LMFDB - Embedded newform 983.2.c.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(2,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(982))

chi = DirichletCharacter(H, H._module([674]))

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

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

chi := DirichletCharacter("983.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.c (of order $491$, degree $490$, 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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$39690$
Relative dimension:	$81$ over $\Q(\zeta_{491})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{491}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.682299 + 2.03761i) q^{2} +(-2.29977 - 1.29204i) q^{3} +(-2.08961 - 1.57615i) q^{4} +(-0.572361 + 0.863308i) q^{5} +(4.20182 - 3.80448i) q^{6} +(-1.13382 + 2.50196i) q^{7} +(1.09385 - 0.750669i) q^{8} +(2.05904 + 3.38064i) q^{9} +O(q^{10})$	\(q+(-0.682299 + 2.03761i) q^{2} +(-2.29977 - 1.29204i) q^{3} +(-2.08961 - 1.57615i) q^{4} +(-0.572361 + 0.863308i) q^{5} +(4.20182 - 3.80448i) q^{6} +(-1.13382 + 2.50196i) q^{7} +(1.09385 - 0.750669i) q^{8} +(2.05904 + 3.38064i) q^{9} +(-1.36857 - 1.75528i) q^{10} +(4.92060 + 0.315268i) q^{11} +(2.76918 + 6.32466i) q^{12} +(-0.00240853 - 0.00278287i) q^{13} +(-4.32441 - 4.01737i) q^{14} +(2.43173 - 1.24590i) q^{15} +(-0.655014 - 2.29230i) q^{16} +(3.35687 - 1.48258i) q^{17} +(-8.29332 + 1.88891i) q^{18} +(2.43600 + 1.86199i) q^{19} +(2.55672 - 0.901854i) q^{20} +(5.84018 - 4.28898i) q^{21} +(-3.99971 + 9.81116i) q^{22} +(0.0587654 + 0.554564i) q^{23} +(-3.48551 + 0.313060i) q^{24} +(1.52891 + 3.61726i) q^{25} +(0.00731374 - 0.00300891i) q^{26} +(-0.0889426 - 2.52639i) q^{27} +(6.31272 - 3.44105i) q^{28} +(0.272004 - 0.393651i) q^{29} +(0.879486 + 5.80500i) q^{30} +(4.09593 + 6.09300i) q^{31} +(7.76838 + 0.348167i) q^{32} +(-10.9089 - 7.08268i) q^{33} +(0.730535 + 7.85156i) q^{34} +(-1.51101 - 2.41086i) q^{35} +(1.02581 - 10.3096i) q^{36} +(-2.55978 + 0.634941i) q^{37} +(-5.45609 + 3.69318i) q^{38} +(0.00194349 + 0.00951189i) q^{39} +(0.0219800 + 1.37399i) q^{40} +(-4.54287 - 0.408028i) q^{41} +(4.75453 + 14.8264i) q^{42} +(-7.24202 - 9.92766i) q^{43} +(-9.78524 - 8.41439i) q^{44} +(-4.09705 - 0.157364i) q^{45} +(-1.17008 - 0.258637i) q^{46} +(1.34117 + 4.47597i) q^{47} +(-1.45537 + 6.11807i) q^{48} +(-0.359516 - 0.410060i) q^{49} +(-8.41374 + 0.647282i) q^{50} +(-9.63560 - 0.927630i) q^{51} +(0.000646689 + 0.00961133i) q^{52} +(-5.93986 + 5.44773i) q^{53} +(5.20848 + 1.54252i) q^{54} +(-3.08853 + 4.06755i) q^{55} +(0.637905 + 3.58790i) q^{56} +(-3.19646 - 7.42957i) q^{57} +(0.616520 + 0.822826i) q^{58} +(-3.99860 - 0.307618i) q^{59} +(-7.04510 - 1.22934i) q^{60} +(0.165056 + 0.140106i) q^{61} +(-15.2098 + 4.18867i) q^{62} +(-10.7928 + 1.31857i) q^{63} +(-4.29489 + 11.1424i) q^{64} +(0.00378102 - 0.000486505i) q^{65} +(21.8749 - 17.3956i) q^{66} +(-0.490682 + 0.421941i) q^{67} +(-9.35133 - 2.19291i) q^{68} +(0.581374 - 1.35130i) q^{69} +(5.94335 - 1.43391i) q^{70} +(-7.35049 + 6.00048i) q^{71} +(4.79003 + 2.15228i) q^{72} +(-5.25818 - 3.75895i) q^{73} +(0.452775 - 5.64906i) q^{74} +(1.15751 - 10.2943i) q^{75} +(-2.15551 - 7.73034i) q^{76} +(-6.36787 + 11.9537i) q^{77} +(-0.0207076 - 0.00252987i) q^{78} +(15.5734 - 2.30851i) q^{79} +(2.35386 + 0.746542i) q^{80} +(2.38894 - 4.62619i) q^{81} +(3.93099 - 8.97820i) q^{82} +(-14.5493 + 4.51214i) q^{83} +(-18.9638 - 0.242687i) q^{84} +(-0.641416 + 3.74659i) q^{85} +(25.1699 - 7.98280i) q^{86} +(-1.13416 + 0.553866i) q^{87} +(5.61908 - 3.34888i) q^{88} +(-3.58984 - 2.36351i) q^{89} +(3.11606 - 8.24083i) q^{90} +(0.00969346 - 0.00287077i) q^{91} +(0.751279 - 1.25145i) q^{92} +(-1.54727 - 19.3046i) q^{93} +(-10.0354 - 0.321159i) q^{94} +(-3.00174 + 1.03728i) q^{95} +(-17.4157 - 10.8378i) q^{96} +(-1.94499 + 0.0996450i) q^{97} +(1.08084 - 0.452771i) q^{98} +(9.06589 + 17.2839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9}+O(q^{10}) $ 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9} - 471 q^{10} - 477 q^{11} - 463 q^{12} - 483 q^{13} - 473 q^{14} - 461 q^{15} - 543 q^{16} - 481 q^{17} - 457 q^{18} - 473 q^{19} - 449 q^{20} - 449 q^{21} - 459 q^{22} - 473 q^{23} - 405 q^{24} - 552 q^{25} - 437 q^{26} - 451 q^{27} - 455 q^{28} - 455 q^{29} - 379 q^{30} - 459 q^{31} - 437 q^{32} - 447 q^{33} - 423 q^{34} - 439 q^{35} - 459 q^{36} - 475 q^{37} - 423 q^{38} - 439 q^{39} - 413 q^{40} - 455 q^{41} - 407 q^{42} - 457 q^{43} - 413 q^{44} - 397 q^{45} - 415 q^{46} - 467 q^{47} - 393 q^{48} - 524 q^{49} - 429 q^{50} - 403 q^{51} - 391 q^{52} - 431 q^{53} - 379 q^{54} - 415 q^{55} - 371 q^{56} - 447 q^{57} - 431 q^{58} - 439 q^{59} - 261 q^{60} - 431 q^{61} - 383 q^{62} - 445 q^{63} - 447 q^{64} - 415 q^{65} - 345 q^{66} - 439 q^{67} - 409 q^{68} - 367 q^{69} - 345 q^{70} - 415 q^{71} - 341 q^{72} - 465 q^{73} - 359 q^{74} - 339 q^{75} - 361 q^{76} - 363 q^{77} - 341 q^{78} - 423 q^{79} - 249 q^{80} - 420 q^{81} - 371 q^{82} - 433 q^{83} - 215 q^{84} - 409 q^{85} - 369 q^{86} - 329 q^{87} - 255 q^{88} - 393 q^{89} - 251 q^{90} - 373 q^{91} - 387 q^{92} - 369 q^{93} - 317 q^{94} - 393 q^{95} - 149 q^{96} - 415 q^{97} - 307 q^{98} - 299 q^{99}+O(q^{100}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9 - 471 * q^10 - 477 * q^11 - 463 * q^12 - 483 * q^13 - 473 * q^14 - 461 * q^15 - 543 * q^16 - 481 * q^17 - 457 * q^18 - 473 * q^19 - 449 * q^20 - 449 * q^21 - 459 * q^22 - 473 * q^23 - 405 * q^24 - 552 * q^25 - 437 * q^26 - 451 * q^27 - 455 * q^28 - 455 * q^29 - 379 * q^30 - 459 * q^31 - 437 * q^32 - 447 * q^33 - 423 * q^34 - 439 * q^35 - 459 * q^36 - 475 * q^37 - 423 * q^38 - 439 * q^39 - 413 * q^40 - 455 * q^41 - 407 * q^42 - 457 * q^43 - 413 * q^44 - 397 * q^45 - 415 * q^46 - 467 * q^47 - 393 * q^48 - 524 * q^49 - 429 * q^50 - 403 * q^51 - 391 * q^52 - 431 * q^53 - 379 * q^54 - 415 * q^55 - 371 * q^56 - 447 * q^57 - 431 * q^58 - 439 * q^59 - 261 * q^60 - 431 * q^61 - 383 * q^62 - 445 * q^63 - 447 * q^64 - 415 * q^65 - 345 * q^66 - 439 * q^67 - 409 * q^68 - 367 * q^69 - 345 * q^70 - 415 * q^71 - 341 * q^72 - 465 * q^73 - 359 * q^74 - 339 * q^75 - 361 * q^76 - 363 * q^77 - 341 * q^78 - 423 * q^79 - 249 * q^80 - 420 * q^81 - 371 * q^82 - 433 * q^83 - 215 * q^84 - 409 * q^85 - 369 * q^86 - 329 * q^87 - 255 * q^88 - 393 * q^89 - 251 * q^90 - 373 * q^91 - 387 * q^92 - 369 * q^93 - 317 * q^94 - 393 * q^95 - 149 * q^96 - 415 * q^97 - 307 * q^98 - 299 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/983\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{337}{491}\right)$

Coefficient data

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

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

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

$2$	−0.682299	+	2.03761i	−0.482458	+	1.44081i	0.375371	+	0.926874i	$0.377515\pi$
$2$	−0.682299	+	2.03761i	−0.482458	+	1.44081i	−0.857830	+	0.513934i	$0.828188\pi$
$3$	−2.29977	−	1.29204i	−1.32777	−	0.745963i	−0.346403	−	0.938086i	$-0.612597\pi$
$3$	−2.29977	−	1.29204i	−1.32777	−	0.745963i	−0.981371	+	0.192123i	$0.938463\pi$
$4$	−2.08961	−	1.57615i	−1.04481	−	0.788076i
$5$	−0.572361	+	0.863308i	−0.255967	+	0.386083i	−0.938784	−	0.344507i	$-0.888046\pi$
$5$	−0.572361	+	0.863308i	−0.255967	+	0.386083i	0.682816	+	0.730590i	$0.260755\pi$
$6$	4.20182	−	3.80448i	1.71538	−	1.55317i
$7$	−1.13382	+	2.50196i	−0.428545	+	0.945651i	0.564225	+	0.825621i	$0.309175\pi$
$7$	−1.13382	+	2.50196i	−0.428545	+	0.945651i	−0.992770	+	0.120030i	$0.961701\pi$
$8$	1.09385	−	0.750669i	0.386736	−	0.265402i
$9$	2.05904	+	3.38064i	0.686346	+	1.12688i
$10$	−1.36857	−	1.75528i	−0.432779	−	0.555069i
$11$	4.92060	+	0.315268i	1.48362	+	0.0950568i	0.784579	−	0.620029i	$-0.212879\pi$
$11$	4.92060	+	0.315268i	1.48362	+	0.0950568i	0.699037	+	0.715086i	$0.253612\pi$
$12$	2.76918	+	6.32466i	0.799392	+	1.82577i
$13$	−0.00240853	−	0.00278287i	−0.000668007	−	0.000771828i	0.755796	−	0.654807i	$-0.227250\pi$
$13$	−0.00240853	−	0.00278287i	−0.000668007	−	0.000771828i	−0.756464	+	0.654035i	$0.773075\pi$
$14$	−4.32441	−	4.01737i	−1.15575	−	1.07369i
$15$	2.43173	−	1.24590i	0.627871	−	0.321689i
$16$	−0.655014	−	2.29230i	−0.163753	−	0.573074i
$17$	3.35687	−	1.48258i	0.814161	−	0.359579i	0.0452827	−	0.998974i	$-0.485581\pi$
$17$	3.35687	−	1.48258i	0.814161	−	0.359579i	0.768878	+	0.639396i	$0.220815\pi$
$18$	−8.29332	+	1.88891i	−1.95475	+	0.445220i
$19$	2.43600	+	1.86199i	0.558856	+	0.427170i	0.847908	−	0.530143i	$-0.177862\pi$
$19$	2.43600	+	1.86199i	0.558856	+	0.427170i	−0.289053	+	0.957313i	$0.593340\pi$
$20$	2.55672	−	0.901854i	0.571699	−	0.201661i
$21$	5.84018	−	4.28898i	1.27443	−	0.935932i
$22$	−3.99971	+	9.81116i	−0.852741	+	2.09175i
$23$	0.0587654	+	0.554564i	0.0122534	+	0.115635i	0.998877	−	0.0473813i	$-0.0150876\pi$
$23$	0.0587654	+	0.554564i	0.0122534	+	0.115635i	−0.986623	+	0.163016i	$0.947878\pi$
$24$	−3.48551	+	0.313060i	−0.711477	+	0.0639030i
$25$	1.52891	+	3.61726i	0.305783	+	0.723451i
$26$	0.00731374	−	0.00300891i	0.00143434	−	0.000590096i
$27$	−0.0889426	−	2.52639i	−0.0171170	−	0.486203i
$28$	6.31272	−	3.44105i	1.19299	−	0.650297i
$29$	0.272004	−	0.393651i	0.0505098	−	0.0730992i	−0.796637	−	0.604458i	$-0.793390\pi$
$29$	0.272004	−	0.393651i	0.0505098	−	0.0730992i	0.847147	+	0.531359i	$0.178318\pi$
$30$	0.879486	+	5.80500i	0.160571	+	1.05984i
$31$	4.09593	+	6.09300i	0.735650	+	1.09433i	0.991813	+	0.127701i	$0.0407598\pi$
$31$	4.09593	+	6.09300i	0.735650	+	1.09433i	−0.256162	+	0.966634i	$0.582458\pi$
$32$	7.76838	+	0.348167i	1.37327	+	0.0615478i
$33$	−10.9089	−	7.08268i	−1.89900	−	1.23294i
$34$	0.730535	+	7.85156i	0.125286	+	1.34653i
$35$	−1.51101	−	2.41086i	−0.255406	−	0.407510i
$36$	1.02581	−	10.3096i	0.170969	−	1.71827i
$37$	−2.55978	+	0.634941i	−0.420826	+	0.104384i	−0.445437	−	0.895313i	$-0.646952\pi$
$37$	−2.55978	+	0.634941i	−0.420826	+	0.104384i	0.0246107	+	0.999697i	$0.492165\pi$
$38$	−5.45609	+	3.69318i	−0.885095	+	0.599112i
$39$	0.00194349	+	0.00951189i	0.000311208	+	0.00152312i
$40$	0.0219800	+	1.37399i	0.00347535	+	0.217246i
$41$	−4.54287	−	0.408028i	−0.709477	−	0.0637233i	−0.271147	−	0.962538i	$-0.587403\pi$
