LMFDB - Embedded newform 983.2.c.a.2.19

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			2.19
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555704 + 1.65955i) q^{2} +(0.352885 + 0.198256i) q^{3} +(-0.848581 - 0.640067i) q^{4} +(-0.636799 + 0.960502i) q^{5} +(-0.525115 + 0.475459i) q^{6} +(-1.20682 + 2.66304i) q^{7} +(-1.35223 + 0.927979i) q^{8} +(-1.47531 - 2.42225i) q^{9} +O(q^{10})$	\(q+(-0.555704 + 1.65955i) q^{2} +(0.352885 + 0.198256i) q^{3} +(-0.848581 - 0.640067i) q^{4} +(-0.636799 + 0.960502i) q^{5} +(-0.525115 + 0.475459i) q^{6} +(-1.20682 + 2.66304i) q^{7} +(-1.35223 + 0.927979i) q^{8} +(-1.47531 - 2.42225i) q^{9} +(-1.24013 - 1.59055i) q^{10} +(2.05116 + 0.131420i) q^{11} +(-0.172555 - 0.394107i) q^{12} +(-4.41619 - 5.10255i) q^{13} +(-3.74880 - 3.48264i) q^{14} +(-0.415142 + 0.212698i) q^{15} +(-1.37266 - 4.80377i) q^{16} +(3.75743 - 1.65949i) q^{17} +(4.83968 - 1.10230i) q^{18} +(-5.73496 - 4.38361i) q^{19} +(1.15516 - 0.407471i) q^{20} +(-0.953832 + 0.700487i) q^{21} +(-1.35793 + 3.33096i) q^{22} +(-0.323923 - 3.05683i) q^{23} +(-0.661158 + 0.0593835i) q^{24} +(1.42957 + 3.38221i) q^{25} +(10.9220 - 4.49338i) q^{26} +(-0.0831133 - 2.36081i) q^{27} +(2.72861 - 1.48736i) q^{28} +(-3.34721 + 4.84417i) q^{29} +(-0.122287 - 0.807146i) q^{30} +(2.65328 + 3.94696i) q^{31} +(5.45814 + 0.244626i) q^{32} +(0.697768 + 0.453030i) q^{33} +(0.665987 + 7.15782i) q^{34} +(-1.78935 - 2.85497i) q^{35} +(-0.298480 + 2.99977i) q^{36} +(-6.49138 + 1.61015i) q^{37} +(10.4617 - 7.08145i) q^{38} +(-0.546798 - 2.67615i) q^{39} +(-0.0302308 - 1.88975i) q^{40} +(-1.78480 - 0.160306i) q^{41} +(-0.632445 - 1.97219i) q^{42} +(5.46504 + 7.49169i) q^{43} +(-1.65645 - 1.42440i) q^{44} +(3.26605 + 0.125446i) q^{45} +(5.25297 + 1.16113i) q^{46} +(-3.10525 - 10.3633i) q^{47} +(0.467987 - 1.96732i) q^{48} +(-1.02063 - 1.16412i) q^{49} +(-6.40736 + 0.492928i) q^{50} +(1.65495 + 0.159323i) q^{51} +(0.481524 + 7.15659i) q^{52} +(3.35120 - 3.07355i) q^{53} +(3.96406 + 1.17398i) q^{54} +(-1.43240 + 1.88645i) q^{55} +(-0.839350 - 4.72093i) q^{56} +(-1.15471 - 2.68390i) q^{57} +(-6.17908 - 8.24679i) q^{58} +(-14.4431 - 1.11113i) q^{59} +(0.488423 + 0.0852274i) q^{60} +(4.78150 + 4.05872i) q^{61} +(-8.02461 + 2.20992i) q^{62} +(8.23097 - 1.00559i) q^{63} +(0.154693 - 0.401326i) q^{64} +(7.71324 - 0.992465i) q^{65} +(-1.13958 + 0.906230i) q^{66} +(8.82713 - 7.59051i) q^{67} +(-4.25067 - 0.996794i) q^{68} +(0.491728 - 1.14293i) q^{69} +(5.73231 - 1.38300i) q^{70} +(-1.37982 + 1.12640i) q^{71} +(4.24275 + 1.90637i) q^{72} +(-7.43933 - 5.31820i) q^{73} +(0.935158 - 11.6675i) q^{74} +(-0.166071 + 1.47695i) q^{75} +(2.06078 + 7.39060i) q^{76} +(-2.82535 + 5.30370i) q^{77} +(4.74507 + 0.579710i) q^{78} +(-9.65745 + 1.43156i) q^{79} +(5.48814 + 1.74060i) q^{80} +(-3.46524 + 6.71044i) q^{81} +(1.25785 - 2.87287i) q^{82} +(4.71479 - 1.46219i) q^{83} +(1.25776 + 0.0160961i) q^{84} +(-0.798783 + 4.66578i) q^{85} +(-15.4698 + 4.90633i) q^{86} +(-2.14157 + 1.04583i) q^{87} +(-2.89558 + 1.72572i) q^{88} +(-14.8997 - 9.80983i) q^{89} +(-2.02314 + 5.35047i) q^{90} +(18.9178 - 5.60262i) q^{91} +(-1.68170 + 2.80130i) q^{92} +(0.153797 + 1.91885i) q^{93} +(18.9241 + 0.605621i) q^{94} +(7.86248 - 2.71696i) q^{95} +(1.87760 + 1.16843i) q^{96} +(-8.30051 + 0.425248i) q^{97} +(2.49907 - 1.04688i) q^{98} +(-2.70776 - 5.16230i) 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 $

$2$	−0.555704	+	1.65955i	−0.392942	+	1.17348i	0.548456	+	0.836180i	$0.315216\pi$
$2$	−0.555704	+	1.65955i	−0.392942	+	1.17348i	−0.941398	+	0.337299i	$0.890487\pi$
$3$	0.352885	+	0.198256i	0.203738	+	0.114463i	0.588321	−	0.808627i	$-0.299789\pi$
$3$	0.352885	+	0.198256i	0.203738	+	0.114463i	−0.384583	+	0.923091i	$0.625655\pi$
$4$	−0.848581	−	0.640067i	−0.424291	−	0.320034i
$5$	−0.636799	+	0.960502i	−0.284785	+	0.429550i	−0.947708	−	0.319138i	$-0.896607\pi$
$5$	−0.636799	+	0.960502i	−0.284785	+	0.429550i	0.662923	+	0.748687i	$0.269316\pi$
$6$	−0.525115	+	0.475459i	−0.214377	+	0.194105i
$7$	−1.20682	+	2.66304i	−0.456135	+	1.00653i	0.531107	+	0.847305i	$0.321776\pi$
$7$	−1.20682	+	2.66304i	−0.456135	+	1.00653i	−0.987242	+	0.159228i	$0.949099\pi$
$8$	−1.35223	+	0.927979i	−0.478084	+	0.328090i
$9$	−1.47531	−	2.42225i	−0.491771	−	0.807417i
$10$	−1.24013	−	1.59055i	−0.392163	−	0.502977i
$11$	2.05116	+	0.131420i	0.618447	+	0.0396245i	0.370016	−	0.929025i	$-0.379352\pi$
$11$	2.05116	+	0.131420i	0.618447	+	0.0396245i	0.248430	+	0.968650i	$0.420085\pi$
$12$	−0.172555	−	0.394107i	−0.0498123	−	0.113769i
$13$	−4.41619	−	5.10255i	−1.22483	−	1.41519i	−0.878949	−	0.476916i	$-0.841755\pi$
$13$	−4.41619	−	5.10255i	−1.22483	−	1.41519i	−0.345883	−	0.938278i	$-0.612420\pi$
$14$	−3.74880	−	3.48264i	−1.00191	−	0.930774i
$15$	−0.415142	+	0.212698i	−0.107189	+	0.0549184i
$16$	−1.37266	−	4.80377i	−0.343164	−	1.20094i
$17$	3.75743	−	1.65949i	0.911311	−	0.402485i	0.105337	−	0.994437i	$-0.466408\pi$
$17$	3.75743	−	1.65949i	0.911311	−	0.402485i	0.805974	+	0.591951i	$0.201642\pi$
$18$	4.83968	−	1.10230i	1.14072	−	0.259814i
$19$	−5.73496	−	4.38361i	−1.31569	−	1.00567i	−0.998354	−	0.0573550i	$-0.981733\pi$
$19$	−5.73496	−	4.38361i	−1.31569	−	1.00567i	−0.317335	−	0.948313i	$-0.602788\pi$
$20$	1.15516	−	0.407471i	0.258302	−	0.0911132i
$21$	−0.953832	+	0.700487i	−0.208143	+	0.152859i
$22$	−1.35793	+	3.33096i	−0.289512	+	0.710163i
$23$	−0.323923	−	3.05683i	−0.0675426	−	0.637394i	−0.975752	−	0.218878i	$-0.929760\pi$
$23$	−0.323923	−	3.05683i	−0.0675426	−	0.637394i	0.908210	−	0.418516i	$-0.137449\pi$
$24$	−0.661158	+	0.0593835i	−0.134958	+	0.0121216i
$25$	1.42957	+	3.38221i	0.285913	+	0.676442i
$26$	10.9220	−	4.49338i	2.14199	−	0.881225i
$27$	−0.0831133	−	2.36081i	−0.0159952	−	0.454337i
$28$	2.72861	−	1.48736i	0.515658	−	0.281084i
$29$	−3.34721	+	4.84417i	−0.621562	+	0.899540i	−0.999656	−	0.0262270i	$-0.991651\pi$
$29$	−3.34721	+	4.84417i	−0.621562	+	0.899540i	0.378094	+	0.925767i	$0.376579\pi$
$30$	−0.122287	−	0.807146i	−0.0223264	−	0.147364i
$31$	2.65328	+	3.94696i	0.476544	+	0.708894i	0.988685	−	0.150007i	$-0.0479296\pi$
$31$	2.65328	+	3.94696i	0.476544	+	0.708894i	−0.512141	+	0.858901i	$0.671148\pi$
$32$	5.45814	+	0.244626i	0.964872	+	0.0432441i
$33$	0.697768	+	0.453030i	0.121466	+	0.0788624i
$34$	0.665987	+	7.15782i	0.114216	+	1.22756i
$35$	−1.78935	−	2.85497i	−0.302456	−	0.482578i
$36$	−0.298480	+	2.99977i	−0.0497467	+	0.499962i
$37$	−6.49138	+	1.61015i	−1.06718	+	0.264708i	−0.734692	−	0.678401i	$-0.762673\pi$
$37$	−6.49138	+	1.61015i	−1.06718	+	0.264708i	−0.332485	+	0.943108i	$0.607887\pi$
$38$	10.4617	−	7.08145i	1.69712	−	1.14876i
$39$	−0.546798	−	2.67615i	−0.0875578	−	0.428528i
$40$	−0.0302308	−	1.88975i	−0.00477992	−	0.298796i
$41$	−1.78480	−	0.160306i	−0.278738	−	0.0250355i	−0.0507920	−	0.998709i	$-0.516175\pi$
$41$	−1.78480	−	0.160306i	−0.278738	−	0.0250355i	−0.227946	+	0.973674i	$0.573201\pi$
$42$	−0.632445	−	1.97219i	−0.0975883	−	0.304316i
$43$	5.46504	+	7.49169i	0.833410	+	1.14247i	0.987994	+	0.154493i	$0.0493744\pi$
$43$	5.46504	+	7.49169i	0.833410	+	1.14247i	−0.154584	+	0.987980i	$0.549404\pi$
$44$	−1.65645	−	1.42440i	−0.249720	−	0.214736i
$45$	3.26605	+	0.125446i	0.486875	+	0.0187004i
$46$	5.25297	+	1.16113i	0.774508	+	0.171199i
$47$	−3.10525	−	10.3633i	−0.452948	−	1.51165i	−0.814984	−	0.579484i	$-0.803254\pi$
$47$	−3.10525	−	10.3633i	−0.452948	−	1.51165i	0.362036	−	0.932164i	$-0.382082\pi$
$48$	0.467987	−	1.96732i	0.0675481	−	0.283958i
$49$	−1.02063	−	1.16412i	−0.145804	−	0.166302i
$50$	−6.40736	+	0.492928i	−0.906138	+	0.0697105i
$51$	1.65495	+	0.159323i	0.231739	+	0.0223098i
$52$	0.481524	+	7.15659i	0.0667754	+	0.992441i
$53$	3.35120	−	3.07355i	0.460322	−	0.422184i	−0.411949	−	0.911207i	$-0.635152\pi$
$53$	3.35120	−	3.07355i	0.460322	−	0.422184i	0.872271	+	0.489023i	$0.162647\pi$
$54$	3.96406	+	1.17398i	0.539440	+	0.159758i
$55$	−1.43240	+	1.88645i	−0.193145	+	0.254369i
$56$	−0.839350	−	4.72093i	−0.112163	−	0.630861i
$57$	−1.15471	−	2.68390i	−0.152944	−	0.355491i
$58$	−6.17908	−	8.24679i	−0.811353	−	1.08286i
$59$	−14.4431	−	1.11113i	−1.88034	−	0.144657i	−0.914630	−	0.404292i	$-0.867518\pi$
$59$	−14.4431	−	1.11113i	−1.88034	−	0.144657i	−0.965707	+	0.259635i	$0.916398\pi$
$60$	0.488423	+	0.0852274i	0.0630552	+	0.0110028i
$61$	4.78150	+	4.05872i	0.612209	+	0.519666i	0.898784	−	0.438392i	$-0.144452\pi$
$61$	4.78150	+	4.05872i	0.612209	+	0.519666i	−0.286575	+	0.958058i	$0.592517\pi$
$62$	−8.02461	+	2.20992i	−1.01913	+	0.280660i
$63$	8.23097	−	1.00559i	1.03701	−	0.126692i
$64$	0.154693	−	0.401326i	0.0193367	−	0.0501657i
$65$	7.71324	−	0.992465i	0.956710	−	0.123100i
$66$	−1.13958	+	0.906230i	−0.140272	+	0.111549i
$67$	8.82713	−	7.59051i	1.07841	−	0.927328i	0.0808163	−	0.996729i	$-0.474247\pi$
$67$	8.82713	−	7.59051i	1.07841	−	0.927328i	0.997589	+	0.0694010i	$0.0221088\pi$
$68$	−4.25067	−	0.996794i	−0.515469	−	0.120879i
$69$	0.491728	−	1.14293i	0.0591971	−	0.137593i
$70$	5.73231	−	1.38300i	0.685143	−	0.165300i
$71$	−1.37982	+	1.12640i	−0.163755	+	0.133679i	−0.710717	−	0.703478i	$-0.751629\pi$
$71$	−1.37982	+	1.12640i	−0.163755	+	0.133679i	0.546962	+	0.837157i	$0.315784\pi$
$72$	4.24275	+	1.90637i	0.500013	+	0.224668i
$73$	−7.43933	−	5.31820i	−0.870708	−	0.622449i	0.0559169	−	0.998435i	$-0.482192\pi$
$73$	−7.43933	−	5.31820i	−0.870708	−	0.622449i	−0.926625	+	0.375987i	$0.877304\pi$
$74$	0.935158	−	11.6675i	0.108710	−	1.35632i
