LMFDB - Embedded newform 983.2.c.a.2.10

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			2.10
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.10

$q$-expansion

$f(q)$	$=$	$q+(-0.696245 + 2.07926i) q^{2} +(-2.48076 - 1.39373i) q^{3} +(-2.24185 - 1.69098i) q^{4} +(1.99175 - 3.00421i) q^{5} +(4.62514 - 4.18777i) q^{6} +(1.53695 - 3.39151i) q^{7} +(1.46097 - 1.00260i) q^{8} +(2.65117 + 4.35284i) q^{9} +O(q^{10})$	\(q+(-0.696245 + 2.07926i) q^{2} +(-2.48076 - 1.39373i) q^{3} +(-2.24185 - 1.69098i) q^{4} +(1.99175 - 3.00421i) q^{5} +(4.62514 - 4.18777i) q^{6} +(1.53695 - 3.39151i) q^{7} +(1.46097 - 1.00260i) q^{8} +(2.65117 + 4.35284i) q^{9} +(4.85979 + 6.23303i) q^{10} +(-1.68953 - 0.108250i) q^{11} +(3.20473 + 7.31945i) q^{12} +(3.96988 + 4.58687i) q^{13} +(5.98174 + 5.55703i) q^{14} +(-9.12811 + 4.67678i) q^{15} +(-0.475549 - 1.66424i) q^{16} +(2.61959 - 1.15696i) q^{17} +(-10.8965 + 2.48183i) q^{18} +(5.19566 + 3.97138i) q^{19} +(-9.54526 + 3.36699i) q^{20} +(-8.53964 + 6.27145i) q^{21} +(1.40141 - 3.43760i) q^{22} +(-0.368058 - 3.47333i) q^{23} +(-5.02166 + 0.451033i) q^{24} +(-3.11161 - 7.36176i) q^{25} +(-12.3013 + 5.06082i) q^{26} +(-0.209904 - 5.96226i) q^{27} +(-9.18058 + 5.00431i) q^{28} +(4.78299 - 6.92206i) q^{29} +(-3.36885 - 22.2359i) q^{30} +(2.90512 + 4.32158i) q^{31} +(7.33174 + 0.328597i) q^{32} +(4.04045 + 2.62329i) q^{33} +(0.581738 + 6.25234i) q^{34} +(-7.12761 - 11.3723i) q^{35} +(1.41704 - 14.2415i) q^{36} +(-0.942967 + 0.233898i) q^{37} +(-11.8750 + 8.03806i) q^{38} +(-3.45547 - 16.9119i) q^{39} +(-0.102158 - 6.38598i) q^{40} +(11.9286 + 1.07139i) q^{41} +(-7.09429 - 22.1226i) q^{42} +(-1.14370 - 1.56783i) q^{43} +(3.60462 + 3.09964i) q^{44} +(18.3573 + 0.705086i) q^{45} +(7.47821 + 1.65300i) q^{46} +(-2.01340 - 6.71943i) q^{47} +(-1.13977 + 4.79137i) q^{48} +(-4.52542 - 5.16164i) q^{49} +(17.4735 - 1.34426i) q^{50} +(-8.11106 - 0.780861i) q^{51} +(-1.14356 - 16.9961i) q^{52} +(-1.57986 + 1.44896i) q^{53} +(12.5432 + 3.71475i) q^{54} +(-3.69032 + 4.86010i) q^{55} +(-1.15492 - 6.49583i) q^{56} +(-7.35416 - 17.0934i) q^{57} +(11.0626 + 14.7645i) q^{58} +(-10.1372 - 0.779872i) q^{59} +(28.3722 + 4.95080i) q^{60} +(-7.22504 - 6.13289i) q^{61} +(-11.0084 + 3.03162i) q^{62} +(18.8374 - 2.30139i) q^{63} +(-4.54288 + 11.7857i) q^{64} +(21.6869 - 2.79046i) q^{65} +(-8.26763 + 6.57469i) q^{66} +(-5.31088 + 4.56686i) q^{67} +(-7.82912 - 1.83595i) q^{68} +(-3.92781 + 9.12948i) q^{69} +(28.6086 - 6.90221i) q^{70} +(-2.38566 + 1.94751i) q^{71} +(8.23744 + 3.70128i) q^{72} +(-5.98515 - 4.27864i) q^{73} +(0.170201 - 2.12352i) q^{74} +(-2.54112 + 22.5995i) q^{75} +(-4.93235 - 17.6890i) q^{76} +(-2.96384 + 5.56368i) q^{77} +(37.5700 + 4.58997i) q^{78} +(-12.2282 + 1.81264i) q^{79} +(-5.94691 - 1.88610i) q^{80} +(-0.773557 + 1.49799i) q^{81} +(-10.5329 + 24.0567i) q^{82} +(14.9172 - 4.62626i) q^{83} +(29.7495 + 0.380716i) q^{84} +(1.74182 - 10.1742i) q^{85} +(4.05622 - 1.28645i) q^{86} +(-21.5129 + 10.5058i) q^{87} +(-2.57688 + 1.53578i) q^{88} +(6.07593 + 4.00033i) q^{89} +(-14.2472 + 37.6787i) q^{90} +(21.6579 - 6.41411i) q^{91} +(-5.04820 + 8.40906i) q^{92} +(-1.18380 - 14.7697i) q^{93} +(15.3733 + 0.491986i) q^{94} +(22.2793 - 7.69886i) q^{95} +(-17.7303 - 11.0336i) q^{96} +(2.88782 - 0.147948i) q^{97} +(13.8832 - 5.81576i) q^{98} +(-4.00803 - 7.64124i) 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 $

$2$	−0.696245	+	2.07926i	−0.492319	+	1.47026i	0.352809	+	0.935695i	$0.385227\pi$
$2$	−0.696245	+	2.07926i	−0.492319	+	1.47026i	−0.845128	+	0.534563i	$0.820476\pi$
$3$	−2.48076	−	1.39373i	−1.43227	−	0.804669i	−0.436782	−	0.899568i	$-0.643882\pi$
$3$	−2.48076	−	1.39373i	−1.43227	−	0.804669i	−0.995487	+	0.0948986i	$0.969747\pi$
$4$	−2.24185	−	1.69098i	−1.12093	−	0.845490i
$5$	1.99175	−	3.00421i	0.890737	−	1.34352i	−0.0479847	−	0.998848i	$-0.515280\pi$
$5$	1.99175	−	3.00421i	0.890737	−	1.34352i	0.938722	−	0.344676i	$-0.112011\pi$
$6$	4.62514	−	4.18777i	1.88821	−	1.70965i
$7$	1.53695	−	3.39151i	0.580911	−	1.28187i	−0.356711	−	0.934215i	$-0.616102\pi$
$7$	1.53695	−	3.39151i	0.580911	−	1.28187i	0.937622	−	0.347656i	$-0.113022\pi$
$8$	1.46097	−	1.00260i	0.516529	−	0.354474i
$9$	2.65117	+	4.35284i	0.883723	+	1.45095i
$10$	4.85979	+	6.23303i	1.53680	+	1.97106i
$11$	−1.68953	−	0.108250i	−0.509412	−	0.0326386i	−0.192884	−	0.981222i	$-0.561784\pi$
$11$	−1.68953	−	0.108250i	−0.509412	−	0.0326386i	−0.316528	+	0.948583i	$0.602517\pi$
$12$	3.20473	+	7.31945i	0.925126	+	2.11294i
$13$	3.96988	+	4.58687i	1.10105	+	1.27217i	0.959338	+	0.282260i	$0.0910840\pi$
$13$	3.96988	+	4.58687i	1.10105	+	1.27217i	0.141707	+	0.989909i	$0.454741\pi$
$14$	5.98174	+	5.55703i	1.59869	+	1.48518i
$15$	−9.12811	+	4.67678i	−2.35687	+	1.20754i
$16$	−0.475549	−	1.66424i	−0.118887	−	0.416060i
$17$	2.61959	−	1.15696i	0.635344	−	0.280603i	−0.0611909	−	0.998126i	$-0.519490\pi$
$17$	2.61959	−	1.15696i	0.635344	−	0.280603i	0.696535	+	0.717523i	$0.254724\pi$
$18$	−10.8965	+	2.48183i	−2.56834	+	0.584972i
$19$	5.19566	+	3.97138i	1.19197	+	0.911098i	0.997559	−	0.0698232i	$-0.0222435\pi$
$19$	5.19566	+	3.97138i	1.19197	+	0.911098i	0.194406	+	0.980921i	$0.437722\pi$
$20$	−9.54526	+	3.36699i	−2.13439	+	0.752881i
$21$	−8.53964	+	6.27145i	−1.86350	+	1.36854i
$22$	1.40141	−	3.43760i	0.298781	−	0.732899i
$23$	−0.368058	−	3.47333i	−0.0767454	−	0.724239i	−0.964529	−	0.263978i	$-0.914965\pi$
$23$	−0.368058	−	3.47333i	−0.0767454	−	0.724239i	0.887783	−	0.460262i	$-0.152244\pi$
$24$	−5.02166	+	0.451033i	−1.02504	+	0.0920666i
$25$	−3.11161	−	7.36176i	−0.622322	−	1.47235i
$26$	−12.3013	+	5.06082i	−2.41248	+	0.992508i
$27$	−0.209904	−	5.96226i	−0.0403961	−	1.14744i
$28$	−9.18058	+	5.00431i	−1.73497	+	0.945726i
$29$	4.78299	−	6.92206i	0.888178	−	1.28539i	−0.0695084	−	0.997581i	$-0.522143\pi$
$29$	4.78299	−	6.92206i	0.888178	−	1.28539i	0.957687	−	0.287813i	$-0.0929282\pi$
$30$	−3.36885	−	22.2359i	−0.615064	−	4.05970i
$31$	2.90512	+	4.32158i	0.521774	+	0.776178i	0.994467	−	0.105049i	$-0.0335000\pi$
$31$	2.90512	+	4.32158i	0.521774	+	0.776178i	−0.472693	+	0.881227i	$0.656718\pi$
$32$	7.33174	+	0.328597i	1.29608	+	0.0580883i
$33$	4.04045	+	2.62329i	0.703352	+	0.456655i
$34$	0.581738	+	6.25234i	0.0997672	+	1.07227i
$35$	−7.12761	−	11.3723i	−1.20479	−	1.92228i
$36$	1.41704	−	14.2415i	0.236174	−	2.37358i
$37$	−0.942967	+	0.233898i	−0.155023	+	0.0384526i	−0.317491	−	0.948261i	$-0.602840\pi$
$37$	−0.942967	+	0.233898i	−0.155023	+	0.0384526i	0.162469	+	0.986714i	$0.448054\pi$
$38$	−11.8750	+	8.03806i	−1.92638	+	1.30395i
$39$	−3.45547	−	16.9119i	−0.553318	−	2.70806i
$40$	−0.102158	−	6.38598i	−0.0161526	−	1.00971i
$41$	11.9286	+	1.07139i	1.86293	+	0.167324i	0.963142	−	0.268995i	$-0.0866915\pi$
$41$	11.9286	+	1.07139i	1.86293	+	0.167324i	0.899792	+	0.436319i	$0.143718\pi$
$42$	−7.09429	−	22.1226i	−1.09467	−	3.41359i
$43$	−1.14370	−	1.56783i	−0.174412	−	0.239092i	0.711787	−	0.702395i	$-0.247886\pi$
$43$	−1.14370	−	1.56783i	−0.174412	−	0.239092i	−0.886200	+	0.463303i	$0.846664\pi$
$44$	3.60462	+	3.09964i	0.543417	+	0.467288i
$45$	18.3573	+	0.705086i	2.73655	+	0.105108i
$46$	7.47821	+	1.65300i	1.10260	+	0.243722i
$47$	−2.01340	−	6.71943i	−0.293685	−	0.980129i	−0.969916	−	0.243440i	$-0.921724\pi$
$47$	−2.01340	−	6.71943i	−0.293685	−	0.980129i	0.676231	−	0.736689i	$-0.263612\pi$
$48$	−1.13977	+	4.79137i	−0.164512	+	0.691575i
$49$	−4.52542	−	5.16164i	−0.646489	−	0.737378i
