LMFDB - Embedded newform 128.5.f.b.95.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,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, 5, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
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:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + \cdots + 2097152 $ x^14 - 4x^13 + 15x^12 - 34x^11 + 62x^10 - 312x^9 + 1432x^8 - 4960x^7 + 11456x^6 - 19968x^5 + 31744x^4 - 139264x^3 + 491520x^2 - 1048576*x + 2097152
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{42} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.6
Root			$0.336831 + 2.80830i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.5.f.b.31.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.86839 - 7.86839i) q^{3} +(-27.2309 + 27.2309i) q^{5} +50.3097 q^{7} -42.8233i q^{9} +O(q^{10})$	\(q+(7.86839 - 7.86839i) q^{3} +(-27.2309 + 27.2309i) q^{5} +50.3097 q^{7} -42.8233i q^{9} +(53.1047 + 53.1047i) q^{11} +(125.128 + 125.128i) q^{13} +428.528i q^{15} +286.271 q^{17} +(99.5010 - 99.5010i) q^{19} +(395.857 - 395.857i) q^{21} -100.505 q^{23} -858.049i q^{25} +(300.390 + 300.390i) q^{27} +(-343.872 - 343.872i) q^{29} -208.400i q^{31} +835.697 q^{33} +(-1369.98 + 1369.98i) q^{35} +(1159.47 - 1159.47i) q^{37} +1969.12 q^{39} +2335.63i q^{41} +(2079.41 + 2079.41i) q^{43} +(1166.12 + 1166.12i) q^{45} +1054.04i q^{47} +130.069 q^{49} +(2252.49 - 2252.49i) q^{51} +(-2136.46 + 2136.46i) q^{53} -2892.18 q^{55} -1565.83i q^{57} +(-3721.44 - 3721.44i) q^{59} +(-2496.46 - 2496.46i) q^{61} -2154.43i q^{63} -6814.72 q^{65} +(329.116 - 329.116i) q^{67} +(-790.817 + 790.817i) q^{69} -1040.71 q^{71} -2673.24i q^{73} +(-6751.46 - 6751.46i) q^{75} +(2671.68 + 2671.68i) q^{77} -4475.80i q^{79} +8195.85 q^{81} +(-1457.69 + 1457.69i) q^{83} +(-7795.43 + 7795.43i) q^{85} -5411.44 q^{87} +1146.97i q^{89} +(6295.17 + 6295.17i) q^{91} +(-1639.78 - 1639.78i) q^{93} +5419.01i q^{95} -13101.5 q^{97} +(2274.11 - 2274.11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7	$ 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 94 q^{11} + 2 q^{13} - 4 q^{17} + 706 q^{19} + 164 q^{21} + 1148 q^{23} + 1664 q^{27} - 862 q^{29} - 4 q^{33} - 1340 q^{35} + 1826 q^{37} + 2684 q^{39} - 1694 q^{43} - 1410 q^{45} + 682 q^{49} + 3012 q^{51} + 482 q^{53} - 11780 q^{55} + 2786 q^{59} + 3778 q^{61} - 2020 q^{65} - 7998 q^{67} - 9628 q^{69} + 19964 q^{71} - 17570 q^{75} + 9508 q^{77} + 1454 q^{81} + 17282 q^{83} - 9948 q^{85} - 49284 q^{87} + 28036 q^{91} - 8896 q^{93} - 4 q^{97} - 49214 q^{99}+O(q^{100}) $ 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 94 * q^11 + 2 * q^13 - 4 * q^17 + 706 * q^19 + 164 * q^21 + 1148 * q^23 + 1664 * q^27 - 862 * q^29 - 4 * q^33 - 1340 * q^35 + 1826 * q^37 + 2684 * q^39 - 1694 * q^43 - 1410 * q^45 + 682 * q^49 + 3012 * q^51 + 482 * q^53 - 11780 * q^55 + 2786 * q^59 + 3778 * q^61 - 2020 * q^65 - 7998 * q^67 - 9628 * q^69 + 19964 * q^71 - 17570 * q^75 + 9508 * q^77 + 1454 * q^81 + 17282 * q^83 - 9948 * q^85 - 49284 * q^87 + 28036 * q^91 - 8896 * q^93 - 4 * q^97 - 49214 * 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
$3$	7.86839	−	7.86839i	0.874266	−	0.874266i	−0.118668	−	0.992934i	$-0.537862\pi$
$3$	7.86839	−	7.86839i	0.874266	−	0.874266i	0.992934	+	0.118668i	$0.0378624\pi$
$4$		0			0
$5$	−27.2309	+	27.2309i	−1.08924	+	1.08924i	−0.0936308	+	0.995607i	$0.529847\pi$
$5$	−27.2309	+	27.2309i	−1.08924	+	1.08924i	−0.995607	+	0.0936308i	$0.970153\pi$
$6$		0			0
$7$	50.3097			1.02673			0.513365	−	0.858171i	$-0.328399\pi$
$7$	50.3097			1.02673			0.513365	+	0.858171i	$0.328399\pi$
$8$		0			0
$9$		−	42.8233i		−	0.528682i
$10$		0			0
$11$	53.1047	+	53.1047i	0.438881	+	0.438881i	0.891635	−	0.452754i	$-0.149558\pi$
$11$	53.1047	+	53.1047i	0.438881	+	0.438881i	−0.452754	+	0.891635i	$0.649558\pi$
$12$		0			0
$13$	125.128	+	125.128i	0.740404	+	0.740404i	0.972656	−	0.232252i	$-0.0746094\pi$
$13$	125.128	+	125.128i	0.740404	+	0.740404i	−0.232252	+	0.972656i	$0.574609\pi$
$14$		0			0
$15$			428.528i			1.90457i
$16$		0			0
$17$	286.271			0.990557			0.495279	−	0.868734i	$-0.335066\pi$
$17$	286.271			0.990557			0.495279	+	0.868734i	$0.335066\pi$
$18$		0			0
$19$	99.5010	−	99.5010i	0.275626	−	0.275626i	−0.555734	−	0.831360i	$-0.687563\pi$
$19$	99.5010	−	99.5010i	0.275626	−	0.275626i	0.831360	+	0.555734i	$0.187563\pi$
$20$		0			0
$21$	395.857	−	395.857i	0.897635	−	0.897635i
$22$		0			0
$23$	−100.505			−0.189991			−0.0949957	−	0.995478i	$-0.530284\pi$
$23$	−100.505			−0.189991			−0.0949957	+	0.995478i	$0.530284\pi$
$24$		0			0
$25$		−	858.049i		−	1.37288i
$26$		0			0
$27$	300.390	+	300.390i	0.412057	+	0.412057i
$28$		0			0
$29$	−343.872	−	343.872i	−0.408885	−	0.408885i	0.472465	−	0.881350i	$-0.343364\pi$
$29$	−343.872	−	343.872i	−0.408885	−	0.408885i	−0.881350	+	0.472465i	$0.843364\pi$
$30$		0			0
$31$		−	208.400i		−	0.216858i	−0.994104	−	0.108429i	$-0.965418\pi$
$31$		−	208.400i		−	0.216858i	0.994104	−	0.108429i	$-0.0345820\pi$
$32$		0			0
$33$	835.697			0.767398
$34$		0			0
$35$	−1369.98	+	1369.98i	−1.11835	+	1.11835i
$36$		0			0
$37$	1159.47	−	1159.47i	0.846946	−	0.846946i	−0.142805	−	0.989751i	$-0.545612\pi$
$37$	1159.47	−	1159.47i	0.846946	−	0.846946i	0.989751	+	0.142805i	$0.0456122\pi$
$38$		0			0
$39$	1969.12			1.29462
$40$		0			0
$41$			2335.63i			1.38943i	0.719286	+	0.694714i	$0.244469\pi$
$41$			2335.63i			1.38943i	−0.719286	+	0.694714i	$0.755531\pi$
$42$		0			0
$43$	2079.41	+	2079.41i	1.12461	+	1.12461i	0.991039	+	0.133575i	$0.0426458\pi$
$43$	2079.41	+	2079.41i	1.12461	+	1.12461i	0.133575	+	0.991039i	$0.457354\pi$
$44$		0			0
$45$	1166.12	+	1166.12i	0.575861	+	0.575861i
$46$		0			0
$47$			1054.04i			0.477159i	0.971123	+	0.238580i	$0.0766818\pi$
$47$			1054.04i			0.477159i	−0.971123	+	0.238580i	$0.923318\pi$
$48$		0			0
$49$	130.069			0.0541728
$50$		0			0
$51$	2252.49	−	2252.49i	0.866011	−	0.866011i
$52$		0			0
$53$	−2136.46	+	2136.46i	−0.760576	+	0.760576i	−0.976426	−	0.215850i	$-0.930748\pi$
$53$	−2136.46	+	2136.46i	−0.760576	+	0.760576i	0.215850	+	0.976426i	$0.430748\pi$
$54$		0			0
$55$	−2892.18			−0.956092
$56$		0			0
$57$		−	1565.83i		−	0.481941i
$58$		0			0
$59$	−3721.44	−	3721.44i	−1.06907	−	1.06907i	−0.997431	−	0.0716407i	$-0.977177\pi$
$59$	−3721.44	−	3721.44i	−1.06907	−	1.06907i	−0.0716407	−	0.997431i	$-0.522823\pi$
