LMFDB - Embedded newform 90.12.c.a.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,12,Mod(19,90)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("90.19"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	90.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-4096,-4950] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$69.1508862504$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{1129})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 565x^{2} + 79524 $ x^4 + 565*x^2 + 79524
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.4
Root			$17.3003i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.12.c.a.19.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+32.0000i q^{2} -1024.00 q^{4} +(4222.60 - 5567.57i) q^{5} +17733.1i q^{7} -32768.0i q^{8} +(178162. + 135123. i) q^{10} +92684.6 q^{11} -1.02948e6i q^{13} -567458. q^{14} +1.04858e6 q^{16} +4.19323e6i q^{17} +8.22974e6 q^{19} +(-4.32394e6 + 5.70119e6i) q^{20} +2.96591e6i q^{22} +2.30941e7i q^{23} +(-1.31675e7 - 4.70192e7i) q^{25} +3.29432e7 q^{26} -1.81587e7i q^{28} +6.33811e7 q^{29} -2.97961e8 q^{31} +3.35544e7i q^{32} -1.34183e8 q^{34} +(9.87300e7 + 7.48796e7i) q^{35} -4.43154e8i q^{37} +2.63352e8i q^{38} +(-1.82438e8 - 1.38366e8i) q^{40} -3.17205e8 q^{41} -1.53142e9i q^{43} -9.49091e7 q^{44} -7.39010e8 q^{46} -1.68921e9i q^{47} +1.66287e9 q^{49} +(1.50461e9 - 4.21359e8i) q^{50} +1.05418e9i q^{52} -9.14498e7i q^{53} +(3.91370e8 - 5.16028e8i) q^{55} +5.81077e8 q^{56} +2.02819e9i q^{58} -6.42961e8 q^{59} +4.06590e9 q^{61} -9.53476e9i q^{62} -1.07374e9 q^{64} +(-5.73167e9 - 4.34706e9i) q^{65} +6.00020e9i q^{67} -4.29387e9i q^{68} +(-2.39615e9 + 3.15936e9i) q^{70} -1.58004e9 q^{71} -2.53729e10i q^{73} +1.41809e10 q^{74} -8.42725e9 q^{76} +1.64358e9i q^{77} +1.79005e10 q^{79} +(4.42771e9 - 5.83802e9i) q^{80} -1.01506e10i q^{82} +2.17112e10i q^{83} +(2.33461e10 + 1.77063e10i) q^{85} +4.90053e10 q^{86} -3.03709e9i q^{88} +9.05198e10 q^{89} +1.82558e10 q^{91} -2.36483e10i q^{92} +5.40547e10 q^{94} +(3.47509e10 - 4.58196e10i) q^{95} -9.98403e10i q^{97} +5.32117e10i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4096 q^{4} - 4950 q^{5} + 228800 q^{10} + 452052 q^{11} - 1775232 q^{14} + 4194304 q^{16} + 36378480 q^{19} + 5068800 q^{20} + 55440000 q^{25} + 56098944 q^{26} - 257619420 q^{29} - 300753272 q^{31}+ \cdots - 63907668000 q^{95}+O(q^{100}) $ 4 * q - 4096 * q^4 - 4950 * q^5 + 228800 * q^10 + 452052 * q^11 - 1775232 * q^14 + 4194304 * q^16 + 36378480 * q^19 + 5068800 * q^20 + 55440000 * q^25 + 56098944 * q^26 - 257619420 * q^29 - 300753272 * q^31 + 253100672 * q^34 + 157589100 * q^35 - 234291200 * q^40 - 875749968 * q^41 - 462901248 * q^44 - 270485504 * q^46 + 7080186228 * q^49 + 4717440000 * q^50 - 1003393600 * q^55 + 1817837568 * q^56 + 15671542860 * q^59 - 361352152 * q^61 - 4294967296 * q^64 - 12072791700 * q^65 - 503718400 * q^70 - 422314488 * q^71 + 3000094848 * q^74 - 37251563520 * q^76 - 1904696280 * q^79 - 5190451200 * q^80 + 79162796900 * q^85 + 49155623424 * q^86 + 67118824440 * q^89 + 33451420248 * q^91 + 201866497792 * q^94 - 63907668000 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$			32.0000i			0.707107i
$2$			32.0000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1024.00			−0.500000
$5$	4222.60	−	5567.57i	0.604289	−	0.796765i
$5$	4222.60	−	5567.57i	0.604289	−	0.796765i
$6$		0			0
$7$			17733.1i			0.398790i	0.979919	+	0.199395i	$0.0638977\pi$
$7$			17733.1i			0.398790i	−0.979919	+	0.199395i	$0.936102\pi$
$8$		−	32768.0i		−	0.353553i
$9$		0			0
$10$	178162.	+	135123.i	0.563398	+	0.427297i
$11$	92684.6			0.173519			0.0867597	−	0.996229i	$-0.472349\pi$
$11$	92684.6			0.173519			0.0867597	+	0.996229i	$0.472349\pi$
$12$		0			0
$13$		−	1.02948e6i		−	0.769002i	−0.923125	−	0.384501i	$-0.874373\pi$
$13$		−	1.02948e6i		−	0.769002i	0.923125	−	0.384501i	$-0.125627\pi$
$14$	−567458.			−0.281987
$15$		0			0
$16$	1.04858e6			0.250000
$17$			4.19323e6i			0.716275i	0.933669	+	0.358138i	$0.116588\pi$
$17$			4.19323e6i			0.716275i	−0.933669	+	0.358138i	$0.883412\pi$
$18$		0			0
$19$	8.22974e6			0.762503			0.381251	−	0.924471i	$-0.375493\pi$
$19$	8.22974e6			0.762503			0.381251	+	0.924471i	$0.375493\pi$
$20$	−4.32394e6	+	5.70119e6i	−0.302144	+	0.398383i
$21$		0			0
$22$			2.96591e6i			0.122697i
$23$			2.30941e7i			0.748164i	0.927396	+	0.374082i	$0.122042\pi$
$23$			2.30941e7i			0.748164i	−0.927396	+	0.374082i	$0.877958\pi$
$24$		0			0
$25$	−1.31675e7	−	4.70192e7i	−0.269670	−	0.962953i
$26$	3.29432e7			0.543767
$27$		0			0
$28$		−	1.81587e7i		−	0.199395i
$29$	6.33811e7			0.573813			0.286907	−	0.957959i	$-0.407373\pi$
$29$	6.33811e7			0.573813			0.286907	+	0.957959i	$0.407373\pi$
$30$		0			0
$31$	−2.97961e8			−1.86926			−0.934632	−	0.355617i	$-0.884271\pi$
$31$	−2.97961e8			−1.86926			−0.934632	+	0.355617i	$0.884271\pi$
$32$			3.35544e7i			0.176777i
$33$		0			0
$34$	−1.34183e8			−0.506483
$35$	9.87300e7	+	7.48796e7i	0.317742	+	0.240985i
$36$		0			0
$37$		−	4.43154e8i		−	1.05062i	−0.850911	−	0.525309i	$-0.823950\pi$
$37$		−	4.43154e8i		−	1.05062i	0.850911	−	0.525309i	$-0.176050\pi$
$38$			2.63352e8i			0.539171i
$39$		0			0
$40$	−1.82438e8	−	1.38366e8i	−0.281699	−	0.213648i
$41$	−3.17205e8			−0.427591			−0.213795	−	0.976878i	$-0.568583\pi$
$41$	−3.17205e8			−0.427591			−0.213795	+	0.976878i	$0.568583\pi$
$42$		0			0
$43$		−	1.53142e9i		−	1.58861i	−0.607521	−	0.794304i	$-0.707836\pi$
$43$		−	1.53142e9i		−	1.58861i	0.607521	−	0.794304i	$-0.292164\pi$
$44$	−9.49091e7			−0.0867597
$45$		0			0
$46$	−7.39010e8			−0.529032
$47$		−	1.68921e9i		−	1.07435i	−0.843471	−	0.537175i	$-0.819492\pi$
$47$		−	1.68921e9i		−	1.07435i	0.843471	−	0.537175i	$-0.180508\pi$
$48$		0			0
$49$	1.66287e9			0.840966
$50$	1.50461e9	−	4.21359e8i	0.680910	−	0.190685i
$51$		0			0
$52$			1.05418e9i			0.384501i
$53$		−	9.14498e7i		−	0.0300376i	−0.999887	−	0.0150188i	$-0.995219\pi$
$53$		−	9.14498e7i		−	0.0300376i	0.999887	−	0.0150188i	$-0.00478081\pi$
$54$		0			0
$55$	3.91370e8	−	5.16028e8i	0.104856	−	0.138254i
$56$	5.81077e8			0.140994
$57$		0			0
$58$			2.02819e9i			0.405747i
$59$	−6.42961e8			−0.117084			−0.0585421	−	0.998285i	$-0.518645\pi$
$59$	−6.42961e8			−0.117084			−0.0585421	+	0.998285i	$0.518645\pi$
$60$		0			0
$61$	4.06590e9			0.616371			0.308186	−	0.951326i	$-0.400278\pi$
$61$	4.06590e9			0.616371			0.308186	+	0.951326i	$0.400278\pi$
$62$		−	9.53476e9i		−	1.32177i
$63$		0			0
$64$	−1.07374e9			−0.125000
$65$	−5.73167e9	−	4.34706e9i	−0.612714	−	0.464699i
