LMFDB - Embedded newform 90.9.g.b.73.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [90,9,Mod(37,90)] 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("90.37"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(90, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,32,0,0,-90] 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:	$36.6640749055$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{249})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 125x^{2} + 3844 $ x^4 + 125*x^2 + 3844
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.2
Root			$7.38987i$ of defining polynomial
Character	$\chi$	$=$	90.73
Dual form			90.9.g.b.37.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.00000 - 8.00000i) q^{2} -128.000i q^{4} +(490.341 - 387.544i) q^{5} +(-2624.01 + 2624.01i) q^{7} +(-1024.00 - 1024.00i) q^{8} +(822.379 - 7023.08i) q^{10} -5372.73 q^{11} +(27972.7 + 27972.7i) q^{13} +41984.2i q^{14} -16384.0 q^{16} +(-53444.2 + 53444.2i) q^{17} +144788. i q^{19} +(-49605.6 - 62763.7i) q^{20} +(-42981.8 + 42981.8i) q^{22} +(-52148.7 - 52148.7i) q^{23} +(90244.3 - 380058. i) q^{25} +447564. q^{26} +(335873. + 335873. i) q^{28} -41723.4i q^{29} +244148. q^{31} +(-131072. + 131072. i) q^{32} +855108. i q^{34} +(-269741. + 2.30358e6i) q^{35} +(-2.00653e6 + 2.00653e6i) q^{37} +(1.15830e6 + 1.15830e6i) q^{38} +(-898955. - 105264. i) q^{40} +4.17322e6 q^{41} +(4.01446e6 + 4.01446e6i) q^{43} +687709. i q^{44} -834380. q^{46} +(-2.26940e6 + 2.26940e6i) q^{47} -8.00606e6i q^{49} +(-2.31851e6 - 3.76242e6i) q^{50} +(3.58051e6 - 3.58051e6i) q^{52} +(3.72734e6 + 3.72734e6i) q^{53} +(-2.63447e6 + 2.08217e6i) q^{55} +5.37397e6 q^{56} +(-333787. - 333787. i) q^{58} +1.12165e7i q^{59} +2.02002e7 q^{61} +(1.95319e6 - 1.95319e6i) q^{62} +2.09715e6i q^{64} +(2.45569e7 + 2.87552e6i) q^{65} +(-1.30857e7 + 1.30857e7i) q^{67} +(6.84086e6 + 6.84086e6i) q^{68} +(1.62707e7 + 2.05866e7i) q^{70} -2.61041e7 q^{71} +(-1.85930e7 - 1.85930e7i) q^{73} +3.21044e7i q^{74} +1.85329e7 q^{76} +(1.40981e7 - 1.40981e7i) q^{77} +3.07594e6i q^{79} +(-8.03375e6 + 6.34952e6i) q^{80} +(3.33858e7 - 3.33858e7i) q^{82} +(-2.41522e7 - 2.41522e7i) q^{83} +(-5.49393e6 + 4.69179e7i) q^{85} +6.42313e7 q^{86} +(5.50167e6 + 5.50167e6i) q^{88} +5.76618e6i q^{89} -1.46802e8 q^{91} +(-6.67504e6 + 6.67504e6i) q^{92} +3.63104e7i q^{94} +(5.61117e7 + 7.09955e7i) q^{95} +(2.86891e7 - 2.86891e7i) q^{97} +(-6.40485e7 - 6.40485e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} - 90 q^{5} - 1186 q^{7} - 4096 q^{8} - 1760 q^{10} + 19852 q^{11} + 73704 q^{13} - 65536 q^{16} - 198944 q^{17} - 16640 q^{20} + 158816 q^{22} - 631334 q^{23} + 545600 q^{25} + 1179264 q^{26}+ \cdots - 167860352 q^{98}+O(q^{100}) $ 4 * q + 32 * q^2 - 90 * q^5 - 1186 * q^7 - 4096 * q^8 - 1760 * q^10 + 19852 * q^11 + 73704 * q^13 - 65536 * q^16 - 198944 * q^17 - 16640 * q^20 + 158816 * q^22 - 631334 * q^23 + 545600 * q^25 + 1179264 * q^26 + 151808 * q^28 - 2329892 * q^31 - 524288 * q^32 - 1403870 * q^35 - 976356 * q^37 + 1144000 * q^38 - 40960 * q^40 + 4284652 * q^41 + 7146534 * q^43 - 10101344 * q^46 + 3300186 * q^47 - 7241600 * q^50 + 9434112 * q^52 - 9989164 * q^53 - 21649020 * q^55 + 2428928 * q^56 - 19957760 * q^58 + 85377108 * q^61 - 18639136 * q^62 + 33878940 * q^65 - 57195466 * q^67 + 25464832 * q^68 + 53504320 * q^70 - 113004028 * q^71 - 60875756 * q^73 + 18304000 * q^76 + 90339932 * q^77 + 1474560 * q^80 + 34277216 * q^82 - 71051214 * q^83 + 8601320 * q^85 + 114344544 * q^86 - 20328448 * q^88 - 221467572 * q^91 - 80810752 * q^92 + 159500600 * q^95 + 139631604 * q^97 - 167860352 * q^98

Character values

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

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	8.00000	−	8.00000i	0.500000	−	0.500000i
$2$	8.00000	−	8.00000i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	128.000i		−	0.500000i
$5$	490.341	−	387.544i	0.784546	−	0.620070i
$5$	490.341	−	387.544i	0.784546	−	0.620070i
$6$		0			0
$7$	−2624.01	+	2624.01i	−1.09288	+	1.09288i	−0.0976629	+	0.995220i	$0.531137\pi$
$7$	−2624.01	+	2624.01i	−1.09288	+	1.09288i	−0.995220	+	0.0976629i	$0.968863\pi$
$8$	−1024.00	−	1024.00i	−0.250000	−	0.250000i
$9$		0			0
$10$	822.379	−	7023.08i	0.0822379	−	0.702308i
$11$	−5372.73			−0.366964			−0.183482	−	0.983023i	$-0.558737\pi$
$11$	−5372.73			−0.366964			−0.183482	+	0.983023i	$0.558737\pi$
$12$		0			0
$13$	27972.7	+	27972.7i	0.979403	+	0.979403i	0.999792	−	0.0203888i	$-0.00649040\pi$
$13$	27972.7	+	27972.7i	0.979403	+	0.979403i	−0.0203888	+	0.999792i	$0.506490\pi$
$14$			41984.2i			1.09288i
$15$		0			0
$16$	−16384.0			−0.250000
$17$	−53444.2	+	53444.2i	−0.639890	+	0.639890i	−0.950528	−	0.310638i	$-0.899457\pi$
$17$	−53444.2	+	53444.2i	−0.639890	+	0.639890i	0.310638	+	0.950528i	$0.399457\pi$
$18$		0			0
$19$			144788.i			1.11101i	0.831513	+	0.555505i	$0.187475\pi$
$19$			144788.i			1.11101i	−0.831513	+	0.555505i	$0.812525\pi$
$20$	−49605.6	−	62763.7i	−0.310035	−	0.392273i
$21$		0			0
$22$	−42981.8	+	42981.8i	−0.183482	+	0.183482i
$23$	−52148.7	−	52148.7i	−0.186351	−	0.186351i	0.607765	−	0.794117i	$-0.292066\pi$
$23$	−52148.7	−	52148.7i	−0.186351	−	0.186351i	−0.794117	+	0.607765i	$0.792066\pi$
$24$		0			0
$25$	90244.3	−	380058.i	0.231025	−	0.972948i
$26$	447564.			0.979403
$27$		0			0
$28$	335873.	+	335873.i	0.546441	+	0.546441i
$29$		−	41723.4i		−	0.0589913i	−0.999565	−	0.0294956i	$-0.990610\pi$
$29$		−	41723.4i		−	0.0589913i	0.999565	−	0.0294956i	$-0.00939012\pi$
$30$		0			0
$31$	244148.			0.264367			0.132183	−	0.991225i	$-0.457801\pi$
$31$	244148.			0.264367			0.132183	+	0.991225i	$0.457801\pi$
$32$	−131072.	+	131072.i	−0.125000	+	0.125000i
$33$		0			0
$34$			855108.i			0.639890i
$35$	−269741.	+	2.30358e6i	−0.179753	+	1.53508i
$36$		0			0
$37$	−2.00653e6	+	2.00653e6i	−1.07063	+	1.07063i	−0.0733185	+	0.997309i	$0.523359\pi$
$37$	−2.00653e6	+	2.00653e6i	−1.07063	+	1.07063i	−0.997309	+	0.0733185i	$0.976641\pi$
$38$	1.15830e6	+	1.15830e6i	0.555505	+	0.555505i
$39$		0			0
$40$	−898955.	−	105264.i	−0.351154	−	0.0411189i
$41$	4.17322e6			1.47685			0.738424	−	0.674336i	$-0.235570\pi$
$41$	4.17322e6			1.47685			0.738424	+	0.674336i	$0.235570\pi$
$42$		0			0
$43$	4.01446e6	+	4.01446e6i	1.17423	+	1.17423i	0.981191	+	0.193038i	$0.0618340\pi$
$43$	4.01446e6	+	4.01446e6i	1.17423	+	1.17423i	0.193038	+	0.981191i	$0.438166\pi$
$44$			687709.i			0.183482i
$45$		0			0
$46$	−834380.			−0.186351
$47$	−2.26940e6	+	2.26940e6i	−0.465071	+	0.465071i	−0.900313	−	0.435242i	$-0.856663\pi$
$47$	−2.26940e6	+	2.26940e6i	−0.465071	+	0.465071i	0.435242	+	0.900313i	$0.356663\pi$
$48$		0			0
$49$		−	8.00606e6i		−	1.38878i
$50$	−2.31851e6	−	3.76242e6i	−0.370961	−	0.601987i
$51$		0			0
$52$	3.58051e6	−	3.58051e6i	0.489702	−	0.489702i
$53$	3.72734e6	+	3.72734e6i	0.472384	+	0.472384i	0.902685	−	0.430301i	$-0.141593\pi$
$53$	3.72734e6	+	3.72734e6i	0.472384	+	0.472384i	−0.430301	+	0.902685i	$0.641593\pi$
$54$		0			0
$55$	−2.63447e6	+	2.08217e6i	−0.287901	+	0.227544i
$56$	5.37397e6			0.546441
$57$		0			0
$58$	−333787.	−	333787.i	−0.0294956	−	0.0294956i
$59$			1.12165e7i			0.925653i	0.886449	+	0.462826i	$0.153165\pi$
$59$			1.12165e7i			0.925653i	−0.886449	+	0.462826i	$0.846835\pi$
$60$		0			0
$61$	2.02002e7			1.45893			0.729467	−	0.684016i	$-0.239768\pi$
$61$	2.02002e7			1.45893			0.729467	+	0.684016i	$0.239768\pi$
$62$	1.95319e6	−	1.95319e6i	0.132183	−	0.132183i
$63$		0			0
$64$			2.09715e6i			0.125000i
$65$	2.45569e7	+	2.87552e6i	1.37569	+	0.161088i
