LMFDB - Embedded newform 196.9.h.b.117.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,9,Mod(117,196)] 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("196.117"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	196.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$79.8462075720$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 720x^{10} + 409912x^{8} + 71803008x^{6} + 9498639424x^{4} + 342190245888x^{2} + 9948826238976 $ x^12 + 720x^10 + 409912x^8 + 71803008x^6 + 9498639424x^4 + 342190245888*x^2 + 9948826238976
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{7}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.4
Root			$-3.09370 + 5.35844i$ of defining polynomial
Character	$\chi$	$=$	196.117
Dual form			196.9.h.b.129.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(29.0850 - 16.7923i) q^{3} +(288.955 + 166.829i) q^{5} +(-2716.54 + 4705.19i) q^{9} +(12063.8 + 20895.1i) q^{11} +43091.3i q^{13} +11205.7 q^{15} +(48496.3 - 27999.4i) q^{17} +(-180200. - 104039. i) q^{19} +(79871.0 - 138341. i) q^{23} +(-139649. - 241879. i) q^{25} +402815. i q^{27} -326089. q^{29} +(-1.13023e6 + 652539. i) q^{31} +(701752. + 405157. i) q^{33} +(-797445. + 1.38122e6i) q^{37} +(723601. + 1.25331e6i) q^{39} -4.17224e6i q^{41} +1.46924e6 q^{43} +(-1.56992e6 + 906393. i) q^{45} +(-3.56128e6 - 2.05610e6i) q^{47} +(940345. - 1.62873e6i) q^{51} +(-3.28498e6 - 5.68976e6i) q^{53} +8.05034e6i q^{55} -6.98818e6 q^{57} +(1.10715e7 - 6.39213e6i) q^{59} +(1.43674e6 + 829504. i) q^{61} +(-7.18886e6 + 1.24515e7i) q^{65} +(5.43833e6 + 9.41946e6i) q^{67} -5.36486e6i q^{69} -2.55338e7 q^{71} +(-1.55391e7 + 8.97149e6i) q^{73} +(-8.12339e6 - 4.69004e6i) q^{75} +(-2.66151e7 + 4.60987e7i) q^{79} +(-1.10590e7 - 1.91548e7i) q^{81} -2.08752e6i q^{83} +1.86844e7 q^{85} +(-9.48430e6 + 5.47576e6i) q^{87} +(8.56303e7 + 4.94387e7i) q^{89} +(-2.19152e7 + 3.79583e7i) q^{93} +(-3.47132e7 - 6.01251e7i) q^{95} +2.44104e7i q^{97} -1.31087e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18234 q^{9} - 24492 q^{11} - 306816 q^{15} + 11604 q^{23} + 678714 q^{25} + 2528664 q^{29} - 3184332 q^{37} - 5634240 q^{39} - 15566760 q^{43} - 6877824 q^{51} + 8340660 q^{53} - 35901696 q^{57}+ \cdots - 1191795624 q^{99}+O(q^{100}) $ 12 * q + 18234 * q^9 - 24492 * q^11 - 306816 * q^15 + 11604 * q^23 + 678714 * q^25 + 2528664 * q^29 - 3184332 * q^37 - 5634240 * q^39 - 15566760 * q^43 - 6877824 * q^51 + 8340660 * q^53 - 35901696 * q^57 - 84095232 * q^65 - 16579500 * q^67 - 124177704 * q^71 - 186114540 * q^79 - 131284998 * q^81 - 526421760 * q^85 - 638128512 * q^93 - 85912896 * q^95 - 1191795624 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	29.0850	−	16.7923i	0.359075	−	0.207312i	−0.309600	−	0.950867i	$-0.600195\pi$
$3$	29.0850	−	16.7923i	0.359075	−	0.207312i	0.668675	+	0.743555i	$0.266862\pi$
$4$		0			0
$5$	288.955	+	166.829i	0.462329	+	0.266926i	0.713023	−	0.701141i	$-0.247326\pi$
$5$	288.955	+	166.829i	0.462329	+	0.266926i	−0.250694	+	0.968066i	$0.580659\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2716.54	+	4705.19i	−0.414044	+	0.717145i
$10$		0			0
$11$	12063.8	+	20895.1i	0.823973	+	1.42716i	0.902701	+	0.430268i	$0.141581\pi$
$11$	12063.8	+	20895.1i	0.823973	+	1.42716i	−0.0787280	+	0.996896i	$0.525086\pi$
$12$		0			0
$13$			43091.3i			1.50875i	0.656445	+	0.754374i	$0.272059\pi$
$13$			43091.3i			1.50875i	−0.656445	+	0.754374i	$0.727941\pi$
$14$		0			0
$15$	11205.7			0.221347
$16$		0			0
$17$	48496.3	−	27999.4i	0.580648	−	0.335237i	−0.180743	−	0.983530i	$-0.557850\pi$
$17$	48496.3	−	27999.4i	0.580648	−	0.335237i	0.761391	+	0.648293i	$0.224517\pi$
$18$		0			0
$19$	−180200.	−	104039.i	−1.38274	−	0.798326i	−0.390258	−	0.920705i	$-0.627614\pi$
$19$	−180200.	−	104039.i	−1.38274	−	0.798326i	−0.992483	+	0.122379i	$0.960948\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	79871.0	−	138341.i	0.285416	−	0.494354i	−0.687294	−	0.726379i	$-0.741202\pi$
$23$	79871.0	−	138341.i	0.285416	−	0.494354i	0.972710	+	0.232025i	$0.0745350\pi$
$24$		0			0
$25$	−139649.	−	241879.i	−0.357501	−	0.619211i
$26$		0			0
$27$			402815.i			0.757968i
$28$		0			0
$29$	−326089.			−0.461045			−0.230523	−	0.973067i	$-0.574044\pi$
$29$	−326089.			−0.461045			−0.230523	+	0.973067i	$0.574044\pi$
$30$		0			0
$31$	−1.13023e6	+	652539.i	−1.22383	+	0.706577i	−0.965732	−	0.259542i	$-0.916428\pi$
$31$	−1.13023e6	+	652539.i	−1.22383	+	0.706577i	−0.258096	+	0.966119i	$0.583095\pi$
$32$		0			0
$33$	701752.	+	405157.i	0.591736	+	0.341639i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−797445.	+	1.38122e6i	−0.425495	+	0.736978i	−0.996466	−	0.0839914i	$-0.973233\pi$
$37$	−797445.	+	1.38122e6i	−0.425495	+	0.736978i	0.570972	+	0.820970i	$0.306567\pi$
$38$		0			0
$39$	723601.	+	1.25331e6i	0.312781	+	0.541753i
$40$		0			0
$41$		−	4.17224e6i		−	1.47650i	−0.674526	−	0.738251i	$-0.735652\pi$
$41$		−	4.17224e6i		−	1.47650i	0.674526	−	0.738251i	$-0.264348\pi$
$42$		0			0
$43$	1.46924e6			0.429754			0.214877	−	0.976641i	$-0.431065\pi$
$43$	1.46924e6			0.429754			0.214877	+	0.976641i	$0.431065\pi$
$44$		0			0
$45$	−1.56992e6	+	906393.i	−0.382849	+	0.221038i
$46$		0			0
$47$	−3.56128e6	−	2.05610e6i	−0.729817	−	0.421360i	0.0885380	−	0.996073i	$-0.471781\pi$
$47$	−3.56128e6	−	2.05610e6i	−0.729817	−	0.421360i	−0.818355	+	0.574713i	$0.805114\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	940345.	−	1.62873e6i	0.138997	−	0.240751i
$52$		0			0
$53$	−3.28498e6	−	5.68976e6i	−0.416322	−	0.721091i	0.579244	−	0.815154i	$-0.303348\pi$
$53$	−3.28498e6	−	5.68976e6i	−0.416322	−	0.721091i	−0.995566	+	0.0940630i	$0.970014\pi$
$54$		0			0
$55$			8.05034e6i			0.879758i
$56$		0			0
$57$	−6.98818e6			−0.662010
$58$		0			0
$59$	1.10715e7	−	6.39213e6i	0.913688	−	0.527518i	0.0320721	−	0.999486i	$-0.489789\pi$
$59$	1.10715e7	−	6.39213e6i	0.913688	−	0.527518i	0.881616	+	0.471968i	$0.156456\pi$
$60$		0			0
$61$	1.43674e6	+	829504.i	0.103767	+	0.0599100i	0.550985	−	0.834515i	$-0.314252\pi$
$61$	1.43674e6	+	829504.i	0.103767	+	0.0599100i	−0.447218	+	0.894425i	$0.647585\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.18886e6	+	1.24515e7i	−0.402723	+	0.697537i
$66$		0			0
$67$	5.43833e6	+	9.41946e6i	0.269877	+	0.467441i	0.968830	−	0.247727i	$-0.0796835\pi$
$67$	5.43833e6	+	9.41946e6i	0.269877	+	0.467441i	−0.698953	+	0.715168i	$0.746350\pi$
$68$		0			0
$69$		−	5.36486e6i		−	0.236680i
$70$		0			0
$71$	−2.55338e7			−1.00480			−0.502402	−	0.864634i	$-0.667550\pi$
$71$	−2.55338e7			−1.00480			−0.502402	+	0.864634i	$0.667550\pi$
$72$		0			0
