LMFDB - Embedded newform 560.2.bd.a.141.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.20
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.a.421.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32415 + 0.496608i) q^{2} +(-0.576404 - 0.576404i) q^{3} +(1.50676 + 1.31517i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.477000 - 1.04949i) q^{6} -1.00000i q^{7} +(1.34206 + 2.48976i) q^{8} -2.33552i q^{9} +O(q^{10})$	\(q+(1.32415 + 0.496608i) q^{2} +(-0.576404 - 0.576404i) q^{3} +(1.50676 + 1.31517i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.477000 - 1.04949i) q^{6} -1.00000i q^{7} +(1.34206 + 2.48976i) q^{8} -2.33552i q^{9} +(1.28747 - 0.585162i) q^{10} +(2.93187 - 2.93187i) q^{11} +(-0.110433 - 1.62657i) q^{12} +(-1.89090 - 1.89090i) q^{13} +(0.496608 - 1.32415i) q^{14} -0.815159 q^{15} +(0.540654 + 3.96329i) q^{16} +1.43655 q^{17} +(1.15984 - 3.09258i) q^{18} +(1.45281 + 1.45281i) q^{19} +(1.99541 - 0.135475i) q^{20} +(-0.576404 + 0.576404i) q^{21} +(5.33823 - 2.42625i) q^{22} +8.06848i q^{23} +(0.661539 - 2.20867i) q^{24} -1.00000i q^{25} +(-1.56480 - 3.44287i) q^{26} +(-3.07541 + 3.07541i) q^{27} +(1.31517 - 1.50676i) q^{28} +(2.86338 + 2.86338i) q^{29} +(-1.07939 - 0.404815i) q^{30} -1.31281 q^{31} +(-1.25230 + 5.51650i) q^{32} -3.37988 q^{33} +(1.90221 + 0.713403i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(3.07160 - 3.51906i) q^{36} +(6.64315 - 6.64315i) q^{37} +(1.20227 + 2.64522i) q^{38} +2.17984i q^{39} +(2.70950 + 0.811546i) q^{40} -8.42537i q^{41} +(-1.04949 + 0.477000i) q^{42} +(-1.52206 + 1.52206i) q^{43} +(8.27352 - 0.561717i) q^{44} +(-1.65146 - 1.65146i) q^{45} +(-4.00687 + 10.6839i) q^{46} -7.14252 q^{47} +(1.97282 - 2.59609i) q^{48} -1.00000 q^{49} +(0.496608 - 1.32415i) q^{50} +(-0.828034 - 0.828034i) q^{51} +(-0.362278 - 5.33598i) q^{52} +(-4.13783 + 4.13783i) q^{53} +(-5.59959 + 2.54504i) q^{54} -4.14628i q^{55} +(2.48976 - 1.34206i) q^{56} -1.67481i q^{57} +(2.36958 + 5.21354i) q^{58} +(-5.34634 + 5.34634i) q^{59} +(-1.22825 - 1.07207i) q^{60} +(-3.30135 - 3.30135i) q^{61} +(-1.73836 - 0.651950i) q^{62} -2.33552 q^{63} +(-4.39777 + 6.68279i) q^{64} -2.67413 q^{65} +(-4.47548 - 1.67848i) q^{66} +(5.94425 + 5.94425i) q^{67} +(2.16454 + 1.88931i) q^{68} +(4.65071 - 4.65071i) q^{69} +(-0.585162 - 1.28747i) q^{70} +4.72606i q^{71} +(5.81487 - 3.13439i) q^{72} +14.9033i q^{73} +(12.0956 - 5.49750i) q^{74} +(-0.576404 + 0.576404i) q^{75} +(0.278344 + 4.09973i) q^{76} +(-2.93187 - 2.93187i) q^{77} +(-1.08253 + 2.88645i) q^{78} -10.3784 q^{79} +(3.18477 + 2.42017i) q^{80} -3.46118 q^{81} +(4.18411 - 11.1565i) q^{82} +(-0.898977 - 0.898977i) q^{83} +(-1.62657 + 0.110433i) q^{84} +(1.01580 - 1.01580i) q^{85} +(-2.77131 + 1.25957i) q^{86} -3.30093i q^{87} +(11.2344 + 3.36490i) q^{88} -11.5205i q^{89} +(-1.36666 - 3.00691i) q^{90} +(-1.89090 + 1.89090i) q^{91} +(-10.6114 + 12.1573i) q^{92} +(0.756707 + 0.756707i) q^{93} +(-9.45778 - 3.54703i) q^{94} +2.05459 q^{95} +(3.90156 - 2.45791i) q^{96} -13.1190 q^{97} +(-1.32415 - 0.496608i) q^{98} +(-6.84742 - 6.84742i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) $ 44 * q + 12 * q^4 + 12 * q^6	$ 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) $ 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.32415	+	0.496608i	0.936317	+	0.351155i
$2$	1.32415	+	0.496608i	0.936317	+	0.351155i
$3$	−0.576404	−	0.576404i	−0.332787	−	0.332787i	0.520857	−	0.853644i	$-0.325613\pi$
$3$	−0.576404	−	0.576404i	−0.332787	−	0.332787i	−0.853644	+	0.520857i	$0.825613\pi$
$4$	1.50676	+	1.31517i	0.753380	+	0.657585i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−0.477000	−	1.04949i	−0.194734	−	0.428454i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.34206	+	2.48976i	0.474489	+	0.880262i
$9$		−	2.33552i		−	0.778505i
$10$	1.28747	−	0.585162i	0.407135	−	0.185045i
$11$	2.93187	−	2.93187i	0.883991	−	0.883991i	−0.109947	−	0.993937i	$-0.535068\pi$
$11$	2.93187	−	2.93187i	0.883991	−	0.883991i	0.993937	+	0.109947i	$0.0350681\pi$
$12$	−0.110433	−	1.62657i	−0.0318794	−	0.469551i
$13$	−1.89090	−	1.89090i	−0.524441	−	0.524441i	0.394469	−	0.918909i	$-0.370929\pi$
$13$	−1.89090	−	1.89090i	−0.524441	−	0.524441i	−0.918909	+	0.394469i	$0.870929\pi$
$14$	0.496608	−	1.32415i	0.132724	−	0.353895i
$15$	−0.815159			−0.210473
$16$	0.540654	+	3.96329i	0.135164	+	0.990823i
$17$	1.43655			0.348415			0.174207	−	0.984709i	$-0.444264\pi$
$17$	1.43655			0.348415			0.174207	+	0.984709i	$0.444264\pi$
$18$	1.15984	−	3.09258i	0.273376	−	0.728928i
$19$	1.45281	+	1.45281i	0.333298	+	0.333298i	0.853837	−	0.520540i	$-0.174269\pi$
$19$	1.45281	+	1.45281i	0.333298	+	0.333298i	−0.520540	+	0.853837i	$0.674269\pi$
$20$	1.99541	−	0.135475i	0.446186	−	0.0302931i
$21$	−0.576404	+	0.576404i	−0.125782	+	0.125782i
$22$	5.33823	−	2.42625i	1.13811	−	0.517278i
$23$			8.06848i			1.68239i	0.540729	+	0.841197i	$0.318149\pi$
$23$			8.06848i			1.68239i	−0.540729	+	0.841197i	$0.681851\pi$
$24$	0.661539	−	2.20867i	0.135036	−	0.450844i
$25$		−	1.00000i		−	0.200000i
$26$	−1.56480	−	3.44287i	−0.306883	−	0.675203i
$27$	−3.07541	+	3.07541i	−0.591864	+	0.591864i
$28$	1.31517	−	1.50676i	0.248544	−	0.284751i
$29$	2.86338	+	2.86338i	0.531717	+	0.531717i	0.921083	−	0.389366i	$-0.127306\pi$
$29$	2.86338	+	2.86338i	0.531717	+	0.531717i	−0.389366	+	0.921083i	$0.627306\pi$
$30$	−1.07939	−	0.404815i	−0.197070	−	0.0739087i
$31$	−1.31281			−0.235787			−0.117893	−	0.993026i	$-0.537614\pi$
$31$	−1.31281			−0.235787			−0.117893	+	0.993026i	$0.537614\pi$
$32$	−1.25230	+	5.51650i	−0.221377	+	0.975188i
$33$	−3.37988			−0.588361
$34$	1.90221	+	0.713403i	0.326227	+	0.122348i
$35$	−0.707107	−	0.707107i	−0.119523	−	0.119523i
$36$	3.07160	−	3.51906i	0.511934	−	0.586511i
$37$	6.64315	−	6.64315i	1.09213	−	1.09213i	0.0968262	−	0.995301i	$-0.469131\pi$
$37$	6.64315	−	6.64315i	1.09213	−	1.09213i	0.995301	−	0.0968262i	$-0.0308691\pi$
$38$	1.20227	+	2.64522i	0.195033	+	0.429112i
$39$			2.17984i			0.349054i
$40$	2.70950	+	0.811546i	0.428410	+	0.128317i
$41$		−	8.42537i		−	1.31582i	−0.753096	−	0.657911i	$-0.771440\pi$
$41$		−	8.42537i		−	1.31582i	0.753096	−	0.657911i	$-0.228560\pi$
$42$	−1.04949	+	0.477000i	−0.161941	+	0.0736027i
$43$	−1.52206	+	1.52206i	−0.232112	+	0.232112i	−0.813574	−	0.581462i	$-0.802481\pi$
$43$	−1.52206	+	1.52206i	−0.232112	+	0.232112i	0.581462	+	0.813574i	$0.302481\pi$
$44$	8.27352	−	0.561717i	1.24728	−	0.0846820i
$45$	−1.65146	−	1.65146i	−0.246185	−	0.246185i
$46$	−4.00687	+	10.6839i	−0.590781	+	1.57525i
$47$	−7.14252			−1.04184			−0.520922	−	0.853604i	$-0.674412\pi$
$47$	−7.14252			−1.04184			−0.520922	+	0.853604i	$0.674412\pi$
$48$	1.97282	−	2.59609i	0.284753	−	0.374714i
$49$	−1.00000			−0.142857
$50$	0.496608	−	1.32415i	0.0702310	−	0.187263i
$51$	−0.828034	−	0.828034i	−0.115948	−	0.115948i
$52$	−0.362278	−	5.33598i	−0.0502389	−	0.739968i
$53$	−4.13783	+	4.13783i	−0.568375	+	0.568375i	−0.931673	−	0.363298i	$-0.881651\pi$
$53$	−4.13783	+	4.13783i	−0.568375	+	0.568375i	0.363298	+	0.931673i	$0.381651\pi$
$54$	−5.59959	+	2.54504i	−0.762008	+	0.346336i
$55$		−	4.14628i		−	0.559085i
$56$	2.48976	−	1.34206i	0.332708	−	0.179340i
$57$		−	1.67481i		−	0.221834i
$58$	2.36958	+	5.21354i	0.311141	+	0.684571i
$59$	−5.34634	+	5.34634i	−0.696034	+	0.696034i	−0.963553	−	0.267518i	$-0.913796\pi$
$59$	−5.34634	+	5.34634i	−0.696034	+	0.696034i	0.267518	+	0.963553i	$0.413796\pi$
$60$	−1.22825	−	1.07207i	−0.158566	−	0.138404i
$61$	−3.30135	−	3.30135i	−0.422695	−	0.422695i	0.463436	−	0.886131i	$-0.346617\pi$
$61$	−3.30135	−	3.30135i	−0.422695	−	0.422695i	−0.886131	+	0.463436i	$0.846617\pi$
$62$	−1.73836	−	0.651950i	−0.220771	−	0.0827978i
$63$	−2.33552			−0.294247
$64$	−4.39777	+	6.68279i	−0.549721	+	0.835348i
$65$	−2.67413			−0.331686
$66$	−4.47548	−	1.67848i	−0.550893	−	0.206606i
$67$	5.94425	+	5.94425i	0.726206	+	0.726206i	0.969862	−	0.243656i	$-0.0783467\pi$
$67$	5.94425	+	5.94425i	0.726206	+	0.726206i	−0.243656	+	0.969862i	$0.578347\pi$
$68$	2.16454	+	1.88931i	0.262489	+	0.229112i
$69$	4.65071	−	4.65071i	0.559879	−	0.559879i
$70$	−0.585162	−	1.28747i	−0.0699403	−	0.153882i
$71$			4.72606i			0.560881i	0.959871	+	0.280440i	$0.0904805\pi$
$71$			4.72606i			0.560881i	−0.959871	+	0.280440i	$0.909520\pi$
$72$	5.81487	−	3.13439i	0.685288	−	0.369392i
$73$			14.9033i			1.74430i	0.489237	+	0.872151i	$0.337275\pi$
$73$			14.9033i			1.74430i	−0.489237	+	0.872151i	$0.662725\pi$
$74$	12.0956	−	5.49750i	1.40608	−	0.639072i
$75$	−0.576404	+	0.576404i	−0.0665574	+	0.0665574i
$76$	0.278344	+	4.09973i	0.0319283	+	0.470272i
$77$	−2.93187	−	2.93187i	−0.334117	−	0.334117i
