LMFDB - Embedded newform 336.2.bo.a.5.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.12
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15113 + 0.821523i) q^{2} +(0.961162 - 1.44089i) q^{3} +(0.650200 - 1.89136i) q^{4} +(-1.84766 + 0.495078i) q^{5} +(0.0773035 + 2.44827i) q^{6} +(-2.64062 + 0.164729i) q^{7} +(0.805330 + 2.71135i) q^{8} +(-1.15234 - 2.76986i) q^{9} +O(q^{10})$	\(q+(-1.15113 + 0.821523i) q^{2} +(0.961162 - 1.44089i) q^{3} +(0.650200 - 1.89136i) q^{4} +(-1.84766 + 0.495078i) q^{5} +(0.0773035 + 2.44827i) q^{6} +(-2.64062 + 0.164729i) q^{7} +(0.805330 + 2.71135i) q^{8} +(-1.15234 - 2.76986i) q^{9} +(1.72017 - 2.08779i) q^{10} +(-2.91705 - 0.781622i) q^{11} +(-2.10030 - 2.75477i) q^{12} +(1.32862 + 1.32862i) q^{13} +(2.90437 - 2.35895i) q^{14} +(-1.06254 + 3.13812i) q^{15} +(-3.15448 - 2.45952i) q^{16} +(-1.97936 - 3.42835i) q^{17} +(3.60199 + 2.24180i) q^{18} +(-2.22214 + 0.595421i) q^{19} +(-0.264976 + 3.81648i) q^{20} +(-2.30071 + 3.96318i) q^{21} +(4.00003 - 1.49668i) q^{22} +(-3.20186 + 5.54578i) q^{23} +(4.68082 + 1.44566i) q^{24} +(-1.16140 + 0.670533i) q^{25} +(-2.62090 - 0.437922i) q^{26} +(-5.09865 - 1.00189i) q^{27} +(-1.40537 + 5.10146i) q^{28} +(-3.37288 - 3.37288i) q^{29} +(-1.35491 - 4.48529i) q^{30} +(-0.517256 + 0.298638i) q^{31} +(5.65177 + 0.239754i) q^{32} +(-3.92999 + 3.45189i) q^{33} +(5.09497 + 2.32039i) q^{34} +(4.79740 - 1.61167i) q^{35} +(-5.98805 + 0.378520i) q^{36} +(8.86814 - 2.37621i) q^{37} +(2.06882 - 2.51095i) q^{38} +(3.19141 - 0.637378i) q^{39} +(-2.83030 - 4.61095i) q^{40} -1.57438i q^{41} +(-0.607429 - 6.45221i) q^{42} +(-9.17974 - 9.17974i) q^{43} +(-3.37500 + 5.00899i) q^{44} +(3.50042 + 4.54725i) q^{45} +(-0.870232 - 9.01431i) q^{46} +(0.138984 - 0.240727i) q^{47} +(-6.57587 + 2.18126i) q^{48} +(6.94573 - 0.869970i) q^{49} +(0.786061 - 1.72599i) q^{50} +(-6.84237 - 0.443158i) q^{51} +(3.37676 - 1.64903i) q^{52} +(2.38152 + 0.638126i) q^{53} +(6.69228 - 3.03535i) q^{54} +5.77668 q^{55} +(-2.57321 - 7.02699i) q^{56} +(-1.27790 + 3.77416i) q^{57} +(6.65352 + 1.11172i) q^{58} +(3.11683 - 11.6322i) q^{59} +(5.24445 + 4.05006i) q^{60} +(-0.759622 + 0.203540i) q^{61} +(0.350091 - 0.768709i) q^{62} +(3.49916 + 7.12432i) q^{63} +(-6.70289 + 4.36707i) q^{64} +(-3.11260 - 1.79706i) q^{65} +(1.68812 - 7.20216i) q^{66} +(6.82801 + 1.82956i) q^{67} +(-7.77123 + 1.51457i) q^{68} +(4.91337 + 9.94392i) q^{69} +(-4.19840 + 5.79642i) q^{70} -12.7692 q^{71} +(6.58206 - 5.35504i) q^{72} +(6.33536 + 10.9732i) q^{73} +(-8.25627 + 10.0207i) q^{74} +(-0.150125 + 2.31794i) q^{75} +(-0.318681 + 4.59001i) q^{76} +(7.83158 + 1.58344i) q^{77} +(-3.15011 + 3.35552i) q^{78} +(-1.42550 + 2.46903i) q^{79} +(7.04605 + 2.98264i) q^{80} +(-6.34424 + 6.38362i) q^{81} +(1.29339 + 1.81231i) q^{82} +(9.60276 - 9.60276i) q^{83} +(5.99987 + 6.92832i) q^{84} +(5.35448 + 5.35448i) q^{85} +(18.1084 + 3.02571i) q^{86} +(-8.10183 + 1.61807i) q^{87} +(-0.229937 - 8.53863i) q^{88} +(10.9145 + 6.30150i) q^{89} +(-7.76510 - 2.35880i) q^{90} +(-3.72724 - 3.28951i) q^{91} +(8.40722 + 9.66173i) q^{92} +(-0.0668618 + 1.03235i) q^{93} +(0.0377743 + 0.391286i) q^{94} +(3.81097 - 2.20027i) q^{95} +(5.77772 - 7.91315i) q^{96} +4.81796i q^{97} +(-7.28074 + 6.70752i) q^{98} +(1.19644 + 8.98052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.15113	+	0.821523i	−0.813972	+	0.580904i
$2$	−1.15113	+	0.821523i	−0.813972	+	0.580904i
$3$	0.961162	−	1.44089i	0.554927	−	0.831899i
$3$	0.961162	−	1.44089i	0.554927	−	0.831899i
$4$	0.650200	−	1.89136i	0.325100	−	0.945680i
$5$	−1.84766	+	0.495078i	−0.826297	+	0.221406i	−0.647097	−	0.762407i	$-0.724017\pi$
$5$	−1.84766	+	0.495078i	−0.826297	+	0.221406i	−0.179199	+	0.983813i	$0.557351\pi$
$6$	0.0773035	+	2.44827i	0.0315590	+	0.999502i
$7$	−2.64062	+	0.164729i	−0.998060	+	0.0622615i
$7$	−2.64062	+	0.164729i	−0.998060	+	0.0622615i
$8$	0.805330	+	2.71135i	0.284727	+	0.958609i
$9$	−1.15234	−	2.76986i	−0.384112	−	0.923286i
$10$	1.72017	−	2.08779i	0.543967	−	0.660217i
$11$	−2.91705	−	0.781622i	−0.879525	−	0.235668i	−0.209323	−	0.977847i	$-0.567126\pi$
$11$	−2.91705	−	0.781622i	−0.879525	−	0.235668i	−0.670202	+	0.742179i	$0.733793\pi$
$12$	−2.10030	−	2.75477i	−0.606303	−	0.795234i
$13$	1.32862	+	1.32862i	0.368492	+	0.368492i	0.866927	−	0.498435i	$-0.166092\pi$
$13$	1.32862	+	1.32862i	0.368492	+	0.368492i	−0.498435	+	0.866927i	$0.666092\pi$
$14$	2.90437	−	2.35895i	0.776225	−	0.630457i
$15$	−1.06254	+	3.13812i	−0.274347	+	0.810259i
$16$	−3.15448	−	2.45952i	−0.788620	−	0.614881i
$17$	−1.97936	−	3.42835i	−0.480065	−	0.831498i	0.519673	−	0.854365i	$-0.326054\pi$
$17$	−1.97936	−	3.42835i	−0.480065	−	0.831498i	−0.999739	+	0.0228674i	$0.992720\pi$
$18$	3.60199	+	2.24180i	0.848998	+	0.528397i
$19$	−2.22214	+	0.595421i	−0.509794	+	0.136599i	−0.504542	−	0.863387i	$-0.668339\pi$
$19$	−2.22214	+	0.595421i	−0.509794	+	0.136599i	−0.00525229	+	0.999986i	$0.501672\pi$
$20$	−0.264976	+	3.81648i	−0.0592504	+	0.853391i
$21$	−2.30071	+	3.96318i	−0.502055	+	0.864836i
$22$	4.00003	−	1.49668i	0.852809	−	0.319093i
$23$	−3.20186	+	5.54578i	−0.667634	+	1.15638i	0.310931	+	0.950433i	$0.399359\pi$
$23$	−3.20186	+	5.54578i	−0.667634	+	1.15638i	−0.978564	+	0.205943i	$0.933974\pi$
$24$	4.68082	+	1.44566i	0.955468	+	0.295093i
$25$	−1.16140	+	0.670533i	−0.232280	+	0.134107i
$26$	−2.62090	−	0.437922i	−0.514001	−	0.0858835i
$27$	−5.09865	−	1.00189i	−0.981235	−	0.192814i
$28$	−1.40537	+	5.10146i	−0.265590	+	0.964086i
$29$	−3.37288	−	3.37288i	−0.626328	−	0.626328i	0.320814	−	0.947142i	$-0.396043\pi$
$29$	−3.37288	−	3.37288i	−0.626328	−	0.626328i	−0.947142	+	0.320814i	$0.896043\pi$
$30$	−1.35491	−	4.48529i	−0.247372	−	0.818898i
$31$	−0.517256	+	0.298638i	−0.0929019	+	0.0536369i	−0.545731	−	0.837960i	$-0.683748\pi$
$31$	−0.517256	+	0.298638i	−0.0929019	+	0.0536369i	0.452829	+	0.891597i	$0.350415\pi$
$32$	5.65177	+	0.239754i	0.999101	+	0.0423829i
$33$	−3.92999	+	3.45189i	−0.684124	+	0.600898i
$34$	5.09497	+	2.32039i	0.873781	+	0.397944i
$35$	4.79740	−	1.61167i	0.810909	−	0.272422i
$36$	−5.98805	+	0.378520i	−0.998008	+	0.0630866i
$37$	8.86814	−	2.37621i	1.45791	−	0.390647i	0.559144	−	0.829070i	$-0.311130\pi$
$37$	8.86814	−	2.37621i	1.45791	−	0.390647i	0.898768	+	0.438424i	$0.144463\pi$
$38$	2.06882	−	2.51095i	0.335607	−	0.407329i
$39$	3.19141	−	0.637378i	0.511035	−	0.102062i
$40$	−2.83030	−	4.61095i	−0.447510	−	0.729055i
$41$		−	1.57438i		−	0.245876i	−0.992414	−	0.122938i	$-0.960768\pi$
$41$		−	1.57438i		−	0.245876i	0.992414	−	0.122938i	$-0.0392317\pi$
$42$	−0.607429	−	6.45221i	−0.0937283	−	0.995598i
$43$	−9.17974	−	9.17974i	−1.39990	−	1.39990i	−0.800306	−	0.599592i	$-0.795329\pi$
$43$	−9.17974	−	9.17974i	−1.39990	−	1.39990i	−0.599592	−	0.800306i	$-0.704671\pi$
$44$	−3.37500	+	5.00899i	−0.508800	+	0.755133i
$45$	3.50042	+	4.54725i	0.521811	+	0.677864i
$46$	−0.870232	−	9.01431i	−0.128309	−	1.32909i
$47$	0.138984	−	0.240727i	0.0202728	−	0.0351136i	−0.855711	−	0.517454i	$-0.826880\pi$
$47$	0.138984	−	0.240727i	0.0202728	−	0.0351136i	0.875984	+	0.482340i	$0.160213\pi$
$48$	−6.57587	+	2.18126i	−0.949145	+	0.314838i
$49$	6.94573	−	0.869970i	0.992247	−	0.124281i
$50$	0.786061	−	1.72599i	0.111166	−	0.244091i
$51$	−6.84237	−	0.443158i	−0.958124	−	0.0620545i
$52$	3.37676	−	1.64903i	0.468273	−	0.228679i
$53$	2.38152	+	0.638126i	0.327127	+	0.0876534i	0.418645	−	0.908150i	$-0.362505\pi$
$53$	2.38152	+	0.638126i	0.327127	+	0.0876534i	−0.0915179	+	0.995803i	$0.529172\pi$
$54$	6.69228	−	3.03535i	0.910704	−	0.413059i
$55$	5.77668			0.778927
$56$	−2.57321	−	7.02699i	−0.343859	−	0.939021i
$57$	−1.27790	+	3.77416i	−0.169262	+	0.499900i
$58$	6.65352	+	1.11172i	0.873649	+	0.145976i
$59$	3.11683	−	11.6322i	0.405776	−	1.51438i	−0.396843	−	0.917887i	$-0.629894\pi$
$59$	3.11683	−	11.6322i	0.405776	−	1.51438i	0.802619	−	0.596492i	$-0.203439\pi$
$60$	5.24445	+	4.05006i	0.677055	+	0.522860i
$61$	−0.759622	+	0.203540i	−0.0972596	+	0.0260606i	−0.307121	−	0.951671i	$-0.599366\pi$
$61$	−0.759622	+	0.203540i	−0.0972596	+	0.0260606i	0.209861	+	0.977731i	$0.432699\pi$
$62$	0.350091	−	0.768709i	0.0444616	−	0.0976261i
$63$	3.49916	+	7.12432i	0.440852	+	0.897580i
$64$	−6.70289	+	4.36707i	−0.837861	+	0.545884i
$65$	−3.11260	−	1.79706i	−0.386070	−	0.222898i
$66$	1.68812	−	7.20216i	0.207794	−	0.886524i
$67$	6.82801	+	1.82956i	0.834174	+	0.223516i	0.650534	−	0.759477i	$-0.274545\pi$
$67$	6.82801	+	1.82956i	0.834174	+	0.223516i	0.183640	+	0.982994i	$0.441212\pi$
$68$	−7.77123	+	1.51457i	−0.942400	+	0.183668i
$69$	4.91337	+	9.94392i	0.591500	+	1.19711i
$70$	−4.19840	+	5.79642i	−0.501805	+	0.692805i
$71$	−12.7692			−1.51542			−0.757710	−	0.652592i	$-0.773682\pi$
$71$	−12.7692			−1.51542			−0.757710	+	0.652592i	$0.773682\pi$
$72$	6.58206	−	5.35504i	0.775703	−	0.631098i
$73$	6.33536	+	10.9732i	0.741498	+	1.28431i	0.951813	+	0.306679i	$0.0992177\pi$
$73$	6.33536	+	10.9732i	0.741498	+	1.28431i	−0.210315	+	0.977634i	$0.567449\pi$
$74$	−8.25627	+	10.0207i	−0.959771	+	1.16488i
$75$	−0.150125	+	2.31794i	−0.0173350	+	0.267653i
$76$	−0.318681	+	4.59001i	−0.0365553	+	0.526510i
$77$	7.83158	+	1.58344i	0.892492	+	0.180450i
$78$	−3.15011	+	3.35552i	−0.356680	+	0.379938i
$79$	−1.42550	+	2.46903i	−0.160381	+	0.277788i	−0.935005	−	0.354634i	$-0.884606\pi$