$75$	−0.166071	+	1.47695i	−0.0191762	+	0.170544i
$76$	2.06078	+	7.39060i	0.236387	+	0.847760i
$77$	−2.82535	+	5.30370i	−0.321978	+	0.604413i
$78$	4.74507	+	0.579710i	0.537273	+	0.0656393i
$79$	−9.65745	+	1.43156i	−1.08655	+	0.161063i	−0.665812	−	0.746120i	$-0.731915\pi$
$79$	−9.65745	+	1.43156i	−1.08655	+	0.161063i	−0.420737	+	0.907183i	$0.638228\pi$
$80$	5.48814	+	1.74060i	0.613593	+	0.194605i
$81$	−3.46524	+	6.71044i	−0.385026	+	0.745604i
$82$	1.25785	−	2.87287i	0.138907	−	0.317256i
$83$	4.71479	−	1.46219i	0.517515	−	0.160496i	−0.0263757	−	0.999652i	$-0.508397\pi$
$83$	4.71479	−	1.46219i	0.517515	−	0.160496i	0.543891	+	0.839156i	$0.316951\pi$
$84$	1.25776	+	0.0160961i	0.137233	+	0.00175623i
$85$	−0.798783	+	4.66578i	−0.0866402	+	0.506075i
$86$	−15.4698	+	4.90633i	−1.66815	+	0.529063i
$87$	−2.14157	+	1.04583i	−0.229600	+	0.112125i
$88$	−2.89558	+	1.72572i	−0.308670	+	0.183962i
$89$	−14.8997	−	9.80983i	−1.57937	−	1.03984i	−0.968789	−	0.247885i	$-0.920264\pi$
$89$	−14.8997	−	9.80983i	−1.57937	−	1.03984i	−0.610579	−	0.791955i	$-0.709063\pi$
$90$	−2.02314	+	5.35047i	−0.213258	+	0.563989i
$91$	18.9178	−	5.60262i	1.98313	−	0.587314i
$92$	−1.68170	+	2.80130i	−0.175330	+	0.292056i
$93$	0.153797	+	1.91885i	0.0159480	+	0.198976i
$94$	18.9241	+	0.605621i	1.95187	+	0.0624650i
$95$	7.86248	−	2.71696i	0.806673	−	0.278755i
$96$	1.87760	+	1.16843i	0.191632	+	0.119253i
$97$	−8.30051	+	0.425248i	−0.842789	+	0.0431774i	−0.467781	−	0.883844i	$-0.654946\pi$
$97$	−8.30051	+	0.425248i	−0.842789	+	0.0431774i	−0.375008	+	0.927022i	$0.622360\pi$
$98$	2.49907	−	1.04688i	0.252445	−	0.105751i
$99$	−2.70776	−	5.16230i	−0.272140	−	0.518830i
$100$	0.951738	−	3.78510i	0.0951738	−	0.378510i
$101$	1.86924	+	1.35443i	0.185997	+	0.134771i	0.675865	−	0.737025i	$-0.263770\pi$
$101$	1.86924	+	1.35443i	0.185997	+	0.134771i	−0.489869	+	0.871796i	$0.662955\pi$
$102$	−1.18406	+	2.65793i	−0.117240	+	0.263174i
$103$	−6.08621	−	2.36835i	−0.599692	−	0.233361i	0.0435157	−	0.999053i	$-0.486144\pi$
$103$	−6.08621	−	2.36835i	−0.599692	−	0.233361i	−0.643207	+	0.765692i	$0.722397\pi$
$104$	10.7068	+	2.80167i	1.04988	+	0.274726i
$105$	−0.0654204	−	1.36223i	−0.00638437	−	0.132940i
$106$	3.23843	+	7.26946i	0.314544	+	0.706072i
$107$	0.799563	−	3.78946i	0.0772966	−	0.366341i	−0.922511	−	0.385972i	$-0.873866\pi$
$107$	0.799563	−	3.78946i	0.0772966	−	0.366341i	0.999807	+	0.0196310i	$0.00624915\pi$
$108$	−1.44055	+	2.05653i	−0.138617	+	0.197890i
$109$	11.1860	+	13.2638i	1.07142	+	1.27044i	0.960998	+	0.276554i	$0.0891924\pi$
$109$	11.1860	+	13.2638i	1.07142	+	1.27044i	0.110424	+	0.993885i	$0.464779\pi$
$110$	−2.33467	−	3.42545i	−0.222602	−	0.326604i
$111$	−2.60994	−	0.718757i	−0.247724	−	0.0682214i
$112$	14.4492	+	2.14186i	1.36532	+	0.202386i
$113$	2.12413	+	1.03732i	0.199821	+	0.0975824i	0.536008	−	0.844213i	$-0.319932\pi$
$113$	2.12413	+	1.03732i	0.199821	+	0.0975824i	−0.336187	+	0.941795i	$0.609137\pi$
$114$	5.09574	−	0.424837i	0.477260	−	0.0397896i
$115$	3.14237	+	1.63546i	0.293027	+	0.152507i
$116$	5.94098	−	1.96823i	0.551606	−	0.182746i
$117$	−5.84440	+	18.2250i	−0.540315	+	1.68490i
$118$	9.87009	−	23.3516i	0.908615	−	2.14969i
$119$	−0.115259	+	12.0089i	−0.0105658	+	1.10085i
$120$	0.363987	−	0.672859i	0.0332273	−	0.0614234i
$121$	−6.72009	−	0.864676i	−0.610917	−	0.0786069i
$122$	−9.39274	+	5.67969i	−0.850379	+	0.514215i
$123$	−0.598047	−	0.410416i	−0.0539241	−	0.0370060i
$124$	0.274790	−	5.04759i	0.0246768	−	0.453287i
$125$	−9.82217	−	1.84374i	−0.878522	−	0.164909i
$126$	−2.90516	+	14.2185i	−0.258812	+	1.26669i
$127$	−2.61369	−	6.29577i	−0.231928	−	0.558659i	0.764356	−	0.644795i	$-0.223057\pi$
$127$	−2.61369	−	6.29577i	−0.231928	−	0.558659i	−0.996283	+	0.0861359i	$0.972548\pi$
$128$	9.00053	+	7.44395i	0.795542	+	0.657958i
$129$	0.443258	+	3.72719i	0.0390267	+	0.328160i
$130$	−2.63923	+	13.3520i	−0.231476	+	1.17105i
$131$	−15.7840	−	8.08692i	−1.37905	−	0.706557i	−0.401228	−	0.915978i	$-0.631416\pi$
$131$	−15.7840	−	8.08692i	−1.37905	−	0.706557i	−0.977826	+	0.209421i	$0.932842\pi$
$132$	−0.302143	−	0.831051i	−0.0262982	−	0.0723337i
$133$	18.5948	−	9.98217i	1.61237	−	0.865564i
$134$	7.69155	+	18.8671i	0.664449	+	1.62987i
$135$	2.32049	+	1.42353i	0.199716	+	0.122518i
$136$	−3.54092	+	5.73082i	−0.303631	+	0.491414i
$137$	−3.92878	−	6.94093i	−0.335658	−	0.593004i	0.650363	−	0.759624i	$-0.274617\pi$
$137$	−3.92878	−	6.94093i	−0.335658	−	0.593004i	−0.986021	+	0.166620i	$0.946715\pi$
$138$	1.62350	+	1.45118i	0.138201	+	0.123532i
$139$	−1.84640	+	3.52012i	−0.156609	+	0.298573i	−0.951201	−	0.308571i	$-0.900149\pi$
$139$	−1.84640	+	3.52012i	−0.156609	+	0.298573i	0.794592	+	0.607144i	$0.207685\pi$
$140$	−0.308963	+	3.56798i	−0.0261121	+	0.301549i
$141$	0.958795	−	4.27271i	0.0807451	−	0.359827i
$142$	−1.10255	−	2.91583i	−0.0925238	−	0.244691i
$143$	−8.38772	−	11.0465i	−0.701417	−	0.923755i
$144$	−9.61085	+	10.4120i	−0.800904	+	0.867665i
$145$	−2.52134	−	6.29977i	−0.209386	−	0.523167i
$146$	12.9599	−	9.39059i	1.07257	−	0.777171i
$147$	−0.129372	−	0.613145i	−0.0106704	−	0.0505713i
$148$	6.53907	+	2.78857i	0.537509	+	0.229219i
$149$	5.65551	+	21.8987i	0.463317	+	1.79401i	0.596147	+	0.802875i	$0.296697\pi$
$149$	5.65551	+	21.8987i	0.463317	+	1.79401i	−0.132830	+	0.991139i	$0.542406\pi$
$150$	−2.35879	−	1.09635i	−0.192594	−	0.0895167i
$151$	16.9011	−	6.08353i	1.37539	−	0.495071i	0.456547	−	0.889699i	$-0.349086\pi$
$151$	16.9011	−	6.08353i	1.37539	−	0.495071i	0.918841	+	0.394628i	$0.129127\pi$
$152$	11.8229	+	0.605704i	0.958960	+	0.0491290i
$153$	−9.56308	−	6.65317i	−0.773129	−	0.537877i
$154$	−7.23169	−	7.63609i	−0.582746	−	0.615334i
$155$	−5.48067	+	0.0350677i	−0.440218	+	0.00281671i
$156$	−1.24891	+	2.62092i	−0.0999932	+	0.209842i
$157$	−0.164679	−	0.178406i	−0.0131428	−	0.0142384i	0.728205	−	0.685359i	$-0.240355\pi$
$157$	−0.164679	−	0.178406i	−0.0131428	−	0.0142384i	−0.741348	+	0.671121i	$0.765813\pi$
$158$	2.99094	−	16.8225i	0.237946	−	1.33833i
$159$	1.79194	−	0.420215i	0.142110	−	0.0333252i
$160$	−3.71070	+	5.08678i	−0.293357	+	0.402145i
$161$	8.53137	+	2.82643i	0.672366	+	0.222754i
$162$	−9.21065	−	9.47974i	−0.723657	−	0.744799i
$163$	−5.75417	+	1.46644i	−0.450702	+	0.114860i	−0.465535	−	0.885030i	$-0.654138\pi$
$163$	−5.75417	+	1.46644i	−0.450702	+	0.114860i	0.0148327	+	0.999890i	$0.495278\pi$
$164$	1.41194	+	1.27842i	0.110254	+	0.0998279i
$165$	−0.879474	+	0.381719i	−0.0684670	+	0.0297168i
$166$	−0.193451	+	8.63696i	−0.0150147	+	0.670358i
$167$	−1.78385	−	9.67371i	−0.138038	−	0.748574i	−0.978427	−	0.206591i	$-0.933763\pi$
$167$	−1.78385	−	9.67371i	−0.138038	−	0.748574i	0.840389	−	0.541983i	$-0.182326\pi$
$168$	0.639759	−	1.83235i	0.0493584	−	0.141369i
$169$	−4.66822	+	32.2022i	−0.359094	+	2.47709i
$170$	−7.29921	−	3.91841i	−0.559824	−	0.300528i
$171$	−2.15735	+	20.3587i	−0.164976	+	1.55687i
$172$	0.157658	−	9.85530i	0.0120213	−	0.751460i
$173$	15.2601	−	2.86450i	1.16021	−	0.217784i	0.431178	−	0.902267i	$-0.358098\pi$
$173$	15.2601	−	2.86450i	1.16021	−	0.217784i	0.729029	+	0.684483i	$0.239972\pi$
$174$	−0.545532	−	4.13521i	−0.0413567	−	0.313490i
$175$	−10.7322	−	0.274733i	−0.811277	−	0.0207679i
$176$	−2.18422	−	10.0337i	−0.164642	−	0.756317i
$177$	−4.87649	−	3.25554i	−0.366539	−	0.244702i
$178$	24.5597	−	19.2755i	1.84083	−	1.44476i
$179$	0.508972	+	0.244535i	0.0380424	+	0.0182774i	0.451985	−	0.892026i	$-0.350716\pi$
$179$	0.508972	+	0.244535i	0.0380424	+	0.0182774i	−0.413942	+	0.910303i	$0.635849\pi$
$180$	−2.69122	−	2.19694i	−0.200592	−	0.163751i
$181$	1.70770	+	3.41341i	0.126932	+	0.253716i	0.948746	−	0.316040i	$-0.102353\pi$
$181$	1.70770	+	3.41341i	0.126932	+	0.253716i	−0.821814	+	0.569756i	$0.807038\pi$
$182$	−1.21489	+	34.5085i	−0.0900534	+	2.55794i
$183$	0.882656	+	2.38023i	0.0652478	+	0.175951i
$184$	3.27470	+	3.83293i	0.241414	+	0.282568i
$185$	2.58715	−	7.26033i	0.190211	−	0.533790i
$186$	−3.26990	−	0.811080i	−0.239760	−	0.0594713i
$187$	7.92516	−	2.91007i	0.579545	−	0.212806i
$188$	−3.99817	+	10.7817i	−0.291596	+	0.786337i
$189$	6.38721	+	2.62773i	0.464601	+	0.191139i
$190$	0.139725	+	14.5580i	0.0101367	+	1.05615i
$191$	−7.60844	−	4.02192i	−0.550528	−	0.291016i	0.168842	−	0.985643i	$-0.445997\pi$
$191$	−7.60844	−	4.02192i	−0.550528	−	0.291016i	−0.719370	+	0.694627i	$0.755569\pi$
$192$	0.134154	−	0.110953i	0.00968175	−	0.00800735i
$193$	−12.1349	−	11.5661i	−0.873487	−	0.832545i	0.113468	−	0.993542i	$-0.463804\pi$
$193$	−12.1349	−	11.5661i	−0.873487	−	0.832545i	−0.986955	+	0.160997i	$0.948529\pi$
$194$	3.90690	−	14.0114i	0.280499	−	1.00596i
$195$	2.91865	+	1.17897i	0.209009	+	0.0844279i
$196$	0.120974	+	1.64112i	0.00864097	+	0.117223i
$197$	−18.7685	+	5.03974i	−1.33720	+	0.359067i	−0.855743	−	0.517401i	$-0.826900\pi$
$197$	−18.7685	+	5.03974i	−1.33720	+	0.359067i	−0.481460	+	0.876468i	$0.659893\pi$
$198$	10.0718	−	1.62496i	0.715771	−	0.115481i
$199$	−10.7935	+	16.7414i	−0.765131	+	1.18677i	0.212647	+	0.977129i	$0.431792\pi$
$199$	−10.7935	+	16.7414i	−0.765131	+	1.18677i	−0.977778	+	0.209641i	$0.932771\pi$
$200$	−5.07172	−	3.24690i	−0.358625	−	0.229591i
$201$	4.61983	−	0.928548i	0.325858	−	0.0654947i
$202$	−3.28649	+	2.34944i	−0.231237	+	0.165306i
$203$	−8.86072	−	14.7598i	−0.621901	−	1.03593i
$204$	−1.30238	−	1.19448i	−0.0911848	−	0.0836300i
$205$	1.29053	−	1.61222i	0.0901345	−	0.112602i
$206$	7.31252	−	8.78425i	0.509488	−	0.612028i
$207$	−6.92653	+	5.29440i	−0.481427	+	0.367987i