$78$	−1.08253	+	2.88645i	−0.122572	+	0.326826i
$79$	−10.3784			−1.16766			−0.583832	−	0.811875i	$-0.698447\pi$
$79$	−10.3784			−1.16766			−0.583832	+	0.811875i	$0.698447\pi$
$80$	3.18477	+	2.42017i	0.356068	+	0.270583i
$81$	−3.46118			−0.384576
$82$	4.18411	−	11.1565i	0.462057	−	1.23203i
$83$	−0.898977	−	0.898977i	−0.0986755	−	0.0986755i	0.656046	−	0.754721i	$-0.272228\pi$
$83$	−0.898977	−	0.898977i	−0.0986755	−	0.0986755i	−0.754721	+	0.656046i	$0.772228\pi$
$84$	−1.62657	+	0.110433i	−0.177474	+	0.0120493i
$85$	1.01580	−	1.01580i	0.110178	−	0.110178i
$86$	−2.77131	+	1.25957i	−0.298838	+	0.135823i
$87$		−	3.30093i		−	0.353897i
$88$	11.2344	+	3.36490i	1.19759	+	0.358700i
$89$		−	11.5205i		−	1.22117i	−0.791951	−	0.610585i	$-0.790934\pi$
$89$		−	11.5205i		−	1.22117i	0.791951	−	0.610585i	$-0.209066\pi$
$90$	−1.36666	−	3.00691i	−0.144058	−	0.316956i
$91$	−1.89090	+	1.89090i	−0.198220	+	0.198220i
$92$	−10.6114	+	12.1573i	−1.10632	+	1.26748i
$93$	0.756707	+	0.756707i	0.0784669	+	0.0784669i
$94$	−9.45778	−	3.54703i	−0.975496	−	0.365849i
$95$	2.05459			0.210796
$96$	3.90156	−	2.45791i	0.398201	−	0.250859i
$97$	−13.1190			−1.33203			−0.666016	−	0.745937i	$-0.732002\pi$
$97$	−13.1190			−1.33203			−0.666016	+	0.745937i	$0.732002\pi$
$98$	−1.32415	−	0.496608i	−0.133760	−	0.0501650i
$99$	−6.84742	−	6.84742i	−0.688191	−	0.688191i
$100$	1.31517	−	1.50676i	0.131517	−	0.150676i
$101$	0.844747	−	0.844747i	0.0840554	−	0.0840554i	−0.663829	−	0.747884i	$-0.731070\pi$
$101$	0.844747	−	0.844747i	0.0840554	−	0.0840554i	0.747884	+	0.663829i	$0.231070\pi$
$102$	−0.685235	−	1.50765i	−0.0678484	−	0.149280i
$103$			15.3945i			1.51687i	0.651751	+	0.758433i	$0.274035\pi$
$103$			15.3945i			1.51687i	−0.651751	+	0.758433i	$0.725965\pi$
$104$	2.17018	−	7.24557i	0.212804	−	0.710486i
$105$			0.815159i			0.0795514i
$106$	−7.53400	+	3.42424i	−0.731767	+	0.332591i
$107$	9.46571	−	9.46571i	0.915085	−	0.915085i	−0.0815817	−	0.996667i	$-0.525997\pi$
$107$	9.46571	−	9.46571i	0.915085	−	0.915085i	0.996667	+	0.0815817i	$0.0259971\pi$
$108$	−8.67861	+	0.589219i	−0.835099	+	0.0566976i
$109$	7.59547	+	7.59547i	0.727514	+	0.727514i	0.970124	−	0.242610i	$-0.0780035\pi$
$109$	7.59547	+	7.59547i	0.727514	+	0.727514i	−0.242610	+	0.970124i	$0.578004\pi$
$110$	2.05908	−	5.49031i	0.196325	−	0.523481i
$111$	−7.65828			−0.726892
$112$	3.96329	−	0.540654i	0.374496	−	0.0510870i
$113$	−8.31678			−0.782377			−0.391188	−	0.920311i	$-0.627936\pi$
$113$	−8.31678			−0.782377			−0.391188	+	0.920311i	$0.627936\pi$
$114$	0.831726	−	2.21771i	0.0778983	−	0.207707i
$115$	5.70528	+	5.70528i	0.532020	+	0.532020i
$116$	0.548596	+	8.08027i	0.0509359	+	0.750234i
$117$	−4.41622	+	4.41622i	−0.408280	+	0.408280i
$118$	−9.73441	+	4.42434i	−0.896125	+	0.407293i
$119$		−	1.43655i		−	0.131688i
$120$	−1.09399	−	2.02955i	−0.0998671	−	0.185271i
$121$		−	6.19167i		−	0.562879i
$122$	−2.73202	−	6.01098i	−0.247345	−	0.544208i
$123$	−4.85642	+	4.85642i	−0.437889	+	0.437889i
$124$	−1.97808	−	1.72656i	−0.177637	−	0.155050i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−3.09258	−	1.15984i	−0.275509	−	0.103326i
$127$	−9.91643			−0.879941			−0.439971	−	0.898012i	$-0.645011\pi$
$127$	−9.91643			−0.879941			−0.439971	+	0.898012i	$0.645011\pi$
$128$	−9.14204	+	6.66506i	−0.808050	+	0.589114i
$129$	1.75464			0.154488
$130$	−3.54096	−	1.32800i	−0.310563	−	0.116473i
$131$	3.31544	+	3.31544i	0.289671	+	0.289671i	0.836950	−	0.547279i	$-0.184336\pi$
$131$	3.31544	+	3.31544i	0.289671	+	0.289671i	−0.547279	+	0.836950i	$0.684336\pi$
$132$	−5.09267	−	4.44512i	−0.443260	−	0.386898i
$133$	1.45281	−	1.45281i	0.125975	−	0.125975i
$134$	4.91913	+	10.8231i	0.424948	+	0.934970i
$135$			4.34929i			0.374328i
$136$	1.92793	+	3.57666i	0.165319	+	0.306696i
$137$		−	4.71440i		−	0.402778i	−0.979511	−	0.201389i	$-0.935454\pi$
$137$		−	4.71440i		−	0.402778i	0.979511	−	0.201389i	$-0.0645456\pi$
$138$	8.46782	−	3.84867i	0.720829	−	0.327620i
$139$	13.9064	−	13.9064i	1.17952	−	1.17952i	0.199657	−	0.979866i	$-0.436017\pi$
$139$	13.9064	−	13.9064i	1.17952	−	1.17952i	0.979866	−	0.199657i	$-0.0639829\pi$
$140$	−0.135475	−	1.99541i	−0.0114497	−	0.168643i
$141$	4.11698	+	4.11698i	0.346712	+	0.346712i
$142$	−2.34700	+	6.25803i	−0.196956	+	0.525162i
$143$	−11.0877			−0.927202
$144$	9.25634	−	1.26271i	0.771361	−	0.105226i
$145$	4.04944			0.336287
$146$	−7.40111	+	19.7343i	−0.612520	+	1.63322i
$147$	0.576404	+	0.576404i	0.0475410	+	0.0475410i
$148$	18.7465	−	1.27276i	1.54095	−	0.104620i
$149$	1.93605	−	1.93605i	0.158607	−	0.158607i	−0.623342	−	0.781949i	$-0.714226\pi$
$149$	1.93605	−	1.93605i	0.158607	−	0.158607i	0.781949	+	0.623342i	$0.214226\pi$
$150$	−1.04949	+	0.477000i	−0.0856909	+	0.0389469i
$151$			19.9549i			1.62391i	0.583722	+	0.811953i	$0.301596\pi$
$151$			19.9549i			1.62391i	−0.583722	+	0.811953i	$0.698404\pi$
$152$	−1.66739	+	5.56690i	−0.135243	+	0.451535i
$153$		−	3.35509i		−	0.271243i
$154$	−2.42625	−	5.33823i	−0.195513	−	0.430166i
$155$	−0.928294	+	0.928294i	−0.0745624	+	0.0745624i
$156$	−2.86687	+	3.28450i	−0.229533	+	0.262971i
$157$	12.8265	+	12.8265i	1.02367	+	1.02367i	0.999713	+	0.0239570i	$0.00762649\pi$
$157$	12.8265	+	12.8265i	1.02367	+	1.02367i	0.0239570	+	0.999713i	$0.492374\pi$
$158$	−13.7426	−	5.15401i	−1.09330	−	0.410031i
$159$	4.77013			0.378296
$160$	3.01525	+	4.78626i	0.238376	+	0.378387i
$161$	8.06848			0.635885
$162$	−4.58314	−	1.71885i	−0.360085	−	0.135046i
$163$	−13.0681	−	13.0681i	−1.02357	−	1.02357i	−0.999715	−	0.0238561i	$-0.992406\pi$
$163$	−13.0681	−	13.0681i	−1.02357	−	1.02357i	−0.0238561	−	0.999715i	$-0.507594\pi$
$164$	11.0808	−	12.6950i	0.865265	−	0.991314i
$165$	−2.38994	+	2.38994i	−0.186056	+	0.186056i
$166$	−0.743943	−	1.63682i	−0.0577412	−	0.127042i
$167$		−	6.72568i		−	0.520449i	−0.965548	−	0.260225i	$-0.916203\pi$
$167$		−	6.72568i		−	0.520449i	0.965548	−	0.260225i	$-0.0837966\pi$
$168$	−2.20867	−	0.661539i	−0.170403	−	0.0510388i
$169$		−	5.84900i		−	0.449923i
$170$	1.84952	−	0.840616i	0.141852	−	0.0644723i
$171$	3.39306	−	3.39306i	0.259474	−	0.259474i
$172$	−4.29515	+	0.291612i	−0.327502	+	0.0222352i
$173$	1.72006	+	1.72006i	0.130774	+	0.130774i	0.769464	−	0.638690i	$-0.220523\pi$
$173$	1.72006	+	1.72006i	0.130774	+	0.130774i	−0.638690	+	0.769464i	$0.720523\pi$
$174$	1.63927	−	4.37094i	0.124273	−	0.331360i
$175$	−1.00000			−0.0755929
$176$	13.2050	+	10.0347i	0.995362	+	0.756395i
$177$	6.16331			0.463263
$178$	5.72117	−	15.2549i	0.428820	−	1.14340i
$179$	−5.77336	−	5.77336i	−0.431521	−	0.431521i	0.457624	−	0.889146i	$-0.348700\pi$
$179$	−5.77336	−	5.77336i	−0.431521	−	0.431521i	−0.889146	+	0.457624i	$0.848700\pi$
$180$	−0.316403	−	4.66030i	−0.0235833	−	0.347359i
$181$	16.3185	−	16.3185i	1.21294	−	1.21294i	0.242890	−	0.970054i	$-0.421905\pi$
$181$	16.3185	−	16.3185i	1.21294	−	1.21294i	0.970054	−	0.242890i	$-0.0780953\pi$
$182$	−3.44287	+	1.56480i	−0.255203	+	0.115991i
$183$			3.80583i			0.281335i
$184$	−20.0885	+	10.8284i	−1.48095	+	0.798277i
$185$		−	9.39484i		−	0.690722i
$186$	0.626209	+	1.37778i	0.0459158	+	0.101024i
$187$	4.21177	−	4.21177i	0.307995	−	0.307995i
$188$	−10.7621	−	9.39363i	−0.784904	−	0.685101i
$189$	3.07541	+	3.07541i	0.223703	+	0.223703i
$190$	2.72058	+	1.02032i	0.197372	+	0.0740221i
$191$	9.11341			0.659423			0.329712	−	0.944082i	$-0.393049\pi$
$191$	9.11341			0.659423			0.329712	+	0.944082i	$0.393049\pi$
$192$	6.38688	−	1.31709i	0.460933	−	0.0950530i
$193$	−4.16518			−0.299816			−0.149908	−	0.988700i	$-0.547898\pi$
$193$	−4.16518			−0.299816			−0.149908	+	0.988700i	$0.547898\pi$
$194$	−17.3716	−	6.51500i	−1.24721	−	0.467750i
$195$	1.54138	+	1.54138i	0.110381	+	0.110381i
$196$	−1.50676	−	1.31517i	−0.107626	−	0.0939407i
$197$	−1.10761	+	1.10761i	−0.0789137	+	0.0789137i	−0.745462	−	0.666548i	$-0.767771\pi$
$197$	−1.10761	+	1.10761i	−0.0789137	+	0.0789137i	0.666548	+	0.745462i	$0.267771\pi$
$198$	−5.66654	−	12.4675i	−0.402704	−	0.886027i
$199$			6.87016i			0.487012i	0.969899	+	0.243506i	$0.0782976\pi$
$199$			6.87016i			0.487012i	−0.969899	+	0.243506i	$0.921702\pi$
$200$	2.48976	−	1.34206i	0.176052	−	0.0948977i
$201$		−	6.85259i		−	0.483344i
$202$	1.53808	−	0.699065i	0.108219	−	0.0491861i
$203$	2.86338	−	2.86338i	0.200970	−	0.200970i
$204$	−0.158643	−	2.33666i	−0.0111072	−	0.163599i
$205$	−5.95764	−	5.95764i	−0.416099	−	0.416099i
$206$	−7.64504	+	20.3847i	−0.532655	+	1.42027i
$207$	18.8441			1.30975
$208$	6.47186	−	8.51651i	0.448743	−	0.590514i
$209$	8.51889			0.589264
$210$	−0.404815	+	1.07939i	−0.0279349	+	0.0744853i
$211$	12.8720	+	12.8720i	0.886147	+	0.886147i	0.994151	−	0.108004i	$-0.0344458\pi$
$211$	12.8720	+	12.8720i	0.886147	+	0.886147i	−0.108004	+	0.994151i	$0.534446\pi$
