LMFDB - Embedded newform 2010.2.d.d.401.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2010,2,Mod(401,2010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("2010.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2010 = 2 \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2010.d (of order $2$, degree $1$, 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:	$16.0499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 2 x^{17} - 9 x^{16} + 4 x^{15} + 14 x^{14} - 28 x^{13} - 16 x^{12} + \cdots + 59049 $ x^20 - 2x^19 + 2x^18 + 2x^17 - 9x^16 + 4x^15 + 14x^14 - 28x^13 - 16x^12 + 188x^11 - 288x^10 + 564x^9 - 144x^8 - 756x^7 + 1134x^6 + 972x^5 - 6561x^4 + 4374x^3 + 13122x^2 - 39366*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			401.6
Root			$1.16984 + 1.27729i$ of defining polynomial
Character	$\chi$	$=$	2010.401
Dual form			2010.2.d.d.401.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.16984 + 1.27729i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.16984 + 1.27729i) q^{6} -1.10570i q^{7} +1.00000 q^{8} +(-0.262965 - 2.98845i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.16984 + 1.27729i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.16984 + 1.27729i) q^{6} -1.10570i q^{7} +1.00000 q^{8} +(-0.262965 - 2.98845i) q^{9} +1.00000 q^{10} -0.357335 q^{11} +(-1.16984 + 1.27729i) q^{12} +2.58786i q^{13} -1.10570i q^{14} +(-1.16984 + 1.27729i) q^{15} +1.00000 q^{16} -2.15051i q^{17} +(-0.262965 - 2.98845i) q^{18} +5.30796 q^{19} +1.00000 q^{20} +(1.41231 + 1.29349i) q^{21} -0.357335 q^{22} -0.834453i q^{23} +(-1.16984 + 1.27729i) q^{24} +1.00000 q^{25} +2.58786i q^{26} +(4.12476 + 3.16012i) q^{27} -1.10570i q^{28} +3.88309i q^{29} +(-1.16984 + 1.27729i) q^{30} +2.99195i q^{31} +1.00000 q^{32} +(0.418024 - 0.456423i) q^{33} -2.15051i q^{34} -1.10570i q^{35} +(-0.262965 - 2.98845i) q^{36} +2.73596 q^{37} +5.30796 q^{38} +(-3.30546 - 3.02738i) q^{39} +1.00000 q^{40} +6.20196 q^{41} +(1.41231 + 1.29349i) q^{42} -6.90875i q^{43} -0.357335 q^{44} +(-0.262965 - 2.98845i) q^{45} -0.834453i q^{46} -9.75513i q^{47} +(-1.16984 + 1.27729i) q^{48} +5.77742 q^{49} +1.00000 q^{50} +(2.74683 + 2.51574i) q^{51} +2.58786i q^{52} +11.7716 q^{53} +(4.12476 + 3.16012i) q^{54} -0.357335 q^{55} -1.10570i q^{56} +(-6.20945 + 6.77983i) q^{57} +3.88309i q^{58} -9.47707i q^{59} +(-1.16984 + 1.27729i) q^{60} +15.2529i q^{61} +2.99195i q^{62} +(-3.30435 + 0.290761i) q^{63} +1.00000 q^{64} +2.58786i q^{65} +(0.418024 - 0.456423i) q^{66} +(7.79466 + 2.49867i) q^{67} -2.15051i q^{68} +(1.06584 + 0.976173i) q^{69} -1.10570i q^{70} +15.8888i q^{71} +(-0.262965 - 2.98845i) q^{72} -12.0792 q^{73} +2.73596 q^{74} +(-1.16984 + 1.27729i) q^{75} +5.30796 q^{76} +0.395107i q^{77} +(-3.30546 - 3.02738i) q^{78} +9.34458i q^{79} +1.00000 q^{80} +(-8.86170 + 1.57172i) q^{81} +6.20196 q^{82} -4.47970i q^{83} +(1.41231 + 1.29349i) q^{84} -2.15051i q^{85} -6.90875i q^{86} +(-4.95985 - 4.54258i) q^{87} -0.357335 q^{88} -6.97529i q^{89} +(-0.262965 - 2.98845i) q^{90} +2.86141 q^{91} -0.834453i q^{92} +(-3.82160 - 3.50009i) q^{93} -9.75513i q^{94} +5.30796 q^{95} +(-1.16984 + 1.27729i) q^{96} +14.6528i q^{97} +5.77742 q^{98} +(0.0939666 + 1.06788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8}+O(q^{10}) $ 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8	$ 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8} + 20 q^{10} - 2 q^{12} - 2 q^{15} + 20 q^{16} + 16 q^{19} + 20 q^{20} - 2 q^{21} - 2 q^{24} + 20 q^{25} + 10 q^{27} - 2 q^{30} + 20 q^{32} + 2 q^{33} + 20 q^{37} + 16 q^{38} + 16 q^{39} + 20 q^{40} + 8 q^{41} - 2 q^{42} - 2 q^{48} - 48 q^{49} + 20 q^{50} + 32 q^{51} - 36 q^{53} + 10 q^{54} + 16 q^{57} - 2 q^{60} - 4 q^{63} + 20 q^{64} + 2 q^{66} + 16 q^{67} - 28 q^{69} - 4 q^{73} + 20 q^{74} - 2 q^{75} + 16 q^{76} + 16 q^{78} + 20 q^{80} + 12 q^{81} + 8 q^{82} - 2 q^{84} + 32 q^{87} + 12 q^{91} - 12 q^{93} + 16 q^{95} - 2 q^{96} - 48 q^{98} + 12 q^{99}+O(q^{100}) $ 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8 + 20 * q^10 - 2 * q^12 - 2 * q^15 + 20 * q^16 + 16 * q^19 + 20 * q^20 - 2 * q^21 - 2 * q^24 + 20 * q^25 + 10 * q^27 - 2 * q^30 + 20 * q^32 + 2 * q^33 + 20 * q^37 + 16 * q^38 + 16 * q^39 + 20 * q^40 + 8 * q^41 - 2 * q^42 - 2 * q^48 - 48 * q^49 + 20 * q^50 + 32 * q^51 - 36 * q^53 + 10 * q^54 + 16 * q^57 - 2 * q^60 - 4 * q^63 + 20 * q^64 + 2 * q^66 + 16 * q^67 - 28 * q^69 - 4 * q^73 + 20 * q^74 - 2 * q^75 + 16 * q^76 + 16 * q^78 + 20 * q^80 + 12 * q^81 + 8 * q^82 - 2 * q^84 + 32 * q^87 + 12 * q^91 - 12 * q^93 + 16 * q^95 - 2 * q^96 - 48 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2010\mathbb{Z}\right)^\times$.

$n$	$671$	$1141$	$1207$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.16984	+	1.27729i	−0.675405	+	0.737447i
$3$	−1.16984	+	1.27729i	−0.675405	+	0.737447i
$4$	1.00000			0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.16984	+	1.27729i	−0.477584	+	0.521453i
$7$		−	1.10570i		−	0.417917i	−0.977925	−	0.208959i	$-0.932993\pi$
$7$		−	1.10570i		−	0.417917i	0.977925	−	0.208959i	$-0.0670074\pi$
$8$	1.00000			0.353553
$9$	−0.262965	−	2.98845i	−0.0876550	−	0.996151i
$10$	1.00000			0.316228
$11$	−0.357335			−0.107741			−0.0538703	−	0.998548i	$-0.517156\pi$
$11$	−0.357335			−0.107741			−0.0538703	+	0.998548i	$0.517156\pi$
$12$	−1.16984	+	1.27729i	−0.337703	+	0.368723i
$13$			2.58786i			0.717744i	0.933387	+	0.358872i	$0.116839\pi$
$13$			2.58786i			0.717744i	−0.933387	+	0.358872i	$0.883161\pi$
$14$		−	1.10570i		−	0.295512i
$15$	−1.16984	+	1.27729i	−0.302050	+	0.329796i
$16$	1.00000			0.250000
$17$		−	2.15051i		−	0.521574i	−0.965396	−	0.260787i	$-0.916018\pi$
$17$		−	2.15051i		−	0.521574i	0.965396	−	0.260787i	$-0.0839821\pi$
$18$	−0.262965	−	2.98845i	−0.0619814	−	0.704385i
$19$	5.30796			1.21773			0.608865	−	0.793274i	$-0.291625\pi$
$19$	5.30796			1.21773			0.608865	+	0.793274i	$0.291625\pi$
$20$	1.00000			0.223607
$21$	1.41231	+	1.29349i	0.308191	+	0.282263i
$22$	−0.357335			−0.0761841
$23$		−	0.834453i		−	0.173995i	−0.996209	−	0.0869977i	$-0.972273\pi$
$23$		−	0.834453i		−	0.173995i	0.996209	−	0.0869977i	$-0.0277273\pi$
$24$	−1.16984	+	1.27729i	−0.238792	+	0.260727i
$25$	1.00000			0.200000
$26$			2.58786i			0.507522i
$27$	4.12476	+	3.16012i	0.793811	+	0.608165i
$28$		−	1.10570i		−	0.208959i
$29$			3.88309i			0.721071i	0.932745	+	0.360536i	$0.117406\pi$
$29$			3.88309i			0.721071i	−0.932745	+	0.360536i	$0.882594\pi$
$30$	−1.16984	+	1.27729i	−0.213582	+	0.233201i
$31$			2.99195i			0.537370i	0.963228	+	0.268685i	$0.0865890\pi$
$31$			2.99195i			0.537370i	−0.963228	+	0.268685i	$0.913411\pi$
$32$	1.00000			0.176777
$33$	0.418024	−	0.456423i	0.0727686	−	0.0794530i
$34$		−	2.15051i		−	0.368809i
$35$		−	1.10570i		−	0.186898i
$36$	−0.262965	−	2.98845i	−0.0438275	−	0.498075i
$37$	2.73596			0.449790			0.224895	−	0.974383i	$-0.427796\pi$
$37$	2.73596			0.449790			0.224895	+	0.974383i	$0.427796\pi$
$38$	5.30796			0.861065
$39$	−3.30546	−	3.02738i	−0.529298	−	0.484768i
$40$	1.00000			0.158114
$41$	6.20196			0.968583			0.484292	−	0.874907i	$-0.339077\pi$
$41$	6.20196			0.968583			0.484292	+	0.874907i	$0.339077\pi$
$42$	1.41231	+	1.29349i	0.217924	+	0.199590i
$43$		−	6.90875i		−	1.05357i	−0.849997	−	0.526787i	$-0.823397\pi$
$43$		−	6.90875i		−	1.05357i	0.849997	−	0.526787i	$-0.176603\pi$
$44$	−0.357335			−0.0538703
$45$	−0.262965	−	2.98845i	−0.0392005	−	0.445492i
$46$		−	0.834453i		−	0.123033i
$47$		−	9.75513i		−	1.42293i	−0.702720	−	0.711466i	$-0.748031\pi$
$47$		−	9.75513i		−	1.42293i	0.702720	−	0.711466i	$-0.251969\pi$
$48$	−1.16984	+	1.27729i	−0.168851	+	0.184362i
$49$	5.77742			0.825345