$60$		0			0
$61$	−2496.46	−	2496.46i	−0.670912	−	0.670912i	0.287014	−	0.957926i	$-0.407337\pi$
$61$	−2496.46	−	2496.46i	−0.670912	−	0.670912i	−0.957926	+	0.287014i	$0.907337\pi$
$62$		0			0
$63$		−	2154.43i		−	0.542814i
$64$		0			0
$65$	−6814.72			−1.61295
$66$		0			0
$67$	329.116	−	329.116i	0.0733162	−	0.0733162i	−0.669498	−	0.742814i	$-0.733491\pi$
$67$	329.116	−	329.116i	0.0733162	−	0.0733162i	0.742814	+	0.669498i	$0.233491\pi$
$68$		0			0
$69$	−790.817	+	790.817i	−0.166103	+	0.166103i
$70$		0			0
$71$	−1040.71			−0.206449			−0.103225	−	0.994658i	$-0.532916\pi$
$71$	−1040.71			−0.206449			−0.103225	+	0.994658i	$0.532916\pi$
$72$		0			0
$73$		−	2673.24i		−	0.501639i	−0.968034	−	0.250820i	$-0.919300\pi$
$73$		−	2673.24i		−	0.501639i	0.968034	−	0.250820i	$-0.0807001\pi$
$74$		0			0
$75$	−6751.46	−	6751.46i	−1.20026	−	1.20026i
$76$		0			0
$77$	2671.68	+	2671.68i	0.450612	+	0.450612i
$78$		0			0
$79$		−	4475.80i		−	0.717161i	−0.933499	−	0.358580i	$-0.883261\pi$
$79$		−	4475.80i		−	0.717161i	0.933499	−	0.358580i	$-0.116739\pi$
$80$		0			0
$81$	8195.85			1.24918
$82$		0			0
$83$	−1457.69	+	1457.69i	−0.211597	+	0.211597i	−0.804945	−	0.593349i	$-0.797805\pi$
$83$	−1457.69	+	1457.69i	−0.211597	+	0.211597i	0.593349	+	0.804945i	$0.297805\pi$
$84$		0			0
$85$	−7795.43	+	7795.43i	−1.07895	+	1.07895i
$86$		0			0
$87$	−5411.44			−0.714948
$88$		0			0
$89$			1146.97i			0.144801i	0.997376	+	0.0724003i	$0.0230659\pi$
$89$			1146.97i			0.144801i	−0.997376	+	0.0724003i	$0.976934\pi$
$90$		0			0
$91$	6295.17	+	6295.17i	0.760194	+	0.760194i
$92$		0			0
$93$	−1639.78	−	1639.78i	−0.189592	−	0.189592i
$94$		0			0
$95$			5419.01i			0.600444i
$96$		0			0
$97$	−13101.5			−1.39244			−0.696222	−	0.717826i	$-0.745137\pi$
$97$	−13101.5			−1.39244			−0.696222	+	0.717826i	$0.745137\pi$
$98$		0			0
$99$	2274.11	−	2274.11i	0.232029	−	0.232029i
$100$		0			0
$101$	7488.18	−	7488.18i	0.734063	−	0.734063i	−0.237359	−	0.971422i	$-0.576282\pi$
$101$	7488.18	−	7488.18i	0.734063	−	0.734063i	0.971422	+	0.237359i	$0.0762818\pi$
$102$		0			0
$103$	7141.23			0.673129			0.336565	−	0.941660i	$-0.390735\pi$
$103$	7141.23			0.673129			0.336565	+	0.941660i	$0.390735\pi$
$104$		0			0
$105$			21559.1i			1.95547i
$106$		0			0
$107$	−1794.26	−	1794.26i	−0.156718	−	0.156718i	0.624393	−	0.781111i	$-0.285346\pi$
$107$	−1794.26	−	1794.26i	−0.156718	−	0.156718i	−0.781111	+	0.624393i	$0.785346\pi$
$108$		0			0
$109$	−5362.57	−	5362.57i	−0.451357	−	0.451357i	0.444448	−	0.895805i	$-0.353400\pi$
$109$	−5362.57	−	5362.57i	−0.451357	−	0.451357i	−0.895805	+	0.444448i	$0.853400\pi$
$110$		0			0
$111$		−	18246.3i		−	1.48091i
$112$		0			0
$113$	−5165.40			−0.404527			−0.202263	−	0.979331i	$-0.564830\pi$
$113$	−5165.40			−0.404527			−0.202263	+	0.979331i	$0.564830\pi$
$114$		0			0
$115$	2736.86	−	2736.86i	0.206946	−	0.206946i
$116$		0			0
$117$	5358.40	−	5358.40i	0.391438	−	0.391438i
$118$		0			0
$119$	14402.2			1.01703
$120$		0			0
$121$		−	9000.79i		−	0.614766i
$122$		0			0
$123$	18377.6	+	18377.6i	1.21473	+	1.21473i
$124$		0			0
$125$	6346.13	+	6346.13i	0.406152	+	0.406152i
$126$		0			0
$127$			22886.9i			1.41899i	0.704711	+	0.709495i	$0.251077\pi$
$127$			22886.9i			1.41899i	−0.704711	+	0.709495i	$0.748923\pi$
$128$		0			0
$129$	32723.3			1.96642
$130$		0			0
$131$	−19202.2	+	19202.2i	−1.11894	+	1.11894i	−0.127048	+	0.991897i	$0.540550\pi$
$131$	−19202.2	+	19202.2i	−1.11894	+	1.11894i	−0.991897	+	0.127048i	$0.959450\pi$
$132$		0			0
$133$	5005.87	−	5005.87i	0.282993	−	0.282993i
$134$		0			0
$135$	−16359.8			−0.897656
$136$		0			0
$137$		−	33680.5i		−	1.79448i	−0.441547	−	0.897238i	$-0.645570\pi$
$137$		−	33680.5i		−	1.79448i	0.441547	−	0.897238i	$-0.354430\pi$
$138$		0			0
$139$	−11747.9	−	11747.9i	−0.608036	−	0.608036i	0.334397	−	0.942432i	$-0.391468\pi$
$139$	−11747.9	−	11747.9i	−0.608036	−	0.608036i	−0.942432	+	0.334397i	$0.891468\pi$
$140$		0			0
$141$	8293.64	+	8293.64i	0.417164	+	0.417164i
$142$		0			0
$143$			13289.8i			0.649899i
$144$		0			0
$145$	18727.9			0.890746
$146$		0			0
$147$	1023.43	−	1023.43i	0.0473615	−	0.0473615i
$148$		0			0
$149$	14877.7	−	14877.7i	0.670136	−	0.670136i	−0.287611	−	0.957747i	$-0.592861\pi$
$149$	14877.7	−	14877.7i	0.670136	−	0.670136i	0.957747	+	0.287611i	$0.0928611\pi$
$150$		0			0
$151$	−8005.74			−0.351114			−0.175557	−	0.984469i	$-0.556173\pi$
$151$	−8005.74			−0.351114			−0.175557	+	0.984469i	$0.556173\pi$
$152$		0			0
$153$		−	12259.1i		−	0.523690i
$154$		0			0
$155$	5674.94	+	5674.94i	0.236210	+	0.236210i
$156$		0			0
$157$	−12150.9	−	12150.9i	−0.492958	−	0.492958i	0.416279	−	0.909237i	$-0.363334\pi$
$157$	−12150.9	−	12150.9i	−0.492958	−	0.492958i	−0.909237	+	0.416279i	$0.863334\pi$
$158$		0			0
$159$			33621.0i			1.32989i
$160$		0			0
$161$	−5056.40			−0.195070
$162$		0			0
$163$	23646.5	−	23646.5i	0.890002	−	0.890002i	−0.104520	−	0.994523i	$-0.533331\pi$
$163$	23646.5	−	23646.5i	0.890002	−	0.890002i	0.994523	+	0.104520i	$0.0333307\pi$
$164$		0			0
$165$	−22756.8	+	22756.8i	−0.835879	+	0.835879i
$166$		0			0
$167$	42493.7			1.52367			0.761836	−	0.647770i	$-0.224298\pi$
$167$	42493.7			1.52367			0.761836	+	0.647770i	$0.224298\pi$
$168$		0			0
$169$			2753.14i			0.0963950i
$170$		0			0
$171$	−4260.96	−	4260.96i	−0.145719	−	0.145719i
$172$		0			0
$173$	16142.1	+	16142.1i	0.539347	+	0.539347i	0.923337	−	0.383990i	$-0.125450\pi$
$173$	16142.1	+	16142.1i	0.539347	+	0.539347i	−0.383990	+	0.923337i	$0.625450\pi$
$174$		0			0
$175$		−	43168.2i		−	1.40957i
$176$		0			0
$177$	−58563.5			−1.86931
$178$		0			0
$179$	22442.0	−	22442.0i	0.700415	−	0.700415i	−0.264084	−	0.964500i	$-0.585070\pi$
$179$	22442.0	−	22442.0i	0.700415	−	0.700415i	0.964500	+	0.264084i	$0.0850698\pi$
$180$		0			0
$181$	9891.06	−	9891.06i	0.301916	−	0.301916i	−0.539847	−	0.841763i	$-0.681518\pi$
$181$	9891.06	−	9891.06i	0.301916	−	0.301916i	0.841763	+	0.539847i	$0.181518\pi$
$182$		0			0
$183$	−39286.3			−1.17311
$184$		0			0
$185$			63146.9i			1.84505i
$186$		0			0
$187$	15202.3	+	15202.3i	0.434737	+	0.434737i
$188$		0			0
$189$	15112.5	+	15112.5i	0.423071	+	0.423071i
$190$		0			0
$191$		−	2033.60i		−	0.0557442i	−0.999611	−	0.0278721i	$-0.991127\pi$
$191$		−	2033.60i		−	0.0557442i	0.999611	−	0.0278721i	$-0.00887311\pi$
$192$		0			0