$50$	17.4735	−	1.34426i	2.47112	−	0.190107i
$51$	−8.11106	−	0.780861i	−1.13578	−	0.109342i
$52$	−1.14356	−	16.9961i	−0.158584	−	2.35693i
$53$	−1.57986	+	1.44896i	−0.217010	+	0.199030i	−0.777057	−	0.629431i	$-0.783288\pi$
$53$	−1.57986	+	1.44896i	−0.217010	+	0.199030i	0.560047	+	0.828461i	$0.310783\pi$
$54$	12.5432	+	3.71475i	1.70692	+	0.505513i
$55$	−3.69032	+	4.86010i	−0.497603	+	0.655335i
$56$	−1.15492	−	6.49583i	−0.154332	−	0.868042i
$57$	−7.35416	−	17.0934i	−0.974082	−	2.26407i
$58$	11.0626	+	14.7645i	1.45260	+	1.93868i
$59$	−10.1372	−	0.779872i	−1.31975	−	0.101531i	−0.602375	−	0.798213i	$-0.705779\pi$
$59$	−10.1372	−	0.779872i	−1.31975	−	0.101531i	−0.717379	+	0.696683i	$0.754659\pi$
$60$	28.3722	+	4.95080i	3.66283	+	0.639146i
$61$	−7.22504	−	6.13289i	−0.925072	−	0.785237i	0.0518892	−	0.998653i	$-0.483476\pi$
$61$	−7.22504	−	6.13289i	−0.925072	−	0.785237i	−0.976961	+	0.213416i	$0.931541\pi$
$62$	−11.0084	+	3.03162i	−1.39806	+	0.385016i
$63$	18.8374	−	2.30139i	2.37329	−	0.289948i
$64$	−4.54288	+	11.7857i	−0.567860	+	1.47322i
$65$	21.6869	−	2.79046i	2.68993	−	0.346114i
$66$	−8.26763	+	6.57469i	−1.01768	+	0.809289i
$67$	−5.31088	+	4.56686i	−0.648827	+	0.557931i	−0.913719	−	0.406347i	$-0.866802\pi$
$67$	−5.31088	+	4.56686i	−0.648827	+	0.557931i	0.264892	+	0.964278i	$0.414664\pi$
$68$	−7.82912	−	1.83595i	−0.949421	−	0.222642i
$69$	−3.92781	+	9.12948i	−0.472853	+	1.09906i
$70$	28.6086	−	6.90221i	3.41938	−	0.824972i
$71$	−2.38566	+	1.94751i	−0.283126	+	0.231127i	−0.763296	−	0.646049i	$-0.776420\pi$
$71$	−2.38566	+	1.94751i	−0.283126	+	0.231127i	0.480170	+	0.877175i	$0.340575\pi$
$72$	8.23744	+	3.70128i	0.970791	+	0.436200i
$73$	−5.98515	−	4.27864i	−0.700508	−	0.500777i	0.174640	−	0.984632i	$-0.444124\pi$
$73$	−5.98515	−	4.27864i	−0.700508	−	0.500777i	−0.875148	+	0.483856i	$0.839236\pi$
$74$	0.170201	−	2.12352i	0.0197855	−	0.246855i
$75$	−2.54112	+	22.5995i	−0.293424	+	2.60957i
$76$	−4.93235	−	17.6890i	−0.565779	−	2.02907i
$77$	−2.96384	+	5.56368i	−0.337761	+	0.634040i
$78$	37.5700	+	4.58997i	4.25396	+	0.519712i
$79$	−12.2282	+	1.81264i	−1.37579	+	0.203938i	−0.793264	−	0.608878i	$-0.791620\pi$
$79$	−12.2282	+	1.81264i	−1.37579	+	0.203938i	−0.582521	+	0.812816i	$0.697934\pi$
$80$	−5.94691	−	1.88610i	−0.664884	−	0.210872i
$81$	−0.773557	+	1.49799i	−0.0859508	+	0.166444i
$82$	−10.5329	+	24.0567i	−1.16317	+	2.65662i
$83$	14.9172	−	4.62626i	1.63738	−	0.507798i	0.666126	−	0.745839i	$-0.267951\pi$
$83$	14.9172	−	4.62626i	1.63738	−	0.507798i	0.971255	+	0.238041i	$0.0765054\pi$
$84$	29.7495	+	0.380716i	3.24593	+	0.0415396i
$85$	1.74182	−	10.1742i	0.188927	−	1.10354i
$86$	4.05622	−	1.28645i	0.437393	−	0.138722i
$87$	−21.5129	+	10.5058i	−2.30643	+	1.12634i
$88$	−2.57688	+	1.53578i	−0.274696	+	0.163715i
$89$	6.07593	+	4.00033i	0.644047	+	0.424034i	0.829413	−	0.558636i	$-0.188675\pi$
$89$	6.07593	+	4.00033i	0.644047	+	0.424034i	−0.185366	+	0.982670i	$0.559347\pi$
$90$	−14.2472	+	37.6787i	−1.50179	+	3.97169i
$91$	21.6579	−	6.41411i	2.27036	−	0.672381i
$92$	−5.04820	+	8.40906i	−0.526311	+	0.876706i
$93$	−1.18380	−	14.7697i	−0.122754	−	1.53155i
$94$	15.3733	+	0.491986i	1.58563	+	0.0507445i
$95$	22.2793	−	7.69886i	2.28581	−	0.789886i
$96$	−17.7303	−	11.0336i	−1.80959	−	1.12611i
$97$	2.88782	−	0.147948i	0.293214	−	0.0150218i	0.0959967	−	0.995382i	$-0.469396\pi$
$97$	2.88782	−	0.147948i	0.293214	−	0.0150218i	0.197217	+	0.980360i	$0.436810\pi$
$98$	13.8832	−	5.81576i	1.40241	−	0.587481i
$99$	−4.00803	−	7.64124i	−0.402822	−	0.767973i
$100$	−5.47283	+	21.7656i	−0.547283	+	2.17656i
$101$	10.8434	+	7.85700i	1.07896	+	0.781801i	0.977054	−	0.212994i	$-0.0683214\pi$
$101$	10.8434	+	7.85700i	1.07896	+	0.781801i	0.101903	+	0.994794i	$0.467507\pi$
$102$	7.27090	−	16.3213i	0.719926	−	1.61605i
$103$	−1.60007	−	0.622642i	−0.157659	−	0.0613507i	0.282516	−	0.959263i	$-0.408831\pi$
$103$	−1.60007	−	0.622642i	−0.157659	−	0.0613507i	−0.440175	+	0.897912i	$0.645084\pi$
$104$	10.3987	+	2.72105i	1.01967	+	0.266821i
$105$	1.83195	+	38.1460i	0.178780	+	3.72267i
$106$	−1.91280	−	4.29376i	−0.185788	−	0.417047i
$107$	1.66401	−	7.88642i	0.160866	−	0.762409i	−0.820711	−	0.571343i	$-0.806423\pi$
$107$	1.66401	−	7.88642i	0.160866	−	0.762409i	0.981577	−	0.191066i	$-0.0611945\pi$
$108$	−9.61149	+	13.7214i	−0.924866	+	1.32035i
$109$	−0.00849477	−	0.0100727i	−0.000813651	−	0.000964786i	0.764036	−	0.645174i	$-0.223215\pi$
$109$	−0.00849477	−	0.0100727i	−0.000813651	−	0.000964786i	−0.764849	+	0.644209i	$0.777187\pi$
$110$	−7.53604	−	11.0570i	−0.718533	−	1.05424i
$111$	2.66527	+	0.733994i	0.252976	+	0.0696676i
$112$	−6.37518	−	0.945018i	−0.602398	−	0.0892958i
$113$	3.34067	+	1.63141i	0.314264	+	0.153471i	0.589189	−	0.807995i	$-0.299447\pi$
$113$	3.34067	+	1.63141i	0.314264	+	0.153471i	−0.274925	+	0.961466i	$0.588653\pi$
$114$	40.6619	−	3.39002i	3.80833	−	0.317505i
$115$	−11.1677	−	5.81227i	−1.04139	−	0.541997i
$116$	−22.4278	+	7.43029i	−2.08237	+	0.689885i
$117$	−9.44109	+	29.4408i	−0.872829	+	2.72180i
$118$	8.67955	−	20.5349i	0.799017	−	1.89039i
$119$	0.102337	−	10.6626i	0.00938125	−	0.977434i
$120$	−8.64689	+	15.9845i	−0.789350	+	1.45918i
$121$	−8.06727	−	1.03802i	−0.733388	−	0.0943652i
$122$	17.7823	−	10.7528i	1.60993	−	0.973508i
$123$	−28.0988	−	19.2831i	−2.53358	−	1.73870i
$124$	0.794864	−	14.6008i	0.0713809	−	1.31119i
$125$	−10.6008	−	1.98988i	−0.948161	−	0.177981i
$126$	−8.33026	+	40.7702i	−0.742119	+	3.63210i
$127$	−0.237328	−	0.571667i	−0.0210595	−	0.0507272i	0.912695	−	0.408641i	$-0.133997\pi$
$127$	−0.237328	−	0.571667i	−0.0210595	−	0.0507272i	−0.933755	+	0.357914i	$0.883488\pi$
$128$	−10.0317	−	8.29681i	−0.886689	−	0.733342i
$129$	0.652118	+	5.48341i	0.0574158	+	0.482788i
$130$	−9.29731	+	47.0356i	−0.815428	+	4.12529i
$131$	7.40315	+	3.79300i	0.646817	+	0.331396i	0.748221	−	0.663449i	$-0.230908\pi$
$131$	7.40315	+	3.79300i	0.646817	+	0.331396i	−0.101405	+	0.994845i	$0.532334\pi$
$132$	−4.62216	−	12.7133i	−0.402307	−	1.10655i
$133$	21.4544	−	11.5173i	1.86034	−	0.998678i
$134$	−5.79802	−	14.2224i	−0.500873	−	1.22862i
$135$	−18.3300	−	11.2447i	−1.57759	−	0.967792i
$136$	2.66716	−	4.31669i	0.228707	−	0.370153i
$137$	−2.15525	−	3.80766i	−0.184136	−	0.325310i	0.762856	−	0.646568i	$-0.223797\pi$
$137$	−2.15525	−	3.80766i	−0.184136	−	0.325310i	−0.946992	+	0.321258i	$0.895894\pi$
$138$	−16.2478	−	14.5233i	−1.38311	−	1.23630i
$139$	0.872135	−	1.66271i	0.0739736	−	0.141029i	−0.845772	−	0.533545i	$-0.820860\pi$
$139$	0.872135	−	1.66271i	0.0739736	−	0.141029i	0.919745	+	0.392516i	$0.128395\pi$
$140$	−3.25138	+	37.5477i	−0.274792	+	3.17336i
$141$	−4.37029	+	19.4754i	−0.368045	+	1.64013i
$142$	−2.38837	−	6.31636i	−0.200427	−	0.530057i
$143$	−6.21069	−	8.17939i	−0.519364	−	0.683995i
$144$	5.98341	−	6.48217i	0.498618	−	0.540181i
$145$	−11.2688	−	28.1561i	−0.935826	−	2.33824i
$146$	13.0635	−	9.46569i	1.08115	−	0.783386i
$147$	4.03257	+	19.1120i	0.332601	+	1.57633i
$148$	2.50951	+	1.07017i	0.206280	+	0.0879678i
$149$	1.72563	+	6.68183i	0.141369	+	0.547397i	0.999427	+	0.0338441i	$0.0107750\pi$
$149$	1.72563	+	6.68183i	0.141369	+	0.547397i	−0.858058	+	0.513553i	$0.828329\pi$
$150$	−45.2210	−	21.0185i	−3.69228	−	1.71615i
$151$	−21.0722	+	7.58493i	−1.71483	+	0.617253i	−0.996887	−	0.0788489i	$-0.974876\pi$
$151$	−21.0722	+	7.58493i	−1.71483	+	0.617253i	−0.717943	+	0.696102i	$0.754916\pi$
$152$	11.5724	+	0.592872i	0.938646	+	0.0480883i
$153$	11.9810	+	8.33537i	0.968609	+	0.673875i
