LMFDB - Embedded newform 64.12.e.a.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,12,Mod(17,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$49.1739635558$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	64.17
Dual form			64.12.e.a.49.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(145.072 + 145.072i) q^{3} +(-4652.81 + 4652.81i) q^{5} +43253.0i q^{7} -135056. i q^{9} +O(q^{10})$	\(q+(145.072 + 145.072i) q^{3} +(-4652.81 + 4652.81i) q^{5} +43253.0i q^{7} -135056. i q^{9} +(685114. - 685114. i) q^{11} +(-1.40072e6 - 1.40072e6i) q^{13} -1.34998e6 q^{15} +3.84591e6 q^{17} +(7.81673e6 + 7.81673e6i) q^{19} +(-6.27478e6 + 6.27478e6i) q^{21} -1.99742e7i q^{23} +5.53080e6i q^{25} +(4.52917e7 - 4.52917e7i) q^{27} +(1.18663e8 + 1.18663e8i) q^{29} -5.32181e7 q^{31} +1.98781e8 q^{33} +(-2.01248e8 - 2.01248e8i) q^{35} +(-3.70312e8 + 3.70312e8i) q^{37} -4.06411e8i q^{39} +8.83045e7i q^{41} +(-1.81785e8 + 1.81785e8i) q^{43} +(6.28388e8 + 6.28388e8i) q^{45} +1.92709e9 q^{47} +1.06502e8 q^{49} +(5.57932e8 + 5.57932e8i) q^{51} +(1.39454e9 - 1.39454e9i) q^{53} +6.37541e9i q^{55} +2.26797e9i q^{57} +(2.09985e9 - 2.09985e9i) q^{59} +(1.23678e9 + 1.23678e9i) q^{61} +5.84156e9 q^{63} +1.30346e10 q^{65} +(9.73212e9 + 9.73212e9i) q^{67} +(2.89769e9 - 2.89769e9i) q^{69} -2.30143e9i q^{71} -2.18626e10i q^{73} +(-8.02362e8 + 8.02362e8i) q^{75} +(2.96333e10 + 2.96333e10i) q^{77} +1.21163e8 q^{79} -1.07836e10 q^{81} +(4.69569e10 + 4.69569e10i) q^{83} +(-1.78943e10 + 1.78943e10i) q^{85} +3.44292e10i q^{87} +6.68453e10i q^{89} +(6.05856e10 - 6.05856e10i) q^{91} +(-7.72043e9 - 7.72043e9i) q^{93} -7.27395e10 q^{95} +4.52611e10 q^{97} +(-9.25284e10 - 9.25284e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 - 2 * q^5	$ 42 q + 2 q^{3} - 2 q^{5} + 540846 q^{11} - 2 q^{13} + 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} + 354292 q^{21} + 66463304 q^{27} + 77673206 q^{29} - 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} - 522762058 q^{37} - 3824193658 q^{43} + 97301954 q^{45} + 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} - 2100608058 q^{53} - 955824746 q^{59} + 2150827022 q^{61} - 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} - 16193060732 q^{69} - 28890034486 q^{75} - 22711870540 q^{77} - 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} - 84575506252 q^{85} + 147369662716 q^{91} - 69689773328 q^{93} - 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 - 2 * q^5 + 540846 * q^11 - 2 * q^13 + 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 + 354292 * q^21 + 66463304 * q^27 + 77673206 * q^29 - 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 - 522762058 * q^37 - 3824193658 * q^43 + 97301954 * q^45 + 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 - 2100608058 * q^53 - 955824746 * q^59 + 2150827022 * q^61 - 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 - 16193060732 * q^69 - 28890034486 * q^75 - 22711870540 * q^77 - 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 - 84575506252 * q^85 + 147369662716 * q^91 - 69689773328 * q^93 - 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	145.072	+	145.072i	0.344679	+	0.344679i	0.858123	−	0.513444i	$-0.171631\pi$
$3$	145.072	+	145.072i	0.344679	+	0.344679i	−0.513444	+	0.858123i	$0.671631\pi$
$4$		0			0
$5$	−4652.81	+	4652.81i	−0.665856	+	0.665856i	−0.956754	−	0.290898i	$-0.906046\pi$
$5$	−4652.81	+	4652.81i	−0.665856	+	0.665856i	0.290898	+	0.956754i	$0.406046\pi$
$6$		0			0
$7$			43253.0i			0.972696i	0.873765	+	0.486348i	$0.161671\pi$
$7$			43253.0i			0.972696i	−0.873765	+	0.486348i	$0.838329\pi$
$8$		0			0
$9$		−	135056.i		−	0.762392i
$10$		0			0
$11$	685114.	−	685114.i	1.28263	−	1.28263i	0.343472	−	0.939163i	$-0.388397\pi$
$11$	685114.	−	685114.i	1.28263	−	1.28263i	0.939163	−	0.343472i	$-0.111603\pi$
$12$		0			0
$13$	−1.40072e6	−	1.40072e6i	−1.04632	−	1.04632i	−0.998874	−	0.0474458i	$-0.984892\pi$
$13$	−1.40072e6	−	1.40072e6i	−1.04632	−	1.04632i	−0.0474458	−	0.998874i	$-0.515108\pi$
$14$		0			0
$15$	−1.34998e6			−0.459014
$16$		0			0
$17$	3.84591e6			0.656946			0.328473	−	0.944513i	$-0.393466\pi$
$17$	3.84591e6			0.656946			0.328473	+	0.944513i	$0.393466\pi$
$18$		0			0
$19$	7.81673e6	+	7.81673e6i	0.724236	+	0.724236i	0.969465	−	0.245229i	$-0.0788631\pi$
$19$	7.81673e6	+	7.81673e6i	0.724236	+	0.724236i	−0.245229	+	0.969465i	$0.578863\pi$
$20$		0			0
$21$	−6.27478e6	+	6.27478e6i	−0.335268	+	0.335268i
$22$		0			0
$23$		−	1.99742e7i		−	0.647094i	−0.946212	−	0.323547i	$-0.895125\pi$
$23$		−	1.99742e7i		−	0.647094i	0.946212	−	0.323547i	$-0.104875\pi$
$24$		0			0
$25$			5.53080e6i			0.113271i
$26$		0			0
$27$	4.52917e7	−	4.52917e7i	0.607460	−	0.607460i
$28$		0			0
$29$	1.18663e8	+	1.18663e8i	1.07430	+	1.07430i	0.997008	+	0.0772929i	$0.0246277\pi$
$29$	1.18663e8	+	1.18663e8i	1.07430	+	1.07430i	0.0772929	+	0.997008i	$0.475372\pi$
$30$		0			0
$31$	−5.32181e7			−0.333864			−0.166932	−	0.985968i	$-0.553386\pi$
$31$	−5.32181e7			−0.333864			−0.166932	+	0.985968i	$0.553386\pi$
$32$		0			0
$33$	1.98781e8			0.884196
$34$		0			0
$35$	−2.01248e8	−	2.01248e8i	−0.647676	−	0.647676i
$36$		0			0
$37$	−3.70312e8	+	3.70312e8i	−0.877928	+	0.877928i	−0.993320	−	0.115392i	$-0.963188\pi$
$37$	−3.70312e8	+	3.70312e8i	−0.877928	+	0.877928i	0.115392	+	0.993320i	$0.463188\pi$
$38$		0			0
$39$		−	4.06411e8i		−	0.721290i
$40$		0			0
$41$			8.83045e7i			0.119034i	0.998227	+	0.0595171i	$0.0189561\pi$
$41$			8.83045e7i			0.119034i	−0.998227	+	0.0595171i	$0.981044\pi$
$42$		0			0
$43$	−1.81785e8	+	1.81785e8i	−0.188573	+	0.188573i	−0.795079	−	0.606506i	$-0.792571\pi$
$43$	−1.81785e8	+	1.81785e8i	−0.188573	+	0.188573i	0.606506	+	0.795079i	$0.292571\pi$
$44$		0			0
$45$	6.28388e8	+	6.28388e8i	0.507644	+	0.507644i
$46$		0			0
$47$	1.92709e9			1.22564			0.612821	−	0.790222i	$-0.290035\pi$
$47$	1.92709e9			1.22564			0.612821	+	0.790222i	$0.290035\pi$
$48$		0			0
$49$	1.06502e8			0.0538618
$50$		0			0
$51$	5.57932e8	+	5.57932e8i	0.226436	+	0.226436i
$52$		0			0
$53$	1.39454e9	−	1.39454e9i	0.458051	−	0.458051i	−0.439964	−	0.898015i	$-0.645009\pi$
$53$	1.39454e9	−	1.39454e9i	0.458051	−	0.458051i	0.898015	+	0.439964i	$0.145009\pi$
$54$		0			0
$55$			6.37541e9i			1.70810i
$56$		0			0
$57$			2.26797e9i			0.499259i
$58$		0			0
$59$	2.09985e9	−	2.09985e9i	0.382385	−	0.382385i	−0.489575	−	0.871961i	$-0.662848\pi$
$59$	2.09985e9	−	2.09985e9i	0.382385	−	0.382385i	0.871961	+	0.489575i	$0.162848\pi$
$60$		0			0
$61$	1.23678e9	+	1.23678e9i	0.187491	+	0.187491i	0.794610	−	0.607120i	$-0.207675\pi$
$61$	1.23678e9	+	1.23678e9i	0.187491	+	0.187491i	−0.607120	+	0.794610i	$0.707675\pi$
$62$		0			0
$63$	5.84156e9			0.741576
$64$		0			0
$65$	1.30346e10			1.39340
