LMFDB - Embedded newform 128.14.e.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,14,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, 14, names="a")

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 14 $
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:	$137.255589058$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ 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			128.14.e.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1618.47 - 1618.47i) q^{3} +(23191.8 - 23191.8i) q^{5} +280152. i q^{7} +3.64459e6i q^{9} +O(q^{10})$	\(q+(-1618.47 - 1618.47i) q^{3} +(23191.8 - 23191.8i) q^{5} +280152. i q^{7} +3.64459e6i q^{9} +(6.11068e6 - 6.11068e6i) q^{11} +(-1.15263e7 - 1.15263e7i) q^{13} -7.50707e7 q^{15} +1.68871e8 q^{17} +(5.82970e6 + 5.82970e6i) q^{19} +(4.53419e8 - 4.53419e8i) q^{21} -2.84306e8i q^{23} +1.44980e8i q^{25} +(3.31829e9 - 3.31829e9i) q^{27} +(1.26029e9 + 1.26029e9i) q^{29} -1.42208e9 q^{31} -1.97800e10 q^{33} +(6.49724e9 + 6.49724e9i) q^{35} +(-1.30091e10 + 1.30091e10i) q^{37} +3.73099e10i q^{39} +3.32305e10i q^{41} +(-8.67795e9 + 8.67795e9i) q^{43} +(8.45247e10 + 8.45247e10i) q^{45} -2.33273e10 q^{47} +1.84038e10 q^{49} +(-2.73314e11 - 2.73314e11i) q^{51} +(-2.15973e11 + 2.15973e11i) q^{53} -2.83436e11i q^{55} -1.88704e10i q^{57} +(-1.81979e11 + 1.81979e11i) q^{59} +(1.87363e10 + 1.87363e10i) q^{61} -1.02104e12 q^{63} -5.34631e11 q^{65} +(1.72418e11 + 1.72418e11i) q^{67} +(-4.60142e11 + 4.60142e11i) q^{69} -3.76419e11i q^{71} +1.75034e12i q^{73} +(2.34646e11 - 2.34646e11i) q^{75} +(1.71192e12 + 1.71192e12i) q^{77} -3.85817e12 q^{79} -4.93049e12 q^{81} +(-8.88037e10 - 8.88037e10i) q^{83} +(3.91644e12 - 3.91644e12i) q^{85} -4.07948e12i q^{87} +1.77771e12i q^{89} +(3.22911e12 - 3.22911e12i) q^{91} +(2.30160e12 + 2.30160e12i) q^{93} +2.70403e11 q^{95} +1.04083e13 q^{97} +(2.22709e13 + 2.22709e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 2 q^{3} + 2 q^{5}+O(q^{10}) $ 50 * q - 2 * q^3 + 2 * q^5	$ 50 q - 2 q^{3} + 2 q^{5} - 4723998 q^{11} + 2 q^{13} - 91124996 q^{15} - 4 q^{17} + 422008902 q^{19} - 3188644 q^{21} - 2068699784 q^{27} + 3661663834 q^{29} + 10650044176 q^{31} - 4 q^{33} + 7767977276 q^{35} - 21527986470 q^{37} - 18577860182 q^{43} - 2438217602 q^{45} - 215584306576 q^{47} - 525968913642 q^{49} - 551664571452 q^{51} - 223019793366 q^{53} + 1167423209882 q^{59} - 81543039150 q^{61} + 862914002556 q^{63} - 27850095516 q^{65} + 1390089097910 q^{67} + 168685276844 q^{69} - 1675683188954 q^{75} + 2147852144860 q^{77} - 8517123343488 q^{79} - 9602604240358 q^{81} + 2192965629438 q^{83} - 2809965843748 q^{85} + 3291182399236 q^{91} - 3412032366928 q^{93} - 7322122332660 q^{95} - 4 q^{97} + 19363874529854 q^{99}+O(q^{100}) $ 50 * q - 2 * q^3 + 2 * q^5 - 4723998 * q^11 + 2 * q^13 - 91124996 * q^15 - 4 * q^17 + 422008902 * q^19 - 3188644 * q^21 - 2068699784 * q^27 + 3661663834 * q^29 + 10650044176 * q^31 - 4 * q^33 + 7767977276 * q^35 - 21527986470 * q^37 - 18577860182 * q^43 - 2438217602 * q^45 - 215584306576 * q^47 - 525968913642 * q^49 - 551664571452 * q^51 - 223019793366 * q^53 + 1167423209882 * q^59 - 81543039150 * q^61 + 862914002556 * q^63 - 27850095516 * q^65 + 1390089097910 * q^67 + 168685276844 * q^69 - 1675683188954 * q^75 + 2147852144860 * q^77 - 8517123343488 * q^79 - 9602604240358 * q^81 + 2192965629438 * q^83 - 2809965843748 * q^85 + 3291182399236 * q^91 - 3412032366928 * q^93 - 7322122332660 * q^95 - 4 * q^97 + 19363874529854 * 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
$3$	−1618.47	−	1618.47i	−1.28179	−	1.28179i	−0.939648	−	0.342143i	$-0.888847\pi$
$3$	−1618.47	−	1618.47i	−1.28179	−	1.28179i	−0.342143	−	0.939648i	$-0.611153\pi$
$4$		0			0
$5$	23191.8	−	23191.8i	0.663789	−	0.663789i	−0.292482	−	0.956271i	$-0.594481\pi$
$5$	23191.8	−	23191.8i	0.663789	−	0.663789i	0.956271	+	0.292482i	$0.0944811\pi$
$6$		0			0
$7$			280152.i			0.900029i	0.893021	+	0.450015i	$0.148581\pi$
$7$			280152.i			0.900029i	−0.893021	+	0.450015i	$0.851419\pi$
$8$		0			0
$9$			3.64459e6i			2.28598i
$10$		0			0
$11$	6.11068e6	−	6.11068e6i	1.04001	−	1.04001i	0.0408442	−	0.999166i	$-0.486995\pi$
$11$	6.11068e6	−	6.11068e6i	1.04001	−	1.04001i	0.999166	−	0.0408442i	$-0.0130047\pi$
$12$		0			0
$13$	−1.15263e7	−	1.15263e7i	−0.662303	−	0.662303i	0.293619	−	0.955923i	$-0.405140\pi$
$13$	−1.15263e7	−	1.15263e7i	−0.662303	−	0.662303i	−0.955923	+	0.293619i	$0.905140\pi$
$14$		0			0
$15$	−7.50707e7			−1.70168
$16$		0			0
$17$	1.68871e8			1.69683			0.848414	−	0.529334i	$-0.177558\pi$
$17$	1.68871e8			1.69683			0.848414	+	0.529334i	$0.177558\pi$
$18$		0			0
$19$	5.82970e6	+	5.82970e6i	0.0284281	+	0.0284281i	0.721178	−	0.692750i	$-0.243601\pi$
$19$	5.82970e6	+	5.82970e6i	0.0284281	+	0.0284281i	−0.692750	+	0.721178i	$0.743601\pi$
$20$		0			0
$21$	4.53419e8	−	4.53419e8i	1.15365	−	1.15365i
$22$		0			0
$23$		−	2.84306e8i		−	0.400456i	−0.979749	−	0.200228i	$-0.935832\pi$
$23$		−	2.84306e8i		−	0.400456i	0.979749	−	0.200228i	$-0.0641683\pi$
$24$		0			0
$25$			1.44980e8i			0.118767i
$26$		0			0
$27$	3.31829e9	−	3.31829e9i	1.64835	−	1.64835i
$28$		0			0
$29$	1.26029e9	+	1.26029e9i	0.393444	+	0.393444i	0.875913	−	0.482469i	$-0.160260\pi$
$29$	1.26029e9	+	1.26029e9i	0.393444	+	0.393444i	−0.482469	+	0.875913i	$0.660260\pi$
$30$		0			0
$31$	−1.42208e9			−0.287788			−0.143894	−	0.989593i	$-0.545962\pi$
$31$	−1.42208e9			−0.287788			−0.143894	+	0.989593i	$0.545962\pi$
$32$		0			0
$33$	−1.97800e10			−2.66615
$34$		0			0
$35$	6.49724e9	+	6.49724e9i	0.597430	+	0.597430i
$36$		0			0
$37$	−1.30091e10	+	1.30091e10i	−0.833561	+	0.833561i	−0.988002	−	0.154441i	$-0.950642\pi$
$37$	−1.30091e10	+	1.30091e10i	−0.833561	+	0.833561i	0.154441	+	0.988002i	$0.450642\pi$
$38$		0			0
$39$			3.73099e10i			1.69787i
$40$		0			0
$41$			3.32305e10i			1.09255i	0.837606	+	0.546275i	$0.183955\pi$
$41$			3.32305e10i			1.09255i	−0.837606	+	0.546275i	$0.816045\pi$
$42$		0			0
$43$	−8.67795e9	+	8.67795e9i	−0.209350	+	0.209350i	−0.803991	−	0.594641i	$-0.797294\pi$
$43$	−8.67795e9	+	8.67795e9i	−0.209350	+	0.209350i	0.594641	+	0.803991i	$0.297294\pi$
$44$		0			0
$45$	8.45247e10	+	8.45247e10i	1.51741	+	1.51741i
$46$		0			0
$47$	−2.33273e10			−0.315667			−0.157833	−	0.987466i	$-0.550451\pi$
$47$	−2.33273e10			−0.315667			−0.157833	+	0.987466i	$0.550451\pi$
$48$		0			0
$49$	1.84038e10			0.189947
$50$		0			0
$51$	−2.73314e11	−	2.73314e11i	−2.17498	−	2.17498i
$52$		0			0
$53$	−2.15973e11	+	2.15973e11i	−1.33846	+	1.33846i	−0.440915	+	0.897549i	$0.645346\pi$
$53$	−2.15973e11	+	2.15973e11i	−1.33846	+	1.33846i	−0.897549	+	0.440915i	$0.854654\pi$
$54$		0			0
$55$		−	2.83436e11i		−	1.38069i
$56$		0			0
$57$		−	1.88704e10i		−	0.0728778i
$58$		0			0
$59$	−1.81979e11	+	1.81979e11i	−0.561672	+	0.561672i	−0.929782	−	0.368110i	$-0.880005\pi$
