LMFDB - Embedded newform 128.12.e.b.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,12,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, 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("128.33");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	128.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:	$98.3479271116$
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			33.2
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-457.250 - 457.250i) q^{3} +(-5575.43 + 5575.43i) q^{5} -55452.7i q^{7} +241008. i q^{9} +O(q^{10})$	\(q+(-457.250 - 457.250i) q^{3} +(-5575.43 + 5575.43i) q^{5} -55452.7i q^{7} +241008. i q^{9} +(593916. - 593916. i) q^{11} +(320484. + 320484. i) q^{13} +5.09873e6 q^{15} -9.66759e6 q^{17} +(-6.35824e6 - 6.35824e6i) q^{19} +(-2.53557e7 + 2.53557e7i) q^{21} +1.96028e7i q^{23} -1.33426e7i q^{25} +(2.92004e7 - 2.92004e7i) q^{27} +(7.64662e7 + 7.64662e7i) q^{29} -1.66832e8 q^{31} -5.43136e8 q^{33} +(3.09173e8 + 3.09173e8i) q^{35} +(-2.74973e7 + 2.74973e7i) q^{37} -2.93082e8i q^{39} +6.15454e8i q^{41} +(-8.26623e8 + 8.26623e8i) q^{43} +(-1.34372e9 - 1.34372e9i) q^{45} +1.20677e9 q^{47} -1.09768e9 q^{49} +(4.42051e9 + 4.42051e9i) q^{51} +(-6.02601e8 + 6.02601e8i) q^{53} +6.62267e9i q^{55} +5.81461e9i q^{57} +(-3.88524e9 + 3.88524e9i) q^{59} +(2.43319e9 + 2.43319e9i) q^{61} +1.33645e10 q^{63} -3.57367e9 q^{65} +(-8.86750e9 - 8.86750e9i) q^{67} +(8.96337e9 - 8.96337e9i) q^{69} -2.93481e10i q^{71} -7.45154e9i q^{73} +(-6.10092e9 + 6.10092e9i) q^{75} +(-3.29342e10 - 3.29342e10i) q^{77} -2.31480e10 q^{79} +1.59901e10 q^{81} +(-4.40857e9 - 4.40857e9i) q^{83} +(5.39010e10 - 5.39010e10i) q^{85} -6.99284e10i q^{87} +4.82749e10i q^{89} +(1.77717e10 - 1.77717e10i) q^{91} +(7.62839e10 + 7.62839e10i) q^{93} +7.08998e10 q^{95} +9.19031e10 q^{97} +(1.43138e11 + 1.43138e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−457.250	−	457.250i	−1.08639	−	1.08639i	−0.995897	−	0.0904954i	$-0.971155\pi$
$3$	−457.250	−	457.250i	−1.08639	−	1.08639i	−0.0904954	−	0.995897i	$-0.528845\pi$
$4$		0			0
$5$	−5575.43	+	5575.43i	−0.797890	+	0.797890i	−0.982763	−	0.184872i	$-0.940813\pi$
$5$	−5575.43	+	5575.43i	−0.797890	+	0.797890i	0.184872	+	0.982763i	$0.440813\pi$
$6$		0			0
$7$		−	55452.7i		−	1.24705i	−0.781804	−	0.623525i	$-0.785700\pi$
$7$		−	55452.7i		−	1.24705i	0.781804	−	0.623525i	$-0.214300\pi$
$8$		0			0
$9$			241008.i			1.36050i
$10$		0			0
$11$	593916.	−	593916.i	1.11190	−	1.11190i	0.119004	−	0.992894i	$-0.462030\pi$
$11$	593916.	−	593916.i	1.11190	−	1.11190i	0.992894	−	0.119004i	$-0.0379702\pi$
$12$		0			0
$13$	320484.	+	320484.i	0.239396	+	0.239396i	0.816600	−	0.577204i	$-0.195856\pi$
$13$	320484.	+	320484.i	0.239396	+	0.239396i	−0.577204	+	0.816600i	$0.695856\pi$
$14$		0			0
$15$	5.09873e6			1.73364
$16$		0			0
$17$	−9.66759e6			−1.65139			−0.825694	−	0.564118i	$-0.809216\pi$
$17$	−9.66759e6			−1.65139			−0.825694	+	0.564118i	$0.809216\pi$
$18$		0			0
$19$	−6.35824e6	−	6.35824e6i	−0.589104	−	0.589104i	0.348285	−	0.937389i	$-0.386764\pi$
$19$	−6.35824e6	−	6.35824e6i	−0.589104	−	0.589104i	−0.937389	+	0.348285i	$0.886764\pi$
$20$		0			0
$21$	−2.53557e7	+	2.53557e7i	−1.35478	+	1.35478i
$22$		0			0
$23$			1.96028e7i			0.635060i	0.948248	+	0.317530i	$0.102853\pi$
$23$			1.96028e7i			0.635060i	−0.948248	+	0.317530i	$0.897147\pi$
$24$		0			0
$25$		−	1.33426e7i		−	0.273257i
$26$		0			0
$27$	2.92004e7	−	2.92004e7i	0.391641	−	0.391641i
$28$		0			0
$29$	7.64662e7	+	7.64662e7i	0.692278	+	0.692278i	0.962733	−	0.270454i	$-0.0871739\pi$
$29$	7.64662e7	+	7.64662e7i	0.692278	+	0.692278i	−0.270454	+	0.962733i	$0.587174\pi$
$30$		0			0
$31$	−1.66832e8			−1.04662			−0.523311	−	0.852142i	$-0.675304\pi$
$31$	−1.66832e8			−1.04662			−0.523311	+	0.852142i	$0.675304\pi$
$32$		0			0
$33$	−5.43136e8			−2.41591
$34$		0			0
$35$	3.09173e8	+	3.09173e8i	0.995008	+	0.995008i
$36$		0			0
$37$	−2.74973e7	+	2.74973e7i	−0.0651899	+	0.0651899i	−0.738950	−	0.673760i	$-0.764678\pi$
$37$	−2.74973e7	+	2.74973e7i	−0.0651899	+	0.0651899i	0.673760	+	0.738950i	$0.264678\pi$
$38$		0			0
$39$		−	2.93082e8i		−	0.520157i
$40$		0			0
$41$			6.15454e8i			0.829630i	0.909906	+	0.414815i	$0.136154\pi$
$41$			6.15454e8i			0.829630i	−0.909906	+	0.414815i	$0.863846\pi$
$42$		0			0
$43$	−8.26623e8	+	8.26623e8i	−0.857493	+	0.857493i	−0.991042	−	0.133549i	$-0.957363\pi$
$43$	−8.26623e8	+	8.26623e8i	−0.857493	+	0.857493i	0.133549	+	0.991042i	$0.457363\pi$
$44$		0			0
$45$	−1.34372e9	−	1.34372e9i	−1.08553	−	1.08553i
$46$		0			0
$47$	1.20677e9			0.767514			0.383757	−	0.923434i	$-0.374630\pi$
$47$	1.20677e9			0.767514			0.383757	+	0.923434i	$0.374630\pi$
$48$		0			0
$49$	−1.09768e9			−0.555132
$50$		0			0
$51$	4.42051e9	+	4.42051e9i	1.79406	+	1.79406i
$52$		0			0
$53$	−6.02601e8	+	6.02601e8i	−0.197930	+	0.197930i	−0.799112	−	0.601182i	$-0.794697\pi$
$53$	−6.02601e8	+	6.02601e8i	−0.197930	+	0.197930i	0.601182	+	0.799112i	$0.294697\pi$
$54$		0			0
$55$			6.62267e9i			1.77435i
$56$		0			0
$57$			5.81461e9i			1.28000i
$58$		0			0
$59$	−3.88524e9	+	3.88524e9i	−0.707508	+	0.707508i	−0.966011	−	0.258502i	$-0.916771\pi$
$59$	−3.88524e9	+	3.88524e9i	−0.707508	+	0.707508i	0.258502	+	0.966011i	$0.416771\pi$
$60$		0			0
$61$	2.43319e9	+	2.43319e9i	0.368861	+	0.368861i	0.867062	−	0.498201i	$-0.166006\pi$
$61$	2.43319e9	+	2.43319e9i	0.368861	+	0.368861i	−0.498201	+	0.867062i	$0.666006\pi$
$62$		0			0
$63$	1.33645e10			1.69661
$64$		0			0
$65$	−3.57367e9			−0.382024
$66$		0			0
$67$	−8.86750e9	−	8.86750e9i	−0.802398	−	0.802398i	0.181072	−	0.983470i	$-0.442043\pi$
$67$	−8.86750e9	−	8.86750e9i	−0.802398	−	0.802398i	−0.983470	+	0.181072i	$0.942043\pi$
$68$		0			0
$69$	8.96337e9	−	8.96337e9i	0.689924	−	0.689924i
$70$		0			0
$71$		−	2.93481e10i		−	1.93045i	−0.261418	−	0.965226i	$-0.584190\pi$
$71$		−	2.93481e10i		−	1.93045i	0.261418	−	0.965226i	$-0.415810\pi$
$72$		0			0
$73$		−	7.45154e9i		−	0.420698i	−0.977626	−	0.210349i	$-0.932540\pi$
$73$		−	7.45154e9i		−	0.420698i	0.977626	−	0.210349i	$-0.0674600\pi$
$74$		0			0
$75$	−6.10092e9	+	6.10092e9i	−0.296865	+	0.296865i
$76$		0			0
$77$	−3.29342e10	−	3.29342e10i	−1.38659	−	1.38659i
$78$		0			0
$79$	−2.31480e10			−0.846378			−0.423189	−	0.906042i	$-0.639089\pi$
$79$	−2.31480e10			−0.846378			−0.423189	+	0.906042i	$0.639089\pi$
$80$		0			0
$81$	1.59901e10			0.509546
$82$		0			0
