LMFDB - Embedded newform 1470.2.b.b.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, 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("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.1
Root			$1.73138 + 0.0481063i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.b.881.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.47537 - 0.907353i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.907353 + 1.47537i) q^{6} +1.00000i q^{8} +(1.35342 + 2.67736i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.47537 - 0.907353i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.907353 + 1.47537i) q^{6} +1.00000i q^{8} +(1.35342 + 2.67736i) q^{9} +1.00000i q^{10} -3.28390i q^{11} +(1.47537 + 0.907353i) q^{12} -5.91369i q^{13} +(1.47537 + 0.907353i) q^{15} +1.00000 q^{16} -2.40398 q^{17} +(2.67736 - 1.35342i) q^{18} -5.51442i q^{19} +1.00000 q^{20} -3.28390 q^{22} +6.49749i q^{23} +(0.907353 - 1.47537i) q^{24} +1.00000 q^{25} -5.91369 q^{26} +(0.432512 - 5.17812i) q^{27} -3.80949i q^{29} +(0.907353 - 1.47537i) q^{30} +5.20176i q^{31} -1.00000i q^{32} +(-2.97965 + 4.84496i) q^{33} +2.40398i q^{34} +(-1.35342 - 2.67736i) q^{36} -1.88030 q^{37} -5.51442 q^{38} +(-5.36581 + 8.72488i) q^{39} -1.00000i q^{40} -0.103155 q^{41} -1.48931 q^{43} +3.28390i q^{44} +(-1.35342 - 2.67736i) q^{45} +6.49749 q^{46} -12.4671 q^{47} +(-1.47537 - 0.907353i) q^{48} -1.00000i q^{50} +(3.54676 + 2.18126i) q^{51} +5.91369i q^{52} -2.43784i q^{53} +(-5.17812 - 0.432512i) q^{54} +3.28390i q^{55} +(-5.00352 + 8.13580i) q^{57} -3.80949 q^{58} -3.65385 q^{59} +(-1.47537 - 0.907353i) q^{60} +14.2325i q^{61} +5.20176 q^{62} -1.00000 q^{64} +5.91369i q^{65} +(4.84496 + 2.97965i) q^{66} -3.35472 q^{67} +2.40398 q^{68} +(5.89552 - 9.58619i) q^{69} +13.9116i q^{71} +(-2.67736 + 1.35342i) q^{72} -8.11303i q^{73} +1.88030i q^{74} +(-1.47537 - 0.907353i) q^{75} +5.51442i q^{76} +(8.72488 + 5.36581i) q^{78} +9.15135 q^{79} -1.00000 q^{80} +(-5.33650 + 7.24719i) q^{81} +0.103155i q^{82} -6.54676 q^{83} +2.40398 q^{85} +1.48931i q^{86} +(-3.45655 + 5.62039i) q^{87} +3.28390 q^{88} +11.2408 q^{89} +(-2.67736 + 1.35342i) q^{90} -6.49749i q^{92} +(4.71983 - 7.67451i) q^{93} +12.4671i q^{94} +5.51442i q^{95} +(-0.907353 + 1.47537i) q^{96} +7.90564i q^{97} +(8.79217 - 4.44450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9	$ 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9 - 4 * q^12 - 4 * q^15 + 12 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 2 * q^24 + 12 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^30 + 20 * q^33 + 6 * q^36 + 16 * q^37 - 16 * q^38 + 12 * q^39 - 4 * q^41 + 6 * q^45 - 4 * q^46 - 32 * q^47 + 4 * q^48 + 4 * q^51 - 28 * q^54 - 36 * q^57 - 16 * q^58 - 24 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^64 + 20 * q^66 + 8 * q^67 + 24 * q^68 + 50 * q^69 - 8 * q^72 + 4 * q^75 + 32 * q^78 + 8 * q^79 - 12 * q^80 - 10 * q^81 - 40 * q^83 + 24 * q^85 + 56 * q^87 - 52 * q^89 - 8 * q^90 + 28 * q^93 - 2 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.47537	−	0.907353i	−0.851804	−	0.523860i
$3$	−1.47537	−	0.907353i	−0.851804	−	0.523860i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.907353	+	1.47537i	−0.370425	+	0.602317i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.35342	+	2.67736i	0.451141	+	0.892453i
$10$			1.00000i			0.316228i
$11$		−	3.28390i		−	0.990133i	−0.868855	−	0.495066i	$-0.835144\pi$
$11$		−	3.28390i		−	0.990133i	0.868855	−	0.495066i	$-0.164856\pi$
$12$	1.47537	+	0.907353i	0.425902	+	0.261930i
$13$		−	5.91369i		−	1.64016i	−0.572246	−	0.820082i	$-0.693928\pi$
$13$		−	5.91369i		−	1.64016i	0.572246	−	0.820082i	$-0.306072\pi$
$14$		0			0
$15$	1.47537	+	0.907353i	0.380938	+	0.234277i
$16$	1.00000			0.250000
$17$	−2.40398			−0.583051			−0.291525	−	0.956563i	$-0.594163\pi$
$17$	−2.40398			−0.583051			−0.291525	+	0.956563i	$0.594163\pi$
$18$	2.67736	−	1.35342i	0.631059	−	0.319005i
$19$		−	5.51442i		−	1.26509i	−0.774522	−	0.632547i	$-0.782009\pi$
$19$		−	5.51442i		−	1.26509i	0.774522	−	0.632547i	$-0.217991\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−3.28390			−0.700129
$23$			6.49749i			1.35482i	0.735605	+	0.677410i	$0.236898\pi$
$23$			6.49749i			1.35482i	−0.735605	+	0.677410i	$0.763102\pi$
$24$	0.907353	−	1.47537i	0.185213	−	0.301158i
$25$	1.00000			0.200000
$26$	−5.91369			−1.15977
$27$	0.432512	−	5.17812i	0.0832369	−	0.996530i
$28$		0			0
$29$		−	3.80949i		−	0.707404i	−0.935358	−	0.353702i	$-0.884923\pi$
$29$		−	3.80949i		−	0.707404i	0.935358	−	0.353702i	$-0.115077\pi$
$30$	0.907353	−	1.47537i	0.165659	−	0.269364i
$31$			5.20176i			0.934263i	0.884188	+	0.467132i	$0.154713\pi$
$31$			5.20176i			0.934263i	−0.884188	+	0.467132i	$0.845287\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.97965	+	4.84496i	−0.518691	+	0.843399i
$34$			2.40398i			0.412279i
$35$		0			0
$36$	−1.35342	−	2.67736i	−0.225570	−	0.446226i
$37$	−1.88030			−0.309120			−0.154560	−	0.987983i	$-0.549396\pi$
$37$	−1.88030			−0.309120			−0.154560	+	0.987983i	$0.549396\pi$
$38$	−5.51442			−0.894557
$39$	−5.36581	+	8.72488i	−0.859217	+	1.39710i
$40$		−	1.00000i		−	0.158114i
$41$	−0.103155			−0.0161101			−0.00805504	−	0.999968i	$-0.502564\pi$
$41$	−0.103155			−0.0161101			−0.00805504	+	0.999968i	$0.502564\pi$
$42$		0			0
$43$	−1.48931			−0.227117			−0.113559	−	0.993531i	$-0.536225\pi$
$43$	−1.48931			−0.227117			−0.113559	+	0.993531i	$0.536225\pi$
$44$			3.28390i			0.495066i
$45$	−1.35342	−	2.67736i	−0.201756	−	0.399117i
$46$	6.49749			0.958003
$47$	−12.4671			−1.81851			−0.909254	−	0.416241i	$-0.863347\pi$
$47$	−12.4671			−1.81851			−0.909254	+	0.416241i	$0.863347\pi$
$48$	−1.47537	−	0.907353i	−0.212951	−	0.130965i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	3.54676	+	2.18126i	0.496645	+	0.305437i
$52$			5.91369i			0.820082i
$53$		−	2.43784i		−	0.334863i	−0.985884	−	0.167432i	$-0.946453\pi$
$53$		−	2.43784i		−	0.334863i	0.985884	−	0.167432i	$-0.0535473\pi$
$54$	−5.17812	−	0.432512i	−0.704653	−	0.0588574i
$55$			3.28390i			0.442801i
$56$		0			0
$57$	−5.00352	+	8.13580i	−0.662733	+	1.07761i
$58$	−3.80949			−0.500210
$59$	−3.65385			−0.475691			−0.237846	−	0.971303i	$-0.576441\pi$
$59$	−3.65385			−0.475691			−0.237846	+	0.971303i	$0.576441\pi$
$60$	−1.47537	−	0.907353i	−0.190469	−	0.117139i
$61$			14.2325i			1.82229i	0.412090	+	0.911143i	$0.364799\pi$
$61$			14.2325i			1.82229i	−0.412090	+	0.911143i	$0.635201\pi$
$62$	5.20176			0.660624
$63$		0			0
$64$	−1.00000			−0.125000
$65$			5.91369i			0.733504i
$66$	4.84496	+	2.97965i	0.596373	+	0.366770i
$67$	−3.35472			−0.409844			−0.204922	−	0.978778i	$-0.565694\pi$
$67$	−3.35472			−0.409844			−0.204922	+	0.978778i	$0.565694\pi$
$68$	2.40398			0.291525
$69$	5.89552	−	9.58619i	0.709737	−	1.15404i
$70$		0			0
$71$			13.9116i			1.65100i	0.564403	+	0.825500i	$0.309107\pi$
$71$			13.9116i			1.65100i	−0.564403	+	0.825500i	$0.690893\pi$
$72$	−2.67736	+	1.35342i	−0.315530	+	0.159502i
$73$		−	8.11303i		−	0.949558i	−0.880105	−	0.474779i	$-0.842528\pi$