$66$		0			0
$67$			6.00020e9i			0.542943i	0.962446	+	0.271471i	$0.0875103\pi$
$67$			6.00020e9i			0.542943i	−0.962446	+	0.271471i	$0.912490\pi$
$68$		−	4.29387e9i		−	0.358138i
$69$		0			0
$70$	−2.39615e9	+	3.15936e9i	−0.170402	+	0.224678i
$71$	−1.58004e9			−0.103931			−0.0519657	−	0.998649i	$-0.516549\pi$
$71$	−1.58004e9			−0.103931			−0.0519657	+	0.998649i	$0.516549\pi$
$72$		0			0
$73$		−	2.53729e10i		−	1.43250i	−0.697844	−	0.716250i	$-0.745857\pi$
$73$		−	2.53729e10i		−	1.43250i	0.697844	−	0.716250i	$-0.254143\pi$
$74$	1.41809e10			0.742899
$75$		0			0
$76$	−8.42725e9			−0.381251
$77$			1.64358e9i			0.0691979i
$78$		0			0
$79$	1.79005e10			0.654508			0.327254	−	0.944936i	$-0.393877\pi$
$79$	1.79005e10			0.654508			0.327254	+	0.944936i	$0.393877\pi$
$80$	4.42771e9	−	5.83802e9i	0.151072	−	0.199191i
$81$		0			0
$82$		−	1.01506e10i		−	0.302352i
$83$			2.17112e10i			0.604997i	0.953150	+	0.302499i	$0.0978208\pi$
$83$			2.17112e10i			0.604997i	−0.953150	+	0.302499i	$0.902179\pi$
$84$		0			0
$85$	2.33461e10	+	1.77063e10i	0.570703	+	0.432837i
$86$	4.90053e10			1.12332
$87$		0			0
$88$		−	3.03709e9i		−	0.0613484i
$89$	9.05198e10			1.71830			0.859149	−	0.511726i	$-0.170994\pi$
$89$	9.05198e10			1.71830			0.859149	+	0.511726i	$0.170994\pi$
$90$		0			0
$91$	1.82558e10			0.306671
$92$		−	2.36483e10i		−	0.374082i
$93$		0			0
$94$	5.40547e10			0.759680
$95$	3.47509e10	−	4.58196e10i	0.460772	−	0.607536i
$96$		0			0
$97$		−	9.98403e10i		−	1.18049i	−0.807225	−	0.590244i	$-0.799032\pi$
$97$		−	9.98403e10i		−	1.18049i	0.807225	−	0.590244i	$-0.200968\pi$
$98$			5.32117e10i			0.594653i
$99$		0			0
$100$	1.34835e10	+	4.81476e10i	0.134835	+	0.481476i
$101$	1.98701e11			1.88119			0.940595	−	0.339531i	$-0.110268\pi$
$101$	1.98701e11			1.88119			0.940595	+	0.339531i	$0.110268\pi$
$102$		0			0
$103$		−	1.41496e10i		−	0.120265i	−0.998190	−	0.0601327i	$-0.980848\pi$
$103$		−	1.41496e10i		−	0.120265i	0.998190	−	0.0601327i	$-0.0191524\pi$
$104$	−3.37339e10			−0.271883
$105$		0			0
$106$	2.92639e9			0.0212398
$107$		−	1.45833e11i		−	1.00518i	−0.864524	−	0.502592i	$-0.832380\pi$
$107$		−	1.45833e11i		−	1.00518i	0.864524	−	0.502592i	$-0.167620\pi$
$108$		0			0
$109$	2.34206e10			0.145798			0.0728992	−	0.997339i	$-0.476775\pi$
$109$	2.34206e10			0.145798			0.0728992	+	0.997339i	$0.476775\pi$
$110$	1.65129e10	+	1.25238e10i	0.0977605	+	0.0741443i
$111$		0			0
$112$			1.85945e10i			0.0996976i
$113$		−	2.82794e11i		−	1.44391i	−0.691942	−	0.721953i	$-0.743244\pi$
$113$		−	2.82794e11i		−	1.44391i	0.691942	−	0.721953i	$-0.256756\pi$
$114$		0			0
$115$	1.28578e11	+	9.75169e10i	0.596111	+	0.452107i
$116$	−6.49022e10			−0.286907
$117$		0			0
$118$		−	2.05747e10i		−	0.0827911i
$119$	−7.43589e10			−0.285644
$120$		0			0
$121$	−2.76721e11			−0.969891
$122$			1.30109e11i			0.435840i
$123$		0			0
$124$	3.05112e11			0.934632
$125$	−3.17383e11	−	1.25232e11i	−0.930206	−	0.367038i
$126$		0			0
$127$		−	2.22914e11i		−	0.598709i	−0.954142	−	0.299355i	$-0.903229\pi$
$127$		−	2.22914e11i		−	0.598709i	0.954142	−	0.299355i	$-0.0967714\pi$
$128$		−	3.43597e10i		−	0.0883883i
$129$		0			0
$130$	1.39106e11	−	1.83414e11i	0.328592	−	0.433254i
$131$	5.28629e11			1.19718			0.598589	−	0.801056i	$-0.295728\pi$
$131$	5.28629e11			1.19718			0.598589	+	0.801056i	$0.295728\pi$
$132$		0			0
$133$			1.45939e11i			0.304079i
$134$	−1.92006e11			−0.383919
$135$		0			0
$136$	1.37404e11			0.253241
$137$		−	6.18656e11i		−	1.09518i	−0.836746	−	0.547591i	$-0.815545\pi$
$137$		−	6.18656e11i		−	1.09518i	0.836746	−	0.547591i	$-0.184455\pi$
$138$		0			0
$139$	−3.12179e11			−0.510297			−0.255148	−	0.966902i	$-0.582124\pi$
$139$	−3.12179e11			−0.510297			−0.255148	+	0.966902i	$0.582124\pi$
$140$	−1.01100e11	−	7.66767e10i	−0.158871	−	0.120492i
$141$		0			0
$142$		−	5.05612e10i		−	0.0734906i
$143$		−	9.54166e10i		−	0.133437i
$144$		0			0
$145$	2.67633e11	−	3.52878e11i	0.346749	−	0.457194i
$146$	8.11933e11			1.01293
$147$		0			0
$148$			4.53790e11i			0.525309i
$149$	6.31691e11			0.704661			0.352330	−	0.935876i	$-0.385389\pi$
$149$	6.31691e11			0.704661			0.352330	+	0.935876i	$0.385389\pi$
$150$		0			0
$151$	−1.53380e12			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$151$	−1.53380e12			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$152$		−	2.69672e11i		−	0.269585i
$153$		0			0
$154$	−5.25947e10			−0.0489303
$155$	−1.25817e12	+	1.65892e12i	−1.12958	+	1.48936i
$156$		0			0
$157$		−	1.16558e12i		−	0.975199i	−0.873067	−	0.487599i	$-0.837873\pi$
$157$		−	1.16558e12i		−	0.975199i	0.873067	−	0.487599i	$-0.162127\pi$
$158$			5.72815e11i			0.462807i
$159$		0			0
$160$	1.86817e11	+	1.41687e11i	0.140850	+	0.106824i
$161$	−4.09528e11			−0.298361
$162$		0			0
$163$		−	8.50999e11i		−	0.579292i	−0.957134	−	0.289646i	$-0.906462\pi$
$163$		−	8.50999e11i		−	0.579292i	0.957134	−	0.289646i	$-0.0935375\pi$
$164$	3.24818e11			0.213795
$165$		0			0
$166$	−6.94757e11			−0.427798
$167$			2.62566e12i			1.56422i	0.623139	+	0.782111i	$0.285857\pi$
$167$			2.62566e12i			1.56422i	−0.623139	+	0.782111i	$0.714143\pi$
$168$		0			0
$169$	7.32341e11			0.408636
$170$	−5.66603e11	+	7.47075e11i	−0.306062	+	0.403548i
$171$		0			0
$172$			1.56817e12i			0.794304i
$173$		−	3.19469e11i		−	0.156738i	−0.996924	−	0.0783692i	$-0.975029\pi$
$173$		−	3.19469e11i		−	0.156738i	0.996924	−	0.0783692i	$-0.0249713\pi$
$174$		0			0
$175$	8.33794e11	−	2.33500e11i	0.384016	−	0.107542i
$176$	9.71869e10			0.0433798
$177$		0			0
$178$			2.89663e12i			1.21502i
$179$	−4.74402e12			−1.92955			−0.964773	−	0.263083i	$-0.915261\pi$
$179$	−4.74402e12			−1.92955			−0.964773	+	0.263083i	$0.915261\pi$
$180$		0			0
$181$	−4.43161e12			−1.69563			−0.847813	−	0.530296i	$-0.822081\pi$
$181$	−4.43161e12			−1.69563			−0.847813	+	0.530296i	$0.822081\pi$
$182$			5.84184e11i			0.216849i
$183$		0			0
$184$	7.56746e11			0.264516
$185$	−2.46729e12	−	1.87126e12i	−0.837096	−	0.634877i
$186$		0			0
$187$			3.88648e11i			0.124288i
$188$			1.72975e12i			0.537175i
$189$		0			0
$190$	1.46623e12	+	1.11203e12i	0.429593	+	0.325815i
$191$	−8.61562e11			−0.245247			−0.122623	−	0.992453i	$-0.539131\pi$
$191$	−8.61562e11			−0.245247			−0.122623	+	0.992453i	$0.539131\pi$
$192$		0			0
$193$			2.65521e12i			0.713729i	0.934156	+	0.356864i	$0.116154\pi$
$193$			2.65521e12i			0.713729i	−0.934156	+	0.356864i	$0.883846\pi$
$194$	3.19489e12			0.834731
$195$		0			0
$196$	−1.70277e12			−0.420483
$197$		−	6.13480e11i		−	0.147311i	−0.997284	−	0.0736556i	$-0.976533\pi$