$193$	29257.4			0.785453			0.392727	−	0.919655i	$-0.371532\pi$
$193$	29257.4			0.785453			0.392727	+	0.919655i	$0.371532\pi$
$194$		0			0
$195$	−53620.9	+	53620.9i	−1.41015	+	1.41015i
$196$		0			0
$197$	−28194.9	+	28194.9i	−0.726504	+	0.726504i	−0.969922	−	0.243417i	$-0.921732\pi$
$197$	−28194.9	+	28194.9i	−0.726504	+	0.726504i	0.243417	+	0.969922i	$0.421732\pi$
$198$		0			0
$199$	54100.9			1.36615			0.683075	−	0.730348i	$-0.260642\pi$
$199$	54100.9			1.36615			0.683075	+	0.730348i	$0.260642\pi$
$200$		0			0
$201$		−	5179.24i		−	0.128196i
$202$		0			0
$203$	−17300.1	−	17300.1i	−0.419814	−	0.419814i
$204$		0			0
$205$	−63601.4	−	63601.4i	−1.51342	−	1.51342i
$206$		0			0
$207$			4303.97i			0.100445i
$208$		0			0
$209$	10567.9			0.241934
$210$		0			0
$211$	31994.1	−	31994.1i	0.718630	−	0.718630i	−0.249694	−	0.968325i	$-0.580330\pi$
$211$	31994.1	−	31994.1i	0.718630	−	0.718630i	0.968325	+	0.249694i	$0.0803301\pi$
$212$		0			0
$213$	−8188.73	+	8188.73i	−0.180492	+	0.180492i
$214$		0			0
$215$	−113249.			−2.44994
$216$		0			0
$217$		−	10484.6i		−	0.222654i
$218$		0			0
$219$	−21034.1	−	21034.1i	−0.438566	−	0.438566i
$220$		0			0
$221$	35820.6	+	35820.6i	0.733412	+	0.733412i
$222$		0			0
$223$		−	94185.8i		−	1.89398i	−0.321261	−	0.946991i	$-0.604107\pi$
$223$		−	94185.8i		−	1.89398i	0.321261	−	0.946991i	$-0.395893\pi$
$224$		0			0
$225$	−36744.4			−0.725816
$226$		0			0
$227$	−62683.9	+	62683.9i	−1.21648	+	1.21648i	−0.247622	+	0.968857i	$0.579649\pi$
$227$	−62683.9	+	62683.9i	−1.21648	+	1.21648i	−0.968857	+	0.247622i	$0.920351\pi$
$228$		0			0
$229$	19781.9	−	19781.9i	0.377221	−	0.377221i	−0.492877	−	0.870099i	$-0.664055\pi$
$229$	19781.9	−	19781.9i	0.377221	−	0.377221i	0.870099	+	0.492877i	$0.164055\pi$
$230$		0			0
$231$	42043.7			0.787910
$232$		0			0
$233$			25062.1i			0.461642i	0.972996	+	0.230821i	$0.0741412\pi$
$233$			25062.1i			0.461642i	−0.972996	+	0.230821i	$0.925859\pi$
$234$		0			0
$235$	−28702.6	−	28702.6i	−0.519740	−	0.519740i
$236$		0			0
$237$	−35217.4	−	35217.4i	−0.626989	−	0.626989i
$238$		0			0
$239$		−	93041.8i		−	1.62885i	−0.580265	−	0.814427i	$-0.697051\pi$
$239$		−	93041.8i		−	1.62885i	0.580265	−	0.814427i	$-0.302949\pi$
$240$		0			0
$241$	−80981.9			−1.39429			−0.697146	−	0.716929i	$-0.745547\pi$
$241$	−80981.9			−1.39429			−0.697146	+	0.716929i	$0.745547\pi$
$242$		0			0
$243$	40156.6	−	40156.6i	0.680056	−	0.680056i
$244$		0			0
$245$	−3541.90	+	3541.90i	−0.0590071	+	0.0590071i
$246$		0			0
$247$	24900.8			0.408149
$248$		0			0
$249$			22939.3i			0.369984i
$250$		0			0
$251$	−25910.0	−	25910.0i	−0.411264	−	0.411264i	0.470915	−	0.882179i	$-0.343924\pi$
$251$	−25910.0	−	25910.0i	−0.411264	−	0.411264i	−0.882179	+	0.470915i	$0.843924\pi$
$252$		0			0
$253$	−5337.31	−	5337.31i	−0.0833837	−	0.0833837i
$254$		0			0
$255$			122675.i			1.88658i
$256$		0			0
$257$	15800.6			0.239225			0.119613	−	0.992821i	$-0.461835\pi$
$257$	15800.6			0.239225			0.119613	+	0.992821i	$0.461835\pi$
$258$		0			0
$259$	58332.6	−	58332.6i	0.869584	−	0.869584i
$260$		0			0
$261$	−14725.7	+	14725.7i	−0.216170	+	0.216170i
$262$		0			0
$263$	−82043.7			−1.18613			−0.593067	−	0.805153i	$-0.702083\pi$
$263$	−82043.7			−1.18613			−0.593067	+	0.805153i	$0.702083\pi$
$264$		0			0
$265$		−	116356.i		−	1.65690i
$266$		0			0
$267$	9024.78	+	9024.78i	0.126594	+	0.126594i
$268$		0			0
$269$	30820.2	+	30820.2i	0.425923	+	0.425923i	0.887237	−	0.461314i	$-0.152622\pi$
$269$	30820.2	+	30820.2i	0.425923	+	0.425923i	−0.461314	+	0.887237i	$0.652622\pi$
$270$		0			0
$271$			110808.i			1.50880i	0.656412	+	0.754402i	$0.272073\pi$
$271$			110808.i			1.50880i	−0.656412	+	0.754402i	$0.727927\pi$
$272$		0			0
$273$	99065.7			1.32922
$274$		0			0
$275$	45566.4	−	45566.4i	0.602531	−	0.602531i
$276$		0			0
$277$	−25634.0	+	25634.0i	−0.334084	+	0.334084i	−0.854135	−	0.520051i	$-0.825913\pi$
$277$	−25634.0	+	25634.0i	−0.334084	+	0.334084i	0.520051	+	0.854135i	$0.325913\pi$
$278$		0			0
$279$	−8924.39			−0.114649
$280$		0			0
$281$			48800.5i			0.618033i	0.951057	+	0.309017i	$0.0999999\pi$
$281$			48800.5i			0.618033i	−0.951057	+	0.309017i	$0.900000\pi$
$282$		0			0
$283$	111466.	+	111466.i	1.39178	+	1.39178i	0.821340	+	0.570439i	$0.193227\pi$
$283$	111466.	+	111466.i	1.39178	+	1.39178i	0.570439	+	0.821340i	$0.306773\pi$
$284$		0			0
$285$	42638.9	+	42638.9i	0.524948	+	0.524948i
$286$		0			0
$287$			117505.i			1.42657i
$288$		0			0
$289$	−1569.88			−0.0187963
$290$		0			0
$291$	−103088.	+	103088.i	−1.21737	+	1.21737i
$292$		0			0
$293$	−13093.1	+	13093.1i	−0.152514	+	0.152514i	−0.779240	−	0.626726i	$-0.784395\pi$
$293$	−13093.1	+	13093.1i	−0.152514	+	0.152514i	0.626726	+	0.779240i	$0.284395\pi$
$294$		0			0
$295$	202676.			2.32895
$296$		0			0
$297$			31904.2i			0.361688i
$298$		0			0
$299$	−12576.1	−	12576.1i	−0.140670	−	0.140670i
$300$		0			0
$301$	104615.	+	104615.i	1.15467	+	1.15467i
$302$		0			0
$303$		−	117840.i		−	1.28353i
$304$		0			0
$305$	135962.			1.46156
$306$		0			0
$307$	−25274.9	+	25274.9i	−0.268171	+	0.268171i	−0.828363	−	0.560192i	$-0.810727\pi$
$307$	−25274.9	+	25274.9i	−0.268171	+	0.268171i	0.560192	+	0.828363i	$0.310727\pi$
$308$		0			0
$309$	56190.0	−	56190.0i	0.588494	−	0.588494i
$310$		0			0
$311$	53808.0			0.556322			0.278161	−	0.960534i	$-0.410275\pi$
$311$	53808.0			0.556322			0.278161	+	0.960534i	$0.410275\pi$
$312$		0			0
$313$		−	137345.i		−	1.40192i	−0.713199	−	0.700961i	$-0.752755\pi$
$313$		−	137345.i		−	1.40192i	0.713199	−	0.700961i	$-0.247245\pi$
$314$		0			0
$315$	58667.1	+	58667.1i	0.591253	+	0.591253i
$316$		0			0
$317$	−115546.	−	115546.i	−1.14984	−	1.14984i	−0.986584	−	0.163252i	$-0.947802\pi$
$317$	−115546.	−	115546.i	−1.14984	−	1.14984i	−0.163252	−	0.986584i	$-0.552198\pi$
$318$		0			0
$319$		−	36522.4i		−	0.358904i
$320$		0			0
$321$	−28235.9			−0.274026
$322$		0			0
$323$	28484.2	−	28484.2i	0.273023	−	0.273023i
$324$		0			0
$325$	107366.	−	107366.i	1.01648	−	1.01648i
$326$		0			0
$327$	−84389.7			−0.789213
$328$		0			0
$329$			53028.7i			0.489913i
$330$		0			0
$331$	−68009.3	−	68009.3i	−0.620744	−	0.620744i	0.324978	−	0.945722i	$-0.394643\pi$
$331$	−68009.3	−	68009.3i	−0.620744	−	0.620744i	−0.945722	+	0.324978i	$0.894643\pi$
$332$		0			0
$333$	−49652.2	−	49652.2i	−0.447765	−	0.447765i
$334$		0			0
$335$			17924.3i			0.159718i
$336$		0			0
