LMFDB - Embedded newform 975.2.s.e.818.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(818,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("975.818");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$975 = 3 \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	975.s (of order $4$ , degree $2$ , 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			818.1
Character	$\chi$	$=$	975.818
Dual form			975.2.s.e.857.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57280 + 1.57280i) q^{2} +(-0.0375613 + 1.73164i) q^{3} -2.94741i q^{4} +(-2.66446 - 2.78261i) q^{6} +(-3.19872 - 3.19872i) q^{7} +(1.49009 + 1.49009i) q^{8} +(-2.99718 - 0.130086i) q^{9} +2.81912 q^{11} +(5.10387 + 0.110709i) q^{12} +(3.47350 - 0.966841i) q^{13} +10.0619 q^{14} +1.20758 q^{16} +(2.03377 + 2.03377i) q^{17} +(4.91857 - 4.50937i) q^{18} -1.12487 q^{19} +(5.65918 - 5.41889i) q^{21} +(-4.43391 + 4.43391i) q^{22} +(-2.81355 + 2.81355i) q^{23} +(-2.63628 + 2.52434i) q^{24} +(-3.94248 + 6.98378i) q^{26} +(0.337840 - 5.18516i) q^{27} +(-9.42794 + 9.42794i) q^{28} +0.367259 q^{29} +6.89322i q^{31} +(-4.87948 + 4.87948i) q^{32} +(-0.105890 + 4.88170i) q^{33} -6.39743 q^{34} +(-0.383416 + 8.83392i) q^{36} +(2.07384 + 2.07384i) q^{37} +(1.76920 - 1.76920i) q^{38} +(1.54376 + 6.05118i) q^{39} -3.73081 q^{41} +(-0.377938 + 17.4236i) q^{42} +(3.25333 + 3.25333i) q^{43} -8.30910i q^{44} -8.85031i q^{46} +(1.65930 - 1.65930i) q^{47} +(-0.0453585 + 2.09110i) q^{48} +13.4636i q^{49} +(-3.59815 + 3.44537i) q^{51} +(-2.84968 - 10.2378i) q^{52} +(9.01755 - 9.01755i) q^{53} +(7.62387 + 8.68658i) q^{54} -9.53277i q^{56} +(0.0422518 - 1.94788i) q^{57} +(-0.577625 + 0.577625i) q^{58} -0.0290860i q^{59} +9.93373 q^{61} +(-10.8417 - 10.8417i) q^{62} +(9.17102 + 10.0032i) q^{63} -12.9337i q^{64} +(-7.51141 - 7.84450i) q^{66} +(3.03050 + 3.03050i) q^{67} +(5.99436 - 5.99436i) q^{68} +(-4.76638 - 4.97774i) q^{69} -1.59810 q^{71} +(-4.27223 - 4.65991i) q^{72} +(-1.40984 + 1.40984i) q^{73} -6.52349 q^{74} +3.31547i q^{76} +(-9.01755 - 9.01755i) q^{77} +(-11.9453 - 7.08929i) q^{78} +5.41757i q^{79} +(8.96616 + 0.779780i) q^{81} +(5.86782 - 5.86782i) q^{82} +(4.58566 + 4.58566i) q^{83} +(-15.9717 - 16.6800i) q^{84} -10.2337 q^{86} +(-0.0137947 + 0.635961i) q^{87} +(4.20074 + 4.20074i) q^{88} +14.1084i q^{89} +(-14.2034 - 8.01810i) q^{91} +(8.29269 + 8.29269i) q^{92} +(-11.9366 - 0.258919i) q^{93} +5.21949i q^{94} +(-8.26623 - 8.63279i) q^{96} +(11.2986 + 11.2986i) q^{97} +(-21.1755 - 21.1755i) q^{98} +(-8.44939 - 0.366727i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 4 q^{3} + 24 q^{12} + 24 q^{16} - 24 q^{22} + 16 q^{27} - 8 q^{36} - 12 q^{42} + 64 q^{43} + 20 q^{48} + 16 q^{51} + 72 q^{52} + 8 q^{61} - 72 q^{66} - 84 q^{78} + 112 q^{81} - 48 q^{82} - 20 q^{87}+ \cdots - 40 q^{91}+O(q^{100})$ 32 * q + 4 * q^3 + 24 * q^12 + 24 * q^16 - 24 * q^22 + 16 * q^27 - 8 * q^36 - 12 * q^42 + 64 * q^43 + 20 * q^48 + 16 * q^51 + 72 * q^52 + 8 * q^61 - 72 * q^66 - 84 * q^78 + 112 * q^81 - 48 * q^82 - 20 * q^87 + 8 * q^88 - 40 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$ .

$n$	$301$	$326$	$352$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−1.57280	+	1.57280i	−1.11214	+	1.11214i	−0.119278	+	0.992861i	$0.538058\pi$
$2$	−1.57280	+	1.57280i	−1.11214	+	1.11214i	−0.992861	+	0.119278i	$0.961942\pi$
$3$	−0.0375613	+	1.73164i	−0.0216860	+	0.999765i
$3$	−0.0375613	+	1.73164i	−0.0216860	+	0.999765i
$4$		−	2.94741i		−	1.47371i
$5$		0			0
$5$		0			0
$6$	−2.66446	−	2.78261i	−1.08776	−	1.13600i
$7$	−3.19872	−	3.19872i	−1.20900	−	1.20900i	−0.971351	−	0.237650i	$-0.923623\pi$
$7$	−3.19872	−	3.19872i	−1.20900	−	1.20900i	−0.237650	−	0.971351i	$-0.576377\pi$
$8$	1.49009	+	1.49009i	0.526827	+	0.526827i
$9$	−2.99718	−	0.130086i	−0.999059	−	0.0433619i
$10$		0			0
$11$	2.81912			0.849995			0.424998	−	0.905194i	$-0.360275\pi$
$11$	2.81912			0.849995			0.424998	+	0.905194i	$0.360275\pi$
$12$	5.10387	+	0.110709i	1.47336	+	0.0319589i
$13$	3.47350	−	0.966841i	0.963376	−	0.268154i
$13$	3.47350	−	0.966841i	0.963376	−	0.268154i
$14$	10.0619			2.68915
$15$		0			0
$16$	1.20758			0.301896
$17$	2.03377	+	2.03377i	0.493261	+	0.493261i	0.909332	−	0.416071i	$-0.136593\pi$
$17$	2.03377	+	2.03377i	0.493261	+	0.493261i	−0.416071	+	0.909332i	$0.636593\pi$
$18$	4.91857	−	4.50937i	1.15932	−	1.06287i
$19$	−1.12487			−0.258064			−0.129032	−	0.991640i	$-0.541187\pi$
$19$	−1.12487			−0.258064			−0.129032	+	0.991640i	$0.541187\pi$
$20$		0			0
$21$	5.65918	−	5.41889i	1.23494	−	1.18250i
$22$	−4.43391	+	4.43391i	−0.945313	+	0.945313i
$23$	−2.81355	+	2.81355i	−0.586666	+	0.586666i	−0.936727	−	0.350061i	$-0.886161\pi$
$23$	−2.81355	+	2.81355i	−0.586666	+	0.586666i	0.350061	+	0.936727i	$0.386161\pi$
$24$	−2.63628	+	2.52434i	−0.538128	+	0.515279i
$25$		0			0
$26$	−3.94248	+	6.98378i	−0.773184	+	1.36963i
$27$	0.337840	−	5.18516i	0.0650173	−	0.997884i
$28$	−9.42794	+	9.42794i	−1.78171	+	1.78171i
$29$	0.367259			0.0681982			0.0340991	−	0.999418i	$-0.489144\pi$
$29$	0.367259			0.0681982			0.0340991	+	0.999418i	$0.489144\pi$
$30$		0			0
$31$			6.89322i			1.23806i	0.785368	+	0.619030i	$0.212474\pi$
$31$			6.89322i			1.23806i	−0.785368	+	0.619030i	$0.787526\pi$
$32$	−4.87948	+	4.87948i	−0.862578	+	0.862578i
$33$	−0.105890	+	4.88170i	−0.0184330	+	0.849795i
$34$	−6.39743			−1.09715
$35$		0			0
$36$	−0.383416	+	8.83392i	−0.0639027	+	1.47232i
$37$	2.07384	+	2.07384i	0.340937	+	0.340937i	0.856720	−	0.515782i	$-0.172499\pi$
$37$	2.07384	+	2.07384i	0.340937	+	0.340937i	−0.515782	+	0.856720i	$0.672499\pi$
$38$	1.76920	−	1.76920i	0.287003	−	0.287003i
$39$	1.54376	+	6.05118i	0.247199	+	0.968965i
$40$		0			0
$41$	−3.73081			−0.582654			−0.291327	−	0.956623i	$-0.594097\pi$
$41$	−3.73081			−0.582654			−0.291327	+	0.956623i	$0.594097\pi$
$42$	−0.377938	+	17.4236i	−0.0583171	+	2.68852i
$43$	3.25333	+	3.25333i	0.496128	+	0.496128i	0.910230	−	0.414102i	$-0.135904\pi$
$43$	3.25333	+	3.25333i	0.496128	+	0.496128i	−0.414102	+	0.910230i	$0.635904\pi$
$44$		−	8.30910i		−	1.25264i
$45$		0			0
$46$		−	8.85031i		−	1.30491i
$47$	1.65930	−	1.65930i	0.242033	−	0.242033i	−0.575658	−	0.817691i	$-0.695254\pi$
$47$	1.65930	−	1.65930i	0.242033	−	0.242033i	0.817691	+	0.575658i	$0.195254\pi$
$48$	−0.0453585	+	2.09110i	−0.00654693	+	0.301825i
$49$			13.4636i			1.92337i
$50$		0			0
$51$	−3.59815	+	3.44537i	−0.503842	+	0.482449i
$52$	−2.84968	−	10.2378i	−0.395180	−	1.41973i
$53$	9.01755	−	9.01755i	1.23866	−	1.23866i	0.278105	−	0.960551i	$-0.410294\pi$
$53$	9.01755	−	9.01755i	1.23866	−	1.23866i	0.960551	−	0.278105i	$-0.0897064\pi$
$54$	7.62387	+	8.68658i	1.03748	+	1.18209i
$55$		0			0
$56$		−	9.53277i		−	1.27387i
$57$	0.0422518	−	1.94788i	0.00559639	−	0.258003i
$58$	−0.577625	+	0.577625i	−0.0758459	+	0.0758459i
$59$		−	0.0290860i		−	0.00378667i	−0.999998	−	0.00189334i	$-0.999397\pi$
$59$		−	0.0290860i		−	0.00378667i	0.999998	−	0.00189334i	$-0.000602668\pi$
$60$		0			0
$61$	9.93373			1.27188			0.635942	−	0.771737i	$-0.280612\pi$
$61$	9.93373			1.27188			0.635942	+	0.771737i	$0.280612\pi$
$62$	−10.8417	−	10.8417i	−1.37689	−	1.37689i
$63$	9.17102	+	10.0032i	1.15544	+	1.26029i
$64$		−	12.9337i		−	1.61672i
$65$		0			0
$66$	−7.51141	−	7.84450i	−0.924591	−	0.965591i
$67$	3.03050	+	3.03050i	0.370235	+	0.370235i	0.867563	−	0.497328i	$-0.165685\pi$
$67$	3.03050	+	3.03050i	0.370235	+	0.370235i	−0.497328	+	0.867563i	$0.665685\pi$
