LMFDB - Embedded newform 196.6.e.l.177.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,6,Mod(165,196)] 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("196.165"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} - 1166 x^{6} + 3512 x^{5} + 513939 x^{4} - 1033736 x^{3} - 101466410 x^{2} + \cdots + 7574050372 $ x^8 - 4x^7 - 1166x^6 + 3512x^5 + 513939x^4 - 1033736x^3 - 101466410x^2 + 101983864*x + 7574050372
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$16.9466 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	196.177
Dual form			196.6.e.l.165.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.6044 - 25.2955i) q^{3} +(49.2526 - 85.3080i) q^{5} +(-305.076 + 528.407i) q^{9} +(-64.5760 - 111.849i) q^{11} -126.140 q^{13} -2877.22 q^{15} +(-807.019 - 1397.80i) q^{17} +(-699.734 + 1211.97i) q^{19} +(-1386.61 + 2401.68i) q^{23} +(-3289.14 - 5696.96i) q^{25} +10724.1 q^{27} +3499.94 q^{29} +(-355.228 - 615.273i) q^{31} +(-1886.19 + 3266.97i) q^{33} +(1525.55 - 2642.33i) q^{37} +(1842.19 + 3190.77i) q^{39} -15263.7 q^{41} +7880.58 q^{43} +(30051.6 + 52050.9i) q^{45} +(-8393.83 + 14538.5i) q^{47} +(-23572.0 + 40828.0i) q^{51} +(1615.06 + 2797.37i) q^{53} -12722.2 q^{55} +40876.7 q^{57} +(6081.66 + 10533.8i) q^{59} +(25503.7 - 44173.7i) q^{61} +(-6212.71 + 10760.7i) q^{65} +(-13616.2 - 23583.9i) q^{67} +81002.2 q^{69} -13313.9 q^{71} +(24856.5 + 43052.6i) q^{73} +(-96071.7 + 166401. i) q^{75} +(-10553.0 + 18278.3i) q^{79} +(-82484.8 - 142868. i) q^{81} +79860.2 q^{83} -158991. q^{85} +(-51114.4 - 88532.7i) q^{87} +(18423.3 - 31910.0i) q^{89} +(-10375.8 + 17971.4i) q^{93} +(68927.4 + 119386. i) q^{95} -27968.5 q^{97} +78802.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1480 q^{9} + 444 q^{11} - 7648 q^{15} - 3408 q^{23} - 11904 q^{25} + 41448 q^{29} - 13732 q^{37} - 25608 q^{39} - 57992 q^{43} - 181852 q^{51} - 528 q^{53} + 179080 q^{57} - 110220 q^{65} - 195384 q^{67}+ \cdots + 132824 q^{99}+O(q^{100}) $ 8 * q - 1480 * q^9 + 444 * q^11 - 7648 * q^15 - 3408 * q^23 - 11904 * q^25 + 41448 * q^29 - 13732 * q^37 - 25608 * q^39 - 57992 * q^43 - 181852 * q^51 - 528 * q^53 + 179080 * q^57 - 110220 * q^65 - 195384 * q^67 + 43344 * q^71 + 117304 * q^79 - 182456 * q^81 - 182600 * q^85 - 250152 * q^93 + 255552 * q^95 + 132824 * q^99

Character values

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

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−14.6044	−	25.2955i	−0.936872	−	1.62271i	−0.771262	−	0.636518i	$-0.780374\pi$
$3$	−14.6044	−	25.2955i	−0.936872	−	1.62271i	−0.165610	−	0.986191i	$-0.552959\pi$
$4$		0			0
$5$	49.2526	−	85.3080i	0.881058	−	1.52604i	0.0308909	−	0.999523i	$-0.490166\pi$
$5$	49.2526	−	85.3080i	0.881058	−	1.52604i	0.850167	−	0.526514i	$-0.176501\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−305.076	+	528.407i	−1.25546	+	2.17452i
$10$		0			0
$11$	−64.5760	−	111.849i	−0.160912	−	0.278708i	0.774284	−	0.632839i	$-0.218110\pi$
$11$	−64.5760	−	111.849i	−0.160912	−	0.278708i	−0.935196	+	0.354130i	$0.884777\pi$
$12$		0			0
$13$	−126.140			−0.207011			−0.103506	−	0.994629i	$-0.533006\pi$
$13$	−126.140			−0.207011			−0.103506	+	0.994629i	$0.533006\pi$
$14$		0			0
$15$	−2877.22			−3.30175
$16$		0			0
$17$	−807.019	−	1397.80i	−0.677269	−	1.17307i	−0.975800	−	0.218665i	$-0.929830\pi$
$17$	−807.019	−	1397.80i	−0.677269	−	1.17307i	0.298530	−	0.954400i	$-0.403504\pi$
$18$		0			0
$19$	−699.734	+	1211.97i	−0.444681	+	0.770210i	−0.998030	−	0.0627393i	$-0.980016\pi$
$19$	−699.734	+	1211.97i	−0.444681	+	0.770210i	0.553349	+	0.832950i	$0.313350\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1386.61	+	2401.68i	−0.546555	+	0.946662i	0.451952	+	0.892042i	$0.350728\pi$
$23$	−1386.61	+	2401.68i	−0.546555	+	0.946662i	−0.998507	+	0.0546193i	$0.982605\pi$
$24$		0			0
$25$	−3289.14	−	5696.96i	−1.05252	−	1.82303i
$26$		0			0
$27$	10724.1			2.83106
$28$		0			0
$29$	3499.94			0.772796			0.386398	−	0.922332i	$-0.373719\pi$
$29$	3499.94			0.772796			0.386398	+	0.922332i	$0.373719\pi$
$30$		0			0
$31$	−355.228	−	615.273i	−0.0663901	−	0.114991i	0.830920	−	0.556392i	$-0.187815\pi$
$31$	−355.228	−	615.273i	−0.0663901	−	0.114991i	−0.897310	+	0.441401i	$0.854481\pi$
$32$		0			0
$33$	−1886.19	+	3266.97i	−0.301509	+	0.522228i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1525.55	−	2642.33i	0.183199	−	0.317310i	−0.759769	−	0.650193i	$-0.774688\pi$
$37$	1525.55	−	2642.33i	0.183199	−	0.317310i	0.942968	+	0.332883i	$0.108021\pi$
$38$		0			0
$39$	1842.19	+	3190.77i	0.193943	+	0.335919i
$40$		0			0
$41$	−15263.7			−1.41808			−0.709041	−	0.705168i	$-0.750872\pi$
$41$	−15263.7			−1.41808			−0.709041	+	0.705168i	$0.750872\pi$
$42$		0			0
$43$	7880.58			0.649960			0.324980	−	0.945721i	$-0.394642\pi$
$43$	7880.58			0.649960			0.324980	+	0.945721i	$0.394642\pi$
$44$		0			0
$45$	30051.6	+	52050.9i	2.21226	+	3.83175i
$46$		0			0
$47$	−8393.83	+	14538.5i	−0.554262	+	0.960011i	0.443698	+	0.896176i	$0.353666\pi$
$47$	−8393.83	+	14538.5i	−0.554262	+	0.960011i	−0.997961	+	0.0638343i	$0.979667\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−23572.0	+	40828.0i	−1.26903	+	2.19802i
$52$		0			0
$53$	1615.06	+	2797.37i	0.0789769	+	0.136792i	0.902809	−	0.430042i	$-0.141501\pi$
$53$	1615.06	+	2797.37i	0.0789769	+	0.136792i	−0.823832	+	0.566834i	$0.808168\pi$
$54$		0			0
$55$	−12722.2			−0.567092
$56$		0			0
$57$	40876.7			1.66644
$58$		0			0
$59$	6081.66	+	10533.8i	0.227453	+	0.393961i	0.957053	−	0.289914i	$-0.0936267\pi$
$59$	6081.66	+	10533.8i	0.227453	+	0.393961i	−0.729599	+	0.683875i	$0.760293\pi$
$60$		0			0
$61$	25503.7	−	44173.7i	0.877563	−	1.51998i	0.0235567	−	0.999723i	$-0.492501\pi$
$61$	25503.7	−	44173.7i	0.877563	−	1.51998i	0.854007	−	0.520262i	$-0.174166\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6212.71	+	10760.7i	−0.182389	+	0.315906i
$66$		0			0
$67$	−13616.2	−	23583.9i	−0.370568	−	0.641842i	0.619085	−	0.785324i	$-0.287504\pi$
$67$	−13616.2	−	23583.9i	−0.370568	−	0.641842i	−0.989653	+	0.143482i	$0.954170\pi$
$68$		0			0
$69$	81002.2			2.04821
$70$		0			0
$71$	−13313.9			−0.313443			−0.156721	−	0.987643i	$-0.550092\pi$
$71$	−13313.9			−0.313443			−0.156721	+	0.987643i	$0.550092\pi$
$72$		0			0
$73$	24856.5	+	43052.6i	0.545924	+	0.945568i	0.998548	+	0.0538666i	$0.0171546\pi$