$66$		0			0
$67$	−1.30857e7	+	1.30857e7i	−0.649377	+	0.649377i	−0.952843	−	0.303465i	$-0.901856\pi$
$67$	−1.30857e7	+	1.30857e7i	−0.649377	+	0.649377i	0.303465	+	0.952843i	$0.401856\pi$
$68$	6.84086e6	+	6.84086e6i	0.319945	+	0.319945i
$69$		0			0
$70$	1.62707e7	+	2.05866e7i	0.677664	+	0.857417i
$71$	−2.61041e7			−1.02725			−0.513624	−	0.858015i	$-0.671697\pi$
$71$	−2.61041e7			−1.02725			−0.513624	+	0.858015i	$0.671697\pi$
$72$		0			0
$73$	−1.85930e7	−	1.85930e7i	−0.654722	−	0.654722i	0.299404	−	0.954126i	$-0.403212\pi$
$73$	−1.85930e7	−	1.85930e7i	−0.654722	−	0.654722i	−0.954126	+	0.299404i	$0.903212\pi$
$74$			3.21044e7i			1.07063i
$75$		0			0
$76$	1.85329e7			0.555505
$77$	1.40981e7	−	1.40981e7i	0.401049	−	0.401049i
$78$		0			0
$79$			3.07594e6i			0.0789714i	0.999220	+	0.0394857i	$0.0125720\pi$
$79$			3.07594e6i			0.0789714i	−0.999220	+	0.0394857i	$0.987428\pi$
$80$	−8.03375e6	+	6.34952e6i	−0.196137	+	0.155018i
$81$		0			0
$82$	3.33858e7	−	3.33858e7i	0.738424	−	0.738424i
$83$	−2.41522e7	−	2.41522e7i	−0.508914	−	0.508914i	0.405279	−	0.914193i	$-0.367174\pi$
$83$	−2.41522e7	−	2.41522e7i	−0.508914	−	0.508914i	−0.914193	+	0.405279i	$0.867174\pi$
$84$		0			0
$85$	−5.49393e6	+	4.69179e7i	−0.105246	+	0.898800i
$86$	6.42313e7			1.17423
$87$		0			0
$88$	5.50167e6	+	5.50167e6i	0.0917411	+	0.0917411i
$89$			5.76618e6i			0.0919027i	0.998944	+	0.0459513i	$0.0146319\pi$
$89$			5.76618e6i			0.0919027i	−0.998944	+	0.0459513i	$0.985368\pi$
$90$		0			0
$91$	−1.46802e8			−2.14075
$92$	−6.67504e6	+	6.67504e6i	−0.0931756	+	0.0931756i
$93$		0			0
$94$			3.63104e7i			0.465071i
$95$	5.61117e7	+	7.09955e7i	0.688905	+	0.871639i
$96$		0			0
$97$	2.86891e7	−	2.86891e7i	0.324063	−	0.324063i	−0.526260	−	0.850324i	$-0.676406\pi$
$97$	2.86891e7	−	2.86891e7i	0.324063	−	0.324063i	0.850324	+	0.526260i	$0.176406\pi$
$98$	−6.40485e7	−	6.40485e7i	−0.694392	−	0.694392i
$99$		0			0
$100$	−4.86474e7	−	1.15513e7i	−0.486474	−	0.115513i
$101$	−7.95260e7			−0.764229			−0.382115	−	0.924115i	$-0.624804\pi$
$101$	−7.95260e7			−0.764229			−0.382115	+	0.924115i	$0.624804\pi$
$102$		0			0
$103$	4.96462e7	+	4.96462e7i	0.441100	+	0.441100i	0.892382	−	0.451282i	$-0.149033\pi$
$103$	4.96462e7	+	4.96462e7i	0.441100	+	0.441100i	−0.451282	+	0.892382i	$0.649033\pi$
$104$		−	5.72882e7i		−	0.489702i
$105$		0			0
$106$	5.96374e7			0.472384
$107$	−6.12534e7	+	6.12534e7i	−0.467300	+	0.467300i	−0.901039	−	0.433739i	$-0.857194\pi$
$107$	−6.12534e7	+	6.12534e7i	−0.467300	+	0.467300i	0.433739	+	0.901039i	$0.357194\pi$
$108$		0			0
$109$		−	9.33557e7i		−	0.661355i	−0.943744	−	0.330678i	$-0.892723\pi$
$109$		−	9.33557e7i		−	0.661355i	0.943744	−	0.330678i	$-0.107277\pi$
$110$	−4.41842e6	+	3.77331e7i	−0.0301784	+	0.257722i
$111$		0			0
$112$	4.29918e7	−	4.29918e7i	0.273221	−	0.273221i
$113$	−1.17246e8	−	1.17246e8i	−0.719093	−	0.719093i	0.249327	−	0.968419i	$-0.419791\pi$
$113$	−1.17246e8	−	1.17246e8i	−0.719093	−	0.719093i	−0.968419	+	0.249327i	$0.919791\pi$
$114$		0			0
$115$	−4.57806e7	−	5.36075e6i	−0.261752	−	0.0306503i
$116$	−5.34060e6			−0.0294956
$117$		0			0
$118$	8.97318e7	+	8.97318e7i	0.462826	+	0.462826i
$119$		−	2.80477e8i		−	1.39865i
$120$		0			0
$121$	−1.85493e8			−0.865337
$122$	1.61601e8	−	1.61601e8i	0.729467	−	0.729467i
$123$		0			0
$124$		−	3.12510e7i		−	0.132183i
$125$	−1.03039e8	−	2.21332e8i	−0.422046	−	0.906574i
$126$		0			0
$127$	1.16482e7	−	1.16482e7i	0.0447759	−	0.0447759i	−0.684364	−	0.729140i	$-0.739920\pi$
$127$	1.16482e7	−	1.16482e7i	0.0447759	−	0.0447759i	0.729140	+	0.684364i	$0.239920\pi$
$128$	1.67772e7	+	1.67772e7i	0.0625000	+	0.0625000i
$129$		0			0
$130$	2.19459e8	−	1.73451e8i	0.768387	−	0.607299i
$131$	−3.83537e8			−1.30233			−0.651167	−	0.758934i	$-0.725720\pi$
$131$	−3.83537e8			−1.30233			−0.651167	+	0.758934i	$0.725720\pi$
$132$		0			0
$133$	−3.79925e8	−	3.79925e8i	−1.21420	−	1.21420i
$134$			2.09371e8i			0.649377i
$135$		0			0
$136$	1.09454e8			0.319945
$137$	1.46786e7	−	1.46786e7i	0.0416681	−	0.0416681i	−0.685966	−	0.727634i	$-0.740620\pi$
$137$	1.46786e7	−	1.46786e7i	0.0416681	−	0.0416681i	0.727634	+	0.685966i	$0.240620\pi$
$138$		0			0
$139$		−	4.00314e8i		−	1.07236i	−0.844103	−	0.536181i	$-0.819866\pi$
$139$		−	4.00314e8i		−	1.07236i	0.844103	−	0.536181i	$-0.180134\pi$
$140$	2.94858e8	+	3.45269e7i	0.767540	+	0.0898763i
$141$		0			0
$142$	−2.08833e8	+	2.08833e8i	−0.513624	+	0.513624i
$143$	−1.50290e8	−	1.50290e8i	−0.359406	−	0.359406i
$144$		0			0
$145$	−1.61697e7	−	2.04587e7i	−0.0365788	−	0.0462814i
$146$	−2.97487e8			−0.654722
$147$		0			0
$148$	2.56836e8	+	2.56836e8i	0.535314	+	0.535314i
$149$			5.62457e8i			1.14115i	0.821244	+	0.570577i	$0.193281\pi$
$149$			5.62457e8i			1.14115i	−0.821244	+	0.570577i	$0.806719\pi$
$150$		0			0
$151$	−2.75254e7			−0.0529452			−0.0264726	−	0.999650i	$-0.508427\pi$
$151$	−2.75254e7			−0.0529452			−0.0264726	+	0.999650i	$0.508427\pi$
$152$	1.48263e8	−	1.48263e8i	0.277753	−	0.277753i
$153$		0			0
$154$		−	2.25569e8i		−	0.401049i
$155$	1.19716e8	−	9.46182e7i	0.207408	−	0.163926i
$156$		0			0
$157$	−3.22628e8	+	3.22628e8i	−0.531010	+	0.531010i	−0.920873	−	0.389863i	$-0.872522\pi$
$157$	−3.22628e8	+	3.22628e8i	−0.531010	+	0.531010i	0.389863	+	0.920873i	$0.372522\pi$
$158$	2.46075e7	+	2.46075e7i	0.0394857	+	0.0394857i
$159$		0			0
$160$	−1.34739e7	+	1.15066e8i	−0.0205595	+	0.175577i
$161$	2.73678e8			0.407320
$162$		0			0
$163$	2.36679e8	+	2.36679e8i	0.335281	+	0.335281i	0.854588	−	0.519307i	$-0.173810\pi$
$163$	2.36679e8	+	2.36679e8i	0.335281	+	0.335281i	−0.519307	+	0.854588i	$0.673810\pi$
$164$		−	5.34172e8i		−	0.738424i
$165$		0			0
$166$	−3.86435e8			−0.508914
$167$	5.45436e8	−	5.45436e8i	0.701258	−	0.701258i	−0.263422	−	0.964681i	$-0.584851\pi$
$167$	5.45436e8	−	5.45436e8i	0.701258	−	0.701258i	0.964681	+	0.263422i	$0.0848512\pi$
$168$		0			0
$169$			7.49218e8i			0.918462i
$170$	3.31392e8	+	4.19295e8i	0.396777	+	0.502023i
$171$		0			0
$172$	5.13850e8	−	5.13850e8i	0.587115	−	0.587115i
$173$	6.41655e8	+	6.41655e8i	0.716337	+	0.716337i	0.967853	−	0.251516i	$-0.0809291\pi$
$173$	6.41655e8	+	6.41655e8i	0.716337	+	0.716337i	−0.251516	+	0.967853i	$0.580929\pi$
$174$		0			0
$175$	7.60474e8	+	1.23408e9i	0.810834	+	1.31580i
$176$	8.80267e7			0.0917411
$177$		0			0
$178$	4.61294e7	+	4.61294e7i	0.0459513	+	0.0459513i
$179$			9.41081e8i			0.916673i	0.888779	+	0.458337i	$0.151555\pi$
$179$			9.41081e8i			0.916673i	−0.888779	+	0.458337i	$0.848445\pi$
$180$		0			0
$181$	−4.09543e8			−0.381580			−0.190790	−	0.981631i	$-0.561105\pi$
$181$	−4.09543e8			−0.381580			−0.190790	+	0.981631i	$0.561105\pi$
$182$	−1.17441e9	+	1.17441e9i	−1.07037	+	1.07037i
$183$		0			0
$184$			1.06801e8i			0.0931756i
$185$	−2.06266e8	+	1.76150e9i	−0.176092	+	1.50382i
$186$		0			0
$187$	2.87141e8	−	2.87141e8i	0.234817	−	0.234817i
$188$	2.90483e8	+	2.90483e8i	0.232536	+	0.232536i
$189$		0			0
$190$	1.01686e9	+	1.19071e8i	0.780272	+	0.0913671i
$191$	−5.56054e8			−0.417814			−0.208907	−	0.977935i	$-0.566991\pi$
$191$	−5.56054e8			−0.417814			−0.208907	+	0.977935i	$0.566991\pi$
$192$		0			0
$193$	1.72776e8	+	1.72776e8i	0.124524	+	0.124524i	0.766622	−	0.642098i	$-0.221936\pi$
$193$	1.72776e8	+	1.72776e8i	0.124524	+	0.124524i	−0.642098	+	0.766622i	$0.721936\pi$
$194$		−	4.59026e8i		−	0.324063i
$195$		0			0
$196$	−1.02478e9			−0.694392
$197$	1.39026e9	−	1.39026e9i	0.923060	−	0.923060i	−0.0741846	−	0.997245i	$-0.523635\pi$
$197$	1.39026e9	−	1.39026e9i	0.923060	−	0.923060i	0.997245	+	0.0741846i	$0.0236354\pi$
$198$		0			0