$212$	−11.6767	+	0.792768i	−0.801957	+	0.0544475i
$213$	2.72412	−	2.72412i	0.186654	−	0.186654i
$214$	17.2348	−	7.83330i	1.17815	−	0.535473i
$215$			2.15252i			0.146801i
$216$	−11.7844	−	3.52965i	−0.801828	−	0.240162i
$217$			1.31281i			0.0891191i
$218$	6.28559	+	13.8295i	0.425714	+	0.936654i
$219$	8.59034	−	8.59034i	0.580481	−	0.580481i
$220$	5.45307	−	6.24746i	0.367646	−	0.421203i
$221$	−2.71637	−	2.71637i	−0.182723	−	0.182723i
$222$	−10.1407	−	3.80317i	−0.680602	−	0.255252i
$223$	−19.4690			−1.30374			−0.651869	−	0.758331i	$-0.726015\pi$
$223$	−19.4690			−1.30374			−0.651869	+	0.758331i	$0.726015\pi$
$224$	5.51650	+	1.25230i	0.368587	+	0.0836725i
$225$	−2.33552			−0.155701
$226$	−11.0127	−	4.13018i	−0.732553	−	0.274736i
$227$	11.3381	+	11.3381i	0.752534	+	0.752534i	0.974952	−	0.222417i	$-0.0713948\pi$
$227$	11.3381	+	11.3381i	0.752534	+	0.752534i	−0.222417	+	0.974952i	$0.571395\pi$
$228$	2.20266	−	2.52354i	0.145875	−	0.167126i
$229$	−7.89978	+	7.89978i	−0.522032	+	0.522032i	−0.918185	−	0.396153i	$-0.870345\pi$
$229$	−7.89978	+	7.89978i	−0.522032	+	0.522032i	0.396153	+	0.918185i	$0.370345\pi$
$230$	4.72137	+	10.3879i	0.311318	+	0.684961i
$231$			3.37988i			0.222380i
$232$	−3.28630	+	10.9719i	−0.215756	+	0.720344i
$233$		−	13.8329i		−	0.906220i	−0.891454	−	0.453110i	$-0.850314\pi$
$233$		−	13.8329i		−	0.906220i	0.891454	−	0.453110i	$-0.149686\pi$
$234$	−8.04089	+	3.65462i	−0.525649	+	0.238910i
$235$	−5.05052	+	5.05052i	−0.329460	+	0.329460i
$236$	−15.0870	+	1.02431i	−0.982081	+	0.0666767i
$237$	5.98217	+	5.98217i	0.388583	+	0.388583i
$238$	0.713403	−	1.90221i	0.0462431	−	0.123302i
$239$	5.85778			0.378908			0.189454	−	0.981890i	$-0.439328\pi$
$239$	5.85778			0.378908			0.189454	+	0.981890i	$0.439328\pi$
$240$	−0.440719	−	3.23071i	−0.0284483	−	0.208542i
$241$	1.98422			0.127815			0.0639075	−	0.997956i	$-0.479644\pi$
$241$	1.98422			0.127815			0.0639075	+	0.997956i	$0.479644\pi$
$242$	3.07483	−	8.19871i	0.197658	−	0.527033i
$243$	11.2213	+	11.2213i	0.719846	+	0.719846i
$244$	−0.632507	−	9.31619i	−0.0404921	−	0.596408i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	−8.84238	+	4.01890i	−0.563769	+	0.256236i
$247$		−	5.49424i		−	0.349590i
$248$	−1.76186	−	3.26857i	−0.111878	−	0.207554i
$249$			1.03635i			0.0656759i
$250$	−0.585162	−	1.28747i	−0.0370089	−	0.0814269i
$251$	15.4038	−	15.4038i	0.972279	−	0.972279i	−0.0273470	−	0.999626i	$-0.508706\pi$
$251$	15.4038	−	15.4038i	0.972279	−	0.972279i	0.999626	+	0.0273470i	$0.00870591\pi$
$252$	−3.51906	−	3.07160i	−0.221680	−	0.193493i
$253$	23.6557	+	23.6557i	1.48722	+	1.48722i
$254$	−13.1309	−	4.92458i	−0.823904	−	0.308996i
$255$	−1.17102			−0.0733320
$256$	−15.4154	+	4.28554i	−0.963462	+	0.267846i
$257$	23.0075			1.43517			0.717583	−	0.696473i	$-0.245248\pi$
$257$	23.0075			1.43517			0.717583	+	0.696473i	$0.245248\pi$
$258$	2.32342	+	0.871371i	0.144650	+	0.0542492i
$259$	−6.64315	−	6.64315i	−0.412785	−	0.412785i
$260$	−4.02928	−	3.51694i	−0.249885	−	0.218111i
$261$	6.68748	−	6.68748i	0.413945	−	0.413945i
$262$	2.74367	+	6.03662i	0.169505	+	0.372944i
$263$		−	7.62646i		−	0.470268i	−0.971963	−	0.235134i	$-0.924447\pi$
$263$		−	7.62646i		−	0.470268i	0.971963	−	0.235134i	$-0.0755529\pi$
$264$	−4.53599	−	8.41507i	−0.279171	−	0.517912i
$265$			5.85177i			0.359472i
$266$	2.64522	−	1.20227i	0.162189	−	0.0737156i
$267$	−6.64046	+	6.64046i	−0.406390	+	0.406390i
$268$	1.13886	+	16.7743i	0.0695670	+	1.02465i
$269$	13.0188	+	13.0188i	0.793768	+	0.793768i	0.982105	−	0.188336i	$-0.0603095\pi$
$269$	13.0188	+	13.0188i	0.793768	+	0.793768i	−0.188336	+	0.982105i	$0.560310\pi$
$270$	−2.15989	+	5.75913i	−0.131447	+	0.350489i
$271$	−12.2396			−0.743502			−0.371751	−	0.928333i	$-0.621242\pi$
$271$	−12.2396			−0.743502			−0.371751	+	0.928333i	$0.621242\pi$
$272$	0.776678	+	5.69347i	0.0470930	+	0.345218i
$273$	2.17984			0.131930
$274$	2.34121	−	6.24258i	0.141438	−	0.377128i
$275$	−2.93187	−	2.93187i	−0.176798	−	0.176798i
$276$	13.1240	−	0.891030i	0.789970	−	0.0536337i
$277$	−17.3921	+	17.3921i	−1.04499	+	1.04499i	−0.0460511	+	0.998939i	$0.514664\pi$
$277$	−17.3921	+	17.3921i	−1.04499	+	1.04499i	−0.998939	+	0.0460511i	$0.985336\pi$
$278$	25.3202	−	11.5081i	1.51860	−	0.690212i
$279$			3.06608i			0.183561i
$280$	0.811546	−	2.70950i	0.0484992	−	0.161924i
$281$		−	23.7456i		−	1.41655i	−0.705938	−	0.708273i	$-0.749474\pi$
$281$		−	23.7456i		−	1.41655i	0.705938	−	0.708273i	$-0.250526\pi$
$282$	3.40698	+	7.49603i	0.202883	+	0.446382i
$283$	−1.87152	+	1.87152i	−0.111250	+	0.111250i	−0.760541	−	0.649290i	$-0.775066\pi$
$283$	−1.87152	+	1.87152i	−0.111250	+	0.111250i	0.649290	+	0.760541i	$0.275066\pi$
$284$	−6.21558	+	7.12105i	−0.368827	+	0.422556i
$285$	−1.18427	−	1.18427i	−0.0701502	−	0.0701502i
$286$	−14.6818	−	5.50625i	−0.868155	−	0.325592i
$287$	−8.42537			−0.497334
$288$	12.8839	+	2.92476i	0.759189	+	0.172343i
$289$	−14.9363			−0.878607
$290$	5.36207	+	2.01098i	0.314872	+	0.118089i
$291$	7.56185	+	7.56185i	0.443283	+	0.443283i
$292$	−19.6004	+	22.4557i	−1.14703	+	1.31412i
$293$	−18.5601	+	18.5601i	−1.08429	+	1.08429i	−0.0881889	+	0.996104i	$0.528108\pi$
$293$	−18.5601	+	18.5601i	−1.08429	+	1.08429i	−0.996104	+	0.0881889i	$0.971892\pi$
$294$	0.477000	+	1.04949i	0.0278192	+	0.0612078i
$295$			7.56087i			0.440211i
$296$	25.4553	+	7.62434i	1.47956	+	0.443156i
$297$			18.0334i			1.04640i
$298$	3.52508	−	1.60216i	0.204202	−	0.0928108i
$299$	15.2567	−	15.2567i	0.882316	−	0.882316i
$300$	−1.62657	+	0.110433i	−0.0939102	+	0.00637588i
$301$	1.52206	+	1.52206i	0.0877301	+	0.0877301i
$302$	−9.90977	+	26.4233i	−0.570243	+	1.52049i
$303$	−0.973831			−0.0559451
$304$	−4.97245	+	6.54338i	−0.285189	+	0.375289i
$305$	−4.66882			−0.267336
$306$	1.66616	−	4.44265i	0.0952483	−	0.253969i
$307$	−16.3790	−	16.3790i	−0.934799	−	0.934799i	0.0632014	−	0.998001i	$-0.479869\pi$
$307$	−16.3790	−	16.3790i	−0.934799	−	0.934799i	−0.998001	+	0.0632014i	$0.979869\pi$
$308$	−0.561717	−	8.27352i	−0.0320068	−	0.471428i
$309$	8.87346	−	8.87346i	0.504793	−	0.504793i
$310$	−1.69020	+	0.768205i	−0.0959970	+	0.0436311i
$311$			6.38044i			0.361802i	0.983501	+	0.180901i	$0.0579013\pi$
$311$			6.38044i			0.361802i	−0.983501	+	0.180901i	$0.942099\pi$
$312$	−5.42728	+	2.92547i	−0.307259	+	0.165622i
$313$			15.8278i			0.894637i	0.894375	+	0.447319i	$0.147621\pi$
$313$			15.8278i			0.894637i	−0.894375	+	0.447319i	$0.852379\pi$
$314$	10.6145	+	23.3541i	0.599013	+	1.31795i
$315$	−1.65146	+	1.65146i	−0.0930492	+	0.0930492i
$316$	−15.6378	−	13.6494i	−0.879695	−	0.767838i
$317$	−10.6420	−	10.6420i	−0.597713	−	0.597713i	0.341991	−	0.939703i	$-0.388899\pi$
$317$	−10.6420	−	10.6420i	−0.597713	−	0.597713i	−0.939703	+	0.341991i	$0.888899\pi$
$318$	6.31637	+	2.36888i	0.354205	+	0.132840i
$319$	16.7901			0.940066
$320$	1.61575	+	7.83514i	0.0903232	+	0.437997i
$321$	−10.9122			−0.609057
$322$	10.6839	+	4.00687i	0.595390	+	0.223294i
$323$	2.08704	+	2.08704i	0.116126	+	0.116126i
$324$	−5.21518	−	4.55205i	−0.289732	−	0.252891i
$325$	−1.89090	+	1.89090i	−0.104888	+	0.104888i
$326$	−10.8144	−	23.7939i	−0.598955	−	1.31782i
$327$		−	8.75612i		−	0.484215i
$328$	20.9771	−	11.3073i	1.15827	−	0.624342i
$329$			7.14252i			0.393780i
$330$	−4.35150	+	1.97778i	−0.239542	+	0.108873i
$331$	5.56618	−	5.56618i	0.305945	−	0.305945i	−0.537389	−	0.843334i	$-0.680589\pi$
$331$	5.56618	−	5.56618i	0.305945	−	0.305945i	0.843334	+	0.537389i	$0.180589\pi$
$332$	−0.172235	−	2.53685i	−0.00945263	−	0.139228i
$333$	−15.5152	−	15.5152i	−0.850227	−	0.850227i
$334$	3.34003	−	8.90583i	0.182758	−	0.487306i
$335$	8.40644			0.459293
$336$	−2.59609	−	1.97282i	−0.141629	−	0.107626i
$337$	26.1199			1.42284			0.711420	−	0.702768i	$-0.248053\pi$
$337$	26.1199			1.42284			0.711420	+	0.702768i	$0.248053\pi$
$338$	2.90466	−	7.74498i	0.157993	−	0.421271i
$339$	4.79383	+	4.79383i	0.260365	+	0.260365i
$340$	2.86650	−	0.194616i	0.155458	−	0.0105546i
$341$	−3.84897	+	3.84897i	−0.208433	+	0.208433i
$342$	6.17796	−	2.80791i	0.334066	−	0.151834i
$343$			1.00000i			0.0539949i
$344$	−5.83225	−	1.74687i	−0.314454	−	0.0941848i
$345$		−	6.57709i		−	0.354099i
$346$	1.42343	+	3.13183i	0.0765241	+	0.168368i
$347$	4.74109	−	4.74109i	0.254515	−	0.254515i	−0.568304	−	0.822819i	$-0.692400\pi$
$347$	4.74109	−	4.74109i	0.254515	−	0.254515i	0.822819	+	0.568304i	$0.192400\pi$
$348$	4.34129	−	4.97372i	0.232718	−	0.266619i
$349$	18.3963	+	18.3963i	0.984730	+	0.984730i	0.999885	−	0.0151554i	$-0.00482430\pi$
$349$	18.3963	+	18.3963i	0.984730	+	0.984730i	−0.0151554	+	0.999885i	$0.504824\pi$
$350$	−1.32415	−	0.496608i	−0.0707789	−	0.0265448i
