LMFDB - Embedded newform 75.10.e.g.32.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(32,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.32");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.e (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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			32.3
Character	$\chi$	$=$	75.32
Dual form			75.10.e.g.68.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-27.2604 + 27.2604i) q^{2} +(84.7063 + 111.838i) q^{3} -974.263i q^{4} +(-5357.90 - 739.636i) q^{6} +(4326.79 + 4326.79i) q^{7} +(12601.5 + 12601.5i) q^{8} +(-5332.69 + 18946.8i) q^{9} +O(q^{10})$	\(q+(-27.2604 + 27.2604i) q^{2} +(84.7063 + 111.838i) q^{3} -974.263i q^{4} +(-5357.90 - 739.636i) q^{6} +(4326.79 + 4326.79i) q^{7} +(12601.5 + 12601.5i) q^{8} +(-5332.69 + 18946.8i) q^{9} -91942.2i q^{11} +(108960. - 82526.2i) q^{12} +(9654.93 - 9654.93i) q^{13} -235900. q^{14} -188222. q^{16} +(237066. - 237066. i) q^{17} +(-371128. - 661871. i) q^{18} +814758. i q^{19} +(-117395. + 850408. i) q^{21} +(2.50638e6 + 2.50638e6i) q^{22} +(620173. + 620173. i) q^{23} +(-341907. + 2.47676e6i) q^{24} +526395. i q^{26} +(-2.57070e6 + 1.00852e6i) q^{27} +(4.21543e6 - 4.21543e6i) q^{28} +6.40395e6 q^{29} +364021. q^{31} +(-1.32095e6 + 1.32095e6i) q^{32} +(1.02827e7 - 7.78808e6i) q^{33} +1.29251e7i q^{34} +(1.84592e7 + 5.19545e6i) q^{36} +(1.23325e7 + 1.23325e7i) q^{37} +(-2.22107e7 - 2.22107e7i) q^{38} +(1.89763e6 + 261959. i) q^{39} +1.60364e7i q^{41} +(-1.99822e7 - 2.63827e7i) q^{42} +(-1.16682e7 + 1.16682e7i) q^{43} -8.95759e7 q^{44} -3.38124e7 q^{46} +(1.50179e7 - 1.50179e7i) q^{47} +(-1.59436e7 - 2.10505e7i) q^{48} -2.91138e6i q^{49} +(4.65941e7 + 6.43213e6i) q^{51} +(-9.40644e6 - 9.40644e6i) q^{52} +(-9.74980e6 - 9.74980e6i) q^{53} +(4.25858e7 - 9.75710e7i) q^{54} +1.09048e8i q^{56} +(-9.11213e7 + 6.90151e7i) q^{57} +(-1.74574e8 + 1.74574e8i) q^{58} +1.46287e7 q^{59} -1.55765e8 q^{61} +(-9.92336e6 + 9.92336e6i) q^{62} +(-1.05052e8 + 5.89056e7i) q^{63} -1.68389e8i q^{64} +(-6.80037e7 + 4.92617e8i) q^{66} +(7.46762e7 + 7.46762e7i) q^{67} +(-2.30965e8 - 2.30965e8i) q^{68} +(-1.68267e7 + 1.21892e8i) q^{69} -9.62530e7i q^{71} +(-3.05959e8 + 1.71559e8i) q^{72} +(2.25364e8 - 2.25364e8i) q^{73} -6.72377e8 q^{74} +7.93789e8 q^{76} +(3.97815e8 - 3.97815e8i) q^{77} +(-5.88712e7 + 4.45890e7i) q^{78} +3.61084e8i q^{79} +(-3.30545e8 - 2.02075e8i) q^{81} +(-4.37160e8 - 4.37160e8i) q^{82} +(-5.68314e7 - 5.68314e7i) q^{83} +(8.28521e8 + 1.14374e8i) q^{84} -6.36163e8i q^{86} +(5.42455e8 + 7.16208e8i) q^{87} +(1.15861e9 - 1.15861e9i) q^{88} -7.68861e8 q^{89} +8.35497e7 q^{91} +(6.04212e8 - 6.04212e8i) q^{92} +(3.08348e7 + 4.07115e7i) q^{93} +8.18788e8i q^{94} +(-2.59625e8 - 3.58402e7i) q^{96} +(7.95158e8 + 7.95158e8i) q^{97} +(7.93654e7 + 7.93654e7i) q^{98} +(1.74201e9 + 4.90299e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10788 q^{6}+O(q^{10}) $ 48 * q + 10788 * q^6	$ 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) $ 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−27.2604	+	27.2604i	−1.20475	+	1.20475i	−0.232048	+	0.972704i	$0.574543\pi$
$2$	−27.2604	+	27.2604i	−1.20475	+	1.20475i	−0.972704	+	0.232048i	$0.925457\pi$
$3$	84.7063	+	111.838i	0.603768	+	0.797160i
$3$	84.7063	+	111.838i	0.603768	+	0.797160i
$4$		−	974.263i		−	1.90286i
$5$		0			0
$5$		0			0
$6$	−5357.90	−	739.636i	−1.68777	−	0.232990i
$7$	4326.79	+	4326.79i	0.681122	+	0.681122i	0.960253	−	0.279131i	$-0.0900465\pi$
$7$	4326.79	+	4326.79i	0.681122	+	0.681122i	−0.279131	+	0.960253i	$0.590046\pi$
$8$	12601.5	+	12601.5i	1.08772	+	1.08772i
$9$	−5332.69	+	18946.8i	−0.270929	+	0.962599i
$10$		0			0
$11$		−	91942.2i		−	1.89342i	−0.322083	−	0.946712i	$-0.604383\pi$
$11$		−	91942.2i		−	1.89342i	0.322083	−	0.946712i	$-0.395617\pi$
$12$	108960.	−	82526.2i	1.51688	−	1.14888i
$13$	9654.93	−	9654.93i	0.0937570	−	0.0937570i	−0.658673	−	0.752430i	$-0.728882\pi$
$13$	9654.93	−	9654.93i	0.0937570	−	0.0937570i	0.752430	+	0.658673i	$0.228882\pi$
$14$	−235900.			−1.64117
$15$		0			0
$16$	−188222.			−0.718011
$17$	237066.	−	237066.i	0.688414	−	0.688414i	−0.273467	−	0.961881i	$-0.588171\pi$
$17$	237066.	−	237066.i	0.688414	−	0.688414i	0.961881	+	0.273467i	$0.0881705\pi$
$18$	−371128.	−	661871.i	−0.833292	−	1.48610i
$19$			814758.i			1.43429i	0.696923	+	0.717146i	$0.254552\pi$
$19$			814758.i			1.43429i	−0.696923	+	0.717146i	$0.745448\pi$
$20$		0			0
$21$	−117395.	+	850408.i	−0.131724	+	0.954202i
$22$	2.50638e6	+	2.50638e6i	2.28111	+	2.28111i
$23$	620173.	+	620173.i	0.462102	+	0.462102i	0.899344	−	0.437242i	$-0.144045\pi$
$23$	620173.	+	620173.i	0.462102	+	0.462102i	−0.437242	+	0.899344i	$0.644045\pi$
$24$	−341907.	+	2.47676e6i	−0.210357	+	1.52382i
$25$		0			0
$26$			526395.i			0.225908i
$27$	−2.57070e6	+	1.00852e6i	−0.930924	+	0.365213i
$28$	4.21543e6	−	4.21543e6i	1.29608	−	1.29608i
$29$	6.40395e6			1.68135			0.840673	−	0.541544i	$-0.182160\pi$
$29$	6.40395e6			1.68135			0.840673	+	0.541544i	$0.182160\pi$
$30$		0			0
$31$	364021.			0.0707943			0.0353972	−	0.999373i	$-0.488730\pi$
$31$	364021.			0.0707943			0.0353972	+	0.999373i	$0.488730\pi$
$32$	−1.32095e6	+	1.32095e6i	−0.222695	+	0.222695i
$33$	1.02827e7	−	7.78808e6i	1.50936	−	1.14319i
$34$			1.29251e7i			1.65874i
$35$		0			0
$36$	1.84592e7	+	5.19545e6i	1.83169	+	0.515539i
$37$	1.23325e7	+	1.23325e7i	1.08179	+	1.08179i	0.996343	+	0.0854459i	$0.0272315\pi$
$37$	1.23325e7	+	1.23325e7i	1.08179	+	1.08179i	0.0854459	+	0.996343i	$0.472769\pi$
$38$	−2.22107e7	−	2.22107e7i	−1.72797	−	1.72797i
$39$	1.89763e6	+	261959.i	0.131347	+	0.0181319i
$40$		0			0
$41$			1.60364e7i			0.886299i	0.896448	+	0.443149i	$0.146139\pi$
$41$			1.60364e7i			0.886299i	−0.896448	+	0.443149i	$0.853861\pi$
$42$	−1.99822e7	−	2.63827e7i	−0.990883	−	1.30827i
$43$	−1.16682e7	+	1.16682e7i	−0.520472	+	0.520472i	−0.917714	−	0.397242i	$-0.869967\pi$
$43$	−1.16682e7	+	1.16682e7i	−0.520472	+	0.520472i	0.397242	+	0.917714i	$0.369967\pi$
$44$	−8.95759e7			−3.60292
$45$		0			0
$46$	−3.38124e7			−1.11344
$47$	1.50179e7	−	1.50179e7i	0.448919	−	0.448919i	−0.446076	−	0.894995i	$-0.647179\pi$
$47$	1.50179e7	−	1.50179e7i	0.448919	−	0.448919i	0.894995	+	0.446076i	$0.147179\pi$
$48$	−1.59436e7	−	2.10505e7i	−0.433512	−	0.572370i
$49$		−	2.91138e6i		−	0.0721466i
$50$		0			0
$51$	4.65941e7	+	6.43213e6i	0.964419	+	0.133134i
$52$	−9.40644e6	−	9.40644e6i	−0.178406	−	0.178406i
$53$	−9.74980e6	−	9.74980e6i	−0.169728	−	0.169728i	0.617132	−	0.786860i	$-0.288295\pi$
$53$	−9.74980e6	−	9.74980e6i	−0.169728	−	0.169728i	−0.786860	+	0.617132i	$0.788295\pi$
$54$	4.25858e7	−	9.75710e7i	0.681542	−	1.56152i
$55$		0			0
$56$			1.09048e8i			1.48174i
$57$	−9.11213e7	+	6.90151e7i	−1.14336	+	0.865979i
$58$	−1.74574e8	+	1.74574e8i	−2.02561	+	2.02561i
$59$	1.46287e7			0.157171			0.0785855	−	0.996907i	$-0.474960\pi$
$59$	1.46287e7			0.157171			0.0785855	+	0.996907i	$0.474960\pi$
$60$		0			0
$61$	−1.55765e8			−1.44041			−0.720205	−	0.693761i	$-0.755952\pi$
$61$	−1.55765e8			−1.44041			−0.720205	+	0.693761i	$0.755952\pi$
$62$	−9.92336e6	+	9.92336e6i	−0.0852896	+	0.0852896i
$63$	−1.05052e8	+	5.89056e7i	−0.840183	+	0.471112i
$64$		−	1.68389e8i		−	1.25460i
$65$		0			0
$66$	−6.80037e7	+	4.92617e8i	−0.441149	+	3.19567i
$67$	7.46762e7	+	7.46762e7i	0.452737	+	0.452737i	0.896262	−	0.443525i	$-0.146272\pi$
$67$	7.46762e7	+	7.46762e7i	0.452737	+	0.452737i	−0.443525	+	0.896262i	$0.646272\pi$
$68$	−2.30965e8	−	2.30965e8i	−1.30995	−	1.30995i
$69$	−1.68267e7	+	1.21892e8i	−0.0893670	+	0.647372i
$70$		0			0
$71$		−	9.62530e7i		−	0.449523i	−0.974414	−	0.224761i	$-0.927840\pi$
$71$		−	9.62530e7i		−	0.449523i	0.974414	−	0.224761i	$-0.0721603\pi$
$72$	−3.05959e8	+	1.71559e8i	−1.34173	+	0.752344i
$73$	2.25364e8	−	2.25364e8i	0.928819	−	0.928819i	−0.0688107	−	0.997630i	$-0.521920\pi$
$73$	2.25364e8	−	2.25364e8i	0.928819	−	0.928819i	0.997630	+	0.0688107i	$0.0219204\pi$
$74$	−6.72377e8			−2.60658
$75$		0			0
$76$	7.93789e8			2.72925
$77$	3.97815e8	−	3.97815e8i	1.28965	−	1.28965i
$78$	−5.88712e7	+	4.45890e7i	−0.180085	+	0.136396i
$79$			3.61084e8i			1.04301i	0.853250	+	0.521503i	$0.174628\pi$
