LMFDB - Embedded newform 336.2.bu.a.11.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(11,336)]

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([6, 3, 6, 8]))

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

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

chi := DirichletCharacter("336.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bu (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			11.18
Character	$\chi$	$=$	336.11
Dual form			336.2.bu.a.275.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.863239 - 1.12019i) q^{2} +(1.08000 - 1.35410i) q^{3} +(-0.509638 + 1.93398i) q^{4} +(-1.29824 - 0.347862i) q^{5} +(-2.44915 - 0.0408893i) q^{6} +(-2.01473 - 1.71490i) q^{7} +(2.60636 - 1.09860i) q^{8} +(-0.667192 - 2.92487i) q^{9} +O(q^{10})$	\(q+(-0.863239 - 1.12019i) q^{2} +(1.08000 - 1.35410i) q^{3} +(-0.509638 + 1.93398i) q^{4} +(-1.29824 - 0.347862i) q^{5} +(-2.44915 - 0.0408893i) q^{6} +(-2.01473 - 1.71490i) q^{7} +(2.60636 - 1.09860i) q^{8} +(-0.667192 - 2.92487i) q^{9} +(0.731019 + 1.75456i) q^{10} +(-1.69548 + 0.454301i) q^{11} +(2.06840 + 2.77880i) q^{12} +(-2.23759 + 2.23759i) q^{13} +(-0.181819 + 3.73724i) q^{14} +(-1.87314 + 1.38226i) q^{15} +(-3.48054 - 1.97126i) q^{16} +(-2.32989 - 1.34516i) q^{17} +(-2.70045 + 3.27224i) q^{18} +(1.65097 - 6.16150i) q^{19} +(1.33439 - 2.33348i) q^{20} +(-4.49806 + 0.876052i) q^{21} +(1.97250 + 1.50708i) q^{22} +(-1.09281 + 0.630932i) q^{23} +(1.32726 - 4.71576i) q^{24} +(-2.76571 - 1.59679i) q^{25} +(4.43808 + 0.574943i) q^{26} +(-4.68114 - 2.25542i) q^{27} +(4.34336 - 3.02246i) q^{28} +(4.88450 + 4.88450i) q^{29} +(3.16535 + 0.905049i) q^{30} +(1.30133 + 0.751321i) q^{31} +(0.796362 + 5.60052i) q^{32} +(-1.21595 + 2.78650i) q^{33} +(0.504417 + 3.77110i) q^{34} +(2.01904 + 2.92719i) q^{35} +(5.99666 + 0.200288i) q^{36} +(0.319055 - 1.19073i) q^{37} +(-8.32722 + 3.46945i) q^{38} +(0.613326 + 5.44652i) q^{39} +(-3.76583 + 0.519586i) q^{40} -0.647051 q^{41} +(4.86424 + 4.28242i) q^{42} +(5.04389 - 5.04389i) q^{43} +(-0.0145305 - 3.51054i) q^{44} +(-0.151276 + 4.02927i) q^{45} +(1.65012 + 0.679503i) q^{46} +(-0.880271 - 1.52467i) q^{47} +(-6.42827 + 2.58405i) q^{48} +(1.11824 + 6.91010i) q^{49} +(0.598773 + 4.47652i) q^{50} +(-4.33777 + 1.70213i) q^{51} +(-3.18708 - 5.46780i) q^{52} +(-2.42297 - 9.04263i) q^{53} +(1.51446 + 7.19072i) q^{54} +2.35916 q^{55} +(-7.13507 - 2.25627i) q^{56} +(-6.56026 - 8.89002i) q^{57} +(1.25506 - 9.68804i) q^{58} +(10.7675 - 2.88515i) q^{59} +(-1.71863 - 4.32706i) q^{60} +(-9.85115 - 2.63961i) q^{61} +(-0.281735 - 2.10630i) q^{62} +(-3.67165 + 7.03697i) q^{63} +(5.58618 - 5.72666i) q^{64} +(3.68329 - 2.12655i) q^{65} +(4.17105 - 1.04332i) q^{66} +(13.5990 - 3.64383i) q^{67} +(3.78891 - 3.82040i) q^{68} +(-0.325886 + 2.16118i) q^{69} +(1.53609 - 4.78857i) q^{70} +10.3613i q^{71} +(-4.95219 - 6.89027i) q^{72} +(-4.47539 - 2.58387i) q^{73} +(-1.60926 + 0.670484i) q^{74} +(-5.14919 + 2.02053i) q^{75} +(11.0748 + 6.33307i) q^{76} +(4.19500 + 1.99228i) q^{77} +(5.57167 - 5.38869i) q^{78} +(2.76636 - 1.59716i) q^{79} +(3.83284 + 3.76990i) q^{80} +(-8.10971 + 3.90290i) q^{81} +(0.558559 + 0.724818i) q^{82} +(10.5779 - 10.5779i) q^{83} +(0.598114 - 9.14561i) q^{84} +(2.55682 + 2.55682i) q^{85} +(-10.0042 - 1.29602i) q^{86} +(11.8894 - 1.33885i) q^{87} +(-3.91992 + 3.04671i) q^{88} +(-2.65355 - 4.59608i) q^{89} +(4.64412 - 3.30876i) q^{90} +(8.34536 - 0.670886i) q^{91} +(-0.663274 - 2.43501i) q^{92} +(2.42280 - 0.950703i) q^{93} +(-0.948036 + 2.30223i) q^{94} +(-4.28670 + 7.42479i) q^{95} +(8.44375 + 4.97021i) q^{96} +9.13706 q^{97} +(6.77530 - 7.21771i) q^{98} +(2.45998 + 4.65594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) $ 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7	$ 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) $ 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7 - 4 * q^10 - 2 * q^12 - 16 * q^13 - 20 * q^16 + 16 * q^18 - 4 * q^19 + 2 * q^21 - 40 * q^22 - 22 * q^24 - 8 * q^27 - 4 * q^28 - 26 * q^30 - 4 * q^33 + 16 * q^36 - 4 * q^37 - 4 * q^39 + 8 * q^40 - 18 * q^42 - 16 * q^43 + 18 * q^45 - 20 * q^46 - 88 * q^48 - 16 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^54 - 32 * q^55 - 36 * q^58 - 42 * q^60 - 4 * q^61 - 64 * q^64 - 30 * q^66 - 36 * q^67 - 20 * q^69 + 116 * q^70 - 46 * q^72 - 24 * q^75 - 112 * q^76 - 92 * q^78 - 4 * q^81 - 32 * q^82 + 44 * q^84 - 56 * q^85 - 4 * q^87 - 20 * q^88 + 28 * q^90 - 40 * q^91 - 14 * q^93 + 72 * q^94 + 36 * q^96 - 32 * q^97 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.863239	−	1.12019i	−0.610402	−	0.792092i
$2$	−0.863239	−	1.12019i	−0.610402	−	0.792092i
$3$	1.08000	−	1.35410i	0.623539	−	0.781792i
$3$	1.08000	−	1.35410i	0.623539	−	0.781792i
$4$	−0.509638	+	1.93398i	−0.254819	+	0.966989i
$5$	−1.29824	−	0.347862i	−0.580590	−	0.155569i	−0.0434408	−	0.999056i	$-0.513832\pi$
$5$	−1.29824	−	0.347862i	−0.580590	−	0.155569i	−0.537149	+	0.843487i	$0.680499\pi$
$6$	−2.44915	−	0.0408893i	−0.999861	−	0.0166930i
$7$	−2.01473	−	1.71490i	−0.761495	−	0.648171i
$7$	−2.01473	−	1.71490i	−0.761495	−	0.648171i
$8$	2.60636	−	1.09860i	0.921486	−	0.388412i
$9$	−0.667192	−	2.92487i	−0.222397	−	0.974956i
$10$	0.731019	+	1.75456i	0.231169	+	0.554840i
$11$	−1.69548	+	0.454301i	−0.511205	+	0.136977i	−0.505196	−	0.863005i	$-0.668580\pi$
$11$	−1.69548	+	0.454301i	−0.511205	+	0.136977i	−0.00600969	+	0.999982i	$0.501913\pi$
$12$	2.06840	+	2.77880i	0.597095	+	0.802171i
$13$	−2.23759	+	2.23759i	−0.620595	+	0.620595i	−0.945683	−	0.325089i	$-0.894606\pi$
$13$	−2.23759	+	2.23759i	−0.620595	+	0.620595i	0.325089	+	0.945683i	$0.394606\pi$
$14$	−0.181819	+	3.73724i	−0.0485931	+	0.998819i
$15$	−1.87314	+	1.38226i	−0.483643	+	0.356897i
$16$	−3.48054	−	1.97126i	−0.870135	−	0.492814i
$17$	−2.32989	−	1.34516i	−0.565081	−	0.326249i	0.190102	−	0.981764i	$-0.439118\pi$
$17$	−2.32989	−	1.34516i	−0.565081	−	0.326249i	−0.755182	+	0.655515i	$0.772452\pi$
$18$	−2.70045	+	3.27224i	−0.636503	+	0.771274i
$19$	1.65097	−	6.16150i	0.378759	−	1.41355i	−0.469016	−	0.883190i	$-0.655391\pi$
$19$	1.65097	−	6.16150i	0.378759	−	1.41355i	0.847775	−	0.530357i	$-0.177942\pi$
$20$	1.33439	−	2.33348i	0.298378	−	0.521782i
$21$	−4.49806	+	0.876052i	−0.981557	+	0.191170i
$22$	1.97250	+	1.50708i	0.420539	+	0.321310i
$23$	−1.09281	+	0.630932i	−0.227866	+	0.131558i	−0.609587	−	0.792719i	$-0.708665\pi$
$23$	−1.09281	+	0.630932i	−0.227866	+	0.131558i	0.381721	+	0.924278i	$0.375331\pi$
$24$	1.32726	−	4.71576i	0.270925	−	0.962600i
$25$	−2.76571	−	1.59679i	−0.553143	−	0.319357i
$26$	4.43808	+	0.574943i	0.870380	+	0.112756i
$27$	−4.68114	−	2.25542i	−0.900886	−	0.434055i
$28$	4.34336	−	3.02246i	0.820817	−	0.571191i
$29$	4.88450	+	4.88450i	0.907029	+	0.907029i	0.996031	−	0.0890025i	$-0.0283679\pi$
$29$	4.88450	+	4.88450i	0.907029	+	0.907029i	−0.0890025	+	0.996031i	$0.528368\pi$
$30$	3.16535	+	0.905049i	0.577912	+	0.165239i
$31$	1.30133	+	0.751321i	0.233725	+	0.134941i	0.612289	−	0.790634i	$-0.290249\pi$
$31$	1.30133	+	0.751321i	0.233725	+	0.134941i	−0.378564	+	0.925575i	$0.623582\pi$
$32$	0.796362	+	5.60052i	0.140778	+	0.990041i
$33$	−1.21595	+	2.78650i	−0.211669	+	0.485067i
$34$	0.504417	+	3.77110i	0.0865068	+	0.646739i
$35$	2.01904	+	2.92719i	0.341281	+	0.494786i
$36$	5.99666	+	0.200288i	0.999443	+	0.0333813i
$37$	0.319055	−	1.19073i	0.0524524	−	0.195755i	−0.934728	−	0.355364i	$-0.884357\pi$
$37$	0.319055	−	1.19073i	0.0524524	−	0.195755i	0.987180	+	0.159609i	$0.0510235\pi$
$38$	−8.32722	+	3.46945i	−1.35085	+	0.562820i
$39$	0.613326	+	5.44652i	0.0982107	+	0.872141i
$40$	−3.76583	+	0.519586i	−0.595430	+	0.0821538i
$41$	−0.647051			−0.101052			−0.0505262	−	0.998723i	$-0.516090\pi$
$41$	−0.647051			−0.101052			−0.0505262	+	0.998723i	$0.516090\pi$
$42$	4.86424	+	4.28242i	0.750569	+	0.660792i
$43$	5.04389	−	5.04389i	0.769187	−	0.769187i	−0.208777	−	0.977963i	$-0.566948\pi$
$43$	5.04389	−	5.04389i	0.769187	−	0.769187i	0.977963	+	0.208777i	$0.0669482\pi$
$44$	−0.0145305	−	3.51054i	−0.00219056	−	0.529234i
$45$	−0.151276	+	4.02927i	−0.0225508	+	0.600647i
$46$	1.65012	+	0.679503i	0.243296	+	0.100187i
$47$	−0.880271	−	1.52467i	−0.128401	−	0.222397i	0.794656	−	0.607059i	$-0.207651\pi$
$47$	−0.880271	−	1.52467i	−0.128401	−	0.222397i	−0.923057	+	0.384663i	$0.874318\pi$
$48$	−6.42827	+	2.58405i	−0.927841	+	0.372976i
$49$	1.11824	+	6.91010i	0.159748	+	0.987158i
$50$	0.598773	+	4.47652i	0.0846793	+	0.633076i
$51$	−4.33777	+	1.70213i	−0.607409	+	0.238346i
$52$	−3.18708	−	5.46780i	−0.441969	−	0.758247i
$53$	−2.42297	−	9.04263i	−0.332820	−	1.24210i	−0.906213	−	0.422821i	$-0.861040\pi$
$53$	−2.42297	−	9.04263i	−0.332820	−	1.24210i	0.573393	−	0.819280i	$-0.305627\pi$
$54$	1.51446	+	7.19072i	0.206092	+	0.978533i
$55$	2.35916			0.318110
$56$	−7.13507	−	2.25627i	−0.953464	−	0.301507i
$57$	−6.56026	−	8.89002i	−0.868928	−	1.17751i
$58$	1.25506	−	9.68804i	0.164798	−	1.27210i
$59$	10.7675	−	2.88515i	1.40181	−	0.375615i	0.522817	−	0.852445i	$-0.324881\pi$
$59$	10.7675	−	2.88515i	1.40181	−	0.375615i	0.878995	+	0.476830i	$0.158214\pi$
$60$	−1.71863	−	4.32706i	−0.221874	−	0.558621i
$61$	−9.85115	−	2.63961i	−1.26131	−	0.337967i	−0.434615	−	0.900616i	$-0.643115\pi$
$61$	−9.85115	−	2.63961i	−1.26131	−	0.337967i	−0.826696	+	0.562649i	$0.809782\pi$
$62$	−0.281735	−	2.10630i	−0.0357804	−	0.267500i
$63$	−3.67165	+	7.03697i	−0.462584	+	0.886575i
$64$	5.58618	−	5.72666i	0.698272	−	0.715832i
$65$	3.68329	−	2.12655i	0.456856	−	0.263766i
$66$	4.17105	−	1.04332i	0.513421	−	0.128424i