$66$		0			0
$67$	9.73212e9	+	9.73212e9i	0.880635	+	0.880635i	0.993599	−	0.112964i	$-0.0360344\pi$
$67$	9.73212e9	+	9.73212e9i	0.880635	+	0.880635i	−0.112964	+	0.993599i	$0.536034\pi$
$68$		0			0
$69$	2.89769e9	−	2.89769e9i	0.223040	−	0.223040i
$70$		0			0
$71$		−	2.30143e9i		−	0.151383i	−0.997131	−	0.0756914i	$-0.975884\pi$
$71$		−	2.30143e9i		−	0.151383i	0.997131	−	0.0756914i	$-0.0241164\pi$
$72$		0			0
$73$		−	2.18626e10i		−	1.23432i	−0.786840	−	0.617158i	$-0.788284\pi$
$73$		−	2.18626e10i		−	1.23432i	0.786840	−	0.617158i	$-0.211716\pi$
$74$		0			0
$75$	−8.02362e8	+	8.02362e8i	−0.0390421	+	0.0390421i
$76$		0			0
$77$	2.96333e10	+	2.96333e10i	1.24761	+	1.24761i
$78$		0			0
$79$	1.21163e8			0.00443018			0.00221509	−	0.999998i	$-0.499295\pi$
$79$	1.21163e8			0.00443018			0.00221509	+	0.999998i	$0.499295\pi$
$80$		0			0
$81$	−1.07836e10			−0.343634
$82$		0			0
$83$	4.69569e10	+	4.69569e10i	1.30849	+	1.30849i	0.922505	+	0.385984i	$0.126138\pi$
$83$	4.69569e10	+	4.69569e10i	1.30849	+	1.30849i	0.385984	+	0.922505i	$0.373862\pi$
$84$		0			0
$85$	−1.78943e10	+	1.78943e10i	−0.437432	+	0.437432i
$86$		0			0
$87$			3.44292e10i			0.740579i
$88$		0			0
$89$			6.68453e10i			1.26890i	0.772966	+	0.634448i	$0.218772\pi$
$89$			6.68453e10i			1.26890i	−0.772966	+	0.634448i	$0.781228\pi$
$90$		0			0
$91$	6.05856e10	−	6.05856e10i	1.01775	−	1.01775i
$92$		0			0
$93$	−7.72043e9	−	7.72043e9i	−0.115076	−	0.115076i
$94$		0			0
$95$	−7.27395e10			−0.964474
$96$		0			0
$97$	4.52611e10			0.535156			0.267578	−	0.963536i	$-0.413777\pi$
$97$	4.52611e10			0.535156			0.267578	+	0.963536i	$0.413777\pi$
$98$		0			0
$99$	−9.25284e10	−	9.25284e10i	−0.977871	−	0.977871i
$100$		0			0
$101$	5.15862e10	−	5.15862e10i	0.488389	−	0.488389i	−0.419408	−	0.907798i	$-0.637762\pi$
$101$	5.15862e10	−	5.15862e10i	0.488389	−	0.488389i	0.907798	+	0.419408i	$0.137762\pi$
$102$		0			0
$103$		−	9.16100e10i		−	0.778643i	−0.921102	−	0.389321i	$-0.872710\pi$
$103$		−	9.16100e10i		−	0.778643i	0.921102	−	0.389321i	$-0.127290\pi$
$104$		0			0
$105$		−	5.83908e10i		−	0.446481i
$106$		0			0
$107$	4.25889e10	−	4.25889e10i	0.293553	−	0.293553i	−0.544929	−	0.838482i	$-0.683444\pi$
$107$	4.25889e10	−	4.25889e10i	0.293553	−	0.293553i	0.838482	+	0.544929i	$0.183444\pi$
$108$		0			0
$109$	1.91614e11	+	1.91614e11i	1.19284	+	1.19284i	0.976267	+	0.216569i	$0.0694867\pi$
$109$	1.91614e11	+	1.91614e11i	1.19284	+	1.19284i	0.216569	+	0.976267i	$0.430513\pi$
$110$		0			0
$111$	−1.07444e11			−0.605207
$112$		0			0
$113$	−2.60158e11			−1.32833			−0.664166	−	0.747586i	$-0.731213\pi$
$113$	−2.60158e11			−1.32833			−0.664166	+	0.747586i	$0.731213\pi$
$114$		0			0
$115$	9.29364e10	+	9.29364e10i	0.430871	+	0.430871i
$116$		0			0
$117$	−1.89176e11	+	1.89176e11i	−0.797706	+	0.797706i
$118$		0			0
$119$			1.66347e11i			0.639009i
$120$		0			0
$121$		−	6.53450e11i		−	2.29030i
$122$		0			0
$123$	−1.28105e10	+	1.28105e10i	−0.0410286	+	0.0410286i
$124$		0			0
$125$	−2.52922e11	−	2.52922e11i	−0.741278	−	0.741278i
$126$		0			0
$127$	−2.49589e11			−0.670355			−0.335177	−	0.942155i	$-0.608796\pi$
$127$	−2.49589e11			−0.670355			−0.335177	+	0.942155i	$0.608796\pi$
$128$		0			0
$129$	−5.27435e10			−0.129995
$130$		0			0
$131$	−2.54164e10	−	2.54164e10i	−0.0575602	−	0.0575602i	0.677741	−	0.735301i	$-0.262959\pi$
$131$	−2.54164e10	−	2.54164e10i	−0.0575602	−	0.0575602i	−0.735301	+	0.677741i	$0.762959\pi$
$132$		0			0
$133$	−3.38097e11	+	3.38097e11i	−0.704462	+	0.704462i
$134$		0			0
$135$			4.21468e11i			0.808962i
$136$		0			0
$137$		−	8.74862e11i		−	1.54873i	−0.632737	−	0.774367i	$-0.718069\pi$
$137$		−	8.74862e11i		−	1.54873i	0.632737	−	0.774367i	$-0.281931\pi$
$138$		0			0
$139$	5.58327e11	−	5.58327e11i	0.912657	−	0.912657i	−0.0838239	−	0.996481i	$-0.526713\pi$
$139$	5.58327e11	−	5.58327e11i	0.912657	−	0.912657i	0.996481	+	0.0838239i	$0.0267133\pi$
$140$		0			0
$141$	2.79566e11	+	2.79566e11i	0.422453	+	0.422453i
$142$		0			0
$143$	−1.91931e12			−2.68409
$144$		0			0
$145$	−1.10423e12			−1.43066
$146$		0			0
$147$	1.54505e10	+	1.54505e10i	0.0185651	+	0.0185651i
$148$		0			0
$149$	1.19866e11	−	1.19866e11i	0.133712	−	0.133712i	−0.637083	−	0.770795i	$-0.719859\pi$
$149$	1.19866e11	−	1.19866e11i	0.133712	−	0.133712i	0.770795	+	0.637083i	$0.219859\pi$
$150$		0			0
$151$		−	7.62184e11i		−	0.790108i	−0.918658	−	0.395054i	$-0.870726\pi$
$151$		−	7.62184e11i		−	0.790108i	0.918658	−	0.395054i	$-0.129274\pi$
$152$		0			0
$153$		−	5.19411e11i		−	0.500851i
$154$		0			0
$155$	2.47614e11	−	2.47614e11i	0.222306	−	0.222306i
$156$		0			0
$157$	9.25699e11	+	9.25699e11i	0.774500	+	0.774500i	0.978890	−	0.204390i	$-0.0655209\pi$
$157$	9.25699e11	+	9.25699e11i	0.774500	+	0.774500i	−0.204390	+	0.978890i	$0.565521\pi$
$158$		0			0
$159$	4.04616e11			0.315762
$160$		0			0
$161$	8.63946e11			0.629426
$162$		0			0
$163$	2.21603e11	+	2.21603e11i	0.150850	+	0.150850i	0.778497	−	0.627648i	$-0.215982\pi$
$163$	2.21603e11	+	2.21603e11i	0.150850	+	0.150850i	−0.627648	+	0.778497i	$0.715982\pi$
$164$		0			0
$165$	−9.24891e11	+	9.24891e11i	−0.588747	+	0.588747i
$166$		0			0
$167$			8.35995e11i			0.498039i	0.968498	+	0.249019i	$0.0801083\pi$
$167$			8.35995e11i			0.498039i	−0.968498	+	0.249019i	$0.919892\pi$
$168$		0			0
$169$			2.13190e12i			1.18957i
$170$		0			0
$171$	1.05569e12	−	1.05569e12i	0.552152	−	0.552152i
$172$		0			0
$173$	1.16818e12	+	1.16818e12i	0.573132	+	0.573132i	0.933002	−	0.359870i	$-0.117179\pi$
$173$	1.16818e12	+	1.16818e12i	0.573132	+	0.573132i	−0.359870	+	0.933002i	$0.617179\pi$
$174$		0			0
$175$	−2.39224e11			−0.110178
$176$		0			0
$177$	6.09256e11			0.263601
$178$		0			0
$179$	9.75915e11	+	9.75915e11i	0.396936	+	0.396936i	0.877151	−	0.480215i	$-0.159441\pi$
$179$	9.75915e11	+	9.75915e11i	0.396936	+	0.396936i	−0.480215	+	0.877151i	$0.659441\pi$
$180$		0			0
$181$	2.26186e12	−	2.26186e12i	0.865435	−	0.865435i	−0.126528	−	0.991963i	$-0.540384\pi$
$181$	2.26186e12	−	2.26186e12i	0.865435	−	0.865435i	0.991963	+	0.126528i	$0.0403835\pi$
$182$		0			0
$183$			3.58844e11i			0.129248i
$184$		0			0
$185$		−	3.44599e12i		−	1.16915i
$186$		0			0
$187$	2.63488e12	−	2.63488e12i	0.842622	−	0.842622i
$188$		0			0
$189$	1.95900e12	+	1.95900e12i	0.590874	+	0.590874i
$190$		0			0
$191$	1.55903e12			0.443785			0.221892	−	0.975071i	$-0.428777\pi$
$191$	1.55903e12			0.443785			0.221892	+	0.975071i	$0.428777\pi$
$192$		0			0
$193$	−3.02138e12			−0.812157			−0.406079	−	0.913838i	$-0.633104\pi$
$193$	−3.02138e12			−0.812157			−0.406079	+	0.913838i	$0.633104\pi$
$194$		0			0
$195$	1.89095e12	+	1.89095e12i	0.480275	+	0.480275i
$196$		0			0
$197$	−2.13585e12	+	2.13585e12i	−0.512868	+	0.512868i	−0.915404	−	0.402536i	$-0.868129\pi$
