LMFDB - Embedded newform 983.2.c.a.2.12

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			2.12
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.691522 + 2.06516i) q^{2} +(-1.31722 - 0.740034i) q^{3} +(-2.18995 - 1.65183i) q^{4} +(-2.30250 + 3.47293i) q^{5} +(2.43917 - 2.20852i) q^{6} +(0.363807 - 0.802796i) q^{7} +(1.33432 - 0.915691i) q^{8} +(-0.373111 - 0.612595i) q^{9} +O(q^{10})$	\(q+(-0.691522 + 2.06516i) q^{2} +(-1.31722 - 0.740034i) q^{3} +(-2.18995 - 1.65183i) q^{4} +(-2.30250 + 3.47293i) q^{5} +(2.43917 - 2.20852i) q^{6} +(0.363807 - 0.802796i) q^{7} +(1.33432 - 0.915691i) q^{8} +(-0.373111 - 0.612595i) q^{9} +(-5.57991 - 7.15662i) q^{10} +(-1.49176 - 0.0955789i) q^{11} +(1.66224 + 3.79647i) q^{12} +(0.264935 + 0.306111i) q^{13} +(1.40632 + 1.30647i) q^{14} +(5.60299 - 2.87069i) q^{15} +(-0.538977 - 1.88621i) q^{16} +(-0.645980 + 0.285301i) q^{17} +(1.52312 - 0.346910i) q^{18} +(-4.63566 - 3.54334i) q^{19} +(10.7791 - 3.80219i) q^{20} +(-1.07331 + 0.788231i) q^{21} +(1.22897 - 3.01463i) q^{22} +(0.765731 + 7.22614i) q^{23} +(-2.43524 + 0.218726i) q^{24} +(-4.81310 - 11.3873i) q^{25} +(-0.815376 + 0.335450i) q^{26} +(0.197603 + 5.61284i) q^{27} +(-2.12280 + 1.15714i) q^{28} +(5.18004 - 7.49668i) q^{29} +(2.05383 + 13.5562i) q^{30} +(0.728553 + 1.08378i) q^{31} +(7.50140 + 0.336201i) q^{32} +(1.89425 + 1.22986i) q^{33} +(-0.142481 - 1.53134i) q^{34} +(1.95039 + 3.11191i) q^{35} +(-0.194810 + 1.95787i) q^{36} +(-3.37878 + 0.838088i) q^{37} +(10.5232 - 7.12306i) q^{38} +(-0.122446 - 0.599278i) q^{39} +(0.107859 + 6.74237i) q^{40} +(3.64627 + 0.327498i) q^{41} +(-0.885602 - 2.76163i) q^{42} +(-1.36438 - 1.87034i) q^{43} +(3.10901 + 2.67346i) q^{44} +(2.98659 + 0.114712i) q^{45} +(-15.4526 - 3.41568i) q^{46} +(-1.87742 - 6.26561i) q^{47} +(-0.685911 + 2.88342i) q^{48} +(4.10259 + 4.67937i) q^{49} +(26.8449 - 2.06522i) q^{50} +(1.06203 + 0.102243i) q^{51} +(-0.0745505 - 1.10800i) q^{52} +(-6.30654 + 5.78403i) q^{53} +(-11.7280 - 3.47332i) q^{54} +(3.76673 - 4.96072i) q^{55} +(-0.249679 - 1.40432i) q^{56} +(3.48400 + 8.09791i) q^{57} +(11.8997 + 15.8817i) q^{58} +(-4.44325 - 0.341826i) q^{59} +(-17.0122 - 2.96854i) q^{60} +(5.53208 + 4.69584i) q^{61} +(-2.74198 + 0.755120i) q^{62} +(-0.627529 + 0.0766660i) q^{63} +(-4.47058 + 11.5982i) q^{64} +(-1.67312 + 0.215280i) q^{65} +(-3.84976 + 3.06146i) q^{66} +(6.71684 - 5.77586i) q^{67} +(1.88593 + 0.442256i) q^{68} +(4.33895 - 10.0851i) q^{69} +(-7.77532 + 1.87590i) q^{70} +(-2.96848 + 2.42328i) q^{71} +(-1.05880 - 0.475743i) q^{72} +(11.9983 + 8.57731i) q^{73} +(0.605718 - 7.55726i) q^{74} +(-2.08708 + 18.5615i) q^{75} +(4.29885 + 15.4171i) q^{76} +(-0.619444 + 1.16281i) q^{77} +(1.32228 + 0.161544i) q^{78} +(1.80489 - 0.267546i) q^{79} +(7.79168 + 2.47118i) q^{80} +(2.90608 - 5.62763i) q^{81} +(-3.19781 + 7.30364i) q^{82} +(7.05251 - 2.18718i) q^{83} +(3.65252 + 0.0467428i) q^{84} +(0.496540 - 2.90034i) q^{85} +(4.80604 - 1.52427i) q^{86} +(-12.3711 + 6.04139i) q^{87} +(-2.07801 + 1.23846i) q^{88} +(5.07283 + 3.33990i) q^{89} +(-2.30219 + 6.08844i) q^{90} +(0.342130 - 0.101324i) q^{91} +(10.2595 - 17.0897i) q^{92} +(-0.157634 - 1.96673i) q^{93} +(14.2377 + 0.455646i) q^{94} +(22.9794 - 7.94077i) q^{95} +(-9.63220 - 5.99414i) q^{96} +(10.7263 - 0.549526i) q^{97} +(-12.5007 + 5.23661i) q^{98} +(0.498043 + 0.949510i) 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 $

$2$	−0.691522	+	2.06516i	−0.488980	+	1.46029i	0.360548	+	0.932741i	$0.382590\pi$
$2$	−0.691522	+	2.06516i	−0.488980	+	1.46029i	−0.849527	+	0.527545i	$0.823113\pi$
$3$	−1.31722	−	0.740034i	−0.760498	−	0.427259i	0.0605154	−	0.998167i	$-0.480726\pi$
$3$	−1.31722	−	0.740034i	−0.760498	−	0.427259i	−0.821014	+	0.570908i	$0.806591\pi$
$4$	−2.18995	−	1.65183i	−1.09497	−	0.825916i
$5$	−2.30250	+	3.47293i	−1.02971	+	1.55314i	−0.212198	+	0.977227i	$0.568062\pi$
$5$	−2.30250	+	3.47293i	−1.02971	+	1.55314i	−0.817511	+	0.575914i	$0.804646\pi$
$6$	2.43917	−	2.20852i	0.995788	−	0.901624i
$7$	0.363807	−	0.802796i	0.137506	−	0.303428i	−0.829359	−	0.558716i	$-0.811294\pi$
$7$	0.363807	−	0.802796i	0.137506	−	0.303428i	0.966865	+	0.255287i	$0.0821701\pi$
$8$	1.33432	−	0.915691i	0.471753	−	0.323746i
$9$	−0.373111	−	0.612595i	−0.124370	−	0.204198i
$10$	−5.57991	−	7.15662i	−1.76452	−	2.26312i
$11$	−1.49176	−	0.0955789i	−0.449784	−	0.0288181i	−0.162597	−	0.986693i	$-0.551987\pi$
$11$	−1.49176	−	0.0955789i	−0.449784	−	0.0288181i	−0.287187	+	0.957874i	$0.592720\pi$
$12$	1.66224	+	3.79647i	0.479846	+	1.09595i
$13$	0.264935	+	0.306111i	0.0734798	+	0.0849000i	0.791678	−	0.610939i	$-0.209208\pi$
$13$	0.264935	+	0.306111i	0.0734798	+	0.0849000i	−0.718198	+	0.695839i	$0.755033\pi$
$14$	1.40632	+	1.30647i	0.375854	+	0.349168i
$15$	5.60299	−	2.87069i	1.44669	−	0.741208i
$16$	−0.538977	−	1.88621i	−0.134744	−	0.471554i
$17$	−0.645980	+	0.285301i	−0.156673	+	0.0691956i	−0.480859	−	0.876798i	$-0.659675\pi$
$17$	−0.645980	+	0.285301i	−0.156673	+	0.0691956i	0.324186	+	0.945993i	$0.394909\pi$
$18$	1.52312	−	0.346910i	0.359003	−	0.0817674i
$19$	−4.63566	−	3.54334i	−1.06349	−	0.812898i	−0.0805395	−	0.996751i	$-0.525664\pi$
$19$	−4.63566	−	3.54334i	−1.06349	−	0.812898i	−0.982954	+	0.183853i	$0.941143\pi$
$20$	10.7791	−	3.80219i	2.41027	−	0.850196i
$21$	−1.07331	+	0.788231i	−0.234216	+	0.172006i
$22$	1.22897	−	3.01463i	0.262018	−	0.642722i
$23$	0.765731	+	7.22614i	0.159666	+	1.50675i	0.728924	+	0.684595i	$0.240021\pi$
$23$	0.765731	+	7.22614i	0.159666	+	1.50675i	−0.569258	+	0.822159i	$0.692769\pi$
$24$	−2.43524	+	0.218726i	−0.497091	+	0.0446473i
$25$	−4.81310	−	11.3873i	−0.962620	−	2.27746i
$26$	−0.815376	+	0.335450i	−0.159908	+	0.0657871i
$27$	0.197603	+	5.61284i	0.0380287	+	1.08019i
$28$	−2.12280	+	1.15714i	−0.401172	+	0.218678i
$29$	5.18004	−	7.49668i	0.961909	−	1.39210i	0.0423688	−	0.999102i	$-0.486510\pi$
$29$	5.18004	−	7.49668i	0.961909	−	1.39210i	0.919540	−	0.392997i	$-0.128562\pi$
$30$	2.05383	+	13.5562i	0.374976	+	2.47501i
$31$	0.728553	+	1.08378i	0.130852	+	0.194652i	0.889611	−	0.456720i	$-0.150976\pi$
$31$	0.728553	+	1.08378i	0.130852	+	0.194652i	−0.758759	+	0.651372i	$0.774194\pi$
$32$	7.50140	+	0.336201i	1.32607	+	0.0594325i
$33$	1.89425	+	1.22986i	0.329747	+	0.214090i
$34$	−0.142481	−	1.53134i	−0.0244353	−	0.262623i
$35$	1.95039	+	3.11191i	0.329676	+	0.526009i
$36$	−0.194810	+	1.95787i	−0.0324683	+	0.326312i
$37$	−3.37878	+	0.838088i	−0.555468	+	0.137781i	−0.508416	−	0.861112i	$-0.669769\pi$
$37$	−3.37878	+	0.838088i	−0.555468	+	0.137781i	−0.0470520	+	0.998892i	$0.514983\pi$
$38$	10.5232	−	7.12306i	1.70709	−	1.15551i
$39$	−0.122446	−	0.599278i	−0.0196070	−	0.0959612i
$40$	0.107859	+	6.74237i	0.0170541	+	1.06606i
$41$	3.64627	+	0.327498i	0.569451	+	0.0511466i	0.370450	−	0.928853i	$-0.379204\pi$
$41$	3.64627	+	0.327498i	0.569451	+	0.0511466i	0.199002	+	0.979999i	$0.436230\pi$
$42$	−0.885602	−	2.76163i	−0.136651	−	0.426129i
$43$	−1.36438	−	1.87034i	−0.208065	−	0.285225i	0.691168	−	0.722695i	$-0.257097\pi$
$43$	−1.36438	−	1.87034i	−0.208065	−	0.285225i	−0.899233	+	0.437470i	$0.855875\pi$
$44$	3.10901	+	2.67346i	0.468701	+	0.403039i
$45$	2.98659	+	0.114712i	0.445214	+	0.0171002i
$46$	−15.4526	−	3.41568i	−2.27836	−	0.503614i
$47$	−1.87742	−	6.26561i	−0.273850	−	0.913933i	−0.978825	−	0.204701i	$-0.934378\pi$
$47$	−1.87742	−	6.26561i	−0.273850	−	0.913933i	0.704975	−	0.709232i	$-0.250958\pi$
$48$	−0.685911	+	2.88342i	−0.0990027	+	0.416187i
$49$	4.10259	+	4.67937i	0.586085	+	0.668481i
$50$	26.8449	−	2.06522i	3.79645	−	0.292067i
$51$	1.06203	+	0.102243i	0.148714	+	0.0143169i
$52$	−0.0745505	−	1.10800i	−0.0103383	−	0.153652i
$53$	−6.30654	+	5.78403i	−0.866269	+	0.794498i	−0.979997	−	0.199014i	$-0.936226\pi$
$53$	−6.30654	+	5.78403i	−0.866269	+	0.794498i	0.113727	+	0.993512i	$0.463721\pi$
$54$	−11.7280	−	3.47332i	−1.59598	−	0.472659i
$55$	3.76673	−	4.96072i	0.507905	−	0.668903i
$56$	−0.249679	−	1.40432i	−0.0333647	−	0.187660i
$57$	3.48400	+	8.09791i	0.461467	+	1.07259i
$58$	11.8997	+	15.8817i	1.56251	+	2.08537i
$59$	−4.44325	−	0.341826i	−0.578461	−	0.0445019i	−0.215824	−	0.976432i	$-0.569244\pi$
$59$	−4.44325	−	0.341826i	−0.578461	−	0.0445019i	−0.362637	+	0.931930i	$0.618124\pi$
$60$	−17.0122	−	2.96854i	−2.19626	−	0.383236i
$61$	5.53208	+	4.69584i	0.708310	+	0.601240i	0.927226	−	0.374503i	$-0.122187\pi$
$61$	5.53208	+	4.69584i	0.708310	+	0.601240i	−0.218916	+	0.975744i	$0.570252\pi$
$62$	−2.74198	+	0.755120i	−0.348232	+	0.0959003i
$63$	−0.627529	+	0.0766660i	−0.0790613	+	0.00965901i
$64$	−4.47058	+	11.5982i	−0.558823	+	1.44977i
$65$	−1.67312	+	0.215280i	−0.207524	+	0.0267022i
$66$	−3.84976	+	3.06146i	−0.473873	+	0.376839i
$67$	6.71684	−	5.77586i	0.820593	−	0.705633i	−0.137994	−	0.990433i	$-0.544066\pi$
$67$	6.71684	−	5.77586i	0.820593	−	0.705633i	0.958587	+	0.284800i	$0.0919271\pi$
$68$	1.88593	+	0.442256i	0.228703	+	0.0536315i
$69$	4.33895	−	10.0851i	0.522348	−	1.21410i
$70$	−7.77532	+	1.87590i	−0.929328	+	0.224213i
$71$	−2.96848	+	2.42328i	−0.352294	+	0.287591i	−0.791963	−	0.610569i	$-0.790941\pi$
$71$	−2.96848	+	2.42328i	−0.352294	+	0.287591i	0.439669	+	0.898160i	$0.355096\pi$
$72$	−1.05880	−	0.475743i	−0.124780	−	0.0560668i
$73$	11.9983	+	8.57731i	1.40430	+	1.00390i	0.995840	+	0.0911201i	$0.0290447\pi$
$73$	11.9983	+	8.57731i	1.40430	+	1.00390i	0.408456	+	0.912778i	$0.366067\pi$
$74$	0.605718	−	7.55726i	0.0704133	−	0.878514i
