LMFDB - Embedded newform 256.6.e.b.193.4

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			193.4
Root			$-0.0885219 + 0.618585i$ of defining polynomial
Character	$\chi$	$=$	256.193
Dual form			256.6.e.b.65.4

$q$-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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

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

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	$-0.767873\pi$
$3$	−1.23717	+	1.23717i	−0.0793645	+	0.0793645i	0.666310	+	0.745675i	$0.267873\pi$
$4$		0			0
$5$	9.46137	+	9.46137i	0.169250	+	0.169250i	0.786650	−	0.617400i	$-0.211814\pi$
$5$	9.46137	+	9.46137i	0.169250	+	0.169250i	−0.617400	+	0.786650i	$0.711814\pi$
$6$		0			0
$7$		−	217.226i		−	1.67558i	−0.545991	−	0.837791i	$-0.683847\pi$
$7$		−	217.226i		−	1.67558i	0.545991	−	0.837791i	$-0.316153\pi$
$8$		0			0
$9$			239.939i			0.987403i
$10$		0			0
$11$	282.343	+	282.343i	0.703550	+	0.703550i	0.965171	−	0.261621i	$-0.0842569\pi$
$11$	282.343	+	282.343i	0.703550	+	0.703550i	−0.261621	+	0.965171i	$0.584257\pi$
$12$		0			0
$13$	−339.858	+	339.858i	−0.557749	+	0.557749i	−0.928666	−	0.370917i	$-0.879043\pi$
$13$	−339.858	+	339.858i	−0.557749	+	0.557749i	0.370917	+	0.928666i	$0.379043\pi$
$14$		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	$-0.722340\pi$
$19$	193.135	−	193.135i	0.122738	−	0.122738i	0.765808	+	0.643070i	$0.222340\pi$
$20$		0			0
$21$	268.745	+	268.745i	0.132982	+	0.132982i
$22$		0			0
$23$			1880.50i			0.741230i	0.928787	+	0.370615i	$0.120853\pi$
$23$			1880.50i			0.741230i	−0.928787	+	0.370615i	$0.879147\pi$
$24$		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	0.110473	−	0.993879i	$-0.464763\pi$
$29$	5001.53	−	5001.53i	1.10435	−	1.10435i	0.993879	−	0.110473i	$-0.0352366\pi$
$30$		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	$-0.301002\pi$
$37$	−1878.88	−	1878.88i	−0.225629	−	0.225629i	−0.810864	+	0.585235i	$0.801002\pi$
$38$		0			0
$39$		−	840.924i		−	0.0885310i
$40$		0			0
$41$			15340.6i			1.42522i	0.701558	+	0.712612i	$0.252488\pi$
$41$			15340.6i			1.42522i	−0.701558	+	0.712612i	$0.747512\pi$
$42$		0			0
$43$	11811.3	+	11811.3i	0.974150	+	0.974150i	0.999674	−	0.0255246i	$-0.00812561\pi$
$43$	11811.3	+	11811.3i	0.974150	+	0.974150i	−0.0255246	+	0.999674i	$0.508126\pi$
$44$		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	$-0.0128481\pi$
$53$	19608.0	+	19608.0i	0.958833	+	0.958833i	−0.0403525	+	0.999186i	$0.512848\pi$
$54$		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	$-0.0585234\pi$
$59$	21399.1	+	21399.1i	0.800323	+	0.800323i	−0.182822	+	0.983146i	$0.558523\pi$
$60$		0			0
$61$	29820.9	−	29820.9i	1.02612	−	1.02612i	0.0264659	−	0.999650i	$-0.491575\pi$
$61$	29820.9	−	29820.9i	1.02612	−	1.02612i	0.999650	−	0.0264659i	$-0.00842534\pi$
$62$		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	$-0.680484\pi$
$67$	11258.5	−	11258.5i	0.306404	−	0.306404i	0.843513	+	0.537109i	$0.180484\pi$
