LMFDB - Embedded newform 983.2.c.a.2.5

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			2.5
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.5

$q$-expansion

$f(q)$	$=$	$q+(-0.815103 + 2.43422i) q^{2} +(1.99272 + 1.11954i) q^{3} +(-3.66431 - 2.76391i) q^{4} +(0.269938 - 0.407156i) q^{5} +(-4.34946 + 3.93817i) q^{6} +(0.302286 - 0.667041i) q^{7} +(5.48157 - 3.76178i) q^{8} +(1.15702 + 1.89966i) q^{9} +O(q^{10})$	\(q+(-0.815103 + 2.43422i) q^{2} +(1.99272 + 1.11954i) q^{3} +(-3.66431 - 2.76391i) q^{4} +(0.269938 - 0.407156i) q^{5} +(-4.34946 + 3.93817i) q^{6} +(0.302286 - 0.667041i) q^{7} +(5.48157 - 3.76178i) q^{8} +(1.15702 + 1.89966i) q^{9} +(0.771079 + 0.988963i) q^{10} +(4.53664 + 0.290667i) q^{11} +(-4.20763 - 9.61001i) q^{12} +(0.900447 + 1.04039i) q^{13} +(1.37733 + 1.27954i) q^{14} +(0.993736 - 0.509140i) q^{15} +(2.16687 + 7.58322i) q^{16} +(-3.64166 + 1.60836i) q^{17} +(-5.56728 + 1.26802i) q^{18} +(3.65716 + 2.79541i) q^{19} +(-2.11448 + 0.745859i) q^{20} +(1.34915 - 0.990803i) q^{21} +(-4.40538 + 10.8063i) q^{22} +(0.465205 + 4.39010i) q^{23} +(15.1347 - 1.35935i) q^{24} +(1.85371 + 4.38569i) q^{25} +(-3.26650 + 1.34386i) q^{26} +(-0.0623822 - 1.77195i) q^{27} +(-2.95131 + 1.60875i) q^{28} +(-0.311575 + 0.450920i) q^{29} +(0.429361 + 2.83397i) q^{30} +(0.0749012 + 0.111421i) q^{31} +(-6.94236 - 0.311146i) q^{32} +(8.71483 + 5.65815i) q^{33} +(-0.946769 - 10.1756i) q^{34} +(-0.189991 - 0.303138i) q^{35} +(1.01081 - 10.1588i) q^{36} +(-4.98277 + 1.23595i) q^{37} +(-9.78559 + 6.62377i) q^{38} +(0.629577 + 3.08129i) q^{39} +(-0.0519479 - 3.24730i) q^{40} +(1.33724 + 0.120108i) q^{41} +(1.31214 + 4.09172i) q^{42} +(2.35832 + 3.23288i) q^{43} +(-15.8203 - 13.6040i) q^{44} +(1.08578 + 0.0417038i) q^{45} +(-11.0657 - 2.44598i) q^{46} +(-2.50885 - 8.37293i) q^{47} +(-4.17173 + 17.5371i) q^{48} +(4.26115 + 4.86022i) q^{49} +(-12.1867 + 0.937540i) q^{50} +(-9.05742 - 0.871968i) q^{51} +(-0.423961 - 6.30107i) q^{52} +(2.40305 - 2.20396i) q^{53} +(4.36415 + 1.29247i) q^{54} +(1.34296 - 1.76866i) q^{55} +(-0.852264 - 4.79356i) q^{56} +(4.15811 + 9.66477i) q^{57} +(-0.843671 - 1.12599i) q^{58} +(-13.7131 - 1.05497i) q^{59} +(-5.04857 - 0.880951i) q^{60} +(-0.904609 - 0.767866i) q^{61} +(-0.332276 + 0.0915062i) q^{62} +(1.61690 - 0.197539i) q^{63} +(0.743022 - 1.92765i) q^{64} +(0.666667 - 0.0857803i) q^{65} +(-20.8767 + 16.6018i) q^{66} +(7.74629 - 6.66109i) q^{67} +(17.7895 + 4.17170i) q^{68} +(-3.98786 + 9.26904i) q^{69} +(0.892765 - 0.215391i) q^{70} +(-5.15286 + 4.20648i) q^{71} +(13.4884 + 6.06066i) q^{72} +(9.34847 + 6.68300i) q^{73} +(1.05290 - 13.1366i) q^{74} +(-1.21602 + 10.8147i) q^{75} +(-5.67469 - 20.3513i) q^{76} +(1.56525 - 2.93826i) q^{77} +(-8.01370 - 0.979044i) q^{78} +(3.78412 - 0.560935i) q^{79} +(3.67247 + 1.16475i) q^{80} +(4.92114 - 9.52980i) q^{81} +(-1.38236 + 3.15724i) q^{82} +(0.781737 - 0.242439i) q^{83} +(-7.68218 - 0.0983120i) q^{84} +(-0.328171 + 1.91688i) q^{85} +(-9.79182 + 3.10554i) q^{86} +(-1.12570 + 0.549735i) q^{87} +(25.9613 - 15.4726i) q^{88} +(5.71837 + 3.76492i) q^{89} +(-0.986541 + 2.60904i) q^{90} +(0.966178 - 0.286139i) q^{91} +(10.4292 - 17.3725i) q^{92} +(0.0245168 + 0.305885i) q^{93} +(22.4265 + 0.717709i) q^{94} +(2.12537 - 0.734445i) q^{95} +(-13.4858 - 8.39224i) q^{96} +(-5.66393 + 0.290172i) q^{97} +(-15.3041 + 6.41099i) q^{98} +(4.69682 + 8.95440i) 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 $

$2$	−0.815103	+	2.43422i	−0.576365	+	1.72125i	0.109940	+	0.993938i	$0.464934\pi$
$2$	−0.815103	+	2.43422i	−0.576365	+	1.72125i	−0.686305	+	0.727314i	$0.740769\pi$
$3$	1.99272	+	1.11954i	1.15049	+	0.646365i	0.943302	−	0.331936i	$-0.107702\pi$
$3$	1.99272	+	1.11954i	1.15049	+	0.646365i	0.207193	+	0.978300i	$0.433567\pi$
$4$	−3.66431	−	2.76391i	−1.83215	−	1.38195i
$5$	0.269938	−	0.407156i	0.120720	−	0.182086i	−0.768116	−	0.640310i	$-0.778806\pi$
$5$	0.269938	−	0.407156i	0.120720	−	0.182086i	0.888836	+	0.458225i	$0.151514\pi$
$6$	−4.34946	+	3.93817i	−1.77566	+	1.60775i
$7$	0.302286	−	0.667041i	0.114253	−	0.252118i	−0.844944	−	0.534854i	$-0.820366\pi$
$7$	0.302286	−	0.667041i	0.114253	−	0.252118i	0.959198	+	0.282737i	$0.0912422\pi$
$8$	5.48157	−	3.76178i	1.93803	−	1.32999i
$9$	1.15702	+	1.89966i	0.385673	+	0.633221i
$10$	0.771079	+	0.988963i	0.243836	+	0.312738i
$11$	4.53664	+	0.290667i	1.36785	+	0.0876395i	0.730488	−	0.682925i	$-0.239293\pi$
$11$	4.53664	+	0.290667i	1.36785	+	0.0876395i	0.637362	+	0.770565i	$0.280026\pi$
$12$	−4.20763	−	9.61001i	−1.21464	−	2.77417i
$13$	0.900447	+	1.04039i	0.249739	+	0.288553i	0.867108	−	0.498121i	$-0.165976\pi$
$13$	0.900447	+	1.04039i	0.249739	+	0.288553i	−0.617369	+	0.786674i	$0.711801\pi$
$14$	1.37733	+	1.27954i	0.368107	+	0.341971i
$15$	0.993736	−	0.509140i	0.256582	−	0.131459i
$16$	2.16687	+	7.58322i	0.541717	+	1.89580i
$17$	−3.64166	+	1.60836i	−0.883233	+	0.390085i	−0.795425	−	0.606052i	$-0.792752\pi$
$17$	−3.64166	+	1.60836i	−0.883233	+	0.390085i	−0.0878085	+	0.996137i	$0.527986\pi$
$18$	−5.56728	+	1.26802i	−1.31222	+	0.298875i
$19$	3.65716	+	2.79541i	0.839009	+	0.641310i	0.935226	−	0.354050i	$-0.115196\pi$
$19$	3.65716	+	2.79541i	0.839009	+	0.641310i	−0.0962173	+	0.995360i	$0.530674\pi$
$20$	−2.11448	+	0.745859i	−0.472812	+	0.166779i
$21$	1.34915	−	0.990803i	0.294408	−	0.216211i
$22$	−4.40538	+	10.8063i	−0.939230	+	2.30390i
$23$	0.465205	+	4.39010i	0.0970020	+	0.915400i	0.931341	+	0.364148i	$0.118640\pi$
$23$	0.465205	+	4.39010i	0.0970020	+	0.915400i	−0.834339	+	0.551252i	$0.814150\pi$
$24$	15.1347	−	1.35935i	3.08935	−	0.277477i
$25$	1.85371	+	4.38569i	0.370742	+	0.877138i
$26$	−3.26650	+	1.34386i	−0.640614	+	0.263552i
$27$	−0.0623822	−	1.77195i	−0.0120055	−	0.341011i
$28$	−2.95131	+	1.60875i	−0.557745	+	0.304026i
$29$	−0.311575	+	0.450920i	−0.0578581	+	0.0837337i	−0.850567	−	0.525866i	$-0.823741\pi$
$29$	−0.311575	+	0.450920i	−0.0578581	+	0.0837337i	0.792709	+	0.609600i	$0.208670\pi$
$30$	0.429361	+	2.83397i	0.0783902	+	0.517410i
$31$	0.0749012	+	0.111421i	0.0134527	+	0.0200118i	0.836577	−	0.547849i	$-0.184553\pi$
$31$	0.0749012	+	0.111421i	0.0134527	+	0.0200118i	−0.823125	+	0.567861i	$0.807771\pi$
$32$	−6.94236	−	0.311146i	−1.22725	−	0.0550033i
$33$	8.71483	+	5.65815i	1.51706	+	0.984958i
$34$	−0.946769	−	10.1756i	−0.162370	−	1.74510i
$35$	−0.189991	−	0.303138i	−0.0321144	−	0.0512396i
$36$	1.01081	−	10.1588i	0.168469	−	1.69314i
$37$	−4.98277	+	1.23595i	−0.819163	+	0.203189i	−0.627844	−	0.778339i	$-0.716063\pi$
$37$	−4.98277	+	1.23595i	−0.819163	+	0.203189i	−0.191319	+	0.981528i	$0.561276\pi$
$38$	−9.78559	+	6.62377i	−1.58743	+	1.07452i
$39$	0.629577	+	3.08129i	0.100813	+	0.493401i
$40$	−0.0519479	−	3.24730i	−0.00821369	−	0.513444i
$41$	1.33724	+	0.120108i	0.208842	+	0.0187577i	0.193385	−	0.981123i	$-0.438053\pi$
$41$	1.33724	+	0.120108i	0.208842	+	0.0187577i	0.0154570	+	0.999881i	$0.495080\pi$
$42$	1.31214	+	4.09172i	0.202467	+	0.631367i
$43$	2.35832	+	3.23288i	0.359641	+	0.493010i	0.949182	−	0.314728i	$-0.101913\pi$
$43$	2.35832	+	3.23288i	0.359641	+	0.493010i	−0.589541	+	0.807738i	$0.700691\pi$
$44$	−15.8203	−	13.6040i	−2.38500	−	2.05088i
$45$	1.08578	+	0.0417038i	0.161859	+	0.00621684i
$46$	−11.0657	−	2.44598i	−1.63154	−	0.360639i
$47$	−2.50885	−	8.37293i	−0.365954	−	1.22132i	−0.921021	−	0.389512i	$-0.872644\pi$
$47$	−2.50885	−	8.37293i	−0.365954	−	1.22132i	0.555067	−	0.831805i	$-0.312692\pi$
$48$	−4.17173	+	17.5371i	−0.602138	+	2.53126i
$49$	4.26115	+	4.86022i	0.608736	+	0.694317i