$83$	−4.40857e9	−	4.40857e9i	−0.122848	−	0.122848i	0.643010	−	0.765858i	$-0.277685\pi$
$83$	−4.40857e9	−	4.40857e9i	−0.122848	−	0.122848i	−0.765858	+	0.643010i	$0.777685\pi$
$84$		0			0
$85$	5.39010e10	−	5.39010e10i	1.31763	−	1.31763i
$86$		0			0
$87$		−	6.99284e10i		−	1.50417i
$88$		0			0
$89$			4.82749e10i			0.916382i	0.888854	+	0.458191i	$0.151502\pi$
$89$			4.82749e10i			0.916382i	−0.888854	+	0.458191i	$0.848498\pi$
$90$		0			0
$91$	1.77717e10	−	1.77717e10i	0.298539	−	0.298539i
$92$		0			0
$93$	7.62839e10	+	7.62839e10i	1.13704	+	1.13704i
$94$		0			0
$95$	7.08998e10			0.940081
$96$		0			0
$97$	9.19031e10			1.08664			0.543320	−	0.839526i	$-0.317167\pi$
$97$	9.19031e10			1.08664			0.543320	+	0.839526i	$0.317167\pi$
$98$		0			0
$99$	1.43138e11	+	1.43138e11i	1.51273	+	1.51273i
$100$		0			0
$101$	8.97475e10	−	8.97475e10i	0.849679	−	0.849679i	−0.140414	−	0.990093i	$-0.544843\pi$
$101$	8.97475e10	−	8.97475e10i	0.849679	−	0.849679i	0.990093	+	0.140414i	$0.0448433\pi$
$102$		0			0
$103$			1.00244e11i			0.852031i	0.904716	+	0.426015i	$0.140083\pi$
$103$			1.00244e11i			0.852031i	−0.904716	+	0.426015i	$0.859917\pi$
$104$		0			0
$105$		−	2.82738e11i		−	2.16194i
$106$		0			0
$107$	2.34076e10	−	2.34076e10i	0.161341	−	0.161341i	−0.621819	−	0.783161i	$-0.713606\pi$
$107$	2.34076e10	−	2.34076e10i	0.161341	−	0.161341i	0.783161	+	0.621819i	$0.213606\pi$
$108$		0			0
$109$	−4.45007e10	−	4.45007e10i	−0.277026	−	0.277026i	0.554894	−	0.831921i	$-0.312759\pi$
$109$	−4.45007e10	−	4.45007e10i	−0.277026	−	0.277026i	−0.831921	+	0.554894i	$0.812759\pi$
$110$		0			0
$111$	2.51463e10			0.141644
$112$		0			0
$113$	−2.35044e11			−1.20010			−0.600049	−	0.799963i	$-0.704852\pi$
$113$	−2.35044e11			−1.20010			−0.600049	+	0.799963i	$0.704852\pi$
$114$		0			0
$115$	−1.09294e11	−	1.09294e11i	−0.506708	−	0.506708i
$116$		0			0
$117$	−7.72391e10	+	7.72391e10i	−0.325698	+	0.325698i
$118$		0			0
$119$			5.36094e11i			2.05936i
$120$		0			0
$121$		−	4.20160e11i		−	1.47263i
$122$		0			0
$123$	2.81416e11	−	2.81416e11i	0.901304	−	0.901304i
$124$		0			0
$125$	−1.97847e11	−	1.97847e11i	−0.579861	−	0.579861i
$126$		0			0
$127$	6.24519e11			1.67736			0.838678	−	0.544628i	$-0.183329\pi$
$127$	6.24519e11			1.67736			0.838678	+	0.544628i	$0.183329\pi$
$128$		0			0
$129$	7.55946e11			1.86315
$130$		0			0
$131$	4.84655e11	+	4.84655e11i	1.09759	+	1.09759i	0.994692	+	0.102900i	$0.0328121\pi$
$131$	4.84655e11	+	4.84655e11i	1.09759	+	1.09759i	0.102900	+	0.994692i	$0.467188\pi$
$132$		0			0
$133$	−3.52582e11	+	3.52582e11i	−0.734642	+	0.734642i
$134$		0			0
$135$			3.25609e11i			0.624972i
$136$		0			0
$137$			5.03802e11i			0.891860i	0.895068	+	0.445930i	$0.147127\pi$
$137$			5.03802e11i			0.891860i	−0.895068	+	0.445930i	$0.852873\pi$
$138$		0			0
$139$	−2.16836e11	+	2.16836e11i	−0.354446	+	0.354446i	−0.861761	−	0.507315i	$-0.830638\pi$
$139$	−2.16836e11	+	2.16836e11i	−0.354446	+	0.354446i	0.507315	+	0.861761i	$0.330638\pi$
$140$		0			0
$141$	−5.51796e11	−	5.51796e11i	−0.833822	−	0.833822i
$142$		0			0
$143$	3.80681e11			0.532369
$144$		0			0
$145$	−8.52664e11			−1.10472
$146$		0			0
$147$	5.01913e11	+	5.01913e11i	0.603091	+	0.603091i
$148$		0			0
$149$	4.15167e11	−	4.15167e11i	0.463126	−	0.463126i	−0.436553	−	0.899679i	$-0.643801\pi$
$149$	4.15167e11	−	4.15167e11i	0.463126	−	0.463126i	0.899679	+	0.436553i	$0.143801\pi$
$150$		0			0
$151$			3.26377e11i			0.338334i	0.985587	+	0.169167i	$0.0541078\pi$
$151$			3.26377e11i			0.338334i	−0.985587	+	0.169167i	$0.945892\pi$
$152$		0			0
$153$		−	2.32997e12i		−	2.24671i
$154$		0			0
$155$	9.30160e11	−	9.30160e11i	0.835090	−	0.835090i
$156$		0			0
$157$	7.29021e11	+	7.29021e11i	0.609947	+	0.609947i	0.942932	−	0.332985i	$-0.108056\pi$
$157$	7.29021e11	+	7.29021e11i	0.609947	+	0.609947i	−0.332985	+	0.942932i	$0.608056\pi$
$158$		0			0
$159$	5.51078e11			0.430060
$160$		0			0
$161$	1.08703e12			0.791951
$162$		0			0
$163$	8.04342e11	+	8.04342e11i	0.547531	+	0.547531i	0.925726	−	0.378195i	$-0.123455\pi$
$163$	8.04342e11	+	8.04342e11i	0.547531	+	0.547531i	−0.378195	+	0.925726i	$0.623455\pi$
$164$		0			0
$165$	3.02821e12	−	3.02821e12i	1.92763	−	1.92763i
$166$		0			0
$167$		−	5.08675e11i		−	0.303040i	−0.988454	−	0.151520i	$-0.951583\pi$
$167$		−	5.08675e11i		−	0.303040i	0.988454	−	0.151520i	$-0.0484168\pi$
$168$		0			0
$169$		−	1.58674e12i		−	0.885379i
$170$		0			0
$171$	1.53239e12	−	1.53239e12i	0.801474	−	0.801474i
$172$		0			0
$173$	8.77981e11	+	8.77981e11i	0.430756	+	0.430756i	0.888886	−	0.458129i	$-0.151480\pi$
$173$	8.77981e11	+	8.77981e11i	0.430756	+	0.430756i	−0.458129	+	0.888886i	$0.651480\pi$
$174$		0			0
$175$	−7.39886e11			−0.340766
$176$		0			0
$177$	3.55305e12			1.53726
$178$		0			0
$179$	−1.50802e12	−	1.50802e12i	−0.613360	−	0.613360i	0.330460	−	0.943820i	$-0.392796\pi$
$179$	−1.50802e12	−	1.50802e12i	−0.613360	−	0.613360i	−0.943820	+	0.330460i	$0.892796\pi$
$180$		0			0
$181$	4.49068e11	−	4.49068e11i	0.171822	−	0.171822i	−0.615957	−	0.787780i	$-0.711231\pi$
$181$	4.49068e11	−	4.49068e11i	0.171822	−	0.171822i	0.787780	+	0.615957i	$0.211231\pi$
$182$		0			0
$183$		−	2.22516e12i		−	0.801456i
$184$		0			0
$185$		−	3.06618e11i		−	0.104029i
$186$		0			0
$187$	−5.74173e12	+	5.74173e12i	−1.83618	+	1.83618i
$188$		0			0
$189$	−1.61924e12	−	1.61924e12i	−0.488395	−	0.488395i
$190$		0			0
$191$	4.96899e12			1.41444			0.707220	−	0.706993i	$-0.249949\pi$
$191$	4.96899e12			1.41444			0.707220	+	0.706993i	$0.249949\pi$
$192$		0			0
$193$	−2.71012e12			−0.728489			−0.364244	−	0.931303i	$-0.618673\pi$
$193$	−2.71012e12			−0.728489			−0.364244	+	0.931303i	$0.618673\pi$
$194$		0			0
$195$	1.63406e12	+	1.63406e12i	0.415028	+	0.415028i
$196$		0			0
$197$	5.19796e12	−	5.19796e12i	1.24816	−	1.24816i	0.291623	−	0.956533i	$-0.405805\pi$
$197$	5.19796e12	−	5.19796e12i	1.24816	−	1.24816i	0.956533	−	0.291623i	$-0.0941954\pi$
$198$		0			0
$199$		−	1.24035e12i		−	0.281742i	−0.990028	−	0.140871i	$-0.955010\pi$
$199$		−	1.24035e12i		−	0.281742i	0.990028	−	0.140871i	$-0.0449903\pi$
$200$		0			0
$201$			8.10933e12i			1.74344i
$202$		0			0
$203$	4.24026e12	−	4.24026e12i	0.863305	−	0.863305i
$204$		0			0
$205$	−3.43142e12	−	3.43142e12i	−0.661954	−	0.661954i
$206$		0			0
$207$	−4.72443e12			−0.863997
$208$		0			0
$209$	−7.55252e12			−1.31005
$210$		0			0
$211$	2.59805e12	+	2.59805e12i	0.427656	+	0.427656i	0.887829	−	0.460173i	$-0.152213\pi$
