LMFDB - Embedded newform 525.2.bp.a.59.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(59,525)]

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([15, 21, 5]))

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

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

chi := DirichletCharacter("525.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bp (of order $30$, 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:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			59.19
Character	$\chi$	$=$	525.59
Dual form			525.2.bp.a.89.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169271 + 1.61051i) q^{2} +(-0.223032 - 1.71763i) q^{3} +(-0.608788 - 0.129402i) q^{4} +(-1.76715 + 1.37010i) q^{5} +(2.80401 - 0.0684501i) q^{6} +(1.20608 + 2.35486i) q^{7} +(-0.689378 + 2.12169i) q^{8} +(-2.90051 + 0.766175i) q^{9} +O(q^{10})$	\(q+(-0.169271 + 1.61051i) q^{2} +(-0.223032 - 1.71763i) q^{3} +(-0.608788 - 0.129402i) q^{4} +(-1.76715 + 1.37010i) q^{5} +(2.80401 - 0.0684501i) q^{6} +(1.20608 + 2.35486i) q^{7} +(-0.689378 + 2.12169i) q^{8} +(-2.90051 + 0.766175i) q^{9} +(-1.90744 - 3.07793i) q^{10} +(-2.02867 - 4.55647i) q^{11} +(-0.0864851 + 1.07453i) q^{12} +(-0.747958 + 0.543423i) q^{13} +(-3.99668 + 1.54379i) q^{14} +(2.74747 + 2.72973i) q^{15} +(-4.43746 - 1.97569i) q^{16} +(-1.62665 + 1.46465i) q^{17} +(-0.742958 - 4.80099i) q^{18} +(1.01423 + 4.77158i) q^{19} +(1.25311 - 0.605430i) q^{20} +(3.77579 - 2.59681i) q^{21} +(7.68163 - 2.49591i) q^{22} +(-0.207895 + 1.97799i) q^{23} +(3.79803 + 0.710892i) q^{24} +(1.24563 - 4.84236i) q^{25} +(-0.748580 - 1.29658i) q^{26} +(1.96291 + 4.81113i) q^{27} +(-0.429522 - 1.58968i) q^{28} +(-9.01719 + 2.92986i) q^{29} +(-4.86132 + 3.96275i) q^{30} +(-5.62051 + 5.06073i) q^{31} +(1.70212 - 2.94815i) q^{32} +(-7.37387 + 4.50075i) q^{33} +(-2.08348 - 2.86766i) q^{34} +(-5.35773 - 2.50894i) q^{35} +(1.86494 - 0.0911063i) q^{36} +(2.22670 - 5.00126i) q^{37} +(-7.85635 + 0.825735i) q^{38} +(1.10022 + 1.16352i) q^{39} +(-1.68870 - 4.69386i) q^{40} +(-4.37105 + 3.17575i) q^{41} +(3.54305 + 6.52050i) q^{42} -4.25592i q^{43} +(0.645414 + 3.03644i) q^{44} +(4.07590 - 5.32795i) q^{45} +(-3.15038 - 0.669635i) q^{46} +(0.426941 + 0.384419i) q^{47} +(-2.40380 + 8.06257i) q^{48} +(-4.09075 + 5.68029i) q^{49} +(7.58780 + 2.82576i) q^{50} +(2.87852 + 2.46733i) q^{51} +(0.525668 - 0.234042i) q^{52} +(8.71435 + 1.85229i) q^{53} +(-8.08063 + 2.34690i) q^{54} +(9.82780 + 5.27247i) q^{55} +(-5.82773 + 0.935531i) q^{56} +(7.96961 - 2.80629i) q^{57} +(-3.19221 - 15.0182i) q^{58} +(0.387984 + 3.69142i) q^{59} +(-1.31939 - 2.01735i) q^{60} +(11.5207 + 1.21088i) q^{61} +(-7.19895 - 9.90850i) q^{62} +(-5.30248 - 5.90624i) q^{63} +(-3.39955 - 2.46992i) q^{64} +(0.577206 - 1.98509i) q^{65} +(-6.00031 - 12.6375i) q^{66} +(-2.52623 + 2.27463i) q^{67} +(1.17982 - 0.681167i) q^{68} +(3.44383 - 0.0840690i) q^{69} +(4.94757 - 8.20397i) q^{70} +(8.73597 - 2.83849i) q^{71} +(0.373966 - 6.68217i) q^{72} +(-4.02889 + 1.79378i) q^{73} +(7.67765 + 4.43269i) q^{74} +(-8.59520 - 1.05953i) q^{75} -3.03612i q^{76} +(8.28312 - 10.2727i) q^{77} +(-2.06009 + 1.57496i) q^{78} +(-6.73463 + 7.47956i) q^{79} +(10.5486 - 2.58846i) q^{80} +(7.82595 - 4.44460i) q^{81} +(-4.37468 - 7.57718i) q^{82} +(13.1352 + 4.26788i) q^{83} +(-2.63469 + 1.09231i) q^{84} +(0.867822 - 4.81694i) q^{85} +(6.85419 + 0.720405i) q^{86} +(7.04355 + 14.8347i) q^{87} +(11.0659 - 1.16308i) q^{88} +(1.30275 - 12.3949i) q^{89} +(7.89077 + 7.46613i) q^{90} +(-2.18178 - 1.10593i) q^{91} +(0.382520 - 1.17728i) q^{92} +(9.94602 + 8.52525i) q^{93} +(-0.691379 + 0.622520i) q^{94} +(-8.32986 - 7.04249i) q^{95} +(-5.44347 - 2.26608i) q^{96} +(1.63307 + 5.02608i) q^{97} +(-8.45571 - 7.54970i) q^{98} +(9.37524 + 11.6618i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.169271	+	1.61051i	−0.119693	+	1.13880i	0.755541	+	0.655101i	$0.227374\pi$
$2$	−0.169271	+	1.61051i	−0.119693	+	1.13880i	−0.875234	+	0.483700i	$0.839293\pi$
$3$	−0.223032	−	1.71763i	−0.128768	−	0.991675i
$3$	−0.223032	−	1.71763i	−0.128768	−	0.991675i
$4$	−0.608788	−	0.129402i	−0.304394	−	0.0647009i
$5$	−1.76715	+	1.37010i	−0.790293	+	0.612729i
$5$	−1.76715	+	1.37010i	−0.790293	+	0.612729i
$6$	2.80401	−	0.0684501i	1.14473	−	0.0279446i
$7$	1.20608	+	2.35486i	0.455855	+	0.890054i
$7$	1.20608	+	2.35486i	0.455855	+	0.890054i
$8$	−0.689378	+	2.12169i	−0.243732	+	0.750130i
$9$	−2.90051	+	0.766175i	−0.966838	+	0.255392i
$10$	−1.90744	−	3.07793i	−0.603184	−	0.973326i
$11$	−2.02867	−	4.55647i	−0.611667	−	1.37383i	−0.908092	−	0.418771i	$-0.862461\pi$
$11$	−2.02867	−	4.55647i	−0.611667	−	1.37383i	0.296425	−	0.955056i	$-0.404206\pi$
$12$	−0.0864851	+	1.07453i	−0.0249661	+	0.310191i
$13$	−0.747958	+	0.543423i	−0.207446	+	0.150719i	−0.686658	−	0.726981i	$-0.740923\pi$
$13$	−0.747958	+	0.543423i	−0.207446	+	0.150719i	0.479211	+	0.877700i	$0.340923\pi$
$14$	−3.99668	+	1.54379i	−1.06816	+	0.412595i
$15$	2.74747	+	2.72973i	0.709393	+	0.704814i
$16$	−4.43746	−	1.97569i	−1.10937	−	0.493922i
$17$	−1.62665	+	1.46465i	−0.394522	+	0.355229i	−0.842388	−	0.538872i	$-0.818851\pi$
$17$	−1.62665	+	1.46465i	−0.394522	+	0.355229i	0.447866	+	0.894101i	$0.352184\pi$
$18$	−0.742958	−	4.80099i	−0.175117	−	1.13160i
$19$	1.01423	+	4.77158i	0.232680	+	1.09468i	0.927015	+	0.375024i	$0.122365\pi$
$19$	1.01423	+	4.77158i	0.232680	+	1.09468i	−0.694335	+	0.719652i	$0.744301\pi$
$20$	1.25311	−	0.605430i	0.280204	−	0.135378i
$21$	3.77579	−	2.59681i	0.823945	−	0.566670i
$22$	7.68163	−	2.49591i	1.63773	−	0.532130i
$23$	−0.207895	+	1.97799i	−0.0433492	+	0.412440i	0.951232	+	0.308477i	$0.0998192\pi$
$23$	−0.207895	+	1.97799i	−0.0433492	+	0.412440i	−0.994581	+	0.103963i	$0.966847\pi$
$24$	3.79803	+	0.710892i	0.775270	+	0.145110i
$25$	1.24563	−	4.84236i	0.249126	−	0.968471i
$26$	−0.748580	−	1.29658i	−0.146809	−	0.254280i
$27$	1.96291	+	4.81113i	0.377763	+	0.925902i
$28$	−0.429522	−	1.58968i	−0.0811720	−	0.300421i
$29$	−9.01719	+	2.92986i	−1.67445	+	0.544062i	−0.983822	−	0.179149i	$-0.942666\pi$
$29$	−9.01719	+	2.92986i	−1.67445	+	0.544062i	−0.690627	+	0.723211i	$0.742666\pi$
$30$	−4.86132	+	3.96275i	−0.887552	+	0.723496i
$31$	−5.62051	+	5.06073i	−1.00947	+	0.908933i	−0.995853	−	0.0909740i	$-0.971002\pi$
$31$	−5.62051	+	5.06073i	−1.00947	+	0.908933i	−0.0136193	+	0.999907i	$0.504335\pi$
$32$	1.70212	−	2.94815i	0.300895	−	0.521165i
$33$	−7.37387	+	4.50075i	−1.28363	+	0.783480i
$34$	−2.08348	−	2.86766i	−0.357314	−	0.491800i
$35$	−5.35773	−	2.50894i	−0.905621	−	0.424088i
$36$	1.86494	−	0.0911063i	0.310823	−	0.0151844i
$37$	2.22670	−	5.00126i	0.366068	−	0.822201i	−0.632786	−	0.774327i	$-0.718089\pi$
$37$	2.22670	−	5.00126i	0.366068	−	0.822201i	0.998853	−	0.0478745i	$-0.0152447\pi$
$38$	−7.85635	+	0.825735i	−1.27447	+	0.133952i
$39$	1.10022	+	1.16352i	0.176176	+	0.186312i
$40$	−1.68870	−	4.69386i	−0.267007	−	0.742164i
$41$	−4.37105	+	3.17575i	−0.682644	+	0.495970i	−0.874234	−	0.485505i	$-0.838636\pi$
$41$	−4.37105	+	3.17575i	−0.682644	+	0.495970i	0.191590	+	0.981475i	$0.438636\pi$
$42$	3.54305	+	6.52050i	0.546704	+	1.00614i
$43$		−	4.25592i		−	0.649022i	−0.945882	−	0.324511i	$-0.894800\pi$
$43$		−	4.25592i		−	0.649022i	0.945882	−	0.324511i	$-0.105200\pi$
$44$	0.645414	+	3.03644i	0.0972999	+	0.457760i
$45$	4.07590	−	5.32795i	0.607599	−	0.794244i
$46$	−3.15038	−	0.669635i	−0.464499	−	0.0987322i
$47$	0.426941	+	0.384419i	0.0622757	+	0.0560733i	0.699681	−	0.714456i	$-0.253326\pi$
$47$	0.426941	+	0.384419i	0.0622757	+	0.0560733i	−0.637405	+	0.770529i	$0.719992\pi$
$48$	−2.40380	+	8.06257i	−0.346959	+	1.16373i
$49$	−4.09075	+	5.68029i	−0.584393	+	0.811471i
$50$	7.58780	+	2.82576i	1.07308	+	0.399623i
$51$	2.87852	+	2.46733i	0.403073	+	0.345495i
$52$	0.525668	−	0.234042i	0.0728970	−	0.0324558i
$53$	8.71435	+	1.85229i	1.19701	+	0.254432i	0.762953	−	0.646454i	$-0.223749\pi$
$53$	8.71435	+	1.85229i	1.19701	+	0.254432i	0.434055	+	0.900886i	$0.357082\pi$
$54$	−8.08063	+	2.34690i	−1.09963	+	0.319373i
$55$	9.82780	+	5.27247i	1.32518	+	0.710939i
$56$	−5.82773	+	0.935531i	−0.778763	+	0.125016i
$57$	7.96961	−	2.80629i	1.05560	−	0.371702i
$58$	−3.19221	−	15.0182i	−0.419158	−	1.97198i
$59$	0.387984	+	3.69142i	0.0505112	+	0.480582i	0.990312	+	0.138860i	$0.0443437\pi$
$59$	0.387984	+	3.69142i	0.0505112	+	0.480582i	−0.939801	+	0.341723i	$0.888990\pi$
$60$	−1.31939	−	2.01735i	−0.170333	−	0.260439i
$61$	11.5207	+	1.21088i	1.47508	+	0.155037i	0.807660	−	0.589649i	$-0.200734\pi$
$61$	11.5207	+	1.21088i	1.47508	+	0.155037i	0.667416	+	0.744685i	$0.267400\pi$
$62$	−7.19895	−	9.90850i	−0.914267	−	1.25838i
$63$	−5.30248	−	5.90624i	−0.668050	−	0.744116i
$64$	−3.39955	−	2.46992i	−0.424943	−	0.308739i
$65$	0.577206	−	1.98509i	0.0715936	−	0.246220i
$66$	−6.00031	−	12.6375i	−0.738587	−	1.55557i
$67$	−2.52623	+	2.27463i	−0.308628	+	0.277890i	−0.808860	−	0.588002i	$-0.799915\pi$
$67$	−2.52623	+	2.27463i	−0.308628	+	0.277890i	0.500232	+	0.865892i	$0.333248\pi$
$68$	1.17982	−	0.681167i	0.143074	−	0.0826036i
$69$	3.44383	−	0.0840690i	0.414588	−	0.0101207i
$70$	4.94757	−	8.20397i	0.591348	−	0.980562i
$71$	8.73597	−	2.83849i	1.03677	−	0.336867i	0.259306	−	0.965795i	$-0.416506\pi$
$71$	8.73597	−	2.83849i	1.03677	−	0.336867i	0.777463	+	0.628929i	$0.216506\pi$
$72$	0.373966	−	6.68217i	0.0440723	−	0.787501i
$73$	−4.02889	+	1.79378i	−0.471546	+	0.209946i	−0.628730	−	0.777624i	$-0.716425\pi$