$68$		0			0
$69$	−2326.49	−	2326.49i	−0.0588273	−	0.0588273i
$70$		0			0
$71$			48020.3i			1.13052i	0.824912	+	0.565261i	$0.191224\pi$
$71$			48020.3i			1.13052i	−0.824912	+	0.565261i	$0.808776\pi$
$72$		0			0
$73$		−	8033.35i		−	0.176437i	−0.996101	−	0.0882184i	$-0.971883\pi$
$73$		−	8033.35i		−	0.176437i	0.996101	−	0.0882184i	$-0.0281174\pi$
$74$		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	0.00498026	−	0.999988i	$-0.498415\pi$
$83$	63073.6	−	63073.6i	1.00497	−	1.00497i	0.999988	−	0.00498026i	$-0.00158527\pi$
$84$		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	$0.215148\pi$
$89$			93498.5i			1.25121i	−0.780141	+	0.625604i	$0.784852\pi$
$90$		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	0.997578	+	0.0695559i	$0.0221582\pi$
$101$	109401.	+	109401.i	1.06713	+	1.06713i	0.0695559	+	0.997578i	$0.477842\pi$
$102$		0			0
$103$		−	56607.0i		−	0.525747i	−0.964830	−	0.262873i	$-0.915330\pi$
$103$		−	56607.0i		−	0.525747i	0.964830	−	0.262873i	$-0.0846702\pi$
$104$		0			0
$105$			5085.39i			0.0450144i
$106$		0			0
$107$	105092.	+	105092.i	0.887385	+	0.887385i	0.994271	−	0.106886i	$-0.0340881\pi$
$107$	105092.	+	105092.i	0.887385	+	0.887385i	−0.106886	+	0.994271i	$0.534088\pi$
$108$		0			0
$109$	35671.6	−	35671.6i	0.287579	−	0.287579i	−0.548543	−	0.836122i	$-0.684817\pi$
$109$	35671.6	−	35671.6i	0.287579	−	0.287579i	0.836122	+	0.548543i	$0.184817\pi$
$110$		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	$-0.550346\pi$
$131$	163028.	−	163028.i	0.830011	−	0.830011i	0.987518	+	0.157507i	$0.0503458\pi$
$132$		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	$-0.904644\pi$
$137$		−	129663.i		−	0.590221i	0.955463	−	0.295111i	$-0.0953565\pi$
$138$		0			0
$139$	−293683.	−	293683.i	−1.28927	−	1.28927i	−0.935233	−	0.354032i	$-0.884810\pi$
$139$	−293683.	−	293683.i	−1.28927	−	1.28927i	−0.354032	−	0.935233i	$-0.615190\pi$
$140$		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	$-0.273134\pi$
$149$	−27828.6	−	27828.6i	−0.102690	−	0.102690i	−0.756585	+	0.653895i	$0.773134\pi$
$150$		0			0
$151$			81358.3i			0.290375i	0.989404	+	0.145188i	$0.0463785\pi$
$151$			81358.3i			0.290375i	−0.989404	+	0.145188i	$0.953621\pi$
$152$		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	$-0.903651\pi$
$157$	−202745.	+	202745.i	−0.656448	+	0.656448i	0.298090	+	0.954538i	$0.403651\pi$
$158$		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	−0.139440	+	0.990230i	$0.544530\pi$
$163$	−383196.	+	383196.i	−1.12967	+	1.12967i	−0.990230	+	0.139440i	$0.955470\pi$
$164$		0			0
$165$	−6609.83	−	6609.83i	−0.0189008	−	0.0189008i
$166$		0			0
$167$		−	523932.i		−	1.45373i	−0.686781	−	0.726865i	$-0.740977\pi$
$167$		−	523932.i		−	1.45373i	0.686781	−	0.726865i	$-0.259023\pi$
$168$		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	−0.147497	+	0.989062i	$0.547122\pi$
$173$	−447412.	+	447412.i	−1.13656	+	1.13656i	−0.989062	+	0.147497i	$0.952878\pi$