$154$	−9.50478	−	10.0363i	−0.765917	−	0.808747i
$155$	18.7692	−	0.120094i	1.50758	−	0.00964615i
$156$	−20.8510	+	43.7570i	−1.66941	+	3.50336i
$157$	−13.1533	−	14.2497i	−1.04975	−	1.13725i	−0.990289	−	0.139023i	$-0.955604\pi$
$157$	−13.1533	−	14.2497i	−1.04975	−	1.13725i	−0.0594600	−	0.998231i	$-0.518938\pi$
$158$	4.74491	−	26.6877i	0.377484	−	2.12316i
$159$	5.93870	−	1.39264i	0.470970	−	0.110444i
$160$	15.5901	−	21.3716i	1.23251	−	1.68957i
$161$	−12.3455	−	4.09005i	−0.972963	−	0.322341i
$162$	−2.57614	−	2.65140i	−0.202400	−	0.208313i
$163$	16.7656	−	4.27267i	1.31318	−	0.334662i	0.474969	−	0.880003i	$-0.342459\pi$
$163$	16.7656	−	4.27267i	1.31318	−	0.334662i	0.838214	+	0.545341i	$0.183600\pi$
$164$	−24.9304	−	22.5729i	−1.94674	−	1.76265i
$165$	15.9285	−	6.91344i	1.24003	−	0.538211i
$166$	−0.766859	+	34.2378i	−0.0595198	+	2.65737i
$167$	−3.18442	−	17.2689i	−0.246418	−	1.33631i	−0.844792	−	0.535094i	$-0.820276\pi$
$167$	−3.18442	−	17.2689i	−0.246418	−	1.33631i	0.598374	−	0.801217i	$-0.295814\pi$
$168$	−6.18834	+	17.7242i	−0.477441	+	1.36745i
$169$	−3.41439	+	23.5531i	−0.262646	+	1.81178i
$170$	19.9420	+	10.7054i	1.52948	+	0.821068i
$171$	−3.51224	+	33.1447i	−0.268587	+	2.53464i
$172$	−0.0871660	+	5.44881i	−0.00664634	+	0.415468i
$173$	−11.3130	+	2.12358i	−0.860112	+	0.161453i	−0.595946	−	0.803024i	$-0.703223\pi$
$173$	−11.3130	+	2.12358i	−0.860112	+	0.161453i	−0.264166	+	0.964477i	$0.585097\pi$
$174$	−6.86604	−	52.0456i	−0.520513	−	3.94556i
$175$	−29.7499	−	0.761567i	−2.24888	−	0.0575691i
$176$	0.623300	+	2.86326i	0.0469830	+	0.215826i
$177$	24.0611	+	16.0632i	1.80854	+	1.20738i
$178$	−12.5481	+	9.84822i	−0.940516	+	0.738156i
$179$	−15.0085	−	7.21081i	−1.12179	−	0.538961i	−0.221893	−	0.975071i	$-0.571224\pi$
$179$	−15.0085	−	7.21081i	−1.12179	−	0.538961i	−0.899894	+	0.436110i	$0.856356\pi$
$180$	−39.9621	−	32.6226i	−2.97860	−	2.43154i
$181$	10.2081	+	20.4043i	0.758762	+	1.51664i	0.853474	+	0.521135i	$0.174491\pi$
$181$	10.2081	+	20.4043i	0.758762	+	1.51664i	−0.0947122	+	0.995505i	$0.530193\pi$
$182$	−1.74261	+	49.4982i	−0.129171	+	3.66905i
$183$	9.37603	+	25.2840i	0.693096	+	1.86905i
$184$	−4.02009	−	4.70540i	−0.296365	−	0.346887i
$185$	−1.17547	+	3.29874i	−0.0864225	+	0.242528i
$186$	31.5343	+	7.82193i	2.31221	+	0.573532i
$187$	−4.55111	+	1.67114i	−0.332810	+	0.122206i
$188$	−6.84868	+	18.4686i	−0.499491	+	1.34696i
$189$	−20.5437	−	8.45178i	−1.49433	−	0.614777i
$190$	0.496062	+	51.6848i	0.0359881	+	3.74961i
$191$	−12.3011	−	6.50250i	−0.890073	−	0.470504i	−0.0412305	−	0.999150i	$-0.513128\pi$
$191$	−12.3011	−	6.50250i	−0.890073	−	0.470504i	−0.848843	+	0.528645i	$0.822700\pi$
$192$	27.6959	−	22.9061i	1.99878	−	1.65311i
$193$	2.84175	+	2.70855i	0.204554	+	0.194966i	0.785294	−	0.619123i	$-0.212512\pi$
$193$	2.84175	+	2.70855i	0.204554	+	0.194966i	−0.580740	+	0.814089i	$0.697237\pi$
$194$	−1.70301	+	6.10754i	−0.122269	+	0.438496i
$195$	−57.6892	−	23.3032i	−4.13121	−	1.66878i
$196$	1.41708	+	19.2240i	0.101220	+	1.37314i
$197$	2.01387	−	0.540765i	0.143482	−	0.0385279i	−0.186877	−	0.982383i	$-0.559836\pi$
$197$	2.01387	−	0.540765i	0.143482	−	0.0385279i	0.330359	+	0.943855i	$0.392830\pi$
$198$	18.6787	−	3.01357i	1.32744	−	0.214165i
$199$	−5.64779	+	8.76010i	−0.400361	+	0.620987i	−0.981191	−	0.193038i	$-0.938166\pi$
$199$	−5.64779	+	8.76010i	−0.400361	+	0.620987i	0.580830	+	0.814025i	$0.302728\pi$
$200$	−11.9269	−	7.63557i	−0.843358	−	0.539916i
$201$	19.5400	−	3.92738i	1.37824	−	0.277016i
$202$	−23.8864	+	17.0758i	−1.68064	+	1.20145i
$203$	−16.1251	−	26.8604i	−1.13176	−	1.88523i
$204$	16.8634	+	15.4662i	1.18067	+	1.08285i
$205$	26.9775	−	33.7021i	1.88419	−	2.35386i
$206$	2.40867	−	2.89345i	0.167820	−	0.201596i
$207$	14.1431	−	10.8105i	0.983011	−	0.751380i
$208$	5.74578	−	8.78811i	0.398398	−	0.609346i
$209$	−8.34831	−	7.27220i	−0.577465	−	0.503028i
$210$	−80.5910	−	22.7499i	−5.56131	−	1.56989i
$211$	0.996195	+	6.05143i	0.0685809	+	0.416598i	0.998773	+	0.0495244i	$0.0157705\pi$
$211$	0.996195	+	6.05143i	0.0685809	+	0.416598i	−0.930192	+	0.367073i	$0.880360\pi$
$212$	5.99197	−	0.576853i	0.411530	−	0.0396184i
$213$	8.63256	−	1.50634i	0.591493	−	0.103213i
$214$	15.2394	+	8.95078i	1.04174	+	0.611863i
$215$	−6.98805	+	0.313194i	−0.476581	+	0.0213596i
$216$	−6.28445	−	8.50021i	−0.427603	−	0.578366i
$217$	19.1217	−	3.21070i	1.29806	−	0.217957i
$218$	0.0268581	−	0.0106498i	0.00181906	−	0.000721295i
$219$	8.88446	+	18.9559i	0.600356	+	1.28092i
$220$	16.4915	−	4.65535i	1.11186	−	0.313864i
$221$	15.7063	+	7.42274i	1.05652	+	0.499308i
$222$	−3.38184	+	5.03074i	−0.226974	+	0.337641i
$223$	15.5503	−	21.0329i	1.04132	−	1.40847i	0.132550	−	0.991176i	$-0.457683\pi$
$223$	15.5503	−	21.0329i	1.04132	−	1.40847i	0.908772	−	0.417294i	$-0.137021\pi$
$224$	12.3829	−	24.3606i	0.827369	−	1.62766i
$225$	23.7952	−	33.0616i	1.58634	−	2.20411i
$226$	−5.71806	+	5.81027i	−0.380360	+	0.386493i
$227$	−7.02562	−	11.8745i	−0.466307	−	0.788136i	0.531974	−	0.846761i	$-0.321451\pi$
$227$	−7.02562	−	11.8745i	−0.466307	−	0.788136i	−0.998280	+	0.0586250i	$0.981328\pi$
$228$	−12.4177	+	50.7566i	−0.822380	+	3.36143i
$229$	−1.71641	+	7.88470i	−0.113424	+	0.521035i	0.885034	+	0.465526i	$0.154135\pi$
$229$	−1.71641	+	7.88470i	−0.113424	+	0.521035i	−0.998458	+	0.0555099i	$0.982322\pi$
$230$	19.8607	−	19.1738i	1.30957	−	1.26428i
$231$	15.1068	−	9.67137i	0.993958	−	0.636330i
$232$	0.0476946	−	14.9083i	0.00313130	−	0.978780i
$233$	19.0015	−	11.6567i	1.24483	−	0.763656i	0.265148	−	0.964208i	$-0.414579\pi$
$233$	19.0015	−	11.6567i	1.24483	−	0.763656i	0.979683	+	0.200552i	$0.0642736\pi$
$234$	−54.6417	−	40.1285i	−3.57204	−	2.62328i
$235$	−24.1968	−	7.33473i	−1.57842	−	0.478465i
$236$	21.4074	+	18.8902i	1.39350	+	1.22965i
$237$	32.8617	+	12.5461i	2.13460	+	0.814958i
$238$	22.0990	+	7.63653i	1.43246	+	0.495003i
$239$	4.96424	+	6.12097i	0.321110	+	0.395933i	0.911577	−	0.411128i	$-0.134865\pi$
$239$	4.96424	+	6.12097i	0.321110	+	0.395933i	−0.590468	+	0.807061i	$0.701057\pi$
$240$	12.1242	+	12.9673i	0.782611	+	0.837037i
$241$	−18.5432	−	0.118648i	−1.19447	−	0.00764276i	−0.592104	−	0.805862i	$-0.701703\pi$
$241$	−18.5432	−	0.118648i	−1.19447	−	0.00764276i	−0.602368	+	0.798219i	$0.705776\pi$
$242$	7.77510	−	16.0512i	0.499802	−	1.03181i
$243$	−10.9420	+	7.20409i	−0.701928	+	0.462142i
$244$	5.82687	+	25.9664i	0.373027	+	1.66233i
$245$	−24.5202	+	3.31464i	−1.56654	+	0.211764i
$246$	59.6582	−	44.9989i	3.80367	−	2.86903i
$247$	2.40989	+	39.5977i	0.153338	+	2.51954i
$248$	8.57710	+	3.40099i	0.544647	+	0.215963i
$249$	−43.4539	−	9.31393i	−2.75378	−	0.590246i
$250$	11.5182	−	20.6563i	0.728476	−	1.30642i
$251$	2.53877	−	8.47277i	0.160246	−	0.534796i	−0.839721	−	0.543019i	$-0.817281\pi$
$251$	2.53877	−	8.47277i	0.160246	−	0.534796i	0.999966	+	0.00822235i	$0.00261728\pi$
$252$	−46.1222	−	26.6943i	−2.90543	−	1.68158i
$253$	0.245857	+	5.90813i	0.0154569	+	0.371441i
$254$	1.35388	−	0.0954465i	0.0849501	−	0.00598885i
$255$	−18.5011	+	22.8121i	−1.15858	+	1.42855i
$256$	2.78771	−	1.73480i	0.174232	−	0.108425i
$257$	−16.9407	+	11.7859i	−1.05673	+	0.735184i	−0.965436	−	0.260640i	$-0.916066\pi$
$257$	−16.9407	+	11.7859i	−1.05673	+	0.735184i	−0.0912964	+	0.995824i	$0.529101\pi$
$258$	−11.8555	−	2.46188i	−0.738090	−	0.153270i
$259$	−0.656022	+	3.55757i	−0.0407632	+	0.221057i
$260$	−53.3374	−	30.4164i	−3.30785	−	1.88634i
$261$	42.8111	+	2.46802i	2.64994	+	0.152766i
$262$	−13.0410	+	12.7522i	−0.805679	+	0.787835i