$73$	−4.02889	+	1.79378i	−0.471546	+	0.209946i	0.157184	+	0.987569i	$0.449758\pi$
$74$	7.67765	+	4.43269i	0.892508	+	0.515290i
$75$	−8.59520	−	1.05953i	−0.992488	−	0.122344i
$76$		−	3.03612i		−	0.348267i
$77$	8.28312	−	10.2727i	0.943949	−	1.17068i
$78$	−2.06009	+	1.57496i	−0.233259	+	0.178329i
$79$	−6.73463	+	7.47956i	−0.757705	+	0.841517i	−0.991410	−	0.130791i	$-0.958248\pi$
$79$	−6.73463	+	7.47956i	−0.757705	+	0.841517i	0.233705	+	0.972308i	$0.424915\pi$
$80$	10.5486	−	2.58846i	1.17936	−	0.289398i
$81$	7.82595	−	4.44460i	0.869550	−	0.493845i
$82$	−4.37468	−	7.57718i	−0.483103	−	0.836759i
$83$	13.1352	+	4.26788i	1.44177	+	0.468461i	0.922450	−	0.386117i	$-0.126184\pi$
$83$	13.1352	+	4.26788i	1.44177	+	0.468461i	0.519324	+	0.854577i	$0.326184\pi$
$84$	−2.63469	+	1.09231i	−0.287468	+	0.119181i
$85$	0.867822	−	4.81694i	0.0941285	−	0.522470i
$86$	6.85419	+	0.720405i	0.739107	+	0.0776833i
$87$	7.04355	+	14.8347i	0.755147	+	1.59045i
$88$	11.0659	−	1.16308i	1.17963	−	0.123984i
$89$	1.30275	−	12.3949i	0.138092	−	1.31385i	−0.677628	−	0.735405i	$-0.736992\pi$
$89$	1.30275	−	12.3949i	0.138092	−	1.31385i	0.815719	−	0.578448i	$-0.196341\pi$
$90$	7.89077	+	7.46613i	0.831761	+	0.787000i
$91$	−2.18178	−	1.10593i	−0.228713	−	0.115933i
$92$	0.382520	−	1.17728i	0.0398805	−	0.122739i
$93$	9.94602	+	8.52525i	1.03135	+	0.884027i
$94$	−0.691379	+	0.622520i	−0.0713103	+	0.0642081i
$95$	−8.32986	−	7.04249i	−0.854626	−	0.722544i
$96$	−5.44347	−	2.26608i	−0.555572	−	0.231280i
$97$	1.63307	+	5.02608i	0.165813	+	0.510321i	0.999095	−	0.0425273i	$-0.0135409\pi$
$97$	1.63307	+	5.02608i	0.165813	+	0.510321i	−0.833282	+	0.552848i	$0.813541\pi$
$98$	−8.45571	−	7.54970i	−0.854156	−	0.762635i
$99$	9.37524	+	11.6618i	0.942247	+	1.17205i
$100$	−1.38493	+	2.78678i	−0.138493	+	0.278678i
$101$	2.11983	−	3.67166i	0.210931	−	0.365344i	−0.741075	−	0.671422i	$-0.765684\pi$
$101$	2.11983	−	3.67166i	0.210931	−	0.365344i	0.952006	+	0.306079i	$0.0990171\pi$
$102$	−4.46090	+	4.21823i	−0.441695	+	0.417667i
$103$	−0.463462	+	0.514726i	−0.0456662	+	0.0507175i	−0.765545	−	0.643382i	$-0.777531\pi$
$103$	−0.463462	+	0.514726i	−0.0456662	+	0.0507175i	0.719879	+	0.694100i	$0.244197\pi$
$104$	−0.637349	−	1.96156i	−0.0624972	−	0.192347i
$105$	−3.11448	+	9.76217i	−0.303942	+	0.952690i
$106$	−4.45822	+	13.7210i	−0.433021	+	1.33270i
$107$	4.87141	+	8.43753i	0.470937	+	0.815687i	0.999447	−	0.0332402i	$-0.0105826\pi$
$107$	4.87141	+	8.43753i	0.470937	+	0.815687i	−0.528511	+	0.848927i	$0.677249\pi$
$108$	−0.572429	−	3.18296i	−0.0550820	−	0.306280i
$109$	−1.59077	−	15.1352i	−0.152369	−	1.44969i	−0.757120	−	0.653276i	$-0.773394\pi$
$109$	−1.59077	−	15.1352i	−0.152369	−	1.44969i	0.604752	−	0.796414i	$-0.293272\pi$
$110$	−10.1549	+	14.9353i	−0.968233	+	1.42402i
$111$	−9.08694	−	2.70921i	−0.862494	−	0.257147i
$112$	−0.699459	−	12.8324i	−0.0660926	−	1.21255i
$113$	2.77252	−	2.01435i	0.260816	−	0.189494i	−0.449691	−	0.893184i	$-0.648466\pi$
$113$	2.77252	−	2.01435i	0.260816	−	0.189494i	0.710507	+	0.703690i	$0.248466\pi$
$114$	3.17053	+	13.3101i	0.296947	+	1.24661i
$115$	−2.34268	−	3.78025i	−0.218456	−	0.352510i
$116$	5.86868	−	0.616823i	0.544893	−	0.0572706i
$117$	1.75310	−	2.14927i	0.162075	−	0.198700i
$118$	−6.01074			−0.553333
$119$	−5.41091	−	2.06407i	−0.496018	−	0.189213i
$120$	−7.68568	+	3.94745i	−0.701604	+	0.360351i
$121$	−9.28547	+	10.3126i	−0.844134	+	0.937506i
$122$	−3.90025	+	18.3492i	−0.353112	+	1.66126i
$123$	6.42966	+	6.79956i	0.579743	+	0.613095i
$124$	4.07656	−	2.35360i	0.366086	−	0.211360i
$125$	4.43332	+	10.2638i	0.396529	+	0.918022i
$126$	10.4096	−	7.53993i	0.927361	−	0.671710i
$127$	5.76203	−	7.93075i	0.511297	−	0.703740i	−0.472840	−	0.881148i	$-0.656771\pi$
$127$	5.76203	−	7.93075i	0.511297	−	0.703740i	0.984137	+	0.177408i	$0.0567712\pi$
$128$	9.10902	−	10.1166i	0.805131	−	0.894189i
$129$	−7.31010	+	0.949209i	−0.643619	+	0.0835732i
$130$	3.09930	+	1.26561i	0.271827	+	0.111002i
$131$	−11.8371	+	2.51605i	−1.03421	+	0.219829i	−0.693589	−	0.720371i	$-0.743971\pi$
$131$	−11.8371	+	2.51605i	−1.03421	+	0.219829i	−0.340623	+	0.940200i	$0.610638\pi$
$132$	5.07153	−	1.78581i	0.441420	−	0.155435i
$133$	−10.0132	+	8.14327i	−0.868252	+	0.706111i
$134$	−3.23569	−	4.45354i	−0.279521	−	0.384727i
$135$	−10.0605	−	5.81258i	−0.865871	−	0.500267i
$136$	−1.98614	−	4.46095i	−0.170310	−	0.382523i
$137$	1.46312	+	13.9207i	0.125003	+	1.18933i	0.859653	+	0.510879i	$0.170680\pi$
$137$	1.46312	+	13.9207i	0.125003	+	1.18933i	−0.734650	+	0.678447i	$0.762653\pi$
$138$	−0.447547	+	5.56055i	−0.0380978	+	0.473345i
$139$	−4.02396	+	5.53850i	−0.341308	+	0.469770i	−0.944823	−	0.327582i	$-0.893766\pi$
$139$	−4.02396	+	5.53850i	−0.341308	+	0.469770i	0.603515	+	0.797352i	$0.293766\pi$
$140$	2.93706	+	2.22071i	0.248227	+	0.187684i
$141$	0.565069	−	0.819065i	0.0475874	−	0.0689777i
$142$	3.09266	+	14.5498i	0.259530	+	1.22099i
$143$	3.99345	+	2.30562i	0.333949	+	0.192806i
$144$	14.3846	+	2.33063i	1.19872	+	0.194219i
$145$	11.9205	−	17.5320i	0.989943	−	1.45595i
$146$	−2.20692	−	6.79219i	−0.182646	−	0.562126i
$147$	10.6690	+	5.75951i	0.879966	+	0.475037i
$148$	−2.00276	+	2.75656i	−0.164626	+	0.226588i
$149$	16.2160	−	9.36234i	1.32847	−	0.766993i	0.343407	−	0.939187i	$-0.388419\pi$
$149$	16.2160	−	9.36234i	1.32847	−	0.766993i	0.985063	+	0.172194i	$0.0550856\pi$
$150$	3.16129	−	13.6633i	0.258119	−	1.11560i
$151$	4.58718	−	7.94524i	0.373300	−	0.646574i	−0.616771	−	0.787142i	$-0.711560\pi$
$151$	4.58718	−	7.94524i	0.373300	−	0.646574i	0.990071	+	0.140568i	$0.0448930\pi$
$152$	−10.8230	−	1.13754i	−0.877861	−	0.0922669i
$153$	3.59596	−	5.49453i	0.290716	−	0.444206i
$154$	15.1422	+	15.0789i	1.22019	+	1.21509i
$155$	2.99854	−	16.6437i	0.240849	−	1.33686i
$156$	−0.519239	−	0.850704i	−0.0415724	−	0.0681108i
$157$	−9.22276	+	15.9743i	−0.736057	+	1.27489i	0.218201	+	0.975904i	$0.429981\pi$
$157$	−9.22276	+	15.9743i	−0.736057	+	1.27489i	−0.954258	+	0.298984i	$0.903352\pi$
$158$	−10.9059	−	12.1122i	−0.867628	−	0.963599i
$159$	1.23797	−	15.3812i	0.0981775	−	1.21981i
$160$	1.03138	+	7.54191i	0.0815381	+	0.596240i
$161$	−4.90864	+	1.89605i	−0.386855	+	0.149430i
$162$	5.83336	+	13.3561i	0.458312	+	1.04935i
$163$	−1.31435	+	2.95208i	−0.102948	+	0.231225i	−0.957674	−	0.287854i	$-0.907058\pi$
$163$	−1.31435	+	2.95208i	−0.102948	+	0.231225i	0.854726	+	0.519079i	$0.173725\pi$
$164$	3.07199	−	1.36774i	0.239882	−	0.106802i
$165$	6.86423	−	18.0565i	0.534380	−	1.40569i
$166$	−9.09686	+	20.4319i	−0.706054	+	1.58582i
$167$	0.172067	+	0.0559081i	0.0133150	+	0.00432630i	0.315667	−	0.948870i	$-0.397772\pi$
$167$	0.172067	+	0.0559081i	0.0133150	+	0.00432630i	−0.302352	+	0.953196i	$0.597772\pi$
$168$	2.90667	+	9.80123i	0.224254	+	0.756182i
$169$	−3.75309	+	11.5508i	−0.288699	+	0.888525i
$170$	7.61082	+	2.21300i	0.583723	+	0.169730i
$171$	−6.59766	−	13.0630i	−0.504535	−	0.998949i
$172$	−0.550724	+	2.59095i	−0.0419923	+	0.197558i
$173$	19.4340	+	2.04260i	1.47754	+	0.155296i	0.808749	−	0.588154i	$-0.200145\pi$
$173$	19.4340	+	2.04260i	1.47754	+	0.155296i	0.668791	+	0.743450i	$0.266812\pi$
$174$	−25.0837	+	8.83259i	−1.90159	+	0.669597i
$175$	12.9054	−	2.90698i	0.975557	−	0.219747i
$176$			24.2272i			1.82619i
$177$	6.25397	−	1.48972i	0.470077	−	0.111974i
$178$	19.7415	+	4.19619i	1.47969	+	0.314518i
$179$	0.342685	−	1.61221i	0.0256135	−	0.120502i	−0.963483	−	0.267768i	$-0.913714\pi$
$179$	0.342685	−	1.61221i	0.0256135	−	0.120502i	0.989097	+	0.147266i	$0.0470473\pi$
$180$	−3.17080	+	2.71616i	−0.236338	+	0.202451i
$181$	7.14820	+	2.32259i	0.531322	+	0.172637i	0.562377	−	0.826881i	$-0.309887\pi$
$181$	7.14820	+	2.32259i	0.531322	+	0.172637i	−0.0310557	+	0.999518i	$0.509887\pi$
$182$	2.15042	−	3.32658i	0.159400	−	0.246582i
$183$	−0.489655	−	20.0584i	−0.0361964	−	1.48276i
$184$	−4.05337	−	1.80468i	−0.298818	−	0.133042i
$185$	2.91733	+	11.8888i	0.214486	+	0.874080i
$186$	−15.4136	+	14.5751i	−1.13018	+	1.06870i
$187$	9.97357	+	4.44052i	0.729339	+	0.324723i
$188$	−0.210172	−	0.289276i	−0.0153283	−	0.0210977i
$189$	−8.96212	+	10.4250i	−0.651898	+	0.758307i
$190$	12.7520	−	12.2232i	0.925127	−	0.886765i
$191$	−7.81144	+	17.5448i	−0.565216	+	1.26950i	0.374401	+	0.927267i	$0.377848\pi$
$191$	−7.81144	+	17.5448i	−0.565216	+	1.26950i	−0.939617	+	0.342228i	$0.888818\pi$
$192$	−3.48419	+	6.39004i	−0.251450	+	0.461161i
$193$	7.10307	+	4.10096i	0.511290	+	0.295194i	0.733364	−	0.679836i	$-0.237949\pi$
$193$	7.10307	+	4.10096i	0.511290	+	0.295194i	−0.222074	+	0.975030i	$0.571283\pi$
$194$	−8.37097	+	1.77930i	−0.601001	+	0.127747i
$195$	−3.53839	−	0.548688i	−0.253389	−	0.0392923i
$196$	3.22544	−	2.92874i	0.230388	−	0.209196i
$197$	−0.703068	−	2.16382i	−0.0500915	−	0.154166i	0.922882	−	0.385083i	$-0.125827\pi$
$197$	−0.703068	−	2.16382i	−0.0500915	−	0.154166i	−0.972973	+	0.230917i	$0.925827\pi$
$198$	−20.3683	+	13.1249i	−1.44752	+	0.932746i
$199$	−2.33237	−	1.34659i	−0.165337	−	0.0954575i	0.415048	−	0.909799i	$-0.363765\pi$
$199$	−2.33237	−	1.34659i	−0.165337	−	0.0954575i	−0.580385	+	0.814342i	$0.697098\pi$
$200$	9.41526	+	5.98105i	0.665760	+	0.422924i
$201$	4.47040	+	3.83182i	0.315318	+	0.270275i
$202$	5.55441	+	4.03551i	0.390807	+	0.283938i
$203$	−17.7748	−	17.7006i	−1.24755	−	1.24234i
$204$	−1.43313	−	1.87456i	−0.100339	−	0.131246i
$205$	3.37318	−	11.6008i	0.235593	−	0.810237i