$73$		−	8.11303i		−	0.949558i	0.880105	−	0.474779i	$-0.157472\pi$
$74$			1.88030i			0.218581i
$75$	−1.47537	−	0.907353i	−0.170361	−	0.104772i
$76$			5.51442i			0.632547i
$77$		0			0
$78$	8.72488	+	5.36581i	0.987898	+	0.607558i
$79$	9.15135			1.02961			0.514803	−	0.857308i	$-0.327865\pi$
$79$	9.15135			1.02961			0.514803	+	0.857308i	$0.327865\pi$
$80$	−1.00000			−0.111803
$81$	−5.33650	+	7.24719i	−0.592944	+	0.805244i
$82$			0.103155i			0.0113915i
$83$	−6.54676			−0.718600			−0.359300	−	0.933222i	$-0.616984\pi$
$83$	−6.54676			−0.718600			−0.359300	+	0.933222i	$0.616984\pi$
$84$		0			0
$85$	2.40398			0.260748
$86$			1.48931i			0.160596i
$87$	−3.45655	+	5.62039i	−0.370581	+	0.602569i
$88$	3.28390			0.350065
$89$	11.2408			1.19152			0.595761	−	0.803162i	$-0.296851\pi$
$89$	11.2408			1.19152			0.595761	+	0.803162i	$0.296851\pi$
$90$	−2.67736	+	1.35342i	−0.282218	+	0.142663i
$91$		0			0
$92$		−	6.49749i		−	0.677410i
$93$	4.71983	−	7.67451i	0.489423	−	0.795809i
$94$			12.4671i			1.28588i
$95$			5.51442i			0.565768i
$96$	−0.907353	+	1.47537i	−0.0926063	+	0.150579i
$97$			7.90564i			0.802696i	0.915926	+	0.401348i	$0.131458\pi$
$97$			7.90564i			0.802696i	−0.915926	+	0.401348i	$0.868542\pi$
$98$		0			0
$99$	8.79217	−	4.44450i	0.883647	−	0.446689i
$100$	−1.00000			−0.100000
$101$	−4.91213			−0.488775			−0.244387	−	0.969678i	$-0.578587\pi$
$101$	−4.91213			−0.488775			−0.244387	+	0.969678i	$0.578587\pi$
$102$	2.18126	−	3.54676i	0.215977	−	0.351181i
$103$			4.57642i			0.450928i	0.974251	+	0.225464i	$0.0723898\pi$
$103$			4.57642i			0.450928i	−0.974251	+	0.225464i	$0.927610\pi$
$104$	5.91369			0.579885
$105$		0			0
$106$	−2.43784			−0.236784
$107$			4.93228i			0.476822i	0.971164	+	0.238411i	$0.0766265\pi$
$107$			4.93228i			0.476822i	−0.971164	+	0.238411i	$0.923373\pi$
$108$	−0.432512	+	5.17812i	−0.0416185	+	0.498265i
$109$	7.60166			0.728107			0.364053	−	0.931378i	$-0.381393\pi$
$109$	7.60166			0.728107			0.364053	+	0.931378i	$0.381393\pi$
$110$	3.28390			0.313107
$111$	2.77414	+	1.70610i	0.263310	+	0.161936i
$112$		0			0
$113$		−	3.88234i		−	0.365220i	−0.983185	−	0.182610i	$-0.941545\pi$
$113$		−	3.88234i		−	0.365220i	0.983185	−	0.182610i	$-0.0584546\pi$
$114$	8.13580	+	5.00352i	0.761987	+	0.468623i
$115$		−	6.49749i		−	0.605894i
$116$			3.80949i			0.353702i
$117$	15.8331	−	8.00373i	1.46377	−	0.739945i
$118$			3.65385i			0.336365i
$119$		0			0
$120$	−0.907353	+	1.47537i	−0.0828296	+	0.134682i
$121$	0.216013			0.0196375
$122$	14.2325			1.28855
$123$	0.152191	+	0.0935978i	0.0137226	+	0.00843943i
$124$		−	5.20176i		−	0.467132i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−14.1380			−1.25455			−0.627273	−	0.778799i	$-0.715829\pi$
$127$	−14.1380			−1.25455			−0.627273	+	0.778799i	$0.715829\pi$
$128$			1.00000i			0.0883883i
$129$	2.19728	+	1.35133i	0.193459	+	0.118978i
$130$	5.91369			0.518665
$131$	−5.02155			−0.438735			−0.219368	−	0.975642i	$-0.570399\pi$
$131$	−5.02155			−0.438735			−0.219368	+	0.975642i	$0.570399\pi$
$132$	2.97965	−	4.84496i	0.259346	−	0.421700i
$133$		0			0
$134$			3.35472i			0.289803i
$135$	−0.432512	+	5.17812i	−0.0372247	+	0.445662i
$136$		−	2.40398i		−	0.206140i
$137$			2.92970i			0.250301i	0.992138	+	0.125150i	$0.0399413\pi$
$137$			2.92970i			0.250301i	−0.992138	+	0.125150i	$0.960059\pi$
$138$	−9.58619	−	5.89552i	−0.816031	−	0.501860i
$139$		−	3.36557i		−	0.285464i	−0.989761	−	0.142732i	$-0.954411\pi$
$139$		−	3.36557i		−	0.285464i	0.989761	−	0.142732i	$-0.0455887\pi$
$140$		0			0
$141$	18.3935	+	11.3120i	1.54901	+	0.952644i
$142$	13.9116			1.16743
$143$	−19.4200			−1.62398
$144$	1.35342	+	2.67736i	0.112785	+	0.223113i
$145$			3.80949i			0.316361i
$146$	−8.11303			−0.671439
$147$		0			0
$148$	1.88030			0.154560
$149$		−	9.63094i		−	0.788998i	−0.918896	−	0.394499i	$-0.870918\pi$
$149$		−	9.63094i		−	0.788998i	0.918896	−	0.394499i	$-0.129082\pi$
$150$	−0.907353	+	1.47537i	−0.0740850	+	0.120463i
$151$	−23.5368			−1.91540			−0.957699	−	0.287771i	$-0.907086\pi$
$151$	−23.5368			−1.91540			−0.957699	+	0.287771i	$0.907086\pi$
$152$	5.51442			0.447278
$153$	−3.25360	−	6.43632i	−0.263038	−	0.520345i
$154$		0			0
$155$		−	5.20176i		−	0.417815i
$156$	5.36581	−	8.72488i	0.429608	−	0.698549i
$157$			4.28351i			0.341861i	0.985283	+	0.170931i	$0.0546774\pi$
$157$			4.28351i			0.341861i	−0.985283	+	0.170931i	$0.945323\pi$
$158$		−	9.15135i		−	0.728042i
$159$	−2.21198	+	3.59671i	−0.175422	+	0.285238i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	7.24719	+	5.33650i	0.569393	+	0.419275i
$163$	−22.0893			−1.73017			−0.865083	−	0.501630i	$-0.832734\pi$
$163$	−22.0893			−1.73017			−0.865083	+	0.501630i	$0.832734\pi$
$164$	0.103155			0.00805504
$165$	2.97965	−	4.84496i	0.231966	−	0.377180i
$166$			6.54676i			0.508127i
$167$	12.9338			1.00085			0.500424	−	0.865780i	$-0.333177\pi$
$167$	12.9338			1.00085			0.500424	+	0.865780i	$0.333177\pi$
$168$		0			0
$169$	−21.9718			−1.69014
$170$		−	2.40398i		−	0.184377i
$171$	14.7641	−	7.46334i	1.12904	−	0.570736i
$172$	1.48931			0.113559
$173$	−23.2595			−1.76839			−0.884195	−	0.467119i	$-0.845292\pi$
$173$	−23.2595			−1.76839			−0.884195	+	0.467119i	$0.845292\pi$
$174$	5.62039	+	3.45655i	0.426081	+	0.262040i
$175$		0			0
$176$		−	3.28390i		−	0.247533i
$177$	5.39078	+	3.31533i	0.405196	+	0.249196i
$178$		−	11.2408i		−	0.842533i
$179$		−	9.45455i		−	0.706666i	−0.935498	−	0.353333i	$-0.885048\pi$
$179$		−	9.45455i		−	0.706666i	0.935498	−	0.353333i	$-0.114952\pi$
$180$	1.35342	+	2.67736i	0.100878	+	0.199559i
$181$			8.42502i			0.626227i	0.949716	+	0.313113i	$0.101372\pi$
$181$			8.42502i			0.626227i	−0.949716	+	0.313113i	$0.898628\pi$
$182$		0			0
$183$	12.9139	−	20.9982i	0.954623	−	1.55223i
$184$	−6.49749			−0.479001
$185$	1.88030			0.138243
$186$	−7.67451	−	4.71983i	−0.562722	−	0.346075i
$187$			7.89443i			0.577298i
$188$	12.4671			0.909254
$189$		0			0
$190$	5.51442			0.400058
$191$		−	5.13035i		−	0.371219i	−0.982624	−	0.185609i	$-0.940574\pi$
$191$		−	5.13035i		−	0.371219i	0.982624	−	0.185609i	$-0.0594259\pi$
$192$	1.47537	+	0.907353i	0.106476	+	0.0654825i
$193$	15.2791			1.09981			0.549907	−	0.835226i	$-0.314663\pi$
$193$	15.2791			1.09981			0.549907	+	0.835226i	$0.314663\pi$
$194$	7.90564			0.567592
$195$	5.36581	−	8.72488i	0.384253	−	0.624801i
$196$		0			0
$197$		−	16.0694i		−	1.14489i	−0.819942	−	0.572447i	$-0.805994\pi$
$197$		−	16.0694i		−	1.14489i	0.819942	−	0.572447i	$-0.194006\pi$
$198$	−4.44450	−	8.79217i	−0.315857	−	0.624832i
$199$		−	6.63017i		−	0.470001i	−0.971995	−	0.235000i	$-0.924491\pi$
$199$		−	6.63017i		−	0.470001i	0.971995	−	0.235000i	$-0.0755091\pi$
$200$			1.00000i			0.0707107i
$201$	4.94944	+	3.04391i	0.349107	+	0.214701i
$202$			4.91213i			0.345616i
$203$		0			0
$204$	−3.54676	−	2.18126i	−0.248323	−	0.152719i
$205$	0.103155			0.00720465
$206$	4.57642			0.318854
$207$	−17.3961	+	8.79385i	−1.20911	+	0.611215i
$208$		−	5.91369i		−	0.410041i
$209$	−18.1088			−1.25261
$210$		0			0