$199$			1.80023e8i			0.114793i	0.998351	+	0.0573964i	$0.0182799\pi$
$199$			1.80023e8i			0.114793i	−0.998351	+	0.0573964i	$0.981720\pi$
$200$	−4.81589e8	+	2.96769e8i	−0.300993	+	0.185481i
$201$		0			0
$202$	−6.36208e8	+	6.36208e8i	−0.382115	+	0.382115i
$203$	1.09483e8	+	1.09483e8i	0.0644705	+	0.0644705i
$204$		0			0
$205$	2.04630e9	−	1.61731e9i	1.15866	−	0.915750i
$206$	7.94339e8			0.441100
$207$		0			0
$208$	−4.58305e8	−	4.58305e8i	−0.244851	−	0.244851i
$209$		−	7.77906e8i		−	0.407701i
$210$		0			0
$211$	−4.17651e8			−0.210709			−0.105355	−	0.994435i	$-0.533598\pi$
$211$	−4.17651e8			−0.210709			−0.105355	+	0.994435i	$0.533598\pi$
$212$	4.77100e8	−	4.77100e8i	0.236192	−	0.236192i
$213$		0			0
$214$			9.80055e8i			0.467300i
$215$	3.52423e9	+	4.12675e8i	1.64934	+	0.193132i
$216$		0			0
$217$	−6.40648e8	+	6.40648e8i	−0.288922	+	0.288922i
$218$	−7.46845e8	−	7.46845e8i	−0.330678	−	0.330678i
$219$		0			0
$220$	2.66517e8	+	3.37212e8i	0.113772	+	0.143950i
$221$	−2.98996e9			−1.25342
$222$		0			0
$223$	1.19002e9	+	1.19002e9i	0.481210	+	0.481210i	0.905518	−	0.424308i	$-0.139483\pi$
$223$	1.19002e9	+	1.19002e9i	0.481210	+	0.481210i	−0.424308	+	0.905518i	$0.639483\pi$
$224$		−	6.87869e8i		−	0.273221i
$225$		0			0
$226$	−1.87594e9			−0.719093
$227$	−2.69749e9	+	2.69749e9i	−1.01591	+	1.01591i	−0.0160418	+	0.999871i	$0.505106\pi$
$227$	−2.69749e9	+	2.69749e9i	−1.01591	+	1.01591i	−0.999871	+	0.0160418i	$0.994894\pi$
$228$		0			0
$229$		−	4.90322e9i		−	1.78295i	−0.453069	−	0.891475i	$-0.649671\pi$
$229$		−	4.90322e9i		−	1.78295i	0.453069	−	0.891475i	$-0.350329\pi$
$230$	−4.09131e8	+	3.23359e8i	−0.146201	+	0.115551i
$231$		0			0
$232$	−4.27248e7	+	4.27248e7i	−0.0147478	+	0.0147478i
$233$	2.60187e9	+	2.60187e9i	0.882798	+	0.882798i	0.993818	−	0.111020i	$-0.0354117\pi$
$233$	2.60187e9	+	2.60187e9i	0.882798	+	0.882798i	−0.111020	+	0.993818i	$0.535412\pi$
$234$		0			0
$235$	−2.33288e8	+	1.99227e9i	−0.0764929	+	0.653247i
$236$	1.43571e9			0.462826
$237$		0			0
$238$	−2.24381e9	−	2.24381e9i	−0.699324	−	0.699324i
$239$		−	4.57968e9i		−	1.40360i	−0.712374	−	0.701800i	$-0.752380\pi$
$239$		−	4.57968e9i		−	1.40360i	0.712374	−	0.701800i	$-0.247620\pi$
$240$		0			0
$241$	5.82501e9			1.72675			0.863373	−	0.504566i	$-0.168348\pi$
$241$	5.82501e9			1.72675			0.863373	+	0.504566i	$0.168348\pi$
$242$	−1.48394e9	+	1.48394e9i	−0.432669	+	0.432669i
$243$		0			0
$244$		−	2.58562e9i		−	0.729467i
$245$	−3.10270e9	−	3.92570e9i	−0.861144	−	1.08957i
$246$		0			0
$247$	−4.05012e9	+	4.05012e9i	−1.08813	+	1.08813i
$248$	−2.50008e8	−	2.50008e8i	−0.0660917	−	0.0660917i
$249$		0			0
$250$	−2.59496e9	−	9.46344e8i	−0.664310	−	0.242264i
$251$	4.01845e9			1.01243			0.506214	−	0.862408i	$-0.331045\pi$
$251$	4.01845e9			1.01243			0.506214	+	0.862408i	$0.331045\pi$
$252$		0			0
$253$	2.80181e8	+	2.80181e8i	0.0683843	+	0.0683843i
$254$		−	1.86372e8i		−	0.0447759i
$255$		0			0
$256$	2.68435e8			0.0625000
$257$	1.77795e9	−	1.77795e9i	0.407556	−	0.407556i	−0.473330	−	0.880885i	$-0.656948\pi$
$257$	1.77795e9	−	1.77795e9i	0.407556	−	0.407556i	0.880885	+	0.473330i	$0.156948\pi$
$258$		0			0
$259$		−	1.05303e10i		−	2.34014i
$260$	3.68067e8	−	3.14328e9i	0.0805440	−	0.687843i
$261$		0			0
$262$	−3.06830e9	+	3.06830e9i	−0.651167	+	0.651167i
$263$	−1.87568e9	−	1.87568e9i	−0.392046	−	0.392046i	0.483370	−	0.875416i	$-0.339412\pi$
$263$	−1.87568e9	−	1.87568e9i	−0.392046	−	0.392046i	−0.875416	+	0.483370i	$0.839412\pi$
$264$		0			0
$265$	3.27218e9	+	3.83161e8i	0.663519	+	0.0776958i
$266$	−6.07880e9			−1.21420
$267$		0			0
$268$	1.67497e9	+	1.67497e9i	0.324689	+	0.324689i
$269$		−	5.91528e9i		−	1.12971i	−0.825191	−	0.564854i	$-0.808932\pi$
$269$		−	5.91528e9i		−	1.12971i	0.825191	−	0.564854i	$-0.191068\pi$
$270$		0			0
$271$	−1.60432e9			−0.297449			−0.148725	−	0.988879i	$-0.547517\pi$
$271$	−1.60432e9			−0.297449			−0.148725	+	0.988879i	$0.547517\pi$
$272$	8.75630e8	−	8.75630e8i	0.159972	−	0.159972i
$273$		0			0
$274$		−	2.34858e8i		−	0.0416681i
$275$	−4.84858e8	+	2.04195e9i	−0.0847781	+	0.357037i
$276$		0			0
$277$	−1.67266e9	+	1.67266e9i	−0.284111	+	0.284111i	−0.834746	−	0.550635i	$-0.814386\pi$
$277$	−1.67266e9	+	1.67266e9i	−0.284111	+	0.284111i	0.550635	+	0.834746i	$0.314386\pi$
$278$	−3.20251e9	−	3.20251e9i	−0.536181	−	0.536181i
$279$		0			0
$280$	2.63508e9	−	2.08265e9i	0.428708	−	0.338832i
$281$	−9.29346e9			−1.49057			−0.745285	−	0.666747i	$-0.767686\pi$
$281$	−9.29346e9			−1.49057			−0.745285	+	0.666747i	$0.767686\pi$
$282$		0			0
$283$	4.61061e9	+	4.61061e9i	0.718808	+	0.718808i	0.968361	−	0.249553i	$-0.0802836\pi$
$283$	4.61061e9	+	4.61061e9i	0.718808	+	0.718808i	−0.249553	+	0.968361i	$0.580284\pi$
$284$			3.34132e9i			0.513624i
$285$		0			0
$286$	−2.40464e9			−0.359406
$287$	−1.09506e10	+	1.09506e10i	−1.61402	+	1.61402i
$288$		0			0
$289$			1.26318e9i			0.181082i
$290$	−2.93027e8	−	3.43124e7i	−0.0414301	−	0.00485132i
$291$		0			0
$292$	−2.37990e9	+	2.37990e9i	−0.327361	+	0.327361i
$293$	6.99292e9	+	6.99292e9i	0.948829	+	0.948829i	0.998753	−	0.0499241i	$-0.0158979\pi$
$293$	6.99292e9	+	6.99292e9i	0.948829	+	0.948829i	−0.0499241	+	0.998753i	$0.515898\pi$
$294$		0			0
$295$	4.34688e9	+	5.49990e9i	0.573970	+	0.726217i
$296$	4.10937e9			0.535314
$297$		0			0
$298$	4.49966e9	+	4.49966e9i	0.570577	+	0.570577i
$299$		−	2.91749e9i		−	0.365026i
$300$		0			0
$301$	−2.10680e10			−2.56659
$302$	−2.20204e8	+	2.20204e8i	−0.0264726	+	0.0264726i
$303$		0			0
$304$		−	2.37221e9i		−	0.277753i
$305$	9.90498e9	−	7.82845e9i	1.14460	−	0.904642i
$306$		0			0
$307$	2.31844e9	−	2.31844e9i	0.261001	−	0.261001i	−0.564459	−	0.825461i	$-0.690915\pi$
$307$	2.31844e9	−	2.31844e9i	0.261001	−	0.261001i	0.825461	+	0.564459i	$0.190915\pi$
$308$	−1.80456e9	−	1.80456e9i	−0.200524	−	0.200524i
$309$		0			0
$310$	2.00782e8	−	1.71467e9i	0.0217410	−	0.185667i
$311$	1.45111e10			1.55117			0.775584	−	0.631245i	$-0.217456\pi$
$311$	1.45111e10			1.55117			0.775584	+	0.631245i	$0.217456\pi$
$312$		0			0
$313$	2.03082e9	+	2.03082e9i	0.211590	+	0.211590i	0.804943	−	0.593353i	$-0.202196\pi$
$313$	2.03082e9	+	2.03082e9i	0.211590	+	0.211590i	−0.593353	+	0.804943i	$0.702196\pi$
$314$			5.16204e9i			0.531010i
$315$		0			0
$316$	3.93720e8			0.0394857
$317$	−9.69018e8	+	9.69018e8i	−0.0959611	+	0.0959611i	−0.753458	−	0.657497i	$-0.771615\pi$
$317$	−9.69018e8	+	9.69018e8i	−0.0959611	+	0.0959611i	0.657497	+	0.753458i	$0.271615\pi$
$318$		0			0
$319$			2.24168e8i			0.0216477i
$320$	8.12739e8	+	1.02832e9i	0.0775088	+	0.0980683i
$321$		0			0
$322$	2.18942e9	−	2.18942e9i	0.203660	−	0.203660i
$323$	−7.73808e9	−	7.73808e9i	−0.710924	−	0.710924i
$324$		0			0
$325$	1.31556e10	−	8.10688e9i	1.17918	−	0.726641i
$326$	3.78686e9			0.335281
$327$		0			0
$328$	−4.27338e9	−	4.27338e9i	−0.369212	−	0.369212i
$329$		−	1.19099e10i		−	1.01654i
$330$		0			0
$331$	−7.63072e9			−0.635702			−0.317851	−	0.948141i	$-0.602961\pi$
$331$	−7.63072e9			−0.635702			−0.317851	+	0.948141i	$0.602961\pi$
$332$	−3.09148e9	+	3.09148e9i	−0.254457	+	0.254457i
$333$		0			0
$334$		−	8.72698e9i		−	0.701258i
$335$	−1.34517e9	+	1.14877e10i	−0.106807	+	0.912126i
$336$		0			0
$337$	−2.47412e9	+	2.47412e9i	−0.191824	+	0.191824i	−0.796484	−	0.604660i	$-0.793309\pi$
$337$	−2.47412e9	+	2.47412e9i	−0.191824	+	0.191824i	0.604660	+	0.796484i	$0.293309\pi$
$338$	5.99374e9	+	5.99374e9i	0.459231	+	0.459231i
$339$		0			0
$340$	6.00549e9	+	7.03222e8i	0.449400	+	0.0526232i
$341$	−1.31174e9			−0.0970132
$342$		0			0
$343$	5.88110e9	+	5.88110e9i	0.424895	+	0.424895i
