LMFDB - Embedded newform 128.13.f.a.95.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,13,Mod(31,128)]

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([2, 1]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	128.f (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:	$116.991208611$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.14
Character	$\chi$	$=$	128.95
Dual form			128.13.f.a.31.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(193.300 - 193.300i) q^{3} +(10355.8 - 10355.8i) q^{5} +108466. q^{7} +456712. i q^{9} +O(q^{10})$	\(q+(193.300 - 193.300i) q^{3} +(10355.8 - 10355.8i) q^{5} +108466. q^{7} +456712. i q^{9} +(-1.04650e6 - 1.04650e6i) q^{11} +(1.27642e6 + 1.27642e6i) q^{13} -4.00356e6i q^{15} +1.95112e7 q^{17} +(-2.72724e7 + 2.72724e7i) q^{19} +(2.09664e7 - 2.09664e7i) q^{21} +1.76773e8 q^{23} +2.96535e7i q^{25} +(1.91009e8 + 1.91009e8i) q^{27} +(3.27663e8 + 3.27663e8i) q^{29} +1.40311e9i q^{31} -4.04575e8 q^{33} +(1.12326e9 - 1.12326e9i) q^{35} +(-3.08303e9 + 3.08303e9i) q^{37} +4.93464e8 q^{39} -1.10296e9i q^{41} +(-4.13826e9 - 4.13826e9i) q^{43} +(4.72963e9 + 4.72963e9i) q^{45} +7.39074e9i q^{47} -2.07645e9 q^{49} +(3.77150e9 - 3.77150e9i) q^{51} +(2.73431e10 - 2.73431e10i) q^{53} -2.16748e10 q^{55} +1.05435e10i q^{57} +(4.52570e9 + 4.52570e9i) q^{59} +(-2.45297e9 - 2.45297e9i) q^{61} +4.95376e10i q^{63} +2.64369e10 q^{65} +(-2.12998e9 + 2.12998e9i) q^{67} +(3.41701e10 - 3.41701e10i) q^{69} -5.19641e10 q^{71} +2.15045e11i q^{73} +(5.73201e9 + 5.73201e9i) q^{75} +(-1.13509e11 - 1.13509e11i) q^{77} -3.83696e10i q^{79} -1.68871e11 q^{81} +(3.95415e11 - 3.95415e11i) q^{83} +(2.02055e11 - 2.02055e11i) q^{85} +1.26674e11 q^{87} +7.22335e11i q^{89} +(1.38448e11 + 1.38448e11i) q^{91} +(2.71220e11 + 2.71220e11i) q^{93} +5.64857e11i q^{95} -1.01704e12 q^{97} +(4.77948e11 - 4.77948e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 46 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	$ 46 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 2668318 q^{11} + 2 q^{13} - 4 q^{17} + 51868606 q^{19} + 1062884 q^{21} - 298270076 q^{23} + 970053760 q^{27} - 704570398 q^{29} - 4 q^{33} - 3815032900 q^{35} - 364298398 q^{37} - 15553507196 q^{39} + 363863518 q^{43} - 489344130 q^{45} + 67229109258 q^{49} + 33806024892 q^{51} + 11168756642 q^{53} + 74491808260 q^{55} + 104334793054 q^{59} + 106371743810 q^{61} - 75186419620 q^{65} - 43778233922 q^{67} + 214340079908 q^{69} + 188251854340 q^{71} + 308961520610 q^{75} + 341607754084 q^{77} - 941431788274 q^{81} - 1025936323202 q^{83} - 436332718748 q^{85} - 2368412421756 q^{87} - 2028231531652 q^{91} - 1534541270080 q^{93} - 4 q^{97} + 4950023059646 q^{99}+O(q^{100}) $ 46 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 2668318 * q^11 + 2 * q^13 - 4 * q^17 + 51868606 * q^19 + 1062884 * q^21 - 298270076 * q^23 + 970053760 * q^27 - 704570398 * q^29 - 4 * q^33 - 3815032900 * q^35 - 364298398 * q^37 - 15553507196 * q^39 + 363863518 * q^43 - 489344130 * q^45 + 67229109258 * q^49 + 33806024892 * q^51 + 11168756642 * q^53 + 74491808260 * q^55 + 104334793054 * q^59 + 106371743810 * q^61 - 75186419620 * q^65 - 43778233922 * q^67 + 214340079908 * q^69 + 188251854340 * q^71 + 308961520610 * q^75 + 341607754084 * q^77 - 941431788274 * q^81 - 1025936323202 * q^83 - 436332718748 * q^85 - 2368412421756 * q^87 - 2028231531652 * q^91 - 1534541270080 * q^93 - 4 * q^97 + 4950023059646 * 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
$3$	193.300	−	193.300i	0.265157	−	0.265157i	−0.561988	−	0.827145i	$-0.689963\pi$
$3$	193.300	−	193.300i	0.265157	−	0.265157i	0.827145	+	0.561988i	$0.189963\pi$
$4$		0			0
$5$	10355.8	−	10355.8i	0.662774	−	0.662774i	−0.293259	−	0.956033i	$-0.594740\pi$
$5$	10355.8	−	10355.8i	0.662774	−	0.662774i	0.956033	+	0.293259i	$0.0947398\pi$
$6$		0			0
$7$	108466.			0.921944			0.460972	−	0.887415i	$-0.347501\pi$
$7$	108466.			0.921944			0.460972	+	0.887415i	$0.347501\pi$
$8$		0			0
$9$			456712.i			0.859383i
$10$		0			0
$11$	−1.04650e6	−	1.04650e6i	−0.590721	−	0.590721i	0.347105	−	0.937826i	$-0.387165\pi$
$11$	−1.04650e6	−	1.04650e6i	−0.590721	−	0.590721i	−0.937826	+	0.347105i	$0.887165\pi$
$12$		0			0
$13$	1.27642e6	+	1.27642e6i	0.264445	+	0.264445i	0.826857	−	0.562412i	$-0.190127\pi$
$13$	1.27642e6	+	1.27642e6i	0.264445	+	0.264445i	−0.562412	+	0.826857i	$0.690127\pi$
$14$		0			0
$15$		−	4.00356e6i		−	0.351479i
$16$		0			0
$17$	1.95112e7			0.808332			0.404166	−	0.914686i	$-0.367562\pi$
$17$	1.95112e7			0.808332			0.404166	+	0.914686i	$0.367562\pi$
$18$		0			0
$19$	−2.72724e7	+	2.72724e7i	−0.579698	+	0.579698i	−0.934820	−	0.355122i	$-0.884439\pi$
$19$	−2.72724e7	+	2.72724e7i	−0.579698	+	0.579698i	0.355122	+	0.934820i	$0.384439\pi$
$20$		0			0
$21$	2.09664e7	−	2.09664e7i	0.244460	−	0.244460i
$22$		0			0
$23$	1.76773e8			1.19412			0.597060	−	0.802197i	$-0.296335\pi$
$23$	1.76773e8			1.19412			0.597060	+	0.802197i	$0.296335\pi$
$24$		0			0
$25$			2.96535e7i			0.121461i
$26$		0			0
$27$	1.91009e8	+	1.91009e8i	0.493029	+	0.493029i
$28$		0			0
$29$	3.27663e8	+	3.27663e8i	0.550858	+	0.550858i	0.926688	−	0.375830i	$-0.122642\pi$
$29$	3.27663e8	+	3.27663e8i	0.550858	+	0.550858i	−0.375830	+	0.926688i	$0.622642\pi$
$30$		0			0
$31$			1.40311e9i			1.58096i	0.612487	+	0.790480i	$0.290169\pi$
$31$			1.40311e9i			1.58096i	−0.612487	+	0.790480i	$0.709831\pi$
$32$		0			0
$33$	−4.04575e8			−0.313268
$34$		0			0
$35$	1.12326e9	−	1.12326e9i	0.611041	−	0.611041i
$36$		0			0
$37$	−3.08303e9	+	3.08303e9i	−1.20162	+	1.20162i	−0.227949	+	0.973673i	$0.573202\pi$
$37$	−3.08303e9	+	3.08303e9i	−1.20162	+	1.20162i	−0.973673	+	0.227949i	$0.926798\pi$
$38$		0			0
$39$	4.93464e8			0.140239
$40$		0			0
$41$		−	1.10296e9i		−	0.232197i	−0.993238	−	0.116098i	$-0.962961\pi$
$41$		−	1.10296e9i		−	0.232197i	0.993238	−	0.116098i	$-0.0370388\pi$
$42$		0			0
$43$	−4.13826e9	−	4.13826e9i	−0.654646	−	0.654646i	0.299462	−	0.954108i	$-0.403193\pi$
$43$	−4.13826e9	−	4.13826e9i	−0.654646	−	0.654646i	−0.954108	+	0.299462i	$0.903193\pi$
$44$		0			0
$45$	4.72963e9	+	4.72963e9i	0.569577	+	0.569577i
$46$		0			0
$47$			7.39074e9i			0.685647i	0.939400	+	0.342824i	$0.111383\pi$
$47$			7.39074e9i			0.685647i	−0.939400	+	0.342824i	$0.888617\pi$
$48$		0			0
$49$	−2.07645e9			−0.150019
$50$		0			0
$51$	3.77150e9	−	3.77150e9i	0.214335	−	0.214335i
$52$		0			0
$53$	2.73431e10	−	2.73431e10i	1.23365	−	1.23365i	0.271103	−	0.962550i	$-0.412611\pi$
$53$	2.73431e10	−	2.73431e10i	1.23365	−	1.23365i	0.962550	−	0.271103i	$-0.0873885\pi$
$54$		0			0
$55$	−2.16748e10			−0.783029
$56$		0			0
$57$			1.05435e10i			0.307422i
$58$		0			0
$59$	4.52570e9	+	4.52570e9i	0.107294	+	0.107294i	0.758716	−	0.651422i	$-0.225827\pi$
$59$	4.52570e9	+	4.52570e9i	0.107294	+	0.107294i	−0.651422	+	0.758716i	$0.725827\pi$