$351$	11.6306			0.620795
$352$	12.5021	+	19.8452i	0.666363	+	1.05775i
$353$	−29.0370			−1.54548			−0.772740	−	0.634722i	$-0.781115\pi$
$353$	−29.0370			−1.54548			−0.772740	+	0.634722i	$0.781115\pi$
$354$	8.16116	+	3.06075i	0.433761	+	0.162677i
$355$	3.34183	+	3.34183i	0.177366	+	0.177366i
$356$	15.1514	−	17.3586i	0.803023	−	0.920005i
$357$	−0.828034	+	0.828034i	−0.0438242	+	0.0438242i
$358$	−4.77771	−	10.5119i	−0.252510	−	0.555572i
$359$		−	35.0672i		−	1.85078i	−0.379019	−	0.925389i	$-0.623738\pi$
$359$		−	35.0672i		−	1.85078i	0.379019	−	0.925389i	$-0.376262\pi$
$360$	1.89538	−	6.32808i	0.0998952	−	0.333519i
$361$		−	14.7787i		−	0.777825i
$362$	29.7121	−	13.5043i	1.56163	−	0.709769i
$363$	−3.56890	+	3.56890i	−0.187319	+	0.187319i
$364$	−5.33598	+	0.362278i	−0.279682	+	0.0189885i
$365$	10.5382	+	10.5382i	0.551597	+	0.551597i
$366$	−1.89001	+	5.03950i	−0.0987922	+	0.263419i
$367$	17.5405			0.915609			0.457805	−	0.889053i	$-0.348636\pi$
$367$	17.5405			0.915609			0.457805	+	0.889053i	$0.348636\pi$
$368$	−31.9777	+	4.36226i	−1.66696	+	0.227398i
$369$	−19.6776			−1.02437
$370$	4.66555	−	12.4402i	0.242551	−	0.646735i
$371$	4.13783	+	4.13783i	0.214825	+	0.214825i
$372$	0.144978	+	2.13537i	0.00751674	+	0.110714i
$373$	10.3544	−	10.3544i	0.536129	−	0.536129i	−0.386260	−	0.922390i	$-0.626233\pi$
$373$	10.3544	−	10.3544i	0.536129	−	0.536129i	0.922390	+	0.386260i	$0.126233\pi$
$374$	7.66863	−	3.48543i	0.396536	−	0.180227i
$375$			0.815159i			0.0420946i
$376$	−9.58566	−	17.7831i	−0.494343	−	0.917095i
$377$		−	10.8287i		−	0.557708i
$378$	2.54504	+	5.59959i	0.130903	+	0.288012i
$379$	−7.45748	+	7.45748i	−0.383065	+	0.383065i	−0.872205	−	0.489140i	$-0.837311\pi$
$379$	−7.45748	+	7.45748i	−0.383065	+	0.383065i	0.489140	+	0.872205i	$0.337311\pi$
$380$	3.09577	+	2.70213i	0.158810	+	0.138616i
$381$	5.71587	+	5.71587i	0.292833	+	0.292833i
$382$	12.0675	+	4.52579i	0.617429	+	0.231560i
$383$	1.24786			0.0637628			0.0318814	−	0.999492i	$-0.489850\pi$
$383$	1.24786			0.0637628			0.0318814	+	0.999492i	$0.489850\pi$
$384$	9.11128	+	1.42774i	0.464958	+	0.0728593i
$385$	−4.14628			−0.211314
$386$	−5.51533	−	2.06846i	−0.280723	−	0.105282i
$387$	3.55480	+	3.55480i	0.180700	+	0.180700i
$388$	−19.7672	−	17.2537i	−1.00353	−	0.875925i
$389$	16.6140	−	16.6140i	0.842364	−	0.842364i	−0.146802	−	0.989166i	$-0.546898\pi$
$389$	16.6140	−	16.6140i	0.842364	−	0.842364i	0.989166	+	0.146802i	$0.0468979\pi$
$390$	1.27556	+	2.80649i	0.0645906	+	0.142112i
$391$			11.5908i			0.586171i
$392$	−1.34206	−	2.48976i	−0.0677841	−	0.125752i
$393$		−	3.82207i		−	0.192798i
$394$	−2.01669	+	0.916594i	−0.101599	+	0.0461773i
$395$	−7.33865	+	7.33865i	−0.369248	+	0.369248i
$396$	−1.31190	−	19.3229i	−0.0659254	−	0.971014i
$397$	−0.525796	−	0.525796i	−0.0263889	−	0.0263889i	0.693789	−	0.720178i	$-0.255940\pi$
$397$	−0.525796	−	0.525796i	−0.0263889	−	0.0263889i	−0.720178	+	0.693789i	$0.755940\pi$
$398$	−3.41178	+	9.09714i	−0.171017	+	0.455998i
$399$	−1.67481			−0.0838455
$400$	3.96329	−	0.540654i	0.198165	−	0.0270327i
$401$	12.9862			0.648499			0.324249	−	0.945972i	$-0.394888\pi$
$401$	12.9862			0.648499			0.324249	+	0.945972i	$0.394888\pi$
$402$	3.40305	−	9.07387i	0.169729	−	0.452564i
$403$	2.48238	+	2.48238i	0.123656	+	0.123656i
$404$	2.38382	−	0.161845i	0.118599	−	0.00805210i
$405$	−2.44743	+	2.44743i	−0.121614	+	0.121614i
$406$	5.21354	−	2.36958i	0.258744	−	0.117600i
$407$		−	38.9537i		−	1.93086i
$408$	0.950335	−	3.17287i	0.0470486	−	0.157081i
$409$		−	1.62193i		−	0.0801994i	−0.999196	−	0.0400997i	$-0.987232\pi$
$409$		−	1.62193i		−	0.0801994i	0.999196	−	0.0400997i	$-0.0127676\pi$
$410$	−4.93021	−	10.8474i	−0.243486	−	0.535716i
$411$	−2.71740	+	2.71740i	−0.134039	+	0.134039i
$412$	−20.2464	+	23.1958i	−0.997468	+	1.14278i
$413$	5.34634	+	5.34634i	0.263076	+	0.263076i
$414$	24.9524	+	9.35812i	1.22634	+	0.459926i
$415$	−1.27135			−0.0624079
$416$	12.7991	−	8.06318i	0.627528	−	0.395330i
$417$	−16.0314			−0.785060
$418$	11.2803	+	4.23055i	0.551738	+	0.206923i
$419$	−15.0499	−	15.0499i	−0.735234	−	0.735234i	0.236418	−	0.971652i	$-0.424027\pi$
$419$	−15.0499	−	15.0499i	−0.735234	−	0.735234i	−0.971652	+	0.236418i	$0.924027\pi$
$420$	−1.07207	+	1.22825i	−0.0523118	+	0.0599324i
$421$	−4.91730	+	4.91730i	−0.239654	+	0.239654i	−0.816707	−	0.577053i	$-0.804203\pi$
$421$	−4.91730	+	4.91730i	−0.239654	+	0.239654i	0.577053	+	0.816707i	$0.304203\pi$
$422$	10.6522	+	23.4369i	0.518540	+	1.14089i
$423$			16.6815i			0.811081i
$424$	−15.8554	−	4.74898i	−0.770006	−	0.230631i
$425$		−	1.43655i		−	0.0696830i
$426$	4.95998	−	2.25433i	0.240312	−	0.109223i
$427$	−3.30135	+	3.30135i	−0.159764	+	0.159764i
$428$	26.7116	−	1.81354i	1.29115	−	0.0876607i
$429$	6.39101	+	6.39101i	0.308561	+	0.308561i
$430$	−1.06896	+	2.85026i	−0.0515497	+	0.137452i
$431$	29.5936			1.42547			0.712737	−	0.701431i	$-0.247455\pi$
$431$	29.5936			1.42547			0.712737	+	0.701431i	$0.247455\pi$
$432$	−13.8515	−	10.5260i	−0.666431	−	0.506434i
$433$	32.1447			1.54477			0.772387	−	0.635152i	$-0.219062\pi$
$433$	32.1447			1.54477			0.772387	+	0.635152i	$0.219062\pi$
$434$	−0.651950	+	1.73836i	−0.0312946	+	0.0834437i
$435$	−2.33411	−	2.33411i	−0.111912	−	0.111912i
$436$	1.45522	+	21.4339i	0.0696923	+	1.02650i
$437$	−11.7220	+	11.7220i	−0.560738	+	0.560738i
$438$	15.6409	−	7.10888i	0.747353	−	0.339676i
$439$			25.8338i			1.23298i	0.787362	+	0.616491i	$0.211446\pi$
$439$			25.8338i			1.23298i	−0.787362	+	0.616491i	$0.788554\pi$
$440$	10.3232	−	5.56455i	0.492141	−	0.265279i
$441$			2.33552i			0.111215i
$442$	−2.24792	−	4.94587i	−0.106923	−	0.235251i
$443$	15.9032	−	15.9032i	0.755584	−	0.755584i	−0.219932	−	0.975515i	$-0.570583\pi$
$443$	15.9032	−	15.9032i	0.755584	−	0.755584i	0.975515	+	0.219932i	$0.0705834\pi$
$444$	−11.5392	−	10.0719i	−0.547626	−	0.477993i
$445$	−8.14622	−	8.14622i	−0.386168	−	0.386168i
$446$	−25.7799	−	9.66845i	−1.22071	−	0.457814i
$447$	−2.23189			−0.105565
$448$	6.68279	+	4.39777i	0.315732	+	0.207775i
$449$	−39.7227			−1.87463			−0.937314	−	0.348486i	$-0.886696\pi$
$449$	−39.7227			−1.87463			−0.937314	+	0.348486i	$0.886696\pi$
$450$	−3.09258	−	1.15984i	−0.145786	−	0.0546752i
$451$	−24.7020	−	24.7020i	−1.16317	−	1.16317i
$452$	−12.5314	−	10.9380i	−0.589427	−	0.514479i
$453$	11.5021	−	11.5021i	0.540415	−	0.540415i
$454$	9.38276	+	20.6439i	0.440355	+	0.968867i
$455$			2.67413i			0.125365i
$456$	4.16988	−	2.24769i	0.195272	−	0.105258i
$457$			19.4173i			0.908305i	0.890924	+	0.454152i	$0.150058\pi$
$457$			19.4173i			0.908305i	−0.890924	+	0.454152i	$0.849942\pi$
$458$	−14.3836	+	6.53742i	−0.672102	+	0.305474i
$459$	−4.41799	+	4.41799i	−0.206214	+	0.206214i
$460$	1.09307	+	16.0999i	0.0509649	+	0.750661i
$461$	−17.8949	−	17.8949i	−0.833450	−	0.833450i	0.154537	−	0.987987i	$-0.450611\pi$
$461$	−17.8949	−	17.8949i	−0.833450	−	0.833450i	−0.987987	+	0.154537i	$0.950611\pi$
$462$	−1.67848	+	4.47548i	−0.0780898	+	0.208218i
$463$	5.40153			0.251030			0.125515	−	0.992092i	$-0.459942\pi$
$463$	5.40153			0.251030			0.125515	+	0.992092i	$0.459942\pi$
$464$	−9.80033	+	12.8965i	−0.454969	+	0.598706i
$465$	1.07015			0.0496268
$466$	6.86951	−	18.3168i	0.318224	−	0.848510i
$467$	−7.02850	−	7.02850i	−0.325240	−	0.325240i	0.525533	−	0.850773i	$-0.323866\pi$
$467$	−7.02850	−	7.02850i	−0.325240	−	0.325240i	−0.850773	+	0.525533i	$0.823866\pi$
$468$	−12.4623	+	0.846105i	−0.576069	+	0.0391112i
$469$	5.94425	−	5.94425i	0.274480	−	0.274480i
$470$	−9.19579	+	4.17953i	−0.424170	+	0.192787i
$471$		−	14.7866i		−	0.681329i
$472$	−20.4862	−	6.13599i	−0.942953	−	0.282432i
$473$			8.92495i			0.410370i
$474$	4.95051	+	10.8921i	0.227384	+	0.500290i
$475$	1.45281	−	1.45281i	0.0666595	−	0.0666595i
$476$	1.88931	−	2.16454i	0.0865964	−	0.0992115i
$477$	9.66397	+	9.66397i	0.442483	+	0.442483i
$478$	7.75659	+	2.90902i	0.354778	+	0.133055i
$479$	−31.6205			−1.44478			−0.722388	−	0.691488i	$-0.756956\pi$
$479$	−31.6205			−1.44478			−0.722388	+	0.691488i	$0.756956\pi$
$480$	1.02082	−	4.49682i	0.0465938	−	0.205251i
$481$	−25.1231			−1.14551
$482$	2.62741	+	0.985382i	0.119675	+	0.0448829i
$483$	−4.65071	−	4.65071i	−0.211614	−	0.211614i
$484$	8.14310	−	9.32936i	0.370141	−	0.424062i
$485$	−9.27653	+	9.27653i	−0.421226	+	0.421226i
$486$	9.28611	+	20.4313i	0.421227	+	0.926782i
$487$		−	6.89453i		−	0.312421i	−0.987724	−	0.156211i	$-0.950072\pi$
$487$		−	6.89453i		−	0.312421i	0.987724	−	0.156211i	$-0.0499279\pi$
$488$	3.78896	−	12.6502i	0.171518	−	0.572646i
$489$			15.0650i			0.681263i
$490$	−1.28747	+	0.585162i	−0.0581621	+	0.0264349i
$491$	−14.0393	+	14.0393i	−0.633584	+	0.633584i	−0.948965	−	0.315381i	$-0.897868\pi$
