LMFDB - Embedded newform 525.2.bg.b.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.b.361.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23117 - 0.548154i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.122944 + 0.136543i) q^{4} +(-0.120990 + 2.23279i) q^{5} +(0.416458 - 1.28173i) q^{6} +(2.20566 - 1.46119i) q^{7} +(-0.909436 + 2.79896i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(1.23117 - 0.548154i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.122944 + 0.136543i) q^{4} +(-0.120990 + 2.23279i) q^{5} +(0.416458 - 1.28173i) q^{6} +(2.20566 - 1.46119i) q^{7} +(-0.909436 + 2.79896i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(1.07495 + 2.81528i) q^{10} +(-0.103281 + 0.982652i) q^{11} +(0.0192058 + 0.182731i) q^{12} +(5.74597 - 4.17469i) q^{13} +(1.91459 - 3.00802i) q^{14} +(1.57833 + 1.58394i) q^{15} +(0.376174 + 3.57905i) q^{16} +(-3.97524 + 0.844964i) q^{17} +(-0.673844 - 1.16713i) q^{18} +(4.88959 + 5.43044i) q^{19} +(-0.289998 - 0.291029i) q^{20} +(0.389998 - 2.61685i) q^{21} +(0.411488 + 1.26643i) q^{22} +(5.33547 - 2.37551i) q^{23} +(1.47150 + 2.54871i) q^{24} +(-4.97072 - 0.540292i) q^{25} +(4.78591 - 8.28944i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.0716572 + 0.480813i) q^{28} +(0.937317 + 2.88477i) q^{29} +(2.81144 + 1.08494i) q^{30} +(-5.26917 + 1.12000i) q^{31} +(-0.517989 - 0.897184i) q^{32} +(0.661144 + 0.734275i) q^{33} +(-4.43105 + 3.21934i) q^{34} +(2.99567 + 5.10157i) q^{35} +(0.148646 + 0.107998i) q^{36} +(-1.08619 - 10.3344i) q^{37} +(8.99665 + 4.00557i) q^{38} +(0.742404 - 7.06350i) q^{39} +(-6.13945 - 2.36923i) q^{40} +(-4.87030 + 3.53848i) q^{41} +(-0.954281 - 3.43558i) q^{42} -3.84084 q^{43} +(-0.121477 - 0.134914i) q^{44} +(2.23321 - 0.113063i) q^{45} +(5.26676 - 5.84932i) q^{46} +(-10.6407 - 2.26175i) q^{47} +(2.91146 + 2.11530i) q^{48} +(2.72985 - 6.44577i) q^{49} +(-6.41599 + 2.05953i) q^{50} +(-2.03203 + 3.51957i) q^{51} +(-0.136407 + 1.29783i) q^{52} +(2.07576 - 2.30537i) q^{53} +(-1.31824 - 0.280200i) q^{54} +(-2.18156 - 0.349496i) q^{55} +(2.08390 + 7.50240i) q^{56} +7.30738 q^{57} +(2.73530 + 3.03785i) q^{58} +(-2.54704 - 1.13401i) q^{59} +(-0.410323 + 0.0207738i) q^{60} +(-4.36307 + 1.94257i) q^{61} +(-5.87334 + 4.26723i) q^{62} +(-1.68374 - 2.04084i) q^{63} +(-6.95246 - 5.05126i) q^{64} +(8.62601 + 13.3346i) q^{65} +(1.21648 + 0.541612i) q^{66} +(0.807222 - 0.171580i) q^{67} +(0.373359 - 0.646676i) q^{68} +(1.80478 - 5.55455i) q^{69} +(6.48463 + 4.63883i) q^{70} +(-3.34340 - 10.2899i) q^{71} +(2.87868 + 0.611883i) q^{72} +(-0.318097 + 3.02649i) q^{73} +(-7.00215 - 12.1281i) q^{74} +(-3.72758 + 3.33244i) q^{75} -1.34264 q^{76} +(1.20804 + 2.31831i) q^{77} +(-2.95786 - 9.10335i) q^{78} +(-7.99462 - 1.69931i) q^{79} +(-8.03679 + 0.406887i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-4.05656 + 7.02616i) q^{82} +(1.50735 - 4.63916i) q^{83} +(0.309365 + 0.374978i) q^{84} +(-1.40566 - 8.97812i) q^{85} +(-4.72875 + 2.10537i) q^{86} +(2.77099 + 1.23372i) q^{87} +(-2.65647 - 1.18274i) q^{88} +(-5.06008 + 2.25289i) q^{89} +(2.68749 - 1.36334i) q^{90} +(6.57363 - 17.6039i) q^{91} +(-0.331606 + 1.02058i) q^{92} +(-2.69345 + 4.66518i) q^{93} +(-14.3404 + 3.04814i) q^{94} +(-12.7166 + 10.2604i) q^{95} +(-1.01334 - 0.215392i) q^{96} +(1.86989 + 5.75493i) q^{97} +(-0.172346 - 9.43224i) q^{98} +0.988064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.23117	−	0.548154i	0.870572	−	0.387603i	0.0776889	−	0.996978i	$-0.475246\pi$
$2$	1.23117	−	0.548154i	0.870572	−	0.387603i	0.792883	+	0.609374i	$0.208579\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.122944	+	0.136543i	−0.0614721	+	0.0682717i
$5$	−0.120990	+	2.23279i	−0.0541085	+	0.998535i
$5$	−0.120990	+	2.23279i	−0.0541085	+	0.998535i
$6$	0.416458	−	1.28173i	0.170018	−	0.523263i
$7$	2.20566	−	1.46119i	0.833660	−	0.552277i
$7$	2.20566	−	1.46119i	0.833660	−	0.552277i
$8$	−0.909436	+	2.79896i	−0.321534	+	0.989580i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	1.07495	+	2.81528i	0.339930	+	0.890269i
$11$	−0.103281	+	0.982652i	−0.0311403	+	0.296281i	0.967857	+	0.251503i	$0.0809247\pi$
$11$	−0.103281	+	0.982652i	−0.0311403	+	0.296281i	−0.998997	+	0.0447780i	$0.985742\pi$
$12$	0.0192058	+	0.182731i	0.00554423	+	0.0527498i
$13$	5.74597	−	4.17469i	1.59364	−	1.15785i	0.695151	−	0.718864i	$-0.255338\pi$
$13$	5.74597	−	4.17469i	1.59364	−	1.15785i	0.898494	−	0.438987i	$-0.144662\pi$
$14$	1.91459	−	3.00802i	0.511696	−	0.803927i
$15$	1.57833	+	1.58394i	0.407523	+	0.408972i
$16$	0.376174	+	3.57905i	0.0940434	+	0.894763i
$17$	−3.97524	+	0.844964i	−0.964138	+	0.204934i	−0.662977	−	0.748640i	$-0.730707\pi$
$17$	−3.97524	+	0.844964i	−0.964138	+	0.204934i	−0.301161	+	0.953573i	$0.597374\pi$
$18$	−0.673844	−	1.16713i	−0.158827	−	0.275096i
$19$	4.88959	+	5.43044i	1.12175	+	1.24583i	0.966143	+	0.258009i	$0.0830663\pi$
$19$	4.88959	+	5.43044i	1.12175	+	1.24583i	0.155606	+	0.987819i	$0.450267\pi$
$20$	−0.289998	−	0.291029i	−0.0648455	−	0.0650761i
$21$	0.389998	−	2.61685i	0.0851046	−	0.571043i
$22$	0.411488	+	1.26643i	0.0877295	+	0.270004i
$23$	5.33547	−	2.37551i	1.11252	−	0.495327i	0.233620	−	0.972328i	$-0.424943\pi$
$23$	5.33547	−	2.37551i	1.11252	−	0.495327i	0.878903	+	0.477001i	$0.158276\pi$
$24$	1.47150	+	2.54871i	0.300368	+	0.520253i
$25$	−4.97072	−	0.540292i	−0.994145	−	0.108058i
$26$	4.78591	−	8.28944i	0.938595	−	1.62569i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.0716572	+	0.480813i	−0.0135419	+	0.0908650i
$29$	0.937317	+	2.88477i	0.174055	+	0.535688i	0.999589	−	0.0286654i	$-0.00912573\pi$
$29$	0.937317	+	2.88477i	0.174055	+	0.535688i	−0.825534	+	0.564353i	$0.809126\pi$
$30$	2.81144	+	1.08494i	0.513297	+	0.198082i
$31$	−5.26917	+	1.12000i	−0.946372	+	0.201158i	−0.655151	−	0.755498i	$-0.727395\pi$
$31$	−5.26917	+	1.12000i	−0.946372	+	0.201158i	−0.291221	+	0.956656i	$0.594062\pi$
$32$	−0.517989	−	0.897184i	−0.0915684	−	0.158601i
$33$	0.661144	+	0.734275i	0.115090	+	0.127821i
$34$	−4.43105	+	3.21934i	−0.759918	+	0.552113i
$35$	2.99567	+	5.10157i	0.506360	+	0.862322i
$36$	0.148646	+	0.107998i	0.0247744	+	0.0179997i
$37$	−1.08619	−	10.3344i	−0.178569	−	1.69897i	−0.606440	−	0.795129i	$-0.707403\pi$
$37$	−1.08619	−	10.3344i	−0.178569	−	1.69897i	0.427871	−	0.903840i	$-0.359264\pi$
$38$	8.99665	+	4.00557i	1.45945	+	0.649789i
$39$	0.742404	−	7.06350i	0.118880	−	1.13106i
$40$	−6.13945	−	2.36923i	−0.970733	−	0.374608i
$41$	−4.87030	+	3.53848i	−0.760613	+	0.552618i	−0.899098	−	0.437747i	$-0.855777\pi$
$41$	−4.87030	+	3.53848i	−0.760613	+	0.552618i	0.138485	+	0.990364i	$0.455777\pi$
$42$	−0.954281	−	3.43558i	−0.147249	−	0.530121i
$43$	−3.84084			−0.585723			−0.292862	−	0.956155i	$-0.594608\pi$
$43$	−3.84084			−0.585723			−0.292862	+	0.956155i	$0.594608\pi$
$44$	−0.121477	−	0.134914i	−0.0183133	−	0.0203390i
$45$	2.23321	−	0.113063i	0.332907	−	0.0168544i
$46$	5.26676	−	5.84932i	0.776541	−	0.862436i
$47$	−10.6407	−	2.26175i	−1.55211	−	0.329911i	−0.649496	−	0.760365i	$-0.725020\pi$
$47$	−10.6407	−	2.26175i	−1.55211	−	0.329911i	−0.902612	+	0.430454i	$0.858353\pi$
$48$	2.91146	+	2.11530i	0.420234	+	0.305318i
$49$	2.72985	−	6.44577i	0.389979	−	0.920824i
$50$	−6.41599	+	2.05953i	−0.907358	+	0.291261i
$51$	−2.03203	+	3.51957i	−0.284541	+	0.492839i
$52$	−0.136407	+	1.29783i	−0.0189163	+	0.179976i
$53$	2.07576	−	2.30537i	0.285128	−	0.316666i	−0.583518	−	0.812100i	$-0.698324\pi$
$53$	2.07576	−	2.30537i	0.285128	−	0.316666i	0.868646	+	0.495434i	$0.164991\pi$
$54$	−1.31824	−	0.280200i	−0.179389	−	0.0381304i
$55$	−2.18156	−	0.349496i	−0.294162	−	0.0471260i
$56$	2.08390	+	7.50240i	0.278473	+	1.00255i
$57$	7.30738			0.967886
$58$	2.73530	+	3.03785i	0.359162	+	0.398890i
$59$	−2.54704	−	1.13401i	−0.331596	−	0.147636i	0.234184	−	0.972192i	$-0.424758\pi$
$59$	−2.54704	−	1.13401i	−0.331596	−	0.147636i	−0.565780	+	0.824556i	$0.691425\pi$
$60$	−0.410323	+	0.0207738i	−0.0529725	+	0.00268189i
$61$	−4.36307	+	1.94257i	−0.558634	+	0.248720i	−0.666576	−	0.745437i	$-0.732241\pi$
$61$	−4.36307	+	1.94257i	−0.558634	+	0.248720i	0.107941	+	0.994157i	$0.465574\pi$
$62$	−5.87334	+	4.26723i	−0.745915	+	0.541939i
$63$	−1.68374	−	2.04084i	−0.212131	−	0.257122i
$64$	−6.95246	−	5.05126i	−0.869057	−	0.631407i
$65$	8.62601	+	13.3346i	1.06992	+	1.65396i
$66$	1.21648	+	0.541612i	0.149738	+	0.0666678i
$67$	0.807222	−	0.171580i	0.0986179	−	0.0209619i	−0.158338	−	0.987385i	$-0.550614\pi$
$67$	0.807222	−	0.171580i	0.0986179	−	0.0209619i	0.256956	+	0.966423i	$0.417280\pi$
$68$	0.373359	−	0.646676i	0.0452764	−	0.0784210i
$69$	1.80478	−	5.55455i	0.217270	−	0.668690i
$70$	6.48463	+	4.63883i	0.775062	+	0.554446i
$71$	−3.34340	−	10.2899i	−0.396788	−	1.22119i	−0.927560	−	0.373673i	$-0.878098\pi$
$71$	−3.34340	−	10.2899i	−0.396788	−	1.22119i	0.530772	−	0.847514i	$-0.321902\pi$
$72$	2.87868	+	0.611883i	0.339256	+	0.0721111i
$73$	−0.318097	+	3.02649i	−0.0372304	+	0.354224i	0.960009	+	0.279969i	$0.0903244\pi$
$73$	−0.318097	+	3.02649i	−0.0372304	+	0.354224i	−0.997239	+	0.0742544i	$0.976342\pi$
$74$	−7.00215	−	12.1281i	−0.813983	−	1.40986i
$75$	−3.72758	+	3.33244i	−0.430424	+	0.384797i
$76$	−1.34264			−0.154011
$77$	1.20804	+	2.31831i	0.137669	+	0.264196i
$78$	−2.95786	−	9.10335i	−0.334911	−	1.03075i
$79$	−7.99462	−	1.69931i	−0.899466	−	0.191187i	−0.265100	−	0.964221i	$-0.585405\pi$
$79$	−7.99462	−	1.69931i	−0.899466	−	0.191187i	−0.634365	+	0.773034i	$0.718738\pi$
$80$	−8.03679	+	0.406887i	−0.898541	+	0.0454913i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−4.05656	+	7.02616i	−0.447972	+	0.775910i
