LMFDB - Embedded newform 819.2.fy.a.50.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

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

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

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.13
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.572772 - 2.13762i) q^{2} +(1.16473 + 1.28195i) q^{3} +(-2.50928 + 1.44873i) q^{4} +(0.0776352 + 0.289738i) q^{5} +(2.07319 - 3.22402i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.40439 + 1.40439i) q^{8} +(-0.286797 + 2.98626i) q^{9} +O(q^{10})$	\(q+(-0.572772 - 2.13762i) q^{2} +(1.16473 + 1.28195i) q^{3} +(-2.50928 + 1.44873i) q^{4} +(0.0776352 + 0.289738i) q^{5} +(2.07319 - 3.22402i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.40439 + 1.40439i) q^{8} +(-0.286797 + 2.98626i) q^{9} +(0.574882 - 0.331908i) q^{10} +(3.00314 - 0.804690i) q^{11} +(-4.77984 - 1.52939i) q^{12} +(0.516596 - 3.56835i) q^{13} +(-1.91653 - 1.10651i) q^{14} +(-0.281006 + 0.436992i) q^{15} +(-0.699811 + 1.21211i) q^{16} +(-2.52643 + 4.37590i) q^{17} +(6.54774 - 1.09739i) q^{18} +(6.13911 - 1.64497i) q^{19} +(-0.614562 - 0.614562i) q^{20} +(1.73007 + 0.0828860i) q^{21} +(-3.44023 - 5.95866i) q^{22} +0.206800 q^{23} +(-0.164621 + 3.43611i) q^{24} +(4.25221 - 2.45501i) q^{25} +(-7.92365 + 0.939569i) q^{26} +(-4.16228 + 3.11053i) q^{27} +(-0.749919 + 2.79874i) q^{28} +(3.50782 + 2.02524i) q^{29} +(1.09507 + 0.350386i) q^{30} +(2.85055 - 0.763803i) q^{31} +(6.82873 + 1.82975i) q^{32} +(4.52943 + 2.91263i) q^{33} +(10.8011 + 2.89413i) q^{34} +(0.259772 + 0.149980i) q^{35} +(-3.60664 - 7.90885i) q^{36} +(-0.802929 - 0.215144i) q^{37} +(-7.03262 - 12.1809i) q^{38} +(5.17615 - 3.49392i) q^{39} +(-0.297876 + 0.515937i) q^{40} +(1.54465 - 1.54465i) q^{41} +(-0.813756 - 3.74569i) q^{42} -10.6346i q^{43} +(-6.36995 + 6.36995i) q^{44} +(-0.887500 + 0.148743i) q^{45} +(-0.118449 - 0.442059i) q^{46} +(-1.89014 + 7.05411i) q^{47} +(-2.36896 + 0.514658i) q^{48} -1.00000i q^{49} +(-7.68342 - 7.68342i) q^{50} +(-8.55230 + 1.85800i) q^{51} +(3.87330 + 9.70240i) q^{52} -1.18836i q^{53} +(9.03316 + 7.11573i) q^{54} +(0.466299 + 0.807654i) q^{55} +1.98611 q^{56} +(9.25919 + 5.95409i) q^{57} +(2.32001 - 8.65838i) q^{58} +(2.04385 - 7.62776i) q^{59} +(0.0720381 - 1.50364i) q^{60} +12.1772 q^{61} +(-3.26543 - 5.65589i) q^{62} +(1.90881 + 2.31440i) q^{63} -12.8460i q^{64} +(1.07399 - 0.127352i) q^{65} +(3.63176 - 11.3505i) q^{66} +(2.10266 + 2.10266i) q^{67} -14.6405i q^{68} +(0.240867 + 0.265107i) q^{69} +(0.171808 - 0.641197i) q^{70} +(-3.05972 - 11.4190i) q^{71} +(-4.59666 + 3.79111i) q^{72} +(-4.73676 + 4.73676i) q^{73} +1.83958i q^{74} +(8.09989 + 2.59169i) q^{75} +(-13.0216 + 13.0216i) q^{76} +(1.55454 - 2.69254i) q^{77} +(-10.4334 - 9.06339i) q^{78} +(4.19096 + 7.25895i) q^{79} +(-0.405524 - 0.108660i) q^{80} +(-8.83550 - 1.71290i) q^{81} +(-4.18661 - 2.41714i) q^{82} +(-3.04444 - 0.815755i) q^{83} +(-4.46130 + 2.29842i) q^{84} +(-1.46401 - 0.392279i) q^{85} +(-22.7328 + 6.09123i) q^{86} +(1.48941 + 6.85572i) q^{87} +(5.34770 + 3.08749i) q^{88} +(-2.29317 + 8.55823i) q^{89} +(0.826290 + 1.81194i) q^{90} +(-2.15792 - 2.88849i) q^{91} +(-0.518919 + 0.299598i) q^{92} +(4.29929 + 2.76464i) q^{93} +16.1616 q^{94} +(0.953222 + 1.65103i) q^{95} +(5.60799 + 10.8853i) q^{96} +(5.89987 + 5.89987i) q^{97} +(-2.13762 + 0.572772i) q^{98} +(1.54172 + 9.19895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−0.572772	−	2.13762i	−0.405011	−	1.51152i	−0.804035	−	0.594582i	$-0.797318\pi$
$2$	−0.572772	−	2.13762i	−0.405011	−	1.51152i	0.399024	−	0.916940i	$-0.369349\pi$
$3$	1.16473	+	1.28195i	0.672459	+	0.740135i
$3$	1.16473	+	1.28195i	0.672459	+	0.740135i
$4$	−2.50928	+	1.44873i	−1.25464	+	0.724367i
$5$	0.0776352	+	0.289738i	0.0347195	+	0.129575i	0.981110	−	0.193449i	$-0.0619673\pi$
$5$	0.0776352	+	0.289738i	0.0347195	+	0.129575i	−0.946391	+	0.323024i	$0.895301\pi$
$6$	2.07319	−	3.22402i	0.846377	−	1.31620i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	1.40439	+	1.40439i	0.496528	+	0.496528i
$9$	−0.286797	+	2.98626i	−0.0955989	+	0.995420i
$10$	0.574882	−	0.331908i	0.181794	−	0.104959i
$11$	3.00314	−	0.804690i	0.905482	−	0.242623i	0.224113	−	0.974563i	$-0.428052\pi$
$11$	3.00314	−	0.804690i	0.905482	−	0.242623i	0.681369	+	0.731940i	$0.261385\pi$
$12$	−4.77984	−	1.52939i	−1.37982	−	0.441496i
$13$	0.516596	−	3.56835i	0.143278	−	0.989682i
$13$	0.516596	−	3.56835i	0.143278	−	0.989682i
$14$	−1.91653	−	1.10651i	−0.512215	−	0.295727i
$15$	−0.281006	+	0.436992i	−0.0725555	+	0.112831i
$16$	−0.699811	+	1.21211i	−0.174953	+	0.303027i
$17$	−2.52643	+	4.37590i	−0.612748	+	1.06131i	0.378027	+	0.925795i	$0.376603\pi$
$17$	−2.52643	+	4.37590i	−0.612748	+	1.06131i	−0.990775	+	0.135517i	$0.956731\pi$
$18$	6.54774	−	1.09739i	1.54332	−	0.258656i
$19$	6.13911	−	1.64497i	1.40841	−	0.377382i	0.527051	−	0.849833i	$-0.323298\pi$
$19$	6.13911	−	1.64497i	1.40841	−	0.377382i	0.881357	+	0.472452i	$0.156631\pi$
$20$	−0.614562	−	0.614562i	−0.137420	−	0.137420i
$21$	1.73007	+	0.0828860i	0.377531	+	0.0180872i
$22$	−3.44023	−	5.95866i	−0.733460	−	1.27039i
$23$	0.206800			0.0431208			0.0215604	−	0.999768i	$-0.493137\pi$
$23$	0.206800			0.0431208			0.0215604	+	0.999768i	$0.493137\pi$
$24$	−0.164621	+	3.43611i	−0.0336031	+	0.701392i
$25$	4.25221	−	2.45501i	0.850441	−	0.491002i
$26$	−7.92365	+	0.939569i	−1.55396	+	0.184265i
$27$	−4.16228	+	3.11053i	−0.801031	+	0.598623i
$28$	−0.749919	+	2.79874i	−0.141721	+	0.528912i
$29$	3.50782	+	2.02524i	0.651386	+	0.376078i	0.788987	−	0.614410i	$-0.210606\pi$
$29$	3.50782	+	2.02524i	0.651386	+	0.376078i	−0.137601	+	0.990488i	$0.543939\pi$
$30$	1.09507	+	0.350386i	0.199932	+	0.0639715i
$31$	2.85055	−	0.763803i	0.511974	−	0.137183i	0.00642230	−	0.999979i	$-0.497956\pi$
$31$	2.85055	−	0.763803i	0.511974	−	0.137183i	0.505552	+	0.862796i	$0.331289\pi$
$32$	6.82873	+	1.82975i	1.20716	+	0.323458i
$33$	4.52943	+	2.91263i	0.788473	+	0.507025i
$34$	10.8011	+	2.89413i	1.85237	+	0.496340i
$35$	0.259772	+	0.149980i	0.0439095	+	0.0253512i
$36$	−3.60664	−	7.90885i	−0.601107	−	1.31814i
$37$	−0.802929	−	0.215144i	−0.132001	−	0.0353695i	0.192214	−	0.981353i	$-0.438433\pi$
$37$	−0.802929	−	0.215144i	−0.132001	−	0.0353695i	−0.324214	+	0.945984i	$0.605100\pi$
$38$	−7.03262	−	12.1809i	−1.14084	−	1.97600i
$39$	5.17615	−	3.49392i	0.828847	−	0.559475i
$40$	−0.297876	+	0.515937i	−0.0470984	+	0.0815768i
$41$	1.54465	−	1.54465i	0.241234	−	0.241234i	−0.576126	−	0.817361i	$-0.695436\pi$
$41$	1.54465	−	1.54465i	0.241234	−	0.241234i	0.817361	+	0.576126i	$0.195436\pi$
$42$	−0.813756	−	3.74569i	−0.125565	−	0.577973i
$43$		−	10.6346i		−	1.62177i	−0.585207	−	0.810884i	$-0.698987\pi$
$43$		−	10.6346i		−	1.62177i	0.585207	−	0.810884i	$-0.301013\pi$
$44$	−6.36995	+	6.36995i	−0.960305	+	0.960305i
$45$	−0.887500	+	0.148743i	−0.132301	+	0.0221733i
$46$	−0.118449	−	0.442059i	−0.0174644	−	0.0651780i
$47$	−1.89014	+	7.05411i	−0.275706	+	1.02895i	0.679661	+	0.733526i	$0.262127\pi$
$47$	−1.89014	+	7.05411i	−0.275706	+	1.02895i	−0.955367	+	0.295422i	$0.904540\pi$
$48$	−2.36896	+	0.514658i	−0.341929	+	0.0742845i
$49$		−	1.00000i		−	0.142857i
$50$	−7.68342	−	7.68342i	−1.08660	−	1.08660i
$51$	−8.55230	+	1.85800i	−1.19756	+	0.260172i
$52$	3.87330	+	9.70240i	0.537131	+	1.34548i
$53$		−	1.18836i		−	0.163233i	−0.996664	−	0.0816167i	$-0.973992\pi$
$53$		−	1.18836i		−	0.163233i	0.996664	−	0.0816167i	$-0.0260083\pi$
$54$	9.03316	+	7.11573i	1.22926	+	0.968328i
$55$	0.466299	+	0.807654i	0.0628758	+	0.108904i
$56$	1.98611			0.265405
$57$	9.25919	+	5.95409i	1.22641	+	0.788638i
$58$	2.32001	−	8.65838i	0.304632	−	1.13690i
$59$	2.04385	−	7.62776i	0.266087	−	0.993049i	−0.695495	−	0.718531i	$-0.744815\pi$
$59$	2.04385	−	7.62776i	0.266087	−	0.993049i	0.961582	−	0.274519i	$-0.0885185\pi$
$60$	0.0720381	−	1.50364i	0.00930007	−	0.194119i
$61$	12.1772			1.55913			0.779563	−	0.626323i	$-0.215441\pi$
$61$	12.1772			1.55913			0.779563	+	0.626323i	$0.215441\pi$
$62$	−3.26543	−	5.65589i	−0.414710	−	0.718299i
$63$	1.90881	+	2.31440i	0.240487	+	0.291587i
$64$		−	12.8460i		−	1.60575i
$65$	1.07399	−	0.127352i	0.133213	−	0.0157960i
$66$	3.63176	−	11.3505i	0.447039	−	1.39714i
$67$	2.10266	+	2.10266i	0.256881	+	0.256881i	0.823784	−	0.566904i	$-0.191859\pi$
$67$	2.10266	+	2.10266i	0.256881	+	0.256881i	−0.566904	+	0.823784i	$0.691859\pi$
$68$		−	14.6405i		−	1.77542i
$69$	0.240867	+	0.265107i	0.0289969	+	0.0319152i
$70$	0.171808	−	0.641197i	0.0205350	−	0.0766378i
$71$	−3.05972	−	11.4190i	−0.363122	−	1.35519i	−0.869948	−	0.493143i	$-0.835848\pi$
$71$	−3.05972	−	11.4190i	−0.363122	−	1.35519i	0.506826	−	0.862048i	$-0.330819\pi$
$72$	−4.59666	+	3.79111i	−0.541722	+	0.446786i
$73$	−4.73676	+	4.73676i	−0.554396	+	0.554396i	−0.927706	−	0.373311i	$-0.878223\pi$
$73$	−4.73676	+	4.73676i	−0.554396	+	0.554396i	0.373311	+	0.927706i	$0.378223\pi$
$74$			1.83958i			0.213847i
$75$	8.09989	+	2.59169i	0.935294	+	0.299262i
$76$	−13.0216	+	13.0216i	−1.49368	+	1.49368i
$77$	1.55454	−	2.69254i	0.177156	−	0.306844i
$78$	−10.4334	−	9.06339i	−1.18135	−	1.02623i