$211$	−10.9980			−0.757135			−0.378568	−	0.925574i	$-0.623583\pi$
$211$	−10.9980			−0.757135			−0.378568	+	0.925574i	$0.623583\pi$
$212$			2.43784i			0.167432i
$213$	12.6227	−	20.5247i	0.864893	−	1.40633i
$214$	4.93228			0.337164
$215$	1.48931			0.101570
$216$	5.17812	+	0.432512i	0.352326	+	0.0294287i
$217$		0			0
$218$		−	7.60166i		−	0.514849i
$219$	−7.36138	+	11.9697i	−0.497436	+	0.808838i
$220$		−	3.28390i		−	0.221400i
$221$			14.2164i			0.956299i
$222$	1.70610	−	2.77414i	0.114506	−	0.186188i
$223$			22.0431i			1.47612i	0.674737	+	0.738058i	$0.264257\pi$
$223$			22.0431i			1.47612i	−0.674737	+	0.738058i	$0.735743\pi$
$224$		0			0
$225$	1.35342	+	2.67736i	0.0902282	+	0.178491i
$226$	−3.88234			−0.258250
$227$	−6.24839			−0.414720			−0.207360	−	0.978265i	$-0.566487\pi$
$227$	−6.24839			−0.414720			−0.207360	+	0.978265i	$0.566487\pi$
$228$	5.00352	−	8.13580i	0.331366	−	0.538806i
$229$			12.1852i			0.805221i	0.915371	+	0.402611i	$0.131897\pi$
$229$			12.1852i			0.805221i	−0.915371	+	0.402611i	$0.868103\pi$
$230$	−6.49749			−0.428432
$231$		0			0
$232$	3.80949			0.250105
$233$		−	16.1655i		−	1.05903i	−0.848299	−	0.529517i	$-0.822373\pi$
$233$		−	16.1655i		−	1.05903i	0.848299	−	0.529517i	$-0.177627\pi$
$234$	−8.00373	−	15.8331i	−0.523220	−	1.03504i
$235$	12.4671			0.813262
$236$	3.65385			0.237846
$237$	−13.5016	−	8.30350i	−0.877024	−	0.539370i
$238$		0			0
$239$			5.36347i			0.346934i	0.984840	+	0.173467i	$0.0554970\pi$
$239$			5.36347i			0.346934i	−0.984840	+	0.173467i	$0.944503\pi$
$240$	1.47537	+	0.907353i	0.0952346	+	0.0585694i
$241$			16.0919i			1.03657i	0.855207	+	0.518286i	$0.173430\pi$
$241$			16.0919i			1.03657i	−0.855207	+	0.518286i	$0.826570\pi$
$242$		−	0.216013i		−	0.0138858i
$243$	14.4491	−	5.85020i	0.926907	−	0.375290i
$244$		−	14.2325i		−	0.911143i
$245$		0			0
$246$	0.0935978	−	0.152191i	0.00596758	−	0.00970337i
$247$	−32.6106			−2.07496
$248$	−5.20176			−0.330312
$249$	9.65888	+	5.94022i	0.612106	+	0.376446i
$250$			1.00000i			0.0632456i
$251$	−1.05846			−0.0668093			−0.0334047	−	0.999442i	$-0.510635\pi$
$251$	−1.05846			−0.0668093			−0.0334047	+	0.999442i	$0.510635\pi$
$252$		0			0
$253$	21.3371			1.34145
$254$			14.1380i			0.887098i
$255$	−3.54676	−	2.18126i	−0.222106	−	0.136596i
$256$	1.00000			0.0625000
$257$	2.46181			0.153564			0.0767819	−	0.997048i	$-0.475535\pi$
$257$	2.46181			0.153564			0.0767819	+	0.997048i	$0.475535\pi$
$258$	1.35133	−	2.19728i	0.0841299	−	0.136796i
$259$		0			0
$260$		−	5.91369i		−	0.366752i
$261$	10.1994	−	5.15584i	0.631324	−	0.319139i
$262$			5.02155i			0.310233i
$263$		−	30.6984i		−	1.89294i	−0.322789	−	0.946471i	$-0.604620\pi$
$263$		−	30.6984i		−	1.89294i	0.322789	−	0.946471i	$-0.395380\pi$
$264$	−4.84496	−	2.97965i	−0.298187	−	0.183385i
$265$			2.43784i			0.149755i
$266$		0			0
$267$	−16.5843	−	10.1994i	−1.01494	−	0.624191i
$268$	3.35472			0.204922
$269$	16.7530			1.02145			0.510724	−	0.859745i	$-0.329377\pi$
$269$	16.7530			1.02145			0.510724	+	0.859745i	$0.329377\pi$
$270$	5.17812	+	0.432512i	0.315130	+	0.0263218i
$271$		−	15.2626i		−	0.927139i	−0.886060	−	0.463570i	$-0.846568\pi$
$271$		−	15.2626i		−	0.927139i	0.886060	−	0.463570i	$-0.153432\pi$
$272$	−2.40398			−0.145763
$273$		0			0
$274$	2.92970			0.176989
$275$		−	3.28390i		−	0.198027i
$276$	−5.89552	+	9.58619i	−0.354868	+	0.577021i
$277$	−3.51222			−0.211029			−0.105514	−	0.994418i	$-0.533649\pi$
$277$	−3.51222			−0.211029			−0.105514	+	0.994418i	$0.533649\pi$
$278$	−3.36557			−0.201854
$279$	−13.9270	+	7.04018i	−0.833786	+	0.421484i
$280$		0			0
$281$			4.15840i			0.248069i	0.992278	+	0.124035i	$0.0395834\pi$
$281$			4.15840i			0.248069i	−0.992278	+	0.124035i	$0.960417\pi$
$282$	11.3120	−	18.3935i	0.673621	−	1.09532i
$283$			0.172611i			0.0102607i	0.999987	+	0.00513033i	$0.00163304\pi$
$283$			0.172611i			0.0102607i	−0.999987	+	0.00513033i	$0.998367\pi$
$284$		−	13.9116i		−	0.825500i
$285$	5.00352	−	8.13580i	0.296383	−	0.481923i
$286$			19.4200i			1.14833i
$287$		0			0
$288$	2.67736	−	1.35342i	0.157765	−	0.0797512i
$289$	−11.2209			−0.660052
$290$	3.80949			0.223701
$291$	7.17320	−	11.6637i	0.420501	−	0.683740i
$292$			8.11303i			0.474779i
$293$	−4.38021			−0.255895			−0.127947	−	0.991781i	$-0.540839\pi$
$293$	−4.38021			−0.255895			−0.127947	+	0.991781i	$0.540839\pi$
$294$		0			0
$295$	3.65385			0.212736
$296$		−	1.88030i		−	0.109290i
$297$	−17.0044	−	1.42032i	−0.986697	−	0.0824156i
$298$	−9.63094			−0.557906
$299$	38.4242			2.22213
$300$	1.47537	+	0.907353i	0.0851804	+	0.0523860i
$301$		0			0
$302$			23.5368i			1.35439i
$303$	7.24719	+	4.45703i	0.416340	+	0.256050i
$304$		−	5.51442i		−	0.316274i
$305$		−	14.2325i		−	0.814951i
$306$	−6.43632	+	3.25360i	−0.367940	+	0.185996i
$307$			4.76658i			0.272043i	0.990706	+	0.136022i	$0.0434316\pi$
$307$			4.76658i			0.272043i	−0.990706	+	0.136022i	$0.956568\pi$
$308$		0			0
$309$	4.15243	−	6.75190i	0.236223	−	0.384102i
$310$	−5.20176			−0.295440
$311$	5.97021			0.338540			0.169270	−	0.985570i	$-0.445859\pi$
$311$	5.97021			0.338540			0.169270	+	0.985570i	$0.445859\pi$
$312$	−8.72488	−	5.36581i	−0.493949	−	0.303779i
$313$		−	26.7217i		−	1.51040i	−0.655493	−	0.755201i	$-0.727539\pi$
$313$		−	26.7217i		−	1.51040i	0.655493	−	0.755201i	$-0.272461\pi$
$314$	4.28351			0.241733
$315$		0			0
$316$	−9.15135			−0.514803
$317$		−	23.7721i		−	1.33518i	−0.744531	−	0.667588i	$-0.767327\pi$
$317$		−	23.7721i		−	1.33518i	0.744531	−	0.667588i	$-0.232673\pi$
$318$	3.59671	+	2.21198i	0.201694	+	0.124042i
$319$	−12.5100			−0.700423
$320$	1.00000			0.0559017
$321$	4.47532	−	7.27694i	0.249788	−	0.406159i
$322$		0			0
$323$			13.2566i			0.737615i
$324$	5.33650	−	7.24719i	0.296472	−	0.402622i
$325$		−	5.91369i		−	0.328033i
$326$			22.0893i			1.22341i
$327$	−11.2152	−	6.89738i	−0.620204	−	0.381426i
$328$		−	0.103155i		−	0.00569577i
$329$		0			0
$330$	−4.84496	−	2.97965i	−0.266706	−	0.164025i
$331$	4.55932			0.250603			0.125301	−	0.992119i	$-0.460010\pi$
$331$	4.55932			0.250603			0.125301	+	0.992119i	$0.460010\pi$
$332$	6.54676			0.359300
$333$	−2.54485	−	5.03425i	−0.139457	−	0.275875i
$334$		−	12.9338i		−	0.707707i
$335$	3.35472			0.183288
$336$		0			0
$337$	12.8779			0.701503			0.350751	−	0.936469i	$-0.385926\pi$
$337$	12.8779			0.701503			0.350751	+	0.936469i	$0.385926\pi$
$338$			21.9718i			1.19511i
$339$	−3.52265	+	5.72789i	−0.191324	+	0.311096i
$340$	−2.40398			−0.130374
$341$	17.0820			0.925045
$342$	−7.46334	−	14.7641i	−0.403571	−	0.798350i
$343$		0			0
$344$		−	1.48931i		−	0.0802981i
$345$	−5.89552	+	9.58619i	−0.317404	+	0.516103i
$346$			23.2595i			1.25044i
$347$			18.7893i			1.00866i	0.863511	+	0.504331i	$0.168261\pi$
$347$			18.7893i			1.00866i	−0.863511	+	0.504331i	$0.831739\pi$
$348$	3.45655	−	5.62039i	0.185290	−	0.301285i
$349$			8.52974i			0.456586i	0.973592	+	0.228293i	$0.0733145\pi$
$349$			8.52974i			0.456586i	−0.973592	+	0.228293i	$0.926686\pi$
$350$		0			0
$351$	−30.6218	−	2.55774i	−1.63447	−	0.136522i
$352$	−3.28390			−0.175032