$208$	−18.4496	+	28.2185i	−1.27925	+	1.95660i
$209$	−11.1872	−	9.74514i	−0.773834	−	0.674086i
$210$	2.29704	+	0.648427i	0.158511	+	0.0447457i
$211$	−0.285567	−	1.73469i	−0.0196592	−	0.119421i	0.975081	−	0.221848i	$-0.0712088\pi$
$211$	−0.285567	−	1.73469i	−0.0196592	−	0.119421i	−0.994741	+	0.102427i	$0.967339\pi$
$212$	−4.81104	+	0.463164i	−0.330424	+	0.0318102i
$213$	−0.710236	+	0.123933i	−0.0486646	+	0.00849173i
$214$	5.84447	+	3.43273i	0.399520	+	0.234657i
$215$	−10.6759	+	0.478478i	−0.728092	+	0.0326319i
$216$	2.30317	+	3.11521i	0.156711	+	0.211963i
$217$	−13.7129	+	2.30252i	−0.930894	+	0.156306i
$218$	−28.2280	+	11.1930i	−1.91184	+	0.758083i
$219$	−1.57087	−	3.35161i	−0.106149	−	0.226481i
$220$	2.42297	−	0.683975i	0.163356	−	0.0461136i
$221$	−25.0612	−	11.8439i	−1.68580	−	0.796704i
$222$	2.64316	−	3.93190i	0.177398	−	0.263892i
$223$	−3.83771	+	5.19080i	−0.256992	+	0.347602i	−0.913588	−	0.406640i	$-0.866700\pi$
$223$	−3.83771	+	5.19080i	−0.256992	+	0.347602i	0.656596	+	0.754242i	$0.271996\pi$
$224$	−7.23844	+	14.2400i	−0.483639	+	0.951451i
$225$	6.08351	−	8.45258i	0.405567	−	0.563506i
$226$	−2.90186	+	2.94865i	−0.193029	+	0.196142i
$227$	5.01979	+	8.48428i	0.333175	+	0.563121i	0.979872	−	0.199625i	$-0.0639725\pi$
$227$	5.01979	+	8.48428i	0.333175	+	0.563121i	−0.646697	+	0.762747i	$0.723850\pi$
$228$	−0.738015	+	3.01660i	−0.0488762	+	0.199779i
$229$	−1.97883	+	9.09015i	−0.130764	+	0.600694i	0.864428	+	0.502757i	$0.167681\pi$
$229$	−1.97883	+	9.09015i	−0.130764	+	0.600694i	−0.995193	+	0.0979376i	$0.968775\pi$
$230$	−4.46035	+	4.30609i	−0.294107	+	0.283935i
$231$	−2.04852	+	1.31146i	−0.134782	+	0.0862874i
$232$	0.0308931	−	9.65656i	0.00202823	−	0.633984i
$233$	5.91079	−	3.62604i	0.387229	−	0.237550i	−0.315625	−	0.948884i	$-0.602214\pi$
$233$	5.91079	−	3.62604i	0.387229	−	0.237550i	0.702854	+	0.711334i	$0.251909\pi$
$234$	−26.9975	−	19.8268i	−1.76488	−	1.29612i
$235$	11.9314	+	3.61675i	0.778321	+	0.235931i
$236$	11.5450	+	10.1875i	0.751514	+	0.663148i
$237$	−3.69179	−	1.40947i	−0.239808	−	0.0915551i
$238$	−19.8653	−	6.86465i	−1.28767	−	0.444969i
$239$	−11.7675	−	14.5095i	−0.761175	−	0.938539i	0.238292	−	0.971194i	$-0.423413\pi$
$239$	−11.7675	−	14.5095i	−0.761175	−	0.938539i	−0.999467	+	0.0326542i	$0.989604\pi$
$240$	1.59160	+	1.70229i	0.102737	+	0.109882i
$241$	−0.935040	−	0.00598280i	−0.0602312	−	0.000385386i	−0.0237202	−	0.999719i	$-0.507551\pi$
$241$	−0.935040	−	0.00598280i	−0.0602312	−	0.000385386i	−0.0365110	+	0.999333i	$0.511624\pi$
$242$	5.16935	−	10.6718i	0.332298	−	0.686010i
$243$	−8.47231	+	5.57808i	−0.543499	+	0.357834i
$244$	−1.45964	−	6.50464i	−0.0934439	−	0.416417i
$245$	1.76807	−	0.239008i	0.112958	−	0.0152696i
$246$	1.01344	−	0.764418i	0.0646147	−	0.0487375i
$247$	2.95909	+	48.6218i	0.188282	+	3.09373i
$248$	−7.25053	−	2.87498i	−0.460409	−	0.182562i
$249$	1.95367	+	0.418750i	0.123809	+	0.0265372i
$250$	8.51799	−	15.2758i	0.538725	−	0.966127i
$251$	0.152768	−	0.509840i	0.00964261	−	0.0321808i	−0.952965	−	0.303080i	$-0.901985\pi$
$251$	0.152768	−	0.509840i	0.00964261	−	0.0321808i	0.962608	+	0.270899i	$0.0873211\pi$
$252$	−7.62830	−	4.41505i	−0.480537	−	0.278122i
$253$	−0.262689	−	6.31261i	−0.0165151	−	0.396870i
$254$	11.9006	−	0.838971i	0.746709	−	0.0526417i
$255$	−1.20690	+	1.48812i	−0.0755789	+	0.0931899i
$256$	−16.6249	+	10.3457i	−1.03906	+	0.646606i
$257$	8.94973	−	6.22645i	0.558269	−	0.388395i	−0.257933	−	0.966163i	$-0.583041\pi$
$257$	8.94973	−	6.22645i	0.558269	−	0.388395i	0.816201	+	0.577767i	$0.196076\pi$
$258$	−6.43177	−	1.33560i	−0.400424	−	0.0831510i
$259$	3.54604	−	19.2300i	0.220340	−	1.19489i
$260$	−7.18056	−	4.09480i	−0.445319	−	0.253949i
$261$	16.6720	+	0.961122i	1.03197	+	0.0594919i
$262$	22.1919	−	21.7004i	1.37102	−	1.34065i
$263$	2.07839	+	8.49533i	0.128159	+	0.523845i	0.999453	+	0.0330821i	$0.0105323\pi$
$263$	2.07839	+	8.49533i	0.128159	+	0.523845i	−0.871293	+	0.490763i	$0.836718\pi$
$264$	−1.36394	+	0.0349156i	−0.0839448	+	0.00214891i
$265$	0.818111	+	5.17606i	0.0502561	+	0.317963i
$266$	6.23272	+	36.4060i	0.382153	+	2.23220i
$267$	−3.31304	−	6.41571i	−0.202755	−	0.392635i
$268$	−12.3490	+	0.791211i	−0.754333	+	0.0483309i
$269$	−10.0155	−	11.2771i	−0.610653	−	0.687578i	0.358643	−	0.933475i	$-0.383239\pi$
$269$	−10.0155	−	11.2771i	−0.610653	−	0.687578i	−0.969296	+	0.245896i	$0.920918\pi$
$270$	−3.65192	+	3.05990i	−0.222249	+	0.186220i
$271$	−6.01783	+	0.115527i	−0.365557	+	0.00701776i	−0.201649	−	0.979458i	$-0.564630\pi$
$271$	−6.01783	+	0.115527i	−0.365557	+	0.00701776i	−0.163908	+	0.986476i	$0.552410\pi$
$272$	−13.1295	−	15.7719i	−0.796091	−	0.956314i
$273$	7.78658	+	1.77349i	0.471265	+	0.107337i
$274$	13.7021	−	2.66290i	0.827771	−	0.160872i
$275$	2.48777	+	7.12531i	0.150018	+	0.429673i
$276$	−1.14882	+	0.655132i	−0.0691511	+	0.0394343i
$277$	6.87975	−	3.41441i	0.413364	−	0.205152i	−0.225881	−	0.974155i	$-0.572526\pi$
$277$	6.87975	−	3.41441i	0.413364	−	0.205152i	0.639245	+	0.769003i	$0.279247\pi$
$278$	−4.81576	−	5.02033i	−0.288830	−	0.301099i
$279$	5.64610	−	12.2499i	0.338023	−	0.733383i
$280$	5.06896	+	2.20008i	0.302928	+	0.131480i
$281$	−9.56948	−	21.1166i	−0.570867	−	1.25971i	−0.943390	−	0.331685i	$-0.892383\pi$
$281$	−9.56948	−	21.1166i	−0.570867	−	1.25971i	0.372523	−	0.928023i	$-0.378493\pi$
$282$	6.55796	+	3.96553i	0.390521	+	0.236144i
$283$	16.9070	+	13.4450i	1.00501	+	0.799221i	0.979702	−	0.200459i	$-0.0642433\pi$
$283$	16.9070	+	13.4450i	1.00501	+	0.799221i	0.0253126	+	0.999680i	$0.491942\pi$
$284$	1.89187	−	0.0726647i	0.112262	−	0.00431186i
$285$	3.31321	+	0.600008i	0.196258	+	0.0355414i
$286$	22.9933	−	7.78125i	1.35962	−	0.460115i
$287$	2.58083	−	4.55952i	0.152341	−	0.269140i
$288$	−7.45992	−	13.5819i	−0.439580	−	0.800320i
$289$	−0.0860916	+	0.0944737i	−0.00506421	+	0.00555728i
$290$	11.8559	−	0.683479i	0.696202	−	0.0401353i
$291$	−3.01344	−	1.49556i	−0.176651	−	0.0876714i
$292$	2.90887	+	9.27460i	0.170229	+	0.542755i
$293$	18.5848	−	4.86313i	1.08573	−	0.284107i	0.333331	−	0.942810i	$-0.391828\pi$
$293$	18.5848	−	4.86313i	1.08573	−	0.284107i	0.752403	+	0.658703i	$0.228895\pi$
$294$	1.08944	+	0.126029i	0.0635372	+	0.00735013i
$295$	10.2646	−	13.1651i	0.597629	−	0.766502i
$296$	7.28363	−	8.20116i	0.423352	−	0.476683i
$297$	0.139778	−	4.85330i	0.00811073	−	0.281617i
$298$	−39.4848	−	2.78361i	−2.28729	−	0.161250i
$299$	−14.1671	+	15.1524i	−0.819307	+	0.876286i
$300$	1.08627	−	1.14702i	0.0627160	−	0.0662232i
$301$	−26.5460	+	5.51246i	−1.53008	+	0.317733i
$302$	0.703941	+	31.4288i	0.0405073	+	1.80852i
$303$	0.391104	+	0.848548i	0.0224683	+	0.0487478i
$304$	−13.1857	+	33.5666i	−0.756254	+	1.92518i
$305$	−6.94327	+	2.00806i	−0.397570	+	0.114981i
$306$	16.3555	−	12.1732i	0.934982	−	0.695896i
$307$	−3.94577	+	3.90808i	−0.225197	+	0.223046i	−0.807411	−	0.589990i	$-0.799132\pi$
$307$	−3.94577	+	3.90808i	−0.225197	+	0.223046i	0.582214	+	0.813036i	$0.302187\pi$
$308$	5.79226	−	2.69221i	0.330045	−	0.153403i
$309$	−1.67819	−	2.04238i	−0.0954690	−	0.116187i
$310$	2.98743	−	9.11493i	0.169675	−	0.517693i
$311$	−13.9560	+	9.31706i	−0.791375	+	0.528322i	−0.884060	−	0.467374i	$-0.845200\pi$
$311$	−13.9560	+	9.31706i	−0.791375	+	0.528322i	0.0926854	+	0.995695i	$0.470455\pi$
$312$	3.22281	+	3.11135i	0.182456	+	0.176145i
$313$	−1.21367	−	0.243938i	−0.0686009	−	0.0137882i	0.162630	−	0.986687i	$-0.448002\pi$
$313$	−1.21367	−	0.243938i	−0.0686009	−	0.0137882i	−0.231231	+	0.972899i	$0.574275\pi$
$314$	0.387586	−	0.174152i	0.0218728	−	0.00982795i
$315$	−4.27561	+	8.54623i	−0.240903	+	0.481525i
$316$	9.11143	+	4.96662i	0.512558	+	0.279394i
$317$	1.37586	−	0.693843i	0.0772759	−	0.0389701i	−0.411221	−	0.911536i	$-0.634898\pi$
$317$	1.37586	−	0.693843i	0.0772759	−	0.0389701i	0.488497	+	0.872565i	$0.337545\pi$
$318$	−0.298420	+	3.20732i	−0.0167346	+	0.179858i
$319$	−7.50227	+	9.49626i	−0.420046	+	0.531688i
$320$	0.286966	+	0.404147i	0.0160419	+	0.0225925i
$321$	1.03344	−	1.17873i	0.0576808	−	0.0657901i
$322$	−9.43151	+	12.5876i	−0.525598	+	0.701478i
$323$	−28.8232	−	6.95399i	−1.60377	−	0.386930i
$324$	7.23566	−	3.47637i	0.401981	−	0.193132i
$325$	10.9447	−	22.2309i	0.607101	−	1.23315i
$326$	0.763991	−	10.3642i	0.0423136	−	0.574022i
$327$	1.31775	+	6.89828i	0.0728716	+	0.381476i
$328$	2.56221	−	1.43948i	0.141474	−	0.0794822i
$329$	31.3454	+	4.23727i	1.72813	+	0.233608i
$330$	−0.144754	−	1.67165i	−0.00796844	−	0.0920215i
$331$	1.11620	+	0.467583i	0.0613518	+	0.0257007i	0.416837	−	0.908981i	$-0.363139\pi$
$331$	1.11620	+	0.467583i	0.0613518	+	0.0257007i	−0.355485	+	0.934682i	$0.615684\pi$
$332$	−4.93678	−	1.77699i	−0.270941	−	0.0975252i
$333$	13.4770	+	13.3483i	0.738536	+	0.731481i
$334$	17.0453	+	2.41533i	0.932676	+	0.132161i
$335$	1.66960	+	13.3121i	0.0912198	+	0.727318i
$336$	4.67427	+	3.62047i	0.255002	+	0.197513i
$337$	12.3933	−	19.7739i	0.675105	−	1.07715i	−0.316593	−	0.948561i	$-0.602539\pi$
$337$	12.3933	−	19.7739i	0.675105	−	1.07715i	0.991698	−	0.128591i	$-0.0410456\pi$
$338$	−50.8470	−	25.6420i	−2.76571	−	1.39474i
$339$	0.543920	+	0.787175i	0.0295417	+	0.0427535i
$340$	3.66425	−	3.44802i	0.198722	−	0.186995i
$341$	4.92359	+	8.44451i	0.266627	+	0.457296i
$342$	−32.5874	−	14.8936i	−1.76212	−	0.805355i
$343$	−15.2542	+	4.62398i	−0.823650	+	0.249672i
$344$	−14.3421	−	5.05902i	−0.773274	−	0.272764i
$345$	0.784657	+	1.20012i	0.0422445	+	0.0646125i
$346$	−3.72633	+	26.9168i	−0.200329	+	1.44705i
