LMFDB - Embedded newform 983.2.c.a.2.4

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			2.4
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.862858 + 2.57683i) q^{2} +(1.07786 + 0.605560i) q^{3} +(-4.29883 - 3.24251i) q^{4} +(1.73663 - 2.61941i) q^{5} +(-2.49047 + 2.25496i) q^{6} +(-1.58443 + 3.49630i) q^{7} +(7.58350 - 5.20426i) q^{8} +(-0.765444 - 1.25675i) q^{9} +O(q^{10})$	\(q+(-0.862858 + 2.57683i) q^{2} +(1.07786 + 0.605560i) q^{3} +(-4.29883 - 3.24251i) q^{4} +(1.73663 - 2.61941i) q^{5} +(-2.49047 + 2.25496i) q^{6} +(-1.58443 + 3.49630i) q^{7} +(7.58350 - 5.20426i) q^{8} +(-0.765444 - 1.25675i) q^{9} +(5.25132 + 6.73519i) q^{10} +(-0.162710 - 0.0104250i) q^{11} +(-2.67002 - 6.09819i) q^{12} +(-0.748119 - 0.864391i) q^{13} +(-7.64223 - 7.09963i) q^{14} +(3.45806 - 1.77174i) q^{15} +(3.90820 + 13.6772i) q^{16} +(6.25017 - 2.76042i) q^{17} +(3.89890 - 0.888025i) q^{18} +(0.449946 + 0.343924i) q^{19} +(-15.9590 + 5.62935i) q^{20} +(-3.82502 + 2.80907i) q^{21} +(0.167259 - 0.410281i) q^{22} +(-0.836680 - 7.89568i) q^{23} +(11.3255 - 1.01722i) q^{24} +(-1.89881 - 4.49240i) q^{25} +(2.87291 - 1.18193i) q^{26} +(-0.194503 - 5.52480i) q^{27} +(18.1480 - 9.89243i) q^{28} +(5.78597 - 8.37361i) q^{29} +(1.58165 + 10.4396i) q^{30} +(4.19827 + 6.24523i) q^{31} +(-20.2395 - 0.907105i) q^{32} +(-0.169067 - 0.109767i) q^{33} +(1.72014 + 18.4875i) q^{34} +(6.40667 + 10.2221i) q^{35} +(-0.784516 + 7.88451i) q^{36} +(-0.185888 + 0.0461086i) q^{37} +(-1.27447 + 0.862678i) q^{38} +(-0.282931 - 1.38473i) q^{39} +(-0.462355 - 28.9022i) q^{40} +(-1.36157 - 0.122293i) q^{41} +(-3.93804 - 12.2803i) q^{42} +(0.0951545 + 0.130442i) q^{43} +(0.665659 + 0.572405i) q^{44} +(-4.62124 - 0.177497i) q^{45} +(21.0678 + 4.65686i) q^{46} +(0.850979 + 2.84002i) q^{47} +(-4.06985 + 17.1088i) q^{48} +(-5.09895 - 5.81580i) q^{49} +(13.2146 - 1.01662i) q^{50} +(8.40844 + 0.809490i) q^{51} +(0.413235 + 6.14165i) q^{52} +(-8.86230 + 8.12805i) q^{53} +(14.4043 + 4.26592i) q^{54} +(-0.309875 + 0.408100i) q^{55} +(6.18009 + 34.7600i) q^{56} +(0.276715 + 0.643173i) q^{57} +(16.5849 + 22.1347i) q^{58} +(6.33010 + 0.486984i) q^{59} +(-20.6105 - 3.59643i) q^{60} +(9.84991 + 8.36098i) q^{61} +(-19.7154 + 5.42948i) q^{62} +(5.60677 - 0.684985i) q^{63} +(9.56921 - 24.8257i) q^{64} +(-3.56340 + 0.458504i) q^{65} +(0.428733 - 0.340942i) q^{66} +(-0.395660 + 0.340231i) q^{67} +(-35.8191 - 8.39968i) q^{68} +(3.87948 - 9.01713i) q^{69} +(-31.8686 + 7.68872i) q^{70} +(7.05451 - 5.75886i) q^{71} +(-12.3452 - 5.54699i) q^{72} +(2.46400 + 1.76146i) q^{73} +(0.0415811 - 0.518788i) q^{74} +(0.673755 - 5.99204i) q^{75} +(-0.819063 - 2.93742i) q^{76} +(0.294252 - 0.552365i) q^{77} +(3.81234 + 0.465758i) q^{78} +(2.54140 - 0.376721i) q^{79} +(42.6133 + 13.5151i) q^{80} +(1.11044 - 2.15037i) q^{81} +(1.48997 - 3.40302i) q^{82} +(2.31539 - 0.718067i) q^{83} +(25.5515 + 0.326994i) q^{84} +(3.62356 - 21.1656i) q^{85} +(-0.418231 + 0.132645i) q^{86} +(11.3072 - 5.52187i) q^{87} +(-1.28817 + 0.767727i) q^{88} +(1.88577 + 1.24157i) q^{89} +(4.44485 - 11.7550i) q^{90} +(4.20751 - 1.24608i) q^{91} +(-22.0051 + 36.6551i) q^{92} +(0.743301 + 9.27382i) q^{93} +(-8.05252 - 0.257702i) q^{94} +(1.68227 - 0.581326i) q^{95} +(-21.2662 - 13.2340i) q^{96} +(-6.78154 + 0.347429i) q^{97} +(19.3860 - 8.12093i) q^{98} +(0.111444 + 0.212466i) 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 $

$2$	−0.862858	+	2.57683i	−0.610133	+	1.82210i	−0.0420633	+	0.999115i	$0.513393\pi$
$2$	−0.862858	+	2.57683i	−0.610133	+	1.82210i	−0.568069	+	0.822981i	$0.692310\pi$
$3$	1.07786	+	0.605560i	0.622306	+	0.349620i	0.768703	−	0.639606i	$-0.220902\pi$
$3$	1.07786	+	0.605560i	0.622306	+	0.349620i	−0.146398	+	0.989226i	$0.546768\pi$
$4$	−4.29883	−	3.24251i	−2.14941	−	1.62126i
$5$	1.73663	−	2.61941i	0.776645	−	1.17144i	−0.204633	−	0.978839i	$-0.565600\pi$
$5$	1.73663	−	2.61941i	0.776645	−	1.17144i	0.981278	−	0.192598i	$-0.0616913\pi$
$6$	−2.49047	+	2.25496i	−1.01673	+	0.920585i
$7$	−1.58443	+	3.49630i	−0.598859	+	1.32148i	0.327506	+	0.944849i	$0.393792\pi$
$7$	−1.58443	+	3.49630i	−0.598859	+	1.32148i	−0.926365	+	0.376627i	$0.877084\pi$
$8$	7.58350	−	5.20426i	2.68117	−	1.83998i
$9$	−0.765444	−	1.25675i	−0.255148	−	0.418917i
$10$	5.25132	+	6.73519i	1.66061	+	2.12985i
$11$	−0.162710	−	0.0104250i	−0.0490589	−	0.00314326i	0.0393911	−	0.999224i	$-0.487458\pi$
$11$	−0.162710	−	0.0104250i	−0.0490589	−	0.00314326i	−0.0884501	+	0.996081i	$0.528191\pi$
$12$	−2.67002	−	6.09819i	−0.770768	−	1.76040i
$13$	−0.748119	−	0.864391i	−0.207491	−	0.239739i	0.642823	−	0.766015i	$-0.277763\pi$
$13$	−0.748119	−	0.864391i	−0.207491	−	0.239739i	−0.850314	+	0.526276i	$0.823588\pi$
$14$	−7.64223	−	7.09963i	−2.04247	−	1.89745i
$15$	3.45806	−	1.77174i	0.892868	−	0.457461i
$16$	3.90820	+	13.6772i	0.977049	+	3.41930i
$17$	6.25017	−	2.76042i	1.51589	−	0.669501i	0.531750	−	0.846901i	$-0.321535\pi$
$17$	6.25017	−	2.76042i	1.51589	−	0.669501i	0.984139	+	0.177401i	$0.0567688\pi$
$18$	3.89890	−	0.888025i	0.918980	−	0.209309i
$19$	0.449946	+	0.343924i	0.103225	+	0.0789015i	0.657609	−	0.753359i	$-0.271568\pi$
$19$	0.449946	+	0.343924i	0.103225	+	0.0789015i	−0.554385	+	0.832261i	$0.687046\pi$
$20$	−15.9590	+	5.62935i	−3.56853	+	1.25876i
$21$	−3.82502	+	2.80907i	−0.834688	+	0.612989i
$22$	0.167259	−	0.410281i	0.0356598	−	0.0874723i
$23$	−0.836680	−	7.89568i	−0.174460	−	1.64636i	−0.645144	−	0.764061i	$-0.723203\pi$
$23$	−0.836680	−	7.89568i	−0.174460	−	1.64636i	0.470684	−	0.882302i	$-0.344007\pi$
$24$	11.3255	−	1.01722i	2.31180	−	0.207640i
$25$	−1.89881	−	4.49240i	−0.379762	−	0.898480i
$26$	2.87291	−	1.18193i	0.563424	−	0.231796i
$27$	−0.194503	−	5.52480i	−0.0374322	−	1.06325i
$28$	18.1480	−	9.89243i	3.42965	−	1.86949i
$29$	5.78597	−	8.37361i	1.07443	−	1.55494i	0.268174	−	0.963370i	$-0.413580\pi$
$29$	5.78597	−	8.37361i	1.07443	−	1.55494i	0.806254	−	0.591570i	$-0.201492\pi$
$30$	1.58165	+	10.4396i	0.288769	+	1.90600i
$31$	4.19827	+	6.24523i	0.754031	+	1.12168i	0.988745	+	0.149613i	$0.0478027\pi$
$31$	4.19827	+	6.24523i	0.754031	+	1.12168i	−0.234714	+	0.972065i	$0.575415\pi$
$32$	−20.2395	−	0.907105i	−3.57788	−	0.160355i
$33$	−0.169067	−	0.109767i	−0.0294307	−	0.0191081i
$34$	1.72014	+	18.4875i	0.295001	+	3.17058i
$35$	6.40667	+	10.2221i	1.08292	+	1.72784i
$36$	−0.784516	+	7.88451i	−0.130753	+	1.31409i
$37$	−0.185888	+	0.0461086i	−0.0305599	+	0.00758021i	−0.255999	−	0.966677i	$-0.582404\pi$
$37$	−0.185888	+	0.0461086i	−0.0305599	+	0.00758021i	0.225439	+	0.974257i	$0.427618\pi$
$38$	−1.27447	+	0.862678i	−0.206747	+	0.139945i
$39$	−0.282931	−	1.38473i	−0.0453052	−	0.221734i
$40$	−0.462355	−	28.9022i	−0.0731048	−	4.56984i
$41$	−1.36157	−	0.122293i	−0.212642	−	0.0190989i	−0.0173749	−	0.999849i	$-0.505531\pi$
$41$	−1.36157	−	0.122293i	−0.212642	−	0.0190989i	−0.195267	+	0.980750i	$0.562557\pi$
$42$	−3.93804	−	12.2803i	−0.607653	−	1.89489i
$43$	0.0951545	+	0.130442i	0.0145109	+	0.0198922i	0.815081	−	0.579346i	$-0.196692\pi$
$43$	0.0951545	+	0.130442i	0.0145109	+	0.0198922i	−0.800571	+	0.599239i	$0.795470\pi$
$44$	0.665659	+	0.572405i	0.100352	+	0.0862933i
$45$	−4.62124	−	0.177497i	−0.688894	−	0.0264597i
$46$	21.0678	+	4.65686i	3.10627	+	0.686617i
$47$	0.850979	+	2.84002i	0.124128	+	0.414259i	0.997324	−	0.0731104i	$-0.0232926\pi$
$47$	0.850979	+	2.84002i	0.124128	+	0.414259i	−0.873196	+	0.487369i	$0.837957\pi$
$48$	−4.06985	+	17.1088i	−0.587433	+	2.46945i
$49$	−5.09895	−	5.81580i	−0.728422	−	0.830829i
$50$	13.2146	−	1.01662i	1.86882	−	0.143771i
$51$	8.40844	+	0.809490i	1.17742	+	0.113351i
$52$	0.413235	+	6.14165i	0.0573054	+	0.851694i
$53$	−8.86230	+	8.12805i	−1.21733	+	1.11647i	−0.227566	+	0.973763i	$0.573077\pi$
$53$	−8.86230	+	8.12805i	−1.21733	+	1.11647i	−0.989765	+	0.142710i	$0.954418\pi$
$54$	14.4043	+	4.26592i	1.96018	+	0.580518i
$55$	−0.309875	+	0.408100i	−0.0417835	+	0.0550282i
$56$	6.18009	+	34.7600i	0.825849	+	4.64499i
$57$	0.276715	+	0.643173i	0.0366518	+	0.0851903i
$58$	16.5849	+	22.1347i	2.17771	+	2.90643i
$59$	6.33010	+	0.486984i	0.824109	+	0.0633999i	0.481902	−	0.876225i	$-0.339946\pi$
$59$	6.33010	+	0.486984i	0.824109	+	0.0633999i	0.342206	+	0.939625i	$0.388826\pi$
$60$	−20.6105	−	3.59643i	−2.66080	−	0.464297i
$61$	9.84991	+	8.36098i	1.26115	+	1.07051i	0.994283	+	0.106781i	$0.0340545\pi$
$61$	9.84991	+	8.36098i	1.26115	+	1.07051i	0.266870	+	0.963733i	$0.414011\pi$
$62$	−19.7154	+	5.42948i	−2.50386	+	0.689544i
$63$	5.60677	−	0.684985i	0.706386	−	0.0863001i
$64$	9.56921	−	24.8257i	1.19615	−	3.10321i
$65$	−3.56340	+	0.458504i	−0.441986	+	0.0568704i
$66$	0.428733	−	0.340942i	0.0527734	−	0.0419671i
$67$	−0.395660	+	0.340231i	−0.0483376	+	0.0415658i	−0.675836	−	0.737052i	$-0.736217\pi$
$67$	−0.395660	+	0.340231i	−0.0483376	+	0.0415658i	0.627499	+	0.778618i	$0.284079\pi$
$68$	−35.8191	−	8.39968i	−4.34370	−	1.01861i
$69$	3.87948	−	9.01713i	0.467034	−	1.08554i
$70$	−31.8686	+	7.68872i	−3.80902	+	0.918978i
$71$	7.05451	−	5.75886i	0.837216	−	0.683451i	−0.113492	−	0.993539i	$-0.536204\pi$
$71$	7.05451	−	5.75886i	0.837216	−	0.683451i	0.950708	+	0.310088i	$0.100358\pi$
$72$	−12.3452	−	5.54699i	−1.45489	−	0.653719i
$73$	2.46400	+	1.76146i	0.288390	+	0.206163i	0.716543	−	0.697543i	$-0.245724\pi$
$73$	2.46400	+	1.76146i	0.288390	+	0.206163i	−0.428153	+	0.903706i	$0.640836\pi$
$74$	0.0415811	−	0.518788i	0.00483370	−	0.0603079i