$41$	−4.54287	−	0.408028i	−0.709477	−	0.0637233i	−0.438329	+	0.898815i	$0.644430\pi$
$42$	4.75453	+	14.8264i	0.733640	+	2.28776i
$43$	−7.24202	−	9.92766i	−1.10440	−	1.51395i	−0.834454	−	0.551078i	$-0.814217\pi$
$43$	−7.24202	−	9.92766i	−1.10440	−	1.51395i	−0.269944	−	0.962876i	$-0.587005\pi$
$44$	−9.78524	−	8.41439i	−1.47518	−	1.26852i
$45$	−4.09705	−	0.157364i	−0.610752	−	0.0234584i
$46$	−1.17008	−	0.258637i	−0.172519	−	0.0381340i
$47$	1.34117	+	4.47597i	0.195630	+	0.652887i	0.998397	+	0.0565943i	$0.0180241\pi$
$47$	1.34117	+	4.47597i	0.195630	+	0.652887i	−0.802767	+	0.596293i	$0.796640\pi$
$48$	−1.45537	+	6.11807i	−0.210064	+	0.883067i
$49$	−0.359516	−	0.410060i	−0.0513595	−	0.0585800i
$50$	−8.41374	+	0.647282i	−1.18988	+	0.0915395i
$51$	−9.63560	−	0.927630i	−1.34925	−	0.129894i
$52$	0.000646689		0.00961133i	8.96796e−5		0.00133285i
$53$	−5.93986	+	5.44773i	−0.815902	+	0.748304i	−0.970868	−	0.239616i	$-0.922978\pi$
$53$	−5.93986	+	5.44773i	−0.815902	+	0.748304i	0.154966	+	0.987920i	$0.450473\pi$
$54$	5.20848	+	1.54252i	0.708784	+	0.209910i
$55$	−3.08853	+	4.06755i	−0.416457	+	0.548468i
$56$	0.637905	+	3.58790i	0.0852437	+	0.479454i
$57$	−3.19646	−	7.42957i	−0.423381	−	0.984071i
$58$	0.616520	+	0.822826i	0.0809530	+	0.108042i
$59$	−3.99860	−	0.307618i	−0.520573	−	0.0400485i	−0.186242	−	0.982504i	$-0.559631\pi$
$59$	−3.99860	−	0.307618i	−0.520573	−	0.0400485i	−0.334332	+	0.942455i	$0.608511\pi$
$60$	−7.04510	−	1.22934i	−0.909519	−	0.158706i
$61$	0.165056	+	0.140106i	0.0211333	+	0.0179387i	0.657638	−	0.753334i	$-0.271555\pi$
$61$	0.165056	+	0.140106i	0.0211333	+	0.0179387i	−0.636505	+	0.771272i	$0.719621\pi$
$62$	−15.2098	+	4.18867i	−1.93165	+	0.531961i
$63$	−10.7928	+	1.31857i	−1.35977	+	0.166124i
$64$	−4.29489	+	11.1424i	−0.536861	+	1.39280i
$65$	0.00378102		0.000486505i	0.000468978		6.03435e-5i
$66$	21.8749	−	17.3956i	2.69261	−	2.14125i
$67$	−0.490682	+	0.421941i	−0.0599464	+	0.0515483i	−0.681462	−	0.731853i	$-0.738656\pi$
$67$	−0.490682	+	0.421941i	−0.0599464	+	0.0515483i	0.621516	+	0.783402i	$0.286517\pi$
$68$	−9.35133	−	2.19291i	−1.13402	−	0.265930i
$69$	0.581374	−	1.35130i	0.0699892	−	0.162677i
$70$	5.94335	−	1.43391i	0.710367	−	0.171385i
$71$	−7.35049	+	6.00048i	−0.872342	+	0.712126i	−0.958786	−	0.284131i	$-0.908295\pi$
$71$	−7.35049	+	6.00048i	−0.872342	+	0.712126i	0.0864434	+	0.996257i	$0.472450\pi$
$72$	4.79003	+	2.15228i	0.564511	+	0.253648i
$73$	−5.25818	−	3.75895i	−0.615424	−	0.439952i	0.230636	−	0.973040i	$-0.425919\pi$
$73$	−5.25818	−	3.75895i	−0.615424	−	0.439952i	−0.846060	+	0.533088i	$0.821031\pi$
$74$	0.452775	−	5.64906i	0.0526340	−	0.656690i
$75$	1.15751	−	10.2943i	0.133657	−	1.18868i
$76$	−2.15551	−	7.73034i	−0.247254	−	0.886731i
$77$	−6.36787	+	11.9537i	−0.725686	+	1.36225i
$78$	−0.0207076	−	0.00252987i	−0.00234467	−	0.000286451i
$79$	15.5734	−	2.30851i	1.75215	−	0.259728i	0.807984	−	0.589204i	$-0.200559\pi$
$79$	15.5734	−	2.30851i	1.75215	−	0.259728i	0.944164	+	0.329476i	$0.106872\pi$
$80$	2.35386	+	0.746542i	0.263170	+	0.0834660i
$81$	2.38894	−	4.62619i	0.265438	−	0.514022i
$82$	3.93099	−	8.97820i	0.434106	−	0.991476i
$83$	−14.5493	+	4.51214i	−1.59699	+	0.495272i	−0.961029	−	0.276448i	$-0.910843\pi$
$83$	−14.5493	+	4.51214i	−1.59699	+	0.495272i	−0.635962	+	0.771720i	$0.719397\pi$
$84$	−18.9638	−	0.242687i	−2.06912	−	0.0264794i
$85$	−0.641416	+	3.74659i	−0.0695714	+	0.406374i
$86$	25.1699	−	7.98280i	2.71414	−	0.860807i
$87$	−1.13416	+	0.553866i	−0.121595	+	0.0593807i
$88$	5.61908	−	3.34888i	0.598996	−	0.356992i
$89$	−3.58984	−	2.36351i	−0.380522	−	0.250532i	0.345186	−	0.938534i	$-0.387816\pi$
$89$	−3.58984	−	2.36351i	−0.380522	−	0.250532i	−0.725708	+	0.688002i	$0.758488\pi$
$90$	3.11606	−	8.24083i	0.328461	−	0.868660i
$91$	0.00969346	−	0.00287077i	0.00101615	−	0.000300939i
$92$	0.751279	−	1.25145i	0.0783263	−	0.130472i
$93$	−1.54727	−	19.3046i	−0.160445	−	2.00180i
$94$	−10.0354	−	0.321159i	−1.03507	−	0.0331250i
$95$	−3.00174	+	1.03728i	−0.307972	+	0.106423i
$96$	−17.4157	−	10.8378i	−1.77748	−	1.10613i
$97$	−1.94499	+	0.0996450i	−0.197484	+	0.0101174i	−0.149656	−	0.988738i	$-0.547817\pi$
$97$	−1.94499	+	0.0996450i	−0.197484	+	0.0101174i	−0.0478282	+	0.998856i	$0.515230\pi$
$98$	1.08084	−	0.452771i	0.109181	−	0.0457368i
$99$	9.06589	+	17.2839i	0.911156	+	1.73710i
$100$	2.50651	−	9.96847i	0.250651	−	0.996847i
$101$	8.96714	+	6.49750i	0.892264	+	0.646525i	0.935802	−	0.352527i	$-0.114677\pi$
$101$	8.96714	+	6.49750i	0.892264	+	0.646525i	−0.0435376	+	0.999052i	$0.513863\pi$
$102$	8.46451	−	19.0007i	0.838111	−	1.88135i
$103$	14.2167	+	5.53222i	1.40082	+	0.545106i	0.939628	−	0.342197i	$-0.111171\pi$
$103$	14.2167	+	5.53222i	1.40082	+	0.545106i	0.461188	+	0.887303i	$0.347424\pi$
$104$	−0.00472360	−	0.00123604i	−0.000463187	−	0.000121203i
$105$	0.360026	+	7.49672i	0.0351350	+	0.731605i
$106$	−7.04761	−	15.8201i	−0.684524	−	1.53658i
$107$	−1.11066	+	5.26387i	−0.107371	+	0.508878i	0.891110	+	0.453788i	$0.149927\pi$
$107$	−1.11066	+	5.26387i	−0.107371	+	0.508878i	−0.998481	+	0.0550901i	$0.982455\pi$
$108$	−3.79611	+	5.41936i	−0.365281	+	0.521478i
$109$	−2.48112	−	2.94198i	−0.237648	−	0.281791i	0.632522	−	0.774542i	$-0.282020\pi$
$109$	−2.48112	−	2.94198i	−0.237648	−	0.281791i	−0.870170	+	0.492751i	$0.835991\pi$
$110$	−6.18078	−	9.06850i	−0.589314	−	0.864648i
$111$	6.70729	+	1.84714i	0.636628	+	0.175322i
$112$	6.47790	+	0.960244i	0.612104	+	0.0907345i
$113$	−10.3755	−	5.06686i	−0.976045	−	0.476650i	−0.119562	−	0.992827i	$-0.538149\pi$
$113$	−10.3755	−	5.06686i	−0.976045	−	0.476650i	−0.856482	+	0.516177i	$0.827355\pi$
$114$	17.3195	−	1.44395i	1.62212	−	0.135238i
$115$	−0.512394	−	0.266678i	−0.0477810	−	0.0248678i
$116$	−1.18884	+	0.393859i	−0.110381	+	0.0365689i
$117$	0.00444862	−	0.0138724i	0.000411275	−	0.00128251i
$118$	3.35505	−	7.93770i	0.308857	−	0.730725i
$119$	−0.0967435	+	10.0797i	−0.00886846	+	0.924007i
$120$	1.72470	−	3.18826i	0.157443	−	0.291047i
$121$	13.2028	+	1.69881i	1.20026	+	0.154437i
$122$	−0.398099	+	0.240726i	−0.0360422	+	0.0217943i
$123$	9.92037	+	6.80796i	0.894489	+	0.613853i
$124$	1.04458	−	19.1878i	0.0938060	−	1.72312i
$125$	−9.08804	−	1.70593i	−0.812859	−	0.152583i
$126$	4.67719	−	22.8912i	0.416677	−	2.03931i
$127$	5.69576	+	13.7197i	0.505417	+	1.21743i	0.947297	+	0.320356i	$0.103803\pi$
$127$	5.69576	+	13.7197i	0.505417	+	1.21743i	−0.441880	+	0.897074i	$0.645688\pi$
$128$	−7.78885	−	6.44182i	−0.688443	−	0.569381i
$129$	3.82802	+	32.1884i	0.337038	+	2.83403i
$130$	−0.00158848	+	0.00803619i	−0.000139319	+	0.000704821i
$131$	8.32484	+	4.26523i	0.727345	+	0.372655i	0.779850	−	0.625966i	$-0.215295\pi$
$131$	8.32484	+	4.26523i	0.727345	+	0.372655i	−0.0525057	+	0.998621i	$0.516721\pi$
$132$	11.6320	+	31.9942i	1.01244	+	2.78473i
$133$	−7.42061	+	3.98359i	−0.643449	+	0.345421i
$134$	−0.524960	−	1.28771i	−0.0453496	−	0.111241i
$135$	2.23196	+	1.36922i	0.192096	+	0.117844i
$136$	2.55900	−	4.14163i	0.219432	−	0.355142i
$137$	−8.75661	−	15.4702i	−0.748128	−	1.32171i	−0.940300	−	0.340347i	$-0.889455\pi$
$137$	−8.75661	−	15.4702i	−0.748128	−	1.32171i	0.192172	−	0.981361i	$-0.438447\pi$
$138$	2.35675	+	2.10660i	0.200620	+	0.179326i
$139$	−9.36297	+	17.8503i	−0.794157	+	1.51404i	0.0624346	+	0.998049i	$0.480114\pi$
$139$	−9.36297	+	17.8503i	−0.794157	+	1.51404i	−0.856591	+	0.515995i	$0.827422\pi$
$140$	−0.642465	+	7.41934i	−0.0542982	+	0.627049i
$141$	2.69876	−	12.0266i	0.227277	−	1.01282i
$142$	−7.21142	−	19.0716i	−0.605169	−	1.60045i
$143$	−0.0109741	−	0.0144527i	−0.000917698	−	0.00120859i
$144$	6.40075	−	6.93429i	0.533395	−	0.577858i
$145$	0.184158	+	0.460134i	0.0152935	+	0.0382120i
$146$	11.2469	−	8.14940i	0.930802	−	0.674449i
$147$	0.296990	+	1.40756i	0.0244953	+	0.116093i
$148$	6.34972	+	2.70783i	0.521944	+	0.222582i
$149$	−1.74981	−	6.77544i	−0.143350	−	0.555066i	−0.999279	−	0.0379724i	$-0.987910\pi$
$149$	−1.74981	−	6.77544i	−0.143350	−	0.555066i	0.855929	−	0.517093i	$-0.172986\pi$
$150$	20.1860	+	9.38233i	1.64818	+	0.766064i
$151$	−4.86840	+	1.75238i	−0.396185	+	0.142607i	−0.529179	−	0.848510i	$-0.677500\pi$
$151$	−4.86840	+	1.75238i	−0.396185	+	0.142607i	0.132994	+	0.991117i	$0.457541\pi$
$152$	4.06236	+	0.208121i	0.329501	+	0.0168809i
$153$	11.9240	+	8.29570i	0.963998	+	0.670667i
$154$	−20.0121	−	21.1312i	−1.61262	−	1.70280i
$155$	−7.60449	+	0.0486569i	−0.610807	+	0.00390821i
$156$	0.0109310	−	0.0229394i	0.000875183	−	0.00183662i
$157$	4.51430	+	4.89060i	0.360280	+	0.390312i	0.888562	−	0.458757i	$-0.151705\pi$
$157$	4.51430	+	4.89060i	0.360280	+	0.390312i	−0.528282	+	0.849069i	$0.677163\pi$
$158$	−5.92189	+	33.3077i	−0.471120	+	2.64982i
$159$	20.6990	−	4.85398i	1.64154	−	0.384946i
$160$	−4.74689	+	6.50723i	−0.375275	+	0.514442i
$161$	−1.45412	−	0.481749i	−0.114601	−	0.0379671i
$162$	7.79641	+	8.02419i	0.612544	+	0.630440i
$163$	14.7292	−	3.75370i	1.15368	−	0.294013i	0.378407	−	0.925639i	$-0.376472\pi$
$163$	14.7292	−	3.75370i	1.15368	−	0.294013i	0.775273	+	0.631627i	$0.217612\pi$
$164$	8.84972	+	8.01287i	0.691047	+	0.625700i
$165$	12.3584	−	5.36391i	0.962097	−	0.417580i
$166$	0.732961	−	32.7244i	0.0568888	−	2.53991i
$167$	2.41935	+	13.1200i	0.187215	+	1.01525i	0.935883	+	0.352310i	$0.114604\pi$
$167$	2.41935	+	13.1200i	0.187215	+	1.01525i	−0.748669	+	0.662944i	$0.769307\pi$
$168$	3.16869	−	9.07556i	0.244470	−	0.700195i
$169$	1.86506	−	12.8655i	0.143466	−	0.989654i
$170$	−7.19645	−	3.86325i	−0.551942	−	0.296298i
$171$	−1.27893	+	12.0691i	−0.0978022	+	0.922951i
$172$	−0.514464	+	32.1595i	−0.0392275	+	2.45214i
$173$	−17.6890	+	3.32043i	−1.34487	+	0.252448i	−0.806986	−	0.590570i	$-0.798903\pi$
$173$	−17.6890	+	3.32043i	−1.34487	+	0.252448i	−0.537885	+	0.843018i	$0.680777\pi$
$174$	−0.354727	−	2.68888i	−0.0268918	−	0.203844i
$175$	−10.7837	−	0.276053i	−0.815174	−	0.0208677i
$176$	−2.50037	−	11.4860i	−0.188473	−	0.865788i
$177$	8.79841	+	5.87382i	0.661329	+	0.441504i
$178$	7.26526	−	5.70208i	0.544555	−	0.427389i
$179$	0.671019	+	0.322390i	0.0501543	+	0.0240966i	0.457970	−	0.888968i	$-0.348577\pi$
$179$	0.671019	+	0.322390i	0.0501543	+	0.0240966i	−0.407815	+	0.913064i	$0.633709\pi$
$180$	8.31322	+	6.78640i	0.619631	+	0.505828i
$181$	−4.68513	−	9.36479i	−0.348243	−	0.696080i	0.649700	−	0.760191i	$-0.274894\pi$
