LMFDB - Embedded newform 100.9.b.d.51.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(51,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.51"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{61}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.8
Root			$-2.93811 - 7.65619i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.d.51.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.64016 + 15.3124i) q^{2} +75.7492i q^{3} +(-212.938 - 142.104i) q^{4} +(-1159.90 - 351.488i) q^{6} +210.345i q^{7} +(3164.01 - 2601.20i) q^{8} +823.060 q^{9} -141.724i q^{11} +(10764.2 - 16129.9i) q^{12} +17655.5 q^{13} +(-3220.88 - 976.035i) q^{14} +(25149.0 + 60518.5i) q^{16} +102231. q^{17} +(-3819.13 + 12603.0i) q^{18} -107088. i q^{19} -15933.5 q^{21} +(2170.13 + 657.620i) q^{22} +455526. i q^{23} +(197039. + 239671. i) q^{24} +(-81924.3 + 270348. i) q^{26} +559337. i q^{27} +(29890.8 - 44790.4i) q^{28} +865184. q^{29} -429788. i q^{31} +(-1.04338e6 + 104276. i) q^{32} +10735.4 q^{33} +(-474366. + 1.56539e6i) q^{34} +(-175261. - 116960. i) q^{36} +2.51809e6 q^{37} +(1.63978e6 + 496908. i) q^{38} +1.33739e6i q^{39} -2.98042e6 q^{41} +(73933.8 - 243979. i) q^{42} +2.22228e6i q^{43} +(-20139.5 + 30178.3i) q^{44} +(-6.97518e6 - 2.11371e6i) q^{46} -7.63886e6i q^{47} +(-4.58423e6 + 1.90502e6i) q^{48} +5.72056e6 q^{49} +7.74388e6i q^{51} +(-3.75952e6 - 2.50891e6i) q^{52} -1.55615e7 q^{53} +(-8.56477e6 - 2.59541e6i) q^{54} +(547149. + 665534. i) q^{56} +8.11187e6 q^{57} +(-4.01459e6 + 1.32480e7i) q^{58} -6.38433e6i q^{59} +2.03289e6 q^{61} +(6.58108e6 + 1.99429e6i) q^{62} +173127. i q^{63} +(3.24473e6 - 1.64605e7i) q^{64} +(-49814.2 + 164385. i) q^{66} +2.03503e7i q^{67} +(-2.17688e7 - 1.45274e7i) q^{68} -3.45057e7 q^{69} +4.44463e7i q^{71} +(2.60417e6 - 2.14094e6i) q^{72} -1.79865e7 q^{73} +(-1.16843e7 + 3.85579e7i) q^{74} +(-1.52177e7 + 2.28032e7i) q^{76} +29810.9 q^{77} +(-2.04786e7 - 6.20570e6i) q^{78} -2.03988e7i q^{79} -3.69692e7 q^{81} +(1.38296e7 - 4.56374e7i) q^{82} +5.09090e7i q^{83} +(3.39284e6 + 2.26421e6i) q^{84} +(-3.40284e7 - 1.03117e7i) q^{86} +6.55370e7i q^{87} +(-368651. - 448415. i) q^{88} -2.68313e7 q^{89} +3.71375e6i q^{91} +(6.47319e7 - 9.69986e7i) q^{92} +3.25561e7 q^{93} +(1.16969e8 + 3.54456e7i) q^{94} +(-7.89880e6 - 7.90351e7i) q^{96} -3.38260e7 q^{97} +(-2.65443e7 + 8.75953e7i) q^{98} -116647. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9} + 64040 q^{12} - 51392 q^{13} + 68472 q^{14} - 81424 q^{16} - 27552 q^{17} + 616994 q^{18} + 414496 q^{21} + 389120 q^{22} + 163792 q^{24}+ \cdots + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9 + 64040 * q^12 - 51392 * q^13 + 68472 * q^14 - 81424 * q^16 - 27552 * q^17 + 616994 * q^18 + 414496 * q^21 + 389120 * q^22 + 163792 * q^24 + 1037124 * q^26 - 1288520 * q^28 + 2764896 * q^29 + 4379904 * q^32 + 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 - 9009472 * q^37 + 3087360 * q^38 - 8576448 * q^41 + 4067400 * q^42 + 16921200 * q^44 - 7974152 * q^46 + 2696640 * q^48 - 32803600 * q^49 - 6679352 * q^52 - 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 - 11957760 * q^57 - 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 + 19358000 * q^66 - 16095192 * q^68 + 7527264 * q^69 + 42242664 * q^72 - 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 + 104032400 * q^78 + 140586672 * q^81 - 83921012 * q^82 + 69761824 * q^84 - 101724672 * q^86 - 44728480 * q^88 + 106647456 * q^89 + 13876200 * q^92 - 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 - 171851232 * q^97 + 285387714 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−4.64016	+	15.3124i	−0.290010	+	0.957024i
$2$	−4.64016	+	15.3124i	−0.290010	+	0.957024i
$3$			75.7492i			0.935175i	0.883947	+	0.467588i	$0.154877\pi$
$3$			75.7492i			0.935175i	−0.883947	+	0.467588i	$0.845123\pi$
$4$	−212.938	−	142.104i	−0.831788	−	0.555093i
$5$		0			0
$5$		0			0
$6$	−1159.90	−	351.488i	−0.894985	−	0.271210i
$7$			210.345i			0.0876072i	0.999040	+	0.0438036i	$0.0139476\pi$
$7$			210.345i			0.0876072i	−0.999040	+	0.0438036i	$0.986052\pi$
$8$	3164.01	−	2601.20i	0.772464	−	0.635059i
$9$	823.060			0.125447
$10$		0			0
$11$		−	141.724i		−	0.00967991i	−0.999988	−	0.00483996i	$-0.998459\pi$
$11$		−	141.724i		−	0.00967991i	0.999988	−	0.00483996i	$-0.00154061\pi$
$12$	10764.2	−	16129.9i	0.519109	−	0.777868i
$13$	17655.5			0.618168			0.309084	−	0.951035i	$-0.399978\pi$
$13$	17655.5			0.618168			0.309084	+	0.951035i	$0.399978\pi$
$14$	−3220.88	−	976.035i	−0.0838422	−	0.0254070i
$15$		0			0
$16$	25149.0	+	60518.5i	0.383744	+	0.923440i
$17$	102231.			1.22401			0.612005	−	0.790854i	$-0.290363\pi$
$17$	102231.			1.22401			0.612005	+	0.790854i	$0.290363\pi$
$18$	−3819.13	+	12603.0i	−0.0363810	+	0.120056i
$19$		−	107088.i		−	0.821728i	−0.911697	−	0.410864i	$-0.865227\pi$
$19$		−	107088.i		−	0.821728i	0.911697	−	0.410864i	$-0.134773\pi$
$20$		0			0
$21$	−15933.5			−0.0819281
$22$	2170.13	+	657.620i	0.00926391	+	0.00280727i
$23$			455526.i			1.62780i	0.581004	+	0.813901i	$0.302660\pi$
$23$			455526.i			1.62780i	−0.581004	+	0.813901i	$0.697340\pi$
$24$	197039.	+	239671.i	0.593891	+	0.722389i
$25$		0			0
$26$	−81924.3	+	270348.i	−0.179275	+	0.591601i
$27$			559337.i			1.05249i
$28$	29890.8	−	44790.4i	0.0486302	−	0.0728707i
$29$	865184.			1.22325			0.611627	−	0.791146i	$-0.290515\pi$
$29$	865184.			1.22325			0.611627	+	0.791146i	$0.290515\pi$
$30$		0			0
$31$		−	429788.i		−	0.465380i	−0.972551	−	0.232690i	$-0.925247\pi$
$31$		−	429788.i		−	0.465380i	0.972551	−	0.232690i	$-0.0747528\pi$
$32$	−1.04338e6	+	104276.i	−0.995043	+	0.0994450i
$33$	10735.4			0.00905241
$34$	−474366.	+	1.56539e6i	−0.354975	+	1.17141i
$35$		0			0
$36$	−175261.	−	116960.i	−0.104346	−	0.0696349i
$37$	2.51809e6			1.34358			0.671791	−	0.740741i	$-0.265525\pi$
$37$	2.51809e6			1.34358			0.671791	+	0.740741i	$0.265525\pi$
$38$	1.63978e6	+	496908.i	0.786414	+	0.238310i
$39$			1.33739e6i			0.578095i
$40$		0			0
$41$	−2.98042e6			−1.05473			−0.527366	−	0.849638i	$-0.676820\pi$
$41$	−2.98042e6			−1.05473			−0.527366	+	0.849638i	$0.676820\pi$
$42$	73933.8	−	243979.i	0.0237600	−	0.0784071i
$43$			2.22228e6i			0.650018i	0.945711	+	0.325009i	$0.105367\pi$
$43$			2.22228e6i			0.650018i	−0.945711	+	0.325009i	$0.894633\pi$
$44$	−20139.5	+	30178.3i	−0.00537325	+	0.00805164i
$45$		0			0
$46$	−6.97518e6	−	2.11371e6i	−1.55784	−	0.472079i
$47$		−	7.63886e6i		−	1.56544i	−0.622372	−	0.782722i	$-0.713831\pi$
$47$		−	7.63886e6i		−	1.56544i	0.622372	−	0.782722i	$-0.286169\pi$
$48$	−4.58423e6	+	1.90502e6i	−0.863578	+	0.358868i
$49$	5.72056e6			0.992325
$50$		0			0
$51$			7.74388e6i			1.14466i
$52$	−3.75952e6	−	2.50891e6i	−0.514185	−	0.343141i
$53$	−1.55615e7			−1.97219			−0.986094	−	0.166186i	$-0.946855\pi$
$53$	−1.55615e7			−1.97219			−0.986094	+	0.166186i	$0.946855\pi$
$54$	−8.56477e6	−	2.59541e6i	−1.00726	−	0.305233i
$55$		0			0
$56$	547149.	+	665534.i	0.0556357	+	0.0676734i
$57$	8.11187e6			0.768460
$58$	−4.01459e6	+	1.32480e7i	−0.354756	+	1.17068i
$59$		−	6.38433e6i		−	0.526874i	−0.964677	−	0.263437i	$-0.915144\pi$
$59$		−	6.38433e6i		−	0.526874i	0.964677	−	0.263437i	$-0.0848562\pi$
$60$		0			0
$61$	2.03289e6			0.146823			0.0734116	−	0.997302i	$-0.476611\pi$
$61$	2.03289e6			0.146823			0.0734116	+	0.997302i	$0.476611\pi$
$62$	6.58108e6	+	1.99429e6i	0.445380	+	0.134965i
$63$			173127.i			0.0109901i
$64$	3.24473e6	−	1.64605e7i	0.193401	−	0.981120i
$65$		0			0
$66$	−49814.2	+	164385.i	−0.00262529	+	0.00866337i
$67$			2.03503e7i			1.00988i	0.863154	+	0.504941i	$0.168486\pi$
$67$			2.03503e7i			1.00988i	−0.863154	+	0.504941i	$0.831514\pi$
$68$	−2.17688e7	−	1.45274e7i	−1.01812	−	0.679439i