$79$	−1.42550	+	2.46903i	−0.160381	+	0.277788i	0.774624	+	0.632421i	$0.217939\pi$
$80$	7.04605	+	2.98264i	0.787772	+	0.333469i
$81$	−6.34424	+	6.38362i	−0.704916	+	0.709291i
$82$	1.29339	+	1.81231i	0.142831	+	0.200136i
$83$	9.60276	−	9.60276i	1.05404	−	1.05404i	0.0555860	−	0.998454i	$-0.482297\pi$
$83$	9.60276	−	9.60276i	1.05404	−	1.05404i	0.998454	−	0.0555860i	$-0.0177027\pi$
$84$	5.99987	+	6.92832i	0.654639	+	0.755941i
$85$	5.35448	+	5.35448i	0.580775	+	0.580775i
$86$	18.1084	+	3.02571i	1.95268	+	0.326270i
$87$	−8.10183	+	1.61807i	−0.868607	+	0.173475i
$88$	−0.229937	−	8.53863i	−0.0245114	−	0.910221i
$89$	10.9145	+	6.30150i	1.15694	+	0.667958i	0.950568	−	0.310516i	$-0.100502\pi$
$89$	10.9145	+	6.30150i	1.15694	+	0.667958i	0.206369	+	0.978474i	$0.433835\pi$
$90$	−7.76510	−	2.35880i	−0.818514	−	0.248640i
$91$	−3.72724	−	3.28951i	−0.390720	−	0.344835i
$92$	8.40722	+	9.66173i	0.876513	+	1.00731i
$93$	−0.0668618	+	1.03235i	−0.00693325	+	0.107050i
$94$	0.0377743	+	0.391286i	0.00389612	+	0.0403580i
$95$	3.81097	−	2.20027i	0.390997	−	0.225742i
$96$	5.77772	−	7.91315i	0.589687	−	0.807632i
$97$			4.81796i			0.489190i	0.969625	+	0.244595i	$0.0786550\pi$
$97$			4.81796i			0.489190i	−0.969625	+	0.244595i	$0.921345\pi$
$98$	−7.28074	+	6.70752i	−0.735465	+	0.677562i
$99$	1.19644	+	8.98052i	0.120247	+	0.902576i
$100$	0.513079	+	2.63260i	0.0513079	+	0.263260i
$101$	0.369220	−	1.37795i	0.0367388	−	0.137111i	−0.945121	−	0.326722i	$-0.894056\pi$
$101$	0.369220	−	1.37795i	0.0367388	−	0.137111i	0.981859	+	0.189611i	$0.0607226\pi$
$102$	8.24052	−	5.11103i	0.815933	−	0.506068i
$103$	5.26506	−	9.11935i	0.518782	−	0.898556i	−0.480980	−	0.876732i	$-0.659719\pi$
$103$	5.26506	−	9.11935i	0.518782	−	0.898556i	0.999762	−	0.0218249i	$-0.00694763\pi$
$104$	−2.53238	+	4.67233i	−0.248320	+	0.458160i
$105$	2.28883	−	8.46161i	0.223367	−	0.825769i
$106$	−3.26567	+	1.22191i	−0.317190	+	0.118682i
$107$	1.05468	+	3.93611i	0.101960	+	0.380518i	0.997983	−	0.0634896i	$-0.0202230\pi$
$107$	1.05468	+	3.93611i	0.101960	+	0.380518i	−0.896023	+	0.444008i	$0.853556\pi$
$108$	−5.21008	+	8.99195i	−0.501340	+	0.865250i
$109$	−15.9501	−	4.27381i	−1.52774	−	0.409356i	−0.605458	−	0.795877i	$-0.707010\pi$
$109$	−15.9501	−	4.27381i	−1.52774	−	0.409356i	−0.922281	+	0.386521i	$0.873677\pi$
$110$	−6.64970	+	4.74567i	−0.634024	+	0.452482i
$111$	5.09985	−	15.0619i	0.484057	−	1.42962i
$112$	8.73493	+	5.97503i	0.825373	+	0.564587i
$113$		−	6.91772i		−	0.650765i	−0.945583	−	0.325382i	$-0.894507\pi$
$113$		−	6.91772i		−	0.650765i	0.945583	−	0.325382i	$-0.105493\pi$
$114$	−1.62953	−	5.39437i	−0.152619	−	0.505229i
$115$	3.17034	−	11.8319i	0.295636	−	1.10333i
$116$	−8.57237	+	4.18628i	−0.795924	+	0.388686i
$117$	2.14907	−	5.21110i	0.198682	−	0.481766i
$118$	5.96821	+	15.9507i	0.549419	+	1.46838i
$119$	5.79148	+	8.72692i	0.530904	+	0.799995i
$120$	−9.36426	−	0.353705i	−0.854836	−	0.0322887i
$121$	−1.62801	−	0.939930i	−0.148001	−	0.0854482i
$122$	0.707211	−	0.858348i	0.0640279	−	0.0777112i
$123$	−2.26850	−	1.51323i	−0.204544	−	0.136443i
$124$	0.228512	+	1.17249i	0.0205210	+	0.105293i
$125$	8.57679	−	8.57679i	0.767131	−	0.767131i
$126$	−9.88077	−	5.32638i	−0.880249	−	0.474512i
$127$	−15.8387			−1.40545			−0.702727	−	0.711459i	$-0.748035\pi$
$127$	−15.8387			−1.40545			−0.702727	+	0.711459i	$0.748035\pi$
$128$	4.12824	−	10.5336i	0.364889	−	0.931051i
$129$	−22.0502	+	4.40380i	−1.94141	+	0.387733i
$130$	5.05933	−	0.488422i	0.443733	−	0.0428375i
$131$	0.264933	+	0.988744i	0.0231473	+	0.0863870i	0.976533	−	0.215367i	$-0.0690947\pi$
$131$	0.264933	+	0.988744i	0.0231473	+	0.0863870i	−0.953386	+	0.301754i	$0.902428\pi$
$132$	3.97349	+	9.67745i	0.345848	+	0.842314i
$133$	5.76974	−	1.93833i	0.500300	−	0.168074i
$134$	−9.36295	+	3.50331i	−0.808836	+	0.302639i
$135$	9.91656	−	0.673079i	0.853482	−	0.0579294i
$136$	7.70144	−	8.12771i	0.660393	−	0.696945i
$137$	0.161917	+	0.280448i	0.0138335	+	0.0239603i	0.872859	−	0.487972i	$-0.162263\pi$
$137$	0.161917	+	0.280448i	0.0138335	+	0.0239603i	−0.859026	+	0.511932i	$0.828930\pi$
$138$	−13.8251	−	7.41030i	−1.17687	−	0.630807i
$139$	−6.37163	+	6.37163i	−0.540435	+	0.540435i	−0.923656	−	0.383222i	$-0.874814\pi$
$139$	−6.37163	+	6.37163i	−0.540435	+	0.540435i	0.383222	+	0.923656i	$0.374814\pi$
$140$	0.0710165	−	10.1215i	0.00600199	−	0.855424i
$141$	−0.213275	−	0.431637i	−0.0179610	−	0.0363504i
$142$	14.6990	−	10.4902i	1.23351	−	0.880314i
$143$	−2.83717	−	4.91413i	−0.237256	−	0.410940i
$144$	−3.17751	+	11.5717i	−0.264793	+	0.964305i
$145$	7.90175	+	4.56208i	0.656205	+	0.378860i
$146$	−16.3075	−	7.42690i	−1.34962	−	0.614654i
$147$	5.42244	−	10.8442i	0.447235	−	0.894417i
$148$	1.27180	−	18.3178i	0.104541	−	1.50572i
$149$	2.45451	+	9.16037i	0.201082	+	0.750447i	0.990608	+	0.136731i	$0.0436595\pi$
$149$	2.45451	+	9.16037i	0.201082	+	0.750447i	−0.789527	+	0.613716i	$0.789674\pi$
$150$	−1.73143	−	2.79158i	−0.141370	−	0.227932i
$151$	−9.24406	+	5.33706i	−0.752271	+	0.434324i	−0.826514	−	0.562916i	$-0.809679\pi$
$151$	−9.24406	+	5.33706i	−0.752271	+	0.434324i	0.0742427	+	0.997240i	$0.476346\pi$
$152$	−3.40395	−	5.54550i	−0.276097	−	0.449799i
$153$	−7.21517	+	9.43317i	−0.583312	+	0.762626i
$154$	−10.3160	+	4.61107i	−0.831287	+	0.371571i
$155$	0.807862	−	0.807862i	0.0648890	−	0.0648890i
$156$	0.869546	−	6.45053i	0.0696194	−	0.516456i
$157$	4.50275	−	16.8045i	0.359359	−	1.34115i	−0.515551	−	0.856859i	$-0.672413\pi$
$157$	4.50275	−	16.8045i	0.359359	−	1.34115i	0.874910	−	0.484286i	$-0.160921\pi$
$158$	−0.387435	−	4.01325i	−0.0308227	−	0.319277i
$159$	3.20850	−	2.81817i	0.254450	−	0.223495i
$160$	−10.5612	+	2.35508i	−0.834938	+	0.186186i
$161$	7.54134	−	15.1717i	0.594341	−	1.19570i
$162$	2.05875	−	12.5603i	0.161751	−	0.986832i
$163$	1.73984	+	6.49316i	0.136274	+	0.508583i	0.999989	+	0.00460262i	$0.00146506\pi$
$163$	1.73984	+	6.49316i	0.136274	+	0.508583i	−0.863715	+	0.503981i	$0.831868\pi$
$164$	−2.97771	−	1.02366i	−0.232520	−	0.0799344i
$165$	5.55232	−	8.32356i	0.432247	−	0.647988i
$166$	−3.16514	+	18.9429i	−0.245662	+	1.47026i
$167$			20.1663i			1.56052i	0.625458	+	0.780258i	$0.284912\pi$
$167$			20.1663i			1.56052i	−0.625458	+	0.780258i	$0.715088\pi$
$168$	−12.5984	−	3.04636i	−0.971988	−	0.235032i
$169$		−	9.46955i		−	0.728427i
$170$	−10.5625	−	1.76487i	−0.810109	−	0.135360i
$171$	4.20989	+	5.46889i	0.321938	+	0.418217i
$172$	−23.3309	+	11.3935i	−1.77896	+	0.868748i
$173$	0.964239	+	3.59859i	0.0733097	+	0.273596i	0.992845	−	0.119412i	$-0.0381011\pi$
$173$	0.964239	+	3.59859i	0.0733097	+	0.273596i	−0.919535	+	0.393008i	$0.871434\pi$
$174$	7.99698	−	8.51845i	0.606249	−	0.645782i
$175$	2.95635	−	1.96194i	0.223479	−	0.148309i
$176$	7.27937	+	9.64018i	0.548703	+	0.726656i
$177$	−13.7649	−	15.6714i	−1.03463	−	1.17793i
$178$	−17.7409	+	1.71268i	−1.32973	+	0.128371i
$179$	4.55771	−	17.0096i	0.340659	−	1.27136i	−0.556943	−	0.830551i	$-0.688026\pi$
$179$	4.55771	−	17.0096i	0.340659	−	1.27136i	0.897602	−	0.440807i	$-0.145308\pi$
$180$	10.8765	−	3.66392i	0.810683	−	0.273093i
$181$	−5.93458	+	5.93458i	−0.441114	+	0.441114i	−0.892386	−	0.451272i	$-0.850970\pi$
$181$	−5.93458	+	5.93458i	−0.441114	+	0.441114i	0.451272	+	0.892386i	$0.350970\pi$
$182$	6.99294	+	0.724647i	0.518351	+	0.0537144i
$183$	−0.436840	+	1.29017i	−0.0322922	+	0.0953720i
$184$	−17.6151	−	4.21519i	−1.29860	−	0.310748i
$185$	−15.2089	+	8.78084i	−1.11818	+	0.645580i
$186$	−0.771132	−	1.24330i	−0.0565421	−	0.0911629i
$187$	3.09423	+	11.5478i	0.226272	+	0.844459i
$188$	−0.364933	−	0.419388i	−0.0266155	−	0.0305870i
$189$	13.6286	+	1.80572i	0.991337	+	0.131347i
$190$	−2.57935	+	5.66359i	−0.187126	+	0.410880i
$191$	−18.0708	−	10.4332i	−1.30755	−	0.754917i	−0.325867	−	0.945416i	$-0.605656\pi$
$191$	−18.0708	−	10.4332i	−1.30755	−	0.754917i	−0.981688	+	0.190498i	$0.938990\pi$
$192$	−0.150080	+	13.8556i	−0.0108311	+	0.999941i
$193$	−8.59743	−	14.8912i	−0.618856	−	1.07189i	−0.989695	−	0.143193i	$-0.954263\pi$
$193$	−8.59743	−	14.8912i	−0.618856	−	1.07189i	0.370838	−	0.928697i	$-0.379070\pi$
$194$	−3.95807	−	5.54610i	−0.284173	−	0.398187i
$195$	−5.58108	+	2.75765i	−0.399669	+	0.197480i
$196$	2.87069	−	13.7025i	0.205049	−	0.978752i
$197$	6.99696	−	6.99696i	0.498513	−	0.498513i	−0.412462	−	0.910975i	$-0.635331\pi$
$197$	6.99696	−	6.99696i	0.498513	−	0.498513i	0.910975	+	0.412462i	$0.135331\pi$
$198$	−8.75497	−	9.35484i	−0.622188	−	0.664820i
$199$	−0.686010	−	1.18820i	−0.0486300	−	0.0842296i	0.840686	−	0.541523i	$-0.182152\pi$
$199$	−0.686010	−	1.18820i	−0.0486300	−	0.0842296i	−0.889316	+	0.457294i	$0.848819\pi$
$200$	−2.75336	−	2.60896i	−0.194692	−	0.184481i
$201$	9.19902	−	8.07992i	0.648849	−	0.569913i
$202$	0.706996	+	1.88952i	0.0497441	+	0.132946i
$203$	9.46209	+	8.35087i	0.664109	+	0.586116i
$204$	−5.28708	+	12.6532i	−0.370170	+	0.885904i
$205$	0.779439	+	2.90890i	0.0544384	+	0.203167i
$206$	1.43099	+	14.8229i	0.0997017	+	1.03276i
$207$	19.0507	+	2.47809i	1.32411	+	0.172239i
$208$	−0.923331	−	7.45887i	−0.0640215	−	0.517179i
$209$	6.94750			0.480569
$210$	4.31667	+	11.6207i	0.297878	+	0.801907i
$211$	−10.0240	+	10.0240i	−0.690081	+	0.690081i	−0.962250	−	0.272169i	$-0.912259\pi$
$211$	−10.0240	+	10.0240i	−0.690081	+	0.690081i	0.272169	+	0.962250i	$0.412259\pi$