$59$	−1.81979e11	+	1.81979e11i	−0.561672	+	0.561672i	0.368110	+	0.929782i	$0.380005\pi$
$60$		0			0
$61$	1.87363e10	+	1.87363e10i	0.0465628	+	0.0465628i	0.730005	−	0.683442i	$-0.239518\pi$
$61$	1.87363e10	+	1.87363e10i	0.0465628	+	0.0465628i	−0.683442	+	0.730005i	$0.739518\pi$
$62$		0			0
$63$	−1.02104e12			−2.05745
$64$		0			0
$65$	−5.34631e11			−0.879260
$66$		0			0
$67$	1.72418e11	+	1.72418e11i	0.232861	+	0.232861i	0.813886	−	0.581025i	$-0.197348\pi$
$67$	1.72418e11	+	1.72418e11i	0.232861	+	0.232861i	−0.581025	+	0.813886i	$0.697348\pi$
$68$		0			0
$69$	−4.60142e11	+	4.60142e11i	−0.513301	+	0.513301i
$70$		0			0
$71$		−	3.76419e11i		−	0.348732i	−0.984681	−	0.174366i	$-0.944212\pi$
$71$		−	3.76419e11i		−	0.348732i	0.984681	−	0.174366i	$-0.0557876\pi$
$72$		0			0
$73$			1.75034e12i			1.35371i	0.736118	+	0.676854i	$0.236657\pi$
$73$			1.75034e12i			1.35371i	−0.736118	+	0.676854i	$0.763343\pi$
$74$		0			0
$75$	2.34646e11	−	2.34646e11i	0.152235	−	0.152235i
$76$		0			0
$77$	1.71192e12	+	1.71192e12i	0.936039	+	0.936039i
$78$		0			0
$79$	−3.85817e12			−1.78569			−0.892843	−	0.450368i	$-0.851293\pi$
$79$	−3.85817e12			−1.78569			−0.892843	+	0.450368i	$0.851293\pi$
$80$		0			0
$81$	−4.93049e12			−1.93971
$82$		0			0
$83$	−8.88037e10	−	8.88037e10i	−0.0298142	−	0.0298142i	0.692043	−	0.721857i	$-0.256711\pi$
$83$	−8.88037e10	−	8.88037e10i	−0.0298142	−	0.0298142i	−0.721857	+	0.692043i	$0.756711\pi$
$84$		0			0
$85$	3.91644e12	−	3.91644e12i	1.12634	−	1.12634i
$86$		0			0
$87$		−	4.07948e12i		−	1.00863i
$88$		0			0
$89$			1.77771e12i			0.379162i	0.981865	+	0.189581i	$0.0607130\pi$
$89$			1.77771e12i			0.379162i	−0.981865	+	0.189581i	$0.939287\pi$
$90$		0			0
$91$	3.22911e12	−	3.22911e12i	0.596092	−	0.596092i
$92$		0			0
$93$	2.30160e12	+	2.30160e12i	0.368885	+	0.368885i
$94$		0			0
$95$	2.70403e11			0.0377406
$96$		0			0
$97$	1.04083e13			1.26871			0.634357	−	0.773040i	$-0.281265\pi$
$97$	1.04083e13			1.26871			0.634357	+	0.773040i	$0.281265\pi$
$98$		0			0
$99$	2.22709e13	+	2.22709e13i	2.37744	+	2.37744i
$100$		0			0
$101$	−9.06482e12	+	9.06482e12i	−0.849709	+	0.849709i	−0.990097	−	0.140388i	$-0.955165\pi$
$101$	−9.06482e12	+	9.06482e12i	−0.849709	+	0.849709i	0.140388	+	0.990097i	$0.455165\pi$
$102$		0			0
$103$		−	8.19498e11i		−	0.0676248i	−0.999428	−	0.0338124i	$-0.989235\pi$
$103$		−	8.19498e11i		−	0.0676248i	0.999428	−	0.0338124i	$-0.0107649\pi$
$104$		0			0
$105$		−	2.10312e13i		−	1.53156i
$106$		0			0
$107$	−6.05091e11	+	6.05091e11i	−0.0389786	+	0.0389786i	−0.726327	−	0.687349i	$-0.758774\pi$
$107$	−6.05091e11	+	6.05091e11i	−0.0389786	+	0.0389786i	0.687349	+	0.726327i	$0.258774\pi$
$108$		0			0
$109$	3.15980e12	+	3.15980e12i	0.180463	+	0.180463i	0.791557	−	0.611095i	$-0.209271\pi$
$109$	3.15980e12	+	3.15980e12i	0.180463	+	0.180463i	−0.611095	+	0.791557i	$0.709271\pi$
$110$		0			0
$111$	4.21099e13			2.13690
$112$		0			0
$113$	−2.68934e13			−1.21517			−0.607583	−	0.794256i	$-0.707861\pi$
$113$	−2.68934e13			−1.21517			−0.607583	+	0.794256i	$0.707861\pi$
$114$		0			0
$115$	−6.59358e12	−	6.59358e12i	−0.265819	−	0.265819i
$116$		0			0
$117$	4.20085e13	−	4.20085e13i	1.51401	−	1.51401i
$118$		0			0
$119$			4.73096e13i			1.52719i
$120$		0			0
$121$		−	4.01582e13i		−	1.16324i
$122$		0			0
$123$	5.37826e13	−	5.37826e13i	1.40042	−	1.40042i
$124$		0			0
$125$	3.16727e13	+	3.16727e13i	0.742626	+	0.742626i
$126$		0			0
$127$	−1.14677e13			−0.242522			−0.121261	−	0.992621i	$-0.538694\pi$
$127$	−1.14677e13			−0.242522			−0.121261	+	0.992621i	$0.538694\pi$
$128$		0			0
$129$	2.80901e13			0.536685
$130$		0			0
$131$	4.72158e12	+	4.72158e12i	0.0816252	+	0.0816252i	0.746741	−	0.665115i	$-0.231618\pi$
$131$	4.72158e12	+	4.72158e12i	0.0816252	+	0.0816252i	−0.665115	+	0.746741i	$0.731618\pi$
$132$		0			0
$133$	−1.63320e12	+	1.63320e12i	−0.0255861	+	0.0255861i
$134$		0			0
$135$		−	1.53915e14i		−	2.18832i
$136$		0			0
$137$			7.52684e13i			0.972589i	0.873795	+	0.486294i	$0.161652\pi$
$137$			7.52684e13i			0.972589i	−0.873795	+	0.486294i	$0.838348\pi$
$138$		0			0
$139$	−9.08475e12	+	9.08475e12i	−0.106836	+	0.106836i	−0.758504	−	0.651668i	$-0.774069\pi$
$139$	−9.08475e12	+	9.08475e12i	−0.106836	+	0.106836i	0.651668	+	0.758504i	$0.274069\pi$
$140$		0			0
$141$	3.77546e13	+	3.77546e13i	0.404619	+	0.404619i
$142$		0			0
$143$	−1.40867e14			−1.37760
$144$		0			0
$145$	5.84568e13			0.522328
$146$		0			0
$147$	−2.97861e13	−	2.97861e13i	−0.243473	−	0.243473i
$148$		0			0
$149$	−1.58746e14	+	1.58746e14i	−1.18848	+	1.18848i	−0.210991	+	0.977488i	$0.567669\pi$
$149$	−1.58746e14	+	1.58746e14i	−1.18848	+	1.18848i	−0.977488	+	0.210991i	$0.932331\pi$
$150$		0			0
$151$			2.06050e14i			1.41456i	0.706931	+	0.707282i	$0.250079\pi$
$151$			2.06050e14i			1.41456i	−0.706931	+	0.707282i	$0.749921\pi$
$152$		0			0
$153$			6.15466e14i			3.87891i
$154$		0			0
$155$	−3.29807e13	+	3.29807e13i	−0.191031	+	0.191031i
$156$		0			0
$157$	−2.21440e13	−	2.21440e13i	−0.118007	−	0.118007i	0.645637	−	0.763644i	$-0.276592\pi$
$157$	−2.21440e13	−	2.21440e13i	−0.118007	−	0.118007i	−0.763644	+	0.645637i	$0.776592\pi$
$158$		0			0
$159$	6.99093e14			3.43126
$160$		0			0
$161$	7.96489e13			0.360422
$162$		0			0
$163$	−1.00342e13	−	1.00342e13i	−0.0419049	−	0.0419049i	0.685844	−	0.727749i	$-0.259433\pi$
$163$	−1.00342e13	−	1.00342e13i	−0.0419049	−	0.0419049i	−0.727749	+	0.685844i	$0.759433\pi$
$164$		0			0
$165$	−4.58734e14	+	4.58734e14i	−1.76976	+	1.76976i
$166$		0			0
$167$		−	5.57674e14i		−	1.98941i	−0.102794	−	0.994703i	$-0.532778\pi$
$167$		−	5.57674e14i		−	1.98941i	0.102794	−	0.994703i	$-0.467222\pi$
$168$		0			0
$169$		−	3.71653e13i		−	0.122708i
$170$		0			0
$171$	−2.12469e13	+	2.12469e13i	−0.0649860	+	0.0649860i
$172$		0			0
$173$	−9.90725e13	−	9.90725e13i	−0.280966	−	0.280966i	0.552528	−	0.833494i	$-0.313663\pi$
$173$	−9.90725e13	−	9.90725e13i	−0.280966	−	0.280966i	−0.833494	+	0.552528i	$0.813663\pi$
$174$		0			0
$175$	−4.06164e13			−0.106894
$176$		0			0
$177$	5.89055e14			1.43989
$178$		0			0
$179$	−5.30408e14	−	5.30408e14i	−1.20522	−	1.20522i	−0.972558	−	0.232659i	$-0.925258\pi$
$179$	−5.30408e14	−	5.30408e14i	−1.20522	−	1.20522i	−0.232659	−	0.972558i	$-0.574742\pi$
$180$		0			0
$181$	3.17091e14	−	3.17091e14i	0.670306	−	0.670306i	−0.287480	−	0.957787i	$-0.592818\pi$
$181$	3.17091e14	−	3.17091e14i	0.670306	−	0.670306i	0.957787	+	0.287480i	$0.0928176\pi$
$182$		0			0
$183$		−	6.06482e13i		−	0.119367i
$184$		0			0
$185$			6.03412e14i			1.10662i
$186$		0			0
$187$	1.03192e15	−	1.03192e15i	1.76472	−	1.76472i
$188$		0			0
$189$	9.29627e14	+	9.29627e14i	1.48357	+	1.48357i
$190$		0			0
$191$	6.39305e14			0.952777			0.476388	−	0.879235i	$-0.341946\pi$
$191$	6.39305e14			0.952777			0.476388	+	0.879235i	$0.341946\pi$
$192$		0			0
$193$	−5.53349e13			−0.0770684			−0.0385342	−	0.999257i	$-0.512269\pi$