$50$	−12.1867	+	0.937540i	−1.72346	+	0.132588i
$51$	−9.05742	−	0.871968i	−1.26829	−	0.122100i
$52$	−0.423961	−	6.30107i	−0.0587929	−	0.873802i
$53$	2.40305	−	2.20396i	0.330085	−	0.302737i	−0.493708	−	0.869628i	$-0.664359\pi$
$53$	2.40305	−	2.20396i	0.330085	−	0.302737i	0.823793	+	0.566891i	$0.191854\pi$
$54$	4.36415	+	1.29247i	0.593886	+	0.175883i
$55$	1.34296	−	1.76866i	0.181085	−	0.238486i
$56$	−0.852264	−	4.79356i	−0.113889	−	0.640567i
$57$	4.15811	+	9.66477i	0.550756	+	1.28013i
$58$	−0.843671	−	1.12599i	−0.110779	−	0.147849i
$59$	−13.7131	−	1.05497i	−1.78530	−	0.137345i	−0.858476	−	0.512854i	$-0.828588\pi$
$59$	−13.7131	−	1.05497i	−1.78530	−	0.137345i	−0.926819	+	0.375508i	$0.877468\pi$
$60$	−5.04857	−	0.880951i	−0.651768	−	0.113730i
$61$	−0.904609	−	0.767866i	−0.115823	−	0.0983152i	0.587353	−	0.809331i	$-0.300170\pi$
$61$	−0.904609	−	0.767866i	−0.115823	−	0.0983152i	−0.703176	+	0.711016i	$0.748235\pi$
$62$	−0.332276	+	0.0915062i	−0.0421991	+	0.0116213i
$63$	1.61690	−	0.197539i	0.203711	−	0.0248876i
$64$	0.743022	−	1.92765i	0.0928777	−	0.240956i
$65$	0.666667	−	0.0857803i	0.0826899	−	0.0106397i
$66$	−20.8767	+	16.6018i	−2.56974	+	2.04354i
$67$	7.74629	−	6.66109i	0.946360	−	0.813782i	−0.0362725	−	0.999342i	$-0.511548\pi$
$67$	7.74629	−	6.66109i	0.946360	−	0.813782i	0.982633	+	0.185560i	$0.0594099\pi$
$68$	17.7895	+	4.17170i	2.15730	+	0.505893i
$69$	−3.98786	+	9.26904i	−0.480082	+	1.11586i
$70$	0.892765	−	0.215391i	0.106706	−	0.0257442i
$71$	−5.15286	+	4.20648i	−0.611532	+	0.499217i	−0.886802	−	0.462150i	$-0.847078\pi$
$71$	−5.15286	+	4.20648i	−0.611532	+	0.499217i	0.275269	+	0.961367i	$0.411233\pi$
$72$	13.4884	+	6.06066i	1.58962	+	0.714256i
$73$	9.34847	+	6.68300i	1.09416	+	0.782186i	0.977489	−	0.210985i	$-0.0676672\pi$
$73$	9.34847	+	6.68300i	1.09416	+	0.782186i	0.116666	+	0.993171i	$0.462779\pi$
$74$	1.05290	−	13.1366i	0.122397	−	1.52710i
$75$	−1.21602	+	10.8147i	−0.140414	+	1.24878i
$76$	−5.67469	−	20.3513i	−0.650932	−	2.33445i
$77$	1.56525	−	2.93826i	0.178377	−	0.334846i
$78$	−8.01370	−	0.979044i	−0.907373	−	0.110855i
$79$	3.78412	−	0.560935i	0.425747	−	0.0631101i	0.0696775	−	0.997570i	$-0.477803\pi$
$79$	3.78412	−	0.560935i	0.425747	−	0.0631101i	0.356070	+	0.934459i	$0.384117\pi$
$80$	3.67247	+	1.16475i	0.410595	+	0.130223i
$81$	4.92114	−	9.52980i	0.546793	−	1.05887i
$82$	−1.38236	+	3.15724i	−0.152656	+	0.348659i
$83$	0.781737	−	0.242439i	0.0858067	−	0.0266111i	−0.253008	−	0.967464i	$-0.581420\pi$
$83$	0.781737	−	0.242439i	0.0858067	−	0.0266111i	0.338815	+	0.940853i	$0.389974\pi$
$84$	−7.68218	−	0.0983120i	−0.838194	−	0.0107267i
$85$	−0.328171	+	1.91688i	−0.0355951	+	0.207915i
$86$	−9.79182	+	3.10554i	−1.05588	+	0.334878i
$87$	−1.12570	+	0.549735i	−0.120688	+	0.0589378i
$88$	25.9613	−	15.4726i	2.76749	−	1.64938i
$89$	5.71837	+	3.76492i	0.606146	+	0.399080i	0.815498	−	0.578760i	$-0.196463\pi$
$89$	5.71837	+	3.76492i	0.606146	+	0.399080i	−0.209352	+	0.977840i	$0.567135\pi$
$90$	−0.986541	+	2.60904i	−0.103991	+	0.275017i
$91$	0.966178	−	0.286139i	0.101283	−	0.0299955i
$92$	10.4292	−	17.3725i	1.08732	−	1.81121i
$93$	0.0245168	+	0.305885i	0.00254228	+	0.0317188i
$94$	22.4265	+	0.717709i	2.31312	+	0.0740260i
$95$	2.12537	−	0.734445i	0.218059	−	0.0753525i
$96$	−13.4858	−	8.39224i	−1.37639	−	0.856530i
$97$	−5.66393	+	0.290172i	−0.575085	+	0.0294625i	−0.336540	−	0.941669i	$-0.609257\pi$
$97$	−5.66393	+	0.290172i	−0.575085	+	0.0294625i	−0.238544	+	0.971132i	$0.576670\pi$
$98$	−15.3041	+	6.41099i	−1.54595	+	0.647608i
$99$	4.69682	+	8.95440i	0.472048	+	0.899951i
$100$	5.32909	−	21.1940i	0.532909	−	2.11940i
$101$	3.30001	+	2.39115i	0.328363	+	0.237928i	0.738744	−	0.673986i	$-0.235419\pi$
$101$	3.30001	+	2.39115i	0.328363	+	0.237928i	−0.410381	+	0.911914i	$0.634604\pi$
$102$	9.50529	−	21.3370i	0.941164	−	2.11268i
$103$	5.34010	+	2.07802i	0.526176	+	0.204753i	0.610982	−	0.791644i	$-0.290775\pi$
$103$	5.34010	+	2.07802i	0.526176	+	0.204753i	−0.0848063	+	0.996397i	$0.527027\pi$
$104$	8.84959	+	2.31570i	0.867774	+	0.227073i
$105$	−0.0392249	−	0.816769i	−0.00382796	−	0.0797085i
$106$	3.40618	+	7.64601i	0.330837	+	0.742646i
$107$	1.27253	−	6.03104i	0.123020	−	0.583043i	−0.872510	−	0.488596i	$-0.837509\pi$
$107$	1.27253	−	6.03104i	0.123020	−	0.583043i	0.995530	−	0.0944462i	$-0.0301080\pi$
$108$	−4.66891	+	6.66538i	−0.449266	+	0.641376i
$109$	−8.74361	−	10.3677i	−0.837486	−	0.993048i	−0.999980	−	0.00633862i	$-0.997982\pi$
$109$	−8.74361	−	10.3677i	−0.837486	−	0.993048i	0.162494	−	0.986710i	$-0.448046\pi$
$110$	3.21065	+	4.71070i	0.306123	+	0.449148i
$111$	−11.3129	−	3.11550i	−1.07378	−	0.295710i
$112$	5.71333	+	0.846909i	0.539859	+	0.0800254i
$113$	−3.90923	−	1.90907i	−0.367749	−	0.179590i	0.245658	−	0.969357i	$-0.420996\pi$
$113$	−3.90923	−	1.90907i	−0.367749	−	0.179590i	−0.613407	+	0.789767i	$0.710202\pi$
$114$	−26.9154	+	2.24397i	−2.52086	+	0.210167i
$115$	1.91303	+	0.995646i	0.178391	+	0.0928445i
$116$	2.38801	−	0.791143i	0.221721	−	0.0734558i
$117$	−0.934560	+	2.91430i	−0.0864001	+	0.269427i
$118$	13.7456	−	32.5208i	1.26539	−	2.99378i
$119$	−0.0279808	+	2.91532i	−0.00256499	+	0.267247i
$120$	3.53196	−	6.52911i	0.322422	−	0.596023i
$121$	9.58659	+	1.23351i	0.871508	+	0.112137i
$122$	2.60650	−	1.57612i	0.235982	−	0.142696i
$123$	2.53028	+	1.73643i	0.228148	+	0.156569i
$124$	0.0334968	−	0.615302i	0.00300811	−	0.0552557i
$125$	4.68667	+	0.879743i	0.419189	+	0.0786866i
$126$	−0.837090	+	4.09691i	−0.0745739	+	0.364982i
$127$	−7.19045	−	17.3201i	−0.638049	−	1.53691i	−0.831338	−	0.555767i	$-0.812425\pi$
$127$	−7.19045	−	17.3201i	−0.638049	−	1.53691i	0.193289	−	0.981142i	$-0.438084\pi$
$128$	−6.62356	−	5.47806i	−0.585445	−	0.484196i
$129$	1.08013	+	9.08245i	0.0951006	+	0.799665i
$130$	−0.334595	+	1.69273i	−0.0293459	+	0.148463i
$131$	−2.21693	−	1.13585i	−0.193694	−	0.0992393i	0.356430	−	0.934322i	$-0.383994\pi$
$131$	−2.21693	−	1.13585i	−0.193694	−	0.0992393i	−0.550124	+	0.835083i	$0.685420\pi$
$132$	−16.2952	−	44.8202i	−1.41831	−	3.90110i
$133$	2.97016	−	1.59446i	0.257545	−	0.138257i
$134$	9.90052	+	24.2856i	0.855274	+	2.09796i
$135$	−0.738298	−	0.452917i	−0.0635426	−	0.0389809i
$136$	−13.9117	+	22.5155i	−1.19292	+	1.93069i
$137$	−2.98115	−	5.26676i	−0.254697	−	0.449970i	0.713326	−	0.700832i	$-0.247188\pi$
$137$	−2.98115	−	5.26676i	−0.254697	−	0.449970i	−0.968023	+	0.250863i	$0.919286\pi$
$138$	−19.3123	−	17.2625i	−1.64398	−	1.46948i
$139$	5.23028	−	9.97142i	0.443626	−	0.845765i	−0.556265	−	0.831005i	$-0.687766\pi$
$139$	5.23028	−	9.97142i	0.443626	−	0.845765i	0.999891	−	0.0147600i	$-0.00469841\pi$
$140$	−0.141659	+	1.63591i	−0.0119723	+	0.138259i
$141$	4.37437	−	19.4936i	0.368388	−	1.64166i
$142$	−6.03937	−	15.9719i	−0.506812	−	1.34033i
$143$	3.78260	+	4.98162i	0.316317	+	0.416584i
$144$	−11.8984	+	12.8903i	−0.991536	+	1.07419i
$145$	0.0994885	+	0.248580i	0.00826207	+	0.0206435i
$146$	−23.8878	+	17.3089i	−1.97697	+	1.43249i
$147$	3.05007	+	14.4556i	0.251566	+	1.19227i
$148$	21.6745	+	9.24303i	1.78163	+	0.759773i
$149$	2.25159	+	8.71839i	0.184457	+	0.714239i	0.992195	+	0.124696i	$0.0397957\pi$
$149$	2.25159	+	8.71839i	0.184457	+	0.714239i	−0.807738	+	0.589542i	$0.799308\pi$
$150$	−25.3342	−	11.7752i	−2.06853	−	0.961440i
$151$	14.2267	−	5.12090i	1.15775	−	0.416733i	0.311882	−	0.950121i	$-0.399041\pi$
$151$	14.2267	−	5.12090i	1.15775	−	0.416733i	0.845871	+	0.533388i	$0.179081\pi$
$152$	30.5627	+	1.56577i	2.47896	+	0.127001i
$153$	−7.26882	−	5.05702i	−0.587649	−	0.408836i
$154$	5.87653	+	6.20515i	0.473544	+	0.500025i
