LMFDB - Embedded newform 380.2.bb.a.319.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			319.48
Character	$\chi$	$=$	380.319
Dual form			380.2.bb.a.299.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22813 - 0.701203i) q^{2} +(0.372293 - 0.0656453i) q^{3} +(1.01663 - 1.72234i) q^{4} +(-1.50958 - 1.64960i) q^{5} +(0.411195 - 0.341674i) q^{6} +(-0.391468 + 0.678043i) q^{7} +(0.0408455 - 2.82813i) q^{8} +(-2.68479 + 0.977182i) q^{9} +O(q^{10})$	\(q+(1.22813 - 0.701203i) q^{2} +(0.372293 - 0.0656453i) q^{3} +(1.01663 - 1.72234i) q^{4} +(-1.50958 - 1.64960i) q^{5} +(0.411195 - 0.341674i) q^{6} +(-0.391468 + 0.678043i) q^{7} +(0.0408455 - 2.82813i) q^{8} +(-2.68479 + 0.977182i) q^{9} +(-3.01067 - 0.967405i) q^{10} +(4.68866 - 2.70700i) q^{11} +(0.265420 - 0.707953i) q^{12} +(0.952816 - 5.40369i) q^{13} +(-0.00533007 + 1.10723i) q^{14} +(-0.670294 - 0.515036i) q^{15} +(-1.93293 - 3.50197i) q^{16} +(-0.973914 + 2.67581i) q^{17} +(-2.61207 + 3.08269i) q^{18} +(4.05553 + 1.59770i) q^{19} +(-4.37585 + 0.922986i) q^{20} +(-0.101230 + 0.278128i) q^{21} +(3.86015 - 6.61226i) q^{22} +(0.999845 + 0.838970i) q^{23} +(-0.170447 - 1.05557i) q^{24} +(-0.442338 + 4.98040i) q^{25} +(-2.61889 - 7.30457i) q^{26} +(-1.91755 + 1.10710i) q^{27} +(0.769844 + 1.36356i) q^{28} +(2.22363 + 6.10938i) q^{29} +(-1.18436 - 0.162522i) q^{30} +(-4.09542 + 7.09348i) q^{31} +(-4.82949 - 2.94551i) q^{32} +(1.56785 - 1.31559i) q^{33} +(0.680186 + 3.96916i) q^{34} +(1.70945 - 0.377795i) q^{35} +(-1.04639 + 5.61755i) q^{36} -6.57613 q^{37} +(6.10105 - 0.881558i) q^{38} -2.07430i q^{39} +(-4.72694 + 4.20191i) q^{40} +(5.74859 - 1.01363i) q^{41} +(0.0706998 + 0.412562i) q^{42} +(6.47766 - 5.43540i) q^{43} +(0.104247 - 10.8275i) q^{44} +(5.66485 + 2.95368i) q^{45} +(1.81623 + 0.329273i) q^{46} +(4.66931 - 1.69949i) q^{47} +(-0.949504 - 1.17687i) q^{48} +(3.19351 + 5.53131i) q^{49} +(2.94902 + 6.42676i) q^{50} +(-0.186927 + 1.06012i) q^{51} +(-8.33834 - 7.13462i) q^{52} +(3.38541 + 2.84069i) q^{53} +(-1.57871 + 2.70425i) q^{54} +(-11.5434 - 3.64797i) q^{55} +(1.90160 + 1.13482i) q^{56} +(1.61473 + 0.328587i) q^{57} +(7.01484 + 5.94393i) q^{58} +(2.21110 + 0.804774i) q^{59} +(-1.56851 + 0.630875i) q^{60} +(-6.61169 - 5.54787i) q^{61} +(-0.0557615 + 11.5835i) q^{62} +(0.388437 - 2.20293i) q^{63} +(-7.99666 - 0.231033i) q^{64} +(-10.3523 + 6.58553i) q^{65} +(1.00304 - 2.71510i) q^{66} +(2.60934 + 7.16910i) q^{67} +(3.61855 + 4.39772i) q^{68} +(0.427310 + 0.246707i) q^{69} +(1.83452 - 1.66265i) q^{70} +(8.81899 - 7.40001i) q^{71} +(2.65394 + 7.63284i) q^{72} +(-8.11016 + 1.43004i) q^{73} +(-8.07637 + 4.61120i) q^{74} +(0.162260 + 1.88320i) q^{75} +(6.87476 - 5.36075i) q^{76} +4.23882i q^{77} +(-1.45451 - 2.54752i) q^{78} +(-1.40179 - 7.94996i) q^{79} +(-2.85892 + 8.47506i) q^{80} +(5.92476 - 4.97146i) q^{81} +(6.34928 - 5.27580i) q^{82} +(-8.17090 + 14.1524i) q^{83} +(0.376119 + 0.457107i) q^{84} +(5.88420 - 2.43278i) q^{85} +(4.14412 - 11.2176i) q^{86} +(1.22890 + 2.12851i) q^{87} +(-7.46424 - 13.3707i) q^{88} +(-6.44549 - 1.13651i) q^{89} +(9.02833 - 0.344697i) q^{90} +(3.29093 + 2.76142i) q^{91} +(2.46146 - 0.869155i) q^{92} +(-1.05904 + 2.90970i) q^{93} +(4.54286 - 5.36134i) q^{94} +(-3.48659 - 9.10185i) q^{95} +(-1.99134 - 0.779560i) q^{96} +(-6.86096 - 2.49719i) q^{97} +(7.80063 + 4.55390i) q^{98} +(-9.94282 + 11.8494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$	$-1$

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 $

$2$	1.22813	−	0.701203i	0.868422	−	0.495825i
$2$	1.22813	−	0.701203i	0.868422	−	0.495825i
$3$	0.372293	−	0.0656453i	0.214943	−	0.0379003i	−0.0651394	−	0.997876i	$-0.520749\pi$
$3$	0.372293	−	0.0656453i	0.214943	−	0.0379003i	0.280083	+	0.959976i	$0.409638\pi$
$4$	1.01663	−	1.72234i	0.508315	−	0.861171i
$5$	−1.50958	−	1.64960i	−0.675105	−	0.737722i
$5$	−1.50958	−	1.64960i	−0.675105	−	0.737722i
$6$	0.411195	−	0.341674i	0.167870	−	0.139488i
$7$	−0.391468	+	0.678043i	−0.147961	+	0.256276i	−0.930474	−	0.366359i	$-0.880604\pi$
$7$	−0.391468	+	0.678043i	−0.147961	+	0.256276i	0.782513	+	0.622635i	$0.213938\pi$
$8$	0.0408455	−	2.82813i	0.0144411	−	0.999896i
$9$	−2.68479	+	0.977182i	−0.894928	+	0.325727i
$10$	−3.01067	−	0.967405i	−0.952057	−	0.305920i
$11$	4.68866	−	2.70700i	1.41368	−	0.816191i	0.417952	−	0.908469i	$-0.362748\pi$
$11$	4.68866	−	2.70700i	1.41368	−	0.816191i	0.995733	+	0.0922780i	$0.0294149\pi$
$12$	0.265420	−	0.707953i	0.0766202	−	0.204368i
$13$	0.952816	−	5.40369i	0.264263	−	1.49871i	−0.506861	−	0.862028i	$-0.669194\pi$
$13$	0.952816	−	5.40369i	0.264263	−	1.49871i	0.771124	−	0.636685i	$-0.219695\pi$
$14$	−0.00533007	+	1.10723i	−0.00142452	+	0.295919i
$15$	−0.670294	−	0.515036i	−0.173069	−	0.132982i
$16$	−1.93293	−	3.50197i	−0.483233	−	0.875492i
$17$	−0.973914	+	2.67581i	−0.236209	+	0.648978i	0.763785	+	0.645471i	$0.223339\pi$
$17$	−0.973914	+	2.67581i	−0.236209	+	0.648978i	−0.999994	+	0.00350771i	$0.998883\pi$
$18$	−2.61207	+	3.08269i	−0.615672	+	0.726597i
$19$	4.05553	+	1.59770i	0.930403	+	0.366538i
$19$	4.05553	+	1.59770i	0.930403	+	0.366538i
$20$	−4.37585	+	0.922986i	−0.978471	+	0.206386i
$21$	−0.101230	+	0.278128i	−0.0220903	+	0.0606926i
$22$	3.86015	−	6.61226i	0.822987	−	1.40974i
$23$	0.999845	+	0.838970i	0.208482	+	0.174937i	0.741050	−	0.671450i	$-0.234328\pi$
$23$	0.999845	+	0.838970i	0.208482	+	0.174937i	−0.532568	+	0.846388i	$0.678773\pi$
$24$	−0.170447	−	1.05557i	−0.0347924	−	0.215468i
$25$	−0.442338	+	4.98040i	−0.0884676	+	0.996079i
$26$	−2.61889	−	7.30457i	−0.513607	−	1.43254i
$27$	−1.91755	+	1.10710i	−0.369032	+	0.213061i
$28$	0.769844	+	1.36356i	0.145487	+	0.257689i
$29$	2.22363	+	6.10938i	0.412918	+	1.13448i	0.955631	+	0.294566i	$0.0951750\pi$
$29$	2.22363	+	6.10938i	0.412918	+	1.13448i	−0.542713	+	0.839918i	$0.682603\pi$
$30$	−1.18436	−	0.162522i	−0.216233	−	0.0296723i
$31$	−4.09542	+	7.09348i	−0.735559	+	1.27403i	0.218918	+	0.975743i	$0.429747\pi$
$31$	−4.09542	+	7.09348i	−0.735559	+	1.27403i	−0.954478	+	0.298283i	$0.903586\pi$
$32$	−4.82949	−	2.94551i	−0.853741	−	0.520698i
$33$	1.56785	−	1.31559i	0.272928	−	0.229014i
$34$	0.680186	+	3.96916i	0.116651	+	0.680706i
$35$	1.70945	−	0.377795i	0.288950	−	0.0638590i
$36$	−1.04639	+	5.61755i	−0.174398	+	0.936259i
$37$	−6.57613			−1.08111			−0.540555	−	0.841309i	$-0.681786\pi$
$37$	−6.57613			−1.08111			−0.540555	+	0.841309i	$0.681786\pi$
$38$	6.10105	−	0.881558i	0.989722	−	0.143008i
$39$		−	2.07430i		−	0.332154i
$40$	−4.72694	+	4.20191i	−0.747394	+	0.664381i
$41$	5.74859	−	1.01363i	0.897779	−	0.158303i	0.294330	−	0.955704i	$-0.404904\pi$
$41$	5.74859	−	1.01363i	0.897779	−	0.158303i	0.603449	+	0.797401i	$0.293793\pi$
$42$	0.0706998	+	0.412562i	0.0109092	+	0.0636597i
$43$	6.47766	−	5.43540i	0.987834	−	0.828891i	0.00258100	−	0.999997i	$-0.499178\pi$
$43$	6.47766	−	5.43540i	0.987834	−	0.828891i	0.985253	+	0.171106i	$0.0547340\pi$
$44$	0.104247	−	10.8275i	0.0157159	−	1.63231i
$45$	5.66485	+	2.95368i	0.844466	+	0.440308i
$46$	1.81623	+	0.329273i	0.267789	+	0.0485487i
$47$	4.66931	−	1.69949i	0.681089	−	0.247896i	0.0217742	−	0.999763i	$-0.493069\pi$
$47$	4.66931	−	1.69949i	0.681089	−	0.247896i	0.659315	+	0.751867i	$0.270846\pi$
$48$	−0.949504	−	1.17687i	−0.137049	−	0.169867i
$49$	3.19351	+	5.53131i	0.456215	+	0.790188i
$50$	2.94902	+	6.42676i	0.417054	+	0.908882i
$51$	−0.186927	+	1.06012i	−0.0261750	+	0.148446i
$52$	−8.33834	−	7.13462i	−1.15632	−	0.989394i
$53$	3.38541	+	2.84069i	0.465021	+	0.390199i	0.844975	−	0.534807i	$-0.179616\pi$
$53$	3.38541	+	2.84069i	0.465021	+	0.390199i	−0.379953	+	0.925006i	$0.624060\pi$
$54$	−1.57871	+	2.70425i	−0.214835	+	0.368002i
$55$	−11.5434	−	3.64797i	−1.55651	−	0.491892i
$56$	1.90160	+	1.13482i	0.254113	+	0.151646i
$57$	1.61473	+	0.328587i	0.213876	+	0.0435224i
$58$	7.01484	+	5.94393i	0.921094	+	0.780476i
$59$	2.21110	+	0.804774i	0.287860	+	0.104773i	0.481915	−	0.876218i	$-0.339942\pi$
$59$	2.21110	+	0.804774i	0.287860	+	0.104773i	−0.194054	+	0.980991i	$0.562164\pi$
$60$	−1.56851	+	0.630875i	−0.202494	+	0.0814456i
$61$	−6.61169	−	5.54787i	−0.846540	−	0.710332i	0.112485	−	0.993653i	$-0.464119\pi$
$61$	−6.61169	−	5.54787i	−0.846540	−	0.710332i	−0.959025	+	0.283322i	$0.908564\pi$
$62$	−0.0557615	+	11.5835i	−0.00708172	+	1.47110i
$63$	0.388437	−	2.20293i	0.0489384	−	0.277544i
$64$	−7.99666	−	0.231033i	−0.999583	−	0.0288791i
$65$	−10.3523	+	6.58553i	−1.28404	+	0.816835i
$66$	1.00304	−	2.71510i	0.123466	−	0.334206i
$67$	2.60934	+	7.16910i	0.318781	+	0.875845i	0.990803	+	0.135313i	$0.0432040\pi$
$67$	2.60934	+	7.16910i	0.318781	+	0.875845i	−0.672021	+	0.740532i	$0.734574\pi$
$68$	3.61855	+	4.39772i	0.438813	+	0.533301i
$69$	0.427310	+	0.246707i	0.0514420	+	0.0297001i
$70$	1.83452	−	1.66265i	0.219267	−	0.198725i
$71$	8.81899	−	7.40001i	1.04662	−	0.878220i	0.0538870	−	0.998547i	$-0.482839\pi$
$71$	8.81899	−	7.40001i	1.04662	−	0.878220i	0.992734	+	0.120328i	$0.0383945\pi$
$72$	2.65394	+	7.63284i	0.312770	+	0.899539i
$73$	−8.11016	+	1.43004i	−0.949223	+	0.167374i	−0.626763	−	0.779210i	$-0.715621\pi$
$73$	−8.11016	+	1.43004i	−0.949223	+	0.167374i	−0.322459	+	0.946583i	$0.604510\pi$
$74$	−8.07637	+	4.61120i	−0.938859	+	0.536041i
$75$	0.162260	+	1.88320i	0.0187362	+	0.217454i
$76$	6.87476	−	5.36075i	0.788590	−	0.614920i
$77$			4.23882i			0.483058i