$197$	−2.13585e12	+	2.13585e12i	−0.512868	+	0.512868i	0.402536	+	0.915404i	$0.368129\pi$
$198$		0			0
$199$			2.41327e12i			0.548169i	0.961706	+	0.274084i	$0.0883748\pi$
$199$			2.41327e12i			0.548169i	−0.961706	+	0.274084i	$0.911625\pi$
$200$		0			0
$201$			2.82371e12i			0.607074i
$202$		0			0
$203$	−5.13253e12	+	5.13253e12i	−1.04497	+	1.04497i
$204$		0			0
$205$	−4.10864e11	−	4.10864e11i	−0.0792597	−	0.0792597i
$206$		0			0
$207$	−2.69763e12			−0.493339
$208$		0			0
$209$	1.07107e13			1.85786
$210$		0			0
$211$	5.23620e12	+	5.23620e12i	0.861912	+	0.861912i	0.991560	−	0.129648i	$-0.0413848\pi$
$211$	5.23620e12	+	5.23620e12i	0.861912	+	0.861912i	−0.129648	+	0.991560i	$0.541385\pi$
$212$		0			0
$213$	3.33872e11	−	3.33872e11i	0.0521785	−	0.0521785i
$214$		0			0
$215$		−	1.69162e12i		−	0.251126i
$216$		0			0
$217$		−	2.30184e12i		−	0.324749i
$218$		0			0
$219$	3.17164e12	−	3.17164e12i	0.425443	−	0.425443i
$220$		0			0
$221$	−5.38706e12	−	5.38706e12i	−0.687376	−	0.687376i
$222$		0			0
$223$	6.20344e12			0.753279			0.376639	−	0.926360i	$-0.377080\pi$
$223$	6.20344e12			0.753279			0.376639	+	0.926360i	$0.377080\pi$
$224$		0			0
$225$	7.46965e11			0.0863568
$226$		0			0
$227$	−9.21304e12	−	9.21304e12i	−1.01452	−	1.01452i	−0.999893	−	0.0146273i	$-0.995344\pi$
$227$	−9.21304e12	−	9.21304e12i	−1.01452	−	1.01452i	−0.0146273	−	0.999893i	$-0.504656\pi$
$228$		0			0
$229$	2.22123e12	−	2.22123e12i	0.233077	−	0.233077i	−0.580899	−	0.813976i	$-0.697299\pi$
$229$	2.22123e12	−	2.22123e12i	0.233077	−	0.233077i	0.813976	+	0.580899i	$0.197299\pi$
$230$		0			0
$231$			8.59788e12i			0.860054i
$232$		0			0
$233$			3.09041e12i			0.294821i	0.989075	+	0.147411i	$0.0470939\pi$
$233$			3.09041e12i			0.294821i	−0.989075	+	0.147411i	$0.952906\pi$
$234$		0			0
$235$	−8.96638e12	+	8.96638e12i	−0.816101	+	0.816101i
$236$		0			0
$237$	1.75773e10	+	1.75773e10i	0.00152699	+	0.00152699i
$238$		0			0
$239$	2.10296e13			1.74439			0.872194	−	0.489160i	$-0.162696\pi$
$239$	2.10296e13			1.74439			0.872194	+	0.489160i	$0.162696\pi$
$240$		0			0
$241$	−1.90768e13			−1.51151			−0.755757	−	0.654852i	$-0.772731\pi$
$241$	−1.90768e13			−1.51151			−0.755757	+	0.654852i	$0.772731\pi$
$242$		0			0
$243$	−9.58768e12	−	9.58768e12i	−0.725904	−	0.725904i
$244$		0			0
$245$	−4.95536e11	+	4.95536e11i	−0.0358642	+	0.0358642i
$246$		0			0
$247$		−	2.18982e13i		−	1.51557i
$248$		0			0
$249$			1.36242e13i			0.902019i
$250$		0			0
$251$	−7.66376e12	+	7.66376e12i	−0.485553	+	0.485553i	−0.906900	−	0.421347i	$-0.861558\pi$
$251$	−7.66376e12	+	7.66376e12i	−0.485553	+	0.485553i	0.421347	+	0.906900i	$0.361558\pi$
$252$		0			0
$253$	−1.36846e13	−	1.36846e13i	−0.829985	−	0.829985i
$254$		0			0
$255$	−5.19190e12			−0.301547
$256$		0			0
$257$	7.28346e12			0.405234			0.202617	−	0.979258i	$-0.435055\pi$
$257$	7.28346e12			0.405234			0.202617	+	0.979258i	$0.435055\pi$
$258$		0			0
$259$	−1.60171e13	−	1.60171e13i	−0.853957	−	0.853957i
$260$		0			0
$261$	1.60261e13	−	1.60261e13i	0.819039	−	0.819039i
$262$		0			0
$263$		−	2.25606e13i		−	1.10559i	−0.833317	−	0.552795i	$-0.813561\pi$
$263$		−	2.25606e13i		−	1.10559i	0.833317	−	0.552795i	$-0.186439\pi$
$264$		0			0
$265$			1.29771e13i			0.609993i
$266$		0			0
$267$	−9.69735e12	+	9.69735e12i	−0.437362	+	0.437362i
$268$		0			0
$269$	−1.76010e13	−	1.76010e13i	−0.761904	−	0.761904i	0.214762	−	0.976666i	$-0.431102\pi$
$269$	−1.76010e13	−	1.76010e13i	−0.761904	−	0.761904i	−0.976666	+	0.214762i	$0.931102\pi$
$270$		0			0
$271$	−2.19742e13			−0.913236			−0.456618	−	0.889663i	$-0.650939\pi$
$271$	−2.19742e13			−0.913236			−0.456618	+	0.889663i	$0.650939\pi$
$272$		0			0
$273$	1.75785e13			0.701596
$274$		0			0
$275$	3.78923e12	+	3.78923e12i	0.145285	+	0.145285i
$276$		0			0
$277$	−2.95361e13	+	2.95361e13i	−1.08821	+	1.08821i	−0.0925024	+	0.995712i	$0.529487\pi$
$277$	−2.95361e13	+	2.95361e13i	−1.08821	+	1.08821i	−0.995712	+	0.0925024i	$0.970513\pi$
$278$		0			0
$279$			7.18740e12i			0.254536i
$280$		0			0
$281$			4.87360e13i			1.65945i	0.558169	+	0.829727i	$0.311504\pi$
$281$			4.87360e13i			1.65945i	−0.558169	+	0.829727i	$0.688496\pi$
$282$		0			0
$283$	1.02370e13	−	1.02370e13i	0.335233	−	0.335233i	−0.519337	−	0.854570i	$-0.673821\pi$
$283$	1.02370e13	−	1.02370e13i	0.335233	−	0.335233i	0.854570	+	0.519337i	$0.173821\pi$
$284$		0			0
$285$	−1.05524e13	−	1.05524e13i	−0.332434	−	0.332434i
$286$		0			0
$287$	−3.81944e12			−0.115784
$288$		0			0
$289$	−1.94809e13			−0.568422
$290$		0			0
$291$	6.56610e12	+	6.56610e12i	0.184457	+	0.184457i
$292$		0			0
$293$	3.01060e13	−	3.01060e13i	0.814480	−	0.814480i	−0.170822	−	0.985302i	$-0.554642\pi$
$293$	3.01060e13	−	3.01060e13i	0.814480	−	0.814480i	0.985302	+	0.170822i	$0.0546422\pi$
$294$		0			0
$295$			1.95404e13i			0.509228i
$296$		0			0
$297$		−	6.20599e13i		−	1.55830i
$298$		0			0
$299$	−2.79784e13	+	2.79784e13i	−0.677067	+	0.677067i
$300$		0			0
$301$	−7.86273e12	−	7.86273e12i	−0.183425	−	0.183425i
$302$		0			0
$303$	1.49674e13			0.336675
$304$		0			0
$305$	−1.15090e13			−0.249684
$306$		0			0
$307$	1.69140e13	+	1.69140e13i	0.353986	+	0.353986i	0.861590	−	0.507605i	$-0.169469\pi$
$307$	1.69140e13	+	1.69140e13i	0.353986	+	0.353986i	−0.507605	+	0.861590i	$0.669469\pi$
$308$		0			0
$309$	1.32900e13	−	1.32900e13i	0.268382	−	0.268382i
$310$		0			0
$311$		−	2.82033e13i		−	0.549691i	−0.961488	−	0.274845i	$-0.911373\pi$
$311$		−	2.82033e13i		−	0.549691i	0.961488	−	0.274845i	$-0.0886266\pi$
$312$		0			0
$313$		−	4.08430e13i		−	0.768465i	−0.923236	−	0.384232i	$-0.874466\pi$
$313$		−	4.08430e13i		−	0.768465i	0.923236	−	0.384232i	$-0.125534\pi$
$314$		0			0
$315$	−2.71797e13	+	2.71797e13i	−0.493783	+	0.493783i
$316$		0			0
$317$	1.25175e13	+	1.25175e13i	0.219630	+	0.219630i	0.808342	−	0.588713i	$-0.200365\pi$
$317$	1.25175e13	+	1.25175e13i	0.219630	+	0.219630i	−0.588713	+	0.808342i	$0.700365\pi$
$318$		0			0
$319$	1.62595e14			2.75587
$320$		0			0
$321$	1.23569e13			0.202363
$322$		0			0
$323$	3.00624e13	+	3.00624e13i	0.475784	+	0.475784i
$324$		0			0
$325$	7.74713e12	−	7.74713e12i	0.118517	−	0.118517i
$326$		0			0
$327$			5.55954e13i			0.822292i
$328$		0			0
$329$			8.33524e13i			1.19218i
$330$		0			0
$331$	8.71388e13	−	8.71388e13i	1.20547	−	1.20547i	0.232996	−	0.972478i	$-0.425147\pi$
$331$	8.71388e13	−	8.71388e13i	1.20547	−	1.20547i	0.972478	−	0.232996i	$-0.0748529\pi$
$332$		0			0
$333$	5.00127e13	+	5.00127e13i	0.669326	+	0.669326i
$334$		0			0
$335$	−9.05635e13			−1.17275
$336$		0			0
$337$	1.31167e14			1.64384			0.821919	−	0.569604i	$-0.192904\pi$
$337$	1.31167e14			1.64384			0.821919	+	0.569604i	$0.192904\pi$
$338$		0			0
$339$	−3.77416e13	−	3.77416e13i	−0.457848	−	0.457848i
$340$		0			0
$341$	−3.64605e13	+	3.64605e13i	−0.428226	+	0.428226i
