LMFDB - Embedded newform 525.2.t.g.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$-0.385731i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.g.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.334053 - 0.192865i) q^{2} +(-1.42561 + 0.983691i) q^{3} +(-0.925606 + 1.60320i) q^{4} +(-0.286507 + 0.603555i) q^{6} +(-2.36975 - 1.17656i) q^{7} +1.48553i q^{8} +(1.06470 - 2.80471i) q^{9} +O(q^{10})$	\(q+(0.334053 - 0.192865i) q^{2} +(-1.42561 + 0.983691i) q^{3} +(-0.925606 + 1.60320i) q^{4} +(-0.286507 + 0.603555i) q^{6} +(-2.36975 - 1.17656i) q^{7} +1.48553i q^{8} +(1.06470 - 2.80471i) q^{9} +(-2.20164 - 1.27112i) q^{11} +(-0.257501 - 3.19604i) q^{12} +3.06718i q^{13} +(-1.01854 + 0.0640110i) q^{14} +(-1.56470 - 2.71015i) q^{16} +(3.23065 - 5.59565i) q^{17} +(-0.185264 - 1.14227i) q^{18} +(-1.03570 + 0.597960i) q^{19} +(4.53570 - 0.653796i) q^{21} -0.980620 q^{22} +(2.64657 - 1.52800i) q^{23} +(-1.46130 - 2.11778i) q^{24} +(0.591553 + 1.02460i) q^{26} +(1.24112 + 5.04575i) q^{27} +(4.07971 - 2.71015i) q^{28} -7.77029i q^{29} +(-5.95299 - 3.43696i) q^{31} +(-3.61840 - 2.08909i) q^{32} +(4.38907 - 0.353622i) q^{33} -2.49232i q^{34} +(3.51101 + 4.30299i) q^{36} +(-1.77604 - 3.07619i) q^{37} +(-0.230652 + 0.399500i) q^{38} +(-3.01716 - 4.37259i) q^{39} +2.31252 q^{41} +(1.38907 - 1.09318i) q^{42} -5.46130 q^{43} +(4.07571 - 2.35311i) q^{44} +(0.589395 - 1.02086i) q^{46} +(1.61009 + 2.78876i) q^{47} +(4.89660 + 2.32442i) q^{48} +(4.23143 + 5.57629i) q^{49} +(0.898757 + 11.1552i) q^{51} +(-4.91730 - 2.83900i) q^{52} +(-11.4790 - 6.62740i) q^{53} +(1.38775 + 1.44618i) q^{54} +(1.74781 - 3.52034i) q^{56} +(0.888288 - 1.87126i) q^{57} +(-1.49862 - 2.59569i) q^{58} +(-1.98146 + 3.43199i) q^{59} +(-8.08933 + 4.67038i) q^{61} -2.65148 q^{62} +(-5.82298 + 5.39378i) q^{63} +4.64717 q^{64} +(1.39798 - 0.964627i) q^{66} +(-1.75966 + 3.04782i) q^{67} +(5.98062 + 10.3587i) q^{68} +(-2.26989 + 4.78173i) q^{69} -0.921861i q^{71} +(4.16649 + 1.58165i) q^{72} +(-0.256722 - 0.148218i) q^{73} +(-1.18658 - 0.685073i) q^{74} -2.21390i q^{76} +(3.72180 + 5.60260i) q^{77} +(-1.85121 - 0.878771i) q^{78} +(-4.14741 - 7.18352i) q^{79} +(-6.73281 - 5.97238i) q^{81} +(0.772502 - 0.446004i) q^{82} -2.11171 q^{83} +(-3.15010 + 7.87677i) q^{84} +(-1.82436 + 1.05330i) q^{86} +(7.64357 + 11.0774i) q^{87} +(1.88829 - 3.27061i) q^{88} +(9.41507 + 16.3074i) q^{89} +(3.60871 - 7.26845i) q^{91} +5.65729i q^{92} +(11.8675 - 0.956152i) q^{93} +(1.07571 + 0.621062i) q^{94} +(7.21343 - 0.581177i) q^{96} -12.3692i q^{97} +(2.48899 + 1.04668i) q^{98} +(-5.90923 + 4.82161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	$ 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.334053	−	0.192865i	0.236211	−	0.136376i	−0.377223	−	0.926122i	$-0.623121\pi$
$2$	0.334053	−	0.192865i	0.236211	−	0.136376i	0.613434	+	0.789746i	$0.289788\pi$
$3$	−1.42561	+	0.983691i	−0.823074	+	0.567934i
$3$	−1.42561	+	0.983691i	−0.823074	+	0.567934i
$4$	−0.925606	+	1.60320i	−0.462803	+	0.801598i
$5$		0			0
$5$		0			0
$6$	−0.286507	+	0.603555i	−0.116966	+	0.246400i
$7$	−2.36975	−	1.17656i	−0.895681	−	0.444696i
$7$	−2.36975	−	1.17656i	−0.895681	−	0.444696i
$8$			1.48553i			0.525214i
$9$	1.06470	−	2.80471i	0.354901	−	0.934904i
$10$		0			0
$11$	−2.20164	−	1.27112i	−0.663821	−	0.383257i	0.129910	−	0.991526i	$-0.458531\pi$
$11$	−2.20164	−	1.27112i	−0.663821	−	0.383257i	−0.793731	+	0.608269i	$0.791864\pi$
$12$	−0.257501	−	3.19604i	−0.0743340	−	0.922616i
$13$			3.06718i			0.850683i	0.905033	+	0.425342i	$0.139846\pi$
$13$			3.06718i			0.850683i	−0.905033	+	0.425342i	$0.860154\pi$
$14$	−1.01854	+	0.0640110i	−0.272216	+	0.0171077i
$15$		0			0
$16$	−1.56470	−	2.71015i	−0.391176	−	0.677537i
$17$	3.23065	−	5.59565i	0.783548	−	1.35715i	−0.146314	−	0.989238i	$-0.546741\pi$
$17$	3.23065	−	5.59565i	0.783548	−	1.35715i	0.929863	−	0.367907i	$-0.119926\pi$
$18$	−0.185264	−	1.14227i	−0.0436672	−	0.269235i
$19$	−1.03570	+	0.597960i	−0.237605	+	0.137181i	−0.614076	−	0.789247i	$-0.710471\pi$
$19$	−1.03570	+	0.597960i	−0.237605	+	0.137181i	0.376470	+	0.926429i	$0.377138\pi$
$20$		0			0
$21$	4.53570	−	0.653796i	0.989770	−	0.142670i
$22$	−0.980620			−0.209069
$23$	2.64657	−	1.52800i	0.551848	−	0.318609i	−0.198019	−	0.980198i	$-0.563451\pi$
$23$	2.64657	−	1.52800i	0.551848	−	0.318609i	0.749867	+	0.661589i	$0.230118\pi$
$24$	−1.46130	−	2.11778i	−0.298287	−	0.432290i
$25$		0			0
$26$	0.591553	+	1.02460i	0.116013	+	0.200941i
$27$	1.24112	+	5.04575i	0.238854	+	0.971056i
$28$	4.07971	−	2.71015i	0.770992	−	0.512170i
$29$		−	7.77029i		−	1.44291i	−0.692463	−	0.721454i	$-0.743474\pi$
$29$		−	7.77029i		−	1.44291i	0.692463	−	0.721454i	$-0.256526\pi$
$30$		0			0
$31$	−5.95299	−	3.43696i	−1.06919	−	0.617297i	−0.141229	−	0.989977i	$-0.545105\pi$
$31$	−5.95299	−	3.43696i	−1.06919	−	0.617297i	−0.927960	+	0.372680i	$0.878439\pi$
$32$	−3.61840	−	2.08909i	−0.639649	−	0.369302i
$33$	4.38907	−	0.353622i	0.764039	−	0.0615576i
$34$		−	2.49232i		−	0.427430i
$35$		0			0
$36$	3.51101	+	4.30299i	0.585168	+	0.717165i
$37$	−1.77604	−	3.07619i	−0.291979	−	0.505722i	0.682299	−	0.731074i	$-0.260980\pi$
$37$	−1.77604	−	3.07619i	−0.291979	−	0.505722i	−0.974278	+	0.225351i	$0.927647\pi$
$38$	−0.230652	+	0.399500i	−0.0374166	+	0.0648075i
$39$	−3.01716	−	4.37259i	−0.483132	−	0.700175i
$40$		0			0
$41$	2.31252			0.361154			0.180577	−	0.983561i	$-0.442203\pi$
$41$	2.31252			0.361154			0.180577	+	0.983561i	$0.442203\pi$
$42$	1.38907	−	1.09318i	0.214338	−	0.168682i
$43$	−5.46130			−0.832841			−0.416420	−	0.909172i	$-0.636716\pi$
$43$	−5.46130			−0.832841			−0.416420	+	0.909172i	$0.636716\pi$
$44$	4.07571	−	2.35311i	0.614437	−	0.354745i
$45$		0			0
$46$	0.589395	−	1.02086i	0.0869016	−	0.150518i
$47$	1.61009	+	2.78876i	0.234856	+	0.406782i	0.959231	−	0.282624i	$-0.0912048\pi$
$47$	1.61009	+	2.78876i	0.234856	+	0.406782i	−0.724375	+	0.689406i	$0.757871\pi$
$48$	4.89660	+	2.32442i	0.706763	+	0.335501i
$49$	4.23143	+	5.57629i	0.604490	+	0.796613i
$50$		0			0
$51$	0.898757	+	11.1552i	0.125851	+	1.56203i
$52$	−4.91730	−	2.83900i	−0.681906	−	0.393699i
$53$	−11.4790	−	6.62740i	−1.57676	−	0.910344i	−0.995307	−	0.0967651i	$-0.969150\pi$
$53$	−11.4790	−	6.62740i	−1.57676	−	0.910344i	−0.581455	−	0.813579i	$-0.697516\pi$
$54$	1.38775	+	1.44618i	0.188849	+	0.196800i
$55$		0			0
$56$	1.74781	−	3.52034i	0.233561	−	0.470425i
$57$	0.888288	−	1.87126i	0.117657	−	0.247855i
$58$	−1.49862	−	2.59569i	−0.196779	−	0.340830i
$59$	−1.98146	+	3.43199i	−0.257964	+	0.446807i	−0.965696	−	0.259674i	$-0.916385\pi$
$59$	−1.98146	+	3.43199i	−0.257964	+	0.446807i	0.707732	+	0.706481i	$0.249718\pi$
$60$		0			0
$61$	−8.08933	+	4.67038i	−1.03573	+	0.597981i	−0.918622	−	0.395138i	$-0.870697\pi$
$61$	−8.08933	+	4.67038i	−1.03573	+	0.597981i	−0.117111	+	0.993119i	$0.537363\pi$
$62$	−2.65148			−0.336739
$63$	−5.82298	+	5.39378i	−0.733627	+	0.679552i
$64$	4.64717			0.580896
$65$		0			0
$66$	1.39798	−	0.964627i	0.172079	−	0.118737i
$67$	−1.75966	+	3.04782i	−0.214977	+	0.372350i	−0.953265	−	0.302134i	$-0.902301\pi$
$67$	−1.75966	+	3.04782i	−0.214977	+	0.372350i	0.738289	+	0.674485i	$0.235634\pi$
$68$	5.98062	+	10.3587i	0.725257	+	1.25618i
$69$	−2.26989	+	4.78173i	−0.273262	+	0.575652i
$70$		0			0
$71$		−	0.921861i		−	0.109405i	−0.998503	−	0.0547024i	$-0.982579\pi$
$71$		−	0.921861i		−	0.109405i	0.998503	−	0.0547024i	$-0.0174210\pi$
$72$	4.16649	+	1.58165i	0.491025	+	0.186399i
$73$	−0.256722	−	0.148218i	−0.0300470	−	0.0173477i	0.484901	−	0.874569i	$-0.338856\pi$
$73$	−0.256722	−	0.148218i	−0.0300470	−	0.0173477i	−0.514948	+	0.857221i	$0.672189\pi$
$74$	−1.18658	−	0.685073i	−0.137937	−	0.0796381i
$75$		0			0
$76$		−	2.21390i		−	0.253952i
$77$	3.72180	+	5.60260i	0.424139	+	0.638475i
$78$	−1.85121	−	0.878771i	−0.209608	−	0.0995012i
$79$	−4.14741	−	7.18352i	−0.466620	−	0.808210i	0.532653	−	0.846334i	$-0.321195\pi$
$79$	−4.14741	−	7.18352i	−0.466620	−	0.808210i	−0.999273	+	0.0381242i	$0.987862\pi$
$80$		0			0
$81$	−6.73281	−	5.97238i	−0.748090	−	0.663597i
$82$	0.772502	−	0.446004i	0.0853085	−	0.0492529i
$83$	−2.11171			−0.231790			−0.115895	−	0.993261i	$-0.536974\pi$
$83$	−2.11171			−0.231790			−0.115895	+	0.993261i	$0.536974\pi$