$68$	5.99436	−	5.99436i	0.726923	−	0.726923i
$69$	−4.76638	−	4.97774i	−0.573805	−	0.599250i
$70$		0			0
$71$	−1.59810			−0.189660			−0.0948300	−	0.995493i	$-0.530231\pi$
$71$	−1.59810			−0.189660			−0.0948300	+	0.995493i	$0.530231\pi$
$72$	−4.27223	−	4.65991i	−0.503488	−	0.549176i
$73$	−1.40984	+	1.40984i	−0.165009	+	0.165009i	−0.784782	−	0.619772i	$-0.787225\pi$
$73$	−1.40984	+	1.40984i	−0.165009	+	0.165009i	0.619772	+	0.784782i	$0.287225\pi$
$74$	−6.52349			−0.758340
$75$		0			0
$76$			3.31547i			0.380310i
$77$	−9.01755	−	9.01755i	−1.02765	−	1.02765i
$78$	−11.9453	−	7.08929i	−1.35254	−	0.802704i
$79$			5.41757i			0.609525i	0.952428	+	0.304762i	$0.0985770\pi$
$79$			5.41757i			0.609525i	−0.952428	+	0.304762i	$0.901423\pi$
$80$		0			0
$81$	8.96616	+	0.779780i	0.996239	+	0.0866422i
$82$	5.86782	−	5.86782i	0.647992	−	0.647992i
$83$	4.58566	+	4.58566i	0.503341	+	0.503341i	0.912475	−	0.409133i	$-0.134169\pi$
$83$	4.58566	+	4.58566i	0.503341	+	0.503341i	−0.409133	+	0.912475i	$0.634169\pi$
$84$	−15.9717	−	16.6800i	−1.74266	−	1.81993i
$85$		0			0
$86$	−10.2337			−1.10353
$87$	−0.0137947	+	0.635961i	−0.00147895	+	0.0681822i
$88$	4.20074	+	4.20074i	0.447801	+	0.447801i
$89$			14.1084i			1.49549i	0.663988	+	0.747744i	$0.268863\pi$
$89$			14.1084i			1.49549i	−0.663988	+	0.747744i	$0.731137\pi$
$90$		0			0
$91$	−14.2034	−	8.01810i	−1.48892	−	0.840525i
$92$	8.29269	+	8.29269i	0.864573	+	0.864573i
$93$	−11.9366	−	0.258919i	−1.23777	−	0.0268486i
$94$			5.21949i			0.538349i
$95$		0			0
$96$	−8.26623	−	8.63279i	−0.843669	−	0.881081i
$97$	11.2986	+	11.2986i	1.14720	+	1.14720i	0.987100	+	0.160104i	$0.0511829\pi$
$97$	11.2986	+	11.2986i	1.14720	+	1.14720i	0.160104	+	0.987100i	$0.448817\pi$
$98$	−21.1755	−	21.1755i	−2.13905	−	2.13905i
$99$	−8.44939	−	0.366727i	−0.849196	−	0.0368574i
$100$		0			0
$101$		−	12.5178i		−	1.24557i	−0.782392	−	0.622786i	$-0.786001\pi$
$101$		−	12.5178i		−	1.24557i	0.782392	−	0.622786i	$-0.213999\pi$
$102$	0.240296	−	11.0781i	0.0237929	−	1.09689i
$103$	−2.86517	−	2.86517i	−0.282313	−	0.282313i	0.551718	−	0.834031i	$-0.313973\pi$
$103$	−2.86517	−	2.86517i	−0.282313	−	0.282313i	−0.834031	+	0.551718i	$0.813973\pi$
$104$	6.61652	+	3.73516i	0.648803	+	0.366262i
$105$		0			0
$106$			28.3656i			2.75511i
$107$	9.17516	+	9.17516i	0.886997	+	0.886997i	0.994233	−	0.107237i	$-0.0342003\pi$
$107$	9.17516	+	9.17516i	0.886997	+	0.886997i	−0.107237	+	0.994233i	$0.534200\pi$
$108$	−15.2828	−	0.995754i	−1.47059	−	0.0958165i
$109$	6.92360			0.663160			0.331580	−	0.943427i	$-0.392418\pi$
$109$	6.92360			0.663160			0.331580	+	0.943427i	$0.392418\pi$
$110$		0			0
$111$	−3.66905	+	3.51326i	−0.348251	+	0.333464i
$112$	−3.86272	−	3.86272i	−0.364993	−	0.364993i
$113$	−3.53841	+	3.53841i	−0.332866	+	0.332866i	−0.853674	−	0.520808i	$-0.825631\pi$
$113$	−3.53841	+	3.53841i	−0.332866	+	0.332866i	0.520808	+	0.853674i	$0.325631\pi$
$114$	2.99718	+	3.13009i	0.280711	+	0.293159i
$115$		0			0
$116$		−	1.08246i		−	0.100504i
$117$	−10.5365	+	2.44594i	−0.974098	+	0.226127i
$118$	0.0457465	+	0.0457465i	0.00421131	+	0.00421131i
$119$		−	13.0109i		−	1.19271i
$120$		0			0
$121$	−3.05259			−0.277508
$122$	−15.6238	+	15.6238i	−1.41451	+	1.41451i
$123$	0.140134	−	6.46043i	0.0126355	−	0.582517i
$124$	20.3172			1.82454
$125$		0			0
$126$	−30.1573	−	1.30891i	−2.68663	−	0.116607i
$127$	−7.34242	+	7.34242i	−0.651534	+	0.651534i	−0.953362	−	0.301828i	$-0.902403\pi$
$127$	−7.34242	+	7.34242i	−0.651534	+	0.651534i	0.301828	+	0.953362i	$0.402403\pi$
$128$	10.5832	+	10.5832i	0.935436	+	0.935436i
$129$	−5.75581	+	5.51141i	−0.506771	+	0.485253i
$130$		0			0
$131$			2.08869i			0.182490i	0.995828	+	0.0912448i	$0.0290846\pi$
$131$			2.08869i			0.182490i	−0.995828	+	0.0912448i	$0.970915\pi$
$132$	14.3884	+	0.312101i	1.25235	+	0.0271649i
$133$	3.59815	+	3.59815i	0.312000	+	0.312000i
$134$	−9.53277			−0.823506
$135$		0			0
$136$			6.06101i			0.519727i
$137$	3.91340	−	3.91340i	0.334344	−	0.334344i	−0.519890	−	0.854233i	$-0.674027\pi$
$137$	3.91340	−	3.91340i	0.334344	−	0.334344i	0.854233	+	0.519890i	$0.174027\pi$
$138$	15.3256	+	0.332429i	1.30460	+	0.0282983i
$139$		−	17.1532i		−	1.45492i	−0.686152	−	0.727458i	$-0.740701\pi$
$139$		−	17.1532i		−	1.45492i	0.686152	−	0.727458i	$-0.259299\pi$
$140$		0			0
$141$	2.81098	+	2.93563i	0.236727	+	0.247225i
$142$	2.51350	−	2.51350i	0.210928	−	0.210928i
$143$	9.79220	−	2.72564i	0.818865	−	0.227929i
$144$	−3.61934	−	0.157089i	−0.301612	−	0.0130908i
$145$		0			0
$146$		−	4.43480i		−	0.367026i
$147$	−23.3141	−	0.505710i	−1.92291	−	0.0417102i
$148$	6.11247	−	6.11247i	0.502442	−	0.502442i
$149$		−	2.94675i		−	0.241407i	−0.992689	−	0.120704i	$-0.961485\pi$
$149$		−	2.94675i		−	0.241407i	0.992689	−	0.120704i	$-0.0385151\pi$
$150$		0			0
$151$		−	1.12487i		−	0.0915410i	−0.998952	−	0.0457705i	$-0.985426\pi$
$151$		−	1.12487i		−	0.0915410i	0.998952	−	0.0457705i	$-0.0145743\pi$
$152$	−1.67617	−	1.67617i	−0.135955	−	0.135955i
$153$	−5.83100	−	6.36013i	−0.471409	−	0.514186i
$154$	28.3656			2.28577
$155$		0			0
$156$	17.8353	−	4.55008i	1.42797	−	0.364298i
$157$	−12.5551	+	12.5551i	−1.00200	+	1.00200i	−0.00200511	+	0.999998i	$0.500638\pi$
$157$	−12.5551	+	12.5551i	−1.00200	+	1.00200i	−0.999998	+	0.00200511i	$0.999362\pi$
$158$	−8.52077	−	8.52077i	−0.677876	−	0.677876i
$159$	15.2765	+	15.9539i	1.21150	+	1.26523i
$160$		0			0
$161$	17.9995			1.41856
$162$	−15.3284	+	12.8755i	−1.20431	+	1.01160i
$163$	−4.81938	+	4.81938i	−0.377483	+	0.377483i	−0.870193	−	0.492710i	$-0.836006\pi$
$163$	−4.81938	+	4.81938i	−0.377483	+	0.377483i	0.492710	+	0.870193i	$0.336006\pi$
$164$			10.9962i			0.858661i
$165$		0			0
$166$	−14.4247			−1.11957
$167$	11.8176	−	11.8176i	0.914477	−	0.914477i	−0.0821438	−	0.996620i	$-0.526177\pi$
$167$	11.8176	−	11.8176i	0.914477	−	0.914477i	0.996620	+	0.0821438i	$0.0261767\pi$
$168$	16.5074	+	0.358063i	1.27357	+	0.0276252i
$169$	11.1304	−	6.71665i	0.856187	−	0.516665i
$170$		0			0
$171$	3.37145	+	0.146330i	0.257821	+	0.0111901i
$172$	9.58891	−	9.58891i	0.731147	−	0.731147i
$173$	4.16058	−	4.16058i	0.316323	−	0.316323i	−0.531030	−	0.847353i	$-0.678195\pi$
$173$	4.16058	−	4.16058i	0.316323	−	0.316323i	0.847353	+	0.531030i	$0.178195\pi$
$174$	−0.978544	−	1.02194i	−0.0741833	−	0.0774729i
$175$		0			0
$176$	3.40432			0.256610
$177$	0.0503666	+	0.00109251i	0.00378578	+	8.21180e-5i
$178$	−22.1897	−	22.1897i	−1.66319	−	1.66319i
$179$	5.51726			0.412379			0.206190	−	0.978512i	$-0.433894\pi$
$179$	5.51726			0.412379			0.206190	+	0.978512i	$0.433894\pi$
$180$		0			0
$181$	15.5001			1.15211			0.576056	−	0.817411i	$-0.304591\pi$
$181$	15.5001			1.15211			0.576056	+	0.817411i	$0.304591\pi$
$182$	34.9500	−	9.72826i	2.59067	−	0.721106i
$183$	−0.373124	+	17.2017i	−0.0275821	+	1.27158i
$184$	−8.38490			−0.618143
$185$		0			0
$186$	19.1811	−	18.3667i	1.40643	−	1.34671i
$187$	5.73343	+	5.73343i	0.419270	+	0.419270i
$188$	−4.89063	−	4.89063i	−0.356686	−	0.356686i
$189$	−17.6665	+	15.5052i	−1.28505	+	1.12784i
$190$		0			0
$191$			18.2212i			1.31844i	0.751951	+	0.659219i	$0.229113\pi$
$191$			18.2212i			1.31844i	−0.751951	+	0.659219i	$0.770887\pi$
$192$	22.3966	+	0.485808i	1.61634	+	0.0350602i
$193$	6.02609	−	6.02609i	0.433767	−	0.433767i	−0.456140	−	0.889908i	$-0.650769\pi$
$193$	6.02609	−	6.02609i	0.433767	−	0.433767i	0.889908	+	0.456140i	$0.150769\pi$
$194$	−35.5411			−2.55170
$195$		0			0
$196$	39.6827			2.83448