$342$		0			0
$343$			9.01319e13i			1.02509i
$344$		0			0
$345$			2.69649e13i			0.297025i
$346$		0			0
$347$	−1.77089e13	+	1.77089e13i	−0.188964	+	0.188964i	−0.795248	−	0.606284i	$-0.792659\pi$
$347$	−1.77089e13	+	1.77089e13i	−0.188964	+	0.188964i	0.606284	+	0.795248i	$0.292659\pi$
$348$		0			0
$349$	6.42641e13	+	6.42641e13i	0.664399	+	0.664399i	0.956414	−	0.292015i	$-0.0943257\pi$
$349$	6.42641e13	+	6.42641e13i	0.664399	+	0.664399i	−0.292015	+	0.956414i	$0.594326\pi$
$350$		0			0
$351$	−1.26882e14			−1.27120
$352$		0			0
$353$	−5.20465e13			−0.505395			−0.252697	−	0.967545i	$-0.581318\pi$
$353$	−5.20465e13			−0.505395			−0.252697	+	0.967545i	$0.581318\pi$
$354$		0			0
$355$	1.07081e13	+	1.07081e13i	0.100799	+	0.100799i
$356$		0			0
$357$	−2.41322e13	+	2.41322e13i	−0.220253	+	0.220253i
$358$		0			0
$359$		−	6.76326e13i		−	0.598599i	−0.954159	−	0.299300i	$-0.903247\pi$
$359$		−	6.76326e13i		−	0.598599i	0.954159	−	0.299300i	$-0.0967530\pi$
$360$		0			0
$361$			5.71224e12i			0.0490362i
$362$		0			0
$363$	9.47971e13	−	9.47971e13i	0.789421	−	0.789421i
$364$		0			0
$365$	1.01723e14	+	1.01723e14i	0.821877	+	0.821877i
$366$		0			0
$367$	9.78016e13			0.766801			0.383400	−	0.923582i	$-0.374753\pi$
$367$	9.78016e13			0.766801			0.383400	+	0.923582i	$0.374753\pi$
$368$		0			0
$369$	1.19260e13			0.0907508
$370$		0			0
$371$	6.03181e13	+	6.03181e13i	0.445545	+	0.445545i
$372$		0			0
$373$	−2.41318e13	+	2.41318e13i	−0.173058	+	0.173058i	−0.788322	−	0.615264i	$-0.789050\pi$
$373$	−2.41318e13	+	2.41318e13i	−0.173058	+	0.173058i	0.615264	+	0.788322i	$0.289050\pi$
$374$		0			0
$375$		−	7.33835e13i		−	0.511007i
$376$		0			0
$377$		−	3.32428e14i		−	2.24813i
$378$		0			0
$379$	4.15025e13	−	4.15025e13i	0.272620	−	0.272620i	−0.557534	−	0.830154i	$-0.688252\pi$
$379$	4.15025e13	−	4.15025e13i	0.272620	−	0.272620i	0.830154	+	0.557534i	$0.188252\pi$
$380$		0			0
$381$	−3.62082e13	−	3.62082e13i	−0.231057	−	0.231057i
$382$		0			0
$383$	−2.16012e14			−1.33932			−0.669661	−	0.742667i	$-0.733561\pi$
$383$	−2.16012e14			−1.33932			−0.669661	+	0.742667i	$0.733561\pi$
$384$		0			0
$385$	−2.75756e14			−1.66146
$386$		0			0
$387$	2.45510e13	+	2.45510e13i	0.143767	+	0.143767i
$388$		0			0
$389$	−1.03236e14	+	1.03236e14i	−0.587638	+	0.587638i	−0.936991	−	0.349353i	$-0.886401\pi$
$389$	−1.03236e14	+	1.03236e14i	−0.587638	+	0.587638i	0.349353	+	0.936991i	$0.386401\pi$
$390$		0			0
$391$		−	7.68191e13i		−	0.425106i
$392$		0			0
$393$		−	7.37440e12i		−	0.0396796i
$394$		0			0
$395$	−5.63749e11	+	5.63749e11i	−0.00294986	+	0.00294986i
$396$		0			0
$397$	1.40605e13	+	1.40605e13i	0.0715571	+	0.0715571i	0.741980	−	0.670422i	$-0.233887\pi$
$397$	1.40605e13	+	1.40605e13i	0.0715571	+	0.0715571i	−0.670422	+	0.741980i	$0.733887\pi$
$398$		0			0
$399$	−9.80965e13			−0.485627
$400$		0			0
$401$	3.66210e13			0.176375			0.0881874	−	0.996104i	$-0.471893\pi$
$401$	3.66210e13			0.176375			0.0881874	+	0.996104i	$0.471893\pi$
$402$		0			0
$403$	7.45439e13	+	7.45439e13i	0.349329	+	0.349329i
$404$		0			0
$405$	5.01741e13	−	5.01741e13i	0.228811	−	0.228811i
$406$		0			0
$407$			5.07412e14i			2.25212i
$408$		0			0
$409$		−	1.86904e14i		−	0.807495i	−0.914870	−	0.403748i	$-0.867707\pi$
$409$		−	1.86904e14i		−	0.807495i	0.914870	−	0.403748i	$-0.132293\pi$
$410$		0			0
$411$	1.26918e14	−	1.26918e14i	0.533816	−	0.533816i
$412$		0			0
$413$	9.08247e13	+	9.08247e13i	0.371945	+	0.371945i
$414$		0			0
$415$	−4.36964e14			−1.74253
$416$		0			0
$417$	1.61995e14			0.629148
$418$		0			0
$419$	−4.88266e13	−	4.88266e13i	−0.184705	−	0.184705i	0.608697	−	0.793403i	$-0.291692\pi$
$419$	−4.88266e13	−	4.88266e13i	−0.184705	−	0.184705i	−0.793403	+	0.608697i	$0.791692\pi$
$420$		0			0
$421$	−1.10431e12	+	1.10431e12i	−0.00406947	+	0.00406947i	−0.709139	−	0.705069i	$-0.750916\pi$
$421$	−1.10431e12	+	1.10431e12i	−0.00406947	+	0.00406947i	0.705069	+	0.709139i	$0.250916\pi$
$422$		0			0
$423$		−	2.60264e14i		−	0.934420i
$424$		0			0
$425$			2.12709e13i			0.0744128i
$426$		0			0
$427$	−5.34947e13	+	5.34947e13i	−0.182372	+	0.182372i
$428$		0			0
$429$	−2.78438e14	−	2.78438e14i	−0.925151	−	0.925151i
$430$		0			0
$431$	1.91371e14			0.619800			0.309900	−	0.950769i	$-0.399704\pi$
$431$	1.91371e14			0.619800			0.309900	+	0.950769i	$0.399704\pi$
$432$		0			0
$433$	−4.41594e14			−1.39425			−0.697124	−	0.716951i	$-0.745537\pi$
$433$	−4.41594e14			−1.39425			−0.697124	+	0.716951i	$0.745537\pi$
$434$		0			0
$435$	−1.60193e14	−	1.60193e14i	−0.493119	−	0.493119i
$436$		0			0
$437$	1.56133e14	−	1.56133e14i	0.468649	−	0.468649i
$438$		0			0
$439$		−	5.26739e14i		−	1.54184i	−0.636930	−	0.770922i	$-0.719796\pi$
$439$		−	5.26739e14i		−	1.54184i	0.636930	−	0.770922i	$-0.280204\pi$
$440$		0			0
$441$		−	1.43837e13i		−	0.0410638i
$442$		0			0
$443$	−2.17125e14	+	2.17125e14i	−0.604629	+	0.604629i	−0.941537	−	0.336909i	$-0.890619\pi$
$443$	−2.17125e14	+	2.17125e14i	−0.604629	+	0.604629i	0.336909	+	0.941537i	$0.390619\pi$
$444$		0			0
$445$	−3.11019e14	−	3.11019e14i	−0.844902	−	0.844902i
$446$		0			0
$447$	3.47782e13			0.0921755
$448$		0			0
$449$	−2.53750e14			−0.656223			−0.328112	−	0.944639i	$-0.606412\pi$
$449$	−2.53750e14			−0.656223			−0.328112	+	0.944639i	$0.606412\pi$
$450$		0			0
$451$	6.04987e13	+	6.04987e13i	0.152677	+	0.152677i
$452$		0			0
$453$	1.10571e14	−	1.10571e14i	0.272334	−	0.272334i
$454$		0			0
$455$			5.63787e14i			1.35535i
$456$		0			0
$457$			1.31008e14i			0.307439i	0.988115	+	0.153719i	$0.0491252\pi$
$457$			1.31008e14i			0.307439i	−0.988115	+	0.153719i	$0.950875\pi$
$458$		0			0
$459$	1.74188e14	−	1.74188e14i	0.399069	−	0.399069i
$460$		0			0
$461$	4.84798e14	+	4.84798e14i	1.08444	+	1.08444i	0.996089	+	0.0883504i	$0.0281595\pi$
$461$	4.84798e14	+	4.84798e14i	1.08444	+	1.08444i	0.0883504	+	0.996089i	$0.471840\pi$
$462$		0			0
$463$	4.46724e13			0.0975761			0.0487881	−	0.998809i	$-0.484464\pi$
$463$	4.46724e13			0.0975761			0.0487881	+	0.998809i	$0.484464\pi$
$464$		0			0
$465$	7.18434e13			0.153248
$466$		0			0
$467$	−4.14973e14	−	4.14973e14i	−0.864523	−	0.864523i	0.127336	−	0.991860i	$-0.459357\pi$
$467$	−4.14973e14	−	4.14973e14i	−0.864523	−	0.864523i	−0.991860	+	0.127336i	$0.959357\pi$
$468$		0			0
$469$	−4.20944e14	+	4.20944e14i	−0.856591	+	0.856591i
$470$		0			0
$471$			2.68585e14i			0.533908i
$472$		0			0
$473$			2.49086e14i			0.483742i
$474$		0			0
$475$	−4.32328e13	+	4.32328e13i	−0.0820348	+	0.0820348i
$476$		0			0
$477$	−1.88340e14	−	1.88340e14i	−0.349215	−	0.349215i
$478$		0			0
$479$	2.13619e14			0.387074			0.193537	−	0.981093i	$-0.438004\pi$
$479$	2.13619e14			0.387074			0.193537	+	0.981093i	$0.438004\pi$
$480$		0			0
$481$	1.03741e15			1.83719
$482$		0			0