$84$	−3.15010	+	7.87677i	−0.343705	+	0.859426i
$85$		0			0
$86$	−1.82436	+	1.05330i	−0.196726	+	0.113580i
$87$	7.64357	+	11.0774i	0.819477	+	1.18762i
$88$	1.88829	−	3.27061i	0.201292	−	0.348648i
$89$	9.41507	+	16.3074i	0.997996	+	1.72858i	0.553799	+	0.832651i	$0.313178\pi$
$89$	9.41507	+	16.3074i	0.997996	+	1.72858i	0.444197	+	0.895929i	$0.353489\pi$
$90$		0			0
$91$	3.60871	−	7.26845i	0.378296	−	0.761941i
$92$			5.65729i			0.589813i
$93$	11.8675	−	0.956152i	1.23061	−	0.0991483i
$94$	1.07571	+	0.621062i	0.110951	+	0.0640576i
$95$		0			0
$96$	7.21343	−	0.581177i	0.736218	−	0.0593161i
$97$		−	12.3692i		−	1.25590i	−0.778252	−	0.627952i	$-0.783894\pi$
$97$		−	12.3692i		−	1.25590i	0.778252	−	0.627952i	$-0.216106\pi$
$98$	2.48899	+	1.04668i	0.251426	+	0.105730i
$99$	−5.90923	+	4.82161i	−0.593900	+	0.484590i
$100$		0			0
$101$	−3.48815	+	6.04166i	−0.347084	+	0.601167i	−0.985730	−	0.168333i	$-0.946162\pi$
$101$	−3.48815	+	6.04166i	−0.347084	+	0.601167i	0.638646	+	0.769501i	$0.279495\pi$
$102$	2.45168	+	3.55307i	0.242752	+	0.351806i
$103$	−3.26767	+	1.88659i	−0.321973	+	0.185891i	−0.652272	−	0.757985i	$-0.726184\pi$
$103$	−3.26767	+	1.88659i	−0.321973	+	0.185891i	0.330299	+	0.943876i	$0.392850\pi$
$104$	−4.55639			−0.446791
$105$		0			0
$106$	−5.11279			−0.496598
$107$	−11.4607	+	6.61684i	−1.10795	+	0.639674i	−0.938297	−	0.345830i	$-0.887597\pi$
$107$	−11.4607	+	6.61684i	−1.10795	+	0.639674i	−0.169651	+	0.985504i	$0.554264\pi$
$108$	−9.23812	−	2.68062i	−0.888939	−	0.257943i
$109$	−1.25081	+	2.16647i	−0.119806	+	0.207510i	−0.919691	−	0.392644i	$-0.871561\pi$
$109$	−1.25081	+	2.16647i	−0.119806	+	0.207510i	0.799885	+	0.600154i	$0.204894\pi$
$110$		0			0
$111$	5.55795	+	2.63836i	0.527537	+	0.250422i
$112$	0.519317	+	8.26333i	0.0490709	+	0.780812i
$113$		−	7.18425i		−	0.675837i	−0.941175	−	0.337919i	$-0.890277\pi$
$113$		−	7.18425i		−	0.675837i	0.941175	−	0.337919i	$-0.109723\pi$
$114$	−0.0641665	−	0.796420i	−0.00600975	−	0.0745916i
$115$		0			0
$116$	12.4573	+	7.19223i	1.15663	+	0.667782i
$117$	8.60256	+	3.26564i	0.795307	+	0.301909i
$118$			1.52862i			0.140721i
$119$	−14.2394	+	9.45925i	−1.30533	+	0.867128i
$120$		0			0
$121$	−2.26851	−	3.92917i	−0.206228	−	0.357197i
$122$	−1.80151	+	3.12030i	−0.163101	+	0.282499i
$123$	−3.29674	+	2.27480i	−0.297257	+	0.205112i
$124$	11.0202	−	6.36254i	0.989648	−	0.571373i
$125$		0			0
$126$	−0.904910	+	2.92486i	−0.0806158	+	0.260567i
$127$	11.1965			0.993528			0.496764	−	0.867886i	$-0.334522\pi$
$127$	11.1965			0.993528			0.496764	+	0.867886i	$0.334522\pi$
$128$	8.78920	−	5.07445i	0.776863	−	0.448522i
$129$	7.78567	−	5.37223i	0.685490	−	0.472999i
$130$		0			0
$131$	−7.83183	−	13.5651i	−0.684270	−	1.18519i	−0.973666	−	0.227981i	$-0.926787\pi$
$131$	−7.83183	−	13.5651i	−0.684270	−	1.18519i	0.289395	−	0.957210i	$-0.406546\pi$
$132$	−3.49562	+	7.36385i	−0.304255	+	0.640941i
$133$	3.15788	−	0.198460i	0.273823	−	0.0172086i
$134$			1.35751i			0.117271i
$135$		0			0
$136$	8.31252	+	4.79923i	0.712792	+	0.411531i
$137$	5.04755	+	2.91420i	0.431241	+	0.248977i	0.699875	−	0.714265i	$-0.253239\pi$
$137$	5.04755	+	2.91420i	0.431241	+	0.248977i	−0.268634	+	0.963242i	$0.586572\pi$
$138$	0.163968	+	2.03513i	0.0139579	+	0.173242i
$139$			12.0365i			1.02092i	0.859900	+	0.510462i	$0.170525\pi$
$139$			12.0365i			1.02092i	−0.859900	+	0.510462i	$0.829475\pi$
$140$		0			0
$141$	−5.03863	−	2.39184i	−0.424330	−	0.201429i
$142$	−0.177795	−	0.307950i	−0.0149202	−	0.0258426i
$143$	3.89876	−	6.75285i	0.326030	−	0.564701i
$144$	−9.26713	+	1.50304i	−0.772261	+	0.125253i
$145$		0			0
$146$	−0.114345			−0.00946324
$147$	−11.5177	−	3.78717i	−0.949964	−	0.312361i
$148$	6.57565			0.540515
$149$	16.1925	−	9.34874i	1.32654	−	0.765879i	0.341778	−	0.939781i	$-0.388971\pi$
$149$	16.1925	−	9.34874i	1.32654	−	0.765879i	0.984763	+	0.173902i	$0.0556377\pi$
$150$		0			0
$151$	2.97531	−	5.15339i	0.242127	−	0.419377i	−0.719193	−	0.694811i	$-0.755488\pi$
$151$	2.97531	−	5.15339i	0.242127	−	0.419377i	0.961320	+	0.275434i	$0.0888215\pi$
$152$	−0.888288	−	1.53856i	−0.0720497	−	0.124794i
$153$	−12.2545	−	15.0188i	−0.990718	−	1.21419i
$154$	2.32383	+	1.15376i	0.187259	+	0.0929722i
$155$		0			0
$156$	9.80283	−	0.789801i	0.784854	−	0.0632347i
$157$	−5.55364	−	3.20639i	−0.443228	−	0.255898i	0.261738	−	0.965139i	$-0.415704\pi$
$157$	−5.55364	−	3.20639i	−0.443228	−	0.255898i	−0.704966	+	0.709241i	$0.749038\pi$
$158$	−2.77091	−	1.59978i	−0.220441	−	0.127272i
$159$	22.8838	−	1.84372i	1.81481	−	0.146217i
$160$		0			0
$161$	−8.06948	+	0.507134i	−0.635964	+	0.0399678i
$162$	−3.40098	−	0.696562i	−0.267206	−	0.0547271i
$163$	−8.22174	−	14.2405i	−0.643976	−	1.11540i	−0.984537	−	0.175177i	$-0.943950\pi$
$163$	−8.22174	−	14.2405i	−0.643976	−	1.11540i	0.340560	−	0.940223i	$-0.389383\pi$
$164$	−2.14048	+	3.70742i	−0.167143	+	0.289501i
$165$		0			0
$166$	−0.705423	+	0.407276i	−0.0547514	+	0.0316108i
$167$	4.81089			0.372278			0.186139	−	0.982523i	$-0.440402\pi$
$167$	4.81089			0.372278			0.186139	+	0.982523i	$0.440402\pi$
$168$	0.971234	+	6.73792i	0.0749323	+	0.519842i
$169$	3.59239			0.276338
$170$		0			0
$171$	0.574394	+	3.54148i	0.0439250	+	0.270824i
$172$	5.05501	−	8.75554i	0.385441	−	0.667604i
$173$	3.40761	+	5.90215i	0.259075	+	0.448732i	0.965994	−	0.258563i	$-0.0832488\pi$
$173$	3.40761	+	5.90215i	0.259075	+	0.448732i	−0.706919	+	0.707294i	$0.749916\pi$
$174$	4.68980	+	2.22625i	0.355533	+	0.168771i
$175$		0			0
$176$			7.95571i			0.599684i
$177$	−0.551236	−	6.84181i	−0.0414335	−	0.514262i
$178$	6.29026	+	3.63168i	0.471475	+	0.272206i
$179$	−17.2931	−	9.98420i	−1.29255	−	0.746254i	−0.313444	−	0.949607i	$-0.601483\pi$
$179$	−17.2931	−	9.98420i	−1.29255	−	0.746254i	−0.979106	+	0.203353i	$0.934816\pi$
$180$		0			0
$181$			5.18808i			0.385627i	0.981235	+	0.192813i	$0.0617612\pi$
$181$			5.18808i			0.385627i	−0.981235	+	0.192813i	$0.938239\pi$
$182$	−0.196333	−	3.12404i	−0.0145532	−	0.231569i
$183$	6.93799	−	14.6155i	0.512871	−	1.08041i
$184$	2.26989	+	3.93156i	0.167338	+	0.289838i
$185$		0			0
$186$	3.77997	−	2.60824i	0.277161	−	0.191245i
$187$	−14.2255	+	8.21309i	−1.04027	+	0.600601i
$188$	−5.96124			−0.434768
$189$	2.99547	−	13.4174i	0.217888	−	0.975974i
$190$		0			0
$191$	−7.48332	+	4.32049i	−0.541474	+	0.312620i	−0.745676	−	0.666309i	$-0.767873\pi$
$191$	−7.48332	+	4.32049i	−0.541474	+	0.312620i	0.204202	+	0.978929i	$0.434540\pi$
$192$	−6.62503	+	4.57138i	−0.478120	+	0.329911i
$193$	−11.8861	+	20.5873i	−0.855578	+	1.48190i	0.0205300	+	0.999789i	$0.493465\pi$
$193$	−11.8861	+	20.5873i	−0.855578	+	1.48190i	−0.876108	+	0.482115i	$0.839869\pi$
$194$	−2.38559	−	4.13197i	−0.171276	−	0.296658i
$195$		0			0
$196$	−12.8565	+	1.62237i	−0.918323	+	0.115883i
$197$		−	11.6843i		−	0.832475i	−0.909256	−	0.416238i	$-0.863348\pi$
$197$		−	11.6843i		−	0.832475i	0.909256	−	0.416238i	$-0.136652\pi$
$198$	−1.04407	+	2.75036i	−0.0741989	+	0.195459i
$199$	−12.2341	−	7.06338i	−0.867254	−	0.500709i	−0.000819396	−	1.00000i	$-0.500261\pi$
$199$	−12.2341	−	7.06338i	−0.867254	−	0.500709i	−0.866435	+	0.499290i	$0.833594\pi$
$200$		0			0
$201$	−0.489531	−	6.07595i	−0.0345289	−	0.428564i
$202$			2.69098i			0.189336i
$203$	−9.14219	+	18.4137i	−0.641656	+	1.29239i
$204$	−18.7158	−	8.88440i	−1.31037	−	0.622032i
$205$		0			0
$206$	−0.727715	+	1.26044i	−0.0507023	+	0.0878190i
$207$	−1.46778	−	9.04972i	−0.102018	−	0.628999i
$208$	8.31252	−	4.79923i	0.576369	−	0.332767i
$209$	3.04032			0.210303
$210$		0			0
$211$	4.49838			0.309681			0.154841	−	0.987939i	$-0.450514\pi$
$211$	4.49838			0.309681			0.154841	+	0.987939i	$0.450514\pi$
$212$	21.2501	−	12.2687i	1.45946	−	0.842620i
$213$	0.906827	+	1.31421i	0.0621347	+	0.0900482i
$214$	−2.55232	+	4.42075i	−0.174473	+	0.302196i
$215$		0			0
$216$	−7.49562	+	1.84372i	−0.510012	+	0.125449i
$217$	10.0633	+	15.1488i	0.683143	+	1.02837i
$218$			0.964952i			0.0653548i
$219$	0.511785	−	0.0412339i	0.0345832	−	0.00278633i
$220$		0			0
$221$	17.1629	+	9.90900i	1.15450	+	0.666551i
$222$	2.36550	−	0.190585i	0.158762	−	0.0127912i
$223$			7.20662i			0.482591i	0.970452	+	0.241296i	$0.0775724\pi$
$223$			7.20662i			0.482591i	−0.970452	+	0.241296i	$0.922428\pi$
$224$	6.11678	+	9.20786i	0.408695	+	0.615226i
