.15749 q^{21} +(-0.419168 + 0.474240i) q^{22} +(-0.570237 - 0.987679i) q^{23} +(2.28060 + 0.176192i) q^{24} +1.00000 q^{25} +(4.01282 + 3.14599i) q^{26} -4.32338i q^{27} +(-7.74954 + 0.959056i) q^{28} +(-8.04039 + 4.64212i) q^{29} +(-0.856940 - 0.757426i) q^{30} +5.19873i q^{31} +(5.65086 - 0.260274i) q^{32} +(-0.313451 - 0.180971i) q^{33} +(-11.1098 - 2.25477i) q^{34} +(3.38125 + 1.95217i) q^{35} +(-0.576264 - 4.65644i) q^{36} +(-2.59519 - 4.49501i) q^{37} +(2.38799 + 0.484651i) q^{38} +(-1.30666 + 2.60670i) q^{39} +(-2.33328 - 1.59869i) q^{40} +(4.37099 - 2.52359i) q^{41} +(-1.41891 - 4.23393i) q^{42} +(-0.587643 - 0.339276i) q^{43} +(-0.824282 - 0.348956i) q^{44} +(-1.17299 + 2.03168i) q^{45} +(1.06814 - 1.20848i) q^{46} -8.71152i q^{47} +(0.788592 + 3.13727i) q^{48} +(4.12190 + 7.13934i) q^{49} +(0.449378 + 1.34092i) q^{50} -6.48262i q^{51} +(-2.41523 + 6.79460i) q^{52} +11.8993i q^{53} +(5.79729 - 1.94283i) q^{54} +(0.223776 + 0.387591i) q^{55} +(-4.76849 - 9.96051i) q^{56} +1.39340i q^{57} +(-9.83788 - 8.69543i) q^{58} +(4.67021 - 8.08904i) q^{59} +(0.630555 - 1.48946i) q^{60} +(6.84304 + 3.95083i) q^{61} +(-6.97107 + 2.33620i) q^{62} +(-7.93234 + 4.57974i) q^{63} +(2.88838 + 7.46038i) q^{64} +(3.01089 - 1.98356i) q^{65} +(0.101809 - 0.501636i) q^{66} +(-5.35905 - 9.28215i) q^{67} +(-1.96903 - 15.9105i) q^{68} +(0.798751 + 0.461159i) q^{69} +(-1.09823 + 5.41124i) q^{70} +(9.05690 + 5.22901i) q^{71} +(5.98494 - 2.86523i) q^{72} -0.118228i q^{73} +(4.86121 - 5.49990i) q^{74} +(-0.700368 + 0.404358i) q^{75} +(0.423233 + 3.41988i) q^{76} +1.74739i q^{77} +(-4.08256 - 0.580734i) q^{78} +17.2905 q^{79} +(1.09519 - 3.84715i) q^{80} +(-1.77078 - 3.06708i) q^{81} +(5.34816 + 4.72709i) q^{82} +10.1833 q^{83} +(5.03973 - 3.80528i) q^{84} +(-4.00797 + 6.94201i) q^{85} +(0.190867 - 0.940443i) q^{86} +(3.75415 - 6.50238i) q^{87} +(0.0975065 - 1.26211i) q^{88} +(7.70585 - 4.44897i) q^{89} +(-3.25143 - 0.659890i) q^{90} +(14.0528 - 0.829158i) q^{91} +(2.10048 + 0.889227i) q^{92} +(-2.10215 - 3.64103i) q^{93} +(11.6814 - 3.91477i) q^{94} +(0.861493 - 1.49215i) q^{95} +(-3.85244 + 2.46726i) q^{96} +(7.84192 + 4.52754i) q^{97} +(-7.72097 + 8.73539i) q^{98} -1.04995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

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 $

$2$	0.449378	+	1.34092i	0.317759	+	0.948172i
$2$	0.449378	+	1.34092i	0.317759	+	0.948172i
$3$	−0.700368	+	0.404358i	−0.404358	+	0.233456i	−0.688362	−	0.725367i	$-0.741670\pi$
$3$	−0.700368	+	0.404358i	−0.404358	+	0.233456i	0.284005	+	0.958823i	$0.408337\pi$
$4$	−1.59612	+	1.20516i	−0.798059	+	0.602579i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.856940	−	0.757426i	−0.349844	−	0.309218i
$7$	3.38125	+	1.95217i	1.27799	+	0.737849i	0.976479	−	0.215613i	$-0.0691749\pi$
$7$	3.38125	+	1.95217i	1.27799	+	0.737849i	0.301513	+	0.953462i	$0.402508\pi$
$8$	−2.33328	−	1.59869i	−0.824939	−	0.565222i
$9$	−1.17299	+	2.03168i	−0.390997	+	0.677226i
$10$	0.449378	+	1.34092i	0.142106	+	0.424035i
$11$	0.223776	+	0.387591i	0.0674710	+	0.116863i	0.897787	−	0.440429i	$-0.145174\pi$
$11$	0.223776	+	0.387591i	0.0674710	+	0.116863i	−0.830316	+	0.557292i	$0.811840\pi$
$12$	0.630555	−	1.48946i	0.182025	−	0.429969i
$13$	3.01089	−	1.98356i	0.835072	−	0.550141i
$13$	3.01089	−	1.98356i	0.835072	−	0.550141i
$14$	−1.09823	+	5.41124i	−0.293515	+	1.44621i
$15$	−0.700368	+	0.404358i	−0.180834	+	0.104405i
$16$	1.09519	−	3.84715i	0.273796	−	0.961788i
$17$	−4.00797	+	6.94201i	−0.972076	+	1.68369i	−0.282812	+	0.959175i	$0.591267\pi$
$17$	−4.00797	+	6.94201i	−0.972076	+	1.68369i	−0.689264	+	0.724510i	$0.742066\pi$
$18$	−3.25143	−	0.659890i	−0.766369	−	0.155538i
$19$	0.861493	−	1.49215i	0.197640	−	0.342323i	−0.750123	−	0.661299i	$-0.770006\pi$
$19$	0.861493	−	1.49215i	0.197640	−	0.342323i	0.947763	+	0.318976i	$0.103339\pi$
$20$	−1.59612	+	1.20516i	−0.356903	+	0.269482i
$21$	−3.15749			−0.689021
$22$	−0.419168	+	0.474240i	−0.0893669	+	0.101108i
$23$	−0.570237	−	0.987679i	−0.118903	−	0.205945i	0.800430	−	0.599426i	$-0.204604\pi$
$23$	−0.570237	−	0.987679i	−0.118903	−	0.205945i	−0.919333	+	0.393480i	$0.871271\pi$
$24$	2.28060	+	0.176192i	0.465525	+	0.0359650i
$25$	1.00000			0.200000
$26$	4.01282	+	3.14599i	0.786980	+	0.616979i
$27$		−	4.32338i		−	0.832034i
$28$	−7.74954	+	0.959056i	−1.46453	+	0.181245i
$29$	−8.04039	+	4.64212i	−1.49306	+	0.862020i	−0.999968	−	0.00795571i	$-0.997468\pi$
$29$	−8.04039	+	4.64212i	−1.49306	+	0.862020i	−0.493094	+	0.869976i	$0.664134\pi$
$30$	−0.856940	−	0.757426i	−0.156455	−	0.138286i
$31$			5.19873i			0.933720i	0.884331	+	0.466860i	$0.154615\pi$
$31$			5.19873i			0.933720i	−0.884331	+	0.466860i	$0.845385\pi$
$32$	5.65086	−	0.260274i	0.998941	−	0.0460104i
$33$	−0.313451	−	0.180971i	−0.0545648	−	0.0315030i
$34$	−11.1098	−	2.25477i	−1.90531	−	0.386690i
$35$	3.38125	+	1.95217i	0.571535	+	0.329976i
$36$	−0.576264	−	4.65644i	−0.0960440	−	0.776073i
$37$	−2.59519	−	4.49501i	−0.426647	−	0.738974i	0.569926	−	0.821696i	$-0.306972\pi$
$37$	−2.59519	−	4.49501i	−0.426647	−	0.738974i	−0.996573	+	0.0827219i	$0.973639\pi$
$38$	2.38799	+	0.484651i	0.387382	+	0.0786207i
$39$	−1.30666	+	2.60670i	−0.209234	+	0.417406i
$40$	−2.33328	−	1.59869i	−0.368924	−	0.252775i
$41$	4.37099	−	2.52359i	0.682635	−	0.394119i	−0.118212	−	0.992988i	$-0.537716\pi$
$41$	4.37099	−	2.52359i	0.682635	−	0.394119i	0.800847	+	0.598869i	$0.204383\pi$
$42$	−1.41891	−	4.23393i	−0.218942	−	0.653310i
$43$	−0.587643	−	0.339276i	−0.0896147	−	0.0517391i	0.454523	−	0.890735i	$-0.349810\pi$
$43$	−0.587643	−	0.339276i	−0.0896147	−	0.0517391i	−0.544138	+	0.838996i	$0.683143\pi$
$44$	−0.824282	−	0.348956i	−0.124265	−	0.0526071i
$45$	−1.17299	+	2.03168i	−0.174859	+	0.302865i
$46$	1.06814	−	1.20848i	0.157489	−	0.178181i
$47$		−	8.71152i		−	1.27071i	−0.772222	−	0.635353i	$-0.780855\pi$
$47$		−	8.71152i		−	1.27071i	0.772222	−	0.635353i	$-0.219145\pi$
$48$	0.788592	+	3.13727i	0.113823	+	0.452826i
$49$	4.12190	+	7.13934i	0.588843	+	1.01991i
$50$	0.449378	+	1.34092i	0.0635517	+	0.189634i
$51$		−	6.48262i		−	0.907748i
$52$	−2.41523	+	6.79460i	−0.334933	+	0.942242i
$53$			11.8993i			1.63450i	0.576286	+	0.817248i	$0.304501\pi$
$53$			11.8993i			1.63450i	−0.576286	+	0.817248i	$0.695499\pi$
$54$	5.79729	−	1.94283i	0.788911	−	0.264386i
$55$	0.223776	+	0.387591i	0.0301739	+	0.0522628i
$56$	−4.76849	−	9.96051i	−0.637217	−	1.33103i
$57$			1.39340i			0.184561i
$58$	−9.83788	−	8.69543i	−1.29178	−	1.14177i
$59$	4.67021	−	8.08904i	0.608009	−	1.05310i	−0.383559	−	0.923516i	$-0.625302\pi$
$59$	4.67021	−	8.08904i	0.608009	−	1.05310i	0.991568	−	0.129586i	$-0.0413650\pi$
$60$	0.630555	−	1.48946i	0.0814043	−	0.192288i
$61$	6.84304	+	3.95083i	0.876162	+	0.505852i	0.869391	−	0.494125i	$-0.164511\pi$
$61$	6.84304	+	3.95083i	0.876162	+	0.505852i	0.00677098	+	0.999977i	$0.497845\pi$
$62$	−6.97107	+	2.33620i	−0.885327	+	0.296697i
$63$	−7.93234	+	4.57974i	−0.999381	+	0.576993i
$64$	2.88838	+	7.46038i	0.361048	+	0.932547i