$353$	5.61974			0.299109			0.149554	−	0.988754i	$-0.452216\pi$
$353$	5.61974			0.299109			0.149554	+	0.988754i	$0.452216\pi$
$354$	3.31533	−	5.39078i	0.176208	−	0.286517i
$355$		−	13.9116i		−	0.738349i
$356$	−11.2408			−0.595761
$357$		0			0
$358$	−9.45455			−0.499689
$359$		−	27.0657i		−	1.42847i	−0.699905	−	0.714236i	$-0.746774\pi$
$359$		−	27.0657i		−	1.42847i	0.699905	−	0.714236i	$-0.253226\pi$
$360$	2.67736	−	1.35342i	0.141109	−	0.0713316i
$361$	−11.4088			−0.600464
$362$	8.42502			0.442809
$363$	−0.318698	−	0.196000i	−0.0167273	−	0.0102873i
$364$		0			0
$365$			8.11303i			0.424655i
$366$	−20.9982	−	12.9139i	−1.09759	−	0.675021i
$367$		−	18.7870i		−	0.980675i	−0.871533	−	0.490337i	$-0.836874\pi$
$367$		−	18.7870i		−	0.980675i	0.871533	−	0.490337i	$-0.163126\pi$
$368$			6.49749i			0.338705i
$369$	−0.139612	−	0.276183i	−0.00726792	−	0.0143775i
$370$		−	1.88030i		−	0.0977523i
$371$		0			0
$372$	−4.71983	+	7.67451i	−0.244712	+	0.397905i
$373$	−13.3367			−0.690549			−0.345275	−	0.938502i	$-0.612214\pi$
$373$	−13.3367			−0.690549			−0.345275	+	0.938502i	$0.612214\pi$
$374$	7.89443			0.408211
$375$	1.47537	+	0.907353i	0.0761877	+	0.0468555i
$376$		−	12.4671i		−	0.642940i
$377$	−22.5281			−1.16026
$378$		0			0
$379$	−33.4683			−1.71915			−0.859576	−	0.511008i	$-0.829272\pi$
$379$	−33.4683			−1.71915			−0.859576	+	0.511008i	$0.829272\pi$
$380$		−	5.51442i		−	0.282884i
$381$	20.8588	+	12.8282i	1.06863	+	0.657207i
$382$	−5.13035			−0.262491
$383$	−9.28481			−0.474431			−0.237216	−	0.971457i	$-0.576235\pi$
$383$	−9.28481			−0.474431			−0.237216	+	0.971457i	$0.576235\pi$
$384$	0.907353	−	1.47537i	0.0463031	−	0.0752896i
$385$		0			0
$386$		−	15.2791i		−	0.777686i
$387$	−2.01566	−	3.98741i	−0.102462	−	0.202691i
$388$		−	7.90564i		−	0.401348i
$389$			19.4580i			0.986559i	0.869871	+	0.493279i	$0.164202\pi$
$389$			19.4580i			0.986559i	−0.869871	+	0.493279i	$0.835798\pi$
$390$	−8.72488	−	5.36581i	−0.441801	−	0.271708i
$391$		−	15.6198i		−	0.789929i
$392$		0			0
$393$	7.40864	+	4.55632i	0.373717	+	0.229836i
$394$	−16.0694			−0.809563
$395$	−9.15135			−0.460454
$396$	−8.79217	+	4.44450i	−0.441823	+	0.223345i
$397$		−	2.29058i		−	0.114961i	−0.998347	−	0.0574804i	$-0.981693\pi$
$397$		−	2.29058i		−	0.114961i	0.998347	−	0.0574804i	$-0.0183067\pi$
$398$	−6.63017			−0.332341
$399$		0			0
$400$	1.00000			0.0500000
$401$			1.50904i			0.0753578i	0.999290	+	0.0376789i	$0.0119964\pi$
$401$			1.50904i			0.0753578i	−0.999290	+	0.0376789i	$0.988004\pi$
$402$	3.04391	−	4.94944i	0.151816	−	0.246856i
$403$	30.7616			1.53234
$404$	4.91213			0.244387
$405$	5.33650	−	7.24719i	0.265173	−	0.360116i
$406$		0			0
$407$			6.17473i			0.306070i
$408$	−2.18126	+	3.54676i	−0.107988	+	0.175591i
$409$			19.2437i			0.951540i	0.879570	+	0.475770i	$0.157831\pi$
$409$			19.2437i			0.951540i	−0.879570	+	0.475770i	$0.842169\pi$
$410$		−	0.103155i		−	0.00509446i
$411$	2.65827	−	4.32238i	0.131123	−	0.213207i
$412$		−	4.57642i		−	0.225464i
$413$		0			0
$414$	8.79385	+	17.3961i	0.432194	+	0.854972i
$415$	6.54676			0.321368
$416$	−5.91369			−0.289943
$417$	−3.05376	+	4.96546i	−0.149543	+	0.243160i
$418$			18.1088i			0.885730i
$419$	−1.34919			−0.0659121			−0.0329560	−	0.999457i	$-0.510492\pi$
$419$	−1.34919			−0.0659121			−0.0329560	+	0.999457i	$0.510492\pi$
$420$		0			0
$421$	−23.3783			−1.13939			−0.569695	−	0.821856i	$-0.692939\pi$
$421$	−23.3783			−1.13939			−0.569695	+	0.821856i	$0.692939\pi$
$422$			10.9980i			0.535376i
$423$	−16.8732	−	33.3788i	−0.820403	−	1.62293i
$424$	2.43784			0.118392
$425$	−2.40398			−0.116610
$426$	−20.5247	−	12.6227i	−0.994424	−	0.611572i
$427$		0			0
$428$		−	4.93228i		−	0.238411i
$429$	28.6516	+	17.6208i	1.38331	+	0.850738i
$430$		−	1.48931i		−	0.0718208i
$431$			7.75984i			0.373778i	0.982381	+	0.186889i	$0.0598405\pi$
$431$			7.75984i			0.373778i	−0.982381	+	0.186889i	$0.940160\pi$
$432$	0.432512	−	5.17812i	0.0208092	−	0.249132i
$433$		−	34.0914i		−	1.63833i	−0.573560	−	0.819164i	$-0.694438\pi$
$433$		−	34.0914i		−	1.63833i	0.573560	−	0.819164i	$-0.305562\pi$
$434$		0			0
$435$	3.45655	−	5.62039i	0.165729	−	0.269477i
$436$	−7.60166			−0.364053
$437$	35.8299			1.71398
$438$	11.9697	+	7.36138i	0.571935	+	0.351740i
$439$		−	11.9593i		−	0.570787i	−0.958410	−	0.285393i	$-0.907876\pi$
$439$		−	11.9593i		−	0.570787i	0.958410	−	0.285393i	$-0.0921242\pi$
$440$	−3.28390			−0.156554
$441$		0			0
$442$	14.2164			0.676205
$443$			3.60614i			0.171333i	0.996324	+	0.0856663i	$0.0273019\pi$
$443$			3.60614i			0.171333i	−0.996324	+	0.0856663i	$0.972698\pi$
$444$	−2.77414	−	1.70610i	−0.131655	−	0.0809679i
$445$	−11.2408			−0.532864
$446$	22.0431			1.04377
$447$	−8.73866	+	14.2092i	−0.413325	+	0.672072i
$448$		0			0
$449$		−	19.0134i		−	0.897296i	−0.893708	−	0.448648i	$-0.851906\pi$
$449$		−	19.0134i		−	0.897296i	0.893708	−	0.448648i	$-0.148094\pi$
$450$	2.67736	−	1.35342i	0.126212	−	0.0638009i
$451$			0.338750i			0.0159511i
$452$			3.88234i			0.182610i
$453$	34.7255	+	21.3562i	1.63154	+	1.00340i
$454$			6.24839i			0.293251i
$455$		0			0
$456$	−8.13580	−	5.00352i	−0.380994	−	0.234311i
$457$	37.8904			1.77244			0.886219	−	0.463266i	$-0.153322\pi$
$457$	37.8904			1.77244			0.886219	+	0.463266i	$0.153322\pi$
$458$	12.1852			0.569377
$459$	−1.03975	+	12.4481i	−0.0485313	+	0.581028i
$460$			6.49749i			0.302947i
$461$	32.6110			1.51884			0.759422	−	0.650598i	$-0.225482\pi$
$461$	32.6110			1.51884			0.759422	+	0.650598i	$0.225482\pi$
$462$		0			0
$463$	5.80289			0.269683			0.134841	−	0.990867i	$-0.456947\pi$
$463$	5.80289			0.269683			0.134841	+	0.990867i	$0.456947\pi$
$464$		−	3.80949i		−	0.176851i
$465$	−4.71983	+	7.67451i	−0.218877	+	0.355897i
$466$	−16.1655			−0.748851
$467$	−22.2926			−1.03158			−0.515790	−	0.856715i	$-0.672502\pi$
$467$	−22.2926			−1.03158			−0.515790	+	0.856715i	$0.672502\pi$
$468$	−15.8331	+	8.00373i	−0.731884	+	0.369972i
$469$		0			0
$470$		−	12.4671i		−	0.575063i
$471$	3.88666	−	6.31976i	0.179088	−	0.291199i
$472$		−	3.65385i		−	0.168182i
$473$			4.89073i			0.224876i
$474$	−8.30350	+	13.5016i	−0.381392	+	0.620149i
$475$		−	5.51442i		−	0.253019i
$476$		0			0
$477$	6.52697	−	3.29943i	0.298850	−	0.151070i
$478$	5.36347			0.245319
$479$	42.3883			1.93677			0.968385	−	0.249459i	$-0.0802529\pi$
$479$	42.3883			1.93677			0.968385	+	0.249459i	$0.0802529\pi$
$480$	0.907353	−	1.47537i	0.0414148	−	0.0673410i
$481$			11.1195i			0.507007i
$482$	16.0919			0.732968
$483$		0			0
$484$	−0.216013			−0.00981876
$485$		−	7.90564i		−	0.358977i
$486$	−5.85020	−	14.4491i	−0.265370	−	0.655422i
$487$	17.5505			0.795289			0.397644	−	0.917540i	$-0.369828\pi$
$487$	17.5505			0.795289			0.397644	+	0.917540i	$0.369828\pi$
$488$	−14.2325			−0.644275
$489$	32.5898	+	20.0428i	1.47376	+	0.906365i
$490$		0			0
$491$			31.2732i			1.41134i	0.708542	+	0.705669i	$0.249353\pi$
$491$			31.2732i			1.41134i	−0.708542	+	0.705669i	$0.750647\pi$
$492$	−0.152191	−	0.0935978i	−0.00686132	−	0.00421972i
$493$			9.15793i			0.412452i
$494$			32.6106i			1.46722i
