LMFDB - Embedded newform 315.2.bv.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(23,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	315.23
Dual form			315.2.bv.a.137.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76155 - 1.76155i) q^{2} +(1.72928 + 0.0979388i) q^{3} +4.20612i q^{4} +(-2.22663 + 0.205270i) q^{5} +(-2.87369 - 3.21874i) q^{6} +(0.0218295 - 2.64566i) q^{7} +(3.88619 - 3.88619i) q^{8} +(2.98082 + 0.338727i) q^{9} +O(q^{10})$	\(q+(-1.76155 - 1.76155i) q^{2} +(1.72928 + 0.0979388i) q^{3} +4.20612i q^{4} +(-2.22663 + 0.205270i) q^{5} +(-2.87369 - 3.21874i) q^{6} +(0.0218295 - 2.64566i) q^{7} +(3.88619 - 3.88619i) q^{8} +(2.98082 + 0.338727i) q^{9} +(4.28391 + 3.56072i) q^{10} +(-3.47671 - 2.00728i) q^{11} +(-0.411942 + 7.27356i) q^{12} +(0.824568 - 0.220942i) q^{13} +(-4.69892 + 4.62201i) q^{14} +(-3.87056 + 0.136896i) q^{15} -5.27921 q^{16} +(1.54367 - 5.76106i) q^{17} +(-4.65417 - 5.84754i) q^{18} +(-6.15483 - 3.55349i) q^{19} +(-0.863390 - 9.36546i) q^{20} +(0.296862 - 4.57295i) q^{21} +(2.58848 + 9.66033i) q^{22} +(-3.69281 - 0.989485i) q^{23} +(7.10092 - 6.33971i) q^{24} +(4.91573 - 0.914118i) q^{25} +(-1.84172 - 1.06332i) q^{26} +(5.12149 + 0.877691i) q^{27} +(11.1280 + 0.0918175i) q^{28} +(0.190223 + 0.329475i) q^{29} +(7.05934 + 6.57704i) q^{30} -2.43295 q^{31} +(1.52721 + 1.52721i) q^{32} +(-5.81562 - 3.81166i) q^{33} +(-12.8677 + 7.42914i) q^{34} +(0.494468 + 5.89538i) q^{35} +(-1.42473 + 12.5377i) q^{36} +(-0.332572 - 1.24118i) q^{37} +(4.58238 + 17.1017i) q^{38} +(1.44755 - 0.301314i) q^{39} +(-7.85538 + 9.45082i) q^{40} +(-1.09948 - 0.634783i) q^{41} +(-8.57842 + 7.53255i) q^{42} +(-0.267479 + 0.998246i) q^{43} +(8.44287 - 14.6235i) q^{44} +(-6.70669 - 0.142347i) q^{45} +(4.76204 + 8.24810i) q^{46} +(8.17492 + 8.17492i) q^{47} +(-9.12923 - 0.517039i) q^{48} +(-6.99905 - 0.115507i) q^{49} +(-10.2696 - 7.04904i) q^{50} +(3.23367 - 9.81130i) q^{51} +(0.929310 + 3.46823i) q^{52} +(5.20020 + 1.39339i) q^{53} +(-7.47567 - 10.5679i) q^{54} +(8.15338 + 3.75580i) q^{55} +(-10.1967 - 10.3664i) q^{56} +(-10.2954 - 6.74777i) q^{57} +(0.245300 - 0.915474i) q^{58} +5.52975 q^{59} +(-0.575800 - 16.2801i) q^{60} +3.92134 q^{61} +(4.28576 + 4.28576i) q^{62} +(0.961227 - 7.87884i) q^{63} +5.17790i q^{64} +(-1.79065 + 0.661215i) q^{65} +(3.53008 + 16.9589i) q^{66} +(-2.33305 + 2.33305i) q^{67} +(24.2317 + 6.49287i) q^{68} +(-6.28899 - 2.07277i) q^{69} +(9.51398 - 11.2560i) q^{70} +6.69543i q^{71} +(12.9004 - 10.2677i) q^{72} +(4.38125 - 16.3510i) q^{73} +(-1.60055 + 2.77224i) q^{74} +(8.59020 - 1.09933i) q^{75} +(14.9464 - 25.8879i) q^{76} +(-5.38648 + 9.15439i) q^{77} +(-3.08071 - 2.01915i) q^{78} -9.66184i q^{79} +(11.7548 - 1.08366i) q^{80} +(8.77053 + 2.01937i) q^{81} +(0.818581 + 3.05499i) q^{82} +(1.20089 + 0.321778i) q^{83} +(19.2344 + 1.24864i) q^{84} +(-2.25461 + 13.1446i) q^{85} +(2.22964 - 1.28728i) q^{86} +(0.296680 + 0.588385i) q^{87} +(-21.3119 + 5.71050i) q^{88} +(3.03201 - 5.25159i) q^{89} +(11.5634 + 12.0649i) q^{90} +(-0.566539 - 2.18635i) q^{91} +(4.16189 - 15.5324i) q^{92} +(-4.20725 - 0.238280i) q^{93} -28.8011i q^{94} +(14.4339 + 6.64889i) q^{95} +(2.49140 + 2.79055i) q^{96} +(8.70133 + 2.33151i) q^{97} +(12.1257 + 12.5326i) q^{98} +(-9.68352 - 7.16099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.76155	−	1.76155i	−1.24560	−	1.24560i	−0.957642	−	0.287963i	$-0.907022\pi$
$2$	−1.76155	−	1.76155i	−1.24560	−	1.24560i	−0.287963	−	0.957642i	$-0.592978\pi$
$3$	1.72928	+	0.0979388i	0.998400	+	0.0565450i
$3$	1.72928	+	0.0979388i	0.998400	+	0.0565450i
$4$			4.20612i			2.10306i
$5$	−2.22663	+	0.205270i	−0.995778	+	0.0917994i
$5$	−2.22663	+	0.205270i	−0.995778	+	0.0917994i
$6$	−2.87369	−	3.21874i	−1.17318	−	1.31404i
$7$	0.0218295	−	2.64566i	0.00825078	−	0.999966i
$7$	0.0218295	−	2.64566i	0.00825078	−	0.999966i
$8$	3.88619	−	3.88619i	1.37398	−	1.37398i
$9$	2.98082	+	0.338727i	0.993605	+	0.112909i
$10$	4.28391	+	3.56072i	1.35469	+	1.12600i
$11$	−3.47671	−	2.00728i	−1.04827	−	0.605218i	−0.126104	−	0.992017i	$-0.540247\pi$
$11$	−3.47671	−	2.00728i	−1.04827	−	0.605218i	−0.922164	+	0.386799i	$0.873581\pi$
$12$	−0.411942	+	7.27356i	−0.118917	+	2.09970i
$13$	0.824568	−	0.220942i	0.228694	−	0.0612784i	−0.142652	−	0.989773i	$-0.545563\pi$
$13$	0.824568	−	0.220942i	0.228694	−	0.0612784i	0.371346	+	0.928495i	$0.378896\pi$
$14$	−4.69892	+	4.62201i	−1.25584	+	1.23528i
$15$	−3.87056	+	0.136896i	−0.999375	+	0.0353463i
$16$	−5.27921			−1.31980
$17$	1.54367	−	5.76106i	0.374395	−	1.39726i	−0.479831	−	0.877361i	$-0.659302\pi$
$17$	1.54367	−	5.76106i	0.374395	−	1.39726i	0.854226	−	0.519901i	$-0.174031\pi$
$18$	−4.65417	−	5.84754i	−1.09700	−	1.37828i
$19$	−6.15483	−	3.55349i	−1.41201	−	0.815227i	−0.416436	−	0.909165i	$-0.636721\pi$
$19$	−6.15483	−	3.55349i	−1.41201	−	0.815227i	−0.995578	+	0.0939386i	$0.970054\pi$
$20$	−0.863390	−	9.36546i	−0.193060	−	2.09418i
$21$	0.296862	−	4.57295i	0.0647806	−	0.997900i
$22$	2.58848	+	9.66033i	0.551866	+	2.05959i
$23$	−3.69281	−	0.989485i	−0.770004	−	0.206322i	−0.147631	−	0.989043i	$-0.547165\pi$
$23$	−3.69281	−	0.989485i	−0.770004	−	0.206322i	−0.622373	+	0.782721i	$0.713831\pi$
$24$	7.10092	−	6.33971i	1.44947	−	1.29409i
$25$	4.91573	−	0.914118i	0.983146	−	0.182824i
$26$	−1.84172	−	1.06332i	−0.361191	−	0.208534i
$27$	5.12149	+	0.877691i	0.985631	+	0.168912i
$28$	11.1280	+	0.0918175i	2.10299	+	0.0173519i
$29$	0.190223	+	0.329475i	0.0353234	+	0.0611820i	0.883147	−	0.469097i	$-0.155421\pi$
$29$	0.190223	+	0.329475i	0.0353234	+	0.0611820i	−0.847823	+	0.530279i	$0.822087\pi$
$30$	7.05934	+	6.57704i	1.28885	+	1.20080i
$31$	−2.43295			−0.436971			−0.218485	−	0.975840i	$-0.570112\pi$
$31$	−2.43295			−0.436971			−0.218485	+	0.975840i	$0.570112\pi$
$32$	1.52721	+	1.52721i	0.269975	+	0.269975i
$33$	−5.81562	−	3.81166i	−1.01237	−	0.663524i
$34$	−12.8677	+	7.42914i	−2.20678	+	1.27409i
$35$	0.494468	+	5.89538i	0.0835804	+	0.996501i
$36$	−1.42473	+	12.5377i	−0.237454	+	2.08961i
$37$	−0.332572	−	1.24118i	−0.0546745	−	0.204048i	0.933185	−	0.359395i	$-0.117017\pi$
$37$	−0.332572	−	1.24118i	−0.0546745	−	0.204048i	−0.987860	+	0.155347i	$0.950350\pi$
$38$	4.58238	+	17.1017i	0.743361	+	2.77426i
$39$	1.44755	−	0.301314i	0.231793	−	0.0482488i
$40$	−7.85538	+	9.45082i	−1.24205	+	1.49431i
$41$	−1.09948	−	0.634783i	−0.171709	−	0.0991365i	0.411682	−	0.911327i	$-0.364941\pi$
$41$	−1.09948	−	0.634783i	−0.171709	−	0.0991365i	−0.583392	+	0.812191i	$0.698275\pi$
$42$	−8.57842	+	7.53255i	−1.32368	+	1.16230i
$43$	−0.267479	+	0.998246i	−0.0407902	+	0.152231i	−0.983317	−	0.181899i	$-0.941776\pi$
$43$	−0.267479	+	0.998246i	−0.0407902	+	0.152231i	0.942527	+	0.334130i	$0.108442\pi$
$44$	8.44287	−	14.6235i	1.27281	−	2.20457i
$45$	−6.70669	−	0.142347i	−0.999775	−	0.0212198i
$46$	4.76204	+	8.24810i	0.702125	+	1.21612i
$47$	8.17492	+	8.17492i	1.19243	+	1.19243i	0.976382	+	0.216053i	$0.0693184\pi$
$47$	8.17492	+	8.17492i	1.19243	+	1.19243i	0.216053	+	0.976382i	$0.430682\pi$
$48$	−9.12923	−	0.517039i	−1.31769	−	0.0746282i
$49$	−6.99905	−	0.115507i	−0.999864	−	0.0165010i
$50$	−10.2696	−	7.04904i	−1.45234	−	0.996885i
$51$	3.23367	−	9.81130i	0.452804	−	1.37386i
$52$	0.929310	+	3.46823i	0.128872	+	0.480957i
$53$	5.20020	+	1.39339i	0.714302	+	0.191397i	0.597628	−	0.801774i	$-0.296110\pi$
$53$	5.20020	+	1.39339i	0.714302	+	0.191397i	0.116674	+	0.993170i	$0.462777\pi$
$54$	−7.47567	−	10.5679i	−1.01731	−	1.43810i
$55$	8.15338	+	3.75580i	1.09940	+	0.506432i
$56$	−10.1967	−	10.3664i	−1.36259	−	1.38527i
$57$	−10.2954	−	6.74777i	−1.36366	−	0.893765i
$58$	0.245300	−	0.915474i	0.0322095	−	0.120208i
$59$	5.52975			0.719912			0.359956	−	0.932969i	$-0.382792\pi$
$59$	5.52975			0.719912			0.359956	+	0.932969i	$0.382792\pi$
$60$	−0.575800	−	16.2801i	−0.0743355	−	2.10175i
$61$	3.92134			0.502076			0.251038	−	0.967977i	$-0.419228\pi$
$61$	3.92134			0.502076			0.251038	+	0.967977i	$0.419228\pi$
$62$	4.28576	+	4.28576i	0.544293	+	0.544293i
$63$	0.961227	−	7.87884i	0.121103	−	0.992640i
$64$			5.17790i			0.647238i
$65$	−1.79065	+	0.661215i	−0.222103	+	0.0820136i
$66$	3.53008	+	16.9589i	0.434523	+	2.08750i
$67$	−2.33305	+	2.33305i	−0.285028	+	0.285028i	−0.835110	−	0.550082i	$-0.814596\pi$
$67$	−2.33305	+	2.33305i	−0.285028	+	0.285028i	0.550082	+	0.835110i	$0.314596\pi$
$68$	24.2317	+	6.49287i	2.93853	+	0.787376i
$69$	−6.28899	−	2.07277i	−0.757106	−	0.249532i
$70$	9.51398	−	11.2560i	1.13714	−	1.34535i
$71$			6.69543i			0.794601i	0.917689	+	0.397301i	$0.130053\pi$
$71$			6.69543i			0.794601i	−0.917689	+	0.397301i	$0.869947\pi$
$72$	12.9004	−	10.2677i	1.52033	−	1.21006i
$73$	4.38125	−	16.3510i	0.512786	−	1.91374i	0.124454	−	0.992225i	$-0.460282\pi$
$73$	4.38125	−	16.3510i	0.512786	−	1.91374i	0.388333	−	0.921519i	$-0.373051\pi$
$74$	−1.60055	+	2.77224i	−0.186060	+	0.322266i
$75$	8.59020	−	1.09933i	0.991911	−	0.126939i
$76$	14.9464	−	25.8879i	1.71447	−	2.96955i
$77$	−5.38648	+	9.15439i	−0.613847	+	1.04324i
$78$	−3.08071	−	2.01915i	−0.348821	−	0.228623i
$79$		−	9.66184i		−	1.08704i	−0.839396	−	0.543521i	$-0.817091\pi$
$79$		−	9.66184i		−	1.08704i	0.839396	−	0.543521i	$-0.182909\pi$