$67$	13.5990	−	3.64383i	1.66138	−	0.445165i	0.698611	−	0.715501i	$-0.253802\pi$
$67$	13.5990	−	3.64383i	1.66138	−	0.445165i	0.962766	+	0.270337i	$0.0871350\pi$
$68$	3.78891	−	3.82040i	0.459473	−	0.463292i
$69$	−0.325886	+	2.16118i	−0.0392320	+	0.260176i
$70$	1.53609	−	4.78857i	0.183597	−	0.572344i
$71$			10.3613i			1.22966i	0.788659	+	0.614830i	$0.210776\pi$
$71$			10.3613i			1.22966i	−0.788659	+	0.614830i	$0.789224\pi$
$72$	−4.95219	−	6.89027i	−0.583621	−	0.812026i
$73$	−4.47539	−	2.58387i	−0.523805	−	0.302419i	0.214685	−	0.976683i	$-0.431127\pi$
$73$	−4.47539	−	2.58387i	−0.523805	−	0.302419i	−0.738490	+	0.674265i	$0.764461\pi$
$74$	−1.60926	+	0.670484i	−0.187073	+	0.0779421i
$75$	−5.14919	+	2.02053i	−0.594577	+	0.233311i
$76$	11.0748	+	6.33307i	1.27037	+	0.726453i
$77$	4.19500	+	1.99228i	0.478065	+	0.227041i
$78$	5.57167	−	5.38869i	0.630868	−	0.610149i
$79$	2.76636	−	1.59716i	0.311240	−	0.179695i	−0.336241	−	0.941776i	$-0.609156\pi$
$79$	2.76636	−	1.59716i	0.311240	−	0.179695i	0.647481	+	0.762081i	$0.275822\pi$
$80$	3.83284	+	3.76990i	0.428525	+	0.421488i
$81$	−8.10971	+	3.90290i	−0.901079	+	0.433655i
$82$	0.558559	+	0.724818i	0.0616826	+	0.0800428i
$83$	10.5779	−	10.5779i	1.16108	−	1.16108i	0.176836	−	0.984240i	$-0.443414\pi$
$83$	10.5779	−	10.5779i	1.16108	−	1.16108i	0.984240	−	0.176836i	$-0.0565863\pi$
$84$	0.598114	−	9.14561i	0.0652596	−	0.997868i
$85$	2.55682	+	2.55682i	0.277326	+	0.277326i
$86$	−10.0042	−	1.29602i	−1.07878	−	0.139753i
$87$	11.8894	−	1.33885i	1.27468	−	0.143540i
$88$	−3.91992	+	3.04671i	−0.417865	+	0.324781i
$89$	−2.65355	−	4.59608i	−0.281276	−	0.487183i	0.690424	−	0.723405i	$-0.257424\pi$
$89$	−2.65355	−	4.59608i	−0.281276	−	0.487183i	−0.971699	+	0.236222i	$0.924091\pi$
$90$	4.64412	−	3.30876i	0.489533	−	0.348774i
$91$	8.34536	−	0.670886i	0.874831	−	0.0703280i
$92$	−0.663274	−	2.43501i	−0.0691510	−	0.253867i
$93$	2.42280	−	0.950703i	0.251233	−	0.0985833i
$94$	−0.948036	+	2.30223i	−0.0977825	+	0.237457i
$95$	−4.28670	+	7.42479i	−0.439807	+	0.761767i
$96$	8.44375	+	4.97021i	0.861787	+	0.507270i
$97$	9.13706			0.927728			0.463864	−	0.885906i	$-0.346463\pi$
$97$	9.13706			0.927728			0.463864	+	0.885906i	$0.346463\pi$
$98$	6.77530	−	7.21771i	0.684409	−	0.729098i
$99$	2.45998	+	4.65594i	0.247237	+	0.467939i
$100$	4.49766	−	4.53505i	0.449766	−	0.453505i
$101$	−4.18758	−	15.6283i	−0.416680	−	1.55507i	−0.781448	−	0.623971i	$-0.785518\pi$
$101$	−4.18758	−	15.6283i	−0.416680	−	1.55507i	0.364768	−	0.931098i	$-0.381148\pi$
$102$	5.65124	+	3.38977i	0.559556	+	0.335637i
$103$	−7.10560	−	12.3073i	−0.700135	−	1.21267i	−0.968419	−	0.249330i	$-0.919790\pi$
$103$	−7.10560	−	12.3073i	−0.700135	−	1.21267i	0.268283	−	0.963340i	$-0.413544\pi$
$104$	−3.37374	+	8.29014i	−0.330823	+	0.812915i
$105$	6.14429	+	0.427379i	0.599622	+	0.0417079i
$106$	−8.03784	+	10.5201i	−0.780704	+	1.02181i
$107$	−1.16641	+	4.35309i	−0.112761	+	0.420830i	−0.999110	−	0.0421888i	$-0.986567\pi$
$107$	−1.16641	+	4.35309i	−0.112761	+	0.420830i	0.886349	+	0.463018i	$0.153234\pi$
$108$	6.74761	−	7.90378i	0.649289	−	0.760542i
$109$	1.39155	+	5.19333i	0.133286	+	0.497431i	0.999999	−	0.00137662i	$-0.000438192\pi$
$109$	1.39155	+	5.19333i	0.133286	+	0.497431i	−0.866713	+	0.498807i	$0.833772\pi$
$110$	−2.03652	−	2.64271i	−0.194175	−	0.251972i
$111$	−1.26779	−	1.71803i	−0.120334	−	0.163068i
$112$	3.63183	+	9.94031i	0.343175	+	0.939271i
$113$		−	11.1607i		−	1.04991i	−0.851129	−	0.524956i	$-0.824082\pi$
$113$		−	11.1607i		−	1.04991i	0.851129	−	0.524956i	$-0.175918\pi$
$114$	−4.29541	+	15.0229i	−0.402302	+	1.40703i
$115$	1.63820	−	0.438954i	0.152763	−	0.0409327i
$116$	−11.9358	+	6.95719i	−1.10821	+	0.645959i
$117$	8.03754	+	5.05174i	0.743071	+	0.467034i
$118$	−12.5269	−	9.57107i	−1.15319	−	0.881088i
$119$	2.38727	+	6.70565i	0.218840	+	0.614706i
$120$	−3.36353	+	5.66048i	−0.307047	+	0.516728i
$121$	−6.85803	+	3.95949i	−0.623457	+	0.359953i
$122$	5.54704	+	13.3137i	0.502205	+	1.20537i
$123$	−0.698816	+	0.876174i	−0.0630101	+	0.0790019i
$124$	−2.11624	+	2.13384i	−0.190044	+	0.191624i
$125$	7.78697	+	7.78697i	0.696488	+	0.696488i
$126$	11.0522	−	1.96166i	0.984611	−	0.174759i
$127$		−	11.9885i		−	1.06381i	−0.846805	−	0.531903i	$-0.821477\pi$
$127$		−	11.9885i		−	1.06381i	0.846805	−	0.531903i	$-0.178523\pi$
$128$	−11.2371	−	1.31409i	−0.993232	−	0.116150i
$129$	−1.38254	−	12.2774i	−0.121726	−	1.08096i
$130$	−5.56169	−	2.29025i	−0.487792	−	0.200868i
$131$	6.84952	+	1.83532i	0.598445	+	0.160353i	0.545310	−	0.838234i	$-0.316412\pi$
$131$	6.84952	+	1.83532i	0.598445	+	0.160353i	0.0531352	+	0.998587i	$0.483079\pi$
$132$	−4.76933	−	3.77172i	−0.415117	−	0.328286i
$133$	−13.8926	+	9.58249i	−1.20464	+	0.830908i
$134$	−15.8209	−	12.0879i	−1.36672	−	1.04423i
$135$	5.29266	+	4.55646i	0.455520	+	0.392157i
$136$	−7.55030	−	0.946365i	−0.647433	−	0.0811501i
$137$	−10.1618	+	17.6008i	−0.868184	+	1.50374i	−0.00433311	+	0.999991i	$0.501379\pi$
$137$	−10.1618	+	17.6008i	−0.868184	+	1.50374i	−0.863851	+	0.503748i	$0.831954\pi$
$138$	2.70224	−	1.50056i	0.230030	−	0.127736i
$139$	−9.03597	+	9.03597i	−0.766421	+	0.766421i	−0.977475	−	0.211053i	$-0.932311\pi$
$139$	−9.03597	+	9.03597i	−0.766421	+	0.766421i	0.211053	+	0.977475i	$0.432311\pi$
$140$	−6.69011	+	2.41298i	−0.565417	+	0.203934i
$141$	−3.01526	−	0.454673i	−0.253931	−	0.0382904i
$142$	11.6066	−	8.94428i	0.974004	−	0.750587i
$143$	2.77723	−	4.81031i	0.232244	−	0.402258i
$144$	−3.44347	+	11.4953i	−0.286956	+	0.957944i
$145$	−4.64211	−	8.04037i	−0.385506	−	0.667717i
$146$	0.968915	+	7.24376i	0.0801880	+	0.599498i
$147$	10.5647	+	5.94871i	0.871361	+	0.490642i
$148$	2.14024	+	1.22389i	0.175927	+	0.100603i
$149$	19.9378	+	5.34232i	1.63337	+	0.437660i	0.954890	−	0.296959i	$-0.0959725\pi$
$149$	19.9378	+	5.34232i	1.63337	+	0.437660i	0.678480	+	0.734619i	$0.262639\pi$
$150$	6.70835	+	4.02385i	0.547735	+	0.328546i
$151$	−2.98937	+	5.17775i	−0.243272	+	0.421359i	−0.961644	−	0.274300i	$-0.911554\pi$
$151$	−2.98937	+	5.17775i	−0.243272	+	0.421359i	0.718372	+	0.695659i	$0.244887\pi$
$152$	−2.46598	−	17.8728i	−0.200018	−	1.44968i
$153$	−2.37994	+	7.71209i	−0.192406	+	0.623486i
$154$	−1.38956	−	6.41900i	−0.111974	−	0.517257i
$155$	−1.42808	−	1.42808i	−0.114706	−	0.114706i
$156$	−10.8460	−	1.58959i	−0.868376	−	0.127269i
$157$	2.73451	+	10.2053i	0.218237	+	0.814473i	0.985002	+	0.172544i	$0.0551988\pi$
$157$	2.73451	+	10.2053i	0.218237	+	0.814473i	−0.766764	+	0.641929i	$0.778134\pi$
$158$	−4.17715	−	1.72011i	−0.332316	−	0.136845i
$159$	−14.8615	−	6.48511i	−1.17859	−	0.514303i
$160$	0.914339	−	7.54783i	0.0722849	−	0.596708i
$161$	3.28369	+	0.602899i	0.258791	+	0.0475151i
$162$	11.3726	+	5.71526i	0.893515	+	0.449033i
$163$	−6.19475	+	23.1191i	−0.485210	+	1.81083i	0.0939039	+	0.995581i	$0.470065\pi$
$163$	−6.19475	+	23.1191i	−0.485210	+	1.81083i	−0.579114	+	0.815247i	$0.696601\pi$
$164$	0.329761	−	1.25138i	0.0257500	−	0.0977165i
$165$	2.54790	−	3.19455i	0.198354	−	0.248696i
$166$	−20.9805	−	2.71797i	−1.62840	−	0.210956i
$167$		−	16.0299i		−	1.24043i	−0.784431	−	0.620216i	$-0.787045\pi$
$167$		−	16.0299i		−	1.24043i	0.784431	−	0.620216i	$-0.212955\pi$
$168$	−10.7611	+	7.22485i	−0.830238	+	0.557409i
$169$			2.98642i			0.229725i
$170$	0.656969	−	5.07126i	0.0503873	−	0.388948i
$171$	−19.1231	−	0.717962i	−1.46238	−	0.0549039i
$172$	7.18422	+	12.3253i	0.547792	+	0.939798i
$173$	3.54360	−	13.2249i	0.269415	−	1.00547i	−0.690077	−	0.723736i	$-0.742423\pi$
$173$	3.54360	−	13.2249i	0.269415	−	1.00547i	0.959492	−	0.281735i	$-0.0909100\pi$
$174$	−11.7631	−	12.1626i	−0.891761	−	0.922044i
$175$	2.83383	+	7.96001i	0.214217	+	0.601720i
$176$	6.79671	+	1.76100i	0.512322	+	0.132741i
$177$	7.72216	−	17.6963i	0.580433	−	1.33014i
$178$	−2.85782	+	6.93998i	−0.214203	+	0.520174i
$179$	−0.963734	−	3.59671i	−0.0720329	−	0.268830i	0.920511	−	0.390716i	$-0.127773\pi$
$179$	−0.963734	−	3.59671i	−0.0720329	−	0.268830i	−0.992544	+	0.121886i	$0.961106\pi$
$180$	−7.71541	−	2.34603i	−0.575073	−	0.174863i
$181$	3.63641	+	3.63641i	0.270292	+	0.270292i	0.829218	−	0.558925i	$-0.188786\pi$
$181$	3.63641	+	3.63641i	0.270292	+	0.270292i	−0.558925	+	0.829218i	$0.688786\pi$
$182$	−7.95555	−	8.76922i	−0.589705	−	0.650018i
$183$	−14.2136	+	10.4887i	−1.05070	+	0.775347i
$184$	−2.15510	+	2.84499i	−0.158876	+	0.209735i
$185$	−0.828420	+	1.43486i	−0.0609066	+	0.105493i
$186$	−3.15642	−	1.89331i	−0.231440	−	0.138824i
$187$	4.56138	+	1.22222i	0.333561	+	0.0893774i
$188$	3.39731	−	0.925393i	0.247774	−	0.0674913i
$189$	5.56341	+	12.5717i	0.404678	+	0.914459i
$190$	12.0176	−	1.60746i	0.871848	−	0.116617i
$191$	3.78402	+	6.55412i	0.273802	+	0.474239i	0.969832	−	0.243773i	$-0.0783853\pi$
$191$	3.78402	+	6.55412i	0.273802	+	0.474239i	−0.696030	+	0.718013i	$0.745052\pi$
$192$	−1.72141	−	13.7491i	−0.124232	−	0.992253i
$193$	−3.72177	+	6.44629i	−0.267899	+	0.464014i	−0.968319	−	0.249716i	$-0.919663\pi$
$193$	−3.72177	+	6.44629i	−0.267899	+	0.464014i	0.700420	+	0.713731i	$0.252996\pi$
$194$	−7.88746	−	10.2352i	−0.566287	−	0.734846i
$195$	1.09839	−	7.28423i	0.0786575	−	0.521634i
$196$	−13.9339	−	1.35900i	−0.995277	−	0.0970715i
$197$	−11.7428	+	11.7428i	−0.836639	+	0.836639i	−0.988415	−	0.151776i	$-0.951501\pi$
$197$	−11.7428	+	11.7428i	−0.836639	+	0.836639i	0.151776	+	0.988415i	$0.451501\pi$
$198$	3.09197	−	6.77482i	0.219737	−	0.481466i
$199$	−8.72142	+	15.1059i	−0.618245	+	1.07083i	0.371561	+	0.928409i	$0.378823\pi$
$199$	−8.72142	+	15.1059i	−0.618245	+	1.07083i	−0.989806	+	0.142423i	$0.954511\pi$
$200$	−8.96265	−	1.12339i	−0.633755	−	0.0794357i
$201$	9.75278	−	22.3497i	0.687908	−	1.57643i