$73$	24856.5	+	43052.6i	0.545924	+	0.945568i	−0.452624	+	0.891701i	$0.649512\pi$
$74$		0			0
$75$	−96071.7	+	166401.i	−1.97216	+	3.41588i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−10553.0	+	18278.3i	−0.190242	+	0.329509i	−0.945330	−	0.326114i	$-0.894261\pi$
$79$	−10553.0	+	18278.3i	−0.190242	+	0.329509i	0.755088	+	0.655623i	$0.227594\pi$
$80$		0			0
$81$	−82484.8	−	142868.i	−1.39689	−	2.41948i
$82$		0			0
$83$	79860.2			1.27243			0.636216	−	0.771511i	$-0.280499\pi$
$83$	79860.2			1.27243			0.636216	+	0.771511i	$0.280499\pi$
$84$		0			0
$85$	−158991.			−2.38685
$86$		0			0
$87$	−51114.4	−	88532.7i	−0.724011	−	1.25402i
$88$		0			0
$89$	18423.3	−	31910.0i	0.246542	−	0.427024i	−0.716022	−	0.698078i	$-0.754039\pi$
$89$	18423.3	−	31910.0i	0.246542	−	0.427024i	0.962564	+	0.271054i	$0.0873722\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−10375.8	+	17971.4i	−0.124398	+	0.215464i
$94$		0			0
$95$	68927.4	+	119386.i	0.783579	+	1.35720i
$96$		0			0
$97$	−27968.5			−0.301814			−0.150907	−	0.988548i	$-0.548219\pi$
$97$	−27968.5			−0.301814			−0.150907	+	0.988548i	$0.548219\pi$
$98$		0			0
$99$	78802.4			0.808074
$100$		0			0
$101$	−46765.8	−	81000.7i	−0.456168	−	0.790106i	0.542587	−	0.840000i	$-0.317445\pi$
$101$	−46765.8	−	81000.7i	−0.456168	−	0.790106i	−0.998755	+	0.0498939i	$0.984112\pi$
$102$		0			0
$103$	89706.9	−	155377.i	0.833168	−	1.44309i	−0.0623449	−	0.998055i	$-0.519858\pi$
$103$	89706.9	−	155377.i	0.833168	−	1.44309i	0.895513	−	0.445035i	$-0.146809\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−94451.5	+	163595.i	−0.797534	+	1.38137i	0.123683	+	0.992322i	$0.460529\pi$
$107$	−94451.5	+	163595.i	−0.797534	+	1.38137i	−0.921218	+	0.389048i	$0.872804\pi$
$108$		0			0
$109$	−52339.8	−	90655.1i	−0.421954	−	0.730846i	0.574176	−	0.818732i	$-0.305322\pi$
$109$	−52339.8	−	90655.1i	−0.421954	−	0.730846i	−0.996131	+	0.0878853i	$0.971989\pi$
$110$		0			0
$111$	−89119.0			−0.686535
$112$		0			0
$113$	25226.6			0.185850			0.0929252	−	0.995673i	$-0.470378\pi$
$113$	25226.6			0.185850			0.0929252	+	0.995673i	$0.470378\pi$
$114$		0			0
$115$	136588.	+	236578.i	0.963093	+	1.66813i
$116$		0			0
$117$	38482.2	−	66653.1i	0.259893	−	0.450149i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	72185.4	−	125029.i	0.448214	−	0.776330i
$122$		0			0
$123$	222917.	+	386104.i	1.32856	+	2.30113i
$124$		0			0
$125$	−340166.			−1.94722
$126$		0			0
$127$	5481.01			0.0301544			0.0150772	−	0.999886i	$-0.495201\pi$
$127$	5481.01			0.0301544			0.0150772	+	0.999886i	$0.495201\pi$
$128$		0			0
$129$	−115091.	−	199343.i	−0.608930	−	1.05470i
$130$		0			0
$131$	−97652.3	+	169139.i	−0.497169	+	0.861123i	−0.999995	−	0.00326538i	$-0.998961\pi$
$131$	−97652.3	+	169139.i	−0.497169	+	0.861123i	0.502825	+	0.864388i	$0.332294\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	528188.	−	914848.i	2.49433	−	4.32031i
$136$		0			0
$137$	86918.5	+	150547.i	0.395650	+	0.685285i	0.993184	−	0.116558i	$-0.0371861\pi$
$137$	86918.5	+	150547.i	0.395650	+	0.685285i	−0.597534	+	0.801843i	$0.703853\pi$
$138$		0			0
$139$	−283445.			−1.24432			−0.622160	−	0.782890i	$-0.713745\pi$
$139$	−283445.			−1.24432			−0.622160	+	0.782890i	$0.713745\pi$
$140$		0			0
$141$	490347.			2.07709
$142$		0			0
$143$	8145.60	+	14108.6i	0.0333106	+	0.0576957i
$144$		0			0
$145$	172381.	−	298573.i	0.680878	−	1.17932i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−113528.	+	196636.i	−0.418926	+	0.725601i	−0.995832	−	0.0912095i	$-0.970927\pi$
$149$	−113528.	+	196636.i	−0.418926	+	0.725601i	0.576906	+	0.816811i	$0.304260\pi$
$150$		0			0
$151$	−166354.	−	288133.i	−0.593731	−	1.02837i	−0.993725	−	0.111855i	$-0.964321\pi$
$151$	−166354.	−	288133.i	−0.593731	−	1.02837i	0.399993	−	0.916518i	$-0.369012\pi$
$152$		0			0
$153$	984809.			3.40113
$154$		0			0
$155$	−69983.6			−0.233974
$156$		0			0
$157$	−221740.	−	384065.i	−0.717952	−	1.24353i	−0.961810	−	0.273718i	$-0.911746\pi$
$157$	−221740.	−	384065.i	−0.717952	−	1.24353i	0.243858	−	0.969811i	$-0.421587\pi$
$158$		0			0
$159$	47174.0	−	81707.8i	0.147982	−	0.256313i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−100862.	+	174699.i	−0.297345	+	0.515017i	−0.975528	−	0.219877i	$-0.929434\pi$
$163$	−100862.	+	174699.i	−0.297345	+	0.515017i	0.678183	+	0.734893i	$0.262768\pi$
$164$		0			0
$165$	185799.	+	321814.i	0.531293	+	0.920226i
$166$		0			0
$167$	−567965.			−1.57591			−0.787953	−	0.615735i	$-0.788859\pi$
$167$	−567965.			−1.57591			−0.787953	+	0.615735i	$0.788859\pi$
$168$		0			0
$169$	−355382.			−0.957146
$170$		0			0
$171$	−426944.	−	739488.i	−1.11656	−	1.93393i
$172$		0			0
$173$	150793.	−	261181.i	0.383059	−	0.663477i	−0.608439	−	0.793601i	$-0.708204\pi$
$173$	150793.	−	261181.i	0.383059	−	0.663477i	0.991498	+	0.130123i	$0.0415373\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	177638.	−	307678.i	0.426189	−	0.738181i
$178$		0			0
$179$	−233371.	−	404210.i	−0.544395	−	0.942920i	−0.998645	−	0.0520455i	$-0.983426\pi$
$179$	−233371.	−	404210.i	−0.544395	−	0.942920i	0.454250	−	0.890874i	$-0.349907\pi$
$180$		0			0
$181$	−530851.			−1.20442			−0.602208	−	0.798340i	$-0.705712\pi$
$181$	−530851.			−1.20442			−0.602208	+	0.798340i	$0.705712\pi$
$182$		0			0
$183$	−1.48986e6			−3.28866
$184$		0			0
$185$	−150275.	−	260284.i	−0.322818	−	0.559136i
$186$		0			0
$187$	−104228.	+	180528.i	−0.217962	+	0.377521i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−261604.	+	453112.i	−0.518874	+	0.898716i	0.480886	+	0.876783i	$0.340315\pi$
$191$	−261604.	+	453112.i	−0.518874	+	0.898716i	−0.999759	+	0.0219325i	$0.993018\pi$
$192$		0			0
$193$	478344.	+	828516.i	0.924373	+	1.60106i	0.792567	+	0.609785i	$0.208744\pi$
$193$	478344.	+	828516.i	0.924373	+	1.60106i	0.131806	+	0.991275i	$0.457922\pi$
$194$		0			0
$195$	362931.			0.683499
$196$		0			0
$197$	−84916.4			−0.155893			−0.0779464	−	0.996958i	$-0.524836\pi$
$197$	−84916.4			−0.155893			−0.0779464	+	0.996958i	$0.524836\pi$
$198$		0			0
$199$	282757.	+	489750.i	0.506152	+	0.876681i	0.999975	+	0.00711842i	$0.00226588\pi$
$199$	282757.	+	489750.i	0.506152	+	0.876681i	−0.493823	+	0.869563i	$0.664401\pi$
$200$		0			0
$201$	−397711.	+	688856.i	−0.694349	+	1.20265i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−751779.	+	1.30212e6i	−1.24941	+	2.16404i