$155$	0.0655845		0.000419639i	0.00526788		3.37062e-5i
$156$	6.20945	−	13.0309i	0.497154	−	1.04331i
$157$	−6.31058	−	6.83661i	−0.503639	−	0.545621i	0.430472	−	0.902604i	$-0.358347\pi$
$157$	−6.31058	−	6.83661i	−0.503639	−	0.545621i	−0.934111	+	0.356983i	$0.883805\pi$
$158$	−1.71901	+	9.66860i	−0.136757	+	0.769192i
$159$	7.25602	−	1.70156i	0.575440	−	0.134942i
$160$	−2.00069	+	2.74263i	−0.158169	+	0.216824i
$161$	3.06900	+	1.01676i	0.241871	+	0.0801315i
$162$	19.1864	+	19.7469i	1.50742	+	1.55146i
$163$	−3.45726	+	0.881074i	−0.270793	+	0.0690111i	−0.379928	−	0.925016i	$-0.624051\pi$
$163$	−3.45726	+	0.881074i	−0.270793	+	0.0690111i	0.109135	+	0.994027i	$0.465192\pi$
$164$	−4.56811	−	4.13613i	−0.356709	−	0.322978i
$165$	4.65622	−	2.02094i	0.362486	−	0.157330i
$166$	−0.0470476	+	2.10053i	−0.00365160	+	0.163033i
$167$	−0.836598	−	4.53682i	−0.0647379	−	0.351070i	0.935258	−	0.353967i	$-0.115167\pi$
$167$	−0.836598	−	4.53682i	−0.0647379	−	0.351070i	−0.999996	+	0.00289696i	$0.999078\pi$
$168$	3.66825	−	10.5064i	0.283012	−	0.810583i
$169$	1.59345	−	10.9919i	0.122573	−	0.845529i
$170$	−4.39862	−	2.36130i	−0.337359	−	0.181103i
$171$	−1.07892	+	10.1817i	−0.0825073	+	0.778614i
$172$	0.293781	−	18.3645i	0.0224006	−	1.40028i
$173$	−20.2092	+	3.79350i	−1.53648	+	0.288415i	−0.883307	−	0.468795i	$-0.844688\pi$
$173$	−20.2092	+	3.79350i	−1.53648	+	0.288415i	−0.653172	+	0.757210i	$0.726562\pi$
$174$	−0.420612	−	3.18829i	−0.0318865	−	0.241704i
$175$	3.48579	+	0.0892327i	0.263501	+	0.00674536i
$176$	7.62612	+	35.0322i	0.574841	+	2.64065i
$177$	−26.1453	−	17.4546i	−1.96520	−	1.31197i
$178$	−13.8257	+	10.8510i	−1.03628	+	0.813315i
$179$	11.9980	+	5.76443i	0.896772	+	0.430854i	0.824062	−	0.566500i	$-0.191703\pi$
$179$	11.9980	+	5.76443i	0.896772	+	0.430854i	0.0727104	+	0.997353i	$0.476835\pi$
$180$	−3.86338	−	3.15382i	−0.287959	−	0.235072i
$181$	9.10655	+	18.2025i	0.676884	+	1.35298i	0.923399	+	0.383841i	$0.125399\pi$
$181$	9.10655	+	18.2025i	0.676884	+	1.35298i	−0.246515	+	0.969139i	$0.579285\pi$
$182$	−0.0910104	+	2.58512i	−0.00674614	+	0.191622i
$183$	−0.942974	−	2.54288i	−0.0697066	−	0.187975i
$184$	19.0647	+	22.3146i	1.40547	+	1.64506i
$185$	−0.841817	+	2.36240i	−0.0618916	+	0.173687i
$186$	−0.764575	−	0.189649i	−0.0560614	−	0.0139057i
$187$	−16.9884	+	6.23805i	−1.24232	+	0.456171i
$188$	−13.9488	+	37.6152i	−1.01732	+	2.74337i
$189$	−1.20082	−	0.494023i	−0.0873467	−	0.0359349i
$190$	0.0554013	+	5.77227i	0.00401923	+	0.418765i
$191$	−14.6382	−	7.73796i	−1.05919	−	0.559899i	−0.155385	−	0.987854i	$-0.549662\pi$
$191$	−14.6382	−	7.73796i	−1.05919	−	0.559899i	−0.903800	+	0.427955i	$0.859234\pi$
$192$	3.63870	−	3.00941i	0.262601	−	0.217185i
$193$	−6.44268	−	6.14070i	−0.463754	−	0.442017i	0.421706	−	0.906733i	$-0.361431\pi$
$193$	−6.44268	−	6.14070i	−0.463754	−	0.442017i	−0.885460	+	0.464716i	$0.846157\pi$
$194$	3.91034	−	14.0238i	0.280746	−	1.00685i
$195$	1.42451	+	0.575423i	0.102011	+	0.0412069i
$196$	−2.18096	−	29.5868i	−0.155783	−	2.11334i
$197$	−9.72918	+	2.61249i	−0.693175	+	0.186132i	−0.588647	−	0.808390i	$-0.700339\pi$
$197$	−9.72918	+	2.61249i	−0.693175	+	0.186132i	−0.104528	+	0.994522i	$0.533333\pi$
$198$	−25.6253	+	4.13432i	−1.82111	+	0.293814i
$199$	−4.66418	+	7.23445i	−0.330635	+	0.512837i	−0.965713	−	0.259611i	$-0.916406\pi$
$199$	−4.66418	+	7.23445i	−0.330635	+	0.512837i	0.635078	+	0.772448i	$0.280968\pi$
$200$	26.6593	+	17.0672i	1.88509	+	1.20683i
$201$	22.8935	−	4.60140i	1.61478	−	0.324558i
$202$	−8.51042	+	6.08390i	−0.598791	+	0.428062i
$203$	0.206597	+	0.344140i	0.0145003	+	0.0241539i
$204$	30.7791	+	28.2290i	2.15497	+	1.97643i
$205$	0.409876	−	0.512045i	0.0286270	−	0.0357628i
$206$	−9.41109	+	11.3052i	−0.655702	+	0.787669i
$207$	−7.80146	+	5.96317i	−0.542239	+	0.414469i
$208$	−5.93838	+	9.08268i	−0.411752	+	0.629771i
$209$	15.7787	+	13.7448i	1.09143	+	0.950746i
$210$	2.02017	+	0.570269i	0.139405	+	0.0393523i
$211$	1.09056	+	6.62466i	0.0750774	+	0.456061i	0.997548	+	0.0699923i	$0.0222975\pi$
$211$	1.09056	+	6.62466i	0.0750774	+	0.456061i	−0.922470	+	0.386068i	$0.873833\pi$
$212$	−14.8971	+	1.43416i	−1.02314	+	0.0984984i
$213$	−14.9775	+	2.61350i	−1.02624	+	0.179074i
$214$	13.6436	+	8.01353i	0.932659	+	0.547794i
$215$	1.95289	−	0.0875255i	0.133186	−	0.00596919i
$216$	−7.00763	−	9.47837i	−0.476809	−	0.644922i
$217$	0.0969641	−	0.0162812i	0.00658235	−	0.00110524i
$218$	32.3642	−	12.8331i	2.19198	−	0.869166i
$219$	11.1470	+	23.7833i	0.753243	+	1.60712i
$220$	−9.80944	+	2.76909i	−0.661352	+	0.186692i
$221$	−4.95245	−	2.34052i	−0.333138	−	0.157440i
$222$	16.8050	−	24.9987i	1.12788	−	1.67780i
$223$	7.45817	−	10.0878i	0.499436	−	0.675526i	−0.480003	−	0.877267i	$-0.659365\pi$
$223$	7.45817	−	10.0878i	0.499436	−	0.675526i	0.979439	+	0.201741i	$0.0646598\pi$
$224$	−2.30612	+	4.53678i	−0.154084	+	0.303126i
$225$	−6.18655	+	8.59575i	−0.412437	+	0.573050i
$226$	7.83351	−	7.95983i	0.521077	−	0.529480i
$227$	−7.54000	−	12.7439i	−0.500448	−	0.845840i	0.499341	−	0.866406i	$-0.333576\pi$
$227$	−7.54000	−	12.7439i	−0.500448	−	0.845840i	−0.999789	+	0.0205656i	$0.993453\pi$
$228$	11.4759	−	46.9073i	0.760013	−	3.10651i
$229$	3.63461	−	16.6963i	0.240182	−	1.10332i	−0.686398	−	0.727226i	$-0.740809\pi$
$229$	3.63461	−	16.6963i	0.240182	−	1.10332i	0.926580	−	0.376099i	$-0.122735\pi$
$230$	−3.98294	+	3.84518i	−0.262627	+	0.253544i
$231$	6.40859	−	4.10277i	0.421654	−	0.269942i
$232$	−0.0116573	+	3.64382i	−0.000765338	+	0.239229i
$233$	3.63271	−	2.22853i	0.237987	−	0.145996i	−0.398794	−	0.917041i	$-0.630571\pi$
$233$	3.63271	−	2.22853i	0.237987	−	0.145996i	0.636781	+	0.771045i	$0.280266\pi$
$234$	−6.33228	−	4.65038i	−0.413954	−	0.304005i
$235$	−4.08632	−	1.23868i	−0.266562	−	0.0808026i
$236$	47.3332	+	41.7675i	3.08113	+	2.71884i
$237$	8.16867	+	3.11868i	0.530612	+	0.202580i
$238$	−7.07373	−	2.44440i	−0.458522	−	0.158447i
$239$	5.99116	+	7.38718i	0.387536	+	0.477837i	0.932783	−	0.360438i	$-0.117373\pi$
$239$	5.99116	+	7.38718i	0.387536	+	0.477837i	−0.545247	+	0.838275i	$0.683564\pi$
$240$	6.01422	+	6.43248i	0.388216	+	0.415215i
$241$	−6.40876	−	0.0410061i	−0.412825	−	0.00264143i	−0.200152	−	0.979765i	$-0.564144\pi$
$241$	−6.40876	−	0.0410061i	−0.412825	−	0.00264143i	−0.212673	+	0.977123i	$0.568217\pi$
$242$	−10.8167	+	22.3304i	−0.695323	+	1.43545i
$243$	16.0327	−	10.5558i	1.02850	−	0.677153i
$244$	1.19245	+	5.31395i	0.0763389	+	0.340191i
$245$	3.12912	−	0.422994i	0.199912	−	0.0270241i
$246$	−6.28930	+	4.74388i	−0.400991	+	0.302459i
$247$	0.384753	+	6.32200i	0.0244812	+	0.402259i
$248$	0.829719	+	0.329000i	0.0526872	+	0.0208915i
$249$	1.82920	+	0.392071i	0.115921	+	0.0248465i
$250$	−5.96161	+	10.6913i	−0.377045	+	0.676177i
$251$	−4.72868	+	15.7813i	−0.298472	+	0.996105i	0.669029	+	0.743236i	$0.266710\pi$
$251$	−4.72868	+	15.7813i	−0.298472	+	0.996105i	−0.967501	+	0.252869i	$0.918626\pi$
$252$	−6.47081	−	3.74513i	−0.407623	−	0.235921i
$253$	0.834411	+	20.0516i	0.0524590	+	1.26063i
$254$	48.0218	−	3.38546i	3.01316	−	0.212423i
$255$	−2.79997	+	3.45240i	−0.175341	+	0.216198i
$256$	22.2417	−	13.8410i	1.39010	−	0.865064i
$257$	22.5152	−	15.6642i	1.40446	−	0.977103i	0.406475	−	0.913662i	$-0.366758\pi$
$257$	22.5152	−	15.6642i	1.40446	−	0.977103i	0.997986	−	0.0634412i	$-0.0202075\pi$
$258$	−22.9891	−	4.77385i	−1.43124	−	0.297207i
$259$	−0.681793	+	3.69733i	−0.0423646	+	0.229741i
$260$	−2.67996	−	1.52828i	−0.166204	−	0.0947801i
$261$	−1.21709	−	0.0701641i	−0.0753362	−	0.00434305i
$262$	4.57193	−	4.47067i	0.282454	−	0.276199i