$174$		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	$-0.855333\pi$
$179$	−196974.	+	196974.i	−0.459489	+	0.459489i	0.438998	+	0.898488i	$0.355333\pi$
$180$		0			0
$181$	259968.	+	259968.i	0.589826	+	0.589826i	0.937584	−	0.347758i	$-0.113057\pi$
$181$	259968.	+	259968.i	0.589826	+	0.589826i	−0.347758	+	0.937584i	$0.613057\pi$
$182$		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	−0.914128	−	0.405425i	$-0.867124\pi$
$197$	−718774.	−	718774.i	−1.31955	−	1.31955i	−0.405425	−	0.914128i	$-0.632876\pi$
$198$		0			0
$199$		−	285135.i		−	0.510408i	−0.966887	−	0.255204i	$-0.917857\pi$
$199$		−	285135.i		−	0.510408i	0.966887	−	0.255204i	$-0.0821426\pi$
$200$		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	0.0518587	−	0.998654i	$-0.483485\pi$
$211$	679372.	−	679372.i	1.05051	−	1.05051i	0.998654	−	0.0518587i	$-0.0165145\pi$
$212$		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	−0.238936	+	0.971035i	$0.576799\pi$
$227$	−939376.	+	939376.i	−1.20997	+	1.20997i	−0.971035	+	0.238936i	$0.923201\pi$
$228$		0			0
$229$	80627.5	+	80627.5i	0.101600	+	0.101600i	0.756080	−	0.654480i	$-0.227112\pi$
$229$	80627.5	+	80627.5i	0.101600	+	0.101600i	−0.654480	+	0.756080i	$0.727112\pi$
$230$		0			0
$231$			151756.i			0.187119i
$232$		0			0
$233$		−	293436.i		−	0.354098i	−0.984202	−	0.177049i	$-0.943345\pi$
$233$		−	293436.i		−	0.354098i	0.984202	−	0.177049i	$-0.0566551\pi$
$234$		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	$-0.0875594\pi$
$251$	689488.	+	689488.i	0.690784	+	0.690784i	−0.271620	+	0.962405i	$0.587559\pi$
$252$		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	$-0.720022\pi$
$263$		−	1.72852e6i		−	1.54094i	0.637478	−	0.770468i	$-0.279978\pi$
$264$		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	$-0.787809\pi$
$269$	−198893.	+	198893.i	−0.167587	+	0.167587i	0.618331	+	0.785918i	$0.287809\pi$
$270$		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	$-0.324390\pi$
$277$	−418236.	−	418236.i	−0.327508	−	0.327508i	−0.851638	+	0.524130i	$0.824390\pi$
$278$		0			0
$279$			969107.i			0.745352i
$280$		0			0
$281$			1.87424e6i			1.41599i	0.706219	+	0.707994i	$0.250399\pi$
$281$			1.87424e6i			1.41599i	−0.706219	+	0.707994i	$0.749601\pi$
$282$		0			0
$283$	1.11383e6	+	1.11383e6i	0.826706	+	0.826706i	0.987060	−	0.160353i	$-0.0512634\pi$
$283$	1.11383e6	+	1.11383e6i	0.826706	+	0.826706i	−0.160353	+	0.987060i	$0.551263\pi$
$284$		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	$-0.325510\pi$
$293$	−488382.	−	488382.i	−0.332346	−	0.332346i	−0.853477	+	0.521131i	$0.825510\pi$
$294$		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	$-0.695652\pi$
$307$	396811.	−	396811.i	0.240291	−	0.240291i	0.816971	+	0.576679i	$0.195652\pi$
$308$		0			0
$309$	70032.4	+	70032.4i	0.0417256	+	0.0417256i
$310$		0			0
$311$			1.80244e6i			1.05672i	0.849020	+	0.528361i	$0.177193\pi$
$311$			1.80244e6i			1.05672i	−0.849020	+	0.528361i	$0.822807\pi$