$69$	−3.45057e7			−1.52228
$70$		0			0
$71$			4.44463e7i			1.74905i	0.484979	+	0.874526i	$0.338827\pi$
$71$			4.44463e7i			1.74905i	−0.484979	+	0.874526i	$0.661173\pi$
$72$	2.60417e6	−	2.14094e6i	0.0969036	−	0.0796664i
$73$	−1.79865e7			−0.633366			−0.316683	−	0.948531i	$-0.602569\pi$
$73$	−1.79865e7			−0.633366			−0.316683	+	0.948531i	$0.602569\pi$
$74$	−1.16843e7	+	3.85579e7i	−0.389652	+	1.28584i
$75$		0			0
$76$	−1.52177e7	+	2.28032e7i	−0.456136	+	0.683504i
$77$	29810.9			0.000848031
$78$	−2.04786e7	−	6.20570e6i	−0.553251	−	0.167653i
$79$		−	2.03988e7i		−	0.523716i	−0.965106	−	0.261858i	$-0.915665\pi$
$79$		−	2.03988e7i		−	0.523716i	0.965106	−	0.261858i	$-0.0843352\pi$
$80$		0			0
$81$	−3.69692e7			−0.858816
$82$	1.38296e7	−	4.56374e7i	0.305883	−	1.00940i
$83$			5.09090e7i			1.07271i	0.843992	+	0.536355i	$0.180199\pi$
$83$			5.09090e7i			1.07271i	−0.843992	+	0.536355i	$0.819801\pi$
$84$	3.39284e6	+	2.26421e6i	0.0681469	+	0.0454777i
$85$		0			0
$86$	−3.40284e7	−	1.03117e7i	−0.622082	−	0.188512i
$87$			6.55370e7i			1.14396i
$88$	−368651.	−	448415.i	−0.00614731	−	0.00747738i
$89$	−2.68313e7			−0.427644			−0.213822	−	0.976873i	$-0.568591\pi$
$89$	−2.68313e7			−0.427644			−0.213822	+	0.976873i	$0.568591\pi$
$90$		0			0
$91$			3.71375e6i			0.0541560i
$92$	6.47319e7	−	9.69986e7i	0.903581	−	1.35399i
$93$	3.25561e7			0.435212
$94$	1.16969e8	+	3.54456e7i	1.49817	+	0.453994i
$95$		0			0
$96$	−7.89880e6	−	7.90351e7i	−0.0929985	−	0.930540i
$97$	−3.38260e7			−0.382089			−0.191044	−	0.981581i	$-0.561187\pi$
$97$	−3.38260e7			−0.382089			−0.191044	+	0.981581i	$0.561187\pi$
$98$	−2.65443e7	+	8.75953e7i	−0.287784	+	0.949678i
$99$		−	116647.i		−	0.00121432i
$100$		0			0
$101$	5.46440e7			0.525118			0.262559	−	0.964916i	$-0.415434\pi$
$101$	5.46440e7			0.525118			0.262559	+	0.964916i	$0.415434\pi$
$102$	−1.18577e8	−	3.59329e7i	−1.09547	−	0.331964i
$103$			5.49350e6i			0.0488090i	0.999702	+	0.0244045i	$0.00776897\pi$
$103$			5.49350e6i			0.0488090i	−0.999702	+	0.0244045i	$0.992231\pi$
$104$	5.58622e7	−	4.59255e7i	0.477513	−	0.392573i
$105$		0			0
$106$	7.22080e7	−	2.38284e8i	0.571955	−	1.88743i
$107$			4.58185e7i			0.349547i	0.984609	+	0.174773i	$0.0559193\pi$
$107$			4.58185e7i			0.349547i	−0.984609	+	0.174773i	$0.944081\pi$
$108$	7.94838e7	−	1.19104e8i	0.584230	−	0.875449i
$109$	1.34989e8			0.956295			0.478147	−	0.878280i	$-0.341308\pi$
$109$	1.34989e8			0.956295			0.478147	+	0.878280i	$0.341308\pi$
$110$		0			0
$111$			1.90743e8i			1.25648i
$112$	−1.27298e7	+	5.28997e6i	−0.0809000	+	0.0336187i
$113$	1.52579e8			0.935796			0.467898	−	0.883783i	$-0.345011\pi$
$113$	1.52579e8			0.935796			0.467898	+	0.883783i	$0.345011\pi$
$114$	−3.76404e7	+	1.24212e8i	−0.222861	+	0.735434i
$115$		0			0
$116$	−1.84230e8	−	1.22946e8i	−1.01749	−	0.679020i
$117$	1.45315e7			0.0775475
$118$	9.77592e7	+	2.96243e7i	0.504231	+	0.152799i
$119$			2.15037e7i			0.107232i
$120$		0			0
$121$	2.14339e8			0.999906
$122$	−9.43293e6	+	3.11284e7i	−0.0425802	+	0.140513i
$123$		−	2.25765e8i		−	0.986360i
$124$	−6.10746e7	+	9.15182e7i	−0.258329	+	0.387098i
$125$		0			0
$126$	−2.65098e6	−	803335.i	−0.0105178	−	0.00318724i
$127$			3.88910e8i			1.49498i	0.664275	+	0.747488i	$0.268740\pi$
$127$			3.88910e8i			1.49498i	−0.664275	+	0.747488i	$0.731260\pi$
$128$	2.36993e8	+	1.26064e8i	0.882866	+	0.469624i
$129$	−1.68336e8			−0.607880
$130$		0			0
$131$			5.32310e8i			1.80750i	0.428056	+	0.903752i	$0.359199\pi$
$131$			5.32310e8i			1.80750i	−0.428056	+	0.903752i	$0.640801\pi$
$132$	−2.28598e6	−	1.52555e6i	−0.00752969	−	0.00502493i
$133$	2.25255e7			0.0719894
$134$	−3.11611e8	−	9.44285e7i	−0.966482	−	0.292876i
$135$		0			0
$136$	3.23459e8	−	2.65922e8i	0.945504	−	0.777318i
$137$	5.11356e8			1.45158			0.725790	−	0.687916i	$-0.241474\pi$
$137$	5.11356e8			1.45158			0.725790	+	0.687916i	$0.241474\pi$
$138$	1.60112e8	−	5.28364e8i	0.441476	−	1.45686i
$139$		−	4.03705e8i		−	1.08145i	−0.841201	−	0.540723i	$-0.818151\pi$
$139$		−	4.03705e8i		−	1.08145i	0.841201	−	0.540723i	$-0.181849\pi$
$140$		0			0
$141$	5.78638e8			1.46396
$142$	−6.80579e8	−	2.06238e8i	−1.67388	−	0.507243i
$143$		−	2.50220e6i		−	0.00598381i
$144$	2.06992e7	+	4.98104e7i	0.0481396	+	0.115843i
$145$		0			0
$146$	8.34602e7	−	2.75416e8i	0.183683	−	0.606146i
$147$			4.33327e8i			0.927998i
$148$	−5.36196e8	−	3.57830e8i	−1.11758	−	0.745813i
$149$	2.52732e8			0.512761			0.256381	−	0.966576i	$-0.417470\pi$
$149$	2.52732e8			0.512761			0.256381	+	0.966576i	$0.417470\pi$
$150$		0			0
$151$		−	1.14787e8i		−	0.220792i	−0.993888	−	0.110396i	$-0.964788\pi$
$151$		−	1.14787e8i		−	0.220792i	0.993888	−	0.110396i	$-0.0352119\pi$
$152$	−2.78559e8	−	3.38829e8i	−0.521846	−	0.634756i
$153$	8.41419e7			0.153549
$154$	−138327.	+	456475.i	−0.000245937	+	0.000811585i
$155$		0			0
$156$	1.90048e8	−	2.84781e8i	0.320897	−	0.480853i
$157$	−3.48763e8			−0.574026			−0.287013	−	0.957927i	$-0.592662\pi$
$157$	−3.48763e8			−0.574026			−0.287013	+	0.957927i	$0.592662\pi$
$158$	3.12354e8	+	9.46536e7i	0.501209	+	0.151883i
$159$		−	1.17877e9i		−	1.84434i
$160$		0			0
$161$	−9.58175e7			−0.142607
$162$	1.71543e8	−	5.66086e8i	0.249065	−	0.821907i
$163$			2.96216e8i			0.419622i	0.977742	+	0.209811i	$0.0672848\pi$
$163$			2.96216e8i			0.419622i	−0.977742	+	0.209811i	$0.932715\pi$
$164$	6.34645e8	+	4.23529e8i	0.877314	+	0.585475i
$165$		0			0
$166$	−7.79538e8	−	2.36226e8i	−1.02661	−	0.311097i
$167$			1.56004e8i			0.200572i	0.994959	+	0.100286i	$0.0319757\pi$
$167$			1.56004e8i			0.200572i	−0.994959	+	0.100286i	$0.968024\pi$
$168$	−5.04137e7	+	4.14461e7i	−0.0632865	+	0.0520292i
$169$	−5.04014e8			−0.617868
$170$		0			0
$171$		−	8.81402e7i		−	0.103084i
$172$	3.15795e8	−	4.73208e8i	0.360820	−	0.540677i
$173$	−4.66034e8			−0.520276			−0.260138	−	0.965572i	$-0.583768\pi$
$173$	−4.66034e8			−0.520276			−0.260138	+	0.965572i	$0.583768\pi$
$174$	−1.00353e9	−	3.04102e8i	−1.09479	−	0.331759i
$175$		0			0
$176$	8.57691e6	−	3.56421e6i	0.00893882	−	0.00371461i
$177$	4.83608e8			0.492720
$178$	1.24502e8	−	4.10851e8i	0.124021	−	0.409265i
$179$			1.44673e9i			1.40921i	0.709600	+	0.704605i	$0.248876\pi$
$179$			1.44673e9i			1.40921i	−0.709600	+	0.704605i	$0.751124\pi$
$180$		0			0
$181$	−5.80491e8			−0.540855			−0.270428	−	0.962740i	$-0.587165\pi$
$181$	−5.80491e8			−0.540855			−0.270428	+	0.962740i	$0.587165\pi$
$182$	−5.68663e7	−	1.72324e7i	−0.0518286	−	0.0157058i
$183$			1.53990e8i			0.137305i
$184$	1.18491e9	+	1.44129e9i	1.03375	+	1.25742i
$185$		0			0
$186$	−1.51066e8	+	4.98512e8i	−0.126216	+	0.416508i
$187$		−	1.44885e7i		−	0.0118483i
$188$	−1.08551e9	+	1.62660e9i	−0.868966	+	1.30212i
$189$	−1.17654e8			−0.0922058
$190$		0			0
$191$			2.29528e9i			1.72465i	0.506351	+	0.862327i	$0.330994\pi$
$191$			2.29528e9i			1.72465i	−0.506351	+	0.862327i	$0.669006\pi$
$192$	1.24687e9	+	2.45786e8i	0.917519	+	0.180864i
$193$	1.42541e9			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$193$	1.42541e9			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$194$	1.56958e8	−	5.17957e8i	0.110810	−	0.365668i
$195$		0			0
$196$	−1.21812e9	−	8.12913e8i	−0.825404	−	0.550833i
$197$	−1.42075e9			−0.943305			−0.471652	−	0.881785i	$-0.656342\pi$
$197$	−1.42075e9			−0.943305			−0.471652	+	0.881785i	$0.656342\pi$
$198$	1.78614e6	+	541261.i	0.00116213	+	0.000352165i
$199$			1.90032e9i			1.21176i	0.795557	+	0.605878i	$0.207178\pi$
$199$			1.90032e9i			1.21176i	−0.795557	+	0.605878i	$0.792822\pi$
$200$		0			0
$201$	−1.54152e9			−0.944417
$202$	−2.53557e8	+	8.36729e8i	−0.152289	+	0.502550i
$203$			1.81987e8i			0.107166i
$204$	1.10044e9	−	1.64897e9i	0.635395	−	0.952118i
$205$		0			0
$206$	−8.41185e7	−	2.54907e7i	−0.0467114	−	0.0141551i
