LMFDB - Embedded newform 983.2.c.a.2.1

Newspace parameters

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.c (of order $491$, degree $490$, minimal)

Newform invariants

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			2.1
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.1

$q$-expansion

$f(q)$	$=$	$q+(-0.882111 + 2.63433i) q^{2} +(2.23553 + 1.25595i) q^{3} +(-4.56485 - 3.44317i) q^{4} +(-1.70964 + 2.57870i) q^{5} +(-5.28058 + 4.78124i) q^{6} +(0.512184 - 1.13021i) q^{7} +(8.51597 - 5.84418i) q^{8} +(1.85965 + 3.05328i) q^{9} +O(q^{10})$	\(q+(-0.882111 + 2.63433i) q^{2} +(2.23553 + 1.25595i) q^{3} +(-4.56485 - 3.44317i) q^{4} +(-1.70964 + 2.57870i) q^{5} +(-5.28058 + 4.78124i) q^{6} +(0.512184 - 1.13021i) q^{7} +(8.51597 - 5.84418i) q^{8} +(1.85965 + 3.05328i) q^{9} +(-5.28506 - 6.77846i) q^{10} +(-5.61398 - 0.359694i) q^{11} +(-5.88041 - 13.4306i) q^{12} +(-3.50154 - 4.04575i) q^{13} +(2.52555 + 2.34623i) q^{14} +(-7.06070 + 3.61755i) q^{15} +(4.74153 + 16.5935i) q^{16} +(4.33448 - 1.91435i) q^{17} +(-9.68377 + 2.20560i) q^{18} +(-2.94335 - 2.24980i) q^{19} +(16.6832 - 5.88481i) q^{20} +(2.56450 - 1.88335i) q^{21} +(5.89971 - 14.4718i) q^{22} +(0.301498 + 2.84521i) q^{23} +(26.3777 - 2.36918i) q^{24} +(-1.78022 - 4.21182i) q^{25} +(13.7466 - 5.65542i) q^{26} +(0.0518778 + 1.47357i) q^{27} +(-6.22956 + 3.39572i) q^{28} +(-5.24199 + 7.58635i) q^{29} +(-3.30148 - 21.7913i) q^{30} +(-3.68375 - 5.47985i) q^{31} +(-27.2593 - 1.22172i) q^{32} +(-12.0985 - 7.85502i) q^{33} +(1.21953 + 13.1071i) q^{34} +(2.03883 + 3.25303i) q^{35} +(2.02394 - 20.3409i) q^{36} +(0.575850 - 0.142837i) q^{37} +(8.52307 - 5.76919i) q^{38} +(-2.74654 - 13.4422i) q^{39} +(0.511138 + 31.9516i) q^{40} +(2.12981 + 0.191293i) q^{41} +(2.69919 + 8.41706i) q^{42} +(-6.55657 - 8.98801i) q^{43} +(24.3885 + 20.9719i) q^{44} +(-11.0529 - 0.424529i) q^{45} +(-7.76116 - 1.71554i) q^{46} +(0.913525 + 3.04876i) q^{47} +(-10.2409 + 43.0506i) q^{48} +(3.59967 + 4.10574i) q^{49} +(12.6657 - 0.974389i) q^{50} +(12.0942 + 1.16432i) q^{51} +(2.05382 + 30.5247i) q^{52} +(-4.16760 + 3.82231i) q^{53} +(-3.92763 - 1.16319i) q^{54} +(10.5254 - 13.8619i) q^{55} +(-2.24342 - 12.6181i) q^{56} +(-3.75432 - 8.72622i) q^{57} +(-15.3609 - 20.5011i) q^{58} +(-10.1968 - 0.784455i) q^{59} +(44.6869 + 7.79763i) q^{60} +(4.69205 + 3.98279i) q^{61} +(17.6852 - 4.87036i) q^{62} +(4.40334 - 0.537962i) q^{63} +(14.8503 - 38.5265i) q^{64} +(16.4192 - 2.11266i) q^{65} +(31.3649 - 24.9424i) q^{66} +(-7.89844 + 6.79192i) q^{67} +(-26.3777 - 6.18564i) q^{68} +(-2.89944 + 6.73922i) q^{69} +(-10.3680 + 2.50142i) q^{70} +(-2.07112 + 1.69074i) q^{71} +(33.6807 + 15.1335i) q^{72} +(3.88781 + 2.77930i) q^{73} +(-0.131685 + 1.64298i) q^{74} +(1.31012 - 11.6515i) q^{75} +(5.68953 + 20.4045i) q^{76} +(-3.28192 + 6.16077i) q^{77} +(37.8339 + 4.62221i) q^{78} +(0.943524 - 0.139862i) q^{79} +(-50.8962 - 16.1420i) q^{80} +(3.18623 - 6.17013i) q^{81} +(-2.38265 + 5.44186i) q^{82} +(2.00102 - 0.620574i) q^{83} +(-18.1913 - 0.232801i) q^{84} +(-2.47388 + 14.4502i) q^{85} +(29.4610 - 9.34373i) q^{86} +(-21.2468 + 10.3758i) q^{87} +(-49.9106 + 29.7460i) q^{88} +(1.29335 + 0.851528i) q^{89} +(10.8682 - 28.7424i) q^{90} +(-6.36599 + 1.88532i) q^{91} +(8.42024 - 14.0261i) q^{92} +(-1.35270 - 16.8770i) q^{93} +(-8.83726 - 0.282816i) q^{94} +(10.8336 - 3.74368i) q^{95} +(-59.4046 - 36.9676i) q^{96} +(-10.7528 + 0.550884i) q^{97} +(-13.9912 + 5.86099i) q^{98} +(-9.34181 - 17.8100i) 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 $

$2$	−0.882111	+	2.63433i	−0.623747	+	1.86275i	−0.133778	+	0.991011i	$0.542711\pi$
$2$	−0.882111	+	2.63433i	−0.623747	+	1.86275i	−0.489969	+	0.871740i	$0.662992\pi$
$3$	2.23553	+	1.25595i	1.29069	+	0.725126i	0.974674	−	0.223630i	$-0.0717906\pi$
$3$	2.23553	+	1.25595i	1.29069	+	0.725126i	0.316012	+	0.948755i	$0.397656\pi$
$4$	−4.56485	−	3.44317i	−2.28243	−	1.72159i
$5$	−1.70964	+	2.57870i	−0.764575	+	1.15323i	0.219523	+	0.975607i	$0.429550\pi$
$5$	−1.70964	+	2.57870i	−0.764575	+	1.15323i	−0.984098	+	0.177624i	$0.943159\pi$
$6$	−5.28058	+	4.78124i	−2.15579	+	1.95193i
$7$	0.512184	−	1.13021i	0.193587	−	0.427180i	−0.788645	−	0.614848i	$-0.789217\pi$
$7$	0.512184	−	1.13021i	0.193587	−	0.427180i	0.982232	+	0.187668i	$0.0600929\pi$
$8$	8.51597	−	5.84418i	3.01085	−	2.06623i
$9$	1.85965	+	3.05328i	0.619884	+	1.01776i
$10$	−5.28506	−	6.77846i	−1.67128	−	2.14354i
$11$	−5.61398	−	0.359694i	−1.69268	−	0.108452i	−0.812460	−	0.583018i	$-0.801872\pi$
$11$	−5.61398	−	0.359694i	−1.69268	−	0.108452i	−0.880220	+	0.474566i	$0.842605\pi$
$12$	−5.88041	−	13.4306i	−1.69753	−	3.87707i
$13$	−3.50154	−	4.04575i	−0.971153	−	1.12209i	−0.992491	−	0.122316i	$-0.960968\pi$
$13$	−3.50154	−	4.04575i	−0.971153	−	1.12209i	0.0213379	−	0.999772i	$-0.493207\pi$
$14$	2.52555	+	2.34623i	0.674981	+	0.627057i
$15$	−7.06070	+	3.61755i	−1.82306	+	0.934046i
$16$	4.74153	+	16.5935i	1.18538	+	4.14839i
$17$	4.33448	−	1.91435i	1.05127	−	0.464298i	0.194984	−	0.980806i	$-0.437534\pi$
$17$	4.33448	−	1.91435i	1.05127	−	0.464298i	0.856282	+	0.516509i	$0.172769\pi$
$18$	−9.68377	+	2.20560i	−2.28249	+	0.519865i
$19$	−2.94335	−	2.24980i	−0.675252	−	0.516139i	0.212091	−	0.977250i	$-0.431973\pi$
$19$	−2.94335	−	2.24980i	−0.675252	−	0.516139i	−0.887343	+	0.461110i	$0.847451\pi$
$20$	16.6832	−	5.88481i	3.73047	−	1.31588i
$21$	2.56450	−	1.88335i	0.559620	−	0.410980i
$22$	5.89971	−	14.4718i	1.25782	−	3.08540i
$23$	0.301498	+	2.84521i	0.0628666	+	0.593267i	0.980593	+	0.196054i	$0.0628127\pi$
$23$	0.301498	+	2.84521i	0.0628666	+	0.593267i	−0.917727	+	0.397213i	$0.869977\pi$
$24$	26.3777	−	2.36918i	5.38434	−	0.483607i
$25$	−1.78022	−	4.21182i	−0.356044	−	0.842364i
$26$	13.7466	−	5.65542i	2.69593	−	1.10912i
$27$	0.0518778	+	1.47357i	0.00998388	+	0.283589i
$28$	−6.22956	+	3.39572i	−1.17728	+	0.641731i
$29$	−5.24199	+	7.58635i	−0.973414	+	1.40875i	−0.0616204	+	0.998100i	$0.519627\pi$
$29$	−5.24199	+	7.58635i	−0.973414	+	1.40875i	−0.911793	+	0.410650i	$0.865302\pi$
$30$	−3.30148	−	21.7913i	−0.602766	−	3.97852i
$31$	−3.68375	−	5.47985i	−0.661620	−	0.984209i	−0.999081	−	0.0428697i	$-0.986350\pi$
$31$	−3.68375	−	5.47985i	−0.661620	−	0.984209i	0.337460	−	0.941340i	$-0.390432\pi$
$32$	−27.2593	−	1.22172i	−4.81881	−	0.215972i
$33$	−12.0985	−	7.85502i	−2.10608	−	1.36738i
$34$	1.21953	+	13.1071i	0.209147	+	2.24785i
$35$	2.03883	+	3.25303i	0.344626	+	0.549862i
$36$	2.02394	−	20.3409i	0.337323	−	3.39015i
$37$	0.575850	−	0.142837i	0.0946692	−	0.0234822i	−0.193128	−	0.981174i	$-0.561863\pi$
$37$	0.575850	−	0.142837i	0.0946692	−	0.0234822i	0.287797	+	0.957691i	$0.407077\pi$
$38$	8.52307	−	5.76919i	1.38263	−	0.935886i
$39$	−2.74654	−	13.4422i	−0.439798	−	2.15247i
$40$	0.511138	+	31.9516i	0.0808180	+	5.05199i
$41$	2.12981	+	0.191293i	0.332620	+	0.0298750i	0.254511	−	0.967070i	$-0.418085\pi$
$41$	2.12981	+	0.191293i	0.332620	+	0.0298750i	0.0781086	+	0.996945i	$0.475112\pi$
$42$	2.69919	+	8.41706i	0.416494	+	1.29878i
$43$	−6.55657	−	8.98801i	−0.999867	−	1.37066i	−0.927725	−	0.373265i	$-0.878238\pi$
$43$	−6.55657	−	8.98801i	−0.999867	−	1.37066i	−0.0721425	−	0.997394i	$-0.522984\pi$
$44$	24.3885	+	20.9719i	3.67671	+	3.16163i
$45$	−11.0529	−	0.424529i	−1.64766	−	0.0632851i
$46$	−7.76116	−	1.71554i	−1.14432	−	0.252943i
$47$	0.913525	+	3.04876i	0.133251	+	0.444707i	0.998383	−	0.0568371i	$-0.0181016\pi$
$47$	0.913525	+	3.04876i	0.133251	+	0.444707i	−0.865132	+	0.501544i	$0.832766\pi$
$48$	−10.2409	+	43.0506i	−1.47815	+	6.21381i
$49$	3.59967	+	4.10574i	0.514239	+	0.586534i
$50$	12.6657	−	0.974389i	1.79120	−	0.137799i
$51$	12.0942	+	1.16432i	1.69353	+	0.163038i
$52$	2.05382	+	30.5247i	0.284814	+	4.23301i
$53$	−4.16760	+	3.82231i	−0.572464	+	0.525035i	−0.909088	−	0.416605i	$-0.863220\pi$