$78$	−1.45451	−	2.54752i	−0.164690	−	0.288450i
$79$	−1.40179	−	7.94996i	−0.157714	−	0.894441i	−0.956262	−	0.292510i	$-0.905509\pi$
$79$	−1.40179	−	7.94996i	−0.157714	−	0.894441i	0.798548	−	0.601931i	$-0.205602\pi$
$80$	−2.85892	+	8.47506i	−0.319637	+	0.947540i
$81$	5.92476	−	4.97146i	0.658306	−	0.552385i
$82$	6.34928	−	5.27580i	0.701161	−	0.582615i
$83$	−8.17090	+	14.1524i	−0.896873	+	1.55343i	−0.0654039	+	0.997859i	$0.520834\pi$
$83$	−8.17090	+	14.1524i	−0.896873	+	1.55343i	−0.831469	+	0.555571i	$0.812500\pi$
$84$	0.376119	+	0.457107i	0.0410379	+	0.0498745i
$85$	5.88420	−	2.43278i	0.638231	−	0.263872i
$86$	4.14412	−	11.2176i	0.446872	−	1.20962i
$87$	1.22890	+	2.12851i	0.131751	+	0.228200i
$88$	−7.46424	−	13.3707i	−0.795691	−	1.42532i
$89$	−6.44549	−	1.13651i	−0.683220	−	0.120470i	−0.178744	−	0.983896i	$-0.557203\pi$
$89$	−6.44549	−	1.13651i	−0.683220	−	0.120470i	−0.504476	+	0.863425i	$0.668314\pi$
$90$	9.02833	−	0.344697i	0.951670	−	0.0363342i
$91$	3.29093	+	2.76142i	0.344983	+	0.289475i
$92$	2.46146	−	0.869155i	0.256625	−	0.0906157i
$93$	−1.05904	+	2.90970i	−0.109818	+	0.301721i
$94$	4.54286	−	5.36134i	0.468560	−	0.552980i
$95$	−3.48659	−	9.10185i	−0.357716	−	0.933830i
$96$	−1.99134	−	0.779560i	−0.203241	−	0.0795635i
$97$	−6.86096	−	2.49719i	−0.696625	−	0.253551i	−0.0306559	−	0.999530i	$-0.509760\pi$
$97$	−6.86096	−	2.49719i	−0.696625	−	0.253551i	−0.665969	+	0.745979i	$0.731982\pi$
$98$	7.80063	+	4.55390i	0.787982	+	0.460014i
$99$	−9.94282	+	11.8494i	−0.999291	+	1.19091i
$100$	8.12826	+	5.82507i	0.812826	+	0.582507i
$101$	−0.528541	+	2.99750i	−0.0525918	+	0.298263i	−0.999747	−	0.0225143i	$-0.992833\pi$
$101$	−0.528541	+	2.99750i	−0.0525918	+	0.298263i	0.947155	+	0.320777i	$0.103944\pi$
$102$	0.513785	+	1.43304i	0.0508723	+	0.141892i
$103$	−2.29198	+	1.32328i	−0.225836	+	0.130386i	−0.608649	−	0.793439i	$-0.708288\pi$
$103$	−2.29198	+	1.32328i	−0.225836	+	0.130386i	0.382814	+	0.923825i	$0.374955\pi$
$104$	−15.2434	−	2.91540i	−1.49474	−	0.285879i
$105$	0.611615	−	0.252868i	0.0596875	−	0.0246774i
$106$	6.14963	+	1.11490i	0.597305	+	0.108288i
$107$	1.93032	+	1.11447i	0.186611	+	0.107740i	0.590395	−	0.807114i	$-0.298972\pi$
$107$	1.93032	+	1.11447i	0.186611	+	0.107740i	−0.403784	+	0.914854i	$0.632305\pi$
$108$	−0.0426345	+	4.42818i	−0.00410251	+	0.426101i
$109$	−2.25510	−	2.68752i	−0.215999	−	0.257418i	0.647155	−	0.762359i	$-0.275959\pi$
$109$	−2.25510	−	2.68752i	−0.215999	−	0.257418i	−0.863154	+	0.504941i	$0.831514\pi$
$110$	−16.7348	+	3.61405i	−1.59560	+	0.344586i
$111$	−2.44825	+	0.431692i	−0.232377	+	0.0409744i
$112$	3.13116	+	0.0602993i	0.295867	+	0.00569775i
$113$	17.6333			1.65880			0.829401	−	0.558654i	$-0.188682\pi$
$113$	17.6333			1.65880			0.829401	+	0.558654i	$0.188682\pi$
$114$	2.21351	−	0.728703i	0.207314	−	0.0682493i
$115$	−0.125384	−	2.91583i	−0.0116922	−	0.271903i
$116$	12.7831	+	2.38112i	1.18688	+	0.221081i
$117$	2.72228	+	15.4388i	0.251675	+	1.42732i
$118$	3.27984	−	0.562058i	0.301933	−	0.0517416i
$119$	−1.43305	−	1.70785i	−0.131368	−	0.156558i
$120$	−1.48397	+	1.87464i	−0.135467	+	0.171131i
$121$	9.15570	−	15.8581i	0.832336	−	1.44165i
$122$	−12.0102	−	2.17739i	−1.08735	−	0.197132i
$123$	2.07362	−	0.754736i	0.186972	−	0.0680522i
$124$	8.05388	+	14.2652i	0.723259	+	1.28105i
$125$	8.88339	−	6.78862i	0.794554	−	0.607193i
$126$	−1.06765	−	2.97787i	−0.0951139	−	0.265290i
$127$	7.62797	+	1.34502i	0.676873	+	0.119351i	0.501508	−	0.865153i	$-0.332779\pi$
$127$	7.62797	+	1.34502i	0.676873	+	0.119351i	0.175364	+	0.984504i	$0.443890\pi$
$128$	−9.98298	+	5.32354i	−0.882379	+	0.470539i
$129$	2.05478	−	2.44879i	0.180913	−	0.215604i
$130$	−8.09616	+	15.3469i	−0.710081	+	1.34602i
$131$	2.19367	−	6.02705i	0.191662	−	0.526586i	−0.806222	−	0.591613i	$-0.798491\pi$
$131$	2.19367	−	6.02705i	0.191662	−	0.526586i	0.997883	+	0.0650274i	$0.0207135\pi$
$132$	−0.671964	−	4.03784i	−0.0584869	−	0.351449i
$133$	−2.67092	+	2.12437i	−0.231598	+	0.184207i
$134$	8.23161	+	6.97494i	0.711103	+	0.602543i
$135$	4.72095	+	1.49193i	0.406315	+	0.128405i
$136$	7.52775	+	2.86365i	0.645500	+	0.245556i
$137$	−8.61310	+	10.2647i	−0.735867	+	0.876972i	−0.996069	−	0.0885819i	$-0.971767\pi$
$137$	−8.61310	+	10.2647i	−0.735867	+	0.876972i	0.260202	+	0.965554i	$0.416211\pi$
$138$	0.697785	+	0.00335906i	0.0593994	+	0.000285943i
$139$	−12.4906	−	2.20243i	−1.05944	−	0.186808i	−0.383332	−	0.923611i	$-0.625224\pi$
$139$	−12.4906	−	2.20243i	−1.05944	−	0.186808i	−0.676108	+	0.736803i	$0.736335\pi$
$140$	1.08718	−	3.32833i	0.0918837	−	0.281296i
$141$	1.62679	−	0.939227i	0.137000	−	0.0790972i
$142$	5.64200	−	15.2721i	0.473466	−	1.28161i
$143$	−10.1603	−	27.9153i	−0.849651	−	2.33440i
$144$	8.61156	+	7.51321i	0.717630	+	0.626101i
$145$	6.72127	−	12.8907i	0.558171	−	1.07051i
$146$	−8.95762	+	7.44315i	−0.741338	+	0.616000i
$147$	1.55202	+	1.84963i	0.128009	+	0.152555i
$148$	−6.68549	+	11.3264i	−0.549544	+	0.931021i
$149$	−1.59318	−	9.03536i	−0.130518	−	0.740205i	−0.977876	−	0.209184i	$-0.932919\pi$
$149$	−1.59318	−	9.03536i	−0.130518	−	0.740205i	0.847358	−	0.531022i	$-0.178192\pi$
$150$	1.51978	+	2.19905i	0.124090	+	0.179552i
$151$	−14.7358			−1.19918			−0.599592	−	0.800306i	$-0.704671\pi$
$151$	−14.7358			−1.19918			−0.599592	+	0.800306i	$0.704671\pi$
$152$	4.68416	−	11.4043i	0.379936	−	0.925013i
$153$		−	8.13566i		−	0.657729i
$154$	2.97227	+	5.20584i	0.239512	+	0.419498i
$155$	17.8837	−	3.95238i	1.43646	−	0.317463i
$156$	−3.57266	−	2.10879i	−0.286042	−	0.168839i
$157$	−5.04556	−	6.01306i	−0.402679	−	0.479895i	0.526156	−	0.850388i	$-0.323633\pi$
$157$	−5.04556	−	6.01306i	−0.402679	−	0.479895i	−0.928835	+	0.370494i	$0.879189\pi$
$158$	−7.29613	−	8.78068i	−0.580449	−	0.698554i
$159$	1.44684	+	0.835334i	0.114742	+	0.0662463i
$160$	2.43159	+	12.4132i	0.192234	+	0.981349i
$161$	−0.960264	+	0.349508i	−0.0756794	+	0.0275451i
$162$	3.79040	−	10.2601i	0.297802	−	0.806108i
$163$	7.09640	+	12.2913i	0.555833	+	0.962730i	0.997838	+	0.0657180i	$0.0209338\pi$
$163$	7.09640	+	12.2913i	0.555833	+	0.962730i	−0.442006	+	0.897012i	$0.645733\pi$
$164$	4.09836	−	10.9315i	0.320028	−	0.853609i
$165$	−4.53699	−	0.600345i	−0.353204	−	0.0467368i
$166$	−0.111252	+	23.1105i	−0.00863480	+	1.79373i
$167$	−2.94658	+	3.51160i	−0.228013	+	0.271735i	−0.867906	−	0.496729i	$-0.834534\pi$
$167$	−2.94658	+	3.51160i	−0.228013	+	0.271735i	0.639893	+	0.768464i	$0.278979\pi$
$168$	0.782449	+	0.297653i	0.0603673	+	0.0229645i
$169$	−16.0760	−	5.85117i	−1.23661	−	0.450090i
$170$	5.52072	−	7.11380i	0.423420	−	0.545603i
$171$	−12.4495	−	0.326495i	−0.952036	−	0.0249677i
$172$	−2.77625	−	16.6825i	−0.211687	−	1.27203i
$173$	−7.42248	−	2.70156i	−0.564321	−	0.205396i	0.0440771	−	0.999028i	$-0.485965\pi$
$173$	−7.42248	−	2.70156i	−0.564321	−	0.205396i	−0.608398	+	0.793632i	$0.708187\pi$
$174$	3.00177	+	1.75239i	0.227563	+	0.132848i
$175$	−3.20376	−	2.24959i	−0.242181	−	0.170053i
$176$	−18.5427	−	11.1871i	−1.39771	−	0.843259i
$177$	0.876006	+	0.154463i	0.0658446	+	0.0116102i
$178$	−8.71285	+	3.12380i	−0.653056	+	0.234139i
$179$	−0.556613	−	0.964081i	−0.0416032	−	0.0720588i	0.844474	−	0.535597i	$-0.179913\pi$
$179$	−0.556613	−	0.964081i	−0.0416032	−	0.0720588i	−0.886077	+	0.463538i	$0.846580\pi$
$180$	10.8463	−	6.75402i	0.808436	−	0.503415i
$181$	−2.04457	−	5.61742i	−0.151972	−	0.417540i	0.840222	−	0.542242i	$-0.182425\pi$
$181$	−2.04457	−	5.61742i	−0.151972	−	0.417540i	−0.992194	+	0.124703i	$0.960202\pi$
$182$	5.97802	+	1.08378i	0.443121	+	0.0803354i
$183$	−2.82568	−	1.63141i	−0.208880	−	0.120597i
$184$	2.41356	−	2.79343i	0.177930	−	0.205934i
$185$	9.92719	+	10.8480i	0.729862	+	0.797558i
$186$	0.739640	+	4.31610i	0.0542330	+	0.316472i
$187$	2.67706	+	15.1823i	0.195766	+	1.11024i
$188$	1.81985	−	9.76991i	0.132726	−	0.712544i
$189$		−	1.73357i		−	0.126099i
$190$	−10.6642	−	8.73350i	−0.773665	−	0.633594i
$191$			17.9351i			1.29774i	0.760901	+	0.648868i	$0.224757\pi$
$191$			17.9351i			1.29774i	−0.760901	+	0.648868i	$0.775243\pi$
$192$	−2.99227	+	0.438931i	−0.215948	+	0.0316771i
$193$	−1.67511	−	9.50001i	−0.120577	−	0.683826i	−0.983837	−	0.179066i	$-0.942692\pi$
$193$	−1.67511	−	9.50001i	−0.120577	−	0.683826i	0.863260	−	0.504759i	$-0.168419\pi$
$194$	−10.1772	+	1.74405i	−0.730682	+	0.125215i
$195$	−3.42176	+	3.13132i	−0.245037	+	0.224239i
$196$	12.7734	+	0.122983i	0.912388	+	0.00878448i
$197$	−7.45576	−	4.30458i	−0.531201	−	0.306689i	0.210305	−	0.977636i	$-0.432554\pi$
$197$	−7.45576	−	4.30458i	−0.531201	−	0.306689i	−0.741505	+	0.670947i	$0.765888\pi$
$198$	−3.90229	+	21.5246i	−0.277324	+	1.52969i
$199$	3.48466	+	9.57402i	0.247021	+	0.678684i	0.999792	+	0.0204017i	$0.00649452\pi$
$199$	3.48466	+	9.57402i	0.247021	+	0.678684i	−0.752771	+	0.658282i	$0.771283\pi$
$200$	14.0671	+	1.45442i	0.994698	+	0.102843i
$201$	1.44206	+	2.49771i	0.101715	+	0.176175i
$202$	1.45274	+	4.05195i	0.102214	+	0.285094i
$203$	−5.01290	−	0.883910i	−0.351837	−	0.0620383i
$204$	1.63585	+	1.39970i	0.114532	+	0.0979985i
$205$	−10.3500	−	7.95270i	−0.722878	−	0.555441i
$206$	−1.88698	+	3.23230i	−0.131472	+	0.225205i
$207$	−3.50419	−	1.27542i	−0.243558	−	0.0886480i
$208$	−20.7653	+	7.10822i	−1.43981	+	0.492866i
$209$	23.3400	−	3.48724i	1.61446	−	0.241218i
$210$	0.573834	−	0.739422i	0.0395983	−	0.0510249i
$211$	−5.41102	−	1.96945i	−0.372510	−	0.135583i	0.148979	−	0.988840i	$-0.452401\pi$