$344$		−	8.22161e9i		−	0.587115i
$345$		0			0
$346$	1.02665e10			0.716337
$347$	2.63557e9	−	2.63557e9i	0.181785	−	0.181785i	−0.610348	−	0.792133i	$-0.708971\pi$
$347$	2.63557e9	−	2.63557e9i	0.181785	−	0.181785i	0.792133	+	0.610348i	$0.208971\pi$
$348$		0			0
$349$		−	2.46965e10i		−	1.66469i	−0.554257	−	0.832346i	$-0.686998\pi$
$349$		−	2.46965e10i		−	1.66469i	0.554257	−	0.832346i	$-0.313002\pi$
$350$	1.59564e10	+	3.78883e9i	1.06332	+	0.252484i
$351$		0			0
$352$	7.04214e8	−	7.04214e8i	0.0458705	−	0.0458705i
$353$	1.25084e10	+	1.25084e10i	0.805566	+	0.805566i	0.983959	−	0.178393i	$-0.0570898\pi$
$353$	1.25084e10	+	1.25084e10i	0.805566	+	0.805566i	−0.178393	+	0.983959i	$0.557090\pi$
$354$		0			0
$355$	−1.27999e10	+	1.01165e10i	−0.805923	+	0.636966i
$356$	7.38071e8			0.0459513
$357$		0			0
$358$	7.52864e9	+	7.52864e9i	0.458337	+	0.458337i
$359$			2.30279e10i			1.38636i	0.720763	+	0.693181i	$0.243792\pi$
$359$			2.30279e10i			1.38636i	−0.720763	+	0.693181i	$0.756208\pi$
$360$		0			0
$361$	−3.97999e9			−0.234344
$362$	−3.27635e9	+	3.27635e9i	−0.190790	+	0.190790i
$363$		0			0
$364$			1.87906e10i			1.07037i
$365$	−1.63225e10	−	1.91131e9i	−0.919634	−	0.107686i
$366$		0			0
$367$	−9.47400e9	+	9.47400e9i	−0.522239	+	0.522239i	−0.918247	−	0.396008i	$-0.870395\pi$
$367$	−9.47400e9	+	9.47400e9i	−0.522239	+	0.522239i	0.396008	+	0.918247i	$0.370395\pi$
$368$	8.54405e8	+	8.54405e8i	0.0465878	+	0.0465878i
$369$		0			0
$370$	1.24419e10	+	1.57421e10i	0.663864	+	0.839956i
$371$	−1.95612e10			−1.03252
$372$		0			0
$373$	6.05089e9	+	6.05089e9i	0.312597	+	0.312597i	0.845915	−	0.533318i	$-0.179055\pi$
$373$	6.05089e9	+	6.05089e9i	0.312597	+	0.312597i	−0.533318	+	0.845915i	$0.679055\pi$
$374$		−	4.59426e9i		−	0.234817i
$375$		0			0
$376$	4.64773e9			0.232536
$377$	1.16712e9	−	1.16712e9i	0.0577763	−	0.0577763i
$378$		0			0
$379$			4.27189e9i			0.207044i	0.994627	+	0.103522i	$0.0330113\pi$
$379$			4.27189e9i			0.207044i	−0.994627	+	0.103522i	$0.966989\pi$
$380$	9.08743e9	−	7.18230e9i	0.435819	−	0.344452i
$381$		0			0
$382$	−4.44843e9	+	4.44843e9i	−0.208907	+	0.208907i
$383$	2.68406e10	+	2.68406e10i	1.24738	+	1.24738i	0.956874	+	0.290502i	$0.0938224\pi$
$383$	2.68406e10	+	2.68406e10i	1.24738	+	1.24738i	0.290502	+	0.956874i	$0.406178\pi$
$384$		0			0
$385$	1.44925e9	−	1.23765e10i	0.0659628	−	0.563320i
$386$	2.76441e9			0.124524
$387$		0			0
$388$	−3.67221e9	−	3.67221e9i	−0.162032	−	0.162032i
$389$		−	9.16592e8i		−	0.0400293i	−0.999800	−	0.0200146i	$-0.993629\pi$
$389$		−	9.16592e8i		−	0.0400293i	0.999800	−	0.0200146i	$-0.00637128\pi$
$390$		0			0
$391$	5.57410e9			0.238489
$392$	−8.19821e9	+	8.19821e9i	−0.347196	+	0.347196i
$393$		0			0
$394$		−	2.22441e10i		−	0.923060i
$395$	1.19206e9	+	1.50826e9i	0.0489678	+	0.0619567i
$396$		0			0
$397$	5.24090e9	−	5.24090e9i	0.210981	−	0.210981i	−0.593703	−	0.804684i	$-0.702335\pi$
$397$	5.24090e9	−	5.24090e9i	0.210981	−	0.210981i	0.804684	+	0.593703i	$0.202335\pi$
$398$	1.44018e9	+	1.44018e9i	0.0573964	+	0.0573964i
$399$		0			0
$400$	−1.47856e9	+	6.22687e9i	−0.0577563	+	0.243237i
$401$	−1.76862e10			−0.684000			−0.342000	−	0.939700i	$-0.611104\pi$
$401$	−1.76862e10			−0.684000			−0.342000	+	0.939700i	$0.611104\pi$
$402$		0			0
$403$	6.82950e9	+	6.82950e9i	0.258922	+	0.258922i
$404$			1.01793e10i			0.382115i
$405$		0			0
$406$	1.75172e9			0.0644705
$407$	1.07805e10	−	1.07805e10i	0.392882	−	0.392882i
$408$		0			0
$409$			2.18253e9i			0.0779950i	0.999239	+	0.0389975i	$0.0124164\pi$
$409$			2.18253e9i			0.0779950i	−0.999239	+	0.0389975i	$0.987584\pi$
$410$	3.43197e9	−	2.93089e10i	0.121453	−	1.03720i
$411$		0			0
$412$	6.35471e9	−	6.35471e9i	0.220550	−	0.220550i
$413$	−2.94321e10	−	2.94321e10i	−1.01163	−	1.01163i
$414$		0			0
$415$	−2.12029e10	−	2.48278e9i	−0.714829	−	0.0837040i
$416$	−7.33289e9			−0.244851
$417$		0			0
$418$	−6.22325e9	−	6.22325e9i	−0.203851	−	0.203851i
$419$		−	3.02443e10i		−	0.981268i	−0.871366	−	0.490634i	$-0.836765\pi$
$419$		−	3.02443e10i		−	0.981268i	0.871366	−	0.490634i	$-0.163235\pi$
$420$		0			0
$421$	1.77840e10			0.566109			0.283055	−	0.959104i	$-0.408652\pi$
$421$	1.77840e10			0.566109			0.283055	+	0.959104i	$0.408652\pi$
$422$	−3.34121e9	+	3.34121e9i	−0.105355	+	0.105355i
$423$		0			0
$424$		−	7.63359e9i		−	0.236192i
$425$	1.54889e10	+	2.51349e10i	0.474749	+	0.770410i
$426$		0			0
$427$	−5.30055e10	+	5.30055e10i	−1.59444	+	1.59444i
$428$	7.84044e9	+	7.84044e9i	0.233650	+	0.233650i
$429$		0			0
$430$	3.14953e10	−	2.48925e10i	0.921237	−	0.728105i
$431$	2.12717e10			0.616443			0.308221	−	0.951315i	$-0.400266\pi$
$431$	2.12717e10			0.616443			0.308221	+	0.951315i	$0.400266\pi$
$432$		0			0
$433$	−2.24808e10	−	2.24808e10i	−0.639529	−	0.639529i	0.310910	−	0.950439i	$-0.399366\pi$
$433$	−2.24808e10	−	2.24808e10i	−0.639529	−	0.639529i	−0.950439	+	0.310910i	$0.899366\pi$
$434$			1.02504e10i			0.288922i
$435$		0			0
$436$	−1.19495e10			−0.330678
$437$	7.55051e9	−	7.55051e9i	0.207038	−	0.207038i
$438$		0			0
$439$			1.46904e10i			0.395526i	0.980250	+	0.197763i	$0.0633676\pi$
$439$			1.46904e10i			0.395526i	−0.980250	+	0.197763i	$0.936632\pi$
$440$	4.82984e9	+	5.65557e8i	0.128861	+	0.0150892i
$441$		0			0
$442$	−2.39197e10	+	2.39197e10i	−0.626710	+	0.626710i
$443$	−1.79953e10	−	1.79953e10i	−0.467245	−	0.467245i	0.433776	−	0.901021i	$-0.357181\pi$
$443$	−1.79953e10	−	1.79953e10i	−0.467245	−	0.467245i	−0.901021	+	0.433776i	$0.857181\pi$
$444$		0			0
$445$	2.23465e9	+	2.82740e9i	0.0569861	+	0.0721019i
$446$	1.90403e10			0.481210
$447$		0			0
$448$	−5.50295e9	−	5.50295e9i	−0.136610	−	0.136610i
$449$		−	2.81226e10i		−	0.691943i	−0.938245	−	0.345972i	$-0.887549\pi$
$449$		−	2.81226e10i		−	0.691943i	0.938245	−	0.345972i	$-0.112451\pi$
$450$		0			0
$451$	−2.24216e10			−0.541951
$452$	−1.50075e10	+	1.50075e10i	−0.359546	+	0.359546i
$453$		0			0
$454$			4.31599e10i			1.01591i
$455$	−7.19829e10	+	5.68921e10i	−1.67951	+	1.32741i
$456$		0			0
$457$	5.32217e10	−	5.32217e10i	1.22018	−	1.22018i	0.252614	−	0.967567i	$-0.418710\pi$
$457$	5.32217e10	−	5.32217e10i	1.22018	−	1.22018i	0.967567	−	0.252614i	$-0.0812901\pi$
$458$	−3.92258e10	−	3.92258e10i	−0.891475	−	0.891475i
$459$		0			0
$460$	−6.86176e8	+	5.85992e9i	−0.0153251	+	0.130876i
$461$	−2.80695e9			−0.0621485			−0.0310743	−	0.999517i	$-0.509893\pi$
$461$	−2.80695e9			−0.0621485			−0.0310743	+	0.999517i	$0.509893\pi$
$462$		0			0
$463$	−1.84228e10	−	1.84228e10i	−0.400896	−	0.400896i	0.477653	−	0.878549i	$-0.341488\pi$
$463$	−1.84228e10	−	1.84228e10i	−0.400896	−	0.400896i	−0.878549	+	0.477653i	$0.841488\pi$
$464$			6.83596e8i			0.0147478i
$465$		0			0
$466$	4.16299e10			0.882798
$467$	1.19286e10	−	1.19286e10i	0.250796	−	0.250796i	−0.570501	−	0.821297i	$-0.693251\pi$
$467$	1.19286e10	−	1.19286e10i	0.250796	−	0.250796i	0.821297	+	0.570501i	$0.193251\pi$
$468$		0			0
$469$		−	6.86739e10i		−	1.41939i
$470$	1.40719e10	+	1.78045e10i	0.288377	+	0.364870i
$471$		0			0
$472$	1.14857e10	−	1.14857e10i	0.231413	−	0.231413i
$473$	−2.15686e10	−	2.15686e10i	−0.430900	−	0.430900i
$474$		0			0
$475$	5.50278e10	+	1.30663e10i	1.08095	+	0.256672i
$476$	−3.59010e10			−0.699324
$477$		0			0
$478$	−3.66374e10	−	3.66374e10i	−0.701800	−	0.701800i
$479$		−	8.08280e10i		−	1.53539i	−0.640813	−	0.767697i	$-0.721403\pi$
$479$		−	8.08280e10i		−	1.53539i	0.640813	−	0.767697i	$-0.278597\pi$
$480$		0			0
$481$	−1.12256e11			−2.09715
$482$	4.66001e10	−	4.66001e10i	0.863373	−	0.863373i
$483$		0			0
$484$			2.37431e10i			0.432669i
$485$	2.94916e9	−	2.51857e10i	0.0533006	−	0.455185i