$225$		0			0
$226$	−1.38559	−	2.39992i	−0.0921682	−	0.159640i
$227$	−0.931518	+	1.61344i	−0.0618270	+	0.107087i	−0.895282	−	0.445500i	$-0.853026\pi$
$227$	−0.931518	+	1.61344i	−0.0618270	+	0.107087i	0.833455	+	0.552587i	$0.186359\pi$
$228$	2.17780	+	3.15615i	0.144228	+	0.209021i
$229$	−17.4126	+	10.0532i	−1.15066	+	0.664333i	−0.949047	−	0.315133i	$-0.897951\pi$
$229$	−17.4126	+	10.0532i	−1.15066	+	0.664333i	−0.201610	+	0.979466i	$0.564617\pi$
$230$		0			0
$231$	−10.8170	−	4.32599i	−0.711709	−	0.284629i
$232$	11.5430			0.757836
$233$	−1.35559	+	0.782650i	−0.0888077	+	0.0512731i	−0.543746	−	0.839250i	$-0.682995\pi$
$233$	−1.35559	+	0.782650i	−0.0888077	+	0.0512731i	0.454938	+	0.890523i	$0.349661\pi$
$234$	3.50354	−	0.568240i	0.229033	−	0.0371470i
$235$		0			0
$236$	−3.66811	−	6.35334i	−0.238773	−	0.413568i
$237$	12.9789	+	6.16110i	0.843073	+	0.400207i
$238$	−2.93236	+	5.90618i	−0.190077	+	0.382841i
$239$		−	5.69230i		−	0.368205i	−0.982907	−	0.184102i	$-0.941062\pi$
$239$		−	5.69230i		−	0.368205i	0.982907	−	0.184102i	$-0.0589378\pi$
$240$		0			0
$241$	11.5466	+	6.66646i	0.743785	+	0.429424i	0.823444	−	0.567398i	$-0.192050\pi$
$241$	11.5466	+	6.66646i	0.743785	+	0.429424i	−0.0796592	+	0.996822i	$0.525383\pi$
$242$	−1.51560	−	0.875033i	−0.0974266	−	0.0562492i
$243$	15.4733	+	1.89125i	0.992613	+	0.121324i
$244$		−	17.2917i		−	1.10699i
$245$		0			0
$246$	−0.662553	+	1.39573i	−0.0422428	+	0.0889884i
$247$	−1.83405	−	3.17667i	−0.116698	−	0.202127i
$248$	5.10571	−	8.84335i	0.324213	−	0.561554i
$249$	3.01047	−	2.07727i	0.190781	−	0.131642i
$250$		0			0
$251$	5.32590			0.336168			0.168084	−	0.985773i	$-0.446242\pi$
$251$	5.32590			0.336168			0.168084	+	0.985773i	$0.446242\pi$
$252$	−3.25750	−	14.3279i	−0.205203	−	0.902573i
$253$	−7.76907			−0.488437
$254$	3.74022	−	2.15941i	0.234682	−	0.135494i
$255$		0			0
$256$	−2.68980	+	4.65887i	−0.168112	+	0.291179i
$257$	−3.25003	−	5.62922i	−0.202731	−	0.351141i	0.746676	−	0.665188i	$-0.231648\pi$
$257$	−3.25003	−	5.62922i	−0.202731	−	0.351141i	−0.949408	+	0.314047i	$0.898315\pi$
$258$	1.56470	−	3.29619i	0.0974142	−	0.205212i
$259$	0.589458	+	9.37941i	0.0366271	+	0.582808i
$260$		0			0
$261$	−21.7934	−	8.27307i	−1.34898	−	0.512090i
$262$	−5.23249	−	3.02098i	−0.323264	−	0.186637i
$263$	12.8401	+	7.41326i	0.791757	+	0.457121i	0.840581	−	0.541686i	$-0.182214\pi$
$263$	12.8401	+	7.41326i	0.791757	+	0.457121i	−0.0488236	+	0.998807i	$0.515547\pi$
$264$	0.525316	+	6.52009i	0.0323309	+	0.401284i
$265$		0			0
$266$	1.01662	−	0.675341i	0.0623331	−	0.0414078i
$267$	−29.4636	−	13.9864i	−1.80314	−	0.855953i
$268$	−3.25750	−	5.64216i	−0.198984	−	0.344650i
$269$	12.3042	−	21.3115i	0.750201	−	1.29939i	−0.197525	−	0.980298i	$-0.563290\pi$
$269$	12.3042	−	21.3115i	0.750201	−	1.29939i	0.947725	−	0.319088i	$-0.103376\pi$
$270$		0			0
$271$	3.30121	−	1.90595i	0.200534	−	0.115778i	−0.396371	−	0.918091i	$-0.629730\pi$
$271$	3.30121	−	1.90595i	0.200534	−	0.115778i	0.596905	+	0.802312i	$0.296397\pi$
$272$	−20.2201			−1.22602
$273$	2.00531	+	13.9118i	0.121367	+	0.841981i
$274$	2.24819			0.135818
$275$		0			0
$276$	−5.56503	−	8.06507i	−0.334975	−	0.485460i
$277$	−9.38769	+	16.2600i	−0.564052	+	0.976966i	0.433086	+	0.901353i	$0.357425\pi$
$277$	−9.38769	+	16.2600i	−0.564052	+	0.976966i	−0.997137	+	0.0756131i	$0.975909\pi$
$278$	2.32143	+	4.02083i	0.139230	+	0.241153i
$279$	−15.9779	+	13.0371i	−0.956570	+	0.780509i
$280$		0			0
$281$		−	23.6885i		−	1.41314i	−0.707643	−	0.706570i	$-0.750242\pi$
$281$		−	23.6885i		−	1.41314i	0.707643	−	0.706570i	$-0.249758\pi$
$282$	−2.14447	+	0.172777i	−0.127701	+	0.0102887i
$283$	4.36831	+	2.52204i	0.259669	+	0.149920i	0.624184	−	0.781278i	$-0.285432\pi$
$283$	4.36831	+	2.52204i	0.259669	+	0.149920i	−0.364515	+	0.931198i	$0.618765\pi$
$284$	1.47792	+	0.853280i	0.0876987	+	0.0506329i
$285$		0			0
$286$		−	3.00774i		−	0.177851i
$287$	−5.48008	−	2.72080i	−0.323479	−	0.160604i
$288$	−9.71181	+	7.92431i	−0.572274	+	0.466945i
$289$	−12.3742	−	21.4328i	−0.727895	−	1.26075i
$290$		0			0
$291$	12.1675	+	17.6336i	0.713270	+	1.03370i
$292$	0.475246	−	0.274384i	0.0278117	−	0.0160571i
$293$	−6.29421			−0.367712			−0.183856	−	0.982953i	$-0.558858\pi$
$293$	−6.29421			−0.367712			−0.183856	+	0.982953i	$0.558858\pi$
$294$	−4.57793	+	0.956251i	−0.266990	+	0.0557697i
$295$		0			0
$296$	4.56977	−	2.63836i	0.265613	−	0.153352i
$297$	3.68125	−	12.6866i	0.213608	−	0.736149i
$298$	3.60610	−	6.24594i	0.208896	−	0.361818i
$299$	4.68664	+	8.11750i	0.271036	+	0.469447i
$300$		0			0
$301$	12.9419	+	6.42553i	0.745960	+	0.370361i
$302$		−	2.29534i		−	0.132082i
$303$	−0.970393	−	12.0443i	−0.0557476	−	0.691926i
$304$	3.24112	+	1.87126i	0.185891	+	0.107324i
$305$		0			0
$306$	−6.99025	−	2.65359i	−0.399606	−	0.151696i
$307$		−	16.0397i		−	0.915432i	−0.889099	−	0.457716i	$-0.848668\pi$
$307$		−	16.0397i		−	0.915432i	0.889099	−	0.457716i	$-0.151332\pi$
$308$	−12.4270	+	0.780986i	−0.708093	+	0.0445008i
$309$	2.80258	−	5.90390i	0.159433	−	0.335861i
$310$		0			0
$311$	9.03624	−	15.6512i	0.512398	−	0.887499i	−0.487499	−	0.873124i	$-0.662091\pi$
$311$	9.03624	−	15.6512i	0.512398	−	0.887499i	0.999897	−	0.0143755i	$-0.00457602\pi$
$312$	6.49562	−	4.48208i	0.367742	−	0.253748i
$313$	16.1272	−	9.31104i	0.911563	−	0.526291i	0.0306290	−	0.999531i	$-0.490249\pi$
$313$	16.1272	−	9.31104i	0.911563	−	0.526291i	0.880934	+	0.473240i	$0.156916\pi$
$314$	−2.47361			−0.139594
$315$		0			0
$316$	15.3555			0.863812
$317$	2.28327	−	1.31825i	0.128241	−	0.0740402i	−0.434507	−	0.900669i	$-0.643077\pi$
$317$	2.28327	−	1.31825i	0.128241	−	0.0740402i	0.562748	+	0.826628i	$0.309744\pi$
$318$	7.28882	−	5.02940i	0.408737	−	0.282035i
$319$	−9.87698	+	17.1074i	−0.553005	+	0.957832i
$320$		0			0
$321$	9.82952	−	20.7068i	0.548630	−	1.15574i
$322$	−2.59782	+	1.72573i	−0.144771	+	0.0961713i
$323$			7.72720i			0.429953i
$324$	15.8068	−	5.26595i	0.878157	−	0.292553i
$325$		0			0
$326$	−5.49299	−	3.17138i	−0.304228	−	0.175646i
$327$	−0.347971	−	4.31894i	−0.0192429	−	0.238838i
$328$			3.43531i			0.189683i
$329$	−0.534381	−	8.50303i	−0.0294614	−	0.468787i
$330$		0			0
$331$	15.1704	+	26.2759i	0.833842	+	1.44426i	0.894970	+	0.446126i	$0.147197\pi$
$331$	15.1704	+	26.2759i	0.833842	+	1.44426i	−0.0611286	+	0.998130i	$0.519470\pi$
$332$	1.95461	−	3.38549i	0.107273	−	0.185803i
$333$	−10.5188	+	1.70604i	−0.576426	+	0.0934906i
$334$	1.60709	−	0.927855i	0.0879362	−	0.0507700i
$335$		0			0
$336$	−8.86891	−	11.2694i	−0.483839	−	0.614797i
$337$	1.84215			0.100348			0.0501741	−	0.998740i	$-0.484022\pi$
$337$	1.84215			0.100348			0.0501741	+	0.998740i	$0.484022\pi$
$338$	1.20005	−	0.692849i	0.0652741	−	0.0376860i
$339$	7.06708	+	10.2419i	0.383831	+	0.556264i
$340$		0			0
$341$	8.73758	+	15.1339i	0.473167	+	0.819549i
$342$	0.874907	+	1.07226i	0.0473096	+	0.0579812i
$343$	−3.46661	−	18.1929i	−0.187180	−	0.982326i
$344$		−	8.11293i		−	0.437420i
$345$		0			0
$346$	2.27664	+	1.31442i	0.122393	+	0.0706636i
$347$	−7.09309	−	4.09520i	−0.380777	−	0.219842i	0.297379	−	0.954759i	$-0.403887\pi$
$347$	−7.09309	−	4.09520i	−0.380777	−	0.219842i	−0.678156	+	0.734918i	$0.737221\pi$
$348$	−24.8341	+	2.00086i	−1.33125	+	0.107257i
$349$		−	36.3291i		−	1.94465i	−0.233627	−	0.972326i	$-0.575059\pi$
$349$		−	36.3291i		−	1.94465i	0.233627	−	0.972326i	$-0.424941\pi$
$350$		0			0
$351$	−15.4762	+	3.80674i	−0.826061	+	0.203189i
$352$	5.31096	+	9.19885i	0.283075	+	0.490300i
$353$	−2.85736	+	4.94910i	−0.152082	+	0.263414i	−0.931993	−	0.362477i	$-0.881931\pi$
$353$	−2.85736	+	4.94910i	−0.152082	+	0.263414i	0.779911	+	0.625891i	$0.215265\pi$
$354$	−1.50369	−	2.17921i	−0.0799203	−	0.115824i
$355$		0			0
$356$	−34.8586			−1.84750
$357$	10.9948	−	27.4924i	0.581909	−	1.45505i
$358$	−7.70242			−0.407086
$359$	4.16181	−	2.40282i	0.219652	−	0.126816i	−0.386137	−	0.922441i	$-0.626191\pi$
$359$	4.16181	−	2.40282i	0.219652	−	0.126816i	0.605789	+	0.795625i	$0.292858\pi$
$360$		0			0
$361$	−8.78489	+	15.2159i	−0.462362	+	0.800835i
$362$	1.00060	+	1.73309i	0.0525904	+	0.0910892i
$363$	7.09909	+	3.36994i	0.372605	+	0.176876i
$364$	8.31252	+	12.5132i	0.435694	+	0.655870i
$365$		0			0
$366$	−0.501174	−	6.22045i	−0.0261968	−	0.325148i