$202$	−13.8917	+	18.1818i	−0.977416	+	1.27927i
$203$	−1.46450	−	18.2174i	−0.102788	−	1.27861i
$204$	−1.08119	−	9.25662i	−0.0756988	−	0.648093i
$205$	0.840026	+	0.225084i	0.0586700	+	0.0157206i
$206$	−7.65260	+	18.5837i	−0.533182	+	1.29479i
$207$	2.57451	+	2.77536i	0.178941	+	0.192901i
$208$	12.1989	−	3.37715i	0.845838	−	0.234163i
$209$			11.1967i			0.774493i
$210$	−4.82525	−	7.25169i	−0.332974	−	0.500414i
$211$	−5.21906	−	5.21906i	−0.359295	−	0.359295i	0.504258	−	0.863553i	$-0.331766\pi$
$211$	−5.21906	−	5.21906i	−0.359295	−	0.359295i	−0.863553	+	0.504258i	$0.831766\pi$
$212$	18.7231	−	0.0774969i	1.28591	−	0.00532251i
$213$	14.0303	+	11.1902i	0.961339	+	0.766742i
$214$	5.88317	−	2.45116i	0.402165	−	0.167558i
$215$	−8.30275	+	4.79360i	−0.566243	+	0.326921i
$216$	−14.6785	−	0.735733i	−0.998746	−	0.0500603i
$217$	−1.33338	−	3.74535i	−0.0905154	−	0.254251i
$218$	4.61626	−	6.04188i	0.312653	−	0.409208i
$219$	−8.33225	+	3.26956i	−0.563041	+	0.220936i
$220$	−1.20232	+	4.56257i	−0.0810603	+	0.307609i
$221$	8.22323	−	2.20341i	0.553155	−	0.148217i
$222$	−0.830102	+	2.90323i	−0.0557128	+	0.194852i
$223$		−	16.5573i		−	1.10876i	−0.832264	−	0.554379i	$-0.812956\pi$
$223$		−	16.5573i		−	1.10876i	0.832264	−	0.554379i	$-0.187044\pi$
$224$	7.99988	−	12.6492i	0.534514	−	0.845159i
$225$	−2.82512	+	9.15471i	−0.188342	+	0.610314i
$226$	−12.5021	+	9.63437i	−0.831627	+	0.640869i
$227$	−3.78676	−	14.1324i	−0.251336	−	0.937999i	−0.970092	−	0.242736i	$-0.921955\pi$
$227$	−3.78676	−	14.1324i	−0.251336	−	0.937999i	0.718756	−	0.695262i	$-0.244712\pi$
$228$	20.5365	−	8.15672i	1.36006	−	0.540192i
$229$	−4.35292	+	16.2453i	−0.287649	+	1.07352i	0.659233	+	0.751939i	$0.270881\pi$
$229$	−4.35292	+	16.2453i	−0.287649	+	1.07352i	−0.946882	+	0.321582i	$0.895785\pi$
$230$	−1.90587	−	1.45617i	−0.125669	−	0.0960169i
$231$	7.22836	−	3.52880i	0.475591	−	0.232178i
$232$	18.0968	+	7.36466i	1.18812	+	0.483513i
$233$	12.0628	+	20.8935i	0.790263	+	1.36878i	0.925804	+	0.378005i	$0.123390\pi$
$233$	12.0628	+	20.8935i	0.790263	+	1.36878i	−0.135540	+	0.990772i	$0.543277\pi$
$234$	−1.27942	−	13.3644i	−0.0836384	−	0.873659i
$235$	0.612425	+	2.28560i	0.0399502	+	0.149096i
$236$	0.0922796	+	22.2945i	0.00600689	+	1.45125i
$237$	0.824957	−	5.47088i	0.0535867	−	0.355372i
$238$	5.45080	−	8.46276i	0.353323	−	0.548560i
$239$	1.99871			0.129286			0.0646430	−	0.997908i	$-0.479409\pi$
$239$	1.99871			0.129286			0.0646430	+	0.997908i	$0.479409\pi$
$240$	9.24432	−	1.11856i	0.596718	−	0.0722029i
$241$	4.60494	−	7.97598i	0.296630	−	0.513778i	−0.678733	−	0.734385i	$-0.737471\pi$
$241$	4.60494	−	7.97598i	0.296630	−	0.513778i	0.975363	+	0.220607i	$0.0708038\pi$
$242$	10.3555	+	4.26429i	0.665676	+	0.274119i
$243$	−3.47357	+	15.1965i	−0.222830	+	0.974857i
$244$	10.1255	−	17.7067i	0.648216	−	1.13355i
$245$	0.952022	−	9.35995i	0.0608224	−	0.597985i
$246$	1.58472	+	0.0264574i	0.101038	+	0.00168686i
$247$	10.0927	+	17.4811i	0.642184	+	1.11229i
$248$	4.21712	+	0.528579i	0.267787	+	0.0335648i
$249$	−2.89942	−	25.7478i	−0.183743	−	1.63170i
$250$	2.00085	−	15.4449i	0.126545	−	0.976820i
$251$	8.56031	+	8.56031i	0.540322	+	0.540322i	0.923623	−	0.383301i	$-0.125213\pi$
$251$	8.56031	+	8.56031i	0.540322	+	0.540322i	−0.383301	+	0.923623i	$0.625213\pi$
$252$	−11.7381	−	10.6872i	−0.739434	−	0.673230i
$253$	1.56619	−	1.56619i	0.0984658	−	0.0984658i
$254$	−13.4294	+	10.3489i	−0.842633	+	0.649350i
$255$	6.22356	−	0.700828i	0.389735	−	0.0438875i
$256$	8.22830	+	13.7221i	0.514269	+	0.857629i
$257$	−16.0274	+	9.25344i	−0.999764	+	0.577214i	−0.908178	−	0.418583i	$-0.862527\pi$
$257$	−16.0274	+	9.25344i	−0.999764	+	0.577214i	−0.0915854	+	0.995797i	$0.529193\pi$
$258$	−12.5595	+	12.1470i	−0.781919	+	0.756239i
$259$	−2.68479	+	1.85185i	−0.166825	+	0.115068i
$260$	2.23555	+	8.20717i	0.138643	+	0.508987i
$261$	11.0276	−	17.5454i	0.682592	−	1.08603i
$262$	−3.85687	−	9.25707i	−0.238278	−	0.571903i
$263$	−17.2099	−	9.93615i	−1.06121	−	0.612689i	−0.135443	−	0.990785i	$-0.543246\pi$
$263$	−17.2099	−	9.93615i	−1.06121	−	0.612689i	−0.925767	+	0.378096i	$0.876579\pi$
$264$	−0.107956	+	8.59843i	−0.00664424	+	0.529197i
$265$			12.5823i			0.772927i
$266$	22.7268	+	7.29035i	1.39347	+	0.447000i
$267$	−9.08940	−	1.37060i	−0.556262	−	0.0838791i
$268$	0.116545	+	28.1571i	0.00711914	+	1.71997i
$269$	6.96476	−	1.86620i	0.424649	−	0.113784i	−0.0401642	−	0.999193i	$-0.512788\pi$
$269$	6.96476	−	1.86620i	0.424649	−	0.113784i	0.464813	+	0.885409i	$0.346121\pi$
$270$	0.535250	−	9.86208i	0.0325743	−	0.600187i
$271$	21.5262	−	12.4282i	1.30763	−	0.754958i	0.325926	−	0.945395i	$-0.394324\pi$
$271$	21.5262	−	12.4282i	1.30763	−	0.754958i	0.981699	+	0.190437i	$0.0609905\pi$
$272$	5.45761	+	9.27469i	0.330916	+	0.562360i
$273$	8.10455	−	12.0250i	0.490510	−	0.727788i
$274$	28.4883	−	3.81055i	1.72104	−	0.230204i
$275$	5.41462	+	1.45084i	0.326514	+	0.0874892i
$276$	−4.01359	−	1.73167i	−0.241590	−	0.104235i
$277$	29.0852	−	7.79335i	1.74756	−	0.468257i	0.763456	−	0.645860i	$-0.223501\pi$
$277$	29.0852	−	7.79335i	1.74756	−	0.468257i	0.984102	+	0.177603i	$0.0568343\pi$
$278$	17.9222	+	2.32178i	1.07490	+	0.139251i
$279$	1.32928	−	4.30748i	0.0795820	−	0.257882i
$280$	8.47815	+	5.41119i	0.506666	+	0.323381i
$281$	−11.6190			−0.693131			−0.346565	−	0.938026i	$-0.612652\pi$
$281$	−11.6190			−0.693131			−0.346565	+	0.938026i	$0.612652\pi$
$282$	2.09357	+	3.77015i	0.124670	+	0.224509i
$283$	−3.63549	−	13.5678i	−0.216107	−	0.806524i	−0.985774	−	0.168078i	$-0.946244\pi$
$283$	−3.63549	−	13.5678i	−0.216107	−	0.806524i	0.769666	−	0.638446i	$-0.220423\pi$
$284$	−20.0385	−	5.28051i	−1.18907	−	0.313341i
$285$	5.42428	+	13.8234i	0.321307	+	0.818829i
$286$	−7.78586	+	1.04143i	−0.460388	+	0.0615808i
$287$	1.30363	+	1.10963i	0.0769508	+	0.0654992i
$288$	15.8495	−	6.06588i	0.933938	−	0.357435i
$289$	−4.88108	−	8.45429i	−0.287123	−	0.497311i
$290$	−4.99947	+	12.1408i	−0.293579	+	0.712932i
$291$	9.86804	−	12.3725i	0.578475	−	0.725290i
$292$	7.27797	−	7.33846i	0.425911	−	0.429451i
$293$	−8.04909	+	8.04909i	−0.470233	+	0.470233i	−0.901990	−	0.431757i	$-0.857894\pi$
$293$	−8.04909	+	8.04909i	−0.470233	+	0.470233i	0.431757	+	0.901990i	$0.357894\pi$
$294$	−2.45618	−	16.9696i	−0.143248	−	0.989687i
$295$	−14.9824			−0.872312
$296$	−0.476560	−	3.45398i	−0.0276995	−	0.200759i
$297$	8.96140	+	1.69735i	0.519993	+	0.0984904i
$298$	−11.2267	−	26.9458i	−0.650345	−	1.56093i
$299$	1.03348	−	3.85701i	0.0597679	−	0.223057i
$300$	−1.28344	−	10.9882i	−0.0740996	−	0.634401i
$301$	−18.8118	+	1.51229i	−1.08430	+	0.0871670i
$302$	8.38059	−	1.12097i	0.482249	−	0.0645049i
$303$	−25.6849	−	11.2081i	−1.47556	−	0.643890i
$304$	−17.8922	+	18.1909i	−1.02619	+	1.04332i
$305$	11.8709	+	6.85368i	0.679727	+	0.392440i
$306$	10.6934	−	3.99141i	0.611303	−	0.228173i
$307$	−14.1474	−	14.1474i	−0.807436	−	0.807436i	0.176809	−	0.984245i	$-0.443422\pi$
$307$	−14.1474	−	14.1474i	−0.807436	−	0.807436i	−0.984245	+	0.176809i	$0.943422\pi$
$308$	−5.99095	+	7.09770i	−0.341366	+	0.404429i
$309$	−24.3394	−	3.67014i	−1.38462	−	0.208787i
$310$	−0.366941	+	2.83248i	−0.0208409	+	0.160874i
$311$	−10.7939	−	6.23188i	−0.612068	−	0.353378i	0.161706	−	0.986839i	$-0.448300\pi$
$311$	−10.7939	−	6.23188i	−0.612068	−	0.353378i	−0.773774	+	0.633461i	$0.781634\pi$
$312$	7.58206	+	13.5218i	0.429250	+	0.765519i
$313$	3.52697	−	2.03630i	0.199356	−	0.115098i	−0.396999	−	0.917819i	$-0.629948\pi$
$313$	3.52697	−	2.03630i	0.199356	−	0.115098i	0.596355	+	0.802721i	$0.296615\pi$
$314$	9.07133	−	11.8728i	0.511925	−	0.670020i
$315$	7.21456	−	7.85844i	0.406495	−	0.442773i
$316$	1.67903	+	6.16406i	0.0944529	+	0.346756i
$317$	1.04473	−	3.89898i	0.0586778	−	0.218989i	−0.930361	−	0.366645i	$-0.880506\pi$
$317$	1.04473	−	3.89898i	0.0586778	−	0.218989i	0.989039	+	0.147656i	$0.0471730\pi$
$318$	5.56446	+	22.2458i	0.312039	+	1.24748i
$319$	−10.5006	−	6.06252i	−0.587920	−	0.339436i
$320$	−9.24427	+	5.49135i	−0.516771	+	0.306976i
$321$	4.63482	+	6.28079i	0.258690	+	0.350559i
$322$	−2.15925	−	4.19879i	−0.120330	−	0.233990i
$323$	−12.1348	+	12.1348i	−0.675198	+	0.675198i
$324$	−3.41511	−	17.6731i	−0.189728	−	0.981837i
$325$	9.76146	−	2.61558i	0.541469	−	0.145086i
$326$	31.2453	−	13.0180i	1.73052	−	0.721002i
$327$	8.53518	+	3.72450i	0.471997	+	0.205966i
$328$	−1.68644	+	0.710847i	−0.0931183	+	0.0392500i
$329$	−0.841159	+	4.58138i	−0.0463746	+	0.252580i
$330$	−5.77795	−	0.0964645i	−0.318065	−	0.00531020i
$331$	−0.932529	−	0.249870i	−0.0512564	−	0.0137341i	0.233100	−	0.972453i	$-0.425113\pi$
$331$	−0.932529	−	0.249870i	−0.0512564	−	0.0137341i	−0.284356	+	0.958719i	$0.591780\pi$
$332$	15.0665	+	25.8483i	0.826884	+	1.41861i
$333$	−3.69560	−	0.138748i	−0.202518	−	0.00760337i
$334$	−17.9565	+	13.8376i	−0.982535	+	0.757162i
$335$	−18.9222			−1.03383
$336$	17.3826	+	5.81769i	0.948298	+	0.317381i
$337$	−1.89991			−0.103495			−0.0517473	−	0.998660i	$-0.516479\pi$
$337$	−1.89991			−0.103495			−0.0517473	+	0.998660i	$0.516479\pi$
$338$	3.34535	−	2.57800i	0.181963	−	0.140224i
$339$	−15.1128	−	12.0536i	−0.820813	−	0.654662i
$340$	−6.24788	+	3.64178i	−0.338839	+	0.197503i
$341$	−2.54769	−	0.682653i	−0.137965	−	0.0369677i
$342$	15.7036	+	22.0412i	0.849151	+	1.19185i
$343$	9.59719	−	15.8396i	0.518200	−	0.855260i
$344$	7.60498	−	18.6874i	0.410033	−	1.00756i
$345$	1.17487	−	2.69236i	0.0632528	−	0.144952i
$346$	−17.8734	+	7.44676i	−0.960877	+	0.400340i
$347$	26.8839	−	7.20351i	1.44320	−	0.386705i	0.549548	−	0.835462i	$-0.314800\pi$
$347$	26.8839	−	7.20351i	1.44320	−	0.386705i	0.893654	+	0.448758i	$0.148133\pi$
$348$	−3.46997	+	23.6761i	−0.186010	+	1.26917i