$483$	1.25334e14	+	1.25334e14i	0.216950	+	0.216950i
$484$		0			0
$485$	−2.10591e14	+	2.10591e14i	−0.356337	+	0.356337i
$486$		0			0
$487$		−	6.10255e14i		−	1.00949i	−0.863269	−	0.504745i	$-0.831587\pi$
$487$		−	6.10255e14i		−	1.00949i	0.863269	−	0.504745i	$-0.168413\pi$
$488$		0			0
$489$			6.42967e13i			0.103990i
$490$		0			0
$491$	−1.94984e14	+	1.94984e14i	−0.308355	+	0.308355i	−0.844271	−	0.535916i	$-0.819966\pi$
$491$	−1.94984e14	+	1.94984e14i	−0.308355	+	0.308355i	0.535916	+	0.844271i	$0.319966\pi$
$492$		0			0
$493$	4.56367e14	+	4.56367e14i	0.705758	+	0.705758i
$494$		0			0
$495$	8.61035e14			1.30224
$496$		0			0
$497$	9.95438e13			0.147250
$498$		0			0
$499$	2.61674e14	+	2.61674e14i	0.378623	+	0.378623i	0.870605	−	0.491982i	$-0.163727\pi$
$499$	2.61674e14	+	2.61674e14i	0.378623	+	0.378623i	−0.491982	+	0.870605i	$0.663727\pi$
$500$		0			0
$501$	−1.21279e14	+	1.21279e14i	−0.171664	+	0.171664i
$502$		0			0
$503$		−	7.38472e14i		−	1.02261i	−0.859399	−	0.511305i	$-0.829162\pi$
$503$		−	7.38472e14i		−	1.02261i	0.859399	−	0.511305i	$-0.170838\pi$
$504$		0			0
$505$			4.80042e14i			0.650394i
$506$		0			0
$507$	−3.09278e14	+	3.09278e14i	−0.410020	+	0.410020i
$508$		0			0
$509$	−3.46018e14	−	3.46018e14i	−0.448901	−	0.448901i	0.446088	−	0.894989i	$-0.352817\pi$
$509$	−3.46018e14	−	3.46018e14i	−0.448901	−	0.448901i	−0.894989	+	0.446088i	$0.852817\pi$
$510$		0			0
$511$	9.45624e14			1.20061
$512$		0			0
$513$	7.08066e14			0.879889
$514$		0			0
$515$	4.26244e14	+	4.26244e14i	0.518464	+	0.518464i
$516$		0			0
$517$	1.32028e15	−	1.32028e15i	1.57205	−	1.57205i
$518$		0			0
$519$			3.38938e14i			0.395094i
$520$		0			0
$521$			8.53908e14i			0.974549i	0.873249	+	0.487275i	$0.162009\pi$
$521$			8.53908e14i			0.974549i	−0.873249	+	0.487275i	$0.837991\pi$
$522$		0			0
$523$	−3.68665e14	+	3.68665e14i	−0.411976	+	0.411976i	−0.882427	−	0.470450i	$-0.844092\pi$
$523$	−3.68665e14	+	3.68665e14i	−0.411976	+	0.411976i	0.470450	+	0.882427i	$0.344092\pi$
$524$		0			0
$525$	−3.47046e13	−	3.47046e13i	−0.0379761	−	0.0379761i
$526$		0			0
$527$	−2.04672e14			−0.219331
$528$		0			0
$529$	5.53839e14			0.581270
$530$		0			0
$531$	−2.83596e14	−	2.83596e14i	−0.291528	−	0.291528i
$532$		0			0
$533$	1.23690e14	−	1.23690e14i	0.124548	−	0.124548i
$534$		0			0
$535$			3.96317e14i			0.390928i
$536$		0			0
$537$			2.83155e14i			0.273631i
$538$		0			0
$539$	7.29663e13	−	7.29663e13i	0.0690851	−	0.0690851i
$540$		0			0
$541$	−3.90393e14	−	3.90393e14i	−0.362174	−	0.362174i	0.502439	−	0.864613i	$-0.332436\pi$
$541$	−3.90393e14	−	3.90393e14i	−0.362174	−	0.362174i	−0.864613	+	0.502439i	$0.832436\pi$
$542$		0			0
$543$	6.56264e14			0.596595
$544$		0			0
$545$	−1.78309e15			−1.58852
$546$		0			0
$547$	−7.12794e14	−	7.12794e14i	−0.622348	−	0.622348i	0.323783	−	0.946131i	$-0.395045\pi$
$547$	−7.12794e14	−	7.12794e14i	−0.622348	−	0.622348i	−0.946131	+	0.323783i	$0.895045\pi$
$548$		0			0
$549$	1.67034e14	−	1.67034e14i	0.142941	−	0.142941i
$550$		0			0
$551$			1.85511e15i			1.55610i
$552$		0			0
$553$			5.24067e12i			0.00430922i
$554$		0			0
$555$	4.99915e14	−	4.99915e14i	0.402981	−	0.402981i
$556$		0			0
$557$	−1.72156e15	−	1.72156e15i	−1.36057	−	1.36057i	−0.873196	−	0.487370i	$-0.837956\pi$
$557$	−1.72156e15	−	1.72156e15i	−1.36057	−	1.36057i	−0.487370	−	0.873196i	$-0.662044\pi$
$558$		0			0
$559$	5.09260e14			0.394616
$560$		0			0
$561$	7.64494e14			0.580869
$562$		0			0
$563$	1.43337e15	+	1.43337e15i	1.06798	+	1.06798i	0.997515	+	0.0704611i	$0.0224471\pi$
$563$	1.43337e15	+	1.43337e15i	1.06798	+	1.06798i	0.0704611	+	0.997515i	$0.477553\pi$
$564$		0			0
$565$	1.21047e15	−	1.21047e15i	0.884478	−	0.884478i
$566$		0			0
$567$		−	4.66424e14i		−	0.334252i
$568$		0			0
$569$			2.36411e15i			1.66169i	0.556501	+	0.830847i	$0.312144\pi$
$569$			2.36411e15i			1.66169i	−0.556501	+	0.830847i	$0.687856\pi$
$570$		0			0
$571$	−1.65021e15	+	1.65021e15i	−1.13773	+	1.13773i	−0.148877	+	0.988856i	$0.547566\pi$
$571$	−1.65021e15	+	1.65021e15i	−1.13773	+	1.13773i	−0.988856	+	0.148877i	$0.952434\pi$
$572$		0			0
$573$	2.26172e14	+	2.26172e14i	0.152963	+	0.152963i
$574$		0			0
$575$	1.10474e14			0.0732968
$576$		0			0
$577$	2.92060e13			0.0190110			0.00950552	−	0.999955i	$-0.496974\pi$
$577$	2.92060e13			0.0190110			0.00950552	+	0.999955i	$0.496974\pi$
$578$		0			0
$579$	−4.38316e14	−	4.38316e14i	−0.279934	−	0.279934i
$580$		0			0
$581$	−2.03103e15	+	2.03103e15i	−1.27276	+	1.27276i
$582$		0			0
$583$		−	1.91084e15i		−	1.17503i
$584$		0			0
$585$		−	1.76040e15i		−	1.06232i
$586$		0			0
$587$	−8.11373e14	+	8.11373e14i	−0.480519	+	0.480519i	−0.905297	−	0.424778i	$-0.860352\pi$
$587$	−8.11373e14	+	8.11373e14i	−0.480519	+	0.480519i	0.424778	+	0.905297i	$0.360352\pi$
$588$		0			0
$589$	−4.15991e14	−	4.15991e14i	−0.241797	−	0.241797i
$590$		0			0
$591$	−6.19701e14			−0.353550
$592$		0			0
$593$	−9.56120e14			−0.535441			−0.267720	−	0.963497i	$-0.586270\pi$
$593$	−9.56120e14			−0.535441			−0.267720	+	0.963497i	$0.586270\pi$
$594$		0			0
$595$	−7.73982e14	−	7.73982e14i	−0.425488	−	0.425488i
$596$		0			0
$597$	−3.50097e14	+	3.50097e14i	−0.188943	+	0.188943i
$598$		0			0
$599$		−	2.61157e15i		−	1.38374i	−0.722024	−	0.691868i	$-0.756788\pi$
$599$		−	2.61157e15i		−	1.38374i	0.722024	−	0.691868i	$-0.243212\pi$
$600$		0			0
$601$		−	3.71453e15i		−	1.93239i	−0.257815	−	0.966194i	$-0.583002\pi$
$601$		−	3.71453e15i		−	1.93239i	0.257815	−	0.966194i	$-0.416998\pi$
$602$		0			0
$603$	1.31438e15	−	1.31438e15i	0.671390	−	0.671390i
$604$		0			0
$605$	3.04038e15	+	3.04038e15i	1.52501	+	1.52501i
$606$		0			0
$607$	−2.62166e15			−1.29133			−0.645666	−	0.763620i	$-0.723420\pi$
$607$	−2.62166e15			−1.29133			−0.645666	+	0.763620i	$0.723420\pi$
$608$		0			0
$609$	−1.48917e15			−0.720358
$610$		0			0
$611$	−2.69932e15	−	2.69932e15i	−1.28241	−	1.28241i
$612$		0			0
$613$	1.37113e14	−	1.37113e14i	0.0639803	−	0.0639803i	−0.674393	−	0.738373i	$-0.735594\pi$
$613$	1.37113e14	−	1.37113e14i	0.0639803	−	0.0639803i	0.738373	+	0.674393i	$0.235594\pi$
$614$		0			0
$615$		−	1.19209e14i		−	0.0546384i
$616$		0			0
$617$			1.11737e15i			0.503071i	0.967848	+	0.251535i	$0.0809355\pi$
$617$			1.11737e15i			0.503071i	−0.967848	+	0.251535i	$0.919065\pi$
$618$		0			0
$619$	1.57470e15	−	1.57470e15i	0.696466	−	0.696466i	−0.267181	−	0.963646i	$-0.586092\pi$
$619$	1.57470e15	−	1.57470e15i	0.696466	−	0.696466i	0.963646	+	0.267181i	$0.0860920\pi$
$620$		0			0
$621$	−9.04667e14	−	9.04667e14i	−0.393084	−	0.393084i
$622$		0			0
$623$	−2.89126e15			−1.23425
$624$		0			0
$625$	2.08354e15			0.873899
$626$		0			0
$627$	1.55382e15	+	1.55382e15i	0.640366	+	0.640366i
$628$		0			0
$629$	−1.42419e15	+	1.42419e15i	−0.576751	+	0.576751i
$630$		0			0