$206$	−0.750520	−	0.833537i	−0.0522912	−	0.0580753i
$207$	−0.912486	−	5.89648i	−0.0634221	−	0.409834i
$208$	4.39267	−	0.933691i	0.304577	−	0.0647398i
$209$	19.6840	−	14.3013i	1.36157	−	0.989240i
$210$	−15.1949	−	6.66835i	−1.04855	−	0.460160i
$211$	−16.0190	−	11.6385i	−1.10279	−	0.801226i	−0.121279	−	0.992618i	$-0.538700\pi$
$211$	−16.0190	−	11.6385i	−1.10279	−	0.801226i	−0.981514	+	0.191393i	$0.938700\pi$
$212$	−5.06550	−	2.25530i	−0.347900	−	0.154895i
$213$	−6.82388	−	14.3721i	−0.467565	−	0.984760i
$214$	−14.4133	+	6.41721i	−0.985272	+	0.438672i
$215$	5.83106	+	7.52084i	0.397675	+	0.512917i
$216$	−11.5609	+	0.848005i	−0.786620	+	0.0576994i
$217$	−18.6961	−	7.13189i	−1.26917	−	0.484144i
$218$	24.6446			1.66915
$219$	3.97962	+	6.52007i	0.268918	+	0.440586i
$220$	−5.30078	−	4.48155i	−0.357378	−	0.302146i
$221$	0.420747	−	1.97946i	0.0283025	−	0.133153i
$222$	5.90136	−	14.1760i	0.396074	−	0.951431i
$223$	−21.1118	−	15.3386i	−1.41375	−	1.02715i	−0.992764	−	0.120082i	$-0.961684\pi$
$223$	−21.1118	−	15.3386i	−1.41375	−	1.02715i	−0.420986	−	0.907067i	$-0.638316\pi$
$224$	8.99538	+	0.452549i	0.601029	+	0.0302372i
$225$	0.0971333	+	14.9997i	0.00647556	+	0.999979i
$226$	2.77482	+	4.80613i	0.184578	+	0.319699i
$227$	6.38753	+	14.3466i	0.423955	+	0.952219i	0.991647	+	0.128978i	$0.0411698\pi$
$227$	6.38753	+	14.3466i	0.423955	+	0.952219i	−0.567692	+	0.823241i	$0.692164\pi$
$228$	−5.21494	+	0.677154i	−0.345368	+	0.0448456i
$229$	2.10166	+	1.89234i	0.138881	+	0.125049i	0.735644	−	0.677369i	$-0.236880\pi$
$229$	2.10166	+	1.89234i	0.138881	+	0.125049i	−0.596762	+	0.802418i	$0.703546\pi$
$230$	6.48466	−	3.13301i	0.427586	−	0.206585i
$231$	−19.4921	−	11.9362i	−1.28249	−	0.785345i
$232$		−	21.1514i		−	1.38866i
$233$	−22.2076	+	4.72036i	−1.45487	+	0.309241i	−0.866429	−	0.499301i	$-0.833590\pi$
$233$	−22.2076	+	4.72036i	−1.45487	+	0.309241i	−0.588438	+	0.808542i	$0.700257\pi$
$234$	3.16467	+	3.18720i	0.206881	+	0.208354i
$235$	−1.28116	−	0.0943723i	−0.0835738	−	0.00615617i
$236$	0.241477	−	2.29750i	0.0157188	−	0.149554i
$237$	14.3492	+	9.89942i	0.932079	+	0.643037i
$238$	4.24011	−	8.36493i	0.274846	−	0.542218i
$239$	7.10886	−	9.78451i	0.459834	−	0.632907i	−0.514640	−	0.857406i	$-0.672075\pi$
$239$	7.10886	−	9.78451i	0.459834	−	0.632907i	0.974474	+	0.224499i	$0.0720745\pi$
$240$	−6.79869	−	17.5412i	−0.438853	−	1.13228i
$241$	−4.39706	+	0.462150i	−0.283240	+	0.0297697i	−0.245083	−	0.969502i	$-0.578815\pi$
$241$	−4.39706	+	0.462150i	−0.283240	+	0.0297697i	−0.0381566	+	0.999272i	$0.512149\pi$
$242$	−15.0367	−	16.6999i	−0.966596	−	1.07351i
$243$	−9.37963	−	12.4508i	−0.601703	−	0.798720i
$244$	−6.85698	−	2.22797i	−0.438973	−	0.142631i
$245$	−0.553631	−	15.6427i	−0.0353702	−	0.999374i
$246$	−12.0391	+	9.20405i	−0.767585	+	0.586829i
$247$	−3.35159	−	3.01779i	−0.213257	−	0.192017i
$248$	−6.86263	−	15.4137i	−0.435777	−	0.978772i
$249$	4.40107	−	23.5133i	0.278907	−	1.49009i
$250$	−17.2804	+	5.40254i	−1.09291	+	0.341686i
$251$	−1.44280			−0.0910686			−0.0455343	−	0.998963i	$-0.514499\pi$
$251$	−1.44280			−0.0910686			−0.0455343	+	0.998963i	$0.514499\pi$
$252$	2.46381	+	4.28180i	0.155205	+	0.269728i
$253$	9.43442	−	3.06543i	0.593137	−	0.192722i
$254$	11.7972	+	10.6222i	0.740221	+	0.666498i
$255$	−8.46727	−	0.416265i	−0.530241	−	0.0260675i
$256$	9.12749	+	10.1371i	0.570468	+	0.633569i
$257$	−22.7405	+	13.1292i	−1.41851	+	0.818979i	−0.996168	−	0.0874565i	$-0.972126\pi$
$257$	−22.7405	+	13.1292i	−1.41851	+	0.818979i	−0.422345	+	0.906435i	$0.638793\pi$
$258$	−0.291318	−	11.9337i	−0.0181367	−	0.742957i
$259$	14.4628	−	0.788327i	0.898678	−	0.0489843i
$260$	−0.608270	+	1.13381i	−0.0377233	+	0.0703157i
$261$	23.9097	−	15.4068i	1.47997	−	0.953660i
$262$	−2.04844	−	19.4896i	−0.126553	−	1.20407i
$263$	1.28537	+	12.2294i	0.0792590	+	0.754099i	0.959905	+	0.280325i	$0.0904422\pi$
$263$	1.28537	+	12.2294i	0.0792590	+	0.754099i	−0.880646	+	0.473775i	$0.842891\pi$
$264$	−4.46580	−	18.7478i	−0.274851	−	1.15385i
$265$	−17.9374	+	8.66629i	−1.10188	+	0.532366i
$266$	−11.4199	−	17.5047i	−0.700197	−	1.07328i
$267$	−21.5804	+	0.526809i	−1.32070	+	0.0322402i
$268$	1.83228	−	1.05787i	0.111924	−	0.0646195i
$269$	14.3873	+	15.9787i	0.877206	+	0.974236i	0.999834	−	0.0182163i	$-0.00579876\pi$
$269$	14.3873	+	15.9787i	0.877206	+	0.974236i	−0.122628	+	0.992453i	$0.539132\pi$
$270$	11.0642	−	15.2186i	0.673344	−	0.926176i
$271$	−9.65650	−	8.69475i	−0.586590	−	0.528168i	0.321518	−	0.946903i	$-0.395807\pi$
$271$	−9.65650	−	8.69475i	−0.586590	−	0.528168i	−0.908108	+	0.418735i	$0.862474\pi$
$272$	10.1119	−	3.28556i	0.613124	−	0.199216i
$273$	−1.41297	+	3.99416i	−0.0855166	+	0.241737i
$274$	−22.6671			−1.36937
$275$	−24.5910	+	4.14788i	−1.48289	+	0.250127i
$276$	−2.10744	−	0.394458i	−0.126853	−	0.0237436i
$277$	4.40547	+	9.89485i	0.264699	+	0.594524i	0.996179	−	0.0873395i	$-0.0278365\pi$
$277$	4.40547	+	9.89485i	0.264699	+	0.594524i	−0.731479	+	0.681863i	$0.761170\pi$
$278$	−8.23866	−	7.41812i	−0.494122	−	0.444909i
$279$	12.4249	−	18.9850i	0.743862	−	1.13660i
$280$	9.01669	−	9.63782i	0.538850	−	0.575970i
$281$	−10.7012	−	3.47705i	−0.638383	−	0.207423i	−0.0280980	−	0.999605i	$-0.508945\pi$
$281$	−10.7012	−	3.47705i	−0.638383	−	0.207423i	−0.610285	+	0.792182i	$0.708945\pi$
$282$	1.22346	+	1.04869i	0.0728560	+	0.0624487i
$283$	17.0731	+	18.9616i	1.01489	+	1.12715i	0.991849	+	0.127415i	$0.0406681\pi$
$283$	17.0731	+	18.9616i	1.01489	+	1.12715i	0.0230409	+	0.999735i	$0.492665\pi$
$284$	−5.68565	+	0.597586i	−0.337381	+	0.0354602i
$285$	−10.2386	+	15.8783i	−0.606480	+	0.940551i
$286$	−4.38920	+	6.04121i	−0.259539	+	0.357224i
$287$	−12.7503	−	6.46302i	−0.752626	−	0.381500i
$288$	−2.67821	+	9.85528i	−0.157815	+	0.580728i
$289$	−1.27617	+	12.1419i	−0.0750687	+	0.714231i
$290$	26.2176	+	22.1657i	1.53955	+	1.30161i
$291$	8.26872	−	3.92599i	0.484721	−	0.230146i
$292$	2.68485	−	0.570683i	0.157119	−	0.0333967i
$293$		−	21.9658i		−	1.28326i	−0.767015	−	0.641629i	$-0.778259\pi$
$293$		−	21.9658i		−	1.28326i	0.767015	−	0.641629i	$-0.221741\pi$
$294$	−11.0817	+	16.2076i	−0.646298	+	0.945248i
$295$	−5.74326	−	5.99171i	−0.334385	−	0.348851i
$296$	9.07607	+	8.17213i	0.527536	+	0.474995i
$297$	17.9397	−	18.7042i	1.04096	−	1.08533i
$298$	12.3332	+	27.7008i	0.714444	+	1.60467i
$299$	−0.919391	−	1.59243i	−0.0531697	−	0.0920927i
$300$	5.09554	+	1.75726i	0.294191	+	0.101455i
$301$	10.0221	−	5.13297i	0.577665	−	0.295860i
$302$	12.0194	+	8.73260i	0.691638	+	0.502504i
$303$	−6.77934	−	2.82219i	−0.389463	−	0.162131i
$304$	4.92653	−	23.1775i	0.282556	−	1.32932i
$305$	−22.0178	+	13.6448i	−1.26074	+	0.781298i
$306$	8.24029	+	6.72138i	0.471066	+	0.384236i
$307$	−8.99324			−0.513271			−0.256636	−	0.966508i	$-0.582614\pi$
$307$	−8.99324			−0.513271			−0.256636	+	0.966508i	$0.582614\pi$
$308$	−6.37197	+	5.18204i	−0.363077	+	0.295274i
$309$	0.987477	+	0.681256i	0.0561756	+	0.0387553i
$310$	26.2973	+	7.64648i	1.49359	+	0.434291i
$311$	−17.6885	+	7.87542i	−1.00302	+	0.446574i	−0.841478	−	0.540291i	$-0.818314\pi$
$311$	−17.6885	+	7.87542i	−1.00302	+	0.446574i	−0.161544	+	0.986866i	$0.551647\pi$
$312$	−3.22708	+	1.53222i	−0.182698	+	0.0867450i
$313$	−5.35639	−	2.38482i	−0.302761	−	0.134798i	0.249733	−	0.968315i	$-0.419657\pi$
$313$	−5.35639	−	2.38482i	−0.302761	−	0.134798i	−0.552494	+	0.833517i	$0.686324\pi$
$314$	−24.1656	−	17.5573i	−1.36374	−	0.990817i
$315$	17.4624	+	3.17225i	0.983897	+	0.178736i
$316$	5.06783	−	3.68199i	0.285088	−	0.207128i
$317$	−15.0577	+	3.20061i	−0.845725	+	0.179764i	−0.610342	−	0.792138i	$-0.708968\pi$
$317$	−15.0577	+	3.20061i	−0.845725	+	0.179764i	−0.235383	+	0.971903i	$0.575635\pi$
$318$	24.5619	+	4.59735i	1.37736	+	0.257807i
$319$	31.6427	+	35.1428i	1.77165	+	1.96762i
$320$	9.39155	−	0.293027i	0.525003	−	0.0163807i
$321$	13.4061	−	10.2491i	0.748254	−	0.572050i
$322$	−2.22271	−	8.22635i	−0.123867	−	0.458437i
$323$	−8.63848	−	6.27623i	−0.480658	−	0.349219i
$324$	−5.33948	+	1.69313i	−0.296638	+	0.0940625i
$325$	1.69977	+	4.29878i	0.0942864	+	0.238454i
$326$	−4.53187	−	2.61648i	−0.250997	−	0.144913i
$327$	−25.6419	+	6.10801i	−1.41800	+	0.337773i
$328$	−3.72465	−	11.4633i	−0.205660	−	0.632955i
$329$	−0.390330	+	1.46903i	−0.0215196	+	0.0809900i
$330$	27.9182	+	14.1113i	1.53684	+	0.776804i
$331$	−15.9278	+	3.38555i	−0.875470	+	0.186087i	−0.623665	−	0.781691i	$-0.714357\pi$
$331$	−15.9278	+	3.38555i	−0.875470	+	0.186087i	−0.251804	+	0.967778i	$0.581024\pi$
$332$	−7.44427	−	4.29795i	−0.408557	−	0.235881i
$333$	−2.62674	+	16.2123i	−0.143945	+	0.888426i
$334$	−0.119166	+	0.267652i	−0.00652050	+	0.0146453i
$335$	1.34775	−	7.48080i	0.0736352	−	0.408720i
$336$	−21.8854	+	4.06347i	−1.19395	+	0.221680i
$337$	8.16802	+	11.2423i	0.444940	+	0.612408i	0.971301	−	0.237854i	$-0.0764439\pi$
$337$	8.16802	+	11.2423i	0.444940	+	0.612408i	−0.526361	+	0.850261i	$0.676444\pi$
$338$	−17.9674	−	7.99960i	−0.977297	−	0.435121i
$339$	−4.07827	−	4.31289i	−0.221501	−	0.234244i
$340$	−1.15164	+	2.82019i	−0.0624564	+	0.152946i
$341$	34.4612	+	15.3431i	1.86618	+	0.830876i
$342$	22.1548	−	8.41439i	1.19799	−	0.454998i
$343$	−18.3101	−	2.78228i	−0.988651	−	0.150229i
$344$	9.02974	+	2.93394i	0.486851	+	0.158187i
$345$	−5.97058	+	4.86697i	−0.321445	+	0.262029i
$346$	−6.57923	+	30.9529i	−0.353702	+	1.66404i
$347$	−28.5155	−	6.06115i	−1.53079	−	0.325380i	−0.635938	−	0.771740i	$-0.719387\pi$