$207$			3.74925e8i			0.204203i
$208$	4.44019e8	+	1.06848e9i	0.237218	+	0.570841i
$209$	−1.51770e7			−0.00795426
$210$		0			0
$211$		−	1.67947e9i		−	0.847311i	−0.905823	−	0.423655i	$-0.860747\pi$
$211$		−	1.67947e9i		−	0.847311i	0.905823	−	0.423655i	$-0.139253\pi$
$212$	3.31364e9	+	2.21135e9i	1.64044	+	1.09475i
$213$	−3.36677e9			−1.63567
$214$	−7.01590e8	−	2.12605e8i	−0.334525	−	0.101372i
$215$		0			0
$216$	1.45495e9	+	1.76975e9i	0.668393	+	0.813011i
$217$	9.04039e7			0.0407707
$218$	−6.26370e8	+	2.06700e9i	−0.277335	+	0.915197i
$219$		−	1.36246e9i		−	0.592308i
$220$		0			0
$221$	1.80493e9			0.756644
$222$	−2.92073e9	−	8.85079e8i	−1.20249	−	0.364393i
$223$			1.10738e9i			0.447795i	0.974613	+	0.223897i	$0.0718780\pi$
$223$			1.10738e9i			0.447795i	−0.974613	+	0.223897i	$0.928122\pi$
$224$	−2.19339e7	−	2.19469e8i	−0.00871210	−	0.0871730i
$225$		0			0
$226$	−7.07991e8	+	2.33635e9i	−0.271390	+	0.895579i
$227$		−	4.15603e9i		−	1.56522i	−0.622512	−	0.782610i	$-0.713888\pi$
$227$		−	4.15603e9i		−	1.56522i	0.622512	−	0.782610i	$-0.286112\pi$
$228$	−1.72732e9	−	1.15273e9i	−0.639196	−	0.426567i
$229$	1.34641e9			0.489594			0.244797	−	0.969574i	$-0.421279\pi$
$229$	1.34641e9			0.489594			0.244797	+	0.969574i	$0.421279\pi$
$230$		0			0
$231$			2.25815e6i			0.000793057i
$232$	2.73745e9	−	2.25052e9i	0.944920	−	0.776838i
$233$	−2.57794e8			−0.0874681			−0.0437341	−	0.999043i	$-0.513925\pi$
$233$	−2.57794e8			−0.0874681			−0.0437341	+	0.999043i	$0.513925\pi$
$234$	−6.74286e7	+	2.22512e8i	−0.0224896	+	0.0742148i
$235$		0			0
$236$	−9.07237e8	+	1.35946e9i	−0.292464	+	0.438248i
$237$	1.54519e9			0.489766
$238$	−3.29273e8	−	9.97806e7i	−0.102624	−	0.0310984i
$239$		−	3.82549e8i		−	0.117245i	−0.998280	−	0.0586227i	$-0.981329\pi$
$239$		−	3.82549e8i		−	0.117245i	0.998280	−	0.0586227i	$-0.0186709\pi$
$240$		0			0
$241$	−5.49743e9			−1.62964			−0.814820	−	0.579714i	$-0.803164\pi$
$241$	−5.49743e9			−1.62964			−0.814820	+	0.579714i	$0.803164\pi$
$242$	−9.94566e8	+	3.28204e9i	−0.289983	+	0.956934i
$243$			8.69420e8i			0.249347i
$244$	−4.32879e8	−	2.88881e8i	−0.122126	−	0.0815005i
$245$		0			0
$246$	3.45699e9	+	1.04758e9i	0.943970	+	0.286054i
$247$		−	1.89070e9i		−	0.507966i
$248$	−1.11797e9	−	1.35986e9i	−0.295544	−	0.359490i
$249$	−3.85632e9			−1.00317
$250$		0			0
$251$		−	7.22250e9i		−	1.81967i	−0.414971	−	0.909835i	$-0.636208\pi$
$251$		−	7.22250e9i		−	1.81967i	0.414971	−	0.909835i	$-0.363792\pi$
$252$	2.46019e7	−	3.68652e7i	0.00610052	−	0.00914143i
$253$	6.45587e7			0.0157570
$254$	−5.95514e9	−	1.80460e9i	−1.43073	−	0.433558i
$255$		0			0
$256$	−3.03002e9	+	3.04396e9i	−0.705482	+	0.708728i
$257$	1.49317e9			0.342277			0.171138	−	0.985247i	$-0.445256\pi$
$257$	1.49317e9			0.342277			0.171138	+	0.985247i	$0.445256\pi$
$258$	7.81106e8	−	2.57762e9i	0.176291	−	0.581756i
$259$			5.29667e8i			0.117707i
$260$		0			0
$261$	7.12099e8			0.153454
$262$	−8.15093e9	−	2.47000e9i	−1.72982	−	0.524195i
$263$		−	4.58536e9i		−	0.958409i	−0.877703	−	0.479205i	$-0.840925\pi$
$263$		−	4.58536e9i		−	0.958409i	0.877703	−	0.479205i	$-0.159075\pi$
$264$	3.39671e7	−	2.79250e7i	0.00699266	−	0.00574881i
$265$		0			0
$266$	−1.04522e8	+	3.44919e8i	−0.0208776	+	0.0688955i
$267$		−	2.03245e9i		−	0.399922i
$268$	2.89185e9	−	4.33334e9i	0.560579	−	0.840009i
$269$	5.70969e9			1.09044			0.545222	−	0.838292i	$-0.316445\pi$
$269$	5.70969e9			1.09044			0.545222	+	0.838292i	$0.316445\pi$
$270$		0			0
$271$		−	8.61657e9i		−	1.59756i	−0.601623	−	0.798780i	$-0.705479\pi$
$271$		−	8.61657e9i		−	1.59756i	0.601623	−	0.798780i	$-0.294521\pi$
$272$	2.57100e9	+	6.18684e9i	0.469706	+	1.13030i
$273$	−2.81313e8			−0.0506453
$274$	−2.37277e9	+	7.83008e9i	−0.420973	+	1.38920i
$275$		0			0
$276$	7.34757e9	+	4.90339e9i	1.26621	+	0.845007i
$277$	−5.74438e9			−0.975717			−0.487858	−	0.872923i	$-0.662222\pi$
$277$	−5.74438e9			−0.975717			−0.487858	+	0.872923i	$0.662222\pi$
$278$	6.18168e9	+	1.87326e9i	1.03497	+	0.313630i
$279$		−	3.53742e8i		−	0.0583807i
$280$		0			0
$281$	7.75176e9			1.24330			0.621648	−	0.783296i	$-0.286463\pi$
$281$	7.75176e9			1.24330			0.621648	+	0.783296i	$0.286463\pi$
$282$	−2.68497e9	+	8.86032e9i	−0.424564	+	1.40105i
$283$		−	3.56052e9i		−	0.555096i	−0.960712	−	0.277548i	$-0.910478\pi$
$283$		−	3.56052e9i		−	0.555096i	0.960712	−	0.277548i	$-0.0895217\pi$
$284$	6.31599e9	−	9.46431e9i	0.970886	−	1.45484i
$285$		0			0
$286$	3.83146e7	+	1.16106e7i	0.00572665	+	0.00173537i
$287$		−	6.26917e8i		−	0.0924022i
$288$	−8.58763e8	+	8.58251e7i	−0.124826	+	0.0124751i
$289$	3.47533e9			0.498201
$290$		0			0
$291$		−	2.56229e9i		−	0.357320i
$292$	3.83000e9	+	2.55595e9i	0.526826	+	0.351577i
$293$	5.61859e9			0.762355			0.381177	−	0.924502i	$-0.375519\pi$
$293$	5.61859e9			0.762355			0.381177	+	0.924502i	$0.375519\pi$
$294$	−6.63527e9	−	2.01071e9i	−0.888116	−	0.269129i
$295$		0			0
$296$	7.96726e9	−	6.55005e9i	1.03787	−	0.853253i
$297$	7.92712e7			0.0101880
$298$	−1.17272e9	+	3.86993e9i	−0.148706	+	0.490725i
$299$			8.04253e9i			1.00625i
$300$		0			0
$301$	−4.67446e8			−0.0569463
$302$	1.75766e9	+	5.32628e8i	0.211303	+	0.0640319i
$303$			4.13924e9i			0.491077i
$304$	6.48084e9	−	2.69317e9i	0.758817	−	0.315333i
$305$		0			0
$306$	−3.90432e8	+	1.28841e9i	−0.0445307	+	0.146950i
$307$		−	1.17341e10i		−	1.32099i	−0.750832	−	0.660493i	$-0.770347\pi$
$307$		−	1.17341e10i		−	1.32099i	0.750832	−	0.660493i	$-0.229653\pi$
$308$	−6.34786e6	−	4.23623e6i	−0.000705382	−	0.000470736i
$309$	−4.16128e8			−0.0456450
$310$		0			0
$311$			8.30766e9i			0.888050i	0.896014	+	0.444025i	$0.146450\pi$
$311$			8.30766e9i			0.888050i	−0.896014	+	0.444025i	$0.853550\pi$
$312$	3.47882e9	+	4.23152e9i	0.367124	+	0.446558i
$313$	8.58561e9			0.894528			0.447264	−	0.894402i	$-0.352399\pi$
$313$	8.58561e9			0.894528			0.447264	+	0.894402i	$0.352399\pi$
$314$	1.61831e9	−	5.34038e9i	0.166473	−	0.549356i
$315$		0			0
$316$	−2.89874e9	+	4.34367e9i	−0.290711	+	0.435621i
$317$	2.51112e9			0.248674			0.124337	−	0.992240i	$-0.460320\pi$
$317$	2.51112e9			0.248674			0.124337	+	0.992240i	$0.460320\pi$
$318$	1.80498e10	+	5.46969e9i	1.76508	+	0.534878i
$319$		−	1.22617e8i		−	0.0118410i
$320$		0			0
$321$	−3.47071e9			−0.326888
$322$	4.44609e8	−	1.46719e9i	0.0413575	−	0.136478i
$323$		−	1.09477e10i		−	1.00580i
$324$	7.87214e9	+	5.25346e9i	0.714353	+	0.476722i
$325$		0			0
$326$	−4.53577e9	−	1.37449e9i	−0.401588	−	0.121694i
$327$			1.02253e10i			0.894303i
$328$	−9.43009e9	+	7.75267e9i	−0.814743	+	0.669817i
$329$	1.60680e9			0.137144
$330$		0			0
$331$		−	1.38910e10i		−	1.15724i	−0.815599	−	0.578618i	$-0.803592\pi$
$331$		−	1.38910e10i		−	1.15724i	0.815599	−	0.578618i	$-0.196408\pi$
$332$	7.23437e9	−	1.08405e10i	0.595454	−	0.892268i
$333$	2.07254e9			0.168549
$334$	−2.38879e9	−	7.23883e8i	−0.191952	−	0.0581678i
$335$		0			0
$336$	−4.00711e8	−	9.64270e8i	−0.0314394	−	0.0756557i
$337$	−1.74804e10			−1.35529			−0.677643	−	0.735391i	$-0.736999\pi$
$337$	−1.74804e10			−1.35529			−0.677643	+	0.735391i	$0.736999\pi$
$338$	2.33871e9	−	7.71766e9i	0.179188	−	0.591315i
$339$			1.15577e10i			0.875133i
$340$		0			0
$341$	−6.09112e7			−0.00450484
$342$	1.34964e9	+	4.08985e8i	0.0986535	+	0.0298953i
$343$			2.41589e9i			0.174542i
$344$	5.78060e9	+	7.03133e9i	0.412799	+	0.502115i
$345$		0			0
$346$	2.16247e9	−	7.13609e9i	0.150885	−	0.497916i
$347$			4.08751e8i			0.0281930i	0.999901	+	0.0140965i	$0.00448720\pi$
$347$			4.08751e8i			0.0281930i	−0.999901	+	0.0140965i	$0.995513\pi$
$348$	9.31306e9	−	1.39553e10i	0.635002	−	0.951530i
$349$	−1.52539e10			−1.02820			−0.514102	−	0.857729i	$-0.671875\pi$
$349$	−1.52539e10			−1.02820			−0.514102	+	0.857729i	$0.671875\pi$
$350$		0			0
