LMFDB - Embedded newform 256.6.e.a.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,6,Mod(65,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("256.65");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	256.e (of order $4$, degree $2$, 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:	$41.0582578721$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{14} + 68094 x^{12} - 631280 x^{10} + 1162609411 x^{8} - 7070628176 x^{6} + \cdots + 25477586689 $ x^16 - 4x^14 + 68094x^12 - 631280x^10 + 1162609411x^8 - 7070628176x^6 + 161314599870x^4 + 124044132812*x^2 + 25477586689
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			65.5
Root			$0.0885219 + 0.618585i$ of defining polynomial
Character	$\chi$	$=$	256.65
Dual form			256.6.e.a.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23717 + 1.23717i) q^{3} +(-9.46137 + 9.46137i) q^{5} +217.226i q^{7} -239.939i q^{9} +O(q^{10})$	\(q+(1.23717 + 1.23717i) q^{3} +(-9.46137 + 9.46137i) q^{5} +217.226i q^{7} -239.939i q^{9} +(-282.343 + 282.343i) q^{11} +(339.858 + 339.858i) q^{13} -23.4106 q^{15} -473.078 q^{17} +(-193.135 - 193.135i) q^{19} +(-268.745 + 268.745i) q^{21} -1880.50i q^{23} +2945.96i q^{25} +(597.477 - 597.477i) q^{27} +(-5001.53 - 5001.53i) q^{29} +4038.97 q^{31} -698.612 q^{33} +(-2055.25 - 2055.25i) q^{35} +(1878.88 - 1878.88i) q^{37} +840.924i q^{39} -15340.6i q^{41} +(-11811.3 + 11811.3i) q^{43} +(2270.15 + 2270.15i) q^{45} +4380.31 q^{47} -30379.9 q^{49} +(-585.278 - 585.278i) q^{51} +(-19608.0 + 19608.0i) q^{53} -5342.70i q^{55} -477.882i q^{57} +(-21399.1 + 21399.1i) q^{59} +(-29820.9 - 29820.9i) q^{61} +52120.8 q^{63} -6431.05 q^{65} +(-11258.5 - 11258.5i) q^{67} +(2326.49 - 2326.49i) q^{69} -48020.3i q^{71} +8033.35i q^{73} +(-3644.66 + 3644.66i) q^{75} +(-61332.1 - 61332.1i) q^{77} +74631.9 q^{79} -56826.8 q^{81} +(-63073.6 - 63073.6i) q^{83} +(4475.97 - 4475.97i) q^{85} -12375.5i q^{87} -93498.5i q^{89} +(-73825.8 + 73825.8i) q^{91} +(4996.90 + 4996.90i) q^{93} +3654.65 q^{95} -158815. q^{97} +(67745.0 + 67745.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 160 q^{5}+O(q^{10}) $ 16 * q - 160 * q^5	$ 16 q - 160 q^{5} - 576 q^{13} - 384 q^{17} - 1120 q^{21} - 14624 q^{29} - 78208 q^{33} - 39552 q^{37} - 190336 q^{45} - 196112 q^{49} - 26432 q^{53} - 274944 q^{61} - 630624 q^{65} - 315040 q^{69} - 426912 q^{77} - 1012880 q^{81} - 451488 q^{85} - 1128512 q^{93} - 833152 q^{97}+O(q^{100}) $ 16 * q - 160 * q^5 - 576 * q^13 - 384 * q^17 - 1120 * q^21 - 14624 * q^29 - 78208 * q^33 - 39552 * q^37 - 190336 * q^45 - 196112 * q^49 - 26432 * q^53 - 274944 * q^61 - 630624 * q^65 - 315040 * q^69 - 426912 * q^77 - 1012880 * q^81 - 451488 * q^85 - 1128512 * q^93 - 833152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.23717	+	1.23717i	0.0793645	+	0.0793645i	0.745675	−	0.666310i	$-0.232127\pi$
$3$	1.23717	+	1.23717i	0.0793645	+	0.0793645i	−0.666310	+	0.745675i	$0.732127\pi$
$4$		0			0
$5$	−9.46137	+	9.46137i	−0.169250	+	0.169250i	−0.786650	−	0.617400i	$-0.788186\pi$
$5$	−9.46137	+	9.46137i	−0.169250	+	0.169250i	0.617400	+	0.786650i	$0.288186\pi$
$6$		0			0
$7$			217.226i			1.67558i	0.545991	+	0.837791i	$0.316153\pi$
$7$			217.226i			1.67558i	−0.545991	+	0.837791i	$0.683847\pi$
$8$		0			0
$9$		−	239.939i		−	0.987403i
$10$		0			0
$11$	−282.343	+	282.343i	−0.703550	+	0.703550i	−0.965171	−	0.261621i	$-0.915743\pi$
$11$	−282.343	+	282.343i	−0.703550	+	0.703550i	0.261621	+	0.965171i	$0.415743\pi$
$12$		0			0
$13$	339.858	+	339.858i	0.557749	+	0.557749i	0.928666	−	0.370917i	$-0.120957\pi$
$13$	339.858	+	339.858i	0.557749	+	0.557749i	−0.370917	+	0.928666i	$0.620957\pi$
$14$		0			0
$15$	−23.4106			−0.0268649
$16$		0			0
$17$	−473.078			−0.397018			−0.198509	−	0.980099i	$-0.563610\pi$
$17$	−473.078			−0.397018			−0.198509	+	0.980099i	$0.563610\pi$
$18$		0			0
$19$	−193.135	−	193.135i	−0.122738	−	0.122738i	0.643070	−	0.765808i	$-0.277660\pi$
$19$	−193.135	−	193.135i	−0.122738	−	0.122738i	−0.765808	+	0.643070i	$0.777660\pi$
$20$		0			0
$21$	−268.745	+	268.745i	−0.132982	+	0.132982i
$22$		0			0
$23$		−	1880.50i		−	0.741230i	−0.928787	−	0.370615i	$-0.879147\pi$
$23$		−	1880.50i		−	0.741230i	0.928787	−	0.370615i	$-0.120853\pi$
$24$		0			0
$25$			2945.96i			0.942709i
$26$		0			0
$27$	597.477	−	597.477i	0.157729	−	0.157729i
$28$		0			0
$29$	−5001.53	−	5001.53i	−1.10435	−	1.10435i	−0.993879	−	0.110473i	$-0.964763\pi$
$29$	−5001.53	−	5001.53i	−1.10435	−	1.10435i	−0.110473	−	0.993879i	$-0.535237\pi$
$30$		0			0
$31$	4038.97			0.754861			0.377430	−	0.926038i	$-0.376808\pi$
$31$	4038.97			0.754861			0.377430	+	0.926038i	$0.376808\pi$
$32$		0			0
$33$	−698.612			−0.111674
$34$		0			0
$35$	−2055.25	−	2055.25i	−0.283593	−	0.283593i
$36$		0			0
$37$	1878.88	−	1878.88i	0.225629	−	0.225629i	−0.585235	−	0.810864i	$-0.698998\pi$
$37$	1878.88	−	1878.88i	0.225629	−	0.225629i	0.810864	+	0.585235i	$0.198998\pi$
$38$		0			0
$39$			840.924i			0.0885310i
$40$		0			0
$41$		−	15340.6i		−	1.42522i	−0.701558	−	0.712612i	$-0.747512\pi$
$41$		−	15340.6i		−	1.42522i	0.701558	−	0.712612i	$-0.252488\pi$
$42$		0			0
$43$	−11811.3	+	11811.3i	−0.974150	+	0.974150i	−0.999674	−	0.0255246i	$-0.991874\pi$
$43$	−11811.3	+	11811.3i	−0.974150	+	0.974150i	0.0255246	+	0.999674i	$0.491874\pi$
$44$		0			0
$45$	2270.15	+	2270.15i	0.167118	+	0.167118i
$46$		0			0
$47$	4380.31			0.289242			0.144621	−	0.989487i	$-0.453804\pi$
$47$	4380.31			0.289242			0.144621	+	0.989487i	$0.453804\pi$
$48$		0			0
$49$	−30379.9			−1.80758
$50$		0			0
$51$	−585.278	−	585.278i	−0.0315092	−	0.0315092i
$52$		0			0
$53$	−19608.0	+	19608.0i	−0.958833	+	0.958833i	−0.999186	−	0.0403525i	$-0.987152\pi$
$53$	−19608.0	+	19608.0i	−0.958833	+	0.958833i	0.0403525	+	0.999186i	$0.487152\pi$
$54$		0			0
$55$		−	5342.70i		−	0.238152i
$56$		0			0
$57$		−	477.882i		−	0.0194820i
$58$		0			0
$59$	−21399.1	+	21399.1i	−0.800323	+	0.800323i	−0.983146	−	0.182822i	$-0.941477\pi$
$59$	−21399.1	+	21399.1i	−0.800323	+	0.800323i	0.182822	+	0.983146i	$0.441477\pi$
$60$		0			0
$61$	−29820.9	−	29820.9i	−1.02612	−	1.02612i	−0.999650	−	0.0264659i	$-0.991575\pi$
$61$	−29820.9	−	29820.9i	−1.02612	−	1.02612i	−0.0264659	−	0.999650i	$-0.508425\pi$
$62$		0			0
$63$	52120.8			1.65447
$64$		0			0
$65$	−6431.05			−0.188798
$66$		0			0
$67$	−11258.5	−	11258.5i	−0.306404	−	0.306404i	0.537109	−	0.843513i	$-0.319516\pi$