$211$	2.59805e12	+	2.59805e12i	0.427656	+	0.427656i	−0.460173	+	0.887829i	$0.652213\pi$
$212$		0			0
$213$	−1.34194e13	+	1.34194e13i	−2.09723	+	2.09723i
$214$		0			0
$215$		−	9.21755e12i		−	1.36837i
$216$		0			0
$217$			9.25129e12i			1.30519i
$218$		0			0
$219$	−3.40722e12	+	3.40722e12i	−0.457043	+	0.457043i
$220$		0			0
$221$	−3.09831e12	−	3.09831e12i	−0.395336	−	0.395336i
$222$		0			0
$223$	3.31901e12			0.403025			0.201512	−	0.979486i	$-0.435414\pi$
$223$	3.31901e12			0.403025			0.201512	+	0.979486i	$0.435414\pi$
$224$		0			0
$225$	3.21568e12			0.371766
$226$		0			0
$227$	−2.66770e12	−	2.66770e12i	−0.293762	−	0.293762i	0.544803	−	0.838564i	$-0.316605\pi$
$227$	−2.66770e12	−	2.66770e12i	−0.293762	−	0.293762i	−0.838564	+	0.544803i	$0.816605\pi$
$228$		0			0
$229$	−5.06633e12	+	5.06633e12i	−0.531616	+	0.531616i	−0.921053	−	0.389437i	$-0.872670\pi$
$229$	−5.06633e12	+	5.06633e12i	−0.531616	+	0.531616i	0.389437	+	0.921053i	$0.372670\pi$
$230$		0			0
$231$			3.01184e13i			3.01277i
$232$		0			0
$233$		−	1.26560e13i		−	1.20737i	−0.797224	−	0.603683i	$-0.793699\pi$
$233$		−	1.26560e13i		−	1.20737i	0.797224	−	0.603683i	$-0.206301\pi$
$234$		0			0
$235$	−6.72826e12	+	6.72826e12i	−0.612392	+	0.612392i
$236$		0			0
$237$	1.05844e13	+	1.05844e13i	0.919498	+	0.919498i
$238$		0			0
$239$	3.75926e12			0.311828			0.155914	−	0.987771i	$-0.450168\pi$
$239$	3.75926e12			0.311828			0.155914	+	0.987771i	$0.450168\pi$
$240$		0			0
$241$	−5.53115e12			−0.438250			−0.219125	−	0.975697i	$-0.570320\pi$
$241$	−5.53115e12			−0.438250			−0.219125	+	0.975697i	$0.570320\pi$
$242$		0			0
$243$	−1.24842e13	−	1.24842e13i	−0.945207	−	0.945207i
$244$		0			0
$245$	6.12002e12	−	6.12002e12i	0.442934	−	0.442934i
$246$		0			0
$247$		−	4.07543e12i		−	0.282059i
$248$		0			0
$249$			4.03164e12i			0.266922i
$250$		0			0
$251$	3.06972e12	−	3.06972e12i	0.194488	−	0.194488i	−0.603144	−	0.797632i	$-0.706086\pi$
$251$	3.06972e12	−	3.06972e12i	0.194488	−	0.194488i	0.797632	+	0.603144i	$0.206086\pi$
$252$		0			0
$253$	1.16424e13	+	1.16424e13i	0.706122	+	0.706122i
$254$		0			0
$255$	−4.92924e13			−2.86292
$256$		0			0
$257$	1.71375e12			0.0953489			0.0476745	−	0.998863i	$-0.484819\pi$
$257$	1.71375e12			0.0953489			0.0476745	+	0.998863i	$0.484819\pi$
$258$		0			0
$259$	1.52480e12	+	1.52480e12i	0.0812950	+	0.0812950i
$260$		0			0
$261$	−1.84290e13	+	1.84290e13i	−0.941842	+	0.941842i
$262$		0			0
$263$		−	1.01496e13i		−	0.497384i	−0.968583	−	0.248692i	$-0.919999\pi$
$263$		−	1.01496e13i		−	0.497384i	0.968583	−	0.248692i	$-0.0800007\pi$
$264$		0			0
$265$		−	6.71951e12i		−	0.315853i
$266$		0			0
$267$	2.20737e13	−	2.20737e13i	0.995550	−	0.995550i
$268$		0			0
$269$	1.30252e13	+	1.30252e13i	0.563828	+	0.563828i	0.930393	−	0.366564i	$-0.119466\pi$
$269$	1.30252e13	+	1.30252e13i	0.563828	+	0.563828i	−0.366564	+	0.930393i	$0.619466\pi$
$270$		0			0
$271$	−1.84540e13			−0.766934			−0.383467	−	0.923554i	$-0.625270\pi$
$271$	−1.84540e13			−0.766934			−0.383467	+	0.923554i	$0.625270\pi$
$272$		0			0
$273$	−1.62522e13			−0.648661
$274$		0			0
$275$	−7.92441e12	−	7.92441e12i	−0.303834	−	0.303834i
$276$		0			0
$277$	−1.56562e13	+	1.56562e13i	−0.576828	+	0.576828i	−0.934028	−	0.357200i	$-0.883732\pi$
$277$	−1.56562e13	+	1.56562e13i	−0.576828	+	0.576828i	0.357200	+	0.934028i	$0.383732\pi$
$278$		0			0
$279$		−	4.02078e13i		−	1.42393i
$280$		0			0
$281$			5.12053e13i			1.74353i	0.489922	+	0.871766i	$0.337025\pi$
$281$			5.12053e13i			1.74353i	−0.489922	+	0.871766i	$0.662975\pi$
$282$		0			0
$283$	−3.68160e10	+	3.68160e10i	−0.00120562	+	0.00120562i	−0.707709	−	0.706504i	$-0.750271\pi$
$283$	−3.68160e10	+	3.68160e10i	−0.00120562	+	0.00120562i	0.706504	+	0.707709i	$0.250271\pi$
$284$		0			0
$285$	−3.24189e13	−	3.24189e13i	−1.02130	−	1.02130i
$286$		0			0
$287$	3.41286e13			1.03459
$288$		0			0
$289$	5.91905e13			1.72708
$290$		0			0
$291$	−4.20227e13	−	4.20227e13i	−1.18052	−	1.18052i
$292$		0			0
$293$	−7.30934e12	+	7.30934e12i	−0.197745	+	0.197745i	−0.799033	−	0.601287i	$-0.794655\pi$
$293$	−7.30934e12	+	7.30934e12i	−0.197745	+	0.197745i	0.601287	+	0.799033i	$0.294655\pi$
$294$		0			0
$295$		−	4.33237e13i		−	1.12903i
$296$		0			0
$297$		−	3.46851e13i		−	0.870929i
$298$		0			0
$299$	−6.28237e12	+	6.28237e12i	−0.152031	+	0.152031i
$300$		0			0
$301$	4.58385e13	+	4.58385e13i	1.06934	+	1.06934i
$302$		0			0
$303$	−8.20741e13			−1.84617
$304$		0			0
$305$	−2.71322e13			−0.588621
$306$		0			0
$307$	−5.00023e13	−	5.00023e13i	−1.04648	−	1.04648i	−0.998866	−	0.0476101i	$-0.984840\pi$
$307$	−5.00023e13	−	5.00023e13i	−1.04648	−	1.04648i	−0.0476101	−	0.998866i	$-0.515160\pi$
$308$		0			0
$309$	4.58367e13	−	4.58367e13i	0.925639	−	0.925639i
$310$		0			0
$311$			8.72624e13i			1.70077i	0.526163	+	0.850384i	$0.323630\pi$
$311$			8.72624e13i			1.70077i	−0.526163	+	0.850384i	$0.676370\pi$
$312$		0			0
$313$			5.00784e13i			0.942229i	0.882072	+	0.471114i	$0.156148\pi$
$313$			5.00784e13i			0.942229i	−0.882072	+	0.471114i	$0.843852\pi$
$314$		0			0
$315$	−7.45130e13	+	7.45130e13i	−1.35371	+	1.35371i
$316$		0			0
$317$	−5.46587e13	−	5.46587e13i	−0.959033	−	0.959033i	0.0401607	−	0.999193i	$-0.487213\pi$
$317$	−5.46587e13	−	5.46587e13i	−0.959033	−	0.959033i	−0.999193	+	0.0401607i	$0.987213\pi$
$318$		0			0
$319$	9.08290e13			1.53949
$320$		0			0
$321$	−2.14062e13			−0.350560
$322$		0			0
$323$	6.14689e13	+	6.14689e13i	0.972840	+	0.972840i
$324$		0			0
$325$	4.27610e12	−	4.27610e12i	0.0654168	−	0.0654168i
$326$		0			0
$327$			4.06959e13i			0.601919i
$328$		0			0
$329$		−	6.69187e13i		−	0.957128i
$330$		0			0
$331$	1.49745e13	−	1.49745e13i	0.207156	−	0.207156i	−0.595901	−	0.803058i	$-0.703205\pi$
$331$	1.49745e13	−	1.49745e13i	0.207156	−	0.207156i	0.803058	+	0.595901i	$0.203205\pi$
$332$		0			0
$333$	−6.62706e12	−	6.62706e12i	−0.0886906	−	0.0886906i
$334$		0			0
$335$	9.88802e13			1.28045
$336$		0			0
$337$	−6.74796e12			−0.0845684			−0.0422842	−	0.999106i	$-0.513463\pi$
$337$	−6.74796e12			−0.0845684			−0.0422842	+	0.999106i	$0.513463\pi$
$338$		0			0
$339$	1.07474e14	+	1.07474e14i	1.30378	+	1.30378i
$340$		0			0
$341$	−9.90842e13	+	9.90842e13i	−1.16374	+	1.16374i
$342$		0			0
$343$		−	4.87789e13i		−	0.554772i
$344$		0			0
$345$			9.99492e13i			1.10097i
$346$		0			0
$347$	9.73980e13	−	9.73980e13i	1.03929	−	1.03929i	0.0400971	−	0.999196i	$-0.487233\pi$