$83$	1.50735	−	4.63916i	0.165454	−	0.509214i	−0.833616	−	0.552345i	$-0.813733\pi$
$83$	1.50735	−	4.63916i	0.165454	−	0.509214i	0.999069	+	0.0431307i	$0.0137332\pi$
$84$	0.309365	+	0.374978i	0.0337545	+	0.0409135i
$85$	−1.40566	−	8.97812i	−0.152466	−	0.973814i
$86$	−4.72875	+	2.10537i	−0.509914	+	0.227028i
$87$	2.77099	+	1.23372i	0.297081	+	0.132269i
$88$	−2.65647	−	1.18274i	−0.283181	−	0.126080i
$89$	−5.06008	+	2.25289i	−0.536368	+	0.238806i	−0.657000	−	0.753891i	$-0.728175\pi$
$89$	−5.06008	+	2.25289i	−0.536368	+	0.238806i	0.120632	+	0.992697i	$0.461508\pi$
$90$	2.68749	−	1.36334i	0.283287	−	0.143709i
$91$	6.57363	−	17.6039i	0.689103	−	1.84539i
$92$	−0.331606	+	1.02058i	−0.0345723	+	0.106403i
$93$	−2.69345	+	4.66518i	−0.279297	+	0.483757i
$94$	−14.3404	+	3.04814i	−1.47910	+	0.314392i
$95$	−12.7166	+	10.2604i	−1.30470	+	1.05270i
$96$	−1.01334	−	0.215392i	−0.103424	−	0.0219834i
$97$	1.86989	+	5.75493i	0.189858	+	0.584324i	0.999998	−	0.00191260i	$-0.000608800\pi$
$97$	1.86989	+	5.75493i	0.189858	+	0.584324i	−0.810140	+	0.586237i	$0.800609\pi$
$98$	−0.172346	−	9.43224i	−0.0174096	−	0.952800i
$99$	0.988064			0.0993042
$100$	0.684895	−	0.612293i	0.0684895	−	0.0612293i
$101$	8.87953	+	15.3798i	0.883546	+	1.53035i	0.847371	+	0.531002i	$0.178184\pi$
$101$	8.87953	+	15.3798i	0.883546	+	1.53035i	0.0361755	+	0.999345i	$0.488482\pi$
$102$	−0.572510	+	5.44707i	−0.0566870	+	0.539340i
$103$	10.7497	+	2.28492i	1.05920	+	0.225139i	0.704400	−	0.709803i	$-0.251216\pi$
$103$	10.7497	+	2.28492i	1.05920	+	0.225139i	0.354798	+	0.934943i	$0.384550\pi$
$104$	6.45918	+	19.8793i	0.633375	+	1.94933i
$105$	5.79570	+	1.18740i	0.565602	+	0.115878i
$106$	1.29193	−	3.97614i	0.125483	−	0.386197i
$107$	−0.294449	+	0.510000i	−0.0284654	+	0.0493036i	−0.879907	−	0.475146i	$-0.842395\pi$
$107$	−0.294449	+	0.510000i	−0.0284654	+	0.0493036i	0.851442	+	0.524449i	$0.175729\pi$
$108$	0.179722	−	0.0382011i	0.0172938	−	0.00367590i
$109$	7.78478	+	3.46601i	0.745647	+	0.331983i	0.744147	−	0.668016i	$-0.232856\pi$
$109$	7.78478	+	3.46601i	0.745647	+	0.331983i	0.00149943	+	0.999999i	$0.499523\pi$
$110$	−2.87746	+	0.765541i	−0.274355	+	0.0729915i
$111$	−8.40678	−	6.10788i	−0.797936	−	0.579735i
$112$	6.05938	+	7.34450i	0.572558	+	0.693990i
$113$	8.10198	−	5.88643i	0.762170	−	0.553749i	−0.137405	−	0.990515i	$-0.543876\pi$
$113$	8.10198	−	5.88643i	0.762170	−	0.553749i	0.899575	+	0.436766i	$0.143876\pi$
$114$	8.99665	−	4.00557i	0.842614	−	0.375156i
$115$	4.65847	+	12.2004i	0.434405	+	1.13770i
$116$	−0.509133	−	0.226681i	−0.0472718	−	0.0210468i
$117$	−4.75244	−	5.27812i	−0.439363	−	0.487962i
$118$	−3.75746			−0.345903
$119$	−7.53337	+	7.67228i	−0.690583	+	0.703317i
$120$	−5.86878	+	2.97718i	−0.535743	+	0.271778i
$121$	9.80469	+	2.08405i	0.891335	+	0.189459i
$122$	−4.30688	+	4.78327i	−0.389927	+	0.433057i
$123$	−0.629264	+	5.98704i	−0.0567388	+	0.539834i
$124$	0.494886	−	0.857168i	0.0444421	−	0.0769759i
$125$	1.80777	−	11.0332i	0.161692	−	0.986841i
$126$	−3.19167	−	1.58968i	−0.284337	−	0.141620i
$127$	−0.223187	−	0.162155i	−0.0198046	−	0.0143889i	0.577839	−	0.816151i	$-0.303896\pi$
$127$	−0.223187	−	0.162155i	−0.0198046	−	0.0143889i	−0.597644	+	0.801762i	$0.703896\pi$
$128$	−9.30187	−	1.97717i	−0.822177	−	0.174759i
$129$	−2.57003	+	2.85430i	−0.226278	+	0.251307i
$130$	17.9296	+	11.6889i	1.57253	+	1.02518i
$131$	6.66990	+	7.40767i	0.582752	+	0.647211i	0.960363	−	0.278753i	$-0.0899210\pi$
$131$	6.66990	+	7.40767i	0.582752	+	0.647211i	−0.377611	+	0.925964i	$0.623254\pi$
$132$	−0.181544			−0.0158014
$133$	18.7197	+	4.83308i	1.62320	+	0.419081i
$134$	0.899778	−	0.653727i	0.0777290	−	0.0564734i
$135$	1.41029	−	1.73525i	0.121378	−	0.149347i
$136$	1.25021	−	11.8950i	0.107205	−	1.01999i
$137$	−8.30361	−	3.69701i	−0.709425	−	0.315857i	0.0201117	−	0.999798i	$-0.493598\pi$
$137$	−8.30361	−	3.69701i	−0.709425	−	0.315857i	−0.729537	+	0.683941i	$0.760264\pi$
$138$	−0.822748	−	7.82792i	−0.0700370	−	0.666357i
$139$	−8.33183	−	6.05343i	−0.706697	−	0.513445i	0.175409	−	0.984496i	$-0.443875\pi$
$139$	−8.33183	−	6.05343i	−0.706697	−	0.513445i	−0.882106	+	0.471050i	$0.843875\pi$
$140$	−1.06488	−	0.218169i	−0.0899992	−	0.0184387i
$141$	−8.80084	+	6.39419i	−0.741165	+	0.538488i
$142$	−9.75676	−	10.8360i	−0.818769	−	0.909335i
$143$	3.50882	+	6.07745i	0.293422	+	0.508222i
$144$	3.52012	−	0.748226i	0.293344	−	0.0623521i
$145$	−6.55449	+	1.74381i	−0.544321	+	0.144815i
$146$	1.26735	+	3.90050i	0.104887	+	0.322808i
$147$	−2.96351	−	6.34174i	−0.244426	−	0.523058i
$148$	1.54464	+	1.12225i	0.126968	+	0.0922480i
$149$	3.50097	−	6.06386i	0.286811	−	0.496771i	−0.686236	−	0.727379i	$-0.740738\pi$
$149$	3.50097	−	6.06386i	0.286811	−	0.496771i	0.973047	+	0.230608i	$0.0740716\pi$
$150$	−2.76261	+	6.14610i	−0.225566	+	0.501827i
$151$	−6.79942	−	11.7769i	−0.553329	−	0.958394i	−0.998031	−	0.0627156i	$-0.980024\pi$
$151$	−6.79942	−	11.7769i	−0.553329	−	0.958394i	0.444702	−	0.895678i	$-0.353309\pi$
$152$	−19.6463	+	8.74711i	−1.59353	+	0.709484i
$153$	1.25586	+	3.86514i	0.101530	+	0.312478i
$154$	2.75809	+	2.19205i	0.222254	+	0.176640i
$155$	−1.86320	−	11.9005i	−0.149656	−	0.955870i
$156$	0.873199	+	0.969786i	0.0699119	+	0.0776450i
$157$	−5.71974	−	9.90688i	−0.456485	−	0.790655i	0.542287	−	0.840193i	$-0.317558\pi$
$157$	−5.71974	−	9.90688i	−0.456485	−	0.790655i	−0.998772	+	0.0495378i	$0.984225\pi$
$158$	−10.7743	+	2.29014i	−0.857154	+	0.182194i
$159$	−0.324266	−	3.08518i	−0.0257159	−	0.244671i
$160$	2.06590	−	1.04801i	0.163323	−	0.0828526i
$161$	8.29717	−	13.0357i	0.653909	−	1.02736i
$162$	−1.09030	+	0.792151i	−0.0856623	+	0.0622373i
$163$	0.742357	+	7.06305i	0.0581459	+	0.553221i	0.984353	+	0.176207i	$0.0563827\pi$
$163$	0.742357	+	7.06305i	0.0581459	+	0.553221i	−0.926207	+	0.377015i	$0.876951\pi$
$164$	0.115619	−	1.10004i	0.00902834	−	0.0858989i
$165$	−1.71948	+	1.38736i	−0.133861	+	0.108006i
$166$	−0.687159	−	6.53788i	−0.0533339	−	0.507438i
$167$	−3.60831	+	11.1053i	−0.279220	+	0.859350i	0.708852	+	0.705357i	$0.249213\pi$
$167$	−3.60831	+	11.1053i	−0.279220	+	0.859350i	−0.988072	+	0.153993i	$0.950787\pi$
$168$	6.96977	+	3.47144i	0.537729	+	0.267828i
$169$	11.5709	−	35.6115i	0.890068	−	2.73935i
$170$	−6.65201	−	10.2831i	−0.510186	−	0.788679i
$171$	4.88959	−	5.43044i	0.373916	−	0.415276i
$172$	0.472209	−	0.524442i	0.0360056	−	0.0399883i
$173$	−11.3177	+	5.03895i	−0.860467	+	0.383104i	−0.789040	−	0.614341i	$-0.789422\pi$
$173$	−11.3177	+	5.03895i	−0.860467	+	0.383104i	−0.0714263	+	0.997446i	$0.522755\pi$
$174$	4.08784			0.309898
$175$	−11.7532	+	6.07146i	−0.888457	+	0.458960i
$176$	−3.55581			−0.268029
$177$	−2.54704	+	1.13401i	−0.191447	+	0.0852378i
$178$	−4.99491	+	5.54741i	−0.374384	+	0.415796i
$179$	−1.65839	+	1.84183i	−0.123954	+	0.137664i	−0.801927	−	0.597422i	$-0.796192\pi$
$179$	−1.65839	+	1.84183i	−0.123954	+	0.137664i	0.677973	+	0.735086i	$0.262858\pi$
$180$	−0.259122	+	0.318830i	−0.0193138	+	0.0237642i
$181$	1.91021	−	5.87903i	0.141985	−	0.436985i	−0.854626	−	0.519244i	$-0.826214\pi$
$181$	1.91021	−	5.87903i	0.141985	−	0.436985i	0.996611	+	0.0822592i	$0.0262135\pi$
$182$	−1.55636	−	25.2768i	−0.115365	−	1.87364i
$183$	−1.47586	+	4.54223i	−0.109099	+	0.335771i
$184$	1.79667	+	17.0941i	0.132452	+	1.26020i
$185$	23.2060	−	1.17488i	1.70614	−	0.0863786i
$186$	−0.758861	+	7.22008i	−0.0556424	+	0.529402i
$187$	−0.419739	−	3.99355i	−0.0306943	−	0.292037i
$188$	1.61704	−	1.17485i	0.117935	−	0.0856847i
$189$	−2.64328	−	0.114327i	−0.192270	−	0.00831604i
$190$	−10.0321	+	19.6030i	−0.727806	+	1.42215i
$191$	−1.30336	−	12.4006i	−0.0943077	−	0.897277i	−0.934733	−	0.355350i	$-0.884362\pi$
$191$	−1.30336	−	12.4006i	−0.0943077	−	0.897277i	0.840426	−	0.541927i	$-0.182305\pi$
$192$	−8.40592	+	1.78673i	−0.606645	+	0.128946i
$193$	6.92685	+	11.9976i	0.498605	+	0.863610i	0.999999	−	0.00160976i	$-0.000512404\pi$
$193$	6.92685	+	11.9976i	0.498605	+	0.863610i	−0.501393	+	0.865219i	$0.667179\pi$
$194$	5.45675	+	6.06033i	0.391771	+	0.435106i
$195$	15.6815	+	2.51225i	1.12298	+	0.179906i
$196$	0.544507	+	1.16521i	0.0388933	+	0.0832295i
$197$	2.51609	+	7.74372i	0.179264	+	0.551717i	0.999802	−	0.0198738i	$-0.00632645\pi$
$197$	2.51609	+	7.74372i	0.179264	+	0.551717i	−0.820539	+	0.571591i	$0.806326\pi$
$198$	1.21648	−	0.541612i	0.0864514	−	0.0384907i
$199$	2.14639	+	3.71765i	0.152153	+	0.263537i	0.932019	−	0.362410i	$-0.118046\pi$
$199$	2.14639	+	3.71765i	0.152153	+	0.263537i	−0.779866	+	0.625947i	$0.784713\pi$
$200$	6.03281	−	13.4215i	0.426584	−	0.949041i
$201$	0.412628	−	0.714693i	0.0291045	−	0.0504105i
$202$	19.3627	+	14.0679i	1.36236	+	0.989811i
$203$	6.28259	+	4.99321i	0.440951	+	0.350455i
$204$	−0.230748	−	0.710170i	−0.0161556	−	0.0497219i
$205$	−7.31143	−	11.3025i	−0.510653	−	0.789400i
$206$	14.4872	−	3.07935i	1.00937	−	0.214549i
$207$	−2.92020	−	5.05794i	−0.202968	−	0.351551i
$208$	17.1029	+	18.9947i	1.18587	+	1.31705i
$209$	−5.84123	+	4.24390i	−0.404046	+	0.293557i
$210$	7.78639	−	1.71504i	0.537312	−	0.118349i
$211$	−14.6410	−	10.6373i	−1.00793	−	0.732303i	−0.0441550	−	0.999025i	$-0.514060\pi$
$211$	−14.6410	−	10.6373i	−1.00793	−	0.732303i	−0.963774	+	0.266722i	$0.914060\pi$
$212$	0.0595797	+	0.566863i	0.00409195	+	0.0389323i
$213$	−9.88406	−	4.40067i	−0.677245	−	0.301529i
$214$	−0.0829590	+	0.789303i	−0.00567096	+	0.0539556i
$215$	0.464705	−	8.57581i	0.0316926	−	0.584865i
$216$	2.38093	−	1.72985i	0.162002	−	0.117701i
$217$	−9.98547	+	10.1696i	−0.677858	+	0.690357i
$218$	11.4843			0.777817
$219$	2.03627	+	2.26151i	0.137599	+	0.152819i
$220$	0.315932	−	0.254909i	0.0213001	−	0.0171860i
$221$	−19.3142	+	21.4505i	−1.29921	+	1.44292i