$67$	−11258.5	−	11258.5i	−0.306404	−	0.306404i	−0.843513	+	0.537109i	$0.819516\pi$
$68$		0			0
$69$	2326.49	−	2326.49i	0.0588273	−	0.0588273i
$70$		0			0
$71$		−	48020.3i		−	1.13052i	−0.824912	−	0.565261i	$-0.808776\pi$
$71$		−	48020.3i		−	1.13052i	0.824912	−	0.565261i	$-0.191224\pi$
$72$		0			0
$73$			8033.35i			0.176437i	0.996101	+	0.0882184i	$0.0281174\pi$
$73$			8033.35i			0.176437i	−0.996101	+	0.0882184i	$0.971883\pi$
$74$		0			0
$75$	−3644.66	+	3644.66i	−0.0748176	+	0.0748176i
$76$		0			0
$77$	−61332.1	−	61332.1i	−1.17886	−	1.17886i
$78$		0			0
$79$	74631.9			1.34542			0.672708	−	0.739908i	$-0.265131\pi$
$79$	74631.9			1.34542			0.672708	+	0.739908i	$0.265131\pi$
$80$		0			0
$81$	−56826.8			−0.962366
$82$		0			0
$83$	−63073.6	−	63073.6i	−1.00497	−	1.00497i	−0.999988	−	0.00498026i	$-0.998415\pi$
$83$	−63073.6	−	63073.6i	−1.00497	−	1.00497i	−0.00498026	−	0.999988i	$-0.501585\pi$
$84$		0			0
$85$	4475.97	−	4475.97i	0.0671954	−	0.0671954i
$86$		0			0
$87$		−	12375.5i		−	0.175293i
$88$		0			0
$89$		−	93498.5i		−	1.25121i	−0.780141	−	0.625604i	$-0.784852\pi$
$89$		−	93498.5i		−	1.25121i	0.780141	−	0.625604i	$-0.215148\pi$
$90$		0			0
$91$	−73825.8	+	73825.8i	−0.934555	+	0.934555i
$92$		0			0
$93$	4996.90	+	4996.90i	0.0599091	+	0.0599091i
$94$		0			0
$95$	3654.65			0.0415467
$96$		0			0
$97$	−158815.			−1.71381			−0.856907	−	0.515472i	$-0.827617\pi$
$97$	−158815.			−1.71381			−0.856907	+	0.515472i	$0.827617\pi$
$98$		0			0
$99$	67745.0	+	67745.0i	0.694687	+	0.694687i
$100$		0			0
$101$	−109401.	+	109401.i	−1.06713	+	1.06713i	−0.0695559	+	0.997578i	$0.522158\pi$
$101$	−109401.	+	109401.i	−1.06713	+	1.06713i	−0.997578	+	0.0695559i	$0.977842\pi$
$102$		0			0
$103$			56607.0i			0.525747i	0.964830	+	0.262873i	$0.0846702\pi$
$103$			56607.0i			0.525747i	−0.964830	+	0.262873i	$0.915330\pi$
$104$		0			0
$105$		−	5085.39i		−	0.0450144i
$106$		0			0
$107$	−105092.	+	105092.i	−0.887385	+	0.887385i	−0.994271	−	0.106886i	$-0.965912\pi$
$107$	−105092.	+	105092.i	−0.887385	+	0.887385i	0.106886	+	0.994271i	$0.465912\pi$
$108$		0			0
$109$	−35671.6	−	35671.6i	−0.287579	−	0.287579i	0.548543	−	0.836122i	$-0.315183\pi$
$109$	−35671.6	−	35671.6i	−0.287579	−	0.287579i	−0.836122	+	0.548543i	$0.815183\pi$
$110$		0			0
$111$	4648.98			0.0358138
$112$		0			0
$113$	78832.7			0.580779			0.290389	−	0.956909i	$-0.406215\pi$
$113$	78832.7			0.580779			0.290389	+	0.956909i	$0.406215\pi$
$114$		0			0
$115$	17792.1	+	17792.1i	0.125453	+	0.125453i
$116$		0			0
$117$	81545.1	−	81545.1i	0.550723	−	0.550723i
$118$		0			0
$119$		−	102765.i		−	0.665237i
$120$		0			0
$121$			1616.01i			0.0100342i
$122$		0			0
$123$	18978.9	−	18978.9i	0.113112	−	0.113112i
$124$		0			0
$125$	−57439.7	−	57439.7i	−0.328804	−	0.328804i
$126$		0			0
$127$	146680.			0.806977			0.403488	−	0.914985i	$-0.367798\pi$
$127$	146680.			0.806977			0.403488	+	0.914985i	$0.367798\pi$
$128$		0			0
$129$	−29225.1			−0.154626
$130$		0			0
$131$	−163028.	−	163028.i	−0.830011	−	0.830011i	0.157507	−	0.987518i	$-0.449654\pi$
$131$	−163028.	−	163028.i	−0.830011	−	0.830011i	−0.987518	+	0.157507i	$0.949654\pi$
$132$		0			0
$133$	41953.9	−	41953.9i	0.205657	−	0.205657i
$134$		0			0
$135$			11305.9i			0.0533914i
$136$		0			0
$137$			129663.i			0.590221i	0.955463	+	0.295111i	$0.0953565\pi$
$137$			129663.i			0.590221i	−0.955463	+	0.295111i	$0.904644\pi$
$138$		0			0
$139$	293683.	−	293683.i	1.28927	−	1.28927i	0.354032	−	0.935233i	$-0.384810\pi$
$139$	293683.	−	293683.i	1.28927	−	1.28927i	0.935233	−	0.354032i	$-0.115190\pi$
$140$		0			0
$141$	5419.19	+	5419.19i	0.0229555	+	0.0229555i
$142$		0			0
$143$	−191913.			−0.784809
$144$		0			0
$145$	94642.6			0.373824
$146$		0			0
$147$	−37585.1	−	37585.1i	−0.143457	−	0.143457i
$148$		0			0
$149$	27828.6	−	27828.6i	0.102690	−	0.102690i	−0.653895	−	0.756585i	$-0.726866\pi$
$149$	27828.6	−	27828.6i	0.102690	−	0.102690i	0.756585	+	0.653895i	$0.226866\pi$
$150$		0			0
$151$		−	81358.3i		−	0.290375i	−0.989404	−	0.145188i	$-0.953621\pi$
$151$		−	81358.3i		−	0.290375i	0.989404	−	0.145188i	$-0.0463785\pi$
$152$		0			0
$153$			113510.i			0.392017i
$154$		0			0
$155$	−38214.2	+	38214.2i	−0.127760	+	0.127760i
$156$		0			0
$157$	202745.	+	202745.i	0.656448	+	0.656448i	0.954538	−	0.298090i	$-0.0963495\pi$
$157$	202745.	+	202745.i	0.656448	+	0.656448i	−0.298090	+	0.954538i	$0.596349\pi$
$158$		0			0
$159$	−48516.8			−0.152195
$160$		0			0
$161$	408492.			1.24199
$162$		0			0
$163$	383196.	+	383196.i	1.12967	+	1.12967i	0.990230	+	0.139440i	$0.0445304\pi$
$163$	383196.	+	383196.i	1.12967	+	1.12967i	0.139440	+	0.990230i	$0.455470\pi$
$164$		0			0
$165$	6609.83	−	6609.83i	0.0189008	−	0.0189008i
$166$		0			0
$167$			523932.i			1.45373i	0.686781	+	0.726865i	$0.259023\pi$
$167$			523932.i			1.45373i	−0.686781	+	0.726865i	$0.740977\pi$
$168$		0			0
$169$		−	140286.i		−	0.377832i
$170$		0			0
$171$	−46340.7	+	46340.7i	−0.121191	+	0.121191i
$172$		0			0
$173$	447412.	+	447412.i	1.13656	+	1.13656i	0.989062	+	0.147497i	$0.0471217\pi$
$173$	447412.	+	447412.i	1.13656	+	1.13656i	0.147497	+	0.989062i	$0.452878\pi$
$174$		0			0
$175$	−639939.			−1.57959
$176$		0			0
$177$	−52948.6			−0.127035
$178$		0			0
$179$	196974.	+	196974.i	0.459489	+	0.459489i	0.898488	−	0.438998i	$-0.144667\pi$
$179$	196974.	+	196974.i	0.459489	+	0.459489i	−0.438998	+	0.898488i	$0.644667\pi$
$180$		0			0
$181$	−259968.	+	259968.i	−0.589826	+	0.589826i	−0.937584	−	0.347758i	$-0.886943\pi$
$181$	−259968.	+	259968.i	−0.589826	+	0.589826i	0.347758	+	0.937584i	$0.386943\pi$
$182$		0			0
$183$		−	73787.1i		−	0.162874i
$184$		0			0
$185$			35553.5i			0.0763754i
$186$		0			0
$187$	133570.	−	133570.i	0.279322	−	0.279322i
$188$		0			0
$189$	129787.	+	129787.i	0.264288	+	0.264288i
$190$		0			0
$191$	−187212.			−0.371322			−0.185661	−	0.982614i	$-0.559443\pi$
$191$	−187212.			−0.371322			−0.185661	+	0.982614i	$0.559443\pi$
$192$		0			0
$193$	592251.			1.14449			0.572246	−	0.820082i	$-0.306072\pi$
$193$	592251.			1.14449			0.572246	+	0.820082i	$0.306072\pi$
$194$		0			0
$195$	−7956.29	−	7956.29i	−0.0149839	−	0.0149839i
$196$		0			0
$197$	718774.	−	718774.i	1.31955	−	1.31955i	0.405425	−	0.914128i	$-0.367124\pi$
$197$	718774.	−	718774.i	1.31955	−	1.31955i	0.914128	−	0.405425i	$-0.132876\pi$
$198$		0			0
$199$			285135.i			0.510408i	0.966887	+	0.255204i	$0.0821426\pi$
$199$			285135.i			0.510408i	−0.966887	+	0.255204i	$0.917857\pi$