$347$	−2.29876	−	1.01526i	−0.123404	−	0.0545020i	0.341385	−	0.939924i	$-0.389104\pi$
$347$	−2.29876	−	1.01526i	−0.123404	−	0.0545020i	−0.464789	+	0.885422i	$0.653870\pi$
$348$	2.48670	+	0.483273i	0.133301	+	0.0259062i
$349$	4.38046	+	30.2172i	0.234481	+	1.61749i	0.687634	+	0.726057i	$0.258649\pi$
$349$	4.38046	+	30.2172i	0.234481	+	1.61749i	−0.453153	+	0.891433i	$0.649701\pi$
$350$	6.41985	−	17.6579i	0.343155	−	0.943855i
$351$	−11.6791	+	10.8499i	−0.623384	+	0.579123i
$352$	11.1633	+	1.21907i	0.595009	+	0.0649768i
$353$	15.0108	+	15.0589i	0.798943	+	0.801503i	0.983422	−	0.181334i	$-0.0580414\pi$
$353$	15.0108	+	15.0589i	0.798943	+	0.801503i	−0.184479	+	0.982836i	$0.559060\pi$
$354$	8.11262	−	6.28365i	0.431181	−	0.333972i
$355$	−0.203242	−	2.04262i	−0.0107870	−	0.108411i
$356$	6.36469	+	17.8613i	0.337328	+	0.946645i
$357$	−2.42151	+	4.21491i	−0.128160	+	0.223076i
$358$	−0.688656	+	0.708775i	−0.0363966	+	0.0374599i
$359$	1.61414	−	0.840086i	0.0851910	−	0.0443380i	−0.418542	−	0.908198i	$-0.637459\pi$
$359$	1.61414	−	0.840086i	0.0851910	−	0.0443380i	0.503733	+	0.863860i	$0.331960\pi$
$360$	−4.53285	+	2.86120i	−0.238902	+	0.150798i
$361$	8.68769	+	31.9455i	0.457247	+	1.68134i
$362$	−6.61369	+	0.937166i	−0.347608	+	0.0492564i
$363$	−2.19999	−	1.63743i	−0.115470	−	0.0859428i
$364$	−19.6394	−	7.35440i	−1.02938	−	0.385475i
$365$	9.84551	−	3.75887i	0.515337	−	0.196748i
$366$	−4.44060	+	0.142111i	−0.232114	+	0.00742826i
$367$	3.01836	+	26.8439i	0.157557	+	1.40124i	0.783511	+	0.621378i	$0.213427\pi$
$367$	3.01836	+	26.8439i	0.157557	+	1.40124i	−0.625954	+	0.779860i	$0.715290\pi$
$368$	−14.2397	+	5.75204i	−0.742296	+	0.299846i
$369$	2.24483	+	4.55972i	0.116861	+	0.237370i
$370$	10.6112	+	8.32810i	0.551650	+	0.432957i
$371$	4.14067	+	12.6336i	0.214973	+	0.655903i
$372$	1.09769	−	1.72674i	0.0569123	−	0.0895275i
$373$	−1.25876	+	30.2489i	−0.0651759	+	1.56623i	0.587900	+	0.808934i	$0.299955\pi$
$373$	−1.25876	+	30.2489i	−0.0651759	+	1.56623i	−0.653076	+	0.757293i	$0.726522\pi$
$374$	0.425365	+	14.7693i	0.0219951	+	0.763704i
$375$	−3.10057	−	2.59793i	−0.160113	−	0.134157i
$376$	13.8160	+	11.1320i	0.712504	+	0.574087i
$377$	39.4996	−	4.31347i	2.03433	−	0.222155i
$378$	−7.91025	+	9.13965i	−0.406859	+	0.470093i
$379$	−19.4070	−	6.01865i	−0.996869	−	0.309157i	−0.245757	−	0.969332i	$-0.579036\pi$
$379$	−19.4070	−	6.01865i	−0.996869	−	0.309157i	−0.751112	+	0.660174i	$0.770482\pi$
$380$	−8.41099	−	2.72695i	−0.431475	−	0.139890i
$381$	0.325840	−	2.73987i	0.0166933	−	0.140368i
$382$	10.9026	−	10.3916i	0.557826	−	0.531680i
$383$	2.51575	+	4.72252i	0.128549	+	0.241310i	0.938568	−	0.345093i	$-0.112153\pi$
$383$	2.51575	+	4.72252i	0.128549	+	0.241310i	−0.810020	+	0.586403i	$0.800544\pi$
$384$	1.70035	+	4.41127i	0.0867706	+	0.225112i
$385$	−3.29504	−	6.09115i	−0.167931	−	0.310434i
$386$	25.9379	−	13.7111i	1.32020	−	0.697876i
$387$	10.0841	−	24.2903i	0.512605	−	1.23474i
$388$	7.31584	+	4.95202i	0.371406	+	0.251401i
$389$	22.8444	+	8.38831i	1.15825	+	0.425304i	0.850404	−	0.526130i	$-0.176358\pi$
$389$	22.8444	+	8.38831i	1.15825	+	0.425304i	0.307851	+	0.951435i	$0.400390\pi$
$390$	−3.57847	+	4.18849i	−0.181203	+	0.212092i
$391$	−6.28990	−	10.9483i	−0.318094	−	0.553679i
$392$	2.46039	+	0.627025i	0.124269	+	0.0316696i
$393$	−3.96666	−	5.98303i	−0.200091	−	0.301804i
$394$	2.06605	−	33.9479i	0.104086	−	1.71027i
$395$	4.77484	−	10.1876i	0.240248	−	0.512595i
$396$	−1.00646	+	6.11378i	−0.0505765	+	0.307229i
$397$	0.141204	−	2.09863i	0.00708683	−	0.105327i	−0.992810	−	0.119702i	$-0.961806\pi$
$397$	0.141204	−	2.09863i	0.00708683	−	0.105327i	0.999897	+	0.0143751i	$0.00457588\pi$
$398$	−21.7853	−	27.2156i	−1.09200	−	1.36420i
$399$	8.54085	+	0.163962i	0.427577	+	0.00820838i
$400$	14.2851	−	11.5099i	0.714254	−	0.575497i
$401$	9.73012	−	9.76130i	0.485899	−	0.487456i	−0.422029	−	0.906582i	$-0.638682\pi$
$401$	9.73012	−	9.76130i	0.485899	−	0.487456i	0.907928	+	0.419126i	$0.137664\pi$
$402$	−1.02629	+	8.18283i	−0.0511865	+	0.408122i
$403$	8.42214	−	30.9690i	0.419537	−	1.54268i
$404$	−0.719277	−	2.34579i	−0.0357854	−	0.116707i
$405$	−4.23873	−	7.60157i	−0.210624	−	0.377725i
$406$	29.4185	−	6.50273i	1.46002	−	0.322725i
$407$	−13.5264	+	2.44958i	−0.670481	+	0.121421i
$408$	−2.38571	+	1.32031i	−0.118110	+	0.0653653i
$409$	−17.3304	−	19.2638i	−0.856931	−	0.952535i	0.142374	−	0.989813i	$-0.454526\pi$
$409$	−17.3304	−	19.2638i	−0.856931	−	0.952535i	−0.999305	+	0.0372778i	$0.988131\pi$
$410$	1.95840	+	3.03761i	0.0967186	+	0.150017i
$411$	−0.0103278	−	3.22826i	−0.000509433	−	0.159238i
$412$	3.64874	+	5.90532i	0.179760	+	0.290934i
$413$	20.3893	−	37.1217i	1.00329	−	1.82664i
$414$	−4.93723	−	14.4370i	−0.242651	−	0.709541i
$415$	−1.59793	+	5.45968i	−0.0784395	+	0.268005i
$416$	−22.8560	−	28.9308i	−1.12061	−	1.41845i
$417$	−1.34945	+	0.876139i	−0.0660829	+	0.0429047i
$418$	22.3893	−	13.1503i	1.09510	−	0.643201i
$419$	15.9171	−	13.5110i	0.777601	−	0.660057i	−0.167853	−	0.985812i	$-0.553684\pi$
$419$	15.9171	−	13.5110i	0.777601	−	0.660057i	0.945454	+	0.325755i	$0.105618\pi$
$420$	−0.816402	+	1.19783i	−0.0398364	+	0.0584483i
$421$	12.3108	−	1.26472i	0.599989	−	0.0616386i	0.202558	−	0.979270i	$-0.435075\pi$
$421$	12.3108	−	1.26472i	0.599989	−	0.0616386i	0.397432	+	0.917632i	$0.369902\pi$
$422$	3.03749	+	0.490061i	0.147863	+	0.0238558i
$423$	−20.5214	+	22.8109i	−0.997783	+	1.10910i
$424$	−1.67939	+	7.26597i	−0.0815582	+	0.352867i
$425$	10.9842	+	10.3361i	0.532814	+	0.501373i
$426$	0.189009	−	1.24754i	0.00915750	−	0.0604436i
$427$	−16.5789	+	7.83517i	−0.802311	+	0.379170i
$428$	−3.10400	+	2.70389i	−0.150038	+	0.130697i
$429$	−0.769869	−	5.56107i	−0.0371696	−	0.268491i
$430$	5.13859	−	17.9831i	0.247805	−	0.867222i
$431$	5.15639	+	26.0865i	0.248375	+	1.25654i	0.877629	+	0.479341i	$0.159124\pi$
$431$	5.15639	+	26.0865i	0.248375	+	1.25654i	−0.629254	+	0.777200i	$0.716640\pi$
$432$	−11.2267	+	3.63983i	−0.540144	+	0.175122i
$433$	22.8141	−	0.291961i	1.09638	−	0.0140308i	0.537486	−	0.843273i	$-0.319374\pi$
$433$	22.8141	−	0.291961i	1.09638	−	0.0140308i	0.558890	+	0.829242i	$0.311227\pi$
$434$	3.79917	−	24.0368i	0.182366	−	1.15380i
$435$	0.359224	−	2.72297i	0.0172235	−	0.130556i
$436$	−1.00252	−	18.4152i	−0.0480118	−	0.881926i
$437$	−11.5423	+	18.9508i	−0.552142	+	0.906538i
$438$	6.43510	−	0.744427i	0.307481	−	0.0355701i
$439$	−17.4894	+	6.80572i	−0.834723	+	0.324819i	−0.741606	−	0.670836i	$-0.765936\pi$
$439$	−17.4894	+	6.80572i	−0.834723	+	0.324819i	−0.0931169	+	0.995655i	$0.529683\pi$
$440$	0.186342	−	3.88015i	0.00888352	−	0.184979i
$441$	−1.31404	+	4.18965i	−0.0625731	+	0.199507i
$442$	33.5820	−	35.0086i	1.59733	−	1.66519i
$443$	−6.10144	−	15.5323i	−0.289888	−	0.737961i	−0.999445	−	0.0333133i	$-0.989394\pi$
$443$	−6.10144	−	15.5323i	−0.289888	−	0.737961i	0.709557	−	0.704648i	$-0.248895\pi$
$444$	1.75469	+	2.28046i	0.0832740	+	0.108226i
$445$	18.9105	−	8.06434i	0.896444	−	0.382287i
$446$	−6.48176	−	9.25341i	−0.306920	−	0.438162i
$447$	−2.34581	+	8.84898i	−0.110953	+	0.418543i
$448$	0.882058	+	0.896282i	0.0416733	+	0.0423453i
$449$	4.31318	−	0.667589i	0.203551	−	0.0315055i	−0.0503687	−	0.998731i	$-0.516040\pi$
$449$	4.31318	−	0.667589i	0.203551	−	0.0315055i	0.253920	+	0.967225i	$0.418280\pi$
$450$	10.6468	+	14.7930i	0.501897	+	0.697349i
$451$	−3.63983	−	0.563369i	−0.171393	−	0.0265280i
$452$	−1.13854	−	2.23983i	−0.0535526	−	0.105353i
$453$	7.17023	+	1.20395i	0.336887	+	0.0565664i
$454$	−16.8696	+	3.61584i	−0.791729	+	0.169700i
$455$	−6.66552	+	21.7384i	−0.312485	+	1.01911i
$456$	4.05203	+	2.55770i	0.189754	+	0.119775i
$457$	−0.711794	−	0.0593430i	−0.0332963	−	0.00277595i	0.0664230	−	0.997792i	$-0.478841\pi$
$457$	−0.711794	−	0.0593430i	−0.0332963	−	0.00277595i	−0.0997193	+	0.995016i	$0.531794\pi$
$458$	−13.9859	−	8.33539i	−0.653519	−	0.389487i
$459$	−4.23003	−	8.73263i	−0.197441	−	0.407604i
$460$	−1.61975	−	3.39915i	−0.0755214	−	0.158486i
$461$	6.59705	−	16.4833i	0.307255	−	0.767702i	−0.691708	−	0.722177i	$-0.743142\pi$
$461$	6.59705	−	16.4833i	0.307255	−	0.767702i	0.998963	−	0.0455246i	$-0.0144959\pi$
$462$	−1.03806	−	4.12839i	−0.0482948	−	0.192070i
$463$	−2.93639	+	2.62472i	−0.136466	+	0.121981i	−0.731868	−	0.681447i	$-0.761351\pi$
$463$	−2.93639	+	2.62472i	−0.136466	+	0.121981i	0.595402	+	0.803428i	$0.296993\pi$
$464$	27.8649	+	9.42987i	1.29359	+	0.437770i
$465$	−1.94100	−	1.07420i	−0.0900117	−	0.0498149i
$466$	2.73294	+	11.8243i	0.126601	+	0.547748i
$467$	−11.2553	+	19.3042i	−0.520834	+	0.893290i	0.479046	+	0.877790i	$0.340983\pi$
$467$	−11.2553	+	19.3042i	−0.520834	+	0.893290i	−0.999880	+	0.0154999i	$0.995066\pi$
$468$	16.6247	−	11.7246i	0.768475	−	0.541969i
$469$	9.56104	+	32.6673i	0.441488	+	1.50844i
$470$	−12.6325	+	17.7909i	−0.582695	+	0.820635i
$471$	−0.0227427	−	0.0956055i	−0.00104793	−	0.00440527i
$472$	20.5615	−	11.9004i	0.946420	−	0.547762i
$473$	10.2251	+	16.0848i	0.470150	+	0.739582i
$474$	4.39063	−	5.34346i	0.201668	−	0.245433i
$475$	6.62778	−	25.6635i	0.304104	−	1.17752i
$476$	7.78429	−	10.1167i	0.356792	−	0.463700i
$477$	−12.3890	−	3.58300i	−0.567251	−	0.164054i
$478$	30.6184	−	11.4657i	1.40045	−	0.524431i
$479$	−2.30671	+	2.03547i	−0.105396	+	0.0930031i	−0.712710	−	0.701459i	$-0.752532\pi$
$479$	−2.30671	+	2.03547i	−0.105396	+	0.0930031i	0.607314	+	0.794462i	$0.292247\pi$
$480$	−2.31794	+	1.05938i	−0.105799	+	0.0483539i
$481$	36.8831	+	26.0119i	1.68172	+	1.18604i
$482$	0.529534	−	1.54842i	0.0241196	−	0.0705286i