$263$	2.47330	+	10.1095i	0.152510	+	0.623377i	0.996242	+	0.0866123i	$0.0276041\pi$
$263$	2.47330	+	10.1095i	0.152510	+	0.623377i	−0.843732	+	0.536764i	$0.819646\pi$
$264$	8.53307	−	0.218438i	0.525174	−	0.0134439i
$265$	1.20632	+	7.63219i	0.0741035	+	0.468842i
$266$	9.00996	+	52.6282i	0.552436	+	3.22684i
$267$	−9.49756	−	18.3920i	−0.581241	−	1.12557i
$268$	19.6287	−	1.25763i	1.19901	−	0.0768219i
$269$	18.0518	+	20.3259i	1.10064	+	1.23929i	0.968754	+	0.248025i	$0.0797814\pi$
$269$	18.0518	+	20.3259i	1.10064	+	1.23929i	0.131886	+	0.991265i	$0.457897\pi$
$270$	36.1429	−	30.2837i	2.19958	−	1.84301i
$271$	8.86938	−	0.170269i	0.538776	−	0.0103431i	0.250904	−	0.968012i	$-0.419272\pi$
$271$	8.86938	−	0.170269i	0.538776	−	0.0103431i	0.287872	+	0.957669i	$0.407052\pi$
$272$	−3.17120	−	3.80944i	−0.192282	−	0.230981i
$273$	−62.6676	−	14.2733i	−3.79282	−	0.863862i
$274$	9.41770	−	1.83027i	0.568944	−	0.110571i
$275$	4.46025	+	12.7747i	0.268963	+	0.770346i
$276$	24.2433	−	13.8251i	1.45928	−	0.832171i
$277$	−7.00211	+	3.47513i	−0.420716	+	0.208801i	−0.642484	−	0.766299i	$-0.722096\pi$
$277$	−7.00211	+	3.47513i	−0.420716	+	0.208801i	0.221768	+	0.975099i	$0.428817\pi$
$278$	2.84999	+	2.97105i	0.170931	+	0.178192i
$279$	−11.1092	+	24.1027i	−0.665089	+	1.44299i
$280$	−21.8151	−	9.46844i	−1.30370	−	0.565848i
$281$	−2.04361	−	4.50955i	−0.121912	−	0.269017i	0.839894	−	0.542751i	$-0.182617\pi$
$281$	−2.04361	−	4.50955i	−0.121912	−	0.269017i	−0.961806	+	0.273734i	$0.911741\pi$
$282$	−37.4517	−	22.6466i	−2.23022	−	1.34859i
$283$	17.9784	+	14.2970i	1.06870	+	0.849868i	0.989142	−	0.146962i	$-0.0469494\pi$
$283$	17.9784	+	14.2970i	1.06870	+	0.849868i	0.0795615	+	0.996830i	$0.474648\pi$
$284$	8.64150	−	0.331911i	0.512778	−	0.0196953i
$285$	−65.9998	−	11.9523i	−3.90949	−	0.707992i
$286$	21.3312	−	7.21879i	1.26134	−	0.426856i
$287$	21.9673	−	38.8093i	1.29669	−	2.29084i
$288$	18.0073	+	32.7850i	1.06109	+	1.93188i
$289$	−5.92675	+	6.50380i	−0.348633	+	0.382576i
$290$	66.3897	−	3.82730i	3.89854	−	0.224747i
$291$	−7.37019	−	3.65781i	−0.432048	−	0.214425i
$292$	6.18271	+	19.7128i	0.361816	+	1.15361i
$293$	2.75319	−	0.720435i	0.160843	−	0.0420883i	−0.171852	−	0.985123i	$-0.554975\pi$
$293$	2.75319	−	0.720435i	0.160843	−	0.0420883i	0.332695	+	0.943035i	$0.392042\pi$
$294$	−42.5465	−	4.92188i	−2.48136	−	0.287050i
$295$	−22.5337	+	28.9011i	−1.31196	+	1.68269i
$296$	−1.14314	+	1.28714i	−0.0664434	+	0.0748134i
$297$	−0.290774	+	10.0961i	−0.0168724	+	0.585837i
$298$	−15.0947	−	1.06415i	−0.874414	−	0.0616448i
$299$	14.4706	−	15.4769i	0.836854	−	0.895053i
$300$	43.9122	−	46.3678i	2.53527	−	2.67704i
$301$	−7.07511	+	1.46920i	−0.407803	+	0.0846832i
$302$	−1.09964	−	49.0955i	−0.0632772	−	2.82513i
$303$	−15.9493	−	34.6041i	−0.916266	−	1.98795i
$304$	4.13855	−	10.5354i	0.237362	−	0.604247i
$305$	−32.8150	+	9.49039i	−1.87898	+	0.543418i
$306$	−25.6731	+	19.1082i	−1.46764	+	1.09234i
$307$	17.4677	−	17.3009i	0.996936	−	0.987413i	−0.00298498	−	0.999996i	$-0.500950\pi$
$307$	17.4677	−	17.3009i	0.996936	−	0.987413i	0.999921	+	0.0125822i	$0.00400514\pi$
$308$	16.0526	−	7.46114i	0.914680	−	0.425138i
$309$	3.10159	+	3.77468i	0.176444	+	0.214734i
$310$	−12.8182	+	39.1096i	−0.728028	+	2.22128i
$311$	−15.0236	+	10.0298i	−0.851912	+	0.568736i	−0.902845	−	0.429966i	$-0.858526\pi$
$311$	−15.0236	+	10.0298i	−0.851912	+	0.568736i	0.0509338	+	0.998702i	$0.483780\pi$
$312$	−22.0042	−	21.2432i	−1.24574	−	1.20266i
$313$	−15.0670	−	3.02835i	−0.851638	−	0.171172i	−0.248325	−	0.968677i	$-0.579880\pi$
$313$	−15.0670	−	3.02835i	−0.851638	−	0.171172i	−0.603313	+	0.797504i	$0.706153\pi$
$314$	38.7869	−	17.4279i	2.18887	−	0.983511i
$315$	30.6055	−	61.1753i	1.72442	−	3.44684i
$316$	30.4790	+	16.6141i	1.71458	+	0.934614i
$317$	−2.36674	+	1.19354i	−0.132929	+	0.0670359i	−0.515496	−	0.856892i	$-0.672392\pi$
$317$	−2.36674	+	1.19354i	−0.132929	+	0.0670359i	0.382567	+	0.923928i	$0.375040\pi$
$318$	−1.23913	+	13.3177i	−0.0694867	+	0.746821i
$319$	−8.83030	+	11.1773i	−0.494402	+	0.625807i
$320$	26.3586	+	37.1220i	1.47349	+	2.07518i
$321$	−15.1195	+	17.2452i	−0.843890	+	0.962531i
$322$	17.0998	−	22.8219i	0.952933	−	1.27181i
$323$	18.2052	+	4.39225i	1.01297	+	0.244391i
$324$	4.26728	−	2.05021i	0.237071	−	0.113901i
$325$	21.4147	−	43.4978i	1.18788	−	2.41283i
$326$	−2.78897	+	37.8349i	−0.154467	+	2.09548i
$327$	0.00703495	+	0.0368273i	0.000389034	+	0.00203655i
$328$	18.5015	−	10.3944i	1.02157	−	0.573934i
$329$	−25.8835	−	3.49893i	−1.42700	−	0.192902i
$330$	3.28473	+	37.9329i	0.180818	+	2.08814i
$331$	29.7667	+	12.4695i	1.63613	+	0.685384i	0.996523	−	0.0833200i	$-0.0265524\pi$
$331$	29.7667	+	12.4695i	1.63613	+	0.685384i	0.639604	+	0.768704i	$0.279098\pi$
$332$	−41.2652	−	14.8534i	−2.26472	−	0.815186i
$333$	−3.51808	−	3.48448i	−0.192790	−	0.190948i
$334$	38.1238	+	5.40217i	2.08604	+	0.295594i
$335$	3.14189	+	25.0510i	0.171660	+	1.36869i
$336$	14.4982	+	11.2296i	0.790942	+	0.612627i
$337$	−7.26251	+	11.5876i	−0.395614	+	0.631216i	−0.984167	−	0.177243i	$-0.943282\pi$
$337$	−7.26251	+	11.5876i	−0.395614	+	0.631216i	0.588553	+	0.808459i	$0.299698\pi$
$338$	−46.5957	−	23.4981i	−2.53447	−	1.27813i
$339$	−6.01367	−	8.70314i	−0.326618	−	0.472690i
$340$	−21.1092	+	19.8636i	−1.14481	+	1.07725i
$341$	−4.44047	−	7.61591i	−0.240465	−	0.412424i
$342$	−66.4710	−	30.3797i	−3.59434	−	1.64274i
$343$	0.482674	−	0.146312i	0.0260619	−	0.00790011i
$344$	−3.24282	−	1.14387i	−0.174841	−	0.0616732i
$345$	19.6037	+	29.9836i	1.05543	+	1.61426i
$346$	3.46114	−	25.0012i	0.186072	−	1.34407i
$347$	7.05899	+	3.11764i	0.378946	+	0.167364i	0.584719	−	0.811236i	$-0.301205\pi$
$347$	7.05899	+	3.11764i	0.378946	+	0.167364i	−0.205772	+	0.978600i	$0.565971\pi$
$348$	65.9939	+	12.8255i	3.53764	+	0.687517i
$349$	0.778180	+	5.36802i	0.0416550	+	0.287343i	0.999999	+	0.00172533i	$0.000549190\pi$
$349$	0.778180	+	5.36802i	0.0416550	+	0.287343i	−0.958344	+	0.285618i	$0.907801\pi$
$350$	22.2967	−	61.3275i	1.19181	−	3.27809i
$351$	26.5148	−	24.6322i	1.41526	−	1.31477i
$352$	−12.3516	−	1.34883i	−0.658343	−	0.0718931i
$353$	−22.7116	−	22.7844i	−1.20882	−	1.21269i	−0.970393	−	0.241530i	$-0.922351\pi$
$353$	−22.7116	−	22.7844i	−1.20882	−	1.21269i	−0.238425	−	0.971161i	$-0.576631\pi$
$354$	−50.1520	+	38.8454i	−2.66555	+	2.06461i
$355$	1.09909	+	11.0460i	0.0583334	+	0.586260i
$356$	−6.85685	−	19.2424i	−0.363412	−	1.01985i
$357$	−15.1146	+	26.3086i	−0.799948	+	1.39240i
$358$	25.4427	−	26.1860i	1.34469	−	1.38398i
$359$	−2.15512	+	1.12164i	−0.113743	+	0.0591979i	−0.517591	−	0.855628i	$-0.673171\pi$
$359$	−2.15512	+	1.12164i	−0.113743	+	0.0591979i	0.403849	+	0.914826i	$0.367672\pi$
$360$	27.5263	−	17.3750i	1.45076	−	0.915743i
$361$	6.23692	+	22.9338i	0.328259	+	1.20704i
$362$	−49.5332	+	7.01890i	−2.60341	+	0.368905i
$363$	18.5663	+	13.8186i	0.974476	+	0.725291i
$364$	−59.3999	−	22.2436i	−3.11340	−	1.16588i
$365$	−24.7748	+	9.45868i	−1.29677	+	0.495090i
$366$	−59.1000	+	1.89136i	−3.08921	+	0.0988630i
$367$	−0.647308	−	5.75684i	−0.0337892	−	0.300505i	−0.999208	−	0.0397996i	$-0.987328\pi$
$367$	−0.647308	−	5.75684i	−0.0337892	−	0.300505i	0.965418	−	0.260705i	$-0.0839550\pi$
$368$	−5.60543	+	2.26428i	−0.292203	+	0.118034i
$369$	26.9611	+	54.7637i	1.40354	+	2.85088i
$370$	−6.04052	−	4.74084i	−0.314031	−	0.246465i
$371$	2.48602	+	7.58507i	0.129068	+	0.393797i
$372$	−22.3214	+	35.1133i	−1.15731	+	1.82054i
$373$	0.206975	−	4.97377i	0.0107168	−	0.257532i	−0.985445	−	0.169997i	$-0.945624\pi$