$65$	3.01089	−	1.98356i	0.373455	−	0.246031i
$66$	0.101809	−	0.501636i	0.0125318	−	0.0617472i
$67$	−5.35905	−	9.28215i	−0.654713	−	1.13400i	−0.981966	−	0.189059i	$-0.939456\pi$
$67$	−5.35905	−	9.28215i	−0.654713	−	1.13400i	0.327253	−	0.944937i	$-0.393877\pi$
$68$	−1.96903	−	15.9105i	−0.238780	−	1.92943i
$69$	0.798751	+	0.461159i	0.0961583	+	0.0555170i
$70$	−1.09823	+	5.41124i	−0.131264	+	0.646766i
$71$	9.05690	+	5.22901i	1.07486	+	0.620569i	0.929504	−	0.368811i	$-0.120235\pi$
$71$	9.05690	+	5.22901i	1.07486	+	0.620569i	0.145352	+	0.989380i	$0.453568\pi$
$72$	5.98494	−	2.86523i	0.705331	−	0.337670i
$73$		−	0.118228i		−	0.0138376i	−0.999976	−	0.00691879i	$-0.997798\pi$
$73$		−	0.118228i		−	0.0138376i	0.999976	−	0.00691879i	$-0.00220234\pi$
$74$	4.86121	−	5.49990i	0.565104	−	0.639350i
$75$	−0.700368	+	0.404358i	−0.0808715	+	0.0466912i
$76$	0.423233	+	3.41988i	0.0485481	+	0.392287i
$77$			1.74739i			0.199134i
$78$	−4.08256	−	0.580734i	−0.462259	−	0.0657551i
$79$	17.2905			1.94533			0.972666	−	0.232210i	$-0.0745957\pi$
$79$	17.2905			1.94533			0.972666	+	0.232210i	$0.0745957\pi$
$80$	1.09519	−	3.84715i	0.122445	−	0.430125i
$81$	−1.77078	−	3.06708i	−0.196753	−	0.340787i
$82$	5.34816	+	4.72709i	0.590606	+	0.522020i
$83$	10.1833			1.11776			0.558879	−	0.829250i	$-0.311232\pi$
$83$	10.1833			1.11776			0.558879	+	0.829250i	$0.311232\pi$
$84$	5.03973	−	3.80528i	0.549879	−	0.415190i
$85$	−4.00797	+	6.94201i	−0.434726	+	0.752967i
$86$	0.190867	−	0.940443i	0.0205817	−	0.101411i
$87$	3.75415	−	6.50238i	0.402488	−	0.697129i
$88$	0.0975065	−	1.26211i	0.0103942	−	0.134541i
$89$	7.70585	−	4.44897i	0.816818	−	0.471590i	−0.0324998	−	0.999472i	$-0.510347\pi$
$89$	7.70585	−	4.44897i	0.816818	−	0.471590i	0.849318	+	0.527882i	$0.177013\pi$
$90$	−3.25143	−	0.659890i	−0.342731	−	0.0695585i
$91$	14.0528	−	0.829158i	1.47314	−	0.0869194i
$92$	2.10048	+	0.889227i	0.218990	+	0.0927083i
$93$	−2.10215	−	3.64103i	−0.217982	−	0.377557i
$94$	11.6814	−	3.91477i	1.20485	−	0.403778i
$95$	0.861493	−	1.49215i	0.0883873	−	0.153091i
$96$	−3.85244	+	2.46726i	−0.393188	+	0.251813i
$97$	7.84192	+	4.52754i	0.796227	+	0.459702i	0.842150	−	0.539243i	$-0.181290\pi$
$97$	7.84192	+	4.52754i	0.796227	+	0.459702i	−0.0459234	+	0.998945i	$0.514623\pi$
$98$	−7.72097	+	8.73539i	−0.779935	+	0.882407i
$99$	−1.04995			−0.105524
$100$	−1.59612	+	1.20516i	−0.159612	+	0.120516i
$101$	−0.0227944	+	0.0131604i	−0.00226813	+	0.00130951i	−0.501134	−	0.865370i	$-0.667083\pi$
$101$	−0.0227944	+	0.0131604i	−0.00226813	+	0.00130951i	0.498866	+	0.866679i	$0.333750\pi$
$102$	8.69265	−	2.91315i	0.860701	−	0.288445i
$103$	−13.0895			−1.28974			−0.644872	−	0.764291i	$-0.723089\pi$
$103$	−13.0895			−1.28974			−0.644872	+	0.764291i	$0.723089\pi$
$104$	−10.1964	−	0.185279i	−0.999835	−	0.0181681i
$105$	−3.15749			−0.308140
$106$	−15.9560	+	5.34729i	−1.54978	+	0.519375i
$107$	4.81312	−	2.77886i	0.465302	−	0.268642i	−0.248969	−	0.968511i	$-0.580092\pi$
$107$	4.81312	−	2.77886i	0.465302	−	0.268642i	0.714271	+	0.699869i	$0.246758\pi$
$108$	5.21035	+	6.90062i	0.501366	+	0.664012i
$109$	0.584348			0.0559704			0.0279852	−	0.999608i	$-0.491091\pi$
$109$	0.584348			0.0559704			0.0279852	+	0.999608i	$0.491091\pi$
$110$	−0.419168	+	0.474240i	−0.0399661	+	0.0452170i
$111$	3.63518	+	2.09877i	0.345036	+	0.199207i
$112$	11.2134	−	10.8702i	1.05956	−	1.02714i
$113$	−5.65275	+	9.79084i	−0.531766	+	0.921045i	0.467547	+	0.883968i	$0.345138\pi$
$113$	−5.65275	+	9.79084i	−0.531766	+	0.921045i	−0.999312	+	0.0370767i	$0.988195\pi$
$114$	−1.86844	+	0.626166i	−0.174995	+	0.0586458i
$115$	−0.570237	−	0.987679i	−0.0531749	−	0.0921016i
$116$	7.23892	−	17.0993i	0.672117	−	1.58763i
$117$	0.498213	+	8.44386i	0.0460598	+	0.780636i
$118$	12.9454	+	2.62732i	1.19172	+	0.241865i
$119$	−27.1039	+	15.6485i	−2.48461	+	1.43449i
$120$	2.28060	+	0.176192i	0.208189	+	0.0160840i
$121$	5.39985	−	9.35281i	0.490895	−	0.850256i
$122$	−2.22262	+	10.9514i	−0.201227	+	0.991491i
$123$	−2.04087	+	3.53489i	−0.184019	+	0.318730i
$124$	−6.26530	−	8.29779i	−0.562640	−	0.745163i
$125$	1.00000			0.0894427
$126$	−9.70568	−	8.57858i	−0.864650	−	0.764240i
$127$	−5.85718	−	10.1449i	−0.519740	−	0.900217i	−0.999737	−	0.0229463i	$-0.992695\pi$
$127$	−5.85718	−	10.1449i	−0.519740	−	0.900217i	0.479996	−	0.877271i	$-0.340638\pi$
$128$	−8.70577	+	7.22562i	−0.769489	+	0.638660i
$129$	0.548755			0.0483152
$130$	4.01282	+	3.14599i	0.351948	+	0.275921i
$131$			11.7108i			1.02318i	0.859229	+	0.511591i	$0.170944\pi$
$131$			11.7108i			1.02318i	−0.859229	+	0.511591i	$0.829056\pi$
$132$	0.718403	−	0.0889071i	0.0625290	−	0.00773837i
$133$	5.82584	−	3.36355i	0.505165	−	0.291657i
$134$	10.0384	−	11.3572i	0.867182	−	0.981117i
$135$		−	4.32338i		−	0.372097i
$136$	20.4498	−	9.79015i	1.75356	−	0.839498i
$137$	−6.49995	−	3.75275i	−0.555329	−	0.320619i	0.195940	−	0.980616i	$-0.437224\pi$
$137$	−6.49995	−	3.75275i	−0.555329	−	0.320619i	−0.751268	+	0.659997i	$0.770558\pi$
$138$	−0.259435	+	1.27829i	−0.0220846	+	0.108816i
$139$	7.07331	+	4.08378i	0.599950	+	0.346381i	0.769022	−	0.639222i	$-0.220744\pi$
$139$	7.07331	+	4.08378i	0.599950	+	0.346381i	−0.169072	+	0.985604i	$0.554077\pi$
$140$	−7.74954	+	0.959056i	−0.654956	+	0.0810550i
$141$	3.52257	+	6.10127i	0.296654	+	0.513819i
$142$	−2.94169	+	14.4944i	−0.246861	+	1.21634i
$143$	1.44258	+	0.723122i	0.120634	+	0.0604705i
$144$	6.53153	+	6.73773i	0.544294	+	0.561478i
$145$	−8.04039	+	4.64212i	−0.667718	+	0.385507i
$146$	0.158534	−	0.0531293i	0.0131204	−	0.00439701i
$147$	−5.77369	−	3.33344i	−0.476206	−	0.274938i
$148$	9.55943	+	4.04694i	0.785780	+	0.332656i
$149$	−2.65141	+	4.59238i	−0.217212	+	0.376223i	−0.953955	−	0.299951i	$-0.903030\pi$
$149$	−2.65141	+	4.59238i	−0.217212	+	0.376223i	0.736742	+	0.676173i	$0.236363\pi$
$150$	−0.856940	−	0.757426i	−0.0699689	−	0.0618436i
$151$		−	4.32338i		−	0.351831i	−0.984405	−	0.175916i	$-0.943711\pi$
$151$		−	4.32338i		−	0.351831i	0.984405	−	0.175916i	$-0.0562886\pi$
$152$	−4.39559	+	2.10434i	−0.356529	+	0.170685i
$153$	−9.40262	−	16.2858i	−0.760157	−	1.31663i
$154$	−2.34311	+	0.785240i	−0.188813	+	0.0632764i
$155$			5.19873i			0.417572i
$156$	−1.05590	−	5.73534i	−0.0845395	−	0.459195i
$157$		−	9.05130i		−	0.722372i	−0.932494	−	0.361186i	$-0.882372\pi$
$157$		−	9.05130i		−	0.722372i	0.932494	−	0.361186i	$-0.117628\pi$
$158$	7.76997	+	23.1851i	0.618146	+	1.84451i
$159$	−4.81158	−	8.33390i	−0.381583	−	0.660921i
$160$	5.65086	−	0.260274i	0.446740	−	0.0205765i
$161$		−	4.45279i		−	0.350929i
$162$	3.31695	−	3.75275i	0.260604	−	0.294844i
$163$	7.29415	−	12.6338i	0.571322	−	0.989558i	−0.425109	−	0.905142i	$-0.639764\pi$
$163$	7.29415	−	12.6338i	0.571322	−	0.989558i	0.996431	−	0.0844159i	$-0.0269024\pi$
$164$	−3.93529	+	9.29570i	−0.307295	+	0.725872i
$165$	−0.313451	−	0.180971i	−0.0244021	−	0.0140886i
$166$	4.57613	+	13.6549i	0.355177	+	1.05983i
$167$	−3.06989	+	1.77240i	−0.237556	+	0.137153i	−0.614053	−	0.789265i	$-0.710462\pi$
$167$	−3.06989	+	1.77240i	−0.237556	+	0.137153i	0.376497	+	0.926418i	$0.377128\pi$