$197$	−6.72726	+	6.72726i	−0.479297	+	0.479297i	−0.904907	−	0.425610i	$-0.860060\pi$
$197$	−6.72726	+	6.72726i	−0.479297	+	0.479297i	0.425610	+	0.904907i	$0.360060\pi$
$198$	13.8660	−	12.7124i	0.985414	−	0.903433i
$199$			5.43933i			0.385584i	0.981240	+	0.192792i	$0.0617543\pi$
$199$			5.43933i			0.385584i	−0.981240	+	0.192792i	$0.938246\pi$
$200$		0			0
$201$	−5.36158	+	5.13392i	−0.378177	+	0.362119i
$202$	19.6881	+	19.6881i	1.38525	+	1.38525i
$203$	−1.17476	−	1.17476i	−0.0824517	−	0.0824517i
$204$	10.1549	+	10.6052i	0.710987	+	0.742516i
$205$		0			0
$206$	9.01268			0.627943
$207$	8.79871	−	8.06671i	0.611553	−	0.560675i
$208$	4.19455	−	1.16754i	0.290839	−	0.0809545i
$209$	−3.17115			−0.219353
$210$		0			0
$211$	1.26400			0.0870171			0.0435086	−	0.999053i	$-0.486146\pi$
$211$	1.26400			0.0870171			0.0435086	+	0.999053i	$0.486146\pi$
$212$	−26.5784	−	26.5784i	−1.82541	−	1.82541i
$213$	0.0600269	−	2.76735i	0.00411298	−	0.189615i
$214$	−28.8614			−1.97293
$215$		0			0
$216$	8.22978	−	7.22295i	0.559965	−	0.491460i
$217$	22.0495	−	22.0495i	1.49682	−	1.49682i
$218$	−10.8894	+	10.8894i	−0.737527	+	0.737527i
$219$	−2.38838	−	2.49429i	−0.161392	−	0.168549i
$220$		0			0
$221$	9.03063	+	5.09797i	0.607466	+	0.342927i
$222$	0.245031	−	11.2964i	0.0164454	−	0.758161i
$223$	−13.6651	+	13.6651i	−0.915086	+	0.915086i	−0.996667	−	0.0815806i	$-0.974003\pi$
$223$	−13.6651	+	13.6651i	−0.915086	+	0.915086i	0.0815806	+	0.996667i	$0.474003\pi$
$224$	31.2161			2.08571
$225$		0			0
$226$		−	11.1304i		−	0.740386i
$227$	0.319120	−	0.319120i	0.0211808	−	0.0211808i	−0.696437	−	0.717618i	$-0.745232\pi$
$227$	0.319120	−	0.319120i	0.0211808	−	0.0211808i	0.717618	+	0.696437i	$0.245232\pi$
$228$	−5.74121	−	0.124533i	−0.380221	−	0.00824743i
$229$	−9.97519			−0.659179			−0.329589	−	0.944124i	$-0.606910\pi$
$229$	−9.97519			−0.659179			−0.329589	+	0.944124i	$0.606910\pi$
$230$		0			0
$231$	15.9539	−	15.2765i	1.04969	−	1.00512i
$232$	0.547249	+	0.547249i	0.0359287	+	0.0359287i
$233$	−6.00827	+	6.00827i	−0.393615	+	0.393615i	−0.875974	−	0.482359i	$-0.839780\pi$
$233$	−6.00827	+	6.00827i	−0.393615	+	0.393615i	0.482359	+	0.875974i	$0.339780\pi$
$234$	12.7248	−	20.4188i	0.831847	−	1.33482i
$235$		0			0
$236$	−0.0857284			−0.00558044
$237$	−9.38131	−	0.203491i	−0.609381	−	0.0132182i
$238$	20.4636	+	20.4636i	1.32646	+	1.32646i
$239$			6.04966i			0.391320i	0.980672	+	0.195660i	$0.0626849\pi$
$239$			6.04966i			0.391320i	−0.980672	+	0.195660i	$0.937315\pi$
$240$		0			0
$241$			25.5460i			1.64556i	0.568360	+	0.822780i	$0.307578\pi$
$241$			25.5460i			1.64556i	−0.568360	+	0.822780i	$0.692422\pi$
$242$	4.80112	−	4.80112i	0.308627	−	0.308627i
$243$	−1.68708	+	15.4969i	−0.108226	+	0.994126i
$244$		−	29.2788i		−	1.87438i
$245$		0			0
$246$	9.94057	+	10.3814i	0.633788	+	0.661892i
$247$	−3.90725	+	1.08758i	−0.248613	+	0.0692007i
$248$	−10.2715	+	10.2715i	−0.652243	+	0.652243i
$249$	−8.11297	+	7.76848i	−0.514138	+	0.492307i
$250$		0			0
$251$			7.41987i			0.468338i	0.972196	+	0.234169i	$0.0752369\pi$
$251$			7.41987i			0.468338i	−0.972196	+	0.234169i	$0.924763\pi$
$252$	29.4836	−	27.0308i	1.85730	−	1.70278i
$253$	−7.93172	+	7.93172i	−0.498663	+	0.498663i
$254$		−	23.0963i		−	1.44919i
$255$		0			0
$256$	−7.42324			−0.463953
$257$	9.78767	+	9.78767i	0.610538	+	0.610538i	0.943086	−	0.332548i	$-0.107908\pi$
$257$	9.78767	+	9.78767i	0.610538	+	0.610538i	−0.332548	+	0.943086i	$0.607908\pi$
$258$	0.384391	−	17.7211i	0.0239311	−	1.10327i
$259$		−	13.2673i		−	0.824388i
$260$		0			0
$261$	−1.10074	−	0.0477751i	−0.0681341	−	0.00295720i
$262$	−3.28509	−	3.28509i	−0.202954	−	0.202954i
$263$	−7.39630	+	7.39630i	−0.456076	+	0.456076i	−0.897365	−	0.441289i	$-0.854521\pi$
$263$	−7.39630	+	7.39630i	−0.456076	+	0.456076i	0.441289	+	0.897365i	$0.354521\pi$
$264$	−7.43197	+	7.11640i	−0.457406	+	0.437984i
$265$		0			0
$266$	−11.3184			−0.693974
$267$	−24.4307	−	0.529930i	−1.49514	−	0.0324312i
$268$	8.93215	−	8.93215i	0.545618	−	0.545618i
$269$	18.8601			1.14992			0.574962	−	0.818180i	$-0.305017\pi$
$269$	18.8601			1.14992			0.574962	+	0.818180i	$0.305017\pi$
$270$		0			0
$271$		−	25.2837i		−	1.53587i	−0.640525	−	0.767937i	$-0.721283\pi$
$271$		−	25.2837i		−	1.53587i	0.640525	−	0.767937i	$-0.278717\pi$
$272$	2.45595	+	2.45595i	0.148914	+	0.148914i
$273$	14.4180	−	24.2941i	0.872616	−	1.47034i
$274$			12.3100i			0.743674i
$275$		0			0
$276$	−14.6715	+	14.0485i	−0.883119	+	0.845620i
$277$	23.1897	−	23.1897i	1.39334	−	1.39334i	0.575612	−	0.817723i	$-0.304764\pi$
$277$	23.1897	−	23.1897i	1.39334	−	1.39334i	0.817723	−	0.575612i	$-0.195236\pi$
$278$	26.9786	+	26.9786i	1.61807	+	1.61807i
$279$	0.896710	−	20.6602i	0.0536846	−	1.23689i
$280$		0			0
$281$	10.5921			0.631871			0.315935	−	0.948781i	$-0.397682\pi$
$281$	10.5921			0.631871			0.315935	+	0.948781i	$0.397682\pi$
$282$	−9.03829	−	0.196051i	−0.538222	−	0.0116747i
$283$	−10.2884	−	10.2884i	−0.611583	−	0.611583i	0.331776	−	0.943358i	$-0.392352\pi$
$283$	−10.2884	−	10.2884i	−0.611583	−	0.611583i	−0.943358	+	0.331776i	$0.892352\pi$
$284$			4.71027i			0.279503i
$285$		0			0
$286$	−11.1143	+	19.6881i	−0.657203	+	1.16418i
$287$	11.9338	+	11.9338i	0.704430	+	0.704430i
$288$	15.2594	−	13.9899i	0.899169	−	0.824363i
$289$		−	8.72757i		−	0.513386i
$290$		0			0
$291$	−19.9896	+	19.1408i	−1.17181	+	1.12206i
$292$	4.15538	+	4.15538i	0.243175	+	0.243175i
$293$	17.5225	+	17.5225i	1.02368	+	1.02368i	0.999713	+	0.0239636i	$0.00762857\pi$
$293$	17.5225	+	17.5225i	1.02368	+	1.02368i	0.0239636	+	0.999713i	$0.492371\pi$
$294$	37.4639	−	35.8731i	2.18494	−	2.09216i
$295$		0			0
$296$			6.18043i			0.359230i
$297$	0.952410	−	14.6176i	0.0552644	−	0.848197i
$298$	4.63465	+	4.63465i	0.268478	+	0.268478i
$299$	−7.05261	+	12.4931i	−0.407863	+	0.722496i
$300$		0			0
$301$		−	20.8130i		−	1.19964i
$302$	1.76920	+	1.76920i	0.101806	+	0.101806i
$303$	21.6764	+	0.470187i	1.24528	+	0.0270115i
$304$	−1.35838			−0.0779085
$305$		0			0
$306$	19.1742	+	0.832214i	1.09612	+	0.0475745i
$307$	3.40185	+	3.40185i	0.194154	+	0.194154i	0.797488	−	0.603335i	$-0.206162\pi$
$307$	3.40185	+	3.40185i	0.194154	+	0.194154i	−0.603335	+	0.797488i	$0.706162\pi$
$308$	−26.5784	+	26.5784i	−1.51445	+	1.51445i
$309$	5.06907	−	4.85383i	0.288369	−	0.276125i
$310$		0			0
$311$		−	16.9575i		−	0.961573i	−0.876838	−	0.480787i	$-0.840351\pi$
$311$		−	16.9575i		−	0.961573i	0.876838	−	0.480787i	$-0.159649\pi$
$312$	−6.71649	+	11.3172i	−0.380246	+	0.640708i
$313$	15.7739	+	15.7739i	0.891595	+	0.891595i	0.994673	−	0.103078i	$-0.0328693\pi$
$313$	15.7739	+	15.7739i	0.891595	+	0.891595i	−0.103078	+	0.994673i	$0.532869\pi$
$314$		−	39.4933i		−	2.22873i
$315$		0			0
$316$	15.9678			0.898260
$317$	9.13373	−	9.13373i	0.513001	−	0.513001i	−0.402443	−	0.915445i	$-0.631839\pi$
$317$	9.13373	−	9.13373i	0.513001	−	0.513001i	0.915445	+	0.402443i	$0.131839\pi$
$318$	−49.1192	−	1.06545i	−2.75447	−	0.0597475i
$319$	1.03534			0.0579682
$320$		0			0
$321$	−16.2327	+	15.5435i	−0.906023	+	0.867553i
$322$	−28.3096	+	28.3096i	−1.57763	+	1.57763i
$323$	−2.28773	−	2.28773i	−0.127293	−	0.127293i
$324$	2.29833	−	26.4270i	0.127685	−	1.46816i
$325$		0			0
$326$		−	15.1599i		−	0.839627i
$327$	−0.260060	+	11.9892i	−0.0143813	+	0.663004i
$328$	−5.55925	−	5.55925i	−0.306958	−	0.306958i
$329$	−10.6152			−0.585237
$330$		0			0
$331$			10.6346i			0.584533i	0.956337	+	0.292266i	$0.0944094\pi$
$331$			10.6346i			0.584533i	−0.956337	+	0.292266i	$0.905591\pi$
