LMFDB - Embedded newform 315.2.cc.a.92.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(92,315)]

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([2, 3, 0]))

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

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

chi := DirichletCharacter("315.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cc (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:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			92.10
Character	$\chi$	$=$	315.92
Dual form			315.2.cc.a.113.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.352695 - 1.31628i) q^{2} +(-0.672895 - 1.59600i) q^{3} +(0.123861 - 0.0715111i) q^{4} +(-0.441766 - 2.19200i) q^{5} +(-1.86345 + 1.44862i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-2.06498 - 2.06498i) q^{8} +(-2.09442 + 2.14788i) q^{9} +O(q^{10})$	\(q+(-0.352695 - 1.31628i) q^{2} +(-0.672895 - 1.59600i) q^{3} +(0.123861 - 0.0715111i) q^{4} +(-0.441766 - 2.19200i) q^{5} +(-1.86345 + 1.44862i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-2.06498 - 2.06498i) q^{8} +(-2.09442 + 2.14788i) q^{9} +(-2.72946 + 1.35459i) q^{10} +(0.158548 + 0.0915380i) q^{11} +(-0.197477 - 0.149562i) q^{12} +(3.39699 + 0.910219i) q^{13} +(0.681355 + 1.18014i) q^{14} +(-3.20116 + 2.18004i) q^{15} +(-1.84675 + 3.19866i) q^{16} +(1.38265 - 1.38265i) q^{17} +(3.56590 + 1.99929i) q^{18} -1.45904i q^{19} +(-0.211470 - 0.239911i) q^{20} +(1.06304 + 1.36746i) q^{21} +(0.0645700 - 0.240979i) q^{22} +(1.47404 - 5.50117i) q^{23} +(-1.90619 + 4.68521i) q^{24} +(-4.60969 + 1.93670i) q^{25} -4.79240i q^{26} +(4.83734 + 1.89740i) q^{27} +(-0.101132 + 0.101132i) q^{28} +(-4.54468 + 7.87162i) q^{29} +(3.99857 + 3.44472i) q^{30} +(1.88724 + 3.26879i) q^{31} +(-0.779952 - 0.208988i) q^{32} +(0.0394080 - 0.314639i) q^{33} +(-2.30761 - 1.33230i) q^{34} +(0.994044 + 2.00297i) q^{35} +(-0.105820 + 0.415813i) q^{36} +(-3.48013 - 3.48013i) q^{37} +(-1.92050 + 0.514598i) q^{38} +(-0.833107 - 6.03407i) q^{39} +(-3.61418 + 5.43865i) q^{40} +(6.39810 - 3.69394i) q^{41} +(1.42502 - 1.88155i) q^{42} +(0.0844810 + 0.315287i) q^{43} +0.0261839 q^{44} +(5.63339 + 3.64210i) q^{45} -7.76095 q^{46} +(-3.12468 - 11.6614i) q^{47} +(6.34773 + 0.795044i) q^{48} +(0.866025 - 0.500000i) q^{49} +(4.17505 + 5.38456i) q^{50} +(-3.13709 - 1.27633i) q^{51} +(0.485845 - 0.130182i) q^{52} +(2.57090 + 2.57090i) q^{53} +(0.791393 - 7.03648i) q^{54} +(0.130609 - 0.387976i) q^{55} +(2.52907 + 1.46016i) q^{56} +(-2.32863 + 0.981784i) q^{57} +(11.9641 + 3.20578i) q^{58} +(-0.942273 - 1.63206i) q^{59} +(-0.240601 + 0.498941i) q^{60} +(5.43752 - 9.41806i) q^{61} +(3.63701 - 3.63701i) q^{62} +(1.46715 - 2.61677i) q^{63} +8.48734i q^{64} +(0.494523 - 7.84828i) q^{65} +(-0.428050 + 0.0590997i) q^{66} +(3.33370 - 12.4415i) q^{67} +(0.0723815 - 0.270132i) q^{68} +(-9.77174 + 1.34916i) q^{69} +(2.28586 - 2.01487i) q^{70} -7.67717i q^{71} +(8.76026 - 0.110387i) q^{72} +(-6.71246 + 6.71246i) q^{73} +(-3.35339 + 5.80824i) q^{74} +(6.19281 + 6.05386i) q^{75} +(-0.104338 - 0.180718i) q^{76} +(-0.176838 - 0.0473836i) q^{77} +(-7.64867 + 3.22479i) q^{78} +(-0.0598459 - 0.0345520i) q^{79} +(7.82729 + 2.63500i) q^{80} +(-0.226780 - 8.99714i) q^{81} +(-7.11883 - 7.11883i) q^{82} +(-10.8877 + 2.91735i) q^{83} +(0.229458 + 0.0933553i) q^{84} +(-3.64158 - 2.41996i) q^{85} +(0.385209 - 0.222401i) q^{86} +(15.6212 + 1.95653i) q^{87} +(-0.138375 - 0.516423i) q^{88} +17.3034 q^{89} +(2.80715 - 8.69965i) q^{90} -3.51682 q^{91} +(-0.210820 - 0.786791i) q^{92} +(3.94707 - 5.21158i) q^{93} +(-14.2476 + 8.22587i) q^{94} +(-3.19822 + 0.644556i) q^{95} +(0.191282 + 1.38543i) q^{96} +(9.28455 - 2.48779i) q^{97} +(-0.963581 - 0.963581i) q^{98} +(-0.528680 + 0.148824i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3}+O(q^{10}) $ 144 * q + 4 * q^3	$ 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) $ 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.352695	−	1.31628i	−0.249393	−	0.930748i	−0.971124	−	0.238574i	$-0.923320\pi$
$2$	−0.352695	−	1.31628i	−0.249393	−	0.930748i	0.721731	−	0.692174i	$-0.243347\pi$
$3$	−0.672895	−	1.59600i	−0.388496	−	0.921450i
$3$	−0.672895	−	1.59600i	−0.388496	−	0.921450i
$4$	0.123861	−	0.0715111i	0.0619305	−	0.0357556i
$5$	−0.441766	−	2.19200i	−0.197564	−	0.980290i
$5$	−0.441766	−	2.19200i	−0.197564	−	0.980290i
$6$	−1.86345	+	1.44862i	−0.760750	+	0.591396i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	−2.06498	−	2.06498i	−0.730079	−	0.730079i
$9$	−2.09442	+	2.14788i	−0.698141	+	0.715960i
$10$	−2.72946	+	1.35459i	−0.863132	+	0.428360i
$11$	0.158548	+	0.0915380i	0.0478042	+	0.0275997i	0.523712	−	0.851896i	$-0.324547\pi$
$11$	0.158548	+	0.0915380i	0.0478042	+	0.0275997i	−0.475907	+	0.879495i	$0.657880\pi$
$12$	−0.197477	−	0.149562i	−0.0570067	−	0.0431749i
$13$	3.39699	+	0.910219i	0.942154	+	0.252449i	0.697030	−	0.717042i	$-0.254505\pi$
$13$	3.39699	+	0.910219i	0.942154	+	0.252449i	0.245124	+	0.969492i	$0.421171\pi$
$14$	0.681355	+	1.18014i	0.182100	+	0.315406i
$15$	−3.20116	+	2.18004i	−0.826536	+	0.562884i
$16$	−1.84675	+	3.19866i	−0.461688	+	0.799666i
$17$	1.38265	−	1.38265i	0.335342	−	0.335342i	−0.519269	−	0.854611i	$-0.673796\pi$
$17$	1.38265	−	1.38265i	0.335342	−	0.335342i	0.854611	+	0.519269i	$0.173796\pi$
$18$	3.56590	+	1.99929i	0.840490	+	0.471238i
$19$		−	1.45904i		−	0.334727i	−0.985895	−	0.167364i	$-0.946475\pi$
$19$		−	1.45904i		−	0.334727i	0.985895	−	0.167364i	$-0.0535254\pi$
$20$	−0.211470	−	0.239911i	−0.0472861	−	0.0536458i
$21$	1.06304	+	1.36746i	0.231975	+	0.298404i
$22$	0.0645700	−	0.240979i	0.0137664	−	0.0513768i
$23$	1.47404	−	5.50117i	0.307358	−	1.14707i	−0.623539	−	0.781792i	$-0.714306\pi$
$23$	1.47404	−	5.50117i	0.307358	−	1.14707i	0.930897	−	0.365282i	$-0.119028\pi$
$24$	−1.90619	+	4.68521i	−0.389099	+	0.956365i
$25$	−4.60969	+	1.93670i	−0.921937	+	0.387340i
$26$		−	4.79240i		−	0.939867i
$27$	4.83734	+	1.89740i	0.930947	+	0.365154i
$28$	−0.101132	+	0.101132i	−0.0191122	+	0.0191122i
$29$	−4.54468	+	7.87162i	−0.843926	+	1.46172i	0.0426239	+	0.999091i	$0.486428\pi$
$29$	−4.54468	+	7.87162i	−0.843926	+	1.46172i	−0.886550	+	0.462632i	$0.846905\pi$
$30$	3.99857	+	3.44472i	0.730036	+	0.628917i
$31$	1.88724	+	3.26879i	0.338958	+	0.587092i	0.984237	−	0.176855i	$-0.0565923\pi$
$31$	1.88724	+	3.26879i	0.338958	+	0.587092i	−0.645279	+	0.763947i	$0.723259\pi$
$32$	−0.779952	−	0.208988i	−0.137877	−	0.0369441i
$33$	0.0394080	−	0.314639i	0.00686005	−	0.0547716i
$34$	−2.30761	−	1.33230i	−0.395751	−	0.228487i
$35$	0.994044	+	2.00297i	0.168024	+	0.338563i
$36$	−0.105820	+	0.415813i	−0.0176366	+	0.0693022i
$37$	−3.48013	−	3.48013i	−0.572130	−	0.572130i	0.360593	−	0.932723i	$-0.382574\pi$
$37$	−3.48013	−	3.48013i	−0.572130	−	0.572130i	−0.932723	+	0.360593i	$0.882574\pi$
$38$	−1.92050	+	0.514598i	−0.311547	+	0.0834788i
$39$	−0.833107	−	6.03407i	−0.133404	−	0.966224i
$40$	−3.61418	+	5.43865i	−0.571452	+	0.859927i
$41$	6.39810	−	3.69394i	0.999215	−	0.576897i	0.0911992	−	0.995833i	$-0.470930\pi$
$41$	6.39810	−	3.69394i	0.999215	−	0.576897i	0.908016	+	0.418936i	$0.137597\pi$
$42$	1.42502	−	1.88155i	0.219886	−	0.290330i
$43$	0.0844810	+	0.315287i	0.0128832	+	0.0480809i	0.972068	−	0.234698i	$-0.0754103\pi$
$43$	0.0844810	+	0.315287i	0.0128832	+	0.0480809i	−0.959185	+	0.282779i	$0.908744\pi$
$44$	0.0261839			0.00394738
$45$	5.63339	+	3.64210i	0.839776	+	0.542933i
$46$	−7.76095			−1.14429
$47$	−3.12468	−	11.6614i	−0.455781	−	1.70100i	−0.685782	−	0.727807i	$-0.740540\pi$
$47$	−3.12468	−	11.6614i	−0.455781	−	1.70100i	0.230002	−	0.973190i	$-0.426127\pi$
$48$	6.34773	+	0.795044i	0.916217	+	0.114755i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	4.17505	+	5.38456i	0.590441	+	0.761491i
$51$	−3.13709	−	1.27633i	−0.439281	−	0.178722i
$52$	0.485845	−	0.130182i	0.0673745	−	0.0180529i
$53$	2.57090	+	2.57090i	0.353141	+	0.353141i	0.861277	−	0.508136i	$-0.169665\pi$
$53$	2.57090	+	2.57090i	0.353141	+	0.353141i	−0.508136	+	0.861277i	$0.669665\pi$
$54$	0.791393	−	7.03648i	0.107695	−	0.957544i
$55$	0.130609	−	0.387976i	0.0176114	−	0.0523147i
$56$	2.52907	+	1.46016i	0.337961	+	0.195122i
$57$	−2.32863	+	0.981784i	−0.308435	+	0.130040i
$58$	11.9641	+	3.20578i	1.57097	+	0.420939i
$59$	−0.942273	−	1.63206i	−0.122674	−	0.212477i	0.798148	−	0.602462i	$-0.205813\pi$
$59$	−0.942273	−	1.63206i	−0.122674	−	0.212477i	−0.920821	+	0.389985i	$0.872480\pi$
$60$	−0.240601	+	0.498941i	−0.0310615	+	0.0644129i
$61$	5.43752	−	9.41806i	0.696203	−	1.20586i	−0.273571	−	0.961852i	$-0.588205\pi$
$61$	5.43752	−	9.41806i	0.696203	−	1.20586i	0.969774	−	0.244007i	$-0.0784619\pi$
$62$	3.63701	−	3.63701i	0.461901	−	0.461901i
$63$	1.46715	−	2.61677i	0.184843	−	0.329682i
$64$			8.48734i			1.06092i
$65$	0.494523	−	7.84828i	0.0613380	−	0.973459i
$66$	−0.428050	+	0.0590997i	−0.0526894	+	0.00727467i
$67$	3.33370	−	12.4415i	0.407277	−	1.51998i	−0.392541	−	0.919734i	$-0.628404\pi$
$67$	3.33370	−	12.4415i	0.407277	−	1.51998i	0.799818	−	0.600243i	$-0.204929\pi$
$68$	0.0723815	−	0.270132i	0.00877755	−	0.0327583i
$69$	−9.77174	+	1.34916i	−1.17638	+	0.162419i
$70$	2.28586	−	2.01487i	0.273213	−	0.240823i
$71$		−	7.67717i		−	0.911112i	−0.890207	−	0.455556i	$-0.849440\pi$
$71$		−	7.67717i		−	0.911112i	0.890207	−	0.455556i	$-0.150560\pi$