$200$		0			0
$201$		−	27857.4i		−	0.0486351i
$202$		0			0
$203$	1.08646e6	−	1.08646e6i	1.85043	−	1.85043i
$204$		0			0
$205$	145143.	+	145143.i	0.241219	+	0.241219i
$206$		0			0
$207$	−451204.			−0.731893
$208$		0			0
$209$	109061.			0.172704
$210$		0			0
$211$	−679372.	−	679372.i	−1.05051	−	1.05051i	−0.998654	−	0.0518587i	$-0.983485\pi$
$211$	−679372.	−	679372.i	−1.05051	−	1.05051i	−0.0518587	−	0.998654i	$-0.516515\pi$
$212$		0			0
$213$	59409.2	−	59409.2i	0.0897232	−	0.0897232i
$214$		0			0
$215$		−	223502.i		−	0.329750i
$216$		0			0
$217$			877368.i			1.26483i
$218$		0			0
$219$	−9938.61	+	9938.61i	−0.0140028	+	0.0140028i
$220$		0			0
$221$	−160779.	−	160779.i	−0.221437	−	0.221437i
$222$		0			0
$223$	−20550.5			−0.0276732			−0.0138366	−	0.999904i	$-0.504404\pi$
$223$	−20550.5			−0.0276732			−0.0138366	+	0.999904i	$0.504404\pi$
$224$		0			0
$225$	706851.			0.930833
$226$		0			0
$227$	939376.	+	939376.i	1.20997	+	1.20997i	0.971035	+	0.238936i	$0.0767986\pi$
$227$	939376.	+	939376.i	1.20997	+	1.20997i	0.238936	+	0.971035i	$0.423201\pi$
$228$		0			0
$229$	−80627.5	+	80627.5i	−0.101600	+	0.101600i	−0.756080	−	0.654480i	$-0.772888\pi$
$229$	−80627.5	+	80627.5i	−0.101600	+	0.101600i	0.654480	+	0.756080i	$0.272888\pi$
$230$		0			0
$231$		−	151756.i		−	0.187119i
$232$		0			0
$233$			293436.i			0.354098i	0.984202	+	0.177049i	$0.0566551\pi$
$233$			293436.i			0.354098i	−0.984202	+	0.177049i	$0.943345\pi$
$234$		0			0
$235$	−41443.8	+	41443.8i	−0.0489542	+	0.0489542i
$236$		0			0
$237$	92332.3	+	92332.3i	0.106778	+	0.106778i
$238$		0			0
$239$	109538.			0.124042			0.0620211	−	0.998075i	$-0.480245\pi$
$239$	109538.			0.124042			0.0620211	+	0.998075i	$0.480245\pi$
$240$		0			0
$241$	734422.			0.814522			0.407261	−	0.913312i	$-0.366484\pi$
$241$	734422.			0.814522			0.407261	+	0.913312i	$0.366484\pi$
$242$		0			0
$243$	−215491.	−	215491.i	−0.234107	−	0.234107i
$244$		0			0
$245$	287436.	−	287436.i	0.305933	−	0.305933i
$246$		0			0
$247$		−	131277.i		−	0.136914i
$248$		0			0
$249$		−	156065.i		−	0.159517i
$250$		0			0
$251$	−689488.	+	689488.i	−0.690784	+	0.690784i	−0.962405	−	0.271620i	$-0.912441\pi$
$251$	−689488.	+	689488.i	−0.690784	+	0.690784i	0.271620	+	0.962405i	$0.412441\pi$
$252$		0			0
$253$	530945.	+	530945.i	0.521493	+	0.521493i
$254$		0			0
$255$	11075.1			0.0106659
$256$		0			0
$257$	−1.75709e6			−1.65944			−0.829719	−	0.558181i	$-0.811499\pi$
$257$	−1.75709e6			−1.65944			−0.829719	+	0.558181i	$0.811499\pi$
$258$		0			0
$259$	408140.	+	408140.i	0.378059	+	0.378059i
$260$		0			0
$261$	−1.20006e6	+	1.20006e6i	−1.09044	+	1.09044i
$262$		0			0
$263$			1.72852e6i			1.54094i	0.637478	+	0.770468i	$0.279978\pi$
$263$			1.72852e6i			1.54094i	−0.637478	+	0.770468i	$0.720022\pi$
$264$		0			0
$265$		−	371037.i		−	0.324565i
$266$		0			0
$267$	115674.	−	115674.i	0.0993015	−	0.0993015i
$268$		0			0
$269$	198893.	+	198893.i	0.167587	+	0.167587i	0.785918	−	0.618331i	$-0.212191\pi$
$269$	198893.	+	198893.i	0.167587	+	0.167587i	−0.618331	+	0.785918i	$0.712191\pi$
$270$		0			0
$271$	−1.61535e6			−1.33612			−0.668059	−	0.744109i	$-0.732874\pi$
$271$	−1.61535e6			−1.33612			−0.668059	+	0.744109i	$0.732874\pi$
$272$		0			0
$273$	−182670.			−0.148341
$274$		0			0
$275$	−831772.	−	831772.i	−0.663243	−	0.663243i
$276$		0			0
$277$	418236.	−	418236.i	0.327508	−	0.327508i	−0.524130	−	0.851638i	$-0.675610\pi$
$277$	418236.	−	418236.i	0.327508	−	0.327508i	0.851638	+	0.524130i	$0.175610\pi$
$278$		0			0
$279$		−	969107.i		−	0.745352i
$280$		0			0
$281$		−	1.87424e6i		−	1.41599i	−0.706219	−	0.707994i	$-0.749601\pi$
$281$		−	1.87424e6i		−	1.41599i	0.706219	−	0.707994i	$-0.250399\pi$
$282$		0			0
$283$	−1.11383e6	+	1.11383e6i	−0.826706	+	0.826706i	−0.987060	−	0.160353i	$-0.948737\pi$
$283$	−1.11383e6	+	1.11383e6i	−0.826706	+	0.826706i	0.160353	+	0.987060i	$0.448737\pi$
$284$		0			0
$285$	4521.42	+	4521.42i	0.00329733	+	0.00329733i
$286$		0			0
$287$	3.33237e6			2.38808
$288$		0			0
$289$	−1.19605e6			−0.842376
$290$		0			0
$291$	−196482.	−	196482.i	−0.136016	−	0.136016i
$292$		0			0
$293$	488382.	−	488382.i	0.332346	−	0.332346i	−0.521131	−	0.853477i	$-0.674490\pi$
$293$	488382.	−	488382.i	0.332346	−	0.332346i	0.853477	+	0.521131i	$0.174490\pi$
$294$		0			0
$295$		−	404930.i		−	0.270910i
$296$		0			0
$297$			337387.i			0.221941i
$298$		0			0
$299$	639102.	−	639102.i	0.413421	−	0.413421i
$300$		0			0
$301$	−2.56571e6	−	2.56571e6i	−1.63227	−	1.63227i
$302$		0			0
$303$	−270696.			−0.169385
$304$		0			0
$305$	564294.			0.347341
$306$		0			0
$307$	−396811.	−	396811.i	−0.240291	−	0.240291i	0.576679	−	0.816971i	$-0.304348\pi$
$307$	−396811.	−	396811.i	−0.240291	−	0.240291i	−0.816971	+	0.576679i	$0.804348\pi$
$308$		0			0
$309$	−70032.4	+	70032.4i	−0.0417256	+	0.0417256i
$310$		0			0
$311$		−	1.80244e6i		−	1.05672i	−0.849020	−	0.528361i	$-0.822807\pi$
$311$		−	1.80244e6i		−	1.05672i	0.849020	−	0.528361i	$-0.177193\pi$
$312$		0			0
$313$			346574.i			0.199956i	0.994990	+	0.0999780i	$0.0318773\pi$
$313$			346574.i			0.199956i	−0.994990	+	0.0999780i	$0.968123\pi$
$314$		0			0
$315$	−493135.	+	493135.i	−0.280020	+	0.280020i
$316$		0			0
$317$	−1.44830e6	−	1.44830e6i	−0.809487	−	0.809487i	0.175069	−	0.984556i	$-0.443985\pi$
$317$	−1.44830e6	−	1.44830e6i	−0.809487	−	0.809487i	−0.984556	+	0.175069i	$0.943985\pi$
$318$		0			0
$319$	2.82429e6			1.55393
$320$		0			0
$321$	−260034.			−0.140854
$322$		0			0
$323$	91368.1	+	91368.1i	0.0487291	+	0.0487291i
$324$		0			0
$325$	−1.00121e6	+	1.00121e6i	−0.525795	+	0.525795i
$326$		0			0
$327$		−	88263.8i		−	0.0456471i
$328$		0			0
$329$			951516.i			0.484648i
$330$		0			0
$331$	−881414.	+	881414.i	−0.442191	+	0.442191i	−0.892748	−	0.450557i	$-0.851225\pi$
$331$	−881414.	+	881414.i	−0.442191	+	0.442191i	0.450557	+	0.892748i	$0.351225\pi$
$332$		0			0
$333$	−450816.	−	450816.i	−0.222786	−	0.222786i
$334$		0			0
$335$	213042.			0.103718
$336$		0			0
$337$	−2.66445e6			−1.27801			−0.639003	−	0.769205i	$-0.720653\pi$
$337$	−2.66445e6			−1.27801			−0.639003	+	0.769205i	$0.720653\pi$
$338$		0			0
$339$	97529.5	+	97529.5i	0.0460932	+	0.0460932i
$340$		0			0
$341$	−1.14038e6	+	1.14038e6i	−0.531083	+	0.531083i
$342$		0			0
$343$		−	2.94839e6i		−	1.35316i
$344$		0			0
$345$			44023.7i			0.0199131i
$346$		0			0
$347$	−1.42569e6	+	1.42569e6i	−0.635626	+	0.635626i	−0.949473	−	0.313848i	$-0.898382\pi$