$181$	−4.68513	−	9.36479i	−0.348243	−	0.696080i	−0.997943	+	0.0641111i	$0.979579\pi$
$182$	−0.000764319		0.0217102i	−5.66551e−5		0.00160927i
$183$	−0.198569	−	0.535472i	−0.0146786	−	0.0395832i
$184$	0.480575	+	0.562498i	0.0354284	+	0.0414679i
$185$	0.916970	−	2.57330i	0.0674170	−	0.189193i
$186$	40.3910	+	10.0188i	2.96161	+	0.734613i
$187$	16.9852	−	6.23687i	1.24208	−	0.456085i
$188$	4.25227	−	11.4669i	0.310129	−	0.836312i
$189$	6.42175	+	2.64194i	0.467114	+	0.192173i
$190$	−0.0654967	−	6.82412i	−0.00475163	−	0.495074i
$191$	5.76275	+	3.04627i	0.416978	+	0.220420i	0.662644	−	0.748935i	$-0.269434\pi$
$191$	5.76275	+	3.04627i	0.416978	+	0.220420i	−0.245666	+	0.969355i	$0.579007\pi$
$192$	24.2737	−	20.0757i	1.75180	−	1.44884i
$193$	8.95436	+	8.53465i	0.644549	+	0.614338i	0.940063	−	0.341001i	$-0.110766\pi$
$193$	8.95436	+	8.53465i	0.644549	+	0.614338i	−0.295514	+	0.955338i	$0.595491\pi$
$194$	1.12403	−	4.03112i	0.0807004	−	0.289418i
$195$	−0.00932407	−	0.00376640i	−0.000667711	−	0.000269717i
$196$	0.104934	+	1.42352i	0.00749525	+	0.101680i
$197$	−1.78091	+	0.478211i	−0.126884	+	0.0340711i	−0.322216	−	0.946666i	$-0.604428\pi$
$197$	−1.78091	+	0.478211i	−0.126884	+	0.0340711i	0.195332	+	0.980737i	$0.437422\pi$
$198$	−41.4036	+	6.67994i	−2.94242	+	0.474723i
$199$	−2.00007	+	3.10225i	−0.141781	+	0.219912i	−0.904133	−	0.427250i	$-0.859482\pi$
$199$	−2.00007	+	3.10225i	−0.141781	+	0.219912i	0.762352	+	0.647163i	$0.224044\pi$
$200$	4.38777	+	2.80904i	0.310262	+	0.198629i
$201$	1.67362	−	0.336385i	0.118048	−	0.0237268i
$202$	−19.3576	+	13.8383i	−1.36200	+	0.973661i
$203$	0.676494	+	1.12687i	0.0474806	+	0.0790910i
$204$	18.6726	+	17.1255i	1.30734	+	1.19903i
$205$	2.95241	−	3.68836i	0.206205	−	0.257606i
$206$	−20.9726	+	25.1935i	−1.46123	+	1.75532i
$207$	−1.75378	+	1.34053i	−0.121896	+	0.0931734i
$208$	−0.00480153	+	0.00734389i	−0.000332926	+	0.000509207i
$209$	11.3995	+	9.93011i	0.788522	+	0.686880i
$210$	−15.5210	−	4.38141i	−1.07105	−	0.302346i
$211$	−2.83179	−	17.2018i	−0.194948	−	1.18422i	−0.886790	−	0.462172i	$-0.847070\pi$
$211$	−2.83179	−	17.2018i	−0.194948	−	1.18422i	0.691842	−	0.722049i	$-0.256799\pi$
$212$	20.9985	−	2.02154i	1.44218	−	0.138840i
$213$	24.6573	−	4.30258i	1.68949	−	0.294808i
$214$	−9.96792	−	5.85462i	−0.681393	−	0.400214i
$215$	12.7157	−	0.569897i	0.867202	−	0.0388667i
$216$	−1.99377	−	2.69673i	−0.135659	−	0.183489i
$217$	−19.8885	+	3.33946i	−1.35012	+	0.226697i
$218$	7.68748	−	3.04824i	0.520662	−	0.206453i
$219$	7.23589	+	15.4385i	0.488956	+	1.04324i
$220$	12.8649	−	3.63161i	0.867351	−	0.244843i
$221$	−0.0122110	−	0.00577087i	−0.000821398	−	0.000388191i
$222$	−8.34012	+	12.4066i	−0.559752	+	0.832673i
$223$	−7.17849	+	9.70947i	−0.480707	+	0.650194i	−0.975805	−	0.218643i	$-0.929837\pi$
$223$	−7.17849	+	9.70947i	−0.480707	+	0.650194i	0.495098	+	0.868837i	$0.335132\pi$
$224$	−9.67907	+	19.0414i	−0.646710	+	1.27226i
$225$	−9.08057	+	12.6168i	−0.605371	+	0.841119i
$226$	17.4035	−	17.6841i	1.15766	−	1.17633i
$227$	−4.49163	−	7.59160i	−0.298120	−	0.503872i	0.673884	−	0.738837i	$-0.264625\pi$
$227$	−4.49163	−	7.59160i	−0.298120	−	0.503872i	−0.972004	+	0.234965i	$0.924502\pi$
$228$	−5.03077	+	20.5630i	−0.333171	+	1.36182i
$229$	−0.558658	+	2.56631i	−0.0369172	+	0.169587i	−0.991888	−	0.127112i	$-0.959429\pi$
$229$	−0.558658	+	2.56631i	−0.0369172	+	0.169587i	0.954971	+	0.296698i	$0.0958856\pi$
$230$	0.892992	−	0.862107i	0.0588821	−	0.0568456i
$231$	30.0893	−	19.2631i	1.97973	−	1.26742i
$232$	0.00203079	−	0.634782i	0.000133328	−	0.0416755i
$233$	−13.1416	+	8.06189i	−0.860938	+	0.528152i	−0.881796	−	0.471631i	$-0.843666\pi$
$233$	−13.1416	+	8.06189i	−0.860938	+	0.528152i	0.0208583	+	0.999782i	$0.493360\pi$
$234$	0.0252313	+	0.0185297i	0.00164942	+	0.00121132i
$235$	−4.63177	−	1.40402i	−0.302144	−	0.0915883i
$236$	7.87068	+	6.94520i	0.512337	+	0.452094i
$237$	−38.7980	−	14.8125i	−2.52020	−	0.962177i
$238$	−20.4726	−	7.07451i	−1.32704	−	0.458573i
$239$	−6.63585	−	8.18210i	−0.429238	−	0.529256i	0.515585	−	0.856838i	$-0.327575\pi$
$239$	−6.63585	−	8.18210i	−0.429238	−	0.529256i	−0.944823	+	0.327582i	$0.893766\pi$
$240$	−4.44878	−	4.75818i	−0.287168	−	0.307139i
$241$	−6.06095	−	0.0387806i	−0.390420	−	0.00249808i	−0.188935	−	0.981990i	$-0.560503\pi$
$241$	−6.06095	−	0.0387806i	−0.390420	−	0.00249808i	−0.201485	+	0.979492i	$0.564577\pi$
$242$	−12.4698	+	25.7431i	−0.801588	+	1.65483i
$243$	−17.8055	+	11.7230i	−1.14222	+	0.752029i
$244$	−0.124076	−	0.552921i	−0.00794312	−	0.0353972i
$245$	0.559781	−	0.0756712i	0.0357631	−	0.00483446i
$246$	−20.6406	+	15.5688i	−1.31600	+	0.992630i
$247$	−0.000685503	−	0.0112637i	−4.36175e−5	−	0.000716693i
$248$	9.05417	+	3.59016i	0.574941	+	0.227976i
$249$	39.2899	+	8.42142i	2.48990	+	0.533686i
$250$	9.67678	−	17.3539i	0.612013	−	1.09756i
$251$	−7.20678	+	24.0516i	−0.454888	+	1.51812i	0.356884	+	0.934149i	$0.383839\pi$
$251$	−7.20678	+	24.0516i	−0.454888	+	1.51812i	−0.811772	+	0.583974i	$0.801497\pi$
$252$	24.6311	+	14.2558i	1.55161	+	0.898031i
$253$	0.114325	+	2.74731i	0.00718753	+	0.172722i
$254$	−31.8417	+	2.24479i	−1.99793	+	0.140851i
$255$	6.31587	−	7.78755i	0.395515	−	0.487676i
$256$	−1.83698	+	1.14316i	−0.114811	+	0.0714472i
$257$	6.10195	−	4.24521i	0.380629	−	0.264809i	−0.365224	−	0.930920i	$-0.619008\pi$
$257$	6.10195	−	4.24521i	0.380629	−	0.264809i	0.745853	+	0.666111i	$0.232042\pi$
$258$	−68.1992	−	14.1621i	−4.24590	−	0.881692i
$259$	1.31375	−	7.12438i	0.0816323	−	0.442687i
$260$	−0.00866768	−	0.00494285i	−0.000537547	−	0.000306543i
$261$	1.89086	+	0.109006i	0.117041	+	0.00674731i
$262$	−14.3709	+	14.0526i	−0.887838	+	0.868174i
$263$	3.62787	+	14.8287i	0.223704	+	0.914379i	0.968884	+	0.247516i	$0.0796142\pi$
$263$	3.62787	+	14.8287i	0.223704	+	0.914379i	−0.745180	+	0.666864i	$0.767636\pi$
$264$	−17.2495	+	0.441570i	−1.06163	+	0.0271768i
$265$	−1.30333	−	8.24600i	−0.0800631	−	0.506548i
$266$	−3.05392	−	17.8383i	−0.187248	−	1.09374i
$267$	5.20205	+	10.0738i	0.318360	+	0.616505i
$268$	1.69038	−	0.108304i	0.103256	−	0.00661574i
$269$	−16.2590	−	18.3072i	−0.991327	−	1.11621i	−0.993225	−	0.116209i	$-0.962926\pi$
$269$	−16.2590	−	18.3072i	−0.991327	−	1.11621i	0.00189758	−	0.999998i	$-0.499396\pi$
$270$	−4.31280	+	3.61364i	−0.262468	+	0.219919i
$271$	−13.8237	+	0.265379i	−0.839727	+	0.0161206i	−0.437283	−	0.899324i	$-0.644059\pi$
$271$	−13.8237	+	0.265379i	−0.839727	+	0.0161206i	−0.402444	+	0.915445i	$0.631839\pi$
$272$	−5.59731	−	6.72384i	−0.339387	−	0.407692i
$273$	−0.0260019	−	0.00592227i	−0.00157371	−	0.000358432i
$274$	37.4969	−	7.28727i	2.26527	−	0.440240i
$275$	6.38276	+	18.2811i	0.384895	+	1.10239i
$276$	−3.34470	+	1.90736i	−0.201327	+	0.114809i
$277$	24.9413	−	12.3783i	1.49858	−	0.743740i	0.505679	−	0.862722i	$-0.331242\pi$
$277$	24.9413	−	12.3783i	1.49858	−	0.743740i	0.992896	+	0.118982i	$0.0379629\pi$
$278$	−29.9837	−	31.2573i	−1.79830	−	1.87469i
$279$	−12.1646	+	26.3926i	−0.728275	+	1.58008i
$280$	−3.46258	−	1.50287i	−0.206929	−	0.0898134i
$281$	4.39975	+	9.70873i	0.262467	+	0.579174i	0.994809	−	0.101763i	$-0.0324483\pi$
$281$	4.39975	+	9.70873i	0.262467	+	0.579174i	−0.732342	+	0.680937i	$0.761573\pi$
$282$	22.6641	+	13.7047i	1.34963	+	0.816105i
$283$	8.53162	+	6.78463i	0.507152	+	0.403304i	0.842422	−	0.538818i	$-0.181129\pi$
$283$	8.53162	+	6.78463i	0.507152	+	0.403304i	−0.335270	+	0.942122i	$0.608828\pi$
$284$	24.8173	−	0.953209i	1.47264	−	0.0565626i
$285$	8.24354	+	1.49287i	0.488305	+	0.0884299i
$286$	0.0369366	−	0.0124999i	0.00218411	−	0.000739132i
$287$	6.17168	−	10.9034i	0.364303	−	0.643609i
$288$	14.8184	+	26.9790i	0.873180	+	1.58975i
$289$	−2.37993	+	2.61164i	−0.139996	+	0.153626i
$290$	−1.06322	+	0.0612937i	−0.0624347	+	0.00359929i
$291$	4.60178	+	2.28386i	0.269761	+	0.133882i
$292$	5.06289	+	16.1424i	0.296283	+	0.944665i
$293$	0.152060	−	0.0397899i	0.00888343	−	0.00232455i	−0.248705	−	0.968579i	$-0.580005\pi$
$293$	0.152060	−	0.0397899i	0.00888343	−	0.00232455i	0.257588	+	0.966255i	$0.417072\pi$
$294$	−3.07069	−	0.355224i	−0.179086	−	0.0207171i
$295$	2.55421	−	3.27596i	0.148712	−	0.190734i
$296$	−2.32340	+	2.61608i	−0.135045	+	0.152057i
$297$	0.358837	−	12.4594i	0.0208218	−	0.722966i
$298$	14.9996	+	1.05745i	0.868904	+	0.0612563i
$299$	0.00140174	−	0.00149922i	8.10646e−5	−	8.67022e-5i
$300$	−18.6441	+	19.6867i	−1.07642	+	1.13661i
$301$	33.0497	−	6.86302i	1.90496	−	0.395578i
$302$	−0.248966	−	11.1156i	−0.0143264	−	0.639629i
$303$	−12.2273	−	26.5287i	−0.702442	−	1.52403i
$304$	2.67263	−	6.80366i	0.153286	−	0.390216i
$305$	−0.215426	+	0.0623033i	−0.0123353	+	0.00356748i
$306$	−25.0391	+	18.6363i	−1.43139	+	1.06537i
$307$	−13.5334	+	13.4041i	−0.772391	+	0.765014i	−0.976865	−	0.213858i	$-0.931397\pi$
$307$	−13.5334	+	13.4041i	−0.772391	+	0.765014i	0.204473	+	0.978872i	$0.434452\pi$
$308$	32.1472	−	14.9418i	1.83176	−	0.851389i
$309$	−25.5474	−	31.0915i	−1.45334	−	1.76873i
$310$	5.08939	−	15.5282i	0.289058	−	0.881942i
$311$	13.0865	−	8.73652i	0.742065	−	0.495403i	−0.125891	−	0.992044i	$-0.540179\pi$
$311$	13.0865	−	8.73652i	0.742065	−	0.495403i	0.867956	+	0.496641i	$0.165434\pi$
$312$	0.00926618	+	0.00894570i	0.000524594	+	0.000506451i
$313$	19.2416	+	3.86740i	1.08760	+	0.218599i	0.707760	−	0.706453i	$-0.249706\pi$
$313$	19.2416	+	3.86740i	1.08760	+	0.218599i	0.379840	+	0.925052i	$0.375979\pi$
$314$	−13.0452	+	5.86153i	−0.736185	+	0.330786i
$315$	5.03905	−	10.0722i	0.283918	−	0.567506i
$316$	−36.1810	−	19.7222i	−2.03534	−	1.10946i
$317$	−11.6614	+	5.88084i	−0.654972	+	0.330301i	−0.746387	−	0.665512i	$-0.768213\pi$
$317$	−11.6614	+	5.88084i	−0.654972	+	0.330301i	0.0914155	+	0.995813i	$0.470861\pi$
$318$	−4.23239	+	45.4884i	−0.237341	+	2.55087i
$319$	1.46253	−	1.85124i	0.0818858	−	0.103650i
$320$	−7.16107	−	10.0853i	−0.400316	−	0.563783i
$321$	9.35542	−	10.6707i	0.522169	−	0.595579i
$322$	1.97376	−	2.63424i	0.109994	−	0.146801i
$323$	10.9379	+	2.63891i	0.608600	+	0.146833i
$324$	−12.2836	+	5.90162i	−0.682420	+	0.327868i
$325$	0.00638390	−	0.0129670i	0.000354115	−	0.000719282i
$326$	−2.40113	+	32.5735i	−0.132986	+	1.80408i
$327$	1.90483	+	9.97160i	0.105337	+	0.551431i
$328$	−5.27553	+	2.96387i	−0.291292	+	0.163652i