$222$	−13.6983	−	2.91166i	−0.919368	−	0.195418i
$223$	−15.0017	−	10.8994i	−1.00459	−	0.729878i	−0.0415228	−	0.999138i	$-0.513221\pi$
$223$	−15.0017	−	10.8994i	−1.00459	−	0.729878i	−0.963068	+	0.269260i	$0.913221\pi$
$224$	−2.45346	−	1.22200i	−0.163929	−	0.0816483i
$225$	−0.0177507	+	4.99997i	−0.00118338	+	0.333331i
$226$	6.74828	−	11.6884i	0.448889	−	0.777498i
$227$	0.544971	−	5.18505i	0.0361710	−	0.344144i	−0.961437	−	0.275024i	$-0.911314\pi$
$227$	0.544971	−	5.18505i	0.0361710	−	0.344144i	0.997608	−	0.0691200i	$-0.0220191\pi$
$228$	−0.898399	+	0.997773i	−0.0594979	+	0.0660792i
$229$	−3.69114	−	0.784575i	−0.243917	−	0.0518462i	0.0843307	−	0.996438i	$-0.473125\pi$
$229$	−3.69114	−	0.784575i	−0.243917	−	0.0518462i	−0.328248	+	0.944592i	$0.606458\pi$
$230$	12.4231	+	12.4673i	0.819155	+	0.822068i
$231$	2.53117	+	0.653503i	0.166539	+	0.0429973i
$232$	−8.92676			−0.586071
$233$	−6.91235	−	7.67695i	−0.452843	−	0.502933i	0.472884	−	0.881125i	$-0.343213\pi$
$233$	−6.91235	−	7.67695i	−0.452843	−	0.502933i	−0.925728	+	0.378191i	$0.876546\pi$
$234$	−8.74430	−	3.89321i	−0.571633	−	0.254507i
$235$	6.33745	−	23.4849i	0.413410	−	1.53198i
$236$	0.467986	−	0.208361i	0.0304633	−	0.0135631i
$237$	−6.61228	+	4.80410i	−0.429514	+	0.312060i
$238$	−5.06930	+	13.5754i	−0.328594	+	0.879960i
$239$	9.10789	+	6.61727i	0.589140	+	0.428036i	0.842008	−	0.539465i	$-0.181374\pi$
$239$	9.10789	+	6.61727i	0.589140	+	0.428036i	−0.252867	+	0.967501i	$0.581374\pi$
$240$	−5.07529	+	6.24476i	−0.327608	+	0.403098i
$241$	2.11771	+	0.942867i	0.136414	+	0.0607354i	0.473808	−	0.880628i	$-0.342879\pi$
$241$	2.11771	+	0.942867i	0.136414	+	0.0607354i	−0.337394	+	0.941363i	$0.609546\pi$
$242$	13.2137	−	2.80865i	0.849406	−	0.180547i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.271170	−	0.834576i	0.0173599	−	0.0534282i
$245$	14.0618	+	6.87507i	0.898374	+	0.439232i
$246$	2.50709	+	7.71603i	0.159846	+	0.491956i
$247$	50.7658	+	10.7906i	3.23015	+	0.686590i
$248$	1.65715	−	15.7668i	0.105229	−	1.00119i
$249$	−2.43895	−	4.22439i	−0.154562	−	0.267710i
$250$	−3.82223	−	14.5748i	−0.241739	−	0.921788i
$251$	−19.4064			−1.22492			−0.612459	−	0.790502i	$-0.709820\pi$
$251$	−19.4064			−1.22492			−0.612459	+	0.790502i	$0.709820\pi$
$252$	0.485669	+	0.0210061i	0.0305943	+	0.00132326i
$253$	1.78324	+	5.48826i	0.112112	+	0.345044i
$254$	−0.363667	−	0.0772999i	−0.0228185	−	0.00485023i
$255$	−7.61262	−	4.96293i	−0.476721	−	0.310791i
$256$	4.27581	−	0.908852i	0.267238	−	0.0568032i
$257$	−10.5179	+	18.2175i	−0.656088	+	1.13638i	0.325531	+	0.945531i	$0.394457\pi$
$257$	−10.5179	+	18.2175i	−0.656088	+	1.13638i	−0.981620	+	0.190847i	$0.938877\pi$
$258$	−1.59955	+	4.92292i	−0.0995838	+	0.306487i
$259$	−17.4963	−	21.2071i	−1.08717	−	1.31774i
$260$	−2.88127	−	0.461593i	−0.178689	−	0.0286268i
$261$	2.77099	−	1.23372i	0.171520	−	0.0763655i
$262$	12.2724	+	5.46400i	0.758189	+	0.337567i
$263$	26.6980	+	11.8867i	1.64627	+	0.732967i	0.999557	−	0.0297647i	$-0.00947579\pi$
$263$	26.6980	+	11.8867i	1.64627	+	0.732967i	0.646715	+	0.762732i	$0.276142\pi$
$264$	−2.65647	+	1.18274i	−0.163495	+	0.0727924i
$265$	4.89626	+	4.91367i	0.300775	+	0.301844i
$266$	25.6964	−	4.31090i	1.57555	−	0.264318i
$267$	−1.71163	+	5.26786i	−0.104750	+	0.322388i
$268$	−0.0758151	+	0.131316i	−0.00463114	+	0.00802138i
$269$	25.4342	−	5.40621i	1.55075	−	0.329623i	0.648631	−	0.761103i	$-0.275342\pi$
$269$	25.4342	−	5.40621i	1.55075	−	0.329623i	0.902122	+	0.431481i	$0.142009\pi$
$270$	0.785123	−	2.90945i	0.0477810	−	0.177063i
$271$	22.3650	+	4.75383i	1.35858	+	0.288775i	0.828887	−	0.559416i	$-0.188974\pi$
$271$	22.3650	+	4.75383i	1.35858	+	0.288775i	0.529691	+	0.848190i	$0.322308\pi$
$272$	−4.51955	−	13.9097i	−0.274038	−	0.843402i
$273$	−8.68362	−	16.6645i	−0.525556	−	1.00858i
$274$	−12.2497			−0.740033
$275$	1.04430	−	4.82869i	0.0629736	−	0.291181i
$276$	0.536550	+	0.929331i	0.0322965	+	0.0559392i
$277$	0.248937	−	2.36848i	0.0149572	−	0.142308i	−0.984495	−	0.175415i	$-0.943873\pi$
$277$	0.248937	−	2.36848i	0.0149572	−	0.142308i	0.999452	+	0.0331065i	$0.0105400\pi$
$278$	−13.5762	−	2.88570i	−0.814244	−	0.173073i
$279$	1.66464	+	5.12324i	0.0996594	+	0.306720i
$280$	−17.0034	+	3.74520i	−1.01615	+	0.223818i
$281$	−0.657786	+	2.02446i	−0.0392402	+	0.120769i	−0.968758	−	0.248009i	$-0.920224\pi$
$281$	−0.657786	+	2.02446i	−0.0392402	+	0.120769i	0.929517	+	0.368778i	$0.120224\pi$
$282$	−7.33037	+	12.6966i	−0.436517	+	0.756070i
$283$	−27.2754	+	5.79756i	−1.62135	+	0.344629i	−0.927017	−	0.375020i	$-0.877636\pi$
$283$	−27.2754	+	5.79756i	−1.62135	+	0.344629i	−0.694337	+	0.719650i	$0.744302\pi$
$284$	1.81607	+	0.808566i	0.107764	+	0.0479796i
$285$	−0.884122	+	16.3159i	−0.0523708	+	0.966468i
$286$	7.65134	+	5.55903i	0.452433	+	0.328712i
$287$	−5.57183	+	14.9211i	−0.328895	+	0.880765i
$288$	−0.838124	+	0.608933i	−0.0493869	+	0.0358817i
$289$	−0.441680	+	0.196649i	−0.0259812	+	0.0115676i
$290$	−7.11384	+	5.73980i	−0.417739	+	0.337053i
$291$	5.52794	+	2.46120i	0.324054	+	0.144278i
$292$	−0.374139	−	0.415523i	−0.0218948	−	0.0243167i
$293$	18.9881			1.10930			0.554649	−	0.832085i	$-0.312853\pi$
$293$	18.9881			1.10930			0.554649	+	0.832085i	$0.312853\pi$
$294$	−7.12484	−	6.18332i	−0.415529	−	0.360619i
$295$	2.84019	−	5.54980i	0.165362	−	0.323122i
$296$	29.9134	+	6.35829i	1.73868	+	0.369568i
$297$	0.661144	−	0.734275i	0.0383635	−	0.0426070i
$298$	0.986376	−	9.38474i	0.0571392	−	0.543643i
$299$	20.7405	−	35.9235i	1.19945	−	2.07751i
$300$	0.00326146	−	0.918680i	0.000188300	−	0.0530400i
$301$	−8.47159	+	5.61220i	−0.488294	+	0.323482i
$302$	−14.8269	−	10.7723i	−0.853189	−	0.619878i
$303$	17.3710	+	3.69232i	0.997937	+	0.212118i
$304$	−17.5965	+	19.5429i	−1.00923	+	1.12086i
$305$	−3.80946	−	9.97687i	−0.218129	−	0.571274i
$306$	3.66488	+	4.07026i	0.209507	+	0.232681i
$307$	25.5790			1.45987			0.729936	−	0.683515i	$-0.239550\pi$
$307$	25.5790			1.45987			0.729936	+	0.683515i	$0.239550\pi$
$308$	−0.465070	−	0.120073i	−0.0264998	−	0.00684178i
$309$	8.89097	−	6.45967i	0.505789	−	0.367478i
$310$	−8.81723	−	13.6302i	−0.500785	−	0.774146i
$311$	0.283001	−	2.69257i	0.0160475	−	0.152682i	−0.983564	−	0.180561i	$-0.942209\pi$
$311$	0.283001	−	2.69257i	0.0160475	−	0.152682i	0.999611	+	0.0278792i	$0.00887538\pi$
$312$	19.0952	+	8.50175i	1.08106	+	0.481317i
$313$	2.97289	+	28.2852i	0.168038	+	1.59877i	0.675674	+	0.737201i	$0.263853\pi$
$313$	2.97289	+	28.2852i	0.168038	+	1.59877i	−0.507636	+	0.861572i	$0.669481\pi$
$314$	−12.4725	−	9.06180i	−0.703864	−	0.511387i
$315$	4.76049	−	3.51252i	0.268223	−	0.197908i
$316$	1.21492	−	0.882692i	0.0683447	−	0.0496553i
$317$	4.39931	+	4.88593i	0.247090	+	0.274421i	0.853913	−	0.520416i	$-0.174223\pi$
$317$	4.39931	+	4.88593i	0.247090	+	0.274421i	−0.606823	+	0.794837i	$0.707556\pi$
$318$	−2.09038	−	3.62065i	−0.117223	−	0.203036i
$319$	−2.93153	+	0.623115i	−0.164134	+	0.0348878i
$320$	12.1196	−	14.9122i	0.677505	−	0.833619i
$321$	0.181979	+	0.560075i	0.0101571	+	0.0312603i
$322$	3.06969	−	20.5973i	0.171067	−	1.14784i
$323$	−24.0258	−	17.4558i	−1.33683	−	0.971266i
$324$	0.0918686	−	0.159121i	0.00510381	−	0.00884006i
$325$	−30.8172	+	17.6467i	−1.70943	+	0.978864i
$326$	4.78561	+	8.28892i	0.265051	+	0.459081i
$327$	7.78478	−	3.46601i	0.430499	−	0.191671i
$328$	−5.47482	−	16.8498i	−0.302297	−	0.930373i
$329$	−26.7746	+	10.5594i	−1.47613	+	0.582161i
$330$	−1.35649	+	2.65062i	−0.0746722	+	0.145912i
$331$	−2.23782	−	2.48535i	−0.123002	−	0.136607i	0.678498	−	0.734602i	$-0.262631\pi$
$331$	−2.23782	−	2.48535i	−0.123002	−	0.136607i	−0.801500	+	0.597995i	$0.795964\pi$
$332$	0.448126	+	0.776177i	0.0245941	+	0.0425982i
$333$	−10.1643	+	2.16048i	−0.556999	+	0.118394i
$334$	1.64492	+	15.6504i	0.0900063	+	0.856352i
$335$	0.285437	+	1.82312i	0.0155951	+	0.0996076i
$336$	9.51255	+	0.411435i	0.518952	+	0.0224456i
$337$	7.97445	−	5.79378i	0.434396	−	0.315607i	−0.349008	−	0.937120i	$-0.613481\pi$
$337$	7.97445	−	5.79378i	0.434396	−	0.315607i	0.783404	+	0.621512i	$0.213481\pi$
$338$	−5.27483	−	50.1866i	−0.286913	−	2.72979i
$339$	1.04681	−	9.95974i	0.0568549	−	0.540939i
$340$	1.39872	+	0.911874i	0.0758563	+	0.0494533i
$341$	−0.556363	−	5.29344i	−0.0301287	−	0.286656i
$342$	3.04322	−	9.36606i	0.164558	−	0.506459i
$343$	−3.39736	−	18.2060i	−0.183440	−	0.983031i
$344$	3.49300	−	10.7504i	0.188330	−	0.579620i
$345$	12.1838	+	4.70176i	0.655954	+	0.253134i
$346$	−11.1719	+	12.4077i	−0.600605	+	0.667040i
$347$	1.23342	−	1.36986i	0.0662136	−	0.0735377i	−0.709128	−	0.705080i	$-0.750911\pi$
$347$	1.23342	−	1.36986i	0.0662136	−	0.0735377i	0.775341	+	0.631542i	$0.217578\pi$
$348$	−0.509133	+	0.226681i	−0.0272924	+	0.0121514i
$349$	−11.2404			−0.601687			−0.300843	−	0.953674i	$-0.597268\pi$
$349$	−11.2404			−0.601687			−0.300843	+	0.953674i	$0.597268\pi$
$350$	−11.1421	+	13.9176i	−0.595571	+	0.743926i
$351$	−7.10241			−0.379098
$352$	0.935117	−	0.416341i	0.0498419	−	0.0221911i
$353$	3.77907	−	4.19708i	0.201140	−	0.223388i	−0.634133	−	0.773224i	$-0.718643\pi$
$353$	3.77907	−	4.19708i	0.201140	−	0.223388i	0.835273	+	0.549836i	$0.185310\pi$
$354$	−2.51423	+	2.79234i	−0.133630	+	0.148411i
$355$	23.3798	−	6.22013i	1.24087	−	0.330130i
$356$	0.314490	−	0.967901i	0.0166679	−	0.0512986i
$357$	0.660805	+	10.7321i	0.0349735	+	0.568005i
$358$	−1.03216	+	3.17666i	−0.0545513	+	0.167892i
$359$	−0.529665	−	5.03943i	−0.0279546	−	0.265971i	−0.999568	−	0.0293956i	$-0.990642\pi$
$359$	−0.529665	−	5.03943i	−0.0279546	−	0.265971i	0.971613	−	0.236575i	$-0.0760249\pi$
$360$	−1.71450	+	6.35347i	−0.0903622	+	0.334857i
$361$	−3.59554	+	34.2093i	−0.189239	+	1.80049i