$72$	8.76026	−	0.110387i	1.03241	−	0.0130092i
$73$	−6.71246	+	6.71246i	−0.785634	+	0.785634i	−0.980775	−	0.195141i	$-0.937484\pi$
$73$	−6.71246	+	6.71246i	−0.785634	+	0.785634i	0.195141	+	0.980775i	$0.437484\pi$
$74$	−3.35339	+	5.80824i	−0.389824	+	0.675194i
$75$	6.19281	+	6.05386i	0.715084	+	0.699039i
$76$	−0.104338	−	0.180718i	−0.0119684	−	0.0207298i
$77$	−0.176838	−	0.0473836i	−0.0201525	−	0.00539986i
$78$	−7.64867	+	3.22479i	−0.866041	+	0.365135i
$79$	−0.0598459	−	0.0345520i	−0.00673319	−	0.00388741i	0.496630	−	0.867963i	$-0.334571\pi$
$79$	−0.0598459	−	0.0345520i	−0.00673319	−	0.00388741i	−0.503363	+	0.864075i	$0.667904\pi$
$80$	7.82729	+	2.63500i	0.875118	+	0.294602i
$81$	−0.226780	−	8.99714i	−0.0251978	−	0.999682i
$82$	−7.11883	−	7.11883i	−0.786143	−	0.786143i
$83$	−10.8877	+	2.91735i	−1.19508	+	0.320221i	−0.800892	−	0.598809i	$-0.795641\pi$
$83$	−10.8877	+	2.91735i	−1.19508	+	0.320221i	−0.394188	+	0.919030i	$0.628974\pi$
$84$	0.229458	+	0.0933553i	0.0250359	+	0.0101859i
$85$	−3.64158	−	2.41996i	−0.394984	−	0.262481i
$86$	0.385209	−	0.222401i	0.0415382	−	0.0239821i
$87$	15.6212	+	1.95653i	1.67477	+	0.209762i
$88$	−0.138375	−	0.516423i	−0.0147508	−	0.0550508i
$89$	17.3034			1.83416			0.917079	−	0.398706i	$-0.130541\pi$
$89$	17.3034			1.83416			0.917079	+	0.398706i	$0.130541\pi$
$90$	2.80715	−	8.69965i	0.295899	−	0.917024i
$91$	−3.51682			−0.368663
$92$	−0.210820	−	0.786791i	−0.0219795	−	0.0820286i
$93$	3.94707	−	5.21158i	0.409292	−	0.540416i
$94$	−14.2476	+	8.22587i	−1.46953	+	0.848434i
$95$	−3.19822	+	0.644556i	−0.328130	+	0.0661301i
$96$	0.191282	+	1.38543i	0.0195227	+	0.141400i
$97$	9.28455	−	2.48779i	0.942703	−	0.252596i	0.245440	−	0.969412i	$-0.421068\pi$
$97$	9.28455	−	2.48779i	0.942703	−	0.252596i	0.697263	+	0.716815i	$0.254401\pi$
$98$	−0.963581	−	0.963581i	−0.0973364	−	0.0973364i
$99$	−0.528680	+	0.148824i	−0.0531344	+	0.0149574i
$100$	−0.432464	+	0.569525i	−0.0432464	+	0.0569525i
$101$	3.74683	+	2.16323i	0.372823	+	0.215250i	0.674691	−	0.738100i	$-0.264277\pi$
$101$	3.74683	+	2.16323i	0.372823	+	0.215250i	−0.301868	+	0.953350i	$0.597610\pi$
$102$	−0.573567	+	4.57943i	−0.0567916	+	0.453432i
$103$	13.2061	+	3.53856i	1.30123	+	0.348665i	0.841917	−	0.539607i	$-0.181427\pi$
$103$	13.2061	+	3.53856i	1.30123	+	0.348665i	0.459318	+	0.888272i	$0.348094\pi$
$104$	−5.13511	−	8.89427i	−0.503539	−	0.872155i
$105$	2.52785	−	2.93428i	0.246692	−	0.286356i
$106$	2.47727	−	4.29077i	0.240614	−	0.416756i
$107$	−7.08139	+	7.08139i	−0.684584	+	0.684584i	−0.961030	−	0.276446i	$-0.910843\pi$
$107$	−7.08139	+	7.08139i	−0.684584	+	0.684584i	0.276446	+	0.961030i	$0.410843\pi$
$108$	0.734843	−	0.110910i	0.0707103	−	0.0106724i
$109$			2.05188i			0.196535i	0.995160	+	0.0982673i	$0.0313300\pi$
$109$			2.05188i			0.196535i	−0.995160	+	0.0982673i	$0.968670\pi$
$110$	−0.556749	−	0.0350809i	−0.0530839	−	0.00334484i
$111$	−3.21252	+	7.89605i	−0.304919	+	0.749460i
$112$	0.955948	−	3.56765i	0.0903286	−	0.337111i
$113$	−1.71126	+	6.38650i	−0.160982	+	0.600791i	0.837537	+	0.546380i	$0.183995\pi$
$113$	−1.71126	+	6.38650i	−0.160982	+	0.600791i	−0.998519	+	0.0544108i	$0.982672\pi$
$114$	2.11360	+	2.71885i	0.197956	+	0.254644i
$115$	−12.7097	−	0.800844i	−1.18519	−	0.0746791i
$116$			1.29998i			0.120700i
$117$	−9.06977	+	5.38993i	−0.838500	+	0.498299i
$118$	−1.81591	+	1.81591i	−0.167168	+	0.167168i
$119$	−0.977683	+	1.69340i	−0.0896240	+	0.155233i
$120$	11.1121	+	2.10858i	1.01439	+	0.192486i
$121$	−5.48324	−	9.49725i	−0.498477	−	0.863387i
$122$	−14.3146	−	3.83557i	−1.29598	−	0.347256i
$123$	−10.2008	−	7.72572i	−0.919773	−	0.696605i
$124$	0.467510	+	0.269917i	0.0419836	+	0.0242392i
$125$	6.28164	+	9.24884i	0.561847	+	0.827241i
$126$	−3.96185	−	1.00825i	−0.352949	−	0.0898218i
$127$	3.63437	+	3.63437i	0.322498	+	0.322498i	0.849725	−	0.527227i	$-0.176768\pi$
$127$	3.63437	+	3.63437i	0.322498	+	0.322498i	−0.527227	+	0.849725i	$0.676768\pi$
$128$	9.61178	−	2.57547i	0.849570	−	0.227642i
$129$	0.446351	−	0.346987i	0.0392991	−	0.0305505i
$130$	−10.5049	+	2.11712i	−0.921343	+	0.185684i
$131$	−3.48450	+	2.01178i	−0.304442	+	0.175770i	−0.644437	−	0.764658i	$-0.722908\pi$
$131$	−3.48450	+	2.01178i	−0.304442	+	0.175770i	0.339994	+	0.940427i	$0.389575\pi$
$132$	−0.0176191	−	0.0417895i	−0.00153354	−	0.00363731i
$133$	0.377628	+	1.40933i	0.0327445	+	0.122204i
$134$	−17.5523			−1.51629
$135$	2.02211	−	11.4416i	0.174036	−	0.984739i
$136$	−5.71029			−0.489653
$137$	5.58973	+	20.8612i	0.477563	+	1.78229i	0.611440	+	0.791291i	$0.290591\pi$
$137$	5.58973	+	20.8612i	0.477563	+	1.78229i	−0.133877	+	0.990998i	$0.542743\pi$
$138$	5.22231	+	12.3865i	0.444552	+	1.05441i
$139$	11.6517	−	6.72709i	0.988280	−	0.570584i	0.0835205	−	0.996506i	$-0.473384\pi$
$139$	11.6517	−	6.72709i	0.988280	−	0.570584i	0.904760	+	0.425922i	$0.140050\pi$
$140$	0.266358	+	0.177004i	0.0225113	+	0.0149596i
$141$	−16.5091	+	12.8339i	−1.39031	+	1.08081i
$142$	−10.1053	+	2.70770i	−0.848016	+	0.227225i
$143$	0.455267	+	0.455267i	0.0380713	+	0.0380713i
$144$	−3.00247	−	10.6660i	−0.250206	−	0.888830i
$145$	19.2622	+	6.48450i	1.59964	+	0.538509i
$146$	11.2029	+	6.46800i	0.927159	+	0.535296i
$147$	−1.38074	−	1.04573i	−0.113882	−	0.0862502i
$148$	−0.679921	−	0.182184i	−0.0558891	−	0.0149754i
$149$	6.08064	+	10.5320i	0.498146	+	0.862814i	0.999998	−	0.00213984i	$-0.000681133\pi$
$149$	6.08064	+	10.5320i	0.498146	+	0.862814i	−0.501852	+	0.864954i	$0.667348\pi$
$150$	5.78437	−	10.2866i	0.472292	−	0.839898i
$151$	7.20688	−	12.4827i	0.586488	−	1.01583i	−0.408201	−	0.912892i	$-0.633844\pi$
$151$	7.20688	−	12.4827i	0.586488	−	1.01583i	0.994688	−	0.102934i	$-0.0328231\pi$
$152$	−3.01289	+	3.01289i	−0.244378	+	0.244378i
$153$	0.0739122	+	5.86563i	0.00597544	+	0.474208i
$154$			0.249479i			0.0201036i
$155$	6.33145	−	5.58085i	0.508554	−	0.448265i
$156$	−0.534692	−	0.687809i	−0.0428096	−	0.0550688i
$157$	−4.17242	+	15.5717i	−0.332995	+	1.24275i	0.573031	+	0.819533i	$0.305767\pi$
$157$	−4.17242	+	15.5717i	−0.332995	+	1.24275i	−0.906026	+	0.423221i	$0.860899\pi$
$158$	−0.0243727	+	0.0909601i	−0.00193899	+	0.00723639i
$159$	2.37321	−	5.83311i	0.188208	−	0.462596i
$160$	−0.113543	+	1.80198i	−0.00897637	+	0.142459i
$161$			5.69524i			0.448847i
$162$	−11.7627	+	3.47175i	−0.924168	+	0.272767i
$163$	−0.640110	+	0.640110i	−0.0501373	+	0.0501373i	−0.731731	−	0.681594i	$-0.761287\pi$
$163$	−0.640110	+	0.640110i	−0.0501373	+	0.0501373i	0.681594	+	0.731731i	$0.261287\pi$
$164$	0.528316	−	0.915071i	0.0412546	−	0.0714550i
$165$	−0.707095	+	0.0526146i	−0.0550473	+	0.00409604i
$166$	7.68008	+	13.3023i	0.596090	+	1.03246i
$167$	−8.47961	−	2.27211i	−0.656172	−	0.175821i	−0.0846543	−	0.996410i	$-0.526979\pi$
$167$	−8.47961	−	2.27211i	−0.656172	−	0.175821i	−0.571518	+	0.820590i	$0.693645\pi$
$168$	0.628612	−	5.01892i	0.0484985	−	0.387218i
$169$	−0.547322	−	0.315997i	−0.0421017	−	0.0243074i
$170$	−1.90097	+	5.64683i	−0.145797	+	0.433092i
$171$	3.13385	+	3.05585i	0.239652	+	0.233687i
$172$	0.0330105	+	0.0330105i	0.00251702	+	0.00251702i
$173$	−14.7364	+	3.94862i	−1.12039	+	0.300208i	−0.771042	−	0.636785i	$-0.780264\pi$
$173$	−14.7364	+	3.94862i	−1.12039	+	0.300208i	−0.349349	+	0.936993i	$0.613597\pi$
$174$	−2.93419	−	21.2519i	−0.222440	−	1.61110i
$175$	3.95136	−	3.06378i	0.298695	−	0.231600i
$176$	−0.585599	+	0.338096i	−0.0441412	+	0.0254849i
$177$	−1.97072	+	2.60208i	−0.148129	+	0.195584i
$178$	−6.10283	−	22.7761i	−0.457426	−	1.70714i
$179$	0.441944			0.0330325			0.0165162	−	0.999864i	$-0.494742\pi$
$179$	0.441944			0.0330325			0.0165162	+	0.999864i	$0.494742\pi$
$180$	0.958208	+	0.0482644i	0.0714206	+	0.00359742i
$181$	13.3171			0.989854			0.494927	−	0.868935i	$-0.335195\pi$
$181$	13.3171			0.989854			0.494927	+	0.868935i	$0.335195\pi$
$182$	1.24036	+	4.62910i	0.0919420	+	0.343132i
$183$	−18.6901	−	2.34090i	−1.38161	−	0.173045i
$184$	−14.4036	+	8.31595i	−1.06185	+	0.613060i
$185$	−6.09103	+	9.16584i	−0.447821	+	0.673886i
$186$	−8.25199	−	3.35734i	−0.605065	−	0.246172i
$187$	0.345783	−	0.0926521i	0.0252861	−	0.00677540i
$188$	−1.22095	−	1.22095i	−0.0890468	−	0.0890468i
$189$	−5.16360	−	0.580750i	−0.375596	−	0.0422433i
$190$	1.97641	+	3.98240i	0.143384	+	0.288914i
$191$	−6.57188	−	3.79428i	−0.475525	−	0.274544i	0.243025	−	0.970020i	$-0.421860\pi$
$191$	−6.57188	−	3.79428i	−0.475525	−	0.274544i	−0.718550	+	0.695476i	$0.755194\pi$
$192$	13.5458	−	5.71109i	0.977583	−	0.412163i
$193$	21.8356	+	5.85082i	1.57176	+	0.421152i	0.936362	−	0.351035i	$-0.114170\pi$
$193$	21.8356	+	5.85082i	1.57176	+	0.421152i	0.635396	+	0.772186i	$0.280837\pi$
$194$	−6.54923	−	11.3436i	−0.470207	−	0.814423i
$195$	−12.8586	+	4.49181i	−0.920824	+	0.321665i
$196$	0.0715111	−	0.123861i	0.00510794	−	0.00884721i
$197$	−8.54290	+	8.54290i	−0.608656	+	0.608656i	−0.942595	−	0.333938i	$-0.891622\pi$
$197$	−8.54290	+	8.54290i	−0.608656	+	0.608656i	0.333938	+	0.942595i	$0.391622\pi$
$198$	0.382356	+	0.643400i	0.0271729	+	0.0457244i
$199$		−	18.7301i		−	1.32775i	−0.747846	−	0.663873i	$-0.768912\pi$
$199$		−	18.7301i		−	1.32775i	0.747846	−	0.663873i	$-0.231088\pi$
$200$	13.5181	+	5.51965i	0.955876	+	0.390298i
$201$	−22.0999	+	3.05128i	−1.55881	+	0.215220i
$202$	1.52592	−	5.69482i	0.107364	−	0.400686i
$203$	2.35250	−	8.77965i	0.165113	−	0.616211i
$204$	−0.479835	+	0.0662495i	−0.0335952	+	0.00463839i