$197$		−	6.13480e11i		−	0.147311i	0.997284	−	0.0736556i	$-0.0234666\pi$
$198$		0			0
$199$	6.69462e12			1.52067			0.760333	−	0.649533i	$-0.225036\pi$
$199$	6.69462e12			1.52067			0.760333	+	0.649533i	$0.225036\pi$
$200$	−1.54072e12	+	4.31472e11i	−0.340455	+	0.0953427i
$201$		0			0
$202$			6.35843e12i			1.33020i
$203$			1.12394e12i			0.228831i
$204$		0			0
$205$	−1.33943e12	+	1.76606e12i	−0.258388	+	0.340690i
$206$	4.52788e11			0.0850405
$207$		0			0
$208$		−	1.07948e12i		−	0.192251i
$209$	7.62771e11			0.132309
$210$		0			0
$211$	−2.93358e12			−0.482886			−0.241443	−	0.970415i	$-0.577621\pi$
$211$	−2.93358e12			−0.482886			−0.241443	+	0.970415i	$0.577621\pi$
$212$			9.36446e10i			0.0150188i
$213$		0			0
$214$	4.66666e12			0.710772
$215$	−8.52626e12	−	6.46655e12i	−1.26575	−	0.959978i
$216$		0			0
$217$		−	5.28377e12i		−	0.745444i
$218$			7.49460e11i			0.103095i
$219$		0			0
$220$	−4.00763e11	+	5.28413e11i	−0.0524279	+	0.0691271i
$221$	4.31683e12			0.550817
$222$		0			0
$223$		−	1.03502e13i		−	1.25682i	−0.777884	−	0.628408i	$-0.783707\pi$
$223$		−	1.03502e13i		−	1.25682i	0.777884	−	0.628408i	$-0.216293\pi$
$224$	−5.95023e11			−0.0704968
$225$		0			0
$226$	9.04942e12			1.02100
$227$			7.14950e12i			0.787288i	0.919263	+	0.393644i	$0.128786\pi$
$227$			7.14950e12i			0.787288i	−0.919263	+	0.393644i	$0.871214\pi$
$228$		0			0
$229$	−1.34181e13			−1.40798			−0.703990	−	0.710210i	$-0.748600\pi$
$229$	−1.34181e13			−1.40798			−0.703990	+	0.710210i	$0.748600\pi$
$230$	−3.12054e12	+	4.11449e12i	−0.319688	+	0.421514i
$231$		0			0
$232$		−	2.07687e12i		−	0.202874i
$233$			2.18579e12i			0.208522i	0.994550	+	0.104261i	$0.0332477\pi$
$233$			2.18579e12i			0.208522i	−0.994550	+	0.104261i	$0.966752\pi$
$234$		0			0
$235$	−9.40479e12	−	7.13286e12i	−0.856005	−	0.649218i
$236$	6.58392e11			0.0585421
$237$		0			0
$238$		−	2.37948e12i		−	0.201981i
$239$	1.55254e13			1.28781			0.643907	−	0.765104i	$-0.277312\pi$
$239$	1.55254e13			1.28781			0.643907	+	0.765104i	$0.277312\pi$
$240$		0			0
$241$	−1.45886e13			−1.15590			−0.577951	−	0.816071i	$-0.696148\pi$
$241$	−1.45886e13			−1.15590			−0.577951	+	0.816071i	$0.696148\pi$
$242$		−	8.85508e12i		−	0.685817i
$243$		0			0
$244$	−4.16348e12			−0.308186
$245$	7.02161e12	−	9.25811e12i	0.508187	−	0.670053i
$246$		0			0
$247$		−	8.47232e12i		−	0.586366i
$248$			9.76359e12i			0.660884i
$249$		0			0
$250$	4.00743e12	−	1.01563e13i	0.259535	−	0.657755i
$251$	−7.86073e12			−0.498032			−0.249016	−	0.968499i	$-0.580107\pi$
$251$	−7.86073e12			−0.498032			−0.249016	+	0.968499i	$0.580107\pi$
$252$		0			0
$253$			2.14046e12i			0.129821i
$254$	7.13323e12			0.423351
$255$		0			0
$256$	1.09951e12			0.0625000
$257$		−	1.74113e13i		−	0.968719i	−0.874869	−	0.484360i	$-0.839053\pi$
$257$		−	1.74113e13i		−	0.968719i	0.874869	−	0.484360i	$-0.160947\pi$
$258$		0			0
$259$	7.85848e12			0.418977
$260$	5.86923e12	+	4.45139e12i	0.306357	+	0.232350i
$261$		0			0
$262$			1.69161e13i			0.846533i
$263$		−	1.44399e13i		−	0.707633i	−0.935315	−	0.353817i	$-0.884884\pi$
$263$		−	1.44399e13i		−	0.707633i	0.935315	−	0.353817i	$-0.115116\pi$
$264$		0			0
$265$	−5.09153e11	−	3.86155e11i	−0.0239329	−	0.0181514i
$266$	−4.67003e12			−0.215016
$267$		0			0
$268$		−	6.14420e12i		−	0.271471i
$269$	3.70372e13			1.60325			0.801623	−	0.597830i	$-0.203970\pi$
$269$	3.70372e13			1.60325			0.801623	+	0.597830i	$0.203970\pi$
$270$		0			0
$271$	4.68050e13			1.94519			0.972594	−	0.232510i	$-0.0746940\pi$
$271$	4.68050e13			1.94519			0.972594	+	0.232510i	$0.0746940\pi$
$272$			4.39692e12i			0.179069i
$273$		0			0
$274$	1.97970e13			0.774410
$275$	−1.22042e12	−	4.35796e12i	−0.0467930	−	0.167091i
$276$		0			0
$277$			2.71382e12i			0.0999867i	0.998750	+	0.0499934i	$0.0159200\pi$
$277$			2.71382e12i			0.0999867i	−0.998750	+	0.0499934i	$0.984080\pi$
$278$		−	9.98974e12i		−	0.360834i
$279$		0			0
$280$	2.45365e12	−	3.23519e12i	0.0852009	−	0.112339i
$281$	−1.90126e12			−0.0647376			−0.0323688	−	0.999476i	$-0.510305\pi$
$281$	−1.90126e12			−0.0647376			−0.0323688	+	0.999476i	$0.510305\pi$
$282$		0			0
$283$			2.31481e13i			0.758036i	0.925389	+	0.379018i	$0.123738\pi$
$283$			2.31481e13i			0.758036i	−0.925389	+	0.379018i	$0.876262\pi$
$284$	1.61796e12			0.0519657
$285$		0			0
$286$	3.05333e12			0.0943541
$287$		−	5.62501e12i		−	0.170519i
$288$		0			0
$289$	1.66887e13			0.486950
$290$	1.12921e13	+	8.56425e12i	0.323285	+	0.245189i
$291$		0			0
$292$			2.59819e13i			0.716250i
$293$		−	2.15915e13i		−	0.584131i	−0.956398	−	0.292066i	$-0.905657\pi$
$293$		−	2.15915e13i		−	0.584131i	0.956398	−	0.292066i	$-0.0943426\pi$
$294$		0			0
$295$	−2.71496e12	+	3.57973e12i	−0.0707527	+	0.0932887i
$296$	−1.45213e13			−0.371450
$297$		0			0
$298$			2.02141e13i			0.498270i
$299$	2.37748e13			0.575340
$300$		0			0
$301$	2.71567e13			0.633522
$302$		−	4.90817e13i		−	1.12430i
$303$		0			0
$304$	8.62951e12			0.190626
$305$	1.71686e13	−	2.26372e13i	0.372466	−	0.491103i
$306$		0			0
$307$		−	9.13551e13i		−	1.91193i	−0.293482	−	0.955965i	$-0.594814\pi$
$307$		−	9.13551e13i		−	1.91193i	0.293482	−	0.955965i	$-0.405186\pi$
$308$		−	1.68303e12i		−	0.0345989i
$309$		0			0
$310$	−5.30854e13	−	4.02614e13i	−1.05314	−	0.798730i
$311$	−9.13888e13			−1.78119			−0.890596	−	0.454795i	$-0.849713\pi$
$311$	−9.13888e13			−1.78119			−0.890596	+	0.454795i	$0.849713\pi$
$312$		0			0
$313$			1.00924e14i			1.89889i	0.313927	+	0.949447i	$0.398355\pi$
$313$			1.00924e14i			1.89889i	−0.313927	+	0.949447i	$0.601645\pi$
$314$	3.72985e13			0.689570
$315$		0			0
$316$	−1.83301e13			−0.327254
$317$			8.27651e13i			1.45218i	0.687598	+	0.726092i	$0.258665\pi$
$317$			8.27651e13i			1.45218i	−0.687598	+	0.726092i	$0.741335\pi$
$318$		0			0
$319$	5.87445e12			0.0995677
$320$	−4.53398e12	+	5.97813e12i	−0.0755361	+	0.0995957i
$321$		0			0
$322$		−	1.31049e13i		−	0.210973i
$323$			3.45092e13i			0.546162i
$324$		0			0
$325$	−4.84051e13	+	1.35556e13i	−0.740513	+	0.207377i
$326$	2.72320e13			0.409621
$327$		0			0
$328$			1.03942e13i			0.151176i
$329$	2.99549e13			0.428440
$330$		0			0
$331$	6.66951e13			0.922656			0.461328	−	0.887230i	$-0.347373\pi$
$331$	6.66951e13			0.922656			0.461328	+	0.887230i	$0.347373\pi$
$332$		−	2.22322e13i		−	0.302499i
$333$		0			0
$334$	−8.40212e13			−1.10607
$335$	3.34065e13	+	2.53364e13i	0.432598	+	0.328094i
$336$		0			0
$337$		−	8.05140e13i		−	1.00904i	−0.863401	−	0.504518i	$-0.831670\pi$
$337$		−	8.05140e13i		−	1.00904i	0.863401	−	0.504518i	$-0.168330\pi$
$338$			2.34349e13i			0.288949i