$362$	−0.870810	−	8.28520i	−0.0457688	−	0.435461i
$363$	8.10937	−	5.89180i	0.425631	−	0.309239i
$364$	1.59550	+	3.06188i	0.0836271	+	0.160486i
$365$	−6.71904	−	1.07642i	−0.351690	−	0.0563424i
$366$	0.672801	+	6.40127i	0.0351679	+	0.334600i
$367$	−6.84632	+	1.45523i	−0.357375	+	0.0759624i	−0.383100	−	0.923707i	$-0.625144\pi$
$367$	−6.84632	+	1.45523i	−0.357375	+	0.0759624i	0.0257257	+	0.999669i	$0.491810\pi$
$368$	10.5091	+	18.2023i	0.547826	+	0.948862i
$369$	4.02818	+	4.47375i	0.209699	+	0.232894i
$370$	27.9267	−	14.1670i	1.45184	−	0.736505i
$371$	1.20984	−	8.11793i	0.0628120	−	0.421462i
$372$	−0.305856	−	0.941329i	−0.0158579	−	0.0488056i
$373$	−16.4016	+	7.30247i	−0.849243	+	0.378107i	−0.784751	−	0.619811i	$-0.787209\pi$
$373$	−16.4016	+	7.30247i	−0.849243	+	0.378107i	−0.0644919	+	0.997918i	$0.520543\pi$
$374$	−2.70585	−	4.68667i	−0.139916	−	0.242342i
$375$	−6.98965	−	8.72610i	−0.360944	−	0.450614i
$376$	16.0076	−	27.7260i	0.825529	−	1.42986i
$377$	17.4288	+	12.6628i	0.897629	+	0.652165i
$378$	−3.31701	+	1.30817i	−0.170608	+	0.0672849i
$379$	−0.0637096	−	0.196078i	−0.00327254	−	0.0100719i	0.949407	−	0.314049i	$-0.101685\pi$
$379$	−0.0637096	−	0.196078i	−0.00327254	−	0.0100719i	−0.952679	+	0.303977i	$0.901685\pi$
$380$	0.162446	−	2.99783i	0.00833330	−	0.153785i
$381$	−0.269845	+	0.0573574i	−0.0138246	+	0.00293851i
$382$	−8.40211	−	14.5529i	−0.429889	−	0.744590i
$383$	14.7048	+	16.3314i	0.751383	+	0.834495i	0.990646	−	0.136460i	$-0.0435725\pi$
$383$	14.7048	+	16.3314i	0.751383	+	0.834495i	−0.239263	+	0.970955i	$0.576906\pi$
$384$	−7.69349	+	5.58965i	−0.392607	+	0.285246i
$385$	−5.32246	+	2.41680i	−0.271258	+	0.123172i
$386$	15.1047	+	10.9742i	0.768810	+	0.558573i
$387$	0.401478	+	3.81980i	0.0204083	+	0.194172i
$388$	−1.01569	−	0.452214i	−0.0515638	−	0.0229577i
$389$	−2.50688	+	23.8514i	−0.127104	+	1.20931i	0.726045	+	0.687647i	$0.241356\pi$
$389$	−2.50688	+	23.8514i	−0.127104	+	1.20931i	−0.853149	+	0.521667i	$0.825310\pi$
$390$	20.6838	−	5.50286i	1.04736	−	0.278648i
$391$	−19.2026	+	13.9515i	−0.971117	+	0.705558i
$392$	15.5588	+	13.5028i	0.785837	+	0.681992i
$393$	9.96801			0.502819
$394$	7.34249	+	8.15466i	0.369909	+	0.410826i
$395$	4.76148	−	17.6447i	0.239576	−	0.887803i
$396$	−0.121477	+	0.134914i	−0.00610444	+	0.00677966i
$397$	22.5109	+	4.78485i	1.12979	+	0.240145i	0.734631	−	0.678467i	$-0.237356\pi$
$397$	22.5109	+	4.78485i	1.12979	+	0.240145i	0.395161	+	0.918612i	$0.370689\pi$
$398$	4.68042	+	3.40052i	0.234608	+	0.170453i
$399$	16.1176	−	10.6775i	0.806888	−	0.534541i
$400$	0.0638805	−	17.9937i	0.00319403	−	0.899686i
$401$	−6.34458	+	10.9891i	−0.316833	+	0.548771i	−0.979826	−	0.199855i	$-0.935953\pi$
$401$	−6.34458	+	10.9891i	−0.316833	+	0.548771i	0.662992	+	0.748626i	$0.269286\pi$
$402$	0.116255	−	1.10609i	0.00579828	−	0.0551670i
$403$	−25.6009	+	28.4326i	−1.27527	+	1.41633i
$404$	−3.19170	−	0.678416i	−0.158793	−	0.0337524i
$405$	−0.345877	−	2.20916i	−0.0171868	−	0.109774i
$406$	10.4720	+	2.70368i	0.519717	+	0.134182i
$407$	10.2673			0.508932
$408$	−8.00313	−	8.88838i	−0.396214	−	0.440040i
$409$	24.6014	+	10.9532i	1.21646	+	0.541603i	0.911712	−	0.410830i	$-0.134761\pi$
$409$	24.6014	+	10.9532i	1.21646	+	0.541603i	0.304748	+	0.952433i	$0.401428\pi$
$410$	−15.1972	−	9.90754i	−0.750534	−	0.489299i
$411$	−8.30361	+	3.69701i	−0.409587	+	0.182360i
$412$	−1.63360	+	1.18688i	−0.0804818	+	0.0584734i
$413$	−7.27491	+	1.22046i	−0.357975	+	0.0600547i
$414$	−6.36781	−	4.62648i	−0.312961	−	0.227379i
$415$	10.1759	+	3.92690i	0.499516	+	0.192764i
$416$	−6.72181	−	2.99274i	−0.329564	−	0.146731i
$417$	−10.0737	+	2.14122i	−0.493309	+	0.104856i
$418$	−4.86526	+	8.42688i	−0.237968	+	0.412172i
$419$	7.63928	−	23.5113i	0.373203	−	1.14860i	−0.571479	−	0.820616i	$-0.693630\pi$
$419$	7.63928	−	23.5113i	0.373203	−	1.14860i	0.944683	−	0.327986i	$-0.106370\pi$
$420$	−0.874678	+	0.645380i	−0.0426799	+	0.0314913i
$421$	3.01291	+	9.27278i	0.146840	+	0.451927i	0.997243	−	0.0742046i	$-0.0236418\pi$
$421$	3.01291	+	9.27278i	0.146840	+	0.451927i	−0.850403	+	0.526132i	$0.823642\pi$
$422$	−23.8565	−	5.07086i	−1.16132	−	0.246846i
$423$	−1.13711	+	10.8188i	−0.0552880	+	0.526030i
$424$	4.56485	+	7.90655i	0.221689	+	0.383976i
$425$	20.2164	−	2.05229i	0.980637	−	0.0995506i
$426$	−14.5812			−0.706464
$427$	−6.78499	+	10.6599i	−0.328349	+	0.515869i
$428$	−0.0334364	−	0.102907i	−0.00161621	−	0.00497418i
$429$	6.86428	+	1.45905i	0.331411	+	0.0704435i
$430$	−4.12873	−	10.8130i	−0.199105	−	0.521451i
$431$	−14.0382	+	2.98391i	−0.676195	+	0.143730i	−0.533194	−	0.845993i	$-0.679008\pi$
$431$	−14.0382	+	2.98391i	−0.676195	+	0.143730i	−0.143001	+	0.989723i	$0.545675\pi$
$432$	1.79938	−	3.11662i	0.0865729	−	0.149949i
$433$	−10.5432	+	32.4486i	−0.506673	+	1.55938i	0.291266	+	0.956642i	$0.405923\pi$
$433$	−10.5432	+	32.4486i	−0.506673	+	1.55938i	−0.797939	+	0.602738i	$0.794077\pi$
$434$	−6.71935	+	17.9941i	−0.322539	+	0.863745i
$435$	−3.08991	+	6.03777i	−0.148150	+	0.289489i
$436$	−1.43035	+	0.636834i	−0.0685015	+	0.0304988i
$437$	38.9883	+	17.3587i	1.86506	+	0.830380i
$438$	3.74666	+	1.66812i	0.179022	+	0.0797059i
$439$	−21.3850	+	9.52121i	−1.02065	+	0.454422i	−0.847682	−	0.530505i	$-0.822002\pi$
$439$	−21.3850	+	9.52121i	−1.02065	+	0.454422i	−0.172968	+	0.984927i	$0.555336\pi$
$440$	2.96221	−	5.78825i	0.141218	−	0.275944i
$441$	−6.69580	−	2.04113i	−0.318848	−	0.0971969i
$442$	−12.0209	+	36.9965i	−0.571775	+	1.75974i
$443$	0.00547773	−	0.00948770i	0.000260255	−	0.000450774i	−0.865895	−	0.500225i	$-0.833250\pi$
$443$	0.00547773	−	0.00948770i	0.000260255	−	0.000450774i	0.866156	+	0.499775i	$0.166584\pi$
$444$	1.86756	−	0.396961i	0.0886302	−	0.0188389i
$445$	−4.41802	−	11.5707i	−0.209434	−	0.548504i
$446$	−24.4443	−	5.19580i	−1.15747	−	0.246028i
$447$	−2.16372	−	6.65924i	−0.102340	−	0.314971i
$448$	−22.7156	−	0.982490i	−1.07321	−	0.0464183i
$449$	−1.01468			−0.0478857			−0.0239428	−	0.999713i	$-0.507622\pi$
$449$	−1.01468			−0.0478857			−0.0239428	+	0.999713i	$0.507622\pi$
$450$	2.71890	+	6.16556i	0.128170	+	0.290647i
$451$	−2.97408	−	5.15127i	−0.140044	−	0.242564i
$452$	−0.192338	+	1.82997i	−0.00904682	+	0.0860747i
$453$	−13.3017	−	2.82736i	−0.624967	−	0.132841i
$454$	−2.17125	−	6.68243i	−0.101902	−	0.313622i
$455$	38.5105	+	16.8074i	1.80540	+	0.787945i
$456$	−6.64559	+	20.4530i	−0.311208	+	0.957800i
$457$	−5.81081	+	10.0646i	−0.271818	+	0.470803i	−0.969327	−	0.245773i	$-0.920958\pi$
$457$	−5.81081	+	10.0646i	−0.271818	+	0.470803i	0.697509	+	0.716576i	$0.254292\pi$
$458$	−4.97450	+	1.05736i	−0.232443	+	0.0494073i
$459$	3.71270	+	1.65300i	0.173294	+	0.0771554i
$460$	−2.23862	−	0.863887i	−0.104376	−	0.0402789i
$461$	15.3315	+	11.1390i	0.714059	+	0.518794i	0.884481	−	0.466577i	$-0.154513\pi$
$461$	15.3315	+	11.1390i	0.714059	+	0.518794i	−0.170422	+	0.985371i	$0.554513\pi$
$462$	3.47453	−	0.582896i	0.161650	−	0.0271188i
$463$	17.5576	−	12.7564i	0.815972	−	0.592838i	−0.0995838	−	0.995029i	$-0.531751\pi$
$463$	17.5576	−	12.7564i	0.815972	−	0.592838i	0.915556	+	0.402191i	$0.131751\pi$
$464$	−9.97213	+	4.43988i	−0.462945	+	0.206116i
$465$	−10.0905	−	6.57835i	−0.467936	−	0.305064i
$466$	−12.7185	−	5.66262i	−0.589171	−	0.262316i
$467$	−26.9450	−	29.9255i	−1.24687	−	1.38479i	−0.893352	−	0.449358i	$-0.851653\pi$
$467$	−26.9450	−	29.9255i	−1.24687	−	1.38479i	−0.353516	−	0.935429i	$-0.615014\pi$
$468$	1.30498			0.0603225
$469$	1.52974	−	1.55795i	0.0706370	−	0.0719395i
$470$	−5.07082	−	32.3879i	−0.233899	−	1.49394i
$471$	−11.1895	−	2.37840i	−0.515585	−	0.109591i
$472$	5.49043	−	6.09774i	0.252717	−	0.280671i
$473$	0.396686	−	3.77421i	0.0182396	−	0.173538i
$474$	−5.50748	+	9.53924i	−0.252967	+	0.438152i
$475$	−21.3708	−	29.6350i	−0.980558	−	1.35975i
$476$	−0.121415	−	1.97189i	−0.00556502	−	0.0903816i
$477$	−2.50971	−	1.82341i	−0.114912	−	0.0834884i
$478$	14.8407	+	3.15448i	0.678797	+	0.144283i
$479$	−15.6797	+	17.4140i	−0.716423	+	0.795668i	−0.985899	−	0.167339i	$-0.946483\pi$
$479$	−15.6797	+	17.4140i	−0.716423	+	0.795668i	0.269477	+	0.963007i	$0.413149\pi$
$480$	0.603530	−	2.23652i	0.0275472	−	0.102083i
$481$	−49.3842	−	54.8468i	−2.25173	−	2.50080i
$482$	3.12411			0.142299
$483$	−4.13552	−	14.8886i	−0.188173	−	0.677454i
$484$	−1.48999	+	1.08254i	−0.0677269	+	0.0492065i
$485$	−13.0758	+	3.47878i	−0.593741	+	0.157963i
$486$	−0.140872	+	1.34031i	−0.00639007	+	0.0607975i
$487$	7.62472	+	3.39475i	0.345509	+	0.153831i	0.572153	−	0.820147i	$-0.306109\pi$
$487$	7.62472	+	3.39475i	0.345509	+	0.153831i	−0.226643	+	0.973978i	$0.572775\pi$
$488$	−1.46922	−	13.9787i	−0.0665085	−	0.632786i
$489$	5.74561	+	4.17443i	0.259825	+	0.188774i
$490$	21.0811	+	0.756396i	0.952346	+	0.0341705i
$491$	11.0575	−	8.03375i	0.499018	−	0.362558i	−0.309624	−	0.950859i	$-0.600203\pi$
$491$	11.0575	−	8.03375i	0.499018	−	0.362558i	0.808642	+	0.588301i	$0.200203\pi$
$492$	−0.740127	−	0.821994i	−0.0333675	−	0.0370583i
$493$	−6.16359	−	10.6756i	−0.277594	−	0.480807i
$494$	68.4165	−	14.5424i	3.07820	−	0.654292i
$495$	−0.119546	+	2.20614i	−0.00537320	+	0.0991587i
$496$	−5.99065	−	18.4373i	−0.268988	−	0.827861i
$497$	−22.4099	−	17.8107i	−1.00522	−	0.798919i
$498$	−5.31839	−	3.86404i	−0.238323	−	0.173152i
$499$	−8.63647	+	14.9588i	−0.386622	+	0.669648i	−0.991993	−	0.126295i	$-0.959691\pi$
$499$	−8.63647	+	14.9588i	−0.386622	+	0.669648i	0.605371	+	0.795943i	$0.293025\pi$
$500$	1.28426	+	1.60331i	0.0574338	+	0.0717022i
$501$	5.83838	+	10.1124i	0.260839	+	0.451787i
$502$	−23.8926	+	10.6377i	−1.06638	+	0.474783i
$503$	−7.49161	−	23.0568i	−0.334035	−	1.02805i	−0.967196	−	0.254033i	$-0.918243\pi$