$332$	13.5158	−	13.5158i	0.741777	−	0.741777i
$333$	−5.94590	−	6.48545i	−0.325833	−	0.355400i
$334$			37.1736i			2.03405i
$335$		0			0
$336$	6.83394	−	6.54376i	0.372822	−	0.356992i
$337$	−2.87201	+	2.87201i	−0.156448	+	0.156448i	−0.780991	−	0.624543i	$-0.785285\pi$
$337$	−2.87201	+	2.87201i	−0.156448	+	0.156448i	0.624543	+	0.780991i	$0.285285\pi$
$338$	−6.94201	+	28.0699i	−0.377596	+	1.52680i
$339$	−5.99436	−	6.26017i	−0.325569	−	0.340006i
$340$		0			0
$341$			19.4328i			1.05234i
$342$	−5.53277	+	5.07247i	−0.299178	+	0.274288i
$343$	20.6751	−	20.6751i	1.11635	−	1.11635i
$344$			9.69553i			0.522748i
$345$		0			0
$346$			13.0875i			0.703590i
$347$	−12.2533	−	12.2533i	−0.657790	−	0.657790i	0.297066	−	0.954857i	$-0.403992\pi$
$347$	−12.2533	−	12.2533i	−0.657790	−	0.657790i	−0.954857	+	0.297066i	$0.903992\pi$
$348$	1.87444	+	0.0406587i	0.100481	+	0.00217954i
$349$	14.7082			0.787311			0.393656	−	0.919258i	$-0.371210\pi$
$349$	14.7082			0.787311			0.393656	+	0.919258i	$0.371210\pi$
$350$		0			0
$351$	−3.83974	−	18.3373i	−0.204950	−	0.978772i
$352$	−13.7558	+	13.7558i	−0.733187	+	0.733187i
$353$	−20.3803	−	20.3803i	−1.08474	−	1.08474i	−0.996061	−	0.0886743i	$-0.971737\pi$
$353$	−20.3803	−	20.3803i	−1.08474	−	1.08474i	−0.0886743	−	0.996061i	$-0.528263\pi$
$354$	−0.0809349	+	0.0774983i	−0.00430164	+	0.00411899i
$355$		0			0
$356$	41.5833			2.20391
$357$	22.5302	+	0.488707i	1.19243	+	0.0258651i
$358$	−8.67756	+	8.67756i	−0.458623	+	0.458623i
$359$			11.3546i			0.599274i	0.954053	+	0.299637i	$0.0968656\pi$
$359$			11.3546i			0.599274i	−0.954053	+	0.299637i	$0.903134\pi$
$360$		0			0
$361$	−17.7347			−0.933403
$362$	−24.3785	+	24.3785i	−1.28131	+	1.28131i
$363$	0.114659	−	5.28599i	0.00601805	−	0.277443i
$364$	−23.6326	+	41.8633i	−1.23869	+	2.19423i
$365$		0			0
$366$	−26.4680	−	27.6417i	−1.38350	−	1.44485i
$367$	7.61351	−	7.61351i	0.397422	−	0.397422i	−0.479901	−	0.877323i	$-0.659327\pi$
$367$	7.61351	−	7.61351i	0.397422	−	0.397422i	0.877323	+	0.479901i	$0.159327\pi$
$368$	−3.39760	+	3.39760i	−0.177112	+	0.177112i
$369$	11.1819	+	0.485325i	0.582106	+	0.0252650i
$370$		0			0
$371$	−57.6892			−2.99507
$372$	−0.763140	+	35.1821i	−0.0395670	+	1.82411i
$373$	−3.82793	−	3.82793i	−0.198203	−	0.198203i	0.601026	−	0.799229i	$-0.294759\pi$
$373$	−3.82793	−	3.82793i	−0.198203	−	0.198203i	−0.799229	+	0.601026i	$0.794759\pi$
$374$	−18.0351			−0.932573
$375$		0			0
$376$	4.94501			0.255019
$377$	1.27567	−	0.355081i	0.0657005	−	0.0182876i
$378$	3.39931	−	52.1725i	0.174842	−	2.68346i
$379$	−34.1628			−1.75482			−0.877412	−	0.479738i	$-0.840732\pi$
$379$	−34.1628			−1.75482			−0.877412	+	0.479738i	$0.840732\pi$
$380$		0			0
$381$	−12.4387	−	12.9902i	−0.637252	−	0.665510i
$382$	−28.6583	−	28.6583i	−1.46629	−	1.46629i
$383$	−14.2931	−	14.2931i	−0.730343	−	0.730343i	0.240344	−	0.970688i	$-0.422740\pi$
$383$	−14.2931	−	14.2931i	−0.730343	−	0.730343i	−0.970688	+	0.240344i	$0.922740\pi$
$384$	−18.7239	+	17.9289i	−0.955502	+	0.914930i
$385$		0			0
$386$			18.9557i			0.964819i
$387$	−9.32760	−	10.1740i	−0.474149	−	0.517175i
$388$	33.3018	−	33.3018i	1.69064	−	1.69064i
$389$	33.9053			1.71907			0.859533	−	0.511080i	$-0.170755\pi$
$389$	33.9053			1.71907			0.859533	+	0.511080i	$0.170755\pi$
$390$		0			0
$391$	−11.4442			−0.578759
$392$	−20.0620	+	20.0620i	−1.01328	+	1.01328i
$393$	−3.61686	−	0.0784539i	−0.182447	−	0.00395748i
$394$		−	21.1613i		−	1.06609i
$395$		0			0
$396$	−1.08089	+	24.9038i	−0.0543170	+	1.25147i
$397$	3.85818	+	3.85818i	0.193636	+	0.193636i	0.797265	−	0.603629i	$-0.206279\pi$
$397$	3.85818	+	3.85818i	0.193636	+	0.193636i	−0.603629	+	0.797265i	$0.706279\pi$
$398$	−8.55499	−	8.55499i	−0.428823	−	0.428823i
$399$	−6.36587	+	6.09557i	−0.318692	+	0.305160i
$400$		0			0
$401$	−11.0143			−0.550028			−0.275014	−	0.961440i	$-0.588682\pi$
$401$	−11.0143			−0.550028			−0.275014	+	0.961440i	$0.588682\pi$
$402$	0.358063	−	16.5074i	0.0178586	−	0.823312i
$403$	6.66465	+	23.9436i	0.331990	+	1.19272i
$404$	−36.8952			−1.83561
$405$		0			0
$406$	3.69532			0.183396
$407$	5.84640	+	5.84640i	0.289795	+	0.289795i
$408$	−10.4955	−	0.227660i	−0.519605	−	0.0112708i
$409$	32.6861			1.61622			0.808111	−	0.589030i	$-0.200490\pi$
$409$	32.6861			1.61622			0.808111	+	0.589030i	$0.200490\pi$
$410$		0			0
$411$	6.62961	+	6.92360i	0.327015	+	0.341516i
$412$	−8.44483	+	8.44483i	−0.416047	+	0.416047i
$413$	−0.0930378	+	0.0930378i	−0.00457809	+	0.00457809i
$414$	−1.15130	+	26.5260i	−0.0565832	+	1.30368i
$415$		0			0
$416$	−12.2312	+	21.6665i	−0.599683	+	1.06229i
$417$	29.7033	+	0.644298i	1.45457	+	0.0315514i
$418$	4.98759	−	4.98759i	0.243951	−	0.243951i
$419$	−25.4271			−1.24220			−0.621099	−	0.783732i	$-0.713313\pi$
$419$	−25.4271			−1.24220			−0.621099	+	0.783732i	$0.713313\pi$
$420$		0			0
$421$		−	4.27667i		−	0.208432i	−0.994555	−	0.104216i	$-0.966767\pi$
$421$		−	4.27667i		−	0.208432i	0.994555	−	0.104216i	$-0.0332334\pi$
$422$	−1.98802	+	1.98802i	−0.0967752	+	0.0967752i
$423$	−5.18905	+	4.75735i	−0.252300	+	0.231310i
$424$	26.8740			1.30512
$425$		0			0
$426$	4.25808	+	4.44690i	0.206305	+	0.215453i
$427$	−31.7752	−	31.7752i	−1.53771	−	1.53771i
$428$	27.0430	−	27.0430i	1.30717	−	1.30717i
$429$	4.35202	+	17.0590i	0.210118	+	0.823616i
$430$		0			0
$431$	17.6300			0.849205			0.424603	−	0.905380i	$-0.360414\pi$
$431$	17.6300			0.849205			0.424603	+	0.905380i	$0.360414\pi$
$432$	0.407970	−	6.26151i	0.0196285	−	0.301257i
$433$	−21.8405	−	21.8405i	−1.04959	−	1.04959i	−0.998705	−	0.0508807i	$-0.983797\pi$
$433$	−21.8405	−	21.8405i	−1.04959	−	1.04959i	−0.0508807	−	0.998705i	$-0.516203\pi$
$434$			69.3589i			3.32933i
$435$		0			0
$436$		−	20.4067i		−	0.977304i
$437$	3.16489	−	3.16489i	0.151397	−	0.151397i
$438$	7.67949	+	0.166577i	0.366940	+	0.00795935i
$439$			23.4447i			1.11896i	0.828845	+	0.559478i	$0.188998\pi$
$439$			23.4447i			1.11896i	−0.828845	+	0.559478i	$0.811002\pi$
$440$		0			0
$441$	1.75142	−	40.3527i	0.0834008	−	1.92156i
$442$	−22.2215	+	6.18530i	−1.05697	+	0.294205i
$443$	11.4089	−	11.4089i	0.542054	−	0.542054i	−0.382076	−	0.924131i	$-0.624791\pi$
$443$	11.4089	−	11.4089i	0.542054	−	0.542054i	0.924131	+	0.382076i	$0.124791\pi$
$444$	10.3550	+	10.8142i	0.491428	+	0.513220i
$445$		0			0
$446$		−	42.9852i		−	2.03541i
$447$	5.10272	+	0.110684i	0.241350	+	0.00523517i
$448$	−41.3713	+	41.3713i	−1.95461	+	1.95461i
$449$		−	20.1684i		−	0.951808i	−0.879497	−	0.475904i	$-0.842121\pi$
$449$		−	20.1684i		−	0.951808i	0.879497	−	0.475904i	$-0.157879\pi$
$450$		0			0
$451$	−10.5176			−0.495253
$452$	10.4292	+	10.4292i	0.490546	+	0.490546i
$453$	1.94788	+	0.0422518i	0.0915195	+	0.00198516i
$454$			1.00383i			0.0471119i
$455$		0			0
$456$	2.96548	−	2.83956i	0.138871	−	0.132975i
$457$	−9.04890	−	9.04890i	−0.423290	−	0.423290i	0.463045	−	0.886335i	$-0.346757\pi$
$457$	−9.04890	−	9.04890i	−0.423290	−	0.423290i	−0.886335	+	0.463045i	$0.846757\pi$
$458$	15.6890	−	15.6890i	0.733098	−	0.733098i
$459$	11.2325	−	9.85833i	0.524288	−	0.460147i
$460$		0			0
$461$	17.6354			0.821365			0.410682	−	0.911779i	$-0.365291\pi$
$461$	17.6354			0.821365			0.410682	+	0.911779i	$0.365291\pi$
$462$	−1.06545	+	49.1192i	−0.0495693	+	2.28523i
$463$	−21.8211	+	21.8211i	−1.01411	+	1.01411i	−0.0142127	+	0.999899i	$0.504524\pi$
$463$	−21.8211	+	21.8211i	−1.01411	+	1.01411i	−0.999899	+	0.0142127i	$0.995476\pi$
$464$	0.443496			0.0205888
$465$		0			0