$211$	−5.41102	−	1.96945i	−0.372510	−	0.135583i	−0.521489	+	0.853258i	$0.674623\pi$
$212$	8.33435	−	2.94290i	0.572405	−	0.202119i
$213$	2.79747	−	3.33390i	0.191680	−	0.228435i
$214$	3.15216	+	0.0151741i	0.215477	+	0.00103728i
$215$	−18.7448	−	2.48035i	−1.27838	−	0.169159i
$216$	3.05269	+	5.46829i	0.207709	+	0.372070i
$217$	−3.20645	−	5.55374i	−0.217668	−	0.377012i
$218$	−4.65406	−	1.71936i	−0.315213	−	0.116449i
$219$	−2.92548	+	1.06479i	−0.197686	+	0.0719517i
$220$	−18.0184	+	16.1730i	−1.21480	+	1.09038i
$221$	13.5313	+	7.81227i	0.910211	+	0.525510i
$222$	−2.70407	+	2.24689i	−0.181485	+	0.150802i
$223$	−16.5421	−	19.7141i	−1.10774	−	1.32015i	−0.942616	−	0.333880i	$-0.891642\pi$
$223$	−16.5421	−	19.7141i	−1.10774	−	1.32015i	−0.165124	−	0.986273i	$-0.552803\pi$
$224$	3.88777	−	2.12153i	0.259763	−	0.141750i
$225$	−3.67917	−	13.8035i	−0.245278	−	0.920236i
$226$	21.6561	−	12.3645i	1.44054	−	0.822476i
$227$			24.1263i			1.60132i	0.599121	+	0.800658i	$0.295517\pi$
$227$			24.1263i			1.60132i	−0.599121	+	0.800658i	$0.704483\pi$
$228$	2.20752	−	2.44706i	0.146196	−	0.162061i
$229$	14.1748			0.936697			0.468349	−	0.883544i	$-0.344849\pi$
$229$	14.1748			0.936697			0.468349	+	0.883544i	$0.344849\pi$
$230$	−2.19858	−	3.49311i	−0.144970	−	0.230329i
$231$	0.278258	+	1.57808i	0.0183080	+	0.103830i
$232$	17.3690	−	6.03919i	1.14033	−	0.396492i
$233$	6.46106	+	7.70000i	0.423278	+	0.504443i	0.934971	−	0.354725i	$-0.115426\pi$
$233$	6.46106	+	7.70000i	0.423278	+	0.504443i	−0.511692	+	0.859169i	$0.670981\pi$
$234$	14.1691	+	17.0521i	0.926261	+	1.11473i
$235$	−9.85218	−	5.13697i	−0.642685	−	0.335099i
$236$	3.63396	−	2.99011i	0.236551	−	0.194640i
$237$	−1.04375	−	2.86769i	−0.0677992	−	0.186277i
$238$	−2.95753	−	1.09261i	−0.191708	−	0.0708231i
$239$	12.2570	−	7.07658i	0.792839	−	0.457746i	−0.0481219	−	0.998841i	$-0.515324\pi$
$239$	12.2570	−	7.07658i	0.792839	−	0.457746i	0.840961	+	0.541096i	$0.181990\pi$
$240$	−0.508009	+	3.34288i	−0.0327918	+	0.215782i
$241$	−20.5308	−	3.62013i	−1.32250	−	0.233193i	−0.532570	−	0.846386i	$-0.678774\pi$
$241$	−20.5308	−	3.62013i	−1.32250	−	0.233193i	−0.789933	+	0.613193i	$0.789885\pi$
$242$	0.124660	−	25.8959i	0.00801346	−	1.66465i
$243$	6.14916	−	7.32828i	0.394468	−	0.470109i
$244$	−16.2770	+	5.74748i	−1.04203	+	0.367944i
$245$	4.30359	−	13.6180i	0.274946	−	0.870019i
$246$	2.01746	−	2.38094i	0.128629	−	0.151803i
$247$	12.4977	−	20.3925i	0.795207	−	1.29754i
$248$	19.8940	+	11.8721i	1.26327	+	0.753881i
$249$	−2.11293	+	5.80523i	−0.133901	+	0.367891i
$250$	6.14979	−	14.5664i	0.388947	−	0.921260i
$251$	16.9121	−	20.1551i	1.06748	−	1.27218i	0.106875	−	0.994272i	$-0.465916\pi$
$251$	16.9121	−	20.1551i	1.06748	−	1.27218i	0.960609	−	0.277905i	$-0.0896400\pi$
$252$	−3.39931	−	2.90859i	−0.214137	−	0.183224i
$253$	6.95903	+	1.22706i	0.437510	+	0.0771449i
$254$	10.3113	−	3.69689i	0.646988	−	0.231964i
$255$	2.03095	−	1.29198i	0.127183	−	0.0809067i
$256$	−8.52756	+	13.5381i	−0.532972	+	0.846133i
$257$	−15.4681	+	5.62993i	−0.964874	+	0.351185i	−0.775942	−	0.630805i	$-0.782725\pi$
$257$	−15.4681	+	5.62993i	−0.964874	+	0.351185i	−0.188932	+	0.981990i	$0.560503\pi$
$258$	0.806446	−	4.44826i	0.0502071	−	0.276936i
$259$	2.57435	−	4.45890i	0.159962	−	0.277062i
$260$	0.818145	+	24.5252i	0.0507392	+	1.52099i
$261$	−11.9400	−	14.2295i	−0.739065	−	0.880783i
$262$	−1.53207	−	8.94023i	−0.0946514	−	0.552329i
$263$	3.24686	+	18.4139i	0.200210	+	1.13545i	0.904801	+	0.425834i	$0.140019\pi$
$263$	3.24686	+	18.4139i	0.200210	+	1.13545i	−0.704591	+	0.709613i	$0.748870\pi$
$264$	−3.65661	−	4.48783i	−0.225049	−	0.276207i
$265$	−0.424543	−	9.87280i	−0.0260795	−	0.606482i
$266$	−1.79063	+	4.48188i	−0.109791	+	0.274801i
$267$	−2.47422			−0.151420
$268$	15.0004	+	2.79414i	0.916294	+	0.170679i
$269$	−19.6178	+	3.45915i	−1.19612	+	0.210908i	−0.736020	−	0.676960i	$-0.763297\pi$
$269$	−19.6178	+	3.45915i	−1.19612	+	0.210908i	−0.460098	+	0.887868i	$0.652186\pi$
$270$	6.84410	−	1.47805i	0.416519	−	0.0899515i
$271$	3.55791	+	4.24015i	0.216128	+	0.257571i	0.863205	−	0.504853i	$-0.168453\pi$
$271$	3.55791	+	4.24015i	0.216128	+	0.257571i	−0.647077	+	0.762424i	$0.724009\pi$
$272$	11.2531	−	1.76153i	0.682319	−	0.106809i
$273$	1.40646	+	0.812023i	0.0851231	+	0.0491458i
$274$	−3.38042	+	18.6460i	−0.204218	+	1.12644i
$275$	11.4080	+	24.5488i	0.687926	+	1.48035i
$276$	0.859330	−	0.485164i	0.0517256	−	0.0292034i
$277$	0.0967603	−	0.0558646i	0.00581376	−	0.00335658i	−0.497090	−	0.867699i	$-0.665598\pi$
$277$	0.0967603	−	0.0558646i	0.00581376	−	0.00335658i	0.502904	+	0.864342i	$0.332265\pi$
$278$	−16.8845	+	6.05357i	−1.01267	+	0.363069i
$279$	4.06371	−	23.0464i	0.243288	−	1.37975i
$280$	−0.998631	−	4.84998i	−0.0596796	−	0.289842i
$281$	−5.41648	+	6.45511i	−0.323120	+	0.385080i	−0.903013	−	0.429613i	$-0.858650\pi$
$281$	−5.41648	+	6.45511i	−0.323120	+	0.385080i	0.579893	+	0.814693i	$0.303094\pi$
$282$	1.33933	−	2.29421i	0.0797557	−	0.136618i
$283$	−8.29217	−	3.01810i	−0.492918	−	0.179408i	0.0835878	−	0.996500i	$-0.473362\pi$
$283$	−8.29217	−	3.01810i	−0.492918	−	0.179408i	−0.576506	+	0.817093i	$0.695584\pi$
$284$	−3.77971	−	22.7124i	−0.224285	−	1.34773i
$285$	−1.89552	−	3.15968i	−0.112281	−	0.187163i
$286$	−32.0526	−	27.1593i	−1.89531	−	1.60596i
$287$	−1.56310	+	4.29459i	−0.0922671	+	0.253502i
$288$	15.8444	+	3.18878i	0.933643	+	0.187900i
$289$	6.81132	+	5.71538i	0.400666	+	0.336199i
$290$	−0.784377	−	20.5445i	−0.0460602	−	1.20641i
$291$	−2.71822	−	0.479295i	−0.159345	−	0.0280968i
$292$	−5.78201	+	15.4223i	−0.338366	+	0.902522i
$293$	−3.71853	−	6.44069i	−0.217239	−	0.376269i	0.736724	−	0.676194i	$-0.236372\pi$
$293$	−3.71853	−	6.44069i	−0.217239	−	0.376269i	−0.953963	+	0.299925i	$0.903038\pi$
$294$	3.20306	+	1.18331i	0.186806	+	0.0690121i
$295$	−2.01028	−	4.86229i	−0.117043	−	0.283093i
$296$	−0.268605	+	18.5982i	−0.0156124	+	1.08100i
$297$	−5.99381	+	10.3816i	−0.347796	+	0.602401i
$298$	−8.29225	−	9.97949i	−0.480357	−	0.578097i
$299$	5.48620	−	4.60346i	0.317275	−	0.266225i
$300$	3.40848	+	1.63505i	0.196789	+	0.0943997i
$301$	1.14964	+	6.51991i	0.0662640	+	0.375802i
$302$	−18.0976	+	10.3328i	−1.04140	+	0.594586i
$303$			1.15064i			0.0661028i
$304$	−2.24396	−	17.2906i	−0.128700	−	0.991684i
$305$	0.829131	+	19.2816i	0.0474759	+	1.10406i
$306$	−5.70475	−	9.99168i	−0.326119	−	0.571186i
$307$	25.1762	−	4.43925i	1.43688	−	0.253361i	0.599674	−	0.800244i	$-0.295297\pi$
$307$	25.1762	−	4.43925i	1.43688	−	0.253361i	0.837209	+	0.546883i	$0.184186\pi$
$308$	7.30070	+	4.30930i	0.415996	+	0.245545i
$309$	−0.766421	+	0.643104i	−0.0436002	+	0.0365849i
$310$	19.1922	−	17.3942i	1.09004	−	0.987923i
$311$	2.88719	+	1.66692i	0.163718	+	0.0945224i	0.579620	−	0.814887i	$-0.303201\pi$
$311$	2.88719	+	1.66692i	0.163718	+	0.0945224i	−0.415903	+	0.909409i	$0.636534\pi$
$312$	−5.86640	−	0.0847259i	−0.332119	−	0.00479666i
$313$	7.11060	+	19.5362i	0.401915	+	1.10425i	0.961338	+	0.275370i	$0.0888002\pi$
$313$	7.11060	+	19.5362i	0.401915	+	1.10425i	−0.559424	+	0.828882i	$0.688978\pi$
$314$	−10.4130	−	3.84689i	−0.587640	−	0.217093i
$315$	−4.22033	+	2.68474i	−0.237789	+	0.151268i
$316$	−15.1177	−	5.66780i	−0.850435	−	0.318838i
$317$	−1.75352	+	9.94473i	−0.0984877	+	0.558552i	0.895135	+	0.445795i	$0.147079\pi$
$317$	−1.75352	+	9.94473i	−0.0984877	+	0.558552i	−0.993623	+	0.112756i	$0.964032\pi$
$318$	2.36265	+	0.0113736i	0.132491	+	0.000637797i
$319$	26.9640	+	22.6255i	1.50969	+	1.26678i
$320$	11.6905	+	13.5400i	0.653518	+	0.756911i
$321$	0.791803	+	0.288193i	0.0441941	+	0.0160853i
$322$	−0.934258	+	1.10258i	−0.0520642	+	0.0614445i
$323$	−8.22488	+	9.29580i	−0.457645	+	0.517232i
$324$	−2.53928	−	15.2586i	−0.141071	−	0.847700i
$325$	26.4910	+	7.13565i	1.46946	+	0.395815i
$326$	17.3340	+	10.1194i	0.960043	+	0.560461i
$327$	−1.01598	−	0.852508i	−0.0561838	−	0.0471438i
$328$	−2.63188	−	16.2992i	−0.145321	−	0.899972i
$329$	−0.675560	+	3.83129i	−0.0372448	+	0.211226i
$330$	−5.99299	+	2.44404i	−0.329903	+	0.134540i
$331$	−1.67568	−	2.90236i	−0.0921036	−	0.159528i	0.816292	−	0.577639i	$-0.196026\pi$
$331$	−1.67568	−	2.90236i	−0.0921036	−	0.159528i	−0.908396	+	0.418111i	$0.862692\pi$
$332$	16.0685	+	28.4609i	0.881876	+	1.56199i
$333$	17.6555	−	6.42608i	0.967515	−	0.352147i
$334$	−1.15645	+	6.37886i	−0.0632784	+	0.349036i
$335$	7.88712	−	15.1267i	0.430919	−	0.826459i
$336$	1.16967	−	0.183097i	0.0638106	−	0.00998877i
$337$	11.3807	−	9.54953i	0.619946	−	0.520196i	−0.277841	−	0.960627i	$-0.589619\pi$
$337$	11.3807	−	9.54953i	0.619946	−	0.520196i	0.897786	+	0.440431i	$0.145174\pi$
$338$	−23.8463	+	4.08648i	−1.29707	+	0.222275i
$339$	6.56475	−	1.15754i	0.356548	−	0.0628691i
$340$	1.79197	−	12.6078i	0.0971834	−	0.683757i
$341$			44.3452i			2.40143i
$342$	−15.5186	+	8.32863i	−0.839149	+	0.450361i
$343$	−10.4812			−0.565930
$344$	−15.1074	−	18.5417i	−0.814539	−	0.999701i
$345$	−0.238090	−	1.07731i	−0.0128184	−	0.0580006i
$346$	−11.0101	+	1.88678i	−0.591909	+	0.101434i
$347$	21.1986	−	17.7878i	1.13800	−	0.954897i	0.138630	−	0.990344i	$-0.455730\pi$
$347$	21.1986	−	17.7878i	1.13800	−	0.954897i	0.999372	+	0.0354472i	$0.0112856\pi$
$348$	4.91535	+	0.0473251i	0.263491	+	0.00253689i
$349$	−2.17555	+	3.76817i	−0.116455	+	0.201706i	−0.918360	−	0.395745i	$-0.870486\pi$