$79$			3.61084e8i			1.04301i	−0.853250	+	0.521503i	$0.825372\pi$
$80$		0			0
$81$	−3.30545e8	−	2.02075e8i	−0.853195	−	0.521592i
$82$	−4.37160e8	−	4.37160e8i	−1.06777	−	1.06777i
$83$	−5.68314e7	−	5.68314e7i	−0.131443	−	0.131443i	0.638325	−	0.769767i	$-0.279628\pi$
$83$	−5.68314e7	−	5.68314e7i	−0.131443	−	0.131443i	−0.769767	+	0.638325i	$0.779628\pi$
$84$	8.28521e8	+	1.14374e8i	1.81571	+	0.250652i
$85$		0			0
$86$		−	6.36163e8i		−	1.25408i
$87$	5.42455e8	+	7.16208e8i	1.01514	+	1.34030i
$88$	1.15861e9	−	1.15861e9i	2.05952	−	2.05952i
$89$	−7.68861e8			−1.29895			−0.649475	−	0.760383i	$-0.725011\pi$
$89$	−7.68861e8			−1.29895			−0.649475	+	0.760383i	$0.725011\pi$
$90$		0			0
$91$	8.35497e7			0.127720
$92$	6.04212e8	−	6.04212e8i	0.879314	−	0.879314i
$93$	3.08348e7	+	4.07115e7i	0.0427433	+	0.0564344i
$94$			8.18788e8i			1.08167i
$95$		0			0
$96$	−2.59625e8	−	3.58402e7i	−0.311980	−	0.0430675i
$97$	7.95158e8	+	7.95158e8i	0.911970	+	0.911970i	0.996427	−	0.0844572i	$-0.0269156\pi$
$97$	7.95158e8	+	7.95158e8i	0.911970	+	0.911970i	−0.0844572	+	0.996427i	$0.526916\pi$
$98$	7.93654e7	+	7.93654e7i	0.0869188	+	0.0869188i
$99$	1.74201e9	+	4.90299e8i	1.82261	+	0.512983i
$100$		0			0
$101$			4.77004e8i			0.456117i	0.973647	+	0.228058i	$0.0732377\pi$
$101$			4.77004e8i			0.456117i	−0.973647	+	0.228058i	$0.926762\pi$
$102$	−1.44552e9	+	1.09483e9i	−1.32228	+	1.00149i
$103$	−3.62626e8	+	3.62626e8i	−0.317461	+	0.317461i	−0.847791	−	0.530330i	$-0.822068\pi$
$103$	−3.62626e8	+	3.62626e8i	−0.317461	+	0.317461i	0.530330	+	0.847791i	$0.322068\pi$
$104$	2.43333e8			0.203963
$105$		0			0
$106$	5.31568e8			0.408961
$107$	−4.08959e8	+	4.08959e8i	−0.301615	+	0.301615i	−0.841646	−	0.540030i	$-0.818413\pi$
$107$	−4.08959e8	+	4.08959e8i	−0.301615	+	0.301615i	0.540030	+	0.841646i	$0.318413\pi$
$108$	9.82561e8	+	2.50454e9i	0.694948	+	1.77142i
$109$			7.00571e7i			0.0475371i	0.999717	+	0.0237686i	$0.00756648\pi$
$109$			7.00571e7i			0.0475371i	−0.999717	+	0.0237686i	$0.992434\pi$
$110$		0			0
$111$	−3.34607e8	+	2.42388e9i	−0.209210	+	1.51551i
$112$	−8.14398e8	−	8.14398e8i	−0.489053	−	0.489053i
$113$	7.73021e8	+	7.73021e8i	0.446004	+	0.446004i	0.894024	−	0.448020i	$-0.147871\pi$
$113$	7.73021e8	+	7.73021e8i	0.446004	+	0.446004i	−0.448020	+	0.894024i	$0.647871\pi$
$114$	6.02624e8	−	4.36539e9i	0.334176	−	2.42076i
$115$		0			0
$116$		−	6.23913e9i		−	3.19936i
$117$	1.31444e8	+	2.34417e8i	0.0648490	+	0.115652i
$118$	−3.98786e8	+	3.98786e8i	−0.189352	+	0.189352i
$119$	2.05147e9			0.937787
$120$		0			0
$121$	−6.09542e9			−2.58505
$122$	4.24623e9	−	4.24623e9i	1.73534	−	1.73534i
$123$	−1.79349e9	+	1.35839e9i	−0.706522	+	0.535119i
$124$		−	3.54652e8i		−	0.134712i
$125$		0			0
$126$	1.25798e9	−	4.46957e9i	0.444639	−	1.57979i
$127$	1.95164e9	+	1.95164e9i	0.665706	+	0.665706i	0.956719	−	0.291013i	$-0.0939923\pi$
$127$	1.95164e9	+	1.95164e9i	0.665706	+	0.665706i	−0.291013	+	0.956719i	$0.593992\pi$
$128$	3.91403e9	+	3.91403e9i	1.28878	+	1.28878i
$129$	−2.29333e9	−	3.16585e8i	−0.729144	−	0.100655i
$130$		0			0
$131$		−	2.25437e9i		−	0.668812i	−0.942429	−	0.334406i	$-0.891464\pi$
$131$		−	2.25437e9i		−	0.668812i	0.942429	−	0.334406i	$-0.108536\pi$
$132$	−7.58764e9	−	1.00180e10i	−2.17532	−	2.87210i
$133$	−3.52529e9	+	3.52529e9i	−0.976927	+	0.976927i
$134$	−4.07141e9			−1.09087
$135$		0			0
$136$	5.97478e9			1.49760
$137$	−3.14001e9	+	3.14001e9i	−0.761533	+	0.761533i	−0.976599	−	0.215067i	$-0.931003\pi$
$137$	−3.14001e9	+	3.14001e9i	−0.761533	+	0.761533i	0.215067	+	0.976599i	$0.431003\pi$
$138$	−2.86412e9	−	3.78153e9i	−0.672258	−	0.887588i
$139$		−	3.85704e9i		−	0.876370i	−0.898885	−	0.438185i	$-0.855621\pi$
$139$		−	3.85704e9i		−	0.876370i	0.898885	−	0.438185i	$-0.144379\pi$
$140$		0			0
$141$	2.95169e9	+	4.07468e8i	0.628904	+	0.0868176i
$142$	2.62390e9	+	2.62390e9i	0.541564	+	0.541564i
$143$	−8.87695e8	−	8.87695e8i	−0.177522	−	0.177522i
$144$	1.00373e9	−	3.56622e9i	0.194530	−	0.691157i
$145$		0			0
$146$			1.22870e10i			2.23799i
$147$	3.25604e8	−	2.46612e8i	0.0575124	−	0.0435598i
$148$	1.20151e10	−	1.20151e10i	2.05849	−	2.05849i
$149$	5.00475e9			0.831848			0.415924	−	0.909399i	$-0.363458\pi$
$149$	5.00475e9			0.831848			0.415924	+	0.909399i	$0.363458\pi$
$150$		0			0
$151$	−2.35429e9			−0.368522			−0.184261	−	0.982877i	$-0.558989\pi$
$151$	−2.35429e9			−0.368522			−0.184261	+	0.982877i	$0.558989\pi$
$152$	−1.02672e10	+	1.02672e10i	−1.56011	+	1.56011i
$153$	3.22746e9	+	5.75586e9i	0.476156	+	0.849178i
$154$			2.16892e10i			3.10742i
$155$		0			0
$156$	2.55217e8	−	1.84879e9i	0.0345024	−	0.249934i
$157$	5.77365e9	+	5.77365e9i	0.758406	+	0.758406i	0.976032	−	0.217626i	$-0.0698313\pi$
$157$	5.77365e9	+	5.77365e9i	0.758406	+	0.758406i	−0.217626	+	0.976032i	$0.569831\pi$
$158$	−9.84332e9	−	9.84332e9i	−1.25656	−	1.25656i
$159$	2.64534e8	−	1.91627e9i	0.0328242	−	0.237777i
$160$		0			0
$161$			5.36672e9i			0.629495i
$162$	1.45195e10	−	3.50215e9i	1.65628	−	0.399500i
$163$	2.90534e9	−	2.90534e9i	0.322369	−	0.322369i	−0.527306	−	0.849675i	$-0.676798\pi$
$163$	2.90534e9	−	2.90534e9i	0.322369	−	0.322369i	0.849675	+	0.527306i	$0.176798\pi$
$164$	1.56237e10			1.68650
$165$		0			0
$166$	3.09850e9			0.316712
$167$	1.25312e9	−	1.25312e9i	0.124671	−	0.124671i	−0.642018	−	0.766690i	$-0.721903\pi$
$167$	1.25312e9	−	1.25312e9i	0.124671	−	0.124671i	0.766690	+	0.642018i	$0.221903\pi$
$168$	−1.21958e10	+	9.23706e9i	−1.18118	+	0.894627i
$169$			1.04181e10i			0.982419i
$170$		0			0
$171$	−1.54371e10	−	4.34485e9i	−1.38065	−	0.388591i
$172$	1.13679e10	+	1.13679e10i	0.990384	+	0.990384i
$173$	2.41960e9	+	2.41960e9i	0.205369	+	0.205369i	0.802296	−	0.596926i	$-0.203612\pi$
$173$	2.41960e9	+	2.41960e9i	0.205369	+	0.205369i	−0.596926	+	0.802296i	$0.703612\pi$
$174$	−3.43117e10	−	4.73659e9i	−2.83773	−	0.391737i
$175$		0			0
$176$			1.73056e10i			1.35950i
$177$	1.23915e9	+	1.63605e9i	0.0948948	+	0.125291i
$178$	2.09595e10	−	2.09595e10i	1.56491	−	1.56491i
$179$	2.06402e9			0.150271			0.0751354	−	0.997173i	$-0.476061\pi$
$179$	2.06402e9			0.150271			0.0751354	+	0.997173i	$0.476061\pi$
$180$		0			0
$181$	1.80551e10			1.25039			0.625197	−	0.780467i	$-0.285019\pi$
$181$	1.80551e10			1.25039			0.625197	+	0.780467i	$0.285019\pi$
$182$	−2.27760e9	+	2.27760e9i	−0.153871	+	0.153871i
$183$	−1.31943e10	−	1.74205e10i	−0.869673	−	1.14824i
$184$			1.56302e10i			1.00528i
$185$		0			0
$186$	−1.95038e9	−	2.69243e8i	−0.119485	−	0.0164944i
$187$	−2.17964e10	−	2.17964e10i	−1.30346	−	1.30346i
$188$	−1.46314e10	−	1.46314e10i	−0.854230	−	0.854230i
$189$	−1.54865e10	−	6.75924e9i	−0.882827	−	0.385318i
$190$		0			0
$191$			1.96853e10i			1.07027i	0.844768	+	0.535133i	$0.179738\pi$
$191$			1.96853e10i			1.07027i	−0.844768	+	0.535133i	$0.820262\pi$
$192$	1.88324e10	−	1.42636e10i	1.00011	−	0.757485i
$193$	−9.69122e9	+	9.69122e9i	−0.502771	+	0.502771i	−0.912298	−	0.409527i	$-0.865694\pi$
$193$	−9.69122e9	+	9.69122e9i	−0.502771	+	0.502771i	0.409527	+	0.912298i	$0.365694\pi$
$194$	−4.33527e10			−2.19740
$195$		0			0
$196$	−2.83645e9			−0.137285
$197$	−1.35999e10	+	1.35999e10i	−0.643337	+	0.643337i	−0.951374	−	0.308037i	$-0.900328\pi$
$197$	−1.35999e10	+	1.35999e10i	−0.643337	+	0.643337i	0.308037	+	0.951374i	$0.400328\pi$
$198$	−6.08538e10	+	3.41223e10i	−2.81381	+	1.57777i
$199$		−	1.69665e10i		−	0.766926i	−0.923556	−	0.383463i	$-0.874731\pi$
$199$		−	1.69665e10i		−	0.766926i	0.923556	−	0.383463i	$-0.125269\pi$
$200$		0			0
$201$	−2.02613e9	+	1.46772e10i	−0.0875559	+	0.634252i
$202$	−1.30033e10	−	1.30033e10i	−0.549508	−	0.549508i
$203$	2.77085e10	+	2.77085e10i	1.14520	+	1.14520i
$204$	6.26659e9	−	4.53950e10i	0.253335	−	1.83515i
$205$		0			0
$206$		−	1.97707e10i		−	0.764925i
$207$	−1.50575e10	+	8.44313e9i	−0.570016	+	0.319622i
$208$	−1.81727e9	+	1.81727e9i	−0.0673186	+	0.0673186i
$209$	7.49106e10			2.71572
$210$		0			0
$211$	4.01946e10			1.39603			0.698017	−	0.716081i	$-0.254066\pi$
$211$	4.01946e10			1.39603			0.698017	+	0.716081i	$0.254066\pi$
$212$	−9.49887e9	+	9.49887e9i	−0.322969	+	0.322969i
$213$	1.07648e10	−	8.15323e9i	0.358342	−	0.271407i
$214$		−	2.22968e10i		−	0.726743i
$215$		0			0
$216$	−4.51035e10	−	1.96858e10i	−1.40984	−	0.615336i