$206$		0			0
$207$	−846042.	−	1.46539e6i	−1.37235	−	2.37699i
$208$		0			0
$209$	180744.			0.286219
$210$		0			0
$211$	−303148.			−0.468758			−0.234379	−	0.972145i	$-0.575306\pi$
$211$	−303148.			−0.468758			−0.234379	+	0.972145i	$0.575306\pi$
$212$		0			0
$213$	194441.	+	336781.i	0.293656	+	0.508626i
$214$		0			0
$215$	388139.	−	672277.i	0.572653	−	0.991863i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	726026.	−	1.25751e6i	1.02292	−	1.77175i
$220$		0			0
$221$	101797.	+	176318.i	0.140202	+	0.242837i
$222$		0			0
$223$	796568.			1.07266			0.536328	−	0.844009i	$-0.319811\pi$
$223$	796568.			1.07266			0.536328	+	0.844009i	$0.319811\pi$
$224$		0			0
$225$	4.01375e6			5.28560
$226$		0			0
$227$	336673.	+	583134.i	0.433654	+	0.751111i	0.997185	−	0.0749845i	$-0.0238907\pi$
$227$	336673.	+	583134.i	0.433654	+	0.751111i	−0.563531	+	0.826095i	$0.690557\pi$
$228$		0			0
$229$	295397.	−	511643.i	0.372235	−	0.644730i	−0.617674	−	0.786434i	$-0.711925\pi$
$229$	295397.	−	511643.i	0.372235	−	0.644730i	0.989909	+	0.141704i	$0.0452581\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	239549.	−	414912.i	0.289072	−	0.500687i	−0.684517	−	0.728997i	$-0.739987\pi$
$233$	239549.	−	414912.i	0.289072	−	0.500687i	0.973588	+	0.228310i	$0.0733201\pi$
$234$		0			0
$235$	826836.	+	1.43212e6i	0.976674	+	1.69165i
$236$		0			0
$237$	616478.			0.712930
$238$		0			0
$239$	−349286.			−0.395536			−0.197768	−	0.980249i	$-0.563369\pi$
$239$	−349286.			−0.395536			−0.197768	+	0.980249i	$0.563369\pi$
$240$		0			0
$241$	168824.	+	292412.i	0.187237	+	0.324304i	0.944328	−	0.329005i	$-0.106713\pi$
$241$	168824.	+	292412.i	0.187237	+	0.324304i	−0.757091	+	0.653309i	$0.773380\pi$
$242$		0			0
$243$	−1.10631e6	+	1.91618e6i	−1.20188	+	2.08171i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	88264.2	−	152878.i	0.0920539	−	0.159442i
$248$		0			0
$249$	−1.16631e6	−	2.02011e6i	−1.19211	−	2.06479i
$250$		0			0
$251$	−1.67737e6			−1.68053			−0.840264	−	0.542178i	$-0.817600\pi$
$251$	−1.67737e6			−1.68053			−0.840264	+	0.542178i	$0.817600\pi$
$252$		0			0
$253$	358167.			0.351790
$254$		0			0
$255$	2.32197e6	+	4.02177e6i	2.23618	+	3.87317i
$256$		0			0
$257$	−377745.	+	654274.i	−0.356752	+	0.617912i	−0.987416	−	0.158144i	$-0.949449\pi$
$257$	−377745.	+	654274.i	−0.356752	+	0.617912i	0.630664	+	0.776056i	$0.282782\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.06775e6	+	1.84939e6i	−0.970213	+	1.68046i
$262$		0			0
$263$	−37403.4	−	64784.7i	−0.0333443	−	0.0577541i	0.848872	−	0.528599i	$-0.177282\pi$
$263$	−37403.4	−	64784.7i	−0.0333443	−	0.0577541i	−0.882216	+	0.470845i	$0.843949\pi$
$264$		0			0
$265$	318185.			0.278333
$266$		0			0
$267$	−1.07624e6			−0.923914
$268$		0			0
$269$	303609.	+	525866.i	0.255820	+	0.443092i	0.965118	−	0.261816i	$-0.0843214\pi$
$269$	303609.	+	525866.i	0.255820	+	0.443092i	−0.709298	+	0.704909i	$0.750988\pi$
$270$		0			0
$271$	−740143.	+	1.28196e6i	−0.612198	+	1.06036i	0.378671	+	0.925531i	$0.376381\pi$
$271$	−740143.	+	1.28196e6i	−0.612198	+	1.06036i	−0.990869	+	0.134827i	$0.956952\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−424799.	+	735774.i	−0.338729	+	0.586695i
$276$		0			0
$277$	662452.	+	1.14740e6i	0.518746	+	0.898494i	0.999763	+	0.0217830i	$0.00693429\pi$
$277$	662452.	+	1.14740e6i	0.518746	+	0.898494i	−0.481017	+	0.876711i	$0.659732\pi$
$278$		0			0
$279$	433486.			0.333399
$280$		0			0
$281$	−649433.			−0.490646			−0.245323	−	0.969441i	$-0.578894\pi$
$281$	−649433.			−0.490646			−0.245323	+	0.969441i	$0.578894\pi$
$282$		0			0
$283$	−1.10766e6	−	1.91852e6i	−0.822128	−	1.42397i	−0.904095	−	0.427332i	$-0.859454\pi$
$283$	−1.10766e6	−	1.91852e6i	−0.822128	−	1.42397i	0.0819671	−	0.996635i	$-0.473880\pi$
$284$		0			0
$285$	2.01328e6	−	3.48711e6i	1.46823	−	2.54304i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−592631.	+	1.02647e6i	−0.417388	+	0.722937i
$290$		0			0
$291$	408462.	+	707477.i	0.282761	+	0.489756i
$292$		0			0
$293$	−513832.			−0.349665			−0.174833	−	0.984598i	$-0.555938\pi$
$293$	−513832.			−0.349665			−0.174833	+	0.984598i	$0.555938\pi$
$294$		0			0
$295$	1.19815e6			0.801598
$296$		0			0
$297$	−692517.	−	1.19947e6i	−0.455553	−	0.789042i
$298$		0			0
$299$	174906.	−	302947.i	0.113143	−	0.195969i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.36597e6	+	2.36593e6i	−0.854741	+	1.48046i
$304$		0			0
$305$	−2.51225e6	−	4.35134e6i	−1.54637	−	2.67839i
$306$		0			0
$307$	835478.			0.505928			0.252964	−	0.967476i	$-0.418594\pi$
$307$	835478.			0.505928			0.252964	+	0.967476i	$0.418594\pi$
$308$		0			0
$309$	−5.24045e6			−3.12229
$310$		0			0
$311$	−1.05910e6	−	1.83441e6i	−0.620920	−	1.07547i	−0.989315	−	0.145796i	$-0.953426\pi$
$311$	−1.05910e6	−	1.83441e6i	−0.620920	−	1.07547i	0.368395	−	0.929670i	$-0.379908\pi$
$312$		0			0
$313$	−847910.	+	1.46862e6i	−0.489203	+	0.847324i	−0.999923	−	0.0124227i	$-0.996046\pi$
$313$	−847910.	+	1.46862e6i	−0.489203	+	0.847324i	0.510720	+	0.859747i	$0.329379\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−552747.	+	957387.i	−0.308943	+	0.535105i	−0.978131	−	0.207988i	$-0.933309\pi$
$317$	−552747.	+	957387.i	−0.308943	+	0.535105i	0.669188	+	0.743093i	$0.266642\pi$
$318$		0			0
$319$	−226012.	−	391464.i	−0.124353	−	0.215385i
$320$		0			0
$321$	5.51762e6			2.98875
$322$		0			0
$323$	2.25879e6			1.20468
$324$		0			0
$325$	414891.	+	718613.i	0.217884	+	0.377387i
$326$		0			0
$327$	−1.52878e6	+	2.64792e6i	−0.790634	+	1.36942i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.43821e6	−	2.49105e6i	0.721526	−	1.24972i	−0.238861	−	0.971054i	$-0.576774\pi$
$331$	1.43821e6	−	2.49105e6i	0.721526	−	1.24972i	0.960388	−	0.278667i	$-0.0898925\pi$
$332$		0			0
$333$	930819.	+	1.61223e6i	0.459997	+	0.796738i
$334$		0			0
$335$	−2.68253e6			−1.30597
$336$		0			0
$337$	−1.71881e6			−0.824430			−0.412215	−	0.911087i	$-0.635245\pi$
$337$	−1.71881e6			−0.824430			−0.412215	+	0.911087i	$0.635245\pi$
$338$		0			0
$339$	−368420.	−	638121.i	−0.174118	−	0.301581i
$340$		0			0
$341$	−45878.4	+	79463.8i	−0.0213660	+	0.0370069i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	3.98957e6	−	6.91014e6i	1.80459	−	3.12564i
$346$		0			0
$347$	−117937.	−	204273.i	−0.0525808	−	0.0910726i	0.838537	−	0.544845i	$-0.183411\pi$