$347$	−28.5155	−	6.06115i	−1.53079	−	0.325380i	−0.894853	+	0.446360i	$0.852720\pi$
$348$	−2.36838	−	9.94265i	−0.126959	−	0.532982i
$349$		−	36.3047i		−	1.94335i	−0.236325	−	0.971674i	$-0.575943\pi$
$349$		−	36.3047i		−	1.94335i	0.236325	−	0.971674i	$-0.424057\pi$
$350$	2.49720	+	21.2763i	0.133481	+	1.13727i
$351$	−4.08266	−	2.53183i	−0.217916	−	0.135139i
$352$	−16.8862	−	1.77481i	−0.900038	−	0.0945978i
$353$	5.08540	−	23.9249i	0.270669	−	1.27340i	−0.607221	−	0.794533i	$-0.707716\pi$
$353$	5.08540	−	23.9249i	0.270669	−	1.27340i	0.877889	−	0.478863i	$-0.158951\pi$
$354$	1.34059	+	10.3242i	0.0712516	+	0.548727i
$355$	−11.5487	+	16.9852i	−0.612943	+	0.901482i
$356$	−2.39702	+	7.37726i	−0.127042	+	0.390994i
$357$	−2.33850	+	9.75431i	−0.123767	+	0.516253i
$358$	2.53847	+	0.824798i	0.134162	+	0.0435919i
$359$	3.59489	−	8.07426i	0.189731	−	0.426143i	−0.793484	−	0.608591i	$-0.791735\pi$
$359$	3.59489	−	8.07426i	0.189731	−	0.426143i	0.983216	+	0.182447i	$0.0584019\pi$
$360$	8.49442	+	12.3208i	0.447695	+	0.649361i
$361$	−4.38195	+	1.95097i	−0.230629	+	0.102683i
$362$	−4.95054	+	11.1191i	−0.260194	+	0.584406i
$363$	19.7841	+	13.6490i	1.03840	+	0.716386i
$364$	1.18513	+	0.955601i	0.0621179	+	0.0500871i
$365$	4.66198	−	8.68987i	0.244019	−	0.454848i
$366$	32.3871	+	2.60671i	1.69290	+	0.136255i
$367$	13.0435	+	14.4863i	0.680867	+	0.756180i	0.980209	−	0.197966i	$-0.0634337\pi$
$367$	13.0435	+	14.4863i	0.680867	+	0.756180i	−0.299342	+	0.954146i	$0.596767\pi$
$368$	4.83042	−	8.36654i	0.251803	−	0.436136i
$369$	10.2451	−	12.5603i	0.533339	−	0.653864i
$370$	−19.6408	+	2.68595i	−1.02108	+	0.139636i
$371$	6.14829	+	22.7551i	0.319203	+	1.18139i
$372$	−4.95183	−	6.47710i	−0.256740	−	0.335822i
$373$	23.5427	+	2.47444i	1.21900	+	0.128122i	0.692096	−	0.721805i	$-0.256687\pi$
$373$	23.5427	+	2.47444i	1.21900	+	0.128122i	0.526900	+	0.849927i	$0.323354\pi$
$374$	−8.83973	+	15.3109i	−0.457091	+	0.791705i
$375$	16.6407	−	9.90398i	0.859319	−	0.511439i
$376$	−1.10994	+	0.640825i	−0.0572409	+	0.0330480i
$377$	5.15232	−	7.09156i	0.265358	−	0.365234i
$378$	−15.2725	−	16.1982i	−0.785533	−	0.833146i
$379$	−1.05613	−	3.25044i	−0.0542499	−	0.166964i	0.920261	−	0.391306i	$-0.127977\pi$
$379$	−1.05613	−	3.25044i	−0.0542499	−	0.166964i	−0.974510	+	0.224342i	$0.927977\pi$
$380$	4.15980	+	5.36528i	0.213393	+	0.275233i
$381$	−14.9072	−	8.12822i	−0.763720	−	0.416421i
$382$	−26.9337	−	15.5502i	−1.37805	−	0.795618i
$383$	4.25999	+	20.0417i	0.217675	+	1.02408i	0.942256	+	0.334892i	$0.108700\pi$
$383$	4.25999	+	20.0417i	0.217675	+	1.02408i	−0.724581	+	0.689190i	$0.757967\pi$
$384$	−19.4082	−	13.3896i	−0.990420	−	0.683286i
$385$	−0.562838	+	29.5021i	−0.0286849	+	1.50357i
$386$	−7.80697	+	10.7454i	−0.397365	+	0.546925i
$387$	3.26078	+	12.3444i	0.165755	+	0.627499i
$388$	−0.343810	−	3.27114i	−0.0174543	−	0.166067i
$389$	2.64496	+	5.94068i	0.134105	+	0.301205i	0.968099	−	0.250569i	$-0.0806178\pi$
$389$	2.64496	+	5.94068i	0.134105	+	0.301205i	−0.833994	+	0.551774i	$0.813951\pi$
$390$	1.48261	−	5.60573i	0.0750750	−	0.283857i
$391$	−2.55889	−	3.52201i	−0.129408	−	0.178115i
$392$	−9.23174	−	12.5952i	−0.466273	−	0.636152i
$393$	6.96171	+	19.7706i	0.351172	+	0.997295i
$394$	3.60386	−	0.766024i	0.181560	−	0.0385917i
$395$	1.65331	−	22.4446i	0.0831869	−	1.12931i
$396$	−4.19847	−	8.31272i	−0.210981	−	0.417730i
$397$	4.15504	−	4.61464i	0.208535	−	0.231602i	−0.629799	−	0.776758i	$-0.716863\pi$
$397$	4.15504	−	4.61464i	0.208535	−	0.231602i	0.838335	+	0.545156i	$0.183530\pi$
$398$	2.56350	−	3.52836i	0.128497	−	0.176861i
$399$	16.2204	+	15.3827i	0.812036	+	0.770099i
$400$	−15.0944	+	19.0268i	−0.754720	+	0.951341i
$401$	−17.2247	+	9.94470i	−0.860162	+	0.496615i	−0.864066	−	0.503378i	$-0.832090\pi$
$401$	−17.2247	+	9.94470i	−0.860162	+	0.496615i	0.00390469	+	0.999992i	$0.498757\pi$
$402$	−6.92788	+	6.55100i	−0.345531	+	0.326734i
$403$	1.45379	−	6.83953i	0.0724182	−	0.340701i
$404$	−1.76565	+	1.96095i	−0.0878442	+	0.0975609i
$405$	−7.74005	+	18.5766i	−0.384606	+	0.923081i
$406$	31.5157	−	25.6303i	1.56410	−	1.27201i
$407$	−27.3053			−1.35347
$408$	−7.21929	+	4.40640i	−0.357408	+	0.218149i
$409$	25.5572	−	2.68617i	1.26372	−	0.132823i	0.551141	−	0.834412i	$-0.314192\pi$
$409$	25.5572	−	2.68617i	1.26372	−	0.132823i	0.712582	+	0.701589i	$0.247526\pi$
$410$	18.1122	+	7.39622i	0.894500	+	0.365273i
$411$	23.5843	−	5.61788i	1.16333	−	0.277109i
$412$	0.348756	−	0.253386i	0.0171820	−	0.0124834i
$413$	−8.22485	+	5.36579i	−0.404718	+	0.264033i
$414$	9.65078	−	0.471461i	0.474310	−	0.0231710i
$415$	−29.0593	+	10.4546i	−1.42646	+	0.513196i
$416$	0.328983	+	3.13007i	0.0161297	+	0.153464i
$417$	10.4106	+	5.67641i	0.509808	+	0.277975i
$418$	19.7004	+	34.1221i	0.963577	+	1.66896i
$419$	3.11612	−	9.59043i	0.152232	−	0.468523i	−0.845638	−	0.533758i	$-0.820780\pi$
$419$	3.11612	−	9.59043i	0.152232	−	0.468523i	0.997870	+	0.0652344i	$0.0207795\pi$
$420$	3.15930	−	5.54007i	0.154158	−	0.270328i
$421$	−1.88187	−	5.79179i	−0.0917165	−	0.282274i	0.894668	−	0.446733i	$-0.147412\pi$
$421$	−1.88187	−	5.79179i	−0.0917165	−	0.282274i	−0.986384	+	0.164458i	$0.947412\pi$
$422$	21.4554	−	23.8286i	1.04443	−	1.15996i
$423$	−1.53288	−	0.787901i	−0.0745311	−	0.0383091i
$424$	−9.93747	+	17.2122i	−0.482606	+	0.835899i
$425$	5.06613	+	9.70125i	0.245744	+	0.470580i
$426$	24.3015	−	8.55713i	1.17741	−	0.414594i
$427$	11.0434	+	28.5901i	0.534429	+	1.38357i
$428$	−1.87382	−	5.76703i	−0.0905746	−	0.278760i
$429$	3.06954	−	7.37351i	0.148199	−	0.355996i
$430$	−13.0994	+	8.11790i	−0.631710	+	0.391480i
$431$	−0.260741	+	0.234772i	−0.0125594	+	0.0113086i	−0.675386	−	0.737464i	$-0.736023\pi$
$431$	−0.260741	+	0.234772i	−0.0125594	+	0.0113086i	0.662827	+	0.748773i	$0.269356\pi$
$432$	0.794919	−	25.2273i	0.0382455	−	1.21375i
$433$	−2.96863	+	9.13650i	−0.142663	+	0.439072i	−0.996703	−	0.0811354i	$-0.974145\pi$
$433$	−2.96863	+	9.13650i	−0.142663	+	0.439072i	0.854040	+	0.520207i	$0.174145\pi$
$434$	14.6507	−	28.9030i	0.703254	−	1.38739i
$435$	−32.7721	−	16.5648i	−1.57130	−	0.794221i
$436$	−0.990079	+	9.41997i	−0.0474162	+	0.451135i
$437$	−9.64901	+	1.01415i	−0.461575	+	0.0485135i
$438$	−11.1743	+	5.30555i	−0.533927	+	0.253509i
$439$	−17.6583	−	1.85596i	−0.842783	−	0.0885801i	−0.326710	−	0.945125i	$-0.605940\pi$
$439$	−17.6583	−	1.85596i	−0.842783	−	0.0885801i	−0.516073	+	0.856544i	$0.672607\pi$
$440$	−17.9616	+	17.2168i	−0.856286	+	0.820779i
$441$	7.51318	−	19.6100i	0.357770	−	0.933810i
$442$	3.11671	+	1.01268i	0.148247	+	0.0481683i
$443$	−5.19292	−	8.99439i	−0.246723	−	0.427337i	0.715892	−	0.698211i	$-0.246020\pi$
$443$	−5.19292	−	8.99439i	−0.246723	−	0.427337i	−0.962615	+	0.270875i	$0.912687\pi$
$444$	5.18144	+	2.82520i	0.245900	+	0.134078i
$445$	14.6801	+	23.6885i	0.695904	+	1.12294i
$446$	28.2766	−	31.4043i	1.33893	−	1.48704i
$447$	−19.6977	−	25.7651i	−0.931672	−	1.21865i
$448$	1.71619	−	10.9844i	0.0810824	−	0.518963i
$449$			33.1764i			1.56569i	0.622216	+	0.782846i	$0.286233\pi$
$449$			33.1764i			1.56569i	−0.622216	+	0.782846i	$0.713767\pi$
$450$	−24.1736	−	2.38258i	−1.13955	−	0.112316i
$451$	23.3377	+	13.4740i	1.09893	+	0.634466i
$452$	−1.94853	+	0.867543i	−0.0916513	+	0.0408058i
$453$	−14.6701	−	6.10704i	−0.689260	−	0.286934i
$454$	−24.1866	+	7.85870i	−1.13513	+	0.368827i
$455$	5.37077	−	1.03493i	0.251786	−	0.0485184i
$456$	0.460001	+	18.8436i	0.0215415	+	0.882434i
$457$	19.2626	−	11.1213i	0.901068	−	0.520232i	0.0235213	−	0.999723i	$-0.492512\pi$
$457$	19.2626	−	11.1213i	0.901068	−	0.520232i	0.877546	+	0.479492i	$0.159179\pi$
$458$	−3.40338	+	3.06442i	−0.159029	+	0.143191i
$459$	−10.2396	−	4.95107i	−0.477943	−	0.231096i
$460$	0.937021	+	2.60451i	0.0436888	+	0.121436i
$461$	20.9810	+	15.2436i	0.977184	+	0.709966i	0.957078	−	0.289832i	$-0.0935994\pi$
$461$	20.9810	+	15.2436i	0.977184	+	0.709966i	0.0201067	+	0.999798i	$0.493599\pi$
$462$	22.5228	−	29.3717i	1.04786	−	1.36650i
$463$	2.00748	+	2.76306i	0.0932955	+	0.128410i	0.853113	−	0.521726i	$-0.174712\pi$
$463$	2.00748	+	2.76306i	0.0932955	+	0.128410i	−0.759818	+	0.650136i	$0.774712\pi$
$464$	45.8019	+	4.81398i	2.12630	+	0.223483i
$465$	−29.2566	−	1.43830i	−1.35674	−	0.0666996i
$466$	−3.84308	−	36.5645i	−0.178027	−	1.69382i
$467$	−3.10103	−	14.5892i	−0.143498	−	0.675107i	−0.989807	−	0.142414i	$-0.954514\pi$
$467$	−3.10103	−	14.5892i	−0.143498	−	0.675107i	0.846309	−	0.532693i	$-0.178820\pi$
$468$	−1.34539	+	1.08160i	−0.0621906	+	0.0499968i
$469$	−8.40327	−	3.20555i	−0.388027	−	0.148018i
$470$	0.368851	−	2.04735i	0.0170138	−	0.0944371i
$471$	29.4949	+	12.2785i	1.35905	+	0.565764i
$472$	−8.09952	−	1.72161i	−0.372810	−	0.0792433i
$473$	−19.3920	+	8.63386i	−0.891644	+	0.396985i
$474$	−18.3720	+	21.4338i	−0.843854	+	0.984485i
$475$	24.3690	+	1.03235i	1.11813	+	0.0473673i
$476$	3.02700	+	1.95676i	0.138742	+	0.0896880i
$477$	−26.6953	+	1.30412i	−1.22229	+	0.0597115i
$478$	14.5547	+	13.1051i	0.665717	+	0.599414i
$479$	−5.80850	−	1.23463i	−0.265397	−	0.0564119i	0.0732910	−	0.997311i	$-0.476650\pi$
$479$	−5.80850	−	1.23463i	−0.265397	−	0.0564119i	−0.338688	+	0.940899i	$0.609983\pi$
$480$	12.7242	−	3.45363i	0.580777	−	0.157636i
$481$	1.05232	+	4.95077i	0.0479816	+	0.225736i
$482$		−	7.15973i		−	0.326117i
$483$	4.35150	+	8.00835i	0.198000	+	0.364393i
$484$	6.98734	−	5.07660i	0.317607	−	0.230755i
$485$	−9.77213	−	6.64435i	−0.443730	−	0.301704i
$486$	21.6398	−	12.9984i	0.981602	−	0.589619i