$367$	21.2836	+	12.2881i	1.11099	+	0.641433i	0.939087	−	0.343680i	$-0.111673\pi$
$367$	21.2836	+	12.2881i	1.11099	+	0.641433i	0.171908	+	0.985113i	$0.445007\pi$
$368$	−8.28219	−	4.78173i	−0.431739	−	0.249265i
$369$	2.46214	−	6.48594i	0.128174	−	0.337644i
$370$		0			0
$371$	19.4048	+	29.2110i	1.00745	+	1.51656i
$372$	−9.45176	+	19.9110i	−0.490051	+	1.03234i
$373$	13.2513	+	22.9519i	0.686126	+	1.18840i	0.973082	+	0.230461i	$0.0740233\pi$
$373$	13.2513	+	22.9519i	0.686126	+	1.18840i	−0.286956	+	0.957944i	$0.592643\pi$
$374$	−3.16804	+	5.48721i	−0.163816	+	0.283737i
$375$		0			0
$376$	−4.14279	+	2.39184i	−0.213648	+	0.123350i
$377$	23.8329			1.22746
$378$	−1.58711	−	5.05985i	−0.0816322	−	0.260250i
$379$	13.0939			0.672588			0.336294	−	0.941757i	$-0.390826\pi$
$379$	13.0939			0.672588			0.336294	+	0.941757i	$0.390826\pi$
$380$		0			0
$381$	−15.9618	+	11.0139i	−0.817747	+	0.564258i
$382$	−1.66655	+	2.88655i	−0.0852680	+	0.147689i
$383$	−8.48299	−	14.6930i	−0.433461	−	0.750776i	0.563708	−	0.825974i	$-0.309374\pi$
$383$	−8.48299	−	14.6930i	−0.433461	−	0.750776i	−0.997169	+	0.0751982i	$0.976041\pi$
$384$	−7.53825	+	15.8800i	−0.384685	+	0.810374i
$385$		0			0
$386$			9.16964i			0.466723i
$387$	−5.81467	+	15.3174i	−0.295576	+	0.778626i
$388$	19.8303	+	11.4490i	1.00673	+	0.581236i
$389$	−2.13457	−	1.23239i	−0.108227	−	0.0624848i	0.444910	−	0.895576i	$-0.353236\pi$
$389$	−2.13457	−	1.23239i	−0.108227	−	0.0624848i	−0.553136	+	0.833091i	$0.686569\pi$
$390$		0			0
$391$		−	19.7457i		−	0.998583i
$392$	−8.28375	+	6.28592i	−0.418393	+	0.317487i
$393$	24.5090	+	11.6344i	1.23632	+	0.586879i
$394$	−2.25351	−	3.90319i	−0.113530	−	0.196640i
$395$		0			0
$396$	−2.26037	−	13.9366i	−0.113588	−	0.700339i
$397$	−2.90437	+	1.67684i	−0.145766	+	0.0841582i	−0.571109	−	0.820874i	$-0.693487\pi$
$397$	−2.90437	+	1.67684i	−0.145766	+	0.0841582i	0.425343	+	0.905032i	$0.360153\pi$
$398$	−5.44912			−0.273140
$399$	−4.30667	+	3.38930i	−0.215603	+	0.169677i
$400$		0			0
$401$	−5.40992	+	3.12342i	−0.270158	+	0.155976i	−0.628960	−	0.777438i	$-0.716519\pi$
$401$	−5.40992	+	3.12342i	−0.270158	+	0.155976i	0.358801	+	0.933414i	$0.383186\pi$
$402$	−1.33537	−	1.93527i	−0.0666022	−	0.0965226i
$403$	10.5418	−	18.2589i	0.525124	−	0.909541i
$404$	−6.45731	−	11.1844i	−0.321263	−	0.556444i
$405$		0			0
$406$	0.497384	+	7.91434i	0.0246848	+	0.392782i
$407$			9.03024i			0.447612i
$408$	−16.5713	+	1.33513i	−0.820403	+	0.0660988i
$409$	−10.2147	−	5.89748i	−0.505086	−	0.291611i	0.225726	−	0.974191i	$-0.427525\pi$
$409$	−10.2147	−	5.89748i	−0.505086	−	0.291611i	−0.730811	+	0.682579i	$0.760858\pi$
$410$		0			0
$411$	−10.0625	+	0.810722i	−0.496346	+	0.0399899i
$412$		−	6.98495i		−	0.344124i
$413$	8.73350	−	5.80166i	0.429748	−	0.285481i
$414$	−2.23569	−	2.74000i	−0.109878	−	0.134664i
$415$		0			0
$416$	6.40761	−	11.0983i	0.314159	−	0.544139i
$417$	−11.8402	−	17.1593i	−0.579817	−	0.840295i
$418$	1.01563	−	0.586372i	0.0496759	−	0.0286804i
$419$	−12.0419			−0.588284			−0.294142	−	0.955762i	$-0.595034\pi$
$419$	−12.0419			−0.588284			−0.294142	+	0.955762i	$0.595034\pi$
$420$		0			0
$421$	11.4264			0.556888			0.278444	−	0.960453i	$-0.410181\pi$
$421$	11.4264			0.556888			0.278444	+	0.960453i	$0.410181\pi$
$422$	1.50270	−	0.867582i	0.0731501	−	0.0422332i
$423$	9.53594	−	1.54664i	0.463653	−	0.0752000i
$424$	9.84521	−	17.0524i	0.478126	−	0.828138i
$425$		0			0
$426$	0.556394	+	0.264120i	0.0269574	+	0.0127967i
$427$	24.6647	−	1.55007i	1.19361	−	0.0750133i
$428$		−	24.4983i		−	1.18417i
$429$	1.08462	+	13.4621i	0.0523660	+	0.649955i
$430$		0			0
$431$	−28.2346	−	16.3013i	−1.36001	−	0.785205i	−0.370389	−	0.928877i	$-0.620776\pi$
$431$	−28.2346	−	16.3013i	−1.36001	−	0.785205i	−0.989625	+	0.143672i	$0.954109\pi$
$432$	11.7327	−	11.2587i	0.564492	−	0.541686i
$433$			4.37644i			0.210318i	0.994455	+	0.105159i	$0.0335352\pi$
$433$			4.37644i			0.210318i	−0.994455	+	0.105159i	$0.966465\pi$
$434$	6.28335	+	3.11962i	0.301611	+	0.149747i
$435$		0			0
$436$	−2.31551	−	4.01059i	−0.110893	−	0.192072i
$437$	−1.82736	+	3.16508i	−0.0874146	+	0.151407i
$438$	0.163011	−	0.112480i	0.00778895	−	0.00537450i
$439$	−12.8416	+	7.41409i	−0.612895	+	0.353855i	−0.774098	−	0.633066i	$-0.781796\pi$
$439$	−12.8416	+	7.41409i	−0.612895	+	0.353855i	0.161202	+	0.986921i	$0.448463\pi$
$440$		0			0
$441$	20.1451	−	5.93084i	0.959291	−	0.282421i
$442$	7.64441			0.363607
$443$	13.7806	−	7.95622i	0.654735	−	0.378011i	−0.135533	−	0.990773i	$-0.543275\pi$
$443$	13.7806	−	7.95622i	0.654735	−	0.378011i	0.790268	+	0.612762i	$0.209941\pi$
$444$	−9.37428	+	6.46841i	−0.444884	+	0.306977i
$445$		0			0
$446$	1.38991	+	2.40739i	0.0658141	+	0.113993i
$447$	−13.8878	+	29.2560i	−0.656872	+	1.38376i
$448$	−11.0126	−	5.46765i	−0.520298	−	0.258322i
$449$			35.1881i			1.66063i	0.557294	+	0.830315i	$0.311839\pi$
$449$			35.1881i			1.66063i	−0.557294	+	0.830315i	$0.688161\pi$
$450$		0			0
$451$	−5.09134	−	2.93948i	−0.239742	−	0.138415i
$452$	11.5178	+	6.64978i	0.541750	+	0.312779i
$453$	0.827721	+	10.2735i	0.0388897	+	0.482690i
$454$			0.718630i			0.0337270i
$455$		0			0
$456$	2.77982	+	1.31958i	0.130177	+	0.0617950i
$457$	7.02954	+	12.1755i	0.328828	+	0.569547i	0.982280	−	0.187421i	$-0.0600129\pi$
$457$	7.02954	+	12.1755i	0.328828	+	0.569547i	−0.653451	+	0.756968i	$0.726680\pi$
$458$	−3.87782	+	6.71658i	−0.181199	+	0.313845i
$459$	32.2439	+	9.35619i	1.50502	+	0.436710i
$460$		0			0
$461$	13.5161			0.629506			0.314753	−	0.949174i	$-0.398078\pi$
$461$	13.5161			0.629506			0.314753	+	0.949174i	$0.398078\pi$
$462$	−4.44780	+	0.641126i	−0.206930	+	0.0298279i
$463$	−17.8381			−0.829009			−0.414504	−	0.910047i	$-0.636045\pi$
$463$	−17.8381			−0.829009			−0.414504	+	0.910047i	$0.636045\pi$
$464$	−21.0586	+	12.1582i	−0.977623	+	0.564431i
$465$		0			0
$466$	−0.301892	+	0.522893i	−0.0139849	+	0.0242225i
$467$	4.59471	+	7.95827i	0.212618	+	0.368265i	0.952533	−	0.304435i	$-0.0984678\pi$
$467$	4.59471	+	7.95827i	0.212618	+	0.368265i	−0.739915	+	0.672700i	$0.765134\pi$
$468$	−13.1980	+	10.7689i	−0.610080	+	0.497792i
$469$	7.75588	−	5.15223i	0.358133	−	0.237908i
$470$		0			0
$471$	11.0714	−	0.892008i	0.510143	−	0.0411016i
$472$	−5.09833	−	2.94352i	−0.234670	−	0.135487i
$473$	12.0238	+	6.94197i	0.552857	+	0.319192i
$474$	5.52391	−	0.445055i	0.253722	−	0.0204420i
$475$		0			0
$476$	−1.98494	−	31.5842i	−0.0909794	−	1.44766i
$477$	−30.8097	+	25.1391i	−1.41068	+	1.15104i
$478$	−1.09785	−	1.90153i	−0.0502144	−	0.0869739i
$479$	−9.44037	+	16.3512i	−0.431341	+	0.747105i	−0.996989	−	0.0775419i	$-0.975293\pi$
$479$	−9.44037	+	16.3512i	−0.431341	+	0.747105i	0.565648	+	0.824647i	$0.308626\pi$
$480$		0			0
$481$	9.43523	−	5.44743i	0.430210	−	0.248382i
$482$	5.14291			0.234253
$483$	11.0050	−	8.66085i	0.500746	−	0.394082i
$484$	8.39897			0.381772
$485$		0			0
$486$	5.53366	−	2.35249i	0.251012	−	0.106711i
$487$	−2.61762	+	4.53386i	−0.118616	+	0.205449i	−0.919219	−	0.393746i	$-0.871179\pi$
$487$	−2.61762	+	4.53386i	−0.118616	+	0.205449i	0.800604	+	0.599194i	$0.204512\pi$
$488$	−6.93799	−	12.0170i	−0.314068	−	0.543982i
$489$	25.7292	+	12.2136i	1.16351	+	0.552320i
$490$		0			0
$491$			19.5201i			0.880930i	0.897770	+	0.440465i	$0.145186\pi$
$491$			19.5201i			0.880930i	−0.897770	+	0.440465i	$0.854814\pi$
$492$	−0.595474	−	7.39088i	−0.0268460	−	0.333207i
$493$	−43.4799	−	25.1031i	−1.95823	−	1.13059i
$494$	−1.22534	−	0.707451i	−0.0551307	−	0.0318297i
$495$		0			0
$496$			21.5113i			0.965887i
$497$	−1.08462	+	2.18458i	−0.0486519	+	0.0979918i
$498$	0.605021	−	1.27453i	0.0271116	−	0.0571132i
$499$	18.3175	+	31.7269i	0.820005	+	1.42029i	0.905678	+	0.423967i	$0.139363\pi$
$499$	18.3175	+	31.7269i	0.820005	+	1.42029i	−0.0856728	+	0.996323i	$0.527304\pi$
$500$		0			0
$501$	−6.85844	+	4.73243i	−0.306413	+	0.211430i
$502$	1.77913	−	1.02718i	0.0794064	−	0.0458453i
$503$	40.7156			1.81542			0.907708	−	0.419602i	$-0.137830\pi$
$503$	40.7156			1.81542			0.907708	+	0.419602i	$0.137830\pi$
$504$	−8.01263	−	8.65022i	−0.356911	−	0.385312i
$505$		0			0
$506$	−2.59528	+	1.49838i	−0.115374	+	0.0666113i
$507$	−5.12134	+	3.53381i	−0.227447	+	0.156942i
$508$	−10.3635	+	17.9502i	−0.459807	+	0.796410i