$347$	−117937.	−	204273.i	−0.0525808	−	0.0910726i	−0.891118	+	0.453772i	$0.850078\pi$
$348$		0			0
$349$	−611300.			−0.268652			−0.134326	−	0.990937i	$-0.542887\pi$
$349$	−611300.			−0.268652			−0.134326	+	0.990937i	$0.542887\pi$
$350$		0			0
$351$	−1.35273e6			−0.586062
$352$		0			0
$353$	−1.63376e6	−	2.82975e6i	−0.697831	−	1.20868i	−0.969217	−	0.246208i	$-0.920815\pi$
$353$	−1.63376e6	−	2.82975e6i	−0.697831	−	1.20868i	0.271386	−	0.962471i	$-0.412518\pi$
$354$		0			0
$355$	−655742.	+	1.13578e6i	−0.276161	+	0.478325i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.72140e6	−	2.98156e6i	0.704932	−	1.22098i	−0.261785	−	0.965126i	$-0.584311\pi$
$359$	1.72140e6	−	2.98156e6i	0.704932	−	1.22098i	0.966716	−	0.255851i	$-0.0823556\pi$
$360$		0			0
$361$	258795.	+	448247.i	0.104517	+	0.181029i
$362$		0			0
$363$	−4.21689e6			−1.67968
$364$		0			0
$365$	4.89698e6			1.92396
$366$		0			0
$367$	70805.1	+	122638.i	0.0274410	+	0.0475292i	0.879420	−	0.476047i	$-0.157931\pi$
$367$	70805.1	+	122638.i	0.0274410	+	0.0475292i	−0.851979	+	0.523576i	$0.824598\pi$
$368$		0			0
$369$	4.65660e6	−	8.06547e6i	1.78034	−	3.08364i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.45342e6	+	2.51740e6i	−0.540903	+	0.936871i	0.457950	+	0.888978i	$0.348584\pi$
$373$	−1.45342e6	+	2.51740e6i	−0.540903	+	0.936871i	−0.998852	+	0.0478929i	$0.984749\pi$
$374$		0			0
$375$	4.96792e6	+	8.60469e6i	1.82430	+	3.15978i
$376$		0			0
$377$	−441481.			−0.159977
$378$		0			0
$379$	1.38009e6			0.493526			0.246763	−	0.969076i	$-0.420633\pi$
$379$	1.38009e6			0.493526			0.246763	+	0.969076i	$0.420633\pi$
$380$		0			0
$381$	−80046.8	−	138645.i	−0.0282508	−	0.0489319i
$382$		0			0
$383$	−976785.	+	1.69184e6i	−0.340253	+	0.589336i	−0.984480	−	0.175499i	$-0.943846\pi$
$383$	−976785.	+	1.69184e6i	−0.340253	+	0.589336i	0.644227	+	0.764835i	$0.277179\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.40418e6	+	4.16415e6i	−0.815997	+	1.41335i
$388$		0			0
$389$	−2.09471e6	−	3.62815e6i	−0.701860	−	1.21566i	−0.967813	−	0.251671i	$-0.919020\pi$
$389$	−2.09471e6	−	3.62815e6i	−0.701860	−	1.21566i	0.265952	−	0.963986i	$-0.414314\pi$
$390$		0			0
$391$	4.47608e6			1.48066
$392$		0			0
$393$	5.70461e6			1.86314
$394$		0			0
$395$	1.03952e6	+	1.80051e6i	0.335229	+	0.580633i
$396$		0			0
$397$	2.93554e6	−	5.08451e6i	0.934786	−	1.61910i	0.159772	−	0.987154i	$-0.448924\pi$
$397$	2.93554e6	−	5.08451e6i	0.934786	−	1.61910i	0.775015	−	0.631943i	$-0.217742\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.35003e6	−	2.33832e6i	0.419258	−	0.726176i	−0.576607	−	0.817022i	$-0.695624\pi$
$401$	1.35003e6	−	2.33832e6i	0.419258	−	0.726176i	0.995865	+	0.0908453i	$0.0289569\pi$
$402$		0			0
$403$	44808.4	+	77610.4i	0.0137435	+	0.0238044i
$404$		0			0
$405$	−1.62504e7			−4.92295
$406$		0			0
$407$	−394056.			−0.117916
$408$		0			0
$409$	2.59713e6	+	4.49836e6i	0.767690	+	1.32968i	0.938813	+	0.344428i	$0.111927\pi$
$409$	2.59713e6	+	4.49836e6i	0.767690	+	1.32968i	−0.171123	+	0.985250i	$0.554740\pi$
$410$		0			0
$411$	2.53878e6	−	4.39730e6i	0.741346	−	1.28405i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	3.93332e6	−	6.81271e6i	1.12109	−	1.94178i
$416$		0			0
$417$	4.13955e6	+	7.16990e6i	1.16577	+	2.01917i
$418$		0			0
$419$	−1.48129e6			−0.412198			−0.206099	−	0.978531i	$-0.566077\pi$
$419$	−1.48129e6			−0.412198			−0.206099	+	0.978531i	$0.566077\pi$
$420$		0			0
$421$	−4.52469e6			−1.24418			−0.622090	−	0.782946i	$-0.713716\pi$
$421$	−4.52469e6			−1.24418			−0.622090	+	0.782946i	$0.713716\pi$
$422$		0			0
$423$	−5.12151e6	−	8.87072e6i	−1.39171	−	2.41050i
$424$		0			0
$425$	−5.30880e6	+	9.19511e6i	−1.42569	+	2.46936i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	237923.	−	412095.i	0.0624156	−	0.108107i
$430$		0			0
$431$	2.11918e6	+	3.67052e6i	0.549508	+	0.951776i	0.998308	+	0.0581438i	$0.0185182\pi$
$431$	2.11918e6	+	3.67052e6i	0.549508	+	0.951776i	−0.448800	+	0.893632i	$0.648148\pi$
$432$		0			0
$433$	3.31287e6			0.849152			0.424576	−	0.905392i	$-0.360423\pi$
$433$	3.31287e6			0.849152			0.424576	+	0.905392i	$0.360423\pi$
$434$		0			0
$435$	−1.00701e7			−2.55158
$436$		0			0
$437$	−1.94051e6	−	3.36107e6i	−0.486086	−	0.841925i
$438$		0			0
$439$	3.30334e6	−	5.72154e6i	0.818072	−	1.41694i	−0.0890295	−	0.996029i	$-0.528377\pi$
$439$	3.30334e6	−	5.72154e6i	0.818072	−	1.41694i	0.907101	−	0.420913i	$-0.138290\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−785203.	+	1.36001e6i	−0.190096	+	0.329256i	−0.945282	−	0.326255i	$-0.894213\pi$
$443$	−785203.	+	1.36001e6i	−0.190096	+	0.329256i	0.755186	+	0.655511i	$0.227547\pi$
$444$		0			0
$445$	−1.81479e6	−	3.14331e6i	−0.434436	−	0.752465i
$446$		0			0
$447$	6.63203e6			1.56992
$448$		0			0
$449$	2.10265e6			0.492211			0.246106	−	0.969243i	$-0.420849\pi$
$449$	2.10265e6			0.492211			0.246106	+	0.969243i	$0.420849\pi$
$450$		0			0
$451$	985671.	+	1.70723e6i	0.228187	+	0.395231i
$452$		0			0
$453$	−4.85898e6	+	8.41601e6i	−1.11250	+	1.92691i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.15955e6	−	5.47249e6i	0.707675	−	1.22573i	−0.258042	−	0.966134i	$-0.583077\pi$
$457$	3.15955e6	−	5.47249e6i	0.707675	−	1.22573i	0.965717	−	0.259596i	$-0.0835894\pi$
$458$		0			0
$459$	−8.65452e6	−	1.49901e7i	−1.91739	−	3.32102i
$460$		0			0
$461$	5.38278e6			1.17965			0.589826	−	0.807530i	$-0.299196\pi$
$461$	5.38278e6			1.17965			0.589826	+	0.807530i	$0.299196\pi$
$462$		0			0
$463$	2.50782e6			0.543682			0.271841	−	0.962342i	$-0.412368\pi$
$463$	2.50782e6			0.543682			0.271841	+	0.962342i	$0.412368\pi$
$464$		0			0
$465$	1.02207e6	+	1.77027e6i	0.219203	+	0.379671i
$466$		0			0
$467$	−796459.	+	1.37951e6i	−0.168994	+	0.292706i	−0.938066	−	0.346455i	$-0.887385\pi$
$467$	−796459.	+	1.37951e6i	−0.168994	+	0.292706i	0.769072	+	0.639162i	$0.220719\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−6.47676e6	+	1.12181e7i	−1.34526	+	2.33006i
$472$		0			0
$473$	−508896.	−	881434.i	−0.104587	−	0.181149i
$474$		0			0
$475$	9.20609e6			1.87215
$476$		0			0
$477$	−1.97087e6			−0.396608
$478$		0			0
$479$	−4.50323e6	−	7.79982e6i	−0.896779	−	1.55327i	−0.831588	−	0.555393i	$-0.812568\pi$
$479$	−4.50323e6	−	7.79982e6i	−0.896779	−	1.55327i	−0.0651909	−	0.997873i	$-0.520766\pi$
$480$		0			0
$481$	−192433.	+	333303.i	−0.0379242	+	0.0656866i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.37752e6	+	2.38593e6i	−0.265915	+	0.460579i