$486$		0			0
$487$	7.93140e10	−	7.93140e10i	1.41005	−	1.41005i	0.650797	−	0.759252i	$-0.274435\pi$
$487$	7.93140e10	−	7.93140e10i	1.41005	−	1.41005i	0.759252	−	0.650797i	$-0.225565\pi$
$488$	−2.06850e10	−	2.06850e10i	−0.364733	−	0.364733i
$489$		0			0
$490$	−5.62272e10	−	6.58402e9i	−0.975355	−	0.114211i
$491$	−6.00911e10			−1.03391			−0.516957	−	0.856011i	$-0.672935\pi$
$491$	−6.00911e10			−1.03391			−0.516957	+	0.856011i	$0.672935\pi$
$492$		0			0
$493$	2.22988e9	+	2.22988e9i	0.0377479	+	0.0377479i
$494$			6.48019e10i			1.08813i
$495$		0			0
$496$	−4.00013e9			−0.0660917
$497$	6.84974e10	−	6.84974e10i	1.12266	−	1.12266i
$498$		0			0
$499$			1.08749e11i			1.75397i	0.480516	+	0.876986i	$0.340449\pi$
$499$			1.08749e11i			1.75397i	−0.480516	+	0.876986i	$0.659551\pi$
$500$	−2.83304e10	+	1.31889e10i	−0.453287	+	0.211023i
$501$		0			0
$502$	3.21476e10	−	3.21476e10i	0.506214	−	0.506214i
$503$	4.36650e10	+	4.36650e10i	0.682122	+	0.682122i	0.960478	−	0.278356i	$-0.0897896\pi$
$503$	4.36650e10	+	4.36650e10i	0.682122	+	0.682122i	−0.278356	+	0.960478i	$0.589790\pi$
$504$		0			0
$505$	−3.89949e10	+	3.08198e10i	−0.599573	+	0.473876i
$506$	4.48289e9			0.0683843
$507$		0			0
$508$	−1.49097e9	−	1.49097e9i	−0.0223880	−	0.0223880i
$509$			6.95461e10i			1.03610i	0.855350	+	0.518050i	$0.173342\pi$
$509$			6.95461e10i			1.03610i	−0.855350	+	0.518050i	$0.826658\pi$
$510$		0			0
$511$	9.75763e10			1.43107
$512$	2.14748e9	−	2.14748e9i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	2.84472e10i		−	0.407556i
$515$	4.35836e10	+	5.10349e9i	0.619576	+	0.0725502i
$516$		0			0
$517$	1.21929e10	−	1.21929e10i	0.170665	−	0.170665i
$518$	−8.42424e10	−	8.42424e10i	−1.17007	−	1.17007i
$519$		0			0
$520$	−2.22017e10	−	2.80908e10i	−0.303650	−	0.384194i
$521$	−1.18226e10			−0.160459			−0.0802294	−	0.996776i	$-0.525565\pi$
$521$	−1.18226e10			−0.160459			−0.0802294	+	0.996776i	$0.525565\pi$
$522$		0			0
$523$	5.44052e10	+	5.44052e10i	0.727166	+	0.727166i	0.970054	−	0.242888i	$-0.0780948\pi$
$523$	5.44052e10	+	5.44052e10i	0.727166	+	0.727166i	−0.242888	+	0.970054i	$0.578095\pi$
$524$			4.90928e10i			0.651167i
$525$		0			0
$526$	−3.00109e10			−0.392046
$527$	−1.30483e10	+	1.30483e10i	−0.169166	+	0.169166i
$528$		0			0
$529$		−	7.28720e10i		−	0.930546i
$530$	2.92427e10	−	2.31121e10i	0.370607	−	0.292912i
$531$		0			0
$532$	−4.86304e10	+	4.86304e10i	−0.607102	+	0.607102i
$533$	1.16736e11	+	1.16736e11i	1.44643	+	1.44643i
$534$		0			0
$535$	−6.29669e9	+	5.37735e10i	−0.0768595	+	0.656377i
$536$	2.67995e10			0.324689
$537$		0			0
$538$	−4.73223e10	−	4.73223e10i	−0.564854	−	0.564854i
$539$			4.30144e10i			0.509634i
$540$		0			0
$541$	1.29671e11			1.51375			0.756873	−	0.653562i	$-0.226726\pi$
$541$	1.29671e11			1.51375			0.756873	+	0.653562i	$0.226726\pi$
$542$	−1.28345e10	+	1.28345e10i	−0.148725	+	0.148725i
$543$		0			0
$544$		−	1.40101e10i		−	0.159972i
$545$	−3.61794e10	−	4.57761e10i	−0.410087	−	0.518864i
$546$		0			0
$547$	2.70067e10	−	2.70067e10i	0.301664	−	0.301664i	−0.540001	−	0.841664i	$-0.681576\pi$
$547$	2.70067e10	−	2.70067e10i	0.301664	−	0.301664i	0.841664	+	0.540001i	$0.181576\pi$
$548$	−1.87887e9	−	1.87887e9i	−0.0208340	−	0.0208340i
$549$		0			0
$550$	1.24567e10	+	2.02144e10i	0.136130	+	0.220908i
$551$	6.04105e9			0.0655399
$552$		0			0
$553$	−8.07130e9	−	8.07130e9i	−0.0863064	−	0.0863064i
$554$			2.67625e10i			0.284111i
$555$		0			0
$556$	−5.12402e10			−0.536181
$557$	−1.51528e9	+	1.51528e9i	−0.0157425	+	0.0157425i	−0.714934	−	0.699192i	$-0.753543\pi$
$557$	−1.51528e9	+	1.51528e9i	−0.0157425	+	0.0157425i	0.699192	+	0.714934i	$0.253543\pi$
$558$		0			0
$559$			2.24591e11i			2.30009i
$560$	4.41944e9	−	3.77419e10i	0.0449382	−	0.383770i
$561$		0			0
$562$	−7.43477e10	+	7.43477e10i	−0.745285	+	0.745285i
$563$	1.16988e11	+	1.16988e11i	1.16441	+	1.16441i	0.983500	+	0.180911i	$0.0579045\pi$
$563$	1.16988e11	+	1.16988e11i	1.16441	+	1.16441i	0.180911	+	0.983500i	$0.442095\pi$
$564$		0			0
$565$	−1.02929e11	−	1.20526e10i	−1.01005	−	0.118273i
$566$	7.37698e10			0.718808
$567$		0			0
$568$	2.67306e10	+	2.67306e10i	0.256812	+	0.256812i
$569$			6.87794e10i			0.656159i	0.944650	+	0.328080i	$0.106401\pi$
$569$			6.87794e10i			0.656159i	−0.944650	+	0.328080i	$0.893599\pi$
$570$		0			0
$571$	−1.03730e10			−0.0975795			−0.0487897	−	0.998809i	$-0.515536\pi$
$571$	−1.03730e10			−0.0975795			−0.0487897	+	0.998809i	$0.515536\pi$
$572$	−1.92371e10	+	1.92371e10i	−0.179703	+	0.179703i
$573$		0			0
$574$			1.75209e11i			1.61402i
$575$	−2.45257e10	+	1.51134e10i	−0.224362	+	0.138258i
$576$		0			0
$577$	5.84784e10	−	5.84784e10i	0.527584	−	0.527584i	−0.392267	−	0.919851i	$-0.628309\pi$
$577$	5.84784e10	−	5.84784e10i	0.527584	−	0.527584i	0.919851	+	0.392267i	$0.128309\pi$
$578$	1.01055e10	+	1.01055e10i	0.0905410	+	0.0905410i
$579$		0			0
$580$	−2.61872e9	+	2.06972e9i	−0.0231407	+	0.0182894i
$581$	1.26751e11			1.11237
$582$		0			0
$583$	−2.00260e10	−	2.00260e10i	−0.173348	−	0.173348i
$584$			3.80784e10i			0.327361i
$585$		0			0
$586$	1.11887e11			0.948829
$587$	−2.36584e10	+	2.36584e10i	−0.199266	+	0.199266i	−0.799685	−	0.600420i	$-0.795000\pi$
$587$	−2.36584e10	+	2.36584e10i	−0.199266	+	0.199266i	0.600420	+	0.799685i	$0.295000\pi$
$588$		0			0
$589$			3.53497e10i			0.293714i
$590$	7.87742e10	+	9.22419e9i	0.650094	+	0.0761237i
$591$		0			0
$592$	3.28749e10	−	3.28749e10i	0.267657	−	0.267657i
$593$	−1.22246e11	−	1.22246e11i	−0.988589	−	0.988589i	0.0113464	−	0.999936i	$-0.496388\pi$
$593$	−1.22246e11	−	1.22246e11i	−0.988589	−	0.988589i	−0.999936	+	0.0113464i	$0.996388\pi$
$594$		0			0
$595$	−1.08697e11	−	1.37529e11i	−0.867261	−	1.09730i
$596$	7.19945e10			0.570577
$597$		0			0
$598$	−2.33399e10	−	2.33399e10i	−0.182513	−	0.182513i
$599$			9.59446e10i			0.745269i	0.927978	+	0.372635i	$0.121546\pi$
$599$			9.59446e10i			0.745269i	−0.927978	+	0.372635i	$0.878454\pi$
$600$		0			0
$601$	1.94971e11			1.49442			0.747210	−	0.664588i	$-0.231393\pi$
$601$	1.94971e11			1.49442			0.747210	+	0.664588i	$0.231393\pi$
$602$	−1.68544e11	+	1.68544e11i	−1.28329	+	1.28329i
$603$		0			0
$604$			3.52326e9i			0.0264726i
$605$	−9.09547e10	+	7.18866e10i	−0.678897	+	0.536570i
$606$		0			0
$607$	−1.26277e11	+	1.26277e11i	−0.930188	+	0.930188i	−0.997717	−	0.0675290i	$-0.978488\pi$
$607$	−1.26277e11	+	1.26277e11i	−0.930188	+	0.930188i	0.0675290	+	0.997717i	$0.478488\pi$
$608$	−1.89776e10	−	1.89776e10i	−0.138876	−	0.138876i
$609$		0			0
$610$	1.66122e10	−	1.41867e11i	0.119980	−	1.02462i
$611$	−1.26963e11			−0.910984
$612$		0			0
$613$	1.84169e11	+	1.84169e11i	1.30429	+	1.30429i	0.925468	+	0.378826i	$0.123672\pi$
$613$	1.84169e11	+	1.84169e11i	1.30429	+	1.30429i	0.378826	+	0.925468i	$0.376328\pi$
$614$		−	3.70951e10i		−	0.261001i
$615$		0			0
$616$	−2.88729e10			−0.200524
$617$	1.20679e11	−	1.20679e11i	0.832707	−	0.832707i	−0.155180	−	0.987886i	$-0.549596\pi$
$617$	1.20679e11	−	1.20679e11i	0.832707	−	0.832707i	0.987886	+	0.155180i	$0.0495956\pi$
$618$		0			0
$619$		−	1.43750e11i		−	0.979143i	−0.871963	−	0.489572i	$-0.837153\pi$
$619$		−	1.43750e11i		−	0.979143i	0.871963	−	0.489572i	$-0.162847\pi$
$620$	−1.21111e10	−	1.53237e10i	−0.0819630	−	0.103704i
$621$		0			0
$622$	1.16089e11	−	1.16089e11i	0.775584	−	0.775584i
$623$	−1.51305e10	−	1.51305e10i	−0.100439	−	0.100439i
$624$		0			0
$625$	−1.36300e11	−	6.85961e10i	−0.893255	−	0.449551i
$626$	3.24932e10			0.211590
$627$		0			0
$628$	4.12963e10	+	4.12963e10i	0.265505	+	0.265505i
$629$		−	2.14475e11i		−	1.37017i
$630$		0			0