$347$	9.73980e13	−	9.73980e13i	1.03929	−	1.03929i	0.999196	−	0.0400971i	$-0.0127667\pi$
$348$		0			0
$349$	8.34720e12	+	8.34720e12i	0.0862980	+	0.0862980i	0.748938	−	0.662640i	$-0.230564\pi$
$349$	8.34720e12	+	8.34720e12i	0.0862980	+	0.0862980i	−0.662640	+	0.748938i	$0.730564\pi$
$350$		0			0
$351$	1.87165e13			0.187515
$352$		0			0
$353$	−9.06184e13			−0.879945			−0.439973	−	0.898011i	$-0.645012\pi$
$353$	−9.06184e13			−0.879945			−0.439973	+	0.898011i	$0.645012\pi$
$354$		0			0
$355$	1.63628e14	+	1.63628e14i	1.54029	+	1.54029i
$356$		0			0
$357$	2.45129e14	−	2.45129e14i	2.23728	−	2.23728i
$358$		0			0
$359$		−	7.14917e13i		−	0.632756i	−0.948633	−	0.316378i	$-0.897533\pi$
$359$		−	7.14917e13i		−	0.632756i	0.948633	−	0.316378i	$-0.102467\pi$
$360$		0			0
$361$		−	3.56358e13i		−	0.305912i
$362$		0			0
$363$	−1.92118e14	+	1.92118e14i	−1.59986	+	1.59986i
$364$		0			0
$365$	4.15455e13	+	4.15455e13i	0.335671	+	0.335671i
$366$		0			0
$367$	4.19051e12			0.0328552			0.0164276	−	0.999865i	$-0.494771\pi$
$367$	4.19051e12			0.0328552			0.0164276	+	0.999865i	$0.494771\pi$
$368$		0			0
$369$	−1.48329e14			−1.12871
$370$		0			0
$371$	3.34159e13	+	3.34159e13i	0.246829	+	0.246829i
$372$		0			0
$373$	−1.12134e14	+	1.12134e14i	−0.804153	+	0.804153i	−0.983742	−	0.179589i	$-0.942523\pi$
$373$	−1.12134e14	+	1.12134e14i	−0.804153	+	0.804153i	0.179589	+	0.983742i	$0.442523\pi$
$374$		0			0
$375$			1.80931e14i			1.25991i
$376$		0			0
$377$			4.90124e13i			0.331458i
$378$		0			0
$379$	1.04153e14	−	1.04153e14i	0.684154	−	0.684154i	−0.276779	−	0.960934i	$-0.589267\pi$
$379$	1.04153e14	−	1.04153e14i	0.684154	−	0.684154i	0.960934	+	0.276779i	$0.0892671\pi$
$380$		0			0
$381$	−2.85561e14	−	2.85561e14i	−1.82227	−	1.82227i
$382$		0			0
$383$	−1.29233e14			−0.801274			−0.400637	−	0.916237i	$-0.631211\pi$
$383$	−1.29233e14			−0.801274			−0.400637	+	0.916237i	$0.631211\pi$
$384$		0			0
$385$	3.67245e14			2.21270
$386$		0			0
$387$	−1.99223e14	−	1.99223e14i	−1.16662	−	1.16662i
$388$		0			0
$389$	2.24630e14	−	2.24630e14i	1.27863	−	1.27863i	0.337198	−	0.941434i	$-0.390521\pi$
$389$	2.24630e14	−	2.24630e14i	1.27863	−	1.27863i	0.941434	−	0.337198i	$-0.109479\pi$
$390$		0			0
$391$		−	1.89512e14i		−	1.04873i
$392$		0			0
$393$		−	4.43217e14i		−	2.38483i
$394$		0			0
$395$	1.29060e14	−	1.29060e14i	0.675316	−	0.675316i
$396$		0			0
$397$	2.06448e14	+	2.06448e14i	1.05066	+	1.05066i	0.998646	+	0.0520169i	$0.0165650\pi$
$397$	2.06448e14	+	2.06448e14i	1.05066	+	1.05066i	0.0520169	+	0.998646i	$0.483435\pi$
$398$		0			0
$399$	3.22436e14			1.59622
$400$		0			0
$401$	1.77354e14			0.854177			0.427089	−	0.904210i	$-0.359539\pi$
$401$	1.77354e14			0.854177			0.427089	+	0.904210i	$0.359539\pi$
$402$		0			0
$403$	−5.34670e13	−	5.34670e13i	−0.250558	−	0.250558i
$404$		0			0
$405$	−8.91516e13	+	8.91516e13i	−0.406562	+	0.406562i
$406$		0			0
$407$			3.26621e13i			0.144969i
$408$		0			0
$409$		−	3.56385e14i		−	1.53972i	−0.638213	−	0.769860i	$-0.720326\pi$
$409$		−	3.56385e14i		−	1.53972i	0.638213	−	0.769860i	$-0.279674\pi$
$410$		0			0
$411$	2.30363e14	−	2.30363e14i	0.968910	−	0.968910i
$412$		0			0
$413$	2.15447e14	+	2.15447e14i	0.882298	+	0.882298i
$414$		0			0
$415$	4.91593e13			0.196039
$416$		0			0
$417$	1.98296e14			0.770135
$418$		0			0
$419$	−2.71801e14	−	2.71801e14i	−1.02819	−	1.02819i	−0.999591	−	0.0286012i	$-0.990895\pi$
$419$	−2.71801e14	−	2.71801e14i	−1.02819	−	1.02819i	−0.0286012	−	0.999591i	$-0.509105\pi$
$420$		0			0
$421$	−5.71653e13	+	5.71653e13i	−0.210660	+	0.210660i	−0.804548	−	0.593888i	$-0.797592\pi$
$421$	−5.71653e13	+	5.71653e13i	−0.210660	+	0.210660i	0.593888	+	0.804548i	$0.297592\pi$
$422$		0			0
$423$			2.90841e14i			1.04420i
$424$		0			0
$425$			1.28991e14i			0.451254i
$426$		0			0
$427$	1.34927e14	−	1.34927e14i	0.459988	−	0.459988i
$428$		0			0
$429$	−1.74066e14	−	1.74066e14i	−0.578361	−	0.578361i
$430$		0			0
$431$	4.62177e13			0.149687			0.0748434	−	0.997195i	$-0.476154\pi$
$431$	4.62177e13			0.149687			0.0748434	+	0.997195i	$0.476154\pi$
$432$		0			0
$433$	−2.17070e14			−0.685356			−0.342678	−	0.939453i	$-0.611334\pi$
$433$	−2.17070e14			−0.685356			−0.342678	+	0.939453i	$0.611334\pi$
$434$		0			0
$435$	3.89880e14	+	3.89880e14i	1.20016	+	1.20016i
$436$		0			0
$437$	1.24639e14	−	1.24639e14i	0.374117	−	0.374117i
$438$		0			0
$439$			2.67074e14i			0.781766i	0.920440	+	0.390883i	$0.127830\pi$
$439$			2.67074e14i			0.781766i	−0.920440	+	0.390883i	$0.872170\pi$
$440$		0			0
$441$		−	2.64549e14i		−	0.755255i
$442$		0			0
$443$	−2.39831e14	+	2.39831e14i	−0.667858	+	0.667858i	−0.957220	−	0.289362i	$-0.906557\pi$
$443$	−2.39831e14	+	2.39831e14i	−0.667858	+	0.667858i	0.289362	+	0.957220i	$0.406557\pi$
$444$		0			0
$445$	−2.69153e14	−	2.69153e14i	−0.731172	−	0.731172i
$446$		0			0
$447$	−3.79670e14			−1.00627
$448$		0			0
$449$	5.87700e14			1.51985			0.759925	−	0.650011i	$-0.225236\pi$
$449$	5.87700e14			1.51985			0.759925	+	0.650011i	$0.225236\pi$
$450$		0			0
$451$	3.65528e14	+	3.65528e14i	0.922464	+	0.922464i
$452$		0			0
$453$	1.49236e14	−	1.49236e14i	0.367564	−	0.367564i
$454$		0			0
$455$			1.98170e14i			0.476403i
$456$		0			0
$457$			4.52197e14i			1.06118i	0.847629	+	0.530589i	$0.178029\pi$
$457$			4.52197e14i			1.06118i	−0.847629	+	0.530589i	$0.821971\pi$
$458$		0			0
$459$	−2.82297e14	+	2.82297e14i	−0.646751	+	0.646751i
$460$		0			0
$461$	5.12674e14	+	5.12674e14i	1.14680	+	1.14680i	0.987179	+	0.159616i	$0.0510257\pi$
$461$	5.12674e14	+	5.12674e14i	1.14680	+	1.14680i	0.159616	+	0.987179i	$0.448974\pi$
$462$		0			0
$463$	2.55229e14			0.557486			0.278743	−	0.960366i	$-0.410082\pi$
$463$	2.55229e14			0.557486			0.278743	+	0.960366i	$0.410082\pi$
$464$		0			0
$465$	−8.50631e14			−1.81447
$466$		0			0
$467$	−1.22952e14	−	1.22952e14i	−0.256148	−	0.256148i	0.567337	−	0.823485i	$-0.307974\pi$
$467$	−1.22952e14	−	1.22952e14i	−0.256148	−	0.256148i	−0.823485	+	0.567337i	$0.807974\pi$
$468$		0			0
$469$	−4.91727e14	+	4.91727e14i	−1.00063	+	1.00063i
$470$		0			0
$471$		−	6.66690e14i		−	1.32528i
$472$		0			0
$473$			9.81888e14i			1.90689i
$474$		0			0
$475$	−8.48358e13	+	8.48358e13i	−0.160977	+	0.160977i
$476$		0			0
$477$	−1.45232e14	−	1.45232e14i	−0.269284	−	0.269284i
$478$		0			0
$479$	2.71050e14			0.491139			0.245569	−	0.969379i	$-0.421025\pi$
$479$	2.71050e14			0.491139			0.245569	+	0.969379i	$0.421025\pi$
$480$		0			0
$481$	−1.76249e13			−0.0312124
$482$		0			0