$75$	−2.08708	+	18.5615i	−0.240995	+	2.14330i
$76$	4.29885	+	15.4171i	0.493112	+	1.76846i
$77$	−0.619444	+	1.16281i	−0.0705922	+	0.132515i
$78$	1.32228	+	0.161544i	0.149718	+	0.0182913i
$79$	1.80489	−	0.267546i	0.203066	−	0.0301012i	−0.0443241	−	0.999017i	$-0.514113\pi$
$79$	1.80489	−	0.267546i	0.203066	−	0.0301012i	0.247390	+	0.968916i	$0.420427\pi$
$80$	7.79168	+	2.47118i	0.871136	+	0.276286i
$81$	2.90608	−	5.62763i	0.322898	−	0.625293i
$82$	−3.19781	+	7.30364i	−0.353139	+	0.806552i
$83$	7.05251	−	2.18718i	0.774113	−	0.240074i	0.116258	−	0.993219i	$-0.462910\pi$
$83$	7.05251	−	2.18718i	0.774113	−	0.240074i	0.657855	+	0.753145i	$0.271464\pi$
$84$	3.65252	+	0.0467428i	0.398523	+	0.00510006i
$85$	0.496540	−	2.90034i	0.0538573	−	0.314587i
$86$	4.80604	−	1.52427i	0.518249	−	0.164366i
$87$	−12.3711	+	6.04139i	−1.32632	+	0.647705i
$88$	−2.07801	+	1.23846i	−0.221517	+	0.132021i
$89$	5.07283	+	3.33990i	0.537719	+	0.354029i	0.789495	−	0.613757i	$-0.210342\pi$
$89$	5.07283	+	3.33990i	0.537719	+	0.354029i	−0.251776	+	0.967786i	$0.581015\pi$
$90$	−2.30219	+	6.08844i	−0.242672	+	0.641778i
$91$	0.342130	−	0.101324i	0.0358650	−	0.0106216i
$92$	10.2595	−	17.0897i	1.06962	−	1.78173i
$93$	−0.157634	−	1.96673i	−0.0163459	−	0.203940i
$94$	14.2377	+	0.455646i	1.46851	+	0.0469963i
$95$	22.9794	−	7.94077i	2.35763	−	0.814705i
$96$	−9.63220	−	5.99414i	−0.983083	−	0.611774i
$97$	10.7263	−	0.549526i	1.08909	−	0.0557959i	0.501656	−	0.865067i	$-0.332724\pi$
$97$	10.7263	−	0.549526i	1.08909	−	0.0557959i	0.587435	+	0.809271i	$0.300138\pi$
$98$	−12.5007	+	5.23661i	−1.26276	+	0.528977i
$99$	0.498043	+	0.949510i	0.0500552	+	0.0954293i
$100$	−8.26949	+	32.8881i	−0.826949	+	3.28881i
$101$	5.63911	+	4.08604i	0.561112	+	0.406576i	0.830964	−	0.556326i	$-0.187789\pi$
$101$	5.63911	+	4.08604i	0.561112	+	0.406576i	−0.269852	+	0.962902i	$0.586975\pi$
$102$	−0.945565	+	2.12256i	−0.0936249	+	0.210164i
$103$	−4.10279	−	1.59654i	−0.404260	−	0.157312i	0.151882	−	0.988399i	$-0.451467\pi$
$103$	−4.10279	−	1.59654i	−0.404260	−	0.157312i	−0.556142	+	0.831087i	$0.687719\pi$
$104$	0.633811	+	0.165851i	0.0621503	+	0.0162630i
$105$	−0.266173	−	5.54243i	−0.0259758	−	0.540886i
$106$	−7.58382	−	17.0238i	−0.736606	−	1.65349i
$107$	0.913116	−	4.32763i	0.0882743	−	0.418368i	−0.911698	−	0.410862i	$-0.865228\pi$
$107$	0.913116	−	4.32763i	0.0882743	−	0.418368i	0.999972	−	0.00750617i	$-0.00238931\pi$
$108$	8.83873	−	12.6182i	0.850507	−	1.21419i
$109$	−8.25526	−	9.78867i	−0.790711	−	0.937584i	0.208471	−	0.978029i	$-0.433151\pi$
$109$	−8.25526	−	9.78867i	−0.790711	−	0.937584i	−0.999182	+	0.0404440i	$0.987123\pi$
$110$	7.63988	+	11.2093i	0.728434	+	1.06877i
$111$	5.07082	+	1.39646i	0.481301	+	0.132547i
$112$	−1.71033	−	0.253529i	−0.161611	−	0.0239562i
$113$	3.99452	+	1.95072i	0.375773	+	0.183508i	0.617005	−	0.786959i	$-0.288346\pi$
$113$	3.99452	+	1.95072i	0.375773	+	0.183508i	−0.241232	+	0.970467i	$0.577551\pi$
$114$	−19.1327	+	1.59511i	−1.79194	+	0.149396i
$115$	−26.8589	−	13.9788i	−2.50461	−	1.30353i
$116$	−23.7273	+	7.86080i	−2.20302	+	0.729857i
$117$	0.0886719	−	0.276512i	0.00819772	−	0.0255635i
$118$	3.77853	−	8.93961i	0.347841	−	0.822958i
$119$	−0.00597354	+	0.622384i	−0.000547593	+	0.0570539i
$120$	4.84751	−	8.96102i	0.442515	−	0.818025i
$121$	−8.69383	−	1.11864i	−0.790348	−	0.101694i
$122$	−13.5232	+	8.17732i	−1.22433	+	0.740340i
$123$	−4.56058	−	3.12975i	−0.411214	−	0.282200i
$124$	0.194723	−	3.57686i	0.0174867	−	0.321212i
$125$	30.1528	+	5.66003i	2.69695	+	0.506249i
$126$	0.275623	−	1.34896i	0.0245545	−	0.120175i
$127$	−4.42839	−	10.6669i	−0.392956	−	0.946537i	−0.989576	−	0.144013i	$-0.953999\pi$
$127$	−4.42839	−	10.6669i	−0.392956	−	0.946537i	0.596620	−	0.802524i	$-0.296510\pi$
$128$	−9.28787	−	7.68159i	−0.820939	−	0.678963i
$129$	0.413069	+	3.47334i	0.0363687	+	0.305811i
$130$	0.712409	−	3.60411i	0.0624824	−	0.316102i
$131$	−15.9024	−	8.14758i	−1.38940	−	0.711858i	−0.409679	−	0.912230i	$-0.634359\pi$
$131$	−15.9024	−	8.14758i	−1.38940	−	0.711858i	−0.979720	+	0.200372i	$0.935785\pi$
$132$	−2.11680	−	5.82231i	−0.184244	−	0.506767i
$133$	−4.53106	+	2.43240i	−0.392893	+	0.210916i
$134$	7.28320	+	17.8655i	0.629173	+	1.54334i
$135$	−19.9480	−	12.2373i	−1.71685	−	1.05322i
$136$	−0.600696	+	0.972200i	−0.0515092	+	0.0833654i
$137$	−2.34834	−	4.14878i	−0.200632	−	0.354454i	0.751706	−	0.659498i	$-0.229231\pi$
$137$	−2.34834	−	4.14878i	−0.200632	−	0.354454i	−0.952338	+	0.305044i	$0.901329\pi$
$138$	17.8268	+	15.9347i	1.51752	+	1.35645i
$139$	1.15063	−	2.19365i	0.0975949	−	0.186063i	−0.831873	−	0.554966i	$-0.812731\pi$
$139$	1.15063	−	2.19365i	0.0975949	−	0.186063i	0.929468	+	0.368904i	$0.120267\pi$
$140$	0.869106	−	10.0366i	0.0734528	−	0.848251i
$141$	−2.16379	+	9.64255i	−0.182224	+	0.812049i
$142$	−2.95169	−	7.80613i	−0.247700	−	0.655075i
$143$	−0.365963	−	0.481968i	−0.0306034	−	0.0403042i
$144$	−0.954388	+	1.03394i	−0.0795323	+	0.0861619i
$145$	14.1084	+	35.2510i	1.17164	+	2.92744i
$146$	−26.0106	+	18.8470i	−2.15265	+	1.55979i
$147$	−1.94113	−	9.19983i	−0.160102	−	0.758789i
$148$	8.78374	+	3.74581i	0.722019	+	0.307903i
$149$	−2.74542	−	10.6306i	−0.224914	−	0.870890i	−0.977247	−	0.212107i	$-0.931968\pi$
$149$	−2.74542	−	10.6306i	−0.224914	−	0.870890i	0.752333	−	0.658783i	$-0.228929\pi$
$150$	−36.8891	−	17.1458i	−3.01198	−	1.39995i
$151$	5.22217	−	1.87972i	0.424974	−	0.152969i	−0.117441	−	0.993080i	$-0.537469\pi$
$151$	5.22217	−	1.87972i	0.424974	−	0.152969i	0.542415	+	0.840110i	$0.317510\pi$
$152$	−9.43005	−	0.483117i	−0.764878	−	0.0391859i
$153$	0.415796	+	0.289275i	0.0336151	+	0.0233865i
$154$	−1.97303	−	2.08336i	−0.158991	−	0.167882i
$155$	−5.44137	+	0.0348163i	−0.437061	+	0.00279651i
$156$	−0.721756	+	1.51465i	−0.0577867	+	0.121269i
$157$	−16.1112	−	17.4542i	−1.28582	−	1.39300i	−0.877078	−	0.480347i	$-0.840511\pi$
$157$	−16.1112	−	17.4542i	−1.28582	−	1.39300i	−0.408738	−	0.912652i	$-0.634031\pi$
$158$	−0.695597	+	3.91239i	−0.0553388	+	0.311253i
$159$	12.5875	−	2.95180i	0.998253	−	0.234093i
$160$	−18.4396	+	25.2777i	−1.45778	+	1.99838i
$161$	6.07969	+	2.01419i	0.479147	+	0.158740i
$162$	9.61232	+	9.89315i	0.755215	+	0.777279i
$163$	−11.1603	+	2.84417i	−0.874139	+	0.222772i	−0.657477	−	0.753474i	$-0.728376\pi$
$163$	−11.1603	+	2.84417i	−0.874139	+	0.222772i	−0.216662	+	0.976247i	$0.569517\pi$
$164$	−7.44417	−	6.74023i	−0.581292	−	0.526323i
$165$	−8.63272	+	3.74686i	−0.672056	+	0.291693i
$166$	−0.360093	+	16.0770i	−0.0279486	+	1.24782i
$167$	−4.11646	−	22.3233i	−0.318541	−	1.72743i	−0.629494	−	0.777005i	$-0.716738\pi$
$167$	−4.11646	−	22.3233i	−0.318541	−	1.72743i	0.310953	−	0.950425i	$-0.399352\pi$
$168$	−0.710362	+	2.03457i	−0.0548056	+	0.156971i
$169$	1.84155	−	12.7033i	0.141658	−	0.977178i
$170$	5.64629	+	3.03108i	0.433051	+	0.232474i
$171$	−0.441017	+	4.16184i	−0.0337254	+	0.318264i
$172$	−0.101577	+	6.34968i	−0.00774520	+	0.484158i
$173$	21.2829	−	3.99504i	1.61811	−	0.303737i	0.704305	−	0.709897i	$-0.251259\pi$
$173$	21.2829	−	3.99504i	1.61811	−	0.303737i	0.913802	+	0.406160i	$0.133132\pi$
$174$	−3.92155	−	29.7259i	−0.297292	−	2.25352i
$175$	−10.8927	−	0.278843i	−0.823413	−	0.0210786i
$176$	0.623745	+	2.86530i	0.0470165	+	0.215980i
$177$	5.59978	+	3.73841i	0.420905	+	0.280996i
$178$	−10.4054	+	8.16657i	−0.779917	+	0.612111i
$179$	−11.8424	−	5.68965i	−0.885140	−	0.425265i	−0.0653053	−	0.997865i	$-0.520802\pi$
$179$	−11.8424	−	5.68965i	−0.885140	−	0.425265i	−0.819834	+	0.572601i	$0.805935\pi$
$180$	−6.35099	−	5.18455i	−0.473375	−	0.386434i
$181$	−6.01872	−	12.0304i	−0.447368	−	0.894214i	−0.998222	−	0.0596123i	$-0.981014\pi$
$181$	−6.01872	−	12.0304i	−0.447368	−	0.894214i	0.550854	−	0.834602i	$-0.314302\pi$
$182$	−0.0273413	+	0.776619i	−0.00202667	+	0.0575669i
$183$	−3.81189	−	10.2794i	−0.281783	−	0.759874i
$184$	7.63864	+	8.94080i	0.563128	+	0.659124i
$185$	4.86902	−	13.6640i	0.357977	−	1.00459i
$186$	4.17061	+	1.03450i	0.305804	+	0.0758530i
$187$	0.990919	−	0.363859i	0.0724631	−	0.0266080i
$188$	−6.23829	+	16.8225i	−0.454974	+	1.22691i
$189$	4.57785	+	1.88335i	0.332990	+	0.136994i
$190$	0.508178	+	52.9472i	0.0368671	+	3.84119i
$191$	−3.96899	−	2.09806i	−0.287186	−	0.151810i	0.317537	−	0.948246i	$-0.397144\pi$
$191$	−3.96899	−	2.09806i	−0.287186	−	0.151810i	−0.604724	+	0.796435i	$0.706716\pi$
$192$	14.4718	−	11.9690i	1.04441	−	0.863788i
$193$	10.1661	+	9.68962i	0.731774	+	0.697474i	0.961200	−	0.275852i	$-0.0889600\pi$
$193$	10.1661	+	9.68962i	0.731774	+	0.697474i	−0.229427	+	0.973326i	$0.573685\pi$
$194$	−6.28262	+	22.5315i	−0.451066	+	1.61767i
$195$	2.36318	+	0.954591i	0.169231	+	0.0683597i
$196$	−1.25494	−	17.0244i	−0.0896384	−	1.21603i
$197$	18.3444	−	4.92585i	1.30698	−	0.350952i	0.462540	−	0.886598i	$-0.346938\pi$
$197$	18.3444	−	4.92585i	1.30698	−	0.350952i	0.844442	+	0.535646i	$0.179932\pi$
$198$	−2.30529	+	0.371930i	−0.163830	+	0.0264319i
$199$	11.6544	−	18.0768i	0.826160	−	1.28143i	−0.130858	−	0.991401i	$-0.541773\pi$
$199$	11.6544	−	18.0768i	0.826160	−	1.28143i	0.957018	−	0.290028i	$-0.0936647\pi$
$200$	−16.8495	−	10.7870i	−1.19144	−	0.762756i
$201$	−13.1219	+	2.63739i	−0.925547	+	0.186027i
$202$	−12.3379	+	8.82005i	−0.868089	+	0.620577i
$203$	−4.13378	−	6.88585i	−0.290134	−	0.483292i
$204$	−2.15691	−	1.97820i	−0.151014	−	0.138502i
$205$	−9.53291	+	11.9092i	−0.665807	+	0.831772i
$206$	6.13427	−	7.36886i	0.427395	−	0.513413i
$207$	4.14099	−	3.16524i	0.287819	−	0.219999i