$168$	7.36731	+	5.04785i	0.568400	+	0.389450i
$169$	5.13096	−	11.9446i	0.394689	−	0.918815i
$170$	−11.1098	−	2.25477i	−0.852080	−	0.172933i
$171$	2.02104	+	3.50055i	0.154553	+	0.267694i
$172$	1.34683	−	0.166679i	0.102695	−	0.0127091i
$173$	−9.91643	−	5.72526i	−0.753932	−	0.435283i	0.0731806	−	0.997319i	$-0.476685\pi$
$173$	−9.91643	−	5.72526i	−0.753932	−	0.435283i	−0.827113	+	0.562036i	$0.810018\pi$
$174$	10.4062	+	2.11198i	0.788892	+	0.160109i
$175$	3.38125	+	1.95217i	0.255598	+	0.147570i
$176$	1.73620	−	0.436416i	0.130871	−	0.0328961i
$177$			7.55374i			0.567774i
$178$	9.42855	+	8.33363i	0.706699	+	0.624632i
$179$	−0.746881	+	0.431212i	−0.0558245	+	0.0322303i	−0.527652	−	0.849460i	$-0.676928\pi$
$179$	−0.746881	+	0.431212i	−0.0558245	+	0.0322303i	0.471828	+	0.881691i	$0.343594\pi$
$180$	−0.576264	−	4.65644i	−0.0429522	−	0.347070i
$181$			4.43168i			0.329404i	0.986343	+	0.164702i	$0.0526663\pi$
$181$			4.43168i			0.329404i	−0.986343	+	0.164702i	$0.947334\pi$
$182$	7.42687	+	18.4711i	0.550516	+	1.36917i
$183$	−6.39020			−0.472377
$184$	−0.248471	+	3.21616i	−0.0183175	+	0.237099i
$185$	−2.59519	−	4.49501i	−0.190802	−	0.330479i
$186$	3.93765	−	4.45500i	0.288723	−	0.326657i
$187$	−3.58755			−0.262348
$188$	10.4988	+	13.9046i	0.765701	+	1.01410i
$189$	8.43994	−	14.6184i	0.613915	−	1.06333i
$190$	2.38799	+	0.484651i	0.173243	+	0.0351603i
$191$	10.8557	−	18.8026i	0.785490	−	1.36051i	−0.143216	−	0.989691i	$-0.545744\pi$
$191$	10.8557	−	18.8026i	0.785490	−	1.36051i	0.928706	−	0.370817i	$-0.120922\pi$
$192$	−5.03959	−	4.05707i	−0.363701	−	0.292794i
$193$	14.6746	−	8.47239i	1.05630	−	0.609856i	0.131894	−	0.991264i	$-0.457894\pi$
$193$	14.6746	−	8.47239i	1.05630	−	0.609856i	0.924407	+	0.381408i	$0.124561\pi$
$194$	−2.54706	+	12.5499i	−0.182868	+	0.901034i
$195$	−1.30666	+	2.60670i	−0.0935722	+	0.186670i
$196$	−15.1831	−	6.42768i	−1.08450	−	0.459120i
$197$	−7.87779	−	13.6447i	−0.561269	−	0.972147i	−0.997386	−	0.0722567i	$-0.976980\pi$
$197$	−7.87779	−	13.6447i	−0.561269	−	0.972147i	0.436117	−	0.899890i	$-0.356353\pi$
$198$	−0.471824	−	1.40789i	−0.0335311	−	0.100055i
$199$	−3.09592	+	5.36228i	−0.219464	+	0.380122i	−0.954644	−	0.297749i	$-0.903764\pi$
$199$	−3.09592	+	5.36228i	−0.219464	+	0.380122i	0.735180	+	0.677871i	$0.237097\pi$
$200$	−2.33328	−	1.59869i	−0.164988	−	0.113044i
$201$	7.50662	+	4.33395i	0.529476	+	0.305693i
$202$	−0.0278903	−	0.0246515i	−0.00196235	−	0.00173447i
$203$	−36.2487			−2.54416
$204$	7.81258	+	10.3470i	0.546990	+	0.724437i
$205$	4.37099	−	2.52359i	0.305283	−	0.176255i
$206$	−5.88212	−	17.5519i	−0.409827	−	1.22290i
$207$	2.67553			0.185962
$208$	−4.33358	−	13.7557i	−0.300480	−	0.953788i
$209$	0.771125			0.0533399
$210$	−1.41891	−	4.23393i	−0.0979140	−	0.292169i
$211$	1.17103	−	0.676093i	0.0806169	−	0.0465442i	−0.459150	−	0.888359i	$-0.651846\pi$
$211$	1.17103	−	0.676093i	0.0806169	−	0.0465442i	0.539767	+	0.841815i	$0.318513\pi$
$212$	−14.3406	−	18.9927i	−0.984914	−	1.30442i
$213$	−8.45755			−0.579502
$214$	5.88913	+	5.20524i	0.402572	+	0.355823i
$215$	−0.587643	−	0.339276i	−0.0400769	−	0.0231384i
$216$	−6.91174	+	10.0876i	−0.470284	+	0.686377i
$217$	−10.1488	+	17.5782i	−0.688944	+	1.19329i
$218$	0.262593	+	0.783562i	0.0177851	+	0.0530695i
$219$	0.0478065	+	0.0828034i	0.00323047	+	0.00559533i
$220$	−0.824282	−	0.348956i	−0.0555731	−	0.0235266i
$221$	1.70234	+	28.8517i	0.114512	+	1.94078i
$222$	−1.18071	+	5.81762i	−0.0792439	+	0.390453i
$223$	9.67467	−	5.58567i	0.647864	−	0.374044i	−0.139774	−	0.990183i	$-0.544637\pi$
$223$	9.67467	−	5.58567i	0.647864	−	0.374044i	0.787637	+	0.616139i	$0.211304\pi$
$224$	19.6151	+	10.1514i	1.31059	+	0.678267i
$225$	−1.17299	+	2.03168i	−0.0781993	+	0.135445i
$226$	−15.6689	−	3.18007i	−1.04228	−	0.211535i
$227$	5.19436	−	8.99690i	0.344762	−	0.597145i	−0.640548	−	0.767918i	$-0.721293\pi$
$227$	5.19436	−	8.99690i	0.344762	−	0.597145i	0.985311	+	0.170772i	$0.0546263\pi$
$228$	−1.67927	−	2.22404i	−0.111213	−	0.147291i
$229$	−23.1100			−1.52715			−0.763574	−	0.645720i	$-0.776557\pi$
$229$	−23.1100			−1.52715			−0.763574	+	0.645720i	$0.776557\pi$
$230$	1.06814	−	1.20848i	0.0704313	−	0.0796850i
$231$	−0.706571	−	1.22382i	−0.0464889	−	0.0805212i
$232$	26.1818	+	2.02272i	1.71892	+	0.132798i
$233$	−8.57015			−0.561449			−0.280725	−	0.959788i	$-0.590575\pi$
$233$	−8.57015			−0.561449			−0.280725	+	0.959788i	$0.590575\pi$
$234$	−11.0986	+	4.46255i	−0.725541	+	0.291726i
$235$		−	8.71152i		−	0.568277i
$236$	2.29437	+	18.5394i	0.149351	+	1.20681i
$237$	−12.1097	+	6.99154i	−0.786609	+	0.454149i
$238$	−33.1632	−	29.3120i	−2.14965	−	1.90002i
$239$		−	1.02636i		−	0.0663899i	−0.999449	−	0.0331950i	$-0.989432\pi$
$239$		−	1.02636i		−	0.0663899i	0.999449	−	0.0331950i	$-0.0105682\pi$
$240$	0.788592	+	3.13727i	0.0509034	+	0.202510i
$241$	14.2112	+	8.20484i	0.915424	+	0.528520i	0.882172	−	0.470927i	$-0.156080\pi$
$241$	14.2112	+	8.20484i	0.915424	+	0.528520i	0.0332518	+	0.999447i	$0.489414\pi$
$242$	14.9679	+	3.03780i	0.962175	+	0.195277i
$243$	13.7129	+	7.91712i	0.879680	+	0.507883i
$244$	−15.6837	+	1.94096i	−1.00405	+	0.124257i
$245$	4.12190	+	7.13934i	0.263338	+	0.456115i
$246$	−5.65712	−	1.14813i	−0.360685	−	0.0732023i
$247$	−0.365908	−	6.20153i	−0.0232822	−	0.394594i
$248$	8.31116	−	12.1301i	0.527759	−	0.770262i
$249$	−7.13202	+	4.11768i	−0.451974	+	0.260947i
$250$	0.449378	+	1.34092i	0.0284212	+	0.0848071i
$251$	1.63097	+	0.941643i	0.102946	+	0.0594360i	0.550589	−	0.834776i	$-0.314403\pi$
$251$	1.63097	+	0.941643i	0.102946	+	0.0594360i	−0.447643	+	0.894212i	$0.647736\pi$
$252$	7.14164	−	16.8695i	0.449881	−	1.06268i
$253$	0.255211	−	0.442038i	0.0160449	−	0.0277907i
$254$	10.9714	−	12.4129i	0.688408	−	0.778855i
$255$		−	6.48262i		−	0.405957i
$256$	−13.6011	−	8.42668i	−0.850071	−	0.526668i
$257$	−8.29410	−	14.3658i	−0.517372	−	0.896114i	−0.999796	−	0.0201769i	$-0.993577\pi$
$257$	−8.29410	−	14.3658i	−0.517372	−	0.896114i	0.482424	−	0.875938i	$-0.339756\pi$
$258$	0.246599	+	0.735835i	0.0153526	+	0.0458111i
$259$		−	20.2650i		−	1.25920i
$260$	−2.41523	+	6.79460i	−0.149786	+	0.421383i
$261$		−	21.7806i		−	1.34819i
$262$	−15.7033	+	5.26260i	−0.970151	+	0.325125i
$263$	10.2539	+	17.7602i	0.632281	+	1.09514i	0.987084	+	0.160202i	$0.0512147\pi$
$263$	10.2539	+	17.7602i	0.632281	+	1.09514i	−0.354803	+	0.934941i	$0.615452\pi$
$264$	0.442052	+	0.923367i	0.0272064	+	0.0568293i
$265$			11.8993i			0.730969i
$266$	7.12825	+	6.30047i	0.437061	+	0.386306i
$267$	−3.59795	+	6.23184i	−0.220191	+	0.381382i
$268$	19.7401	+	8.35690i	1.20582	+	0.510479i
$269$	−4.99021	−	2.88110i	−0.304258	−	0.175664i	0.340096	−	0.940391i	$-0.389540\pi$
$269$	−4.99021	−	2.88110i	−0.304258	−	0.175664i	−0.644354	+	0.764727i	$0.722874\pi$
$270$	5.79729	−	1.94283i	0.352812	−	0.118237i
$271$	−8.20521	+	4.73728i	−0.498431	+	0.287769i	−0.728065	−	0.685508i	$-0.759580\pi$
$271$	−8.20521	+	4.73728i	−0.498431	+	0.287769i	0.229634	+	0.973277i	$0.426247\pi$
$272$	22.3175	+	23.0221i	1.35320	+	1.39592i