$486$		0			0
$487$	−2.29630e6	−	3.97731e6i	−0.438740	−	0.759919i	0.558853	−	0.829267i	$-0.311242\pi$
$487$	−2.29630e6	−	3.97731e6i	−0.438740	−	0.759919i	−0.997593	+	0.0693474i	$0.977908\pi$
$488$		0			0
$489$	5.89214e6			1.11430
$490$		0			0
$491$	8.27422e6			1.54890			0.774450	−	0.632635i	$-0.218027\pi$
$491$	8.27422e6			1.54890			0.774450	+	0.632635i	$0.218027\pi$
$492$		0			0
$493$	−2.82451e6	−	4.89220e6i	−0.523391	−	0.906540i
$494$		0			0
$495$	3.88122e6	−	6.72248e6i	0.711960	−	1.23315i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.00519e6	−	6.93719e6i	0.720065	−	1.24719i	−0.240908	−	0.970548i	$-0.577445\pi$
$499$	4.00519e6	−	6.93719e6i	0.720065	−	1.24719i	0.960973	−	0.276642i	$-0.0892215\pi$
$500$		0			0
$501$	8.29478e6	+	1.43670e7i	1.47642	+	2.55724i
$502$		0			0
$503$	−8.70461e6			−1.53401			−0.767007	−	0.641639i	$-0.778255\pi$
$503$	−8.70461e6			−1.53401			−0.767007	+	0.641639i	$0.778255\pi$
$504$		0			0
$505$	−9.21335e6			−1.60764
$506$		0			0
$507$	5.19013e6	+	8.98957e6i	0.896723	+	1.55317i
$508$		0			0
$509$	122453.	−	212095.i	0.0209496	−	0.0362858i	−0.855361	−	0.518033i	$-0.826664\pi$
$509$	122453.	−	212095.i	0.0209496	−	0.0362858i	0.876310	+	0.481747i	$0.159998\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−7.50398e6	+	1.29973e7i	−1.25892	+	2.18051i
$514$		0			0
$515$	−8.83660e6	−	1.53054e7i	−1.46814	−	2.54289i
$516$		0			0
$517$	2.16816e6			0.356751
$518$		0			0
$519$	−8.80895e6			−1.43551
$520$		0			0
$521$	−1.10639e6	−	1.91632e6i	−0.178572	−	0.309296i	0.762820	−	0.646611i	$-0.223814\pi$
$521$	−1.10639e6	−	1.91632e6i	−0.178572	−	0.309296i	−0.941392	+	0.337316i	$0.890481\pi$
$522$		0			0
$523$	−2.54949e6	+	4.41584e6i	−0.407566	+	0.705926i	−0.994616	−	0.103625i	$-0.966956\pi$
$523$	−2.54949e6	+	4.41584e6i	−0.407566	+	0.705926i	0.587050	+	0.809551i	$0.300289\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−573352.	+	993074.i	−0.0899279	+	0.155760i
$528$		0			0
$529$	−627193.	−	1.08633e6i	−0.0974455	−	0.168781i
$530$		0			0
$531$	−7.42148e6			−1.14223
$532$		0			0
$533$	1.92536e6			0.293558
$534$		0			0
$535$	9.30396e6	+	1.61149e7i	1.40535	+	2.43413i
$536$		0			0
$537$	−6.81648e6	+	1.18065e7i	−1.02006	+	1.76679i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.63298e6	+	4.56045e6i	−0.386771	+	0.669908i	−0.992013	−	0.126134i	$-0.959743\pi$
$541$	−2.63298e6	+	4.56045e6i	−0.386771	+	0.669908i	0.605242	+	0.796042i	$0.293076\pi$
$542$		0			0
$543$	7.75275e6	+	1.34282e7i	1.12838	+	1.95442i
$544$		0			0
$545$	−1.03115e7			−1.48706
$546$		0			0
$547$	8.54636e6			1.22127			0.610636	−	0.791911i	$-0.290914\pi$
$547$	8.54636e6			1.22127			0.610636	+	0.791911i	$0.290914\pi$
$548$		0			0
$549$	1.55611e7	+	2.69527e7i	2.20349	+	3.81655i
$550$		0			0
$551$	−2.44902e6	+	4.24183e6i	−0.343648	+	0.595216i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.38934e6	+	7.60257e6i	−0.604877	+	1.04768i
$556$		0			0
$557$	−798468.	−	1.38299e6i	−0.109049	−	0.188878i	0.806337	−	0.591457i	$-0.201447\pi$
$557$	−798468.	−	1.38299e6i	−0.109049	−	0.188878i	−0.915385	+	0.402579i	$0.868114\pi$
$558$		0			0
$559$	−994054.			−0.134549
$560$		0			0
$561$	6.08875e6			0.816810
$562$		0			0
$563$	899521.	+	1.55802e6i	0.119603	+	0.207158i	0.919610	−	0.392832i	$-0.128505\pi$
$563$	899521.	+	1.55802e6i	0.119603	+	0.207158i	−0.800008	+	0.599990i	$0.795171\pi$
$564$		0			0
$565$	1.24248e6	−	2.15204e6i	0.163745	−	0.283614i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.02679e6	−	1.77846e6i	0.132954	−	0.230284i	−0.791860	−	0.610703i	$-0.790887\pi$
$569$	1.02679e6	−	1.77846e6i	0.132954	−	0.230284i	0.924814	+	0.380419i	$0.124220\pi$
$570$		0			0
$571$	1.61429e6	+	2.79603e6i	0.207201	+	0.358882i	0.950832	−	0.309708i	$-0.100231\pi$
$571$	1.61429e6	+	2.79603e6i	0.207201	+	0.358882i	−0.743631	+	0.668590i	$0.766898\pi$
$572$		0			0
$573$	1.52823e7			1.94447
$574$		0			0
$575$	1.82430e7			2.30105
$576$		0			0
$577$	−4.13400e6	−	7.16030e6i	−0.516929	−	0.895348i	−0.999807	−	0.0196599i	$-0.993742\pi$
$577$	−4.13400e6	−	7.16030e6i	−0.516929	−	0.895348i	0.482877	−	0.875688i	$-0.339592\pi$
$578$		0			0
$579$	1.39718e7	−	2.41999e7i	1.73204	−	2.99998i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	208589.	−	361286.i	0.0254167	−	0.0440231i
$584$		0			0
$585$	−3.79070e6	−	6.56568e6i	−0.457962	−	0.793214i
$586$		0			0
$587$	−1.12852e7			−1.35180			−0.675901	−	0.736993i	$-0.736245\pi$
$587$	−1.12852e7			−1.35180			−0.675901	+	0.736993i	$0.736245\pi$
$588$		0			0
$589$	994260.			0.118090
$590$		0			0
$591$	1.24015e6	+	2.14801e6i	0.146051	+	0.252969i
$592$		0			0
$593$	−4.50699e6	+	7.80634e6i	−0.526320	+	0.911614i	0.473209	+	0.880950i	$0.343095\pi$
$593$	−4.50699e6	+	7.80634e6i	−0.526320	+	0.911614i	−0.999530	+	0.0306638i	$0.990238\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.25899e6	−	1.43050e7i	0.948399	−	1.64268i
$598$		0			0
$599$	−4.96319e6	−	8.59650e6i	−0.565190	−	0.978937i	−0.997032	−	0.0769881i	$-0.975470\pi$
$599$	−4.96319e6	−	8.59650e6i	−0.565190	−	0.978937i	0.431842	−	0.901949i	$-0.357864\pi$
$600$		0			0
$601$	−7.45600e6			−0.842015			−0.421008	−	0.907057i	$-0.638323\pi$
$601$	−7.45600e6			−0.842015			−0.421008	+	0.907057i	$0.638323\pi$
$602$		0			0
$603$	1.66159e7			1.86093
$604$		0			0
$605$	−7.11064e6	−	1.23160e7i	−0.789805	−	1.36798i
$606$		0			0
$607$	123512.	−	213929.i	0.0136062	−	0.0235667i	−0.859142	−	0.511737i	$-0.829002\pi$
$607$	123512.	−	213929.i	0.0136062	−	0.0235667i	0.872748	+	0.488170i	$0.162336\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.05880e6	−	1.83389e6i	0.114738	−	0.198733i
$612$		0			0
$613$	4.60940e6	+	7.98372e6i	0.495443	+	0.858132i	0.999986	−	0.00525443i	$-0.00167255\pi$
$613$	4.60940e6	+	7.98372e6i	0.495443	+	0.858132i	−0.504544	+	0.863386i	$0.668339\pi$
$614$		0			0
$615$	4.39171e7			4.68215
$616$		0			0
$617$	−1.17574e7			−1.24336			−0.621682	−	0.783270i	$-0.713550\pi$
$617$	−1.17574e7			−1.24336			−0.621682	+	0.783270i	$0.713550\pi$
$618$		0			0
$619$	1.31564e6	+	2.27875e6i	0.138010	+	0.239040i	0.926743	−	0.375695i	$-0.122596\pi$
$619$	1.31564e6	+	2.27875e6i	0.138010	+	0.239040i	−0.788733	+	0.614735i	$0.789263\pi$
$620$		0			0