$50$	1.00000			0.141421
$51$	2.74683	+	2.51574i	0.384633	+	0.352274i
$52$			2.58786i			0.358872i
$53$	11.7716			1.61695			0.808476	−	0.588529i	$-0.200293\pi$
$53$	11.7716			1.61695			0.808476	+	0.588529i	$0.200293\pi$
$54$	4.12476	+	3.16012i	0.561309	+	0.430038i
$55$	−0.357335			−0.0481831
$56$		−	1.10570i		−	0.147756i
$57$	−6.20945	+	6.77983i	−0.822462	+	0.898011i
$58$			3.88309i			0.509874i
$59$		−	9.47707i		−	1.23381i	−0.787038	−	0.616905i	$-0.788386\pi$
$59$		−	9.47707i		−	1.23381i	0.787038	−	0.616905i	$-0.211614\pi$
$60$	−1.16984	+	1.27729i	−0.151025	+	0.164898i
$61$			15.2529i			1.95293i	0.215677	+	0.976465i	$0.430804\pi$
$61$			15.2529i			1.95293i	−0.215677	+	0.976465i	$0.569196\pi$
$62$			2.99195i			0.379978i
$63$	−3.30435	+	0.290761i	−0.416308	+	0.0366325i
$64$	1.00000			0.125000
$65$			2.58786i			0.320985i
$66$	0.418024	−	0.456423i	0.0514552	−	0.0561817i
$67$	7.79466	+	2.49867i	0.952269	+	0.305261i
$67$	7.79466	+	2.49867i	0.952269	+	0.305261i
$68$		−	2.15051i		−	0.260787i
$69$	1.06584	+	0.976173i	0.128312	+	0.117517i
$70$		−	1.10570i		−	0.132157i
$71$			15.8888i			1.88566i	0.333279	+	0.942828i	$0.391845\pi$
$71$			15.8888i			1.88566i	−0.333279	+	0.942828i	$0.608155\pi$
$72$	−0.262965	−	2.98845i	−0.0309907	−	0.352193i
$73$	−12.0792			−1.41377			−0.706883	−	0.707330i	$-0.749899\pi$
$73$	−12.0792			−1.41377			−0.706883	+	0.707330i	$0.749899\pi$
$74$	2.73596			0.318049
$75$	−1.16984	+	1.27729i	−0.135081	+	0.147489i
$76$	5.30796			0.608865
$77$			0.395107i			0.0450266i
$78$	−3.30546	−	3.02738i	−0.374270	−	0.342783i
$79$			9.34458i			1.05135i	0.850686	+	0.525674i	$0.176187\pi$
$79$			9.34458i			1.05135i	−0.850686	+	0.525674i	$0.823813\pi$
$80$	1.00000			0.111803
$81$	−8.86170	+	1.57172i	−0.984633	+	0.174635i
$82$	6.20196			0.684892
$83$		−	4.47970i		−	0.491711i	−0.969307	−	0.245855i	$-0.920931\pi$
$83$		−	4.47970i		−	0.491711i	0.969307	−	0.245855i	$-0.0790689\pi$
$84$	1.41231	+	1.29349i	0.154096	+	0.141132i
$85$		−	2.15051i		−	0.233255i
$86$		−	6.90875i		−	0.744989i
$87$	−4.95985	−	4.54258i	−0.531752	−	0.487015i
$88$	−0.357335			−0.0380921
$89$		−	6.97529i		−	0.739379i	−0.929155	−	0.369689i	$-0.879464\pi$
$89$		−	6.97529i		−	0.739379i	0.929155	−	0.369689i	$-0.120536\pi$
$90$	−0.262965	−	2.98845i	−0.0277189	−	0.315011i
$91$	2.86141			0.299957
$92$		−	0.834453i		−	0.0869977i
$93$	−3.82160	−	3.50009i	−0.396281	−	0.362942i
$94$		−	9.75513i		−	1.00617i
$95$	5.30796			0.544585
$96$	−1.16984	+	1.27729i	−0.119396	+	0.130363i
$97$			14.6528i			1.48777i	0.668310	+	0.743883i	$0.267018\pi$
$97$			14.6528i			1.48777i	−0.668310	+	0.743883i	$0.732982\pi$
$98$	5.77742			0.583607
$99$	0.0939666	+	1.06788i	0.00944400	+	0.107326i
$100$	1.00000			0.100000
$101$	−4.74192			−0.471838			−0.235919	−	0.971773i	$-0.575810\pi$
$101$	−4.74192			−0.471838			−0.235919	+	0.971773i	$0.575810\pi$
$102$	2.74683	+	2.51574i	0.271977	+	0.249095i
$103$	18.2963			1.80279			0.901396	−	0.432996i	$-0.142544\pi$
$103$	18.2963			1.80279			0.901396	+	0.432996i	$0.142544\pi$
$104$			2.58786i			0.253761i
$105$	1.41231	+	1.29349i	0.137827	+	0.126232i
$106$	11.7716			1.14336
$107$		−	14.5849i		−	1.40998i	−0.709219	−	0.704988i	$-0.750952\pi$
$107$		−	14.5849i		−	1.40998i	0.709219	−	0.704988i	$-0.249048\pi$
$108$	4.12476	+	3.16012i	0.396905	+	0.304082i
$109$			1.55580i			0.149018i	0.997220	+	0.0745091i	$0.0237390\pi$
$109$			1.55580i			0.149018i	−0.997220	+	0.0745091i	$0.976261\pi$
$110$	−0.357335			−0.0340706
$111$	−3.20063	+	3.49463i	−0.303790	+	0.331696i
$112$		−	1.10570i		−	0.104479i
$113$	−9.97721			−0.938577			−0.469288	−	0.883045i	$-0.655490\pi$
$113$	−9.97721			−0.938577			−0.469288	+	0.883045i	$0.655490\pi$
$114$	−6.20945	+	6.77983i	−0.581568	+	0.634990i
$115$		−	0.834453i		−	0.0778131i
$116$			3.88309i			0.360536i
$117$	7.73371	−	0.680517i	0.714981	−	0.0629138i
$118$		−	9.47707i		−	0.872435i
$119$	−2.37782			−0.217975
$120$	−1.16984	+	1.27729i	−0.106791	+	0.116601i
$121$	−10.8723			−0.988392
$122$			15.2529i			1.38093i
$123$	−7.25528	+	7.92173i	−0.654186	+	0.714278i
$124$			2.99195i			0.268685i
$125$	1.00000			0.0894427
$126$	−3.30435	+	0.290761i	−0.294374	+	0.0259031i
$127$	−22.0307			−1.95491			−0.977454	−	0.211148i	$-0.932280\pi$
$127$	−22.0307			−1.95491			−0.977454	+	0.211148i	$0.932280\pi$
$128$	1.00000			0.0883883
$129$	8.82451	+	8.08210i	0.776955	+	0.711590i
$130$			2.58786i			0.226971i
$131$		−	3.60469i		−	0.314943i	−0.987524	−	0.157472i	$-0.949666\pi$
$131$		−	3.60469i		−	0.314943i	0.987524	−	0.157472i	$-0.0503343\pi$
$132$	0.418024	−	0.456423i	0.0363843	−	0.0397265i
$133$		−	5.86904i		−	0.508910i
$134$	7.79466	+	2.49867i	0.673356	+	0.215852i
$135$	4.12476	+	3.16012i	0.355003	+	0.271980i
$136$		−	2.15051i		−	0.184404i
$137$	22.9849			1.96373			0.981865	−	0.189583i	$-0.0607136\pi$
$137$	22.9849			1.96373			0.981865	+	0.189583i	$0.0607136\pi$
$138$	1.06584	+	0.976173i	0.0907305	+	0.0830974i
$139$		−	8.81597i		−	0.747761i	−0.927477	−	0.373881i	$-0.878027\pi$
$139$		−	8.81597i		−	0.747761i	0.927477	−	0.373881i	$-0.121973\pi$
$140$		−	1.10570i		−	0.0934491i
$141$	12.4602	+	11.4119i	1.04934	+	0.961056i
$142$			15.8888i			1.33336i
$143$		−	0.924735i		−	0.0773302i
$144$	−0.262965	−	2.98845i	−0.0219137	−	0.249038i
$145$			3.88309i			0.322473i
$146$	−12.0792			−0.999684
$147$	−6.75863	+	7.37947i	−0.557443	+	0.608648i
$148$	2.73596			0.224895
$149$			10.1468i			0.831256i	0.909535	+	0.415628i	$0.136438\pi$
$149$			10.1468i			0.831256i	−0.909535	+	0.415628i	$0.863562\pi$
$150$	−1.16984	+	1.27729i	−0.0955168	+	0.104291i
$151$	1.34157			0.109176			0.0545879	−	0.998509i	$-0.482615\pi$
$151$	1.34157			0.109176			0.0545879	+	0.998509i	$0.482615\pi$
$152$	5.30796			0.430533
$153$	−6.42669	+	0.565508i	−0.519567	+	0.0457186i
$154$			0.395107i			0.0318386i
$155$			2.99195i			0.240319i
$156$	−3.30546	−	3.02738i	−0.264649	−	0.242384i
$157$	16.5368			1.31978			0.659888	−	0.751364i	$-0.270604\pi$
$157$	16.5368			1.31978			0.659888	+	0.751364i	$0.270604\pi$
$158$			9.34458i			0.743415i
$159$	−13.7708	+	15.0358i	−1.09210	+	1.19242i
$160$	1.00000			0.0790569
$161$	−0.922658			−0.0727156
$162$	−8.86170	+	1.57172i	−0.696241	+	0.123486i
$163$	−14.0394			−1.09965			−0.549825	−	0.835280i	$-0.685306\pi$
$163$	−14.0394			−1.09965			−0.549825	+	0.835280i	$0.685306\pi$
$164$	6.20196			0.484292
$165$	0.418024	−	0.456423i	0.0325431	−	0.0355324i
$166$		−	4.47970i		−	0.347692i
$167$			9.21767i			0.713285i	0.934241	+	0.356642i	$0.116079\pi$
$167$			9.21767i			0.713285i	−0.934241	+	0.356642i	$0.883921\pi$
$168$	1.41231	+	1.29349i	0.108962	+	0.0997952i
$169$	6.30297			0.484844
$170$		−	2.15051i		−	0.164936i
$171$	−1.39581	−	15.8626i	−0.106740	−	1.21304i
$172$		−	6.90875i		−	0.526787i
$173$			6.73609i			0.512135i	0.966659	+	0.256068i	$0.0824270\pi$
$173$			6.73609i			0.512135i	−0.966659	+	0.256068i	$0.917573\pi$
$174$	−4.95985	−	4.54258i	−0.376005	−	0.344372i
$175$		−	1.10570i		−	0.0835834i
$176$	−0.357335			−0.0269352
$177$	12.1050	+	11.0866i	0.909868	+	0.833321i
$178$		−	6.97529i		−	0.522820i
$179$	−19.0886			−1.42675			−0.713374	−	0.700784i	$-0.752834\pi$
$179$	−19.0886			−1.42675			−0.713374	+	0.700784i	$0.752834\pi$
$180$	−0.262965	−	2.98845i	−0.0196002	−	0.222746i
$181$	12.3626			0.918908			0.459454	−	0.888201i	$-0.348045\pi$
$181$	12.3626			0.918908			0.459454	+	0.888201i	$0.348045\pi$
$182$	2.86141			0.212102
$183$	−19.4824	−	17.8434i	−1.44018	−	1.31902i
$184$		−	0.834453i		−	0.0615167i
$185$	2.73596			0.201152
$186$	−3.82160	−	3.50009i	−0.280213	−	0.256639i
$187$			0.768452i			0.0561947i
$188$		−	9.75513i		−	0.711466i
$189$	3.49416	−	4.56077i	0.254162	−	0.331747i
$190$	5.30796			0.385080