$53$	−4.16760	+	3.82231i	−0.572464	+	0.525035i	0.336624	+	0.941639i	$0.390715\pi$
$54$	−3.92763	−	1.16319i	−0.534483	−	0.158290i
$55$	10.5254	−	13.8619i	1.41925	−	1.86913i
$56$	−2.24342	−	12.6181i	−0.299790	−	1.68617i
$57$	−3.75432	−	8.72622i	−0.497271	−	1.15582i
$58$	−15.3609	−	20.5011i	−2.01699	−	2.69193i
$59$	−10.1968	−	0.784455i	−1.32751	−	0.102127i	−0.606517	−	0.795070i	$-0.707434\pi$
$59$	−10.1968	−	0.784455i	−1.32751	−	0.102127i	−0.720992	+	0.692943i	$0.756314\pi$
$60$	44.6869	+	7.79763i	5.76905	+	1.00667i
$61$	4.69205	+	3.98279i	0.600756	+	0.509945i	0.895165	−	0.445735i	$-0.147058\pi$
$61$	4.69205	+	3.98279i	0.600756	+	0.509945i	−0.294409	+	0.955680i	$0.595123\pi$
$62$	17.6852	−	4.87036i	2.24602	−	0.618537i
$63$	4.40334	−	0.537962i	0.554769	−	0.0677768i
$64$	14.8503	−	38.5265i	1.85628	−	4.81582i
$65$	16.4192	−	2.11266i	2.03655	−	0.262043i
$66$	31.3649	−	24.9424i	3.86075	−	3.07020i
$67$	−7.89844	+	6.79192i	−0.964948	+	0.829766i	−0.985440	−	0.170024i	$-0.945615\pi$
$67$	−7.89844	+	6.79192i	−0.964948	+	0.829766i	0.0204916	+	0.999790i	$0.493477\pi$
$68$	−26.3777	−	6.18564i	−3.19876	−	0.750119i
$69$	−2.89944	+	6.73922i	−0.349052	+	0.811307i
$70$	−10.3680	+	2.50142i	−1.23922	+	0.298977i
$71$	−2.07112	+	1.69074i	−0.245797	+	0.200654i	−0.747271	−	0.664519i	$-0.768636\pi$
$71$	−2.07112	+	1.69074i	−0.245797	+	0.200654i	0.501474	+	0.865173i	$0.332791\pi$
$72$	33.6807	+	15.1335i	3.96930	+	1.78350i
$73$	3.88781	+	2.77930i	0.455034	+	0.325293i	0.785866	−	0.618397i	$-0.212217\pi$
$73$	3.88781	+	2.77930i	0.455034	+	0.325293i	−0.330832	+	0.943690i	$0.607329\pi$
$74$	−0.131685	+	1.64298i	−0.0153081	+	0.190992i
$75$	1.31012	−	11.6515i	0.151279	−	1.34540i
$76$	5.68953	+	20.4045i	0.652633	+	2.34055i
$77$	−3.28192	+	6.16077i	−0.374010	+	0.702085i
$78$	37.8339	+	4.62221i	4.28384	+	0.523362i
$79$	0.943524	−	0.139862i	0.106155	−	0.0157357i	−0.0933430	−	0.995634i	$-0.529755\pi$
$79$	0.943524	−	0.139862i	0.106155	−	0.0157357i	0.199498	+	0.979898i	$0.436069\pi$
$80$	−50.8962	−	16.1420i	−5.69036	−	1.80473i
$81$	3.18623	−	6.17013i	0.354025	−	0.685570i
$82$	−2.38265	+	5.44186i	−0.263120	+	0.600953i
$83$	2.00102	−	0.620574i	0.219641	−	0.0681168i	−0.184426	−	0.982846i	$-0.559042\pi$
$83$	2.00102	−	0.620574i	0.219641	−	0.0681168i	0.404066	+	0.914730i	$0.367596\pi$
$84$	−18.1913	−	0.232801i	−1.98483	−	0.0254007i
$85$	−2.47388	+	14.4502i	−0.268330	+	1.56734i
$86$	29.4610	−	9.34373i	3.17686	−	1.00756i
$87$	−21.2468	+	10.3758i	−2.27789	+	1.11241i
$88$	−49.9106	+	29.7460i	−5.32049	+	3.17093i
$89$	1.29335	+	0.851528i	0.137095	+	0.0902617i	0.616597	−	0.787279i	$-0.288511\pi$
$89$	1.29335	+	0.851528i	0.137095	+	0.0902617i	−0.479502	+	0.877541i	$0.659183\pi$
$90$	10.8682	−	28.7424i	1.14561	−	3.02971i
$91$	−6.36599	+	1.88532i	−0.667337	+	0.197636i
$92$	8.42024	−	14.0261i	0.877871	−	1.46232i
$93$	−1.35270	−	16.8770i	−0.140268	−	1.75006i
$94$	−8.83726	−	0.282816i	−0.911494	−	0.0291703i
$95$	10.8336	−	3.74368i	1.11151	−	0.384094i
$96$	−59.4046	−	36.9676i	−6.06296	−	3.77299i
$97$	−10.7528	+	0.550884i	−1.09178	+	0.0559338i	−0.588736	−	0.808325i	$-0.700374\pi$
$97$	−10.7528	+	0.550884i	−1.09178	+	0.0559338i	−0.503047	+	0.864259i	$0.667788\pi$
$98$	−13.9912	+	5.86099i	−1.41332	+	0.592050i
$99$	−9.34181	−	17.8100i	−0.938887	−	1.78997i
$100$	−6.37558	+	25.3559i	−0.637558	+	2.53559i
$101$	0.656115	+	0.475414i	0.0652859	+	0.0473054i	0.618915	−	0.785458i	$-0.287572\pi$
$101$	0.656115	+	0.475414i	0.0652859	+	0.0473054i	−0.553630	+	0.832763i	$0.686758\pi$
$102$	−13.7356	+	30.8331i	−1.36003	+	3.05293i
$103$	−2.06687	−	0.804290i	−0.203655	−	0.0792490i	0.258647	−	0.965972i	$-0.416724\pi$
$103$	−2.06687	−	0.804290i	−0.203655	−	0.0792490i	−0.462301	+	0.886723i	$0.652976\pi$
$104$	−53.4631	−	13.9898i	−5.24249	−	1.37182i
$105$	0.472222	+	9.83294i	0.0460842	+	0.959597i
$106$	−6.39293	−	14.3505i	−0.620937	−	1.39385i
$107$	−1.18362	+	5.60968i	−0.114425	+	0.542309i	0.882922	+	0.469520i	$0.155573\pi$
$107$	−1.18362	+	5.60968i	−0.114425	+	0.542309i	−0.997347	+	0.0727891i	$0.976810\pi$
$108$	4.83694	−	6.90526i	0.465435	−	0.664459i
$109$	3.73367	+	4.42719i	0.357620	+	0.424048i	0.913261	−	0.407374i	$-0.133556\pi$
$109$	3.73367	+	4.42719i	0.357620	+	0.424048i	−0.555641	+	0.831422i	$0.687527\pi$
$110$	27.2321	+	39.9552i	2.59648	+	3.80958i
$111$	1.46673	+	0.403926i	0.139216	+	0.0383389i
$112$	21.1828	+	3.14000i	2.00158	+	0.296702i
$113$	−3.47355	−	1.69630i	−0.326764	−	0.159575i	0.268122	−	0.963385i	$-0.413597\pi$
$113$	−3.47355	−	1.69630i	−0.326764	−	0.159575i	−0.594886	+	0.803810i	$0.702803\pi$
$114$	26.2995	−	2.19261i	2.46317	−	0.205357i
$115$	−7.85240	−	4.08681i	−0.732240	−	0.381097i
$116$	50.0500	−	16.5815i	4.64703	−	1.53955i
$117$	5.84116	−	18.2149i	0.540016	−	1.68397i
$118$	11.0612	−	26.1697i	1.01827	−	2.40912i
$119$	0.0564293	−	5.87938i	0.00517287	−	0.538962i
$120$	−38.9871	+	72.0709i	−3.55902	+	6.57914i
$121$	20.4774	+	2.63483i	1.86158	+	0.239530i
$122$	−14.6309	+	8.84715i	−1.32462	+	0.800983i
$123$	4.52099	+	3.10258i	0.407644	+	0.279750i
$124$	−2.05229	+	37.6985i	−0.184301	+	3.38542i
$125$	−1.29968	−	0.243965i	−0.116247	−	0.0218209i
$126$	−2.46707	+	12.0744i	−0.219784	+	1.07567i
$127$	6.25149	+	15.0584i	0.554730	+	1.33621i	0.915033	+	0.403378i	$0.132164\pi$
$127$	6.25149	+	15.0584i	0.554730	+	1.33621i	−0.360303	+	0.932835i	$0.617327\pi$
$128$	46.3380	+	38.3242i	4.09574	+	3.38741i
$129$	−3.36889	−	28.3278i	−0.296615	−	2.49412i
$130$	−8.91809	+	45.1171i	−0.782169	+	3.95703i
$131$	−10.4108	−	5.33394i	−0.909592	−	0.466029i	−0.0628439	−	0.998023i	$-0.520017\pi$
$131$	−10.4108	−	5.33394i	−0.909592	−	0.466029i	−0.846748	+	0.531995i	$0.821443\pi$
$132$	28.1816	+	77.5141i	2.45290	+	6.74674i
$133$	−4.05029	+	2.17431i	−0.351205	+	0.188536i
$134$	−10.9249	−	26.7983i	−0.943764	−	2.31502i
$135$	−3.88860	−	2.38550i	−0.334677	−	0.205311i
$136$	25.7245	−	41.6340i	2.20586	−	3.57009i
$137$	−7.69532	−	13.5952i	−0.657456	−	1.16152i	−0.976856	−	0.213899i	$-0.931384\pi$
$137$	−7.69532	−	13.5952i	−0.657456	−	1.16152i	0.319400	−	0.947620i	$-0.396519\pi$
$138$	−15.1957	−	13.5828i	−1.29354	−	1.15625i
$139$	−3.23762	+	6.17247i	−0.274612	+	0.523542i	−0.983303	−	0.181977i	$-0.941750\pi$
$139$	−3.23762	+	6.17247i	−0.274612	+	0.523542i	0.708691	+	0.705519i	$0.249286\pi$
$140$	1.89376	−	21.8697i	0.160052	−	1.84832i
$141$	−1.78689	+	7.96295i	−0.150483	+	0.670601i
$142$	−2.62700	−	6.94744i	−0.220453	−	0.583016i
$143$	18.2024	+	23.9722i	1.52216	+	2.00466i
$144$	−41.8472	+	45.3355i	−3.48727	+	3.77795i
$145$	−10.6010	−	26.4875i	−0.880366	−	2.19967i
$146$	−10.7511	+	7.79012i	−0.889766	+	0.644715i
$147$	2.89056	+	13.6995i	0.238409	+	1.12992i
$148$	−3.12048	−	1.33072i	−0.256502	−	0.109385i
$149$	1.37462	+	5.32266i	0.112613	+	0.436050i	0.999672	−	0.0256063i	$-0.00815162\pi$
$149$	1.37462	+	5.32266i	0.112613	+	0.436050i	−0.887059	+	0.461656i	$0.847255\pi$
$150$	29.5383	+	13.7292i	2.41179	+	1.12099i
$151$	−0.0511521	+	0.0184122i	−0.00416270	+	0.00149836i	−0.340758	−	0.940151i	$-0.610684\pi$
$151$	−0.0511521	+	0.0184122i	−0.00416270	+	0.00149836i	0.336596	+	0.941649i	$0.390724\pi$
$152$	−38.2137	−	1.95775i	−3.09954	−	0.158795i
$153$	13.9057	+	9.67437i	1.12421	+	0.782127i
$154$	−13.3345	−	14.0801i	−1.07452	−	1.13461i
$155$	20.4288	−	0.130712i	1.64088	−	0.0104991i
$156$	−33.7462	+	70.8184i	−2.70186	+	5.67001i
$157$	3.01596	+	3.26736i	0.240700	+	0.260764i	0.843501	−	0.537127i	$-0.180491\pi$
$157$	3.01596	+	3.26736i	0.240700	+	0.260764i	−0.602801	+	0.797891i	$0.705949\pi$
$158$	−0.463850	+	2.60893i	−0.0369019	+	0.207555i
$159$	−14.1175	+	3.31058i	−1.11959	+	0.262546i
$160$	49.7541	−	68.2049i	3.93341	−	5.39207i
$161$	3.37011	+	1.11651i	0.265602	+	0.0879935i
$162$	13.4436	+	13.8363i	1.05623	+	1.08708i