$503$	−7.49161	−	23.0568i	−0.334035	−	1.02805i	0.633161	−	0.774020i	$-0.281757\pi$
$504$	7.24347	−	2.85670i	0.322650	−	0.127247i
$505$	−35.4142	+	17.9653i	−1.57591	+	0.799447i
$506$	5.20389	+	5.77951i	0.231341	+	0.256931i
$507$	−18.7221	−	32.4276i	−0.831477	−	1.44016i
$508$	0.0495806	−	0.0105387i	0.00219978	−	0.000467579i
$509$	0.352952	+	3.35811i	0.0156443	+	0.148846i	0.999556	−	0.0298125i	$-0.00949102\pi$
$509$	0.352952	+	3.35811i	0.0156443	+	0.148846i	−0.983911	+	0.178658i	$0.942824\pi$
$510$	−12.0929	−	1.93734i	−0.535483	−	0.0857868i
$511$	3.72066	+	7.14020i	0.164592	+	0.315864i
$512$	20.1531	−	14.6421i	0.890648	−	0.647094i
$513$	−0.763829	−	7.26734i	−0.0337239	−	0.320861i
$514$	−2.96335	+	28.1944i	−0.130708	+	1.24360i
$515$	−6.40235	+	23.7254i	−0.282121	+	1.04546i
$516$	−0.0737663	−	0.701840i	−0.00324738	−	0.0308968i
$517$	3.32150	−	10.2225i	0.146079	−	0.449586i
$518$	−33.1658	−	16.5189i	−1.45722	−	0.725800i
$519$	−3.82833	+	11.7824i	−0.168045	+	0.517189i
$520$	−45.1679	+	12.0168i	−1.98074	+	0.526972i
$521$	14.0687	−	15.6249i	0.616360	−	0.684537i	−0.351453	−	0.936205i	$-0.614312\pi$
$521$	14.0687	−	15.6249i	0.616360	−	0.684537i	0.967814	+	0.251668i	$0.0809791\pi$
$522$	2.73530	−	3.03785i	0.119721	−	0.132963i
$523$	18.5137	−	8.24281i	0.809545	−	0.360433i	0.0401404	−	0.999194i	$-0.487219\pi$
$523$	18.5137	−	8.24281i	0.809545	−	0.360433i	0.769405	+	0.638761i	$0.220553\pi$
$524$	−1.83149			−0.0800092
$525$	−3.35244	+	12.7969i	−0.146312	+	0.558503i
$526$	39.3857			1.71730
$527$	19.9999	−	8.90453i	0.871209	−	0.387887i
$528$	−2.37930	+	2.64248i	−0.103546	+	0.114999i
$529$	7.43426	−	8.25658i	0.323228	−	0.358982i
$530$	8.72159	+	3.36568i	0.378842	+	0.146196i
$531$	−0.861565	+	2.65162i	−0.0373887	+	0.115071i
$532$	−2.96140	+	1.96185i	−0.128393	+	0.0850568i
$533$	−13.2125	+	40.6640i	−0.572298	+	1.76135i
$534$	0.780282	+	7.42389i	0.0337661	+	0.321263i
$535$	−1.10310	−	0.719148i	−0.0476911	−	0.0310915i
$536$	−0.253871	+	2.41542i	−0.0109656	+	0.104330i
$537$	0.259065	+	2.46484i	0.0111795	+	0.106366i
$538$	28.3505	−	20.5979i	1.22228	−	0.888037i
$539$	6.05200	+	3.34822i	0.260678	+	0.144218i
$540$	0.0635505	+	0.405904i	0.00273478	+	0.0174673i
$541$	3.61464	+	34.3910i	0.155406	+	1.47859i	0.742925	+	0.669375i	$0.233438\pi$
$541$	3.61464	+	34.3910i	0.155406	+	1.47859i	−0.587519	+	0.809210i	$0.699895\pi$
$542$	30.1411	−	6.40668i	1.29467	−	0.275191i
$543$	−3.09079	−	5.35341i	−0.132638	−	0.229737i
$544$	2.81722	+	3.12884i	0.120787	+	0.134148i
$545$	−8.68076	+	16.9624i	−0.371843	+	0.726591i
$546$	−19.8257	−	15.7569i	−0.848463	−	0.674332i
$547$	3.15876	+	9.72167i	0.135059	+	0.415669i	0.995599	−	0.0937138i	$-0.0298739\pi$
$547$	3.15876	+	9.72167i	0.135059	+	0.415669i	−0.860540	+	0.509382i	$0.829874\pi$
$548$	1.52568	−	0.679277i	0.0651739	−	0.0290173i
$549$	2.38799	+	4.13612i	0.101917	+	0.176525i
$550$	−1.36115	−	6.51739i	−0.0580396	−	0.277903i
$551$	−11.0824	+	19.1954i	−0.472128	+	0.817750i
$552$	13.9056	+	10.1030i	0.591862	+	0.430013i
$553$	−20.1164	+	7.93356i	−0.855437	+	0.337369i
$554$	−0.991807	−	3.05247i	−0.0421379	−	0.129687i
$555$	14.6548	−	18.0316i	0.622060	−	0.765399i
$556$	1.85091	−	0.393422i	0.0784959	−	0.0166848i
$557$	−20.7997	−	36.0261i	−0.881311	−	1.52647i	−0.849885	−	0.526969i	$-0.823329\pi$
$557$	−20.7997	−	36.0261i	−0.881311	−	1.52647i	−0.0314259	−	0.999506i	$-0.510005\pi$
$558$	4.85779	+	5.39512i	0.205647	+	0.228394i
$559$	−22.0694	+	16.0343i	−0.933435	+	0.678180i
$560$	−17.1319	+	12.6407i	−0.723954	+	0.534168i
$561$	−3.24864	−	2.36028i	−0.137158	−	0.0996510i
$562$	0.299865	+	2.85303i	0.0126491	+	0.120348i
$563$	−32.3294	−	14.3940i	−1.36252	−	0.606634i	−0.410274	−	0.911962i	$-0.634567\pi$
$563$	−32.3294	−	14.3940i	−1.36252	−	0.606634i	−0.952247	+	0.305329i	$0.901234\pi$
$564$	0.208929	−	1.98782i	0.00879749	−	0.0837025i
$565$	12.1629	+	18.8022i	0.511698	+	0.791016i
$566$	−30.4028	+	22.0889i	−1.27793	+	0.928467i
$567$	−1.85366	+	1.88784i	−0.0778464	+	0.0792818i
$568$	31.8416			1.33604
$569$	−6.50686	−	7.22660i	−0.272782	−	0.302955i	0.591152	−	0.806560i	$-0.298673\pi$
$569$	−6.50686	−	7.22660i	−0.272782	−	0.302955i	−0.863934	+	0.503605i	$0.832007\pi$
$570$	7.85509	+	20.5723i	0.329014	+	0.861678i
$571$	−12.9796	+	14.4153i	−0.543180	+	0.603263i	−0.950768	−	0.309903i	$-0.899703\pi$
$571$	−12.9796	+	14.4153i	−0.543180	+	0.603263i	0.407588	+	0.913166i	$0.366370\pi$
$572$	−1.26122	−	0.268081i	−0.0527344	−	0.0112090i
$573$	−10.0876	−	7.32905i	−0.421414	−	0.306176i
$574$	1.31917	+	21.4247i	0.0550612	+	0.894250i
$575$	−27.8046	+	8.92527i	−1.15953	+	0.372209i
$576$	−4.29685	+	7.44237i	−0.179036	+	0.310099i
$577$	3.15055	−	29.9755i	0.131159	−	1.24790i	−0.708864	−	0.705345i	$-0.750792\pi$
$577$	3.15055	−	29.9755i	0.131159	−	1.24790i	0.840023	−	0.542551i	$-0.182541\pi$
$578$	−0.435991	+	0.484217i	−0.0181348	+	0.0201408i
$579$	13.5510	+	2.88034i	0.563158	+	0.119703i
$580$	0.567731	−	1.10936i	0.0235737	−	0.0460638i
$581$	−3.45398	−	12.4349i	−0.143295	−	0.515888i
$582$	8.15498			0.338035
$583$	2.05099	+	2.27785i	0.0849431	+	0.0943389i
$584$	−8.18172	−	3.64274i	−0.338562	−	0.150738i
$585$	12.3599	−	9.97260i	0.511020	−	0.412316i
$586$	23.3777	−	10.4084i	0.965723	−	0.429968i
$587$	−29.2894	+	21.2800i	−1.20890	+	0.878319i	−0.995131	−	0.0985644i	$-0.968575\pi$
$587$	−29.2894	+	21.2800i	−1.20890	+	0.878319i	−0.213772	+	0.976884i	$0.568575\pi$
$588$	1.23027	+	0.375032i	0.0507354	+	0.0154661i
$589$	−31.8462	−	23.1376i	−1.31220	−	0.953368i
$590$	0.454617	−	8.38964i	0.0187163	−	0.345396i
$591$	7.43829	+	3.31174i	0.305971	+	0.136227i
$592$	36.5788	−	7.77507i	1.50338	−	0.319554i
$593$	1.28766	−	2.23030i	0.0528779	−	0.0915873i	−0.838375	−	0.545094i	$-0.816494\pi$
$593$	1.28766	−	2.23030i	0.0528779	−	0.0915873i	0.891253	+	0.453507i	$0.149827\pi$
$594$	0.411488	−	1.26643i	0.0168835	−	0.0519622i
$595$	−16.2191	−	17.7487i	−0.664920	−	0.727627i
$596$	0.397556	+	1.22355i	0.0162845	+	0.0501186i
$597$	4.19897	+	0.892518i	0.171852	+	0.0365283i
$598$	5.84349	−	55.5971i	0.238958	−	2.27353i
$599$	3.67827	+	6.37096i	0.150290	+	0.260310i	0.931334	−	0.364166i	$-0.118646\pi$
$599$	3.67827	+	6.37096i	0.150290	+	0.260310i	−0.781044	+	0.624476i	$0.785313\pi$
$600$	−5.93736	−	13.4640i	−0.242392	−	0.549664i
$601$	31.9828			1.30461			0.652303	−	0.757958i	$-0.273803\pi$
$601$	31.9828			1.30461			0.652303	+	0.757958i	$0.273803\pi$
$602$	−7.35365	+	11.5533i	−0.299712	+	0.470879i
$603$	−0.255018	−	0.784865i	−0.0103851	−	0.0319622i
$604$	2.44401	+	0.519491i	0.0994454	+	0.0211378i
$605$	−5.83952	+	21.6397i	−0.237410	+	0.879778i
$606$	23.4107	−	4.97609i	0.950993	−	0.202140i
$607$	−3.41087	+	5.90780i	−0.138443	+	0.239790i	−0.926907	−	0.375290i	$-0.877543\pi$
$607$	−3.41087	+	5.90780i	−0.138443	+	0.239790i	0.788464	+	0.615080i	$0.210876\pi$
$608$	2.33935	−	7.19977i	0.0948730	−	0.291989i
$609$	7.91455	−	1.32776i	0.320714	−	0.0538037i
$610$	−10.1590	−	10.1951i	−0.411325	−	0.412787i
$611$	−70.5833	+	31.4257i	−2.85550	+	1.27135i
$612$	−0.682160	−	0.303717i	−0.0275747	−	0.0122770i
$613$	4.74265	+	2.11157i	0.191554	+	0.0852853i	0.500272	−	0.865868i	$-0.333233\pi$
$613$	4.74265	+	2.11157i	0.191554	+	0.0852853i	−0.308718	+	0.951154i	$0.599900\pi$
$614$	31.4923	−	14.0213i	1.27092	−	0.565852i
$615$	−13.2917	−	2.12939i	−0.535973	−	0.0858653i
$616$	−7.58747	+	1.27289i	−0.305708	+	0.0512863i
$617$	7.37782	−	22.7066i	0.297020	−	0.914133i	−0.685516	−	0.728058i	$-0.740423\pi$
$617$	7.37782	−	22.7066i	0.297020	−	0.914133i	0.982535	−	0.186075i	$-0.0595768\pi$
$618$	7.40544	−	12.8266i	0.297890	−	0.515961i
$619$	3.18637	−	0.677284i	0.128071	−	0.0272224i	−0.143430	−	0.989660i	$-0.545813\pi$
$619$	3.18637	−	0.677284i	0.128071	−	0.0272224i	0.271501	+	0.962438i	$0.412480\pi$
$620$	1.85400	+	1.20869i	0.0744585	+	0.0485420i
$621$	−5.71278	−	1.21429i	−0.229246	−	0.0487277i
$622$	−1.12752	−	3.47015i	−0.0452095	−	0.139140i
$623$	−7.86891	+	12.3629i	−0.315261	+	0.495307i
$624$	25.5599			1.02321
$625$	24.4162	+	5.37129i	0.976647	+	0.214852i
$626$	19.1648	+	33.1944i	0.765979	+	1.32671i
$627$	−0.754712	+	7.18060i	−0.0301403	+	0.286766i
$628$	2.05593	+	0.437001i	0.0820404	+	0.0174382i
$629$	13.0501	+	40.1641i	0.520341	+	1.60145i
$630$	3.93559	−	6.93400i	0.156798	−	0.276257i
$631$	−15.0151	+	46.2118i	−0.597743	+	1.83966i	−0.0571732	+	0.998364i	$0.518209\pi$
$631$	−15.0151	+	46.2118i	−0.597743	+	1.83966i	−0.540570	+	0.841299i	$0.681791\pi$
$632$	12.0269	−	20.8312i	0.478404	−	0.828620i
$633$	−17.7018	+	3.76264i	−0.703584	+	0.149551i
$634$	8.09456	+	3.60393i	0.321476	+	0.143130i
$635$	0.389061	−	0.478710i	0.0154394	−	0.0189970i
$636$	0.461128	+	0.335029i	0.0182849	+	0.0132848i
$637$	−11.2234	−	48.4334i	−0.444688	−	1.91900i
$638$	−3.26766	+	2.37409i	−0.129368	+	0.0939912i
$639$	−9.88406	+	4.40067i	−0.391007	+	0.174088i
$640$	5.54005	−	20.5299i	0.218990	−	0.811517i
$641$	−22.0578	−	9.82076i	−0.871230	−	0.387897i	−0.0780976	−	0.996946i	$-0.524885\pi$
$641$	−22.0578	−	9.82076i	−0.871230	−	0.387897i	−0.793133	+	0.609049i	$0.791551\pi$
$642$	0.531056	+	0.589797i	0.0209591	+	0.0232774i
$643$	30.1335			1.18835			0.594174	−	0.804336i	$-0.297479\pi$
$643$	30.1335			1.18835			0.594174	+	0.804336i	$0.297479\pi$
$644$	0.759848	+	2.73559i	0.0299422	+	0.107797i
$645$	−6.06212	−	6.08368i	−0.238696	−	0.239545i
$646$	−39.1484	−	8.32126i	−1.54027	−	0.327396i
$647$	16.9136	−	18.7845i	0.664943	−	0.738494i	−0.312448	−	0.949935i	$-0.601149\pi$
$647$	16.9136	−	18.7845i	0.664943	−	0.738494i	0.977391	+	0.211441i	$0.0678155\pi$
$648$	0.307627	−	2.92687i	0.0120847	−	0.114978i