$373$	0.206975	−	4.97377i	0.0107168	−	0.257532i	0.996161	−	0.0875355i	$-0.0278991\pi$
$374$	−0.306048	−	10.6265i	−0.0158254	−	0.549482i
$375$	23.5246	+	19.7110i	1.21481	+	1.01787i
$376$	−9.67843	−	7.79821i	−0.499127	−	0.402162i
$377$	50.7384	−	5.54079i	2.61316	−	0.285365i
$378$	31.8769	−	36.8312i	1.63957	−	1.89439i
$379$	−3.51141	−	1.08899i	−0.180369	−	0.0559376i	0.204703	−	0.978824i	$-0.434377\pi$
$379$	−3.51141	−	1.08899i	−0.180369	−	0.0559376i	−0.385072	+	0.922887i	$0.625823\pi$
$380$	−62.9655	−	20.4142i	−3.23006	−	1.04723i
$381$	−0.207994	+	1.74894i	−0.0106558	+	0.0896009i
$382$	22.0849	−	21.0498i	1.12996	−	1.07700i
$383$	7.25336	+	13.6159i	0.370629	+	0.695739i	0.996446	−	0.0842307i	$-0.0268433\pi$
$383$	7.25336	+	13.6159i	0.370629	+	0.695739i	−0.625817	+	0.779970i	$0.715234\pi$
$384$	13.3229	+	34.5639i	0.679879	+	1.76383i
$385$	10.8112	+	19.9855i	0.550992	+	1.01855i
$386$	−7.61034	+	4.02292i	−0.387356	+	0.204761i
$387$	3.79237	−	9.13492i	0.192777	−	0.464354i
$388$	−6.72424	−	4.55157i	−0.341372	−	0.231071i
$389$	−3.86470	−	1.41909i	−0.195948	−	0.0719509i	0.244834	−	0.969565i	$-0.421266\pi$
$389$	−3.86470	−	1.41909i	−0.195948	−	0.0719509i	−0.440782	+	0.897614i	$0.645299\pi$
$390$	88.6192	−	103.726i	4.48741	−	5.25238i
$391$	−4.98265	−	8.67288i	−0.251984	−	0.438606i
$392$	−11.7866	−	3.00378i	−0.595312	−	0.151714i
$393$	−13.0791	−	19.7275i	−0.659751	−	0.995122i
$394$	−0.277753	+	4.56386i	−0.0139930	+	0.229924i
$395$	−18.9100	+	40.3466i	−0.951467	+	2.03006i
$396$	−3.93577	+	23.9080i	−0.197780	+	1.20142i
$397$	0.318095	−	4.72764i	0.0159647	−	0.237274i	−0.982683	−	0.185293i	$-0.940677\pi$
$397$	0.318095	−	4.72764i	0.0159647	−	0.237274i	0.998648	−	0.0519809i	$-0.0165535\pi$
$398$	−14.2823	−	17.8424i	−0.715906	−	0.894359i
$399$	−69.2753	−	1.32991i	−3.46811	−	0.0665787i
$400$	−10.7720	+	8.67935i	−0.538601	+	0.433968i
$401$	−4.10756	+	4.12072i	−0.205122	+	0.205779i	−0.803284	−	0.595596i	$-0.796916\pi$
$401$	−4.10756	+	4.12072i	−0.205122	+	0.205779i	0.598163	+	0.801375i	$0.295898\pi$
$402$	−5.43858	+	43.3631i	−0.271252	+	2.16276i
$403$	−8.28955	+	30.4815i	−0.412932	+	1.51839i
$404$	−11.0232	−	35.9502i	−0.548425	−	1.78859i
$405$	2.95956	+	5.30756i	0.147062	+	0.263735i
$406$	67.0767	−	14.8268i	3.32896	−	0.735841i
$407$	1.61849	−	0.293101i	0.0802255	−	0.0145285i
$408$	−12.6329	+	6.99137i	−0.625421	+	0.346124i
$409$	5.90326	+	6.56186i	0.291897	+	0.324463i	0.871462	−	0.490463i	$-0.163172\pi$
$409$	5.90326	+	6.56186i	0.291897	+	0.324463i	−0.579564	+	0.814926i	$0.696777\pi$
$410$	51.2925	+	79.5580i	2.53316	+	3.92909i
$411$	0.0398291	+	12.4497i	0.00196462	+	0.614100i
$412$	2.53424	+	4.10155i	0.124853	+	0.202069i
$413$	−18.2253	+	33.1819i	−0.896809	+	1.63277i
$414$	12.6308	+	36.9338i	0.620768	+	1.81520i
$415$	15.8131	−	54.0289i	0.776236	−	2.65218i
$416$	27.5988	+	34.9342i	1.35314	+	1.71279i
$417$	−4.48092	+	2.90927i	−0.219432	+	0.142467i
$418$	20.9333	−	12.2951i	1.02388	−	0.601372i
$419$	6.42049	−	5.44996i	0.313662	−	0.266248i	−0.476462	−	0.879195i	$-0.658081\pi$
$419$	6.42049	−	5.44996i	0.313662	−	0.266248i	0.790124	+	0.612947i	$0.210016\pi$
$420$	60.3972	−	88.6155i	2.94708	−	4.32399i
$421$	−10.1186	+	1.03951i	−0.493151	+	0.0506628i	−0.345581	−	0.938389i	$-0.612318\pi$
$421$	−10.1186	+	1.03951i	−0.493151	+	0.0506628i	−0.147570	+	0.989052i	$0.547145\pi$
$422$	−13.2761	−	2.14193i	−0.646270	−	0.104267i
$423$	23.9107	−	26.5783i	1.16258	−	1.29228i
$424$	−0.855379	+	3.70085i	−0.0415409	+	0.179729i
$425$	−16.6684	−	15.6848i	−0.808536	−	0.760825i
$426$	−2.87831	+	18.9981i	−0.139454	+	0.920461i
$427$	−31.9043	+	15.0779i	−1.54396	+	0.729670i
$428$	−17.0662	+	14.8664i	−0.824928	+	0.718593i
$429$	4.00741	+	28.9471i	0.193480	+	1.39758i
$430$	4.21418	−	14.7480i	0.203226	−	0.711213i
$431$	1.48112	+	7.49307i	0.0713431	+	0.360928i	0.999949	−	0.0101402i	$-0.00322777\pi$
$431$	1.48112	+	7.49307i	0.0713431	+	0.360928i	−0.928606	+	0.371068i	$0.878992\pi$
$432$	−9.82282	+	3.18468i	−0.472601	+	0.153223i
$433$	17.0003	−	0.217559i	0.816980	−	0.0104552i	0.396810	−	0.917901i	$-0.370117\pi$
$433$	17.0003	−	0.217559i	0.816980	−	0.0104552i	0.420170	+	0.907445i	$0.361970\pi$
$434$	−6.63748	+	41.9944i	−0.318609	+	2.01579i
$435$	−11.2866	+	85.5543i	−0.541153	+	4.10201i
$436$	0.00201132	+	0.0369459i	9.63250e−5	+	0.00176939i
$437$	11.8816	−	19.5079i	0.568375	−	0.933191i
$438$	−45.6001	+	5.27513i	−2.17886	+	0.252055i
$439$	32.9219	−	12.8111i	1.57128	−	0.611438i	0.590581	−	0.806978i	$-0.298898\pi$
$439$	32.9219	−	12.8111i	1.57128	−	0.611438i	0.980696	+	0.195540i	$0.0626459\pi$
$440$	−0.518683	+	10.8004i	−0.0247272	+	0.514887i
$441$	10.4701	−	33.3828i	0.498578	−	1.58966i
$442$	−26.3692	+	27.4893i	−1.25426	+	1.30753i
$443$	4.70104	+	11.9673i	0.223353	+	0.568585i	0.997959	−	0.0638596i	$-0.0203410\pi$
$443$	4.70104	+	11.9673i	0.223353	+	0.568585i	−0.774606	+	0.632444i	$0.782052\pi$
$444$	−4.73396	−	6.15242i	−0.224664	−	0.291981i
$445$	24.1195	−	10.2857i	1.14338	−	0.487590i
$446$	32.9062	+	46.9771i	1.55815	+	2.22443i
$447$	5.03177	−	18.9811i	0.237995	−	0.897775i
$448$	32.9893	+	33.5213i	1.55860	+	1.58373i
$449$	−3.05474	+	0.472811i	−0.144162	+	0.0223133i	−0.224631	−	0.974444i	$-0.572118\pi$
$449$	−3.05474	+	0.472811i	−0.144162	+	0.0223133i	0.0804691	+	0.996757i	$0.474358\pi$
$450$	52.1764	+	72.4953i	2.45962	+	3.41746i
$451$	−20.0377	−	3.10142i	−0.943540	−	0.146040i
$452$	−4.73060	−	9.30640i	−0.222509	−	0.437736i
$453$	62.8464	+	10.5525i	2.95278	+	0.495799i
$454$	29.5816	−	6.34055i	1.38834	−	0.297577i
$455$	23.8677	−	77.8402i	1.11894	−	3.64920i
$456$	−27.8821	−	17.5995i	−1.30570	−	0.824174i
$457$	−2.86585	−	0.238929i	−0.134059	−	0.0111766i	0.0158651	−	0.999874i	$-0.494950\pi$
$457$	−2.86585	−	0.238929i	−0.134059	−	0.0111766i	−0.149924	+	0.988698i	$0.547903\pi$
$458$	−15.1993	−	9.05855i	−0.710216	−	0.423278i
$459$	−7.44795	−	15.3758i	−0.347640	−	0.717683i
$460$	15.2079	+	31.9146i	0.709070	+	1.48803i
$461$	−3.36444	+	8.40633i	−0.156698	+	0.391522i	−0.985879	−	0.167457i	$-0.946444\pi$
$461$	−3.36444	+	8.40633i	−0.156698	+	0.391522i	0.829182	+	0.558979i	$0.188807\pi$
$462$	9.59124	+	38.1447i	0.446225	+	1.77465i
$463$	11.4419	−	10.2275i	0.531750	−	0.475310i	−0.356742	−	0.934203i	$-0.616112\pi$
$463$	11.4419	−	10.2275i	0.531750	−	0.475310i	0.888492	+	0.458893i	$0.151754\pi$
$464$	−13.7945	−	4.66826i	−0.640395	−	0.216718i
$465$	−46.7293	−	25.8612i	−2.16702	−	1.19929i
$466$	11.0076	+	47.6250i	0.509917	+	2.20619i
$467$	−21.2173	+	36.3902i	−0.981822	+	1.68394i	−0.297554	+	0.954705i	$0.596171\pi$
$467$	−21.2173	+	36.3902i	−0.981822	+	1.68394i	−0.684268	+	0.729231i	$0.739878\pi$
$468$	70.9493	−	50.0371i	3.27963	−	2.31297i
$469$	7.32603	+	25.0309i	0.338284	+	1.15582i
$470$	32.0977	−	45.2046i	1.48056	−	2.08513i
$471$	12.7700	+	53.6824i	0.588410	+	2.47355i
$472$	−15.5920	+	9.02425i	−0.717682	+	0.415375i
$473$	1.76259	+	2.77270i	0.0810442	+	0.127489i
$474$	−48.9664	+	59.5928i	−2.24910	+	2.73719i
$475$	13.0695	−	50.6066i	0.599671	−	2.32199i
$476$	−18.2596	+	23.7308i	−0.836927	+	1.08770i
$477$	−10.4956	−	3.03541i	−0.480559	−	0.138982i
$478$	−16.1834	+	6.06024i	−0.740212	+	0.277189i
$479$	20.8459	−	18.3947i	0.952473	−	0.840477i	−0.0348185	−	0.999394i	$-0.511085\pi$
$479$	20.8459	−	18.3947i	0.952473	−	0.840477i	0.987292	+	0.158917i	$0.0508002\pi$
$480$	−68.4616	+	31.2895i	−3.12483	+	1.42816i
$481$	−4.81632	−	3.39672i	−0.219605	−	0.154877i
$482$	13.1573	−	38.4735i	0.599299	−	1.75242i