$337$	−146703.			−1.29176			−0.645878	−	0.763440i	$-0.723509\pi$
$337$	−146703.			−1.29176			−0.645878	+	0.763440i	$0.723509\pi$
$338$		0			0
$339$	−40643.4	+	40643.4i	−0.353664	+	0.353664i
$340$		0			0
$341$	11067.0	−	11067.0i	0.0951749	−	0.0951749i
$342$		0			0
$343$	−114250.			−0.971108
$344$		0			0
$345$		−	43069.4i		−	0.361851i
$346$		0			0
$347$	80120.9	+	80120.9i	0.665406	+	0.665406i	0.956649	−	0.291243i	$-0.0940688\pi$
$347$	80120.9	+	80120.9i	0.665406	+	0.665406i	−0.291243	+	0.956649i	$0.594069\pi$
$348$		0			0
$349$	−100990.	−	100990.i	−0.829143	−	0.829143i	0.158255	−	0.987398i	$-0.449413\pi$
$349$	−100990.	−	100990.i	−0.829143	−	0.829143i	−0.987398	+	0.158255i	$0.949413\pi$
$350$		0			0
$351$			75174.4i			0.610177i
$352$		0			0
$353$	129855.			1.04210			0.521052	−	0.853525i	$-0.325540\pi$
$353$	129855.			1.04210			0.521052	+	0.853525i	$0.325540\pi$
$354$		0			0
$355$	28339.6	−	28339.6i	0.224873	−	0.224873i
$356$		0			0
$357$	113322.	−	113322.i	0.889158	−	0.889158i
$358$		0			0
$359$	−55943.2			−0.434068			−0.217034	−	0.976164i	$-0.569638\pi$
$359$	−55943.2			−0.434068			−0.217034	+	0.976164i	$0.569638\pi$
$360$		0			0
$361$			110520.i			0.848061i
$362$		0			0
$363$	−70821.8	−	70821.8i	−0.537469	−	0.537469i
$364$		0			0
$365$	72794.8	+	72794.8i	0.546405	+	0.546405i
$366$		0			0
$367$		−	144947.i		−	1.07616i	−0.842892	−	0.538082i	$-0.819149\pi$
$367$		−	144947.i		−	1.07616i	0.842892	−	0.538082i	$-0.180851\pi$
$368$		0			0
$369$	100019.			0.734566
$370$		0			0
$371$	−107485.	+	107485.i	−0.780906	+	0.780906i
$372$		0			0
$373$	−24034.7	+	24034.7i	−0.172751	+	0.172751i	−0.788187	−	0.615436i	$-0.788980\pi$
$373$	−24034.7	+	24034.7i	−0.172751	+	0.172751i	0.615436	+	0.788187i	$0.288980\pi$
$374$		0			0
$375$	99867.8			0.710171
$376$		0			0
$377$		−	86056.2i		−	0.605480i
$378$		0			0
$379$	27907.2	+	27907.2i	0.194284	+	0.194284i	0.797544	−	0.603260i	$-0.206132\pi$
$379$	27907.2	+	27907.2i	0.194284	+	0.194284i	−0.603260	+	0.797544i	$0.706132\pi$
$380$		0			0
$381$	180083.	+	180083.i	1.24057	+	1.24057i
$382$		0			0
$383$			96652.7i			0.658895i	0.944174	+	0.329448i	$0.106863\pi$
$383$			96652.7i			0.658895i	−0.944174	+	0.329448i	$0.893137\pi$
$384$		0			0
$385$	−145505.			−0.981648
$386$		0			0
$387$	89047.2	−	89047.2i	0.594564	−	0.594564i
$388$		0			0
$389$	−133129.	+	133129.i	−0.879777	+	0.879777i	−0.993511	−	0.113734i	$-0.963719\pi$
$389$	−133129.	+	133129.i	−0.879777	+	0.879777i	0.113734	+	0.993511i	$0.463719\pi$
$390$		0			0
$391$	−28771.8			−0.188197
$392$		0			0
$393$			302181.i			1.95651i
$394$		0			0
$395$	121880.	+	121880.i	0.781159	+	0.781159i
$396$		0			0
$397$	−33406.1	−	33406.1i	−0.211956	−	0.211956i	0.593142	−	0.805098i	$-0.297887\pi$
$397$	−33406.1	−	33406.1i	−0.211956	−	0.211956i	−0.805098	+	0.593142i	$0.797887\pi$
$398$		0			0
$399$		−	78776.3i		−	0.494823i
$400$		0			0
$401$	−87329.7			−0.543092			−0.271546	−	0.962425i	$-0.587535\pi$
$401$	−87329.7			−0.543092			−0.271546	+	0.962425i	$0.587535\pi$
$402$		0			0
$403$	26076.8	−	26076.8i	0.160562	−	0.160562i
$404$		0			0
$405$	−223181.	+	223181.i	−1.36065	+	1.36065i
$406$		0			0
$407$	123146.			0.743418
$408$		0			0
$409$		−	47133.9i		−	0.281765i	−0.990026	−	0.140883i	$-0.955006\pi$
$409$		−	47133.9i		−	0.281765i	0.990026	−	0.140883i	$-0.0449940\pi$
$410$		0			0
$411$	−265012.	−	265012.i	−1.56885	−	1.56885i
$412$		0			0
$413$	−187224.	−	187224.i	−1.09765	−	1.09765i
$414$		0			0
$415$		−	79388.5i		−	0.460958i
$416$		0			0
$417$	−184874.			−1.06317
$418$		0			0
$419$	70487.1	−	70487.1i	0.401497	−	0.401497i	−0.477264	−	0.878760i	$-0.658371\pi$
$419$	70487.1	−	70487.1i	0.401497	−	0.401497i	0.878760	+	0.477264i	$0.158371\pi$
$420$		0			0
$421$	−109929.	+	109929.i	−0.620225	+	0.620225i	−0.945589	−	0.325364i	$-0.894513\pi$
$421$	−109929.	+	109929.i	−0.620225	+	0.620225i	0.325364	+	0.945589i	$0.394513\pi$
$422$		0			0
$423$	45137.6			0.252266
$424$		0			0
$425$		−	245634.i		−	1.35991i
$426$		0			0
$427$	−125596.	−	125596.i	−0.688845	−	0.688845i
$428$		0			0
$429$	104569.	+	104569.i	0.568184	+	0.568184i
$430$		0			0
$431$			8391.44i			0.0451733i	0.999745	+	0.0225867i	$0.00719017\pi$
$431$			8391.44i			0.0451733i	−0.999745	+	0.0225867i	$0.992810\pi$
$432$		0			0
$433$	112221.			0.598545			0.299272	−	0.954168i	$-0.403256\pi$
$433$	112221.			0.598545			0.299272	+	0.954168i	$0.403256\pi$
$434$		0			0
$435$	147359.	−	147359.i	0.778749	−	0.778749i
$436$		0			0
$437$	−10000.4	+	10000.4i	−0.0523666	+	0.0523666i
$438$		0			0
$439$	−95834.1			−0.497269			−0.248634	−	0.968597i	$-0.579982\pi$
$439$	−95834.1			−0.497269			−0.248634	+	0.968597i	$0.579982\pi$
$440$		0			0
$441$		−	5569.98i		−	0.0286402i
$442$		0			0
$443$	−48800.8	−	48800.8i	−0.248668	−	0.248668i	0.571756	−	0.820424i	$-0.306262\pi$
$443$	−48800.8	−	48800.8i	−0.248668	−	0.248668i	−0.820424	+	0.571756i	$0.806262\pi$
$444$		0			0
$445$	−31233.0	−	31233.0i	−0.157722	−	0.157722i
$446$		0			0
$447$		−	234127.i		−	1.17175i
$448$		0			0
$449$	−246669.			−1.22355			−0.611776	−	0.791031i	$-0.709545\pi$
$449$	−246669.			−1.22355			−0.611776	+	0.791031i	$0.709545\pi$
$450$		0			0
$451$	−124033.	+	124033.i	−0.609794	+	0.609794i
$452$		0			0
$453$	−62992.3	+	62992.3i	−0.306967	+	0.306967i
$454$		0			0
$455$	−342847.			−1.65606
$456$		0			0
$457$			6030.04i			0.0288727i	0.999896	+	0.0144364i	$0.00459540\pi$
$457$			6030.04i			0.0288727i	−0.999896	+	0.0144364i	$0.995405\pi$
$458$		0			0
$459$	85992.8	+	85992.8i	0.408166	+	0.408166i
$460$		0			0
$461$	−13122.6	−	13122.6i	−0.0617473	−	0.0617473i	0.675559	−	0.737306i	$-0.263902\pi$
$461$	−13122.6	−	13122.6i	−0.0617473	−	0.0617473i	−0.737306	+	0.675559i	$0.763902\pi$
$462$		0			0
$463$			408077.i			1.90362i	0.306689	+	0.951810i	$0.400779\pi$
$463$			408077.i			1.90362i	−0.306689	+	0.951810i	$0.599221\pi$
$464$		0			0
$465$	89305.3			0.413020
$466$		0			0
$467$	108240.	−	108240.i	0.496311	−	0.496311i	−0.413977	−	0.910288i	$-0.635860\pi$
$467$	108240.	−	108240.i	0.496311	−	0.496311i	0.910288	+	0.413977i	$0.135860\pi$
$468$		0			0
$469$	16557.8	−	16557.8i	0.0752759	−	0.0752759i
$470$		0			0
$471$	−191216.			−0.861953
$472$		0			0
$473$			220853.i			0.987144i
$474$		0			0
$475$	−85376.7	−	85376.7i	−0.378401	−	0.378401i
$476$		0			0
$477$	91490.1	+	91490.1i	0.402103	+	0.402103i
$478$		0			0