$349$	15.3784	−	15.3784i	0.823186	−	0.823186i	−0.163377	−	0.986564i	$-0.552239\pi$
$349$	15.3784	−	15.3784i	0.823186	−	0.823186i	0.986564	+	0.163377i	$0.0522388\pi$
$350$	6.47042	−	10.0458i	0.345859	−	0.536971i
$351$	15.5211	−	5.42777i	0.828457	−	0.289713i
$352$	−3.89454	−	9.13376i	−0.207579	−	0.486831i
$353$	0.267982	+	0.154719i	0.0142632	+	0.00823487i	0.507115	−	0.861879i	$-0.330712\pi$
$353$	0.267982	+	0.154719i	0.0142632	+	0.00823487i	−0.492851	+	0.870113i	$0.664045\pi$
$354$	−26.4892	+	6.62588i	−1.40789	+	0.352162i
$355$	3.60430	−	13.4514i	0.191296	−	0.713928i
$356$	10.2411	−	2.78957i	0.542775	−	0.147847i
$357$	11.6584	+	4.00951i	0.617028	+	0.212206i
$358$	−3.19705	+	4.18438i	−0.168969	+	0.221151i
$359$	−22.8245	+	13.1777i	−1.20463	+	0.695494i	−0.961581	−	0.274520i	$-0.911481\pi$
$359$	−22.8245	+	13.1777i	−1.20463	+	0.695494i	−0.243049	+	0.970014i	$0.578148\pi$
$360$	4.03225	+	10.6679i	0.212518	+	0.562247i
$361$	−18.7840	−	10.8449i	−0.988629	−	0.570785i
$362$	0.934370	−	7.21256i	0.0491094	−	0.379083i
$363$	−2.04513	+	13.5627i	−0.107342	+	0.711859i
$364$	−2.95563	+	16.4816i	−0.154917	+	0.863873i
$365$	4.91129	+	4.91129i	0.257069	+	0.257069i
$366$	24.0190	+	6.86760i	1.25549	+	0.358975i
$367$	−2.70497	−	1.56172i	−0.141199	−	0.0815210i	0.427737	−	0.903903i	$-0.359311\pi$
$367$	−2.70497	−	1.56172i	−0.141199	−	0.0815210i	−0.568935	+	0.822382i	$0.692644\pi$
$368$	5.04729	−	0.0417833i	0.263108	−	0.00217810i
$369$	0.431707	+	1.89254i	0.0224738	+	0.0985216i
$370$	2.32244	−	0.310646i	0.120738	−	0.0161497i
$371$	−10.6256	+	22.3736i	−0.551654	+	1.16158i
$372$	0.603887	+	5.17016i	0.0313101	+	0.268060i
$373$	2.61531	−	9.76047i	0.135416	−	0.505378i	−0.864580	−	0.502495i	$-0.832416\pi$
$373$	2.61531	−	9.76047i	0.135416	−	0.505378i	0.999996	−	0.00288320i	$-0.000917753\pi$
$374$	−2.56844	−	6.16466i	−0.132811	−	0.318767i
$375$	18.9543	−	2.13442i	0.978796	−	0.110221i
$376$	−3.96930	−	3.00678i	−0.204701	−	0.155063i
$377$	−21.8590			−1.12579
$378$	9.28014	−	17.0845i	0.477319	−	0.878730i
$379$	9.94404	−	9.94404i	0.510791	−	0.510791i	−0.403978	−	0.914769i	$-0.632373\pi$
$379$	9.94404	−	9.94404i	0.510791	−	0.510791i	0.914769	+	0.403978i	$0.132373\pi$
$380$	−12.1747	−	12.0743i	−0.624549	−	0.619401i
$381$	−16.2337	−	12.9476i	−0.831676	−	0.663325i
$382$	4.07532	−	9.89658i	0.208512	−	0.506353i
$383$	−1.06026	−	1.83643i	−0.0541769	−	0.0938372i	0.837665	−	0.546184i	$-0.183920\pi$
$383$	−1.06026	−	1.83643i	−0.0541769	−	0.0938372i	−0.891842	+	0.452347i	$0.850587\pi$
$384$	−13.9155	+	13.7970i	−0.710124	+	0.704076i
$385$	−4.75307	−	4.04573i	−0.242239	−	0.206190i
$386$	10.4338	−	1.39561i	0.531068	−	0.0710348i
$387$	−18.1180	−	11.3875i	−0.920988	−	0.578858i
$388$	−4.65659	+	17.6709i	−0.236402	+	0.897102i
$389$	−6.77320	−	25.2779i	−0.343415	−	1.28164i	−0.894453	−	0.447162i	$-0.852435\pi$
$389$	−6.77320	−	25.2779i	−0.343415	−	1.28164i	0.551038	−	0.834480i	$-0.314232\pi$
$390$	−9.10787	+	5.05762i	−0.461195	+	0.256103i
$391$	3.39482			0.171684
$392$	10.5059	+	16.7817i	0.530630	+	0.847604i
$393$	9.88271	−	7.29281i	0.498517	−	0.367873i
$394$	23.2910	+	3.01729i	1.17338	+	0.152009i
$395$	−4.14699	+	1.11118i	−0.208658	+	0.0559097i
$396$	−10.2582	+	2.38471i	−0.515493	+	0.119836i
$397$	−3.65377	−	0.979024i	−0.183377	−	0.0491358i	0.165962	−	0.986132i	$-0.446927\pi$
$397$	−3.65377	−	0.979024i	−0.183377	−	0.0491358i	−0.349339	+	0.936996i	$0.613594\pi$
$398$	24.4502	−	3.27042i	1.22558	−	0.163931i
$399$	−2.02836	+	29.1611i	−0.101545	+	1.45988i
$400$	6.47850	+	11.0096i	0.323925	+	0.550480i
$401$	16.7071	−	9.64585i	0.834313	−	0.481691i	−0.0210141	−	0.999779i	$-0.506689\pi$
$401$	16.7071	−	9.64585i	0.834313	−	0.481691i	0.855327	+	0.518088i	$0.173356\pi$
$402$	−33.4549	+	8.36823i	−1.66858	+	0.417369i
$403$	−4.59298	+	1.23068i	−0.228792	+	0.0613047i
$404$	32.3588	−	0.133937i	1.60991	−	0.00666361i
$405$	11.8860	−	2.24583i	0.590620	−	0.111596i
$406$	−19.1426	+	17.3664i	−0.950033	+	0.861882i
$407$			2.16380i			0.107256i
$408$	−9.43581	+	9.20181i	−0.467142	+	0.455558i
$409$	28.0242	+	16.1798i	1.38571	+	0.800039i	0.992828	−	0.119551i	$-0.0381456\pi$
$409$	28.0242	+	16.1798i	1.38571	+	0.800039i	0.392880	+	0.919590i	$0.371479\pi$
$410$	−0.473006	−	1.13529i	−0.0233601	−	0.0560679i
$411$	12.8585	+	32.7691i	0.634264	+	1.61638i
$412$	27.4232	−	7.46983i	1.35105	−	0.368012i
$413$	−26.6414	−	12.6524i	−1.31094	−	0.622586i
$414$	0.886512	−	5.27973i	0.0435697	−	0.259485i
$415$	−17.4123	+	10.0530i	−0.854736	+	0.493482i
$416$	−14.3136	−	10.7497i	−0.701780	−	0.527048i
$417$	2.47677	+	21.9945i	0.121288	+	1.07708i
$418$	12.5424	−	9.66544i	0.613470	−	0.472752i
$419$	−16.2689	+	16.2689i	−0.794786	+	0.794786i	−0.982268	−	0.187482i	$-0.939967\pi$
$419$	−16.2689	+	16.2689i	−0.794786	+	0.794786i	0.187482	+	0.982268i	$0.439967\pi$
$420$	−3.95790	+	11.6651i	−0.193126	+	0.569200i
$421$	−2.80080	−	2.80080i	−0.136503	−	0.136503i	0.635554	−	0.772057i	$-0.280772\pi$
$421$	−2.80080	−	2.80080i	−0.136503	−	0.136503i	−0.772057	+	0.635554i	$0.780772\pi$
$422$	−1.34103	+	10.3516i	−0.0652803	+	0.503909i
$423$	−3.87216	+	3.59193i	−0.188271	+	0.174646i
$424$	−16.2493	−	20.9065i	−0.789136	−	1.01531i
$425$	4.29587	+	7.44066i	0.208380	+	0.360925i
$426$	0.423666	−	25.3764i	0.0205267	−	1.22949i
$427$	15.3207	+	22.2118i	0.741421	+	1.07491i
$428$	−7.82434	−	4.47431i	−0.378204	−	0.216274i
$429$	−3.51424	−	8.95581i	−0.169669	−	0.432390i
$430$	12.5370	+	5.16262i	0.604587	+	0.248963i
$431$	−12.5434	+	21.7258i	−0.604193	+	1.04649i	0.387985	+	0.921666i	$0.373171\pi$
$431$	−12.5434	+	21.7258i	−0.604193	+	1.04649i	−0.992178	+	0.124828i	$0.960162\pi$
$432$	11.8469	+	17.0778i	0.569984	+	0.821656i
$433$	3.82357			0.183749			0.0918745	−	0.995771i	$-0.470714\pi$
$433$	3.82357			0.183749			0.0918745	+	0.995771i	$0.470714\pi$
$434$	−3.04447	+	4.72676i	−0.146139	+	0.226892i
$435$	−15.9010	−	2.39772i	−0.762394	−	0.114962i
$436$	−10.7530	+	0.0445077i	−0.514974	+	0.00213153i
$437$	2.08330	+	7.77498i	0.0996578	+	0.371928i
$438$	10.8552	+	6.51127i	0.518683	+	0.311120i
$439$	4.45359	+	7.71384i	0.212558	+	0.368161i	0.952514	−	0.304493i	$-0.0984872\pi$
$439$	4.45359	+	7.71384i	0.212558	+	0.368161i	−0.739956	+	0.672655i	$0.765154\pi$
$440$	6.14882	−	2.59177i	0.293134	−	0.123558i
$441$	19.4651	−	7.88107i	0.926908	−	0.375289i
$442$	−9.56684	−	7.30949i	−0.455048	−	0.347677i
$443$	−0.0135207	+	0.0504601i	−0.000642390	+	0.00239743i	−0.966246	−	0.257620i	$-0.917062\pi$
$443$	−0.0135207	+	0.0504601i	−0.000642390	+	0.00239743i	0.965604	+	0.260018i	$0.0837284\pi$
$444$	3.96874	−	1.57631i	0.188348	−	0.0748085i
$445$	1.84614	+	6.88987i	0.0875152	+	0.326611i
$446$	−18.5473	+	14.2929i	−0.878239	+	0.676789i
$447$	28.7669	−	21.2282i	1.36063	−	1.00406i
$448$	−21.0753	+	1.95791i	−0.995712	+	0.0925027i
$449$			3.26054i			0.153874i	0.997036	+	0.0769372i	$0.0245141\pi$
$449$			3.26054i			0.153874i	−0.997036	+	0.0769372i	$0.975486\pi$
$450$	12.6937	−	4.73803i	0.598389	−	0.223353i
$451$	1.09706	−	0.293956i	0.0516585	−	0.0138419i
$452$	21.5846	+	5.68792i	1.01525	+	0.267537i
$453$	3.78268	+	9.63990i	0.177726	+	0.452922i
$454$	−12.5620	+	16.4415i	−0.589565	+	0.771637i
$455$	−11.0676	−	2.03206i	−0.518859	−	0.0952644i
$456$	−26.8649	−	15.9635i	−1.25806	−	0.747558i
$457$	24.4680	−	14.1266i	1.14457	−	0.660816i	0.197009	−	0.980402i	$-0.436877\pi$
$457$	24.4680	−	14.1266i	1.14457	−	0.660816i	0.947557	+	0.319586i	$0.103544\pi$
$458$	21.9554	−	9.14751i	1.02591	−	0.427435i
$459$	7.87264	+	11.5518i	0.367463	+	0.539190i
$460$	0.0140397	+	3.39195i	0.000654602	+	0.158150i
$461$	−21.3994	−	21.3994i	−0.996670	−	0.996670i	0.00332414	−	0.999994i	$-0.498942\pi$
$461$	−21.3994	−	21.3994i	−0.996670	−	0.996670i	−0.999994	+	0.00332414i	$0.998942\pi$
$462$	−10.1927	−	5.05092i	−0.474208	−	0.234990i
$463$			31.0542i			1.44321i	0.692305	+	0.721605i	$0.256595\pi$
$463$			31.0542i			1.44321i	−0.692305	+	0.721605i	$0.743405\pi$
$464$	−7.37210	−	26.6293i	−0.342241	−	1.23623i
$465$	−3.47609	+	0.391438i	−0.161200	+	0.0181525i
$466$	12.9915	−	31.5487i	0.601818	−	1.46147i
$467$	−3.31436	−	0.888079i	−0.153370	−	0.0410954i	0.181317	−	0.983425i	$-0.441964\pi$
$467$	−3.31436	−	0.888079i	−0.153370	−	0.0410954i	−0.334687	+	0.942329i	$0.608631\pi$
$468$	−13.8662	+	12.9699i	−0.640965	+	0.599532i
$469$	−33.6470	−	15.9795i	−1.55367	−	0.737866i
$470$	2.03163	−	2.65905i	0.0937122	−	0.122653i
$471$	16.7723	+	7.31896i	0.772828	+	0.337240i
$472$	24.8944	−	19.3489i	1.14586	−	0.890604i
$473$	−6.26035	+	10.8432i	−0.287851	+	0.498573i
$474$	−6.84054	+	3.79857i	−0.314197	+	0.174474i
$475$	−14.4047	+	14.4047i	−0.660934	+	0.660934i
$476$	−14.1852	+	1.19947i	−0.650179	+	0.0549776i
$477$	−24.8319	+	13.1200i	−1.13698	+	0.600725i
$478$	−1.72537	−	2.23893i	−0.0789165	−	0.102406i
$479$	16.5690	−	28.6984i	0.757058	−	1.31126i	−0.187287	−	0.982305i	$-0.559969\pi$
$479$	16.5690	−	28.6984i	0.757058	−	1.31126i	0.944345	−	0.328958i	$-0.106697\pi$
$480$	−9.23305	−	9.38978i	−0.421429	−	0.428583i
$481$	1.95045	+	3.37828i	0.0889328	+	0.154036i
$482$	−12.9098	+	1.72679i	−0.588023	+	0.0786531i
$483$	4.36278	−	3.79533i	0.198513	−	0.172693i
$484$	−4.16245	−	15.2812i	−0.189202	−	0.694599i
$485$	−11.8621	−	3.17843i	−0.538629	−	0.144325i
$486$	20.0215	−	9.22718i	0.908192	−	0.418553i
$487$	15.0956	−	26.1463i	0.684046	−	1.18480i	−0.289689	−	0.957121i	$-0.593552\pi$
$487$	15.0956	−	26.1463i	0.684046	−	1.18480i	0.973736	−	0.227682i	$-0.0731147\pi$
$488$	−28.5755	+	3.94267i	−1.29355	+	0.178476i
$489$	24.6153	+	33.3570i	1.11314	+	1.50846i
$490$	−11.3067	+	7.01343i	−0.510785	+	0.316834i
