LMFDB - Embedded newform 256.6.e.c.193.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [256,6,Mod(65,256)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [24,0,0,0,-160] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$41.0582578721$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.7
Character	$\chi$	$=$	256.193
Dual form			256.6.e.c.65.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.14100 - 4.14100i) q^{3} +(30.9040 + 30.9040i) q^{5} -106.094i q^{7} +208.704i q^{9} +(-242.499 - 242.499i) q^{11} +(76.4407 - 76.4407i) q^{13} +255.947 q^{15} +1146.65 q^{17} +(1107.85 - 1107.85i) q^{19} +(-439.337 - 439.337i) q^{21} -199.505i q^{23} -1214.88i q^{25} +(1870.51 + 1870.51i) q^{27} +(-785.771 + 785.771i) q^{29} -2486.00 q^{31} -2008.37 q^{33} +(3278.74 - 3278.74i) q^{35} +(8899.35 + 8899.35i) q^{37} -633.081i q^{39} -14420.5i q^{41} +(-2925.13 - 2925.13i) q^{43} +(-6449.80 + 6449.80i) q^{45} +25229.5 q^{47} +5550.98 q^{49} +(4748.26 - 4748.26i) q^{51} +(2017.41 + 2017.41i) q^{53} -14988.4i q^{55} -9175.20i q^{57} +(9031.27 + 9031.27i) q^{59} +(-28207.7 + 28207.7i) q^{61} +22142.4 q^{63} +4724.65 q^{65} +(49993.9 - 49993.9i) q^{67} +(-826.149 - 826.149i) q^{69} -79547.5i q^{71} -69785.1i q^{73} +(-5030.83 - 5030.83i) q^{75} +(-25727.7 + 25727.7i) q^{77} +41295.6 q^{79} -35223.6 q^{81} +(24978.6 - 24978.6i) q^{83} +(35436.0 + 35436.0i) q^{85} +6507.75i q^{87} -80681.9i q^{89} +(-8109.93 - 8109.93i) q^{91} +(-10294.5 + 10294.5i) q^{93} +68474.0 q^{95} +86279.9 q^{97} +(50610.5 - 50610.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 160 q^{5} - 1040 q^{13} + 384 q^{17} + 7376 q^{21} - 14624 q^{29} + 78208 q^{33} - 35248 q^{37} - 118288 q^{45} + 100072 q^{49} - 104144 q^{53} - 174640 q^{61} + 464496 q^{65} - 29968 q^{69} - 667920 q^{77}+ \cdots + 833152 q^{97}+O(q^{100}) $ 24 * q - 160 * q^5 - 1040 * q^13 + 384 * q^17 + 7376 * q^21 - 14624 * q^29 + 78208 * q^33 - 35248 * q^37 - 118288 * q^45 + 100072 * q^49 - 104144 * q^53 - 174640 * q^61 + 464496 * q^65 - 29968 * q^69 - 667920 * q^77 + 750440 * q^81 - 419856 * q^85 - 391136 * q^93 + 833152 * q^97

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
$3$	4.14100	−	4.14100i	0.265645	−	0.265645i	−0.561698	−	0.827343i	$-0.689852\pi$
$3$	4.14100	−	4.14100i	0.265645	−	0.265645i	0.827343	+	0.561698i	$0.189852\pi$
$4$		0			0
$5$	30.9040	+	30.9040i	0.552828	+	0.552828i	0.927256	−	0.374428i	$-0.122161\pi$
$5$	30.9040	+	30.9040i	0.552828	+	0.552828i	−0.374428	+	0.927256i	$0.622161\pi$
$6$		0			0
$7$		−	106.094i		−	0.818366i	−0.912452	−	0.409183i	$-0.865814\pi$