$60$		0			0
$61$	−2.45297e9	−	2.45297e9i	−0.0476117	−	0.0476117i	0.682900	−	0.730512i	$-0.260718\pi$
$61$	−2.45297e9	−	2.45297e9i	−0.0476117	−	0.0476117i	−0.730512	+	0.682900i	$0.760718\pi$
$62$		0			0
$63$			4.95376e10i			0.792304i
$64$		0			0
$65$	2.64369e10			0.350534
$66$		0			0
$67$	−2.12998e9	+	2.12998e9i	−0.0235465	+	0.0235465i	−0.718782	−	0.695236i	$-0.755300\pi$
$67$	−2.12998e9	+	2.12998e9i	−0.0235465	+	0.0235465i	0.695236	+	0.718782i	$0.255300\pi$
$68$		0			0
$69$	3.41701e10	−	3.41701e10i	0.316629	−	0.316629i
$70$		0			0
$71$	−5.19641e10			−0.405652			−0.202826	−	0.979215i	$-0.565013\pi$
$71$	−5.19641e10			−0.405652			−0.202826	+	0.979215i	$0.565013\pi$
$72$		0			0
$73$			2.15045e11i			1.42100i	0.703699	+	0.710498i	$0.251530\pi$
$73$			2.15045e11i			1.42100i	−0.703699	+	0.710498i	$0.748470\pi$
$74$		0			0
$75$	5.73201e9	+	5.73201e9i	0.0322062	+	0.0322062i
$76$		0			0
$77$	−1.13509e11	−	1.13509e11i	−0.544612	−	0.544612i
$78$		0			0
$79$		−	3.83696e10i		−	0.157843i	−0.996881	−	0.0789214i	$-0.974852\pi$
$79$		−	3.83696e10i		−	0.157843i	0.996881	−	0.0789214i	$-0.0251476\pi$
$80$		0			0
$81$	−1.68871e11			−0.597923
$82$		0			0
$83$	3.95415e11	−	3.95415e11i	1.20944	−	1.20944i	0.238232	−	0.971208i	$-0.423432\pi$
$83$	3.95415e11	−	3.95415e11i	1.20944	−	1.20944i	0.971208	−	0.238232i	$-0.0765677\pi$
$84$		0			0
$85$	2.02055e11	−	2.02055e11i	0.535741	−	0.535741i
$86$		0			0
$87$	1.26674e11			0.292128
$88$		0			0
$89$			7.22335e11i			1.45344i	0.686931	+	0.726722i	$0.258957\pi$
$89$			7.22335e11i			1.45344i	−0.686931	+	0.726722i	$0.741043\pi$
$90$		0			0
$91$	1.38448e11	+	1.38448e11i	0.243803	+	0.243803i
$92$		0			0
$93$	2.71220e11	+	2.71220e11i	0.419203	+	0.419203i
$94$		0			0
$95$			5.64857e11i			0.768417i
$96$		0			0
$97$	−1.01704e12			−1.22098			−0.610491	−	0.792023i	$-0.709028\pi$
$97$	−1.01704e12			−1.22098			−0.610491	+	0.792023i	$0.709028\pi$
$98$		0			0
$99$	4.77948e11	−	4.77948e11i	0.507656	−	0.507656i
$100$		0			0
$101$	−8.69714e9	+	8.69714e9i	−0.00819310	+	0.00819310i	−0.711191	−	0.702998i	$-0.751844\pi$
$101$	−8.69714e9	+	8.69714e9i	−0.00819310	+	0.00819310i	0.702998	+	0.711191i	$0.251844\pi$
$102$		0			0
$103$	5.80891e10			0.0486487			0.0243243	−	0.999704i	$-0.492257\pi$
$103$	5.80891e10			0.0486487			0.0243243	+	0.999704i	$0.492257\pi$
$104$		0			0
$105$		−	4.34249e11i		−	0.324044i
$106$		0			0
$107$	−5.86672e11	−	5.86672e11i	−0.390924	−	0.390924i	0.484093	−	0.875017i	$-0.339150\pi$
$107$	−5.86672e11	−	5.86672e11i	−0.390924	−	0.390924i	−0.875017	+	0.484093i	$0.839150\pi$
$108$		0			0
$109$	2.77381e11	+	2.77381e11i	0.165393	+	0.165393i	0.784951	−	0.619558i	$-0.212688\pi$
$109$	2.77381e11	+	2.77381e11i	0.165393	+	0.165393i	−0.619558	+	0.784951i	$0.712688\pi$
$110$		0			0
$111$			1.19190e12i			0.637237i
$112$		0			0
$113$	3.16225e12			1.51889			0.759443	−	0.650574i	$-0.225471\pi$
$113$	3.16225e12			1.51889			0.759443	+	0.650574i	$0.225471\pi$
$114$		0			0
$115$	1.83063e12	−	1.83063e12i	0.791432	−	0.791432i
$116$		0			0
$117$	−5.82958e11	+	5.82958e11i	−0.227259	+	0.227259i
$118$		0			0
$119$	2.11629e12			0.745237
$120$		0			0
$121$		−	9.48110e11i		−	0.302097i
$122$		0			0
$123$	−2.13202e11	−	2.13202e11i	−0.0615687	−	0.0615687i
$124$		0			0
$125$	2.83537e12	+	2.83537e12i	0.743275	+	0.743275i
$126$		0			0
$127$		−	7.23090e12i		−	1.72334i	−0.507472	−	0.861668i	$-0.669420\pi$
$127$		−	7.23090e12i		−	1.72334i	0.507472	−	0.861668i	$-0.330580\pi$
$128$		0			0
$129$	−1.59985e12			−0.347168
$130$		0			0
$131$	−2.05134e12	+	2.05134e12i	−0.405891	+	0.405891i	−0.880303	−	0.474412i	$-0.842661\pi$
$131$	−2.05134e12	+	2.05134e12i	−0.405891	+	0.405891i	0.474412	+	0.880303i	$0.342661\pi$
$132$		0			0
$133$	−2.95812e12	+	2.95812e12i	−0.534449	+	0.534449i
$134$		0			0
$135$	3.95613e12			0.653533
$136$		0			0
$137$			1.23880e13i			1.87360i	0.349867	+	0.936799i	$0.386227\pi$
$137$			1.23880e13i			1.87360i	−0.349867	+	0.936799i	$0.613773\pi$
$138$		0			0
$139$	7.00348e12	+	7.00348e12i	0.971014	+	0.971014i	0.999592	−	0.0285781i	$-0.00909792\pi$
$139$	7.00348e12	+	7.00348e12i	0.971014	+	0.971014i	−0.0285781	+	0.999592i	$0.509098\pi$
$140$		0			0
$141$	1.42863e12	+	1.42863e12i	0.181804	+	0.181804i
$142$		0			0
$143$		−	2.67155e12i		−	0.312426i
$144$		0			0
$145$	6.78646e12			0.730189
$146$		0			0
$147$	−4.01378e11	+	4.01378e11i	−0.0397786	+	0.0397786i
$148$		0			0
$149$	−8.99648e12	+	8.99648e12i	−0.822158	+	0.822158i	−0.986417	−	0.164259i	$-0.947477\pi$
$149$	−8.99648e12	+	8.99648e12i	−0.822158	+	0.822158i	0.164259	+	0.986417i	$0.447477\pi$
$150$		0			0
$151$	2.30291e13			1.94274			0.971369	−	0.237574i	$-0.0763522\pi$
$151$	2.30291e13			1.94274			0.971369	+	0.237574i	$0.0763522\pi$
$152$		0			0
$153$			8.91097e12i			0.694667i
$154$		0			0
$155$	1.45304e13	+	1.45304e13i	1.04782	+	1.04782i
$156$		0			0
$157$	1.75120e13	+	1.75120e13i	1.16934	+	1.16934i	0.982366	+	0.186970i	$0.0598666\pi$
$157$	1.75120e13	+	1.75120e13i	1.16934	+	1.16934i	0.186970	+	0.982366i	$0.440133\pi$
$158$		0			0
$159$		−	1.05708e13i		−	0.654224i
$160$		0			0
$161$	1.91738e13			1.10091
$162$		0			0
$163$	6.45525e12	−	6.45525e12i	0.344182	−	0.344182i	−0.513755	−	0.857937i	$-0.671746\pi$
$163$	6.45525e12	−	6.45525e12i	0.344182	−	0.344182i	0.857937	+	0.513755i	$0.171746\pi$
$164$		0			0
$165$	−4.18972e12	+	4.18972e12i	−0.207626	+	0.207626i
$166$		0			0
$167$	1.01980e13			0.470127			0.235063	−	0.971980i	$-0.424470\pi$
$167$	1.01980e13			0.470127			0.235063	+	0.971980i	$0.424470\pi$
$168$		0			0
$169$		−	2.00396e13i		−	0.860138i
$170$		0			0
$171$	−1.24556e13	−	1.24556e13i	−0.498183	−	0.498183i
$172$		0			0
$173$	8.50657e12	+	8.50657e12i	0.317306	+	0.317306i	0.847731	−	0.530426i	$-0.177968\pi$
$173$	8.50657e12	+	8.50657e12i	0.317306	+	0.317306i	−0.530426	+	0.847731i	$0.677968\pi$
$174$		0			0
$175$			3.21639e12i			0.111980i
$176$		0			0
$177$	1.74963e12			0.0568993
$178$		0			0
$179$	3.91848e13	−	3.91848e13i	1.19124	−	1.19124i	0.214521	−	0.976719i	$-0.431181\pi$
$179$	3.91848e13	−	3.91848e13i	1.19124	−	1.19124i	0.976719	−	0.214521i	$-0.0688190\pi$
$180$		0			0
$181$	−1.73583e13	+	1.73583e13i	−0.493669	+	0.493669i	−0.909460	−	0.415791i	$-0.863505\pi$
$181$	−1.73583e13	+	1.73583e13i	−0.493669	+	0.493669i	0.415791	+	0.909460i	$0.363505\pi$
$182$		0			0
$183$	−9.48317e11			−0.0252492
$184$		0			0
$185$			6.38548e13i			1.59281i
$186$		0			0
$187$	−2.04184e13	−	2.04184e13i	−0.477499	−	0.477499i
$188$		0			0
$189$	2.07180e13	+	2.07180e13i	0.454545	+	0.454545i
$190$		0			0
$191$		−	3.63298e13i		−	0.748278i	−0.927373	−	0.374139i	$-0.877938\pi$
$191$		−	3.63298e13i		−	0.748278i	0.927373	−	0.374139i	$-0.122062\pi$
$192$		0			0
$193$	−5.66249e13			−1.09563			−0.547814	−	0.836600i	$-0.684540\pi$
$193$	−5.66249e13			−1.09563			−0.547814	+	0.836600i	$0.684540\pi$