$621$	−1.48701e7	+	2.57557e7i	−1.54733	+	2.68006i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−6.47551e6	+	1.12159e7i	−0.663092	+	1.14851i
$626$		0			0
$627$	−2.63965e6	−	4.57202e6i	−0.268150	−	0.464450i
$628$		0			0
$629$	−4.92460e6			−0.496300
$630$		0			0
$631$	−2.00147e6			−0.200113			−0.100057	−	0.994982i	$-0.531902\pi$
$631$	−2.00147e6			−0.200113			−0.100057	+	0.994982i	$0.531902\pi$
$632$		0			0
$633$	4.42729e6	+	7.66829e6i	0.439166	+	0.760658i
$634$		0			0
$635$	269954.	−	467574.i	0.0265678	−	0.0460168i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.06174e6	−	7.03514e6i	0.393514	−	0.681586i
$640$		0			0
$641$	−7.74386e6	−	1.34128e7i	−0.744410	−	1.28936i	−0.950470	−	0.310817i	$-0.899398\pi$
$641$	−7.74386e6	−	1.34128e7i	−0.744410	−	1.28936i	0.206060	−	0.978539i	$-0.433936\pi$
$642$		0			0
$643$	4.97821e6			0.474838			0.237419	−	0.971407i	$-0.423699\pi$
$643$	4.97821e6			0.474838			0.237419	+	0.971407i	$0.423699\pi$
$644$		0			0
$645$	−2.26741e7			−2.14601
$646$		0			0
$647$	6.40683e6	+	1.10970e7i	0.601704	+	1.04218i	0.992563	+	0.121731i	$0.0388446\pi$
$647$	6.40683e6	+	1.10970e7i	0.601704	+	1.04218i	−0.390859	+	0.920450i	$0.627822\pi$
$648$		0			0
$649$	785459.	−	1.36046e6i	0.0732001	−	0.126786i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.90750e6	−	3.30389e6i	0.175058	−	0.303210i	−0.765123	−	0.643884i	$-0.777322\pi$
$653$	1.90750e6	−	3.30389e6i	0.175058	−	0.303210i	0.940181	+	0.340674i	$0.110655\pi$
$654$		0			0
$655$	9.61927e6	+	1.66611e7i	0.876070	+	1.51740i
$656$		0			0
$657$	−3.03324e7			−2.74154
$658$		0			0
$659$	−1.25889e7			−1.12921			−0.564604	−	0.825362i	$-0.690971\pi$
$659$	−1.25889e7			−1.12921			−0.564604	+	0.825362i	$0.690971\pi$
$660$		0			0
$661$	−8.75648e6	−	1.51667e7i	−0.779518	−	1.35016i	−0.932220	−	0.361892i	$-0.882131\pi$
$661$	−8.75648e6	−	1.51667e7i	−0.779518	−	1.35016i	0.152702	−	0.988272i	$-0.451203\pi$
$662$		0			0
$663$	2.97337e6	−	5.15003e6i	0.262703	−	0.455015i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.85304e6	+	8.40571e6i	−0.422376	+	0.731577i
$668$		0			0
$669$	−1.16334e7	−	2.01496e7i	−1.00494	−	1.74061i
$670$		0			0
$671$	−6.58771e6			−0.564843
$672$		0			0
$673$	−2.20008e7			−1.87241			−0.936205	−	0.351453i	$-0.885688\pi$
$673$	−2.20008e7			−1.87241			−0.936205	+	0.351453i	$0.885688\pi$
$674$		0			0
$675$	−3.52729e7	−	6.10945e7i	−2.97977	−	5.16111i
$676$		0			0
$677$	5.14532e6	−	8.91195e6i	0.431460	−	0.747311i	−0.565539	−	0.824721i	$-0.691332\pi$
$677$	5.14532e6	−	8.91195e6i	0.431460	−	0.747311i	0.996999	+	0.0774107i	$0.0246653\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	9.83379e6	−	1.70326e7i	0.812556	−	1.40739i
$682$		0			0
$683$	1.07660e7	+	1.86473e7i	0.883085	+	1.52955i	0.847893	+	0.530168i	$0.177871\pi$
$683$	1.07660e7	+	1.86473e7i	0.883085	+	1.52955i	0.0351926	+	0.999381i	$0.488796\pi$
$684$		0			0
$685$	1.71239e7			1.39436
$686$		0			0
$687$	−1.72564e7			−1.39495
$688$		0			0
$689$	−203724.	−	352860.i	−0.0163491	−	0.0283175i
$690$		0			0
$691$	−4.43434e6	+	7.68050e6i	−0.353292	+	0.611920i	−0.986824	−	0.161797i	$-0.948271\pi$
$691$	−4.43434e6	+	7.68050e6i	−0.353292	+	0.611920i	0.633532	+	0.773716i	$0.281604\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.39604e7	+	2.41802e7i	−1.09632	+	1.89888i
$696$		0			0
$697$	1.23181e7	+	2.13356e7i	0.960423	+	1.66350i
$698$		0			0
$699$	−1.39939e7			−1.08329
$700$		0			0
$701$	1.79181e7			1.37720			0.688598	−	0.725143i	$-0.258227\pi$
$701$	1.79181e7			1.37720			0.688598	+	0.725143i	$0.258227\pi$
$702$		0			0
$703$	2.13496e6	+	3.69786e6i	0.162930	+	0.282203i
$704$		0			0
$705$	2.41509e7	−	4.18305e7i	1.83004	−	3.16972i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.24392e6	+	2.15452e6i	−0.0929341	+	0.160967i	−0.908745	−	0.417353i	$-0.862958\pi$
$709$	−1.24392e6	+	2.15452e6i	−0.0929341	+	0.160967i	0.815810	+	0.578319i	$0.196291\pi$
$710$		0			0
$711$	−6.43891e6	−	1.11525e7i	−0.477682	−	0.827369i
$712$		0			0
$713$	1.97025e6			0.145143
$714$		0			0
$715$	1.60477e6			0.117394
$716$		0			0
$717$	5.10110e6	+	8.83537e6i	0.370566	+	0.641840i
$718$		0			0
$719$	6.48481e6	−	1.12320e7i	0.467816	−	0.810281i	−0.531507	−	0.847054i	$-0.678374\pi$
$719$	6.48481e6	−	1.12320e7i	0.467816	−	0.810281i	0.999324	+	0.0367721i	$0.0117076\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	4.93114e6	−	8.54099e6i	0.350834	−	0.607662i
$724$		0			0
$725$	−1.15118e7	−	1.99390e7i	−0.813387	−	1.40883i
$726$		0			0
$727$	3.25820e6			0.228634			0.114317	−	0.993444i	$-0.463532\pi$
$727$	3.25820e6			0.228634			0.114317	+	0.993444i	$0.463532\pi$
$728$		0			0
$729$	2.45400e7			1.71024
$730$		0			0
$731$	−6.35978e6	−	1.10155e7i	−0.440198	−	0.762446i
$732$		0			0
$733$	3.25223e6	−	5.63302e6i	0.223574	−	0.387241i	−0.732317	−	0.680964i	$-0.761561\pi$
$733$	3.25223e6	−	5.63302e6i	0.223574	−	0.387241i	0.955891	+	0.293723i	$0.0948943\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.75855e6	+	3.04591e6i	−0.119258	+	0.206561i
$738$		0			0
$739$	7.92777e6	+	1.37313e7i	0.533998	+	0.924912i	0.999211	+	0.0397134i	$0.0126445\pi$
$739$	7.92777e6	+	1.37313e7i	0.533998	+	0.924912i	−0.465213	+	0.885199i	$0.654022\pi$
$740$		0			0
$741$	−5.15618e6			−0.344971
$742$		0			0
$743$	2.11717e6			0.140696			0.0703482	−	0.997522i	$-0.477589\pi$
$743$	2.11717e6			0.140696			0.0703482	+	0.997522i	$0.477589\pi$
$744$		0			0
$745$	1.11831e7	+	1.93697e7i	0.738196	+	1.27859i
$746$		0			0
$747$	−2.43634e7	+	4.21987e7i	−1.59748	+	2.76692i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	2.27681e6	−	3.94355e6i	0.147308	−	0.255145i	−0.782924	−	0.622118i	$-0.786272\pi$
$751$	2.27681e6	−	3.94355e6i	0.147308	−	0.255145i	0.930232	+	0.366973i	$0.119606\pi$
$752$		0			0
$753$	2.44970e7	+	4.24301e7i	1.57444	+	2.72701i
$754$		0			0
$755$	−3.27734e7			−2.09245
$756$		0			0
$757$	6.04759e6			0.383568			0.191784	−	0.981437i	$-0.438573\pi$
$757$	6.04759e6			0.383568			0.191784	+	0.981437i	$0.438573\pi$
$758$		0			0
$759$	−5.23080e6	−	9.06001e6i	−0.329582	−	0.570853i
$760$		0			0
$761$	6.76130e6	−	1.17109e7i	0.423222	−	0.733043i	−0.573030	−	0.819534i	$-0.694232\pi$
$761$	6.76130e6	−	1.17109e7i	0.423222	−	0.733043i	0.996253	+	0.0864916i	$0.0275656\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	4.85044e7	−	8.40121e7i	2.99659	−	5.19025i
$766$		0			0
$767$	−767139.	−	1.32872e6i	−0.0470854	−	0.0815542i