$351$			9.87536e9i			0.650616i
$352$	1.47783e7	+	1.47871e8i	0.000962619	+	0.00963193i
$353$	2.36311e9			0.152190			0.0760950	−	0.997101i	$-0.475755\pi$
$353$	2.36311e9			0.152190			0.0760950	+	0.997101i	$0.475755\pi$
$354$	−2.24402e9	+	7.40518e9i	−0.142894	+	0.471544i
$355$		0			0
$356$	5.71340e9	+	3.81283e9i	0.355709	+	0.237382i
$357$	−1.62889e9			−0.100281
$358$	−2.21529e10	−	6.71306e9i	−1.34865	−	0.408685i
$359$		−	1.95665e10i		−	1.17797i	−0.808143	−	0.588987i	$-0.799527\pi$
$359$		−	1.95665e10i		−	1.17797i	0.808143	−	0.588987i	$-0.200473\pi$
$360$		0			0
$361$	5.51562e9			0.324762
$362$	2.69357e9	−	8.88870e9i	0.156854	−	0.517611i
$363$			1.62360e10i			0.935088i
$364$	5.27737e8	−	7.90797e8i	0.0300616	−	0.0450463i
$365$		0			0
$366$	−2.35795e9	−	7.14537e8i	−0.131404	−	0.0398199i
$367$			2.40655e10i			1.32657i	0.748367	+	0.663285i	$0.230838\pi$
$367$			2.40655e10i			1.32657i	−0.748367	+	0.663285i	$0.769162\pi$
$368$	−2.75677e10	+	1.14560e10i	−1.50318	+	0.624659i
$369$	−2.45307e9			−0.132313
$370$		0			0
$371$		−	3.27329e9i		−	0.172778i
$372$	−6.93243e9	−	4.62635e9i	−0.362004	−	0.241583i
$373$	−1.70488e10			−0.880760			−0.440380	−	0.897811i	$-0.645156\pi$
$373$	−1.70488e10			−0.880760			−0.440380	+	0.897811i	$0.645156\pi$
$374$	2.21853e8	+	6.72289e7i	0.0113391	+	0.00343613i
$375$		0			0
$376$	−1.98702e10	−	2.41695e10i	−0.994148	−	1.20925i
$377$	1.52753e10			0.756176
$378$	5.45932e8	−	1.80156e9i	0.0267406	−	0.0882431i
$379$		−	1.60429e10i		−	0.777545i	−0.921334	−	0.388772i	$-0.872899\pi$
$379$		−	1.60429e10i		−	0.777545i	0.921334	−	0.388772i	$-0.127101\pi$
$380$		0			0
$381$	−2.94596e10			−1.39806
$382$	−3.51462e10	−	1.06505e10i	−1.65054	−	0.500167i
$383$			1.23891e10i			0.575765i	0.957666	+	0.287883i	$0.0929513\pi$
$383$			1.23891e10i			0.575765i	−0.957666	+	0.287883i	$0.907049\pi$
$384$	−9.54923e9	+	1.79520e10i	−0.439181	+	0.825635i
$385$		0			0
$386$	−6.61413e9	+	2.18264e10i	−0.297936	+	0.983180i
$387$			1.82907e9i			0.0815430i
$388$	7.20284e9	+	4.80681e9i	0.317817	+	0.212095i
$389$	−1.27527e10			−0.556935			−0.278467	−	0.960446i	$-0.589826\pi$
$389$	−1.27527e10			−0.556935			−0.278467	+	0.960446i	$0.589826\pi$
$390$		0			0
$391$			4.65686e10i			1.99245i
$392$	1.80999e10	−	1.48803e10i	0.766535	−	0.630184i
$393$	−4.03221e10			−1.69033
$394$	6.59250e9	−	2.17550e10i	0.273568	−	0.902765i
$395$		0			0
$396$	−1.65760e7	+	2.48386e7i	−0.000674060	+	0.00101006i
$397$	1.95226e10			0.785914			0.392957	−	0.919557i	$-0.371452\pi$
$397$	1.95226e10			0.785914			0.392957	+	0.919557i	$0.371452\pi$
$398$	−2.90985e10	−	8.81781e9i	−1.15968	−	0.351422i
$399$			1.70629e9i			0.0673227i
$400$		0			0
$401$	2.44896e10			0.947119			0.473559	−	0.880762i	$-0.342969\pi$
$401$	2.44896e10			0.947119			0.473559	+	0.880762i	$0.342969\pi$
$402$	7.15288e9	−	2.36043e10i	0.273891	−	0.903830i
$403$		−	7.58813e9i		−	0.287683i
$404$	−1.16358e10	−	7.76512e9i	−0.436787	−	0.291489i
$405$		0			0
$406$	−2.78666e9	−	8.44450e8i	−0.102560	−	0.0310792i
$407$		−	3.56873e8i		−	0.0130058i
$408$	2.01434e10	+	2.45017e10i	0.726929	+	0.884212i
$409$	1.79748e10			0.642350			0.321175	−	0.947020i	$-0.395922\pi$
$409$	1.79748e10			0.642350			0.321175	+	0.947020i	$0.395922\pi$
$410$		0			0
$411$			3.87348e10i			1.35748i
$412$	7.80647e8	−	1.16977e9i	0.0270935	−	0.0405988i
$413$	1.34291e9			0.0461580
$414$	−5.74099e9	−	1.73971e9i	−0.195427	−	0.0592210i
$415$		0			0
$416$	−1.84214e10	+	1.84104e9i	−0.615104	+	0.0614737i
$417$	3.05803e10			1.01134
$418$	7.04236e7	−	2.32395e8i	0.00230682	−	0.00761241i
$419$		−	3.49871e10i		−	1.13515i	−0.823323	−	0.567573i	$-0.807883\pi$
$419$		−	3.49871e10i		−	1.13515i	0.823323	−	0.567573i	$-0.192117\pi$
$420$		0			0
$421$	1.17473e10			0.373947			0.186973	−	0.982365i	$-0.440132\pi$
$421$	1.17473e10			0.373947			0.186973	+	0.982365i	$0.440132\pi$
$422$	2.57167e10	+	7.79302e9i	0.810896	+	0.245729i
$423$		−	6.28724e9i		−	0.196381i
$424$	−4.92368e10	+	4.04786e10i	−1.52344	+	1.25246i
$425$		0			0
$426$	1.56224e10	−	5.15533e10i	0.474361	−	1.56537i
$427$			4.27608e8i			0.0128628i
$428$	6.51098e9	−	9.75649e9i	0.194031	−	0.290749i
$429$	1.89540e8			0.00559591
$430$		0			0
$431$			4.11908e10i			1.19369i	0.802357	+	0.596845i	$0.203579\pi$
$431$			4.11908e10i			1.19369i	−0.802357	+	0.596845i	$0.796421\pi$
$432$	−3.38502e10	+	1.40668e10i	−0.971911	+	0.403887i
$433$	1.38879e10			0.395079			0.197540	−	0.980295i	$-0.436705\pi$
$433$	1.38879e10			0.395079			0.197540	+	0.980295i	$0.436705\pi$
$434$	−4.19488e8	+	1.38430e9i	−0.0118239	+	0.0390185i
$435$		0			0
$436$	−2.87442e10	−	1.91824e10i	−0.795435	−	0.530833i
$437$	4.87815e10			1.33761
$438$	2.08625e10	+	6.32204e9i	0.566853	+	0.171775i
$439$			2.26777e10i			0.610577i	0.952260	+	0.305289i	$0.0987530\pi$
$439$			2.26777e10i			0.610577i	−0.952260	+	0.305289i	$0.901247\pi$
$440$		0			0
$441$	4.70836e9			0.124485
$442$	−8.37517e9	+	2.76378e10i	−0.219434	+	0.724126i
$443$			4.08182e10i			1.05984i	0.848049	+	0.529919i	$0.177778\pi$
$443$			4.08182e10i			1.05984i	−0.848049	+	0.529919i	$0.822222\pi$
$444$	2.71053e10	−	4.06164e10i	0.697466	−	1.04513i
$445$		0			0
$446$	−1.69567e10	−	5.13844e9i	−0.428550	−	0.129865i
$447$			1.91442e10i			0.479521i
$448$	3.46237e9	+	6.82514e8i	0.0859532	+	0.0169434i
$449$	4.15880e10			1.02325			0.511626	−	0.859208i	$-0.329043\pi$
$449$	4.15880e10			1.02325			0.511626	+	0.859208i	$0.329043\pi$
$450$		0			0
$451$			4.22396e8i			0.0102097i
$452$	−3.24898e10	−	2.16821e10i	−0.778384	−	0.519454i
$453$	8.69500e9			0.206479
$454$	6.36387e10	+	1.92847e10i	1.49795	+	0.453929i
$455$		0			0
$456$	2.56660e10	−	2.11006e10i	0.593608	−	0.488017i
$457$	−7.96321e10			−1.82567			−0.912837	−	0.408324i	$-0.866113\pi$
$457$	−7.96321e10			−1.82567			−0.912837	+	0.408324i	$0.866113\pi$
$458$	−6.24756e9	+	2.06168e10i	−0.141987	+	0.468553i
$459$			5.71813e10i			1.28826i
$460$		0			0
$461$	−2.32904e10			−0.515671			−0.257836	−	0.966189i	$-0.583009\pi$
$461$	−2.32904e10			−0.515671			−0.257836	+	0.966189i	$0.583009\pi$
$462$	−3.45776e7	−	1.04782e7i	−0.000758974	−	0.000229995i
$463$		−	3.77433e10i		−	0.821327i	−0.911787	−	0.410664i	$-0.865297\pi$
$463$		−	3.77433e10i		−	0.821327i	0.911787	−	0.410664i	$-0.134703\pi$
$464$	2.17585e10	+	5.23597e10i	0.469416	+	1.12960i
$465$		0			0
$466$	1.19621e9	−	3.94745e9i	0.0253666	−	0.0837091i
$467$			3.59265e10i			0.755349i	0.925938	+	0.377674i	$0.123276\pi$
$467$			3.59265e10i			0.755349i	−0.925938	+	0.377674i	$0.876724\pi$
$468$	−3.09431e9	−	2.06499e9i	−0.0645031	−	0.0430461i
$469$	−4.28058e9			−0.0884731
$470$		0			0
$471$		−	2.64185e10i		−	0.536814i
$472$	−1.66069e10	−	2.02001e10i	−0.334596	−	0.406991i
$473$	3.14950e8			0.00629212
$474$	−7.16994e9	+	2.36605e10i	−0.142037	+	0.468718i
$475$		0			0
$476$	3.05576e9	−	4.57895e9i	0.0595238	−	0.0891945i
$477$	−1.28081e10			−0.247406
$478$	5.85774e9	+	1.77509e9i	0.112207	+	0.0340024i
$479$		−	4.40663e10i		−	0.837076i	−0.908199	−	0.418538i	$-0.862543\pi$
$479$		−	4.40663e10i		−	0.837076i	0.908199	−	0.418538i	$-0.137457\pi$
$480$		0			0
$481$	4.44581e10			0.830559
$482$	2.55090e10	−	8.41787e10i	0.472612	−	1.55960i
$483$		−	7.25810e9i		−	0.133363i
$484$	−4.56408e10	−	3.04584e10i	−0.831710	−	0.555041i
$485$		0			0
$486$	−1.33129e10	−	4.03425e9i	−0.238631	−	0.0723132i
$487$			3.99322e10i			0.709916i	0.934882	+	0.354958i	$0.115505\pi$
$487$			3.99322e10i			0.709916i	−0.934882	+	0.354958i	$0.884495\pi$
$488$	6.43209e9	−	5.28795e9i	0.113416	−	0.0932413i
$489$	−2.24381e10			−0.392420
$490$		0			0
$491$		−	7.96737e10i		−	1.37085i	−0.728145	−	0.685423i	$-0.759617\pi$
$491$		−	7.96737e10i		−	1.37085i	0.728145	−	0.685423i	$-0.240383\pi$
$492$	−3.20820e10	+	4.80738e10i	−0.547521	+	0.820443i