$208$	0.434597	−	0.664712i	0.0301339	−	0.0460895i
$209$	6.57664	+	5.72890i	0.454916	+	0.396277i
$210$	11.6300	+	3.28302i	0.802549	+	0.226550i
$211$	0.921193	+	5.59582i	0.0634175	+	0.385232i	0.999445	+	0.0333060i	$0.0106036\pi$
$211$	0.921193	+	5.59582i	0.0634175	+	0.385232i	−0.936028	+	0.351926i	$0.885527\pi$
$212$	23.3652	−	2.24940i	1.60473	−	0.154489i
$213$	5.70346	−	0.995225i	0.390795	−	0.0681917i
$214$	8.30580	+	4.87838i	0.567773	+	0.333479i
$215$	9.63704	−	0.431917i	0.657241	−	0.0294565i
$216$	5.40329	+	7.30837i	0.367647	+	0.497272i
$217$	1.13510	−	0.190594i	0.0770559	−	0.0129384i
$218$	25.9238	−	10.2793i	1.75578	−	0.696203i
$219$	−9.45694	−	20.1774i	−0.639040	−	1.36346i
$220$	−16.4432	+	4.64173i	−1.10860	+	0.312945i
$221$	−0.258477	−	0.122155i	−0.0173870	−	0.00821707i
$222$	−6.39050	+	9.50634i	−0.428902	+	0.638024i
$223$	12.8515	−	17.3827i	0.860602	−	1.16403i	−0.124528	−	0.992216i	$-0.539742\pi$
$223$	12.8515	−	17.3827i	0.860602	−	1.16403i	0.985129	−	0.171815i	$-0.0549631\pi$
$224$	2.99896	−	5.89978i	0.200376	−	0.394196i
$225$	−5.17999	+	7.19722i	−0.345333	+	0.479815i
$226$	−6.79084	+	6.90034i	−0.451720	+	0.459004i
$227$	6.47419	+	10.9425i	0.429707	+	0.726277i	0.995135	−	0.0985208i	$-0.0314111\pi$
$227$	6.47419	+	10.9425i	0.429707	+	0.726277i	−0.565428	+	0.824798i	$0.691289\pi$
$228$	5.74662	−	23.4890i	0.380579	−	1.55560i
$229$	1.28588	−	5.90698i	0.0849736	−	0.390344i	−0.914939	−	0.403593i	$-0.867761\pi$
$229$	1.28588	−	5.90698i	0.0849736	−	0.390344i	0.999912	+	0.0132489i	$0.00421736\pi$
$230$	47.4420	−	45.8012i	3.12824	−	3.02004i
$231$	1.67647	−	1.07327i	0.110303	−	0.0706160i
$232$	0.0471761	−	14.7463i	0.00309726	−	0.968140i
$233$	2.10190	−	1.28943i	0.137700	−	0.0844737i	−0.452349	−	0.891841i	$-0.649414\pi$
$233$	2.10190	−	1.28943i	0.137700	−	0.0844737i	0.590049	+	0.807367i	$0.299108\pi$
$234$	0.509721	+	0.374335i	0.0333215	+	0.0244711i
$235$	26.0828	+	7.90642i	1.70145	+	0.515758i
$236$	9.16585	+	8.08808i	0.596646	+	0.526489i
$237$	−2.57543	−	0.983263i	−0.167292	−	0.0638698i
$238$	−1.28119	−	0.442729i	−0.0830472	−	0.0286978i
$239$	4.75330	+	5.86089i	0.307466	+	0.379109i	0.906922	−	0.421298i	$-0.138425\pi$
$239$	4.75330	+	5.86089i	0.307466	+	0.379109i	−0.599457	+	0.800407i	$0.704617\pi$
$240$	−8.43462	−	9.02120i	−0.544452	−	0.582316i
$241$	15.5598	+	0.0995584i	1.00229	+	0.00641312i	0.506684	−	0.862132i	$-0.330871\pi$
$241$	15.5598	+	0.0995584i	1.00229	+	0.00641312i	0.495610	+	0.868545i	$0.334945\pi$
$242$	8.32213	−	17.1805i	0.534967	−	1.10441i
$243$	6.08010	−	4.00308i	0.390039	−	0.256797i
$244$	−4.35823	−	19.4217i	−0.279007	−	1.24335i
$245$	−25.6973	+	3.47376i	−1.64174	+	0.221931i
$246$	9.61717	−	7.25402i	0.613168	−	0.462500i
$247$	−0.143493	−	2.35778i	−0.00913025	−	0.150022i
$248$	1.96453	+	0.778974i	0.124748	+	0.0494649i
$249$	−10.9083	−	2.33809i	−0.691286	−	0.148171i
$250$	−32.5402	+	58.3562i	−2.05802	+	3.69077i
$251$	−6.31177	+	21.0646i	−0.398395	+	1.32959i	0.490486	+	0.871449i	$0.336819\pi$
$251$	−6.31177	+	21.0646i	−0.398395	+	1.32959i	−0.888881	+	0.458137i	$0.848517\pi$
$252$	1.50090	+	0.868679i	0.0945476	+	0.0547216i
$253$	−0.451624	−	10.8529i	−0.0283934	−	0.682315i
$254$	25.0912	−	1.76889i	1.57436	−	0.110990i
$255$	−2.80041	+	3.45294i	−0.175368	+	0.216232i
$256$	1.17971	−	0.734138i	0.0737321	−	0.0458836i
$257$	−22.8821	+	15.9194i	−1.42735	+	0.993027i	−0.431489	+	0.902118i	$0.642012\pi$
$257$	−22.8821	+	15.9194i	−1.42735	+	0.993027i	−0.995859	+	0.0909086i	$0.971023\pi$
$258$	−7.45864	−	1.54884i	−0.464354	−	0.0964266i
$259$	−0.556409	+	3.01737i	−0.0345735	+	0.187490i
$260$	4.01965	+	2.29225i	0.249288	+	0.142160i
$261$	−6.52516	−	0.376169i	−0.403897	−	0.0232843i
$262$	27.8229	−	27.2067i	1.71890	−	1.68083i
$263$	−2.02831	−	8.29063i	−0.125071	−	0.511222i	−0.999653	−	0.0263441i	$-0.991613\pi$
$263$	−2.02831	−	8.29063i	−0.125071	−	0.511222i	0.874582	−	0.484878i	$-0.161136\pi$
$264$	3.65371	−	0.0935313i	0.224870	−	0.00575645i
$265$	−5.56673	−	35.2199i	−0.341962	−	2.16354i
$266$	−1.88995	−	11.0394i	−0.115880	−	0.676869i
$267$	−4.21041	−	8.15346i	−0.257673	−	0.498984i
$268$	−24.2503	+	1.55374i	−1.48132	+	0.0949098i
$269$	−17.3355	−	19.5193i	−1.05697	−	1.19011i	−0.981201	−	0.192989i	$-0.938182\pi$
$269$	−17.3355	−	19.5193i	−1.05697	−	1.19011i	−0.0757655	−	0.997126i	$-0.524140\pi$
$270$	39.0664	−	32.7333i	2.37750	−	1.99208i
$271$	26.1892	−	0.502766i	1.59088	−	0.0305409i	0.783813	−	0.620997i	$-0.213272\pi$
$271$	26.1892	−	0.502766i	1.59088	−	0.0305409i	0.807070	+	0.590456i	$0.201052\pi$
$272$	0.886306	+	1.06469i	0.0537402	+	0.0645561i
$273$	−0.525644	−	0.119722i	−0.0318134	−	0.00724591i
$274$	10.1918	−	1.98071i	0.615709	−	0.119659i
$275$	6.09163	+	17.4472i	0.367339	+	1.05211i
$276$	−26.1610	+	14.9186i	−1.57471	+	0.897996i
$277$	−9.87488	+	4.90088i	−0.593324	+	0.294466i	−0.716132	−	0.697965i	$-0.754089\pi$
$277$	−9.87488	+	4.90088i	−0.593324	+	0.294466i	0.122808	+	0.992430i	$0.460810\pi$
$278$	3.73454	+	3.89318i	0.223983	+	0.233497i
$279$	0.392085	−	0.850677i	0.0234735	−	0.0509287i
$280$	5.45199	+	2.36633i	0.325819	+	0.141415i
$281$	−0.900952	−	1.98809i	−0.0537463	−	0.118599i	0.882031	−	0.471192i	$-0.156176\pi$
$281$	−0.900952	−	1.98809i	−0.0537463	−	0.118599i	−0.935777	+	0.352592i	$0.885300\pi$
$282$	−18.4171	−	11.1366i	−1.09672	−	0.663175i
$283$	11.1020	+	8.82866i	0.659944	+	0.524809i	0.894372	−	0.447324i	$-0.147623\pi$
$283$	11.1020	+	8.82866i	0.659944	+	0.524809i	−0.234428	+	0.972134i	$0.575322\pi$
$284$	10.5037	−	0.403436i	0.623279	−	0.0239395i
$285$	−36.1454	−	6.54577i	−2.14107	−	0.387738i
$286$	1.24841	−	0.422480i	0.0738201	−	0.0249818i
$287$	1.58945	−	2.80806i	0.0938223	−	0.165755i
$288$	−2.59290	−	4.72076i	−0.152788	−	0.278173i
$289$	−11.1146	+	12.1967i	−0.653798	+	0.717454i
$290$	−82.5551	+	4.75921i	−4.84780	+	0.279470i
$291$	−14.5356	−	7.21398i	−0.852091	−	0.422891i
$292$	−12.1074	−	38.6031i	−0.708533	−	2.25907i
$293$	−21.3509	+	5.58695i	−1.24733	+	0.326393i	−0.817191	−	0.576367i	$-0.804470\pi$
$293$	−21.3509	+	5.58695i	−1.24733	+	0.326393i	−0.430143	+	0.902761i	$0.641537\pi$
$294$	20.3414	+	2.35314i	1.18633	+	0.137238i
$295$	11.4177	−	14.6440i	0.664765	−	0.852608i
$296$	−3.74094	+	4.21219i	−0.217438	+	0.244829i
$297$	0.241692	−	8.39192i	0.0140244	−	0.486949i
$298$	23.8523	+	1.68155i	1.38173	+	0.0974094i
$299$	−2.00913	+	2.14886i	−0.116191	+	0.124272i
$300$	35.2311	−	37.2012i	2.03407	−	2.14781i
$301$	−1.99787	+	0.414873i	−0.115155	+	0.0239129i
$302$	0.270668	+	12.0845i	0.0155752	+	0.695383i
$303$	−4.40415	−	9.55535i	−0.253012	−	0.548941i
$304$	−4.18499	+	10.6536i	−0.240026	+	0.611028i
$305$	−29.0459	+	8.40034i	−1.66316	+	0.481002i
$306$	−0.884930	+	0.658643i	−0.0505881	+	0.0376521i
$307$	−16.1656	+	16.0111i	−0.922617	+	0.913804i	−0.996511	−	0.0834619i	$-0.973402\pi$
$307$	−16.1656	+	16.0111i	−0.922617	+	0.913804i	0.0738941	+	0.997266i	$0.476457\pi$
$308$	3.27732	−	1.52328i	0.186743	−	0.0867968i
$309$	4.22279	+	5.13920i	0.240226	+	0.292359i
$310$	3.69093	−	11.2614i	0.209631	−	0.639602i
$311$	11.6129	−	7.75279i	0.658508	−	0.439620i	−0.180621	−	0.983553i	$-0.557811\pi$
$311$	11.6129	−	7.75279i	0.658508	−	0.439620i	0.839129	+	0.543933i	$0.183065\pi$
$312$	−0.712135	−	0.687505i	−0.0403167	−	0.0389223i
$313$	−3.92845	−	0.789586i	−0.222049	−	0.0446300i	0.0847588	−	0.996401i	$-0.472988\pi$
$313$	−3.92845	−	0.789586i	−0.222049	−	0.0446300i	−0.306808	+	0.951771i	$0.599261\pi$
$314$	47.1870	−	21.2022i	2.66291	−	1.19651i
$315$	1.17863	−	2.35589i	0.0664083	−	0.132739i
$316$	−4.39456	−	2.39546i	−0.247213	−	0.134755i
$317$	13.0700	−	6.59116i	0.734083	−	0.370197i	−0.0434357	−	0.999056i	$-0.513830\pi$
$317$	13.0700	−	6.59116i	0.734083	−	0.370197i	0.777519	+	0.628860i	$0.216478\pi$
$318$	−2.60859	+	28.0364i	−0.146283	+	1.57220i
$319$	−8.44392	+	10.6882i	−0.472769	+	0.598424i
$320$	−29.9861	−	42.2308i	−1.67628	−	2.36077i
$321$	−4.40537	+	5.02472i	−0.245884	+	0.280452i
$322$	−8.36386	+	11.1626i	−0.466099	+	0.622070i
$323$	4.00546	+	0.966370i	0.222870	+	0.0537703i
$324$	−15.6601	+	7.52387i	−0.870005	+	0.417993i
$325$	2.21063	−	4.49025i	0.122623	−	0.249074i
$326$	1.84392	−	25.0145i	0.102125	−	1.38542i
$327$	3.63006	+	19.0030i	0.200743	+	1.05087i
$328$	5.16517	−	2.90187i	0.285199	−	0.160229i
$329$	−5.71302	−	0.772286i	−0.314969	−	0.0425775i
$330$	−1.76814	−	20.4189i	−0.0973331	−	1.12403i
$331$	−13.1583	−	5.51210i	−0.723246	−	0.302972i	−0.00618282	−	0.999981i	$-0.501968\pi$
$331$	−13.1583	−	5.51210i	−0.723246	−	0.302972i	−0.717063	+	0.697009i	$0.754514\pi$
$332$	−19.0575	−	6.85974i	−1.04592	−	0.376477i
$333$	1.77407	+	1.75712i	0.0972184	+	0.0962898i
$334$	48.9477	+	6.93594i	2.67830	+	0.379518i
$335$	4.59361	+	36.6260i	0.250976	+	2.00109i
$336$	2.06526	+	1.59966i	0.112669	+	0.0872683i
$337$	6.73973	−	10.7535i	0.367137	−	0.585779i	−0.611533	−	0.791219i	$-0.709447\pi$
$337$	6.73973	−	10.7535i	0.367137	−	0.585779i	0.978670	+	0.205439i	$0.0658624\pi$
$338$	24.9609	+	12.5877i	1.35769	+	0.684681i
$339$	−3.81807	−	5.52561i	−0.207369	−	0.300110i
$340$	−5.87828	+	5.53141i	−0.318795	+	0.299983i
$341$	−0.983243	−	1.68637i	−0.0532456	−	0.0913223i
$342$	−8.28988	−	3.78878i	−0.448265	−	0.204874i
$343$	11.1535	−	3.38094i	0.602233	−	0.182554i
$344$	−3.53317	−	1.24629i	−0.190496	−	0.0671953i
$345$	25.0344	+	38.2898i	1.34780	+	2.06145i
$346$	−6.46720	+	46.7151i	−0.347679	+	2.51142i