$483$	−4.97043e14	−	4.97043e14i	−0.860369	−	0.860369i
$484$		0			0
$485$	−5.12399e14	+	5.12399e14i	−0.867019	+	0.867019i
$486$		0			0
$487$		−	3.77246e14i		−	0.624045i	−0.950075	−	0.312022i	$-0.898994\pi$
$487$		−	3.77246e14i		−	0.624045i	0.950075	−	0.312022i	$-0.101006\pi$
$488$		0			0
$489$		−	7.35571e14i		−	1.18967i
$490$		0			0
$491$	4.41994e14	−	4.41994e14i	0.698985	−	0.698985i	−0.265207	−	0.964192i	$-0.585440\pi$
$491$	4.41994e14	−	4.41994e14i	0.698985	−	0.698985i	0.964192	+	0.265207i	$0.0854402\pi$
$492$		0			0
$493$	−7.39245e14	−	7.39245e14i	−1.14322	−	1.14322i
$494$		0			0
$495$	−1.59611e15			−2.41399
$496$		0			0
$497$	−1.62743e15			−2.40737
$498$		0			0
$499$	5.44840e14	+	5.44840e14i	0.788344	+	0.788344i	0.981223	−	0.192878i	$-0.0617823\pi$
$499$	5.44840e14	+	5.44840e14i	0.788344	+	0.788344i	−0.192878	+	0.981223i	$0.561782\pi$
$500$		0			0
$501$	−2.32592e14	+	2.32592e14i	−0.329220	+	0.329220i
$502$		0			0
$503$			3.71015e14i			0.513768i	0.966442	+	0.256884i	$0.0826958\pi$
$503$			3.71015e14i			0.513768i	−0.966442	+	0.256884i	$0.917304\pi$
$504$		0			0
$505$			1.00076e15i			1.35590i
$506$		0			0
$507$	−7.25537e14	+	7.25537e14i	−0.961869	+	0.961869i
$508$		0			0
$509$	7.69790e14	+	7.69790e14i	0.998676	+	0.998676i	0.999999	−	0.00132283i	$-0.000421071\pi$
$509$	7.69790e14	+	7.69790e14i	0.998676	+	0.998676i	−0.00132283	+	0.999999i	$0.500421\pi$
$510$		0			0
$511$	−4.13208e14			−0.524631
$512$		0			0
$513$	−3.71326e14			−0.461434
$514$		0			0
$515$	−5.58905e14	−	5.58905e14i	−0.679827	−	0.679827i
$516$		0			0
$517$	7.16720e14	−	7.16720e14i	0.853398	−	0.853398i
$518$		0			0
$519$		−	8.02914e14i		−	0.935941i
$520$		0			0
$521$			1.01193e14i			0.115489i	0.998331	+	0.0577447i	$0.0183909\pi$
$521$			1.01193e14i			0.115489i	−0.998331	+	0.0577447i	$0.981609\pi$
$522$		0			0
$523$	−2.30526e14	+	2.30526e14i	−0.257608	+	0.257608i	−0.824081	−	0.566472i	$-0.808308\pi$
$523$	−2.30526e14	+	2.30526e14i	−0.257608	+	0.257608i	0.566472	+	0.824081i	$0.308308\pi$
$524$		0			0
$525$	3.38313e14	+	3.38313e14i	0.370205	+	0.370205i
$526$		0			0
$527$	1.61286e15			1.72838
$528$		0			0
$529$	5.68541e14			0.596699
$530$		0			0
$531$	−9.36373e14	−	9.36373e14i	−0.962562	−	0.962562i
$532$		0			0
$533$	−1.97243e14	+	1.97243e14i	−0.198610	+	0.198610i
$534$		0			0
$535$			2.61015e14i			0.257465i
$536$		0			0
$537$			1.37908e15i			1.33270i
$538$		0			0
$539$	−6.51928e14	+	6.51928e14i	−0.617250	+	0.617250i
$540$		0			0
$541$	3.94835e14	+	3.94835e14i	0.366295	+	0.366295i	0.866124	−	0.499829i	$-0.166604\pi$
$541$	3.94835e14	+	3.94835e14i	0.366295	+	0.366295i	−0.499829	+	0.866124i	$0.666604\pi$
$542$		0			0
$543$	−4.10672e14			−0.373333
$544$		0			0
$545$	4.96221e14			0.442073
$546$		0			0
$547$	−2.85865e14	−	2.85865e14i	−0.249592	−	0.249592i	0.571211	−	0.820803i	$-0.306474\pi$
$547$	−2.85865e14	−	2.85865e14i	−0.249592	−	0.249592i	−0.820803	+	0.571211i	$0.806474\pi$
$548$		0			0
$549$	−5.86419e14	+	5.86419e14i	−0.501834	+	0.501834i
$550$		0			0
$551$		−	9.72382e14i		−	0.815648i
$552$		0			0
$553$			1.28362e15i			1.05547i
$554$		0			0
$555$	−1.40201e14	+	1.40201e14i	−0.113016	+	0.113016i
$556$		0			0
$557$	−6.89000e13	−	6.89000e13i	−0.0544522	−	0.0544522i	0.679356	−	0.733809i	$-0.262259\pi$
$557$	−6.89000e13	−	6.89000e13i	−0.0544522	−	0.0544522i	−0.733809	+	0.679356i	$0.762259\pi$
$558$		0			0
$559$	−5.29838e14			−0.410562
$560$		0			0
$561$	5.25081e15			3.98961
$562$		0			0
$563$	−2.79657e14	−	2.79657e14i	−0.208367	−	0.208367i	0.595206	−	0.803573i	$-0.297070\pi$
$563$	−2.79657e14	−	2.79657e14i	−0.208367	−	0.208367i	−0.803573	+	0.595206i	$0.797070\pi$
$564$		0			0
$565$	1.31047e15	−	1.31047e15i	0.957547	−	0.957547i
$566$		0			0
$567$		−	8.86694e14i		−	0.635429i
$568$		0			0
$569$		−	1.64126e15i		−	1.15361i	−0.816881	−	0.576807i	$-0.804299\pi$
$569$		−	1.64126e15i		−	1.15361i	0.816881	−	0.576807i	$-0.195701\pi$
$570$		0			0
$571$	1.29829e15	−	1.29829e15i	0.895100	−	0.895100i	−0.0998976	−	0.994998i	$-0.531852\pi$
$571$	1.29829e15	−	1.29829e15i	0.895100	−	0.895100i	0.994998	+	0.0998976i	$0.0318515\pi$
$572$		0			0
$573$	−2.27207e15	−	2.27207e15i	−1.53664	−	1.53664i
$574$		0			0
$575$	2.61553e14			0.173535
$576$		0			0
$577$	−1.84725e15			−1.20242			−0.601212	−	0.799089i	$-0.705315\pi$
$577$	−1.84725e15			−1.20242			−0.601212	+	0.799089i	$0.705315\pi$
$578$		0			0
$579$	1.23920e15	+	1.23920e15i	0.791424	+	0.791424i
$580$		0			0
$581$	−2.44467e14	+	2.44467e14i	−0.153198	+	0.153198i
$582$		0			0
$583$			7.15788e14i			0.440157i
$584$		0			0
$585$		−	8.61282e14i		−	0.519742i
$586$		0			0
$587$	−7.54803e14	+	7.54803e14i	−0.447017	+	0.447017i	−0.894362	−	0.447345i	$-0.852370\pi$
$587$	−7.54803e14	+	7.54803e14i	−0.447017	+	0.447017i	0.447345	+	0.894362i	$0.352370\pi$
$588$		0			0
$589$	1.06076e15	+	1.06076e15i	0.616570	+	0.616570i
$590$		0			0
$591$	−4.75354e15			−2.71198
$592$		0			0
$593$	−2.83705e15			−1.58879			−0.794393	−	0.607404i	$-0.792211\pi$
$593$	−2.83705e15			−1.58879			−0.794393	+	0.607404i	$0.792211\pi$
$594$		0			0
$595$	−2.98896e15	−	2.98896e15i	−1.64315	−	1.64315i
$596$		0			0
$597$	−5.67150e14	+	5.67150e14i	−0.306083	+	0.306083i
$598$		0			0
$599$		−	1.42147e15i		−	0.753167i	−0.926383	−	0.376584i	$-0.877099\pi$
$599$		−	1.42147e15i		−	0.753167i	0.926383	−	0.376584i	$-0.122901\pi$
$600$		0			0
$601$		−	1.37212e15i		−	0.713810i	−0.934141	−	0.356905i	$-0.883832\pi$
$601$		−	1.37212e15i		−	0.713810i	0.934141	−	0.356905i	$-0.116168\pi$
$602$		0			0
$603$	2.13714e15	−	2.13714e15i	1.09166	−	1.09166i
$604$		0			0
$605$	2.34257e15	+	2.34257e15i	1.17500	+	1.17500i
$606$		0			0
$607$	9.58569e14			0.472156			0.236078	−	0.971734i	$-0.424138\pi$
$607$	9.58569e14			0.472156			0.236078	+	0.971734i	$0.424138\pi$
$608$		0			0
$609$	−3.87772e15			−1.87578
$610$		0			0
$611$	3.86750e14	+	3.86750e14i	0.183740	+	0.183740i
$612$		0			0
$613$	−1.16692e15	+	1.16692e15i	−0.544512	+	0.544512i	−0.924848	−	0.380336i	$-0.875808\pi$
$613$	−1.16692e15	+	1.16692e15i	−0.544512	+	0.544512i	0.380336	+	0.924848i	$0.375808\pi$
$614$		0			0
$615$			3.13803e15i			1.43828i
$616$		0			0
$617$		−	1.66121e15i		−	0.747920i	−0.927445	−	0.373960i	$-0.878000\pi$
$617$		−	1.66121e15i		−	0.747920i	0.927445	−	0.373960i	$-0.122000\pi$
$618$		0			0
$619$	1.32258e15	−	1.32258e15i	0.584958	−	0.584958i	−0.351304	−	0.936262i	$-0.614262\pi$