$79$	4.19096	+	7.25895i	0.471519	+	0.816696i	0.999469	−	0.0325800i	$-0.0103724\pi$
$79$	4.19096	+	7.25895i	0.471519	+	0.816696i	−0.527950	+	0.849276i	$0.677039\pi$
$80$	−0.405524	−	0.108660i	−0.0453390	−	0.0121485i
$81$	−8.83550	−	1.71290i	−0.981722	−	0.190322i
$82$	−4.18661	−	2.41714i	−0.462334	−	0.266929i
$83$	−3.04444	−	0.815755i	−0.334171	−	0.0895408i	0.0878321	−	0.996135i	$-0.472006\pi$
$83$	−3.04444	−	0.815755i	−0.334171	−	0.0895408i	−0.422003	+	0.906595i	$0.638673\pi$
$84$	−4.46130	+	2.29842i	−0.486768	+	0.250778i
$85$	−1.46401	−	0.392279i	−0.158794	−	0.0425486i
$86$	−22.7328	+	6.09123i	−2.45134	+	0.656834i
$87$	1.48941	+	6.85572i	0.159682	+	0.735011i
$88$	5.34770	+	3.08749i	0.570066	+	0.329128i
$89$	−2.29317	+	8.55823i	−0.243076	+	0.907170i	0.731265	+	0.682093i	$0.238930\pi$
$89$	−2.29317	+	8.55823i	−0.243076	+	0.907170i	−0.974341	+	0.225077i	$0.927737\pi$
$90$	0.826290	+	1.81194i	0.0870986	+	0.190995i
$91$	−2.15792	−	2.88849i	−0.226211	−	0.302796i
$92$	−0.518919	+	0.299598i	−0.0541010	+	0.0312352i
$93$	4.29929	+	2.76464i	0.445815	+	0.286680i
$94$	16.1616			1.66694
$95$	0.953222	+	1.65103i	0.0977985	+	0.169392i
$96$	5.60799	+	10.8853i	0.572363	+	1.11097i
$97$	5.89987	+	5.89987i	0.599041	+	0.599041i	0.940057	−	0.341016i	$-0.110771\pi$
$97$	5.89987	+	5.89987i	0.599041	+	0.599041i	−0.341016	+	0.940057i	$0.610771\pi$
$98$	−2.13762	+	0.572772i	−0.215932	+	0.0578587i
$99$	1.54172	+	9.19895i	0.154949	+	0.924529i
$100$	−7.11331	+	12.3206i	−0.711331	+	1.23206i
$101$	−0.469798	+	0.813714i	−0.0467466	+	0.0809676i	−0.888452	−	0.458970i	$-0.848219\pi$
$101$	−0.469798	+	0.813714i	−0.0467466	+	0.0809676i	0.841705	+	0.539937i	$0.181552\pi$
$102$	8.87020	+	17.2173i	0.878281	+	1.70477i
$103$	−9.07192	−	5.23768i	−0.893883	−	0.516084i	−0.0186725	−	0.999826i	$-0.505944\pi$
$103$	−9.07192	−	5.23768i	−0.893883	−	0.516084i	−0.875211	+	0.483742i	$0.839277\pi$
$104$	5.73687	−	4.28586i	0.562547	−	0.420264i
$105$	0.110299	+	0.507702i	0.0107641	+	0.0495466i
$106$	−2.54025	+	0.680658i	−0.246731	+	0.0661114i
$107$	−11.8182	+	6.82326i	−1.14251	+	0.659629i	−0.947051	−	0.321083i	$-0.895953\pi$
$107$	−11.8182	+	6.82326i	−1.14251	+	0.659629i	−0.195460	+	0.980712i	$0.562620\pi$
$108$	5.93799	−	13.8352i	0.571383	−	1.33130i
$109$	−6.05433	−	6.05433i	−0.579900	−	0.579900i	0.354976	−	0.934875i	$-0.384489\pi$
$109$	−6.05433	−	6.05433i	−0.579900	−	0.579900i	−0.934875	+	0.354976i	$0.884489\pi$
$110$	1.45937	−	1.45937i	0.139145	−	0.139145i
$111$	−0.659393	−	1.27990i	−0.0625868	−	0.121483i
$112$	0.362249	+	1.35193i	0.0342293	+	0.127745i
$113$	−16.9978	+	9.81368i	−1.59902	+	0.923193i	−0.607341	+	0.794442i	$0.707764\pi$
$113$	−16.9978	+	9.81368i	−1.59902	+	0.923193i	−0.991677	+	0.128752i	$0.958903\pi$
$114$	7.42414	−	23.2029i	0.695334	−	2.17315i
$115$	0.0160550	+	0.0599179i	0.00149713	+	0.00558737i
$116$	−11.7361			−1.08967
$117$	10.5079	+	2.56608i	0.971452	+	0.237234i
$118$	−17.4759			−1.60878
$119$	1.30777	+	4.88068i	0.119883	+	0.447411i
$120$	−1.00835	+	0.219066i	−0.0920496	+	0.0199979i
$121$	−1.15493	+	0.666802i	−0.104994	+	0.0606183i
$122$	−6.97474	−	26.0301i	−0.631464	−	2.35665i
$123$	3.77928	+	0.181062i	0.340766	+	0.0163258i
$124$	−6.04628	+	6.04628i	−0.542972	+	0.542972i
$125$	2.10195	+	2.10195i	0.188004	+	0.188004i
$126$	3.85398	−	5.40592i	0.343340	−	0.481598i
$127$	−8.03784	+	4.64065i	−0.713243	+	0.411791i	−0.812261	−	0.583295i	$-0.801763\pi$
$127$	−8.03784	+	4.64065i	−0.713243	+	0.411791i	0.0990176	+	0.995086i	$0.468430\pi$
$128$	−13.8023	+	3.69832i	−1.21996	+	0.326888i
$129$	13.6331	−	12.3865i	1.20033	−	1.09057i
$130$	−0.887383	−	2.22284i	−0.0778287	−	0.194956i
$131$	−10.3878	−	5.99737i	−0.907582	−	0.523993i	−0.0279298	−	0.999610i	$-0.508891\pi$
$131$	−10.3878	−	5.99737i	−0.907582	−	0.523993i	−0.879652	+	0.475617i	$0.842225\pi$
$132$	−15.5852	−	0.746676i	−1.35652	−	0.0649898i
$133$	3.17784	−	5.50417i	0.275553	−	0.477272i
$134$	3.29033	−	5.69902i	0.284241	−	0.492320i
$135$	−1.22438	−	0.964486i	−0.105378	−	0.0830097i
$136$	−9.69358	+	2.59739i	−0.831218	+	0.222724i
$137$	4.99475	+	4.99475i	0.426730	+	0.426730i	0.887513	−	0.460783i	$-0.152431\pi$
$137$	4.99475	+	4.99475i	0.426730	+	0.426730i	−0.460783	+	0.887513i	$0.652431\pi$
$138$	0.428736	−	0.666726i	0.0364964	−	0.0567555i
$139$	5.31510	+	9.20603i	0.450821	+	0.780845i	0.998437	−	0.0558846i	$-0.0177979\pi$
$139$	5.31510	+	9.20603i	0.450821	+	0.780845i	−0.547616	+	0.836730i	$0.684465\pi$
$140$	−0.869122			−0.0734542
$141$	−11.2445	+	5.79308i	−0.946961	+	0.487866i
$142$	−22.6570	+	13.0810i	−1.90133	+	1.09774i
$143$	−1.32000	−	11.1320i	−0.110384	−	0.930902i
$144$	−3.41897	−	2.43745i	−0.284914	−	0.203121i
$145$	−0.314460	+	1.17358i	−0.0261145	+	0.0974606i
$146$	12.8384	+	7.41228i	1.06252	+	0.613445i
$147$	1.28195	−	1.16473i	0.105734	−	0.0960655i
$148$	2.32646	−	0.623373i	0.191234	−	0.0512409i
$149$	−21.9355	−	5.87760i	−1.79702	−	0.481511i	−0.803518	−	0.595281i	$-0.797041\pi$
$149$	−21.9355	−	5.87760i	−1.79702	−	0.481511i	−0.993507	+	0.113770i	$0.963707\pi$
$150$	0.900639	−	18.7989i	0.0735369	−	1.53492i
$151$	10.3077	+	2.76195i	0.838831	+	0.224764i	0.652563	−	0.757735i	$-0.273694\pi$
$151$	10.3077	+	2.76195i	0.838831	+	0.224764i	0.186268	+	0.982499i	$0.440361\pi$
$152$	10.9319	+	6.31154i	0.886695	+	0.511934i
$153$	−12.3430	−	8.79956i	−0.997872	−	0.711402i
$154$	−6.64602	−	1.78080i	−0.535552	−	0.143501i
$155$	0.442606	+	0.766616i	0.0355510	+	0.0615761i
$156$	−7.92664	+	16.2661i	−0.634639	+	1.30233i
$157$	−5.94363	+	10.2947i	−0.474354	+	0.821605i	−0.999569	−	0.0293649i	$-0.990652\pi$
$157$	−5.94363	+	10.2947i	−0.474354	+	0.821605i	0.525215	+	0.850969i	$0.323985\pi$
$158$	13.1164	−	13.1164i	1.04348	−	1.04348i
$159$	1.52342	−	1.38412i	0.120815	−	0.109768i
$160$			2.12060i			0.167648i
$161$	0.146230	−	0.146230i	0.0115245	−	0.0115245i
$162$	1.39921	+	19.8680i	0.109932	+	1.56098i
$163$	−0.408776	−	1.52557i	−0.0320178	−	0.119492i	0.948067	−	0.318070i	$-0.103035\pi$
$163$	−0.408776	−	1.52557i	−0.0320178	−	0.119492i	−0.980085	+	0.198577i	$0.936368\pi$
$164$	−1.63818	+	6.11376i	−0.127920	+	0.477405i
$165$	−0.492259	+	1.53847i	−0.0383223	+	0.119770i
$166$			6.97508i			0.541371i
$167$	14.6953	+	14.6953i	1.13716	+	1.13716i	0.988958	+	0.148199i	$0.0473476\pi$
$167$	14.6953	+	14.6953i	1.13716	+	1.13716i	0.148199	+	0.988958i	$0.452652\pi$
$168$	2.31329	+	2.54610i	0.178474	+	0.196436i
$169$	−12.4663	−	3.68679i	−0.958943	−	0.283599i
$170$			3.35417i			0.257253i
$171$	3.15163	+	18.8047i	0.241011	+	1.43803i
$172$	15.4068	+	26.6853i	1.17475	+	2.03473i
$173$	21.0148			1.59772			0.798862	−	0.601515i	$-0.205436\pi$
$173$	21.0148			1.59772			0.798862	+	0.601515i	$0.205436\pi$
$174$	13.8018	−	7.11056i	1.04631	−	0.539050i
$175$	1.27081	−	4.74272i	0.0960640	−	0.358516i
$176$	−1.12626	+	4.20327i	−0.0848952	+	0.316833i
$177$	12.1590	−	6.26418i	0.913923	−	0.470845i
$178$	19.6077			1.46966
$179$	−0.122924	−	0.212910i	−0.00918775	−	0.0159137i	0.861395	−	0.507936i	$-0.169591\pi$
$179$	−0.122924	−	0.212910i	−0.00918775	−	0.0159137i	−0.870583	+	0.492022i	$0.836258\pi$
$180$	2.01150	−	1.65899i	0.149928	−	0.123654i
$181$		−	23.7795i		−	1.76752i	−0.467943	−	0.883759i	$-0.655005\pi$
$181$		−	23.7795i		−	1.76752i	0.467943	−	0.883759i	$-0.344995\pi$
$182$	−4.93849	+	6.26724i	−0.366065	+	0.464559i
$183$	14.1831	+	15.6105i	1.04845	+	1.15396i
$184$	0.290429	+	0.290429i	0.0214107	+	0.0214107i
$185$		−	0.249342i		−	0.0183320i
$186$	3.44722	−	10.7737i	0.252763	−	0.789968i
$187$	−4.06598	+	15.1744i	−0.297334	+	1.10967i
$188$	−5.47663	−	20.4391i	−0.399424	−	1.49067i
$189$	−0.743697	+	5.14266i	−0.0540960	+	0.374073i
$190$	2.98328	−	2.98328i	0.216430	−	0.216430i
$191$		−	14.8921i		−	1.07755i	−0.842449	−	0.538777i	$-0.818887\pi$
$191$		−	14.8921i		−	1.07755i	0.842449	−	0.538777i	$-0.181113\pi$
$192$	16.4679	−	14.9621i	1.18847	−	1.07980i
$193$	−17.3601	+	17.3601i	−1.24960	+	1.24960i	−0.293710	+	0.955895i	$0.594890\pi$
$193$	−17.3601	+	17.3601i	−1.24960	+	1.24960i	−0.955895	+	0.293710i	$0.905110\pi$
$194$	9.23237	−	15.9909i	0.662845	−	1.14808i
$195$	1.41417	+	1.22848i	0.101271	+	0.0879731i
$196$	1.44873	+	2.50928i	0.103481	+	0.179234i
$197$	9.38467	+	2.51461i	0.668630	+	0.179159i	0.577138	−	0.816647i	$-0.304170\pi$
$197$	9.38467	+	2.51461i	0.668630	+	0.179159i	0.0914923	+	0.995806i	$0.470836\pi$
$198$	18.7808	−	8.56451i	1.33469	−	0.608653i
$199$	18.8817	+	10.9014i	1.33849	+	0.772777i	0.986583	−	0.163258i	$-0.0522004\pi$
$199$	18.8817	+	10.9014i	1.33849	+	0.772777i	0.351906	+	0.936035i	$0.385534\pi$
$200$	9.41957	+	2.52397i	0.666064	+	0.178471i
$201$	−0.246470	+	5.14454i	−0.0173847	+	0.362868i
$202$	2.00849	+	0.538174i	0.141317	+	0.0378658i
$203$	3.91247	−	1.04834i	0.274601	−	0.0735792i
$204$	18.7684	−	17.0522i	1.31405	−	1.19389i
$205$	0.567465	+	0.327626i	0.0396335	+	0.0228824i
$206$	−5.99999	+	22.3923i	−0.418039	+	1.56014i
$207$	−0.0593095	+	0.617558i	−0.00412230	+	0.0429233i
$208$	3.96371	+	3.12334i	0.274834	+	0.216565i
$209$	17.1129	−	9.88016i	1.18373	−	0.683425i
$210$	1.02209	−	0.526574i	0.0705312	−	0.0363370i