$479$		−	223150.i		−	0.972583i	−0.873797	−	0.486291i	$-0.838349\pi$
$479$		−	223150.i		−	0.972583i	0.873797	−	0.486291i	$-0.161651\pi$
$480$		0			0
$481$	290165.			1.25416
$482$		0			0
$483$	−39785.8	+	39785.8i	−0.170543	+	0.170543i
$484$		0			0
$485$	356767.	−	356767.i	1.51670	−	1.51670i
$486$		0			0
$487$	225880.			0.952399			0.476200	−	0.879337i	$-0.342014\pi$
$487$	225880.			0.952399			0.476200	+	0.879337i	$0.342014\pi$
$488$		0			0
$489$		−	372120.i		−	1.55620i
$490$		0			0
$491$	101698.	+	101698.i	0.421842	+	0.421842i	0.885837	−	0.463996i	$-0.153585\pi$
$491$	101698.	+	101698.i	0.421842	+	0.421842i	−0.463996	+	0.885837i	$0.653585\pi$
$492$		0			0
$493$	−98440.7	−	98440.7i	−0.405024	−	0.405024i
$494$		0			0
$495$			123853.i			0.505469i
$496$		0			0
$497$	−52357.9			−0.211968
$498$		0			0
$499$	−226481.	+	226481.i	−0.909559	+	0.909559i	−0.996236	−	0.0866770i	$-0.972375\pi$
$499$	−226481.	+	226481.i	−0.909559	+	0.909559i	0.0866770	+	0.996236i	$0.472375\pi$
$500$		0			0
$501$	334357.	−	334357.i	1.33209	−	1.33209i
$502$		0			0
$503$	125734.			0.496956			0.248478	−	0.968637i	$-0.420070\pi$
$503$	125734.			0.496956			0.248478	+	0.968637i	$0.420070\pi$
$504$		0			0
$505$			407820.i			1.59914i
$506$		0			0
$507$	21662.8	+	21662.8i	0.0842749	+	0.0842749i
$508$		0			0
$509$	82499.2	+	82499.2i	0.318430	+	0.318430i	0.848164	−	0.529734i	$-0.177708\pi$
$509$	82499.2	+	82499.2i	0.318430	+	0.318430i	−0.529734	+	0.848164i	$0.677708\pi$
$510$		0			0
$511$		−	134490.i		−	0.515048i
$512$		0			0
$513$	59778.1			0.227147
$514$		0			0
$515$	−194462.	+	194462.i	−0.733198	+	0.733198i
$516$		0			0
$517$	−55974.7	+	55974.7i	−0.209416	+	0.209416i
$518$		0			0
$519$	254025.			0.943066
$520$		0			0
$521$			225057.i			0.829120i	0.910022	+	0.414560i	$0.136064\pi$
$521$			225057.i			0.829120i	−0.910022	+	0.414560i	$0.863936\pi$
$522$		0			0
$523$	230384.	+	230384.i	0.842264	+	0.842264i	0.989153	−	0.146889i	$-0.0469260\pi$
$523$	230384.	+	230384.i	0.842264	+	0.842264i	−0.146889	+	0.989153i	$0.546926\pi$
$524$		0			0
$525$	−339664.	−	339664.i	−1.23234	−	1.23234i
$526$		0			0
$527$		−	59659.0i		−	0.214810i
$528$		0			0
$529$	−269740.			−0.963903
$530$		0			0
$531$	−159364.	+	159364.i	−0.565199	+	0.565199i
$532$		0			0
$533$	−292253.	+	292253.i	−1.02874	+	1.02874i
$534$		0			0
$535$	97718.9			0.341406
$536$		0			0
$537$		−	353165.i		−	1.22470i
$538$		0			0
$539$	6907.27	+	6907.27i	0.0237755	+	0.0237755i
$540$		0			0
$541$	183995.	+	183995.i	0.628655	+	0.628655i	0.947730	−	0.319074i	$-0.103372\pi$
$541$	183995.	+	183995.i	0.628655	+	0.628655i	−0.319074	+	0.947730i	$0.603372\pi$
$542$		0			0
$543$		−	155654.i		−	0.527909i
$544$		0			0
$545$	292056.			0.983271
$546$		0			0
$547$	416851.	−	416851.i	1.39318	−	1.39318i	0.575075	−	0.818100i	$-0.304973\pi$
$547$	416851.	−	416851.i	1.39318	−	1.39318i	0.818100	−	0.575075i	$-0.195027\pi$
$548$		0			0
$549$	−106907.	+	106907.i	−0.354699	+	0.354699i
$550$		0			0
$551$	−68431.2			−0.225399
$552$		0			0
$553$		−	225176.i		−	0.736330i
$554$		0			0
$555$	496864.	+	496864.i	1.61307	+	1.61307i
$556$		0			0
$557$	233211.	+	233211.i	0.751691	+	0.751691i	0.974795	−	0.223104i	$-0.0716189\pi$
$557$	233211.	+	233211.i	0.751691	+	0.751691i	−0.223104	+	0.974795i	$0.571619\pi$
$558$		0			0
$559$			520386.i			1.66534i
$560$		0			0
$561$	239236.			0.760152
$562$		0			0
$563$	82256.5	−	82256.5i	0.259510	−	0.259510i	−0.565345	−	0.824855i	$-0.691257\pi$
$563$	82256.5	−	82256.5i	0.259510	−	0.259510i	0.824855	+	0.565345i	$0.191257\pi$
$564$		0			0
$565$	140659.	−	140659.i	0.440626	−	0.440626i
$566$		0			0
$567$	412331.			1.28257
$568$		0			0
$569$		−	130218.i		−	0.402203i	−0.979570	−	0.201102i	$-0.935548\pi$
$569$		−	130218.i		−	0.402203i	0.979570	−	0.201102i	$-0.0644522\pi$
$570$		0			0
$571$	−62508.2	−	62508.2i	−0.191719	−	0.191719i	0.604720	−	0.796438i	$-0.293285\pi$
$571$	−62508.2	−	62508.2i	−0.191719	−	0.191719i	−0.796438	+	0.604720i	$0.793285\pi$
$572$		0			0
$573$	−16001.2	−	16001.2i	−0.0487353	−	0.0487353i
$574$		0			0
$575$			86238.6i			0.260835i
$576$		0			0
$577$	522256.			1.56867			0.784336	−	0.620336i	$-0.213004\pi$
$577$	522256.			1.56867			0.784336	+	0.620336i	$0.213004\pi$
$578$		0			0
$579$	230208.	−	230208.i	0.686695	−	0.686695i
$580$		0			0
$581$	−73336.0	+	73336.0i	−0.217252	+	0.217252i
$582$		0			0
$583$	−226912.			−0.667606
$584$		0			0
$585$			291829.i			0.852739i
$586$		0			0
$587$	−309702.	−	309702.i	−0.898811	−	0.898811i	0.0965202	−	0.995331i	$-0.469229\pi$
$587$	−309702.	−	309702.i	−0.898811	−	0.898811i	−0.995331	+	0.0965202i	$0.969229\pi$
$588$		0			0
$589$	−20736.0	−	20736.0i	−0.0597717	−	0.0597717i
$590$		0			0
$591$			443697.i			1.27032i
$592$		0			0
$593$	−447350.			−1.27215			−0.636075	−	0.771628i	$-0.719443\pi$
$593$	−447350.			−1.27215			−0.636075	+	0.771628i	$0.719443\pi$
$594$		0			0
$595$	−392186.	+	392186.i	−1.10779	+	1.10779i
$596$		0			0
$597$	425687.	−	425687.i	1.19438	−	1.19438i
$598$		0			0
$599$	462149.			1.28804			0.644019	−	0.765009i	$-0.277266\pi$
$599$	462149.			1.28804			0.644019	+	0.765009i	$0.277266\pi$
$600$		0			0
$601$			374481.i			1.03677i	0.855149	+	0.518383i	$0.173466\pi$
$601$			374481.i			1.03677i	−0.855149	+	0.518383i	$0.826534\pi$
$602$		0			0
$603$	−14093.8	−	14093.8i	−0.0387610	−	0.0387610i
$604$		0			0
$605$	245100.	+	245100.i	0.669627	+	0.669627i
$606$		0			0
$607$			86755.6i			0.235462i	0.993046	+	0.117731i	$0.0375620\pi$
$607$			86755.6i			0.235462i	−0.993046	+	0.117731i	$0.962438\pi$
$608$		0			0
$609$	−272248.			−0.734058
$610$		0			0
$611$	−131891.	+	131891.i	−0.353290	+	0.353290i
$612$		0			0
$613$	112325.	−	112325.i	0.298920	−	0.298920i	−0.541671	−	0.840591i	$-0.682208\pi$
$613$	112325.	−	112325.i	0.298920	−	0.298920i	0.840591	+	0.541671i	$0.182208\pi$
$614$		0			0
$615$	−1.00088e6			−2.64626
$616$		0			0
$617$		−	602706.i		−	1.58320i	−0.611041	−	0.791599i	$-0.709249\pi$
$617$		−	602706.i		−	1.58320i	0.611041	−	0.791599i	$-0.290751\pi$
$618$		0			0
$619$	150969.	+	150969.i	0.394010	+	0.394010i	0.876114	−	0.482104i	$-0.160127\pi$
$619$	150969.	+	150969.i	0.394010	+	0.394010i	−0.482104	+	0.876114i	$0.660127\pi$
$620$		0			0
$621$	−30190.8	−	30190.8i	−0.0782873	−	0.0782873i
$622$		0			0
$623$			57703.6i			0.148671i
$624$		0			0
$625$	190658.			0.488084
$626$		0			0