$163$	5.40228	−	1.37676i	0.423139	−	0.107836i	−0.0294268	−	0.999567i	$-0.509368\pi$
$163$	5.40228	−	1.37676i	0.423139	−	0.107836i	0.452566	+	0.891731i	$0.350509\pi$
$164$	−9.06359	−	8.20651i	−0.707747	−	0.640821i
$165$	40.9398	−	17.7691i	3.18716	−	1.38333i
$166$	−0.130329	+	5.81877i	−0.0101155	+	0.451624i
$167$	−3.25199	−	17.6353i	−0.251646	−	1.36466i	−0.834016	−	0.551740i	$-0.813964\pi$
$167$	−3.25199	−	17.6353i	−0.251646	−	1.36466i	0.582370	−	0.812924i	$-0.302126\pi$
$168$	10.8326	−	31.0259i	0.835751	−	2.39370i
$169$	−2.24222	+	15.4672i	−0.172478	+	1.18978i
$170$	−35.8843	−	19.2637i	−2.75220	−	1.47746i
$171$	1.39566	−	13.1707i	0.106729	−	1.00719i
$172$	−1.01749	+	63.6043i	−0.0775832	+	4.84978i
$173$	−4.35682	+	0.817826i	−0.331243	+	0.0621782i	−0.347473	−	0.937690i	$-0.612960\pi$
$173$	−4.35682	+	0.817826i	−0.331243	+	0.0621782i	0.0162295	+	0.999868i	$0.494834\pi$
$174$	−8.59134	−	65.1236i	−0.651308	−	4.93700i
$175$	−5.67205	−	0.145199i	−0.428767	−	0.0109760i
$176$	−20.6503	−	94.8614i	−1.55657	−	7.15044i
$177$	−21.8100	−	14.5604i	−1.63934	−	1.09443i
$178$	−3.38408	+	2.65597i	−0.253648	+	0.199073i
$179$	−5.84110	−	2.80635i	−0.436584	−	0.209757i	0.201876	−	0.979411i	$-0.435296\pi$
$179$	−5.84110	−	2.80635i	−0.436584	−	0.209757i	−0.638461	+	0.769655i	$0.720428\pi$
$180$	48.9929	+	39.9948i	3.65172	+	2.98104i
$181$	−7.47304	−	14.9374i	−0.555467	−	1.11029i	−0.978896	−	0.204357i	$-0.934490\pi$
$181$	−7.47304	−	14.9374i	−0.555467	−	1.11029i	0.423430	−	0.905929i	$-0.360826\pi$
$182$	0.648949	−	18.4332i	0.0481033	−	1.36636i
$183$	5.48703	+	14.7967i	0.405613	+	1.09380i
$184$	19.1954	+	22.4677i	1.41511	+	1.65634i
$185$	−0.616165	+	1.72915i	−0.0453013	+	0.127129i
$186$	45.6528	+	11.3239i	3.34742	+	0.830311i
$187$	−25.0223	+	9.18803i	−1.82981	+	0.671895i
$188$	6.32729	−	17.0626i	0.461465	−	1.24441i
$189$	1.69202	+	0.696106i	0.123076	+	0.0506343i
$190$	0.305611	+	31.8417i	0.0221714	+	2.31004i
$191$	11.7871	+	6.23080i	0.852883	+	0.450845i	0.835816	−	0.549010i	$-0.184995\pi$
$191$	11.7871	+	6.23080i	0.852883	+	0.450845i	0.0170666	+	0.999854i	$0.494567\pi$
$192$	81.5858	−	67.4761i	5.88795	−	4.86967i
$193$	−13.2376	−	12.6172i	−0.952867	−	0.908204i	0.0429958	−	0.999075i	$-0.486310\pi$
$193$	−13.2376	−	12.6172i	−0.952867	−	0.908204i	−0.995863	+	0.0908712i	$0.971035\pi$
$194$	8.03397	−	28.8124i	0.576805	−	2.06861i
$195$	39.3590	+	15.8988i	2.81856	+	1.13854i
$196$	−2.29519	−	31.1364i	−0.163942	−	2.22403i
$197$	11.8755	−	3.18882i	0.846095	−	0.227194i	0.189917	−	0.981800i	$-0.439178\pi$
$197$	11.8755	−	3.18882i	0.846095	−	0.227194i	0.656178	+	0.754606i	$0.272172\pi$
$198$	55.1579	−	8.89902i	3.91990	−	0.632426i
$199$	−8.98047	+	13.9293i	−0.636609	+	0.987423i	0.361867	+	0.932230i	$0.382140\pi$
$199$	−8.98047	+	13.9293i	−0.636609	+	0.987423i	−0.998476	+	0.0551929i	$0.982423\pi$
$200$	−39.7749	−	25.4638i	−2.81251	−	1.80056i
$201$	−26.1876	+	5.26349i	−1.84713	+	0.371258i
$202$	−1.83116	+	1.30905i	−0.128840	+	0.0921047i
$203$	5.88933	+	9.81017i	0.413350	+	0.688539i
$204$	−51.1993	−	46.9574i	−3.58467	−	3.28767i
$205$	−4.13450	+	5.16509i	−0.288766	+	0.360746i
$206$	3.94197	−	4.73534i	0.274650	−	0.329927i
$207$	−8.12654	+	6.21165i	−0.564834	+	0.431740i
$208$	50.5306	−	77.2860i	3.50367	−	5.35882i
$209$	15.7147	+	13.6890i	1.08701	+	0.946891i
$210$	−26.3197	−	7.42975i	−1.81624	−	0.512702i
$211$	1.41000	+	8.56509i	0.0970683	+	0.589645i	0.990179	+	0.139808i	$0.0446485\pi$
$211$	1.41000	+	8.56509i	0.0970683	+	0.589645i	−0.893110	+	0.449838i	$0.851482\pi$
$212$	32.1853	−	3.09852i	2.21050	−	0.212807i
$213$	−6.75355	+	1.17846i	−0.462746	+	0.0807468i
$214$	−13.7337	−	8.06642i	−0.938814	−	0.551409i
$215$	34.3868	−	1.54116i	2.34516	−	0.105107i
$216$	9.05360	+	12.2457i	0.616019	+	0.833214i
$217$	−8.08015	+	1.35673i	−0.548516	+	0.0921008i
$218$	−14.9562	+	5.93043i	−1.01296	+	0.401659i
$219$	5.20065	+	11.0961i	0.351427	+	0.749808i
$220$	−95.7758	+	27.0364i	−6.45721	+	1.82279i
$221$	−22.9223	−	10.8330i	−1.54192	−	0.728710i
$222$	−2.35789	+	3.50754i	−0.158251	+	0.235410i
$223$	−10.0494	+	13.5926i	−0.672958	+	0.910229i	−0.999388	−	0.0349927i	$-0.988859\pi$
$223$	−10.0494	+	13.5926i	−0.672958	+	0.910229i	0.326429	+	0.945222i	$0.394155\pi$
$224$	−15.3426	+	30.1831i	−1.02512	+	2.01669i
$225$	9.54929	−	13.2680i	0.636619	−	0.884536i
$226$	7.53267	−	7.65414i	0.501066	−	0.509146i
$227$	−6.26778	−	10.5936i	−0.416007	−	0.703122i	0.577562	−	0.816347i	$-0.304004\pi$
$227$	−6.26778	−	10.5936i	−0.416007	−	0.703122i	−0.993569	+	0.113225i	$0.963882\pi$
$228$	−12.9080	+	52.7607i	−0.854851	+	3.49416i
$229$	2.48237	−	11.4033i	0.164040	−	0.753551i	−0.819532	−	0.573033i	$-0.805767\pi$
$229$	2.48237	−	11.4033i	0.164040	−	0.753551i	0.983572	−	0.180517i	$-0.0577772\pi$
$230$	17.6927	−	17.0808i	1.16662	−	1.12627i
$231$	−15.0745	+	9.65066i	−0.991828	+	0.634967i
$232$	−0.304691	+	95.2402i	−0.0200040	+	6.25283i
$233$	5.57666	−	3.42106i	0.365339	−	0.224121i	−0.328090	−	0.944647i	$-0.606405\pi$
$233$	5.57666	−	3.42106i	0.365339	−	0.224121i	0.693429	+	0.720525i	$0.256099\pi$
$234$	42.8314	+	31.4551i	2.79998	+	2.05628i
$235$	−9.42365	−	2.85657i	−0.614731	−	0.186342i
$236$	43.8458	+	38.6902i	2.85412	+	2.51852i
$237$	2.28494	+	0.872357i	0.148423	+	0.0566656i
$238$	15.4384	+	5.33492i	1.00073	+	0.345812i
$239$	−5.73771	−	7.07468i	−0.371142	−	0.457623i	0.556636	−	0.830757i	$-0.312092\pi$
$239$	−5.73771	−	7.07468i	−0.371142	−	0.457623i	−0.927778	+	0.373134i	$0.878283\pi$
$240$	−93.5064	−	100.009i	−6.03581	−	6.45557i
$241$	20.0752	+	0.128450i	1.29316	+	0.00827418i	0.651459	−	0.758684i	$-0.274157\pi$
$241$	20.0752	+	0.128450i	1.29316	+	0.00827418i	0.641697	+	0.766958i	$0.278231\pi$
$242$	−25.0043	+	51.6199i	−1.60734	+	3.31825i
$243$	18.5669	−	12.2243i	1.19107	−	0.784187i
$244$	−7.70509	−	34.3364i	−0.493268	−	2.19816i
$245$	−16.7416	+	2.26313i	−1.06958	+	0.144586i
$246$	−12.1612	+	9.17296i	−0.775372	+	0.584847i
$247$	1.20415	+	19.7858i	0.0766184	+	1.25894i
$248$	−63.3958	−	25.1377i	−4.02564	−	1.59625i
$249$	5.25277	+	1.12588i	0.332881	+	0.0713498i
$250$	1.78915	−	3.20858i	0.113156	−	0.202929i
$251$	−1.96092	+	6.54430i	−0.123772	+	0.413073i	−0.997277	−	0.0737430i	$-0.976506\pi$
$251$	−1.96092	+	6.54430i	−0.123772	+	0.413073i	0.873505	+	0.486816i	$0.161842\pi$
$252$	−21.9529	−	12.7057i	−1.38290	−	0.800387i
$253$	−0.669200	−	16.0814i	−0.0420722	−	1.01103i
$254$	−45.1832	+	3.18534i	−2.83504	+	0.199866i
$255$	−23.6792	+	29.1968i	−1.48285	+	1.82838i
$256$	−71.7220	+	44.6327i	−4.48262	+	2.78955i
$257$	7.27297	−	5.05991i	0.453675	−	0.315628i	−0.322023	−	0.946732i	$-0.604363\pi$
$257$	7.27297	−	5.05991i	0.453675	−	0.315628i	0.775699	+	0.631103i	$0.217398\pi$
$258$	77.5963	+	16.1134i	4.83094	+	1.00318i
$259$	0.133505	−	0.723992i	0.00829561	−	0.0449867i
$260$	−82.2253	−	46.8901i	−5.09940	−	2.90800i
$261$	−32.9116	−	1.89732i	−2.03717	−	0.117441i
$262$	23.2348	−	22.7202i	1.43545	−	1.40366i
$263$	−2.98946	−	12.2192i	−0.184338	−	0.753471i	−0.987488	−	0.157695i	$-0.949594\pi$
$263$	−2.98946	−	12.2192i	−0.184338	−	0.753471i	0.803150	−	0.595777i	$-0.203156\pi$
$264$	−148.936	+	3.81263i	−9.16640	+	0.234651i
$265$	−2.73150	−	17.2818i	−0.167795	−	1.06161i
$266$	−2.15503	−	12.5878i	−0.132133	−	0.771806i
$267$	1.82185	+	3.52801i	0.111495	+	0.215910i
$268$	59.4410	−	3.80844i	3.63094	−	0.232638i
$269$	6.66597	+	7.50569i	0.406431	+	0.457630i	0.915037	−	0.403369i	$-0.132161\pi$
$269$	6.66597	+	7.50569i	0.406431	+	0.457630i	−0.508606	+	0.860999i	$0.669839\pi$
$270$	9.71437	−	8.13956i	0.591198	−	0.495358i
$271$	−9.67609	+	0.185756i	−0.587780	+	0.0112839i	−0.312236	−	0.950005i	$-0.601078\pi$
$271$	−9.67609	+	0.185756i	−0.587780	+	0.0112839i	−0.275544	+	0.961288i	$0.588858\pi$
$272$	52.3179	+	62.8475i	3.17224	+	3.81069i