$205$	−10.9236	−	12.3927i	−0.762935	−	0.865547i
$206$		−	18.6309i		−	1.29808i
$207$	8.72861	+	14.6878i	0.606680	+	1.02088i
$208$	−9.18487	+	9.18487i	−0.636856	+	0.636856i
$209$	0.133558	−	0.231329i	0.00923839	−	0.0160014i
$210$	−4.75388	−	2.29244i	−0.328049	−	0.158193i
$211$	2.37164	+	4.10781i	0.163271	+	0.282793i	0.936040	−	0.351894i	$-0.114462\pi$
$211$	2.37164	+	4.10781i	0.163271	+	0.282793i	−0.772769	+	0.634687i	$0.781129\pi$
$212$	0.502283	+	0.134586i	0.0344969	+	0.00924342i
$213$	−12.2527	+	5.16593i	−0.839544	+	0.353964i
$214$	11.8186	+	6.82349i	0.807906	+	0.466444i
$215$	0.653788	−	0.324465i	0.0445880	−	0.0221284i
$216$	−6.07091	−	13.9071i	−0.413073	−	0.946257i
$217$	−2.66895	−	2.66895i	−0.181180	−	0.181180i
$218$	2.70084	−	0.723689i	0.182924	−	0.0490144i
$219$	15.2299	+	6.19629i	1.02914	+	0.418707i
$220$	−0.0115672	−	0.0573951i	−0.000779860	−	0.00386958i
$221$	5.95536	−	3.43833i	0.400601	−	0.231287i
$222$	11.5264	+	1.44367i	0.773603	+	0.0968926i
$223$	1.31473	+	4.90663i	0.0880407	+	0.328572i	0.995873	−	0.0907619i	$-0.0289302\pi$
$223$	1.31473	+	4.90663i	0.0880407	+	0.328572i	−0.907832	+	0.419334i	$0.862264\pi$
$224$	0.807466			0.0539511
$225$	5.49483	−	13.9573i	0.366322	−	0.930488i
$226$	9.00995			0.599333
$227$	−3.71343	−	13.8587i	−0.246469	−	0.919834i	−0.972640	−	0.232319i	$-0.925369\pi$
$227$	−3.71343	−	13.8587i	−0.246469	−	0.919834i	0.726171	−	0.687514i	$-0.241298\pi$
$228$	−0.218218	+	0.288128i	−0.0144518	+	0.0190817i
$229$	−2.97696	+	1.71875i	−0.196723	+	0.113578i	−0.595126	−	0.803632i	$-0.702898\pi$
$229$	−2.97696	+	1.71875i	−0.196723	+	0.113578i	0.398403	+	0.917210i	$0.369565\pi$
$230$	3.42853	+	17.0120i	0.226070	+	1.12174i
$231$	0.0433693	+	0.314117i	0.00285349	+	0.0206674i
$232$	25.6394	−	6.87005i	1.68331	−	0.451041i
$233$	−1.71635	−	1.71635i	−0.112442	−	0.112442i	0.648647	−	0.761089i	$-0.275335\pi$
$233$	−1.71635	−	1.71635i	−0.112442	−	0.112442i	−0.761089	+	0.648647i	$0.775335\pi$
$234$	10.2935	+	10.0373i	0.672907	+	0.656160i
$235$	−24.1815	+	12.0009i	−1.57742	+	0.782853i
$236$	−0.233422	−	0.134766i	−0.0151945	−	0.00877252i
$237$	−0.0148750	+	0.118764i	−0.000966234	+	0.00771454i
$238$	2.57380	+	0.689648i	0.166835	+	0.0447032i
$239$	13.5506	+	23.4703i	0.876513	+	1.51817i	0.855142	+	0.518394i	$0.173470\pi$
$239$	13.5506	+	23.4703i	0.876513	+	1.51817i	0.0213715	+	0.999772i	$0.493197\pi$
$240$	−1.06148	−	14.2654i	−0.0685185	−	0.920829i
$241$	−6.13250	+	10.6218i	−0.395029	+	0.684211i	−0.993105	−	0.117229i	$-0.962599\pi$
$241$	−6.13250	+	10.6218i	−0.395029	+	0.684211i	0.598076	+	0.801440i	$0.295932\pi$
$242$	−10.5671	+	10.5671i	−0.679279	+	0.679279i
$243$	−14.2068	+	6.41608i	−0.911368	+	0.411591i
$244$		−	1.55537i		−	0.0995725i
$245$	−1.47858	−	1.67744i	−0.0944629	−	0.107168i
$246$	−6.57142	+	16.1519i	−0.418978	+	1.02981i
$247$	1.32805	−	4.95635i	0.0845018	−	0.315365i
$248$	2.85287	−	10.6471i	0.181158	−	0.676090i
$249$	11.9824	+	15.4137i	0.759352	+	0.976802i
$250$	9.95852	−	11.5304i	0.629832	−	0.729246i
$251$			1.18960i			0.0750869i	0.999295	+	0.0375434i	$0.0119533\pi$
$251$			1.18960i			0.0750869i	−0.999295	+	0.0375434i	$0.988047\pi$
$252$	−0.00540620	−	0.429033i	−0.000340558	−	0.0270265i
$253$	0.737273	−	0.737273i	0.0463519	−	0.0463519i
$254$	3.50201	−	6.06565i	0.219735	−	0.380593i
$255$	−1.41185	+	7.44033i	−0.0884134	+	0.465931i
$256$	1.70728	+	2.95710i	0.106705	+	0.184819i
$257$	5.43112	+	1.45527i	0.338784	+	0.0907769i	0.424200	−	0.905568i	$-0.360555\pi$
$257$	5.43112	+	1.45527i	0.338784	+	0.0907769i	−0.0854160	+	0.996345i	$0.527222\pi$
$258$	−0.614157	−	0.465141i	−0.0382357	−	0.0289584i
$259$	4.26227	+	2.46082i	0.264845	+	0.152908i
$260$	−0.499987	−	1.00746i	−0.0310079	−	0.0624800i
$261$	−7.38881	−	26.2479i	−0.457356	−	1.62471i
$262$	3.87702	+	3.87702i	0.239523	+	0.239523i
$263$	−2.62386	+	0.703061i	−0.161794	+	0.0433526i	−0.338807	−	0.940856i	$-0.610023\pi$
$263$	−2.62386	+	0.703061i	−0.161794	+	0.0433526i	0.177013	+	0.984209i	$0.443357\pi$
$264$	−0.731098	+	0.568345i	−0.0449960	+	0.0349792i
$265$	4.49967	−	6.77115i	0.276413	−	0.415948i
$266$	1.72188	−	0.994126i	0.105575	−	0.0609538i
$267$	−11.6434	−	27.6162i	−0.712564	−	1.69009i
$268$	−0.476794	−	1.77942i	−0.0291248	−	0.108695i
$269$	−6.36961			−0.388362			−0.194181	−	0.980966i	$-0.562205\pi$
$269$	−6.36961			−0.388362			−0.194181	+	0.980966i	$0.562205\pi$
$270$	−15.7735	+	1.37375i	−0.959948	+	0.0836038i
$271$	22.8991			1.39102			0.695511	−	0.718516i	$-0.255178\pi$
$271$	22.8991			1.39102			0.695511	+	0.718516i	$0.255178\pi$
$272$	1.86923	+	6.97605i	0.113339	+	0.422985i
$273$	2.36645	+	5.61284i	0.143224	+	0.339704i
$274$	25.4876	−	14.7153i	1.53976	−	0.888981i
$275$	−0.908140	−	0.114901i	−0.0547629	−	0.00692877i
$276$	−1.11386	+	0.865896i	−0.0670463	+	0.0521208i
$277$	19.6129	−	5.25525i	1.17842	−	0.315757i	0.384122	−	0.923283i	$-0.374504\pi$
$277$	19.6129	−	5.25525i	1.17842	−	0.315757i	0.794300	+	0.607525i	$0.207838\pi$
$278$	−12.9642	−	12.9642i	−0.777540	−	0.777540i
$279$	−10.9736	−	2.79267i	−0.656975	−	0.167193i
$280$	2.08340	−	6.18876i	0.124507	−	0.369849i
$281$	16.1738	+	9.33795i	0.964849	+	0.557056i	0.897662	−	0.440685i	$-0.145264\pi$
$281$	16.1738	+	9.33795i	0.964849	+	0.557056i	0.0671868	+	0.997740i	$0.478598\pi$
$282$	22.7156	+	17.2040i	1.35270	+	1.02449i
$283$	18.8480	+	5.05030i	1.12040	+	0.300209i	0.771044	−	0.636782i	$-0.219735\pi$
$283$	18.8480	+	5.05030i	1.12040	+	0.300209i	0.349352	+	0.936991i	$0.386402\pi$
$284$	−0.549003	−	0.950901i	−0.0325773	−	0.0564256i
$285$	3.18078	+	4.67063i	0.188413	+	0.276664i
$286$	0.438687	−	0.759828i	0.0259401	−	0.0449296i
$287$	−5.22403	+	5.22403i	−0.308365	+	0.308365i
$288$	2.08243	−	1.23754i	0.122708	−	0.0729225i
$289$			13.1765i			0.775091i
$290$	1.74170	−	27.6415i	0.102276	−	1.62316i
$291$	−10.2180	−	13.1441i	−0.598992	−	0.770521i
$292$	−0.351396	+	1.31143i	−0.0205639	+	0.0767455i
$293$	5.66448	−	21.1401i	0.330923	−	1.23502i	−0.577300	−	0.816532i	$-0.695894\pi$
$293$	5.66448	−	21.1401i	0.330923	−	1.23502i	0.908222	−	0.418488i	$-0.137440\pi$
$294$	−0.889485	+	2.18626i	−0.0518758	+	0.127505i
$295$	−3.16121	+	2.78645i	−0.184053	+	0.162233i
$296$			14.3728i			0.835401i
$297$	0.593269	+	0.743630i	0.0344250	+	0.0431498i
$298$	11.7184	−	11.7184i	0.678828	−	0.678828i
$299$	10.0146	−	17.3457i	0.579157	−	1.00313i
$300$	1.19996	+	0.306982i	0.0692800	+	0.0177236i
$301$	−0.163205	−	0.282679i	−0.00940697	−	0.0162933i
$302$	−18.9725	−	5.08366i	−1.09174	−	0.292532i
$303$	0.931292	−	7.43556i	0.0535013	−	0.427162i
$304$	4.66699	+	2.69449i	0.267670	+	0.154540i
$305$	−23.0464	−	7.75843i	−1.31964	−	0.444247i
$306$	7.69472	−	2.16607i	0.439878	−	0.123826i
$307$	−2.08355	−	2.08355i	−0.118915	−	0.118915i	0.645145	−	0.764060i	$-0.276797\pi$
$307$	−2.08355	−	2.08355i	−0.118915	−	0.118915i	−0.764060	+	0.645145i	$0.776797\pi$
$308$	−0.0252918	+	0.00677690i	−0.00144113	+	0.000386150i
$309$	−3.23878	−	23.4580i	−0.184248	−	1.33448i
$310$	−9.57902	−	6.36560i	−0.544052	−	0.361542i
$311$	−9.48346	+	5.47528i	−0.537758	+	0.310474i	−0.744170	−	0.667991i	$-0.767155\pi$
$311$	−9.48346	+	5.47528i	−0.537758	+	0.310474i	0.206412	+	0.978465i	$0.433821\pi$
$312$	−10.7399	+	14.1805i	−0.608025	+	0.802815i
$313$	−3.10949	−	11.6048i	−0.175759	−	0.655942i	−0.996421	−	0.0845279i	$-0.973062\pi$
$313$	−3.10949	−	11.6048i	−0.175759	−	0.655942i	0.820662	−	0.571414i	$-0.193605\pi$
$314$	21.9682			1.23974
$315$	−6.38408	−	2.05997i	−0.359702	−	0.116066i
$316$	−0.00988342			−0.000555986
$317$	−1.49429	−	5.57677i	−0.0839277	−	0.313223i	0.911181	−	0.412006i	$-0.135172\pi$
$317$	−1.49429	−	5.57677i	−0.0839277	−	0.313223i	−0.995109	+	0.0987832i	$0.968505\pi$
$318$	−8.51500	−	1.06649i	−0.477498	−	0.0598058i
$319$	−1.44110	+	0.832022i	−0.0806864	+	0.0465843i
$320$	18.6042	−	3.74942i	1.04001	−	0.209599i
$321$	16.0669	+	6.53685i	0.896768	+	0.364852i
$322$	7.49650	−	2.00868i	0.417764	−	0.111939i
$323$	−2.01735	−	2.01735i	−0.112248	−	0.112248i
$324$	−0.671485	−	1.09818i	−0.0373047	−	0.0610098i
$325$	−17.4219	+	2.38311i	−0.966390	+	0.132191i
$326$	1.06832	+	0.616798i	0.0591690	+	0.0341613i
$327$	3.27480	−	1.38070i	0.181097	−	0.0763530i
$328$	−20.8398	−	5.58402i	−1.15069	−	0.308326i
$329$	6.03641	+	10.4554i	0.332798	+	0.576423i
$330$	0.318645	+	0.912176i	0.0175408	+	0.0502136i
$331$	−16.4827	+	28.5488i	−0.905969	+	1.56919i	−0.0863589	+	0.996264i	$0.527523\pi$
$331$	−16.4827	+	28.5488i	−0.905969	+	1.56919i	−0.819611	+	0.572921i	$0.805810\pi$
$332$	−1.13994	+	1.13994i	−0.0625622	+	0.0625622i
$333$	14.7638	−	0.186037i	0.809050	−	0.0101948i
$334$			11.9629i			0.654580i
$335$	−28.7445	−	1.81120i	−1.57048	−	0.0989566i
$336$	−6.33721	+	0.874961i	−0.345723	+	0.0477331i
$337$	1.70970	−	6.38069i	0.0931333	−	0.347578i	−0.903597	−	0.428385i	$-0.859083\pi$
$337$	1.70970	−	6.38069i	0.0931333	−	0.347578i	0.996730	+	0.0808063i	$0.0257495\pi$
$338$	−0.222901	+	0.831878i	−0.0121242	+	0.0452482i
$339$	11.3443	−	1.56628i	0.616140	−	0.0850687i
$340$	−0.624103	−	0.0393249i	−0.0338467	−	0.00213269i
$341$			0.691015i			0.0374206i
$342$	2.91706	−	5.20280i	0.157736	−	0.281335i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	0.476610	−	0.825512i	0.0256971	−	0.0445086i
$345$	7.27417	+	20.8236i	0.391628	+	1.12110i
$346$	10.3949	+	18.0046i	0.558836	+	0.967932i