$347$	18.5580	+	8.19624i	0.996245	+	0.439997i	0.836977	−	0.547238i	$-0.184321\pi$
$347$	18.5580	+	8.19624i	0.996245	+	0.439997i	0.159268	+	0.987235i	$0.449087\pi$
$348$	37.0714	+	7.20457i	1.98723	+	0.386206i
$349$	1.52355	+	10.5097i	0.0815536	+	0.562571i	0.989616	+	0.143736i	$0.0459117\pi$
$349$	1.52355	+	10.5097i	0.0815536	+	0.562571i	−0.908062	+	0.418835i	$0.862439\pi$
$350$	8.10842	−	22.3024i	0.433413	−	1.19211i
$351$	−1.66580	+	1.54753i	−0.0889139	+	0.0826009i
$352$	−11.1582	−	1.21851i	−0.594733	−	0.0649467i
$353$	16.0189	+	16.0702i	0.852599	+	0.855330i	0.990836	−	0.135069i	$-0.0431255\pi$
$353$	16.0189	+	16.0702i	0.852599	+	0.855330i	−0.138238	+	0.990399i	$0.544144\pi$
$354$	−11.5928	+	8.97922i	−0.616149	+	0.477240i
$355$	−1.58096	−	15.8889i	−0.0839088	−	0.843296i
$356$	−5.59229	−	15.6937i	−0.296391	−	0.831763i
$357$	0.468454	−	0.815397i	0.0247932	−	0.0431554i
$358$	19.9393	−	20.5218i	1.05382	−	1.08461i
$359$	20.8294	−	10.8408i	1.09933	−	0.572153i	0.187315	−	0.982300i	$-0.440021\pi$
$359$	20.8294	−	10.8408i	1.09933	−	0.572153i	0.912020	+	0.410147i	$0.134522\pi$
$360$	4.09010	−	2.58173i	0.215567	−	0.136069i
$361$	3.94804	+	14.5173i	0.207792	+	0.764070i
$362$	29.0068	−	4.11029i	1.52456	−	0.216032i
$363$	10.6239	+	7.90722i	0.557609	+	0.415022i
$364$	−0.916617	−	0.343248i	−0.0480438	−	0.0179911i
$365$	−57.4145	+	21.9200i	−3.00521	+	1.14735i
$366$	23.8645	−	0.763729i	1.24742	−	0.0399208i
$367$	−2.71266	−	24.1251i	−0.141600	−	1.25932i	−0.839593	−	0.543216i	$-0.817206\pi$
$367$	−2.71266	−	24.1251i	−0.141600	−	1.25932i	0.697993	−	0.716105i	$-0.254077\pi$
$368$	13.2173	−	5.33906i	0.689001	−	0.278318i
$369$	−1.15984	−	2.35588i	−0.0603788	−	0.122642i
$370$	24.8512	+	19.5042i	1.29195	+	1.01398i
$371$	2.34904	+	7.16713i	0.121956	+	0.372099i
$372$	−2.90350	+	4.56742i	−0.150539	+	0.236810i
$373$	0.0365456	−	0.878220i	0.00189226	−	0.0454725i	−0.997930	−	0.0643028i	$-0.979518\pi$
$373$	0.0365456	−	0.878220i	0.00189226	−	0.0454725i	0.999823	+	0.0188303i	$0.00599423\pi$
$374$	0.0661842	+	2.29802i	0.00342230	+	0.118828i
$375$	−35.5293	−	29.7696i	−1.83473	−	1.53730i
$376$	−8.24243	−	6.64118i	−0.425071	−	0.342493i
$377$	3.66719	−	0.400469i	0.188870	−	0.0206252i
$378$	−7.05510	+	8.15160i	−0.362875	+	0.419273i
$379$	0.807477	+	0.250422i	0.0414773	+	0.0128633i	0.316879	−	0.948466i	$-0.397365\pi$
$379$	0.807477	+	0.250422i	0.0414773	+	0.0128633i	−0.275402	+	0.961329i	$0.588811\pi$
$380$	−63.4405	−	20.5682i	−3.25443	−	1.05513i
$381$	−2.06073	+	17.3279i	−0.105574	+	0.887734i
$382$	7.07747	−	6.74573i	0.362115	−	0.345142i
$383$	−8.30666	−	15.5931i	−0.424450	−	0.796771i	0.575326	−	0.817924i	$-0.304875\pi$
$383$	−8.30666	−	15.5931i	−0.424450	−	0.796771i	−0.999776	+	0.0211531i	$0.993266\pi$
$384$	6.54954	+	16.9917i	0.334230	+	0.867104i
$385$	−2.61209	−	4.82866i	−0.133124	−	0.246091i
$386$	−27.0407	+	14.2940i	−1.37633	+	0.727548i
$387$	−0.636699	+	1.53366i	−0.0323652	+	0.0779601i
$388$	−24.3978	−	16.5146i	−1.23861	−	0.838403i
$389$	−4.27200	−	1.56865i	−0.216599	−	0.0795339i	0.234090	−	0.972215i	$-0.424789\pi$
$389$	−4.27200	−	1.56865i	−0.216599	−	0.0795339i	−0.450689	+	0.892681i	$0.648822\pi$
$390$	−3.60557	+	4.22021i	−0.182575	+	0.213699i
$391$	−2.55627	−	4.44947i	−0.129276	−	0.225020i
$392$	9.75902	+	2.48706i	0.492905	+	0.125616i
$393$	14.9175	+	22.5005i	0.752488	+	1.13500i
$394$	−2.51290	+	41.2903i	−0.126598	+	2.08018i
$395$	−3.22659	+	6.88427i	−0.162347	+	0.346385i
$396$	0.477742	−	2.90206i	0.0240074	−	0.145834i
$397$	−0.0825104	+	1.22630i	−0.00414108	+	0.0615463i	−0.999340	−	0.0363271i	$-0.988434\pi$
$397$	−0.0825104	+	1.22630i	−0.00414108	+	0.0615463i	0.995199	+	0.0978734i	$0.0312040\pi$
$398$	29.2721	+	36.5687i	1.46728	+	1.83302i
$399$	7.76847	+	0.149135i	0.388910	+	0.00746607i
$400$	−18.8848	+	15.2160i	−0.944239	+	0.760802i
$401$	3.62698	−	3.63860i	0.181123	−	0.181703i	−0.611824	−	0.790994i	$-0.709564\pi$
$401$	3.62698	−	3.63860i	0.181123	−	0.181703i	0.792947	+	0.609291i	$0.208546\pi$
$402$	3.62745	−	28.9226i	0.180921	−	1.44253i
$403$	−0.138737	+	0.510149i	−0.00691097	+	0.0254123i
$404$	−5.59991	−	18.2631i	−0.278606	−	0.908622i
$405$	12.8531	+	23.0502i	0.638676	+	1.14538i
$406$	17.0790	−	3.77517i	0.847614	−	0.187358i
$407$	5.12045	−	0.927291i	0.253811	−	0.0459641i
$408$	1.51071	−	0.836067i	0.0747913	−	0.0413915i
$409$	−12.3758	−	13.7565i	−0.611944	−	0.680216i	0.355099	−	0.934829i	$-0.384447\pi$
$409$	−12.3758	−	13.7565i	−0.611944	−	0.680216i	−0.967043	+	0.254613i	$0.918052\pi$
$410$	−18.0021	−	27.9224i	−0.889058	−	1.37899i
$411$	0.0230428	+	7.20271i	0.00113662	+	0.355284i
$412$	6.34769	+	10.2735i	0.312728	+	0.506137i
$413$	−1.89090	+	3.44266i	−0.0930450	+	0.169402i
$414$	3.67312	+	10.7406i	0.180524	+	0.527873i
$415$	−8.64247	+	29.5288i	−0.424242	+	1.44951i
$416$	1.88447	+	2.38533i	0.0923937	+	0.116951i
$417$	−3.13900	+	2.03802i	−0.153718	+	0.0998021i
$418$	−16.3790	+	9.62013i	−0.801122	+	0.470536i
$419$	−16.4816	+	13.9902i	−0.805179	+	0.683467i	−0.952135	−	0.305676i	$-0.901117\pi$
$419$	−16.4816	+	13.9902i	−0.805179	+	0.683467i	0.146957	+	0.989143i	$0.453052\pi$
$420$	−8.57226	+	12.5773i	−0.418284	+	0.613710i
$421$	−3.64913	+	0.374885i	−0.177848	+	0.0182708i	−0.190710	−	0.981646i	$-0.561079\pi$
$421$	−3.64913	+	0.374885i	−0.177848	+	0.0182708i	0.0128620	+	0.999917i	$0.495906\pi$
$422$	−12.1933	−	1.96723i	−0.593559	−	0.0957632i
$423$	−3.13780	+	3.48787i	−0.152565	+	0.169586i
$424$	−3.11854	+	13.4926i	−0.151450	+	0.655258i
$425$	6.35797	+	5.98280i	0.308407	+	0.290208i
$426$	−1.88877	+	12.4667i	−0.0915113	+	0.604016i
$427$	5.78240	−	2.73275i	0.279830	−	0.132247i
$428$	−9.14821	+	7.96899i	−0.442195	+	0.385195i
$429$	0.125382	+	0.905685i	0.00605350	+	0.0437269i
$430$	−5.77225	+	20.2007i	−0.278363	+	0.974163i
$431$	−1.07366	−	5.43170i	−0.0517164	−	0.261636i	0.946399	−	0.323000i	$-0.104691\pi$
$431$	−1.07366	−	5.43170i	−0.0517164	−	0.261636i	−0.998115	+	0.0613638i	$0.980455\pi$
$432$	10.4805	−	3.39791i	0.504244	−	0.163482i
$433$	38.2971	−	0.490103i	1.84044	−	0.0235529i	0.915214	−	0.402968i	$-0.132022\pi$
$433$	38.2971	−	0.490103i	1.84044	−	0.0235529i	0.925226	+	0.379415i	$0.123875\pi$
$434$	−0.391343	+	2.47597i	−0.0187850	+	0.118850i
$435$	7.50304	−	56.8741i	0.359743	−	2.72690i
$436$	1.90936	+	35.0730i	0.0914420	+	1.67969i
$437$	22.0550	−	36.2112i	1.05503	−	1.73221i
$438$	48.2091	−	5.57694i	2.30352	−	0.266477i
$439$	−0.874946	+	0.340471i	−0.0417589	+	0.0162498i	−0.383433	−	0.923568i	$-0.625258\pi$
$439$	−0.874946	+	0.340471i	−0.0417589	+	0.0162498i	0.341675	+	0.939818i	$0.389006\pi$
$440$	0.483527	−	10.0683i	0.0230513	−	0.479989i
$441$	1.33584	−	4.25915i	0.0636112	−	0.202817i
$442$	0.431012	−	0.449321i	0.0205012	−	0.0213720i
$443$	−9.97343	−	25.3891i	−0.473852	−	1.20627i	−0.945830	−	0.324664i	$-0.894749\pi$
$443$	−9.97343	−	25.3891i	−0.473852	−	1.20627i	0.471978	−	0.881611i	$-0.343540\pi$
$444$	−8.79811	−	11.4343i	−0.417540	−	0.542649i
$445$	−23.2794	+	9.92746i	−1.10355	+	0.470607i
$446$	27.0109	+	38.5609i	1.27900	+	1.82591i
$447$	−4.25065	+	16.0345i	−0.201049	+	0.758407i
$448$	7.68455	+	7.80846i	0.363061	+	0.368915i
$449$	−33.8138	+	5.23366i	−1.59577	+	0.246992i	−0.888134	−	0.459585i	$-0.847998\pi$
$449$	−33.8138	+	5.23366i	−1.59577	+	0.246992i	−0.707637	+	0.706577i	$0.750239\pi$
$450$	−11.2813	−	15.6745i	−0.531805	−	0.738904i
$451$	−5.40807	−	0.837056i	−0.254656	−	0.0394154i
$452$	−5.52554	−	10.8703i	−0.259899	−	0.511294i
$453$	−8.26982	−	1.38858i	−0.388550	−	0.0652410i
$454$	−27.0749	+	5.80326i	−1.27069	+	0.272360i
$455$	−0.435864	+	1.42149i	−0.0204336	+	0.0666405i
$456$	12.0639	+	7.61493i	0.564946	+	0.356602i
$457$	12.6446	+	1.05419i	0.591490	+	0.0493131i	0.375085	−	0.926991i	$-0.377614\pi$
$457$	12.6446	+	1.05419i	0.591490	+	0.0493131i	0.216405	+	0.976304i	$0.430567\pi$
$458$	11.3096	+	6.74036i	0.528464	+	0.314956i
$459$	−1.72899	−	3.56940i	−0.0807025	−	0.166605i
$460$	35.7290	+	74.9794i	1.66587	+	3.49593i
$461$	−6.50694	+	16.2581i	−0.303058	+	0.757216i	0.696168	+	0.717879i	$0.254887\pi$
$461$	−6.50694	+	16.2581i	−0.303058	+	0.757216i	−0.999226	+	0.0393368i	$0.987475\pi$
$462$	1.05716	+	4.20435i	0.0491834	+	0.195604i
$463$	−0.630172	+	0.563285i	−0.0292866	+	0.0261781i	−0.680947	−	0.732333i	$-0.738431\pi$
$463$	−0.630172	+	0.563285i	−0.0292866	+	0.0261781i	0.651660	+	0.758511i	$0.274073\pi$
$464$	−16.9323	−	5.73012i	−0.786061	−	0.266014i
$465$	7.19326	+	3.98094i	0.333579	+	0.184612i
$466$	1.20937	+	5.23243i	0.0560231	+	0.242387i
$467$	11.6664	−	20.0092i	0.539856	−	0.925915i	−0.459433	−	0.888212i	$-0.651947\pi$
$467$	11.6664	−	20.0092i	0.539856	−	0.925915i	0.999289	−	0.0377021i	$-0.0120038\pi$
$468$	−0.650938	+	0.459075i	−0.0300896	+	0.0212208i
$469$	−2.19320	−	7.49355i	−0.101273	−	0.346020i
$470$	−34.3648	+	48.3975i	−1.58513	+	2.23241i
$471$	8.30535	+	34.9140i	0.382690	+	1.60875i
$472$	−6.24171	+	3.61253i	−0.287298	+	0.166280i
$473$	1.85656	+	2.92052i	0.0853649	+	0.134286i
$474$	3.81156	−	4.63872i	0.175071	−	0.213064i
$475$	−18.0373	+	69.8422i	−0.827606	+	3.20458i
$476$	1.04116	−	1.35312i	0.0477213	−	0.0620203i
$477$	5.89631	+	1.70527i	0.269974	+	0.0780788i
$478$	−15.3907	+	5.76338i	−0.703953	+	0.263611i
$479$	−6.17088	+	5.44528i	−0.281955	+	0.248801i	−0.790825	−	0.612042i	$-0.790348\pi$
$479$	−6.17088	+	5.44528i	−0.281955	+	0.248801i	0.508870	+	0.860843i	$0.330063\pi$
$480$	42.9954	−	19.6504i	1.96246	−	0.896915i
$481$	−1.15171	−	0.812243i	−0.0525133	−	0.0370351i