$73$	−1.55391e7	+	8.97149e6i	−0.547185	+	0.315917i	−0.747986	−	0.663715i	$-0.768979\pi$
$73$	−1.55391e7	+	8.97149e6i	−0.547185	+	0.315917i	0.200801	+	0.979632i	$0.435645\pi$
$74$		0			0
$75$	−8.12339e6	−	4.69004e6i	−0.256739	−	0.148229i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−2.66151e7	+	4.60987e7i	−0.683313	+	1.18353i	0.290650	+	0.956829i	$0.406128\pi$
$79$	−2.66151e7	+	4.60987e7i	−0.683313	+	1.18353i	−0.973964	+	0.226704i	$0.927205\pi$
$80$		0			0
$81$	−1.10590e7	−	1.91548e7i	−0.256908	−	0.444977i
$82$		0			0
$83$		−	2.08752e6i		−	0.0439864i	−0.999758	−	0.0219932i	$-0.992999\pi$
$83$		−	2.08752e6i		−	0.0439864i	0.999758	−	0.0219932i	$-0.00700122\pi$
$84$		0			0
$85$	1.86844e7			0.357934
$86$		0			0
$87$	−9.48430e6	+	5.47576e6i	−0.165550	+	0.0955801i
$88$		0			0
$89$	8.56303e7	+	4.94387e7i	1.36479	+	0.787964i	0.990258	−	0.139248i	$-0.0444684\pi$
$89$	8.56303e7	+	4.94387e7i	1.36479	+	0.787964i	0.374537	+	0.927212i	$0.377802\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.19152e7	+	3.79583e7i	−0.292964	+	0.507428i
$94$		0			0
$95$	−3.47132e7	−	6.01251e7i	−0.426187	−	0.738178i
$96$		0			0
$97$			2.44104e7i			0.275733i	0.990451	+	0.137867i	$0.0440245\pi$
$97$			2.44104e7i			0.275733i	−0.990451	+	0.137867i	$0.955976\pi$
$98$		0			0
$99$	−1.31087e8			−1.36464
$100$		0			0
$101$	7.17174e7	−	4.14061e7i	0.689190	−	0.397904i	−0.114118	−	0.993467i	$-0.536404\pi$
$101$	7.17174e7	−	4.14061e7i	0.689190	−	0.397904i	0.803309	+	0.595563i	$0.203071\pi$
$102$		0			0
$103$	−7.55715e7	−	4.36312e7i	−0.671443	−	0.387658i	0.125180	−	0.992134i	$-0.460049\pi$
$103$	−7.55715e7	−	4.36312e7i	−0.671443	−	0.387658i	−0.796623	+	0.604476i	$0.793382\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.07324e8	+	1.85891e8i	−0.818769	+	1.41815i	0.0878202	+	0.996136i	$0.472010\pi$
$107$	−1.07324e8	+	1.85891e8i	−0.818769	+	1.41815i	−0.906589	+	0.422014i	$0.861323\pi$
$108$		0			0
$109$	4.22065e7	+	7.31038e7i	0.299002	+	0.517886i	0.975908	−	0.218183i	$-0.0700131\pi$
$109$	4.22065e7	+	7.31038e7i	0.299002	+	0.517886i	−0.676906	+	0.736069i	$0.736680\pi$
$110$		0			0
$111$			5.35636e7i			0.352840i
$112$		0			0
$113$	−2.83510e8			−1.73882			−0.869411	−	0.494090i	$-0.835501\pi$
$113$	−2.83510e8			−1.73882			−0.869411	+	0.494090i	$0.835501\pi$
$114$		0			0
$115$	4.61583e7	−	2.66495e7i	0.263912	−	0.152370i
$116$		0			0
$117$	−2.02753e8	−	1.17059e8i	−1.08199	−	0.624687i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.83891e8	+	3.18508e8i	−0.857864	+	1.48586i
$122$		0			0
$123$	−7.00613e7	−	1.21350e8i	−0.306096	−	0.530174i
$124$		0			0
$125$		−	2.23525e8i		−	0.915556i
$126$		0			0
$127$	−6.18914e7			−0.237911			−0.118956	−	0.992900i	$-0.537955\pi$
$127$	−6.18914e7			−0.237911			−0.118956	+	0.992900i	$0.537955\pi$
$128$		0			0
$129$	4.27330e7	−	2.46719e7i	0.154314	−	0.0890930i
$130$		0			0
$131$	3.72190e8	+	2.14884e8i	1.26380	+	0.729658i	0.973808	−	0.227370i	$-0.0730128\pi$
$131$	3.72190e8	+	2.14884e8i	1.26380	+	0.729658i	0.289996	+	0.957028i	$0.406346\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−6.72011e7	+	1.16396e8i	−0.202321	+	0.350430i
$136$		0			0
$137$	−1.46094e8	−	2.53043e8i	−0.414716	−	0.718309i	0.580682	−	0.814130i	$-0.302786\pi$
$137$	−1.46094e8	−	2.53043e8i	−0.414716	−	0.718309i	−0.995399	+	0.0958207i	$0.969452\pi$
$138$		0			0
$139$		−	9.34937e6i		−	0.0250451i	−0.999922	−	0.0125226i	$-0.996014\pi$
$139$		−	9.34937e6i		−	0.0250451i	0.999922	−	0.0125226i	$-0.00398616\pi$
$140$		0			0
$141$	−1.38106e8			−0.349412
$142$		0			0
$143$	−9.00398e8	+	5.19845e8i	−2.15323	+	1.24317i
$144$		0			0
$145$	−9.42251e7	−	5.44009e7i	−0.213154	−	0.123065i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.06007e8	+	7.03224e8i	−0.823736	+	1.42675i	0.0791449	+	0.996863i	$0.474781\pi$
$149$	−4.06007e8	+	7.03224e8i	−0.823736	+	1.42675i	−0.902881	+	0.429890i	$0.858552\pi$
$150$		0			0
$151$	−5.38132e6	−	9.32072e6i	−0.0103510	−	0.0179284i	0.860804	−	0.508937i	$-0.169962\pi$
$151$	−5.38132e6	−	9.32072e6i	−0.0103510	−	0.0179284i	−0.871154	+	0.491009i	$0.836628\pi$
$152$		0			0
$153$			3.04246e8i			0.555212i
$154$		0			0
$155$	−4.35448e8			−0.754414
$156$		0			0
$157$	3.97061e8	−	2.29243e8i	0.653520	−	0.377310i	−0.136283	−	0.990670i	$-0.543516\pi$
$157$	3.97061e8	−	2.29243e8i	0.653520	−	0.377310i	0.789804	+	0.613360i	$0.210182\pi$
$158$		0			0
$159$	−1.91088e8	−	1.10325e8i	−0.298981	−	0.172617i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.28605e8	+	5.69161e8i	−0.465505	+	0.806278i	−0.999224	−	0.0393835i	$-0.987461\pi$
$163$	−3.28605e8	+	5.69161e8i	−0.465505	+	0.806278i	0.533719	+	0.845662i	$0.320794\pi$
$164$		0			0
$165$	1.35183e8	+	2.34144e8i	0.182384	+	0.315899i
$166$		0			0
$167$		−	4.94686e8i		−	0.636010i	−0.948089	−	0.318005i	$-0.896987\pi$
$167$		−	4.94686e8i		−	0.636010i	0.948089	−	0.318005i	$-0.103013\pi$
$168$		0			0
$169$	−1.04113e9			−1.27632
$170$		0			0
$171$	9.79043e8	−	5.65251e8i	1.14503	−	0.661084i
$172$		0			0
$173$	−6.87736e8	−	3.97065e8i	−0.767781	−	0.443279i	0.0643014	−	0.997931i	$-0.479518\pi$
$173$	−6.87736e8	−	3.97065e8i	−0.767781	−	0.443279i	−0.832082	+	0.554652i	$0.812851\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.14676e8	−	3.71831e8i	0.218721	−	0.378837i
$178$		0			0
$179$	−9.27018e7	−	1.60564e8i	−0.0902976	−	0.156400i	0.817339	−	0.576157i	$-0.195448\pi$
$179$	−9.27018e7	−	1.60564e8i	−0.0902976	−	0.156400i	−0.907636	+	0.419757i	$0.862115\pi$
$180$		0			0
$181$			1.44977e9i			1.35078i	0.737462	+	0.675389i	$0.236024\pi$
$181$			1.44977e9i			1.35078i	−0.737462	+	0.675389i	$0.763976\pi$
$182$		0			0
$183$	5.57170e7			0.0496802
$184$		0			0
$185$	−4.60852e8	+	2.66073e8i	−0.393437	+	0.227151i
$186$		0			0
$187$	1.17010e9	+	6.75557e8i	0.956878	+	0.552454i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.69822e7	−	9.86960e7i	0.0428159	−	0.0741594i	−0.843823	−	0.536621i	$-0.819700\pi$
$191$	5.69822e7	−	9.86960e7i	0.0428159	−	0.0741594i	0.886639	+	0.462462i	$0.153034\pi$
$192$		0			0
$193$	−4.63518e8	−	8.02837e8i	−0.334070	−	0.578626i	0.649236	−	0.760587i	$-0.275089\pi$
$193$	−4.63518e8	−	8.02837e8i	−0.334070	−	0.578626i	−0.983306	+	0.181961i	$0.941756\pi$
$194$		0			0
$195$			4.82869e8i			0.333957i
$196$		0			0
$197$	2.50846e9			1.66549			0.832747	−	0.553654i	$-0.186767\pi$
$197$	2.50846e9			1.66549			0.832747	+	0.553654i	$0.186767\pi$
$198$		0			0
$199$	1.13458e9	−	6.55049e8i	0.723472	−	0.417697i	−0.0925571	−	0.995707i	$-0.529504\pi$
$199$	1.13458e9	−	6.55049e8i	0.723472	−	0.417697i	0.816029	+	0.578010i	$0.196171\pi$
$200$		0			0