$339$		0			0
$340$	−2.39064e13	−	1.81313e13i	−0.285352	−	0.216419i
$341$	−2.76164e13			−0.324353
$342$		0			0
$343$			6.45518e13i			0.734160i
$344$	−5.01814e13			−0.561658
$345$		0			0
$346$	1.02230e13			0.110831
$347$			1.32024e14i			1.40877i	0.709817	+	0.704386i	$0.248778\pi$
$347$			1.32024e14i			1.40877i	−0.709817	+	0.704386i	$0.751222\pi$
$348$		0			0
$349$	−3.92975e13			−0.406280			−0.203140	−	0.979150i	$-0.565115\pi$
$349$	−3.92975e13			−0.406280			−0.203140	+	0.979150i	$0.565115\pi$
$350$	7.47199e12	+	2.66814e13i	0.0760435	+	0.271541i
$351$		0			0
$352$			3.10998e12i			0.0306742i
$353$			1.33047e14i			1.29195i	0.763360	+	0.645973i	$0.223548\pi$
$353$			1.33047e14i			1.29195i	−0.763360	+	0.645973i	$0.776452\pi$
$354$		0			0
$355$	−6.67186e12	+	8.79697e12i	−0.0628045	+	0.0828089i
$356$	−9.26922e13			−0.859149
$357$		0			0
$358$		−	1.51809e14i		−	1.36440i
$359$	−6.12598e13			−0.542196			−0.271098	−	0.962552i	$-0.587387\pi$
$359$	−6.12598e13			−0.542196			−0.271098	+	0.962552i	$0.587387\pi$
$360$		0			0
$361$	−4.87616e13			−0.418590
$362$		−	1.41812e14i		−	1.19899i
$363$		0			0
$364$	−1.86939e13			−0.153335
$365$	−1.41265e14	−	1.07140e14i	−1.14137	−	0.865643i
$366$		0			0
$367$			3.85669e13i			0.302379i	0.988505	+	0.151189i	$0.0483103\pi$
$367$			3.85669e13i			0.302379i	−0.988505	+	0.151189i	$0.951690\pi$
$368$			2.42159e13i			0.187041i
$369$		0			0
$370$	5.98803e13	−	7.89532e13i	0.448926	−	0.591917i
$371$	1.62168e12			0.0119787
$372$		0			0
$373$			1.48417e14i			1.06435i	0.846635	+	0.532174i	$0.178625\pi$
$373$			1.48417e14i			1.06435i	−0.846635	+	0.532174i	$0.821375\pi$
$374$	−1.24367e13			−0.0878846
$375$		0			0
$376$	−5.53521e13			−0.379840
$377$		−	6.52493e13i		−	0.441264i
$378$		0			0
$379$	−2.32826e13			−0.152938			−0.0764691	−	0.997072i	$-0.524365\pi$
$379$	−2.32826e13			−0.152938			−0.0764691	+	0.997072i	$0.524365\pi$
$380$	−3.55849e13	+	4.69193e13i	−0.230386	+	0.303768i
$381$		0			0
$382$		−	2.75700e13i		−	0.173416i
$383$		−	1.04288e12i		−	0.00646605i	−0.999995	−	0.00323303i	$-0.998971\pi$
$383$		−	1.04288e12i		−	0.00646605i	0.999995	−	0.00323303i	$-0.00102911\pi$
$384$		0			0
$385$	9.15076e12	+	6.94019e12i	0.0551345	+	0.0418155i
$386$	−8.49666e13			−0.504682
$387$		0			0
$388$			1.02236e14i			0.590244i
$389$	−1.43212e14			−0.815187			−0.407593	−	0.913163i	$-0.633632\pi$
$389$	−1.43212e14			−0.815187			−0.407593	+	0.913163i	$0.633632\pi$
$390$		0			0
$391$	−9.68387e13			−0.535892
$392$		−	5.44888e13i		−	0.297326i
$393$		0			0
$394$	1.96313e13			0.104165
$395$	7.55864e13	−	9.96620e13i	0.395512	−	0.521490i
$396$		0			0
$397$			5.28208e13i			0.268817i	0.990926	+	0.134409i	$0.0429135\pi$
$397$			5.28208e13i			0.268817i	−0.990926	+	0.134409i	$0.957087\pi$
$398$			2.14228e14i			1.07527i
$399$		0			0
$400$	−1.38071e13	−	4.93032e13i	−0.0674175	−	0.240738i
$401$	2.10904e14			1.01576			0.507880	−	0.861428i	$-0.330429\pi$
$401$	2.10904e14			1.01576			0.507880	+	0.861428i	$0.330429\pi$
$402$		0			0
$403$			3.06744e14i			1.43747i
$404$	−2.03470e14			−0.940595
$405$		0			0
$406$	−3.59661e13			−0.161808
$407$		−	4.10736e13i		−	0.182303i
$408$		0			0
$409$	9.65539e13			0.417149			0.208575	−	0.978006i	$-0.433118\pi$
$409$	9.65539e13			0.417149			0.208575	+	0.978006i	$0.433118\pi$
$410$	−5.65139e13	−	4.28617e13i	−0.240904	−	0.182708i
$411$		0			0
$412$			1.44892e13i			0.0601327i
$413$		−	1.14017e13i		−	0.0466921i
$414$		0			0
$415$	1.20878e14	+	9.16774e13i	0.482041	+	0.365593i
$416$	3.45435e13			0.135942
$417$		0			0
$418$			2.44087e13i			0.0935566i
$419$	−1.21273e13			−0.0458761			−0.0229381	−	0.999737i	$-0.507302\pi$
$419$	−1.21273e13			−0.0458761			−0.0229381	+	0.999737i	$0.507302\pi$
$420$		0			0
$421$	1.96716e13			0.0724916			0.0362458	−	0.999343i	$-0.488460\pi$
$421$	1.96716e13			0.0724916			0.0362458	+	0.999343i	$0.488460\pi$
$422$		−	9.38746e13i		−	0.341452i
$423$		0			0
$424$	−2.99663e12			−0.0106199
$425$	1.97162e14	−	5.52143e13i	0.689739	−	0.193158i
$426$		0			0
$427$			7.21008e13i			0.245803i
$428$			1.49333e14i			0.502592i
$429$		0			0
$430$	2.06930e14	−	2.72840e14i	0.678807	−	0.895019i
$431$	2.13646e14			0.691941			0.345971	−	0.938245i	$-0.387550\pi$
$431$	2.13646e14			0.691941			0.345971	+	0.938245i	$0.387550\pi$
$432$		0			0
$433$		−	1.18328e13i		−	0.0373598i	−0.999826	−	0.0186799i	$-0.994054\pi$
$433$		−	1.18328e13i		−	0.0373598i	0.999826	−	0.0186799i	$-0.00594634\pi$
$434$	1.69081e14			0.527109
$435$		0			0
$436$	−2.39827e13			−0.0728992
$437$			1.90058e14i			0.570477i
$438$		0			0
$439$	1.12906e14			0.330494			0.165247	−	0.986252i	$-0.447158\pi$
$439$	1.12906e14			0.330494			0.165247	+	0.986252i	$0.447158\pi$
$440$	−1.69092e13	−	1.28244e13i	−0.0488803	−	0.0370721i
$441$		0			0
$442$			1.38139e14i			0.389487i
$443$			5.15214e14i			1.43472i	0.696703	+	0.717360i	$0.254649\pi$
$443$			5.15214e14i			1.43472i	−0.696703	+	0.717360i	$0.745351\pi$
$444$		0			0
$445$	3.82228e14	−	5.03975e14i	1.03835	−	1.36908i
$446$	3.31206e14			0.888703
$447$		0			0
$448$		−	1.90407e13i		−	0.0498488i
$449$	−5.91800e14			−1.53045			−0.765227	−	0.643761i	$-0.777373\pi$
$449$	−5.91800e14			−1.53045			−0.765227	+	0.643761i	$0.777373\pi$
$450$		0			0
$451$	−2.94000e13			−0.0741953
$452$			2.89581e14i			0.721953i
$453$		0			0
$454$	−2.28784e14			−0.556697
$455$	7.70867e13	−	1.01640e14i	0.185318	−	0.244345i
$456$		0			0
$457$		−	6.79879e14i		−	1.59549i	−0.602998	−	0.797743i	$-0.706027\pi$
$457$		−	6.79879e14i		−	1.59549i	0.602998	−	0.797743i	$-0.293973\pi$
$458$		−	4.29380e14i		−	0.995592i
$459$		0			0
$460$	−1.31664e14	−	9.98573e13i	−0.298056	−	0.226054i
$461$	8.70498e14			1.94721			0.973604	−	0.228243i	$-0.0732979\pi$
$461$	8.70498e14			1.94721			0.973604	+	0.228243i	$0.0732979\pi$
$462$		0			0
$463$			6.66296e14i			1.45537i	0.685914	+	0.727683i	$0.259403\pi$
$463$			6.66296e14i			1.45537i	−0.685914	+	0.727683i	$0.740597\pi$
$464$	6.64599e13			0.143453
$465$		0			0
$466$	−6.99453e13			−0.147447
$467$		−	2.78736e14i		−	0.580697i	−0.956921	−	0.290349i	$-0.906229\pi$
$467$		−	2.78736e14i		−	0.580697i	0.956921	−	0.290349i	$-0.0937713\pi$
$468$		0			0
$469$	−1.06402e14			−0.216520
$470$	2.28251e14	−	3.00953e14i	0.459066	−	0.605287i
$471$		0			0
$472$			2.10685e13i			0.0413955i
$473$		−	1.41939e14i		−	0.275654i
$474$		0			0
$475$	−1.08365e14	−	3.86956e14i	−0.205624	−	0.734254i
$476$	7.61435e13			0.142822
$477$		0			0
$478$			4.96811e14i			0.910622i
$479$	3.12280e14			0.565847			0.282923	−	0.959143i	$-0.408696\pi$