$193$	−5.53349e13			−0.0770684			−0.0385342	+	0.999257i	$0.512269\pi$
$194$		0			0
$195$	8.65286e14	+	8.65286e14i	1.12703	+	1.12703i
$196$		0			0
$197$	5.99596e14	−	5.99596e14i	0.730851	−	0.730851i	−0.239938	−	0.970788i	$-0.577127\pi$
$197$	5.99596e14	−	5.99596e14i	0.730851	−	0.730851i	0.970788	+	0.239938i	$0.0771270\pi$
$198$		0			0
$199$			1.20057e15i			1.37039i	0.728361	+	0.685194i	$0.240283\pi$
$199$			1.20057e15i			1.37039i	−0.728361	+	0.685194i	$0.759717\pi$
$200$		0			0
$201$		−	5.58109e14i		−	0.596959i
$202$		0			0
$203$	−3.53072e14	+	3.53072e14i	−0.354111	+	0.354111i
$204$		0			0
$205$	7.70676e14	+	7.70676e14i	0.725223	+	0.725223i
$206$		0			0
$207$	1.03618e15			0.915434
$208$		0			0
$209$	7.12470e13			0.0591310
$210$		0			0
$211$	1.27423e15	+	1.27423e15i	0.994055	+	0.994055i	0.999982	−	0.00592775i	$-0.00188687\pi$
$211$	1.27423e15	+	1.27423e15i	0.994055	+	0.994055i	−0.00592775	+	0.999982i	$0.501887\pi$
$212$		0			0
$213$	−6.09223e14	+	6.09223e14i	−0.447002	+	0.447002i
$214$		0			0
$215$			4.02515e14i			0.277928i
$216$		0			0
$217$		−	3.98399e14i		−	0.259018i
$218$		0			0
$219$	2.83288e15	−	2.83288e15i	1.73517	−	1.73517i
$220$		0			0
$221$	−1.94646e15	−	1.94646e15i	−1.12381	−	1.12381i
$222$		0			0
$223$	1.82750e15			0.995118			0.497559	−	0.867430i	$-0.334230\pi$
$223$	1.82750e15			0.995118			0.497559	+	0.867430i	$0.334230\pi$
$224$		0			0
$225$	−5.28391e14			−0.271500
$226$		0			0
$227$	4.93795e14	+	4.93795e14i	0.239540	+	0.239540i	0.816660	−	0.577119i	$-0.195823\pi$
$227$	4.93795e14	+	4.93795e14i	0.239540	+	0.239540i	−0.577119	+	0.816660i	$0.695823\pi$
$228$		0			0
$229$	3.01763e14	−	3.01763e14i	0.138272	−	0.138272i	−0.634583	−	0.772855i	$-0.718828\pi$
$229$	3.01763e14	−	3.01763e14i	0.138272	−	0.138272i	0.772855	+	0.634583i	$0.218828\pi$
$230$		0			0
$231$		−	5.54139e15i		−	2.39961i
$232$		0			0
$233$			1.79737e15i			0.735910i	0.929844	+	0.367955i	$0.119942\pi$
$233$			1.79737e15i			0.735910i	−0.929844	+	0.367955i	$0.880058\pi$
$234$		0			0
$235$	−5.41004e14	+	5.41004e14i	−0.209536	+	0.209536i
$236$		0			0
$237$	6.24434e15	+	6.24434e15i	2.28888	+	2.28888i
$238$		0			0
$239$	3.25399e15			1.12935			0.564677	−	0.825312i	$-0.309001\pi$
$239$	3.25399e15			1.12935			0.564677	+	0.825312i	$0.309001\pi$
$240$		0			0
$241$	3.53433e15			1.16197			0.580987	−	0.813913i	$-0.302667\pi$
$241$	3.53433e15			1.16197			0.580987	+	0.813913i	$0.302667\pi$
$242$		0			0
$243$	2.68943e15	+	2.68943e15i	0.837953	+	0.837953i
$244$		0			0
$245$	4.26819e14	−	4.26819e14i	0.126085	−	0.126085i
$246$		0			0
$247$		−	1.34390e14i		−	0.0376561i
$248$		0			0
$249$			2.87453e14i			0.0764312i
$250$		0			0
$251$	−2.55285e15	+	2.55285e15i	−0.644386	+	0.644386i	−0.951631	−	0.307244i	$-0.900593\pi$
$251$	−2.55285e15	+	2.55285e15i	−0.644386	+	0.644386i	0.307244	+	0.951631i	$0.400593\pi$
$252$		0			0
$253$	−1.73730e15	−	1.73730e15i	−0.416478	−	0.416478i
$254$		0			0
$255$	−1.26773e16			−2.88745
$256$		0			0
$257$	−7.39918e15			−1.60184			−0.800918	−	0.598774i	$-0.795655\pi$
$257$	−7.39918e15			−1.60184			−0.800918	+	0.598774i	$0.795655\pi$
$258$		0			0
$259$	−3.64454e15	−	3.64454e15i	−0.750229	−	0.750229i
$260$		0			0
$261$	−4.59323e15	+	4.59323e15i	−0.899404	+	0.899404i
$262$		0			0
$263$			3.39984e15i			0.633500i	0.948509	+	0.316750i	$0.102592\pi$
$263$			3.39984e15i			0.633500i	−0.948509	+	0.316750i	$0.897408\pi$
$264$		0			0
$265$			1.00176e16i			1.77692i
$266$		0			0
$267$	2.87717e15	−	2.87717e15i	0.486007	−	0.486007i
$268$		0			0
$269$	−1.43403e15	−	1.43403e15i	−0.230764	−	0.230764i	0.582247	−	0.813012i	$-0.302173\pi$
$269$	−1.43403e15	−	1.43403e15i	−0.230764	−	0.230764i	−0.813012	+	0.582247i	$0.802173\pi$
$270$		0			0
$271$	−5.45457e15			−0.836489			−0.418244	−	0.908335i	$-0.637354\pi$
$271$	−5.45457e15			−0.836489			−0.418244	+	0.908335i	$0.637354\pi$
$272$		0			0
$273$	−1.04524e16			−1.52813
$274$		0			0
$275$	8.85926e14	+	8.85926e14i	0.123519	+	0.123519i
$276$		0			0
$277$	−5.38672e14	+	5.38672e14i	−0.0716483	+	0.0716483i	−0.742023	−	0.670375i	$-0.766133\pi$
$277$	−5.38672e14	+	5.38672e14i	−0.0716483	+	0.0716483i	0.670375	+	0.742023i	$0.266133\pi$
$278$		0			0
$279$		−	5.18289e15i		−	0.657878i
$280$		0			0
$281$			3.85917e15i			0.467631i	0.972281	+	0.233815i	$0.0751211\pi$
$281$			3.85917e15i			0.467631i	−0.972281	+	0.233815i	$0.924879\pi$
$282$		0			0
$283$	−3.17394e15	+	3.17394e15i	−0.367271	+	0.367271i	−0.866481	−	0.499210i	$-0.833624\pi$
$283$	−3.17394e15	+	3.17394e15i	−0.367271	+	0.367271i	0.499210	+	0.866481i	$0.333624\pi$
$284$		0			0
$285$	−4.37640e14	−	4.37640e14i	−0.0483755	−	0.0483755i
$286$		0			0
$287$	−9.30958e15			−0.983327
$288$		0			0
$289$	1.86129e16			1.87922
$290$		0			0
$291$	−1.68456e16	−	1.68456e16i	−1.62623	−	1.62623i
$292$		0			0
$293$	7.92902e15	−	7.92902e15i	0.732117	−	0.732117i	−0.238922	−	0.971039i	$-0.576794\pi$
$293$	7.92902e15	−	7.92902e15i	0.732117	−	0.732117i	0.971039	+	0.238922i	$0.0767941\pi$
$294$		0			0
$295$			8.44085e15i			0.745664i
$296$		0			0
$297$		−	4.05541e16i		−	3.42861i
$298$		0			0
$299$	−3.27699e15	+	3.27699e15i	−0.265224	+	0.265224i
$300$		0			0
$301$	−2.43115e15	−	2.43115e15i	−0.188421	−	0.188421i
$302$		0			0
$303$	2.93423e16			2.17830
$304$		0			0
$305$	8.69056e14			0.0618157
$306$		0			0
$307$	−2.07369e15	−	2.07369e15i	−0.141366	−	0.141366i	0.632882	−	0.774248i	$-0.281872\pi$
$307$	−2.07369e15	−	2.07369e15i	−0.141366	−	0.141366i	−0.774248	+	0.632882i	$0.781872\pi$
$308$		0			0
$309$	−1.32634e15	+	1.32634e15i	−0.0866809	+	0.0866809i
$310$		0			0
$311$			2.05444e16i			1.28751i	0.765231	+	0.643756i	$0.222625\pi$
$311$			2.05444e16i			1.28751i	−0.765231	+	0.643756i	$0.777375\pi$
$312$		0			0
$313$		−	5.07483e15i		−	0.305059i	−0.988299	−	0.152529i	$-0.951258\pi$
$313$		−	5.07483e15i		−	0.305059i	0.988299	−	0.152529i	$-0.0487418\pi$
$314$		0			0
$315$	−2.36798e16	+	2.36798e16i	−1.36571	+	1.36571i
$316$		0			0
$317$	−1.70053e16	−	1.70053e16i	−0.941236	−	0.941236i	0.0571311	−	0.998367i	$-0.481805\pi$
$317$	−1.70053e16	−	1.70053e16i	−0.941236	−	0.941236i	−0.998367	+	0.0571311i	$0.981805\pi$
$318$		0			0
$319$	1.54024e16			0.818371
$320$		0			0
$321$	1.95865e15			0.0999249
$322$		0			0
$323$	9.84469e14	+	9.84469e14i	0.0482376	+	0.0482376i
$324$		0			0
$325$	1.67108e15	−	1.67108e15i	0.0786601	−	0.0786601i
$326$		0			0
$327$		−	1.02281e16i		−	0.462631i
$328$		0			0
$329$		−	6.53520e15i		−	0.284109i
$330$		0			0
$331$	1.04623e16	−	1.04623e16i	0.437265	−	0.437265i	−0.453825	−	0.891091i	$-0.649941\pi$
$331$	1.04623e16	−	1.04623e16i	0.437265	−	0.437265i	0.891091	+	0.453825i	$0.149941\pi$
$332$		0			0
$333$	−4.74129e16	−	4.74129e16i	−1.90550	−	1.90550i
$334$		0			0
$335$	7.99740e15			0.309142
$336$		0			0
$337$	1.07783e16			0.400824			0.200412	−	0.979712i	$-0.435772\pi$