$347$	30.0088	+	8.04084i	1.61096	+	0.431655i	0.948328	−	0.317291i	$-0.102773\pi$
$347$	30.0088	+	8.04084i	1.61096	+	0.431655i	0.662630	+	0.748947i	$0.269440\pi$
$348$	2.07477	−	0.874752i	0.111219	−	0.0468916i
$349$	−13.1407	−	7.58681i	−0.703408	−	0.406113i	0.105207	−	0.994450i	$-0.466449\pi$
$349$	−13.1407	−	7.58681i	−0.703408	−	0.406113i	−0.808615	+	0.588337i	$0.799783\pi$
$350$	−5.42641	−	4.12050i	−0.290054	−	0.220250i
$351$	14.7053	+	10.8485i	0.784912	+	0.579049i
$352$	−0.104530	−	0.104530i	−0.00557147	−	0.00557147i
$353$	31.0016	−	8.30687i	1.65005	−	0.442130i	0.690424	−	0.723405i	$-0.257424\pi$
$353$	31.0016	−	8.30687i	1.65005	−	0.442130i	0.959627	+	0.281275i	$0.0907574\pi$
$354$	4.12012	+	1.67628i	0.218982	+	0.0890930i
$355$	−16.8283	+	3.39151i	−0.893154	+	0.180003i
$356$	2.14322	−	1.23739i	0.113590	−	0.0655814i
$357$	3.36054	+	0.420902i	0.177858	+	0.0222765i
$358$	−0.155872	−	0.581721i	−0.00823807	−	0.0307449i
$359$	34.0346			1.79628			0.898140	−	0.439710i	$-0.144919\pi$
$359$	34.0346			1.79628			0.898140	+	0.439710i	$0.144919\pi$
$360$	−4.11195	−	19.1537i	−0.216719	−	1.00949i
$361$	16.8712			0.887958
$362$	−4.69688	−	17.5290i	−0.246863	−	0.921304i
$363$	−11.4680	+	15.1419i	−0.601912	+	0.794744i
$364$	−0.435596	+	0.251492i	−0.0228315	+	0.0131817i
$365$	17.6790	+	11.7483i	0.925362	+	0.614936i
$366$	3.51063	+	25.4269i	0.183503	+	1.32909i
$367$	−11.3802	+	3.04933i	−0.594044	+	0.159173i	−0.543301	−	0.839538i	$-0.682826\pi$
$367$	−11.3802	+	3.04933i	−0.594044	+	0.159173i	−0.0507430	+	0.998712i	$0.516159\pi$
$368$	14.8742	+	14.8742i	0.775373	+	0.775373i
$369$	−5.46618	+	21.4790i	−0.284558	+	1.11815i
$370$	14.2131	+	4.78473i	0.738901	+	0.248746i
$371$	−3.14870	−	1.81790i	−0.163472	−	0.0943808i
$372$	0.116202	−	0.927771i	0.00602478	−	0.0481027i
$373$	−19.8756	−	5.32564i	−1.02912	−	0.275751i	−0.295521	−	0.955336i	$-0.595493\pi$
$373$	−19.8756	−	5.32564i	−1.02912	−	0.275751i	−0.733597	+	0.679585i	$0.762160\pi$
$374$	−0.243912	−	0.422467i	−0.0126124	−	0.0218453i
$375$	10.5342	−	16.2490i	0.543986	−	0.839094i
$376$	−17.6282	+	30.5330i	−0.909107	+	1.57462i
$377$	−22.6031	+	22.6031i	−1.16412	+	1.16412i
$378$	1.05675	+	7.00155i	0.0543533	+	0.360121i
$379$		−	25.3546i		−	1.30238i	−0.758915	−	0.651190i	$-0.774270\pi$
$379$		−	25.3546i		−	1.30238i	0.758915	−	0.651190i	$-0.225730\pi$
$380$	−0.350041	+	0.308543i	−0.0179567	+	0.0158279i
$381$	3.35489	−	8.24599i	0.171876	−	0.422455i
$382$	−2.67645	+	9.98864i	−0.136939	+	0.511063i
$383$	−1.73269	+	6.46650i	−0.0885365	+	0.330423i	−0.995960	−	0.0897937i	$-0.971379\pi$
$383$	−1.73269	+	6.46650i	−0.0885365	+	0.330423i	0.907424	+	0.420217i	$0.138046\pi$
$384$	−10.5782	−	13.6074i	−0.539815	−	0.694398i
$385$	−0.0257435	+	0.408560i	−0.00131201	+	0.0208222i
$386$		−	30.8052i		−	1.56794i
$387$	−0.854139	−	0.478890i	−0.0434183	−	0.0243434i
$388$	0.972088	−	0.972088i	0.0493503	−	0.0493503i
$389$	−7.30232	+	12.6480i	−0.370242	+	0.641279i	−0.989603	−	0.143828i	$-0.954059\pi$
$389$	−7.30232	+	12.6480i	−0.370242	+	0.641279i	0.619360	+	0.785107i	$0.287392\pi$
$390$	10.4476	+	15.3412i	0.529037	+	0.776834i
$391$	−5.56813	−	9.64429i	−0.281593	−	0.487733i
$392$	−2.82081	−	0.755834i	−0.142472	−	0.0381754i
$393$	5.55550	+	4.20754i	0.280238	+	0.212243i
$394$	14.2579	+	8.23178i	0.718301	+	0.414711i
$395$	−0.0493000	+	0.146446i	−0.00248055	+	0.00736849i
$396$	−0.0548403	+	0.0562400i	−0.00275583	+	0.00282617i
$397$	−23.9632	−	23.9632i	−1.20268	−	1.20268i	−0.973349	−	0.229328i	$-0.926347\pi$
$397$	−23.9632	−	23.9632i	−1.20268	−	1.20268i	−0.229328	−	0.973349i	$-0.573653\pi$
$398$	−24.6541	+	6.60603i	−1.23580	+	0.331131i
$399$	1.99518	−	1.55102i	0.0998840	−	0.0776483i
$400$	2.31808	−	18.3214i	0.115904	−	0.916072i
$401$	−15.9504	+	9.20898i	−0.796526	+	0.459875i	−0.842255	−	0.539079i	$-0.818772\pi$
$401$	−15.9504	+	9.20898i	−0.796526	+	0.459875i	0.0457289	+	0.998954i	$0.485439\pi$
$402$	11.8109	+	28.0134i	0.589072	+	1.39718i
$403$	3.43560	+	12.8218i	0.171139	+	0.638701i
$404$	0.618781			0.0307855
$405$	−19.6215	+	4.47174i	−0.975001	+	0.222202i
$406$	−12.3862			−0.614715
$407$	−0.233205	−	0.870334i	−0.0115596	−	0.0431409i
$408$	3.84243	+	9.11361i	0.190228	+	0.451191i
$409$	−16.5144	+	9.53459i	−0.816585	+	0.471455i	−0.849237	−	0.528011i	$-0.822938\pi$
$409$	−16.5144	+	9.53459i	−0.816585	+	0.471455i	0.0326527	+	0.999467i	$0.489604\pi$
$410$	−12.4596	+	18.7493i	−0.615335	+	0.925962i
$411$	29.5331	−	22.9586i	1.45676	−	1.13246i
$412$	1.88877	−	0.506093i	0.0930528	−	0.0249334i
$413$	1.33258	+	1.33258i	0.0655717	+	0.0655717i
$414$	16.2547	−	16.6696i	0.798876	−	0.819266i
$415$	11.2046	+	22.5770i	0.550014	+	1.10826i
$416$	−2.45926	−	1.41986i	−0.120575	−	0.0696142i
$417$	−18.5768	−	14.0694i	−0.909708	−	0.688981i
$418$	−0.351598	−	0.0942105i	−0.0171972	−	0.00460798i
$419$	3.42893	+	5.93908i	0.167514	+	0.290143i	0.937545	−	0.347863i	$-0.113093\pi$
$419$	3.42893	+	5.93908i	0.167514	+	0.290143i	−0.770031	+	0.638006i	$0.779759\pi$
$420$	0.103268	−	0.544212i	0.00503894	−	0.0265548i
$421$	−1.53201	+	2.65352i	−0.0746658	+	0.129325i	−0.900941	−	0.433942i	$-0.857122\pi$
$421$	−1.53201	+	2.65352i	−0.0746658	+	0.129325i	0.826275	+	0.563267i	$0.190456\pi$
$422$	4.57054	−	4.57054i	0.222490	−	0.222490i
$423$	31.5918	+	17.7126i	1.53605	+	0.861215i
$424$		−	10.6177i		−	0.515642i
$425$	−3.69581	+	9.05137i	−0.179273	+	0.439056i
$426$	11.1213	+	14.3060i	0.538828	+	0.693128i
$427$	−2.81467	+	10.5045i	−0.136211	+	0.508347i
$428$	−0.370709	+	1.38351i	−0.0179189	+	0.0668743i
$429$	0.420259	−	1.03295i	0.0202903	−	0.0498714i
$430$	−0.657674	−	0.746128i	−0.0317159	−	0.0359815i
$431$		−	12.6529i		−	0.609469i	−0.952437	−	0.304734i	$-0.901432\pi$
$431$		−	12.6529i		−	0.609469i	0.952437	−	0.304734i	$-0.0985677\pi$
$432$	−15.0025	+	11.9690i	−0.721808	+	0.575860i
$433$	−11.6961	+	11.6961i	−0.562079	+	0.562079i	−0.929898	−	0.367818i	$-0.880105\pi$
$433$	−11.6961	+	11.6961i	−0.562079	+	0.562079i	0.367818	+	0.929898i	$0.380105\pi$
$434$	−2.57175	+	4.45441i	−0.123448	+	0.213819i
$435$	−2.61221	−	35.1059i	−0.125246	−	1.68320i
$436$	0.146732	+	0.254148i	0.00702721	+	0.0121715i
$437$	−8.02645	−	2.15068i	−0.383957	−	0.102881i
$438$	2.78454	−	22.2321i	0.133050	−	1.06229i
$439$	−18.0480	−	10.4200i	−0.861385	−	0.497321i	0.00309081	−	0.999995i	$-0.499016\pi$
$439$	−18.0480	−	10.4200i	−0.861385	−	0.497321i	−0.864476	+	0.502674i	$0.832349\pi$
$440$	−1.07087	+	0.531455i	−0.0510516	+	0.0253361i
$441$	−0.739884	+	2.90733i	−0.0352326	+	0.138444i
$442$	−6.62622	−	6.62622i	−0.315177	−	0.315177i
$443$	−11.5443	+	3.09328i	−0.548486	+	0.146966i	−0.522411	−	0.852694i	$-0.674967\pi$
$443$	−11.5443	+	3.09328i	−0.548486	+	0.146966i	−0.0260747	+	0.999660i	$0.508301\pi$
$444$	0.166750	+	1.20774i	0.00791359	+	0.0573170i
$445$	−7.64406	−	37.9290i	−0.362363	−	1.79801i
$446$	5.99478	−	3.46109i	0.283861	−	0.163887i
$447$	12.7174	−	16.7916i	0.601512	−	0.794216i
$448$	−2.19669	−	8.19814i	−0.103784	−	0.387326i
$449$	−5.14260			−0.242694			−0.121347	−	0.992610i	$-0.538721\pi$
$449$	−5.14260			−0.242694			−0.121347	+	0.992610i	$0.538721\pi$
$450$	−20.3097	−	2.31004i	−0.957408	−	0.108896i
$451$	1.35255			0.0636889
$452$	0.244748	+	0.913412i	0.0115120	+	0.0429633i
$453$	−24.7718	−	3.10263i	−1.16388	−	0.145774i
$454$	−16.9322	+	9.77579i	−0.794666	+	0.458801i
$455$	1.55361	+	7.70885i	0.0728344	+	0.361396i
$456$	6.83593	+	2.78121i	0.320122	+	0.130242i
$457$	−26.4648	+	7.09122i	−1.23797	+	0.331713i	−0.817679	−	0.575675i	$-0.804739\pi$
$457$	−26.4648	+	7.09122i	−1.23797	+	0.331713i	−0.420293	+	0.907388i	$0.638073\pi$
$458$	3.31231	+	3.31231i	0.154774	+	0.154774i
$459$	9.31180	−	4.06492i	0.434638	−	0.189734i
$460$	−1.63151	+	0.809694i	−0.0760695	+	0.0377522i
$461$	16.9768	+	9.80158i	0.790690	+	0.456505i	0.840205	−	0.542268i	$-0.182434\pi$
$461$	16.9768	+	9.80158i	0.790690	+	0.456505i	−0.0495155	+	0.998773i	$0.515768\pi$
$462$	0.398169	−	0.167874i	0.0185245	−	0.00781019i
$463$	−18.7589	−	5.02644i	−0.871802	−	0.233599i	−0.204935	−	0.978776i	$-0.565698\pi$
$463$	−18.7589	−	5.02644i	−0.871802	−	0.233599i	−0.666867	+	0.745177i	$0.732365\pi$
$464$	−16.7858	−	29.0738i	−0.779261	−	1.34972i
$465$	−13.1674	−	6.34966i	−0.610625	−	0.294458i
$466$	−1.65385	+	2.86454i	−0.0766129	+	0.132697i
$467$	−14.3556	+	14.3556i	−0.664296	+	0.664296i	−0.956390	−	0.292094i	$-0.905648\pi$
$467$	−14.3556	+	14.3556i	−0.664296	+	0.664296i	0.292094	+	0.956390i	$0.405648\pi$
$468$	−0.737950	+	1.31619i	−0.0341117	+	0.0608410i
$469$			12.8804i			0.594763i
$470$	24.3252	+	27.5968i	1.12204	+	1.27295i
$471$	27.6600	−	3.81893i	1.27450	−	0.175967i
$472$	−1.42440	+	5.31595i	−0.0655635	+	0.244686i
$473$	−0.0154664	+	0.0577216i	−0.000711148	+	0.00265404i
$474$	0.161572	−	0.0223079i	0.00742127	−	0.00102463i
$475$	2.82573	+	6.72573i	0.129653	+	0.308598i
$476$			0.279661i			0.0128182i
$477$	−10.9066	+	0.137432i	−0.499377	+	0.00629259i
$478$	26.1141	−	26.1141i	1.19443	−	1.19443i
$479$	9.75324	−	16.8931i	0.445637	−	0.771866i	−0.552459	−	0.833540i	$-0.686311\pi$
$479$	9.75324	−	16.8931i	0.445637	−	0.771866i	0.998096	+	0.0616740i	$0.0196439\pi$
$480$	2.95235	−	1.03133i	0.134756	−	0.0470734i
$481$	−8.65427	−	14.9896i	−0.394601	−	0.683469i
$482$	16.1441	+	4.32581i	0.735345	+	0.197035i
$483$	9.08959	−	3.83230i	0.413591	−	0.174376i
$484$	−1.35832	−	0.784226i	−0.0617418	−	0.0356466i