$211$	−4.32162			−0.297513			−0.148756	−	0.988874i	$-0.547527\pi$
$211$	−4.32162			−0.297513			−0.148756	+	0.988874i	$0.547527\pi$
$212$	1.72161	+	2.98192i	0.118241	+	0.204799i
$213$	11.0749	−	17.2226i	0.758839	−	1.18007i
$214$	21.3546	+	21.3546i	1.45977	+	1.45977i
$215$	3.08126	−	0.825622i	0.210140	−	0.0563070i
$216$	−10.2139	−	1.47707i	−0.694967	−	0.100502i
$217$	1.47555	−	2.55573i	0.100167	−	0.173494i
$218$	−9.47408	+	16.4096i	−0.641665	+	1.11140i
$219$	−11.5893	−	0.555236i	−0.783135	−	0.0375194i
$220$	−2.34015	−	1.35109i	−0.157773	−	0.0910902i
$221$	14.3096	+	11.2757i	0.962568	+	0.758489i
$222$	−2.35825	+	2.14262i	−0.158276	+	0.143803i
$223$	−9.12408	+	2.44479i	−0.610993	+	0.163715i	−0.551030	−	0.834485i	$-0.685765\pi$
$223$	−9.12408	+	2.44479i	−0.610993	+	0.163715i	−0.0599633	+	0.998201i	$0.519098\pi$
$224$	6.12247	−	3.53481i	0.409075	−	0.236179i
$225$	6.11179	+	13.4023i	0.407452	+	0.893485i
$226$	30.7137	+	30.7137i	2.04305	+	2.04305i
$227$	−10.8762	+	10.8762i	−0.721878	+	0.721878i	−0.968988	−	0.247109i	$-0.920519\pi$
$227$	−10.8762	+	10.8762i	−0.721878	+	0.721878i	0.247109	+	0.968988i	$0.420519\pi$
$228$	−31.8598	−	1.52638i	−2.10997	−	0.101087i
$229$	−5.78003	−	21.5714i	−0.381955	−	1.42548i	−0.842911	−	0.538053i	$-0.819160\pi$
$229$	−5.78003	−	21.5714i	−0.381955	−	1.42548i	0.460956	−	0.887423i	$-0.347507\pi$
$230$	0.118886	−	0.0686386i	0.00783908	−	0.00452590i
$231$	5.26234	−	1.14325i	0.346236	−	0.0752202i
$232$	2.08213	+	7.77060i	0.136698	+	0.510165i
$233$	12.0801			0.791395			0.395698	−	0.918381i	$-0.370503\pi$
$233$	12.0801			0.791395			0.395698	+	0.918381i	$0.370503\pi$
$234$	−0.533318	−	23.9316i	−0.0348641	−	1.56445i
$235$	−2.19059			−0.142898
$236$	5.92199	+	22.1012i	0.385489	+	1.43866i
$237$	−4.42427	+	13.8273i	−0.287388	+	0.898182i
$238$	9.68396	−	5.59104i	0.627718	−	0.362413i
$239$	1.11181	+	4.14932i	0.0719168	+	0.268397i	0.992517	−	0.122110i	$-0.0389662\pi$
$239$	1.11181	+	4.14932i	0.0719168	+	0.268397i	−0.920600	+	0.390508i	$0.872300\pi$
$240$	−0.333031	−	0.646422i	−0.0214970	−	0.0417264i
$241$	0.565180	−	0.565180i	0.0364064	−	0.0364064i	−0.688669	−	0.725076i	$-0.741805\pi$
$241$	0.565180	−	0.565180i	0.0364064	−	0.0364064i	0.725076	+	0.688669i	$0.241805\pi$
$242$	2.08688	+	2.08688i	0.134150	+	0.134150i
$243$	−8.09514	−	13.3217i	−0.519303	−	0.854590i
$244$	−30.5559	+	17.6415i	−1.95614	+	1.12938i
$245$	0.289738	−	0.0776352i	0.0185107	−	0.00495993i
$246$	−1.77763	−	8.18235i	−0.113337	−	0.521688i
$247$	−2.69839	−	22.7563i	−0.171694	−	1.44795i
$248$	5.07597	+	2.93061i	0.322325	+	0.186094i
$249$	−2.50020	−	4.85296i	−0.158444	−	0.307544i
$250$	3.28922	−	5.69709i	0.208028	−	0.360316i
$251$	−2.21548	+	3.83732i	−0.139840	+	0.242210i	−0.927436	−	0.373982i	$-0.877992\pi$
$251$	−2.21548	+	3.83732i	−0.139840	+	0.242210i	0.787596	+	0.616192i	$0.211325\pi$
$252$	−8.14268	−	3.04212i	−0.512941	−	0.191636i
$253$	0.621050	−	0.166410i	0.0390451	−	0.0104621i
$254$	14.5238	+	14.5238i	0.911303	+	0.911303i
$255$	−1.20229	−	2.33368i	−0.0752905	−	0.146141i
$256$	2.96517	+	5.13583i	0.185323	+	0.320989i
$257$	−10.1178			−0.631132			−0.315566	−	0.948904i	$-0.602194\pi$
$257$	−10.1178			−0.631132			−0.315566	+	0.948904i	$0.602194\pi$
$258$	−34.2862	−	22.0476i	−2.13457	−	1.37263i
$259$	−0.719886	+	0.415627i	−0.0447316	+	0.0258258i
$260$	−2.51045	+	1.87549i	−0.155692	+	0.116313i
$261$	−7.05393	+	9.89444i	−0.436627	+	0.612450i
$262$	−6.87026	+	25.6401i	−0.424446	+	1.58405i
$263$	17.5401	+	10.1268i	1.08157	+	0.624443i	0.931319	−	0.364205i	$-0.118659\pi$
$263$	17.5401	+	10.1268i	1.08157	+	0.624443i	0.150249	+	0.988648i	$0.451993\pi$
$264$	2.27062	+	10.4516i	0.139747	+	0.643251i
$265$	0.344313	−	0.0922583i	0.0211510	−	0.00566738i
$266$	−13.5860	−	3.64035i	−0.833010	−	0.223204i
$267$	−13.6422	+	7.02831i	−0.834887	+	0.430126i
$268$	−8.32234	−	2.22997i	−0.508368	−	0.136217i
$269$	−15.6346	−	9.02664i	−0.953258	−	0.550364i	−0.0591666	−	0.998248i	$-0.518844\pi$
$269$	−15.6346	−	9.02664i	−0.953258	−	0.550364i	−0.894092	+	0.447884i	$0.852178\pi$
$270$	−1.36041	+	3.16969i	−0.0827918	+	0.192901i
$271$	−8.64999	−	2.31776i	−0.525450	−	0.140794i	−0.0136635	−	0.999907i	$-0.504349\pi$
$271$	−8.64999	−	2.31776i	−0.525450	−	0.140794i	−0.511786	+	0.859113i	$0.671016\pi$
$272$	−3.53604	−	6.12460i	−0.214404	−	0.371359i
$273$	1.18951	−	6.13067i	0.0719926	−	0.371045i
$274$	7.81600	−	13.5377i	0.472182	−	0.817843i
$275$	10.7945	−	10.7945i	0.650930	−	0.650930i
$276$	−0.988471	−	0.316277i	−0.0594990	−	0.0190376i
$277$		−	21.5821i		−	1.29674i	−0.761325	−	0.648370i	$-0.775451\pi$
$277$		−	21.5821i		−	1.29674i	0.761325	−	0.648370i	$-0.224549\pi$
$278$	16.6346	−	16.6346i	0.997677	−	0.997677i
$279$	1.46338	+	8.73154i	0.0876105	+	0.522744i
$280$	0.154192	+	0.575453i	0.00921475	+	0.0343899i
$281$	−4.25599	+	15.8836i	−0.253891	+	0.947534i	0.714813	+	0.699315i	$0.246512\pi$
$281$	−4.25599	+	15.8836i	−0.253891	+	0.947534i	−0.968704	+	0.248218i	$0.920155\pi$
$282$	18.8239	+	20.7184i	1.12095	+	1.23376i
$283$			11.1717i			0.664088i	0.943264	+	0.332044i	$0.107738\pi$
$283$			11.1717i			0.664088i	−0.943264	+	0.332044i	$0.892262\pi$
$284$	24.2209	+	24.2209i	1.43724	+	1.43724i
$285$	−1.00629	+	3.14499i	−0.0596074	+	0.186293i
$286$	−23.0398	+	9.19774i	−1.36237	+	0.543874i
$287$		−	2.18447i		−	0.128945i
$288$	−7.42257	+	19.8676i	−0.437379	+	1.17071i
$289$	−4.26566	−	7.38834i	−0.250921	−	0.434608i
$290$	2.68878			0.157891
$291$	−0.691574	+	14.4351i	−0.0405408	+	0.846201i
$292$	5.02355	−	18.7481i	0.293981	−	1.09715i
$293$	5.19093	−	19.3728i	0.303258	−	1.13177i	−0.631177	−	0.775639i	$-0.717428\pi$
$293$	5.19093	−	19.3728i	0.303258	−	1.13177i	0.934435	−	0.356134i	$-0.115905\pi$
$294$	−3.22402	−	2.07319i	−0.188028	−	0.120911i
$295$	2.36873			0.137913
$296$	−0.825481	−	1.42978i	−0.0479801	−	0.0831040i
$297$	−9.99691	+	12.6907i	−0.580080	+	0.736391i
$298$			50.2561i			2.91126i
$299$	0.106832	−	0.737935i	0.00617826	−	0.0426759i
$300$	−24.0795	+	5.23131i	−1.39023	+	0.302030i
$301$	−7.51983	−	7.51983i	−0.433436	−	0.433436i
$302$		−	23.6159i		−	1.35894i
$303$	−1.59033	+	0.345501i	−0.0913621	+	0.0198485i
$304$	−2.30233	+	8.59243i	−0.132048	+	0.492810i
$305$	0.945377	+	3.52819i	0.0541321	+	0.202024i
$306$	−11.7403	+	31.4247i	−0.671151	+	1.79643i
$307$	9.40782	−	9.40782i	0.536933	−	0.536933i	−0.385694	−	0.922627i	$-0.626038\pi$
$307$	9.40782	−	9.40782i	0.536933	−	0.536933i	0.922627	+	0.385694i	$0.126038\pi$
$308$			9.00846i			0.513305i
$309$	−3.85192	−	17.7303i	−0.219128	−	1.00864i
$310$	1.38522	−	1.38522i	0.0786751	−	0.0786751i
$311$	−6.80279	+	11.7828i	−0.385751	+	0.668140i	−0.991873	−	0.127231i	$-0.959391\pi$
$311$	−6.80279	+	11.7828i	−0.385751	+	0.668140i	0.606122	+	0.795372i	$0.292724\pi$
$312$	12.1762	+	2.36250i	0.689341	+	0.133751i
$313$	−5.00263	−	8.66480i	−0.282765	−	0.489764i	0.689300	−	0.724476i	$-0.257918\pi$
$313$	−5.00263	−	8.66480i	−0.282765	−	0.489764i	−0.972065	+	0.234713i	$0.924585\pi$
$314$	25.4104	+	6.80870i	1.43399	+	0.384237i
$315$	−0.522380	+	0.732734i	−0.0294328	+	0.0412849i
$316$	−21.0326	−	12.1432i	−1.18317	−	0.683106i
$317$	−27.5625	−	7.38536i	−1.54807	−	0.414803i	−0.619205	−	0.785229i	$-0.712545\pi$
$317$	−27.5625	−	7.38536i	−1.54807	−	0.414803i	−0.928862	+	0.370426i	$0.879212\pi$
$318$	−3.83128	−	2.46369i	−0.214848	−	0.138157i
$319$	12.1642	+	3.25938i	0.681064	+	0.182490i
$320$	3.72197	−	0.997300i	0.208065	−	0.0557508i
$321$	−22.5122	−	7.20312i	−1.25651	−	0.402039i
$322$	−0.396339	−	0.228826i	−0.0220871	−	0.0127520i
$323$	−8.31179	+	31.0200i	−0.462480	+	1.72600i
$324$	24.6523	−	8.50213i	1.36957	−	0.472341i
$325$	−6.56367	−	16.4416i	−0.364087	−	0.912017i
$326$	−3.02695	+	1.74761i	−0.167647	+	0.0967913i
$327$	0.709680	−	14.8130i	0.0392454	−	0.819162i
$328$	4.33861			0.239559
$329$	3.65148	+	6.32455i	0.201313	+	0.348684i
$330$	3.57062	+	0.171065i	0.196556	+	0.00941683i
$331$	−18.8882	−	18.8882i	−1.03819	−	1.03819i	−0.999241	−	0.0389489i	$-0.987599\pi$
$331$	−18.8882	−	18.8882i	−1.03819	−	1.03819i	−0.0389489	−	0.999241i	$-0.512401\pi$
$332$	8.82116	−	2.36362i	0.484124	−	0.129721i
$333$	0.872754	−	2.33605i	0.0478266	−	0.128015i
$334$	22.9958	−	39.8300i	1.25828	−	2.17940i
$335$	−0.445980	+	0.772461i	−0.0243665	+	0.0422040i
$336$	−1.31119	+	2.03902i	−0.0715311	+	0.111238i
$337$	−17.2381	−	9.95241i	−0.939018	−	0.542142i	−0.0493656	−	0.998781i	$-0.515720\pi$
$337$	−17.2381	−	9.95241i	−0.939018	−	0.542142i	−0.889652	+	0.456639i	$0.849053\pi$
$338$	−0.740618	+	28.7598i	−0.0402843	+	1.56432i
$339$	−32.3785	−	10.3600i	−1.75856	−	0.562679i
$340$	4.24191	−	1.13662i	0.230050	−	0.0616416i
$341$	7.94599	−	4.58762i	0.430299	−	0.248433i
$342$	38.3921	−	17.5078i	2.07601	−	0.946714i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	14.9352	−	14.9352i	0.805253	−	0.805253i
$345$	−0.0581121	+	0.0903700i	−0.00312865	+	0.00486536i
$346$	−12.0367	−	44.9215i	−0.647096	−	2.41499i
$347$	−23.5787	+	13.6132i	−1.26577	+	0.730794i	−0.974185	−	0.225750i	$-0.927517\pi$
$347$	−23.5787	+	13.6132i	−1.26577	+	0.730794i	−0.291587	+	0.956544i	$0.594183\pi$
$348$	−13.6695	−	15.0452i	−0.732760	−	0.806505i