$631$			2.16645e15i			0.862159i	0.902314	+	0.431079i	$0.141867\pi$
$631$			2.16645e15i			0.862159i	−0.902314	+	0.431079i	$0.858133\pi$
$632$		0			0
$633$			1.51925e15i			0.594166i
$634$		0			0
$635$	1.16129e15	−	1.16129e15i	0.446360	−	0.446360i
$636$		0			0
$637$	−1.49181e14	−	1.49181e14i	−0.0563567	−	0.0563567i
$638$		0			0
$639$	−3.10821e14			−0.115413
$640$		0			0
$641$	−8.53695e14			−0.311590			−0.155795	−	0.987789i	$-0.549794\pi$
$641$	−8.53695e14			−0.311590			−0.155795	+	0.987789i	$0.549794\pi$
$642$		0			0
$643$	−9.15616e14	−	9.15616e14i	−0.328513	−	0.328513i	0.523508	−	0.852021i	$-0.324623\pi$
$643$	−9.15616e14	−	9.15616e14i	−0.328513	−	0.328513i	−0.852021	+	0.523508i	$0.824623\pi$
$644$		0			0
$645$	2.45406e14	−	2.45406e14i	0.0865578	−	0.0865578i
$646$		0			0
$647$			2.43835e15i			0.845518i	0.906242	+	0.422759i	$0.138938\pi$
$647$			2.43835e15i			0.845518i	−0.906242	+	0.422759i	$0.861062\pi$
$648$		0			0
$649$		−	2.87727e15i		−	0.980922i
$650$		0			0
$651$	3.33932e14	−	3.33932e14i	0.111934	−	0.111934i
$652$		0			0
$653$	−1.10464e15	−	1.10464e15i	−0.364080	−	0.364080i	0.501233	−	0.865313i	$-0.332880\pi$
$653$	−1.10464e15	−	1.10464e15i	−0.364080	−	0.364080i	−0.865313	+	0.501233i	$0.832880\pi$
$654$		0			0
$655$	2.36516e14			0.0766537
$656$		0			0
$657$	−2.95266e15			−0.941032
$658$		0			0
$659$	2.32279e15	+	2.32279e15i	0.728014	+	0.728014i	0.970224	−	0.242210i	$-0.0778723\pi$
$659$	2.32279e15	+	2.32279e15i	0.728014	+	0.728014i	−0.242210	+	0.970224i	$0.577872\pi$
$660$		0			0
$661$	−6.73212e14	+	6.73212e14i	−0.207512	+	0.207512i	−0.803209	−	0.595697i	$-0.796876\pi$
$661$	−6.73212e14	+	6.73212e14i	−0.207512	+	0.207512i	0.595697	+	0.803209i	$0.296876\pi$
$662$		0			0
$663$		−	1.56302e15i		−	0.473848i
$664$		0			0
$665$		−	3.14621e15i		−	0.938141i
$666$		0			0
$667$	2.37020e15	−	2.37020e15i	0.695174	−	0.695174i
$668$		0			0
$669$	8.99942e14	+	8.99942e14i	0.259640	+	0.259640i
$670$		0			0
$671$	1.69468e15			0.480964
$672$		0			0
$673$	2.99678e15			0.836704			0.418352	−	0.908285i	$-0.362608\pi$
$673$	2.99678e15			0.836704			0.418352	+	0.908285i	$0.362608\pi$
$674$		0			0
$675$	2.50499e14	+	2.50499e14i	0.0688075	+	0.0688075i
$676$		0			0
$677$	−1.70658e15	+	1.70658e15i	−0.461199	+	0.461199i	−0.899048	−	0.437849i	$-0.855740\pi$
$677$	−1.70658e15	+	1.70658e15i	−0.461199	+	0.461199i	0.437849	+	0.899048i	$0.355740\pi$
$678$		0			0
$679$			1.95768e15i			0.520545i
$680$		0			0
$681$		−	2.67310e15i		−	0.699368i
$682$		0			0
$683$	−5.32703e15	+	5.32703e15i	−1.37142	+	1.37142i	−0.513084	+	0.858339i	$0.671497\pi$
$683$	−5.32703e15	+	5.32703e15i	−1.37142	+	1.37142i	−0.858339	+	0.513084i	$0.828503\pi$
$684$		0			0
$685$	4.07057e15	+	4.07057e15i	1.03123	+	1.03123i
$686$		0			0
$687$	6.44475e14			0.160673
$688$		0			0
$689$	−3.90674e15			−0.958536
$690$		0			0
$691$	2.15825e15	+	2.15825e15i	0.521161	+	0.521161i	0.917922	−	0.396761i	$-0.129866\pi$
$691$	2.15825e15	+	2.15825e15i	0.521161	+	0.521161i	−0.396761	+	0.917922i	$0.629866\pi$
$692$		0			0
$693$	4.00213e15	−	4.00213e15i	0.951171	−	0.951171i
$694$		0			0
$695$			5.19558e15i			1.21540i
$696$		0			0
$697$			3.39611e14i			0.0781991i
$698$		0			0
$699$	−4.48331e14	+	4.48331e14i	−0.101619	+	0.101619i
$700$		0			0
$701$	1.52455e15	+	1.52455e15i	0.340167	+	0.340167i	0.856430	−	0.516263i	$-0.172677\pi$
$701$	1.52455e15	+	1.52455e15i	0.340167	+	0.340167i	−0.516263	+	0.856430i	$0.672677\pi$
$702$		0			0
$703$	−5.78926e15			−1.27165
$704$		0			0
$705$	−2.60153e15			−0.562587
$706$		0			0
$707$	2.23126e15	+	2.23126e15i	0.475054	+	0.475054i
$708$		0			0
$709$	−5.50134e14	+	5.50134e14i	−0.115323	+	0.115323i	−0.762413	−	0.647091i	$-0.775986\pi$
$709$	−5.50134e14	+	5.50134e14i	−0.115323	+	0.115323i	0.647091	+	0.762413i	$0.275986\pi$
$710$		0			0
$711$		−	1.63637e13i		−	0.00337754i
$712$		0			0
$713$			1.06299e15i			0.216042i
$714$		0			0
$715$	8.93020e15	−	8.93020e15i	1.78722	−	1.78722i
$716$		0			0
$717$	3.05080e15	+	3.05080e15i	0.601255	+	0.601255i
$718$		0			0
$719$	2.96713e15			0.575875			0.287937	−	0.957649i	$-0.407031\pi$
$719$	2.96713e15			0.575875			0.287937	+	0.957649i	$0.407031\pi$
$720$		0			0
$721$	3.96241e15			0.757383
$722$		0			0
$723$	−2.76750e15	−	2.76750e15i	−0.520988	−	0.520988i
$724$		0			0
$725$	−6.56301e14	+	6.56301e14i	−0.121687	+	0.121687i
$726$		0			0
$727$		−	8.35407e15i		−	1.52566i	−0.646597	−	0.762832i	$-0.723808\pi$
$727$		−	8.35407e15i		−	1.52566i	0.646597	−	0.762832i	$-0.276192\pi$
$728$		0			0
$729$		−	8.71516e14i		−	0.156774i
$730$		0			0
$731$	−6.99127e14	+	6.99127e14i	−0.123883	+	0.123883i
$732$		0			0
$733$	−2.90697e15	−	2.90697e15i	−0.507421	−	0.507421i	0.406313	−	0.913734i	$-0.366814\pi$
$733$	−2.90697e15	−	2.90697e15i	−0.507421	−	0.507421i	−0.913734	+	0.406313i	$0.866814\pi$
$734$		0			0
$735$	−1.43776e14			−0.0247233
$736$		0			0
$737$	1.33352e16			2.25907
$738$		0			0
$739$	5.27620e15	+	5.27620e15i	0.880596	+	0.880596i	0.993595	−	0.113000i	$-0.0360459\pi$
$739$	5.27620e15	+	5.27620e15i	0.880596	+	0.880596i	−0.113000	+	0.993595i	$0.536046\pi$
$740$		0			0
$741$	3.17680e15	−	3.17680e15i	0.522384	−	0.522384i
$742$		0			0
$743$			9.75338e15i			1.58022i	0.612967	+	0.790109i	$0.289976\pi$
$743$			9.75338e15i			1.58022i	−0.612967	+	0.790109i	$0.710024\pi$
$744$		0			0
$745$			1.11543e15i			0.178066i
$746$		0			0
$747$	6.34179e15	−	6.34179e15i	0.997582	−	0.997582i
$748$		0			0
$749$	1.84210e15	+	1.84210e15i	0.285538	+	0.285538i
$750$		0			0
$751$	−2.77812e14			−0.0424357			−0.0212179	−	0.999775i	$-0.506754\pi$
$751$	−2.77812e14			−0.0424357			−0.0212179	+	0.999775i	$0.506754\pi$
$752$		0			0
$753$	−2.22359e15			−0.334720
$754$		0			0
$755$	3.54630e15	+	3.54630e15i	0.526099	+	0.526099i
$756$		0			0
$757$	−4.77158e15	+	4.77158e15i	−0.697646	+	0.697646i	−0.963902	−	0.266256i	$-0.914213\pi$
$757$	−4.77158e15	+	4.77158e15i	−0.697646	+	0.697646i	0.266256	+	0.963902i	$0.414213\pi$
$758$		0			0
$759$		−	3.97050e15i		−	0.572157i
$760$		0			0
$761$			1.30767e16i			1.85730i	0.370957	+	0.928650i	$0.379030\pi$
$761$			1.30767e16i			1.85730i	−0.370957	+	0.928650i	$0.620970\pi$
$762$		0			0
$763$	−8.28787e15	+	8.28787e15i	−1.16027	+	1.16027i
$764$		0			0
$765$	2.41672e15	+	2.41672e15i	0.333495	+	0.333495i
$766$		0			0
$767$	−5.88261e15			−0.800195
$768$		0			0
$769$	−6.05417e15			−0.811819			−0.405910	−	0.913913i	$-0.633045\pi$
$769$	−6.05417e15			−0.811819			−0.405910	+	0.913913i	$0.633045\pi$
$770$		0			0
$771$	1.05662e15	+	1.05662e15i	0.139676	+	0.139676i
$772$		0			0
$773$	−1.19006e15	+	1.19006e15i	−0.155090	+	0.155090i	−0.780387	−	0.625297i	$-0.784978\pi$
$773$	−1.19006e15	+	1.19006e15i	−0.155090	+	0.155090i	0.625297	+	0.780387i	$0.284978\pi$
$774$		0			0
$775$		−	2.94339e14i		−	0.0378171i