$491$	−11.8604	−	11.8604i	−0.535251	−	0.535251i	0.386879	−	0.922130i	$-0.373553\pi$
$491$	−11.8604	−	11.8604i	−0.535251	−	0.535251i	−0.922130	+	0.386879i	$0.873553\pi$
$492$	−1.33836	−	1.79803i	−0.0603378	−	0.0810613i
$493$	−4.80989	−	17.9508i	−0.216627	−	0.808462i
$494$	10.8697	−	26.3961i	0.489049	−	1.18762i
$495$	−1.57402	−	6.90025i	−0.0707468	−	0.310143i
$496$	−3.04827	−	5.18025i	−0.136871	−	0.232600i
$497$	17.7686	−	20.8752i	0.797031	−	0.936380i
$498$	−26.3394	+	25.4744i	−1.18030	+	1.14153i
$499$	1.33307	−	4.97507i	0.0596762	−	0.222715i	−0.929647	−	0.368451i	$-0.879888\pi$
$499$	1.33307	−	4.97507i	0.0596762	−	0.222715i	0.989324	+	0.145736i	$0.0465550\pi$
$500$	−19.0284	+	11.0913i	−0.850974	+	0.496018i
$501$	−21.7061	−	17.3123i	−0.969759	−	0.773458i
$502$	2.19956	−	16.9787i	0.0981710	−	0.757799i
$503$		−	19.4647i		−	0.867889i	−0.900940	−	0.433945i	$-0.857121\pi$
$503$		−	19.4647i		−	0.867889i	0.900940	−	0.433945i	$-0.142879\pi$
$504$	−1.83883	+	22.3745i	−0.0819079	+	0.996640i
$505$			21.7459i			0.967679i
$506$	−3.10643	−	0.402431i	−0.138098	−	0.0178902i
$507$	4.04393	+	3.22534i	0.179597	+	0.143242i
$508$	23.1855	+	6.10979i	1.02869	+	0.271078i
$509$	−0.829975	+	3.09751i	−0.0367880	+	0.137295i	−0.981877	−	0.189517i	$-0.939308\pi$
$509$	−0.829975	+	3.09751i	−0.0367880	+	0.137295i	0.945089	+	0.326812i	$0.105974\pi$
$510$	−6.15748	−	6.36657i	−0.272658	−	0.281917i
$511$	4.58561	+	12.8806i	0.202855	+	0.569805i
$512$	8.26828	−	21.0627i	0.365410	−	0.930847i
$513$	−21.6252	+	25.1193i	−0.954775	+	1.10904i
$514$	24.2011	+	9.96579i	1.06746	+	0.439572i
$515$	4.94353	+	18.4495i	0.217838	+	0.812983i
$516$	24.4488	+	3.58321i	1.07630	+	0.157742i
$517$	2.18514	+	2.18514i	0.0961024	+	0.0961024i
$518$	4.39203	+	1.40888i	0.192975	+	0.0619028i
$519$	−14.0808	−	19.0813i	−0.618079	−	0.837578i
$520$	7.26374	−	9.58898i	0.318536	−	0.420505i
$521$	9.04830	−	15.6721i	0.396413	−	0.686608i	−0.596867	−	0.802340i	$-0.703588\pi$
$521$	9.04830	−	15.6721i	0.396413	−	0.686608i	0.993280	+	0.115732i	$0.0369214\pi$
$522$	−29.1736	+	2.79289i	−1.27689	+	0.122242i
$523$	−16.0144	−	4.29104i	−0.700261	−	0.187634i	−0.108913	−	0.994051i	$-0.534737\pi$
$523$	−16.0144	−	4.29104i	−0.700261	−	0.187634i	−0.591347	+	0.806417i	$0.701404\pi$
$524$	−7.04025	+	12.3115i	−0.307555	+	0.537829i
$525$	13.8392	+	4.75953i	0.603993	+	0.207723i
$526$	3.72592	+	27.8556i	0.162458	+	1.21456i
$527$	−2.02130	−	3.50099i	−0.0880490	−	0.152505i
$528$	9.72504	−	7.30157i	0.423228	−	0.317760i
$529$	−10.7038	+	18.5396i	−0.465385	+	0.806070i
$530$	14.0946	−	10.8616i	0.612229	−	0.471796i
$531$	−15.6227	−	29.5686i	−0.677967	−	1.28317i
$532$	−11.4521	−	31.7516i	−0.496513	−	1.37661i
$533$	1.44783	−	1.44783i	0.0627125	−	0.0627125i
$534$	6.31100	+	11.3650i	0.273104	+	0.491811i
$535$	3.02855	−	5.24560i	0.130936	−	0.226787i
$536$	31.4406	−	24.4369i	1.35803	−	1.05551i
$537$	−5.91115	−	2.57945i	−0.255085	−	0.111312i
$538$	−8.10275	−	6.19086i	−0.349334	−	0.266907i
$539$	−5.03522	−	11.2079i	−0.216882	−	0.482758i
$540$	−11.5094	+	7.91375i	−0.495287	+	0.340554i
$541$	0.600025	+	0.160776i	0.0257971	+	0.00691230i	0.271695	−	0.962384i	$-0.412416\pi$
$541$	0.600025	+	0.160776i	0.0257971	+	0.00691230i	−0.245897	+	0.969296i	$0.579083\pi$
$542$	−32.5042	−	13.3849i	−1.39617	−	0.574932i
$543$	8.85141	−	0.996747i	0.379850	−	0.0427745i
$544$	5.67817	−	14.1198i	0.243449	−	0.605382i
$545$		−	7.22624i		−	0.309538i
$546$	−20.4664	+	1.30186i	−0.875883	+	0.0557147i
$547$	−7.58948	−	7.58948i	−0.324503	−	0.324503i	0.525989	−	0.850492i	$-0.323695\pi$
$547$	−7.58948	−	7.58948i	−0.324503	−	0.324503i	−0.850492	+	0.525989i	$0.823695\pi$
$548$	−28.8607	−	28.6228i	−1.23287	−	1.22270i
$549$	−1.14789	+	30.5744i	−0.0489909	+	1.30489i
$550$	−3.04890	−	7.31781i	−0.130005	−	0.312033i
$551$	38.1600	−	22.0317i	1.62567	−	0.938582i
$552$	1.52489	+	5.99082i	0.0649036	+	0.254986i
$553$	−8.31244	−	1.52620i	−0.353481	−	0.0649005i
$554$	−33.8374	−	25.8533i	−1.43762	−	1.09840i
$555$	1.04826	+	2.67142i	0.0444962	+	0.113396i
$556$	−12.8703	−	22.0804i	−0.545822	−	0.936419i
$557$	−15.5368	+	4.16308i	−0.658316	+	0.176395i	−0.572486	−	0.819914i	$-0.694021\pi$
$557$	−15.5368	+	4.16308i	−0.658316	+	0.176395i	−0.0858302	+	0.996310i	$0.527354\pi$
$558$	−5.97267	+	2.22935i	−0.252843	+	0.0943757i
$559$			22.5723i			0.954706i
$560$	−1.25712	−	14.1683i	−0.0531230	−	0.598718i
$561$	6.58130	−	4.85658i	0.277863	−	0.205045i
$562$	10.0300	+	13.0154i	0.423088	+	0.549023i
$563$	6.94636	+	25.9242i	0.292754	+	1.09257i	0.942985	+	0.332836i	$0.108006\pi$
$563$	6.94636	+	25.9242i	0.292754	+	1.09257i	−0.650230	+	0.759737i	$0.725328\pi$
$564$	2.41602	−	5.59973i	0.101733	−	0.235791i
$565$	−3.88239	+	14.4893i	−0.163333	+	0.609568i
$566$	−12.0602	+	15.7847i	−0.506929	+	0.663481i
$567$	23.0319	+	6.04407i	0.967250	+	0.253827i
$568$	11.3829	+	27.0052i	0.477615	+	1.13311i
$569$	4.96684	+	8.60283i	0.208221	+	0.360649i	0.951154	−	0.308716i	$-0.0998994\pi$
$569$	4.96684	+	8.60283i	0.208221	+	0.360649i	−0.742933	+	0.669366i	$0.766566\pi$
$570$	10.8024	−	18.0091i	0.452461	−	0.754319i
$571$	−8.08460	−	30.1721i	−0.338330	−	1.26266i	−0.900214	−	0.435448i	$-0.856590\pi$
$571$	−8.08460	−	30.1721i	−0.338330	−	1.26266i	0.561884	−	0.827216i	$-0.310077\pi$
$572$	7.88765	+	7.82262i	0.329799	+	0.327080i
$573$	12.9617	+	1.95450i	0.541483	+	0.0816505i
$574$	0.117646	−	2.41818i	0.00491045	−	0.100933i
$575$	4.02985			0.168057
$576$	−20.4768	−	12.5180i	−0.853199	−	0.521585i
$577$	4.14251	−	7.17503i	0.172455	−	0.298700i	−0.766823	−	0.641859i	$-0.778163\pi$
$577$	4.14251	−	7.17503i	0.172455	−	0.298700i	0.939278	+	0.343159i	$0.111497\pi$
$578$	−5.25684	+	12.7658i	−0.218656	+	0.530987i
$579$	4.70943	+	12.0017i	0.195717	+	0.498772i
$580$	17.9157	−	4.88006i	0.743909	−	0.202634i
$581$	−39.4516	+	3.17153i	−1.63673	+	0.131577i
$582$	−22.3780	−	0.373608i	−0.927598	−	0.0154865i
$583$	8.21616	+	14.2308i	0.340279	+	0.589380i
$584$	−14.5031	−	1.81783i	−0.600142	−	0.0752225i
$585$	−8.67733	−	9.35432i	−0.358764	−	0.386753i
$586$	15.9648	+	2.06820i	0.659498	+	0.0854365i
$587$	8.75969	+	8.75969i	0.361551	+	0.361551i	0.864384	−	0.502833i	$-0.167709\pi$
$587$	8.75969	+	8.75969i	0.361551	+	0.361551i	−0.502833	+	0.864384i	$0.667709\pi$
$588$	−16.8888	+	17.4002i	−0.696484	+	0.717572i
$589$	6.77772	−	6.77772i	0.279271	−	0.279271i
$590$	12.9334	+	16.7831i	0.532461	+	0.690951i
$591$	3.21872	+	28.5832i	0.132400	+	1.17576i
$592$	−3.45772	+	3.51545i	−0.142111	+	0.144484i
$593$	−39.3709	+	22.7308i	−1.61677	+	0.933442i	−0.629020	+	0.777389i	$0.716543\pi$
$593$	−39.3709	+	22.7308i	−1.61677	+	0.933442i	−0.987749	+	0.156052i	$0.950123\pi$
$594$	−5.83448	−	11.5037i	−0.239392	−	0.472001i
$595$	−0.766600	−	9.53597i	−0.0314275	−	0.390937i
$596$	−20.4930	+	35.8366i	−0.839426	+	1.46793i
$597$	11.0359	+	28.1242i	0.451668	+	1.15105i
$598$	−5.21272	+	2.17183i	−0.213164	+	0.0888127i
$599$	6.95678	+	4.01650i	0.284246	+	0.164110i	0.635344	−	0.772229i	$-0.280858\pi$
$599$	6.95678	+	4.01650i	0.284246	+	0.164110i	−0.351098	+	0.936339i	$0.614192\pi$
$600$	−11.2009	+	10.9231i	−0.457274	+	0.445934i
$601$		−	6.16511i		−	0.251480i	−0.992063	−	0.125740i	$-0.959869\pi$
$601$		−	6.16511i		−	0.251480i	0.992063	−	0.125740i	$-0.0401305\pi$
$602$	17.9332	+	19.7673i	0.730901	+	0.805655i
$603$	−19.7308	−	37.3440i	−0.803502	−	1.52077i
$604$	−8.49015	−	8.42016i	−0.345459	−	0.342611i
$605$	10.2807	−	2.75471i	0.417970	−	0.111995i
$606$	9.61697	+	38.4471i	0.390663	+	1.56181i
$607$	9.26416	−	5.34866i	0.376021	−	0.217096i	−0.300065	−	0.953919i	$-0.597008\pi$
$607$	9.26416	−	5.34866i	0.376021	−	0.217096i	0.676085	+	0.736823i	$0.263675\pi$
$608$	35.8224	+	4.33950i	1.45279	+	0.175990i
$609$	−26.2498	−	17.6917i	−1.06370	−	0.716903i
$610$	−2.57004	−	19.2140i	−0.104058	−	0.777952i
$611$	5.38127	+	1.44191i	0.217703	+	0.0583333i
$612$	−13.7021	−	8.53311i	−0.553875	−	0.344931i
$613$	−4.06758	+	1.08991i	−0.164288	+	0.0440209i	−0.340025	−	0.940416i	$-0.610436\pi$
$613$	−4.06758	+	1.08991i	−0.164288	+	0.0440209i	0.175737	+	0.984437i	$0.443769\pi$
$614$	−3.63515	+	28.0604i	−0.146703	+	1.13242i
$615$	1.21202	−	0.894391i	0.0488732	−	0.0360653i
$616$	13.1224	+	0.583979i	0.528715	+	0.0235292i
$617$	31.6199			1.27297			0.636485	−	0.771289i	$-0.280388\pi$
$617$	31.6199			1.27297			0.636485	+	0.771289i	$0.280388\pi$
$618$	16.8994	+	30.4328i	0.679795	+	1.22419i
$619$	4.39003	+	16.3838i	0.176450	+	0.658520i	0.996300	+	0.0859422i	$0.0273900\pi$
$619$	4.39003	+	16.3838i	0.176450	+	0.658520i	−0.819850	+	0.572578i	$0.805943\pi$
$620$	3.48967	−	2.03407i	0.140148	−	0.0816900i
$621$	6.53860	−	0.488751i	0.262385	−	0.0196129i
$622$	2.33687	+	17.4708i	0.0937001	+	0.700517i
$623$	−2.53564	+	13.8104i	−0.101588	+	0.553302i
$624$	8.60177	−	20.1658i	0.344347	−	0.807280i
$625$	0.583375	+	1.01043i	0.0233350	+	0.0404174i
$626$	−5.32565	−	2.19305i	−0.212856	−	0.0876521i
$627$	15.1615	+	12.0925i	0.605493	+	0.482927i
$628$	−21.1305	+	0.0874613i	−0.843197	+	0.00349009i
$629$	−2.34509	+	2.34509i	−0.0935048	+	0.0935048i
$630$	−15.0308	−	1.29795i	−0.598842	−	0.0517115i
$631$	23.4033			0.931669			0.465835	−	0.884872i	$-0.345754\pi$
$631$	23.4033			0.931669			0.465835	+	0.884872i	$0.345754\pi$
$632$	5.45550	−	7.20189i	0.217008	−	0.286476i
$633$	−12.7038	+	1.43055i	−0.504929	+	0.0568594i
$634$	−5.26944	+	2.19546i	−0.209276	+	0.0871929i
$635$	−4.17034	+	15.5639i	−0.165495	+	0.617635i
$636$	20.1160	−	25.4367i	0.797652	−	1.00863i
$637$	−17.9641	−	12.9598i	−0.711764	−	0.513486i
$638$	2.27336	+	16.9960i	0.0900033	+	0.672879i
$639$	30.3055	−	6.91298i	1.19887	−	0.273473i
$640$	14.1313	+	5.61497i	0.558591	+	0.221951i