$337$	1.07783e16			0.400824			0.200412	+	0.979712i	$0.435772\pi$
$338$		0			0
$339$	4.35262e16	+	4.35262e16i	1.55759	+	1.55759i
$340$		0			0
$341$	−8.68989e15	+	8.68989e15i	−0.299303	+	0.299303i
$342$		0			0
$343$			3.22995e16i			1.07099i
$344$		0			0
$345$			2.13431e16i			0.681448i
$346$		0			0
$347$	6.91963e15	−	6.91963e15i	0.212785	−	0.212785i	−0.592664	−	0.805450i	$-0.701924\pi$
$347$	6.91963e15	−	6.91963e15i	0.212785	−	0.212785i	0.805450	+	0.592664i	$0.201924\pi$
$348$		0			0
$349$	−5.92482e15	−	5.92482e15i	−0.175513	−	0.175513i	0.613883	−	0.789397i	$-0.289606\pi$
$349$	−5.92482e15	−	5.92482e15i	−0.175513	−	0.175513i	−0.789397	+	0.613883i	$0.789606\pi$
$350$		0			0
$351$	−7.64951e16			−2.18342
$352$		0			0
$353$	1.12830e16			0.310376			0.155188	−	0.987885i	$-0.450402\pi$
$353$	1.12830e16			0.310376			0.155188	+	0.987885i	$0.450402\pi$
$354$		0			0
$355$	−8.72984e15	−	8.72984e15i	−0.231485	−	0.231485i
$356$		0			0
$357$	7.65693e16	−	7.65693e16i	1.95754	−	1.95754i
$358$		0			0
$359$			1.94203e16i			0.478787i	0.970923	+	0.239393i	$0.0769486\pi$
$359$			1.94203e16i			0.478787i	−0.970923	+	0.239393i	$0.923051\pi$
$360$		0			0
$361$		−	4.19850e16i		−	0.998384i
$362$		0			0
$363$	−6.49950e16	+	6.49950e16i	−1.49103	+	1.49103i
$364$		0			0
$365$	4.05937e16	+	4.05937e16i	0.898576	+	0.898576i
$366$		0			0
$367$	−6.87228e16			−1.46815			−0.734077	−	0.679066i	$-0.762385\pi$
$367$	−6.87228e16			−1.46815			−0.734077	+	0.679066i	$0.762385\pi$
$368$		0			0
$369$	−1.21111e17			−2.49754
$370$		0			0
$371$	−6.05053e16	−	6.05053e16i	−1.20466	−	1.20466i
$372$		0			0
$373$	−1.10241e16	+	1.10241e16i	−0.211950	+	0.211950i	−0.805096	−	0.593145i	$-0.797886\pi$
$373$	−1.10241e16	+	1.10241e16i	−0.211950	+	0.211950i	0.593145	+	0.805096i	$0.297886\pi$
$374$		0			0
$375$		−	1.02523e17i		−	1.90378i
$376$		0			0
$377$		−	2.90528e16i		−	0.521159i
$378$		0			0
$379$	6.02648e16	−	6.02648e16i	1.04450	−	1.04450i	0.0455383	−	0.998963i	$-0.485500\pi$
$379$	6.02648e16	−	6.02648e16i	1.04450	−	1.04450i	0.998963	−	0.0455383i	$-0.0145003\pi$
$380$		0			0
$381$	1.85601e16	+	1.85601e16i	0.310863	+	0.310863i
$382$		0			0
$383$	−1.66637e16			−0.269762			−0.134881	−	0.990862i	$-0.543065\pi$
$383$	−1.66637e16			−0.269762			−0.134881	+	0.990862i	$0.543065\pi$
$384$		0			0
$385$	7.94052e16			1.24267
$386$		0			0
$387$	−3.16275e16	−	3.16275e16i	−0.478568	−	0.478568i
$388$		0			0
$389$	−4.34057e16	+	4.34057e16i	−0.635147	+	0.635147i	−0.949354	−	0.314207i	$-0.898261\pi$
$389$	−4.34057e16	+	4.34057e16i	−0.635147	+	0.635147i	0.314207	+	0.949354i	$0.398261\pi$
$390$		0			0
$391$		−	4.80111e16i		−	0.679505i
$392$		0			0
$393$		−	1.52835e16i		−	0.209253i
$394$		0			0
$395$	−8.94781e16	+	8.94781e16i	−1.18532	+	1.18532i
$396$		0			0
$397$	1.58492e16	+	1.58492e16i	0.203174	+	0.203174i	0.801358	−	0.598185i	$-0.204111\pi$
$397$	1.58492e16	+	1.58492e16i	0.203174	+	0.203174i	−0.598185	+	0.801358i	$0.704111\pi$
$398$		0			0
$399$	5.28659e15			0.0655922
$400$		0			0
$401$	−1.10363e17			−1.32551			−0.662757	−	0.748835i	$-0.730614\pi$
$401$	−1.10363e17			−1.32551			−0.662757	+	0.748835i	$0.730614\pi$
$402$		0			0
$403$	1.63913e16	+	1.63913e16i	0.190603	+	0.190603i
$404$		0			0
$405$	−1.14347e17	+	1.14347e17i	−1.28756	+	1.28756i
$406$		0			0
$407$			1.58989e17i			1.73382i
$408$		0			0
$409$			1.19187e17i			1.25900i	0.777000	+	0.629501i	$0.216741\pi$
$409$			1.19187e17i			1.25900i	−0.777000	+	0.629501i	$0.783259\pi$
$410$		0			0
$411$	1.21820e17	−	1.21820e17i	1.24666	−	1.24666i
$412$		0			0
$413$	−5.09817e16	−	5.09817e16i	−0.505521	−	0.505521i
$414$		0			0
$415$	−4.11904e15			−0.0395807
$416$		0			0
$417$	2.94068e16			0.273882
$418$		0			0
$419$	1.10185e17	+	1.10185e17i	0.994788	+	0.994788i	0.999986	−	0.00519871i	$-0.00165481\pi$
$419$	1.10185e17	+	1.10185e17i	0.994788	+	0.994788i	−0.00519871	+	0.999986i	$0.501655\pi$
$420$		0			0
$421$	−2.48438e16	+	2.48438e16i	−0.217462	+	0.217462i	−0.807428	−	0.589966i	$-0.799141\pi$
$421$	−2.48438e16	+	2.48438e16i	−0.217462	+	0.217462i	0.589966	+	0.807428i	$0.299141\pi$
$422$		0			0
$423$		−	8.50184e16i		−	0.721607i
$424$		0			0
$425$			2.44829e16i			0.201528i
$426$		0			0
$427$	−5.24900e15	+	5.24900e15i	−0.0419078	+	0.0419078i
$428$		0			0
$429$	2.27989e17	+	2.27989e17i	1.76580	+	1.76580i
$430$		0			0
$431$	−8.64799e16			−0.649850			−0.324925	−	0.945740i	$-0.605339\pi$
$431$	−8.64799e16			−0.649850			−0.324925	+	0.945740i	$0.605339\pi$
$432$		0			0
$433$	−9.69670e16			−0.707054			−0.353527	−	0.935424i	$-0.615018\pi$
$433$	−9.69670e16			−0.707054			−0.353527	+	0.935424i	$0.615018\pi$
$434$		0			0
$435$	−9.46108e16	−	9.46108e16i	−0.669515	−	0.669515i
$436$		0			0
$437$	1.65742e15	−	1.65742e15i	0.0113842	−	0.0113842i
$438$		0			0
$439$			1.62353e16i			0.108253i	0.998534	+	0.0541265i	$0.0172374\pi$
$439$			1.62353e16i			0.108253i	−0.998534	+	0.0541265i	$0.982763\pi$
$440$		0			0
$441$			6.70743e16i			0.434216i
$442$		0			0
$443$	−1.31609e17	+	1.31609e17i	−0.827299	+	0.827299i	−0.987142	−	0.159844i	$-0.948901\pi$
$443$	−1.31609e17	+	1.31609e17i	−0.827299	+	0.827299i	0.159844	+	0.987142i	$0.448901\pi$
$444$		0			0
$445$	4.12283e16	+	4.12283e16i	0.251684	+	0.251684i
$446$		0			0
$447$	5.13851e17			3.04676
$448$		0			0
$449$	2.24709e17			1.29425			0.647127	−	0.762382i	$-0.275970\pi$
$449$	2.24709e17			1.29425			0.647127	+	0.762382i	$0.275970\pi$
$450$		0			0
$451$	2.03061e17	+	2.03061e17i	1.13626	+	1.13626i
$452$		0			0
$453$	3.33487e17	−	3.33487e17i	1.81318	−	1.81318i
$454$		0			0
$455$		−	1.49778e17i		−	0.791360i
$456$		0			0
$457$		−	5.26167e16i		−	0.270189i	−0.990833	−	0.135095i	$-0.956866\pi$
$457$		−	5.26167e16i		−	0.270189i	0.990833	−	0.135095i	$-0.0431338\pi$
$458$		0			0
$459$	5.60364e17	−	5.60364e17i	2.79697	−	2.79697i
$460$		0			0
$461$	1.37938e17	+	1.37938e17i	0.669313	+	0.669313i	0.957557	−	0.288244i	$-0.0930714\pi$
$461$	1.37938e17	+	1.37938e17i	0.669313	+	0.669313i	−0.288244	+	0.957557i	$0.593071\pi$
$462$		0			0
$463$	−2.61647e17			−1.23435			−0.617176	−	0.786825i	$-0.711723\pi$
$463$	−2.61647e17			−1.23435			−0.617176	+	0.786825i	$0.711723\pi$
$464$		0			0
$465$	1.06757e17			0.489723
$466$		0			0
$467$	1.41604e17	+	1.41604e17i	0.631706	+	0.631706i	0.948496	−	0.316790i	$-0.102605\pi$
$467$	1.41604e17	+	1.41604e17i	0.631706	+	0.631706i	−0.316790	+	0.948496i	$0.602605\pi$
$468$		0			0
$469$	−4.83033e16	+	4.83033e16i	−0.209582	+	0.209582i
$470$		0			0
$471$			7.16788e16i			0.302521i
$472$		0			0
$473$			1.06056e17i			0.435451i
$474$		0			0
$475$	−8.45189e14	+	8.45189e14i	−0.00337633	+	0.00337633i
$476$		0			0
$477$	−7.87133e17	−	7.87133e17i	−3.05970	−	3.05970i
$478$		0			0
$479$	4.39019e17			1.66074			0.830372	−	0.557210i	$-0.188128\pi$
$479$	4.39019e17			1.66074			0.830372	+	0.557210i	$0.188128\pi$
$480$		0			0