$312$		0			0
$313$		−	346574.i		−	0.199956i	−0.994990	−	0.0999780i	$-0.968123\pi$
$313$		−	346574.i		−	0.199956i	0.994990	−	0.0999780i	$-0.0318773\pi$
$314$		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	$-0.556015\pi$
$317$	1.44830e6	−	1.44830e6i	0.809487	−	0.809487i	0.984556	+	0.175069i	$0.0560148\pi$
$318$		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	$-0.148775\pi$
$331$	881414.	+	881414.i	0.442191	+	0.442191i	−0.450557	+	0.892748i	$0.648775\pi$
$332$		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	$-0.101618\pi$
$347$	1.42569e6	+	1.42569e6i	0.635626	+	0.635626i	−0.313848	+	0.949473i	$0.601618\pi$
$348$		0			0
$349$	−297231.	+	297231.i	−0.130626	+	0.130626i	−0.769397	−	0.638771i	$-0.779443\pi$
$349$	−297231.	+	297231.i	−0.130626	+	0.130626i	0.638771	+	0.769397i	$0.279443\pi$
$350$		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	$-0.762663\pi$
$359$		−	3.31336e6i		−	1.35685i	0.734669	−	0.678426i	$-0.237337\pi$
$360$		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	$-0.147371\pi$
$373$	1.20408e6	+	1.20408e6i	0.448109	+	0.448109i	−0.446617	+	0.894725i	$0.647371\pi$
$374$		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	0.999980	+	0.00630982i	$0.00200849\pi$
$379$	2.81398e6	+	2.81398e6i	1.00629	+	1.00629i	0.00630982	+	0.999980i	$0.497992\pi$
$380$		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	$-0.381313\pi$
$389$	−1.69223e6	−	1.69223e6i	−0.567002	−	0.567002i	−0.931287	+	0.364286i	$0.881313\pi$
$390$		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	$-0.903085\pi$
$397$	−2.05447e6	+	2.05447e6i	−0.654221	+	0.654221i	0.299786	+	0.954007i	$0.403085\pi$
$398$		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	$-0.770208\pi$
$409$		−	4.47118e6i		−	1.32164i	0.750544	−	0.660821i	$-0.229792\pi$
$410$		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	$-0.578054\pi$
$419$	2.61373e6	−	2.61373e6i	0.727321	−	0.727321i	0.970085	+	0.242765i	$0.0780543\pi$
$420$		0			0
$421$	295751.	+	295751.i	0.0813244	+	0.0813244i	0.746599	−	0.665274i	$-0.231685\pi$
$421$	295751.	+	295751.i	0.0813244	+	0.0813244i	−0.665274	+	0.746599i	$0.731685\pi$
$422$		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	$0.164068\pi$
$439$			3.98071e6i			0.985824i	−0.870079	+	0.492912i	$0.835932\pi$
$440$		0			0
$441$		−	7.28932e6i		−	1.78481i
$442$		0			0
$443$	−713863.	−	713863.i	−0.172825	−	0.172825i	0.615395	−	0.788219i	$-0.288997\pi$
$443$	−713863.	−	713863.i	−0.172825	−	0.172825i	−0.788219	+	0.615395i	$0.788997\pi$
$444$		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	$-0.957315\pi$
$457$		−	1.19382e6i		−	0.267393i	0.991022	−	0.133696i	$-0.0426847\pi$
$458$		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	$-0.921649\pi$
$461$	−3.31361e6	+	3.31361e6i	−0.726189	+	0.726189i	0.243669	+	0.969858i	$0.421649\pi$
$462$		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	$-0.649256\pi$