$495$	−8.79217	+	4.44450i	−0.395179	+	0.199765i
$496$			5.20176i			0.233566i
$497$		0			0
$498$	5.94022	−	9.65888i	0.266187	−	0.432825i
$499$	−5.36424			−0.240136			−0.120068	−	0.992766i	$-0.538311\pi$
$499$	−5.36424			−0.240136			−0.120068	+	0.992766i	$0.538311\pi$
$500$	1.00000			0.0447214
$501$	−19.0821	−	11.7355i	−0.852527	−	0.524305i
$502$			1.05846i			0.0472413i
$503$	21.3393			0.951470			0.475735	−	0.879589i	$-0.342182\pi$
$503$	21.3393			0.951470			0.475735	+	0.879589i	$0.342182\pi$
$504$		0			0
$505$	4.91213			0.218587
$506$		−	21.3371i		−	0.948550i
$507$	32.4165	+	19.9362i	1.43967	+	0.885396i
$508$	14.1380			0.627273
$509$	−32.3815			−1.43528			−0.717642	−	0.696412i	$-0.754778\pi$
$509$	−32.3815			−1.43528			−0.717642	+	0.696412i	$0.754778\pi$
$510$	−2.18126	+	3.54676i	−0.0965877	+	0.157053i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−28.5543	−	2.38505i	−1.26070	−	0.105303i
$514$		−	2.46181i		−	0.108586i
$515$		−	4.57642i		−	0.201661i
$516$	−2.19728	−	1.35133i	−0.0967297	−	0.0594889i
$517$			40.9406i			1.80056i
$518$		0			0
$519$	34.3164	+	21.1046i	1.50632	+	0.926389i
$520$	−5.91369			−0.259333
$521$	26.0646			1.14191			0.570955	−	0.820982i	$-0.306573\pi$
$521$	26.0646			1.14191			0.570955	+	0.820982i	$0.306573\pi$
$522$	−5.15584	−	10.1994i	−0.225665	−	0.446414i
$523$		−	12.9907i		−	0.568042i	−0.958818	−	0.284021i	$-0.908331\pi$
$523$		−	12.9907i		−	0.568042i	0.958818	−	0.284021i	$-0.0916686\pi$
$524$	5.02155			0.219368
$525$		0			0
$526$	−30.6984			−1.33851
$527$		−	12.5049i		−	0.544723i
$528$	−2.97965	+	4.84496i	−0.129673	+	0.210850i
$529$	−19.2174			−0.835539
$530$	2.43784			0.105893
$531$	−4.94521	−	9.78268i	−0.214604	−	0.424532i
$532$		0			0
$533$			0.610026i			0.0264232i
$534$	−10.1994	+	16.5843i	−0.441369	+	0.717673i
$535$		−	4.93228i		−	0.213241i
$536$		−	3.35472i		−	0.144902i
$537$	−8.57861	+	13.9489i	−0.370194	+	0.601941i
$538$		−	16.7530i		−	0.722273i
$539$		0			0
$540$	0.432512	−	5.17812i	0.0186123	−	0.222831i
$541$	21.2463			0.913448			0.456724	−	0.889609i	$-0.349023\pi$
$541$	21.2463			0.913448			0.456724	+	0.889609i	$0.349023\pi$
$542$	−15.2626			−0.655587
$543$	7.64446	−	12.4300i	0.328055	−	0.533423i
$544$			2.40398i			0.103070i
$545$	−7.60166			−0.325619
$546$		0			0
$547$	5.49150			0.234800			0.117400	−	0.993085i	$-0.462544\pi$
$547$	5.49150			0.234800			0.117400	+	0.993085i	$0.462544\pi$
$548$		−	2.92970i		−	0.125150i
$549$	−38.1055	+	19.2626i	−1.62630	+	0.822108i
$550$	−3.28390			−0.140026
$551$	−21.0071			−0.894933
$552$	9.58619	+	5.89552i	0.408015	+	0.250930i
$553$		0			0
$554$			3.51222i			0.149220i
$555$	−2.77414	−	1.70610i	−0.117756	−	0.0724199i
$556$			3.36557i			0.142732i
$557$		−	35.4536i		−	1.50222i	−0.660179	−	0.751109i	$-0.729519\pi$
$557$		−	35.4536i		−	1.50222i	0.660179	−	0.751109i	$-0.270481\pi$
$558$	7.04018	+	13.9270i	0.298034	+	0.589576i
$559$			8.80731i			0.372509i
$560$		0			0
$561$	7.16303	−	11.6472i	0.302423	−	0.491745i
$562$	4.15840			0.175412
$563$	−39.1466			−1.64983			−0.824916	−	0.565255i	$-0.808778\pi$
$563$	−39.1466			−1.64983			−0.824916	+	0.565255i	$0.808778\pi$
$564$	−18.3935	−	11.3120i	−0.774507	−	0.476322i
$565$			3.88234i			0.163331i
$566$	0.172611			0.00725538
$567$		0			0
$568$	−13.9116			−0.583716
$569$		−	42.0049i		−	1.76094i	−0.474103	−	0.880469i	$-0.657228\pi$
$569$		−	42.0049i		−	1.76094i	0.474103	−	0.880469i	$-0.342772\pi$
$570$	−8.13580	−	5.00352i	−0.340771	−	0.209575i
$571$	−19.6836			−0.823735			−0.411867	−	0.911244i	$-0.635123\pi$
$571$	−19.6836			−0.823735			−0.411867	+	0.911244i	$0.635123\pi$
$572$	19.4200			0.811990
$573$	−4.65503	+	7.56915i	−0.194467	+	0.316206i
$574$		0			0
$575$			6.49749i			0.270964i
$576$	−1.35342	−	2.67736i	−0.0563926	−	0.111557i
$577$			25.3786i			1.05652i	0.849082	+	0.528261i	$0.177156\pi$
$577$			25.3786i			1.05652i	−0.849082	+	0.528261i	$0.822844\pi$
$578$			11.2209i			0.466727i
$579$	−22.5423	−	13.8635i	−0.936826	−	0.576149i
$580$		−	3.80949i		−	0.158180i
$581$		0			0
$582$	−11.6637	−	7.17320i	−0.483477	−	0.297339i
$583$	−8.00562			−0.331559
$584$	8.11303			0.335719
$585$	−15.8331	+	8.00373i	−0.654617	+	0.330913i
$586$			4.38021i			0.180945i
$587$	−30.1344			−1.24378			−0.621889	−	0.783105i	$-0.713635\pi$
$587$	−30.1344			−1.24378			−0.621889	+	0.783105i	$0.713635\pi$
$588$		0			0
$589$	28.6847			1.18193
$590$		−	3.65385i		−	0.150427i
$591$	−14.5806	+	23.7082i	−0.599765	+	0.975226i
$592$	−1.88030			−0.0772800
$593$	1.01122			0.0415259			0.0207629	−	0.999784i	$-0.493390\pi$
$593$	1.01122			0.0415259			0.0207629	+	0.999784i	$0.493390\pi$
$594$	−1.42032	+	17.0044i	−0.0582766	+	0.697700i
$595$		0			0
$596$			9.63094i			0.394499i
$597$	−6.01590	+	9.78195i	−0.246215	+	0.400348i
$598$		−	38.4242i		−	1.57128i
$599$		−	20.4477i		−	0.835471i	−0.908569	−	0.417735i	$-0.862824\pi$
$599$		−	20.4477i		−	0.835471i	0.908569	−	0.417735i	$-0.137176\pi$
$600$	0.907353	−	1.47537i	0.0370425	−	0.0602317i
$601$		−	43.8623i		−	1.78918i	−0.446886	−	0.894591i	$-0.647467\pi$
$601$		−	43.8623i		−	1.78918i	0.446886	−	0.894591i	$-0.352533\pi$
$602$		0			0
$603$	−4.54035	−	8.98178i	−0.184897	−	0.365766i
$604$	23.5368			0.957699
$605$	−0.216013			−0.00878217
$606$	4.45703	−	7.24719i	0.181054	−	0.294397i
$607$			37.5611i			1.52456i	0.647248	+	0.762280i	$0.275920\pi$
$607$			37.5611i			1.52456i	−0.647248	+	0.762280i	$0.724080\pi$
$608$	−5.51442			−0.223639
$609$		0			0
$610$	−14.2325			−0.576257
$611$			73.7264i			2.98265i
$612$	3.25360	+	6.43632i	0.131519	+	0.260173i
$613$	45.3115			1.83011			0.915057	−	0.403325i	$-0.132146\pi$
$613$	45.3115			1.83011			0.915057	+	0.403325i	$0.132146\pi$
$614$	4.76658			0.192364
$615$	−0.152191	−	0.0935978i	−0.00613695	−	0.00377423i
$616$		0			0
$617$			28.3334i			1.14066i	0.821416	+	0.570329i	$0.193184\pi$
$617$			28.3334i			1.14066i	−0.821416	+	0.570329i	$0.806816\pi$
$618$	−6.75190	−	4.15243i	−0.271601	−	0.167035i
$619$		−	15.7473i		−	0.632937i	−0.948603	−	0.316468i	$-0.897503\pi$
$619$		−	15.7473i		−	0.632937i	0.948603	−	0.316468i	$-0.102497\pi$
$620$			5.20176i			0.208908i
$621$	33.6448	+	2.81024i	1.35012	+	0.112771i
$622$		−	5.97021i		−	0.239384i
$623$		0			0
$624$	−5.36581	+	8.72488i	−0.214804	+	0.349275i
$625$	1.00000			0.0400000
$626$	−26.7217			−1.06802
$627$	26.7171	+	16.4311i	1.06698	+	0.656193i
$628$		−	4.28351i		−	0.170931i
$629$	4.52021			0.180233
$630$		0			0
$631$	18.3939			0.732252			0.366126	−	0.930565i	$-0.380684\pi$
$631$	18.3939			0.732252			0.366126	+	0.930565i	$0.380684\pi$
$632$			9.15135i			0.364021i
$633$	16.2261	+	9.97909i	0.644931	+	0.396633i
$634$	−23.7721			−0.944112
$635$	14.1380			0.561050
$636$	2.21198	−	3.59671i	0.0877108	−	0.142619i
$637$		0			0
$638$			12.5100i			0.495274i
$639$	−37.2463	+	18.8282i	−1.47344	+	0.744833i
$640$		−	1.00000i		−	0.0395285i
$641$		−	22.8881i		−	0.904026i	−0.892011	−	0.452013i	$-0.850706\pi$
$641$		−	22.8881i		−	0.904026i	0.892011	−	0.452013i	$-0.149294\pi$
$642$	−7.27694	−	4.47532i	−0.287198	−	0.176627i