$201$	3.16348e8	+	1.82644e8i	0.193812	+	0.111898i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.96049e8	−	1.20559e9i	0.394116	−	0.682629i
$206$		0			0
$207$	4.33946e8	+	7.51616e8i	0.236349	+	0.409369i
$208$		0			0
$209$		−	5.02040e9i		−	2.63120i
$210$		0			0
$211$	−9.73665e8			−0.491224			−0.245612	−	0.969368i	$-0.578989\pi$
$211$	−9.73665e8			−0.491224			−0.245612	+	0.969368i	$0.578989\pi$
$212$		0			0
$213$	−7.42651e8	+	4.28770e8i	−0.360800	+	0.208308i
$214$		0			0
$215$	4.24546e8	+	2.45112e8i	0.198687	+	0.114712i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.01303e8	+	5.21872e8i	−0.130987	+	0.226876i
$220$		0			0
$221$	1.20653e9	+	2.08977e9i	0.505789	+	0.876052i
$222$		0			0
$223$			1.64534e9i			0.665329i	0.943045	+	0.332665i	$0.107948\pi$
$223$			1.64534e9i			0.665329i	−0.943045	+	0.332665i	$0.892052\pi$
$224$		0			0
$225$	1.51745e9			0.592085
$226$		0			0
$227$	−5.18290e8	+	2.99235e8i	−0.195195	+	0.112696i	−0.594412	−	0.804160i	$-0.702615\pi$
$227$	−5.18290e8	+	2.99235e8i	−0.195195	+	0.112696i	0.399217	+	0.916856i	$0.369282\pi$
$228$		0			0
$229$	4.62374e8	+	2.66951e8i	0.168132	+	0.0970712i	0.581705	−	0.813400i	$-0.302386\pi$
$229$	4.62374e8	+	2.66951e8i	0.168132	+	0.0970712i	−0.413573	+	0.910471i	$0.635719\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.20796e9	−	2.09225e9i	0.409854	−	0.709888i	−0.585019	−	0.811019i	$-0.698913\pi$
$233$	1.20796e9	−	2.09225e9i	0.409854	−	0.709888i	0.994873	+	0.101132i	$0.0322464\pi$
$234$		0			0
$235$	−6.86033e8	−	1.18824e9i	−0.224944	−	0.389614i
$236$		0			0
$237$			1.78771e9i			0.566636i
$238$		0			0
$239$	1.20541e9			0.369440			0.184720	−	0.982791i	$-0.440862\pi$
$239$	1.20541e9			0.369440			0.184720	+	0.982791i	$0.440862\pi$
$240$		0			0
$241$	−2.39853e9	+	1.38479e9i	−0.711013	+	0.410504i	−0.811436	−	0.584441i	$-0.801314\pi$
$241$	−2.39853e9	+	1.38479e9i	−0.711013	+	0.410504i	0.100423	+	0.994945i	$0.467980\pi$
$242$		0			0
$243$	−2.93210e9	−	1.69285e9i	−0.840918	−	0.485504i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.48316e9	−	7.76507e9i	1.20447	−	2.08621i
$248$		0			0
$249$	−3.50542e7	−	6.07157e7i	−0.00911890	−	0.0157944i
$250$		0			0
$251$			5.72275e9i			1.44182i	0.693031	+	0.720908i	$0.256275\pi$
$251$			5.72275e9i			1.44182i	−0.693031	+	0.720908i	$0.743725\pi$
$252$		0			0
$253$	3.85419e9			0.940700
$254$		0			0
$255$	5.43436e8	−	3.13753e8i	0.128525	−	0.0742039i
$256$		0			0
$257$	2.02347e8	+	1.16825e8i	0.0463835	+	0.0267796i	0.523012	−	0.852325i	$-0.324808\pi$
$257$	2.02347e8	+	1.16825e8i	0.0463835	+	0.0267796i	−0.476629	+	0.879105i	$0.658141\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	8.85833e8	−	1.53431e9i	0.190893	−	0.330636i
$262$		0			0
$263$	−1.52500e8	−	2.64137e8i	−0.0318747	−	0.0552086i	0.849648	−	0.527350i	$-0.176814\pi$
$263$	−1.52500e8	−	2.64137e8i	−0.0318747	−	0.0552086i	−0.881523	+	0.472142i	$0.843481\pi$
$264$		0			0
$265$		−	2.19211e9i		−	0.444508i
$266$		0			0
$267$	3.32075e9			0.653417
$268$		0			0
$269$	5.30888e9	−	3.06509e9i	1.01390	−	0.585374i	0.101567	−	0.994829i	$-0.467614\pi$
$269$	5.30888e9	−	3.06509e9i	1.01390	−	0.585374i	0.912331	+	0.409455i	$0.134281\pi$
$270$		0			0
$271$	−2.97369e9	−	1.71686e9i	−0.551339	−	0.318316i	0.198323	−	0.980137i	$-0.436451\pi$
$271$	−2.97369e9	−	1.71686e9i	−0.551339	−	0.318316i	−0.749662	+	0.661821i	$0.769784\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.36939e9	−	5.83596e9i	0.589143	−	1.02043i
$276$		0			0
$277$	3.65202e9	+	6.32549e9i	0.620318	+	1.07442i	0.989426	+	0.145036i	$0.0463297\pi$
$277$	3.65202e9	+	6.32549e9i	0.620318	+	1.07442i	−0.369109	+	0.929386i	$0.620337\pi$
$278$		0			0
$279$		−	7.09059e9i		−	1.17022i
$280$		0			0
$281$	4.46382e9			0.715947			0.357974	−	0.933732i	$-0.383468\pi$
$281$	4.46382e9			0.715947			0.357974	+	0.933732i	$0.383468\pi$
$282$		0			0
$283$	−4.34990e9	+	2.51142e9i	−0.678163	+	0.391537i	−0.799162	−	0.601115i	$-0.794723\pi$
$283$	−4.34990e9	+	2.51142e9i	−0.678163	+	0.391537i	0.121000	+	0.992653i	$0.461390\pi$
$284$		0			0
$285$	−2.01927e9	−	1.16583e9i	−0.306066	−	0.176707i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−1.91995e9	+	3.32545e9i	−0.275232	+	0.476715i
$290$		0			0
$291$	4.09906e8	+	7.09979e8i	0.0571627	+	0.0990087i
$292$		0			0
$293$			4.99782e9i			0.678125i	0.940764	+	0.339063i	$0.110110\pi$
$293$			4.99782e9i			0.678125i	−0.940764	+	0.339063i	$0.889890\pi$
$294$		0			0
$295$	4.26556e9			0.563232
$296$		0			0
$297$	−8.41687e9	+	4.85948e9i	−1.08174	+	0.624546i
$298$		0			0
$299$	5.96128e9	+	3.44175e9i	0.745856	+	0.430620i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.39060e9	−	2.40859e9i	0.164980	−	0.285755i
$304$		0			0
$305$	2.76770e8	+	4.79379e8i	0.0319830	+	0.0553962i
$306$		0			0
$307$		−	1.40127e10i		−	1.57750i	−0.614714	−	0.788750i	$-0.710729\pi$
$307$		−	1.40127e10i		−	1.57750i	0.614714	−	0.788750i	$-0.289271\pi$
$308$		0			0
$309$	−2.93067e9			−0.321464
$310$		0			0
$311$	7.96537e9	−	4.59881e9i	0.851461	−	0.491591i	−0.00968271	−	0.999953i	$-0.503082\pi$
$311$	7.96537e9	−	4.59881e9i	0.851461	−	0.491591i	0.861143	+	0.508362i	$0.169749\pi$
$312$		0			0
$313$	1.42010e10	+	8.19895e9i	1.47959	+	0.854242i	0.999733	−	0.0231053i	$-0.00735529\pi$
$313$	1.42010e10	+	8.19895e9i	1.47959	+	0.854242i	0.479857	+	0.877347i	$0.340689\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.75687e9	−	8.23915e9i	0.471069	−	0.815916i	−0.528383	−	0.849006i	$-0.677202\pi$
$317$	4.75687e9	−	8.23915e9i	0.471069	−	0.815916i	0.999452	+	0.0330904i	$0.0105349\pi$
$318$		0			0
$319$	−3.93386e9	−	6.81365e9i	−0.379889	−	0.657987i
$320$		0			0
$321$			7.20885e9i			0.678962i
$322$		0			0
$323$	−1.16521e10			−1.07052
$324$		0			0
$325$	1.04229e10	−	6.01766e9i	0.934232	−	0.539379i
$326$		0			0
$327$	2.45516e9	+	1.41748e9i	0.214728	+	0.123973i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.45808e9	+	4.25751e9i	−0.204778	+	0.354686i	−0.950062	−	0.312061i	$-0.898981\pi$
$331$	−2.45808e9	+	4.25751e9i	−0.204778	+	0.354686i	0.745284	+	0.666747i	$0.232314\pi$
$332$		0			0
$333$	−4.33258e9	−	7.50426e9i	−0.352347	−	0.610282i
$334$		0			0
$335$			3.62907e9i			0.288149i
$336$		0			0
$337$	2.07250e10			1.60685			0.803425	−	0.595406i	$-0.203009\pi$
$337$	2.07250e10			1.60685			0.803425	+	0.595406i	$0.203009\pi$
$338$		0			0
$339$	−8.24591e9	+	4.76078e9i	−0.624366	+	0.360478i
$340$		0			0
$341$	−2.72697e10	−	1.57442e10i	−2.01680	−	1.16440i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	8.95011e8	−	1.55020e9i	0.0631760	−	0.109424i
$346$		0			0