$491$	−14.0393	+	14.0393i	−0.633584	+	0.633584i	0.315381	+	0.948965i	$0.397868\pi$
$492$	−13.7045	+	0.930442i	−0.617846	+	0.0419476i
$493$	4.11340	+	4.11340i	0.185258	+	0.185258i
$494$	2.72848	−	7.27521i	0.122760	−	0.327327i
$495$	−9.68371			−0.435250
$496$	−0.709774	−	5.20304i	−0.0318698	−	0.233623i
$497$	4.72606			0.211993
$498$	−0.514659	+	1.37228i	−0.0230624	+	0.0614935i
$499$	0.917846	+	0.917846i	0.0410884	+	0.0410884i	0.727352	−	0.686264i	$-0.240751\pi$
$499$	0.917846	+	0.917846i	0.0410884	+	0.0410884i	−0.686264	+	0.727352i	$0.740751\pi$
$500$	−0.135475	−	1.99541i	−0.00605861	−	0.0892373i
$501$	−3.87671	+	3.87671i	−0.173199	+	0.173199i
$502$	28.0466	−	12.7473i	1.25178	−	0.568941i
$503$		−	9.74277i		−	0.434408i	−0.976126	−	0.217204i	$-0.930306\pi$
$503$		−	9.74277i		−	0.434408i	0.976126	−	0.217204i	$-0.0696938\pi$
$504$	−3.13439	−	5.81487i	−0.139617	−	0.259015i
$505$		−	1.19465i		−	0.0531613i
$506$	19.5761	+	43.0714i	0.870265	+	1.91476i
$507$	−3.37139	+	3.37139i	−0.149729	+	0.149729i
$508$	−14.9417	−	13.0418i	−0.662930	−	0.578636i
$509$	−6.51544	−	6.51544i	−0.288792	−	0.288792i	0.547811	−	0.836602i	$-0.315461\pi$
$509$	−6.51544	−	6.51544i	−0.288792	−	0.288792i	−0.836602	+	0.547811i	$0.815461\pi$
$510$	−1.55061	−	0.581537i	−0.0686620	−	0.0257509i
$511$	14.9033			0.659284
$512$	−22.5406	−	1.98070i	−0.996161	−	0.0875352i
$513$	−8.93599			−0.394534
$514$	30.4654	+	11.4257i	1.34377	+	0.503966i
$515$	10.8856	+	10.8856i	0.479675	+	0.479675i
$516$	2.64383	+	2.30766i	0.116388	+	0.101589i
$517$	−20.9409	+	20.9409i	−0.920980	+	0.920980i
$518$	−5.49750	−	12.0956i	−0.241546	−	0.531450i
$519$		−	1.98290i		−	0.0870399i
$520$	−3.58884	−	6.65794i	−0.157381	−	0.291970i
$521$			10.2045i			0.447066i	0.974696	+	0.223533i	$0.0717590\pi$
$521$			10.2045i			0.447066i	−0.974696	+	0.223533i	$0.928241\pi$
$522$	12.1763	−	5.53419i	0.532942	−	0.242225i
$523$	22.0914	−	22.0914i	0.965988	−	0.965988i	−0.0334527	−	0.999440i	$-0.510650\pi$
$523$	22.0914	−	22.0914i	0.965988	−	0.965988i	0.999440	+	0.0334527i	$0.0106503\pi$
$524$	0.635206	+	9.35594i	0.0277491	+	0.408716i
$525$	0.576404	+	0.576404i	0.0251563	+	0.0251563i
$526$	3.78736	−	10.0986i	0.165137	−	0.440320i
$527$	−1.88591			−0.0821517
$528$	−1.82735	−	13.3955i	−0.0795250	−	0.582962i
$529$	−42.1003			−1.83045
$530$	−2.90604	+	7.74864i	−0.126230	+	0.336580i
$531$	12.4865	+	12.4865i	0.541867	+	0.541867i
$532$	4.09973	−	0.278344i	0.177746	−	0.0120678i
$533$	−15.9315	+	15.9315i	−0.690071	+	0.690071i
$534$	−12.0907	+	5.49528i	−0.523216	+	0.237804i
$535$		−	13.3865i		−	0.578751i
$536$	−6.82222	+	22.7773i	−0.294675	+	0.983828i
$537$			6.65558i			0.287209i
$538$	10.7736	+	23.7041i	0.464483	+	1.02195i
$539$	−2.93187	+	2.93187i	−0.126284	+	0.126284i
$540$	−5.72006	+	6.55334i	−0.246152	+	0.282011i
$541$	−20.4475	−	20.4475i	−0.879106	−	0.879106i	0.114336	−	0.993442i	$-0.463526\pi$
$541$	−20.4475	−	20.4475i	−0.879106	−	0.879106i	−0.993442	+	0.114336i	$0.963526\pi$
$542$	−16.2071	−	6.07828i	−0.696154	−	0.261084i
$543$	−18.8121			−0.807304
$544$	−1.79899	+	7.92473i	−0.0771309	+	0.339770i
$545$	10.7416			0.460120
$546$	2.88645	+	1.08253i	0.123529	+	0.0463279i
$547$	−14.3509	−	14.3509i	−0.613602	−	0.613602i	0.330281	−	0.943883i	$-0.392856\pi$
$547$	−14.3509	−	14.3509i	−0.613602	−	0.613602i	−0.943883	+	0.330281i	$0.892856\pi$
$548$	6.20024	−	7.10347i	0.264861	−	0.303445i
$549$	−7.71037	+	7.71037i	−0.329070	+	0.329070i
$550$	−2.42625	−	5.33823i	−0.103456	−	0.227623i
$551$			8.31991i			0.354440i
$552$	17.8206	+	5.33761i	0.758496	+	0.227184i
$553$			10.3784i			0.441335i
$554$	−31.6669	+	14.3927i	−1.34540	+	0.611489i
$555$	−5.41522	+	5.41522i	−0.229863	+	0.229863i
$556$	39.2428	−	2.66432i	1.66427	−	0.112993i
$557$	−18.6540	−	18.6540i	−0.790394	−	0.790394i	0.191164	−	0.981558i	$-0.438774\pi$
$557$	−18.6540	−	18.6540i	−0.790394	−	0.790394i	−0.981558	+	0.191164i	$0.938774\pi$
$558$	−1.52264	+	4.05996i	−0.0644585	+	0.171872i
$559$	5.75612			0.243458
$560$	2.42017	−	3.18477i	0.102271	−	0.134581i
$561$	−4.85537			−0.204994
$562$	11.7923	−	31.4429i	0.497427	−	1.32634i
$563$	−19.7090	−	19.7090i	−0.830637	−	0.830637i	0.156967	−	0.987604i	$-0.449829\pi$
$563$	−19.7090	−	19.7090i	−0.830637	−	0.830637i	−0.987604	+	0.156967i	$0.949829\pi$
$564$	0.788773	+	11.6178i	0.0332133	+	0.489199i
$565$	−5.88085	+	5.88085i	−0.247409	+	0.247409i
$566$	−3.40759	+	1.54877i	−0.143232	+	0.0650995i
$567$			3.46118i			0.145356i
$568$	−11.7667	+	6.34265i	−0.493722	+	0.266131i
$569$			16.5605i			0.694251i	0.937819	+	0.347125i	$0.112842\pi$
$569$			16.5605i			0.694251i	−0.937819	+	0.347125i	$0.887158\pi$
$570$	−0.980037	−	2.15628i	−0.0410492	−	0.0903164i
$571$	4.59853	−	4.59853i	0.192443	−	0.192443i	−0.604308	−	0.796751i	$-0.706550\pi$
$571$	4.59853	−	4.59853i	0.192443	−	0.192443i	0.796751	+	0.604308i	$0.206550\pi$
$572$	−16.7065	−	14.5822i	−0.698535	−	0.609714i
$573$	−5.25301	−	5.25301i	−0.219448	−	0.219448i
$574$	−11.1565	−	4.18411i	−0.465662	−	0.174641i
$575$	8.06848			0.336479
$576$	15.6078	+	10.2711i	0.650323	+	0.427961i
$577$	36.0984			1.50280			0.751399	−	0.659849i	$-0.229380\pi$
$577$	36.0984			1.50280			0.751399	+	0.659849i	$0.229380\pi$
$578$	−19.7780	−	7.41750i	−0.822655	−	0.308527i
$579$	2.40083	+	2.40083i	0.0997749	+	0.0997749i
$580$	6.10153	+	5.32570i	0.253352	+	0.221138i
$581$	−0.898977	+	0.898977i	−0.0372958	+	0.0372958i
$582$	6.25776	+	13.7683i	0.259393	+	0.570715i
$583$			24.2631i			1.00488i
$584$	−37.1056	+	20.0011i	−1.53544	+	0.827651i
$585$			6.24548i			0.258219i
$586$	−33.7935	+	15.3593i	−1.39600	+	0.634487i
$587$	17.1069	−	17.1069i	0.706077	−	0.706077i	−0.259631	−	0.965708i	$-0.583601\pi$
$587$	17.1069	−	17.1069i	0.706077	−	0.706077i	0.965708	+	0.259631i	$0.0836010\pi$
$588$	0.110433	+	1.62657i	0.00455420	+	0.0670787i
$589$	−1.90726	−	1.90726i	−0.0785872	−	0.0785872i
$590$	−3.75479	+	10.0117i	−0.154582	+	0.412177i
$591$	1.27686			0.0525230
$592$	29.9204	+	22.7371i	1.22972	+	0.934490i
$593$	−14.3899			−0.590923			−0.295462	−	0.955355i	$-0.595473\pi$
$593$	−14.3899			−0.590923			−0.295462	+	0.955355i	$0.595473\pi$
$594$	−8.95554	+	23.8790i	−0.367450	+	0.979766i
$595$	−1.01580	−	1.01580i	−0.0416435	−	0.0416435i
$596$	5.46339	−	0.370927i	0.223789	−	0.0151938i
$597$	3.95999	−	3.95999i	0.162072	−	0.162072i
$598$	27.7788	−	12.6256i	1.13596	−	0.516298i
$599$			19.5613i			0.799253i	0.916678	+	0.399627i	$0.130860\pi$
$599$			19.5613i			0.799253i	−0.916678	+	0.399627i	$0.869140\pi$
$600$	−2.20867	−	0.661539i	−0.0901687	−	0.0270072i
$601$			47.6643i			1.94427i	0.234425	+	0.972134i	$0.424679\pi$
$601$			47.6643i			1.94427i	−0.234425	+	0.972134i	$0.575321\pi$
$602$	1.25957	+	2.77131i	0.0513363	+	0.112950i
$603$	13.8829	−	13.8829i	0.565355	−	0.565355i
$604$	−26.2441	+	30.0673i	−1.06786	+	1.22342i
$605$	−4.37817	−	4.37817i	−0.177998	−	0.177998i
$606$	−1.28950	−	0.483613i	−0.0523824	−	0.0196454i
$607$	−32.9334			−1.33673			−0.668363	−	0.743835i	$-0.733005\pi$
$607$	−32.9334			−1.33673			−0.668363	+	0.743835i	$0.733005\pi$
$608$	−9.83378	+	6.19508i	−0.398812	+	0.251244i
$609$	−3.30093			−0.133761
$610$	−6.18223	−	2.31857i	−0.250311	−	0.0938763i
$611$	13.5058	+	13.5058i	0.546385	+	0.546385i
$612$	4.41251	−	5.05532i	0.178365	−	0.204349i
$613$	−14.2556	+	14.2556i	−0.575780	+	0.575780i	−0.933738	−	0.357958i	$-0.883473\pi$
$613$	−14.2556	+	14.2556i	−0.575780	+	0.575780i	0.357958	+	0.933738i	$0.383473\pi$
$614$	−13.5544	−	29.8223i	−0.547009	−	1.20353i
$615$			6.86801i			0.276945i
$616$	3.36490	−	11.2344i	0.135576	−	0.452645i
$617$			2.44103i			0.0982722i	0.998792	+	0.0491361i	$0.0156468\pi$
$617$			2.44103i			0.0982722i	−0.998792	+	0.0491361i	$0.984353\pi$
$618$	16.1564	−	7.34318i	0.649907	−	0.295386i
$619$	−11.0216	+	11.0216i	−0.442995	+	0.442995i	−0.893017	−	0.450023i	$-0.851416\pi$
$619$	−11.0216	+	11.0216i	−0.442995	+	0.442995i	0.450023	+	0.893017i	$0.351416\pi$
$620$	−2.61958	+	0.177852i	−0.105205	+	0.00714271i
$621$	−24.8139	−	24.8139i	−0.995748	−	0.995748i
$622$	−3.16858	+	8.44868i	−0.127048	+	0.338761i
$623$	−11.5205			−0.461559
$624$	−8.63936	+	1.17854i	−0.345851	+	0.0471794i
$625$	−1.00000			−0.0400000
$626$	−7.86019	+	20.9584i	−0.314156	+	0.837664i
$627$	−4.91033	−	4.91033i	−0.196100	−	0.196100i
$628$	2.45744	+	36.1956i	0.0980626	+	1.44436i
$629$	9.54323	−	9.54323i	0.380513	−	0.380513i
$630$	−3.00691	+	1.36666i	−0.119798	+	0.0544489i
$631$		−	26.6244i		−	1.05990i	−0.848029	−	0.529950i	$-0.822211\pi$
$631$		−	26.6244i		−	1.05990i	0.848029	−	0.529950i	$-0.177789\pi$
$632$	−13.9284	−	25.8397i	−0.554043	−	1.02785i
$633$		−	14.8390i		−	0.589797i
$634$	−8.80670	−	19.3765i	−0.349759	−	0.769539i