$329$	−12.7193	−	1.71940i	−0.701239	−	0.0947935i
$330$	2.49747	+	28.8413i	0.137481	+	1.58766i
$331$	25.6312	+	10.7371i	1.40882	+	0.590162i	0.953833	−	0.300338i	$-0.0970995\pi$
$331$	25.6312	+	10.7371i	1.40882	+	0.590162i	0.454983	+	0.890500i	$0.349645\pi$
$332$	37.5142	+	13.5032i	2.05886	+	0.741086i
$333$	−7.41720	−	7.34635i	−0.406460	−	0.402578i
$334$	−28.3841	−	4.02206i	−1.55311	−	0.220077i
$335$	−0.0834181	−	0.665113i	−0.00455762	−	0.0363390i
$336$	−13.6570	−	10.5781i	−0.745051	−	0.577082i
$337$	−5.61566	+	8.95998i	−0.305904	+	0.488081i	−0.964380	−	0.264521i	$-0.914786\pi$
$337$	−5.61566	+	8.95998i	−0.305904	+	0.488081i	0.658475	+	0.752602i	$0.271202\pi$
$338$	24.9424	+	12.5784i	1.35669	+	0.684174i
$339$	17.3147	+	25.0582i	0.940403	+	1.36098i
$340$	7.24550	−	6.81795i	0.392942	−	0.369755i
$341$	18.2335	+	31.2725i	0.987399	+	1.69350i
$342$	−23.7196	−	10.8407i	−1.28261	−	0.586199i
$343$	−16.9677	+	5.14340i	−0.916171	+	0.277718i
$344$	−15.3741	−	5.42305i	−0.828916	−	0.292391i
$345$	0.833831	+	1.27533i	0.0448919	+	0.0686617i
$346$	5.30344	−	38.3089i	0.285115	−	2.05950i
$347$	1.82088	+	0.804200i	0.0977497	+	0.0431717i	0.452305	−	0.891863i	$-0.350602\pi$
$347$	1.82088	+	0.804200i	0.0977497	+	0.0431717i	−0.354555	+	0.935035i	$0.615368\pi$
$348$	3.24294	+	0.630243i	0.173840	+	0.0337846i
$349$	−1.04397	−	7.20150i	−0.0558825	−	0.385487i	−0.998646	−	0.0520247i	$-0.983433\pi$
$349$	−1.04397	−	7.20150i	−0.0558825	−	0.385487i	0.942763	−	0.333463i	$-0.108217\pi$
$350$	7.92022	−	21.7847i	0.423354	−	1.16444i
$351$	−0.00681637	+	0.00633240i	−0.000363831	+	0.000337998i
$352$	38.1153	+	4.16231i	2.03155	+	0.221852i
$353$	−6.25175	−	6.27179i	−0.332747	−	0.333814i	0.521915	−	0.852997i	$-0.325218\pi$
$353$	−6.25175	−	6.27179i	−0.332747	−	0.333814i	−0.854663	+	0.519184i	$0.826236\pi$
$354$	−17.9717	+	13.9200i	−0.955186	+	0.739842i
$355$	−0.973137	−	9.78018i	−0.0516487	−	0.519078i
$356$	3.77612	+	10.5970i	0.200134	+	0.561638i
$357$	13.2460	−	23.0561i	0.701050	−	1.22026i
$358$	−1.11474	+	1.14731i	−0.0589159	+	0.0606372i
$359$	−8.05747	+	4.19355i	−0.425257	+	0.221327i	−0.660839	−	0.750528i	$-0.729799\pi$
$359$	−8.05747	+	4.19355i	−0.425257	+	0.221327i	0.235582	+	0.971855i	$0.424300\pi$
$360$	−4.59970	+	2.90340i	−0.242426	+	0.153022i
$361$	−2.51897	−	9.26250i	−0.132577	−	0.487500i
$362$	22.2785	−	3.15688i	1.17093	−	0.165922i
$363$	−28.1685	−	20.9655i	−1.47847	−	1.10040i
$364$	−0.0247804	−	0.00927956i	−0.00129884	−	0.000486381i
$365$	6.25471	−	2.38796i	0.327386	−	0.124991i
$366$	1.22657	−	0.0392535i	0.0641137	−	0.00205181i
$367$	0.474417	+	4.21923i	0.0247643	+	0.220242i	1.00000		0.000928212i	$-0.000295459\pi$
$367$	0.474417	+	4.21923i	0.0247643	+	0.220242i	−0.975235	+	0.221170i	$0.929012\pi$
$368$	1.23273	−	0.497954i	0.0642606	−	0.0259577i
$369$	−7.97453	−	16.1980i	−0.415138	−	0.843232i
$370$	4.61773	+	3.62419i	0.240065	+	0.188412i
$371$	−6.89525	−	21.0380i	−0.357983	−	1.09224i
$372$	−27.1938	+	42.7780i	−1.40993	+	2.21793i
$373$	1.45190	−	34.8903i	0.0751767	−	1.80655i	−0.389451	−	0.921047i	$-0.627335\pi$
$373$	1.45190	−	34.8903i	0.0751767	−	1.80655i	0.464628	−	0.885506i	$-0.346188\pi$
$374$	1.11932	+	38.8647i	0.0578789	+	2.00964i
$375$	18.6963	+	15.6654i	0.965472	+	0.808958i
$376$	4.82702	+	3.88928i	0.248934	+	0.200574i
$377$	−0.00175061		0.000191172i	−9.01609e−5		9.84585e-6i
$378$	−9.76481	+	11.2824i	−0.502247	+	0.580306i
$379$	25.3546	+	7.86319i	1.30238	+	0.403905i	0.867883	−	0.496768i	$-0.165480\pi$
$379$	25.3546	+	7.86319i	1.30238	+	0.403905i	0.434497	+	0.900673i	$0.356926\pi$
$380$	7.90740	+	2.56368i	0.405641	+	0.131514i
$381$	4.62757	−	38.9115i	0.237077	−	1.99349i
$382$	−10.1390	+	9.66379i	−0.518758	+	0.494442i
$383$	5.06058	+	9.49964i	0.258584	+	0.485409i	0.977845	−	0.209331i	$-0.0671286\pi$
$383$	5.06058	+	9.49964i	0.258584	+	0.485409i	−0.719261	+	0.694740i	$0.755520\pi$
$384$	9.58946	+	24.8782i	0.489360	+	1.26956i
$385$	−6.67498	−	12.3392i	−0.340188	−	0.628866i
$386$	−23.4999	+	12.4223i	−1.19611	+	0.632280i
$387$	18.6503	−	44.9241i	0.948047	−	2.28362i
$388$	4.22134	+	2.85738i	0.214306	+	0.145062i
$389$	11.8385	+	4.34704i	0.600238	+	0.220404i	0.626719	−	0.779245i	$-0.284397\pi$
$389$	11.8385	+	4.34704i	0.600238	+	0.220404i	−0.0264806	+	0.999649i	$0.508430\pi$
$390$	0.0140363	−	0.0164290i	0.000710754	−	0.000831916i
$391$	1.01945	+	1.77447i	0.0515560	+	0.0897390i
$392$	−0.701078	−	0.178668i	−0.0354098	−	0.00902410i
$393$	−13.6344	−	20.5651i	−0.687763	−	1.03737i
$394$	0.240704	−	3.95508i	0.0121265	−	0.199254i
$395$	−6.92067	+	14.7660i	−0.348216	+	0.742957i
$396$	8.29790	−	50.4060i	0.416985	−	2.53299i
$397$	0.790959	−	11.7555i	0.0396971	−	0.589993i	−0.933289	−	0.359127i	$-0.883074\pi$
$397$	0.790959	−	11.7555i	0.0396971	−	0.589993i	0.972986	−	0.230866i	$-0.0741557\pi$
$398$	−4.95652	−	6.19203i	−0.248448	−	0.310378i
$399$	22.2127	+	0.426427i	1.11203	+	0.0213480i
$400$	7.29037	−	5.87408i	0.364519	−	0.293704i
$401$	−21.4601	+	21.5288i	−1.07166	+	1.07510i	−0.0747032	+	0.997206i	$0.523801\pi$
$401$	−21.4601	+	21.5288i	−1.07166	+	1.07510i	−0.996962	+	0.0778931i	$0.975181\pi$
$402$	−0.456490	+	3.63971i	−0.0227677	+	0.181532i
$403$	0.00709081	−	0.0260736i	0.000353219	−	0.00129882i
$404$	−8.49683	−	27.7108i	−0.422733	−	1.37867i
$405$	2.62649	+	4.71025i	0.130512	+	0.234054i
$406$	−2.75770	+	0.609568i	−0.136862	+	0.0302523i
$407$	−12.7958	+	2.31727i	−0.634266	+	0.114863i
$408$	−11.2363	+	6.21846i	−0.556279	+	0.307859i
$409$	7.18375	+	7.98521i	0.355214	+	0.394843i	0.894345	−	0.447379i	$-0.147642\pi$
$409$	7.18375	+	7.98521i	0.355214	+	0.394843i	−0.539131	+	0.842222i	$0.681247\pi$
$410$	5.50101	+	8.53243i	0.271675	+	0.421387i
$411$	0.150016	+	46.8919i	0.00739974	+	2.31301i
$412$	−20.9879	−	33.9679i	−1.03400	−	1.67348i
$413$	5.30335	−	9.65554i	0.260961	−	0.475118i
$414$	−1.53488	−	4.48817i	−0.0754352	−	0.220582i
$415$	4.43207	−	15.1431i	0.217562	−	0.743345i
$416$	−0.0177415	−	0.0224569i	−0.000869849	−	0.00110104i
$417$	44.5961	−	28.9543i	2.18388	−	1.41790i
$418$	−28.0116	+	16.4525i	−1.37009	+	0.804718i
$419$	−5.96100	+	5.05993i	−0.291214	+	0.247194i	−0.780828	−	0.624746i	$-0.785203\pi$
$419$	−5.96100	+	5.05993i	−0.291214	+	0.247194i	0.489614	+	0.871939i	$0.337138\pi$
$420$	11.0636	−	16.2327i	0.539851	−	0.792075i
$421$	6.31974	−	0.649245i	0.308005	−	0.0316423i	0.0530398	−	0.998592i	$-0.483109\pi$
$421$	6.31974	−	0.649245i	0.308005	−	0.0316423i	0.254966	+	0.966950i	$0.417936\pi$
$422$	36.9827	+	5.96669i	1.80029	+	0.290454i
$423$	−12.3701	+	13.7502i	−0.601456	+	0.668558i
$424$	−2.40789	+	10.4179i	−0.116937	+	0.505938i
$425$	10.4952	+	9.87593i	0.509094	+	0.479053i
$426$	−8.05668	+	53.1777i	−0.390347	+	2.57647i
$427$	−0.537684	+	0.254108i	−0.0260204	+	0.0122972i
$428$	10.6175	−	9.24889i	0.513216	−	0.447062i
$429$	0.00656435	+	0.0474169i	0.000316930	+	0.00228931i
$430$	−7.51466	+	26.2985i	−0.362389	+	1.26822i
$431$	−2.05918	−	10.4175i	−0.0991871	−	0.501793i	−0.997986	−	0.0634318i	$-0.979795\pi$
$431$	−2.05918	−	10.4175i	−0.0991871	−	0.501793i	0.898799	−	0.438361i	$-0.144441\pi$
$432$	−5.73297	+	1.85870i	−0.275828	+	0.0894267i
$433$	22.7531	−	0.291181i	1.09345	−	0.0139933i	0.536009	−	0.844212i	$-0.319931\pi$
$433$	22.7531	−	0.291181i	1.09345	−	0.0139933i	0.557437	+	0.830219i	$0.311785\pi$
$434$	6.76537	−	42.8035i	0.324748	−	2.05463i
$435$	0.170992	−	1.29614i	0.00819844	−	0.0621453i
$436$	0.547567	+	10.0582i	0.0262237	+	0.481702i
$437$	−0.889441	+	1.46034i	−0.0425477	+	0.0698573i
$438$	−36.3948	+	4.21023i	−1.73901	+	0.201173i
$439$	−26.6833	+	10.3834i	−1.27353	+	0.495573i	−0.901552	−	0.432671i	$-0.857571\pi$
$439$	−26.6833	+	10.3834i	−1.27353	+	0.495573i	−0.371973	+	0.928243i	$0.621319\pi$
$440$	−0.325019	+	6.76777i	−0.0154947	+	0.322641i
$441$	0.646010	−	2.05973i	0.0307624	−	0.0980822i
$442$	0.0200903	−	0.0209437i	0.000955599	−	0.000996192i
$443$	−7.69544	−	19.5901i	−0.365622	−	0.930755i	−0.988877	−	0.148736i	$-0.952479\pi$
$443$	−7.69544	−	19.5901i	−0.365622	−	0.930755i	0.623255	−	0.782018i	$-0.285810\pi$
$444$	−11.1043	−	14.4315i	−0.526986	−	0.684889i
$445$	4.09512	−	1.74636i	0.194128	−	0.0827853i
$446$	−14.8862	−	21.2517i	−0.704884	−	1.00630i
$447$	−4.73002	+	17.8428i	−0.223722	+	0.843935i
$448$	−23.0081	−	23.3791i	−1.08703	−	1.10456i
$449$	−26.7215	+	4.13592i	−1.26106	+	0.195186i	−0.748310	−	0.663349i	$-0.769134\pi$
$449$	−26.7215	+	4.13592i	−1.26106	+	0.195186i	−0.512754	+	0.858535i	$0.671375\pi$
$450$	−19.5124	−	27.1111i	−0.919825	−	1.27803i
$451$	−22.2250	−	3.43996i	−1.04653	−	0.161981i
$452$	13.6946	+	26.9411i	0.644142	+	1.26720i
$453$	13.4604	+	2.26012i	0.632423	+	0.106190i
$454$	18.5334	−	3.97245i	0.869814	−	0.186436i
$455$	−0.00306979	+	0.0100116i	−0.000143914	+	0.000469349i
$456$	−9.07361	−	5.72739i	−0.424911	−	0.268210i
$457$	−26.1759	−	2.18231i	−1.22446	−	0.102084i	−0.546673	−	0.837346i	$-0.684106\pi$
$457$	−26.1759	−	2.18231i	−1.22446	−	0.102084i	−0.677783	+	0.735262i	$0.737059\pi$
$458$	−4.84798	−	2.88932i	−0.226531	−	0.135009i
$459$	−4.04414	−	8.34888i	−0.188764	−	0.389692i
$460$	0.650382	+	1.36486i	0.0303242	+	0.0636371i
$461$	10.5921	−	26.4652i	0.493323	−	1.23261i	−0.447675	−	0.894196i	$-0.647748\pi$
$461$	10.5921	−	26.4652i	0.493323	−	1.23261i	0.940998	−	0.338411i	$-0.109890\pi$
$462$	18.7209	+	74.4536i	0.870973	+	3.46389i
$463$	3.72542	−	3.33001i	0.173135	−	0.154759i	−0.575357	−	0.817903i	$-0.695137\pi$
$463$	3.72542	−	3.33001i	0.173135	−	0.154759i	0.748492	+	0.663144i	$0.230778\pi$
$464$	−1.08053	−	0.365667i	−0.0501624	−	0.0169757i
$465$	17.5515	+	9.71344i	0.813929	+	0.450450i
$466$	−7.46047	−	32.2782i	−0.345599	−	1.49526i
$467$	8.79683	−	15.0876i	0.407069	−	0.698169i	−0.586679	−	0.809820i	$-0.699565\pi$
$467$	8.79683	−	15.0876i	0.407069	−	0.698169i	0.993748	+	0.111651i	$0.0356137\pi$
$468$	−0.0311609	+	0.0219763i	−0.00144041	+	0.00101586i
$469$	−0.499332	−	1.70607i	−0.0230570	−	0.0787791i
$470$	6.02111	−	8.47979i	0.277733	−	0.391144i
$471$	−4.06298	−	17.0799i	−0.187212	−	0.787002i
$472$	−4.60480	+	2.66514i	−0.211953	+	0.122673i
$473$	−32.5052	−	51.1332i	−1.49459	−	2.35111i
$474$	56.6540	−	68.9488i	2.60221	−	3.16692i
$475$	−3.01088	+	11.6584i	−0.138149	+	0.534926i
$476$	16.0893	−	20.9103i	0.737454	−	0.958420i
$477$	−30.6472	−	8.86346i	−1.40324	−	0.405830i