$467$	2.07444e6	−	2.07444e6i	0.440159	−	0.440159i	0.892065	+	0.451906i	$0.149256\pi$
$468$		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	$-0.787725\pi$
$487$		−	6.47468e6i		−	1.23708i	0.785755	−	0.618538i	$-0.212275\pi$
$488$		0			0
$489$		−	948157.i		−	0.179311i
$490$		0			0
$491$	−3.39527e6	−	3.39527e6i	−0.635581	−	0.635581i	0.313881	−	0.949462i	$-0.398371\pi$
$491$	−3.39527e6	−	3.39527e6i	−0.635581	−	0.635581i	−0.949462	+	0.313881i	$0.898371\pi$
$492$		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	$-0.851680\pi$
$499$	−2.47024e6	+	2.47024e6i	−0.444107	+	0.444107i	0.449283	+	0.893390i	$0.351680\pi$
$500$		0			0
$501$	648193.	+	648193.i	0.115374	+	0.115374i
$502$		0			0
$503$		−	9.84544e6i		−	1.73506i	−0.497383	−	0.867531i	$-0.665706\pi$
$503$		−	9.84544e6i		−	1.73506i	0.497383	−	0.867531i	$-0.334294\pi$
$504$		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	$-0.865150\pi$
$509$	−2.92555e6	+	2.92555e6i	−0.500511	+	0.500511i	0.411086	+	0.911597i	$0.365150\pi$
$510$		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	$-0.995876\pi$
$521$		−	160551.i		−	0.0259130i	0.999916	−	0.0129565i	$-0.00412430\pi$
$522$		0			0
$523$	2.69862e6	+	2.69862e6i	0.431408	+	0.431408i	0.889107	−	0.457699i	$-0.151326\pi$
$523$	2.69862e6	+	2.69862e6i	0.431408	+	0.431408i	−0.457699	+	0.889107i	$0.651326\pi$
$524$		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	$-0.979442\pi$
$541$	−6.35404e6	+	6.35404e6i	−0.933376	+	0.933376i	0.0645390	+	0.997915i	$0.479442\pi$
$542$		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	$-0.649152\pi$
$547$	3.08327e6	−	3.08327e6i	0.440599	−	0.440599i	0.892213	+	0.451614i	$0.149152\pi$
$548$		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	$-0.618583\pi$
$557$	4.15476e6	−	4.15476e6i	0.567424	−	0.567424i	0.931406	+	0.363982i	$0.118583\pi$
$558$		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	$-0.686910\pi$
$563$	2.09434e6	−	2.09434e6i	0.278469	−	0.278469i	0.832497	+	0.554029i	$0.186910\pi$
$564$		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	$0.0719583\pi$
$569$			3.46207e6i			0.448286i	−0.974556	+	0.224143i	$0.928042\pi$
$570$		0			0
$571$	−5.29256e6	−	5.29256e6i	−0.679321	−	0.679321i	0.280525	−	0.959847i	$-0.409491\pi$
$571$	−5.29256e6	−	5.29256e6i	−0.679321	−	0.679321i	−0.959847	+	0.280525i	$0.909491\pi$
$572$		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	$-0.293767\pi$
$587$	−1.61821e6	−	1.61821e6i	−0.193839	−	0.193839i	−0.797353	+	0.603514i	$0.793767\pi$
$588$		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	$-0.841765\pi$
$599$		−	8.37554e6i		−	0.953774i	0.878965	−	0.476887i	$-0.158235\pi$
$600$		0			0
$601$		−	3.75444e6i		−	0.423994i	−0.977270	−	0.211997i	$-0.932003\pi$
$601$		−	3.75444e6i		−	0.423994i	0.977270	−	0.211997i	$-0.0679967\pi$
$602$		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	$-0.00310758\pi$
$613$	9.21233e6	+	9.21233e6i	0.990190	+	0.990190i	−0.00976261	+	0.999952i	$0.503108\pi$