$80$	11.7548	−	1.08366i	1.31423	−	0.121157i
$81$	8.77053	+	2.01937i	0.974503	+	0.224374i
$82$	0.818581	+	3.05499i	0.0903972	+	0.337367i
$83$	1.20089	+	0.321778i	0.131815	+	0.0353197i	0.324123	−	0.946015i	$-0.394931\pi$
$83$	1.20089	+	0.321778i	0.131815	+	0.0353197i	−0.192308	+	0.981335i	$0.561597\pi$
$84$	19.2344	+	1.24864i	2.09864	+	0.136238i
$85$	−2.25461	+	13.1446i	−0.244547	+	1.42573i
$86$	2.22964	−	1.28728i	0.240428	−	0.138811i
$87$	0.296680	+	0.588385i	0.0318074	+	0.0630815i
$88$	−21.3119	+	5.71050i	−2.27185	+	0.608741i
$89$	3.03201	−	5.25159i	0.321392	−	0.556668i	−0.659383	−	0.751807i	$-0.729182\pi$
$89$	3.03201	−	5.25159i	0.321392	−	0.556668i	0.980776	+	0.195139i	$0.0625158\pi$
$90$	11.5634	+	12.0649i	1.21889	+	1.27176i
$91$	−0.566539	−	2.18635i	−0.0593894	−	0.229192i
$92$	4.16189	−	15.5324i	0.433908	−	1.61936i
$93$	−4.20725	−	0.238280i	−0.436271	−	0.0247085i
$94$		−	28.8011i		−	2.97060i
$95$	14.4339	+	6.64889i	1.48089	+	0.682162i
$96$	2.49140	+	2.79055i	0.254278	+	0.284809i
$97$	8.70133	+	2.33151i	0.883486	+	0.236729i	0.671911	−	0.740632i	$-0.265474\pi$
$97$	8.70133	+	2.33151i	0.883486	+	0.236729i	0.211576	+	0.977362i	$0.432141\pi$
$98$	12.1257	+	12.5326i	1.22488	+	1.26599i
$99$	−9.68352	−	7.16099i	−0.973231	−	0.719707i
$100$	3.84489	+	20.6761i	0.384489	+	2.06761i
$101$	7.57290	+	4.37222i	0.753532	+	0.435052i	0.826969	−	0.562248i	$-0.190063\pi$
$101$	7.57290	+	4.37222i	0.753532	+	0.435052i	−0.0734370	+	0.997300i	$0.523397\pi$
$102$	−22.9794	+	11.5868i	−2.27530	+	1.14727i
$103$	−1.19153	+	4.44686i	−0.117405	+	0.438162i	−0.999456	−	0.0329930i	$-0.989496\pi$
$103$	−1.19153	+	4.44686i	−0.117405	+	0.438162i	0.882050	+	0.471155i	$0.156163\pi$
$104$	2.34581	−	4.06305i	0.230025	−	0.398415i
$105$	0.277687	+	10.2432i	0.0270995	+	0.999633i
$106$	−6.70589	−	11.6149i	−0.651333	−	1.12814i
$107$	−12.3032	+	3.29664i	−1.18940	+	0.318698i	−0.798647	−	0.601799i	$-0.794451\pi$
$107$	−12.3032	+	3.29664i	−1.18940	+	0.318698i	−0.390749	+	0.920497i	$0.627784\pi$
$108$	−3.69168	+	21.5416i	−0.355232	+	2.07284i
$109$	−6.82361	+	3.93961i	−0.653583	+	0.377347i	−0.789828	−	0.613329i	$-0.789830\pi$
$109$	−6.82361	+	3.93961i	−0.653583	+	0.377347i	0.136244	+	0.990675i	$0.456497\pi$
$110$	−7.74655	−	20.9786i	−0.738604	−	2.00023i
$111$	−0.453551	−	2.17891i	−0.0430491	−	0.206813i
$112$	−0.115243	+	13.9670i	−0.0108894	+	1.31976i
$113$	−4.31517	−	16.1044i	−0.405937	−	1.51498i	−0.802321	−	0.596893i	$-0.796402\pi$
$113$	−4.31517	−	16.1044i	−0.405937	−	1.51498i	0.396384	−	0.918085i	$-0.370265\pi$
$114$	6.24930	+	30.0224i	0.585301	+	2.81185i
$115$	8.42562	+	1.44519i	0.785693	+	0.134765i
$116$	−1.38581	+	0.800099i	−0.128669	+	0.0742873i
$117$	2.53272	−	0.379285i	0.234150	−	0.0350649i
$118$	−9.74093	−	9.74093i	−0.896725	−	0.896725i
$119$	−15.2081	−	4.20979i	−1.39413	−	0.385911i
$120$	−14.5098	+	15.5738i	−1.32455	+	1.42168i
$121$	2.55836	+	4.43120i	0.232578	+	0.402837i
$122$	−6.90764	−	6.90764i	−0.625388	−	0.625388i
$123$	−1.83913	−	1.20540i	−0.165829	−	0.108687i
$124$		−	10.2333i		−	0.918976i
$125$	−10.7578	+	3.04445i	−0.962211	+	0.272304i
$126$	−15.5722	+	12.1857i	−1.38728	+	1.08559i
$127$	5.28214	−	5.28214i	0.468714	−	0.468714i	−0.432784	−	0.901498i	$-0.642469\pi$
$127$	5.28214	−	5.28214i	0.468714	−	0.468714i	0.901498	+	0.432784i	$0.142469\pi$
$128$	12.1756	−	12.1756i	1.07618	−	1.07618i
$129$	−0.560313	+	1.70005i	−0.0493328	+	0.149681i
$130$	4.31909	+	1.98956i	0.378809	+	0.174496i
$131$	−0.893294	+	0.515744i	−0.0780475	+	0.0450607i	−0.538516	−	0.842615i	$-0.681015\pi$
$131$	−0.893294	+	0.515744i	−0.0780475	+	0.0450607i	0.460468	+	0.887676i	$0.347681\pi$
$132$	16.0323	−	24.4612i	1.39543	−	2.12907i
$133$	−9.53569	+	16.2060i	−0.826849	+	1.40524i
$134$	8.21959			0.710064
$135$	−11.5838	−	0.903003i	−0.996975	−	0.0777181i
$136$	−16.3896	−	28.3876i	−1.40540	−	2.43422i
$137$	8.12249	−	2.17642i	0.693951	−	0.185944i	0.105432	−	0.994427i	$-0.466378\pi$
$137$	8.12249	−	2.17642i	0.693951	−	0.185944i	0.588520	+	0.808483i	$0.299711\pi$
$138$	7.42709	+	14.7297i	0.632236	+	1.25387i
$139$	11.8061	+	6.81624i	1.00138	+	0.578146i	0.908656	−	0.417546i	$-0.137110\pi$
$139$	11.8061	+	6.81624i	1.00138	+	0.578146i	0.0927224	+	0.995692i	$0.470443\pi$
$140$	−24.7967	+	2.07979i	−2.09570	+	0.175775i
$141$	13.3361	+	14.9374i	1.12310	+	1.25795i
$142$	11.7943	−	11.7943i	0.989759	−	0.989759i
$143$	−3.31028	−	0.886987i	−0.276819	−	0.0741736i
$144$	−15.7364	−	1.78821i	−1.31136	−	0.149018i
$145$	−0.491186	−	0.694571i	−0.0407908	−	0.0576810i
$146$	−36.5210	+	21.0854i	−3.02250	+	1.74504i
$147$	−12.0920	−	0.885222i	−0.997331	−	0.0730119i
$148$	5.22054	−	1.39884i	0.429125	−	0.114984i
$149$	9.48078	+	16.4212i	0.776695	+	1.34528i	0.933837	+	0.357700i	$0.116439\pi$
$149$	9.48078	+	16.4212i	0.776695	+	1.34528i	−0.157141	+	0.987576i	$0.550228\pi$
$150$	−17.0686	−	13.1955i	−1.39364	−	1.07741i
$151$	−6.29701	+	10.9067i	−0.512443	+	0.887578i	0.487453	+	0.873149i	$0.337926\pi$
$151$	−6.29701	+	10.9067i	−0.512443	+	0.887578i	−0.999896	+	0.0144284i	$0.995407\pi$
$152$	−37.7284	+	10.1093i	−3.06018	+	0.819972i
$153$	6.55283	−	16.6498i	0.529765	−	1.34605i
$154$	25.6145	−	6.63736i	2.06407	−	0.534854i
$155$	5.41727	−	0.499411i	0.435126	−	0.0401137i
$156$	1.26736	+	6.08856i	0.101470	+	0.487475i
$157$	7.38741	−	7.38741i	0.589580	−	0.589580i	−0.347938	−	0.937518i	$-0.613118\pi$
$157$	7.38741	−	7.38741i	0.589580	−	0.589580i	0.937518	+	0.347938i	$0.113118\pi$
$158$	−17.0198	+	17.0198i	−1.35402	+	1.35402i
$159$	8.85613	+	2.91886i	0.702337	+	0.231481i
$160$	−3.71402	−	3.08704i	−0.293619	−	0.244052i
$161$	−2.69846	+	9.74832i	−0.212668	+	0.768275i
$162$	−11.8925	−	19.0069i	−0.934364	−	1.49333i
$163$	1.82569	−	0.489193i	0.142999	−	0.0383166i	−0.186609	−	0.982434i	$-0.559750\pi$
$163$	1.82569	−	0.489193i	0.142999	−	0.0383166i	0.329609	+	0.944118i	$0.393083\pi$
$164$	2.66997	−	4.62453i	0.208490	−	0.361115i
$165$	13.7316	+	7.29336i	1.06901	+	0.567787i
$166$	−1.54860	−	2.68226i	−0.120195	−	0.208184i
$167$	4.81079	−	1.28905i	0.372270	−	0.0997494i	−0.0678333	−	0.997697i	$-0.521609\pi$
$167$	4.81079	−	1.28905i	0.372270	−	0.0997494i	0.440103	+	0.897947i	$0.354942\pi$
$168$	−16.6177	−	18.9250i	−1.28208	−	1.46010i
$169$	−10.6272	+	6.13564i	−0.817480	+	0.471972i
$170$	27.1265	−	19.1833i	2.08051	−	1.47129i
$171$	−17.1427	−	12.6771i	−1.31094	−	0.969443i
$172$	−4.19874	−	1.12505i	−0.320151	−	0.0857843i
$173$	3.44427	−	3.44427i	0.261863	−	0.261863i	−0.563947	−	0.825811i	$-0.690718\pi$
$173$	3.44427	−	3.44427i	0.261863	−	0.261863i	0.825811	+	0.563947i	$0.190718\pi$
$174$	0.513854	−	1.55909i	0.0389551	−	0.118194i
$175$	−2.31114	−	13.0253i	−0.174706	−	0.984621i
$176$	18.3543	+	10.5969i	1.38351	+	0.798769i
$177$	9.56248	+	0.541577i	0.718760	+	0.0407074i
$178$	−14.5920	+	3.90991i	−1.09372	+	0.293060i
$179$	2.91370	+	5.04668i	0.217780	+	0.377207i	0.954129	−	0.299396i	$-0.0967850\pi$
$179$	2.91370	+	5.04668i	0.217780	+	0.377207i	−0.736349	+	0.676602i	$0.763452\pi$
$180$	0.598729	−	28.2092i	0.0446266	−	2.10259i
$181$	1.68895			0.125539			0.0627695	−	0.998028i	$-0.480007\pi$
$181$	1.68895			0.125539			0.0627695	+	0.998028i	$0.480007\pi$
$182$	−2.85338	+	4.84935i	−0.211507	+	0.359458i
$183$	6.78110	+	0.384051i	0.501273	+	0.0283899i
$184$	−18.1963	+	10.5056i	−1.34145	+	0.774486i
$185$	0.995290	+	2.69537i	0.0731751	+	0.198167i
$186$	6.99154	+	7.83103i	0.512645	+	0.574199i
$187$	−16.9310	+	16.9310i	−1.23812	+	1.23812i
$188$	−34.3847	+	34.3847i	−2.50776	+	2.50776i
$189$	2.43387	−	13.5306i	0.177038	−	0.984204i
$190$	−13.7137	−	37.1384i	−0.994898	−	2.69431i
$191$			12.9996i			0.940614i	0.882503	+	0.470307i	$0.155857\pi$
$191$			12.9996i			0.940614i	−0.882503	+	0.470307i	$0.844143\pi$
$192$	−0.507118	+	8.95404i	−0.0365981	+	0.646202i
$193$	13.2429	+	13.2429i	0.953244	+	0.953244i	0.998955	−	0.0457107i	$-0.0145552\pi$
$193$	13.2429	+	13.2429i	0.953244	+	0.953244i	−0.0457107	+	0.998955i	$0.514555\pi$
$194$	−11.2208	−	19.4349i	−0.805603	−	1.39535i
$195$	−3.16130	+	0.968051i	−0.226385	+	0.0693236i
$196$	0.485836	−	29.4388i	0.0347026	−	2.10277i
$197$	−5.87731	−	5.87731i	−0.418741	−	0.418741i	0.466028	−	0.884770i	$-0.345684\pi$
$197$	−5.87731	−	5.87731i	−0.418741	−	0.418741i	−0.884770	+	0.466028i	$0.845684\pi$
$198$	4.44356	+	29.6725i	0.315790	+	2.10873i
$199$	−7.74324	+	4.47056i	−0.548904	+	0.316910i	−0.748680	−	0.662932i	$-0.769312\pi$
$199$	−7.74324	+	4.47056i	−0.548904	+	0.316910i	0.199776	+	0.979842i	$0.435979\pi$
$200$	15.5510	−	22.6559i	1.09962	−	1.60202i
$201$	−4.26300	+	3.80601i	−0.300689	+	0.268455i
$202$	−5.63817	−	21.0419i	−0.396700	−	1.48050i
$203$	0.875832	−	0.496072i	0.0614714	−	0.0348174i
$204$	41.2675	+	13.6012i	2.88930	+	0.952275i
$205$	2.57843	+	1.18774i	0.180085	+	0.0829550i
$206$	9.93231	−	5.73442i	0.692017	−	0.399536i
$207$	−10.6724	−	4.20033i	−0.741784	−	0.291943i
$208$	−4.35307	+	1.16640i	−0.301831	+	0.0808754i
$209$	14.2657	+	24.7089i	0.986780	+	1.70915i
$210$	17.5547	−	18.5331i	1.21139	−	1.27890i
$211$	1.32751	−	2.29932i	0.0913896	−	0.158291i	−0.816706	−	0.577053i	$-0.804202\pi$
$211$	1.32751	−	2.29932i	0.0913896	−	0.158291i	0.908096	+	0.418762i	$0.137536\pi$
$212$	−5.86076	+	21.8727i	−0.402519	+	1.50222i