$482$	−10.9655	+	32.0645i	−0.499466	+	1.46050i
$483$	−6.51773	−	7.15231i	−0.296567	−	0.325442i
$484$	17.1912	+	16.8105i	0.781420	+	0.764114i
$485$	−22.7888	+	38.5170i	−1.03479	+	1.74896i
$486$	4.06245	+	15.3246i	0.184276	+	0.695137i
$487$	−15.9480	+	18.9103i	−0.722671	+	0.856906i	−0.994423	−	0.105461i	$-0.966368\pi$
$487$	−15.9480	+	18.9103i	−0.722671	+	0.856906i	0.271753	+	0.962367i	$0.412397\pi$
$488$	11.6815	+	1.20007i	0.528796	+	0.0543247i
$489$	16.8053	+	4.51258i	0.759963	+	0.204066i
$490$	10.5964	−	55.4712i	0.478697	−	2.50593i
$491$	−1.39060	−	4.15287i	−0.0627568	−	0.187416i	0.912230	−	0.409678i	$-0.134359\pi$
$491$	−1.39060	−	4.15287i	−0.0627568	−	0.187416i	−0.974987	+	0.222261i	$0.928656\pi$
$492$	4.81763	+	14.3873i	0.217195	+	0.648630i
$493$	−1.20739	+	6.32057i	−0.0543781	+	0.284664i
$494$	4.96842	+	1.33412i	0.223540	+	0.0600251i
$495$	−4.44432	−	0.456578i	−0.199757	−	0.0205216i
$496$	1.65156	−	1.95834i	0.0741573	−	0.0879320i
$497$	0.865449	+	3.26469i	0.0388207	+	0.146441i
$498$	12.3719	−	20.9105i	0.554396	−	0.937022i
$499$	−14.4985	−	14.1774i	−0.649043	−	0.634669i	0.298457	−	0.954423i	$-0.403528\pi$
$499$	−14.4985	−	14.1774i	−0.649043	−	0.634669i	−0.947501	+	0.319754i	$0.896400\pi$
$500$	−56.6837	−	62.2026i	−2.53497	−	2.78178i
$501$	−11.0977	+	32.4511i	−0.495810	+	1.44981i
$502$	−39.1370	−	27.6014i	−1.74677	−	1.23191i
$503$	−13.9029	+	6.35413i	−0.619900	+	0.283317i	−0.700747	−	0.713410i	$-0.747150\pi$
$503$	−13.9029	+	6.35413i	−0.619900	+	0.283317i	0.0808472	+	0.996727i	$0.474237\pi$
$504$	−0.767122	+	0.676920i	−0.0341703	+	0.0301524i
$505$	−27.1746	+	10.1761i	−1.20925	+	0.452831i
$506$	22.7252	+	6.57233i	1.01026	+	0.292176i
$507$	−11.8266	+	15.3703i	−0.525238	+	0.682618i
$508$	−7.92204	+	30.6750i	−0.351484	+	1.36098i
$509$	−5.54440	+	6.74762i	−0.245751	+	0.299083i	−0.880896	−	0.473311i	$-0.843059\pi$
$509$	−5.54440	+	6.74762i	−0.245751	+	0.299083i	0.635144	+	0.772394i	$0.280941\pi$
$510$	−5.19432	−	8.17106i	−0.230008	−	0.361821i
$511$	11.2509	−	6.51171i	0.497710	−	0.288061i
$512$	−4.87830	−	20.5074i	−0.215592	−	0.906306i
$513$	18.9722	−	26.7194i	0.837642	−	1.17969i
$514$	−17.0526	−	58.2638i	−0.752158	−	2.56991i
$515$	14.9913	−	10.5727i	0.660597	−	0.465887i
$516$	4.83278	−	8.28876i	0.212751	−	0.364892i
$517$	2.20181	+	9.52626i	0.0968353	+	0.418964i
$518$	−5.84658	−	3.23565i	−0.256884	−	0.142166i
$519$	−30.9907	−	10.4877i	−1.36034	−	0.460359i
$520$	−2.03534	+	1.81931i	−0.0892555	+	0.0797820i
$521$	7.74967	+	30.8207i	0.339519	+	1.35028i	0.865979	+	0.500081i	$0.166696\pi$
$521$	7.74967	+	30.8207i	0.339519	+	1.35028i	−0.526459	+	0.850200i	$0.676481\pi$
$522$	5.28914	−	13.2153i	0.231499	−	0.578420i
$523$	15.6914	+	32.9294i	0.686138	+	1.43990i	0.887699	+	0.460424i	$0.152303\pi$
$523$	15.6914	+	32.9294i	0.686138	+	1.43990i	−0.201561	+	0.979476i	$0.564602\pi$
$524$	21.3670	+	44.1109i	0.933422	+	1.92699i
$525$	14.1418	+	8.42829i	0.617198	+	0.367841i
$526$	18.5241	+	1.54437i	0.807688	+	0.0673377i
$527$	−0.779833	−	0.492241i	−0.0339700	−	0.0214424i
$528$	1.29881	−	4.23583i	0.0565235	−	0.184341i
$529$	−29.1415	+	6.24620i	−1.26702	+	0.271574i
$530$	76.5840	+	12.8592i	3.32660	+	0.558566i
$531$	1.44842	+	2.84945i	0.0628563	+	0.123656i
$532$	13.9407	+	2.15773i	0.604407	+	0.0935495i
$533$	0.865774	+	1.20293i	0.0375008	+	0.0521047i
$534$	19.7497	−	3.05685i	0.854655	−	0.132283i
$535$	12.9271	+	13.1356i	0.558888	+	0.567900i
$536$	3.67351	−	13.8574i	0.158671	−	0.598548i
$537$	11.3885	+	16.2583i	0.491449	+	0.701597i
$538$	52.2984	−	22.3025i	2.25474	−	0.961530i
$539$	−5.67286	−	7.37264i	−0.244347	−	0.317562i
$540$	23.4711	+	59.7498i	1.01003	+	2.57122i
$541$	−5.90987	+	6.16091i	−0.254085	+	0.264878i	−0.836443	−	0.548054i	$-0.815369\pi$
$541$	−5.90987	+	6.16091i	−0.254085	+	0.264878i	0.582358	+	0.812933i	$0.302130\pi$
$542$	−17.0721	+	54.4325i	−0.733311	+	2.33808i
$543$	−0.974936	+	20.3008i	−0.0418385	+	0.871190i
$544$	−4.94167	+	1.92297i	−0.211872	+	0.0824468i
$545$	53.0031	−	6.13152i	2.27040	−	0.262645i
$546$	0.610739	−	1.00275i	0.0261372	−	0.0429136i
$547$	−2.06186	−	37.8742i	−0.0881589	−	1.61939i	−0.628411	−	0.777882i	$-0.716294\pi$
$547$	−2.06186	−	37.8742i	−0.0881589	−	1.61939i	0.540252	−	0.841504i	$-0.318329\pi$
$548$	−1.71035	+	12.9647i	−0.0730625	+	0.553824i
$549$	0.812567	−	5.14099i	0.0346795	−	0.219412i
$550$	−40.2437	+	0.515016i	−1.71600	+	0.0219603i
$551$	−50.5762	+	16.3974i	−2.15462	+	0.698554i
$552$	−3.44528	−	17.4299i	−0.146641	−	0.741864i
$553$	0.441846	−	1.54629i	0.0187892	−	0.0657551i
$554$	−3.29239	−	23.7822i	−0.139880	−	1.01041i
$555$	−16.5254	+	14.3952i	−0.701463	+	0.611043i
$556$	−6.14335	+	2.90333i	−0.260536	+	0.123129i
$557$	−4.95420	+	32.6999i	−0.209916	+	1.38554i	0.600471	+	0.799646i	$0.294980\pi$
$557$	−4.95420	+	32.6999i	−0.209916	+	1.38554i	−0.810387	+	0.585894i	$0.800743\pi$
$558$	1.48565	+	1.39798i	0.0628924	+	0.0591812i
$559$	0.211061	−	0.913171i	0.00892695	−	0.0386230i
$560$	4.81852	−	5.35610i	0.203620	−	0.226336i
$561$	−1.57453	−	0.254030i	−0.0664766	−	0.0107252i
$562$	4.72874	−	0.485797i	0.199470	−	0.0204921i
$563$	−9.06852	+	13.3054i	−0.382193	+	0.560757i	−0.968399	−	0.249404i	$-0.919765\pi$
$563$	−9.06852	+	13.3054i	−0.382193	+	0.560757i	0.586207	+	0.810161i	$0.300621\pi$
$564$	20.6665	−	17.5425i	0.870215	−	0.738672i
$565$	−15.9721	+	9.38115i	−0.671951	+	0.394668i
$566$	−25.9098	+	16.8221i	−1.08907	+	0.707086i
$567$	−3.46059	−	4.38036i	−0.145331	−	0.183958i
$568$	−1.74192	+	5.95164i	−0.0730894	+	0.249725i
$569$	−6.64948	−	19.4439i	−0.278761	−	0.815129i	−0.993303	−	0.115537i	$-0.963141\pi$
$569$	−6.64948	−	19.4439i	−0.278761	−	0.815129i	0.714543	−	0.699592i	$-0.246635\pi$
$570$	38.5133	−	70.1193i	1.61315	−	2.93697i
$571$	−19.2157	−	31.0997i	−0.804150	−	1.30148i	−0.950024	−	0.312178i	$-0.898941\pi$
$571$	−19.2157	−	31.0997i	−0.804150	−	1.30148i	0.145874	−	0.989303i	$-0.453401\pi$
$572$	0.00531064	+	1.66000i	0.000222049	+	0.0694079i
$573$	3.67541	+	5.70080i	0.153542	+	0.238154i
$574$	4.69995	+	5.22430i	0.196172	+	0.218058i
$575$	78.6008	−	43.4998i	3.27788	−	1.81407i
$576$	8.77302	−	1.58875i	0.365542	−	0.0661981i
$577$	11.2503	−	2.48679i	0.468357	−	0.103527i	0.0246452	−	0.999696i	$-0.492154\pi$
$577$	11.2503	−	2.48679i	0.468357	−	0.103527i	0.443711	+	0.896170i	$0.353662\pi$
$578$	−17.5021	−	31.3876i	−0.727993	−	1.30555i
$579$	−6.22039	−	20.2867i	−0.258511	−	0.843085i
$580$	27.3320	−	100.503i	1.13490	−	4.17314i
$581$	0.809888	−	6.45744i	0.0335998	−	0.267900i
$582$	24.9497	−	25.0296i	1.03420	−	1.03751i
$583$	9.96070	−	8.02565i	0.412530	−	0.332388i
$584$	23.8637	+	0.458122i	0.987488	+	0.0189572i
$585$	0.756138	+	0.944619i	0.0312624	+	0.0390552i
$586$	3.22670	−	47.9565i	0.133294	−	1.98106i
$587$	4.70909	−	28.6055i	0.194365	−	1.18068i	−0.693460	−	0.720495i	$-0.743915\pi$
$587$	4.70909	−	28.6055i	0.194365	−	1.18068i	0.887825	−	0.460182i	$-0.152216\pi$
$588$	−10.9456	+	23.3536i	−0.451389	+	0.963085i
$589$	0.462868	−	7.60553i	0.0190721	−	0.313380i
$590$	22.3466	+	33.7060i	0.919994	+	1.38765i
$591$	−27.8089	−	7.08703i	−1.14391	−	0.291522i
$592$	3.40190	+	5.92139i	0.139817	+	0.243368i
$593$	13.3987	−	15.6828i	0.550218	−	0.644014i	−0.413637	−	0.910442i	$-0.635742\pi$
$593$	13.3987	−	15.6828i	0.550218	−	0.644014i	0.963855	+	0.266428i	$0.0858435\pi$
$594$	17.1635	+	6.30233i	0.704226	+	0.258588i
$595$	−2.14774	−	1.45378i	−0.0880488	−	0.0595994i
$596$	−11.5476	+	27.8154i	−0.473007	+	1.13936i
$597$	−28.7289	+	15.1865i	−1.17580	+	0.621541i
$598$	−3.04837	−	5.63515i	−0.124657	−	0.230439i
$599$	2.03743	+	5.28576i	0.0832469	+	0.215970i	0.968437	−	0.249260i	$-0.0801874\pi$
$599$	2.03743	+	5.28576i	0.0832469	+	0.215970i	−0.885190	+	0.465230i	$0.845971\pi$
$600$	14.2117	+	26.6781i	0.580192	+	1.08913i
$601$	18.7611	−	17.8818i	0.765282	−	0.729412i	−0.203025	−	0.979174i	$-0.565077\pi$
$601$	18.7611	−	17.8818i	0.765282	−	0.729412i	0.968307	+	0.249762i	$0.0803523\pi$
$602$	0.524796	−	4.41281i	0.0213891	−	0.179853i
$603$	−6.04439	−	1.95967i	−0.246147	−	0.0798038i
$604$	−14.5413	−	4.50966i	−0.591676	−	0.183496i
$605$	23.9025	−	27.6174i	0.971774	−	1.12281i
$606$	22.7788	−	2.48752i	0.925328	−	0.101049i
$607$	−9.96780	−	8.03137i	−0.404581	−	0.325983i	0.403581	−	0.914944i	$-0.367765\pi$
$607$	−9.96780	−	8.03137i	−0.404581	−	0.325983i	−0.808162	+	0.588961i	$0.799537\pi$
$608$	−33.5826	−	28.1385i	−1.36196	−	1.14117i
$609$	0.349332	+	12.1293i	0.0141556	+	0.491505i
$610$	2.73788	−	65.7933i	0.110853	−	2.66389i
$611$	1.42058	−	2.23468i	0.0574705	−	0.0904055i
$612$	−0.432738	−	1.32032i	−0.0174924	−	0.0533709i
$613$	11.6230	+	9.12220i	0.469448	+	0.368442i	0.823996	−	0.566596i	$-0.191740\pi$
$613$	11.6230	+	9.12220i	0.469448	+	0.368442i	−0.354548	+	0.935038i	$0.615365\pi$
$614$	−21.8867	−	44.4564i	−0.883274	−	1.79412i
$615$	21.3701	−	8.63233i	0.861727	−	0.348089i
$616$	0.238239	+	2.11878i	0.00959891	+	0.0853681i
$617$	45.6909	−	1.46223i	1.83945	−	0.0588673i	0.907203	−	0.420694i	$-0.138213\pi$
$617$	45.6909	−	1.46223i	1.83945	−	0.0588673i	0.932245	+	0.361827i	$0.117847\pi$
$618$	−13.5334	+	5.16686i	−0.544393	+	0.207841i
$619$	25.4700	+	9.53781i	1.02373	+	0.383357i	0.805534	−	0.592549i	$-0.201878\pi$
$619$	25.4700	+	9.53781i	1.02373	+	0.383357i	0.218192	+	0.975906i	$0.429984\pi$
$620$	11.9738	+	8.91199i	0.480881	+	0.357914i
$621$	−40.4078	+	5.72583i	−1.62151	+	0.229770i
$622$	7.98012	+	29.3437i	0.319974	+	1.17658i