$641$	24.0222	+	13.8692i	0.948819	+	0.547801i	0.892714	−	0.450624i	$-0.148798\pi$
$641$	24.0222	+	13.8692i	0.948819	+	0.547801i	0.0561053	+	0.998425i	$0.482132\pi$
$642$	3.03470	−	10.6137i	0.119770	−	0.418889i
$643$	25.6488	+	25.6488i	1.01149	+	1.01149i	0.999933	+	0.0115574i	$0.00367891\pi$
$643$	25.6488	+	25.6488i	1.01149	+	1.01149i	0.0115574	+	0.999933i	$0.496321\pi$
$644$	−2.83948	+	6.04333i	−0.111891	+	0.238140i
$645$	−2.47596	+	16.4199i	−0.0974909	+	0.646532i
$646$	24.0685	+	3.11801i	0.946961	+	0.122677i
$647$	−29.3985	−	16.9732i	−1.15577	−	0.667286i	−0.205486	−	0.978660i	$-0.565877\pi$
$647$	−29.3985	−	16.9732i	−1.15577	−	0.667286i	−0.950287	+	0.311374i	$0.899211\pi$
$648$	−16.8491	+	19.0816i	−0.661894	+	0.749597i
$649$	−16.9454	+	9.78340i	−0.665163	+	0.384032i
$650$	−11.3564	−	8.67680i	−0.445435	−	0.340332i
$651$	−6.51164	−	2.23946i	−0.255211	−	0.0877712i
$652$	−41.5548	−	23.7629i	−1.62741	−	0.930626i
$653$	−4.33005	+	16.1600i	−0.169448	+	0.632389i	0.827983	+	0.560754i	$0.189488\pi$
$653$	−4.33005	+	16.1600i	−0.169448	+	0.632389i	−0.997431	+	0.0716355i	$0.977178\pi$
$654$	−3.19576	−	12.7761i	−0.124964	−	0.499586i
$655$	−8.25387	−	4.76537i	−0.322505	−	0.186199i
$656$	2.25209	+	1.27550i	0.0879292	+	0.0498000i
$657$	−4.57152	+	14.8139i	−0.178352	+	0.577944i
$658$	5.85812	−	3.01257i	0.228373	−	0.117442i
$659$	30.8207	−	30.8207i	1.20060	−	1.20060i	0.226619	−	0.973983i	$-0.427233\pi$
$659$	30.8207	−	30.8207i	1.20060	−	1.20060i	0.973983	−	0.226619i	$-0.0727673\pi$
$660$	4.87969	+	6.55565i	0.189942	+	0.255178i
$661$	−8.76018	+	2.34728i	−0.340732	+	0.0912988i	−0.425127	−	0.905134i	$-0.639771\pi$
$661$	−8.76018	+	2.34728i	−0.340732	+	0.0912988i	0.0843957	+	0.996432i	$0.473104\pi$
$662$	0.525094	+	1.26030i	0.0204083	+	0.0489831i
$663$	5.89746	−	13.5148i	0.229038	−	0.524871i
$664$	15.9490	−	39.1906i	0.618939	−	1.52089i
$665$	21.3693	−	7.60765i	0.828666	−	0.295012i
$666$	3.03476	+	4.25954i	0.117595	+	0.165054i
$667$	−8.41960	−	2.25603i	−0.326008	−	0.0873537i
$668$	31.0015	+	8.16944i	1.19948	+	0.316085i
$669$	−22.4203	−	17.8819i	−0.866819	−	0.691355i
$670$	16.3344	+	21.1964i	0.631053	+	0.818890i
$671$	17.9016			0.691082
$672$	−8.48843	−	24.4938i	−0.327448	−	0.944869i
$673$	24.3045			0.936869			0.468435	−	0.883498i	$-0.344818\pi$
$673$	24.3045			0.936869			0.468435	+	0.883498i	$0.344818\pi$
$674$	1.64007	+	2.12825i	0.0631733	+	0.0819772i
$675$	9.34529	+	13.7126i	0.359700	+	0.527799i
$676$	−5.77567	−	1.52199i	−0.222141	−	0.0585382i
$677$	44.1978	+	11.8428i	1.69866	+	0.455155i	0.972602	−	0.232478i	$-0.0746833\pi$
$677$	44.1978	+	11.8428i	1.69866	+	0.455155i	0.726059	+	0.687632i	$0.241350\pi$
$678$	−0.456354	+	27.3343i	−0.0175262	+	1.04977i
$679$	−18.4087	−	15.6691i	−0.706460	−	0.601326i
$680$	9.47288	+	3.85507i	0.363268	+	0.147835i
$681$	−23.2264	−	10.1353i	−0.890038	−	0.388387i
$682$	1.43457	+	3.44319i	0.0549325	+	0.131846i
$683$	28.6057	−	7.66489i	1.09457	−	0.293289i	0.334017	−	0.942567i	$-0.391596\pi$
$683$	28.6057	−	7.66489i	1.09457	−	0.293289i	0.760551	+	0.649278i	$0.224929\pi$
$684$	11.1344	−	36.6178i	0.425733	−	1.40011i
$685$	19.3151	−	19.3151i	0.737993	−	0.737993i
$686$	−26.0280	+	2.92274i	−0.993754	+	0.111591i
$687$	17.2967	+	23.4393i	0.659910	+	0.894264i
$688$	−27.4983	+	7.61267i	−1.04836	+	0.290230i
$689$	25.6553	+	14.8121i	0.977388	+	0.564295i
$690$	−4.03014	+	1.00808i	−0.153425	+	0.0383769i
$691$	−0.290046	+	1.08247i	−0.0110339	+	0.0411790i	−0.971223	−	0.238171i	$-0.923452\pi$
$691$	−0.290046	+	1.08247i	−0.0110339	+	0.0411790i	0.960189	+	0.279350i	$0.0901189\pi$
$692$	23.7707	+	13.5932i	0.903628	+	0.516735i
$693$	3.02828	−	13.5991i	0.115035	−	0.516585i
$694$	−31.2765	−	23.8966i	−1.18724	−	0.907103i
$695$	14.8741	−	8.58757i	0.564207	−	0.325745i
$696$	29.5171	−	16.5511i	1.11884	−	0.627369i
$697$	1.50756	+	0.870387i	0.0571027	+	0.0329683i
$698$	−30.5019	−	3.95145i	−1.15451	−	0.149565i
$699$	41.3198	+	6.23064i	1.56286	+	0.235664i
$700$	−16.8387	+	1.42384i	−0.636443	+	0.0538161i
$701$	1.57176	+	1.57176i	0.0593645	+	0.0593645i	0.736166	−	0.676801i	$-0.236634\pi$
$701$	1.57176	+	1.57176i	0.0593645	+	0.0593645i	−0.676801	+	0.736166i	$0.736634\pi$
$702$	−19.4786	−	12.7011i	−0.735171	−	0.479373i
$703$	−6.80994	−	3.93172i	−0.256842	−	0.148288i
$704$	−6.86960	+	12.2472i	−0.258908	+	0.461584i
$705$	3.75636	+	1.63917i	0.141473	+	0.0617346i
$706$	−0.0580176	−	0.433749i	−0.00218352	−	0.0163244i
$707$	−18.3641	+	38.6679i	−0.690652	+	1.45426i
$708$	30.2888	+	23.9532i	1.13832	+	0.900216i
$709$	6.76881	−	25.2615i	0.254208	−	0.948717i	−0.714322	−	0.699818i	$-0.753265\pi$
$709$	6.76881	−	25.2615i	0.254208	−	0.948717i	0.968529	−	0.248899i	$-0.0800687\pi$
$710$	−18.1795	+	7.57431i	−0.682264	+	0.284259i
$711$	−6.51718	−	7.02564i	−0.244414	−	0.263482i
$712$	−11.9653	−	9.06384i	−0.448419	−	0.339682i
$713$	−1.89613			−0.0710107
$714$	−5.57258	−	16.5208i	−0.208549	−	0.618274i
$715$	−5.27883	+	5.27883i	−0.197417	+	0.197417i
$716$	7.44710	−	0.0308244i	0.278311	−	0.00115196i
$717$	2.15862	−	2.70647i	0.0806150	−	0.101075i
$718$	34.4645	+	14.1922i	1.28620	+	0.529647i
$719$	12.3167	+	21.3332i	0.459337	+	0.795595i	0.998926	−	0.0463335i	$-0.0147537\pi$
$719$	12.3167	+	21.3332i	0.459337	+	0.795595i	−0.539589	+	0.841929i	$0.681420\pi$
$720$	8.46923	−	13.7258i	0.315630	−	0.511531i
$721$	−6.78988	+	36.9811i	−0.252868	+	1.37725i
$722$	4.06670	+	30.4033i	0.151347	+	1.13149i
$723$	−5.82697	−	14.8496i	−0.216707	−	0.552264i
$724$	−8.88599	+	5.17949i	−0.330245	+	0.192494i
$725$	−5.70963	−	21.3086i	−0.212050	−	0.791383i
$726$	16.9582	−	9.41695i	0.629379	−	0.349496i
$727$	19.3950			0.719319			0.359660	−	0.933084i	$-0.382893\pi$
$727$	19.3950			0.719319			0.359660	+	0.933084i	$0.382893\pi$
$728$	21.0139	−	10.9167i	0.778828	−	0.404601i
$729$	16.8262	+	21.1158i	0.623193	+	0.782068i
$730$	1.26195	−	9.74118i	0.0467067	−	0.360537i
$731$	−18.5366	+	4.96685i	−0.685599	+	0.183706i
$732$	−13.0411	−	32.8341i	−0.482014	−	1.21358i
$733$	47.2679	+	12.6654i	1.74588	+	0.467807i	0.983739	−	0.179602i	$-0.0574811\pi$
$733$	47.2679	+	12.6654i	1.74588	+	0.467807i	0.762142	+	0.647410i	$0.224148\pi$
$734$	0.585623	+	4.37821i	0.0216157	+	0.161603i
$735$	−11.6462	−	11.3979i	−0.429575	−	0.420418i
$736$	−4.40382	−	5.61783i	−0.162327	−	0.207076i
$737$	−21.4013	+	12.3561i	−0.788327	+	0.455141i
$738$	1.74733	−	2.11731i	0.0643201	−	0.0779391i
$739$	3.41774	−	0.915781i	0.125724	−	0.0336875i	−0.195409	−	0.980722i	$-0.562603\pi$
$739$	3.41774	−	0.915781i	0.125724	−	0.0336875i	0.321132	+	0.947034i	$0.395937\pi$
$740$	−2.35280	−	2.33341i	−0.0864908	−	0.0857777i
$741$	34.5713	+	5.21303i	1.27001	+	0.191505i
$742$	34.2350	−	7.41108i	1.25681	−	0.272069i
$743$		−	38.2184i		−	1.40210i	−0.713113	−	0.701049i	$-0.752715\pi$
$743$		−	38.2184i		−	1.40210i	0.713113	−	0.701049i	$-0.247285\pi$
$744$	5.27025	−	5.13955i	0.193217	−	0.188425i
$745$	−24.0256	−	13.8712i	−0.880231	−	0.508202i
$746$	−13.1912	+	5.49598i	−0.482964	+	0.201222i
$747$	−37.9965	−	23.8815i	−1.39022	−	0.873778i
$748$	−4.68839	+	8.19871i	−0.171424	+	0.299775i
$749$	9.81511	−	6.77002i	0.358636	−	0.247371i
$750$	−18.7530	−	19.3899i	−0.684765	−	0.708017i
$751$	−2.09970	+	1.21226i	−0.0766190	+	0.0442360i	−0.537820	−	0.843060i	$-0.680752\pi$
$751$	−2.09970	+	1.21226i	−0.0766190	+	0.0442360i	0.461201	+	0.887296i	$0.347419\pi$
$752$	0.0582956	+	7.04193i	0.00212582	+	0.256793i
$753$	20.8367	−	2.34640i	0.759332	−	0.0855074i
$754$	18.8695	+	24.4861i	0.687187	+	0.891732i
$755$	5.68206	−	5.68206i	0.206791	−	0.206791i
$756$	−27.1488	+	4.35248i	−0.987391	+	0.158298i
$757$	3.73965	+	3.73965i	0.135920	+	0.135920i	0.771793	−	0.635873i	$-0.219360\pi$
$757$	3.73965	+	3.73965i	0.135920	+	0.135920i	−0.635873	+	0.771793i	$0.719360\pi$
$758$	−19.7233	−	2.55510i	−0.716381	−	0.0928055i
$759$	−0.429296	−	3.81228i	−0.0155825	−	0.138377i
$760$	−3.01584	+	24.0610i	−0.109396	+	0.872784i
$761$	−1.73621	−	3.00720i	−0.0629376	−	0.109011i	0.832840	−	0.553514i	$-0.186714\pi$
$761$	−1.73621	−	3.00720i	−0.0629376	−	0.109011i	−0.895777	+	0.444503i	$0.853380\pi$
$762$	−0.490201	+	29.3616i	−0.0177581	+	1.06366i
$763$	6.10245	−	12.8495i	0.220924	−	0.465183i
$764$	−14.6040	+	3.97799i	−0.528354	+	0.143919i
$765$	5.77246	−	9.18424i	0.208704	−	0.332057i
$766$	−1.14188	+	2.77297i	−0.0412579	+	0.100191i
$767$	−17.6375	+	30.5490i	−0.636853	+	1.10306i
$768$	27.4677	+	3.67788i	0.991154	+	0.132714i
$769$	−17.8238			−0.642742			−0.321371	−	0.946953i	$-0.604144\pi$
$769$	−17.8238			−0.642742			−0.321371	+	0.946953i	$0.604144\pi$
$770$	−0.428941	+	8.81676i	−0.0154580	+	0.317734i
$771$	−4.77954	+	31.6965i	−0.172131	+	1.14152i
$772$	−10.5702	−	10.4831i	−0.380431	−	0.377295i
$773$	−1.80558	−	6.73850i	−0.0649421	−	0.242367i	0.925823	−	0.377958i	$-0.123373\pi$
$773$	−1.80558	−	6.73850i	−0.0649421	−	0.242367i	−0.990765	+	0.135591i	$0.956707\pi$
$774$	2.88403	+	30.1256i	0.103664	+	1.08284i
$775$	−2.39940	−	4.15588i	−0.0861889	−	0.149284i
$776$	23.8144	−	10.0379i	0.854888	−	0.360341i
$777$	−0.391987	+	5.63549i	−0.0140625	+	0.202172i
$778$	−22.4691	+	29.4081i	−0.805557	+	1.05433i
$779$	−1.06826	+	3.98681i	−0.0382744	+	0.142842i
$780$	13.5278	+	5.83658i	0.484371	+	0.208983i
$781$	−4.70715	−	17.5673i	−0.168435	−	0.628609i
$782$	−2.93054	−	3.80283i	−0.104796	−	0.135989i
$783$	−11.8485	−	33.8816i	−0.423430	−	1.21083i
$784$	9.72951	−	26.2552i	0.347482	−	0.937687i
$785$		−	14.2002i		−	0.506825i
$786$	−16.7004	−	4.77505i	−0.595685	−	0.170320i
$787$	−28.5882	+	7.66019i	−1.01906	+	0.273056i	−0.729410	−	0.684077i	$-0.760205\pi$