$217$	1.57504e9	+	1.57504e9i	0.0482195	+	0.0482195i
$218$	−1.90979e9	−	1.90979e9i	−0.0572705	−	0.0572705i
$219$	4.42941e10	+	6.11461e9i	1.30121	+	0.179627i
$220$		0			0
$221$		−	4.57772e9i		−	0.129087i
$222$	−5.69546e10	−	7.51977e10i	−1.57377	−	2.07786i
$223$	3.27645e10	−	3.27645e10i	0.887220	−	0.887220i	−0.107036	−	0.994255i	$-0.534136\pi$
$223$	3.27645e10	−	3.27645e10i	0.887220	−	0.887220i	0.994255	+	0.107036i	$0.0341359\pi$
$224$	−1.14309e10			−0.303365
$225$		0			0
$226$	−4.21458e10			−1.07465
$227$	−4.23963e10	+	4.23963e10i	−1.05977	+	1.05977i	−0.0616737	+	0.998096i	$0.519644\pi$
$227$	−4.23963e10	+	4.23963e10i	−1.05977	+	1.05977i	−0.998096	+	0.0616737i	$0.980356\pi$
$228$	6.72389e10	+	8.87761e10i	1.64783	+	2.17565i
$229$		−	2.44093e10i		−	0.586537i	−0.956030	−	0.293268i	$-0.905257\pi$
$229$		−	2.44093e10i		−	0.586537i	0.956030	−	0.293268i	$-0.0947430\pi$
$230$		0			0
$231$	7.81884e10	+	1.07936e10i	1.80671	+	0.249409i
$232$	8.06994e10	+	8.06994e10i	1.82883	+	1.82883i
$233$	−1.13130e10	−	1.13130e10i	−0.251464	−	0.251464i	0.570107	−	0.821571i	$-0.306902\pi$
$233$	−1.13130e10	−	1.13130e10i	−0.251464	−	0.251464i	−0.821571	+	0.570107i	$0.806902\pi$
$234$	−9.97353e9	−	2.80710e9i	−0.217459	−	0.0612050i
$235$		0			0
$236$		−	1.42522e10i		−	0.299074i
$237$	−4.03831e10	+	3.05861e10i	−0.831443	+	0.629733i
$238$	−5.59241e10	+	5.59241e10i	−1.12980	+	1.12980i
$239$	−3.06039e10			−0.606718			−0.303359	−	0.952876i	$-0.598108\pi$
$239$	−3.06039e10			−0.606718			−0.303359	+	0.952876i	$0.598108\pi$
$240$		0			0
$241$	−3.99405e10			−0.762670			−0.381335	−	0.924437i	$-0.624536\pi$
$241$	−3.99405e10			−0.762670			−0.381335	+	0.924437i	$0.624536\pi$
$242$	1.66164e11	−	1.66164e11i	3.11435	−	3.11435i
$243$	−5.39946e9	−	5.40847e10i	−0.0993395	−	0.995054i
$244$			1.51756e11i			2.74090i
$245$		0			0
$246$	1.18611e10	−	8.59215e10i	0.206499	−	1.49587i
$247$	7.86643e9	+	7.86643e9i	0.134475	+	0.134475i
$248$	4.58721e9	+	4.58721e9i	0.0770044	+	0.0770044i
$249$	1.54196e9	−	1.11699e10i	0.0254200	−	0.184142i
$250$		0			0
$251$		−	7.38428e10i		−	1.17429i	−0.809481	−	0.587146i	$-0.800251\pi$
$251$		−	7.38428e10i		−	1.17429i	0.809481	−	0.587146i	$-0.199749\pi$
$252$	5.73895e10	+	1.02349e11i	0.896459	+	1.59875i
$253$	5.70201e10	−	5.70201e10i	0.874954	−	0.874954i
$254$	−1.06405e11			−1.60402
$255$		0			0
$256$	−1.27181e11			−1.85073
$257$	3.99676e10	−	3.99676e10i	0.571491	−	0.571491i	−0.361054	−	0.932545i	$-0.617583\pi$
$257$	3.99676e10	−	3.99676e10i	0.571491	−	0.571491i	0.932545	+	0.361054i	$0.117583\pi$
$258$	7.11475e10	−	5.38870e10i	0.999702	−	0.757173i
$259$			1.06720e11i			1.47366i
$260$		0			0
$261$	−3.41503e10	+	1.21335e11i	−0.455525	+	1.61846i
$262$	6.14550e10	+	6.14550e10i	0.805753	+	0.805753i
$263$	3.71068e10	+	3.71068e10i	0.478248	+	0.478248i	0.904571	−	0.426323i	$-0.140191\pi$
$263$	3.71068e10	+	3.71068e10i	0.478248	+	0.478248i	−0.426323	+	0.904571i	$0.640191\pi$
$264$	2.27719e11	+	3.14356e10i	2.88523	+	0.398295i
$265$		0			0
$266$		−	1.92202e11i		−	2.35391i
$267$	−6.51273e10	−	8.59882e10i	−0.784265	−	1.03547i
$268$	7.27543e10	−	7.27543e10i	0.861494	−	0.861494i
$269$	1.04901e11			1.22150			0.610749	−	0.791824i	$-0.290868\pi$
$269$	1.04901e11			1.22150			0.610749	+	0.791824i	$0.290868\pi$
$270$		0			0
$271$	1.51320e11			1.70425			0.852126	−	0.523336i	$-0.175313\pi$
$271$	1.51320e11			1.70425			0.852126	+	0.523336i	$0.175313\pi$
$272$	−4.46212e10	+	4.46212e10i	−0.494289	+	0.494289i
$273$	7.07718e9	+	9.34407e9i	0.0771132	+	0.101813i
$274$		−	1.71196e11i		−	1.83492i
$275$		0			0
$276$	1.18755e11	+	1.63936e10i	1.23186	+	0.170053i
$277$	−2.72604e10	−	2.72604e10i	−0.278210	−	0.278210i	0.554184	−	0.832394i	$-0.313030\pi$
$277$	−2.72604e10	−	2.72604e10i	−0.278210	−	0.278210i	−0.832394	+	0.554184i	$0.813030\pi$
$278$	1.05145e11	+	1.05145e11i	1.05581	+	1.05581i
$279$	−1.94121e9	+	6.89704e9i	−0.0191802	+	0.0681466i
$280$		0			0
$281$		−	8.63409e10i		−	0.826111i	−0.910706	−	0.413055i	$-0.864462\pi$
$281$		−	8.63409e10i		−	0.826111i	0.910706	−	0.413055i	$-0.135538\pi$
$282$	−9.15720e10	+	6.93565e10i	−0.862267	+	0.653080i
$283$	−3.72420e10	+	3.72420e10i	−0.345139	+	0.345139i	−0.858295	−	0.513156i	$-0.828476\pi$
$283$	−3.72420e10	+	3.72420e10i	−0.345139	+	0.345139i	0.513156	+	0.858295i	$0.328476\pi$
$284$	−9.37758e10			−0.855378
$285$		0			0
$286$	4.83979e10			0.427740
$287$	−6.93862e10	+	6.93862e10i	−0.603677	+	0.603677i
$288$	−1.79836e10	−	3.20720e10i	−0.154032	−	0.274701i
$289$			6.18698e9i			0.0521721i
$290$		0			0
$291$	−2.15744e10	+	1.56284e11i	−0.176368	+	1.27760i
$292$	−2.19564e11	−	2.19564e11i	−1.76741	−	1.76741i
$293$	−3.40595e10	−	3.40595e10i	−0.269981	−	0.269981i	0.559111	−	0.829093i	$-0.311142\pi$
$293$	−3.40595e10	−	3.40595e10i	−0.269981	−	0.269981i	−0.829093	+	0.559111i	$0.811142\pi$
$294$	−2.15336e9	+	1.55989e10i	−0.0168094	+	0.121767i
$295$		0			0
$296$			3.10815e11i			2.35337i
$297$	9.27252e10	+	2.36356e11i	0.691502	+	1.76263i
$298$	−1.36432e11	+	1.36432e11i	−1.00217	+	1.00217i
$299$	1.19755e10			0.0866506
$300$		0			0
$301$	−1.00972e11			−0.709009
$302$	6.41790e10	−	6.41790e10i	0.443978	−	0.443978i
$303$	−5.33474e10	+	4.04052e10i	−0.363598	+	0.275389i
$304$		−	1.53356e11i		−	1.02984i
$305$		0			0
$306$	−2.44889e11	−	6.89254e10i	−1.59670	−	0.449400i
$307$	−6.41669e10	−	6.41669e10i	−0.412277	−	0.412277i	0.470254	−	0.882531i	$-0.344162\pi$
$307$	−6.41669e10	−	6.41669e10i	−0.412277	−	0.412277i	−0.882531	+	0.470254i	$0.844162\pi$
$308$	−3.87576e11	−	3.87576e11i	−2.45402	−	2.45402i
$309$	−7.12722e10	−	9.83883e9i	−0.444741	−	0.0613946i
$310$		0			0
$311$			3.89435e10i			0.236055i	0.993010	+	0.118027i	$0.0376571\pi$
$311$			3.89435e10i			0.236055i	−0.993010	+	0.118027i	$0.962343\pi$
$312$	2.06118e10	+	2.72140e10i	0.123146	+	0.162591i
$313$	−1.12579e11	+	1.12579e11i	−0.662993	+	0.662993i	−0.956084	−	0.293092i	$-0.905316\pi$
$313$	−1.12579e11	+	1.12579e11i	−0.662993	+	0.662993i	0.293092	+	0.956084i	$0.405316\pi$
$314$	−3.14784e11			−1.82738
$315$		0			0
$316$	3.51791e11			1.98469
$317$	1.63509e11	−	1.63509e11i	0.909444	−	0.909444i	−0.0867832	−	0.996227i	$-0.527659\pi$
$317$	1.63509e11	−	1.63509e11i	0.909444	−	0.909444i	0.996227	+	0.0867832i	$0.0276587\pi$
$318$	4.50271e10	+	5.94497e10i	0.246918	+	0.326008i
$319$		−	5.88793e11i		−	3.18350i
$320$		0			0
$321$	−8.03788e10	−	1.10960e10i	−0.422541	−	0.0583301i
$322$	−1.46299e11	−	1.46299e11i	−0.758386	−	0.758386i
$323$	1.93152e11	+	1.93152e11i	0.987386	+	0.987386i
$324$	−1.96875e11	+	3.22038e11i	−0.992515	+	1.62351i
$325$		0			0
$326$			1.58402e11i			0.776750i
$327$	−7.83508e9	+	5.93428e9i	−0.0378947	+	0.0287014i
$328$	−2.02083e11	+	2.02083e11i	−0.964046	+	0.964046i
$329$	1.29958e11			0.611537
$330$		0			0
$331$	−1.88672e11			−0.863934			−0.431967	−	0.901889i	$-0.642180\pi$
$331$	−1.88672e11			−0.863934			−0.431967	+	0.901889i	$0.642180\pi$
$332$	−5.53688e10	+	5.53688e10i	−0.250117	+	0.250117i
$333$	−2.99427e11	+	1.67896e11i	−1.33442	+	0.748241i
$334$			6.83210e10i			0.300397i
$335$		0			0
$336$	2.20964e10	−	1.60066e11i	0.0945791	−	0.685128i
$337$	5.30750e10	+	5.30750e10i	0.224159	+	0.224159i	0.810247	−	0.586088i	$-0.199333\pi$
$337$	5.30750e10	+	5.30750e10i	0.224159	+	0.224159i	−0.586088	+	0.810247i	$0.699333\pi$
$338$	−2.84001e11	−	2.84001e11i	−1.18357	−	1.18357i
$339$	−2.09738e10	+	1.51933e11i	−0.0862537	+	0.624819i
$340$		0			0
$341$		−	3.34688e10i		−	0.134044i
$342$	5.39264e11	−	3.02379e11i	2.13150	−	1.19518i
$343$	1.87199e11	−	1.87199e11i	0.730262	−	0.730262i
$344$	−2.94075e11			−1.13226
$345$		0			0
$346$	−1.31919e11			−0.494839
$347$	−3.42159e11	+	3.42159e11i	−1.26691	+	1.26691i	−0.319234	+	0.947676i	$0.603426\pi$
$347$	−3.42159e11	+	3.42159e11i	−1.26691	+	1.26691i	−0.947676	+	0.319234i	$0.896574\pi$
$348$	6.97775e11	−	5.28494e11i	2.55040	−	1.93167i
$349$			4.38934e11i			1.58374i	0.610688	+	0.791871i	$0.290893\pi$
$349$			4.38934e11i			1.58374i	−0.610688	+	0.791871i	$0.709107\pi$
$350$		0			0
$351$	−1.50828e10	+	3.45571e10i	−0.0530394	+	0.121522i
$352$	1.21451e11	+	1.21451e11i	0.421656	+	0.421656i
$353$	3.50214e11	+	3.50214e11i	1.20046	+	1.20046i	0.974027	+	0.226432i	$0.0727062\pi$