$623$	4.52679	−	2.85737i	0.181362	−	0.114478i
$624$	−1.06437	+	0.553956i	−0.0426089	+	0.0221760i
$625$	−46.0087	+	47.3528i	−1.84035	+	1.89411i
$626$	4.34723	−	7.56684i	0.173750	−	0.302432i
$627$	−4.42332	−	12.4132i	−0.176650	−	0.495735i
$628$	6.45134	+	64.8369i	0.257436	+	2.58728i
$629$	1.94352	−	1.50536i	0.0774931	−	0.0600225i
$630$	4.05022	+	4.06320i	0.161365	+	0.161882i
$631$	45.6034	+	4.98003i	1.81544	+	0.198252i	0.951980	−	0.306159i	$-0.0990440\pi$
$631$	45.6034	+	4.98003i	1.81544	+	0.198252i	0.863464	+	0.504411i	$0.168290\pi$
$632$	2.16331	−	2.00971i	0.0860518	−	0.0799420i
$633$	2.92769	−	8.05266i	0.116365	−	0.320064i
$634$	4.57360	+	31.5495i	0.181641	+	1.25299i
$635$	47.2418	+	9.18114i	1.87473	+	0.364342i
$636$	−32.4418	−	14.3281i	−1.28640	−	0.568147i
$637$	−0.345486	+	2.49558i	−0.0136886	+	0.0988785i
$638$	−16.2336	−	24.8291i	−0.642695	−	0.982994i
$639$	2.59206	+	0.914322i	0.102540	+	0.0361700i
$640$	48.0629	−	14.5692i	1.89985	−	0.575899i
$641$	−19.2889	−	8.81573i	−0.761866	−	0.348201i	−0.00346990	−	0.999994i	$-0.501105\pi$
$641$	−19.2889	−	8.81573i	−0.761866	−	0.348201i	−0.758397	+	0.651793i	$0.774017\pi$
$642$	−7.33041	−	12.5725i	−0.289308	−	0.496196i
$643$	15.3028	−	14.3998i	0.603484	−	0.567873i	−0.321962	−	0.946753i	$-0.604342\pi$
$643$	15.3028	−	14.3998i	0.603484	−	0.567873i	0.925446	+	0.378880i	$0.123691\pi$
$644$	−9.98711	−	14.4536i	−0.393547	−	0.569552i
$645$	−13.0138	−	6.56281i	−0.512416	−	0.258410i
$646$	−4.76557	+	7.60363i	−0.187499	+	0.299161i
$647$	−22.6783	−	17.5655i	−0.891576	−	0.690573i	0.0599303	−	0.998203i	$-0.480912\pi$
$647$	−22.6783	−	17.5655i	−0.891576	−	0.690573i	−0.951506	+	0.307630i	$0.900464\pi$
$648$	−1.27553	−	10.1701i	−0.0501076	−	0.399521i
$649$	6.59561	+	0.934604i	0.258900	+	0.0366864i
$650$	7.74436	+	7.67039i	0.303759	+	0.300857i
$651$	−1.63623	−	0.588961i	−0.0641289	−	0.0230832i
$652$	29.1385	+	12.2063i	1.14115	+	0.478036i
$653$	3.30926	+	38.2161i	0.129501	+	1.49551i	0.723096	+	0.690747i	$0.242718\pi$
$653$	3.30926	+	38.2161i	0.129501	+	1.49551i	−0.593595	+	0.804764i	$0.702292\pi$
$654$	−41.7545	−	5.64437i	−1.63273	−	0.220712i
$655$	64.9112	−	36.4681i	2.53629	−	1.42492i
$656$	−1.34752	−	7.05416i	−0.0526120	−	0.275419i
$657$	0.777714	−	10.5504i	0.0303415	−	0.411610i
$658$	5.54557	−	11.2642i	0.216189	−	0.439125i
$659$	8.06809	−	3.87630i	0.314288	−	0.150999i	−0.269284	−	0.963061i	$-0.586787\pi$
$659$	8.06809	−	3.87630i	0.314288	−	0.150999i	0.583572	+	0.812061i	$0.301655\pi$
$660$	25.0944	+	6.05436i	0.976798	+	0.235666i
$661$	−2.81663	+	3.75916i	−0.109554	+	0.146214i	−0.851711	−	0.524013i	$-0.824435\pi$
$661$	−2.81663	+	3.75916i	−0.109554	+	0.146214i	0.742156	+	0.670227i	$0.233803\pi$
$662$	20.4826	−	23.3622i	0.796078	−	0.907998i
$663$	0.250072	+	0.352187i	0.00971198	+	0.0136778i
$664$	7.40751	−	9.37632i	0.287467	−	0.363872i
$665$	1.98523	−	21.3366i	0.0769840	−	0.827400i
$666$	−4.85554	+	2.44864i	−0.188148	+	0.0948829i
$667$	58.1386	+	31.6912i	2.25113	+	1.22709i
$668$	−27.8596	+	55.6866i	−1.07792	+	2.15458i
$669$	−29.7921	+	13.3863i	−1.15183	+	0.517544i
$670$	−78.8150	−	15.8412i	−3.04489	−	0.611997i
$671$	−7.80373	−	7.53383i	−0.301260	−	0.290840i
$672$	−8.31633	+	5.55199i	−0.320809	+	0.214172i
$673$	−7.43230	+	22.6766i	−0.286494	+	0.874119i	0.700541	+	0.713612i	$0.252942\pi$
$673$	−7.43230	+	22.6766i	−0.286494	+	0.874119i	−0.987035	+	0.160507i	$0.948687\pi$
$674$	17.5469	+	21.3549i	0.675883	+	0.822559i
$675$	62.9641	−	29.2653i	2.42349	−	1.12642i
$676$	−25.0167	+	24.7777i	−0.962179	+	0.952988i
$677$	35.1539	−	26.1646i	1.35107	−	1.00559i	0.353540	−	0.935420i	$-0.384978\pi$
$677$	35.1539	−	26.1646i	1.35107	−	1.00559i	0.997535	−	0.0701696i	$-0.0223541\pi$
$678$	14.0515	−	4.06383i	0.539646	−	0.156070i
$679$	3.46114	−	8.81095i	0.132826	−	0.338133i
$680$	−1.99328	−	4.32466i	−0.0764387	−	0.165843i
$681$	−0.430148	−	19.2048i	−0.0164833	−	0.735929i
$682$	4.16256	−	0.864386i	0.159393	−	0.0330990i
$683$	−32.3018	+	34.1082i	−1.23600	+	1.30511i	−0.299643	+	0.954052i	$0.596867\pi$
$683$	−32.3018	+	34.1082i	−1.23600	+	1.30511i	−0.936353	+	0.351061i	$0.885821\pi$
$684$	7.84047	−	8.38574i	0.299788	−	0.320637i
$685$	19.8155	+	1.39696i	0.757110	+	0.0533750i
$686$	−0.730720	+	25.3717i	−0.0278990	+	0.968697i
$687$	−6.06516	+	6.82920i	−0.231400	+	0.260550i
$688$	−2.79250	+	3.58158i	−0.106463	+	0.136546i
$689$	−3.44138	−	0.398107i	−0.131106	−	0.0151667i
$690$	−96.3861	+	25.2216i	−3.66936	+	0.960171i
$691$	−11.3152	−	36.0771i	−0.430450	−	1.37244i	−0.878206	−	0.478283i	$-0.841259\pi$
$691$	−11.3152	−	36.0771i	−0.430450	−	1.37244i	0.447756	−	0.894156i	$-0.352223\pi$
$692$	−53.2076	−	26.4068i	−2.02265	−	1.00384i
$693$	0.943454	−	0.0543891i	0.0358388	−	0.00206607i
$694$	−29.7598	+	32.6572i	−1.12966	+	1.23965i
$695$	4.96906	+	9.04691i	0.188487	+	0.343169i
$696$	−10.9749	+	19.3892i	−0.416002	+	0.734946i
$697$	−2.44885	+	0.828725i	−0.0927568	+	0.0313902i
$698$	−22.7577	−	4.12132i	−0.861393	−	0.155994i
$699$	−3.72290	+	0.142993i	−0.140813	+	0.00540848i
$700$	23.3939	+	18.6036i	0.884208	+	0.703151i
$701$	−2.35523	−	1.42418i	−0.0889558	−	0.0537906i	0.472266	−	0.881456i	$-0.343436\pi$
$701$	−2.35523	−	1.42418i	−0.0889558	−	0.0537906i	−0.561222	+	0.827666i	$0.689668\pi$
$702$	−2.04395	−	4.51029i	−0.0771438	−	0.170230i
$703$	18.6325	+	8.08708i	0.702738	+	0.305010i
$704$	7.77760	−	16.8745i	0.293129	−	0.635981i
$705$	−28.5058	−	29.7166i	−1.07359	−	1.11919i
$706$	−44.2649	+	21.9686i	−1.66593	+	0.826798i
$707$	5.33180	−	3.04053i	0.200523	−	0.114351i
$708$	−6.08800	−	17.4368i	−0.228801	−	0.655316i
$709$	0.0483761	−	0.00940158i	0.00181680	−	0.000353084i	−0.189866	−	0.981810i	$-0.560805\pi$
$709$	0.0483761	−	0.00940158i	0.00181680	−	0.000353084i	0.191682	+	0.981457i	$0.438606\pi$
$710$	33.9064	+	7.72260i	1.27248	+	0.289824i
$711$	−0.837322	−	1.00584i	−0.0314020	−	0.0377220i
$712$	9.82709	−	0.188655i	0.368286	−	0.00707014i
$713$	−7.27364	+	6.09450i	−0.272400	+	0.228241i
$714$	1.35998	+	1.53130i	0.0508958	+	0.0573073i
$715$	2.51647	−	0.161233i	0.0941107	−	0.00602977i
$716$	16.5358	+	32.0216i	0.617973	+	1.19671i
$717$	−1.92390	−	11.2377i	−0.0718492	−	0.419680i
$718$	7.98385	+	50.5126i	0.297955	+	1.88511i
$719$	−25.0172	+	0.640414i	−0.932982	+	0.0238834i	−0.489125	−	0.872214i	$-0.662684\pi$
$719$	−25.0172	+	0.640414i	−0.932982	+	0.0238834i	−0.443858	+	0.896097i	$0.646390\pi$
$720$	−1.39333	−	5.69517i	−0.0519264	−	0.212246i
$721$	−2.77432	+	2.71287i	−0.103321	+	0.101033i
$722$	−32.7107	−	1.88574i	−1.21737	−	0.0701799i
$723$	−20.4220	−	11.6459i	−0.759503	−	0.433116i
$724$	−6.69155	+	36.2879i	−0.248690	+	1.34863i
$725$	−110.299	−	22.9044i	−4.09641	−	0.850649i
$726$	−23.6763	+	16.4719i	−0.878709	+	0.611331i
$727$	−25.5692	+	15.9118i	−0.948308	+	0.590134i	−0.912435	−	0.409222i	$-0.865800\pi$
$727$	−25.5692	+	15.9118i	−0.948308	+	0.590134i	−0.0358734	+	0.999356i	$0.511421\pi$
$728$	0.363729	−	0.448483i	0.0134807	−	0.0166219i
$729$	−29.9253	+	2.10968i	−1.10834	+	0.0781364i
$730$	−5.56486	−	133.728i	−0.205965	−	4.94949i
$731$	1.41497	+	0.818946i	0.0523345	+	0.0302898i
$732$	−8.63197	+	28.8079i	−0.319047	+	1.06477i
$733$	22.1174	−	39.6644i	0.816924	−	1.46504i	−0.0671758	−	0.997741i	$-0.521399\pi$
$733$	22.1174	−	39.6644i	0.816924	−	1.46504i	0.884100	−	0.467297i	$-0.154772\pi$
$734$	51.6980	+	11.0810i	1.90821	+	0.409006i
$735$	36.4198	+	14.4412i	1.34336	+	0.532671i
$736$	3.31462	+	54.4635i	0.122178	+	2.00755i
$737$	−10.5720	+	7.97423i	−0.389424	+	0.293735i
$738$	5.66731	−	0.766107i	0.208617	−	0.0282008i
$739$	−2.37743	−	10.5946i	−0.0874552	−	0.389729i	0.912351	−	0.409409i	$-0.134265\pi$
$739$	−2.37743	−	10.5946i	−0.0874552	−	0.389729i	−0.999806	+	0.0196795i	$0.993735\pi$
$740$	−33.2335	+	21.8806i	−1.22169	+	0.804346i
$741$	−1.55583	+	3.21191i	−0.0571548	+	0.117993i
$742$	−16.4257	−	0.105099i	−0.603005	−	0.00385829i
$743$	−31.7317	−	33.9385i	−1.16412	−	1.24508i	−0.964173	−	0.265275i	$-0.914537\pi$
$743$	−31.7317	−	33.9385i	−1.16412	−	1.24508i	−0.199949	−	0.979806i	$-0.564078\pi$
$744$	−2.01125	−	2.47990i	−0.0737360	−	0.0909175i
$745$	43.2405	+	14.9422i	1.58421	+	0.547441i
$746$	1.78839	+	0.682780i	0.0654775	+	0.0249984i
$747$	−3.97123	−	3.50427i	−0.145300	−	0.128215i
$748$	−2.77110	−	0.839998i	−0.101321	−	0.0307134i
$749$	−3.14201	−	2.30747i	−0.114807	−	0.0843130i
$750$	86.0482	−	52.7873i	3.14204	−	1.92752i
$751$	−0.0548659	+	17.1499i	−0.00200208	+	0.625810i	0.948778	+	0.315943i	$0.102321\pi$
$751$	−0.0548659	+	17.1499i	−0.00200208	+	0.625810i	−0.950780	+	0.309866i	$0.899716\pi$
$752$	−10.8064	+	6.91823i	−0.394069	+	0.252282i
$753$	23.9025	−	23.0758i	0.871057	−	0.840930i
$754$	−1.70891	+	7.85026i	−0.0622350	+	0.285890i
$755$	−5.49592	+	22.4643i	−0.200017	+	0.817559i
$756$	−6.91428	−	11.6863i	−0.251470	−	0.425026i
$757$	−6.20619	+	6.30627i	−0.225568	+	0.229205i	−0.816250	−	0.577700i	$-0.803951\pi$
$757$	−6.20619	+	6.30627i	−0.225568	+	0.229205i	0.590682	+	0.806905i	$0.298859\pi$
$758$	−1.07555	+	1.49439i	−0.0390656	+	0.0542788i
$759$	−7.43661	+	14.6299i	−0.269932	+	0.531031i
$760$	23.3905	−	31.6375i	0.848463	−	1.14761i
$761$	7.14532	−	10.6292i	0.259018	−	0.385308i	−0.677731	−	0.735310i	$-0.737037\pi$
$761$	7.14532	−	10.6292i	0.259018	−	0.385308i	0.936749	+	0.350001i	$0.113819\pi$
$762$	−34.3597	−	16.2383i	−1.24472	−	0.588252i
$763$	−10.8616	+	3.06611i	−0.393217	+	0.111001i
$764$	5.22625	+	11.1508i	0.189079	+	0.403420i
$765$	−1.96200	+	0.777973i	−0.0709363	+	0.0281277i