$509$	8.86384	+	15.3526i	0.392883	+	0.680493i	0.992828	−	0.119548i	$-0.0381445\pi$
$509$	8.86384	+	15.3526i	0.392883	+	0.680493i	−0.599946	+	0.800041i	$0.704811\pi$
$510$		0			0
$511$	0.433979	+	0.653288i	0.0191981	+	0.0288998i
$512$			22.3729i			0.988751i
$513$	−4.30258	−	4.48373i	−0.189964	−	0.197962i
$514$	−2.17136	−	1.25364i	−0.0957747	−	0.0552956i
$515$		0			0
$516$	1.40629	+	17.4545i	0.0619084	+	0.768393i
$517$		−	8.18648i		−	0.360041i
$518$	2.00587	+	3.01953i	0.0881330	+	0.132671i
$519$	−10.6638	−	5.06210i	−0.468088	−	0.222202i
$520$		0			0
$521$	1.75780	−	3.04461i	0.0770108	−	0.133387i	−0.824948	−	0.565208i	$-0.808796\pi$
$521$	1.75780	−	3.04461i	0.0770108	−	0.133387i	0.901959	+	0.431822i	$0.142129\pi$
$522$	−8.87574	+	1.43956i	−0.388481	+	0.0630078i
$523$	−4.20527	+	2.42791i	−0.183884	+	0.106165i	−0.589116	−	0.808048i	$-0.700524\pi$
$523$	−4.20527	+	2.42791i	−0.183884	+	0.106165i	0.405232	+	0.914214i	$0.367191\pi$
$524$	28.9968			1.26673
$525$		0			0
$526$	5.71904			0.249362
$527$	−38.4641	+	22.2073i	−1.67552	+	0.967363i
$528$	−7.82596	−	11.3417i	−0.340581	−	0.493584i
$529$	−6.83045	+	11.8307i	−0.296976	+	0.514378i
$530$		0			0
$531$	7.51608	+	9.21148i	0.326170	+	0.399744i
$532$	−2.60478	+	5.24639i	−0.112932	+	0.227460i
$533$			7.09290i			0.307228i
$534$	−12.5399	+	1.01032i	−0.542654	+	0.0437209i
$535$		0			0
$536$	−4.52763	−	2.61403i	−0.195564	−	0.112909i
$537$	34.4746	−	2.77757i	1.48769	−	0.119861i
$538$		−	9.49222i		−	0.409239i
$539$	−2.22797	−	17.6557i	−0.0959656	−	0.760483i
$540$		0			0
$541$	0.0193171	+	0.0334581i	0.000830506	+	0.00143848i	0.866440	−	0.499281i	$-0.166402\pi$
$541$	0.0193171	+	0.0334581i	0.000830506	+	0.00143848i	−0.865610	+	0.500719i	$0.833069\pi$
$542$	0.735184	−	1.27338i	0.0315789	−	0.0546962i
$543$	−5.10346	−	7.39615i	−0.219011	−	0.317399i
$544$	−23.3796	+	13.4982i	−1.00239	+	0.578731i
$545$		0			0
$546$	3.35299	+	4.26052i	0.143495	+	0.182333i
$547$	36.3881			1.55584			0.777921	−	0.628362i	$-0.216274\pi$
$547$	36.3881			1.55584			0.777921	+	0.628362i	$0.216274\pi$
$548$	−9.34408	+	5.39480i	−0.399159	+	0.230455i
$549$	4.48632	+	27.6608i	0.191471	+	1.18053i
$550$		0			0
$551$	4.64633	+	8.04767i	0.197940	+	0.342842i
$552$	−7.10340	−	3.37199i	−0.302341	−	0.143521i
$553$	1.37650	+	21.9028i	0.0585349	+	0.931402i
$554$			7.24224i			0.307693i
$555$		0			0
$556$	−19.2969	−	11.1411i	−0.818370	−	0.472486i
$557$	15.0477	+	8.68779i	0.637591	+	0.368114i	0.783686	−	0.621157i	$-0.213337\pi$
$557$	15.0477	+	8.68779i	0.637591	+	0.368114i	−0.146095	+	0.989271i	$0.546670\pi$
$558$	−2.82305	+	7.43665i	−0.119509	+	0.314818i
$559$		−	16.7508i		−	0.708484i
$560$		0			0
$561$	12.2008	−	25.7021i	0.515118	−	1.08514i
$562$	−4.56870	−	7.91322i	−0.192719	−	0.333799i
$563$	−10.4546	+	18.1078i	−0.440607	+	0.763153i	−0.997735	−	0.0672735i	$-0.978570\pi$
$563$	−10.4546	+	18.1078i	−0.440607	+	0.763153i	0.557128	+	0.830427i	$0.311903\pi$
$564$	8.49838	−	5.86402i	0.357846	−	0.246920i
$565$		0			0
$566$	1.94566			0.0817822
$567$	8.92824	+	22.0746i	0.374951	+	0.927045i
$568$	1.36945			0.0574610
$569$	−24.8873	+	14.3687i	−1.04333	+	0.602367i	−0.920775	−	0.390094i	$-0.872442\pi$
$569$	−24.8873	+	14.3687i	−1.04333	+	0.602367i	−0.122556	+	0.992462i	$0.539109\pi$
$570$		0			0
$571$	15.2499	−	26.4136i	0.638188	−	1.10537i	−0.347643	−	0.937627i	$-0.613018\pi$
$571$	15.2499	−	26.4136i	0.638188	−	1.10537i	0.985830	−	0.167746i	$-0.0536490\pi$
$572$	7.21742	+	12.5009i	0.301776	+	0.522691i
$573$	6.41823	−	13.5206i	0.268125	−	0.564831i
$574$	−2.35539	+	0.148026i	−0.0983119	+	0.00617850i
$575$		0			0
$576$	4.94786	−	13.0340i	0.206161	−	0.543082i
$577$	−20.3570	−	11.7531i	−0.847473	−	0.489289i	0.0123245	−	0.999924i	$-0.496077\pi$
$577$	−20.3570	−	11.7531i	−0.847473	−	0.489289i	−0.859797	+	0.510635i	$0.829410\pi$
$578$	−8.26728	−	4.77312i	−0.343874	−	0.198536i
$579$	−3.30667	−	41.0416i	−0.137420	−	1.70563i
$580$		0			0
$581$	5.00423	+	2.48455i	0.207610	+	0.103076i
$582$	7.46549	+	3.54387i	0.309455	+	0.146898i
$583$	16.8485	+	29.1824i	0.697792	+	1.20861i
$584$	0.220183	−	0.381368i	0.00911124	−	0.0157811i
$585$		0			0
$586$	−2.10260	+	1.21394i	−0.0868575	+	0.0501472i
$587$	−24.4613			−1.00963			−0.504813	−	0.863229i	$-0.668439\pi$
$587$	−24.4613			−1.00963			−0.504813	+	0.863229i	$0.668439\pi$
$588$	16.7324	−	14.9597i	0.690034	−	0.616928i
$589$	8.22067			0.338727
$590$		0			0
$591$	11.4938	+	16.6573i	0.472791	+	0.685189i
$592$	−5.55795	+	9.62665i	−0.228430	+	0.395653i
$593$	1.87506	+	3.24770i	0.0769995	+	0.133367i	0.901954	−	0.431832i	$-0.142133\pi$
$593$	1.87506	+	3.24770i	0.0769995	+	0.133367i	−0.824955	+	0.565199i	$0.808799\pi$
$594$	−1.21707	−	4.94797i	−0.0499369	−	0.203018i
$595$		0			0
$596$			34.6130i			1.41780i
$597$	24.3892	−	1.96501i	0.998184	−	0.0804224i
$598$	3.13117	+	1.80778i	0.128043	+	0.0739257i
$599$	28.6663	+	16.5505i	1.17127	+	0.676235i	0.953980	−	0.299871i	$-0.0969438\pi$
$599$	28.6663	+	16.5505i	1.17127	+	0.676235i	0.217294	+	0.976106i	$0.430277\pi$
$600$		0			0
$601$			3.36032i			0.137070i	0.997649	+	0.0685352i	$0.0218325\pi$
$601$			3.36032i			0.137070i	−0.997649	+	0.0685352i	$0.978167\pi$
$602$	5.56255	−	0.349583i	0.226712	−	0.0142480i
$603$	6.67473	+	8.18036i	0.271816	+	0.333130i
$604$	5.50793	+	9.54001i	0.224114	+	0.388177i
$605$		0			0
$606$	−2.64709	−	3.83627i	−0.107531	−	0.155838i
$607$	−38.5420	+	22.2522i	−1.56437	+	0.903190i	−0.567565	+	0.823329i	$0.692114\pi$
$607$	−38.5420	+	22.2522i	−1.56437	+	0.903190i	−0.996806	+	0.0798612i	$0.974552\pi$
$608$	4.99676			0.202645
$609$	−5.08019	−	35.2437i	−0.205860	−	1.42815i
$610$		0			0
$611$	−8.55364	+	4.93844i	−0.346043	+	0.199788i
$612$	35.4209	−	5.74492i	1.43180	−	0.232225i
$613$	20.1567	−	34.9125i	0.814123	−	1.41010i	−0.0958333	−	0.995397i	$-0.530552\pi$
$613$	20.1567	−	34.9125i	0.814123	−	1.41010i	0.909956	−	0.414705i	$-0.136115\pi$
$614$	−3.09349	−	5.35809i	−0.124843	−	0.216235i
$615$		0			0
$616$	−8.32283	+	5.52885i	−0.335336	+	0.222764i
$617$		−	37.7372i		−	1.51924i	−0.650366	−	0.759621i	$-0.725384\pi$
$617$		−	37.7372i		−	1.51924i	0.650366	−	0.759621i	$-0.274616\pi$
$618$	−0.202448	−	2.51274i	−0.00814365	−	0.101077i
$619$	12.7122	+	7.33941i	0.510948	+	0.294996i	0.733223	−	0.679988i	$-0.238015\pi$
$619$	12.7122	+	7.33941i	0.510948	+	0.294996i	−0.222275	+	0.974984i	$0.571348\pi$
$620$		0			0
$621$	10.9946	+	11.4575i	0.441198	+	0.459774i
$622$		−	6.97111i		−	0.279516i
$623$	−3.12481	−	49.7218i	−0.125193	−	1.99206i
$624$	−7.12941	+	15.0188i	−0.285405	+	0.601232i
$625$		0			0
$626$	3.59155	−	6.22075i	0.143547	−	0.248631i
$627$	−4.33429	+	2.99073i	−0.173095	+	0.119438i
$628$	10.2810	−	5.93571i	0.410255	−	0.236861i
$629$	−22.9511			−0.915118
$630$		0			0
$631$	−35.8363			−1.42662			−0.713311	−	0.700848i	$-0.752805\pi$
$631$	−35.8363			−1.42662			−0.713311	+	0.700848i	$0.752805\pi$
$632$	10.6713	−	6.16110i	0.424483	−	0.245076i
$633$	−6.41292	+	4.42502i	−0.254891	+	0.175879i
$634$	0.508489	−	0.880729i	0.0201947	−	0.0349782i
$635$		0			0
$636$	−18.2256	+	38.3939i	−0.722691	+	1.52242i
$637$	−17.1035	+	12.9786i	−0.677665	+	0.514230i
$638$			7.61971i			0.301667i
$639$	−2.58555	−	0.981510i	−0.102283	−	0.0388279i
$640$		0			0
$641$	−13.5251	−	7.80872i	−0.534209	−	0.308426i	0.208519	−	0.978018i	$-0.433136\pi$
$641$	−13.5251	−	7.80872i	−0.534209	−	0.308426i	−0.742729	+	0.669592i	$0.766469\pi$
$642$	−0.710047	−	8.81293i	−0.0280233	−	0.347819i
$643$			29.3208i			1.15630i	0.815931	+	0.578149i	$0.196225\pi$
$643$			29.3208i			1.15630i	−0.815931	+	0.578149i	$0.803775\pi$
$644$	6.65612	−	13.4064i	0.262288	−	0.528285i
$645$		0			0
$646$	1.49031	+	2.58129i	0.0586355	+	0.101560i
$647$	−3.33405	+	5.77475i	−0.131075	+	0.227029i	−0.924091	−	0.382172i	$-0.875176\pi$
$647$	−3.33405	+	5.77475i	−0.131075	+	0.227029i	0.793016	+	0.609201i	$0.208510\pi$
$648$	8.87215	−	10.0018i	0.348531	−	0.392908i
$649$	8.72495	−	5.03735i	0.342484	−	0.197733i
$650$		0			0
$651$	−29.2480	−	11.6970i	−1.14632	−	0.458441i
$652$	30.4404			1.19214
$653$	−38.2165	+	22.0643i	−1.49553	+	0.863444i	−0.999987	−	0.00514013i	$-0.998364\pi$
$653$	−38.2165	+	22.0643i	−1.49553	+	0.863444i	−0.495542	+	0.868584i	$0.665031\pi$
$654$	−0.949214	−	1.37564i	−0.0371172	−	0.0537918i
$655$		0			0