$478$	21.1996	−	7.93865i	0.969646	−	0.363106i
$479$	−2.09438	+	1.84811i	−0.0956947	+	0.0844425i	−0.708147	−	0.706065i	$-0.750468\pi$
$479$	−2.09438	+	1.84811i	−0.0956947	+	0.0844425i	0.612452	+	0.790508i	$0.290183\pi$
$480$	19.3244	−	8.83195i	0.882034	−	0.403122i
$481$	0.00793228	+	0.00559426i	0.000361681	+	0.000255076i
$482$	4.21440	−	12.3234i	0.191961	−	0.561315i
$483$	2.72171	+	2.98671i	0.123842	+	0.135900i
$484$	−24.9112	−	24.3595i	−1.13233	−	1.10725i
$485$	1.02721	−	1.73616i	0.0466433	−	0.0788350i
$486$	−11.7382	−	44.2793i	−0.532454	−	2.00855i
$487$	1.00403	−	1.19052i	0.0454968	−	0.0539477i	−0.741218	−	0.671264i	$-0.765752\pi$
$487$	1.00403	−	1.19052i	0.0454968	−	0.0539477i	0.786715	+	0.617316i	$0.211780\pi$
$488$	0.285721	+	0.0293529i	0.0129340	+	0.00132874i
$489$	−38.7237	−	10.3981i	−1.75115	−	0.470220i
$490$	−0.227750	+	1.19225i	−0.0102887	+	0.0538602i
$491$	−6.46970	−	19.3211i	−0.291974	−	0.871947i	−0.988071	−	0.154000i	$-0.950784\pi$
$491$	−6.46970	−	19.3211i	−0.291974	−	0.871947i	0.696097	−	0.717947i	$-0.254918\pi$
$492$	−9.99936	−	29.8620i	−0.450806	−	1.34628i
$493$	0.329462	−	1.72470i	0.0148382	−	0.0776767i
$494$	0.0234188	+	0.00628843i	0.00105366	+	0.000282930i
$495$	−20.1103	−	2.06599i	−0.903892	−	0.0928594i
$496$	11.2841	−	13.3801i	0.506670	−	0.600784i
$497$	−6.67880	−	25.1941i	−0.299585	−	1.13011i
$498$	−43.9671	+	74.3117i	−1.97021	+	3.32999i
$499$	−20.4153	−	19.9632i	−0.913916	−	0.893675i	0.0807597	−	0.996734i	$-0.474265\pi$
$499$	−20.4153	−	19.9632i	−0.913916	−	0.893675i	−0.994675	+	0.103059i	$0.967137\pi$
$500$	16.3017	+	17.8889i	0.729033	+	0.800014i
$501$	11.3877	−	33.2989i	0.508763	−	1.48768i
$502$	−44.0906	−	31.0950i	−1.96786	−	1.38784i
$503$	38.3657	−	17.5345i	1.71064	−	0.781826i	0.713983	−	0.700163i	$-0.246889\pi$
$503$	38.3657	−	17.5345i	1.71064	−	0.781826i	0.996660	−	0.0816626i	$-0.0260230\pi$
$504$	−10.8159	+	9.54416i	−0.481781	+	0.425130i
$505$	−10.7418	+	4.02250i	−0.478003	+	0.178999i
$506$	−5.67596	−	1.64154i	−0.252327	−	0.0729752i
$507$	−20.9120	+	27.1780i	−0.928735	+	1.20702i
$508$	9.72244	−	37.6463i	0.431364	−	1.67029i
$509$	−7.34064	+	8.93367i	−0.325368	+	0.395978i	−0.909516	−	0.415670i	$-0.863547\pi$
$509$	−7.34064	+	8.93367i	−0.325368	+	0.395978i	0.584147	+	0.811648i	$0.301429\pi$
$510$	11.5587	+	18.1827i	0.511828	+	0.805144i
$511$	15.3666	−	8.89376i	0.679777	−	0.393437i
$512$	−5.75419	−	24.1894i	−0.254302	−	1.06903i
$513$	4.48745	−	6.31987i	0.198126	−	0.279029i
$514$	4.48674	+	15.3299i	0.197902	+	0.676173i
$515$	−12.9131	+	9.10700i	−0.569020	+	0.401302i
$516$	42.7347	−	73.2948i	1.88129	−	3.22662i
$517$	5.18824	+	22.4473i	0.228179	+	0.987229i
$518$	13.6203	+	7.53786i	0.598444	+	0.331195i
$519$	44.9709	+	15.2188i	1.97400	+	0.668030i
$520$	0.00377068	−	0.00337046i	0.000165355	−	0.000147805i
$521$	8.56973	+	34.0822i	0.375447	+	1.49317i	0.806714	+	0.590942i	$0.201244\pi$
$521$	8.56973	+	34.0822i	0.375447	+	1.49317i	−0.431267	+	0.902224i	$0.641933\pi$
$522$	−1.51224	+	3.77846i	−0.0661891	+	0.165379i
$523$	−5.07440	−	10.6489i	−0.221888	−	0.465645i	0.761262	−	0.648444i	$-0.224580\pi$
$523$	−5.07440	−	10.6489i	−0.221888	−	0.465645i	−0.983150	+	0.182799i	$0.941484\pi$
$524$	−10.6731	−	22.0339i	−0.466255	−	0.962555i
$525$	24.4435	+	14.5679i	1.06680	+	0.635797i
$526$	−32.6905	−	2.72544i	−1.42537	−	0.118835i
$527$	22.7829	+	14.3809i	0.992437	+	0.626440i
$528$	−9.09012	+	29.6457i	−0.395597	+	1.29016i
$529$	22.1851	−	4.75517i	0.964570	−	0.206746i
$530$	17.6914	+	2.97055i	0.768465	+	0.129032i
$531$	−7.19332	−	14.1512i	−0.312163	−	0.614112i
$532$	21.7849	+	3.37185i	0.944497	+	0.146188i
$533$	0.00980616	+	0.0136249i	0.000424752	+	0.000590162i
$534$	−24.0758	+	3.72643i	−1.04186	+	0.161258i
$535$	−3.90865	−	3.97167i	−0.168986	−	0.171710i
$536$	−0.219997	+	0.829882i	−0.00950241	+	0.0358455i
$537$	−1.12665	−	1.60841i	−0.0486184	−	0.0694080i
$538$	48.3963	−	20.6385i	2.08651	−	0.889790i
$539$	−1.63976	−	2.13108i	−0.0706293	−	0.0917923i
$540$	−2.50583	−	6.37904i	−0.107834	−	0.274510i
$541$	−7.42333	+	7.73866i	−0.319154	+	0.332711i	−0.861798	−	0.507252i	$-0.830661\pi$
$541$	−7.42333	+	7.73866i	−0.319154	+	0.332711i	0.542644	+	0.839963i	$0.317423\pi$
$542$	8.89113	−	28.3483i	0.381907	−	1.21766i
$543$	−1.32501	+	27.5903i	−0.0568617	+	1.18401i
$544$	26.5936	−	10.3485i	1.14019	−	0.443688i
$545$	3.95993	−	0.458094i	0.169625	−	0.0196226i
$546$	0.0298084	−	0.0489411i	0.00127568	−	0.00209448i
$547$	−0.115815	−	2.12740i	−0.00495189	−	0.0909609i	0.995009	−	0.0997833i	$-0.0318149\pi$
$547$	−0.115815	−	2.12740i	−0.00495189	−	0.0909609i	−0.999961	+	0.00882234i	$0.997192\pi$
$548$	−6.08544	+	46.1285i	−0.259957	+	1.97051i
$549$	−0.133792	+	0.846480i	−0.00571009	+	0.0361269i
$550$	−41.6047	+	0.532432i	−1.77403	+	0.0227030i
$551$	1.39558	−	0.452463i	0.0594535	−	0.0192756i
$552$	−0.378439	−	1.91454i	−0.0161074	−	0.0814883i
$553$	−11.8817	+	41.5815i	−0.505262	+	1.76823i
$554$	8.20477	+	59.2663i	0.348587	+	2.51798i
$555$	−5.43364	+	4.73323i	−0.230645	+	0.200915i
$556$	47.6998	−	22.5428i	2.02292	−	0.956028i
$557$	−4.89369	+	32.3006i	−0.207352	+	1.36862i	0.609964	+	0.792429i	$0.291184\pi$
$557$	−4.89369	+	32.3006i	−0.207352	+	1.36862i	−0.817316	+	0.576189i	$0.804539\pi$
$558$	−45.4780	−	42.7943i	−1.92524	−	1.81163i
$559$	−0.0101847	+	0.0440647i	−0.000430766	+	0.00186374i
$560$	−4.53668	+	5.04282i	−0.191710	+	0.213098i
$561$	−47.1204	−	7.60228i	−1.98943	−	0.320969i
$562$	−22.7846	+	2.34072i	−0.961109	+	0.0987374i
$563$	2.46867	−	3.62206i	0.104042	−	0.152652i	−0.770771	−	0.637112i	$-0.780129\pi$
$563$	2.46867	−	3.62206i	0.104042	−	0.152652i	0.874813	+	0.484461i	$0.160984\pi$
$564$	−24.5950	+	20.8772i	−1.03564	+	0.879089i
$565$	10.3128	−	6.05718i	0.433862	−	0.254828i
$566$	−19.6455	+	12.7550i	−0.825764	+	0.536132i
$567$	8.86590	+	11.2223i	0.372333	+	0.471293i
$568$	−3.53598	+	12.0814i	−0.148367	+	0.506926i
$569$	−3.28936	−	9.61848i	−0.137897	−	0.403228i	0.855521	−	0.517767i	$-0.173237\pi$
$569$	−3.28936	−	9.61848i	−0.137897	−	0.403228i	−0.993419	+	0.114540i	$0.963461\pi$
$570$	−8.66644	+	15.7785i	−0.362997	+	0.660891i
$571$	12.7037	+	20.5604i	0.531635	+	0.860428i	0.999730	−	0.0232505i	$-0.00740153\pi$
$571$	12.7037	+	20.5604i	0.531635	+	0.860428i	−0.468095	+	0.883678i	$0.655059\pi$
$572$	0.000151953		0.0474973i	6.35347e−6		0.00198596i
$573$	−9.31711	−	14.4515i	−0.389228	−	0.603718i
$574$	18.0060	+	20.0149i	0.751557	+	0.835405i
$575$	−1.91615	+	1.06045i	−0.0799091	+	0.0442238i
$576$	−46.5117	+	8.42307i	−1.93799	+	0.350961i
$577$	−20.7429	+	4.58506i	−0.863540	+	0.190879i	−0.625354	−	0.780341i	$-0.715045\pi$
$577$	−20.7429	+	4.58506i	−0.863540	+	0.190879i	−0.238185	+	0.971220i	$0.576553\pi$
$578$	−3.69769	−	6.63129i	−0.153804	−	0.275825i
$579$	−9.56584	−	31.1972i	−0.397543	−	1.29651i
$580$	0.340421	−	1.25176i	0.0141352	−	0.0519766i
$581$	5.20712	−	41.5177i	0.216028	−	1.72244i
$582$	−7.79340	+	7.81837i	−0.323047	+	0.324082i
$583$	−30.9451	+	24.9335i	−1.28162	+	1.03264i
$584$	−8.57341	−	0.164587i	−0.354770	−	0.00681068i
$585$	0.00942996	+	0.0117806i	0.000389881	+	0.000487066i
$586$	−0.0226739	+	0.336987i	−0.000936649	+	0.0139208i
$587$	−0.585457	+	3.55638i	−0.0241644	+	0.146788i	−0.996068	−	0.0885914i	$-0.971763\pi$
$587$	−0.585457	+	3.55638i	−0.0241644	+	0.146788i	0.971904	+	0.235379i	$0.0756331\pi$
$588$	1.59793	−	3.40935i	0.0658974	−	0.140599i
$589$	−1.36746	+	22.4691i	−0.0563450	+	0.925823i
$590$	4.93239	+	7.43967i	0.203063	+	0.306286i
$591$	4.71355	+	1.20124i	0.193890	+	0.0494123i
$592$	3.13217	+	5.45189i	0.128731	+	0.224071i
$593$	−11.8296	+	13.8462i	−0.485785	+	0.568597i	−0.948040	−	0.318150i	$-0.896938\pi$
$593$	−11.8296	+	13.8462i	−0.485785	+	0.568597i	0.462256	+	0.886747i	$0.347040\pi$
$594$	25.1425	+	9.23218i	1.03161	+	0.378801i
$595$	−8.64654	−	5.85276i	−0.354474	−	0.239940i
$596$	−7.02270	+	16.9160i	−0.287661	+	0.692907i
$597$	8.60795	−	4.55027i	0.352300	−	0.186230i
$598$	0.00209843	+	0.00387911i	8.58111e−5	+	0.000158629i
$599$	1.79920	+	4.66772i	0.0735132	+	0.190718i	0.964954	−	0.262420i	$-0.0845205\pi$
$599$	1.79920	+	4.66772i	0.0735132	+	0.190718i	−0.891441	+	0.453138i	$0.850305\pi$
$600$	−6.46147	−	12.1294i	−0.263788	−	0.495179i
$601$	−25.8947	+	24.6810i	−1.05627	+	1.00676i	−0.0563018	+	0.998414i	$0.517931\pi$
$601$	−25.8947	+	24.6810i	−1.05627	+	1.00676i	−0.999965	+	0.00834379i	$0.997344\pi$
$602$	−8.56563	+	72.0252i	−0.349109	+	2.93553i
$603$	−2.43677	−	0.790030i	−0.0992328	−	0.0321725i
$604$	12.9351	+	4.01154i	0.526322	+	0.163227i
$605$	−9.02337	+	10.4258i	−0.366852	+	0.423868i
$606$	62.3979	−	6.81404i	2.53474	−	0.276801i
$607$	22.4488	+	18.0877i	0.911168	+	0.734156i	0.964406	−	0.264426i	$-0.0851823\pi$
$607$	22.4488	+	18.0877i	0.911168	+	0.734156i	−0.0532381	+	0.998582i	$0.516954\pi$
$608$	18.2755	+	15.3128i	0.741168	+	0.621016i
$609$	−0.0998115	−	3.46561i	−0.00404457	−	0.140434i
$610$	0.0200353	−	0.481465i	0.000811207	−	0.0194939i
$611$	0.00922575	−	0.0145128i	0.000373234	−	0.000587126i
$612$	−11.8413	−	36.1288i	−0.478655	−	1.46042i
$613$	31.4490	+	24.6825i	1.27021	+	0.996916i	0.999412	+	0.0342813i	$0.0109142\pi$
$613$	31.4490	+	24.6825i	1.27021	+	0.996916i	0.270802	+	0.962635i	$0.412711\pi$
$614$	−18.0786	−	36.7214i	−0.729592	−	1.48196i
$615$	−11.5554	+	4.66773i	−0.465959	+	0.188221i
$616$	2.00773	+	17.8557i	0.0808936	+	0.719428i
$617$	37.7351	−	1.20762i	1.51916	−	0.0486171i	0.738788	−	0.673937i	$-0.235398\pi$
$617$	37.7351	−	1.20762i	1.51916	−	0.0486171i	0.780368	+	0.625320i	$0.215032\pi$
$618$	80.7833	−	30.8419i	3.24958	−	1.24064i
$619$	−0.0544529	−	0.0203911i	−0.00218865	−	0.000819588i	0.349596	−	0.936901i	$-0.386319\pi$
$619$	−0.0544529	−	0.0203911i	−0.00218865	−	0.000819588i	−0.351784	+	0.936081i	$0.614425\pi$
$620$	15.9671	+	11.8841i	0.641255	+	0.477279i
$621$	1.39581	−	0.197788i	0.0560121	−	0.00793697i
$622$	8.87277	+	32.6260i	0.355766	+	1.30818i
$623$	9.98365	−	6.30182i	0.399987	−	0.252477i
$624$	0.0205311	−	0.0106855i	0.000821901	−	0.000427762i
$625$	−7.00871	+	7.21347i	−0.280348	+	0.288539i
$626$	−21.0088	+	36.5682i	−0.839680	+	1.46156i
$627$	−13.3862	−	37.5657i	−0.534592	−	1.50023i
$628$	−1.72482	−	17.3347i	−0.0688277	−	0.691729i
$629$	−7.65151	+	5.92650i	−0.305086	+	0.236305i