$194$		0			0
$195$	5.11024e12	−	5.11024e12i	0.0929467	−	0.0929467i
$196$		0			0
$197$	2.02663e13	−	2.02663e13i	0.346718	−	0.346718i	−0.512167	−	0.858886i	$-0.671157\pi$
$197$	2.02663e13	−	2.02663e13i	0.346718	−	0.346718i	0.858886	+	0.512167i	$0.171157\pi$
$198$		0			0
$199$	9.99830e13			1.60993			0.804966	−	0.593321i	$-0.202183\pi$
$199$	9.99830e13			1.60993			0.804966	+	0.593321i	$0.202183\pi$
$200$		0			0
$201$			8.23448e11i			0.0124871i
$202$		0			0
$203$	3.55403e13	+	3.55403e13i	0.507860	+	0.507860i
$204$		0			0
$205$	−1.14221e13	−	1.14221e13i	−0.153894	−	0.153894i
$206$		0			0
$207$			8.07341e13i			1.02621i
$208$		0			0
$209$	5.70810e13			0.684879
$210$		0			0
$211$	8.39250e13	−	8.39250e13i	0.951036	−	0.951036i	−0.0478204	−	0.998856i	$-0.515228\pi$
$211$	8.39250e13	−	8.39250e13i	0.951036	−	0.951036i	0.998856	+	0.0478204i	$0.0152275\pi$
$212$		0			0
$213$	−1.00446e13	+	1.00446e13i	−0.107561	+	0.107561i
$214$		0			0
$215$	−8.57103e13			−0.867765
$216$		0			0
$217$			1.52189e14i			1.45756i
$218$		0			0
$219$	4.15682e13	+	4.15682e13i	0.376787	+	0.376787i
$220$		0			0
$221$	2.49045e13	+	2.49045e13i	0.213759	+	0.213759i
$222$		0			0
$223$			5.73361e13i			0.466229i	0.972449	+	0.233114i	$0.0748917\pi$
$223$			5.73361e13i			0.466229i	−0.972449	+	0.233114i	$0.925108\pi$
$224$		0			0
$225$	−1.35431e13			−0.104381
$226$		0			0
$227$	4.84010e13	−	4.84010e13i	0.353752	−	0.353752i	−0.507751	−	0.861504i	$-0.669523\pi$
$227$	4.84010e13	−	4.84010e13i	0.353752	−	0.353752i	0.861504	+	0.507751i	$0.169523\pi$
$228$		0			0
$229$	1.33346e14	−	1.33346e14i	0.924630	−	0.924630i	−0.0727222	−	0.997352i	$-0.523169\pi$
$229$	1.33346e14	−	1.33346e14i	0.924630	−	0.924630i	0.997352	+	0.0727222i	$0.0231686\pi$
$230$		0			0
$231$	−4.38826e13			−0.288815
$232$		0			0
$233$			1.15358e14i			0.720964i	0.932766	+	0.360482i	$0.117388\pi$
$233$			1.15358e14i			0.720964i	−0.932766	+	0.360482i	$0.882612\pi$
$234$		0			0
$235$	7.65374e13	+	7.65374e13i	0.454429	+	0.454429i
$236$		0			0
$237$	−7.41682e12	−	7.41682e12i	−0.0418531	−	0.0418531i
$238$		0			0
$239$		−	7.96873e13i		−	0.427565i	−0.976881	−	0.213782i	$-0.931422\pi$
$239$		−	7.96873e13i		−	0.427565i	0.976881	−	0.213782i	$-0.0685783\pi$
$240$		0			0
$241$	−1.28218e14			−0.654403			−0.327201	−	0.944955i	$-0.606106\pi$
$241$	−1.28218e14			−0.654403			−0.327201	+	0.944955i	$0.606106\pi$
$242$		0			0
$243$	−1.34153e14	+	1.34153e14i	−0.651572	+	0.651572i
$244$		0			0
$245$	−2.15034e13	+	2.15034e13i	−0.0994286	+	0.0994286i
$246$		0			0
$247$	−6.96223e13			−0.306596
$248$		0			0
$249$		−	1.52867e14i		−	0.641383i
$250$		0			0
$251$	−3.05704e14	−	3.05704e14i	−1.22253	−	1.22253i	−0.966731	−	0.255796i	$-0.917662\pi$
$251$	−3.05704e14	−	3.05704e14i	−1.22253	−	1.22253i	−0.255796	−	0.966731i	$-0.582338\pi$
$252$		0			0
$253$	−1.84992e14	−	1.84992e14i	−0.705392	−	0.705392i
$254$		0			0
$255$		−	7.81141e13i		−	0.284111i
$256$		0			0
$257$	1.72780e14			0.599646			0.299823	−	0.953995i	$-0.403072\pi$
$257$	1.72780e14			0.599646			0.299823	+	0.953995i	$0.403072\pi$
$258$		0			0
$259$	−3.34404e14	+	3.34404e14i	−1.10783	+	1.10783i
$260$		0			0
$261$	−1.49648e14	+	1.49648e14i	−0.473398	+	0.473398i
$262$		0			0
$263$	5.64678e13			0.170634			0.0853171	−	0.996354i	$-0.472810\pi$
$263$	5.64678e13			0.170634			0.0853171	+	0.996354i	$0.472810\pi$
$264$		0			0
$265$		−	5.66323e14i		−	1.63527i
$266$		0			0
$267$	1.39627e14	+	1.39627e14i	0.385391	+	0.385391i
$268$		0			0
$269$	−5.37736e12	−	5.37736e12i	−0.0141924	−	0.0141924i	0.699975	−	0.714167i	$-0.253194\pi$
$269$	−5.37736e12	−	5.37736e12i	−0.0141924	−	0.0141924i	−0.714167	+	0.699975i	$0.753194\pi$
$270$		0			0
$271$			2.83332e14i			0.715287i	0.933858	+	0.357644i	$0.116420\pi$
$271$			2.83332e14i			0.715287i	−0.933858	+	0.357644i	$0.883580\pi$
$272$		0			0
$273$	5.35240e13			0.129292
$274$		0			0
$275$	3.10324e13	−	3.10324e13i	0.0717495	−	0.0717495i
$276$		0			0
$277$	2.01391e14	−	2.01391e14i	0.445823	−	0.445823i	−0.448140	−	0.893963i	$-0.647914\pi$
$277$	2.01391e14	−	2.01391e14i	0.445823	−	0.445823i	0.893963	+	0.448140i	$0.147914\pi$
$278$		0			0
$279$	−6.40816e14			−1.35865
$280$		0			0
$281$		−	7.86654e14i		−	1.59789i	−0.601407	−	0.798943i	$-0.705393\pi$
$281$		−	7.86654e14i		−	1.59789i	0.601407	−	0.798943i	$-0.294607\pi$
$282$		0			0
$283$	−4.30440e14	−	4.30440e14i	−0.837903	−	0.837903i	0.150679	−	0.988583i	$-0.451854\pi$
$283$	−4.30440e14	−	4.30440e14i	−0.837903	−	0.837903i	−0.988583	+	0.150679i	$0.951854\pi$
$284$		0			0
$285$	1.09187e14	+	1.09187e14i	0.203751	+	0.203751i
$286$		0			0
$287$		−	1.19633e14i		−	0.214073i
$288$		0			0
$289$	−2.01937e14			−0.346600
$290$		0			0
$291$	−1.96594e14	+	1.96594e14i	−0.323752	+	0.323752i
$292$		0			0
$293$	−3.41236e14	+	3.41236e14i	−0.539323	+	0.539323i	−0.923330	−	0.384007i	$-0.874544\pi$
$293$	−3.41236e14	+	3.41236e14i	−0.539323	+	0.539323i	0.384007	+	0.923330i	$0.374544\pi$
$294$		0			0
$295$	9.37349e13			0.142223
$296$		0			0
$297$		−	3.99782e14i		−	0.582485i
$298$		0			0
$299$	2.25637e14	+	2.25637e14i	0.315779	+	0.315779i
$300$		0			0
$301$	−4.48859e14	−	4.48859e14i	−0.603547	−	0.603547i
$302$		0			0
$303$			3.36231e12i			0.00434492i
$304$		0			0
$305$	−5.08052e13			−0.0631116
$306$		0			0
$307$	−7.30337e14	+	7.30337e14i	−0.872354	+	0.872354i	−0.992729	−	0.120374i	$-0.961591\pi$
$307$	−7.30337e14	+	7.30337e14i	−0.872354	+	0.872354i	0.120374	+	0.992729i	$0.461591\pi$
$308$		0			0
$309$	1.12286e13	−	1.12286e13i	0.0128995	−	0.0128995i
$310$		0			0
$311$	−5.34246e13			−0.0590444			−0.0295222	−	0.999564i	$-0.509399\pi$
$311$	−5.34246e13			−0.0590444			−0.0295222	+	0.999564i	$0.509399\pi$
$312$		0			0
$313$		−	7.70410e13i		−	0.0819324i	−0.999161	−	0.0409662i	$-0.986956\pi$
$313$		−	7.70410e13i		−	0.0819324i	0.999161	−	0.0409662i	$-0.0130436\pi$
$314$		0			0
$315$	5.13004e14	+	5.13004e14i	0.525118	+	0.525118i
$316$		0			0
$317$	−4.90262e14	−	4.90262e14i	−0.483140	−	0.483140i	0.422993	−	0.906133i	$-0.360979\pi$
$317$	−4.90262e14	−	4.90262e14i	−0.483140	−	0.483140i	−0.906133	+	0.422993i	$0.860979\pi$
$318$		0			0
$319$		−	6.85798e14i		−	0.650807i
$320$		0			0
$321$	−2.26807e14			−0.207313
$322$		0			0
$323$	−5.32116e14	+	5.32116e14i	−0.468588	+	0.468588i
$324$		0			0
$325$	−3.78505e13	+	3.78505e13i	−0.0321197	+	0.0321197i
$326$		0			0
$327$	1.07235e14			0.0877104
$328$		0			0
$329$			8.01643e14i			0.632128i
$330$		0			0
$331$	−5.78696e14	−	5.78696e14i	−0.440030	−	0.440030i	0.451992	−	0.892022i	$-0.350714\pi$
$331$	−5.78696e14	−	5.78696e14i	−0.440030	−	0.440030i	−0.892022	+	0.451992i	$0.850714\pi$
$332$		0			0
$333$	−1.40806e15	−	1.40806e15i	−1.03265	−	1.03265i
$334$		0			0
$335$			4.41155e13i			0.0312121i
$336$		0			0
$337$	−1.67966e15			−1.14668			−0.573338	−	0.819319i	$-0.694352\pi$