$353$	3.50214e11	+	3.50214e11i	1.20046	+	1.20046i	0.226432	+	0.974027i	$0.427294\pi$
$354$	−7.83792e10	−	1.08199e10i	−0.265269	−	0.0366193i
$355$		0			0
$356$			7.49073e11i			2.47172i
$357$	1.73773e11	+	2.29434e11i	0.566206	+	0.747567i
$358$	−5.62660e10	+	5.62660e10i	−0.181039	+	0.181039i
$359$	5.21576e11			1.65727			0.828633	−	0.559792i	$-0.189119\pi$
$359$	5.21576e11			1.65727			0.828633	+	0.559792i	$0.189119\pi$
$360$		0			0
$361$	−3.41143e11			−1.05719
$362$	−4.92191e11	+	4.92191e11i	−1.50642	+	1.50642i
$363$	−5.16320e11	−	6.81702e11i	−1.56077	−	2.06070i
$364$		−	8.13994e10i		−	0.243033i
$365$		0			0
$366$	8.34574e11	+	1.15210e11i	2.43108	+	0.335601i
$367$	2.50492e11	+	2.50492e11i	0.720769	+	0.720769i	0.968762	−	0.247993i	$-0.0797709\pi$
$367$	2.50492e11	+	2.50492e11i	0.720769	+	0.720769i	−0.247993	+	0.968762i	$0.579771\pi$
$368$	−1.16730e11	−	1.16730e11i	−0.331794	−	0.331794i
$369$	−3.03840e11	−	8.55173e10i	−0.853151	−	0.240124i
$370$		0			0
$371$		−	8.43707e10i		−	0.231211i
$372$	3.96637e10	−	3.00412e10i	0.107387	−	0.0813345i
$373$	−4.62167e11	+	4.62167e11i	−1.23626	+	1.23626i	−0.274739	+	0.961519i	$0.588591\pi$
$373$	−4.62167e11	+	4.62167e11i	−1.23626	+	1.23626i	−0.961519	+	0.274739i	$0.911409\pi$
$374$	1.18836e12			3.14069
$375$		0			0
$376$	3.78496e11			0.976598
$377$	6.18297e10	−	6.18297e10i	0.157638	−	0.157638i
$378$	6.06429e11	−	2.37909e11i	1.52780	−	0.599375i
$379$			4.65005e11i			1.15766i	0.815448	+	0.578830i	$0.196491\pi$
$379$			4.65005e11i			1.15766i	−0.815448	+	0.578830i	$0.803509\pi$
$380$		0			0
$381$	−5.29522e10	+	3.83584e11i	−0.128742	+	0.932606i
$382$	−5.36630e11	−	5.36630e11i	−1.28941	−	1.28941i
$383$	6.64390e10	+	6.64390e10i	0.157771	+	0.157771i	0.781578	−	0.623807i	$-0.214415\pi$
$383$	6.64390e10	+	6.64390e10i	0.157771	+	0.157771i	−0.623807	+	0.781578i	$0.714415\pi$
$384$	−1.06196e11	+	7.69283e11i	−0.249241	+	1.80549i
$385$		0			0
$386$		−	5.28374e11i		−	1.21143i
$387$	−1.58853e11	−	2.83299e11i	−0.359995	−	0.642017i
$388$	7.74693e11	−	7.74693e11i	1.73535	−	1.73535i
$389$	−2.98459e11			−0.660863			−0.330432	−	0.943830i	$-0.607194\pi$
$389$	−2.98459e11			−0.660863			−0.330432	+	0.943830i	$0.607194\pi$
$390$		0			0
$391$	2.94044e11			0.636235
$392$	3.66877e10	−	3.66877e10i	0.0784754	−	0.0784754i
$393$	2.52125e11	−	1.90959e11i	0.533150	−	0.403807i
$394$		−	7.41481e11i		−	1.55013i
$395$		0			0
$396$	4.77681e11	−	1.69718e12i	0.976134	−	3.46816i
$397$	3.95199e11	+	3.95199e11i	0.798470	+	0.798470i	0.982854	−	0.184384i	$-0.0590291\pi$
$397$	3.95199e11	+	3.95199e11i	0.798470	+	0.798470i	−0.184384	+	0.982854i	$0.559029\pi$
$398$	4.62514e11	+	4.62514e11i	0.923956	+	0.923956i
$399$	−6.92877e11	−	9.56488e10i	−1.36860	−	0.188930i
$400$		0			0
$401$		−	5.38579e11i		−	1.04016i	−0.854118	−	0.520079i	$-0.825902\pi$
$401$		−	5.38579e11i		−	1.04016i	0.854118	−	0.520079i	$-0.174098\pi$
$402$	−3.44874e11	−	4.55341e11i	−0.658633	−	0.869600i
$403$	3.51459e9	−	3.51459e9i	0.00663747	−	0.00663747i
$404$	4.64728e11			0.867925
$405$		0			0
$406$	−1.51069e12			−2.75937
$407$	1.13387e12	−	1.13387e12i	2.04828	−	2.04828i
$408$	5.06102e11	+	6.68211e11i	0.904205	+	1.19383i
$409$		−	2.38720e11i		−	0.421826i	−0.977505	−	0.210913i	$-0.932356\pi$
$409$		−	2.38720e11i		−	0.421826i	0.977505	−	0.210913i	$-0.0676437\pi$
$410$		0			0
$411$	−6.17152e11	−	8.51954e10i	−1.06685	−	0.147275i
$412$	3.53293e11	+	3.53293e11i	0.604084	+	0.604084i
$413$	6.32954e10	+	6.32954e10i	0.107053	+	0.107053i
$414$	1.80311e11	−	6.40638e11i	0.301662	−	1.07179i
$415$		0			0
$416$			2.55073e10i			0.0417585i
$417$	4.31366e11	−	3.26716e11i	0.698607	−	0.529124i
$418$	−2.04210e12	+	2.04210e12i	−3.27177	+	3.27177i
$419$	−5.63091e11			−0.892514			−0.446257	−	0.894905i	$-0.647243\pi$
$419$	−5.63091e11			−0.892514			−0.446257	+	0.894905i	$0.647243\pi$
$420$		0			0
$421$	−4.73400e10			−0.0734444			−0.0367222	−	0.999326i	$-0.511692\pi$
$421$	−4.73400e10			−0.0734444			−0.0367222	+	0.999326i	$0.511692\pi$
$422$	−1.09572e12	+	1.09572e12i	−1.68188	+	1.68188i
$423$	2.04456e11	+	3.64627e11i	0.310504	+	0.553755i
$424$		−	2.45724e11i		−	0.369234i
$425$		0			0
$426$	−7.11922e10	+	5.15714e11i	−0.104734	+	0.758692i
$427$	−6.73963e11	−	6.73963e11i	−0.981095	−	0.981095i
$428$	3.98434e11	+	3.98434e11i	0.573931	+	0.573931i
$429$	2.40851e10	−	1.74472e11i	0.0343314	−	0.248695i
$430$		0			0
$431$		−	8.32690e11i		−	1.16235i	−0.813780	−	0.581173i	$-0.802594\pi$
$431$		−	8.32690e11i		−	1.16235i	0.813780	−	0.581173i	$-0.197406\pi$
$432$	4.83863e11	−	1.89825e11i	0.668414	−	0.262227i
$433$	5.06995e11	−	5.06995e11i	0.693119	−	0.693119i	−0.269798	−	0.962917i	$-0.586957\pi$
$433$	5.06995e11	−	5.06995e11i	0.693119	−	0.693119i	0.962917	+	0.269798i	$0.0869569\pi$
$434$	−8.58726e10			−0.116185
$435$		0			0
$436$	6.82541e10			0.0904564
$437$	−5.05291e11	+	5.05291e11i	−0.662789	+	0.662789i
$438$	−1.37416e12	+	1.04079e12i	−1.78404	+	1.35123i
$439$		−	1.14488e11i		−	0.147119i	−0.997291	−	0.0735597i	$-0.976564\pi$
$439$		−	1.14488e11i		−	0.147119i	0.997291	−	0.0735597i	$-0.0234359\pi$
$440$		0			0
$441$	5.51614e10	+	1.55255e10i	0.0694483	+	0.0195466i
$442$	1.24791e11	+	1.24791e11i	0.155518	+	0.155518i
$443$	−7.66465e11	−	7.66465e11i	−0.945531	−	0.945531i	0.0530606	−	0.998591i	$-0.483102\pi$
$443$	−7.66465e11	−	7.66465e11i	−0.945531	−	0.945531i	−0.998591	+	0.0530606i	$0.983102\pi$
$444$	2.36150e12	+	3.25996e11i	2.88380	+	0.398096i
$445$		0			0
$446$			1.78635e12i			2.13776i
$447$	4.23933e11	+	5.59723e11i	0.502243	+	0.663116i
$448$	7.28584e11	−	7.28584e11i	0.854533	−	0.854533i
$449$	5.33889e11			0.619930			0.309965	−	0.950748i	$-0.399683\pi$
$449$	5.33889e11			0.619930			0.309965	+	0.950748i	$0.399683\pi$
$450$		0			0
$451$	1.47442e12			1.67814
$452$	7.53126e11	−	7.53126e11i	0.848682	−	0.848682i
$453$	−1.99423e11	−	2.63300e11i	−0.222502	−	0.293771i
$454$		−	2.31148e12i		−	2.55352i
$455$		0			0
$456$	−2.01796e12	−	2.78571e11i	−2.18560	−	0.301713i
$457$	−8.13858e11	−	8.13858e11i	−0.872822	−	0.872822i	0.119957	−	0.992779i	$-0.461724\pi$
$457$	−8.13858e11	−	8.13858e11i	−0.872822	−	0.872822i	−0.992779	+	0.119957i	$0.961724\pi$
$458$	6.65408e11	+	6.65408e11i	0.706632	+	0.706632i
$459$	−3.70341e11	+	8.48511e11i	−0.389444	+	0.892279i
$460$		0			0
$461$		−	3.41270e11i		−	0.351920i	−0.984397	−	0.175960i	$-0.943697\pi$
$461$		−	3.41270e11i		−	0.351920i	0.984397	−	0.175960i	$-0.0563030\pi$
$462$	−2.42569e12	+	1.83721e12i	−2.47711	+	1.87616i
$463$	1.58976e11	−	1.58976e11i	0.160774	−	0.160774i	−0.622135	−	0.782910i	$-0.713735\pi$
$463$	1.58976e11	−	1.58976e11i	0.160774	−	0.160774i	0.782910	+	0.622135i	$0.213735\pi$
$464$	−1.20537e12			−1.20722
$465$		0			0
$466$	6.16794e11			0.605903
$467$	2.84198e11	−	2.84198e11i	0.276500	−	0.276500i	−0.555210	−	0.831710i	$-0.687362\pi$
$467$	2.84198e11	−	2.84198e11i	0.276500	−	0.276500i	0.831710	+	0.555210i	$0.187362\pi$
$468$	2.28384e11	−	1.28061e11i	0.220069	−	0.123398i
$469$			6.46217e11i			0.616738i
$470$		0			0
$471$	−1.56652e11	+	1.13478e12i	−0.146670	+	1.06247i
$472$	1.84344e11	+	1.84344e11i	0.170958	+	0.170958i
$473$	1.07280e12	+	1.07280e12i	0.985473	+	0.985473i
$474$	2.67071e11	−	1.93465e12i	0.243010	−	1.76036i
$475$		0			0
$476$		−	1.99867e12i		−	1.78448i
$477$	2.36721e11	−	1.32735e11i	0.209365	−	0.117396i
$478$	8.34276e11	−	8.34276e11i	0.730945	−	0.730945i
$479$	−4.37648e11			−0.379853			−0.189926	−	0.981798i	$-0.560825\pi$
$479$	−4.37648e11			−0.379853			−0.189926	+	0.981798i	$0.560825\pi$
$480$		0			0
$481$	2.38138e11			0.202851
$482$	1.08880e12	−	1.08880e12i	0.918829	−	0.918829i
$483$	−6.00206e11	+	4.54595e11i	−0.501809	+	0.380069i
$484$			5.93854e12i			4.91899i
$485$		0			0
$486$	1.62157e12	+	1.32718e12i	1.31847	+	1.07911i
$487$	−6.53169e11	−	6.53169e11i	−0.526193	−	0.526193i	0.393242	−	0.919435i	$-0.371353\pi$
$487$	−6.53169e11	−	6.53169e11i	−0.526193	−	0.526193i	−0.919435	+	0.393242i	$0.871353\pi$
$488$	−1.96288e12	−	1.96288e12i	−1.56676	−	1.56676i
$489$	5.71030e11	+	7.88284e10i	0.451616	+	0.0623437i
$490$		0			0
$491$		−	1.57439e12i		−	1.22249i	−0.791442	−	0.611244i	$-0.790670\pi$
$491$		−	1.57439e12i		−	1.22249i	0.791442	−	0.611244i	$-0.209330\pi$