$483$	2.45024	+	2.68880i	0.111490	+	0.122345i
$484$	5.14909	+	5.03506i	0.234050	+	0.228866i
$485$	4.87730	−	8.24345i	0.221467	−	0.374316i
$486$	−4.54900	−	17.1600i	−0.206347	−	0.778392i
$487$	19.5200	−	23.1459i	0.884537	−	1.04884i	−0.113930	−	0.993489i	$-0.536344\pi$
$487$	19.5200	−	23.1459i	0.884537	−	1.04884i	0.998467	−	0.0553499i	$-0.0176274\pi$
$488$	−10.2321	−	1.05117i	−0.463184	−	0.0475842i
$489$	−2.32129	−	0.623316i	−0.104973	−	0.0281873i
$490$	−0.585878	+	3.06702i	−0.0264673	+	0.138554i
$491$	−0.357943	−	1.06896i	−0.0161537	−	0.0482414i	0.939867	−	0.341542i	$-0.110949\pi$
$491$	−0.357943	−	1.06896i	−0.0161537	−	0.0482414i	−0.956020	+	0.293300i	$0.905246\pi$
$492$	0.244798	+	0.731062i	0.0110363	+	0.0329588i
$493$	−4.53806	+	23.7563i	−0.204384	+	1.06993i
$494$	−82.3346	−	22.1085i	−3.70441	−	0.994710i
$495$	6.68270	+	0.686532i	0.300365	+	0.0308573i
$496$	15.3182	−	18.1636i	0.687809	−	0.815569i
$497$	−1.33445	−	5.03389i	−0.0598584	−	0.225801i
$498$	−1.78060	+	3.00951i	−0.0797904	+	0.134859i
$499$	−25.3097	−	24.7492i	−1.13302	−	1.10792i	−0.993041	−	0.117770i	$-0.962425\pi$
$499$	−25.3097	−	24.7492i	−1.13302	−	1.10792i	−0.139977	−	0.990155i	$-0.544703\pi$
$500$	7.15480	+	7.85141i	0.319972	+	0.351126i
$501$	1.28838	−	3.76737i	0.0575605	−	0.168314i
$502$	0.761210	+	0.536845i	0.0339745	+	0.0239606i
$503$	21.5915	−	9.86811i	0.962719	−	0.439997i	0.128670	−	0.991688i	$-0.458929\pi$
$503$	21.5915	−	9.86811i	0.962719	−	0.439997i	0.834049	+	0.551690i	$0.186017\pi$
$504$	−10.1970	+	8.99796i	−0.454209	+	0.400801i
$505$	−2.49127	+	0.932911i	−0.110860	+	0.0415140i
$506$	10.6221	+	3.07200i	0.472208	+	0.136567i
$507$	−8.03163	+	10.4382i	−0.356697	+	0.463576i
$508$	−1.81178	+	7.01541i	−0.0803848	+	0.311259i
$509$	13.3369	−	16.2312i	0.591148	−	0.719436i	−0.388209	−	0.921571i	$-0.626906\pi$
$509$	13.3369	−	16.2312i	0.591148	−	0.719436i	0.979358	+	0.202136i	$0.0647882\pi$
$510$	−1.79893	−	2.82986i	−0.0796582	−	0.125308i
$511$	23.1405	−	13.3931i	1.02368	−	0.592476i
$512$	−2.52466	−	10.6131i	−0.111575	−	0.469039i
$513$	−9.87219	+	13.9035i	−0.435868	+	0.613852i
$514$	5.35971	+	18.3126i	0.236407	+	0.807733i
$515$	6.15050	−	4.33765i	0.271023	−	0.191140i
$516$	2.00951	−	3.44654i	0.0884637	−	0.151725i
$517$	−5.00741	−	21.6649i	−0.220226	−	0.952821i
$518$	29.9425	+	16.5710i	1.31560	+	0.728087i
$519$	5.95299	+	2.01457i	0.261307	+	0.0884300i
$520$	−9.50906	+	8.49977i	−0.417000	+	0.372739i
$521$	−6.80505	−	27.0639i	−0.298135	−	1.18569i	−0.916576	−	0.399861i	$-0.869058\pi$
$521$	−6.80505	−	27.0639i	−0.298135	−	1.18569i	0.618441	−	0.785831i	$-0.287765\pi$
$522$	−10.8597	+	27.1339i	−0.475316	+	1.18762i
$523$	4.97101	+	10.4320i	0.217367	+	0.456157i	0.982142	−	0.188140i	$-0.0602458\pi$
$523$	4.97101	+	10.4320i	0.217367	+	0.456157i	−0.764775	+	0.644297i	$0.777150\pi$
$524$	8.21783	+	16.9652i	0.358998	+	0.741129i
$525$	−3.73276	−	2.22467i	−0.162911	−	0.0970925i
$526$	−15.2534	−	1.27169i	−0.665080	−	0.0554483i
$527$	16.5195	+	10.4273i	0.719599	+	0.454221i
$528$	1.21846	−	3.97378i	0.0530266	−	0.172936i
$529$	13.2499	−	2.83999i	0.576083	−	0.123478i
$530$	−9.04456	−	1.51866i	−0.392871	−	0.0659665i
$531$	18.6167	+	36.6242i	0.807896	+	1.58935i
$532$	−22.1684	−	3.43121i	−0.961123	−	0.148762i
$533$	7.06403	+	9.81495i	0.305977	+	0.425133i
$534$	12.4883	−	1.93292i	0.540420	−	0.0836456i
$535$	3.13062	+	3.18110i	0.135349	+	0.137531i
$536$	−4.89243	+	18.4555i	−0.211321	+	0.797155i
$537$	0.131128	+	0.187200i	0.00565860	+	0.00807827i
$538$	24.2806	−	10.3544i	1.04681	−	0.446410i
$539$	−1.94048	−	2.52191i	−0.0835823	−	0.108626i
$540$	−1.05797	−	2.69325i	−0.0455277	−	0.115899i
$541$	−16.3956	+	17.0921i	−0.704904	+	0.734847i	−0.973571	−	0.228386i	$-0.926655\pi$
$541$	−16.3956	+	17.0921i	−0.704904	+	0.734847i	0.268667	+	0.963233i	$0.413417\pi$
$542$	3.15241	−	10.0511i	0.135408	−	0.431731i
$543$	−0.0741068	+	1.54310i	−0.00318023	+	0.0662209i
$544$	20.9145	−	8.13857i	0.896704	−	0.348938i
$545$	−19.8631	+	2.29781i	−0.850842	+	0.0984274i
$546$	−7.27023	+	11.9367i	−0.311137	+	0.510843i
$547$	−0.972140	−	17.8572i	−0.0415657	−	0.763518i	−0.943445	−	0.331530i	$-0.892435\pi$
$547$	−0.972140	−	17.8572i	−0.0415657	−	0.763518i	0.901879	−	0.431988i	$-0.142188\pi$
$548$	−1.10877	+	8.40463i	−0.0473643	+	0.359028i
$549$	2.77703	−	17.5699i	0.118521	−	0.749864i
$550$	−13.2073	+	0.169019i	−0.563160	+	0.00720699i
$551$	40.4311	−	13.1083i	1.72242	−	0.558430i
$552$	0.395690	+	2.00181i	0.0168417	+	0.0852029i
$553$	7.84251	−	27.4458i	0.333497	−	1.16711i
$554$	1.84327	+	13.3147i	0.0783131	+	0.565687i
$555$	2.35237	−	2.04915i	0.0998527	−	0.0869815i
$556$	3.81993	−	1.80529i	0.162001	−	0.0765614i
$557$	−5.64636	+	37.2685i	−0.239244	+	1.57912i	0.475489	+	0.879722i	$0.342271\pi$
$557$	−5.64636	+	37.2685i	−0.239244	+	1.57912i	−0.714733	+	0.699397i	$0.753452\pi$
$558$	17.1918	+	16.1773i	0.727785	+	0.684839i
$559$	14.0921	−	60.9704i	0.596033	−	2.57877i
$560$	−11.2585	+	12.5145i	−0.475757	+	0.528836i
$561$	3.37361	+	0.544290i	0.142434	+	0.0229799i
$562$	40.3618	−	4.14648i	1.70256	−	0.174909i
$563$	22.4150	−	32.8875i	0.944679	−	1.38604i	0.0223024	−	0.999751i	$-0.492900\pi$
$563$	22.4150	−	32.8875i	0.944679	−	1.38604i	0.922377	−	0.386292i	$-0.126244\pi$
$564$	−3.54843	+	3.01205i	−0.149416	+	0.126830i
$565$	−2.34899	+	1.37967i	−0.0988226	+	0.0580431i
$566$	−31.7079	+	20.5865i	−1.33278	+	0.865316i
$567$	−13.6882	−	17.3263i	−0.574851	−	0.727638i
$568$	0.820555	−	2.80360i	0.0344297	−	0.117636i
$569$	3.64532	+	10.6593i	0.152820	+	0.446863i	0.995851	−	0.0910022i	$-0.0290070\pi$
$569$	3.64532	+	10.6593i	0.152820	+	0.446863i	−0.843031	+	0.537865i	$0.819231\pi$
$570$	−2.83690	+	5.16501i	−0.118825	+	0.216338i
$571$	18.3834	+	29.7527i	0.769320	+	1.24511i	0.964432	+	0.264330i	$0.0851508\pi$
$571$	18.3834	+	29.7527i	0.769320	+	1.24511i	−0.195112	+	0.980781i	$0.562507\pi$
$572$	0.0471642	+	14.7426i	0.00197204	+	0.616417i
$573$	−1.88754	−	2.92770i	−0.0788530	−	0.122306i
$574$	6.13256	+	6.81675i	0.255968	+	0.284526i
$575$	9.87579	−	5.46552i	0.411849	−	0.227928i
$576$	−1.20033	+	0.217375i	−0.0500138	+	0.00905729i
$577$	−0.573920	+	0.126861i	−0.0238926	+	0.00528127i	−0.227762	−	0.973717i	$-0.573141\pi$
$577$	−0.573920	+	0.126861i	−0.0238926	+	0.00528127i	0.203870	+	0.978998i	$0.434648\pi$
$578$	−0.108942	−	0.195373i	−0.00453140	−	0.00812643i
$579$	−1.98917	−	6.48731i	−0.0826672	−	0.269604i
$580$	−1.89271	+	6.95969i	−0.0785906	+	0.288985i
$581$	−1.79604	+	14.3202i	−0.0745122	+	0.594104i
$582$	4.15654	−	4.16985i	0.172294	−	0.172846i
$583$	7.27775	−	5.86391i	0.301414	−	0.242858i
$584$	14.9948	+	0.287862i	0.620491	+	0.0119118i
$585$	−13.7834	−	17.2192i	−0.569875	−	0.711927i
$586$	−2.25703	+	33.5448i	−0.0932369	+	1.38572i
$587$	−2.92843	+	17.7889i	−0.120869	+	0.734225i	0.855449	+	0.517887i	$0.173281\pi$
$587$	−2.92843	+	17.7889i	−0.120869	+	0.734225i	−0.976318	+	0.216339i	$0.930589\pi$
$588$	−0.282672	+	0.603110i	−0.0116572	+	0.0248718i
$589$	2.08544	−	34.2666i	0.0859291	−	1.41193i
$590$	16.1440	+	24.3505i	0.664640	+	1.00250i
$591$	−7.62231	−	1.94253i	−0.313540	−	0.0799049i
$592$	16.6453	+	28.9730i	0.684116	+	1.19078i
$593$	−16.5912	+	19.4195i	−0.681317	+	0.797461i	−0.988017	−	0.154345i	$-0.950673\pi$
$593$	−16.5912	+	19.4195i	−0.681317	+	0.797461i	0.306700	+	0.951806i	$0.400775\pi$
$594$	7.97662	+	2.92897i	0.327284	+	0.120177i
$595$	−11.4612	−	7.75794i	−0.469862	−	0.318045i
$596$	9.21750	−	22.2028i	0.377563	−	0.909461i
$597$	−7.12796	+	3.76793i	−0.291728	+	0.154211i
$598$	−17.2734	−	31.9313i	−0.706362	−	1.30577i
$599$	−4.85760	−	12.6022i	−0.198476	−	0.514913i	0.797623	−	0.603156i	$-0.206091\pi$
$599$	−4.85760	−	12.6022i	−0.198476	−	0.514913i	−0.996099	+	0.0882435i	$0.971875\pi$
$600$	−1.14602	−	2.15128i	−0.0467860	−	0.0878258i
$601$	16.4739	−	15.7018i	0.671985	−	0.640488i	−0.275120	−	0.961410i	$-0.588718\pi$
$601$	16.4739	−	15.7018i	0.671985	−	0.640488i	0.947106	+	0.320922i	$0.103993\pi$
$602$	5.60349	−	47.1176i	0.228381	−	1.92037i
$603$	−31.4089	−	10.1831i	−1.27907	−	0.414690i
$604$	−18.2358	−	5.65543i	−0.742004	−	0.230116i
$605$	5.10987	−	5.90404i	0.207746	−	0.240033i
$606$	−1.62555	+	0.177515i	−0.0660333	+	0.00721104i
$607$	−16.2593	−	13.1006i	−0.659943	−	0.531736i	0.238325	−	0.971186i	$-0.423402\pi$
$607$	−16.2593	−	13.1006i	−0.659943	−	0.531736i	−0.898267	+	0.439449i	$0.855174\pi$
$608$	−30.2299	−	25.3293i	−1.22598	−	1.02724i
$609$	−0.200602	−	6.96521i	−0.00812880	−	0.282244i
$610$	0.525933	−	12.6386i	0.0212944	−	0.511721i
$611$	−39.1661	+	61.6112i	−1.58449	+	2.49252i
$612$	3.85658	+	11.7668i	0.155893	+	0.475643i
$613$	−20.9676	−	16.4562i	−0.846872	−	0.664660i	0.0968863	−	0.995295i	$-0.469112\pi$
$613$	−20.9676	−	16.4562i	−0.846872	−	0.664660i	−0.943759	+	0.330635i	$0.892737\pi$
$614$	−4.29297	−	8.71993i	−0.173250	−	0.351908i
$615$	0.775041	−	0.313073i	0.0312527	−	0.0126243i
$616$	−1.10121	−	9.79367i	−0.0443692	−	0.394598i
$617$	6.08651	−	0.194785i	0.245034	−	0.00784174i	0.0907718	−	0.995872i	$-0.471067\pi$
$617$	6.08651	−	0.194785i	0.245034	−	0.00784174i	0.154262	+	0.988030i	$0.450700\pi$
$618$	4.32201	−	1.65008i	0.173857	−	0.0663760i
$619$	0.224040	+	0.0838966i	0.00900491	+	0.00337209i	0.355189	−	0.934795i	$-0.384417\pi$
$619$	0.224040	+	0.0838966i	0.00900491	+	0.00337209i	−0.346184	+	0.938167i	$0.612523\pi$
$620$	4.67324	+	3.47824i	0.187682	+	0.139689i
$621$	−7.18967	+	1.01878i	−0.288511	+	0.0408823i
$622$	−7.70669	−	28.3383i	−0.309010	−	1.13626i