$630$	17.0851	+	17.1399i	0.680688	+	0.682869i
$631$	−37.7516	−	4.12259i	−1.50287	−	0.164118i	−0.680362	−	0.732876i	$-0.738177\pi$
$631$	−37.7516	−	4.12259i	−1.50287	−	0.164118i	−0.822504	+	0.568759i	$0.807424\pi$
$632$	15.3021	−	14.2157i	0.608686	−	0.565469i
$633$	−15.7130	+	43.2190i	−0.624537	+	1.71780i
$634$	−4.02628	−	27.7740i	−0.159904	−	1.10304i
$635$	−15.1044	−	2.93544i	−0.599400	−	0.116489i
$636$	−50.9036	−	22.4819i	−2.01846	−	0.891464i
$637$	−0.000275235		0.00198813i	−1.09052e−5		7.87725e-5i
$638$	2.77424	+	4.24316i	0.109833	+	0.167988i
$639$	−35.4204	−	12.4942i	−1.40121	−	0.494262i
$640$	10.0193	−	3.03713i	0.396048	−	0.120053i
$641$	−17.1469	−	7.83677i	−0.677263	−	0.309534i	0.0471618	−	0.998887i	$-0.484982\pi$
$641$	−17.1469	−	7.83677i	−0.677263	−	0.309534i	−0.724425	+	0.689353i	$0.757895\pi$
$642$	15.3595	+	26.3433i	0.606191	+	1.03969i
$643$	−24.2641	+	22.8323i	−0.956883	+	0.900418i	−0.995102	−	0.0988514i	$-0.968483\pi$
$643$	−24.2641	+	22.8323i	−0.956883	+	0.900418i	0.0382194	+	0.999269i	$0.487831\pi$
$644$	2.27925	+	3.29859i	0.0898150	+	0.129983i
$645$	−29.9795	−	15.1186i	−1.18044	−	0.595294i
$646$	−12.8400	+	20.4866i	−0.505182	+	0.806035i
$647$	4.66064	+	3.60991i	0.183229	+	0.141920i	0.699840	−	0.714300i	$-0.253255\pi$
$647$	4.66064	+	3.60991i	0.183229	+	0.141920i	−0.516611	+	0.856220i	$0.672807\pi$
$648$	−0.859586	−	6.85369i	−0.0337677	−	0.269238i
$649$	−19.5785	−	2.77429i	−0.768524	−	0.108901i
$650$	0.0220661	+	0.0218553i	0.000865503	+	0.000857236i
$651$	50.0537	+	18.0168i	1.96176	+	0.706135i
$652$	−36.6947	−	15.3717i	−1.43708	−	0.602001i
$653$	0.608262	+	7.02436i	0.0238031	+	0.274884i	0.998647	+	0.0519967i	$0.0165585\pi$
$653$	0.608262	+	7.02436i	0.0238031	+	0.274884i	−0.974844	+	0.222888i	$0.928452\pi$
$654$	−21.6179	−	2.92231i	−0.845327	−	0.114271i
$655$	−8.44702	+	4.74566i	−0.330052	+	0.185428i
$656$	2.04032	+	10.6809i	0.0796610	+	0.417018i
$657$	1.88088	−	25.5159i	0.0733801	−	0.995468i
$658$	12.1818	−	24.7439i	0.474898	−	0.964618i
$659$	41.2278	−	19.8079i	1.60601	−	0.771605i	0.606287	−	0.795246i	$-0.292658\pi$
$659$	41.2278	−	19.8079i	1.60601	−	0.771605i	0.999720	+	0.0236417i	$0.00752609\pi$
$660$	−34.2785	−	8.27016i	−1.33429	−	0.321915i
$661$	−26.5005	+	35.3684i	−1.03075	+	1.37567i	−0.106315	+	0.994332i	$0.533905\pi$
$661$	−26.5005	+	35.3684i	−1.03075	+	1.37567i	−0.924436	+	0.381338i	$0.875463\pi$
$662$	−39.3661	+	44.9005i	−1.53001	+	1.74511i
$663$	0.0206262	+	0.0290488i	0.000801055	+	0.00112816i
$664$	−12.5277	+	15.8573i	−0.486168	+	0.615384i
$665$	0.808204	−	8.68633i	0.0313408	−	0.336841i
$666$	20.0298	−	10.1010i	0.776137	−	0.391404i
$667$	0.234289	+	0.127710i	0.00907171	+	0.00494497i
$668$	15.6236	−	31.2289i	0.604494	−	1.20828i
$669$	29.0539	−	13.0546i	1.12329	−	0.504721i
$670$	1.41216	+	0.283832i	0.0545564	+	0.0109654i
$671$	0.768005	+	0.741442i	0.0296485	+	0.0286231i
$672$	46.8620	−	31.2851i	1.80774	−	1.20685i
$673$	−9.71998	+	29.6565i	−0.374678	+	1.14318i	0.571796	+	0.820396i	$0.306247\pi$
$673$	−9.71998	+	29.6565i	−0.374678	+	1.14318i	−0.946474	+	0.322780i	$0.895383\pi$
$674$	−14.4254	−	17.5559i	−0.555646	−	0.676229i
$675$	9.00260	−	4.18435i	0.346510	−	0.161056i
$676$	−24.1752	+	23.9443i	−0.929817	+	0.920935i
$677$	24.9055	−	18.5369i	0.957195	−	0.712429i	−0.000564283	−	1.00000i	$-0.500180\pi$
$677$	24.9055	−	18.5369i	0.957195	−	0.712429i	0.957759	+	0.287571i	$0.0928476\pi$
$678$	−62.8727	+	18.1834i	−2.41461	+	0.698328i
$679$	1.95597	−	4.97926i	0.0750632	−	0.191087i
$680$	2.11083	+	4.57971i	0.0809467	+	0.175624i
$681$	0.521030	+	23.2623i	0.0199659	+	0.891415i
$682$	−76.1619	+	15.8156i	−2.91639	+	0.605610i
$683$	16.2288	−	17.1364i	0.620980	−	0.655705i	−0.337347	−	0.941380i	$-0.609530\pi$
$683$	16.2288	−	17.1364i	0.620980	−	0.655705i	0.958326	+	0.285675i	$0.0922179\pi$
$684$	21.6953	−	23.2041i	0.829539	−	0.887230i
$685$	18.3675	+	1.29488i	0.701786	+	0.0494747i
$686$	1.09681	−	38.0830i	0.0418764	−	1.45401i
$687$	4.60058	−	5.18013i	0.175523	−	0.197634i
$688$	−18.0135	+	23.1036i	−0.686759	+	0.880817i
$689$	0.0294667	+	0.00340877i	0.00112259	+	0.000129864i
$690$	−3.16756	+	0.828864i	−0.120587	+	0.0315543i
$691$	−3.38353	−	10.7880i	−0.128716	−	0.410395i	0.867487	−	0.497460i	$-0.165734\pi$
$691$	−3.38353	−	10.7880i	−0.128716	−	0.410395i	−0.996203	+	0.0870652i	$0.972251\pi$
$692$	42.1967	+	20.9422i	1.60408	+	0.796101i
$693$	−53.5228	+	3.08553i	−2.03316	+	0.117210i
$694$	−2.88103	+	3.16153i	−0.109362	+	0.120010i
$695$	−10.0513	−	18.3000i	−0.381269	−	0.694157i
$696$	−0.824837	+	1.45723i	−0.0312654	+	0.0552361i
$697$	−15.8547	+	5.36547i	−0.600541	+	0.203232i
$698$	15.3862	+	2.78637i	0.582375	+	0.105465i
$699$	40.6391	−	1.56091i	1.53711	−	0.0590390i
$700$	22.0988	+	17.5737i	0.835254	+	0.664222i
$701$	37.8439	+	22.8838i	1.42934	+	0.864309i	0.999259	−	0.0384802i	$-0.0122517\pi$
$701$	37.8439	+	22.8838i	1.42934	+	0.864309i	0.430084	+	0.902789i	$0.358484\pi$
$702$	−0.00825217	−	0.0182097i	−0.000311458	−	0.000687281i
$703$	−7.41788	−	3.21959i	−0.279771	−	0.121429i
$704$	−24.6462	+	53.4730i	−0.928890	+	2.01534i
$705$	8.83797	+	9.21339i	0.332857	+	0.346996i
$706$	17.0450	−	8.45941i	0.641498	−	0.318374i
$707$	−26.4236	+	15.0684i	−0.993762	+	0.566705i
$708$	−9.12725	−	26.1416i	−0.343023	−	0.982463i
$709$	45.2104	−	8.78635i	1.69791	−	0.329978i	0.753179	−	0.657815i	$-0.228519\pi$
$709$	45.2104	−	8.78635i	1.69791	−	0.329978i	0.944734	+	0.327837i	$0.106320\pi$
$710$	20.5922	+	4.69013i	0.772810	+	0.176017i
$711$	39.8705	+	47.8949i	1.49526	+	1.79620i
$712$	−5.70098	+	0.109444i	−0.213653	+	0.00410159i
$713$	−3.13826	+	2.62951i	−0.117529	+	0.0984759i
$714$	37.9416	+	42.7212i	1.41993	+	1.59880i
$715$	0.0187583	−	0.00120186i	0.000701519	−	4.49470e-5i
$716$	−0.894034	−	1.73130i	−0.0334116	−	0.0647017i
$717$	4.68931	+	27.3908i	0.175125	+	1.02293i
$718$	−3.04721	−	19.2793i	−0.113721	−	0.719495i
$719$	39.2457	−	1.00465i	1.46362	−	0.0374672i	0.714376	−	0.699762i	$-0.246711\pi$
$719$	39.2457	−	1.00465i	1.46362	−	0.0374672i	0.749243	+	0.662295i	$0.230418\pi$
$720$	2.32290	+	9.49474i	0.0865694	+	0.353848i
$721$	−29.9606	+	29.2971i	−1.11579	+	1.09108i
$722$	20.5921	+	1.18711i	0.766357	+	0.0441797i
$723$	13.8887	+	7.92020i	0.516526	+	0.294556i
$724$	−4.97023	+	26.9533i	−0.184717	+	1.00171i
$725$	1.83981	+	0.382049i	0.0683287	+	0.0141890i
$726$	61.9389	−	43.0918i	2.29877	−	1.59929i
$727$	−4.19936	+	2.61327i	−0.155746	+	0.0969209i	−0.603997	−	0.796987i	$-0.706426\pi$
$727$	−4.19936	+	2.61327i	−0.155746	+	0.0969209i	0.448251	+	0.893908i	$0.352047\pi$
$728$	0.00844823	−	0.0104168i	0.000313112	−	0.000386072i
$729$	40.5141	−	2.85618i	1.50052	−	0.105784i
$730$	0.598148	+	14.3740i	0.0221385	+	0.532004i
$731$	−39.0291	−	22.5890i	−1.44354	−	0.835484i
$732$	−0.429054	+	1.43190i	−0.0158583	+	0.0529247i
$733$	15.6969	−	28.1502i	0.579780	−	1.03975i	−0.411925	−	0.911218i	$-0.635144\pi$
$733$	15.6969	−	28.1502i	0.579780	−	1.03975i	0.991705	−	0.128535i	$-0.0410275\pi$
$734$	−8.92084	−	1.91210i	−0.329274	−	0.0705768i
$735$	−1.38514	−	0.549236i	−0.0510917	−	0.0202589i
$736$	0.263431	+	4.32852i	0.00971020	+	0.159551i
$737$	−2.54747	+	1.92151i	−0.0938374	+	0.0707796i
$738$	38.4462	−	5.19715i	1.41522	−	0.191310i
$739$	−9.05717	−	40.3617i	−0.333173	−	1.48473i	−0.799795	−	0.600273i	$-0.795059\pi$
$739$	−9.05717	−	40.3617i	−0.333173	−	1.48473i	0.466622	−	0.884457i	$-0.345471\pi$
$740$	−5.97202	+	3.93192i	−0.219536	+	0.144540i
$741$	−0.0129767	+	0.0267897i	−0.000476712	+	0.000984144i
$742$	47.5720	+	0.304386i	1.74642	+	0.0111744i
$743$	−26.4499	−	28.2894i	−0.970352	−	1.03784i	−0.999268	−	0.0382538i	$-0.987820\pi$
$743$	−26.4499	−	28.2894i	−0.970352	−	1.03784i	0.0289156	−	0.999582i	$-0.490795\pi$
$744$	−16.1839	−	19.9550i	−0.593330	−	0.731584i
$745$	6.85082	+	2.36737i	0.250994	+	0.0867338i
$746$	70.1023	+	26.7640i	2.56663	+	0.979901i
$747$	−45.2115	−	39.8953i	−1.65420	−	1.45969i
$748$	−45.3228	−	13.7386i	−1.65717	−	0.502334i
$749$	−11.9107	−	8.74712i	−0.435207	−	0.319613i
$750$	−44.6765	+	27.4073i	−1.63135	+	1.00077i
$751$	−0.0453925	+	14.1887i	−0.00165640	+	0.517755i	0.965077	+	0.261967i	$0.0843713\pi$
$751$	−0.0453925	+	14.1887i	−0.00165640	+	0.517755i	−0.966733	+	0.255787i	$0.917665\pi$
$752$	9.38176	−	6.00619i	0.342118	−	0.219023i
$753$	47.6497	−	46.0017i	1.73645	−	1.67639i
$754$	0.000804904	−	0.00369750i	2.93129e−5	−	0.000134655i
$755$	1.27364	−	5.20593i	0.0463524	−	0.189463i
$756$	−9.25488	−	15.6423i	−0.336597	−	0.568905i
$757$	22.0622	−	22.4179i	0.801864	−	0.814794i	−0.183898	−	0.982945i	$-0.558871\pi$
$757$	22.0622	−	22.4179i	0.801864	−	0.814794i	0.985761	+	0.168152i	$0.0537798\pi$
$758$	−33.3216	+	46.2979i	−1.21029	+	1.68161i
$759$	3.28673	−	6.46590i	0.119301	−	0.234697i
$760$	−2.50481	+	3.38795i	−0.0908590	+	0.122894i
$761$	−7.85952	+	11.6916i	−0.284907	+	0.423821i	−0.944854	−	0.327491i	$-0.893797\pi$
$761$	−7.85952	+	11.6916i	−0.284907	+	0.423821i	0.659947	+	0.751312i	$0.270579\pi$
$762$	76.1290	+	35.9784i	2.75786	+	1.30336i
$763$	10.1739	−	2.87196i	0.368319	−	0.103972i
$764$	−7.24055	−	15.4485i	−0.261954	−	0.558907i
$765$	−13.9866	+	5.54596i	−0.505686	+	0.200515i
$766$	−22.8094	+	3.82990i	−0.824137	+	0.138380i
$767$	0.00877470	+	0.0118685i	0.000316836	+	0.000428546i
$768$	5.70164	−	0.255539i	0.205740	−	0.00922096i
$769$	36.1755	+	21.2476i	1.30452	+	0.766207i	0.983508	−	0.180867i	$-0.0578903\pi$
$769$	36.1755	+	21.2476i	1.30452	+	0.766207i	0.321015	+	0.947074i	$0.395976\pi$
$770$	29.6969	−	5.18196i	1.07020	−	0.186745i
$771$	−19.5181	+	1.87903i	−0.702927	+	0.0676716i
$772$	−5.25925	−	31.9476i	−0.189285	−	1.14982i
$773$	−32.9566	−	9.30326i	−1.18537	−	0.334615i	−0.378643	−	0.925543i	$-0.623609\pi$
$773$	−32.9566	−	9.30326i	−1.18537	−	0.334615i	−0.806724	+	0.590928i	$0.798762\pi$
$774$	78.8128	+	68.6537i	2.83287	+	2.46771i
$775$	−15.7776	+	24.1317i	−0.566749	+	0.866836i
$776$	−2.05274	+	1.56904i	−0.0736889	+	0.0563253i
$777$	−12.2263	+	14.6870i	−0.438617	+	0.526894i
$778$	−16.9350	+	21.1564i	−0.607150	+	0.758493i
$779$	−10.3067	−	9.45274i	−0.369274	−	0.338680i
$780$	0.0135473	+	0.0225665i	0.000485071	+	0.000808009i
$781$	−38.0605	+	27.2086i	−1.36191	+	0.973600i
$782$	−4.31126	+	0.866528i	−0.154170	+	0.0309870i