$485$	−9.55482	−	19.2527i	−0.433862	−	0.874218i
$486$	13.4560	+	16.4372i	0.610377	+	0.745606i
$487$	−29.7056	−	29.7056i	−1.34609	−	1.34609i	−0.889864	−	0.456227i	$-0.849201\pi$
$487$	−29.7056	−	29.7056i	−1.34609	−	1.34609i	−0.456227	−	0.889864i	$-0.650799\pi$
$488$	−30.6764	+	8.21972i	−1.38866	+	0.372089i
$489$	1.45234	+	0.590887i	0.0656771	+	0.0267208i
$490$	−1.68649	+	2.53784i	−0.0761877	+	0.114648i
$491$	−16.9298	+	9.77445i	−0.764033	+	0.441115i	−0.830742	−	0.556658i	$-0.812083\pi$
$491$	−16.9298	+	9.77445i	−0.764033	+	0.441115i	0.0667088	+	0.997772i	$0.478750\pi$
$492$	−1.81595	−	0.227445i	−0.0818695	−	0.0102540i
$493$	4.60000	+	17.1674i	0.207173	+	0.773182i
$494$	−6.99232			−0.314599
$495$	0.559774	+	1.09312i	0.0251600	+	0.0491321i
$496$	−13.9410			−0.625970
$497$	1.98700	+	7.41557i	0.0891290	+	0.332634i
$498$	16.0625	−	21.2084i	0.719780	−	0.950373i
$499$	−12.6730	+	7.31674i	−0.567320	+	0.327542i	−0.756078	−	0.654481i	$-0.772887\pi$
$499$	−12.6730	+	7.31674i	−0.567320	+	0.327542i	0.188758	+	0.982024i	$0.439554\pi$
$500$	1.43944	+	0.696363i	0.0643739	+	0.0311423i
$501$	2.07962	+	15.0623i	0.0929104	+	0.672936i
$502$	1.56584	−	0.419566i	0.0698870	−	0.0187262i
$503$	1.91349	+	1.91349i	0.0853183	+	0.0853183i	0.748478	−	0.663160i	$-0.230785\pi$
$503$	1.91349	+	1.91349i	0.0853183	+	0.0853183i	−0.663160	+	0.748478i	$0.730785\pi$
$504$	−8.43319	+	2.37395i	−0.375644	+	0.105744i
$505$	3.08657	−	9.16867i	0.137351	−	0.408000i
$506$	−1.23049	−	0.710422i	−0.0547018	−	0.0315821i
$507$	−0.136040	+	1.08616i	−0.00604173	+	0.0482380i
$508$	0.710054	+	0.190258i	0.0315035	+	0.00844135i
$509$	−5.04165	−	8.73240i	−0.223467	−	0.387057i	0.732391	−	0.680884i	$-0.238404\pi$
$509$	−5.04165	−	8.73240i	−0.223467	−	0.387057i	−0.955859	+	0.293827i	$0.905071\pi$
$510$	10.2915	−	0.765784i	0.455714	−	0.0339095i
$511$	4.74643	−	8.22105i	0.209970	−	0.363678i
$512$	17.3628	−	17.3628i	0.767336	−	0.767336i
$513$	2.76839	−	7.05789i	0.122227	−	0.311614i
$514$		−	7.66213i		−	0.337962i
$515$	1.92250	−	30.5109i	0.0847156	−	1.34447i
$516$	0.0304721	−	0.0748973i	0.00134146	−	0.00329717i
$517$	0.572053	−	2.13493i	0.0251589	−	0.0938942i
$518$	1.73584	−	6.47825i	0.0762685	−	0.284638i
$519$	16.2181	+	20.8623i	0.711894	+	0.915755i
$520$	−17.2277	+	15.1853i	−0.755484	+	0.665921i
$521$		−	32.4283i		−	1.42071i	−0.703845	−	0.710354i	$-0.748535\pi$
$521$		−	32.4283i		−	1.42071i	0.703845	−	0.710354i	$-0.251465\pi$
$522$	−31.9436	+	18.9832i	−1.39813	+	0.830874i
$523$	−18.9284	+	18.9284i	−0.827679	+	0.827679i	−0.987195	−	0.159516i	$-0.949007\pi$
$523$	−18.9284	+	18.9284i	−0.827679	+	0.827679i	0.159516	+	0.987195i	$0.449007\pi$
$524$	−0.287729	+	0.498361i	−0.0125695	+	0.0217710i
$525$	−7.54864	−	4.24476i	−0.329450	−	0.185256i
$526$	1.85085	+	3.20576i	0.0807007	+	0.139778i
$527$	7.12899	+	1.91021i	0.310544	+	0.0832099i
$528$	0.933647	+	0.707112i	0.0406318	+	0.0307731i
$529$	−8.17156	−	4.71785i	−0.355285	−	0.205124i
$530$	−10.4997	−	3.53466i	−0.456078	−	0.153536i
$531$	5.47900	+	1.39435i	0.237768	+	0.0605094i
$532$	0.147556	+	0.147556i	0.00639736	+	0.00639736i
$533$	25.0965	−	6.72460i	1.08705	−	0.291275i
$534$	−32.2440	+	25.0660i	−1.39533	+	1.08471i
$535$	18.6507	+	12.3941i	0.806340	+	0.535842i
$536$	−32.5755	+	18.8075i	−1.40705	+	0.812360i
$537$	−0.297382	−	0.705343i	−0.0128330	−	0.0304378i
$538$	2.24653	+	8.38417i	0.0968548	+	0.361467i
$539$	0.183076			0.00788564
$540$	−0.567744	−	1.56178i	−0.0244318	−	0.0672081i
$541$	3.89921			0.167640			0.0838200	−	0.996481i	$-0.473288\pi$
$541$	3.89921			0.167640			0.0838200	+	0.996481i	$0.473288\pi$
$542$	−8.07641	−	30.1416i	−0.346911	−	1.29469i
$543$	−8.96103	−	21.2541i	−0.384554	−	0.912101i
$544$	−1.36736	+	0.789446i	−0.0586251	+	0.0338472i
$545$	4.49771	−	0.906452i	0.192661	−	0.0388281i
$546$	6.55341	−	5.09452i	0.280460	−	0.218025i
$547$	−3.84960	+	1.03150i	−0.164597	+	0.0441036i	−0.340176	−	0.940362i	$-0.610487\pi$
$547$	−3.84960	+	1.03150i	−0.164597	+	0.0441036i	0.175579	+	0.984465i	$0.443820\pi$
$548$	2.18415	+	2.18415i	0.0933025	+	0.0933025i
$549$	8.84039	+	31.4045i	0.377299	+	1.34031i
$550$	0.169056	+	1.23589i	0.00720856	+	0.0526985i
$551$	11.4850	+	6.63089i	0.489279	+	0.282485i
$552$	22.9644	+	17.3924i	0.977429	+	0.740271i
$553$	0.0667494	+	0.0178854i	0.00283847	+	0.000760567i
$554$	−13.8347	−	23.9624i	−0.587781	−	1.01807i
$555$	18.7273	+	3.55362i	0.794929	+	0.150843i
$556$	0.962123	−	1.66645i	0.0408031	−	0.0706731i
$557$	31.6273	−	31.6273i	1.34009	−	1.34009i	0.444128	−	0.895964i	$-0.353514\pi$
$557$	31.6273	−	31.6273i	1.34009	−	1.34009i	0.895964	−	0.444128i	$-0.146486\pi$
$558$	0.194423	+	15.4293i	0.00823058	+	0.653175i
$559$			1.14792i			0.0485520i
$560$	−8.24257	−	0.519367i	−0.348312	−	0.0219473i
$561$	−0.380548	−	0.489523i	−0.0160668	−	0.0206677i
$562$	6.58690	−	24.5827i	0.277852	−	1.03696i
$563$	4.27444	−	15.9524i	0.180146	−	0.672315i	−0.815471	−	0.578798i	$-0.803522\pi$
$563$	4.27444	−	15.9524i	0.180146	−	0.672315i	0.995618	−	0.0935178i	$-0.0298112\pi$
$564$	−1.12706	+	2.77020i	−0.0474579	+	0.116647i
$565$	14.7551	+	0.929727i	0.620754	+	0.0391139i
$566$		−	26.5904i		−	1.11768i
$567$	2.54768	+	8.63188i	0.106993	+	0.362505i
$568$	−15.8532	+	15.8532i	−0.665184	+	0.665184i
$569$	−11.2852	+	19.5465i	−0.473099	+	0.819432i	−0.999526	−	0.0307885i	$-0.990198\pi$
$569$	−11.2852	+	19.5465i	−0.473099	+	0.819432i	0.526427	+	0.850221i	$0.323532\pi$
$570$	5.02600	−	5.83409i	0.210516	−	0.244363i
$571$	20.6071	+	35.6926i	0.862381	+	1.49369i	0.869624	+	0.493714i	$0.164361\pi$
$571$	20.6071	+	35.6926i	0.862381	+	1.49369i	−0.00724345	+	0.999974i	$0.502306\pi$
$572$	0.0889465	+	0.0238331i	0.00371904	+	0.000996514i
$573$	−1.63347	+	13.0419i	−0.0682393	+	0.544832i
$574$	8.71875	+	5.03377i	0.363914	+	0.210106i
$575$	3.85928	+	28.2134i	0.160943	+	1.17658i
$576$	−18.2298	−	17.7761i	−0.759575	−	0.740670i
$577$	28.4165	+	28.4165i	1.18299	+	1.18299i	0.978965	+	0.204028i	$0.0654034\pi$
$577$	28.4165	+	28.4165i	1.18299	+	1.18299i	0.204028	+	0.978965i	$0.434597\pi$
$578$	17.3440	−	4.64731i	0.721414	−	0.193302i
$579$	−5.35515	−	38.7865i	−0.222552	−	1.61191i
$580$	2.84955	−	0.574288i	0.118321	−	0.0238460i
$581$	9.76164	−	5.63589i	0.404981	−	0.233816i
$582$	−13.6974	+	18.0856i	−0.567776	+	0.749673i
$583$	0.172277	+	0.642948i	0.00713500	+	0.0266282i
$584$	27.7221			1.14715
$585$	15.8214	+	17.4998i	0.654135	+	0.723528i
$586$	−29.8241			−1.23202
$587$	3.04399	+	11.3603i	0.125639	+	0.468890i	0.999862	−	0.0166345i	$-0.00529517\pi$
$587$	3.04399	+	11.3603i	0.125639	+	0.468890i	−0.874223	+	0.485525i	$0.838629\pi$
$588$	−0.245801	−	0.0307862i	−0.0101367	−	0.00126960i
$589$	4.76930	−	2.75356i	0.196516	−	0.113458i
$590$	4.78268	+	3.17826i	0.196900	+	0.130847i
$591$	19.3829	+	7.88598i	0.797308	+	0.324386i
$592$	17.5587	−	4.70484i	0.721659	−	0.193368i
$593$	33.3410	+	33.3410i	1.36915	+	1.36915i	0.861651	+	0.507501i	$0.169431\pi$
$593$	33.3410	+	33.3410i	1.36915	+	1.36915i	0.507501	+	0.861651i	$0.330569\pi$
$594$	0.769580	−	1.04318i	0.0315762	−	0.0428022i
$595$	4.14382	+	1.39499i	0.169880	+	0.0571890i
$596$	1.50631	+	0.869667i	0.0617008	+	0.0356230i
$597$	−29.8933	+	12.6034i	−1.22345	+	0.515824i
$598$	−26.3638	−	7.06417i	−1.07810	−	0.288875i
$599$	−15.7308	−	27.2465i	−0.642743	−	1.11326i	−0.984818	−	0.173590i	$-0.944463\pi$
$599$	−15.7308	−	27.2465i	−0.642743	−	1.11326i	0.342075	−	0.939673i	$-0.388870\pi$
$600$	−0.286929	−	25.2891i	−0.0117138	−	1.03242i
$601$	−11.8240	+	20.4797i	−0.482310	+	0.835385i	−0.999794	−	0.0203077i	$-0.993535\pi$
$601$	−11.8240	+	20.4797i	−0.482310	+	0.835385i	0.517484	+	0.855693i	$0.326869\pi$
$602$	−0.314522	+	0.314522i	−0.0128190	+	0.0128190i
$603$	19.7408	+	33.2183i	0.803906	+	1.35275i
$604$		−	2.06149i		−	0.0838808i
$605$	−18.3956	+	16.2148i	−0.747888	+	0.659226i
$606$	−10.1157	+	1.39665i	−0.410923	+	0.0567350i
$607$	0.758873	−	2.83215i	0.0308017	−	0.114954i	−0.948813	−	0.315837i	$-0.897715\pi$
$607$	0.758873	−	2.83215i	0.0308017	−	0.114954i	0.979615	+	0.200884i	$0.0643813\pi$
$608$	−0.304922	+	1.13798i	−0.0123662	+	0.0461514i
$609$	−15.5953	+	2.15320i	−0.631953	+	0.0872521i
$610$	−2.08387	+	33.0719i	−0.0843734	+	1.33904i
$611$		−	42.4579i		−	1.71766i
$612$	0.428613	+	0.721237i	0.0173256	+	0.0291543i
$613$	13.6365	−	13.6365i	0.550773	−	0.550773i	−0.375891	−	0.926664i	$-0.622663\pi$
$613$	13.6365	−	13.6365i	0.550773	−	0.550773i	0.926664	+	0.375891i	$0.122663\pi$
$614$	−2.00767	+	3.47739i	−0.0810231	+	0.140336i
$615$	−12.4284	+	25.7730i	−0.501161	+	1.03927i
$616$	0.267320	+	0.463012i	0.0107706	+	0.0186553i
$617$	−5.86604	−	1.57180i	−0.236158	−	0.0632783i	0.138799	−	0.990321i	$-0.455676\pi$
$617$	−5.86604	−	1.57180i	−0.236158	−	0.0632783i	−0.374957	+	0.927042i	$0.622342\pi$
$618$	−29.7349	+	12.5366i	−1.19611	+	0.504298i
$619$	−21.8393	−	12.6089i	−0.877795	−	0.506795i	−0.00786399	−	0.999969i	$-0.502503\pi$
$619$	−21.8393	−	12.6089i	−0.877795	−	0.506795i	−0.869931	+	0.493174i	$0.835837\pi$
$620$	0.385126	−	1.14402i	0.0154670	−	0.0459449i
$621$	17.5683	−	23.8142i	0.704993	−	0.955632i
$622$	10.5517	+	10.5517i	0.423087	+	0.423087i
$623$	−16.7138	+	4.47845i	−0.669625	+	0.179425i
$624$	20.8395	+	8.47858i	0.834247	+	0.339415i
$625$	17.4984	−	17.8551i	0.699936	−	0.714206i
$626$	−14.1784	+	8.18591i	−0.566683	+	0.327175i
$627$	−0.459071	−	0.0574980i	−0.0183335	−	0.00229625i