$768$		0			0
$769$	−6.83797e6			−0.416976			−0.208488	−	0.978025i	$-0.566854\pi$
$769$	−6.83797e6			−0.416976			−0.208488	+	0.978025i	$0.566854\pi$
$770$		0			0
$771$	2.20669e7			1.33692
$772$		0			0
$773$	2.63202e6	+	4.55880e6i	0.158431	+	0.274411i	0.934303	−	0.356479i	$-0.116023\pi$
$773$	2.63202e6	+	4.55880e6i	0.158431	+	0.274411i	−0.775872	+	0.630891i	$0.782690\pi$
$774$		0			0
$775$	−2.33679e6	+	4.04744e6i	−0.139754	+	0.242062i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.06805e7	−	1.84992e7i	0.630594	−	1.09222i
$780$		0			0
$781$	859756.	+	1.48914e6i	0.0504368	+	0.0873591i
$782$		0			0
$783$	3.75335e7			2.18784
$784$		0			0
$785$	−4.36852e7			−2.53023
$786$		0			0
$787$	−9.38998e6	−	1.62639e7i	−0.540416	−	0.936027i	−0.998880	−	0.0473147i	$-0.984934\pi$
$787$	−9.38998e6	−	1.62639e7i	−0.540416	−	0.936027i	0.458464	−	0.888713i	$-0.348400\pi$
$788$		0			0
$789$	−1.09251e6	+	1.89228e6i	−0.0624787	+	0.108216i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.21703e6	+	5.57206e6i	−0.181665	+	0.314654i
$794$		0			0
$795$	−4.64689e6	−	8.04865e6i	−0.260762	−	0.451653i
$796$		0			0
$797$	−2.71298e7			−1.51286			−0.756432	−	0.654072i	$-0.773059\pi$
$797$	−2.71298e7			−1.51286			−0.756432	+	0.654072i	$0.773059\pi$
$798$		0			0
$799$	2.70959e7			1.50154
$800$		0			0
$801$	1.12410e7	+	1.94700e7i	0.619047	+	1.07222i
$802$		0			0
$803$	3.21026e6	−	5.56034e6i	0.175692	−	0.304307i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	8.86804e6	−	1.53599e7i	0.479340	−	0.830242i
$808$		0			0
$809$	−2.26690e6	−	3.92639e6i	−0.121776	−	0.210922i	0.798692	−	0.601740i	$-0.205526\pi$
$809$	−2.26690e6	−	3.92639e6i	−0.121776	−	0.210922i	−0.920468	+	0.390818i	$0.872192\pi$
$810$		0			0
$811$	−1.91621e7			−1.02303			−0.511517	−	0.859273i	$-0.670916\pi$
$811$	−1.91621e7			−1.02303			−0.511517	+	0.859273i	$0.670916\pi$
$812$		0			0
$813$	4.32373e7			2.29421
$814$		0			0
$815$	9.93548e6	+	1.72088e7i	0.523956	+	0.907518i
$816$		0			0
$817$	−5.51430e6	+	9.55106e6i	−0.289025	+	0.500606i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.61069e7	+	2.78980e7i	−0.833977	+	1.44449i	0.0608845	+	0.998145i	$0.480608\pi$
$821$	−1.61069e7	+	2.78980e7i	−0.833977	+	1.44449i	−0.894861	+	0.446345i	$0.852725\pi$
$822$		0			0
$823$	1.45197e6	+	2.51489e6i	0.0747238	+	0.129425i	0.900966	−	0.433889i	$-0.142859\pi$
$823$	1.45197e6	+	2.51489e6i	0.0747238	+	0.129425i	−0.826242	+	0.563315i	$0.809526\pi$
$824$		0			0
$825$	2.48157e7			1.26938
$826$		0			0
$827$	3.30382e7			1.67978			0.839890	−	0.542756i	$-0.182619\pi$
$827$	3.30382e7			1.67978			0.839890	+	0.542756i	$0.182619\pi$
$828$		0			0
$829$	−1.77939e6	−	3.08199e6i	−0.0899257	−	0.155756i	0.817554	−	0.575852i	$-0.195330\pi$
$829$	−1.77939e6	−	3.08199e6i	−0.0899257	−	0.155756i	−0.907480	+	0.420096i	$0.861996\pi$
$830$		0			0
$831$	1.93494e7	−	3.35141e7i	0.971997	−	1.68355i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.79738e7	+	4.84520e7i	−1.38846	+	2.40489i
$836$		0			0
$837$	−3.80949e6	−	6.59822e6i	−0.187955	−	0.325547i
$838$		0			0
$839$	7.33186e6			0.359591			0.179796	−	0.983704i	$-0.442456\pi$
$839$	7.33186e6			0.359591			0.179796	+	0.983704i	$0.442456\pi$
$840$		0			0
$841$	−8.26160e6			−0.402786
$842$		0			0
$843$	9.48457e6	+	1.64278e7i	0.459673	+	0.796176i
$844$		0			0
$845$	−1.75035e7	+	3.03169e7i	−0.843301	+	1.46064i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.23533e7	+	5.60376e7i	−1.54046	+	2.66815i
$850$		0			0
$851$	4.23069e6	+	7.32776e6i	0.200257	+	0.346855i
$852$		0			0
$853$	3.34015e6			0.157178			0.0785892	−	0.996907i	$-0.474958\pi$
$853$	3.34015e6			0.157178			0.0785892	+	0.996907i	$0.474958\pi$
$854$		0			0
$855$	−8.41124e7			−3.93500
$856$		0			0
$857$	−1.48338e7	−	2.56928e7i	−0.689921	−	1.19498i	−0.971863	−	0.235546i	$-0.924312\pi$
$857$	−1.48338e7	−	2.56928e7i	−0.689921	−	1.19498i	0.281942	−	0.959431i	$-0.409021\pi$
$858$		0			0
$859$	1.52227e7	−	2.63664e7i	0.703895	−	1.21918i	−0.263194	−	0.964743i	$-0.584776\pi$
$859$	1.52227e7	−	2.63664e7i	0.703895	−	1.21918i	0.967089	−	0.254438i	$-0.0818906\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.10120e7	−	1.90733e7i	0.503314	−	0.871766i	−0.496678	−	0.867935i	$-0.665447\pi$
$863$	1.10120e7	−	1.90733e7i	0.503314	−	0.871766i	0.999993	−	0.00383127i	$-0.00121953\pi$
$864$		0			0
$865$	−1.48539e7	−	2.57277e7i	−0.674994	−	1.16912i
$866$		0			0
$867$	3.46200e7			1.56416
$868$		0			0
$869$	2.72587e6			0.122449
$870$		0			0
$871$	1.71754e6	+	2.97486e6i	0.0767116	+	0.132868i
$872$		0			0
$873$	8.53251e6	−	1.47787e7i	0.378914	−	0.656299i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.04283e6	−	1.39306e7i	0.353110	−	0.611605i	−0.633683	−	0.773593i	$-0.718457\pi$
$877$	8.04283e6	−	1.39306e7i	0.353110	−	0.611605i	0.986793	+	0.161989i	$0.0517908\pi$
$878$		0			0
$879$	7.50420e6	+	1.29977e7i	0.327591	+	0.567405i
$880$		0			0
$881$	−2.03474e7			−0.883221			−0.441610	−	0.897207i	$-0.645593\pi$
$881$	−2.03474e7			−0.883221			−0.441610	+	0.897207i	$0.645593\pi$
$882$		0			0
$883$	−3.79836e7			−1.63943			−0.819717	−	0.572769i	$-0.805869\pi$
$883$	−3.79836e7			−1.63943			−0.819717	+	0.572769i	$0.805869\pi$
$884$		0			0
$885$	−1.74983e7	−	3.03079e7i	−0.750995	−	1.30076i
$886$		0			0
$887$	−4.17498e6	+	7.23127e6i	−0.178174	+	0.308607i	−0.941255	−	0.337696i	$-0.890352\pi$
$887$	−4.17498e6	+	7.23127e6i	−0.178174	+	0.308607i	0.763081	+	0.646303i	$0.223686\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.06531e7	+	1.84517e7i	−0.449553	+	0.778648i
$892$		0			0
$893$	−1.17469e7	−	2.03462e7i	−0.492940	−	0.853797i
$894$		0			0
$895$	−4.59765e7			−1.91857
$896$		0			0
$897$	−1.02176e7			−0.424002
$898$		0			0
$899$	−1.24328e6	−	2.15342e6i	−0.0513060	−	0.0888646i
$900$		0			0
$901$	2.60678e6	−	4.51507e6i	0.106977	−	0.185290i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.61458e7	+	4.52859e7i	−1.06116	+	1.83798i
$906$		0			0
$907$	−1.34802e7	−	2.33485e7i	−0.544101	−	0.942411i	−0.998663	−	0.0516955i	$-0.983537\pi$
$907$	−1.34802e7	−	2.33485e7i	−0.544101	−	0.942411i	0.454562	−	0.890715i	$-0.349796\pi$
$908$		0			0
$909$	5.70685e7			2.29080
$910$		0			0
$911$	−3.84152e7			−1.53358			−0.766792	−	0.641896i	$-0.778148\pi$
$911$	−3.84152e7			−1.53358			−0.766792	+	0.641896i	$0.778148\pi$