$347$	1.34176e9	+	2.32400e9i	0.0925459	+	0.160294i	0.908582	−	0.417707i	$-0.137166\pi$
$347$	1.34176e9	+	2.32400e9i	0.0925459	+	0.160294i	−0.816036	+	0.578001i	$0.803833\pi$
$348$		0			0
$349$			1.30154e10i			0.877312i	0.898655	+	0.438656i	$0.144545\pi$
$349$			1.30154e10i			0.877312i	−0.898655	+	0.438656i	$0.855455\pi$
$350$		0			0
$351$	−1.73578e10			−1.14358
$352$		0			0
$353$	1.46630e10	−	8.46571e9i	0.944333	−	0.545211i	0.0530172	−	0.998594i	$-0.483116\pi$
$353$	1.46630e10	−	8.46571e9i	0.944333	−	0.545211i	0.891316	+	0.453383i	$0.149783\pi$
$354$		0			0
$355$	−7.37812e9	−	4.25976e9i	−0.464550	−	0.268208i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.37086e10	+	2.37440e10i	−0.825307	+	1.42947i	0.0763783	+	0.997079i	$0.475664\pi$
$359$	−1.37086e10	+	2.37440e10i	−0.825307	+	1.42947i	−0.901685	+	0.432394i	$0.857669\pi$
$360$		0			0
$361$	1.31563e10	+	2.27874e10i	0.774650	+	1.34173i
$362$		0			0
$363$			1.23518e10i			0.711382i
$364$		0			0
$365$	−5.98680e9			−0.337305
$366$		0			0
$367$	−8.30961e9	+	4.79756e9i	−0.458054	+	0.264457i	−0.711226	−	0.702964i	$-0.751860\pi$
$367$	−8.30961e9	+	4.79756e9i	−0.458054	+	0.264457i	0.253172	+	0.967421i	$0.418526\pi$
$368$		0			0
$369$	1.96312e10	+	1.13341e10i	1.05887	+	0.611336i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.94764e9	+	1.54978e10i	−0.462246	+	0.800634i	−0.999073	−	0.0430589i	$-0.986290\pi$
$373$	−8.94764e9	+	1.54978e10i	−0.462246	+	0.800634i	0.536826	+	0.843693i	$0.319623\pi$
$374$		0			0
$375$	−3.75348e9	−	6.50122e9i	−0.189806	−	0.328753i
$376$		0			0
$377$		−	1.40516e10i		−	0.695601i
$378$		0			0
$379$	−2.75716e10			−1.33630			−0.668152	−	0.744025i	$-0.732914\pi$
$379$	−2.75716e10			−1.33630			−0.668152	+	0.744025i	$0.732914\pi$
$380$		0			0
$381$	−1.80011e9	+	1.03930e9i	−0.0854279	+	0.0493218i
$382$		0			0
$383$	−2.79841e9	−	1.61566e9i	−0.130052	−	0.0750855i	0.433563	−	0.901123i	$-0.357256\pi$
$383$	−2.79841e9	−	1.61566e9i	−0.130052	−	0.0750855i	−0.563614	+	0.826038i	$0.690590\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.99126e9	+	6.91306e9i	−0.177937	+	0.308196i
$388$		0			0
$389$	−3.21609e9	−	5.57042e9i	−0.140452	−	0.243271i	0.787215	−	0.616679i	$-0.211522\pi$
$389$	−3.21609e9	−	5.57042e9i	−0.140452	−	0.243271i	−0.927667	+	0.373408i	$0.878189\pi$
$390$		0			0
$391$		−	8.94535e9i		−	0.382728i
$392$		0			0
$393$	1.44336e10			0.605067
$394$		0			0
$395$	−1.53812e10	+	8.88032e9i	−0.631831	+	0.364788i
$396$		0			0
$397$	2.22744e10	+	1.28601e10i	0.896694	+	0.517707i	0.876126	−	0.482082i	$-0.160119\pi$
$397$	2.22744e10	+	1.28601e10i	0.896694	+	0.517707i	0.0205680	+	0.999788i	$0.493453\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.62503e10	+	2.81463e10i	−0.628469	+	1.08854i	0.359390	+	0.933187i	$0.382985\pi$
$401$	−1.62503e10	+	2.81463e10i	−0.628469	+	1.08854i	−0.987859	+	0.155353i	$0.950349\pi$
$402$		0			0
$403$	−2.81188e10	−	4.87031e10i	−1.06605	−	1.84645i
$404$		0			0
$405$		−	7.37985e9i		−	0.274301i
$406$		0			0
$407$	−3.84809e10			−1.40238
$408$		0			0
$409$	−2.22688e10	+	1.28569e10i	−0.795798	+	0.459454i	−0.842000	−	0.539478i	$-0.818622\pi$
$409$	−2.22688e10	+	1.28569e10i	−0.795798	+	0.459454i	0.0462015	+	0.998932i	$0.485288\pi$
$410$		0			0
$411$	−8.49832e9	−	4.90651e9i	−0.297828	−	0.171951i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3.48258e8	−	6.03201e8i	0.0117411	−	0.0203362i
$416$		0			0
$417$	−1.56997e8	−	2.71927e8i	−0.00519215	−	0.00899307i
$418$		0			0
$419$		−	1.24082e10i		−	0.402581i	−0.979532	−	0.201291i	$-0.935486\pi$
$419$		−	1.24082e10i		−	0.402581i	0.979532	−	0.201291i	$-0.0645136\pi$
$420$		0			0
$421$	−2.05827e10			−0.655201			−0.327600	−	0.944816i	$-0.606240\pi$
$421$	−2.05827e10			−0.655201			−0.327600	+	0.944816i	$0.606240\pi$
$422$		0			0
$423$	1.93487e10	−	1.11710e10i	0.604352	−	0.348923i
$424$		0			0
$425$	−1.35449e10	−	7.82017e9i	−0.415165	−	0.239696i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.74587e10	+	3.02394e10i	−0.515447	+	0.892780i
$430$		0			0
$431$	2.11740e9	+	3.66744e9i	0.0613611	+	0.106280i	0.895074	−	0.445918i	$-0.147123\pi$
$431$	2.11740e9	+	3.66744e9i	0.0613611	+	0.106280i	−0.833713	+	0.552198i	$0.813789\pi$
$432$		0			0
$433$		−	4.21039e10i		−	1.19776i	−0.800838	−	0.598882i	$-0.795612\pi$
$433$		−	4.21039e10i		−	1.19776i	0.800838	−	0.598882i	$-0.204388\pi$
$434$		0			0
$435$	−3.65405e9			−0.102051
$436$		0			0
$437$	−2.87856e10	+	1.66193e10i	−0.789312	+	0.455710i
$438$		0			0
$439$	−3.53153e10	−	2.03893e10i	−0.950835	−	0.548965i	−0.0574951	−	0.998346i	$-0.518311\pi$
$439$	−3.53153e10	−	2.03893e10i	−0.950835	−	0.548965i	−0.893340	+	0.449381i	$0.851645\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.94488e8	−	3.36863e8i	0.00504984	−	0.00874658i	−0.863489	−	0.504367i	$-0.831726\pi$
$443$	1.94488e8	−	3.36863e8i	0.00504984	−	0.00874658i	0.868539	+	0.495620i	$0.165059\pi$
$444$		0			0
$445$	1.64956e10	+	2.85711e10i	0.420656	+	0.728597i
$446$		0			0
$447$			2.72711e10i			0.683081i
$448$		0			0
$449$	2.69794e10			0.663814			0.331907	−	0.943312i	$-0.392308\pi$
$449$	2.69794e10			0.663814			0.331907	+	0.943312i	$0.392308\pi$
$450$		0			0
$451$	8.71794e10	−	5.03330e10i	2.10721	−	1.21660i
$452$		0			0
$453$	−3.13032e8	−	1.80729e8i	−0.00743354	−	0.00429176i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.17232e10	+	5.49462e10i	−0.727298	+	1.25972i	0.230724	+	0.973019i	$0.425891\pi$
$457$	−3.17232e10	+	5.49462e10i	−0.727298	+	1.25972i	−0.958021	+	0.286697i	$0.907443\pi$
$458$		0			0
$459$	1.12786e10	+	1.95351e10i	0.254099	+	0.440113i
$460$		0			0
$461$			5.53281e10i			1.22502i	0.790464	+	0.612508i	$0.209839\pi$
$461$			5.53281e10i			1.22502i	−0.790464	+	0.612508i	$0.790161\pi$
$462$		0			0
$463$	−6.29238e10			−1.36928			−0.684638	−	0.728883i	$-0.740040\pi$
$463$	−6.29238e10			−1.36928			−0.684638	+	0.728883i	$0.740040\pi$
$464$		0			0
$465$	−1.26650e10	+	7.31216e9i	−0.270891	+	0.156399i
$466$		0			0
$467$	8.04918e10	+	4.64719e10i	1.69233	+	0.977065i	0.952634	+	0.304119i	$0.0983619\pi$
$467$	8.04918e10	+	4.64719e10i	1.69233	+	0.977065i	0.739692	+	0.672946i	$0.234971\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.69903e9	−	1.33351e10i	0.156442	−	0.270965i
$472$		0			0
$473$	1.77246e10	+	3.07000e10i	0.354106	+	0.613329i
$474$		0			0
$475$			5.81156e10i			1.14161i
$476$		0			0
$477$	3.56951e10			0.689502
$478$		0			0
$479$	−2.53604e10	+	1.46419e10i	−0.481742	+	0.278134i	−0.721142	−	0.692787i	$-0.756383\pi$
$479$	−2.53604e10	+	1.46419e10i	−0.481742	+	0.278134i	0.239400	+	0.970921i	$0.423049\pi$
$480$		0			0