$337$	−1.67966e15			−1.14668			−0.573338	+	0.819319i	$0.694352\pi$
$338$		0			0
$339$	6.11261e14	−	6.11261e14i	0.402744	−	0.402744i
$340$		0			0
$341$	1.46835e15	−	1.46835e15i	0.933907	−	0.933907i
$342$		0			0
$343$	−1.72653e15			−1.06025
$344$		0			0
$345$		−	7.07720e14i		−	0.419707i
$346$		0			0
$347$	−8.18570e14	−	8.18570e14i	−0.468899	−	0.468899i	0.432659	−	0.901558i	$-0.357575\pi$
$347$	−8.18570e14	−	8.18570e14i	−0.468899	−	0.468899i	−0.901558	+	0.432659i	$0.857575\pi$
$348$		0			0
$349$	6.99278e14	+	6.99278e14i	0.386988	+	0.386988i	0.873612	−	0.486624i	$-0.161772\pi$
$349$	6.99278e14	+	6.99278e14i	0.386988	+	0.386988i	−0.486624	+	0.873612i	$0.661772\pi$
$350$		0			0
$351$			4.87618e14i			0.260758i
$352$		0			0
$353$	2.63707e15			1.36293			0.681464	−	0.731851i	$-0.261344\pi$
$353$	2.63707e15			1.36293			0.681464	+	0.731851i	$0.261344\pi$
$354$		0			0
$355$	−5.38132e14	+	5.38132e14i	−0.268856	+	0.268856i
$356$		0			0
$357$	4.09079e14	−	4.09079e14i	0.197605	−	0.197605i
$358$		0			0
$359$	−1.92584e15			−0.899606			−0.449803	−	0.893128i	$-0.648506\pi$
$359$	−1.92584e15			−0.899606			−0.449803	+	0.893128i	$0.648506\pi$
$360$		0			0
$361$			7.25748e14i			0.327901i
$362$		0			0
$363$	−1.83269e14	−	1.83269e14i	−0.0801032	−	0.0801032i
$364$		0			0
$365$	2.22698e15	+	2.22698e15i	0.941800	+	0.941800i
$366$		0			0
$367$			2.57502e15i			1.05386i	0.849907	+	0.526932i	$0.176658\pi$
$367$			2.57502e15i			1.05386i	−0.849907	+	0.526932i	$0.823342\pi$
$368$		0			0
$369$	5.03734e14			0.199546
$370$		0			0
$371$	2.96580e15	−	2.96580e15i	1.13736	−	1.13736i
$372$		0			0
$373$	1.06739e15	−	1.06739e15i	0.396341	−	0.396341i	−0.480599	−	0.876940i	$-0.659581\pi$
$373$	1.06739e15	−	1.06739e15i	0.396341	−	0.396341i	0.876940	+	0.480599i	$0.159581\pi$
$374$		0			0
$375$	1.09615e15			0.394169
$376$		0			0
$377$			8.36475e14i			0.291343i
$378$		0			0
$379$	1.11549e15	+	1.11549e15i	0.376383	+	0.376383i	0.869795	−	0.493413i	$-0.164251\pi$
$379$	1.11549e15	+	1.11549e15i	0.376383	+	0.376383i	−0.493413	+	0.869795i	$0.664251\pi$
$380$		0			0
$381$	−1.39773e15	−	1.39773e15i	−0.456955	−	0.456955i
$382$		0			0
$383$			2.81468e15i			0.891737i	0.895099	+	0.445868i	$0.147105\pi$
$383$			2.81468e15i			0.891737i	−0.895099	+	0.445868i	$0.852895\pi$
$384$		0			0
$385$	−2.35097e15			−0.721909
$386$		0			0
$387$	1.88999e15	−	1.88999e15i	0.562592	−	0.562592i
$388$		0			0
$389$	−1.52369e15	+	1.52369e15i	−0.439743	+	0.439743i	−0.891926	−	0.452182i	$-0.850646\pi$
$389$	−1.52369e15	+	1.52369e15i	−0.439743	+	0.439743i	0.452182	+	0.891926i	$0.350646\pi$
$390$		0			0
$391$	3.44904e15			0.965245
$392$		0			0
$393$			7.93045e14i			0.215250i
$394$		0			0
$395$	−3.97350e14	−	3.97350e14i	−0.104614	−	0.104614i
$396$		0			0
$397$	3.63476e15	+	3.63476e15i	0.928395	+	0.928395i	0.997602	−	0.0692069i	$-0.0220469\pi$
$397$	3.63476e15	+	3.63476e15i	0.928395	+	0.928395i	−0.0692069	+	0.997602i	$0.522047\pi$
$398$		0			0
$399$			1.14361e15i			0.283426i
$400$		0			0
$401$	−2.07327e15			−0.498643			−0.249322	−	0.968421i	$-0.580208\pi$
$401$	−2.07327e15			−0.498643			−0.249322	+	0.968421i	$0.580208\pi$
$402$		0			0
$403$	−1.79096e15	+	1.79096e15i	−0.418077	+	0.418077i
$404$		0			0
$405$	−1.74880e15	+	1.74880e15i	−0.396288	+	0.396288i
$406$		0			0
$407$	6.45278e15			1.41965
$408$		0			0
$409$			8.49663e15i			1.81513i	0.419915	+	0.907563i	$0.362060\pi$
$409$			8.49663e15i			1.81513i	−0.419915	+	0.907563i	$0.637940\pi$
$410$		0			0
$411$	2.39459e15	+	2.39459e15i	0.496798	+	0.496798i
$412$		0			0
$413$	4.90884e14	+	4.90884e14i	0.0989187	+	0.0989187i
$414$		0			0
$415$		−	8.18971e15i		−	1.60317i
$416$		0			0
$417$	2.70754e15			0.514942
$418$		0			0
$419$	4.45210e15	−	4.45210e15i	0.822774	−	0.822774i	−0.163731	−	0.986505i	$-0.552353\pi$
$419$	4.45210e15	−	4.45210e15i	0.822774	−	0.822774i	0.986505	+	0.163731i	$0.0523530\pi$
$420$		0			0
$421$	−2.32236e15	+	2.32236e15i	−0.417097	+	0.417097i	−0.884202	−	0.467105i	$-0.845297\pi$
$421$	−2.32236e15	+	2.32236e15i	−0.417097	+	0.417097i	0.467105	+	0.884202i	$0.345297\pi$
$422$		0			0
$423$	−3.37544e15			−0.589234
$424$		0			0
$425$			5.78575e14i			0.0981807i
$426$		0			0
$427$	−2.66064e14	−	2.66064e14i	−0.0438953	−	0.0438953i
$428$		0			0
$429$	−5.16410e14	−	5.16410e14i	−0.0828420	−	0.0828420i
$430$		0			0
$431$		−	9.18668e15i		−	1.43316i	−0.697504	−	0.716581i	$-0.745706\pi$
$431$		−	9.18668e15i		−	1.43316i	0.697504	−	0.716581i	$-0.254294\pi$
$432$		0			0
$433$	1.08227e15			0.164213			0.0821064	−	0.996624i	$-0.473835\pi$
$433$	1.08227e15			0.164213			0.0821064	+	0.996624i	$0.473835\pi$
$434$		0			0
$435$	1.31182e15	−	1.31182e15i	0.193615	−	0.193615i
$436$		0			0
$437$	−4.82101e15	+	4.82101e15i	−0.692229	+	0.692229i
$438$		0			0
$439$	7.75977e15			1.08408			0.542041	−	0.840352i	$-0.317652\pi$
$439$	7.75977e15			1.08408			0.542041	+	0.840352i	$0.317652\pi$
$440$		0			0
$441$		−	9.48341e14i		−	0.128924i
$442$		0			0
$443$	2.77707e15	+	2.77707e15i	0.367421	+	0.367421i	0.866536	−	0.499115i	$-0.166341\pi$
$443$	2.77707e15	+	2.77707e15i	0.367421	+	0.367421i	−0.499115	+	0.866536i	$0.666341\pi$
$444$		0			0
$445$	7.48039e15	+	7.48039e15i	0.963306	+	0.963306i
$446$		0			0
$447$			3.47803e15i			0.436002i
$448$		0			0
$449$	9.97047e15			1.21685			0.608426	−	0.793611i	$-0.291801\pi$
$449$	9.97047e15			1.21685			0.608426	+	0.793611i	$0.291801\pi$
$450$		0			0
$451$	−1.15425e15	+	1.15425e15i	−0.137164	+	0.137164i
$452$		0			0
$453$	4.45151e15	−	4.45151e15i	0.515131	−	0.515131i
$454$		0			0
$455$	2.86750e15			0.323173
$456$		0			0
$457$		−	8.85500e15i		−	0.972056i	−0.873943	−	0.486028i	$-0.838445\pi$
$457$		−	8.85500e15i		−	0.972056i	0.873943	−	0.486028i	$-0.161555\pi$
$458$		0			0
$459$	3.72682e15	+	3.72682e15i	0.398531	+	0.398531i
$460$		0			0
$461$	−1.19649e16	−	1.19649e16i	−1.24654	−	1.24654i	−0.957239	−	0.289297i	$-0.906578\pi$
$461$	−1.19649e16	−	1.19649e16i	−1.24654	−	1.24654i	−0.289297	−	0.957239i	$-0.593422\pi$
$462$		0			0
$463$		−	7.12165e15i		−	0.722927i	−0.932386	−	0.361464i	$-0.882277\pi$
$463$		−	7.12165e15i		−	0.722927i	0.932386	−	0.361464i	$-0.117723\pi$
$464$		0			0
$465$	5.61743e15			0.555674
$466$		0			0
$467$	−9.50281e15	+	9.50281e15i	−0.916117	+	0.916117i	−0.996744	−	0.0806275i	$-0.974308\pi$
$467$	−9.50281e15	+	9.50281e15i	−0.916117	+	0.916117i	0.0806275	+	0.996744i	$0.474308\pi$
$468$		0			0
$469$	−2.31030e14	+	2.31030e14i	−0.0217086	+	0.0217086i
$470$		0			0
$471$	6.77014e15			0.620115
$472$		0			0
$473$			8.66136e15i			0.773427i
$474$		0			0
$475$	−8.08723e14	−	8.08723e14i	−0.0704106	−	0.0704106i
$476$		0			0
$477$	1.24879e16	+	1.24879e16i	1.06018	+	1.06018i
$478$		0			0
$479$			1.86901e15i			0.154739i	0.997002	+	0.0773694i	$0.0246521\pi$
$479$			1.86901e15i			0.154739i	−0.997002	+	0.0773694i	$0.975348\pi$
$480$		0			0