$273$	−16.5993	−	3.78069i	−1.00463	−	0.228818i
$274$	42.6024	−	8.27950i	2.57371	−	0.500183i
$275$	8.47915	+	24.2854i	0.511312	+	1.46447i
$276$	36.4398	−	20.7803i	2.19342	−	1.25083i
$277$	11.8119	−	5.86223i	0.709709	−	0.352227i	−0.0533322	−	0.998577i	$-0.516984\pi$
$277$	11.8119	−	5.86223i	0.709709	−	0.352227i	0.763041	+	0.646350i	$0.223705\pi$
$278$	−13.4044	−	13.9738i	−0.803940	−	0.838091i
$279$	9.88103	−	21.4381i	0.591562	−	1.28347i
$280$	36.3739	+	15.7874i	2.17376	+	0.943478i
$281$	2.89093	+	6.37928i	0.172458	+	0.380556i	0.976969	−	0.213382i	$-0.0684480\pi$
$281$	2.89093	+	6.37928i	0.172458	+	0.380556i	−0.804510	+	0.593938i	$0.797572\pi$
$282$	−19.4008	−	11.7314i	−1.15530	−	0.698597i
$283$	−13.9721	−	11.1111i	−0.830557	−	0.660486i	0.112303	−	0.993674i	$-0.464177\pi$
$283$	−13.9721	−	11.1111i	−0.830557	−	0.660486i	−0.942861	+	0.333187i	$0.891876\pi$
$284$	15.2759	−	0.586731i	0.906456	−	0.0348161i
$285$	28.9209	+	5.23744i	1.71313	+	0.310239i
$286$	−79.2073	+	26.8048i	−4.68362	+	1.58500i
$287$	1.30705	−	2.30916i	0.0771529	−	0.136305i
$288$	−46.9625	−	85.5023i	−2.76729	−	5.03827i
$289$	3.67253	−	4.03010i	0.216031	−	0.237065i
$290$	79.1280	−	4.56165i	4.64656	−	0.267869i
$291$	−24.7302	−	12.2735i	−1.44971	−	0.719487i
$292$	−8.17766	−	26.0735i	−0.478562	−	1.52584i
$293$	0.649919	−	0.170066i	0.0379687	−	0.00993537i	−0.234116	−	0.972209i	$-0.575220\pi$
$293$	0.649919	−	0.170066i	0.0379687	−	0.00993537i	0.272085	+	0.962273i	$0.412287\pi$
$294$	−38.6389	−	4.46984i	−2.25347	−	0.260686i
$295$	19.4558	−	24.9534i	1.13276	−	1.45284i
$296$	4.06916	−	4.58176i	0.236515	−	0.266309i
$297$	0.238793	−	8.29126i	0.0138562	−	0.481108i
$298$	−15.2342	−	1.07399i	−0.882494	−	0.0622144i
$299$	10.4553	−	11.1824i	0.604645	−	0.646695i
$300$	−46.0987	+	48.6766i	−2.66151	+	2.81034i
$301$	−13.5165	+	2.80681i	−0.779080	+	0.161782i
$302$	−0.00338194	−	0.150993i	−0.000194609	−	0.00868867i
$303$	0.869668	+	1.88685i	0.0499611	+	0.108397i
$304$	23.3762	−	59.5082i	1.34071	−	3.41303i
$305$	−18.2922	+	5.29027i	−1.04741	+	0.302920i
$306$	−37.7518	+	28.0982i	−2.15813	+	1.60627i
$307$	19.6710	−	19.4831i	1.12268	−	1.11196i	0.129963	−	0.991519i	$-0.458514\pi$
$307$	19.6710	−	19.4831i	1.12268	−	1.11196i	0.992720	−	0.120441i	$-0.0384310\pi$
$308$	36.1941	−	16.8228i	2.06235	−	0.958567i
$309$	−3.61040	−	4.39391i	−0.205389	−	0.249961i
$310$	−17.6761	+	53.9314i	−1.00394	+	3.06310i
$311$	−15.3415	+	10.2420i	−0.869936	+	0.580770i	−0.908218	−	0.418497i	$-0.862557\pi$
$311$	−15.3415	+	10.2420i	−0.869936	+	0.580770i	0.0382821	+	0.999267i	$0.487811\pi$
$312$	−101.948	−	98.4220i	−5.77166	−	5.57205i
$313$	−25.3297	−	5.09105i	−1.43172	−	0.287763i	−0.581221	−	0.813746i	$-0.697425\pi$
$313$	−25.3297	−	5.09105i	−1.43172	−	0.287763i	−0.850496	+	0.525982i	$0.823698\pi$
$314$	−11.2677	+	5.06285i	−0.635874	+	0.285713i
$315$	−6.14090	+	12.2746i	−0.346001	+	0.691598i
$316$	−4.78861	−	2.61026i	−0.269381	−	0.146839i
$317$	9.19562	−	4.63733i	0.516477	−	0.260458i	−0.172799	−	0.984957i	$-0.555281\pi$
$317$	9.19562	−	4.63733i	0.516477	−	0.260458i	0.689276	+	0.724499i	$0.257929\pi$
$318$	3.73199	−	40.1103i	0.209280	−	2.24927i
$319$	32.1572	−	40.7041i	1.80046	−	2.27899i
$320$	73.9599	+	104.161i	4.13448	+	5.82278i
$321$	−9.69154	+	11.0541i	−0.540929	+	0.616977i
$322$	−5.91407	+	7.89309i	−0.329578	+	0.439865i
$323$	−17.0648	−	4.11711i	−0.949511	−	0.229082i
$324$	−35.7895	+	17.1950i	−1.98830	+	0.955279i
$325$	−10.8065	+	21.9502i	−0.599434	+	1.21758i
$326$	−1.13858	+	15.4458i	−0.0630599	+	0.855465i
$327$	2.78638	+	14.5865i	0.154087	+	0.806633i
$328$	19.2553	−	10.8179i	1.06320	−	0.597319i
$329$	3.91364	+	0.529046i	0.215766	+	0.0291672i
$330$	10.6963	+	123.523i	0.588812	+	6.79974i
$331$	3.13127	+	1.31171i	0.172110	+	0.0720981i	0.470745	−	0.882269i	$-0.343985\pi$
$331$	3.13127	+	1.31171i	0.172110	+	0.0720981i	−0.298634	+	0.954368i	$0.596531\pi$
$332$	−11.2711	−	4.05704i	−0.618583	−	0.222659i
$333$	1.50700	+	1.49261i	0.0825832	+	0.0817944i
$334$	49.3259	+	6.98953i	2.69899	+	0.382450i
$335$	−4.01085	−	31.9795i	−0.219136	−	1.74723i
$336$	43.4111	+	33.6242i	2.36827	+	1.83435i
$337$	−11.4349	+	18.2448i	−0.622898	+	0.993856i	0.374870	+	0.927078i	$0.377687\pi$
$337$	−11.4349	+	18.2448i	−0.622898	+	0.993856i	−0.997768	+	0.0667783i	$0.978728\pi$
$338$	−38.7678	−	19.5505i	−2.10869	−	1.06341i
$339$	−5.63475	−	8.15476i	−0.306038	−	0.442906i
$340$	61.0474	−	57.4450i	3.31076	−	3.11539i
$341$	18.7094	+	32.0888i	1.01317	+	1.73771i
$342$	33.4649	+	15.2947i	1.80958	+	0.827042i
$343$	14.7965	−	4.48524i	0.798936	−	0.242180i
$344$	−108.363	−	38.2239i	−5.84254	−	2.06089i
$345$	−12.4214	−	18.9985i	−0.668748	−	1.02284i
$346$	1.68878	−	12.1987i	0.0907893	−	0.655807i
$347$	15.9089	+	7.02625i	0.854034	+	0.377189i	0.784304	−	0.620377i	$-0.213020\pi$
$347$	15.9089	+	7.02625i	0.854034	+	0.377189i	0.0697302	+	0.997566i	$0.477786\pi$
$348$	132.714	+	25.7921i	7.11422	+	1.38260i
$349$	1.51313	+	10.4378i	0.0809961	+	0.558725i	0.989905	+	0.141731i	$0.0452667\pi$
$349$	1.51313	+	10.4378i	0.0809961	+	0.558725i	−0.908909	+	0.416994i	$0.863084\pi$
$350$	5.38588	−	14.8140i	0.287887	−	0.791840i
$351$	5.78004	−	5.36966i	0.308516	−	0.286611i
$352$	152.594	+	16.6637i	8.13327	+	0.888178i
$353$	−22.0759	−	22.1466i	−1.17498	−	1.17875i	−0.980223	−	0.197896i	$-0.936589\pi$
$353$	−22.0759	−	22.1466i	−1.17498	−	1.17875i	−0.194759	−	0.980851i	$-0.562392\pi$
$354$	57.5957	−	44.6109i	3.06118	−	2.37104i
$355$	−0.819029	−	8.23137i	−0.0434696	−	0.436876i
$356$	−2.97199	−	8.34032i	−0.157515	−	0.442036i
$357$	7.51039	−	13.0727i	0.397492	−	0.691880i
$358$	12.5453	−	12.9119i	0.663042	−	0.682413i
$359$	−27.2945	+	14.2055i	−1.44055	+	0.749739i	−0.989740	−	0.142881i	$-0.954363\pi$
$359$	−27.2945	+	14.2055i	−1.44055	+	0.749739i	−0.450809	+	0.892621i	$0.648864\pi$
$360$	−96.6068	+	60.9796i	−5.09162	+	3.21390i
$361$	−1.38430	−	5.09020i	−0.0728578	−	0.267905i
$362$	45.9420	−	6.51002i	2.41466	−	0.342159i
$363$	42.4686	+	31.6089i	2.22902	+	1.65904i
$364$	35.5513	+	13.3130i	1.86339	+	0.697789i
$365$	−13.8138	+	5.27390i	−0.723046	+	0.276048i
$366$	−43.8195	+	1.40234i	−2.29048	+	0.0733016i
$367$	−1.64916	−	14.6668i	−0.0860854	−	0.765602i	−0.960091	−	0.279686i	$-0.909770\pi$
$367$	−1.64916	−	14.6668i	−0.0860854	−	0.765602i	0.874006	−	0.485915i	$-0.161514\pi$
$368$	−45.7825	+	18.4935i	−2.38658	+	0.964043i
$369$	3.37662	+	6.85864i	0.175780	+	0.357046i
$370$	−4.01161	−	3.14848i	−0.208554	−	0.163682i
$371$	2.18545	+	6.66800i	0.113463	+	0.346185i
$372$	−51.9355	+	81.6986i	−2.69273	+	4.23587i
$373$	−0.161075	+	3.87076i	−0.00834014	+	0.200420i	0.989927	+	0.141578i	$0.0452175\pi$
$373$	−0.161075	+	3.87076i	−0.00834014	+	0.200420i	−0.998267	+	0.0588424i	$0.981259\pi$
$374$	−2.13187	−	74.0218i	−0.110236	−	3.82757i
$375$	−2.59907	−	2.17773i	−0.134215	−	0.112458i
$376$	25.5970	+	20.6243i	1.32007	+	1.06362i
$377$	49.0475	−	5.35614i	2.52608	−	0.275855i
$378$	−3.32632	+	3.84329i	−0.171087	+	0.197678i
$379$	31.5059	+	9.77088i	1.61835	+	0.501896i	0.966547	−	0.256491i	$-0.0825663\pi$
$379$	31.5059	+	9.77088i	1.61835	+	0.501896i	0.651804	+	0.758387i	$0.274012\pi$
$380$	−62.3441	−	20.2127i	−3.19819	−	1.03689i
$381$	−4.93720	+	41.5151i	−0.252940	+	2.12688i
$382$	−26.8115	+	25.5548i	−1.37179	+	1.30750i
$383$	−7.02148	−	13.1806i	−0.358781	−	0.673497i	0.636421	−	0.771342i	$-0.280414\pi$
$383$	−7.02148	−	13.1806i	−0.358781	−	0.673497i	−0.995202	+	0.0978447i	$0.968805\pi$
$384$	55.4568	+	143.873i	2.83002	+	7.34201i
$385$	−10.2759	−	18.9958i	−0.523708	−	0.968116i
$386$	44.9149	−	23.7426i	2.28611	−	1.20847i
$387$	15.2500	−	36.7336i	0.775201	−	1.86728i
$388$	50.9818	+	34.5091i	2.58821	+	1.75193i
$389$	18.6529	+	6.84923i	0.945740	+	0.347270i	0.770633	−	0.637279i	$-0.219940\pi$