$487$	−2.10952	+	0.221720i	−0.0955915	+	0.0100471i	−0.152203	−	0.988349i	$-0.548637\pi$
$487$	−2.10952	+	0.221720i	−0.0955915	+	0.0100471i	0.0566119	+	0.998396i	$0.481970\pi$
$488$	−10.5112	+	23.6086i	−0.475821	+	1.06871i
$489$	5.36373	+	1.59916i	0.242556	+	0.0723166i
$490$	25.2864	+	1.75623i	1.14232	+	0.0793383i
$491$	2.33799	+	3.21796i	0.105512	+	0.145225i	0.858508	−	0.512801i	$-0.171392\pi$
$491$	2.33799	+	3.21796i	0.105512	+	0.145225i	−0.752996	+	0.658025i	$0.771392\pi$
$492$	−3.03442	−	4.97150i	−0.136802	−	0.224132i
$493$	10.3766	−	17.9729i	0.467340	−	0.809457i
$494$	5.42750	−	4.88694i	0.244195	−	0.219874i
$495$	−32.5453	−	7.76304i	−1.46280	−	0.348923i
$496$	34.9392	−	11.3524i	1.56882	−	0.509739i
$497$	17.2205	+	17.1486i	0.772445	+	0.769218i
$498$	37.1234	+	11.0681i	1.66354	+	0.495973i
$499$	5.76751	+	9.98962i	0.258189	+	0.447197i	0.965757	−	0.259449i	$-0.0835409\pi$
$499$	5.76751	+	9.98962i	0.258189	+	0.447197i	−0.707568	+	0.706646i	$0.750208\pi$
$500$	−1.37080	−	6.82215i	−0.0613040	−	0.305096i
$501$	0.0576528	−	0.308018i	0.00257574	−	0.0137612i
$502$	0.244224	−	2.32364i	0.0109003	−	0.103709i
$503$	4.60416	−	1.49598i	0.205289	−	0.0667025i	−0.204567	−	0.978852i	$-0.565579\pi$
$503$	4.60416	−	1.49598i	0.205289	−	0.0667025i	0.409857	+	0.912150i	$0.365579\pi$
$504$	16.1866	−	7.17858i	0.721009	−	0.319759i
$505$	1.28450	+	9.39275i	0.0571593	+	0.417972i
$506$	3.33992	+	15.7131i	0.148478	+	0.698532i
$507$	20.6771	+	3.87021i	0.918303	+	0.171882i
$508$	−4.53410	+	4.08252i	−0.201168	+	0.181133i
$509$	−21.8063	−	9.70879i	−0.966547	−	0.430335i	−0.138110	−	0.990417i	$-0.544103\pi$
$509$	−21.8063	−	9.70879i	−0.966547	−	0.430335i	−0.828437	+	0.560082i	$0.810770\pi$
$510$	2.10366	−	13.5661i	0.0931518	−	0.600719i
$511$	−9.08325	−	7.32404i	−0.401819	−	0.323996i
$512$	4.15575	−	3.01933i	0.183660	−	0.133437i
$513$	−20.9658	+	14.2458i	−0.925665	+	0.628967i
$514$	−17.2954	−	38.8461i	−0.762868	−	1.71343i
$515$	0.113777	−	1.54459i	0.00501360	−	0.0680627i
$516$	4.57313	+	0.368074i	0.201321	+	0.0162035i
$517$	0.885472	−	2.72520i	0.0389430	−	0.119854i
$518$	−1.17854	+	23.4260i	−0.0517819	+	1.02928i
$519$	−0.825988	−	33.8360i	−0.0362568	−	1.48524i
$520$	3.81383	+	2.59313i	0.167248	+	0.113716i
$521$	−13.4308	−	2.85481i	−0.588415	−	0.125072i	−0.0959237	−	0.995389i	$-0.530580\pi$
$521$	−13.4308	−	2.85481i	−0.588415	−	0.125072i	−0.492492	+	0.870317i	$0.663914\pi$
$522$	20.7656	+	41.1147i	0.908887	+	1.79954i
$523$	−0.0888052	+	0.844925i	−0.00388318	+	0.0369460i	−0.996292	−	0.0860374i	$-0.972580\pi$
$523$	−0.0888052	+	0.844925i	−0.00388318	+	0.0369460i	0.992409	+	0.122983i	$0.0392462\pi$
$524$	7.53186			0.329031
$525$	−7.87144	−	21.5184i	−0.343538	−	0.939139i
$526$	−19.9132			−0.868256
$527$	1.73045	−	16.4641i	0.0753795	−	0.717188i
$528$	41.6134	−	5.40345i	1.81099	−	0.235155i
$529$	18.6282	+	3.95954i	0.809920	+	0.172154i
$530$	−10.9209	−	30.3552i	−0.474371	−	1.31855i
$531$	−3.95363	−	10.4098i	−0.171573	−	0.451745i
$532$	7.14965	−	3.66180i	0.309977	−	0.158759i
$533$	1.54358	−	4.75066i	0.0668600	−	0.205774i
$534$	2.80450	−	34.8445i	0.121363	−	1.50787i
$535$	−20.1688	−	8.23602i	−0.871973	−	0.356074i
$536$	−3.08452	−	6.92795i	−0.133231	−	0.299242i
$537$	−2.84561	−	0.229032i	−0.122797	−	0.00988348i
$538$	−28.1691	+	20.4661i	−1.21446	+	0.882354i
$539$	34.1809	+	7.11594i	1.47227	+	0.306505i
$540$	5.37256	+	4.84048i	0.231198	+	0.208301i
$541$	31.8089	+	14.1622i	1.36757	+	0.608881i	0.953508	−	0.301368i	$-0.0974432\pi$
$541$	31.8089	+	14.1622i	1.36757	+	0.608881i	0.414061	+	0.910249i	$0.364110\pi$
$542$	15.6375	−	14.0801i	0.671689	−	0.604792i
$543$	2.39507	−	12.7960i	0.102782	−	0.549128i
$544$	1.54925	+	7.28863i	0.0664234	+	0.312497i
$545$	23.5479	+	24.5666i	1.00868	+	1.05232i
$546$	−6.19345	−	2.95169i	−0.265055	−	0.126321i
$547$	−11.1170	+	3.61213i	−0.475328	+	0.154443i	−0.536877	−	0.843661i	$-0.680396\pi$
$547$	−11.1170	+	3.61213i	−0.475328	+	0.154443i	0.0615488	+	0.998104i	$0.480396\pi$
$548$	0.910631	−	8.66408i	0.0389002	−	0.370111i
$549$	−34.3437	+	5.31472i	−1.46575	+	0.226827i
$550$	−2.51765	−	40.3061i	−0.107353	−	1.71866i
$551$	−23.1256	−	40.0547i	−0.985183	−	1.70639i
$552$	−2.19573	+	7.36469i	−0.0934566	+	0.313462i
$553$	−25.7358	−	6.83819i	−1.09440	−	0.290789i
$554$	−16.6815	+	5.42013i	−0.708727	+	0.230279i
$555$	19.7699	−	7.66248i	0.839184	−	0.325254i
$556$	3.16643	−	2.85106i	0.134286	−	0.120912i
$557$	12.4523	−	21.5681i	0.527622	−	0.913869i	−0.471859	−	0.881674i	$-0.656417\pi$
$557$	12.4523	−	21.5681i	0.527622	−	0.913869i	0.999482	−	0.0321949i	$-0.0102497\pi$
$558$	28.4723	+	23.2241i	1.20533	+	0.983154i
$559$	2.31277	+	3.18325i	0.0978196	+	0.134637i
$560$	18.8178	+	21.7185i	0.795199	+	0.917775i
$561$	5.40274	−	18.1213i	0.228104	−	0.765081i
$562$	7.41122	−	16.6459i	0.312624	−	0.702164i
$563$	12.8329	−	1.34879i	0.540841	−	0.0568447i	0.169830	−	0.985473i	$-0.445678\pi$
$563$	12.8329	−	1.34879i	0.540841	−	0.0568447i	0.371011	+	0.928629i	$0.379011\pi$
$564$	−0.449995	+	0.425515i	−0.0189482	+	0.0179174i
$565$	−2.13958	+	7.35829i	−0.0900126	+	0.309566i
$566$	−33.4278	+	24.2867i	−1.40507	+	1.02085i
$567$	19.9051	+	13.0685i	0.835937	+	0.548825i
$568$			20.4918i			0.859817i
$569$	0.201435	+	0.947675i	0.00844458	+	0.0397286i	0.982168	−	0.188005i	$-0.0602020\pi$
$569$	0.201435	+	0.947675i	0.00844458	+	0.0397286i	−0.973724	+	0.227733i	$0.926869\pi$
$570$	−23.8391	−	19.1770i	−0.998509	−	0.803238i
$571$	−29.2937	−	6.22657i	−1.22590	−	0.260574i	−0.450926	−	0.892561i	$-0.648906\pi$
$571$	−29.2937	−	6.22657i	−1.22590	−	0.260574i	−0.774979	+	0.631987i	$0.782239\pi$
$572$	−2.13281	−	1.92039i	−0.0891774	−	0.0802957i
$573$	31.8777	+	9.50411i	1.33171	+	0.397040i
$574$	12.5670	−	19.4404i	0.524536	−	0.811429i
$575$	9.31919	+	3.47055i	0.388637	+	0.144732i
$576$	11.7528	+	4.55937i	0.489701	+	0.189974i
$577$	−4.28989	+	1.90998i	−0.178591	+	0.0795137i	−0.494084	−	0.869414i	$-0.664497\pi$
$577$	−4.28989	+	1.90998i	−0.178591	+	0.0795137i	0.315494	+	0.948928i	$0.397830\pi$
$578$	−19.3386	−	4.11056i	−0.804381	−	0.170977i
$579$	5.45972	−	13.1151i	0.226898	−	0.545045i
$580$	−9.52572	+	9.13072i	−0.395534	+	0.379133i
$581$	5.79179	+	36.0790i	0.240284	+	1.49681i
$582$	4.92319	+	13.9814i	0.204073	+	0.579548i
$583$	−9.23863	−	43.4644i	−0.382625	−	1.80011i
$584$	−1.02841	−	9.78464i	−0.0425558	−	0.404891i
$585$	−0.153267	+	6.20002i	−0.00633683	+	0.256339i
$586$	35.3762	+	3.71818i	1.46138	+	0.153597i
$587$	11.9322	+	16.4233i	0.492495	+	0.677861i	0.980846	−	0.194787i	$-0.0624014\pi$
$587$	11.9322	+	16.4233i	0.492495	+	0.677861i	−0.488351	+	0.872647i	$0.662401\pi$
$588$	−5.74988	−	4.88691i	−0.237121	−	0.201533i
$589$	−29.8482	−	21.6860i	−1.22987	−	0.893554i
$590$	10.6219	−	8.23534i	0.437295	−	0.339044i
$591$	−3.55984	+	1.69021i	−0.146432	+	0.0695261i
$592$	−19.7618	+	17.7936i	−0.812206	+	0.731314i
$593$	26.8233	−	15.4864i	1.10150	−	0.635952i	0.164886	−	0.986313i	$-0.447274\pi$
$593$	26.8233	−	15.4864i	1.10150	−	0.635952i	0.936615	+	0.350361i	$0.113941\pi$
$594$	27.0865	+	32.0580i	1.11137	+	1.31536i
$595$	12.3899	−	3.76600i	0.507936	−	0.154391i
$596$	−11.0836	+	3.60129i	−0.454003	+	0.147515i
$597$	−1.79276	+	4.30649i	−0.0733727	+	0.176253i
$598$	2.72025	−	1.21113i	0.111239	−	0.0495269i
$599$	−19.1621	−	11.0632i	−0.782940	−	0.452031i	0.0545309	−	0.998512i	$-0.482634\pi$
$599$	−19.1621	−	11.0632i	−0.782940	−	0.452031i	−0.837471	+	0.546481i	$0.815967\pi$
$600$	8.17333	−	17.5059i	0.333675	−	0.714676i
$601$			25.5231i			1.04111i	0.853829	+	0.520554i	$0.174275\pi$
$601$			25.5231i			1.04111i	−0.853829	+	0.520554i	$0.825725\pi$
$602$	6.57024	+	17.0095i	0.267783	+	0.693257i
$603$	5.58460	−	8.53312i	0.227423	−	0.347496i
$604$	−3.82075	+	4.24337i	−0.155464	+	0.172660i
$605$	2.27952	−	30.9459i	0.0926757	−	1.25813i
$606$	5.69271	−	10.4405i	0.231250	−	0.424115i
$607$	9.50630	+	16.4654i	0.385849	+	0.668310i	0.991887	−	0.127126i	$-0.0405753\pi$
$607$	9.50630	+	16.4654i	0.385849	+	0.668310i	−0.606038	+	0.795436i	$0.707242\pi$
$608$	15.7937	+	5.13168i	0.640519	+	0.208117i
$609$	−26.4387	+	34.4784i	−1.07135	+	1.39714i
$610$	−18.2480	−	37.7696i	−0.738842	−	1.52924i
$611$	−0.528236	−	0.0555199i	−0.0213701	−	0.00224609i
$612$	−2.90018	+	2.87968i	−0.117233	+	0.116404i
$613$	−41.9951	+	4.41386i	−1.69616	+	0.178274i	−0.902679	−	0.430315i	$-0.858402\pi$
$613$	−41.9951	+	4.41386i	−1.69616	+	0.178274i	−0.793486	+	0.608589i	$0.791736\pi$
$614$	1.52230	−	14.4837i	0.0614349	−	0.584514i
$615$	−20.6783	−	3.20652i	−0.833828	−	0.129299i
$616$	16.0853	+	24.6560i	0.648094	+	0.993418i
$617$	3.70275	−	11.3959i	0.149067	−	0.458782i	−0.848444	−	0.529285i	$-0.822460\pi$
$617$	3.70275	−	11.3959i	0.149067	−	0.458782i	0.997512	+	0.0705029i	$0.0224604\pi$
$618$	−1.26432	+	1.47502i	−0.0508584	+	0.0593341i
$619$	−19.9126	+	17.9294i	−0.800355	+	0.720643i	−0.964008	−	0.265875i	$-0.914339\pi$
$619$	−19.9126	+	17.9294i	−0.800355	+	0.720643i	0.163652	+	0.986518i	$0.447673\pi$
$620$	−3.97921	+	9.74448i	−0.159809	+	0.391348i
$621$	−9.92446	+	2.88242i	−0.398255	+	0.115668i
$622$	−9.68928	−	29.8205i	−0.388505	−	1.19569i
$623$	30.7594	−	11.8814i	1.23235	−	0.476017i
$624$	−2.58345	−	7.33675i	−0.103421	−	0.293705i
$625$	−21.8968	−	12.0635i	−0.875873	−	0.482542i
$626$	4.74746	−	8.22283i	0.189746	−	0.328651i
$627$	−28.9545	−	30.6202i	−1.15633	−	1.22285i
$628$	7.68181	−	8.53151i	0.306537	−	0.340444i