$614$		0			0
$615$		−	359134.i		−	0.0382885i
$616$		0			0
$617$			1.42219e7i			1.50399i	0.659167	+	0.751997i	$0.270909\pi$
$617$			1.42219e7i			1.50399i	−0.659167	+	0.751997i	$0.729091\pi$
$618$		0			0
$619$	9.69068e6	+	9.69068e6i	1.01655	+	1.01655i	0.999861	+	0.0166871i	$0.00531192\pi$
$619$	9.69068e6	+	9.69068e6i	1.01655	+	1.01655i	0.0166871	+	0.999861i	$0.494688\pi$
$620$		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	$-0.732411\pi$
$631$		−	1.49041e7i		−	1.49016i	0.666974	−	0.745081i	$-0.267589\pi$
$632$		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	$-0.648025\pi$
$643$	4.66909e6	−	4.66909e6i	0.445353	−	0.445353i	0.893806	+	0.448453i	$0.148025\pi$
$644$		0			0
$645$	−276510.	−	276510.i	−0.0261704	−	0.0261704i
$646$		0			0
$647$		−	1.22769e7i		−	1.15299i	−0.817100	−	0.576496i	$-0.804419\pi$
$647$		−	1.22769e7i		−	1.15299i	0.817100	−	0.576496i	$-0.195581\pi$
$648$		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	$-0.869123\pi$
$653$	−5.63324e6	+	5.63324e6i	−0.516982	+	0.516982i	0.399675	+	0.916657i	$0.369123\pi$
$654$		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	$-0.686209\pi$
$659$	3.13854e6	−	3.13854e6i	0.281523	−	0.281523i	0.833716	+	0.552193i	$0.186209\pi$
$660$		0			0
$661$	2.25214e6	+	2.25214e6i	0.200489	+	0.200489i	0.800210	−	0.599720i	$-0.204722\pi$
$661$	2.25214e6	+	2.25214e6i	0.200489	+	0.200489i	−0.599720	+	0.800210i	$0.704722\pi$
$662$		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	$-0.353209\pi$
$677$	−5.37302e6	−	5.37302e6i	−0.450554	−	0.450554i	−0.895538	+	0.444984i	$0.853209\pi$
$678$		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	$-0.0974488\pi$
$683$	7.95020e6	+	7.95020e6i	0.652118	+	0.652118i	−0.301384	+	0.953503i	$0.597449\pi$
$684$		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	$-0.962912\pi$
$691$	−1.10073e7	+	1.10073e7i	−0.876968	+	0.876968i	0.116251	+	0.993220i	$0.462912\pi$
$692$		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	$-0.570533\pi$
$701$	9.83300e6	−	9.83300e6i	0.755772	−	0.755772i	0.975550	+	0.219778i	$0.0705332\pi$
$702$		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	$-0.146535\pi$
$709$	6.04507e6	+	6.04507e6i	0.451633	+	0.451633i	−0.444263	+	0.895896i	$0.646535\pi$
$710$		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	$0.0595434\pi$
$727$			5.30046e6i			0.371944i	−0.982555	+	0.185972i	$0.940457\pi$
$728$		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	$-0.561566\pi$
$733$	1.14793e7	−	1.14793e7i	0.789143	−	0.789143i	0.981354	+	0.192210i	$0.0615656\pi$
$734$		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	$-0.766759\pi$
$739$	−1.10488e6	+	1.10488e6i	−0.0744226	+	0.0744226i	0.668916	+	0.743338i	$0.266759\pi$
$740$		0			0
$741$	−162412.	−	162412.i	−0.0108661	−	0.0108661i
$742$		0			0
$743$		−	2.73631e6i		−	0.181842i	−0.995858	−	0.0909209i	$-0.971019\pi$
$743$		−	2.73631e6i		−	0.181842i	0.995858	−	0.0909209i	$-0.0289810\pi$