$75$	0.673755	−	5.99204i	0.0777985	−	0.691902i
$76$	−0.819063	−	2.93742i	−0.0939530	−	0.336946i
$77$	0.294252	−	0.552365i	0.0335331	−	0.0629479i
$78$	3.81234	+	0.465758i	0.431662	+	0.0527367i
$79$	2.54140	−	0.376721i	0.285929	−	0.0423844i	−0.00212735	−	0.999998i	$-0.500677\pi$
$79$	2.54140	−	0.376721i	0.285929	−	0.0423844i	0.288057	+	0.957613i	$0.406991\pi$
$80$	42.6133	+	13.5151i	4.76431	+	1.51103i
$81$	1.11044	−	2.15037i	0.123382	−	0.238930i
$82$	1.48997	−	3.40302i	0.164540	−	0.375801i
$83$	2.31539	−	0.718067i	0.254147	−	0.0788181i	−0.166504	−	0.986041i	$-0.553248\pi$
$83$	2.31539	−	0.718067i	0.254147	−	0.0788181i	0.420651	+	0.907223i	$0.361802\pi$
$84$	25.5515	+	0.326994i	2.78790	+	0.0356779i
$85$	3.62356	−	21.1656i	0.393030	−	2.29573i
$86$	−0.418231	+	0.132645i	−0.0450990	+	0.0143034i
$87$	11.3072	−	5.52187i	1.21226	−	0.592006i
$88$	−1.28817	+	0.767727i	−0.137319	+	0.0818400i
$89$	1.88577	+	1.24157i	0.199891	+	0.131606i	0.645899	−	0.763423i	$-0.276483\pi$
$89$	1.88577	+	1.24157i	0.199891	+	0.131606i	−0.446008	+	0.895029i	$0.647155\pi$
$90$	4.44485	−	11.7550i	0.468529	−	1.23909i
$91$	4.20751	−	1.24608i	0.441067	−	0.130624i
$92$	−22.0051	+	36.6551i	−2.29419	+	3.82156i
$93$	0.743301	+	9.27382i	0.0770767	+	0.961650i
$94$	−8.05252	−	0.257702i	−0.830554	−	0.0265800i
$95$	1.68227	−	0.581326i	0.172597	−	0.0596428i
$96$	−21.2662	−	13.2340i	−2.17047	−	1.35069i
$97$	−6.78154	+	0.347429i	−0.688561	+	0.0352761i	−0.392309	−	0.919834i	$-0.628323\pi$
$97$	−6.78154	+	0.347429i	−0.688561	+	0.0352761i	−0.296252	+	0.955110i	$0.595737\pi$
$98$	19.3860	−	8.12093i	1.95828	−	0.820338i
$99$	0.111444	+	0.212466i	0.0112005	+	0.0213536i
$100$	−6.40400	+	25.4690i	−0.640400	+	2.54690i
$101$	−7.18862	−	5.20880i	−0.715295	−	0.518295i	0.168772	−	0.985655i	$-0.446020\pi$
$101$	−7.18862	−	5.20880i	−0.715295	−	0.518295i	−0.884067	+	0.467360i	$0.845205\pi$
$102$	−9.34121	+	20.9687i	−0.924918	+	2.07621i
$103$	−7.72308	−	3.00532i	−0.760977	−	0.296123i	−0.0494459	−	0.998777i	$-0.515746\pi$
$103$	−7.72308	−	3.00532i	−0.760977	−	0.296123i	−0.711531	+	0.702654i	$0.751998\pi$
$104$	−10.1719	−	2.66170i	−0.997434	−	0.261001i
$105$	0.715451	+	14.8976i	0.0698209	+	1.45386i
$106$	−13.2977	−	29.8500i	−1.29159	−	2.89929i
$107$	4.01119	−	19.0107i	0.387776	−	1.83783i	−0.142227	−	0.989834i	$-0.545426\pi$
$107$	4.01119	−	19.0107i	0.387776	−	1.83783i	0.530003	−	0.847996i	$-0.322191\pi$
$108$	−17.0781	+	24.3808i	−1.64334	+	2.34605i
$109$	−10.9351	−	12.9663i	−1.04739	−	1.24194i	−0.969529	−	0.244978i	$-0.921219\pi$
$109$	−10.9351	−	12.9663i	−1.04739	−	1.24194i	−0.0778617	−	0.996964i	$-0.524809\pi$
$110$	−0.784228	−	1.15063i	−0.0747732	−	0.109708i
$111$	−0.228284	−	0.0628677i	−0.0216678	−	0.00596714i
$112$	−54.0118	−	8.00638i	−5.10364	−	0.756532i
$113$	12.9500	+	6.32412i	1.21823	+	0.594923i	0.931728	−	0.363156i	$-0.118301\pi$
$113$	12.9500	+	6.32412i	1.21823	+	0.594923i	0.286505	+	0.958079i	$0.407506\pi$
$114$	−1.89611	+	0.158081i	−0.177587	+	0.0148056i
$115$	−22.1350	−	11.5203i	−2.06410	−	1.07427i
$116$	−52.0244	+	17.2356i	−4.83035	+	1.60028i
$117$	−0.513680	+	1.60184i	−0.0474897	+	0.148090i
$118$	−6.71685	+	15.8914i	−0.618336	+	1.46292i
$119$	−0.251714	+	26.2262i	−0.0230746	+	2.40415i
$120$	17.0036	−	31.4326i	1.55221	−	2.86939i
$121$	−10.8837	−	1.40041i	−0.989426	−	0.127310i
$122$	−30.0439	+	18.1672i	−2.72005	+	1.64478i
$123$	−1.39354	−	0.956329i	−0.125651	−	0.0862293i
$124$	2.20264	−	40.4601i	0.197803	−	3.63342i
$125$	0.379291	+	0.0711973i	0.0339248	+	0.00636808i
$126$	−3.07275	+	15.0387i	−0.273742	+	1.33976i
$127$	5.74940	+	13.8489i	0.510177	+	1.22889i	0.944611	+	0.328191i	$0.106439\pi$
$127$	5.74940	+	13.8489i	0.510177	+	1.22889i	−0.434435	+	0.900703i	$0.643052\pi$
$128$	24.4905	+	20.2551i	2.16468	+	1.79031i
$129$	0.0235735	+	0.198220i	0.00207553	+	0.0174523i
$130$	1.89322	−	9.57791i	0.166047	−	0.840039i
$131$	10.0344	+	5.14110i	0.876706	+	0.449180i	0.835192	−	0.549958i	$-0.185356\pi$
$131$	10.0344	+	5.14110i	0.876706	+	0.449180i	0.0415135	+	0.999138i	$0.486782\pi$
$132$	0.370865	+	1.02007i	0.0322797	+	0.0887858i
$133$	−1.91537	+	1.02822i	−0.166084	+	0.0891581i
$134$	−0.535319	−	1.31312i	−0.0462445	−	0.113436i
$135$	−14.8095	−	9.08506i	−1.27460	−	0.781918i
$136$	33.0322	−	53.4611i	2.83249	−	4.58425i
$137$	−1.42800	−	2.52282i	−0.122002	−	0.215539i	0.802560	−	0.596572i	$-0.203471\pi$
$137$	−1.42800	−	2.52282i	−0.122002	−	0.215539i	−0.924562	+	0.381032i	$0.875569\pi$
$138$	19.8882	+	17.7773i	1.69300	+	1.51330i
$139$	−5.98676	+	11.4137i	−0.507791	+	0.968093i	0.487680	+	0.873023i	$0.337843\pi$
$139$	−5.98676	+	11.4137i	−0.507791	+	0.968093i	−0.995471	+	0.0950706i	$0.969692\pi$
$140$	5.60402	−	64.7166i	0.473626	−	5.46955i
$141$	−0.802561	+	3.57647i	−0.0675878	+	0.301193i
$142$	8.75258	+	23.1474i	0.734501	+	1.94248i
$143$	0.112715	+	0.148444i	0.00942572	+	0.0124135i
$144$	14.1973	−	15.3808i	1.18311	−	1.28173i
$145$	−11.8858	−	29.6977i	−0.987065	−	2.46626i
$146$	−6.66506	+	4.82943i	−0.551605	+	0.399687i
$147$	−1.97416	−	9.35637i	−0.162826	−	0.771701i
$148$	0.948609	+	0.404533i	0.0779752	+	0.0332524i
$149$	−4.81599	−	18.6480i	−0.394542	−	1.52771i	−0.792251	−	0.610196i	$-0.791091\pi$
$149$	−4.81599	−	18.6480i	−0.394542	−	1.52771i	0.397709	−	0.917512i	$-0.369805\pi$
$150$	14.8591	+	6.90644i	1.21324	+	0.563908i
$151$	9.34745	−	3.36461i	0.760684	−	0.273808i	0.0705683	−	0.997507i	$-0.477519\pi$
$151$	9.34745	−	3.36461i	0.760684	−	0.273808i	0.690116	+	0.723699i	$0.257559\pi$
$152$	5.20203	+	0.266508i	0.421940	+	0.0216167i
$153$	−8.25332	−	5.74195i	−0.667241	−	0.464209i
$154$	1.16945	+	1.23485i	0.0942373	+	0.0995071i
$155$	23.6497	−	0.151321i	1.89959	−	0.0121544i
$156$	−3.27373	+	6.87011i	−0.262108	+	0.550049i
$157$	−14.1867	−	15.3693i	−1.13223	−	1.22660i	−0.970844	−	0.239712i	$-0.922947\pi$
$157$	−14.1867	−	15.3693i	−1.13223	−	1.22660i	−0.161381	−	0.986892i	$-0.551595\pi$
$158$	−1.22212	+	6.87381i	−0.0972265	+	0.546851i
$159$	−14.4744	+	3.39428i	−1.14789	+	0.269184i
$160$	−37.5247	+	51.4404i	−2.96659	+	4.06672i
$161$	28.9313	+	9.58489i	2.28011	+	0.755395i
$162$	4.58300	+	4.71689i	0.360074	+	0.370594i
$163$	11.3736	−	2.89854i	0.890851	−	0.227031i	0.226107	−	0.974103i	$-0.427400\pi$
$163$	11.3736	−	2.89854i	0.890851	−	0.227031i	0.664744	+	0.747071i	$0.268541\pi$
$164$	5.45663	+	4.94063i	0.426091	+	0.385799i
$165$	−0.581132	+	0.252229i	−0.0452411	+	0.0196360i
$166$	−0.147512	+	6.58595i	−0.0114492	+	0.511169i
$167$	−1.20353	−	6.52668i	−0.0931320	−	0.505050i	−0.997011	−	0.0772612i	$-0.975382\pi$
$167$	−1.20353	−	6.52668i	−0.0931320	−	0.505050i	0.903879	−	0.427788i	$-0.140707\pi$
$168$	−14.3879	+	41.2090i	−1.11005	+	3.17934i
$169$	1.67757	−	11.5722i	0.129044	−	0.890168i
$170$	51.4136	+	27.6002i	3.94324	+	2.11684i
$171$	0.0878173	−	0.828724i	0.00671556	−	0.0633741i
$172$	0.0139062	−	0.869286i	0.00106034	−	0.0662824i
$173$	−20.0389	+	3.76152i	−1.52353	+	0.285983i	−0.878338	−	0.478040i	$-0.841347\pi$
$173$	−20.0389	+	3.76152i	−1.52353	+	0.285983i	−0.645188	+	0.764024i	$0.723221\pi$
$174$	4.47240	+	33.9014i	0.339052	+	2.57006i
$175$	18.7153	+	0.479093i	1.41474	+	0.0362161i
$176$	−0.493318	−	2.26616i	−0.0371853	−	0.170818i
$177$	6.52809	+	4.35816i	0.490681	+	0.327579i
$178$	−4.82647	+	3.78801i	−0.361759	+	0.283923i
$179$	7.72700	+	3.71243i	0.577543	+	0.277480i	0.699006	−	0.715116i	$-0.253626\pi$
$179$	7.72700	+	3.71243i	0.577543	+	0.277480i	−0.121463	+	0.992596i	$0.538759\pi$
$180$	19.2904	+	15.7475i	1.43782	+	1.17375i
$181$	10.0265	+	20.0413i	0.745264	+	1.48966i	0.867650	+	0.497176i	$0.165630\pi$
$181$	10.0265	+	20.0413i	0.745264	+	1.48966i	−0.122386	+	0.992483i	$0.539055\pi$
$182$	−0.419552	+	11.9172i	−0.0310993	+	0.883365i
$183$	5.55380	+	14.9767i	0.410549	+	1.10711i
$184$	−47.4361	−	55.5225i	−3.49704	−	4.09318i
$185$	−0.202042	+	0.566992i	−0.0148544	+	0.0416861i
$186$	−24.5384	−	6.08663i	−1.79925	−	0.446293i
$187$	−1.04574	+	0.383991i	−0.0764723	+	0.0280802i
$188$	5.55058	−	14.9680i	0.404818	−	1.09166i
$189$	19.6245	+	8.07364i	1.42747	+	0.587271i
$190$	0.0464201	+	4.83652i	0.00336767	+	0.350878i
$191$	−8.43695	−	4.45988i	−0.610476	−	0.322706i	0.133360	−	0.991068i	$-0.457423\pi$
$191$	−8.43695	−	4.45988i	−0.610476	−	0.322706i	−0.743836	+	0.668362i	$0.766996\pi$
$192$	25.3478	−	20.9640i	1.82932	−	1.51295i
$193$	−3.72887	−	3.55409i	−0.268410	−	0.255829i	0.543772	−	0.839233i	$-0.316995\pi$
$193$	−3.72887	−	3.55409i	−0.268410	−	0.255829i	−0.812182	+	0.583404i	$0.801721\pi$
$194$	4.95624	−	17.7747i	0.355837	−	1.27615i
$195$	−4.11852	−	1.66365i	−0.294933	−	0.119136i
$196$	3.06168	+	41.5345i	0.218692	+	2.96675i
$197$	8.18798	−	2.19864i	0.583369	−	0.156647i	0.0444608	−	0.999011i	$-0.485843\pi$
$197$	8.18798	−	2.19864i	0.583369	−	0.156647i	0.538908	+	0.842364i	$0.318837\pi$
$198$	−0.643649	+	0.103845i	−0.0457421	+	0.00737991i
$199$	−6.76895	+	10.4991i	−0.479838	+	0.744261i	−0.993512	−	0.113725i	$-0.963722\pi$
$199$	−6.76895	+	10.4991i	−0.479838	+	0.744261i	0.513674	+	0.857985i	$0.328284\pi$
$200$	−37.7792	−	24.1862i	−2.67140	−	1.71022i
$201$	−0.632498	+	0.127127i	−0.0446130	+	0.00896684i
$202$	19.6250	−	14.0294i	1.38081	−	0.987106i
$203$	20.1091	+	33.4969i	1.41139	+	2.35102i
$204$	−33.5216	−	30.7443i	−2.34698	−	2.15253i
$205$	−2.68489	+	3.35414i	−0.187521	+	0.234264i
$206$	14.4081	−	17.3079i	1.00386	−	1.20590i
$207$	−9.28246	+	7.09520i	−0.645176	+	0.493150i