$479$	3.12280e14			0.565847			0.282923	+	0.959143i	$0.408696\pi$
$480$		0			0
$481$	−4.56216e14			−0.807928
$482$		−	4.66837e14i		−	0.817347i
$483$		0			0
$484$	2.83363e14			0.484946
$485$	−5.55868e14	−	4.21585e14i	−0.940572	−	0.713356i
$486$		0			0
$487$		−	5.72468e14i		−	0.946982i	−0.880799	−	0.473491i	$-0.842994\pi$
$487$		−	5.72468e14i		−	0.946982i	0.880799	−	0.473491i	$-0.157006\pi$
$488$		−	1.33231e14i		−	0.217920i
$489$		0			0
$490$	2.96260e14	+	2.24691e14i	0.473799	+	0.359342i
$491$	4.72897e14			0.747856			0.373928	−	0.927458i	$-0.378011\pi$
$491$	4.72897e14			0.747856			0.373928	+	0.927458i	$0.378011\pi$
$492$		0			0
$493$			2.65772e14i			0.411008i
$494$	2.71114e14			0.414624
$495$		0			0
$496$	−3.12435e14			−0.467316
$497$		−	2.80189e13i		−	0.0414468i
$498$		0			0
$499$	−2.15127e14			−0.311274			−0.155637	−	0.987814i	$-0.549743\pi$
$499$	−2.15127e14			−0.311274			−0.155637	+	0.987814i	$0.549743\pi$
$500$	3.25001e14	+	1.28238e14i	0.465103	+	0.183519i
$501$		0			0
$502$		−	2.51544e14i		−	0.352162i
$503$		−	5.75007e14i		−	0.796250i	−0.917331	−	0.398125i	$-0.869661\pi$
$503$		−	5.75007e14i		−	0.796250i	0.917331	−	0.398125i	$-0.130339\pi$
$504$		0			0
$505$	8.39034e14	−	1.10628e15i	1.13678	−	1.49887i
$506$	−6.84948e13			−0.0917973
$507$		0			0
$508$			2.28264e14i			0.299355i
$509$	−5.10104e14			−0.661776			−0.330888	−	0.943670i	$-0.607348\pi$
$509$	−5.10104e14			−0.661776			−0.330888	+	0.943670i	$0.607348\pi$
$510$		0			0
$511$	4.49939e14			0.571267
$512$			3.51844e13i			0.0441942i
$513$		0			0
$514$	5.57160e14			0.684988
$515$	−7.87791e13	−	5.97482e13i	−0.0958233	−	0.0726750i
$516$		0			0
$517$		−	1.56564e14i		−	0.186420i
$518$			2.51471e14i			0.296261i
$519$		0			0
$520$	−1.42444e14	+	1.87815e14i	−0.164296	+	0.216627i
$521$	−1.40565e15			−1.60424			−0.802122	−	0.597160i	$-0.796296\pi$
$521$	−1.40565e15			−1.60424			−0.802122	+	0.597160i	$0.796296\pi$
$522$		0			0
$523$			1.00053e15i			1.11807i	0.829144	+	0.559035i	$0.188828\pi$
$523$			1.00053e15i			1.11807i	−0.829144	+	0.559035i	$0.811172\pi$
$524$	−5.41316e14			−0.598589
$525$		0			0
$526$	4.62077e14			0.500372
$527$		−	1.24942e15i		−	1.33891i
$528$		0			0
$529$	4.19475e14			0.440250
$530$	1.23570e13	−	1.62929e13i	0.0128350	−	0.0169231i
$531$		0			0
$532$		−	1.49441e14i		−	0.152039i
$533$			3.26555e14i			0.328818i
$534$		0			0
$535$	−8.11935e14	−	6.15794e14i	−0.800895	−	0.607421i
$536$	1.96614e14			0.191959
$537$		0			0
$538$			1.18519e15i			1.13367i
$539$	1.54122e14			0.145924
$540$		0			0
$541$	−2.10941e14			−0.195693			−0.0978466	−	0.995202i	$-0.531195\pi$
$541$	−2.10941e14			−0.195693			−0.0978466	+	0.995202i	$0.531195\pi$
$542$			1.49776e15i			1.37546i
$543$		0			0
$544$	−1.40702e14			−0.126621
$545$	9.88958e13	−	1.30396e14i	0.0881043	−	0.116167i
$546$		0			0
$547$			2.52114e14i			0.220123i	0.993925	+	0.110062i	$0.0351048\pi$
$547$			2.52114e14i			0.220123i	−0.993925	+	0.110062i	$0.964895\pi$
$548$			6.33504e14i			0.547591i
$549$		0			0
$550$	1.39455e14	−	3.90535e13i	0.118151	−	0.0330876i
$551$	5.21610e14			0.437534
$552$		0			0
$553$			3.17430e14i			0.261012i
$554$	−8.68423e13			−0.0707013
$555$		0			0
$556$	3.19672e14			0.255148
$557$		−	5.86436e14i		−	0.463465i	−0.972780	−	0.231733i	$-0.925561\pi$
$557$		−	5.86436e14i		−	0.463465i	0.972780	−	0.231733i	$-0.0744395\pi$
$558$		0			0
$559$	−1.57656e15			−1.22164
$560$	1.03526e14	+	7.85169e13i	0.0794356	+	0.0602461i
$561$		0			0
$562$		−	6.08403e13i		−	0.0457764i
$563$			2.38879e15i			1.77984i	0.456117	+	0.889920i	$0.349240\pi$
$563$			2.38879e15i			1.77984i	−0.456117	+	0.889920i	$0.650760\pi$
$564$		0			0
$565$	−1.57448e15	−	1.19413e15i	−1.15045	−	0.872537i
$566$	−7.40739e14			−0.536012
$567$		0			0
$568$			5.17747e13i			0.0367453i
$569$	2.07492e14			0.145843			0.0729213	−	0.997338i	$-0.476768\pi$
$569$	2.07492e14			0.145843			0.0729213	+	0.997338i	$0.476768\pi$
$570$		0			0
$571$	−4.55927e14			−0.314338			−0.157169	−	0.987572i	$-0.550237\pi$
$571$	−4.55927e14			−0.314338			−0.157169	+	0.987572i	$0.550237\pi$
$572$			9.77066e13i			0.0667184i
$573$		0			0
$574$	1.80000e14			0.120575
$575$	1.08586e15	−	3.04090e14i	0.720447	−	0.201757i
$576$		0			0
$577$		−	1.28823e14i		−	0.0838542i	−0.999121	−	0.0419271i	$-0.986650\pi$
$577$		−	1.28823e14i		−	0.0838542i	0.999121	−	0.0419271i	$-0.0133497\pi$
$578$			5.34038e14i			0.344326i
$579$		0			0
$580$	−2.74056e14	+	3.61347e14i	−0.173374	+	0.228597i
$581$	−3.85005e14			−0.241267
$582$		0			0
$583$		−	8.47599e12i		−	0.00521211i
$584$	−8.31419e14			−0.506465
$585$		0			0
$586$	6.90927e14			0.413043
$587$		−	3.49044e14i		−	0.206714i	−0.994644	−	0.103357i	$-0.967042\pi$
$587$		−	3.49044e14i		−	0.206714i	0.994644	−	0.103357i	$-0.0329584\pi$
$588$		0			0
$589$	−2.45214e15			−1.42532
$590$	−1.14551e14	−	8.68789e13i	−0.0659650	−	0.0500297i
$591$		0			0
$592$		−	4.64681e14i		−	0.262655i
$593$			1.98920e15i			1.11398i	0.830518	+	0.556991i	$0.188044\pi$
$593$			1.98920e15i			1.11398i	−0.830518	+	0.556991i	$0.811956\pi$
$594$		0			0
$595$	−3.13988e14	+	4.13998e14i	−0.172611	+	0.227591i
$596$	−6.46851e14			−0.352330
$597$		0			0
$598$			7.60792e14i			0.406827i
$599$	−1.03318e15			−0.547432			−0.273716	−	0.961811i	$-0.588253\pi$
$599$	−1.03318e15			−0.547432			−0.273716	+	0.961811i	$0.588253\pi$
$600$		0			0
$601$	1.38171e15			0.718797			0.359398	−	0.933184i	$-0.382982\pi$
$601$	1.38171e15			0.718797			0.359398	+	0.933184i	$0.382982\pi$
$602$			8.69015e14i			0.447967i
$603$		0			0
$604$	1.57061e15			0.794998
$605$	−1.16848e15	+	1.54066e15i	−0.586094	+	0.772776i
$606$		0			0
$607$			1.68888e15i			0.831882i	0.909392	+	0.415941i	$0.136548\pi$
$607$			1.68888e15i			0.831882i	−0.909392	+	0.415941i	$0.863452\pi$
$608$			2.76144e14i			0.134793i
$609$		0			0
$610$	7.24389e14	+	5.49397e14i	0.347262	+	0.263373i
$611$	−1.73900e15			−0.826177
$612$		0			0
$613$			5.46218e14i			0.254878i	0.991846	+	0.127439i	$0.0406758\pi$
$613$			5.46218e14i			0.254878i	−0.991846	+	0.127439i	$0.959324\pi$
$614$	2.92336e15			1.35194
$615$		0			0
$616$	5.38569e13			0.0244651
$617$		−	4.52349e14i		−	0.203660i	−0.994802	−	0.101830i	$-0.967530\pi$
$617$		−	4.52349e14i		−	0.203660i	0.994802	−	0.101830i	$-0.0324698\pi$
$618$		0			0
$619$	2.14770e15			0.949892			0.474946	−	0.880015i	$-0.342468\pi$
$619$	2.14770e15			0.949892			0.474946	+	0.880015i	$0.342468\pi$
$620$	1.28837e15	−	1.69873e15i	0.564788	−	0.744682i
$621$		0			0
$622$		−	2.92444e15i		−	1.25949i
$623$			1.60519e15i			0.685241i
$624$		0			0