$191$	11.6132			0.840300			0.420150	−	0.907455i	$-0.361977\pi$
$191$	11.6132			0.840300			0.420150	+	0.907455i	$0.361977\pi$
$192$	−1.16984	+	1.27729i	−0.0844257	+	0.0921808i
$193$	−0.896082			−0.0645014			−0.0322507	−	0.999480i	$-0.510267\pi$
$193$	−0.896082			−0.0645014			−0.0322507	+	0.999480i	$0.510267\pi$
$194$			14.6528i			1.05201i
$195$	−3.30546	−	3.02738i	−0.236709	−	0.216795i
$196$	5.77742			0.412673
$197$	4.56961			0.325571			0.162785	−	0.986661i	$-0.447952\pi$
$197$	4.56961			0.325571			0.162785	+	0.986661i	$0.447952\pi$
$198$	0.0939666	+	1.06788i	0.00667792	+	0.0758909i
$199$	1.24326			0.0881324			0.0440662	−	0.999029i	$-0.485969\pi$
$199$	1.24326			0.0881324			0.0440662	+	0.999029i	$0.485969\pi$
$200$	1.00000			0.0707107
$201$	−12.3100	+	7.03304i	−0.868281	+	0.496073i
$202$	−4.74192			−0.333640
$203$	4.29355			0.301348
$204$	2.74683	+	2.51574i	0.192317	+	0.176137i
$205$	6.20196			0.433164
$206$	18.2963			1.27477
$207$	−2.49372	+	0.219432i	−0.173326	+	0.0152516i
$208$			2.58786i			0.179436i
$209$	−1.89672			−0.131199
$210$	1.41231	+	1.29349i	0.0974587	+	0.0892595i
$211$	1.28602			0.0885332			0.0442666	−	0.999020i	$-0.485905\pi$
$211$	1.28602			0.0885332			0.0442666	+	0.999020i	$0.485905\pi$
$212$	11.7716			0.808476
$213$	−20.2947	−	18.5873i	−1.39057	−	1.27358i
$214$		−	14.5849i		−	0.997003i
$215$		−	6.90875i		−	0.471173i
$216$	4.12476	+	3.16012i	0.280654	+	0.215019i
$217$	3.30821			0.224576
$218$			1.55580i			0.105372i
$219$	14.1307	−	15.4287i	0.954865	−	1.04258i
$220$	−0.357335			−0.0240915
$221$	5.56521			0.374357
$222$	−3.20063	+	3.49463i	−0.214812	+	0.234544i
$223$	−23.6116			−1.58115			−0.790574	−	0.612366i	$-0.790218\pi$
$223$	−23.6116			−1.58115			−0.790574	+	0.612366i	$0.790218\pi$
$224$		−	1.10570i		−	0.0738780i
$225$	−0.262965	−	2.98845i	−0.0175310	−	0.199230i
$226$	−9.97721			−0.663674
$227$		−	16.9703i		−	1.12636i	−0.826335	−	0.563178i	$-0.809578\pi$
$227$		−	16.9703i		−	1.12636i	0.826335	−	0.563178i	$-0.190422\pi$
$228$	−6.20945	+	6.77983i	−0.411231	+	0.449005i
$229$		−	19.9276i		−	1.31685i	−0.752646	−	0.658425i	$-0.771223\pi$
$229$		−	19.9276i		−	1.31685i	0.752646	−	0.658425i	$-0.228777\pi$
$230$		−	0.834453i		−	0.0550222i
$231$	−0.504668	−	0.462211i	−0.0332047	−	0.0304112i
$232$			3.88309i			0.254937i
$233$	−25.2606			−1.65488			−0.827440	−	0.561555i	$-0.810203\pi$
$233$	−25.2606			−1.65488			−0.827440	+	0.561555i	$0.810203\pi$
$234$	7.73371	−	0.680517i	0.505568	−	0.0444868i
$235$		−	9.75513i		−	0.636355i
$236$		−	9.47707i		−	0.616905i
$237$	−11.9358	−	10.9316i	−0.775312	−	0.710086i
$238$	−2.37782			−0.154131
$239$	−4.75090			−0.307310			−0.153655	−	0.988125i	$-0.549104\pi$
$239$	−4.75090			−0.307310			−0.153655	+	0.988125i	$0.549104\pi$
$240$	−1.16984	+	1.27729i	−0.0755126	+	0.0824490i
$241$	18.6505			1.20139			0.600693	−	0.799480i	$-0.294891\pi$
$241$	18.6505			1.20139			0.600693	+	0.799480i	$0.294891\pi$
$242$	−10.8723			−0.698899
$243$	8.35919	−	13.1577i	0.536243	−	0.844064i
$244$			15.2529i			0.976465i
$245$	5.77742			0.369106
$246$	−7.25528	+	7.92173i	−0.462580	+	0.505071i
$247$			13.7363i			0.874018i
$248$			2.99195i			0.189989i
$249$	5.72190	+	5.24052i	0.362611	+	0.332104i
$250$	1.00000			0.0632456
$251$	−8.50442			−0.536794			−0.268397	−	0.963308i	$-0.586494\pi$
$251$	−8.50442			−0.536794			−0.268397	+	0.963308i	$0.586494\pi$
$252$	−3.30435	+	0.290761i	−0.208154	+	0.0183162i
$253$			0.298179i			0.0187464i
$254$	−22.0307			−1.38233
$255$	2.74683	+	2.51574i	0.172013	+	0.157542i
$256$	1.00000			0.0625000
$257$		−	21.3562i		−	1.33217i	−0.745878	−	0.666083i	$-0.767970\pi$
$257$		−	21.3562i		−	1.33217i	0.745878	−	0.666083i	$-0.232030\pi$
$258$	8.82451	+	8.08210i	0.549390	+	0.503170i
$259$		−	3.02517i		−	0.187975i
$260$			2.58786i			0.160492i
$261$	11.6044	−	1.02112i	0.718296	−	0.0632055i
$262$		−	3.60469i		−	0.222699i
$263$		−	16.0248i		−	0.988134i	−0.869424	−	0.494067i	$-0.835510\pi$
$263$		−	16.0248i		−	0.988134i	0.869424	−	0.494067i	$-0.164490\pi$
$264$	0.418024	−	0.456423i	0.0257276	−	0.0280909i
$265$	11.7716			0.723123
$266$		−	5.86904i		−	0.359854i
$267$	8.90950	+	8.15995i	0.545252	+	0.499381i
$268$	7.79466	+	2.49867i	0.476134	+	0.152630i
$269$			5.66646i			0.345490i	0.984967	+	0.172745i	$0.0552637\pi$
$269$			5.66646i			0.345490i	−0.984967	+	0.172745i	$0.944736\pi$
$270$	4.12476	+	3.16012i	0.251025	+	0.192319i
$271$		−	14.0485i		−	0.853388i	−0.904396	−	0.426694i	$-0.859678\pi$
$271$		−	14.0485i		−	0.853388i	0.904396	−	0.426694i	$-0.140322\pi$
$272$		−	2.15051i		−	0.130394i
$273$	−3.34738	+	3.65487i	−0.202593	+	0.221203i
$274$	22.9849			1.38857
$275$	−0.357335			−0.0215481
$276$	1.06584	+	0.976173i	0.0641562	+	0.0587587i
$277$	−25.5204			−1.53337			−0.766685	−	0.642023i	$-0.778095\pi$
$277$	−25.5204			−1.53337			−0.766685	+	0.642023i	$0.778095\pi$
$278$		−	8.81597i		−	0.528747i
$279$	8.94129	−	0.786777i	0.535301	−	0.0471031i
$280$		−	1.10570i		−	0.0660785i
$281$	−10.2431			−0.611053			−0.305526	−	0.952184i	$-0.598832\pi$
$281$	−10.2431			−0.611053			−0.305526	+	0.952184i	$0.598832\pi$
$282$	12.4602	+	11.4119i	0.741993	+	0.679569i
$283$	−8.28611			−0.492558			−0.246279	−	0.969199i	$-0.579208\pi$
$283$	−8.28611			−0.492558			−0.246279	+	0.969199i	$0.579208\pi$
$284$			15.8888i			0.942828i
$285$	−6.20945	+	6.77983i	−0.367816	+	0.401603i
$286$		−	0.924735i		−	0.0546807i
$287$		−	6.85753i		−	0.404787i
$288$	−0.262965	−	2.98845i	−0.0154954	−	0.176096i
$289$	12.3753			0.727960
$290$			3.88309i			0.228023i
$291$	−18.7159	−	17.1414i	−1.09715	−	1.00484i
$292$	−12.0792			−0.706883
$293$		−	26.8620i		−	1.56930i	−0.619941	−	0.784648i	$-0.712844\pi$
$293$		−	26.8620i		−	1.56930i	0.619941	−	0.784648i	$-0.287156\pi$
$294$	−6.75863	+	7.37947i	−0.394172	+	0.430379i
$295$		−	9.47707i		−	0.551776i
$296$	2.73596			0.159025
$297$	−1.47392	−	1.12922i	−0.0855257	−	0.0655241i
$298$			10.1468i			0.587787i
$299$	2.15945			0.124884
$300$	−1.16984	+	1.27729i	−0.0675405	+	0.0737447i
$301$	−7.63903			−0.440306
$302$	1.34157			0.0771989
$303$	5.54727	−	6.05683i	0.318682	−	0.347956i
$304$	5.30796			0.304433
$305$			15.2529i			0.873377i
$306$	−6.42669	+	0.565508i	−0.367389	+	0.0323279i
$307$	−5.37690			−0.306876			−0.153438	−	0.988158i	$-0.549034\pi$
$307$	−5.37690			−0.306876			−0.153438	+	0.988158i	$0.549034\pi$
$308$			0.395107i			0.0225133i
$309$	−21.4037	+	23.3698i	−1.21762	+	1.32946i
$310$			2.99195i			0.169931i
$311$	−12.7194			−0.721249			−0.360625	−	0.932711i	$-0.617436\pi$
$311$	−12.7194			−0.721249			−0.360625	+	0.932711i	$0.617436\pi$
$312$	−3.30546	−	3.02738i	−0.187135	−	0.171391i
$313$			1.01542i			0.0573951i	0.999588	+	0.0286975i	$0.00913596\pi$
$313$			1.01542i			0.0573951i	−0.999588	+	0.0286975i	$0.990864\pi$
$314$	16.5368			0.933223
$315$	−3.30435	+	0.290761i	−0.186179	+	0.0163826i
$316$			9.34458i			0.525674i
$317$			12.9163i			0.725453i	0.931896	+	0.362726i	$0.118154\pi$
$317$			12.9163i			0.725453i	−0.931896	+	0.362726i	$0.881846\pi$
$318$	−13.7708	+	15.0358i	−0.772230	+	0.843165i
$319$		−	1.38756i		−	0.0776887i
$320$	1.00000			0.0559017
$321$	18.6292	+	17.0620i	1.03978	+	0.952305i
$322$	−0.922658			−0.0514177
$323$		−	11.4148i		−	0.635137i
$324$	−8.86170	+	1.57172i	−0.492317	+	0.0873176i
$325$			2.58786i			0.143549i
$326$	−14.0394			−0.777571
$327$	−1.98721	−	1.82003i	−0.109893	−	0.100648i
$328$	6.20196			0.342446
$329$	−10.7863			−0.594668
$330$	0.418024	−	0.456423i	0.0230115	−	0.0251252i
$331$		−	0.685019i		−	0.0376520i	−0.999823	−	0.0188260i	$-0.994007\pi$
$331$		−	0.685019i		−	0.0376520i	0.999823	−	0.0188260i	$-0.00599286\pi$
$332$		−	4.47970i		−	0.245855i