$481$	−5.95184e10	−	3.43630e10i	−1.11191	−	0.641964i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.07236e9	+	7.05353e9i	−0.0736002	+	0.127479i
$486$		0			0
$487$	−4.93709e10	−	8.55129e10i	−0.877718	−	1.52025i	−0.853839	−	0.520537i	$-0.825732\pi$
$487$	−4.93709e10	−	8.55129e10i	−0.877718	−	1.52025i	−0.0238790	−	0.999715i	$-0.507602\pi$
$488$		0			0
$489$			2.20721e10i			0.386019i
$490$		0			0
$491$	−1.84236e10			−0.316992			−0.158496	−	0.987360i	$-0.550665\pi$
$491$	−1.84236e10			−0.316992			−0.158496	+	0.987360i	$0.550665\pi$
$492$		0			0
$493$	−1.58141e10	+	9.13027e9i	−0.267705	+	0.154560i
$494$		0			0
$495$	−3.78783e10	−	2.18691e10i	−0.630914	−	0.364258i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.64036e10	−	8.03734e10i	0.748427	−	1.29631i	−0.200149	−	0.979765i	$-0.564143\pi$
$499$	4.64036e10	−	8.03734e10i	0.748427	−	1.29631i	0.948576	−	0.316548i	$-0.102524\pi$
$500$		0			0
$501$	−8.30690e9	−	1.43880e10i	−0.131852	−	0.228375i
$502$		0			0
$503$		−	1.06679e11i		−	1.66651i	−0.552886	−	0.833257i	$-0.686473\pi$
$503$		−	1.06679e11i		−	1.66651i	0.552886	−	0.833257i	$-0.313527\pi$
$504$		0			0
$505$	2.76308e10			0.424843
$506$		0			0
$507$	−3.02814e10	+	1.74830e10i	−0.458293	+	0.264596i
$508$		0			0
$509$	7.70815e10	+	4.45031e10i	1.14836	+	0.663008i	0.948488	−	0.316813i	$-0.102613\pi$
$509$	7.70815e10	+	4.45031e10i	1.14836	+	0.663008i	0.199875	+	0.979821i	$0.435946\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	4.19084e10	−	7.25874e10i	0.605106	−	1.04807i
$514$		0			0
$515$	−1.45579e10	−	2.52150e10i	−0.206952	−	0.358451i
$516$		0			0
$517$		−	9.92176e10i		−	1.38876i
$518$		0			0
$519$	−2.66704e10			−0.367588
$520$		0			0
$521$	9.39145e10	−	5.42215e10i	1.27462	−	0.735904i	0.298768	−	0.954326i	$-0.403424\pi$
$521$	9.39145e10	−	5.42215e10i	1.27462	−	0.735904i	0.975854	+	0.218422i	$0.0700910\pi$
$522$		0			0
$523$	3.02486e10	+	1.74640e10i	0.404295	+	0.233420i	0.688335	−	0.725393i	$-0.258342\pi$
$523$	3.02486e10	+	1.74640e10i	0.404295	+	0.233420i	−0.284041	+	0.958812i	$0.591675\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.65414e10	+	6.32915e10i	−0.473742	+	0.820546i
$528$		0			0
$529$	2.63967e10	+	4.57205e10i	0.337076	+	0.583832i
$530$		0			0
$531$			6.94579e10i			0.873662i
$532$		0			0
$533$	1.79787e11			2.22767
$534$		0			0
$535$	−6.20237e10	+	3.58094e10i	−0.757081	+	0.437101i
$536$		0			0
$537$	−5.39247e9	−	3.11334e9i	−0.0648471	−	0.0374395i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	4.23798e10	−	7.34040e10i	0.494732	−	0.856901i	−0.505250	−	0.862973i	$-0.668600\pi$
$541$	4.23798e10	−	7.34040e10i	0.494732	−	0.856901i	0.999982	+	0.00607251i	$0.00193295\pi$
$542$		0			0
$543$	2.43449e10	+	4.21665e10i	0.280032	+	0.485030i
$544$		0			0
$545$			2.81650e10i			0.319245i
$546$		0			0
$547$	−1.64069e10			−0.183264			−0.0916320	−	0.995793i	$-0.529208\pi$
$547$	−1.64069e10			−0.183264			−0.0916320	+	0.995793i	$0.529208\pi$
$548$		0			0
$549$	−7.80594e9	+	4.50676e9i	−0.0859282	+	0.0496107i
$550$		0			0
$551$	5.87612e10	+	3.39258e10i	0.637506	+	0.368065i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−8.93594e9	+	1.54775e10i	−0.0941821	+	0.163128i
$556$		0			0
$557$	8.08990e10	+	1.40121e11i	0.840471	+	1.45574i	0.889497	+	0.456941i	$0.151055\pi$
$557$	8.08990e10	+	1.40121e11i	0.840471	+	1.45574i	−0.0490265	+	0.998797i	$0.515612\pi$
$558$		0			0
$559$			6.33116e10i			0.648390i
$560$		0			0
$561$	4.53765e10			0.458121
$562$		0			0
$563$	−3.64217e10	+	2.10281e10i	−0.362515	+	0.209298i	−0.670184	−	0.742195i	$-0.733785\pi$
$563$	−3.64217e10	+	2.10281e10i	−0.362515	+	0.209298i	0.307668	+	0.951494i	$0.400451\pi$
$564$		0			0
$565$	−8.19218e10	−	4.72976e10i	−0.803907	−	0.464136i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.41355e10	−	1.28406e11i	0.707256	−	1.22500i	−0.258615	−	0.965981i	$-0.583266\pi$
$569$	7.41355e10	−	1.28406e11i	0.707256	−	1.22500i	0.965871	−	0.259023i	$-0.0834007\pi$
$570$		0			0
$571$	4.01866e9	+	6.96052e9i	0.0378039	+	0.0654782i	0.884308	−	0.466903i	$-0.154630\pi$
$571$	4.01866e9	+	6.96052e9i	0.0378039	+	0.0654782i	−0.846504	+	0.532382i	$0.821297\pi$
$572$		0			0
$573$		−	3.82744e9i		−	0.0355050i
$574$		0			0
$575$	−4.46156e10			−0.408146
$576$		0			0
$577$	1.29943e11	−	7.50226e10i	1.17233	−	0.676845i	0.218102	−	0.975926i	$-0.430014\pi$
$577$	1.29943e11	−	7.50226e10i	1.17233	−	0.676845i	0.954228	+	0.299081i	$0.0966802\pi$
$578$		0			0
$579$	−2.69629e10	−	1.55670e10i	−0.239912	−	0.138513i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	7.92587e10	−	1.37280e11i	0.686077	−	1.18832i
$584$		0			0
$585$	−3.90577e10	−	6.76499e10i	−0.333490	−	0.577622i
$586$		0			0
$587$		−	1.31985e11i		−	1.11166i	−0.831296	−	0.555830i	$-0.812401\pi$
$587$		−	1.31985e11i		−	1.11166i	0.831296	−	0.555830i	$-0.187599\pi$
$588$		0			0
$589$	2.71557e11			2.25632
$590$		0			0
$591$	7.29588e10	−	4.21228e10i	0.598036	−	0.345276i
$592$		0			0
$593$	−1.53587e11	−	8.86738e10i	−1.24204	−	0.717094i	−0.272534	−	0.962146i	$-0.587862\pi$
$593$	−1.53587e11	−	8.86738e10i	−1.24204	−	0.717094i	−0.969510	+	0.245052i	$0.921195\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.19995e10	−	3.81042e10i	0.173187	−	0.299969i
$598$		0			0
$599$	−4.47106e10	−	7.74410e10i	−0.347299	−	0.601539i	0.638470	−	0.769647i	$-0.279568\pi$
$599$	−4.47106e10	−	7.74410e10i	−0.347299	−	0.601539i	−0.985769	+	0.168108i	$0.946234\pi$
$600$		0			0
$601$			6.85319e10i			0.525285i	0.964893	+	0.262642i	$0.0845939\pi$
$601$			6.85319e10i			0.525285i	−0.964893	+	0.262642i	$0.915406\pi$
$602$		0			0
$603$	−5.90938e10			−0.446964
$604$		0			0
$605$	−1.06273e11	+	6.13565e10i	−0.793230	+	0.457972i
$606$		0			0
$607$	3.17573e9	+	1.83351e9i	0.0233932	+	0.0135061i	0.511651	−	0.859193i	$-0.329034\pi$
$607$	3.17573e9	+	1.83351e9i	0.0233932	+	0.0135061i	−0.488258	+	0.872699i	$0.662367\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.86002e10	−	1.53460e11i	0.635726	−	1.10111i
$612$		0			0
$613$	3.24622e10	+	5.62261e10i	0.229898	+	0.398196i	0.957778	−	0.287510i	$-0.0928273\pi$
$613$	3.24622e10	+	5.62261e10i	0.229898	+	0.398196i	−0.727879	+	0.685705i	$0.759494\pi$
$614$		0			0
$615$		−	4.67529e10i		−	0.326820i
$616$		0			0
$617$	−9.79839e10			−0.676105			−0.338052	−	0.941127i	$-0.609768\pi$
$617$	−9.79839e10			−0.676105			−0.338052	+	0.941127i	$0.609768\pi$
$618$		0			0
$619$	−1.01257e11	+	5.84609e10i	−0.689705	+	0.398202i	−0.803502	−	0.595303i	$-0.797032\pi$
$619$	−1.01257e11	+	5.84609e10i	−0.689705	+	0.398202i	0.113796	+	0.993504i	$0.463699\pi$
$620$		0			0