$7$		−	106.094i		−	0.818366i	0.912452	−	0.409183i	$-0.134186\pi$
$8$		0			0
$9$			208.704i			0.858865i
$10$		0			0
$11$	−242.499	−	242.499i	−0.604265	−	0.604265i	0.337176	−	0.941441i	$-0.390528\pi$
$11$	−242.499	−	242.499i	−0.604265	−	0.604265i	−0.941441	+	0.337176i	$0.890528\pi$
$12$		0			0
$13$	76.4407	−	76.4407i	0.125449	−	0.125449i	−0.641595	−	0.767044i	$-0.721727\pi$
$13$	76.4407	−	76.4407i	0.125449	−	0.125449i	0.767044	+	0.641595i	$0.221727\pi$
$14$		0			0
$15$	255.947			0.293712
$16$		0			0
$17$	1146.65			0.962293			0.481147	−	0.876640i	$-0.340220\pi$
$17$	1146.65			0.962293			0.481147	+	0.876640i	$0.340220\pi$
$18$		0			0
$19$	1107.85	−	1107.85i	0.704039	−	0.704039i	−0.261236	−	0.965275i	$-0.584130\pi$
$19$	1107.85	−	1107.85i	0.704039	−	0.704039i	0.965275	+	0.261236i	$0.0841302\pi$
$20$		0			0
$21$	−439.337	−	439.337i	−0.217395	−	0.217395i
$22$		0			0
$23$		−	199.505i		−	0.0786383i	−0.999227	−	0.0393191i	$-0.987481\pi$
$23$		−	199.505i		−	0.0786383i	0.999227	−	0.0393191i	$-0.0125189\pi$
$24$		0			0
$25$		−	1214.88i		−	0.388763i
$26$		0			0
$27$	1870.51	+	1870.51i	0.493798	+	0.493798i
$28$		0			0
$29$	−785.771	+	785.771i	−0.173501	+	0.173501i	−0.788516	−	0.615015i	$-0.789150\pi$
$29$	−785.771	+	785.771i	−0.173501	+	0.173501i	0.615015	+	0.788516i	$0.289150\pi$
$30$		0			0
$31$	−2486.00			−0.464619			−0.232310	−	0.972642i	$-0.574628\pi$
$31$	−2486.00			−0.464619			−0.232310	+	0.972642i	$0.574628\pi$
$32$		0			0
$33$	−2008.37			−0.321040
$34$		0			0
$35$	3278.74	−	3278.74i	0.452415	−	0.452415i
$36$		0			0
$37$	8899.35	+	8899.35i	1.06870	+	1.06870i	0.997459	+	0.0712366i	$0.0226945\pi$
$37$	8899.35	+	8899.35i	1.06870	+	1.06870i	0.0712366	+	0.997459i	$0.477305\pi$
$38$		0			0
$39$		−	633.081i		−	0.0666497i
$40$		0			0
$41$		−	14420.5i		−	1.33974i	−0.742480	−	0.669868i	$-0.766351\pi$
$41$		−	14420.5i		−	1.33974i	0.742480	−	0.669868i	$-0.233649\pi$
$42$		0			0
$43$	−2925.13	−	2925.13i	−0.241254	−	0.241254i	0.576115	−	0.817369i	$-0.304568\pi$
$43$	−2925.13	−	2925.13i	−0.241254	−	0.241254i	−0.817369	+	0.576115i	$0.804568\pi$
$44$		0			0
$45$	−6449.80	+	6449.80i	−0.474805	+	0.474805i
$46$		0			0
$47$	25229.5			1.66595			0.832977	−	0.553307i	$-0.186634\pi$
$47$	25229.5			1.66595			0.832977	+	0.553307i	$0.186634\pi$
$48$		0			0
$49$	5550.98			0.330278
$50$		0			0
$51$	4748.26	−	4748.26i	0.255629	−	0.255629i
$52$		0			0
$53$	2017.41	+	2017.41i	0.0986519	+	0.0986519i	0.754710	−	0.656058i	$-0.227777\pi$
$53$	2017.41	+	2017.41i	0.0986519	+	0.0986519i	−0.656058	+	0.754710i	$0.727777\pi$
$54$		0			0
$55$		−	14988.4i		−	0.668109i
$56$		0			0
$57$		−	9175.20i		−	0.374049i
$58$		0			0