$623$	44.1052	−	27.8398i	1.76704	−	1.11538i
$624$	−12.1051	+	6.30014i	−0.484591	+	0.252207i
$625$	−4.76831	+	4.90762i	−0.190732	+	0.196305i
$626$	1.07927	−	1.87859i	0.0431363	−	0.0750837i
$627$	−2.01576	−	5.65685i	−0.0805018	−	0.225913i
$628$	0.0255516	+	0.256798i	0.00101962	+	0.0102473i
$629$	−21.7189	+	16.8224i	−0.865989	+	0.670754i
$630$	−11.8069	−	11.8447i	−0.470399	−	0.471906i
$631$	−47.2837	−	5.16352i	−1.88233	−	0.205557i	−0.906218	−	0.422811i	$-0.861044\pi$
$631$	−47.2837	−	5.16352i	−1.88233	−	0.205557i	−0.976115	+	0.217254i	$0.930290\pi$
$632$	11.7306	−	10.8977i	0.466618	−	0.433488i
$633$	0.243140	−	0.668762i	0.00966395	−	0.0265809i
$634$	0.386896	+	2.66888i	0.0153656	+	0.105995i
$635$	7.71150	+	1.49868i	0.306021	+	0.0594733i
$636$	−1.78957	−	0.790374i	−0.0709611	−	0.0313404i
$637$	−1.43267	+	10.3488i	−0.0567646	+	0.410033i
$638$	−11.5905	−	17.7275i	−0.458871	−	0.701838i
$639$	4.76410	+	1.68048i	0.188465	+	0.0664790i
$640$	−12.8815	+	3.90474i	−0.509184	+	0.154348i
$641$	28.9169	+	13.2161i	1.14215	+	0.522004i	0.894599	−	0.446870i	$-0.147462\pi$
$641$	28.9169	+	13.2161i	1.14215	+	0.522004i	0.247552	+	0.968875i	$0.420374\pi$
$642$	1.38187	+	2.37006i	0.0545380	+	0.0935389i
$643$	5.92848	−	5.57864i	0.233796	−	0.220000i	−0.559509	−	0.828824i	$-0.689010\pi$
$643$	5.92848	−	5.57864i	0.233796	−	0.220000i	0.793305	+	0.608824i	$0.208358\pi$
$644$	−5.43046	−	7.85911i	−0.213990	−	0.309692i
$645$	−3.86224	−	1.94772i	−0.152075	−	0.0766913i
$646$	27.5577	−	43.9692i	1.08424	−	1.72995i
$647$	−27.7483	−	21.4925i	−1.09090	−	0.844959i	−0.102183	−	0.994766i	$-0.532583\pi$
$647$	−27.7483	−	21.4925i	−1.09090	−	0.844959i	−0.988715	+	0.149807i	$0.952135\pi$
$648$	−1.54137	−	12.2897i	−0.0605506	−	0.482785i
$649$	−29.4791	−	4.17722i	−1.15716	−	0.163970i
$650$	30.8113	+	30.5170i	1.20852	+	1.19698i
$651$	−5.29558	−	1.90614i	−0.207550	−	0.0747076i
$652$	5.82150	+	2.43867i	0.227988	+	0.0955055i
$653$	−2.98912	−	34.5191i	−0.116973	−	1.35084i	−0.790858	−	0.612000i	$-0.790365\pi$
$653$	−2.98912	−	34.5191i	−0.116973	−	1.35084i	0.673885	−	0.738837i	$-0.264624\pi$
$654$	−12.1803	−	1.64653i	−0.476288	−	0.0643846i
$655$	17.8187	−	10.0108i	0.696235	−	0.391155i
$656$	1.67984	+	8.79380i	0.0655867	+	0.343340i
$657$	−1.90669	+	25.8659i	−0.0743869	+	1.00913i
$658$	−24.4507	+	49.6646i	−0.953189	+	1.93613i
$659$	−13.1961	+	6.34004i	−0.514046	+	0.246973i	−0.672104	−	0.740457i	$-0.734609\pi$
$659$	−13.1961	+	6.34004i	−0.514046	+	0.246973i	0.158058	+	0.987430i	$0.449477\pi$
$660$	0.990631	+	0.239003i	0.0385603	+	0.00930318i
$661$	−10.2408	+	13.6677i	−0.398322	+	0.531612i	−0.954009	−	0.299780i	$-0.903087\pi$
$661$	−10.2408	+	13.6677i	−0.398322	+	0.531612i	0.555686	+	0.831392i	$0.312456\pi$
$662$	−1.39625	+	1.59255i	−0.0542669	+	0.0618962i
$663$	−6.49561	−	9.14805i	−0.252268	−	0.355281i
$664$	−5.01857	+	6.35243i	−0.194758	+	0.246522i
$665$	−2.25322	+	24.2169i	−0.0873763	+	0.939093i
$666$	−29.6413	+	14.9481i	−1.14858	+	0.579226i
$667$	15.8921	+	8.66273i	0.615343	+	0.335422i
$668$	−4.67808	+	9.35071i	−0.181000	+	0.361790i
$669$	−2.38338	+	1.07091i	−0.0921468	+	0.0414037i
$670$	−23.0199	−	4.62681i	−0.889336	−	0.178749i
$671$	9.27421	+	8.95345i	0.358027	+	0.345644i
$672$	−5.37751	+	3.59003i	−0.207442	+	0.138488i
$673$	−11.7295	+	35.7877i	−0.452138	+	1.37951i	0.427562	+	0.903986i	$0.359373\pi$
$673$	−11.7295	+	35.7877i	−0.452138	+	1.37951i	−0.879700	+	0.475529i	$0.842257\pi$
$674$	25.9288	+	31.5557i	0.998739	+	1.21548i
$675$	7.86593	−	3.65603i	0.302760	−	0.140721i
$676$	24.5729	−	24.3382i	0.945113	−	0.936085i
$677$	15.7108	−	11.6934i	0.603815	−	0.449412i	−0.251258	−	0.967920i	$-0.580844\pi$
$677$	15.7108	−	11.6934i	0.603815	−	0.449412i	0.855073	+	0.518508i	$0.173512\pi$
$678$	−1.60861	+	0.465226i	−0.0617784	+	0.0178669i
$679$	8.88476	−	22.6177i	0.340966	−	0.867989i
$680$	−3.24962	−	7.05044i	−0.124617	−	0.270372i
$681$	0.0893496	+	3.98918i	0.00342388	+	0.152866i
$682$	−16.7501	+	3.47829i	−0.641396	+	0.133191i
$683$	10.2568	−	10.8304i	0.392465	−	0.414412i	−0.499645	−	0.866231i	$-0.666536\pi$
$683$	10.2568	−	10.8304i	0.392465	−	0.414412i	0.892110	+	0.451818i	$0.149224\pi$
$684$	14.8616	−	15.8952i	0.568248	−	0.607766i
$685$	9.16862	+	0.646373i	0.350315	+	0.0246966i
$686$	0.803094	−	27.8847i	0.0306623	−	1.06464i
$687$	−2.50048	+	2.81547i	−0.0953991	+	0.107417i
$688$	28.4868	−	36.5363i	1.08605	−	1.39293i
$689$	−30.4825	−	3.52628i	−1.16129	−	0.134341i
$690$	−2.42770	+	0.635263i	−0.0924210	+	0.0241840i
$691$	−11.1383	−	35.5131i	−0.423720	−	1.35098i	−0.885769	−	0.464127i	$-0.846368\pi$
$691$	−11.1383	−	35.5131i	−0.423720	−	1.35098i	0.462049	−	0.886854i	$-0.347114\pi$
$692$	−14.7829	−	7.33675i	−0.561963	−	0.278901i
$693$	17.0152	−	0.980906i	0.646352	−	0.0372615i
$694$	2.96230	−	3.25072i	0.112447	−	0.123396i
$695$	−2.20530	−	4.01508i	−0.0836518	−	0.152301i
$696$	1.92537	−	3.40153i	0.0729811	−	0.128935i
$697$	−6.97227	+	2.35951i	−0.264094	+	0.0893729i
$698$	−52.5812	−	9.52222i	−1.99023	−	0.360421i
$699$	2.80472	−	0.107726i	0.106084	−	0.00407459i
$700$	8.93128	+	7.10245i	0.337571	+	0.268447i
$701$	39.4356	+	23.8463i	1.48946	+	0.900661i	0.999583	+	0.0288707i	$0.00919112\pi$
$701$	39.4356	+	23.8463i	1.48946	+	0.900661i	0.489879	+	0.871791i	$0.337041\pi$
$702$	−11.5158	−	25.4113i	−0.434635	−	0.959089i
$703$	44.2861	+	19.2215i	1.67028	+	0.724953i
$704$	0.370042	−	0.802852i	0.0139465	−	0.0302586i
$705$	3.49338	+	3.64178i	0.131568	+	0.137157i
$706$	−33.3325	+	16.5428i	−1.25448	+	0.622598i
$707$	−5.86274	+	3.34330i	−0.220491	+	0.125738i
$708$	2.05433	+	5.88387i	0.0772064	+	0.221129i
$709$	12.4256	−	2.41484i	0.466654	−	0.0906912i	0.0480206	−	0.998846i	$-0.484709\pi$
$709$	12.4256	−	2.41484i	0.466654	−	0.0906912i	0.418634	+	0.908155i	$0.362509\pi$
$710$	3.50277	+	0.797799i	0.131456	+	0.0299409i
$711$	17.7154	+	21.2808i	0.664378	+	0.798091i
$712$	29.2511	−	0.561546i	1.09623	−	0.0210448i
$713$	11.2057	−	9.38916i	0.419658	−	0.351627i
$714$	−5.64920	−	6.36085i	−0.211416	−	0.238049i
$715$	15.9515	−	1.02203i	0.596552	−	0.0382217i
$716$	−0.275386	−	0.533285i	−0.0102916	−	0.0199298i
$717$	−1.27598	−	7.45315i	−0.0476524	−	0.278343i
$718$	0.497180	+	3.14558i	0.0185546	+	0.117392i
$719$	−41.4841	+	1.06195i	−1.54710	+	0.0396041i	−0.789758	−	0.613418i	$-0.789794\pi$
$719$	−41.4841	+	1.06195i	−1.54710	+	0.0396041i	−0.757339	+	0.653022i	$0.773501\pi$
$720$	−3.88056	−	15.8616i	−0.144620	−	0.591126i
$721$	13.6520	−	13.3496i	0.508426	−	0.497165i
$722$	−57.8429	−	3.33458i	−2.15269	−	0.124100i
$723$	−0.328776	−	0.187489i	−0.0122273	−	0.00697277i
$724$	0.735688	−	3.98959i	0.0273416	−	0.148272i
$725$	−21.1691	−	4.39591i	−0.786200	−	0.163260i
$726$	3.93994	−	2.74107i	0.146225	−	0.101731i
$727$	−31.5785	+	19.6514i	−1.17118	+	0.728828i	−0.968157	−	0.250345i	$-0.919456\pi$
$727$	−31.5785	+	19.6514i	−1.17118	+	0.728828i	−0.203024	+	0.979174i	$0.565077\pi$
$728$	−20.3821	+	25.1314i	−0.755409	+	0.931430i
$729$	18.5053	−	1.30459i	0.685381	−	0.0483182i
$730$	0.766847	+	18.4279i	0.0283823	+	0.682048i
$731$	32.9669	+	19.0803i	1.21932	+	0.705712i
$732$	0.774498	−	2.58477i	0.0286263	−	0.0955360i
$733$	−11.4692	+	20.5684i	−0.423624	+	0.759709i	−0.998276	−	0.0586880i	$-0.981308\pi$
$733$	−11.4692	+	20.5684i	−0.423624	+	0.759709i	0.574653	+	0.818397i	$0.305137\pi$
$734$	−46.2260	−	9.90811i	−1.70623	−	0.365715i
$735$	0.671311	+	0.266188i	0.0247617	+	0.00981851i
$736$	−1.02024	−	16.7639i	−0.0376065	−	0.617925i
$737$	19.1033	−	14.4093i	0.703681	−	0.530772i
$738$	−8.81454	+	1.19155i	−0.324468	+	0.0438615i
$739$	9.29249	+	41.4104i	0.341830	+	1.52331i	0.780786	+	0.624798i	$0.214819\pi$
$739$	9.29249	+	41.4104i	0.341830	+	1.52331i	−0.438957	+	0.898508i	$0.644652\pi$
$740$	−6.84251	+	4.50504i	−0.251536	+	0.165608i
$741$	−8.59534	+	17.7446i	−0.315758	+	0.651863i
$742$	−23.2670	−	0.148873i	−0.854159	−	0.00546529i
$743$	21.2273	+	22.7036i	0.778755	+	0.832913i	0.989486	−	0.144631i	$-0.0461995\pi$
$743$	21.2273	+	22.7036i	0.778755	+	0.832913i	−0.210731	+	0.977544i	$0.567584\pi$
$744$	−1.98862	−	2.45200i	−0.0729065	−	0.0898947i
$745$	−24.6352	−	8.51296i	−0.902564	−	0.311891i
$746$	−49.5000	−	18.8984i	−1.81232	−	0.691919i
$747$	−10.4976	−	9.26321i	−0.384086	−	0.338923i
$748$	−8.58778	−	2.60320i	−0.314001	−	0.0951825i
$749$	9.12653	+	6.70246i	0.333476	+	0.244902i
$750$	6.03439	−	3.70187i	0.220345	−	0.135173i
$751$	0.0964966	−	30.1628i	0.00352121	−	1.10066i	−0.833181	−	0.553000i	$-0.813483\pi$
$751$	0.0964966	−	30.1628i	0.00352121	−	1.10066i	0.836702	−	0.547658i	$-0.184480\pi$
$752$	−45.5207	+	29.1422i	−1.65997	+	1.06271i
$753$	0.154988	−	0.149628i	0.00564809	−	0.00545274i
$754$	−14.7916	+	67.9485i	−0.538680	+	2.47454i
$755$	−4.91932	+	20.1075i	−0.179033	+	0.731787i
$756$	−3.73814	−	6.31809i	−0.135955	−	0.229787i
$757$	−16.4915	+	16.7574i	−0.599393	+	0.609058i	−0.944103	−	0.329651i	$-0.893069\pi$
$757$	−16.4915	+	16.7574i	−0.599393	+	0.609058i	0.344710	+	0.938709i	$0.387977\pi$
$758$	20.7728	−	28.8622i	0.754501	−	1.04832i
$759$	1.15881	−	2.27971i	0.0420623	−	0.0827481i
$760$	−8.11056	+	10.9702i	−0.294201	+	0.397930i
$761$	−15.4231	+	22.9429i	−0.559085	+	0.831681i	−0.997755	−	0.0669675i	$-0.978668\pi$
$761$	−15.4231	+	22.9429i	−0.559085	+	0.831681i	0.438670	+	0.898648i	$0.355450\pi$
$762$	4.36587	+	2.06330i	0.158159	+	0.0747455i
$763$	−48.8214	+	13.7817i	−1.76745	+	0.498931i
$764$	3.88208	+	8.28284i	0.140449	+	0.299663i
$765$	12.4801	−	4.94863i	0.451221	−	0.178918i