$389$	18.6529	+	6.84923i	0.945740	+	0.347270i	0.175107	+	0.984549i	$0.443973\pi$
$390$	−76.6017	+	89.6600i	−3.87888	+	4.54011i
$391$	6.75355	+	11.7553i	0.341542	+	0.594492i
$392$	54.6493	+	13.9273i	2.76021	+	0.703433i
$393$	−16.5744	−	24.9996i	−0.836067	−	1.26107i
$394$	−2.07511	+	34.0969i	−0.104543	+	1.71778i
$395$	−1.25243	+	2.67218i	−0.0630164	+	0.134452i
$396$	−18.6788	+	113.465i	−0.938647	+	5.70185i
$397$	−1.36541	+	20.2933i	−0.0685280	+	1.01849i	0.823735	+	0.566974i	$0.191886\pi$
$397$	−1.36541	+	20.2933i	−0.0685280	+	1.01849i	−0.892264	+	0.451515i	$0.850884\pi$
$398$	−28.7726	−	35.9447i	−1.44224	−	1.80175i
$399$	−11.7854	−	0.226249i	−0.590007	−	0.0113266i
$400$	61.4481	−	49.5106i	3.07240	−	2.47553i
$401$	−8.03677	+	8.06252i	−0.401337	+	0.402623i	−0.879692	−	0.475543i	$-0.842251\pi$
$401$	−8.03677	+	8.06252i	−0.401337	+	0.402623i	0.478355	+	0.878166i	$0.341233\pi$
$402$	9.23459	−	73.6297i	0.460579	−	3.67231i
$403$	−9.27128	+	34.0914i	−0.461836	+	1.69821i
$404$	−1.35814	−	4.42931i	−0.0675698	−	0.220366i
$405$	10.4636	+	18.7651i	0.519942	+	0.932443i
$406$	−31.0382	+	6.86076i	−1.54040	+	0.340494i
$407$	−3.28419	+	0.594752i	−0.162791	+	0.0294808i
$408$	109.798	−	60.7653i	5.43583	−	3.00833i
$409$	−20.3703	−	22.6430i	−1.00725	−	1.11962i	−0.992807	−	0.119727i	$-0.961798\pi$
$409$	−20.3703	−	22.6430i	−1.00725	−	1.11962i	−0.0144411	−	0.999896i	$-0.504597\pi$
$410$	−9.95947	−	15.4478i	−0.491863	−	0.762913i
$411$	−0.128152	−	40.0576i	−0.00632126	−	1.97589i
$412$	6.66564	+	10.7880i	0.328393	+	0.531489i
$413$	−6.10923	+	11.1228i	−0.300616	+	0.547315i
$414$	−9.19503	−	26.8873i	−0.451911	−	1.32144i
$415$	−1.82076	+	6.22101i	−0.0893775	+	0.305377i
$416$	90.5068	+	114.562i	4.43746	+	5.61687i
$417$	−14.9902	+	9.73245i	−0.734071	+	0.476600i
$418$	−49.9235	+	29.3224i	−2.44184	+	1.43421i
$419$	−11.8441	+	10.0537i	−0.578620	+	0.491155i	−0.888037	−	0.459772i	$-0.847931\pi$
$419$	−11.8441	+	10.0537i	−0.578620	+	0.491155i	0.309417	+	0.950926i	$0.399866\pi$
$420$	31.7009	−	46.5119i	1.54684	−	2.26955i
$421$	26.3377	−	2.70574i	1.28362	−	0.131870i	0.563730	−	0.825959i	$-0.309366\pi$
$421$	26.3377	−	2.70574i	1.28362	−	0.131870i	0.719889	+	0.694089i	$0.244193\pi$
$422$	−23.8070	−	3.84096i	−1.15891	−	0.186975i
$423$	−7.60988	+	8.45888i	−0.370005	+	0.411285i
$424$	−13.1529	+	56.9068i	−0.638761	+	2.76364i
$425$	−15.7792	−	14.8481i	−0.765404	−	0.720238i
$426$	2.85293	−	18.8306i	0.138225	−	0.912346i
$427$	6.90460	−	3.26310i	0.334137	−	0.157912i
$428$	24.7182	−	21.5320i	1.19480	−	1.04079i
$429$	10.5840	+	76.4521i	0.510998	+	3.69114i
$430$	−26.2730	+	91.9456i	−1.26700	+	4.43401i
$431$	4.59950	+	23.2691i	0.221550	+	1.12083i	0.915965	+	0.401258i	$0.131427\pi$
$431$	4.59950	+	23.2691i	0.221550	+	1.12083i	−0.694415	+	0.719575i	$0.744337\pi$
$432$	−24.2058	+	7.84782i	−1.16460	+	0.377578i
$433$	−17.8877	+	0.228916i	−0.859628	+	0.0110010i	−0.441368	−	0.897326i	$-0.645507\pi$
$433$	−17.8877	+	0.228916i	−0.859628	+	0.0110010i	−0.418260	+	0.908327i	$0.637360\pi$
$434$	3.55351	−	22.4825i	0.170574	−	1.07920i
$435$	9.56817	−	72.5281i	0.458759	−	3.47745i
$436$	−1.80006	−	33.0651i	−0.0862071	−	1.58353i
$437$	5.51373	−	9.05276i	0.263758	−	0.433052i
$438$	−33.8184	+	3.91220i	−1.61591	+	0.186932i
$439$	18.8372	−	7.33020i	0.899050	−	0.349852i	0.131858	−	0.991269i	$-0.457906\pi$
$439$	18.8372	−	7.33020i	0.899050	−	0.349852i	0.767192	+	0.641417i	$0.221653\pi$
$440$	8.62327	−	179.560i	0.411098	−	8.56017i
$441$	−5.84185	+	18.6261i	−0.278183	+	0.886955i
$442$	48.7578	−	50.8290i	2.31917	−	2.41769i
$443$	−1.84701	−	4.70190i	−0.0877542	−	0.223394i	0.880159	−	0.474679i	$-0.157436\pi$
$443$	−1.84701	−	4.70190i	−0.0877542	−	0.223394i	−0.967913	+	0.251285i	$0.919147\pi$
$444$	−5.30461	−	6.89406i	−0.251746	−	0.327178i
$445$	−4.40700	+	1.87936i	−0.208912	+	0.0890901i
$446$	−26.9427	−	38.4636i	−1.27577	−	1.82131i
$447$	−3.61202	+	13.6254i	−0.170843	+	0.644462i
$448$	−35.9371	−	36.5166i	−1.69787	−	1.72525i
$449$	36.3305	−	5.62320i	1.71454	−	0.265375i	0.781178	−	0.624308i	$-0.214619\pi$
$449$	36.3305	−	5.62320i	1.71454	−	0.265375i	0.933363	+	0.358933i	$0.116859\pi$
$450$	26.5288	+	36.8598i	1.25058	+	1.73759i
$451$	−11.8879	−	1.84000i	−0.559779	−	0.0866420i
$452$	10.0156	+	19.7034i	0.471093	+	0.926770i
$453$	−0.137477	−	0.0230837i	−0.00645924	−	0.00108456i
$454$	33.4359	−	7.16666i	1.56922	−	0.336348i
$455$	6.02188	−	19.6392i	0.282310	−	0.920701i
$456$	−82.9692	−	52.3713i	−3.88539	−	2.45251i
$457$	15.3452	+	1.27934i	0.717816	+	0.0598450i	0.436415	−	0.899745i	$-0.356248\pi$
$457$	15.3452	+	1.27934i	0.717816	+	0.0598450i	0.281401	+	0.959590i	$0.409201\pi$
$458$	27.8503	+	16.5983i	1.30136	+	0.775590i
$459$	3.04579	+	6.28785i	0.142165	+	0.293492i
$460$	21.7734	+	45.6929i	1.01519	+	2.13044i
$461$	−12.6275	+	31.5510i	−0.588124	+	1.46947i	0.273472	+	0.961880i	$0.411828\pi$
$461$	−12.6275	+	31.5510i	−0.588124	+	1.46947i	−0.861596	+	0.507595i	$0.830535\pi$
$462$	−12.1256	−	48.2241i	−0.564135	−	2.24359i
$463$	8.30159	−	7.42046i	0.385808	−	0.344858i	−0.450835	−	0.892607i	$-0.648874\pi$
$463$	8.30159	−	7.42046i	0.385808	−	0.344858i	0.836642	+	0.547749i	$0.184515\pi$
$464$	−150.739	−	51.0123i	−6.99790	−	2.36819i
$465$	45.8334	+	25.3654i	2.12547	+	1.17629i
$466$	4.09297	+	17.7085i	0.189603	+	0.820331i
$467$	−7.87025	+	13.4984i	−0.364192	+	0.624631i	−0.987550	−	0.157306i	$-0.949719\pi$
$467$	−7.87025	+	13.4984i	−0.364192	+	0.624631i	0.623358	+	0.781937i	$0.285768\pi$
$468$	−89.3810	+	63.0361i	−4.13164	+	2.91385i
$469$	3.63087	+	12.4056i	0.167658	+	0.572839i
$470$	15.8379	−	22.3052i	0.730546	−	1.02886i
$471$	2.63862	+	11.0922i	0.121581	+	0.511102i
$472$	−91.4201	+	52.9115i	−4.20795	+	2.43545i
$473$	33.5755	+	52.8169i	1.54380	+	2.42852i
$474$	−4.31364	+	5.24976i	−0.198132	+	0.241130i
$475$	−4.23594	+	16.4020i	−0.194358	+	0.752576i
$476$	−20.5013	+	26.6442i	−0.939676	+	1.22124i
$477$	−19.4209	−	5.61669i	−0.889221	−	0.257171i
$478$	23.6983	−	8.87436i	1.08394	−	0.405904i
$479$	−12.2564	+	10.8153i	−0.560011	+	0.494162i	−0.893788	−	0.448490i	$-0.851962\pi$
$479$	−12.2564	+	10.8153i	−0.560011	+	0.494162i	0.333777	+	0.942652i	$0.391677\pi$
$480$	196.889	−	89.9855i	8.98672	−	4.10726i
$481$	−2.59424	−	1.82960i	−0.118287	−	0.0834224i
$482$	−18.0469	+	52.7713i	−0.822014	+	2.40367i
$483$	6.13171	+	6.72871i	0.279002	+	0.306167i
$484$	−84.4040	−	82.5347i	−3.83655	−	3.75158i
$485$	16.9629	−	28.6701i	0.770246	−	1.30184i
$486$	15.8246	+	59.6945i	0.717820	+	2.70780i
$487$	−23.9280	+	28.3726i	−1.08428	+	1.28569i	−0.128468	+	0.991714i	$0.541006\pi$
$487$	−23.9280	+	28.3726i	−1.08428	+	1.28569i	−0.955814	+	0.293973i	$0.905022\pi$
$488$	63.2335	+	6.49616i	2.86245	+	0.294067i
$489$	13.8061	+	3.70723i	0.624334	+	0.167647i
$490$	8.80614	−	46.0993i	0.397821	−	2.08255i
$491$	5.91571	+	17.6666i	0.266972	+	0.797284i	0.993872	+	0.110540i	$0.0352580\pi$
$491$	5.91571	+	17.6666i	0.266972	+	0.797284i	−0.726899	+	0.686744i	$0.759039\pi$
$492$	−9.95495	−	29.7294i	−0.448804	−	1.34030i
$493$	−8.19841	+	42.9179i	−0.369238	+	1.93292i
$494$	−53.1846	−	14.2812i	−2.39289	−	0.642540i
$495$	61.8978	+	6.35894i	2.78210	+	0.285813i
$496$	73.4635	−	87.1093i	3.29861	−	3.91132i
$497$	0.850097	+	3.20678i	0.0381321	+	0.143844i
$498$	−7.59946	+	12.8444i	−0.340540	+	0.575570i
$499$	−9.71930	−	9.50404i	−0.435095	−	0.425459i	0.448448	−	0.893809i	$-0.351977\pi$
$499$	−9.71930	−	9.50404i	−0.435095	−	0.425459i	−0.883543	+	0.468350i	$0.844849\pi$
$500$	5.09284	+	5.58869i	0.227759	+	0.249934i
$501$	14.8793	−	43.5087i	0.664757	−	1.94383i
$502$	−15.5101	−	10.9385i	−0.692249	−	0.488210i
$503$	22.4029	−	10.2389i	0.998897	−	0.456532i	0.152052	−	0.988372i	$-0.451412\pi$
$503$	22.4029	−	10.2389i	0.998897	−	0.456532i	0.846845	+	0.531840i	$0.178499\pi$
$504$	34.3548	−	30.3152i	1.53028	−	1.35035i