$776$		0			0
$777$		−	4.64726e15i		−	0.588683i
$778$		0			0
$779$	−6.90253e14	+	6.90253e14i	−0.0862089	+	0.0862089i
$780$		0			0
$781$	−1.57674e15	−	1.57674e15i	−0.194169	−	0.194169i
$782$		0			0
$783$	1.07489e16			1.30519
$784$		0			0
$785$	−8.61420e15			−1.03141
$786$		0			0
$787$	−4.94174e15	−	4.94174e15i	−0.583470	−	0.583470i	0.352385	−	0.935855i	$-0.385371\pi$
$787$	−4.94174e15	−	4.94174e15i	−0.583470	−	0.583470i	−0.935855	+	0.352385i	$0.885371\pi$
$788$		0			0
$789$	3.27290e15	−	3.27290e15i	0.381074	−	0.381074i
$790$		0			0
$791$		−	1.12526e16i		−	1.29206i
$792$		0			0
$793$		−	3.46479e15i		−	0.392350i
$794$		0			0
$795$	−1.88260e15	+	1.88260e15i	−0.210252	+	0.210252i
$796$		0			0
$797$	−5.72084e15	−	5.72084e15i	−0.630142	−	0.630142i	0.317961	−	0.948104i	$-0.397002\pi$
$797$	−5.72084e15	−	5.72084e15i	−0.630142	−	0.630142i	−0.948104	+	0.317961i	$0.897002\pi$
$798$		0			0
$799$	7.41141e15			0.805181
$800$		0			0
$801$	9.02782e15			0.967396
$802$		0			0
$803$	−1.49784e16	−	1.49784e16i	−1.58318	−	1.58318i
$804$		0			0
$805$	−4.01978e15	+	4.01978e15i	−0.419107	+	0.419107i
$806$		0			0
$807$		−	5.10681e15i		−	0.525225i
$808$		0			0
$809$			7.80980e14i			0.0792361i	0.999215	+	0.0396180i	$0.0126141\pi$
$809$			7.80980e14i			0.0792361i	−0.999215	+	0.0396180i	$0.987386\pi$
$810$		0			0
$811$	−3.66369e15	+	3.66369e15i	−0.366695	+	0.366695i	−0.866270	−	0.499576i	$-0.833489\pi$
$811$	−3.66369e15	+	3.66369e15i	−0.366695	+	0.366695i	0.499576	+	0.866270i	$0.333489\pi$
$812$		0			0
$813$	−3.18784e15	−	3.18784e15i	−0.314773	−	0.314773i
$814$		0			0
$815$	−2.06216e15			−0.200888
$816$		0			0
$817$	−2.84192e15			−0.273143
$818$		0			0
$819$	−8.18242e15	−	8.18242e15i	−0.775926	−	0.775926i
$820$		0			0
$821$	8.26565e15	−	8.26565e15i	0.773374	−	0.773374i	−0.205321	−	0.978695i	$-0.565824\pi$
$821$	8.26565e15	−	8.26565e15i	0.773374	−	0.773374i	0.978695	+	0.205321i	$0.0658237\pi$
$822$		0			0
$823$			5.04163e15i			0.465449i	0.972543	+	0.232724i	$0.0747640\pi$
$823$			5.04163e15i			0.465449i	−0.972543	+	0.232724i	$0.925236\pi$
$824$		0			0
$825$			1.09942e15i			0.100154i
$826$		0			0
$827$	−1.05064e16	+	1.05064e16i	−0.944440	+	0.944440i	−0.998536	−	0.0540957i	$-0.982772\pi$
$827$	−1.05064e16	+	1.05064e16i	−0.944440	+	0.944440i	0.0540957	+	0.998536i	$0.482772\pi$
$828$		0			0
$829$	−1.11651e16	−	1.11651e16i	−0.990401	−	0.990401i	0.00955324	−	0.999954i	$-0.496959\pi$
$829$	−1.11651e16	−	1.11651e16i	−0.990401	−	0.990401i	−0.999954	+	0.00955324i	$0.996959\pi$
$830$		0			0
$831$	−8.56970e15			−0.750170
$832$		0			0
$833$	4.09599e14			0.0353843
$834$		0			0
$835$	−3.88973e15	−	3.88973e15i	−0.331622	−	0.331622i
$836$		0			0
$837$	−2.41034e15	+	2.41034e15i	−0.202809	+	0.202809i
$838$		0			0
$839$			1.14888e16i			0.954080i	0.878882	+	0.477040i	$0.158290\pi$
$839$			1.14888e16i			0.954080i	−0.878882	+	0.477040i	$0.841710\pi$
$840$		0			0
$841$			1.59613e16i			1.30825i
$842$		0			0
$843$	−7.07021e15	+	7.07021e15i	−0.571980	+	0.571980i
$844$		0			0
$845$	−9.91933e15	−	9.91933e15i	−0.792082	−	0.792082i
$846$		0			0
$847$	2.82637e16			2.22777
$848$		0			0
$849$	2.97019e15			0.231096
$850$		0			0
$851$	7.39671e15	+	7.39671e15i	0.568102	+	0.568102i
$852$		0			0
$853$	4.44810e15	−	4.44810e15i	0.337252	−	0.337252i	−0.518080	−	0.855332i	$-0.673353\pi$
$853$	4.44810e15	−	4.44810e15i	0.337252	−	0.337252i	0.855332	+	0.518080i	$0.173353\pi$
$854$		0			0
$855$			9.82388e15i			0.735308i
$856$		0			0
$857$		−	3.92912e15i		−	0.290336i	−0.989407	−	0.145168i	$-0.953628\pi$
$857$		−	3.92912e15i		−	0.290336i	0.989407	−	0.145168i	$-0.0463722\pi$
$858$		0			0
$859$	−4.10362e15	+	4.10362e15i	−0.299368	+	0.299368i	−0.840766	−	0.541399i	$-0.817895\pi$
$859$	−4.10362e15	+	4.10362e15i	−0.299368	+	0.299368i	0.541399	+	0.840766i	$0.317895\pi$
$860$		0			0
$861$	−5.54092e14	−	5.54092e14i	−0.0399084	−	0.0399084i
$862$		0			0
$863$	−1.39006e16			−0.988493			−0.494246	−	0.869322i	$-0.664556\pi$
$863$	−1.39006e16			−0.988493			−0.494246	+	0.869322i	$0.664556\pi$
$864$		0			0
$865$	−1.08706e16			−0.763248
$866$		0			0
$867$	−2.82612e15	−	2.82612e15i	−0.195923	−	0.195923i
$868$		0			0
$869$	8.30105e13	−	8.30105e13i	0.00568230	−	0.00568230i
$870$		0			0
$871$		−	2.72640e16i		−	1.84285i
$872$		0			0
$873$		−	6.11276e15i		−	0.407999i
$874$		0			0
$875$	1.09396e16	−	1.09396e16i	0.721039	−	0.721039i
$876$		0			0
$877$	−1.01754e16	−	1.01754e16i	−0.662296	−	0.662296i	0.293625	−	0.955921i	$-0.405138\pi$
$877$	−1.01754e16	−	1.01754e16i	−0.662296	−	0.662296i	−0.955921	+	0.293625i	$0.905138\pi$
$878$		0			0
$879$	8.73504e15			0.561469
$880$		0			0
$881$	−7.33273e15			−0.465477			−0.232738	−	0.972539i	$-0.574769\pi$
$881$	−7.33273e15			−0.465477			−0.232738	+	0.972539i	$0.574769\pi$
$882$		0			0
$883$	1.96400e16	+	1.96400e16i	1.23128	+	1.23128i	0.963471	+	0.267813i	$0.0863008\pi$
$883$	1.96400e16	+	1.96400e16i	1.23128	+	1.23128i	0.267813	+	0.963471i	$0.413699\pi$
$884$		0			0
$885$	−2.83475e15	+	2.83475e15i	−0.175520	+	0.175520i
$886$		0			0
$887$			3.76810e15i			0.230432i	0.993340	+	0.115216i	$0.0367560\pi$
$887$			3.76810e15i			0.230432i	−0.993340	+	0.115216i	$0.963244\pi$
$888$		0			0
$889$		−	1.07955e16i		−	0.652052i
$890$		0			0
$891$	−7.38800e15	+	7.38800e15i	−0.440757	+	0.440757i
$892$		0			0
$893$	1.50635e16	+	1.50635e16i	0.887654	+	0.887654i
$894$		0			0
$895$	−9.08150e15			−0.528605
$896$		0			0
$897$	−8.11774e15			−0.466742
$898$		0			0
$899$	−6.31502e15	−	6.31502e15i	−0.358671	−	0.358671i
$900$		0			0
$901$	5.36328e15	−	5.36328e15i	0.300915	−	0.300915i
$902$		0			0
$903$		−	2.28132e15i		−	0.126445i
$904$		0			0
$905$			2.10481e16i			1.15251i
$906$		0			0
$907$	1.08569e16	−	1.08569e16i	0.587309	−	0.587309i	−0.349593	−	0.936902i	$-0.613680\pi$
$907$	1.08569e16	−	1.08569e16i	0.587309	−	0.587309i	0.936902	+	0.349593i	$0.113680\pi$
$908$		0			0
$909$	−6.96700e15	−	6.96700e15i	−0.372344	−	0.372344i
$910$		0			0
$911$	7.63729e14			0.0403263			0.0201631	−	0.999797i	$-0.493581\pi$
$911$	7.63729e14			0.0403263			0.0201631	+	0.999797i	$0.493581\pi$
$912$		0			0
$913$	6.43417e16			3.35663
$914$		0			0
$915$	−1.66964e15	−	1.66964e15i	−0.0860608	−	0.0860608i
$916$		0			0
$917$	1.09934e15	−	1.09934e15i	0.0559886	−	0.0559886i
$918$		0			0
$919$		−	2.80095e16i		−	1.40952i	−0.709447	−	0.704759i	$-0.751055\pi$
$919$		−	2.80095e16i		−	1.40952i	0.709447	−	0.704759i	$-0.248945\pi$
$920$		0			0
$921$			4.90748e15i			0.244023i
$922$		0			0
$923$	−3.22367e15	+	3.22367e15i	−0.158395	+	0.158395i
$924$		0			0
$925$	−2.04812e15	−	2.04812e15i	−0.0994436	−	0.0994436i
$926$		0			0
$927$	−1.23724e16			−0.593631
$928$		0			0
$929$	−8.81107e15			−0.417775			−0.208888	−	0.977940i	$-0.566984\pi$