$627$	83152.6	−	83152.6i	0.211515	−	0.211515i
$628$		0			0
$629$	331922.	−	331922.i	0.838948	−	0.838948i
$630$		0			0
$631$	−693714.			−1.74230			−0.871148	−	0.491020i	$-0.836624\pi$
$631$	−693714.			−1.74230			−0.871148	+	0.491020i	$0.836624\pi$
$632$		0			0
$633$		−	503485.i		−	1.25655i
$634$		0			0
$635$	−623231.	−	623231.i	−1.54562	−	1.54562i
$636$		0			0
$637$	16275.3	+	16275.3i	0.0401098	+	0.0401098i
$638$		0			0
$639$			44566.7i			0.109146i
$640$		0			0
$641$	−17843.0			−0.0434261			−0.0217131	−	0.999764i	$-0.506912\pi$
$641$	−17843.0			−0.0434261			−0.0217131	+	0.999764i	$0.506912\pi$
$642$		0			0
$643$	230136.	−	230136.i	0.556626	−	0.556626i	−0.371719	−	0.928345i	$-0.621232\pi$
$643$	230136.	−	230136.i	0.556626	−	0.556626i	0.928345	+	0.371719i	$0.121232\pi$
$644$		0			0
$645$	−891085.	+	891085.i	−2.14190	+	2.14190i
$646$		0			0
$647$	568528.			1.35814			0.679068	−	0.734075i	$-0.262384\pi$
$647$	568528.			1.35814			0.679068	+	0.734075i	$0.262384\pi$
$648$		0			0
$649$		−	395251.i		−	0.938391i
$650$		0			0
$651$	−82496.7	−	82496.7i	−0.194659	−	0.194659i
$652$		0			0
$653$	−371799.	−	371799.i	−0.871932	−	0.871932i	0.120751	−	0.992683i	$-0.461470\pi$
$653$	−371799.	−	371799.i	−0.871932	−	0.871932i	−0.992683	+	0.120751i	$0.961470\pi$
$654$		0			0
$655$		−	1.04579e6i		−	2.43759i
$656$		0			0
$657$	−114477.			−0.265208
$658$		0			0
$659$	71107.3	−	71107.3i	0.163736	−	0.163736i	−0.620484	−	0.784219i	$-0.713064\pi$
$659$	71107.3	−	71107.3i	0.163736	−	0.163736i	0.784219	+	0.620484i	$0.213064\pi$
$660$		0			0
$661$	−570193.	+	570193.i	−1.30502	+	1.30502i	−0.380065	+	0.924960i	$0.624098\pi$
$661$	−570193.	+	570193.i	−1.30502	+	1.30502i	−0.924960	+	0.380065i	$0.875902\pi$
$662$		0			0
$663$	563701.			1.28239
$664$		0			0
$665$			272629.i			0.616494i
$666$		0			0
$667$	34561.0	+	34561.0i	0.0776846	+	0.0776846i
$668$		0			0
$669$	−741091.	−	741091.i	−1.65584	−	1.65584i
$670$		0			0
$671$		−	265148.i		−	0.588901i
$672$		0			0
$673$	−57084.2			−0.126033			−0.0630167	−	0.998012i	$-0.520072\pi$
$673$	−57084.2			−0.126033			−0.0630167	+	0.998012i	$0.520072\pi$
$674$		0			0
$675$	257749.	−	257749.i	0.565704	−	0.565704i
$676$		0			0
$677$	107264.	−	107264.i	0.234032	−	0.234032i	−0.580341	−	0.814373i	$-0.697081\pi$
$677$	107264.	−	107264.i	0.234032	−	0.234032i	0.814373	+	0.580341i	$0.197081\pi$
$678$		0			0
$679$	−659134.			−1.42966
$680$		0			0
$681$			986444.i			2.12705i
$682$		0			0
$683$	−41763.8	−	41763.8i	−0.0895280	−	0.0895280i	0.660924	−	0.750452i	$-0.270164\pi$
$683$	−41763.8	−	41763.8i	−0.0895280	−	0.0895280i	−0.750452	+	0.660924i	$0.770164\pi$
$684$		0			0
$685$	917153.	+	917153.i	1.95461	+	1.95461i
$686$		0			0
$687$		−	311303.i		−	0.659583i
$688$		0			0
$689$	−534662.			−1.12627
$690$		0			0
$691$	−473605.	+	473605.i	−0.991882	+	0.991882i	−0.999967	−	0.00808568i	$-0.997426\pi$
$691$	−473605.	+	473605.i	−0.991882	+	0.991882i	0.00808568	+	0.999967i	$0.497426\pi$
$692$		0			0
$693$	114410.	−	114410.i	0.238231	−	0.238231i
$694$		0			0
$695$	639811.			1.32459
$696$		0			0
$697$			668623.i			1.37631i
$698$		0			0
$699$	197198.	+	197198.i	0.403598	+	0.403598i
$700$		0			0
$701$	139642.	+	139642.i	0.284170	+	0.284170i	0.834770	−	0.550599i	$-0.185601\pi$
$701$	139642.	+	139642.i	0.284170	+	0.284170i	−0.550599	+	0.834770i	$0.685601\pi$
$702$		0			0
$703$		−	230737.i		−	0.466880i
$704$		0			0
$705$	−451687.			−0.908782
$706$		0			0
$707$	376728.	−	376728.i	0.753684	−	0.753684i
$708$		0			0
$709$	161047.	−	161047.i	0.320377	−	0.320377i	−0.528535	−	0.848912i	$-0.677258\pi$
$709$	161047.	−	161047.i	0.320377	−	0.320377i	0.848912	+	0.528535i	$0.177258\pi$
$710$		0			0
$711$	−191668.			−0.379150
$712$		0			0
$713$			20945.4i			0.0412011i
$714$		0			0
$715$	−361893.	−	361893.i	−0.707894	−	0.707894i
$716$		0			0
$717$	−732090.	−	732090.i	−1.42405	−	1.42405i
$718$		0			0
$719$			132212.i			0.255749i	0.991790	+	0.127874i	$0.0408154\pi$
$719$			132212.i			0.255749i	−0.991790	+	0.127874i	$0.959185\pi$
$720$		0			0
$721$	359273.			0.691122
$722$		0			0
$723$	−637198.	+	637198.i	−1.21898	+	1.21898i
$724$		0			0
$725$	−295059.	+	295059.i	−0.561349	+	0.561349i
$726$		0			0
$727$	98417.4			0.186210			0.0931050	−	0.995656i	$-0.470321\pi$
$727$	98417.4			0.186210			0.0931050	+	0.995656i	$0.470321\pi$
$728$		0			0
$729$			31927.4i			0.0600770i
$730$		0			0
$731$	595275.	+	595275.i	1.11399	+	1.11399i
$732$		0			0
$733$	369797.	+	369797.i	0.688265	+	0.688265i	0.961848	−	0.273584i	$-0.0882090\pi$
$733$	369797.	+	369797.i	0.688265	+	0.688265i	−0.273584	+	0.961848i	$0.588209\pi$
$734$		0			0
$735$			55738.2i			0.103176i
$736$		0			0
$737$	34955.2			0.0643542
$738$		0			0
$739$	−117481.	+	117481.i	−0.215120	+	0.215120i	−0.806438	−	0.591318i	$-0.798608\pi$
$739$	−117481.	+	117481.i	−0.215120	+	0.215120i	0.591318	+	0.806438i	$0.298608\pi$
$740$		0			0
$741$	195929.	−	195929.i	0.356831	−	0.356831i
$742$		0			0
$743$	−273733.			−0.495849			−0.247925	−	0.968779i	$-0.579749\pi$
$743$	−273733.			−0.495849			−0.247925	+	0.968779i	$0.579749\pi$
$744$		0			0
$745$			810267.i			1.45988i
$746$		0			0
$747$	62423.0	+	62423.0i	0.111867	+	0.111867i
$748$		0			0
$749$	−90268.8	−	90268.8i	−0.160907	−	0.160907i
$750$		0			0
$751$			875863.i			1.55295i	0.630150	+	0.776473i	$0.282993\pi$
$751$			875863.i			1.55295i	−0.630150	+	0.776473i	$0.717007\pi$
$752$		0			0
$753$	−407741.			−0.719108
$754$		0			0
$755$	218004.	−	218004.i	0.382446	−	0.382446i
$756$		0			0
$757$	−66071.4	+	66071.4i	−0.115298	+	0.115298i	−0.762402	−	0.647104i	$-0.775980\pi$
$757$	−66071.4	+	66071.4i	−0.115298	+	0.115298i	0.647104	+	0.762402i	$0.275980\pi$
$758$		0			0
$759$	−83992.1			−0.145799
$760$		0			0
$761$		−	333176.i		−	0.575314i	−0.957734	−	0.287657i	$-0.907124\pi$
$761$		−	333176.i		−	0.575314i	0.957734	−	0.287657i	$-0.0928763\pi$
$762$		0			0
$763$	−269790.	−	269790.i	−0.463422	−	0.463422i
$764$		0			0
$765$	333826.	+	333826.i	0.570423	+	0.570423i
$766$		0			0
$767$		−	931313.i		−	1.58309i
$768$		0			0
$769$	−110911.			−0.187552			−0.0937762	−	0.995593i	$-0.529894\pi$
$769$	−110911.			−0.187552			−0.0937762	+	0.995593i	$0.529894\pi$
$770$		0			0
$771$	124325.	−	124325.i	0.209146	−	0.209146i
$772$		0			0
$773$	800998.	−	800998.i	1.34052	−	1.34052i	0.444972	−	0.895544i	$-0.353213\pi$