$208$	8.89865	−	13.6104i	0.617010	−	0.943710i
$209$	−0.0696254	−	0.0606505i	−0.00481609	−	0.00419529i
$210$	−39.0060	−	11.0109i	−2.69167	−	0.759827i
$211$	0.488964	+	2.97023i	0.0336616	+	0.204479i	0.998239	−	0.0593213i	$-0.0188936\pi$
$211$	0.488964	+	2.97023i	0.0336616	+	0.204479i	−0.964577	+	0.263800i	$0.915024\pi$
$212$	64.4528	−	6.20494i	4.42663	−	0.426157i
$213$	11.0911	−	1.93535i	0.759953	−	0.132608i
$214$	45.5262	+	26.7397i	3.11211	+	1.82789i
$215$	0.506929	−	0.0227198i	0.0345723	−	0.00154948i
$216$	−30.2275	−	40.8851i	−2.05672	−	2.78188i
$217$	−28.4871	+	4.78324i	−1.93383	+	0.324707i
$218$	42.8473	−	16.9898i	2.90198	−	1.15070i
$219$	1.58919	+	3.39071i	0.107388	+	0.229123i
$220$	2.65537	−	0.749579i	0.179025	−	0.0505366i
$221$	−7.06195	−	3.33746i	−0.475038	−	0.224502i
$222$	0.358976	−	0.534004i	0.0240929	−	0.0358400i
$223$	6.92168	−	9.36212i	0.463510	−	0.626934i	−0.508728	−	0.860927i	$-0.669884\pi$
$223$	6.92168	−	9.36212i	0.463510	−	0.626934i	0.972238	+	0.233993i	$0.0751794\pi$
$224$	35.2397	−	69.3262i	2.35455	−	4.63205i
$225$	−4.19239	+	5.82501i	−0.279493	+	0.388334i
$226$	−27.4702	+	27.9132i	−1.82729	+	1.85676i
$227$	7.80564	+	13.1928i	0.518079	+	0.875640i	1.00000		0.000574849i	$-0.000182980\pi$
$227$	7.80564	+	13.1928i	0.518079	+	0.875640i	−0.481921	+	0.876215i	$0.660061\pi$
$228$	0.895947	−	3.66214i	0.0593355	−	0.242531i
$229$	−1.50108	+	6.89551i	−0.0991940	+	0.455668i	0.900586	+	0.434679i	$0.143138\pi$
$229$	−1.50108	+	6.89551i	−0.0991940	+	0.455668i	−0.999780	+	0.0209899i	$0.993318\pi$
$230$	48.7852	−	47.0979i	3.21680	−	3.10554i
$231$	0.651654	−	0.417188i	0.0428757	−	0.0274489i
$232$	0.299485	−	93.6129i	0.0196622	−	6.14599i
$233$	−12.1294	+	7.44094i	−0.794626	+	0.487472i	−0.859942	−	0.510393i	$-0.829500\pi$
$233$	−12.1294	+	7.44094i	−0.794626	+	0.487472i	0.0653156	+	0.997865i	$0.479195\pi$
$234$	−3.68444	−	2.70583i	−0.240860	−	0.176885i
$235$	8.91701	+	2.70300i	0.581682	+	0.176324i
$236$	−25.6329	−	22.6189i	−1.66856	−	1.47236i
$237$	2.96741	+	1.13291i	0.192754	+	0.0735907i
$238$	−67.3632	−	23.2781i	−4.36651	−	1.50889i
$239$	−2.31318	−	2.85218i	−0.149627	−	0.184492i	0.696365	−	0.717688i	$-0.254799\pi$
$239$	−2.31318	−	2.85218i	−0.149627	−	0.184492i	−0.845992	+	0.533196i	$0.820991\pi$
$240$	37.7472	+	40.3723i	2.43657	+	2.60602i
$241$	17.2686	+	0.110492i	1.11237	+	0.00711743i	0.561502	−	0.827475i	$-0.310224\pi$
$241$	17.2686	+	0.110492i	1.11237	+	0.00711743i	0.550867	+	0.834593i	$0.314297\pi$
$242$	12.9997	−	26.8371i	0.835652	−	1.72515i
$243$	−11.3529	+	7.47462i	−0.728288	+	0.479497i
$244$	−15.2325	−	67.8809i	−0.975159	−	4.34563i
$245$	−24.0890	+	3.25635i	−1.53899	+	0.208040i
$246$	3.66672	−	2.76573i	0.233782	−	0.176337i
$247$	−0.0393288	−	0.646225i	−0.00250243	−	0.0411183i
$248$	64.3393	+	25.5119i	4.08555	+	1.62000i
$249$	2.93051	+	0.628126i	0.185713	+	0.0398059i
$250$	−0.510738	+	0.915936i	−0.0323019	+	0.0579289i
$251$	−6.43000	+	21.4592i	−0.405858	+	1.35449i	0.474530	+	0.880239i	$0.342618\pi$
$251$	−6.43000	+	21.4592i	−0.405858	+	1.35449i	−0.880388	+	0.474253i	$0.842718\pi$
$252$	−26.3236	−	15.2354i	−1.65823	−	0.959739i
$253$	0.0538239	+	1.29343i	0.00338388	+	0.0813172i
$254$	−40.6473	+	2.86557i	−2.55044	+	0.179802i
$255$	16.7227	−	20.6194i	1.04722	−	1.29124i
$256$	−28.1472	+	17.5160i	−1.75920	+	1.09475i
$257$	−3.52116	+	2.44972i	−0.219644	+	0.152809i	−0.675787	−	0.737097i	$-0.736196\pi$
$257$	−3.52116	+	2.44972i	−0.219644	+	0.152809i	0.456143	+	0.889907i	$0.349231\pi$
$258$	−0.531121	−	0.110291i	−0.0330662	−	0.00686643i
$259$	0.133318	−	0.722977i	0.00828399	−	0.0449236i
$260$	16.8051	+	9.58335i	1.04221	+	0.594334i
$261$	−14.9524	−	0.861988i	−0.925529	−	0.0533557i
$262$	−21.9060	+	21.4208i	−1.35336	+	1.32338i
$263$	−0.0358002	−	0.146331i	−0.00220753	−	0.00902318i	0.970238	−	0.242152i	$-0.0778532\pi$
$263$	−0.0358002	−	0.146331i	−0.00220753	−	0.00902318i	−0.972446	+	0.233129i	$0.925104\pi$
$264$	−1.85337	+	0.0474445i	−0.114067	+	0.00292001i
$265$	5.90016	+	37.3294i	0.362444	+	2.29313i
$266$	−0.996863	−	5.82279i	−0.0611216	−	0.357018i
$267$	1.28076	+	2.48019i	0.0783811	+	0.151785i
$268$	2.80408	−	0.179660i	0.171286	−	0.0109745i
$269$	−7.30264	−	8.22257i	−0.445250	−	0.501339i	0.481798	−	0.876282i	$-0.339984\pi$
$269$	−7.30264	−	8.22257i	−0.445250	−	0.501339i	−0.927048	+	0.374943i	$0.877662\pi$
$270$	36.1892	−	30.3225i	2.20240	−	1.84537i
$271$	10.3464	−	0.198623i	0.628496	−	0.0120655i	0.296027	−	0.955180i	$-0.404338\pi$
$271$	10.3464	−	0.198623i	0.628496	−	0.0120655i	0.332469	+	0.943114i	$0.392118\pi$
$272$	62.1817	+	74.6965i	3.77032	+	4.52914i
$273$	5.28970	+	1.20480i	0.320147	+	0.0729176i
$274$	7.73305	−	1.50287i	0.467171	−	0.0907915i
$275$	0.262123	+	0.750754i	0.0158066	+	0.0452722i
$276$	−45.9154	+	26.1838i	−2.76378	+	1.57608i
$277$	−4.59624	+	2.28110i	−0.276161	+	0.137058i	−0.577326	−	0.816514i	$-0.695904\pi$
$277$	−4.59624	+	2.28110i	−0.276161	+	0.137058i	0.301165	+	0.953572i	$0.402625\pi$
$278$	−24.2453	−	25.2752i	−1.45414	−	1.51591i
$279$	4.63516	−	10.0566i	0.277500	−	0.602070i
$280$	101.783	+	44.1770i	6.08271	+	2.64008i
$281$	−4.71219	−	10.3982i	−0.281105	−	0.620303i	0.715852	−	0.698252i	$-0.246039\pi$
$281$	−4.71219	−	10.3982i	−0.281105	−	0.620303i	−0.996957	+	0.0779491i	$0.975163\pi$
$282$	−8.52348	−	5.15405i	−0.507566	−	0.306919i
$283$	−9.94557	−	7.90904i	−0.591203	−	0.470144i	0.280718	−	0.959790i	$-0.409427\pi$
$283$	−9.94557	−	7.90904i	−0.591203	−	0.470144i	−0.871921	+	0.489646i	$0.837126\pi$
$284$	−48.9993	+	1.88201i	−2.90757	+	0.111677i
$285$	2.16529	+	0.392124i	0.128260	+	0.0232274i
$286$	−0.479773	+	0.162362i	−0.0283696	+	0.00960066i
$287$	2.58489	−	4.56670i	0.152581	−	0.269564i
$288$	14.3522	+	26.1304i	0.845714	+	1.53975i
$289$	19.9942	−	21.9409i	1.17613	−	1.29064i
$290$	86.7818	−	5.00288i	5.09600	−	0.293779i
$291$	−7.51997	−	3.73215i	−0.440829	−	0.218782i
$292$	−4.88077	−	15.5618i	−0.285625	−	0.910683i
$293$	−2.20334	+	0.576555i	−0.128721	+	0.0336827i	−0.316949	−	0.948443i	$-0.602658\pi$
$293$	−2.20334	+	0.576555i	−0.128721	+	0.0336827i	0.188228	+	0.982125i	$0.439726\pi$
$294$	25.8132	+	2.98613i	1.50546	+	0.174155i
$295$	12.2687	−	15.7354i	0.714309	−	0.916152i
$296$	−1.16972	+	1.31708i	−0.0679887	+	0.0765534i
$297$	−0.0259484	+	0.900969i	−0.00150568	+	0.0522795i
$298$	52.2084	+	3.68061i	3.02435	+	0.213212i
$299$	−6.19901	+	6.63012i	−0.358498	+	0.383430i
$300$	−22.3256	+	23.5741i	−1.28897	+	1.36105i
$301$	−0.606829	+	0.126012i	−0.0349770	+	0.00726324i
$302$	0.604521	+	26.9900i	0.0347863	+	1.55310i
$303$	−4.59412	−	9.96752i	−0.263926	−	0.572619i
$304$	−2.94543	+	7.49812i	−0.168932	+	0.430047i
$305$	39.0065	−	11.2810i	2.23351	−	0.645950i
$306$	21.9175	−	16.3129i	1.25294	−	0.932548i
$307$	−10.9405	+	10.8360i	−0.624406	+	0.618442i	−0.944329	−	0.329002i	$-0.893288\pi$
$307$	−10.9405	+	10.8360i	−0.624406	+	0.618442i	0.319924	+	0.947443i	$0.396343\pi$
$308$	−3.05599	+	1.42041i	−0.174131	+	0.0809351i
$309$	−6.50453	−	7.91611i	−0.370030	−	0.450332i
$310$	−20.0164	+	61.0718i	−1.13685	+	3.46865i
$311$	−3.49198	+	2.33125i	−0.198012	+	0.132193i	−0.650296	−	0.759681i	$-0.725355\pi$
$311$	−3.49198	+	2.33125i	−0.198012	+	0.132193i	0.452284	+	0.891874i	$0.350610\pi$
$312$	−9.35208	−	9.02863i	−0.529457	−	0.511146i
$313$	−15.9936	−	3.21458i	−0.904010	−	0.181699i	−0.277147	−	0.960828i	$-0.589389\pi$
$313$	−15.9936	−	3.21458i	−0.904010	−	0.181699i	−0.626864	+	0.779129i	$0.715662\pi$
$314$	51.8453	−	23.2953i	2.92580	−	1.31463i
$315$	7.94263	−	15.8760i	0.447516	−	0.894511i
$316$	−12.1465	−	6.62105i	−0.683296	−	0.372463i
$317$	−18.2800	+	9.21854i	−1.02670	+	0.517765i	−0.881772	−	0.471677i	$-0.843649\pi$
$317$	−18.2800	+	9.21854i	−1.02670	+	0.517765i	−0.144933	+	0.989441i	$0.546297\pi$
$318$	3.74284	−	40.2268i	0.209888	−	2.25581i
$319$	−1.02873	+	1.30215i	−0.0575979	+	0.0729065i
$320$	−48.4106	−	68.1788i	−2.70623	−	3.81131i
$321$	15.8356	−	18.0619i	0.883858	−	1.00812i
$322$	−49.6623	+	66.2807i	−2.76757	+	3.69368i
$323$	3.76161	+	0.907539i	0.209302	+	0.0504968i
$324$	−11.7462	+	5.64345i	−0.652567	+	0.313525i
$325$	−2.46265	+	5.00216i	−0.136603	+	0.277470i
$326$	−2.34477	+	31.8089i	−0.129865	+	1.76173i
$327$	−3.93469	−	20.5977i	−0.217589	−	1.13906i
$328$	−10.9619	+	6.15857i	−0.605271	+	0.340050i
$329$	−11.2779	−	1.52454i	−0.621769	−	0.0840507i
$330$	−0.148518	−	1.71512i	−0.00817563	−	0.0944142i
$331$	−23.9134	−	10.0175i	−1.31440	−	0.550610i	−0.386103	−	0.922456i	$-0.626179\pi$
$331$	−23.9134	−	10.0175i	−1.31440	−	0.550610i	−0.928294	+	0.371846i	$0.878725\pi$
$332$	−12.2818	−	4.42083i	−0.674050	−	0.242624i
$333$	0.200234	+	0.198322i	0.0109728	+	0.0108680i
$334$	17.8566	+	2.53030i	0.977071	+	0.138452i
$335$	0.204089	+	1.62725i	0.0111506	+	0.0889063i
$336$	−53.3691	−	41.3372i	−2.91152	−	2.25513i
$337$	2.22209	−	3.54543i	0.121045	−	0.193132i	−0.781288	−	0.624170i	$-0.785437\pi$
$337$	2.22209	−	3.54543i	0.121045	−	0.193132i	0.902334	+	0.431038i	$0.141853\pi$
$338$	28.3721	+	14.3080i	1.54324	+	0.778251i
$339$	10.1287	+	14.6585i	0.550116	+	0.796143i
$340$	−84.2068	+	79.2378i	−4.56675	+	4.29727i
$341$	−0.617994	−	1.05993i	−0.0334662	−	0.0573984i
$342$	2.05971	+	0.941362i	0.111376	+	0.0509030i
$343$	2.69827	−	0.817923i	0.145693	−	0.0441637i
$344$	1.40046	+	0.493996i	0.0755075	+	0.0266345i
$345$	−16.8824	−	25.8214i	−0.908916	−	1.39018i
$346$	7.59787	−	54.8824i	0.408464	−	2.95050i