$481$	−7.87052e15			−0.635525
$482$		0			0
$483$	3.70628e15	−	3.70628e15i	0.291915	−	0.291915i
$484$		0			0
$485$	−1.05323e16	+	1.05323e16i	−0.809235	+	0.809235i
$486$		0			0
$487$	−7.14064e14			−0.0535258			−0.0267629	−	0.999642i	$-0.508520\pi$
$487$	−7.14064e14			−0.0535258			−0.0267629	+	0.999642i	$0.508520\pi$
$488$		0			0
$489$		−	2.49559e15i		−	0.182524i
$490$		0			0
$491$	−9.85977e14	−	9.85977e14i	−0.0703684	−	0.0703684i	0.671047	−	0.741415i	$-0.265845\pi$
$491$	−9.85977e14	−	9.85977e14i	−0.0703684	−	0.0703684i	−0.741415	+	0.671047i	$0.765845\pi$
$492$		0			0
$493$	6.39309e15	+	6.39309e15i	0.445276	+	0.445276i
$494$		0			0
$495$		−	9.89911e15i		−	0.672923i
$496$		0			0
$497$	−5.63633e15			−0.373988
$498$		0			0
$499$	5.93551e15	−	5.93551e15i	0.384463	−	0.384463i	−0.488244	−	0.872707i	$-0.662362\pi$
$499$	5.93551e15	−	5.93551e15i	0.384463	−	0.384463i	0.872707	+	0.488244i	$0.162362\pi$
$500$		0			0
$501$	1.97126e15	−	1.97126e15i	0.124657	−	0.124657i
$502$		0			0
$503$	−1.36287e16			−0.841486			−0.420743	−	0.907180i	$-0.638231\pi$
$503$	−1.36287e16			−0.841486			−0.420743	+	0.907180i	$0.638231\pi$
$504$		0			0
$505$			1.80133e14i			0.0108604i
$506$		0			0
$507$	−3.87364e15	−	3.87364e15i	−0.228072	−	0.228072i
$508$		0			0
$509$	−5.50762e15	−	5.50762e15i	−0.316706	−	0.316706i	0.530794	−	0.847501i	$-0.321894\pi$
$509$	−5.50762e15	−	5.50762e15i	−0.316706	−	0.316706i	−0.847501	+	0.530794i	$0.821894\pi$
$510$		0			0
$511$			2.33251e16i			1.31008i
$512$		0			0
$513$	−1.04186e16			−0.571615
$514$		0			0
$515$	6.01561e14	−	6.01561e14i	0.0322431	−	0.0322431i
$516$		0			0
$517$	7.73440e15	−	7.73440e15i	0.405026	−	0.405026i
$518$		0			0
$519$	3.28863e15			0.168272
$520$		0			0
$521$			1.95062e14i			0.00975320i	0.999988	+	0.00487660i	$0.00155228\pi$
$521$			1.95062e14i			0.00975320i	−0.999988	+	0.00487660i	$0.998448\pi$
$522$		0			0
$523$	−1.16950e16	−	1.16950e16i	−0.571463	−	0.571463i	0.361074	−	0.932537i	$-0.382410\pi$
$523$	−1.16950e16	−	1.16950e16i	−0.571463	−	0.571463i	−0.932537	+	0.361074i	$0.882410\pi$
$524$		0			0
$525$	6.21728e14	+	6.21728e14i	0.0296923	+	0.0296923i
$526$		0			0
$527$			2.73763e16i			1.27794i
$528$		0			0
$529$	9.33392e15			0.425922
$530$		0			0
$531$	−2.06694e15	+	2.06694e15i	−0.0922063	+	0.0922063i
$532$		0			0
$533$	1.40784e15	−	1.40784e15i	0.0614032	−	0.0614032i
$534$		0			0
$535$	−1.21510e16			−0.518189
$536$		0			0
$537$		−	1.51488e16i		−	0.631732i
$538$		0			0
$539$	2.17301e15	+	2.17301e15i	0.0886193	+	0.0886193i
$540$		0			0
$541$	−1.42283e16	−	1.42283e16i	−0.567506	−	0.567506i	0.363923	−	0.931429i	$-0.381437\pi$
$541$	−1.42283e16	−	1.42283e16i	−0.567506	−	0.567506i	−0.931429	+	0.363923i	$0.881437\pi$
$542$		0			0
$543$			6.71071e15i			0.261800i
$544$		0			0
$545$	5.74503e15			0.219237
$546$		0			0
$547$	1.17975e16	−	1.17975e16i	0.440418	−	0.440418i	−0.451734	−	0.892153i	$-0.649194\pi$
$547$	1.17975e16	−	1.17975e16i	0.440418	−	0.440418i	0.892153	+	0.451734i	$0.149194\pi$
$548$		0			0
$549$	1.12030e15	−	1.12030e15i	0.0409167	−	0.0409167i
$550$		0			0
$551$	−1.78723e16			−0.638662
$552$		0			0
$553$		−	4.16179e15i		−	0.145522i
$554$		0			0
$555$	1.23431e16	+	1.23431e16i	0.422344	+	0.422344i
$556$		0			0
$557$	−2.31579e16	−	2.31579e16i	−0.775475	−	0.775475i	0.203583	−	0.979058i	$-0.434741\pi$
$557$	−2.31579e16	−	2.31579e16i	−0.775475	−	0.775475i	−0.979058	+	0.203583i	$0.934741\pi$
$558$		0			0
$559$		−	1.05643e16i		−	0.346235i
$560$		0			0
$561$	−7.89374e15			−0.253224
$562$		0			0
$563$	−4.19200e16	+	4.19200e16i	−1.31635	+	1.31635i	−0.399704	+	0.916644i	$0.630887\pi$
$563$	−4.19200e16	+	4.19200e16i	−1.31635	+	1.31635i	−0.916644	+	0.399704i	$0.869113\pi$
$564$		0			0
$565$	3.27478e16	−	3.27478e16i	1.00668	−	1.00668i
$566$		0			0
$567$	−1.83168e16			−0.551252
$568$		0			0
$569$			8.61572e15i			0.253874i	0.991911	+	0.126937i	$0.0405146\pi$
$569$			8.61572e15i			0.253874i	−0.991911	+	0.126937i	$0.959485\pi$
$570$		0			0
$571$	−3.40328e15	−	3.40328e15i	−0.0981930	−	0.0981930i	0.656304	−	0.754497i	$-0.272119\pi$
$571$	−3.40328e15	−	3.40328e15i	−0.0981930	−	0.0981930i	−0.754497	+	0.656304i	$0.772119\pi$
$572$		0			0
$573$	−7.02254e15	−	7.02254e15i	−0.198411	−	0.198411i
$574$		0			0
$575$			5.24193e15i			0.145039i
$576$		0			0
$577$	−3.44963e16			−0.934797			−0.467398	−	0.884047i	$-0.654809\pi$
$577$	−3.44963e16			−0.934797			−0.467398	+	0.884047i	$0.654809\pi$
$578$		0			0
$579$	−1.09456e16	+	1.09456e16i	−0.290514	+	0.290514i
$580$		0			0
$581$	4.28890e16	−	4.28890e16i	1.11504	−	1.11504i
$582$		0			0
$583$	−5.72291e16			−1.45749
$584$		0			0
$585$			1.20740e16i			0.301243i
$586$		0			0
$587$	−4.67335e16	−	4.67335e16i	−1.14235	−	1.14235i	−0.988019	−	0.154333i	$-0.950677\pi$
$587$	−4.67335e16	−	4.67335e16i	−1.14235	−	1.14235i	−0.154333	−	0.988019i	$-0.549323\pi$
$588$		0			0
$589$	−3.82661e16	−	3.82661e16i	−0.916479	−	0.916479i
$590$		0			0
$591$		−	7.83493e15i		−	0.183870i
$592$		0			0
$593$	−3.96075e16			−0.910854			−0.455427	−	0.890273i	$-0.650513\pi$
$593$	−3.96075e16			−0.910854			−0.455427	+	0.890273i	$0.650513\pi$
$594$		0			0
$595$	2.19160e16	−	2.19160e16i	0.493924	−	0.493924i
$596$		0			0
$597$	1.93267e16	−	1.93267e16i	0.426885	−	0.426885i
$598$		0			0
$599$	−4.64783e15			−0.100621			−0.0503105	−	0.998734i	$-0.516021\pi$
$599$	−4.64783e15			−0.100621			−0.0503105	+	0.998734i	$0.516021\pi$
$600$		0			0
$601$		−	4.13370e16i		−	0.877187i	−0.898686	−	0.438594i	$-0.855477\pi$
$601$		−	4.13370e16i		−	0.877187i	0.898686	−	0.438594i	$-0.144523\pi$
$602$		0			0
$603$	−9.72787e14	−	9.72787e14i	−0.0202355	−	0.0202355i
$604$		0			0
$605$	−9.81848e15	−	9.81848e15i	−0.200222	−	0.200222i
$606$		0			0
$607$		−	6.54144e16i		−	1.30780i	−0.756581	−	0.653900i	$-0.773132\pi$
$607$		−	6.54144e16i		−	1.30780i	0.756581	−	0.653900i	$-0.226868\pi$
$608$		0			0
$609$	1.37398e16			0.269326
$610$		0			0
$611$	−9.43372e15	+	9.43372e15i	−0.181316	+	0.181316i
$612$		0			0
$613$	−6.12990e16	+	6.12990e16i	−1.15529	+	1.15529i	−0.169811	+	0.985477i	$0.554316\pi$
$613$	−6.12990e16	+	6.12990e16i	−1.15529	+	1.15529i	−0.985477	+	0.169811i	$0.945684\pi$
$614$		0			0
$615$	−4.41576e15			−0.0816122
$616$		0			0
$617$		−	6.00477e16i		−	1.08839i	−0.838958	−	0.544196i	$-0.816835\pi$
$617$		−	6.00477e16i		−	1.08839i	0.838958	−	0.544196i	$-0.183165\pi$
$618$		0			0
$619$	5.79727e16	+	5.79727e16i	1.03058	+	1.03058i	0.999518	+	0.0310575i	$0.00988748\pi$
$619$	5.79727e16	+	5.79727e16i	1.03058	+	1.03058i	0.0310575	+	0.999518i	$0.490113\pi$
$620$		0			0
$621$	3.37652e16	+	3.37652e16i	0.588735	+	0.588735i
$622$		0			0
$623$			7.83487e16i			1.34000i
$624$		0			0
$625$	5.14857e16			0.863786
$626$		0			0
$627$	1.10337e16	−	1.10337e16i	0.181601	−	0.181601i
$628$		0			0
$629$	−6.01536e16	+	6.01536e16i	−0.971309	+	0.971309i
$630$		0			0