$744$		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	$-0.0111414\pi$
$757$	1.52053e7	+	1.52053e7i	0.964393	+	0.964393i	−0.0349946	+	0.999388i	$0.511141\pi$
$758$		0			0
$759$		−	1.31374e6i		−	0.0827760i
$760$		0			0
$761$			1.28357e7i			0.803448i	0.915761	+	0.401724i	$0.131589\pi$
$761$			1.28357e7i			0.803448i	−0.915761	+	0.401724i	$0.868411\pi$
$762$		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	$-0.350128\pi$
$773$	−7.26917e6	−	7.26917e6i	−0.437558	−	0.437558i	−0.891190	+	0.453631i	$0.850128\pi$
$774$		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	$-0.738025\pi$
$787$	924212.	−	924212.i	0.0531906	−	0.0531906i	0.733202	+	0.680011i	$0.238025\pi$
$788$		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	$-0.805071\pi$
$797$	−4.36584e6	+	4.36584e6i	−0.243457	+	0.243457i	0.574822	+	0.818279i	$0.305071\pi$
$798$		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	$0.161435\pi$
$809$			1.80829e7i			0.971396i	−0.874127	+	0.485698i	$0.838565\pi$
$810$		0			0
$811$	2.29179e7	+	2.29179e7i	1.22355	+	1.22355i	0.966361	+	0.257191i	$0.0827969\pi$
$811$	2.29179e7	+	2.29179e7i	1.22355	+	1.22355i	0.257191	+	0.966361i	$0.417203\pi$
$812$		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	$-0.298382\pi$
$821$	−4.13555e6	−	4.13555e6i	−0.214129	−	0.214129i	−0.806019	+	0.591890i	$0.798382\pi$
$822$		0			0
$823$			1.35656e7i			0.698133i	0.937098	+	0.349067i	$0.113501\pi$
$823$			1.35656e7i			0.698133i	−0.937098	+	0.349067i	$0.886499\pi$
$824$		0			0
$825$			2.05809e6i			0.105276i
$826$		0			0
$827$	−2.05917e6	−	2.05917e6i	−0.104696	−	0.104696i	0.652819	−	0.757514i	$-0.273586\pi$
$827$	−2.05917e6	−	2.05917e6i	−0.104696	−	0.104696i	−0.757514	+	0.652819i	$0.773586\pi$
$828$		0			0
$829$	−2.41770e7	+	2.41770e7i	−1.22185	+	1.22185i	−0.254871	+	0.966975i	$0.582033\pi$
$829$	−2.41770e7	+	2.41770e7i	−1.22185	+	1.22185i	−0.966975	+	0.254871i	$0.917967\pi$
$830$		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	$0.0779852\pi$
$839$			9.89108e6i			0.485108i	−0.970138	+	0.242554i	$0.922015\pi$
$840$		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	$-0.369922\pi$
$853$	−1.10564e7	−	1.10564e7i	−0.520284	−	0.520284i	−0.917657	+	0.397373i	$0.869922\pi$
$854$		0			0
$855$			876893.i			0.0410234i
$856$		0			0
$857$			1.52495e7i			0.709257i	0.935007	+	0.354628i	$0.115393\pi$
$857$			1.52495e7i			0.709257i	−0.935007	+	0.354628i	$0.884607\pi$
$858$		0			0
$859$	−1.20409e7	−	1.20409e7i	−0.556768	−	0.556768i	0.371617	−	0.928386i	$-0.378803\pi$
$859$	−1.20409e7	−	1.20409e7i	−0.556768	−	0.556768i	−0.928386	+	0.371617i	$0.878803\pi$
$860$		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	0.0246672	−	0.999696i	$-0.492147\pi$
$877$	2.33320e7	−	2.33320e7i	1.02436	−	1.02436i	0.999696	−	0.0246672i	$-0.00785260\pi$
$878$		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	−0.0827776	+	0.996568i	$0.526379\pi$