$347$	−1.42569e6	+	1.42569e6i	−0.635626	+	0.635626i	0.313848	+	0.949473i	$0.398382\pi$
$348$		0			0
$349$	297231.	+	297231.i	0.130626	+	0.130626i	0.769397	−	0.638771i	$-0.220557\pi$
$349$	297231.	+	297231.i	0.130626	+	0.130626i	−0.638771	+	0.769397i	$0.720557\pi$
$350$		0			0
$351$	406115.			0.175947
$352$		0			0
$353$	−1.12097e6			−0.478804			−0.239402	−	0.970921i	$-0.576951\pi$
$353$	−1.12097e6			−0.478804			−0.239402	+	0.970921i	$0.576951\pi$
$354$		0			0
$355$	454338.	+	454338.i	0.191341	+	0.191341i
$356$		0			0
$357$	127137.	−	127137.i	0.0527962	−	0.0527962i
$358$		0			0
$359$			3.31336e6i			1.35685i	0.734669	+	0.678426i	$0.237337\pi$
$359$			3.31336e6i			1.35685i	−0.734669	+	0.678426i	$0.762663\pi$
$360$		0			0
$361$		−	2.40150e6i		−	0.969871i
$362$		0			0
$363$	−1999.28	+	1999.28i	−0.000796356	+	0.000796356i
$364$		0			0
$365$	−76006.5	−	76006.5i	−0.0298620	−	0.0298620i
$366$		0			0
$367$	1.22043e6			0.472986			0.236493	−	0.971633i	$-0.424002\pi$
$367$	1.22043e6			0.472986			0.236493	+	0.971633i	$0.424002\pi$
$368$		0			0
$369$	−3.68081e6			−1.40727
$370$		0			0
$371$	−4.25935e6	−	4.25935e6i	−1.60660	−	1.60660i
$372$		0			0
$373$	−1.20408e6	+	1.20408e6i	−0.448109	+	0.448109i	−0.894725	−	0.446617i	$-0.852629\pi$
$373$	−1.20408e6	+	1.20408e6i	−0.448109	+	0.448109i	0.446617	+	0.894725i	$0.352629\pi$
$374$		0			0
$375$		−	142125.i		−	0.0521907i
$376$		0			0
$377$		−	3.39962e6i		−	1.23190i
$378$		0			0
$379$	−2.81398e6	+	2.81398e6i	−1.00629	+	1.00629i	−0.00630982	+	0.999980i	$0.502008\pi$
$379$	−2.81398e6	+	2.81398e6i	−1.00629	+	1.00629i	−0.999980	+	0.00630982i	$0.997992\pi$
$380$		0			0
$381$	181468.	+	181468.i	0.0640453	+	0.0640453i
$382$		0			0
$383$	432846.			0.150777			0.0753887	−	0.997154i	$-0.475980\pi$
$383$	432846.			0.150777			0.0753887	+	0.997154i	$0.475980\pi$
$384$		0			0
$385$	1.16057e6			0.399043
$386$		0			0
$387$	2.83398e6	+	2.83398e6i	0.961878	+	0.961878i
$388$		0			0
$389$	1.69223e6	−	1.69223e6i	0.567002	−	0.567002i	−0.364286	−	0.931287i	$-0.618687\pi$
$389$	1.69223e6	−	1.69223e6i	0.567002	−	0.567002i	0.931287	+	0.364286i	$0.118687\pi$
$390$		0			0
$391$			889622.i			0.294282i
$392$		0			0
$393$		−	403386.i		−	0.131747i
$394$		0			0
$395$	−706120.	+	706120.i	−0.227712	+	0.227712i
$396$		0			0
$397$	2.05447e6	+	2.05447e6i	0.654221	+	0.654221i	0.954007	−	0.299786i	$-0.0969151\pi$
$397$	2.05447e6	+	2.05447e6i	0.654221	+	0.654221i	−0.299786	+	0.954007i	$0.596915\pi$
$398$		0			0
$399$	103808.			0.0326437
$400$		0			0
$401$	2.95627e6			0.918087			0.459043	−	0.888414i	$-0.348192\pi$
$401$	2.95627e6			0.918087			0.459043	+	0.888414i	$0.348192\pi$
$402$		0			0
$403$	1.37268e6	+	1.37268e6i	0.421023	+	0.421023i
$404$		0			0
$405$	537659.	−	537659.i	0.162881	−	0.162881i
$406$		0			0
$407$			1.06098e6i			0.317482i
$408$		0			0
$409$			4.47118e6i			1.32164i	0.750544	+	0.660821i	$0.229792\pi$
$409$			4.47118e6i			1.32164i	−0.750544	+	0.660821i	$0.770208\pi$
$410$		0			0
$411$	−160415.	+	160415.i	−0.0468426	+	0.0468426i
$412$		0			0
$413$	−4.64843e6	−	4.64843e6i	−1.34101	−	1.34101i
$414$		0			0
$415$	1.19353e6			0.340182
$416$		0			0
$417$	726672.			0.204644
$418$		0			0
$419$	−2.61373e6	−	2.61373e6i	−0.727321	−	0.727321i	0.242765	−	0.970085i	$-0.421946\pi$
$419$	−2.61373e6	−	2.61373e6i	−0.727321	−	0.727321i	−0.970085	+	0.242765i	$0.921946\pi$
$420$		0			0
$421$	−295751.	+	295751.i	−0.0813244	+	0.0813244i	−0.746599	−	0.665274i	$-0.768315\pi$
$421$	−295751.	+	295751.i	−0.0813244	+	0.0813244i	0.665274	+	0.746599i	$0.268315\pi$
$422$		0			0
$423$		−	1.05101e6i		−	0.285598i
$424$		0			0
$425$		−	1.39367e6i		−	0.374273i
$426$		0			0
$427$	6.47786e6	−	6.47786e6i	1.71934	−	1.71934i
$428$		0			0
$429$	−237429.	−	237429.i	−0.0622860	−	0.0622860i
$430$		0			0
$431$	−4.14971e6			−1.07603			−0.538016	−	0.842935i	$-0.680826\pi$
$431$	−4.14971e6			−1.07603			−0.538016	+	0.842935i	$0.680826\pi$
$432$		0			0
$433$	−1.48115e6			−0.379647			−0.189823	−	0.981818i	$-0.560792\pi$
$433$	−1.48115e6			−0.379647			−0.189823	+	0.981818i	$0.560792\pi$
$434$		0			0
$435$	117089.	+	117089.i	0.0296683	+	0.0296683i
$436$		0			0
$437$	−363190.	+	363190.i	−0.0909768	+	0.0909768i
$438$		0			0
$439$		−	3.98071e6i		−	0.985824i	−0.870079	−	0.492912i	$-0.835932\pi$
$439$		−	3.98071e6i		−	0.985824i	0.870079	−	0.492912i	$-0.164068\pi$
$440$		0			0
$441$			7.28932e6i			1.78481i
$442$		0			0
$443$	713863.	−	713863.i	0.172825	−	0.172825i	−0.615395	−	0.788219i	$-0.711003\pi$
$443$	713863.	−	713863.i	0.172825	−	0.172825i	0.788219	+	0.615395i	$0.211003\pi$
$444$		0			0
$445$	884624.	+	884624.i	0.211767	+	0.211767i
$446$		0			0
$447$	68857.5			0.0162998
$448$		0			0
$449$	3.43383e6			0.803827			0.401913	−	0.915678i	$-0.368345\pi$
$449$	3.43383e6			0.803827			0.401913	+	0.915678i	$0.368345\pi$
$450$		0			0
$451$	4.33131e6	+	4.33131e6i	1.00272	+	1.00272i
$452$		0			0
$453$	100654.	−	100654.i	0.0230455	−	0.0230455i
$454$		0			0
$455$		−	1.39699e6i		−	0.316347i
$456$		0			0
$457$			1.19382e6i			0.267393i	0.991022	+	0.133696i	$0.0426847\pi$
$457$			1.19382e6i			0.267393i	−0.991022	+	0.133696i	$0.957315\pi$
$458$		0			0
$459$	−282653.	+	282653.i	−0.0626214	+	0.0626214i
$460$		0			0
$461$	3.31361e6	+	3.31361e6i	0.726189	+	0.726189i	0.969858	−	0.243669i	$-0.0783512\pi$
$461$	3.31361e6	+	3.31361e6i	0.726189	+	0.726189i	−0.243669	+	0.969858i	$0.578351\pi$
$462$		0			0
$463$	−2.87318e6			−0.622888			−0.311444	−	0.950265i	$-0.600813\pi$
$463$	−2.87318e6			−0.622888			−0.311444	+	0.950265i	$0.600813\pi$
$464$		0			0
$465$	−94555.0			−0.0202793
$466$		0			0
$467$	−2.07444e6	−	2.07444e6i	−0.440159	−	0.440159i	0.451906	−	0.892065i	$-0.350744\pi$
$467$	−2.07444e6	−	2.07444e6i	−0.440159	−	0.440159i	−0.892065	+	0.451906i	$0.850744\pi$
$468$		0			0
$469$	2.44564e6	−	2.44564e6i	0.513405	−	0.513405i
$470$		0			0
$471$			501659.i			0.104197i
$472$		0			0
$473$		−	6.66966e6i		−	1.37073i
$474$		0			0
$475$	568970.	−	568970.i	0.115706	−	0.115706i
$476$		0			0
$477$	4.70471e6	+	4.70471e6i	0.946754	+	0.946754i
$478$		0			0
$479$	−5.37108e6			−1.06960			−0.534801	−	0.844978i	$-0.679614\pi$
$479$	−5.37108e6			−1.06960			−0.534801	+	0.844978i	$0.679614\pi$
$480$		0			0
$481$	1.27710e6			0.251688
$482$		0			0
$483$	505374.	+	505374.i	0.0985701	+	0.0985701i
$484$		0			0
$485$	1.50261e6	−	1.50261e6i	0.290063	−	0.290063i
$486$		0			0
$487$			6.47468e6i			1.23708i	0.785755	+	0.618538i	$0.212275\pi$