$912$		0			0
$913$	−5.15705e6	−	8.93227e6i	−0.204750	−	0.354638i
$914$		0			0
$915$	−7.33796e7	+	1.27097e8i	−2.89750	+	5.01861i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.26381e7	−	2.18898e7i	0.493620	−	0.854975i	−0.506353	−	0.862326i	$-0.669007\pi$
$919$	1.26381e7	−	2.18898e7i	0.493620	−	0.854975i	0.999973	+	0.00735108i	$0.00233994\pi$
$920$		0			0
$921$	−1.22016e7	−	2.11339e7i	−0.473990	−	0.820975i
$922$		0			0
$923$	1.67941e6			0.0648861
$924$		0			0
$925$	−2.00710e7			−0.771286
$926$		0			0
$927$	5.47348e7	+	9.48035e7i	2.09201	+	3.62347i
$928$		0			0
$929$	−4.58393e6	+	7.93960e6i	−0.174261	+	0.301828i	−0.939905	−	0.341436i	$-0.889087\pi$
$929$	−4.58393e6	+	7.93960e6i	−0.174261	+	0.301828i	0.765645	+	0.643264i	$0.222420\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−3.09350e7	+	5.35810e7i	−1.16344	+	2.01515i
$934$		0			0
$935$	1.02670e7	+	1.77830e7i	0.384074	+	0.665236i
$936$		0			0
$937$	7.16427e6			0.266577			0.133289	−	0.991077i	$-0.457446\pi$
$937$	7.16427e6			0.266577			0.133289	+	0.991077i	$0.457446\pi$
$938$		0			0
$939$	4.95328e7			1.83328
$940$		0			0
$941$	4.24781e6	+	7.35743e6i	0.156384	+	0.270864i	0.933562	−	0.358416i	$-0.116683\pi$
$941$	4.24781e6	+	7.35743e6i	0.156384	+	0.270864i	−0.777178	+	0.629280i	$0.783350\pi$
$942$		0			0
$943$	2.11648e7	−	3.66585e7i	0.775060	−	1.34244i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.91006e6	−	1.71647e7i	0.359088	−	0.621959i	−0.628720	−	0.777631i	$-0.716421\pi$
$947$	9.91006e6	−	1.71647e7i	0.359088	−	0.621959i	0.987809	+	0.155672i	$0.0497543\pi$
$948$		0			0
$949$	−3.13539e6	−	5.43065e6i	−0.113012	−	0.195743i
$950$		0			0
$951$	3.22901e7			1.15776
$952$		0			0
$953$	4.97501e7			1.77444			0.887221	−	0.461344i	$-0.152633\pi$
$953$	4.97501e7			1.77444			0.887221	+	0.461344i	$0.152633\pi$
$954$		0			0
$955$	2.57694e7	+	4.46339e7i	0.914315	+	1.58364i
$956$		0			0
$957$	−6.60153e6	+	1.14342e7i	−0.233005	+	0.403576i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.40622e7	−	2.43564e7i	0.491185	−	0.850757i
$962$		0			0
$963$	−5.76298e7	−	9.98177e7i	−2.00254	−	3.46850i
$964$		0			0
$965$	9.42388e7			3.25770
$966$		0			0
$967$	−1.50099e7			−0.516192			−0.258096	−	0.966119i	$-0.583095\pi$
$967$	−1.50099e7			−0.516192			−0.258096	+	0.966119i	$0.583095\pi$
$968$		0			0
$969$	−3.29883e7	−	5.71374e7i	−1.12863	−	1.95484i
$970$		0			0
$971$	1.29328e7	−	2.24002e7i	0.440193	−	0.762437i	−0.557511	−	0.830170i	$-0.688243\pi$
$971$	1.29328e7	−	2.24002e7i	0.440193	−	0.762437i	0.997703	+	0.0677334i	$0.0215767\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.21185e7	−	2.09898e7i	0.408259	−	0.707126i
$976$		0			0
$977$	2.54394e7	+	4.40623e7i	0.852649	+	1.47683i	0.878809	+	0.477173i	$0.158338\pi$
$977$	2.54394e7	+	4.40623e7i	0.852649	+	1.47683i	−0.0261610	+	0.999658i	$0.508328\pi$
$978$		0			0
$979$	−4.75880e6			−0.158687
$980$		0			0
$981$	6.38704e7			2.11898
$982$		0			0
$983$	−2.51588e7	−	4.35764e7i	−0.830437	−	1.43836i	−0.897692	−	0.440623i	$-0.854758\pi$
$983$	−2.51588e7	−	4.35764e7i	−0.830437	−	1.43836i	0.0672556	−	0.997736i	$-0.478576\pi$
$984$		0			0
$985$	−4.18235e6	+	7.24405e6i	−0.137350	+	0.237898i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.09273e7	+	1.89266e7i	−0.355239	+	0.615293i
$990$		0			0
$991$	7.09160e6	+	1.22830e7i	0.229382	+	0.397302i	0.957625	−	0.288017i	$-0.0929961\pi$
$991$	7.09160e6	+	1.22830e7i	0.229382	+	0.397302i	−0.728243	+	0.685319i	$0.759663\pi$
$992$		0			0
$993$	−8.40167e7			−2.70391
$994$		0			0
$995$	5.57061e7			1.78380
$996$		0			0
$997$	8.15878e6	+	1.41314e7i	0.259949	+	0.450244i	0.966228	−	0.257689i	$-0.0829611\pi$
$997$	8.15878e6	+	1.41314e7i	0.259949	+	0.450244i	−0.706279	+	0.707933i	$0.749628\pi$
$998$		0			0
$999$	1.63601e7	−	2.83365e7i	0.518648	−	0.898324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.e.l.177.1		8
7.2	even	3		196.6.a.k.1.4	yes	4
7.3	odd	6	inner	196.6.e.l.165.4		8
7.4	even	3	inner	196.6.e.l.165.1		8
7.5	odd	6		196.6.a.k.1.1	✓	4
7.6	odd	2	inner	196.6.e.l.177.4		8
28.19	even	6		784.6.a.bi.1.4		4
28.23	odd	6		784.6.a.bi.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.6.a.k.1.1	✓	4	7.5	odd	6
196.6.a.k.1.4	yes	4	7.2	even	3
196.6.e.l.165.1		8	7.4	even	3	inner
196.6.e.l.165.4		8	7.3	odd	6	inner
196.6.e.l.177.1		8	1.1	even	1	trivial
196.6.e.l.177.4		8	7.6	odd	2	inner
784.6.a.bi.1.1		4	28.23	odd	6
784.6.a.bi.1.4		4	28.19	even	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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-14.6044 - 25.2955i) q^{3} +(49.2526 - 85.3080i) q^{5} +(-305.076 + 528.407i) q^{9} +(-64.5760 - 111.849i) q^{11} -126.140 q^{13} -2877.22 q^{15} +(-807.019 - 1397.80i) q^{17} +(-699.734 + 1211.97i) q^{19} +(-1386.61 + 2401.68i) q^{23} +(-3289.14 - 5696.96i) q^{25} +10724.1 q^{27} +3499.94 q^{29} +(-355.228 - 615.273i) q^{31} +(-1886.19 + 3266.97i) q^{33} +(1525.55 - 2642.33i) q^{37} +(1842.19 + 3190.77i) q^{39} -15263.7 q^{41} +7880.58 q^{43} +(30051.6 + 52050.9i) q^{45} +(-8393.83 + 14538.5i) q^{47} +(-23572.0 + 40828.0i) q^{51} +(1615.06 + 2797.37i) q^{53} -12722.2 q^{55} +40876.7 q^{57} +(6081.66 + 10533.8i) q^{59} +(25503.7 - 44173.7i) q^{61} +(-6212.71 + 10760.7i) q^{65} +(-13616.2 - 23583.9i) q^{67} +81002.2 q^{69} -13313.9 q^{71} +(24856.5 + 43052.6i) q^{73} +(-96071.7 + 166401. i) q^{75} +(-10553.0 + 18278.3i) q^{79} +(-82484.8 - 142868. i) q^{81} +79860.2 q^{83} -158991. q^{85} +(-51114.4 - 88532.7i) q^{87} +(18423.3 - 31910.0i) q^{89} +(-10375.8 + 17971.4i) q^{93} +(68927.4 + 119386. i) q^{95} -27968.5 q^{97} +78802.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1480 q^{9} + 444 q^{11} - 7648 q^{15} - 3408 q^{23} - 11904 q^{25} + 41448 q^{29} - 13732 q^{37} - 25608 q^{39} - 57992 q^{43} - 181852 q^{51} - 528 q^{53} + 179080 q^{57} - 110220 q^{65} - 195384 q^{67}+ \cdots + 132824 q^{99}+O(q^{100}) \) 8 * q - 1480 * q^9 + 444 * q^11 - 7648 * q^15 - 3408 * q^23 - 11904 * q^25 + 41448 * q^29 - 13732 * q^37 - 25608 * q^39 - 57992 * q^43 - 181852 * q^51 - 528 * q^53 + 179080 * q^57 - 110220 * q^65 - 195384 * q^67 + 43344 * q^71 + 117304 * q^79 - 182456 * q^81 - 182600 * q^85 - 250152 * q^93 + 255552 * q^95 + 132824 * q^99

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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