$347$	18.9196	+	8.35593i	1.01565	+	0.448570i	0.843860	−	0.536563i	$-0.180278\pi$
$347$	18.9196	+	8.35593i	1.01565	+	0.448570i	0.171795	+	0.985133i	$0.445043\pi$
$348$	−66.5125	−	12.9263i	−3.56544	−	0.692920i
$349$	2.82283	+	19.4724i	0.151102	+	1.04233i	0.916862	+	0.399204i	$0.130714\pi$
$349$	2.82283	+	19.4724i	0.151102	+	1.04233i	−0.765760	+	0.643127i	$0.777637\pi$
$350$	−17.3832	+	47.8128i	−0.929171	+	2.55570i
$351$	−4.63008	+	4.30134i	−0.247135	+	0.229588i
$352$	3.28372	+	0.358592i	0.175023	+	0.0191130i
$353$	−13.3021	−	13.3448i	−0.708002	−	0.710270i	0.258762	−	0.965941i	$-0.416685\pi$
$353$	−13.3021	−	13.3448i	−0.708002	−	0.710270i	−0.966764	+	0.255671i	$0.917704\pi$
$354$	−16.8631	+	13.0613i	−0.896261	+	0.694202i
$355$	−2.83376	−	28.4797i	−0.150400	−	1.51154i
$356$	−4.08078	−	11.4519i	−0.216281	−	0.606950i
$357$	−16.1528	+	28.1158i	−0.854898	+	1.48805i
$358$	−16.2336	+	16.7079i	−0.857973	+	0.883039i
$359$	1.17555	−	0.611822i	0.0620434	−	0.0322907i	−0.430366	−	0.902655i	$-0.641615\pi$
$359$	1.17555	−	0.611822i	0.0620434	−	0.0322907i	0.492409	+	0.870364i	$0.336116\pi$
$360$	−35.9689	+	22.7041i	−1.89573	+	1.19661i
$361$	−4.90186	−	18.0246i	−0.257993	−	0.948664i
$362$	−60.2945	+	8.54380i	−3.16901	+	0.449052i
$363$	−10.8831	−	8.10018i	−0.571216	−	0.425149i
$364$	−22.1278	−	8.28624i	−1.15981	−	0.434317i
$365$	8.89305	−	3.39524i	0.465483	−	0.177715i
$366$	−43.3846	+	1.38843i	−2.26775	+	0.0725742i
$367$	2.81853	+	25.0666i	0.147126	+	1.30847i	0.821556	+	0.570128i	$0.193106\pi$
$367$	2.81853	+	25.0666i	0.147126	+	1.30847i	−0.674430	+	0.738339i	$0.735611\pi$
$368$	104.721	−	42.3013i	5.45895	−	2.20511i
$369$	0.888517	+	1.80477i	0.0462543	+	0.0939523i
$370$	−1.28671	−	1.00986i	−0.0668928	−	0.0525002i
$371$	−14.3764	−	43.8636i	−0.746383	−	2.27728i
$372$	26.8752	−	42.2767i	1.39341	−	2.19194i
$373$	−0.322471	+	7.74923i	−0.0166969	+	0.401240i	0.970438	+	0.241351i	$0.0775904\pi$
$373$	−0.322471	+	7.74923i	−0.0166969	+	0.401240i	−0.987135	+	0.159889i	$0.948886\pi$
$374$	−0.0871515	−	3.02603i	−0.00450649	−	0.156472i
$375$	0.365710	+	0.306424i	0.0188852	+	0.0158237i
$376$	21.2336	+	17.1085i	1.09504	+	0.882306i
$377$	−11.5667	+	1.26312i	−0.595714	+	0.0650537i
$378$	−37.7376	+	43.6027i	−1.94101	+	2.24268i
$379$	8.41195	+	2.60878i	0.432093	+	0.134004i	0.504580	−	0.863365i	$-0.331647\pi$
$379$	8.41195	+	2.60878i	0.432093	+	0.134004i	−0.0724868	+	0.997369i	$0.523094\pi$
$380$	−9.11673	−	2.95576i	−0.467679	−	0.151627i
$381$	−2.18929	+	18.4089i	−0.112161	+	0.943116i
$382$	18.7723	−	17.8924i	0.960472	−	0.915453i
$383$	7.64238	+	14.3461i	0.390507	+	0.733054i	0.998127	−	0.0611742i	$-0.0194845\pi$
$383$	7.64238	+	14.3461i	0.390507	+	0.733054i	−0.607620	+	0.794228i	$0.707876\pi$
$384$	14.1318	+	36.6627i	0.721163	+	1.87094i
$385$	−0.935865	−	1.73002i	−0.0476961	−	0.0881701i
$386$	12.3758	−	6.54200i	0.629911	−	0.332979i
$387$	0.0910971	−	0.219431i	0.00463073	−	0.0111543i
$388$	30.2792	+	20.4957i	1.53719	+	1.04051i
$389$	26.7439	+	9.82021i	1.35597	+	0.497904i	0.916385	−	0.400297i	$-0.131093\pi$
$389$	26.7439	+	9.82021i	1.35597	+	0.497904i	0.439585	+	0.898201i	$0.355126\pi$
$390$	7.84064	−	9.17724i	0.397026	−	0.464707i
$391$	−27.0248	−	47.0397i	−1.36670	−	2.37890i
$392$	−68.9348	−	17.5679i	−3.48173	−	0.887312i
$393$	7.70244	+	11.6178i	0.388537	+	0.586041i
$394$	−1.39953	+	22.9962i	−0.0705074	+	1.15853i
$395$	3.42668	−	7.31119i	0.172415	−	0.367866i
$396$	0.209845	−	1.27471i	0.0105451	−	0.0640566i
$397$	−2.29688	+	34.1371i	−0.115277	+	1.71329i	0.453880	+	0.891063i	$0.350039\pi$
$397$	−2.29688	+	34.1371i	−0.115277	+	1.71329i	−0.569157	+	0.822229i	$0.692730\pi$
$398$	−21.2137	−	26.5017i	−1.06335	−	1.32841i
$399$	−2.68716	−	0.0515865i	−0.134526	−	0.00258256i
$400$	54.0225	−	43.5276i	2.70113	−	2.17638i
$401$	−13.4233	+	13.4663i	−0.670328	+	0.672476i	−0.958497	−	0.285104i	$-0.907972\pi$
$401$	−13.4233	+	13.4663i	−0.670328	+	0.672476i	0.288169	+	0.957580i	$0.406954\pi$
$402$	0.218171	−	1.73953i	0.0108814	−	0.0867601i
$403$	2.25752	−	8.30112i	0.112455	−	0.413508i
$404$	14.0130	+	45.7009i	0.697175	+	2.27371i
$405$	−3.70428	−	6.64311i	−0.184067	−	0.330099i
$406$	−103.667	+	22.9148i	−5.14492	+	1.13724i
$407$	0.0307266	−	0.00556445i	0.00152306	−	0.000275820i
$408$	67.9782	−	37.6209i	3.36542	−	1.86251i
$409$	−2.56105	−	2.84677i	−0.126636	−	0.140764i	0.676773	−	0.736192i	$-0.263378\pi$
$409$	−2.56105	−	2.84677i	−0.126636	−	0.140764i	−0.803409	+	0.595428i	$0.796983\pi$
$410$	−6.32639	−	9.81265i	−0.312438	−	0.484612i
$411$	−0.0114659	−	3.58400i	−0.000565571	−	0.176786i
$412$	23.4554	+	37.9615i	1.15556	+	1.87023i
$413$	−11.7323	+	21.3603i	−0.577307	+	1.05107i
$414$	−10.2737	−	30.0415i	−0.504924	−	1.47646i
$415$	2.14006	−	7.31197i	0.105051	−	0.358930i
$416$	14.3575	+	18.1735i	0.703934	+	0.891029i
$417$	−13.3646	+	8.67703i	−0.654466	+	0.424916i
$418$	0.216363	−	0.127080i	0.0105827	−	0.00621569i
$419$	−1.07215	+	0.910082i	−0.0523780	+	0.0444604i	−0.672941	−	0.739696i	$-0.734969\pi$
$419$	−1.07215	+	0.910082i	−0.0523780	+	0.0444604i	0.620563	+	0.784157i	$0.286904\pi$
$420$	45.2301	−	66.3621i	2.20700	−	3.23814i
$421$	39.5968	−	4.06789i	1.92983	−	0.198257i	0.940068	−	0.340987i	$-0.110761\pi$
$421$	39.5968	−	4.06789i	1.92983	−	0.198257i	0.989762	+	0.142730i	$0.0455881\pi$
$422$	−8.07569	−	1.30291i	−0.393119	−	0.0634247i
$423$	2.91781	−	3.24334i	0.141869	−	0.157697i
$424$	−24.9068	+	107.761i	−1.20958	+	5.23332i
$425$	−24.2688	−	22.8367i	−1.17721	−	1.10774i
$426$	−4.58301	+	30.2499i	−0.222048	+	1.46561i
$427$	−44.8390	+	21.1908i	−2.16991	+	1.02550i
$428$	−78.8857	+	68.7172i	−3.81308	+	3.32157i
$429$	0.0315999	+	0.228259i	0.00152566	+	0.0110204i
$430$	−0.378863	+	1.32587i	−0.0182704	+	0.0639394i
$431$	−4.93956	−	24.9895i	−0.237930	−	1.20370i	−0.893674	−	0.448718i	$-0.851881\pi$
$431$	−4.93956	−	24.9895i	−0.237930	−	1.20370i	0.655743	−	0.754984i	$-0.272355\pi$
$432$	74.8037	−	24.2523i	3.59899	−	1.16684i
$433$	0.238557	−	0.00305291i	0.0114643	−	0.000146714i	−0.00706399	−	0.999975i	$-0.502249\pi$
$433$	0.238557	−	0.00305291i	0.0114643	−	0.000146714i	0.0185283	+	0.999828i	$0.494102\pi$
$434$	12.2547	−	77.5337i	0.588244	−	3.72173i
$435$	5.17243	−	39.2077i	0.247999	−	1.87987i
$436$	4.96473	+	91.1968i	0.237767	+	4.36753i
$437$	2.33905	−	3.84038i	0.111892	−	0.183710i
$438$	−10.1086	+	1.16938i	−0.483005	+	0.0558752i
$439$	−24.6039	+	9.57421i	−1.17428	+	0.456952i	−0.868760	−	0.495234i	$-0.835082\pi$
$439$	−24.6039	+	9.57421i	−1.17428	+	0.456952i	−0.305518	+	0.952186i	$0.598830\pi$
$440$	−0.226075	+	4.70750i	−0.0107777	+	0.224421i
$441$	−3.40605	+	10.8598i	−0.162193	+	0.517132i
$442$	14.6935	−	15.3177i	0.698901	−	0.728589i
$443$	−8.37026	−	21.3080i	−0.397683	−	1.01237i	−0.979927	−	0.199359i	$-0.936114\pi$
$443$	−8.37026	−	21.3080i	−0.397683	−	1.01237i	0.582244	−	0.813014i	$-0.302175\pi$
$444$	0.777504	+	1.01047i	0.0368987	+	0.0479548i
$445$	6.52706	−	2.78345i	0.309413	−	0.131948i
$446$	18.1522	+	25.9142i	0.859531	+	1.22707i
$447$	6.10152	−	23.0164i	0.288592	−	1.08864i
$448$	71.6363	+	72.7915i	3.38450	+	3.43907i
$449$	15.6612	−	2.42402i	0.739097	−	0.114397i	0.227688	−	0.973734i	$-0.426883\pi$
$449$	15.6612	−	2.42402i	0.739097	−	0.114397i	0.511409	+	0.859338i	$0.329124\pi$
$450$	−11.3926	−	15.8292i	−0.537055	−	0.746198i
$451$	0.220267	+	0.0340927i	0.0103720	+	0.00160536i
$452$	−35.1638	−	69.1768i	−1.65396	−	3.25380i
$453$	12.1128	+	2.03384i	0.569107	+	0.0955582i
$454$	−40.7309	+	8.73028i	−1.91160	+	0.409733i
$455$	4.04291	−	13.1852i	0.189534	−	0.618131i
$456$	5.44570	+	3.43740i	0.255018	+	0.160971i
$457$	30.9159	+	2.57749i	1.44618	+	0.120570i	0.780263	−	0.625452i	$-0.215085\pi$
$457$	30.9159	+	2.57749i	1.44618	+	0.120570i	0.665922	+	0.746022i	$0.268039\pi$
$458$	−16.4734	−	9.81788i	−0.769750	−	0.458759i
$459$	−16.4665	−	33.9940i	−0.768589	−	1.58671i
$460$	57.8000	+	121.297i	2.69494	+	5.65549i
$461$	5.33970	−	13.3417i	0.248695	−	0.621384i	−0.750527	−	0.660840i	$-0.770200\pi$
$461$	5.33970	−	13.3417i	0.248695	−	0.621384i	0.999221	+	0.0394566i	$0.0125627\pi$
$462$	0.512738	+	2.03918i	0.0238547	+	0.0948711i
$463$	−15.0270	+	13.4320i	−0.698362	+	0.624238i	−0.938004	−	0.346623i	$-0.887328\pi$
$463$	−15.0270	+	13.4320i	−0.698362	+	0.624238i	0.239642	+	0.970861i	$0.422970\pi$
$464$	137.140	+	46.4102i	6.36657	+	2.15454i
$465$	25.5828	+	14.1582i	1.18637	+	0.656571i
$466$	−8.70807	−	37.6760i	−0.403393	−	1.74531i
$467$	−3.30322	+	5.66540i	−0.152855	+	0.262163i	−0.930309	−	0.366776i	$-0.880462\pi$
$467$	−3.30322	+	5.66540i	−0.152855	+	0.262163i	0.777455	+	0.628939i	$0.216511\pi$
$468$	7.40221	−	5.22042i	0.342167	−	0.241314i
$469$	−0.562651	−	1.92242i	−0.0259808	−	0.0887690i
$470$	−14.6593	+	20.6453i	−0.676183	+	0.952298i
$471$	−5.98435	−	25.1570i	−0.275744	−	1.15917i
$472$	50.5387	−	29.2504i	2.32623	−	1.34636i
$473$	−0.0141227	−	0.0222162i	−0.000649365	−	0.00102150i
$474$	−5.47978	+	6.66897i	−0.251695	+	0.306316i
$475$	0.690679	−	2.67438i	0.0316905	−	0.122709i
$476$	86.1207	−	111.925i	3.94734	−	5.13010i
$477$	16.9985	+	4.91612i	0.778309	+	0.225094i
$478$	9.34553	−	3.49964i	0.427454	−	0.160070i
$479$	−17.3683	+	15.3261i	−0.793579	+	0.700266i	−0.958203	−	0.286090i	$-0.907644\pi$
$479$	−17.3683	+	15.3261i	−0.793579	+	0.700266i	0.164624	+	0.986356i	$0.447359\pi$
$480$	−71.5968	+	32.7223i	−3.26793	+	1.49356i
$481$	0.178922	+	0.126185i	0.00815816	+	0.00575356i
$482$	−15.1851	+	44.4030i	−0.691662	+	2.02250i