$493$	8.84483e10			1.49728
$494$	2.89511e10	+	8.77315e9i	0.486136	+	0.147315i
$495$		0			0
$496$	2.60102e10	−	1.08088e10i	0.429751	−	0.178587i
$497$	−9.34907e9			−0.153230
$498$	1.78939e10	−	5.90494e10i	0.290930	−	0.960060i
$499$		−	1.56191e10i		−	0.251915i	−0.992036	−	0.125957i	$-0.959800\pi$
$499$		−	1.56191e10i		−	0.251915i	0.992036	−	0.125957i	$-0.0402002\pi$
$500$		0			0
$501$	−1.18172e10			−0.187570
$502$	1.10594e11	+	3.35136e10i	1.74147	+	0.527722i
$503$			6.13884e10i			0.958990i	0.877544	+	0.479495i	$0.159180\pi$
$503$			6.13884e10i			0.958990i	−0.877544	+	0.479495i	$0.840820\pi$
$504$	4.50337e8	+	5.47775e8i	0.00697935	+	0.00848945i
$505$		0			0
$506$	−2.99563e8	+	9.88548e8i	−0.00456968	+	0.0150798i
$507$		−	3.81787e10i		−	0.577815i
$508$	5.52656e10	−	8.28136e10i	0.829850	−	1.24350i
$509$	−1.27845e10			−0.190464			−0.0952322	−	0.995455i	$-0.530359\pi$
$509$	−1.27845e10			−0.190464			−0.0952322	+	0.995455i	$0.530359\pi$
$510$		0			0
$511$		−	3.78337e9i		−	0.0554875i
$512$	−3.25506e10	−	6.05213e10i	−0.473673	−	0.880701i
$513$	5.98985e10			0.864861
$514$	−6.92856e9	+	2.28640e10i	−0.0992637	+	0.327567i
$515$		0			0
$516$	3.58451e10	+	2.39212e10i	0.505628	+	0.337430i
$517$	−1.08261e9			−0.0151534
$518$	−8.11047e9	−	2.45774e9i	−0.112649	−	0.0341364i
$519$		−	3.53017e10i		−	0.486549i
$520$		0			0
$521$	2.70385e10			0.366971			0.183486	−	0.983022i	$-0.441262\pi$
$521$	2.70385e10			0.366971			0.183486	+	0.983022i	$0.441262\pi$
$522$	−3.30425e9	+	1.09039e10i	−0.0445032	+	0.146859i
$523$		−	1.26822e11i		−	1.69508i	−0.530734	−	0.847538i	$-0.678084\pi$
$523$		−	1.26822e11i		−	1.69508i	0.530734	−	0.847538i	$-0.321916\pi$
$524$	7.56433e10	−	1.13349e11i	1.00333	−	1.50346i
$525$		0			0
$526$	7.02128e10	+	2.12768e10i	0.917220	+	0.277948i
$527$		−	4.39375e10i		−	0.569630i
$528$	2.69986e8	+	6.49694e8i	0.00347381	+	0.00835936i
$529$	−1.29193e11			−1.64974
$530$		0			0
$531$		−	5.25468e9i		−	0.0660950i
$532$	−4.79654e9	−	3.20096e9i	−0.0598799	−	0.0399608i
$533$	−5.26208e10			−0.652002
$534$	3.11217e10	+	9.43090e9i	0.382735	+	0.115981i
$535$		0			0
$536$	5.29351e10	+	6.43885e10i	0.641335	+	0.780098i
$537$	−1.09589e11			−1.31786
$538$	−2.64939e10	+	8.74289e10i	−0.316240	+	1.04358i
$539$		−	8.10738e8i		−	0.00960562i
$540$		0			0
$541$	1.86619e10			0.217854			0.108927	−	0.994050i	$-0.465259\pi$
$541$	1.86619e10			0.217854			0.108927	+	0.994050i	$0.465259\pi$
$542$	1.31940e11	+	3.99823e10i	1.52890	+	0.463308i
$543$		−	4.39717e10i		−	0.505795i
$544$	−1.06665e11	+	1.06602e10i	−1.21794	+	0.121722i
$545$		0			0
$546$	1.30534e9	−	4.30757e9i	0.0146877	−	0.0484688i
$547$			2.19453e9i			0.0245128i	0.999925	+	0.0122564i	$0.00390143\pi$
$547$			2.19453e9i			0.0245128i	−0.999925	+	0.0122564i	$0.996099\pi$
$548$	−1.08887e11	−	7.26656e10i	−1.20741	−	0.805762i
$549$	1.67319e9			0.0184186
$550$		0			0
$551$		−	9.26513e10i		−	1.00518i
$552$	−1.09176e11	+	8.97562e10i	−1.17591	+	0.966737i
$553$	4.29078e9			0.0458813
$554$	2.66548e10	−	8.79601e10i	0.282968	−	0.933784i
$555$		0			0
$556$	−5.73680e10	+	8.59640e10i	−0.600303	+	0.899534i
$557$	1.97889e10			0.205590			0.102795	−	0.994703i	$-0.467221\pi$
$557$	1.97889e10			0.205590			0.102795	+	0.994703i	$0.467221\pi$
$558$	5.41663e9	+	1.64142e9i	0.0558717	+	0.0169310i
$559$			3.92355e10i			0.401820i
$560$		0			0
$561$	1.09749e9			0.0110803
$562$	−3.59694e10	+	1.18698e11i	−0.360569	+	1.18986i
$563$			3.05862e10i			0.304433i	0.988347	+	0.152216i	$0.0486411\pi$
$563$			3.05862e10i			0.304433i	−0.988347	+	0.152216i	$0.951359\pi$
$564$	−1.23214e11	−	8.22266e10i	−1.21771	−	0.812636i
$565$		0			0
$566$	5.45200e10	+	1.65214e10i	0.531240	+	0.160983i
$567$		−	7.77629e9i		−	0.0752385i
$568$	1.15614e11	+	1.40629e11i	1.11075	+	1.35108i
$569$	1.99299e11			1.90132			0.950661	−	0.310230i	$-0.100406\pi$
$569$	1.99299e11			1.90132			0.950661	+	0.310230i	$0.100406\pi$
$570$		0			0
$571$			8.63094e10i			0.811921i	0.913891	+	0.405960i	$0.133063\pi$
$571$			8.63094e10i			0.811921i	−0.913891	+	0.405960i	$0.866937\pi$
$572$	−3.55572e8	+	5.32813e8i	−0.00332157	+	0.00497727i
$573$	−1.73866e11			−1.61285
$574$	9.59959e9	+	2.90900e9i	0.0884311	+	0.0267976i
$575$		0			0
$576$	2.67061e9	−	1.35479e10i	0.0242617	−	0.123079i
$577$	8.87088e10			0.800320			0.400160	−	0.916445i	$-0.368955\pi$
$577$	8.87088e10			0.800320			0.400160	+	0.916445i	$0.368955\pi$
$578$	−1.61261e10	+	5.32156e10i	−0.144483	+	0.476791i
$579$			1.07974e11i			0.960734i
$580$		0			0
$581$	−1.07085e10			−0.0939772
$582$	3.92348e10	+	1.18895e10i	0.341963	+	0.103626i
$583$			2.20543e9i			0.0190906i
$584$	−5.69095e10	+	4.67864e10i	−0.489252	+	0.402225i
$585$		0			0
$586$	−2.60712e10	+	8.60340e10i	−0.221091	+	0.729591i
$587$		−	1.67947e11i		−	1.41456i	−0.706936	−	0.707278i	$-0.749923\pi$
$587$		−	1.67947e11i		−	1.41456i	0.706936	−	0.707278i	$-0.250077\pi$
$588$	6.15775e10	−	9.22718e10i	0.515125	−	0.771898i
$589$	−4.60254e10			−0.382416
$590$		0			0
$591$		−	1.07620e11i		−	0.882155i
$592$	6.33275e10	+	1.52391e11i	0.515591	+	1.24072i
$593$	1.04027e11			0.841252			0.420626	−	0.907234i	$-0.361810\pi$
$593$	1.04027e11			0.841252			0.420626	+	0.907234i	$0.361810\pi$
$594$	−3.67831e8	+	1.21383e9i	−0.00295463	+	0.00975017i
$595$		0			0
$596$	−5.38162e10	−	3.59142e10i	−0.426509	−	0.284630i
$597$	−1.43948e11			−1.13320
$598$	−1.23150e11	−	3.73186e10i	−0.963009	−	0.291824i
$599$			1.28089e11i			0.994960i	0.867475	+	0.497480i	$0.165741\pi$
$599$			1.28089e11i			0.994960i	−0.867475	+	0.497480i	$0.834259\pi$
$600$		0			0
$601$	−6.55306e10			−0.502281			−0.251140	−	0.967951i	$-0.580806\pi$
$601$	−6.55306e10			−0.502281			−0.251140	+	0.967951i	$0.580806\pi$
$602$	2.16902e9	−	7.15771e9i	0.0165150	−	0.0544989i
$603$			1.67495e10i			0.126687i
$604$	−1.63116e10	+	2.44424e10i	−0.122560	+	0.183652i
$605$		0			0
$606$	−6.33816e10	−	1.92067e10i	−0.469973	−	0.142417i
$607$		−	2.09475e11i		−	1.54304i	−0.636204	−	0.771521i	$-0.719496\pi$
$607$		−	2.09475e11i		−	1.54304i	0.636204	−	0.771521i	$-0.280504\pi$
$608$	1.11667e10	+	1.11734e11i	0.0817168	+	0.817655i
$609$	−1.37854e10			−0.100219
$610$		0			0
$611$		−	1.34868e11i		−	0.967707i
$612$	−1.79170e10	−	1.19569e10i	−0.127720	−	0.0852339i
$613$	−1.26502e11			−0.895894			−0.447947	−	0.894060i	$-0.647845\pi$
$613$	−1.26502e11			−0.895894			−0.447947	+	0.894060i	$0.647845\pi$
$614$	1.79678e11	+	5.44483e10i	1.26421	+	0.383099i
$615$		0			0
$616$	9.43219e7	−	7.75440e7i	0.000655073	−	0.000538549i
$617$	2.25072e11			1.55303			0.776517	−	0.630096i	$-0.216984\pi$
$617$	2.25072e11			1.55303			0.776517	+	0.630096i	$0.216984\pi$
$618$	1.93090e9	−	6.37191e9i	0.0132375	−	0.0436833i
$619$		−	6.03060e10i		−	0.410769i	−0.978681	−	0.205385i	$-0.934155\pi$
$619$		−	6.03060e10i		−	0.410769i	0.978681	−	0.205385i	$-0.0658445\pi$
$620$		0			0
$621$	−2.54792e11			−1.71325
$622$	−1.27210e11	−	3.85489e10i	−0.849884	−	0.257543i
$623$		−	5.64383e9i		−	0.0374647i
$624$	−8.09369e10	+	3.36340e10i	−0.533836	+	0.221840i
$625$		0			0
$626$	−3.98386e10	+	1.31466e11i	−0.259422	+	0.856084i
$627$		−	1.14964e9i		−	0.00743863i
$628$	7.42647e10	+	4.95605e10i	0.477468	+	0.318638i
$629$	2.57426e11			1.64456
$630$		0			0
$631$		−	1.40158e11i		−	0.884097i	−0.896991	−	0.442049i	$-0.854252\pi$
$631$		−	1.40158e11i		−	0.884097i	0.896991	−	0.442049i	$-0.145748\pi$
$632$	−5.30613e10	−	6.45420e10i	−0.332590	−	0.404552i
$633$	1.27219e11			0.792384
$634$	−1.16520e10	+	3.84512e10i	−0.0721179	+	0.237987i
$635$		0			0
$636$	−1.67508e11	+	2.51005e11i	−1.02378	+	1.53410i
$637$	1.00999e11			0.613424
$638$	1.87756e9	+	5.68963e8i	0.0113321	+	0.00343401i
$639$			3.65820e10i			0.219414i
$640$		0			0