$628$	0.596749	+	2.22710i	0.0238129	+	0.0888708i
$629$	−9.62362			−0.383719
$630$	−0.459861	+	9.12976i	−0.0183213	+	0.363738i
$631$	40.0388			1.59392			0.796959	−	0.604033i	$-0.206441\pi$
$631$	40.0388			1.59392			0.796959	+	0.604033i	$0.206441\pi$
$632$	0.0522312	+	0.194929i	0.00207764	+	0.00775388i
$633$	4.96018	−	6.54926i	0.197150	−	0.260310i
$634$	−6.81354	+	3.93380i	−0.270600	+	0.156231i
$635$	6.36097	−	9.57205i	0.252427	−	0.379855i
$636$	−0.123184	−	0.892205i	−0.00488457	−	0.0353782i
$637$	3.39699	−	0.910219i	0.134593	−	0.0360642i
$638$	1.60344	+	1.60344i	0.0634809	+	0.0634809i
$639$	16.4896	+	16.0792i	0.652320	+	0.636085i
$640$	−9.89158	−	19.9312i	−0.390999	−	0.787851i
$641$	−27.4706	−	15.8601i	−1.08502	−	0.626438i	−0.152775	−	0.988261i	$-0.548821\pi$
$641$	−27.4706	−	15.8601i	−1.08502	−	0.626438i	−0.932247	+	0.361823i	$0.882154\pi$
$642$	2.93758	−	23.4540i	0.115937	−	0.925657i
$643$	26.9602	+	7.22397i	1.06321	+	0.284886i	0.747699	−	0.664037i	$-0.231158\pi$
$643$	26.9602	+	7.22397i	1.06321	+	0.284886i	0.315508	+	0.948923i	$0.397825\pi$
$644$	0.407273	+	0.705417i	0.0160488	+	0.0277973i
$645$	−0.957777	−	0.825113i	−0.0377124	−	0.0324888i
$646$	−1.94388	+	3.36690i	−0.0764809	+	0.132469i
$647$	−3.09376	+	3.09376i	−0.121628	+	0.121628i	−0.765301	−	0.643673i	$-0.777410\pi$
$647$	−3.09376	+	3.09376i	−0.121628	+	0.121628i	0.643673	+	0.765301i	$0.277410\pi$
$648$	−18.1106	+	19.0472i	−0.711451	+	0.748244i
$649$		−	0.345015i		−	0.0135430i
$650$	9.28144	+	22.0915i	0.364048	+	0.866498i
$651$	−2.46372	+	6.05558i	−0.0965608	+	0.237337i
$652$	−0.0335096	+	0.125060i	−0.00131234	+	0.00489771i
$653$	10.6338	−	39.6857i	0.416131	−	1.55302i	−0.366427	−	0.930447i	$-0.619419\pi$
$653$	10.6338	−	39.6857i	0.416131	−	1.55302i	0.782559	−	0.622577i	$-0.213914\pi$
$654$	−2.97239	−	3.82358i	−0.116230	−	0.149514i
$655$	5.94914	+	6.74927i	0.232452	+	0.263716i
$656$			27.2872i			1.06538i
$657$	−0.358827	−	28.4763i	−0.0139992	−	1.11097i
$658$	11.6331	−	11.6331i	0.453507	−	0.453507i
$659$	−2.60962	+	4.52000i	−0.101656	+	0.176074i	−0.912367	−	0.409373i	$-0.865748\pi$
$659$	−2.60962	+	4.52000i	−0.101656	+	0.176074i	0.810711	+	0.585447i	$0.199081\pi$
$660$	−0.0838190	+	0.0570821i	−0.00326265	+	0.00222192i
$661$	−19.4739	−	33.7298i	−0.757447	−	1.31194i	−0.944149	−	0.329519i	$-0.893113\pi$
$661$	−19.4739	−	33.7298i	−0.757447	−	1.31194i	0.186702	−	0.982417i	$-0.440220\pi$
$662$	43.3915	+	11.6267i	1.68646	+	0.451885i
$663$	−9.49491	−	7.19112i	−0.368752	−	0.279280i
$664$	28.5071	+	16.4586i	1.10629	+	0.638717i
$665$	2.92242	−	1.45035i	0.113326	−	0.0562423i
$666$	−5.45199	−	19.3676i	−0.211260	−	0.750479i
$667$	36.6041	+	36.6041i	1.41732	+	1.41732i
$668$	−1.21277	+	0.324962i	−0.0469236	+	0.0125731i
$669$	6.94630	−	5.39995i	0.268560	−	0.208774i
$670$	7.75401	+	38.4746i	0.299564	+	1.48640i
$671$	1.72422	−	0.995479i	0.0665628	−	0.0384300i
$672$	−0.543340	−	1.28871i	−0.0209598	−	0.0497133i
$673$	7.36456	+	27.4849i	0.283883	+	1.05947i	0.949652	+	0.313307i	$0.101437\pi$
$673$	7.36456	+	27.4849i	0.283883	+	1.05947i	−0.665769	+	0.746158i	$0.731896\pi$
$674$	−9.00175			−0.346735
$675$	−25.9733	+	0.622068i	−0.999713	+	0.0239434i
$676$	−0.0903891			−0.00347650
$677$	11.0966	+	41.4130i	0.426476	+	1.59163i	0.760679	+	0.649128i	$0.224866\pi$
$677$	11.0966	+	41.4130i	0.426476	+	1.59163i	−0.334203	+	0.942501i	$0.608467\pi$
$678$	−6.06275	−	14.3799i	−0.232839	−	0.552256i
$679$	−8.32430	+	4.80603i	−0.319457	+	0.184439i
$680$	2.52261	+	12.5169i	0.0967378	+	0.480002i
$681$	−19.6197	+	15.2521i	−0.751829	+	0.584461i
$682$	0.909567	−	0.243718i	0.0348291	−	0.00933244i
$683$	−16.7527	−	16.7527i	−0.641024	−	0.641024i	0.309783	−	0.950807i	$-0.399744\pi$
$683$	−16.7527	−	16.7527i	−0.641024	−	0.641024i	−0.950807	+	0.309783i	$0.899744\pi$
$684$	0.606689	+	0.154396i	0.0231973	+	0.00590347i
$685$	43.2582	−	21.4684i	1.65281	−	0.820266i
$686$	1.18014	+	0.681355i	0.0450580	+	0.0260142i
$687$	4.74630	+	3.59468i	0.181083	+	0.137146i
$688$	−1.16451	−	0.312031i	−0.0443967	−	0.0118961i
$689$	6.39324	+	11.0734i	0.243563	+	0.421863i
$690$	24.8440	−	16.9192i	0.945796	−	0.644103i
$691$	0.281016	−	0.486733i	0.0106903	−	0.0185162i	−0.860631	−	0.509230i	$-0.829930\pi$
$691$	0.281016	−	0.486733i	0.0106903	−	0.0185162i	0.871321	+	0.490713i	$0.163264\pi$
$692$	−1.54290	+	1.54290i	−0.0586522	+	0.0586522i
$693$	0.472148	−	0.280585i	0.0179354	−	0.0106586i
$694$		−	42.3359i		−	1.60705i
$695$	−19.8930	−	22.5686i	−0.754586	−	0.856075i
$696$	−28.2172	−	36.2976i	−1.06957	−	1.37586i
$697$	3.73890	−	13.9538i	0.141621	−	0.528537i
$698$	−5.35167	+	19.9727i	−0.202564	+	0.755977i
$699$	−1.58437	+	3.89422i	−0.0599264	+	0.147293i
$700$	0.270324	−	0.662049i	0.0102173	−	0.0250231i
$701$			0.157967i			0.00596631i	0.999996	+	0.00298316i	$0.000949570\pi$
$701$			0.157967i			0.00596631i	−0.999996	+	0.00298316i	$0.999050\pi$
$702$	9.09310	−	23.1825i	0.343197	−	0.874967i
$703$	−5.07766	+	5.07766i	−0.191508	+	0.191508i
$704$	−0.776914	+	1.34566i	−0.0292811	+	0.0507163i
$705$	35.4250	+	30.5182i	1.33418	+	1.14938i
$706$	−21.8683	−	37.8769i	−0.823023	−	1.42552i
$707$	−4.17904	−	1.11977i	−0.157169	−	0.0421133i
$708$	−0.0580181	+	0.463224i	−0.00218045	+	0.0174090i
$709$	8.31063	+	4.79815i	0.312112	+	0.180198i	0.647871	−	0.761750i	$-0.275659\pi$
$709$	8.31063	+	4.79815i	0.312112	+	0.180198i	−0.335759	+	0.941948i	$0.608993\pi$
$710$	10.3994	+	20.9545i	0.390284	+	0.786410i
$711$	0.199556	−	0.0561752i	0.00748394	−	0.00210673i
$712$	−35.7311	−	35.7311i	−1.33908	−	1.33908i
$713$	20.7640	−	5.56371i	0.777619	−	0.208362i
$714$	−0.631222	−	4.57184i	−0.0236229	−	0.171097i
$715$	0.796822	−	1.19906i	0.0297994	−	0.0448425i
$716$	0.0547397	−	0.0316040i	0.00204572	−	0.00118110i
$717$	28.3404	−	37.4197i	1.05839	−	1.39747i
$718$	−12.0039	−	44.7990i	−0.447980	−	1.67188i
$719$	26.3328			0.982048			0.491024	−	0.871146i	$-0.336623\pi$
$719$	26.3328			0.982048			0.491024	+	0.871146i	$0.336623\pi$
$720$	−22.0533	+	11.2933i	−0.821879	+	0.420875i
$721$	−13.6720			−0.509170
$722$	−5.95039	−	22.2072i	−0.221451	−	0.826465i
$723$	21.0789	+	2.64010i	0.783933	+	0.0981864i
$724$	1.64947	−	0.952322i	0.0613021	−	0.0353928i
$725$	5.70459	−	45.0874i	0.211863	−	1.67450i
$726$	23.9756	+	9.75452i	0.889819	+	0.362024i
$727$	−21.8458	+	5.85357i	−0.810216	+	0.217097i	−0.640064	−	0.768321i	$-0.721092\pi$
$727$	−21.8458	+	5.85357i	−0.810216	+	0.217097i	−0.170152	+	0.985418i	$0.554426\pi$
$728$	7.26214	+	7.26214i	0.269153	+	0.269153i
$729$	19.7998	+	18.3567i	0.733324	+	0.679879i
$730$	9.22876	−	27.4141i	0.341572	−	1.01464i
$731$	0.552741	+	0.319125i	0.0204439	+	0.0118033i
$732$	−2.48237	+	1.04660i	−0.0917511	+	0.0386836i
$733$	−17.6531	−	4.73012i	−0.652031	−	0.174711i	−0.0823837	−	0.996601i	$-0.526253\pi$
$733$	−17.6531	−	4.73012i	−0.652031	−	0.174711i	−0.569647	+	0.821890i	$0.692920\pi$
$734$	8.02751	+	13.9041i	0.296301	+	0.513208i
$735$	−1.68226	+	3.48855i	−0.0620512	+	0.128677i
$736$	−2.29935	+	3.98260i	−0.0847553	+	0.146801i
$737$	1.66743	−	1.66743i	0.0614205	−	0.0614205i
$738$	30.2002	−	0.380550i	1.11169	−	0.0140082i
$739$			35.9390i			1.32204i	0.750369	+	0.661019i	$0.229876\pi$
$739$			35.9390i			1.32204i	−0.750369	+	0.661019i	$0.770124\pi$
$740$	−0.0989808	+	1.57087i	−0.00363861	+	0.0577462i
$741$	−8.80396	+	1.21554i	−0.323422	+	0.0446539i
$742$	−1.28233	+	4.78573i	−0.0470759	+	0.175690i
$743$	2.33243	−	8.70475i	0.0855686	−	0.319346i	−0.909853	−	0.414932i	$-0.863806\pi$
$743$	2.33243	−	8.70475i	0.0855686	−	0.319346i	0.995421	+	0.0955851i	$0.0304722\pi$
$744$	−18.9124	+	2.61118i	−0.693362	+	0.0957306i
$745$	20.3998	−	17.9814i	0.747392	−	0.658788i
$746$			28.0401i			1.02662i
$747$	16.5373	−	29.4956i	0.605069	−	1.07919i
$748$	0.0362033	−	0.0362033i	0.00132372	−	0.00132372i
$749$	5.00730	−	8.67290i	0.182963	−	0.316901i
$750$	−25.1035	−	8.13504i	−0.916652	−	0.297050i
$751$	−1.00086	−	1.73353i	−0.0365217	−	0.0632575i	0.847187	−	0.531295i	$-0.178294\pi$
$751$	−1.00086	−	1.73353i	−0.0365217	−	0.0632575i	−0.883709	+	0.468038i	$0.844961\pi$
$752$	43.0716	+	11.5410i	1.57066	+	0.420857i
$753$	1.89860	−	0.800476i	0.0691888	−	0.0291710i
$754$	37.7240	+	21.7799i	1.37383	+	0.793179i
$755$	−30.5457	−	10.2830i	−1.11167	−	0.374237i
$756$	−0.681098	+	0.297322i	−0.0247713	+	0.0108135i
$757$	19.3813	+	19.3813i	0.704427	+	0.704427i	0.965358	−	0.260931i	$-0.0840294\pi$
$757$	19.3813	+	19.3813i	0.704427	+	0.704427i	−0.260931	+	0.965358i	$0.584029\pi$
$758$	−33.3737	+	8.94246i	−1.21219	+	0.324805i
$759$	−1.67279	−	0.680579i	−0.0607186	−	0.0247034i
$760$	7.93523	+	5.27325i	0.287841	+	0.191281i
$761$	−6.70687	+	3.87221i	−0.243124	+	0.140368i	−0.616612	−	0.787267i	$-0.711495\pi$
$761$	−6.70687	+	3.87221i	−0.243124	+	0.140368i	0.373488	+	0.927635i	$0.378162\pi$
$762$	−12.0373	−	1.50765i	−0.436064	−	0.0546163i
$763$	−0.531066	−	1.98197i	−0.0192259	−	0.0717520i
$764$	−1.08533			−0.0392660
$765$	12.8248	−	2.75325i	0.463681	−	0.0995441i
$766$	9.12282			0.329621
$767$	−1.71535	−	6.40178i	−0.0619377	−	0.231155i
$768$	3.57070	−	4.71464i	0.128847	−	0.170125i
$769$	16.4536	−	9.49951i	0.593333	−	0.342561i	−0.173081	−	0.984908i	$-0.555372\pi$
$769$	16.4536	−	9.49951i	0.593333	−	0.342561i	0.766414	+	0.642347i	$0.222039\pi$
$770$	0.546858	−	0.110212i	0.0197074	−	0.00397175i