$643$			10.5338i			0.415411i	0.978191	+	0.207705i	$0.0665995\pi$
$643$			10.5338i			0.415411i	−0.978191	+	0.207705i	$0.933400\pi$
$644$		0			0
$645$	−2.19728	−	1.35133i	−0.0865177	−	0.0532084i
$646$	13.2566			0.521572
$647$	−24.8945			−0.978704			−0.489352	−	0.872086i	$-0.662767\pi$
$647$	−24.8945			−0.978704			−0.489352	+	0.872086i	$0.662767\pi$
$648$	−7.24719	−	5.33650i	−0.284697	−	0.209637i
$649$			11.9989i			0.470997i
$650$	−5.91369			−0.231954
$651$		0			0
$652$	22.0893			0.865083
$653$			41.4890i			1.62359i	0.583943	+	0.811795i	$0.301509\pi$
$653$			41.4890i			1.62359i	−0.583943	+	0.811795i	$0.698491\pi$
$654$	−6.89738	+	11.2152i	−0.269709	+	0.438551i
$655$	5.02155			0.196208
$656$	−0.103155			−0.00402752
$657$	21.7215	−	10.9804i	0.847436	−	0.428384i
$658$		0			0
$659$		−	2.65098i		−	0.103268i	−0.998666	−	0.0516338i	$-0.983557\pi$
$659$		−	2.65098i		−	0.103268i	0.998666	−	0.0516338i	$-0.0164429\pi$
$660$	−2.97965	+	4.84496i	−0.115983	+	0.188590i
$661$		−	13.1948i		−	0.513219i	−0.966515	−	0.256610i	$-0.917395\pi$
$661$		−	13.1948i		−	0.513219i	0.966515	−	0.256610i	$-0.0826054\pi$
$662$		−	4.55932i		−	0.177203i
$663$	12.8993	−	20.9744i	0.500967	−	0.814579i
$664$		−	6.54676i		−	0.254063i
$665$		0			0
$666$	−5.03425	+	2.54485i	−0.195073	+	0.0986108i
$667$	24.7521			0.958405
$668$	−12.9338			−0.500424
$669$	20.0009	−	32.5217i	0.773278	−	1.25736i
$670$		−	3.35472i		−	0.129604i
$671$	46.7381			1.80430
$672$		0			0
$673$	−2.26483			−0.0873027			−0.0436514	−	0.999047i	$-0.513899\pi$
$673$	−2.26483			−0.0873027			−0.0436514	+	0.999047i	$0.513899\pi$
$674$		−	12.8779i		−	0.496037i
$675$	0.432512	−	5.17812i	0.0166474	−	0.199306i
$676$	21.9718			0.845069
$677$	11.8106			0.453919			0.226960	−	0.973904i	$-0.427121\pi$
$677$	11.8106			0.453919			0.226960	+	0.973904i	$0.427121\pi$
$678$	5.72789	+	3.52265i	0.219978	+	0.135287i
$679$		0			0
$680$			2.40398i			0.0921884i
$681$	9.21868	+	5.66949i	0.353260	+	0.217255i
$682$		−	17.0820i		−	0.654105i
$683$			4.46238i			0.170748i	0.996349	+	0.0853742i	$0.0272086\pi$
$683$			4.46238i			0.170748i	−0.996349	+	0.0853742i	$0.972791\pi$
$684$	−14.7641	+	7.46334i	−0.564519	+	0.285368i
$685$		−	2.92970i		−	0.111938i
$686$		0			0
$687$	11.0563	−	17.9777i	0.421823	−	0.685891i
$688$	−1.48931			−0.0567793
$689$	−14.4166			−0.549231
$690$	9.58619	+	5.89552i	0.364940	+	0.224438i
$691$		−	27.2979i		−	1.03846i	−0.854635	−	0.519230i	$-0.826219\pi$
$691$		−	27.2979i		−	1.03846i	0.854635	−	0.519230i	$-0.173781\pi$
$692$	23.2595			0.884195
$693$		0			0
$694$	18.7893			0.713231
$695$			3.36557i			0.127664i
$696$	−5.62039	−	3.45655i	−0.213040	−	0.131020i
$697$	0.247982			0.00939300
$698$	8.52974			0.322855
$699$	−14.6678	+	23.8500i	−0.554786	+	0.902090i
$700$		0			0
$701$		−	23.5071i		−	0.887851i	−0.896064	−	0.443926i	$-0.853585\pi$
$701$		−	23.5071i		−	0.887851i	0.896064	−	0.443926i	$-0.146415\pi$
$702$	−2.55774	+	30.6218i	−0.0965357	+	1.15575i
$703$			10.3688i			0.391066i
$704$			3.28390i			0.123767i
$705$	−18.3935	−	11.3120i	−0.692740	−	0.426036i
$706$		−	5.61974i		−	0.211502i
$707$		0			0
$708$	−5.39078	−	3.31533i	−0.202598	−	0.124598i
$709$	27.0190			1.01472			0.507360	−	0.861734i	$-0.330622\pi$
$709$	27.0190			1.01472			0.507360	+	0.861734i	$0.330622\pi$
$710$	−13.9116			−0.522092
$711$	12.3856	+	24.5014i	0.464498	+	0.918876i
$712$			11.2408i			0.421266i
$713$	−33.7984			−1.26576
$714$		0			0
$715$	19.4200			0.726266
$716$			9.45455i			0.353333i
$717$	4.86655	−	7.91309i	0.181745	−	0.295520i
$718$	−27.0657			−1.01008
$719$	−34.6720			−1.29305			−0.646524	−	0.762894i	$-0.723778\pi$
$719$	−34.6720			−1.29305			−0.646524	+	0.762894i	$0.723778\pi$
$720$	−1.35342	−	2.67736i	−0.0504391	−	0.0997793i
$721$		0			0
$722$			11.4088i			0.424592i
$723$	14.6011	−	23.7415i	0.543019	−	0.882957i
$724$		−	8.42502i		−	0.313113i
$725$		−	3.80949i		−	0.141481i
$726$	−0.196000	+	0.318698i	−0.00727423	+	0.0118280i
$727$			16.8936i			0.626549i	0.949663	+	0.313274i	$0.101426\pi$
$727$			16.8936i			0.626549i	−0.949663	+	0.313274i	$0.898574\pi$
$728$		0			0
$729$	−26.6259	−	4.47919i	−0.986143	−	0.165896i
$730$	8.11303			0.300277
$731$	3.58027			0.132421
$732$	−12.9139	+	20.9982i	−0.477312	+	0.776115i
$733$			18.0499i			0.666688i	0.942805	+	0.333344i	$0.108177\pi$
$733$			18.0499i			0.666688i	−0.942805	+	0.333344i	$0.891823\pi$
$734$	−18.7870			−0.693442
$735$		0			0
$736$	6.49749			0.239501
$737$			11.0165i			0.405800i
$738$	−0.276183	+	0.139612i	−0.0101664	+	0.00513919i
$739$	26.4469			0.972866			0.486433	−	0.873718i	$-0.338298\pi$
$739$	26.4469			0.972866			0.486433	+	0.873718i	$0.338298\pi$
$740$	−1.88030			−0.0691213
$741$	48.1126	+	29.5893i	1.76746	+	1.08699i
$742$		0			0
$743$		−	48.5084i		−	1.77960i	−0.456350	−	0.889801i	$-0.650843\pi$
$743$		−	48.5084i		−	1.77960i	0.456350	−	0.889801i	$-0.349157\pi$
$744$	7.67451	+	4.71983i	0.281361	+	0.173037i
$745$			9.63094i			0.352851i
$746$			13.3367i			0.488292i
$747$	−8.86053	−	17.5280i	−0.324190	−	0.641316i
$748$		−	7.89443i		−	0.288649i
$749$		0			0
$750$	0.907353	−	1.47537i	0.0331318	−	0.0538728i
$751$	−15.7034			−0.573025			−0.286512	−	0.958077i	$-0.592496\pi$
$751$	−15.7034			−0.573025			−0.286512	+	0.958077i	$0.592496\pi$
$752$	−12.4671			−0.454627
$753$	1.56162	+	0.960395i	0.0569085	+	0.0349988i
$754$			22.5281i			0.820426i
$755$	23.5368			0.856592
$756$		0			0
$757$	5.53921			0.201326			0.100663	−	0.994921i	$-0.467904\pi$
$757$	5.53921			0.201326			0.100663	+	0.994921i	$0.467904\pi$
$758$			33.4683i			1.21562i
$759$	−31.4801	−	19.3603i	−1.14265	−	0.702734i
$760$	−5.51442			−0.200029
$761$	−13.7586			−0.498748			−0.249374	−	0.968407i	$-0.580225\pi$
$761$	−13.7586			−0.498748			−0.249374	+	0.968407i	$0.580225\pi$
$762$	12.8282	−	20.8588i	0.464715	−	0.755634i
$763$		0			0
$764$			5.13035i			0.185609i
$765$	3.25360	+	6.43632i	0.117634	+	0.232706i
$766$			9.28481i			0.335474i
$767$			21.6078i			0.780212i
$768$	−1.47537	−	0.907353i	−0.0532378	−	0.0327413i
$769$		−	11.0157i		−	0.397238i	−0.980077	−	0.198619i	$-0.936354\pi$
$769$		−	11.0157i		−	0.397238i	0.980077	−	0.198619i	$-0.0636455\pi$
$770$		0			0
$771$	−3.63208	−	2.23373i	−0.130806	−	0.0804460i
$772$	−15.2791			−0.549907
$773$	−35.1440			−1.26404			−0.632022	−	0.774951i	$-0.717775\pi$
$773$	−35.1440			−1.26404			−0.632022	+	0.774951i	$0.717775\pi$
$774$	−3.98741	+	2.01566i	−0.143324	+	0.0724515i
$775$			5.20176i			0.186853i
$776$	−7.90564			−0.283796
$777$		0			0
$778$	19.4580			0.697602
$779$			0.568839i			0.0203808i
$780$	−5.36581	+	8.72488i	−0.192127	+	0.312401i
$781$	45.6842			1.63471
$782$	−15.6198			−0.558564
$783$	−19.7260	−	1.64765i	−0.704949	−	0.0588821i
$784$		0			0
$785$		−	4.28351i		−	0.152885i
$786$	4.55632	−	7.40864i	0.162519	−	0.264258i
$787$		−	6.98016i		−	0.248816i	−0.992231	−	0.124408i	$-0.960297\pi$
$787$		−	6.98016i		−	0.248816i	0.992231	−	0.124408i	$-0.0397031\pi$
$788$			16.0694i			0.572447i
$789$	−27.8542	+	45.2914i	−0.991637	+	1.61242i
$790$			9.15135i			0.325590i