$492$	1.32343e12	+	1.74733e12i	1.01825	+	1.34441i
$493$	1.51816e12	−	1.51816e12i	1.15746	−	1.15746i
$494$	−4.28885e11			−0.324018
$495$		0			0
$496$	−6.85168e10			−0.0508311
$497$	4.16467e11	−	4.16467e11i	0.306180	−	0.306180i
$498$	2.62462e11	+	3.46531e11i	0.191221	+	0.252470i
$499$		−	9.09272e11i		−	0.656510i	−0.944589	−	0.328255i	$-0.893539\pi$
$499$		−	9.09272e11i		−	0.656510i	0.944589	−	0.328255i	$-0.106461\pi$
$500$		0			0
$501$	2.46293e11	+	3.39998e10i	0.174656	+	0.0241105i
$502$	2.01299e12	+	2.01299e12i	1.41473	+	1.41473i
$503$	−9.68222e11	−	9.68222e11i	−0.674403	−	0.674403i	0.284325	−	0.958728i	$-0.408230\pi$
$503$	−9.68222e11	−	9.68222e11i	−0.674403	−	0.674403i	−0.958728	+	0.284325i	$0.908230\pi$
$504$	−2.06612e12	−	5.81520e11i	−1.42632	−	0.401446i
$505$		0			0
$506$			3.10879e12i			2.10821i
$507$	−1.16514e12	+	8.82475e11i	−0.783146	+	0.593153i
$508$	1.90141e12	−	1.90141e12i	1.26674	−	1.26674i
$509$	−2.52477e12			−1.66721			−0.833607	−	0.552358i	$-0.813728\pi$
$509$	−2.52477e12			−1.66721			−0.833607	+	0.552358i	$0.813728\pi$
$510$		0			0
$511$	1.95020e12			1.26528
$512$	1.46304e12	−	1.46304e12i	0.940893	−	0.940893i
$513$	−8.21697e11	−	2.09450e12i	−0.523822	−	1.33522i
$514$			2.17907e12i			1.37701i
$515$		0			0
$516$	−3.08437e11	+	2.23431e12i	−0.191533	+	1.38746i
$517$	−1.38078e12	−	1.38078e12i	−0.849994	−	0.849994i
$518$	−2.90924e12	−	2.90924e12i	−1.77540	−	1.77540i
$519$	−6.56490e10	+	4.75559e11i	−0.0397169	+	0.287708i
$520$		0			0
$521$		−	1.49486e12i		−	0.888856i	−0.895815	−	0.444428i	$-0.853407\pi$
$521$		−	1.49486e12i		−	0.888856i	0.895815	−	0.444428i	$-0.146593\pi$
$522$	−2.37668e12	−	4.23859e12i	−1.40105	−	2.49864i
$523$	3.25864e11	−	3.25864e11i	0.190449	−	0.190449i	−0.605441	−	0.795890i	$-0.707003\pi$
$523$	3.25864e11	−	3.25864e11i	0.190449	−	0.190449i	0.795890	+	0.605441i	$0.207003\pi$
$524$	−2.19635e12			−1.27265
$525$		0			0
$526$	−2.02310e12			−1.15234
$527$	8.62970e10	−	8.62970e10i	0.0487358	−	0.0487358i
$528$	−1.93543e12	+	1.46589e12i	−1.08374	+	0.820822i
$529$		−	1.03192e12i		−	0.572924i
$530$		0			0
$531$	−7.80105e10	+	2.77168e11i	−0.0425822	+	0.151293i
$532$	3.43456e12	+	3.43456e12i	1.85895	+	1.85895i
$533$	1.54830e11	+	1.54830e11i	0.0830968	+	0.0830968i
$534$	4.11948e12	+	5.68677e11i	2.19233	+	0.302643i
$535$		0			0
$536$			1.88207e12i			0.984902i
$537$	1.74835e11	+	2.30836e11i	0.0907286	+	0.119790i
$538$	−2.85964e12	+	2.85964e12i	−1.47160	+	1.47160i
$539$	−2.67678e11			−0.136604
$540$		0			0
$541$	8.19017e11			0.411060			0.205530	−	0.978651i	$-0.434108\pi$
$541$	8.19017e11			0.411060			0.205530	+	0.978651i	$0.434108\pi$
$542$	−4.12505e12	+	4.12505e12i	−2.05320	+	2.05320i
$543$	1.52938e12	+	2.01926e12i	0.754948	+	0.996764i
$544$			6.26304e11i			0.306613i
$545$		0			0
$546$	−4.47651e11	−	6.17963e10i	−0.215562	−	0.0297575i
$547$	1.47005e12	+	1.47005e12i	0.702082	+	0.702082i	0.964857	−	0.262775i	$-0.0846377\pi$
$547$	1.47005e12	+	1.47005e12i	0.702082	+	0.702082i	−0.262775	+	0.964857i	$0.584638\pi$
$548$	3.05920e12	+	3.05920e12i	1.44909	+	1.44909i
$549$	8.30648e11	−	2.95126e12i	0.390249	−	1.38654i
$550$		0			0
$551$			5.21767e12i			2.41154i
$552$	−1.74806e12	+	1.32398e12i	−0.801366	+	0.606953i
$553$	−1.56234e12	+	1.56234e12i	−0.710414	+	0.710414i
$554$	1.48626e12			0.670350
$555$		0			0
$556$	−3.75777e12			−1.66761
$557$	1.64728e12	−	1.64728e12i	0.725137	−	0.725137i	−0.244510	−	0.969647i	$-0.578627\pi$
$557$	1.64728e12	−	1.64728e12i	0.725137	−	0.725137i	0.969647	+	0.244510i	$0.0786269\pi$
$558$	−1.35098e11	−	2.40935e11i	−0.0589923	−	0.105207i
$559$			2.25312e11i			0.0975958i
$560$		0			0
$561$	5.91384e11	−	4.28397e12i	0.252079	−	1.82605i
$562$	2.35369e12	+	2.35369e12i	0.995259	+	0.995259i
$563$	6.20715e11	+	6.20715e11i	0.260378	+	0.260378i	0.825208	−	0.564830i	$-0.191058\pi$
$563$	6.20715e11	+	6.20715e11i	0.260378	+	0.260378i	−0.564830	+	0.825208i	$0.691058\pi$
$564$	3.96981e11	−	2.87572e12i	0.165202	−	1.19671i
$565$		0			0
$566$		−	2.03047e12i		−	0.831614i
$567$	−5.55862e11	−	2.30454e12i	−0.225862	−	0.936397i
$568$	1.21293e12	−	1.21293e12i	0.488955	−	0.488955i
$569$	9.03315e11			0.361272			0.180636	−	0.983550i	$-0.442184\pi$
$569$	9.03315e11			0.361272			0.180636	+	0.983550i	$0.442184\pi$
$570$		0			0
$571$	−3.42408e12			−1.34797			−0.673987	−	0.738743i	$-0.735420\pi$
$571$	−3.42408e12			−1.34797			−0.673987	+	0.738743i	$0.735420\pi$
$572$	−8.64849e11	+	8.64849e11i	−0.337799	+	0.337799i
$573$	−2.20157e12	+	1.66747e12i	−0.853173	+	0.646192i
$574$		−	3.78300e12i		−	1.45456i
$575$		0			0
$576$	3.19044e12	+	8.97967e11i	1.20767	+	0.339906i
$577$	−3.10909e12	−	3.10909e12i	−1.16773	−	1.16773i	−0.982741	−	0.184989i	$-0.940775\pi$
$577$	−3.10909e12	−	3.10909e12i	−1.16773	−	1.16773i	−0.184989	−	0.982741i	$-0.559225\pi$
$578$	−1.68660e11	−	1.68660e11i	−0.0628545	−	0.0628545i
$579$	−1.90476e12	−	2.62944e11i	−0.704347	−	0.0972322i
$580$		0			0
$581$		−	4.91795e11i		−	0.179057i
$582$	−3.67225e12	−	4.84850e12i	−1.32672	−	1.75168i
$583$	−8.96418e11	+	8.96418e11i	−0.321368	+	0.321368i
$584$	5.67984e12			2.02059
$585$		0			0
$586$	1.85695e12			0.650521
$587$	−6.90802e11	+	6.90802e11i	−0.240150	+	0.240150i	−0.816912	−	0.576762i	$-0.804316\pi$
$587$	−6.90802e11	+	6.90802e11i	−0.240150	+	0.240150i	0.576762	+	0.816912i	$0.304316\pi$
$588$	−2.40265e11	−	3.17224e11i	−0.0828881	−	0.109438i
$589$			2.96589e11i			0.101540i
$590$		0			0
$591$	−2.67300e12	−	3.68996e11i	−0.901269	−	0.124417i
$592$	−2.32125e12	−	2.32125e12i	−0.776736	−	0.776736i
$593$	1.11597e12	+	1.11597e12i	0.370600	+	0.370600i	0.867696	−	0.497096i	$-0.165600\pi$
$593$	1.11597e12	+	1.11597e12i	0.370600	+	0.370600i	−0.497096	+	0.867696i	$0.665600\pi$
$594$	−8.97089e12	−	3.91543e12i	−2.95663	−	1.29045i
$595$		0			0
$596$		−	4.87594e12i		−	1.58289i
$597$	1.89751e12	−	1.43717e12i	0.611363	−	0.463045i
$598$	−3.26456e11	+	3.26456e11i	−0.104393	+	0.104393i
$599$	−2.92090e12			−0.927036			−0.463518	−	0.886088i	$-0.653413\pi$
$599$	−2.92090e12			−0.927036			−0.463518	+	0.886088i	$0.653413\pi$
$600$		0			0
$601$	2.94381e12			0.920397			0.460198	−	0.887816i	$-0.347778\pi$
$601$	2.94381e12			0.920397			0.460198	+	0.887816i	$0.347778\pi$
$602$	2.75254e12	−	2.75254e12i	0.854181	−	0.854181i
$603$	−1.81310e12	+	1.01665e12i	−0.558464	+	0.313145i
$604$			2.29370e12i			0.701245i
$605$		0			0
$606$	3.52809e11	−	2.55574e12i	0.106271	−	0.769821i
$607$	2.93780e11	+	2.93780e11i	0.0878360	+	0.0878360i	0.749660	−	0.661824i	$-0.230217\pi$
$607$	2.93780e11	+	2.93780e11i	0.0878360	+	0.0878360i	−0.661824	+	0.749660i	$0.730217\pi$
$608$	−1.07625e12	−	1.07625e12i	−0.319410	−	0.319410i
$609$	−7.51794e11	+	5.44597e12i	−0.221473	+	1.60434i
$610$		0			0
$611$		−	2.89993e11i		−	0.0841787i
$612$	5.60772e12	−	3.14439e12i	1.61587	−	0.906057i
$613$	1.80873e12	−	1.80873e12i	0.517370	−	0.517370i	−0.399405	−	0.916775i	$-0.630783\pi$
$613$	1.80873e12	−	1.80873e12i	0.517370	−	0.517370i	0.916775	+	0.399405i	$0.130783\pi$
$614$	3.49844e12			0.993383
$615$		0			0
$616$	1.00261e13			2.80556
$617$	−1.47527e12	+	1.47527e12i	−0.409816	+	0.409816i	−0.881674	−	0.471859i	$-0.843583\pi$
$617$	−1.47527e12	+	1.47527e12i	−0.409816	+	0.409816i	0.471859	+	0.881674i	$0.343583\pi$
$618$	2.21112e12	−	1.67470e12i	0.609768	−	0.461837i
$619$		−	2.33341e12i		−	0.638827i	−0.947615	−	0.319413i	$-0.896514\pi$
$619$		−	2.33341e12i		−	0.638827i	0.947615	−	0.319413i	$-0.103486\pi$
$620$		0			0
$621$	−2.21973e12	−	9.68824e11i	−0.598947	−	0.261416i
$622$	−1.06162e12	−	1.06162e12i	−0.284388	−	0.284388i
$623$	−3.32670e12	−	3.32670e12i	−0.884743	−	0.884743i
$624$	−3.57175e11	−	4.93066e10i	−0.0943085	−	0.0130189i
$625$		0			0
$626$		−	6.13792e12i		−	1.59748i
$627$	6.34540e12	+	8.37789e12i	1.63966	+	2.16486i
$628$	5.62505e12	−	5.62505e12i	1.44314	−	1.44314i
$629$	5.84723e12			1.48944
$630$		0			0
$631$	−6.18612e12			−1.55341			−0.776706	−	0.629864i	$-0.783111\pi$
$631$	−6.18612e12			−1.55341			−0.776706	+	0.629864i	$0.783111\pi$
$632$	−4.55021e12	+	4.55021e12i	−1.13450	+	1.13450i
$633$	3.40473e12	+	4.49530e12i	0.842881	+	1.11286i
$634$			8.91468e12i			2.19131i
$635$		0			0
$636$	−1.86695e12	−	2.57725e11i	−0.452456	−	0.0624597i