$783$	−1.01871	−	0.652174i	−0.0364056	−	0.0233068i
$784$	−0.704491	+	1.09271i	−0.0251604	+	0.0390255i
$785$	−6.80590	+	1.09805i	−0.242913	+	0.0391909i
$786$	51.2064	−	13.7500i	1.82647	−	0.490446i
$787$	1.08872	+	14.7695i	0.0388086	+	0.526474i	0.981330	+	0.192330i	$0.0616043\pi$
$787$	1.08872	+	14.7695i	0.0388086	+	0.526474i	−0.942522	+	0.334145i	$0.891553\pi$
$788$	4.47514	+	1.80771i	0.159420	+	0.0643968i
$789$	10.8161	−	38.7901i	0.385064	−	1.38096i
$790$	−25.3654	−	24.1764i	−0.902459	−	0.860159i
$791$	24.4410	−	20.2141i	0.869024	−	0.718731i
$792$	22.8913	+	12.1006i	0.813406	+	0.429977i
$793$	−7.64735e−6	0	0.000796780i	−2.71566e−7	0	2.82945e-5i
$794$	23.4135	+	9.63245i	0.830915	+	0.341843i
$795$	−7.65683	+	20.6479i	−0.271560	+	0.732305i
$796$	9.06899	−	3.33008i	0.321442	−	0.118031i
$797$	−29.9490	−	7.42869i	−1.06085	−	0.263138i	−0.328806	−	0.944397i	$-0.606646\pi$
$797$	−29.9490	−	7.42869i	−1.06085	−	0.263138i	−0.732042	+	0.681260i	$0.761432\pi$
$798$	−16.0246	+	44.9699i	−0.567264	+	1.59192i
$799$	11.1381	+	13.0368i	0.394039	+	0.461210i
$800$	10.6178	+	28.6326i	0.375395	+	1.01231i
$801$	0.598583	−	17.0025i	0.0211499	−	0.600755i
$802$	−29.2252	−	58.4164i	−1.03198	−	2.06275i
$803$	−24.6883	−	20.1540i	−0.871232	−	0.711220i
$804$	−4.02742	−	1.93497i	−0.142036	−	0.0682412i
$805$	1.24818	−	0.979624i	0.0439926	−	0.0345272i
$806$	0.0482898	+	0.0322383i	0.00170094	+	0.00113555i
$807$	13.7383	+	63.1096i	0.483610	+	2.22156i
$808$	14.6862	+	0.375953i	0.516659	+	0.0132260i
$809$	−1.03776	−	7.86635i	−0.0364857	−	0.276566i	−0.999962	−	0.00877116i	$-0.997208\pi$
$809$	−1.03776	−	7.86635i	−0.0364857	−	0.276566i	0.963476	−	0.267795i	$-0.0862950\pi$
$810$	−11.3897	+	2.13798i	−0.400194	+	0.0751210i
$811$	−0.309889	+	19.3714i	−0.0108817	+	0.680222i	0.934808	+	0.355153i	$0.115571\pi$
$811$	−0.309889	+	19.3714i	−0.0108817	+	0.680222i	−0.945690	+	0.325070i	$0.894612\pi$
$812$	0.362511	−	3.42099i	0.0127216	−	0.120053i
$813$	32.1341	+	17.2505i	1.12699	+	0.605001i
$814$	4.00889	−	27.6540i	0.140511	−	0.969273i
$815$	−5.18981	+	14.8643i	−0.181791	+	0.520674i
$816$	4.18504	+	22.6953i	0.146506	+	0.794493i
$817$	0.843695	−	37.6683i	0.0295171	−	1.31785i
$818$	−21.1722	+	9.18939i	−0.740269	+	0.321300i
$819$	0.0296643	+	0.0268591i	0.00103655	+	0.000938534i
$820$	−11.9828	+	3.05379i	−0.418458	+	0.106643i
$821$	−26.7328	−	27.5138i	−0.932983	−	0.960240i	0.0663119	−	0.997799i	$-0.478877\pi$
$821$	−26.7328	−	27.5138i	−0.932983	−	0.960240i	−0.999294	+	0.0375591i	$0.988042\pi$
$822$	−95.6497	−	31.6886i	−3.33617	−	1.10527i
$823$	13.2624	−	18.1806i	0.462297	−	0.633735i	−0.512005	−	0.858982i	$-0.671097\pi$
$823$	13.2624	−	18.1806i	0.462297	−	0.633735i	0.974302	+	0.225248i	$0.0723191\pi$
$824$	19.7039	−	4.62062i	0.686418	−	0.160967i
$825$	8.94108	−	50.2891i	0.311288	−	1.75084i
$826$	16.0558	+	17.3941i	0.558652	+	0.605219i
$827$	8.93992	−	18.7610i	0.310872	−	0.652382i	−0.686318	−	0.727302i	$-0.740774\pi$
$827$	8.93992	−	18.7610i	0.310872	−	0.652382i	0.997190	+	0.0749193i	$0.0238699\pi$
$828$	5.77761	−	0.0369677i	0.200786	−	0.00128472i
$829$	−29.2347	−	30.8695i	−1.01536	−	1.07214i	−0.997383	−	0.0723046i	$-0.976965\pi$
$829$	−29.2347	−	30.8695i	−1.01536	−	1.07214i	−0.0179807	−	0.999838i	$-0.505724\pi$
$830$	27.8317	+	19.3629i	0.966054	+	0.672097i
$831$	−73.3526	−	3.75797i	−2.54457	−	0.130362i
$832$	0.0413521	−	0.0148847i	0.00143363	−	0.000516033i
$833$	−1.81480	−	0.843506i	−0.0628790	−	0.0292258i
$834$	28.5697	+	110.625i	0.989289	+	3.83063i
$835$	−12.7113	−	5.42072i	−0.439894	−	0.187592i
$836$	−8.16925	−	38.7175i	−0.282540	−	1.33907i
$837$	15.0290	−	10.8898i	0.519477	−	0.376407i
$838$	−6.24298	−	15.5986i	−0.215660	−	0.538844i
$839$	−34.1051	+	36.9480i	−1.17744	+	1.27559i	−0.223799	+	0.974635i	$0.571846\pi$
$839$	−34.1051	+	36.9480i	−1.17744	+	1.27559i	−0.953639	+	0.300952i	$0.902696\pi$
$840$	6.02137	+	7.93005i	0.207757	+	0.273613i
$841$	10.1759	+	26.9114i	0.350892	+	0.927980i
$842$	−2.98904	+	13.3202i	−0.103009	+	0.459043i
$843$	2.42570	−	28.0125i	0.0835455	−	0.964803i
$844$	−21.1953	+	40.4084i	−0.729572	+	1.39092i
$845$	10.0394	+	8.97383i	0.345366	+	0.308709i
$846$	−19.5775	−	34.5873i	−0.673087	−	1.18913i
$847$	−19.2200	+	31.1067i	−0.660408	+	1.06884i
$848$	16.3785	+	10.0476i	0.562440	+	0.345035i
$849$	−10.8547	−	26.6263i	−0.372534	−	0.913813i
$850$	−27.2842	+	14.6469i	−0.935840	+	0.502384i
$851$	−0.502542	−	1.38225i	−0.0172269	−	0.0473829i
$852$	−58.3058	−	29.8730i	−1.99752	−	1.02343i
$853$	3.18140	−	16.0949i	0.108929	−	0.551078i	−0.887064	−	0.461647i	$-0.847259\pi$
$853$	3.18140	−	16.0949i	0.108929	−	0.551078i	0.995993	−	0.0894314i	$-0.0285050\pi$
$854$	−0.150913	−	1.26897i	−0.00516413	−	0.0434232i
$855$	−9.68739	−	8.01202i	−0.331302	−	0.274005i
$856$	2.73653	+	6.59164i	0.0935326	+	0.225298i
$857$	−5.88499	+	28.8025i	−0.201027	+	0.983873i	0.746790	+	0.665060i	$0.231594\pi$
$857$	−5.88499	+	28.8025i	−0.201027	+	0.983873i	−0.947817	+	0.318813i	$0.896716\pi$
$858$	−0.101096	−	0.0189769i	−0.00345136	−	0.000647861i
$859$	2.66723	−	48.9943i	0.0910048	−	1.67166i	−0.500786	−	0.865571i	$-0.666956\pi$
$859$	2.66723	−	48.9943i	0.0910048	−	1.67166i	0.591791	−	0.806092i	$-0.298421\pi$
$860$	−27.4691	−	18.8510i	−0.936689	−	0.642813i
$861$	−28.2812	+	17.1013i	−0.963819	+	0.582811i
$862$	22.6318	+	2.91203i	0.770841	+	0.0991843i
$863$	−17.3469	+	32.0672i	−0.590495	+	1.09158i	0.394483	+	0.918903i	$0.370924\pi$
$863$	−17.3469	+	32.0672i	−0.590495	+	1.09158i	−0.984979	+	0.172676i	$0.944759\pi$
$864$	0.188663	−	19.6569i	0.00641846	−	0.668741i
$865$	7.25794	−	17.1716i	0.246777	−	0.583851i
$866$	−14.9311	+	46.5607i	−0.507380	+	1.58220i
$867$	8.84765	−	2.93121i	0.300482	−	0.0995491i
$868$	46.8227	+	24.3691i	1.58927	+	0.827140i
$869$	77.3584	−	6.44944i	2.62420	−	0.218782i
$870$	2.52437	+	1.23277i	0.0855841	+	0.0417949i
$871$	0.00235603		0.000349243i	7.98311e−5		1.18337e-5i
$872$	−4.92244	−	1.35560i	−0.166695	−	0.0459064i
$873$	−4.34167	−	6.37015i	−0.146943	−	0.215597i
$874$	−2.36873	−	2.80872i	−0.0801235	−	0.0950064i
$875$	14.5724	−	20.8037i	0.492637	−	0.703292i
$876$	9.21326	−	43.6654i	0.311287	−	1.47532i
$877$	3.32169	+	7.45636i	0.112166	+	0.251783i	0.960825	−	0.277157i	$-0.0893921\pi$
$877$	3.32169	+	7.45636i	0.112166	+	0.251783i	−0.848659	+	0.528940i	$0.822590\pi$
$878$	−2.95134	−	61.4548i	−0.0996029	−	2.07400i
$879$	−0.401113	−	0.104960i	−0.0135292	−	0.00354023i
$880$	11.3471	+	4.41553i	0.382509	+	0.148848i
$881$	−6.64891	+	14.9251i	−0.224007	+	0.502840i	−0.990181	−	0.139794i	$-0.955356\pi$
$881$	−6.64891	+	14.9251i	−0.224007	+	0.502840i	0.766173	+	0.642634i	$0.222158\pi$
$882$	3.75615	+	2.72166i	0.126476	+	0.0916432i
$883$	9.39104	−	37.3485i	0.316034	−	1.25688i	−0.580630	−	0.814167i	$-0.697194\pi$
$883$	9.39104	−	37.3485i	0.316034	−	1.25688i	0.896664	−	0.442711i	$-0.145983\pi$
$884$	0.0164204	+	0.0313052i	0.000552278	+	0.00105291i
$885$	−10.1068	+	4.23380i	−0.339736	+	0.142318i
$886$	45.1676	−	2.31401i	1.51744	−	0.0777407i
$887$	22.0486	+	13.7209i	0.740318	+	0.460702i	0.845652	−	0.533735i	$-0.179212\pi$
$887$	22.0486	+	13.7209i	0.740318	+	0.460702i	−0.105333	+	0.994437i	$0.533591\pi$
$888$	8.72339	−	3.01446i	0.292738	−	0.101159i
$889$	−40.7842	−	1.30520i	−1.36786	−	0.0437751i
$890$	0.764299	+	9.53581i	0.0256194	+	0.319641i
$891$	13.2135	−	22.0105i	0.442670	−	0.737379i
$892$	30.3038	−	8.97465i	1.01465	−	0.300494i
$893$	−5.06713	+	13.4007i	−0.169565	+	0.448437i
$894$	−33.1294	−	21.8121i	−1.10801	−	0.729504i
$895$	−0.662387	+	0.394773i	−0.0221412	+	0.0131958i
$896$	24.9483	−	12.1835i	0.833465	−	0.407022i
$897$	−0.00516074	+	0.00163676i	−0.000172312	+	5.46498e-5i
$898$	9.80462	−	57.2699i	0.327184	−	1.91112i
$899$	3.51262	+	0.0449525i	0.117153	+	0.00149925i
$900$	38.8608	−	12.0518i	1.29536	−	0.401728i
$901$	−11.8626	+	27.0937i	−0.395201	+	0.902620i
$902$	22.1734	−	42.9388i	0.738293	−	1.42971i
$903$	−84.8742	−	26.9184i	−2.82444	−	0.895787i
$904$	−15.1528	+	2.24616i	−0.503975	+	0.0747061i
$905$	10.7663	+	1.31533i	0.357883	+	0.0437231i
$906$	−13.7892	+	25.8849i	−0.458117	+	0.859969i
$907$	−3.61059	−	12.9487i	−0.119888	−	0.429956i	0.879015	−	0.476794i	$-0.158201\pi$
$907$	−3.61059	−	12.9487i	−0.119888	−	0.429956i	−0.998902	+	0.0468388i	$0.985085\pi$
$908$	−2.57975	+	22.9430i	−0.0856119	+	0.761390i
$909$	−3.50204	+	43.6933i	−0.116155	+	1.44922i
$910$	−0.0183052	−	0.0130859i	−0.000606810	−	0.000433794i
$911$	−6.78945	−	3.05066i	−0.224944	−	0.101073i	0.294252	−	0.955728i	$-0.404930\pi$
$911$	−6.78945	−	3.05066i	−0.224944	−	0.101073i	−0.519196	+	0.854655i	$0.673769\pi$
$912$	−14.9371	+	12.1937i	−0.494616	+	0.403774i
$913$	−73.0137	+	17.6155i	−2.41640	+	0.582989i
$914$	22.3065	−	51.8473i	0.737832	−	1.71495i
$915$	0.575930	+	0.135057i	0.0190397	+	0.00446486i
$916$	5.21228	−	4.48208i	0.172219	−	0.148092i
$917$	−20.1103	+	15.9924i	−0.664101	+	0.528115i
$918$	19.7711	−	2.54395i	0.652543	−	0.0839629i
$919$	−3.44809	+	8.94550i	−0.113742	+	0.295085i	−0.978215	−	0.207595i	$-0.933437\pi$
$919$	−3.44809	+	8.94550i	−0.113742	+	0.295085i	0.864473	+	0.502679i	$0.167652\pi$
$920$	−0.760672	+	0.0929322i	−0.0250786	+	0.00306388i
$921$	48.4424	−	13.3407i	1.59623	−	0.439590i
$922$	46.6988	+	39.6397i	1.53794	+	1.30547i
$923$	0.0344024	+	0.00600305i	0.00113237	+	0.000197593i
$924$	−93.2367	−	7.17284i	−3.06726	−	0.235969i
$925$	−6.21043	−	8.28863i	−0.204198	−	0.272528i
$926$	4.24341	+	9.86302i	0.139447	+	0.324119i
$927$	10.5703	+	59.4527i	0.347174	+	1.95268i
$928$	2.25009	−	2.96333i	0.0738627	−	0.0972760i
$929$	−19.3514	−	5.73104i	−0.634900	−	0.188029i	−0.0495006	−	0.998774i	$-0.515763\pi$
$929$	−19.3514	−	5.73104i	−0.634900	−	0.188029i	−0.585400	+	0.810745i	$0.699062\pi$
$930$	−31.7675	+	29.1356i	−1.04170	+	0.955393i
$931$	−0.112251	−	1.66832i	−0.00367889	−	0.0546770i
$932$	40.1677	+	3.86699i	1.31574	+	0.126668i
$933$	−41.3839	+	3.18372i	−1.35485	+	0.104230i
$934$	24.7405	+	28.2187i	0.809535	+	0.923346i
$935$	−4.33733	+	18.2332i	−0.141846	+	0.596290i
$936$	−0.00554746	−	0.0185138i	−0.000181324	−	0.000605144i
$937$	46.4400	+	10.2652i	1.51713	+	0.335349i	0.894464	−	0.447140i	$-0.147557\pi$
$937$	46.4400	+	10.2652i	1.51713	+	0.335349i	0.622664	+	0.782489i	$0.286050\pi$
$938$	3.81701	+	0.146607i	0.124630	+	0.00478690i