$263$	−3.07610	−	12.5734i	−0.189680	−	0.775309i	−0.985486	−	0.169757i	$-0.945702\pi$
$263$	−3.07610	−	12.5734i	−0.189680	−	0.775309i	0.795806	−	0.605552i	$-0.207048\pi$
$264$	69.0557	−	1.76776i	4.25008	−	0.108798i
$265$	−0.248678	−	1.57335i	−0.0152762	−	0.0966502i
$266$	1.46028	+	8.52966i	0.0895355	+	0.522987i
$267$	7.18013	+	13.9043i	0.439417	+	0.850932i
$268$	−46.7955	+	2.99823i	−2.85849	+	0.183146i
$269$	13.3062	+	14.9825i	0.811296	+	0.913496i	0.997617	−	0.0689925i	$-0.0219784\pi$
$269$	13.3062	+	14.9825i	0.811296	+	0.913496i	−0.186322	+	0.982489i	$0.559657\pi$
$270$	1.70429	−	1.42800i	0.103720	−	0.0869055i
$271$	−27.7426	+	0.532587i	−1.68524	+	0.0323524i	−0.852954	−	0.521987i	$-0.825191\pi$
$271$	−27.7426	+	0.532587i	−1.68524	+	0.0323524i	−0.832291	+	0.554339i	$0.812971\pi$
$272$	−20.0876	−	24.1304i	−1.21799	−	1.46312i
$273$	2.24566	+	0.511478i	0.135914	+	0.0309560i
$274$	15.2504	−	2.96381i	0.921309	−	0.179050i
$275$	7.13484	+	20.4351i	0.430247	+	1.23228i
$276$	40.2315	−	22.9425i	2.42165	−	1.38098i
$277$	25.8972	−	12.8527i	1.55601	−	0.772246i	0.557684	−	0.830053i	$-0.311690\pi$
$277$	25.8972	−	12.8527i	1.55601	−	0.772246i	0.998328	+	0.0578077i	$0.0184110\pi$
$278$	20.0094	+	20.8594i	1.20008	+	1.25106i
$279$	−0.125000	+	0.271204i	−0.00748357	+	0.0162365i
$280$	−2.18179	−	0.946963i	−0.130387	−	0.0565918i
$281$	−0.0572671	−	0.126369i	−0.00341627	−	0.00753853i	0.909120	−	0.416533i	$-0.136755\pi$
$281$	−0.0572671	−	0.126369i	−0.00341627	−	0.00753853i	−0.912537	+	0.408995i	$0.865879\pi$
$282$	43.8862	+	26.5375i	2.61338	+	1.58028i
$283$	13.7034	+	10.8974i	0.814581	+	0.647781i	0.938796	−	0.344474i	$-0.111943\pi$
$283$	13.7034	+	10.8974i	0.814581	+	0.647781i	−0.124215	+	0.992255i	$0.539641\pi$
$284$	30.5080	−	1.17178i	1.81032	−	0.0695325i
$285$	5.05750	+	0.915892i	0.299581	+	0.0542527i
$286$	−15.2096	+	5.14713i	−0.899360	+	0.304356i
$287$	0.484347	−	0.855690i	0.0285901	−	0.0505098i
$288$	−7.44137	−	13.5481i	−0.438487	−	0.798331i
$289$	−0.775572	+	0.851084i	−0.0456219	+	0.0500637i
$290$	−0.686192	+	0.0395582i	−0.0402946	+	0.00232294i
$291$	−11.6115	−	5.76274i	−0.680676	−	0.337818i
$292$	−15.7845	−	50.3269i	−0.923716	−	2.94516i
$293$	3.84773	−	1.00685i	0.224787	−	0.0588206i	−0.139042	−	0.990287i	$-0.544402\pi$
$293$	3.84773	−	1.00685i	0.224787	−	0.0588206i	0.363828	+	0.931466i	$0.381469\pi$
$294$	−37.6741	−	4.35823i	−2.19720	−	0.254177i
$295$	−4.13123	+	5.29860i	−0.240530	+	0.308496i
$296$	−22.6640	+	25.5191i	−1.31732	+	1.48327i
$297$	0.232041	−	8.05682i	0.0134644	−	0.467504i
$298$	−23.0577	−	1.62553i	−1.33570	−	0.0941646i
$299$	−4.14854	+	4.43705i	−0.239916	+	0.256601i
$300$	34.3468	−	36.2675i	1.98301	−	2.09391i
$301$	2.86935	−	0.595842i	0.165387	−	0.0343438i
$302$	0.869153	+	38.8050i	0.0500141	+	2.23297i
$303$	3.89900	+	8.45935i	0.223991	+	0.485977i
$304$	−13.2736	+	33.7903i	−0.761293	+	1.93801i
$305$	−0.556830	+	0.161040i	−0.0318840	+	0.00922114i
$306$	18.2347	−	13.5719i	1.04241	−	0.775854i
$307$	−18.1393	+	17.9661i	−1.03527	+	1.02538i	−0.0356036	+	0.999366i	$0.511335\pi$
$307$	−18.1393	+	17.9661i	−1.03527	+	1.02538i	−0.999662	+	0.0260107i	$0.991720\pi$
$308$	−13.8567	+	6.44049i	−0.789556	+	0.366981i
$309$	8.31489	+	10.1193i	0.473018	+	0.575669i
$310$	−0.0524367	+	0.159989i	−0.00297820	+	0.00908677i
$311$	0.498262	−	0.332640i	0.0282538	−	0.0188623i	−0.541031	−	0.841003i	$-0.681966\pi$
$311$	0.498262	−	0.332640i	0.0282538	−	0.0188623i	0.569284	+	0.822141i	$0.307220\pi$
$312$	15.0422	+	14.5220i	0.851598	+	0.822145i
$313$	−17.2309	−	3.46327i	−0.973949	−	0.195756i	−0.315951	−	0.948775i	$-0.602324\pi$
$313$	−17.2309	−	3.46327i	−0.973949	−	0.195756i	−0.657998	+	0.753020i	$0.728597\pi$
$314$	21.7856	−	9.78878i	1.22943	−	0.552413i
$315$	0.356035	−	0.711655i	0.0200603	−	0.0400972i
$316$	−15.4166	−	8.40353i	−0.867249	−	0.472736i
$317$	−26.5799	+	13.4042i	−1.49287	+	0.752853i	−0.993532	−	0.113551i	$-0.963777\pi$
$317$	−26.5799	+	13.4042i	−1.49287	+	0.752853i	−0.499342	+	0.866405i	$0.666425\pi$
$318$	−1.77244	+	19.0497i	−0.0993937	+	1.06825i
$319$	−1.54457	+	1.95510i	−0.0864795	+	0.109464i
$320$	−0.584282	−	0.822871i	−0.0326624	−	0.0459999i
$321$	9.28776	−	10.5935i	0.518392	−	0.591272i
$322$	−4.97656	+	6.64186i	−0.277333	+	0.370137i
$323$	−17.8142	−	4.29790i	−0.991206	−	0.239142i
$324$	−44.3721	+	21.3185i	−2.46512	+	1.18436i
$325$	−2.89368	+	5.87767i	−0.160512	+	0.326034i
$326$	0.673297	−	9.13389i	0.0372905	−	0.505879i
$327$	−5.81648	−	30.4487i	−0.321652	−	1.68382i
$328$	7.78201	−	4.37204i	0.429690	−	0.241406i
$329$	−6.34348	−	0.857511i	−0.349727	−	0.0472761i
$330$	1.12411	+	12.9815i	0.0618804	+	0.714609i
$331$	17.0195	+	7.12959i	0.935477	+	0.391878i	0.800746	−	0.599005i	$-0.204437\pi$
$331$	17.0195	+	7.12959i	0.935477	+	0.391878i	0.134732	+	0.990882i	$0.456983\pi$
$332$	−3.53460	−	1.27228i	−0.193986	−	0.0698254i
$333$	−8.11306	−	8.03556i	−0.444593	−	0.440346i
$334$	11.7255	+	1.66152i	0.641593	+	0.0909143i
$335$	−0.621081	−	4.95203i	−0.0339333	−	0.270559i
$336$	10.4369	+	8.08393i	0.569380	+	0.441015i
$337$	3.94762	−	6.29856i	0.215041	−	0.343105i	−0.722263	−	0.691618i	$-0.756898\pi$
$337$	3.94762	−	6.29856i	0.215041	−	0.343105i	0.937304	+	0.348514i	$0.113314\pi$
$338$	25.4578	+	12.8383i	1.38472	+	0.698312i
$339$	−5.65271	−	8.18075i	−0.307013	−	0.444317i
$340$	6.50061	−	6.11702i	0.352545	−	0.331742i
$341$	0.307414	+	0.527250i	0.0166474	+	0.0285522i
$342$	−23.9050	−	10.9255i	−1.29264	−	0.590782i
$343$	9.43598	−	2.86031i	0.509495	−	0.154442i
$344$	25.0887	+	8.84977i	1.35269	+	0.477148i
$345$	2.69747	+	4.12575i	0.145227	+	0.222123i
$346$	7.23839	−	52.2857i	0.389138	−	2.81090i
$347$	−4.12920	−	1.82368i	−0.221667	−	0.0979004i	0.290197	−	0.956967i	$-0.406279\pi$
$347$	−4.12920	−	1.82368i	−0.221667	−	0.0979004i	−0.511864	+	0.859066i	$0.671045\pi$
$348$	5.64434	+	1.09694i	0.302568	+	0.0588021i
$349$	0.0977777	+	0.674488i	0.00523392	+	0.0361045i	0.992108	−	0.125390i	$-0.0400182\pi$
$349$	0.0977777	+	0.674488i	0.00523392	+	0.0361045i	−0.986874	+	0.161495i	$0.948369\pi$
$350$	−3.05849	+	8.41243i	−0.163483	+	0.449663i
$351$	1.78735	−	1.66045i	0.0954016	−	0.0886280i
$352$	−31.4046	−	3.42947i	−1.67387	−	0.182792i
$353$	−7.67873	−	7.70334i	−0.408698	−	0.410007i	0.473569	−	0.880757i	$-0.342965\pi$
$353$	−7.67873	−	7.70334i	−0.408698	−	0.410007i	−0.882267	+	0.470749i	$0.843984\pi$
$354$	63.7993	−	49.4160i	3.39090	−	2.62643i
$355$	0.321737	+	3.23351i	0.0170760	+	0.171617i
$356$	−10.5480	−	29.6009i	−0.559042	−	1.56884i
$357$	−3.31957	+	5.77809i	−0.175690	+	0.305809i
$358$	−23.8115	+	24.5071i	−1.25848	+	1.29524i
$359$	4.44559	−	2.31372i	0.234629	−	0.122114i	−0.340300	−	0.940317i	$-0.610529\pi$
$359$	4.44559	−	2.31372i	0.234629	−	0.122114i	0.574929	+	0.818203i	$0.305030\pi$
$360$	6.10867	−	3.85588i	0.321955	−	0.203223i
$361$	0.574467	+	2.11237i	0.0302351	+	0.111177i
$362$	−51.7316	+	7.33042i	−2.71895	+	0.385278i
$363$	17.7224	+	13.1906i	0.930185	+	0.692325i
$364$	−4.33123	−	1.62193i	−0.227018	−	0.0850121i
$365$	5.24453	−	2.00229i	0.274511	−	0.104804i
$366$	6.95855	−	0.222692i	0.363729	−	0.0116403i
$367$	−1.87304	−	16.6579i	−0.0977719	−	0.869536i	−0.942470	−	0.334292i	$-0.891503\pi$
$367$	−1.87304	−	16.6579i	−0.0977719	−	0.869536i	0.844698	−	0.535244i	$-0.179780\pi$
$368$	−32.2831	+	13.0405i	−1.68287	+	0.679785i
$369$	1.31905	+	2.67928i	0.0686672	+	0.139478i
$370$	−5.06442	−	3.97476i	−0.263287	−	0.206638i
$371$	−0.743721	−	2.26916i	−0.0386121	−	0.117809i
$372$	0.755602	−	1.18862i	0.0391762	−	0.0616271i