$787$	−28.5882	+	7.66019i	−1.01906	+	0.273056i	−0.289649	+	0.957133i	$0.593539\pi$
$788$	−16.7257	−	28.6949i	−0.595830	−	1.02221i
$789$	−32.0413	+	12.5730i	−1.14070	+	0.447609i
$790$	4.82458	+	3.68619i	0.171651	+	0.131149i
$791$	−19.1395	+	22.4858i	−0.680523	+	0.799503i
$792$	11.5266	+	9.43250i	0.409579	+	0.335169i
$793$	27.9491	−	16.1364i	0.992503	−	0.573022i
$794$	2.05738	+	4.93803i	0.0730138	+	0.175244i
$795$	17.0378	+	13.5890i	0.604268	+	0.481951i
$796$	−24.7698	−	24.5656i	−0.877942	−	0.870704i
$797$	−13.5247	−	13.5247i	−0.479071	−	0.479071i	0.425764	−	0.904834i	$-0.360006\pi$
$797$	−13.5247	−	13.5247i	−0.479071	−	0.479071i	−0.904834	+	0.425764i	$0.860006\pi$
$798$	34.4169	−	22.9009i	1.21834	−	0.810683i
$799$			4.73643i			0.167563i
$800$	6.74032	−	16.7610i	0.238306	−	0.592593i
$801$	−11.6725	+	10.8277i	−0.412428	+	0.382580i
$802$	−25.2274	−	10.3884i	−0.890810	−	0.366827i
$803$	8.76177	+	2.34771i	0.309196	+	0.0828488i
$804$	38.2535	+	30.2519i	1.34910	+	1.06690i
$805$	−4.05329	−	1.92498i	−0.142860	−	0.0678465i
$806$	5.34343	+	4.08262i	0.188214	+	0.143804i
$807$	4.99493	−	11.4465i	0.175830	−	0.402936i
$808$	−28.0834	−	36.1323i	−0.987972	−	1.27113i
$809$	0.989810	−	1.71440i	0.0347999	−	0.0602752i	−0.848101	−	0.529835i	$-0.822254\pi$
$809$	0.989810	−	1.71440i	0.0347999	−	0.0602752i	0.882901	+	0.469560i	$0.155587\pi$
$810$	−12.7762	−	11.3759i	−0.448910	−	0.399707i
$811$	−1.70827	+	1.70827i	−0.0599855	+	0.0599855i	−0.736463	−	0.676478i	$-0.763506\pi$
$811$	−1.70827	+	1.70827i	−0.0599855	+	0.0599855i	0.676478	+	0.736463i	$0.263506\pi$
$812$	35.9783	+	6.45194i	1.26259	+	0.226419i
$813$	6.41933	−	42.5712i	0.225136	−	1.49304i
$814$	2.42386	−	1.86788i	0.0849564	−	0.0654691i
$815$	16.0845	−	27.8592i	0.563416	−	0.975864i
$816$	18.4531	+	2.62651i	0.645988	+	0.0919464i
$817$	−22.7507	−	39.4053i	−0.795945	−	1.37862i
$818$	−6.06720	−	45.3594i	−0.212135	−	1.58595i
$819$	−7.53021	−	23.9615i	−0.263127	−	0.837281i
$820$	−0.863417	+	1.50988i	−0.0301518	+	0.0527273i
$821$	−3.31409	−	0.888008i	−0.115663	−	0.0309917i	0.200523	−	0.979689i	$-0.435736\pi$
$821$	−3.31409	−	0.888008i	−0.115663	−	0.0309917i	−0.316186	+	0.948697i	$0.602402\pi$
$822$	25.6075	−	42.6915i	0.893165	−	1.48904i
$823$	16.6739	−	28.8800i	0.581215	−	1.00669i	−0.414120	−	0.910222i	$-0.635911\pi$
$823$	16.6739	−	28.8800i	0.581215	−	1.00669i	0.995336	−	0.0964722i	$-0.0307559\pi$
$824$	−32.0404	−	24.2709i	−1.11618	−	0.845517i
$825$	7.81239	−	5.76505i	0.271993	−	0.200713i
$826$	8.82475	+	40.7654i	0.307052	+	1.41841i
$827$	38.2225	+	38.2225i	1.32913	+	1.32913i	0.906133	+	0.422993i	$0.139020\pi$
$827$	38.2225	+	38.2225i	1.32913	+	1.32913i	0.422993	+	0.906133i	$0.360980\pi$
$828$	−6.67955	+	3.56461i	−0.232131	+	0.123879i
$829$	13.6246	+	50.8478i	0.473203	+	1.76602i	0.628149	+	0.778093i	$0.283813\pi$
$829$	13.6246	+	50.8478i	0.473203	+	1.76602i	−0.154946	+	0.987923i	$0.549520\pi$
$830$	26.2922	+	10.8269i	0.912616	+	0.375807i
$831$	20.8590	−	47.8012i	0.723592	−	1.65820i
$832$	0.314340	+	25.3134i	0.0108978	+	0.877586i
$833$	6.68983	−	17.6040i	0.231789	−	0.609941i
$834$	22.4999	−	21.7610i	0.779108	−	0.753520i
$835$	−5.57619	+	20.8106i	−0.192972	+	0.720181i
$836$	−21.6542	−	5.70627i	−0.748926	−	0.197355i
$837$	−4.39715	−	6.45207i	−0.151988	−	0.223016i
$838$	32.2681	+	4.18025i	1.11468	+	0.144404i
$839$			22.4695i			0.775733i	0.921716	+	0.387866i	$0.126788\pi$
$839$			22.4695i			0.775733i	−0.921716	+	0.387866i	$0.873212\pi$
$840$	16.4837	−	5.63619i	0.568743	−	0.194467i
$841$			18.7167i			0.645403i
$842$	−0.719661	+	5.55519i	−0.0248012	+	0.191444i
$843$	−12.5485	+	15.7333i	−0.432194	+	0.541884i
$844$	12.7534	−	7.43372i	0.438990	−	0.255879i
$845$	1.03886	−	3.87709i	0.0357379	−	0.133376i
$846$	7.36623	+	1.23685i	0.253256	+	0.0425239i
$847$	20.6072	+	3.78356i	0.708071	+	0.130005i
$848$	−9.39211	+	36.2495i	−0.322526	+	1.24481i
$849$	−22.2986	−	9.73046i	−0.765286	−	0.333948i
$850$	4.62657	−	11.2352i	0.158690	−	0.385366i
$851$	0.402605	+	1.50254i	0.0138011	+	0.0515065i
$852$	−28.7920	+	21.4313i	−0.986398	+	0.734224i
$853$	−14.0157	−	14.0157i	−0.479887	−	0.479887i	0.425208	−	0.905096i	$-0.360201\pi$
$853$	−14.0157	−	14.0157i	−0.479887	−	0.479887i	−0.905096	+	0.425208i	$0.860201\pi$
$854$	11.6560	−	36.3361i	0.398859	−	1.24340i
$855$	24.5766	+	7.58428i	0.840501	+	0.259377i
$856$	1.74221	+	12.6271i	0.0595477	+	0.431586i
$857$	1.50938	−	2.61433i	0.0515595	−	0.0893037i	−0.839094	−	0.543987i	$-0.816914\pi$
$857$	1.50938	−	2.61433i	0.0515595	−	0.0893037i	0.890653	+	0.454683i	$0.150247\pi$
$858$	−6.99855	+	11.6676i	−0.238926	+	0.398325i
$859$	−17.4046	−	4.66354i	−0.593836	−	0.159118i	−0.0506304	−	0.998717i	$-0.516123\pi$
$859$	−17.4046	−	4.66354i	−0.593836	−	0.159118i	−0.543206	+	0.839599i	$0.682790\pi$
$860$	−5.03931	−	18.5003i	−0.171839	−	0.630856i
$861$	2.91047	−	0.566850i	0.0991886	−	0.0193182i
$862$	35.1649	−	4.70360i	1.19772	−	0.160205i
$863$	−15.0253	−	26.0246i	−0.511468	−	0.885889i	−0.999912	−	0.0132936i	$-0.995768\pi$
$863$	−15.0253	−	26.0246i	−0.511468	−	0.885889i	0.488443	−	0.872596i	$-0.337565\pi$
$864$	8.90361	−	28.0130i	0.302907	−	0.953020i
$865$	−9.20088	+	15.9364i	−0.312839	+	0.541854i
$866$	−3.30065	−	4.28311i	−0.112161	−	0.145546i
$867$	−16.7196	−	2.52115i	−0.567826	−	0.0856228i
$868$	7.92296	−	0.669947i	0.268923	−	0.0227395i
$869$	−3.96471	+	3.96471i	−0.134494	+	0.134494i
$870$	11.0405	+	19.8819i	0.374306	+	0.674059i
$871$	−22.2755	+	38.5822i	−0.754775	+	1.30731i
$872$	9.33224	+	12.0069i	0.316029	+	0.406605i
$873$	−6.09618	−	26.7247i	−0.206324	−	0.904494i
$874$	6.91105	−	9.04535i	0.233770	−	0.305964i
$875$	−2.33474	−	29.0425i	−0.0789285	−	0.981815i
$876$	−2.07682	−	17.7807i	−0.0701694	−	0.600753i
$877$	10.0934	+	2.70451i	0.340829	+	0.0913248i	0.425174	−	0.905112i	$-0.360213\pi$
$877$	10.0934	+	2.70451i	0.340829	+	0.0913248i	−0.0843447	+	0.996437i	$0.526880\pi$
$878$	4.79643	−	11.6477i	0.161872	−	0.393092i
$879$	2.20627	+	19.5923i	0.0744156	+	0.660833i
$880$	−8.21117	−	4.65052i	−0.276798	−	0.156769i
$881$			33.6914i			1.13509i	0.823341	+	0.567546i	$0.192107\pi$
$881$			33.6914i			1.13509i	−0.823341	+	0.567546i	$0.807893\pi$
$882$	−25.6313	−	15.0013i	−0.863050	−	0.505119i
$883$	−13.1894	−	13.1894i	−0.443859	−	0.443859i	0.449448	−	0.893307i	$-0.351621\pi$
$883$	−13.1894	−	13.1894i	−0.443859	−	0.443859i	−0.893307	+	0.449448i	$0.851621\pi$
$884$	0.0704745	+	17.0265i	0.00237031	+	0.572663i
$885$	−16.1811	+	20.2878i	−0.543921	+	0.681966i
$886$	0.0681963	−	0.0284133i	0.00229110	−	0.000954565i
$887$	−24.0909	+	13.9089i	−0.808892	+	0.467014i	−0.846571	−	0.532276i	$-0.821337\pi$
$887$	−24.0909	+	13.9089i	−0.808892	+	0.467014i	0.0376787	+	0.999290i	$0.488004\pi$
$888$	−5.19173	−	3.08500i	−0.174223	−	0.103526i
$889$	−20.5591	+	24.1535i	−0.689529	+	0.810083i
$890$	6.12429	−	8.01562i	0.205287	−	0.268684i
$891$	11.9767	−	10.3015i	0.401235	−	0.345114i
$892$	32.0215	+	8.43822i	1.07216	+	0.282533i
$893$	−10.8476	+	2.90660i	−0.363001	+	0.0972658i
$894$	−48.6122	−	13.8994i	−1.62584	−	0.464865i
$895$			5.00463i			0.167286i
$896$	20.3862	+	21.9181i	0.681055	+	0.732232i
$897$	−4.10663	−	5.56503i	−0.137116	−	0.185811i
$898$	3.65241	−	2.81462i	0.121883	−	0.0939252i
$899$	2.68650	+	10.0262i	0.0895998	+	0.334391i
$900$	−16.2652	−	10.1293i	−0.542174	−	0.337644i
$901$	−6.51856	+	24.3276i	−0.217165	+	0.810470i
$902$	−1.27631	−	0.975157i	−0.0424965	−	0.0324692i
$903$	−18.2690	+	27.1064i	−0.607955	+	0.902046i
$904$	−12.2611	−	29.0888i	−0.407799	−	0.967480i
$905$	−3.45596	−	5.98590i	−0.114880	−	0.198978i
$906$	7.53314	−	12.5588i	0.250272	−	0.417239i
$907$	14.8320	+	55.3536i	0.492487	+	1.83799i	0.543672	+	0.839298i	$0.317034\pi$
$907$	14.8320	+	55.3536i	0.492487	+	1.83799i	−0.0511845	+	0.998689i	$0.516300\pi$
$908$	29.2616	−	0.121117i	0.971079	−	0.00401940i
$909$	−42.9167	+	22.6752i	−1.42346	+	0.752088i
$910$	7.27772	+	14.1520i	0.241254	+	0.469133i
$911$	6.01012			0.199124			0.0995621	−	0.995031i	$-0.468256\pi$
$911$	6.01012			0.199124			0.0995621	+	0.995031i	$0.468256\pi$
$912$	5.30875	+	43.8740i	0.175790	+	1.45281i
$913$	−13.1290	+	22.7402i	−0.434508	+	0.752589i
$914$	−36.9462	−	15.2141i	−1.22207	−	0.503238i
$915$	22.1012	−	8.67246i	0.730643	−	0.286703i
$916$	−29.1997	−	16.6977i	−0.964785	−	0.551707i
$917$	−10.6525	−	15.4439i	−0.351777	−	0.510003i
$918$	6.14416	−	18.7907i	0.202787	−	0.620187i
$919$	−17.3144	−	29.9894i	−0.571148	−	0.989258i	−0.996448	−	0.0842055i	$-0.973165\pi$
$919$	−17.3144	−	29.9894i	−0.571148	−	0.989258i	0.425300	−	0.905052i	$-0.360169\pi$
$920$	3.78750	−	2.94379i	0.124870	−	0.0970539i
$921$	−34.4363	+	3.87783i	−1.13471	+	0.127779i
$922$	−5.49854	+	42.4442i	−0.181085	+	1.39782i
$923$	−23.1843	−	23.1843i	−0.763121	−	0.763121i
$924$	3.14078	+	15.7779i	0.103324	+	0.519055i
$925$	−2.78376	+	2.78376i	−0.0915294	+	0.0915294i
$926$	34.7865	−	26.8072i	1.14315	−	0.880938i
$927$	−31.2563	+	28.9942i	−1.02659	+	0.952296i
$928$	−23.4659	+	31.2456i	−0.770306	+	1.02569i
$929$	−8.57633	+	4.95155i	−0.281380	+	0.162455i	−0.634048	−	0.773294i	$-0.718608\pi$
$929$	−8.57633	+	4.95155i	−0.281380	+	0.162455i	0.352668	+	0.935749i	$0.385275\pi$
$930$	3.43918	+	3.55596i	0.112775	+	0.116605i
$931$	44.4228	+	4.51834i	1.45590	+	0.148083i
$932$	−46.5552	+	12.6812i	−1.52497	+	0.415386i
$933$	−20.0961	+	7.88567i	−0.657916	+	0.258165i
$934$	1.86627	+	4.47932i	0.0610661	+	0.146568i
$935$	−5.49659	−	3.17346i	−0.179758	−	0.103783i
$936$	26.4985	+	4.33663i	0.866131	+	0.141747i
$937$		−	46.1779i		−	1.50856i	−0.656550	−	0.754282i	$-0.727985\pi$
$937$		−	46.1779i		−	1.50856i	0.656550	−	0.754282i	$-0.272015\pi$