$883$	−2.50070e7	+	2.50070e7i	−1.07935	+	1.07935i	−0.996568	+	0.0827776i	$0.973621\pi$
$884$		0			0
$885$	−500967.	−	500967.i	−0.0215006	−	0.0215006i
$886$		0			0
$887$		−	3.34384e7i		−	1.42704i	−0.700633	−	0.713521i	$-0.747099\pi$
$887$		−	3.34384e7i		−	1.42704i	0.700633	−	0.713521i	$-0.252901\pi$
$888$		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	$-0.394283\pi$
$907$	−1.53434e7	−	1.53434e7i	−0.619304	−	0.619304i	−0.945353	+	0.326049i	$0.894283\pi$
$908$		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	$-0.942093\pi$
$919$		−	9.26403e6i		−	0.361835i	0.983498	−	0.180918i	$-0.0579068\pi$
$920$		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	$0.0504464\pi$
$937$			8.48280e6i			0.315639i	−0.987468	+	0.157819i	$0.949554\pi$
$938$		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	$-0.634160\pi$
$941$	1.36732e7	−	1.36732e7i	0.503379	−	0.503379i	0.912486	+	0.409107i	$0.134160\pi$
$942$		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	$-0.514813\pi$
$947$	2.62841e7	−	2.62841e7i	0.952399	−	0.952399i	0.998917	+	0.0465186i	$0.0148127\pi$
$948$		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	$0.0161981\pi$
$953$			2.85225e6i			0.101732i	−0.998705	+	0.0508658i	$0.983802\pi$
$954$		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	$0.0128882\pi$
$967$			2.35407e6i			0.0809568i	−0.999180	+	0.0404784i	$0.987112\pi$
$968$		0			0
$969$		−	226076.i		−	0.00773472i
$970$		0			0
$971$	3.13394e6	+	3.13394e6i	0.106670	+	0.106670i	0.758427	−	0.651757i	$-0.225968\pi$
$971$	3.13394e6	+	3.13394e6i	0.106670	+	0.106670i	−0.651757	+	0.758427i	$0.725968\pi$
$972$		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	$-0.838975\pi$
$983$		−	2.93611e7i		−	0.969145i	0.874751	−	0.484572i	$-0.161025\pi$
$984$		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	$-0.387005\pi$
$997$	−1.85202e7	−	1.85202e7i	−0.590076	−	0.590076i	−0.937652	+	0.347576i	$0.887005\pi$
$998$		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.b.193.4	yes	16
4.3	odd	2	inner	256.6.e.b.193.5	yes	16
8.3	odd	2		256.6.e.a.193.4	yes	16
8.5	even	2		256.6.e.a.193.5	yes	16
16.3	odd	4	inner	256.6.e.b.65.5	yes	16
16.5	even	4		256.6.e.a.65.5	yes	16
16.11	odd	4		256.6.e.a.65.4	✓	16
16.13	even	4	inner	256.6.e.b.65.4	yes	16
32.3	odd	8		1024.6.a.e.1.5		8
32.13	even	8		1024.6.a.e.1.6		8
32.19	odd	8		1024.6.a.d.1.4		8
32.29	even	8		1024.6.a.d.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.6.e.a.65.4	✓	16	16.11	odd	4
256.6.e.a.65.5	yes	16	16.5	even	4
256.6.e.a.193.4	yes	16	8.3	odd	2
256.6.e.a.193.5	yes	16	8.5	even	2
256.6.e.b.65.4	yes	16	16.13	even	4	inner
256.6.e.b.65.5	yes	16	16.3	odd	4	inner
256.6.e.b.193.4	yes	16	1.1	even	1	trivial
256.6.e.b.193.5	yes	16	4.3	odd	2	inner
1024.6.a.d.1.3		8	32.29	even	8
1024.6.a.d.1.4		8	32.19	odd	8
1024.6.a.e.1.5		8	32.3	odd	8
1024.6.a.e.1.6		8	32.13	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

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