$505$	−2.34767	+	0.879139i	−0.104470	+	0.0391212i
$506$	42.9540	+	12.4227i	1.90954	+	0.552255i
$507$	−24.4387	+	31.7613i	−1.08536	+	1.41057i
$508$	23.3114	−	90.2641i	1.03427	−	4.00482i
$509$	−22.5888	+	27.4908i	−1.00123	+	1.21851i	−0.0254672	+	0.999676i	$0.508107\pi$
$509$	−22.5888	+	27.4908i	−1.00123	+	1.21851i	−0.975762	+	0.218834i	$0.929775\pi$
$510$	−56.0263	−	88.1337i	−2.48089	−	3.90262i
$511$	5.13248	−	2.97054i	0.227048	−	0.131409i
$512$	−26.4784	−	111.309i	−1.17019	−	4.91923i
$513$	3.16254	−	4.45395i	0.139630	−	0.196647i
$514$	6.91389	+	23.6228i	0.304959	+	1.04196i
$515$	5.60763	−	3.95479i	0.247102	−	0.174269i
$516$	−82.1588	+	140.912i	−3.61684	+	6.20329i
$517$	−4.03190	−	17.4443i	−0.177323	−	0.767198i
$518$	1.78947	+	0.990338i	0.0786246	+	0.0435129i
$519$	−10.7670	−	3.64369i	−0.472618	−	0.159940i
$520$	127.478	−	113.948i	5.59030	−	4.99695i
$521$	9.21168	+	36.6352i	0.403571	+	1.60502i	0.746318	+	0.665589i	$0.231820\pi$
$521$	9.21168	+	36.6352i	0.403571	+	1.60502i	−0.342747	+	0.939428i	$0.611357\pi$
$522$	34.0298	−	85.0262i	1.48944	−	3.72150i
$523$	−8.79571	−	18.4583i	−0.384610	−	0.807126i	−0.999824	−	0.0187661i	$-0.994026\pi$
$523$	−8.79571	−	18.4583i	−0.384610	−	0.807126i	0.615214	−	0.788360i	$-0.289070\pi$
$524$	29.1579	+	60.1947i	1.27377	+	2.62962i
$525$	−12.4977	−	7.44844i	−0.545444	−	0.325076i
$526$	34.8265	+	2.90352i	1.51851	+	0.126600i
$527$	−26.4575	−	16.7003i	−1.15250	−	0.727477i
$528$	72.9772	−	238.002i	3.17593	−	10.3577i
$529$	14.4849	−	3.10470i	0.629778	−	0.134987i
$530$	47.9354	+	8.04879i	2.08218	+	0.349617i
$531$	−16.5673	−	32.5925i	−0.718961	−	1.41439i
$532$	25.9755	+	4.02046i	1.12618	+	0.174309i
$533$	−6.68368	−	9.28648i	−0.289502	−	0.402242i
$534$	−10.9010	+	1.68725i	−0.471732	+	0.0730143i
$535$	−12.4421	−	12.6428i	−0.537921	−	0.546595i
$536$	−27.5697	+	104.000i	−1.19083	+	4.49210i
$537$	−9.53332	−	13.6098i	−0.411393	−	0.587308i
$538$	−25.6526	+	10.9395i	−1.10596	+	0.471635i
$539$	−18.7317	−	24.3443i	−0.806830	−	1.04858i
$540$	9.53717	+	24.2786i	0.410415	+	1.04478i
$541$	7.28304	−	7.59241i	0.313122	−	0.326423i	−0.546397	−	0.837526i	$-0.684001\pi$
$541$	7.28304	−	7.59241i	0.313122	−	0.326423i	0.859520	+	0.511103i	$0.170763\pi$
$542$	8.04604	−	25.6538i	0.345607	−	1.10193i
$543$	2.05443	−	42.7788i	0.0881641	−	1.83581i
$544$	−120.494	+	46.8882i	−5.16612	+	2.01032i
$545$	−17.7997	+	2.05911i	−0.762454	+	0.0882024i
$546$	24.6020	−	40.3929i	1.05287	−	1.72866i
$547$	−0.0204301	−	0.375279i	−0.000873527	−	0.0160458i	0.998052	−	0.0623803i	$-0.0198692\pi$
$547$	−0.0204301	−	0.375279i	−0.000873527	−	0.0160458i	−0.998926	+	0.0463346i	$0.985246\pi$
$548$	−11.6827	+	88.5565i	−0.499060	+	3.78295i
$549$	−3.43501	+	21.7328i	−0.146603	+	0.927533i
$550$	−71.4553	+	0.914443i	−3.04687	+	0.0389920i
$551$	32.4968	−	10.5359i	1.38441	−	0.448843i
$552$	14.6936	+	74.3358i	0.625403	+	3.16394i
$553$	0.325183	−	1.13802i	0.0138282	−	0.0483934i
$554$	5.02362	+	36.2876i	0.213433	+	1.54171i
$555$	−3.54919	+	3.09169i	−0.150655	+	0.131235i
$556$	36.0321	−	17.0287i	1.52810	−	0.722178i
$557$	−2.73812	+	18.0728i	−0.116018	+	0.765770i	0.853561	+	0.520992i	$0.174438\pi$
$557$	−2.73812	+	18.0728i	−0.116018	+	0.765770i	−0.969579	+	0.244778i	$0.921285\pi$
$558$	47.7589	+	44.9407i	2.02180	+	1.90249i
$559$	−13.4051	+	57.9981i	−0.566976	+	2.45306i
$560$	−44.3121	+	49.2558i	−1.87253	+	2.08144i
$561$	−67.4779	−	10.8867i	−2.84892	−	0.459637i
$562$	−19.3552	+	1.98842i	−0.816452	+	0.0838764i
$563$	−20.9801	+	30.7823i	−0.884206	+	1.29732i	0.0698091	+	0.997560i	$0.477761\pi$
$563$	−20.9801	+	30.7823i	−0.884206	+	1.29732i	−0.954016	+	0.299757i	$0.903094\pi$
$564$	35.5747	−	30.1971i	1.49796	−	1.27153i
$565$	10.3128	−	6.05718i	0.433862	−	0.254828i
$566$	41.5953	−	27.0060i	1.74838	−	1.13515i
$567$	−5.34163	−	6.76135i	−0.224327	−	0.283950i
$568$	−7.75666	+	26.5023i	−0.325462	+	1.11201i
$569$	−2.64250	−	7.72698i	−0.110779	−	0.323932i	0.876844	−	0.480774i	$-0.159644\pi$
$569$	−2.64250	−	7.72698i	−0.110779	−	0.323932i	−0.987624	+	0.156843i	$0.949868\pi$
$570$	−39.3086	+	71.5671i	−1.64645	+	2.99762i
$571$	14.6411	+	23.6960i	0.612712	+	0.991648i	0.997637	+	0.0687002i	$0.0218852\pi$
$571$	14.6411	+	23.6960i	0.612712	+	0.991648i	−0.384925	+	0.922948i	$0.625773\pi$
$572$	−0.550592	−	172.104i	−0.0230214	−	7.19601i
$573$	18.5248	+	28.7332i	0.773884	+	1.20035i
$574$	4.93011	+	5.48014i	0.205779	+	0.228737i
$575$	11.4468	−	6.33494i	0.477363	−	0.264185i
$576$	145.249	−	26.3039i	6.05203	−	1.09600i
$577$	−5.65877	+	1.25083i	−0.235578	+	0.0520726i	−0.332045	−	0.943264i	$-0.607739\pi$
$577$	−5.65877	+	1.25083i	−0.235578	+	0.0520726i	0.0964673	+	0.995336i	$0.469246\pi$
$578$	7.37702	+	13.2296i	0.306844	+	0.550281i
$579$	−13.7466	−	44.8320i	−0.571289	−	1.86315i
$580$	−42.8089	+	157.413i	−1.77754	+	6.53620i
$581$	0.323511	−	2.57943i	0.0134215	−	0.107013i
$582$	54.1472	−	54.3208i	2.24448	−	2.25167i
$583$	24.7717	−	19.9593i	1.02594	−	0.826631i
$584$	49.3512	+	0.947416i	2.04217	+	0.0392044i
$585$	36.9845	+	46.2036i	1.52912	+	1.91028i
$586$	−0.125291	+	1.86212i	−0.00517571	+	0.0769234i
$587$	−0.674957	+	4.10006i	−0.0278585	+	0.169227i	−0.997014	−	0.0772231i	$-0.975395\pi$
$587$	−0.674957	+	4.10006i	−0.0278585	+	0.169227i	0.969155	+	0.246451i	$0.0792643\pi$
$588$	33.9749	−	72.4891i	1.40110	−	2.98940i
$589$	−1.48599	+	24.4168i	−0.0612292	+	1.00608i
$590$	48.5733	+	73.2645i	1.99973	+	3.01625i
$591$	30.5531	+	7.78639i	1.25679	+	0.320289i
$592$	5.10058	+	8.87813i	0.209632	+	0.364889i
$593$	1.22716	−	1.43636i	0.0503936	−	0.0589842i	−0.734533	−	0.678573i	$-0.762599\pi$
$593$	1.22716	−	1.43636i	0.0503936	−	0.0589842i	0.784927	+	0.619589i	$0.212701\pi$
$594$	21.6313	+	7.94287i	0.887542	+	0.325900i
$595$	15.0647	+	10.1972i	0.617593	+	0.418043i
$596$	12.0519	−	29.0302i	0.493666	−	1.18912i
$597$	−37.5707	+	19.8604i	−1.53767	+	0.812831i
$598$	20.2354	+	37.4068i	0.827486	+	1.52968i
$599$	0.727716	+	1.88794i	0.0297337	+	0.0771390i	0.947152	−	0.320785i	$-0.103947\pi$
$599$	0.727716	+	1.88794i	0.0297337	+	0.0771390i	−0.917418	+	0.397924i	$0.869731\pi$
$600$	−56.9367	−	106.881i	−2.32443	−	4.36339i
$601$	−30.6102	+	29.1754i	−1.24861	+	1.19009i	−0.275112	+	0.961412i	$0.588715\pi$
$601$	−30.6102	+	29.1754i	−1.24861	+	1.19009i	−0.973502	+	0.228677i	$0.926560\pi$
$602$	4.52903	−	38.0829i	0.184589	−	1.55214i
$603$	−35.4260	−	11.4856i	−1.44266	−	0.467728i
$604$	0.296898	+	0.0920765i	0.0120806	+	0.00374654i
$605$	−41.8034	+	48.3005i	−1.69955	+	1.96369i
$606$	−5.73774	+	0.626578i	−0.233080	+	0.0254530i
$607$	31.2863	+	25.2083i	1.26987	+	1.02317i	0.998150	+	0.0607987i	$0.0193648\pi$
$607$	31.2863	+	25.2083i	1.26987	+	1.02317i	0.271721	+	0.962376i	$0.412407\pi$
$608$	77.4851	+	64.9239i	3.14244	+	2.63301i
$609$	0.844654	+	29.3277i	0.0342271	+	1.18842i
$610$	2.19944	−	52.8542i	0.0890527	−	2.14000i
$611$	9.13576	−	14.3713i	0.369593	−	0.581399i
$612$	−30.1668	−	92.0417i	−1.21942	−	3.72056i
$613$	7.91688	+	6.21349i	0.319760	+	0.250960i	0.764391	−	0.644753i	$-0.223040\pi$
$613$	7.91688	+	6.21349i	0.319760	+	0.250960i	−0.444631	+	0.895714i	$0.646665\pi$
$614$	33.9729	+	69.0062i	1.37104	+	2.78486i
$615$	−15.7299	+	6.35400i	−0.634292	+	0.256218i
$616$	8.05588	+	71.6450i	0.324580	+	2.88666i
$617$	−15.2357	+	0.487583i	−0.613366	+	0.0196294i	−0.337126	−	0.941459i	$-0.609455\pi$
$617$	−15.2357	+	0.487583i	−0.613366	+	0.0196294i	−0.276240	+	0.961089i	$0.589088\pi$
$618$	14.7598	−	5.63507i	0.593725	−	0.226676i
$619$	−20.6849	−	7.74593i	−0.831397	−	0.311335i	−0.101452	−	0.994840i	$-0.532349\pi$
$619$	−20.6849	−	7.74593i	−0.831397	−	0.311335i	−0.729946	+	0.683505i	$0.760455\pi$
$620$	−93.7045	−	69.7431i	−3.76326	−	2.80095i
$621$	−4.17697	+	0.591881i	−0.167616	+	0.0237514i
$622$	−13.4479	−	49.4491i	−0.539210	−	1.98273i