$349$	0.981251	+	3.66208i	0.0525251	+	0.196026i	0.987203	−	0.159470i	$-0.0509785\pi$
$349$	0.981251	+	3.66208i	0.0525251	+	0.196026i	−0.934678	+	0.355496i	$0.884312\pi$
$350$	−10.8660			−0.580812
$351$	8.94926	+	16.4594i	0.477676	+	0.878536i
$352$	21.9800			1.17154
$353$	2.44870	+	9.13865i	0.130331	+	0.486402i	0.999973	−	0.00728031i	$-0.00231741\pi$
$353$	2.44870	+	9.13865i	0.130331	+	0.486402i	−0.869643	+	0.493682i	$0.835651\pi$
$354$	−20.3547	−	22.4032i	−1.08184	−	1.19072i
$355$	3.07099	−	1.77304i	0.162991	−	0.0941032i
$356$	−6.64438	−	24.7972i	−0.352152	−	1.31425i
$357$	−4.73359	+	7.36119i	−0.250528	+	0.389595i
$358$	−0.384713	+	0.384713i	−0.0203327	+	0.0203327i
$359$	−8.61833	−	8.61833i	−0.454858	−	0.454858i	0.442105	−	0.896963i	$-0.354232\pi$
$359$	−8.61833	−	8.61833i	−0.454858	−	0.454858i	−0.896963	+	0.442105i	$0.854232\pi$
$360$	−1.45529	−	1.03751i	−0.0767006	−	0.0546813i
$361$	18.5282	−	10.6973i	0.975171	−	0.563015i
$362$	−50.8314	+	13.6202i	−2.67164	+	0.715864i
$363$	−2.20000	−	0.703924i	−0.115470	−	0.0369464i
$364$	9.59947	+	4.12179i	0.503149	+	0.216041i
$365$	−1.74016	−	1.00468i	−0.0910841	−	0.0525874i
$366$	25.2456	−	39.2594i	1.31961	−	2.05212i
$367$	−5.51551	+	9.55314i	−0.287907	+	0.498670i	−0.973310	−	0.229494i	$-0.926293\pi$
$367$	−5.51551	+	9.55314i	−0.287907	+	0.498670i	0.685403	+	0.728164i	$0.259626\pi$
$368$	−0.144721	+	0.250664i	−0.00754410	+	0.0130668i
$369$	4.16974	+	5.05574i	0.217068	+	0.263191i
$370$	−0.532997	+	0.142816i	−0.0277092	+	0.00742466i
$371$	−0.840296	−	0.840296i	−0.0436260	−	0.0436260i
$372$	−14.7933	−	0.708736i	−0.766999	−	0.0367463i
$373$	2.79008	+	4.83256i	0.144465	+	0.250221i	0.929173	−	0.369645i	$-0.120521\pi$
$373$	2.79008	+	4.83256i	0.144465	+	0.250221i	−0.784708	+	0.619865i	$0.787187\pi$
$374$	34.7660			1.79771
$375$	−0.246387	+	5.14280i	−0.0127234	+	0.265573i
$376$	−12.5613	+	7.25225i	−0.647797	+	0.374006i
$377$	9.03890	−	11.4709i	0.465527	−	0.590782i
$378$	11.4190	−	1.35583i	0.587329	−	0.0697366i
$379$	−0.321541	+	1.20001i	−0.0165165	+	0.0616402i	−0.973692	−	0.227867i	$-0.926825\pi$
$379$	−0.321541	+	1.20001i	−0.0165165	+	0.0616402i	0.957176	+	0.289507i	$0.0934915\pi$
$380$	−4.78380	−	2.76193i	−0.245404	−	0.141684i
$381$	−15.3110	−	4.89900i	−0.784407	−	0.250984i
$382$	−31.8336	+	8.52977i	−1.62875	+	0.436421i
$383$	27.9548	+	7.49048i	1.42843	+	0.382746i	0.888465	−	0.458944i	$-0.151772\pi$
$383$	27.9548	+	7.49048i	1.42843	+	0.382746i	0.539961	+	0.841690i	$0.318439\pi$
$384$	−20.8170	−	13.3863i	−1.06232	−	0.683118i
$385$	0.900821	+	0.241374i	0.0459101	+	0.0123016i
$386$	47.0525	+	27.1658i	2.39491	+	1.38270i
$387$	31.7578	+	3.04998i	1.61434	+	0.155039i
$388$	−23.3518	−	6.25708i	−1.18551	−	0.317655i
$389$	−2.26967	−	3.93119i	−0.115077	−	0.199319i	0.802734	−	0.596338i	$-0.203378\pi$
$389$	−2.26967	−	3.93119i	−0.115077	−	0.199319i	−0.917811	+	0.397019i	$0.870045\pi$
$390$	1.81601	−	3.72660i	0.0919573	−	0.188704i
$391$	−0.522465	+	0.904936i	−0.0264222	+	0.0457646i
$392$	1.40439	−	1.40439i	0.0709326	−	0.0709326i
$393$	−4.41062	−	20.3019i	−0.222486	−	1.02410i
$394$		−	21.5011i		−	1.08321i
$395$	−1.77783	+	1.77783i	−0.0894524	+	0.0894524i
$396$	−17.1954	−	20.8492i	−0.864103	−	1.04771i
$397$	6.58895	+	24.5903i	0.330690	+	1.23415i	0.908467	+	0.417956i	$0.137254\pi$
$397$	6.58895	+	24.5903i	0.330690	+	1.23415i	−0.577777	+	0.816194i	$0.696080\pi$
$398$	12.4880	−	46.6058i	0.625967	−	2.33614i
$399$	10.7574	−	2.33706i	0.538544	−	0.116999i
$400$			6.87218i			0.343609i
$401$	−0.115964	−	0.115964i	−0.00579095	−	0.00579095i	0.704205	−	0.709996i	$-0.251303\pi$
$401$	−0.115964	−	0.115964i	−0.00579095	−	0.00579095i	−0.709996	+	0.704205i	$0.751303\pi$
$402$	11.1382	−	2.41979i	0.555524	−	0.120688i
$403$	−1.25293	−	10.5663i	−0.0624130	−	0.526347i
$404$		−	2.72245i		−	0.135447i
$405$	−0.189653	−	2.69296i	−0.00942391	−	0.133814i
$406$	−4.48191	−	7.76289i	−0.222433	−	0.385266i
$407$	−2.58443			−0.128106
$408$	−14.6202	−	9.40143i	−0.723805	−	0.465440i
$409$	−7.00829	+	26.1553i	−0.346538	+	1.29330i	0.544268	+	0.838911i	$0.316807\pi$
$409$	−7.00829	+	26.1553i	−0.346538	+	1.29330i	−0.890806	+	0.454384i	$0.849859\pi$
$410$	0.375310	−	1.40068i	0.0185353	−	0.0691745i
$411$	−0.585477	+	12.2206i	−0.0288795	+	0.602796i
$412$	30.3520			1.49533
$413$	−3.94842	−	6.83886i	−0.194289	−	0.336518i
$414$	1.35407	−	0.226939i	0.0665491	−	0.0111535i
$415$		−	0.945422i		−	0.0464090i
$416$	10.0569	−	23.4221i	0.493080	−	1.14836i
$417$	−5.61100	+	17.5363i	−0.274772	+	0.858754i
$418$	−30.9218	−	30.9218i	−1.51243	−	1.51243i
$419$			29.5727i			1.44472i	0.691517	+	0.722360i	$0.256943\pi$
$419$			29.5727i			1.44472i	−0.691517	+	0.722360i	$0.743057\pi$
$420$	−1.01229	−	1.11417i	−0.0493949	−	0.0543660i
$421$	2.87745	−	10.7388i	0.140238	−	0.523377i	−0.859683	−	0.510828i	$-0.829339\pi$
$421$	2.87745	−	10.7388i	0.140238	−	0.523377i	0.999921	−	0.0125488i	$-0.00399451\pi$
$422$	2.47531	+	9.23797i	0.120496	+	0.449697i
$423$	−20.5233	−	7.66756i	−0.997879	−	0.372809i
$424$	1.66892	−	1.66892i	0.0810500	−	0.0810500i
$425$			24.8096i			1.20344i
$426$	−43.1586	−	13.8093i	−2.09104	−	0.669061i
$427$	8.61056	−	8.61056i	0.416694	−	0.416694i
$428$	19.7702	−	34.2429i	0.955626	−	1.65519i
$429$	12.7332	−	14.6579i	0.614764	−	0.707692i
$430$	−3.52972	−	6.11366i	−0.170218	−	0.294827i
$431$	−36.1109	−	9.67588i	−1.73940	−	0.466071i	−0.757086	−	0.653315i	$-0.773378\pi$
$431$	−36.1109	−	9.67588i	−1.73940	−	0.466071i	−0.982313	+	0.187245i	$0.940044\pi$
$432$	−0.857495	−	7.22192i	−0.0412562	−	0.347465i
$433$	−31.0144	−	17.9062i	−1.49046	−	0.860516i	−0.490518	−	0.871431i	$-0.663192\pi$
$433$	−31.0144	−	17.9062i	−1.49046	−	0.860516i	−0.999940	+	0.0109150i	$0.996526\pi$
$434$	−6.30833	−	1.69031i	−0.302809	−	0.0811376i
$435$	−1.87074	+	0.963785i	−0.0896949	+	0.0462100i
$436$	23.9631	+	6.42090i	1.14763	+	0.307505i
$437$	1.26957	−	0.340180i	0.0607316	−	0.0162730i
$438$	5.45117	+	25.0916i	0.260467	+	1.19892i
$439$	−0.416474	−	0.240452i	−0.0198772	−	0.0114761i	0.490028	−	0.871706i	$-0.336986\pi$
$439$	−0.416474	−	0.240452i	−0.0198772	−	0.0114761i	−0.509906	+	0.860230i	$0.670320\pi$
$440$	−0.479396	+	1.78913i	−0.0228543	+	0.0852935i
$441$	2.98626	+	0.286797i	0.142203	+	0.0136570i
$442$	15.9071	−	37.0469i	0.756622	−	1.76214i
$443$	0.332820	−	0.192154i	0.0158128	−	0.00912951i	−0.492073	−	0.870554i	$-0.663761\pi$
$443$	0.332820	−	0.192154i	0.0158128	−	0.00912951i	0.507886	+	0.861425i	$0.330427\pi$
$444$	3.50884	+	2.25634i	0.166522	+	0.107081i
$445$	−2.65768			−0.125986
$446$	10.4520	+	18.1035i	0.494918	+	0.857223i
$447$	−18.0142	−	34.9660i	−0.852041	−	1.65384i
$448$	−9.08348	−	9.08348i	−0.429154	−	0.429154i
$449$	25.5382	−	6.84293i	1.20522	−	0.322938i	0.400335	−	0.916369i	$-0.368894\pi$
$449$	25.5382	−	6.84293i	1.20522	−	0.322938i	0.804885	+	0.593431i	$0.202227\pi$
$450$	25.1483	−	20.7411i	1.18550	−	0.977745i
$451$	3.39585	−	5.88179i	0.159904	−	0.276962i
$452$	28.4348	−	49.2505i	1.33746	−	2.31655i
$453$	8.46506	+	16.4309i	0.397723	+	0.771992i
$454$	29.4787	+	17.0195i	1.38350	+	0.798766i
$455$	0.669377	−	0.849480i	0.0313809	−	0.0398242i
$456$	4.64166	+	21.3654i	0.217366	+	1.00053i
$457$	26.3157	−	7.05128i	1.23100	−	0.329845i	0.416030	−	0.909351i	$-0.363421\pi$
$457$	26.3157	−	7.05128i	1.23100	−	0.329845i	0.814968	+	0.579506i	$0.196754\pi$
$458$	−42.8006	+	24.7110i	−1.99994	+	1.15467i
$459$	−3.09569	−	26.0723i	−0.144494	−	1.21695i
$460$	−0.127091	−	0.127091i	−0.00592567	−	0.00592567i
$461$	3.78344	−	3.78344i	0.176212	−	0.176212i	−0.613490	−	0.789702i	$-0.710235\pi$
$461$	3.78344	−	3.78344i	0.176212	−	0.176212i	0.789702	+	0.613490i	$0.210235\pi$
$462$	−5.45794	−	10.5940i	−0.253927	−	0.492879i
$463$	3.80565	+	14.2029i	0.176864	+	0.660064i	0.996227	+	0.0867893i	$0.0276607\pi$
$463$	3.80565	+	14.2029i	0.176864	+	0.660064i	−0.819363	+	0.573275i	$0.805673\pi$
$464$	−4.90963	+	2.83457i	−0.227924	+	0.131592i
$465$	−0.467247	+	1.46030i	−0.0216680	+	0.0677199i
$466$	−6.91916	−	25.8226i	−0.320524	−	1.19621i
$467$	0.217737			0.0100756			0.00503782	−	0.999987i	$-0.498396\pi$
$467$	0.217737			0.0100756			0.00503782	+	0.999987i	$0.498396\pi$
$468$	−30.0847	+	8.78408i	−1.39067	+	0.406044i
$469$	2.97361			0.137308
$470$	1.25471	+	4.68264i	0.0578754	+	0.215994i
$471$	−20.1200	+	4.37110i	−0.927081	+	0.201409i
$472$	13.5827	−	7.84200i	0.625197	−	0.360957i
$473$	−8.55759	−	31.9373i	−0.393478	−	1.46848i
$474$	32.0916	+	1.53748i	1.47402	+	0.0706189i
$475$	22.0663	−	22.0663i	1.01247	−	1.01247i
$476$	−10.3524	−	10.3524i	−0.474500	−	0.474500i
$477$	3.54874	+	0.340817i	0.162486	+	0.0156049i
$478$	8.23283	−	4.75323i	0.376561	−	0.217408i
$479$	15.6337	−	4.18904i	0.714322	−	0.191402i	0.116685	−	0.993169i	$-0.462773\pi$
$479$	15.6337	−	4.18904i	0.714322	−	0.191402i	0.597637	+	0.801767i	$0.296106\pi$
$480$	−2.71850	+	2.46993i	−0.124082	+	0.112736i
$481$	−1.18250	+	2.75399i	−0.0539173	+	0.125571i
$482$	−1.53186	−	0.884417i	−0.0697741	−	0.0402841i
$483$	0.357778	+	0.0171408i	0.0162794	+	0.000779935i
$484$	1.93204	−	3.34638i	0.0878198	−	0.152108i
$485$	−1.25138	+	2.16746i	−0.0568223	+	0.0984191i