$273$	−9.50687	+	6.26308i	−0.575382	+	0.379059i
$274$	2.11119	−	10.4023i	0.127542	−	0.628426i
$275$	0.223776	+	0.387591i	0.0134942	+	0.0233726i
$276$	−1.83067	+	0.226557i	−0.110193	+	0.0136372i
$277$	2.14086	+	1.23602i	0.128632	+	0.0742655i	0.562935	−	0.826501i	$-0.309672\pi$
$277$	2.14086	+	1.23602i	0.128632	+	0.0742655i	−0.434303	+	0.900767i	$0.643005\pi$
$278$	−2.29741	+	11.3199i	−0.137790	+	0.678921i
$279$	−10.5621	−	6.09806i	−0.632339	−	0.365081i
$280$	−4.76849	−	9.96051i	−0.284972	−	0.595255i
$281$			5.80779i			0.346464i	0.984881	+	0.173232i	$0.0554210\pi$
$281$			5.80779i			0.346464i	−0.984881	+	0.173232i	$0.944579\pi$
$282$	−6.59833	+	7.46525i	−0.392925	+	0.444549i
$283$	−13.4435	+	7.76159i	−0.799131	+	0.461379i	−0.843167	−	0.537651i	$-0.819312\pi$
$283$	−13.4435	+	7.76159i	−0.799131	+	0.461379i	0.0440362	+	0.999030i	$0.485978\pi$
$284$	−20.7577	+	2.56890i	−1.23174	+	0.152436i
$285$			1.39340i			0.0825382i
$286$	−0.321384	+	2.25933i	−0.0190039	+	0.133597i
$287$	19.7059			1.16320
$288$	−6.09961	+	11.7860i	−0.359423	+	0.694499i
$289$	−23.6277	−	40.9244i	−1.38986	−	2.40732i
$290$	−9.83788	−	8.69543i	−0.577700	−	0.510613i
$291$	−7.32297			−0.429280
$292$	0.142484	+	0.188706i	0.00833824	+	0.0110432i
$293$	−15.6517	+	27.1095i	−0.914381	+	1.58375i	−0.106575	+	0.994305i	$0.533988\pi$
$293$	−15.6517	+	27.1095i	−0.914381	+	1.58375i	−0.807806	+	0.589449i	$0.799345\pi$
$294$	1.87530	−	9.24002i	0.109370	−	0.538889i
$295$	4.67021	−	8.08904i	0.271910	−	0.470962i
$296$	−1.13081	+	14.6370i	−0.0657270	+	0.850759i
$297$	1.67570	−	0.967467i	0.0972341	−	0.0561381i
$298$	−7.34949	−	1.49161i	−0.425745	−	0.0864065i
$299$	−3.67605	−	1.84270i	−0.212591	−	0.106566i
$300$	0.630555	−	1.48946i	0.0364051	−	0.0859938i
$301$	−1.32464	−	2.29435i	−0.0763512	−	0.132244i
$302$	5.79729	−	1.94283i	0.333596	−	0.111797i
$303$	0.0106430	−	0.0184342i	0.000611424	−	0.00105902i
$304$	−4.79703	−	4.94847i	−0.275129	−	0.283814i
$305$	6.84304	+	3.95083i	0.391832	+	0.226224i
$306$	17.6126	−	19.9266i	1.00685	−	1.13913i
$307$	−3.84349			−0.219359			−0.109680	−	0.993967i	$-0.534982\pi$
$307$	−3.84349			−0.219359			−0.109680	+	0.993967i	$0.534982\pi$
$308$	−2.10588	−	2.78904i	−0.119994	−	0.158920i
$309$	9.16744	−	5.29283i	0.521518	−	0.301098i
$310$	−6.97107	+	2.33620i	−0.395930	+	0.132687i
$311$	−21.8342			−1.23810			−0.619052	−	0.785350i	$-0.712483\pi$
$311$	−21.8342			−1.23810			−0.619052	+	0.785350i	$0.712483\pi$
$312$	7.21612	−	3.99321i	0.408532	−	0.226071i
$313$	10.5613			0.596961			0.298481	−	0.954416i	$-0.403520\pi$
$313$	10.5613			0.596961			0.298481	+	0.954416i	$0.403520\pi$
$314$	12.1370	−	4.06746i	0.684933	−	0.229540i
$315$	−7.93234	+	4.57974i	−0.446937	+	0.258039i
$316$	−27.5976	+	20.8378i	−1.55249	+	1.17222i
$317$	19.3125			1.08470			0.542350	−	0.840153i	$-0.317535\pi$
$317$	19.3125			1.08470			0.542350	+	0.840153i	$0.317535\pi$
$318$	9.01285	−	10.1970i	0.505415	−	0.571819i
$319$	−3.59849	−	2.07759i	−0.201477	−	0.116323i
$320$	2.88838	+	7.46038i	0.161466	+	0.417048i
$321$	−2.24730	+	3.89244i	−0.125432	+	0.217255i
$322$	5.97082	−	2.00099i	0.332741	−	0.111511i
$323$	6.90568	+	11.9610i	0.384242	+	0.665527i
$324$	6.52269	+	2.76135i	0.362372	+	0.153408i
$325$	3.01089	−	1.98356i	0.167014	−	0.110028i
$326$	20.2188	+	4.10347i	1.11981	+	0.227270i
$327$	−0.409259	+	0.236286i	−0.0226321	+	0.0130666i
$328$	−14.2332	−	1.09961i	−0.785897	−	0.0607159i
$329$	17.0063	−	29.4558i	0.937589	−	1.62395i
$330$	0.101809	−	0.501636i	0.00560440	−	0.0276142i
$331$	−10.6242	+	18.4017i	−0.583960	+	1.01145i	0.411044	+	0.911615i	$0.365164\pi$
$331$	−10.6242	+	18.4017i	−0.583960	+	1.01145i	−0.995004	+	0.0998329i	$0.968169\pi$
$332$	−16.2537	+	12.2724i	−0.892036	+	0.673537i
$333$	12.1765			0.667270
$334$	−3.75619	−	3.31999i	−0.205530	−	0.181662i
$335$	−5.35905	−	9.28215i	−0.292796	−	0.507138i
$336$	−3.45804	+	12.1473i	−0.188651	+	0.662692i
$337$	−22.4148			−1.22101			−0.610506	−	0.792012i	$-0.709034\pi$
$337$	−22.4148			−1.22101			−0.610506	+	0.792012i	$0.709034\pi$
$338$	18.3225	+	1.51255i	0.996610	+	0.0822719i
$339$		−	9.14292i		−	0.496575i
$340$	−1.96903	−	15.9105i	−0.106786	−	0.862869i
$341$	−2.01498	+	1.16335i	−0.109117	+	0.0629990i
$342$	−3.78574	+	4.28313i	−0.204709	+	0.231605i
$343$			4.85619i			0.262210i
$344$	0.828738	+	1.73108i	0.0446826	+	0.0933337i
$345$	0.798751	+	0.461159i	0.0430033	+	0.0248280i
$346$	3.22086	−	15.8699i	0.173155	−	0.853172i
$347$	−30.6557	−	17.6991i	−1.64569	−	0.950137i	−0.978759	−	0.205015i	$-0.934276\pi$
$347$	−30.6557	−	17.6991i	−1.64569	−	0.950137i	−0.666928	−	0.745123i	$-0.732391\pi$
$348$	1.84433	+	14.9029i	0.0988667	+	0.798881i
$349$	−4.80203	−	8.31737i	−0.257047	−	0.445219i	0.708402	−	0.705809i	$-0.249416\pi$
$349$	−4.80203	−	8.31737i	−0.257047	−	0.445219i	−0.965450	+	0.260590i	$0.916083\pi$
$350$	−1.09823	+	5.41124i	−0.0587029	+	0.289243i
$351$	−8.57568	−	13.0172i	−0.457736	−	0.694808i
$352$	1.36541	+	2.13198i	0.0727764	+	0.113635i
$353$	11.4605	−	6.61673i	0.609981	−	0.352173i	−0.162977	−	0.986630i	$-0.552110\pi$
$353$	11.4605	−	6.61673i	0.609981	−	0.352173i	0.772958	+	0.634457i	$0.218776\pi$
$354$	−10.1289	+	3.39449i	−0.538347	+	0.180415i
$355$	9.05690	+	5.22901i	0.480691	+	0.277527i
$356$	−6.93772	+	16.3879i	−0.367699	+	0.868555i
$357$	12.6551	−	21.9193i	0.669781	−	1.16009i
$358$	−0.913852	−	0.807728i	−0.0482986	−	0.0426898i
$359$			34.1706i			1.80345i	0.432307	+	0.901726i	$0.357700\pi$
$359$			34.1706i			1.80345i	−0.432307	+	0.901726i	$0.642300\pi$
$360$	5.98494	−	2.86523i	0.315434	−	0.151011i
$361$	8.01566	+	13.8835i	0.421877	+	0.730712i
$362$	−5.94252	+	1.99150i	−0.312332	+	0.104671i
$363$			8.73388i			0.458410i
$364$	−21.4307	+	18.2593i	−1.12327	+	0.957048i
$365$		−	0.118228i		−	0.00618836i
$366$	−2.87162	−	8.56873i	−0.150102	−	0.447895i
$367$	7.52014	+	13.0253i	0.392548	+	0.679913i	0.992785	−	0.119909i	$-0.0382603\pi$
$367$	7.52014	+	13.0253i	0.392548	+	0.679913i	−0.600237	+	0.799822i	$0.704927\pi$
$368$	−4.42427	+	1.11210i	−0.230631	+	0.0579720i
$369$			11.8406i			0.616397i
$370$	4.86121	−	5.49990i	0.252722	−	0.285926i
$371$	−23.2294	+	40.2345i	−1.20601	+	2.08887i
$372$	7.74329	+	3.27809i	0.401471	+	0.169961i
$373$	5.64614	+	3.25980i	0.292346	+	0.168786i	0.638999	−	0.769207i	$-0.279349\pi$
$373$	5.64614	+	3.25980i	0.292346	+	0.168786i	−0.346653	+	0.937993i	$0.612682\pi$
$374$	−1.61217	−	4.81061i	−0.0833632	−	0.248751i
$375$	−0.700368	+	0.404358i	−0.0361668	+	0.0208809i
$376$	−13.9270	+	20.3264i	−0.718231	+	1.04825i
$377$	−15.0008	+	29.9255i	−0.772581	+	1.54124i
$378$	23.3948	+	4.74807i	1.20330	+	0.244214i
$379$	6.04540	+	10.4709i	0.310531	+	0.537856i	0.978477	−	0.206354i	$-0.0661597\pi$
$379$	6.04540	+	10.4709i	0.310531	+	0.537856i	−0.667946	+	0.744210i	$0.732826\pi$
$380$	0.423233	+	3.41988i	0.0217114	+	0.175436i
$381$	8.20436	+	4.73679i	0.420322	+	0.242673i
$382$	30.0910	+	6.10709i	1.53959	+	0.312466i
$383$	1.57440	+	0.908980i	0.0804480	+	0.0464467i	0.539684	−	0.841867i	$-0.318544\pi$
$383$	1.57440	+	0.908980i	0.0804480	+	0.0464467i	−0.459236	+	0.888314i	$0.651877\pi$