$212$	2.75539	−	4.08940i	0.189241	−	0.280861i
$213$	−12.2732	+	18.3990i	−0.840947	+	1.26068i
$214$	−4.44768	−	3.66453i	−0.304037	−	0.250502i
$215$	21.5057	+	12.4163i	1.46668	+	0.846786i
$216$	−1.38962	−	14.6311i	−0.0945514	−	0.995520i
$217$	1.31668	−	0.873795i	0.0893822	−	0.0593171i
$218$	21.8716	−	8.18364i	1.48133	−	0.554266i
$219$	21.9005	+	1.41842i	1.47990	+	0.0958480i
$220$	3.75599	−	10.9258i	0.253229	−	0.736615i
$221$	1.92516	−	7.18479i	0.129500	−	0.483301i
$222$	6.50314	+	21.5279i	0.436462	+	1.44486i
$223$			15.9831i			1.07031i	0.844755	+	0.535153i	$0.179746\pi$
$223$			15.9831i			1.07031i	−0.844755	+	0.535153i	$0.820254\pi$
$224$	−14.9637	+	0.297910i	−0.999802	+	0.0199049i
$225$	3.19560	+	2.44423i	0.213040	+	0.162949i
$226$	5.68307	+	7.96320i	0.378032	+	0.529704i
$227$	−2.55625	−	0.684946i	−0.169664	−	0.0454614i	0.172987	−	0.984924i	$-0.444658\pi$
$227$	−2.55625	−	0.684946i	−0.169664	−	0.0454614i	−0.342651	+	0.939463i	$0.611325\pi$
$228$	6.30740	+	4.87093i	0.417718	+	0.322585i
$229$	−1.24906	−	4.66155i	−0.0825401	−	0.308044i	0.912297	−	0.409529i	$-0.134307\pi$
$229$	−1.24906	−	4.66155i	−0.0825401	−	0.308044i	−0.994837	+	0.101486i	$0.967640\pi$
$230$	6.07068	+	16.2245i	0.400288	+	1.06981i
$231$	9.80899	−	9.76251i	0.645384	−	0.642326i
$232$	6.42879	−	11.8613i	0.422070	−	0.778736i
$233$	−5.56619	+	9.64092i	−0.364653	+	0.631597i	−0.988720	−	0.149773i	$-0.952146\pi$
$233$	−5.56619	+	9.64092i	−0.364653	+	0.631597i	0.624067	+	0.781370i	$0.285479\pi$
$234$	1.80718	+	7.76417i	0.118139	+	0.507559i
$235$	−0.137615	+	0.513587i	−0.00897704	+	0.0335028i
$236$	−19.9740	−	13.4583i	−1.30020	−	0.876059i
$237$	2.18747	+	4.42712i	0.142092	+	0.287573i
$238$	−13.8361	−	5.28798i	−0.896862	−	0.342769i
$239$			13.1839i			0.852798i	0.904535	+	0.426399i	$0.140218\pi$
$239$			13.1839i			0.852798i	−0.904535	+	0.426399i	$0.859782\pi$
$240$	11.0701	−	7.28579i	0.714569	−	0.470296i
$241$	−11.7674	+	6.79392i	−0.758006	+	0.437635i	−0.828579	−	0.559872i	$-0.810850\pi$
$241$	−11.7674	+	6.79392i	−0.758006	+	0.437635i	0.0705736	+	0.997507i	$0.477517\pi$
$242$	2.64622	−	0.255463i	0.170106	−	0.0164218i
$243$	3.10026	+	15.2771i	0.198882	+	0.980023i
$244$	−0.108939	+	1.56906i	−0.00697409	+	0.100449i
$245$	−12.4026	+	5.04608i	−0.792374	+	0.322382i
$246$	3.85450	−	0.121705i	0.245754	−	0.00775962i
$247$	−3.74346	−	2.16129i	−0.238191	−	0.137520i
$248$	−1.22628	−	1.16196i	−0.0778686	−	0.0737847i
$249$	−4.60673	−	23.0663i	−0.291940	−	1.46177i
$250$	−2.82697	+	16.9190i	−0.178793	+	1.07005i
$251$	−19.1295	−	19.1295i	−1.20744	−	1.20744i	−0.971853	−	0.235589i	$-0.924298\pi$
$251$	−19.1295	−	19.1295i	−1.20744	−	1.20744i	−0.235589	−	0.971853i	$-0.575702\pi$
$252$	15.7498	−	1.98593i	0.992144	−	0.125102i
$253$	13.6747	−	13.6747i	0.859721	−	0.859721i
$254$	18.2324	−	13.0118i	1.14400	−	0.816435i
$255$	12.8617	−	2.56870i	0.805434	−	0.160858i
$256$	3.90149	+	15.5170i	0.243843	+	0.969815i
$257$	−12.3716	+	21.4282i	−0.771717	+	1.33665i	0.164905	+	0.986309i	$0.447268\pi$
$257$	−12.3716	+	21.4282i	−0.771717	+	1.33665i	−0.936622	+	0.350343i	$0.886065\pi$
$258$	21.7649	−	23.1841i	1.35502	−	1.44338i
$259$	−23.0259	+	7.73550i	−1.43076	+	0.480661i
$260$	−5.42270	+	4.71859i	−0.336301	+	0.292635i
$261$	−5.45571	+	13.2291i	−0.337700	+	0.818860i
$262$	−1.11725	−	0.920524i	−0.0690238	−	0.0568702i
$263$	−4.53545	−	7.85563i	−0.279668	−	0.484399i	0.691634	−	0.722248i	$-0.256891\pi$
$263$	−4.53545	−	7.85563i	−0.279668	−	0.484399i	−0.971302	+	0.237849i	$0.923558\pi$
$264$	−12.5242	−	7.87569i	−0.770814	−	0.484715i
$265$	−4.71615			−0.289711
$266$	−5.04934	+	6.97124i	−0.309595	+	0.427434i
$267$	19.5704	−	9.66988i	1.19769	−	0.591787i
$268$	7.89993	−	11.7246i	0.482565	−	0.716196i
$269$	23.6314	+	6.33202i	1.44083	+	0.386070i	0.892825	−	0.450404i	$-0.148720\pi$
$269$	23.6314	+	6.33202i	1.44083	+	0.386070i	0.548007	+	0.836474i	$0.315387\pi$
$270$	−10.8623	+	8.92148i	−0.661058	+	0.542944i
$271$	−11.2425	−	6.49088i	−0.682935	−	0.394293i	0.118025	−	0.993011i	$-0.462344\pi$
$271$	−11.2425	−	6.49088i	−0.682935	−	0.394293i	−0.800960	+	0.598718i	$0.795677\pi$
$272$	−2.18826	+	15.6830i	−0.132683	+	0.950919i
$273$	−8.32231	+	2.20879i	−0.503689	+	0.133682i
$274$	−0.416782	−	0.189814i	−0.0251787	−	0.0114671i
$275$	3.91196	−	1.04821i	0.235900	−	0.0632093i
$276$	22.0022	−	2.82740i	1.32438	−	0.170189i
$277$	1.72730	−	6.44637i	0.103783	−	0.387325i	−0.894421	−	0.447226i	$-0.852412\pi$
$277$	1.72730	−	6.44637i	0.103783	−	0.387325i	0.998204	+	0.0599012i	$0.0190786\pi$
$278$	2.10013	−	12.5690i	0.125958	−	0.753839i
$279$	1.42324	+	1.08860i	0.0852070	+	0.0651725i
$280$	8.23331	+	11.7095i	0.492034	+	0.699778i
$281$	−8.68701			−0.518224			−0.259112	−	0.965847i	$-0.583430\pi$
$281$	−8.68701			−0.518224			−0.259112	+	0.965847i	$0.583430\pi$
$282$	0.600107	+	0.321660i	0.0357359	+	0.0191546i
$283$	17.1852	+	4.60476i	1.02155	+	0.273724i	0.730449	−	0.682967i	$-0.239311\pi$
$283$	17.1852	+	4.60476i	1.02155	+	0.273724i	0.291104	+	0.956691i	$0.405977\pi$
$284$	−8.30250	+	24.1511i	−0.492663	+	1.43310i
$285$	0.492616	−	7.60601i	0.0291800	−	0.450541i
$286$	7.30303	+	3.32600i	0.431837	+	0.196670i
$287$	0.259345	+	4.15733i	0.0153086	+	0.245399i
$288$	−5.84866	−	15.9309i	−0.344636	−	0.938737i
$289$	0.664262	−	1.15054i	0.0390742	−	0.0676786i
$290$	−12.8438	+	1.23993i	−0.754214	+	0.0728109i
$291$	6.94216	+	4.63084i	0.406957	+	0.271465i
$292$	24.8735	−	4.84769i	1.45561	−	0.283690i
$293$	−23.8168	−	23.8168i	−1.39139	−	1.39139i	−0.822213	−	0.569180i	$-0.807261\pi$
$293$	−23.8168	−	23.8168i	−1.39139	−	1.39139i	−0.569180	−	0.822213i	$-0.692739\pi$
$294$	2.66685	+	16.9378i	0.155534	+	0.987831i
$295$			23.0353i			1.34117i
$296$	13.5845	+	22.1310i	0.789585	+	1.28634i
$297$	14.0899	+	6.90779i	0.817581	+	0.400830i
$298$	−10.3509	−	8.52834i	−0.599613	−	0.494033i
$299$	−11.6223	+	3.11418i	−0.672133	+	0.180098i
$300$	4.28644	+	1.79107i	0.247478	+	0.103407i
$301$	25.7524	+	22.7280i	1.48434	+	1.31002i
$302$	6.25660	−	13.7379i	0.360027	−	0.790525i
$303$	−1.63059	−	1.85644i	−0.0936752	−	0.106650i
$304$	8.47415	+	3.58716i	0.486026	+	0.205738i
$305$	1.30275	−	0.752144i	0.0745954	−	0.0430676i
$306$	0.556030	−	16.7862i	0.0317861	−	0.959605i
$307$	−2.97137	−	2.97137i	−0.169585	−	0.169585i	0.617212	−	0.786797i	$-0.288262\pi$
$307$	−2.97137	−	2.97137i	−0.169585	−	0.169585i	−0.786797	+	0.617212i	$0.788262\pi$
$308$	8.08696	−	13.7828i	0.460797	−	0.785347i
$309$	−8.07942	−	16.3516i	−0.459622	−	0.930207i
$310$	−0.266277	+	1.59363i	−0.0151235	+	0.0905122i
$311$	−6.80884	+	3.93108i	−0.386094	+	0.222911i	−0.680466	−	0.732779i	$-0.738223\pi$
$311$	−6.80884	+	3.93108i	−0.386094	+	0.222911i	0.294372	+	0.955691i	$0.404889\pi$
$312$	4.29830	+	8.13975i	0.243343	+	0.460823i
$313$	4.21826	−	7.30624i	0.238430	−	0.412973i	−0.721834	−	0.692066i	$-0.756700\pi$
$313$	4.21826	−	7.30624i	0.238430	−	0.412973i	0.960264	+	0.279093i	$0.0900338\pi$
$314$	8.62203	+	23.0433i	0.486569	+	1.30041i
$315$	−9.99233	−	11.4309i	−0.563004	−	0.644060i
$316$	3.74297	+	4.30149i	0.210558	+	0.241978i
$317$	−21.0207	+	5.63248i	−1.18064	+	0.316352i	−0.795180	−	0.606373i	$-0.792624\pi$
$317$	−21.0207	+	5.63248i	−1.18064	+	0.316352i	−0.385460	+	0.922725i	$0.625957\pi$
$318$	−1.37821	+	5.87993i	−0.0772859	+	0.329730i
$319$	7.20255	+	12.4752i	0.403265	+	0.698476i
$320$	10.2226	−	11.3873i	0.571460	−	0.636569i
$321$	6.68522	+	2.26356i	0.373133	+	0.126340i
$322$	3.78286	+	23.6600i	0.210811	+	1.31852i
$323$	6.43973	+	6.43973i	0.358316	+	0.358316i
$324$	7.94869	+	16.1499i	0.441594	+	0.897215i
$325$	−2.43394	−	0.652172i	−0.135011	−	0.0361760i
$326$	−7.33706	−	6.04515i	−0.406362	−	0.334810i
$327$	−21.4887	+	18.8745i	−1.18833	+	1.04376i
$328$	4.26869	−	1.26789i	0.235699	−	0.0700077i
$329$	−0.327348	+	0.658562i	−0.0180473	+	0.0363077i
$330$	0.446557	+	14.1429i	0.0245822	+	0.778539i
$331$	−14.0521	+	3.76525i	−0.772373	+	0.206957i	−0.623419	−	0.781888i	$-0.714257\pi$
$331$	−14.0521	+	3.76525i	−0.772373	+	0.206957i	−0.148953	+	0.988844i	$0.547590\pi$
$332$	−11.9186	−	24.4060i	−0.654116	−	1.33945i
$333$	−16.8008	−	21.8253i	−0.920681	−	1.19602i
$334$	−16.5671	−	23.2140i	−0.906510	−	1.27022i
$335$	−13.5216			−0.738763
$336$	17.0051	−	6.84312i	0.927702	−	0.373323i
$337$	21.9594			1.19620			0.598102	−	0.801420i	$-0.295922\pi$
$337$	21.9594			1.19620			0.598102	+	0.801420i	$0.295922\pi$
$338$	7.77945	+	10.9007i	0.423146	+	0.592919i
$339$	−9.96769	−	6.64905i	−0.541371	−	0.361127i
$340$	13.6087	−	6.64576i	0.738037	−	0.360417i
$341$	1.74229	−	0.466844i	0.0943501	−	0.0252810i
$342$	−9.33894	−	2.83689i	−0.504992	−	0.153401i
$343$	−18.1977	+	3.44142i	−0.982584	+	0.185819i
$344$	17.4968	−	32.2823i	0.943365	−	1.74054i
$345$	−14.0012	−	15.9404i	−0.753800	−	0.858205i
$346$	−4.06629	−	3.35030i	−0.218605	−	0.180113i
$347$	11.3221	+	3.03376i	0.607805	+	0.162861i	0.549578	−	0.835443i	$-0.314789\pi$
$347$	11.3221	+	3.03376i	0.607805	+	0.162861i	0.0582269	+	0.998303i	$0.481455\pi$
$348$	−2.20746	+	16.3755i	−0.118332	+	0.877821i
$349$	−2.66234	−	2.66234i	−0.142512	−	0.142512i	0.632252	−	0.774763i	$-0.282131\pi$
$349$	−2.66234	−	2.66234i	−0.142512	−	0.142512i	−0.774763	+	0.632252i	$0.782131\pi$
$350$	−1.79137	+	4.68716i	−0.0957527	+	0.250539i