$213$	−0.655742	+	11.5783i	−0.0449307	+	0.793330i
$214$	27.4799	+	15.8655i	1.87849	+	1.08455i
$215$	0.390666	−	2.27763i	0.0266432	−	0.155333i
$216$	23.3140	−	16.4922i	1.58632	−	1.12215i
$217$	−0.0531101	+	6.43676i	−0.00360535	+	0.436956i
$218$	18.9600	+	5.08031i	1.28413	+	0.344082i
$219$	9.17780	−	27.8464i	0.620179	−	1.88169i
$220$	−15.7974	+	34.2941i	−1.06506	+	2.31211i
$221$		−	5.09145i		−	0.342488i
$222$	−3.03931	+	4.63722i	−0.203985	+	0.311230i
$223$	7.14906	−	26.6807i	0.478737	−	1.78667i	−0.128009	−	0.991773i	$-0.540859\pi$
$223$	7.14906	−	26.6807i	0.478737	−	1.78667i	0.606745	−	0.794896i	$-0.292475\pi$
$224$	4.07382	−	4.00715i	0.272194	−	0.267739i
$225$	14.9625	−	1.05973i	0.997501	−	0.0706485i
$226$	−20.7674	+	35.9702i	−1.38143	+	2.39270i
$227$	−10.8130	+	2.89734i	−0.717684	+	0.192303i	−0.599138	−	0.800646i	$-0.704490\pi$
$227$	−10.8130	+	2.89734i	−0.717684	+	0.192303i	−0.118546	+	0.992949i	$0.537823\pi$
$228$	28.3820	−	43.3037i	1.87964	−	2.86785i
$229$	−4.90510	+	2.83196i	−0.324138	+	0.187141i	−0.653236	−	0.757155i	$-0.726589\pi$
$229$	−4.90510	+	2.83196i	−0.324138	+	0.187141i	0.329098	+	0.944296i	$0.393256\pi$
$230$	−12.2964	−	17.3879i	−0.810799	−	1.14653i
$231$	−10.2113	+	15.3030i	−0.671854	+	1.00686i
$232$	2.01965	+	0.541163i	0.132596	+	0.0355291i
$233$	−4.02180	−	15.0096i	−0.263477	−	0.983309i	−0.963176	−	0.268871i	$-0.913349\pi$
$233$	−4.02180	−	15.0096i	−0.263477	−	0.983309i	0.699699	−	0.714437i	$-0.253317\pi$
$234$	−5.12965	−	3.79339i	−0.335336	−	0.247982i
$235$	−19.8806	−	16.5244i	−1.29686	−	1.07793i
$236$			23.2588i			1.51402i
$237$	0.946268	−	16.7080i	0.0614667	−	1.08530i
$238$	19.3741	+	34.2056i	1.25584	+	2.21722i
$239$	−10.9680	+	18.9971i	−0.709459	+	1.22882i	0.255600	+	0.966783i	$0.417727\pi$
$239$	−10.9680	+	18.9971i	−0.709459	+	1.22882i	−0.965058	+	0.262036i	$0.915606\pi$
$240$	20.4335	−	0.722702i	1.31898	−	0.0466502i
$241$	7.59999	−	13.1636i	0.489558	−	0.847940i	−0.510370	−	0.859955i	$-0.670491\pi$
$241$	7.59999	−	13.1636i	0.489558	−	0.847940i	0.999928	+	0.0120154i	$0.00382473\pi$
$242$	3.29912	−	12.3125i	0.212075	−	0.791475i
$243$	14.9689	+	4.35102i	0.960257	+	0.279118i
$244$			16.4936i			1.05590i
$245$	15.6080	−	1.17950i	0.997157	−	0.0753556i
$246$	1.11635	+	5.36310i	0.0711761	+	0.341939i
$247$	−5.86019	−	1.57023i	−0.372875	−	0.0999115i
$248$	−9.45491	+	9.45491i	−0.600388	+	0.600388i
$249$	2.04516	+	0.674058i	0.129607	+	0.0427167i
$250$	24.3134	+	13.5875i	1.53772	+	0.859352i
$251$		−	2.64900i		−	0.167203i	−0.996499	−	0.0836016i	$-0.973358\pi$
$251$		−	2.64900i		−	0.167203i	0.996499	−	0.0836016i	$-0.0266423\pi$
$252$	33.1393	+	4.04304i	2.08758	+	0.254687i
$253$	10.8527	+	10.8527i	0.682301	+	0.682301i
$254$	−18.6095			−1.16766
$255$	−5.18621	+	22.5099i	−0.324773	+	1.40962i
$256$	−32.5399			−2.03375
$257$	7.27634	−	27.1557i	0.453886	−	1.69392i	−0.237457	−	0.971398i	$-0.576314\pi$
$257$	7.27634	−	27.1557i	0.453886	−	1.69392i	0.691343	−	0.722527i	$-0.257019\pi$
$258$	3.98174	−	2.00770i	0.247893	−	0.124994i
$259$	−3.29099	+	0.852779i	−0.204492	+	0.0529891i
$260$	−2.78115	−	7.53170i	−0.172480	−	0.467096i
$261$	0.455416	+	1.04654i	0.0281896	+	0.0647791i
$262$	2.48209	+	0.665074i	0.153344	+	0.0410884i
$263$	−0.158383	−	0.591094i	−0.00976632	−	0.0364484i	0.960871	−	0.276997i	$-0.0893393\pi$
$263$	−0.158383	−	0.591094i	−0.00976632	−	0.0364484i	−0.970637	+	0.240549i	$0.922673\pi$
$264$	−37.4135	+	7.78779i	−2.30264	+	0.479305i
$265$	−11.8649	−	2.03511i	−0.728856	−	0.125016i
$266$	45.3453	−	11.7501i	2.78030	−	0.720446i
$267$	5.75753	−	8.78452i	0.352355	−	0.537604i
$268$	−9.81311	−	9.81311i	−0.599431	−	0.599431i
$269$	1.59411	+	2.76108i	0.0971947	+	0.168346i	0.910522	−	0.413460i	$-0.135680\pi$
$269$	1.59411	+	2.76108i	0.0971947	+	0.168346i	−0.813328	+	0.581806i	$0.802346\pi$
$270$	18.8148	+	21.9961i	1.14503	+	1.33864i
$271$	8.29620	−	14.3694i	0.503958	−	0.872882i	−0.496031	−	0.868305i	$-0.665210\pi$
$271$	8.29620	−	14.3694i	0.503958	−	0.872882i	0.999990	−	0.00457693i	$-0.00145689\pi$
$272$	−8.14937	+	30.4139i	−0.494128	+	1.84411i
$273$	−0.765575	−	3.83630i	−0.0463347	−	0.232183i
$274$	−18.1420	−	10.4743i	−1.09600	−	0.632777i
$275$	−18.9255	−	6.68912i	−1.14125	−	0.403369i
$276$	8.71830	−	26.4523i	0.524780	−	1.59224i
$277$	3.16929	+	11.8280i	0.190424	+	0.710673i	0.993404	+	0.114667i	$0.0365800\pi$
$277$	3.16929	+	11.8280i	0.190424	+	0.710673i	−0.802980	+	0.596006i	$0.796753\pi$
$278$	−8.78984	−	32.8041i	−0.527180	−	1.96746i
$279$	−7.25217	−	0.824106i	−0.434176	−	0.0493379i
$280$	24.8322	+	20.9890i	1.48401	+	1.25433i
$281$	22.6786	−	13.0935i	1.35289	−	0.781092i	0.364237	−	0.931306i	$-0.381330\pi$
$281$	22.6786	−	13.0935i	1.35289	−	0.781092i	0.988653	+	0.150215i	$0.0479965\pi$
$282$	2.82074	−	49.8051i	0.167973	−	2.96585i
$283$	−9.32584	−	9.32584i	−0.554364	−	0.554364i	0.373333	−	0.927697i	$-0.378215\pi$
$283$	−9.32584	−	9.32584i	−0.554364	−	0.554364i	−0.927697	+	0.373333i	$0.878215\pi$
$284$	−28.1618			−1.67109
$285$	24.3091	+	12.9114i	1.43995	+	0.764808i
$286$	4.26875	+	7.39370i	0.252417	+	0.437198i
$287$	−1.70342	+	2.89499i	−0.100550	+	0.170886i
$288$	4.03503	+	5.06964i	0.237766	+	0.298732i
$289$	−16.0844	−	9.28636i	−0.946144	−	0.546257i
$290$	−0.358273	+	2.08877i	−0.0210385	+	0.122657i
$291$	14.8187	+	4.88404i	0.868687	+	0.286307i
$292$	68.7745	+	18.4281i	4.02472	+	1.07842i
$293$	−4.58630	−	17.1163i	−0.267935	−	0.999946i	−0.960430	−	0.278523i	$-0.910155\pi$
$293$	−4.58630	−	17.1163i	−0.267935	−	0.999946i	0.692495	−	0.721423i	$-0.256512\pi$
$294$	19.7413	+	22.8600i	1.15134	+	1.33322i
$295$	−12.3127	+	1.13509i	−0.716872	+	0.0660875i
$296$	−6.11589	−	3.53101i	−0.355479	−	0.205236i
$297$	−16.0442	−	13.3318i	−0.930978	−	0.773587i
$298$	12.2259	−	45.6276i	0.708226	−	2.64314i
$299$	−3.26359			−0.188738
$300$	4.62390	+	36.1314i	0.266961	+	2.08605i
$301$	2.63518	+	0.729451i	0.151889	+	0.0420448i
$302$	30.3053	−	8.12027i	1.74387	−	0.467269i
$303$	12.6674	+	8.30246i	0.727726	+	0.476964i
$304$	32.4926	+	18.7596i	1.86358	+	1.07594i
$305$	−8.73136	+	0.804933i	−0.499956	+	0.0460903i
$306$	−40.8726	+	17.7863i	−2.33653	+	1.01677i
$307$	−15.5428	+	15.5428i	−0.887075	+	0.887075i	−0.994241	−	0.107166i	$-0.965822\pi$
$307$	−15.5428	+	15.5428i	−0.887075	+	0.887075i	0.107166	+	0.994241i	$0.465822\pi$
$308$	−38.5045	−	22.6562i	−2.19400	−	1.29096i
$309$	−2.49601	+	7.57316i	−0.141993	+	0.430822i
$310$	−10.4225	−	8.66306i	−0.591960	−	0.492028i
$311$		−	2.93291i		−	0.166310i	−0.996537	−	0.0831550i	$-0.973500\pi$
$311$		−	2.93291i		−	0.166310i	0.996537	−	0.0831550i	$-0.0264997\pi$
$312$	4.45448	−	6.79641i	0.252186	−	0.384771i
$313$	−16.1240	−	16.1240i	−0.911383	−	0.911383i	0.0849984	−	0.996381i	$-0.472911\pi$
$313$	−16.1240	−	16.1240i	−0.911383	−	0.911383i	−0.996381	+	0.0849984i	$0.972911\pi$
$314$	−26.0266			−1.46877
$315$	−0.523006	+	17.7405i	−0.0294680	+	0.999566i
$316$	40.6389			2.28611
$317$	2.96823	+	2.96823i	0.166713	+	0.166713i	0.785533	−	0.618820i	$-0.212389\pi$
$317$	2.96823	+	2.96823i	0.166713	+	0.166713i	−0.618820	+	0.785533i	$0.712389\pi$
$318$	−10.4588	−	20.7422i	−0.586500	−	1.16317i
$319$		−	1.52732i		−	0.0855136i
$320$	−1.06287	−	11.5293i	−0.0594161	−	0.644505i
$321$	−21.5986	+	4.49585i	−1.20551	+	0.250934i
$322$	21.9256	−	12.4187i	1.22187	−	0.692067i
$323$	−29.9729	+	29.9729i	−1.66774	+	1.66774i
$324$	−8.49370	+	36.8899i	−0.471872	+	2.04944i
$325$	3.85138	−	1.83984i	0.213636	−	0.102056i
$326$	−4.07779	−	2.35431i	−0.225848	−	0.130393i
$327$	−12.1858	+	6.14440i	−0.673875	+	0.339786i
$328$	−6.73967	+	1.80589i	−0.372136	+	0.0997135i
$329$	21.8065	−	21.4496i	1.20223	−	1.18256i
$330$	−11.3413	−	37.0366i	−0.624320	−	2.03880i
$331$	−13.0819			−0.719048			−0.359524	−	0.933136i	$-0.617061\pi$
$331$	−13.0819			−0.719048			−0.359524	+	0.933136i	$0.617061\pi$
$332$	−1.35344	+	5.05110i	−0.0742795	+	0.277215i
$333$	−0.570916	−	3.81237i	−0.0312860	−	0.208916i
$334$	−10.7452	−	6.20372i	−0.587949	−	0.339453i
$335$	4.71593	−	5.67374i	0.257659	−	0.309990i
$336$	−1.56720	+	24.1416i	−0.0854977	+	1.31703i
$337$	8.66631	+	32.3431i	0.472084	+	1.76184i	0.632263	+	0.774754i	$0.282126\pi$
$337$	8.66631	+	32.3431i	0.472084	+	1.76184i	−0.160179	+	0.987088i	$0.551207\pi$
$338$	29.5286	+	7.91218i	1.60615	+	0.430366i
$339$	−5.88489	−	28.2717i	−0.319623	−	1.53551i
$340$	−55.2878	−	9.48315i	−2.99840	−	0.514296i
$341$	8.45867	+	4.88361i	0.458063	+	0.264463i
$342$	7.86644	+	52.5292i	0.425368	+	2.84045i
$343$	−0.458378	+	18.5146i	−0.0247501	+	0.999694i
$344$	2.83990	+	4.91885i	0.153117	+	0.265207i
$345$	14.4287	+	3.32434i	0.776816	+	0.178976i
$346$	−12.1345			−0.652356
$347$	−22.0297	−	22.0297i	−1.18262	−	1.18262i	−0.979064	−	0.203554i	$-0.934751\pi$
$347$	−22.0297	−	22.0297i	−1.18262	−	1.18262i	−0.203554	−	0.979064i	$-0.565249\pi$
$348$	−2.47482	+	1.24787i	−0.132664	+	0.0668929i
$349$	−0.414023	+	0.239036i	−0.0221621	+	0.0127953i	−0.511040	−	0.859557i	$-0.670740\pi$
$349$	−0.414023	+	0.239036i	−0.0221621	+	0.0127953i	0.488878	+	0.872352i	$0.337406\pi$
$350$	−18.8735	+	27.0159i	−1.00883	+	1.44406i
$351$	4.41693	−	0.407838i	0.235759	−	0.0217688i
$352$	−2.24413	−	8.37522i	−0.119613	−	0.446401i