$621$	5.57257e10	+	3.21733e10i	0.374705	+	0.216336i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.72601e10	+	2.98954e10i	−0.113116	+	0.195923i
$626$		0			0
$627$	−8.43039e10	−	1.46019e11i	−0.545479	−	0.944796i
$628$		0			0
$629$			8.93119e10i			0.570567i
$630$		0			0
$631$	1.32605e11			0.836457			0.418229	−	0.908342i	$-0.362651\pi$
$631$	1.32605e11			0.836457			0.418229	+	0.908342i	$0.362651\pi$
$632$		0			0
$633$	−2.83191e10	+	1.63500e10i	−0.176386	+	0.101837i
$634$		0			0
$635$	−1.78838e10	−	1.03252e10i	−0.109993	−	0.0635046i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.93635e10	−	1.20141e11i	0.416033	−	0.720590i
$640$		0			0
$641$	9.12550e10	+	1.58058e11i	0.540536	+	0.936236i	0.998873	+	0.0474575i	$0.0151119\pi$
$641$	9.12550e10	+	1.58058e11i	0.540536	+	0.936236i	−0.458337	+	0.888778i	$0.651555\pi$
$642$		0			0
$643$			4.16413e10i			0.243602i	0.992555	+	0.121801i	$0.0388669\pi$
$643$			4.16413e10i			0.243602i	−0.992555	+	0.121801i	$0.961133\pi$
$644$		0			0
$645$	1.64639e10			0.0951248
$646$		0			0
$647$	−1.03407e11	+	5.97022e10i	−0.590111	+	0.340701i	−0.765142	−	0.643862i	$-0.777331\pi$
$647$	−1.03407e11	+	5.97022e10i	−0.590111	+	0.340701i	0.175030	+	0.984563i	$0.443998\pi$
$648$		0			0
$649$	2.67128e11	+	1.54227e11i	1.50571	+	0.869322i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.58120e11	+	2.73872e11i	−0.869629	+	1.50624i	−0.00725371	+	0.999974i	$0.502309\pi$
$653$	−1.58120e11	+	2.73872e11i	−0.869629	+	1.50624i	−0.862376	+	0.506269i	$0.831024\pi$
$654$		0			0
$655$	7.16976e10	+	1.24184e11i	0.389529	+	0.674683i
$656$		0			0
$657$		−	9.74857e10i		−	0.523214i
$658$		0			0
$659$	−3.31924e10			−0.175994			−0.0879969	−	0.996121i	$-0.528047\pi$
$659$	−3.31924e10			−0.175994			−0.0879969	+	0.996121i	$0.528047\pi$
$660$		0			0
$661$	−1.45318e11	+	8.38995e10i	−0.761227	+	0.439495i	−0.829736	−	0.558156i	$-0.811509\pi$
$661$	−1.45318e11	+	8.38995e10i	−0.761227	+	0.439495i	0.0685089	+	0.997651i	$0.478176\pi$
$662$		0			0
$663$	7.01840e10	+	4.05207e10i	0.363232	+	0.209712i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.60450e10	+	4.51113e10i	−0.131590	+	0.227920i
$668$		0			0
$669$	2.76290e10	+	4.78548e10i	0.137931	+	0.238903i
$670$		0			0
$671$			4.00279e10i			0.197457i
$672$		0			0
$673$	9.56218e10			0.466119			0.233059	−	0.972462i	$-0.425126\pi$
$673$	9.56218e10			0.466119			0.233059	+	0.972462i	$0.425126\pi$
$674$		0			0
$675$	9.74326e10	−	5.62528e10i	0.469342	−	0.270975i
$676$		0			0
$677$	−6.69694e10	−	3.86648e10i	−0.318803	−	0.184061i	0.332056	−	0.943260i	$-0.392258\pi$
$677$	−6.69694e10	−	3.86648e10i	−0.318803	−	0.184061i	−0.650859	+	0.759199i	$0.725591\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.00496e10	+	1.74065e10i	−0.0467264	+	0.0809325i
$682$		0			0
$683$	2.07611e10	+	3.59593e10i	0.0954042	+	0.165245i	0.909777	−	0.415097i	$-0.136252\pi$
$683$	2.07611e10	+	3.59593e10i	0.0954042	+	0.165245i	−0.814373	+	0.580342i	$0.802919\pi$
$684$		0			0
$685$		−	9.74908e10i		−	0.442793i
$686$		0			0
$687$	1.79309e10			0.0804960
$688$		0			0
$689$	2.45179e11	−	1.41554e11i	1.08794	−	0.628125i
$690$		0			0
$691$	−2.01717e11	−	1.16461e11i	−0.884769	−	0.510822i	−0.0125412	−	0.999921i	$-0.503992\pi$
$691$	−2.01717e11	−	1.16461e11i	−0.884769	−	0.510822i	−0.872228	+	0.489100i	$0.837325\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.55974e9	−	2.70155e9i	0.00668519	−	0.0115791i
$696$		0			0
$697$	−1.16820e11	−	2.02338e11i	−0.494979	−	0.857328i
$698$		0			0
$699$		−	8.11375e10i		−	0.339870i
$700$		0			0
$701$	−1.07467e11			−0.445044			−0.222522	−	0.974928i	$-0.571429\pi$
$701$	−1.07467e11			−0.445044			−0.222522	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$	2.87400e11	−	1.65930e11i	1.17670	−	0.679367i
$704$		0			0
$705$	−3.99066e10	−	2.30401e10i	−0.161543	−	0.0932670i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	3.70870e10	−	6.42366e10i	0.146770	−	0.254213i	−0.783262	−	0.621692i	$-0.786446\pi$
$709$	3.70870e10	−	6.42366e10i	0.146770	−	0.254213i	0.930032	+	0.367479i	$0.119779\pi$
$710$		0			0
$711$	−1.44602e11	−	2.50458e11i	−0.565843	−	0.980069i
$712$		0			0
$713$			2.08476e11i			0.806673i
$714$		0			0
$715$	−3.46900e11			−1.32733
$716$		0			0
$717$	3.50594e10	−	2.02416e10i	0.132656	−	0.0765892i
$718$		0			0
$719$	−1.62257e11	−	9.36794e10i	−0.607140	−	0.350533i	0.164705	−	0.986343i	$-0.447333\pi$
$719$	−1.62257e11	−	9.36794e10i	−0.607140	−	0.350533i	−0.771845	+	0.635810i	$0.780666\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−4.65076e10	+	8.05536e10i	−0.170205	+	0.294803i
$724$		0			0
$725$	4.55379e10	+	7.88740e10i	0.164824	+	0.285484i
$726$		0			0
$727$			3.65939e11i			1.31000i	0.755629	+	0.655000i	$0.227331\pi$
$727$			3.65939e11i			1.31000i	−0.755629	+	0.655000i	$0.772669\pi$
$728$		0			0
$729$	3.14098e10			0.111213
$730$		0			0
$731$	7.12529e10	−	4.11379e10i	0.249536	−	0.144070i
$732$		0			0
$733$	2.60911e11	+	1.50637e11i	0.903807	+	0.521813i	0.878434	−	0.477865i	$-0.158589\pi$
$733$	2.60911e11	+	1.50637e11i	0.903807	+	0.521813i	0.0253739	+	0.999678i	$0.491922\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.31214e11	+	2.27269e11i	−0.444743	+	0.770318i
$738$		0			0
$739$	−1.32861e11	−	2.30121e11i	−0.445470	−	0.771577i	0.552615	−	0.833437i	$-0.313630\pi$
$739$	−1.32861e11	−	2.30121e11i	−0.445470	−	0.771577i	−0.998085	+	0.0618599i	$0.980297\pi$
$740$		0			0
$741$		−	3.01130e11i		−	0.998806i
$742$		0			0
$743$	−4.14572e11			−1.36033			−0.680166	−	0.733058i	$-0.738092\pi$
$743$	−4.14572e11			−1.36033			−0.680166	+	0.733058i	$0.738092\pi$
$744$		0			0
$745$	−2.34636e11	+	1.35467e11i	−0.761674	+	0.439753i
$746$		0			0
$747$	9.82218e9	+	5.67084e9i	0.0315446	+	0.0182123i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.22326e11	+	3.85079e11i	−0.698924	+	1.21057i	0.269916	+	0.962884i	$0.413004\pi$
$751$	−2.22326e11	+	3.85079e11i	−0.698924	+	1.21057i	−0.968840	+	0.247688i	$0.920329\pi$
$752$		0			0
$753$	9.60979e10	+	1.66446e11i	0.298905	+	0.517719i
$754$		0			0
$755$		−	3.59103e9i		−	0.0110518i
$756$		0			0
$757$	−2.60251e11			−0.792517			−0.396258	−	0.918139i	$-0.629692\pi$
$757$	−2.60251e11			−0.792517			−0.396258	+	0.918139i	$0.629692\pi$
$758$		0			0
$759$	1.12099e11	−	6.47205e10i	0.337781	−	0.195018i
$760$		0			0
$761$	4.05348e10	+	2.34028e10i	0.120862	+	0.0697797i	0.559212	−	0.829025i	$-0.311104\pi$
$761$	4.05348e10	+	2.34028e10i	0.120862	+	0.0697797i	−0.438350	+	0.898804i	$0.644437\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5.07568e10	+	8.79134e10i	−0.148200	+	0.256690i
$766$		0			0