$384$	3.17551	−	8.58083i	0.162050	−	0.437889i
$385$			1.74739i			0.0890552i
$386$	17.9552	+	15.8701i	0.913897	+	0.807768i
$387$	1.37860	−	0.795934i	0.0700781	−	0.0404596i
$388$	−17.9730	+	2.22428i	−0.912442	+	0.112921i
$389$			3.63531i			0.184318i	0.995744	+	0.0921589i	$0.0293768\pi$
$389$			3.63531i			0.184318i	−0.995744	+	0.0921589i	$0.970623\pi$
$390$	−4.08256	−	0.580734i	−0.206728	−	0.0294066i
$391$	9.14198			0.462330
$392$	1.79605	−	23.2477i	0.0907140	−	1.17419i
$393$	−4.73537	−	8.20190i	−0.238868	−	0.413731i
$394$	14.7563	−	16.6951i	0.743414	−	0.841087i
$395$	17.2905			0.869979
$396$	1.67584	−	1.26535i	0.0842141	−	0.0635864i
$397$	1.49457	−	2.58868i	0.0750105	−	0.129922i	−0.826080	−	0.563552i	$-0.809434\pi$
$397$	1.49457	−	2.58868i	0.0750105	−	0.129922i	0.901091	+	0.433630i	$0.142768\pi$
$398$	−8.58162	−	1.74167i	−0.430158	−	0.0873021i
$399$	−2.72016	+	4.71145i	−0.136178	+	0.235867i
$400$	1.09519	−	3.84715i	0.0547593	−	0.192358i
$401$	11.2958	−	6.52161i	0.564084	−	0.325674i	−0.190699	−	0.981648i	$-0.561076\pi$
$401$	11.2958	−	6.52161i	0.564084	−	0.325674i	0.754783	+	0.655975i	$0.227742\pi$
$402$	−2.43815	+	12.0133i	−0.121604	+	0.599171i
$403$	10.3120	+	15.6528i	0.513678	+	0.779723i
$404$	0.0205223	−	0.0484764i	0.00102102	−	0.00241179i
$405$	−1.77078	−	3.06708i	−0.0879908	−	0.152404i
$406$	−16.2894	−	48.6066i	−0.808430	−	2.41230i
$407$	1.16148	−	2.01175i	0.0575726	−	0.0997186i
$408$	−10.3637	+	15.1258i	−0.513079	+	0.748837i
$409$	11.7308	+	6.77276i	0.580049	+	0.334892i	0.761153	−	0.648572i	$-0.224634\pi$
$409$	11.7308	+	6.77276i	0.580049	+	0.334892i	−0.181104	+	0.983464i	$0.557967\pi$
$410$	5.34816	+	4.72709i	0.264127	+	0.233454i
$411$	6.06981			0.299402
$412$	20.8923	−	15.7749i	1.02929	−	0.777173i
$413$	31.5823	−	18.2340i	1.55406	−	0.897238i
$414$	1.20232	+	3.58766i	0.0590910	+	0.176324i
$415$	10.1833			0.499876
$416$	16.4979	−	11.9925i	0.808875	−	0.587981i
$417$	−6.60522			−0.323459
$418$	0.346527	+	1.03402i	0.0169492	+	0.0505753i
$419$	−22.8340	+	13.1832i	−1.11551	+	0.644041i	−0.940251	−	0.340481i	$-0.889410\pi$
$419$	−22.8340	+	13.1832i	−1.11551	+	0.644041i	−0.175260	+	0.984522i	$0.556077\pi$
$420$	5.03973	−	3.80528i	0.245914	−	0.185679i
$421$	18.3329			0.893489			0.446744	−	0.894662i	$-0.352583\pi$
$421$	18.3329			0.893489			0.446744	+	0.894662i	$0.352583\pi$
$422$	1.43282	+	1.26643i	0.0697486	+	0.0616488i
$423$	17.6990	+	10.2185i	0.860555	+	0.496841i
$424$	19.0233	−	27.7644i	0.923853	−	1.34836i
$425$	−4.00797	+	6.94201i	−0.194415	+	0.336737i
$426$	−3.80064	−	11.3409i	−0.184142	−	0.549467i
$427$	15.4254	+	26.7175i	0.746485	+	1.29295i
$428$	−4.33334	+	10.2360i	−0.209460	+	0.494774i
$429$	−1.30273	+	0.0768652i	−0.0628966	+	0.00371109i
$430$	0.190867	−	0.940443i	0.00920440	−	0.0453522i
$431$	16.5529	−	9.55682i	0.797325	−	0.460336i	−0.0452099	−	0.998978i	$-0.514396\pi$
$431$	16.5529	−	9.55682i	0.797325	−	0.460336i	0.842535	+	0.538642i	$0.181062\pi$
$432$	−16.6327	−	4.73490i	−0.800240	−	0.227808i
$433$	9.52072	−	16.4904i	0.457537	−	0.792477i	−0.541294	−	0.840834i	$-0.682065\pi$
$433$	9.52072	−	16.4904i	0.457537	−	0.792477i	0.998830	+	0.0483571i	$0.0153986\pi$
$434$	−28.1316	−	5.70941i	−1.35036	−	0.274060i
$435$	3.75415	−	6.50238i	0.179998	−	0.311765i
$436$	−0.932689	+	0.704232i	−0.0446677	+	0.0337266i
$437$	−1.96502			−0.0939996
$438$	−0.0895492	+	0.101315i	−0.00427883	+	0.00484100i
$439$	4.17977	+	7.23957i	0.199490	+	0.345526i	0.948363	−	0.317187i	$-0.102738\pi$
$439$	4.17977	+	7.23957i	0.199490	+	0.345526i	−0.748873	+	0.662713i	$0.769405\pi$
$440$	0.0975065	−	1.26211i	0.00464844	−	0.0601686i
$441$	−19.3398			−0.920942
$442$	−37.9228	+	15.2480i	−1.80380	+	0.725275i
$443$		−	27.0916i		−	1.28716i	−0.765378	−	0.643580i	$-0.777448\pi$
$443$		−	27.0916i		−	1.28716i	0.765378	−	0.643580i	$-0.222552\pi$
$444$	−8.33153	+	1.03108i	−0.395397	+	0.0489329i
$445$	7.70585	−	4.44897i	0.365292	−	0.210902i
$446$	11.8375	+	10.4628i	0.560522	+	0.495430i
$447$		−	4.28848i		−	0.202838i
$448$	−4.79755	+	30.8640i	−0.226663	+	1.45819i
$449$	−0.192996	−	0.111426i	−0.00910804	−	0.00525853i	0.495439	−	0.868643i	$-0.335007\pi$
$449$	−0.192996	−	0.111426i	−0.00910804	−	0.00525853i	−0.504547	+	0.863384i	$0.668341\pi$
$450$	−3.25143	−	0.659890i	−0.153274	−	0.0311075i
$451$	1.95625	+	1.12944i	0.0921160	+	0.0531832i
$452$	−2.77707	−	22.4398i	−0.130622	−	1.05548i
$453$	1.74819	+	3.02795i	0.0821371	+	0.142266i
$454$	14.3983	+	2.92220i	0.675747	+	0.137146i
$455$	14.0528	−	0.829158i	0.658807	−	0.0388715i
$456$	2.22762	−	3.25120i	0.104318	−	0.152251i
$457$	−6.68503	+	3.85960i	−0.312712	+	0.180545i	−0.648140	−	0.761522i	$-0.724453\pi$
$457$	−6.68503	+	3.85960i	−0.312712	+	0.180545i	0.335427	+	0.942066i	$0.391119\pi$
$458$	−10.3851	−	30.9885i	−0.485265	−	1.44800i
$459$	30.0129	+	17.3280i	1.40088	+	0.808800i
$460$	2.10048	+	0.889227i	0.0979352	+	0.0414604i
$461$	5.52913	−	9.57673i	0.257517	−	0.446033i	−0.708059	−	0.706153i	$-0.750429\pi$
$461$	5.52913	−	9.57673i	0.257517	−	0.446033i	0.965576	+	0.260120i	$0.0837622\pi$
$462$	1.32352	−	1.49741i	0.0615756	−	0.0696658i
$463$		−	28.7883i		−	1.33791i	−0.743304	−	0.668954i	$-0.766742\pi$
$463$		−	28.7883i		−	1.33791i	0.743304	−	0.668954i	$-0.233258\pi$
$464$	9.05322	+	36.0166i	0.420285	+	1.67203i
$465$	−2.10215	−	3.64103i	−0.0974847	−	0.168848i
$466$	−3.85124	−	11.4919i	−0.178405	−	0.532350i
$467$		−	33.8862i		−	1.56806i	−0.620720	−	0.784032i	$-0.713160\pi$
$467$		−	33.8862i		−	1.56806i	0.620720	−	0.784032i	$-0.286840\pi$
$468$	−10.9714	−	12.8770i	−0.507153	−	0.595239i
$469$		−	41.8470i		−	1.93232i
$470$	11.6814	−	3.91477i	0.538824	−	0.180575i
$471$	3.65996	+	6.33924i	0.168642	+	0.292097i
$472$	−23.8288	+	11.4078i	−1.09681	+	0.525085i
$473$		−	0.303687i		−	0.0139635i
$474$	−14.8169	−	13.0963i	−0.680563	−	0.601531i
$475$	0.861493	−	1.49215i	0.0395280	−	0.0684645i
$476$	24.4022	−	57.6413i	1.11847	−	2.64198i
$477$	−24.1756	−	13.9578i	−1.10692	−	0.639082i
$478$	1.37627	−	0.461226i	0.0629490	−	0.0210960i
$479$	−14.6419	+	8.45349i	−0.669004	+	0.386250i	−0.795699	−	0.605692i	$-0.792896\pi$
$479$	−14.6419	+	8.45349i	−0.669004	+	0.386250i	0.126695	+	0.991942i	$0.459563\pi$
$480$	−3.85244	+	2.46726i	−0.175839	+	0.112614i
$481$	−16.7300	−	8.38626i	−0.762821	−	0.382380i
$482$	−4.61581	+	22.7431i	−0.210244	+	1.03592i
$483$	1.80052	+	3.11859i	0.0819264	+	0.141901i
$484$	2.65283	+	21.4359i	0.120583	+	0.974358i
$485$	7.84192	+	4.52754i	0.356083	+	0.205585i
$486$	−4.45394	+	21.9456i	−0.202035	+	0.995472i
$487$	28.6541	+	16.5434i	1.29844	+	0.749654i	0.980135	−	0.198334i	$-0.0635530\pi$
$487$	28.6541	+	16.5434i	1.29844	+	0.749654i	0.318305	+	0.947988i	$0.396886\pi$
$488$	−9.65058	−	20.1583i	−0.436861	−	0.912523i
$489$			11.7978i			0.533514i
$490$	−7.72097	+	8.73539i	−0.348798	+	0.394625i
$491$	26.6188	−	15.3683i	1.20129	−	0.693564i	0.240446	−	0.970663i	$-0.422706\pi$
$491$	26.6188	−	15.3683i	1.20129	−	0.693564i	0.960841	+	0.277099i	$0.0893730\pi$