$349$	−2.17555	+	3.76817i	−0.116455	+	0.201706i	0.801906	+	0.597451i	$0.203820\pi$
$350$	−5.51207	−	0.516314i	−0.294632	−	0.0275981i
$351$	4.15533	+	11.4167i	0.221795	+	0.609377i
$352$	−30.6173	−	0.737080i	−1.63191	−	0.0392865i
$353$	−24.4172	+	14.0973i	−1.29960	+	0.750322i	−0.980334	−	0.197344i	$-0.936768\pi$
$353$	−24.4172	+	14.0973i	−1.29960	+	0.750322i	−0.319262	+	0.947667i	$0.603435\pi$
$354$	1.18416	−	0.424556i	0.0629376	−	0.0225649i
$355$	−25.5200	−	3.37687i	−1.35446	−	0.179226i
$356$	−8.51014	+	9.94593i	−0.451036	+	0.527133i
$357$	−0.645628	−	0.541746i	−0.0341703	−	0.0286723i
$358$	−1.35961	−	0.793723i	−0.0718577	−	0.0419496i
$359$	1.16297	−	3.19522i	0.0613790	−	0.168637i	−0.905213	−	0.424959i	$-0.860288\pi$
$359$	1.16297	−	3.19522i	0.0613790	−	0.168637i	0.966591	+	0.256322i	$0.0825107\pi$
$360$	8.58478	−	15.9003i	0.452457	−	0.838020i
$361$	13.8947	+	12.9591i	0.731300	+	0.682056i
$362$	−6.44996	−	5.46529i	−0.339003	−	0.287249i
$363$	2.36759	−	6.50490i	0.124266	−	0.341419i
$364$	8.10177	−	2.86077i	0.424648	−	0.149945i
$365$	14.6019	+	11.2197i	0.764300	+	0.587268i
$366$	−4.61426	−	0.0222125i	−0.241191	−	0.00116107i
$367$	1.34308	−	7.61698i	0.0701082	−	0.397603i	−0.929479	−	0.368875i	$-0.879743\pi$
$367$	1.34308	−	7.61698i	0.0701082	−	0.397603i	0.999587	−	0.0287284i	$-0.00914579\pi$
$368$	1.00541	−	5.12310i	0.0524108	−	0.267060i
$369$	−14.4432	+	8.33880i	−0.751885	+	0.434101i
$370$	19.7986	+	6.36178i	1.02928	+	0.330733i
$371$	−3.25139	+	1.18341i	−0.168804	+	0.0614395i
$372$	3.93484	+	4.78212i	0.204012	+	0.247941i
$373$	−6.03828	+	10.4586i	−0.312651	+	0.541527i	−0.978935	−	0.204171i	$-0.934550\pi$
$373$	−6.03828	+	10.4586i	−0.312651	+	0.541527i	0.666285	+	0.745697i	$0.267884\pi$
$374$	13.9337	+	16.7688i	0.720494	+	0.867094i
$375$	2.86158	−	3.11051i	0.147771	−	0.160626i
$376$	−4.61566	−	13.2749i	−0.238035	−	0.684598i
$377$	35.1319	−	6.19470i	1.80939	−	0.319043i
$378$	−1.21558	−	2.12906i	−0.0625229	−	0.109507i
$379$	−26.4585			−1.35908			−0.679542	−	0.733637i	$-0.737821\pi$
$379$	−26.4585			−1.35908			−0.679542	+	0.733637i	$0.737821\pi$
$380$	−19.2211	−	3.24811i	−0.986020	−	0.166625i
$381$	2.92813			0.150013
$382$	12.5761	+	22.0267i	0.643451	+	1.12698i
$383$	9.24112	−	1.62946i	0.472199	−	0.0832614i	0.0675155	−	0.997718i	$-0.478493\pi$
$383$	9.24112	−	1.62946i	0.472199	−	0.0832614i	0.404684	+	0.914457i	$0.367382\pi$
$384$	−3.36713	+	2.63725i	−0.171828	+	0.134582i
$385$	6.99234	−	6.39883i	0.356363	−	0.326115i
$386$	−8.71869	−	10.4927i	−0.443770	−	0.534065i
$387$	−12.0797	+	20.9227i	−0.614048	+	1.06356i
$388$	−11.2761	+	9.27822i	−0.572455	+	0.471030i
$389$	24.9206	−	9.07036i	1.26353	−	0.459886i	0.378575	−	0.925571i	$-0.376414\pi$
$389$	24.9206	−	9.07036i	1.26353	−	0.459886i	0.884950	+	0.465685i	$0.154192\pi$
$390$	−2.00669	+	6.24503i	−0.101613	+	0.316230i
$391$	−3.21868	+	1.85831i	−0.162776	+	0.0939787i
$392$	15.7737	−	8.80573i	0.796694	−	0.444756i
$393$	0.421039	−	2.38783i	0.0212386	−	0.120450i
$394$	−12.1751	−	0.0586094i	−0.613371	−	0.00295270i
$395$	−10.9981	+	14.3135i	−0.553375	+	0.720190i
$396$	10.3006	+	29.1714i	0.517622	+	1.46592i
$397$	−8.70509	+	23.9170i	−0.436896	+	1.20036i	0.504605	+	0.863351i	$0.331638\pi$
$397$	−8.70509	+	23.9170i	−0.436896	+	1.20036i	−0.941501	+	0.337011i	$0.890584\pi$
$398$	10.9930	+	9.31473i	0.551027	+	0.466905i
$399$	−0.854910	+	0.966223i	−0.0427990	+	0.0483716i
$400$	18.2962	−	8.07771i	0.914810	−	0.403885i
$401$	−9.67470	+	26.5810i	−0.483131	+	1.32739i	0.423663	+	0.905820i	$0.360744\pi$
$401$	−9.67470	+	26.5810i	−0.483131	+	1.32739i	−0.906795	+	0.421573i	$0.861478\pi$
$402$	3.52244	+	2.05635i	0.175683	+	0.102562i
$403$	34.4287	+	28.8891i	1.71502	+	1.43907i
$404$	4.62540	+	3.95768i	0.230122	+	0.196902i
$405$	−17.1448	−	2.26864i	−0.851932	−	0.112730i
$406$	−6.77632	+	2.42950i	−0.336303	+	0.120574i
$407$	−30.8333	+	17.8016i	−1.52835	+	0.882392i
$408$	2.99051	+	0.571956i	0.148053	+	0.0283160i
$409$	−3.73646	−	10.2658i	−0.184756	−	0.507613i	0.812390	−	0.583115i	$-0.198166\pi$
$409$	−3.73646	−	10.2658i	−0.184756	−	0.507613i	−0.997146	+	0.0755020i	$0.975944\pi$
$410$	−18.2877	−	2.50951i	−0.903165	−	0.123936i
$411$	−2.53277	+	4.38688i	−0.124932	+	0.216389i
$412$	−0.0509597	+	5.29286i	−0.00251060	+	0.260760i
$413$	−1.41125	+	1.18418i	−0.0694428	+	0.0582695i
$414$	−5.19795	+	0.890761i	−0.255465	+	0.0437785i
$415$	35.6804	−	7.88551i	1.75148	−	0.387085i
$416$	−20.5182	+	23.2905i	−1.00599	+	1.14191i
$417$	−4.79475			−0.234800
$418$	26.2194	−	20.6489i	1.28243	−	1.00997i
$419$			26.7563i			1.30713i	0.756870	+	0.653566i	$0.226728\pi$
$419$			26.7563i			1.30713i	−0.756870	+	0.653566i	$0.773272\pi$
$420$	0.186261	−	1.31048i	0.00908861	−	0.0639451i
$421$	−14.7693	+	2.60422i	−0.719811	+	0.126922i	−0.521542	−	0.853226i	$-0.674643\pi$
$421$	−14.7693	+	2.60422i	−0.719811	+	0.126922i	−0.198269	+	0.980148i	$0.563532\pi$
$422$	−8.02644	+	1.37547i	−0.390721	+	0.0669570i
$423$	−10.8754	+	9.12554i	−0.528780	+	0.443699i
$424$	8.17213	−	9.45834i	0.396874	−	0.459338i
$425$	−12.8958	−	6.03409i	−0.625537	−	0.292696i
$426$	1.09793	−	6.05607i	0.0531950	−	0.293417i
$427$	6.34996	−	2.31120i	0.307296	−	0.111847i
$428$	3.88191	−	2.19167i	0.187639	−	0.105938i
$429$	−5.61513	−	9.72570i	−0.271101	−	0.469561i
$430$	−24.7603	+	10.0977i	−1.19405	+	0.486953i
$431$	0.580242	−	3.29071i	0.0279493	−	0.158508i	−0.967639	−	0.252339i	$-0.918800\pi$
$431$	0.580242	−	3.29071i	0.0279493	−	0.158508i	0.995588	+	0.0938309i	$0.0299113\pi$
$432$	7.58349	+	4.57524i	0.364861	+	0.220127i
$433$	−2.59278	−	2.17560i	−0.124601	−	0.104553i	0.578358	−	0.815783i	$-0.303694\pi$
$433$	−2.59278	−	2.17560i	−0.124601	−	0.104553i	−0.702959	+	0.711231i	$0.748138\pi$
$434$	−7.83225	−	4.57236i	−0.375960	−	0.219481i
$435$	1.65607	−	5.24034i	0.0794023	−	0.251255i
$436$	−6.92143	+	1.15184i	−0.331476	+	0.0551631i
$437$	2.71448	+	4.99992i	0.129851	+	0.239179i
$438$	−2.84625	+	3.35906i	−0.135999	+	0.160502i
$439$	−20.2943	−	7.38652i	−0.968593	−	0.352539i	−0.191198	−	0.981551i	$-0.561237\pi$
$439$	−20.2943	−	7.38652i	−0.968593	−	0.352539i	−0.777395	+	0.629012i	$0.783460\pi$
$440$	−10.7884	+	32.4972i	−0.514318	+	1.54924i
$441$	−13.9790	−	11.7298i	−0.665666	−	0.558560i
$442$	22.0962	+	0.106369i	1.05101	+	0.00505944i
$443$	3.62348	−	20.5498i	0.172157	−	0.976349i	−0.769218	−	0.638987i	$-0.779354\pi$
$443$	3.62348	−	20.5498i	0.172157	−	0.976349i	0.941375	−	0.337363i	$-0.109535\pi$
$444$	−1.74544	+	4.65559i	−0.0828348	+	0.220945i
$445$	7.85519	+	12.3481i	0.372372	+	0.585357i
$446$	−34.1395	−	12.6122i	−1.61655	−	0.597205i
$447$	−1.18626	−	3.25921i	−0.0561080	−	0.154156i
$448$	3.28709	−	5.33164i	0.155300	−	0.251896i
$449$	7.80786	+	4.50787i	0.368476	+	0.212740i	0.672792	−	0.739831i	$-0.265095\pi$
$449$	7.80786	+	4.50787i	0.368476	+	0.212740i	−0.304317	+	0.952571i	$0.598428\pi$
$450$	−14.1976	−	14.3728i	−0.669281	−	0.677538i
$451$	24.2093	−	20.3140i	1.13997	−	0.956550i
$452$	17.9265	−	30.3706i	0.843193	−	1.42851i
$453$	−5.48604	+	0.967338i	−0.257757	+	0.0454495i
$454$	16.9174	+	29.6303i	0.793973	+	1.39062i
$455$	−0.412695	−	9.59729i	−0.0193475	−	0.449928i
$456$	0.995241	−	4.55324i	0.0466064	−	0.213225i
$457$		−	7.71473i		−	0.360880i	−0.983586	−	0.180440i	$-0.942248\pi$
$457$		−	7.71473i		−	0.360880i	0.983586	−	0.180440i	$-0.0577521\pi$
$458$	17.4086	−	9.93941i	0.813449	−	0.464438i
$459$	−1.09485	−	6.20920i	−0.0511032	−	0.289820i
$460$	−5.14953	−	2.74837i	−0.240098	−	0.128143i
$461$	−3.62669	+	3.04316i	−0.168912	+	0.141734i	−0.723325	−	0.690508i	$-0.757387\pi$
$461$	−3.62669	+	3.04316i	−0.168912	+	0.141734i	0.554413	+	0.832242i	$0.312943\pi$
$462$	1.44829	+	1.74298i	0.0673807	+	0.0810908i
$463$	2.00278	−	3.46891i	0.0930769	−	0.161214i	−0.815727	−	0.578436i	$-0.803663\pi$
$463$	2.00278	−	3.46891i	0.0930769	−	0.161214i	0.908804	+	0.417222i	$0.136996\pi$
$464$	17.0967	−	19.5961i	0.793696	−	0.909727i
$465$	6.39853	−	2.64542i	0.296725	−	0.122679i
$466$	13.3343	+	4.92611i	0.617700	+	0.228198i
$467$	−4.32284	−	7.48738i	−0.200037	−	0.346475i	0.748503	−	0.663131i	$-0.230773\pi$
$467$	−4.32284	−	7.48738i	−0.200037	−	0.346475i	−0.948540	+	0.316657i	$0.897440\pi$
$468$	29.3585	+	11.0068i	1.35710	+	0.508792i
$469$	−5.88243	−	1.03723i	−0.271625	−	0.0478949i
$470$	−15.7019	+	0.599488i	−0.724272	+	0.0276523i
$471$	−2.27315	−	1.90740i	−0.104741	−	0.0878885i
$472$	2.36632	−	6.22041i	0.108919	−	0.286317i
$473$	15.6579	−	43.0198i	0.719952	−	1.97805i
$474$	−3.29271	−	2.79003i	−0.151239	−	0.128150i
$475$	−9.75111	+	19.4914i	−0.447411	+	0.894328i
$476$	−4.39838	+	0.731964i	−0.201600	+	0.0335495i
$477$	−11.8650	−	4.31849i	−0.543259	−	0.197730i
$478$	10.0911	−	17.2856i	0.461557	−	0.790626i
$479$	−5.10197	+	6.08029i	−0.233115	+	0.277815i	−0.869902	−	0.493224i	$-0.835818\pi$
$479$	−5.10197	+	6.08029i	−0.233115	+	0.277815i	0.636788	+	0.771039i	$0.280263\pi$
$480$	1.72013	+	4.46172i	0.0785129	+	0.203649i
$481$	−6.26584	+	35.5353i	−0.285698	+	1.62027i
$482$	−27.7530	+	9.95023i	−1.26411	+	0.453221i
$483$	−0.334556	+	0.193156i	−0.0152228	+	0.00878890i
$484$	−18.0052	−	31.8911i	−0.818418	−	1.44960i
$485$	6.23782	+	15.0875i	0.283245	+	0.685089i
$486$	2.41338	−	13.3119i	0.109473	−	0.603841i
$487$	−27.6299	−	15.9522i	−1.25203	−	0.722861i	−0.280520	−	0.959848i	$-0.590507\pi$
$487$	−27.6299	−	15.9522i	−1.25203	−	0.722861i	−0.971513	+	0.236987i	$0.923840\pi$