$351$	−5.44303	−	8.10529i	−0.290527	−	0.432628i
$352$	−16.2991	−	5.11693i	−0.868746	−	0.272733i
$353$	7.09545	+	12.2897i	0.377652	+	0.654113i	0.990720	−	0.135917i	$-0.0433981\pi$
$353$	7.09545	+	12.2897i	0.377652	+	0.654113i	−0.613068	+	0.790030i	$0.710065\pi$
$354$	28.7196	+	6.73163i	1.52643	+	0.357782i
$355$	23.5930	−	6.32172i	1.25219	−	0.335522i
$356$	19.0150	−	16.5460i	1.00779	−	0.876939i
$357$	18.1411	+	0.0430768i	0.960128	+	0.00227986i
$358$	8.72727	+	23.3245i	0.461250	+	1.23274i
$359$	16.3675	−	28.3493i	0.863843	−	1.49622i	−0.00434871	−	0.999991i	$-0.501384\pi$
$359$	16.3675	−	28.3493i	0.863843	−	1.49622i	0.868192	−	0.496229i	$-0.165282\pi$
$360$	−9.51021	+	13.1529i	−0.501232	+	0.693219i
$361$	−11.8711	+	6.85378i	−0.624795	+	0.360725i
$362$	1.95608	−	11.7069i	0.102809	−	0.615299i
$363$	−2.91911	+	1.44236i	−0.153214	+	0.0757041i
$364$	−8.64510	+	4.91070i	−0.453126	+	0.257391i
$365$	−17.1381	−	17.1381i	−0.897051	−	0.897051i
$366$	−0.557043	−	1.84403i	−0.0291171	−	0.0963888i
$367$	29.1928	−	16.8544i	1.52385	−	0.879795i	0.524248	−	0.851566i	$-0.324347\pi$
$367$	29.1928	−	16.8544i	1.52385	−	0.879795i	0.999601	−	0.0282290i	$-0.00898677\pi$
$368$	23.7402	−	9.61901i	1.23754	−	0.501425i
$369$	−4.36080	+	1.81421i	−0.227014	+	0.0944441i
$370$	10.2937	−	22.6023i	0.535144	−	1.17504i
$371$	−6.39380	−	1.29274i	−0.331950	−	0.0671159i
$372$	1.90907	+	0.797693i	0.0989806	+	0.0413585i
$373$	−7.16791	+	1.92063i	−0.371140	+	0.0994467i	−0.439568	−	0.898209i	$-0.644868\pi$
$373$	−7.16791	+	1.92063i	−0.371140	+	0.0994467i	0.0684277	+	0.997656i	$0.478202\pi$
$374$	−13.0486	−	10.7510i	−0.674729	−	0.555923i
$375$	−4.11454	−	20.6019i	−0.212474	−	1.06388i
$376$	0.764623	+	0.182969i	0.0394324	+	0.00943592i
$377$		−	8.96253i		−	0.461594i
$378$	−17.1718	+	9.11761i	−0.883220	+	0.468959i
$379$	−0.171777	−	0.171777i	−0.00882358	−	0.00882358i	0.702681	−	0.711505i	$-0.251986\pi$
$379$	−0.171777	−	0.171777i	−0.00882358	−	0.00882358i	−0.711505	+	0.702681i	$0.751986\pi$
$380$	−1.68360	−	8.63853i	−0.0863668	−	0.443147i
$381$	−15.2235	+	22.8218i	−0.779925	+	1.16920i
$382$	29.3729	−	2.83563i	1.50285	−	0.145083i
$383$	−7.21803	+	12.5020i	−0.368824	+	0.638822i	−0.989382	−	0.145338i	$-0.953573\pi$
$383$	−7.21803	+	12.5020i	−0.368824	+	0.638822i	0.620558	+	0.784161i	$0.286906\pi$
$384$	−11.2099	−	16.0729i	−0.572054	−	0.820216i
$385$	−15.2540	+	0.951583i	−0.777416	+	0.0484972i
$386$	22.1302	+	10.0787i	1.12640	+	0.512992i
$387$	−14.8484	+	36.0048i	−0.754789	+	1.83022i
$388$	9.11250	+	3.13264i	0.462617	+	0.159036i
$389$	−26.2434	−	7.03189i	−1.33059	−	0.356531i	−0.477656	−	0.878547i	$-0.658513\pi$
$389$	−26.2434	−	7.03189i	−1.33059	−	0.356531i	−0.852936	+	0.522016i	$0.825180\pi$
$390$	4.15907	−	7.75940i	0.210603	−	0.392912i
$391$	25.3505			1.28203
$392$	7.95240	+	18.1317i	0.401657	+	0.915790i
$393$	1.67932	+	0.568603i	0.0847103	+	0.0286822i
$394$	−2.30625	+	13.8026i	−0.116187	+	0.695364i
$395$	1.41146	−	5.26765i	0.0710184	−	0.265044i
$396$	17.7633	+	3.57623i	0.892641	+	0.179712i
$397$	−3.31165	+	0.887355i	−0.166207	+	0.0445350i	−0.340963	−	0.940077i	$-0.610753\pi$
$397$	−3.31165	+	0.887355i	−0.166207	+	0.0445350i	0.174756	+	0.984612i	$0.444086\pi$
$398$	1.76582	+	0.804205i	0.0885128	+	0.0403111i
$399$	2.75273	−	10.1766i	0.137809	−	0.509468i
$400$	5.31280	+	0.741302i	0.265640	+	0.0370651i
$401$	1.91942	+	1.10818i	0.0958513	+	0.0553398i	0.547159	−	0.837028i	$-0.315709\pi$
$401$	1.91942	+	1.10818i	0.0958513	+	0.0553398i	−0.451308	+	0.892368i	$0.649042\pi$
$402$	−3.95143	+	16.8582i	−0.197079	+	0.840812i
$403$	−1.08401	−	0.290460i	−0.0539985	−	0.0144688i
$404$	−2.36613	−	1.59427i	−0.117719	−	0.0793179i
$405$	8.56158	−	14.9356i	0.425429	−	0.742157i
$406$	−17.7525	−	1.83961i	−0.881043	−	0.0912985i
$407$	−27.7261			−1.37433
$408$	−4.30881	−	18.9090i	−0.213318	−	0.936134i
$409$	−9.26494	−	16.0473i	−0.458122	−	0.793490i	0.540740	−	0.841190i	$-0.318144\pi$
$409$	−9.26494	−	16.0473i	−0.458122	−	0.793490i	−0.998862	+	0.0476998i	$0.984811\pi$
$410$	−3.28697	−	2.70820i	−0.162332	−	0.133748i
$411$	0.559724	+	0.0362515i	0.0276091	+	0.00178815i
$412$	−13.8246	−	15.8875i	−0.681091	−	0.782722i
$413$	−6.31420	+	31.2295i	−0.310702	+	1.53670i
$414$	−23.9656	+	12.7979i	−1.17784	+	0.628985i
$415$	−12.9885	+	22.4967i	−0.637579	+	1.10432i
$416$	7.19051	+	7.82759i	0.352544	+	0.383779i
$417$	3.05666	+	15.3050i	0.149685	+	0.749489i
$418$	−7.99747	+	5.70753i	−0.391169	+	0.279164i
$419$	26.3706	−	26.3706i	1.28829	−	1.28829i	0.352459	−	0.935827i	$-0.385346\pi$
$419$	26.3706	−	26.3706i	1.28829	−	1.28829i	0.935827	−	0.352459i	$-0.114654\pi$
$420$	−14.5157	−	9.83074i	−0.708296	−	0.479691i
$421$	5.74913	+	5.74913i	0.280195	+	0.280195i	0.833187	−	0.552992i	$-0.186514\pi$
$421$	5.74913	+	5.74913i	0.280195	+	0.280195i	−0.552992	+	0.833187i	$0.686514\pi$
$422$	3.30398	−	19.7739i	0.160835	−	0.962578i
$423$	−0.826935	−	0.107567i	−0.0402069	−	0.00523008i
$424$	0.187724	+	6.97105i	0.00911667	+	0.338544i
$425$	4.59765	+	2.65445i	0.223019	+	0.128760i
$426$	−0.987101	−	31.2623i	−0.0478252	−	1.51466i
$427$	1.97234	−	0.662603i	0.0954484	−	0.0320656i
$428$	8.13035	+	0.564485i	0.392995	+	0.0272854i
$429$	−9.80771	−	0.635213i	−0.473521	−	0.0306684i
$430$	−34.9561	+	3.37463i	−1.68573	+	0.162739i
$431$	−3.06169	+	1.76767i	−0.147477	+	0.0851456i	−0.571923	−	0.820308i	$-0.693802\pi$
$431$	−3.06169	+	1.76767i	−0.147477	+	0.0851456i	0.424446	+	0.905453i	$0.360469\pi$
$432$	13.6194	+	15.7007i	0.655264	+	0.755400i
$433$		−	32.3146i		−	1.55294i	−0.630153	−	0.776471i	$-0.717008\pi$
$433$		−	32.3146i		−	1.55294i	0.630153	−	0.776471i	$-0.282992\pi$
$434$	−0.797828	+	2.08754i	−0.0382970	+	0.100205i
$435$	14.1683	−	7.00067i	0.679319	−	0.335657i
$436$	−18.4540	+	27.3885i	−0.883788	+	1.31167i
$437$	3.81291	−	14.2300i	0.182396	−	0.680711i
$438$	−26.3755	+	16.3589i	−1.26027	+	0.781660i
$439$	10.8715	−	18.8299i	0.518866	−	0.898702i	−0.480894	−	0.876779i	$-0.659688\pi$
$439$	10.8715	−	18.8299i	0.518866	−	0.898702i	0.999760	−	0.0219234i	$-0.00697899\pi$
$440$	4.65213	+	15.6626i	0.221782	+	0.746686i
$441$	−10.4135	−	18.2362i	−0.495882	−	0.868390i
$442$	3.68636	+	9.85219i	0.175342	+	0.468621i
$443$	7.90185	+	29.4901i	0.375428	+	1.40112i	0.852718	+	0.522372i	$0.174953\pi$
$443$	7.90185	+	29.4901i	0.375428	+	1.40112i	−0.477290	+	0.878746i	$0.658381\pi$
$444$	−25.1716	−	19.4389i	−1.19459	−	0.922531i
$445$	−23.2860	−	6.23947i	−1.10386	−	0.295779i
$446$	−13.1305	−	18.3986i	−0.621746	−	0.871199i
$447$	15.5583	+	5.26791i	0.735882	+	0.249164i
$448$	16.9804	−	12.6359i	0.802248	−	0.596991i
$449$			33.6146i			1.58637i	0.608980	+	0.793185i	$0.291579\pi$
$449$			33.6146i			1.58637i	−0.608980	+	0.793185i	$0.708421\pi$
$450$	−5.68655	−	0.188362i	−0.268066	−	0.00887948i
$451$	−1.23057	+	4.59254i	−0.0579452	+	0.216254i
$452$	−13.0839	−	4.49790i	−0.615415	−	0.211564i
$453$	−1.19491	+	18.4495i	−0.0561418	+	0.866832i
$454$	3.50528	−	1.31156i	0.164511	−	0.0615545i
$455$	8.51521	+	4.23261i	0.399199	+	0.198428i
$456$	−11.2622	−	0.425394i	−0.527401	−	0.0199209i
$457$	18.8296	+	10.8712i	0.880809	+	0.508535i	0.870925	−	0.491416i	$-0.163520\pi$
$457$	18.8296	+	10.8712i	0.880809	+	0.508535i	0.00988408	+	0.999951i	$0.496854\pi$
$458$	5.26740	+	4.33992i	0.246129	+	0.202791i
$459$	6.65723	+	19.4631i	0.310733	+	0.908458i
$460$	−20.3169	−	13.6893i	−0.947283	−	0.638268i
$461$	−23.9734	+	23.9734i	−1.11655	+	1.11655i	−0.124307	+	0.992244i	$0.539671\pi$
$461$	−23.9734	+	23.9734i	−1.11655	+	1.11655i	−0.992244	+	0.124307i	$0.960329\pi$
$462$	−3.27129	+	19.2962i	−0.152194	+	0.897742i
$463$	17.5721			0.816644			0.408322	−	0.912838i	$-0.366114\pi$
$463$	17.5721			0.816644			0.408322	+	0.912838i	$0.366114\pi$
$464$	2.34400	+	18.9353i	0.108818	+	0.879051i
$465$	−0.387555	−	1.94053i	−0.0179725	−	0.0899898i
$466$	−1.51283	−	15.6707i	−0.0700806	−	0.725931i
$467$	6.18216	+	23.0721i	0.286076	+	1.06765i	0.948049	+	0.318123i	$0.103053\pi$
$467$	6.18216	+	23.0721i	0.286076	+	1.06765i	−0.661973	+	0.749528i	$0.730281\pi$
$468$	−8.45874	−	7.45292i	−0.391005	−	0.344511i
$469$	−18.3315	−	3.70640i	−0.846472	−	0.171146i
$470$	−0.263511	−	0.704260i	−0.0121548	−	0.0324851i
$471$	−19.8856	−	22.6398i	−0.916280	−	1.04319i
$472$	34.0490	−	0.916907i	1.56723	−	0.0422041i
$473$	19.6027	+	33.9529i	0.901334	+	1.56116i
$474$	−6.15505	−	3.29913i	−0.282711	−	0.151534i
$475$	2.18154	−	2.18154i	0.100096	−	0.100096i
$476$	20.2714	−	5.27954i	0.929136	−	0.241987i
$477$	−0.976792	−	7.33181i	−0.0447243	−	0.335701i
$478$	−10.8309	−	15.1764i	−0.495394	−	0.694153i
$479$	12.0632	+	20.8940i	0.551180	+	0.954672i	0.998190	+	0.0601429i	$0.0191556\pi$
$479$	12.0632	+	20.8940i	0.551180	+	0.954672i	−0.447010	+	0.894529i	$0.647511\pi$
$480$	−6.75762	+	17.4812i	−0.308442	+	0.797904i
$481$	14.9394	+	8.62529i	0.681180	+	0.393280i
$482$	7.96446	−	17.4879i	0.362771	−	0.796551i
$483$	−14.6124	−	25.4487i	−0.664886	−	1.15796i
$484$	−2.83628	+	2.46800i	−0.128922	+	0.112182i
$485$	−2.38527	−	8.90193i	−0.108309	−	0.404216i
$486$	−16.1193	−	15.0389i	−0.731184	−	0.682180i
$487$	13.9702	−	8.06568i	0.633048	−	0.365491i	−0.148883	−	0.988855i	$-0.547568\pi$
$487$	13.9702	−	8.06568i	0.633048	−	0.365491i	0.781932	+	0.623364i	$0.214235\pi$
$488$	−1.16362	−	1.89569i	−0.0526744	−	0.0858138i