$373$	1.22750	−	29.4978i	0.0635576	−	1.52734i	−0.612488	−	0.790480i	$-0.709831\pi$
$373$	1.22750	−	29.4978i	0.0635576	−	1.52734i	0.676046	−	0.736860i	$-0.263692\pi$
$374$	−1.33745	−	46.4382i	−0.0691577	−	2.40126i
$375$	8.35430	+	6.99998i	0.431414	+	0.361477i
$376$	−45.2496	−	36.4590i	−2.33357	−	1.88023i
$377$	−0.749691	+	0.0818685i	−0.0386110	+	0.00421644i
$378$	2.18135	−	2.52037i	0.112197	−	0.129634i
$379$	7.54506	+	2.33994i	0.387564	+	0.120194i	0.483832	−	0.875161i	$-0.339245\pi$
$379$	7.54506	+	2.33994i	0.387564	+	0.120194i	−0.0962682	+	0.995355i	$0.530691\pi$
$380$	−9.81796	−	3.18311i	−0.503651	−	0.163290i
$381$	5.06194	−	42.5640i	0.259331	−	2.18062i
$382$	30.7675	−	29.3254i	1.57420	−	1.50042i
$383$	−3.31608	−	6.22489i	−0.169444	−	0.318077i	0.783411	−	0.621504i	$-0.213478\pi$
$383$	−3.31608	−	6.22489i	−0.169444	−	0.318077i	−0.952855	+	0.303427i	$0.901869\pi$
$384$	−7.06598	−	18.3315i	−0.360585	−	0.935476i
$385$	−0.773810	−	1.43045i	−0.0394370	−	0.0729025i
$386$	20.1992	−	10.6776i	1.02811	−	0.543474i
$387$	−3.41276	+	8.22053i	−0.173480	+	0.417873i
$388$	21.5564	+	14.5913i	1.09436	+	0.740761i
$389$	−34.1732	−	12.5482i	−1.73265	−	0.636218i	−0.733589	−	0.679593i	$-0.762156\pi$
$389$	−34.1732	−	12.5482i	−1.73265	−	0.636218i	−0.999059	+	0.0433755i	$0.986189\pi$
$390$	−2.56183	+	2.99855i	−0.129723	+	0.151837i
$391$	−8.75499	−	15.2391i	−0.442759	−	0.770672i
$392$	41.6409	+	10.6121i	2.10318	+	0.535991i
$393$	−3.14610	−	4.74536i	−0.158700	−	0.239372i
$394$	1.57093	−	25.8124i	0.0791421	−	1.30041i
$395$	0.793092	−	1.69215i	0.0399048	−	0.0851411i
$396$	7.53855	−	45.7932i	0.378826	−	2.30120i
$397$	1.68746	−	25.0796i	0.0846911	−	1.25871i	−0.731867	−	0.681448i	$-0.761351\pi$
$397$	1.68746	−	25.0796i	0.0846911	−	1.25871i	0.816558	−	0.577263i	$-0.195879\pi$
$398$	−13.8084	−	17.2504i	−0.692154	−	0.864687i
$399$	7.70374	+	0.147892i	0.385669	+	0.00740386i
$400$	−29.2409	+	23.5603i	−1.46205	+	1.17802i
$401$	−12.4031	+	12.4428i	−0.619381	+	0.621366i	−0.946146	−	0.323740i	$-0.895060\pi$
$401$	−12.4031	+	12.4428i	−0.619381	+	0.621366i	0.326765	+	0.945106i	$0.394041\pi$
$402$	−7.45974	+	59.4784i	−0.372058	+	2.96651i
$403$	−0.0484772	+	0.178256i	−0.00241482	+	0.00887954i
$404$	−5.48332	−	17.8828i	−0.272805	−	0.889704i
$405$	−2.55171	−	4.57613i	−0.126795	−	0.227390i
$406$	−1.00611	+	0.222393i	−0.0499324	+	0.0110372i
$407$	−22.9643	+	4.15874i	−1.13830	+	0.206141i
$408$	−52.9290	+	29.2923i	−2.62038	+	1.45019i
$409$	−5.66615	−	6.29830i	−0.280173	−	0.311431i	0.586853	−	0.809693i	$-0.300367\pi$
$409$	−5.66615	−	6.29830i	−0.280173	−	0.311431i	−0.867026	+	0.498263i	$0.833971\pi$
$410$	0.912338	+	1.41510i	0.0450572	+	0.0698867i
$411$	−0.0442533	−	13.8327i	−0.00218285	−	0.682315i
$412$	−13.8243	−	22.3741i	−0.681076	−	1.10229i
$413$	−4.84899	+	8.82831i	−0.238603	+	0.434413i
$414$	−8.15666	−	23.8510i	−0.400878	−	1.17221i
$415$	0.112310	−	0.383732i	0.00551310	−	0.0188367i
$416$	−5.92751	−	7.50295i	−0.290620	−	0.367862i
$417$	21.5858	−	14.0147i	1.05706	−	0.686304i
$418$	−46.3190	+	27.2053i	−2.26554	+	1.33066i
$419$	6.94248	−	5.89304i	0.339162	−	0.287894i	−0.461340	−	0.887223i	$-0.652631\pi$
$419$	6.94248	−	5.89304i	0.339162	−	0.287894i	0.800502	+	0.599329i	$0.204566\pi$
$420$	−2.11374	+	3.10131i	−0.103140	+	0.151328i
$421$	37.4212	−	3.84438i	1.82380	−	0.187364i	0.871062	−	0.491172i	$-0.163432\pi$
$421$	37.4212	−	3.84438i	1.82380	−	0.187364i	0.952733	+	0.303809i	$0.0982584\pi$
$422$	−17.0148	−	2.74512i	−0.828267	−	0.133630i
$423$	13.0029	−	14.4536i	0.632225	−	0.702759i
$424$	4.88168	−	21.1209i	0.237076	−	1.02572i
$425$	−13.8044	−	12.9898i	−0.669610	−	0.630097i
$426$	5.84638	−	38.5888i	0.283258	−	1.86963i
$427$	−0.785649	+	0.371296i	−0.0380202	+	0.0179683i
$428$	−21.3322	+	18.5824i	−1.03113	+	0.898216i
$429$	1.96053	+	14.1617i	0.0946555	+	0.683734i
$430$	−1.37875	+	4.82510i	−0.0664893	+	0.232687i
$431$	2.28034	+	11.5364i	0.109840	+	0.555687i	0.995771	+	0.0918697i	$0.0292843\pi$
$431$	2.28034	+	11.5364i	0.109840	+	0.555687i	−0.885931	+	0.463817i	$0.846479\pi$
$432$	13.3019	−	4.31264i	0.639987	−	0.207492i
$433$	−27.5871	+	0.353044i	−1.32575	+	0.0169662i	−0.672457	−	0.740137i	$-0.734761\pi$
$433$	−27.5871	+	0.353044i	−1.32575	+	0.0169662i	−0.653296	+	0.757103i	$0.726614\pi$
$434$	−0.0394039	+	0.249303i	−0.00189145	+	0.0119669i
$435$	−0.0800422	+	0.606731i	−0.00383773	+	0.0290905i
$436$	3.38381	+	62.1571i	0.162055	+	2.97678i
$437$	−10.5708	+	17.3557i	−0.505670	+	0.830237i
$438$	−66.9796	+	7.74836i	−3.20041	+	0.370231i
$439$	−11.0418	+	4.29676i	−0.526998	+	0.205073i	−0.611346	−	0.791363i	$-0.709372\pi$
$439$	−11.0418	+	4.29676i	−0.526998	+	0.205073i	0.0843482	+	0.996436i	$0.473119\pi$
$440$	0.708216	−	14.7470i	0.0337629	−	0.703033i
$441$	−4.30253	+	13.7181i	−0.204883	+	0.653244i
$442$	9.73409	−	10.1476i	0.463004	−	0.482671i
$443$	−1.68097	−	4.27921i	−0.0798654	−	0.203311i	0.885262	−	0.465093i	$-0.153979\pi$
$443$	−1.68097	−	4.27921i	−0.0798654	−	0.203311i	−0.965127	+	0.261782i	$0.915690\pi$
$444$	32.8432	+	42.6841i	1.55867	+	2.02570i
$445$	3.07652	−	1.31197i	0.145841	−	0.0621935i
$446$	18.4766	+	26.3774i	0.874893	+	1.24900i
$447$	−5.27378	+	19.8940i	−0.249441	+	0.940955i
$448$	−1.06121	−	1.07833i	−0.0501376	−	0.0509461i
$449$	−6.75324	+	1.04526i	−0.318705	+	0.0493289i	−0.310309	−	0.950636i	$-0.600432\pi$
$449$	−6.75324	+	1.04526i	−0.318705	+	0.0493289i	−0.00839641	+	0.999965i	$0.502673\pi$
$450$	−15.8813	−	22.0658i	−0.748650	−	1.04019i
$451$	6.03169	+	0.933579i	0.284021	+	0.0439605i
$452$	9.04813	+	17.8002i	0.425588	+	0.837249i
$453$	34.0828	+	5.72281i	1.60135	+	0.268881i
$454$	37.1672	−	7.96644i	1.74434	−	0.373884i
$455$	0.144305	−	0.470625i	0.00676514	−	0.0220632i
$456$	59.1498	+	37.3362i	2.76994	+	1.74843i
$457$	37.1491	+	3.09715i	1.73776	+	0.144879i	0.909565	−	0.415562i	$-0.136415\pi$
$457$	37.1491	+	3.09715i	1.73776	+	0.144879i	0.828194	+	0.560441i	$0.189368\pi$
$458$	37.6799	+	22.4567i	1.76067	+	1.04933i
$459$	3.07711	+	6.35250i	0.143627	+	0.296509i
$460$	−4.25807	−	8.93580i	−0.198533	−	0.416634i
$461$	−4.87009	+	12.1683i	−0.226823	+	0.566735i	−0.997514	−	0.0704740i	$-0.977549\pi$
$461$	−4.87009	+	12.1683i	−0.226823	+	0.566735i	0.770691	+	0.637209i	$0.219911\pi$
$462$	4.76337	+	18.9441i	0.221612	+	0.881359i
$463$	−20.6281	+	18.4387i	−0.958671	+	0.856918i	−0.989781	−	0.142598i	$-0.954454\pi$
$463$	−20.6281	+	18.4387i	−0.958671	+	0.856918i	0.0311099	+	0.999516i	$0.490096\pi$
$464$	−4.09456	−	1.38566i	−0.190085	−	0.0643276i
$465$	0.131161	+	0.0725880i	0.00608245	+	0.00336619i
$466$	2.46368	+	10.6593i	0.114128	+	0.493782i
$467$	−12.2058	+	20.9343i	−0.564817	+	0.968725i	0.432917	+	0.901434i	$0.357484\pi$
$467$	−12.2058	+	20.9343i	−0.564817	+	0.968725i	−0.997733	+	0.0672910i	$0.978564\pi$
$468$	11.4794	−	8.09585i	0.530634	−	0.374231i
$469$	−2.10163	−	7.18065i	−0.0970441	−	0.331572i
$470$	6.34600	−	8.93735i	0.292719	−	0.412249i
$471$	−4.92135	−	20.6883i	−0.226764	−	0.953269i
$472$	−79.1379	+	45.8029i	−3.64262	+	2.10825i
$473$	9.75917	+	15.3519i	0.448727	+	0.705883i
$474$	−14.2498	+	17.3423i	−0.654517	+	0.796557i
$475$	−5.48049	+	21.2210i	−0.251462	+	0.973688i
$476$	8.16022	−	10.6053i	0.374023	−	0.486094i
$477$	6.96716	+	2.01497i	0.319004	+	0.0922589i
$478$	−22.8654	+	8.56247i	−1.04584	+	0.391638i
$479$	31.5193	−	27.8131i	1.44015	−	1.27081i	0.535584	−	0.844482i	$-0.320092\pi$
$479$	31.5193	−	27.8131i	1.44015	−	1.27081i	0.904568	−	0.426329i	$-0.140193\pi$
$480$	−7.05729	+	3.22544i	−0.322120	+	0.147220i
$481$	−5.77260	−	4.07114i	−0.263208	−	0.185628i
$482$	5.32362	−	15.5669i	0.242484	−	0.709053i