$486$	−23.8401	+	24.9346i	−1.08141	+	1.13106i
$487$	22.2327	−	5.95724i	1.00746	−	0.269948i	0.282893	−	0.959152i	$-0.408706\pi$
$487$	22.2327	−	5.95724i	1.00746	−	0.269948i	0.724568	+	0.689203i	$0.242039\pi$
$488$	17.1015	+	17.1015i	0.774150	+	0.774150i
$489$	1.47960	−	2.30092i	0.0669096	−	0.104051i
$490$	−0.331908	−	0.574882i	−0.0149941	−	0.0259705i
$491$	−7.47382			−0.337289			−0.168644	−	0.985677i	$-0.553939\pi$
$491$	−7.47382			−0.337289			−0.168644	+	0.985677i	$0.553939\pi$
$492$	−9.74558	+	5.02083i	−0.439365	+	0.226357i
$493$	−17.7245	+	10.2332i	−0.798272	+	0.460882i
$494$	−47.0986	+	18.8023i	−2.11907	+	0.845954i
$495$	−2.54560	+	1.16086i	−0.114416	+	0.0521767i
$496$	−1.06903	+	3.98969i	−0.0480011	+	0.179142i
$497$	−10.2380	−	5.91093i	−0.459239	−	0.265142i
$498$	−8.94171	+	8.12410i	−0.400688	+	0.364050i
$499$	−28.1882	+	7.55301i	−1.26188	+	0.338119i	−0.826914	−	0.562329i	$-0.809906\pi$
$499$	−28.1882	+	7.55301i	−1.26188	+	0.338119i	−0.434964	+	0.900448i	$0.643239\pi$
$500$	−8.31954	−	2.22921i	−0.372061	−	0.0996935i
$501$	−1.72256	+	35.9548i	−0.0769584	+	1.60634i
$502$	9.47169	+	2.53793i	0.422742	+	0.113273i
$503$	−21.9217	−	12.6565i	−0.977441	−	0.564326i	−0.0759444	−	0.997112i	$-0.524197\pi$
$503$	−21.9217	−	12.6565i	−0.977441	−	0.564326i	−0.901497	+	0.432786i	$0.857530\pi$
$504$	−0.569610	+	5.93105i	−0.0253725	+	0.264190i
$505$	−0.272237	−	0.0729457i	−0.0121144	−	0.00324604i
$506$	−0.711440	−	1.23225i	−0.0316274	−	0.0547802i
$507$	−9.79357	−	20.2753i	−0.434948	−	0.900456i
$508$	13.4461	−	23.2894i	0.596575	−	1.03330i
$509$	30.8975	−	30.8975i	1.36951	−	1.36951i	0.508366	−	0.861141i	$-0.330250\pi$
$509$	30.8975	−	30.8975i	1.36951	−	1.36951i	0.861141	−	0.508366i	$-0.169750\pi$
$510$	−4.29988	+	3.90671i	−0.190402	+	0.172992i
$511$			6.69879i			0.296337i
$512$	−10.9279	+	10.9279i	−0.482950	+	0.482950i
$513$	−20.4360	+	25.9427i	−0.902269	+	1.14540i
$514$	5.79520	+	21.6280i	0.255615	+	0.953970i
$515$	0.813256	−	3.03511i	0.0358363	−	0.133743i
$516$	−16.2645	+	50.8319i	−0.716004	+	2.23775i
$517$			22.7055i			0.998587i
$518$	1.30078	+	1.30078i	0.0571530	+	0.0571530i
$519$	24.4766	+	26.9399i	1.07440	+	1.18253i
$520$	1.68716	+	1.32946i	0.0739870	+	0.0583006i
$521$		−	41.2350i		−	1.80654i	−0.429073	−	0.903270i	$-0.641160\pi$
$521$		−	41.2350i		−	1.80654i	0.429073	−	0.903270i	$-0.358840\pi$
$522$	25.1908	+	9.41133i	1.10257	+	0.411923i
$523$	8.36684	+	14.4918i	0.365856	+	0.633682i	0.988913	−	0.148495i	$-0.0474429\pi$
$523$	8.36684	+	14.4918i	0.365856	+	0.633682i	−0.623057	+	0.782176i	$0.714110\pi$
$524$	34.7544			1.51825
$525$	7.56008	−	3.89489i	0.329949	−	0.169987i
$526$	11.6007	−	43.2943i	0.505813	−	1.88772i
$527$	−3.85938	+	14.4034i	−0.168117	+	0.627422i
$528$	−6.70017	+	3.45187i	−0.291588	+	0.150223i
$529$	−22.9572			−0.998141
$530$	−0.394426	−	0.683165i	−0.0171328	−	0.0296748i
$531$	22.1923	+	8.29109i	0.963064	+	0.359803i
$532$			18.4153i			0.798407i
$533$	−4.71391	−	6.30983i	−0.204182	−	0.273309i
$534$	22.8377	+	25.1361i	0.988283	+	1.08774i
$535$	−2.89447	−	2.89447i	−0.125139	−	0.125139i
$536$			5.90592i			0.255097i
$537$	0.129767	−	0.405566i	0.00559986	−	0.0175014i
$538$	−10.3404	+	38.5910i	−0.445807	+	1.66377i
$539$	−0.804690	−	3.00314i	−0.0346604	−	0.129355i
$540$	4.46960	+	0.646363i	0.192341	+	0.0278150i
$541$	19.6980	−	19.6980i	0.846884	−	0.846884i	−0.142859	−	0.989743i	$-0.545629\pi$
$541$	19.6980	−	19.6980i	0.846884	−	0.846884i	0.989743	+	0.142859i	$0.0456295\pi$
$542$			19.8179i			0.851252i
$543$	30.4842	−	27.6968i	1.30820	−	1.18858i
$544$	−25.2591	+	25.2591i	−1.08297	+	1.08297i
$545$	1.28414	−	2.22420i	0.0550067	−	0.0952743i
$546$	−13.7863	+	0.968756i	−0.590000	+	0.0414589i
$547$	−6.93495	−	12.0117i	−0.296517	−	0.513583i	0.678820	−	0.734305i	$-0.262492\pi$
$547$	−6.93495	−	12.0117i	−0.296517	−	0.513583i	−0.975337	+	0.220722i	$0.929159\pi$
$548$	−19.7693	−	5.29716i	−0.844502	−	0.226284i
$549$	−3.49237	+	36.3642i	−0.149051	+	1.55199i
$550$	−29.2572	−	16.8916i	−1.24753	−	0.720262i
$551$	24.8664	+	6.66292i	1.05934	+	0.283850i
$552$	−0.0340436	+	0.710587i	−0.00144899	+	0.0302446i
$553$	8.09631	+	2.16940i	0.344290	+	0.0922522i
$554$	−46.1341	+	12.3616i	−1.96005	+	0.525194i
$555$	0.319644	−	0.290417i	0.0135681	−	0.0123275i
$556$	−26.6742	−	15.4003i	−1.13124	−	0.653120i
$557$	−1.73589	+	6.47844i	−0.0735521	+	0.274500i	−0.992901	−	0.118943i	$-0.962049\pi$
$557$	−1.73589	+	6.47844i	−0.0735521	+	0.274500i	0.919349	+	0.393443i	$0.128716\pi$
$558$	17.8265	−	8.12934i	0.754655	−	0.344142i
$559$	−37.9481	−	5.49381i	−1.60503	−	0.232364i
$560$	−0.363583	+	0.209915i	−0.0153642	+	0.00887052i
$561$	−24.1887	+	12.4618i	−1.02125	+	0.526137i
$562$	36.3906			1.53505
$563$	6.64789	+	11.5145i	0.280175	+	0.485278i	0.971428	−	0.237336i	$-0.0762741\pi$
$563$	6.64789	+	11.5145i	0.280175	+	0.485278i	−0.691253	+	0.722613i	$0.742941\pi$
$564$	19.8231	−	30.8268i	0.834702	−	1.29804i
$565$	−4.16303	−	4.16303i	−0.175140	−	0.175140i
$566$	23.8808	−	6.39883i	1.00378	−	0.268963i
$567$	−7.45884	+	5.03644i	−0.313242	+	0.211510i
$568$	11.7398	−	20.3339i	0.492590	−	0.853191i
$569$	2.62541	−	4.54734i	0.110063	−	0.190634i	−0.805733	−	0.592279i	$-0.798228\pi$
$569$	2.62541	−	4.54734i	0.110063	−	0.190634i	0.915795	+	0.401645i	$0.131561\pi$
$570$	7.29915	+	0.349696i	0.305728	+	0.0146472i
$571$	29.2454	+	16.8848i	1.22388	+	0.706608i	0.965743	−	0.259500i	$-0.0835579\pi$
$571$	29.2454	+	16.8848i	1.22388	+	0.706608i	0.258138	+	0.966108i	$0.416891\pi$
$572$	19.4395	+	26.0209i	0.812807	+	1.08799i
$573$	19.0909	−	17.3453i	0.797535	−	0.724610i
$574$	−4.66956	+	1.25120i	−0.194904	+	0.0522243i
$575$	0.879356	−	0.507696i	0.0366717	−	0.0211724i
$576$	38.3614	+	3.68418i	1.59839	+	0.153508i
$577$	7.25160	+	7.25160i	0.301888	+	0.301888i	0.841752	−	0.539864i	$-0.181524\pi$
$577$	7.25160	+	7.25160i	0.301888	+	0.301888i	−0.539864	+	0.841752i	$0.681524\pi$
$578$	−13.3502	+	13.3502i	−0.555294	+	0.555294i
$579$	−42.4746	−	2.03492i	−1.76518	−	0.0845684i
$580$	−0.911137	−	3.40041i	−0.0378329	−	0.141194i
$581$	−2.72957	+	1.57592i	−0.113242	+	0.0653801i
$582$	31.2528	−	6.78971i	1.29547	−	0.281443i
$583$	−0.956259	−	3.56881i	−0.0396042	−	0.147805i
$584$	−13.3045			−0.550546
$585$	0.0722875	+	3.24375i	0.00298872	+	0.134113i
$586$	−44.3849			−1.83352
$587$	−1.87777	−	7.00792i	−0.0775037	−	0.289248i	0.916286	−	0.400525i	$-0.131172\pi$
$587$	−1.87777	−	7.00792i	−0.0775037	−	0.289248i	−0.993789	+	0.111278i	$0.964506\pi$
$588$	−1.52939	+	4.77984i	−0.0630708	+	0.197117i
$589$	16.2434	−	9.37813i	0.669298	−	0.386419i
$590$	−1.35674	−	5.06343i	−0.0558562	−	0.208458i
$591$	7.70701	+	14.9595i	0.317024	+	0.615353i
$592$	0.822676	−	0.822676i	0.0338118	−	0.0338118i
$593$	−24.9169	−	24.9169i	−1.02322	−	1.02322i	−0.999724	−	0.0234920i	$-0.992522\pi$
$593$	−24.9169	−	24.9169i	−1.02322	−	1.02322i	−0.0234920	−	0.999724i	$-0.507478\pi$
$594$	32.8538	+	14.1006i	1.34801	+	0.578557i
$595$	−1.31259	+	0.757825i	−0.0538110	+	0.0310678i
$596$	63.5573	−	17.0301i	2.60341	−	0.697581i
$597$	8.01713	+	36.9026i	0.328119	+	1.51032i
$598$	−1.63861	+	0.194303i	−0.0670078	+	0.00794563i
$599$	19.8330	+	11.4506i	0.810356	+	0.467859i	0.847079	−	0.531466i	$-0.178359\pi$
$599$	19.8330	+	11.4506i	0.810356	+	0.467859i	−0.0367236	+	0.999325i	$0.511692\pi$
$600$	7.73568	+	15.0152i	0.315808	+	0.612992i
$601$	1.12773	−	1.95328i	0.0460009	−	0.0796758i	−0.842108	−	0.539309i	$-0.818686\pi$
$601$	1.12773	−	1.95328i	0.0460009	−	0.0796758i	0.888109	+	0.459633i	$0.152019\pi$
$602$	−11.7673	+	20.3816i	−0.479601	+	0.830694i
$603$	−6.88212	+	5.67605i	−0.280261	+	0.231146i
$604$	−29.8663	+	8.00265i	−1.21524	+	0.325623i
$605$	−0.282862	−	0.282862i	−0.0115000	−	0.0115000i
$606$	1.64945	+	3.20162i	0.0670041	+	0.130057i
$607$	−10.6511	−	18.4482i	−0.432313	−	0.748788i	0.564759	−	0.825256i	$-0.308969\pi$
$607$	−10.6511	−	18.4482i	−0.432313	−	0.748788i	−0.997072	+	0.0764679i	$0.975636\pi$
$608$	44.9322			1.82224
$609$	5.90090	+	3.79455i	0.239117	+	0.153763i
$610$	7.00044	−	4.04170i	0.283439	−	0.163644i
$611$	24.1951	+	10.3888i	0.978830	+	0.420287i
$612$	43.7202	+	4.19884i	1.76729	+	0.169728i
$613$	−7.09311	+	26.4719i	−0.286488	+	1.06919i	0.661257	+	0.750159i	$0.270023\pi$
$613$	−7.09311	+	26.4719i	−0.286488	+	1.06919i	−0.947745	+	0.319029i	$0.896643\pi$
$614$	−25.4988	−	14.7218i	−1.02905	−	0.594122i
$615$	0.240944	+	1.10906i	0.00971582	+	0.0447216i
$616$	5.96458	−	1.59820i	0.240320	−	0.0643935i
$617$	−33.7876	−	9.05335i	−1.36024	−	0.364474i	−0.496333	−	0.868132i	$-0.665321\pi$
$617$	−33.7876	−	9.05335i	−1.36024	−	0.364474i	−0.863903	+	0.503658i	$0.831987\pi$
$618$	−35.6942	+	18.3893i	−1.43583	+	0.739727i
$619$	40.0880	+	10.7415i	1.61127	+	0.431739i	0.948422	−	0.317012i	$-0.102680\pi$
$619$	40.0880	+	10.7415i	1.61127	+	0.431739i	0.662851	+	0.748751i	$0.269346\pi$
$620$	−2.22124	−	1.28244i	−0.0892073	−	0.0515039i
$621$	−0.860759	+	0.643258i	−0.0345411	+	0.0258131i
$622$	29.0835	+	7.79290i	1.16614	+	0.312467i
$623$	4.43007	+	7.67310i	0.177487	+	0.307416i
$624$	0.612688	+	8.71914i	0.0245271	+	0.349045i
$625$	11.8292	−	20.4888i	0.473169	−	0.819553i