$353$	−0.134496	−	0.501945i	−0.00715849	−	0.0267158i	0.962254	−	0.272152i	$-0.0877354\pi$
$353$	−0.134496	−	0.501945i	−0.00715849	−	0.0267158i	−0.969413	+	0.245436i	$0.921069\pi$
$354$	−15.8908	−	17.7988i	−0.844585	−	0.945996i
$355$	−1.37437	−	14.9082i	−0.0729439	−	0.791246i
$356$	22.0888	+	12.7530i	1.17071	+	0.675908i
$357$	−25.8868	−	8.76937i	−1.37007	−	0.464124i
$358$	3.75735	−	14.0226i	0.198582	−	0.741118i
$359$	−4.11787	+	7.13236i	−0.217333	+	0.376432i	−0.953992	−	0.299833i	$-0.903069\pi$
$359$	−4.11787	+	7.13236i	−0.217333	+	0.376432i	0.736659	+	0.676265i	$0.236402\pi$
$360$	−26.6167	+	25.5103i	−1.40282	+	1.34451i
$361$	15.7546	+	27.2877i	0.829189	+	1.43620i
$362$	−2.97518	−	2.97518i	−0.156372	−	0.156372i
$363$	3.99013	+	7.91335i	0.209427	+	0.415343i
$364$	9.19605	−	2.38293i	0.482004	−	0.124899i
$365$	−6.39903	+	37.3070i	−0.334940	+	1.95274i
$366$	−11.2687	−	12.6218i	−0.589025	−	0.659750i
$367$	−0.476903	−	1.77983i	−0.0248941	−	0.0929062i	0.952361	−	0.304973i	$-0.0986473\pi$
$367$	−0.476903	−	1.77983i	−0.0248941	−	0.0929062i	−0.977255	+	0.212066i	$0.931981\pi$
$368$	19.4951	+	5.22370i	1.01625	+	0.272304i
$369$	−3.06232	−	2.26459i	−0.159418	−	0.117890i
$370$	2.99477	−	6.50128i	0.155691	−	0.337985i
$371$	3.79995	−	13.7275i	0.197284	−	0.712699i
$372$	1.00223	−	17.6962i	0.0519635	−	0.917505i
$373$	−4.32811	+	16.1527i	−0.224101	+	0.836356i	0.758662	+	0.651485i	$0.225854\pi$
$373$	−4.32811	+	16.1527i	−0.224101	+	0.836356i	−0.982763	+	0.184871i	$0.940813\pi$
$374$	59.6495			3.08440
$375$	−18.9015	+	4.21109i	−0.976069	+	0.217460i
$376$	63.5386			3.27676
$377$	0.229646	+	0.229646i	0.0118274	+	0.0118274i
$378$	−28.1222	+	19.5474i	−1.44645	+	1.00541i
$379$		−	25.4211i		−	1.30579i	−0.757447	−	0.652897i	$-0.773553\pi$
$379$		−	25.4211i		−	1.30579i	0.757447	−	0.652897i	$-0.226447\pi$
$380$	−27.9661	+	60.7108i	−1.43463	+	3.11440i
$381$	9.65162	−	8.61697i	0.494467	−	0.441461i
$382$	22.8994	−	22.8994i	1.17163	−	1.17163i
$383$	−1.92825	−	0.516674i	−0.0985292	−	0.0264008i	0.209218	−	0.977869i	$-0.432908\pi$
$383$	−1.92825	−	0.516674i	−0.0985292	−	0.0264008i	−0.307747	+	0.951468i	$0.599575\pi$
$384$	22.2474	−	19.8625i	1.13531	−	1.01360i
$385$	10.1146	−	21.4891i	0.515486	−	1.09519i
$386$		−	46.6560i		−	2.37473i
$387$	−1.13544	+	2.88499i	−0.0577176	+	0.146652i
$388$	−9.80663	+	36.5988i	−0.497856	+	1.85802i
$389$	−11.5960	+	20.0848i	−0.587938	+	1.01834i	0.406564	+	0.913622i	$0.366727\pi$
$389$	−11.5960	+	20.0848i	−0.587938	+	1.01834i	−0.994502	+	0.104716i	$0.966607\pi$
$390$	7.27405	+	3.86351i	0.368336	+	0.195637i
$391$	−11.4010	+	19.7471i	−0.576572	+	0.998651i
$392$	−27.6485	+	26.7508i	−1.39646	+	1.35112i
$393$	−1.59527	+	0.804377i	−0.0804706	+	0.0405754i
$394$			20.7064i			1.04317i
$395$	1.98328	+	21.5133i	0.0997898	+	1.08245i
$396$	30.1200	−	40.7301i	1.51359	−	2.04676i
$397$	−0.411706	−	1.53651i	−0.0206629	−	0.0771151i	0.954824	−	0.297170i	$-0.0960429\pi$
$397$	−0.411706	−	1.53651i	−0.0206629	−	0.0771151i	−0.975487	+	0.220055i	$0.929376\pi$
$398$	21.5152	+	5.76499i	1.07846	+	0.288973i
$399$	−18.0771	+	27.0908i	−0.904985	+	1.35624i
$400$	−25.9512	+	4.82582i	−1.29756	+	0.241291i
$401$	27.2539	−	15.7350i	1.36099	−	0.785769i	0.371236	−	0.928538i	$-0.378934\pi$
$401$	27.2539	−	15.7350i	1.36099	−	0.785769i	0.989756	+	0.142769i	$0.0456006\pi$
$402$	14.2140	+	0.805016i	0.708928	+	0.0401506i
$403$	−2.00613	+	0.537541i	−0.0999325	+	0.0267768i
$404$	−18.3901	+	31.8525i	−0.914940	+	1.58472i
$405$	−19.9432	−	2.69605i	−0.990986	−	0.133968i
$406$	−2.41668	−	0.668966i	−0.119938	−	0.0332002i
$407$	−1.33513	+	4.98278i	−0.0661800	+	0.246987i
$408$	−25.5619	−	50.6953i	−1.26550	−	2.50979i
$409$			10.7032i			0.529238i	0.964353	+	0.264619i	$0.0852462\pi$
$409$			10.7032i			0.529238i	−0.964353	+	0.264619i	$0.914754\pi$
$410$	−2.44977	−	6.63428i	−0.120986	−	0.327644i
$411$	14.2592	−	2.96812i	0.703355	−	0.146407i
$412$	−18.7040	−	5.01173i	−0.921481	−	0.246910i
$413$	0.120712	−	14.6298i	0.00593983	−	0.719887i
$414$	11.4009	+	26.1991i	0.560325	+	1.28762i
$415$	−2.73999	−	0.469972i	−0.134501	−	0.0230700i
$416$	1.59671	+	0.921864i	0.0782854	+	0.0451981i
$417$	19.7484	+	12.9435i	0.967085	+	0.633844i
$418$	18.3963	−	68.6558i	0.899791	−	3.35807i
$419$	10.4384	−	18.0798i	0.509948	−	0.883256i	−0.489985	−	0.871731i	$-0.662998\pi$
$419$	10.4384	−	18.0798i	0.509948	−	0.883256i	0.999934	−	0.0115257i	$-0.00366882\pi$
$420$	−43.0841	+	1.16799i	−2.10229	+	0.0569919i
$421$	−5.95259	−	10.3102i	−0.290111	−	0.502488i	0.683724	−	0.729740i	$-0.260359\pi$
$421$	−5.95259	−	10.3102i	−0.290111	−	0.502488i	−0.973836	+	0.227253i	$0.927026\pi$
$422$	−6.38884	+	1.71188i	−0.311004	+	0.0833332i
$423$	21.5989	+	27.1370i	1.05017	+	1.31945i
$424$	25.6240	−	14.7940i	1.24441	−	0.718460i
$425$	2.32198	−	29.7309i	0.112633	−	1.44216i
$426$	21.5508	−	19.2406i	1.04414	−	0.932209i
$427$	0.0856009	−	10.3745i	0.00414252	−	0.502059i
$428$	−13.8661	−	51.7488i	−0.670241	−	2.50137i
$429$	−5.63753	−	1.85805i	−0.272182	−	0.0897076i
$430$	−4.70033	+	3.32397i	−0.226670	+	0.160296i
$431$	19.7495	−	11.4024i	0.951301	−	0.549234i	0.0578160	−	0.998327i	$-0.481586\pi$
$431$	19.7495	−	11.4024i	0.951301	−	0.549234i	0.893485	+	0.449094i	$0.148253\pi$
$432$	−27.0374	−	4.63352i	−1.30084	−	0.222930i
$433$	2.66843	+	2.66843i	0.128236	+	0.128236i	0.768312	−	0.640076i	$-0.221097\pi$
$433$	2.66843	+	2.66843i	0.128236	+	0.128236i	−0.640076	+	0.768312i	$0.721097\pi$
$434$	11.4322	−	11.2451i	0.548765	−	0.539783i
$435$	−0.781372	−	1.24921i	−0.0374639	−	0.0598952i
$436$	−16.5705	−	28.7009i	−0.793583	−	1.37453i
$437$	19.2125	+	19.2125i	0.919057	+	0.919057i
$438$	−65.2201	+	32.8857i	−3.11634	+	1.57134i
$439$		−	8.80239i		−	0.420115i	−0.977689	−	0.210058i	$-0.932635\pi$
$439$		−	8.80239i		−	0.420115i	0.977689	−	0.210058i	$-0.0673651\pi$
$440$	46.2814	−	17.0898i	2.20638	−	0.814725i
$441$	−20.8237	−	2.71507i	−0.991607	−	0.129289i
$442$	−8.96884	+	8.96884i	−0.426604	+	0.426604i
$443$	4.15501	−	4.15501i	0.197411	−	0.197411i	−0.601478	−	0.798889i	$-0.705421\pi$
$443$	4.15501	−	4.15501i	0.197411	−	0.197411i	0.798889	+	0.601478i	$0.205421\pi$
$444$	9.16477	−	1.90769i	0.434941	−	0.0905350i
$445$	−5.67316	+	12.3157i	−0.268934	+	0.583821i
$446$	−59.5928	+	34.4059i	−2.82180	+	1.62917i
$447$	14.7866	+	29.3254i	0.699384	+	1.38704i
$448$	13.6990	+	0.113031i	0.647216	+	0.00534022i
$449$	−7.45249			−0.351705			−0.175852	−	0.984417i	$-0.556268\pi$
$449$	−7.45249			−0.351705			−0.175852	+	0.984417i	$0.556268\pi$
$450$	−28.2240	−	24.4905i	−1.33049	−	1.15449i
$451$	2.54838	+	4.41392i	0.119998	+	0.207843i
$452$	67.7372	−	18.1501i	3.18609	−	0.853710i
$453$	−11.9575	+	18.2441i	−0.561811	+	0.857182i
$454$	24.1515	+	13.9438i	1.13348	+	0.654417i
$455$	1.71026	+	4.75189i	0.0801783	+	0.222772i
$456$	−66.2330	+	13.7867i	−3.10165	+	0.645622i
$457$	−13.0953	+	13.0953i	−0.612571	+	0.612571i	−0.943615	−	0.331044i	$-0.892599\pi$
$457$	−13.0953	+	13.0953i	−0.612571	+	0.612571i	0.331044	+	0.943615i	$0.392599\pi$
$458$	13.6292	+	3.65194i	0.636852	+	0.170644i
$459$	12.9623	−	28.1503i	0.605030	−	1.31395i
$460$	−6.07865	+	35.4392i	−0.283419	+	1.65236i
$461$	18.7995	−	10.8539i	0.875581	−	0.505517i	0.00638217	−	0.999980i	$-0.497968\pi$
$461$	18.7995	−	10.8539i	0.875581	−	0.505517i	0.869199	+	0.494463i	$0.164635\pi$
$462$	44.9446	−	8.96920i	2.09101	−	0.417285i
$463$	−16.9219	+	4.53420i	−0.786426	+	0.210722i	−0.629616	−	0.776907i	$-0.716788\pi$
$463$	−16.9219	+	4.53420i	−0.786426	+	0.210722i	−0.156810	+	0.987629i	$0.550121\pi$
$464$	−1.00423	−	1.73937i	−0.0466200	−	0.0807482i
$465$	9.41688	−	0.333061i	0.436698	−	0.0154453i
$466$	−19.3555	+	33.5247i	−0.896626	+	1.55300i
$467$	32.9223	−	8.82151i	1.52346	−	0.408211i	0.602583	−	0.798056i	$-0.294138\pi$
$467$	32.9223	−	8.82151i	1.52346	−	0.408211i	0.920880	+	0.389846i	$0.127472\pi$
$468$	1.59532	+	10.6529i	0.0737436	+	0.492433i
$469$	6.12154	+	6.22340i	0.282667	+	0.287370i
$470$	5.91199	+	64.1292i	0.272700	+	2.95806i
$471$	13.4984	−	12.0514i	0.621974	−	0.555299i
$472$	21.4897	−	21.4897i	0.989142	−	0.989142i
$473$	2.93371	−	2.93371i	0.134892	−	0.134892i
$474$	−31.0989	+	27.7651i	−1.42842	+	1.27529i
$475$	−33.5038	−	11.8418i	−1.53726	−	0.543337i
$476$	17.7069	−	63.9672i	0.811594	−	2.93193i
$477$	15.0289	+	5.91488i	0.688124	+	0.270824i
$478$	52.7849	−	14.1437i	2.41433	−	0.646917i
$479$	10.3981	−	18.0100i	0.475099	−	0.822896i	−0.524494	−	0.851414i	$-0.675745\pi$
$479$	10.3981	−	18.0100i	0.475099	−	0.822896i	0.999593	+	0.0285178i	$0.00907873\pi$
$480$	−6.12024	−	5.70210i	−0.279349	−	0.260264i
$481$	−0.548456	−	0.949954i	−0.0250075	−	0.0433142i
$482$	−36.5760	+	9.80052i	−1.66599	+	0.446402i
$483$	−5.62112	+	16.5933i	−0.255770	+	0.755021i
$484$	−18.6382	+	10.7608i	−0.847190	+	0.489125i
$485$	−19.8532	−	3.40529i	−0.901487	−	0.154626i
$486$	−18.7040	−	34.0331i	−0.848429	−	1.54377i
$487$	−1.12034	−	0.300195i	−0.0507676	−	0.0136031i	0.233346	−	0.972394i	$-0.425033\pi$
$487$	−1.12034	−	0.300195i	−0.0507676	−	0.0136031i	−0.284113	+	0.958791i	$0.591699\pi$
$488$	15.2391	−	15.2391i	0.689841	−	0.689841i
$489$	3.20505	−	0.667145i	0.144937	−	0.0301694i
$490$	−29.5720	−	25.4165i	−1.33593	−	1.14820i