$481$	2.99894e17			1.10414
$482$		0			0
$483$	−1.28910e17	−	1.28910e17i	−0.461986	−	0.461986i
$484$		0			0
$485$	2.41388e17	−	2.41388e17i	0.842159	−	0.842159i
$486$		0			0
$487$			1.47903e17i			0.502387i	0.967937	+	0.251193i	$0.0808230\pi$
$487$			1.47903e17i			0.502387i	−0.967937	+	0.251193i	$0.919177\pi$
$488$		0			0
$489$			3.24802e16i			0.107427i
$490$		0			0
$491$	−3.10757e17	+	3.10757e17i	−1.00090	+	1.00090i	−0.000902964		1.00000i	$0.500287\pi$
$491$	−3.10757e17	+	3.10757e17i	−1.00090	+	1.00090i	−1.00000		0.000902964i	$0.999713\pi$
$492$		0			0
$493$	2.12826e17	+	2.12826e17i	0.667607	+	0.667607i
$494$		0			0
$495$	1.03301e18			3.15624
$496$		0			0
$497$	1.05454e17			0.313869
$498$		0			0
$499$	−1.91213e16	−	1.91213e16i	−0.0554452	−	0.0554452i	0.678841	−	0.734286i	$-0.262483\pi$
$499$	−1.91213e16	−	1.91213e16i	−0.0554452	−	0.0554452i	−0.734286	+	0.678841i	$0.762483\pi$
$500$		0			0
$501$	−9.02580e17	+	9.02580e17i	−2.55000	+	2.55000i
$502$		0			0
$503$		−	4.17981e17i		−	1.15071i	−0.817905	−	0.575353i	$-0.804865\pi$
$503$		−	4.17981e17i		−	1.15071i	0.817905	−	0.575353i	$-0.195135\pi$
$504$		0			0
$505$			4.20460e17i			1.12806i
$506$		0			0
$507$	−6.01510e16	+	6.01510e16i	−0.157286	+	0.157286i
$508$		0			0
$509$	4.89507e17	+	4.89507e17i	1.24765	+	1.24765i	0.956754	+	0.290897i	$0.0939537\pi$
$509$	4.89507e17	+	4.89507e17i	1.24765	+	1.24765i	0.290897	+	0.956754i	$0.406046\pi$
$510$		0			0
$511$	−4.90362e17			−1.21838
$512$		0			0
$513$	3.86893e16			0.0937192
$514$		0			0
$515$	−1.90057e16	−	1.90057e16i	−0.0448886	−	0.0448886i
$516$		0			0
$517$	−1.42546e17	+	1.42546e17i	−0.328297	+	0.328297i
$518$		0			0
$519$			3.20692e17i			0.720279i
$520$		0			0
$521$		−	5.63176e17i		−	1.23367i	−0.787092	−	0.616835i	$-0.788414\pi$
$521$		−	5.63176e17i		−	1.23367i	0.787092	−	0.616835i	$-0.211586\pi$
$522$		0			0
$523$	−2.55276e16	+	2.55276e16i	−0.0545442	+	0.0545442i	−0.733853	−	0.679309i	$-0.762280\pi$
$523$	−2.55276e16	+	2.55276e16i	−0.0545442	+	0.0545442i	0.679309	+	0.733853i	$0.262280\pi$
$524$		0			0
$525$	6.57365e16	+	6.57365e16i	0.137016	+	0.137016i
$526$		0			0
$527$	−2.40149e17			−0.488327
$528$		0			0
$529$	4.23206e17			0.839635
$530$		0			0
$531$	−6.63237e17	−	6.63237e17i	−1.28397	−	1.28397i
$532$		0			0
$533$	3.83023e17	−	3.83023e17i	0.723600	−	0.723600i
$534$		0			0
$535$			2.80664e16i			0.0517472i
$536$		0			0
$537$			1.71690e18i			3.08967i
$538$		0			0
$539$	1.12460e17	−	1.12460e17i	0.197547	−	0.197547i
$540$		0			0
$541$	1.60118e17	+	1.60118e17i	0.274574	+	0.274574i	0.830938	−	0.556365i	$-0.187804\pi$
$541$	1.60118e17	+	1.60118e17i	0.274574	+	0.274574i	−0.556365	+	0.830938i	$0.687804\pi$
$542$		0			0
$543$	−1.02641e18			−1.71839
$544$		0			0
$545$	1.46563e17			0.239579
$546$		0			0
$547$	−3.14478e17	−	3.14478e17i	−0.501964	−	0.501964i	0.410084	−	0.912048i	$-0.365500\pi$
$547$	−3.14478e17	−	3.14478e17i	−0.501964	−	0.501964i	−0.912048	+	0.410084i	$0.865500\pi$
$548$		0			0
$549$	−6.82859e16	+	6.82859e16i	−0.106441	+	0.106441i
$550$		0			0
$551$			1.46942e16i			0.0223697i
$552$		0			0
$553$		−	1.08087e18i		−	1.60717i
$554$		0			0
$555$	9.76605e17	−	9.76605e17i	1.41845	−	1.41845i
$556$		0			0
$557$	8.33001e17	+	8.33001e17i	1.18192	+	1.18192i	0.979247	+	0.202669i	$0.0649615\pi$
$557$	8.33001e17	+	8.33001e17i	1.18192	+	1.18192i	0.202669	+	0.979247i	$0.435038\pi$
$558$		0			0
$559$	2.00049e17			0.277306
$560$		0			0
$561$	−3.34026e18			−4.52400
$562$		0			0
$563$	5.99285e17	+	5.99285e17i	0.793102	+	0.793102i	0.981997	−	0.188895i	$-0.0604907\pi$
$563$	5.99285e17	+	5.99285e17i	0.793102	+	0.793102i	−0.188895	+	0.981997i	$0.560491\pi$
$564$		0			0
$565$	−6.23707e17	+	6.23707e17i	−0.806614	+	0.806614i
$566$		0			0
$567$		−	1.38129e18i		−	1.74580i
$568$		0			0
$569$			9.75737e17i			1.20532i	0.797997	+	0.602661i	$0.205893\pi$
$569$			9.75737e17i			1.20532i	−0.797997	+	0.602661i	$0.794107\pi$
$570$		0			0
$571$	−9.05961e17	+	9.05961e17i	−1.09389	+	1.09389i	−0.0987843	+	0.995109i	$0.531495\pi$
$571$	−9.05961e17	+	9.05961e17i	−1.09389	+	1.09389i	−0.995109	+	0.0987843i	$0.968505\pi$
$572$		0			0
$573$	−1.03470e18	−	1.03470e18i	−1.22126	−	1.22126i
$574$		0			0
$575$	4.12186e16			0.0475612
$576$		0			0
$577$	3.64354e17			0.411037			0.205518	−	0.978653i	$-0.434112\pi$
$577$	3.64354e17			0.411037			0.205518	+	0.978653i	$0.434112\pi$
$578$		0			0
$579$	8.95580e16	+	8.95580e16i	0.0987856	+	0.0987856i
$580$		0			0
$581$	2.48785e16	−	2.48785e16i	0.0268337	−	0.0268337i
$582$		0			0
$583$			2.63949e18i			2.78403i
$584$		0			0
$585$		−	1.94851e18i		−	2.00997i
$586$		0			0
$587$	−4.75387e17	+	4.75387e17i	−0.479622	+	0.479622i	−0.905011	−	0.425389i	$-0.860137\pi$
$587$	−4.75387e17	+	4.75387e17i	−0.479622	+	0.479622i	0.425389	+	0.905011i	$0.360137\pi$
$588$		0			0
$589$	−8.29031e15	−	8.29031e15i	−0.00818128	−	0.00818128i
$590$		0			0
$591$	−1.94086e18			−1.87360
$592$		0			0
$593$	6.23776e17			0.589078			0.294539	−	0.955639i	$-0.404834\pi$
$593$	6.23776e17			0.589078			0.294539	+	0.955639i	$0.404834\pi$
$594$		0			0
$595$	1.09720e18	+	1.09720e18i	1.01374	+	1.01374i
$596$		0			0
$597$	1.94309e18	−	1.94309e18i	1.75655	−	1.75655i
$598$		0			0
$599$		−	4.82018e17i		−	0.426372i	−0.977012	−	0.213186i	$-0.931616\pi$
$599$		−	4.82018e17i		−	0.426372i	0.977012	−	0.213186i	$-0.0683841\pi$
$600$		0			0
$601$		−	8.49589e17i		−	0.735402i	−0.929944	−	0.367701i	$-0.880145\pi$
$601$		−	8.49589e17i		−	0.735402i	0.929944	−	0.367701i	$-0.119855\pi$
$602$		0			0
$603$	−6.28393e17	+	6.28393e17i	−0.532315	+	0.532315i
$604$		0			0
$605$	−9.31343e17	−	9.31343e17i	−0.772146	−	0.772146i
$606$		0			0
$607$	−1.28182e17			−0.104016			−0.0520082	−	0.998647i	$-0.516562\pi$
$607$	−1.28182e17			−0.104016			−0.0520082	+	0.998647i	$0.516562\pi$
$608$		0			0
$609$	1.14288e18			0.907793
$610$		0			0
$611$	2.68877e17	+	2.68877e17i	0.209067	+	0.209067i
$612$		0			0
$613$	1.66322e18	−	1.66322e18i	1.26607	−	1.26607i	0.317966	−	0.948102i	$-0.397000\pi$
$613$	1.66322e18	−	1.66322e18i	1.26607	−	1.26607i	0.948102	−	0.317966i	$-0.103000\pi$
$614$		0			0
$615$		−	2.49464e18i		−	1.85917i
$616$		0			0
$617$		−	7.52729e17i		−	0.549269i	−0.961549	−	0.274634i	$-0.911443\pi$
$617$		−	7.52729e17i		−	0.549269i	0.961549	−	0.274634i	$-0.0885568\pi$
$618$		0			0
$619$	1.78382e16	−	1.78382e16i	0.0127456	−	0.0127456i	−0.700705	−	0.713451i	$-0.747131\pi$
$619$	1.78382e16	−	1.78382e16i	0.0127456	−	0.0127456i	0.713451	+	0.700705i	$0.247131\pi$
$620$		0			0
$621$	−9.43411e17	−	9.43411e17i	−0.660094	−	0.660094i
$622$		0			0
$623$	−4.98028e17			−0.341257
$624$		0			0
$625$	1.29212e18			0.867127
$626$		0			0
$627$	−1.15311e17	−	1.15311e17i	−0.0757936	−	0.0757936i
$628$		0			0
$629$	−2.19687e18	+	2.19687e18i	−1.41441	+	1.41441i
$630$		0			0
$631$		−	4.00314e17i		−	0.252470i	−0.992000	−	0.126235i	$-0.959711\pi$