$333$	−0.719462	−	8.17630i	−0.0394263	−	0.448058i
$334$			9.21767i			0.504368i
$335$	7.79466	+	2.49867i	0.425868	+	0.136517i
$336$	1.41231	+	1.29349i	0.0770479	+	0.0705659i
$337$			5.93774i			0.323449i	0.986836	+	0.161725i	$0.0517056\pi$
$337$			5.93774i			0.323449i	−0.986836	+	0.161725i	$0.948294\pi$
$338$	6.30297			0.342836
$339$	11.6717	−	12.7438i	0.633920	−	0.692150i
$340$		−	2.15051i		−	0.116628i
$341$		−	1.06913i		−	0.0578965i
$342$	−1.39581	−	15.8626i	−0.0754766	−	0.857751i
$343$		−	14.1280i		−	0.762843i
$344$		−	6.90875i		−	0.372495i
$345$	1.06584	+	0.976173i	0.0573830	+	0.0525554i
$346$			6.73609i			0.362134i
$347$	−8.25511			−0.443158			−0.221579	−	0.975142i	$-0.571121\pi$
$347$	−8.25511			−0.443158			−0.221579	+	0.975142i	$0.571121\pi$
$348$	−4.95985	−	4.54258i	−0.265876	−	0.243508i
$349$	−12.0824			−0.646756			−0.323378	−	0.946270i	$-0.604819\pi$
$349$	−12.0824			−0.646756			−0.323378	+	0.946270i	$0.604819\pi$
$350$		−	1.10570i		−	0.0591024i
$351$	−8.17795	+	10.6743i	−0.436507	+	0.569753i
$352$	−0.357335			−0.0190460
$353$	−31.3728			−1.66980			−0.834902	−	0.550398i	$-0.814476\pi$
$353$	−31.3728			−1.66980			−0.834902	+	0.550398i	$0.814476\pi$
$354$	12.1050	+	11.0866i	0.643374	+	0.589247i
$355$			15.8888i			0.843291i
$356$		−	6.97529i		−	0.369689i
$357$	2.78167	−	3.03718i	0.147221	−	0.160745i
$358$	−19.0886			−1.00886
$359$			25.9535i			1.36977i	0.728649	+	0.684887i	$0.240148\pi$
$359$			25.9535i			1.36977i	−0.728649	+	0.684887i	$0.759852\pi$
$360$	−0.262965	−	2.98845i	−0.0138595	−	0.157505i
$361$	9.17446			0.482867
$362$	12.3626			0.649766
$363$	12.7188	−	13.8871i	0.667565	−	0.728886i
$364$	2.86141			0.149979
$365$	−12.0792			−0.632255
$366$	−19.4824	−	17.8434i	−1.01836	−	0.932688i
$367$		−	5.72011i		−	0.298587i	−0.988793	−	0.149294i	$-0.952300\pi$
$367$		−	5.72011i		−	0.298587i	0.988793	−	0.149294i	$-0.0477000\pi$
$368$		−	0.834453i		−	0.0434988i
$369$	−1.63090	−	18.5343i	−0.0849011	−	0.964855i
$370$	2.73596			0.142236
$371$		−	13.0159i		−	0.675752i
$372$	−3.82160	−	3.50009i	−0.198141	−	0.181471i
$373$		−	19.4974i		−	1.00953i	−0.863255	−	0.504767i	$-0.831578\pi$
$373$		−	19.4974i		−	1.00953i	0.863255	−	0.504767i	$-0.168422\pi$
$374$			0.768452i			0.0397357i
$375$	−1.16984	+	1.27729i	−0.0604101	+	0.0659592i
$376$		−	9.75513i		−	0.503083i
$377$	−10.0489			−0.517545
$378$	3.49416	−	4.56077i	0.179720	−	0.234581i
$379$		−	7.66723i		−	0.393839i	−0.980420	−	0.196920i	$-0.936906\pi$
$379$		−	7.66723i		−	0.393839i	0.980420	−	0.196920i	$-0.0630938\pi$
$380$	5.30796			0.272293
$381$	25.7723	−	28.1397i	1.32036	−	1.44164i
$382$	11.6132			0.594182
$383$	−19.2226			−0.982229			−0.491115	−	0.871095i	$-0.663410\pi$
$383$	−19.2226			−0.982229			−0.491115	+	0.871095i	$0.663410\pi$
$384$	−1.16984	+	1.27729i	−0.0596980	+	0.0651817i
$385$			0.395107i			0.0201365i
$386$	−0.896082			−0.0456094
$387$	−20.6465	+	1.81676i	−1.04952	+	0.0923510i
$388$			14.6528i			0.743883i
$389$			28.5043i			1.44522i	0.691254	+	0.722611i	$0.257058\pi$
$389$			28.5043i			1.44522i	−0.691254	+	0.722611i	$0.742942\pi$
$390$	−3.30546	−	3.02738i	−0.167379	−	0.153297i
$391$	−1.79450			−0.0907515
$392$	5.77742			0.291804
$393$	4.60425	+	4.21690i	0.232254	+	0.212714i
$394$	4.56961			0.230213
$395$			9.34458i			0.470177i
$396$	0.0939666	+	1.06788i	0.00472200	+	0.0536630i
$397$	8.75968			0.439636			0.219818	−	0.975541i	$-0.429454\pi$
$397$	8.75968			0.439636			0.219818	+	0.975541i	$0.429454\pi$
$398$	1.24326			0.0623190
$399$	7.49649	+	6.86581i	0.375294	+	0.343721i
$400$	1.00000			0.0500000
$401$	−9.07728			−0.453298			−0.226649	−	0.973977i	$-0.572777\pi$
$401$	−9.07728			−0.453298			−0.226649	+	0.973977i	$0.572777\pi$
$402$	−12.3100	+	7.03304i	−0.613967	+	0.350776i
$403$	−7.74275			−0.385694
$404$	−4.74192			−0.235919
$405$	−8.86170	+	1.57172i	−0.440341	+	0.0780992i
$406$	4.29355			0.213085
$407$	−0.977656			−0.0484606
$408$	2.74683	+	2.51574i	0.135988	+	0.124548i
$409$		−	20.5072i		−	1.01402i	−0.861941	−	0.507008i	$-0.830751\pi$
$409$		−	20.5072i		−	1.01402i	0.861941	−	0.507008i	$-0.169249\pi$
$410$	6.20196			0.306293
$411$	−26.8885	+	29.3585i	−1.32631	+	1.44815i
$412$	18.2963			0.901396
$413$	−10.4788			−0.515630
$414$	−2.49372	+	0.219432i	−0.122560	+	0.0107845i
$415$		−	4.47970i		−	0.219900i
$416$			2.58786i			0.126880i
$417$	11.2606	+	10.3132i	0.551434	+	0.505042i
$418$	−1.89672			−0.0927717
$419$		−	5.35904i		−	0.261806i	−0.991395	−	0.130903i	$-0.958212\pi$
$419$		−	5.35904i		−	0.261806i	0.991395	−	0.130903i	$-0.0417877\pi$
$420$	1.41231	+	1.29349i	0.0689137	+	0.0631160i
$421$	−4.50590			−0.219604			−0.109802	−	0.993953i	$-0.535022\pi$
$421$	−4.50590			−0.219604			−0.109802	+	0.993953i	$0.535022\pi$
$422$	1.28602			0.0626025
$423$	−29.1528	+	2.56526i	−1.41746	+	0.124727i
$424$	11.7716			0.571679
$425$		−	2.15051i		−	0.104315i
$426$	−20.2947	−	18.5873i	−0.983282	−	0.900559i
$427$	16.8652			0.816163
$428$		−	14.5849i		−	0.704988i
$429$	1.18116	+	1.08179i	0.0570269	+	0.0522292i
$430$		−	6.90875i		−	0.333169i
$431$		−	15.8178i		−	0.761917i	−0.924592	−	0.380959i	$-0.875594\pi$
$431$		−	15.8178i		−	0.761917i	0.924592	−	0.380959i	$-0.124406\pi$
$432$	4.12476	+	3.16012i	0.198453	+	0.152041i
$433$		−	3.60619i		−	0.173302i	−0.996239	−	0.0866512i	$-0.972383\pi$
$433$		−	3.60619i		−	0.173302i	0.996239	−	0.0866512i	$-0.0276166\pi$
$434$	3.30821			0.158799
$435$	−4.95985	−	4.54258i	−0.237807	−	0.217800i
$436$			1.55580i			0.0745091i
$437$		−	4.42924i		−	0.211879i
$438$	14.1307	−	15.4287i	0.675192	−	0.737213i
$439$	−2.26867			−0.108278			−0.0541389	−	0.998533i	$-0.517241\pi$
$439$	−2.26867			−0.108278			−0.0541389	+	0.998533i	$0.517241\pi$
$440$	−0.357335			−0.0170353
$441$	−1.51926	−	17.2655i	−0.0723456	−	0.822169i
$442$	5.56521			0.264710
$443$	−9.02705			−0.428888			−0.214444	−	0.976736i	$-0.568794\pi$
$443$	−9.02705			−0.428888			−0.214444	+	0.976736i	$0.568794\pi$
$444$	−3.20063	+	3.49463i	−0.151895	+	0.165848i
$445$		−	6.97529i		−	0.330660i
$446$	−23.6116			−1.11804
$447$	−12.9604	−	11.8701i	−0.613007	−	0.561435i
$448$		−	1.10570i		−	0.0522396i
$449$			18.8339i			0.888827i	0.895822	+	0.444413i	$0.146588\pi$
$449$			18.8339i			0.888827i	−0.895822	+	0.444413i	$0.853412\pi$
$450$	−0.262965	−	2.98845i	−0.0123963	−	0.140877i
$451$	−2.21618			−0.104356
$452$	−9.97721			−0.469288
$453$	−1.56942	+	1.71359i	−0.0737379	+	0.0805113i
$454$		−	16.9703i		−	0.796454i
$455$	2.86141			0.134145
$456$	−6.20945	+	6.77983i	−0.290784	+	0.317495i
$457$	7.12233			0.333169			0.166584	−	0.986027i	$-0.446726\pi$
$457$	7.12233			0.333169			0.166584	+	0.986027i	$0.446726\pi$
$458$		−	19.9276i		−	0.931154i
$459$	6.79585	−	8.87032i	0.317203	−	0.414031i
$460$		−	0.834453i		−	0.0389066i
$461$		−	1.06535i		−	0.0496181i	−0.999692	−	0.0248090i	$-0.992102\pi$
$461$		−	1.06535i		−	0.0496181i	0.999692	−	0.0248090i	$-0.00789777\pi$
$462$	−0.504668	−	0.462211i	−0.0234793	−	0.0215040i
$463$		−	14.4915i		−	0.673478i	−0.941598	−	0.336739i	$-0.890676\pi$
$463$		−	14.4915i		−	0.673478i	0.941598	−	0.336739i	$-0.109324\pi$
$464$			3.88309i			0.180268i
$465$	−3.82160	−	3.50009i	−0.177222	−	0.162313i
$466$	−25.2606			−1.17018
$467$			14.8441i			0.686903i	0.939170	+	0.343451i	$0.111596\pi$
$467$			14.8441i			0.686903i	−0.939170	+	0.343451i	$0.888404\pi$
$468$	7.73371	−	0.680517i	0.357491	−	0.0314569i
$469$	2.76279	−	8.61859i	0.127574	−	0.397969i
$470$		−	9.75513i		−	0.449971i
$471$	−19.3453	+	21.1223i	−0.891384	+	0.973265i
$472$		−	9.47707i		−	0.436217i
$473$			2.46874i			0.113513i
$474$	−11.9358	−	10.9316i	−0.548229	−	0.502106i
$475$	5.30796			0.243546
$476$	−2.37782			−0.108987
$477$	−3.09551	−	35.1788i	−0.141734	−	1.61073i