$766$	−9.23527	+	1.55068i	−0.333684	+	0.0560285i
$767$	58.1141	+	78.6039i	2.09838	+	2.83822i
$768$	−7.91778	+	0.354863i	−0.285708	+	0.0128050i
$769$	6.14948	+	3.61187i	0.221756	+	0.130248i	0.613124	−	0.789987i	$-0.289913\pi$
$769$	6.14948	+	3.61187i	0.221756	+	0.130248i	−0.391368	+	0.920234i	$0.627998\pi$
$770$	11.9396	−	2.08340i	0.430274	−	0.0750806i
$771$	4.39266	−	0.422886i	0.158198	−	0.0152299i
$772$	2.89436	+	17.5819i	0.104170	+	0.632786i
$773$	−23.2983	−	6.57684i	−0.837982	−	0.236553i	−0.174418	−	0.984672i	$-0.555804\pi$
$773$	−23.2983	−	6.57684i	−0.837982	−	0.236553i	−0.663564	+	0.748119i	$0.730957\pi$
$774$	34.7071	+	30.2333i	1.24752	+	1.08671i
$775$	−9.55640	+	14.6164i	−0.343276	+	0.525037i
$776$	10.8295	−	8.27773i	0.388758	−	0.297153i
$777$	5.06380	−	6.08295i	0.181663	−	0.218225i
$778$	−26.6155	+	33.2499i	−0.954212	+	1.19207i
$779$	9.53301	+	8.74319i	0.341555	+	0.313257i
$780$	−1.72209	−	2.86859i	−0.0616609	−	0.102712i
$781$	−2.97827	+	2.12909i	−0.106571	+	0.0761849i
$782$	21.6645	−	4.35440i	0.774722	−	0.155713i
$783$	11.7143	+	7.49950i	0.418636	+	0.268010i
$784$	−4.19118	+	6.50080i	−0.149685	+	0.232171i
$785$	0.276227	−	0.0445657i	0.00985896	−	0.00159062i
$786$	12.1334	−	3.25807i	0.432785	−	0.116212i
$787$	−4.03428	−	54.7287i	−0.143807	−	1.95087i	−0.279567	−	0.960126i	$-0.590191\pi$
$787$	−4.03428	−	54.7287i	−0.143807	−	1.95087i	0.135760	−	0.990742i	$-0.456652\pi$
$788$	19.1524	+	7.73649i	0.682276	+	0.275601i
$789$	−0.950816	+	3.40993i	−0.0338500	+	0.121397i
$790$	14.2535	+	13.5854i	0.507116	+	0.483346i
$791$	−5.32585	+	4.40478i	−0.189365	+	0.156616i
$792$	8.45201	+	4.46784i	0.300329	+	0.158758i
$793$	−0.406199	−	42.3220i	−0.0144245	−	1.50290i
$794$	3.40431	+	1.40055i	0.120814	+	0.0497037i
$795$	−0.737487	+	1.98875i	−0.0261560	+	0.0705338i
$796$	19.8748	−	7.29791i	0.704444	−	0.258668i
$797$	−29.0587	−	7.20787i	−1.02931	−	0.255316i	−0.310540	−	0.950560i	$-0.600510\pi$
$797$	−29.0587	−	7.20787i	−1.02931	−	0.255316i	−0.718773	+	0.695245i	$0.755296\pi$
$798$	−5.01828	+	14.0828i	−0.177645	+	0.498527i
$799$	−28.8656	−	33.7864i	−1.02119	−	1.19528i
$800$	6.97540	+	18.8103i	0.246618	+	0.665045i
$801$	−1.78011	+	50.5634i	−0.0628971	+	1.78657i
$802$	10.7923	+	21.5720i	0.381089	+	0.761734i
$803$	−14.5603	−	11.8861i	−0.513822	−	0.419453i
$804$	−4.51463	−	2.16905i	−0.159219	−	0.0764965i
$805$	−8.14756	+	6.39454i	−0.287164	+	0.225378i
$806$	46.7144	+	31.1866i	1.64545	+	1.09850i
$807$	−1.29855	−	5.96516i	−0.0457111	−	0.209983i
$808$	−3.78452	−	0.0968801i	−0.133139	−	0.00340823i
$809$	−0.891982	−	6.76135i	−0.0313604	−	0.237716i	0.968579	−	0.248705i	$-0.0800051\pi$
$809$	−0.891982	−	6.76135i	−0.0313604	−	0.237716i	−0.999940	+	0.0109890i	$0.996502\pi$
$810$	14.9707	−	2.81016i	0.526015	−	0.0987391i
$811$	0.381195	−	23.8288i	0.0133856	−	0.836743i	−0.901442	−	0.432899i	$-0.857491\pi$
$811$	0.381195	−	23.8288i	0.0133856	−	0.836743i	0.914828	−	0.403844i	$-0.132326\pi$
$812$	−1.92821	+	18.1963i	−0.0676669	+	0.638566i
$813$	−2.14651	−	1.15230i	−0.0752814	−	0.0404131i
$814$	3.45150	−	23.8090i	0.120975	−	0.834506i
$815$	2.25574	−	6.46072i	0.0790150	−	0.226309i
$816$	−1.50632	−	8.16868i	−0.0527317	−	0.285961i
$817$	1.49890	−	66.9211i	0.0524398	−	2.34127i
$818$	41.5998	−	18.0556i	1.45450	−	0.631299i
$819$	−41.4806	−	37.5581i	−1.44945	−	1.31239i
$820$	−2.12705	+	0.542073i	−0.0742797	+	0.0189300i
$821$	13.1364	+	13.5201i	0.458462	+	0.471856i	0.906529	−	0.422144i	$-0.138722\pi$
$821$	13.1364	+	13.5201i	0.458462	+	0.471856i	−0.448067	+	0.894000i	$0.647887\pi$
$822$	5.36319	+	1.77682i	0.187063	+	0.0619736i
$823$	29.2286	−	40.0678i	1.01885	−	1.39667i	0.103212	−	0.994659i	$-0.467088\pi$
$823$	29.2286	−	40.0678i	1.01885	−	1.39667i	0.915633	−	0.402015i	$-0.131690\pi$
$824$	10.4277	−	2.44533i	0.363266	−	0.0851870i
$825$	−0.534738	+	3.00764i	−0.0186172	+	0.104712i
$826$	50.2748	+	54.4656i	1.74929	+	1.89510i
$827$	18.2306	−	38.2579i	0.633939	−	1.33036i	−0.293348	−	0.956006i	$-0.594769\pi$
$827$	18.2306	−	38.2579i	0.633939	−	1.33036i	0.927287	−	0.374352i	$-0.122135\pi$
$828$	9.26650	−	0.0592911i	0.322033	−	0.00206051i
$829$	27.9276	+	29.4893i	0.969964	+	1.02421i	0.999696	+	0.0246473i	$0.00784627\pi$
$829$	27.9276	+	29.4893i	0.969964	+	1.02421i	−0.0297319	+	0.999558i	$0.509465\pi$
$830$	−8.17263	−	5.68582i	−0.283676	−	0.197358i
$831$	3.10469	+	0.159058i	0.107701	+	0.00551767i
$832$	−2.73094	+	0.983002i	−0.0946784	+	0.0340795i
$833$	−5.76677	−	2.68036i	−0.199807	−	0.0928690i
$834$	−0.704101	−	2.72635i	−0.0243810	−	0.0944059i
$835$	10.4276	+	4.44682i	0.360861	+	0.153888i
$836$	3.25570	+	15.4301i	0.112601	+	0.533661i
$837$	9.09747	−	6.59193i	0.314455	−	0.227850i
$838$	13.5770	+	33.9233i	0.469011	+	1.17186i
$839$	−17.3054	+	18.7479i	−0.597447	+	0.647249i	−0.958431	−	0.285323i	$-0.907899\pi$
$839$	−17.3054	+	18.7479i	−0.597447	+	0.647249i	0.360984	+	0.932572i	$0.382441\pi$
$840$	1.35258	+	1.78133i	0.0466685	+	0.0614617i
$841$	−2.00533	−	5.30335i	−0.0691492	−	0.182874i
$842$	−4.74227	+	21.1331i	−0.163429	+	0.728295i
$843$	0.809555	−	9.34893i	0.0278825	−	0.321994i
$844$	−0.867990	+	1.65481i	−0.0298775	+	0.0569608i
$845$	−27.9576	−	24.9902i	−0.961770	−	0.859688i
$846$	−26.4519	−	46.7323i	−0.909436	−	1.60669i
$847$	10.4126	−	16.8523i	0.357781	−	0.579053i
$848$	−19.3647	−	11.8795i	−0.664986	−	0.407943i
$849$	3.30067	+	8.09644i	0.113279	+	0.277869i
$850$	−23.2572	+	12.4851i	−0.797715	+	0.428235i
$851$	7.02468	+	19.3215i	0.240803	+	0.662333i
$852$	0.682019	+	0.349432i	0.0233656	+	0.0119713i
$853$	−10.7416	+	54.3423i	−0.367786	+	1.86065i	0.127389	+	0.991853i	$0.459340\pi$
$853$	−10.7416	+	54.3423i	−0.367786	+	1.86065i	−0.495174	+	0.868794i	$0.664896\pi$
$854$	−3.78987	−	31.8676i	−0.129687	−	1.09049i
$855$	−18.1808	−	15.0365i	−0.621769	−	0.514238i
$856$	2.43535	+	5.86618i	0.0832385	+	0.200502i
$857$	6.60644	−	32.3334i	0.225672	−	1.10449i	−0.696455	−	0.717601i	$-0.745240\pi$
$857$	6.60644	−	32.3334i	0.225672	−	1.10449i	0.922127	−	0.386888i	$-0.126450\pi$
$858$	9.65668	+	1.81267i	0.329674	+	0.0618836i
$859$	−1.32063	+	24.2587i	−0.0450595	+	0.827695i	0.886192	+	0.463318i	$0.153341\pi$
$859$	−1.32063	+	24.2587i	−0.0450595	+	0.827695i	−0.931252	+	0.364377i	$0.881282\pi$
$860$	9.36564	+	6.42728i	0.319366	+	0.219168i
$861$	1.81469	−	1.09732i	0.0618444	−	0.0373966i
$862$	−46.1572	−	5.93905i	−1.57212	−	0.202285i
$863$	3.00783	−	5.56022i	0.102388	−	0.189272i	−0.823254	−	0.567673i	$-0.807844\pi$
$863$	3.00783	−	5.56022i	0.102388	−	0.189272i	0.925642	+	0.378401i	$0.123526\pi$
$864$	0.123869	−	12.9059i	0.00421411	−	0.439069i
$865$	−6.96628	+	16.4815i	−0.236860	+	0.560388i
$866$	−12.1934	+	38.0234i	−0.414347	+	1.29209i
$867$	−0.0491105	+	0.0162702i	−0.00166788	+	0.000552565i
$868$	13.1103	+	6.82331i	0.444993	+	0.231598i
$869$	−19.9971	+	1.66718i	−0.678354	+	0.0565551i
$870$	4.31927	+	2.10931i	0.146437	+	0.0715124i
$871$	−77.7133	−	11.5197i	−2.63321	−	0.390331i
$872$	−27.4345	−	7.55524i	−0.929048	−	0.255853i
$873$	13.2759	+	19.4785i	0.449321	+	0.659248i
$874$	−25.0356	−	29.6860i	−0.846843	−	1.00414i
$875$	16.7635	−	23.9317i	0.566711	−	0.809040i
$876$	−0.812247	+	3.84957i	−0.0274433	+	0.130065i
$877$	−0.530851	−	1.19163i	−0.0179256	−	0.0402384i	0.904274	−	0.426952i	$-0.140413\pi$
$877$	−0.530851	−	1.19163i	−0.0179256	−	0.0402384i	−0.922200	+	0.386714i	$0.873610\pi$
$878$	−1.57552	−	32.8065i	−0.0531711	−	1.10716i
$879$	7.52244	+	1.96842i	0.253725	+	0.0663930i
$880$	11.0283	+	4.29149i	0.371763	+	0.144666i
$881$	14.8008	−	33.2240i	0.498651	−	1.11935i	−0.472597	−	0.881279i	$-0.656683\pi$
$881$	14.8008	−	33.2240i	0.498651	−	1.11935i	0.971248	−	0.238068i	$-0.0765141\pi$
$882$	−6.22271	−	4.50891i	−0.209530	−	0.151823i
$883$	11.6124	−	46.1830i	0.390788	−	1.55418i	−0.384835	−	0.922985i	$-0.625742\pi$
$883$	11.6124	−	46.1830i	0.390788	−	1.55418i	0.775624	−	0.631195i	$-0.217435\pi$
$884$	13.6856	+	26.0913i	0.460296	+	0.877545i
$885$	6.23230	−	2.61075i	0.209496	−	0.0877594i
$886$	29.1672	−	1.49428i	0.979891	−	0.0502014i
$887$	19.8548	+	12.3557i	0.666659	+	0.414863i	0.819258	−	0.573425i	$-0.194386\pi$
$887$	19.8548	+	12.3557i	0.666659	+	0.414863i	−0.152599	+	0.988288i	$0.548764\pi$
$888$	4.19622	−	1.45005i	0.140816	−	0.0486604i
$889$	19.9201	+	0.637497i	0.668099	+	0.0213810i
$890$	2.87454	+	35.8643i	0.0963547	+	1.20217i
$891$	−7.98962	+	13.3087i	−0.267662	+	0.445860i
$892$	6.57907	−	1.94843i	0.220284	−	0.0652382i
$893$	−27.6203	+	73.0455i	−0.924278	+	2.44437i
$894$	−13.3817	−	8.81040i	−0.447552	−	0.294664i
$895$	−0.558990	+	0.333149i	−0.0186850	+	0.0111360i
$896$	−30.6855	+	14.9852i	−1.02513	+	0.500622i
$897$	−8.00344	+	2.53834i	−0.267227	+	0.0847526i
$898$	−1.28895	+	7.52891i	−0.0430128	+	0.251243i
$899$	−28.0008	−	0.358338i	−0.933880	−	0.0119512i
$900$	−10.5726	+	3.27885i	−0.352419	+	0.109295i
$901$	7.49137	−	17.1099i	0.249574	−	0.570014i
$902$	2.95760	−	5.72740i	0.0984774	−	0.190702i
$903$	−10.4606	−	3.31763i	−0.348106	−	0.110404i
$904$	−3.83491	+	0.568463i	−0.127547	+	0.0189068i
$905$	−4.36604	−	0.533405i	−0.145132	−	0.0177310i
$906$	−5.98253	+	11.2303i	−0.198756	+	0.373102i
$907$	9.51259	+	34.1152i	0.315860	+	1.13278i	0.937073	+	0.349134i	$0.113524\pi$
$907$	9.51259	+	34.1152i	0.315860	+	1.13278i	−0.621212	+	0.783642i	$0.713360\pi$
$908$	1.17081	−	10.4126i	0.0388546	−	0.345554i
$909$	0.523060	−	6.52598i	0.0173488	−	0.216453i
$910$	−32.3718	−	23.1419i	−1.07312	−	0.767145i