$623$	1.62484	−	1.02562i	0.0650978	−	0.0410907i
$624$	210.031	−	109.311i	8.40796	−	4.37596i
$625$	18.7833	−	19.3320i	0.751330	−	0.773281i
$626$	35.7551	−	62.2358i	1.42906	−	2.48744i
$627$	17.9379	+	50.3393i	0.716371	+	2.01036i
$628$	−2.51732	−	25.2995i	−0.100452	−	1.00956i
$629$	2.22257	−	1.72150i	0.0886198	−	0.0686407i
$630$	−26.9185	−	27.0047i	−1.07246	−	1.07589i
$631$	−36.3802	−	3.97283i	−1.44827	−	0.158156i	−0.649762	−	0.760137i	$-0.725132\pi$
$631$	−36.3802	−	3.97283i	−1.44827	−	0.158156i	−0.798510	+	0.601982i	$0.794378\pi$
$632$	7.21764	−	6.70518i	0.287102	−	0.266718i
$633$	−7.60527	+	20.9184i	−0.302282	+	0.831434i
$634$	4.10470	+	28.3149i	0.163018	+	1.12453i
$635$	−49.5189	−	9.62367i	−1.96510	−	0.381904i
$636$	75.8430	+	33.4965i	3.00737	+	1.32822i
$637$	4.00640	−	28.9398i	0.158739	−	1.14664i
$638$	78.8618	+	120.618i	3.12217	+	4.77532i
$639$	−9.01387	−	3.17954i	−0.356583	−	0.125781i
$640$	−178.048	+	53.9714i	−7.03797	+	2.13341i
$641$	10.8997	+	4.98157i	0.430513	+	0.196760i	0.619126	−	0.785291i	$-0.287487\pi$
$641$	10.8997	+	4.98157i	0.430513	+	0.196760i	−0.188613	+	0.982051i	$0.560399\pi$
$642$	−20.5710	−	35.2816i	−0.811873	−	1.39245i
$643$	−10.6996	+	10.0682i	−0.421950	+	0.397051i	−0.866882	−	0.498513i	$-0.833879\pi$
$643$	−10.6996	+	10.0682i	−0.421950	+	0.397051i	0.444932	+	0.895564i	$0.353228\pi$
$644$	−11.5397	−	16.7006i	−0.454729	−	0.658095i
$645$	78.8085	+	39.7430i	3.10308	+	1.56488i
$646$	25.8989	−	41.3226i	1.01898	−	1.62581i
$647$	23.8807	+	18.4969i	0.938847	+	0.727186i	0.962144	−	0.272542i	$-0.0878645\pi$
$647$	23.8807	+	18.4969i	0.938847	+	0.727186i	−0.0232972	+	0.999729i	$0.507416\pi$
$648$	−8.92554	−	71.1655i	−0.350628	−	2.79565i
$649$	56.9625	+	8.07164i	2.23597	+	0.316839i
$650$	−48.2915	−	47.8302i	−1.89415	−	1.87606i
$651$	−19.7674	−	7.11528i	−0.774747	−	0.278870i
$652$	−29.4010	−	12.3163i	−1.15143	−	0.482343i
$653$	1.57696	+	18.2112i	0.0617113	+	0.712658i	0.961225	+	0.275765i	$0.0889312\pi$
$653$	1.57696	+	18.2112i	0.0617113	+	0.712658i	−0.899514	+	0.436892i	$0.856079\pi$
$654$	−40.8834	−	5.52662i	−1.59867	−	0.216108i
$655$	31.5533	−	17.7271i	1.23289	−	0.692656i
$656$	6.92430	+	36.2480i	0.270348	+	1.41525i
$657$	−1.25603	+	17.0391i	−0.0490022	+	0.664760i
$658$	−4.84594	+	9.84313i	−0.188915	+	0.383725i
$659$	−18.5932	+	8.93308i	−0.724288	+	0.347984i	−0.758714	−	0.651424i	$-0.774172\pi$
$659$	−18.5932	+	8.93308i	−0.724288	+	0.347984i	0.0344260	+	0.999407i	$0.489040\pi$
$660$	−248.067	−	59.8494i	−9.65598	−	2.32963i
$661$	−8.71996	+	11.6379i	−0.339167	+	0.452662i	−0.937191	−	0.348816i	$-0.886584\pi$
$661$	−8.71996	+	11.6379i	−0.339167	+	0.452662i	0.598024	+	0.801478i	$0.295953\pi$
$662$	−6.21760	+	7.09172i	−0.241654	+	0.275628i
$663$	−37.6378	−	53.0071i	−1.46173	−	2.05862i
$664$	13.4139	−	16.9791i	0.520561	−	0.658918i
$665$	1.31766	−	14.1618i	0.0510966	−	0.549170i
$666$	−5.26136	+	2.65329i	−0.203874	+	0.102813i
$667$	−23.1652	−	12.6273i	−0.896959	−	0.488930i
$668$	−45.8767	+	91.6999i	−1.77502	+	3.54797i
$669$	−39.5375	+	17.7651i	−1.52861	+	0.686840i
$670$	87.7825	+	17.6436i	3.39134	+	0.681631i
$671$	−24.9085	−	24.0470i	−0.961583	−	0.928326i
$672$	−72.2074	+	48.2057i	−2.78546	+	1.85957i
$673$	3.50708	−	10.7004i	0.135188	−	0.412471i	−0.860019	−	0.510262i	$-0.829548\pi$
$673$	3.50708	−	10.7004i	0.135188	−	0.412471i	0.995207	+	0.0977911i	$0.0311777\pi$
$674$	−37.9759	−	46.2172i	−1.46278	−	1.78022i
$675$	6.11406	−	2.84178i	0.235330	−	0.109380i
$676$	63.4916	−	62.8852i	2.44199	−	2.41866i
$677$	13.1130	−	9.75982i	0.503972	−	0.375100i	−0.314856	−	0.949139i	$-0.601956\pi$
$677$	13.1130	−	9.75982i	0.503972	−	0.375100i	0.818828	+	0.574039i	$0.194624\pi$
$678$	26.4528	−	7.65039i	1.01591	−	0.293811i
$679$	−4.88480	+	12.4351i	−0.187461	+	0.477216i
$680$	63.3820	+	137.515i	2.43059	+	5.27347i
$681$	−0.706755	−	31.5544i	−0.0270829	−	1.20917i
$682$	−101.036	+	20.9809i	−3.86888	+	0.803400i
$683$	20.4778	−	21.6229i	0.783560	−	0.827377i	−0.204912	−	0.978780i	$-0.565691\pi$
$683$	20.4778	−	21.6229i	0.783560	−	0.827377i	0.988472	+	0.151403i	$0.0483792\pi$
$684$	−51.7201	+	55.3170i	−1.97757	+	2.11510i
$685$	48.2143	+	3.39903i	1.84217	+	0.129870i
$686$	−1.23656	+	42.9353i	−0.0472121	+	1.63928i
$687$	19.8714	−	22.3747i	0.758143	−	0.853648i
$688$	118.055	−	151.414i	4.50080	−	5.77259i
$689$	30.0571	+	3.47708i	1.14509	+	0.132466i
$690$	61.0053	−	15.9634i	2.32243	−	0.607717i
$691$	−11.0868	−	35.3491i	−0.421763	−	1.34474i	−0.887903	−	0.460030i	$-0.847838\pi$
$691$	−11.0868	−	35.3491i	−0.421763	−	1.34474i	0.466140	−	0.884711i	$-0.345644\pi$
$692$	22.7042	+	11.2680i	0.863083	+	0.428346i
$693$	−24.9138	+	1.43625i	−0.946397	+	0.0545588i
$694$	−32.5429	+	35.7113i	−1.23531	+	1.35558i
$695$	−10.3818	−	18.9016i	−0.393804	−	0.716978i
$696$	−120.299	+	212.530i	−4.55990	+	8.05593i
$697$	9.59780	−	3.24803i	0.363543	−	0.123028i
$698$	−28.8315	−	5.22125i	−1.09129	−	0.197627i
$699$	16.7635	−	0.643870i	0.634054	−	0.0243534i
$700$	25.3921	+	20.1927i	0.959732	+	0.763211i
$701$	−40.9056	−	24.7352i	−1.54498	−	0.934235i	−0.995087	−	0.0990021i	$-0.968435\pi$
$701$	−40.9056	−	24.7352i	−1.54498	−	0.934235i	−0.549897	−	0.835233i	$-0.685333\pi$
$702$	9.04680	+	19.9632i	0.341449	+	0.753461i
$703$	−2.01628	−	0.875129i	−0.0760456	−	0.0330061i
$704$	−97.2268	+	210.946i	−3.66437	+	7.95032i
$705$	−17.4791	−	18.2216i	−0.658303	−	0.686267i
$706$	77.8149	−	38.6194i	2.92860	−	1.45346i
$707$	0.873370	−	0.498050i	0.0328465	−	0.0187311i
$708$	49.4257	+	141.562i	1.85753	+	5.32021i
$709$	−25.9630	+	5.04574i	−0.975061	+	0.189497i	−0.653113	−	0.757260i	$-0.726537\pi$
$709$	−25.9630	+	5.04574i	−0.975061	+	0.189497i	−0.321948	+	0.946757i	$0.604338\pi$
$710$	22.4066	+	5.10339i	0.840905	+	0.191527i
$711$	2.18166	+	2.62075i	0.0818188	+	0.0982858i
$712$	15.9906	−	0.306978i	0.599273	−	0.0115045i
$713$	14.4807	−	12.1332i	0.542305	−	0.454391i
$714$	27.8127	+	31.3164i	1.04087	+	1.17199i
$715$	−92.9369	+	5.95456i	−3.47564	+	0.222688i
$716$	17.0010	+	32.9225i	0.635358	+	1.23037i
$717$	−3.94137	−	23.0220i	−0.147193	−	0.859772i
$718$	−13.3453	−	84.4335i	−0.498041	−	3.15103i
$719$	−30.6318	+	0.784143i	−1.14237	+	0.0292436i	−0.592188	−	0.805800i	$-0.701736\pi$
$719$	−30.6318	+	0.784143i	−1.14237	+	0.0292436i	−0.550184	+	0.835043i	$0.685442\pi$
$720$	−45.3630	−	185.419i	−1.69058	−	6.91016i
$721$	−1.96763	+	1.92406i	−0.0732785	+	0.0716556i
$722$	14.6304	+	0.843425i	0.544486	+	0.0313890i
$723$	44.7174	+	25.5007i	1.66306	+	0.948380i
$724$	−17.3186	+	93.9178i	−0.643641	+	3.49043i
$725$	41.2842	+	8.57297i	1.53326	+	0.318392i
$726$	−120.730	+	83.9937i	−4.48072	+	3.11730i
$727$	30.3533	−	18.8890i	1.12574	−	0.700552i	0.167320	−	0.985903i	$-0.446489\pi$
$727$	30.3533	−	18.8890i	1.12574	−	0.700552i	0.958423	+	0.285350i	$0.0921099\pi$
$728$	−43.1944	+	53.2593i	−1.60089	+	1.97392i
$729$	36.0789	−	2.54350i	1.33626	−	0.0942038i
$730$	−1.70790	−	41.0422i	−0.0632122	−	1.51904i
$731$	−45.6255	−	26.4068i	−1.68752	−	0.976691i
$732$	25.9000	−	86.4374i	0.957291	−	3.19482i
$733$	−19.2773	+	34.5711i	−0.712023	+	1.27691i	0.239966	+	0.970781i	$0.422864\pi$
$733$	−19.2773	+	34.5711i	−0.712023	+	1.27691i	−0.951989	+	0.306131i	$0.900965\pi$
$734$	40.0920	+	8.59333i	1.47982	+	0.317186i
$735$	−40.2689	−	15.9674i	−1.48534	−	0.588967i
$736$	−4.74257	−	77.9267i	−0.174813	−	2.87241i
$737$	46.7847	−	35.2887i	1.72334	−	1.29988i
$738$	−21.0465	+	2.84506i	−0.774731	+	0.104728i
$739$	−3.52875	−	15.7253i	−0.129807	−	0.578464i	−0.996785	−	0.0801176i	$-0.974470\pi$
$739$	−3.52875	−	15.7253i	−0.129807	−	0.578464i	0.866978	−	0.498346i	$-0.166059\pi$
$740$	8.76645	−	5.77174i	0.322261	−	0.212173i
$741$	−22.1582	+	45.7443i	−0.814001	+	1.68046i
$742$	−19.4935	−	0.124728i	−0.715629	−	0.00457891i