$483$	24.9259	+	27.3527i	1.13417	+	1.24459i
$484$	16.3303	+	15.9687i	0.742288	+	0.725849i
$485$	5.30735	−	8.97030i	0.240994	−	0.407320i
$486$	−7.36087	−	27.7670i	−0.333896	−	1.25954i
$487$	−4.41863	+	5.23938i	−0.200227	+	0.237419i	−0.855283	−	0.518161i	$-0.826617\pi$
$487$	−4.41863	+	5.23938i	−0.200227	+	0.237419i	0.655056	+	0.755581i	$0.272645\pi$
$488$	−16.7044	−	1.71609i	−0.756173	−	0.0776838i
$489$	−47.5464	−	12.7672i	−2.15012	−	0.577353i
$490$	10.1801	−	53.2916i	0.459888	−	2.40747i
$491$	−5.38149	−	16.0712i	−0.242863	−	0.725285i	−0.997599	−	0.0692558i	$-0.977938\pi$
$491$	−5.38149	−	16.0712i	−0.242863	−	0.725285i	0.754736	−	0.656029i	$-0.227765\pi$
$492$	30.3859	+	90.7443i	1.36990	+	4.09107i
$493$	4.52094	−	23.6667i	0.203613	−	1.06589i
$494$	−84.0118	−	22.5589i	−3.77987	−	1.01497i
$495$	−30.9389	−	3.17844i	−1.39060	−	0.142860i
$496$	5.81062	−	6.88993i	0.260904	−	0.309367i
$497$	2.93836	+	11.0842i	0.131803	+	0.497195i
$498$	49.6206	−	83.8672i	2.22355	−	3.75818i
$499$	−1.27902	−	1.25070i	−0.0572570	−	0.0559889i	0.669956	−	0.742401i	$-0.266313\pi$
$499$	−1.27902	−	1.25070i	−0.0572570	−	0.0559889i	−0.727213	+	0.686412i	$0.759185\pi$
$500$	20.4005	+	22.3867i	0.912336	+	1.00116i
$501$	−16.1684	+	47.2784i	−0.722351	+	2.11224i
$502$	15.8495	+	11.1779i	0.707397	+	0.498893i
$503$	−9.53596	+	4.35828i	−0.425187	+	0.194326i	−0.616758	−	0.787153i	$-0.711554\pi$
$503$	−9.53596	+	4.35828i	−0.425187	+	0.194326i	0.191571	+	0.981479i	$0.438642\pi$
$504$	25.2134	−	22.2487i	1.12309	−	0.991036i
$505$	45.2014	−	16.9267i	2.01144	−	0.753227i
$506$	−12.4557	−	3.60231i	−0.553724	−	0.160142i
$507$	41.2969	−	53.6708i	1.83406	−	2.38361i
$508$	−0.434623	+	1.68291i	−0.0192833	+	0.0746670i
$509$	1.16459	−	1.41732i	0.0516196	−	0.0628218i	−0.746181	−	0.665743i	$-0.768115\pi$
$509$	1.16459	−	1.41732i	0.0516196	−	0.0628218i	0.797801	+	0.602921i	$0.205997\pi$
$510$	−34.5510	−	54.3513i	−1.52994	−	2.40672i
$511$	−23.7099	+	13.7226i	−1.04886	+	0.607054i
$512$	−4.35924	−	18.3253i	−0.192653	−	0.809872i
$513$	22.5878	−	31.8115i	0.997278	−	1.40451i
$514$	−12.7111	−	43.4300i	−0.560660	−	1.91562i
$515$	−5.05748	+	3.56680i	−0.222859	+	0.157172i
$516$	7.81039	−	13.3957i	0.343833	−	0.589713i
$517$	2.67432	+	11.5706i	0.117616	+	0.508875i
$518$	−6.94036	−	3.84098i	−0.304942	−	0.168763i
$519$	31.0246	+	10.4992i	1.36183	+	0.460862i
$520$	28.8861	−	25.8202i	1.26674	−	1.13229i
$521$	−5.76926	−	22.9446i	−0.252756	−	1.00522i	−0.955787	−	0.294061i	$-0.904993\pi$
$521$	−5.76926	−	22.9446i	−0.252756	−	1.00522i	0.703031	−	0.711159i	$-0.251830\pi$
$522$	−34.9387	+	87.2971i	−1.52922	+	3.82089i
$523$	5.72284	+	12.0097i	0.250242	+	0.525148i	0.988837	−	0.149001i	$-0.0476059\pi$
$523$	5.72284	+	12.0097i	0.250242	+	0.525148i	−0.738595	+	0.674150i	$0.764510\pi$
$524$	−10.1829	−	21.0219i	−0.444841	−	0.918347i
$525$	72.7409	+	43.3525i	3.17468	+	1.89206i
$526$	−22.7422	−	1.89604i	−0.991609	−	0.0826714i
$527$	12.6101	+	7.95967i	0.549304	+	0.346729i
$528$	2.44435	−	7.97178i	0.106376	−	0.346927i
$529$	10.5607	−	2.26358i	0.459159	−	0.0984163i
$530$	−16.7092	−	2.80563i	−0.725801	−	0.121869i
$531$	−23.4808	−	46.1933i	−1.01898	−	2.00462i
$532$	−67.5732	−	10.4589i	−2.92967	−	0.453451i
$533$	42.4407	+	58.9682i	1.83831	+	2.55420i
$534$	44.8545	−	6.94253i	1.94104	−	0.300433i
$535$	−20.3782	−	20.7068i	−0.881026	−	0.895233i
$536$	−3.18026	+	11.9967i	−0.137366	+	0.518180i
$537$	27.1826	+	38.8060i	1.17301	+	1.67460i
$538$	−54.8312	+	23.3827i	−2.36394	+	1.00810i
$539$	7.08708	+	9.21062i	0.305262	+	0.396730i
$540$	22.0785	+	56.2046i	0.950105	+	2.41866i
$541$	15.3753	−	16.0284i	0.661036	−	0.689116i	−0.303571	−	0.952809i	$-0.598179\pi$
$541$	15.3753	−	16.0284i	0.661036	−	0.689116i	0.964607	+	0.263693i	$0.0849406\pi$
$542$	−5.82122	+	18.5603i	−0.250043	+	0.797233i
$543$	3.11418	−	64.8455i	0.133642	−	2.78279i
$544$	19.5863	−	7.62171i	0.839757	−	0.326778i
$545$	−0.0471799	+	0.00545788i	−0.00202096	+	0.000233790i
$546$	73.3100	−	120.364i	3.13738	−	5.15112i
$547$	0.143673	+	2.63913i	0.00614303	+	0.112841i	0.999998	+	0.00214811i	$0.000683767\pi$
$547$	0.143673	+	2.63913i	0.00614303	+	0.112841i	−0.993855	+	0.110693i	$0.964693\pi$
$548$	−1.60692	+	12.1807i	−0.0686443	+	0.520334i
$549$	7.54069	−	47.7088i	0.321829	−	2.03616i
$550$	−29.6674	+	0.379666i	−1.26502	+	0.0161890i
$551$	52.3409	−	16.9696i	2.22980	−	0.722928i
$552$	3.41485	+	17.2759i	0.145346	+	0.735311i
$553$	−12.6466	+	44.2582i	−0.537787	+	1.88205i
$554$	−2.35052	−	16.9788i	−0.0998641	−	0.721358i
$555$	7.51361	−	6.54509i	0.318935	−	0.277824i
$556$	−4.76681	+	2.25278i	−0.202158	+	0.0955392i
$557$	5.58998	−	36.8964i	0.236855	−	1.56335i	−0.487003	−	0.873400i	$-0.661910\pi$
$557$	5.58998	−	36.8964i	0.236855	−	1.56335i	0.723858	−	0.689949i	$-0.242367\pi$
$558$	−42.3811	−	39.8803i	−1.79414	−	1.68827i
$559$	2.65108	−	11.4701i	0.112129	−	0.485133i
$560$	−15.5368	+	17.2702i	−0.656549	+	0.729798i
$561$	13.6193	+	2.19731i	0.575009	+	0.0927704i
$562$	10.7994	−	1.10945i	0.455544	−	0.0467993i
$563$	−17.6298	+	25.8667i	−0.743009	+	1.09015i	0.249547	+	0.968363i	$0.419718\pi$
$563$	−17.6298	+	25.8667i	−0.743009	+	1.09015i	−0.992556	+	0.121788i	$0.961137\pi$
$564$	42.7301	−	36.2709i	1.79926	−	1.52728i
$565$	11.5549	−	6.78673i	0.486118	−	0.285520i
$566$	−42.2445	+	27.4275i	−1.77567	+	1.15286i
$567$	3.89155	+	4.92586i	0.163430	+	0.206867i
$568$	−1.53279	+	5.23712i	−0.0643146	+	0.219744i
$569$	−12.2839	−	35.9197i	−0.514969	−	1.50583i	−0.830557	−	0.556934i	$-0.811978\pi$
$569$	−12.2839	−	35.9197i	−0.514969	−	1.50583i	0.315588	−	0.948896i	$-0.397798\pi$
$570$	70.8039	−	128.909i	2.96565	−	5.39940i
$571$	3.76444	+	6.09258i	0.157537	+	0.254967i	0.919874	−	0.392213i	$-0.128290\pi$
$571$	3.76444	+	6.09258i	0.157537	+	0.254967i	−0.762337	+	0.647180i	$0.775948\pi$
$572$	0.0922618	+	28.8391i	0.00385766	+	1.20582i
$573$	21.4533	+	33.2755i	0.896224	+	1.39010i
$574$	65.4000	+	72.6964i	2.72974	+	3.03429i
$575$	−24.4246	+	13.5172i	−1.01858	+	0.563707i
$576$	−63.3454	+	11.4716i	−2.63939	+	0.477982i
$577$	−33.8293	+	7.47771i	−1.40833	+	0.311301i	−0.853688	−	0.520785i	$-0.825639\pi$
$577$	−33.8293	+	7.47771i	−1.40833	+	0.311301i	−0.554646	+	0.832086i	$0.687146\pi$
$578$	−9.39661	−	16.8515i	−0.390848	−	0.700930i
$579$	−3.27472	−	10.6799i	−0.136093	−	0.443841i
$580$	−22.3484	+	82.1772i	−0.927966	+	3.41222i
$581$	7.23699	−	57.7023i	0.300241	−	2.39390i
$582$	12.7370	−	12.7778i	0.527966	−	0.529658i
$583$	2.82606	−	2.27704i	0.117043	−	0.0943056i
$584$	−13.0339	−	0.250217i	−0.539345	−	0.0103540i
$585$	69.6421	+	87.0017i	2.87935	+	3.59708i
$586$	−0.418924	+	6.22620i	−0.0173056	+	0.257202i
$587$	−3.44733	+	20.9409i	−0.142286	+	0.864325i	0.815903	+	0.578189i	$0.196240\pi$
$587$	−3.44733	+	20.9409i	−0.142286	+	0.864325i	−0.958189	+	0.286136i	$0.907629\pi$
$588$	23.2776	−	49.6653i	0.959953	−	2.04816i
$589$	−2.06866	+	33.9908i	−0.0852375	+	1.40056i
$590$	−44.4039	−	66.9756i	−1.82808	−	2.75734i
$591$	−5.74960	−	1.46527i	−0.236507	−	0.0602733i
$592$	0.837689	+	1.45809i	0.0344288	+	0.0599273i
$593$	11.8739	−	13.8981i	0.487604	−	0.570726i	−0.460916	−	0.887444i	$-0.652479\pi$
$593$	11.8739	−	13.8981i	0.487604	−	0.570726i	0.948520	+	0.316718i	$0.102581\pi$
$594$	−20.7900	−	7.63398i	−0.853026	−	0.313226i
$595$	−31.8287	−	21.5446i	−1.30485	−	0.883241i
$596$	7.43024	−	17.8977i	0.304354	−	0.733118i
$597$	26.2200	−	13.8602i	1.07311	−	0.567262i
$598$	22.1055	+	40.8638i	0.903960	+	1.67104i