$629$	3.70300	+	11.3967i	0.147648	+	0.454414i
$630$	−8.06483	+	27.5864i	−0.321310	+	1.09907i
$631$	10.4069	−	32.0292i	0.414293	−	1.27506i	−0.498589	−	0.866839i	$-0.666148\pi$
$631$	10.4069	−	32.0292i	0.414293	−	1.27506i	0.912882	−	0.408224i	$-0.133852\pi$
$632$	−11.2266	−	19.4450i	−0.446570	−	0.773482i
$633$	−16.4179	+	30.1105i	−0.652551	+	1.19678i
$634$	−2.60578	−	24.7923i	−0.103489	−	0.984629i
$635$	0.683598	+	21.9094i	0.0271278	+	0.869447i
$636$	−2.74401	+	9.20366i	−0.108807	+	0.364949i
$637$	−0.0270940	−	6.47163i	−0.00107350	−	0.256415i
$638$	−61.9540	+	45.0122i	−2.45278	+	1.78205i
$639$	−23.1640	+	14.9264i	−0.916354	+	0.590477i
$640$	−2.23620	+	30.3578i	−0.0883937	+	1.20000i
$641$	20.0603	−	2.10842i	0.792334	−	0.0832777i	0.300290	−	0.953848i	$-0.402917\pi$
$641$	20.0603	−	2.10842i	0.792334	−	0.0832777i	0.492044	+	0.870570i	$0.336250\pi$
$642$	14.2370	+	23.3255i	0.561891	+	0.920583i
$643$	−28.8063			−1.13601			−0.568005	−	0.823025i	$-0.692284\pi$
$643$	−28.8063			−1.13601			−0.568005	+	0.823025i	$0.692284\pi$
$644$	3.23367	−	0.519104i	0.127424	−	0.0204556i
$645$	11.6175	−	11.6930i	0.457439	−	0.460411i
$646$	11.5702	−	12.8500i	0.455222	−	0.505575i
$647$	−8.10332	+	38.1231i	−0.318574	+	1.49877i	0.469355	+	0.883009i	$0.344486\pi$
$647$	−8.10332	+	38.1231i	−0.318574	+	1.49877i	−0.787930	+	0.615765i	$0.788847\pi$
$648$	4.03502	+	19.6682i	0.158510	+	0.772642i
$649$	16.0328	−	9.25652i	0.629341	−	0.363350i
$650$	−7.21095	+	2.00984i	−0.282837	+	0.0788323i
$651$	−8.08012	+	33.7036i	−0.316685	+	1.32095i
$652$	1.18217	−	1.62711i	0.0462972	−	0.0637226i
$653$	−12.0544	+	13.3878i	−0.471725	+	0.523904i	−0.931309	−	0.364231i	$-0.881332\pi$
$653$	−12.0544	+	13.3878i	−0.471725	+	0.523904i	0.459584	+	0.888134i	$0.347999\pi$
$654$	−5.49655	−	42.3304i	−0.214932	−	1.65525i
$655$	17.4707	−	20.6643i	0.682635	−	0.807421i
$656$	25.6707	−	5.45647i	1.00227	−	0.213039i
$657$	10.3115	−	8.28970i	0.402290	−	0.323412i
$658$	−2.29981	−	0.877294i	−0.0896558	−	0.0342005i
$659$	−6.00295	−	8.26236i	−0.233842	−	0.321856i	0.675929	−	0.736967i	$-0.263743\pi$
$659$	−6.00295	−	8.26236i	−0.233842	−	0.321856i	−0.909771	+	0.415111i	$0.863743\pi$
$660$	−6.51540	+	10.1043i	−0.253612	+	0.393310i
$661$	−1.17298	−	2.63456i	−0.0456236	−	0.102472i	0.889296	−	0.457333i	$-0.151195\pi$
$661$	−1.17298	−	2.63456i	−0.0456236	−	0.102472i	−0.934919	+	0.354860i	$0.884528\pi$
$662$	−2.75635	−	26.2249i	−0.107128	−	1.01926i
$663$	−3.49382	−	0.281204i	−0.135689	−	0.0109211i
$664$	−18.1102	+	24.9266i	−0.702813	+	0.967339i
$665$	6.53763	−	28.1095i	0.253518	−	1.09004i
$666$	−25.6653	−	6.97466i	−0.994511	−	0.270262i
$667$	−3.92061	−	18.4450i	−0.151807	−	0.714195i
$668$	−0.0975179	−	0.0563020i	−0.00377308	−	0.00217839i
$669$	−21.6375	+	39.6833i	−0.836552	+	1.53424i
$670$	11.8198	+	3.43684i	0.456637	+	0.132777i
$671$	−17.8544	−	54.9502i	−0.689262	−	2.12133i
$672$	−1.22895	−	15.5517i	−0.0474078	−	0.599919i
$673$	15.2358	−	20.9703i	0.587298	−	0.808346i	−0.407174	−	0.913351i	$-0.633486\pi$
$673$	15.2358	−	20.9703i	0.587298	−	0.808346i	0.994472	+	0.105005i	$0.0334858\pi$
$674$	−19.4884	+	11.2517i	−0.750666	+	0.433397i
$675$	25.7423	−	3.51226i	0.990820	−	0.135187i
$676$	3.77953	−	6.54634i	0.145367	−	0.251782i
$677$	26.5569	+	2.79125i	1.02067	+	0.107276i	0.600050	−	0.799963i	$-0.295147\pi$
$677$	26.5569	+	2.79125i	1.02067	+	0.107276i	0.420616	+	0.907239i	$0.361814\pi$
$678$	7.63628	−	5.83804i	0.293270	−	0.224209i
$679$	−9.86611	+	9.90750i	−0.378627	+	0.380215i
$680$	9.62178	+	5.16194i	0.368978	+	0.197951i
$681$	23.2176	−	14.1712i	0.889700	−	0.543041i
$682$	−30.5435	+	52.9029i	−1.16957	+	2.02576i
$683$	8.77990	+	9.75107i	0.335954	+	0.373114i	0.887324	−	0.461146i	$-0.152562\pi$
$683$	8.77990	+	9.75107i	0.335954	+	0.373114i	−0.551371	+	0.834260i	$0.685895\pi$
$684$	2.32620	+	8.80631i	0.0889445	+	0.336718i
$685$	−21.6584	−	22.5953i	−0.827524	−	0.863322i
$686$	7.58025	−	29.0176i	0.289415	−	1.10790i
$687$	2.78161	−	4.03193i	0.106125	−	0.153828i
$688$	−8.40837	+	18.8855i	−0.320566	+	0.720003i
$689$	−7.52455	+	3.35014i	−0.286662	+	0.127630i
$690$	−6.82765	−	10.4395i	−0.259924	−	0.397425i
$691$	−2.07692	+	4.66484i	−0.0790098	+	0.177459i	−0.948731	−	0.316084i	$-0.897632\pi$
$691$	−2.07692	+	4.66484i	−0.0790098	+	0.177459i	0.869721	+	0.493543i	$0.164298\pi$
$692$	−11.5669	−	3.75830i	−0.439706	−	0.142869i
$693$	−16.1546	+	36.1424i	−0.613663	+	1.37294i
$694$	14.5884	−	44.8984i	0.553768	−	1.70432i
$695$	−0.477396	−	15.3006i	−0.0181087	−	0.580385i
$696$	−36.3304	+	4.71746i	−1.37710	+	0.178815i
$697$	2.45883	−	11.5679i	0.0931350	−	0.438166i
$698$	58.4691	+	6.14535i	2.21309	+	0.232605i
$699$	13.0609	+	37.0916i	0.494007	+	1.40293i
$700$	−8.23282	+	0.0997493i	−0.311171	+	0.00377017i
$701$		−	42.8024i		−	1.61662i	−0.588754	−	0.808312i	$-0.700381\pi$
$701$		−	42.8024i		−	1.61662i	0.588754	−	0.808312i	$-0.299619\pi$
$702$	4.76861	−	6.14659i	0.179980	−	0.231988i
$703$	26.1223	+	5.55246i	0.985221	+	0.209415i
$704$	−4.35753	+	20.5006i	−0.164231	+	0.772645i
$705$	0.123644	+	2.22161i	0.00465670	+	0.0836707i
$706$	37.6705	+	12.2399i	1.41775	+	0.460654i
$707$	11.2029	+	0.563608i	0.421330	+	0.0211967i
$708$	−4.00011	+	0.0976487i	−0.150333	+	0.00366986i
$709$	29.5418	+	13.1529i	1.10947	+	0.493966i	0.877896	−	0.478852i	$-0.158947\pi$
$709$	29.5418	+	13.1529i	1.10947	+	0.493966i	0.231571	+	0.972818i	$0.425614\pi$
$710$	−25.4000	−	21.4744i	−0.953244	−	0.805921i
$711$	13.8032	−	26.8545i	0.517661	−	1.00712i
$712$	25.4000	+	11.3088i	0.951904	+	0.423815i
$713$	−8.84160	−	12.1694i	−0.331121	−	0.455749i
$714$	−15.3135	−	5.41730i	−0.573095	−	0.202737i
$715$	−10.2160	+	1.39707i	−0.382055	+	0.0522476i
$716$	−0.417245	+	0.937148i	−0.0155932	+	0.0350229i
$717$	−18.3917	−	10.0281i	−0.686850	−	0.374508i
$718$	12.3952	+	7.15634i	0.462583	+	0.267072i
$719$	−21.7581	+	4.62483i	−0.811440	+	0.172477i	−0.594903	−	0.803797i	$-0.702810\pi$
$719$	−21.7581	+	4.62483i	−0.811440	+	0.172477i	−0.216537	+	0.976274i	$0.569476\pi$
$720$	−28.6130	+	15.5899i	−1.06634	+	0.581001i
$721$	−1.77108	−	0.470588i	−0.0659585	−	0.0175256i
$722$	−2.40032	−	7.38741i	−0.0893305	−	0.274931i
$723$	1.77449	+	7.44945i	0.0659940	+	0.277048i
$724$	−4.05119	−	2.33895i	−0.150561	−	0.0869265i
$725$	2.95538	+	47.3139i	0.109760	+	1.75720i
$726$	−25.3307	+	29.5521i	−0.940109	+	1.09678i
$727$	17.9382	+	13.0329i	0.665291	+	0.483363i	0.868446	−	0.495784i	$-0.165119\pi$
$727$	17.9382	+	13.0329i	0.665291	+	0.483363i	−0.203154	+	0.979147i	$0.565119\pi$
$728$	3.85051	−	3.86666i	0.142709	−	0.143308i
$729$	−19.2939	+	18.8877i	−0.714590	+	0.699543i
$730$	13.2060	+	8.97910i	0.488774	+	0.332331i
$731$	6.23342	+	6.92292i	0.230551	+	0.256053i
$732$	−2.29750	+	12.2747i	−0.0849179	+	0.453685i
$733$	−22.5780	+	4.79911i	−0.833939	+	0.177259i	−0.605044	−	0.796192i	$-0.706845\pi$
$733$	−22.5780	+	4.79911i	−0.833939	+	0.177259i	−0.228895	+	0.973451i	$0.573511\pi$
$734$	−25.5382	+	18.5546i	−0.942633	+	0.684863i
$735$	−26.7449	+	4.43976i	−0.986500	+	0.163763i
$736$	5.47757	+	3.97969i	0.201906	+	0.146693i
$737$	15.4892	+	6.89622i	0.570551	+	0.254026i
$738$	18.4943	+	18.6259i	0.680784	+	0.685630i
$739$	46.0398	−	20.4982i	1.69360	−	0.754040i	0.694189	−	0.719793i	$-0.255763\pi$
$739$	46.0398	−	20.4982i	1.69360	−	0.754040i	0.999413	−	0.0342470i	$-0.0109033\pi$
$740$	−0.237604	−	7.61525i	−0.00873451	−	0.279942i
$741$	−4.43593	+	6.42986i	−0.162958	+	0.236207i
$742$	−37.6880	+	6.05009i	−1.38357	+	0.222106i
$743$	38.0175			1.39473			0.697364	−	0.716717i	$-0.254356\pi$
$743$	38.0175			1.39473			0.697364	+	0.716717i	$0.254356\pi$
$744$	−24.9445	+	15.2252i	−0.914509	+	0.558184i
$745$	−15.8288	+	38.7623i	−0.579922	+	1.42014i
$746$	−7.97021	+	37.4969i	−0.291810	+	1.37286i
$747$	−41.3687	−	2.31519i	−1.51360	−	0.0847084i
$748$	−5.49717	−	3.99393i	−0.200997	−	0.146033i
$749$	−13.9939	+	21.6478i	−0.511327	+	0.790994i
$750$	13.1337	+	28.4764i	0.479573	+	1.03981i
$751$	−14.5342	−	25.1739i	−0.530360	−	0.918610i	−0.999373	−	0.0354186i	$-0.988724\pi$
$751$	−14.5342	−	25.1739i	−0.530360	−	0.918610i	0.469013	−	0.883191i	$-0.344610\pi$
$752$	−1.13504	−	2.54935i	−0.0413907	−	0.0929651i
$753$	0.321791	+	2.47820i	0.0117267	+	0.0903105i
$754$	10.5489	+	9.49825i	0.384168	+	0.345906i
$755$	2.77957	+	20.3253i	0.101159	+	0.739715i
$756$	6.80504	−	5.18689i	0.247497	−	0.188645i
$757$			32.7653i			1.19088i	0.803401	+	0.595438i	$0.203022\pi$
$757$			32.7653i			1.19088i	−0.803401	+	0.595438i	$0.796978\pi$
$758$	5.41364	−	1.15070i	0.196632	−	0.0417955i
$759$	−7.36946	−	15.5212i	−0.267494	−	0.563382i
$760$	20.6844	−	12.8184i	0.750302	−	0.464973i
$761$	−1.83718	+	17.4796i	−0.0665979	+	0.633636i	0.909410	+	0.415901i	$0.136534\pi$
$761$	−1.83718	+	17.4796i	−0.0665979	+	0.633636i	−0.976008	+	0.217735i	$0.930133\pi$
$762$	15.6139	−	22.6323i	0.565633	−	0.819882i
$763$	33.7227	−	22.0003i	1.22084	−	0.796464i
$764$	7.02583	−	9.67023i	0.254186	−	0.349856i
$765$	1.17349	+	14.6365i	0.0424275	+	0.529183i
$766$	−32.9984	+	3.46827i	−1.19228	+	0.125314i
$767$	−2.29620	−	2.55019i	−0.0829110	−	0.0920820i
$768$	15.3761	−	17.9386i	0.554836	−	0.647302i
$769$	−18.9093	−	6.14401i	−0.681888	−	0.221559i	−0.0524660	−	0.998623i	$-0.516708\pi$
$769$	−18.9093	−	6.14401i	−0.681888	−	0.221559i	−0.629422	+	0.777064i	$0.716708\pi$
$770$	−47.4181	−	5.90032i	−1.70883	−	0.212633i
$771$	27.6230	+	36.1315i	0.994820	+	1.30125i