$766$	37.9464	−	6.37155i	1.37106	−	0.230214i
$767$	−1.07254	−	1.45069i	−0.0387270	−	0.0523814i
$768$	−2.09723	+	0.0939947i	−0.0756773	+	0.00339174i
$769$	−15.6485	−	9.19112i	−0.564301	−	0.331440i	0.196419	−	0.980520i	$-0.437069\pi$
$769$	−15.6485	−	9.19112i	−0.564301	−	0.331440i	−0.760720	+	0.649080i	$0.775154\pi$
$770$	11.7782	−	2.05524i	0.424458	−	0.0740658i
$771$	41.9218	−	4.03586i	1.50978	−	0.145348i
$772$	−6.25767	−	38.0125i	−0.225219	−	1.36810i
$773$	34.0820	+	9.62095i	1.22585	+	0.346042i	0.822372	−	0.568950i	$-0.192650\pi$
$773$	34.0820	+	9.62095i	1.22585	+	0.346042i	0.403473	+	0.914992i	$0.367803\pi$
$774$	−2.72695	−	2.37544i	−0.0980181	−	0.0853834i
$775$	8.83471	−	13.5126i	0.317352	−	0.485387i
$776$	13.8091	−	10.5552i	0.495718	−	0.378910i
$777$	2.96587	−	3.56279i	0.106400	−	0.127814i
$778$	6.19370	−	7.73759i	0.222055	−	0.277406i
$779$	−15.7424	−	14.4381i	−0.564031	−	0.517300i
$780$	−3.59842	−	5.99408i	−0.128844	−	0.214623i
$781$	4.65989	−	3.33124i	0.166744	−	0.119201i
$782$	10.9566	−	2.20218i	0.391806	−	0.0787498i
$783$	43.1013	+	27.5933i	1.54031	+	0.986106i
$784$	6.61509	−	10.2604i	0.236253	−	0.366444i
$785$	97.7134	−	15.7648i	3.48754	−	0.562670i
$786$	−56.7828	+	15.2474i	−2.02537	+	0.543855i
$787$	2.10705	+	28.5840i	0.0751081	+	1.01891i	0.894905	+	0.446256i	$0.147243\pi$
$787$	2.10705	+	28.5840i	0.0751081	+	1.01891i	−0.819797	+	0.572654i	$0.805914\pi$
$788$	−48.3099	−	19.5145i	−1.72097	−	0.695175i
$789$	−3.46361	+	12.4216i	−0.123308	+	0.442221i
$790$	−11.9858	−	11.4240i	−0.426437	−	0.406449i
$791$	3.01926	−	2.49710i	0.107353	−	0.0887867i
$792$	1.53401	+	0.810895i	0.0545085	+	0.0288139i
$793$	0.0281938	+	2.93752i	0.00100119	+	0.104315i
$794$	−2.47544	−	1.01841i	−0.0878502	−	0.0361420i
$795$	−18.7313	+	50.5120i	−0.664330	+	1.79147i
$796$	−55.3824	+	20.3361i	−1.96298	+	0.720794i
$797$	3.07449	+	0.762612i	0.108904	+	0.0270131i	0.294822	−	0.955552i	$-0.404740\pi$
$797$	3.07449	+	0.762612i	0.108904	+	0.0270131i	−0.185918	+	0.982565i	$0.559526\pi$
$798$	−5.68006	+	15.9400i	−0.201072	+	0.564269i
$799$	3.00036	+	3.51183i	0.106145	+	0.124240i
$800$	−32.2766	−	87.0390i	−1.14115	−	3.07729i
$801$	0.153276	−	4.35375i	0.00541573	−	0.153832i
$802$	5.00614	+	10.0064i	0.176773	+	0.353340i
$803$	−17.0788	−	13.9421i	−0.602699	−	0.492006i
$804$	33.0928	+	15.8994i	1.16709	+	0.560729i
$805$	−20.9936	+	16.4767i	−0.739928	+	0.580726i
$806$	−0.957597	−	0.639292i	−0.0337299	−	0.0225181i
$807$	8.38977	+	38.5402i	0.295334	+	1.35668i
$808$	11.2659	+	0.288396i	0.396333	+	0.0101457i
$809$	7.33357	+	55.5894i	0.257834	+	1.95442i	0.296112	+	0.955153i	$0.404310\pi$
$809$	7.33357	+	55.5894i	0.257834	+	1.95442i	−0.0382773	+	0.999267i	$0.512187\pi$
$810$	−56.4905	+	10.6039i	−1.98488	+	0.372584i
$811$	−0.0108509	+	0.678295i	−0.000381025	+	0.0238182i	−0.999992	−	0.00408500i	$-0.998700\pi$
$811$	−0.0108509	+	0.678295i	−0.000381025	+	0.0238182i	0.999611	+	0.0279031i	$0.00888300\pi$
$812$	−2.32152	+	21.9080i	−0.0814694	+	0.768819i
$813$	−34.8691	−	18.7187i	−1.22291	−	0.656493i
$814$	−1.62590	+	11.2158i	−0.0569879	+	0.393112i
$815$	15.8189	−	45.3075i	0.554112	−	1.58705i
$816$	−0.379558	−	2.05832i	−0.0132872	−	0.0720558i
$817$	−0.302479	+	13.5047i	−0.0105824	+	0.472470i
$818$	36.9675	−	16.0450i	1.29254	−	0.561001i
$819$	−0.189723	−	0.171782i	−0.00662946	−	0.00600256i
$820$	40.5485	−	10.3337i	1.41602	−	0.360868i
$821$	−9.25439	−	9.52475i	−0.322980	−	0.332416i	0.536198	−	0.844092i	$-0.319860\pi$
$821$	−9.25439	−	9.52475i	−0.322980	−	0.332416i	−0.859179	+	0.511676i	$0.829025\pi$
$822$	−14.8907	−	4.93325i	−0.519371	−	0.172067i
$823$	−15.2823	+	20.9495i	−0.532706	+	0.730255i	−0.987022	−	0.160586i	$-0.948662\pi$
$823$	−15.2823	+	20.9495i	−0.532706	+	0.730255i	0.454316	+	0.890841i	$0.349884\pi$
$824$	−6.93637	+	1.62660i	−0.241640	+	0.0566652i
$825$	4.88752	−	27.4899i	0.170162	−	0.957075i
$826$	−5.80203	−	6.28568i	−0.201879	−	0.218707i
$827$	17.5581	−	36.8468i	0.610556	−	1.28129i	−0.330745	−	0.943720i	$-0.607300\pi$
$827$	17.5581	−	36.8468i	0.610556	−	1.28129i	0.941301	−	0.337568i	$-0.109604\pi$
$828$	−14.2970	+	0.0914786i	−0.496855	+	0.00317910i
$829$	6.79356	+	7.17346i	0.235950	+	0.249144i	0.833280	−	0.552851i	$-0.186460\pi$
$829$	6.79356	+	7.17346i	0.235950	+	0.249144i	−0.597330	+	0.801996i	$0.703772\pi$
$830$	−55.0052	−	38.2679i	−1.90926	−	1.32830i
$831$	16.6342	+	0.852198i	0.577035	+	0.0295624i
$832$	−4.73475	+	1.70427i	−0.164148	+	0.0590850i
$833$	−3.98522	−	1.85231i	−0.138080	−	0.0641786i
$834$	−2.03813	−	7.89186i	−0.0705747	−	0.273273i
$835$	87.0054	+	37.1033i	3.01095	+	1.28401i
$836$	−4.93933	−	23.4095i	−0.170830	−	0.809635i
$837$	−5.93910	+	4.30341i	−0.205285	+	0.148748i
$838$	−17.4946	−	43.7116i	−0.604340	−	1.50999i
$839$	11.2430	−	12.1802i	0.388150	−	0.420506i	−0.510014	−	0.860166i	$-0.670360\pi$
$839$	11.2430	−	12.1802i	0.388150	−	0.420506i	0.898164	+	0.439661i	$0.144901\pi$
$840$	−5.43031	−	7.15164i	−0.187364	−	0.246755i
$841$	−19.1106	−	50.5406i	−0.658987	−	1.74278i
$842$	1.74926	−	7.79526i	0.0602833	−	0.268642i
$843$	−0.284501	+	3.28549i	−0.00979875	+	0.113158i
$844$	7.22600	−	13.7762i	0.248729	−	0.474197i
$845$	39.8775	+	35.6449i	1.37183	+	1.22622i
$846$	−5.03313	−	8.89197i	−0.173043	−	0.305712i
$847$	−4.06091	+	6.57240i	−0.139535	+	0.225830i
$848$	14.3090	+	8.77802i	0.491373	+	0.301438i
$849$	−8.09026	−	19.8451i	−0.277657	−	0.681084i
$850$	−16.7521	+	8.99297i	−0.574592	+	0.308456i
$851$	−8.64338	−	23.7738i	−0.296291	−	0.814955i
$852$	−14.1342	−	7.24167i	−0.484231	−	0.248095i
$853$	9.68764	−	49.0103i	0.331698	−	1.67808i	−0.342491	−	0.939521i	$-0.611271\pi$
$853$	9.68764	−	49.0103i	0.331698	−	1.67808i	0.674190	−	0.738558i	$-0.264493\pi$
$854$	1.64490	+	13.8313i	0.0562872	+	0.473298i
$855$	−13.4383	−	11.1143i	−0.459581	−	0.380100i
$856$	−2.74439	−	6.61058i	−0.0938012	−	0.225945i
$857$	−7.07895	+	34.6460i	−0.241812	+	1.18348i	0.659969	+	0.751293i	$0.270569\pi$
$857$	−7.07895	+	34.6460i	−0.241812	+	1.18348i	−0.901782	+	0.432192i	$0.857740\pi$
$858$	−1.95708	−	0.367367i	−0.0668137	−	0.0125417i
$859$	−1.38987	+	25.5305i	−0.0474218	+	0.871089i	0.874813	+	0.484460i	$0.160984\pi$
$859$	−1.38987	+	25.5305i	−0.0474218	+	0.871089i	−0.922235	+	0.386629i	$0.873639\pi$
$860$	−21.8181	−	14.9729i	−0.743991	−	0.510572i
$861$	−4.17172	+	2.52259i	−0.142172	+	0.0859698i
$862$	11.9598	+	1.53887i	0.407351	+	0.0524140i
$863$	7.97942	−	14.7506i	0.271622	−	0.502116i	−0.707151	−	0.707063i	$-0.750020\pi$
$863$	7.97942	−	14.7506i	0.271622	−	0.502116i	0.978773	+	0.204947i	$0.0657021\pi$
$864$	−0.404746	+	42.1706i	−0.0137697	+	1.43467i
$865$	−35.1293	+	83.1125i	−1.19443	+	2.82591i
$866$	−25.4711	+	79.4283i	−0.865544	+	2.69909i
$867$	23.6663	−	7.84061i	0.803751	−	0.266281i
$868$	−2.80065	−	1.45761i	−0.0950603	−	0.0494745i
$869$	−2.71804	+	0.226606i	−0.0922033	+	0.00768708i
$870$	112.265	+	54.8246i	3.80615	+	1.85873i
$871$	3.54758	+	0.525872i	0.120205	+	0.0178185i
$872$	−19.9785	−	5.50194i	−0.676559	−	0.186319i
$873$	−4.33874	−	6.36585i	−0.146844	−	0.215451i
$874$	59.5301	+	70.5878i	2.01364	+	2.38767i
$875$	15.5136	−	22.1474i	0.524457	−	0.748719i
$876$	−12.6194	+	59.8087i	−0.426371	+	2.02075i
$877$	−15.0563	−	33.7975i	−0.508414	−	1.14126i	−0.967500	−	0.252869i	$-0.918626\pi$
$877$	−15.0563	−	33.7975i	−0.508414	−	1.14126i	0.459087	−	0.888391i	$-0.348177\pi$
$878$	−0.0980825	−	2.04234i	−0.00331012	−	0.0689257i
$879$	32.2584	+	8.44115i	1.08805	+	0.284713i
$880$	−11.3872	−	4.43114i	−0.383861	−	0.149374i
$881$	−4.71740	+	10.5894i	−0.158933	+	0.356765i	−0.975339	−	0.220714i	$-0.929161\pi$
$881$	−4.71740	+	10.5894i	−0.158933	+	0.356765i	0.816405	+	0.577479i	$0.195964\pi$
$882$	7.87206	+	5.70401i	0.265066	+	0.192064i
$883$	4.05841	−	16.1405i	0.136577	−	0.543170i	−0.862721	−	0.505681i	$-0.831241\pi$
$883$	4.05841	−	16.1405i	0.136577	−	0.543170i	0.999297	−	0.0374890i	$-0.0119359\pi$
$884$	0.364270	+	0.694474i	0.0122517	+	0.0233577i
$885$	−25.8767	+	10.8399i	−0.869837	+	0.364380i
$886$	59.3294	−	3.03954i	1.99321	−	0.102115i
$887$	−1.79881	−	1.11940i	−0.0603981	−	0.0375859i	0.497817	−	0.867282i	$-0.334135\pi$
$887$	−1.79881	−	1.11940i	−0.0603981	−	0.0375859i	−0.558216	+	0.829696i	$0.688514\pi$
$888$	8.04482	−	2.77997i	0.269966	−	0.0932898i
$889$	−10.1744	−	0.325610i	−0.341240	−	0.0109206i
$890$	−4.40352	−	54.9407i	−0.147606	−	1.84162i
$891$	−4.87308	+	8.11735i	−0.163254	+	0.271941i
$892$	−56.8575	+	16.8387i	−1.90373	+	0.563800i
$893$	−13.4981	+	35.6976i	−0.451697	+	1.19457i
$894$	−30.1744	−	19.8665i	−1.00918	−	0.664435i
$895$	47.0268	−	28.0272i	1.57193	−	0.936847i
$896$	−9.54574	+	4.66165i	−0.318901	+	0.155735i
$897$	4.23670	−	1.34370i	0.141459	−	0.0448647i
$898$	12.5746	−	73.4499i	0.419621	−	2.45105i
$899$	11.8987	+	0.152272i	0.396843	+	0.00507856i
$900$	23.2325	−	7.20506i	0.774418	−	0.240169i
$901$	2.42371	−	5.53563i	0.0807454	−	0.184418i
$902$	5.46845	−	10.5897i	0.182080	−	0.352597i
$903$	2.93866	+	0.932014i	0.0977925	+	0.0310155i
$904$	7.11622	−	1.05486i	0.236682	−	0.0350843i
$905$	55.6389	+	6.79747i	1.84950	+	0.225955i
$906$	8.58639	−	16.1182i	0.285264	−	0.535492i
$907$	5.16402	+	18.5199i	0.171469	+	0.614942i	0.998598	+	0.0529304i	$0.0168561\pi$
$907$	5.16402	+	18.5199i	0.171469	+	0.614942i	−0.827130	+	0.562011i	$0.810028\pi$
$908$	3.89697	−	34.6577i	0.129325	−	1.15016i
$909$	0.399072	−	4.97904i	0.0132364	−	0.165144i
$910$	−2.63419	−	1.88312i	−0.0873225	−	0.0624248i