$929$	−8.81107e15			−0.417775			−0.208888	+	0.977940i	$0.566984\pi$
$930$		0			0
$931$	8.32501e14	+	8.32501e14i	0.0390087	+	0.0390087i
$932$		0			0
$933$	4.09150e15	−	4.09150e15i	0.189467	−	0.189467i
$934$		0			0
$935$			2.45192e16i			1.12213i
$936$		0			0
$937$			1.20088e16i			0.543165i	0.962415	+	0.271583i	$0.0875470\pi$
$937$			1.20088e16i			0.543165i	−0.962415	+	0.271583i	$0.912453\pi$
$938$		0			0
$939$	5.92516e15	−	5.92516e15i	0.264874	−	0.264874i
$940$		0			0
$941$	2.02398e16	+	2.02398e16i	0.894257	+	0.894257i	0.994921	−	0.100664i	$-0.0320966\pi$
$941$	2.02398e16	+	2.02398e16i	0.894257	+	0.894257i	−0.100664	+	0.994921i	$0.532097\pi$
$942$		0			0
$943$	1.76382e15			0.0770263
$944$		0			0
$945$	−1.82297e16			−0.786875
$946$		0			0
$947$	−9.83196e15	−	9.83196e15i	−0.419484	−	0.419484i	0.465542	−	0.885026i	$-0.345859\pi$
$947$	−9.83196e15	−	9.83196e15i	−0.419484	−	0.419484i	−0.885026	+	0.465542i	$0.845859\pi$
$948$		0			0
$949$	−3.06235e16	+	3.06235e16i	−1.29149	+	1.29149i
$950$		0			0
$951$			3.63186e15i			0.151404i
$952$		0			0
$953$			1.24788e16i			0.514236i	0.966380	+	0.257118i	$0.0827729\pi$
$953$			1.24788e16i			0.514236i	−0.966380	+	0.257118i	$0.917227\pi$
$954$		0			0
$955$	−7.25389e15	+	7.25389e15i	−0.295497	+	0.295497i
$956$		0			0
$957$	2.35879e16	+	2.35879e16i	0.949892	+	0.949892i
$958$		0			0
$959$	3.78404e16			1.50645
$960$		0			0
$961$	−2.25763e16			−0.888535
$962$		0			0
$963$	−5.75187e15	−	5.75187e15i	−0.223802	−	0.223802i
$964$		0			0
$965$	1.40579e16	−	1.40579e16i	0.540780	−	0.540780i
$966$		0			0
$967$			2.34176e16i			0.890630i	0.895374	+	0.445315i	$0.146908\pi$
$967$			2.34176e16i			0.890630i	−0.895374	+	0.445315i	$0.853092\pi$
$968$		0			0
$969$			8.72240e15i			0.327986i
$970$		0			0
$971$	2.54807e16	−	2.54807e16i	0.947341	−	0.947341i	−0.0513402	−	0.998681i	$-0.516349\pi$
$971$	2.54807e16	−	2.54807e16i	0.947341	−	0.947341i	0.998681	+	0.0513402i	$0.0163493\pi$
$972$		0			0
$973$	2.41493e16	+	2.41493e16i	0.887738	+	0.887738i
$974$		0			0
$975$	2.24778e15			0.0817010
$976$		0			0
$977$	3.36150e15			0.120813			0.0604065	−	0.998174i	$-0.480760\pi$
$977$	3.36150e15			0.120813			0.0604065	+	0.998174i	$0.480760\pi$
$978$		0			0
$979$	4.57966e16	+	4.57966e16i	1.62753	+	1.62753i
$980$		0			0
$981$	2.58785e16	−	2.58785e16i	0.909409	−	0.909409i
$982$		0			0
$983$		−	9.77577e14i		−	0.0339709i	−0.999856	−	0.0169854i	$-0.994593\pi$
$983$		−	9.77577e14i		−	0.0339709i	0.999856	−	0.0169854i	$-0.00540689\pi$
$984$		0			0
$985$		−	1.98754e16i		−	0.682993i
$986$		0			0
$987$	−1.20921e16	+	1.20921e16i	−0.410919	+	0.410919i
$988$		0			0
$989$	3.63101e15	+	3.63101e15i	0.122025	+	0.122025i
$990$		0			0
$991$	−4.62468e16			−1.53701			−0.768504	−	0.639845i	$-0.778999\pi$
$991$	−4.62468e16			−1.53701			−0.768504	+	0.639845i	$0.778999\pi$
$992$		0			0
$993$	2.52827e16			0.831004
$994$		0			0
$995$	−1.12285e16	−	1.12285e16i	−0.365002	−	0.365002i
$996$		0			0
$997$	2.23825e15	−	2.23825e15i	0.0719590	−	0.0719590i	−0.670211	−	0.742170i	$-0.733797\pi$
$997$	2.23825e15	−	2.23825e15i	0.0719590	−	0.0719590i	0.742170	+	0.670211i	$0.233797\pi$
$998$		0			0
$999$			3.35442e16i			1.06661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.12.e.a.17.13		42
4.3	odd	2		16.12.e.a.13.17	yes	42
8.3	odd	2		128.12.e.b.33.13		42
8.5	even	2		128.12.e.a.33.9		42
16.3	odd	4		128.12.e.b.97.13		42
16.5	even	4	inner	64.12.e.a.49.13		42
16.11	odd	4		16.12.e.a.5.17	✓	42
16.13	even	4		128.12.e.a.97.9		42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.17	✓	42	16.11	odd	4
16.12.e.a.13.17	yes	42	4.3	odd	2
64.12.e.a.17.13		42	1.1	even	1	trivial
64.12.e.a.49.13		42	16.5	even	4	inner
128.12.e.a.33.9		42	8.5	even	2
128.12.e.a.97.9		42	16.13	even	4
128.12.e.b.33.13		42	8.3	odd	2
128.12.e.b.97.13		42	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(145.072 + 145.072i) q^{3} +(-4652.81 + 4652.81i) q^{5} +43253.0i q^{7} -135056. i q^{9} +O(q^{10})\)	\(q+(145.072 + 145.072i) q^{3} +(-4652.81 + 4652.81i) q^{5} +43253.0i q^{7} -135056. i q^{9} +(685114. - 685114. i) q^{11} +(-1.40072e6 - 1.40072e6i) q^{13} -1.34998e6 q^{15} +3.84591e6 q^{17} +(7.81673e6 + 7.81673e6i) q^{19} +(-6.27478e6 + 6.27478e6i) q^{21} -1.99742e7i q^{23} +5.53080e6i q^{25} +(4.52917e7 - 4.52917e7i) q^{27} +(1.18663e8 + 1.18663e8i) q^{29} -5.32181e7 q^{31} +1.98781e8 q^{33} +(-2.01248e8 - 2.01248e8i) q^{35} +(-3.70312e8 + 3.70312e8i) q^{37} -4.06411e8i q^{39} +8.83045e7i q^{41} +(-1.81785e8 + 1.81785e8i) q^{43} +(6.28388e8 + 6.28388e8i) q^{45} +1.92709e9 q^{47} +1.06502e8 q^{49} +(5.57932e8 + 5.57932e8i) q^{51} +(1.39454e9 - 1.39454e9i) q^{53} +6.37541e9i q^{55} +2.26797e9i q^{57} +(2.09985e9 - 2.09985e9i) q^{59} +(1.23678e9 + 1.23678e9i) q^{61} +5.84156e9 q^{63} +1.30346e10 q^{65} +(9.73212e9 + 9.73212e9i) q^{67} +(2.89769e9 - 2.89769e9i) q^{69} -2.30143e9i q^{71} -2.18626e10i q^{73} +(-8.02362e8 + 8.02362e8i) q^{75} +(2.96333e10 + 2.96333e10i) q^{77} +1.21163e8 q^{79} -1.07836e10 q^{81} +(4.69569e10 + 4.69569e10i) q^{83} +(-1.78943e10 + 1.78943e10i) q^{85} +3.44292e10i q^{87} +6.68453e10i q^{89} +(6.05856e10 - 6.05856e10i) q^{91} +(-7.72043e9 - 7.72043e9i) q^{93} -7.27395e10 q^{95} +4.52611e10 q^{97} +(-9.25284e10 - 9.25284e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 - 2 * q^5	\( 42 q + 2 q^{3} - 2 q^{5} + 540846 q^{11} - 2 q^{13} + 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} + 354292 q^{21} + 66463304 q^{27} + 77673206 q^{29} - 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} - 522762058 q^{37} - 3824193658 q^{43} + 97301954 q^{45} + 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} - 2100608058 q^{53} - 955824746 q^{59} + 2150827022 q^{61} - 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} - 16193060732 q^{69} - 28890034486 q^{75} - 22711870540 q^{77} - 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} - 84575506252 q^{85} + 147369662716 q^{91} - 69689773328 q^{93} - 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 - 2 * q^5 + 540846 * q^11 - 2 * q^13 + 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 + 354292 * q^21 + 66463304 * q^27 + 77673206 * q^29 - 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 - 522762058 * q^37 - 3824193658 * q^43 + 97301954 * q^45 + 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 - 2100608058 * q^53 - 955824746 * q^59 + 2150827022 * q^61 - 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 - 16193060732 * q^69 - 28890034486 * q^75 - 22711870540 * q^77 - 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 - 84575506252 * q^85 + 147369662716 * q^91 - 69689773328 * q^93 - 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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