$772$	−3.79359	−	3.41576i	−0.136534	−	0.122936i
$773$	15.5042	+	34.8230i	0.557647	+	1.25249i	0.943939	+	0.330119i	$0.107089\pi$
$773$	15.5042	+	34.8230i	0.557647	+	1.25249i	−0.386293	+	0.922376i	$0.626245\pi$
$774$	−20.4326	+	3.16197i	−0.734436	+	0.113655i
$775$	17.5048	+	33.5203i	0.628790	+	1.20408i
$776$	−11.7896			−0.423221
$777$	−4.57974	−	24.6660i	−0.164297	−	0.884888i
$778$	−10.0152	+	3.25415i	−0.359063	+	0.116667i
$779$	−19.5866	−	17.6359i	−0.701764	−	0.631871i
$780$	2.08313	+	0.791908i	0.0745879	+	0.0283549i
$781$	−30.6559	−	34.0468i	−1.09695	−	1.21829i
$782$	6.10536	−	3.52493i	0.218327	−	0.126051i
$783$	−31.7959	−	37.6318i	−1.13629	−	1.34485i
$784$	29.3750	−	17.1241i	1.04911	−	0.611574i
$785$	−5.58846	−	40.8651i	−0.199461	−	1.45854i
$786$	−33.0191	+	7.86529i	−1.17775	+	0.280546i
$787$	1.30609	+	12.4266i	0.0465569	+	0.442959i	0.992825	+	0.119576i	$0.0381536\pi$
$787$	1.30609	+	12.4266i	0.0465569	+	0.442959i	−0.946268	+	0.323383i	$0.895180\pi$
$788$	0.148017	+	1.40829i	0.00527288	+	0.0501681i
$789$	20.7190	−	4.93535i	0.737615	−	0.175703i
$790$	35.8674	+	6.46189i	1.27611	+	0.229904i
$791$	8.08739	+	4.09943i	0.287554	+	0.145759i
$792$	−31.2058	+	11.8520i	−1.10885	+	0.421141i
$793$	−9.27503	+	5.35494i	−0.329366	+	0.190159i
$794$	6.72858	+	7.47284i	0.238788	+	0.265201i
$795$	18.8861	+	28.8769i	0.669821	+	1.02416i
$796$	1.24567	+	1.12160i	0.0441515	+	0.0397542i
$797$	−14.5708	+	4.73433i	−0.516124	+	0.167699i	−0.555485	−	0.831526i	$-0.687468\pi$
$797$	−14.5708	+	4.73433i	−0.516124	+	0.167699i	0.0393618	+	0.999225i	$0.487468\pi$
$798$	−27.5196	+	23.5192i	−0.974185	+	0.832572i
$799$	−1.25752			−0.0444880
$800$	−12.1558	−	11.9146i	−0.429773	−	0.421243i
$801$	5.71799	+	36.9496i	0.202035	+	1.30555i
$802$	−13.1004	−	29.4239i	−0.462590	−	1.03899i
$803$	16.3466	+	14.7185i	0.576858	+	0.519405i
$804$	−2.22568	−	2.91124i	−0.0784937	−	0.102672i
$805$	6.07651	−	10.0759i	0.214169	−	0.355131i
$806$	10.7690	+	3.49907i	0.379323	+	0.123249i
$807$	24.2366	−	28.2758i	0.853170	−	0.995354i
$808$	6.32875	+	7.02879i	0.222645	+	0.247272i
$809$	21.4909	−	2.25879i	0.755580	−	0.0794147i	0.281097	−	0.959679i	$-0.409302\pi$
$809$	21.4909	−	2.25879i	0.755580	−	0.0794147i	0.474483	+	0.880265i	$0.342635\pi$
$810$	−28.6077	−	15.6099i	−1.00517	−	0.548476i
$811$	−3.26311	+	4.49129i	−0.114583	+	0.157710i	−0.862456	−	0.506131i	$-0.831075\pi$
$811$	−3.26311	+	4.49129i	−0.114583	+	0.157710i	0.747873	+	0.663842i	$0.231075\pi$
$812$	8.53062	+	13.0760i	0.299366	+	0.458877i
$813$	−12.7807	+	18.5255i	−0.448237	+	0.649718i
$814$	4.62200	−	43.9754i	0.162001	−	1.54134i
$815$	−1.72201	−	7.01757i	−0.0603193	−	0.245815i
$816$	−7.89866	−	16.6357i	−0.276508	−	0.582367i
$817$	20.3075	−	4.31649i	0.710468	−	0.151015i
$818$			41.6148i			1.45503i
$819$	7.17562	+	1.53613i	0.250737	+	0.0536767i
$820$	−3.55472	+	6.62594i	−0.124136	+	0.231388i
$821$	4.15163	+	3.73815i	0.144893	+	0.130462i	0.738390	−	0.674374i	$-0.235586\pi$
$821$	4.15163	+	3.73815i	0.144893	+	0.130462i	−0.593497	+	0.804836i	$0.702253\pi$
$822$	5.05549	+	38.9336i	0.176330	+	1.35797i
$823$	17.1068	+	38.4226i	0.596307	+	1.33933i	0.919535	+	0.393007i	$0.128565\pi$
$823$	17.1068	+	38.4226i	0.596307	+	1.33933i	−0.323228	+	0.946321i	$0.604768\pi$
$824$	−0.772589	−	1.33816i	−0.0269144	−	0.0466171i
$825$	12.6091	+	41.3132i	0.438993	+	1.43834i
$826$	−7.24942	−	14.1545i	−0.252240	−	0.492497i
$827$	26.1924	+	19.0299i	0.910798	+	0.661734i	0.941217	−	0.337804i	$-0.109684\pi$
$827$	26.1924	+	19.0299i	0.910798	+	0.661734i	−0.0304183	+	0.999537i	$0.509684\pi$
$828$	−0.207505	+	3.70778i	−0.00721130	+	0.128854i
$829$	9.58075	−	45.0739i	0.332753	−	1.56548i	−0.420215	−	0.907424i	$-0.638045\pi$
$829$	9.58075	−	45.0739i	0.332753	−	1.56548i	0.752969	−	0.658057i	$-0.228621\pi$
$830$	−11.9183	−	48.5698i	−0.413691	−	1.68588i
$831$	16.0131	−	9.77385i	0.555490	−	0.339051i
$832$	3.88493			0.134686
$833$	−1.66538	−	15.2314i	−0.0577021	−	0.527736i
$834$	−10.9041	+	15.8055i	−0.377578	+	0.547298i
$835$	−0.380669	+	0.136952i	−0.0131736	+	0.00473943i
$836$	−13.8340	+	6.15929i	−0.478459	+	0.213024i
$837$	−35.3804	−	17.1072i	−1.22292	−	0.591312i
$838$	14.9180	+	6.64192i	0.515333	+	0.229441i
$839$	9.32957	+	6.77833i	0.322093	+	0.234014i	0.737068	−	0.675819i	$-0.236210\pi$
$839$	9.32957	+	6.77833i	0.322093	+	0.234014i	−0.414975	+	0.909833i	$0.636210\pi$
$840$	−18.5652	−	13.3378i	−0.640561	−	0.460198i
$841$	49.2641	−	35.7924i	1.69876	−	1.23422i
$842$	9.64626	−	2.05038i	0.332432	−	0.0706606i
$843$	−3.58556	+	19.1563i	−0.123493	+	0.659778i
$844$	8.24612	+	9.15825i	0.283843	+	0.315240i
$845$	−9.19356	−	25.5541i	−0.316268	−	0.879089i
$846$	1.52839	−	2.33535i	0.0525473	−	0.0802908i
$847$	−35.4837	−	9.42825i	−1.21923	−	0.323959i
$848$	−35.0101	−	25.4363i	−1.20225	−	0.873486i
$849$	28.7612	−	33.5543i	0.987081	−	1.15158i
$850$	−16.4815	+	6.51691i	−0.565310	+	0.223528i
$851$	9.42953	+	5.44414i	0.323240	+	0.186623i
$852$	2.29452	+	9.63257i	0.0786089	+	0.330007i
$853$	−1.63213	−	5.02317i	−0.0558829	−	0.171990i	0.919219	−	0.393746i	$-0.128821\pi$
$853$	−1.63213	−	5.02317i	−0.0558829	−	0.171990i	−0.975102	+	0.221756i	$0.928821\pi$
$854$	−47.9139	+	12.9461i	−1.63958	+	0.443005i
$855$	29.5566	+	14.0447i	1.01082	+	0.480319i
$856$	−21.2600	+	4.51896i	−0.726654	+	0.154455i
$857$	−21.9450	−	12.6700i	−0.749627	−	0.432797i	0.0759322	−	0.997113i	$-0.475807\pi$
$857$	−21.9450	−	12.6700i	−0.749627	−	0.432797i	−0.825559	+	0.564316i	$0.809140\pi$
$858$	11.3555	+	6.19164i	0.387671	+	0.211379i
$859$	7.43240	−	16.6934i	0.253590	−	0.569573i	−0.741227	−	0.671255i	$-0.765756\pi$
$859$	7.43240	−	16.6934i	0.253590	−	0.569573i	0.994817	+	0.101682i	$0.0324224\pi$
$860$	−2.57666	−	5.33315i	−0.0878635	−	0.181859i
$861$	−8.25735	+	23.3418i	−0.281410	+	0.795485i
$862$	−0.333966	−	0.459665i	−0.0113749	−	0.0156563i
$863$	−16.5921	−	7.38727i	−0.564801	−	0.251466i	0.104415	−	0.994534i	$-0.466703\pi$
$863$	−16.5921	−	7.38727i	−0.564801	−	0.251466i	−0.669216	+	0.743068i	$0.733370\pi$
$864$	17.5251	+	2.40213i	0.596215	+	0.0817222i
$865$	−37.1413	+	23.0170i	−1.26284	+	0.782603i
$866$	−14.2119	−	6.32754i	−0.482940	−	0.215019i
$867$	21.1400	−	0.516058i	0.717951	−	0.0175263i
$868$	10.4591	+	6.76111i	0.355004	+	0.229487i
$869$	47.7427	+	15.5126i	1.61956	+	0.526228i
$870$	32.2251	−	49.9758i	1.09253	−	1.69434i
$871$	0.653428	−	3.07414i	0.0221406	−	0.104163i
$872$	33.2088	+	7.05876i	1.12459	+	0.239040i
$873$	−8.58760	−	13.3270i	−0.290646	−	0.451050i
$874$		−	15.7115i		−	0.531448i
$875$	−18.8229	+	22.8188i	−0.636330	+	0.771417i
$876$	−1.57903	−	4.48431i	−0.0533506	−	0.151511i
$877$	−50.1274	−	5.26860i	−1.69268	−	0.177908i	−0.791447	−	0.611238i	$-0.790672\pi$
$877$	−50.1274	−	5.26860i	−1.69268	−	0.177908i	−0.901235	+	0.433330i	$0.857338\pi$
$878$	5.97807	−	28.1246i	0.201750	−	0.949160i
$879$	−37.7292	+	4.89910i	−1.27257	+	0.165242i
$880$	−33.1938	−	42.8130i	−1.11896	−	1.44323i
$881$	0.723089	−	2.22544i	0.0243615	−	0.0749770i	−0.938137	−	0.346265i	$-0.887450\pi$
$881$	0.723089	−	2.22544i	0.0243615	−	0.0749770i	0.962498	+	0.271288i	$0.0874497\pi$
$882$	30.3103	+	15.4194i	1.02060	+	0.519200i
$883$	22.5789	+	7.33633i	0.759840	+	0.246887i	0.663210	−	0.748433i	$-0.269194\pi$
$883$	22.5789	+	7.33633i	0.759840	+	0.246887i	0.0966302	+	0.995320i	$0.469194\pi$
$884$	−0.512290	+	1.15062i	−0.0172302	+	0.0386996i
$885$	−9.01062	+	11.2011i	−0.302889	+	0.376522i
$886$	15.3646	−	6.84074i	0.516182	−	0.229819i
$887$	−11.3289	+	25.4451i	−0.380387	+	0.854362i	0.617322	+	0.786710i	$0.288217\pi$
$887$	−11.3289	+	25.4451i	−0.380387	+	0.854362i	−0.997709	+	0.0676521i	$0.978449\pi$
$888$	12.0124	−	17.4120i	0.403111	−	0.584308i
$889$	25.6253	+	4.00368i	0.859444	+	0.134279i
$890$	−40.6354	+	19.6326i	−1.36210	+	0.658088i
$891$	−36.1280	−	26.6421i	−1.21033	−	0.892543i
$892$	10.8677	+	12.0699i	0.363879	+	0.404129i
$893$	−1.40127	+	2.42707i	−0.0468917	+	0.0812189i
$894$	44.8291	−	27.3621i	1.49931	−	0.915125i
$895$	1.60332	+	3.31853i	0.0535930	+	0.110926i
$896$	34.8094	+	9.24909i	1.16290	+	0.308990i
$897$	−2.53016	+	1.93434i	−0.0844794	+	0.0645857i
$898$	−53.4309	−	5.61581i	−1.78301	−	0.187402i
$899$	35.8539	−	62.1008i	1.19580	−	2.07118i
$900$	1.88185	−	9.14419i	0.0627284	−	0.304806i
$901$	−16.8882	+	9.75040i	−0.562627	+	0.324833i
$902$	−25.6504	+	35.3047i	−0.854064	+	1.17552i
$903$	−11.0518	−	16.0695i	−0.367781	−	0.534758i
$904$	2.36251	+	7.27106i	0.0785760	+	0.241832i
$905$	−15.8141	+	5.68942i	−0.525679	+	0.189123i
$906$	12.3187	−	22.5925i	0.409260	−	0.750586i
$907$	8.35061	+	4.82122i	0.277277	+	0.160086i	0.632190	−	0.774813i	$-0.282156\pi$
$907$	8.35061	+	4.82122i	0.277277	+	0.160086i	−0.354913	+	0.934899i	$0.615489\pi$
$908$	−2.03217	−	9.56061i	−0.0674399	−	0.317280i
$909$	−3.33547	+	12.2739i	−0.110631	+	0.407098i
$910$	0.757651	+	8.82485i	0.0251159	+	0.292541i
$911$	−26.0874	+	35.9063i	−0.864315	+	1.18963i	0.116208	+	0.993225i	$0.462926\pi$
$911$	−26.0874	+	35.9063i	−0.864315	+	1.18963i	−0.980523	+	0.196403i	$0.937074\pi$
$912$	−40.9092	−	3.29263i	−1.35464	−	0.109030i
$913$	−7.20050	−	68.5082i	−0.238302	−	2.26729i
$914$	14.6503	+	32.9051i	0.484589	+	1.08840i
$915$	28.3474	+	34.7753i	0.937136	+	1.14964i
$916$	−1.03459	−	1.42399i	−0.0341838	−	0.0470500i
$917$	−20.2014	−	24.8402i	−0.667110	−	0.820295i
$918$	9.70701	−	15.6529i	0.320379	−	0.516622i