$491$	−7.95097	−	4.59050i	−0.358822	−	0.207166i	0.309742	−	0.950821i	$-0.399757\pi$
$491$	−7.95097	−	4.59050i	−0.358822	−	0.207166i	−0.668564	+	0.743655i	$0.733091\pi$
$492$	5.07005	−	7.73561i	0.228576	−	0.348748i
$493$	2.19177	−	0.587282i	0.0987122	−	0.0264499i
$494$	7.55697	+	13.0891i	0.340004	+	0.588905i
$495$	23.0315	+	13.9571i	1.03519	+	0.627326i
$496$	12.8441			0.576715
$497$	17.7138	+	0.146158i	0.794574	+	0.00655608i
$498$	−2.41527	−	4.79004i	−0.108231	−	0.214647i
$499$	31.0778	−	17.9428i	1.39123	−	0.803228i	0.397781	−	0.917481i	$-0.369781\pi$
$499$	31.0778	−	17.9428i	1.39123	−	0.803228i	0.993452	+	0.114252i	$0.0364472\pi$
$500$	−12.8053	−	45.2488i	−0.572672	−	2.02359i
$501$	8.44544	−	1.75796i	0.377314	−	0.0785398i
$502$	−4.66634	+	4.66634i	−0.208269	+	0.208269i
$503$	4.53104	−	4.53104i	0.202029	−	0.202029i	−0.598840	−	0.800869i	$-0.704371\pi$
$503$	4.53104	−	4.53104i	0.202029	−	0.202029i	0.800869	+	0.598840i	$0.204371\pi$
$504$	−26.8832	−	34.3542i	−1.19747	−	1.53026i
$505$	−17.7595	−	8.18080i	−0.790287	−	0.364041i
$506$		−	38.2350i		−	1.69975i
$507$	−18.9784	+	9.56941i	−0.842859	+	0.424993i
$508$	22.2173	+	22.2173i	0.985734	+	0.985734i
$509$	−2.75152	−	4.76578i	−0.121959	−	0.211239i	0.798581	−	0.601887i	$-0.205584\pi$
$509$	−2.75152	−	4.76578i	−0.121959	−	0.211239i	−0.920540	+	0.390648i	$0.872251\pi$
$510$	48.7880	−	30.5165i	2.16037	−	1.35129i
$511$	−43.1637	−	11.9482i	−1.90945	−	0.528559i
$512$	32.9696	+	32.9696i	1.45706	+	1.45706i
$513$	−28.4030	−	23.6012i	−1.25402	−	1.04202i
$514$	−60.6537	+	35.0185i	−2.67532	+	1.54460i
$515$	1.74029	−	10.1461i	0.0766864	−	0.447090i
$516$	−7.15062	−	2.35675i	−0.314788	−	0.103750i
$517$	−12.0125	−	44.8312i	−0.528309	−	1.97167i
$518$	7.29946	+	4.29503i	0.320720	+	0.188713i
$519$	6.29344	−	5.61879i	0.276251	−	0.246637i
$520$	−4.38921	+	9.52843i	−0.192480	+	0.417849i
$521$	−4.33094	+	2.50047i	−0.189742	+	0.109547i	−0.591862	−	0.806040i	$-0.701607\pi$
$521$	−4.33094	+	2.50047i	−0.189742	+	0.109547i	0.402120	+	0.915587i	$0.368274\pi$
$522$	1.04129	−	2.64577i	0.0455761	−	0.115802i
$523$	10.1736	−	2.72600i	0.444859	−	0.119200i	−0.0294339	−	0.999567i	$-0.509370\pi$
$523$	10.1736	−	2.72600i	0.444859	−	0.119200i	0.474293	+	0.880367i	$0.342704\pi$
$524$	−2.16928	−	3.75730i	−0.0947654	−	0.164139i
$525$	−2.72092	−	22.7507i	−0.118751	−	0.992924i
$526$	−0.762242	+	1.32024i	−0.0332353	+	0.0575652i
$527$	−3.75567	+	14.0164i	−0.163600	+	0.610562i
$528$	30.7019	+	20.1225i	1.33613	+	0.875721i
$529$	−7.26082	−	4.19204i	−0.315688	−	0.182263i
$530$	17.3157	+	24.4856i	0.752146	+	1.06359i
$531$	16.4832	+	1.87308i	0.715308	+	0.0812845i
$532$	−68.1644	−	40.1083i	−2.95530	−	1.73891i
$533$	−1.04684	−	0.280501i	−0.0453438	−	0.0121498i
$534$	−25.6166	+	5.33221i	−1.10854	+	0.230747i
$535$	26.7180	−	9.86586i	1.15512	−	0.426538i
$536$			18.1334i			0.783244i
$537$	4.54434	+	9.01249i	0.196103	+	0.388917i
$538$	2.05568	−	7.67189i	0.0886266	−	0.330759i
$539$	24.1018	+	14.4506i	1.03814	+	0.622433i
$540$	3.79814	−	48.7229i	0.163446	−	2.09670i
$541$	10.2159	−	17.6945i	0.439217	−	0.760746i	−0.558412	−	0.829564i	$-0.688589\pi$
$541$	10.2159	−	17.6945i	0.439217	−	0.760746i	0.997629	+	0.0688176i	$0.0219226\pi$
$542$	−39.9267	+	10.6983i	−1.71500	+	0.459532i
$543$	2.92067	+	0.165414i	0.125338	+	0.00709859i
$544$	11.1559	−	6.44084i	0.478304	−	0.276149i
$545$	14.3849	−	10.1727i	0.616183	−	0.435752i
$546$	−5.40923	+	8.10643i	−0.231494	+	0.346923i
$547$	40.3704	+	10.8172i	1.72611	+	0.462511i	0.979282	−	0.202501i	$-0.0649071\pi$
$547$	40.3704	+	10.8172i	1.72611	+	0.462511i	0.746832	+	0.665012i	$0.231574\pi$
$548$	9.15427	+	34.1642i	0.391051	+	1.45942i
$549$	11.6888	+	1.32826i	0.498866	+	0.0566889i
$550$	21.5549	+	45.1214i	0.919106	+	1.92398i
$551$		−	2.70382i		−	0.115186i
$552$	−32.4954	+	16.3851i	−1.38310	+	0.697395i
$553$	−25.5619	−	0.210913i	−1.08700	−	0.00896893i
$554$	15.2527	−	26.4184i	0.648024	−	1.12241i
$555$	1.45715	+	4.75852i	0.0618527	+	0.201988i
$556$	−28.6699	+	49.6578i	−1.21588	+	2.10596i
$557$	−6.03469	+	22.5218i	−0.255698	+	0.954278i	0.712003	+	0.702177i	$0.247788\pi$
$557$	−6.03469	+	22.5218i	−0.255698	+	0.954278i	−0.967701	+	0.252102i	$0.918878\pi$
$558$	11.3234	+	14.2268i	0.479356	+	0.602267i
$559$			0.882219i			0.0373139i
$560$	−2.61040	−	31.1230i	−0.110310	−	1.31519i
$561$	−30.9366	+	27.6202i	−1.30614	+	1.16612i
$562$	−63.0143	−	16.8846i	−2.65810	−	0.712235i
$563$	−6.14073	+	6.14073i	−0.258801	+	0.258801i	−0.824566	−	0.565765i	$-0.808581\pi$
$563$	−6.14073	+	6.14073i	−0.258801	+	0.258801i	0.565765	+	0.824566i	$0.308581\pi$
$564$	−62.8284	+	56.0932i	−2.64555	+	2.36195i
$565$	12.9140	+	34.9728i	0.543297	+	1.47132i
$566$			32.8559i			1.38104i
$567$	5.53401	−	23.1598i	0.232407	−	0.972619i
$568$	26.0197	+	26.0197i	1.09176	+	1.09176i
$569$	−21.9460			−0.920022			−0.460011	−	0.887913i	$-0.652155\pi$
$569$	−21.9460			−0.920022			−0.460011	+	0.887913i	$0.652155\pi$
$570$	−20.0776	−	65.5659i	−0.840956	−	2.74625i
$571$	−12.1160			−0.507038			−0.253519	−	0.967330i	$-0.581588\pi$
$571$	−12.1160			−0.507038			−0.253519	+	0.967330i	$0.581588\pi$
$572$	3.73077	−	13.9234i	0.155991	−	0.582168i
$573$	−1.27316	+	22.4799i	−0.0531870	+	0.939110i
$574$	8.10033	−	2.09900i	0.338101	−	0.0876106i
$575$	−19.0574	−	1.48838i	−0.794747	−	0.0620696i
$576$	−1.75390	+	15.4344i	−0.0730790	+	0.643099i
$577$	43.0653	+	11.5393i	1.79283	+	0.480388i	0.992822	−	0.119600i	$-0.0381613\pi$
$577$	43.0653	+	11.5393i	1.79283	+	0.480388i	0.800009	+	0.599988i	$0.204828\pi$
$578$	11.9752	+	44.6920i	0.498102	+	1.85894i
$579$	21.6037	+	24.1977i	0.897818	+	1.00562i
$580$	2.92145	−	2.06599i	0.121307	−	0.0857854i
$581$	0.877530	−	3.17013i	0.0364061	−	0.131519i
$582$	−17.5004	−	34.7073i	−0.725414	−	1.43867i
$583$	−15.2827	−	15.2827i	−0.632944	−	0.632944i
$584$	−46.5169	−	80.5697i	−1.92488	−	3.33400i
$585$	−5.56157	+	1.36442i	−0.229943	+	0.0564117i
$586$	−22.0722	+	38.2303i	−0.911796	+	1.57928i
$587$	−6.88246	+	25.6857i	−0.284069	+	1.06016i	0.665447	+	0.746445i	$0.268241\pi$
$587$	−6.88246	+	25.6857i	−0.284069	+	1.06016i	−0.949517	+	0.313717i	$0.898426\pi$
$588$	3.72335	−	50.8604i	0.153548	−	2.09745i
$589$	14.9744	+	8.64546i	0.617009	+	0.356230i
$590$	23.6889	+	19.6899i	0.975258	+	0.810620i
$591$	−9.58790	−	10.7391i	−0.394394	−	0.441749i
$592$	1.75572	+	6.55243i	0.0721596	+	0.269303i
$593$	4.62447	+	17.2587i	0.189904	+	0.708731i	0.993527	+	0.113593i	$0.0362361\pi$
$593$	4.62447	+	17.2587i	0.189904	+	0.708731i	−0.803623	+	0.595138i	$0.797097\pi$
$594$	4.77808	+	51.7472i	0.196047	+	2.12321i
$595$	34.7269	+	6.25187i	1.42367	+	0.256302i
$596$	−69.0695	+	39.8773i	−2.82920	+	1.63344i
$597$	−13.8281	+	6.97249i	−0.565945	+	0.285365i
$598$	5.74898	+	5.74898i	0.235093	+	0.235093i
$599$	−19.2221			−0.785393			−0.392696	−	0.919668i	$-0.628458\pi$
$599$	−19.2221			−0.785393			−0.392696	+	0.919668i	$0.628458\pi$
$600$	29.1110	−	37.6554i	1.18845	−	1.53727i
$601$	14.3837	+	24.9132i	0.586722	+	1.01623i	0.994658	+	0.103222i	$0.0329153\pi$
$601$	14.3837	+	24.9132i	0.586722	+	1.01623i	−0.407936	+	0.913010i	$0.633751\pi$
$602$	−3.35704	−	5.92697i	−0.136823	−	0.241565i
$603$	−7.74467	+	6.16414i	−0.315387	+	0.251023i
$604$	−45.8751	−	26.4860i	−1.86663	−	1.07770i
$605$	−6.60610	−	9.34148i	−0.268576	−	0.379785i
$606$	−7.68915	−	36.9396i	−0.312350	−	1.50057i
$607$	−13.9459	−	3.73680i	−0.566048	−	0.151672i	−0.0355647	−	0.999367i	$-0.511323\pi$
$607$	−13.9459	−	3.73680i	−0.566048	−	0.151672i	−0.530484	+	0.847695i	$0.677990\pi$
$608$	−3.97279	−	14.8266i	−0.161118	−	0.601300i
$609$	1.56314	−	0.772070i	0.0633418	−	0.0312858i
$610$	16.7987	+	13.9628i	0.680158	+	0.565337i
$611$	8.54696	+	4.93459i	0.345773	+	0.199632i
$612$	70.0310	+	27.5620i	2.83083	+	1.11413i
$613$	10.1110	−	37.7348i	0.408380	−	1.52409i	−0.389357	−	0.921087i	$-0.627303\pi$
$613$	10.1110	−	37.7348i	0.408380	−	1.52409i	0.797736	−	0.603006i	$-0.206031\pi$
$614$	54.7589			2.20989
$615$	4.34249	+	2.30645i	0.175106	+	0.0930052i
$616$	14.6428	+	56.5086i	0.589976	+	2.27680i
$617$	−36.4845	+	9.77600i	−1.46881	+	0.393567i	−0.902524	−	0.430640i	$-0.858288\pi$
$617$	−36.4845	+	9.77600i	−1.46881	+	0.393567i	−0.566288	+	0.824207i	$0.691621\pi$
$618$	17.7374	−	8.94366i	0.713501	−	0.359767i
$619$	28.5902	+	16.5065i	1.14914	+	0.663454i	0.948676	−	0.316248i	$-0.102423\pi$
$619$	28.5902	+	16.5065i	1.14914	+	0.663454i	0.200459	+	0.979702i	$0.435757\pi$
$620$	2.10058	+	22.7857i	0.0843614	+	0.915095i
$621$	−18.0442	−	8.30878i	−0.724090	−	0.333420i
$622$	−5.16647	+	5.16647i	−0.207157	+	0.207157i
$623$	−13.8278	−	8.13631i	−0.553997	−	0.325974i
$624$	−7.64191	+	1.59070i	−0.305921	+	0.0636789i
$625$	23.3288	−	8.98711i	0.933151	−	0.359485i
$626$			56.8065i			2.27044i
$627$	22.2494	+	44.1258i	0.888557	+	1.76222i
$628$	31.0724	+	31.0724i	1.23992	+	1.23992i
$629$	−7.66387			−0.305578
$630$	32.1721	−	30.3295i	1.28177	−	1.20836i
$631$	−5.10513			−0.203232			−0.101616	−	0.994824i	$-0.532401\pi$
$631$	−5.10513			−0.203232			−0.101616	+	0.994824i	$0.532401\pi$
$632$	−37.5478	−	37.5478i	−1.49357	−	1.49357i
$633$	2.52083	−	3.84615i	0.100194	−	0.152871i
$634$		−	10.4574i		−	0.415316i
$635$	−10.6771	+	12.8456i	−0.423707	+	0.509762i
$636$	−12.2771	+	37.2500i	−0.486818	+	1.47706i