$483$	4.97736	+	5.46197i	0.226478	+	0.248528i
$484$	−31.7189	−	31.0164i	−1.44177	−	1.40984i
$485$	−1.41077	+	2.38443i	−0.0640596	+	0.108271i
$486$	12.6267	+	47.6311i	0.572760	+	2.16059i
$487$	−0.149560	+	0.177341i	−0.00677722	+	0.00803608i	−0.767821	−	0.640665i	$-0.778659\pi$
$487$	−0.149560	+	0.177341i	−0.00677722	+	0.00803608i	0.761043	+	0.648701i	$0.224687\pi$
$488$	−7.84722	−	0.806167i	−0.355227	−	0.0364935i
$489$	−7.87573	−	2.11480i	−0.356153	−	0.0956344i
$490$	−1.52089	+	7.96173i	−0.0687070	+	0.359674i
$491$	−9.06372	−	27.0678i	−0.409040	−	1.22155i	−0.929869	−	0.367892i	$-0.880080\pi$
$491$	−9.06372	−	27.0678i	−0.409040	−	1.22155i	0.520829	−	0.853661i	$-0.325623\pi$
$492$	−4.47239	−	13.3563i	−0.201631	−	0.602148i
$493$	0.409410	−	2.14322i	0.0184389	−	0.0965259i
$494$	−15.7027	−	4.21651i	−0.706499	−	0.189710i
$495$	4.91369	+	0.504797i	0.220854	+	0.0226889i
$496$	−0.682630	+	0.809428i	−0.0306510	+	0.0363444i
$497$	1.24826	+	4.70873i	0.0559919	+	0.211215i
$498$	−2.44537	+	4.13309i	−0.109580	+	0.185208i
$499$	4.59277	+	4.49106i	0.205601	+	0.201047i	0.794681	−	0.607027i	$-0.207638\pi$
$499$	4.59277	+	4.49106i	0.205601	+	0.201047i	−0.589080	+	0.808075i	$0.700510\pi$
$500$	−14.7419	−	16.1772i	−0.659277	−	0.723466i
$501$	3.41204	−	9.97720i	0.152439	−	0.445749i
$502$	−34.5607	−	24.3740i	−1.54252	−	1.08786i
$503$	−10.5795	+	4.83524i	−0.471719	+	0.215593i	−0.637318	−	0.770601i	$-0.719956\pi$
$503$	−10.5795	+	4.83524i	−0.471719	+	0.215593i	0.165600	+	0.986193i	$0.447044\pi$
$504$	8.12006	−	7.16526i	0.361696	−	0.319166i
$505$	1.86437	−	0.698154i	0.0829633	−	0.0310675i
$506$	−49.4900	−	14.3129i	−2.20010	−	0.636288i
$507$	15.4811	−	20.1198i	0.687540	−	0.893550i
$508$	−21.5231	+	83.3399i	−0.954934	+	3.69761i
$509$	−8.04392	+	9.78956i	−0.356540	+	0.433915i	−0.919813	−	0.392356i	$-0.871660\pi$
$509$	−8.04392	+	9.78956i	−0.356540	+	0.433915i	0.563273	+	0.826271i	$0.309542\pi$
$510$	−6.12164	−	9.62981i	−0.271071	−	0.426415i
$511$	7.28375	−	4.21564i	0.322214	−	0.186489i
$512$	11.5845	+	48.6988i	0.511967	+	2.15220i
$513$	4.72517	−	6.65467i	0.208621	−	0.293811i
$514$	19.7777	+	67.5748i	0.872359	+	2.98060i
$515$	2.28758	−	1.61332i	0.100803	−	0.0710913i
$516$	21.1451	−	36.2663i	0.930862	−	1.59653i
$517$	−8.94804	−	38.7142i	−0.393534	−	1.70265i
$518$	−8.44436	−	4.67333i	−0.371024	−	0.205335i
$519$	−44.5182	−	15.0656i	−1.95413	−	0.661306i
$520$	3.33169	−	2.97807i	0.146104	−	0.130597i
$521$	7.80332	+	31.0341i	0.341870	+	1.35963i	0.862591	+	0.505902i	$0.168840\pi$
$521$	7.80332	+	31.0341i	0.341870	+	1.35963i	−0.520721	+	0.853727i	$0.674337\pi$
$522$	1.16285	−	2.90548i	0.0508966	−	0.127169i
$523$	−4.21711	−	8.84986i	−0.184402	−	0.386977i	0.789566	−	0.613666i	$-0.210306\pi$
$523$	−4.21711	−	8.84986i	−0.184402	−	0.386977i	−0.973967	+	0.226688i	$0.927210\pi$
$524$	4.98416	+	10.2895i	0.217734	+	0.449499i
$525$	6.84628	+	4.08028i	0.298796	+	0.178078i
$526$	33.1137	+	2.76072i	1.44383	+	0.120373i
$527$	−0.451971	−	0.285290i	−0.0196882	−	0.0124274i
$528$	−24.0231	+	78.3469i	−1.04547	+	3.40961i
$529$	3.43262	−	0.735749i	0.149244	−	0.0319891i
$530$	4.03258	+	0.677106i	0.175164	+	0.0294116i
$531$	−13.8623	−	27.2709i	−0.601571	−	1.18346i
$532$	−15.2905	−	2.36665i	−0.662928	−	0.102607i
$533$	1.07916	+	1.49941i	0.0467435	+	0.0649466i
$534$	−39.6987	+	6.14453i	−1.71793	+	0.265900i
$535$	−2.11207	−	2.14613i	−0.0913127	−	0.0927851i
$536$	17.4042	−	65.6531i	0.751748	−	2.83578i
$537$	17.4551	+	24.9191i	0.753244	+	1.07534i
$538$	−47.3165	+	20.1780i	−2.03996	+	0.869937i
$539$	17.9186	+	23.2877i	0.771810	+	1.00307i
$540$	1.45353	+	3.70022i	0.0625499	+	0.159232i
$541$	15.1272	−	15.7698i	0.650369	−	0.677996i	−0.311894	−	0.950117i	$-0.600963\pi$
$541$	15.1272	−	15.7698i	0.650369	−	0.677996i	0.962263	+	0.272121i	$0.0877250\pi$
$542$	21.3167	−	67.9657i	0.915630	−	2.91938i
$543$	−2.23158	+	46.4675i	−0.0957663	+	1.99411i
$544$	25.7822	−	10.0327i	1.10540	−	0.430150i
$545$	−6.58152	+	0.761365i	−0.281921	+	0.0326133i
$546$	−3.07549	+	5.04952i	−0.131619	+	0.216099i
$547$	−0.765686	−	14.0648i	−0.0327384	−	0.601369i	−0.968542	−	0.248849i	$-0.919948\pi$
$547$	−0.765686	−	14.0648i	−0.0327384	−	0.601369i	0.935804	−	0.352521i	$-0.114675\pi$
$548$	−3.63300	+	27.5387i	−0.155194	+	1.17639i
$549$	0.412035	−	2.60689i	0.0175852	−	0.111259i
$550$	−55.5592	+	0.711014i	−2.36905	+	0.0303177i
$551$	−2.39998	+	0.778104i	−0.102243	+	0.0331484i
$552$	13.0084	+	65.8103i	0.553676	+	2.80107i
$553$	0.769721	−	2.69373i	0.0327318	−	0.114549i
$554$	10.1774	+	73.5157i	0.432398	+	3.12338i
$555$	−4.32229	+	3.76514i	−0.183471	+	0.159821i
$556$	−46.7255	+	22.0824i	−1.98160	+	0.936500i
$557$	3.89400	−	25.7021i	0.164994	−	1.08903i	−0.742768	−	0.669549i	$-0.766487\pi$
$557$	3.89400	−	25.7021i	0.164994	−	1.08903i	0.907762	−	0.419486i	$-0.137790\pi$
$558$	−0.558280	−	0.525337i	−0.0236339	−	0.0222393i
$559$	−1.23993	+	5.36462i	−0.0524433	+	0.226899i
$560$	1.88707	−	2.09760i	0.0797433	−	0.0886399i
$561$	−40.8368	−	6.58850i	−1.72413	−	0.278167i
$562$	0.354288	−	0.0363970i	0.0149447	−	0.00153531i
$563$	22.4645	−	32.9601i	0.946765	−	1.38910i	0.0257105	−	0.999669i	$-0.491815\pi$
$563$	22.4645	−	32.9601i	0.946765	−	1.38910i	0.921054	−	0.389434i	$-0.127329\pi$
$564$	−69.9076	+	59.3403i	−2.94364	+	2.49868i
$565$	−1.83254	+	1.07634i	−0.0770955	+	0.0452818i
$566$	−37.6962	+	24.4745i	−1.58449	+	1.02874i
$567$	−4.86918	−	6.16333i	−0.204486	−	0.258835i
$568$	−12.4219	+	42.4420i	−0.521211	+	1.78083i
$569$	−13.3987	−	39.1795i	−0.561704	−	1.64249i	−0.750799	−	0.660531i	$-0.770331\pi$
$569$	−13.3987	−	39.1795i	−0.561704	−	1.64249i	0.189094	−	0.981959i	$-0.439445\pi$
$570$	−6.35187	+	11.5645i	−0.266050	+	0.484384i
$571$	8.50353	+	13.7626i	0.355862	+	0.575947i	0.978420	−	0.206627i	$-0.0662487\pi$
$571$	8.50353	+	13.7626i	0.355862	+	0.575947i	−0.622558	+	0.782574i	$0.713907\pi$
$572$	−0.0918454	−	28.7090i	−0.00384025	−	1.20038i
$573$	−20.5069	−	31.8076i	−0.856688	−	1.32878i
$574$	1.68814	+	1.87648i	0.0704617	+	0.0783228i
$575$	−18.3913	+	10.1782i	−0.766969	+	0.424461i
$576$	4.52157	−	0.818836i	0.188399	−	0.0341181i
$577$	33.1157	−	7.31996i	1.37862	−	0.304734i	0.536447	−	0.843934i	$-0.319766\pi$
$577$	33.1157	−	7.31996i	1.37862	−	0.304734i	0.842178	+	0.539200i	$0.181273\pi$
$578$	−1.43955	−	2.58163i	−0.0598775	−	0.107382i
$579$	−5.96369	−	19.4495i	−0.247843	−	0.808293i
$580$	0.322497	−	1.18585i	0.0133909	−	0.0492398i
$581$	0.0745915	−	0.594736i	0.00309458	−	0.0246738i
$582$	23.4923	−	23.5676i	0.973787	−	0.976908i
$583$	11.5424	−	9.30009i	0.478038	−	0.385170i
$584$	76.3843	+	1.46638i	3.16080	+	0.0606793i
$585$	0.934301	+	1.16719i	0.0386286	+	0.0482575i
$586$	−0.685415	+	10.1869i	−0.0283142	+	0.420817i
$587$	0.723579	−	4.39541i	0.0298653	−	0.181418i	−0.967608	−	0.252456i	$-0.918762\pi$
$587$	0.723579	−	4.39541i	0.0298653	−	0.181418i	0.997474	+	0.0710383i	$0.0226313\pi$
$588$	28.7774	−	61.3997i	1.18676	−	2.53208i
$589$	−0.0375420	+	0.616864i	−0.00154689	+	0.0254174i
$590$	−9.53056	−	14.3752i	−0.392367	−	0.591819i
$591$	−22.3123	−	5.68623i	−0.917804	−	0.233900i
$592$	−20.1695	−	35.1073i	−0.828962	−	1.44290i
$593$	26.1041	−	30.5541i	1.07197	−	1.25471i	0.106465	−	0.994316i	$-0.466047\pi$
$593$	26.1041	−	30.5541i	1.07197	−	1.25471i	0.965503	−	0.260391i	$-0.0838514\pi$
$594$	19.4229	+	7.13198i	0.796932	+	0.292629i
$595$	1.17944	+	0.798350i	0.0483523	+	0.0327292i
$596$	15.8463	−	38.1701i	0.649091	−	1.56351i
$597$	−17.3936	+	9.19448i	−0.711873	+	0.376305i
$598$	−7.41926	−	13.7151i	−0.303396	−	0.560852i