$466$		−	18.8996i		−	0.875509i
$467$	21.6520	+	21.6520i	1.00194	+	1.00194i	0.999998	+	0.00193691i	$0.000616538\pi$
$467$	21.6520	+	21.6520i	1.00194	+	1.00194i	0.00193691	+	0.999998i	$0.499383\pi$
$468$	7.20920	+	31.0553i	0.333246	+	1.43553i
$469$		−	19.3874i		−	0.895229i
$470$		0			0
$471$	−21.2693	−	22.2125i	−0.980038	−	1.02350i
$472$	0.0433408	−	0.0433408i	0.00199492	−	0.00199492i
$473$	9.17151	+	9.17151i	0.421707	+	0.421707i
$474$	15.0750	−	14.4349i	0.692417	−	0.663016i
$475$		0			0
$476$	−38.3485			−1.75770
$477$	−28.2003	+	25.8542i	−1.29120	+	1.18378i
$478$	−9.51492	−	9.51492i	−0.435202	−	0.435202i
$479$		−	32.2569i		−	1.47386i	−0.675971	−	0.736928i	$-0.736276\pi$
$479$		−	32.2569i		−	1.47386i	0.675971	−	0.736928i	$-0.263724\pi$
$480$		0			0
$481$	9.20857	+	5.19842i	0.419875	+	0.237027i
$482$	−40.1787	−	40.1787i	−1.83009	−	1.83009i
$483$	−0.676085	+	31.1687i	−0.0307629	+	1.41822i
$484$			8.99723i			0.408965i
$485$		0			0
$486$	−21.7201	−	27.0270i	−0.985244	−	1.22597i
$487$	5.05289	+	5.05289i	0.228968	+	0.228968i	0.812262	−	0.583293i	$-0.198236\pi$
$487$	5.05289	+	5.05289i	0.228968	+	0.228968i	−0.583293	+	0.812262i	$0.698236\pi$
$488$	14.8022	+	14.8022i	0.670063	+	0.670063i
$489$	−8.16443	−	8.52647i	−0.369208	−	0.385580i
$490$		0			0
$491$			26.1702i			1.18104i	0.807022	+	0.590522i	$0.201078\pi$
$491$			26.1702i			1.18104i	−0.807022	+	0.590522i	$0.798922\pi$
$492$	−19.0415	−	0.413033i	−0.858459	−	0.0186210i
$493$	0.746919	+	0.746919i	0.0336395	+	0.0336395i
$494$	4.43480	−	7.85588i	0.199531	−	0.353453i
$495$		0			0
$496$			8.32415i			0.373765i
$497$	5.11188	+	5.11188i	0.229299	+	0.229299i
$498$	0.541810	−	24.9784i	0.0242791	−	1.11931i
$499$	−19.6289			−0.878712			−0.439356	−	0.898313i	$-0.644793\pi$
$499$	−19.6289			−0.878712			−0.439356	+	0.898313i	$0.644793\pi$
$500$		0			0
$501$	20.0201	+	20.9078i	0.894430	+	0.934093i
$502$	−11.6700	−	11.6700i	−0.520857	−	0.520857i
$503$	30.7794	−	30.7794i	1.37239	−	1.37239i	0.515489	−	0.856896i	$-0.327610\pi$
$503$	30.7794	−	30.7794i	1.37239	−	1.37239i	0.856896	−	0.515489i	$-0.172390\pi$
$504$	−1.24008	+	28.5714i	−0.0552374	+	1.27267i
$505$		0			0
$506$		−	24.9501i		−	1.10917i
$507$	11.2128	+	19.5262i	0.497977	+	0.867190i
$508$	21.6411	+	21.6411i	0.960170	+	0.960170i
$509$		−	7.50375i		−	0.332598i	−0.986075	−	0.166299i	$-0.946818\pi$
$509$		−	7.50375i		−	0.332598i	0.986075	−	0.166299i	$-0.0531817\pi$
$510$		0			0
$511$	9.01935			0.398993
$512$	−9.49120	+	9.49120i	−0.419456	+	0.419456i
$513$	−0.380028	+	5.83265i	−0.0167786	+	0.257518i
$514$	−30.7881			−1.35801
$515$		0			0
$516$	16.2444	+	16.9647i	0.715120	+	0.746831i
$517$	4.67775	−	4.67775i	0.205727	−	0.205727i
$518$	20.8668	+	20.8668i	0.916834	+	0.916834i
$519$	7.04836	+	7.36091i	0.309389	+	0.323108i
$520$		0			0
$521$		−	3.88636i		−	0.170264i	−0.996370	−	0.0851322i	$-0.972869\pi$
$521$		−	3.88636i		−	0.170264i	0.996370	−	0.0851322i	$-0.0271312\pi$
$522$	1.80639	−	1.65610i	0.0790634	−	0.0724857i
$523$	−26.2758	−	26.2758i	−1.14896	−	1.14896i	−0.986757	−	0.162203i	$-0.948140\pi$
$523$	−26.2758	−	26.2758i	−1.14896	−	1.14896i	−0.162203	−	0.986757i	$-0.551860\pi$
$524$	6.15623			0.268936
$525$		0			0
$526$		−	23.2658i		−	1.01444i
$527$	−14.0192	+	14.0192i	−0.610687	+	0.610687i
$528$	−0.127871	+	5.89507i	−0.00556486	+	0.256550i
$529$			7.16788i			0.311647i
$530$		0			0
$531$	−0.00378367	+	0.0871759i	−0.000164197	+	0.00378311i
$532$	10.6052	−	10.6052i	0.459796	−	0.459796i
$533$	−12.9590	+	3.60710i	−0.561315	+	0.156241i
$534$	39.2582	−	37.5912i	1.69887	−	1.62673i
$535$		0			0
$536$			9.03146i			0.390100i
$537$	−0.207236	+	9.55393i	−0.00894288	+	0.412282i
$538$	−29.6633	+	29.6633i	−1.27887	+	1.27887i
$539$			37.9554i			1.63485i
$540$		0			0
$541$			15.7873i			0.678749i	0.940651	+	0.339374i	$0.110215\pi$
$541$			15.7873i			0.678749i	−0.940651	+	0.339374i	$0.889785\pi$
$542$	39.7662	+	39.7662i	1.70811	+	1.70811i
$543$	−0.582203	+	26.8406i	−0.0249847	+	1.15184i
$544$	−19.8475			−0.850953
$545$		0			0
$546$	15.5331	+	60.8864i	0.664755	+	2.60570i
$547$	12.4325	−	12.4325i	0.531575	−	0.531575i	−0.389466	−	0.921041i	$-0.627340\pi$
$547$	12.4325	−	12.4325i	0.531575	−	0.531575i	0.921041	+	0.389466i	$0.127340\pi$
$548$	−11.5344	−	11.5344i	−0.492725	−	0.492725i
$549$	−29.7732	−	1.29224i	−1.27069	−	0.0551513i
$550$		0			0
$551$	−0.413120			−0.0175995
$552$	0.314948	−	14.5197i	0.0134051	−	0.617997i
$553$	17.3293	−	17.3293i	0.736916	−	0.736916i
$554$			72.9457i			3.09916i
$555$		0			0
$556$	−50.5576			−2.14412
$557$	27.1000	−	27.1000i	1.14826	−	1.14826i	0.161370	−	0.986894i	$-0.448409\pi$
$557$	27.1000	−	27.1000i	1.14826	−	1.14826i	0.986894	−	0.161370i	$-0.0515914\pi$
$558$	31.0841	+	33.9048i	1.31589	+	1.43530i
$559$	14.4459	+	8.15500i	0.610997	+	0.344920i
$560$		0			0
$561$	−10.1436	+	9.71290i	−0.428264	+	0.410079i
$562$	−16.6593	+	16.6593i	−0.702728	+	0.702728i
$563$	−11.3159	+	11.3159i	−0.476908	+	0.476908i	−0.904141	−	0.427234i	$-0.859488\pi$
$563$	−11.3159	+	11.3159i	−0.476908	+	0.476908i	0.427234	+	0.904141i	$0.359488\pi$
$564$	8.65252	−	8.28513i	0.364337	−	0.348867i
$565$		0			0
$566$	32.3633			1.36033
$567$	−26.1859	−	31.1745i	−1.09970	−	1.30921i
$568$	−2.38132	−	2.38132i	−0.0999181	−	0.0999181i
$569$	24.5114			1.02757			0.513787	−	0.857918i	$-0.328242\pi$
$569$	24.5114			1.02757			0.513787	+	0.857918i	$0.328242\pi$
$570$		0			0
$571$	−5.75974			−0.241038			−0.120519	−	0.992711i	$-0.538456\pi$
$571$	−5.75974			−0.241038			−0.120519	+	0.992711i	$0.538456\pi$
$572$	−8.03358	−	28.8617i	−0.335901	−	1.20677i
$573$	−31.5526	−	0.684412i	−1.31813	−	0.0285917i
$574$	−37.5390			−1.56685
$575$		0			0
$576$	−1.68249	+	38.7647i	−0.0701039	+	1.61520i
$577$	12.2388	+	12.2388i	0.509507	+	0.509507i	0.914375	−	0.404868i	$-0.132683\pi$
$577$	12.2388	+	12.2388i	0.509507	+	0.509507i	−0.404868	+	0.914375i	$0.632683\pi$
$578$	13.7267	+	13.7267i	0.570957	+	0.570957i
$579$	10.2087	+	10.6614i	0.424259	+	0.443072i
$580$		0			0
$581$		−	29.3364i		−	1.21708i
$582$	1.33497	−	61.5445i	0.0553363	−	2.55110i
$583$	25.4215	−	25.4215i	1.05285	−	1.05285i
$584$	−4.20158			−0.173863
$585$		0			0
$586$	−55.1189			−2.27694
$587$	−4.62321	+	4.62321i	−0.190820	+	0.190820i	−0.796051	−	0.605230i	$-0.793081\pi$
$587$	−4.62321	+	4.62321i	−0.190820	+	0.190820i	0.605230	+	0.796051i	$0.293081\pi$
$588$	−1.49054	+	68.7163i	−0.0614686	+	2.83381i
$589$		−	7.75401i		−	0.319498i
$590$		0			0
$591$	−11.3965	−	11.9019i	−0.468791	−	0.489579i
$592$	2.50434	+	2.50434i	0.102928	+	0.102928i
$593$	1.14398	+	1.14398i	0.0469777	+	0.0469777i	0.730205	−	0.683228i	$-0.239424\pi$
$593$	1.14398	+	1.14398i	0.0469777	+	0.0469777i	−0.683228	+	0.730205i	$0.739424\pi$
$594$	21.4926	+	24.4885i	0.881851	+	1.00477i
$595$		0			0
$596$	−8.68529			−0.355763
$597$	−9.41898	−	0.204309i	−0.385493	−	0.00836179i
$598$	−8.55685	−	30.7416i	−0.349915	−	1.25712i
$599$	20.1045			0.821447			0.410723	−	0.911760i	$-0.365276\pi$
$599$	20.1045			0.821447			0.410723	+	0.911760i	$0.365276\pi$
$600$		0			0
$601$	−2.94840			−0.120268			−0.0601338	−	0.998190i	$-0.519153\pi$
$601$	−2.94840			−0.120268			−0.0601338	+	0.998190i	$0.519153\pi$
$602$	32.7347	+	32.7347i	1.33417	+	1.33417i
$603$	−8.68874	−	9.47719i	−0.353833	−	0.385941i
$604$	−3.31547			−0.134905
$605$		0			0
$606$	−34.8323	+	33.3532i	−1.41496	+	1.35488i
$607$	−13.2165	+	13.2165i	−0.536440	+	0.536440i	−0.922481	−	0.386041i	$-0.873842\pi$