$637$	−5.79671	+	1.45114i	−0.229674	+	0.0574963i
$638$	−2.69045	+	2.69045i	−0.106516	+	0.106516i
$639$	−2.26792	+	19.9578i	−0.0897176	+	0.789520i
$640$	−24.6112	+	29.6097i	−0.972841	+	1.17043i
$641$	16.2852	+	9.40228i	0.643228	+	0.371368i	0.785857	−	0.618409i	$-0.212222\pi$
$641$	16.2852	+	9.40228i	0.643228	+	0.371368i	−0.142629	+	0.989776i	$0.545556\pi$
$642$	45.9666	+	30.1273i	1.81416	+	1.18903i
$643$	18.2444	−	4.88858i	0.719490	−	0.192787i	0.119546	−	0.992829i	$-0.461856\pi$
$643$	18.2444	−	4.88858i	0.719490	−	0.192787i	0.599944	+	0.800042i	$0.295189\pi$
$644$	−41.0026	−	11.3500i	−1.61573	−	0.447254i
$645$	0.898640	−	3.90039i	0.0353839	−	0.153578i
$646$	105.598			4.15468
$647$	12.3072	−	45.9309i	0.483844	−	1.80573i	−0.101365	−	0.994849i	$-0.532321\pi$
$647$	12.3072	−	45.9309i	0.483844	−	1.80573i	0.585209	−	0.810882i	$-0.301012\pi$
$648$	41.9316	−	26.2363i	1.64723	−	1.03066i
$649$	−19.2253	−	11.0998i	−0.754661	−	0.435704i
$650$	−10.0254	−	3.54343i	−0.393228	−	0.138985i
$651$	−0.722250	+	11.1258i	−0.0283072	+	0.436053i
$652$	2.05761	+	7.67909i	0.0805820	+	0.300736i
$653$	15.0731	+	4.03882i	0.589855	+	0.158051i	0.541387	−	0.840774i	$-0.317899\pi$
$653$	15.0731	+	4.03882i	0.589855	+	0.158051i	0.0484680	+	0.998825i	$0.484566\pi$
$654$	32.2895	+	10.6422i	1.26262	+	0.416142i
$655$	1.88317	−	1.33173i	0.0735814	−	0.0520352i
$656$	5.80437	+	3.35115i	0.226623	+	0.130841i
$657$	18.5982	−	47.2554i	0.725586	−	1.84361i
$658$	−76.1979	−	0.628713i	−2.97050	−	0.0245098i
$659$	−21.7114	−	37.6053i	−0.845758	−	1.46490i	−0.884961	−	0.465664i	$-0.845815\pi$
$659$	−21.7114	−	37.6053i	−0.845758	−	1.46490i	0.0392037	−	0.999231i	$-0.487518\pi$
$660$	−30.6768	+	57.7569i	−1.19409	+	2.24818i
$661$	13.3152			0.517900			0.258950	−	0.965891i	$-0.416623\pi$
$661$	13.3152			0.517900			0.258950	+	0.965891i	$0.416623\pi$
$662$	23.0445	+	23.0445i	0.895649	+	0.895649i
$663$	0.498650	−	8.80453i	0.0193660	−	0.341940i
$664$	5.91739	−	3.41641i	0.229639	−	0.132582i
$665$	17.9058	−	38.0421i	0.694357	−	1.47521i
$666$	−5.70998	+	7.72138i	−0.221257	+	0.299197i
$667$	−0.376445	−	1.40491i	−0.0145760	−	0.0543984i
$668$	5.42188	+	20.2347i	0.209779	+	0.782906i
$669$	14.9758	−	45.4382i	0.578998	−	1.75674i
$670$	−18.3019	+	1.68723i	−0.707066	+	0.0651835i
$671$	−13.6334	−	7.87123i	−0.526311	−	0.303866i
$672$	7.43723	−	6.53049i	0.286897	−	0.251919i
$673$	−3.02428	+	11.2868i	−0.116578	+	0.435073i	−0.999400	−	0.0346334i	$-0.988974\pi$
$673$	−3.02428	+	11.2868i	−0.116578	+	0.435073i	0.882823	+	0.469707i	$0.155640\pi$
$674$	41.7079	−	72.2402i	1.60653	−	2.78259i
$675$	25.9782	−	0.367155i	0.999900	−	0.0141318i
$676$	−25.8072	−	44.6994i	−0.992586	−	1.71921i
$677$	−34.9119	−	34.9119i	−1.34177	−	1.34177i	−0.894296	−	0.447477i	$-0.852323\pi$
$677$	−34.9119	−	34.9119i	−1.34177	−	1.34177i	−0.447477	−	0.894296i	$-0.647677\pi$
$678$	−39.4355	+	60.1685i	−1.51451	+	2.31076i
$679$	6.35834	−	22.9699i	0.244011	−	0.881503i
$680$	42.3206	+	59.8443i	1.62292	+	2.29492i
$681$	−18.9825	+	3.95129i	−0.727410	+	0.151414i
$682$	−6.29764	−	23.5031i	−0.241149	−	0.899980i
$683$	−23.3183	−	6.24813i	−0.892251	−	0.239078i	−0.216566	−	0.976268i	$-0.569486\pi$
$683$	−23.3183	−	6.24813i	−0.892251	−	0.239078i	−0.675686	+	0.737190i	$0.736152\pi$
$684$	53.3214	−	72.1044i	2.03880	−	2.75698i
$685$	−17.6390	+	6.51337i	−0.673952	+	0.248863i
$686$	33.4218	−	31.8069i	1.27605	−	1.21439i
$687$	−8.75965	+	4.41685i	−0.334201	+	0.168513i
$688$	1.41208	−	5.26995i	0.0538350	−	0.200915i
$689$	4.59577			0.175085
$690$	−19.5609	−	31.2729i	−0.744671	−	1.19054i
$691$	−19.0952			−0.726415			−0.363208	−	0.931708i	$-0.618318\pi$
$691$	−19.0952			−0.726415			−0.363208	+	0.931708i	$0.618318\pi$
$692$	14.4870	+	14.4870i	0.550715	+	0.550715i
$693$	−19.1569	+	25.4630i	−0.727712	+	0.967259i
$694$			77.6129i			2.94615i
$695$	−27.6869	−	12.7538i	−1.05022	−	0.483779i
$696$	3.43953	+	1.13362i	0.130375	+	0.0429699i
$697$	−5.35425	+	5.35425i	−0.202807	+	0.202807i
$698$	1.15040	+	0.308248i	0.0435432	+	0.0116674i
$699$	−5.48480	−	26.3496i	−0.207454	−	0.996634i
$700$	54.7860	−	9.72093i	2.07072	−	0.367417i
$701$		−	13.3764i		−	0.505219i	−0.967568	−	0.252610i	$-0.918711\pi$
$701$		−	13.3764i		−	0.505219i	0.967568	−	0.252610i	$-0.0812888\pi$
$702$	−8.49908	−	7.06223i	−0.320777	−	0.266547i
$703$	−2.36358	+	8.82101i	−0.0891442	+	0.332691i
$704$	10.3935	−	18.0021i	0.391720	−	0.678479i
$705$	−32.7607	−	30.5224i	−1.23384	−	1.14954i
$706$	−0.647280	+	1.12112i	−0.0243607	+	0.0421940i
$707$	11.7327	−	19.9399i	0.441254	−	0.749916i
$708$	−2.27794	+	40.2210i	−0.0856101	+	1.51160i
$709$			8.49065i			0.318873i	0.987208	+	0.159437i	$0.0509677\pi$
$709$			8.49065i			0.318873i	−0.987208	+	0.159437i	$0.949032\pi$
$710$	−23.8406	+	28.6826i	−0.894720	+	1.07644i
$711$	3.27272	−	28.8002i	0.122737	−	1.08009i
$712$	−8.62574	−	32.1917i	−0.323263	−	1.20643i
$713$	8.98442	+	2.40737i	0.336469	+	0.0901566i
$714$	30.1532	+	61.0486i	1.12845	+	2.28468i
$715$	7.55283	+	1.29549i	0.282460	+	0.0484485i
$716$	−21.2269	+	12.2554i	−0.793288	+	0.458005i
$717$	−20.8272	+	31.7771i	−0.777807	+	1.18674i
$718$	19.8179	−	5.31018i	0.739596	−	0.198174i
$719$	−11.7155	+	20.2919i	−0.436915	+	0.756760i	−0.997450	−	0.0713715i	$-0.977262\pi$
$719$	−11.7155	+	20.2919i	−0.436915	+	0.756760i	0.560534	+	0.828131i	$0.310596\pi$
$720$	35.4061	+	0.751480i	1.31951	+	0.0280060i
$721$	11.7389	+	3.24946i	0.437178	+	0.121016i
$722$	20.3162	−	75.8212i	0.756092	−	2.82177i
$723$	14.4317	−	22.0192i	0.536722	−	0.818901i
$724$			7.10394i			0.264016i
$725$	1.23626	+	1.44572i	0.0459136	+	0.0536929i
$726$	6.91096	−	20.9686i	0.256490	−	0.778217i
$727$	32.8601	+	8.80483i	1.21871	+	0.326553i	0.810175	−	0.586188i	$-0.199372\pi$
$727$	32.8601	+	8.80483i	1.21871	+	0.326553i	0.408538	+	0.912741i	$0.366039\pi$
$728$	−10.6983	−	6.29490i	−0.396504	−	0.233305i
$729$	25.4593	+	8.99017i	0.942938	+	0.332969i
$730$	76.9904	−	54.4459i	2.84954	−	2.01514i
$731$	5.33805	+	3.08193i	0.197435	+	0.113989i
$732$	−1.61537	+	28.5221i	−0.0597057	+	1.05421i
$733$	−9.66483	+	36.0696i	−0.356978	+	1.33226i	0.520998	+	0.853558i	$0.325560\pi$
$733$	−9.66483	+	36.0696i	−0.356978	+	1.33226i	−0.877976	+	0.478704i	$0.841107\pi$
$734$	−2.29517	+	3.97534i	−0.0847161	+	0.146733i
$735$	27.1061	−	0.511063i	0.999822	−	0.0188509i
$736$	−4.12855	−	7.15085i	−0.152180	−	0.263584i
$737$	12.7945	−	3.42826i	0.471290	−	0.126282i
$738$	1.40523	+	9.38363i	0.0517274	+	0.345416i
$739$	−14.3473	+	8.28342i	−0.527774	+	0.304711i	−0.740110	−	0.672486i	$-0.765226\pi$
$739$	−14.3473	+	8.28342i	−0.527774	+	0.304711i	0.212335	+	0.977197i	$0.431893\pi$
$740$	−11.3370	+	4.18631i	−0.416758	+	0.153892i
$741$	−9.98012	−	3.28931i	−0.366629	−	0.120836i
$742$	−30.8756	+	17.4880i	−1.13348	+	0.642003i
$743$	−9.27093	−	34.5996i	−0.340117	−	1.26934i	−0.898214	−	0.439559i	$-0.855135\pi$
$743$	−9.27093	−	34.5996i	−0.340117	−	1.26934i	0.558096	−	0.829776i	$-0.311532\pi$
$744$	−17.2762	+	15.4242i	−0.633376	+	0.565478i
$745$	−24.4809	−	34.6177i	−0.896911	−	1.26830i
$746$	36.0780	−	20.8297i	1.32091	−	0.762628i
$747$	3.47064	+	1.36594i	0.126984	+	0.0499770i
$748$	−71.2137	−	71.2137i	−2.60383	−	2.60383i
$749$	8.45321	+	32.6221i	0.308874	+	1.19199i
$750$	40.7140	+	25.8779i	1.48667	+	0.944927i
$751$	25.6623	+	44.4484i	0.936431	+	1.62195i	0.772061	+	0.635548i	$0.219226\pi$
$751$	25.6623	+	44.4484i	0.936431	+	1.62195i	0.164370	+	0.986399i	$0.447441\pi$
$752$	−43.1571	−	43.1571i	−1.57378	−	1.57378i
$753$	0.259440	−	4.58086i	0.00945450	−	0.166936i
$754$		−	0.809068i		−	0.0294645i
$755$	11.7823	−	25.5778i	0.428800	−	0.930872i
$756$	56.9112	+	10.2372i	2.06984	+	0.372322i
$757$	−8.38764	+	8.38764i	−0.304854	+	0.304854i	−0.842909	−	0.538055i	$-0.819159\pi$
$757$	−8.38764	+	8.38764i	−0.304854	+	0.304854i	0.538055	+	0.842909i	$0.319159\pi$
$758$	−44.7805	+	44.7805i	−1.62650	+	1.62650i
$759$	17.7044	+	19.8302i	0.642629	+	0.719790i
$760$	81.9319	−	30.2541i	2.97198	−	1.09743i
$761$	29.1050	−	16.8038i	1.05506	−	0.609137i	0.130995	−	0.991383i	$-0.458183\pi$
$761$	29.1050	−	16.8038i	1.05506	−	0.609137i	0.924061	+	0.382246i	$0.124849\pi$
$762$	−32.1810	−	1.82259i	−1.16580	−	0.0660255i
$763$	10.2739	+	18.1390i	0.371941	+	0.656675i
$764$	−54.6777			−1.97817
$765$	−11.1730	+	38.4179i	−0.403961	+	1.38900i
$766$	2.48657	+	4.30686i	0.0898434	+	0.155613i
$767$	4.55965	−	1.22176i	0.164640	−	0.0441150i
$768$	−56.2706	−	3.18692i	−2.03049	−	0.114998i
$769$	26.0569	+	15.0439i	0.939635	+	0.542498i	0.889846	−	0.456261i	$-0.150812\pi$
$769$	26.0569	+	15.0439i	0.939635	+	0.542498i	0.0497890	+	0.998760i	$0.484145\pi$
$770$	−55.6714	+	20.0368i	−2.00626	+	0.722076i
$771$	15.2424	−	46.2471i	0.548942	−	1.66555i
$772$	−55.7012	+	55.7012i	−2.00473	+	2.00473i
$773$	−21.6573	−	5.80307i	−0.778961	−	0.208722i	−0.152634	−	0.988283i	$-0.548776\pi$
$773$	−21.6573	−	5.80307i	−0.778961	−	0.208722i	−0.626326	+	0.779561i	$0.715442\pi$
$774$	7.08218	−	3.08191i	0.254564	−	0.110777i
$775$	−11.9597	+	2.22400i	−0.429606	+	0.0798886i
$776$	42.8758	−	24.7543i	1.53915	−	0.888629i
$777$	−5.77456	+	1.15238i	−0.207161	+	0.0413413i
$778$	55.8072	−	14.9535i	2.00079	−	0.536109i
$779$	4.51139	+	7.81396i	0.161637	+	0.279964i