$641$	−1.84845e11			−1.09490			−0.547452	−	0.836837i	$-0.684402\pi$
$641$	−1.84845e11			−1.09490			−0.547452	+	0.836837i	$0.684402\pi$
$642$	1.61047e10	−	5.31449e10i	0.0948007	−	0.312839i
$643$			2.62671e11i			1.53662i	0.640076	+	0.768312i	$0.278903\pi$
$643$			2.62671e11i			1.53662i	−0.640076	+	0.768312i	$0.721097\pi$
$644$	2.04032e10	+	1.36160e10i	0.118619	+	0.0791602i
$645$		0			0
$646$	1.67636e11	+	5.07992e10i	0.962578	+	0.291693i
$647$		−	2.14765e11i		−	1.22560i	−0.790240	−	0.612798i	$-0.790044\pi$
$647$		−	2.14765e11i		−	1.22560i	0.790240	−	0.612798i	$-0.209956\pi$
$648$	−1.16971e11	+	9.61643e10i	−0.663404	+	0.545398i
$649$	−9.04810e8			−0.00510010
$650$		0			0
$651$			6.84802e9i			0.0381277i
$652$	4.20934e10	−	6.30755e10i	0.232929	−	0.349036i
$653$	−2.41679e11			−1.32919			−0.664593	−	0.747206i	$-0.731395\pi$
$653$	−2.41679e11			−1.32919			−0.664593	+	0.747206i	$0.731395\pi$
$654$	−1.56574e11	−	4.74470e10i	−0.855869	−	0.259357i
$655$		0			0
$656$	−7.49547e10	−	1.80371e11i	−0.404747	−	0.973982i
$657$	−1.48040e10			−0.0794541
$658$	−7.45579e9	+	2.46039e10i	−0.0397732	+	0.131250i
$659$		−	1.45001e11i		−	0.768828i	−0.923161	−	0.384414i	$-0.874403\pi$
$659$		−	1.45001e11i		−	0.768828i	0.923161	−	0.384414i	$-0.125597\pi$
$660$		0			0
$661$	9.94275e10			0.520836			0.260418	−	0.965496i	$-0.416140\pi$
$661$	9.94275e10			0.520836			0.260418	+	0.965496i	$0.416140\pi$
$662$	2.12705e11	+	6.44566e10i	1.10750	+	0.335610i
$663$			1.36722e11i			0.707595i
$664$	1.32425e11	+	1.61077e11i	0.681234	+	0.828630i
$665$		0			0
$666$	−9.61691e9	+	3.17355e10i	−0.0488808	+	0.161305i
$667$			3.94114e11i			1.99121i
$668$	2.21687e10	−	3.32191e10i	0.111336	−	0.166833i
$669$	−8.38835e10			−0.418767
$670$		0			0
$671$		−	2.88108e8i		−	0.00142123i
$672$	1.66246e10	−	1.66147e9i	0.0815220	−	0.00814734i
$673$	−2.01911e10			−0.0984239			−0.0492120	−	0.998788i	$-0.515671\pi$
$673$	−2.01911e10			−0.0984239			−0.0492120	+	0.998788i	$0.515671\pi$
$674$	8.11117e10	−	2.67666e11i	0.393047	−	1.29704i
$675$		0			0
$676$	1.07324e11	+	7.16223e10i	0.513936	+	0.342974i
$677$	−3.25587e10			−0.154993			−0.0774966	−	0.996993i	$-0.524693\pi$
$677$	−3.25587e10			−0.154993			−0.0774966	+	0.996993i	$0.524693\pi$
$678$	−1.76976e11	−	5.36298e10i	−0.837523	−	0.253797i
$679$		−	7.11514e9i		−	0.0334737i
$680$		0			0
$681$	3.14816e11			1.46375
$682$	2.82638e8	−	9.32695e8i	0.00130645	−	0.00431124i
$683$			2.46509e10i			0.113279i	0.998395	+	0.0566396i	$0.0180386\pi$
$683$			2.46509e10i			0.113279i	−0.998395	+	0.0566396i	$0.981961\pi$
$684$	−1.25251e10	+	1.87684e10i	−0.0572210	+	0.0857438i
$685$		0			0
$686$	−3.69930e10	−	1.12101e10i	−0.167041	−	0.0506190i
$687$			1.01990e11i			0.457856i
$688$	−1.34489e11	+	5.58882e10i	−0.600252	+	0.249440i
$689$	−2.74746e11			−1.21914
$690$		0			0
$691$			3.02518e11i			1.32690i	0.748220	+	0.663451i	$0.230909\pi$
$691$			3.02518e11i			1.32690i	−0.748220	+	0.663451i	$0.769091\pi$
$692$	9.92363e10	+	6.62252e10i	0.432759	+	0.288801i
$693$	2.45361e7			0.000106383
$694$	−6.25894e9	−	1.89667e9i	−0.0269813	−	0.00817624i
$695$		0			0
$696$	1.70475e11	+	2.07360e11i	0.726480	+	0.883665i
$697$	−3.04690e11			−1.29100
$698$	7.07805e10	−	2.33573e11i	0.298189	−	0.984015i
$699$		−	1.95277e10i		−	0.0817980i
$700$		0			0
$701$	−1.07716e11			−0.446076			−0.223038	−	0.974810i	$-0.571597\pi$
$701$	−1.07716e11			−0.446076			−0.223038	+	0.974810i	$0.571597\pi$
$702$	−1.51215e11	−	4.58233e10i	−0.622655	−	0.188685i
$703$		−	2.69658e11i		−	1.10406i
$704$	−2.33284e9	−	4.59856e8i	−0.00949715	−	0.00187211i
$705$		0			0
$706$	−1.09652e10	+	3.61849e10i	−0.0441366	+	0.145649i
$707$			1.14941e10i			0.0460041i
$708$	−1.02978e11	−	6.87225e10i	−0.409839	−	0.273505i
$709$	−2.10543e10			−0.0833213			−0.0416606	−	0.999132i	$-0.513265\pi$
$709$	−2.10543e10			−0.0833213			−0.0416606	+	0.999132i	$0.513265\pi$
$710$		0			0
$711$		−	1.67894e10i		−	0.0656988i
$712$	−8.48946e10	+	6.97936e10i	−0.330339	+	0.271579i
$713$	1.95780e11			0.757547
$714$	7.55830e9	−	2.49421e10i	0.0290825	−	0.0959712i
$715$		0			0
$716$	2.05586e11	−	3.08064e11i	0.782242	−	1.17216i
$717$	2.89778e10			0.109645
$718$	2.99610e11	+	9.07918e10i	1.12735	+	0.341624i
$719$			1.84186e11i			0.689193i	0.938751	+	0.344597i	$0.111984\pi$
$719$			1.84186e11i			0.689193i	−0.938751	+	0.344597i	$0.888016\pi$
$720$		0			0
$721$	−1.15553e9			−0.00427602
$722$	−2.55934e10	+	8.44573e10i	−0.0941843	+	0.310805i
$723$		−	4.16426e11i		−	1.52400i
$724$	1.23608e11	+	8.24900e10i	0.449877	+	0.300225i
$725$		0			0
$726$	−2.48612e11	−	7.53376e10i	−0.894901	−	0.271185i
$727$			1.34820e11i			0.482632i	0.970447	+	0.241316i	$0.0775791\pi$
$727$			1.34820e11i			0.482632i	−0.970447	+	0.241316i	$0.922421\pi$
$728$	9.66019e9	+	1.17503e10i	0.0343922	+	0.0418336i
$729$	−3.08413e11			−1.09200
$730$		0			0
$731$			2.27185e11i			0.795628i
$732$	2.18825e10	−	3.27902e10i	0.0762172	−	0.114209i
$733$	5.46288e10			0.189237			0.0946184	−	0.995514i	$-0.469837\pi$
$733$	5.46288e10			0.189237			0.0946184	+	0.995514i	$0.469837\pi$
$734$	−3.68500e11	−	1.11668e11i	−1.26956	−	0.384719i
$735$		0			0
$736$	−4.75002e10	−	4.75285e11i	−0.161877	−	1.61973i
$737$	2.88411e9			0.00977558
$738$	1.13826e10	−	3.75623e10i	0.0383722	−	0.126627i
$739$		−	2.87010e11i		−	0.962320i	−0.876633	−	0.481160i	$-0.840216\pi$
$739$		−	2.87010e11i		−	0.962320i	0.876633	−	0.481160i	$-0.159784\pi$
$740$		0			0
$741$	1.43219e11			0.475037
$742$	5.01218e10	+	1.51886e10i	0.165353	+	0.0501074i
$743$		−	1.72722e11i		−	0.566750i	−0.959009	−	0.283375i	$-0.908546\pi$
$743$		−	1.72722e11i		−	0.566750i	0.959009	−	0.283375i	$-0.0914541\pi$
$744$	1.03008e11	−	8.46850e10i	0.336186	−	0.276385i
$745$		0			0
$746$	7.91090e10	−	2.61057e11i	0.255429	−	0.842908i
$747$			4.19012e10i			0.134569i
$748$	−2.05887e9	+	3.08515e9i	−0.00657692	+	0.00985529i
$749$	−9.63769e9			−0.0306228
$750$		0			0
$751$			1.75776e11i			0.552586i	0.961073	+	0.276293i	$0.0891060\pi$
$751$			1.75776e11i			0.552586i	−0.961073	+	0.276293i	$0.910894\pi$
$752$	4.62293e11	−	1.92110e11i	1.44559	−	0.600729i
$753$	5.47098e11			1.70171
$754$	−7.08796e10	+	2.33901e11i	−0.219299	+	0.723679i
$755$		0			0
$756$	2.50529e10	+	1.67190e10i	0.0766957	+	0.0511828i
$757$	−2.40268e11			−0.731665			−0.365833	−	0.930681i	$-0.619216\pi$
$757$	−2.40268e11			−0.731665			−0.365833	+	0.930681i	$0.619216\pi$
$758$	2.45655e11	+	7.44415e10i	0.744129	+	0.225496i
$759$			4.89027e9i			0.0147355i
$760$		0			0
$761$	5.00466e11			1.49223			0.746115	−	0.665817i	$-0.231917\pi$
$761$	5.00466e11			1.49223			0.746115	+	0.665817i	$0.231917\pi$
$762$	1.36697e11	−	4.51097e11i	0.405453	−	1.33798i
$763$			2.83942e10i			0.0837784i
$764$	3.26168e11	−	4.88752e11i	0.957344	−	1.43455i
$765$		0			0
$766$	−1.89707e11	−	5.74875e10i	−0.551021	−	0.166978i
$767$		−	1.12718e11i		−	0.325697i
$768$	−2.30578e11	−	2.29522e11i	−0.662785	−	0.659749i
$769$	1.02605e11			0.293402			0.146701	−	0.989181i	$-0.453135\pi$
$769$	1.02605e11			0.293402			0.146701	+	0.989181i	$0.453135\pi$
$770$		0			0
$771$			1.13107e11i			0.320089i
$772$	−3.03523e11	−	2.02556e11i	−0.854522	−	0.570264i
$773$	−5.93175e11			−1.66136			−0.830682	−	0.556747i	$-0.812049\pi$
$773$	−5.93175e11			−1.66136			−0.830682	+	0.556747i	$0.812049\pi$
$774$	−2.80074e10	−	8.48718e9i	−0.0780386	−	0.0236483i
$775$		0			0
$776$	−1.07026e11	+	8.79883e10i	−0.295150	+	0.242649i
$777$	−4.01219e10			−0.110077
$778$	5.91747e10	−	1.95274e11i	0.161517	−	0.533000i
$779$			3.19169e11i			0.866704i
$780$		0			0
$781$	6.29910e9			0.0169307
$782$	−7.13077e11	−	2.16086e11i	−1.90682	−	0.577829i
$783$			4.83929e11i			1.28746i
$784$	1.43866e11	+	3.46200e11i	0.380798	+	0.916352i
$785$		0			0
$786$	1.87101e11	−	6.17427e11i	0.490214	−	1.61769i