$607$	−13.2165	+	13.2165i	−0.536440	+	0.536440i	0.386041	+	0.922481i	$0.373842\pi$
$608$	5.48880	−	5.48880i	0.222600	−	0.222600i
$609$	2.07838	−	1.99013i	0.0842204	−	0.0806443i
$610$		0			0
$611$	4.15929	−	7.36784i	0.168267	−	0.298071i
$612$	−18.7459	+	17.1864i	−0.757760	+	0.694718i
$613$	14.8172	−	14.8172i	0.598463	−	0.598463i	−0.341440	−	0.939903i	$-0.610915\pi$
$613$	14.8172	−	14.8172i	0.598463	−	0.598463i	0.939903	+	0.341440i	$0.110915\pi$
$614$	−10.7009			−0.431852
$615$		0			0
$616$		−	26.8740i		−	1.08278i
$617$	−17.5429	+	17.5429i	−0.706252	+	0.706252i	−0.965745	−	0.259493i	$-0.916445\pi$
$617$	−17.5429	+	17.5429i	−0.706252	+	0.706252i	0.259493	+	0.965745i	$0.416445\pi$
$618$	−0.338528	+	15.6067i	−0.0136176	+	0.627795i
$619$	13.6862			0.550096			0.275048	−	0.961430i	$-0.411306\pi$
$619$	13.6862			0.550096			0.275048	+	0.961430i	$0.411306\pi$
$620$		0			0
$621$	13.6382	+	15.5392i	0.547281	+	0.623568i
$622$	26.6708	+	26.6708i	1.06940	+	1.06940i
$623$	45.1288	−	45.1288i	1.80805	−	1.80805i
$624$	1.86421	+	7.30731i	0.0746283	+	0.292527i
$625$		0			0
$626$	−49.6185			−1.98315
$627$	0.119113	−	5.49130i	0.00475690	−	0.219302i
$628$	37.0050	+	37.0050i	1.47666	+	1.47666i
$629$			8.43543i			0.336343i
$630$		0			0
$631$		−	23.8965i		−	0.951306i	−0.879633	−	0.475653i	$-0.842212\pi$
$631$		−	23.8965i		−	0.951306i	0.879633	−	0.475653i	$-0.157788\pi$
$632$	−8.07269	+	8.07269i	−0.321114	+	0.321114i
$633$	−0.0474774	+	2.18879i	−0.00188706	+	0.0869967i
$634$			28.7311i			1.14106i
$635$		0			0
$636$	47.0227	−	45.0261i	1.86457	−	1.78540i
$637$	13.0171	+	46.7657i	0.515758	+	1.85293i
$638$	−1.62839	+	1.62839i	−0.0644687	+	0.0644687i
$639$	4.78980	+	0.207890i	0.189482	+	0.00822402i
$640$		0			0
$641$		−	21.5542i		−	0.851340i	−0.904879	−	0.425670i	$-0.860039\pi$
$641$		−	21.5542i		−	0.851340i	0.904879	−	0.425670i	$-0.139961\pi$
$642$	1.08407	−	49.9777i	0.0427850	−	1.97246i
$643$	12.9420	−	12.9420i	0.510382	−	0.510382i	−0.404261	−	0.914644i	$-0.632471\pi$
$643$	12.9420	−	12.9420i	0.510382	−	0.510382i	0.914644	+	0.404261i	$0.132471\pi$
$644$		−	53.0519i		−	2.09054i
$645$		0			0
$646$	7.19631			0.283135
$647$	4.00836	+	4.00836i	0.157585	+	0.157585i	0.781496	−	0.623911i	$-0.214457\pi$
$647$	4.00836	+	4.00836i	0.157585	+	0.157585i	−0.623911	+	0.781496i	$0.714457\pi$
$648$	12.1985	+	14.5223i	0.479201	+	0.570492i
$649$		−	0.0819968i		−	0.00321865i
$650$		0			0
$651$	37.3536	+	39.0100i	1.46400	+	1.52892i
$652$	14.2047	+	14.2047i	0.556299	+	0.556299i
$653$	−30.3911	+	30.3911i	−1.18929	+	1.18929i	−0.212032	+	0.977263i	$0.568008\pi$
$653$	−30.3911	+	30.3911i	−1.18929	+	1.18929i	−0.977263	+	0.212032i	$0.931992\pi$
$654$	−18.4476	−	19.2657i	−0.721359	−	0.753347i
$655$		0			0
$656$	−4.50526			−0.175901
$657$	4.40894	−	4.04214i	0.172009	−	0.157699i
$658$	16.6957	−	16.6957i	0.650864	−	0.650864i
$659$	−0.825043			−0.0321391			−0.0160695	−	0.999871i	$-0.505115\pi$
$659$	−0.825043			−0.0321391			−0.0160695	+	0.999871i	$0.505115\pi$
$660$		0			0
$661$			7.76920i			0.302187i	0.988519	+	0.151093i	$0.0482794\pi$
$661$			7.76920i			0.302187i	−0.988519	+	0.151093i	$0.951721\pi$
$662$	−16.7262	−	16.7262i	−0.650082	−	0.650082i
$663$	−9.16707	+	15.4464i	−0.356019	+	0.599887i
$664$			13.6661i			0.530348i
$665$		0			0
$666$	19.5520	+	0.848612i	0.757626	+	0.0328830i
$667$	−1.03330	+	1.03330i	−0.0400095	+	0.0400095i
$668$	−34.8315	−	34.8315i	−1.34767	−	1.34767i
$669$	−23.1499	−	24.1764i	−0.895026	−	0.934716i
$670$		0			0
$671$	28.0043			1.08110
$672$	−1.17252	+	54.0552i	−0.0452309	+	2.08522i
$673$	0.296312	+	0.296312i	0.0114220	+	0.0114220i	0.712795	−	0.701373i	$-0.247429\pi$
$673$	0.296312	+	0.296312i	0.0114220	+	0.0114220i	−0.701373	+	0.712795i	$0.747429\pi$
$674$		−	9.03420i		−	0.347984i
$675$		0			0
$676$	−19.7967	−	32.8060i	−0.761413	−	1.26177i
$677$	−33.5761	−	33.5761i	−1.29044	−	1.29044i	−0.934517	−	0.355919i	$-0.884168\pi$
$677$	−33.5761	−	33.5761i	−1.29044	−	1.29044i	−0.355919	−	0.934517i	$-0.615832\pi$
$678$	19.2739	+	0.418074i	0.740211	+	0.0160560i
$679$		−	72.2823i		−	2.77394i
$680$		0			0
$681$	0.540616	+	0.564589i	0.0207164	+	0.0216351i
$682$	−30.5639	−	30.5639i	−1.17035	−	1.17035i
$683$	−18.3743	−	18.3743i	−0.703075	−	0.703075i	0.261994	−	0.965069i	$-0.415620\pi$
$683$	−18.3743	−	18.3743i	−0.703075	−	0.703075i	−0.965069	+	0.261994i	$0.915620\pi$
$684$	0.431295	−	9.93705i	0.0164910	−	0.379953i
$685$		0			0
$686$			65.0358i			2.48308i
$687$	0.374681	−	17.2735i	0.0142950	−	0.659024i
$688$	3.92867	+	3.92867i	0.149779	+	0.149779i
$689$	22.6039	−	40.0410i	0.861142	−	1.52544i
$690$		0			0
$691$		−	50.1745i		−	1.90873i	−0.298647	−	0.954364i	$-0.596535\pi$
$691$		−	50.1745i		−	1.90873i	0.298647	−	0.954364i	$-0.403465\pi$
$692$	−12.2629	−	12.2629i	−0.466167	−	0.466167i
$693$	25.8542	+	28.2003i	0.982118	+	1.07124i
$694$	38.5440			1.46311
$695$		0			0
$696$	−0.968196	+	0.927085i	−0.0366994	+	0.0351411i
$697$	−7.58760	−	7.58760i	−0.287401	−	0.287401i
$698$	−23.1331	+	23.1331i	−0.875600	+	0.875600i
$699$	−10.1785	−	10.6299i	−0.384986	−	0.402058i
$700$		0			0
$701$			25.0442i			0.945906i	0.881088	+	0.472953i	$0.156812\pi$
$701$			25.0442i			0.945906i	−0.881088	+	0.472953i	$0.843188\pi$
$702$	34.8801	+	22.8018i	1.31646	+	0.860598i
$703$	−2.33281	−	2.33281i	−0.0879837	−	0.0879837i
$704$		−	36.4617i		−	1.37420i
$705$		0			0
$706$	64.1084			2.41275
$707$	−40.0410	+	40.0410i	−1.50590	+	1.50590i
$708$	0.00322007	−	0.148451i	0.000121018	−	0.00557913i
$709$	−34.4704			−1.29456			−0.647282	−	0.762251i	$-0.724094\pi$
$709$	−34.4704			−1.29456			−0.647282	+	0.762251i	$0.724094\pi$
$710$		0			0
$711$	0.704749	−	16.2374i	0.0264301	−	0.608951i
$712$	−21.0228	+	21.0228i	−0.787863	+	0.787863i
$713$	−19.3944	−	19.3944i	−0.726327	−	0.726327i
$714$	−36.2042	+	34.6670i	−1.35491	+	1.29738i
$715$		0			0
$716$		−	16.2616i		−	0.607726i
$717$	−10.4759	−	0.227233i	−0.391228	−	0.00848619i
$718$	−17.8586	−	17.8586i	−0.666476	−	0.666476i
$719$	−32.5125			−1.21251			−0.606255	−	0.795270i	$-0.707329\pi$
$719$	−32.5125			−1.21251			−0.606255	+	0.795270i	$0.707329\pi$
$720$		0			0
$721$			18.3297i			0.682634i
$722$	27.8931	−	27.8931i	1.03807	−	1.03807i
$723$	−44.2365	−	0.959541i	−1.64517	−	0.0356857i
$724$		−	45.6851i		−	1.69787i
$725$		0			0
$726$	8.13348	+	8.49416i	0.301862	+	0.315248i
$727$	−24.3971	+	24.3971i	−0.904837	+	0.904837i	−0.995850	−	0.0910132i	$-0.970989\pi$
$727$	−24.3971	+	24.3971i	−0.904837	+	0.904837i	0.0910132	+	0.995850i	$0.470989\pi$
$728$	−9.21667	−	33.1121i	−0.341593	−	1.22722i
$729$	−26.7717	−	3.50351i	−0.991545	−	0.129760i
$730$		0			0
$731$			13.2330i			0.489442i
$732$	50.7005	+	1.09975i	1.87394	+	0.0406480i
$733$	−3.61267	+	3.61267i	−0.133437	+	0.133437i	−0.770671	−	0.637234i	$-0.780079\pi$
$733$	−3.61267	+	3.61267i	−0.133437	+	0.133437i	0.637234	+	0.770671i	$0.280079\pi$
$734$			23.9491i			0.883976i
$735$		0			0
$736$		−	27.4573i		−	1.01209i
$737$	8.54334	+	8.54334i	0.314698	+	0.314698i
$738$	−18.3502	+	16.8236i	−0.675481	+	0.619285i
$739$	8.45473			0.311012			0.155506	−	0.987835i	$-0.450299\pi$
$739$	8.45473			0.311012			0.155506	+	0.987835i	$0.450299\pi$
$740$		0			0
$741$	−1.73653	−	6.80682i	−0.0637930	−	0.250055i
$742$	90.7336	−	90.7336i	3.33094	−	3.33094i
$743$	21.2620	+	21.2620i	0.780028	+	0.780028i	0.979835	−	0.199807i	$-0.0640316\pi$
$743$	21.2620	+	21.2620i	0.780028	+	0.780028i	−0.199807	+	0.979835i	$0.564032\pi$
$744$	−17.4008	−	18.1725i	−0.637945	−	0.666235i