$488$	−15.9602	+	18.4721i	−0.722483	+	0.836194i
$489$	3.44880	+	4.11012i	0.155960	+	0.185866i
$490$	−4.26357	−	19.7424i	−0.192608	−	0.891869i
$491$	10.4740	−	1.84685i	0.472684	−	0.0833470i	0.0677688	−	0.997701i	$-0.478412\pi$
$491$	10.4740	−	1.84685i	0.472684	−	0.0833470i	0.404916	+	0.914354i	$0.367301\pi$
$492$	0.808188	−	4.33877i	0.0364359	−	0.195607i
$493$	−18.5132			−0.833791
$494$	1.04952	−	33.8081i	0.0472201	−	1.52110i
$495$	34.5562	−	1.48596i	1.55319	−	0.0667889i
$496$	32.7573	+	0.630833i	1.47085	+	0.0283253i
$497$	1.56517	+	8.87652i	0.0702074	+	0.398166i
$498$	1.47568	+	8.61119i	0.0661268	+	0.385877i
$499$	11.5993	+	13.8236i	0.519258	+	0.618828i	0.960405	−	0.278607i	$-0.0898727\pi$
$499$	11.5993	+	13.8236i	0.519258	+	0.618828i	−0.441147	+	0.897435i	$0.645428\pi$
$500$	−2.66123	−	22.2018i	−0.119014	−	0.992893i
$501$	−0.866470	+	1.50077i	−0.0387110	+	0.0670495i
$502$	6.63756	−	36.6120i	0.296249	−	1.63407i
$503$	26.0346	−	9.47581i	1.16082	−	0.422505i	0.311432	−	0.950268i	$-0.399191\pi$
$503$	26.0346	−	9.47581i	1.16082	−	0.422505i	0.849392	+	0.527763i	$0.176969\pi$
$504$	−6.21432	−	1.18853i	−0.276808	−	0.0529413i
$505$	5.74254	−	3.65309i	0.255540	−	0.162560i
$506$	9.40704	−	3.37269i	0.418194	−	0.149934i
$507$	−6.36906	−	1.12304i	−0.282860	−	0.0498759i
$508$	10.0714	−	11.7706i	0.446846	−	0.522236i
$509$	3.18794	−	3.79923i	0.141303	−	0.168398i	−0.690752	−	0.723092i	$-0.742720\pi$
$509$	3.18794	−	3.79923i	0.141303	−	0.168398i	0.832054	+	0.554694i	$0.187165\pi$
$510$	1.58834	−	3.01083i	0.0703328	−	0.133322i
$511$	2.20524	−	6.05885i	0.0975541	−	0.268028i
$512$	−0.980019	+	22.6062i	−0.0433111	+	0.999062i
$513$	−9.54548	+	1.42619i	−0.421443	+	0.0629680i
$514$	−15.0492	+	17.7606i	−0.663791	+	0.783386i
$515$	5.64280	+	1.78325i	0.248651	+	0.0785795i
$516$	−2.12871	−	6.02854i	−0.0937111	−	0.265392i
$517$	17.2923	−	20.6082i	0.760515	−	0.906346i
$518$	0.0350512	−	7.28126i	0.00154006	−	0.319920i
$519$	−2.94068	−	0.518521i	−0.129082	−	0.0227606i
$520$	18.2019	+	29.5465i	0.798207	+	1.29570i
$521$	6.43082	−	3.71284i	0.281740	−	0.162662i	−0.352471	−	0.935823i	$-0.614659\pi$
$521$	6.43082	−	3.71284i	0.281740	−	0.162662i	0.634211	+	0.773160i	$0.281325\pi$
$522$	−24.6416	−	9.10339i	−1.07854	−	0.398445i
$523$	8.55118	+	23.4942i	0.373917	+	1.02733i	0.973833	+	0.227266i	$0.0729786\pi$
$523$	8.55118	+	23.4942i	0.373917	+	1.02733i	−0.599916	+	0.800063i	$0.704799\pi$
$524$	−8.15050	−	9.90552i	−0.356056	−	0.432725i
$525$	−1.34041	−	0.627194i	−0.0585003	−	0.0273730i
$526$	16.8994	+	20.3380i	0.736850	+	0.886778i
$527$	−14.9922	−	17.8670i	−0.653070	−	0.778298i
$528$	−7.63769	−	2.94764i	−0.332388	−	0.128279i
$529$	−3.69809	−	20.9729i	−0.160786	−	0.911865i
$530$	−7.44423	−	11.8274i	−0.323357	−	0.513751i
$531$	−6.72273			−0.291742
$532$	0.943564	+	6.75994i	0.0409087	+	0.293081i
$533$		−	32.0294i		−	1.38735i
$534$	−3.03867	+	1.73493i	−0.131496	+	0.0750776i
$535$	−1.07554	−	4.86662i	−0.0464998	−	0.210402i
$536$	20.3817	−	7.08673i	0.880357	−	0.306100i
$537$	−0.270510	−	0.322382i	−0.0116734	−	0.0139118i
$538$	−21.6677	+	18.0043i	−0.934162	+	0.776223i
$539$	29.9465	+	17.2896i	1.28989	+	0.744718i
$540$	7.36906	−	6.61436i	0.317114	−	0.284637i
$541$	11.9507	−	4.34969i	0.513800	−	0.187008i	−0.0720908	−	0.997398i	$-0.522967\pi$
$541$	11.9507	−	4.34969i	0.513800	−	0.187008i	0.585890	+	0.810390i	$0.300745\pi$
$542$	7.34280	+	2.71266i	0.315400	+	0.116519i
$543$	−1.12994	−	1.95711i	−0.0484902	−	0.0839876i
$544$	12.5851	−	10.0541i	0.539583	−	0.431066i
$545$	−1.02907	+	7.77703i	−0.0440807	+	0.333131i
$546$	2.29672	+	0.0110562i	0.0982906	+	0.000473160i
$547$	−12.4947	+	14.8906i	−0.534233	+	0.636674i	−0.963885	−	0.266320i	$-0.914192\pi$
$547$	−12.4947	+	14.8906i	−0.534233	+	0.636674i	0.429651	+	0.902995i	$0.358637\pi$
$548$	8.92300	+	25.2701i	0.381172	+	1.07949i
$549$	23.1722	+	8.43401i	0.988967	+	0.359955i
$550$	31.2242	+	22.1499i	1.33140	+	0.944476i
$551$	−0.742958	+	28.3295i	−0.0316511	+	1.20688i
$552$	0.715174	−	1.19841i	0.0304398	−	0.0510078i
$553$	5.93917	+	2.16168i	0.252559	+	0.0919240i
$554$	0.0796623	−	0.136458i	0.00338453	−	0.00579754i
$555$	4.40794	+	3.38695i	0.187107	+	0.143768i
$556$	−16.4917	+	19.2741i	−0.699402	+	0.817402i
$557$	−1.59202	−	0.280716i	−0.0674561	−	0.0118943i	0.139818	−	0.990177i	$-0.455348\pi$
$557$	−1.59202	−	0.280716i	−0.0674561	−	0.0118943i	−0.207274	+	0.978283i	$0.566459\pi$
$558$	−11.1694	−	31.1536i	−0.472840	−	1.31884i
$559$	−23.1992	−	40.1822i	−0.981221	−	1.69952i
$560$	−4.62727	−	5.25618i	−0.195538	−	0.222114i
$561$	1.99330	+	5.47654i	0.0841571	+	0.231220i
$562$	−2.12582	+	11.7258i	−0.0896725	+	0.494623i
$563$	3.41365	+	1.97087i	0.143868	+	0.0830624i	0.570206	−	0.821502i	$-0.306863\pi$
$563$	3.41365	+	1.97087i	0.143868	+	0.0830624i	−0.426338	+	0.904564i	$0.640197\pi$
$564$	0.0361699	−	3.75673i	0.00152303	−	0.158187i
$565$	−26.6189	−	29.0878i	−1.11986	−	1.22373i
$566$	−12.3002	+	2.10786i	−0.517016	+	0.0885998i
$567$	1.05151	+	5.96341i	0.0441592	+	0.250440i
$568$	−20.5680	−	25.2435i	−0.863014	−	1.05919i
$569$		−	1.68994i		−	0.0708458i	−0.999372	−	0.0354229i	$-0.988722\pi$
$569$		−	1.68994i		−	0.0708458i	0.999372	−	0.0354229i	$-0.0112778\pi$
$570$	−4.54353	−	2.55136i	−0.190308	−	0.106865i
$571$		−	12.1472i		−	0.508345i	−0.967159	−	0.254173i	$-0.918197\pi$
$571$		−	12.1472i		−	0.508345i	0.967159	−	0.254173i	$-0.0818032\pi$
$572$	−58.4091	−	10.8799i	−2.44221	−	0.454913i
$573$	1.17735	+	6.67710i	0.0491846	+	0.278940i
$574$	1.09168	+	6.37039i	0.0455658	+	0.265895i
$575$	−4.62067	+	4.60852i	−0.192695	+	0.192188i
$576$	21.6951	−	7.19392i	0.903962	−	0.299747i
$577$	−19.6381	−	11.3380i	−0.817543	−	0.472009i	0.0320255	−	0.999487i	$-0.489804\pi$
$577$	−19.6381	−	11.3380i	−0.817543	−	0.472009i	−0.849568	+	0.527478i	$0.823138\pi$
$578$	12.3729	+	2.24313i	0.514643	+	0.0933021i
$579$	−1.24726	−	3.42682i	−0.0518344	−	0.142414i
$580$	−15.3692	−	24.6814i	−0.638170	−	1.02484i
$581$	−6.39729	−	11.0804i	−0.265405	−	0.459694i
$582$	−3.67442	+	1.31738i	−0.152309	+	0.0546072i
$583$	23.5628	+	4.15475i	0.975871	+	0.172072i
$584$	3.71308	+	22.9950i	0.153648	+	0.951541i
$585$	21.3583	−	27.7968i	0.883057	−	1.14926i
$586$	−9.08309	−	5.30259i	−0.375219	−	0.219048i
$587$	8.07910	+	2.94055i	0.333460	+	0.121370i	0.503324	−	0.864098i	$-0.332110\pi$
$587$	8.07910	+	2.94055i	0.333460	+	0.121370i	−0.169863	+	0.985468i	$0.554333\pi$
$588$	4.76353	−	0.792730i	0.196445	−	0.0326916i
$589$	−27.9424	+	22.2246i	−1.15135	+	0.915747i
$590$	−5.87834	−	4.56194i	−0.242008	−	0.187812i
$591$	−3.05830	−	1.11313i	−0.125802	−	0.0457881i
$592$	12.7112	+	23.0294i	0.522427	+	0.946503i
$593$	−0.0509110	+	0.0606734i	−0.00209067	+	0.00249156i	−0.767089	−	0.641541i	$-0.778295\pi$
$593$	−0.0509110	+	0.0606734i	−0.00209067	+	0.00249156i	0.764998	+	0.644033i	$0.222740\pi$
$594$	−0.0816093	+	16.9529i	−0.00334847	+	0.695585i
$595$	−0.653950	+	4.94209i	−0.0268093	+	0.202606i
$596$	−17.1817	−	6.44161i	−0.703788	−	0.263859i
$597$	1.92580	+	3.33559i	0.0788178	+	0.136516i
$598$	3.50982	−	9.50061i	0.143527	−	0.388509i
$599$	9.14026	−	3.32678i	0.373461	−	0.135929i	−0.148469	−	0.988917i	$-0.547434\pi$
$599$	9.14026	−	3.32678i	0.373461	−	0.135929i	0.521930	+	0.852988i	$0.325212\pi$
$600$	5.33257	−	0.381973i	0.217701	−	0.0155940i
$601$	−4.69953	−	2.71328i	−0.191698	−	0.110677i	0.401079	−	0.916043i	$-0.368635\pi$
$601$	−4.69953	−	2.71328i	−0.191698	−	0.110677i	−0.592777	+	0.805367i	$0.701969\pi$
$602$	5.98369	+	7.20120i	0.243877	+	0.293499i
$603$	−14.0110	−	16.6977i	−0.570573	−	0.679982i
$604$	−14.9809	+	25.3802i	−0.609563	+	1.03270i
$605$	−39.9808	+	8.83591i	−1.62545	+	0.359231i
$606$	0.806836	+	1.41315i	0.0327755	+	0.0574052i
$607$		−	30.6530i		−	1.24417i	−0.782950	−	0.622084i	$-0.786286\pi$
$607$		−	30.6530i		−	1.24417i	0.782950	−	0.622084i	$-0.213714\pi$
$608$	−14.8801	−	19.6617i	−0.603468	−	0.797387i
$609$	−1.92429			−0.0779763
$610$	14.5386	+	23.0990i	0.588650	+	0.935250i
$611$	−4.73452	−	26.8508i	−0.191538	−	1.08627i
$612$	−14.0124	−	8.27095i	−0.566417	−	0.334333i
$613$	15.4204	+	18.3773i	0.622823	+	0.742252i	0.981553	−	0.191190i	$-0.0612345\pi$
$613$	15.4204	+	18.3773i	0.622823	+	0.742252i	−0.358730	+	0.933441i	$0.616790\pi$
$614$	27.8070	−	23.1056i	1.12220	−	0.932468i
$615$	−4.37530	−	2.28130i	−0.176429	−	0.0919910i
$616$	11.9879	+	0.173137i	0.483008	+	0.00697587i
$617$	−12.2926	−	33.7736i	−0.494881	−	1.35967i	−0.896165	−	0.443721i	$-0.853658\pi$
$617$	−12.2926	−	33.7736i	−0.494881	−	1.35967i	0.401284	−	0.915954i	$-0.368564\pi$
$618$	−0.490322	+	1.32723i	−0.0197236	+	0.0533892i
$619$	11.4612	−	6.61711i	0.460663	−	0.265964i	−0.251660	−	0.967816i	$-0.580976\pi$
$619$	11.4612	−	6.61711i	0.460663	−	0.265964i	0.712323	+	0.701852i	$0.247643\pi$
$620$	11.3738	−	34.8200i	0.456782	−	1.39841i
$621$	−2.84607	−	0.501838i	−0.114209	−	0.0201381i
$622$	4.71471	+	0.0226961i	0.189043	+	0.000910031i
$623$	3.29381	−	3.92541i	0.131964	−	0.157268i
$624$	−7.26414	+	4.00948i	−0.290798	+	0.160508i
$625$	−24.6087	−	4.40604i	−0.984347	−	0.176241i
$626$	22.4316	+	19.0071i	0.896547	+	0.759677i
$627$	8.46040	−	2.83044i	0.337876	−	0.113037i
$628$	−15.4860	+	2.57713i	−0.617959	+	0.102839i
$629$	6.40459	−	17.5965i	0.255368	−	0.701617i
$630$	−3.30058	+	6.25653i	−0.131498	+	0.249266i
$631$	−16.6352	+	19.8251i	−0.662237	+	0.789223i	−0.987705	−	0.156330i	$-0.950034\pi$