$626$	−15.6566	+	15.6566i	−0.625766	+	0.625766i
$627$	32.5979	+	10.4302i	1.30183	+	0.416542i
$628$		−	34.4430i		−	1.37442i
$629$	2.96999	−	2.96999i	0.118421	−	0.118421i
$630$	1.86551	+	0.696958i	0.0743236	+	0.0277675i
$631$	0.381450	+	1.42359i	0.0151853	+	0.0566723i	0.973103	−	0.230372i	$-0.0739941\pi$
$631$	0.381450	+	1.42359i	0.0151853	+	0.0566723i	−0.957917	+	0.287044i	$0.907327\pi$
$632$	−4.30867	+	16.0802i	−0.171390	+	0.639635i
$633$	−5.03354	−	5.54011i	−0.200065	−	0.220200i
$634$			63.1482i			2.50794i
$635$	−1.96859	−	1.96859i	−0.0781213	−	0.0781213i
$636$	−1.81746	+	5.68016i	−0.0720669	+	0.225233i
$637$	−3.56835	−	0.516596i	−0.141383	−	0.0204683i
$638$		−	27.8692i		−	1.10335i
$639$	34.9778	−	5.86219i	1.38370	−	0.231905i
$640$	−2.14309	−	3.71194i	−0.0847130	−	0.146727i
$641$	10.9208			0.431347			0.215673	−	0.976466i	$-0.430805\pi$
$641$	10.9208			0.431347			0.215673	+	0.976466i	$0.430805\pi$
$642$	−2.50316	+	52.2481i	−0.0987919	+	2.06207i
$643$	−3.02408	+	11.2860i	−0.119258	+	0.445078i	−0.999570	−	0.0293176i	$-0.990667\pi$
$643$	−3.02408	+	11.2860i	−0.119258	+	0.445078i	0.880312	+	0.474395i	$0.157333\pi$
$644$	−0.155083	+	0.578779i	−0.00611114	+	0.0228071i
$645$	4.64725	+	2.98840i	0.182985	+	0.117668i
$646$	71.0696			2.79620
$647$	−2.57628	−	4.46224i	−0.101284	−	0.175429i	0.810930	−	0.585143i	$-0.198962\pi$
$647$	−2.57628	−	4.46224i	−0.101284	−	0.175429i	−0.912214	+	0.409714i	$0.865628\pi$
$648$	−10.0029	−	14.8141i	−0.392952	−	0.581953i
$649$		−	24.5519i		−	0.963747i
$650$	−31.3864	+	23.4479i	−1.23107	+	0.919702i
$651$	4.99495	−	1.08516i	0.195767	−	0.0425307i
$652$	3.23588	+	3.23588i	0.126727	+	0.126727i
$653$			13.3628i			0.522925i	0.965214	+	0.261462i	$0.0842048\pi$
$653$			13.3628i			0.522925i	−0.965214	+	0.261462i	$0.915795\pi$
$654$	−32.0710	+	6.96747i	−1.25408	+	0.272450i
$655$	0.931214	−	3.47534i	0.0363855	−	0.135793i
$656$	0.791322	+	2.95325i	0.0308959	+	0.115305i
$657$	−12.7867	−	15.5037i	−0.498857	−	0.604856i
$658$	11.4280	−	11.4280i	0.445509	−	0.445509i
$659$		−	6.76138i		−	0.263386i	−0.991291	−	0.131693i	$-0.957959\pi$
$659$		−	6.76138i		−	0.263386i	0.991291	−	0.131693i	$-0.0420413\pi$
$660$	−0.993622	−	4.57361i	−0.0386767	−	0.178028i
$661$	11.2956	−	11.2956i	0.439350	−	0.439350i	−0.452443	−	0.891793i	$-0.649448\pi$
$661$	11.2956	−	11.2956i	0.439350	−	0.439350i	0.891793	+	0.452443i	$0.149448\pi$
$662$	−29.5571	+	51.1944i	−1.14877	+	1.98973i
$663$	2.21190	+	31.4774i	0.0859030	+	1.22248i
$664$	−3.12995	−	5.42123i	−0.121466	−	0.210385i
$665$	1.84148	+	0.493424i	0.0714096	+	0.0191342i
$666$	−5.49347	−	0.527586i	−0.212868	−	0.0204435i
$667$	0.725418	+	0.418820i	0.0280883	+	0.0162168i
$668$	−58.1642	−	15.5850i	−2.25044	−	0.603004i
$669$	−13.7612	−	8.84909i	−0.532039	−	0.342126i
$670$	1.90667	+	0.510890i	0.0736611	+	0.0197374i
$671$	36.5698	−	9.79885i	1.41176	−	0.378280i
$672$	11.6625	+	3.73160i	0.449890	+	0.143950i
$673$	−38.6090	−	22.2909i	−1.48827	−	0.859251i	−0.488356	−	0.872645i	$-0.662403\pi$
$673$	−38.6090	−	22.2909i	−1.48827	−	0.859251i	−0.999910	+	0.0133936i	$0.995737\pi$
$674$	−11.4009	+	42.5488i	−0.439147	+	1.63892i
$675$	−10.0625	+	23.4451i	−0.387305	+	0.902402i
$676$	36.6225	−	8.80909i	1.40856	−	0.338811i
$677$	17.4845	−	10.0947i	0.671986	−	0.387971i	−0.124843	−	0.992177i	$-0.539843\pi$
$677$	17.4845	−	10.0947i	0.671986	−	0.387971i	0.796829	+	0.604205i	$0.206509\pi$
$678$	−3.60022	+	75.1468i	−0.138266	+	2.88599i
$679$	8.34367			0.320201
$680$	−1.50513	−	2.60695i	−0.0577189	−	0.0999721i
$681$	−26.6106	−	1.27489i	−1.01972	−	0.0488539i
$682$	−14.3578	−	14.3578i	−0.549789	−	0.549789i
$683$	−0.627521	+	0.168144i	−0.0240114	+	0.00643385i	−0.270805	−	0.962634i	$-0.587290\pi$
$683$	−0.627521	+	0.168144i	−0.0240114	+	0.00643385i	0.246793	+	0.969068i	$0.420623\pi$
$684$	−35.1514	−	42.6205i	−1.34405	−	1.62964i
$685$	−1.05940	+	1.83494i	−0.0404777	+	0.0701094i
$686$	−1.10651	+	1.91653i	−0.0422468	+	0.0731736i
$687$	20.9212	−	32.5346i	0.798195	−	1.24127i
$688$	12.8903	+	7.44224i	0.491439	+	0.283733i
$689$	−4.24048	−	0.613901i	−0.161549	−	0.0233878i
$690$	0.226461	+	0.0724598i	0.00862123	+	0.00275850i
$691$	17.7074	−	4.74467i	0.673620	−	0.180496i	0.0942350	−	0.995550i	$-0.469960\pi$
$691$	17.7074	−	4.74467i	0.673620	−	0.180496i	0.579385	+	0.815054i	$0.303293\pi$
$692$	−52.7319	+	30.4448i	−2.00457	+	1.15734i
$693$	7.59480	+	5.41448i	0.288503	+	0.205679i
$694$	42.6050	+	42.6050i	1.61726	+	1.61726i
$695$	−2.25470	+	2.25470i	−0.0855257	+	0.0855257i
$696$	−7.53641	+	11.7199i	−0.285667	+	0.444240i
$697$	2.85680	+	10.6617i	0.108209	+	0.403841i
$698$	7.26608	−	4.19507i	0.275025	−	0.158786i
$699$	14.0701	+	15.4861i	0.532180	+	0.585739i
$700$	3.68212	+	13.7419i	0.139171	+	0.519394i
$701$	−0.840821			−0.0317574			−0.0158787	−	0.999874i	$-0.505055\pi$
$701$	−0.840821			−0.0317574			−0.0158787	+	0.999874i	$0.505055\pi$
$702$	30.0579	−	28.5575i	1.13446	−	1.07783i
$703$	−5.28317			−0.199259
$704$	−10.3370	−	38.5783i	−0.389591	−	1.45398i
$705$	−2.55145	−	2.80823i	−0.0960932	−	0.105764i
$706$	18.1324	−	10.4687i	0.682421	−	0.393996i
$707$	0.243185	+	0.907580i	0.00914592	+	0.0341331i
$708$	−21.4351	+	33.3337i	−0.805580	+	1.25276i
$709$	−19.3975	+	19.3975i	−0.728487	+	0.728487i	−0.970318	−	0.241832i	$-0.922252\pi$
$709$	−19.3975	+	19.3975i	−0.728487	+	0.728487i	0.241832	+	0.970318i	$0.422252\pi$
$710$	−5.54906	−	5.54906i	−0.208252	−	0.208252i
$711$	−22.8791	+	10.4334i	−0.858032	+	0.391285i
$712$	−15.2396	+	8.79861i	−0.571129	+	0.329742i
$713$	0.589494	−	0.157954i	0.0220767	−	0.00591544i
$714$	18.4467	+	5.90230i	0.690349	+	0.220888i
$715$	3.12288	−	1.24669i	0.116789	−	0.0466235i
$716$	0.616900	+	0.356167i	0.0230546	+	0.0133106i
$717$	−4.02427	+	6.25813i	−0.150289	+	0.233714i
$718$	−13.4863	+	23.3590i	−0.503305	+	0.871750i
$719$	−13.2094	+	22.8793i	−0.492626	+	0.853253i	−0.999964	−	0.00849381i	$-0.997296\pi$
$719$	−13.2094	+	22.8793i	−0.492626	+	0.853253i	0.507338	+	0.861747i	$0.330630\pi$
$720$	0.440790	−	1.17984i	0.0164273	−	0.0439699i
$721$	−10.1184	+	2.71122i	−0.376829	+	0.100971i
$722$	−33.4791	−	33.4791i	−1.24596	−	1.24596i
$723$	1.38282	+	0.0662495i	0.0514275	+	0.00246385i
$724$	34.4502	+	59.6694i	1.28033	+	2.21760i
$725$	19.8880			0.738621
$726$	−0.244621	+	5.10593i	−0.00907874	+	0.189499i
$727$	−5.23600	+	3.02300i	−0.194192	+	0.112117i	−0.593944	−	0.804507i	$-0.702430\pi$
$727$	−5.23600	+	3.02300i	−0.194192	+	0.112117i	0.399751	+	0.916624i	$0.369096\pi$
$728$	1.02602	−	7.08715i	0.0380268	−	0.262667i
$729$	7.64915	−	25.8938i	0.283302	−	0.959031i
$730$	−1.15091	+	4.29525i	−0.0425970	+	0.158974i
$731$	46.5361	+	26.8676i	1.72120	+	0.993735i
$732$	−58.2050	−	18.6236i	−2.15132	−	0.688348i
$733$	−21.0877	+	5.65044i	−0.778894	+	0.208704i	−0.626297	−	0.779585i	$-0.715430\pi$
$733$	−21.0877	+	5.65044i	−0.778894	+	0.208704i	−0.152597	+	0.988289i	$0.548764\pi$
$734$	23.5801	+	6.31826i	0.870357	+	0.233211i
$735$	0.436992	+	0.281006i	0.0161187	+	0.0103651i
$736$	1.41218	+	0.378393i	0.0520537	+	0.0139477i
$737$	8.00657	+	4.62260i	0.294926	+	0.170275i
$738$	8.41892	−	11.8091i	0.309905	−	0.434698i
$739$	31.3712	+	8.40589i	1.15401	+	0.309216i	0.784570	−	0.620040i	$-0.212884\pi$
$739$	31.3712	+	8.40589i	1.15401	+	0.309216i	0.369438	+	0.929255i	$0.379550\pi$
$740$	0.361230	+	0.625669i	0.0132791	+	0.0230000i
$741$	26.0295	−	29.9642i	0.956219	−	1.10076i
$742$	−1.31493	+	2.27753i	−0.0482726	+	0.0836106i
$743$	15.6820	−	15.6820i	0.575317	−	0.575317i	−0.358293	−	0.933609i	$-0.616641\pi$
$743$	15.6820	−	15.6820i	0.575317	−	0.575317i	0.933609	+	0.358293i	$0.116641\pi$
$744$	2.15525	+	9.92053i	0.0790152	+	0.363704i
$745$		−	6.81186i		−	0.249567i
$746$	8.73208	−	8.73208i	0.319704	−	0.319704i
$747$	3.30919	−	8.85753i	0.121077	−	0.324080i
$748$	−11.7810	−	43.9674i	−0.430757	−	1.60761i
$749$	−3.53198	+	13.1815i	−0.129056	+	0.481642i
$750$	11.1345	−	2.41897i	0.406573	−	0.0883284i
$751$			26.0458i			0.950424i	0.879871	+	0.475212i	$0.157629\pi$
$751$			26.0458i			0.950424i	−0.879871	+	0.475212i	$0.842371\pi$
$752$	−7.22761	−	7.22761i	−0.263564	−	0.263564i
$753$	−7.49970	+	1.62932i	−0.273304	+	0.0593757i
$754$	−29.6976	−	12.7515i	−1.08152	−	0.464381i
$755$			3.20097i			0.116495i
$756$	−5.58419	−	13.9818i	−0.203095	−	0.508512i
$757$	−6.92747	−	11.9987i	−0.251783	−	0.436101i	0.712234	−	0.701943i	$-0.247684\pi$
$757$	−6.92747	−	11.9987i	−0.251783	−	0.436101i	−0.964017	+	0.265841i	$0.914350\pi$
$758$	2.74932			0.0998599
$759$	0.936686	+	0.602333i	0.0339996	+	0.0218633i
$760$	−0.979995	+	3.65739i	−0.0355482	+	0.132668i
$761$	6.51225	−	24.3040i	0.236069	−	0.881020i	−0.741595	−	0.670847i	$-0.765931\pi$
$761$	6.51225	−	24.3040i	0.236069	−	0.881020i	0.977664	−	0.210173i	$-0.0674028\pi$
$762$	−1.70246	+	35.5351i	−0.0616735	+	1.28730i
$763$	−8.56212			−0.309969
$764$	21.5747	+	37.3684i	0.780544	+	1.35194i
$765$	1.59132	−	4.25940i	0.0575343	−	0.153999i
$766$		−	64.0470i		−	2.31411i
$767$	−26.1627	−	11.2336i	−0.944679	−	0.405624i
$768$	−3.13025	+	9.78307i	−0.112953	+	0.353016i
$769$	17.5161	+	17.5161i	0.631647	+	0.631647i	0.948481	−	0.316834i	$-0.102620\pi$