$478$	−4.75090			−0.217301
$479$		−	3.58488i		−	0.163797i	−0.996641	−	0.0818986i	$-0.973902\pi$
$479$		−	3.58488i		−	0.163797i	0.996641	−	0.0818986i	$-0.0260984\pi$
$480$	−1.16984	+	1.27729i	−0.0533955	+	0.0583003i
$481$			7.08030i			0.322834i
$482$	18.6505			0.849508
$483$	1.07936	−	1.17851i	0.0491125	−	0.0536239i
$484$	−10.8723			−0.494196
$485$			14.6528i			0.665349i
$486$	8.35919	−	13.1577i	0.379181	−	0.596843i
$487$		−	40.8238i		−	1.84990i	−0.380088	−	0.924951i	$-0.624106\pi$
$487$		−	40.8238i		−	1.84990i	0.380088	−	0.924951i	$-0.375894\pi$
$488$			15.2529i			0.690465i
$489$	16.4238	−	17.9325i	0.742710	−	0.810934i
$490$	5.77742			0.260997
$491$		−	5.82397i		−	0.262832i	−0.991327	−	0.131416i	$-0.958048\pi$
$491$		−	5.82397i		−	0.262832i	0.991327	−	0.131416i	$-0.0419524\pi$
$492$	−7.25528	+	7.92173i	−0.327093	+	0.357139i
$493$	8.35060			0.376092
$494$			13.7363i			0.618024i
$495$	0.0939666	+	1.06788i	0.00422349	+	0.0479976i
$496$			2.99195i			0.134342i
$497$	17.5683			0.788048
$498$	5.72190	+	5.24052i	0.256404	+	0.234833i
$499$			26.6192i			1.19164i	0.803119	+	0.595819i	$0.203172\pi$
$499$			26.6192i			1.19164i	−0.803119	+	0.595819i	$0.796828\pi$
$500$	1.00000			0.0447214
$501$	−11.7737	−	10.7832i	−0.526009	−	0.481756i
$502$	−8.50442			−0.379571
$503$	1.50927			0.0672951			0.0336475	−	0.999434i	$-0.489288\pi$
$503$	1.50927			0.0672951			0.0336475	+	0.999434i	$0.489288\pi$
$504$	−3.30435	+	0.290761i	−0.147187	+	0.0129515i
$505$	−4.74192			−0.211013
$506$			0.298179i			0.0132557i
$507$	−7.37344	+	8.05075i	−0.327466	+	0.357546i
$508$	−22.0307			−0.977454
$509$			26.3815i			1.16934i	0.811272	+	0.584669i	$0.198775\pi$
$509$			26.3815i			1.16934i	−0.811272	+	0.584669i	$0.801225\pi$
$510$	2.74683	+	2.51574i	0.121632	+	0.111399i
$511$			13.3561i			0.590837i
$512$	1.00000			0.0441942
$513$	21.8941	+	16.7738i	0.966647	+	0.740581i
$514$		−	21.3562i		−	0.941984i
$515$	18.2963			0.806233
$516$	8.82451	+	8.08210i	0.388477	+	0.355795i
$517$			3.48585i			0.153308i
$518$		−	3.02517i		−	0.132918i
$519$	−8.60397	−	7.88012i	−0.377673	−	0.345899i
$520$			2.58786i			0.113485i
$521$	−19.9200			−0.872709			−0.436355	−	0.899775i	$-0.643731\pi$
$521$	−19.9200			−0.872709			−0.436355	+	0.899775i	$0.643731\pi$
$522$	11.6044	−	1.02112i	0.507912	−	0.0446930i
$523$	26.8214			1.17282			0.586408	−	0.810016i	$-0.300541\pi$
$523$	26.8214			1.17282			0.586408	+	0.810016i	$0.300541\pi$
$524$		−	3.60469i		−	0.157472i
$525$	1.41231	+	1.29349i	0.0616383	+	0.0564527i
$526$		−	16.0248i		−	0.698716i
$527$	6.43420			0.280278
$528$	0.418024	−	0.456423i	0.0181922	−	0.0198632i
$529$	22.3037			0.969726
$530$	11.7716			0.511325
$531$	−28.3218	+	2.49214i	−1.22906	+	0.108149i
$532$		−	5.86904i		−	0.254455i
$533$			16.0498i			0.695195i
$534$	8.90950	+	8.15995i	0.385552	+	0.353115i
$535$		−	14.5849i		−	0.630560i
$536$	7.79466	+	2.49867i	0.336678	+	0.107926i
$537$	22.3305	−	24.3817i	0.963633	−	1.05215i
$538$			5.66646i			0.244298i
$539$	−2.06447			−0.0889232
$540$	4.12476	+	3.16012i	0.177501	+	0.135990i
$541$		−	15.3414i		−	0.659580i	−0.944054	−	0.329790i	$-0.893022\pi$
$541$		−	15.3414i		−	0.659580i	0.944054	−	0.329790i	$-0.106978\pi$
$542$		−	14.0485i		−	0.603436i
$543$	−14.4623	+	15.7907i	−0.620636	+	0.677646i
$544$		−	2.15051i		−	0.0922022i
$545$			1.55580i			0.0666430i
$546$	−3.34738	+	3.65487i	−0.143255	+	0.156414i
$547$		−	22.7451i		−	0.972508i	−0.873817	−	0.486254i	$-0.838363\pi$
$547$		−	22.7451i		−	0.972508i	0.873817	−	0.486254i	$-0.161637\pi$
$548$	22.9849			0.981865
$549$	45.5825	−	4.01097i	1.94541	−	0.171184i
$550$	−0.357335			−0.0152368
$551$			20.6113i			0.878070i
$552$	1.06584	+	0.976173i	0.0453653	+	0.0415487i
$553$	10.3323			0.439376
$554$	−25.5204			−1.08426
$555$	−3.20063	+	3.49463i	−0.135859	+	0.148339i
$556$		−	8.81597i		−	0.373881i
$557$			16.7579i			0.710055i	0.934856	+	0.355027i	$0.115528\pi$
$557$			16.7579i			0.710055i	−0.934856	+	0.355027i	$0.884472\pi$
$558$	8.94129	−	0.786777i	0.378515	−	0.0333069i
$559$	17.8789			0.756196
$560$		−	1.10570i		−	0.0467245i
$561$	−0.981539	−	0.898963i	−0.0414406	−	0.0379542i
$562$	−10.2431			−0.432079
$563$	11.6538			0.491148			0.245574	−	0.969378i	$-0.421024\pi$
$563$	11.6538			0.491148			0.245574	+	0.969378i	$0.421024\pi$
$564$	12.4602	+	11.4119i	0.524668	+	0.480528i
$565$	−9.97721			−0.419744
$566$	−8.28611			−0.348291
$567$	1.73785	+	9.79842i	0.0729830	+	0.411495i
$568$			15.8888i			0.666680i
$569$			47.2424i			1.98051i	0.139282	+	0.990253i	$0.455521\pi$
$569$			47.2424i			1.98051i	−0.139282	+	0.990253i	$0.544479\pi$
$570$	−6.20945	+	6.77983i	−0.260085	+	0.283976i
$571$	15.8046			0.661401			0.330700	−	0.943736i	$-0.392715\pi$
$571$	15.8046			0.661401			0.330700	+	0.943736i	$0.392715\pi$
$572$		−	0.924735i		−	0.0386651i
$573$	−13.5855	+	14.8335i	−0.567543	+	0.619676i
$574$		−	6.85753i		−	0.286228i
$575$		−	0.834453i		−	0.0347991i
$576$	−0.262965	−	2.98845i	−0.0109569	−	0.124519i
$577$			36.9474i			1.53814i	0.639164	+	0.769070i	$0.279280\pi$
$577$			36.9474i			1.53814i	−0.639164	+	0.769070i	$0.720720\pi$
$578$	12.3753			0.514746
$579$	1.04827	−	1.14456i	0.0435646	−	0.0475663i
$580$			3.88309i			0.161236i
$581$	−4.95322			−0.205494
$582$	−18.7159	−	17.1414i	−0.775800	−	0.710533i
$583$	−4.20640			−0.174211
$584$	−12.0792			−0.499842
$585$	7.73371	−	0.680517i	0.319749	−	0.0281359i
$586$		−	26.8620i		−	1.10966i
$587$	−17.7172			−0.731266			−0.365633	−	0.930759i	$-0.619148\pi$
$587$	−17.7172			−0.731266			−0.365633	+	0.930759i	$0.619148\pi$
$588$	−6.75863	+	7.37947i	−0.278721	+	0.304324i
$589$			15.8811i			0.654371i
$590$		−	9.47707i		−	0.390165i
$591$	−5.34569	+	5.83673i	−0.219892	+	0.240091i
$592$	2.73596			0.112447
$593$	−40.8538			−1.67766			−0.838832	−	0.544391i	$-0.816761\pi$
$593$	−40.8538			−1.67766			−0.838832	+	0.544391i	$0.816761\pi$
$594$	−1.47392	−	1.12922i	−0.0604758	−	0.0463325i
$595$	−2.37782			−0.0974813
$596$			10.1468i			0.415628i
$597$	−1.45441	+	1.58801i	−0.0595251	+	0.0649929i
$598$	2.15945			0.0883064
$599$	−13.4434			−0.549282			−0.274641	−	0.961547i	$-0.588559\pi$
$599$	−13.4434			−0.549282			−0.274641	+	0.961547i	$0.588559\pi$
$600$	−1.16984	+	1.27729i	−0.0477584	+	0.0521453i
$601$	5.47259			0.223232			0.111616	−	0.993751i	$-0.464397\pi$
$601$	5.47259			0.223232			0.111616	+	0.993751i	$0.464397\pi$
$602$	−7.63903			−0.311344
$603$	5.41742	−	23.9510i	0.220615	−	0.975361i
$604$	1.34157			0.0545879
$605$	−10.8723			−0.442022
$606$	5.54727	−	6.05683i	0.225342	−	0.246042i
$607$	−10.4948			−0.425971			−0.212985	−	0.977055i	$-0.568319\pi$
$607$	−10.4948			−0.425971			−0.212985	+	0.977055i	$0.568319\pi$
$608$	5.30796			0.215266
$609$	−5.02275	+	5.48413i	−0.203532	+	0.222228i
$610$			15.2529i			0.617571i
$611$	25.2449			1.02130
$612$	−6.42669	+	0.565508i	−0.259783	+	0.0228593i
$613$	−0.227267			−0.00917921			−0.00458960	−	0.999989i	$-0.501461\pi$
$613$	−0.227267			−0.00917921			−0.00458960	+	0.999989i	$0.501461\pi$
$614$	−5.37690			−0.216994
$615$	−7.25528	+	7.92173i	−0.292561	+	0.319435i
$616$			0.395107i			0.0159193i
$617$			13.2924i			0.535131i	0.963540	+	0.267566i	$0.0862192\pi$
$617$			13.2924i			0.535131i	−0.963540	+	0.267566i	$0.913781\pi$
$618$	−21.4037	+	23.3698i	−0.860984	+	0.940072i
$619$	−27.9019			−1.12147			−0.560736	−	0.827995i	$-0.689482\pi$
$619$	−27.9019			−1.12147			−0.560736	+	0.827995i	$0.689482\pi$
$620$			2.99195i			0.120159i
$621$	2.63697	−	3.44192i	0.105818	−	0.138119i
$622$	−12.7194			−0.510000
$623$	−7.71261			−0.308999
$624$	−3.30546	−	3.02738i	−0.132324	−	0.121192i
$625$	1.00000			0.0400000
$626$			1.01542i			0.0405844i
$627$	2.21885	−	2.42267i	0.0886125	−	0.0967523i