$631$	−16.6352	+	19.8251i	−0.662237	+	0.789223i	0.325468	+	0.945553i	$0.394478\pi$
$632$	−22.5408	+	3.63974i	−0.896625	+	0.144781i
$633$	−2.14377	−	0.378004i	−0.0852072	−	0.0150243i
$634$	4.81971	+	13.4430i	0.191415	+	0.533891i
$635$	−9.29629	−	14.6135i	−0.368912	−	0.579918i
$636$	2.90963	−	1.64273i	0.115374	−	0.0651385i
$637$	32.9323	−	11.9864i	1.30483	−	0.474918i
$638$	48.9804	+	8.87989i	1.93915	+	0.351558i
$639$	−16.4459	+	28.4852i	−0.650591	+	1.12686i
$640$	23.8518	+	8.43158i	0.942825	+	0.333287i
$641$	−26.3580	−	31.4123i	−1.04108	−	1.24071i	−0.969965	−	0.243243i	$-0.921789\pi$
$641$	−26.3580	−	31.4123i	−1.04108	−	1.24071i	−0.0711144	−	0.997468i	$-0.522656\pi$
$642$	1.17452	−	0.201275i	0.0463547	−	0.00794369i
$643$	1.17231	+	6.64851i	0.0462314	+	0.262191i	0.999159	−	0.0410070i	$-0.0130566\pi$
$643$	1.17231	+	6.64851i	0.0462314	+	0.262191i	−0.952927	+	0.303198i	$0.901945\pi$
$644$	−0.374261	+	2.00922i	−0.0147479	+	0.0791745i
$645$	−7.14136	+	0.307087i	−0.281191	+	0.0120916i
$646$	−3.58302	+	17.1838i	−0.140972	+	0.676088i
$647$	5.45735			0.214551			0.107275	−	0.994229i	$-0.465787\pi$
$647$	5.45735			0.214551			0.107275	+	0.994229i	$0.465787\pi$
$648$	−13.8180	−	16.9591i	−0.542820	−	0.666215i
$649$	12.5456	−	2.21213i	0.492458	−	0.0868337i
$650$	37.5381	−	9.81204i	1.47236	−	0.384860i
$651$	−1.55832	−	1.85713i	−0.0610752	−	0.0727866i
$652$	28.3843	+	0.273284i	1.11161	+	0.0107026i
$653$	22.5982	+	13.0471i	0.884335	+	0.510571i	0.872085	−	0.489354i	$-0.162767\pi$
$653$	22.5982	+	13.0471i	0.884335	+	0.510571i	0.0122500	+	0.999925i	$0.496101\pi$
$654$	−1.84554	−	0.334587i	−0.0721663	−	0.0130834i
$655$	−13.2537	+	5.47965i	−0.517866	+	0.214108i
$656$	−14.6613	−	18.1721i	−0.572429	−	0.709501i
$657$	20.3766	−	11.7645i	0.794968	−	0.458975i
$658$	1.85683	+	5.17904i	0.0723869	+	0.201900i
$659$	6.75864	−	38.3302i	0.263279	−	1.49313i	−0.510611	−	0.859812i	$-0.670581\pi$
$659$	6.75864	−	38.3302i	0.263279	−	1.49313i	0.773890	−	0.633320i	$-0.218308\pi$
$660$	−5.64643	+	7.20392i	−0.219787	+	0.280412i
$661$	29.3910	−	35.0268i	1.14318	−	1.36238i	0.221159	−	0.975238i	$-0.429016\pi$
$661$	29.3910	−	35.0268i	1.14318	−	1.36238i	0.922018	−	0.387147i	$-0.126539\pi$
$662$	−4.09310	−	2.38950i	−0.159083	−	0.0928705i
$663$	5.55043	+	2.02019i	0.215561	+	0.0784577i
$664$	39.6912	+	23.6865i	1.54032	+	0.919213i
$665$	7.53633	+	1.19903i	0.292246	+	0.0464964i
$666$	17.1773	−	20.2722i	0.665609	−	0.785531i
$667$	−2.90230	+	7.97400i	−0.112377	+	0.308754i
$668$	3.05259	+	8.64501i	0.118108	+	0.334485i
$669$	−7.45264	−	6.25350i	−0.288136	−	0.241774i
$670$	−0.920433	−	24.1081i	−0.0355594	−	0.931376i
$671$	−46.0181	−	8.11423i	−1.77651	−	0.313246i
$672$	1.30812	−	1.04504i	0.0504619	−	0.0403134i
$673$	1.98800	+	3.44332i	0.0766319	+	0.132730i	0.901795	−	0.432165i	$-0.142250\pi$
$673$	1.98800	+	3.44332i	0.0766319	+	0.132730i	−0.825163	+	0.564895i	$0.808917\pi$
$674$	7.28086	−	19.7083i	0.280448	−	0.759135i
$675$	−4.66557	−	10.0398i	−0.179578	−	0.386434i
$676$	−26.4210	+	21.7398i	−1.01619	+	0.836148i
$677$	3.17733	−	5.50330i	0.122115	−	0.211509i	−0.798487	−	0.602013i	$-0.794366\pi$
$677$	3.17733	−	5.50330i	0.122115	−	0.211509i	0.920601	+	0.390503i	$0.127699\pi$
$678$	7.25073	−	6.02484i	0.278463	−	0.231383i
$679$	4.37905	−	3.67446i	0.168052	−	0.141013i
$680$	−6.63988	−	16.7407i	−0.254628	−	0.641975i
$681$	1.58378	+	8.98204i	0.0606904	+	0.344192i
$682$	31.0950	+	54.4619i	1.19069	+	2.08545i
$683$		−	1.07451i		−	0.0411150i	−0.999789	−	0.0205575i	$-0.993456\pi$
$683$		−	1.07451i		−	0.0411150i	0.999789	−	0.0205575i	$-0.00654412\pi$
$684$	−13.2188	+	21.1104i	−0.505435	+	0.807174i
$685$	29.9348	−	1.28723i	1.14375	−	0.0491826i
$686$	−12.8723	+	7.34943i	−0.491466	+	0.280603i
$687$	5.27718	−	0.930509i	0.201337	−	0.0355011i
$688$	−31.5555	−	12.1783i	−1.20304	−	0.464293i
$689$	18.5759	−	15.5870i	0.707684	−	0.593818i
$690$	−1.04782	−	1.15614i	−0.0398899	−	0.0440133i
$691$	0.383098	+	0.221181i	0.0145737	+	0.00841414i	0.507269	−	0.861788i	$-0.330655\pi$
$691$	0.383098	+	0.221181i	0.0145737	+	0.00841414i	−0.492695	+	0.870202i	$0.663988\pi$
$692$	−12.1989	+	10.0376i	−0.463734	+	0.381571i
$693$	−4.14209	−	11.3803i	−0.157345	−	0.432302i
$694$	13.5619	−	36.7103i	0.514804	−	1.39350i
$695$	15.2225	+	23.9292i	0.577421	+	0.907687i
$696$	6.06990	−	3.38854i	0.230079	−	0.128442i
$697$	−2.88635	+	16.3693i	−0.109328	+	0.620032i
$698$	−0.0296215	+	6.15333i	−0.00112119	+	0.232907i
$699$	2.91088	+	2.44251i	0.110099	+	0.0923844i
$700$	−7.13160	+	3.23097i	−0.269549	+	0.122119i
$701$	1.46916	+	0.534731i	0.0554894	+	0.0201965i	0.369616	−	0.929185i	$-0.379489\pi$
$701$	1.46916	+	0.534731i	0.0554894	+	0.0201965i	−0.314126	+	0.949381i	$0.601712\pi$
$702$	13.1087	+	11.1075i	0.494756	+	0.419225i
$703$	−26.6697	−	10.5067i	−1.00587	−	0.396268i
$704$	−38.1191	+	20.5637i	−1.43667	+	0.775025i
$705$	−4.00511	−	1.26571i	−0.150841	−	0.0476693i
$706$	−20.1026	+	34.4348i	−0.756570	+	1.29597i
$707$	−1.82553	−	1.53180i	−0.0686560	−	0.0576093i
$708$	1.15661	−	1.35175i	0.0434681	−	0.0508019i
$709$	−6.78122	+	38.4582i	−0.254674	+	1.44433i	0.542233	+	0.840228i	$0.317579\pi$
$709$	−6.78122	+	38.4582i	−0.254674	+	1.44433i	−0.796907	+	0.604101i	$0.793532\pi$
$710$	−33.7099	+	13.7474i	−1.26511	+	0.515932i
$711$	11.5321	+	19.9741i	0.432487	+	0.749089i
$712$	−3.47748	+	18.1823i	−0.130324	+	0.681409i
$713$	−10.0460	+	3.65644i	−0.376226	+	0.136935i
$714$	−1.17279	−	0.212621i	−0.0438906	−	0.00795714i
$715$	−30.7112	+	58.9009i	−1.14853	+	2.20277i
$716$	−2.22635	−	0.0214353i	−0.0832025	−	0.000801074i
$717$	4.09865	−	3.43917i	0.153067	−	0.128438i
$718$	−0.812220	−	4.73964i	−0.0303118	−	0.176882i
$719$	−41.7510	+	7.36183i	−1.55705	+	0.274550i	−0.884870	−	0.465838i	$-0.845753\pi$
$719$	−41.7510	+	7.36183i	−1.55705	+	0.274550i	−0.672180	+	0.740388i	$0.734642\pi$
$720$	−0.606081	−	25.5474i	−0.0225873	−	0.952095i
$721$		−	2.07208i		−	0.0771683i
$722$	26.1515	+	6.17248i	0.973258	+	0.229716i
$723$	−7.88110			−0.293101
$724$	−11.7537	−	2.18938i	−0.436823	−	0.0813675i
$725$	−31.4107	+	8.37216i	−1.16657	+	0.310934i
$726$	−1.65354	−	9.64905i	−0.0613685	−	0.358110i
$727$	−16.9853	+	14.2524i	−0.629950	+	0.528591i	−0.900914	−	0.433999i	$-0.857102\pi$
$727$	−16.9853	+	14.2524i	−0.629950	+	0.528591i	0.270963	+	0.962590i	$0.412658\pi$
$728$	7.94408	−	9.19440i	0.294427	−	0.340767i
$729$	−9.79311	+	16.9622i	−0.362708	+	0.628229i
$730$	25.8004	+	3.54043i	0.954917	+	0.131037i
$731$	8.23540	+	22.6266i	0.304597	+	0.836874i
$732$	−5.68250	+	3.20825i	−0.210031	+	0.118580i
$733$	−24.8242	+	14.3323i	−0.916902	+	0.529374i	−0.882646	−	0.470039i	$-0.844240\pi$
$733$	−24.8242	+	14.3323i	−0.916902	+	0.529374i	−0.0342569	+	0.999413i	$0.510906\pi$
$734$	−3.69157	−	10.2965i	−0.136258	−	0.380049i
$735$	0.708240	−	5.35238i	0.0261238	−	0.197425i
$736$	−2.35755	−	6.99685i	−0.0869003	−	0.257907i
$737$	31.6411	+	26.5500i	1.16551	+	0.977982i
$738$	−11.8910	+	20.3688i	−0.437715	+	0.749786i
$739$	−5.26194	+	14.4571i	−0.193564	+	0.531812i	−0.998068	−	0.0621352i	$-0.980209\pi$
$739$	−5.26194	+	14.4571i	−0.193564	+	0.531812i	0.804504	+	0.593947i	$0.202431\pi$
$740$	28.7762	−	6.06968i	1.05783	−	0.223126i
$741$	3.31412	−	8.41240i	0.121747	−	0.309037i
$742$	−3.16333	+	3.73327i	−0.116130	+	0.137053i
$743$	1.44776	−	3.97769i	0.0531131	−	0.145927i	−0.910299	−	0.413951i	$-0.864148\pi$
$743$	1.44776	−	3.97769i	0.0531131	−	0.145927i	0.963412	+	0.268024i	$0.0863707\pi$
$744$	8.18575	+	3.11396i	0.300104	+	0.114163i
$745$	−12.4997	+	16.2677i	−0.457952	+	0.596002i
$746$	−0.0822148	+	17.0786i	−0.00301010	+	0.625294i
$747$	8.10763	−	45.9807i	0.296643	−	1.68234i
$748$	28.8708	+	10.8240i	1.05562	+	0.395765i
$749$	−1.51131	+	0.872558i	−0.0552222	+	0.0318826i
$750$	1.33331	−	5.82667i	0.0486855	−	0.212760i
$751$	−15.1597	+	5.51769i	−0.553187	+	0.201343i	−0.603462	−	0.797392i	$-0.706212\pi$
$751$	−15.1597	+	5.51769i	−0.553187	+	0.201343i	0.0502752	+	0.998735i	$0.483990\pi$
$752$	−14.9770	−	13.0668i	−0.546156	−	0.476497i
$753$	4.97318	−	8.61379i	0.181233	−	0.313904i
$754$	38.8030	−	32.2425i	1.41312	−	1.17420i
$755$	22.2449	+	24.3082i	0.809575	+	0.884665i
$756$	−2.98580	−	1.76240i	−0.108593	−	0.0640978i
$757$	18.4535	−	3.25384i	0.670702	−	0.118263i	0.172081	−	0.985083i	$-0.444951\pi$
$757$	18.4535	−	3.25384i	0.670702	−	0.118263i	0.498621	+	0.866820i	$0.333840\pi$
$758$	−32.4946	+	18.5528i	−1.18026	+	0.673868i
$759$	2.67135			0.0969637
$760$	−25.8837	+	9.48876i	−0.938899	+	0.344193i
$761$	−11.3122			−0.410066			−0.205033	−	0.978755i	$-0.565730\pi$
$761$	−11.3122			−0.410066			−0.205033	+	0.978755i	$0.565730\pi$
$762$	3.59614	−	2.05321i	0.130274	−	0.0743801i
$763$	2.70505	−	0.476973i	0.0979294	−	0.0172676i
$764$	30.8904	+	18.2333i	1.11757	+	0.659658i
$765$	−13.4206	+	12.2814i	−0.485221	+	0.444036i
$766$	10.2068	−	8.48109i	0.368785	−	0.306434i
$767$	6.45551	−	11.1813i	0.233095	−	0.403733i
$768$	−2.28604	+	5.59994i	−0.0824902	+	0.202070i
$769$	33.0020	−	12.0117i	1.19008	−	0.433155i	0.330330	−	0.943865i	$-0.392840\pi$
$769$	33.0020	−	12.0117i	1.19008	−	0.433155i	0.859753	+	0.510711i	$0.170618\pi$
$770$	4.10065	−	12.7617i	0.147777	−	0.459899i
$771$	−5.38909	+	3.11139i	−0.194083	+	0.112054i
$772$	−18.0652	−	6.77288i	−0.650182	−	0.243761i