$911$	−10.0044	−	4.49523i	−0.331462	−	0.148934i	0.237299	−	0.971437i	$-0.423738\pi$
$911$	−10.0044	−	4.49523i	−0.331462	−	0.148934i	−0.568761	+	0.822503i	$0.692577\pi$
$912$	13.3966	−	10.9362i	0.443606	−	0.362132i
$913$	−10.7297	+	2.58869i	−0.355102	+	0.0856732i
$914$	−10.9211	+	25.3841i	−0.361238	+	0.839631i
$915$	44.4764	+	10.4299i	1.47035	+	0.344800i
$916$	−12.5734	+	10.8119i	−0.415436	+	0.357236i
$917$	−12.3262	+	9.80223i	−0.407048	+	0.323698i
$918$	8.56701	−	1.10232i	0.282753	−	0.0363820i
$919$	10.4454	−	27.0990i	0.344563	−	0.893912i	−0.646787	−	0.762671i	$-0.723888\pi$
$919$	10.4454	−	27.0990i	0.344563	−	0.893912i	0.991350	−	0.131242i	$-0.0418964\pi$
$920$	−48.6387	+	5.94225i	−1.60357	+	0.195910i
$921$	33.1424	−	9.12717i	1.09208	−	0.300750i
$922$	−29.0758	−	24.6807i	−0.957562	−	0.812815i
$923$	−1.52825	−	0.266672i	−0.0503029	−	0.00877761i
$924$	−5.44424	−	0.418833i	−0.179102	−	0.0137786i
$925$	25.8060	+	34.4414i	0.848496	+	1.13243i
$926$	−0.727494	−	1.69093i	−0.0239069	−	0.0555673i
$927$	0.552766	+	3.10904i	0.0181552	+	0.102114i
$928$	41.3779	−	54.4941i	1.35830	−	1.78885i
$929$	39.5732	+	11.7198i	1.29836	+	0.384515i	0.858158	−	0.513386i	$-0.171609\pi$
$929$	39.5732	+	11.7198i	1.29836	+	0.384515i	0.440197	+	0.897901i	$0.354908\pi$
$930$	−13.1956	+	12.1023i	−0.432699	+	0.396850i
$931$	−2.43762	−	36.2288i	−0.0798898	−	1.18735i
$932$	−6.73299	−	0.648192i	−0.220546	−	0.0212322i
$933$	−21.0341	+	1.61819i	−0.688626	+	0.0529770i
$934$	33.2545	+	37.9297i	1.08812	+	1.24110i
$935$	−1.01793	+	4.27917i	−0.0332899	+	0.139944i
$936$	−0.134883	−	0.450151i	−0.00440877	−	0.0147136i
$937$	−46.1781	−	10.2073i	−1.50857	−	0.333458i	−0.617228	−	0.786784i	$-0.711744\pi$
$937$	−46.1781	−	10.2073i	−1.50857	−	0.333458i	−0.891345	+	0.453326i	$0.850237\pi$
$938$	16.9920	+	0.652645i	0.554808	+	0.0213096i
$939$	4.59032	+	3.94725i	0.149799	+	0.128814i
$940$	−44.0598	−	60.3990i	−1.43707	−	1.97000i
$941$	−15.7455	−	49.1002i	−0.513288	−	1.60062i	−0.772644	−	0.634840i	$-0.781066\pi$
$941$	−15.7455	−	49.1002i	−0.513288	−	1.60062i	0.259356	−	0.965782i	$-0.416490\pi$
$942$	−77.8461	−	6.99193i	−2.53636	−	0.227809i
$943$	0.425514	+	26.5992i	0.0138566	+	0.866189i
$944$	1.75005	+	8.56515i	0.0569593	+	0.278772i
$945$	−17.0813	+	11.5621i	−0.555653	+	0.376116i
$946$	−7.31518	+	1.81449i	−0.237837	+	0.0589942i
$947$	−1.42121	+	14.2834i	−0.0461831	+	0.464147i	0.944554	+	0.328355i	$0.106494\pi$
$947$	−1.42121	+	14.2834i	−0.0461831	+	0.464147i	−0.990737	+	0.135792i	$0.956642\pi$
$948$	4.01588	+	6.40748i	0.130430	+	0.208105i
$949$	0.553165	+	5.94525i	0.0179565	+	0.192991i
$950$	−131.762	−	85.5472i	−4.27492	−	2.77552i
$951$	−22.0937	−	0.990208i	−0.716439	−	0.0321097i
$952$	0.561941	+	0.835929i	0.0182126	+	0.0270926i
$953$	−2.53330	−	16.7209i	−0.0820615	−	0.541643i	−0.991934	−	0.126755i	$-0.959544\pi$
$953$	−2.53330	−	16.7209i	−0.0820615	−	0.541643i	0.909873	−	0.414888i	$-0.136179\pi$
$954$	−7.59907	+	10.9976i	−0.246029	+	0.356059i
$955$	16.4250	−	8.95324i	0.531501	−	0.289720i
$956$	−0.728286	−	20.6867i	−0.0235545	−	0.669056i
$957$	19.0321	−	7.82992i	0.615222	−	0.253105i
$958$	−6.97805	−	16.5094i	−0.225451	−	0.533393i
$959$	−4.18496	+	0.375882i	−0.135140	+	0.0121379i
$960$	8.24614	+	77.8181i	0.266143	+	2.51157i
$961$	11.0589	−	27.1271i	0.356738	−	0.875066i
$962$	2.47384	−	1.81677i	0.0797598	−	0.0585750i
$963$	−2.99178	+	1.05532i	−0.0964088	+	0.0340072i
$964$	−33.9107	−	25.9202i	−1.09219	−	0.834833i
$965$	−57.0588	+	12.9959i	−1.83679	+	0.418352i
$966$	19.2778	−	8.51415i	0.620253	−	0.273938i
$967$	2.65928	+	9.30647i	0.0855168	+	0.299276i	0.992559	−	0.121763i	$-0.0388549\pi$
$967$	2.65928	+	9.30647i	0.0855168	+	0.299276i	−0.907042	+	0.421039i	$0.861665\pi$
$968$	−12.6247	+	6.46824i	−0.405772	+	0.207897i
$969$	−4.56093	−	4.23710i	−0.146518	−	0.136115i
$970$	−63.7845	−	73.6978i	−2.04800	−	2.36629i
$971$	−6.56698	−	14.9987i	−0.210744	−	0.481330i	0.778492	−	0.627654i	$-0.215985\pi$
$971$	−6.56698	−	14.9987i	−0.210744	−	0.481330i	−0.989237	+	0.146324i	$0.953256\pi$
$972$	−19.9275	−	1.27678i	−0.639176	−	0.0409526i
$973$	−1.34245	−	1.72178i	−0.0430368	−	0.0551978i
$974$	−28.0243	−	46.0119i	−0.897956	−	1.47432i
$975$	−6.23482	+	4.27871i	−0.199674	+	0.137029i
$976$	5.87569	−	12.9656i	0.188076	−	0.415020i
$977$	8.71869	−	7.89423i	0.278936	−	0.252559i	−0.519734	−	0.854328i	$-0.673969\pi$
$977$	8.71869	−	7.89423i	0.278936	−	0.252559i	0.798670	+	0.601769i	$0.205537\pi$
$978$	−20.9404	+	31.5850i	−0.669601	+	1.00998i
$979$	−7.24825	−	5.46720i	−0.231655	−	0.174732i
$980$	62.0139	+	34.8403i	1.98096	+	1.11293i
$981$	−2.91636	+	8.70940i	−0.0931122	+	0.278070i
$982$	9.53795			0.304368
$983$	−31.3147	+	1.54664i	−0.998783	+	0.0493301i
$983$	−31.3147	+	1.54664i	−0.998783	+	0.0493301i
$984$	−8.95116			−0.285352
$985$	−25.1308	+	75.0504i	−0.800734	+	2.39131i
$986$	−12.2180	−	6.86426i	−0.389101	−	0.218603i
$987$	6.95380	+	5.24510i	0.221342	+	0.166953i
$988$	−3.58042	+	5.40045i	−0.113908	+	0.171811i
$989$	12.4706	−	11.2913i	0.396542	−	0.359044i
$990$	4.01625	−	8.86248i	0.127645	−	0.281668i
$991$	−20.1438	+	13.8239i	−0.639890	+	0.439132i	−0.841443	−	0.540346i	$-0.818293\pi$
$991$	−20.1438	+	13.8239i	−0.639890	+	0.439132i	0.201553	+	0.979478i	$0.435401\pi$
$992$	5.10080	+	8.37478i	0.161950	+	0.265899i
$993$	13.2533	+	16.9982i	0.420579	+	0.539423i
$994$	−7.34057	−	0.470318i	−0.232829	−	0.0149176i
$995$	35.9451	+	82.0967i	1.13953	+	2.60264i
$996$	20.0265	+	23.1390i	0.634564	+	0.733187i
$997$	1.14584	+	1.06448i	0.0362890	+	0.0337125i	0.698555	−	0.715556i	$-0.253827\pi$
$997$	1.14584	+	1.06448i	0.0362890	+	0.0337125i	−0.662266	+	0.749269i	$0.730405\pi$
$998$	39.3046	−	20.1377i	1.24417	−	0.637448i
$999$	−5.37171	−	18.7989i	−0.169953	−	0.594772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.c.a.2.12	✓	39690
983.492	even	491	inner	983.2.c.a.492.12	yes	39690

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.c.a.2.12	✓	39690	1.1	even	1	trivial
983.2.c.a.492.12	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)

\(f(q)\)	\(=\)	\(q+(-0.691522 + 2.06516i) q^{2} +(-1.31722 - 0.740034i) q^{3} +(-2.18995 - 1.65183i) q^{4} +(-2.30250 + 3.47293i) q^{5} +(2.43917 - 2.20852i) q^{6} +(0.363807 - 0.802796i) q^{7} +(1.33432 - 0.915691i) q^{8} +(-0.373111 - 0.612595i) q^{9} +O(q^{10})\)	\(q+(-0.691522 + 2.06516i) q^{2} +(-1.31722 - 0.740034i) q^{3} +(-2.18995 - 1.65183i) q^{4} +(-2.30250 + 3.47293i) q^{5} +(2.43917 - 2.20852i) q^{6} +(0.363807 - 0.802796i) q^{7} +(1.33432 - 0.915691i) q^{8} +(-0.373111 - 0.612595i) q^{9} +(-5.57991 - 7.15662i) q^{10} +(-1.49176 - 0.0955789i) q^{11} +(1.66224 + 3.79647i) q^{12} +(0.264935 + 0.306111i) q^{13} +(1.40632 + 1.30647i) q^{14} +(5.60299 - 2.87069i) q^{15} +(-0.538977 - 1.88621i) q^{16} +(-0.645980 + 0.285301i) q^{17} +(1.52312 - 0.346910i) q^{18} +(-4.63566 - 3.54334i) q^{19} +(10.7791 - 3.80219i) q^{20} +(-1.07331 + 0.788231i) q^{21} +(1.22897 - 3.01463i) q^{22} +(0.765731 + 7.22614i) q^{23} +(-2.43524 + 0.218726i) q^{24} +(-4.81310 - 11.3873i) q^{25} +(-0.815376 + 0.335450i) q^{26} +(0.197603 + 5.61284i) q^{27} +(-2.12280 + 1.15714i) q^{28} +(5.18004 - 7.49668i) q^{29} +(2.05383 + 13.5562i) q^{30} +(0.728553 + 1.08378i) q^{31} +(7.50140 + 0.336201i) q^{32} +(1.89425 + 1.22986i) q^{33} +(-0.142481 - 1.53134i) q^{34} +(1.95039 + 3.11191i) q^{35} +(-0.194810 + 1.95787i) q^{36} +(-3.37878 + 0.838088i) q^{37} +(10.5232 - 7.12306i) q^{38} +(-0.122446 - 0.599278i) q^{39} +(0.107859 + 6.74237i) q^{40} +(3.64627 + 0.327498i) q^{41} +(-0.885602 - 2.76163i) q^{42} +(-1.36438 - 1.87034i) q^{43} +(3.10901 + 2.67346i) q^{44} +(2.98659 + 0.114712i) q^{45} +(-15.4526 - 3.41568i) q^{46} +(-1.87742 - 6.26561i) q^{47} +(-0.685911 + 2.88342i) q^{48} +(4.10259 + 4.67937i) q^{49} +(26.8449 - 2.06522i) q^{50} +(1.06203 + 0.102243i) q^{51} +(-0.0745505 - 1.10800i) q^{52} +(-6.30654 + 5.78403i) q^{53} +(-11.7280 - 3.47332i) q^{54} +(3.76673 - 4.96072i) q^{55} +(-0.249679 - 1.40432i) q^{56} +(3.48400 + 8.09791i) q^{57} +(11.8997 + 15.8817i) q^{58} +(-4.44325 - 0.341826i) q^{59} +(-17.0122 - 2.96854i) q^{60} +(5.53208 + 4.69584i) q^{61} +(-2.74198 + 0.755120i) q^{62} +(-0.627529 + 0.0766660i) q^{63} +(-4.47058 + 11.5982i) q^{64} +(-1.67312 + 0.215280i) q^{65} +(-3.84976 + 3.06146i) q^{66} +(6.71684 - 5.77586i) q^{67} +(1.88593 + 0.442256i) q^{68} +(4.33895 - 10.0851i) q^{69} +(-7.77532 + 1.87590i) q^{70} +(-2.96848 + 2.42328i) q^{71} +(-1.05880 - 0.475743i) q^{72} +(11.9983 + 8.57731i) q^{73} +(0.605718 - 7.55726i) q^{74} +(-2.08708 + 18.5615i) q^{75} +(4.29885 + 15.4171i) q^{76} +(-0.619444 + 1.16281i) q^{77} +(1.32228 + 0.161544i) q^{78} +(1.80489 - 0.267546i) q^{79} +(7.79168 + 2.47118i) q^{80} +(2.90608 - 5.62763i) q^{81} +(-3.19781 + 7.30364i) q^{82} +(7.05251 - 2.18718i) q^{83} +(3.65252 + 0.0467428i) q^{84} +(0.496540 - 2.90034i) q^{85} +(4.80604 - 1.52427i) q^{86} +(-12.3711 + 6.04139i) q^{87} +(-2.07801 + 1.23846i) q^{88} +(5.07283 + 3.33990i) q^{89} +(-2.30219 + 6.08844i) q^{90} +(0.342130 - 0.101324i) q^{91} +(10.2595 - 17.0897i) q^{92} +(-0.157634 - 1.96673i) q^{93} +(14.2377 + 0.455646i) q^{94} +(22.9794 - 7.94077i) q^{95} +(-9.63220 - 5.99414i) q^{96} +(10.7263 - 0.549526i) q^{97} +(-12.5007 + 5.23661i) q^{98} +(0.498043 + 0.949510i) 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

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