$773$	800998.	−	800998.i	1.34052	−	1.34052i	0.895544	−	0.444972i	$-0.146787\pi$
$774$		0			0
$775$	−178818.			−0.297719
$776$		0			0
$777$		−	917967.i		−	1.52050i
$778$		0			0
$779$	232397.	+	232397.i	0.382962	+	0.382962i
$780$		0			0
$781$	−55266.6	−	55266.6i	−0.0906068	−	0.0906068i
$782$		0			0
$783$		−	206591.i		−	0.336968i
$784$		0			0
$785$	661762.			1.07390
$786$		0			0
$787$	528761.	−	528761.i	0.853709	−	0.853709i	−0.136879	−	0.990588i	$-0.543707\pi$
$787$	528761.	−	528761.i	0.853709	−	0.853709i	0.990588	+	0.136879i	$0.0437071\pi$
$788$		0			0
$789$	−645552.	+	645552.i	−1.03700	+	1.03700i
$790$		0			0
$791$	−259870.			−0.415340
$792$		0			0
$793$		−	624756.i		−	0.993491i
$794$		0			0
$795$	−915532.	−	915532.i	−1.44857	−	1.44857i
$796$		0			0
$797$	−771661.	−	771661.i	−1.21481	−	1.21481i	−0.969424	−	0.245390i	$-0.921084\pi$
$797$	−771661.	−	771661.i	−1.21481	−	1.21481i	−0.245390	−	0.969424i	$-0.578916\pi$
$798$		0			0
$799$			301742.i			0.472653i
$800$		0			0
$801$	49116.8			0.0765536
$802$		0			0
$803$	141961.	−	141961.i	0.220160	−	0.220160i
$804$		0			0
$805$	137691.	−	137691.i	0.212477	−	0.212477i
$806$		0			0
$807$	485011.			0.744740
$808$		0			0
$809$		−	100893.i		−	0.154157i	−0.997025	−	0.0770783i	$-0.975441\pi$
$809$		−	100893.i		−	0.154157i	0.997025	−	0.0770783i	$-0.0245592\pi$
$810$		0			0
$811$	51769.7	+	51769.7i	0.0787107	+	0.0787107i	0.745366	−	0.666655i	$-0.232275\pi$
$811$	51769.7	+	51769.7i	0.0787107	+	0.0787107i	−0.666655	+	0.745366i	$0.732275\pi$
$812$		0			0
$813$	871882.	+	871882.i	1.31910	+	1.31910i
$814$		0			0
$815$			1.28783e6i			1.93885i
$816$		0			0
$817$	413807.			0.619946
$818$		0			0
$819$	269580.	−	269580.i	0.401901	−	0.401901i
$820$		0			0
$821$	−48584.3	+	48584.3i	−0.0720791	+	0.0720791i	−0.742227	−	0.670148i	$-0.766231\pi$
$821$	−48584.3	+	48584.3i	−0.0720791	+	0.0720791i	0.670148	+	0.742227i	$0.266231\pi$
$822$		0			0
$823$	−338093.			−0.499157			−0.249578	−	0.968355i	$-0.580292\pi$
$823$	−338093.			−0.499157			−0.249578	+	0.968355i	$0.580292\pi$
$824$		0			0
$825$		−	717068.i		−	1.05354i
$826$		0			0
$827$	458054.	+	458054.i	0.669740	+	0.669740i	0.957656	−	0.287916i	$-0.0929624\pi$
$827$	458054.	+	458054.i	0.669740	+	0.669740i	−0.287916	+	0.957656i	$0.592962\pi$
$828$		0			0
$829$	−495530.	−	495530.i	−0.721042	−	0.721042i	0.247775	−	0.968818i	$-0.420301\pi$
$829$	−495530.	−	495530.i	−0.721042	−	0.721042i	−0.968818	+	0.247775i	$0.920301\pi$
$830$		0			0
$831$			403396.i			0.584157i
$832$		0			0
$833$	37235.0			0.0536613
$834$		0			0
$835$	−1.15714e6	+	1.15714e6i	−1.65964	+	1.65964i
$836$		0			0
$837$	62601.3	−	62601.3i	0.0893578	−	0.0893578i
$838$		0			0
$839$	696514.			0.989477			0.494739	−	0.869042i	$-0.335264\pi$
$839$	696514.			0.989477			0.494739	+	0.869042i	$0.335264\pi$
$840$		0			0
$841$		−	470785.i		−	0.665626i
$842$		0			0
$843$	383982.	+	383982.i	0.540326	+	0.540326i
$844$		0			0
$845$	−74970.5	−	74970.5i	−0.104997	−	0.104997i
$846$		0			0
$847$		−	452827.i		−	0.631198i
$848$		0			0
$849$	1.75412e6			2.43357
$850$		0			0
$851$	−116533.	+	116533.i	−0.160912	+	0.160912i
$852$		0			0
$853$	−78365.1	+	78365.1i	−0.107702	+	0.107702i	−0.758904	−	0.651202i	$-0.774265\pi$
$853$	−78365.1	+	78365.1i	−0.107702	+	0.107702i	0.651202	+	0.758904i	$0.274265\pi$
$854$		0			0
$855$	232060.			0.317444
$856$		0			0
$857$		−	576243.i		−	0.784593i	−0.919839	−	0.392296i	$-0.871681\pi$
$857$		−	576243.i		−	0.784593i	0.919839	−	0.392296i	$-0.128319\pi$
$858$		0			0
$859$	−74196.4	−	74196.4i	−0.100553	−	0.100553i	0.655040	−	0.755594i	$-0.272652\pi$
$859$	−74196.4	−	74196.4i	−0.100553	−	0.100553i	−0.755594	+	0.655040i	$0.772652\pi$
$860$		0			0
$861$	924574.	+	924574.i	1.24720	+	1.24720i
$862$		0			0
$863$			299840.i			0.402594i	0.979530	+	0.201297i	$0.0645157\pi$
$863$			299840.i			0.402594i	−0.979530	+	0.201297i	$0.935484\pi$
$864$		0			0
$865$	−879131.			−1.17495
$866$		0			0
$867$	−12352.5	+	12352.5i	−0.0164329	+	0.0164329i
$868$		0			0
$869$	237686.	−	237686.i	0.314749	−	0.314749i
$870$		0			0
$871$	82363.5			0.108567
$872$		0			0
$873$			561050.i			0.736161i
$874$		0			0
$875$	319272.	+	319272.i	0.417009	+	0.417009i
$876$		0			0
$877$	438353.	+	438353.i	0.569934	+	0.569934i	0.932110	−	0.362176i	$-0.117966\pi$
$877$	438353.	+	438353.i	0.569934	+	0.569934i	−0.362176	+	0.932110i	$0.617966\pi$
$878$		0			0
$879$			206044.i			0.266675i
$880$		0			0
$881$	−1526.15			−0.00196628			−0.000983142	−	1.00000i	$-0.500313\pi$
$881$	−1526.15			−0.00196628			−0.000983142		1.00000i	$0.500313\pi$
$882$		0			0
$883$	−114980.	+	114980.i	−0.147469	+	0.147469i	−0.776986	−	0.629517i	$-0.783253\pi$
$883$	−114980.	+	114980.i	−0.147469	+	0.147469i	0.629517	+	0.776986i	$0.283253\pi$
$884$		0			0
$885$	1.59474e6	−	1.59474e6i	2.03612	−	2.03612i
$886$		0			0
$887$	−833028.			−1.05880			−0.529398	−	0.848373i	$-0.677582\pi$
$887$	−833028.			−1.05880			−0.529398	+	0.848373i	$0.677582\pi$
$888$		0			0
$889$			1.15143e6i			1.45692i
$890$		0			0
$891$	435238.	+	435238.i	0.548241	+	0.548241i
$892$		0			0
$893$	104878.	+	104878.i	0.131517	+	0.131517i
$894$		0			0
$895$			1.22223e6i			1.52584i
$896$		0			0
$897$	−197907.			−0.245967
$898$		0			0
$899$	−71663.1	+	71663.1i	−0.0886699	+	0.0886699i
$900$		0			0
$901$	−611606.	+	611606.i	−0.753394	+	0.753394i
$902$		0			0
$903$	1.64630e6			2.01898
$904$		0			0
$905$			538686.i			0.657716i
$906$		0			0
$907$	1.13198e6	+	1.13198e6i	1.37602	+	1.37602i	0.851234	+	0.524787i	$0.175855\pi$
$907$	1.13198e6	+	1.13198e6i	1.37602	+	1.37602i	0.524787	+	0.851234i	$0.324145\pi$
$908$		0			0
$909$	−320668.	−	320668.i	−0.388086	−	0.388086i
$910$		0			0
$911$		−	369952.i		−	0.445768i	−0.974845	−	0.222884i	$-0.928453\pi$
$911$		−	369952.i		−	0.445768i	0.974845	−	0.222884i	$-0.0715471\pi$
$912$		0			0
$913$	−154820.			−0.185732
$914$		0			0
$915$	1.06980e6	−	1.06980e6i	1.27780	−	1.27780i
$916$		0			0
$917$	−966058.	+	966058.i	−1.14885	+	1.14885i
$918$		0			0
$919$	815703.			0.965831			0.482915	−	0.875667i	$-0.339578\pi$
$919$	815703.			0.965831			0.482915	+	0.875667i	$0.339578\pi$
$920$		0			0
$921$			397746.i			0.468906i
$922$		0			0
$923$	−130222.	−	130222.i	−0.152856	−	0.152856i
$924$		0			0
$925$	−994881.	−	994881.i	−1.16275	−	1.16275i
$926$		0			0
$927$		−	305811.i		−	0.355872i
$928$		0			0