$649$	1.37740	−	2.38573i	0.0540678	−	0.0936481i
$650$	−28.2682	+	38.6187i	−1.10877	+	1.51475i
$651$	0.875896	+	14.2254i	0.0343291	+	0.557539i
$652$	−1.05568	−	0.766997i	−0.0413437	−	0.0300379i
$653$	4.97862	+	1.05824i	0.194829	+	0.0414121i	0.304292	−	0.952579i	$-0.401580\pi$
$653$	4.97862	+	1.05824i	0.194829	+	0.0414121i	−0.109464	+	0.993991i	$0.534913\pi$
$654$	7.68451	−	8.53452i	0.300488	−	0.333726i
$655$	−17.3468	+	13.9962i	−0.677795	+	0.546878i
$656$	−14.4965	−	16.1000i	−0.565993	−	0.628598i
$657$	3.04316			0.118725
$658$	−27.1760	+	27.6771i	−1.05943	+	1.07897i
$659$	6.25225	−	4.54252i	0.243553	−	0.176952i	−0.459312	−	0.888275i	$-0.651904\pi$
$659$	6.25225	−	4.54252i	0.243553	−	0.176952i	0.702865	+	0.711324i	$0.251904\pi$
$660$	0.0219651	−	0.405350i	0.000854990	−	0.0157782i
$661$	−0.890275	+	8.47040i	−0.0346277	+	0.329460i	0.963470	+	0.267815i	$0.0863015\pi$
$661$	−0.890275	+	8.47040i	−0.0346277	+	0.329460i	−0.998098	+	0.0616456i	$0.980365\pi$
$662$	−4.11751	−	1.83323i	−0.160031	−	0.0712506i
$663$	3.01717	+	28.7064i	0.117177	+	1.11487i
$664$	11.6140	+	8.43804i	0.450709	+	0.327459i
$665$	−13.0562	+	41.2123i	−0.506296	+	1.59815i
$666$	−11.3297	+	8.23152i	−0.439018	+	0.318965i
$667$	11.8538	+	13.1650i	0.458981	+	0.509750i
$668$	−1.07273	−	1.85802i	−0.0415050	−	0.0718888i
$669$	−18.1379	+	3.85534i	−0.701254	+	0.149056i
$670$	1.35077	+	2.08811i	0.0521849	+	0.0806708i
$671$	−1.45824	−	4.48801i	−0.0562949	−	0.173258i
$672$	−2.54981	+	1.00560i	−0.0983610	+	0.0387919i
$673$	3.12793	+	2.27258i	0.120573	+	0.0876014i	0.646437	−	0.762967i	$-0.276258\pi$
$673$	3.12793	+	2.27258i	0.120573	+	0.0876014i	−0.525865	+	0.850568i	$0.676258\pi$
$674$	6.64205	−	11.5044i	0.255842	−	0.443132i
$675$	3.70382	+	3.35882i	0.142560	+	0.129281i
$676$	3.43994	+	5.95815i	0.132305	+	0.229160i
$677$	−8.54988	+	3.80665i	−0.328599	+	0.146302i	−0.564404	−	0.825499i	$-0.690894\pi$
$677$	−8.54988	+	3.80665i	−0.328599	+	0.146302i	0.235805	+	0.971800i	$0.424227\pi$
$678$	−4.17066	−	12.8360i	−0.160173	−	0.492963i
$679$	12.5334	+	9.96114i	0.480987	+	0.382273i
$680$	26.4077	+	4.23064i	1.01269	+	0.162238i
$681$	−3.48859	−	3.87447i	−0.133683	−	0.148470i
$682$	−3.58660	−	6.21217i	−0.137338	−	0.237876i
$683$	−35.9362	+	7.63847i	−1.37506	+	0.292278i	−0.835417	−	0.549617i	$-0.814774\pi$
$683$	−35.9362	+	7.63847i	−1.37506	+	0.292278i	−0.539642	+	0.841895i	$0.681440\pi$
$684$	0.140344	+	1.33528i	0.00536618	+	0.0510558i
$685$	9.25930	−	18.0929i	0.353780	−	0.691296i
$686$	−14.1624	−	20.5525i	−0.540724	−	0.784697i
$687$	−3.05291	+	2.21807i	−0.116476	+	0.0846245i
$688$	−1.44482	−	13.7466i	−0.0550834	−	0.524083i
$689$	2.30307	−	21.9122i	0.0877399	−	0.834789i
$690$	17.5777	−	0.889922i	0.669171	−	0.0338788i
$691$	−1.06425	−	10.1257i	−0.0404862	−	0.385200i	−0.995937	−	0.0900505i	$-0.971297\pi$
$691$	−1.06425	−	10.1257i	−0.0404862	−	0.385200i	0.955451	−	0.295150i	$-0.0953695\pi$
$692$	0.703406	−	2.16486i	0.0267395	−	0.0822957i
$693$	2.17933	−	1.44375i	0.0827860	−	0.0548435i
$694$	0.767667	−	2.36264i	0.0291402	−	0.0896844i
$695$	14.5241	−	17.8709i	0.550932	−	0.677880i
$696$	−5.97317	+	6.63388i	−0.226412	+	0.251456i
$697$	16.3707	−	18.1815i	0.620086	−	0.688675i
$698$	−13.8389	+	6.16149i	−0.523812	+	0.233216i
$699$	−10.3304			−0.390730
$700$	0.615967	−	2.35127i	0.0232814	−	0.0888696i
$701$	−18.9028			−0.713949			−0.356974	−	0.934114i	$-0.616192\pi$
$701$	−18.9028			−0.713949			−0.356974	+	0.934114i	$0.616192\pi$
$702$	−8.74430	+	3.89321i	−0.330032	+	0.146940i
$703$	50.8094	−	56.4296i	1.91631	−	2.12828i
$704$	5.68168	−	6.31014i	0.214136	−	0.237823i
$705$	−13.2121	−	20.4241i	−0.497595	−	0.769216i
$706$	2.35205	−	7.23886i	0.0885205	−	0.272438i
$707$	42.0580	+	20.9479i	1.58175	+	0.787827i
$708$	0.158301	−	0.487202i	0.00594933	−	0.0183102i
$709$	−0.973782	−	9.26492i	−0.0365711	−	0.347951i	−0.997472	−	0.0710590i	$-0.977362\pi$
$709$	−0.973782	−	9.26492i	−0.0365711	−	0.347951i	0.960901	−	0.276892i	$-0.0893045\pi$
$710$	25.3750	−	20.4738i	0.952305	−	0.768367i
$711$	−0.854335	+	8.12846i	−0.0320401	+	0.304841i
$712$	−1.70393	−	16.2118i	−0.0638575	−	0.607563i
$713$	−25.4530	+	18.4927i	−0.953222	+	0.692556i
$714$	6.69644	+	12.8509i	0.250608	+	0.480934i
$715$	−13.9942	+	7.09915i	−0.523354	+	0.265493i
$716$	−0.0476000	−	0.452883i	−0.00177889	−	0.0169250i
$717$	11.0120	−	2.34066i	0.411249	−	0.0874137i
$718$	−3.41449	−	5.91407i	−0.127428	−	0.220711i
$719$	2.83114	+	3.14429i	0.105584	+	0.117262i	0.793620	−	0.608414i	$-0.208194\pi$
$719$	2.83114	+	3.14429i	0.105584	+	0.117262i	−0.688037	+	0.725676i	$0.741527\pi$
$720$	1.24473	+	7.95024i	0.0463884	+	0.296288i
$721$	27.0488	−	10.6676i	1.00735	−	0.397281i
$722$	14.3252	+	44.0885i	0.533130	+	1.64080i
$723$	2.11771	−	0.942867i	0.0787586	−	0.0350656i
$724$	0.567893	+	0.983620i	0.0211056	+	0.0365559i
$725$	−3.10053	−	14.8458i	−0.115151	−	0.551359i
$726$	6.75443	−	11.6990i	0.250680	−	0.434191i
$727$	3.29578	+	2.39453i	0.122234	+	0.0888081i	0.647223	−	0.762301i	$-0.275930\pi$
$727$	3.29578	+	2.39453i	0.122234	+	0.0888081i	−0.524989	+	0.851109i	$0.675930\pi$
$728$	43.2942	+	34.4089i	1.60459	+	1.27528i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−8.86235	+	2.35781i	−0.328010	+	0.0872663i
$731$	15.2683	−	3.24538i	0.564718	−	0.120035i
$732$	−0.438762	−	0.759959i	−0.0162171	−	0.0280889i
$733$	3.75675	+	4.17229i	0.138759	+	0.154107i	0.808519	−	0.588471i	$-0.200270\pi$
$733$	3.75675	+	4.17229i	0.138759	+	0.154107i	−0.669760	+	0.742578i	$0.733603\pi$
$734$	−7.63132	+	5.54448i	−0.281677	+	0.204650i
$735$	14.5183	−	5.84961i	0.535517	−	0.215766i
$736$	−4.89498	−	3.55641i	−0.180432	−	0.131091i
$737$	0.0852331	+	0.810939i	0.00313960	+	0.0298713i
$738$	7.41170	+	3.29990i	0.272828	+	0.121471i
$739$	3.53146	−	33.5996i	0.129907	−	1.23598i	−0.714252	−	0.699889i	$-0.753233\pi$
$739$	3.53146	−	33.5996i	0.129907	−	1.23598i	0.844159	−	0.536093i	$-0.180101\pi$
$740$	−2.69263	+	3.31307i	−0.0989829	+	0.121791i
$741$	41.9879	−	30.5060i	1.54247	−	1.12067i
$742$	−2.96035	−	10.6578i	−0.108678	−	0.391259i
$743$	43.8322			1.60805			0.804024	−	0.594596i	$-0.202688\pi$
$743$	43.8322			1.60805			0.804024	+	0.594596i	$0.202688\pi$
$744$	−10.6081	−	11.7815i	−0.388913	−	0.431932i
$745$	13.1158	+	8.55061i	0.480524	+	0.313270i
$746$	−16.1904	+	17.9812i	−0.592771	+	0.658339i
$747$	−4.77131	−	1.01417i	−0.174573	−	0.0371066i
$748$	0.596897	+	0.433671i	0.0218247	+	0.0158566i
$749$	0.0957534	+	1.55513i	0.00349875	+	0.0568233i
$750$	−13.3887	−	6.91195i	−0.488887	−	0.252389i
$751$	0.315650	−	0.546723i	0.0115182	−	0.0199502i	−0.860209	−	0.509942i	$-0.829667\pi$
$751$	0.315650	−	0.546723i	0.0115182	−	0.0199502i	0.871727	+	0.489992i	$0.163000\pi$
$752$	4.09218	−	38.9345i	0.149226	−	1.41980i
$753$	−12.9854	+	14.4217i	−0.473214	+	0.525557i
$754$	28.3990	+	6.03640i	1.03423	+	0.219833i
$755$	27.1181	−	13.7568i	0.986930	−	0.500661i
$756$	0.340586	−	0.346866i	0.0123870	−	0.0126154i
$757$	14.3485			0.521506			0.260753	−	0.965406i	$-0.416029\pi$
$757$	14.3485			0.521506			0.260753	+	0.965406i	$0.416029\pi$
$758$	−0.185919	−	0.206484i	−0.00675287	−	0.00749982i
$759$	5.27179	+	2.34715i	0.191354	+	0.0851963i
$760$	−17.1535	−	44.9245i	−0.622221	−	1.62958i
$761$	49.8905	−	22.2127i	1.80853	−	0.805209i	0.846436	−	0.532490i	$-0.178744\pi$
$761$	49.8905	−	22.2127i	1.80853	−	0.805209i	0.962094	−	0.272719i	$-0.0879230\pi$
$762$	−0.300786	+	0.218534i	−0.0108963	+	0.00791664i
$763$	22.2351	−	3.73021i	0.804963	−	0.135043i
$764$	1.85346	+	1.34662i	0.0670559	+	0.0487190i
$765$	−8.78201	+	2.33643i	−0.317514	+	0.0844739i
$766$	27.0563	+	12.0463i	0.977585	+	0.435249i
$767$	−19.3694	+	4.11708i	−0.699387	+	0.148659i
$768$	2.18567	−	3.78569i	0.0788685	−	0.136604i
$769$	−8.22735	+	25.3212i	−0.296686	+	0.913105i	0.685964	+	0.727636i	$0.259381\pi$
$769$	−8.22735	+	25.3212i	−0.296686	+	0.913105i	−0.982650	+	0.185470i	$0.940619\pi$
$770$	−5.22809	+	5.89303i	−0.188407	+	0.212370i
$771$	6.50042	+	20.0062i	0.234107	+	0.720507i
$772$	−2.48981	−	0.529226i	−0.0896104	−	0.0190473i
$773$	−2.27999	+	21.6926i	−0.0820054	+	0.780229i	0.873811	+	0.486265i	$0.161641\pi$
$773$	−2.27999	+	21.6926i	−0.0820054	+	0.780229i	−0.955817	+	0.293964i	$0.905025\pi$
$774$	2.58813	+	4.48277i	0.0930284	+	0.161130i
$775$	26.7967	−	2.72030i	0.962567	−	0.0977162i
$776$	−17.8083			−0.639282
$777$	−27.4673	−	1.18801i	−0.985382	−	0.0426196i
$778$	9.98783	+	30.7394i	0.358081	+	1.10206i
$779$	−43.0293	−	9.14615i	−1.54168	−	0.327695i
$780$	−2.27098	+	1.83234i	−0.0813141	+	0.0656082i
$781$	10.4567	−	2.22264i	0.374170	−	0.0795324i
$782$	−15.9942	+	27.7027i	−0.571950	+	0.990647i
$783$	0.937317	−	2.88477i	0.0334970	−	0.103093i
$784$	24.0966	+	7.34556i	0.860594	+	0.262342i
$785$	22.8120	−	11.5724i	0.814197	−	0.413035i
$786$	12.2724	−	5.46400i	0.437740	−	0.194895i
$787$	8.92280	+	3.97269i	0.318063	+	0.141611i	0.559558	−	0.828791i	$-0.310971\pi$
$787$	8.92280	+	3.97269i	0.318063	+	0.141611i	−0.241495	+	0.970402i	$0.577638\pi$
$788$	−1.36669	−	0.608490i	−0.0486864	−	0.0216766i
$789$	26.6980	−	11.8867i	0.950475	−	0.423179i
$790$	−3.80982	−	24.3338i	−0.135547	−	0.865757i
$791$	9.26901	−	24.8220i	0.329568	−	0.882568i
$792$	−0.898581	+	2.76555i	−0.0319297	+	0.0982695i
$793$	−16.9605	+	29.3764i	−0.602284	+	1.04319i
$794$	30.3377	−	6.44848i	1.07665	−	0.228848i
$795$	6.92780	−	0.350741i	0.245704	−	0.0124395i
$796$	−0.771506	−	0.163989i	−0.0273453	−	0.00581242i
$797$	5.21828	+	16.0602i	0.184841	+	0.568882i	0.999946	−	0.0104318i	$-0.00332061\pi$
$797$	5.21828	+	16.0602i	0.184841	+	0.568882i	−0.815105	+	0.579314i	$0.803321\pi$
$798$	13.9906	−	21.9807i	0.495264	−	0.778109i