$489$	11.0282	+	3.73406i	0.498712	+	0.168860i
$490$	10.1315	−	15.9977i	0.457697	−	0.722704i
$491$	−1.51321	+	1.51321i	−0.0682901	+	0.0682901i	−0.740427	−	0.672137i	$-0.765377\pi$
$491$	−1.51321	+	1.51321i	−0.0682901	+	0.0682901i	0.672137	+	0.740427i	$0.265377\pi$
$492$	−4.33704	+	3.30666i	−0.195529	+	0.149076i
$493$	−4.88727	+	18.2396i	−0.220112	+	0.821468i
$494$	6.08476	−	0.587416i	0.273766	−	0.0264291i
$495$	−6.65667	−	16.0006i	−0.299195	−	0.719173i
$496$	2.36618	+	0.330156i	0.106245	+	0.0148245i
$497$	33.7185	−	2.10344i	1.51248	−	0.0943524i
$498$	24.2525	+	22.7678i	1.08678	+	1.02025i
$499$	−1.62172	−	6.05235i	−0.0725982	−	0.270940i	0.920080	−	0.391731i	$-0.128124\pi$
$499$	−1.62172	−	6.05235i	−0.0725982	−	0.270940i	−0.992678	+	0.120791i	$0.961457\pi$
$500$	−10.6452	−	21.7984i	−0.476066	−	0.974855i
$501$	29.0575	+	19.3831i	1.29819	+	0.865972i
$502$	37.7358	+	6.30521i	1.68423	+	0.281415i
$503$			11.5892i			0.516739i	0.966046	+	0.258370i	$0.0831852\pi$
$503$			11.5892i			0.516739i	−0.966046	+	0.258370i	$0.916815\pi$
$504$	−16.4986	+	15.2249i	−0.734905	+	0.678170i
$505$			2.72877i			0.121429i
$506$	−4.50728	+	26.9754i	−0.200373	+	1.19920i
$507$	−13.6446	−	9.10177i	−0.605977	−	0.404224i
$508$	−10.2983	+	29.9566i	−0.456913	+	1.32911i
$509$	−5.08793	−	18.9884i	−0.225519	−	0.841647i	−0.982196	−	0.187858i	$-0.939845\pi$
$509$	−5.08793	−	18.9884i	−0.225519	−	0.841647i	0.756678	−	0.653788i	$-0.226821\pi$
$510$	−12.6953	+	13.5231i	−0.562157	+	0.598814i
$511$	−18.5369	−	27.9323i	−0.820023	−	1.23565i
$512$	−17.2387	−	14.6570i	−0.761851	−	0.647752i
$513$	11.9265	−	0.809499i	0.526566	−	0.0357403i
$514$	−3.36246	−	34.8301i	−0.148312	−	1.53629i
$515$	−5.21323	+	19.4560i	−0.229722	+	0.857335i
$516$	−6.00790	+	44.5683i	−0.264483	+	1.96201i
$517$	−0.593580	+	0.593580i	−0.0261056	+	0.0261056i
$518$	20.1510	−	27.8209i	0.885382	−	1.22238i
$519$	6.11197	+	2.06946i	0.268286	+	0.0908393i
$520$	2.36580	−	9.88658i	0.103747	−	0.433555i
$521$	29.2651	−	16.8962i	1.28213	−	0.740237i	0.304892	−	0.952387i	$-0.401380\pi$
$521$	29.2651	−	16.8962i	1.28213	−	0.740237i	0.977237	+	0.212150i	$0.0680464\pi$
$522$	−4.58777	−	19.7104i	−0.200801	−	0.862700i
$523$	0.596978	+	2.22795i	0.0261040	+	0.0974215i	0.977749	−	0.209779i	$-0.0672745\pi$
$523$	0.596978	+	2.22795i	0.0261040	+	0.0974215i	−0.951645	+	0.307200i	$0.900608\pi$
$524$	2.04233	+	0.141798i	0.0892196	+	0.00619446i
$525$	0.0145928	−	6.14552i	0.000636882	−	0.268213i
$526$	11.6745	+	5.31687i	0.509031	+	0.231827i
$527$	2.04767	+	1.18222i	0.0891980	+	0.0514985i
$528$	20.8871	−	1.22301i	0.908994	−	0.0532249i
$529$	−9.00379	−	15.5950i	−0.391469	−	0.678044i
$530$	5.42890	−	3.87443i	0.235816	−	0.168294i
$531$	−35.8111	+	4.77099i	−1.55407	+	0.207043i
$532$	0.0854102	−	12.1730i	0.00370300	−	0.527765i
$533$	2.09174	−	2.09174i	0.0906035	−	0.0906035i
$534$	−14.5840	+	27.2088i	−0.631113	+	1.17744i
$535$	−3.89736	−	6.75043i	−0.168498	−	0.291846i
$536$	0.538219	+	19.9865i	0.0232475	+	0.863287i
$537$	−20.1283	−	22.9162i	−0.868600	−	0.988905i
$538$	−32.4047	+	12.1248i	−1.39707	+	0.522736i
$539$	−20.9411	−	2.89119i	−0.901995	−	0.124532i
$540$	5.17471	−	19.1934i	0.222684	−	0.825953i
$541$	1.67488	+	6.25072i	0.0720085	+	0.268739i	0.992538	−	0.121933i	$-0.0389093\pi$
$541$	1.67488	+	6.25072i	0.0720085	+	0.268739i	−0.920530	+	0.390672i	$0.872243\pi$
$542$	18.2740	−	1.76415i	0.784936	−	0.0757769i
$543$	2.84700	+	14.2552i	0.122176	+	0.611748i
$544$	−10.3649	−	19.8508i	−0.444393	−	0.851097i
$545$	31.5861			1.35300
$546$	7.76548	−	9.37957i	0.332332	−	0.401408i
$547$	−0.941076	+	0.941076i	−0.0402375	+	0.0402375i	−0.726939	−	0.686702i	$-0.759058\pi$
$547$	−0.941076	+	0.941076i	−0.0402375	+	0.0402375i	0.686702	+	0.726939i	$0.259058\pi$
$548$	0.635707	−	0.123896i	0.0271560	−	0.00529255i
$549$	1.43912	+	1.86950i	0.0614201	+	0.0797883i
$550$	−3.64205	+	4.42039i	−0.155298	+	0.188486i
$551$	9.50329	+	5.48673i	0.404854	+	0.233742i
$552$	−23.0046	+	21.3300i	−0.979141	+	0.907866i
$553$	3.35747	−	6.75459i	0.142774	−	0.287234i
$554$	3.30750	+	8.83963i	0.140522	+	0.375560i
$555$	−1.96594	+	30.3541i	−0.0834493	+	1.28846i
$556$	7.90821	+	16.1939i	0.335383	+	0.686773i
$557$	−3.24812	+	12.1222i	−0.137627	+	0.513632i	0.862346	+	0.506320i	$0.168994\pi$
$557$	−3.24812	+	12.1222i	−0.137627	+	0.513632i	−0.999973	+	0.00731273i	$0.997672\pi$
$558$	−2.53264	−	0.0838916i	−0.107215	−	0.00355141i
$559$		−	24.3928i		−	1.03170i
$560$	−19.0972	−	6.71533i	−0.807006	−	0.283774i
$561$	19.6132	+	6.64087i	0.828069	+	0.280378i
$562$	9.99988	−	7.13658i	0.421819	−	0.301038i
$563$	−34.2923	−	9.18861i	−1.44525	−	0.387254i	−0.550881	−	0.834584i	$-0.685708\pi$
$563$	−34.2923	−	9.18861i	−1.44525	−	0.387254i	−0.894369	+	0.447330i	$0.852375\pi$
$564$	−0.955053	+	0.122729i	−0.0402150	+	0.00516784i
$565$	3.42481	+	12.7816i	0.144083	+	0.537725i
$566$	−23.5653	+	8.81735i	−0.990523	+	0.370621i
$567$	15.7012	−	17.9018i	0.659386	−	0.751804i
$568$	−10.2834	−	34.6217i	−0.431481	−	1.45269i
$569$	3.30179	−	5.71887i	0.138418	−	0.239747i	−0.788480	−	0.615061i	$-0.789132\pi$
$569$	3.30179	−	5.71887i	0.138418	−	0.239747i	0.926898	+	0.375313i	$0.122465\pi$
$570$	5.68144	+	9.16020i	0.237969	+	0.383678i
$571$	5.90951	−	22.0546i	0.247305	−	0.922957i	−0.724905	−	0.688849i	$-0.758116\pi$
$571$	5.90951	−	22.0546i	0.247305	−	0.922957i	0.972211	−	0.234108i	$-0.0752169\pi$
$572$	−11.1391	+	2.17095i	−0.465750	+	0.0907719i
$573$	−32.4020	+	16.0101i	−1.35361	+	0.668830i
$574$	−3.71388	−	4.57256i	−0.155014	−	0.190855i
$575$		−	8.58781i		−	0.358136i
$576$	19.8202	+	13.5337i	0.825840	+	0.563905i
$577$	2.00743	−	1.15899i	0.0835706	−	0.0482495i	−0.457632	−	0.889142i	$-0.651302\pi$
$577$	2.00743	−	1.15899i	0.0835706	−	0.0482495i	0.541203	+	0.840892i	$0.317969\pi$
$578$	0.180540	+	1.87012i	0.00750945	+	0.0777868i
$579$	−29.7201	−	1.92487i	−1.23513	−	0.0799950i
$580$	13.7663	−	11.9788i	0.571612	−	0.497392i
$581$	−23.7754	+	26.9391i	−0.986369	+	1.11762i
$582$	−11.7957	+	0.372445i	−0.488946	+	0.0154384i
$583$	−6.44825	−	3.72290i	−0.267059	−	0.154187i
$584$	−24.6501	+	26.0144i	−1.02003	+	1.07649i
$585$	−1.39084	+	10.6923i	−0.0575042	+	0.442071i
$586$	46.9823	+	7.85019i	1.94082	+	0.324288i
$587$	0.612943	+	0.612943i	0.0252988	+	0.0252988i	0.719643	−	0.694344i	$-0.244305\pi$
$587$	0.612943	+	0.612943i	0.0252988	+	0.0252988i	−0.694344	+	0.719643i	$0.744305\pi$
$588$	−16.9847	−	17.3067i	−0.700435	−	0.713716i
$589$	0.971600	−	0.971600i	0.0400341	−	0.0400341i
$590$	−18.9240	−	26.5166i	−0.779090	−	1.09167i
$591$	−3.35665	−	16.8071i	−0.138074	−	0.691351i
$592$	−33.8187	−	14.3157i	−1.38994	−	0.588371i
$593$	13.6407	−	23.6264i	0.560157	−	0.970221i	−0.437325	−	0.899304i	$-0.644074\pi$
$593$	13.6407	−	23.6264i	0.560157	−	0.970221i	0.997482	−	0.0709174i	$-0.0225927\pi$
$594$	−21.8943	+	3.62344i	−0.898332	+	0.148672i
$595$	−15.0212	−	13.2571i	−0.615808	−	0.543488i
$596$	18.9215	+	1.31371i	0.775054	+	0.0538115i
$597$	−2.37144	−	0.153590i	−0.0970566	−	0.00628603i
$598$	10.8204	−	13.1328i	0.442478	−	0.537040i
$599$	−3.58051	−	6.20163i	−0.146296	−	0.253392i	0.783560	−	0.621316i	$-0.213402\pi$
$599$	−3.58051	−	6.20163i	−0.146296	−	0.253392i	−0.929856	+	0.367925i	$0.880068\pi$
$600$	−6.40566	+	1.45966i	−0.261510	+	0.0595905i
$601$	22.5323			0.919113			0.459556	−	0.888149i	$-0.348008\pi$
$601$	22.5323			0.919113			0.459556	+	0.888149i	$0.348008\pi$
$602$	−48.3159	−	5.00676i	−1.96921	−	0.204060i
$603$	−2.80054	−	21.0209i	−0.114047	−	0.856037i
$604$	4.08381	+	20.9540i	0.166168	+	0.852606i
$605$	3.47333	+	0.930677i	0.141211	+	0.0378374i
$606$	3.40213	+	0.797430i	0.138202	+	0.0323934i
$607$	5.72505	+	3.30536i	0.232373	+	0.134160i	0.611666	−	0.791116i	$-0.290500\pi$
$607$	5.72505	+	3.30536i	0.232373	+	0.134160i	−0.379293	+	0.925276i	$0.623833\pi$
$608$	−12.7018	+	2.83242i	−0.515125	+	0.114870i
$609$	21.1273	−	5.60731i	0.856121	−	0.227220i
$610$	−0.881733	+	1.93606i	−0.0357003	+	0.0783886i
$611$	0.504490	−	0.135178i	0.0204095	−	0.00546870i
$612$	13.1502	+	19.7799i	0.531566	+	0.799556i
$613$	−0.162950	+	0.608136i	−0.00658147	+	0.0245624i	−0.969138	−	0.246517i	$-0.920714\pi$
$613$	−0.162950	+	0.608136i	−0.00658147	+	0.0245624i	0.962557	+	0.271079i	$0.0873806\pi$
$614$	5.86149	+	0.979385i	0.236550	+	0.0395248i
$615$	4.94058	+	1.67284i	0.199224	+	0.0674555i
$616$	2.01373	+	22.5094i	0.0811356	+	0.906929i
$617$	−17.1982			−0.692375			−0.346187	−	0.938165i	$-0.612524\pi$
$617$	−17.1982			−0.692375			−0.346187	+	0.938165i	$0.612524\pi$
$618$	22.7336	+	12.1853i	0.914481	+	0.490166i
$619$	−36.7851	−	9.85653i	−1.47852	−	0.396167i	−0.572674	−	0.819783i	$-0.694094\pi$
$619$	−36.7851	−	9.85653i	−1.47852	−	0.396167i	−0.905842	+	0.423616i	$0.860761\pi$
$620$	−1.00269	−	2.05323i	−0.0402688	−	0.0824597i
$621$	21.8814	−	25.0681i	0.878071	−	1.00595i
$622$	4.60838	−	10.1188i	0.184779	−	0.405727i
$623$	−29.8591	−	14.8419i	−1.19628	−	0.594629i
$624$	−11.6349	−	5.83876i	−0.465768	−	0.233737i
$625$	−8.24810	+	14.2861i	−0.329924	+	0.571445i
$626$	1.14648	+	11.8758i	0.0458226	+	0.474654i
$627$	6.67767	−	10.0106i	0.266680	−	0.399785i
$628$	−28.8557	−	19.4426i	−1.15147	−	0.775845i
$629$	−25.6997	−	25.6997i	−1.02472	−	1.02472i
$630$	20.8932	+	4.94956i	0.832407	+	0.197195i
$631$			8.66282i			0.344861i	0.985022	+	0.172431i	$0.0551621\pi$