$637$	−2.81091e10	−	2.81091e10i	−0.00676425	−	0.00676425i
$638$	1.60508e13	+	1.60508e13i	3.83533	+	3.83533i
$639$	1.82369e12	+	5.13288e11i	0.432710	+	0.121789i
$640$		0			0
$641$			4.01836e12i			0.940129i	0.882632	+	0.470064i	$0.155769\pi$
$641$			4.01836e12i			0.940129i	−0.882632	+	0.470064i	$0.844231\pi$
$642$	2.49364e12	−	1.88868e12i	0.579331	−	0.438784i
$643$	3.17185e12	−	3.17185e12i	0.731752	−	0.731752i	−0.239215	−	0.970967i	$-0.576890\pi$
$643$	3.17185e12	−	3.17185e12i	0.731752	−	0.731752i	0.970967	+	0.239215i	$0.0768901\pi$
$644$	5.22860e12			1.19784
$645$		0			0
$646$	−1.05308e13			−2.37911
$647$	−2.61283e12	+	2.61283e12i	−0.586196	+	0.586196i	−0.936599	−	0.350403i	$-0.886045\pi$
$647$	−2.61283e12	+	2.61283e12i	−0.586196	+	0.586196i	0.350403	+	0.936599i	$0.386045\pi$
$648$	−1.61891e12	−	6.71182e12i	−0.360692	−	1.49538i
$649$		−	1.34500e12i		−	0.297591i
$650$		0			0
$651$	−4.27343e10	+	3.09566e11i	−0.00932529	+	0.0675521i
$652$	−2.83057e12	−	2.83057e12i	−0.613423	−	0.613423i
$653$	−2.87416e12	−	2.87416e12i	−0.618588	−	0.618588i	0.326581	−	0.945169i	$-0.394103\pi$
$653$	−2.87416e12	−	2.87416e12i	−0.618588	−	0.618588i	−0.945169	+	0.326581i	$0.894103\pi$
$654$	5.18168e10	−	3.75359e11i	0.0110757	−	0.0802318i
$655$		0			0
$656$		−	3.01841e12i		−	0.636372i
$657$	3.06814e12	+	5.47173e12i	0.642437	+	1.14572i
$658$	−3.54272e12	+	3.54272e12i	−0.736751	+	0.736751i
$659$	4.54583e12			0.938920			0.469460	−	0.882954i	$-0.344449\pi$
$659$	4.54583e12			0.938920			0.469460	+	0.882954i	$0.344449\pi$
$660$		0			0
$661$	8.55740e12			1.74355			0.871777	−	0.489903i	$-0.162968\pi$
$661$	8.55740e12			1.74355			0.871777	+	0.489903i	$0.162968\pi$
$662$	5.14327e12	−	5.14327e12i	1.04083	−	1.04083i
$663$	5.11965e11	−	3.87761e11i	0.102903	−	0.0779388i
$664$		−	1.43232e12i		−	0.285946i
$665$		0			0
$666$	3.58558e12	−	1.27394e13i	0.706197	−	2.50909i
$667$	3.97156e12	+	3.97156e12i	0.776953	+	0.776953i
$668$	−1.22086e12	−	1.22086e12i	−0.237232	−	0.237232i
$669$	6.43968e12	+	8.88972e11i	1.24293	+	0.171582i
$670$		0			0
$671$			1.43214e13i			2.72731i
$672$	−9.68271e11	−	1.27842e12i	−0.183162	−	0.241830i
$673$	1.52960e12	−	1.52960e12i	0.287416	−	0.287416i	−0.548642	−	0.836057i	$-0.684855\pi$
$673$	1.52960e12	−	1.52960e12i	0.287416	−	0.287416i	0.836057	+	0.548642i	$0.184855\pi$
$674$	−2.89370e12			−0.540111
$675$		0			0
$676$	1.01499e13			1.86940
$677$	−6.67092e12	+	6.67092e12i	−1.22050	+	1.22050i	−0.253041	+	0.967456i	$0.581431\pi$
$677$	−6.67092e12	+	6.67092e12i	−1.22050	+	1.22050i	−0.967456	+	0.253041i	$0.918569\pi$
$678$	−3.57001e12	−	4.71352e12i	−0.648838	−	0.856667i
$679$			6.88096e12i			1.24232i
$680$		0			0
$681$	−8.33277e12	−	1.15031e12i	−1.48466	−	0.204951i
$682$	9.12376e11	+	9.12376e11i	0.161489	+	0.161489i
$683$	−2.46742e12	−	2.46742e12i	−0.433860	−	0.433860i	0.456079	−	0.889939i	$-0.349253\pi$
$683$	−2.46742e12	−	2.46742e12i	−0.433860	−	0.433860i	−0.889939	+	0.456079i	$0.849253\pi$
$684$	−4.23303e12	+	1.50398e13i	−0.739433	+	2.62718i
$685$		0			0
$686$			1.02062e13i			1.75957i
$687$	2.72990e12	−	2.06762e12i	0.467564	−	0.354132i
$688$	2.19622e12	−	2.19622e12i	0.373704	−	0.373704i
$689$	−1.88267e11			−0.0318265
$690$		0			0
$691$	3.99348e12			0.666347			0.333173	−	0.942866i	$-0.391881\pi$
$691$	3.99348e12			0.666347			0.333173	+	0.942866i	$0.391881\pi$
$692$	2.35733e12	−	2.35733e12i	0.390789	−	0.390789i
$693$	5.41591e12	+	9.65875e12i	0.892014	+	1.59082i
$694$		−	1.86548e13i		−	3.05263i
$695$		0			0
$696$	−2.18955e12	+	1.58610e13i	−0.353683	+	2.56207i
$697$	3.80170e12	+	3.80170e12i	0.610141	+	0.610141i
$698$	−1.19655e13	−	1.19655e13i	−1.90802	−	1.90802i
$699$	3.06946e11	−	2.22351e12i	0.0486312	−	0.352283i
$700$		0			0
$701$		−	1.22127e13i		−	1.91020i	−0.296277	−	0.955102i	$-0.595745\pi$
$701$		−	1.22127e13i		−	1.91020i	0.296277	−	0.955102i	$-0.404255\pi$
$702$	−5.30878e11	−	1.35320e12i	−0.0825045	−	0.210303i
$703$	−1.00480e13	+	1.00480e13i	−1.55160	+	1.55160i
$704$	−1.54821e13			−2.37548
$705$		0			0
$706$	−1.90940e13			−2.89251
$707$	−2.06390e12	+	2.06390e12i	−0.310671	+	0.310671i
$708$	1.59395e12	−	1.20725e12i	0.238410	−	0.180571i
$709$		−	2.93664e11i		−	0.0436458i	−0.999762	−	0.0218229i	$-0.993053\pi$
$709$		−	2.93664e11i		−	0.0436458i	0.999762	−	0.0218229i	$-0.00694700\pi$
$710$		0			0
$711$	−6.84141e12	−	1.92555e12i	−1.00400	−	0.282580i
$712$	−9.68880e12	−	9.68880e12i	−1.41290	−	1.41290i
$713$	2.25756e11	+	2.25756e11i	0.0327142	+	0.0327142i
$714$	−1.09916e13	−	1.51734e12i	−1.58277	−	0.218495i
$715$		0			0
$716$		−	2.01089e12i		−	0.285944i
$717$	−2.59234e12	−	3.42270e12i	−0.366317	−	0.483651i
$718$	−1.42184e13	+	1.42184e13i	−1.99660	+	1.99660i
$719$	−2.62311e12			−0.366046			−0.183023	−	0.983109i	$-0.558588\pi$
$719$	−2.62311e12			−0.366046			−0.183023	+	0.983109i	$0.558588\pi$
$720$		0			0
$721$	−3.13801e12			−0.432460
$722$	9.29970e12	−	9.29970e12i	1.27365	−	1.27365i
$723$	−3.38321e12	−	4.46688e12i	−0.460476	−	0.607970i
$724$		−	1.75904e13i		−	2.37932i
$725$		0			0
$726$	3.26586e13	+	4.50839e12i	4.36298	+	0.602291i
$727$	−7.19644e12	−	7.19644e12i	−0.955460	−	0.955460i	0.0435893	−	0.999050i	$-0.486121\pi$
$727$	−7.19644e12	−	7.19644e12i	−0.955460	−	0.955460i	−0.999050	+	0.0435893i	$0.986121\pi$
$728$	1.05285e12	+	1.05285e12i	0.138924	+	0.138924i
$729$	5.59139e12	−	5.18518e12i	0.733239	−	0.679971i
$730$		0			0
$731$			5.53229e12i			0.716600i
$732$	−1.69722e13	+	1.28547e13i	−2.18493	+	1.65487i
$733$	8.37256e12	−	8.37256e12i	1.07125	−	1.07125i	0.0739897	−	0.997259i	$-0.476427\pi$
$733$	8.37256e12	−	8.37256e12i	1.07125	−	1.07125i	0.997259	−	0.0739897i	$-0.0235732\pi$
$734$	−1.36570e13			−1.73670
$735$		0			0
$736$	−1.63843e12			−0.205816
$737$	6.86590e12	−	6.86590e12i	0.857222	−	0.857222i
$738$	1.06140e13	−	5.95156e12i	1.31713	−	0.738546i
$739$			5.57077e12i			0.687092i	0.939136	+	0.343546i	$0.111628\pi$
$739$			5.57077e12i			0.687092i	−0.939136	+	0.343546i	$0.888372\pi$
$740$		0			0
$741$	−2.13433e11	+	1.54611e12i	−0.0260064	+	0.188390i
$742$	2.29998e12	+	2.29998e12i	0.278552	+	0.278552i
$743$	2.82819e12	+	2.82819e12i	0.340455	+	0.340455i	0.856538	−	0.516083i	$-0.172611\pi$
$743$	2.82819e12	+	2.82819e12i	0.340455	+	0.340455i	−0.516083	+	0.856538i	$0.672611\pi$
$744$	−1.24461e11	+	9.01592e11i	−0.0148921	+	0.107878i
$745$		0			0
$746$		−	2.51977e13i		−	2.97877i
$747$	1.37984e12	−	7.73711e11i	0.162138	−	0.0909151i
$748$	−2.12354e13	+	2.12354e13i	−2.48030	+	2.48030i
$749$	−3.53896e12			−0.410873
$750$		0			0
$751$	7.51531e12			0.862119			0.431060	−	0.902323i	$-0.358140\pi$
$751$	7.51531e12			0.862119			0.431060	+	0.902323i	$0.358140\pi$
$752$	−2.82670e12	+	2.82670e12i	−0.322329	+	0.322329i
$753$	8.25846e12	−	6.25495e12i	0.936099	−	0.709000i
$754$			3.37101e12i			0.379830i
$755$		0			0
$756$	−6.58528e12	+	1.50879e13i	−0.733206	+	1.67989i
$757$	−4.07403e12	−	4.07403e12i	−0.450913	−	0.450913i	0.444745	−	0.895657i	$-0.353294\pi$
$757$	−4.07403e12	−	4.07403e12i	−0.450913	−	0.450913i	−0.895657	+	0.444745i	$0.853294\pi$
$758$	−1.26762e13	−	1.26762e13i	−1.39469	−	1.39469i
$759$	1.12070e13	+	1.54708e12i	1.22575	+	0.169210i
$760$		0			0
$761$			1.08913e13i			1.17720i	0.808425	+	0.588599i	$0.200320\pi$
$761$			1.08913e13i			1.17720i	−0.808425	+	0.588599i	$0.799680\pi$
$762$	−9.01317e12	−	1.19002e13i	−0.968457	−	1.27866i
$763$	−3.03122e11	+	3.03122e11i	−0.0323786	+	0.0323786i
$764$	1.91787e13			2.03656
$765$		0			0
$766$	−3.62231e12			−0.380151
$767$	1.41239e11	−	1.41239e11i	0.0147359	−	0.0147359i
$768$	−1.07731e13	−	1.42238e13i	−1.11741	−	1.47533i
$769$		−	1.18841e13i		−	1.22545i	−0.790295	−	0.612727i	$-0.790073\pi$
$769$		−	1.18841e13i		−	1.22545i	0.790295	−	0.612727i	$-0.209927\pi$
$770$		0			0
$771$	7.85543e12	+	1.08441e12i	0.800618	+	0.110522i
$772$	9.44180e12	+	9.44180e12i	0.956703	+	0.956703i
$773$	7.19833e12	+	7.19833e12i	0.725144	+	0.725144i	0.969648	−	0.244504i	$-0.0786253\pi$
$773$	7.19833e12	+	7.19833e12i	0.725144	+	0.725144i	−0.244504	+	0.969648i	$0.578625\pi$
$774$	1.20533e13	+	3.39246e12i	1.20718	+	0.339766i
$775$		0			0
$776$			2.00404e13i			1.98394i
$777$	−1.19354e13	+	9.03986e12i	−1.17474	+	0.889748i
$778$	8.13613e12	−	8.13613e12i	0.796177	−	0.796177i