$599$	−7.23090	−	18.7594i	−0.295446	−	0.766486i	−0.998469	−	0.0553187i	$-0.982383\pi$
$599$	−7.23090	−	18.7594i	−0.295446	−	0.766486i	0.703022	−	0.711168i	$-0.251833\pi$
$600$	34.0170	+	63.8561i	1.38874	+	2.60691i
$601$	9.89972	−	9.43570i	0.403818	−	0.384890i	−0.460647	−	0.887584i	$-0.652383\pi$
$601$	9.89972	−	9.43570i	0.403818	−	0.384890i	0.864465	+	0.502693i	$0.167657\pi$
$602$	−0.888410	+	7.47031i	−0.0362089	+	0.304467i
$603$	21.6164	+	7.00832i	0.880289	+	0.285401i
$604$	−66.2847	−	20.5568i	−2.69709	−	0.836443i
$605$	3.09002	−	3.57027i	0.125627	−	0.145152i
$606$	−23.7700	+	2.59576i	−0.965590	+	0.105445i
$607$	26.8921	+	21.6678i	1.09152	+	0.879469i	0.993285	−	0.115694i	$-0.0369093\pi$
$607$	26.8921	+	21.6678i	1.09152	+	0.879469i	0.0982323	+	0.995164i	$0.468681\pi$
$608$	−24.5195	−	20.5446i	−0.994397	−	0.833194i
$609$	0.0264120	+	0.917066i	0.00107027	+	0.0371614i
$610$	0.0618669	−	1.48671i	0.00250492	−	0.0601951i
$611$	6.45205	−	10.1496i	0.261022	−	0.410608i
$612$	12.6580	+	38.6209i	0.511671	+	1.56116i
$613$	−15.0294	−	11.7957i	−0.607033	−	0.476424i	0.266074	−	0.963953i	$-0.414273\pi$
$613$	−15.0294	−	11.7957i	−0.607033	−	0.476424i	−0.873107	+	0.487528i	$0.837899\pi$
$614$	−28.9479	−	58.7992i	−1.16824	−	2.37294i
$615$	1.39002	−	0.561489i	0.0560510	−	0.0226414i
$616$	−2.47309	−	21.9944i	−0.0996435	−	0.886180i
$617$	−35.6101	+	1.13962i	−1.43361	+	0.0458793i	−0.739095	−	0.673601i	$-0.764747\pi$
$617$	−35.6101	+	1.13962i	−1.43361	+	0.0458793i	−0.694513	+	0.719481i	$0.744380\pi$
$618$	−31.4102	+	11.9920i	−1.26350	+	0.482387i
$619$	−5.39345	−	2.01970i	−0.216781	−	0.0811786i	0.239943	−	0.970787i	$-0.422871\pi$
$619$	−5.39345	−	2.01970i	−0.216781	−	0.0811786i	−0.456724	+	0.889609i	$0.650977\pi$
$620$	−0.241482	−	0.179732i	−0.00969814	−	0.00721821i
$621$	7.75001	−	1.09818i	0.310997	−	0.0440686i
$622$	0.403583	+	1.48401i	0.0161822	+	0.0595035i
$623$	4.23994	−	2.67631i	0.169870	−	0.107224i
$624$	−22.0019	+	11.4510i	−0.880780	+	0.458406i
$625$	−14.9666	+	15.4038i	−0.598662	+	0.616152i
$626$	22.4753	−	39.1209i	0.898296	−	1.56359i
$627$	16.0546	+	45.0543i	0.641161	+	1.79929i
$628$	4.22813	+	42.4933i	0.168721	+	1.69567i
$629$	16.1577	−	12.5150i	0.644251	−	0.499006i
$630$	1.44212	+	1.44674i	0.0574554	+	0.0576395i
$631$	34.0302	+	3.71621i	1.35472	+	0.147940i	0.756817	−	0.653627i	$-0.226753\pi$
$631$	34.0302	+	3.71621i	1.35472	+	0.147940i	0.597905	+	0.801567i	$0.296000\pi$
$632$	18.6328	−	17.3099i	0.741173	−	0.688549i
$633$	−5.24337	+	14.4220i	−0.208405	+	0.573223i
$634$	−10.9633	−	75.6270i	−0.435410	−	3.00353i
$635$	−8.99295	−	1.74772i	−0.356874	−	0.0693562i
$636$	−31.2912	−	13.8199i	−1.24078	−	0.547997i
$637$	−1.21960	+	8.80964i	−0.0483222	+	0.349051i
$638$	−3.50015	−	5.35343i	−0.138572	−	0.211944i
$639$	−13.9528	−	4.92171i	−0.551966	−	0.194700i
$640$	−4.01838	+	1.21808i	−0.158840	+	0.0481490i
$641$	26.7904	+	12.2442i	1.05816	+	0.483617i	0.867189	−	0.497979i	$-0.165924\pi$
$641$	26.7904	+	12.2442i	1.05816	+	0.483617i	0.190970	+	0.981596i	$0.438837\pi$
$642$	18.2164	+	31.2432i	0.718944	+	1.23307i
$643$	−4.38382	+	4.12514i	−0.172881	+	0.162680i	−0.766889	−	0.641779i	$-0.778196\pi$
$643$	−4.38382	+	4.12514i	−0.172881	+	0.162680i	0.594008	+	0.804459i	$0.297545\pi$
$644$	−8.43556	−	12.2082i	−0.332407	−	0.481069i
$645$	3.98954	+	2.01192i	0.157088	+	0.0792192i
$646$	24.9824	−	39.8603i	0.982920	−	1.56828i
$647$	−3.11347	−	2.41154i	−0.122403	−	0.0948076i	0.549312	−	0.835618i	$-0.314890\pi$
$647$	−3.11347	−	2.41154i	−0.122403	−	0.0948076i	−0.671715	+	0.740810i	$0.734442\pi$
$648$	−8.87348	−	70.7505i	−0.348583	−	2.77934i
$649$	−61.9049	−	8.77198i	−2.42998	−	0.344330i
$650$	−11.9489	−	11.8347i	−0.468674	−	0.464197i
$651$	0.211449	+	0.0761111i	0.00828735	+	0.00298303i
$652$	15.1037	+	6.32703i	0.591505	+	0.247785i
$653$	1.91477	+	22.1123i	0.0749309	+	0.865320i	0.934885	+	0.354950i	$0.115502\pi$
$653$	1.91477	+	22.1123i	0.0749309	+	0.865320i	−0.859955	+	0.510371i	$0.829508\pi$
$654$	78.8598	+	10.6603i	3.08366	+	0.416850i
$655$	−1.06090	+	0.596030i	−0.0414529	+	0.0232888i
$656$	1.98683	+	10.4009i	0.0775727	+	0.406086i
$657$	−1.87907	+	25.4913i	−0.0733095	+	0.994510i
$658$	7.25796	−	14.7425i	0.282945	−	0.574721i
$659$	−15.1878	+	7.29698i	−0.591634	+	0.284250i	−0.704891	−	0.709316i	$-0.749004\pi$
$659$	−15.1878	+	7.29698i	−0.591634	+	0.284250i	0.113257	+	0.993566i	$0.463872\pi$
$660$	−22.6475	−	5.46402i	−0.881553	−	0.212686i
$661$	−0.643252	+	0.858503i	−0.0250196	+	0.0333919i	−0.812615	−	0.582800i	$-0.801957\pi$
$661$	−0.643252	+	0.858503i	−0.0250196	+	0.0333919i	0.787596	+	0.616192i	$0.211326\pi$
$662$	−31.2276	+	35.6179i	−1.21370	+	1.38433i
$663$	−7.24854	−	10.2084i	−0.281510	−	0.396463i
$664$	3.37314	−	4.26967i	0.130903	−	0.165695i
$665$	0.152565	−	1.63972i	0.00591623	−	0.0635858i
$666$	26.1733	−	13.1991i	1.01419	−	0.511456i
$667$	−2.12453	−	1.15808i	−0.0822621	−	0.0448409i
$668$	−9.47382	+	18.9366i	−0.366553	+	0.732679i
$669$	26.1556	−	11.7523i	1.01123	−	0.454372i
$670$	12.5606	+	2.52457i	0.485257	+	0.0975327i
$671$	−3.88069	−	3.74648i	−0.149813	−	0.144631i
$672$	−9.67454	+	6.45873i	−0.373203	+	0.249151i
$673$	−6.41741	+	19.5801i	−0.247373	+	0.754757i	0.748428	+	0.663216i	$0.230809\pi$
$673$	−6.41741	+	19.5801i	−0.247373	+	0.754757i	−0.995801	+	0.0915414i	$0.970821\pi$
$674$	12.1144	+	14.7433i	0.466628	+	0.567892i
$675$	7.65557	−	3.55826i	0.294663	−	0.136958i
$676$	−36.2194	+	35.8735i	−1.39306	+	1.37975i
$677$	−28.0715	+	20.8933i	−1.07888	+	0.802995i	−0.981348	−	0.192237i	$-0.938426\pi$
$677$	−28.0715	+	20.8933i	−1.07888	+	0.802995i	−0.0975283	+	0.995233i	$0.531094\pi$
$678$	24.5213	−	7.09177i	0.941734	−	0.272358i
$679$	−1.51857	+	3.86579i	−0.0582773	+	0.148355i
$680$	5.41201	+	11.7420i	0.207541	+	0.450286i
$681$	−0.757863	−	33.8362i	−0.0290414	−	1.29661i
$682$	−1.53401	+	0.318549i	−0.0587404	+	0.0121979i
$683$	31.4984	−	33.2598i	1.20525	−	1.27265i	0.252957	−	0.967478i	$-0.418597\pi$
$683$	31.4984	−	33.2598i	1.20525	−	1.27265i	0.952297	−	0.305174i	$-0.0987147\pi$
$684$	32.0948	−	34.3268i	1.22718	−	1.31252i
$685$	−2.94912	−	0.207908i	−0.112680	−	0.00794376i
$686$	−0.728674	+	25.3007i	−0.0278209	+	0.965985i
$687$	25.9349	−	29.2020i	0.989478	−	1.11412i
$688$	−19.4055	+	24.8889i	−0.739827	+	0.948881i
$689$	4.45681	+	0.515574i	0.169791	+	0.0196418i
$690$	−12.2417	+	3.20332i	−0.466033	+	0.121948i
$691$	−0.689380	−	2.19801i	−0.0262252	−	0.0836161i	0.940141	−	0.340785i	$-0.110693\pi$
$691$	−0.689380	−	2.19801i	−0.0262252	−	0.0836161i	−0.966366	+	0.257169i	$0.917210\pi$
$692$	84.5377	+	41.9559i	3.21364	+	1.59492i
$693$	7.39273	−	0.426183i	0.280827	−	0.0161894i
$694$	7.80496	−	8.56487i	0.296272	−	0.325118i
$695$	−2.64807	−	4.82121i	−0.100447	−	0.182879i
$696$	−4.10262	+	7.24806i	−0.155510	+	0.274737i
$697$	−5.06297	+	1.71338i	−0.191774	+	0.0648989i
$698$	−1.72155	−	0.311765i	−0.0651616	−	0.0118005i
$699$	9.73388	−	0.373869i	0.368169	−	0.0141410i
$700$	−12.5264	−	9.96138i	−0.473452	−	0.376505i
$701$	−34.7799	−	21.0311i	−1.31362	−	0.794332i	−0.325138	−	0.945667i	$-0.605411\pi$
$701$	−34.7799	−	21.0311i	−1.31362	−	0.794332i	−0.988483	+	0.151335i	$0.951643\pi$
$702$	2.58501	+	5.70423i	0.0975650	+	0.215292i
$703$	−21.6778	−	9.40882i	−0.817593	−	0.354860i
$704$	3.93113	−	8.52907i	0.148160	−	0.321451i
$705$	−6.75613	−	7.04313i	−0.254451	−	0.265260i
$706$	25.0106	−	12.4127i	0.941285	−	0.467158i
$707$	2.59254	−	1.47843i	0.0975025	−	0.0556020i
$708$	47.5614	+	136.222i	1.78747	+	5.11954i
$709$	−7.20355	+	1.39996i	−0.270535	+	0.0525767i	−0.324222	−	0.945981i	$-0.605102\pi$