$745$		0			0
$746$	12.0412			0.440858
$747$	−13.1475	−	14.3406i	−0.481042	−	0.524694i
$748$	16.8988	−	16.8988i	0.617881	−	0.617881i
$749$		−	58.6975i		−	2.14476i
$750$		0			0
$751$	−2.03706			−0.0743334			−0.0371667	−	0.999309i	$-0.511833\pi$
$751$	−2.03706			−0.0743334			−0.0371667	+	0.999309i	$0.511833\pi$
$752$	2.00374	−	2.00374i	0.0730688	−	0.0730688i
$753$	−12.8486	−	0.278700i	−0.468228	−	0.0101564i
$754$	−1.44791	+	2.56485i	−0.0527298	+	0.0934065i
$755$		0			0
$756$	45.7002	+	52.0705i	1.66210	+	1.89378i
$757$	9.91296	−	9.91296i	0.360293	−	0.360293i	−0.503628	−	0.863921i	$-0.668002\pi$
$757$	9.91296	−	9.91296i	0.360293	−	0.360293i	0.863921	+	0.503628i	$0.168002\pi$
$758$	53.7313	−	53.7313i	1.95161	−	1.95161i
$759$	−13.4370	−	14.0328i	−0.487732	−	0.509360i
$760$		0			0
$761$	−25.0081			−0.906543			−0.453272	−	0.891372i	$-0.649743\pi$
$761$	−25.0081			−0.906543			−0.453272	+	0.891372i	$0.649743\pi$
$762$	39.9946	+	0.867529i	1.44885	+	0.0314273i
$763$	−22.1466	−	22.1466i	−0.801762	−	0.801762i
$764$	53.7053			1.94299
$765$		0			0
$766$	44.9604			1.62449
$767$	−0.0281215	−	0.101030i	−0.00101541	−	0.00364799i
$768$	0.278827	−	12.8544i	0.0100613	−	0.463844i
$769$	37.0720			1.33685			0.668425	−	0.743780i	$-0.266969\pi$
$769$	37.0720			1.33685			0.668425	+	0.743780i	$0.266969\pi$
$770$		0			0
$771$	−17.3164	+	16.5811i	−0.623635	+	0.597155i
$772$	−17.7614	−	17.7614i	−0.639246	−	0.639246i
$773$	−3.40655	−	3.40655i	−0.122525	−	0.122525i	0.643185	−	0.765711i	$-0.277612\pi$
$773$	−3.40655	−	3.40655i	−0.122525	−	0.122525i	−0.765711	+	0.643185i	$0.777612\pi$
$774$	30.6722	+	1.33126i	1.10249	+	0.0478510i
$775$		0			0
$776$			33.6721i			1.20876i
$777$	22.9742	+	0.498336i	0.824194	+	0.0178777i
$778$	−53.3263	+	53.3263i	−1.91184	+	1.91184i
$779$	4.19669			0.150362
$780$		0			0
$781$	−4.50524			−0.161210
$782$	17.9995	−	17.9995i	0.643660	−	0.643660i
$783$	0.124075	−	1.90429i	0.00443407	−	0.0680539i
$784$			16.2584i			0.580657i
$785$		0			0
$786$	5.81200	−	5.56522i	0.207307	−	0.198505i
$787$	−15.5327	−	15.5327i	−0.553681	−	0.553681i	0.373820	−	0.927501i	$-0.378048\pi$
$787$	−15.5327	−	15.5327i	−0.553681	−	0.553681i	−0.927501	+	0.373820i	$0.878048\pi$
$788$	19.8280	+	19.8280i	0.706344	+	0.706344i
$789$	−12.5299	−	13.0856i	−0.446078	−	0.465859i
$790$		0			0
$791$	22.6367			0.804870
$792$	−12.0439	−	13.1368i	−0.427962	−	0.466797i
$793$	34.5048	−	9.60434i	1.22530	−	0.341060i
$794$	−12.1363			−0.430701
$795$		0			0
$796$	16.0320			0.568238
$797$	−25.0570	−	25.0570i	−0.887565	−	0.887565i	0.106724	−	0.994289i	$-0.465964\pi$
$797$	−25.0570	−	25.0570i	−0.887565	−	0.887565i	−0.994289	+	0.106724i	$0.965964\pi$
$798$	0.425133	−	19.5994i	0.0150495	−	0.693810i
$799$	6.74925			0.238771
$800$		0			0
$801$	1.83530	−	42.2854i	0.0648472	−	1.49408i
$802$	17.3233	−	17.3233i	0.611708	−	0.611708i
$803$	−3.97450	+	3.97450i	−0.140257	+	0.140257i
$804$	15.1318	+	15.8028i	0.533657	+	0.557322i
$805$		0			0
$806$	−48.1408	−	27.1764i	−1.69569	−	0.957248i
$807$	−0.708412	+	32.6590i	−0.0249373	+	1.14965i
$808$	18.6527	−	18.6527i	0.656201	−	0.656201i
$809$	−46.4473			−1.63300			−0.816500	−	0.577345i	$-0.804089\pi$
$809$	−46.4473			−1.63300			−0.816500	+	0.577345i	$0.804089\pi$
$810$		0			0
$811$		−	10.6193i		−	0.372892i	−0.982465	−	0.186446i	$-0.940303\pi$
$811$		−	10.6193i		−	0.372892i	0.982465	−	0.186446i	$-0.0596970\pi$
$812$	−3.46249	+	3.46249i	−0.121510	+	0.121510i
$813$	43.7823	+	0.949689i	1.53551	+	0.0333070i
$814$	−18.3905			−0.644585
$815$		0			0
$816$	−4.34507	+	4.16058i	−0.152108	+	0.145649i
$817$	−3.65959	−	3.65959i	−0.128033	−	0.128033i
$818$	−51.4087	+	51.4087i	−1.79746	+	1.79746i
$819$	41.5271	+	25.8793i	1.45107	+	0.904297i
$820$		0			0
$821$	33.7003			1.17615			0.588075	−	0.808806i	$-0.299886\pi$
$821$	33.7003			1.17615			0.588075	+	0.808806i	$0.299886\pi$
$822$	−21.3165	−	0.462380i	−0.743499	−	0.0161273i
$823$	−21.0331	−	21.0331i	−0.733169	−	0.733169i	0.238078	−	0.971246i	$-0.423483\pi$
$823$	−21.0331	−	21.0331i	−0.733169	−	0.733169i	−0.971246	+	0.238078i	$0.923483\pi$
$824$		−	8.53873i		−	0.297461i
$825$		0			0
$826$		−	0.292660i		−	0.0101829i
$827$	29.1434	−	29.1434i	1.01342	−	1.01342i	0.0135073	−	0.999909i	$-0.495700\pi$
$827$	29.1434	−	29.1434i	1.01342	−	1.01342i	0.999909	−	0.0135073i	$-0.00429965\pi$
$828$	−23.7759	−	25.9334i	−0.826270	−	0.901249i
$829$		−	33.6661i		−	1.16927i	−0.811296	−	0.584636i	$-0.801237\pi$
$829$		−	33.6661i		−	1.16927i	0.811296	−	0.584636i	$-0.198763\pi$
$830$		0			0
$831$	39.2853	+	41.0274i	1.36279	+	1.42322i
$832$	−12.5049	−	44.9253i	−0.433528	−	1.55751i
$833$	−27.3818	+	27.3818i	−0.948723	+	0.948723i
$834$	−47.7307	+	45.7040i	−1.65278	+	1.58260i
$835$		0			0
$836$			9.34669i			0.323262i
$837$	35.7424	+	2.32881i	1.23544	+	0.0804953i
$838$	39.9919	−	39.9919i	1.38150	−	1.38150i
$839$			1.04638i			0.0361250i	0.999837	+	0.0180625i	$0.00574978\pi$
$839$			1.04638i			0.0361250i	−0.999837	+	0.0180625i	$0.994250\pi$
$840$		0			0
$841$	−28.8651			−0.995349
$842$	6.72636	+	6.72636i	0.231806	+	0.231806i
$843$	−0.397853	+	18.3417i	−0.0137028	+	0.631722i
$844$		−	3.72552i		−	0.128238i
$845$		0			0
$846$	0.678980	−	15.6437i	0.0233438	−	0.537843i
$847$	9.76436	+	9.76436i	0.335507	+	0.335507i
$848$	10.8894	−	10.8894i	0.373945	−	0.373945i
$849$	18.2023	−	17.4294i	0.624701	−	0.598176i
$850$		0			0
$851$	−11.6697			−0.400033
$852$	−8.15651	−	0.176924i	−0.279438	−	0.00606132i
$853$	−1.27200	+	1.27200i	−0.0435526	+	0.0435526i	−0.728548	−	0.684995i	$-0.759804\pi$
$853$	−1.27200	+	1.27200i	−0.0435526	+	0.0435526i	0.684995	+	0.728548i	$0.259804\pi$
$854$	99.9522			3.42029
$855$		0			0
$856$			27.3437i			0.934588i
$857$	−32.9950	−	32.9950i	−1.12709	−	1.12709i	−0.990649	−	0.136438i	$-0.956434\pi$
$857$	−32.9950	−	32.9950i	−1.12709	−	1.12709i	−0.136438	−	0.990649i	$-0.543566\pi$
$858$	−33.6753	−	19.9855i	−1.14966	−	0.682295i
$859$			48.5229i			1.65558i	0.561038	+	0.827790i	$0.310402\pi$
$859$			48.5229i			1.65558i	−0.561038	+	0.827790i	$0.689598\pi$
$860$		0			0
$861$	−21.1133	+	20.2168i	−0.719540	+	0.688988i
$862$	−27.7284	+	27.7284i	−0.944435	+	0.944435i
$863$	19.3034	+	19.3034i	0.657097	+	0.657097i	0.954692	−	0.297595i	$-0.0961846\pi$
$863$	19.3034	+	19.3034i	0.657097	+	0.657097i	−0.297595	+	0.954692i	$0.596185\pi$
$864$	23.6524	+	26.9493i	0.804670	+	0.916835i
$865$		0			0
$866$	68.7014			2.33457
$867$	15.1130	+	0.327819i	0.513266	+	0.0111333i
$868$	−64.9889	−	64.9889i	−2.20587	−	2.20587i
$869$			15.2728i			0.518093i
$870$		0			0
$871$	13.4565	+	7.59645i	0.455955	+	0.257396i
$872$	10.3168	+	10.3168i	0.349371	+	0.349371i
$873$	−32.3943	−	35.3339i	−1.09638	−	1.19587i
$874$			9.95549i			0.336749i
$875$		0			0
$876$	−7.35172	+	7.03955i	−0.248391	+	0.237844i
$877$	20.3172	+	20.3172i	0.686062	+	0.686062i	0.961359	−	0.275297i	$-0.0887762\pi$
$877$	20.3172	+	20.3172i	0.686062	+	0.686062i	−0.275297	+	0.961359i	$0.588776\pi$
$878$	−36.8739	−	36.8739i	−1.24443	−	1.24443i
$879$	−31.0009	+	29.6846i	−1.04564	+	1.00124i
$880$		0			0
$881$			14.2114i			0.478796i	0.970922	+	0.239398i	$0.0769500\pi$
$881$			14.2114i			0.478796i	−0.970922	+	0.239398i	$0.923050\pi$
$882$	60.7122	+	66.2215i	2.04429	+	2.22979i
$883$	40.2650	+	40.2650i	1.35503	+	1.35503i	0.879939	+	0.475086i	$0.157583\pi$
$883$	40.2650	+	40.2650i	1.35503	+	1.35503i	0.475086	+	0.879939i	$0.342417\pi$
$884$	15.0258	−	26.6170i	0.505373	−	0.895227i
$885$		0			0