$779$	−1.30658e13			−1.27121
$780$		0			0
$781$	−8.84971e12			−0.851137
$782$	−8.01578e12	+	8.01578e12i	−0.766506	+	0.766506i
$783$	−1.64626e13	+	6.45849e12i	−1.56520	+	0.614049i
$784$			5.47986e11i			0.0518021i
$785$		0			0
$786$	−1.66741e12	+	1.20787e13i	−0.155826	+	1.12880i
$787$	−4.89571e11	−	4.89571e11i	−0.0454914	−	0.0454914i	0.683995	−	0.729487i	$-0.260241\pi$
$787$	−4.89571e11	−	4.89571e11i	−0.0454914	−	0.0454914i	−0.729487	+	0.683995i	$0.760241\pi$
$788$	1.32499e13	+	1.32499e13i	1.22418	+	1.22418i
$789$	−1.00679e12	+	7.29315e12i	−0.0924895	+	0.669991i
$790$		0			0
$791$			6.68940e12i			0.607565i
$792$	1.57735e13	+	2.81305e13i	1.42451	+	2.54047i
$793$	−1.50390e12	+	1.50390e12i	−0.135049	+	0.135049i
$794$	−2.15466e13			−1.92392
$795$		0			0
$796$	−1.65298e13			−1.45935
$797$	−2.15529e12	+	2.15529e12i	−0.189209	+	0.189209i	−0.795354	−	0.606145i	$-0.792715\pi$
$797$	−2.15529e12	+	2.15529e12i	−0.189209	+	0.189209i	0.606145	+	0.795354i	$0.292715\pi$
$798$	2.14955e13	−	1.62807e13i	1.87644	−	1.42122i
$799$		−	7.12047e12i		−	0.618085i
$800$		0			0
$801$	4.10010e12	−	1.45675e13i	0.351923	−	1.25037i
$802$	1.46819e13	+	1.46819e13i	1.25313	+	1.25313i
$803$	−2.07204e13	−	2.07204e13i	−1.75865	−	1.75865i
$804$	1.42995e13	+	1.97398e12i	1.20689	+	0.166606i
$805$		0			0
$806$			1.91619e11i			0.0159930i
$807$	8.88575e12	+	1.17319e13i	0.737502	+	0.973730i
$808$	−6.01097e12	+	6.01097e12i	−0.496128	+	0.496128i
$809$	1.45943e13			1.19789			0.598943	−	0.800791i	$-0.295587\pi$
$809$	1.45943e13			1.19789			0.598943	+	0.800791i	$0.295587\pi$
$810$		0			0
$811$	1.82825e13			1.48403			0.742013	−	0.670385i	$-0.233871\pi$
$811$	1.82825e13			1.48403			0.742013	+	0.670385i	$0.233871\pi$
$812$	2.69954e13	−	2.69954e13i	2.17915	−	2.17915i
$813$	1.28177e13	+	1.69234e13i	1.02897	+	1.35856i
$814$			6.18198e13i			4.93535i
$815$		0			0
$816$	−8.77006e12	−	1.21067e12i	−0.692463	−	0.0955917i
$817$	−9.50679e12	−	9.50679e12i	−0.746508	−	0.746508i
$818$	6.50760e12	+	6.50760e12i	0.508196	+	0.508196i
$819$	−4.45545e11	+	1.58300e12i	−0.0346030	+	0.122943i
$820$		0			0
$821$		−	1.08121e13i		−	0.830549i	−0.909696	−	0.415274i	$-0.863686\pi$
$821$		−	1.08121e13i		−	0.830549i	0.909696	−	0.415274i	$-0.136314\pi$
$822$	1.91463e13	−	1.45014e13i	1.46272	−	1.10786i
$823$	1.68505e13	−	1.68505e13i	1.28030	−	1.28030i	0.339809	−	0.940494i	$-0.389637\pi$
$823$	1.68505e13	−	1.68505e13i	1.28030	−	1.28030i	0.940494	−	0.339809i	$-0.110363\pi$
$824$	−9.13926e12			−0.690619
$825$		0			0
$826$	−3.45092e12			−0.257944
$827$	−2.61775e12	+	2.61775e12i	−0.194605	+	0.194605i	−0.797682	−	0.603078i	$-0.793941\pi$
$827$	−2.61775e12	+	2.61775e12i	−0.194605	+	0.194605i	0.603078	+	0.797682i	$0.293941\pi$
$828$	8.22584e12	+	1.46700e13i	0.608196	+	1.08466i
$829$		−	8.22999e12i		−	0.605207i	−0.953116	−	0.302604i	$-0.902144\pi$
$829$		−	8.22999e12i		−	0.605207i	0.953116	−	0.302604i	$-0.0978558\pi$
$830$		0			0
$831$	7.39635e11	−	5.35789e12i	0.0538038	−	0.389753i
$832$	−1.62578e12	−	1.62578e12i	−0.117627	−	0.117627i
$833$	−6.90189e11	−	6.90189e11i	−0.0496667	−	0.0496667i
$834$	−2.85281e12	+	2.06656e13i	−0.204185	+	1.47911i
$835$		0			0
$836$		−	7.29827e13i		−	5.16763i
$837$	−9.35787e11	+	3.67121e11i	−0.0659041	+	0.0258550i
$838$	1.53501e13	−	1.53501e13i	1.07526	−	1.07526i
$839$	−2.04160e13			−1.42247			−0.711234	−	0.702955i	$-0.751863\pi$
$839$	−2.04160e13			−1.42247			−0.711234	+	0.702955i	$0.751863\pi$
$840$		0			0
$841$	2.65034e13			1.82692
$842$	1.29051e12	−	1.29051e12i	0.0884823	−	0.0884823i
$843$	9.65624e12	−	7.31362e12i	0.658543	−	0.498779i
$844$		−	3.91601e13i		−	2.65646i
$845$		0			0
$846$	−1.55134e13	−	4.36634e12i	−1.04122	−	0.293056i
$847$	−2.63736e13	−	2.63736e13i	−1.76073	−	1.76073i
$848$	1.83513e12	+	1.83513e12i	0.121867	+	0.121867i
$849$	−7.31972e12	−	1.01046e12i	−0.483515	−	0.0667472i
$850$		0			0
$851$			1.52965e13i			0.999793i
$852$	−7.94340e12	−	1.04877e13i	−0.516450	−	0.681873i
$853$	−3.41185e12	+	3.41185e12i	−0.220658	+	0.220658i	−0.808775	−	0.588118i	$-0.799869\pi$
$853$	−3.41185e12	+	3.41185e12i	−0.220658	+	0.220658i	0.588118	+	0.808775i	$0.299869\pi$
$854$	3.67451e13			2.36395
$855$		0			0
$856$	−1.03070e13			−0.656146
$857$	7.15296e12	−	7.15296e12i	0.452972	−	0.452972i	−0.443367	−	0.896340i	$-0.646216\pi$
$857$	7.15296e12	−	7.15296e12i	0.452972	−	0.452972i	0.896340	+	0.443367i	$0.146216\pi$
$858$	4.09961e12	+	5.41275e12i	0.258255	+	0.340977i
$859$		−	2.20120e12i		−	0.137940i	−0.997619	−	0.0689701i	$-0.978029\pi$
$859$		−	2.20120e12i		−	0.137940i	0.997619	−	0.0689701i	$-0.0219713\pi$
$860$		0			0
$861$	−1.36375e13	−	1.88260e12i	−0.845708	−	0.116747i
$862$	2.26995e13	+	2.26995e13i	1.40034	+	1.40034i
$863$	3.81330e12	+	3.81330e12i	0.234020	+	0.234020i	0.814368	−	0.580348i	$-0.197084\pi$
$863$	3.81330e12	+	3.81330e12i	0.234020	+	0.234020i	−0.580348	+	0.814368i	$0.697084\pi$
$864$	2.06356e12	−	4.72796e12i	0.125981	−	0.288643i
$865$		0			0
$866$			2.76418e13i			1.67007i
$867$	−6.91942e11	+	5.24076e11i	−0.0415895	+	0.0314998i
$868$	1.53450e12	−	1.53450e12i	0.0917549	−	0.0917549i
$869$	3.31989e13			1.97485
$870$		0			0
$871$	1.44199e12			0.0848945
$872$	−8.82825e11	+	8.82825e11i	−0.0517071	+	0.0517071i
$873$	−1.93061e13	+	1.08254e13i	−1.12494	+	0.630783i
$874$		−	2.75489e13i		−	1.59699i
$875$		0			0
$876$	5.95724e12	−	4.31541e13i	0.341804	−	2.47602i
$877$	7.78983e12	+	7.78983e12i	0.444662	+	0.444662i	0.893575	−	0.448913i	$-0.148189\pi$
$877$	7.78983e12	+	7.78983e12i	0.444662	+	0.444662i	−0.448913	+	0.893575i	$0.648189\pi$
$878$	3.12099e12	+	3.12099e12i	0.177242	+	0.177242i
$879$	9.24108e11	−	6.69421e12i	0.0522123	−	0.378224i
$880$		0			0
$881$		−	1.60987e13i		−	0.900325i	−0.892947	−	0.450163i	$-0.851366\pi$
$881$		−	1.60987e13i		−	0.900325i	0.892947	−	0.450163i	$-0.148634\pi$
$882$	−1.92696e12	+	1.08049e12i	−0.107217	+	0.0601192i
$883$	1.01063e13	−	1.01063e13i	0.559461	−	0.559461i	−0.369693	−	0.929154i	$-0.620537\pi$
$883$	1.01063e13	−	1.01063e13i	0.559461	−	0.559461i	0.929154	+	0.369693i	$0.120537\pi$
$884$	−4.45990e12			−0.245635
$885$		0			0
$886$	4.17884e13			2.27826
$887$	−1.76653e13	+	1.76653e13i	−0.958221	+	0.958221i	−0.999162	−	0.0409403i	$-0.986965\pi$
$887$	−1.76653e13	+	1.76653e13i	−0.958221	+	0.958221i	0.0409403	+	0.999162i	$0.486965\pi$
$888$	−3.47611e13	+	2.63280e13i	−1.87601	+	1.42089i
$889$			1.68887e13i			0.906854i
$890$		0			0
$891$	−1.85792e13	+	3.03911e13i	−0.987594	+	1.61546i
$892$	−3.19212e13	−	3.19212e13i	−1.68825	−	1.68825i
$893$	1.22359e13	+	1.22359e13i	0.643881	+	0.643881i
$894$	−2.68149e13	−	3.70169e12i	−1.40397	−	0.193812i
$895$		0			0
$896$			3.38704e13i			1.75564i
$897$	1.01440e12	+	1.33932e12i	0.0523169	+	0.0690744i
$898$	−1.45541e13	+	1.45541e13i	−0.746862	+	0.746862i
$899$	2.33117e12			0.119030
$900$		0			0
$901$	−4.62270e12			−0.233687
$902$	−4.01934e13	+	4.01934e13i	−2.02174	+	2.02174i
$903$	−8.55297e12	−	1.12926e13i	−0.428077	−	0.565194i
$904$			1.94825e13i			0.970255i
$905$		0			0
$906$	1.26140e13	+	1.74132e12i	0.621981	+	0.0858620i
$907$	−2.15559e13	−	2.15559e13i	−1.05763	−	1.05763i	−0.998235	−	0.0593936i	$-0.981083\pi$
$907$	−2.15559e13	−	2.15559e13i	−1.05763	−	1.05763i	−0.0593936	−	0.998235i	$-0.518917\pi$
$908$	4.13052e13	+	4.13052e13i	2.01659	+	2.01659i
$909$	−9.03772e12	−	2.54372e12i	−0.439058	−	0.123575i
$910$		0			0
$911$		−	6.36238e11i		−	0.0306046i	−0.999883	−	0.0153023i	$-0.995129\pi$
$911$		−	6.36238e11i		−	0.0306046i	0.999883	−	0.0153023i	$-0.00487107\pi$
$912$	1.71511e13	−	1.29902e13i	0.820945	−	0.621782i
$913$	−5.22520e12	+	5.22520e12i	−0.248877	+	0.248877i
$914$	4.43723e13			2.10307
$915$		0			0
$916$	−2.37811e13			−1.11610
$917$	9.75417e12	−	9.75417e12i	0.455542	−	0.455542i
$918$	−1.30351e13	−	3.32265e13i	−0.605792	−	1.54416i
$919$		−	3.10997e13i		−	1.43826i	−0.694878	−	0.719128i	$-0.744541\pi$
$919$		−	3.10997e13i		−	1.43826i	0.694878	−	0.719128i	$-0.255459\pi$
$920$		0			0
$921$	1.74099e12	−	1.26117e13i	0.0797311	−	0.577570i
$922$	9.30317e12	+	9.30317e12i	0.423977	+	0.423977i
$923$	−9.29316e11	−	9.29316e11i	−0.0421459	−	0.0421459i
$924$	1.05158e13	−	7.61761e13i	0.474590	−	3.43791i
$925$		0			0