$780$	−4.07174	−	13.2968i	−0.145792	−	0.476102i
$781$	13.4396	−	23.2781i	0.480907	−	0.832955i
$782$	54.8688	−	14.7021i	1.96210	−	0.525744i
$783$	0.685046	+	1.85436i	0.0244815	+	0.0662694i
$784$	36.9495	+	0.609786i	1.31962	+	0.0217781i
$785$	−14.9326	+	17.9654i	−0.532967	+	0.641213i
$786$	4.22709	+	1.39319i	0.150775	+	0.0496935i
$787$	2.62147	−	2.62147i	0.0934453	−	0.0934453i	−0.658839	−	0.752284i	$-0.728952\pi$
$787$	2.62147	−	2.62147i	0.0934453	−	0.0934453i	0.752284	+	0.658839i	$0.228952\pi$
$788$	24.7207	−	24.7207i	0.880638	−	0.880638i
$789$	−0.215998	−	1.03768i	−0.00768972	−	0.0369423i
$790$	34.4031	−	41.3904i	1.22401	−	1.47260i
$791$	−42.7011	+	11.0649i	−1.51827	+	0.393423i
$792$	−65.4611	+	9.80304i	−2.32606	+	0.348336i
$793$	3.23341	−	0.866390i	0.114822	−	0.0307664i
$794$	−1.98139	+	3.43188i	−0.0703171	+	0.121793i
$795$	−20.3184	−	4.68131i	−0.720621	−	0.166029i
$796$	−18.8037	−	32.5690i	−0.666481	−	1.15438i
$797$	−10.7040	+	2.86814i	−0.379156	+	0.101595i	−0.443363	−	0.896342i	$-0.646215\pi$
$797$	−10.7040	+	2.86814i	−0.379156	+	0.101595i	0.0642072	+	0.997937i	$0.479548\pi$
$798$	79.5655	−	15.8782i	2.81659	−	0.562081i
$799$	59.7156	−	34.4768i	2.11259	−	1.21970i
$800$	8.90341	+	6.11130i	0.314783	+	0.216067i
$801$	10.8167	−	14.6270i	0.382190	−	0.516820i
$802$	−75.7271	−	20.2910i	−2.67402	−	0.716500i
$803$	−48.0535	+	48.0535i	−1.69577	+	1.69577i
$804$	−16.0085	−	17.9307i	−0.564577	−	0.632367i
$805$	4.00741	−	22.2598i	0.141243	−	0.784554i
$806$	4.48081	+	2.58700i	0.157830	+	0.0911231i
$807$	2.48625	+	4.93081i	0.0875201	+	0.173573i
$808$	46.4210	−	12.4385i	1.63309	−	0.437584i
$809$	3.01700	+	5.22560i	0.106072	+	0.183722i	0.914176	−	0.405318i	$-0.132839\pi$
$809$	3.01700	+	5.22560i	0.106072	+	0.183722i	−0.808104	+	0.589040i	$0.799506\pi$
$810$	30.3817	+	39.8802i	1.06751	+	1.40125i
$811$	−13.9624			−0.490286			−0.245143	−	0.969487i	$-0.578835\pi$
$811$	−13.9624			−0.490286			−0.245143	+	0.969487i	$0.578835\pi$
$812$	2.08654	+	3.68386i	0.0732232	+	0.129278i
$813$	15.7538	−	24.0363i	0.552509	−	0.842989i
$814$	11.1293	−	6.42551i	0.390082	−	0.225214i
$815$	−3.96472	+	1.46401i	−0.138878	+	0.0512820i
$816$	−17.0712	+	51.7959i	−0.597613	+	1.81322i
$817$	5.19355	−	5.19355i	0.181699	−	0.181699i
$818$	18.8542	−	18.8542i	0.659222	−	0.659222i
$819$	−0.948171	−	6.70901i	−0.0331318	−	0.234432i
$820$	−4.99576	+	10.8452i	−0.174459	+	0.378730i
$821$			37.6073i			1.31250i	0.754542	+	0.656252i	$0.227859\pi$
$821$			37.6073i			1.31250i	−0.754542	+	0.656252i	$0.772141\pi$
$822$	−30.3468	−	19.8898i	−1.05847	−	0.693737i
$823$	−16.7687	−	16.7687i	−0.584519	−	0.584519i	0.351623	−	0.936142i	$-0.385630\pi$
$823$	−16.7687	−	16.7687i	−0.584519	−	0.584519i	−0.936142	+	0.351623i	$0.885630\pi$
$824$	12.6508	+	21.9119i	0.440712	+	0.763336i
$825$	−32.0723	−	13.4209i	−1.11661	−	0.467256i
$826$	−25.9838	+	25.5586i	−0.904094	+	0.889296i
$827$	32.3416	+	32.3416i	1.12463	+	1.12463i	0.991037	+	0.133591i	$0.0426508\pi$
$827$	32.3416	+	32.3416i	1.12463	+	1.12463i	0.133591	+	0.991037i	$0.457349\pi$
$828$	17.6671	−	44.8895i	0.613974	−	1.56002i
$829$	13.9171	−	8.03505i	0.483362	−	0.279069i	−0.238455	−	0.971154i	$-0.576641\pi$
$829$	13.9171	−	8.03505i	0.483362	−	0.279069i	0.721816	+	0.692085i	$0.243308\pi$
$830$	3.99875	+	5.65451i	0.138799	+	0.196271i
$831$	4.32218	+	20.7642i	0.149935	+	0.720304i
$832$	1.14402	+	4.26953i	0.0396617	+	0.148019i
$833$	−11.4697	+	40.1436i	−0.397400	+	1.39089i
$834$	−11.9873	−	57.5884i	−0.415086	−	1.99412i
$835$	−10.4472	+	3.85773i	−0.361541	+	0.133502i
$836$	−103.929	+	60.0033i	−3.59445	+	2.07526i
$837$	−12.4603	−	2.13538i	−0.430692	−	0.0738095i
$838$	−50.2362	+	13.4608i	−1.73538	+	0.464994i
$839$	13.4337	+	23.2679i	0.463783	+	0.803297i	0.999146	−	0.0413260i	$-0.0131582\pi$
$839$	13.4337	+	23.2679i	0.463783	+	0.803297i	−0.535362	+	0.844623i	$0.679825\pi$
$840$	40.8862	+	38.7279i	1.41071	+	1.33624i
$841$	14.4276	−	24.9894i	0.497505	−	0.861703i
$842$	−7.67613	+	28.6477i	−0.264537	+	0.987265i
$843$	40.5000	−	20.4212i	1.39489	−	0.703343i
$844$	9.67120	+	5.58367i	0.332897	+	0.192198i
$845$	22.4034	−	15.8432i	0.770701	−	0.545023i
$846$	9.75570	−	85.8507i	0.335408	−	2.95161i
$847$	11.7793	−	6.67182i	0.404742	−	0.229246i
$848$	−27.4529	−	7.35600i	−0.942738	−	0.252606i
$849$	−15.2136	−	17.0404i	−0.522130	−	0.584823i
$850$	−56.4628	+	48.2822i	−1.93666	+	1.65607i
$851$			4.91250i			0.168398i
$852$	−48.6996	−	2.75813i	−1.66842	−	0.0944920i
$853$	−14.2841	+	53.3091i	−0.489079	+	1.82527i	0.0718664	+	0.997414i	$0.477104\pi$
$853$	−14.2841	+	53.3091i	−0.489079	+	1.82527i	−0.560945	+	0.827853i	$0.689562\pi$
$854$	−18.4261	+	18.1245i	−0.630527	+	0.620207i
$855$	40.7727	+	24.7083i	1.39440	+	0.845006i
$856$	−35.0013	+	60.6241i	−1.19632	+	2.07209i
$857$	−34.2490	+	9.17700i	−1.16992	+	0.313480i	−0.790923	−	0.611916i	$-0.790399\pi$
$857$	−34.2490	+	9.17700i	−1.16992	+	0.313480i	−0.379002	+	0.925396i	$0.623732\pi$
$858$	6.65774	+	13.2038i	0.227291	+	0.450772i
$859$	−43.9132	+	25.3533i	−1.49830	+	0.865043i	−0.999998	−	0.00196207i	$-0.999375\pi$
$859$	−43.9132	+	25.3533i	−1.49830	+	0.865043i	−0.498300	+	0.867005i	$0.666042\pi$
$860$	9.57997	+	1.64319i	0.326674	+	0.0560323i
$861$	−3.22922	+	4.83941i	−0.110052	+	0.164927i
$862$	−54.8757	−	14.7039i	−1.86907	−	0.500816i
$863$	7.87659	+	29.3958i	0.268122	+	1.00065i	0.960312	+	0.278930i	$0.0899796\pi$
$863$	7.87659	+	29.3958i	0.268122	+	1.00065i	−0.692189	+	0.721716i	$0.743354\pi$
$864$	6.48118	+	9.16202i	0.220494	+	0.311698i
$865$	−6.96211	+	8.37612i	−0.236719	+	0.284797i
$866$		−	9.40114i		−	0.319464i
$867$	−26.9050	−	17.6340i	−0.913742	−	0.598882i
$868$	−27.0738	−	0.223387i	−0.918944	−	0.00758226i
$869$	−19.3940	+	33.5914i	−0.657897	+	1.13951i
$870$	−0.824126	+	3.57698i	−0.0279405	+	0.121271i
$871$	−1.40829	+	2.43923i	−0.0477181	+	0.0826502i
$872$	−11.2078	+	41.8280i	−0.379543	+	1.41647i
$873$	25.1473	+	9.89719i	0.851108	+	0.334969i
$874$		−	67.6875i		−	2.28956i
$875$	7.81974	+	28.5281i	0.264356	+	0.964425i
$876$	117.125	+	38.6030i	3.95730	+	1.30427i
$877$	20.6340	+	5.52887i	0.696762	+	0.186697i	0.589780	−	0.807564i	$-0.299215\pi$
$877$	20.6340	+	5.52887i	0.696762	+	0.186697i	0.106982	+	0.994261i	$0.465881\pi$
$878$	−15.5059	+	15.5059i	−0.523297	+	0.523297i
$879$	−6.25465	−	30.0481i	−0.210964	−	1.01350i
$880$	−43.0434	−	19.8277i	−1.45099	−	0.668391i
$881$			9.76224i			0.328898i	0.986386	+	0.164449i	$0.0525846\pi$
$881$			9.76224i			0.328898i	−0.986386	+	0.164449i	$0.947415\pi$
$882$	31.8993	+	41.4648i	1.07411	+	1.39619i
$883$	33.9295	+	33.9295i	1.14182	+	1.14182i	0.988118	+	0.153700i	$0.0491189\pi$
$883$	33.9295	+	33.9295i	1.14182	+	1.14182i	0.153700	+	0.988118i	$0.450881\pi$
$884$	21.4152			0.720272
$885$	−21.4032	+	0.756999i	−0.719462	+	0.0254463i
$886$	−14.6385			−0.491791
$887$	−2.17746	+	8.12638i	−0.0731118	+	0.272857i	−0.992799	−	0.119796i	$-0.961776\pi$
$887$	−2.17746	+	8.12638i	−0.0731118	+	0.272857i	0.919687	+	0.392653i	$0.128443\pi$
$888$	−10.2303	−	6.70509i	−0.343305	−	0.225008i
$889$	−13.8594	−	14.0901i	−0.464831	−	0.472565i
$890$	31.6883	−	11.7012i	1.06219	−	0.392225i
$891$	−26.4392	−	24.6257i	−0.885746	−	0.824991i
$892$	112.222	+	30.0698i	3.75747	+	1.00681i
$893$	−21.2657	−	79.3647i	−0.711630	−	2.65584i
$894$	25.6107	−	77.7055i	0.856549	−	2.59886i
$895$	−7.52366	−	10.6390i	−0.251488	−	0.355622i
$896$	−31.9466	−	32.4782i	−1.06726	−	1.08502i
$897$	−5.64366	−	0.319632i	−0.188436	−	0.0106722i
$898$	13.1279	+	13.1279i	0.438085	+	0.438085i
$899$	−0.462802	−	0.801596i	−0.0154353	−	0.0267347i
$900$	4.45734	+	62.9342i	0.148578	+	2.09781i
$901$	16.0548	−	27.8077i	0.534863	−	0.926409i
$902$	3.28625	−	12.2644i	0.109420	−	0.408361i
$903$	4.48552	+	1.51951i	0.149269	+	0.0505661i
$904$	−79.3545	−	45.8153i	−2.63929	−	1.52380i
$905$	−3.76067	+	0.346691i	−0.125009	+	0.0115244i
$906$	53.2016	−	11.0742i	1.76750	−	0.367914i
$907$	−10.9871	−	41.0043i	−0.364819	−	1.36152i	−0.867665	−	0.497149i	$-0.834380\pi$
$907$	−10.9871	−	41.0043i	−0.364819	−	1.36152i	0.502846	−	0.864376i	$-0.332286\pi$
$908$	−12.1865	−	45.4808i	−0.404425	−	1.50933i
$909$	21.0924	+	15.5979i	0.699592	+	0.517350i
$910$	5.35799	−	11.3834i	0.177615	−	0.377356i
$911$	−14.0429	+	8.10766i	−0.465261	+	0.268619i	−0.714254	−	0.699887i	$-0.753234\pi$
$911$	−14.0429	+	8.10766i	−0.465261	+	0.268619i	0.248993	+	0.968505i	$0.419900\pi$
$912$	54.3515	+	35.6229i	1.79976	+	1.17959i
$913$	−3.52926	−	3.52926i	−0.116801	−	0.116801i
$914$	46.1360			1.52604
$915$	−15.1778	+	0.536815i	−0.501763	+	0.0177466i
$916$	−11.9116	−	20.6314i	−0.393569	−	0.681682i
$917$	1.34498	+	2.37461i	0.0444152	+	0.0784166i
$918$	−72.4220	+	26.7545i	−2.39028	+	0.883029i
$919$	7.16338	+	4.13578i	0.236298	+	0.136427i	0.613474	−	0.789715i	$-0.289771\pi$
$919$	7.16338	+	4.13578i	0.236298	+	0.136427i	−0.377176	+	0.926142i	$0.623105\pi$
$920$	38.3599	−	27.1273i	1.26469	−	0.894360i
$921$	−28.4001	+	25.3556i	−0.935815	+	0.835496i
$922$	−52.2360	−	13.9966i	−1.72030	−	0.460953i
$923$	1.47930	+	5.52084i	0.0486919	+	0.181721i
$924$	−64.3661	−	42.9500i	−2.11749	−	1.41295i
$925$	−2.76942	−	5.79727i	−0.0910578	−	0.190613i
$926$	37.7959	+	21.8215i	1.24205	+	0.717099i