$599$	2.23011	+	5.78564i	0.0911198	+	0.236395i	0.971126	−	0.238567i	$-0.0766777\pi$
$599$	2.23011	+	5.78564i	0.0911198	+	0.236395i	−0.880006	+	0.474962i	$0.842462\pi$
$600$	18.9459	+	35.5649i	0.773462	+	1.45193i
$601$	−14.1526	+	13.4893i	−0.577299	+	0.550239i	−0.921361	−	0.388707i	$-0.872922\pi$
$601$	−14.1526	+	13.4893i	−0.577299	+	0.550239i	0.344063	+	0.938947i	$0.388197\pi$
$602$	1.87116	−	15.7339i	0.0762630	−	0.641267i
$603$	−33.9589	−	11.0099i	−1.38291	−	0.448357i
$604$	60.0666	+	18.6284i	2.44408	+	0.757977i
$605$	−19.1864	+	22.1683i	−0.780038	+	0.901270i
$606$	83.0555	−	9.06991i	3.37390	−	0.368440i
$607$	1.63708	+	1.31905i	0.0664470	+	0.0535384i	0.660065	−	0.751209i	$-0.270529\pi$
$607$	1.63708	+	1.31905i	0.0664470	+	0.0535384i	−0.593618	+	0.804747i	$0.702301\pi$
$608$	36.7882	+	30.8244i	1.49196	+	1.25010i
$609$	2.56636	+	89.1081i	0.103994	+	3.61084i
$610$	3.11428	−	74.8385i	0.126093	−	3.03012i
$611$	22.8282	−	35.9105i	0.923530	−	1.45278i
$612$	−12.7647	−	38.9463i	−0.515983	−	1.57431i
$613$	29.1648	+	22.8898i	1.17796	+	0.924509i	0.998246	−	0.0592106i	$-0.0188584\pi$
$613$	29.1648	+	22.8898i	1.17796	+	0.924509i	0.179711	+	0.983719i	$0.442484\pi$
$614$	23.8112	+	48.3656i	0.960942	+	1.95188i
$615$	−113.896	+	46.0076i	−4.59274	+	1.85521i
$616$	1.24809	+	11.0999i	0.0502870	+	0.447228i
$617$	13.6415	−	0.436565i	0.549186	−	0.0175754i	0.243837	−	0.969816i	$-0.421594\pi$
$617$	13.6415	−	0.436565i	0.549186	−	0.0175754i	0.305348	+	0.952241i	$0.401227\pi$
$618$	−10.0080	+	3.82092i	−0.402582	+	0.153700i
$619$	17.9047	+	6.70481i	0.719650	+	0.269489i	0.683596	−	0.729861i	$-0.260415\pi$
$619$	17.9047	+	6.70481i	0.719650	+	0.269489i	0.0360541	+	0.999350i	$0.488521\pi$
$620$	−42.2808	−	31.4691i	−1.69804	−	1.26383i
$621$	−20.6316	+	2.92352i	−0.827919	+	0.117317i
$622$	−10.3944	−	38.2212i	−0.416777	−	1.53253i
$623$	22.9055	−	14.4583i	0.917690	−	0.579259i
$624$	−26.5021	+	13.7932i	−1.06094	+	0.552168i
$625$	0.755440	−	0.777511i	0.0302176	−	0.0311004i
$626$	16.7871	−	29.2198i	0.670946	−	1.16786i
$627$	10.5747	+	29.6759i	0.422313	+	1.18514i
$628$	5.39174	+	54.1878i	0.215154	+	2.16233i
$629$	−2.19958	+	1.70369i	−0.0877029	+	0.0679305i
$630$	105.891	+	106.230i	4.21878	+	4.23230i
$631$	−45.1259	−	4.92788i	−1.79643	−	0.196176i	−0.851703	−	0.524025i	$-0.824430\pi$
$631$	−45.1259	−	4.92788i	−1.79643	−	0.196176i	−0.944730	+	0.327849i	$0.893676\pi$
$632$	−16.0477	+	14.9083i	−0.638343	+	0.593020i
$633$	5.96272	−	16.4006i	0.236997	−	0.651865i
$634$	−0.833852	−	5.75206i	−0.0331165	−	0.228443i
$635$	−2.19011	−	0.425633i	−0.0869117	−	0.0168907i
$636$	−15.6686	−	6.92013i	−0.621301	−	0.274401i
$637$	5.71042	−	41.2486i	0.226255	−	1.63433i
$638$	−17.0924	−	26.1426i	−0.676694	−	1.03500i
$639$	−14.8020	−	5.22124i	−0.585557	−	0.206549i
$640$	−44.9061	+	13.6123i	−1.77507	+	0.538074i
$641$	−32.6862	−	14.9388i	−1.29103	−	0.590046i	−0.352681	−	0.935744i	$-0.614730\pi$
$641$	−32.6862	−	14.9388i	−1.29103	−	0.590046i	−0.938346	+	0.345698i	$0.887642\pi$
$642$	−25.3303	−	43.4443i	−0.999706	−	1.71461i
$643$	−23.3372	+	21.9601i	−0.920330	+	0.866022i	−0.991322	−	0.131455i	$-0.958035\pi$
$643$	−23.3372	+	21.9601i	−0.920330	+	0.866022i	0.0709923	+	0.997477i	$0.477383\pi$
$644$	20.7606	+	30.0453i	0.818083	+	1.18395i
$645$	17.7722	+	8.96248i	0.699780	+	0.352897i
$646$	−21.8079	+	34.7953i	−0.858021	+	1.36900i
$647$	−14.1946	−	10.9944i	−0.558046	−	0.432236i	0.293922	−	0.955829i	$-0.405039\pi$
$647$	−14.1946	−	10.9944i	−0.558046	−	0.432236i	−0.851968	+	0.523593i	$0.824591\pi$
$648$	0.371755	+	2.96409i	0.0146039	+	0.116440i
$649$	17.0427	+	2.41497i	0.668985	+	0.0947958i
$650$	75.5334	+	74.8119i	2.96266	+	2.93437i
$651$	−51.9112	−	18.6854i	−2.03456	−	0.732339i
$652$	−44.8110	−	18.7716i	−1.75493	−	0.735153i
$653$	−3.50027	−	40.4220i	−0.136976	−	1.58183i	−0.674299	−	0.738458i	$-0.735554\pi$
$653$	−3.50027	−	40.4220i	−0.136976	−	1.58183i	0.537323	−	0.843377i	$-0.319436\pi$
$654$	−0.0814715	−	0.0110133i	−0.00318579	−	0.000430655i
$655$	26.1402	−	14.6859i	1.02138	−	0.573827i
$656$	−3.88958	−	20.3616i	−0.151862	−	0.794985i
$657$	2.75660	−	37.3958i	0.107545	−	1.45895i
$658$	25.2964	−	51.3824i	0.986158	−	2.00310i
$659$	−33.1866	+	15.9445i	−1.29277	+	0.621109i	−0.948206	−	0.317655i	$-0.897104\pi$
$659$	−33.1866	+	15.9445i	−1.29277	+	0.621109i	−0.344561	+	0.938764i	$0.611972\pi$
$660$	−47.3997	−	11.4358i	−1.84503	−	0.445138i
$661$	15.0826	−	20.1297i	0.586647	−	0.782956i	−0.404668	−	0.914463i	$-0.632613\pi$
$661$	15.0826	−	20.1297i	0.586647	−	0.782956i	0.991315	+	0.131507i	$0.0419817\pi$
$662$	−46.6522	+	53.2110i	−1.81319	+	2.06810i
$663$	−28.6182	−	40.3043i	−1.11144	−	1.56529i
$664$	17.1553	−	21.7149i	0.665754	−	0.842701i
$665$	8.13136	−	87.3933i	0.315320	−	3.38897i
$666$	9.69459	−	4.88896i	0.375658	−	0.189443i
$667$	−25.8030	−	14.0652i	−0.999097	−	0.544605i
$668$	−22.0624	+	44.0992i	−0.853622	+	1.70625i
$669$	−67.8907	+	30.5049i	−2.62481	+	1.17939i
$670$	−54.2752	−	10.9089i	−2.09683	−	0.421446i
$671$	11.5430	+	11.1438i	0.445614	+	0.430202i
$672$	−64.6712	+	43.1745i	−2.49474	+	1.66549i
$673$	−15.4316	+	47.0831i	−0.594843	+	1.81492i	−0.0154361	+	0.999881i	$0.504914\pi$
$673$	−15.4316	+	47.0831i	−0.594843	+	1.81492i	−0.579407	+	0.815039i	$0.696716\pi$
$674$	−19.0371	−	23.1684i	−0.733282	−	0.892415i
$675$	−43.2396	+	20.0975i	−1.66429	+	0.773554i
$676$	47.4823	−	47.0288i	1.82624	−	1.80880i
$677$	−7.41319	+	5.51755i	−0.284912	+	0.212057i	−0.730030	−	0.683415i	$-0.760494\pi$
$677$	−7.41319	+	5.51755i	−0.284912	+	0.212057i	0.445118	+	0.895472i	$0.353162\pi$
$678$	22.2831	−	6.44447i	0.855776	−	0.247498i
$679$	3.93666	−	10.0215i	0.151075	−	0.384588i
$680$	−7.65592	−	16.6105i	−0.293591	−	0.636983i
$681$	0.879110	+	39.2495i	0.0336876	+	1.50404i
$682$	18.9271	−	3.93035i	0.724756	−	0.150501i
$683$	−21.7605	+	22.9773i	−0.832641	+	0.879203i	−0.994188	−	0.107662i	$-0.965663\pi$
$683$	−21.7605	+	22.9773i	−0.832641	+	0.879203i	0.161547	+	0.986865i	$0.448352\pi$
$684$	63.9209	−	68.3663i	2.44408	−	2.61405i
$685$	−15.7317	−	1.10906i	−0.601079	−	0.0423751i
$686$	−0.0318383	+	1.10547i	−0.00121559	+	0.0422072i
$687$	15.2471	−	17.1678i	0.581714	−	0.654994i
$688$	−2.06536	+	2.64897i	−0.0787411	+	0.100991i
$689$	−12.9180	−	1.49439i	−0.492138	−	0.0569316i
$690$	−75.9927	+	19.8852i	−2.89299	+	0.757017i
$691$	6.24313	+	19.9055i	0.237500	+	0.757241i	0.994585	+	0.103925i	$0.0331401\pi$
$691$	6.24313	+	19.9055i	0.237500	+	0.757241i	−0.757085	+	0.653316i	$0.773377\pi$
$692$	28.9530	+	14.3693i	1.10063	+	0.546240i
$693$	−32.0755	+	1.84912i	−1.21845	+	0.0702421i
$694$	−11.3972	+	12.5068i	−0.432631	+	0.474753i
$695$	−3.25806	−	5.93178i	−0.123585	−	0.225005i
$696$	−20.8965	+	36.9176i	−0.792079	+	1.39936i
$697$	32.4876	−	10.9943i	1.23056	−	0.416437i
$698$	−11.7033	−	2.11942i	−0.442977	−	0.0802212i
$699$	−63.3845	+	2.43454i	−2.39742	+	0.0920826i
$700$	65.4070	+	52.0138i	2.47215	+	1.96594i
$701$	16.8851	+	10.2103i	0.637743	+	0.385636i	0.799047	−	0.601269i	$-0.205338\pi$
$701$	16.8851	+	10.2103i	0.637743	+	0.385636i	−0.161304	+	0.986905i	$0.551570\pi$
$702$	32.7560	+	72.2813i	1.23630	+	2.72808i
$703$	−5.82823	−	2.52963i	−0.219816	−	0.0954068i
$704$	8.95113	−	19.4206i	0.337359	−	0.731941i
$705$	49.8038	+	51.9194i	1.87572	+	1.95540i
$706$	63.1876	−	31.3599i	2.37809	−	1.18024i
$707$	43.3128	−	24.6997i	1.62895	−	0.928927i
$708$	−26.7788	−	76.6982i	−1.00641	−	2.88249i
$709$	27.1250	−	5.27157i	1.01870	−	0.197978i	0.346268	−	0.938136i	$-0.387449\pi$