$487$			6.47468e6i			1.23708i	−0.785755	+	0.618538i	$0.787725\pi$
$488$		0			0
$489$			948157.i			0.179311i
$490$		0			0
$491$	3.39527e6	−	3.39527e6i	0.635581	−	0.635581i	−0.313881	−	0.949462i	$-0.601629\pi$
$491$	3.39527e6	−	3.39527e6i	0.635581	−	0.635581i	0.949462	+	0.313881i	$0.101629\pi$
$492$		0			0
$493$	2.36611e6	+	2.36611e6i	0.438448	+	0.438448i
$494$		0			0
$495$	−1.28192e6			−0.235152
$496$		0			0
$497$	1.04312e7			1.89428
$498$		0			0
$499$	2.47024e6	+	2.47024e6i	0.444107	+	0.444107i	0.893390	−	0.449283i	$-0.148320\pi$
$499$	2.47024e6	+	2.47024e6i	0.444107	+	0.444107i	−0.449283	+	0.893390i	$0.648320\pi$
$500$		0			0
$501$	−648193.	+	648193.i	−0.115374	+	0.115374i
$502$		0			0
$503$			9.84544e6i			1.73506i	0.497383	+	0.867531i	$0.334294\pi$
$503$			9.84544e6i			1.73506i	−0.497383	+	0.867531i	$0.665706\pi$
$504$		0			0
$505$		−	2.07017e6i		−	0.361225i
$506$		0			0
$507$	173558.	−	173558.i	0.0299864	−	0.0299864i
$508$		0			0
$509$	2.92555e6	+	2.92555e6i	0.500511	+	0.500511i	0.911597	−	0.411086i	$-0.134850\pi$
$509$	2.92555e6	+	2.92555e6i	0.500511	+	0.500511i	−0.411086	+	0.911597i	$0.634850\pi$
$510$		0			0
$511$	−1.74505e6			−0.295635
$512$		0			0
$513$	−230788.			−0.0387186
$514$		0			0
$515$	−535580.	−	535580.i	−0.0889828	−	0.0889828i
$516$		0			0
$517$	−1.23675e6	+	1.23675e6i	−0.203496	+	0.203496i
$518$		0			0
$519$			1.10705e6i			0.180405i
$520$		0			0
$521$			160551.i			0.0259130i	0.999916	+	0.0129565i	$0.00412430\pi$
$521$			160551.i			0.0259130i	−0.999916	+	0.0129565i	$0.995876\pi$
$522$		0			0
$523$	−2.69862e6	+	2.69862e6i	−0.431408	+	0.431408i	−0.889107	−	0.457699i	$-0.848674\pi$
$523$	−2.69862e6	+	2.69862e6i	−0.431408	+	0.431408i	0.457699	+	0.889107i	$0.348674\pi$
$524$		0			0
$525$	−791713.	−	791713.i	−0.125363	−	0.125363i
$526$		0			0
$527$	−1.91075e6			−0.299694
$528$		0			0
$529$	2.90007e6			0.450578
$530$		0			0
$531$	5.13448e6	+	5.13448e6i	0.790241	+	0.790241i
$532$		0			0
$533$	5.21363e6	−	5.21363e6i	0.794918	−	0.794918i
$534$		0			0
$535$		−	1.98864e6i		−	0.300380i
$536$		0			0
$537$			487380.i			0.0729343i
$538$		0			0
$539$	8.57756e6	−	8.57756e6i	1.27172	−	1.27172i
$540$		0			0
$541$	6.35404e6	+	6.35404e6i	0.933376	+	0.933376i	0.997915	−	0.0645390i	$-0.0205577\pi$
$541$	6.35404e6	+	6.35404e6i	0.933376	+	0.933376i	−0.0645390	+	0.997915i	$0.520558\pi$
$542$		0			0
$543$	−643250.			−0.0936225
$544$		0			0
$545$	675005.			0.0973455
$546$		0			0
$547$	−3.08327e6	−	3.08327e6i	−0.440599	−	0.440599i	0.451614	−	0.892213i	$-0.350848\pi$
$547$	−3.08327e6	−	3.08327e6i	−0.440599	−	0.440599i	−0.892213	+	0.451614i	$0.850848\pi$
$548$		0			0
$549$	−7.15519e6	+	7.15519e6i	−1.01319	+	1.01319i
$550$		0			0
$551$			1.93194e6i			0.271091i
$552$		0			0
$553$			1.62119e7i			2.25436i
$554$		0			0
$555$	−43985.7	+	43985.7i	−0.00606149	+	0.00606149i
$556$		0			0
$557$	−4.15476e6	−	4.15476e6i	−0.567424	−	0.567424i	0.363982	−	0.931406i	$-0.381417\pi$
$557$	−4.15476e6	−	4.15476e6i	−0.567424	−	0.567424i	−0.931406	+	0.363982i	$0.881417\pi$
$558$		0			0
$559$	−8.02831e6			−1.08666
$560$		0			0
$561$	330498.			0.0443365
$562$		0			0
$563$	−2.09434e6	−	2.09434e6i	−0.278469	−	0.278469i	0.554029	−	0.832497i	$-0.313090\pi$
$563$	−2.09434e6	−	2.09434e6i	−0.278469	−	0.278469i	−0.832497	+	0.554029i	$0.813090\pi$
$564$		0			0
$565$	−745866.	+	745866.i	−0.0982969	+	0.0982969i
$566$		0			0
$567$		−	1.23442e7i		−	1.61252i
$568$		0			0
$569$		−	3.46207e6i		−	0.448286i	−0.974556	−	0.224143i	$-0.928042\pi$
$569$		−	3.46207e6i		−	0.448286i	0.974556	−	0.224143i	$-0.0719583\pi$
$570$		0			0
$571$	5.29256e6	−	5.29256e6i	0.679321	−	0.679321i	−0.280525	−	0.959847i	$-0.590509\pi$
$571$	5.29256e6	−	5.29256e6i	0.679321	−	0.679321i	0.959847	+	0.280525i	$0.0905087\pi$
$572$		0			0
$573$	−231613.	−	231613.i	−0.0294698	−	0.0294698i
$574$		0			0
$575$	5.53988e6			0.698764
$576$		0			0
$577$	2.13325e6			0.266749			0.133374	−	0.991066i	$-0.457419\pi$
$577$	2.13325e6			0.266749			0.133374	+	0.991066i	$0.457419\pi$
$578$		0			0
$579$	732715.	+	732715.i	0.0908320	+	0.0908320i
$580$		0			0
$581$	1.37012e7	−	1.37012e7i	1.68391	−	1.68391i
$582$		0			0
$583$		−	1.10723e7i		−	1.34917i
$584$		0			0
$585$			1.54306e6i			0.186420i
$586$		0			0
$587$	1.61821e6	−	1.61821e6i	0.193839	−	0.193839i	−0.603514	−	0.797353i	$-0.706233\pi$
$587$	1.61821e6	−	1.61821e6i	0.193839	−	0.193839i	0.797353	+	0.603514i	$0.206233\pi$
$588$		0			0
$589$	−780069.	−	780069.i	−0.0926498	−	0.0926498i
$590$		0			0
$591$	1.77849e6			0.209451
$592$		0			0
$593$	1.12281e6			0.131121			0.0655603	−	0.997849i	$-0.479117\pi$
$593$	1.12281e6			0.131121			0.0655603	+	0.997849i	$0.479117\pi$
$594$		0			0
$595$	972295.	+	972295.i	0.112591	+	0.112591i
$596$		0			0
$597$	−352760.	+	352760.i	−0.0405082	+	0.0405082i
$598$		0			0
$599$			8.37554e6i			0.953774i	0.878965	+	0.476887i	$0.158235\pi$
$599$			8.37554e6i			0.953774i	−0.878965	+	0.476887i	$0.841765\pi$
$600$		0			0
$601$			3.75444e6i			0.423994i	0.977270	+	0.211997i	$0.0679967\pi$
$601$			3.75444e6i			0.423994i	−0.977270	+	0.211997i	$0.932003\pi$
$602$		0			0
$603$	−2.70135e6	+	2.70135e6i	−0.302544	+	0.302544i
$604$		0			0
$605$	−15289.7	−	15289.7i	−0.00169828	−	0.00169828i
$606$		0			0
$607$	−1.04209e7			−1.14798			−0.573988	−	0.818864i	$-0.694604\pi$
$607$	−1.04209e7			−1.14798			−0.573988	+	0.818864i	$0.694604\pi$
$608$		0			0
$609$	2.68827e6			0.293717
$610$		0			0
$611$	1.48868e6	+	1.48868e6i	0.161324	+	0.161324i
$612$		0			0
$613$	−9.21233e6	+	9.21233e6i	−0.990190	+	0.990190i	−0.999952	−	0.00976261i	$-0.996892\pi$
$613$	−9.21233e6	+	9.21233e6i	−0.990190	+	0.990190i	0.00976261	+	0.999952i	$0.496892\pi$
$614$		0			0
$615$			359134.i			0.0382885i
$616$		0			0
$617$		−	1.42219e7i		−	1.50399i	−0.659167	−	0.751997i	$-0.729091\pi$
$617$		−	1.42219e7i		−	1.50399i	0.659167	−	0.751997i	$-0.270909\pi$
$618$		0			0
$619$	−9.69068e6	+	9.69068e6i	−1.01655	+	1.01655i	−0.0166871	+	0.999861i	$0.505312\pi$
$619$	−9.69068e6	+	9.69068e6i	−1.01655	+	1.01655i	−0.999861	+	0.0166871i	$0.994688\pi$
$620$		0			0
$621$	−1.12355e6	−	1.12355e6i	−0.116914	−	0.116914i
$622$		0			0
$623$	2.03103e7			2.09650
$624$		0			0
$625$	−8.11922e6			−0.831409
$626$		0			0
$627$	134927.	+	134927.i	0.0137066	+	0.0137066i
$628$		0			0
$629$	−888856.	+	888856.i	−0.0895787	+	0.0895787i
$630$		0			0
$631$			1.49041e7i			1.49016i	0.666974	+	0.745081i	$0.267589\pi$