$773$	1.50636	−	8.54300i	0.0541800	−	0.307270i	−0.945660	−	0.325157i	$-0.894583\pi$
$773$	1.50636	−	8.54300i	0.0541800	−	0.307270i	0.999840	+	0.0178869i	$0.00569388\pi$
$774$	−0.164473	+	34.1663i	−0.00591185	+	1.22808i
$775$	−33.5168	−	23.5345i	−1.20396	−	0.845385i
$776$	−7.34261	+	19.3017i	−0.263584	+	0.692891i
$777$	0.665705	−	1.82901i	0.0238820	−	0.0656153i
$778$	24.2457	−	28.6140i	0.869250	−	1.02586i
$779$	24.9331	+	5.07372i	0.893320	+	0.181785i
$780$	1.91455	+	9.07684i	0.0685519	+	0.325003i
$781$	21.3174	−	58.5691i	0.762797	−	2.09577i
$782$	−2.64993	+	4.53920i	−0.0947611	+	0.162322i
$783$	−11.0276	−	9.25325i	−0.394094	−	0.330684i
$784$	13.1977	−	21.8752i	0.471345	−	0.781257i
$785$	−2.30245	+	17.4003i	−0.0821781	+	0.621045i
$786$	−1.15726	−	3.22781i	−0.0412782	−	0.115132i
$787$	−4.12491	+	2.38152i	−0.147037	+	0.0848920i	−0.571714	−	0.820453i	$-0.693721\pi$
$787$	−4.12491	+	2.38152i	−0.147037	+	0.0848920i	0.424676	+	0.905345i	$0.360388\pi$
$788$	−14.9937	+	8.46521i	−0.534129	+	0.301561i
$789$	2.41757	+	6.64221i	0.0860676	+	0.236469i
$790$	−3.47050	+	25.2908i	−0.123475	+	0.899807i
$791$	−6.90288	+	11.9561i	−0.245438	+	0.425111i
$792$	33.1055	+	28.6036i	1.17635	+	1.01638i
$793$	−36.2787	+	30.4414i	−1.28829	+	1.08101i
$794$	6.07967	+	35.4774i	0.215760	+	1.25905i
$795$	−0.806157	−	3.64771i	−0.0285914	−	0.129371i
$796$	20.0323	+	3.73145i	0.710028	+	0.132258i
$797$	−24.3395			−0.862149			−0.431075	−	0.902316i	$-0.641865\pi$
$797$	−24.3395			−0.862149			−0.431075	+	0.902316i	$0.641865\pi$
$798$	−0.372426	+	1.78612i	−0.0131837	+	0.0632279i
$799$			14.1493i			0.500568i
$800$	16.8061	−	22.7499i	0.594185	−	0.804329i
$801$	18.4153	−	3.24712i	0.650674	−	0.114731i
$802$	6.75685	+	39.4290i	0.238593	+	1.39229i
$803$	−34.1547	+	28.6592i	−1.20529	+	1.01136i
$804$	5.76795	+	0.0555339i	0.203420	+	0.00195853i
$805$	2.02614	+	1.05644i	0.0714121	+	0.0372346i
$806$	62.5403	+	11.3382i	2.20289	+	0.399372i
$807$	−7.07649	+	2.57563i	−0.249104	+	0.0906665i
$808$	8.45575	+	1.61722i	0.297472	+	0.0568935i
$809$	−18.6472	−	32.2980i	−0.655602	−	1.13554i	−0.981742	−	0.190215i	$-0.939081\pi$
$809$	−18.6472	−	32.2980i	−0.655602	−	1.13554i	0.326140	−	0.945321i	$-0.394252\pi$
$810$	−22.6469	+	9.23579i	−0.795731	+	0.324512i
$811$	6.26247	−	35.5162i	0.219905	−	1.24714i	−0.652284	−	0.757975i	$-0.726189\pi$
$811$	6.26247	−	35.5162i	0.219905	−	1.24714i	0.872189	−	0.489169i	$-0.162700\pi$
$812$	−6.61866	+	7.73533i	−0.232269	+	0.271457i
$813$	1.60293	+	1.34502i	0.0562172	+	0.0471718i
$814$	−25.3849	+	43.4831i	−0.889739	+	1.52408i
$815$	9.56314	−	30.2609i	0.334982	−	1.05999i
$816$	4.07381	−	1.39452i	0.142612	−	0.0488179i
$817$	34.9545	−	11.6941i	1.22290	−	0.409124i
$818$	−11.7873	−	9.98781i	−0.412134	−	0.349216i
$819$	−11.5339	−	4.19798i	−0.403026	−	0.146689i
$820$	−24.2194	+	9.74137i	−0.845779	+	0.340184i
$821$	14.8069	+	12.4244i	0.516763	+	0.433616i	0.863502	−	0.504346i	$-0.168266\pi$
$821$	14.8069	+	12.4244i	0.516763	+	0.433616i	−0.346739	+	0.937962i	$0.612711\pi$
$822$	−0.0344851	+	7.16367i	−0.00120281	+	0.249862i
$823$	−9.47272	+	53.7224i	−0.330198	+	1.87265i	0.140097	+	0.990138i	$0.455258\pi$
$823$	−9.47272	+	53.7224i	−0.330198	+	1.87265i	−0.470296	+	0.882509i	$0.655853\pi$
$824$	3.64878	+	6.53607i	0.127111	+	0.227695i
$825$	5.85861	+	8.39046i	0.203971	+	0.292118i
$826$	−0.902852	+	2.44390i	−0.0314142	+	0.0850340i
$827$	−2.07138	−	5.69107i	−0.0720289	−	0.197898i	0.898454	−	0.439068i	$-0.144691\pi$
$827$	−2.07138	−	5.69107i	−0.0720289	−	0.197898i	−0.970483	+	0.241170i	$0.922469\pi$
$828$	−5.75918	+	4.73879i	−0.200145	+	0.164684i
$829$	−0.258335	−	0.149150i	−0.00897234	−	0.00518018i	0.495507	−	0.868604i	$-0.334982\pi$
$829$	−0.258335	−	0.149150i	−0.00897234	−	0.00518018i	−0.504479	+	0.863424i	$0.668316\pi$
$830$	38.2910	−	34.7037i	1.32910	−	1.20458i
$831$	0.0323559	−	0.0271498i	0.00112241	−	0.000941818i
$832$	−8.86777	+	42.9913i	−0.307435	+	1.49046i
$833$	−17.9109	+	3.15818i	−0.620577	+	0.109424i
$834$	−5.88859	+	3.36209i	−0.203905	+	0.116420i
$835$	10.2408	−	0.440368i	0.354398	−	0.0152395i
$836$	17.7219	−	43.7447i	0.612925	−	1.51294i
$837$		−	18.1361i		−	0.626875i
$838$	18.7616	+	32.8603i	0.648109	+	1.13514i
$839$	−2.13709	−	12.1201i	−0.0737807	−	0.418431i	−0.999218	−	0.0395312i	$-0.987414\pi$
$839$	−2.13709	−	12.1201i	−0.0737807	−	0.418431i	0.925438	−	0.378900i	$-0.123698\pi$
$840$	−0.690161	−	1.74006i	−0.0238128	−	0.0600377i
$841$	−10.1647	+	8.52923i	−0.350508	+	0.294111i
$842$	−16.3126	+	13.5546i	−0.562168	+	0.467122i
$843$	−1.59277	+	2.75876i	−0.0548579	+	0.0950166i
$844$	−8.89307	+	7.31743i	−0.306112	+	0.251876i
$845$	14.6159	+	35.3516i	0.502801	+	1.21613i
$846$	−6.95759	+	18.8332i	−0.239207	+	0.647500i
$847$	7.16833	+	12.4159i	0.246307	+	0.426616i
$848$	3.40426	−	17.3464i	0.116903	−	0.595679i
$849$	−3.28524	−	0.579277i	−0.112749	−	0.0198807i
$850$	−20.0689	+	1.63188i	−0.688356	+	0.0559731i
$851$	−6.57511	−	5.51717i	−0.225392	−	0.189126i
$852$	−2.89812	−	8.20754i	−0.0992880	−	0.281186i
$853$	−9.76227	+	26.8216i	−0.334254	+	0.918355i	0.652738	+	0.757584i	$0.273620\pi$
$853$	−9.76227	+	26.8216i	−0.334254	+	0.918355i	−0.986992	+	0.160771i	$0.948602\pi$
$854$	6.17798	−	7.29107i	0.211406	−	0.249495i
$855$	18.2549	+	21.0295i	0.624304	+	0.719193i
$856$	3.23071	−	5.41367i	0.110423	−	0.185035i
$857$	4.28757	+	1.56055i	0.146461	+	0.0533073i	0.414210	−	0.910181i	$-0.364058\pi$
$857$	4.28757	+	1.56055i	0.146461	+	0.0533073i	−0.267750	+	0.963489i	$0.586280\pi$
$858$	−13.7158	−	8.00712i	−0.468251	−	0.273358i
$859$	−12.4711	+	14.8624i	−0.425507	+	0.507100i	−0.935621	−	0.353007i	$-0.885159\pi$
$859$	−12.4711	+	14.8624i	−0.425507	+	0.507100i	0.510113	+	0.860107i	$0.329604\pi$
$860$	−23.3285	+	29.7633i	−0.795495	+	1.01492i
$861$	−0.300013	+	1.70146i	−0.0102244	+	0.0579855i
$862$	−1.59484	−	4.44831i	−0.0543206	−	0.151510i
$863$	22.9706	−	13.2621i	0.781927	−	0.451446i	−0.0551859	−	0.998476i	$-0.517575\pi$
$863$	22.9706	−	13.2621i	0.781927	−	0.451446i	0.837113	+	0.547030i	$0.184242\pi$
$864$	12.5217	+	0.301447i	0.425998	+	0.0102554i
$865$	6.74834	+	16.3223i	0.229450	+	0.554976i
$866$	−4.70982	−	0.853866i	−0.160046	−	0.0290155i
$867$	2.91099	+	1.68066i	0.0988626	+	0.0570783i
$868$	−12.8252	−	0.123481i	−0.435316	−	0.00419123i
$869$	−28.0931	−	33.4800i	−0.952993	−	1.13573i
$870$	−1.64067	−	7.59707i	−0.0556238	−	0.257565i
$871$	41.2258	−	7.26922i	1.39688	−	0.246308i
$872$	−7.69277	+	6.26794i	−0.260510	+	0.212259i
$873$	20.8604			0.706018
$874$	6.83971	+	4.23718i	0.231357	+	0.143325i
$875$	1.12541	+	8.68084i	0.0380459	+	0.293466i
$876$	−1.14020	+	6.12117i	−0.0385237	+	0.206815i
$877$	−7.93741	−	45.0153i	−0.268027	−	1.52006i	−0.760274	−	0.649603i	$-0.774935\pi$
$877$	−7.93741	−	45.0153i	−0.268027	−	1.52006i	0.492246	−	0.870456i	$-0.336176\pi$
$878$	−30.1036	+	5.15878i	−1.01595	+	0.174100i
$879$	−1.80718	−	2.15372i	−0.0609548	−	0.0726431i
$880$	9.53746	+	47.4758i	0.321508	+	1.60041i
$881$	9.13383	−	15.8203i	0.307727	−	0.532998i	−0.670138	−	0.742236i	$-0.733765\pi$
$881$	9.13383	−	15.8203i	0.307727	−	0.532998i	0.977865	+	0.209238i	$0.0670985\pi$
$882$	−25.3930	−	4.60362i	−0.855027	−	0.155012i
$883$	9.93502	−	3.61605i	0.334340	−	0.121690i	−0.169395	−	0.985548i	$-0.554181\pi$
$883$	9.93502	−	3.61605i	0.334340	−	0.121690i	0.503734	+	0.863859i	$0.331959\pi$
$884$	27.2117	−	15.3633i	0.915228	−	0.516723i
$885$	−1.06760	−	1.67823i	−0.0358869	−	0.0564131i
$886$	−9.95944	−	27.7787i	−0.334594	−	0.933243i
$887$	−5.13370	−	0.905209i	−0.172373	−	0.0303940i	0.0867956	−	0.996226i	$-0.472337\pi$
$887$	−5.13370	−	0.905209i	−0.172373	−	0.0303940i	−0.259168	+	0.965832i	$0.583448\pi$
$888$	1.12088	+	6.94160i	0.0376143	+	0.232945i
$889$	−3.89808	+	4.64555i	−0.130738	+	0.155807i
$890$	18.3058	+	9.65706i	0.613610	+	0.323705i
$891$	14.3214	−	39.3478i	0.479786	−	1.31820i
$892$	−50.7716	+	8.44923i	−1.69996	+	0.282901i
$893$	21.6518	+	0.567832i	0.724551	+	0.0190018i
$894$	−3.74225	−	3.17095i	−0.125160	−	0.106052i
$895$	−0.750094	+	2.37354i	−0.0250729	+	0.0793388i
$896$	0.298428	−	8.85288i	0.00996979	−	0.295754i
$897$	1.74028	−	2.07398i	0.0581061	−	0.0692482i
$898$	12.7500	+	0.0613773i	0.425474	+	0.00204819i
$899$	−52.4435	−	9.24720i	−1.74909	−	0.308411i
$900$	−27.5148	−	7.69628i	−0.917159	−	0.256543i
$901$	−10.8982	+	6.29210i	−0.363073	+	0.209620i
$902$	15.4880	−	41.9240i	0.515695	−	1.39592i
$903$	0.856003	+	2.35185i	0.0284860	+	0.0782646i
$904$	0.720241	−	49.8693i	0.0239549	−	1.65863i
$905$	−6.18003	+	11.8527i	−0.205431	+	0.393996i
$906$	−6.05930	+	5.03485i	−0.201307	+	0.167272i
$907$	−20.3039	−	24.1972i	−0.674180	−	0.803456i	0.315166	−	0.949036i	$-0.397940\pi$
$907$	−20.3039	−	24.1972i	−0.674180	−	0.803456i	−0.989346	+	0.145580i	$0.953495\pi$
$908$	41.5537	+	24.5275i	1.37901	+	0.813972i
$909$	−1.51009	−	8.56413i	−0.0500864	−	0.284054i
$910$	−7.23650	−	11.4974i	−0.239887	−	0.381135i
$911$	−1.54324			−0.0511298			−0.0255649	−	0.999673i	$-0.508138\pi$
$911$	−1.54324			−0.0511298			−0.0255649	+	0.999673i	$0.508138\pi$
$912$	−1.97046	−	6.28986i	−0.0652483	−	0.208278i
$913$			88.4745i			2.92808i
$914$	−5.40959	−	9.47473i	−0.178933	−	0.313396i
$915$	1.57442	+	7.12396i	0.0520488	+	0.235511i
$916$	14.4105	−	24.4139i	0.476137	−	0.806657i
$917$	3.22785	+	3.84680i	0.106593	+	0.127032i
$918$	−5.69853	−	6.85802i	−0.188079	−	0.226348i