$631$		−	4.00314e17i		−	0.252470i	0.992000	−	0.126235i	$-0.0402893\pi$
$632$		0			0
$633$		−	4.12460e18i		−	2.54834i
$634$		0			0
$635$	−2.65957e17	+	2.65957e17i	−0.160984	+	0.160984i
$636$		0			0
$637$	−2.12127e17	−	2.12127e17i	−0.125803	−	0.125803i
$638$		0			0
$639$	1.37189e18			0.797193
$640$		0			0
$641$	1.42677e18			0.812411			0.406206	−	0.913782i	$-0.366852\pi$
$641$	1.42677e18			0.812411			0.406206	+	0.913782i	$0.366852\pi$
$642$		0			0
$643$	−1.59416e17	−	1.59416e17i	−0.0889530	−	0.0889530i	0.661230	−	0.750183i	$-0.270035\pi$
$643$	−1.59416e17	−	1.59416e17i	−0.0889530	−	0.0889530i	−0.750183	+	0.661230i	$0.770035\pi$
$644$		0			0
$645$	6.51460e17	−	6.51460e17i	0.356246	−	0.356246i
$646$		0			0
$647$			9.05793e17i			0.485457i	0.970094	+	0.242729i	$0.0780425\pi$
$647$			9.05793e17i			0.485457i	−0.970094	+	0.242729i	$0.921958\pi$
$648$		0			0
$649$			2.22403e18i			1.16829i
$650$		0			0
$651$	−6.44798e17	+	6.44798e17i	−0.332007	+	0.332007i
$652$		0			0
$653$	9.37957e17	+	9.37957e17i	0.473421	+	0.473421i	0.903020	−	0.429599i	$-0.141345\pi$
$653$	9.37957e17	+	9.37957e17i	0.473421	+	0.473421i	−0.429599	+	0.903020i	$0.641345\pi$
$654$		0			0
$655$	2.19004e17			0.108364
$656$		0			0
$657$	−6.37928e18			−3.09454
$658$		0			0
$659$	−2.18336e18	−	2.18336e18i	−1.03841	−	1.03841i	−0.999232	−	0.0391816i	$-0.987525\pi$
$659$	−2.18336e18	−	2.18336e18i	−1.03841	−	1.03841i	−0.0391816	−	0.999232i	$-0.512475\pi$
$660$		0			0
$661$	2.83125e18	−	2.83125e18i	1.32029	−	1.32029i	0.406746	−	0.913541i	$-0.366663\pi$
$661$	2.83125e18	−	2.83125e18i	1.32029	−	1.32029i	0.913541	−	0.406746i	$-0.133337\pi$
$662$		0			0
$663$			6.30057e18i			2.88099i
$664$		0			0
$665$			7.57540e16i			0.0339676i
$666$		0			0
$667$	3.58308e17	−	3.58308e17i	0.157557	−	0.157557i
$668$		0			0
$669$	−2.95775e18	−	2.95775e18i	−1.27553	−	1.27553i
$670$		0			0
$671$	2.28983e17			0.0968515
$672$		0			0
$673$	−2.55518e18			−1.06004			−0.530022	−	0.847984i	$-0.677816\pi$
$673$	−2.55518e18			−1.06004			−0.530022	+	0.847984i	$0.677816\pi$
$674$		0			0
$675$	4.81085e17	+	4.81085e17i	0.195771	+	0.195771i
$676$		0			0
$677$	−8.69311e17	+	8.69311e17i	−0.347015	+	0.347015i	−0.858997	−	0.511981i	$-0.828912\pi$
$677$	−8.69311e17	+	8.69311e17i	−0.347015	+	0.347015i	0.511981	+	0.858997i	$0.328912\pi$
$678$		0			0
$679$			2.91591e18i			1.14188i
$680$		0			0
$681$		−	1.59839e18i		−	0.614081i
$682$		0			0
$683$	−1.07466e18	+	1.07466e18i	−0.405077	+	0.405077i	−0.880018	−	0.474941i	$-0.842470\pi$
$683$	−1.07466e18	+	1.07466e18i	−0.405077	+	0.405077i	0.474941	+	0.880018i	$0.342470\pi$
$684$		0			0
$685$	1.74561e18	+	1.74561e18i	0.645594	+	0.645594i
$686$		0			0
$687$	−9.76789e17			−0.354472
$688$		0			0
$689$	4.97873e18			1.77294
$690$		0			0
$691$	1.57377e18	+	1.57377e18i	0.549965	+	0.549965i	0.926431	−	0.376466i	$-0.122861\pi$
$691$	1.57377e18	+	1.57377e18i	0.549965	+	0.549965i	−0.376466	+	0.926431i	$0.622861\pi$
$692$		0			0
$693$	−6.23924e18	+	6.23924e18i	−2.13976	+	2.13976i
$694$		0			0
$695$			4.21384e17i			0.141833i
$696$		0			0
$697$			5.61167e18i			1.85387i
$698$		0			0
$699$	2.90900e18	−	2.90900e18i	0.943283	−	0.943283i
$700$		0			0
$701$	3.29947e18	+	3.29947e18i	1.05021	+	1.05021i	0.998671	+	0.0515405i	$0.0164131\pi$
$701$	3.29947e18	+	3.29947e18i	1.05021	+	1.05021i	0.0515405	+	0.998671i	$0.483587\pi$
$702$		0			0
$703$	−1.51679e17			−0.0473931
$704$		0			0
$705$	1.75120e18			0.537163
$706$		0			0
$707$	−2.53953e18	−	2.53953e18i	−0.764763	−	0.764763i
$708$		0			0
$709$	6.85820e17	−	6.85820e17i	0.202773	−	0.202773i	−0.598414	−	0.801187i	$-0.704202\pi$
$709$	6.85820e17	−	6.85820e17i	0.202773	−	0.202773i	0.801187	+	0.598414i	$0.204202\pi$
$710$		0			0
$711$		−	1.40614e19i		−	4.08204i
$712$		0			0
$713$			4.04306e17i			0.115247i
$714$		0			0
$715$	−3.26696e18	+	3.26696e18i	−0.914439	+	0.914439i
$716$		0			0
$717$	−5.26650e18	−	5.26650e18i	−1.44760	−	1.44760i
$718$		0			0
$719$	−2.52315e18			−0.681090			−0.340545	−	0.940228i	$-0.610612\pi$
$719$	−2.52315e18			−0.681090			−0.340545	+	0.940228i	$0.610612\pi$
$720$		0			0
$721$	2.29584e17			0.0608643
$722$		0			0
$723$	−5.72022e18	−	5.72022e18i	−1.48941	−	1.48941i
$724$		0			0
$725$	−1.82716e17	+	1.82716e17i	−0.0467283	+	0.0467283i
$726$		0			0
$727$			1.67257e18i			0.420155i	0.977685	+	0.210078i	$0.0673716\pi$
$727$			1.67257e18i			0.420155i	−0.977685	+	0.210078i	$0.932628\pi$
$728$		0			0
$729$		−	8.44753e17i		−	0.208449i
$730$		0			0
$731$	−1.46546e18	+	1.46546e18i	−0.355230	+	0.355230i
$732$		0			0
$733$	−2.10063e18	−	2.10063e18i	−0.500235	−	0.500235i	0.411276	−	0.911511i	$-0.365083\pi$
$733$	−2.10063e18	−	2.10063e18i	−0.500235	−	0.500235i	−0.911511	+	0.411276i	$0.865083\pi$
$734$		0			0
$735$	−1.38159e18			−0.323230
$736$		0			0
$737$	2.10719e18			0.484356
$738$		0			0
$739$	−5.40359e18	−	5.40359e18i	−1.22038	−	1.22038i	−0.967498	−	0.252877i	$-0.918623\pi$
$739$	−5.40359e18	−	5.40359e18i	−1.22038	−	1.22038i	−0.252877	−	0.967498i	$-0.581377\pi$
$740$		0			0
$741$	−2.17506e17	+	2.17506e17i	−0.0482672	+	0.0482672i
$742$		0			0
$743$		−	3.09680e17i		−	0.0675284i	−0.999430	−	0.0337642i	$-0.989250\pi$
$743$		−	3.09680e17i		−	0.0675284i	0.999430	−	0.0337642i	$-0.0107495\pi$
$744$		0			0
$745$			7.36322e18i			1.57780i
$746$		0			0
$747$	3.23653e17	−	3.23653e17i	0.0681546	−	0.0681546i
$748$		0			0
$749$	−1.69518e17	−	1.69518e17i	−0.0350819	−	0.0350819i
$750$		0			0
$751$	5.15109e18			1.04771			0.523853	−	0.851808i	$-0.324494\pi$
$751$	5.15109e18			1.04771			0.523853	+	0.851808i	$0.324494\pi$
$752$		0			0
$753$	8.26344e18			1.65194
$754$		0			0
$755$	4.77868e18	+	4.77868e18i	0.938973	+	0.938973i
$756$		0			0
$757$	−9.97460e16	+	9.97460e16i	−0.0192651	+	0.0192651i	−0.716674	−	0.697409i	$-0.754336\pi$
$757$	−9.97460e16	+	9.97460e16i	−0.0192651	+	0.0192651i	0.697409	+	0.716674i	$0.254336\pi$
$758$		0			0
$759$			5.62356e18i			1.06768i
$760$		0			0
$761$		−	6.64383e18i		−	1.23999i	−0.784605	−	0.619995i	$-0.787134\pi$
$761$		−	6.64383e18i		−	1.23999i	0.784605	−	0.619995i	$-0.212866\pi$
$762$		0			0
$763$	−8.85225e17	+	8.85225e17i	−0.162422	+	0.162422i
$764$		0			0
$765$	1.42738e19	+	1.42738e19i	2.57478	+	2.57478i
$766$		0			0
$767$	4.19507e18			0.743994
$768$		0			0
$769$	−8.40914e18			−1.46633			−0.733163	−	0.680053i	$-0.761957\pi$
$769$	−8.40914e18			−1.46633			−0.733163	+	0.680053i	$0.761957\pi$
$770$		0			0
$771$	1.19754e19	+	1.19754e19i	2.05322	+	2.05322i
$772$		0			0
$773$	−9.74851e17	+	9.74851e17i	−0.164351	+	0.164351i	−0.784491	−	0.620140i	$-0.787076\pi$
$773$	−9.74851e17	+	9.74851e17i	−0.164351	+	0.164351i	0.620140	+	0.784491i	$0.287076\pi$
$774$		0			0
$775$		−	2.06173e17i		−	0.0341799i
$776$		0			0
$777$			1.17972e19i			1.92327i
$778$		0			0
$779$	−1.93724e17	+	1.93724e17i	−0.0310591	+	0.0310591i
$780$		0			0