$771$	−1.33198	−	9.64731i	−0.0479700	−	0.347439i
$772$	3.12297	−	0.836798i	0.112398	−	0.0301170i
$773$	−12.7109	−	12.7109i	−0.457178	−	0.457178i	0.440550	−	0.897728i	$-0.354784\pi$
$773$	−12.7109	−	12.7109i	−0.457178	−	0.457178i	−0.897728	+	0.440550i	$0.854784\pi$
$774$	−0.329101	+	1.29319i	−0.0118293	+	0.0464826i
$775$	−15.0302	−	11.4131i	−0.539902	−	0.409970i
$776$	−24.3096	−	14.0351i	−0.872663	−	0.503832i
$777$	1.05941	−	8.45846i	0.0380061	−	0.303446i
$778$	19.2237	+	5.15099i	0.689205	+	0.184672i
$779$	−5.38962	−	9.33510i	−0.193103	−	0.334465i
$780$	−1.27146	+	1.47589i	−0.0455257	+	0.0528455i
$781$	0.702752	−	1.21720i	0.0251465	−	0.0435549i
$782$	−10.7307	+	10.7307i	−0.383729	+	0.383729i
$783$	−36.9198	+	29.4547i	−1.31941	+	1.05262i
$784$			3.69350i			0.131911i
$785$	35.9763	+	2.26688i	1.28405	+	0.0809083i
$786$	3.57889	−	8.79656i	0.127655	−	0.313763i
$787$	−10.9002	+	40.6801i	−0.388550	+	1.45009i	0.443944	+	0.896054i	$0.353579\pi$
$787$	−10.9002	+	40.6801i	−0.388550	+	1.45009i	−0.832494	+	0.554034i	$0.813088\pi$
$788$	−0.447219	+	1.66904i	−0.0159315	+	0.0594572i
$789$	2.88767	+	3.71459i	0.102804	+	0.132243i
$790$	0.210151	+	0.0132417i	0.00747684	+	0.000471118i
$791$		−	6.61179i		−	0.235088i
$792$	1.39903	+	0.784395i	0.0497124	+	0.0278723i
$793$	27.0437	−	27.0437i	0.960349	−	0.960349i
$794$	−23.0905	+	39.9939i	−0.819450	+	1.41933i
$795$	−13.8345	−	2.62519i	−0.490661	−	0.0931060i
$796$	−1.33941	−	2.31993i	−0.0474743	−	0.0822279i
$797$	−32.6889	−	8.75895i	−1.15790	−	0.310258i	−0.371772	−	0.928324i	$-0.621250\pi$
$797$	−32.6889	−	8.75895i	−1.15790	−	0.310258i	−0.786126	+	0.618066i	$0.787917\pi$
$798$	−2.74527	−	2.07917i	−0.0971814	−	0.0736018i
$799$	−20.4441	−	11.8034i	−0.723259	−	0.417574i
$800$	4.00008	−	0.547166i	0.141424	−	0.0193452i
$801$	−36.2407	+	37.1657i	−1.28050	+	1.31318i
$802$	17.7472	+	17.7472i	0.626676	+	0.626676i
$803$	−1.67870	+	0.449805i	−0.0592399	+	0.0158733i
$804$	−2.51912	+	1.95832i	−0.0888424	+	0.0690648i
$805$	12.4839	−	2.51596i	0.440001	−	0.0886761i
$806$	15.6653	−	9.04439i	0.551788	−	0.318575i
$807$	4.28608	+	10.1659i	0.150877	+	0.357856i
$808$	−3.27009	−	12.2041i	−0.115041	−	0.429340i
$809$	−28.7697			−1.01149			−0.505744	−	0.862684i	$-0.668782\pi$
$809$	−28.7697			−1.01149			−0.505744	+	0.862684i	$0.668782\pi$
$810$	12.8065	+	24.2502i	0.449973	+	0.852064i
$811$	−12.1723			−0.427426			−0.213713	−	0.976897i	$-0.568556\pi$
$811$	−12.1723			−0.427426			−0.213713	+	0.976897i	$0.568556\pi$
$812$	−0.336460	−	1.25569i	−0.0118074	−	0.0440659i
$813$	−15.4087	−	36.5469i	−0.540407	−	1.28176i
$814$	−1.06335	+	0.613925i	−0.0372704	+	0.0215181i
$815$	1.68590	+	1.12034i	0.0590544	+	0.0392437i
$816$	9.87598	−	7.67744i	0.345728	−	0.268764i
$817$	0.460018	−	0.123261i	0.0160940	−	0.00431237i
$818$	18.3747	+	18.3747i	0.642457	+	0.642457i
$819$	7.36571	−	7.55370i	0.257379	−	0.263948i
$820$	−2.23922	−	0.753819i	−0.0781971	−	0.0263245i
$821$	8.44826	+	4.87760i	0.294846	+	0.170230i	0.640125	−	0.768271i	$-0.278882\pi$
$821$	8.44826	+	4.87760i	0.294846	+	0.170230i	−0.345279	+	0.938500i	$0.612216\pi$
$822$	−40.6360	−	30.7763i	−1.41734	−	1.07345i
$823$	−23.0135	−	6.16644i	−0.802200	−	0.214949i	−0.165650	−	0.986185i	$-0.552972\pi$
$823$	−23.0135	−	6.16644i	−0.802200	−	0.214949i	−0.636549	+	0.771236i	$0.719639\pi$
$824$	−19.9632	−	34.5773i	−0.695452	−	1.20456i
$825$	0.427702	+	1.52671i	0.0148907	+	0.0531531i
$826$	1.28404	−	2.22403i	0.0446776	−	0.0773839i
$827$	10.8386	−	10.8386i	0.376896	−	0.376896i	−0.493085	−	0.869981i	$-0.664131\pi$
$827$	10.8386	−	10.8386i	0.376896	−	0.376896i	0.869981	+	0.493085i	$0.164131\pi$
$828$	2.13148	+	1.19506i	0.0740740	+	0.0415311i
$829$		−	36.8679i		−	1.28047i	−0.768177	−	0.640237i	$-0.778836\pi$
$829$		−	36.8679i		−	1.28047i	0.768177	−	0.640237i	$-0.221164\pi$
$830$	25.7657	−	22.7112i	0.894342	−	0.788317i
$831$	−21.5848	−	27.7659i	−0.748767	−	0.963187i
$832$	−7.72534	+	28.8314i	−0.267828	+	0.999548i
$833$	0.506086	−	1.88874i	0.0175348	−	0.0654409i
$834$	−11.9673	+	29.4144i	−0.414393	+	1.01854i
$835$	−1.23444	+	19.5910i	−0.0427194	+	0.677975i
$836$		−	0.0382035i		−	0.00132130i
$837$	2.92701	+	19.3931i	0.101172	+	0.670323i
$838$	6.60810	−	6.60810i	0.228273	−	0.228273i
$839$	5.85897	−	10.1480i	0.202274	−	0.350349i	−0.746987	−	0.664839i	$-0.768500\pi$
$839$	5.85897	−	10.1480i	0.202274	−	0.350349i	0.949261	+	0.314490i	$0.101834\pi$
$840$	−11.2792	+	0.839277i	−0.389168	+	0.0289578i
$841$	−26.8083	−	46.4333i	−0.924423	−	1.60115i
$842$	4.03311	+	1.08067i	0.138990	+	0.0372423i
$843$	4.02008	−	32.0969i	0.138459	−	1.10547i
$844$	0.587508	+	0.339198i	0.0202228	+	0.0116757i
$845$	−0.450874	+	1.33932i	−0.0155106	+	0.0460741i
$846$	12.1724	−	47.8307i	0.418495	−	1.64445i
$847$	7.75447	+	7.75447i	0.266447	+	0.266447i
$848$	−12.9713	+	3.47564i	−0.445435	+	0.119354i
$849$	−4.62244	−	33.4797i	−0.158642	−	1.14902i
$850$	13.2176	+	1.67233i	0.453360	+	0.0573605i
$851$	−24.2747	+	14.0150i	−0.832124	+	0.480427i
$852$	−1.14821	+	1.51606i	−0.0393372	+	0.0519395i
$853$	−0.881163	−	3.28854i	−0.0301704	−	0.112598i	0.949199	−	0.314678i	$-0.101896\pi$
$853$	−0.881163	−	3.28854i	−0.0301704	−	0.112598i	−0.979369	+	0.202080i	$0.935230\pi$
$854$	14.8195			0.507113
$855$	5.31399	−	8.21936i	0.181735	−	0.281096i
$856$	29.2458			0.999601
$857$	−5.93048	−	22.1328i	−0.202581	−	0.756044i	−0.990173	−	0.139846i	$-0.955339\pi$
$857$	−5.93048	−	22.1328i	−0.202581	−	0.756044i	0.787592	−	0.616197i	$-0.211328\pi$
$858$	−1.50787	−	0.188859i	−0.0514780	−	0.00644754i
$859$	−19.0841	+	11.0182i	−0.651141	+	0.375937i	−0.788893	−	0.614530i	$-0.789346\pi$
$859$	−19.0841	+	11.0182i	−0.651141	+	0.375937i	0.137752	+	0.990467i	$0.456012\pi$
$860$	0.0577759	−	0.0869417i	0.00197014	−	0.00296469i
$861$	11.8528	+	4.82232i	0.403941	+	0.164344i
$862$	−16.6547	+	4.46262i	−0.567262	+	0.151997i
$863$	25.1266	+	25.1266i	0.855319	+	0.855319i	0.990782	−	0.135463i	$-0.0432523\pi$
$863$	25.1266	+	25.1266i	0.855319	+	0.855319i	−0.135463	+	0.990782i	$0.543252\pi$
$864$	−3.37636	−	2.49083i	−0.114866	−	0.0847396i
$865$	15.1654	+	30.5578i	0.515639	+	1.03900i
$866$	19.5205	+	11.2702i	0.663333	+	0.382975i
$867$	21.0298	−	8.86644i	0.714208	−	0.301120i
$868$	−0.521439	−	0.139719i	−0.0176988	−	0.00474238i
$869$	−0.00632565	−	0.0109563i	−0.000214583	−	0.000371669i
$870$	−45.2878	+	15.8201i	−1.53540	+	0.536351i
$871$	22.6491	−	39.2294i	0.767435	−	1.32924i
$872$	4.23709	−	4.23709i	0.143486	−	0.143486i
$873$	−14.1023	+	25.1526i	−0.477291	+	0.851286i
$874$			11.3236i			0.383025i
$875$	−8.46137	−	7.30788i	−0.286047	−	0.247052i
$876$	2.32949	−	0.321626i	0.0787061	−	0.0108667i
$877$	5.57305	−	20.7989i	0.188188	−	0.702329i	−0.805737	−	0.592274i	$-0.798230\pi$
$877$	5.57305	−	20.7989i	0.188188	−	0.702329i	0.993925	−	0.110055i	$-0.0351029\pi$
$878$	−7.35019	+	27.4313i	−0.248057	+	0.925761i
$879$	−37.5512	+	5.18459i	−1.26657	+	0.174872i
$880$	0.999802	+	1.13427i	0.0337033	+	0.0382362i
$881$			52.4240i			1.76621i	0.469177	+	0.883104i	$0.344551\pi$
$881$			52.4240i			1.76621i	−0.469177	+	0.883104i	$0.655449\pi$
$882$	4.08780	−	0.0515100i	0.137644	−	0.00173443i
$883$	−36.6950	+	36.6950i	−1.23488	+	1.23488i	−0.272819	+	0.962065i	$0.587956\pi$
$883$	−36.6950	+	36.6950i	−1.23488	+	1.23488i	−0.962065	+	0.272819i	$0.912044\pi$
$884$	0.491758	−	0.851750i	0.0165396	−	0.0286474i
$885$	6.57434	+	3.17030i	0.220994	+	0.106569i
$886$	8.14324	+	14.1045i	0.273577	+	0.473850i
$887$	17.1253	+	4.58871i	0.575011	+	0.154074i	0.534594	−	0.845109i	$-0.320465\pi$
$887$	17.1253	+	4.58871i	0.575011	+	0.154074i	0.0404174	+	0.999183i	$0.487131\pi$
$888$	22.9389	−	9.67138i	0.769780	−	0.324550i
$889$	−4.45117	−	2.56988i	−0.149287	−	0.0861912i
$890$	−47.2290	+	23.4391i	−1.58312	+	0.785680i
$891$	0.787625	−	1.44724i	0.0263864	−	0.0484844i
$892$	0.513722	+	0.513722i	0.0172007	+	0.0172007i
$893$	−17.0146	+	4.55904i	−0.569370	+	0.152562i
$894$	−26.5878	−	10.8173i	−0.889228	−	0.361784i
$895$	−0.195236	−	0.968740i	−0.00652603	−	0.0323814i
$896$	−8.61769	+	4.97543i	−0.287897	+	0.166217i
$897$	−34.4225	−	4.31136i	−1.14933	−	0.143952i
$898$	1.81377	+	6.76908i	0.0605263	+	0.225887i
$899$	−34.3076			−1.14422
$900$	−0.317509	−	2.12171i	−0.0105836	−	0.0707236i
$901$	7.10933			0.236846
$902$	−0.477036	−	1.78032i	−0.0158836	−	0.0592783i
$903$	−0.341336	+	0.450688i	−0.0113589	+	0.0149980i
$904$	16.7217	−	9.65426i	0.556155	−	0.321096i
$905$	−5.88305	−	29.1911i	−0.195559	−	0.970344i
$906$	4.65298	+	33.7008i	0.154585	+	1.11964i
$907$	11.3958	−	3.05350i	0.378392	−	0.101390i	−0.0646096	−	0.997911i	$-0.520580\pi$
$907$	11.3958	−	3.05350i	0.378392	−	0.101390i	0.443002	+	0.896521i	$0.353914\pi$
$908$	−1.45100	−	1.45100i	−0.0481531	−	0.0481531i
$909$	−12.4938	+	3.51701i	−0.414393	+	0.116652i
$910$	9.59902	−	4.76386i	0.318205	−	0.157920i
$911$	−4.20936	−	2.43027i	−0.139462	−	0.0805185i	0.428645	−	0.903473i	$-0.358991\pi$
$911$	−4.20936	−	2.43027i	−0.139462	−	0.0805185i	−0.568108	+	0.822954i	$0.692324\pi$
$912$	1.16000	−	9.26162i	0.0384115	−	0.306683i
$913$	−1.99328	−	0.534097i	−0.0659678	−	0.0176760i
$914$	18.6680	+	32.3340i	0.617483	+	1.06951i
$915$	3.12540	+	42.0027i	0.103323	+	1.38857i
$916$	−0.245819	+	0.425771i	−0.00812210	+	0.0140679i
$917$	2.84508	−	2.84508i	0.0939529	−	0.0939529i
$918$	−8.63479	−	10.8232i	−0.284990	−	0.357220i