$635$	−7.01198	+	7.01198i	−0.278262	+	0.278262i
$636$	7.18744	+	6.27353i	0.285000	+	0.248762i
$637$	1.89090	+	1.89090i	0.0749201	+	0.0749201i
$638$	22.2327	+	8.33811i	0.880200	+	0.330109i
$639$	11.0378			0.436649
$640$	−1.75149	+	11.1773i	−0.0692338	+	0.441822i
$641$	−16.4913			−0.651367			−0.325684	−	0.945479i	$-0.605594\pi$
$641$	−16.4913			−0.651367			−0.325684	+	0.945479i	$0.605594\pi$
$642$	−14.4494	−	5.41907i	−0.570271	−	0.213873i
$643$	−10.1394	−	10.1394i	−0.399859	−	0.399859i	0.478324	−	0.878183i	$-0.341244\pi$
$643$	−10.1394	−	10.1394i	−0.399859	−	0.399859i	−0.878183	+	0.478324i	$0.841244\pi$
$644$	12.1573	+	10.6114i	0.479063	+	0.418149i
$645$	1.24072	−	1.24072i	0.0488533	−	0.0488533i
$646$	1.72712	+	3.80000i	0.0679525	+	0.149509i
$647$		−	18.6188i		−	0.731979i	−0.930619	−	0.365989i	$-0.880731\pi$
$647$		−	18.6188i		−	0.731979i	0.930619	−	0.365989i	$-0.119269\pi$
$648$	−4.64510	−	8.61750i	−0.182477	−	0.338528i
$649$			31.3495i			1.23058i
$650$	−3.44287	+	1.56480i	−0.135041	+	0.0613766i
$651$	0.756707	−	0.756707i	0.0296577	−	0.0296577i
$652$	−2.50372	−	36.8772i	−0.0980531	−	1.44422i
$653$	−30.5099	−	30.5099i	−1.19395	−	1.19395i	−0.975950	−	0.217995i	$-0.930048\pi$
$653$	−30.5099	−	30.5099i	−1.19395	−	1.19395i	−0.217995	−	0.975950i	$-0.569952\pi$
$654$	4.34836	−	11.5944i	0.170034	−	0.453379i
$655$	4.68874			0.183204
$656$	33.3922	−	4.55521i	1.30375	−	0.177851i
$657$	34.8069			1.35795
$658$	−3.54703	+	9.45778i	−0.138278	+	0.368703i
$659$	−21.1337	−	21.1337i	−0.823252	−	0.823252i	0.163321	−	0.986573i	$-0.447779\pi$
$659$	−21.1337	−	21.1337i	−0.823252	−	0.823252i	−0.986573	+	0.163321i	$0.947779\pi$
$660$	−6.74423	+	0.457888i	−0.262519	+	0.0178233i
$661$	19.3455	−	19.3455i	0.752452	−	0.752452i	−0.222485	−	0.974936i	$-0.571417\pi$
$661$	19.3455	−	19.3455i	0.752452	−	0.752452i	0.974936	+	0.222485i	$0.0714167\pi$
$662$	10.1347	−	4.60626i	0.393896	−	0.179027i
$663$			3.13146i			0.121616i
$664$	1.03176	−	3.44471i	0.0400399	−	0.133681i
$665$		−	2.05459i		−	0.0796734i
$666$	−12.8395	−	28.2495i	−0.497521	−	1.09464i
$667$	−23.1032	+	23.1032i	−0.894558	+	0.894558i
$668$	8.84542	−	10.1340i	0.342240	−	0.392096i
$669$	11.2220	+	11.2220i	0.433867	+	0.433867i
$670$	11.1314	+	4.17471i	0.430044	+	0.161283i
$671$	−19.3582			−0.747317
$672$	−2.45791	−	3.90156i	−0.0948157	−	0.150506i
$673$	13.9541			0.537892			0.268946	−	0.963155i	$-0.413325\pi$
$673$	13.9541			0.537892			0.268946	+	0.963155i	$0.413325\pi$
$674$	34.5867	+	12.9713i	1.33223	+	0.499637i
$675$	3.07541	+	3.07541i	0.118373	+	0.118373i
$676$	7.69244	−	8.81305i	0.295863	−	0.338963i
$677$	−15.0295	+	15.0295i	−0.577629	+	0.577629i	−0.934249	−	0.356620i	$-0.883929\pi$
$677$	−15.0295	+	15.0295i	−0.577629	+	0.577629i	0.356620	+	0.934249i	$0.383929\pi$
$678$	3.96711	+	8.72842i	0.152356	+	0.335213i
$679$			13.1190i			0.503461i
$680$	3.89234	+	1.16583i	0.149264	+	0.0447074i
$681$		−	13.0706i		−	0.500867i
$682$	−7.00805	+	3.18519i	−0.268352	+	0.121967i
$683$	3.12623	−	3.12623i	0.119622	−	0.119622i	−0.644762	−	0.764384i	$-0.723043\pi$
$683$	3.12623	−	3.12623i	0.119622	−	0.119622i	0.764384	+	0.644762i	$0.223043\pi$
$684$	9.57499	−	0.650078i	0.366109	−	0.0248563i
$685$	−3.33358	−	3.33358i	−0.127370	−	0.127370i
$686$	−0.496608	+	1.32415i	−0.0189606	+	0.0505564i
$687$	9.10693			0.347451
$688$	−6.85528	−	5.20946i	−0.261355	−	0.198609i
$689$	15.6484			0.596158
$690$	3.26624	−	8.70907i	0.124344	−	0.331549i
$691$	−5.25205	−	5.25205i	−0.199797	−	0.199797i	0.600116	−	0.799913i	$-0.295121\pi$
$691$	−5.25205	−	5.25205i	−0.199797	−	0.199797i	−0.799913	+	0.600116i	$0.795121\pi$
$692$	0.329547	+	4.85390i	0.0125275	+	0.184518i
$693$	−6.84742	+	6.84742i	−0.260112	+	0.260112i
$694$	8.63239	−	3.92346i	0.327681	−	0.148933i
$695$		−	19.6666i		−	0.745996i
$696$	8.21852	−	4.43004i	0.311522	−	0.167920i
$697$		−	12.1035i		−	0.458452i
$698$	15.2237	+	33.4952i	0.576227	+	1.26781i
$699$	−7.97332	+	7.97332i	−0.301579	+	0.301579i
$700$	−1.50676	−	1.31517i	−0.0569502	−	0.0497088i
$701$	15.3965	+	15.3965i	0.581517	+	0.581517i	0.935320	−	0.353803i	$-0.115112\pi$
$701$	15.3965	+	15.3965i	0.581517	+	0.581517i	−0.353803	+	0.935320i	$0.615112\pi$
$702$	15.4007	+	5.77585i	0.581261	+	0.217995i
$703$	19.3025			0.728007
$704$	6.69936	+	32.4867i	0.252492	+	1.22439i
$705$	5.82229			0.219280
$706$	−38.4494	−	14.4200i	−1.44706	−	0.542703i
$707$	−0.844747	−	0.844747i	−0.0317700	−	0.0317700i
$708$	9.28663	+	8.10580i	0.349013	+	0.304635i
$709$	−26.1685	+	26.1685i	−0.982778	+	0.982778i	−0.999854	−	0.0170765i	$-0.994564\pi$
$709$	−26.1685	+	26.1685i	−0.982778	+	0.982778i	0.0170765	+	0.999854i	$0.494564\pi$
$710$	2.76551	+	6.08468i	0.103788	+	0.228354i
$711$			24.2390i			0.909032i
$712$	28.6832	−	15.4612i	1.07495	−	0.579431i
$713$		−	10.5923i		−	0.396687i
$714$	−1.50765	+	0.685235i	−0.0564225	+	0.0256443i
$715$	−7.84020	+	7.84020i	−0.293207	+	0.293207i
$716$	−1.10612	−	16.2920i	−0.0413376	−	0.608861i
$717$	−3.37645	−	3.37645i	−0.126096	−	0.126096i
$718$	17.4147	−	46.4344i	0.649910	−	1.73292i
$719$	−18.8014			−0.701173			−0.350586	−	0.936530i	$-0.614018\pi$
$719$	−18.8014			−0.701173			−0.350586	+	0.936530i	$0.614018\pi$
$720$	5.65235	−	7.43809i	0.210651	−	0.277201i
$721$	15.3945			0.573321
$722$	7.33921	−	19.5692i	0.273137	−	0.728291i
$723$	−1.14372	−	1.14372i	−0.0425352	−	0.0425352i
$724$	46.0496	−	3.12646i	1.71142	−	0.116194i
$725$	2.86338	−	2.86338i	0.106343	−	0.106343i
$726$	−6.49812	+	2.95343i	−0.241168	+	0.109612i
$727$		−	53.4505i		−	1.98237i	−0.132489	−	0.991185i	$-0.542297\pi$
$727$		−	53.4505i		−	1.98237i	0.132489	−	0.991185i	$-0.457703\pi$
$728$	−7.24557	−	2.17018i	−0.268539	−	0.0804323i
$729$		−	2.55244i		−	0.0945348i
$730$	8.72086	+	19.1876i	0.322773	+	0.710165i
$731$	−2.18652	+	2.18652i	−0.0808713	+	0.0808713i
$732$	−5.00531	+	5.73447i	−0.185002	+	0.211952i
$733$	24.6798	+	24.6798i	0.911570	+	0.911570i	0.996396	−	0.0848259i	$-0.0270334\pi$
$733$	24.6798	+	24.6798i	0.911570	+	0.911570i	−0.0848259	+	0.996396i	$0.527033\pi$
$734$	23.2264	+	8.71078i	0.857301	+	0.321521i
$735$	0.815159			0.0300676
$736$	−44.5098	−	10.1041i	−1.64065	−	0.372443i
$737$	34.8555			1.28392
$738$	−26.0561	−	9.77205i	−0.959139	−	0.359714i
$739$	11.8553	+	11.8553i	0.436105	+	0.436105i	0.890699	−	0.454594i	$-0.150216\pi$
$739$	11.8553	+	11.8553i	0.436105	+	0.436105i	−0.454594	+	0.890699i	$0.650216\pi$
$740$	12.3558	−	14.1558i	0.454209	−	0.520376i
$741$	−3.16690	+	3.16690i	−0.116339	+	0.116339i
$742$	3.42424	+	7.53400i	0.125708	+	0.276582i
$743$		−	50.6920i		−	1.85971i	−0.367925	−	0.929855i	$-0.619932\pi$
$743$		−	50.6920i		−	1.85971i	0.367925	−	0.929855i	$-0.380068\pi$
$744$	−0.868472	+	2.89956i	−0.0318397	+	0.106303i
$745$		−	2.73798i		−	0.100312i
$746$	18.8528	−	8.56871i	0.690252	−	0.313723i
$747$	−2.09958	+	2.09958i	−0.0768194	+	0.0768194i
$748$	11.8853	−	0.806935i	0.434571	−	0.0295045i
$749$	−9.46571	−	9.46571i	−0.345870	−	0.345870i
$750$	−0.404815	+	1.07939i	−0.0147817	+	0.0394139i
$751$	−4.54553			−0.165869			−0.0829343	−	0.996555i	$-0.526429\pi$
$751$	−4.54553			−0.165869			−0.0829343	+	0.996555i	$0.526429\pi$
$752$	−3.86163	−	28.3079i	−0.140819	−	1.03228i
$753$	−17.7576			−0.647124
$754$	5.37764	−	14.3389i	0.195842	−	0.522192i
$755$	14.1102	+	14.1102i	0.513524	+	0.513524i
$756$	0.589219	+	8.67861i	0.0214297	+	0.315638i
$757$	11.0294	−	11.0294i	0.400869	−	0.400869i	−0.477670	−	0.878539i	$-0.658519\pi$
$757$	11.0294	−	11.0294i	0.400869	−	0.400869i	0.878539	+	0.477670i	$0.158519\pi$
$758$	−13.5783	+	6.17139i	−0.493186	+	0.224155i
$759$		−	27.2705i		−	0.989856i
$760$	2.75737	+	5.11542i	0.100020	+	0.185556i
$761$		−	28.7744i		−	1.04307i	−0.853229	−	0.521536i	$-0.825359\pi$
$761$		−	28.7744i		−	1.04307i	0.853229	−	0.521536i	$-0.174641\pi$
$762$	4.73014	+	10.4072i	0.171355	+	0.377015i
$763$	7.59547	−	7.59547i	0.274974	−	0.274974i
$764$	13.7317	+	11.9857i	0.496796	+	0.433627i
$765$	−2.37241	−	2.37241i	−0.0857745	−	0.0857745i
$766$	1.65236	+	0.619699i	0.0597022	+	0.0223906i
$767$	20.2188			0.730058
$768$	11.3557	+	6.41529i	0.409764	+	0.231492i
$769$	29.5774			1.06659			0.533294	−	0.845930i	$-0.320954\pi$
$769$	29.5774			1.06659			0.533294	+	0.845930i	$0.320954\pi$
$770$	−5.49031	−	2.05908i	−0.197857	−	0.0742040i
$771$	−13.2616	−	13.2616i	−0.477605	−	0.477605i
$772$	−6.27592	−	5.47792i	−0.225875	−	0.197155i
$773$	18.4444	−	18.4444i	0.663398	−	0.663398i	−0.292781	−	0.956180i	$-0.594581\pi$
$773$	18.4444	−	18.4444i	0.663398	−	0.663398i	0.956180	+	0.292781i	$0.0945807\pi$
$774$	2.94175	+	6.47243i	0.105739	+	0.232647i
$775$			1.31281i			0.0471574i
$776$	−17.6064	−	32.6631i	−0.632034	−	1.17254i
$777$			7.65828i			0.274739i