$938$	11.1453	+	51.4851i	0.363907	+	1.68105i
$939$	1.05178	−	6.97509i	0.0343234	−	0.227623i
$940$	−4.73242	+	0.0195880i	−0.154355	+	0.000638890i
$941$	17.0486	−	4.56816i	0.555769	−	0.148918i	0.0300073	−	0.999550i	$-0.490447\pi$
$941$	17.0486	−	4.56816i	0.555769	−	0.148918i	0.525762	+	0.850632i	$0.323780\pi$
$942$	−6.27993	−	25.1062i	−0.204611	−	0.818003i
$943$	0.707102	−	0.408245i	0.0230264	−	0.0132943i
$944$	−43.1642	−	11.1837i	−1.40487	−	0.363997i
$945$	−2.84940	−	18.2564i	−0.0926910	−	0.593881i
$946$	17.5506	−	2.34755i	0.570621	−	0.0763254i
$947$	2.33004	+	0.624333i	0.0757162	+	0.0202881i	0.296478	−	0.955040i	$-0.404188\pi$
$947$	2.33004	+	0.624333i	0.0757162	+	0.0202881i	−0.220762	+	0.975328i	$0.570854\pi$
$948$	10.1601	+	4.38362i	0.329986	+	0.142373i
$949$	15.7957	−	4.23244i	0.512750	−	0.137391i
$950$	28.5707	+	3.70126i	0.926955	+	0.120085i
$951$	−4.15132	−	5.62558i	−0.134616	−	0.182422i
$952$	13.5889	+	14.8547i	0.440418	+	0.481443i
$953$	8.71845			0.282418			0.141209	−	0.989980i	$-0.454901\pi$
$953$	8.71845			0.282418			0.141209	+	0.989980i	$0.454901\pi$
$954$	36.1328	+	16.4907i	1.16984	+	0.533906i
$955$	−2.63263	−	9.82512i	−0.0851900	−	0.317933i
$956$	−1.01862	+	3.86547i	−0.0329445	+	0.125018i
$957$	−19.5499	+	7.67135i	−0.631959	+	0.247980i
$958$	−46.4506	+	6.21316i	−1.50075	+	0.200738i
$959$	50.6569	−	18.0343i	1.63580	−	0.582357i
$960$	−2.54798	+	18.4484i	−0.0822356	+	0.595418i
$961$	−14.3710	−	24.8914i	−0.463582	−	0.802947i
$962$	2.10060	−	5.10113i	0.0677260	−	0.164467i
$963$	13.5104	+	0.507239i	0.435368	+	0.0163455i
$964$	13.0785	+	12.9707i	0.421231	+	0.417758i
$965$	7.07416	−	7.07416i	0.227725	−	0.227725i
$966$	−8.01760	−	1.61086i	−0.257962	−	0.0518284i
$967$	4.07858			0.131158			0.0655792	−	0.997847i	$-0.479110\pi$
$967$	4.07858			0.131158			0.0655792	+	0.997847i	$0.479110\pi$
$968$	−13.5246	+	17.8540i	−0.434697	+	0.573850i
$969$	3.32617	+	29.5374i	0.106852	+	0.948876i
$970$	6.67936	+	16.0315i	0.214461	+	0.514740i
$971$	−6.19107	+	23.1054i	−0.198681	+	0.741488i	0.792602	+	0.609739i	$0.208726\pi$
$971$	−6.19107	+	23.1054i	−0.198681	+	0.741488i	−0.991283	+	0.131749i	$0.957941\pi$
$972$	−27.6195	−	14.4625i	−0.885895	−	0.463886i
$973$	33.7008	−	2.70922i	1.08040	−	0.0868536i
$974$	−42.3199	+	5.66064i	−1.35602	+	0.181379i
$975$	7.00064	−	16.0429i	0.224200	−	0.513783i
$976$	29.0840	+	28.6064i	0.930955	+	0.915668i
$977$	−48.8994	−	28.2321i	−1.56443	−	0.903223i	−0.996800	−	0.0799390i	$-0.974527\pi$
$977$	−48.8994	−	28.2321i	−1.56443	−	0.903223i	−0.567629	−	0.823284i	$-0.692139\pi$
$978$	16.1172	−	56.3688i	0.515370	−	1.80248i
$979$	6.58703	+	6.58703i	0.210522	+	0.210522i
$980$	17.6167	+	6.61137i	0.562746	+	0.211193i
$981$	14.2614	−	7.53504i	0.455331	−	0.240575i
$982$	−3.04750	+	23.5242i	−0.0972496	+	0.750686i
$983$	31.2115	+	18.0200i	0.995493	+	0.574748i	0.906912	−	0.421321i	$-0.138433\pi$
$983$	31.2115	+	18.0200i	0.995493	+	0.574748i	0.0885811	+	0.996069i	$0.471767\pi$
$984$	−0.858803	+	3.05134i	−0.0273776	+	0.0972731i
$985$	19.3298	−	11.1601i	0.615899	−	0.355589i
$986$	−15.9561	+	20.8838i	−0.508147	+	0.665075i
$987$	5.29521	+	6.08691i	0.168548	+	0.193749i
$988$	−38.9516	+	10.6101i	−1.23922	+	0.337551i
$989$	−2.32965	+	8.69436i	−0.0740784	+	0.276464i
$990$	−6.37081	+	7.71975i	−0.202478	+	0.245350i
$991$	−34.9307	−	20.1672i	−1.10961	−	0.640633i	−0.170881	−	0.985292i	$-0.554661\pi$
$991$	−34.9307	−	20.1672i	−1.10961	−	0.640633i	−0.938728	+	0.344659i	$0.887995\pi$
$992$	−3.17146	+	7.88643i	−0.100694	+	0.250394i
$993$	−1.34548	+	0.992880i	−0.0426976	+	0.0315081i
$994$	−38.7227	−	1.88388i	−1.22821	−	0.0597531i
$995$	16.5773	−	16.5773i	0.525534	−	0.525534i
$996$	51.2732	+	7.51460i	1.62465	+	0.238109i
$997$	−3.67266	+	0.984086i	−0.116314	+	0.0311663i	−0.316507	−	0.948590i	$-0.602510\pi$
$997$	−3.67266	+	0.984086i	−0.116314	+	0.0311663i	0.200192	+	0.979757i	$0.435843\pi$
$998$	−6.72376	+	2.80139i	−0.212837	+	0.0886764i
$999$	−4.17914	+	4.85438i	−0.132222	+	0.153586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bu.a.11.18	✓	240
3.2	odd	2	inner	336.2.bu.a.11.43	yes	240
7.2	even	3	inner	336.2.bu.a.107.23	yes	240
16.3	odd	4	inner	336.2.bu.a.179.38	yes	240
21.2	odd	6	inner	336.2.bu.a.107.38	yes	240
48.35	even	4	inner	336.2.bu.a.179.23	yes	240
112.51	odd	12	inner	336.2.bu.a.275.43	yes	240
336.275	even	12	inner	336.2.bu.a.275.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bu.a.11.18	✓	240	1.1	even	1	trivial
336.2.bu.a.11.43	yes	240	3.2	odd	2	inner
336.2.bu.a.107.23	yes	240	7.2	even	3	inner
336.2.bu.a.107.38	yes	240	21.2	odd	6	inner
336.2.bu.a.179.23	yes	240	48.35	even	4	inner
336.2.bu.a.179.38	yes	240	16.3	odd	4	inner
336.2.bu.a.275.18	yes	240	336.275	even	12	inner
336.2.bu.a.275.43	yes	240	112.51	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.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.863239 - 1.12019i) q^{2} +(1.08000 - 1.35410i) q^{3} +(-0.509638 + 1.93398i) q^{4} +(-1.29824 - 0.347862i) q^{5} +(-2.44915 - 0.0408893i) q^{6} +(-2.01473 - 1.71490i) q^{7} +(2.60636 - 1.09860i) q^{8} +(-0.667192 - 2.92487i) q^{9} +O(q^{10})\)	\(q+(-0.863239 - 1.12019i) q^{2} +(1.08000 - 1.35410i) q^{3} +(-0.509638 + 1.93398i) q^{4} +(-1.29824 - 0.347862i) q^{5} +(-2.44915 - 0.0408893i) q^{6} +(-2.01473 - 1.71490i) q^{7} +(2.60636 - 1.09860i) q^{8} +(-0.667192 - 2.92487i) q^{9} +(0.731019 + 1.75456i) q^{10} +(-1.69548 + 0.454301i) q^{11} +(2.06840 + 2.77880i) q^{12} +(-2.23759 + 2.23759i) q^{13} +(-0.181819 + 3.73724i) q^{14} +(-1.87314 + 1.38226i) q^{15} +(-3.48054 - 1.97126i) q^{16} +(-2.32989 - 1.34516i) q^{17} +(-2.70045 + 3.27224i) q^{18} +(1.65097 - 6.16150i) q^{19} +(1.33439 - 2.33348i) q^{20} +(-4.49806 + 0.876052i) q^{21} +(1.97250 + 1.50708i) q^{22} +(-1.09281 + 0.630932i) q^{23} +(1.32726 - 4.71576i) q^{24} +(-2.76571 - 1.59679i) q^{25} +(4.43808 + 0.574943i) q^{26} +(-4.68114 - 2.25542i) q^{27} +(4.34336 - 3.02246i) q^{28} +(4.88450 + 4.88450i) q^{29} +(3.16535 + 0.905049i) q^{30} +(1.30133 + 0.751321i) q^{31} +(0.796362 + 5.60052i) q^{32} +(-1.21595 + 2.78650i) q^{33} +(0.504417 + 3.77110i) q^{34} +(2.01904 + 2.92719i) q^{35} +(5.99666 + 0.200288i) q^{36} +(0.319055 - 1.19073i) q^{37} +(-8.32722 + 3.46945i) q^{38} +(0.613326 + 5.44652i) q^{39} +(-3.76583 + 0.519586i) q^{40} -0.647051 q^{41} +(4.86424 + 4.28242i) q^{42} +(5.04389 - 5.04389i) q^{43} +(-0.0145305 - 3.51054i) q^{44} +(-0.151276 + 4.02927i) q^{45} +(1.65012 + 0.679503i) q^{46} +(-0.880271 - 1.52467i) q^{47} +(-6.42827 + 2.58405i) q^{48} +(1.11824 + 6.91010i) q^{49} +(0.598773 + 4.47652i) q^{50} +(-4.33777 + 1.70213i) q^{51} +(-3.18708 - 5.46780i) q^{52} +(-2.42297 - 9.04263i) q^{53} +(1.51446 + 7.19072i) q^{54} +2.35916 q^{55} +(-7.13507 - 2.25627i) q^{56} +(-6.56026 - 8.89002i) q^{57} +(1.25506 - 9.68804i) q^{58} +(10.7675 - 2.88515i) q^{59} +(-1.71863 - 4.32706i) q^{60} +(-9.85115 - 2.63961i) q^{61} +(-0.281735 - 2.10630i) q^{62} +(-3.67165 + 7.03697i) q^{63} +(5.58618 - 5.72666i) q^{64} +(3.68329 - 2.12655i) q^{65} +(4.17105 - 1.04332i) q^{66} +(13.5990 - 3.64383i) q^{67} +(3.78891 - 3.82040i) q^{68} +(-0.325886 + 2.16118i) q^{69} +(1.53609 - 4.78857i) q^{70} +10.3613i q^{71} +(-4.95219 - 6.89027i) q^{72} +(-4.47539 - 2.58387i) q^{73} +(-1.60926 + 0.670484i) q^{74} +(-5.14919 + 2.02053i) q^{75} +(11.0748 + 6.33307i) q^{76} +(4.19500 + 1.99228i) q^{77} +(5.57167 - 5.38869i) q^{78} +(2.76636 - 1.59716i) q^{79} +(3.83284 + 3.76990i) q^{80} +(-8.10971 + 3.90290i) q^{81} +(0.558559 + 0.724818i) q^{82} +(10.5779 - 10.5779i) q^{83} +(0.598114 - 9.14561i) q^{84} +(2.55682 + 2.55682i) q^{85} +(-10.0042 - 1.29602i) q^{86} +(11.8894 - 1.33885i) q^{87} +(-3.91992 + 3.04671i) q^{88} +(-2.65355 - 4.59608i) q^{89} +(4.64412 - 3.30876i) q^{90} +(8.34536 - 0.670886i) q^{91} +(-0.663274 - 2.43501i) q^{92} +(2.42280 - 0.950703i) q^{93} +(-0.948036 + 2.30223i) q^{94} +(-4.28670 + 7.42479i) q^{95} +(8.44375 + 4.97021i) q^{96} +9.13706 q^{97} +(6.77530 - 7.21771i) q^{98} +(2.45998 + 4.65594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7}+O(q^{10}) \) 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7	\( 240 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 16 q^{7} - 4 q^{10} - 2 q^{12} - 16 q^{13} - 20 q^{16} + 16 q^{18} - 4 q^{19} + 2 q^{21} - 40 q^{22} - 22 q^{24} - 8 q^{27} - 4 q^{28} - 26 q^{30} - 4 q^{33} + 16 q^{36} - 4 q^{37} - 4 q^{39} + 8 q^{40} - 18 q^{42} - 16 q^{43} + 18 q^{45} - 20 q^{46} - 88 q^{48} - 16 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{54} - 32 q^{55} - 36 q^{58} - 42 q^{60} - 4 q^{61} - 64 q^{64} - 30 q^{66} - 36 q^{67} - 20 q^{69} + 116 q^{70} - 46 q^{72} - 24 q^{75} - 112 q^{76} - 92 q^{78} - 4 q^{81} - 32 q^{82} + 44 q^{84} - 56 q^{85} - 4 q^{87} - 20 q^{88} + 28 q^{90} - 40 q^{91} - 14 q^{93} + 72 q^{94} + 36 q^{96} - 32 q^{97} + 28 q^{99}+O(q^{100}) \) 240 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 16 * q^7 - 4 * q^10 - 2 * q^12 - 16 * q^13 - 20 * q^16 + 16 * q^18 - 4 * q^19 + 2 * q^21 - 40 * q^22 - 22 * q^24 - 8 * q^27 - 4 * q^28 - 26 * q^30 - 4 * q^33 + 16 * q^36 - 4 * q^37 - 4 * q^39 + 8 * q^40 - 18 * q^42 - 16 * q^43 + 18 * q^45 - 20 * q^46 - 88 * q^48 - 16 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^54 - 32 * q^55 - 36 * q^58 - 42 * q^60 - 4 * q^61 - 64 * q^64 - 30 * q^66 - 36 * q^67 - 20 * q^69 + 116 * q^70 - 46 * q^72 - 24 * q^75 - 112 * q^76 - 92 * q^78 - 4 * q^81 - 32 * q^82 + 44 * q^84 - 56 * q^85 - 4 * q^87 - 20 * q^88 + 28 * q^90 - 40 * q^91 - 14 * q^93 + 72 * q^94 + 36 * q^96 - 32 * q^97 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more