$919$			34.7802i			1.14729i	0.819103	+	0.573646i	$0.194472\pi$
$919$			34.7802i			1.14729i	−0.819103	+	0.573646i	$0.805528\pi$
$920$	24.5916	+	27.8990i	0.810760	+	0.919803i
$921$	−1.92333	+	4.72736i	−0.0633760	+	0.155772i
$922$	6.91394	−	25.8032i	0.227698	−	0.849782i
$923$	6.98790	−	26.0792i	0.230010	−	0.858408i
$924$	0.0278346	+	0.0358055i	0.000915692	+	0.00117791i
$925$	22.7823	+	9.30234i	0.749077	+	0.305859i
$926$			26.4648i			0.869686i
$927$	−35.2596	+	20.9539i	−1.15808	+	0.688215i
$928$	5.18971	−	5.18971i	0.170360	−	0.170360i
$929$	2.61251	−	4.52500i	0.0857137	−	0.148461i	−0.819981	−	0.572390i	$-0.806016\pi$
$929$	2.61251	−	4.52500i	0.0857137	−	0.148461i	0.905695	+	0.423930i	$0.139350\pi$
$930$	−3.71381	+	19.5715i	−0.121781	+	0.641774i
$931$	−0.729522	−	1.26357i	−0.0239091	−	0.0414118i
$932$	−0.335327	−	0.0898507i	−0.0109840	−	0.00294316i
$933$	15.1199	+	11.4513i	0.495004	+	0.374899i
$934$	23.9590	+	13.8327i	0.783963	+	0.452621i
$935$	−0.355848	−	0.717023i	−0.0116375	−	0.0234492i
$936$	29.8589	+	7.59877i	0.975970	+	0.248374i
$937$	−2.93968	−	2.93968i	−0.0960353	−	0.0960353i	0.657457	−	0.753492i	$-0.271632\pi$
$937$	−2.93968	−	2.93968i	−0.0960353	−	0.0960353i	−0.753492	+	0.657457i	$0.771632\pi$
$938$	16.9542	−	4.54287i	0.553575	−	0.148330i
$939$	−16.4289	+	12.7716i	−0.536136	+	0.416784i
$940$	−2.13694	+	3.21569i	−0.0696993	+	0.104884i
$941$	−25.1347	+	14.5115i	−0.819368	+	0.473063i	−0.850199	−	0.526462i	$-0.823518\pi$
$941$	−25.1347	+	14.5115i	−0.819368	+	0.473063i	0.0308303	+	0.999525i	$0.490185\pi$
$942$	−14.7823	−	35.0612i	−0.481634	−	1.14236i
$943$	−10.8900	−	40.6421i	−0.354627	−	1.32349i
$944$	6.96057			0.226547
$945$	1.00810	+	11.5751i	0.0327936	+	0.376539i
$946$	0.0814325			0.00264760
$947$	13.7165	+	51.1907i	0.445727	+	1.66348i	0.714010	+	0.700135i	$0.246877\pi$
$947$	13.7165	+	51.1907i	0.445727	+	1.66348i	−0.268283	+	0.963340i	$0.586456\pi$
$948$	0.00665051	+	0.0157739i	0.000215998	+	0.000512313i
$949$	−28.9119	+	16.6923i	−0.938521	+	0.541855i
$950$	7.85630	−	6.09157i	0.254892	−	0.197637i
$951$	−7.89502	+	6.13747i	−0.256013	+	0.199021i
$952$	5.51571	−	1.47793i	0.178765	−	0.0479000i
$953$	22.7166	+	22.7166i	0.735864	+	0.735864i	0.971775	−	0.235911i	$-0.0758074\pi$
$953$	22.7166	+	22.7166i	0.735864	+	0.735864i	−0.235911	+	0.971775i	$0.575807\pi$
$954$	4.02759	+	14.3076i	0.130398	+	0.463225i
$955$	−5.41380	+	16.0817i	−0.175187	+	0.520392i
$956$	3.35677	+	1.93803i	0.108566	+	0.0626805i
$957$	2.29762	+	1.74014i	0.0742715	+	0.0562507i
$958$	−25.6759	−	6.87984i	−0.829551	−	0.222278i
$959$	−10.7985	−	18.7036i	−0.348703	−	0.603971i
$960$	−18.5028	−	27.1693i	−0.597174	−	0.876886i
$961$	8.37668	−	14.5088i	0.270215	−	0.468027i
$962$	−16.6782	+	16.6782i	−0.537726	+	0.537726i
$963$	−0.378548	−	30.0414i	−0.0121986	−	0.968071i
$964$			1.75417i			0.0564980i
$965$	3.17876	−	50.4482i	0.102328	−	1.62398i
$966$	−8.25022	−	10.6128i	−0.265446	−	0.341461i
$967$	−14.6518	+	54.6811i	−0.471169	+	1.75843i	0.164412	+	0.986392i	$0.447427\pi$
$967$	−14.6518	+	54.6811i	−0.471169	+	1.75843i	−0.635581	+	0.772034i	$0.719239\pi$
$968$	−8.28884	+	30.9344i	−0.266413	+	0.994268i
$969$	−1.86222	+	4.57715i	−0.0598232	+	0.147039i
$970$	−21.9719	+	19.3671i	−0.705475	+	0.621840i
$971$			50.3139i			1.61465i	0.590107	+	0.807325i	$0.299086\pi$
$971$			50.3139i			1.61465i	−0.590107	+	0.807325i	$0.700914\pi$
$972$	−1.30085	+	1.81065i	−0.0417248	+	0.0580766i
$973$	−9.51354	+	9.51354i	−0.304990	+	0.304990i
$974$	−28.6238	+	49.5778i	−0.917165	+	1.58858i
$975$	15.5265	+	26.2017i	0.497247	+	0.839125i
$976$	20.0835	+	34.7856i	0.642856	+	1.11346i
$977$	−29.1091	−	7.79975i	−0.931282	−	0.249536i	−0.238881	−	0.971049i	$-0.576781\pi$
$977$	−29.1091	−	7.79975i	−0.931282	−	0.249536i	−0.692401	+	0.721513i	$0.743447\pi$
$978$	0.265537	−	2.12009i	0.00849095	−	0.0677928i
$979$	2.74343	+	1.58392i	0.0876804	+	0.0506223i
$980$	−0.303094	−	0.102034i	−0.00968198	−	0.00325937i
$981$	−4.40720	−	4.29751i	−0.140711	−	0.137209i
$982$	18.8370	+	18.8370i	0.601111	+	0.601111i
$983$	7.44685	−	1.99538i	0.237518	−	0.0636426i	−0.138097	−	0.990419i	$-0.544098\pi$
$983$	7.44685	−	1.99538i	0.237518	−	0.0636426i	0.375614	+	0.926776i	$0.377432\pi$
$984$	5.11094	+	37.0178i	0.162931	+	1.18008i
$985$	22.5000	+	14.9520i	0.716908	+	0.476411i
$986$	20.9747	−	12.1097i	0.667970	−	0.385653i
$987$	12.6249	−	16.6695i	0.401854	−	0.530595i
$988$	−0.189941	−	0.708868i	−0.00604282	−	0.0225521i
$989$	1.85898			0.0591121
$990$	1.24142	−	1.12236i	0.0394548	−	0.0356708i
$991$	8.12399			0.258067			0.129034	−	0.991640i	$-0.458813\pi$
$991$	8.12399			0.258067			0.129034	+	0.991640i	$0.458813\pi$
$992$	−0.788818	−	2.94391i	−0.0250450	−	0.0934692i
$993$	56.6550	+	7.09595i	1.79789	+	0.225183i
$994$	9.06014	−	5.23087i	0.287370	−	0.165913i
$995$	−41.0564	+	8.27435i	−1.30158	+	0.262315i
$996$	2.58640	+	1.05228i	0.0819531	+	0.0333428i
$997$	45.2386	−	12.1217i	1.43272	−	0.383897i	0.542743	−	0.839899i	$-0.317386\pi$
$997$	45.2386	−	12.1217i	1.43272	−	0.383897i	0.889979	+	0.456002i	$0.150719\pi$
$998$	14.1005	+	14.1005i	0.446345	+	0.446345i
$999$	−10.2314	−	23.4378i	−0.323707	−	0.741539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cc.a.92.10	✓	144
3.2	odd	2		945.2.cf.a.197.27		144
5.3	odd	4	inner	315.2.cc.a.218.10	yes	144
9.4	even	3		945.2.cf.a.827.27		144
9.5	odd	6	inner	315.2.cc.a.302.10	yes	144
15.8	even	4		945.2.cf.a.8.27		144
45.13	odd	12		945.2.cf.a.638.27		144
45.23	even	12	inner	315.2.cc.a.113.10	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cc.a.92.10	✓	144	1.1	even	1	trivial
315.2.cc.a.113.10	yes	144	45.23	even	12	inner
315.2.cc.a.218.10	yes	144	5.3	odd	4	inner
315.2.cc.a.302.10	yes	144	9.5	odd	6	inner
945.2.cf.a.8.27		144	15.8	even	4
945.2.cf.a.197.27		144	3.2	odd	2
945.2.cf.a.638.27		144	45.13	odd	12
945.2.cf.a.827.27		144	9.4	even	3

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.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.352695 - 1.31628i) q^{2} +(-0.672895 - 1.59600i) q^{3} +(0.123861 - 0.0715111i) q^{4} +(-0.441766 - 2.19200i) q^{5} +(-1.86345 + 1.44862i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-2.06498 - 2.06498i) q^{8} +(-2.09442 + 2.14788i) q^{9} +O(q^{10})\)	\(q+(-0.352695 - 1.31628i) q^{2} +(-0.672895 - 1.59600i) q^{3} +(0.123861 - 0.0715111i) q^{4} +(-0.441766 - 2.19200i) q^{5} +(-1.86345 + 1.44862i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-2.06498 - 2.06498i) q^{8} +(-2.09442 + 2.14788i) q^{9} +(-2.72946 + 1.35459i) q^{10} +(0.158548 + 0.0915380i) q^{11} +(-0.197477 - 0.149562i) q^{12} +(3.39699 + 0.910219i) q^{13} +(0.681355 + 1.18014i) q^{14} +(-3.20116 + 2.18004i) q^{15} +(-1.84675 + 3.19866i) q^{16} +(1.38265 - 1.38265i) q^{17} +(3.56590 + 1.99929i) q^{18} -1.45904i q^{19} +(-0.211470 - 0.239911i) q^{20} +(1.06304 + 1.36746i) q^{21} +(0.0645700 - 0.240979i) q^{22} +(1.47404 - 5.50117i) q^{23} +(-1.90619 + 4.68521i) q^{24} +(-4.60969 + 1.93670i) q^{25} -4.79240i q^{26} +(4.83734 + 1.89740i) q^{27} +(-0.101132 + 0.101132i) q^{28} +(-4.54468 + 7.87162i) q^{29} +(3.99857 + 3.44472i) q^{30} +(1.88724 + 3.26879i) q^{31} +(-0.779952 - 0.208988i) q^{32} +(0.0394080 - 0.314639i) q^{33} +(-2.30761 - 1.33230i) q^{34} +(0.994044 + 2.00297i) q^{35} +(-0.105820 + 0.415813i) q^{36} +(-3.48013 - 3.48013i) q^{37} +(-1.92050 + 0.514598i) q^{38} +(-0.833107 - 6.03407i) q^{39} +(-3.61418 + 5.43865i) q^{40} +(6.39810 - 3.69394i) q^{41} +(1.42502 - 1.88155i) q^{42} +(0.0844810 + 0.315287i) q^{43} +0.0261839 q^{44} +(5.63339 + 3.64210i) q^{45} -7.76095 q^{46} +(-3.12468 - 11.6614i) q^{47} +(6.34773 + 0.795044i) q^{48} +(0.866025 - 0.500000i) q^{49} +(4.17505 + 5.38456i) q^{50} +(-3.13709 - 1.27633i) q^{51} +(0.485845 - 0.130182i) q^{52} +(2.57090 + 2.57090i) q^{53} +(0.791393 - 7.03648i) q^{54} +(0.130609 - 0.387976i) q^{55} +(2.52907 + 1.46016i) q^{56} +(-2.32863 + 0.981784i) q^{57} +(11.9641 + 3.20578i) q^{58} +(-0.942273 - 1.63206i) q^{59} +(-0.240601 + 0.498941i) q^{60} +(5.43752 - 9.41806i) q^{61} +(3.63701 - 3.63701i) q^{62} +(1.46715 - 2.61677i) q^{63} +8.48734i q^{64} +(0.494523 - 7.84828i) q^{65} +(-0.428050 + 0.0590997i) q^{66} +(3.33370 - 12.4415i) q^{67} +(0.0723815 - 0.270132i) q^{68} +(-9.77174 + 1.34916i) q^{69} +(2.28586 - 2.01487i) q^{70} -7.67717i q^{71} +(8.76026 - 0.110387i) q^{72} +(-6.71246 + 6.71246i) q^{73} +(-3.35339 + 5.80824i) q^{74} +(6.19281 + 6.05386i) q^{75} +(-0.104338 - 0.180718i) q^{76} +(-0.176838 - 0.0473836i) q^{77} +(-7.64867 + 3.22479i) q^{78} +(-0.0598459 - 0.0345520i) q^{79} +(7.82729 + 2.63500i) q^{80} +(-0.226780 - 8.99714i) q^{81} +(-7.11883 - 7.11883i) q^{82} +(-10.8877 + 2.91735i) q^{83} +(0.229458 + 0.0933553i) q^{84} +(-3.64158 - 2.41996i) q^{85} +(0.385209 - 0.222401i) q^{86} +(15.6212 + 1.95653i) q^{87} +(-0.138375 - 0.516423i) q^{88} +17.3034 q^{89} +(2.80715 - 8.69965i) q^{90} -3.51682 q^{91} +(-0.210820 - 0.786791i) q^{92} +(3.94707 - 5.21158i) q^{93} +(-14.2476 + 8.22587i) q^{94} +(-3.19822 + 0.644556i) q^{95} +(0.191282 + 1.38543i) q^{96} +(9.28455 - 2.48779i) q^{97} +(-0.963581 - 0.963581i) q^{98} +(-0.528680 + 0.148824i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3}+O(q^{10}) \) 144 * q + 4 * q^3	\( 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) \) 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more