$778$	30.2502	−	13.7488i	1.08452	−	0.492920i
$779$	12.2405	−	12.2405i	0.438560	−	0.438560i
$780$	0.295314	+	4.34967i	0.0105739	+	0.155743i
$781$	13.8562	+	13.8562i	0.495813	+	0.495813i
$782$	−5.75608	+	15.3480i	−0.205837	+	0.548842i
$783$	−17.6122			−0.629408
$784$	−0.540654	−	3.96329i	−0.0193091	−	0.141546i
$785$	18.1395			0.647426
$786$	1.89807	−	5.06100i	0.0677019	−	0.180520i
$787$	−13.4883	−	13.4883i	−0.480806	−	0.480806i	0.424583	−	0.905389i	$-0.360421\pi$
$787$	−13.4883	−	13.4883i	−0.480806	−	0.480806i	−0.905389	+	0.424583i	$0.860421\pi$
$788$	−3.12559	+	0.212207i	−0.111345	+	0.00755955i
$789$	−4.39593	+	4.39593i	−0.156499	+	0.156499i
$790$	−13.3619	+	6.07306i	−0.475396	+	0.216070i
$791$			8.31678i			0.295711i
$792$	7.85878	−	26.2380i	0.279250	−	0.932328i
$793$			12.4851i			0.443357i
$794$	−0.435119	−	0.957348i	−0.0154418	−	0.0339750i
$795$	3.37299	−	3.37299i	0.119628	−	0.119628i
$796$	−9.03543	+	10.3517i	−0.320252	+	0.366906i
$797$	−28.1865	−	28.1865i	−0.998417	−	0.998417i	0.00158140	−	0.999999i	$-0.499497\pi$
$797$	−28.1865	−	28.1865i	−0.998417	−	0.998417i	−0.999999	+	0.00158140i	$0.999497\pi$
$798$	−2.21771	−	0.831726i	−0.0785060	−	0.0294428i
$799$	−10.2606			−0.362994
$800$	5.51650	+	1.25230i	0.195038	+	0.0442753i
$801$	−26.9063			−0.950688
$802$	17.1957	+	6.44904i	0.607201	+	0.227724i
$803$	43.6945	+	43.6945i	1.54195	+	1.54195i
$804$	9.01232	−	10.3252i	0.317840	−	0.364142i
$805$	5.70528	−	5.70528i	0.201085	−	0.201085i
$806$	2.05428	+	4.51983i	0.0723590	+	0.159204i
$807$		−	15.0081i		−	0.528312i
$808$	3.23691	+	0.969515i	0.113874	+	0.0341074i
$809$		−	8.11833i		−	0.285425i	−0.989764	−	0.142713i	$-0.954418\pi$
$809$		−	8.11833i		−	0.285425i	0.989764	−	0.142713i	$-0.0455825\pi$
$810$	−4.45618	+	2.02535i	−0.156574	+	0.0711637i
$811$	−33.0046	+	33.0046i	−1.15895	+	1.15895i	−0.174247	+	0.984702i	$0.555749\pi$
$811$	−33.0046	+	33.0046i	−1.15895	+	1.15895i	−0.984702	+	0.174247i	$0.944251\pi$
$812$	8.08027	−	0.548596i	0.283562	−	0.0192520i
$813$	7.05495	+	7.05495i	0.247428	+	0.247428i
$814$	19.3447	−	51.5806i	0.678032	−	1.80790i
$815$	−18.4811			−0.647363
$816$	2.83406	−	3.72942i	0.0992120	−	0.130556i
$817$	−4.42253			−0.154725
$818$	0.805465	−	2.14769i	0.0281624	−	0.0750921i
$819$	4.41622	+	4.41622i	0.154315	+	0.154315i
$820$	−1.14142	−	16.8120i	−0.0398603	−	0.587102i
$821$	22.7948	−	22.7948i	0.795543	−	0.795543i	−0.186846	−	0.982389i	$-0.559827\pi$
$821$	22.7948	−	22.7948i	0.795543	−	0.795543i	0.982389	+	0.186846i	$0.0598265\pi$
$822$	−4.94773	+	2.24877i	−0.172572	+	0.0784348i
$823$		−	23.0983i		−	0.805155i	−0.915386	−	0.402577i	$-0.868114\pi$
$823$		−	23.0983i		−	0.805155i	0.915386	−	0.402577i	$-0.131886\pi$
$824$	−38.3286	+	20.6603i	−1.33524	+	0.719735i
$825$			3.37988i			0.117672i
$826$	4.42434	+	9.73441i	0.153942	+	0.338703i
$827$	−34.0200	+	34.0200i	−1.18299	+	1.18299i	−0.204027	+	0.978965i	$0.565403\pi$
$827$	−34.0200	+	34.0200i	−1.18299	+	1.18299i	−0.978965	+	0.204027i	$0.934597\pi$
$828$	28.3935	+	24.7832i	0.986742	+	0.861274i
$829$	35.5005	+	35.5005i	1.23298	+	1.23298i	0.962812	+	0.270173i	$0.0870809\pi$
$829$	35.5005	+	35.5005i	1.23298	+	1.23298i	0.270173	+	0.962812i	$0.412919\pi$
$830$	−1.68346	−	0.631361i	−0.0584336	−	0.0219148i
$831$	20.0498			0.695519
$832$	20.9522	−	4.32074i	0.726387	−	0.149795i
$833$	−1.43655			−0.0497736
$834$	−21.2280	−	7.96132i	−0.735066	−	0.275678i
$835$	−4.75578	−	4.75578i	−0.164580	−	0.164580i
$836$	12.8359	+	11.2038i	0.443940	+	0.387491i
$837$	4.03742	−	4.03742i	0.139554	−	0.139554i
$838$	−12.4544	−	27.4022i	−0.430231	−	0.946593i
$839$			36.1815i			1.24912i	0.780976	+	0.624562i	$0.214722\pi$
$839$			36.1815i			1.24912i	−0.780976	+	0.624562i	$0.785278\pi$
$840$	−2.02955	+	1.09399i	−0.0700260	+	0.0377462i
$841$		−	12.6021i		−	0.434554i
$842$	−8.95322	+	4.06928i	−0.308548	+	0.140237i
$843$	−13.6871	+	13.6871i	−0.471409	+	0.471409i
$844$	2.46615	+	36.3240i	0.0848885	+	1.25032i
$845$	−4.13587	−	4.13587i	−0.142278	−	0.142278i
$846$	−8.28415	+	22.0888i	−0.284815	+	0.759429i
$847$	−6.19167			−0.212748
$848$	−18.6366	−	14.1623i	−0.639982	−	0.486335i
$849$	2.15750			0.0740453
$850$	0.713403	−	1.90221i	0.0244695	−	0.0652454i
$851$	53.6001	+	53.6001i	1.83739	+	1.83739i
$852$	7.68729	−	0.521915i	0.263362	−	0.0178805i
$853$	36.9036	−	36.9036i	1.26355	−	1.26355i	0.314197	−	0.949358i	$-0.398265\pi$
$853$	36.9036	−	36.9036i	1.26355	−	1.26355i	0.949358	−	0.314197i	$-0.101735\pi$
$854$	−6.01098	+	2.73202i	−0.205691	+	0.0934877i
$855$		−	4.79852i		−	0.164106i
$856$	36.2708	+	10.8638i	1.23971	+	0.371317i
$857$			27.8872i			0.952608i	0.879281	+	0.476304i	$0.158024\pi$
$857$			27.8872i			0.952608i	−0.879281	+	0.476304i	$0.841976\pi$
$858$	5.28884	+	11.6365i	0.180558	+	0.397264i
$859$	20.6313	−	20.6313i	0.703931	−	0.703931i	−0.261321	−	0.965252i	$-0.584158\pi$
$859$	20.6313	−	20.6313i	0.703931	−	0.703931i	0.965252	+	0.261321i	$0.0841581\pi$
$860$	−2.83093	+	3.24333i	−0.0965338	+	0.110597i
$861$	4.85642	+	4.85642i	0.165506	+	0.165506i
$862$	39.1865	+	14.6964i	1.33470	+	0.500562i
$863$	27.8828			0.949141			0.474570	−	0.880218i	$-0.342603\pi$
$863$	27.8828			0.949141			0.474570	+	0.880218i	$0.342603\pi$
$864$	−13.1142	−	20.8168i	−0.446154	−	0.708204i
$865$	2.43254			0.0827088
$866$	42.5645	+	15.9633i	1.44640	+	0.542455i
$867$	8.60936	+	8.60936i	0.292389	+	0.292389i
$868$	−1.72656	+	1.97808i	−0.0586034	+	0.0671406i
$869$	−30.4281	+	30.4281i	−1.03220	+	1.03220i
$870$	−1.93158	−	4.24986i	−0.0654868	−	0.144084i
$871$		−	22.4800i		−	0.761704i
$872$	−8.71732	+	29.1044i	−0.295206	+	0.985600i
$873$			30.6396i			1.03699i
$874$	−21.3429	+	9.70045i	−0.721935	+	0.328123i
$875$	−0.707107	+	0.707107i	−0.0239046	+	0.0239046i
$876$	24.2413	−	1.64582i	0.819039	−	0.0556072i
$877$	4.71301	+	4.71301i	0.159147	+	0.159147i	0.782189	−	0.623042i	$-0.214103\pi$
$877$	4.71301	+	4.71301i	0.159147	+	0.159147i	−0.623042	+	0.782189i	$0.714103\pi$
$878$	−12.8293	+	34.2079i	−0.432968	+	1.15446i
$879$	21.3962			0.721677
$880$	16.4329	−	2.24171i	0.553954	−	0.0755679i
$881$	46.3283			1.56084			0.780419	−	0.625256i	$-0.215006\pi$
$881$	46.3283			1.56084			0.780419	+	0.625256i	$0.215006\pi$
$882$	−1.15984	+	3.09258i	−0.0390537	+	0.104133i
$883$	1.42256	+	1.42256i	0.0478728	+	0.0478728i	0.730638	−	0.682765i	$-0.239223\pi$
$883$	1.42256	+	1.42256i	0.0478728	+	0.0478728i	−0.682765	+	0.730638i	$0.739223\pi$
$884$	−0.520430	−	7.66542i	−0.0175040	−	0.257816i
$885$	4.35812	−	4.35812i	0.146497	−	0.146497i
$886$	28.9559	−	13.1606i	0.972793	−	0.442139i
$887$			8.23550i			0.276521i	0.990396	+	0.138261i	$0.0441511\pi$
$887$			8.23550i			0.276521i	−0.990396	+	0.138261i	$0.955849\pi$
$888$	−10.2778	−	19.0673i	−0.344902	−	0.639855i
$889$			9.91643i			0.332587i
$890$	−6.74136	−	14.8323i	−0.225971	−	0.497180i
$891$	−10.1477	+	10.1477i	−0.339962	+	0.339962i
$892$	−29.3351	−	25.6050i	−0.982211	−	0.857319i
$893$	−10.3767	−	10.3767i	−0.347244	−	0.347244i
$894$	−2.95536	−	1.10837i	−0.0988421	−	0.0370696i
$895$	−8.16476			−0.272918
$896$	6.66506	+	9.14204i	0.222664	+	0.305414i
$897$	−17.5880			−0.587247
$898$	−52.5989	−	19.7266i	−1.75525	−	0.658285i
$899$	−3.75907	−	3.75907i	−0.125372	−	0.125372i
$900$	−3.51906	−	3.07160i	−0.117302	−	0.102387i
$901$	−5.94420	+	5.94420i	−0.198030	+	0.198030i
$902$	−20.4420	−	44.9765i	−0.680645	−	1.49755i
$903$		−	1.75464i		−	0.0583909i
$904$	−11.1616	−	20.7068i	−0.371229	−	0.688696i
$905$		−	23.0778i		−	0.767133i
$906$	20.9426	−	9.51849i	0.695770	−	0.316231i
$907$	5.51759	−	5.51759i	0.183209	−	0.183209i	−0.609544	−	0.792752i	$-0.708647\pi$
$907$	5.51759	−	5.51759i	0.183209	−	0.183209i	0.792752	+	0.609544i	$0.208647\pi$
$908$	2.17226	+	31.9952i	0.0720891	+	1.06180i
$909$	−1.97292	−	1.97292i	−0.0654376	−	0.0654376i
$910$	−1.32800	+	3.54096i	−0.0440227	+	0.117382i
$911$	8.65180			0.286647			0.143323	−	0.989676i	$-0.454221\pi$
$911$	8.65180			0.286647			0.143323	+	0.989676i	$0.454221\pi$
$912$	6.63778	−	0.905495i	0.219799	−	0.0299839i
$913$	−5.27136			−0.174456
$914$	−9.64281	+	25.7115i	−0.318956	+	0.850462i
$915$	2.69113	+	2.69113i	0.0889659	+	0.0889659i
$916$	−22.2926	+	1.51352i	−0.736569	+	0.0500081i
$917$	3.31544	−	3.31544i	0.109485	−	0.109485i
$918$	−8.04410	+	3.65608i	−0.265495	+	0.120669i
$919$			37.6570i			1.24219i	0.783735	+	0.621095i	$0.213312\pi$
$919$			37.6570i			1.24219i	−0.783735	+	0.621095i	$0.786688\pi$
$920$	−6.54794	+	21.8615i	−0.215879	+	0.720754i
$921$			18.8819i			0.622178i
$922$	−14.8088	−	32.5824i	−0.487703	−	1.07304i
$923$	8.93651	−	8.93651i	0.294149	−	0.294149i
$924$	−4.44512	+	5.09267i	−0.146234	+	0.167536i
$925$	−6.64315	−	6.64315i	−0.218426	−	0.218426i