$926$			8.66750e12i			0.387386i
$927$	−4.93684e12	−	8.80438e12i	−0.219579	−	0.391598i
$928$	−8.45928e12	+	8.45928e12i	−0.374427	+	0.374427i
$929$	−7.26334e12			−0.319938			−0.159969	−	0.987122i	$-0.551139\pi$
$929$	−7.26334e12			−0.319938			−0.159969	+	0.987122i	$0.551139\pi$
$930$		0			0
$931$	2.37207e12			0.103479
$932$	−1.10218e13	+	1.10218e13i	−0.478500	+	0.478500i
$933$	−4.35538e12	+	3.29876e12i	−0.188174	+	0.142522i
$934$			1.54948e13i			0.666229i
$935$		0			0
$936$	−1.29762e12	+	4.61040e12i	−0.0552594	+	0.196335i
$937$	1.57470e13	+	1.57470e13i	0.667374	+	0.667374i	0.957107	−	0.289733i	$-0.0935665\pi$
$937$	1.57470e13	+	1.57470e13i	0.667374	+	0.667374i	−0.289733	+	0.957107i	$0.593567\pi$
$938$	−1.76162e13	−	1.76162e13i	−0.743016	−	0.743016i
$939$	−2.21269e13	−	3.05452e12i	−0.928805	−	0.128218i
$940$		0			0
$941$		−	4.63214e13i		−	1.92587i	−0.269725	−	0.962937i	$-0.586933\pi$
$941$		−	4.63214e13i		−	1.92587i	0.269725	−	0.962937i	$-0.413067\pi$
$942$	−2.66642e13	−	3.52050e13i	−1.10332	−	1.45672i
$943$	−9.94536e12	+	9.94536e12i	−0.409560	+	0.409560i
$944$	−2.75345e12			−0.112851
$945$		0			0
$946$	−5.84902e13			−2.37450
$947$	2.05905e11	−	2.05905e11i	0.00831939	−	0.00831939i	−0.702935	−	0.711254i	$-0.748127\pi$
$947$	2.05905e11	−	2.05905e11i	0.00831939	−	0.00831939i	0.711254	+	0.702935i	$0.248127\pi$
$948$	2.97989e13	+	3.93438e13i	1.19829	+	1.58212i
$949$		−	4.35174e12i		−	0.174167i
$950$		0			0
$951$	3.21369e13	+	4.43637e12i	1.27407	+	0.175880i
$952$	2.58516e13	+	2.58516e13i	1.02005	+	1.02005i
$953$	2.44874e13	+	2.44874e13i	0.961668	+	0.961668i	0.999292	−	0.0376244i	$-0.0119791\pi$
$953$	2.44874e13	+	2.44874e13i	0.961668	+	0.961668i	−0.0376244	+	0.999292i	$0.511979\pi$
$954$	−2.83469e12	+	1.00715e13i	−0.110799	+	0.393666i
$955$		0			0
$956$			2.98163e13i			1.15450i
$957$	6.58497e13	−	4.98745e13i	2.53776	−	1.92209i
$958$	1.19305e13	−	1.19305e13i	0.457628	−	0.457628i
$959$	−2.71723e13			−1.03739
$960$		0			0
$961$	−2.63071e13			−0.994988
$962$	−6.49175e12	+	6.49175e12i	−0.244385	+	0.244385i
$963$	−5.56763e12	−	9.92934e12i	−0.208618	−	0.372051i
$964$			3.89126e13i			1.45125i
$965$		0			0
$966$	3.96942e12	−	2.87543e13i	0.146666	−	1.06244i
$967$	3.11592e13	+	3.11592e13i	1.14596	+	1.14596i	0.987340	+	0.158615i	$0.0507029\pi$
$967$	3.11592e13	+	3.11592e13i	1.14596	+	1.14596i	0.158615	+	0.987340i	$0.449297\pi$
$968$	−7.68114e13	−	7.68114e13i	−2.81181	−	2.81181i
$969$	−5.24063e12	+	3.79629e13i	−0.190953	+	1.38326i
$970$		0			0
$971$			1.57661e13i			0.569166i	0.958651	+	0.284583i	$0.0918552\pi$
$971$			1.57661e13i			0.569166i	−0.958651	+	0.284583i	$0.908145\pi$
$972$	−5.26928e13	+	5.26050e12i	−1.89345	+	0.189029i
$973$	1.66886e13	−	1.66886e13i	0.596915	−	0.596915i
$974$	3.56113e13			1.26787
$975$		0			0
$976$	2.93185e13			1.03423
$977$	3.01099e13	−	3.01099e13i	1.05727	−	1.05727i	0.0590076	−	0.998258i	$-0.481206\pi$
$977$	3.01099e13	−	3.01099e13i	1.05727	−	1.05727i	0.998258	−	0.0590076i	$-0.0187936\pi$
$978$	−1.77154e13	+	1.34176e13i	−0.619194	+	0.468977i
$979$			7.06907e13i			2.45946i
$980$		0			0
$981$	−1.32736e12	−	3.73593e11i	−0.0457592	−	0.0128792i
$982$	4.29184e13	+	4.29184e13i	1.47279	+	1.47279i
$983$	−3.58883e13	−	3.58883e13i	−1.22592	−	1.22592i	−0.965494	−	0.260424i	$-0.916138\pi$
$983$	−3.58883e13	−	3.58883e13i	−1.22592	−	1.22592i	−0.260424	−	0.965494i	$-0.583862\pi$
$984$	−3.97184e13	−	5.48296e12i	−1.35056	−	0.186439i
$985$		0			0
$986$			8.27715e13i			2.78891i
$987$	1.10083e13	+	1.45344e13i	0.369227	+	0.487493i
$988$	7.66397e12	−	7.66397e12i	0.255887	−	0.255887i
$989$	−1.44727e13			−0.481022
$990$		0			0
$991$	9.77081e11			0.0321810			0.0160905	−	0.999871i	$-0.494878\pi$
$991$	9.77081e11			0.0321810			0.0160905	+	0.999871i	$0.494878\pi$
$992$	−4.80852e11	+	4.80852e11i	−0.0157655	+	0.0157655i
$993$	−1.59817e13	−	2.11007e13i	−0.521615	−	0.688694i
$994$			2.27061e13i			0.737742i
$995$		0			0
$996$	−1.08824e13	−	1.50228e12i	−0.350396	−	0.0483707i
$997$	1.78419e13	+	1.78419e13i	0.571892	+	0.571892i	0.932657	−	0.360765i	$-0.117484\pi$
$997$	1.78419e13	+	1.78419e13i	0.571892	+	0.571892i	−0.360765	+	0.932657i	$0.617484\pi$
$998$	2.47872e13	+	2.47872e13i	0.790933	+	0.790933i
$999$	−4.41406e13	−	1.92656e13i	−1.40215	−	0.611980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.e.g.32.3	✓	48
3.2	odd	2	inner	75.10.e.g.32.21	yes	48
5.2	odd	4	inner	75.10.e.g.68.4	yes	48
5.3	odd	4	inner	75.10.e.g.68.21	yes	48
5.4	even	2	inner	75.10.e.g.32.22	yes	48
15.2	even	4	inner	75.10.e.g.68.22	yes	48
15.8	even	4	inner	75.10.e.g.68.3	yes	48
15.14	odd	2	inner	75.10.e.g.32.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.10.e.g.32.3	✓	48	1.1	even	1	trivial
75.10.e.g.32.4	yes	48	15.14	odd	2	inner
75.10.e.g.32.21	yes	48	3.2	odd	2	inner
75.10.e.g.32.22	yes	48	5.4	even	2	inner
75.10.e.g.68.3	yes	48	15.8	even	4	inner
75.10.e.g.68.4	yes	48	5.2	odd	4	inner
75.10.e.g.68.21	yes	48	5.3	odd	4	inner
75.10.e.g.68.22	yes	48	15.2	even	4	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.2604 + 27.2604i) q^{2} +(84.7063 + 111.838i) q^{3} -974.263i q^{4} +(-5357.90 - 739.636i) q^{6} +(4326.79 + 4326.79i) q^{7} +(12601.5 + 12601.5i) q^{8} +(-5332.69 + 18946.8i) q^{9} +O(q^{10})\)	\(q+(-27.2604 + 27.2604i) q^{2} +(84.7063 + 111.838i) q^{3} -974.263i q^{4} +(-5357.90 - 739.636i) q^{6} +(4326.79 + 4326.79i) q^{7} +(12601.5 + 12601.5i) q^{8} +(-5332.69 + 18946.8i) q^{9} -91942.2i q^{11} +(108960. - 82526.2i) q^{12} +(9654.93 - 9654.93i) q^{13} -235900. q^{14} -188222. q^{16} +(237066. - 237066. i) q^{17} +(-371128. - 661871. i) q^{18} +814758. i q^{19} +(-117395. + 850408. i) q^{21} +(2.50638e6 + 2.50638e6i) q^{22} +(620173. + 620173. i) q^{23} +(-341907. + 2.47676e6i) q^{24} +526395. i q^{26} +(-2.57070e6 + 1.00852e6i) q^{27} +(4.21543e6 - 4.21543e6i) q^{28} +6.40395e6 q^{29} +364021. q^{31} +(-1.32095e6 + 1.32095e6i) q^{32} +(1.02827e7 - 7.78808e6i) q^{33} +1.29251e7i q^{34} +(1.84592e7 + 5.19545e6i) q^{36} +(1.23325e7 + 1.23325e7i) q^{37} +(-2.22107e7 - 2.22107e7i) q^{38} +(1.89763e6 + 261959. i) q^{39} +1.60364e7i q^{41} +(-1.99822e7 - 2.63827e7i) q^{42} +(-1.16682e7 + 1.16682e7i) q^{43} -8.95759e7 q^{44} -3.38124e7 q^{46} +(1.50179e7 - 1.50179e7i) q^{47} +(-1.59436e7 - 2.10505e7i) q^{48} -2.91138e6i q^{49} +(4.65941e7 + 6.43213e6i) q^{51} +(-9.40644e6 - 9.40644e6i) q^{52} +(-9.74980e6 - 9.74980e6i) q^{53} +(4.25858e7 - 9.75710e7i) q^{54} +1.09048e8i q^{56} +(-9.11213e7 + 6.90151e7i) q^{57} +(-1.74574e8 + 1.74574e8i) q^{58} +1.46287e7 q^{59} -1.55765e8 q^{61} +(-9.92336e6 + 9.92336e6i) q^{62} +(-1.05052e8 + 5.89056e7i) q^{63} -1.68389e8i q^{64} +(-6.80037e7 + 4.92617e8i) q^{66} +(7.46762e7 + 7.46762e7i) q^{67} +(-2.30965e8 - 2.30965e8i) q^{68} +(-1.68267e7 + 1.21892e8i) q^{69} -9.62530e7i q^{71} +(-3.05959e8 + 1.71559e8i) q^{72} +(2.25364e8 - 2.25364e8i) q^{73} -6.72377e8 q^{74} +7.93789e8 q^{76} +(3.97815e8 - 3.97815e8i) q^{77} +(-5.88712e7 + 4.45890e7i) q^{78} +3.61084e8i q^{79} +(-3.30545e8 - 2.02075e8i) q^{81} +(-4.37160e8 - 4.37160e8i) q^{82} +(-5.68314e7 - 5.68314e7i) q^{83} +(8.28521e8 + 1.14374e8i) q^{84} -6.36163e8i q^{86} +(5.42455e8 + 7.16208e8i) q^{87} +(1.15861e9 - 1.15861e9i) q^{88} -7.68861e8 q^{89} +8.35497e7 q^{91} +(6.04212e8 - 6.04212e8i) q^{92} +(3.08348e7 + 4.07115e7i) q^{93} +8.18788e8i q^{94} +(-2.59625e8 - 3.58402e7i) q^{96} +(7.95158e8 + 7.95158e8i) q^{97} +(7.93654e7 + 7.93654e7i) q^{98} +(1.74201e9 + 4.90299e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10788 q^{6}+O(q^{10}) \) 48 * q + 10788 * q^6	\( 48 q + 10788 q^{6} - 3683496 q^{16} + 2202288 q^{21} - 50381304 q^{31} + 225716076 q^{36} - 336695184 q^{46} + 673842108 q^{51} + 69620856 q^{61} - 445930020 q^{66} + 4632842472 q^{76} - 4102516332 q^{81} + 11717060616 q^{91} - 14562582156 q^{96}+O(q^{100}) \) 48 * q + 10788 * q^6 - 3683496 * q^16 + 2202288 * q^21 - 50381304 * q^31 + 225716076 * q^36 - 336695184 * q^46 + 673842108 * q^51 + 69620856 * q^61 - 445930020 * q^66 + 4632842472 * q^76 - 4102516332 * q^81 + 11717060616 * q^91 - 14562582156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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