$628$	16.5368			0.659888
$629$		−	5.88371i		−	0.234599i
$630$	−3.30435	+	0.290761i	−0.131648	+	0.0115842i
$631$			8.34969i			0.332396i	0.986092	+	0.166198i	$0.0531491\pi$
$631$			8.34969i			0.332396i	−0.986092	+	0.166198i	$0.946851\pi$
$632$			9.34458i			0.371707i
$633$	−1.50443	+	1.64263i	−0.0597958	+	0.0652885i
$634$			12.9163i			0.512973i
$635$	−22.0307			−0.874262
$636$	−13.7708	+	15.0358i	−0.546049	+	0.596208i
$637$			14.9512i			0.592387i
$638$		−	1.38756i		−	0.0549342i
$639$	47.4830	−	4.17820i	1.87840	−	0.165287i
$640$	1.00000			0.0395285
$641$	37.1089			1.46572			0.732858	−	0.680382i	$-0.238186\pi$
$641$	37.1089			1.46572			0.732858	+	0.680382i	$0.238186\pi$
$642$	18.6292	+	17.0620i	0.735237	+	0.673382i
$643$	−9.38800			−0.370227			−0.185113	−	0.982717i	$-0.559265\pi$
$643$	−9.38800			−0.370227			−0.185113	+	0.982717i	$0.559265\pi$
$644$	−0.922658			−0.0363578
$645$	8.82451	+	8.08210i	0.347465	+	0.318233i
$646$		−	11.4148i		−	0.449109i
$647$	5.26994			0.207183			0.103591	−	0.994620i	$-0.466967\pi$
$647$	5.26994			0.207183			0.103591	+	0.994620i	$0.466967\pi$
$648$	−8.86170	+	1.57172i	−0.348120	+	0.0617428i
$649$			3.38649i			0.132931i
$650$			2.58786i			0.101504i
$651$	−3.87006	+	4.22556i	−0.151680	+	0.165613i
$652$	−14.0394			−0.549825
$653$	−3.08390			−0.120682			−0.0603412	−	0.998178i	$-0.519219\pi$
$653$	−3.08390			−0.120682			−0.0603412	+	0.998178i	$0.519219\pi$
$654$	−1.98721	−	1.82003i	−0.0777061	−	0.0711687i
$655$		−	3.60469i		−	0.140847i
$656$	6.20196			0.242146
$657$	3.17641	+	36.0982i	0.123924	+	1.40832i
$658$	−10.7863			−0.420494
$659$		−	0.0528055i		−	0.00205701i	−0.999999	−	0.00102850i	$-0.999673\pi$
$659$		−	0.0528055i		−	0.00205701i	0.999999	−	0.00102850i	$-0.000327383\pi$
$660$	0.418024	−	0.456423i	0.0162716	−	0.0177662i
$661$		−	32.0793i		−	1.24774i	−0.781528	−	0.623870i	$-0.785559\pi$
$661$		−	32.0793i		−	1.24774i	0.781528	−	0.623870i	$-0.214441\pi$
$662$		−	0.685019i		−	0.0266240i
$663$	−6.51039	+	7.10842i	−0.252843	+	0.276068i
$664$		−	4.47970i		−	0.173846i
$665$		−	5.86904i		−	0.227592i
$666$	−0.719462	−	8.17630i	−0.0278786	−	0.316825i
$667$	3.24025			0.125463
$668$			9.21767i			0.356642i
$669$	27.6217	−	30.1590i	1.06792	−	1.16601i
$670$	7.79466	+	2.49867i	0.301134	+	0.0965319i
$671$		−	5.45039i		−	0.210410i
$672$	1.41231	+	1.29349i	0.0544811	+	0.0498976i
$673$			35.6698i			1.37497i	0.726199	+	0.687485i	$0.241285\pi$
$673$			35.6698i			1.37497i	−0.726199	+	0.687485i	$0.758715\pi$
$674$			5.93774i			0.228713i
$675$	4.12476	+	3.16012i	0.158762	+	0.121633i
$676$	6.30297			0.242422
$677$	−5.61881			−0.215948			−0.107974	−	0.994154i	$-0.534436\pi$
$677$	−5.61881			−0.215948			−0.107974	+	0.994154i	$0.534436\pi$
$678$	11.6717	−	12.7438i	0.448249	−	0.489424i
$679$	16.2017			0.621762
$680$		−	2.15051i		−	0.0824681i
$681$	21.6760	+	19.8524i	0.830628	+	0.760747i
$682$		−	1.06913i		−	0.0409390i
$683$	13.4427			0.514371			0.257185	−	0.966362i	$-0.417205\pi$
$683$	13.4427			0.514371			0.257185	+	0.966362i	$0.417205\pi$
$684$	−1.39581	−	15.8626i	−0.0533700	−	0.606521i
$685$	22.9849			0.878206
$686$		−	14.1280i		−	0.539411i
$687$	25.4534	+	23.3120i	0.971107	+	0.889408i
$688$		−	6.90875i		−	0.263393i
$689$			30.4633i			1.16056i
$690$	1.06584	+	0.976173i	0.0405759	+	0.0371623i
$691$	−24.5919			−0.935519			−0.467759	−	0.883856i	$-0.654939\pi$
$691$	−24.5919			−0.935519			−0.467759	+	0.883856i	$0.654939\pi$
$692$			6.73609i			0.256068i
$693$	1.18076	−	0.103899i	0.0448533	−	0.00394681i
$694$	−8.25511			−0.313360
$695$		−	8.81597i		−	0.334409i
$696$	−4.95985	−	4.54258i	−0.188003	−	0.172186i
$697$		−	13.3373i		−	0.505188i
$698$	−12.0824			−0.457325
$699$	29.5508	−	32.2653i	1.11771	−	1.22039i
$700$		−	1.10570i		−	0.0417917i
$701$	−22.9680			−0.867489			−0.433744	−	0.901036i	$-0.642808\pi$
$701$	−22.9680			−0.867489			−0.433744	+	0.901036i	$0.642808\pi$
$702$	−8.17795	+	10.6743i	−0.308657	+	0.402876i
$703$	14.5224			0.547723
$704$	−0.357335			−0.0134676
$705$	12.4602	+	11.4119i	0.469278	+	0.429797i
$706$	−31.3728			−1.18073
$707$			5.24316i			0.197189i
$708$	12.1050	+	11.0866i	0.454934	+	0.416661i
$709$	52.1284			1.95772			0.978861	−	0.204526i	$-0.0655652\pi$
$709$	52.1284			1.95772			0.978861	+	0.204526i	$0.0655652\pi$
$710$			15.8888i			0.596297i
$711$	27.9258	−	2.45730i	1.04730	−	0.0921558i
$712$		−	6.97529i		−	0.261410i
$713$	2.49664			0.0934998
$714$	2.78167	−	3.03718i	0.104101	−	0.113664i
$715$		−	0.924735i		−	0.0345831i
$716$	−19.0886			−0.713374
$717$	5.55778	−	6.06830i	0.207559	−	0.226625i
$718$			25.9535i			0.968576i
$719$		−	37.8793i		−	1.41266i	−0.707884	−	0.706329i	$-0.750350\pi$
$719$		−	37.8793i		−	1.41266i	0.707884	−	0.706329i	$-0.249650\pi$
$720$	−0.262965	−	2.98845i	−0.00980012	−	0.111373i
$721$		−	20.2303i		−	0.753417i
$722$	9.17446			0.341438
$723$	−21.8181	+	23.8222i	−0.811423	+	0.885958i
$724$	12.3626			0.459454
$725$			3.88309i			0.144214i
$726$	12.7188	−	13.8871i	0.472040	−	0.515400i
$727$			20.6312i			0.765170i	0.923920	+	0.382585i	$0.124966\pi$
$727$			20.6312i			0.765170i	−0.923920	+	0.382585i	$0.875034\pi$
$728$	2.86141			0.106051
$729$	7.02732	+	26.0695i	0.260271	+	0.965536i
$730$	−12.0792			−0.447072
$731$	−14.8573			−0.549517
$732$	−19.4824	−	17.8434i	−0.720091	−	0.659510i
$733$			13.3520i			0.493166i	0.969122	+	0.246583i	$0.0793077\pi$
$733$			13.3520i			0.493166i	−0.969122	+	0.246583i	$0.920692\pi$
$734$		−	5.72011i		−	0.211133i
$735$	−6.75863	+	7.37947i	−0.249296	+	0.272196i
$736$		−	0.834453i		−	0.0307583i
$737$	−2.78531	−	0.892861i	−0.102598	−	0.0328890i
$738$	−1.63090	−	18.5343i	−0.0600342	−	0.682255i
$739$			41.7359i			1.53528i	0.640881	+	0.767640i	$0.278569\pi$
$739$			41.7359i			1.53528i	−0.640881	+	0.767640i	$0.721431\pi$
$740$	2.73596			0.100576
$741$	−17.5453	−	16.0692i	−0.644542	−	0.590317i
$742$		−	13.0159i		−	0.477829i
$743$			39.1259i			1.43539i	0.696358	+	0.717695i	$0.254803\pi$
$743$			39.1259i			1.43539i	−0.696358	+	0.717695i	$0.745197\pi$
$744$	−3.82160	−	3.50009i	−0.140107	−	0.128319i
$745$			10.1468i			0.371749i
$746$		−	19.4974i		−	0.713849i
$747$	−13.3874	+	1.17800i	−0.489818	+	0.0431009i
$748$			0.768452i			0.0280974i
$749$	−16.1266			−0.589253
$750$	−1.16984	+	1.27729i	−0.0427164	+	0.0466402i
$751$	39.9206			1.45673			0.728363	−	0.685192i	$-0.240282\pi$
$751$	39.9206			1.45673			0.728363	+	0.685192i	$0.240282\pi$
$752$		−	9.75513i		−	0.355733i
$753$	9.94878	−	10.8627i	0.362554	−	0.395857i
$754$	−10.0489			−0.365959
$755$	1.34157			0.0488249
$756$	3.49416	−	4.56077i	0.127081	−	0.165873i
$757$		−	8.22832i		−	0.299063i	−0.988757	−	0.149532i	$-0.952223\pi$
$757$		−	8.22832i		−	0.299063i	0.988757	−	0.149532i	$-0.0477766\pi$
$758$		−	7.66723i		−	0.278486i
$759$	−0.380863	−	0.348821i	−0.0138244	−	0.0126614i
$760$	5.30796			0.192540
$761$			33.0672i			1.19868i	0.800493	+	0.599342i	$0.204571\pi$
$761$			33.0672i			1.19868i	−0.800493	+	0.599342i	$0.795429\pi$
$762$	25.7723	−	28.1397i	0.933633	−	1.01939i
$763$	1.72025			0.0622773
$764$	11.6132			0.420150
$765$	−6.42669	+	0.565508i	−0.232357	+	0.0204460i
$766$	−19.2226			−0.694541
$767$	24.5254			0.885559
$768$	−1.16984	+	1.27729i	−0.0422128	+	0.0460904i
$769$		−	25.2179i		−	0.909382i	−0.890649	−	0.454691i	$-0.849750\pi$
$769$		−	25.2179i		−	0.909382i	0.890649	−	0.454691i	$-0.150250\pi$
$770$			0.395107i			0.0142387i
$771$	27.2782	+	24.9833i	0.982401	+	0.899752i
$772$	−0.896082			−0.0322507
$773$		−	20.0081i		−	0.719641i	−0.933021	−	0.359821i	$-0.882838\pi$
$773$		−	20.0081i		−	0.719641i	0.933021	−	0.359821i	$-0.117162\pi$
$774$	−20.6465	+	1.81676i	−0.742122	+	0.0653020i
$775$			2.99195i			0.107474i