$926$	7.15245	+	2.68245i	0.235044	+	0.0881506i
$927$	35.9541			1.18089
$928$	−19.3817	+	12.2101i	−0.636234	+	0.400815i
$929$	41.6931			1.36791			0.683953	−	0.729526i	$-0.260259\pi$
$929$	41.6931			1.36791			0.683953	+	0.729526i	$0.260259\pi$
$930$	1.41704	+	0.531443i	0.0464664	+	0.0174267i
$931$	−1.45281	−	1.45281i	−0.0476140	−	0.0476140i
$932$	18.1926	−	20.8428i	0.595917	−	0.682729i
$933$	3.67771	−	3.67771i	0.120403	−	0.120403i
$934$	−5.81640	−	12.7972i	−0.190318	−	0.418738i
$935$		−	5.95635i		−	0.194793i
$936$	−16.9221	−	5.06850i	−0.553118	−	0.165669i
$937$			39.2632i			1.28267i	0.767260	+	0.641336i	$0.221619\pi$
$937$			39.2632i			1.28267i	−0.767260	+	0.641336i	$0.778381\pi$
$938$	10.8231	−	4.91913i	0.353386	−	0.160615i
$939$	9.12318	−	9.12318i	0.297724	−	0.297724i
$940$	−14.2522	+	0.967631i	−0.464856	+	0.0315606i
$941$	−30.6071	−	30.6071i	−0.997762	−	0.997762i	0.00223595	−	0.999998i	$-0.499288\pi$
$941$	−30.6071	−	30.6071i	−0.997762	−	0.997762i	−0.999998	+	0.00223595i	$0.999288\pi$
$942$	7.34313	−	19.5797i	0.239252	−	0.637940i
$943$	67.9799			2.21373
$944$	−24.0796	−	18.2986i	−0.783726	−	0.595569i
$945$	4.34929			0.141483
$946$	−4.43220	+	11.8180i	−0.144103	+	0.384236i
$947$	31.8816	+	31.8816i	1.03601	+	1.03601i	0.999327	+	0.0366857i	$0.0116800\pi$
$947$	31.8816	+	31.8816i	1.03601	+	1.03601i	0.0366857	+	0.999327i	$0.488320\pi$
$948$	1.14612	+	16.8813i	0.0372244	+	0.548278i
$949$	28.1807	−	28.1807i	0.914783	−	0.914783i
$950$	2.64522	−	1.20227i	0.0858223	−	0.0390066i
$951$			12.2682i			0.397822i
$952$	3.57666	−	1.92793i	0.115920	−	0.0624847i
$953$		−	32.5418i		−	1.05413i	−0.849824	−	0.527066i	$-0.823292\pi$
$953$		−	32.5418i		−	1.05413i	0.849824	−	0.527066i	$-0.176708\pi$
$954$	7.99736	+	17.5958i	0.258924	+	0.569684i
$955$	6.44415	−	6.44415i	0.208528	−	0.208528i
$956$	8.82626	+	7.70397i	0.285462	+	0.249164i
$957$	−9.67789	−	9.67789i	−0.312842	−	0.312842i
$958$	−41.8703	−	15.7030i	−1.35277	−	0.507341i
$959$	−4.71440			−0.152236
$960$	3.58488	−	5.44753i	0.115702	−	0.175818i
$961$	−29.2765			−0.944405
$962$	−33.2668	−	12.4763i	−1.07256	−	0.402253i
$963$	−22.1073	−	22.1073i	−0.712399	−	0.712399i
$964$	2.98975	+	2.60959i	0.0962934	+	0.0840493i
$965$	−2.94522	+	2.94522i	−0.0948101	+	0.0948101i
$966$	−3.84867	−	8.46782i	−0.123829	−	0.272448i
$967$		−	47.9565i		−	1.54218i	−0.636727	−	0.771089i	$-0.719712\pi$
$967$		−	47.9565i		−	1.54218i	0.636727	−	0.771089i	$-0.280288\pi$
$968$	15.4157	−	8.30957i	0.495481	−	0.267080i
$969$		−	2.40595i		−	0.0772904i
$970$	−16.8903	+	7.67674i	−0.542316	+	0.246485i
$971$	16.5904	−	16.5904i	0.532413	−	0.532413i	−0.388877	−	0.921290i	$-0.627137\pi$
$971$	16.5904	−	16.5904i	0.532413	−	0.532413i	0.921290	+	0.388877i	$0.127137\pi$
$972$	2.14989	+	31.6657i	0.0689577	+	1.01568i
$973$	−13.9064	−	13.9064i	−0.445818	−	0.445818i
$974$	3.42388	−	9.12942i	0.109708	−	0.292525i
$975$	2.17984			0.0698109
$976$	11.2993	−	14.8691i	0.361683	−	0.475949i
$977$	23.3811			0.748028			0.374014	−	0.927423i	$-0.377981\pi$
$977$	23.3811			0.748028			0.374014	+	0.927423i	$0.377981\pi$
$978$	−7.48140	+	19.9484i	−0.239229	+	0.637878i
$979$	−33.7765	−	33.7765i	−1.07950	−	1.07950i
$980$	−1.99541	+	0.135475i	−0.0637409	+	0.00432758i
$981$	17.7393	−	17.7393i	0.566374	−	0.566374i
$982$	−25.5622	+	11.6181i	−0.815722	+	0.370749i
$983$			7.77765i			0.248068i	0.992278	+	0.124034i	$0.0395833\pi$
$983$			7.77765i			0.248068i	−0.992278	+	0.124034i	$0.960417\pi$
$984$	−18.6089	−	5.57371i	−0.593230	−	0.177683i
$985$			1.56639i			0.0499094i
$986$	3.40402	+	7.48951i	0.108406	+	0.238515i
$987$	4.11698	−	4.11698i	0.131045	−	0.131045i
$988$	7.22586	−	8.27850i	0.229885	−	0.263374i
$989$	−12.2807	−	12.2807i	−0.390504	−	0.390504i
$990$	−12.8227	−	4.80901i	−0.407533	−	0.152840i
$991$	−22.8347			−0.725370			−0.362685	−	0.931912i	$-0.618140\pi$
$991$	−22.8347			−0.725370			−0.362685	+	0.931912i	$0.618140\pi$
$992$	1.64402	−	7.24209i	0.0521977	−	0.229937i
$993$	−6.41674			−0.203629
$994$	6.25803	+	2.34700i	0.198493	+	0.0744424i
$995$	4.85793	+	4.85793i	0.154007	+	0.154007i
$996$	−1.36297	+	1.56153i	−0.0431875	+	0.0494789i
$997$	−8.83919	+	8.83919i	−0.279940	+	0.279940i	−0.833085	−	0.553145i	$-0.813428\pi$
$997$	−8.83919	+	8.83919i	−0.279940	+	0.279940i	0.553145	+	0.833085i	$0.313428\pi$
$998$	0.759558	+	1.67118i	0.0240434	+	0.0529002i
$999$			40.8609i			1.29278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.a.141.20	✓	44
4.3	odd	2		2240.2.bd.a.1681.13		44
16.5	even	4	inner	560.2.bd.a.421.20	yes	44
16.11	odd	4		2240.2.bd.a.561.13		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.20	✓	44	1.1	even	1	trivial
560.2.bd.a.421.20	yes	44	16.5	even	4	inner
2240.2.bd.a.561.13		44	16.11	odd	4
2240.2.bd.a.1681.13		44	4.3	odd	2

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32415 + 0.496608i) q^{2} +(-0.576404 - 0.576404i) q^{3} +(1.50676 + 1.31517i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.477000 - 1.04949i) q^{6} -1.00000i q^{7} +(1.34206 + 2.48976i) q^{8} -2.33552i q^{9} +O(q^{10})\)	\(q+(1.32415 + 0.496608i) q^{2} +(-0.576404 - 0.576404i) q^{3} +(1.50676 + 1.31517i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-0.477000 - 1.04949i) q^{6} -1.00000i q^{7} +(1.34206 + 2.48976i) q^{8} -2.33552i q^{9} +(1.28747 - 0.585162i) q^{10} +(2.93187 - 2.93187i) q^{11} +(-0.110433 - 1.62657i) q^{12} +(-1.89090 - 1.89090i) q^{13} +(0.496608 - 1.32415i) q^{14} -0.815159 q^{15} +(0.540654 + 3.96329i) q^{16} +1.43655 q^{17} +(1.15984 - 3.09258i) q^{18} +(1.45281 + 1.45281i) q^{19} +(1.99541 - 0.135475i) q^{20} +(-0.576404 + 0.576404i) q^{21} +(5.33823 - 2.42625i) q^{22} +8.06848i q^{23} +(0.661539 - 2.20867i) q^{24} -1.00000i q^{25} +(-1.56480 - 3.44287i) q^{26} +(-3.07541 + 3.07541i) q^{27} +(1.31517 - 1.50676i) q^{28} +(2.86338 + 2.86338i) q^{29} +(-1.07939 - 0.404815i) q^{30} -1.31281 q^{31} +(-1.25230 + 5.51650i) q^{32} -3.37988 q^{33} +(1.90221 + 0.713403i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(3.07160 - 3.51906i) q^{36} +(6.64315 - 6.64315i) q^{37} +(1.20227 + 2.64522i) q^{38} +2.17984i q^{39} +(2.70950 + 0.811546i) q^{40} -8.42537i q^{41} +(-1.04949 + 0.477000i) q^{42} +(-1.52206 + 1.52206i) q^{43} +(8.27352 - 0.561717i) q^{44} +(-1.65146 - 1.65146i) q^{45} +(-4.00687 + 10.6839i) q^{46} -7.14252 q^{47} +(1.97282 - 2.59609i) q^{48} -1.00000 q^{49} +(0.496608 - 1.32415i) q^{50} +(-0.828034 - 0.828034i) q^{51} +(-0.362278 - 5.33598i) q^{52} +(-4.13783 + 4.13783i) q^{53} +(-5.59959 + 2.54504i) q^{54} -4.14628i q^{55} +(2.48976 - 1.34206i) q^{56} -1.67481i q^{57} +(2.36958 + 5.21354i) q^{58} +(-5.34634 + 5.34634i) q^{59} +(-1.22825 - 1.07207i) q^{60} +(-3.30135 - 3.30135i) q^{61} +(-1.73836 - 0.651950i) q^{62} -2.33552 q^{63} +(-4.39777 + 6.68279i) q^{64} -2.67413 q^{65} +(-4.47548 - 1.67848i) q^{66} +(5.94425 + 5.94425i) q^{67} +(2.16454 + 1.88931i) q^{68} +(4.65071 - 4.65071i) q^{69} +(-0.585162 - 1.28747i) q^{70} +4.72606i q^{71} +(5.81487 - 3.13439i) q^{72} +14.9033i q^{73} +(12.0956 - 5.49750i) q^{74} +(-0.576404 + 0.576404i) q^{75} +(0.278344 + 4.09973i) q^{76} +(-2.93187 - 2.93187i) q^{77} +(-1.08253 + 2.88645i) q^{78} -10.3784 q^{79} +(3.18477 + 2.42017i) q^{80} -3.46118 q^{81} +(4.18411 - 11.1565i) q^{82} +(-0.898977 - 0.898977i) q^{83} +(-1.62657 + 0.110433i) q^{84} +(1.01580 - 1.01580i) q^{85} +(-2.77131 + 1.25957i) q^{86} -3.30093i q^{87} +(11.2344 + 3.36490i) q^{88} -11.5205i q^{89} +(-1.36666 - 3.00691i) q^{90} +(-1.89090 + 1.89090i) q^{91} +(-10.6114 + 12.1573i) q^{92} +(0.756707 + 0.756707i) q^{93} +(-9.45778 - 3.54703i) q^{94} +2.05459 q^{95} +(3.90156 - 2.45791i) q^{96} -13.1190 q^{97} +(-1.32415 - 0.496608i) q^{98} +(-6.84742 - 6.84742i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) 44 * q + 12 * q^4 + 12 * q^6	\( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) 44 * q + 12 * q^4 + 12 * q^6 - 4 * q^10 + 12 * q^11 - 16 * q^12 + 4 * q^14 + 8 * q^15 - 8 * q^16 - 20 * q^18 + 8 * q^19 - 36 * q^22 + 12 * q^24 + 44 * q^26 - 24 * q^27 - 4 * q^28 + 12 * q^29 - 40 * q^32 - 16 * q^34 + 4 * q^36 + 28 * q^37 - 16 * q^38 + 4 * q^42 - 44 * q^43 - 32 * q^44 - 16 * q^46 - 32 * q^48 - 44 * q^49 + 4 * q^50 - 8 * q^51 + 16 * q^52 - 12 * q^53 - 80 * q^54 + 8 * q^56 + 4 * q^58 + 24 * q^59 - 16 * q^61 + 28 * q^63 + 72 * q^64 - 40 * q^65 - 20 * q^66 - 28 * q^67 + 56 * q^68 + 40 * q^69 + 12 * q^72 + 24 * q^74 - 12 * q^77 + 84 * q^78 - 16 * q^79 + 20 * q^81 + 48 * q^82 + 16 * q^85 - 64 * q^86 + 28 * q^88 - 36 * q^90 - 16 * q^92 + 88 * q^93 + 96 * q^94 - 32 * q^95 + 48 * q^96 + 28 * q^99

Introduction

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