$483$	25.3798	+	27.8509i	1.15482	+	1.26726i
$484$	42.2463	+	41.3106i	1.92028	+	1.87776i
$485$	−10.8670	+	18.3670i	−0.493444	+	0.834002i
$486$	−9.46492	−	35.7040i	−0.429337	−	1.61957i
$487$	5.07800	−	6.02124i	0.230106	−	0.272848i	−0.637118	−	0.770767i	$-0.719873\pi$
$487$	5.07800	−	6.02124i	0.230106	−	0.272848i	0.867224	+	0.497918i	$0.165902\pi$
$488$	118.209	+	12.1440i	5.35109	+	0.549733i
$489$	14.0145	+	3.76317i	0.633756	+	0.170177i
$490$	12.3943	−	64.8830i	0.559918	−	2.93112i
$491$	13.3509	+	39.8710i	0.602517	+	1.79935i	0.600861	+	0.799353i	$0.294824\pi$
$491$	13.3509	+	39.8710i	0.602517	+	1.79935i	0.00165588	+	0.999999i	$0.499473\pi$
$492$	2.88966	+	8.62965i	0.130276	+	0.389055i
$493$	13.0486	−	68.3082i	0.587680	−	3.07645i
$494$	1.69915	+	0.456257i	0.0764483	+	0.0205280i
$495$	0.750072	+	0.0770570i	0.0337132	+	0.00346346i
$496$	−69.0096	+	81.8281i	−3.09862	+	3.67419i
$497$	8.95731	+	33.7892i	0.401790	+	1.51565i
$498$	−4.14719	+	7.00944i	−0.185840	+	0.314100i
$499$	19.3010	+	18.8735i	0.864030	+	0.844894i	0.989099	−	0.147254i	$-0.0470435\pi$
$499$	19.3010	+	18.8735i	0.864030	+	0.844894i	−0.125069	+	0.992148i	$0.539915\pi$
$500$	−1.39965	−	1.53592i	−0.0625941	−	0.0686885i
$501$	2.65505	−	7.76369i	0.118619	−	0.346856i
$502$	−49.7486	−	35.0853i	−2.22039	−	1.56593i
$503$	−29.0221	+	13.2641i	−1.29403	+	0.591419i	−0.939155	−	0.343494i	$-0.888389\pi$
$503$	−29.0221	+	13.2641i	−1.29403	+	0.591419i	−0.354876	+	0.934913i	$0.615477\pi$
$504$	38.9541	−	34.3736i	1.73515	−	1.53112i
$505$	−26.1280	+	9.78420i	−1.16268	+	0.435391i
$506$	−3.37939	−	0.977351i	−0.150232	−	0.0434485i
$507$	8.81585	−	11.4574i	0.391526	−	0.508840i
$508$	20.1897	−	78.1766i	0.895773	−	3.46853i
$509$	−8.05147	+	9.79875i	−0.356875	+	0.434322i	−0.919921	−	0.392103i	$-0.871748\pi$
$509$	−8.05147	+	9.79875i	−0.356875	+	0.434322i	0.563046	+	0.826426i	$0.309629\pi$
$510$	38.7033	+	60.8833i	1.71381	+	2.69596i
$511$	−10.0626	+	5.82398i	−0.445144	+	0.257638i
$512$	−6.13904	−	25.8072i	−0.271310	−	1.14053i
$513$	1.81259	−	2.55276i	0.0800280	−	0.112707i
$514$	−3.27426	−	11.1872i	−0.144421	−	0.493446i
$515$	−21.2843	+	15.0108i	−0.937898	+	0.661455i
$516$	0.541394	−	0.928552i	0.0238335	−	0.0408772i
$517$	−0.108856	−	0.470971i	−0.00478747	−	0.0207133i
$518$	1.74796	+	0.967365i	0.0768008	+	0.0425036i
$519$	−23.8770	−	8.08031i	−1.04808	−	0.354686i
$520$	−24.6369	+	22.0219i	−1.08040	+	0.965725i
$521$	1.04421	+	4.15288i	0.0457478	+	0.181941i	0.988410	−	0.151807i	$-0.0485093\pi$
$521$	1.04421	+	4.15288i	0.0457478	+	0.181941i	−0.942662	+	0.333748i	$0.891686\pi$
$522$	15.1230	−	37.7860i	0.661915	−	1.65385i
$523$	−0.0361617	−	0.0758874i	−0.00158124	−	0.00331832i	0.901954	−	0.431833i	$-0.142133\pi$
$523$	−0.0361617	−	0.0758874i	−0.00158124	−	0.00331832i	−0.903535	+	0.428514i	$0.859037\pi$
$524$	−26.4659	−	54.6372i	−1.15617	−	2.38684i
$525$	19.8825	+	11.8496i	0.867741	+	0.517161i
$526$	0.407962	+	0.0340122i	0.0177880	+	0.00148300i
$527$	43.4794	+	27.4448i	1.89399	+	1.19551i
$528$	0.840566	−	2.74135i	0.0365809	−	0.119302i
$529$	−39.1525	+	8.39196i	−1.70228	+	0.364868i
$530$	−101.283	−	17.0063i	−4.39944	−	0.738705i
$531$	−4.23332	−	8.32811i	−0.183710	−	0.361409i
$532$	11.5679	+	1.79046i	0.501530	+	0.0776264i
$533$	0.912910	+	1.26842i	0.0395425	+	0.0549414i
$534$	−7.49614	+	1.16025i	−0.324390	+	0.0502088i
$535$	−42.8308	−	43.5215i	−1.85174	−	1.88160i
$536$	−1.22984	+	4.63925i	−0.0531209	+	0.200385i
$537$	6.08056	+	8.68066i	0.262396	+	0.374598i
$538$	27.4893	−	11.7228i	1.18515	−	0.505404i
$539$	0.769021	+	0.999447i	0.0331241	+	0.0430492i
$540$	34.2051	+	87.0751i	1.47195	+	3.74712i
$541$	−9.82491	+	10.2423i	−0.422406	+	0.440349i	−0.898452	−	0.439071i	$-0.855308\pi$
$541$	−9.82491	+	10.2423i	−0.422406	+	0.440349i	0.476047	+	0.879420i	$0.342069\pi$
$542$	−8.41562	+	26.8322i	−0.361482	+	1.15254i
$543$	−1.32901	+	27.6735i	−0.0570331	+	1.18758i
$544$	−129.005	+	50.2001i	−5.53102	+	2.15231i
$545$	−52.9542	+	6.12586i	−2.26831	+	0.262403i
$546$	−7.66882	+	12.5911i	−0.328195	+	0.538850i
$547$	0.583397	+	10.7164i	0.0249443	+	0.458200i	0.984356	+	0.176191i	$0.0563776\pi$
$547$	0.583397	+	10.7164i	0.0249443	+	0.458200i	−0.959412	+	0.282009i	$0.908999\pi$
$548$	−2.04158	+	15.4755i	−0.0872120	+	0.661079i
$549$	2.96810	−	18.7787i	0.126676	−	0.801457i
$550$	−2.16074	+	0.0276519i	−0.0921343	+	0.00117908i
$551$	5.48326	−	1.77774i	0.233595	−	0.0757343i
$552$	−17.5075	−	88.5712i	−0.745167	−	3.76984i
$553$	−2.70954	+	9.48237i	−0.115222	+	0.403231i
$554$	−1.91212	−	13.8120i	−0.0812382	−	0.586816i
$555$	−0.561122	+	0.488792i	−0.0238183	+	0.0207481i
$556$	62.7450	−	29.6531i	2.66098	−	1.25757i
$557$	−1.07291	+	7.08171i	−0.0454608	+	0.300062i	0.954537	+	0.298092i	$0.0963501\pi$
$557$	−1.07291	+	7.08171i	−0.0454608	+	0.300062i	−0.999998	+	0.00197010i	$0.999373\pi$
$558$	21.9146	+	20.6214i	0.927717	+	0.872973i
$559$	0.0415657	−	0.179837i	0.00175804	−	0.00760628i
$560$	−114.771	+	127.575i	−4.84994	+	5.39103i
$561$	−1.35970	−	0.219370i	−0.0574065	−	0.00926181i
$562$	30.8603	−	3.17037i	1.30176	−	0.133734i
$563$	9.98291	−	14.6470i	0.420730	−	0.617299i	−0.556152	−	0.831081i	$-0.687723\pi$
$563$	9.98291	−	14.6470i	0.420730	−	0.617299i	0.976881	+	0.213782i	$0.0685781\pi$
$564$	15.0468	−	12.7723i	0.633586	−	0.537812i
$565$	39.0548	−	22.9387i	1.64305	−	0.965039i
$566$	28.9619	−	18.8037i	1.21736	−	0.790378i
$567$	5.75892	+	7.28956i	0.241852	+	0.306133i
$568$	23.5272	−	80.3858i	0.987181	−	3.37291i
$569$	−3.86626	−	11.3054i	−0.162082	−	0.473947i	0.835003	−	0.550245i	$-0.185466\pi$
$569$	−3.86626	−	11.3054i	−0.162082	−	0.473947i	−0.997085	+	0.0762984i	$0.975690\pi$
$570$	−2.87877	+	5.24123i	−0.120578	+	0.219531i
$571$	7.83152	+	12.6750i	0.327739	+	0.530431i	0.972184	−	0.234220i	$-0.0752536\pi$
$571$	7.83152	+	12.6750i	0.327739	+	0.530431i	−0.644445	+	0.764651i	$0.722911\pi$
$572$	−0.00321076	−	1.00362i	−0.000134249	−	0.0419633i
$573$	−6.39317	−	9.91623i	−0.267078	−	0.414256i
$574$	9.53722	+	10.6013i	0.398076	+	0.442488i
$575$	−33.8818	+	18.7511i	−1.41297	+	0.781975i
$576$	−38.5244	+	6.97660i	−1.60518	+	0.290692i
$577$	40.7465	−	9.00670i	1.69630	−	0.374954i	0.741211	−	0.671272i	$-0.234252\pi$
$577$	40.7465	−	9.00670i	1.69630	−	0.374954i	0.955089	+	0.296318i	$0.0957589\pi$
$578$	39.2859	+	70.4536i	1.63408	+	2.93048i
$579$	−1.86700	−	6.08888i	−0.0775900	−	0.253045i
$580$	−45.2001	+	166.205i	−1.87683	+	6.90130i
$581$	−1.15800	+	9.23301i	−0.0480419	+	0.383050i
$582$	16.1058	−	16.1574i	0.667606	−	0.669745i
$583$	1.52672	−	1.23013i	0.0632303	−	0.0509466i
$584$	27.8528	+	0.534703i	1.15256	+	0.0221262i
$585$	3.30381	+	4.12735i	0.136596	+	0.170645i
$586$	0.415488	−	6.17513i	0.0171636	−	0.255092i
$587$	−2.73977	+	16.6429i	−0.113082	+	0.686924i	0.868472	+	0.495739i	$0.165103\pi$
$587$	−2.73977	+	16.6429i	−0.113082	+	0.686924i	−0.981554	+	0.191185i	$0.938767\pi$
$588$	−21.8516	+	46.6227i	−0.901144	+	1.92269i
$589$	−0.258890	+	4.25390i	−0.0106674	+	0.175279i
$590$	29.9614	+	45.1917i	1.23349	+	1.86051i
$591$	10.1569	+	2.58847i	0.417801	+	0.106476i
$592$	−1.35712	−	2.36223i	−0.0557775	−	0.0970871i
$593$	−22.0003	+	25.7508i	−0.903446	+	1.05746i	0.0946337	+	0.995512i	$0.469832\pi$
$593$	−22.0003	+	25.7508i	−0.903446	+	1.05746i	−0.998080	+	0.0619445i	$0.980270\pi$
$594$	−2.29926	−	0.844273i	−0.0943396	−	0.0346409i
$595$	68.2600	+	46.2045i	2.79839	+	1.89420i
$596$	−39.7634	+	95.7806i	−1.62877	+	3.92333i
$597$	−13.6538	+	7.21759i	−0.558814	+	0.295396i
$598$	−11.7358	−	21.6947i	−0.479915	−	0.887161i
$599$	11.9654	+	31.0423i	0.488894	+	1.26835i	0.928890	+	0.370355i	$0.120764\pi$
$599$	11.9654	+	31.0423i	0.488894	+	1.26835i	−0.439996	+	0.898000i	$0.645020\pi$
$600$	−26.0747	−	48.9470i	−1.06450	−	1.99825i
$601$	22.7927	−	21.7244i	0.929735	−	0.886157i	−0.0639960	−	0.997950i	$-0.520384\pi$
$601$	22.7927	−	21.7244i	0.929735	−	0.886157i	0.993731	+	0.111793i	$0.0356594\pi$
$602$	0.198894	−	1.67243i	0.00810633	−	0.0681631i
$603$	0.730441	+	0.236818i	0.0297458	+	0.00964397i
$604$	−51.0928	−	15.8453i	−2.07894	−	0.644738i
$605$	−22.5692	+	26.0769i	−0.917569	+	1.06018i
$606$	29.6487	−	3.23773i	1.20440	−	0.131524i
$607$	−11.3381	−	9.13547i	−0.460200	−	0.370797i	0.369294	−	0.929312i	$-0.379599\pi$
$607$	−11.3381	−	9.13547i	−0.460200	−	0.370797i	−0.829494	+	0.558515i	$0.811371\pi$
$608$	−8.79473	−	7.36900i	−0.356673	−	0.298853i
$609$	1.39056	+	48.2824i	0.0563484	+	1.95650i
$610$	−4.58775	+	110.247i	−0.185753	+	4.46378i
$611$	1.81825	−	2.86025i	0.0735586	−	0.115713i
$612$	16.8612	+	51.4451i	0.681575	+	2.07955i
$613$	−9.74253	−	7.64633i	−0.393497	−	0.308833i	0.401026	−	0.916067i	$-0.368654\pi$
$613$	−9.74253	−	7.64633i	−0.393497	−	0.308833i	−0.794523	+	0.607234i	$0.792279\pi$
$614$	−18.4824	−	37.5417i	−0.745889	−	1.51506i
$615$	−4.92508	+	1.98945i	−0.198598	+	0.0802225i
$616$	−0.643191	−	5.72022i	−0.0259149	−	0.230474i
$617$	−37.4711	+	1.19918i	−1.50853	+	0.0482770i	−0.775251	−	0.631653i	$-0.782377\pi$
$617$	−37.4711	+	1.19918i	−1.50853	+	0.0482770i	−0.733277	+	0.679930i	$0.762010\pi$
$618$	26.0110	−	9.93061i	1.04632	−	0.399468i
$619$	7.34101	+	2.74900i	0.295060	+	0.110492i	0.493841	−	0.869552i	$-0.335592\pi$
$619$	7.34101	+	2.74900i	0.295060	+	0.110492i	−0.198781	+	0.980044i	$0.563698\pi$
$620$	−102.157	−	76.0339i	−4.10270	−	3.05359i
$621$	−43.4593	+	6.15823i	−1.74396	+	0.247121i
$622$	−2.99415	−	11.0098i	−0.120054	−	0.441452i