$767$	2.75445e11	+	4.77085e11i	0.795891	+	1.37852i
$768$		0			0
$769$		−	3.82049e11i		−	1.09248i	−0.837628	−	0.546240i	$-0.816058\pi$
$769$		−	3.82049e11i		−	1.09248i	0.837628	−	0.546240i	$-0.183942\pi$
$770$		0			0
$771$	7.84702e9			0.0222069
$772$		0			0
$773$	−3.11909e10	+	1.80080e10i	−0.0873593	+	0.0504369i	−0.543043	−	0.839705i	$-0.682728\pi$
$773$	−3.11909e10	+	1.80080e10i	−0.0873593	+	0.0504369i	0.455684	+	0.890142i	$0.349395\pi$
$774$		0			0
$775$	3.15671e11	+	1.82253e11i	0.875040	+	0.505205i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.34074e11	+	7.51839e11i	−1.17873	+	2.04162i
$780$		0			0
$781$	−3.08034e11	−	5.33531e11i	−0.827932	−	1.43402i
$782$		0			0
$783$		−	1.31353e11i		−	0.349458i
$784$		0			0
$785$	1.52977e11			0.402855
$786$		0			0
$787$	−2.83447e11	+	1.63648e11i	−0.738879	+	0.426592i	−0.821661	−	0.569976i	$-0.806953\pi$
$787$	−2.83447e11	+	1.63648e11i	−0.738879	+	0.426592i	0.0827828	+	0.996568i	$0.473619\pi$
$788$		0			0
$789$	−8.87092e9	−	5.12163e9i	−0.0228908	−	0.0132160i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.57444e10	+	6.19112e10i	−0.0903890	+	0.156558i
$794$		0			0
$795$	−3.68106e10	−	6.37577e10i	−0.0921518	−	0.159612i
$796$		0			0
$797$			6.29152e11i			1.55927i	0.626232	+	0.779636i	$0.284596\pi$
$797$			6.29152e11i			1.55927i	−0.626232	+	0.779636i	$0.715404\pi$
$798$		0			0
$799$	−2.30278e11			−0.565023
$800$		0			0
$801$	−4.65236e11	+	2.68604e11i	−1.13017	+	0.652503i
$802$		0			0
$803$	−3.74920e11	−	2.16460e11i	−0.901731	−	0.520615i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.02939e11	−	1.78296e11i	0.242710	−	0.420386i
$808$		0			0
$809$	1.37743e11	+	2.38579e11i	0.321571	+	0.556977i	0.980812	−	0.194954i	$-0.0624558\pi$
$809$	1.37743e11	+	2.38579e11i	0.321571	+	0.556977i	−0.659241	+	0.751931i	$0.729122\pi$
$810$		0			0
$811$		−	3.31344e11i		−	0.765942i	−0.923760	−	0.382971i	$-0.874901\pi$
$811$		−	3.31344e11i		−	0.765942i	0.923760	−	0.382971i	$-0.125099\pi$
$812$		0			0
$813$	−1.15320e11			−0.263962
$814$		0			0
$815$	−1.89905e11	+	1.09642e11i	−0.430433	+	0.248510i
$816$		0			0
$817$	−2.64758e11	−	1.52858e11i	−0.594238	−	0.343084i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.26039e10	+	9.11126e10i	−0.115783	+	0.200542i	−0.918093	−	0.396366i	$-0.870271\pi$
$821$	−5.26039e10	+	9.11126e10i	−0.115783	+	0.200542i	0.802309	+	0.596908i	$0.203604\pi$
$822$		0			0
$823$	−1.32796e11	−	2.30010e11i	−0.289459	−	0.501357i	0.684222	−	0.729274i	$-0.260142\pi$
$823$	−1.32796e11	−	2.30010e11i	−0.289459	−	0.501357i	−0.973681	+	0.227917i	$0.926809\pi$
$824$		0			0
$825$		−	2.26319e11i		−	0.488546i
$826$		0			0
$827$	2.81754e11			0.602349			0.301175	−	0.953569i	$-0.402621\pi$
$827$	2.81754e11			0.602349			0.301175	+	0.953569i	$0.402621\pi$
$828$		0			0
$829$	1.39457e11	−	8.05154e10i	0.295272	−	0.170475i	−0.345045	−	0.938586i	$-0.612136\pi$
$829$	1.39457e11	−	8.05154e10i	0.295272	−	0.170475i	0.640317	+	0.768111i	$0.278803\pi$
$830$		0			0
$831$	2.12438e11	+	1.22651e11i	0.445481	+	0.257198i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.25278e10	−	1.42942e11i	0.169767	−	0.294046i
$836$		0			0
$837$	−2.62853e11	−	4.55274e11i	−0.535563	−	0.927623i
$838$		0			0
$839$		−	1.23152e11i		−	0.248539i	−0.992248	−	0.124270i	$-0.960341\pi$
$839$		−	1.23152e11i		−	0.248539i	0.992248	−	0.124270i	$-0.0396588\pi$
$840$		0			0
$841$	−3.93913e11			−0.787437
$842$		0			0
$843$	1.29830e11	−	7.49575e10i	0.257078	−	0.148424i
$844$		0			0
$845$	−3.00841e11	−	1.73690e11i	−0.590078	−	0.340682i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−8.43448e10	+	1.46089e11i	−0.162341	+	0.281182i
$850$		0			0
$851$	1.27386e11	+	2.20638e11i	0.242886	+	0.420690i
$852$		0			0
$853$			9.07583e11i			1.71431i	0.515056	+	0.857156i	$0.327771\pi$
$853$			9.07583e11i			1.71431i	−0.515056	+	0.857156i	$0.672229\pi$
$854$		0			0
$855$	3.77200e11			0.705841
$856$		0			0
$857$	6.57594e11	−	3.79662e11i	1.21909	−	0.703840i	0.254364	−	0.967109i	$-0.418134\pi$
$857$	6.57594e11	−	3.79662e11i	1.21909	−	0.703840i	0.964722	+	0.263269i	$0.0848006\pi$
$858$		0			0
$859$	1.38342e11	+	7.98719e10i	0.254087	+	0.146697i	0.621634	−	0.783308i	$-0.286469\pi$
$859$	1.38342e11	+	7.98719e10i	0.254087	+	0.146697i	−0.367547	+	0.930005i	$0.619802\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.48166e11	+	4.29837e11i	−0.447404	+	0.774926i	−0.998216	−	0.0597030i	$-0.980985\pi$
$863$	−2.48166e11	+	4.29837e11i	−0.447404	+	0.774926i	0.550812	+	0.834629i	$0.314318\pi$
$864$		0			0
$865$	−1.32483e11	−	2.29468e11i	−0.236645	−	0.409881i
$866$		0			0
$867$			1.28961e11i			0.228235i
$868$		0			0
$869$	−1.28432e12			−2.25213
$870$		0			0
$871$	−4.05897e11	+	2.34345e11i	−0.705251	+	0.407177i
$872$		0			0
$873$	−1.14856e11	−	6.63120e10i	−0.197740	−	0.114165i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.87067e11	−	4.97215e11i	0.485272	−	0.840515i	−0.514585	−	0.857439i	$-0.672054\pi$
$877$	2.87067e11	−	4.97215e11i	0.485272	−	0.840515i	0.999857	+	0.0169241i	$0.00538738\pi$
$878$		0			0
$879$	8.39246e10	+	1.45362e11i	0.140583	+	0.243497i
$880$		0			0
$881$		−	1.34834e11i		−	0.223819i	−0.993718	−	0.111909i	$-0.964303\pi$
$881$		−	1.34834e11i		−	0.223819i	0.993718	−	0.111909i	$-0.0356967\pi$
$882$		0			0
$883$	2.79034e11			0.459002			0.229501	−	0.973308i	$-0.426291\pi$
$883$	2.79034e11			0.459002			0.229501	+	0.973308i	$0.426291\pi$
$884$		0			0
$885$	1.24064e11	−	7.16283e10i	0.202242	−	0.116765i
$886$		0			0
$887$	2.45349e11	+	1.41652e11i	0.396360	+	0.228838i	0.684912	−	0.728626i	$-0.259841\pi$
$887$	2.45349e11	+	1.41652e11i	0.396360	+	0.228838i	−0.288552	+	0.957464i	$0.593174\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.66828e11	−	4.62160e11i	0.423370	−	0.733299i
$892$		0			0
$893$	4.27829e11	+	7.41021e11i	0.672766	+	1.16526i
$894$		0			0
$895$		−	6.18612e10i		−	0.0964109i
$896$		0			0
$897$	2.31179e11			0.357091
$898$		0			0
$899$	3.68555e11	−	2.12785e11i	0.564240	−	0.325764i
$900$		0			0
$901$	−3.18619e11	−	1.83955e11i	−0.483474	−	0.279134i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.41863e11	+	4.18918e11i	−0.360557	+	0.624504i
$906$		0			0
$907$	2.48996e11	+	4.31274e11i	0.367929	+	0.637272i	0.989242	−	0.146291i	$-0.0467336\pi$
$907$	2.48996e11	+	4.31274e11i	0.367929	+	0.637272i	−0.621313	+	0.783563i	$0.713400\pi$
$908$		0			0
$909$			4.49925e11i			0.658999i
$910$		0			0
$911$	7.98004e11			1.15859			0.579297	−	0.815117i	$-0.303327\pi$
$911$	7.98004e11			1.15859			0.579297	+	0.815117i	$0.303327\pi$
$912$		0			0
$913$	4.36190e10	−	2.51834e10i	0.0627758	−	0.0362436i
$914$		0			0