$776$			14.6528i			0.526004i
$777$	3.86403	+	3.53895i	0.138621	+	0.126959i
$778$			28.5043i			1.02193i
$779$	32.9198			1.17947
$780$	−3.30546	−	3.02738i	−0.118355	−	0.108397i
$781$		−	5.67764i		−	0.203162i
$782$	−1.79450			−0.0641710
$783$	−12.2710	+	16.0168i	−0.438530	+	0.572394i
$784$	5.77742			0.206336
$785$	16.5368			0.590222
$786$	4.60425	+	4.21690i	0.164228	+	0.150412i
$787$		−	2.81803i		−	0.100452i	−0.998738	−	0.0502259i	$-0.984006\pi$
$787$		−	2.81803i		−	0.100452i	0.998738	−	0.0502259i	$-0.0159941\pi$
$788$	4.56961			0.162785
$789$	20.4685	+	18.7464i	0.728696	+	0.667391i
$790$			9.34458i			0.332465i
$791$			11.0318i			0.392247i
$792$	0.0939666	+	1.06788i	0.00333896	+	0.0379454i
$793$	−39.4723			−1.40170
$794$	8.75968			0.310870
$795$	−13.7708	+	15.0358i	−0.488401	+	0.533265i
$796$	1.24326			0.0440662
$797$		−	34.3198i		−	1.21567i	−0.794063	−	0.607836i	$-0.792038\pi$
$797$		−	34.3198i		−	1.21567i	0.794063	−	0.607836i	$-0.207962\pi$
$798$	7.49649	+	6.86581i	0.265373	+	0.243047i
$799$	−20.9785			−0.742165
$800$	1.00000			0.0353553
$801$	−20.8453	+	1.83426i	−0.736533	+	0.0648102i
$802$	−9.07728			−0.320530
$803$	4.31633			0.152320
$804$	−12.3100	+	7.03304i	−0.434140	+	0.248036i
$805$	−0.922658			−0.0325194
$806$	−7.74275			−0.272727
$807$	−7.23774	−	6.62883i	−0.254780	−	0.233346i
$808$	−4.74192			−0.166820
$809$	6.24459			0.219548			0.109774	−	0.993957i	$-0.464987\pi$
$809$	6.24459			0.219548			0.109774	+	0.993957i	$0.464987\pi$
$810$	−8.86170	+	1.57172i	−0.311368	+	0.0552245i
$811$			42.1703i			1.48080i	0.672166	+	0.740400i	$0.265364\pi$
$811$			42.1703i			1.48080i	−0.672166	+	0.740400i	$0.734636\pi$
$812$	4.29355			0.150674
$813$	17.9441	+	16.4345i	0.629328	+	0.576383i
$814$	−0.977656			−0.0342668
$815$	−14.0394			−0.491779
$816$	2.74683	+	2.51574i	0.0961583	+	0.0880685i
$817$		−	36.6714i		−	1.28297i
$818$		−	20.5072i		−	0.717018i
$819$	−0.752451	−	8.55119i	−0.0262928	−	0.298803i
$820$	6.20196			0.216582
$821$			23.5569i			0.822143i	0.911603	+	0.411072i	$0.134845\pi$
$821$			23.5569i			0.822143i	−0.911603	+	0.411072i	$0.865155\pi$
$822$	−26.8885	+	29.3585i	−0.937845	+	1.02399i
$823$	26.0001			0.906306			0.453153	−	0.891433i	$-0.350299\pi$
$823$	26.0001			0.906306			0.453153	+	0.891433i	$0.350299\pi$
$824$	18.2963			0.637383
$825$	0.418024	−	0.456423i	0.0145537	−	0.0158906i
$826$	−10.4788			−0.364605
$827$		−	54.3627i		−	1.89038i	−0.326527	−	0.945188i	$-0.605879\pi$
$827$		−	54.3627i		−	1.89038i	0.326527	−	0.945188i	$-0.394121\pi$
$828$	−2.49372	+	0.219432i	−0.0866628	+	0.00762578i
$829$	−31.7307			−1.10205			−0.551026	−	0.834488i	$-0.685764\pi$
$829$	−31.7307			−1.10205			−0.551026	+	0.834488i	$0.685764\pi$
$830$		−	4.47970i		−	0.155493i
$831$	29.8547	−	32.5971i	1.03565	−	1.13078i
$832$			2.58786i			0.0897180i
$833$		−	12.4244i		−	0.430479i
$834$	11.2606	+	10.3132i	0.389923	+	0.357119i
$835$			9.21767i			0.318991i
$836$	−1.89672			−0.0655995
$837$	−9.45490	+	12.3411i	−0.326809	+	0.426570i
$838$		−	5.35904i		−	0.185125i
$839$		−	24.8638i		−	0.858392i	−0.903211	−	0.429196i	$-0.858797\pi$
$839$		−	24.8638i		−	0.858392i	0.903211	−	0.429196i	$-0.141203\pi$
$840$	1.41231	+	1.29349i	0.0487293	+	0.0446298i
$841$	13.9216			0.480056
$842$	−4.50590			−0.155284
$843$	11.9828	−	13.0835i	0.412708	−	0.450619i
$844$	1.28602			0.0442666
$845$	6.30297			0.216829
$846$	−29.1528	+	2.56526i	−1.00229	+	0.0881954i
$847$			12.0216i			0.413066i
$848$	11.7716			0.404238
$849$	9.69339	−	10.5838i	0.332676	−	0.363235i
$850$		−	2.15051i		−	0.0737617i
$851$		−	2.28303i		−	0.0782613i
$852$	−20.2947	−	18.5873i	−0.695285	−	0.636791i
$853$	6.68029			0.228729			0.114364	−	0.993439i	$-0.463517\pi$
$853$	6.68029			0.228729			0.114364	+	0.993439i	$0.463517\pi$
$854$	16.8652			0.577114
$855$	−1.39581	−	15.8626i	−0.0477356	−	0.542489i
$856$		−	14.5849i		−	0.498502i
$857$	5.16006			0.176264			0.0881321	−	0.996109i	$-0.471910\pi$
$857$	5.16006			0.176264			0.0881321	+	0.996109i	$0.471910\pi$
$858$	1.18116	+	1.08179i	0.0403241	+	0.0369316i
$859$	−38.6569			−1.31896			−0.659478	−	0.751724i	$-0.729223\pi$
$859$	−38.6569			−1.31896			−0.659478	+	0.751724i	$0.729223\pi$
$860$		−	6.90875i		−	0.235586i
$861$	8.75909	+	8.02219i	0.298509	+	0.273396i
$862$		−	15.8178i		−	0.538757i
$863$			27.1070i			0.922731i	0.887210	+	0.461366i	$0.152640\pi$
$863$			27.1070i			0.922731i	−0.887210	+	0.461366i	$0.847360\pi$
$864$	4.12476	+	3.16012i	0.140327	+	0.107509i
$865$			6.73609i			0.229034i
$866$		−	3.60619i		−	0.122543i
$867$	−14.4771	+	15.8069i	−0.491668	+	0.536832i
$868$	3.30821			0.112288
$869$		−	3.33915i		−	0.113273i
$870$	−4.95985	−	4.54258i	−0.168155	−	0.154008i
$871$	−6.46620	+	20.1715i	−0.219099	+	0.683485i
$872$			1.55580i			0.0526859i
$873$	43.7892	−	3.85317i	1.48204	−	0.130410i
$874$		−	4.42924i		−	0.149821i
$875$		−	1.10570i		−	0.0373796i
$876$	14.1307	−	15.4287i	0.477433	−	0.521289i
$877$	34.3329			1.15934			0.579671	−	0.814851i	$-0.303181\pi$
$877$	34.3329			1.15934			0.579671	+	0.814851i	$0.303181\pi$
$878$	−2.26867			−0.0765639
$879$	34.3107	+	31.4242i	1.15727	+	1.05991i
$880$	−0.357335			−0.0120458
$881$		−	21.3255i		−	0.718474i	−0.933246	−	0.359237i	$-0.883037\pi$
$881$		−	21.3255i		−	0.718474i	0.933246	−	0.359237i	$-0.116963\pi$
$882$	−1.51926	−	17.2655i	−0.0511561	−	0.581361i
$883$			51.3084i			1.72667i	0.504634	+	0.863333i	$0.331627\pi$
$883$			51.3084i			1.72667i	−0.504634	+	0.863333i	$0.668373\pi$
$884$	5.56521			0.187178
$885$	12.1050	+	11.0866i	0.406906	+	0.372673i
$886$	−9.02705			−0.303270
$887$			51.2841i			1.72195i	0.508645	+	0.860976i	$0.330147\pi$
$887$			51.2841i			1.72195i	−0.508645	+	0.860976i	$0.669853\pi$
$888$	−3.20063	+	3.49463i	−0.107406	+	0.117272i
$889$			24.3594i			0.816989i
$890$		−	6.97529i		−	0.233812i
$891$	3.16660	−	0.561630i	0.106085	−	0.0188153i
$892$	−23.6116			−0.790574
$893$		−	51.7799i		−	1.73275i
$894$	−12.9604	−	11.8701i	−0.433461	−	0.396994i
$895$	−19.0886			−0.638061
$896$		−	1.10570i		−	0.0369390i
$897$	−2.52620	+	2.75825i	−0.0843474	+	0.0920954i
$898$			18.8339i			0.628495i
$899$	−11.6180			−0.387482
$900$	−0.262965	−	2.98845i	−0.00876550	−	0.0996151i
$901$		−	25.3149i		−	0.843361i
$902$	−2.21618			−0.0737907
$903$	8.93642	−	9.75730i	0.297385	−	0.324702i
$904$	−9.97721			−0.331837
$905$	12.3626			0.410948
$906$	−1.56942	+	1.71359i	−0.0521406	+	0.0569301i
$907$	−47.9347			−1.59165			−0.795823	−	0.605529i	$-0.792962\pi$
$907$	−47.9347			−1.59165			−0.795823	+	0.605529i	$0.792962\pi$
$908$		−	16.9703i		−	0.563178i
$909$	1.24696	+	14.1710i	0.0413590	+	0.470022i
$910$	2.86141			0.0948549
$911$		−	54.9975i		−	1.82215i	−0.412244	−	0.911074i	$-0.635255\pi$
$911$		−	54.9975i		−	1.82215i	0.412244	−	0.911074i	$-0.364745\pi$
$912$	−6.20945	+	6.77983i	−0.205615	+	0.224503i
$913$			1.60075i			0.0529772i
$914$	7.12233			0.235586
$915$	−19.4824	−	17.8434i	−0.644069	−	0.589883i
$916$		−	19.9276i		−	0.658425i
$917$	−3.98572			−0.131620
$918$	6.79585	−	8.87032i	0.224297	−	0.292764i
$919$		−	43.8279i		−	1.44575i	−0.690979	−	0.722874i	$-0.742820\pi$
$919$		−	43.8279i		−	1.44575i	0.690979	−	0.722874i	$-0.257180\pi$
$920$		−	0.834453i		−	0.0275111i
$921$	6.29009	−	6.86788i	0.207266	−	0.226304i
$922$		−	1.06535i		−	0.0350853i
$923$	−41.1181			−1.35342
$924$	−0.504668	−	0.462211i	−0.0166024	−	0.0152056i
$925$	2.73596			0.0899579
$926$		−	14.4915i		−	0.476221i
$927$	−4.81129	−	54.6777i	−0.158024	−	1.79585i
$928$			3.88309i			0.127469i
$929$	−51.5178			−1.69024			−0.845121	−	0.534574i	$-0.820472\pi$
$929$	−51.5178			−1.69024			−0.845121	+	0.534574i	$0.820472\pi$
$930$	−3.82160	−	3.50009i	−0.125315	−	0.114772i
$931$	30.6663			1.00505