$631$			1.49041e7i			1.49016i	−0.666974	+	0.745081i	$0.732411\pi$
$632$		0			0
$633$		−	1.68100e6i		−	0.166747i
$634$		0			0
$635$	−1.38779e6	+	1.38779e6i	−0.136581	+	0.136581i
$636$		0			0
$637$	−1.03249e7	−	1.03249e7i	−1.00817	−	1.00817i
$638$		0			0
$639$	−1.15219e7			−1.11628
$640$		0			0
$641$	−1.23159e7			−1.18391			−0.591956	−	0.805970i	$-0.701644\pi$
$641$	−1.23159e7			−1.18391			−0.591956	+	0.805970i	$0.701644\pi$
$642$		0			0
$643$	−4.66909e6	−	4.66909e6i	−0.445353	−	0.445353i	0.448453	−	0.893806i	$-0.351975\pi$
$643$	−4.66909e6	−	4.66909e6i	−0.445353	−	0.445353i	−0.893806	+	0.448453i	$0.851975\pi$
$644$		0			0
$645$	276510.	−	276510.i	0.0261704	−	0.0261704i
$646$		0			0
$647$			1.22769e7i			1.15299i	0.817100	+	0.576496i	$0.195581\pi$
$647$			1.22769e7i			1.15299i	−0.817100	+	0.576496i	$0.804419\pi$
$648$		0			0
$649$		−	1.20838e7i		−	1.12614i
$650$		0			0
$651$	−1.08545e6	+	1.08545e6i	−0.100383	+	0.100383i
$652$		0			0
$653$	5.63324e6	+	5.63324e6i	0.516982	+	0.516982i	0.916657	−	0.399675i	$-0.130877\pi$
$653$	5.63324e6	+	5.63324e6i	0.516982	+	0.516982i	−0.399675	+	0.916657i	$0.630877\pi$
$654$		0			0
$655$	3.08494e6			0.280959
$656$		0			0
$657$	1.92751e6			0.174214
$658$		0			0
$659$	−3.13854e6	−	3.13854e6i	−0.281523	−	0.281523i	0.552193	−	0.833716i	$-0.313791\pi$
$659$	−3.13854e6	−	3.13854e6i	−0.281523	−	0.281523i	−0.833716	+	0.552193i	$0.813791\pi$
$660$		0			0
$661$	−2.25214e6	+	2.25214e6i	−0.200489	+	0.200489i	−0.800210	−	0.599720i	$-0.795278\pi$
$661$	−2.25214e6	+	2.25214e6i	−0.200489	+	0.200489i	0.599720	+	0.800210i	$0.295278\pi$
$662$		0			0
$663$		−	397823.i		−	0.0351484i
$664$		0			0
$665$			793884.i			0.0696150i
$666$		0			0
$667$	−9.40536e6	+	9.40536e6i	−0.818579	+	0.818579i
$668$		0			0
$669$	−25424.4	−	25424.4i	−0.00219627	−	0.00219627i
$670$		0			0
$671$	1.68394e7			1.44385
$672$		0			0
$673$	−5.80254e6			−0.493834			−0.246917	−	0.969037i	$-0.579417\pi$
$673$	−5.80254e6			−0.493834			−0.246917	+	0.969037i	$0.579417\pi$
$674$		0			0
$675$	1.76015e6	+	1.76015e6i	0.148693	+	0.148693i
$676$		0			0
$677$	5.37302e6	−	5.37302e6i	0.450554	−	0.450554i	−0.444984	−	0.895538i	$-0.646791\pi$
$677$	5.37302e6	−	5.37302e6i	0.450554	−	0.450554i	0.895538	+	0.444984i	$0.146791\pi$
$678$		0			0
$679$		−	3.44988e7i		−	2.87163i
$680$		0			0
$681$			2.32434e6i			0.192057i
$682$		0			0
$683$	−7.95020e6	+	7.95020e6i	−0.652118	+	0.652118i	−0.953503	−	0.301384i	$-0.902551\pi$
$683$	−7.95020e6	+	7.95020e6i	−0.652118	+	0.652118i	0.301384	+	0.953503i	$0.402551\pi$
$684$		0			0
$685$	−1.22679e6	−	1.22679e6i	−0.0998950	−	0.0998950i
$686$		0			0
$687$	−199500.			−0.0161269
$688$		0			0
$689$	−1.33278e7			−1.06958
$690$		0			0
$691$	1.10073e7	+	1.10073e7i	0.876968	+	0.876968i	0.993220	−	0.116251i	$-0.0370878\pi$
$691$	1.10073e7	+	1.10073e7i	0.876968	+	0.876968i	−0.116251	+	0.993220i	$0.537088\pi$
$692$		0			0
$693$	−1.47159e7	+	1.47159e7i	−1.16401	+	1.16401i
$694$		0			0
$695$			5.55729e6i			0.436417i
$696$		0			0
$697$			7.25731e6i			0.565840i
$698$		0			0
$699$	−363030.	+	363030.i	−0.0281028	+	0.0281028i
$700$		0			0
$701$	−9.83300e6	−	9.83300e6i	−0.755772	−	0.755772i	0.219778	−	0.975550i	$-0.429467\pi$
$701$	−9.83300e6	−	9.83300e6i	−0.755772	−	0.755772i	−0.975550	+	0.219778i	$0.929467\pi$
$702$		0			0
$703$	−725755.			−0.0553862
$704$		0			0
$705$	−102546.			−0.00777045
$706$		0			0
$707$	−2.37647e7	−	2.37647e7i	−1.78807	−	1.78807i
$708$		0			0
$709$	−6.04507e6	+	6.04507e6i	−0.451633	+	0.451633i	−0.895896	−	0.444263i	$-0.853465\pi$
$709$	−6.04507e6	+	6.04507e6i	−0.451633	+	0.451633i	0.444263	+	0.895896i	$0.353465\pi$
$710$		0			0
$711$		−	1.79071e7i		−	1.32847i
$712$		0			0
$713$		−	7.59528e6i		−	0.559526i
$714$		0			0
$715$	1.81576e6	−	1.81576e6i	0.132829	−	0.132829i
$716$		0			0
$717$	135517.	+	135517.i	0.00984454	+	0.00984454i
$718$		0			0
$719$	2.40812e7			1.73722			0.868611	−	0.495495i	$-0.165013\pi$
$719$	2.40812e7			1.73722			0.868611	+	0.495495i	$0.165013\pi$
$720$		0			0
$721$	−1.22965e7			−0.880932
$722$		0			0
$723$	908604.	+	908604.i	0.0646441	+	0.0646441i
$724$		0			0
$725$	1.47343e7	−	1.47343e7i	1.04108	−	1.04108i
$726$		0			0
$727$		−	5.30046e6i		−	0.371944i	−0.982555	−	0.185972i	$-0.940457\pi$
$727$		−	5.30046e6i		−	0.371944i	0.982555	−	0.185972i	$-0.0595434\pi$
$728$		0			0
$729$			1.32757e7i			0.925207i
$730$		0			0
$731$	5.58766e6	−	5.58766e6i	0.386755	−	0.386755i
$732$		0			0
$733$	−1.14793e7	−	1.14793e7i	−0.789143	−	0.789143i	0.192210	−	0.981354i	$-0.438434\pi$
$733$	−1.14793e7	−	1.14793e7i	−0.789143	−	0.789143i	−0.981354	+	0.192210i	$0.938434\pi$
$734$		0			0
$735$	711214.			0.0485604
$736$		0			0
$737$	6.35752e6			0.431141
$738$		0			0
$739$	1.10488e6	+	1.10488e6i	0.0744226	+	0.0744226i	0.743338	−	0.668916i	$-0.233241\pi$
$739$	1.10488e6	+	1.10488e6i	0.0744226	+	0.0744226i	−0.668916	+	0.743338i	$0.733241\pi$
$740$		0			0
$741$	162412.	−	162412.i	0.0108661	−	0.0108661i
$742$		0			0
$743$			2.73631e6i			0.181842i	0.995858	+	0.0909209i	$0.0289810\pi$
$743$			2.73631e6i			0.181842i	−0.995858	+	0.0909209i	$0.971019\pi$
$744$		0			0
$745$			526594.i			0.0347605i
$746$		0			0
$747$	−1.51338e7	+	1.51338e7i	−0.992308	+	0.992308i
$748$		0			0
$749$	−2.28288e7	−	2.28288e7i	−1.48689	−	1.48689i
$750$		0			0
$751$	2.79880e7			1.81080			0.905402	−	0.424555i	$-0.139570\pi$
$751$	2.79880e7			1.81080			0.905402	+	0.424555i	$0.139570\pi$
$752$		0			0
$753$	−1.70603e6			−0.109647
$754$		0			0
$755$	769761.	+	769761.i	0.0491460	+	0.0491460i
$756$		0			0
$757$	−1.52053e7	+	1.52053e7i	−0.964393	+	0.964393i	−0.999388	−	0.0349946i	$-0.988859\pi$
$757$	−1.52053e7	+	1.52053e7i	−0.964393	+	0.964393i	0.0349946	+	0.999388i	$0.488859\pi$
$758$		0			0
$759$			1.31374e6i			0.0827760i
$760$		0			0
$761$		−	1.28357e7i		−	0.803448i	−0.915761	−	0.401724i	$-0.868411\pi$
$761$		−	1.28357e7i		−	0.803448i	0.915761	−	0.401724i	$-0.131589\pi$
$762$		0			0
$763$	7.74879e6	−	7.74879e6i	0.481862	−	0.481862i
$764$		0			0
$765$	−1.07396e6	−	1.07396e6i	−0.0663490	−	0.0663490i
$766$		0			0
$767$	−1.45453e7			−0.892760
$768$		0			0
$769$	479067.			0.0292133			0.0146066	−	0.999893i	$-0.495350\pi$
$769$	479067.			0.0292133			0.0146066	+	0.999893i	$0.495350\pi$
$770$		0			0
$771$	−2.17382e6	−	2.17382e6i	−0.131700	−	0.131700i
$772$		0			0
$773$	7.26917e6	−	7.26917e6i	0.437558	−	0.437558i	−0.453631	−	0.891190i	$-0.649872\pi$