$799$	44.2105			1.56406
$800$	2.09004	+	4.73952i	0.0738941	+	0.167567i
$801$	2.76948	+	4.79687i	0.0978546	+	0.169489i
$802$	−1.78754	+	17.0074i	−0.0631204	+	0.600551i
$803$	−2.94113	−	0.625157i	−0.103790	−	0.0220613i
$804$	0.0468563	+	0.144209i	0.00165249	+	0.00508585i
$805$	28.1021	+	20.1030i	0.990469	+	0.708539i
$806$	−15.9337	+	49.0387i	−0.561239	+	1.72732i
$807$	13.0012	−	22.5188i	0.457665	−	0.792699i
$808$	−51.1227	+	10.8665i	−1.79849	+	0.382281i
$809$	17.8807	+	7.96101i	0.628652	+	0.279894i	0.696229	−	0.717820i	$-0.254860\pi$
$809$	17.8807	+	7.96101i	0.628652	+	0.279894i	−0.0675762	+	0.997714i	$0.521527\pi$
$810$	−1.63679	−	2.53026i	−0.0575110	−	0.0889043i
$811$	−24.3035	−	17.6575i	−0.853411	−	0.620040i	0.0726731	−	0.997356i	$-0.476847\pi$
$811$	−24.3035	−	17.6575i	−0.853411	−	0.620040i	−0.926085	+	0.377316i	$0.876847\pi$
$812$	−1.45420	+	0.243960i	−0.0510323	+	0.00856130i
$813$	18.4979	−	13.4395i	0.648750	−	0.471345i
$814$	12.6409	−	5.62808i	0.443062	−	0.197264i
$815$	−15.8602	+	0.802968i	−0.555557	+	0.0281267i
$816$	−13.3611	−	5.94876i	−0.467733	−	0.208248i
$817$	−18.7801	−	20.8575i	−0.657034	−	0.729710i
$818$	36.2927			1.26894
$819$	−18.1946	−	4.69751i	−0.635770	−	0.164144i
$820$	2.44218	+	0.391248i	0.0852845	+	0.0136630i
$821$	−3.94160	−	0.837813i	−0.137563	−	0.0292399i	0.138616	−	0.990346i	$-0.455735\pi$
$821$	−3.94160	−	0.837813i	−0.137563	−	0.0292399i	−0.276178	+	0.961106i	$0.589068\pi$
$822$	−8.19666	+	9.10332i	−0.285891	+	0.317515i
$823$	−1.37562	+	13.0881i	−0.0479510	+	0.456223i	0.944032	+	0.329853i	$0.106999\pi$
$823$	−1.37562	+	13.0881i	−0.0479510	+	0.456223i	−0.991983	+	0.126370i	$0.959667\pi$
$824$	−16.1715	+	28.0099i	−0.563362	+	0.975772i
$825$	−2.88964	−	4.00709i	−0.100604	−	0.139509i
$826$	−8.28768	+	5.49036i	−0.288365	+	0.191034i
$827$	27.9460	+	20.3039i	0.971777	+	0.706037i	0.955856	−	0.293836i	$-0.0949320\pi$
$827$	27.9460	+	20.3039i	0.971777	+	0.706037i	0.0159209	+	0.999873i	$0.494932\pi$
$828$	1.04965	+	0.223110i	0.0364778	+	0.00775360i
$829$	−14.8470	+	16.4892i	−0.515656	+	0.572694i	−0.943590	−	0.331116i	$-0.892575\pi$
$829$	−14.8470	+	16.4892i	−0.515656	+	0.572694i	0.427934	+	0.903810i	$0.359242\pi$
$830$	14.6809	−	0.743263i	0.509580	−	0.0257990i
$831$	−1.59355	−	1.76982i	−0.0552797	−	0.0613944i
$832$	−61.0360			−2.11604
$833$	−5.40539	+	27.9301i	−0.187286	+	0.967721i
$834$	−11.2287	+	8.15814i	−0.388819	+	0.282493i
$835$	−24.3591	−	9.40025i	−0.842983	−	0.325309i
$836$	0.138669	−	1.31934i	0.00479596	−	0.0456305i
$837$	4.92117	+	2.19105i	0.170101	+	0.0757336i
$838$	−3.48252	−	33.1340i	−0.120302	−	1.14460i
$839$	−29.3740	−	21.3415i	−1.01410	−	0.736790i	−0.0490380	−	0.998797i	$-0.515616\pi$
$839$	−29.3740	−	21.3415i	−1.01410	−	0.736790i	−0.965066	+	0.262007i	$0.915616\pi$
$840$	−8.59429	+	15.1420i	−0.296531	+	0.522450i
$841$	16.0182	−	11.6379i	0.552351	−	0.401307i
$842$	8.79232	+	9.76486i	0.303003	+	0.336519i
$843$	1.06432	+	1.84346i	0.0366571	+	0.0634920i
$844$	3.25248	−	0.691336i	0.111955	−	0.0237968i
$845$	78.1132	+	30.1440i	2.68717	+	1.03699i
$846$	4.53042	+	13.9432i	0.155759	+	0.479377i
$847$	24.6710	−	9.72980i	0.847705	−	0.334320i
$848$	9.03187	+	6.56204i	0.310156	+	0.225341i
$849$	−13.9424	+	24.1489i	−0.478501	+	0.828788i
$850$	23.7649	−	13.6084i	0.815129	−	0.466764i
$851$	−30.3448	−	52.5588i	−1.04021	−	1.80169i
$852$	1.81607	−	0.808566i	0.0622175	−	0.0277010i
$853$	−5.06522	−	15.5891i	−0.173430	−	0.533762i	0.826129	−	0.563482i	$-0.190538\pi$
$853$	−5.06522	−	15.5891i	−0.173430	−	0.533762i	−0.999558	+	0.0297199i	$0.990538\pi$
$854$	−2.51024	+	16.8434i	−0.0858985	+	0.576370i
$855$	11.5334	+	11.5745i	0.394436	+	0.395838i
$856$	−1.15969	−	1.28796i	−0.0396372	−	0.0440216i
$857$	26.7673	+	46.3623i	0.914354	+	1.58371i	0.807845	+	0.589395i	$0.200634\pi$
$857$	26.7673	+	46.3623i	0.914354	+	1.58371i	0.106509	+	0.994312i	$0.466033\pi$
$858$	9.25091	−	1.96634i	0.315821	−	0.0671298i
$859$	3.72461	+	35.4373i	0.127082	+	1.20910i	0.853219	+	0.521554i	$0.174647\pi$
$859$	3.72461	+	35.4373i	0.127082	+	1.20910i	−0.726137	+	0.687551i	$0.758686\pi$
$860$	1.11384	+	1.11780i	0.0379815	+	0.0381166i
$861$	7.36026	+	14.1248i	0.250837	+	0.481373i
$862$	−15.6478	+	11.3688i	−0.532966	+	0.387222i
$863$	−0.599384	−	5.70276i	−0.0204033	−	0.194124i	0.979572	−	0.201092i	$-0.0644489\pi$
$863$	−0.599384	−	5.70276i	−0.0204033	−	0.194124i	−0.999976	+	0.00696732i	$0.997782\pi$
$864$	−0.108289	+	1.03030i	−0.00368407	+	0.0350516i
$865$	−9.88160	−	25.8797i	−0.335985	−	0.879935i
$866$	4.80633	+	45.7292i	0.163326	+	1.55394i
$867$	−0.149403	+	0.459816i	−0.00507400	+	0.0156162i
$868$	−0.160935	−	2.61374i	−0.00546248	−	0.0887162i
$869$	2.49552	−	7.68043i	0.0846548	−	0.260541i
$870$	−0.494589	+	9.12729i	−0.0167681	+	0.309444i
$871$	3.92198	−	4.35580i	0.132891	−	0.147591i
$872$	−16.7810	+	18.6371i	−0.568275	+	0.631133i
$873$	5.52794	−	2.46120i	0.187093	−	0.0832990i
$874$	57.5167			1.94553
$875$	−12.1343	−	26.9770i	−0.410214	−	0.911989i
$876$	−0.559142			−0.0188916
$877$	20.0187	−	8.91291i	0.675984	−	0.300968i	−0.0398825	−	0.999204i	$-0.512698\pi$
$877$	20.0187	−	8.91291i	0.675984	−	0.300968i	0.715867	+	0.698237i	$0.246032\pi$
$878$	−21.1096	+	23.4445i	−0.712413	+	0.791215i
$879$	12.7055	−	14.1109i	0.428547	−	0.475950i
$880$	0.430219	−	7.93939i	0.0145027	−	0.267637i
$881$	−0.277952	+	0.855447i	−0.00936443	+	0.0288207i	−0.955630	−	0.294571i	$-0.904823\pi$
$881$	−0.277952	+	0.855447i	−0.00936443	+	0.0288207i	0.946265	+	0.323392i	$0.104823\pi$
$882$	−9.36256	+	1.15734i	−0.315254	+	0.0389697i
$883$	15.1913	−	46.7542i	0.511230	−	1.57340i	−0.278810	−	0.960346i	$-0.589940\pi$
$883$	15.1913	−	46.7542i	0.511230	−	1.57340i	0.790039	−	0.613056i	$-0.210060\pi$
$884$	−0.554366	−	5.27444i	−0.0186453	−	0.177399i
$885$	−2.22385	−	5.82421i	−0.0747540	−	0.195779i
$886$	0.00154331	−	0.0146837i	5.18487e−5	−	0.000493307i
$887$	0.0994782	+	0.946471i	0.00334015	+	0.0317794i	0.996065	−	0.0886254i	$-0.0282474\pi$
$887$	0.0994782	+	0.946471i	0.00334015	+	0.0317794i	−0.992725	+	0.120405i	$0.961581\pi$
$888$	24.7411	−	17.9755i	0.830258	−	0.603217i
$889$	−0.729212	−	0.0315397i	−0.0244570	−	0.00105781i
$890$	−11.7819	−	11.8238i	−0.394930	−	0.396334i
$891$	−0.103281	−	0.982652i	−0.00346004	−	0.0329201i
$892$	3.33262	−	0.708369i	0.111584	−	0.0237180i
$893$	−39.7464	−	68.8428i	−1.33006	−	2.30374i
$894$	−6.31421	−	7.01264i	−0.211179	−	0.234538i
$895$	−3.91176	−	3.92568i	−0.130756	−	0.131221i
$896$	−23.4058	+	9.23082i	−0.781932	+	0.308380i
$897$	−12.8183	−	39.4507i	−0.427991	−	1.31722i
$898$	−1.24925	+	0.556200i	−0.0416879	+	0.0185606i
$899$	−8.16982	−	14.1505i	−0.272479	−	0.471947i
$900$	−0.680530	−	0.617141i	−0.0226843	−	0.0205714i
$901$	−6.30370	+	10.9183i	−0.210007	+	0.363742i
$902$	−6.48530	−	4.71185i	−0.215937	−	0.156887i
$903$	−1.49792	+	10.0509i	−0.0498478	+	0.334473i
$904$	9.10763	+	28.0304i	0.302915	+	0.932278i
$905$	12.8955	+	4.97642i	0.428662	+	0.165422i
$906$	−17.9265	+	3.81040i	−0.595568	+	0.126592i
$907$	26.5813	+	46.0402i	0.882618	+	1.52874i	0.848420	+	0.529324i	$0.177554\pi$
$907$	26.5813	+	46.0402i	0.882618	+	1.52874i	0.0341978	+	0.999415i	$0.489112\pi$
$908$	0.640983	+	0.711884i	0.0212718	+	0.0236247i
$909$	14.3674	−	10.4385i	0.476536	−	0.346224i
$910$	56.6262	−	0.416773i	1.87714	−	0.0138159i
$911$	−11.1737	−	8.11816i	−0.370201	−	0.268967i	0.387093	−	0.922040i	$-0.373479\pi$
$911$	−11.1737	−	8.11816i	−0.370201	−	0.268967i	−0.757294	+	0.653074i	$0.773479\pi$
$912$	2.74884	+	26.1535i	0.0910232	+	0.866028i
$913$	4.40300	+	1.96034i	0.145718	+	0.0648778i
$914$	−1.63716	+	15.5765i	−0.0541524	+	0.515225i
$915$	−9.96328	−	3.84485i	−0.329376	−	0.127107i
$916$	0.560932	−	0.407541i	0.0185337	−	0.0134655i
$917$	25.5355	+	6.59281i	0.843257	+	0.217714i
$918$	5.47707			0.180770
$919$	5.54021	+	6.15303i	0.182755	+	0.202970i	0.827560	−	0.561377i	$-0.189728\pi$
$919$	5.54021	+	6.15303i	0.182755	+	0.202970i	−0.644805	+	0.764347i	$0.723062\pi$
$920$	−38.3850	+	1.94336i	−1.26552	+	0.0640706i
$921$	17.1157	−	19.0089i	0.563982	−	0.626366i
$922$	24.9816	+	5.31001i	0.822726	+	0.174876i
$923$	−62.1682	−	45.1679i	−2.04629	−	1.48672i
$924$	−0.400424	+	0.265270i	−0.0131730	+	0.00872675i
$925$	−0.184453	+	51.9564i	−0.00606479	+	1.70832i
$926$	14.6240	−	25.3296i	0.480576	−	0.832382i
$927$	1.14875	−	10.9296i	0.0377299	−	0.358976i
$928$	2.10264	−	2.33522i	0.0690227	−	0.0766575i
$929$	52.0666	+	11.0671i	1.70825	+	0.363099i	0.955450	−	0.295152i	$-0.0953703\pi$
$929$	52.0666	+	11.0671i	1.70825	+	0.363099i	0.752798	+	0.658251i	$0.228704\pi$
$930$	−16.0291	−	2.56794i	−0.525616	−	0.0842060i
$931$	48.3512	−	16.6928i	1.58465	−	0.547086i
$932$	1.89807			0.0621733
$933$	−1.81161	−	2.01199i	−0.0593093	−	0.0658697i
$934$	−49.5778	−	22.0735i	−1.62224	−	0.722266i
$935$	8.96755	−	0.454009i	0.293270	−	0.0148477i
$936$	19.0952	−	8.50175i	0.624148	−	0.277888i
$937$	7.32227	−	5.31994i	0.239208	−	0.173795i	−0.461722	−	0.887024i	$-0.652768\pi$
$937$	7.32227	−	5.31994i	0.239208	−	0.173795i	0.700930	+	0.713230i	$0.252768\pi$
$938$	1.02938	−	2.75665i	0.0336106	−	0.0900077i
$939$	23.0092	+	16.7172i	0.750878	+	0.545545i
$940$	2.42755	+	3.75266i	0.0791779	+	0.122398i
$941$	35.9159	+	15.9908i	1.17082	+	0.521284i	0.897662	−	0.440684i	$-0.145264\pi$
$941$	35.9159	+	15.9908i	1.17082	+	0.521284i	0.273162	+	0.961968i	$0.411931\pi$
$942$	−15.0800	+	3.20534i	−0.491332	+	0.104436i
$943$	−17.5797	+	30.4489i	−0.572473	+	0.991553i
$944$	3.10057	−	9.54257i	0.100915	−	0.310584i
$945$	0.575079	−	5.88806i	0.0187073	−	0.191539i
$946$	−1.58046	−	4.86416i	−0.0513852	−	0.158147i