$631$			8.66282i			0.344861i	−0.985022	+	0.172431i	$0.944838\pi$
$632$	−7.84241	−	1.87664i	−0.311955	−	0.0746487i
$633$	4.80881	+	24.0782i	0.191133	+	0.957022i
$634$	19.5703	−	23.7527i	0.777238	−	0.943340i
$635$	29.2644	−	7.84137i	1.16132	−	0.311175i
$636$	−3.24401	−	7.90079i	−0.128633	−	0.313287i
$637$	10.3841	+	8.07236i	0.411432	+	0.319839i
$638$	−18.5397	−	8.44350i	−0.733995	−	0.334281i
$639$	14.7144	+	35.3688i	0.582091	+	1.39917i
$640$	−2.41260	+	21.5063i	−0.0953663	+	0.850113i
$641$	16.3876	−	9.46139i	0.647272	−	0.373703i	−0.140138	−	0.990132i	$-0.544755\pi$
$641$	16.3876	−	9.46139i	0.647272	−	0.373703i	0.787410	+	0.616429i	$0.211421\pi$
$642$	−9.55513	+	2.88641i	−0.377111	+	0.113918i
$643$	31.8131	+	31.8131i	1.25459	+	1.25459i	0.953641	+	0.300947i	$0.0973027\pi$
$643$	31.8131	+	31.8131i	1.25459	+	1.25459i	0.300947	+	0.953641i	$0.402697\pi$
$644$	−23.7918	−	24.1280i	−0.937529	−	0.950778i
$645$	38.5610	−	19.0533i	1.51834	−	0.750222i
$646$	−12.7034	−	2.12258i	−0.499807	−	0.0835118i
$647$	35.5083	−	20.5007i	1.39598	−	0.805967i	0.402007	−	0.915636i	$-0.368313\pi$
$647$	35.5083	−	20.5007i	1.39598	−	0.805967i	0.993968	+	0.109670i	$0.0349793\pi$
$648$	−22.4175	−	12.0606i	−0.880641	−	0.473784i
$649$	−18.1839	+	31.4955i	−0.713781	+	1.23631i
$650$	3.33755	−	1.24880i	0.130910	−	0.0489820i
$651$	0.00649925	−	2.73705i	0.000254726	−	0.107274i
$652$	13.4121	+	0.931196i	0.525260	+	0.0364684i
$653$	21.8978	−	5.86749i	0.856926	−	0.229613i	0.196500	−	0.980504i	$-0.437042\pi$
$653$	21.8978	−	5.86749i	0.856926	−	0.229613i	0.660426	+	0.750891i	$0.270376\pi$
$654$	9.23043	−	39.3804i	0.360939	−	1.53990i
$655$	−0.979011	−	1.69570i	−0.0382531	−	0.0662563i
$656$	−3.87222	+	4.96634i	−0.151185	+	0.193903i
$657$	23.0937	−	30.1928i	0.900970	−	1.17794i
$658$	−0.164203	−	1.02701i	−0.00640131	−	0.0400372i
$659$	−1.24714	−	1.24714i	−0.0485815	−	0.0485815i	0.682399	−	0.730980i	$-0.260937\pi$
$659$	−1.24714	−	1.24714i	−0.0485815	−	0.0485815i	−0.730980	+	0.682399i	$0.760937\pi$
$660$	−12.1327	−	15.9134i	−0.472266	−	0.619429i
$661$	−0.728902	−	0.195309i	−0.0283510	−	0.00759663i	0.244616	−	0.969620i	$-0.421338\pi$
$661$	−0.728902	−	0.195309i	−0.0283510	−	0.00759663i	−0.272967	+	0.962023i	$0.588005\pi$
$662$	13.0825	−	15.8784i	0.508468	−	0.617132i
$663$	−8.50211	−	9.67969i	−0.330195	−	0.375928i
$664$	33.7699	+	18.3031i	1.31053	+	0.710298i
$665$	−9.70087	+	6.43784i	−0.376184	+	0.249649i
$666$	37.2699	+	11.3215i	1.44418	+	0.438698i
$667$	29.5047	−	7.90576i	1.14243	−	0.306112i
$668$	38.1417	+	13.1121i	1.47575	+	0.507324i
$669$	23.0299	+	15.3623i	0.890387	+	0.593942i
$670$	15.5651	−	11.1083i	0.601332	−	0.429151i
$671$	2.37495			0.0916840
$672$	−13.9532	+	21.8474i	−0.538258	+	0.842780i
$673$	10.6344			0.409926			0.204963	−	0.978770i	$-0.434293\pi$
$673$	10.6344			0.409926			0.204963	+	0.978770i	$0.434293\pi$
$674$	−25.2781	+	18.0401i	−0.973677	+	0.694881i
$675$	6.59336	−	2.25522i	0.253779	−	0.0868035i
$676$	−17.9103	−	6.15710i	−0.688858	−	0.236812i
$677$	35.1233	−	9.41125i	1.34990	−	0.361704i	0.489800	−	0.871835i	$-0.337070\pi$
$677$	35.1233	−	9.41125i	1.34990	−	0.361704i	0.860097	+	0.510131i	$0.170403\pi$
$678$	16.9365	−	0.534765i	0.650441	−	0.0205375i
$679$	−0.793656	−	12.7224i	−0.0304577	−	0.488241i
$680$	−10.2058	+	18.8300i	−0.391373	+	0.722098i
$681$	−3.44390	+	3.02494i	−0.131971	+	0.115916i
$682$	−1.62207	+	1.96873i	−0.0621124	+	0.0753864i
$683$	21.2293	+	5.68836i	0.812315	+	0.217659i	0.640984	−	0.767554i	$-0.278527\pi$
$683$	21.2293	+	5.68836i	0.812315	+	0.217659i	0.171331	+	0.985213i	$0.445193\pi$
$684$	13.0809	−	4.40653i	0.500161	−	0.168488i
$685$	−0.438010	−	0.438010i	−0.0167355	−	0.0167355i
$686$	18.1207	−	18.9114i	0.691852	−	0.722039i
$687$	−7.91734	−	2.68075i	−0.302065	−	0.102277i
$688$	6.37952	+	51.5351i	0.243217	+	1.96476i
$689$	2.31631	+	4.01196i	0.0882442	+	0.152843i
$690$	29.2127	+	6.84720i	1.11211	+	0.260668i
$691$	−18.2590	+	4.89250i	−0.694607	+	0.186119i	−0.588814	−	0.808269i	$-0.700405\pi$
$691$	−18.2590	+	4.89250i	−0.694607	+	0.186119i	−0.105793	+	0.994388i	$0.533738\pi$
$692$	7.43317	+	0.516080i	0.282567	+	0.0196184i
$693$	−4.63870	−	23.5170i	−0.176210	−	0.893339i
$694$	−15.5256	+	5.80915i	−0.589342	+	0.220512i
$695$	8.61812	−	14.9270i	0.326904	−	0.566214i
$696$	−10.9118	−	20.6639i	−0.413611	−	0.783261i
$697$	−5.39752	+	3.11626i	−0.204446	+	0.118037i
$698$	5.25187	+	0.877524i	0.198786	+	0.0332148i
$699$	8.54151	+	17.2867i	0.323070	+	0.653845i
$700$	−1.78851	−	6.86718i	−0.0675993	−	0.259555i
$701$	−13.7542	−	13.7542i	−0.519490	−	0.519490i	0.397927	−	0.917417i	$-0.369730\pi$
$701$	−13.7542	−	13.7542i	−0.519490	−	0.519490i	−0.917417	+	0.397927i	$0.869730\pi$
$702$	12.9243	+	4.85867i	0.487797	+	0.183379i
$703$	−18.2914	+	10.5605i	−0.689873	+	0.398299i
$704$	22.9661	−	7.49986i	0.865567	−	0.282662i
$705$	0.607753	+	0.691929i	0.0228893	+	0.0260596i
$706$	−18.2640	−	8.31794i	−0.687376	−	0.313050i
$707$	−0.747982	+	3.69946i	−0.0281308	+	0.139132i
$708$	−38.5902	+	15.8448i	−1.45031	+	0.595486i
$709$	44.4485	−	11.9099i	1.66930	−	0.447287i	0.704378	−	0.709825i	$-0.251226\pi$
$709$	44.4485	−	11.9099i	1.66930	−	0.447287i	0.964922	+	0.262538i	$0.0845595\pi$
$710$	−21.9652	+	26.6593i	−0.824338	+	1.00051i
$711$	8.48152	+	1.10327i	0.318082	+	0.0413758i
$712$	−8.29581	+	34.6679i	−0.310899	+	1.29924i
$713$		−	3.82478i		−	0.143239i
$714$	−20.9181	+	14.8537i	−0.782842	+	0.555887i
$715$	7.67500	+	7.67500i	0.287029	+	0.287029i
$716$	−29.2079	−	19.6799i	−1.09155	−	0.735473i
$717$	18.9966	+	12.6719i	0.709441	+	0.473240i
$718$	4.44851	+	46.0800i	0.166017	+	1.71969i
$719$	0.517463	−	0.896272i	0.0192981	−	0.0334253i	−0.856215	−	0.516620i	$-0.827190\pi$
$719$	0.517463	−	0.896272i	0.0192981	−	0.0334253i	0.875513	+	0.483194i	$0.160524\pi$
$720$	0.142074	−	22.9536i	0.00529479	−	0.855429i
$721$	−12.4008	+	24.9480i	−0.461830	+	0.929113i
$722$	8.03464	−	17.6420i	0.299018	−	0.656566i
$723$	−1.52109	+	23.4856i	−0.0565698	+	0.873440i
$724$	7.36576	+	15.0831i	0.273746	+	0.560559i
$725$	6.17888	+	1.65563i	0.229478	+	0.0614884i
$726$	2.17535	−	4.05846i	0.0807349	−	0.150624i
$727$	−40.7074			−1.50976			−0.754878	−	0.655866i	$-0.772304\pi$
$727$	−40.7074			−1.50976			−0.754878	+	0.655866i	$0.772304\pi$
$728$	5.91738	−	12.7550i	0.219313	−	0.472732i
$729$	24.9924	+	10.2166i	0.925646	+	0.378392i
$730$	33.8076	+	5.64885i	1.25128	+	0.209073i
$731$	−13.3014	+	49.6414i	−0.491969	+	1.83605i
$732$	2.15614	+	1.66509i	0.0796931	+	0.0615435i
$733$	−38.3920	+	10.2871i	−1.41804	+	0.379963i	−0.884789	−	0.465993i	$-0.845697\pi$
$733$	−38.3920	+	10.2871i	−1.41804	+	0.379963i	−0.533253	+	0.845956i	$0.679031\pi$
$734$	−19.7583	+	43.3842i	−0.729294	+	1.60134i
$735$	−4.65006	+	22.7209i	−0.171520	+	0.838074i
$736$	−19.4258	+	30.5758i	−0.716044	+	1.12704i
$737$	−18.4876	−	10.6738i	−0.681001	−	0.393176i
$738$	3.52943	−	5.67089i	0.129920	−	0.208748i
$739$	41.6644	+	11.1639i	1.53265	+	0.410672i	0.923883	−	0.382676i	$-0.124997\pi$
$739$	41.6644	+	11.1639i	1.53265	+	0.410672i	0.608768	+	0.793348i	$0.291664\pi$
$740$	6.71892	+	34.4747i	0.246992	+	1.26732i
$741$	−6.71226	+	3.31658i	−0.246581	+	0.121837i
$742$	8.42212	−	3.76454i	0.309186	−	0.138201i
$743$	−26.3486			−0.966635			−0.483317	−	0.875445i	$-0.660568\pi$
$743$	−26.3486			−0.966635			−0.483317	+	0.875445i	$0.660568\pi$
$744$	−2.85291	+	0.650096i	−0.104593	+	0.0238337i
$745$	−9.07019	−	15.7100i	−0.332306	−	0.575571i
$746$	6.67335	−	8.09950i	0.244329	−	0.296544i
$747$	−37.6639	−	15.5327i	−1.37805	−	0.568311i
$748$	23.8529	+	1.65609i	0.872149	+	0.0605527i
$749$	−3.43339	−	10.2200i	−0.125453	−	0.373432i
$750$	21.6613	+	20.3353i	0.790959	+	0.742539i
$751$	4.52777	−	7.84232i	0.165221	−	0.286170i	−0.771513	−	0.636213i	$-0.780500\pi$
$751$	4.52777	−	7.84232i	0.165221	−	0.286170i	0.936734	+	0.350043i	$0.113833\pi$
$752$	−1.03049	+	0.417534i	−0.0375782	+	0.0152259i
$753$	−45.9500	+	9.17698i	−1.67451	+	0.334428i
$754$	7.36293	+	10.3170i	0.268142	+	0.375724i
$755$	14.4376	−	14.4376i	0.525438	−	0.525438i
$756$	12.2766	−	24.6025i	0.446495	−	0.894786i
$757$	−25.3277	−	25.3277i	−0.920551	−	0.920551i	0.0765170	−	0.997068i	$-0.475620\pi$
$757$	−25.3277	−	25.3277i	−0.920551	−	0.920551i	−0.997068	+	0.0765170i	$0.975620\pi$
$758$	0.338856	+	0.0566188i	0.0123078	+	0.00205649i
$759$	−6.56016	−	32.8474i	−0.238119	−	1.19228i
$760$	9.03479	+	8.56095i	0.327726	+	0.310538i
$761$	23.2431	+	13.4194i	0.842561	+	0.486453i	0.858134	−	0.513426i	$-0.171624\pi$
$761$	23.2431	+	13.4194i	0.842561	+	0.486453i	−0.0155731	+	0.999879i	$0.504957\pi$
$762$	−1.22438	−	38.7773i	−0.0443548	−	1.40475i
$763$	42.8220	+	8.65806i	1.55026	+	0.313443i
$764$	−31.4825	+	27.3947i	−1.13900	+	0.991104i
$765$	8.66099	−	21.0013i	0.313139	−	0.759304i
$766$	−1.96179	−	20.3212i	−0.0708822	−	0.734235i
$767$	19.5958	−	11.3136i	0.707563	−	0.408511i
$768$	26.1083	+	9.29276i	0.942103	+	0.335324i
$769$		−	5.97807i		−	0.215575i	−0.994174	−	0.107787i	$-0.965623\pi$
$769$		−	5.97807i		−	0.215575i	0.994174	−	0.107787i	$-0.0343766\pi$
$770$	16.7776	−	13.6269i	0.604622	−	0.491080i
$771$	18.9846	+	38.4220i	0.683713	+	1.38373i
$772$	−33.7546	+	6.57858i	−1.21486	+	0.236768i
$773$	5.60499	−	20.9181i	0.201598	−	0.752372i	−0.788862	−	0.614570i	$-0.789330\pi$