$911$	13.9211	+	6.25508i	0.461226	+	0.207240i	0.627150	−	0.778899i	$-0.284221\pi$
$911$	13.9211	+	6.25508i	0.461226	+	0.207240i	−0.165924	+	0.986139i	$0.553061\pi$
$912$	−11.3078	+	9.23102i	−0.374440	+	0.305670i
$913$	9.86292	−	2.37956i	0.326415	−	0.0787520i
$914$	0.494029	−	1.14828i	0.0163410	−	0.0379817i
$915$	−2.84829	−	0.667931i	−0.0941614	−	0.0220811i
$916$	7.49750	−	6.44715i	0.247724	−	0.213020i
$917$	40.5842	−	32.2739i	1.34021	−	1.06578i
$918$	16.8429	−	2.16718i	0.555898	−	0.0715275i
$919$	−11.9804	+	31.0811i	−0.395197	+	1.02527i	0.582048	+	0.813155i	$0.302252\pi$
$919$	−11.9804	+	31.0811i	−0.395197	+	1.02527i	−0.977244	+	0.212117i	$0.931964\pi$
$920$	−5.76686	+	0.704545i	−0.190128	+	0.0232282i
$921$	−2.16720	+	0.596832i	−0.0714118	+	0.0196663i
$922$	23.6888	+	20.1079i	0.780148	+	0.662219i
$923$	11.8411	+	2.06621i	0.389755	+	0.0680102i
$924$	2.57775	+	0.198310i	0.0848018	+	0.00652393i
$925$	−14.7257	−	19.6534i	−0.484179	−	0.646200i
$926$	−2.72409	−	6.33165i	−0.0895192	−	0.208071i
$927$	3.24231	+	18.2364i	0.106491	+	0.598961i
$928$	−19.4546	+	25.6214i	−0.638627	+	0.841063i
$929$	−40.2294	−	11.9141i	−1.31988	−	0.390890i	−0.453939	−	0.891033i	$-0.649982\pi$
$929$	−40.2294	−	11.9141i	−1.31988	−	0.390890i	−0.865943	+	0.500142i	$0.833281\pi$
$930$	2.86131	−	2.62425i	0.0938261	−	0.0860525i
$931$	0.750229	+	11.1502i	0.0245878	+	0.365432i
$932$	−7.33670	−	0.706312i	−0.240322	−	0.0231360i
$933$	−6.77205	+	0.520984i	−0.221707	+	0.0170562i
$934$	−25.7816	−	29.4062i	−0.843599	−	0.962199i
$935$	−2.25160	+	9.46527i	−0.0736353	+	0.309547i
$936$	−9.00946	−	30.0678i	−0.294484	−	0.982796i
$937$	46.3029	+	10.2349i	1.51265	+	0.334359i	0.892833	−	0.450389i	$-0.148715\pi$
$937$	46.3029	+	10.2349i	1.51265	+	0.334359i	0.619816	+	0.784747i	$0.287207\pi$
$938$	−59.5261	−	2.28634i	−1.94360	−	0.0746516i
$939$	−0.379925	−	0.326700i	−0.0123984	−	0.0106615i
$940$	−7.80983	−	10.7060i	−0.254728	−	0.349192i
$941$	−12.4399	−	38.7922i	−0.405530	−	1.26459i	−0.914773	−	0.403968i	$-0.867631\pi$
$941$	−12.4399	−	38.7922i	−0.405530	−	1.26459i	0.509243	−	0.860623i	$-0.329925\pi$
$942$	0.171300	+	0.0153857i	0.00558126	+	0.000501294i
$943$	0.0881089	+	5.50775i	0.00286922	+	0.179357i
$944$	14.4878	+	70.9068i	0.471539	+	2.30782i
$945$	−6.59131	+	4.46160i	−0.214415	+	0.145136i
$946$	−32.3757	+	8.03062i	−1.05262	+	0.261098i
$947$	2.62396	−	26.3712i	0.0852672	−	0.856949i	−0.855479	−	0.517837i	$-0.826737\pi$
$947$	2.62396	−	26.3712i	0.0852672	−	0.856949i	0.940746	−	0.339111i	$-0.110126\pi$
$948$	2.23063	+	3.55905i	0.0724474	+	0.115592i
$949$	5.71712	+	61.4458i	0.185586	+	1.99462i
$950$	38.9067	+	25.2604i	1.26230	+	0.819557i
$951$	0.623079	+	0.0279255i	0.0202047	+	0.000905545i
$952$	−10.9881	−	16.3457i	−0.356127	−	0.529766i
$953$	1.23625	+	8.15981i	0.0400461	+	0.264322i	0.999867	−	0.0162901i	$-0.00518552\pi$
$953$	1.23625	+	8.15981i	0.0400461	+	0.264322i	−0.959821	+	0.280612i	$0.909463\pi$
$954$	12.8308	−	18.5690i	0.415411	−	0.601194i
$955$	8.70811	−	4.74677i	0.281788	−	0.153602i
$956$	0.698633	+	19.8444i	0.0225954	+	0.641815i
$957$	−4.53013	+	1.86372i	−0.146438	+	0.0602455i
$958$	−2.09612	−	4.95921i	−0.0677226	−	0.160225i
$959$	23.2253	−	2.08603i	0.749983	−	0.0673615i
$960$	0.0211415	+	0.199510i	0.000682338	+	0.00643917i
$961$	3.16410	−	7.76144i	0.102068	−	0.250369i
$962$	−63.6641	+	46.7544i	−2.05261	+	1.50742i
$963$	−10.3586	+	3.65389i	−0.333802	+	0.117745i
$964$	0.789628	+	0.603565i	0.0254322	+	0.0194395i
$965$	18.8367	−	4.29030i	0.606376	−	0.138110i
$966$	−5.82381	+	2.57212i	−0.187378	+	0.0827565i
$967$	1.36559	+	4.77906i	0.0439145	+	0.153684i	0.980398	−	0.197028i	$-0.0631290\pi$
$967$	1.36559	+	4.77906i	0.0439145	+	0.153684i	−0.936483	+	0.350712i	$0.885940\pi$
$968$	9.88948	−	5.06687i	0.317860	−	0.162855i
$969$	−8.79263	−	8.16835i	−0.282460	−	0.262405i
$970$	10.9701	+	12.6750i	0.352228	+	0.406971i
$971$	−14.0794	−	32.1566i	−0.451829	−	1.03196i	−0.982818	−	0.184576i	$-0.940909\pi$
$971$	−14.0794	−	32.1566i	−0.451829	−	1.03196i	0.530989	−	0.847379i	$-0.321820\pi$
$972$	10.7598	+	0.689391i	0.345120	+	0.0221122i
$973$	−7.14594	−	9.16517i	−0.229088	−	0.293822i
$974$	27.5643	+	45.2567i	0.883218	+	1.45012i
$975$	8.26963	−	5.67513i	0.264840	−	0.181749i
$976$	12.9338	−	28.5405i	0.414001	−	0.913559i
$977$	−29.1750	+	26.4161i	−0.933390	+	0.845126i	−0.988168	−	0.153373i	$-0.950986\pi$
$977$	−29.1750	+	26.4161i	−0.933390	+	0.845126i	0.0547785	+	0.998499i	$0.482555\pi$
$978$	2.32437	−	3.50592i	0.0743253	−	0.112107i
$979$	−29.2725	−	22.0796i	−0.935552	−	0.705667i
$980$	−1.65333	−	0.928866i	−0.0528138	−	0.0296715i
$981$	15.6254	−	46.6634i	0.498879	−	1.48985i
$982$	1.97290			0.0629577
$983$	0.507534	−	31.3487i	0.0161878	−	0.999869i
$983$	0.507534	−	31.3487i	0.0161878	−	0.999869i
$984$	1.18955			0.0379215
$985$	7.11110	−	21.2365i	0.226579	−	0.676652i
$986$	−36.9029	−	20.7326i	−1.17523	−	0.660260i
$987$	10.2213	+	7.70969i	0.325347	+	0.245402i
$988$	28.6102	−	43.1535i	0.910211	−	1.37290i
$989$	21.1306	−	19.1324i	0.671914	−	0.608376i
$990$	−4.85293	+	10.7088i	−0.154236	+	0.340347i
$991$	37.5793	−	25.7892i	1.19375	−	0.819221i	0.206504	−	0.978446i	$-0.433792\pi$
$991$	37.5793	−	25.7892i	1.19375	−	0.819221i	0.987242	+	0.159225i	$0.0508995\pi$
$992$	13.5165	+	22.1921i	0.429148	+	0.704600i
$993$	0.301189	+	0.386296i	0.00955795	+	0.0122587i
$994$	9.09555	+	0.582761i	0.288493	+	0.0184841i
$995$	−9.20691	−	21.0281i	−0.291879	−	0.666636i
$996$	−1.38982	−	1.60582i	−0.0440381	−	0.0508824i
$997$	18.9044	+	17.5621i	0.598708	+	0.556199i	0.920565	−	0.390589i	$-0.127729\pi$
$997$	18.9044	+	17.5621i	0.598708	+	0.556199i	−0.321857	+	0.946788i	$0.604307\pi$
$998$	55.1371	−	28.2495i	1.74534	−	0.894222i
$999$	4.34078	+	15.1911i	0.137336	+	0.480624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.c.a.2.19	✓	39690
983.492	even	491	inner	983.2.c.a.492.19	yes	39690

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.c.a.2.19	✓	39690	1.1	even	1	trivial
983.2.c.a.492.19	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)

\(f(q)\)	\(=\)	\(q+(-0.555704 + 1.65955i) q^{2} +(0.352885 + 0.198256i) q^{3} +(-0.848581 - 0.640067i) q^{4} +(-0.636799 + 0.960502i) q^{5} +(-0.525115 + 0.475459i) q^{6} +(-1.20682 + 2.66304i) q^{7} +(-1.35223 + 0.927979i) q^{8} +(-1.47531 - 2.42225i) q^{9} +O(q^{10})\)	\(q+(-0.555704 + 1.65955i) q^{2} +(0.352885 + 0.198256i) q^{3} +(-0.848581 - 0.640067i) q^{4} +(-0.636799 + 0.960502i) q^{5} +(-0.525115 + 0.475459i) q^{6} +(-1.20682 + 2.66304i) q^{7} +(-1.35223 + 0.927979i) q^{8} +(-1.47531 - 2.42225i) q^{9} +(-1.24013 - 1.59055i) q^{10} +(2.05116 + 0.131420i) q^{11} +(-0.172555 - 0.394107i) q^{12} +(-4.41619 - 5.10255i) q^{13} +(-3.74880 - 3.48264i) q^{14} +(-0.415142 + 0.212698i) q^{15} +(-1.37266 - 4.80377i) q^{16} +(3.75743 - 1.65949i) q^{17} +(4.83968 - 1.10230i) q^{18} +(-5.73496 - 4.38361i) q^{19} +(1.15516 - 0.407471i) q^{20} +(-0.953832 + 0.700487i) q^{21} +(-1.35793 + 3.33096i) q^{22} +(-0.323923 - 3.05683i) q^{23} +(-0.661158 + 0.0593835i) q^{24} +(1.42957 + 3.38221i) q^{25} +(10.9220 - 4.49338i) q^{26} +(-0.0831133 - 2.36081i) q^{27} +(2.72861 - 1.48736i) q^{28} +(-3.34721 + 4.84417i) q^{29} +(-0.122287 - 0.807146i) q^{30} +(2.65328 + 3.94696i) q^{31} +(5.45814 + 0.244626i) q^{32} +(0.697768 + 0.453030i) q^{33} +(0.665987 + 7.15782i) q^{34} +(-1.78935 - 2.85497i) q^{35} +(-0.298480 + 2.99977i) q^{36} +(-6.49138 + 1.61015i) q^{37} +(10.4617 - 7.08145i) q^{38} +(-0.546798 - 2.67615i) q^{39} +(-0.0302308 - 1.88975i) q^{40} +(-1.78480 - 0.160306i) q^{41} +(-0.632445 - 1.97219i) q^{42} +(5.46504 + 7.49169i) q^{43} +(-1.65645 - 1.42440i) q^{44} +(3.26605 + 0.125446i) q^{45} +(5.25297 + 1.16113i) q^{46} +(-3.10525 - 10.3633i) q^{47} +(0.467987 - 1.96732i) q^{48} +(-1.02063 - 1.16412i) q^{49} +(-6.40736 + 0.492928i) q^{50} +(1.65495 + 0.159323i) q^{51} +(0.481524 + 7.15659i) q^{52} +(3.35120 - 3.07355i) q^{53} +(3.96406 + 1.17398i) q^{54} +(-1.43240 + 1.88645i) q^{55} +(-0.839350 - 4.72093i) q^{56} +(-1.15471 - 2.68390i) q^{57} +(-6.17908 - 8.24679i) q^{58} +(-14.4431 - 1.11113i) q^{59} +(0.488423 + 0.0852274i) q^{60} +(4.78150 + 4.05872i) q^{61} +(-8.02461 + 2.20992i) q^{62} +(8.23097 - 1.00559i) q^{63} +(0.154693 - 0.401326i) q^{64} +(7.71324 - 0.992465i) q^{65} +(-1.13958 + 0.906230i) q^{66} +(8.82713 - 7.59051i) q^{67} +(-4.25067 - 0.996794i) q^{68} +(0.491728 - 1.14293i) q^{69} +(5.73231 - 1.38300i) q^{70} +(-1.37982 + 1.12640i) q^{71} +(4.24275 + 1.90637i) q^{72} +(-7.43933 - 5.31820i) q^{73} +(0.935158 - 11.6675i) q^{74} +(-0.166071 + 1.47695i) q^{75} +(2.06078 + 7.39060i) q^{76} +(-2.82535 + 5.30370i) q^{77} +(4.74507 + 0.579710i) q^{78} +(-9.65745 + 1.43156i) q^{79} +(5.48814 + 1.74060i) q^{80} +(-3.46524 + 6.71044i) q^{81} +(1.25785 - 2.87287i) q^{82} +(4.71479 - 1.46219i) q^{83} +(1.25776 + 0.0160961i) q^{84} +(-0.798783 + 4.66578i) q^{85} +(-15.4698 + 4.90633i) q^{86} +(-2.14157 + 1.04583i) q^{87} +(-2.89558 + 1.72572i) q^{88} +(-14.8997 - 9.80983i) q^{89} +(-2.02314 + 5.35047i) q^{90} +(18.9178 - 5.60262i) q^{91} +(-1.68170 + 2.80130i) q^{92} +(0.153797 + 1.91885i) q^{93} +(18.9241 + 0.605621i) q^{94} +(7.86248 - 2.71696i) q^{95} +(1.87760 + 1.16843i) q^{96} +(-8.30051 + 0.425248i) q^{97} +(2.49907 - 1.04688i) q^{98} +(-2.70776 - 5.16230i) 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

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Database

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