$623$	−7.32877	+	4.62602i	−0.293621	+	0.185338i
$624$	17.8334	−	9.28149i	0.713909	−	0.371557i
$625$	17.8387	−	18.3599i	0.713548	−	0.734394i
$626$	22.0836	−	38.4390i	0.882639	−	1.53633i
$627$	−0.0383192	−	0.107535i	−0.00153032	−	0.00429455i
$628$	11.1511	+	112.071i	0.444979	+	4.47211i
$629$	−1.03455	+	0.801317i	−0.0412504	+	0.0319506i
$630$	34.0564	+	34.1656i	1.35684	+	1.36119i
$631$	16.2829	+	1.77814i	0.648213	+	0.0707868i	0.426732	−	0.904378i	$-0.359665\pi$
$631$	16.2829	+	1.77814i	0.648213	+	0.0707868i	0.221481	+	0.975165i	$0.428911\pi$
$632$	17.3121	−	16.0829i	0.688639	−	0.639745i
$633$	−1.27162	+	3.49760i	−0.0505422	+	0.139017i
$634$	−7.98163	−	55.0587i	−0.316991	−	2.18666i
$635$	46.2606	+	8.99045i	1.83580	+	0.356775i
$636$	73.2288	+	32.3419i	2.90371	+	1.28244i
$637$	−1.21250	+	8.75840i	−0.0480412	+	0.347020i
$638$	−2.46778	−	3.77444i	−0.0977003	−	0.149431i
$639$	−12.6373	−	4.45766i	−0.499923	−	0.176342i
$640$	95.5874	−	28.9752i	3.77842	−	1.14535i
$641$	16.1805	+	7.39509i	0.639092	+	0.292088i	0.708726	−	0.705484i	$-0.249270\pi$
$641$	16.1805	+	7.39509i	0.639092	+	0.292088i	−0.0696332	+	0.997573i	$0.522183\pi$
$642$	32.8786	+	56.3906i	1.29762	+	2.22556i
$643$	36.0718	−	33.9433i	1.42253	−	1.33859i	0.564060	−	0.825734i	$-0.309239\pi$
$643$	36.0718	−	33.9433i	1.42253	−	1.33859i	0.858474	−	0.512857i	$-0.171413\pi$
$644$	−93.2915	−	135.014i	−3.67620	−	5.32029i
$645$	0.560159	+	0.282487i	0.0220562	+	0.0111229i
$646$	−5.58432	+	8.90997i	−0.219712	+	0.350558i
$647$	−18.8702	−	14.6160i	−0.741865	−	0.574613i	0.169834	−	0.985473i	$-0.445677\pi$
$647$	−18.8702	−	14.6160i	−0.741865	−	0.574613i	−0.911699	+	0.410859i	$0.865229\pi$
$648$	−2.77006	−	22.0864i	−0.108818	−	0.867634i
$649$	−1.02489	−	0.145228i	−0.0402306	−	0.00570072i
$650$	−10.7648	−	10.6620i	−0.422231	−	0.418198i
$651$	−33.6017	−	12.0949i	−1.31696	−	0.474038i
$652$	−58.2918	−	24.4188i	−2.28288	−	0.956314i
$653$	1.88062	+	21.7178i	0.0735943	+	0.849885i	0.937897	+	0.346913i	$0.112770\pi$
$653$	1.88062	+	21.7178i	0.0735943	+	0.849885i	−0.864303	+	0.502972i	$0.832240\pi$
$654$	56.4719	+	7.63388i	2.20823	+	0.298508i
$655$	30.8926	−	17.3559i	1.20707	−	0.678152i
$656$	−3.64867	−	19.1004i	−0.142457	−	0.745747i
$657$	0.327655	−	4.44493i	0.0127830	−	0.173413i
$658$	13.6597	−	27.7457i	0.532510	−	1.08164i
$659$	20.9558	−	10.0682i	0.816320	−	0.392200i	0.0220439	−	0.999757i	$-0.492983\pi$
$659$	20.9558	−	10.0682i	0.816320	−	0.392200i	0.794276	+	0.607557i	$0.207850\pi$
$660$	3.31604	+	0.800040i	0.129077	+	0.0311415i
$661$	−19.5160	+	26.0466i	−0.759083	+	1.01309i	0.240021	+	0.970768i	$0.422846\pi$
$661$	−19.5160	+	26.0466i	−0.759083	+	1.01309i	−0.999104	+	0.0423270i	$0.986523\pi$
$662$	46.4472	−	52.9771i	1.80522	−	2.05901i
$663$	−5.59080	−	7.87377i	−0.217129	−	0.305792i
$664$	13.8217	−	17.4953i	0.536387	−	0.678950i
$665$	−0.632953	+	6.80278i	−0.0245449	+	0.263801i
$666$	−0.683815	+	0.344847i	−0.0264973	+	0.0133625i
$667$	−70.9563	−	38.6781i	−2.74744	−	1.49762i
$668$	−15.9891	+	31.9595i	−0.618636	+	1.23655i
$669$	13.1300	−	5.89961i	0.507634	−	0.228092i
$670$	−4.36925	−	0.878184i	−0.168799	−	0.0339272i
$671$	−1.51552	−	1.46310i	−0.0585059	−	0.0564824i
$672$	79.9648	−	53.3845i	3.08471	−	2.05935i
$673$	7.17410	−	21.8888i	0.276541	−	0.843752i	−0.713210	−	0.700950i	$-0.752759\pi$
$673$	7.17410	−	21.8888i	0.276541	−	0.843752i	0.989751	−	0.142802i	$-0.0456112\pi$
$674$	7.21862	+	8.78516i	0.278051	+	0.338392i
$675$	−24.4503	+	11.3643i	−0.941092	+	0.437414i
$676$	−44.7345	+	44.3073i	−1.72056	+	1.70413i
$677$	5.90799	−	4.39725i	0.227063	−	0.169000i	−0.477523	−	0.878619i	$-0.658465\pi$
$677$	5.90799	−	4.39725i	0.227063	−	0.169000i	0.704585	+	0.709619i	$0.251133\pi$
$678$	−46.5123	+	13.4518i	−1.78629	+	0.516612i
$679$	9.53018	−	24.2608i	0.365735	−	0.931042i
$680$	−82.6720	−	179.367i	−3.17033	−	6.87842i
$681$	0.424372	+	18.9469i	0.0162620	+	0.726046i
$682$	3.26450	−	0.677898i	0.125004	−	0.0259580i
$683$	−34.6150	+	36.5507i	−1.32451	+	1.39857i	−0.466865	+	0.884329i	$0.654617\pi$
$683$	−34.6150	+	36.5507i	−1.32451	+	1.39857i	−0.857643	+	0.514246i	$0.828072\pi$
$684$	−3.06466	+	3.27779i	−0.117180	+	0.125329i
$685$	−9.08821	−	0.640704i	−0.347243	−	0.0244800i
$686$	−0.220576	+	7.65875i	−0.00842164	+	0.292412i
$687$	−5.79361	+	6.52344i	−0.221040	+	0.248885i
$688$	−1.41219	+	1.81124i	−0.0538394	+	0.0690528i
$689$	13.6559	+	1.57974i	0.520247	+	0.0601834i
$690$	81.1045	−	21.2228i	3.08759	−	0.807939i
$691$	1.25206	+	3.99203i	0.0476305	+	0.151864i	0.974959	−	0.222384i	$-0.0713837\pi$
$691$	1.25206	+	3.99203i	0.0476305	+	0.151864i	−0.927329	+	0.374248i	$0.877901\pi$
$692$	98.3403	+	48.8061i	3.73834	+	1.85533i
$693$	−0.919419	+	0.0530035i	−0.0349258	+	0.00201344i
$694$	−37.8567	+	41.5425i	−1.43702	+	1.57693i
$695$	19.5003	+	35.5031i	0.739687	+	1.34671i
$696$	57.0110	−	100.721i	2.16100	−	3.81781i
$697$	−8.84764	+	2.99417i	−0.335128	+	0.113412i
$698$	−52.6127	−	9.52793i	−1.99142	−	0.360637i
$699$	−17.5798	+	0.675224i	−0.664930	+	0.0255393i
$700$	−78.9004	−	62.7442i	−2.98215	−	2.37151i
$701$	−7.34376	−	4.44069i	−0.277370	−	0.167723i	0.371917	−	0.928266i	$-0.378701\pi$
$701$	−7.34376	−	4.44069i	−0.277370	−	0.167723i	−0.649287	+	0.760543i	$0.724933\pi$
$702$	−7.08872	−	15.6424i	−0.267547	−	0.590383i
$703$	−0.0994976	−	0.0431850i	−0.00375262	−	0.00162875i
$704$	−1.81581	+	3.93963i	−0.0684361	+	0.148481i
$705$	7.97450	+	8.31325i	0.300337	+	0.313095i
$706$	45.8651	−	22.7628i	1.72616	−	0.856688i
$707$	29.6014	−	16.8806i	1.11327	−	0.634859i
$708$	−13.9318	−	39.9024i	−0.523587	−	1.49962i
$709$	−18.8250	+	3.65852i	−0.706990	+	0.137399i	−0.531470	−	0.847077i	$-0.678360\pi$
$709$	−18.8250	+	3.65852i	−0.706990	+	0.137399i	−0.175520	+	0.984476i	$0.556161\pi$
$710$	75.8325	+	17.2718i	2.84594	+	0.648200i
$711$	−2.41874	−	2.90554i	−0.0907099	−	0.108966i
$712$	20.7622	−	0.398580i	0.778095	−	0.0149374i
$713$	45.7977	−	38.3734i	1.71514	−	1.43710i
$714$	−58.5122	−	65.8831i	−2.18976	−	2.46561i
$715$	0.584581	−	0.0374547i	0.0218621	−	0.00140073i
$716$	−21.1794	−	41.0140i	−0.791512	−	1.53276i
$717$	−0.766126	−	4.47503i	−0.0286115	−	0.167123i
$718$	0.562226	+	3.55712i	0.0209821	+	0.132751i
$719$	6.68661	−	0.171171i	0.249368	−	0.00638358i	0.0992934	−	0.995058i	$-0.468342\pi$
$719$	6.68661	−	0.171171i	0.249368	−	0.00638358i	0.150075	+	0.988675i	$0.452048\pi$
$720$	−15.6331	−	63.8993i	−0.582609	−	2.38139i
$721$	22.7442	−	22.2405i	0.847037	−	0.828278i
$722$	50.6760	+	2.92142i	1.88597	+	0.108724i
$723$	18.5463	+	10.5763i	0.689745	+	0.393336i
$724$	21.8820	−	118.665i	0.813240	−	4.41016i
$725$	−48.6041	−	10.0930i	−1.80511	−	0.374844i
$726$	30.2634	−	21.0547i	1.12318	−	0.781412i
$727$	8.15301	−	5.07364i	0.302379	−	0.188171i	−0.368717	−	0.929542i	$-0.620203\pi$
$727$	8.15301	−	5.07364i	0.302379	−	0.188171i	0.671096	+	0.741371i	$0.265824\pi$
$728$	25.4227	−	31.3466i	0.942229	−	1.16178i
$729$	−24.0057	+	1.69236i	−0.889101	+	0.0626801i
$730$	1.07552	+	25.8455i	0.0398067	+	0.956585i
$731$	0.954806	+	0.552616i	0.0353148	+	0.0204392i
$732$	24.6874	−	82.3906i	0.912472	−	3.04524i
$733$	0.476736	−	0.854959i	0.0176087	−	0.0315786i	−0.864446	−	0.502725i	$-0.832331\pi$
$733$	0.476736	−	0.854959i	0.0176087	−	0.0315786i	0.882055	+	0.471147i	$0.156160\pi$
$734$	−67.0244	−	14.3661i	−2.47392	−	0.530261i
$735$	−27.9366	−	11.0774i	−1.03046	−	0.408597i
$736$	9.77181	+	160.564i	0.360194	+	5.91846i
$737$	0.0679248	−	0.0512342i	0.00250204	−	0.00188724i
$738$	−5.41724	+	0.732302i	−0.199411	+	0.0269564i
$739$	3.89573	+	17.3607i	0.143307	+	0.638623i	0.993662	+	0.112413i	$0.0358579\pi$
$739$	3.89573	+	17.3607i	0.143307	+	0.638623i	−0.850355	+	0.526210i	$0.823613\pi$
$740$	2.70702	−	1.78228i	0.0995121	−	0.0655177i
$741$	0.348937	−	0.720359i	0.0128185	−	0.0264631i
$742$	125.434	+	0.802581i	4.60482	+	0.0294637i
$743$	−7.83864	−	8.38378i	−0.287572	−	0.307571i	0.570298	−	0.821438i	$-0.306828\pi$
$743$	−7.83864	−	8.38378i	−0.287572	−	0.307571i	−0.857870	+	0.513867i	$0.828213\pi$
$744$	53.9002	+	66.4597i	1.97608	+	2.43653i
$745$	−57.2105	−	19.7697i	−2.09603	−	0.724306i
$746$	−19.6902	−	7.51744i	−0.720910	−	0.275233i
$747$	−2.67473	−	2.36022i	−0.0978632	−	0.0863560i
$748$	5.74056	+	1.74013i	0.209896	+	0.0636253i
$749$	60.1115	+	44.1454i	2.19643	+	1.61304i
$750$	−1.10516	+	0.677973i	−0.0403548	+	0.0247561i
$751$	−0.000640873		0.200324i	−2.33858e−5		0.00730991i	0.999977	+	0.00685411i	$0.00218175\pi$
$751$	−0.000640873		0.200324i	−2.33858e−5		0.00730991i	−1.00000		0.000455805i	$0.999855\pi$
$752$	−35.5177	+	22.7383i	−1.29520	+	0.829182i
$753$	−19.9255	+	19.2364i	−0.726126	+	0.701012i
$754$	6.72555	−	30.8952i	0.244930	−	1.12514i
$755$	7.41976	−	30.3279i	0.270033	−	1.10375i
$756$	−58.1836	−	98.3400i	−2.11612	−	3.57659i
$757$	−22.5679	+	22.9318i	−0.820243	+	0.833470i	−0.988334	−	0.152302i	$-0.951331\pi$
$757$	−22.5679	+	22.9318i	−0.820243	+	0.833470i	0.168091	+	0.985771i	$0.446240\pi$
$758$	−13.9807	+	19.4252i	−0.507803	+	0.705554i
$759$	−0.725234	+	1.42674i	−0.0263243	+	0.0517872i
$760$	9.73211	−	13.1634i	0.353021	−	0.477488i
$761$	8.41917	−	12.5241i	0.305195	−	0.454000i	−0.645665	−	0.763620i	$-0.723420\pi$
$761$	8.41917	−	12.5241i	0.305195	−	0.454000i	0.950860	+	0.309620i	$0.100202\pi$
$762$	−45.5476	−	21.5257i	−1.65001	−	0.779793i
$763$	62.6598	−	17.6881i	2.26844	−	0.640353i
$764$	21.8078	+	46.5292i	0.788977	+	1.68337i
$765$	−29.3735	+	11.6472i	−1.06200	+	0.421105i