$773$	5.60499	−	20.9181i	0.201598	−	0.752372i	0.990460	−	0.137802i	$-0.0440038\pi$
$774$	−12.4862	−	53.6445i	−0.448809	−	1.92821i
$775$	0.400493	−	0.693675i	0.0143861	−	0.0249175i
$776$	−13.0632	+	3.88005i	−0.468942	+	0.139286i
$777$	−10.9856	+	40.6129i	−0.394107	+	1.45698i
$778$	35.9864	−	13.4649i	1.29017	−	0.482741i
$779$	0.937416	+	3.49848i	0.0335864	+	0.125346i
$780$	1.58689	+	12.3488i	0.0568199	+	0.442160i
$781$	37.2483	+	9.98066i	1.33285	+	0.357136i
$782$	−29.1818	+	20.8260i	−1.04354	+	0.744738i
$783$	13.8179	+	20.5764i	0.493810	+	0.735339i
$784$	−24.0499	−	14.3389i	−0.858924	−	0.512103i
$785$			33.2781i			1.18775i
$786$	−2.40023	+	0.725061i	−0.0856134	+	0.0258621i
$787$	4.13339	−	15.4260i	0.147340	−	0.549879i	−0.852301	−	0.523052i	$-0.824793\pi$
$787$	4.13339	−	15.4260i	0.147340	−	0.549879i	0.999640	−	0.0268264i	$-0.00854015\pi$
$788$	−8.68435	−	17.7832i	−0.309367	−	0.633500i
$789$	−15.6784	−	1.01544i	−0.558166	−	0.0361506i
$790$	2.70272	+	7.22330i	0.0961584	+	0.256993i
$791$	1.13955	+	18.2671i	0.0405176	+	0.649502i
$792$	−23.3858	+	10.4763i	−0.830980	+	0.372258i
$793$	−1.27968	−	0.738821i	−0.0454426	−	0.0262363i
$794$	3.08316	−	3.74206i	0.109417	−	0.132801i
$795$	−4.53298	+	6.79546i	−0.160768	+	0.241010i
$796$	−2.69337	+	0.524921i	−0.0954638	+	0.0186053i
$797$	−4.34882	+	4.34882i	−0.154043	+	0.154043i	−0.779921	−	0.625878i	$-0.784741\pi$
$797$	−4.34882	+	4.34882i	−0.154043	+	0.154043i	0.625878	+	0.779921i	$0.284741\pi$
$798$	5.19157	+	13.9760i	0.183780	+	0.494747i
$799$	−1.10039			−0.0389292
$800$	−6.72472	+	3.51125i	−0.237755	+	0.124141i
$801$	4.87707	−	37.4931i	0.172323	−	1.32475i
$802$	−3.11990	+	0.301191i	−0.110167	+	0.0106354i
$803$	−9.90372	−	36.9612i	−0.349495	−	1.30433i
$804$	−9.30082	−	22.6522i	−0.328015	−	0.798882i
$805$	−6.42261	+	31.7657i	−0.226367	+	1.11959i
$806$	1.48646	−	0.556183i	0.0523582	−	0.0195907i
$807$	31.8374	−	27.9642i	1.12073	−	0.984387i
$808$	4.03345	−	0.108617i	0.141896	−	0.00382113i
$809$	−1.23933	−	2.14659i	−0.0435726	−	0.0754700i	0.843417	−	0.537260i	$-0.180541\pi$
$809$	−1.23933	−	2.14659i	−0.0435726	−	0.0754700i	−0.886989	+	0.461790i	$0.847207\pi$
$810$	2.41446	+	24.2264i	0.0848356	+	0.851228i
$811$	11.6016	−	11.6016i	0.407386	−	0.407386i	−0.473440	−	0.880826i	$-0.656988\pi$
$811$	11.6016	−	11.6016i	0.407386	−	0.407386i	0.880826	+	0.473440i	$0.156988\pi$
$812$	21.9468	−	12.4665i	0.770180	−	0.437488i
$813$	−20.1585	+	9.96049i	−0.706991	+	0.349329i
$814$	31.9164	−	22.7777i	1.11867	−	0.798356i
$815$	−6.42924	−	11.1358i	−0.225206	−	0.390069i
$816$	20.4942	+	18.2269i	0.717439	+	0.638069i
$817$	25.8645	+	14.9329i	0.904884	+	0.522435i
$818$	23.8484	+	10.8612i	0.833840	+	0.379753i
$819$	−4.81646	+	14.1145i	−0.168301	+	0.493202i
$820$	6.00857	+	0.417171i	0.209829	+	0.0145683i
$821$	0.826924	+	3.08612i	0.0288599	+	0.107706i	0.978853	−	0.204563i	$-0.0655774\pi$
$821$	0.826924	+	3.08612i	0.0288599	+	0.107706i	−0.949993	+	0.312270i	$0.898911\pi$
$822$	−0.674096	+	0.418096i	−0.0235118	+	0.0145828i
$823$	−7.70076	+	4.44604i	−0.268432	+	0.154979i	−0.628175	−	0.778072i	$-0.716198\pi$
$823$	−7.70076	+	4.44604i	−0.268432	+	0.154979i	0.359743	+	0.933051i	$0.382864\pi$
$824$	28.9659	+	6.93135i	1.00908	+	0.241465i
$825$	2.24968	−	6.64421i	0.0783237	−	0.231322i
$826$	−18.3873	−	41.1365i	−0.639776	−	1.43132i
$827$	10.6462	−	10.6462i	0.370206	−	0.370206i	−0.497346	−	0.867552i	$-0.665692\pi$
$827$	10.6462	−	10.6462i	0.370206	−	0.370206i	0.867552	+	0.497346i	$0.165692\pi$
$828$	17.0737	−	34.4204i	0.593352	−	1.19619i
$829$	−3.03526	+	11.3277i	−0.105419	+	0.393429i	−0.998392	−	0.0566805i	$-0.981948\pi$
$829$	−3.03526	+	11.3277i	−0.105419	+	0.393429i	0.892973	+	0.450109i	$0.148615\pi$
$830$	−3.53013	−	36.5670i	−0.122533	−	1.26926i
$831$	−7.62831	−	8.68486i	−0.264623	−	0.301274i
$832$	−14.7077	−	3.10341i	−0.509899	−	0.107591i
$833$	−16.7307	−	22.0904i	−0.579683	−	0.765388i
$834$	−16.0920	−	15.1069i	−0.557221	−	0.523110i
$835$	−9.98389	−	37.2604i	−0.345507	−	1.28945i
$836$	4.51726	−	13.1402i	0.156233	−	0.454464i
$837$	2.93651	−	1.00442i	0.101501	−	0.0347177i
$838$	−8.69192	+	52.0200i	−0.300257	+	1.79700i
$839$			26.7713i			0.924248i	0.886815	+	0.462124i	$0.152912\pi$
$839$			26.7713i			0.924248i	−0.886815	+	0.462124i	$0.847088\pi$
$840$	24.7857	−	0.608561i	0.855188	−	0.0209974i
$841$		−	6.24740i		−	0.215427i
$842$	−11.3410	−	1.89495i	−0.390838	−	0.0653044i
$843$	−8.34962	+	12.5170i	−0.287576	+	0.431110i
$844$	12.4414	+	25.4766i	0.428250	+	0.876941i
$845$	4.68816	+	17.4965i	0.161278	+	0.601897i
$846$	1.04028	−	0.555522i	0.0357655	−	0.0190993i
$847$	4.45378	+	2.21382i	0.153034	+	0.0760677i
$848$	−5.94297	−	7.87036i	−0.204082	−	0.270269i
$849$	23.1527	−	20.3361i	0.794598	−	0.697932i
$850$	−7.47319	+	0.721453i	−0.256328	+	0.0247456i
$851$	−15.2166	+	56.7890i	−0.521617	+	1.94670i
$852$	26.8190	+	35.1761i	0.918804	+	1.20511i
$853$	−8.42520	+	8.42520i	−0.288473	+	0.288473i	−0.836476	−	0.548003i	$-0.815388\pi$
$853$	−8.42520	+	8.42520i	−0.288473	+	0.288473i	0.548003	+	0.836476i	$0.315388\pi$
$854$	−1.72608	+	2.38307i	−0.0590652	+	0.0815469i
$855$	−10.4859	−	8.02041i	−0.358612	−	0.274292i
$856$	−9.82282	+	6.02947i	−0.335737	+	0.206083i
$857$	−37.5658	+	21.6886i	−1.28322	+	0.740870i	−0.977436	−	0.211230i	$-0.932253\pi$
$857$	−37.5658	+	21.6886i	−1.28322	+	0.740870i	−0.305788	+	0.952100i	$0.598920\pi$
$858$	11.8118	−	7.32605i	0.403248	−	0.250107i
$859$	−9.70555	−	36.2216i	−0.331149	−	1.23587i	−0.907984	−	0.419005i	$-0.862379\pi$
$859$	−9.70555	−	36.2216i	−0.331149	−	1.23587i	0.576835	−	0.816861i	$-0.304288\pi$
$860$	37.4667	−	32.6019i	1.27760	−	1.11172i
$861$	6.23953	+	3.62217i	0.212643	+	0.123443i
$862$	2.07223	−	4.55007i	0.0705803	−	0.154976i
$863$	−1.77594	−	1.02534i	−0.0604537	−	0.0349030i	0.469469	−	0.882949i	$-0.344446\pi$
$863$	−1.77594	−	1.02534i	−0.0604537	−	0.0349030i	−0.529922	+	0.848046i	$0.677779\pi$
$864$	−28.5762	−	6.88488i	−0.972182	−	0.234228i
$865$	−3.56316	−	6.17158i	−0.121151	−	0.209840i
$866$	26.5472	+	37.1983i	0.902111	+	1.26405i
$867$	−1.01933	−	2.06298i	−0.0346184	−	0.0700625i
$868$	−0.796555	−	3.05846i	−0.0270368	−	0.103811i
$869$	6.08810	−	6.08810i	0.206525	−	0.206525i
$870$	−10.5584	+	19.6983i	−0.357962	+	0.667834i
$871$	6.64103	+	11.5026i	0.225023	+	0.389751i
$872$	−1.25727	−	46.6881i	−0.0425764	−	1.58106i
$873$	13.3451	−	5.55191i	0.451662	−	0.187904i
$874$	7.30109	+	19.5129i	0.246963	+	0.660034i
$875$	−21.2352	+	24.0609i	−0.717880	+	0.813405i
$876$	16.9224	−	40.4994i	0.571756	−	1.36835i
$877$	−5.58155	−	20.8306i	−0.188476	−	0.703401i	−0.993860	−	0.110648i	$-0.964708\pi$
$877$	−5.58155	−	20.8306i	−0.188476	−	0.703401i	0.805384	−	0.592753i	$-0.201959\pi$
$878$	2.95475	+	30.6068i	0.0997179	+	1.03293i
$879$	−57.2092	+	11.4256i	−1.92962	+	0.385377i
$880$	−18.2224	−	14.2079i	−0.614277	−	0.478947i
$881$	16.5133			0.556346			0.278173	−	0.960531i	$-0.410271\pi$
$881$	16.5133			0.556346			0.278173	+	0.960531i	$0.410271\pi$
$882$	26.9688	+	12.4373i	0.908085	+	0.418785i
$883$	20.9255	−	20.9255i	0.704198	−	0.704198i	−0.261111	−	0.965309i	$-0.584089\pi$
$883$	20.9255	−	20.9255i	0.704198	−	0.704198i	0.965309	+	0.261111i	$0.0840887\pi$
$884$	−12.3373	−	8.31272i	−0.414948	−	0.279587i
$885$	33.1914	+	22.1406i	1.11572	+	0.744250i
$886$	−33.3229	−	27.4554i	−1.11950	−	0.922382i
$887$	−44.9530	−	25.9536i	−1.50937	−	0.871438i	−0.999940	−	0.0109283i	$-0.996521\pi$
$887$	−44.9530	−	25.9536i	−1.50937	−	0.871438i	−0.509434	−	0.860510i	$-0.670145\pi$
$888$	44.9453	+	1.69767i	1.50827	+	0.0569699i
$889$	41.8239	−	2.60908i	1.40273	−	0.0875058i
$890$	31.9311	−	11.9476i	1.07033	−	0.400483i
$891$	23.4961	−	13.6626i	0.787148	−	0.457713i
$892$	30.2298	+	10.3922i	1.01217	+	0.347957i
$893$	−0.165507	+	0.617682i	−0.00553849	+	0.0206699i
$894$	−22.2373	+	6.71744i	−0.743727	+	0.224665i
$895$			33.6843i			1.12594i
$896$	−9.16592	+	28.4954i	−0.306212	+	0.951963i
$897$	−6.68369	+	19.7397i	−0.223162	+	0.659088i
$898$	−27.6152	−	38.6948i	−0.921530	−	1.29126i
$899$	2.75191	+	0.737372i	0.0917813	+	0.0245927i
$900$	6.70070	−	4.45480i	0.223357	−	0.148493i
$901$	−2.52616	−	9.42778i	−0.0841588	−	0.314085i
$902$	−2.35633	−	6.29755i	−0.0784574	−	0.209685i
$903$	57.5008	−	15.2610i	1.91351	−	0.507856i
$904$	18.7564	−	5.57105i	0.623829	−	0.185290i
$905$	8.02698	−	13.9031i	0.266826	−	0.462156i
$906$	−13.7812	−	22.2194i	−0.457849	−	0.738190i
$907$	−5.65148	+	21.0916i	−0.187654	+	0.700335i	0.806393	+	0.591381i	$0.201417\pi$
$907$	−5.65148	+	21.0916i	−0.187654	+	0.700335i	−0.994047	+	0.108954i	$0.965250\pi$
$908$	−2.95755	+	4.38944i	−0.0981499	+	0.145669i
$909$	−4.24219	+	0.565172i	−0.140705	+	0.0187456i
$910$	−13.2793	+	2.12315i	−0.440205	+	0.0703818i
$911$		−	5.98219i		−	0.198199i	−0.995078	−	0.0990994i	$-0.968404\pi$
$911$		−	5.98219i		−	0.198199i	0.995078	−	0.0990994i	$-0.0315962\pi$
$912$	13.3137	−	8.76248i	0.440862	−	0.290155i
$913$	−35.5175	+	20.5060i	−1.17546	+	0.678651i
$914$	−30.6062	+	2.95469i	−1.01236	+	0.0977325i
$915$	0.168397	−	2.60006i	0.00556703	−	0.0859552i
$916$	−9.62880	−	0.668522i	−0.318145	−	0.0220886i
$917$	−0.862462	−	2.56725i	−0.0284810	−	0.0847782i
$918$	−23.6527	−	16.9355i	−0.780655	−	0.558953i
$919$	−28.2043	−	16.2838i	−0.930374	−	0.537152i	−0.0434443	−	0.999056i	$-0.513833\pi$