$947$	−13.5038	−	2.87032i	−0.438814	−	0.0932728i	−0.0167934	−	0.999859i	$-0.505346\pi$
$947$	−13.5038	−	2.87032i	−0.438814	−	0.0932728i	−0.422021	+	0.906586i	$0.638679\pi$
$948$	0.156973	−	1.49350i	0.00509825	−	0.0485066i
$949$	10.8069	+	18.7181i	0.350806	+	0.607614i
$950$	−42.5557	−	24.7714i	−1.38069	−	0.803690i
$951$	6.57467			0.213198
$952$	−14.6233	−	28.0630i	−0.473943	−	0.909528i
$953$	10.1148	+	31.1301i	0.327650	+	1.00840i	0.970230	+	0.242185i	$0.0778641\pi$
$953$	10.1148	+	31.1301i	0.327650	+	1.00840i	−0.642580	+	0.766219i	$0.722136\pi$
$954$	−4.08941	−	0.869230i	−0.132399	−	0.0281424i
$955$	27.8457	−	1.40977i	0.901066	−	0.0456192i
$956$	−2.02331	+	0.430067i	−0.0654384	+	0.0139094i
$957$	−1.49851	+	2.59549i	−0.0484399	+	0.0839004i
$958$	−9.75883	+	30.0346i	−0.315294	+	0.970374i
$959$	−23.7170	+	3.97881i	−0.765860	+	0.128483i
$960$	−2.97237	−	18.9848i	−0.0959328	−	0.612733i
$961$	−1.81010	+	0.805909i	−0.0583903	+	0.0259971i
$962$	−90.8651	−	40.4557i	−2.92961	−	1.30435i
$963$	0.537985	+	0.239526i	0.0173363	+	0.00771863i
$964$	−0.389103	+	0.173240i	−0.0125322	+	0.00557968i
$965$	−27.6263	+	14.0146i	−0.889323	+	0.451146i
$966$	−13.2528	−	16.0635i	−0.426401	−	0.516836i
$967$	−5.70799	+	17.5674i	−0.183557	+	0.564930i	−0.999921	−	0.0126085i	$-0.995986\pi$
$967$	−5.70799	+	17.5674i	−0.183557	+	0.564930i	0.816364	+	0.577538i	$0.195986\pi$
$968$	−14.7499	+	25.5476i	−0.474080	+	0.821130i
$969$	−29.0486	+	6.17447i	−0.933175	+	0.198353i
$970$	−14.1917	+	11.4505i	−0.455667	+	0.367655i
$971$	−38.0686	−	8.09173i	−1.22168	−	0.259676i	−0.448453	−	0.893806i	$-0.648025\pi$
$971$	−38.0686	−	8.09173i	−1.22168	−	0.259676i	−0.773226	+	0.634131i	$0.781358\pi$
$972$	−0.0567779	−	0.174744i	−0.00182115	−	0.00560493i
$973$	−27.2224	−	1.17742i	−0.872710	−	0.0377463i
$974$	11.2482			0.360416
$975$	−7.50664	+	34.7096i	−0.240405	+	1.11160i
$976$	−8.59382	−	14.8849i	−0.275081	−	0.476455i
$977$	5.98412	−	56.9351i	0.191449	−	1.82151i	−0.303770	−	0.952745i	$-0.598245\pi$
$977$	5.98412	−	56.9351i	0.191449	−	1.82151i	0.495219	−	0.868768i	$-0.335088\pi$
$978$	9.36207	+	1.98997i	0.299366	+	0.0636322i
$979$	−1.69120	−	5.20498i	−0.0540510	−	0.166352i
$980$	−2.66756	+	1.07479i	−0.0852120	+	0.0343329i
$981$	2.63329	−	8.10443i	0.0840745	−	0.258755i
$982$	9.20999	−	15.9522i	0.293903	−	0.509054i
$983$	10.7669	−	2.28858i	0.343412	−	0.0729945i	−0.0329772	−	0.999456i	$-0.510499\pi$
$983$	10.7669	−	2.28858i	0.343412	−	0.0729945i	0.376389	+	0.926462i	$0.377166\pi$
$984$	−16.1852	−	7.20611i	−0.515965	−	0.229722i
$985$	−17.5945	+	4.68098i	−0.560609	+	0.149149i
$986$	−13.4403	−	9.76498i	−0.428028	−	0.310980i
$987$	−10.0685	+	26.9631i	−0.320485	+	0.858244i
$988$	−7.71474	+	5.60509i	−0.245439	+	0.178322i
$989$	−20.4927	+	9.12395i	−0.651631	+	0.290125i
$990$	1.06212	+	2.78168i	0.0337565	+	0.0884075i
$991$	−2.96901	−	1.32189i	−0.0943136	−	0.0419911i	0.359038	−	0.933323i	$-0.383105\pi$
$991$	−2.96901	−	1.32189i	−0.0943136	−	0.0419911i	−0.453351	+	0.891332i	$0.649772\pi$
$992$	3.73422	+	4.14727i	0.118562	+	0.131676i
$993$	−3.34437			−0.106131
$994$	−37.3535	−	9.64400i	−1.18478	−	0.305889i
$995$	−8.56043	+	4.34264i	−0.271384	+	0.137671i
$996$	0.876667	+	0.186341i	0.0277782	+	0.00590445i
$997$	−0.143145	+	0.158979i	−0.00453345	+	0.00503491i	−0.745407	−	0.666609i	$-0.767745\pi$
$997$	−0.143145	+	0.158979i	−0.00453345	+	0.00503491i	0.740874	+	0.671644i	$0.234412\pi$
$998$	−2.43327	+	23.1510i	−0.0770238	+	0.732833i
$999$	−5.19568	+	8.99917i	−0.164384	+	0.284721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.b.16.15	✓	160
7.4	even	3	inner	525.2.bg.b.466.6	yes	160
25.11	even	5	inner	525.2.bg.b.436.6	yes	160
175.11	even	15	inner	525.2.bg.b.361.15	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.b.16.15	✓	160	1.1	even	1	trivial
525.2.bg.b.361.15	yes	160	175.11	even	15	inner
525.2.bg.b.436.6	yes	160	25.11	even	5	inner
525.2.bg.b.466.6	yes	160	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23117 - 0.548154i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.122944 + 0.136543i) q^{4} +(-0.120990 + 2.23279i) q^{5} +(0.416458 - 1.28173i) q^{6} +(2.20566 - 1.46119i) q^{7} +(-0.909436 + 2.79896i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(1.23117 - 0.548154i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.122944 + 0.136543i) q^{4} +(-0.120990 + 2.23279i) q^{5} +(0.416458 - 1.28173i) q^{6} +(2.20566 - 1.46119i) q^{7} +(-0.909436 + 2.79896i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(1.07495 + 2.81528i) q^{10} +(-0.103281 + 0.982652i) q^{11} +(0.0192058 + 0.182731i) q^{12} +(5.74597 - 4.17469i) q^{13} +(1.91459 - 3.00802i) q^{14} +(1.57833 + 1.58394i) q^{15} +(0.376174 + 3.57905i) q^{16} +(-3.97524 + 0.844964i) q^{17} +(-0.673844 - 1.16713i) q^{18} +(4.88959 + 5.43044i) q^{19} +(-0.289998 - 0.291029i) q^{20} +(0.389998 - 2.61685i) q^{21} +(0.411488 + 1.26643i) q^{22} +(5.33547 - 2.37551i) q^{23} +(1.47150 + 2.54871i) q^{24} +(-4.97072 - 0.540292i) q^{25} +(4.78591 - 8.28944i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.0716572 + 0.480813i) q^{28} +(0.937317 + 2.88477i) q^{29} +(2.81144 + 1.08494i) q^{30} +(-5.26917 + 1.12000i) q^{31} +(-0.517989 - 0.897184i) q^{32} +(0.661144 + 0.734275i) q^{33} +(-4.43105 + 3.21934i) q^{34} +(2.99567 + 5.10157i) q^{35} +(0.148646 + 0.107998i) q^{36} +(-1.08619 - 10.3344i) q^{37} +(8.99665 + 4.00557i) q^{38} +(0.742404 - 7.06350i) q^{39} +(-6.13945 - 2.36923i) q^{40} +(-4.87030 + 3.53848i) q^{41} +(-0.954281 - 3.43558i) q^{42} -3.84084 q^{43} +(-0.121477 - 0.134914i) q^{44} +(2.23321 - 0.113063i) q^{45} +(5.26676 - 5.84932i) q^{46} +(-10.6407 - 2.26175i) q^{47} +(2.91146 + 2.11530i) q^{48} +(2.72985 - 6.44577i) q^{49} +(-6.41599 + 2.05953i) q^{50} +(-2.03203 + 3.51957i) q^{51} +(-0.136407 + 1.29783i) q^{52} +(2.07576 - 2.30537i) q^{53} +(-1.31824 - 0.280200i) q^{54} +(-2.18156 - 0.349496i) q^{55} +(2.08390 + 7.50240i) q^{56} +7.30738 q^{57} +(2.73530 + 3.03785i) q^{58} +(-2.54704 - 1.13401i) q^{59} +(-0.410323 + 0.0207738i) q^{60} +(-4.36307 + 1.94257i) q^{61} +(-5.87334 + 4.26723i) q^{62} +(-1.68374 - 2.04084i) q^{63} +(-6.95246 - 5.05126i) q^{64} +(8.62601 + 13.3346i) q^{65} +(1.21648 + 0.541612i) q^{66} +(0.807222 - 0.171580i) q^{67} +(0.373359 - 0.646676i) q^{68} +(1.80478 - 5.55455i) q^{69} +(6.48463 + 4.63883i) q^{70} +(-3.34340 - 10.2899i) q^{71} +(2.87868 + 0.611883i) q^{72} +(-0.318097 + 3.02649i) q^{73} +(-7.00215 - 12.1281i) q^{74} +(-3.72758 + 3.33244i) q^{75} -1.34264 q^{76} +(1.20804 + 2.31831i) q^{77} +(-2.95786 - 9.10335i) q^{78} +(-7.99462 - 1.69931i) q^{79} +(-8.03679 + 0.406887i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-4.05656 + 7.02616i) q^{82} +(1.50735 - 4.63916i) q^{83} +(0.309365 + 0.374978i) q^{84} +(-1.40566 - 8.97812i) q^{85} +(-4.72875 + 2.10537i) q^{86} +(2.77099 + 1.23372i) q^{87} +(-2.65647 - 1.18274i) q^{88} +(-5.06008 + 2.25289i) q^{89} +(2.68749 - 1.36334i) q^{90} +(6.57363 - 17.6039i) q^{91} +(-0.331606 + 1.02058i) q^{92} +(-2.69345 + 4.66518i) q^{93} +(-14.3404 + 3.04814i) q^{94} +(-12.7166 + 10.2604i) q^{95} +(-1.01334 - 0.215392i) q^{96} +(1.86989 + 5.75493i) q^{97} +(-0.172346 - 9.43224i) q^{98} +0.988064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9	\( 160 q + 2 q^{2} + 20 q^{3} + 20 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 30 q^{8} + 20 q^{9} - 6 q^{10} + 12 q^{11} + 20 q^{12} + 12 q^{14} + 4 q^{15} + 12 q^{16} - 6 q^{17} - 8 q^{18} + 12 q^{19} - 7 q^{21} + 14 q^{23} - 30 q^{24} - 4 q^{25} - 56 q^{26} - 40 q^{27} - 27 q^{28} - 2 q^{29} + 4 q^{30} + 27 q^{31} - 78 q^{32} - 8 q^{33} + 76 q^{34} + 21 q^{35} - 40 q^{36} + 14 q^{37} - 17 q^{38} + 10 q^{40} - 6 q^{41} - 2 q^{42} + 28 q^{43} - 22 q^{44} + 3 q^{45} - 22 q^{46} + 7 q^{47} - 24 q^{48} + 152 q^{49} - 62 q^{50} + 4 q^{51} + 13 q^{52} - 26 q^{53} + 2 q^{54} + 64 q^{55} - 33 q^{56} + 56 q^{57} + 48 q^{59} + 15 q^{60} + 36 q^{61} - 88 q^{62} - 7 q^{63} - 2 q^{64} + 46 q^{65} + 15 q^{66} + 42 q^{67} - 28 q^{68} - 8 q^{69} - 32 q^{70} + 36 q^{71} + 15 q^{72} + 10 q^{73} - 16 q^{74} + q^{75} - 76 q^{76} + 12 q^{77} - 8 q^{78} - 10 q^{79} + 100 q^{80} + 20 q^{81} + 14 q^{82} - 74 q^{83} - 6 q^{84} + 90 q^{85} + 6 q^{86} - 4 q^{87} + 102 q^{88} + 33 q^{89} - 18 q^{90} - 31 q^{91} - 94 q^{92} - 98 q^{93} - 30 q^{94} - 106 q^{95} + 47 q^{96} - 26 q^{97} + 26 q^{98} + 16 q^{99}+O(q^{100}) \) 160 * q + 2 * q^2 + 20 * q^3 + 20 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 30 * q^8 + 20 * q^9 - 6 * q^10 + 12 * q^11 + 20 * q^12 + 12 * q^14 + 4 * q^15 + 12 * q^16 - 6 * q^17 - 8 * q^18 + 12 * q^19 - 7 * q^21 + 14 * q^23 - 30 * q^24 - 4 * q^25 - 56 * q^26 - 40 * q^27 - 27 * q^28 - 2 * q^29 + 4 * q^30 + 27 * q^31 - 78 * q^32 - 8 * q^33 + 76 * q^34 + 21 * q^35 - 40 * q^36 + 14 * q^37 - 17 * q^38 + 10 * q^40 - 6 * q^41 - 2 * q^42 + 28 * q^43 - 22 * q^44 + 3 * q^45 - 22 * q^46 + 7 * q^47 - 24 * q^48 + 152 * q^49 - 62 * q^50 + 4 * q^51 + 13 * q^52 - 26 * q^53 + 2 * q^54 + 64 * q^55 - 33 * q^56 + 56 * q^57 + 48 * q^59 + 15 * q^60 + 36 * q^61 - 88 * q^62 - 7 * q^63 - 2 * q^64 + 46 * q^65 + 15 * q^66 + 42 * q^67 - 28 * q^68 - 8 * q^69 - 32 * q^70 + 36 * q^71 + 15 * q^72 + 10 * q^73 - 16 * q^74 + q^75 - 76 * q^76 + 12 * q^77 - 8 * q^78 - 10 * q^79 + 100 * q^80 + 20 * q^81 + 14 * q^82 - 74 * q^83 - 6 * q^84 + 90 * q^85 + 6 * q^86 - 4 * q^87 + 102 * q^88 + 33 * q^89 - 18 * q^90 - 31 * q^91 - 94 * q^92 - 98 * q^93 - 30 * q^94 - 106 * q^95 + 47 * q^96 - 26 * q^97 + 26 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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