$619$	1.32258e15	−	1.32258e15i	0.584958	−	0.584958i	0.936262	+	0.351304i	$0.114262\pi$
$620$		0			0
$621$	5.72409e14	+	5.72409e14i	0.248715	+	0.248715i
$622$		0			0
$623$	2.67698e15			1.14277
$624$		0			0
$625$	2.85766e15			1.19859
$626$		0			0
$627$	3.45339e15	+	3.45339e15i	1.42323	+	1.42323i
$628$		0			0
$629$	2.65832e14	−	2.65832e14i	0.107654	−	0.107654i
$630$		0			0
$631$			3.87984e15i			1.54402i	0.635612	+	0.772009i	$0.280748\pi$
$631$			3.87984e15i			1.54402i	−0.635612	+	0.772009i	$0.719252\pi$
$632$		0			0
$633$		−	2.37592e15i		−	0.929204i
$634$		0			0
$635$	−3.48196e15	+	3.48196e15i	−1.33835	+	1.33835i
$636$		0			0
$637$	−3.51788e14	−	3.51788e14i	−0.132897	−	0.132897i
$638$		0			0
$639$	7.07312e15			2.62637
$640$		0			0
$641$	−5.57445e14			−0.203462			−0.101731	−	0.994812i	$-0.532438\pi$
$641$	−5.57445e14			−0.203462			−0.101731	+	0.994812i	$0.532438\pi$
$642$		0			0
$643$	3.17954e15	+	3.17954e15i	1.14079	+	1.14079i	0.988307	+	0.152480i	$0.0487260\pi$
$643$	3.17954e15	+	3.17954e15i	1.14079	+	1.14079i	0.152480	+	0.988307i	$0.451274\pi$
$644$		0			0
$645$	−4.21472e15	+	4.21472e15i	−1.48659	+	1.48659i
$646$		0			0
$647$			2.20708e15i			0.765324i	0.923888	+	0.382662i	$0.124993\pi$
$647$			2.20708e15i			0.765324i	−0.923888	+	0.382662i	$0.875007\pi$
$648$		0			0
$649$			4.61501e15i			1.57335i
$650$		0			0
$651$	4.23015e15	−	4.23015e15i	1.41795	−	1.41795i
$652$		0			0
$653$	−2.46010e15	−	2.46010e15i	−0.810832	−	0.810832i	0.173926	−	0.984759i	$-0.444355\pi$
$653$	−2.46010e15	−	2.46010e15i	−0.810832	−	0.810832i	−0.984759	+	0.173926i	$0.944355\pi$
$654$		0			0
$655$	−5.40432e15			−1.75152
$656$		0			0
$657$	1.79588e15			0.572358
$658$		0			0
$659$	−9.41322e13	−	9.41322e13i	−0.0295032	−	0.0295032i	0.692201	−	0.721704i	$-0.256641\pi$
$659$	−9.41322e13	−	9.41322e13i	−0.0295032	−	0.0295032i	−0.721704	+	0.692201i	$0.756641\pi$
$660$		0			0
$661$	1.97944e15	−	1.97944e15i	0.610148	−	0.610148i	−0.332837	−	0.942984i	$-0.608006\pi$
$661$	1.97944e15	−	1.97944e15i	0.610148	−	0.610148i	0.942984	+	0.332837i	$0.108006\pi$
$662$		0			0
$663$			2.83340e15i			0.858981i
$664$		0			0
$665$		−	3.93159e15i		−	1.17233i
$666$		0			0
$667$	−1.49895e15	+	1.49895e15i	−0.439638	+	0.439638i
$668$		0			0
$669$	−1.51762e15	−	1.51762e15i	−0.437843	−	0.437843i
$670$		0			0
$671$	2.89022e15			0.820272
$672$		0			0
$673$	1.41200e15			0.394231			0.197116	−	0.980380i	$-0.436843\pi$
$673$	1.41200e15			0.394231			0.197116	+	0.980380i	$0.436843\pi$
$674$		0			0
$675$	−3.89610e14	−	3.89610e14i	−0.107019	−	0.107019i
$676$		0			0
$677$	4.85721e15	−	4.85721e15i	1.31265	−	1.31265i	0.393194	−	0.919456i	$-0.371370\pi$
$677$	4.85721e15	−	4.85721e15i	1.31265	−	1.31265i	0.919456	−	0.393194i	$-0.128630\pi$
$678$		0			0
$679$		−	5.09628e15i		−	1.35509i
$680$		0			0
$681$			2.43961e15i			0.638281i
$682$		0			0
$683$	8.68637e14	−	8.68637e14i	0.223627	−	0.223627i	−0.586397	−	0.810024i	$-0.699454\pi$
$683$	8.68637e14	−	8.68637e14i	0.223627	−	0.223627i	0.810024	+	0.586397i	$0.199454\pi$
$684$		0			0
$685$	−2.80891e15	−	2.80891e15i	−0.711606	−	0.711606i
$686$		0			0
$687$	4.63316e15			1.15509
$688$		0			0
$689$	−3.86248e14			−0.0947676
$690$		0			0
$691$	4.10027e15	+	4.10027e15i	0.990110	+	0.990110i	0.999952	−	0.00984162i	$-0.00313273\pi$
$691$	4.10027e15	+	4.10027e15i	0.990110	+	0.990110i	−0.00984162	+	0.999952i	$0.503133\pi$
$692$		0			0
$693$	7.93741e15	−	7.93741e15i	1.88645	−	1.88645i
$694$		0			0
$695$		−	2.41791e15i		−	0.565618i
$696$		0			0
$697$		−	5.94996e15i		−	1.37004i
$698$		0			0
$699$	−5.78696e15	+	5.78696e15i	−1.31167	+	1.31167i
$700$		0			0
$701$	−4.09473e14	−	4.09473e14i	−0.0913643	−	0.0913643i	0.659947	−	0.751312i	$-0.270579\pi$
$701$	−4.09473e14	−	4.09473e14i	−0.0913643	−	0.0913643i	−0.751312	+	0.659947i	$0.770579\pi$
$702$		0			0
$703$	3.49669e14			0.0768073
$704$		0			0
$705$	6.15299e15			1.33060
$706$		0			0
$707$	−4.97674e15	−	4.97674e15i	−1.05959	−	1.05959i
$708$		0			0
$709$	4.23628e13	−	4.23628e13i	0.00888035	−	0.00888035i	−0.702653	−	0.711533i	$-0.748001\pi$
$709$	4.23628e13	−	4.23628e13i	0.00888035	−	0.00888035i	0.711533	+	0.702653i	$0.248001\pi$
$710$		0			0
$711$		−	5.57885e15i		−	1.15149i
$712$		0			0
$713$		−	3.27037e15i		−	0.664668i
$714$		0			0
$715$	−2.12246e15	+	2.12246e15i	−0.424772	+	0.424772i
$716$		0			0
$717$	−1.71892e15	−	1.71892e15i	−0.338767	−	0.338767i
$718$		0			0
$719$	3.44205e15			0.668049			0.334025	−	0.942564i	$-0.391593\pi$
$719$	3.44205e15			0.668049			0.334025	+	0.942564i	$0.391593\pi$
$720$		0			0
$721$	5.55882e15			1.06252
$722$		0			0
$723$	2.52912e15	+	2.52912e15i	0.476111	+	0.476111i
$724$		0			0
$725$	1.02026e15	−	1.02026e15i	0.189170	−	0.189170i
$726$		0			0
$727$			8.86644e14i			0.161924i	0.996717	+	0.0809618i	$0.0257992\pi$
$727$			8.86644e14i			0.161924i	−0.996717	+	0.0809618i	$0.974201\pi$
$728$		0			0
$729$			8.58422e15i			1.54419i
$730$		0			0
$731$	7.99145e15	−	7.99145e15i	1.41605	−	1.41605i
$732$		0			0
$733$	7.89968e15	+	7.89968e15i	1.37892	+	1.37892i	0.846455	+	0.532461i	$0.178733\pi$
$733$	7.89968e15	+	7.89968e15i	1.37892	+	1.37892i	0.532461	+	0.846455i	$0.321267\pi$
$734$		0			0
$735$	−5.59676e15			−0.962401
$736$		0			0
$737$	−1.05331e16			−1.78437
$738$		0			0
$739$	−3.16961e15	−	3.16961e15i	−0.529007	−	0.529007i	0.391269	−	0.920276i	$-0.372036\pi$
$739$	−3.16961e15	−	3.16961e15i	−0.529007	−	0.529007i	−0.920276	+	0.391269i	$0.872036\pi$
$740$		0			0
$741$	−1.86349e15	+	1.86349e15i	−0.306427	+	0.306427i
$742$		0			0
$743$			1.94649e15i			0.315364i	0.987490	+	0.157682i	$0.0504022\pi$
$743$			1.94649e15i			0.315364i	−0.987490	+	0.157682i	$0.949598\pi$
$744$		0			0
$745$			4.62947e15i			0.739047i
$746$		0			0
$747$	1.06250e15	−	1.06250e15i	0.167134	−	0.167134i
$748$		0			0
$749$	−1.29801e15	−	1.29801e15i	−0.201201	−	0.201201i
$750$		0			0
$751$	−8.22162e14			−0.125585			−0.0627925	−	0.998027i	$-0.520001\pi$
$751$	−8.22162e14			−0.125585			−0.0627925	+	0.998027i	$0.520001\pi$
$752$		0			0
$753$	−2.80726e15			−0.422581
$754$		0			0
$755$	−1.81969e15	−	1.81969e15i	−0.269954	−	0.269954i
$756$		0			0
$757$	−1.22234e15	+	1.22234e15i	−0.178716	+	0.178716i	−0.790796	−	0.612080i	$-0.790333\pi$
$757$	−1.22234e15	+	1.22234e15i	−0.178716	+	0.178716i	0.612080	+	0.790796i	$0.290333\pi$
$758$		0			0
$759$		−	1.06470e16i		−	1.53425i
$760$		0			0
$761$		−	7.64079e15i		−	1.08523i	−0.839981	−	0.542616i	$-0.817434\pi$