$709$	27.1250	−	5.27157i	1.01870	−	0.197978i	0.672434	+	0.740157i	$0.265249\pi$
$710$	−23.7327	−	5.40542i	−0.890672	−	0.202862i
$711$	−40.3093	−	48.4220i	−1.51172	−	1.81597i
$712$	12.8875	−	0.247406i	0.482978	−	0.00927194i
$713$	13.9410	−	11.6810i	0.522095	−	0.437457i
$714$	−44.1790	−	49.7444i	−1.65336	−	1.86164i
$715$	−36.9427	+	2.36696i	−1.38158	+	0.0885192i
$716$	21.4534	+	41.5446i	0.801752	+	1.55259i
$717$	−3.78412	−	22.1035i	−0.141321	−	0.825469i
$718$	−0.831691	−	5.26199i	−0.0310384	−	0.196376i
$719$	15.3307	−	0.392452i	0.571740	−	0.0146360i	0.261348	−	0.965245i	$-0.415833\pi$
$719$	15.3307	−	0.392452i	0.571740	−	0.0146360i	0.310392	+	0.950609i	$0.399540\pi$
$720$	−7.55637	−	30.8863i	−0.281609	−	1.15106i
$721$	−4.57091	+	4.46968i	−0.170230	+	0.166460i
$722$	−52.0277	−	2.99934i	−1.93627	−	0.111624i
$723$	45.8359	+	26.1385i	1.70465	+	0.972101i
$724$	11.6182	−	63.0051i	0.431789	−	2.34157i
$725$	−65.8414	−	13.6724i	−2.44529	−	0.507782i
$726$	−41.6592	+	28.9829i	−1.54612	+	1.07566i
$727$	24.5511	−	15.2782i	0.910548	−	0.566636i	0.00930850	−	0.999957i	$-0.497037\pi$
$727$	24.5511	−	15.2782i	0.910548	−	0.566636i	0.901240	+	0.433320i	$0.142658\pi$
$728$	25.2106	−	31.0851i	0.934368	−	1.15209i
$729$	42.2303	−	2.97716i	1.56408	−	0.110265i
$730$	−2.41769	−	58.0989i	−0.0894826	−	2.15034i
$731$	−4.80993	−	2.78386i	−0.177902	−	0.102965i
$732$	21.7351	−	72.5376i	0.803351	−	2.68107i
$733$	1.17072	−	2.09953i	0.0432416	−	0.0775477i	−0.850911	−	0.525309i	$-0.823950\pi$
$733$	1.17072	−	2.09953i	0.0432416	−	0.0775477i	0.894153	+	0.447761i	$0.147779\pi$
$734$	12.4207	+	2.66225i	0.458455	+	0.0982654i
$735$	65.4484	+	25.9516i	2.41410	+	0.957240i
$736$	−1.55718	−	25.5865i	−0.0573983	−	0.943130i
$737$	9.46725	−	7.14094i	0.348731	−	0.263040i
$738$	−132.640	+	17.9302i	−4.88253	+	0.660020i
$739$	10.4789	+	46.6975i	0.385473	+	1.71780i	0.655720	+	0.755005i	$0.272365\pi$
$739$	10.4789	+	46.6975i	0.385473	+	1.71780i	−0.270246	+	0.962791i	$0.587105\pi$
$740$	8.21333	−	5.40757i	0.301928	−	0.198786i
$741$	49.2100	−	101.591i	1.80778	−	3.73204i
$742$	−17.5022	−	0.111987i	−0.642527	−	0.00411117i
$743$	−10.1841	−	10.8924i	−0.373619	−	0.399603i	0.515789	−	0.856715i	$-0.327499\pi$
$743$	−10.1841	−	10.8924i	−0.373619	−	0.399603i	−0.889409	+	0.457113i	$0.848884\pi$
$744$	−16.5377	−	20.3912i	−0.606301	−	0.747578i
$745$	23.5107	+	8.12436i	0.861364	+	0.297654i
$746$	10.1977	+	3.89332i	0.373363	+	0.142544i
$747$	59.6855	+	52.6674i	2.18378	+	1.92700i
$748$	13.0288	+	3.94939i	0.476380	+	0.144404i
$749$	−24.1894	−	17.7645i	−0.883861	−	0.649101i
$750$	−57.3632	+	35.1901i	−2.09461	+	1.28496i
$751$	−0.0831003	+	25.9754i	−0.00303237	+	0.947857i	0.879041	+	0.476745i	$0.158184\pi$
$751$	−0.0831003	+	25.9754i	−0.00303237	+	0.947857i	−0.882074	+	0.471111i	$0.843853\pi$
$752$	−10.2253	+	6.54620i	−0.372877	+	0.238715i
$753$	−18.1068	+	17.4806i	−0.659849	+	0.637027i
$754$	−23.8056	+	109.356i	−0.866950	+	3.98252i
$755$	−19.1837	+	78.4126i	−0.698168	+	2.85373i
$756$	31.7641	+	53.6866i	1.15525	+	1.95256i
$757$	−1.23171	+	1.25158i	−0.0447674	+	0.0454893i	−0.734760	−	0.678327i	$-0.762705\pi$
$757$	−1.23171	+	1.25158i	−0.0447674	+	0.0454893i	0.689993	+	0.723816i	$0.257614\pi$
$758$	4.70909	−	6.54294i	0.171042	−	0.237650i
$759$	7.62442	−	14.9993i	0.276749	−	0.544441i
$760$	24.8304	−	33.5851i	0.900694	−	1.21826i
$761$	−15.0637	+	22.4084i	−0.546059	+	0.812303i	−0.996765	−	0.0803693i	$-0.974390\pi$
$761$	−15.0637	+	22.4084i	−0.546059	+	0.812303i	0.450706	+	0.892672i	$0.351172\pi$
$762$	−3.49169	−	1.65016i	−0.126490	−	0.0597791i
$763$	−0.0472176	+	0.0133290i	−0.00170939	+	0.000482541i
$764$	16.5815	+	35.3785i	0.599899	+	1.27995i
$765$	48.9044	−	19.3916i	1.76814	−	0.701104i
$766$	−33.3611	+	5.60163i	−1.20538	+	0.202395i
$767$	−36.6663	−	49.5941i	−1.32395	−	1.79074i
$768$	−9.33350	+	0.418313i	−0.336794	+	0.0150946i
$769$	−10.0837	−	5.92264i	−0.363628	−	0.213576i	0.313250	−	0.949671i	$-0.398582\pi$
$769$	−10.0837	−	5.92264i	−0.363628	−	0.213576i	−0.676878	+	0.736095i	$0.736668\pi$
$770$	−49.0823	+	8.56461i	−1.76880

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)

\(f(q)\)	\(=\)	\(q+(-0.696245 + 2.07926i) q^{2} +(-2.48076 - 1.39373i) q^{3} +(-2.24185 - 1.69098i) q^{4} +(1.99175 - 3.00421i) q^{5} +(4.62514 - 4.18777i) q^{6} +(1.53695 - 3.39151i) q^{7} +(1.46097 - 1.00260i) q^{8} +(2.65117 + 4.35284i) q^{9} +O(q^{10})\)	\(q+(-0.696245 + 2.07926i) q^{2} +(-2.48076 - 1.39373i) q^{3} +(-2.24185 - 1.69098i) q^{4} +(1.99175 - 3.00421i) q^{5} +(4.62514 - 4.18777i) q^{6} +(1.53695 - 3.39151i) q^{7} +(1.46097 - 1.00260i) q^{8} +(2.65117 + 4.35284i) q^{9} +(4.85979 + 6.23303i) q^{10} +(-1.68953 - 0.108250i) q^{11} +(3.20473 + 7.31945i) q^{12} +(3.96988 + 4.58687i) q^{13} +(5.98174 + 5.55703i) q^{14} +(-9.12811 + 4.67678i) q^{15} +(-0.475549 - 1.66424i) q^{16} +(2.61959 - 1.15696i) q^{17} +(-10.8965 + 2.48183i) q^{18} +(5.19566 + 3.97138i) q^{19} +(-9.54526 + 3.36699i) q^{20} +(-8.53964 + 6.27145i) q^{21} +(1.40141 - 3.43760i) q^{22} +(-0.368058 - 3.47333i) q^{23} +(-5.02166 + 0.451033i) q^{24} +(-3.11161 - 7.36176i) q^{25} +(-12.3013 + 5.06082i) q^{26} +(-0.209904 - 5.96226i) q^{27} +(-9.18058 + 5.00431i) q^{28} +(4.78299 - 6.92206i) q^{29} +(-3.36885 - 22.2359i) q^{30} +(2.90512 + 4.32158i) q^{31} +(7.33174 + 0.328597i) q^{32} +(4.04045 + 2.62329i) q^{33} +(0.581738 + 6.25234i) q^{34} +(-7.12761 - 11.3723i) q^{35} +(1.41704 - 14.2415i) q^{36} +(-0.942967 + 0.233898i) q^{37} +(-11.8750 + 8.03806i) q^{38} +(-3.45547 - 16.9119i) q^{39} +(-0.102158 - 6.38598i) q^{40} +(11.9286 + 1.07139i) q^{41} +(-7.09429 - 22.1226i) q^{42} +(-1.14370 - 1.56783i) q^{43} +(3.60462 + 3.09964i) q^{44} +(18.3573 + 0.705086i) q^{45} +(7.47821 + 1.65300i) q^{46} +(-2.01340 - 6.71943i) q^{47} +(-1.13977 + 4.79137i) q^{48} +(-4.52542 - 5.16164i) q^{49} +(17.4735 - 1.34426i) q^{50} +(-8.11106 - 0.780861i) q^{51} +(-1.14356 - 16.9961i) q^{52} +(-1.57986 + 1.44896i) q^{53} +(12.5432 + 3.71475i) q^{54} +(-3.69032 + 4.86010i) q^{55} +(-1.15492 - 6.49583i) q^{56} +(-7.35416 - 17.0934i) q^{57} +(11.0626 + 14.7645i) q^{58} +(-10.1372 - 0.779872i) q^{59} +(28.3722 + 4.95080i) q^{60} +(-7.22504 - 6.13289i) q^{61} +(-11.0084 + 3.03162i) q^{62} +(18.8374 - 2.30139i) q^{63} +(-4.54288 + 11.7857i) q^{64} +(21.6869 - 2.79046i) q^{65} +(-8.26763 + 6.57469i) q^{66} +(-5.31088 + 4.56686i) q^{67} +(-7.82912 - 1.83595i) q^{68} +(-3.92781 + 9.12948i) q^{69} +(28.6086 - 6.90221i) q^{70} +(-2.38566 + 1.94751i) q^{71} +(8.23744 + 3.70128i) q^{72} +(-5.98515 - 4.27864i) q^{73} +(0.170201 - 2.12352i) q^{74} +(-2.54112 + 22.5995i) q^{75} +(-4.93235 - 17.6890i) q^{76} +(-2.96384 + 5.56368i) q^{77} +(37.5700 + 4.58997i) q^{78} +(-12.2282 + 1.81264i) q^{79} +(-5.94691 - 1.88610i) q^{80} +(-0.773557 + 1.49799i) q^{81} +(-10.5329 + 24.0567i) q^{82} +(14.9172 - 4.62626i) q^{83} +(29.7495 + 0.380716i) q^{84} +(1.74182 - 10.1742i) q^{85} +(4.05622 - 1.28645i) q^{86} +(-21.5129 + 10.5058i) q^{87} +(-2.57688 + 1.53578i) q^{88} +(6.07593 + 4.00033i) q^{89} +(-14.2472 + 37.6787i) q^{90} +(21.6579 - 6.41411i) q^{91} +(-5.04820 + 8.40906i) q^{92} +(-1.18380 - 14.7697i) q^{93} +(15.3733 + 0.491986i) q^{94} +(22.2793 - 7.69886i) q^{95} +(-17.7303 - 11.0336i) q^{96} +(2.88782 - 0.147948i) q^{97} +(13.8832 - 5.81576i) q^{98} +(-4.00803 - 7.64124i) 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

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