$919$	37.9219	+	21.8942i	1.25093	+	0.722225i	0.971294	−	0.237882i	$-0.0764530\pi$
$919$	37.9219	+	21.8942i	1.25093	+	0.722225i	0.279635	+	0.960106i	$0.409786\pi$
$920$	−8.25148	+	0.235505i	−0.272043	+	0.00776437i
$921$	9.08152	−	3.30540i	0.299246	−	0.108917i
$922$	−2.32020	+	6.28045i	−0.0764116	+	0.206836i
$923$	−31.5845	−	54.7059i	−1.03961	−	1.80067i
$924$	3.00088	+	1.12507i	0.0987218	+	0.0370120i
$925$	2.90887	−	32.7517i	0.0956431	−	1.07687i
$926$	0.0272690	−	5.66464i	0.000896114	−	0.186152i
$927$	4.86039	−	5.79239i	0.159636	−	0.190247i
$928$	7.25624	−	36.0549i	0.238198	−	1.18356i
$929$	−19.6655	−	7.15767i	−0.645205	−	0.234836i	−0.00136932	−	0.999999i	$-0.500436\pi$
$929$	−19.6655	−	7.15767i	−0.645205	−	0.234836i	−0.643836	+	0.765164i	$0.722658\pi$
$930$	6.00328	−	7.73561i	0.196855	−	0.253661i
$931$	4.11397	+	27.5347i	0.134830	+	0.902413i
$932$	19.8305	−	3.30013i	0.649571	−	0.108099i
$933$	1.18431	+	0.431052i	0.0387725	+	0.0141120i
$934$	−10.5592	−	6.16432i	−0.345508	−	0.201703i
$935$	21.0035	−	27.3350i	0.686888	−	0.893951i
$936$	43.7742	−	7.06836i	1.43080	−	0.231037i
$937$	38.2697	+	6.74797i	1.25022	+	0.220447i	0.759289	−	0.650754i	$-0.225547\pi$
$937$	38.2697	+	6.74797i	1.25022	+	0.220447i	0.490927	+	0.871201i	$0.336658\pi$
$938$	−7.95172	+	2.85092i	−0.259633	+	0.0930857i
$939$	3.92968	+	6.80641i	0.128240	+	0.222119i
$940$	−18.8636	+	11.7464i	−0.615264	+	0.383126i
$941$	−5.77427	−	15.8647i	−0.188236	−	0.517174i	0.809295	−	0.587402i	$-0.199849\pi$
$941$	−5.77427	−	15.8647i	−0.188236	−	0.517174i	−0.997531	+	0.0702286i	$0.977627\pi$
$942$	−4.12922	−	0.748605i	−0.134537	−	0.0243909i
$943$	6.59811	+	3.80942i	0.214864	+	0.124052i
$944$	−1.45561	−	9.29877i	−0.0473760	−	0.302649i
$945$	−2.85969	+	2.61696i	−0.0930258	+	0.0851298i
$946$	−10.9356	−	63.8135i	−0.355546	−	2.07475i
$947$	−9.28634	−	52.6654i	−0.301765	−	1.71140i	−0.638353	−	0.769744i	$-0.720384\pi$
$947$	−9.28634	−	52.6654i	−0.301765	−	1.71140i	0.336587	−	0.941652i	$-0.390727\pi$
$948$	−6.00026	−	1.11768i	−0.194879	−	0.0363004i
$949$			45.1873i			1.46684i
$950$	1.69178	+	30.7756i	0.0548885	+	0.998492i
$951$			3.81746i			0.123790i
$952$	−4.88855	+	3.98311i	−0.158439	+	0.129093i
$953$	−1.55231	−	8.80356i	−0.0502841	−	0.285175i	0.949289	−	0.314406i	$-0.101805\pi$
$953$	−1.55231	−	8.80356i	−0.0502841	−	0.285175i	−0.999573	+	0.0292307i	$0.990694\pi$
$954$	−17.5999	+	3.01605i	−0.569818	+	0.0976484i
$955$	29.5856	−	27.0744i	0.957369	−	0.876108i
$956$	0.272521	−	28.3050i	0.00881395	−	0.915449i
$957$	11.5237	+	6.65324i	0.372510	+	0.215069i
$958$	−2.00239	+	11.0449i	−0.0646942	+	0.356845i
$959$	−3.58815	−	9.85835i	−0.115867	−	0.318343i
$960$	5.24112	+	4.27343i	0.169157	+	0.137924i
$961$	−18.0449	−	31.2547i	−0.582095	−	1.00822i
$962$	17.2222	+	48.0358i	0.555266	+	1.54874i
$963$	−6.27152	−	1.10584i	−0.202097	−	0.0356352i
$964$	−27.1073	+	31.6807i	−0.873067	+	1.02037i
$965$	−13.1425	+	17.1043i	−0.423071	+	0.550606i
$966$	−0.275438	+	0.471813i	−0.00886208	+	0.0151803i
$967$	32.8331	+	11.9503i	1.05584	+	0.384294i	0.810864	−	0.585235i	$-0.198998\pi$
$967$	32.8331	+	11.9503i	1.05584	+	0.384294i	0.244976	+	0.969529i	$0.421220\pi$
$968$	−44.4749	−	26.5413i	−1.42948	−	0.853069i
$969$	−2.45184	+	4.00068i	−0.0787644	+	0.128520i
$970$	18.2403	+	14.1555i	0.585661	+	0.454507i
$971$	34.5801	+	12.5861i	1.10973	+	0.403908i	0.830893	−	0.556432i	$-0.187830\pi$
$971$	34.5801	+	12.5861i	1.10973	+	0.403908i	0.278834	+	0.960339i	$0.410052\pi$
$972$	−6.37040	−	18.0411i	−0.204331	−	0.578668i
$973$	6.38302	−	7.60699i	0.204630	−	0.243869i
$974$	−45.1190	−	0.217198i	−1.44571	−	0.00695947i
$975$	10.3308	+	0.917542i	0.330852	+	0.0293849i
$976$	−6.64851	+	33.8776i	−0.212814	+	1.08439i
$977$	−20.0222	−	34.6795i	−0.640568	−	1.10950i	−0.985306	−	0.170797i	$-0.945366\pi$
$977$	−20.0222	−	34.6795i	−0.640568	−	1.10950i	0.344738	−	0.938699i	$-0.387968\pi$
$978$	7.11763	+	2.62947i	0.227597	+	0.0840813i
$979$	−33.2973	+	12.1192i	−1.06418	+	0.387332i
$980$	−19.0796	−	21.2567i	−0.609477	−	0.679019i
$981$	8.68065	+	5.01177i	0.277152	+	0.160014i
$982$	11.5685	−	9.61257i	0.369164	−	0.306749i
$983$	19.9627	+	23.7906i	0.636710	+	0.758802i	0.983847	−	0.179013i	$-0.0572904\pi$
$983$	19.9627	+	23.7906i	0.636710	+	0.758802i	−0.347137	+	0.937815i	$0.612846\pi$
$984$	−2.04979	−	5.89530i	−0.0653451	−	0.187935i
$985$	4.15423	+	18.7971i	0.132365	+	0.598926i
$986$	−22.7366	+	12.9815i	−0.724082	+	0.413415i
$987$			1.47071i			0.0468132i
$988$	−22.4174	−	42.2569i	−0.713193	−	1.34437i
$989$	11.0368			0.350950
$990$	41.3977	−	26.0559i	1.31571	−	0.828110i
$991$	2.95064	+	16.7339i	0.0937302	+	0.531570i	0.995129	+	0.0985806i	$0.0314302\pi$
$991$	2.95064	+	16.7339i	0.0937302	+	0.531570i	−0.901399	+	0.432990i	$0.857459\pi$
$992$	40.6727	−	22.1948i	1.29136	−	0.704684i
$993$	−0.814369	−	0.970528i	−0.0258432	−	0.0307988i
$994$	8.14648	+	9.80406i	0.258391	+	0.310966i
$995$	10.5329	−	20.2010i	0.333915	−	0.640416i
$996$	7.85052	+	9.54095i	0.248753	+	0.302317i
$997$	13.9350	+	38.2861i	0.441325	+	1.21253i	0.938621	+	0.344950i	$0.112104\pi$
$997$	13.9350	+	38.2861i	0.441325	+	1.21253i	−0.497296	+	0.867581i	$0.665674\pi$
$998$	23.9387	+	8.84370i	0.757766	+	0.279942i
$999$	12.6100	−	7.28040i	0.398964	−	0.230342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.319.48	yes	336
4.3	odd	2	inner	380.2.bb.a.319.35	yes	336
5.4	even	2	inner	380.2.bb.a.319.9	yes	336
19.14	odd	18	inner	380.2.bb.a.299.22	yes	336
20.19	odd	2	inner	380.2.bb.a.319.22	yes	336
76.71	even	18	inner	380.2.bb.a.299.9	✓	336
95.14	odd	18	inner	380.2.bb.a.299.35	yes	336
380.299	even	18	inner	380.2.bb.a.299.48	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.299.9	✓	336	76.71	even	18	inner
380.2.bb.a.299.22	yes	336	19.14	odd	18	inner
380.2.bb.a.299.35	yes	336	95.14	odd	18	inner
380.2.bb.a.299.48	yes	336	380.299	even	18	inner
380.2.bb.a.319.9	yes	336	5.4	even	2	inner
380.2.bb.a.319.22	yes	336	20.19	odd	2	inner
380.2.bb.a.319.35	yes	336	4.3	odd	2	inner
380.2.bb.a.319.48	yes	336	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22813 - 0.701203i) q^{2} +(0.372293 - 0.0656453i) q^{3} +(1.01663 - 1.72234i) q^{4} +(-1.50958 - 1.64960i) q^{5} +(0.411195 - 0.341674i) q^{6} +(-0.391468 + 0.678043i) q^{7} +(0.0408455 - 2.82813i) q^{8} +(-2.68479 + 0.977182i) q^{9} +O(q^{10})\)	\(q+(1.22813 - 0.701203i) q^{2} +(0.372293 - 0.0656453i) q^{3} +(1.01663 - 1.72234i) q^{4} +(-1.50958 - 1.64960i) q^{5} +(0.411195 - 0.341674i) q^{6} +(-0.391468 + 0.678043i) q^{7} +(0.0408455 - 2.82813i) q^{8} +(-2.68479 + 0.977182i) q^{9} +(-3.01067 - 0.967405i) q^{10} +(4.68866 - 2.70700i) q^{11} +(0.265420 - 0.707953i) q^{12} +(0.952816 - 5.40369i) q^{13} +(-0.00533007 + 1.10723i) q^{14} +(-0.670294 - 0.515036i) q^{15} +(-1.93293 - 3.50197i) q^{16} +(-0.973914 + 2.67581i) q^{17} +(-2.61207 + 3.08269i) q^{18} +(4.05553 + 1.59770i) q^{19} +(-4.37585 + 0.922986i) q^{20} +(-0.101230 + 0.278128i) q^{21} +(3.86015 - 6.61226i) q^{22} +(0.999845 + 0.838970i) q^{23} +(-0.170447 - 1.05557i) q^{24} +(-0.442338 + 4.98040i) q^{25} +(-2.61889 - 7.30457i) q^{26} +(-1.91755 + 1.10710i) q^{27} +(0.769844 + 1.36356i) q^{28} +(2.22363 + 6.10938i) q^{29} +(-1.18436 - 0.162522i) q^{30} +(-4.09542 + 7.09348i) q^{31} +(-4.82949 - 2.94551i) q^{32} +(1.56785 - 1.31559i) q^{33} +(0.680186 + 3.96916i) q^{34} +(1.70945 - 0.377795i) q^{35} +(-1.04639 + 5.61755i) q^{36} -6.57613 q^{37} +(6.10105 - 0.881558i) q^{38} -2.07430i q^{39} +(-4.72694 + 4.20191i) q^{40} +(5.74859 - 1.01363i) q^{41} +(0.0706998 + 0.412562i) q^{42} +(6.47766 - 5.43540i) q^{43} +(0.104247 - 10.8275i) q^{44} +(5.66485 + 2.95368i) q^{45} +(1.81623 + 0.329273i) q^{46} +(4.66931 - 1.69949i) q^{47} +(-0.949504 - 1.17687i) q^{48} +(3.19351 + 5.53131i) q^{49} +(2.94902 + 6.42676i) q^{50} +(-0.186927 + 1.06012i) q^{51} +(-8.33834 - 7.13462i) q^{52} +(3.38541 + 2.84069i) q^{53} +(-1.57871 + 2.70425i) q^{54} +(-11.5434 - 3.64797i) q^{55} +(1.90160 + 1.13482i) q^{56} +(1.61473 + 0.328587i) q^{57} +(7.01484 + 5.94393i) q^{58} +(2.21110 + 0.804774i) q^{59} +(-1.56851 + 0.630875i) q^{60} +(-6.61169 - 5.54787i) q^{61} +(-0.0557615 + 11.5835i) q^{62} +(0.388437 - 2.20293i) q^{63} +(-7.99666 - 0.231033i) q^{64} +(-10.3523 + 6.58553i) q^{65} +(1.00304 - 2.71510i) q^{66} +(2.60934 + 7.16910i) q^{67} +(3.61855 + 4.39772i) q^{68} +(0.427310 + 0.246707i) q^{69} +(1.83452 - 1.66265i) q^{70} +(8.81899 - 7.40001i) q^{71} +(2.65394 + 7.63284i) q^{72} +(-8.11016 + 1.43004i) q^{73} +(-8.07637 + 4.61120i) q^{74} +(0.162260 + 1.88320i) q^{75} +(6.87476 - 5.36075i) q^{76} +4.23882i q^{77} +(-1.45451 - 2.54752i) q^{78} +(-1.40179 - 7.94996i) q^{79} +(-2.85892 + 8.47506i) q^{80} +(5.92476 - 4.97146i) q^{81} +(6.34928 - 5.27580i) q^{82} +(-8.17090 + 14.1524i) q^{83} +(0.376119 + 0.457107i) q^{84} +(5.88420 - 2.43278i) q^{85} +(4.14412 - 11.2176i) q^{86} +(1.22890 + 2.12851i) q^{87} +(-7.46424 - 13.3707i) q^{88} +(-6.44549 - 1.13651i) q^{89} +(9.02833 - 0.344697i) q^{90} +(3.29093 + 2.76142i) q^{91} +(2.46146 - 0.869155i) q^{92} +(-1.05904 + 2.90970i) q^{93} +(4.54286 - 5.36134i) q^{94} +(-3.48659 - 9.10185i) q^{95} +(-1.99134 - 0.779560i) q^{96} +(-6.86096 - 2.49719i) q^{97} +(7.80063 + 4.55390i) q^{98} +(-9.94282 + 11.8494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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