$656$	−3.61840	−	6.26726i	−0.141275	−	0.244695i
$657$	−0.689043	+	0.562222i	−0.0268821	+	0.0219344i
$658$	−1.81845	−	2.73740i	−0.0708906	−	0.106715i
$659$		−	7.10057i		−	0.276599i	−0.990390	−	0.138299i	$-0.955836\pi$
$659$		−	7.10057i		−	0.276599i	0.990390	−	0.138299i	$-0.0441636\pi$
$660$		0			0
$661$	−20.5558	−	11.8679i	−0.799527	−	0.461607i	0.0437789	−	0.999041i	$-0.486060\pi$
$661$	−20.5558	−	11.8679i	−0.799527	−	0.461607i	−0.843306	+	0.537434i	$0.819394\pi$
$662$	10.1354	+	5.85170i	0.393925	+	0.227433i
$663$	−34.2149	+	2.75665i	−1.32880	+	0.107059i
$664$		−	3.13701i		−	0.121740i
$665$		0			0
$666$	−3.18479	+	2.59862i	−0.123408	+	0.100694i
$667$	−11.8730	−	20.5646i	−0.459724	−	0.796265i
$668$	−4.45299	+	7.71281i	−0.172291	+	0.298418i
$669$	−7.08909	−	10.2738i	−0.274080	−	0.397208i
$670$		0			0
$671$	23.7464			0.916721
$672$	−17.7778	−	7.10976i	−0.685794	−	0.274265i
$673$	14.7915			0.570171			0.285086	−	0.958502i	$-0.407978\pi$
$673$	14.7915			0.570171			0.285086	+	0.958502i	$0.407978\pi$
$674$	0.615374	−	0.355286i	0.0237033	−	0.0136851i
$675$		0			0
$676$	−3.32514	+	5.75931i	−0.127890	+	0.221512i
$677$	−18.2590	−	31.6255i	−0.701749	−	1.21547i	−0.967852	−	0.251521i	$-0.919069\pi$
$677$	−18.2590	−	31.6255i	−0.701749	−	1.21547i	0.266103	−	0.963945i	$-0.414264\pi$
$678$	4.33609	+	2.05834i	0.166526	+	0.0790501i
$679$	−14.5531	+	29.3119i	−0.558496	+	1.12489i
$680$		0			0
$681$	−0.259145	−	3.21645i	−0.00993047	−	0.123255i
$682$	5.83763	+	3.37035i	0.223534	+	0.129058i
$683$	18.9828	+	10.9597i	0.726356	+	0.419362i	0.817088	−	0.576514i	$-0.195587\pi$
$683$	18.9828	+	10.9597i	0.726356	+	0.419362i	−0.0907317	+	0.995875i	$0.528921\pi$
$684$	−6.20936	−	2.35715i	−0.237421	−	0.0901279i
$685$		0			0
$686$	−4.66682	−	5.40881i	−0.178180	−	0.206509i
$687$	14.9343	−	31.4605i	0.569779	−	1.20029i
$688$	8.54532	+	14.8009i	0.325787	+	0.564280i
$689$	20.3275	−	35.2082i	0.774414	−	1.34132i
$690$		0			0
$691$	27.2031	−	15.7057i	1.03485	−	0.597473i	0.116482	−	0.993193i	$-0.462838\pi$
$691$	27.2031	−	15.7057i	1.03485	−	0.597473i	0.918371	+	0.395720i	$0.129505\pi$
$692$	−12.6164			−0.479604
$693$	19.6763	−	4.47347i	0.747440	−	0.169933i
$694$	−3.15929			−0.119925
$695$		0			0
$696$	−16.4558	+	11.3548i	−0.623755	+	0.430401i
$697$	7.47093	−	12.9400i	0.282982	−	0.490139i
$698$	−7.00663	−	12.1358i	−0.265205	−	0.459348i
$699$	1.16265	−	2.44923i	0.0439755	−	0.0926385i
$700$		0			0
$701$		−	29.6988i		−	1.12171i	−0.827915	−	0.560854i	$-0.810473\pi$
$701$		−	29.6988i		−	1.12171i	0.827915	−	0.560854i	$-0.189527\pi$
$702$	−4.43569	+	4.25648i	−0.167414	+	0.160651i
$703$	3.67888	+	2.12400i	0.138751	+	0.0801082i
$704$	−10.2314	−	5.90711i	−0.385611	−	0.222633i
$705$		0			0
$706$			2.20435i			0.0829617i
$707$	15.3744	−	10.2132i	0.578214	−	0.384107i
$708$	11.4790	+	5.44908i	0.431407	+	0.204789i
$709$	−6.66342	−	11.5414i	−0.250250	−	0.433446i	0.713344	−	0.700814i	$-0.247180\pi$
$709$	−6.66342	−	11.5414i	−0.250250	−	0.433446i	−0.963595	+	0.267368i	$0.913846\pi$
$710$		0			0
$711$	−24.5635	+	3.98396i	−0.921202	+	0.149410i
$712$	−24.2251	+	13.9864i	−0.907875	+	0.524162i
$713$	−21.0067			−0.786706
$714$	−1.62947	−	11.3044i	−0.0609814	−	0.423057i
$715$		0			0
$716$	32.0133	−	18.4829i	1.19639	−	0.690737i
$717$	5.59947	+	8.11498i	0.209116	+	0.303060i
$718$	0.926842	−	1.60534i	0.0345895	−	0.0599107i
$719$	−25.5863	−	44.3167i	−0.954207	−	1.65273i	−0.736173	−	0.676794i	$-0.763369\pi$
$719$	−25.5863	−	44.3167i	−0.954207	−	1.65273i	−0.218034	−	0.975941i	$-0.569964\pi$
$720$		0			0
$721$	9.96323	−	0.626148i	0.371050	−	0.0233190i
$722$			6.77720i			0.252221i
$723$	−23.0187	+	1.85459i	−0.856074	+	0.0689728i
$724$	−8.31751	−	4.80211i	−0.309118	−	0.178469i
$725$		0			0
$726$	3.02141	−	0.243431i	0.112135	−	0.00903459i
$727$		−	51.6371i		−	1.91511i	−0.288246	−	0.957556i	$-0.593072\pi$
$727$		−	51.6371i		−	1.91511i	0.288246	−	0.957556i	$-0.406928\pi$
$728$	10.7975	+	5.36085i	0.400182	+	0.198686i
$729$	−23.9192	+	12.5248i	−0.885898	+	0.463880i
$730$		0			0
$731$	−17.6436	+	30.5596i	−0.652571	+	1.13029i
$732$	17.0097	+	24.6512i	0.628697	+	0.911134i
$733$	−19.0043	+	10.9721i	−0.701940	+	0.405265i	−0.808069	−	0.589087i	$-0.799487\pi$
$733$	−19.0043	+	10.9721i	−0.701940	+	0.405265i	0.106130	+	0.994352i	$0.466154\pi$
$734$	9.47979			0.349905
$735$		0			0
$736$	−12.7685			−0.470652
$737$	7.74829	−	4.47347i	0.285412	−	0.164783i
$738$	−0.428427	−	2.64151i	−0.0157706	−	0.0972352i
$739$	19.2874	−	33.4068i	0.709500	−	1.22889i	−0.255543	−	0.966798i	$-0.582254\pi$
$739$	19.2874	−	33.4068i	0.709500	−	1.22889i	0.965043	−	0.262092i	$-0.0844125\pi$
$740$		0			0
$741$	5.73950	+	2.72454i	0.210846	+	0.100089i
$742$	12.1160	+	6.01548i	0.444793	+	0.220835i
$743$			3.81873i			0.140096i	0.997544	+	0.0700478i	$0.0223152\pi$
$743$			3.81873i			0.140096i	−0.997544	+	0.0700478i	$0.977685\pi$
$744$	1.42039	+	17.6296i	0.0520741	+	0.646332i
$745$		0			0
$746$	8.85325	+	5.11143i	0.324141	+	0.187143i
$747$	−2.24835	+	5.92274i	−0.0822628	+	0.216702i
$748$		−	30.4083i		−	1.11184i
$749$	34.9441	−	2.19609i	1.27683	−	0.0802435i
$750$		0			0
$751$	−10.5271	−	18.2334i	−0.384139	−	0.665348i	0.607511	−	0.794312i	$-0.292168\pi$
$751$	−10.5271	−	18.2334i	−0.384139	−	0.665348i	−0.991649	+	0.128964i	$0.958835\pi$
$752$	5.03863	−	8.72717i	0.183740	−	0.318247i
$753$	−7.59263	+	5.23904i	−0.276691	+	0.190921i
$754$	7.96145	−	4.59654i	0.289939	−	0.167396i
$755$		0			0
$756$	18.7381	+	17.2216i	0.681500	+	0.626342i
$757$	−28.6903			−1.04277			−0.521383	−	0.853323i	$-0.674584\pi$
$757$	−28.6903			−1.04277			−0.521383	+	0.853323i	$0.674584\pi$
$758$	4.37405	−	2.52536i	0.158873	−	0.0917251i
$759$	11.0756	−	7.64236i	0.402020	−	0.277400i
$760$		0			0
$761$	5.34875	+	9.26431i	0.193892	+	0.335831i	0.946537	−	0.322596i	$-0.104556\pi$
$761$	5.34875	+	9.26431i	0.193892	+	0.335831i	−0.752645	+	0.658427i	$0.771222\pi$
$762$	−3.20788	+	6.75769i	−0.116209	+	0.244805i
$763$	5.51308	−	3.66234i	0.199587	−	0.132585i
$764$		−	15.9963i		−	0.578726i
$765$		0			0
$766$	−5.66753	−	3.27215i	−0.204776	−	0.118228i
$767$	−10.5265	−	6.07750i	−0.380092	−	0.219446i
$768$	−0.748293	−	9.28763i	−0.0270017	−	0.335139i
$769$			38.6874i			1.39510i	0.716535	+	0.697551i	$0.245727\pi$
$769$			38.6874i			1.39510i	−0.716535	+	0.697551i	$0.754273\pi$
$770$		0			0
$771$	10.1707	+	4.82802i	0.366288	+	0.173877i
$772$	−22.0036	−	38.1114i	−0.791928	−	1.37166i
$773$	−11.4438	+	19.8212i	−0.411603	+	0.712918i	−0.995065	−	0.0992225i	$-0.968364\pi$
$773$	−11.4438	+	19.8212i	−0.411603	+	0.712918i	0.583462	+	0.812141i	$0.301698\pi$
$774$	1.01179	+	6.23826i	0.0363679	+	0.224230i
$775$		0			0
$776$	18.3748			0.659618
$777$	−10.0668	−	12.7915i	−0.361144	−	0.458892i
$778$	−0.950743			−0.0340858
$779$	−2.39507	+	1.38279i	−0.0858121	+	0.0495437i
$780$		0			0
$781$	−1.17180	+	2.02961i	−0.0419302	+	0.0726252i
$782$	−3.80826	−	6.59610i	−0.136183	−	0.235876i
$783$	39.2070	−	9.64387i	1.40114	−	0.344644i
$784$	8.49163	−	20.1930i	0.303272	−	0.721180i
$785$		0			0
$786$	10.4312	−	0.840427i	0.372068	−	0.0299770i
$787$	−28.1627	−	16.2597i	−1.00389	−	0.579597i	−0.0944937	−	0.995525i	$-0.530123\pi$
$787$	−28.1627	−	16.2597i	−1.00389	−	0.579597i	−0.909397	+	0.415929i	$0.863457\pi$
$788$	18.7323	+	10.8151i	0.667311	+	0.385272i
$789$	−25.5973	+	2.06235i	−0.911289	+	0.0734214i
$790$		0			0
$791$	−8.45267	+	17.0249i	−0.300542	+	0.605335i
$792$	−7.16265	−	8.77834i	−0.254514	−	0.311925i
$793$	−14.3249	−	24.8115i	−0.508692	−	0.881081i
$794$	−0.646809	+	1.12031i	−0.0229544	+	0.0397582i
$795$		0			0
$796$	22.6480	−	13.0758i	0.802736	−	0.463460i
$797$	31.9080			1.13024			0.565120	−	0.825009i	$-0.308830\pi$
$797$	31.9080			1.13024			0.565120	+	0.825009i	$0.308830\pi$
$798$	−0.784974	+	1.96281i	−0.0277878	+	0.0694828i
$799$	20.8066			0.736084
$800$		0			0
$801$	55.7618	−	9.04402i	1.97025	−	0.319555i
$802$	−1.20480	+	2.08677i	−0.0425429	+	0.0736865i
$803$	0.376807	+	0.652648i	0.0132972	+	0.0230315i
$804$	10.1941	+	4.83912i	0.359516	+	0.170663i
$805$		0			0
$806$		−	8.13258i		−	0.286458i
$807$	3.42299	+	42.4853i	0.120495	+	1.49555i
$808$	−8.97507	−	5.18176i	−0.315742	−	0.182294i
$809$	17.9862	+	10.3843i	0.632360	+	0.365093i	0.781666	−	0.623698i	$-0.214370\pi$