$492$	−1.00263	−	8.10167i	−0.0452023	−	0.365252i
$493$		−	74.4220i		−	3.35180i
$494$	8.15130	−	3.27749i	0.366744	−	0.147461i
$495$	−1.04995			−0.0471916
$496$	20.0003	+	5.69357i	0.898040	+	0.255649i
$497$	20.4158	+	35.3611i	0.915772	+	1.58616i
$498$	−8.72644	−	7.71306i	−0.391041	−	0.345630i
$499$	−6.58714			−0.294881			−0.147440	−	0.989071i	$-0.547103\pi$
$499$	−6.58714			−0.294881			−0.147440	+	0.989071i	$0.547103\pi$
$500$	−1.59612	+	1.20516i	−0.0713806	+	0.0538963i
$501$	1.43337	−	2.48267i	0.0640383	−	0.110918i
$502$	−0.529741	+	2.61015i	−0.0236435	+	0.116497i
$503$	−20.7723	+	35.9786i	−0.926190	+	1.60421i	−0.136555	+	0.990633i	$0.543603\pi$
$503$	−20.7723	+	35.9786i	−0.926190	+	1.60421i	−0.789636	+	0.613576i	$0.789730\pi$
$504$	25.8300	+	1.99554i	1.15056	+	0.0888885i
$505$	−0.0227944	+	0.0131604i	−0.00101434	+	0.000585629i
$506$	0.707422	+	0.143574i	0.0314487	+	0.00638264i
$507$	1.23633	+	10.4404i	0.0549072	+	0.463672i
$508$	21.5750	+	9.13367i	0.957236	+	0.405241i
$509$	8.56097	+	14.8280i	0.379458	+	0.657241i	0.990984	−	0.133984i	$-0.0427770\pi$
$509$	8.56097	+	14.8280i	0.379458	+	0.657241i	−0.611525	+	0.791225i	$0.709444\pi$
$510$	8.69265	−	2.91315i	0.384917	−	0.128996i
$511$	0.230801	−	0.399760i	0.0102100	−	0.0176843i
$512$	5.18743	−	22.0248i	0.229254	−	0.973367i
$513$	−6.45112	−	3.72456i	−0.284824	−	0.164443i
$514$	15.5362	−	17.5774i	0.685271	−	0.775305i
$515$	−13.0895			−0.576791
$516$	−0.875877	+	0.661337i	−0.0385584	+	0.0291137i
$517$	3.37651	−	1.94943i	0.148499	−	0.0857357i
$518$	27.1737	−	9.10665i	1.19394	−	0.400123i
$519$	9.26020			0.406478
$520$	−10.1964	−	0.185279i	−0.447140	−	0.00812504i
$521$	−23.5385			−1.03124			−0.515621	−	0.856817i	$-0.672439\pi$
$521$	−23.5385			−1.03124			−0.515621	+	0.856817i	$0.672439\pi$
$522$	29.2060	−	9.78775i	1.27831	−	0.428398i
$523$	1.93140	−	1.11509i	0.0844542	−	0.0487597i	−0.457178	−	0.889375i	$-0.651140\pi$
$523$	1.93140	−	1.11509i	0.0844542	−	0.0487597i	0.541632	+	0.840615i	$0.317806\pi$
$524$	−14.1134	−	18.6919i	−0.616548	−	0.816559i
$525$	−3.15749			−0.137804
$526$	−19.2071	+	21.7307i	−0.837471	+	0.947503i
$527$	−36.0897	−	20.8364i	−1.57209	−	0.907647i
$528$	−1.03951	+	1.00770i	−0.0452388	+	0.0438544i
$529$	10.8497	−	18.7922i	0.471724	−	0.817051i
$530$	−15.9560	+	5.34729i	−0.693084	+	0.232272i
$531$	10.9562	+	18.9767i	0.475459	+	0.823519i
$532$	−5.24512	+	12.3897i	−0.227405	+	0.537161i
$533$	8.15489	−	16.2684i	0.353227	−	0.704663i
$534$	−9.97322	−	2.02410i	−0.431583	−	0.0875915i
$535$	4.81312	−	2.77886i	0.208089	−	0.120140i
$536$	−2.33511	+	30.2253i	−0.100862	+	1.30553i
$537$	0.348728	−	0.604014i	0.0150487	−	0.0260651i
$538$	1.62082	−	7.98616i	0.0698786	−	0.344308i
$539$	−1.84476	+	3.19522i	−0.0794596	+	0.137628i
$540$	5.21035	+	6.90062i	0.224218	+	0.296955i
$541$	−27.5466			−1.18432			−0.592161	−	0.805820i	$-0.701725\pi$
$541$	−27.5466			−1.18432			−0.592161	+	0.805820i	$0.701725\pi$
$542$	−10.0395	−	8.87367i	−0.431235	−	0.381157i
$543$	−1.79198	−	3.10381i	−0.0769014	−	0.133197i
$544$	−20.8417	+	40.2715i	−0.893580	+	1.72663i
$545$	0.584348			0.0250307
$546$	−12.6705	−	9.93343i	−0.542245	−	0.425112i
$547$			40.5419i			1.73345i	0.498788	+	0.866724i	$0.333779\pi$
$547$			40.5419i			1.73345i	−0.498788	+	0.866724i	$0.666221\pi$
$548$	14.8974	−	1.84364i	0.636383	−	0.0787566i
$549$	−16.0536	+	9.26857i	−0.685153	+	0.395573i
$550$	−0.419168	+	0.474240i	−0.0178734	+	0.0202217i
$551$			15.9966i			0.681479i
$552$	−1.12646	−	2.35297i	−0.0479453	−	0.100149i
$553$	58.4634	+	33.7539i	2.48612	+	1.43536i
$554$	−0.695351	+	3.42615i	−0.0295426	+	0.145563i
$555$	3.63518	+	2.09877i	0.154305	+	0.0890879i
$556$	−16.2114	+	2.00627i	−0.687518	+	0.0850848i
$557$	14.4872	+	25.0925i	0.613841	+	1.06320i	0.990587	+	0.136887i	$0.0437098\pi$
$557$	14.4872	+	25.0925i	0.613841	+	1.06320i	−0.376746	+	0.926317i	$0.622957\pi$
$558$	3.43059	−	16.9033i	0.145228	−	0.715574i
$559$	−2.44230	+	0.144103i	−0.103298	+	0.00609491i
$560$	11.2134	−	10.8702i	0.473851	−	0.459350i
$561$	2.51261	−	1.45065i	0.106082	−	0.0612466i
$562$	−7.78776	+	2.60990i	−0.328507	+	0.110092i
$563$	−23.2595	−	13.4289i	−0.980272	−	0.565961i	−0.0779201	−	0.996960i	$-0.524828\pi$
$563$	−23.2595	−	13.4289i	−0.980272	−	0.565961i	−0.902352	+	0.430999i	$0.858161\pi$
$564$	−12.9754	−	5.49309i	−0.546364	−	0.231301i
$565$	−5.65275	+	9.79084i	−0.237813	+	0.411904i
$566$	−16.4489	−	14.5387i	−0.691397	−	0.611106i
$567$		−	13.8274i		−	0.580697i
$568$	−12.7727	−	26.6799i	−0.535932	−	1.11946i
$569$	−3.53392	−	6.12094i	−0.148150	−	0.256603i	0.782394	−	0.622784i	$-0.213998\pi$
$569$	−3.53392	−	6.12094i	−0.148150	−	0.256603i	−0.930544	+	0.366181i	$0.880665\pi$
$570$	−1.86844	+	0.626166i	−0.0782604	+	0.0262272i
$571$		−	14.6144i		−	0.611594i	−0.952097	−	0.305797i	$-0.901077\pi$
$571$		−	14.6144i		−	0.611594i	0.952097	−	0.305797i	$-0.0989230\pi$
$572$	−3.17400	+	0.584345i	−0.132712	+	0.0244327i
$573$			17.5583i			0.733509i
$574$	8.85540	+	26.4240i	0.369617	+	1.10292i
$575$	−0.570237	−	0.987679i	−0.0237805	−	0.0411891i
$576$	−18.5451	−	2.88268i	−0.772714	−	0.120112i
$577$			5.48671i			0.228415i	0.993457	+	0.114207i	$0.0364328\pi$
$577$			5.48671i			0.228415i	−0.993457	+	0.114207i	$0.963567\pi$
$578$	44.2584	−	50.0733i	1.84091	−	2.08278i
$579$	−6.85175	+	11.8676i	−0.284749	+	0.493200i
$580$	7.23892	−	17.0993i	0.300580	−	0.710010i
$581$	34.4321	+	19.8794i	1.42848	+	0.824736i
$582$	−3.29079	−	9.81950i	−0.136408	−	0.407031i
$583$	−4.61207	+	2.66278i	−0.191012	+	0.110281i
$584$	−0.189010	+	0.275860i	−0.00782131	+	0.0114152i
$585$	0.498213	+	8.44386i	0.0205986	+	0.349111i
$586$	−43.3851	−	8.80518i	−1.79222	−	0.363738i
$587$	−9.53461	−	16.5144i	−0.393536	−	0.681623i	0.599378	−	0.800466i	$-0.295415\pi$
$587$	−9.53461	−	16.5144i	−0.393536	−	0.681623i	−0.992913	+	0.118843i	$0.962081\pi$
$588$	13.2328	−	1.63765i	0.545712	−	0.0675354i
$589$	7.75728	+	4.47867i	0.319633	+	0.184540i
$590$	12.9454	+	2.62732i	0.532954	+	0.108165i
$591$	11.0347	+	6.37089i	0.453907	+	0.262063i
$592$	−20.1352	+	5.06123i	−0.827551	+	0.208015i
$593$		−	28.8284i		−	1.18384i	−0.805997	−	0.591920i	$-0.798370\pi$
$593$		−	28.8284i		−	1.18384i	0.805997	−	0.591920i	$-0.201630\pi$
$594$	2.05032	+	1.81222i	0.0841256	+	0.0743563i
$595$	−27.1039	+	15.6485i	−1.11115	+	0.641524i
$596$	−1.30258	−	10.5254i	−0.0533558	−	0.431135i
$597$		−	5.00743i		−	0.204940i
$598$	0.818967	−	5.75734i	0.0334901	−	0.235435i
$599$	−4.08040			−0.166721			−0.0833603	−	0.996519i	$-0.526565\pi$
$599$	−4.08040			−0.166721			−0.0833603	+	0.996519i	$0.526565\pi$
$600$	2.28060	+	0.176192i	0.0931049	+	0.00719300i
$601$	−8.92004	−	15.4500i	−0.363856	−	0.630217i	0.624736	−	0.780836i	$-0.285207\pi$
$601$	−8.92004	−	15.4500i	−0.363856	−	0.630217i	−0.988592	+	0.150619i	$0.951873\pi$
$602$	2.48127	−	2.80727i	0.101129	−	0.114416i
$603$	25.1445			1.02396
$604$	5.21035	+	6.90062i	0.212006	+	0.280782i
$605$	5.39985	−	9.35281i	0.219535	−	0.380246i
$606$	0.0295015	+	0.00598744i	0.00119842	+	0.000243223i