$939$	−39.2544	−	33.7552i	−1.28102	−	1.10156i
$940$	7.46567	+	10.2342i	0.243503	+	0.333804i
$941$	−7.97373	−	24.8650i	−0.259936	−	0.810576i	−0.991649	−	0.128964i	$-0.958835\pi$
$941$	−7.97373	−	24.8650i	−0.259936	−	0.810576i	0.731713	−	0.681613i	$-0.238721\pi$
$942$	37.5744	+	3.37484i	1.22424	+	0.109958i
$943$	−0.0406856	−	2.54329i	−0.00132491	−	0.0828208i
$944$	1.91398	+	9.36748i	0.0622949	+	0.304885i
$945$	−5.95637	+	4.03181i	−0.193761	+	0.131155i
$946$	126.368	−	31.3449i	4.10857	−	1.01911i
$947$	−2.92373	+	29.3839i	−0.0950083	+	0.954849i	0.825572	+	0.564296i	$0.190852\pi$
$947$	−2.92373	+	29.3839i	−0.0950083	+	0.954849i	−0.920581	+	0.390552i	$0.872284\pi$
$948$	57.7261	+	92.1041i	1.87486	+	2.99140i
$949$	0.00220386	+	0.0236864i	7.15402e−5	+	0.000768892i
$950$	−21.7011	−	14.0895i	−0.704076	−	0.457125i
$951$	34.4170	+	1.54251i	1.11605	+	0.0500195i
$952$	7.46072	+	11.0984i	0.241803	+	0.359700i
$953$	−0.485950	−	3.20749i	−0.0157415	−	0.103901i	0.979481	−	0.201539i	$-0.0645943\pi$
$953$	−0.485950	−	3.20749i	−0.0157415	−	0.103901i	−0.995222	+	0.0976381i	$0.968871\pi$
$954$	38.9708	−	56.3996i	1.26173	−	1.82601i
$955$	−5.92824	+	3.23147i	−0.191833	+	0.104568i
$956$	0.970141	+	27.5565i	0.0313766	+	0.891242i
$957$	−5.75537	+	2.36779i	−0.186045	+	0.0765398i
$958$	−2.33674	−	5.52850i	−0.0754967	−	0.178618i
$959$	48.6342	−	4.36820i	1.57048	−	0.141056i
$960$	3.43823	+	32.4462i	0.110968	+	1.04720i
$961$	−8.64534	+	21.2067i	−0.278882	+	0.684088i
$962$	−0.0168111	+	0.0123460i	−0.000542012	+	0.000398049i
$963$	−20.0822	+	7.08376i	−0.647139	+	0.228271i
$964$	12.6039	+	9.63401i	0.405945	+	0.310290i
$965$	−12.4932	+	2.84548i	−0.402169	+	0.0915991i
$966$	−7.94277	+	3.50797i	−0.255554	+	0.112867i
$967$	0.653176	+	2.28587i	0.0210047	+	0.0735085i	0.971316	−	0.237794i	$-0.0764242\pi$
$967$	0.653176	+	2.28587i	0.0210047	+	0.0735085i	−0.950311	+	0.311302i	$0.899235\pi$
$968$	15.7172	−	8.05270i	0.505170	−	0.258824i
$969$	−21.7450	−	20.2011i	−0.698551	−	0.648953i
$970$	2.83675	+	3.27764i	0.0910827	+	0.105239i
$971$	21.5912	+	49.3132i	0.692894	+	1.58254i	0.808000	+	0.589183i	$0.200550\pi$
$971$	21.5912	+	49.3132i	0.692894	+	1.58254i	−0.115106	+	0.993353i	$0.536721\pi$
$972$	55.6838	+	3.56772i	1.78606	+	0.114435i
$973$	−34.0448	−	43.6649i	−1.09143	−	1.39983i
$974$	1.74078	+	2.85811i	0.0557781	+	0.0915796i
$975$	−0.0314355	+	0.0215730i	−0.00100674	+	0.000690888i
$976$	0.213051	−	0.470129i	0.00681959	−	0.0150485i
$977$	9.74512	−	8.82359i	0.311774	−	0.282292i	−0.500293	−	0.865856i	$-0.666774\pi$
$977$	9.74512	−	8.82359i	0.311774	−	0.282292i	0.812067	+	0.583565i	$0.198342\pi$
$978$	47.6085	−	71.8093i	1.52235	−	2.29621i
$979$	−16.9190	−	12.7617i	−0.540734	−	0.407864i
$980$	−1.28900	−	0.724176i	−0.0411755	−	0.0231330i
$981$	4.83708	−	14.4454i	0.154436	−	0.461207i
$982$	43.7831			1.39717
$983$	29.6302	+	10.2495i	0.945057	+	0.326907i
$983$	29.6302	+	10.2495i	0.945057	+	0.326907i
$984$	15.9620			0.508849
$985$	0.606479	−	1.81118i	0.0193240	−	0.0577091i
$986$	3.28948	+	1.84808i	0.104758	+	0.0588548i
$987$	27.0300	+	20.3882i	0.860375	+	0.648963i
$988$	−0.0163209	+	0.0246173i	−0.000519237	+	0.000783180i
$989$	5.07994	−	4.59956i	0.161533	−	0.146258i
$990$	17.9309	−	39.5674i	0.569883	−	1.25753i
$991$	40.0598	−	27.4915i	1.27254	−	0.873295i	0.276398	−	0.961043i	$-0.410859\pi$
$991$	40.0598	−	27.4915i	1.27254	−	0.873295i	0.996143	+	0.0877483i	$0.0279671\pi$
$992$	29.6974	+	48.7588i	0.942892	+	1.54809i
$993$	−45.0731	−	57.8094i	−1.43035	−	1.83453i
$994$	55.8927	+	3.58110i	1.77281	+	0.113586i
$995$	−1.53343	−	3.50228i	−0.0486131	−	0.111030i
$996$	−68.8273	−	79.5244i	−2.18088	−	2.51983i
$997$	25.6279	+	23.8083i	0.811642	+	0.754015i	0.972485	−	0.232965i	$-0.0748428\pi$
$997$	25.6279	+	23.8083i	0.811642	+	0.754015i	−0.160843	+	0.986980i	$0.551421\pi$
$998$	54.6066	−	27.9776i	1.72854	−	0.885617i
$999$	1.83178	+	6.41053i	0.0579549	+	0.202820i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.c.a.2.13	✓	39690
983.492	even	491	inner	983.2.c.a.492.13	yes	39690

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.c.a.2.13	✓	39690	1.1	even	1	trivial
983.2.c.a.492.13	yes	39690	983.492	even	491	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.c (of order \(491\), degree \(490\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.682299 + 2.03761i) q^{2} +(-2.29977 - 1.29204i) q^{3} +(-2.08961 - 1.57615i) q^{4} +(-0.572361 + 0.863308i) q^{5} +(4.20182 - 3.80448i) q^{6} +(-1.13382 + 2.50196i) q^{7} +(1.09385 - 0.750669i) q^{8} +(2.05904 + 3.38064i) q^{9} +O(q^{10})\)	\(q+(-0.682299 + 2.03761i) q^{2} +(-2.29977 - 1.29204i) q^{3} +(-2.08961 - 1.57615i) q^{4} +(-0.572361 + 0.863308i) q^{5} +(4.20182 - 3.80448i) q^{6} +(-1.13382 + 2.50196i) q^{7} +(1.09385 - 0.750669i) q^{8} +(2.05904 + 3.38064i) q^{9} +(-1.36857 - 1.75528i) q^{10} +(4.92060 + 0.315268i) q^{11} +(2.76918 + 6.32466i) q^{12} +(-0.00240853 - 0.00278287i) q^{13} +(-4.32441 - 4.01737i) q^{14} +(2.43173 - 1.24590i) q^{15} +(-0.655014 - 2.29230i) q^{16} +(3.35687 - 1.48258i) q^{17} +(-8.29332 + 1.88891i) q^{18} +(2.43600 + 1.86199i) q^{19} +(2.55672 - 0.901854i) q^{20} +(5.84018 - 4.28898i) q^{21} +(-3.99971 + 9.81116i) q^{22} +(0.0587654 + 0.554564i) q^{23} +(-3.48551 + 0.313060i) q^{24} +(1.52891 + 3.61726i) q^{25} +(0.00731374 - 0.00300891i) q^{26} +(-0.0889426 - 2.52639i) q^{27} +(6.31272 - 3.44105i) q^{28} +(0.272004 - 0.393651i) q^{29} +(0.879486 + 5.80500i) q^{30} +(4.09593 + 6.09300i) q^{31} +(7.76838 + 0.348167i) q^{32} +(-10.9089 - 7.08268i) q^{33} +(0.730535 + 7.85156i) q^{34} +(-1.51101 - 2.41086i) q^{35} +(1.02581 - 10.3096i) q^{36} +(-2.55978 + 0.634941i) q^{37} +(-5.45609 + 3.69318i) q^{38} +(0.00194349 + 0.00951189i) q^{39} +(0.0219800 + 1.37399i) q^{40} +(-4.54287 - 0.408028i) q^{41} +(4.75453 + 14.8264i) q^{42} +(-7.24202 - 9.92766i) q^{43} +(-9.78524 - 8.41439i) q^{44} +(-4.09705 - 0.157364i) q^{45} +(-1.17008 - 0.258637i) q^{46} +(1.34117 + 4.47597i) q^{47} +(-1.45537 + 6.11807i) q^{48} +(-0.359516 - 0.410060i) q^{49} +(-8.41374 + 0.647282i) q^{50} +(-9.63560 - 0.927630i) q^{51} +(0.000646689 + 0.00961133i) q^{52} +(-5.93986 + 5.44773i) q^{53} +(5.20848 + 1.54252i) q^{54} +(-3.08853 + 4.06755i) q^{55} +(0.637905 + 3.58790i) q^{56} +(-3.19646 - 7.42957i) q^{57} +(0.616520 + 0.822826i) q^{58} +(-3.99860 - 0.307618i) q^{59} +(-7.04510 - 1.22934i) q^{60} +(0.165056 + 0.140106i) q^{61} +(-15.2098 + 4.18867i) q^{62} +(-10.7928 + 1.31857i) q^{63} +(-4.29489 + 11.1424i) q^{64} +(0.00378102 - 0.000486505i) q^{65} +(21.8749 - 17.3956i) q^{66} +(-0.490682 + 0.421941i) q^{67} +(-9.35133 - 2.19291i) q^{68} +(0.581374 - 1.35130i) q^{69} +(5.94335 - 1.43391i) q^{70} +(-7.35049 + 6.00048i) q^{71} +(4.79003 + 2.15228i) q^{72} +(-5.25818 - 3.75895i) q^{73} +(0.452775 - 5.64906i) q^{74} +(1.15751 - 10.2943i) q^{75} +(-2.15551 - 7.73034i) q^{76} +(-6.36787 + 11.9537i) q^{77} +(-0.0207076 - 0.00252987i) q^{78} +(15.5734 - 2.30851i) q^{79} +(2.35386 + 0.746542i) q^{80} +(2.38894 - 4.62619i) q^{81} +(3.93099 - 8.97820i) q^{82} +(-14.5493 + 4.51214i) q^{83} +(-18.9638 - 0.242687i) q^{84} +(-0.641416 + 3.74659i) q^{85} +(25.1699 - 7.98280i) q^{86} +(-1.13416 + 0.553866i) q^{87} +(5.61908 - 3.34888i) q^{88} +(-3.58984 - 2.36351i) q^{89} +(3.11606 - 8.24083i) q^{90} +(0.00969346 - 0.00287077i) q^{91} +(0.751279 - 1.25145i) q^{92} +(-1.54727 - 19.3046i) q^{93} +(-10.0354 - 0.321159i) q^{94} +(-3.00174 + 1.03728i) q^{95} +(-17.4157 - 10.8378i) q^{96} +(-1.94499 + 0.0996450i) q^{97} +(1.08084 - 0.452771i) q^{98} +(9.06589 + 17.2839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9}+O(q^{10}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9} - 471 q^{10} - 477 q^{11} - 463 q^{12} - 483 q^{13} - 473 q^{14} - 461 q^{15} - 543 q^{16} - 481 q^{17} - 457 q^{18} - 473 q^{19} - 449 q^{20} - 449 q^{21} - 459 q^{22} - 473 q^{23} - 405 q^{24} - 552 q^{25} - 437 q^{26} - 451 q^{27} - 455 q^{28} - 455 q^{29} - 379 q^{30} - 459 q^{31} - 437 q^{32} - 447 q^{33} - 423 q^{34} - 439 q^{35} - 459 q^{36} - 475 q^{37} - 423 q^{38} - 439 q^{39} - 413 q^{40} - 455 q^{41} - 407 q^{42} - 457 q^{43} - 413 q^{44} - 397 q^{45} - 415 q^{46} - 467 q^{47} - 393 q^{48} - 524 q^{49} - 429 q^{50} - 403 q^{51} - 391 q^{52} - 431 q^{53} - 379 q^{54} - 415 q^{55} - 371 q^{56} - 447 q^{57} - 431 q^{58} - 439 q^{59} - 261 q^{60} - 431 q^{61} - 383 q^{62} - 445 q^{63} - 447 q^{64} - 415 q^{65} - 345 q^{66} - 439 q^{67} - 409 q^{68} - 367 q^{69} - 345 q^{70} - 415 q^{71} - 341 q^{72} - 465 q^{73} - 359 q^{74} - 339 q^{75} - 361 q^{76} - 363 q^{77} - 341 q^{78} - 423 q^{79} - 249 q^{80} - 420 q^{81} - 371 q^{82} - 433 q^{83} - 215 q^{84} - 409 q^{85} - 369 q^{86} - 329 q^{87} - 255 q^{88} - 393 q^{89} - 251 q^{90} - 373 q^{91} - 387 q^{92} - 369 q^{93} - 317 q^{94} - 393 q^{95} - 149 q^{96} - 415 q^{97} - 307 q^{98} - 299 q^{99}+O(q^{100}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9 - 471 * q^10 - 477 * q^11 - 463 * q^12 - 483 * q^13 - 473 * q^14 - 461 * q^15 - 543 * q^16 - 481 * q^17 - 457 * q^18 - 473 * q^19 - 449 * q^20 - 449 * q^21 - 459 * q^22 - 473 * q^23 - 405 * q^24 - 552 * q^25 - 437 * q^26 - 451 * q^27 - 455 * q^28 - 455 * q^29 - 379 * q^30 - 459 * q^31 - 437 * q^32 - 447 * q^33 - 423 * q^34 - 439 * q^35 - 459 * q^36 - 475 * q^37 - 423 * q^38 - 439 * q^39 - 413 * q^40 - 455 * q^41 - 407 * q^42 - 457 * q^43 - 413 * q^44 - 397 * q^45 - 415 * q^46 - 467 * q^47 - 393 * q^48 - 524 * q^49 - 429 * q^50 - 403 * q^51 - 391 * q^52 - 431 * q^53 - 379 * q^54 - 415 * q^55 - 371 * q^56 - 447 * q^57 - 431 * q^58 - 439 * q^59 - 261 * q^60 - 431 * q^61 - 383 * q^62 - 445 * q^63 - 447 * q^64 - 415 * q^65 - 345 * q^66 - 439 * q^67 - 409 * q^68 - 367 * q^69 - 345 * q^70 - 415 * q^71 - 341 * q^72 - 465 * q^73 - 359 * q^74 - 339 * q^75 - 361 * q^76 - 363 * q^77 - 341 * q^78 - 423 * q^79 - 249 * q^80 - 420 * q^81 - 371 * q^82 - 433 * q^83 - 215 * q^84 - 409 * q^85 - 369 * q^86 - 329 * q^87 - 255 * q^88 - 393 * q^89 - 251 * q^90 - 373 * q^91 - 387 * q^92 - 369 * q^93 - 317 * q^94 - 393 * q^95 - 149 * q^96 - 415 * q^97 - 307 * q^98 - 299 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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