$809$	17.9862	+	10.3843i	0.632360	+	0.365093i	−0.149305	+	0.988791i	$0.547704\pi$
$810$		0			0
$811$		−	5.77041i		−	0.202627i	−0.994855	−	0.101313i	$-0.967696\pi$
$811$		−	5.77041i		−	0.202627i	0.994855	−	0.101313i	$-0.0323044\pi$
$812$	−21.0586	−	31.7005i	−0.739013	−	1.11247i
$813$	−2.83135	+	5.96450i	−0.0992998	+	0.209184i
$814$	1.74162	+	3.01657i	0.0610437	+	0.105731i
$815$		0			0
$816$	28.8258	−	19.8903i	1.00911	−	0.696299i
$817$	5.65626	−	3.26564i	0.197887	−	0.114250i
$818$	−4.54968			−0.159076
$819$	−16.5437	−	17.8602i	−0.578084	−	0.624084i
$820$		0			0
$821$	12.7908	−	7.38477i	0.446402	−	0.257730i	−0.259907	−	0.965634i	$-0.583692\pi$
$821$	12.7908	−	7.38477i	0.446402	−	0.257730i	0.706309	+	0.707903i	$0.250359\pi$
$822$	−3.20504	+	2.21153i	−0.111789	+	0.0771359i
$823$	13.7054	−	23.7385i	0.477741	−	0.827472i	−0.521933	−	0.852986i	$-0.674789\pi$
$823$	13.7054	−	23.7385i	0.477741	−	0.827472i	0.999674	+	0.0255145i	$0.00812240\pi$
$824$	−2.80258	−	4.85422i	−0.0976326	−	0.169105i
$825$		0			0
$826$	1.79851	−	3.62245i	0.0625781	−	0.126041i
$827$		−	27.6521i		−	0.961557i	−0.876842	−	0.480779i	$-0.840354\pi$
$827$		−	27.6521i		−	0.961557i	0.876842	−	0.480779i	$-0.159646\pi$
$828$	15.8671	+	6.02334i	0.551419	+	0.209326i
$829$	−18.6252	−	10.7533i	−0.646880	−	0.373476i	0.140380	−	0.990098i	$-0.455168\pi$
$829$	−18.6252	−	10.7533i	−0.646880	−	0.373476i	−0.787260	+	0.616621i	$0.788501\pi$
$830$		0			0
$831$	−2.61162	−	32.4149i	−0.0905963	−	1.12446i
$832$			14.2537i			0.494158i
$833$	44.8733	−	5.66257i	1.55477	−	0.196196i
$834$	−7.26469	−	3.44855i	−0.251556	−	0.119414i
$835$		0			0
$836$	−2.81414	+	4.87423i	−0.0973289	+	0.168579i
$837$	9.95368	−	34.3030i	0.344050	−	1.18569i
$838$	−4.02262	+	2.32246i	−0.138959	+	0.0802281i
$839$	26.4538			0.913286			0.456643	−	0.889650i	$-0.349052\pi$
$839$	26.4538			0.913286			0.456643	+	0.889650i	$0.349052\pi$
$840$		0			0
$841$	−31.3775			−1.08198
$842$	3.81701	−	2.20375i	0.131543	−	0.0759463i
$843$	23.3022	+	33.7705i	0.802570	+	1.16312i
$844$	−4.16373	+	7.21179i	−0.143321	+	0.248240i
$845$		0			0
$846$	2.88721	−	2.35581i	0.0992644	−	0.0809944i
$847$	0.752905	+	11.9802i	0.0258701	+	0.411644i
$848$			41.4797i			1.42442i
$849$	−8.70840	+	0.701625i	−0.298871	+	0.0240797i
$850$		0			0
$851$	−9.40081	−	5.42756i	−0.322256	−	0.186054i
$852$	−2.94630	+	0.237380i	−0.100939	+	0.00813250i
$853$		−	6.05997i		−	0.207490i	−0.994604	−	0.103745i	$-0.966917\pi$
$853$		−	6.05997i		−	0.207490i	0.994604	−	0.103745i	$-0.0330825\pi$
$854$	7.94034	−	5.27477i	0.271713	−	0.180499i
$855$		0			0
$856$	−9.82952	−	17.0252i	−0.335966	−	0.581910i
$857$	−5.16988	+	8.95449i	−0.176600	+	0.305880i	−0.940714	−	0.339202i	$-0.889843\pi$
$857$	−5.16988	+	8.95449i	−0.176600	+	0.305880i	0.764114	+	0.645081i	$0.223176\pi$
$858$	2.95869	+	4.28785i	0.101008	+	0.146385i
$859$	−30.7393	+	17.7473i	−1.04881	+	0.605531i	−0.922316	−	0.386436i	$-0.873706\pi$
$859$	−30.7393	+	17.7473i	−1.04881	+	0.605531i	−0.126495	+	0.991967i	$0.540373\pi$
$860$		0			0
$861$	10.4889	−	1.51191i	0.357460	−	0.0515259i
$862$	−12.5758			−0.428334
$863$	−13.1125	+	7.57049i	−0.446354	+	0.257702i	−0.706289	−	0.707924i	$-0.749632\pi$
$863$	−13.1125	+	7.57049i	−0.446354	+	0.257702i	0.259935	+	0.965626i	$0.416299\pi$
$864$	6.05014	−	20.8504i	0.205830	−	0.709344i
$865$		0			0
$866$	0.844064	+	1.46196i	0.0286824	+	0.0496795i
$867$	38.7240	+	18.3823i	1.31514	+	0.624295i
$868$	−33.6011	+	2.11169i	−1.14050	+	0.0716756i
$869$			21.0874i			0.715342i
$870$		0			0
$871$	−9.34821	−	5.39719i	−0.316752	−	0.182877i
$872$	−3.21835	−	1.85812i	−0.108987	−	0.0629238i
$873$	−34.6921	−	13.1696i	−1.17415	−	0.445722i
$874$			1.40974i			0.0476852i
$875$		0			0
$876$	−0.407605	+	0.858658i	−0.0137717	+	0.0290114i
$877$	9.79476	+	16.9650i	0.330745	+	0.572868i	0.982658	−	0.185426i	$-0.0593665\pi$
$877$	9.79476	+	16.9650i	0.330745	+	0.572868i	−0.651913	+	0.758294i	$0.726033\pi$
$878$	−2.85984	+	4.95339i	−0.0965150	+	0.167169i
$879$	8.97306	−	6.19156i	0.302654	−	0.208836i
$880$		0			0
$881$	−28.7481			−0.968548			−0.484274	−	0.874917i	$-0.660916\pi$
$881$	−28.7481			−0.968548			−0.484274	+	0.874917i	$0.660916\pi$
$882$	5.58567	−	5.86651i	0.188079	−	0.197536i
$883$	−5.77550			−0.194361			−0.0971805	−	0.995267i	$-0.530982\pi$
$883$	−5.77550			−0.194361			−0.0971805	+	0.995267i	$0.530982\pi$
$884$	−31.7721	+	18.3437i	−1.06861	+	0.616964i
$885$		0			0
$886$	3.06896	−	5.31559i	0.103104	−	0.178581i
$887$	−6.56917	−	11.3781i	−0.220571	−	0.382041i	0.734410	−	0.678706i	$-0.237459\pi$
$887$	−6.56917	−	11.3781i	−0.220571	−	0.382041i	−0.954982	+	0.296665i	$0.904125\pi$
$888$	−3.91937	+	8.25651i	−0.131525	+	0.277070i
$889$	−26.5329	−	13.1733i	−0.889884	−	0.441818i
$890$		0			0
$891$	7.23165	+	21.7073i	0.242269	+	0.727221i
$892$	−11.5536	−	6.67049i	−0.386844	−	0.223345i
$893$	−3.33514	−	1.92554i	−0.111606	−	0.0644358i
$894$	1.00320	+	12.4515i	0.0335522	+	0.416442i
$895$		0			0
$896$	−26.7986	+	1.68418i	−0.895278	+	0.0562646i
$897$	−14.6664	−	6.96215i	−0.489698	−	0.232460i
$898$	6.78657	+	11.7547i	0.226471	+	0.392259i
$899$	−26.7062	+	46.2565i	−0.890702	+	1.54274i
$900$		0			0
$901$	−74.1693	+	42.8217i	−2.47094	+	1.42660i
$902$	−2.26770			−0.0755061
$903$	−24.7708	+	3.57058i	−0.824321	+	0.118821i
$904$	10.6724			0.354959
$905$		0			0
$906$	2.25790	+	3.27225i	0.0750138	+	0.108713i
$907$	−3.08504	+	5.34345i	−0.102437	+	0.177426i	−0.912688	−	0.408657i	$-0.865997\pi$
$907$	−3.08504	+	5.34345i	−0.102437	+	0.177426i	0.810251	+	0.586083i	$0.199331\pi$
$908$	−1.72444	−	2.98681i	−0.0572274	−	0.0991208i
$909$	13.2313	+	16.2158i	0.438853	+	0.537845i
$910$		0			0
$911$		−	53.7961i		−	1.78234i	−0.453665	−	0.891172i	$-0.649884\pi$
$911$		−	53.7961i		−	1.78234i	0.453665	−	0.891172i	$-0.350116\pi$
$912$	−6.46130	+	0.520579i	−0.213955	+	0.0172381i
$913$	4.64924	+	2.68424i	0.153867	+	0.0888354i
$914$	4.69648	+	2.71151i	0.155346	+	0.0896888i
$915$		0			0
$916$		−	37.2211i		−	1.22982i
$917$	2.59934	+	41.3606i	0.0858379	+	1.36585i
$918$	12.5756	−	3.09327i	0.415058	−	0.102093i
$919$	0.310140	+	0.537179i	0.0102306	+	0.0177199i	0.871095	−	0.491114i	$-0.163410\pi$
$919$	0.310140	+	0.537179i	0.0102306	+	0.0177199i	−0.860865	+	0.508834i	$0.830077\pi$
$920$		0			0
$921$	15.7781	+	22.8662i	0.519905	+	0.753468i
$922$	4.51508	−	2.60678i	0.148696	−	0.0858498i
$923$	2.82752			0.0930688
$924$	16.9477	−	13.3377i	0.557540	−	0.438778i
$925$		0			0
$926$	−5.95888	+	3.44036i	−0.195821	+	0.113057i
$927$	1.81224	+	11.1735i	0.0595216	+	0.366986i
$928$	−16.2328	+	28.1161i	−0.532868	+	0.922955i
$929$	−26.4805	−	45.8655i	−0.868796	−	1.50480i	−0.863228	−	0.504814i	$-0.831561\pi$
$929$	−26.4805	−	45.8655i	−0.868796	−	1.50480i	−0.00556817	−	0.999984i	$-0.501772\pi$
$930$		0			0
$931$	−7.71688	−	3.24512i	−0.252911	−	0.106355i
$932$		−	2.89770i		−	0.0949174i
$933$	2.51385	+	31.2013i	0.0822998	+	1.02149i
$934$	3.06975	+	1.77232i	0.100445	+	0.0579921i
$935$		0			0
$936$	−4.85121	+	12.7794i	−0.158567	+	0.417707i
$937$			0.667265i			0.0217986i	0.999941	+	0.0108993i	$0.00346942\pi$
$937$			0.667265i			0.0217986i	−0.999941	+	0.0108993i	$0.996531\pi$
$938$	1.59719	−	3.21696i	0.0521500	−	0.105037i
$939$	−13.8318	+	29.1380i	−0.451385	+	0.950884i
$940$		0			0
$941$	−12.4842	+	21.6232i	−0.406972	+	0.704896i	−0.994549	−	0.104272i	$-0.966749\pi$
$941$	−12.4842	+	21.6232i	−0.406972	+	0.704896i	0.587577	+	0.809168i	$0.300082\pi$
$942$	3.52639	−	2.43327i	0.114896	−	0.0792801i
$943$	6.12023	−	3.53352i	0.199302	−	0.115067i
$944$	12.4016			0.403638
$945$		0			0
$946$	5.35547			0.174121
$947$	47.6286	−	27.4984i	1.54772	−	0.893577i	0.549405	−	0.835556i	$-0.314854\pi$
$947$	47.6286	−	27.4984i	1.54772	−	0.893577i	0.998315	−	0.0580209i	$-0.0184790\pi$
$948$	−21.8908	+	15.1050i	−0.710981	+	0.490589i
$949$	0.454613	−	0.787412i	0.0147574	−	0.0255605i
$950$		0			0
$951$	−1.95830	+	4.12534i	−0.0635022	+	0.133773i
$952$	−14.0520	−	21.1531i	−0.455428	−	0.685577i
$953$		−	35.8657i		−	1.16180i	−0.813974	−	0.580902i	$-0.802700\pi$
$953$		−	35.8657i		−	1.16180i	0.813974	−	0.580902i	$-0.197300\pi$
$954$	−5.44361	+	14.3399i	−0.176243	+	0.464271i
$955$		0			0
$956$	9.12588	+	5.26883i	0.295152	+	0.170406i