$743$	1.03705	+	1.10918i	0.0380458	+	0.0406917i	0.749196	−	0.662349i	$-0.230440\pi$
$743$	1.03705	+	1.10918i	0.0380458	+	0.0406917i	−0.711150	+	0.703041i	$0.751825\pi$
$744$	−110.152	−	135.819i	−4.03836	−	4.97935i
$745$	−16.0757	−	5.55512i	−0.588967	−	0.203524i
$746$	−10.0548	−	3.83876i	−0.368131	−	0.140547i
$747$	5.61600	+	4.95564i	0.205479	+	0.181317i
$748$	145.859	+	44.2140i	5.33313	+	1.61662i
$749$	5.73391	+	4.21094i	0.209512	+	0.153864i
$750$	8.02953	−	4.92580i	0.293197	−	0.179865i
$751$	−0.144756	+	45.2478i	−0.00528223	+	1.65111i	0.561669	+	0.827362i	$0.310160\pi$
$751$	−0.144756	+	45.2478i	−0.00528223	+	1.65111i	−0.566951	+	0.823752i	$0.691877\pi$
$752$	−46.2582	+	29.6144i	−1.68686	+	1.07993i
$753$	−12.6031	+	12.1672i	−0.459281	+	0.443396i
$754$	−29.1555	+	133.932i	−1.06178	+	4.87751i
$755$	0.0399722	−	0.163384i	0.00145474	−	0.00594617i
$756$	−5.32701	−	9.00353i	−0.193741	−	0.327455i
$757$	30.8329	−	31.3301i	1.12064	−	1.13871i	0.131566	−	0.991307i	$-0.458000\pi$
$757$	30.8329	−	31.3301i	1.12064	−	1.13871i	0.989076	−	0.147405i	$-0.0470921\pi$
$758$	−53.5314	+	74.3780i	−1.94435	+	2.70153i
$759$	18.7015	−	36.7910i	0.678821	−	1.33543i
$760$	70.3803	−	95.1948i	2.55296	−	3.45308i
$761$	17.1434	−	25.5020i	0.621446	−	0.924448i	−0.378553	−	0.925580i	$-0.623578\pi$
$761$	17.1434	−	25.5020i	0.621446	−	0.924448i	0.999999	+	0.00113206i	$0.000360345\pi$
$762$	−105.009	−	49.6271i	−3.80408	−	1.79780i
$763$	6.91599	−	1.95230i	0.250376	−	0.0706781i
$764$	−32.3525	−	69.0276i	−1.17047	−	2.49733i
$765$	−48.7211	+	19.3189i	−1.76151	+	0.698476i
$766$	40.9157	−	6.87012i	1.47835	−	0.248228i
$767$	32.5308	+	44.0005i	1.17462	+	1.58876i
$768$	−216.394	+	9.69843i	−7.80843	+	0.349962i
$769$	6.06715	+	3.56352i	0.218787	+	0.128504i	0.611752	−	0.791050i	$-0.290465\pi$
$769$	6.06715	+	3.56352i	0.218787	+	0.128504i	−0.392965	+	0.919553i	$0.628551\pi$
$770$	59.1057	−	10.3136i	2.13002	−	0.371678i

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)

\(f(q)\)	\(=\)	\(q+(-0.882111 + 2.63433i) q^{2} +(2.23553 + 1.25595i) q^{3} +(-4.56485 - 3.44317i) q^{4} +(-1.70964 + 2.57870i) q^{5} +(-5.28058 + 4.78124i) q^{6} +(0.512184 - 1.13021i) q^{7} +(8.51597 - 5.84418i) q^{8} +(1.85965 + 3.05328i) q^{9} +O(q^{10})\)	\(q+(-0.882111 + 2.63433i) q^{2} +(2.23553 + 1.25595i) q^{3} +(-4.56485 - 3.44317i) q^{4} +(-1.70964 + 2.57870i) q^{5} +(-5.28058 + 4.78124i) q^{6} +(0.512184 - 1.13021i) q^{7} +(8.51597 - 5.84418i) q^{8} +(1.85965 + 3.05328i) q^{9} +(-5.28506 - 6.77846i) q^{10} +(-5.61398 - 0.359694i) q^{11} +(-5.88041 - 13.4306i) q^{12} +(-3.50154 - 4.04575i) q^{13} +(2.52555 + 2.34623i) q^{14} +(-7.06070 + 3.61755i) q^{15} +(4.74153 + 16.5935i) q^{16} +(4.33448 - 1.91435i) q^{17} +(-9.68377 + 2.20560i) q^{18} +(-2.94335 - 2.24980i) q^{19} +(16.6832 - 5.88481i) q^{20} +(2.56450 - 1.88335i) q^{21} +(5.89971 - 14.4718i) q^{22} +(0.301498 + 2.84521i) q^{23} +(26.3777 - 2.36918i) q^{24} +(-1.78022 - 4.21182i) q^{25} +(13.7466 - 5.65542i) q^{26} +(0.0518778 + 1.47357i) q^{27} +(-6.22956 + 3.39572i) q^{28} +(-5.24199 + 7.58635i) q^{29} +(-3.30148 - 21.7913i) q^{30} +(-3.68375 - 5.47985i) q^{31} +(-27.2593 - 1.22172i) q^{32} +(-12.0985 - 7.85502i) q^{33} +(1.21953 + 13.1071i) q^{34} +(2.03883 + 3.25303i) q^{35} +(2.02394 - 20.3409i) q^{36} +(0.575850 - 0.142837i) q^{37} +(8.52307 - 5.76919i) q^{38} +(-2.74654 - 13.4422i) q^{39} +(0.511138 + 31.9516i) q^{40} +(2.12981 + 0.191293i) q^{41} +(2.69919 + 8.41706i) q^{42} +(-6.55657 - 8.98801i) q^{43} +(24.3885 + 20.9719i) q^{44} +(-11.0529 - 0.424529i) q^{45} +(-7.76116 - 1.71554i) q^{46} +(0.913525 + 3.04876i) q^{47} +(-10.2409 + 43.0506i) q^{48} +(3.59967 + 4.10574i) q^{49} +(12.6657 - 0.974389i) q^{50} +(12.0942 + 1.16432i) q^{51} +(2.05382 + 30.5247i) q^{52} +(-4.16760 + 3.82231i) q^{53} +(-3.92763 - 1.16319i) q^{54} +(10.5254 - 13.8619i) q^{55} +(-2.24342 - 12.6181i) q^{56} +(-3.75432 - 8.72622i) q^{57} +(-15.3609 - 20.5011i) q^{58} +(-10.1968 - 0.784455i) q^{59} +(44.6869 + 7.79763i) q^{60} +(4.69205 + 3.98279i) q^{61} +(17.6852 - 4.87036i) q^{62} +(4.40334 - 0.537962i) q^{63} +(14.8503 - 38.5265i) q^{64} +(16.4192 - 2.11266i) q^{65} +(31.3649 - 24.9424i) q^{66} +(-7.89844 + 6.79192i) q^{67} +(-26.3777 - 6.18564i) q^{68} +(-2.89944 + 6.73922i) q^{69} +(-10.3680 + 2.50142i) q^{70} +(-2.07112 + 1.69074i) q^{71} +(33.6807 + 15.1335i) q^{72} +(3.88781 + 2.77930i) q^{73} +(-0.131685 + 1.64298i) q^{74} +(1.31012 - 11.6515i) q^{75} +(5.68953 + 20.4045i) q^{76} +(-3.28192 + 6.16077i) q^{77} +(37.8339 + 4.62221i) q^{78} +(0.943524 - 0.139862i) q^{79} +(-50.8962 - 16.1420i) q^{80} +(3.18623 - 6.17013i) q^{81} +(-2.38265 + 5.44186i) q^{82} +(2.00102 - 0.620574i) q^{83} +(-18.1913 - 0.232801i) q^{84} +(-2.47388 + 14.4502i) q^{85} +(29.4610 - 9.34373i) q^{86} +(-21.2468 + 10.3758i) q^{87} +(-49.9106 + 29.7460i) q^{88} +(1.29335 + 0.851528i) q^{89} +(10.8682 - 28.7424i) q^{90} +(-6.36599 + 1.88532i) q^{91} +(8.42024 - 14.0261i) q^{92} +(-1.35270 - 16.8770i) q^{93} +(-8.83726 - 0.282816i) q^{94} +(10.8336 - 3.74368i) q^{95} +(-59.4046 - 36.9676i) q^{96} +(-10.7528 + 0.550884i) q^{97} +(-13.9912 + 5.86099i) q^{98} +(-9.34181 - 17.8100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9}+O(q^{10}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9} - 471 q^{10} - 477 q^{11} - 463 q^{12} - 483 q^{13} - 473 q^{14} - 461 q^{15} - 543 q^{16} - 481 q^{17} - 457 q^{18} - 473 q^{19} - 449 q^{20} - 449 q^{21} - 459 q^{22} - 473 q^{23} - 405 q^{24} - 552 q^{25} - 437 q^{26} - 451 q^{27} - 455 q^{28} - 455 q^{29} - 379 q^{30} - 459 q^{31} - 437 q^{32} - 447 q^{33} - 423 q^{34} - 439 q^{35} - 459 q^{36} - 475 q^{37} - 423 q^{38} - 439 q^{39} - 413 q^{40} - 455 q^{41} - 407 q^{42} - 457 q^{43} - 413 q^{44} - 397 q^{45} - 415 q^{46} - 467 q^{47} - 393 q^{48} - 524 q^{49} - 429 q^{50} - 403 q^{51} - 391 q^{52} - 431 q^{53} - 379 q^{54} - 415 q^{55} - 371 q^{56} - 447 q^{57} - 431 q^{58} - 439 q^{59} - 261 q^{60} - 431 q^{61} - 383 q^{62} - 445 q^{63} - 447 q^{64} - 415 q^{65} - 345 q^{66} - 439 q^{67} - 409 q^{68} - 367 q^{69} - 345 q^{70} - 415 q^{71} - 341 q^{72} - 465 q^{73} - 359 q^{74} - 339 q^{75} - 361 q^{76} - 363 q^{77} - 341 q^{78} - 423 q^{79} - 249 q^{80} - 420 q^{81} - 371 q^{82} - 433 q^{83} - 215 q^{84} - 409 q^{85} - 369 q^{86} - 329 q^{87} - 255 q^{88} - 393 q^{89} - 251 q^{90} - 373 q^{91} - 387 q^{92} - 369 q^{93} - 317 q^{94} - 393 q^{95} - 149 q^{96} - 415 q^{97} - 307 q^{98} - 299 q^{99}+O(q^{100}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9 - 471 * q^10 - 477 * q^11 - 463 * q^12 - 483 * q^13 - 473 * q^14 - 461 * q^15 - 543 * q^16 - 481 * q^17 - 457 * q^18 - 473 * q^19 - 449 * q^20 - 449 * q^21 - 459 * q^22 - 473 * q^23 - 405 * q^24 - 552 * q^25 - 437 * q^26 - 451 * q^27 - 455 * q^28 - 455 * q^29 - 379 * q^30 - 459 * q^31 - 437 * q^32 - 447 * q^33 - 423 * q^34 - 439 * q^35 - 459 * q^36 - 475 * q^37 - 423 * q^38 - 439 * q^39 - 413 * q^40 - 455 * q^41 - 407 * q^42 - 457 * q^43 - 413 * q^44 - 397 * q^45 - 415 * q^46 - 467 * q^47 - 393 * q^48 - 524 * q^49 - 429 * q^50 - 403 * q^51 - 391 * q^52 - 431 * q^53 - 379 * q^54 - 415 * q^55 - 371 * q^56 - 447 * q^57 - 431 * q^58 - 439 * q^59 - 261 * q^60 - 431 * q^61 - 383 * q^62 - 445 * q^63 - 447 * q^64 - 415 * q^65 - 345 * q^66 - 439 * q^67 - 409 * q^68 - 367 * q^69 - 345 * q^70 - 415 * q^71 - 341 * q^72 - 465 * q^73 - 359 * q^74 - 339 * q^75 - 361 * q^76 - 363 * q^77 - 341 * q^78 - 423 * q^79 - 249 * q^80 - 420 * q^81 - 371 * q^82 - 433 * q^83 - 215 * q^84 - 409 * q^85 - 369 * q^86 - 329 * q^87 - 255 * q^88 - 393 * q^89 - 251 * q^90 - 373 * q^91 - 387 * q^92 - 369 * q^93 - 317 * q^94 - 393 * q^95 - 149 * q^96 - 415 * q^97 - 307 * q^98 - 299 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more