$886$			35.8880i			1.20568i
$887$	−29.2301	−	29.2301i	−0.981451	−	0.981451i	0.0183797	−	0.999831i	$-0.494149\pi$
$887$	−29.2301	−	29.2301i	−0.981451	−	0.981451i	−0.999831	+	0.0183797i	$0.994149\pi$
$888$	−10.7023	−	0.232145i	−0.359146	−	0.00779029i
$889$	46.9726			1.57541
$890$		0			0
$891$	25.2766	+	2.19829i	0.846799	+	0.0736455i
$892$	40.2768	+	40.2768i	1.34857	+	1.34857i
$893$	−1.86650	+	1.86650i	−0.0624600	+	0.0624600i
$894$	−8.19965	+	7.85148i	−0.274237	+	0.262593i
$895$		0			0
$896$		−	67.7056i		−	2.26189i
$897$	−21.3687	−	12.6819i	−0.713481	−	0.423435i
$898$	31.7210	+	31.7210i	1.05854	+	1.05854i
$899$			2.53160i			0.0844334i
$900$		0			0
$901$	36.6792			1.22196
$902$	16.5421	−	16.5421i	0.550791	−	0.550791i
$903$	36.0406	+	0.781763i	1.19936	+	0.0260154i
$904$	−10.5451			−0.350725
$905$		0			0
$906$	−3.13009	+	2.99718i	−0.103990	+	0.0995746i
$907$	−9.52059	+	9.52059i	−0.316126	+	0.316126i	−0.847277	−	0.531151i	$-0.821760\pi$
$907$	−9.52059	+	9.52059i	−0.316126	+	0.316126i	0.531151	+	0.847277i	$0.321760\pi$
$908$	−0.940579	−	0.940579i	−0.0312142	−	0.0312142i
$909$	−1.62839	+	37.5182i	−0.0540104	+	1.24440i
$910$		0			0
$911$		−	1.77346i		−	0.0587574i	−0.999568	−	0.0293787i	$-0.990647\pi$
$911$		−	1.77346i		−	0.0587574i	0.999568	−	0.0293787i	$-0.00935287\pi$
$912$	0.0510226	−	2.35223i	0.00168953	−	0.0778901i
$913$	12.9275	+	12.9275i	0.427838	+	0.427838i
$914$	28.4643			0.941514
$915$		0			0
$916$			29.4010i			0.971436i
$917$	6.68112	−	6.68112i	0.220630	−	0.220630i
$918$	−2.16131	+	33.1717i	−0.0713338	+	1.09483i
$919$			30.1726i			0.995301i	0.867378	+	0.497651i	$0.165804\pi$
$919$			30.1726i			0.995301i	−0.867378	+	0.497651i	$0.834196\pi$
$920$		0			0
$921$	−6.01856	+	5.76301i	−0.198318	+	0.189898i
$922$	−27.7371	+	27.7371i	−0.913472	+	0.913472i
$923$	−5.55102	+	1.54511i	−0.182714	+	0.0508580i
$924$	−45.0261	−	47.0227i	−1.48125	−	1.54693i
$925$		0			0
$926$		−	68.6405i		−	2.25567i
$927$	8.21470	+	8.96013i	0.269806	+	0.294289i
$928$	−1.79203	+	1.79203i	−0.0588262	+	0.0588262i
$929$			21.8725i			0.717614i	0.933412	+	0.358807i	$0.116816\pi$
$929$			21.8725i			0.717614i	−0.933412	+	0.358807i	$0.883184\pi$
$930$		0			0
$931$		−	15.1448i		−	0.496352i
$932$	17.7088	+	17.7088i	0.580073	+	0.580073i
$933$	29.3644	+	0.636947i	0.961347	+	0.0208527i
$934$	−68.1086			−2.22858
$935$		0			0
$936$	−19.3450	−	12.0556i	−0.632311	−	0.394051i
$937$	−8.75074	+	8.75074i	−0.285874	+	0.285874i	−0.835446	−	0.549572i	$-0.814791\pi$
$937$	−8.75074	+	8.75074i	−0.285874	+	0.285874i	0.549572	+	0.835446i	$0.314791\pi$
$938$	30.4926	+	30.4926i	0.995619	+	0.995619i
$939$	−27.9073	+	26.7223i	−0.910720	+	0.872050i
$940$		0			0
$941$	−20.4642			−0.667114			−0.333557	−	0.942730i	$-0.608249\pi$
$941$	−20.4642			−0.667114			−0.333557	+	0.942730i	$0.608249\pi$
$942$	68.3882	+	1.48342i	2.22821	+	0.0483324i
$943$	10.4968	−	10.4968i	0.341823	−	0.341823i
$944$		−	0.0351238i		−	0.00114318i
$945$		0			0
$946$	−28.8500			−0.937993
$947$	−38.3259	+	38.3259i	−1.24542	+	1.24542i	−0.287704	+	0.957719i	$0.592892\pi$
$947$	−38.3259	+	38.3259i	−1.24542	+	1.24542i	−0.957719	+	0.287704i	$0.907108\pi$
$948$	−0.599773	+	27.6506i	−0.0194797	+	0.898049i
$949$	−3.53399	+	6.26017i	−0.114718	+	0.203214i
$950$		0			0
$951$	15.4733	+	16.1594i	0.501756	+	0.524006i
$952$	19.3874	−	19.3874i	0.628351	−	0.628351i
$953$	−6.53740	+	6.53740i	−0.211767	+	0.211767i	−0.805018	−	0.593251i	$-0.797844\pi$
$953$	−6.53740	+	6.53740i	−0.211767	+	0.211767i	0.593251	+	0.805018i	$0.297844\pi$
$954$	3.68996	−	85.0169i	0.119467	−	2.75252i
$955$		0			0
$956$	17.8309			0.576691
$957$	−0.0388889	+	1.79285i	−0.00125710	+	0.0579545i
$958$	50.7338	+	50.7338i	1.63913	+	1.63913i
$959$	−25.0357			−0.808444
$960$		0			0
$961$	−16.5165			−0.532791
$962$	−22.6593	+	6.30717i	−0.730566	+	0.203351i
$963$	−26.3060	−	28.6932i	−0.847700	−	0.924624i
$964$	75.2945			2.42507
$965$		0			0
$966$	−47.9588	−	50.0855i	−1.54305	−	1.61148i
$967$	13.4620	+	13.4620i	0.432909	+	0.432909i	0.889617	−	0.456708i	$-0.150971\pi$
$967$	13.4620	+	13.4620i	0.432909	+	0.432909i	−0.456708	+	0.889617i	$0.650971\pi$
$968$	−4.54864	−	4.54864i	−0.146199	−	0.146199i
$969$	4.04747	−	3.87561i	0.130024	−	0.124503i
$970$		0			0
$971$		−	22.3416i		−	0.716977i	−0.933534	−	0.358489i	$-0.883292\pi$
$971$		−	22.3416i		−	0.716977i	0.933534	−	0.358489i	$-0.116708\pi$
$972$	45.6757	+	4.97253i	1.46505	+	0.159494i
$973$	−54.8683	+	54.8683i	−1.75900	+	1.75900i
$974$	−15.8944			−0.509289
$975$		0			0
$976$	11.9958			0.383977
$977$	26.2653	−	26.2653i	0.840303	−	0.840303i	−0.148595	−	0.988898i	$-0.547475\pi$
$977$	26.2653	−	26.2653i	0.840303	−	0.840303i	0.988898	+	0.148595i	$0.0474751\pi$
$978$	26.2515	+	0.569425i	0.839430	+	0.0182082i
$979$			39.7732i			1.27116i
$980$		0			0
$981$	−20.7513	−	0.900661i	−0.662537	−	0.0287559i
$982$	−41.1605	−	41.1605i	−1.31348	−	1.31348i
$983$	17.4667	+	17.4667i	0.557100	+	0.557100i	0.928481	−	0.371381i	$-0.121116\pi$
$983$	17.4667	+	17.4667i	0.557100	+	0.557100i	−0.371381	+	0.928481i	$0.621116\pi$
$984$	9.83545	−	9.41782i	0.313543	−	0.300229i
$985$		0			0
$986$	−2.34951			−0.0748237
$987$	0.398722	−	18.3818i	0.0126915	−	0.585099i
$988$	3.20553	+	11.5163i	0.101982	+	0.366382i
$989$	−18.3068			−0.582123
$990$		0			0
$991$	−24.4390			−0.776332			−0.388166	−	0.921589i	$-0.626891\pi$
$991$	−24.4390			−0.776332			−0.388166	+	0.921589i	$0.626891\pi$
$992$	−33.6353	−	33.6353i	−1.06792	−	1.06792i
$993$	−18.4154	−	0.399451i	−0.584396	−	0.0126762i
$994$	−16.0800			−0.510025
$995$		0			0
$996$	22.8969	+	23.9123i	0.725517	+	0.757689i
$997$	17.4390	−	17.4390i	0.552298	−	0.552298i	−0.374806	−	0.927103i	$-0.622291\pi$
$997$	17.4390	−	17.4390i	0.552298	−	0.552298i	0.927103	+	0.374806i	$0.122291\pi$
$998$	30.8724	−	30.8724i	0.977250	−	0.977250i
$999$	11.4538	−	10.0526i	0.362383	−	0.318049i

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.s.e.818.1		32
3.2	odd	2	inner	975.2.s.e.818.16		32
5.2	odd	4	inner	975.2.s.e.857.2		32
5.3	odd	4		195.2.s.b.77.15	yes	32
5.4	even	2		195.2.s.b.38.16	yes	32
13.12	even	2	inner	975.2.s.e.818.15		32
15.2	even	4	inner	975.2.s.e.857.15		32
15.8	even	4		195.2.s.b.77.2	yes	32
15.14	odd	2		195.2.s.b.38.1	✓	32
39.38	odd	2	inner	975.2.s.e.818.2		32
65.12	odd	4	inner	975.2.s.e.857.16		32
65.38	odd	4		195.2.s.b.77.1	yes	32
65.64	even	2		195.2.s.b.38.2	yes	32
195.38	even	4		195.2.s.b.77.16	yes	32
195.77	even	4	inner	975.2.s.e.857.1		32
195.194	odd	2		195.2.s.b.38.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.s.b.38.1	✓	32	15.14	odd	2
195.2.s.b.38.2	yes	32	65.64	even	2
195.2.s.b.38.15	yes	32	195.194	odd	2
195.2.s.b.38.16	yes	32	5.4	even	2
195.2.s.b.77.1	yes	32	65.38	odd	4
195.2.s.b.77.2	yes	32	15.8	even	4
195.2.s.b.77.15	yes	32	5.3	odd	4
195.2.s.b.77.16	yes	32	195.38	even	4
975.2.s.e.818.1		32	1.1	even	1	trivial
975.2.s.e.818.2		32	39.38	odd	2	inner
975.2.s.e.818.15		32	13.12	even	2	inner
975.2.s.e.818.16		32	3.2	odd	2	inner
975.2.s.e.857.1		32	195.77	even	4	inner
975.2.s.e.857.2		32	5.2	odd	4	inner
975.2.s.e.857.15		32	15.2	even	4	inner
975.2.s.e.857.16		32	65.12	odd	4	inner

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Elliptic curves over $\Q$
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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	975.2.s.e.818.1

Level	$975$
Weight	$2$
Character	975.818
Analytic conductor	$7.785$
Analytic rank	$0$
Dimension	$32$
Inner twists	$8$