$919$	24.9925	−	5.31232i	0.824427	−	0.175237i	0.223666	−	0.974666i	$-0.428198\pi$
$919$	24.9925	−	5.31232i	0.824427	−	0.175237i	0.600761	+	0.799429i	$0.294864\pi$
$920$	9.63550	−	2.36441i	0.317673	−	0.0779522i
$921$	2.00578	+	15.4471i	0.0660928	+	0.508998i
$922$	−28.1014	+	31.2098i	−0.925472	+	1.02784i
$923$	−4.99164	+	6.87040i	−0.164302	+	0.226142i
$924$	10.3220	+	9.78893i	0.339568	+	0.322032i
$925$	−21.4442	−	17.0122i	−0.705082	−	0.559357i
$926$	−4.78974	+	2.76535i	−0.157400	+	0.0908752i
$927$	0.949906	−	1.84806i	0.0311990	−	0.0606984i
$928$	−6.71063	+	31.5710i	−0.220287	+	1.03637i
$929$	31.6112	−	35.1077i	1.03713	−	1.15185i	0.0489090	−	0.998803i	$-0.484426\pi$
$929$	31.6112	−	35.1077i	1.03713	−	1.15185i	0.988219	−	0.153044i	$-0.0489078\pi$
$930$	7.26869	−	46.8745i	0.238350	−	1.53707i
$931$	−31.2530	−	13.7582i	−1.02427	−	0.450908i
$932$	14.1305			0.462860
$933$	17.4722	+	28.6258i	0.572013	+	0.937167i
$934$	24.0209	−	2.52470i	0.785988	−	0.0826107i
$935$	−23.7087	+	5.81777i	−0.775359	+	0.190262i
$936$	3.35154	+	5.20121i	0.109548	+	0.170007i
$937$	−8.61894	+	6.26202i	−0.281568	+	0.204571i	−0.719601	−	0.694388i	$-0.755675\pi$
$937$	−8.61894	+	6.26202i	−0.281568	+	0.204571i	0.438033	+	0.898959i	$0.355675\pi$
$938$	6.58499	−	12.9909i	0.215007	−	0.424169i
$939$	−2.90159	+	9.73220i	−0.0946899	+	0.317598i
$940$	0.767743	+	0.223237i	0.0250410	+	0.00728120i
$941$	−1.78529	−	16.9859i	−0.0581987	−	0.553723i	−0.984307	−	0.176465i	$-0.943534\pi$
$941$	−1.78529	−	16.9859i	−0.0581987	−	0.553723i	0.926108	−	0.377258i	$-0.123133\pi$
$942$	−24.7673	+	45.4234i	−0.806962	+	1.47997i
$943$	−5.37290	−	9.30614i	−0.174966	−	0.303049i
$944$	5.57143	−	17.1471i	0.181335	−	0.558090i
$945$	1.55407	−	30.7015i	0.0505538	−	0.998721i
$946$	−10.6224	−	32.6924i	−0.345364	−	1.06292i
$947$	8.03043	−	8.91870i	0.260954	−	0.289819i	−0.598403	−	0.801196i	$-0.704198\pi$
$947$	8.03043	−	8.91870i	0.260954	−	0.289819i	0.859357	+	0.511377i	$0.170864\pi$
$948$	−7.45459	−	7.88345i	−0.242114	−	0.256043i
$949$	2.03866	−	3.53106i	0.0661777	−	0.114623i
$950$	−5.78758	+	39.0718i	−0.187774	+	1.26766i
$951$	8.85583	+	25.1497i	0.287170	+	0.815536i
$952$	8.10948	−	10.0573i	0.262830	−	0.325961i
$953$	−18.2231	−	56.0848i	−0.590303	−	1.81676i	−0.576842	−	0.816856i	$-0.695715\pi$
$953$	−18.2231	−	56.0848i	−0.590303	−	1.81676i	−0.0134604	−	0.999909i	$-0.504285\pi$
$954$	2.41844	−	43.2137i	0.0783000	−	1.39909i
$955$	−10.2342	−	41.7067i	−0.331171	−	1.34960i
$956$	−5.59392	+	5.03679i	−0.180920	+	0.162901i
$957$	53.3050	−	62.1885i	1.72311	−	2.01027i
$958$	2.97160	−	9.14564i	0.0960080	−	0.295482i
$959$	−31.0167	+	20.2349i	−1.00158	+	0.653419i
$960$	−2.59793	−	16.0659i	−0.0838479	−	0.518523i
$961$	2.73875	−	26.0575i	0.0883469	−	0.840564i
$962$	−8.15139	+	0.856745i	−0.262811	+	0.0276226i
$963$	−20.5942	−	20.7408i	−0.663639	−	0.668363i
$964$	2.73668	+	0.287637i	0.0881425	+	0.00926415i
$965$	−18.1709	+	2.48494i	−0.584943	+	0.0799932i
$966$	−13.6341	+	5.65254i	−0.438670	+	0.181867i
$967$	51.7662	+	16.8199i	1.66469	+	0.540890i	0.981847	−	0.189677i	$-0.0607440\pi$
$967$	51.7662	+	16.8199i	1.66469	+	0.540890i	0.682841	+	0.730567i	$0.260744\pi$
$968$	−15.4788	−	26.8101i	−0.497509	−	0.861711i
$969$	−8.85358	+	16.2375i	−0.284418	+	0.521625i
$970$	12.3549	−	14.6134i	0.396692	−	0.469208i
$971$	−16.4320	+	18.2496i	−0.527328	+	0.585657i	−0.946684	−	0.322165i	$-0.895589\pi$
$971$	−16.4320	+	18.2496i	−0.527328	+	0.585657i	0.419356	+	0.907822i	$0.362256\pi$
$972$	4.09904	+	8.79364i	0.131477	+	0.282056i
$973$	−17.8956	−	2.79600i	−0.573707	−	0.0896356i
$974$		−	3.43493i		−	0.110062i
$975$	7.00462	−	3.87835i	0.224327	−	0.124207i
$976$	−48.7304	−	28.1345i	−1.55982	−	0.900564i
$977$	40.0025	−	17.8103i	1.27979	−	0.569801i	0.349611	−	0.936895i	$-0.386314\pi$
$977$	40.0025	−	17.8103i	1.27979	−	0.569801i	0.930184	+	0.367094i	$0.119647\pi$
$978$	−3.48339	+	8.36764i	−0.111386	+	0.267568i
$979$	−59.1197	+	19.2092i	−1.88947	+	0.613927i
$980$	−1.68715	+	9.59471i	−0.0538939	+	0.306492i
$981$	16.2103	+	42.6810i	0.517554	+	1.36270i
$982$	−5.57831	+	3.22064i	−0.178011	+	0.102775i
$983$	−20.3896	+	18.3589i	−0.650328	+	0.585558i	−0.926842	−	0.375452i	$-0.877488\pi$
$983$	−20.3896	+	18.3589i	−0.650328	+	0.585558i	0.276514	+	0.961010i	$0.410821\pi$
$984$	−18.8590	+	8.95427i	−0.601203	+	0.285452i
$985$	4.20709	+	2.86052i	0.134049	+	0.0911436i
$986$	27.1890	+	19.7539i	0.865873	+	0.629094i
$987$	2.61030	+	0.342803i	0.0830868	+	0.0109115i
$988$	1.64990	+	2.27089i	0.0524903	+	0.0722467i
$989$	8.41818	+	0.884787i	0.267683	+	0.0281346i
$990$	18.0114	−	51.1004i	0.572441	−	1.62408i
$991$	0.743292	+	7.07195i	0.0236115	+	0.224648i	0.999964	+	0.00846434i	$0.00269431\pi$
$991$	0.743292	+	7.07195i	0.0236115	+	0.224648i	−0.976353	+	0.216184i	$0.930639\pi$
$992$	5.35304	+	25.1841i	0.169959	+	0.799595i
$993$	9.36754	+	26.6029i	0.297270	+	0.844219i
$994$	−30.5328	+	24.8310i	−0.968443	+	0.787592i
$995$	5.96662	−	0.815958i	0.189155	−	0.0258676i
$996$	−5.72198	+	13.7451i	−0.181308	+	0.435530i
$997$	33.7985	+	7.18409i	1.07041	+	0.227522i	0.709232	−	0.704975i	$-0.249042\pi$
$997$	33.7985	+	7.18409i	1.07041	+	0.227522i	0.361177	+	0.932497i	$0.382375\pi$
$998$	−17.0646	+	7.59767i	−0.540172	+	0.240500i
$999$	28.4325	+	0.895915i	0.899565	+	0.0283455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bp.a.59.19	✓	608
3.2	odd	2	inner	525.2.bp.a.59.58	yes	608
7.5	odd	6	inner	525.2.bp.a.509.58	yes	608
21.5	even	6	inner	525.2.bp.a.509.19	yes	608
25.14	even	10	inner	525.2.bp.a.164.19	yes	608
75.14	odd	10	inner	525.2.bp.a.164.58	yes	608
175.89	odd	30	inner	525.2.bp.a.89.58	yes	608
525.89	even	30	inner	525.2.bp.a.89.19	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bp.a.59.19	✓	608	1.1	even	1	trivial
525.2.bp.a.59.58	yes	608	3.2	odd	2	inner
525.2.bp.a.89.19	yes	608	525.89	even	30	inner
525.2.bp.a.89.58	yes	608	175.89	odd	30	inner
525.2.bp.a.164.19	yes	608	25.14	even	10	inner
525.2.bp.a.164.58	yes	608	75.14	odd	10	inner
525.2.bp.a.509.19	yes	608	21.5	even	6	inner
525.2.bp.a.509.58	yes	608	7.5	odd	6	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.bp (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.169271 + 1.61051i) q^{2} +(-0.223032 - 1.71763i) q^{3} +(-0.608788 - 0.129402i) q^{4} +(-1.76715 + 1.37010i) q^{5} +(2.80401 - 0.0684501i) q^{6} +(1.20608 + 2.35486i) q^{7} +(-0.689378 + 2.12169i) q^{8} +(-2.90051 + 0.766175i) q^{9} +O(q^{10})\)	\(q+(-0.169271 + 1.61051i) q^{2} +(-0.223032 - 1.71763i) q^{3} +(-0.608788 - 0.129402i) q^{4} +(-1.76715 + 1.37010i) q^{5} +(2.80401 - 0.0684501i) q^{6} +(1.20608 + 2.35486i) q^{7} +(-0.689378 + 2.12169i) q^{8} +(-2.90051 + 0.766175i) q^{9} +(-1.90744 - 3.07793i) q^{10} +(-2.02867 - 4.55647i) q^{11} +(-0.0864851 + 1.07453i) q^{12} +(-0.747958 + 0.543423i) q^{13} +(-3.99668 + 1.54379i) q^{14} +(2.74747 + 2.72973i) q^{15} +(-4.43746 - 1.97569i) q^{16} +(-1.62665 + 1.46465i) q^{17} +(-0.742958 - 4.80099i) q^{18} +(1.01423 + 4.77158i) q^{19} +(1.25311 - 0.605430i) q^{20} +(3.77579 - 2.59681i) q^{21} +(7.68163 - 2.49591i) q^{22} +(-0.207895 + 1.97799i) q^{23} +(3.79803 + 0.710892i) q^{24} +(1.24563 - 4.84236i) q^{25} +(-0.748580 - 1.29658i) q^{26} +(1.96291 + 4.81113i) q^{27} +(-0.429522 - 1.58968i) q^{28} +(-9.01719 + 2.92986i) q^{29} +(-4.86132 + 3.96275i) q^{30} +(-5.62051 + 5.06073i) q^{31} +(1.70212 - 2.94815i) q^{32} +(-7.37387 + 4.50075i) q^{33} +(-2.08348 - 2.86766i) q^{34} +(-5.35773 - 2.50894i) q^{35} +(1.86494 - 0.0911063i) q^{36} +(2.22670 - 5.00126i) q^{37} +(-7.85635 + 0.825735i) q^{38} +(1.10022 + 1.16352i) q^{39} +(-1.68870 - 4.69386i) q^{40} +(-4.37105 + 3.17575i) q^{41} +(3.54305 + 6.52050i) q^{42} -4.25592i q^{43} +(0.645414 + 3.03644i) q^{44} +(4.07590 - 5.32795i) q^{45} +(-3.15038 - 0.669635i) q^{46} +(0.426941 + 0.384419i) q^{47} +(-2.40380 + 8.06257i) q^{48} +(-4.09075 + 5.68029i) q^{49} +(7.58780 + 2.82576i) q^{50} +(2.87852 + 2.46733i) q^{51} +(0.525668 - 0.234042i) q^{52} +(8.71435 + 1.85229i) q^{53} +(-8.08063 + 2.34690i) q^{54} +(9.82780 + 5.27247i) q^{55} +(-5.82773 + 0.935531i) q^{56} +(7.96961 - 2.80629i) q^{57} +(-3.19221 - 15.0182i) q^{58} +(0.387984 + 3.69142i) q^{59} +(-1.31939 - 2.01735i) q^{60} +(11.5207 + 1.21088i) q^{61} +(-7.19895 - 9.90850i) q^{62} +(-5.30248 - 5.90624i) q^{63} +(-3.39955 - 2.46992i) q^{64} +(0.577206 - 1.98509i) q^{65} +(-6.00031 - 12.6375i) q^{66} +(-2.52623 + 2.27463i) q^{67} +(1.17982 - 0.681167i) q^{68} +(3.44383 - 0.0840690i) q^{69} +(4.94757 - 8.20397i) q^{70} +(8.73597 - 2.83849i) q^{71} +(0.373966 - 6.68217i) q^{72} +(-4.02889 + 1.79378i) q^{73} +(7.67765 + 4.43269i) q^{74} +(-8.59520 - 1.05953i) q^{75} -3.03612i q^{76} +(8.28312 - 10.2727i) q^{77} +(-2.06009 + 1.57496i) q^{78} +(-6.73463 + 7.47956i) q^{79} +(10.5486 - 2.58846i) q^{80} +(7.82595 - 4.44460i) q^{81} +(-4.37468 - 7.57718i) q^{82} +(13.1352 + 4.26788i) q^{83} +(-2.63469 + 1.09231i) q^{84} +(0.867822 - 4.81694i) q^{85} +(6.85419 + 0.720405i) q^{86} +(7.04355 + 14.8347i) q^{87} +(11.0659 - 1.16308i) q^{88} +(1.30275 - 12.3949i) q^{89} +(7.89077 + 7.46613i) q^{90} +(-2.18178 - 1.10593i) q^{91} +(0.382520 - 1.17728i) q^{92} +(9.94602 + 8.52525i) q^{93} +(-0.691379 + 0.622520i) q^{94} +(-8.32986 - 7.04249i) q^{95} +(-5.44347 - 2.26608i) q^{96} +(1.63307 + 5.02608i) q^{97} +(-8.45571 - 7.54970i) q^{98} +(9.37524 + 11.6618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more