$625$	−2.03742e15	+	1.23825e15i	−0.854556	+	0.519359i
$626$	−3.22957e15			−1.34272
$627$		0			0
$628$			1.19355e15i			0.487599i
$629$	1.85825e15			0.752532
$630$		0			0
$631$	4.15753e15			1.65453			0.827263	−	0.561815i	$-0.189897\pi$
$631$	4.15753e15			1.65453			0.827263	+	0.561815i	$0.189897\pi$
$632$		−	5.86562e14i		−	0.231404i
$633$		0			0
$634$	−2.64848e15			−1.02685
$635$	−1.24109e15	−	9.41274e14i	−0.477031	−	0.361793i
$636$		0			0
$637$		−	1.71188e15i		−	0.646705i
$638$			1.87982e14i			0.0704050i
$639$		0			0
$640$	−1.91300e14	−	1.45087e14i	−0.0704248	−	0.0534121i
$641$	−3.37785e15			−1.23288			−0.616440	−	0.787402i	$-0.711426\pi$
$641$	−3.37785e15			−1.23288			−0.616440	+	0.787402i	$0.711426\pi$
$642$		0			0
$643$			4.67438e15i			1.67712i	0.544810	+	0.838560i	$0.316602\pi$
$643$			4.67438e15i			1.67712i	−0.544810	+	0.838560i	$0.683398\pi$
$644$	4.19357e14			0.149180
$645$		0			0
$646$	−1.10429e15			−0.386195
$647$		−	1.48014e15i		−	0.513252i	−0.966511	−	0.256626i	$-0.917389\pi$
$647$		−	1.48014e15i		−	0.513252i	0.966511	−	0.256626i	$-0.0826109\pi$
$648$		0			0
$649$	−5.95926e13			−0.0203164
$650$	−4.33779e14	−	1.54896e15i	−0.146638	−	0.523622i
$651$		0			0
$652$			8.71423e14i			0.289646i
$653$		−	2.76712e15i		−	0.912023i	−0.889974	−	0.456012i	$-0.849278\pi$
$653$		−	2.76712e15i		−	0.912023i	0.889974	−	0.456012i	$-0.150722\pi$
$654$		0			0
$655$	2.23219e15	−	2.94318e15i	0.723441	−	0.953870i
$656$	−3.32613e14			−0.106898
$657$		0			0
$658$			9.58557e14i			0.302953i
$659$	−1.23830e14			−0.0388110			−0.0194055	−	0.999812i	$-0.506177\pi$
$659$	−1.23830e14			−0.0388110			−0.0194055	+	0.999812i	$0.506177\pi$
$660$		0			0
$661$	−3.27129e15			−1.00835			−0.504175	−	0.863602i	$-0.668203\pi$
$661$	−3.27129e15			−1.00835			−0.504175	+	0.863602i	$0.668203\pi$
$662$			2.13424e15i			0.652416i
$663$		0			0
$664$	7.11431e14			0.213899
$665$	8.12523e14	+	6.16240e14i	0.242279	+	0.183751i
$666$		0			0
$667$			1.46373e15i			0.429307i
$668$		−	2.68868e15i		−	0.782111i
$669$		0			0
$670$	−8.10765e14	+	1.06901e15i	−0.231998	+	0.305893i
$671$	3.76846e14			0.106952
$672$		0			0
$673$		−	3.59624e15i		−	1.00407i	−0.864846	−	0.502037i	$-0.832584\pi$
$673$		−	3.59624e15i		−	1.00407i	0.864846	−	0.502037i	$-0.167416\pi$
$674$	2.57645e15			0.713497
$675$		0			0
$676$	−7.49917e14			−0.204318
$677$		−	2.53490e15i		−	0.685051i	−0.939509	−	0.342525i	$-0.888718\pi$
$677$		−	2.53490e15i		−	0.685051i	0.939509	−	0.342525i	$-0.111282\pi$
$678$		0			0
$679$	1.77048e15			0.470767
$680$	5.80201e14	−	7.65005e14i	0.153031	−	0.201774i
$681$		0			0
$682$		−	8.83726e14i		−	0.229353i
$683$			2.47450e15i			0.637051i	0.947914	+	0.318525i	$0.103188\pi$
$683$			2.47450e15i			0.637051i	−0.947914	+	0.318525i	$0.896812\pi$
$684$		0			0
$685$	−3.44441e15	−	2.61234e15i	−0.872603	−	0.661806i
$686$	−2.06566e15			−0.519129
$687$		0			0
$688$		−	1.60581e15i		−	0.397152i
$689$	−9.41453e13			−0.0230990
$690$		0			0
$691$	3.64400e15			0.879932			0.439966	−	0.898015i	$-0.354991\pi$
$691$	3.64400e15			0.879932			0.439966	+	0.898015i	$0.354991\pi$
$692$			3.27136e14i			0.0783692i
$693$		0			0
$694$	−4.22477e15			−0.996152
$695$	−1.31821e15	+	1.73808e15i	−0.308367	+	0.406587i
$696$		0			0
$697$		−	1.33011e15i		−	0.306273i
$698$		−	1.25752e15i		−	0.287283i
$699$		0			0
$700$	−8.53805e14	+	2.39104e14i	−0.192008	+	0.0537709i
$701$	6.80102e15			1.51749			0.758744	−	0.651389i	$-0.225813\pi$
$701$	6.80102e15			1.51749			0.758744	+	0.651389i	$0.225813\pi$
$702$		0			0
$703$		−	3.64704e15i		−	0.801099i
$704$	−9.95194e13			−0.0216899
$705$		0			0
$706$	−4.25751e15			−0.913544
$707$			3.52358e15i			0.750200i
$708$		0			0
$709$	3.93607e15			0.825104			0.412552	−	0.910934i	$-0.364638\pi$
$709$	3.93607e15			0.825104			0.412552	+	0.910934i	$0.364638\pi$
$710$	−2.81503e14	−	2.13500e14i	−0.0585547	−	0.0444095i
$711$		0			0
$712$		−	2.96615e15i		−	0.607510i
$713$		−	6.88113e15i		−	1.39852i
$714$		0			0
$715$	−5.31238e14	−	4.02906e14i	−0.106318	−	0.0806344i
$716$	4.85788e15			0.964773
$717$		0			0
$718$		−	1.96031e15i		−	0.383390i
$719$	7.85788e15			1.52509			0.762546	−	0.646933i	$-0.223949\pi$
$719$	7.85788e15			1.52509			0.762546	+	0.646933i	$0.223949\pi$
$720$		0			0
$721$	2.50917e14			0.0479607
$722$		−	1.56037e15i		−	0.295988i
$723$		0			0
$724$	4.53797e15			0.847813
$725$	−8.34569e14	−	2.98013e15i	−0.154740	−	0.552555i
$726$		0			0
$727$			4.90765e14i			0.0896261i	0.998995	+	0.0448130i	$0.0142692\pi$
$727$			4.90765e14i			0.0896261i	−0.998995	+	0.0448130i	$0.985731\pi$
$728$		−	5.98205e14i		−	0.108424i
$729$		0			0
$730$	3.42847e15	−	4.52049e15i	0.612102	−	0.807068i
$731$	6.42158e15			1.13788
$732$		0			0
$733$			6.34430e15i			1.10742i	0.832710	+	0.553710i	$0.186788\pi$
$733$			6.34430e15i			1.10742i	−0.832710	+	0.553710i	$0.813212\pi$
$734$	−1.23414e15			−0.213814
$735$		0			0
$736$	−7.74908e14			−0.132258
$737$			5.56126e14i			0.0942111i
$738$		0			0
$739$	9.30410e15			1.55285			0.776426	−	0.630208i	$-0.217030\pi$
$739$	9.30410e15			1.55285			0.776426	+	0.630208i	$0.217030\pi$
$740$	2.52650e15	+	1.91617e15i	0.418548	+	0.317439i
$741$		0			0
$742$			5.18939e13i			0.00847023i
$743$			4.15515e15i			0.673206i	0.941647	+	0.336603i	$0.109278\pi$
$743$			4.15515e15i			0.673206i	−0.941647	+	0.336603i	$0.890722\pi$
$744$		0			0
$745$	2.66738e15	−	3.51698e15i	0.425819	−	0.561449i
$746$	−4.74933e15			−0.752608
$747$		0			0
$748$		−	3.97976e14i		−	0.0621438i
$749$	2.58607e15			0.400857
$750$		0			0
$751$	3.04610e14			0.0465291			0.0232646	−	0.999729i	$-0.492594\pi$
$751$	3.04610e14			0.0465291			0.0232646	+	0.999729i	$0.492594\pi$
$752$		−	1.77127e15i		−	0.268587i
$753$		0			0
$754$	2.08798e15			0.312020
$755$	−6.47663e15	+	8.53954e15i	−0.960817	+	1.26685i
$756$		0			0
$757$			7.96714e15i			1.16486i	0.812880	+	0.582432i	$0.197899\pi$
$757$			7.96714e15i			1.16486i	−0.812880	+	0.582432i	$0.802101\pi$
$758$		−	7.45044e14i		−	0.108144i
$759$		0			0
$760$	−1.50142e15	−	1.13872e15i	−0.214796	−	0.162907i
$761$	1.18903e16			1.68880			0.844401	−	0.535711i	$-0.179956\pi$
$761$	1.18903e16			1.68880			0.844401	+	0.535711i	$0.179956\pi$
$762$		0			0
$763$			4.15319e14i			0.0581430i
$764$	8.82239e14			0.122623
$765$		0			0
$766$	3.33720e13			0.00457219
$767$			6.61912e14i			0.0900380i
$768$		0			0
$769$	−1.11777e16			−1.49885			−0.749424	−	0.662091i	$-0.769669\pi$
$769$	−1.11777e16			−1.49885			−0.749424	+	0.662091i	$0.769669\pi$
$770$	−2.22086e14	+	2.92824e14i	−0.0295680	+	0.0389859i
$771$		0			0
$772$		−	2.71893e15i		−	0.356864i