$929$	329861.			0.382208			0.191104	−	0.981570i	$-0.438793\pi$
$929$	329861.			0.382208			0.191104	+	0.981570i	$0.438793\pi$
$930$		0			0
$931$	12942.0	−	12942.0i	0.0149314	−	0.0149314i
$932$		0			0
$933$	423383.	−	423383.i	0.486374	−	0.486374i
$934$		0			0
$935$	−827947.			−0.947064
$936$		0			0
$937$			884572.i			1.00752i	0.863844	+	0.503760i	$0.168051\pi$
$937$			884572.i			1.00752i	−0.863844	+	0.503760i	$0.831949\pi$
$938$		0			0
$939$	−1.08068e6	−	1.08068e6i	−1.22565	−	1.22565i
$940$		0			0
$941$	441727.	+	441727.i	0.498856	+	0.498856i	0.911082	−	0.412226i	$-0.135249\pi$
$941$	441727.	+	441727.i	0.498856	+	0.498856i	−0.412226	+	0.911082i	$0.635249\pi$
$942$		0			0
$943$		−	234743.i		−	0.263979i
$944$		0			0
$945$	−823056.			−0.921650
$946$		0			0
$947$	98614.4	−	98614.4i	0.109961	−	0.109961i	−0.649985	−	0.759947i	$-0.725225\pi$
$947$	98614.4	−	98614.4i	0.109961	−	0.109961i	0.759947	+	0.649985i	$0.225225\pi$
$948$		0			0
$949$	334497.	−	334497.i	0.371416	−	0.371416i
$950$		0			0
$951$	−1.81832e6			−2.01053
$952$		0			0
$953$		−	327664.i		−	0.360780i	−0.983595	−	0.180390i	$-0.942264\pi$
$953$		−	327664.i		−	0.360780i	0.983595	−	0.180390i	$-0.0577360\pi$
$954$		0			0
$955$	55377.0	+	55377.0i	0.0607187	+	0.0607187i
$956$		0			0
$957$	−287373.	−	287373.i	−0.313778	−	0.313778i
$958$		0			0
$959$		−	1.69446e6i		−	1.84244i
$960$		0			0
$961$	880090.			0.952973
$962$		0			0
$963$	−76836.2	+	76836.2i	−0.0828539	+	0.0828539i
$964$		0			0
$965$	−796705.	+	796705.i	−0.855545	+	0.855545i
$966$		0			0
$967$	386677.			0.413519			0.206760	−	0.978392i	$-0.433708\pi$
$967$	386677.			0.413519			0.206760	+	0.978392i	$0.433708\pi$
$968$		0			0
$969$		−	448251.i		−	0.477390i
$970$		0			0
$971$	−718740.	−	718740.i	−0.762313	−	0.762313i	0.214427	−	0.976740i	$-0.431212\pi$
$971$	−718740.	−	718740.i	−0.762313	−	0.762313i	−0.976740	+	0.214427i	$0.931212\pi$
$972$		0			0
$973$	−591032.	−	591032.i	−0.624288	−	0.624288i
$974$		0			0
$975$		−	1.68960e6i		−	1.77735i
$976$		0			0
$977$	−1.27845e6			−1.33935			−0.669675	−	0.742654i	$-0.733567\pi$
$977$	−1.27845e6			−1.33935			−0.669675	+	0.742654i	$0.733567\pi$
$978$		0			0
$979$	−60909.2	+	60909.2i	−0.0635503	+	0.0635503i
$980$		0			0
$981$	−229643.	+	229643.i	−0.238625	+	0.238625i
$982$		0			0
$983$	−414529.			−0.428991			−0.214495	−	0.976725i	$-0.568811\pi$
$983$	−414529.			−0.428991			−0.214495	+	0.976725i	$0.568811\pi$
$984$		0			0
$985$		−	1.53555e6i		−	1.58267i
$986$		0			0
$987$	417251.	+	417251.i	0.428314	+	0.428314i
$988$		0			0
$989$	−208992.	−	208992.i	−0.213667	−	0.213667i
$990$		0			0
$991$			176697.i			0.179921i	0.995945	+	0.0899605i	$0.0286741\pi$
$991$			176697.i			0.179921i	−0.995945	+	0.0899605i	$0.971326\pi$
$992$		0			0
$993$	−1.07025e6			−1.08539
$994$		0			0
$995$	−1.47322e6	+	1.47322e6i	−1.48806	+	1.48806i
$996$		0			0
$997$	1.20434e6	−	1.20434e6i	1.21160	−	1.21160i	0.241102	−	0.970500i	$-0.422491\pi$
$997$	1.20434e6	−	1.20434e6i	1.21160	−	1.21160i	0.970500	−	0.241102i	$-0.0775089\pi$
$998$		0			0
$999$	696585.			0.697980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.f.b.95.6		14
4.3	odd	2		128.5.f.a.95.2		14
8.3	odd	2		64.5.f.a.47.6		14
8.5	even	2		16.5.f.a.3.6	✓	14
16.3	odd	4		16.5.f.a.11.6	yes	14
16.5	even	4		128.5.f.a.31.2		14
16.11	odd	4	inner	128.5.f.b.31.6		14
16.13	even	4		64.5.f.a.15.6		14
24.5	odd	2		144.5.m.a.19.2		14
24.11	even	2		576.5.m.a.559.1		14
48.29	odd	4		576.5.m.a.271.1		14
48.35	even	4		144.5.m.a.91.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.5.f.a.3.6	✓	14	8.5	even	2
16.5.f.a.11.6	yes	14	16.3	odd	4
64.5.f.a.15.6		14	16.13	even	4
64.5.f.a.47.6		14	8.3	odd	2
128.5.f.a.31.2		14	16.5	even	4
128.5.f.a.95.2		14	4.3	odd	2
128.5.f.b.31.6		14	16.11	odd	4	inner
128.5.f.b.95.6		14	1.1	even	1	trivial
144.5.m.a.19.2		14	24.5	odd	2
144.5.m.a.91.2		14	48.35	even	4
576.5.m.a.271.1		14	48.29	odd	4
576.5.m.a.559.1		14	24.11	even	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(7.86839 - 7.86839i) q^{3} +(-27.2309 + 27.2309i) q^{5} +50.3097 q^{7} -42.8233i q^{9} +O(q^{10})\)	\(q+(7.86839 - 7.86839i) q^{3} +(-27.2309 + 27.2309i) q^{5} +50.3097 q^{7} -42.8233i q^{9} +(53.1047 + 53.1047i) q^{11} +(125.128 + 125.128i) q^{13} +428.528i q^{15} +286.271 q^{17} +(99.5010 - 99.5010i) q^{19} +(395.857 - 395.857i) q^{21} -100.505 q^{23} -858.049i q^{25} +(300.390 + 300.390i) q^{27} +(-343.872 - 343.872i) q^{29} -208.400i q^{31} +835.697 q^{33} +(-1369.98 + 1369.98i) q^{35} +(1159.47 - 1159.47i) q^{37} +1969.12 q^{39} +2335.63i q^{41} +(2079.41 + 2079.41i) q^{43} +(1166.12 + 1166.12i) q^{45} +1054.04i q^{47} +130.069 q^{49} +(2252.49 - 2252.49i) q^{51} +(-2136.46 + 2136.46i) q^{53} -2892.18 q^{55} -1565.83i q^{57} +(-3721.44 - 3721.44i) q^{59} +(-2496.46 - 2496.46i) q^{61} -2154.43i q^{63} -6814.72 q^{65} +(329.116 - 329.116i) q^{67} +(-790.817 + 790.817i) q^{69} -1040.71 q^{71} -2673.24i q^{73} +(-6751.46 - 6751.46i) q^{75} +(2671.68 + 2671.68i) q^{77} -4475.80i q^{79} +8195.85 q^{81} +(-1457.69 + 1457.69i) q^{83} +(-7795.43 + 7795.43i) q^{85} -5411.44 q^{87} +1146.97i q^{89} +(6295.17 + 6295.17i) q^{91} +(-1639.78 - 1639.78i) q^{93} +5419.01i q^{95} -13101.5 q^{97} +(2274.11 - 2274.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7	\( 14 q + 2 q^{3} + 2 q^{5} - 4 q^{7} - 94 q^{11} + 2 q^{13} - 4 q^{17} + 706 q^{19} + 164 q^{21} + 1148 q^{23} + 1664 q^{27} - 862 q^{29} - 4 q^{33} - 1340 q^{35} + 1826 q^{37} + 2684 q^{39} - 1694 q^{43} - 1410 q^{45} + 682 q^{49} + 3012 q^{51} + 482 q^{53} - 11780 q^{55} + 2786 q^{59} + 3778 q^{61} - 2020 q^{65} - 7998 q^{67} - 9628 q^{69} + 19964 q^{71} - 17570 q^{75} + 9508 q^{77} + 1454 q^{81} + 17282 q^{83} - 9948 q^{85} - 49284 q^{87} + 28036 q^{91} - 8896 q^{93} - 4 q^{97} - 49214 q^{99}+O(q^{100}) \) 14 * q + 2 * q^3 + 2 * q^5 - 4 * q^7 - 94 * q^11 + 2 * q^13 - 4 * q^17 + 706 * q^19 + 164 * q^21 + 1148 * q^23 + 1664 * q^27 - 862 * q^29 - 4 * q^33 - 1340 * q^35 + 1826 * q^37 + 2684 * q^39 - 1694 * q^43 - 1410 * q^45 + 682 * q^49 + 3012 * q^51 + 482 * q^53 - 11780 * q^55 + 2786 * q^59 + 3778 * q^61 - 2020 * q^65 - 7998 * q^67 - 9628 * q^69 + 19964 * q^71 - 17570 * q^75 + 9508 * q^77 + 1454 * q^81 + 17282 * q^83 - 9948 * q^85 - 49284 * q^87 + 28036 * q^91 - 8896 * q^93 - 4 * q^97 - 49214 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more