$766$	−43.5619	+	7.31444i	−1.57396	+	0.264281i
$767$	−4.31472	−	5.83600i	−0.155796	−	0.210726i
$768$	−40.9459	+	1.83513i	−1.47751	+	0.0662196i
$769$	40.5162	+	23.7970i	1.46105	+	0.858143i	0.999579	−	0.0290118i	$-0.00923603\pi$
$769$	40.5162	+	23.7970i	1.46105	+	0.858143i	0.461472	+	0.887155i	$0.347322\pi$
$770$	5.26550	−	0.918802i	0.189755	−	0.0331113i
$771$	−5.27879	+	0.508195i	−0.190111	+	0.0183022i
$772$	4.50558	+	27.3693i	0.162159	+	0.985044i
$773$	−28.5982	−	8.07293i	−1.02860	−	0.290363i	−0.284677	−	0.958623i	$-0.591886\pi$
$773$	−28.5982	−	8.07293i	−1.02860	−	0.290363i	−0.743927	+	0.668260i	$0.767039\pi$
$774$	0.486834	+	0.424080i	0.0174989	+	0.0152432i
$775$	20.0844	−	30.7188i	0.721452	−	1.10345i
$776$	−49.6197	+	37.9276i	−1.78124	+	1.36152i
$777$	0.581505	−	0.698539i	0.0208614	−	0.0250600i
$778$	−48.3812	+	60.4411i	−1.73455	+	2.16692i
$779$	−0.570575	−	0.523302i	−0.0204430	−	0.0187493i
$780$	12.3104	+	20.5061i	0.440783	+	0.734235i
$781$	−1.20788	+	0.863482i	−0.0432212	+	0.0308978i
$782$	144.532	−	29.0498i	5.16846	−	1.03882i
$783$	−47.3879	−	30.3377i	−1.69351	−	1.08418i
$784$	59.6162	−	92.4687i	2.12915	−	3.30245i
$785$	−64.8957	+	10.4701i	−2.31623	+	0.373694i
$786$	−36.5833	+	9.82336i	−1.30488	+	0.350388i
$787$	1.55017	+	21.0295i	0.0552576	+	0.749619i	0.951811	+	0.306684i	$0.0992196\pi$
$787$	1.55017	+	21.0295i	0.0552576	+	0.749619i	−0.896554	+	0.442935i	$0.853937\pi$
$788$	−42.3278	−	17.0980i	−1.50787	−	0.609093i
$789$	0.0500247	−	0.179405i	0.00178093	−	0.00638697i
$790$	15.8830	+	15.1385i	0.565091	+	0.538604i
$791$	−42.6294	+	35.2569i	−1.51573	+	1.25359i
$792$	1.95086	+	1.03125i	0.0693208	+	0.0366439i
$793$	−0.141752	−	14.7692i	−0.00503376	−	0.524469i
$794$	−85.9837	−	35.3741i	−3.05145	−	1.25538i
$795$	−16.2456	+	43.8090i	−0.576173	+	1.55374i
$796$	63.1420	−	23.1853i	2.23801	−	0.821783i
$797$	52.9868	+	13.1431i	1.87689	+	0.465552i	0.999888	−	0.0149359i	$-0.00475442\pi$
$797$	52.9868	+	13.1431i	1.87689	+	0.465552i	0.877001	+	0.480488i	$0.159541\pi$
$798$	2.45157	−	6.87984i	0.0867845	−	0.243544i
$799$	13.1584	+	15.4015i	0.465511	+	0.544867i
$800$	34.3560	+	92.6465i	1.21467	+	3.27555i
$801$	0.116892	−	3.32029i	0.00413019	−	0.117317i
$802$	−23.1180	−	46.2091i	−0.816326	−	1.63170i
$803$	−0.382555	−	0.312294i	−0.0135001	−	0.0110206i
$804$	3.13121	+	1.50439i	0.110429	+	0.0530556i
$805$	75.3498	−	59.1376i	2.65573	−	2.08433i
$806$	19.4427	+	12.9799i	0.684839	+	0.457199i
$807$	−2.89200	−	13.2850i	−0.101803	−	0.467654i
$808$	−81.6228	−	2.08946i	−2.87148	−	0.0735071i
$809$	−1.17181	−	8.88252i	−0.0411988	−	0.312293i	−0.999636	−	0.0269882i	$-0.991408\pi$
$809$	−1.17181	−	8.88252i	−0.0411988	−	0.312293i	0.958437	−	0.285304i	$-0.0920947\pi$
$810$	20.3144	−	3.81326i	0.713777	−	0.133984i
$811$	0.0672444	−	4.20349i	0.00236127	−	0.147605i	−0.995964	−	0.0897539i	$-0.971392\pi$
$811$	0.0672444	−	4.20349i	0.00236127	−	0.147605i	0.998325	−	0.0578507i	$-0.0184247\pi$
$812$	22.1684	−	209.202i	0.777959	−	7.34153i
$813$	11.2723	+	6.05125i	0.395335	+	0.212227i
$814$	−0.0121740	+	0.0839786i	−0.000426700	+	0.00294345i
$815$	12.1593	−	34.8259i	0.425922	−	1.21990i
$816$	21.7903	+	118.168i	0.762812	+	4.13669i
$817$	−0.00204757	+	0.0914176i	−7.16354e−5	+	0.00319830i
$818$	9.54548	−	4.14303i	0.333750	−	0.144858i
$819$	−4.78662	−	4.33399i	−0.167258	−	0.151442i
$820$	22.4177	−	5.71310i	0.782860	−	0.199510i
$821$	36.2955	+	37.3559i	1.26672	+	1.30373i	0.932471	+	0.361246i	$0.117649\pi$
$821$	36.2955	+	37.3559i	1.26672	+	1.30373i	0.334252	+	0.942484i	$0.391516\pi$
$822$	9.24526	+	3.06294i	0.322465	+	0.106832i
$823$	−21.3938	+	29.3275i	−0.745742	+	1.02229i	0.252758	+	0.967530i	$0.418662\pi$
$823$	−21.3938	+	29.3275i	−0.745742	+	1.02229i	−0.998499	+	0.0547635i	$0.982560\pi$
$824$	−74.2084	+	17.4021i	−2.58517	+	0.606230i
$825$	−0.172094	+	0.967942i	−0.00599154	+	0.0336994i
$826$	−44.9187	−	48.6630i	−1.56292	−	1.69320i
$827$	3.12916	−	6.56673i	0.108812	−	0.228348i	−0.841091	−	0.540894i	$-0.818086\pi$
$827$	3.12916	−	6.56673i	0.108812	−	0.228348i	0.949903	+	0.312546i	$0.101182\pi$
$828$	62.9099	−	0.402526i	2.18627	−	0.0139887i
$829$	−19.2889	−	20.3675i	−0.669930	−	0.707393i	0.299131	−	0.954212i	$-0.403303\pi$
$829$	−19.2889	−	20.3675i	−0.669930	−	0.707393i	−0.969062	+	0.246819i	$0.920615\pi$
$830$	16.9951	+	11.8238i	0.589910	+	0.410409i
$831$	−6.33547	−	0.324576i	−0.219775	−	0.0112594i
$832$	−28.6180	+	10.3011i	−0.992151	+	0.357125i
$833$	−47.9234	−	22.2745i	−1.66045	−	0.771766i
$834$	−10.8275	−	41.9253i	−0.374926	−	1.45175i
$835$	−19.1861	−	8.18189i	−0.663964	−	0.283146i
$836$	0.102647	+	0.486487i	0.00355013	+	0.0168255i
$837$	33.6871	−	24.4093i	1.16440	−	0.843709i
$838$	−1.42002	−	3.54802i	−0.0490536	−	0.122564i
$839$	17.9285	−	19.4230i	0.618962	−	0.670557i	−0.344381	−	0.938830i	$-0.611911\pi$
$839$	17.9285	−	19.4230i	0.618962	−	0.670557i	0.963343	+	0.268273i	$0.0864530\pi$
$840$	82.9567	+	109.253i	2.86228	+	3.76958i
$841$	−26.3830	−	69.7734i	−0.909759	−	2.40598i
$842$	−23.6841	+	105.544i	−0.816209	+	3.63730i
$843$	1.21762	−	14.0613i	0.0419370	−	0.484298i
$844$	7.52904	−	14.3540i	0.259160	−	0.494084i
$845$	−27.3990	−	24.4909i	−0.942554	−	0.842511i
$846$	5.83989	+	10.3173i	0.200780	+	0.354715i
$847$	22.1407	−	35.8338i	0.760764	−	1.23126i
$848$	−145.804	−	89.4454i	−5.00695	−	3.07157i
$849$	−5.93058	−	14.5475i	−0.203537	−	0.499269i
$850$	79.7870	−	42.8318i	2.73667	−	1.46912i
$851$	0.519588	+	1.42914i	0.0178112	+	0.0489902i
$852$	−53.9543	−	27.6434i	−1.84844	−	0.947049i
$853$	−0.547507	+	2.76987i	−0.0187463	+	0.0948385i	−0.989245	−	0.146268i	$-0.953274\pi$
$853$	−0.547507	+	2.76987i	−0.0187463	+	0.0948385i	0.970499	+	0.241106i	$0.0775102\pi$
$854$	−15.9155	−	133.827i	−0.544616	−	4.57947i
$855$	−2.01826	−	1.66922i	−0.0690232	−	0.0570860i
$856$	−68.5175	−	165.043i	−2.34188	−	5.64104i
$857$	−3.06957	+	15.0232i	−0.104855	+	0.513183i	0.893134	+	0.449791i	$0.148501\pi$
$857$	−3.06957	+	15.0232i	−0.104855	+	0.513183i	−0.997989	+	0.0633919i	$0.979808\pi$
$858$	−0.615451	−	0.115527i	−0.0210111	−	0.00394403i
$859$	−2.55448	+	46.9230i	−0.0871576	+	1.60099i	0.553288	+	0.832990i	$0.313373\pi$
$859$	−2.55448	+	46.9230i	−0.0871576	+	1.60099i	−0.640446	+	0.768003i	$0.721250\pi$
$860$	−2.25287	−	1.54606i	−0.0768222	−	0.0527200i
$861$	5.55158	−	3.35698i	0.189197	−	0.114405i
$862$	68.6559	+	8.83397i	2.33843	+	0.300886i
$863$	−17.4331	+	32.2265i	−0.593430	+	1.09700i	0.390861	+	0.920450i	$0.372177\pi$
$863$	−17.4331	+	32.2265i	−0.593430	+	1.09700i	−0.984291	+	0.176554i	$0.943505\pi$
$864$	−1.07492	+	111.996i	−0.0365694	+	3.81018i
$865$	−24.9471	+	59.0224i	−0.848228	+	2.00682i
$866$	−0.197974	+	0.617356i	−0.00672744	+	0.0209786i
$867$	34.8376	−	11.5416i	1.18315	−	0.391974i
$868$	137.971	+	71.8074i	4.68303	+	2.43730i
$869$	−0.417438	+	0.0348022i	−0.0141606	+	0.00118058i
$870$	96.5686	+	47.1592i	3.27398	+	1.59885i
$871$	0.590093	+	0.0874717i	0.0199945	+	0.00296387i
$872$	−150.406	−	41.4206i	−5.09338	−	1.40268i
$873$	5.62752	+	8.25676i	0.190463	+	0.279449i
$874$	7.87776	+	9.34104i	0.266469	+	0.315965i
$875$	−0.849888	+	1.21331i	−0.0287315	+	0.0410173i
$876$	4.16277	−	19.7291i	0.140647	−	0.666584i
$877$	12.0509	+	27.0513i	0.406931	+	0.913459i	0.994544	+	0.104316i	$0.0332654\pi$
$877$	12.0509	+	27.0513i	0.406931	+	0.913459i	−0.587613	+	0.809142i	$0.699932\pi$
$878$	−3.44150	−	71.6612i	−0.116145	−	2.41845i
$879$	−2.72405	−	0.712808i	−0.0918798	−	0.0240424i
$880$	−6.79272	−	2.64328i	−0.228983	−	0.0891050i
$881$	13.8650	−	31.1234i	0.467123	−	1.04857i	−0.514456	−	0.857517i	$-0.672006\pi$
$881$	13.8650	−	31.1234i	0.467123	−	1.04857i	0.981579	−	0.191057i	$-0.0611915\pi$
$882$	−25.0449	−	18.1473i	−0.843306	−	0.611050i
$883$	−8.11243	+	32.2634i	−0.273005	+	1.08575i	0.667128	+	0.744943i	$0.267523\pi$
$883$	−8.11243	+	32.2634i	−0.273005	+	1.08575i	−0.940133	+	0.340808i	$0.889299\pi$
$884$	19.5363	+	37.2457i	0.657078	+	1.25271i
$885$	22.7527	−	9.53125i	0.764824	−	0.320390i
$886$	62.1295	−	3.18299i	2.08728	−	0.106935i
$887$	−6.79912	−	4.23111i	−0.228292	−	0.142067i	0.409408	−	0.912351i	$-0.365735\pi$
$887$	−6.79912	−	4.23111i	−0.228292	−	0.142067i	−0.637700	+	0.770285i	$0.720114\pi$
$888$	−2.05837	+	0.711292i	−0.0690744	+	0.0238694i
$889$	−57.5295	−	1.84110i	−1.92948	−	0.0617485i
$890$	1.54056	+	19.2209i	0.0516397	+	0.644285i
$891$	−0.203098	+	0.338311i	−0.00680403	+	0.0113338i
$892$	−60.1119	+	17.8025i	−2.01270	+	0.596071i
$893$	−0.593854	+	1.57053i	−0.0198726	+	0.0525557i
$894$	54.0448	+	35.5825i	1.80753	+	1.19006i
$895$	23.1433	−	13.7931i	0.773596	−	0.461051i
$896$	−109.621	+	53.5334i	−3.66219	+	1.78843i
$897$	−10.6966	+	3.39250i	−0.357150	+	0.113272i
$898$	−7.26707	+	42.4478i	−0.242505	+	1.41650i
$899$	76.5862	+	0.980105i	2.55429	+	0.0326883i
$900$	36.9100	−	11.4468i	1.23033	−	0.381561i
$901$	−32.9540	+	75.2653i	−1.09786	+	2.50745i
$902$	−0.277910	+	0.538173i	−0.00925339	+	0.0179192i
$903$	−0.730388	−	0.231647i	−0.0243058	−	0.00770873i
$904$	131.119	−	19.4362i	4.36094	−	0.646439i
$905$	69.9088	+	8.54084i	2.32385	+	0.283907i
$906$	−15.6925	+	29.4576i	−0.521347	+	0.978664i
$907$	−6.23135	−	22.3476i	−0.206909	−	0.742041i	−0.992388	−	0.123153i	$-0.960700\pi$
$907$	−6.23135	−	22.3476i	−0.206909	−	0.742041i	0.785479	−	0.618888i	$-0.212417\pi$
$908$	9.22286	−	82.0236i	0.306071	−	2.72205i
$909$	−1.04367	+	13.0213i	−0.0346162	+	0.431891i
$910$	30.4876	+	21.7948i	1.01065	+	0.722492i