$781$	−2.30018e18	−	2.30018e18i	−0.362685	−	0.362685i
$782$		0			0
$783$	8.36401e18			1.29707
$784$		0			0
$785$	−1.02712e18			−0.156664
$786$		0			0
$787$	6.94241e17	+	6.94241e17i	0.104154	+	0.104154i	0.757263	−	0.653110i	$-0.226536\pi$
$787$	6.94241e17	+	6.94241e17i	0.104154	+	0.104154i	−0.653110	+	0.757263i	$0.726536\pi$
$788$		0			0
$789$	5.50255e18	−	5.50255e18i	0.812014	−	0.812014i
$790$		0			0
$791$		−	7.53424e18i		−	1.09368i
$792$		0			0
$793$		−	4.31918e17i		−	0.0616774i
$794$		0			0
$795$	1.62133e19	−	1.62133e19i	2.27763	−	2.27763i
$796$		0			0
$797$	−6.70874e18	−	6.70874e18i	−0.927176	−	0.927176i	0.0703467	−	0.997523i	$-0.477589\pi$
$797$	−6.70874e18	−	6.70874e18i	−0.927176	−	0.927176i	−0.997523	+	0.0703467i	$0.977589\pi$
$798$		0			0
$799$	−3.93931e18			−0.535632
$800$		0			0
$801$	−6.47900e18			−0.866756
$802$		0			0
$803$	1.06958e19	+	1.06958e19i	1.40787	+	1.40787i
$804$		0			0
$805$	1.84721e18	−	1.84721e18i	0.239245	−	0.239245i
$806$		0			0
$807$			4.64188e18i			0.591583i
$808$		0			0
$809$		−	9.13910e18i		−	1.14614i	−0.819506	−	0.573070i	$-0.805752\pi$
$809$		−	9.13910e18i		−	1.14614i	0.819506	−	0.573070i	$-0.194248\pi$
$810$		0			0
$811$	1.07286e19	−	1.07286e19i	1.32406	−	1.32406i	0.413609	−	0.910455i	$-0.364268\pi$
$811$	1.07286e19	−	1.07286e19i	1.32406	−	1.32406i	0.910455	−	0.413609i	$-0.135732\pi$
$812$		0			0
$813$	8.82807e18	+	8.82807e18i	1.07220	+	1.07220i
$814$		0			0
$815$	−4.65424e17			−0.0556320
$816$		0			0
$817$	−1.01180e17			−0.0119028
$818$		0			0
$819$	1.17688e19	+	1.17688e19i	1.36265	+	1.36265i
$820$		0			0
$821$	2.75052e18	−	2.75052e18i	0.313462	−	0.313462i	−0.532787	−	0.846249i	$-0.678855\pi$
$821$	2.75052e18	−	2.75052e18i	0.313462	−	0.313462i	0.846249	+	0.532787i	$0.178855\pi$
$822$		0			0
$823$		−	6.70129e18i		−	0.751726i	−0.926675	−	0.375863i	$-0.877346\pi$
$823$		−	6.70129e18i		−	0.751726i	0.926675	−	0.375863i	$-0.122654\pi$
$824$		0			0
$825$		−	2.86769e18i		−	0.316652i
$826$		0			0
$827$	−2.96497e18	+	2.96497e18i	−0.322281	+	0.322281i	−0.849641	−	0.527361i	$-0.823182\pi$
$827$	−2.96497e18	+	2.96497e18i	−0.322281	+	0.322281i	0.527361	+	0.849641i	$0.323182\pi$
$828$		0			0
$829$	7.17012e18	+	7.17012e18i	0.767224	+	0.767224i	0.977617	−	0.210393i	$-0.0674744\pi$
$829$	7.17012e18	+	7.17012e18i	0.767224	+	0.767224i	−0.210393	+	0.977617i	$0.567474\pi$
$830$		0			0
$831$	1.74365e18			0.183676
$832$		0			0
$833$	3.10788e18			0.322308
$834$		0			0
$835$	−1.29335e19	−	1.29335e19i	−1.32055	−	1.32055i
$836$		0			0
$837$	−4.71888e18	+	4.71888e18i	−0.474377	+	0.474377i
$838$		0			0
$839$			7.39990e18i			0.732442i	0.930528	+	0.366221i	$0.119349\pi$
$839$			7.39990e18i			0.732442i	−0.930528	+	0.366221i	$0.880651\pi$
$840$		0			0
$841$		−	7.08398e18i		−	0.690404i
$842$		0			0
$843$	6.24596e18	−	6.24596e18i	0.599405	−	0.599405i
$844$		0			0
$845$	−8.61931e17	−	8.61931e17i	−0.0814524	−	0.0814524i
$846$		0			0
$847$	1.12504e19			1.04695
$848$		0			0
$849$	1.02739e19			0.941529
$850$		0			0
$851$	3.69857e18	+	3.69857e18i	0.333805	+	0.333805i
$852$		0			0
$853$	1.16573e19	−	1.16573e19i	1.03617	−	1.03617i	0.0368450	−	0.999321i	$-0.488269\pi$
$853$	1.16573e19	−	1.16573e19i	1.03617	−	1.03617i	0.999321	−	0.0368450i	$-0.0117308\pi$
$854$		0			0
$855$			9.85508e17i			0.0862741i
$856$		0			0
$857$		−	4.81231e18i		−	0.414934i	−0.978242	−	0.207467i	$-0.933478\pi$
$857$		−	4.81231e18i		−	0.414934i	0.978242	−	0.207467i	$-0.0665219\pi$
$858$		0			0
$859$	−7.90944e18	+	7.90944e18i	−0.671723	+	0.671723i	−0.958113	−	0.286390i	$-0.907545\pi$
$859$	−7.90944e18	+	7.90944e18i	−0.671723	+	0.671723i	0.286390	+	0.958113i	$0.407545\pi$
$860$		0			0
$861$	1.50673e19	+	1.50673e19i	1.26042	+	1.26042i
$862$		0			0
$863$	1.79865e19			1.48210			0.741050	−	0.671450i	$-0.234328\pi$
$863$	1.79865e19			1.48210			0.741050	+	0.671450i	$0.234328\pi$
$864$		0			0
$865$	−4.59535e18			−0.373004
$866$		0			0
$867$	−3.01245e19	−	3.01245e19i	−2.40877	−	2.40877i
$868$		0			0
$869$	−2.35761e19	+	2.35761e19i	−1.85713	+	1.85713i
$870$		0			0
$871$		−	3.97468e18i		−	0.308450i
$872$		0			0
$873$			3.79340e19i			2.90025i
$874$		0			0
$875$	−8.87317e18	+	8.87317e18i	−0.668385	+	0.668385i
$876$		0			0
$877$	−7.71684e18	−	7.71684e18i	−0.572719	−	0.572719i	0.360168	−	0.932887i	$-0.382719\pi$
$877$	−7.71684e18	−	7.71684e18i	−0.572719	−	0.572719i	−0.932887	+	0.360168i	$0.882719\pi$
$878$		0			0
$879$	−2.56658e19			−1.87684
$880$		0			0
$881$	−5.75567e18			−0.414717			−0.207359	−	0.978265i	$-0.566487\pi$
$881$	−5.75567e18			−0.414717			−0.207359	+	0.978265i	$0.566487\pi$
$882$		0			0
$883$	1.11808e19	+	1.11808e19i	0.793834	+	0.793834i	0.982115	−	0.188282i	$-0.0602917\pi$
$883$	1.11808e19	+	1.11808e19i	0.793834	+	0.793834i	−0.188282	+	0.982115i	$0.560292\pi$
$884$		0			0
$885$	1.36613e19	−	1.36613e19i	0.955785	−	0.955785i
$886$		0			0
$887$		−	4.78085e18i		−	0.329611i	−0.986326	−	0.164805i	$-0.947300\pi$
$887$		−	4.78085e18i		−	0.329611i	0.986326	−	0.164805i	$-0.0526996\pi$
$888$		0			0
$889$		−	3.21269e18i		−	0.218277i
$890$		0			0
$891$	−3.01287e19	+	3.01287e19i	−2.01732	+	2.01732i
$892$		0			0
$893$	−1.35991e17	−	1.35991e17i	−0.00897381	−	0.00897381i
$894$		0			0
$895$	−2.46023e19			−1.60002
$896$		0			0
$897$	1.06074e19			0.679922
$898$		0			0
$899$	−1.79223e18	−	1.79223e18i	−0.113229	−	0.113229i
$900$		0			0
$901$	−3.64717e19	+	3.64717e19i	−2.27114	+	2.27114i
$902$		0			0
$903$			7.86949e18i			0.483032i
$904$		0			0
$905$		−	1.47079e19i		−	0.889884i
$906$		0			0
$907$	2.20607e19	−	2.20607e19i	1.31575	−	1.31575i	0.398636	−	0.917109i	$-0.369484\pi$
$907$	2.20607e19	−	2.20607e19i	1.31575	−	1.31575i	0.917109	−	0.398636i	$-0.130516\pi$
$908$		0			0
$909$	−3.30375e19	−	3.30375e19i	−1.94241	−	1.94241i
$910$		0			0
$911$	−7.76869e18			−0.450276			−0.225138	−	0.974327i	$-0.572283\pi$
$911$	−7.76869e18			−0.450276			−0.225138	+	0.974327i	$0.572283\pi$
$912$		0			0
$913$	−1.08530e18			−0.0620141
$914$		0			0
$915$	−1.40654e18	−	1.40654e18i	−0.0792349	−	0.0792349i
$916$		0			0
$917$	−1.32276e18	+	1.32276e18i	−0.0734650	+	0.0734650i
$918$		0			0
$919$		−	5.73390e18i		−	0.313978i	−0.987600	−	0.156989i	$-0.949821\pi$
$919$		−	5.73390e18i		−	0.313978i	0.987600	−	0.156989i	$-0.0501788\pi$
$920$		0			0
$921$			6.71243e18i			0.362403i
$922$		0			0
$923$	−4.33870e18	+	4.33870e18i	−0.230966	+	0.230966i
$924$		0			0
$925$	−1.88606e18	−	1.88606e18i	−0.0989998	−	0.0989998i
$926$		0			0
$927$	2.98673e18			0.154589
$928$		0			0
$929$	−3.14027e19			−1.60274			−0.801372	−	0.598166i	$-0.795896\pi$
$929$	−3.14027e19			−1.60274			−0.801372	+	0.598166i	$0.795896\pi$
$930$		0			0
$931$	1.07289e17	+	1.07289e17i	0.00539985	+	0.00539985i
$932$		0			0
$933$	3.32506e19	−	3.32506e19i	1.65032	−	1.65032i
$934$		0			0
$935$		−	4.78642e19i		−	2.34280i
$936$		0			0