$761$		−	7.64079e15i		−	1.08523i	0.839981	−	0.542616i	$-0.182566\pi$
$762$		0			0
$763$	−2.46768e15	+	2.46768e15i	−0.345466	+	0.345466i
$764$		0			0
$765$	1.29906e16	+	1.29906e16i	1.79263	+	1.79263i
$766$		0			0
$767$	−2.49031e15			−0.338750
$768$		0			0
$769$	4.51581e15			0.605537			0.302768	−	0.953064i	$-0.402089\pi$
$769$	4.51581e15			0.605537			0.302768	+	0.953064i	$0.402089\pi$
$770$		0			0
$771$	−7.83613e14	−	7.83613e14i	−0.103586	−	0.103586i
$772$		0			0
$773$	1.07717e15	−	1.07717e15i	0.140377	−	0.140377i	−0.633426	−	0.773803i	$-0.718352\pi$
$773$	1.07717e15	−	1.07717e15i	0.140377	−	0.140377i	0.773803	+	0.633426i	$0.218352\pi$
$774$		0			0
$775$			2.22598e15i			0.285997i
$776$		0			0
$777$		−	1.39443e15i		−	0.176637i
$778$		0			0
$779$	3.91321e15	−	3.91321e15i	0.488739	−	0.488739i
$780$		0			0
$781$	−1.74303e16	−	1.74303e16i	−2.14647	−	2.14647i
$782$		0			0
$783$	4.46569e15			0.542249
$784$		0			0
$785$	−8.12921e15			−0.973342
$786$		0			0
$787$	4.70724e15	+	4.70724e15i	0.555783	+	0.555783i	0.928104	−	0.372321i	$-0.121438\pi$
$787$	4.70724e15	+	4.70724e15i	0.555783	+	0.555783i	−0.372321	+	0.928104i	$0.621438\pi$
$788$		0			0
$789$	−4.64090e15	+	4.64090e15i	−0.540354	+	0.540354i
$790$		0			0
$791$			1.30338e16i			1.49658i
$792$		0			0
$793$			1.55960e15i			0.176608i
$794$		0			0
$795$	−3.07250e15	+	3.07250e15i	−0.343141	+	0.343141i
$796$		0			0
$797$	−7.24872e15	−	7.24872e15i	−0.798436	−	0.798436i	0.184412	−	0.982849i	$-0.440962\pi$
$797$	−7.24872e15	−	7.24872e15i	−0.798436	−	0.798436i	−0.982849	+	0.184412i	$0.940962\pi$
$798$		0			0
$799$	−1.16666e16			−1.26746
$800$		0			0
$801$	−1.16346e16			−1.24673
$802$		0			0
$803$	−4.42559e15	−	4.42559e15i	−0.467773	−	0.467773i
$804$		0			0
$805$	−6.06064e15	+	6.06064e15i	−0.631890	+	0.631890i
$806$		0			0
$807$		−	1.19115e16i		−	1.22508i
$808$		0			0
$809$			1.03410e16i			1.04917i	0.851360	+	0.524583i	$0.175779\pi$
$809$			1.03410e16i			1.04917i	−0.851360	+	0.524583i	$0.824221\pi$
$810$		0			0
$811$	−1.11196e16	+	1.11196e16i	−1.11295	+	1.11295i	−0.120200	+	0.992750i	$0.538354\pi$
$811$	−1.11196e16	+	1.11196e16i	−1.11295	+	1.11295i	−0.992750	+	0.120200i	$0.961646\pi$
$812$		0			0
$813$	8.43807e15	+	8.43807e15i	0.833192	+	0.833192i
$814$		0			0
$815$	−8.96910e15			−0.873740
$816$		0			0
$817$	1.05117e16			1.01031
$818$		0			0
$819$	4.28312e15	+	4.28312e15i	0.406161	+	0.406161i
$820$		0			0
$821$	−7.05917e15	+	7.05917e15i	−0.660490	+	0.660490i	−0.955496	−	0.295005i	$-0.904679\pi$
$821$	−7.05917e15	+	7.05917e15i	−0.660490	+	0.660490i	0.295005	+	0.955496i	$0.404679\pi$
$822$		0			0
$823$			1.30797e16i			1.20753i	0.797163	+	0.603764i	$0.206333\pi$
$823$			1.30797e16i			1.20753i	−0.797163	+	0.603764i	$0.793667\pi$
$824$		0			0
$825$			7.24687e15i			0.660167i
$826$		0			0
$827$	−8.30624e15	+	8.30624e15i	−0.746662	+	0.746662i	−0.973851	−	0.227189i	$-0.927047\pi$
$827$	−8.30624e15	+	8.30624e15i	−0.746662	+	0.746662i	0.227189	+	0.973851i	$0.427047\pi$
$828$		0			0
$829$	1.07494e16	+	1.07494e16i	0.953531	+	0.953531i	0.998967	−	0.0454367i	$-0.0144679\pi$
$829$	1.07494e16	+	1.07494e16i	0.953531	+	0.953531i	−0.0454367	+	0.998967i	$0.514468\pi$
$830$		0			0
$831$	1.43176e16			1.25332
$832$		0			0
$833$	1.06119e16			0.916739
$834$		0			0
$835$	2.83608e15	+	2.83608e15i	0.241793	+	0.241793i
$836$		0			0
$837$	−4.87156e15	+	4.87156e15i	−0.409900	+	0.409900i
$838$		0			0
$839$			7.21546e15i			0.599202i	0.954065	+	0.299601i	$0.0968535\pi$
$839$			7.21546e15i			0.599202i	−0.954065	+	0.299601i	$0.903146\pi$
$840$		0			0
$841$		−	5.06335e14i		−	0.0415011i
$842$		0			0
$843$	2.34136e16	−	2.34136e16i	1.89416	−	1.89416i
$844$		0			0
$845$	8.84676e15	+	8.84676e15i	0.706435	+	0.706435i
$846$		0			0
$847$	−2.32990e16			−1.83645
$848$		0			0
$849$	3.36682e13			0.00261956
$850$		0			0
$851$	−5.39023e14	−	5.39023e14i	−0.0413995	−	0.0413995i
$852$		0			0
$853$	−2.11551e15	+	2.11551e15i	−0.160397	+	0.160397i	−0.782742	−	0.622346i	$-0.786180\pi$
$853$	−2.11551e15	+	2.11551e15i	−0.160397	+	0.160397i	0.622346	+	0.782742i	$0.286180\pi$
$854$		0			0
$855$			1.70874e16i			1.27898i
$856$		0			0
$857$		−	5.60408e15i		−	0.414104i	−0.978330	−	0.207052i	$-0.933613\pi$
$857$		−	5.60408e15i		−	0.414104i	0.978330	−	0.207052i	$-0.0663870\pi$
$858$		0			0
$859$	2.84823e14	−	2.84823e14i	0.0207784	−	0.0207784i	−0.696641	−	0.717420i	$-0.745323\pi$
$859$	2.84823e14	−	2.84823e14i	0.0207784	−	0.0207784i	0.717420	+	0.696641i	$0.245323\pi$
$860$		0			0
$861$	−1.56053e16	−	1.56053e16i	−1.12397	−	1.12397i
$862$		0			0
$863$	2.14058e15			0.152220			0.0761102	−	0.997099i	$-0.475750\pi$
$863$	2.14058e15			0.152220			0.0761102	+	0.997099i	$0.475750\pi$
$864$		0			0
$865$	−9.79024e15			−0.687392
$866$		0			0
$867$	−2.70648e16	−	2.70648e16i	−1.87629	−	1.87629i
$868$		0			0
$869$	−1.37479e16	+	1.37479e16i	−0.941086	+	0.941086i
$870$		0			0
$871$		−	5.68378e15i		−	0.384182i
$872$		0			0
$873$			2.21494e16i			1.47837i
$874$		0			0
$875$	−1.09711e16	+	1.09711e16i	−0.723115	+	0.723115i
$876$		0			0
$877$	6.91657e14	+	6.91657e14i	0.0450187	+	0.0450187i	0.729258	−	0.684239i	$-0.239866\pi$
$877$	6.91657e14	+	6.91657e14i	0.0450187	+	0.0450187i	−0.684239	+	0.729258i	$0.739866\pi$
$878$		0			0
$879$	6.68439e15			0.429658
$880$		0			0
$881$	−1.27110e16			−0.806889			−0.403444	−	0.915004i	$-0.632187\pi$
$881$	−1.27110e16			−0.806889			−0.403444	+	0.915004i	$0.632187\pi$
$882$		0			0
$883$	−1.13706e16	−	1.13706e16i	−0.712850	−	0.712850i	0.254280	−	0.967131i	$-0.418161\pi$
$883$	−1.13706e16	−	1.13706e16i	−0.712850	−	0.712850i	−0.967131	+	0.254280i	$0.918161\pi$
$884$		0			0
$885$	−1.98098e16	+	1.98098e16i	−1.22657	+	1.22657i
$886$		0			0
$887$			4.64514e15i			0.284066i	0.989862	+	0.142033i	$0.0453639\pi$
$887$			4.64514e15i			0.284066i	−0.989862	+	0.142033i	$0.954636\pi$
$888$		0			0
$889$		−	3.46313e16i		−	2.09175i
$890$		0			0
$891$	9.49676e15	−	9.49676e15i	0.566563	−	0.566563i
$892$		0			0
$893$	−7.67294e15	−	7.67294e15i	−0.452146	−	0.452146i
$894$		0			0
$895$	1.68157e16			0.978788
$896$		0			0
$897$	5.74523e15			0.330331
$898$		0			0
$899$	−1.27570e16	−	1.27570e16i	−0.724554	−	0.724554i
$900$		0			0
$901$	5.82570e15	−	5.82570e15i	0.326860	−	0.326860i
$902$		0			0
$903$		−	4.19193e16i		−	2.32344i
$904$		0			0
$905$			5.00749e15i			0.274191i
$906$		0			0
$907$	−1.40963e16	+	1.40963e16i	−0.762543	+	0.762543i	−0.976781	−	0.214239i	$-0.931273\pi$