$631$	2.13796e16			0.338706			0.169353	−	0.985555i	$-0.445832\pi$
$631$	2.13796e16			0.338706			0.169353	+	0.985555i	$0.445832\pi$
$632$		0			0
$633$		−	3.24453e16i		−	0.504348i
$634$		0			0
$635$	−7.48821e16	−	7.48821e16i	−1.14218	−	1.14218i
$636$		0			0
$637$	−2.65044e15	−	2.65044e15i	−0.0396717	−	0.0396717i
$638$		0			0
$639$		−	2.37326e16i		−	0.348611i
$640$		0			0
$641$	5.35879e16			0.772536			0.386268	−	0.922387i	$-0.373764\pi$
$641$	5.35879e16			0.772536			0.386268	+	0.922387i	$0.373764\pi$
$642$		0			0
$643$	−6.25235e16	+	6.25235e16i	−0.884662	+	0.884662i	−0.994004	−	0.109342i	$-0.965126\pi$
$643$	−6.25235e16	+	6.25235e16i	−0.884662	+	0.884662i	0.109342	+	0.994004i	$0.465126\pi$
$644$		0			0
$645$	−1.65678e16	+	1.65678e16i	−0.230094	+	0.230094i
$646$		0			0
$647$	1.26602e17			1.72589			0.862946	−	0.505296i	$-0.168617\pi$
$647$	1.26602e17			1.72589			0.862946	+	0.505296i	$0.168617\pi$
$648$		0			0
$649$		−	9.47228e15i		−	0.126761i
$650$		0			0
$651$	2.94181e16	+	2.94181e16i	0.386482	+	0.386482i
$652$		0			0
$653$	3.31039e16	+	3.31039e16i	0.426973	+	0.426973i	0.887596	−	0.460623i	$-0.152374\pi$
$653$	3.31039e16	+	3.31039e16i	0.426973	+	0.426973i	−0.460623	+	0.887596i	$0.652374\pi$
$654$		0			0
$655$			4.24866e16i			0.538028i
$656$		0			0
$657$	−9.82137e16			−1.22118
$658$		0			0
$659$	−2.08651e16	+	2.08651e16i	−0.254746	+	0.254746i	−0.822913	−	0.568167i	$-0.807653\pi$
$659$	−2.08651e16	+	2.08651e16i	−0.254746	+	0.254746i	0.568167	+	0.822913i	$0.307653\pi$
$660$		0			0
$661$	−2.23011e16	+	2.23011e16i	−0.267373	+	0.267373i	−0.828041	−	0.560668i	$-0.810544\pi$
$661$	−2.23011e16	+	2.23011e16i	−0.267373	+	0.267373i	0.560668	+	0.828041i	$0.310544\pi$
$662$		0			0
$663$	9.62806e15			0.113359
$664$		0			0
$665$			6.12677e16i			0.708438i
$666$		0			0
$667$	5.79219e16	+	5.79219e16i	0.657791	+	0.657791i
$668$		0			0
$669$	1.10830e16	+	1.10830e16i	0.123624	+	0.123624i
$670$		0			0
$671$			5.13407e15i			0.0562505i
$672$		0			0
$673$	6.52403e16			0.702143			0.351072	−	0.936349i	$-0.385817\pi$
$673$	6.52403e16			0.702143			0.351072	+	0.936349i	$0.385817\pi$
$674$		0			0
$675$	−5.66410e15	+	5.66410e15i	−0.0598837	+	0.0598837i
$676$		0			0
$677$	4.27547e15	−	4.27547e15i	0.0444070	−	0.0444070i	−0.684555	−	0.728962i	$-0.740003\pi$
$677$	4.27547e15	−	4.27547e15i	0.0444070	−	0.0444070i	0.728962	+	0.684555i	$0.240003\pi$
$678$		0			0
$679$	−1.10314e17			−1.12568
$680$		0			0
$681$		−	1.87118e16i		−	0.187600i
$682$		0			0
$683$	3.96458e15	+	3.96458e15i	0.0390547	+	0.0390547i	0.726364	−	0.687310i	$-0.241208\pi$
$683$	3.96458e15	+	3.96458e15i	0.0390547	+	0.0390547i	−0.687310	+	0.726364i	$0.741208\pi$
$684$		0			0
$685$	1.28288e17	+	1.28288e17i	1.24177	+	1.24177i
$686$		0			0
$687$		−	5.15515e16i		−	0.490344i
$688$		0			0
$689$	6.98029e16			0.652466
$690$		0			0
$691$	8.10550e16	−	8.10550e16i	0.744581	−	0.744581i	−0.228875	−	0.973456i	$-0.573505\pi$
$691$	8.10550e16	−	8.10550e16i	0.744581	−	0.744581i	0.973456	+	0.228875i	$0.0735047\pi$
$692$		0			0
$693$	5.18410e16	−	5.18410e16i	0.468030	−	0.468030i
$694$		0			0
$695$	1.45054e17			1.28713
$696$		0			0
$697$		−	2.15200e16i		−	0.187692i
$698$		0			0
$699$	2.22987e16	+	2.22987e16i	0.191169	+	0.191169i
$700$		0			0
$701$	−8.57205e16	−	8.57205e16i	−0.722398	−	0.722398i	0.246695	−	0.969093i	$-0.420655\pi$
$701$	−8.57205e16	−	8.57205e16i	−0.722398	−	0.722398i	−0.969093	+	0.246695i	$0.920655\pi$
$702$		0			0
$703$		−	1.68163e17i		−	1.39315i
$704$		0			0
$705$	2.95893e16			0.240990
$706$		0			0
$707$	−9.43343e14	+	9.43343e14i	−0.00755358	+	0.00755358i
$708$		0			0
$709$	1.22404e16	−	1.22404e16i	0.0963645	−	0.0963645i	−0.657281	−	0.753646i	$-0.728294\pi$
$709$	1.22404e16	−	1.22404e16i	0.0963645	−	0.0963645i	0.753646	+	0.657281i	$0.228294\pi$
$710$		0			0
$711$	1.75238e16			0.135647
$712$		0			0
$713$			2.48031e17i			1.88786i
$714$		0			0
$715$	−2.76662e16	−	2.76662e16i	−0.207068	−	0.207068i
$716$		0			0
$717$	−1.54035e16	−	1.54035e16i	−0.113372	−	0.113372i
$718$		0			0
$719$		−	5.05188e16i		−	0.365662i	−0.983144	−	0.182831i	$-0.941474\pi$
$719$		−	5.05188e16i		−	0.365662i	0.983144	−	0.182831i	$-0.0585261\pi$
$720$		0			0
$721$	6.30068e15			0.0448514
$722$		0			0
$723$	−2.47844e16	+	2.47844e16i	−0.173520	+	0.173520i
$724$		0			0
$725$	−9.71637e15	+	9.71637e15i	−0.0669077	+	0.0669077i
$726$		0			0
$727$	−1.34730e17			−0.912553			−0.456277	−	0.889838i	$-0.650817\pi$
$727$	−1.34730e17			−0.912553			−0.456277	+	0.889838i	$0.650817\pi$
$728$		0			0
$729$		−	3.78817e16i		−	0.252385i
$730$		0			0
$731$	−8.07422e16	−	8.07422e16i	−0.529171	−	0.529171i
$732$		0			0
$733$	7.84822e16	+	7.84822e16i	0.505997	+	0.505997i	0.913295	−	0.407299i	$-0.133529\pi$
$733$	7.84822e16	+	7.84822e16i	0.505997	+	0.505997i	−0.407299	+	0.913295i	$0.633529\pi$
$734$		0			0
$735$			8.31321e15i			0.0527284i
$736$		0			0
$737$	4.45804e15			0.0278189
$738$		0			0
$739$	1.59444e17	−	1.59444e17i	0.978907	−	0.978907i	−0.0208752	−	0.999782i	$-0.506645\pi$
$739$	1.59444e17	−	1.59444e17i	0.978907	−	0.978907i	0.999782	+	0.0208752i	$0.00664526\pi$
$740$		0			0
$741$	−1.34580e16	+	1.34580e16i	−0.0812961	+	0.0812961i
$742$		0			0
$743$	2.88342e17			1.71386			0.856930	−	0.515432i	$-0.172369\pi$
$743$	2.88342e17			1.71386			0.856930	+	0.515432i	$0.172369\pi$
$744$		0			0
$745$			1.86332e17i			1.08981i
$746$		0			0
$747$	1.80591e17	+	1.80591e17i	1.03937	+	1.03937i
$748$		0			0
$749$	−6.36338e16	−	6.36338e16i	−0.360410	−	0.360410i
$750$		0			0
$751$			1.84338e17i			1.02748i	0.857944	+	0.513742i	$0.171741\pi$
$751$			1.84338e17i			1.02748i	−0.857944	+	0.513742i	$0.828259\pi$
$752$		0			0
$753$	−1.18185e17			−0.648323
$754$		0			0
$755$	2.38485e17	−	2.38485e17i	1.28760	−	1.28760i
$756$		0			0
$757$	−9.33249e16	+	9.33249e16i	−0.495932	+	0.495932i	−0.910169	−	0.414237i	$-0.864048\pi$
$757$	−9.33249e16	+	9.33249e16i	−0.495932	+	0.495932i	0.414237	+	0.910169i	$0.364048\pi$
$758$		0			0
$759$	−7.15178e16			−0.374079
$760$		0			0
$761$			1.95329e17i			1.00568i	0.864380	+	0.502840i	$0.167711\pi$
$761$			1.95329e17i			1.00568i	−0.864380	+	0.502840i	$0.832289\pi$
$762$		0			0
$763$	3.00864e16	+	3.00864e16i	0.152483	+	0.152483i
$764$		0			0
$765$	9.22807e16	+	9.22807e16i	0.460407	+	0.460407i
$766$		0			0
$767$			1.15534e16i			0.0567465i
$768$		0			0
$769$	−2.10306e17			−1.01694			−0.508468	−	0.861081i	$-0.669788\pi$
$769$	−2.10306e17			−1.01694			−0.508468	+	0.861081i	$0.669788\pi$
$770$		0			0
$771$	3.33983e16	−	3.33983e16i	0.159000	−	0.159000i
$772$		0			0
$773$	6.25995e16	−	6.25995e16i	0.293423	−	0.293423i	−0.545008	−	0.838431i	$-0.683473\pi$
$773$	6.25995e16	−	6.25995e16i	0.293423	−	0.293423i	0.838431	+	0.545008i	$0.183473\pi$
$774$		0			0
$775$	−4.16071e16			−0.192025
$776$		0			0
$777$			1.29280e17i			0.587497i
$778$		0			0