$787$			1.93252e11i			0.503761i	0.967758	+	0.251880i	$0.0810489\pi$
$787$			1.93252e11i			0.503761i	−0.967758	+	0.251880i	$0.918951\pi$
$788$	3.02531e11	+	2.01894e11i	0.784630	+	0.523622i
$789$	3.47338e11			0.896280
$790$		0			0
$791$			3.20942e10i			0.0819825i
$792$	−3.03422e8	−	3.69073e8i	−0.000771164	−	0.000938018i
$793$	3.58917e10			0.0907613
$794$	−9.05879e10	+	2.98937e11i	−0.227923	+	0.752139i
$795$		0			0
$796$	2.70043e11	−	4.04651e11i	0.672638	−	1.00793i
$797$	4.34328e11			1.07643			0.538213	−	0.842809i	$-0.319099\pi$
$797$	4.34328e11			1.07643			0.538213	+	0.842809i	$0.319099\pi$
$798$	−2.61274e10	−	7.91746e9i	−0.0644294	−	0.0195243i
$799$		−	7.80925e11i		−	1.91612i
$800$		0			0
$801$	−2.20838e10			−0.0536468
$802$	−1.13636e11	+	3.74994e11i	−0.274674	+	0.906415i
$803$			2.54911e9i			0.00613093i
$804$	3.28247e11	+	2.19055e11i	0.785555	+	0.524239i
$805$		0			0
$806$	1.16192e11	+	3.52101e10i	0.275320	+	0.0834310i
$807$			4.32504e11i			1.01976i
$808$	1.72894e11	−	1.42140e11i	0.405635	−	0.333481i
$809$	7.57515e11			1.76847			0.884234	−	0.467044i	$-0.154681\pi$
$809$	7.57515e11			1.76847			0.884234	+	0.467044i	$0.154681\pi$
$810$		0			0
$811$		−	1.15001e11i		−	0.265838i	−0.991127	−	0.132919i	$-0.957565\pi$
$811$		−	1.15001e11i		−	0.265838i	0.991127	−	0.132919i	$-0.0424350\pi$
$812$	2.58611e10	−	3.87520e10i	0.0594870	−	0.0891394i
$813$	6.52698e11			1.49400
$814$	5.46457e9	+	1.65595e9i	0.0124468	+	0.00377180i
$815$		0			0
$816$	−4.68649e11	+	1.94751e11i	−1.05703	+	0.439258i
$817$	2.37981e11			0.534138
$818$	−8.34061e10	+	2.75238e11i	−0.186288	+	0.614744i
$819$			3.05663e9i			0.00679373i
$820$		0			0
$821$	−2.18337e11			−0.480568			−0.240284	−	0.970703i	$-0.577240\pi$
$821$	−2.18337e11			−0.480568			−0.240284	+	0.970703i	$0.577240\pi$
$822$	−5.93122e11	−	1.79736e11i	−1.29914	−	0.393683i
$823$		−	2.44330e11i		−	0.532572i	−0.963894	−	0.266286i	$-0.914203\pi$
$823$		−	2.44330e11i		−	0.532572i	0.963894	−	0.266286i	$-0.0857965\pi$
$824$	1.42897e10	+	1.73815e10i	0.0309966	+	0.0377032i
$825$		0			0
$826$	−6.23132e9	+	2.05632e10i	−0.0133863	+	0.0441743i
$827$			6.25569e11i			1.33738i	0.743543	+	0.668688i	$0.233144\pi$
$827$			6.25569e11i			1.33738i	−0.743543	+	0.668688i	$0.766856\pi$
$828$	5.32782e10	−	7.98357e10i	0.113352	−	0.169854i
$829$	−7.91341e11			−1.67550			−0.837752	−	0.546051i	$-0.816131\pi$
$829$	−7.91341e11			−1.67550			−0.837752	+	0.546051i	$0.816131\pi$
$830$		0			0
$831$		−	4.35132e11i		−	0.912466i
$832$	5.72874e10	−	2.90618e11i	0.119554	−	0.606497i
$833$	5.84816e11			1.21462
$834$	−1.41898e11	+	4.68257e11i	−0.293299	+	0.967878i
$835$		0			0
$836$	3.23175e9	+	2.15670e9i	0.00661626	+	0.00441535i
$837$	2.40396e11			0.489808
$838$	5.35735e11	+	1.62346e11i	1.08636	+	0.329204i
$839$			1.97673e11i			0.398933i	0.979905	+	0.199466i	$0.0639209\pi$
$839$			1.97673e11i			0.398933i	−0.979905	+	0.199466i	$0.936079\pi$
$840$		0			0
$841$	2.48297e11			0.496350
$842$	−5.45094e10	+	1.79879e11i	−0.108448	+	0.357876i
$843$			5.87189e11i			1.16270i
$844$	−2.38659e11	+	3.57623e11i	−0.470336	+	0.704783i
$845$		0			0
$846$	9.62726e10	+	2.91738e10i	0.187941	+	0.0569524i
$847$			4.50851e10i			0.0875990i
$848$	−3.91357e11	−	9.41760e11i	−0.756815	−	1.82120i
$849$	2.69707e11			0.519112
$850$		0			0
$851$			1.14705e12i			2.18708i
$852$	7.16914e11	+	4.78431e11i	1.36053	+	0.907949i
$853$	−9.60505e11			−1.81428			−0.907138	−	0.420833i	$-0.861738\pi$
$853$	−9.60505e11			−1.81428			−0.907138	+	0.420833i	$0.861738\pi$
$854$	−6.54770e9	−	1.98417e9i	−0.0123100	−	0.00373033i
$855$		0			0
$856$	1.19183e11	+	1.44970e11i	0.221983	+	0.270012i
$857$	−1.83889e10			−0.0340904			−0.0170452	−	0.999855i	$-0.505426\pi$
$857$	−1.83889e10			−0.0340904			−0.0170452	+	0.999855i	$0.505426\pi$
$858$	−8.79495e8	+	2.90230e9i	−0.00162287	+	0.00535542i
$859$		−	2.58648e11i		−	0.475048i	−0.971382	−	0.237524i	$-0.923664\pi$
$859$		−	2.58648e11i		−	0.475048i	0.971382	−	0.237524i	$-0.0763358\pi$
$860$		0			0
$861$	4.74884e10			0.0864123
$862$	−6.30729e11	−	1.91132e11i	−1.14239	−	0.346182i
$863$			4.58083e11i			0.825849i	0.910765	+	0.412925i	$0.135493\pi$
$863$			4.58083e11i			0.825849i	−0.910765	+	0.412925i	$0.864507\pi$
$864$	−5.83252e10	−	5.83600e11i	−0.104665	−	1.04727i
$865$		0			0
$866$	−6.44420e10	+	2.12656e11i	−0.114577	+	0.378100i
$867$			2.63254e11i			0.465906i
$868$	−1.92504e10	−	1.28467e10i	−0.0339126	−	0.0226315i
$869$	−2.89099e9			−0.00506953
$870$		0			0
$871$			3.59294e11i			0.624277i
$872$	4.27106e11	−	3.51133e11i	0.738703	−	0.607303i
$873$	−2.78409e10			−0.0479320
$874$	−2.26354e11	+	7.46961e11i	−0.387921	+	1.28012i
$875$		0			0
$876$	−1.93611e11	+	2.90120e11i	−0.328786	+	0.492675i
$877$	9.94220e11			1.68068			0.840338	−	0.542062i	$-0.182356\pi$
$877$	9.94220e11			1.68068			0.840338	+	0.542062i	$0.182356\pi$
$878$	−3.47249e11	−	1.05228e11i	−0.584337	−	0.177074i
$879$			4.25604e11i			0.712935i
$880$		0			0
$881$	4.02463e11			0.668071			0.334036	−	0.942560i	$-0.391589\pi$
$881$	4.02463e11			0.668071			0.334036	+	0.942560i	$0.391589\pi$
$882$	−2.18476e10	+	7.20962e10i	−0.0361018	+	0.119135i
$883$		−	7.19682e11i		−	1.18385i	−0.805992	−	0.591926i	$-0.798368\pi$
$883$		−	7.19682e11i		−	1.18385i	0.805992	−	0.591926i	$-0.201632\pi$
$884$	−3.84338e11	−	2.56488e11i	−0.629368	−	0.420008i
$885$		0			0
$886$	−6.25024e11	−	1.89403e11i	−1.01429	−	0.307363i
$887$		−	4.82885e11i		−	0.780097i	−0.920794	−	0.390049i	$-0.872458\pi$
$887$		−	4.82885e11i		−	0.780097i	0.920794	−	0.390049i	$-0.127542\pi$
$888$	4.96161e11	+	6.03514e11i	0.797941	+	0.970589i
$889$	−8.18053e10			−0.130971
$890$		0			0
$891$			5.23941e9i			0.00831326i
$892$	1.57364e11	−	2.35804e11i	0.248568	−	0.372470i
$893$	−8.18034e11			−1.28637
$894$	−2.93144e11	−	8.88324e10i	−0.458913	−	0.139066i
$895$		0			0
$896$	−2.65169e10	+	4.98502e10i	−0.0411425	+	0.0773455i
$897$	−6.09215e11			−0.941024
$898$	−1.92975e11	+	6.36811e11i	−0.296753	+	0.979277i
$899$		−	3.71846e11i		−	0.569278i
$900$		0			0
$901$	−1.59086e12			−2.41398
$902$	−6.46789e9	−	1.95999e9i	−0.00977094	−	0.00296092i
$903$		−	3.54086e10i		−	0.0532547i
$904$	4.82762e11	−	3.96889e11i	0.722869	−	0.594285i
$905$		0			0
$906$	−4.03462e10	+	1.33141e11i	−0.0598811	+	0.197606i
$907$		−	1.11961e12i		−	1.65439i	−0.561917	−	0.827194i	$-0.689936\pi$
$907$		−	1.11961e12i		−	1.65439i	0.561917	−	0.827194i	$-0.310064\pi$
$908$	−5.90588e11	+	8.84976e11i	−0.868842	+	1.30193i
$909$	4.49753e10			0.0658746
$910$		0			0
$911$		−	1.90411e10i		−	0.0276451i	−0.999904	−	0.0138225i	$-0.995600\pi$
$911$		−	1.90411e10i		−	0.0276451i	0.999904	−	0.0138225i	$-0.00439999\pi$
$912$	2.04006e11	+	4.90918e11i	0.294892	+	0.709626i
$913$	7.21501e9			0.0103837
$914$	3.69506e11	−	1.21936e12i	0.529464	−	1.74721i
$915$		0			0
$916$	−2.86702e11	−	1.91330e11i	−0.407238	−	0.271770i
$917$	−1.11969e11			−0.158351
$918$	−8.75582e11	−	2.65330e11i	−1.23289	−	0.373608i
$919$		−	1.16760e11i		−	0.163694i	−0.996645	−	0.0818470i	$-0.973918\pi$
$919$		−	1.16760e11i		−	0.163694i	0.996645	−	0.0818470i	$-0.0260819\pi$
$920$		0			0
$921$	8.88852e11			1.23535
$922$	1.08071e11	−	3.56631e11i	0.149550	−	0.493509i
$923$			7.84722e11i			1.08121i
$924$	3.20891e8	−	4.80845e8i	0.000440220	−	0.000659656i
$925$		0			0
$926$	5.77940e11	+	1.75135e11i	0.786030	+	0.238193i
$927$			4.52148e9i			0.00612296i
$928$	−9.02714e11	+	9.02177e10i	−1.21719	+	0.121647i
$929$	−8.06361e11			−1.08260			−0.541298	−	0.840831i	$-0.682067\pi$
$929$	−8.06361e11			−1.08260			−0.541298	+	0.840831i	$0.682067\pi$
$930$		0			0
$931$		−	6.12606e11i		−	0.815422i
$932$	5.48942e10	+	3.66336e10i	0.0727550	+	0.0485529i
$933$	−6.29299e11			−0.830482