$911$	−19.7241	−	8.86249i	−0.653488	−	0.293628i	0.0559103	−	0.998436i	$-0.482194\pi$
$911$	−19.7241	−	8.86249i	−0.653488	−	0.293628i	−0.709398	+	0.704808i	$0.751033\pi$
$912$	−7.71534	+	6.29833i	−0.255480	+	0.208558i
$913$	−0.384223	+	0.0926988i	−0.0127159	+	0.00306788i
$914$	−33.3178	+	77.4411i	−1.10205	+	2.56152i
$915$	48.8751	+	11.4614i	1.61576	+	0.378901i
$916$	28.8117	−	24.7754i	0.951964	−	0.818601i
$917$	−33.8736	+	26.9374i	−1.11860	+	0.889550i
$918$	101.805	−	13.0993i	3.36007	−	0.432341i
$919$	1.27155	−	3.29883i	0.0419446	−	0.108818i	−0.910523	−	0.413459i	$-0.864320\pi$
$919$	1.27155	−	3.29883i	0.0419446	−	0.108818i	0.952467	+	0.304641i	$0.0985364\pi$
$920$	−227.815	+	27.8325i	−7.51085	+	0.917610i
$921$	−18.3542	+	5.05460i	−0.604791	+	0.166555i
$922$	29.7718	+	25.2715i	0.980483	+	0.832272i
$923$	−10.2555	−	1.78954i	−0.337564	−	0.0589033i
$924$	−4.15409	−	0.319580i	−0.136659	−	0.0105134i
$925$	0.560105	+	0.747533i	0.0184162	+	0.0245787i
$926$	−21.6459	−	50.3119i	−0.711328	−	1.65335i
$927$	2.13465	+	12.0064i	0.0701113	+	0.394341i
$928$	−124.701	+	164.230i	−4.09352	+	5.39110i
$929$	4.26595	+	1.26338i	0.139961	+	0.0414503i	0.353188	−	0.935553i	$-0.385098\pi$
$929$	4.26595	+	1.26338i	0.139961	+	0.0414503i	−0.213226	+	0.977003i	$0.568397\pi$
$930$	−58.5576	+	53.7061i	−1.92018	+	1.76109i
$931$	−0.294061	−	4.37045i	−0.00963747	−	0.143236i
$932$	76.2697	+	7.34257i	2.49830	+	0.240514i
$933$	−5.17559	+	0.398166i	−0.169441	+	0.0130354i
$934$	−11.7486	−	13.4003i	−0.384425	−	0.438471i
$935$	−0.810241	+	3.40608i	−0.0264977	+	0.111391i
$936$	4.44091	+	14.8209i	0.145156	+	0.484436i
$937$	30.7431	+	6.79553i	1.00433	+	0.222000i	0.687269	−	0.726403i	$-0.258810\pi$
$937$	30.7431	+	6.79553i	1.00433	+	0.222000i	0.317066	+	0.948404i	$0.397302\pi$
$938$	5.43924	+	0.208916i	0.177597	+	0.00682134i
$939$	−15.2923	−	13.1499i	−0.499045	−	0.429132i
$940$	−29.5682	−	40.5332i	−0.964407	−	1.32205i
$941$	15.2934	+	47.6903i	0.498549	+	1.55466i	0.799285	+	0.600952i	$0.205212\pi$
$941$	15.2934	+	47.6903i	0.498549	+	1.55466i	−0.300736	+	0.953707i	$0.597232\pi$
$942$	69.9889	+	6.28622i	2.28036	+	0.204816i
$943$	0.173616	+	10.8529i	0.00565371	+	0.353418i
$944$	18.0787	+	88.4812i	0.588411	+	2.87982i
$945$	55.2288	−	37.3838i	1.79659	−	1.21610i
$946$	0.0694333	−	0.0172226i	0.00225747	−	0.000559953i
$947$	−2.38442	+	23.9637i	−0.0774831	+	0.778717i	0.877008	+	0.480476i	$0.159536\pi$
$947$	−2.38442	+	23.9637i	−0.0774831	+	0.778717i	−0.954491	+	0.298241i	$0.903600\pi$
$948$	−9.08289	−	14.4921i	−0.294998	−	0.470680i
$949$	−0.320780	−	3.44764i	−0.0104130	−	0.111915i
$950$	6.29548	+	4.08738i	0.204252	+	0.132612i
$951$	−25.2857	−	1.13327i	−0.819945	−	0.0367487i
$952$	134.579	+	200.196i	4.36172	+	6.48839i
$953$	6.61597	+	43.6684i	0.214312	+	1.41456i	0.798038	+	0.602607i	$0.205871\pi$
$953$	6.61597	+	43.6684i	0.214312	+	1.41456i	−0.583726	+	0.811951i	$0.698406\pi$
$954$	−27.3353	+	39.5604i	−0.885014	+	1.28082i
$955$	−26.3341	+	14.3547i	−0.852153	+	0.464507i
$956$	0.695714	+	19.7615i	0.0225010	+	0.639133i
$957$	−1.89736	+	0.780586i	−0.0613331	+	0.0252328i
$958$	−24.5063	−	57.9795i	−0.791763	−	1.87323i
$959$	11.0831	−	0.995455i	0.357892	−	0.0321449i
$960$	−10.8937	−	102.803i	−0.351593	−	3.31795i
$961$	−9.67485	+	23.7321i	−0.312092	+	0.765551i
$962$	−0.479543	+	0.352173i	−0.0154611	+	0.0113545i
$963$	−26.9620	+	9.51054i	−0.868838	+	0.306473i
$964$	−73.8765	−	56.4687i	−2.37940	−	1.81873i
$965$	−15.7853	+	3.59530i	−0.508147	+	0.115737i
$966$	−93.6661	+	41.3682i	−3.01366	+	1.33100i
$967$	−10.0063	−	35.0181i	−0.321780	−	1.12611i	−0.940302	−	0.340340i	$-0.889458\pi$
$967$	−10.0063	−	35.0181i	−0.321780	−	1.12611i	0.618522	−	0.785767i	$-0.287732\pi$
$968$	−89.8245	+	46.0215i	−2.88707	+	1.47919i
$969$	3.50494	+	3.25609i	0.112595	+	0.104601i
$970$	−37.9520	−	43.8505i	−1.21857	−	1.40795i
$971$	−19.8174	−	45.2619i	−0.635970	−	1.45252i	−0.876268	−	0.481824i	$-0.839974\pi$
$971$	−19.8174	−	45.2619i	−0.635970	−	1.45252i	0.240298	−	0.970699i	$-0.422755\pi$
$972$	73.0407	+	4.67979i	2.34278	+	0.150104i
$973$	−30.4199	−	39.0157i	−0.975217	−	1.25078i
$974$	11.1341	+	18.2806i	0.356760	+	0.585749i
$975$	−5.68352	+	3.90037i	−0.182018	+	0.124912i
$976$	−75.8594	+	167.396i	−2.42820	+	5.35820i
$977$	27.6655	−	25.0493i	0.885097	−	0.801400i	−0.0959064	−	0.995390i	$-0.530575\pi$
$977$	27.6655	−	25.0493i	0.885097	−	0.801400i	0.981003	+	0.193991i	$0.0621432\pi$
$978$	−21.7896	+	32.8658i	−0.696753	+	1.05093i
$979$	−0.293890	−	0.221675i	−0.00939277	−	0.00708476i
$980$	114.113	+	64.1104i	3.64521	+	2.04793i
$981$	−7.92515	+	23.6676i	−0.253031	+	0.755648i
$982$	−114.261			−3.64621
$983$	−25.8931	+	17.6789i	−0.825863	+	0.563871i
$983$	−25.8931	+	17.6789i	−0.825863	+	0.563871i
$984$	−15.5449			−0.495552
$985$	8.46035	−	25.2659i	0.269569	−	0.805039i
$986$	164.760	+	92.5643i	5.24702	+	2.94785i
$987$	−11.2328	−	8.47267i	−0.357544	−	0.269688i
$988$	−1.92633	+	2.90553i	−0.0612846	+	0.0924373i
$989$	0.950312	−	0.860447i	0.0302182	−	0.0273606i
$990$	−0.845769	+	1.86632i	−0.0268803	+	0.0593156i
$991$	28.9510	−	19.8680i	0.919660	−	0.631127i	−0.00983888	−	0.999952i	$-0.503132\pi$
$991$	28.9510	−	19.8680i	0.919660	−	0.631127i	0.929499	+	0.368825i	$0.120240\pi$
$992$	−79.3059	−	130.209i	−2.51797	−	4.13414i
$993$	−19.7092	−	25.2785i	−0.625453	−	0.802187i
$994$	−94.7980	−	6.07380i	−3.00681	−	0.192649i
$995$	15.7463	+	35.9637i	0.499190	+	1.14013i
$996$	−10.5610	−	12.2024i	−0.334639	−	0.386648i
$997$	−12.4693	−	11.5840i	−0.394907	−	0.366868i	0.457981	−	0.888962i	$-0.348573\pi$
$997$	−12.4693	−	11.5840i	−0.394907	−	0.366868i	−0.852888	+	0.522094i	$0.825151\pi$
$998$	−65.2878	+	33.4502i	−2.06665	+	1.05885i
$999$	0.290897	+	1.01803i	0.00920357	+	0.0322090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.c.a.2.4	✓	39690
983.492	even	491	inner	983.2.c.a.492.4	yes	39690

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.c.a.2.4	✓	39690	1.1	even	1	trivial
983.2.c.a.492.4	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)

\(f(q)\)	\(=\)	\(q+(-0.862858 + 2.57683i) q^{2} +(1.07786 + 0.605560i) q^{3} +(-4.29883 - 3.24251i) q^{4} +(1.73663 - 2.61941i) q^{5} +(-2.49047 + 2.25496i) q^{6} +(-1.58443 + 3.49630i) q^{7} +(7.58350 - 5.20426i) q^{8} +(-0.765444 - 1.25675i) q^{9} +O(q^{10})\)	\(q+(-0.862858 + 2.57683i) q^{2} +(1.07786 + 0.605560i) q^{3} +(-4.29883 - 3.24251i) q^{4} +(1.73663 - 2.61941i) q^{5} +(-2.49047 + 2.25496i) q^{6} +(-1.58443 + 3.49630i) q^{7} +(7.58350 - 5.20426i) q^{8} +(-0.765444 - 1.25675i) q^{9} +(5.25132 + 6.73519i) q^{10} +(-0.162710 - 0.0104250i) q^{11} +(-2.67002 - 6.09819i) q^{12} +(-0.748119 - 0.864391i) q^{13} +(-7.64223 - 7.09963i) q^{14} +(3.45806 - 1.77174i) q^{15} +(3.90820 + 13.6772i) q^{16} +(6.25017 - 2.76042i) q^{17} +(3.89890 - 0.888025i) q^{18} +(0.449946 + 0.343924i) q^{19} +(-15.9590 + 5.62935i) q^{20} +(-3.82502 + 2.80907i) q^{21} +(0.167259 - 0.410281i) q^{22} +(-0.836680 - 7.89568i) q^{23} +(11.3255 - 1.01722i) q^{24} +(-1.89881 - 4.49240i) q^{25} +(2.87291 - 1.18193i) q^{26} +(-0.194503 - 5.52480i) q^{27} +(18.1480 - 9.89243i) q^{28} +(5.78597 - 8.37361i) q^{29} +(1.58165 + 10.4396i) q^{30} +(4.19827 + 6.24523i) q^{31} +(-20.2395 - 0.907105i) q^{32} +(-0.169067 - 0.109767i) q^{33} +(1.72014 + 18.4875i) q^{34} +(6.40667 + 10.2221i) q^{35} +(-0.784516 + 7.88451i) q^{36} +(-0.185888 + 0.0461086i) q^{37} +(-1.27447 + 0.862678i) q^{38} +(-0.282931 - 1.38473i) q^{39} +(-0.462355 - 28.9022i) q^{40} +(-1.36157 - 0.122293i) q^{41} +(-3.93804 - 12.2803i) q^{42} +(0.0951545 + 0.130442i) q^{43} +(0.665659 + 0.572405i) q^{44} +(-4.62124 - 0.177497i) q^{45} +(21.0678 + 4.65686i) q^{46} +(0.850979 + 2.84002i) q^{47} +(-4.06985 + 17.1088i) q^{48} +(-5.09895 - 5.81580i) q^{49} +(13.2146 - 1.01662i) q^{50} +(8.40844 + 0.809490i) q^{51} +(0.413235 + 6.14165i) q^{52} +(-8.86230 + 8.12805i) q^{53} +(14.4043 + 4.26592i) q^{54} +(-0.309875 + 0.408100i) q^{55} +(6.18009 + 34.7600i) q^{56} +(0.276715 + 0.643173i) q^{57} +(16.5849 + 22.1347i) q^{58} +(6.33010 + 0.486984i) q^{59} +(-20.6105 - 3.59643i) q^{60} +(9.84991 + 8.36098i) q^{61} +(-19.7154 + 5.42948i) q^{62} +(5.60677 - 0.684985i) q^{63} +(9.56921 - 24.8257i) q^{64} +(-3.56340 + 0.458504i) q^{65} +(0.428733 - 0.340942i) q^{66} +(-0.395660 + 0.340231i) q^{67} +(-35.8191 - 8.39968i) q^{68} +(3.87948 - 9.01713i) q^{69} +(-31.8686 + 7.68872i) q^{70} +(7.05451 - 5.75886i) q^{71} +(-12.3452 - 5.54699i) q^{72} +(2.46400 + 1.76146i) q^{73} +(0.0415811 - 0.518788i) q^{74} +(0.673755 - 5.99204i) q^{75} +(-0.819063 - 2.93742i) q^{76} +(0.294252 - 0.552365i) q^{77} +(3.81234 + 0.465758i) q^{78} +(2.54140 - 0.376721i) q^{79} +(42.6133 + 13.5151i) q^{80} +(1.11044 - 2.15037i) q^{81} +(1.48997 - 3.40302i) q^{82} +(2.31539 - 0.718067i) q^{83} +(25.5515 + 0.326994i) q^{84} +(3.62356 - 21.1656i) q^{85} +(-0.418231 + 0.132645i) q^{86} +(11.3072 - 5.52187i) q^{87} +(-1.28817 + 0.767727i) q^{88} +(1.88577 + 1.24157i) q^{89} +(4.44485 - 11.7550i) q^{90} +(4.20751 - 1.24608i) q^{91} +(-22.0051 + 36.6551i) q^{92} +(0.743301 + 9.27382i) q^{93} +(-8.05252 - 0.257702i) q^{94} +(1.68227 - 0.581326i) q^{95} +(-21.2662 - 13.2340i) q^{96} +(-6.78154 + 0.347429i) q^{97} +(19.3860 - 8.12093i) q^{98} +(0.111444 + 0.212466i) 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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