$631$	−1.08715e11			−0.685760			−0.342880	−	0.939379i	$-0.611402\pi$
$631$	−1.08715e11			−0.685760			−0.342880	+	0.939379i	$0.611402\pi$
$632$	3.14976e9	−	3.14976e9i	0.0197428	−	0.0197428i
$633$		0			0
$634$			1.55043e10i			0.0959611i
$635$	1.19741e9	−	1.02258e10i	0.00736456	−	0.0628930i
$636$		0			0
$637$	2.23952e11	−	2.23952e11i	1.36018	−	1.36018i
$638$	1.79335e9	+	1.79335e9i	0.0108239	+	0.0108239i
$639$		0			0
$640$	1.47285e10	+	1.72465e9i	0.0877885	+	0.0102797i
$641$	3.25454e11			1.92778			0.963890	−	0.266299i	$-0.0858010\pi$
$641$	3.25454e11			1.92778			0.963890	+	0.266299i	$0.0858010\pi$
$642$		0			0
$643$	4.11926e10	+	4.11926e10i	0.240977	+	0.240977i	0.817254	−	0.576278i	$-0.195495\pi$
$643$	4.11926e10	+	4.11926e10i	0.240977	+	0.240977i	−0.576278	+	0.817254i	$0.695495\pi$
$644$		−	3.50307e10i		−	0.203660i
$645$		0			0
$646$	−1.23809e11			−0.710924
$647$	8.13749e10	−	8.13749e10i	0.464380	−	0.464380i	−0.435708	−	0.900088i	$-0.643502\pi$
$647$	8.13749e10	−	8.13749e10i	0.464380	−	0.464380i	0.900088	+	0.435708i	$0.143502\pi$
$648$		0			0
$649$		−	6.02630e10i		−	0.339682i
$650$	4.03901e10	−	1.70100e11i	0.226267	−	0.952908i
$651$		0			0
$652$	3.02949e10	−	3.02949e10i	0.167640	−	0.167640i
$653$	−1.29147e11	−	1.29147e11i	−0.710285	−	0.710285i	0.256310	−	0.966595i	$-0.417493\pi$
$653$	−1.29147e11	−	1.29147e11i	−0.710285	−	0.710285i	−0.966595	+	0.256310i	$0.917493\pi$
$654$		0			0
$655$	−1.88064e11	+	1.48638e11i	−1.02174	+	0.807539i
$656$	−6.83741e10			−0.369212
$657$		0			0
$658$	−9.52788e10	−	9.52788e10i	−0.508268	−	0.508268i
$659$			2.74018e10i			0.145291i	0.997358	+	0.0726453i	$0.0231441\pi$
$659$			2.74018e10i			0.145291i	−0.997358	+	0.0726453i	$0.976856\pi$
$660$		0			0
$661$	−1.19547e11			−0.626228			−0.313114	−	0.949716i	$-0.601372\pi$
$661$	−1.19547e11			−0.626228			−0.313114	+	0.949716i	$0.601372\pi$
$662$	−6.10457e10	+	6.10457e10i	−0.317851	+	0.317851i
$663$		0			0
$664$			4.94637e10i			0.254457i
$665$	−3.33531e11	−	3.90553e10i	−1.70549	−	0.199707i
$666$		0			0
$667$	−2.17582e9	+	2.17582e9i	−0.0109931	+	0.0109931i
$668$	−6.98158e10	−	6.98158e10i	−0.350629	−	0.350629i
$669$		0			0
$670$	8.11404e10	+	1.02663e11i	0.402660	+	0.509466i
$671$	−1.08530e11			−0.535377
$672$		0			0
$673$	−2.17592e11	−	2.17592e11i	−1.06068	−	1.06068i	−0.998036	−	0.0626416i	$-0.980047\pi$
$673$	−2.17592e11	−	2.17592e11i	−1.06068	−	1.06068i	−0.0626416	−	0.998036i	$-0.519953\pi$
$674$			3.95860e10i			0.191824i
$675$		0			0
$676$	9.58998e10			0.459231
$677$	−1.34337e11	+	1.34337e11i	−0.639503	+	0.639503i	−0.950433	−	0.310930i	$-0.899360\pi$
$677$	−1.34337e11	+	1.34337e11i	−0.639503	+	0.639503i	0.310930	+	0.950433i	$0.399360\pi$
$678$		0			0
$679$			1.50561e11i			0.708327i
$680$	5.36697e10	−	4.24182e10i	0.251012	−	0.198388i
$681$		0			0
$682$	−1.04939e10	+	1.04939e10i	−0.0485066	+	0.0485066i
$683$	2.62510e11	+	2.62510e11i	1.20632	+	1.20632i	0.972210	+	0.234110i	$0.0752177\pi$
$683$	2.62510e11	+	2.62510e11i	1.20632	+	1.20632i	0.234110	+	0.972210i	$0.424782\pi$
$684$		0			0
$685$	1.50893e9	−	1.28862e10i	0.00685339	−	0.0585277i
$686$	9.40976e10			0.424895
$687$		0			0
$688$	−6.57728e10	−	6.57728e10i	−0.293557	−	0.293557i
$689$			2.08528e11i			0.925310i
$690$		0			0
$691$	3.13746e11			1.37615			0.688075	−	0.725639i	$-0.258456\pi$
$691$	3.13746e11			1.37615			0.688075	+	0.725639i	$0.258456\pi$
$692$	8.21319e10	−	8.21319e10i	0.358169	−	0.358169i
$693$		0			0
$694$		−	4.21692e10i		−	0.181785i
$695$	−1.55139e11	−	1.96290e11i	−0.664940	−	0.841318i
$696$		0			0
$697$	−2.23035e11	+	2.23035e11i	−0.945021	+	0.945021i
$698$	−1.97572e11	−	1.97572e11i	−0.832346	−	0.832346i
$699$		0			0
$700$	1.57962e11	−	9.73406e10i	0.657901	−	0.405417i
$701$	−2.56197e11			−1.06097			−0.530483	−	0.847696i	$-0.677989\pi$
$701$	−2.56197e11			−1.06097			−0.530483	+	0.847696i	$0.677989\pi$
$702$		0			0
$703$	−2.90521e11	−	2.90521e11i	−1.18948	−	1.18948i
$704$		−	1.12674e10i		−	0.0458705i
$705$		0			0
$706$	2.00134e11			0.805566
$707$	2.08677e11	−	2.08677e11i	0.835213	−	0.835213i
$708$		0			0
$709$			1.51234e10i			0.0598499i	0.999552	+	0.0299250i	$0.00952683\pi$
$709$			1.51234e10i			0.0598499i	−0.999552	+	0.0299250i	$0.990473\pi$
$710$	−2.14675e10	+	1.83331e11i	−0.0844787	+	0.721445i
$711$		0			0
$712$	5.90457e9	−	5.90457e9i	0.0229757	−	0.0229757i
$713$	−1.27320e10	−	1.27320e10i	−0.0492651	−	0.0492651i
$714$		0			0
$715$	−1.31937e11	−	1.54494e10i	−0.504828	−	0.0591136i
$716$	1.20458e11			0.458337
$717$		0			0
$718$	1.84223e11	+	1.84223e11i	0.693181	+	0.693181i
$719$		−	4.20879e11i		−	1.57486i	−0.616404	−	0.787430i	$-0.711411\pi$
$719$		−	4.20879e11i		−	1.57486i	0.616404	−	0.787430i	$-0.288589\pi$
$720$		0			0
$721$	−2.60544e11			−0.964140
$722$	−3.18399e10	+	3.18399e10i	−0.117172	+	0.117172i
$723$		0			0
$724$			5.24215e10i			0.190790i
$725$	−1.58573e10	−	3.76530e9i	−0.0573954	−	0.0136285i
$726$		0			0
$727$	2.08188e11	−	2.08188e11i	0.745277	−	0.745277i	−0.228312	−	0.973588i	$-0.573320\pi$
$727$	2.08188e11	−	2.08188e11i	0.745277	−	0.745277i	0.973588	+	0.228312i	$0.0733205\pi$
$728$	1.50325e11	+	1.50325e11i	0.535186	+	0.535186i
$729$		0			0
$730$	−1.45870e11	+	1.15289e11i	−0.513660	+	0.405974i
$731$	−4.29099e11			−1.50275
$732$		0			0
$733$	−2.48791e11	−	2.48791e11i	−0.861826	−	0.861826i	0.129725	−	0.991550i	$-0.458591\pi$
$733$	−2.48791e11	−	2.48791e11i	−0.861826	−	0.861826i	−0.991550	+	0.129725i	$0.958591\pi$
$734$			1.51584e11i			0.522239i
$735$		0			0
$736$	1.36705e10			0.0465878
$737$	7.03058e10	−	7.03058e10i	0.238298	−	0.238298i
$738$		0			0
$739$		−	1.15406e11i		−	0.386946i	−0.981106	−	0.193473i	$-0.938025\pi$
$739$		−	1.15406e11i		−	0.386946i	0.981106	−	0.193473i	$-0.0619752\pi$
$740$	2.25472e11	+	2.64020e10i	0.751910	+	0.0880461i
$741$		0			0
$742$	−1.56489e11	+	1.56489e11i	−0.516261	+	0.516261i
$743$	−1.60556e11	−	1.60556e11i	−0.526833	−	0.526833i	0.392794	−	0.919627i	$-0.371509\pi$
$743$	−1.60556e11	−	1.60556e11i	−0.526833	−	0.526833i	−0.919627	+	0.392794i	$0.871509\pi$
$744$		0			0
$745$	2.17977e11	+	2.75796e11i	0.707596	+	0.895289i
$746$	9.68143e10			0.312597
$747$		0			0
$748$	−3.67541e10	−	3.67541e10i	−0.117408	−	0.117408i
$749$		−	3.21459e11i		−	1.02141i
$750$		0			0
$751$	−5.98277e10			−0.188080			−0.0940400	−	0.995568i	$-0.529978\pi$
$751$	−5.98277e10			−0.188080			−0.0940400	+	0.995568i	$0.529978\pi$
$752$	3.71818e10	−	3.71818e10i	0.116268	−	0.116268i
$753$		0			0
$754$		−	1.86739e10i		−	0.0577763i
$755$	−1.34969e10	+	1.06673e10i	−0.0415379	+	0.0328297i
$756$		0			0
$757$	−2.88999e11	+	2.88999e11i	−0.880060	+	0.880060i	−0.993540	−	0.113480i	$-0.963800\pi$
$757$	−2.88999e11	+	2.88999e11i	−0.880060	+	0.880060i	0.113480	+	0.993540i	$0.463800\pi$
$758$	3.41752e10	+	3.41752e10i	0.103522	+	0.103522i
$759$		0			0
$760$	1.52410e10	−	1.30158e11i	0.0456836	−	0.390136i
$761$	1.15311e11			0.343819			0.171910	−	0.985113i	$-0.445006\pi$
$761$	1.15311e11			0.343819			0.171910	+	0.985113i	$0.445006\pi$
$762$		0			0
$763$	2.44966e11	+	2.44966e11i	0.722783	+	0.722783i
$764$			7.11748e10i			0.208907i
$765$		0			0
$766$	4.29450e11			1.24738
$767$	−3.13755e11	+	3.13755e11i	−0.906587	+	0.906587i
$768$		0			0
$769$			1.71633e11i			0.490791i	0.969423	+	0.245395i	$0.0789178\pi$
$769$			1.71633e11i			0.490791i	−0.969423	+	0.245395i	$0.921082\pi$
$770$	−8.74181e10	−	1.10606e11i	−0.248679	−	0.314641i
$771$		0			0
$772$	2.21153e10	−	2.21153e10i	0.0622621	−	0.0622621i
$773$	3.60143e11	+	3.60143e11i	1.00869	+	1.00869i	0.999962	+	0.00872501i	$0.00277729\pi$