$773$		−	6.96394e15i		−	0.907545i	−0.891118	−	0.453772i	$-0.850078\pi$
$773$		−	6.96394e15i		−	0.907545i	0.891118	−	0.453772i	$-0.149922\pi$
$774$		0			0
$775$	3.92340e15	+	1.40099e16i	0.504084	+	1.80001i
$776$	−3.27157e15			−0.417365
$777$		0			0
$778$		−	4.58279e15i		−	0.576424i
$779$	−2.61051e15			−0.326039
$780$		0			0
$781$	−1.46445e14			−0.0180341
$782$		−	3.09884e15i		−	0.378933i
$783$		0			0
$784$	1.74364e15			0.210242
$785$	−6.48943e15	−	4.92177e15i	−0.777005	−	0.589302i
$786$		0			0
$787$			1.62122e16i			1.91418i	0.289795	+	0.957089i	$0.406413\pi$
$787$			1.62122e16i			1.91418i	−0.289795	+	0.957089i	$0.593587\pi$
$788$			6.28203e14i			0.0736556i
$789$		0			0
$790$	3.18918e15	+	2.41877e15i	0.368749	+	0.279669i
$791$	5.01481e15			0.575816
$792$		0			0
$793$		−	4.18574e15i		−	0.473991i
$794$	−1.69027e15			−0.190083
$795$		0			0
$796$	−6.85529e15			−0.760333
$797$		−	5.20007e15i		−	0.572781i	−0.958113	−	0.286391i	$-0.907545\pi$
$797$		−	5.20007e15i		−	0.572781i	0.958113	−	0.286391i	$-0.0924555\pi$
$798$		0			0
$799$	7.08325e15			0.769530
$800$	1.57770e15	−	4.41827e14i	0.170228	−	0.0476714i
$801$		0			0
$802$			6.74894e15i			0.718251i
$803$		−	2.35168e15i		−	0.248566i
$804$		0			0
$805$	−1.72927e15	+	2.28008e15i	−0.180296	+	0.237724i
$806$	−9.81580e15			−1.01644
$807$		0			0
$808$		−	6.51104e15i		−	0.665101i
$809$	−1.16758e16			−1.18459			−0.592296	−	0.805720i	$-0.701778\pi$
$809$	−1.16758e16			−1.18459			−0.592296	+	0.805720i	$0.701778\pi$
$810$		0			0
$811$	−6.13788e15			−0.614333			−0.307167	−	0.951656i	$-0.599381\pi$
$811$	−6.13788e15			−0.614333			−0.307167	+	0.951656i	$0.599381\pi$
$812$		−	1.15092e15i		−	0.114416i
$813$		0			0
$814$	1.31435e15			0.128907
$815$	−4.73799e15	−	3.59343e15i	−0.461559	−	0.350059i
$816$		0			0
$817$		−	1.26032e16i		−	1.21132i
$818$			3.08972e15i			0.294969i
$819$		0			0
$820$	1.37157e15	−	1.80844e15i	0.129194	−	0.170345i
$821$	−1.81708e15			−0.170015			−0.0850075	−	0.996380i	$-0.527091\pi$
$821$	−1.81708e15			−0.170015			−0.0850075	+	0.996380i	$0.527091\pi$
$822$		0			0
$823$		−	2.50540e15i		−	0.231302i	−0.993290	−	0.115651i	$-0.963105\pi$
$823$		−	2.50540e15i		−	0.231302i	0.993290	−	0.115651i	$-0.0368954\pi$
$824$	−4.63655e14			−0.0425202
$825$		0			0
$826$	3.64853e14			0.0330163
$827$			1.93870e16i			1.74273i	0.490631	+	0.871367i	$0.336766\pi$
$827$			1.93870e16i			1.74273i	−0.490631	+	0.871367i	$0.663234\pi$
$828$		0			0
$829$	−8.91873e15			−0.791139			−0.395570	−	0.918436i	$-0.629453\pi$
$829$	−8.91873e15			−0.791139			−0.395570	+	0.918436i	$0.629453\pi$
$830$	−2.93368e15	+	3.86811e15i	−0.258513	+	0.340854i
$831$		0			0
$832$			1.10539e15i			0.0961253i
$833$			6.97278e15i			0.602363i
$834$		0			0
$835$	1.46186e16	+	1.10871e16i	1.24632	+	0.945242i
$836$	−7.81077e14			−0.0661545
$837$		0			0
$838$		−	3.88073e14i		−	0.0324393i
$839$	−1.40832e16			−1.16953			−0.584764	−	0.811204i	$-0.698813\pi$
$839$	−1.40832e16			−1.16953			−0.584764	+	0.811204i	$0.698813\pi$
$840$		0			0
$841$	−8.18335e15			−0.670738
$842$			6.29491e14i			0.0512593i
$843$		0			0
$844$	3.00399e15			0.241443
$845$	3.09238e15	−	4.07736e15i	0.246934	−	0.325587i
$846$		0			0
$847$		−	4.90712e15i		−	0.386783i
$848$		−	9.58920e13i		−	0.00750940i
$849$		0			0
$850$	1.76686e15	+	6.30920e15i	0.136583	+	0.487719i
$851$	1.02342e16			0.786035
$852$		0			0
$853$		−	2.18003e16i		−	1.65288i	−0.563023	−	0.826441i	$-0.690362\pi$
$853$		−	2.18003e16i		−	1.65288i	0.563023	−	0.826441i	$-0.309638\pi$
$854$	−2.30723e15			−0.173809
$855$		0			0
$856$	−4.77866e15			−0.355386
$857$			9.84653e15i			0.727593i	0.931478	+	0.363797i	$0.118520\pi$
$857$			9.84653e15i			0.727593i	−0.931478	+	0.363797i	$0.881480\pi$
$858$		0			0
$859$	−1.89097e16			−1.37950			−0.689751	−	0.724046i	$-0.742280\pi$
$859$	−1.89097e16			−1.37950			−0.689751	+	0.724046i	$0.742280\pi$
$860$	8.73089e15	+	6.62175e15i	0.632874	+	0.479989i
$861$		0			0
$862$			6.83666e15i			0.489276i
$863$			2.09992e15i			0.149329i	0.997209	+	0.0746643i	$0.0237885\pi$
$863$			2.09992e15i			0.149329i	−0.997209	+	0.0746643i	$0.976211\pi$
$864$		0			0
$865$	−1.77867e15	−	1.34899e15i	−0.124884	−	0.0947153i
$866$	3.78650e14			0.0264174
$867$		0			0
$868$			5.41058e15i			0.372722i
$869$	1.65910e15			0.113570
$870$		0			0
$871$	6.17706e15			0.417524
$872$		−	7.67447e14i		−	0.0515475i
$873$		0			0
$874$	−6.08186e15			−0.403388
$875$	2.22075e15	−	5.62818e15i	0.146371	−	0.370957i
$876$		0			0
$877$		−	1.35726e16i		−	0.883413i	−0.897160	−	0.441706i	$-0.854373\pi$
$877$		−	1.35726e16i		−	0.883413i	0.897160	−	0.441706i	$-0.145627\pi$
$878$			3.61300e15i			0.233694i
$879$		0			0
$880$	4.10381e14	−	5.41095e14i	0.0262140	−	0.0345636i
$881$	−8.32387e15			−0.528394			−0.264197	−	0.964469i	$-0.585107\pi$
$881$	−8.32387e15			−0.528394			−0.264197	+	0.964469i	$0.585107\pi$
$882$		0			0
$883$		−	1.83191e16i		−	1.14847i	−0.818689	−	0.574237i	$-0.805299\pi$
$883$		−	1.83191e16i		−	1.14847i	0.818689	−	0.574237i	$-0.194701\pi$
$884$	−4.42043e15			−0.275409
$885$		0			0
$886$	−1.64868e16			−1.01450
$887$		−	3.28697e15i		−	0.201009i	−0.994937	−	0.100504i	$-0.967954\pi$
$887$		−	3.28697e15i		−	0.201009i	0.994937	−	0.100504i	$-0.0320457\pi$
$888$		0			0
$889$	3.95294e15			0.238760
$890$	1.61272e16	+	1.22313e16i	0.968086	+	0.734223i
$891$		0			0
$892$			1.05986e16i			0.628408i
$893$		−	1.39018e16i		−	0.819194i
$894$		0			0
$895$	−2.00321e16	+	2.64127e16i	−1.16600	+	1.53740i
$896$	6.09304e14			0.0352484
$897$		0			0
$898$		−	1.89376e16i		−	1.08219i
$899$	−1.88851e16			−1.07261
$900$		0			0
$901$	3.83470e14			0.0215152
$902$		−	9.40800e14i		−	0.0524640i
$903$		0			0
$904$	−9.26660e15			−0.510498
$905$	−1.87129e16	+	2.46733e16i	−1.02465	+	1.35102i
$906$		0			0
$907$		−	7.53749e15i		−	0.407743i	−0.978998	−	0.203872i	$-0.934648\pi$
$907$		−	7.53749e15i		−	0.407743i	0.978998	−	0.203872i	$-0.0653525\pi$
$908$		−	7.32109e15i		−	0.393644i
$909$		0			0
$910$	3.25249e15	+	2.46677e15i	0.172778	+	0.131039i
$911$	1.55366e16			0.820360			0.410180	−	0.912005i	$-0.365466\pi$
$911$	1.55366e16			0.820360			0.410180	+	0.912005i	$0.365466\pi$
$912$		0			0
$913$			2.01229e15i			0.104979i
$914$	2.17561e16			1.12818
$915$		0			0
$916$	1.37402e16			0.703990
$917$			9.37421e15i			0.477423i
$918$		0			0
$919$	6.33154e15			0.318621			0.159310	−	0.987229i	$-0.449073\pi$
$919$	6.33154e15			0.318621			0.159310	+	0.987229i	$0.449073\pi$
$920$	3.19543e15	−	4.21323e15i	0.159844	−	0.210757i
$921$		0			0
$922$			2.78559e16i			1.37688i