$769$	17.5161	+	17.5161i	0.631647	+	0.631647i	−0.316834	+	0.948481i	$0.602620\pi$
$770$		−	2.06386i		−	0.0743764i
$771$	−11.7845	−	12.9705i	−0.424410	−	0.467123i
$772$	18.4111	−	68.7113i	0.662632	−	2.47298i
$773$	−11.2983	−	42.1657i	−0.406370	−	1.51659i	−0.801514	−	0.597975i	$-0.795972\pi$
$773$	−11.2983	−	42.1657i	−0.406370	−	1.51659i	0.395144	−	0.918619i	$-0.370695\pi$
$774$	−11.6703	−	69.6329i	−0.419480	−	2.50290i
$775$	10.2460	−	10.2460i	0.368046	−	0.368046i
$776$			16.5715i			0.594881i
$777$	−1.37129	−	0.438765i	−0.0491947	−	0.0157406i
$778$	−7.10336	+	7.10336i	−0.254668	+	0.254668i
$779$	6.94189	−	12.0237i	0.248719	−	0.430794i
$780$	−5.32830	−	1.03383i	−0.190784	−	0.0370171i
$781$	−18.3776	−	31.8309i	−0.657602	−	1.13900i
$782$	2.23366	+	0.598507i	0.0798754	+	0.0214026i
$783$	−20.9001	+	2.48158i	−0.746910	+	0.0886843i
$784$	1.21211	+	0.699811i	0.0432896	+	0.0249932i
$785$	−3.44420	−	0.922870i	−0.122929	−	0.0329386i
$786$	−40.8714	+	21.0566i	−1.45784	+	0.751063i
$787$	31.6776	+	8.48799i	1.12918	+	0.302564i	0.774595	−	0.632458i	$-0.217954\pi$
$787$	31.6776	+	8.48799i	1.12918	+	0.302564i	0.354590	+	0.935022i	$0.384621\pi$
$788$	−27.1918	+	7.28601i	−0.968666	+	0.259553i
$789$	7.44748	+	34.2805i	0.265137	+	1.22042i
$790$	4.81861	+	2.78203i	0.171438	+	0.0989801i
$791$	−5.07993	+	18.9586i	−0.180622	+	0.674089i
$792$	−10.7538	+	15.0841i	−0.382118	+	0.535991i
$793$	6.29068	−	43.4524i	0.223389	−	1.54304i
$794$	48.7906	−	28.1693i	1.73151	−	0.999690i
$795$	0.519303	+	0.333936i	0.0184178	+	0.0118435i
$796$	−63.1727			−2.23910
$797$	−12.8052	−	22.1792i	−0.453583	−	0.785628i	0.545023	−	0.838421i	$-0.316521\pi$
$797$	−12.8052	−	22.1792i	−0.453583	−	0.785628i	−0.998605	+	0.0527928i	$0.983188\pi$
$798$	−11.1573	−	21.6566i	−0.394963	−	0.766635i
$799$	−26.0928	−	26.0928i	−0.923096	−	0.923096i
$800$	33.5292	−	8.98413i	1.18544	−	0.317637i
$801$	−24.8994	−	9.30247i	−0.879778	−	0.328687i
$802$	−0.181465	+	0.314307i	−0.00640775	+	0.0110986i
$803$	−10.4135	+	18.0368i	−0.367486	+	0.636504i
$804$	−6.83460	−	13.2662i	−0.241038	−	0.467861i
$805$	0.0537209	+	0.0310158i	0.00189341	+	0.00109316i
$806$	−21.8691	+	8.73039i	−0.770307	+	0.307515i
$807$	−6.63841	−	30.5564i	−0.233683	−	1.07564i
$808$	−1.80256	+	0.482993i	−0.0634137	+	0.0169916i
$809$	−23.2486	+	13.4226i	−0.817378	+	0.471913i	−0.849511	−	0.527570i	$-0.823103\pi$
$809$	−23.2486	+	13.4226i	−0.817378	+	0.471913i	0.0321336	+	0.999484i	$0.489770\pi$
$810$	−5.64789	+	1.94786i	−0.198447	+	0.0684408i
$811$	16.5073	+	16.5073i	0.579650	+	0.579650i	0.934807	−	0.355157i	$-0.115572\pi$
$811$	16.5073	+	16.5073i	0.579650	+	0.579650i	−0.355157	+	0.934807i	$0.615572\pi$
$812$	−8.29871	+	8.29871i	−0.291227	+	0.291227i
$813$	−7.10368	−	13.7884i	−0.249137	−	0.483582i
$814$	1.48029	+	5.52453i	0.0518842	+	0.193635i
$815$	0.410282	−	0.236876i	0.0143715	−	0.00829741i
$816$	3.73290	−	11.6666i	0.130678	−	0.408411i
$817$	−17.4937	−	65.2872i	−0.612025	−	2.28411i
$818$	59.9241			2.09520
$819$	9.24468	−	5.61569i	0.323035	−	0.196228i
$820$	−1.89857			−0.0663010
$821$	2.58982	+	9.66532i	0.0903852	+	0.337322i	0.996279	−	0.0861819i	$-0.0274666\pi$
$821$	2.58982	+	9.66532i	0.0903852	+	0.337322i	−0.905894	+	0.423504i	$0.860800\pi$
$822$	26.4582	−	5.74808i	0.922836	−	0.200487i
$823$	−34.9807	+	20.1961i	−1.21935	+	0.703993i	−0.964779	−	0.263060i	$-0.915268\pi$
$823$	−34.9807	+	20.1961i	−1.21935	+	0.703993i	−0.254573	+	0.967054i	$0.581935\pi$
$824$	−5.38479	−	20.0963i	−0.187588	−	0.700088i
$825$	26.4106	+	1.26531i	0.919500	+	0.0440525i
$826$	−12.3573	+	12.3573i	−0.429966	+	0.429966i
$827$	6.11318	+	6.11318i	0.212576	+	0.212576i	0.805361	−	0.592785i	$-0.201972\pi$
$827$	6.11318	+	6.11318i	0.212576	+	0.212576i	−0.592785	+	0.805361i	$0.701972\pi$
$828$	−0.745853	−	1.63555i	−0.0259202	−	0.0568393i
$829$	−23.8858	+	13.7905i	−0.829587	+	0.478962i	−0.853711	−	0.520747i	$-0.825654\pi$
$829$	−23.8858	+	13.7905i	−0.829587	+	0.478962i	0.0241243	+	0.999709i	$0.492320\pi$
$830$	−2.02095	+	0.541512i	−0.0701482	+	0.0187961i
$831$	27.6671	−	25.1373i	0.959763	−	0.872004i
$832$	−45.8390	−	6.63618i	−1.58918	−	0.230068i
$833$	4.37590	+	2.52643i	0.151616	+	0.0875355i
$834$	40.6996	+	1.94988i	1.40931	+	0.0675190i
$835$	−3.11692	+	5.39867i	−0.107866	+	0.186829i
$836$	−28.6274	+	49.5841i	−0.990100	+	1.71490i
$837$	−9.48895	+	12.0459i	−0.327986	+	0.416367i
$838$	63.2150	−	16.9384i	2.18373	−	0.585128i
$839$	−1.22194	−	1.22194i	−0.0421860	−	0.0421860i	0.685699	−	0.727885i	$-0.259497\pi$
$839$	−1.22194	−	1.22194i	−0.0421860	−	0.0421860i	−0.727885	+	0.685699i	$0.759497\pi$
$840$	−0.558110	+	0.867916i	−0.0192566	+	0.0299459i
$841$	−6.29679	−	10.9064i	−0.217131	−	0.376081i
$842$	−24.6035			−0.847894
$843$	−25.3190	+	13.0441i	−0.872034	+	0.449264i
$844$	10.8442	−	6.26088i	0.373271	−	0.215508i
$845$	0.100386	−	3.89818i	0.00345337	−	0.134101i
$846$	−4.63509	+	48.2627i	−0.159358	+	1.65931i
$847$	−0.345162	+	1.28816i	−0.0118599	+	0.0442618i
$848$	1.44042	+	0.831626i	0.0494641	+	0.0285581i
$849$	−14.3216	+	13.0120i	−0.491515	+	0.446572i
$850$	53.0334	−	14.2103i	1.81903	−	0.487408i
$851$	−0.166046	−	0.0444918i	−0.00569197	−	0.00152516i
$852$	−2.83913	+	59.2608i	−0.0972671	+	2.03024i
$853$	27.7337	+	7.43122i	0.949584	+	0.254440i	0.700186	−	0.713961i	$-0.253101\pi$
$853$	27.7337	+	7.43122i	0.949584	+	0.254440i	0.249398	+	0.968401i	$0.419767\pi$
$854$	−23.3380	−	13.4742i	−0.798608	−	0.461077i
$855$	−5.20378	+	2.37306i	−0.177966	+	0.0811569i
$856$	−26.1800	−	7.01490i	−0.894813	−	0.239764i
$857$	5.48908	+	9.50736i	0.187503	+	0.324765i	0.944417	−	0.328749i	$-0.106627\pi$
$857$	5.48908	+	9.50736i	0.187503	+	0.324765i	−0.756914	+	0.653515i	$0.773294\pi$
$858$	−38.6263	−	18.8230i	−1.31868	−	0.642606i
$859$	−9.41900	+	16.3142i	−0.321372	+	0.556633i	−0.980771	−	0.195160i	$-0.937477\pi$
$859$	−9.41900	+	16.3142i	−0.321372	+	0.556633i	0.659399	+	0.751793i	$0.270811\pi$
$860$	−6.53564	+	6.53564i	−0.222864	+	0.222864i
$861$	2.80038	−	2.54432i	0.0954369	−	0.0867103i
$862$			82.7332i			2.81790i
$863$	27.4276	−	27.4276i	0.933647	−	0.933647i	−0.0642849	−	0.997932i	$-0.520477\pi$
$863$	27.4276	−	27.4276i	0.933647	−	0.933647i	0.997932	+	0.0642849i	$0.0204766\pi$
$864$	−34.1146	+	13.6251i	−1.16060	+	0.463534i
$865$	1.63149	+	6.08879i	0.0554722	+	0.207025i
$866$	−20.5123	+	76.5531i	−0.697037	+	2.60138i
$867$	4.50314	−	14.0738i	0.152934	−	0.477971i
$868$			8.55073i			0.290231i
$869$	18.4272	+	18.4272i	0.625102	+	0.625102i
$870$	3.13171	+	3.44688i	0.106175	+	0.116860i
$871$	8.58924	−	6.41680i	0.291035	−	0.217425i
$872$		−	17.0053i		−	0.575873i
$873$	−19.3106	+	15.9265i	−0.653565	+	0.539030i
$874$	−1.45435	−	2.51900i	−0.0491940	−	0.0852065i
$875$	2.97260			0.100492
$876$	29.8853	−	15.3966i	1.00973	−	0.520204i
$877$	7.16235	−	26.7302i	0.241855	−	0.902616i	−0.733083	−	0.680139i	$-0.761919\pi$
$877$	7.16235	−	26.7302i	0.241855	−	0.902616i	0.974938	−	0.222477i	$-0.0714141\pi$
$878$	−0.275448	+	1.02799i	−0.00929592	+	0.0346929i
$879$	30.8811	−	15.9096i	1.04159	−	0.536619i
$880$	−1.30529			−0.0440012
$881$	22.8206	+	39.5265i	0.768846	+	1.33168i	0.938189	+	0.346124i	$0.112502\pi$
$881$	22.8206	+	39.5265i	0.768846	+	1.33168i	−0.169343	+	0.985557i	$0.554164\pi$
$882$	−1.09739	−	6.54774i	−0.0369509	−	0.220474i
$883$		−	29.8798i		−	1.00553i	−0.864422	−	0.502767i	$-0.832315\pi$
$883$		−	29.8798i		−	1.00553i	0.864422	−	0.502767i	$-0.167685\pi$
$884$	−52.2423	−	7.56321i	−1.75710	−	0.254378i
$885$	2.75894	+	3.03659i	0.0927406	+	0.102074i
$886$	−0.601382	−	0.601382i	−0.0202038	−	0.0202038i
$887$		−	29.7975i		−	1.00050i	−0.865881	−	0.500251i	$-0.833241\pi$
$887$		−	29.7975i		−	1.00050i	0.865881	−	0.500251i	$-0.166759\pi$
$888$	0.871437	−	2.72353i	0.0292435	−	0.0913957i
$889$	−2.40218	+	8.96505i	−0.0805664	+	0.300678i
$890$	1.52224	+	5.68109i	0.0510257	+	0.190431i
$891$	−27.9126	+	1.96575i	−0.935108	+	0.0658552i
$892$	19.3530	−	19.3530i	0.647987	−	0.647987i
$893$			46.4152i			1.55323i
$894$	−64.4259	+	58.5350i	−2.15472	+	1.95770i
$895$	0.0521450	−	0.0521450i	0.00174302	−	0.00174302i
$896$	−7.14460	+	12.3748i	−0.238684	+	0.413413i
$897$	1.07043	−	0.722543i	0.0357405	−	0.0241250i
$898$	−29.2551	−	50.6713i	−0.976255	−	1.69092i
$899$	11.5461	+	3.09377i	0.385084	+	0.103183i
$900$	−34.7525	−	24.7757i	−1.15842	−	0.825857i
$901$	5.20013	+	3.00230i	0.173241	+	0.100021i
$902$	−14.5180	−	3.89010i	−0.483398	−	0.129526i
$903$	0.881463	−	18.3986i	0.0293333	−	0.612268i
$904$	−37.6539	−	10.0893i	−1.25235	−	0.335566i
$905$	6.88984	−	1.84613i	0.229026	−	0.0613673i
$906$	30.2744	−	27.5062i	1.00580	−	0.913833i
$907$	−30.1864	−	17.4281i	−1.00232	−	0.578692i	−0.0933889	−	0.995630i	$-0.529770\pi$
$907$	−30.1864	−	17.4281i	−1.00232	−	0.578692i	−0.908935	+	0.416938i	$0.863103\pi$
$908$	11.5347	−	43.0481i	0.382793	−	1.42860i
$909$	−2.29522	−	1.63631i	−0.0761278	−	0.0542729i
$910$	−2.19926	−	0.944313i	−0.0729048	−	0.0313037i
$911$	22.6487	−	13.0763i	0.750386	−	0.433236i	−0.0754471	−	0.997150i	$-0.524038\pi$
$911$	22.6487	−	13.0763i	0.750386	−	0.433236i	0.825834	+	0.563914i	$0.190705\pi$
$912$	−13.6967	+	7.05640i	−0.453542	+	0.233661i