$927$	−5.05801	+	12.8517i	−0.166127	+	0.422104i
$928$	−0.212668	+	0.793688i	−0.00698117	+	0.0260541i
$929$	45.5759			1.49530			0.747649	−	0.664095i	$-0.231183\pi$
$929$	45.5759			1.49530			0.747649	+	0.664095i	$0.231183\pi$
$930$	−17.1750	−	16.0016i	−0.563191	−	0.524714i
$931$	42.6675	+	25.5820i	1.39837	+	0.838415i
$932$	63.1320	−	16.9162i	2.06796	−	0.554108i
$933$	0.287246	−	5.07182i	0.00940400	−	0.166044i
$934$	−73.5339	−	42.4548i	−2.40610	−	1.38916i
$935$	34.2235	−	41.1744i	1.11923	−	1.34655i
$936$	8.36868	−	11.3166i	0.273539	−	0.369896i
$937$	14.2833	−	14.2833i	0.466615	−	0.466615i	−0.434201	−	0.900816i	$-0.642969\pi$
$937$	14.2833	−	14.2833i	0.466615	−	0.466615i	0.900816	+	0.434201i	$0.142969\pi$
$938$	0.179429	−	21.7462i	0.00585858	−	0.710040i
$939$	−26.3038	−	29.4621i	−0.858390	−	0.961459i
$940$	69.5037	−	83.6200i	2.26696	−	2.72738i
$941$			23.0022i			0.749852i	0.927055	+	0.374926i	$0.122332\pi$
$941$			23.0022i			0.749852i	−0.927055	+	0.374926i	$0.877668\pi$
$942$	−45.0073	−	2.54901i	−1.46642	−	0.0830513i
$943$	3.43205	+	3.43205i	0.111763	+	0.111763i
$944$	−29.1927			−0.950142
$945$	−2.64191	+	30.6271i	−0.0859413	+	0.996300i
$946$	−10.3358			−0.336044
$947$	14.7359	+	14.7359i	0.478853	+	0.478853i	0.904765	−	0.425912i	$-0.140047\pi$
$947$	14.7359	+	14.7359i	0.478853	+	0.478853i	−0.425912	+	0.904765i	$0.640047\pi$
$948$	70.2759	+	3.98012i	2.28246	+	0.129268i
$949$		−	14.4505i		−	0.469085i
$950$	38.1587	+	79.8784i	1.23803	+	2.59160i
$951$	4.84220	+	5.42361i	0.157019	+	0.175873i
$952$	−75.4617	+	42.7416i	−2.44573	+	1.38526i
$953$	21.8776	−	21.8776i	0.708686	−	0.708686i	−0.257573	−	0.966259i	$-0.582923\pi$
$953$	21.8776	−	21.8776i	0.708686	−	0.708686i	0.966259	+	0.257573i	$0.0829229\pi$
$954$	−16.0547	−	36.8935i	−0.519791	−	1.19447i
$955$	−2.66841	−	28.9451i	−0.0863479	−	0.936643i
$956$	−79.9040	−	46.1326i	−2.58428	−	1.49203i
$957$	0.149584	−	2.64116i	0.00483536	−	0.0853767i
$958$	−50.0422	+	13.4088i	−1.61679	+	0.433217i
$959$	−5.58075	−	21.5369i	−0.180212	−	0.695462i
$960$	−0.708833	−	20.0414i	−0.0228775	−	0.646834i
$961$	−25.0808			−0.809057
$962$	−0.707259	+	2.63953i	−0.0228029	+	0.0851018i
$963$	−37.7903	+	5.65924i	−1.21777	+	0.182366i
$964$	55.3675	+	31.9665i	1.78327	+	1.02957i
$965$	−32.2053	−	26.7686i	−1.03673	−	0.861712i
$966$	39.1318	−	19.3280i	1.25905	−	0.621869i
$967$	4.44378	+	16.5844i	0.142902	+	0.533318i	0.999840	+	0.0178982i	$0.00569749\pi$
$967$	4.44378	+	16.5844i	0.142902	+	0.533318i	−0.856938	+	0.515420i	$0.827636\pi$
$968$	27.1628	+	7.27825i	0.873045	+	0.233932i
$969$	−54.7670	+	48.8960i	−1.75937	+	1.57077i
$970$	28.9738	+	40.9710i	0.930293	+	1.31550i
$971$	17.9592	+	10.3687i	0.576338	+	0.332749i	0.759677	−	0.650301i	$-0.225357\pi$
$971$	17.9592	+	10.3687i	0.576338	+	0.332749i	−0.183339	+	0.983050i	$0.558691\pi$
$972$	−18.3009	+	62.9611i	−0.587003	+	2.01948i
$973$	18.2912	−	31.0861i	0.586388	−	0.996574i
$974$	1.44473	+	2.50235i	0.0462922	+	0.0801805i
$975$	6.84031	−	2.80441i	0.219065	−	0.0898129i
$976$	−20.7016			−0.662642
$977$	−12.6478	−	12.6478i	−0.404639	−	0.404639i	0.475225	−	0.879864i	$-0.342367\pi$
$977$	−12.6478	−	12.6478i	−0.404639	−	0.404639i	−0.879864	+	0.475225i	$0.842367\pi$
$978$	−6.82106	−	4.47064i	−0.218113	−	0.142955i
$979$	−21.0829	+	12.1722i	−0.673811	+	0.389025i
$980$	4.96113	+	65.6490i	0.158477	+	2.09708i
$981$	−21.6744	+	9.43192i	−0.692010	+	0.301138i
$982$	5.91965	+	22.0924i	0.188904	+	0.704998i
$983$	−9.93626	−	37.0826i	−0.316917	−	1.18275i	−0.922191	−	0.386734i	$-0.873603\pi$
$983$	−9.93626	−	37.0826i	−0.316917	−	1.18275i	0.605274	−	0.796017i	$-0.293064\pi$
$984$	−11.8316	+	2.46281i	−0.377179	+	0.0785116i
$985$	14.2930	+	11.8801i	0.455413	+	0.378533i
$986$	−4.89544	−	2.82638i	−0.155902	−	0.0900103i
$987$	39.8103	−	34.9567i	1.26718	−	1.11268i
$988$	6.60459	−	24.6487i	0.210120	−	0.784178i
$989$	1.97550	−	3.42167i	0.0628172	−	0.108803i
$990$	−15.9850	−	65.1574i	−0.508037	−	2.07084i
$991$	−1.87792	−	3.25265i	−0.0596540	−	0.103324i	0.834656	−	0.550771i	$-0.185666\pi$
$991$	−1.87792	−	3.25265i	−0.0596540	−	0.103324i	−0.894310	+	0.447448i	$0.852333\pi$
$992$	−3.71563	−	3.71563i	−0.117971	−	0.117971i
$993$	−22.6223	−	1.28123i	−0.717897	−	0.0406585i
$994$	−30.9464	−	31.4613i	−0.981559	−	0.997891i
$995$	16.3236	−	11.5437i	0.517494	−	0.365961i
$996$	−2.83517	+	8.60220i	−0.0898358	+	0.272571i
$997$	−0.0688813	−	0.257069i	−0.00218149	−	0.00814144i	0.964827	−	0.262887i	$-0.0846748\pi$
$997$	−0.0688813	−	0.257069i	−0.00218149	−	0.00814144i	−0.967008	+	0.254746i	$0.918008\pi$
$998$	−86.3522	−	23.1380i	−2.73343	−	0.732420i
$999$	−0.613895	−	6.64857i	−0.0194228	−	0.210351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bv.a.23.4	✓	176
3.2	odd	2		945.2.by.a.233.41		176
5.2	odd	4	inner	315.2.bv.a.212.41	yes	176
7.4	even	3		315.2.bx.a.158.41	yes	176
9.2	odd	6		315.2.bx.a.128.41	yes	176
9.7	even	3		945.2.ca.a.548.4		176
15.2	even	4		945.2.by.a.422.4		176
21.11	odd	6		945.2.ca.a.368.4		176
35.32	odd	12		315.2.bx.a.32.41	yes	176
45.2	even	12		315.2.bx.a.2.41	yes	176
45.7	odd	12		945.2.ca.a.737.4		176
63.11	odd	6	inner	315.2.bv.a.263.41	yes	176
63.25	even	3		945.2.by.a.683.4		176
105.32	even	12		945.2.ca.a.557.4		176
315.137	even	12	inner	315.2.bv.a.137.4	yes	176
315.277	odd	12		945.2.by.a.872.41		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bv.a.23.4	✓	176	1.1	even	1	trivial
315.2.bv.a.137.4	yes	176	315.137	even	12	inner
315.2.bv.a.212.41	yes	176	5.2	odd	4	inner
315.2.bv.a.263.41	yes	176	63.11	odd	6	inner
315.2.bx.a.2.41	yes	176	45.2	even	12
315.2.bx.a.32.41	yes	176	35.32	odd	12
315.2.bx.a.128.41	yes	176	9.2	odd	6
315.2.bx.a.158.41	yes	176	7.4	even	3
945.2.by.a.233.41		176	3.2	odd	2
945.2.by.a.422.4		176	15.2	even	4
945.2.by.a.683.4		176	63.25	even	3
945.2.by.a.872.41		176	315.277	odd	12
945.2.ca.a.368.4		176	21.11	odd	6
945.2.ca.a.548.4		176	9.7	even	3
945.2.ca.a.557.4		176	105.32	even	12
945.2.ca.a.737.4		176	45.7	odd	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76155 - 1.76155i) q^{2} +(1.72928 + 0.0979388i) q^{3} +4.20612i q^{4} +(-2.22663 + 0.205270i) q^{5} +(-2.87369 - 3.21874i) q^{6} +(0.0218295 - 2.64566i) q^{7} +(3.88619 - 3.88619i) q^{8} +(2.98082 + 0.338727i) q^{9} +O(q^{10})\)	\(q+(-1.76155 - 1.76155i) q^{2} +(1.72928 + 0.0979388i) q^{3} +4.20612i q^{4} +(-2.22663 + 0.205270i) q^{5} +(-2.87369 - 3.21874i) q^{6} +(0.0218295 - 2.64566i) q^{7} +(3.88619 - 3.88619i) q^{8} +(2.98082 + 0.338727i) q^{9} +(4.28391 + 3.56072i) q^{10} +(-3.47671 - 2.00728i) q^{11} +(-0.411942 + 7.27356i) q^{12} +(0.824568 - 0.220942i) q^{13} +(-4.69892 + 4.62201i) q^{14} +(-3.87056 + 0.136896i) q^{15} -5.27921 q^{16} +(1.54367 - 5.76106i) q^{17} +(-4.65417 - 5.84754i) q^{18} +(-6.15483 - 3.55349i) q^{19} +(-0.863390 - 9.36546i) q^{20} +(0.296862 - 4.57295i) q^{21} +(2.58848 + 9.66033i) q^{22} +(-3.69281 - 0.989485i) q^{23} +(7.10092 - 6.33971i) q^{24} +(4.91573 - 0.914118i) q^{25} +(-1.84172 - 1.06332i) q^{26} +(5.12149 + 0.877691i) q^{27} +(11.1280 + 0.0918175i) q^{28} +(0.190223 + 0.329475i) q^{29} +(7.05934 + 6.57704i) q^{30} -2.43295 q^{31} +(1.52721 + 1.52721i) q^{32} +(-5.81562 - 3.81166i) q^{33} +(-12.8677 + 7.42914i) q^{34} +(0.494468 + 5.89538i) q^{35} +(-1.42473 + 12.5377i) q^{36} +(-0.332572 - 1.24118i) q^{37} +(4.58238 + 17.1017i) q^{38} +(1.44755 - 0.301314i) q^{39} +(-7.85538 + 9.45082i) q^{40} +(-1.09948 - 0.634783i) q^{41} +(-8.57842 + 7.53255i) q^{42} +(-0.267479 + 0.998246i) q^{43} +(8.44287 - 14.6235i) q^{44} +(-6.70669 - 0.142347i) q^{45} +(4.76204 + 8.24810i) q^{46} +(8.17492 + 8.17492i) q^{47} +(-9.12923 - 0.517039i) q^{48} +(-6.99905 - 0.115507i) q^{49} +(-10.2696 - 7.04904i) q^{50} +(3.23367 - 9.81130i) q^{51} +(0.929310 + 3.46823i) q^{52} +(5.20020 + 1.39339i) q^{53} +(-7.47567 - 10.5679i) q^{54} +(8.15338 + 3.75580i) q^{55} +(-10.1967 - 10.3664i) q^{56} +(-10.2954 - 6.74777i) q^{57} +(0.245300 - 0.915474i) q^{58} +5.52975 q^{59} +(-0.575800 - 16.2801i) q^{60} +3.92134 q^{61} +(4.28576 + 4.28576i) q^{62} +(0.961227 - 7.87884i) q^{63} +5.17790i q^{64} +(-1.79065 + 0.661215i) q^{65} +(3.53008 + 16.9589i) q^{66} +(-2.33305 + 2.33305i) q^{67} +(24.2317 + 6.49287i) q^{68} +(-6.28899 - 2.07277i) q^{69} +(9.51398 - 11.2560i) q^{70} +6.69543i q^{71} +(12.9004 - 10.2677i) q^{72} +(4.38125 - 16.3510i) q^{73} +(-1.60055 + 2.77224i) q^{74} +(8.59020 - 1.09933i) q^{75} +(14.9464 - 25.8879i) q^{76} +(-5.38648 + 9.15439i) q^{77} +(-3.08071 - 2.01915i) q^{78} -9.66184i q^{79} +(11.7548 - 1.08366i) q^{80} +(8.77053 + 2.01937i) q^{81} +(0.818581 + 3.05499i) q^{82} +(1.20089 + 0.321778i) q^{83} +(19.2344 + 1.24864i) q^{84} +(-2.25461 + 13.1446i) q^{85} +(2.22964 - 1.28728i) q^{86} +(0.296680 + 0.588385i) q^{87} +(-21.3119 + 5.71050i) q^{88} +(3.03201 - 5.25159i) q^{89} +(11.5634 + 12.0649i) q^{90} +(-0.566539 - 2.18635i) q^{91} +(4.16189 - 15.5324i) q^{92} +(-4.20725 - 0.238280i) q^{93} -28.8011i q^{94} +(14.4339 + 6.64889i) q^{95} +(2.49140 + 2.79055i) q^{96} +(8.70133 + 2.33151i) q^{97} +(12.1257 + 12.5326i) q^{98} +(-9.68352 - 7.16099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

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