$919$	−28.2043	−	16.2838i	−0.930374	−	0.537152i	−0.886930	+	0.461904i	$0.847166\pi$
$920$	34.6335	−	0.932648i	1.14183	−	0.0307485i
$921$	−7.13740	+	1.42546i	−0.235185	+	0.0469704i
$922$	7.90179	−	47.2911i	0.260232	−	1.55745i
$923$	−16.9653	−	16.9653i	−0.558421	−	0.558421i
$924$	−12.0866	−	24.8999i	−0.397621	−	0.819147i
$925$	−8.70611	+	8.70611i	−0.286255	+	0.286255i
$926$	−20.2278	+	14.4359i	−0.664725	+	0.474392i
$927$	−31.3264	−	4.07491i	−1.02890	−	0.133838i
$928$	−18.2541	−	19.8714i	−0.599219	−	0.652310i
$929$	11.9866	−	20.7615i	0.393269	−	0.681162i	−0.599610	−	0.800293i	$-0.704677\pi$
$929$	11.9866	−	20.7615i	0.393269	−	0.681162i	0.992879	+	0.119131i	$0.0380108\pi$
$930$	2.04031	+	1.91541i	0.0669045	+	0.0628089i
$931$	−14.9164	+	6.06883i	−0.488865	+	0.198898i
$932$	14.6153	+	16.7962i	0.478740	+	0.550177i
$933$	−0.880128	+	13.5892i	−0.0288141	+	0.444891i
$934$	−26.0708	−	21.4802i	−0.853061	−	0.702855i
$935$	−11.4341	−	19.8045i	−0.373936	−	0.647676i
$936$	15.8599	+	1.63023i	0.518396	+	0.0532858i
$937$	−34.0643			−1.11283			−0.556416	−	0.830904i	$-0.687824\pi$
$937$	−34.0643			−1.11283			−0.556416	+	0.830904i	$0.687824\pi$
$938$	24.1469	−	10.7932i	0.788424	−	0.352412i
$939$	−6.47307	−	13.1005i	−0.211241	−	0.427520i
$940$	0.881901	+	0.594215i	0.0287644	+	0.0193811i
$941$	−27.6261	−	7.40239i	−0.900585	−	0.241311i	−0.221317	−	0.975202i	$-0.571036\pi$
$941$	−27.6261	−	7.40239i	−0.900585	−	0.241311i	−0.679267	+	0.733891i	$0.737702\pi$
$942$	41.4900	+	9.72490i	1.35182	+	0.316855i
$943$	8.73114	+	5.04093i	0.284325	+	0.164155i
$944$	−38.4416	+	29.0275i	−1.25117	+	0.944765i
$945$	−26.0750	+	3.41088i	−0.848219	+	0.110956i
$946$	−50.4584	−	22.9801i	−1.64054	−	0.747148i
$947$	−24.6127	+	6.59494i	−0.799804	+	0.214307i	−0.635498	−	0.772103i	$-0.719205\pi$
$947$	−24.6127	+	6.59494i	−0.799804	+	0.214307i	−0.164306	+	0.986409i	$0.552538\pi$
$948$	9.79558	−	1.25878i	0.318146	−	0.0408834i
$949$	−6.16188	+	22.9964i	−0.200023	+	0.746496i
$950$	−0.719051	+	4.30342i	−0.0233291	+	0.139621i
$951$	−12.0885	+	35.7023i	−0.391996	+	1.15773i
$952$	−18.9977	+	22.7308i	−0.615719	+	0.736710i
$953$	−5.93311			−0.192192			−0.0960962	−	0.995372i	$-0.530636\pi$
$953$	−5.93311			−0.192192			−0.0960962	+	0.995372i	$0.530636\pi$
$954$	7.14767	+	7.63741i	0.231414	+	0.247270i
$955$	38.5538	+	10.3305i	1.24757	+	0.334286i
$956$	24.9355	+	8.57219i	0.806473	+	0.277244i
$957$	24.8982	+	1.61257i	0.804845	+	0.0521271i
$958$	−31.0512	−	14.1416i	−1.00322	−	0.456893i
$959$	−0.473758	−	0.713884i	−0.0152985	−	0.0230525i
$960$	−6.58230	−	25.6747i	−0.212443	−	0.828646i
$961$	−15.3216	+	26.5378i	−0.494246	+	0.856059i
$962$	−24.2831	+	2.34427i	−0.782919	+	0.0755821i
$963$	9.68713	−	7.45703i	0.312163	−	0.240299i
$964$	5.19857	+	26.6738i	0.167435	+	0.859106i
$965$	23.2574	+	23.2574i	0.748682	+	0.748682i
$966$	37.7274	+	17.2904i	1.21386	+	0.556309i
$967$			15.0819i			0.485002i	0.970151	+	0.242501i	$0.0779678\pi$
$967$			15.0819i			0.485002i	−0.970151	+	0.242501i	$0.922032\pi$
$968$	1.23740	−	5.17106i	0.0397716	−	0.166204i
$969$	15.4686	−	3.08933i	0.496922	−	0.0992436i
$970$	10.0589	+	8.28773i	0.322972	+	0.266103i
$971$	−3.19635	+	0.856459i	−0.102576	+	0.0274851i	−0.309742	−	0.950821i	$-0.600243\pi$
$971$	−3.19635	+	0.856459i	−0.102576	+	0.0274851i	0.207166	+	0.978306i	$0.433576\pi$
$972$	30.9102	+	4.06943i	0.991445	+	0.130527i
$973$	15.7755	−	17.8746i	0.505738	−	0.573034i
$974$	−9.45533	+	20.7614i	−0.302968	+	0.665240i
$975$	−3.27912	+	2.88020i	−0.105016	+	0.0922401i
$976$	2.89682	+	1.22625i	0.0927251	+	0.0392512i
$977$	−34.6710	+	20.0173i	−1.10922	+	0.640411i	−0.938628	−	0.344930i	$-0.887903\pi$
$977$	−34.6710	+	20.0173i	−1.10922	+	0.640411i	−0.170596	+	0.985341i	$0.554569\pi$
$978$	−15.7625	+	4.76153i	−0.504029	+	0.152257i
$979$	−26.9129	−	26.9129i	−0.860139	−	0.860139i
$980$	1.47978	+	26.7388i	0.0472697	+	0.854138i
$981$	6.54200	+	49.1043i	0.208870	+	1.56778i
$982$	0.498764	−	2.98503i	0.0159162	−	0.0952562i
$983$	37.0193	−	21.3731i	1.18073	−	0.681695i	0.224548	−	0.974463i	$-0.427910\pi$
$983$	37.0193	−	21.3731i	1.18073	−	0.681695i	0.956184	+	0.292768i	$0.0945762\pi$
$984$	2.27601	−	7.36937i	0.0725564	−	0.234927i
$985$	−9.46394	+	16.3920i	−0.301546	+	0.522293i
$986$	−9.35833	−	25.0111i	−0.298030	−	0.796516i
$987$	0.634281	+	1.10466i	0.0201894	+	0.0351616i
$988$	−6.52178	+	5.67496i	−0.207485	+	0.180545i
$989$	80.3011	−	21.5166i	2.55343	−	0.684188i
$990$	20.8075	+	12.9501i	0.661307	+	0.411582i
$991$	1.32563	+	2.29605i	0.0421099	+	0.0729365i	0.886312	−	0.463088i	$-0.153259\pi$
$991$	1.32563	+	2.29605i	0.0421099	+	0.0729365i	−0.844202	+	0.536025i	$0.819925\pi$
$992$	−2.99501	+	1.56382i	−0.0950917	+	0.0496513i
$993$	−8.08102	+	23.8665i	−0.256443	+	0.757382i
$994$	−37.0863	+	30.1218i	−1.17631	+	0.955406i
$995$	1.85576	+	1.85576i	0.0588317	+	0.0588317i
$996$	−46.6220	−	6.28475i	−1.47728	−	0.199140i
$997$	−31.4435	−	8.42525i	−0.995824	−	0.266830i	−0.276129	−	0.961121i	$-0.589052\pi$
$997$	−31.4435	−	8.42525i	−0.995824	−	0.266830i	−0.719695	+	0.694290i	$0.755718\pi$
$998$	6.83895	+	5.63475i	0.216483	+	0.178365i
$999$	−47.5962	+	3.23056i	−1.50588	+	0.102210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.12	✓	240
3.2	odd	2	inner	336.2.bo.a.5.49	yes	240
7.3	odd	6	inner	336.2.bo.a.101.29	yes	240
16.13	even	4	inner	336.2.bo.a.173.32	yes	240
21.17	even	6	inner	336.2.bo.a.101.32	yes	240
48.29	odd	4	inner	336.2.bo.a.173.29	yes	240
112.45	odd	12	inner	336.2.bo.a.269.49	yes	240
336.269	even	12	inner	336.2.bo.a.269.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.12	✓	240	1.1	even	1	trivial
336.2.bo.a.5.49	yes	240	3.2	odd	2	inner
336.2.bo.a.101.29	yes	240	7.3	odd	6	inner
336.2.bo.a.101.32	yes	240	21.17	even	6	inner
336.2.bo.a.173.29	yes	240	48.29	odd	4	inner
336.2.bo.a.173.32	yes	240	16.13	even	4	inner
336.2.bo.a.269.12	yes	240	336.269	even	12	inner
336.2.bo.a.269.49	yes	240	112.45	odd	12	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15113 + 0.821523i) q^{2} +(0.961162 - 1.44089i) q^{3} +(0.650200 - 1.89136i) q^{4} +(-1.84766 + 0.495078i) q^{5} +(0.0773035 + 2.44827i) q^{6} +(-2.64062 + 0.164729i) q^{7} +(0.805330 + 2.71135i) q^{8} +(-1.15234 - 2.76986i) q^{9} +O(q^{10})\)	\(q+(-1.15113 + 0.821523i) q^{2} +(0.961162 - 1.44089i) q^{3} +(0.650200 - 1.89136i) q^{4} +(-1.84766 + 0.495078i) q^{5} +(0.0773035 + 2.44827i) q^{6} +(-2.64062 + 0.164729i) q^{7} +(0.805330 + 2.71135i) q^{8} +(-1.15234 - 2.76986i) q^{9} +(1.72017 - 2.08779i) q^{10} +(-2.91705 - 0.781622i) q^{11} +(-2.10030 - 2.75477i) q^{12} +(1.32862 + 1.32862i) q^{13} +(2.90437 - 2.35895i) q^{14} +(-1.06254 + 3.13812i) q^{15} +(-3.15448 - 2.45952i) q^{16} +(-1.97936 - 3.42835i) q^{17} +(3.60199 + 2.24180i) q^{18} +(-2.22214 + 0.595421i) q^{19} +(-0.264976 + 3.81648i) q^{20} +(-2.30071 + 3.96318i) q^{21} +(4.00003 - 1.49668i) q^{22} +(-3.20186 + 5.54578i) q^{23} +(4.68082 + 1.44566i) q^{24} +(-1.16140 + 0.670533i) q^{25} +(-2.62090 - 0.437922i) q^{26} +(-5.09865 - 1.00189i) q^{27} +(-1.40537 + 5.10146i) q^{28} +(-3.37288 - 3.37288i) q^{29} +(-1.35491 - 4.48529i) q^{30} +(-0.517256 + 0.298638i) q^{31} +(5.65177 + 0.239754i) q^{32} +(-3.92999 + 3.45189i) q^{33} +(5.09497 + 2.32039i) q^{34} +(4.79740 - 1.61167i) q^{35} +(-5.98805 + 0.378520i) q^{36} +(8.86814 - 2.37621i) q^{37} +(2.06882 - 2.51095i) q^{38} +(3.19141 - 0.637378i) q^{39} +(-2.83030 - 4.61095i) q^{40} -1.57438i q^{41} +(-0.607429 - 6.45221i) q^{42} +(-9.17974 - 9.17974i) q^{43} +(-3.37500 + 5.00899i) q^{44} +(3.50042 + 4.54725i) q^{45} +(-0.870232 - 9.01431i) q^{46} +(0.138984 - 0.240727i) q^{47} +(-6.57587 + 2.18126i) q^{48} +(6.94573 - 0.869970i) q^{49} +(0.786061 - 1.72599i) q^{50} +(-6.84237 - 0.443158i) q^{51} +(3.37676 - 1.64903i) q^{52} +(2.38152 + 0.638126i) q^{53} +(6.69228 - 3.03535i) q^{54} +5.77668 q^{55} +(-2.57321 - 7.02699i) q^{56} +(-1.27790 + 3.77416i) q^{57} +(6.65352 + 1.11172i) q^{58} +(3.11683 - 11.6322i) q^{59} +(5.24445 + 4.05006i) q^{60} +(-0.759622 + 0.203540i) q^{61} +(0.350091 - 0.768709i) q^{62} +(3.49916 + 7.12432i) q^{63} +(-6.70289 + 4.36707i) q^{64} +(-3.11260 - 1.79706i) q^{65} +(1.68812 - 7.20216i) q^{66} +(6.82801 + 1.82956i) q^{67} +(-7.77123 + 1.51457i) q^{68} +(4.91337 + 9.94392i) q^{69} +(-4.19840 + 5.79642i) q^{70} -12.7692 q^{71} +(6.58206 - 5.35504i) q^{72} +(6.33536 + 10.9732i) q^{73} +(-8.25627 + 10.0207i) q^{74} +(-0.150125 + 2.31794i) q^{75} +(-0.318681 + 4.59001i) q^{76} +(7.83158 + 1.58344i) q^{77} +(-3.15011 + 3.35552i) q^{78} +(-1.42550 + 2.46903i) q^{79} +(7.04605 + 2.98264i) q^{80} +(-6.34424 + 6.38362i) q^{81} +(1.29339 + 1.81231i) q^{82} +(9.60276 - 9.60276i) q^{83} +(5.99987 + 6.92832i) q^{84} +(5.35448 + 5.35448i) q^{85} +(18.1084 + 3.02571i) q^{86} +(-8.10183 + 1.61807i) q^{87} +(-0.229937 - 8.53863i) q^{88} +(10.9145 + 6.30150i) q^{89} +(-7.76510 - 2.35880i) q^{90} +(-3.72724 - 3.28951i) q^{91} +(8.40722 + 9.66173i) q^{92} +(-0.0668618 + 1.03235i) q^{93} +(0.0377743 + 0.391286i) q^{94} +(3.81097 - 2.20027i) q^{95} +(5.77772 - 7.91315i) q^{96} +4.81796i q^{97} +(-7.28074 + 6.70752i) q^{98} +(1.19644 + 8.98052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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