$779$	3.00803e16	+	3.00803e16i	0.134604	+	0.134604i
$780$		0			0
$781$	5.43804e16	+	5.43804e16i	0.239627	+	0.239627i
$782$		0			0
$783$			1.25174e17i			0.543178i
$784$		0			0
$785$	3.62704e17			1.55001
$786$		0			0
$787$	−1.42157e17	+	1.42157e17i	−0.598301	+	0.598301i	−0.939860	−	0.341559i	$-0.889045\pi$
$787$	−1.42157e17	+	1.42157e17i	−0.598301	+	0.598301i	0.341559	+	0.939860i	$0.389045\pi$
$788$		0			0
$789$	1.09152e16	−	1.09152e16i	0.0452449	−	0.0452449i
$790$		0			0
$791$	3.42996e17			1.40033
$792$		0			0
$793$		−	6.26207e15i		−	0.0251813i
$794$		0			0
$795$	−1.09470e17	−	1.09470e17i	−0.433603	−	0.433603i
$796$		0			0
$797$	6.47111e16	+	6.47111e16i	0.252481	+	0.252481i	0.821987	−	0.569506i	$-0.192865\pi$
$797$	6.47111e16	+	6.47111e16i	0.252481	+	0.252481i	−0.569506	+	0.821987i	$0.692865\pi$
$798$		0			0
$799$			1.44202e17i			0.554230i
$800$		0			0
$801$	−3.29899e17			−1.24907
$802$		0			0
$803$	2.25045e17	−	2.25045e17i	0.839413	−	0.839413i
$804$		0			0
$805$	1.98561e17	−	1.98561e17i	0.729656	−	0.729656i
$806$		0			0
$807$	−2.07888e15			−0.00752643
$808$		0			0
$809$		−	3.42899e17i		−	1.22314i	−0.791192	−	0.611568i	$-0.790539\pi$
$809$		−	3.42899e17i		−	1.22314i	0.791192	−	0.611568i	$-0.209461\pi$
$810$		0			0
$811$	2.40290e16	+	2.40290e16i	0.0844522	+	0.0844522i	0.748071	−	0.663619i	$-0.230980\pi$
$811$	2.40290e16	+	2.40290e16i	0.0844522	+	0.0844522i	−0.663619	+	0.748071i	$0.730980\pi$
$812$		0			0
$813$	5.47680e16	+	5.47680e16i	0.189664	+	0.189664i
$814$		0			0
$815$		−	1.33699e17i		−	0.456229i
$816$		0			0
$817$	2.25720e17			0.758994
$818$		0			0
$819$	−6.32310e16	+	6.32310e16i	−0.209521	+	0.209521i
$820$		0			0
$821$	−8.18964e16	+	8.18964e16i	−0.267427	+	0.267427i	−0.828063	−	0.560635i	$-0.810557\pi$
$821$	−8.18964e16	+	8.18964e16i	−0.267427	+	0.267427i	0.560635	+	0.828063i	$0.310557\pi$
$822$		0			0
$823$	5.02910e16			0.161842			0.0809210	−	0.996721i	$-0.474214\pi$
$823$	5.02910e16			0.161842			0.0809210	+	0.996721i	$0.474214\pi$
$824$		0			0
$825$		−	1.19971e16i		−	0.0380498i
$826$		0			0
$827$	−1.53905e17	−	1.53905e17i	−0.481081	−	0.481081i	0.424396	−	0.905477i	$-0.360487\pi$
$827$	−1.53905e17	−	1.53905e17i	−0.481081	−	0.481081i	−0.905477	+	0.424396i	$0.860487\pi$
$828$		0			0
$829$	−5.98178e16	−	5.98178e16i	−0.184291	−	0.184291i	0.608932	−	0.793223i	$-0.291598\pi$
$829$	−5.98178e16	−	5.98178e16i	−0.184291	−	0.184291i	−0.793223	+	0.608932i	$0.791598\pi$
$830$		0			0
$831$		−	7.78577e16i		−	0.236426i
$832$		0			0
$833$	−4.05140e16			−0.121265
$834$		0			0
$835$	1.05609e17	−	1.05609e17i	0.311588	−	0.311588i
$836$		0			0
$837$	−2.68007e17	+	2.68007e17i	−0.779459	+	0.779459i
$838$		0			0
$839$	−6.70932e17			−1.92356			−0.961782	−	0.273816i	$-0.911714\pi$
$839$	−6.70932e17			−1.92356			−0.961782	+	0.273816i	$0.911714\pi$
$840$		0			0
$841$		−	1.39088e17i		−	0.393111i
$842$		0			0
$843$	−1.52060e17	−	1.52060e17i	−0.423691	−	0.423691i
$844$		0			0
$845$	−2.07527e17	−	2.07527e17i	−0.570077	−	0.570077i
$846$		0			0
$847$		−	1.02838e17i		−	0.278517i
$848$		0			0
$849$	−1.66408e17			−0.444352
$850$		0			0
$851$	−5.44996e17	+	5.44996e17i	−1.43488	+	1.43488i
$852$		0			0
$853$	1.04290e17	−	1.04290e17i	0.270737	−	0.270737i	−0.558660	−	0.829397i	$-0.688684\pi$
$853$	1.04290e17	−	1.04290e17i	0.270737	−	0.270737i	0.829397	+	0.558660i	$0.188684\pi$
$854$		0			0
$855$	−2.57977e17			−0.660365
$856$		0			0
$857$			7.69097e16i			0.194132i	0.995278	+	0.0970658i	$0.0309457\pi$
$857$			7.69097e16i			0.194132i	−0.995278	+	0.0970658i	$0.969054\pi$
$858$		0			0
$859$	−4.11016e16	−	4.11016e16i	−0.102306	−	0.102306i	0.654101	−	0.756407i	$-0.273047\pi$
$859$	−4.11016e16	−	4.11016e16i	−0.102306	−	0.102306i	−0.756407	+	0.654101i	$0.773047\pi$
$860$		0			0
$861$	−2.31251e16	−	2.31251e16i	−0.0567629	−	0.0567629i
$862$		0			0
$863$			7.36833e16i			0.178363i	0.996015	+	0.0891814i	$0.0284251\pi$
$863$			7.36833e16i			0.178363i	−0.996015	+	0.0891814i	$0.971575\pi$
$864$		0			0
$865$	1.76186e17			0.420604
$866$		0			0
$867$	−3.90343e16	+	3.90343e16i	−0.0919035	+	0.0919035i
$868$		0			0
$869$	−4.01537e16	+	4.01537e16i	−0.0932411	+	0.0932411i
$870$		0			0
$871$	−5.43752e15			−0.0124535
$872$		0			0
$873$		−	4.64496e17i		−	1.04929i
$874$		0			0
$875$	3.07541e17	+	3.07541e17i	0.685258	+	0.685258i
$876$		0			0
$877$	−1.20503e17	−	1.20503e17i	−0.264851	−	0.264851i	0.562170	−	0.827021i	$-0.309966\pi$
$877$	−1.20503e17	−	1.20503e17i	−0.264851	−	0.264851i	−0.827021	+	0.562170i	$0.809966\pi$
$878$		0			0
$879$			1.31921e17i			0.286011i
$880$		0			0
$881$	3.54308e17			0.757749			0.378874	−	0.925448i	$-0.376311\pi$
$881$	3.54308e17			0.757749			0.378874	+	0.925448i	$0.376311\pi$
$882$		0			0
$883$	−5.08816e17	+	5.08816e17i	−1.07349	+	1.07349i	−0.0764093	+	0.997077i	$0.524346\pi$
$883$	−5.08816e17	+	5.08816e17i	−1.07349	+	1.07349i	−0.997077	+	0.0764093i	$0.975654\pi$
$884$		0			0
$885$	1.81189e16	−	1.81189e16i	0.0377114	−	0.0377114i
$886$		0			0
$887$	8.31898e16			0.170816			0.0854080	−	0.996346i	$-0.472781\pi$
$887$	8.31898e16			0.170816			0.0854080	+	0.996346i	$0.472781\pi$
$888$		0			0
$889$		−	7.84306e17i		−	1.58882i
$890$		0			0
$891$	1.76723e17	+	1.76723e17i	0.353206	+	0.353206i
$892$		0			0
$893$	−2.01563e17	−	2.01563e17i	−0.397468	−	0.397468i
$894$		0			0
$895$		−	8.11583e17i		−	1.57905i
$896$		0			0
$897$	8.72310e16			0.167462
$898$		0			0
$899$	−4.59747e17	+	4.59747e17i	−0.870885	+	0.870885i
$900$		0			0
$901$	5.33496e17	−	5.33496e17i	0.997201	−	0.997201i
$902$		0			0
$903$	−1.73529e17			−0.320070
$904$		0			0
$905$			3.59520e17i			0.654382i
$906$		0			0
$907$	−8.85242e16	−	8.85242e16i	−0.159008	−	0.159008i	0.623119	−	0.782127i	$-0.285865\pi$
$907$	−8.85242e16	−	8.85242e16i	−0.159008	−	0.159008i	−0.782127	+	0.623119i	$0.785865\pi$
$908$		0			0
$909$	−3.97209e15	−	3.97209e15i	−0.00704102	−	0.00704102i
$910$		0			0
$911$			2.64384e17i			0.462515i	0.972893	+	0.231257i	$0.0742839\pi$
$911$			2.64384e17i			0.462515i	−0.972893	+	0.231257i	$0.925716\pi$
$912$		0			0
$913$	−8.27602e17			−1.42888
$914$		0			0
$915$	−9.82063e15	+	9.82063e15i	−0.0167345	+	0.0167345i
$916$		0			0
$917$	−2.22500e17	+	2.22500e17i	−0.374209	+	0.374209i
$918$		0			0
$919$	6.73471e17			1.11796			0.558979	−	0.829182i	$-0.311193\pi$
$919$	6.73471e17			1.11796			0.558979	+	0.829182i	$0.311193\pi$
$920$		0			0
$921$			2.82348e17i			0.462622i
$922$		0			0
$923$	−6.63283e16	−	6.63283e16i	−0.107273	−	0.107273i
$924$		0			0
$925$	−9.14228e16	−	9.14228e16i	−0.145950	−	0.145950i
$926$		0			0
$927$			2.65299e16i			0.0418079i
$928$		0			0
$929$	7.06289e17			1.09872			0.549361	−	0.835585i	$-0.314871\pi$
$929$	7.06289e17			1.09872			0.549361	+	0.835585i	$0.314871\pi$
$930$		0			0
$931$	5.66299e16	−	5.66299e16i	0.0869656	−	0.0869656i
$932$		0			0
$933$	−1.03270e16	+	1.03270e16i	−0.0156561	+	0.0156561i