$773$	3.60143e11	+	3.60143e11i	1.00869	+	1.00869i	0.00872501	+	0.999962i	$0.497223\pi$
$774$		0			0
$775$	2.20330e10	−	9.27905e10i	0.0610754	−	0.257215i
$776$	−5.87553e10			−0.162032
$777$		0			0
$778$	−7.33273e9	−	7.33273e9i	−0.0200146	−	0.0200146i
$779$			6.04232e11i			1.64079i
$780$		0			0
$781$	1.40250e11			0.376963
$782$	4.45928e10	−	4.45928e10i	0.119244	−	0.119244i
$783$		0			0
$784$			1.31171e11i			0.347196i
$785$	−3.31653e10	+	2.83230e11i	−0.0873383	+	0.745866i
$786$		0			0
$787$	3.81822e11	−	3.81822e11i	0.995318	−	0.995318i	−0.00467136	−	0.999989i	$-0.501487\pi$
$787$	3.81822e11	−	3.81822e11i	0.995318	−	0.995318i	0.999989	+	0.00467136i	$0.00148694\pi$
$788$	−1.77953e11	−	1.77953e11i	−0.461530	−	0.461530i
$789$		0			0
$790$	2.16026e10	+	2.52959e9i	0.0554622	+	0.00649444i
$791$	6.15310e11			1.57177
$792$		0			0
$793$	5.65054e11	+	5.65054e11i	1.42888	+	1.42888i
$794$		−	8.38543e10i		−	0.210981i
$795$		0			0
$796$	2.30429e10			0.0573964
$797$	−4.32433e11	+	4.32433e11i	−1.07173	+	1.07173i	−0.0745090	+	0.997220i	$0.523739\pi$
$797$	−4.32433e11	+	4.32433e11i	−1.07173	+	1.07173i	−0.997220	+	0.0745090i	$0.976261\pi$
$798$		0			0
$799$		−	2.42573e11i		−	0.595189i
$800$	3.79864e10	+	6.16434e10i	0.0927403	+	0.150497i
$801$		0			0
$802$	−1.41489e11	+	1.41489e11i	−0.342000	+	0.342000i
$803$	9.98949e10	+	9.98949e10i	0.240260	+	0.240260i
$804$		0			0
$805$	1.34195e11	−	1.06062e11i	0.319561	−	0.252567i
$806$	1.09272e11			0.258922
$807$		0			0
$808$	8.14346e10	+	8.14346e10i	0.191057	+	0.191057i
$809$		−	4.04427e11i		−	0.944160i	−0.881556	−	0.472080i	$-0.843503\pi$
$809$		−	4.04427e11i		−	0.944160i	0.881556	−	0.472080i	$-0.156497\pi$
$810$		0			0
$811$	−6.23463e11			−1.44121			−0.720605	−	0.693346i	$-0.756136\pi$
$811$	−6.23463e11			−1.44121			−0.720605	+	0.693346i	$0.756136\pi$
$812$	1.40138e10	−	1.40138e10i	0.0322353	−	0.0322353i
$813$		0			0
$814$		−	1.72488e11i		−	0.392882i
$815$	2.07777e11	+	2.43299e10i	0.470941	+	0.0551456i
$816$		0			0
$817$	−5.81245e11	+	5.81245e11i	−1.30458	+	1.30458i
$818$	1.74602e10	+	1.74602e10i	0.0389975	+	0.0389975i
$819$		0			0
$820$	−2.07015e11	−	2.61927e11i	−0.457875	−	0.579328i
$821$	−3.67266e11			−0.808366			−0.404183	−	0.914678i	$-0.632444\pi$
$821$	−3.67266e11			−0.808366			−0.404183	+	0.914678i	$0.632444\pi$
$822$		0			0
$823$	1.17460e11	+	1.17460e11i	0.256030	+	0.256030i	0.823437	−	0.567407i	$-0.192053\pi$
$823$	1.17460e11	+	1.17460e11i	0.256030	+	0.256030i	−0.567407	+	0.823437i	$0.692053\pi$
$824$		−	1.01675e11i		−	0.220550i
$825$		0			0
$826$	−4.70914e11			−1.01163
$827$	5.29740e11	−	5.29740e11i	1.13251	−	1.13251i	0.142748	−	0.989759i	$-0.454406\pi$
$827$	5.29740e11	−	5.29740e11i	1.13251	−	1.13251i	0.989759	−	0.142748i	$-0.0455939\pi$
$828$		0			0
$829$		−	2.39704e11i		−	0.507525i	−0.967267	−	0.253762i	$-0.918332\pi$
$829$		−	2.39704e11i		−	0.507525i	0.967267	−	0.253762i	$-0.0816681\pi$
$830$	−1.89485e11	+	1.49761e11i	−0.399267	+	0.315563i
$831$		0			0
$832$	−5.86631e10	+	5.86631e10i	−0.122425	+	0.122425i
$833$	4.27878e11	+	4.27878e11i	0.888669	+	0.888669i
$834$		0			0
$835$	5.60694e10	−	4.78831e11i	0.115340	−	0.984999i
$836$	−9.95720e10			−0.203851
$837$		0			0
$838$	−2.41954e11	−	2.41954e11i	−0.490634	−	0.490634i
$839$		−	5.22857e11i		−	1.05520i	−0.849493	−	0.527601i	$-0.823092\pi$
$839$		−	5.22857e11i		−	1.05520i	0.849493	−	0.527601i	$-0.176908\pi$
$840$		0			0
$841$	4.98506e11			0.996520
$842$	1.42272e11	−	1.42272e11i	0.283055	−	0.283055i
$843$		0			0
$844$			5.34594e10i			0.105355i
$845$	2.90355e11	+	3.67372e11i	0.569511	+	0.720576i
$846$		0			0
$847$	4.86735e11	−	4.86735e11i	0.945712	−	0.945712i
$848$	−6.10687e10	−	6.10687e10i	−0.118096	−	0.118096i
$849$		0			0
$850$	3.24990e11	+	7.71686e10i	0.622579	+	0.147831i
$851$	2.09276e11			0.399025
$852$		0			0
$853$	−2.94110e11	−	2.94110e11i	−0.555537	−	0.555537i	0.372496	−	0.928034i	$-0.378502\pi$
$853$	−2.94110e11	−	2.94110e11i	−0.555537	−	0.555537i	−0.928034	+	0.372496i	$0.878502\pi$
$854$			8.48087e11i			1.59444i
$855$		0			0
$856$	1.25447e11			0.233650
$857$	1.69558e11	−	1.69558e11i	0.314336	−	0.314336i	−0.532251	−	0.846587i	$-0.678654\pi$
$857$	1.69558e11	−	1.69558e11i	0.314336	−	0.314336i	0.846587	+	0.532251i	$0.178654\pi$
$858$		0			0
$859$			3.81187e11i			0.700109i	0.936729	+	0.350055i	$0.113837\pi$
$859$			3.81187e11i			0.700109i	−0.936729	+	0.350055i	$0.886163\pi$
$860$	5.28224e10	−	4.51102e11i	0.0965661	−	0.824671i
$861$		0			0
$862$	1.70174e11	−	1.70174e11i	0.308221	−	0.308221i
$863$	−8.42734e10	−	8.42734e10i	−0.151931	−	0.151931i	0.627049	−	0.778980i	$-0.284263\pi$
$863$	−8.42734e10	−	8.42734e10i	−0.151931	−	0.151931i	−0.778980	+	0.627049i	$0.784263\pi$
$864$		0			0
$865$	5.63300e11	+	6.59605e10i	1.00618	+	0.117820i
$866$	−3.59693e11			−0.639529
$867$		0			0
$868$	8.20029e10	+	8.20029e10i	0.144461	+	0.144461i
$869$		−	1.65262e10i		−	0.0289797i
$870$		0			0
$871$	−7.32085e11			−1.27200
$872$	−9.55962e10	+	9.55962e10i	−0.165339	+	0.165339i
$873$		0			0
$874$		−	1.20808e11i		−	0.207038i
$875$	8.51151e11	+	3.10402e11i	1.45203	+	0.529533i
$876$		0			0
$877$	3.72176e10	−	3.72176e10i	0.0629144	−	0.0629144i	−0.674950	−	0.737864i	$-0.735835\pi$
$877$	3.72176e10	−	3.72176e10i	0.0629144	−	0.0629144i	0.737864	+	0.674950i	$0.235835\pi$
$878$	1.17523e11	+	1.17523e11i	0.197763	+	0.197763i
$879$		0			0
$880$	4.31631e10	−	3.41142e10i	0.0719751	−	0.0568859i
$881$	4.91908e10			0.0816545			0.0408273	−	0.999166i	$-0.487001\pi$
$881$	4.91908e10			0.0816545			0.0408273	+	0.999166i	$0.487001\pi$
$882$		0			0
$883$	4.82360e11	+	4.82360e11i	0.793467	+	0.793467i	0.982056	−	0.188589i	$-0.0603914\pi$
$883$	4.82360e11	+	4.82360e11i	0.793467	+	0.793467i	−0.188589	+	0.982056i	$0.560391\pi$
$884$			3.82715e11i			0.626710i
$885$		0			0
$886$	−2.87925e11			−0.467245
$887$	−7.58872e11	+	7.58872e11i	−1.22595	+	1.22595i	−0.260472	+	0.965481i	$0.583878\pi$
$887$	−7.58872e11	+	7.58872e11i	−1.22595	+	1.22595i	−0.965481	+	0.260472i	$0.916122\pi$
$888$		0			0
$889$			6.11301e10i			0.0978697i
$890$	4.04964e10	+	4.74198e9i	0.0645440	+	0.00755788i
$891$		0			0
$892$	1.52322e11	−	1.52322e11i	0.240605	−	0.240605i
$893$	−3.28582e11	−	3.28582e11i	−0.516699	−	0.516699i
$894$		0			0
$895$	3.64710e11	+	4.61451e11i	0.568402	+	0.719173i
$896$	−8.80472e10			−0.136610
$897$		0			0
$898$	−2.24981e11	−	2.24981e11i	−0.345972	−	0.345972i
$899$		−	1.01867e10i		−	0.0155953i
$900$		0			0
$901$	−3.98410e11			−0.604548
$902$	−1.79373e11	+	1.79373e11i	−0.270975	+	0.270975i
$903$		0			0
$904$			2.40120e11i			0.359546i
$905$	−2.00816e11	+	1.58716e11i	−0.299367	+	0.236606i
$906$		0			0
$907$	−8.25250e11	+	8.25250e11i	−1.21943	+	1.21943i	−0.251597	+	0.967832i	$0.580956\pi$
$907$	−8.25250e11	+	8.25250e11i	−1.21943	+	1.21943i	−0.967832	+	0.251597i	$0.919044\pi$
$908$	3.45279e11	+	3.45279e11i	0.507957	+	0.507957i
$909$		0			0
$910$	−1.20726e11	+	1.03100e12i	−0.176050	+	1.50346i
$911$	−5.86650e11			−0.851737			−0.425869	−	0.904785i	$-0.640031\pi$
$911$	−5.86650e11			−0.851737			−0.425869	+	0.904785i	$0.640031\pi$
$912$		0			0
$913$	1.29763e11	+	1.29763e11i	0.186753	+	0.186753i
$914$		−	8.51548e11i		−	1.22018i
$915$		0			0
$916$	−6.27612e11			−0.891475
$917$	1.00641e12	−	1.00641e12i	1.42330	−	1.42330i
$918$		0			0
$919$		−	1.27566e12i		−	1.78843i	−0.447640	−	0.894214i	$-0.647735\pi$
$919$		−	1.27566e12i		−	1.78843i	0.447640	−	0.894214i	$-0.352265\pi$
$920$	4.13899e10	+	5.23688e10i	0.0577755	+	0.0731006i
$921$		0			0
$922$	−2.24556e10	+	2.24556e10i	−0.0310743	+	0.0310743i