$934$	−5.50120e11	−	1.66705e11i	−0.722887	−	0.219059i
$935$		0			0
$936$	4.59779e10	−	3.77994e10i	0.0599027	−	0.0492472i
$937$	−1.43350e12			−1.85968			−0.929842	−	0.367959i	$-0.880057\pi$
$937$	−1.43350e12			−1.85968			−0.929842	+	0.367959i	$0.880057\pi$
$938$	1.98626e10	−	6.55458e10i	0.0256581	−	0.0846708i
$939$			6.50353e11i			0.836540i
$940$		0			0
$941$	−1.41766e12			−1.80806			−0.904029	−	0.427472i	$-0.859404\pi$
$941$	−1.41766e12			−1.80806			−0.904029	+	0.427472i	$0.859404\pi$
$942$	4.04530e11	+	1.22586e11i	0.513744	+	0.155682i
$943$		−	1.35766e12i		−	1.71690i
$944$	3.86370e11	−	1.60560e11i	0.486537	−	0.202185i
$945$		0			0
$946$	−1.46142e9	+	4.82263e9i	−0.00182478	+	0.00602170i
$947$		−	7.59493e11i		−	0.944331i	−0.881510	−	0.472165i	$-0.843473\pi$
$947$		−	7.59493e11i		−	0.944331i	0.881510	−	0.472165i	$-0.156527\pi$
$948$	−3.29030e11	−	2.19578e11i	−0.407382	−	0.271866i
$949$	−3.17560e11			−0.391527
$950$		0			0
$951$			1.90215e11i			0.232553i
$952$	5.59354e10	+	6.80379e10i	0.0680987	+	0.0828330i
$953$	−3.72618e11			−0.451743			−0.225872	−	0.974157i	$-0.572523\pi$
$953$	−3.72618e11			−0.451743			−0.225872	+	0.974157i	$0.572523\pi$
$954$	5.94315e10	−	1.96122e11i	0.0717502	−	0.236773i
$955$		0			0
$956$	−5.43617e10	+	8.14592e10i	−0.0650821	+	0.0975234i
$957$	9.28814e9			0.0110734
$958$	6.74760e11	+	2.04475e11i	0.801101	+	0.242760i
$959$			1.07561e11i			0.127169i
$960$		0			0
$961$	6.68173e11			0.783421
$962$	−2.06293e11	+	6.80759e11i	−0.240870	+	0.794865i
$963$			3.77114e10i			0.0438497i
$964$	1.17061e12	+	7.81206e11i	1.35552	+	0.904601i
$965$		0			0
$966$	1.11139e11	+	3.36787e10i	0.127631	+	0.0386765i
$967$		−	7.07203e11i		−	0.808794i	−0.914584	−	0.404397i	$-0.867481\pi$
$967$		−	7.07203e11i		−	0.808794i	0.914584	−	0.404397i	$-0.132519\pi$
$968$	6.78171e11	−	5.57538e11i	0.772392	−	0.634999i
$969$	8.29281e11			0.940603
$970$		0			0
$971$		−	1.48456e12i		−	1.67001i	−0.550240	−	0.835007i	$-0.685464\pi$
$971$		−	1.48456e12i		−	1.67001i	0.550240	−	0.835007i	$-0.314536\pi$
$972$	1.23548e11	−	1.85133e11i	0.138411	−	0.207404i
$973$	8.49173e10			0.0947425
$974$	−6.11457e11	−	1.85292e11i	−0.679407	−	0.205883i
$975$		0			0
$976$	5.11252e10	+	1.23027e11i	0.0563424	+	0.135582i
$977$	4.31329e10			0.0473402			0.0236701	−	0.999720i	$-0.492465\pi$
$977$	4.31329e10			0.0473402			0.0236701	+	0.999720i	$0.492465\pi$
$978$	1.04116e11	−	3.43581e11i	0.113806	−	0.375555i
$979$			3.80263e9i			0.00413955i
$980$		0			0
$981$	1.11104e11			0.119965
$982$	1.21999e12	+	3.69699e11i	1.31193	+	0.397559i
$983$			1.13842e12i			1.21923i	0.792696	+	0.609617i	$0.208677\pi$
$983$			1.13842e12i			1.21923i	−0.792696	+	0.609617i	$0.791323\pi$
$984$	−5.87259e11	−	7.14322e11i	−0.626396	−	0.761927i
$985$		0			0
$986$	−4.10414e11	+	1.35435e12i	−0.434225	+	1.43293i
$987$			1.21714e11i			0.128254i
$988$	−2.68676e11	+	4.02602e11i	−0.281968	+	0.422520i
$989$	−1.01231e12			−1.05810
$990$		0			0
$991$			6.27241e11i			0.650339i	0.945656	+	0.325170i	$0.105421\pi$
$991$			6.27241e11i			0.650339i	−0.945656	+	0.325170i	$0.894579\pi$
$992$	4.48165e10	+	4.48432e11i	0.0462797	+	0.463073i
$993$	1.05223e12			1.08222
$994$	4.33812e10	−	1.43156e11i	0.0444381	−	0.146644i
$995$		0			0
$996$	8.21156e11	+	5.47997e11i	0.834427	+	0.556854i
$997$	−2.64260e11			−0.267455			−0.133728	−	0.991018i	$-0.542695\pi$
$997$	−2.64260e11			−0.267455			−0.133728	+	0.991018i	$0.542695\pi$
$998$	2.39165e11	+	7.24750e10i	0.241088	+	0.0730578i
$999$			1.40846e12i			1.41411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.d.51.8		16
4.3	odd	2	inner	100.9.b.d.51.7		16
5.2	odd	4		100.9.d.c.99.3		32
5.3	odd	4		100.9.d.c.99.30		32
5.4	even	2		20.9.b.a.11.9	✓	16
15.14	odd	2		180.9.c.a.91.8		16
20.3	even	4		100.9.d.c.99.4		32
20.7	even	4		100.9.d.c.99.29		32
20.19	odd	2		20.9.b.a.11.10	yes	16
40.19	odd	2		320.9.b.d.191.5		16
40.29	even	2		320.9.b.d.191.12		16
60.59	even	2		180.9.c.a.91.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.9	✓	16	5.4	even	2
20.9.b.a.11.10	yes	16	20.19	odd	2
100.9.b.d.51.7		16	4.3	odd	2	inner
100.9.b.d.51.8		16	1.1	even	1	trivial
100.9.d.c.99.3		32	5.2	odd	4
100.9.d.c.99.4		32	20.3	even	4
100.9.d.c.99.29		32	20.7	even	4
100.9.d.c.99.30		32	5.3	odd	4
180.9.c.a.91.7		16	60.59	even	2
180.9.c.a.91.8		16	15.14	odd	2
320.9.b.d.191.5		16	40.19	odd	2
320.9.b.d.191.12		16	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.64016 + 15.3124i) q^{2} +75.7492i q^{3} +(-212.938 - 142.104i) q^{4} +(-1159.90 - 351.488i) q^{6} +210.345i q^{7} +(3164.01 - 2601.20i) q^{8} +823.060 q^{9} -141.724i q^{11} +(10764.2 - 16129.9i) q^{12} +17655.5 q^{13} +(-3220.88 - 976.035i) q^{14} +(25149.0 + 60518.5i) q^{16} +102231. q^{17} +(-3819.13 + 12603.0i) q^{18} -107088. i q^{19} -15933.5 q^{21} +(2170.13 + 657.620i) q^{22} +455526. i q^{23} +(197039. + 239671. i) q^{24} +(-81924.3 + 270348. i) q^{26} +559337. i q^{27} +(29890.8 - 44790.4i) q^{28} +865184. q^{29} -429788. i q^{31} +(-1.04338e6 + 104276. i) q^{32} +10735.4 q^{33} +(-474366. + 1.56539e6i) q^{34} +(-175261. - 116960. i) q^{36} +2.51809e6 q^{37} +(1.63978e6 + 496908. i) q^{38} +1.33739e6i q^{39} -2.98042e6 q^{41} +(73933.8 - 243979. i) q^{42} +2.22228e6i q^{43} +(-20139.5 + 30178.3i) q^{44} +(-6.97518e6 - 2.11371e6i) q^{46} -7.63886e6i q^{47} +(-4.58423e6 + 1.90502e6i) q^{48} +5.72056e6 q^{49} +7.74388e6i q^{51} +(-3.75952e6 - 2.50891e6i) q^{52} -1.55615e7 q^{53} +(-8.56477e6 - 2.59541e6i) q^{54} +(547149. + 665534. i) q^{56} +8.11187e6 q^{57} +(-4.01459e6 + 1.32480e7i) q^{58} -6.38433e6i q^{59} +2.03289e6 q^{61} +(6.58108e6 + 1.99429e6i) q^{62} +173127. i q^{63} +(3.24473e6 - 1.64605e7i) q^{64} +(-49814.2 + 164385. i) q^{66} +2.03503e7i q^{67} +(-2.17688e7 - 1.45274e7i) q^{68} -3.45057e7 q^{69} +4.44463e7i q^{71} +(2.60417e6 - 2.14094e6i) q^{72} -1.79865e7 q^{73} +(-1.16843e7 + 3.85579e7i) q^{74} +(-1.52177e7 + 2.28032e7i) q^{76} +29810.9 q^{77} +(-2.04786e7 - 6.20570e6i) q^{78} -2.03988e7i q^{79} -3.69692e7 q^{81} +(1.38296e7 - 4.56374e7i) q^{82} +5.09090e7i q^{83} +(3.39284e6 + 2.26421e6i) q^{84} +(-3.40284e7 - 1.03117e7i) q^{86} +6.55370e7i q^{87} +(-368651. - 448415. i) q^{88} -2.68313e7 q^{89} +3.71375e6i q^{91} +(6.47319e7 - 9.69986e7i) q^{92} +3.25561e7 q^{93} +(1.16969e8 + 3.54456e7i) q^{94} +(-7.89880e6 - 7.90351e7i) q^{96} -3.38260e7 q^{97} +(-2.65443e7 + 8.75953e7i) q^{98} -116647. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 4368 q^{6} + 14184 q^{8} - 38800 q^{9} + 64040 q^{12} - 51392 q^{13} + 68472 q^{14} - 81424 q^{16} - 27552 q^{17} + 616994 q^{18} + 414496 q^{21} + 389120 q^{22} + 163792 q^{24}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 4368 * q^6 + 14184 * q^8 - 38800 * q^9 + 64040 * q^12 - 51392 * q^13 + 68472 * q^14 - 81424 * q^16 - 27552 * q^17 + 616994 * q^18 + 414496 * q^21 + 389120 * q^22 + 163792 * q^24 + 1037124 * q^26 - 1288520 * q^28 + 2764896 * q^29 + 4379904 * q^32 + 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 - 9009472 * q^37 + 3087360 * q^38 - 8576448 * q^41 + 4067400 * q^42 + 16921200 * q^44 - 7974152 * q^46 + 2696640 * q^48 - 32803600 * q^49 - 6679352 * q^52 - 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 - 11957760 * q^57 - 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 + 19358000 * q^66 - 16095192 * q^68 + 7527264 * q^69 + 42242664 * q^72 - 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 + 104032400 * q^78 + 140586672 * q^81 - 83921012 * q^82 + 69761824 * q^84 - 101724672 * q^86 - 44728480 * q^88 + 106647456 * q^89 + 13876200 * q^92 - 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 - 171851232 * q^97 + 285387714 * q^98

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