$607$	13.6841	−	23.7016i	0.555421	−	0.962018i	−0.442449	−	0.896793i	$-0.645890\pi$
$607$	13.6841	−	23.7016i	0.555421	−	0.962018i	0.997871	−	0.0652243i	$-0.0207763\pi$
$608$	4.47981	−	8.65616i	0.181680	−	0.351054i
$609$	25.3875	−	14.6575i	1.02875	−	0.593950i
$610$	−2.22262	+	10.9514i	−0.0899914	+	0.443408i
$611$	−17.2798	−	26.2294i	−0.699067	−	1.06113i
$612$	34.6347	+	14.6624i	1.40002	+	0.592694i
$613$	−2.05530	−	3.55988i	−0.0830127	−	0.143782i	0.821530	−	0.570165i	$-0.193121\pi$
$613$	−2.05530	−	3.55988i	−0.0830127	−	0.143782i	−0.904543	+	0.426383i	$0.859788\pi$
$614$	−1.72718	−	5.15380i	−0.0697033	−	0.207990i
$615$	−2.04087	+	3.53489i	−0.0822958	+	0.142540i
$616$	2.79353	−	4.07715i	0.112555	−	0.164273i
$617$	−26.8289	−	15.4897i	−1.08009	−	0.623591i	−0.149170	−	0.988812i	$-0.547660\pi$
$617$	−26.8289	−	15.4897i	−1.08009	−	0.623591i	−0.930921	+	0.365220i	$0.880994\pi$
$618$	11.2169	+	9.91430i	0.451210	+	0.398812i
$619$	−43.4702			−1.74722			−0.873608	−	0.486631i	$-0.838226\pi$
$619$	−43.4702			−1.74722			−0.873608	+	0.486631i	$0.838226\pi$
$620$	−6.26530	−	8.29779i	−0.251620	−	0.333247i
$621$	−4.27011	+	2.46535i	−0.171354	+	0.0989310i
$622$	−9.81182	−	29.2779i	−0.393418	−	1.17393i
$623$	34.7405			1.39185
$624$	8.59733	+	7.88176i	0.344169	+	0.315523i
$625$	1.00000			0.0400000
$626$	4.74603	+	14.1619i	0.189690	+	0.566022i
$627$	−0.540071	+	0.311810i	−0.0215684	+	0.0124525i
$628$	10.9083	+	14.4469i	0.435287	+	0.576496i
$629$	41.6059			1.65893
$630$	−9.70568	−	8.57858i	−0.386683	−	0.341779i
$631$	2.39053	+	1.38018i	0.0951657	+	0.0549439i	0.546828	−	0.837245i	$-0.315835\pi$
$631$	2.39053	+	1.38018i	0.0951657	+	0.0549439i	−0.451662	+	0.892189i	$0.649169\pi$
$632$	−40.3435	−	27.6421i	−1.60478	−	1.09954i
$633$	−0.546767	+	0.947028i	−0.0217320	+	0.0376410i
$634$	8.67863	+	25.8965i	0.344673	+	1.02848i
$635$	−5.85718	−	10.1449i	−0.232435	−	0.402589i
$636$	17.7235	+	7.50317i	0.702783	+	0.297520i
$637$	26.5719	+	13.3197i	1.05282	+	0.527747i
$638$	1.16879	−	5.75890i	0.0462729	−	0.227997i
$639$	−21.2473	+	12.2671i	−0.840531	+	0.485281i
$640$	−8.70577	+	7.22562i	−0.344126	+	0.285618i
$641$	5.00752	−	8.67328i	0.197785	−	0.342574i	−0.750025	−	0.661410i	$-0.769958\pi$
$641$	5.00752	−	8.67328i	0.197785	−	0.342574i	0.947810	+	0.318836i	$0.103292\pi$
$642$	−6.22933	−	1.26427i	−0.245852	−	0.0498966i
$643$	14.2515	−	24.6843i	0.562024	−	0.973454i	−0.435296	−	0.900287i	$-0.643356\pi$
$643$	14.2515	−	24.6843i	0.562024	−	0.973454i	0.997320	−	0.0731662i	$-0.0233104\pi$
$644$	5.36631	+	7.10717i	0.211462	+	0.280062i
$645$	0.548755			0.0216072
$646$	−12.9354	+	14.6350i	−0.508938	+	0.575805i
$647$	−7.53191	−	13.0456i	−0.296110	−	0.512877i	0.679133	−	0.734016i	$-0.262356\pi$
$647$	−7.53191	−	13.0456i	−0.296110	−	0.512877i	−0.975242	+	0.221138i	$0.929023\pi$
$648$	−0.771587	+	9.98728i	−0.0303108	+	0.392338i
$649$	4.18032			0.164092
$650$	4.01282	+	3.14599i	0.157396	+	0.123396i
$651$		−	16.4150i		−	0.643353i
$652$	3.58345	+	28.9557i	0.140339	+	1.13399i
$653$	−14.7901	+	8.53909i	−0.578783	+	0.334161i	−0.760650	−	0.649163i	$-0.775119\pi$
$653$	−14.7901	+	8.53909i	−0.578783	+	0.334161i	0.181867	+	0.983323i	$0.441786\pi$
$654$	−0.500751	−	0.442600i	−0.0195809	−	0.0173070i
$655$			11.7108i			0.457581i
$656$	−4.92160	−	19.5797i	−0.192156	−	0.764458i
$657$	0.240202	+	0.138681i	0.00937117	+	0.00541045i
$658$	47.1401	+	9.56726i	1.83771	+	0.372971i
$659$	32.4049	+	18.7090i	1.26232	+	0.728799i	0.973522	−	0.228593i	$-0.0734124\pi$
$659$	32.4049	+	18.7090i	1.26232	+	0.728799i	0.288794	+	0.957391i	$0.406746\pi$
$660$	0.718403	−	0.0889071i	0.0279638	−	0.00346070i
$661$	−8.83203	−	15.2975i	−0.343526	−	0.595005i	0.641559	−	0.767074i	$-0.278288\pi$
$661$	−8.83203	−	15.2975i	−0.343526	−	0.595005i	−0.985085	+	0.172069i	$0.944955\pi$
$662$	−29.4494	−	5.97688i	−1.14458	−	0.232298i
$663$	−12.8587	−	19.5185i	−0.499390	−	0.758035i
$664$	−23.7604	−	16.2799i	−0.922081	−	0.631781i
$665$	5.82584	−	3.36355i	0.225917	−	0.130433i
$666$	5.47187	+	16.3277i	0.212031	+	0.632687i
$667$	9.16985	+	5.29422i	0.355058	+	0.204993i
$668$	2.76388	−	6.52868i	0.106938	−	0.252602i
$669$	−4.51722	+	7.82405i	−0.174646	+	0.302495i
$670$	10.0384	−	11.3572i	0.387815	−	0.438769i
$671$			3.53641i			0.136521i
$672$	−17.8426	+	0.821814i	−0.688291	+	0.0317022i
$673$	11.1111	+	19.2450i	0.428302	+	0.741841i	0.996722	−	0.0808970i	$-0.0257785\pi$
$673$	11.1111	+	19.2450i	0.428302	+	0.741841i	−0.568420	+	0.822738i	$0.692445\pi$
$674$	−10.0727	−	30.0564i	−0.387987	−	1.15773i
$675$		−	4.32338i		−	0.166407i
$676$	6.20551	+	25.2486i	0.238673	+	0.971100i
$677$		−	5.99382i		−	0.230361i	−0.993345	−	0.115181i	$-0.963255\pi$
$677$		−	5.99382i		−	0.230361i	0.993345	−	0.115181i	$-0.0367447\pi$
$678$	12.2599	−	4.10863i	0.470839	−	0.157791i
$679$	17.6770	+	30.6175i	0.678381	+	1.17499i
$680$	20.4498	−	9.79015i	0.784216	−	0.375435i
$681$			8.40152i			0.321947i
$682$	−2.46545	−	2.17914i	−0.0944069	−	0.0834436i
$683$	4.56662	−	7.90963i	0.174737	−	0.302653i	−0.765333	−	0.643634i	$-0.777426\pi$
$683$	4.56662	−	7.90963i	0.174737	−	0.302653i	0.940070	+	0.340981i	$0.110759\pi$
$684$	−7.44455	−	3.15161i	−0.284649	−	0.120505i
$685$	−6.49995	−	3.75275i	−0.248350	−	0.143385i
$686$	−6.51175	+	2.18227i	−0.248620	+	0.0833193i
$687$	16.1855	−	9.34469i	0.617514	−	0.356522i
$688$	−1.94882	+	1.88918i	−0.0742981	+	0.0720243i
$689$	23.6030	+	35.8276i	0.899204	+	1.36492i
$690$	−0.259435	+	1.27829i	−0.00987651	+	0.0486638i
$691$	9.65327	+	16.7200i	0.367228	+	0.636057i	0.989131	−	0.147037i	$-0.0469736\pi$
$691$	9.65327	+	16.7200i	0.367228	+	0.636057i	−0.621903	+	0.783094i	$0.713640\pi$
$692$	22.7276	−	2.81269i	0.863975	−	0.106923i
$693$	−3.55013	−	2.04967i	−0.134858	−	0.0778606i
$694$	9.95700	−	49.0604i	0.377962	−	1.86231i
$695$	7.07331	+	4.08378i	0.268306	+	0.154906i
$696$	−19.1548	+	9.17015i	−0.726060	+	0.347594i
$697$			40.4580i			1.53246i
$698$	8.99497	−	10.1768i	0.340465	−	0.385197i
$699$	6.00226	−	3.46541i	0.227026	−	0.131074i
$700$	−7.74954	+	0.959056i	−0.292905	+	0.0362489i
$701$			11.3698i			0.429432i	0.976677	+	0.214716i	$0.0688825\pi$
$701$			11.3698i			0.429432i	−0.976677	+	0.214716i	$0.931117\pi$
$702$	13.6013	−	17.3489i	0.513348	−	0.654794i
$703$	−8.94296			−0.337290
$704$	−2.24523	+	2.78896i	−0.0846202	+	0.105113i
$705$	3.52257	+	6.10127i	0.132668	+	0.229787i
$706$	14.0226	+	12.3942i	0.527747	+	0.466461i
$707$	−0.102765			−0.00386487
$708$	−9.10345	−	12.0567i	−0.342129	−	0.453117i
$709$	−2.70275	+	4.68129i	−0.101504	+	0.175810i	−0.912304	−	0.409513i	$-0.865699\pi$
$709$	−2.70275	+	4.68129i	−0.101504	+	0.175810i	0.810801	+	0.585322i	$0.199032\pi$
$710$	−2.94169	+	14.4944i	−0.110400	+	0.543964i
$711$	−20.2816	+	35.1287i	−0.760618	+	1.31743i
$712$	−25.0924	−	1.93856i	−0.940378	−	0.0726507i
$713$	5.13468	−	2.96451i	0.192295	−	0.111022i
$714$	35.0790	+	7.11941i	1.31280	+	0.266437i
$715$	1.44258	+	0.723122i	0.0539493	+	0.0270432i
$716$	0.672432	−	1.58838i	0.0251299	−	0.0593604i
$717$	0.415018	+	0.718832i	0.0154991	+	0.0268453i
$718$	−45.8199	+	15.3555i	−1.70998	+	0.573063i