$913$	−9.79932			−0.324310
$914$	−30.1458	−	52.2141i	−0.997136	−	1.72709i
$915$	−3.42186	+	5.32133i	−0.113123	+	0.175918i
$916$	45.7549	+	45.7549i	1.51178	+	1.51178i
$917$	−11.5860	+	3.10447i	−0.382605	+	0.102519i
$918$	−53.9593	+	21.5509i	−1.78092	+	0.711284i
$919$	−2.19076	+	3.79450i	−0.0722664	+	0.125169i	−0.899894	−	0.436108i	$-0.856357\pi$
$919$	−2.19076	+	3.79450i	−0.0722664	+	0.125169i	0.827628	+	0.561277i	$0.189690\pi$
$920$	−0.0616008	+	0.106696i	−0.00203092	+	0.00351766i
$921$	23.0180	+	1.10277i	0.758467	+	0.0363375i
$922$	−10.2546	−	5.92049i	−0.337717	−	0.194981i
$923$	−42.3278	+	5.01913i	−1.39324	+	0.165207i
$924$	−11.5484	+	10.4924i	−0.379915	+	0.345176i
$925$	−3.94240	+	1.05636i	−0.129625	+	0.0347330i
$926$	28.1805	−	16.2700i	0.926070	−	0.534667i
$927$	18.2429	−	25.5890i	0.599174	−	0.840452i
$928$	20.2483	+	20.2483i	0.664682	+	0.664682i
$929$	23.8912	−	23.8912i	0.783845	−	0.783845i	−0.196632	−	0.980477i	$-0.563000\pi$
$929$	23.8912	−	23.8912i	0.783845	−	0.783845i	0.980477	+	0.196632i	$0.0630004\pi$
$930$	3.38919	+	0.162373i	0.111136	+	0.00532443i
$931$	−1.64497	−	6.13911i	−0.0539117	−	0.201201i
$932$	−30.3124	+	17.5009i	−0.992916	+	0.573260i
$933$	−23.0284	+	5.00294i	−0.753916	+	0.163789i
$934$	−0.124713	−	0.465437i	−0.00408075	−	0.0152296i
$935$	−4.71228			−0.154108
$936$	11.1534	+	18.3610i	0.364560	+	0.600147i
$937$	9.98183			0.326092			0.163046	−	0.986618i	$-0.447868\pi$
$937$	9.98183			0.326092			0.163046	+	0.986618i	$0.447868\pi$
$938$	−1.70320	−	6.35643i	−0.0556114	−	0.207545i
$939$	5.28113	−	16.5053i	0.172343	−	0.538630i
$940$	5.49680	−	3.17358i	0.179286	−	0.103511i
$941$	6.57919	+	24.5539i	0.214475	+	0.800433i	0.986351	+	0.164659i	$0.0526524\pi$
$941$	6.57919	+	24.5539i	0.214475	+	0.800433i	−0.771875	+	0.635774i	$0.780681\pi$
$942$	20.8679	+	40.5052i	0.679913	+	1.31973i
$943$	0.319434	−	0.319434i	0.0104022	−	0.0104022i
$944$	7.81536	+	7.81536i	0.254368	+	0.254368i
$945$	−1.54776	+	0.183774i	−0.0503487	+	0.00597815i
$946$	−63.3682	+	36.5856i	−2.06028	+	1.18950i
$947$	46.5466	−	12.4721i	1.51256	−	0.405289i	0.595276	−	0.803522i	$-0.297043\pi$
$947$	46.5466	−	12.4721i	1.51256	−	0.405289i	0.917285	+	0.398232i	$0.130376\pi$
$948$	−8.93038	−	41.1062i	−0.290045	−	1.33507i
$949$	14.4554	+	19.3494i	0.469243	+	0.628108i
$950$	−59.8083	−	34.5303i	−1.94044	−	1.12031i
$951$	−22.6353	−	43.9358i	−0.734001	−	1.42472i
$952$	−5.01777	+	8.69103i	−0.162627	+	0.281678i
$953$	−20.5154	+	35.5337i	−0.664559	+	1.15105i	0.314846	+	0.949143i	$0.398047\pi$
$953$	−20.5154	+	35.5337i	−0.664559	+	1.15105i	−0.979405	+	0.201907i	$0.935286\pi$
$954$	−1.30409	−	7.78106i	−0.0422214	−	0.251921i
$955$	4.31481	−	1.15615i	0.139624	−	0.0374121i
$956$	−8.80109	−	8.80109i	−0.284648	−	0.284648i
$957$	9.98965	+	19.3902i	0.322920	+	0.626796i
$958$	−17.9091	−	31.0195i	−0.578617	−	1.00219i
$959$	7.06364			0.228097
$960$	5.61359	+	3.60980i	0.181178	+	0.116506i
$961$	−19.3045	+	11.1455i	−0.622727	+	0.359532i
$962$	6.56427	+	0.950321i	0.211641	+	0.0306396i
$963$	−16.9866	−	37.2492i	−0.547385	−	1.20034i
$964$	−0.599399	+	2.23699i	−0.0193053	+	0.0720485i
$965$	−6.37763	−	3.68213i	−0.205303	−	0.118532i
$966$	−0.168285	−	0.774609i	−0.00541447	−	0.0249226i
$967$	19.6125	−	5.25516i	0.630696	−	0.168994i	0.0707103	−	0.997497i	$-0.477473\pi$
$967$	19.6125	−	5.25516i	0.630696	−	0.168994i	0.559985	+	0.828502i	$0.310807\pi$
$968$	−2.55843	−	0.685530i	−0.0822312	−	0.0220338i
$969$	−49.4471	+	25.4747i	−1.58847	+	0.818365i
$970$	5.34994	+	1.43351i	0.171776	+	0.0460273i
$971$	12.5863	+	7.26668i	0.403912	+	0.233199i	0.688171	−	0.725549i	$-0.258414\pi$
$971$	12.5863	+	7.26668i	0.403912	+	0.233199i	−0.284258	+	0.958748i	$0.591747\pi$
$972$	39.6126	+	21.7003i	1.27057	+	0.696037i
$973$	10.2680	+	2.75130i	0.329177	+	0.0882026i
$974$	−25.4686	−	44.1129i	−0.816066	−	1.41347i
$975$	13.4324	−	27.5644i	0.430182	−	0.882767i
$976$	−8.52172	+	14.7600i	−0.272774	+	0.472458i
$977$	23.0683	−	23.0683i	0.738020	−	0.738020i	−0.234175	−	0.972195i	$-0.575239\pi$
$977$	23.0683	−	23.0683i	0.738020	−	0.738020i	0.972195	+	0.234175i	$0.0752388\pi$
$978$	−5.76594	−	1.84490i	−0.184375	−	0.0589935i
$979$			27.5469i			0.880402i
$980$	−0.614562	+	0.614562i	−0.0196315	+	0.0196315i
$981$	19.8162	−	16.3434i	0.632681	−	0.521806i
$982$	4.28080	+	15.9762i	0.136606	+	0.509820i
$983$	−1.24477	+	4.64556i	−0.0397021	+	0.148170i	−0.982932	−	0.183972i	$-0.941105\pi$
$983$	−1.24477	+	4.64556i	−0.0397021	+	0.148170i	0.943229	+	0.332142i	$0.107771\pi$
$984$	5.05331	+	5.56188i	0.161094	+	0.177306i
$985$			2.91432i			0.0928580i
$986$	32.0269	+	32.0269i	1.01994	+	1.01994i
$987$	−3.85476	+	12.0474i	−0.122698	+	0.383474i
$988$	39.7388	+	53.1926i	1.26426	+	1.69228i
$989$		−	2.19924i		−	0.0699319i
$990$	3.93951	+	4.77660i	0.125206	+	0.151810i
$991$	23.9532	+	41.4881i	0.760897	+	1.31791i	0.942389	+	0.334520i	$0.108574\pi$
$991$	23.9532	+	41.4881i	0.760897	+	1.31791i	−0.181492	+	0.983392i	$0.558093\pi$
$992$	20.8632			0.662407
$993$	2.21405	−	46.2135i	0.0702607	−	1.46654i
$994$	−6.77124	+	25.2706i	−0.214771	+	0.801535i
$995$	−1.69266	+	6.31709i	−0.0536609	+	0.200265i
$996$	13.3043	+	8.55531i	0.421564	+	0.271085i
$997$	−54.2732			−1.71885			−0.859425	−	0.511263i	$-0.829178\pi$
$997$	−54.2732			−1.71885			−0.859425	+	0.511263i	$0.829178\pi$
$998$	32.2909	+	55.9294i	1.02215	+	1.77041i
$999$	4.01123	−	1.60205i	0.126910	−	0.0506865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.13	yes	336
9.2	odd	6		819.2.ew.a.596.72	✓	336
13.6	odd	12		819.2.ew.a.617.72	yes	336
117.110	even	12	inner	819.2.fy.a.344.13	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.72	✓	336	9.2	odd	6
819.2.ew.a.617.72	yes	336	13.6	odd	12
819.2.fy.a.50.13	yes	336	1.1	even	1	trivial
819.2.fy.a.344.13	yes	336	117.110	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.572772 - 2.13762i) q^{2} +(1.16473 + 1.28195i) q^{3} +(-2.50928 + 1.44873i) q^{4} +(0.0776352 + 0.289738i) q^{5} +(2.07319 - 3.22402i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.40439 + 1.40439i) q^{8} +(-0.286797 + 2.98626i) q^{9} +O(q^{10})\)	\(q+(-0.572772 - 2.13762i) q^{2} +(1.16473 + 1.28195i) q^{3} +(-2.50928 + 1.44873i) q^{4} +(0.0776352 + 0.289738i) q^{5} +(2.07319 - 3.22402i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.40439 + 1.40439i) q^{8} +(-0.286797 + 2.98626i) q^{9} +(0.574882 - 0.331908i) q^{10} +(3.00314 - 0.804690i) q^{11} +(-4.77984 - 1.52939i) q^{12} +(0.516596 - 3.56835i) q^{13} +(-1.91653 - 1.10651i) q^{14} +(-0.281006 + 0.436992i) q^{15} +(-0.699811 + 1.21211i) q^{16} +(-2.52643 + 4.37590i) q^{17} +(6.54774 - 1.09739i) q^{18} +(6.13911 - 1.64497i) q^{19} +(-0.614562 - 0.614562i) q^{20} +(1.73007 + 0.0828860i) q^{21} +(-3.44023 - 5.95866i) q^{22} +0.206800 q^{23} +(-0.164621 + 3.43611i) q^{24} +(4.25221 - 2.45501i) q^{25} +(-7.92365 + 0.939569i) q^{26} +(-4.16228 + 3.11053i) q^{27} +(-0.749919 + 2.79874i) q^{28} +(3.50782 + 2.02524i) q^{29} +(1.09507 + 0.350386i) q^{30} +(2.85055 - 0.763803i) q^{31} +(6.82873 + 1.82975i) q^{32} +(4.52943 + 2.91263i) q^{33} +(10.8011 + 2.89413i) q^{34} +(0.259772 + 0.149980i) q^{35} +(-3.60664 - 7.90885i) q^{36} +(-0.802929 - 0.215144i) q^{37} +(-7.03262 - 12.1809i) q^{38} +(5.17615 - 3.49392i) q^{39} +(-0.297876 + 0.515937i) q^{40} +(1.54465 - 1.54465i) q^{41} +(-0.813756 - 3.74569i) q^{42} -10.6346i q^{43} +(-6.36995 + 6.36995i) q^{44} +(-0.887500 + 0.148743i) q^{45} +(-0.118449 - 0.442059i) q^{46} +(-1.89014 + 7.05411i) q^{47} +(-2.36896 + 0.514658i) q^{48} -1.00000i q^{49} +(-7.68342 - 7.68342i) q^{50} +(-8.55230 + 1.85800i) q^{51} +(3.87330 + 9.70240i) q^{52} -1.18836i q^{53} +(9.03316 + 7.11573i) q^{54} +(0.466299 + 0.807654i) q^{55} +1.98611 q^{56} +(9.25919 + 5.95409i) q^{57} +(2.32001 - 8.65838i) q^{58} +(2.04385 - 7.62776i) q^{59} +(0.0720381 - 1.50364i) q^{60} +12.1772 q^{61} +(-3.26543 - 5.65589i) q^{62} +(1.90881 + 2.31440i) q^{63} -12.8460i q^{64} +(1.07399 - 0.127352i) q^{65} +(3.63176 - 11.3505i) q^{66} +(2.10266 + 2.10266i) q^{67} -14.6405i q^{68} +(0.240867 + 0.265107i) q^{69} +(0.171808 - 0.641197i) q^{70} +(-3.05972 - 11.4190i) q^{71} +(-4.59666 + 3.79111i) q^{72} +(-4.73676 + 4.73676i) q^{73} +1.83958i q^{74} +(8.09989 + 2.59169i) q^{75} +(-13.0216 + 13.0216i) q^{76} +(1.55454 - 2.69254i) q^{77} +(-10.4334 - 9.06339i) q^{78} +(4.19096 + 7.25895i) q^{79} +(-0.405524 - 0.108660i) q^{80} +(-8.83550 - 1.71290i) q^{81} +(-4.18661 - 2.41714i) q^{82} +(-3.04444 - 0.815755i) q^{83} +(-4.46130 + 2.29842i) q^{84} +(-1.46401 - 0.392279i) q^{85} +(-22.7328 + 6.09123i) q^{86} +(1.48941 + 6.85572i) q^{87} +(5.34770 + 3.08749i) q^{88} +(-2.29317 + 8.55823i) q^{89} +(0.826290 + 1.81194i) q^{90} +(-2.15792 - 2.88849i) q^{91} +(-0.518919 + 0.299598i) q^{92} +(4.29929 + 2.76464i) q^{93} +16.1616 q^{94} +(0.953222 + 1.65103i) q^{95} +(5.60799 + 10.8853i) q^{96} +(5.89987 + 5.89987i) q^{97} +(-2.13762 + 0.572772i) q^{98} +(1.54172 + 9.19895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Introduction

L-functions

Modular forms

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