$932$	−25.2606			−0.827440
$933$	14.8796	−	16.2464i	0.487136	−	0.531883i
$934$			14.8441i			0.485714i
$935$			0.768452i			0.0251311i
$936$	7.73371	−	0.680517i	0.252784	−	0.0222434i
$937$			40.7276i			1.33051i	0.746615	+	0.665257i	$0.231678\pi$
$937$			40.7276i			1.33051i	−0.746615	+	0.665257i	$0.768322\pi$
$938$	2.76279	−	8.61859i	0.0902082	−	0.281407i
$939$	−1.29699	−	1.18788i	−0.0423258	−	0.0387649i
$940$		−	9.75513i		−	0.318177i
$941$	0.0284249			0.000926625			0.000463313	−	1.00000i	$-0.499853\pi$
$941$	0.0284249			0.000926625			0.000463313		1.00000i	$0.499853\pi$
$942$	−19.3453	+	21.1223i	−0.630304	+	0.688202i
$943$		−	5.17524i		−	0.168529i
$944$		−	9.47707i		−	0.308452i
$945$	3.49416	−	4.56077i	0.113665	−	0.148362i
$946$			2.46874i			0.0802656i
$947$		−	5.63009i		−	0.182953i	−0.995807	−	0.0914767i	$-0.970841\pi$
$947$		−	5.63009i		−	0.182953i	0.995807	−	0.0914767i	$-0.0291587\pi$
$948$	−11.9358	−	10.9316i	−0.387656	−	0.355043i
$949$		−	31.2594i		−	1.01472i
$950$	5.30796			0.172213
$951$	−16.4980	−	15.1100i	−0.534983	−	0.489975i
$952$	−2.37782			−0.0770657
$953$			43.1847i			1.39889i	0.714686	+	0.699445i	$0.246569\pi$
$953$			43.1847i			1.39889i	−0.714686	+	0.699445i	$0.753431\pi$
$954$	−3.09551	−	35.1788i	−0.100221	−	1.13896i
$955$	11.6132			0.375794
$956$	−4.75090			−0.153655
$957$	1.77233	+	1.62322i	0.0572912	+	0.0524713i
$958$		−	3.58488i		−	0.115822i
$959$		−	25.4145i		−	0.820676i
$960$	−1.16984	+	1.27729i	−0.0377563	+	0.0412245i
$961$	22.0483			0.711234
$962$			7.08030i			0.228278i
$963$	−43.5863	+	3.83532i	−1.40455	+	0.123591i
$964$	18.6505			0.600693
$965$	−0.896082			−0.0288459
$966$	1.07936	−	1.17851i	0.0347278	−	0.0379178i
$967$	−22.0124			−0.707873			−0.353936	−	0.935270i	$-0.615157\pi$
$967$	−22.0124			−0.707873			−0.353936	+	0.935270i	$0.615157\pi$
$968$	−10.8723			−0.349449
$969$	14.5801	+	13.3535i	0.468379	+	0.428975i
$970$			14.6528i			0.470473i
$971$			2.80062i			0.0898761i	0.998990	+	0.0449380i	$0.0143090\pi$
$971$			2.80062i			0.0898761i	−0.998990	+	0.0449380i	$0.985691\pi$
$972$	8.35919	−	13.1577i	0.268121	−	0.422032i
$973$	−9.74786			−0.312502
$974$		−	40.8238i		−	1.30808i
$975$	−3.30546	−	3.02738i	−0.105860	−	0.0969536i
$976$			15.2529i			0.488232i
$977$			17.7902i			0.569158i	0.958653	+	0.284579i	$0.0918538\pi$
$977$			17.7902i			0.569158i	−0.958653	+	0.284579i	$0.908146\pi$
$978$	16.4238	−	17.9325i	0.525175	−	0.573417i
$979$			2.49252i			0.0796612i
$980$	5.77742			0.184553
$981$	4.64942	−	0.409120i	0.148445	−	0.0130622i
$982$		−	5.82397i		−	0.185850i
$983$	59.2259			1.88901			0.944506	−	0.328494i	$-0.106541\pi$
$983$	59.2259			1.88901			0.944506	+	0.328494i	$0.106541\pi$
$984$	−7.25528	+	7.92173i	−0.231290	+	0.252536i
$985$	4.56961			0.145600
$986$	8.35060			0.265937
$987$	12.6182	−	13.7773i	0.401642	−	0.438536i
$988$			13.7363i			0.437009i
$989$	−5.76502			−0.183317
$990$	0.0939666	+	1.06788i	0.00298646	+	0.0339394i
$991$			44.7858i			1.42267i	0.702854	+	0.711334i	$0.251909\pi$
$991$			44.7858i			1.42267i	−0.702854	+	0.711334i	$0.748091\pi$
$992$			2.99195i			0.0949944i
$993$	0.874971	+	0.801360i	0.0277664	+	0.0254304i
$994$	17.5683			0.557234
$995$	1.24326			0.0394140
$996$	5.72190	+	5.24052i	0.181305	+	0.166052i
$997$	−53.5257			−1.69518			−0.847588	−	0.530654i	$-0.821946\pi$
$997$	−53.5257			−1.69518			−0.847588	+	0.530654i	$0.821946\pi$
$998$			26.6192i			0.842616i
$999$	11.2852	+	8.64597i	0.357048	+	0.273546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2010.2.d.d.401.6	yes	20
3.2	odd	2		2010.2.d.c.401.16	yes	20
67.66	odd	2		2010.2.d.c.401.15	✓	20
201.200	even	2	inner	2010.2.d.d.401.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2010.2.d.c.401.15	✓	20	67.66	odd	2
2010.2.d.c.401.16	yes	20	3.2	odd	2
2010.2.d.d.401.5	yes	20	201.200	even	2	inner
2010.2.d.d.401.6	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2010.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.16984 + 1.27729i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.16984 + 1.27729i) q^{6} -1.10570i q^{7} +1.00000 q^{8} +(-0.262965 - 2.98845i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.16984 + 1.27729i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.16984 + 1.27729i) q^{6} -1.10570i q^{7} +1.00000 q^{8} +(-0.262965 - 2.98845i) q^{9} +1.00000 q^{10} -0.357335 q^{11} +(-1.16984 + 1.27729i) q^{12} +2.58786i q^{13} -1.10570i q^{14} +(-1.16984 + 1.27729i) q^{15} +1.00000 q^{16} -2.15051i q^{17} +(-0.262965 - 2.98845i) q^{18} +5.30796 q^{19} +1.00000 q^{20} +(1.41231 + 1.29349i) q^{21} -0.357335 q^{22} -0.834453i q^{23} +(-1.16984 + 1.27729i) q^{24} +1.00000 q^{25} +2.58786i q^{26} +(4.12476 + 3.16012i) q^{27} -1.10570i q^{28} +3.88309i q^{29} +(-1.16984 + 1.27729i) q^{30} +2.99195i q^{31} +1.00000 q^{32} +(0.418024 - 0.456423i) q^{33} -2.15051i q^{34} -1.10570i q^{35} +(-0.262965 - 2.98845i) q^{36} +2.73596 q^{37} +5.30796 q^{38} +(-3.30546 - 3.02738i) q^{39} +1.00000 q^{40} +6.20196 q^{41} +(1.41231 + 1.29349i) q^{42} -6.90875i q^{43} -0.357335 q^{44} +(-0.262965 - 2.98845i) q^{45} -0.834453i q^{46} -9.75513i q^{47} +(-1.16984 + 1.27729i) q^{48} +5.77742 q^{49} +1.00000 q^{50} +(2.74683 + 2.51574i) q^{51} +2.58786i q^{52} +11.7716 q^{53} +(4.12476 + 3.16012i) q^{54} -0.357335 q^{55} -1.10570i q^{56} +(-6.20945 + 6.77983i) q^{57} +3.88309i q^{58} -9.47707i q^{59} +(-1.16984 + 1.27729i) q^{60} +15.2529i q^{61} +2.99195i q^{62} +(-3.30435 + 0.290761i) q^{63} +1.00000 q^{64} +2.58786i q^{65} +(0.418024 - 0.456423i) q^{66} +(7.79466 + 2.49867i) q^{67} -2.15051i q^{68} +(1.06584 + 0.976173i) q^{69} -1.10570i q^{70} +15.8888i q^{71} +(-0.262965 - 2.98845i) q^{72} -12.0792 q^{73} +2.73596 q^{74} +(-1.16984 + 1.27729i) q^{75} +5.30796 q^{76} +0.395107i q^{77} +(-3.30546 - 3.02738i) q^{78} +9.34458i q^{79} +1.00000 q^{80} +(-8.86170 + 1.57172i) q^{81} +6.20196 q^{82} -4.47970i q^{83} +(1.41231 + 1.29349i) q^{84} -2.15051i q^{85} -6.90875i q^{86} +(-4.95985 - 4.54258i) q^{87} -0.357335 q^{88} -6.97529i q^{89} +(-0.262965 - 2.98845i) q^{90} +2.86141 q^{91} -0.834453i q^{92} +(-3.82160 - 3.50009i) q^{93} -9.75513i q^{94} +5.30796 q^{95} +(-1.16984 + 1.27729i) q^{96} +14.6528i q^{97} +5.77742 q^{98} +(0.0939666 + 1.06788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8}+O(q^{10}) \) 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8	\( 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8} + 20 q^{10} - 2 q^{12} - 2 q^{15} + 20 q^{16} + 16 q^{19} + 20 q^{20} - 2 q^{21} - 2 q^{24} + 20 q^{25} + 10 q^{27} - 2 q^{30} + 20 q^{32} + 2 q^{33} + 20 q^{37} + 16 q^{38} + 16 q^{39} + 20 q^{40} + 8 q^{41} - 2 q^{42} - 2 q^{48} - 48 q^{49} + 20 q^{50} + 32 q^{51} - 36 q^{53} + 10 q^{54} + 16 q^{57} - 2 q^{60} - 4 q^{63} + 20 q^{64} + 2 q^{66} + 16 q^{67} - 28 q^{69} - 4 q^{73} + 20 q^{74} - 2 q^{75} + 16 q^{76} + 16 q^{78} + 20 q^{80} + 12 q^{81} + 8 q^{82} - 2 q^{84} + 32 q^{87} + 12 q^{91} - 12 q^{93} + 16 q^{95} - 2 q^{96} - 48 q^{98} + 12 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8 + 20 * q^10 - 2 * q^12 - 2 * q^15 + 20 * q^16 + 16 * q^19 + 20 * q^20 - 2 * q^21 - 2 * q^24 + 20 * q^25 + 10 * q^27 - 2 * q^30 + 20 * q^32 + 2 * q^33 + 20 * q^37 + 16 * q^38 + 16 * q^39 + 20 * q^40 + 8 * q^41 - 2 * q^42 - 2 * q^48 - 48 * q^49 + 20 * q^50 + 32 * q^51 - 36 * q^53 + 10 * q^54 + 16 * q^57 - 2 * q^60 - 4 * q^63 + 20 * q^64 + 2 * q^66 + 16 * q^67 - 28 * q^69 - 4 * q^73 + 20 * q^74 - 2 * q^75 + 16 * q^76 + 16 * q^78 + 20 * q^80 + 12 * q^81 + 8 * q^82 - 2 * q^84 + 32 * q^87 + 12 * q^91 - 12 * q^93 + 16 * q^95 - 2 * q^96 - 48 * q^98 + 12 * q^99

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