$791$		0			0
$792$	4.44450	+	8.79217i	0.157928	+	0.312416i
$793$	84.1667			2.98885
$794$	−2.29058			−0.0812895
$795$	2.21198	−	3.59671i	0.0784509	−	0.127562i
$796$			6.63017i			0.235000i
$797$	−0.975566			−0.0345563			−0.0172782	−	0.999851i	$-0.505500\pi$
$797$	−0.975566			−0.0345563			−0.0172782	+	0.999851i	$0.505500\pi$
$798$		0			0
$799$	29.9706			1.06028
$800$		−	1.00000i		−	0.0353553i
$801$	15.2135	+	30.0956i	0.537544	+	1.06338i
$802$	1.50904			0.0532860
$803$	−26.6424			−0.940188
$804$	−4.94944	−	3.04391i	−0.174553	−	0.107350i
$805$		0			0
$806$		−	30.7616i		−	1.08353i
$807$	−24.7168	−	15.2009i	−0.870074	−	0.535096i
$808$		−	4.91213i		−	0.172808i
$809$		−	29.3199i		−	1.03083i	−0.856940	−	0.515416i	$-0.827637\pi$
$809$		−	29.3199i		−	1.03083i	0.856940	−	0.515416i	$-0.172363\pi$
$810$	−7.24719	−	5.33650i	−0.254640	−	0.187505i
$811$			1.54090i			0.0541084i	0.999634	+	0.0270542i	$0.00861267\pi$
$811$			1.54090i			0.0541084i	−0.999634	+	0.0270542i	$0.991387\pi$
$812$		0			0
$813$	−13.8486	+	22.5180i	−0.485692	+	0.789741i
$814$	6.17473			0.216424
$815$	22.0893			0.773753
$816$	3.54676	+	2.18126i	0.124161	+	0.0763593i
$817$			8.21267i			0.287325i
$818$	19.2437			0.672841
$819$		0			0
$820$	−0.103155			−0.00360232
$821$		−	31.4943i		−	1.09916i	−0.835442	−	0.549579i	$-0.814788\pi$
$821$		−	31.4943i		−	1.09916i	0.835442	−	0.549579i	$-0.185212\pi$
$822$	−4.32238	−	2.65827i	−0.150760	−	0.0927177i
$823$	−46.9378			−1.63615			−0.818074	−	0.575113i	$-0.804958\pi$
$823$	−46.9378			−1.63615			−0.818074	+	0.575113i	$0.804958\pi$
$824$	−4.57642			−0.159427
$825$	−2.97965	+	4.84496i	−0.103738	+	0.168680i
$826$		0			0
$827$		−	7.83421i		−	0.272422i	−0.990680	−	0.136211i	$-0.956507\pi$
$827$		−	7.83421i		−	0.272422i	0.990680	−	0.136211i	$-0.0434925\pi$
$828$	17.3961	−	8.79385i	0.604557	−	0.305607i
$829$			12.1173i			0.420852i	0.977610	+	0.210426i	$0.0674851\pi$
$829$			12.1173i			0.420852i	−0.977610	+	0.210426i	$0.932515\pi$
$830$		−	6.54676i		−	0.227241i
$831$	5.18181	+	3.18682i	0.179755	+	0.110550i
$832$			5.91369i			0.205020i
$833$		0			0
$834$	4.96546	+	3.05376i	0.171940	+	0.105743i
$835$	−12.9338			−0.447593
$836$	18.1088			0.626306
$837$	26.9353	+	2.24982i	0.931021	+	0.0777652i
$838$			1.34919i			0.0466069i
$839$	−12.4633			−0.430279			−0.215140	−	0.976583i	$-0.569021\pi$
$839$	−12.4633			−0.430279			−0.215140	+	0.976583i	$0.569021\pi$
$840$		0			0
$841$	14.4878			0.499580
$842$			23.3783i			0.805671i
$843$	3.77314	−	6.13517i	0.129954	−	0.211307i
$844$	10.9980			0.378568
$845$	21.9718			0.755852
$846$	−33.3788	+	16.8732i	−1.14759	+	0.580113i
$847$		0			0
$848$		−	2.43784i		−	0.0837158i
$849$	0.156619	−	0.254665i	0.00537515	−	0.00874007i
$850$			2.40398i			0.0824558i
$851$		−	12.2173i		−	0.418802i
$852$	−12.6227	+	20.5247i	−0.432446	+	0.703164i
$853$			21.5297i			0.737162i	0.929596	+	0.368581i	$0.120156\pi$
$853$			21.5297i			0.737162i	−0.929596	+	0.368581i	$0.879844\pi$
$854$		0			0
$855$	−14.7641	+	7.46334i	−0.504921	+	0.255241i
$856$	−4.93228			−0.168582
$857$	−50.3563			−1.72014			−0.860069	−	0.510177i	$-0.829580\pi$
$857$	−50.3563			−1.72014			−0.860069	+	0.510177i	$0.829580\pi$
$858$	17.6208	−	28.6516i	0.601563	−	0.978150i
$859$		−	11.9773i		−	0.408659i	−0.978902	−	0.204329i	$-0.934499\pi$
$859$		−	11.9773i		−	0.408659i	0.978902	−	0.204329i	$-0.0655013\pi$
$860$	−1.48931			−0.0507850
$861$		0			0
$862$	7.75984			0.264301
$863$			51.8999i			1.76669i	0.468722	+	0.883346i	$0.344715\pi$
$863$			51.8999i			1.76669i	−0.468722	+	0.883346i	$0.655285\pi$
$864$	−5.17812	−	0.432512i	−0.176163	−	0.0147143i
$865$	23.2595			0.790848
$866$	−34.0914			−1.15847
$867$	16.5549	+	10.1813i	0.562235	+	0.345775i
$868$		0			0
$869$		−	30.0521i		−	1.01945i
$870$	−5.62039	−	3.45655i	−0.190549	−	0.117188i
$871$			19.8388i			0.672211i
$872$			7.60166i			0.257425i
$873$	−21.1662	+	10.6997i	−0.716368	+	0.362129i
$874$		−	35.8299i		−	1.21196i
$875$		0			0
$876$	7.36138	−	11.9697i	0.248718	−	0.404419i
$877$	−8.61953			−0.291061			−0.145530	−	0.989354i	$-0.546489\pi$
$877$	−8.61953			−0.291061			−0.145530	+	0.989354i	$0.546489\pi$
$878$	−11.9593			−0.403607
$879$	6.46243	+	3.97440i	0.217972	+	0.134053i
$880$			3.28390i			0.110700i
$881$	−21.7764			−0.733667			−0.366833	−	0.930287i	$-0.619558\pi$
$881$	−21.7764			−0.733667			−0.366833	+	0.930287i	$0.619558\pi$
$882$		0			0
$883$	24.1748			0.813546			0.406773	−	0.913529i	$-0.366654\pi$
$883$	24.1748			0.813546			0.406773	+	0.913529i	$0.366654\pi$
$884$		−	14.2164i		−	0.478149i
$885$	−5.39078	−	3.31533i	−0.181209	−	0.111444i
$886$	3.60614			0.121151
$887$	19.7429			0.662903			0.331452	−	0.943472i	$-0.392462\pi$
$887$	19.7429			0.662903			0.331452	+	0.943472i	$0.392462\pi$
$888$	−1.70610	+	2.77414i	−0.0572529	+	0.0930941i
$889$		0			0
$890$			11.2408i			0.376792i
$891$	23.7990	+	17.5245i	0.797298	+	0.587093i
$892$		−	22.0431i		−	0.738058i
$893$			68.7486i			2.30059i
$894$	14.2092	+	8.73866i	0.475226	+	0.292265i
$895$			9.45455i			0.316031i
$896$		0			0
$897$	−56.6898	−	34.8643i	−1.89282	−	1.16408i
$898$	−19.0134			−0.634484
$899$	19.8160			0.660901
$900$	−1.35342	−	2.67736i	−0.0451141	−	0.0892453i
$901$			5.86052i			0.195242i
$902$	0.338750			0.0112791
$903$		0			0
$904$	3.88234			0.129125
$905$		−	8.42502i		−	0.280057i
$906$	21.3562	−	34.7255i	0.709512	−	1.15368i
$907$	−21.1423			−0.702019			−0.351010	−	0.936372i	$-0.614162\pi$
$907$	−21.1423			−0.702019			−0.351010	+	0.936372i	$0.614162\pi$
$908$	6.24839			0.207360
$909$	−6.64818	−	13.1515i	−0.220506	−	0.436208i
$910$		0			0
$911$			48.9326i			1.62121i	0.585594	+	0.810604i	$0.300861\pi$
$911$			48.9326i			1.62121i	−0.585594	+	0.810604i	$0.699139\pi$
$912$	−5.00352	+	8.13580i	−0.165683	+	0.269403i
$913$			21.4989i			0.711509i
$914$		−	37.8904i		−	1.25330i
$915$	−12.9139	+	20.9982i	−0.426920	+	0.694179i
$916$		−	12.1852i		−	0.402611i
$917$		0			0
$918$	12.4481	+	1.03975i	0.410849	+	0.0343168i
$919$	−22.4405			−0.740245			−0.370123	−	0.928983i	$-0.620684\pi$
$919$	−22.4405			−0.740245			−0.370123	+	0.928983i	$0.620684\pi$
$920$	6.49749			0.214216
$921$	4.32497	−	7.03246i	0.142513	−	0.231727i
$922$		−	32.6110i		−	1.07399i
$923$	82.2688			2.70791
$924$		0			0
$925$	−1.88030			−0.0618240
$926$		−	5.80289i		−	0.190695i
$927$	−12.2527	+	6.19383i	−0.402432	+	0.203432i
$928$	−3.80949			−0.125052
$929$	17.0461			0.559265			0.279632	−	0.960107i	$-0.409787\pi$
$929$	17.0461			0.559265			0.279632	+	0.960107i	$0.409787\pi$
$930$	7.67451	+	4.71983i	0.251657	+	0.154769i
$931$		0			0
$932$			16.1655i			0.529517i
$933$	−8.80826	−	5.41709i	−0.288369	−	0.177347i
$934$			22.2926i			0.729437i
$935$		−	7.89443i		−	0.258175i
$936$	8.00373	+	15.8331i	0.261610	+	0.517520i
$937$		−	38.9259i		−	1.27165i	−0.771832	−	0.635827i	$-0.780659\pi$
$937$		−	38.9259i		−	1.27165i	0.771832	−	0.635827i	$-0.219341\pi$
$938$		0			0
$939$	−24.2460	+	39.4244i	−0.791240	+	1.28657i
$940$	−12.4671			−0.406631
$941$	−36.1355			−1.17798			−0.588992	−	0.808139i	$-0.700475\pi$