$915$	1.60997e10	+	9.29518e9i	0.0229686	+	0.0132609i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.56291e11	−	2.70704e11i	0.219115	−	0.379518i	−0.735423	−	0.677609i	$-0.763016\pi$
$919$	1.56291e11	−	2.70704e11i	0.219115	−	0.379518i	0.954538	+	0.298091i	$0.0963497\pi$
$920$		0			0
$921$	−2.35305e11	−	4.07561e11i	−0.327034	−	0.566440i
$922$		0			0
$923$		−	1.10028e12i		−	1.51600i
$924$		0			0
$925$	4.45450e11			0.608460
$926$		0			0
$927$	4.10586e11	−	2.37052e11i	0.556013	−	0.321014i
$928$		0			0
$929$	1.00462e12	+	5.80018e11i	1.34878	+	0.778716i	0.988076	−	0.153966i	$-0.0492048\pi$
$929$	1.00462e12	+	5.80018e11i	1.34878	+	0.778716i	0.360699	+	0.932682i	$0.382538\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.54449e11	−	2.67513e11i	0.203825	−	0.353036i
$934$		0			0
$935$	2.25404e11	+	3.90412e11i	0.294928	+	0.510830i
$936$		0			0
$937$		−	9.95746e11i		−	1.29179i	−0.763428	−	0.645893i	$-0.776485\pi$
$937$		−	9.95746e11i		−	1.29179i	0.763428	−	0.645893i	$-0.223515\pi$
$938$		0			0
$939$	5.50715e11			0.708377
$940$		0			0
$941$	−4.92448e11	+	2.84315e11i	−0.628061	+	0.362611i	−0.780001	−	0.625779i	$-0.784781\pi$
$941$	−4.92448e11	+	2.84315e11i	−0.628061	+	0.362611i	0.151940	+	0.988390i	$0.451448\pi$
$942$		0			0
$943$	−5.77190e11	−	3.33241e11i	−0.729915	−	0.421417i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.65811e11	−	9.80013e11i	0.703512	−	1.21852i	−0.263714	−	0.964601i	$-0.584948\pi$
$947$	5.65811e11	−	9.80013e11i	0.703512	−	1.21852i	0.967226	−	0.253917i	$-0.0817191\pi$
$948$		0			0
$949$	−3.86593e11	−	6.69599e11i	−0.476639	−	0.825563i
$950$		0			0
$951$		−	3.19515e11i		−	0.390633i
$952$		0			0
$953$	1.59922e11			0.193882			0.0969411	−	0.995290i	$-0.469094\pi$
$953$	1.59922e11			0.193882			0.0969411	+	0.995290i	$0.469094\pi$
$954$		0			0
$955$	3.29306e10	−	1.90125e10i	0.0395901	−	0.0228573i
$956$		0			0
$957$	−2.28833e11	−	1.32117e11i	−0.272817	−	0.157511i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	4.25169e11	−	7.36414e11i	0.498503	−	0.863433i
$962$		0			0
$963$	−5.83100e11	−	1.00996e12i	−0.678012	−	1.17435i
$964$		0			0
$965$		−	3.09312e11i		−	0.356687i
$966$		0			0
$967$	1.40368e12			1.60532			0.802660	−	0.596436i	$-0.203417\pi$
$967$	1.40368e12			1.60532			0.802660	+	0.596436i	$0.203417\pi$
$968$		0			0
$969$	−3.38901e11	+	1.95665e11i	−0.384395	+	0.221931i
$970$		0			0
$971$	1.36401e12	+	7.87511e11i	1.53441	+	0.885890i	0.999151	+	0.0411996i	$0.0131180\pi$
$971$	1.36401e12	+	7.87511e11i	1.53441	+	0.885890i	0.535255	+	0.844690i	$0.320215\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.02100e11	−	3.50048e11i	0.223639	−	0.387355i
$976$		0			0
$977$	3.15641e11	+	5.46706e11i	0.346429	+	0.600033i	0.985612	−	0.169021i	$-0.0540607\pi$
$977$	3.15641e11	+	5.46706e11i	0.346429	+	0.600033i	−0.639183	+	0.769055i	$0.720727\pi$
$978$		0			0
$979$			2.38567e12i			2.59705i
$980$		0			0
$981$	−4.58623e11			−0.495199
$982$		0			0
$983$	−1.28656e12	+	7.42796e11i	−1.37790	+	0.795528i	−0.991906	−	0.126975i	$-0.959473\pi$
$983$	−1.28656e12	+	7.42796e11i	−1.37790	+	0.795528i	−0.385990	+	0.922503i	$0.626140\pi$
$984$		0			0
$985$	7.24834e11	+	4.18483e11i	0.770005	+	0.444563i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.17350e11	−	2.03256e11i	0.122658	−	0.212451i
$990$		0			0
$991$	6.13950e11	+	1.06339e12i	0.636558	+	1.10255i	0.986183	+	0.165662i	$0.0529760\pi$
$991$	6.13950e11	+	1.06339e12i	0.636558	+	1.10255i	−0.349624	+	0.936890i	$0.613691\pi$
$992$		0			0
$993$			1.65107e11i			0.169812i
$994$		0			0
$995$	4.37123e11			0.445976
$996$		0			0
$997$	1.50902e12	−	8.71236e11i	1.52727	−	0.881770i	0.527795	−	0.849372i	$-0.323019\pi$
$997$	1.50902e12	−	8.71236e11i	1.52727	−	0.881770i	0.999475	−	0.0323977i	$-0.0103143\pi$
$998$		0			0
$999$	−5.56375e11	−	3.21223e11i	−0.558606	−	0.322511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.9.h.b.117.4		12
7.2	even	3		28.9.b.a.13.4	yes	6
7.3	odd	6	inner	196.9.h.b.129.4		12
7.4	even	3	inner	196.9.h.b.129.3		12
7.5	odd	6		28.9.b.a.13.3	✓	6
7.6	odd	2	inner	196.9.h.b.117.3		12
21.2	odd	6		252.9.d.b.181.4		6
21.5	even	6		252.9.d.b.181.3		6
28.19	even	6		112.9.c.d.97.4		6
28.23	odd	6		112.9.c.d.97.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.b.a.13.3	✓	6	7.5	odd	6
28.9.b.a.13.4	yes	6	7.2	even	3
112.9.c.d.97.3		6	28.23	odd	6
112.9.c.d.97.4		6	28.19	even	6
196.9.h.b.117.3		12	7.6	odd	2	inner
196.9.h.b.117.4		12	1.1	even	1	trivial
196.9.h.b.129.3		12	7.4	even	3	inner
196.9.h.b.129.4		12	7.3	odd	6	inner
252.9.d.b.181.3		6	21.5	even	6
252.9.d.b.181.4		6	21.2	odd	6

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(29.0850 - 16.7923i) q^{3} +(288.955 + 166.829i) q^{5} +(-2716.54 + 4705.19i) q^{9} +(12063.8 + 20895.1i) q^{11} +43091.3i q^{13} +11205.7 q^{15} +(48496.3 - 27999.4i) q^{17} +(-180200. - 104039. i) q^{19} +(79871.0 - 138341. i) q^{23} +(-139649. - 241879. i) q^{25} +402815. i q^{27} -326089. q^{29} +(-1.13023e6 + 652539. i) q^{31} +(701752. + 405157. i) q^{33} +(-797445. + 1.38122e6i) q^{37} +(723601. + 1.25331e6i) q^{39} -4.17224e6i q^{41} +1.46924e6 q^{43} +(-1.56992e6 + 906393. i) q^{45} +(-3.56128e6 - 2.05610e6i) q^{47} +(940345. - 1.62873e6i) q^{51} +(-3.28498e6 - 5.68976e6i) q^{53} +8.05034e6i q^{55} -6.98818e6 q^{57} +(1.10715e7 - 6.39213e6i) q^{59} +(1.43674e6 + 829504. i) q^{61} +(-7.18886e6 + 1.24515e7i) q^{65} +(5.43833e6 + 9.41946e6i) q^{67} -5.36486e6i q^{69} -2.55338e7 q^{71} +(-1.55391e7 + 8.97149e6i) q^{73} +(-8.12339e6 - 4.69004e6i) q^{75} +(-2.66151e7 + 4.60987e7i) q^{79} +(-1.10590e7 - 1.91548e7i) q^{81} -2.08752e6i q^{83} +1.86844e7 q^{85} +(-9.48430e6 + 5.47576e6i) q^{87} +(8.56303e7 + 4.94387e7i) q^{89} +(-2.19152e7 + 3.79583e7i) q^{93} +(-3.47132e7 - 6.01251e7i) q^{95} +2.44104e7i q^{97} -1.31087e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18234 q^{9} - 24492 q^{11} - 306816 q^{15} + 11604 q^{23} + 678714 q^{25} + 2528664 q^{29} - 3184332 q^{37} - 5634240 q^{39} - 15566760 q^{43} - 6877824 q^{51} + 8340660 q^{53} - 35901696 q^{57}+ \cdots - 1191795624 q^{99}+O(q^{100}) \) 12 * q + 18234 * q^9 - 24492 * q^11 - 306816 * q^15 + 11604 * q^23 + 678714 * q^25 + 2528664 * q^29 - 3184332 * q^37 - 5634240 * q^39 - 15566760 * q^43 - 6877824 * q^51 + 8340660 * q^53 - 35901696 * q^57 - 84095232 * q^65 - 16579500 * q^67 - 124177704 * q^71 - 186114540 * q^79 - 131284998 * q^81 - 526421760 * q^85 - 638128512 * q^93 - 85912896 * q^95 - 1191795624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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