$907$	−1.40963e16	+	1.40963e16i	−0.762543	+	0.762543i	0.214239	+	0.976781i	$0.431273\pi$
$908$		0			0
$909$	2.16299e16	+	2.16299e16i	1.15599	+	1.15599i
$910$		0			0
$911$	−2.45183e16			−1.29461			−0.647305	−	0.762231i	$-0.724104\pi$
$911$	−2.45183e16			−1.29461			−0.647305	+	0.762231i	$0.724104\pi$
$912$		0			0
$913$	−5.23664e15			−0.273189
$914$		0			0
$915$	1.24062e16	+	1.24062e16i	0.639474	+	0.639474i
$916$		0			0
$917$	2.68755e16	−	2.68755e16i	1.36875	−	1.36875i
$918$		0			0
$919$		−	1.71814e16i		−	0.864615i	−0.901726	−	0.432307i	$-0.857700\pi$
$919$		−	1.71814e16i		−	0.864615i	0.901726	−	0.432307i	$-0.142300\pi$
$920$		0			0
$921$			4.57271e16i			2.27377i
$922$		0			0
$923$	9.40559e15	−	9.40559e15i	0.462143	−	0.462143i
$924$		0			0
$925$	3.66887e14	+	3.66887e14i	0.0178136	+	0.0178136i
$926$		0			0
$927$	−2.41597e16			−1.15918
$928$		0			0
$929$	1.37942e16			0.654047			0.327024	−	0.945016i	$-0.393954\pi$
$929$	1.37942e16			0.654047			0.327024	+	0.945016i	$0.393954\pi$
$930$		0			0
$931$	6.97930e15	+	6.97930e15i	0.327031	+	0.327031i
$932$		0			0
$933$	3.99007e16	−	3.99007e16i	1.84770	−	1.84770i
$934$		0			0
$935$		−	6.40252e16i		−	2.93013i
$936$		0			0
$937$		−	3.53690e16i		−	1.59976i	−0.600160	−	0.799880i	$-0.704896\pi$
$937$		−	3.53690e16i		−	1.59976i	0.600160	−	0.799880i	$-0.295104\pi$
$938$		0			0
$939$	2.28983e16	−	2.28983e16i	1.02363	−	1.02363i
$940$		0			0
$941$	2.22717e16	+	2.22717e16i	0.984034	+	0.984034i	0.999875	−	0.0158400i	$-0.00504226\pi$
$941$	2.22717e16	+	2.22717e16i	0.984034	+	0.984034i	−0.0158400	+	0.999875i	$0.505042\pi$
$942$		0			0
$943$	−1.20646e16			−0.526865
$944$		0			0
$945$	1.80559e16			0.779371
$946$		0			0
$947$	2.09342e16	+	2.09342e16i	0.893163	+	0.893163i	0.994820	−	0.101656i	$-0.0324142\pi$
$947$	2.09342e16	+	2.09342e16i	0.893163	+	0.893163i	−0.101656	+	0.994820i	$0.532414\pi$
$948$		0			0
$949$	2.38810e15	−	2.38810e15i	0.100714	−	0.100714i
$950$		0			0
$951$			4.99854e16i			2.08377i
$952$		0			0
$953$			2.34667e16i			0.967035i	0.875335	+	0.483517i	$0.160641\pi$
$953$			2.34667e16i			0.967035i	−0.875335	+	0.483517i	$0.839359\pi$
$954$		0			0
$955$	−2.77043e16	+	2.77043e16i	−1.12857	+	1.12857i
$956$		0			0
$957$	−4.15315e16	−	4.15315e16i	−1.67249	−	1.67249i
$958$		0			0
$959$	2.79372e16			1.11219
$960$		0			0
$961$	2.42445e15			0.0954191
$962$		0			0
$963$	5.64141e15	+	5.64141e15i	0.219504	+	0.219504i
$964$		0			0
$965$	1.51101e16	−	1.51101e16i	0.581254	−	0.581254i
$966$		0			0
$967$			3.94438e16i			1.50014i	0.661357	+	0.750071i	$0.269981\pi$
$967$			3.94438e16i			1.50014i	−0.661357	+	0.750071i	$0.730019\pi$
$968$		0			0
$969$		−	5.62133e16i		−	2.11377i
$970$		0			0
$971$	−1.82080e16	+	1.82080e16i	−0.676948	+	0.676948i	−0.959308	−	0.282360i	$-0.908883\pi$
$971$	−1.82080e16	+	1.82080e16i	−0.676948	+	0.676948i	0.282360	+	0.959308i	$0.408883\pi$
$972$		0			0
$973$	1.20241e16	+	1.20241e16i	0.442012	+	0.442012i
$974$		0			0
$975$	−3.91049e15			−0.142137
$976$		0			0
$977$	−1.68239e16			−0.604652			−0.302326	−	0.953205i	$-0.597763\pi$
$977$	−1.68239e16			−0.604652			−0.302326	+	0.953205i	$0.597763\pi$
$978$		0			0
$979$	2.86712e16	+	2.86712e16i	1.01892	+	1.01892i
$980$		0			0
$981$	1.07250e16	−	1.07250e16i	0.376893	−	0.376893i
$982$		0			0
$983$		−	1.79195e16i		−	0.622704i	−0.950295	−	0.311352i	$-0.899218\pi$
$983$		−	1.79195e16i		−	0.622704i	0.950295	−	0.311352i	$-0.100782\pi$
$984$		0			0
$985$			5.79617e16i			1.99178i
$986$		0			0
$987$	−3.05986e16	+	3.05986e16i	−1.03982	+	1.03982i
$988$		0			0
$989$	−1.62041e16	−	1.62041e16i	−0.544560	−	0.544560i
$990$		0			0
$991$	5.56476e16			1.84945			0.924723	−	0.380641i	$-0.124296\pi$
$991$	5.56476e16			1.84945			0.924723	+	0.380641i	$0.124296\pi$
$992$		0			0
$993$	−1.36942e16			−0.450106
$994$		0			0
$995$	6.91548e15	+	6.91548e15i	0.224800	+	0.224800i
$996$		0			0
$997$	−1.04105e16	+	1.04105e16i	−0.334695	+	0.334695i	−0.854366	−	0.519671i	$-0.826055\pi$
$997$	−1.04105e16	+	1.04105e16i	−0.334695	+	0.334695i	0.519671	+	0.854366i	$0.326055\pi$
$998$		0			0
$999$			1.60586e15i			0.0510620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.2		42
4.3	odd	2		128.12.e.a.33.20		42
8.3	odd	2		64.12.e.a.17.2		42
8.5	even	2		16.12.e.a.13.21	yes	42
16.3	odd	4		64.12.e.a.49.2		42
16.5	even	4	inner	128.12.e.b.97.2		42
16.11	odd	4		128.12.e.a.97.20		42
16.13	even	4		16.12.e.a.5.21	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.21	✓	42	16.13	even	4
16.12.e.a.13.21	yes	42	8.5	even	2
64.12.e.a.17.2		42	8.3	odd	2
64.12.e.a.49.2		42	16.3	odd	4
128.12.e.a.33.20		42	4.3	odd	2
128.12.e.a.97.20		42	16.11	odd	4
128.12.e.b.33.2		42	1.1	even	1	trivial
128.12.e.b.97.2		42	16.5	even	4	inner

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-457.250 - 457.250i) q^{3} +(-5575.43 + 5575.43i) q^{5} -55452.7i q^{7} +241008. i q^{9} +O(q^{10})\)	\(q+(-457.250 - 457.250i) q^{3} +(-5575.43 + 5575.43i) q^{5} -55452.7i q^{7} +241008. i q^{9} +(593916. - 593916. i) q^{11} +(320484. + 320484. i) q^{13} +5.09873e6 q^{15} -9.66759e6 q^{17} +(-6.35824e6 - 6.35824e6i) q^{19} +(-2.53557e7 + 2.53557e7i) q^{21} +1.96028e7i q^{23} -1.33426e7i q^{25} +(2.92004e7 - 2.92004e7i) q^{27} +(7.64662e7 + 7.64662e7i) q^{29} -1.66832e8 q^{31} -5.43136e8 q^{33} +(3.09173e8 + 3.09173e8i) q^{35} +(-2.74973e7 + 2.74973e7i) q^{37} -2.93082e8i q^{39} +6.15454e8i q^{41} +(-8.26623e8 + 8.26623e8i) q^{43} +(-1.34372e9 - 1.34372e9i) q^{45} +1.20677e9 q^{47} -1.09768e9 q^{49} +(4.42051e9 + 4.42051e9i) q^{51} +(-6.02601e8 + 6.02601e8i) q^{53} +6.62267e9i q^{55} +5.81461e9i q^{57} +(-3.88524e9 + 3.88524e9i) q^{59} +(2.43319e9 + 2.43319e9i) q^{61} +1.33645e10 q^{63} -3.57367e9 q^{65} +(-8.86750e9 - 8.86750e9i) q^{67} +(8.96337e9 - 8.96337e9i) q^{69} -2.93481e10i q^{71} -7.45154e9i q^{73} +(-6.10092e9 + 6.10092e9i) q^{75} +(-3.29342e10 - 3.29342e10i) q^{77} -2.31480e10 q^{79} +1.59901e10 q^{81} +(-4.40857e9 - 4.40857e9i) q^{83} +(5.39010e10 - 5.39010e10i) q^{85} -6.99284e10i q^{87} +4.82749e10i q^{89} +(1.77717e10 - 1.77717e10i) q^{91} +(7.62839e10 + 7.62839e10i) q^{93} +7.08998e10 q^{95} +9.19031e10 q^{97} +(1.43138e11 + 1.43138e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 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

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Database

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