$941$	−36.1355			−1.17798			−0.588992	+	0.808139i	$0.700475\pi$
$942$	−6.31976	−	3.88666i	−0.205909	−	0.126634i
$943$		−	0.670248i		−	0.0218263i
$944$	−3.65385			−0.118923
$945$		0			0
$946$	4.89073			0.159011
$947$			9.05604i			0.294282i	0.989116	+	0.147141i	$0.0470071\pi$
$947$			9.05604i			0.294282i	−0.989116	+	0.147141i	$0.952993\pi$
$948$	13.5016	+	8.30350i	0.438512	+	0.269685i
$949$	−47.9780			−1.55743
$950$	−5.51442			−0.178911
$951$	−21.5697	+	35.0727i	−0.699446	+	1.13731i
$952$		0			0
$953$			45.8921i			1.48659i	0.668963	+	0.743296i	$0.266739\pi$
$953$			45.8921i			1.48659i	−0.668963	+	0.743296i	$0.733261\pi$
$954$	−3.29943	−	6.52697i	−0.106823	−	0.211319i
$955$			5.13035i			0.166014i
$956$		−	5.36347i		−	0.173467i
$957$	18.4568	+	11.3509i	0.596624	+	0.366924i
$958$		−	42.3883i		−	1.36950i
$959$		0			0
$960$	−1.47537	−	0.907353i	−0.0476173	−	0.0292847i
$961$	3.94171			0.127152
$962$	11.1195			0.358508
$963$	−13.2055	+	6.67546i	−0.425541	+	0.215114i
$964$		−	16.0919i		−	0.518286i
$965$	−15.2791			−0.491852
$966$		0			0
$967$	−13.6246			−0.438137			−0.219068	−	0.975710i	$-0.570302\pi$
$967$	−13.6246			−0.438137			−0.219068	+	0.975710i	$0.570302\pi$
$968$			0.216013i			0.00694291i
$969$	12.0284	−	19.5583i	0.386407	−	0.628303i
$970$	−7.90564			−0.253835
$971$	−34.4743			−1.10633			−0.553166	−	0.833071i	$-0.686581\pi$
$971$	−34.4743			−1.10633			−0.553166	+	0.833071i	$0.686581\pi$
$972$	−14.4491	+	5.85020i	−0.463454	+	0.187645i
$973$		0			0
$974$		−	17.5505i		−	0.562354i
$975$	−5.36581	+	8.72488i	−0.171843	+	0.279420i
$976$			14.2325i			0.455571i
$977$			7.04521i			0.225396i	0.993629	+	0.112698i	$0.0359493\pi$
$977$			7.04521i			0.225396i	−0.993629	+	0.112698i	$0.964051\pi$
$978$	20.0428	−	32.5898i	0.640897	−	1.04211i
$979$		−	36.9136i		−	1.17976i
$980$		0			0
$981$	10.2883	+	20.3524i	0.328479	+	0.649801i
$982$	31.2732			0.997967
$983$	52.9665			1.68937			0.844685	−	0.535263i	$-0.179788\pi$
$983$	52.9665			1.68937			0.844685	+	0.535263i	$0.179788\pi$
$984$	−0.0935978	+	0.152191i	−0.00298379	+	0.00485168i
$985$			16.0694i			0.512012i
$986$	9.15793			0.291648
$987$		0			0
$988$	32.6106			1.03748
$989$		−	9.67676i		−	0.307703i
$990$	4.44450	+	8.79217i	0.141256	+	0.279434i
$991$	−30.8776			−0.980859			−0.490429	−	0.871481i	$-0.663160\pi$
$991$	−30.8776			−0.980859			−0.490429	+	0.871481i	$0.663160\pi$
$992$	5.20176			0.165156
$993$	−6.72668	−	4.13691i	−0.213465	−	0.131281i
$994$		0			0
$995$			6.63017i			0.210191i
$996$	−9.65888	−	5.94022i	−0.306053	−	0.188223i
$997$			24.8993i			0.788569i	0.918988	+	0.394285i	$0.129008\pi$
$997$			24.8993i			0.788569i	−0.918988	+	0.394285i	$0.870992\pi$
$998$			5.36424i			0.169802i
$999$	−0.813253	+	9.73644i	−0.0257302	+	0.308047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.b.881.1		12
3.2	odd	2		1470.2.b.a.881.12		12
7.4	even	3		210.2.r.a.131.5	yes	12
7.5	odd	6		210.2.r.b.101.1	yes	12
7.6	odd	2		1470.2.b.a.881.6		12
21.5	even	6		210.2.r.a.101.5	✓	12
21.11	odd	6		210.2.r.b.131.1	yes	12
21.20	even	2	inner	1470.2.b.b.881.7		12
35.4	even	6		1050.2.s.g.551.2		12
35.12	even	12		1050.2.u.e.899.4		12
35.18	odd	12		1050.2.u.g.299.1		12
35.19	odd	6		1050.2.s.f.101.6		12
35.32	odd	12		1050.2.u.f.299.6		12
35.33	even	12		1050.2.u.h.899.3		12
105.32	even	12		1050.2.u.h.299.3		12
105.47	odd	12		1050.2.u.g.899.1		12
105.53	even	12		1050.2.u.e.299.4		12
105.68	odd	12		1050.2.u.f.899.6		12
105.74	odd	6		1050.2.s.f.551.6		12
105.89	even	6		1050.2.s.g.101.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.5	✓	12	21.5	even	6
210.2.r.a.131.5	yes	12	7.4	even	3
210.2.r.b.101.1	yes	12	7.5	odd	6
210.2.r.b.131.1	yes	12	21.11	odd	6
1050.2.s.f.101.6		12	35.19	odd	6
1050.2.s.f.551.6		12	105.74	odd	6
1050.2.s.g.101.2		12	105.89	even	6
1050.2.s.g.551.2		12	35.4	even	6
1050.2.u.e.299.4		12	105.53	even	12
1050.2.u.e.899.4		12	35.12	even	12
1050.2.u.f.299.6		12	35.32	odd	12
1050.2.u.f.899.6		12	105.68	odd	12
1050.2.u.g.299.1		12	35.18	odd	12
1050.2.u.g.899.1		12	105.47	odd	12
1050.2.u.h.299.3		12	105.32	even	12
1050.2.u.h.899.3		12	35.33	even	12
1470.2.b.a.881.6		12	7.6	odd	2
1470.2.b.a.881.12		12	3.2	odd	2
1470.2.b.b.881.1		12	1.1	even	1	trivial
1470.2.b.b.881.7		12	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.47537 - 0.907353i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.907353 + 1.47537i) q^{6} +1.00000i q^{8} +(1.35342 + 2.67736i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.47537 - 0.907353i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-0.907353 + 1.47537i) q^{6} +1.00000i q^{8} +(1.35342 + 2.67736i) q^{9} +1.00000i q^{10} -3.28390i q^{11} +(1.47537 + 0.907353i) q^{12} -5.91369i q^{13} +(1.47537 + 0.907353i) q^{15} +1.00000 q^{16} -2.40398 q^{17} +(2.67736 - 1.35342i) q^{18} -5.51442i q^{19} +1.00000 q^{20} -3.28390 q^{22} +6.49749i q^{23} +(0.907353 - 1.47537i) q^{24} +1.00000 q^{25} -5.91369 q^{26} +(0.432512 - 5.17812i) q^{27} -3.80949i q^{29} +(0.907353 - 1.47537i) q^{30} +5.20176i q^{31} -1.00000i q^{32} +(-2.97965 + 4.84496i) q^{33} +2.40398i q^{34} +(-1.35342 - 2.67736i) q^{36} -1.88030 q^{37} -5.51442 q^{38} +(-5.36581 + 8.72488i) q^{39} -1.00000i q^{40} -0.103155 q^{41} -1.48931 q^{43} +3.28390i q^{44} +(-1.35342 - 2.67736i) q^{45} +6.49749 q^{46} -12.4671 q^{47} +(-1.47537 - 0.907353i) q^{48} -1.00000i q^{50} +(3.54676 + 2.18126i) q^{51} +5.91369i q^{52} -2.43784i q^{53} +(-5.17812 - 0.432512i) q^{54} +3.28390i q^{55} +(-5.00352 + 8.13580i) q^{57} -3.80949 q^{58} -3.65385 q^{59} +(-1.47537 - 0.907353i) q^{60} +14.2325i q^{61} +5.20176 q^{62} -1.00000 q^{64} +5.91369i q^{65} +(4.84496 + 2.97965i) q^{66} -3.35472 q^{67} +2.40398 q^{68} +(5.89552 - 9.58619i) q^{69} +13.9116i q^{71} +(-2.67736 + 1.35342i) q^{72} -8.11303i q^{73} +1.88030i q^{74} +(-1.47537 - 0.907353i) q^{75} +5.51442i q^{76} +(8.72488 + 5.36581i) q^{78} +9.15135 q^{79} -1.00000 q^{80} +(-5.33650 + 7.24719i) q^{81} +0.103155i q^{82} -6.54676 q^{83} +2.40398 q^{85} +1.48931i q^{86} +(-3.45655 + 5.62039i) q^{87} +3.28390 q^{88} +11.2408 q^{89} +(-2.67736 + 1.35342i) q^{90} -6.49749i q^{92} +(4.71983 - 7.67451i) q^{93} +12.4671i q^{94} +5.51442i q^{95} +(-0.907353 + 1.47537i) q^{96} +7.90564i q^{97} +(8.79217 - 4.44450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9	\( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9 - 4 * q^12 - 4 * q^15 + 12 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 2 * q^24 + 12 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^30 + 20 * q^33 + 6 * q^36 + 16 * q^37 - 16 * q^38 + 12 * q^39 - 4 * q^41 + 6 * q^45 - 4 * q^46 - 32 * q^47 + 4 * q^48 + 4 * q^51 - 28 * q^54 - 36 * q^57 - 16 * q^58 - 24 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^64 + 20 * q^66 + 8 * q^67 + 24 * q^68 + 50 * q^69 - 8 * q^72 + 4 * q^75 + 32 * q^78 + 8 * q^79 - 12 * q^80 - 10 * q^81 - 40 * q^83 + 24 * q^85 + 56 * q^87 - 52 * q^89 - 8 * q^90 + 28 * q^93 - 2 * q^96 + 48 * q^99

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