$934$		0			0
$935$	−4.22900e17			−0.632947
$936$		0			0
$937$		−	5.68113e17i		−	0.839454i	−0.907650	−	0.419727i	$-0.862126\pi$
$937$		−	5.68113e17i		−	0.839454i	0.907650	−	0.419727i	$-0.137874\pi$
$938$		0			0
$939$	−1.48920e16	−	1.48920e16i	−0.0217250	−	0.0217250i
$940$		0			0
$941$	−4.35025e17	−	4.35025e17i	−0.626581	−	0.626581i	0.320626	−	0.947206i	$-0.396107\pi$
$941$	−4.35025e17	−	4.35025e17i	−0.626581	−	0.626581i	−0.947206	+	0.320626i	$0.896107\pi$
$942$		0			0
$943$		−	1.94973e17i		−	0.277271i
$944$		0			0
$945$	4.29105e17			0.602521
$946$		0			0
$947$	−2.99509e17	+	2.99509e17i	−0.415250	+	0.415250i	−0.883563	−	0.468312i	$-0.844862\pi$
$947$	−2.99509e17	+	2.99509e17i	−0.415250	+	0.415250i	0.468312	+	0.883563i	$0.344862\pi$
$948$		0			0
$949$	−2.74489e17	+	2.74489e17i	−0.375775	+	0.375775i
$950$		0			0
$951$	−1.89535e17			−0.256216
$952$		0			0
$953$		−	6.34898e17i		−	0.847514i	−0.905776	−	0.423757i	$-0.860711\pi$
$953$		−	6.34898e17i		−	0.847514i	0.905776	−	0.423757i	$-0.139289\pi$
$954$		0			0
$955$	−3.76226e17	−	3.76226e17i	−0.495939	−	0.495939i
$956$		0			0
$957$	−1.32564e17	−	1.32564e17i	−0.172566	−	0.172566i
$958$		0			0
$959$			1.34367e18i			1.72735i
$960$		0			0
$961$	−1.18105e18			−1.49944
$962$		0			0
$963$	2.67940e17	−	2.67940e17i	0.335954	−	0.335954i
$964$		0			0
$965$	−5.86398e17	+	5.86398e17i	−0.726154	+	0.726154i
$966$		0			0
$967$	−1.28709e18			−1.57416			−0.787082	−	0.616849i	$-0.788409\pi$
$967$	−1.28709e18			−1.57416			−0.787082	+	0.616849i	$0.788409\pi$
$968$		0			0
$969$			2.05716e17i			0.248499i
$970$		0			0
$971$	−6.58185e17	−	6.58185e17i	−0.785295	−	0.785295i	0.195424	−	0.980719i	$-0.437392\pi$
$971$	−6.58185e17	−	6.58185e17i	−0.785295	−	0.785295i	−0.980719	+	0.195424i	$0.937392\pi$
$972$		0			0
$973$	7.59638e17	+	7.59638e17i	0.895220	+	0.895220i
$974$		0			0
$975$			1.46330e16i			0.0170335i
$976$		0			0
$977$	−1.36846e18			−1.57349			−0.786744	−	0.617280i	$-0.788235\pi$
$977$	−1.36846e18			−1.57349			−0.786744	+	0.617280i	$0.788235\pi$
$978$		0			0
$979$	7.55923e17	−	7.55923e17i	0.858581	−	0.858581i
$980$		0			0
$981$	−1.26683e17	+	1.26683e17i	−0.142136	+	0.142136i
$982$		0			0
$983$	8.26375e17			0.915917			0.457958	−	0.888974i	$-0.348581\pi$
$983$	8.26375e17			0.915917			0.457958	+	0.888974i	$0.348581\pi$
$984$		0			0
$985$		−	4.19749e17i		−	0.459592i
$986$		0			0
$987$	1.54957e17	+	1.54957e17i	0.167613	+	0.167613i
$988$		0			0
$989$	−7.31530e17	−	7.31530e17i	−0.781726	−	0.781726i
$990$		0			0
$991$		−	6.10527e17i		−	0.644560i	−0.946644	−	0.322280i	$-0.895551\pi$
$991$		−	6.10527e17i		−	0.644560i	0.946644	−	0.322280i	$-0.104449\pi$
$992$		0			0
$993$	−2.23723e17			−0.233354
$994$		0			0
$995$	1.03541e18	−	1.03541e18i	1.06702	−	1.06702i
$996$		0			0
$997$	1.25089e18	−	1.25089e18i	1.27365	−	1.27365i	0.329484	−	0.944161i	$-0.393125\pi$
$997$	1.25089e18	−	1.25089e18i	1.27365	−	1.27365i	0.944161	−	0.329484i	$-0.106875\pi$
$998$		0			0
$999$	−1.17778e18			−1.18487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.13.f.a.95.14		46
4.3	odd	2		128.13.f.b.95.10		46
8.3	odd	2		16.13.f.a.3.18	✓	46
8.5	even	2		64.13.f.a.47.10		46
16.3	odd	4		64.13.f.a.15.10		46
16.5	even	4		128.13.f.b.31.10		46
16.11	odd	4	inner	128.13.f.a.31.14		46
16.13	even	4		16.13.f.a.11.18	yes	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.13.f.a.3.18	✓	46	8.3	odd	2
16.13.f.a.11.18	yes	46	16.13	even	4
64.13.f.a.15.10		46	16.3	odd	4
64.13.f.a.47.10		46	8.5	even	2
128.13.f.a.31.14		46	16.11	odd	4	inner
128.13.f.a.95.14		46	1.1	even	1	trivial
128.13.f.b.31.10		46	16.5	even	4
128.13.f.b.95.10		46	4.3	odd	2

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:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(193.300 - 193.300i) q^{3} +(10355.8 - 10355.8i) q^{5} +108466. q^{7} +456712. i q^{9} +O(q^{10})\)	\(q+(193.300 - 193.300i) q^{3} +(10355.8 - 10355.8i) q^{5} +108466. q^{7} +456712. i q^{9} +(-1.04650e6 - 1.04650e6i) q^{11} +(1.27642e6 + 1.27642e6i) q^{13} -4.00356e6i q^{15} +1.95112e7 q^{17} +(-2.72724e7 + 2.72724e7i) q^{19} +(2.09664e7 - 2.09664e7i) q^{21} +1.76773e8 q^{23} +2.96535e7i q^{25} +(1.91009e8 + 1.91009e8i) q^{27} +(3.27663e8 + 3.27663e8i) q^{29} +1.40311e9i q^{31} -4.04575e8 q^{33} +(1.12326e9 - 1.12326e9i) q^{35} +(-3.08303e9 + 3.08303e9i) q^{37} +4.93464e8 q^{39} -1.10296e9i q^{41} +(-4.13826e9 - 4.13826e9i) q^{43} +(4.72963e9 + 4.72963e9i) q^{45} +7.39074e9i q^{47} -2.07645e9 q^{49} +(3.77150e9 - 3.77150e9i) q^{51} +(2.73431e10 - 2.73431e10i) q^{53} -2.16748e10 q^{55} +1.05435e10i q^{57} +(4.52570e9 + 4.52570e9i) q^{59} +(-2.45297e9 - 2.45297e9i) q^{61} +4.95376e10i q^{63} +2.64369e10 q^{65} +(-2.12998e9 + 2.12998e9i) q^{67} +(3.41701e10 - 3.41701e10i) q^{69} -5.19641e10 q^{71} +2.15045e11i q^{73} +(5.73201e9 + 5.73201e9i) q^{75} +(-1.13509e11 - 1.13509e11i) q^{77} -3.83696e10i q^{79} -1.68871e11 q^{81} +(3.95415e11 - 3.95415e11i) q^{83} +(2.02055e11 - 2.02055e11i) q^{85} +1.26674e11 q^{87} +7.22335e11i q^{89} +(1.38448e11 + 1.38448e11i) q^{91} +(2.71220e11 + 2.71220e11i) q^{93} +5.64857e11i q^{95} -1.01704e12 q^{97} +(4.77948e11 - 4.77948e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 46 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	\( 46 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 2668318 q^{11} + 2 q^{13} - 4 q^{17} + 51868606 q^{19} + 1062884 q^{21} - 298270076 q^{23} + 970053760 q^{27} - 704570398 q^{29} - 4 q^{33} - 3815032900 q^{35} - 364298398 q^{37} - 15553507196 q^{39} + 363863518 q^{43} - 489344130 q^{45} + 67229109258 q^{49} + 33806024892 q^{51} + 11168756642 q^{53} + 74491808260 q^{55} + 104334793054 q^{59} + 106371743810 q^{61} - 75186419620 q^{65} - 43778233922 q^{67} + 214340079908 q^{69} + 188251854340 q^{71} + 308961520610 q^{75} + 341607754084 q^{77} - 941431788274 q^{81} - 1025936323202 q^{83} - 436332718748 q^{85} - 2368412421756 q^{87} - 2028231531652 q^{91} - 1534541270080 q^{93} - 4 q^{97} + 4950023059646 q^{99}+O(q^{100}) \) 46 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 + 2668318 * q^11 + 2 * q^13 - 4 * q^17 + 51868606 * q^19 + 1062884 * q^21 - 298270076 * q^23 + 970053760 * q^27 - 704570398 * q^29 - 4 * q^33 - 3815032900 * q^35 - 364298398 * q^37 - 15553507196 * q^39 + 363863518 * q^43 - 489344130 * q^45 + 67229109258 * q^49 + 33806024892 * q^51 + 11168756642 * q^53 + 74491808260 * q^55 + 104334793054 * q^59 + 106371743810 * q^61 - 75186419620 * q^65 - 43778233922 * q^67 + 214340079908 * q^69 + 188251854340 * q^71 + 308961520610 * q^75 + 341607754084 * q^77 - 941431788274 * q^81 - 1025936323202 * q^83 - 436332718748 * q^85 - 2368412421756 * q^87 - 2028231531652 * q^91 - 1534541270080 * q^93 - 4 * q^97 + 4950023059646 * q^99

Introduction

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