$923$	−7.30203e11	−	7.30203e11i	−1.00609	−	1.00609i
$924$		0			0
$925$	5.81519e11	+	9.43674e11i	0.794322	+	1.28901i
$926$	−2.94765e11			−0.400896
$927$		0			0
$928$	5.46877e9	+	5.46877e9i	0.00737391	+	0.00737391i
$929$			1.11916e12i			1.50255i	0.659991	+	0.751274i	$0.270560\pi$
$929$			1.11916e12i			1.50255i	−0.659991	+	0.751274i	$0.729440\pi$
$930$		0			0
$931$	1.15918e12			1.54295
$932$	3.33039e11	−	3.33039e11i	0.441399	−	0.441399i
$933$		0			0
$934$		−	1.90857e11i		−	0.250796i
$935$	2.95174e10	−	2.52077e11i	0.0386217	−	0.329828i
$936$		0			0
$937$	3.48571e11	−	3.48571e11i	0.452202	−	0.452202i	−0.443883	−	0.896085i	$-0.646399\pi$
$937$	3.48571e11	−	3.48571e11i	0.452202	−	0.452202i	0.896085	+	0.443883i	$0.146399\pi$
$938$	−5.49391e11	−	5.49391e11i	−0.709693	−	0.709693i
$939$		0			0
$940$	2.55011e11	+	2.98609e10i	0.326623	+	0.0382465i
$941$	−3.10729e11			−0.396299			−0.198150	−	0.980172i	$-0.563493\pi$
$941$	−3.10729e11			−0.396299			−0.198150	+	0.980172i	$0.563493\pi$
$942$		0			0
$943$	−2.17628e11	−	2.17628e11i	−0.275213	−	0.275213i
$944$		−	1.83771e11i		−	0.231413i
$945$		0			0
$946$	−3.45097e11			−0.430900
$947$	4.81109e11	−	4.81109e11i	0.598197	−	0.598197i	−0.341636	−	0.939832i	$-0.610981\pi$
$947$	4.81109e11	−	4.81109e11i	0.598197	−	0.598197i	0.939832	+	0.341636i	$0.110981\pi$
$948$		0			0
$949$		−	1.04019e12i		−	1.28247i
$950$	5.44753e11	−	3.35692e11i	0.668813	−	0.412142i
$951$		0			0
$952$	−2.87208e11	+	2.87208e11i	−0.349662	+	0.349662i
$953$	−2.19961e11	−	2.19961e11i	−0.266670	−	0.266670i	0.561087	−	0.827757i	$-0.310383\pi$
$953$	−2.19961e11	−	2.19961e11i	−0.266670	−	0.266670i	−0.827757	+	0.561087i	$0.810383\pi$
$954$		0			0
$955$	−2.72656e11	+	2.15495e11i	−0.327794	+	0.259074i
$956$	−5.86199e11			−0.701800
$957$		0			0
$958$	−6.46624e11	−	6.46624e11i	−0.767697	−	0.767697i
$959$			7.70338e10i			0.0910767i
$960$		0			0
$961$	−7.93283e11			−0.930110
$962$	−8.98049e11	+	8.98049e11i	−1.04858	+	1.04858i
$963$		0			0
$964$		−	7.45601e11i		−	0.863373i
$965$	1.51677e11	+	1.77609e10i	0.174909	+	0.0204812i
$966$		0			0
$967$	6.94014e11	−	6.94014e11i	0.793711	−	0.793711i	−0.188384	−	0.982095i	$-0.560325\pi$
$967$	6.94014e11	−	6.94014e11i	0.793711	−	0.793711i	0.982095	+	0.188384i	$0.0603251\pi$
$968$	1.89945e11	+	1.89945e11i	0.216334	+	0.216334i
$969$		0			0
$970$	−1.77893e11	−	2.25079e11i	−0.200942	−	0.254243i
$971$	−1.29419e12			−1.45587			−0.727935	−	0.685646i	$-0.759520\pi$
$971$	−1.29419e12			−1.45587			−0.727935	+	0.685646i	$0.759520\pi$
$972$		0			0
$973$	1.05043e12	+	1.05043e12i	1.17197	+	1.17197i
$974$		−	1.26902e12i		−	1.41005i
$975$		0			0
$976$	−3.30960e11			−0.364733
$977$	−2.00533e11	+	2.00533e11i	−0.220093	+	0.220093i	−0.808538	−	0.588444i	$-0.799741\pi$
$977$	−2.00533e11	+	2.00533e11i	−0.220093	+	0.220093i	0.588444	+	0.808538i	$0.299741\pi$
$978$		0			0
$979$		−	3.09801e10i		−	0.0337250i
$980$	−5.02490e11	+	3.97146e11i	−0.544783	+	0.430572i
$981$		0			0
$982$	−4.80729e11	+	4.80729e11i	−0.516957	+	0.516957i
$983$	−4.14637e11	−	4.14637e11i	−0.444072	−	0.444072i	0.449306	−	0.893378i	$-0.351671\pi$
$983$	−4.14637e11	−	4.14637e11i	−0.444072	−	0.444072i	−0.893378	+	0.449306i	$0.851671\pi$
$984$		0			0
$985$	1.42915e11	−	1.22049e12i	0.151821	−	1.29655i
$986$	3.56780e10			0.0377479
$987$		0			0
$988$	5.18415e11	+	5.18415e11i	0.544064	+	0.544064i
$989$		−	4.18698e11i		−	0.437638i
$990$		0			0
$991$	−6.51779e11			−0.675780			−0.337890	−	0.941186i	$-0.609713\pi$
$991$	−6.51779e11			−0.675780			−0.337890	+	0.941186i	$0.609713\pi$
$992$	−3.20010e10	+	3.20010e10i	−0.0330459	+	0.0330459i
$993$		0			0
$994$		−	1.09596e12i		−	1.12266i
$995$	6.97667e10	+	8.82725e10i	0.0711796	+	0.0900603i
$996$		0			0
$997$	−6.71342e11	+	6.71342e11i	−0.679459	+	0.679459i	−0.959878	−	0.280419i	$-0.909527\pi$
$997$	−6.71342e11	+	6.71342e11i	−0.679459	+	0.679459i	0.280419	+	0.959878i	$0.409527\pi$
$998$	8.69991e11	+	8.69991e11i	0.876986	+	0.876986i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.9.g.b.73.2		4
3.2	odd	2		10.9.c.a.3.2	✓	4
5.2	odd	4	inner	90.9.g.b.37.2		4
12.11	even	2		80.9.p.b.33.1		4
15.2	even	4		10.9.c.a.7.2	yes	4
15.8	even	4		50.9.c.e.7.1		4
15.14	odd	2		50.9.c.e.43.1		4
60.47	odd	4		80.9.p.b.17.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.9.c.a.3.2	✓	4	3.2	odd	2
10.9.c.a.7.2	yes	4	15.2	even	4
50.9.c.e.7.1		4	15.8	even	4
50.9.c.e.43.1		4	15.14	odd	2
80.9.p.b.17.1		4	60.47	odd	4
80.9.p.b.33.1		4	12.11	even	2
90.9.g.b.37.2		4	5.2	odd	4	inner
90.9.g.b.73.2		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 8.00000i) q^{2} -128.000i q^{4} +(490.341 - 387.544i) q^{5} +(-2624.01 + 2624.01i) q^{7} +(-1024.00 - 1024.00i) q^{8} +(822.379 - 7023.08i) q^{10} -5372.73 q^{11} +(27972.7 + 27972.7i) q^{13} +41984.2i q^{14} -16384.0 q^{16} +(-53444.2 + 53444.2i) q^{17} +144788. i q^{19} +(-49605.6 - 62763.7i) q^{20} +(-42981.8 + 42981.8i) q^{22} +(-52148.7 - 52148.7i) q^{23} +(90244.3 - 380058. i) q^{25} +447564. q^{26} +(335873. + 335873. i) q^{28} -41723.4i q^{29} +244148. q^{31} +(-131072. + 131072. i) q^{32} +855108. i q^{34} +(-269741. + 2.30358e6i) q^{35} +(-2.00653e6 + 2.00653e6i) q^{37} +(1.15830e6 + 1.15830e6i) q^{38} +(-898955. - 105264. i) q^{40} +4.17322e6 q^{41} +(4.01446e6 + 4.01446e6i) q^{43} +687709. i q^{44} -834380. q^{46} +(-2.26940e6 + 2.26940e6i) q^{47} -8.00606e6i q^{49} +(-2.31851e6 - 3.76242e6i) q^{50} +(3.58051e6 - 3.58051e6i) q^{52} +(3.72734e6 + 3.72734e6i) q^{53} +(-2.63447e6 + 2.08217e6i) q^{55} +5.37397e6 q^{56} +(-333787. - 333787. i) q^{58} +1.12165e7i q^{59} +2.02002e7 q^{61} +(1.95319e6 - 1.95319e6i) q^{62} +2.09715e6i q^{64} +(2.45569e7 + 2.87552e6i) q^{65} +(-1.30857e7 + 1.30857e7i) q^{67} +(6.84086e6 + 6.84086e6i) q^{68} +(1.62707e7 + 2.05866e7i) q^{70} -2.61041e7 q^{71} +(-1.85930e7 - 1.85930e7i) q^{73} +3.21044e7i q^{74} +1.85329e7 q^{76} +(1.40981e7 - 1.40981e7i) q^{77} +3.07594e6i q^{79} +(-8.03375e6 + 6.34952e6i) q^{80} +(3.33858e7 - 3.33858e7i) q^{82} +(-2.41522e7 - 2.41522e7i) q^{83} +(-5.49393e6 + 4.69179e7i) q^{85} +6.42313e7 q^{86} +(5.50167e6 + 5.50167e6i) q^{88} +5.76618e6i q^{89} -1.46802e8 q^{91} +(-6.67504e6 + 6.67504e6i) q^{92} +3.63104e7i q^{94} +(5.61117e7 + 7.09955e7i) q^{95} +(2.86891e7 - 2.86891e7i) q^{97} +(-6.40485e7 - 6.40485e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} - 90 q^{5} - 1186 q^{7} - 4096 q^{8} - 1760 q^{10} + 19852 q^{11} + 73704 q^{13} - 65536 q^{16} - 198944 q^{17} - 16640 q^{20} + 158816 q^{22} - 631334 q^{23} + 545600 q^{25} + 1179264 q^{26}+ \cdots - 167860352 q^{98}+O(q^{100}) \) 4 * q + 32 * q^2 - 90 * q^5 - 1186 * q^7 - 4096 * q^8 - 1760 * q^10 + 19852 * q^11 + 73704 * q^13 - 65536 * q^16 - 198944 * q^17 - 16640 * q^20 + 158816 * q^22 - 631334 * q^23 + 545600 * q^25 + 1179264 * q^26 + 151808 * q^28 - 2329892 * q^31 - 524288 * q^32 - 1403870 * q^35 - 976356 * q^37 + 1144000 * q^38 - 40960 * q^40 + 4284652 * q^41 + 7146534 * q^43 - 10101344 * q^46 + 3300186 * q^47 - 7241600 * q^50 + 9434112 * q^52 - 9989164 * q^53 - 21649020 * q^55 + 2428928 * q^56 - 19957760 * q^58 + 85377108 * q^61 - 18639136 * q^62 + 33878940 * q^65 - 57195466 * q^67 + 25464832 * q^68 + 53504320 * q^70 - 113004028 * q^71 - 60875756 * q^73 + 18304000 * q^76 + 90339932 * q^77 + 1474560 * q^80 + 34277216 * q^82 - 71051214 * q^83 + 8601320 * q^85 + 114344544 * q^86 - 20328448 * q^88 - 221467572 * q^91 - 80810752 * q^92 + 159500600 * q^95 + 139631604 * q^97 - 167860352 * q^98

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