$957$	−2.74774	−	34.1043i	−0.0888219	−	1.10244i
$958$			7.28288i			0.235299i
$959$	−8.53270	−	12.8447i	−0.275535	−	0.414775i
$960$		0			0
$961$	8.12541	+	14.0736i	0.262110	+	0.453988i
$962$	2.10124	−	3.63946i	0.0677468	−	0.117341i
$963$	6.35607	+	39.1889i	0.204821	+	1.26285i
$964$	−21.3753	+	12.3410i	−0.688451	+	0.397478i
$965$		0			0
$966$	2.00588	−	5.01567i	0.0645382	−	0.161376i
$967$	−11.8780			−0.381971			−0.190986	−	0.981593i	$-0.561168\pi$
$967$	−11.8780			−0.381971			−0.190986	+	0.981593i	$0.561168\pi$
$968$	5.83690	−	3.36994i	0.187605	−	0.108314i
$969$	−7.60118	−	11.0159i	−0.244185	−	0.353883i
$970$		0			0
$971$	2.61333	+	4.52642i	0.0838658	+	0.145260i	0.904907	−	0.425609i	$-0.139940\pi$
$971$	2.61333	+	4.52642i	0.0838658	+	0.145260i	−0.821042	+	0.570868i	$0.806607\pi$
$972$	−17.3542	+	23.0562i	−0.556637	+	0.739528i
$973$	14.1616	−	28.5235i	0.454001	−	0.914422i
$974$			2.01940i			0.0647056i
$975$		0			0
$976$	25.3148	+	14.6155i	0.810308	+	0.467831i
$977$	−15.5190	−	8.95992i	−0.496498	−	0.286653i	0.230768	−	0.973009i	$-0.425876\pi$
$977$	−15.5190	−	8.95992i	−0.496498	−	0.286653i	−0.727266	+	0.686355i	$0.759209\pi$
$978$	10.9505	−	0.882267i	0.350158	−	0.0282118i
$979$		−	47.8708i		−	1.52996i
$980$		0			0
$981$	4.74457	+	5.81481i	0.151482	+	0.185653i
$982$	3.76475	+	6.52074i	0.120138	+	0.208085i
$983$	20.9414	−	36.2715i	0.667926	−	1.15688i	−0.310556	−	0.950555i	$-0.600515\pi$
$983$	20.9414	−	36.2715i	0.667926	−	1.15688i	0.978483	−	0.206328i	$-0.0661513\pi$
$984$	−3.37929	−	4.89740i	−0.107728	−	0.156123i
$985$		0			0
$986$	−19.3661			−0.616742
$987$	9.12617	+	11.5963i	0.290489	+	0.369114i
$988$	6.79044			0.216033
$989$	−14.4537	+	8.34485i	−0.459601	+	0.265351i
$990$		0			0
$991$	−4.88415	+	8.45960i	−0.155150	+	0.268728i	−0.933114	−	0.359581i	$-0.882919\pi$
$991$	−4.88415	+	8.45960i	−0.155150	+	0.268728i	0.777964	+	0.628309i	$0.216253\pi$
$992$	14.3602	+	24.8726i	0.455937	+	0.789706i
$993$	−47.4744	−	22.5361i	−1.50656	−	0.715162i
$994$	0.0590093	+	0.938951i	0.00187166	+	0.0297817i
$995$		0			0
$996$	0.543767	+	6.74911i	0.0172299	+	0.213854i
$997$	30.4616	+	17.5870i	0.964728	+	0.556986i	0.897625	−	0.440760i	$-0.145291\pi$
$997$	30.4616	+	17.5870i	0.964728	+	0.556986i	0.0671032	+	0.997746i	$0.478624\pi$
$998$	12.2380	+	7.06563i	0.387388	+	0.223659i
$999$	13.3174	−	12.7794i	0.421344	−	0.404322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.g.101.2		8
3.2	odd	2		525.2.t.f.101.3		8
5.2	odd	4		525.2.q.f.374.5		16
5.3	odd	4		525.2.q.f.374.4		16
5.4	even	2		105.2.s.c.101.3	yes	8
7.5	odd	6		525.2.t.f.26.3		8
15.2	even	4		525.2.q.e.374.4		16
15.8	even	4		525.2.q.e.374.5		16
15.14	odd	2		105.2.s.d.101.2	yes	8
21.5	even	6	inner	525.2.t.g.26.2		8
35.4	even	6		735.2.b.d.146.4		8
35.9	even	6		735.2.s.l.656.2		8
35.12	even	12		525.2.q.e.299.5		16
35.19	odd	6		105.2.s.d.26.2	yes	8
35.24	odd	6		735.2.b.c.146.4		8
35.33	even	12		525.2.q.e.299.4		16
35.34	odd	2		735.2.s.k.521.3		8
105.44	odd	6		735.2.s.k.656.3		8
105.47	odd	12		525.2.q.f.299.4		16
105.59	even	6		735.2.b.d.146.5		8
105.68	odd	12		525.2.q.f.299.5		16
105.74	odd	6		735.2.b.c.146.5		8
105.89	even	6		105.2.s.c.26.3	✓	8
105.104	even	2		735.2.s.l.521.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.3	✓	8	105.89	even	6
105.2.s.c.101.3	yes	8	5.4	even	2
105.2.s.d.26.2	yes	8	35.19	odd	6
105.2.s.d.101.2	yes	8	15.14	odd	2
525.2.q.e.299.4		16	35.33	even	12
525.2.q.e.299.5		16	35.12	even	12
525.2.q.e.374.4		16	15.2	even	4
525.2.q.e.374.5		16	15.8	even	4
525.2.q.f.299.4		16	105.47	odd	12
525.2.q.f.299.5		16	105.68	odd	12
525.2.q.f.374.4		16	5.3	odd	4
525.2.q.f.374.5		16	5.2	odd	4
525.2.t.f.26.3		8	7.5	odd	6
525.2.t.f.101.3		8	3.2	odd	2
525.2.t.g.26.2		8	21.5	even	6	inner
525.2.t.g.101.2		8	1.1	even	1	trivial
735.2.b.c.146.4		8	35.24	odd	6
735.2.b.c.146.5		8	105.74	odd	6
735.2.b.d.146.4		8	35.4	even	6
735.2.b.d.146.5		8	105.59	even	6
735.2.s.k.521.3		8	35.34	odd	2
735.2.s.k.656.3		8	105.44	odd	6
735.2.s.l.521.2		8	105.104	even	2
735.2.s.l.656.2		8	35.9	even	6

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.334053 - 0.192865i) q^{2} +(-1.42561 + 0.983691i) q^{3} +(-0.925606 + 1.60320i) q^{4} +(-0.286507 + 0.603555i) q^{6} +(-2.36975 - 1.17656i) q^{7} +1.48553i q^{8} +(1.06470 - 2.80471i) q^{9} +O(q^{10})\)	\(q+(0.334053 - 0.192865i) q^{2} +(-1.42561 + 0.983691i) q^{3} +(-0.925606 + 1.60320i) q^{4} +(-0.286507 + 0.603555i) q^{6} +(-2.36975 - 1.17656i) q^{7} +1.48553i q^{8} +(1.06470 - 2.80471i) q^{9} +(-2.20164 - 1.27112i) q^{11} +(-0.257501 - 3.19604i) q^{12} +3.06718i q^{13} +(-1.01854 + 0.0640110i) q^{14} +(-1.56470 - 2.71015i) q^{16} +(3.23065 - 5.59565i) q^{17} +(-0.185264 - 1.14227i) q^{18} +(-1.03570 + 0.597960i) q^{19} +(4.53570 - 0.653796i) q^{21} -0.980620 q^{22} +(2.64657 - 1.52800i) q^{23} +(-1.46130 - 2.11778i) q^{24} +(0.591553 + 1.02460i) q^{26} +(1.24112 + 5.04575i) q^{27} +(4.07971 - 2.71015i) q^{28} -7.77029i q^{29} +(-5.95299 - 3.43696i) q^{31} +(-3.61840 - 2.08909i) q^{32} +(4.38907 - 0.353622i) q^{33} -2.49232i q^{34} +(3.51101 + 4.30299i) q^{36} +(-1.77604 - 3.07619i) q^{37} +(-0.230652 + 0.399500i) q^{38} +(-3.01716 - 4.37259i) q^{39} +2.31252 q^{41} +(1.38907 - 1.09318i) q^{42} -5.46130 q^{43} +(4.07571 - 2.35311i) q^{44} +(0.589395 - 1.02086i) q^{46} +(1.61009 + 2.78876i) q^{47} +(4.89660 + 2.32442i) q^{48} +(4.23143 + 5.57629i) q^{49} +(0.898757 + 11.1552i) q^{51} +(-4.91730 - 2.83900i) q^{52} +(-11.4790 - 6.62740i) q^{53} +(1.38775 + 1.44618i) q^{54} +(1.74781 - 3.52034i) q^{56} +(0.888288 - 1.87126i) q^{57} +(-1.49862 - 2.59569i) q^{58} +(-1.98146 + 3.43199i) q^{59} +(-8.08933 + 4.67038i) q^{61} -2.65148 q^{62} +(-5.82298 + 5.39378i) q^{63} +4.64717 q^{64} +(1.39798 - 0.964627i) q^{66} +(-1.75966 + 3.04782i) q^{67} +(5.98062 + 10.3587i) q^{68} +(-2.26989 + 4.78173i) q^{69} -0.921861i q^{71} +(4.16649 + 1.58165i) q^{72} +(-0.256722 - 0.148218i) q^{73} +(-1.18658 - 0.685073i) q^{74} -2.21390i q^{76} +(3.72180 + 5.60260i) q^{77} +(-1.85121 - 0.878771i) q^{78} +(-4.14741 - 7.18352i) q^{79} +(-6.73281 - 5.97238i) q^{81} +(0.772502 - 0.446004i) q^{82} -2.11171 q^{83} +(-3.15010 + 7.87677i) q^{84} +(-1.82436 + 1.05330i) q^{86} +(7.64357 + 11.0774i) q^{87} +(1.88829 - 3.27061i) q^{88} +(9.41507 + 16.3074i) q^{89} +(3.60871 - 7.26845i) q^{91} +5.65729i q^{92} +(11.8675 - 0.956152i) q^{93} +(1.07571 + 0.621062i) q^{94} +(7.21343 - 0.581177i) q^{96} -12.3692i q^{97} +(2.48899 + 1.04668i) q^{98} +(-5.90923 + 4.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9	\( 8 q + 3 q^{2} - q^{3} + 3 q^{4} + 5 q^{6} - 2 q^{7} - 5 q^{9} + 9 q^{12} - 12 q^{14} + q^{16} + 12 q^{17} + 19 q^{18} + 9 q^{19} + 19 q^{21} + 40 q^{22} - 27 q^{23} + 16 q^{24} - 6 q^{26} - 4 q^{27} - 3 q^{28} - 21 q^{31} - 21 q^{32} - 2 q^{33} + 9 q^{36} - 7 q^{37} + 12 q^{38} - 3 q^{39} - 30 q^{41} - 26 q^{42} - 16 q^{43} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} - 6 q^{51} - 30 q^{52} - 24 q^{53} + 17 q^{54} - 21 q^{56} - 6 q^{57} + 13 q^{58} - 12 q^{59} + 15 q^{61} - 24 q^{62} + 2 q^{63} + 38 q^{64} + 22 q^{66} - 4 q^{67} - 13 q^{69} + 14 q^{72} - 15 q^{73} + 54 q^{74} + 36 q^{77} + 6 q^{78} - 29 q^{79} - 41 q^{81} - 27 q^{82} - 30 q^{83} - 3 q^{84} + 9 q^{86} - 32 q^{87} + 2 q^{88} - 3 q^{89} - 3 q^{91} + 9 q^{93} - 24 q^{94} - 3 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 - q^3 + 3 * q^4 + 5 * q^6 - 2 * q^7 - 5 * q^9 + 9 * q^12 - 12 * q^14 + q^16 + 12 * q^17 + 19 * q^18 + 9 * q^19 + 19 * q^21 + 40 * q^22 - 27 * q^23 + 16 * q^24 - 6 * q^26 - 4 * q^27 - 3 * q^28 - 21 * q^31 - 21 * q^32 - 2 * q^33 + 9 * q^36 - 7 * q^37 + 12 * q^38 - 3 * q^39 - 30 * q^41 - 26 * q^42 - 16 * q^43 - 7 * q^46 + 6 * q^47 + 25 * q^48 - 4 * q^49 - 6 * q^51 - 30 * q^52 - 24 * q^53 + 17 * q^54 - 21 * q^56 - 6 * q^57 + 13 * q^58 - 12 * q^59 + 15 * q^61 - 24 * q^62 + 2 * q^63 + 38 * q^64 + 22 * q^66 - 4 * q^67 - 13 * q^69 + 14 * q^72 - 15 * q^73 + 54 * q^74 + 36 * q^77 + 6 * q^78 - 29 * q^79 - 41 * q^81 - 27 * q^82 - 30 * q^83 - 3 * q^84 + 9 * q^86 - 32 * q^87 + 2 * q^88 - 3 * q^89 - 3 * q^91 + 9 * q^93 - 24 * q^94 - 3 * q^96 + 39 * q^98 - 34 * q^99

Introduction

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