$937$			1.70737e19i			0.824175i	0.911144	+	0.412087i	$0.135200\pi$
$937$			1.70737e19i			0.824175i	−0.911144	+	0.412087i	$0.864800\pi$
$938$		0			0
$939$	−8.21347e18	+	8.21347e18i	−0.391021	+	0.391021i
$940$		0			0
$941$	8.30753e18	+	8.30753e18i	0.390067	+	0.390067i	0.874711	−	0.484644i	$-0.161051\pi$
$941$	8.30753e18	+	8.30753e18i	0.390067	+	0.390067i	−0.484644	+	0.874711i	$0.661051\pi$
$942$		0			0
$943$	9.44762e18			0.437518
$944$		0			0
$945$	4.31195e19			1.96955
$946$		0			0
$947$	−2.74831e19	−	2.74831e19i	−1.23820	−	1.23820i	−0.960735	−	0.277467i	$-0.910505\pi$
$947$	−2.74831e19	−	2.74831e19i	−1.23820	−	1.23820i	−0.277467	−	0.960735i	$-0.589495\pi$
$948$		0			0
$949$	2.01749e19	−	2.01749e19i	0.896565	−	0.896565i
$950$		0			0
$951$			5.50451e19i			2.41293i
$952$		0			0
$953$		−	3.25341e18i		−	0.140681i	−0.997523	−	0.0703405i	$-0.977591\pi$
$953$		−	3.25341e18i		−	0.140681i	0.997523	−	0.0703405i	$-0.0224086\pi$
$954$		0			0
$955$	1.48267e19	−	1.48267e19i	0.632443	−	0.632443i
$956$		0			0
$957$	−2.49284e19	−	2.49284e19i	−1.04898	−	1.04898i
$958$		0			0
$959$	−2.10866e19			−0.875358
$960$		0			0
$961$	−2.23952e19			−0.917178
$962$		0			0
$963$	−2.20531e18	−	2.20531e18i	−0.0891042	−	0.0891042i
$964$		0			0
$965$	−1.28332e18	+	1.28332e18i	−0.0511572	+	0.0511572i
$966$		0			0
$967$			3.03010e19i			1.19175i	0.803077	+	0.595875i	$0.203195\pi$
$967$			3.03010e19i			1.19175i	−0.803077	+	0.595875i	$0.796805\pi$
$968$		0			0
$969$		−	3.18667e18i		−	0.123661i
$970$		0			0
$971$	−8.31667e18	+	8.31667e18i	−0.318438	+	0.318438i	−0.848167	−	0.529729i	$-0.822294\pi$
$971$	−8.31667e18	+	8.31667e18i	−0.318438	+	0.318438i	0.529729	+	0.848167i	$0.322294\pi$
$972$		0			0
$973$	−2.54511e18	−	2.54511e18i	−0.0961553	−	0.0961553i
$974$		0			0
$975$	−5.40918e18			−0.201652
$976$		0			0
$977$	2.14881e19			0.790466			0.395233	−	0.918581i	$-0.370664\pi$
$977$	2.14881e19			0.790466			0.395233	+	0.918581i	$0.370664\pi$
$978$		0			0
$979$	1.08630e19	+	1.08630e19i	0.394332	+	0.394332i
$980$		0			0
$981$	−1.15162e19	+	1.15162e19i	−0.412534	+	0.412534i
$982$		0			0
$983$		−	3.65878e19i		−	1.29341i	−0.762738	−	0.646707i	$-0.776145\pi$
$983$		−	3.65878e19i		−	1.29341i	0.762738	−	0.646707i	$-0.223855\pi$
$984$		0			0
$985$		−	2.78115e19i		−	0.970262i
$986$		0			0
$987$	−1.05770e19	+	1.05770e19i	−0.364169	+	0.364169i
$988$		0			0
$989$	2.46719e18	+	2.46719e18i	0.0838354	+	0.0838354i
$990$		0			0
$991$	4.57991e19			1.53595			0.767976	−	0.640478i	$-0.221264\pi$
$991$	4.57991e19			1.53595			0.767976	+	0.640478i	$0.221264\pi$
$992$		0			0
$993$	−3.38659e19			−1.12097
$994$		0			0
$995$	2.78435e19	+	2.78435e19i	0.909649	+	0.909649i
$996$		0			0
$997$	−1.28554e19	+	1.28554e19i	−0.414541	+	0.414541i	−0.883317	−	0.468776i	$-0.844695\pi$
$997$	−1.28554e19	+	1.28554e19i	−0.414541	+	0.414541i	0.468776	+	0.883317i	$0.344695\pi$
$998$		0			0
$999$			8.63363e19i			2.74801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.14.e.a.33.2		50
4.3	odd	2		128.14.e.b.33.24		50
8.3	odd	2		16.14.e.a.13.20	yes	50
8.5	even	2		64.14.e.a.17.24		50
16.3	odd	4		16.14.e.a.5.20	✓	50
16.5	even	4	inner	128.14.e.a.97.2		50
16.11	odd	4		128.14.e.b.97.24		50
16.13	even	4		64.14.e.a.49.24		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.14.e.a.5.20	✓	50	16.3	odd	4
16.14.e.a.13.20	yes	50	8.3	odd	2
64.14.e.a.17.24		50	8.5	even	2
64.14.e.a.49.24		50	16.13	even	4
128.14.e.a.33.2		50	1.1	even	1	trivial
128.14.e.a.97.2		50	16.5	even	4	inner
128.14.e.b.33.24		50	4.3	odd	2
128.14.e.b.97.24		50	16.11	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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1618.47 - 1618.47i) q^{3} +(23191.8 - 23191.8i) q^{5} +280152. i q^{7} +3.64459e6i q^{9} +O(q^{10})\)	\(q+(-1618.47 - 1618.47i) q^{3} +(23191.8 - 23191.8i) q^{5} +280152. i q^{7} +3.64459e6i q^{9} +(6.11068e6 - 6.11068e6i) q^{11} +(-1.15263e7 - 1.15263e7i) q^{13} -7.50707e7 q^{15} +1.68871e8 q^{17} +(5.82970e6 + 5.82970e6i) q^{19} +(4.53419e8 - 4.53419e8i) q^{21} -2.84306e8i q^{23} +1.44980e8i q^{25} +(3.31829e9 - 3.31829e9i) q^{27} +(1.26029e9 + 1.26029e9i) q^{29} -1.42208e9 q^{31} -1.97800e10 q^{33} +(6.49724e9 + 6.49724e9i) q^{35} +(-1.30091e10 + 1.30091e10i) q^{37} +3.73099e10i q^{39} +3.32305e10i q^{41} +(-8.67795e9 + 8.67795e9i) q^{43} +(8.45247e10 + 8.45247e10i) q^{45} -2.33273e10 q^{47} +1.84038e10 q^{49} +(-2.73314e11 - 2.73314e11i) q^{51} +(-2.15973e11 + 2.15973e11i) q^{53} -2.83436e11i q^{55} -1.88704e10i q^{57} +(-1.81979e11 + 1.81979e11i) q^{59} +(1.87363e10 + 1.87363e10i) q^{61} -1.02104e12 q^{63} -5.34631e11 q^{65} +(1.72418e11 + 1.72418e11i) q^{67} +(-4.60142e11 + 4.60142e11i) q^{69} -3.76419e11i q^{71} +1.75034e12i q^{73} +(2.34646e11 - 2.34646e11i) q^{75} +(1.71192e12 + 1.71192e12i) q^{77} -3.85817e12 q^{79} -4.93049e12 q^{81} +(-8.88037e10 - 8.88037e10i) q^{83} +(3.91644e12 - 3.91644e12i) q^{85} -4.07948e12i q^{87} +1.77771e12i q^{89} +(3.22911e12 - 3.22911e12i) q^{91} +(2.30160e12 + 2.30160e12i) q^{93} +2.70403e11 q^{95} +1.04083e13 q^{97} +(2.22709e13 + 2.22709e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 2 q^{3} + 2 q^{5}+O(q^{10}) \) 50 * q - 2 * q^3 + 2 * q^5	\( 50 q - 2 q^{3} + 2 q^{5} - 4723998 q^{11} + 2 q^{13} - 91124996 q^{15} - 4 q^{17} + 422008902 q^{19} - 3188644 q^{21} - 2068699784 q^{27} + 3661663834 q^{29} + 10650044176 q^{31} - 4 q^{33} + 7767977276 q^{35} - 21527986470 q^{37} - 18577860182 q^{43} - 2438217602 q^{45} - 215584306576 q^{47} - 525968913642 q^{49} - 551664571452 q^{51} - 223019793366 q^{53} + 1167423209882 q^{59} - 81543039150 q^{61} + 862914002556 q^{63} - 27850095516 q^{65} + 1390089097910 q^{67} + 168685276844 q^{69} - 1675683188954 q^{75} + 2147852144860 q^{77} - 8517123343488 q^{79} - 9602604240358 q^{81} + 2192965629438 q^{83} - 2809965843748 q^{85} + 3291182399236 q^{91} - 3412032366928 q^{93} - 7322122332660 q^{95} - 4 q^{97} + 19363874529854 q^{99}+O(q^{100}) \) 50 * q - 2 * q^3 + 2 * q^5 - 4723998 * q^11 + 2 * q^13 - 91124996 * q^15 - 4 * q^17 + 422008902 * q^19 - 3188644 * q^21 - 2068699784 * q^27 + 3661663834 * q^29 + 10650044176 * q^31 - 4 * q^33 + 7767977276 * q^35 - 21527986470 * q^37 - 18577860182 * q^43 - 2438217602 * q^45 - 215584306576 * q^47 - 525968913642 * q^49 - 551664571452 * q^51 - 223019793366 * q^53 + 1167423209882 * q^59 - 81543039150 * q^61 + 862914002556 * q^63 - 27850095516 * q^65 + 1390089097910 * q^67 + 168685276844 * q^69 - 1675683188954 * q^75 + 2147852144860 * q^77 - 8517123343488 * q^79 - 9602604240358 * q^81 + 2192965629438 * q^83 - 2809965843748 * q^85 + 3291182399236 * q^91 - 3412032366928 * q^93 - 7322122332660 * q^95 - 4 * q^97 + 19363874529854 * q^99

Introduction

L-functions

Modular forms

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Database

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