$773$	7.26917e6	−	7.26917e6i	0.437558	−	0.437558i	0.891190	+	0.453631i	$0.149872\pi$
$774$		0			0
$775$			1.18987e7i			0.711614i
$776$		0			0
$777$			1.00988e6i			0.0600089i
$778$		0			0
$779$	−2.96282e6	+	2.96282e6i	−0.174929	+	0.174929i
$780$		0			0
$781$	1.35582e7	+	1.35582e7i	0.795378	+	0.795378i
$782$		0			0
$783$	−5.97660e6			−0.348377
$784$		0			0
$785$	−3.83649e6			−0.222208
$786$		0			0
$787$	−924212.	−	924212.i	−0.0531906	−	0.0531906i	0.680011	−	0.733202i	$-0.261975\pi$
$787$	−924212.	−	924212.i	−0.0531906	−	0.0531906i	−0.733202	+	0.680011i	$0.761975\pi$
$788$		0			0
$789$	−2.13847e6	+	2.13847e6i	−0.122296	+	0.122296i
$790$		0			0
$791$			1.71245e7i			0.973142i
$792$		0			0
$793$		−	2.02697e7i		−	1.14463i
$794$		0			0
$795$	459035.	−	459035.i	0.0257590	−	0.0257590i
$796$		0			0
$797$	4.36584e6	+	4.36584e6i	0.243457	+	0.243457i	0.818279	−	0.574822i	$-0.194929\pi$
$797$	4.36584e6	+	4.36584e6i	0.243457	+	0.243457i	−0.574822	+	0.818279i	$0.694929\pi$
$798$		0			0
$799$	−2.07223e6			−0.114834
$800$		0			0
$801$	−2.24339e7			−1.23545
$802$		0			0
$803$	−2.26816e6	−	2.26816e6i	−0.124132	−	0.124132i
$804$		0			0
$805$	−3.86489e6	+	3.86489e6i	−0.210207	+	0.210207i
$806$		0			0
$807$			492129.i			0.0266008i
$808$		0			0
$809$		−	1.80829e7i		−	0.971396i	−0.874127	−	0.485698i	$-0.838565\pi$
$809$		−	1.80829e7i		−	0.971396i	0.874127	−	0.485698i	$-0.161435\pi$
$810$		0			0
$811$	−2.29179e7	+	2.29179e7i	−1.22355	+	1.22355i	−0.257191	+	0.966361i	$0.582797\pi$
$811$	−2.29179e7	+	2.29179e7i	−1.22355	+	1.22355i	−0.966361	+	0.257191i	$0.917203\pi$
$812$		0			0
$813$	−1.99847e6	−	1.99847e6i	−0.106040	−	0.106040i
$814$		0			0
$815$	−7.25112e6			−0.382394
$816$		0			0
$817$	4.56235e6			0.239130
$818$		0			0
$819$	1.77137e7	+	1.77137e7i	0.922782	+	0.922782i
$820$		0			0
$821$	4.13555e6	−	4.13555e6i	0.214129	−	0.214129i	−0.591890	−	0.806019i	$-0.701618\pi$
$821$	4.13555e6	−	4.13555e6i	0.214129	−	0.214129i	0.806019	+	0.591890i	$0.201618\pi$
$822$		0			0
$823$		−	1.35656e7i		−	0.698133i	−0.937098	−	0.349067i	$-0.886499\pi$
$823$		−	1.35656e7i		−	0.698133i	0.937098	−	0.349067i	$-0.113501\pi$
$824$		0			0
$825$		−	2.05809e6i		−	0.105276i
$826$		0			0
$827$	2.05917e6	−	2.05917e6i	0.104696	−	0.104696i	−0.652819	−	0.757514i	$-0.726414\pi$
$827$	2.05917e6	−	2.05917e6i	0.104696	−	0.104696i	0.757514	+	0.652819i	$0.226414\pi$
$828$		0			0
$829$	2.41770e7	+	2.41770e7i	1.22185	+	1.22185i	0.966975	+	0.254871i	$0.0820329\pi$
$829$	2.41770e7	+	2.41770e7i	1.22185	+	1.22185i	0.254871	+	0.966975i	$0.417967\pi$
$830$		0			0
$831$	1.03486e6			0.0519850
$832$		0			0
$833$	1.43721e7			0.717641
$834$		0			0
$835$	−4.95711e6	−	4.95711e6i	−0.246044	−	0.246044i
$836$		0			0
$837$	2.41320e6	−	2.41320e6i	0.119064	−	0.119064i
$838$		0			0
$839$		−	9.89108e6i		−	0.485108i	−0.970138	−	0.242554i	$-0.922015\pi$
$839$		−	9.89108e6i		−	0.485108i	0.970138	−	0.242554i	$-0.0779852\pi$
$840$		0			0
$841$			2.95194e7i			1.43919i
$842$		0			0
$843$	2.31875e6	−	2.31875e6i	0.112379	−	0.112379i
$844$		0			0
$845$	1.32730e6	+	1.32730e6i	0.0639481	+	0.0639481i
$846$		0			0
$847$	−351039.			−0.0168131
$848$		0			0
$849$	−2.75598e6			−0.131222
$850$		0			0
$851$	−3.53322e6	−	3.53322e6i	−0.167243	−	0.167243i
$852$		0			0
$853$	1.10564e7	−	1.10564e7i	0.520284	−	0.520284i	−0.397373	−	0.917657i	$-0.630078\pi$
$853$	1.10564e7	−	1.10564e7i	0.520284	−	0.520284i	0.917657	+	0.397373i	$0.130078\pi$
$854$		0			0
$855$		−	876893.i		−	0.0410234i
$856$		0			0
$857$		−	1.52495e7i		−	0.709257i	−0.935007	−	0.354628i	$-0.884607\pi$
$857$		−	1.52495e7i		−	0.709257i	0.935007	−	0.354628i	$-0.115393\pi$
$858$		0			0
$859$	1.20409e7	−	1.20409e7i	0.556768	−	0.556768i	−0.371617	−	0.928386i	$-0.621197\pi$
$859$	1.20409e7	−	1.20409e7i	0.556768	−	0.556768i	0.928386	+	0.371617i	$0.121197\pi$
$860$		0			0
$861$	4.12271e6	+	4.12271e6i	0.189529	+	0.189529i
$862$		0			0
$863$	−3.08994e7			−1.41229			−0.706145	−	0.708067i	$-0.749567\pi$
$863$	−3.08994e7			−1.41229			−0.706145	+	0.708067i	$0.749567\pi$
$864$		0			0
$865$	−8.46626e6			−0.384726
$866$		0			0
$867$	−1.47972e6	−	1.47972e6i	−0.0668548	−	0.0668548i
$868$		0			0
$869$	−2.10718e7	+	2.10718e7i	−0.946568	+	0.946568i
$870$		0			0
$871$		−	7.65259e6i		−	0.341793i
$872$		0			0
$873$			3.81060e7i			1.69222i
$874$		0			0
$875$	1.24774e7	−	1.24774e7i	0.550938	−	0.550938i
$876$		0			0
$877$	−2.33320e7	−	2.33320e7i	−1.02436	−	1.02436i	−0.999696	−	0.0246672i	$-0.992147\pi$
$877$	−2.33320e7	−	2.33320e7i	−1.02436	−	1.02436i	−0.0246672	−	0.999696i	$-0.507853\pi$
$878$		0			0
$879$	1.20842e6			0.0527529
$880$		0			0
$881$	3.57739e7			1.55284			0.776419	−	0.630218i	$-0.217034\pi$
$881$	3.57739e7			1.55284			0.776419	+	0.630218i	$0.217034\pi$
$882$		0			0
$883$	2.50070e7	+	2.50070e7i	1.07935	+	1.07935i	0.996568	+	0.0827776i	$0.0263791\pi$
$883$	2.50070e7	+	2.50070e7i	1.07935	+	1.07935i	0.0827776	+	0.996568i	$0.473621\pi$
$884$		0			0
$885$	500967.	−	500967.i	0.0215006	−	0.0215006i
$886$		0			0
$887$			3.34384e7i			1.42704i	0.700633	+	0.713521i	$0.252901\pi$
$887$			3.34384e7i			1.42704i	−0.700633	+	0.713521i	$0.747099\pi$
$888$		0			0
$889$			3.18626e7i			1.35216i
$890$		0			0
$891$	1.60446e7	−	1.60446e7i	0.677073	−	0.677073i
$892$		0			0
$893$	−845993.	−	845993.i	−0.0355008	−	0.0355008i
$894$		0			0
$895$	−3.72728e6			−0.155537
$896$		0			0
$897$	1.58135e6			0.0656218
$898$		0			0
$899$	−2.02010e7	−	2.02010e7i	−0.833632	−	0.833632i
$900$		0			0
$901$	9.27610e6	−	9.27610e6i	0.380674	−	0.380674i
$902$		0			0
$903$		−	6.34844e6i		−	0.259088i
$904$		0			0
$905$		−	4.91931e6i		−	0.199656i
$906$		0			0
$907$	1.53434e7	−	1.53434e7i	0.619304	−	0.619304i	−0.326049	−	0.945353i	$-0.605717\pi$
$907$	1.53434e7	−	1.53434e7i	0.619304	−	0.619304i	0.945353	+	0.326049i	$0.105717\pi$
$908$		0			0
$909$	2.62496e7	+	2.62496e7i	1.05369	+	1.05369i
$910$		0			0
$911$	479747.			0.0191521			0.00957604	−	0.999954i	$-0.496952\pi$
$911$	479747.			0.0191521			0.00957604	+	0.999954i	$0.496952\pi$
$912$		0			0
$913$	3.56167e7			1.41409
$914$		0			0
$915$	698127.	+	698127.i	0.0275665	+	0.0275665i
$916$		0			0
$917$	3.54138e7	−	3.54138e7i	1.39075	−	1.39075i
$918$		0			0
$919$			9.26403e6i			0.361835i	0.983498	+	0.180918i	$0.0579068\pi$
$919$			9.26403e6i			0.361835i	−0.983498	+	0.180918i	$0.942093\pi$
$920$		0			0
$921$		−	981845.i		−	0.0381412i
$922$		0			0
$923$	1.63201e7	−	1.63201e7i	0.630547	−	0.630547i