$923$			1.62661e15i			0.0799234i
$924$		0			0
$925$	−2.08367e16	+	5.83522e15i	−1.01170	+	0.283320i
$926$	−2.13215e16			−1.02910
$927$		0			0
$928$			2.12672e15i			0.101437i
$929$	−4.05211e16			−1.92130			−0.960650	−	0.277762i	$-0.910407\pi$
$929$	−4.05211e16			−1.92130			−0.960650	+	0.277762i	$0.910407\pi$
$930$		0			0
$931$	1.36849e16			0.641239
$932$		−	2.23825e15i		−	0.104261i
$933$		0			0
$934$	8.91955e15			0.410615
$935$	2.16383e15	+	1.64110e15i	0.0990281	+	0.0751056i
$936$		0			0
$937$		−	2.81645e16i		−	1.27390i	−0.770907	−	0.636948i	$-0.780197\pi$
$937$		−	2.81645e16i		−	1.27390i	0.770907	−	0.636948i	$-0.219803\pi$
$938$		−	3.40486e15i		−	0.153103i
$939$		0			0
$940$	9.63051e15	+	7.30404e15i	0.428002	+	0.324609i
$941$	−1.99421e16			−0.881107			−0.440553	−	0.897726i	$-0.645218\pi$
$941$	−1.99421e16			−0.881107			−0.440553	+	0.897726i	$0.645218\pi$
$942$		0			0
$943$		−	7.32554e15i		−	0.319908i
$944$	−6.74193e14			−0.0292711
$945$		0			0
$946$	4.54204e15			0.194917
$947$		−	1.16923e16i		−	0.498858i	−0.968393	−	0.249429i	$-0.919757\pi$
$947$		−	1.16923e16i		−	0.498858i	0.968393	−	0.249429i	$-0.0802429\pi$
$948$		0			0
$949$	−2.61208e16			−1.10160
$950$	1.23826e16	−	3.46768e15i	0.519196	−	0.145398i
$951$		0			0
$952$			2.43659e15i			0.100990i
$953$		−	1.31930e16i		−	0.543666i	−0.962344	−	0.271833i	$-0.912370\pi$
$953$		−	1.31930e16i		−	0.543666i	0.962344	−	0.271833i	$-0.0876299\pi$
$954$		0			0
$955$	−3.63803e15	+	4.79680e15i	−0.148200	+	0.195404i
$956$	−1.58980e16			−0.643907
$957$		0			0
$958$			9.99296e15i			0.400114i
$959$	1.09707e16			0.436748
$960$		0			0
$961$	6.33724e16			2.49415
$962$		−	1.45989e16i		−	0.571291i
$963$		0			0
$964$	1.49388e16			0.577951
$965$	1.47830e16	+	1.12119e16i	0.568674	+	0.431298i
$966$		0			0
$967$			4.22542e16i			1.60703i	0.595284	+	0.803516i	$0.297040\pi$
$967$			4.22542e16i			1.60703i	−0.595284	+	0.803516i	$0.702960\pi$
$968$			9.06760e15i			0.342908i
$969$		0			0
$970$	1.34907e16	−	1.77878e16i	0.504419	−	0.665085i
$971$	3.97016e16			1.47606			0.738028	−	0.674771i	$-0.235757\pi$
$971$	3.97016e16			1.47606			0.738028	+	0.674771i	$0.235757\pi$
$972$		0			0
$973$		−	5.53590e15i		−	0.203501i
$974$	1.83190e16			0.669617
$975$		0			0
$976$	4.26340e15			0.154093
$977$			7.32402e15i			0.263226i	0.991301	+	0.131613i	$0.0420157\pi$
$977$			7.32402e15i			0.263226i	−0.991301	+	0.131613i	$0.957984\pi$
$978$		0			0
$979$	8.38979e15			0.298158
$980$	−7.19013e15	+	9.48031e15i	−0.254093	+	0.335026i
$981$		0			0
$982$			1.51327e16i			0.528814i
$983$		−	4.23299e16i		−	1.47097i	−0.677543	−	0.735483i	$-0.736955\pi$
$983$		−	4.23299e16i		−	1.47097i	0.677543	−	0.735483i	$-0.263045\pi$
$984$		0			0
$985$	−3.41559e15	−	2.59048e15i	−0.117372	−	0.0890185i
$986$	−8.50469e15			−0.290627
$987$		0			0
$988$			8.67565e15i			0.293183i
$989$	3.53666e16			1.18854
$990$		0			0
$991$	1.94163e16			0.645299			0.322649	−	0.946519i	$-0.395427\pi$
$991$	1.94163e16			0.645299			0.322649	+	0.946519i	$0.395427\pi$
$992$		−	9.99792e15i		−	0.330442i
$993$		0			0
$994$	8.96605e14			0.0293073
$995$	2.82687e16	−	3.72727e16i	0.918922	−	1.21161i
$996$		0			0
$997$			1.08203e16i			0.347869i	0.984757	+	0.173934i	$0.0556481\pi$
$997$			1.08203e16i			0.347869i	−0.984757	+	0.173934i	$0.944352\pi$
$998$		−	6.88408e15i		−	0.220104i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.12.c.a.19.4		4
3.2	odd	2		30.12.c.a.19.1	✓	4
5.4	even	2	inner	90.12.c.a.19.2		4
12.11	even	2		240.12.f.a.49.1		4
15.2	even	4		150.12.a.r.1.1		2
15.8	even	4		150.12.a.k.1.2		2
15.14	odd	2		30.12.c.a.19.3	yes	4
60.59	even	2		240.12.f.a.49.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.12.c.a.19.1	✓	4	3.2	odd	2
30.12.c.a.19.3	yes	4	15.14	odd	2
90.12.c.a.19.2		4	5.4	even	2	inner
90.12.c.a.19.4		4	1.1	even	1	trivial
150.12.a.k.1.2		2	15.8	even	4
150.12.a.r.1.1		2	15.2	even	4
240.12.f.a.49.1		4	12.11	even	2
240.12.f.a.49.3		4	60.59	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+32.0000i q^{2} -1024.00 q^{4} +(4222.60 - 5567.57i) q^{5} +17733.1i q^{7} -32768.0i q^{8} +(178162. + 135123. i) q^{10} +92684.6 q^{11} -1.02948e6i q^{13} -567458. q^{14} +1.04858e6 q^{16} +4.19323e6i q^{17} +8.22974e6 q^{19} +(-4.32394e6 + 5.70119e6i) q^{20} +2.96591e6i q^{22} +2.30941e7i q^{23} +(-1.31675e7 - 4.70192e7i) q^{25} +3.29432e7 q^{26} -1.81587e7i q^{28} +6.33811e7 q^{29} -2.97961e8 q^{31} +3.35544e7i q^{32} -1.34183e8 q^{34} +(9.87300e7 + 7.48796e7i) q^{35} -4.43154e8i q^{37} +2.63352e8i q^{38} +(-1.82438e8 - 1.38366e8i) q^{40} -3.17205e8 q^{41} -1.53142e9i q^{43} -9.49091e7 q^{44} -7.39010e8 q^{46} -1.68921e9i q^{47} +1.66287e9 q^{49} +(1.50461e9 - 4.21359e8i) q^{50} +1.05418e9i q^{52} -9.14498e7i q^{53} +(3.91370e8 - 5.16028e8i) q^{55} +5.81077e8 q^{56} +2.02819e9i q^{58} -6.42961e8 q^{59} +4.06590e9 q^{61} -9.53476e9i q^{62} -1.07374e9 q^{64} +(-5.73167e9 - 4.34706e9i) q^{65} +6.00020e9i q^{67} -4.29387e9i q^{68} +(-2.39615e9 + 3.15936e9i) q^{70} -1.58004e9 q^{71} -2.53729e10i q^{73} +1.41809e10 q^{74} -8.42725e9 q^{76} +1.64358e9i q^{77} +1.79005e10 q^{79} +(4.42771e9 - 5.83802e9i) q^{80} -1.01506e10i q^{82} +2.17112e10i q^{83} +(2.33461e10 + 1.77063e10i) q^{85} +4.90053e10 q^{86} -3.03709e9i q^{88} +9.05198e10 q^{89} +1.82558e10 q^{91} -2.36483e10i q^{92} +5.40547e10 q^{94} +(3.47509e10 - 4.58196e10i) q^{95} -9.98403e10i q^{97} +5.32117e10i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4096 q^{4} - 4950 q^{5} + 228800 q^{10} + 452052 q^{11} - 1775232 q^{14} + 4194304 q^{16} + 36378480 q^{19} + 5068800 q^{20} + 55440000 q^{25} + 56098944 q^{26} - 257619420 q^{29} - 300753272 q^{31}+ \cdots - 63907668000 q^{95}+O(q^{100}) \) 4 * q - 4096 * q^4 - 4950 * q^5 + 228800 * q^10 + 452052 * q^11 - 1775232 * q^14 + 4194304 * q^16 + 36378480 * q^19 + 5068800 * q^20 + 55440000 * q^25 + 56098944 * q^26 - 257619420 * q^29 - 300753272 * q^31 + 253100672 * q^34 + 157589100 * q^35 - 234291200 * q^40 - 875749968 * q^41 - 462901248 * q^44 - 270485504 * q^46 + 7080186228 * q^49 + 4717440000 * q^50 - 1003393600 * q^55 + 1817837568 * q^56 + 15671542860 * q^59 - 361352152 * q^61 - 4294967296 * q^64 - 12072791700 * q^65 - 503718400 * q^70 - 422314488 * q^71 + 3000094848 * q^74 - 37251563520 * q^76 - 1904696280 * q^79 - 5190451200 * q^80 + 79162796900 * q^85 + 49155623424 * q^86 + 67118824440 * q^89 + 33451420248 * q^91 + 201866497792 * q^94 - 63907668000 * q^95

Introduction

L-functions

Modular forms

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