$709$	−7.20355	+	1.39996i	−0.270535	+	0.0525767i	0.0536866	+	0.998558i	$0.482903\pi$
$710$	−8.13331	−	1.85247i	−0.305238	−	0.0695218i
$711$	5.44389	+	6.53954i	0.204162	+	0.245252i
$712$	45.5084	−	0.873645i	1.70550	−	0.0327412i
$713$	−0.454306	+	0.380658i	−0.0170139	+	0.0142557i
$714$	−11.3593	−	12.7903i	−0.425112	−	0.478665i
$715$	3.04937	−	0.195376i	0.114040	−	0.00730665i
$716$	−28.0320	−	54.2840i	−1.04761	−	2.02869i
$717$	3.66846	+	21.4279i	0.137001	+	0.800239i
$718$	2.00850	+	12.7075i	0.0749564	+	0.474238i
$719$	17.2176	−	0.440753i	0.642107	−	0.0164373i	0.296819	−	0.954934i	$-0.404074\pi$
$719$	17.2176	−	0.440753i	0.642107	−	0.0164373i	0.345289	+	0.938497i	$0.387781\pi$
$720$	2.03650	+	8.32409i	0.0758959	+	0.310221i
$721$	3.00036	−	2.93391i	0.111739	−	0.109265i
$722$	−5.61022	−	0.323423i	−0.208791	−	0.0120366i
$723$	−12.7249	−	7.25655i	−0.473245	−	0.269874i
$724$	16.9408	−	91.8692i	0.629601	−	3.41429i
$725$	−2.55516	−	0.530598i	−0.0948964	−	0.0197059i
$726$	−46.5543	+	32.3885i	−1.72779	+	1.20205i
$727$	−19.6026	+	12.1987i	−0.727020	+	0.452426i	−0.840985	−	0.541058i	$-0.818024\pi$
$727$	−19.6026	+	12.1987i	−0.727020	+	0.452426i	0.113965	+	0.993485i	$0.463645\pi$
$728$	4.21977	−	5.20304i	0.156395	−	0.192837i
$729$	11.6696	−	0.822686i	0.432207	−	0.0304699i
$730$	0.599165	+	14.3984i	0.0221761	+	0.532909i
$731$	−13.7879	−	7.98004i	−0.509963	−	0.295153i
$732$	−3.57295	+	11.9242i	−0.132060	+	0.440731i
$733$	19.8169	−	35.5388i	0.731954	−	1.31266i	−0.210260	−	0.977646i	$-0.567431\pi$
$733$	19.8169	−	35.5388i	0.731954	−	1.31266i	0.942214	−	0.335011i	$-0.108740\pi$
$734$	42.0757	+	9.01853i	1.55304	+	0.332880i
$735$	6.70899	+	2.66025i	0.247465	+	0.0981249i
$736$	−1.86366	−	30.6224i	−0.0686954	−	1.12876i
$737$	37.0783	−	27.9674i	1.36580	−	1.03019i
$738$	−7.59711	+	1.02698i	−0.279653	+	0.0378035i
$739$	−0.437837	−	1.95114i	−0.0161061	−	0.0717740i	0.967022	−	0.254694i	$-0.0819747\pi$
$739$	−0.437837	−	1.95114i	−0.0161061	−	0.0717740i	−0.983128	+	0.182920i	$0.941445\pi$
$740$	9.61413	−	6.32984i	0.353422	−	0.232690i
$741$	−6.31100	+	13.0287i	−0.231840	+	0.478621i
$742$	6.12984	+	0.0392215i	0.225034	+	0.00143986i
$743$	−10.9376	−	11.6983i	−0.401263	−	0.429169i	0.497595	−	0.867410i	$-0.334217\pi$
$743$	−10.9376	−	11.6983i	−0.401263	−	0.429169i	−0.898858	+	0.438241i	$0.855602\pi$
$744$	1.28507	+	1.58450i	0.0471128	+	0.0580907i
$745$	4.15754	+	1.43668i	0.152320	+	0.0526359i
$746$	70.8036	+	27.0318i	2.59230	+	0.989704i
$747$	1.36504	+	1.20453i	0.0499441	+	0.0440714i
$748$	79.4922	+	24.0964i	2.90652	+	0.881050i
$749$	−3.63828	−	2.67193i	−0.132940	−	0.0976301i
$750$	−23.8491	+	14.6305i	−0.870846	+	0.534230i
$751$	0.0936698	−	29.2792i	0.00341806	−	1.06841i	−0.843639	−	0.536911i	$-0.819591\pi$
$751$	0.0936698	−	29.2792i	0.00341806	−	1.06841i	0.847057	−	0.531503i	$-0.178372\pi$
$752$	58.0574	−	37.1682i	2.11714	−	1.35539i
$753$	−27.0906	+	26.1537i	−0.987237	+	0.953093i
$754$	0.411790	−	1.89164i	0.0149965	−	0.0688895i
$755$	1.75533	−	7.17482i	0.0638829	−	0.261118i
$756$	3.03473	+	5.12921i	0.110372	+	0.186547i
$757$	−13.3231	+	13.5380i	−0.484238	+	0.492046i	−0.911051	−	0.412293i	$-0.864728\pi$
$757$	−13.3231	+	13.5380i	−0.484238	+	0.492046i	0.426813	+	0.904340i	$0.359636\pi$
$758$	−11.8459	+	16.4590i	−0.430263	+	0.597819i
$759$	−20.7857	+	40.8912i	−0.754473	+	1.48426i
$760$	8.88755	−	12.0211i	0.322385	−	0.436051i
$761$	27.2934	−	40.6010i	0.989385	−	1.47178i	0.111006	−	0.993820i	$-0.464593\pi$
$761$	27.2934	−	40.6010i	0.989385	−	1.47178i	0.878379	−	0.477965i	$-0.158625\pi$
$762$	99.4840	+	47.0159i	3.60392	+	1.70321i
$763$	−9.55877	+	2.69833i	−0.346051	+	0.0976860i
$764$	32.2520	+	68.8130i	1.16684	+	2.48957i
$765$	−4.02113	+	1.59446i	−0.145384	+	0.0576478i
$766$	17.8557	−	2.99813i	0.645152	−	0.108327i
$767$	−11.2503	−	15.2170i	−0.406226	−	0.549453i
$768$	59.8168	−	2.68090i	2.15845	−	0.0967386i
$769$	13.2410	+	7.77706i	0.477483	+	0.280448i	0.725393	−	0.688335i	$-0.241658\pi$
$769$	13.2410	+	7.77706i	0.477483	+	0.280448i	−0.247910	+	0.968783i	$0.579744\pi$
$770$	4.11276	−	0.717

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)

\(f(q)\)	\(=\)	\(q+(-0.815103 + 2.43422i) q^{2} +(1.99272 + 1.11954i) q^{3} +(-3.66431 - 2.76391i) q^{4} +(0.269938 - 0.407156i) q^{5} +(-4.34946 + 3.93817i) q^{6} +(0.302286 - 0.667041i) q^{7} +(5.48157 - 3.76178i) q^{8} +(1.15702 + 1.89966i) q^{9} +O(q^{10})\)	\(q+(-0.815103 + 2.43422i) q^{2} +(1.99272 + 1.11954i) q^{3} +(-3.66431 - 2.76391i) q^{4} +(0.269938 - 0.407156i) q^{5} +(-4.34946 + 3.93817i) q^{6} +(0.302286 - 0.667041i) q^{7} +(5.48157 - 3.76178i) q^{8} +(1.15702 + 1.89966i) q^{9} +(0.771079 + 0.988963i) q^{10} +(4.53664 + 0.290667i) q^{11} +(-4.20763 - 9.61001i) q^{12} +(0.900447 + 1.04039i) q^{13} +(1.37733 + 1.27954i) q^{14} +(0.993736 - 0.509140i) q^{15} +(2.16687 + 7.58322i) q^{16} +(-3.64166 + 1.60836i) q^{17} +(-5.56728 + 1.26802i) q^{18} +(3.65716 + 2.79541i) q^{19} +(-2.11448 + 0.745859i) q^{20} +(1.34915 - 0.990803i) q^{21} +(-4.40538 + 10.8063i) q^{22} +(0.465205 + 4.39010i) q^{23} +(15.1347 - 1.35935i) q^{24} +(1.85371 + 4.38569i) q^{25} +(-3.26650 + 1.34386i) q^{26} +(-0.0623822 - 1.77195i) q^{27} +(-2.95131 + 1.60875i) q^{28} +(-0.311575 + 0.450920i) q^{29} +(0.429361 + 2.83397i) q^{30} +(0.0749012 + 0.111421i) q^{31} +(-6.94236 - 0.311146i) q^{32} +(8.71483 + 5.65815i) q^{33} +(-0.946769 - 10.1756i) q^{34} +(-0.189991 - 0.303138i) q^{35} +(1.01081 - 10.1588i) q^{36} +(-4.98277 + 1.23595i) q^{37} +(-9.78559 + 6.62377i) q^{38} +(0.629577 + 3.08129i) q^{39} +(-0.0519479 - 3.24730i) q^{40} +(1.33724 + 0.120108i) q^{41} +(1.31214 + 4.09172i) q^{42} +(2.35832 + 3.23288i) q^{43} +(-15.8203 - 13.6040i) q^{44} +(1.08578 + 0.0417038i) q^{45} +(-11.0657 - 2.44598i) q^{46} +(-2.50885 - 8.37293i) q^{47} +(-4.17173 + 17.5371i) q^{48} +(4.26115 + 4.86022i) q^{49} +(-12.1867 + 0.937540i) q^{50} +(-9.05742 - 0.871968i) q^{51} +(-0.423961 - 6.30107i) q^{52} +(2.40305 - 2.20396i) q^{53} +(4.36415 + 1.29247i) q^{54} +(1.34296 - 1.76866i) q^{55} +(-0.852264 - 4.79356i) q^{56} +(4.15811 + 9.66477i) q^{57} +(-0.843671 - 1.12599i) q^{58} +(-13.7131 - 1.05497i) q^{59} +(-5.04857 - 0.880951i) q^{60} +(-0.904609 - 0.767866i) q^{61} +(-0.332276 + 0.0915062i) q^{62} +(1.61690 - 0.197539i) q^{63} +(0.743022 - 1.92765i) q^{64} +(0.666667 - 0.0857803i) q^{65} +(-20.8767 + 16.6018i) q^{66} +(7.74629 - 6.66109i) q^{67} +(17.7895 + 4.17170i) q^{68} +(-3.98786 + 9.26904i) q^{69} +(0.892765 - 0.215391i) q^{70} +(-5.15286 + 4.20648i) q^{71} +(13.4884 + 6.06066i) q^{72} +(9.34847 + 6.68300i) q^{73} +(1.05290 - 13.1366i) q^{74} +(-1.21602 + 10.8147i) q^{75} +(-5.67469 - 20.3513i) q^{76} +(1.56525 - 2.93826i) q^{77} +(-8.01370 - 0.979044i) q^{78} +(3.78412 - 0.560935i) q^{79} +(3.67247 + 1.16475i) q^{80} +(4.92114 - 9.52980i) q^{81} +(-1.38236 + 3.15724i) q^{82} +(0.781737 - 0.242439i) q^{83} +(-7.68218 - 0.0983120i) q^{84} +(-0.328171 + 1.91688i) q^{85} +(-9.79182 + 3.10554i) q^{86} +(-1.12570 + 0.549735i) q^{87} +(25.9613 - 15.4726i) q^{88} +(5.71837 + 3.76492i) q^{89} +(-0.986541 + 2.60904i) q^{90} +(0.966178 - 0.286139i) q^{91} +(10.4292 - 17.3725i) q^{92} +(0.0245168 + 0.305885i) q^{93} +(22.4265 + 0.717709i) q^{94} +(2.12537 - 0.734445i) q^{95} +(-13.4858 - 8.39224i) q^{96} +(-5.66393 + 0.290172i) q^{97} +(-15.3041 + 6.41099i) q^{98} +(4.69682 + 8.95440i) 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

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