$924$		0			0
$925$	5.53511e6	+	5.53511e6i	0.212702	+	0.212702i
$926$		0			0
$927$	1.35822e7			0.519124
$928$		0			0
$929$	3.65567e7			1.38972			0.694861	−	0.719144i	$-0.255466\pi$
$929$	3.65567e7			1.38972			0.694861	+	0.719144i	$0.255466\pi$
$930$		0			0
$931$	5.86744e6	+	5.86744e6i	0.221858	+	0.221858i
$932$		0			0
$933$	2.22993e6	−	2.22993e6i	0.0838662	−	0.0838662i
$934$		0			0
$935$			2.52752e6i			0.0945507i
$936$		0			0
$937$		−	8.48280e6i		−	0.315639i	−0.987468	−	0.157819i	$-0.949554\pi$
$937$		−	8.48280e6i		−	0.315639i	0.987468	−	0.157819i	$-0.0504464\pi$
$938$		0			0
$939$	−428770.	+	428770.i	−0.0158694	+	0.0158694i
$940$		0			0
$941$	−1.36732e7	−	1.36732e7i	−0.503379	−	0.503379i	0.409107	−	0.912486i	$-0.365840\pi$
$941$	−1.36732e7	−	1.36732e7i	−0.503379	−	0.503379i	−0.912486	+	0.409107i	$0.865840\pi$
$942$		0			0
$943$	−2.88480e7			−1.05642
$944$		0			0
$945$	−2.45593e6			−0.0894617
$946$		0			0
$947$	−2.62841e7	−	2.62841e7i	−0.952399	−	0.952399i	0.0465186	−	0.998917i	$-0.485187\pi$
$947$	−2.62841e7	−	2.62841e7i	−0.952399	−	0.952399i	−0.998917	+	0.0465186i	$0.985187\pi$
$948$		0			0
$949$	−2.73020e6	+	2.73020e6i	−0.0984075	+	0.0984075i
$950$		0			0
$951$		−	3.58358e6i		−	0.128489i
$952$		0			0
$953$		−	2.85225e6i		−	0.101732i	−0.998705	−	0.0508658i	$-0.983802\pi$
$953$		−	2.85225e6i		−	0.101732i	0.998705	−	0.0508658i	$-0.0161981\pi$
$954$		0			0
$955$	1.77128e6	−	1.77128e6i	0.0628463	−	0.0628463i
$956$		0			0
$957$	3.49413e6	+	3.49413e6i	0.123327	+	0.123327i
$958$		0			0
$959$	−2.81661e7			−0.988964
$960$		0			0
$961$	−1.23158e7			−0.430185
$962$		0			0
$963$	2.52158e7	+	2.52158e7i	0.876206	+	0.876206i
$964$		0			0
$965$	−5.60351e6	+	5.60351e6i	−0.193705	+	0.193705i
$966$		0			0
$967$		−	2.35407e6i		−	0.0809568i	−0.999180	−	0.0404784i	$-0.987112\pi$
$967$		−	2.35407e6i		−	0.0809568i	0.999180	−	0.0404784i	$-0.0128882\pi$
$968$		0			0
$969$			226076.i			0.00773472i
$970$		0			0
$971$	−3.13394e6	+	3.13394e6i	−0.106670	+	0.106670i	−0.758427	−	0.651757i	$-0.774032\pi$
$971$	−3.13394e6	+	3.13394e6i	−0.106670	+	0.106670i	0.651757	+	0.758427i	$0.274032\pi$
$972$		0			0
$973$	6.37955e7	+	6.37955e7i	2.16027	+	2.16027i
$974$		0			0
$975$	−2.47733e6			−0.0834589
$976$		0			0
$977$	574910.			0.0192692			0.00963460	−	0.999954i	$-0.496933\pi$
$977$	574910.			0.0192692			0.00963460	+	0.999954i	$0.496933\pi$
$978$		0			0
$979$	2.63986e7	+	2.63986e7i	0.880288	+	0.880288i
$980$		0			0
$981$	−8.55901e6	+	8.55901e6i	−0.283956	+	0.283956i
$982$		0			0
$983$			2.93611e7i			0.969145i	0.874751	+	0.484572i	$0.161025\pi$
$983$			2.93611e7i			0.969145i	−0.874751	+	0.484572i	$0.838975\pi$
$984$		0			0
$985$			1.36012e7i			0.446669i
$986$		0			0
$987$	−1.17719e6	+	1.17719e6i	−0.0384638	+	0.0384638i
$988$		0			0
$989$	2.22111e7	+	2.22111e7i	0.722069	+	0.722069i
$990$		0			0
$991$	−5.12370e7			−1.65730			−0.828648	−	0.559770i	$-0.810889\pi$
$991$	−5.12370e7			−1.65730			−0.828648	+	0.559770i	$0.810889\pi$
$992$		0			0
$993$	−2.18092e6			−0.0701885
$994$		0			0
$995$	−2.69776e6	−	2.69776e6i	−0.0863866	−	0.0863866i
$996$		0			0
$997$	1.85202e7	−	1.85202e7i	0.590076	−	0.590076i	−0.347576	−	0.937652i	$-0.612995\pi$
$997$	1.85202e7	−	1.85202e7i	0.590076	−	0.590076i	0.937652	+	0.347576i	$0.112995\pi$
$998$		0			0
$999$		−	2.24517e6i		−	0.0711764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.6.e.a.65.5	yes	16
4.3	odd	2	inner	256.6.e.a.65.4	✓	16
8.3	odd	2		256.6.e.b.65.5	yes	16
8.5	even	2		256.6.e.b.65.4	yes	16
16.3	odd	4		256.6.e.b.193.5	yes	16
16.5	even	4	inner	256.6.e.a.193.5	yes	16
16.11	odd	4	inner	256.6.e.a.193.4	yes	16
16.13	even	4		256.6.e.b.193.4	yes	16
32.5	even	8		1024.6.a.d.1.3		8
32.11	odd	8		1024.6.a.d.1.4		8
32.21	even	8		1024.6.a.e.1.6		8
32.27	odd	8		1024.6.a.e.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.6.e.a.65.4	✓	16	4.3	odd	2	inner
256.6.e.a.65.5	yes	16	1.1	even	1	trivial
256.6.e.a.193.4	yes	16	16.11	odd	4	inner
256.6.e.a.193.5	yes	16	16.5	even	4	inner
256.6.e.b.65.4	yes	16	8.5	even	2
256.6.e.b.65.5	yes	16	8.3	odd	2
256.6.e.b.193.4	yes	16	16.13	even	4
256.6.e.b.193.5	yes	16	16.3	odd	4
1024.6.a.d.1.3		8	32.5	even	8
1024.6.a.d.1.4		8	32.11	odd	8
1024.6.a.e.1.5		8	32.27	odd	8
1024.6.a.e.1.6		8	32.21	even	8

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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	256.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23717 + 1.23717i) q^{3} +(-9.46137 + 9.46137i) q^{5} +217.226i q^{7} -239.939i q^{9} +O(q^{10})\)	\(q+(1.23717 + 1.23717i) q^{3} +(-9.46137 + 9.46137i) q^{5} +217.226i q^{7} -239.939i q^{9} +(-282.343 + 282.343i) q^{11} +(339.858 + 339.858i) q^{13} -23.4106 q^{15} -473.078 q^{17} +(-193.135 - 193.135i) q^{19} +(-268.745 + 268.745i) q^{21} -1880.50i q^{23} +2945.96i q^{25} +(597.477 - 597.477i) q^{27} +(-5001.53 - 5001.53i) q^{29} +4038.97 q^{31} -698.612 q^{33} +(-2055.25 - 2055.25i) q^{35} +(1878.88 - 1878.88i) q^{37} +840.924i q^{39} -15340.6i q^{41} +(-11811.3 + 11811.3i) q^{43} +(2270.15 + 2270.15i) q^{45} +4380.31 q^{47} -30379.9 q^{49} +(-585.278 - 585.278i) q^{51} +(-19608.0 + 19608.0i) q^{53} -5342.70i q^{55} -477.882i q^{57} +(-21399.1 + 21399.1i) q^{59} +(-29820.9 - 29820.9i) q^{61} +52120.8 q^{63} -6431.05 q^{65} +(-11258.5 - 11258.5i) q^{67} +(2326.49 - 2326.49i) q^{69} -48020.3i q^{71} +8033.35i q^{73} +(-3644.66 + 3644.66i) q^{75} +(-61332.1 - 61332.1i) q^{77} +74631.9 q^{79} -56826.8 q^{81} +(-63073.6 - 63073.6i) q^{83} +(4475.97 - 4475.97i) q^{85} -12375.5i q^{87} -93498.5i q^{89} +(-73825.8 + 73825.8i) q^{91} +(4996.90 + 4996.90i) q^{93} +3654.65 q^{95} -158815. q^{97} +(67745.0 + 67745.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 160 q^{5}+O(q^{10}) \) 16 * q - 160 * q^5	\( 16 q - 160 q^{5} - 576 q^{13} - 384 q^{17} - 1120 q^{21} - 14624 q^{29} - 78208 q^{33} - 39552 q^{37} - 190336 q^{45} - 196112 q^{49} - 26432 q^{53} - 274944 q^{61} - 630624 q^{65} - 315040 q^{69} - 426912 q^{77} - 1012880 q^{81} - 451488 q^{85} - 1128512 q^{93} - 833152 q^{97}+O(q^{100}) \) 16 * q - 160 * q^5 - 576 * q^13 - 384 * q^17 - 1120 * q^21 - 14624 * q^29 - 78208 * q^33 - 39552 * q^37 - 190336 * q^45 - 196112 * q^49 - 26432 * q^53 - 274944 * q^61 - 630624 * q^65 - 315040 * q^69 - 426912 * q^77 - 1012880 * q^81 - 451488 * q^85 - 1128512 * q^93 - 833152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more