$719$	3.58826	−	6.21504i	0.133819	−	0.231782i	−0.791326	−	0.611394i	$-0.790609\pi$
$719$	3.58826	−	6.21504i	0.133819	−	0.231782i	0.925146	+	0.379612i	$0.123942\pi$
$720$	6.53153	+	6.73773i	0.243416	+	0.251100i
$721$	−44.2587	−	25.5528i	−1.64828	−	0.951636i
$722$	−15.0146	+	16.9873i	−0.558786	+	0.632202i
$723$	−13.2708			−0.493545
$724$	−5.34088	−	7.07349i	−0.198492	−	0.262884i
$725$	−8.04039	+	4.64212i	−0.298613	+	0.172404i
$726$	−11.7114	+	3.92482i	−0.434651	+	0.145664i
$727$	−13.9387			−0.516958			−0.258479	−	0.966017i	$-0.583221\pi$
$727$	−13.9387			−0.516958			−0.258479	+	0.966017i	$0.583221\pi$
$728$	−34.1147	−	20.5314i	−1.26438	−	0.760946i
$729$	−2.18071			−0.0807670
$730$	0.158534	−	0.0531293i	0.00586762	−	0.00196640i
$731$	4.71051	−	2.71962i	0.174225	−	0.100589i
$732$	10.1995	−	7.70120i	0.376985	−	0.284645i
$733$	−51.7217			−1.91039			−0.955193	−	0.295983i	$-0.904353\pi$
$733$	−51.7217			−1.91039			−0.955193	+	0.295983i	$0.904353\pi$
$734$	−14.0864	+	15.9372i	−0.519939	+	0.588251i
$735$	−5.77369	−	3.33344i	−0.212966	−	0.122956i
$736$	−3.47940	−	5.43282i	−0.128252	−	0.200256i
$737$	2.39845	−	4.15424i	0.0883482	−	0.153024i
$738$	−15.8773	+	5.32091i	−0.584450	+	0.195865i
$739$	−3.70149	−	6.41116i	−0.136161	−	0.235838i	0.789879	−	0.613263i	$-0.210143\pi$
$739$	−3.70149	−	6.41116i	−0.136161	−	0.235838i	−0.926041	+	0.377424i	$0.876810\pi$
$740$	9.55943	+	4.04694i	0.351412	+	0.148768i
$741$	2.76391	+	4.19539i	0.101535	+	0.154122i
$742$	−64.3900	−	13.0682i	−2.36383	−	0.479749i
$743$	−38.2295	+	22.0718i	−1.40251	+	0.809737i	−0.994649	−	0.103309i	$-0.967057\pi$
$743$	−38.2295	+	22.0718i	−1.40251	+	0.809737i	−0.407856	+	0.913046i	$0.633724\pi$
$744$	−0.915974	+	11.8562i	−0.0335812	+	0.434670i
$745$	−2.65141	+	4.59238i	−0.0971403	+	0.168252i
$746$	−1.83387	+	9.03589i	−0.0671427	+	0.330827i
$747$	−11.9449	+	20.6891i	−0.437039	+	0.756974i
$748$	5.72616	−	4.32357i	0.209369	−	0.158085i
$749$	21.6991			0.792869
$750$	−0.856940	−	0.757426i	−0.0312910	−	0.0276573i
$751$	−0.525634	−	0.910425i	−0.0191807	−	0.0332219i	0.856276	−	0.516519i	$-0.172772\pi$
$751$	−0.525634	−	0.910425i	−0.0191807	−	0.0332219i	−0.875456	+	0.483297i	$0.839439\pi$
$752$	−33.5145	−	9.54072i	−1.22215	−	0.347914i
$753$	−1.52304			−0.0555027
$754$	−46.8687	−	6.66696i	−1.70686	−	0.242796i
$755$		−	4.32338i		−	0.157344i
$756$	4.14636	+	33.5042i	0.150802	+	1.21854i
$757$	−25.1218	+	14.5041i	−0.913068	+	0.527160i	−0.881417	−	0.472339i	$-0.843410\pi$
$757$	−25.1218	+	14.5041i	−0.913068	+	0.527160i	−0.0316510	+	0.999499i	$0.510076\pi$
$758$	−11.3240	+	12.8118i	−0.411306	+	0.465345i
$759$			0.412785i			0.0149832i
$760$	−4.39559	+	2.10434i	−0.159445	+	0.0763325i
$761$	9.61433	+	5.55084i	0.348519	+	0.201218i	0.664033	−	0.747703i	$-0.268843\pi$
$761$	9.61433	+	5.55084i	0.348519	+	0.201218i	−0.315514	+	0.948921i	$0.602177\pi$
$762$	−2.66478	+	13.1300i	−0.0965348	+	0.475649i
$763$	1.97583	+	1.14074i	0.0715297	+	0.0412977i
$764$	5.33316	+	43.0940i	0.192947	+	1.55909i
$765$	−9.40262	−	16.2858i	−0.339953	−	0.588815i
$766$	−0.511366	+	2.51962i	−0.0184764	+	0.0910374i
$767$	−1.98361	−	33.6189i	−0.0716241	−	1.21391i
$768$	12.9332	+	0.402055i	0.466686	+	0.0145079i
$769$	−13.7216	+	7.92220i	−0.494815

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.449378 + 1.34092i) q^{2} +(-0.700368 + 0.404358i) q^{3} +(-1.59612 + 1.20516i) q^{4} +1.00000 q^{5} +(-0.856940 - 0.757426i) q^{6} +(3.38125 + 1.95217i) q^{7} +(-2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +O(q^{10})\)	\(q+(0.449378 + 1.34092i) q^{2} +(-0.700368 + 0.404358i) q^{3} +(-1.59612 + 1.20516i) q^{4} +1.00000 q^{5} +(-0.856940 - 0.757426i) q^{6} +(3.38125 + 1.95217i) q^{7} +(-2.33328 - 1.59869i) q^{8} +(-1.17299 + 2.03168i) q^{9} +(0.449378 + 1.34092i) q^{10} +(0.223776 + 0.387591i) q^{11} +(0.630555 - 1.48946i) q^{12} +(3.01089 - 1.98356i) q^{13} +(-1.09823 + 5.41124i) q^{14} +(-0.700368 + 0.404358i) q^{15} +(1.09519 - 3.84715i) q^{16} +(-4.00797 + 6.94201i) q^{17} +(-3.25143 - 0.659890i) q^{18} +(0.861493 - 1.49215i) q^{19} +(-1.59612 + 1.20516i) q^{20} -3.15749 q^{21} +(-0.419168 + 0.474240i) q^{22} +(-0.570237 - 0.987679i) q^{23} +(2.28060 + 0.176192i) q^{24} +1.00000 q^{25} +(4.01282 + 3.14599i) q^{26} -4.32338i q^{27} +(-7.74954 + 0.959056i) q^{28} +(-8.04039 + 4.64212i) q^{29} +(-0.856940 - 0.757426i) q^{30} +5.19873i q^{31} +(5.65086 - 0.260274i) q^{32} +(-0.313451 - 0.180971i) q^{33} +(-11.1098 - 2.25477i) q^{34} +(3.38125 + 1.95217i) q^{35} +(-0.576264 - 4.65644i) q^{36} +(-2.59519 - 4.49501i) q^{37} +(2.38799 + 0.484651i) q^{38} +(-1.30666 + 2.60670i) q^{39} +(-2.33328 - 1.59869i) q^{40} +(4.37099 - 2.52359i) q^{41} +(-1.41891 - 4.23393i) q^{42} +(-0.587643 - 0.339276i) q^{43} +(-0.824282 - 0.348956i) q^{44} +(-1.17299 + 2.03168i) q^{45} +(1.06814 - 1.20848i) q^{46} -8.71152i q^{47} +(0.788592 + 3.13727i) q^{48} +(4.12190 + 7.13934i) q^{49} +(0.449378 + 1.34092i) q^{50} -6.48262i q^{51} +(-2.41523 + 6.79460i) q^{52} +11.8993i q^{53} +(5.79729 - 1.94283i) q^{54} +(0.223776 + 0.387591i) q^{55} +(-4.76849 - 9.96051i) q^{56} +1.39340i q^{57} +(-9.83788 - 8.69543i) q^{58} +(4.67021 - 8.08904i) q^{59} +(0.630555 - 1.48946i) q^{60} +(6.84304 + 3.95083i) q^{61} +(-6.97107 + 2.33620i) q^{62} +(-7.93234 + 4.57974i) q^{63} +(2.88838 + 7.46038i) q^{64} +(3.01089 - 1.98356i) q^{65} +(0.101809 - 0.501636i) q^{66} +(-5.35905 - 9.28215i) q^{67} +(-1.96903 - 15.9105i) q^{68} +(0.798751 + 0.461159i) q^{69} +(-1.09823 + 5.41124i) q^{70} +(9.05690 + 5.22901i) q^{71} +(5.98494 - 2.86523i) q^{72} -0.118228i q^{73} +(4.86121 - 5.49990i) q^{74} +(-0.700368 + 0.404358i) q^{75} +(0.423233 + 3.41988i) q^{76} +1.74739i q^{77} +(-4.08256 - 0.580734i) q^{78} +17.2905 q^{79} +(1.09519 - 3.84715i) q^{80} +(-1.77078 - 3.06708i) q^{81} +(5.34816 + 4.72709i) q^{82} +10.1833 q^{83} +(5.03973 - 3.80528i) q^{84} +(-4.00797 + 6.94201i) q^{85} +(0.190867 - 0.940443i) q^{86} +(3.75415 - 6.50238i) q^{87} +(0.0975065 - 1.26211i) q^{88} +(7.70585 - 4.44897i) q^{89} +(-3.25143 - 0.659890i) q^{90} +(14.0528 - 0.829158i) q^{91} +(2.10048 + 0.889227i) q^{92} +(-2.10215 - 3.64103i) q^{93} +(11.6814 - 3.91477i) q^{94} +(0.861493 - 1.49215i) q^{95} +(-3.85244 + 2.46726i) q^{96} +(7.84192 + 4.52754i) q^{97} +(-7.72097 + 8.73539i) q^{98} -1.04995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30} - 30 q^{32} - 16 q^{34} + 15 q^{36} + 4 q^{37} - 24 q^{39} - 61 q^{42} + 24 q^{44} + 28 q^{45} - 19 q^{46} - 51 q^{48} + 20 q^{49} - 64 q^{52} - 5 q^{54} - 8 q^{55} - 23 q^{56} - q^{58} - 16 q^{59} + 6 q^{60} + 10 q^{62} - 30 q^{64} + 14 q^{66} - 36 q^{67} - 51 q^{68} - 4 q^{70} - 81 q^{72} + 70 q^{74} - 60 q^{76} + 143 q^{78} + 14 q^{80} - 28 q^{81} + 21 q^{82} + 40 q^{83} + 31 q^{84} - 28 q^{86} - 36 q^{87} - 19 q^{88} + 18 q^{90} + 16 q^{91} - 18 q^{92} + 43 q^{94} - 16 q^{95} - 48 q^{96} + 24 q^{97} + 56 q^{98} - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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