$59$	9031.27	+	9031.27i	0.337768	+	0.337768i	0.855527	−	0.517758i	$-0.173233\pi$
$59$	9031.27	+	9031.27i	0.337768	+	0.337768i	−0.517758	+	0.855527i	$0.673233\pi$
$60$		0			0
$61$	−28207.7	+	28207.7i	−0.970606	+	0.970606i	−0.999580	−	0.0289740i	$-0.990776\pi$
$61$	−28207.7	+	28207.7i	−0.970606	+	0.970606i	0.0289740	+	0.999580i	$0.490776\pi$
$62$		0			0
$63$	22142.4			0.702866
$64$		0			0
$65$	4724.65			0.138703
$66$		0			0
$67$	49993.9	−	49993.9i	1.36060	−	1.36060i	0.487447	−	0.873153i	$-0.337928\pi$
$67$	49993.9	−	49993.9i	1.36060	−	1.36060i	0.873153	−	0.487447i	$-0.162072\pi$
$68$		0			0
$69$	−826.149	−	826.149i	−0.0208899	−	0.0208899i
$70$		0			0
$71$		−	79547.5i		−	1.87275i	−0.350997	−	0.936376i	$-0.614157\pi$
$71$		−	79547.5i		−	1.87275i	0.350997	−	0.936376i	$-0.385843\pi$
$72$		0			0
$73$		−	69785.1i		−	1.53269i	−0.642426	−	0.766347i	$-0.722072\pi$
$73$		−	69785.1i		−	1.53269i	0.642426	−	0.766347i	$-0.277928\pi$
$74$		0			0
$75$	−5030.83	−	5030.83i	−0.103273	−	0.103273i
$76$		0			0
$77$	−25727.7	+	25727.7i	−0.494510	+	0.494510i
$78$		0			0
$79$	41295.6			0.744450			0.372225	−	0.928143i	$-0.378595\pi$
$79$	41295.6			0.744450			0.372225	+	0.928143i	$0.378595\pi$
$80$		0			0
$81$	−35223.6			−0.596515
$82$		0			0
$83$	24978.6	−	24978.6i	0.397991	−	0.397991i	−0.479533	−	0.877524i	$-0.659194\pi$
$83$	24978.6	−	24978.6i	0.397991	−	0.397991i	0.877524	+	0.479533i	$0.159194\pi$
$84$		0			0
$85$	35436.0	+	35436.0i	0.531983	+	0.531983i
$86$		0			0
$87$			6507.75i			0.0921792i
$88$		0			0
$89$		−	80681.9i		−	1.07970i	−0.841763	−	0.539848i	$-0.818482\pi$
$89$		−	80681.9i		−	1.07970i	0.841763	−	0.539848i	$-0.181518\pi$
$90$		0			0
$91$	−8109.93	−	8109.93i	−0.102663	−	0.102663i
$92$		0			0
$93$	−10294.5	+	10294.5i	−0.123424	+	0.123424i
$94$		0			0
$95$	68474.0			0.778424
$96$		0			0
$97$	86279.9			0.931065			0.465533	−	0.885031i	$-0.345863\pi$
$97$	86279.9			0.931065			0.465533	+	0.885031i	$0.345863\pi$
$98$		0			0
$99$	50610.5	−	50610.5i	0.518982	−	0.518982i
$100$		0			0
$101$	106616.	+	106616.i	1.03997	+	1.03997i	0.999167	+	0.0408028i	$0.0129915\pi$
$101$	106616.	+	106616.i	1.03997	+	1.03997i	0.0408028	+	0.999167i	$0.487008\pi$
$102$		0			0
$103$			54346.7i			0.504754i	0.967629	+	0.252377i	$0.0812123\pi$
$103$			54346.7i			0.504754i	−0.967629	+	0.252377i	$0.918788\pi$
$104$		0			0
$105$		−	27154.5i		−	0.240364i
$106$		0			0
$107$	86694.5	+	86694.5i	0.732036	+	0.732036i	0.971023	−	0.238987i	$-0.0768154\pi$
$107$	86694.5	+	86694.5i	0.732036	+	0.732036i	−0.238987	+	0.971023i	$0.576815\pi$
$108$		0			0
$109$	−128900.	+	128900.i	−1.03917	+	1.03917i	−0.0399673	+	0.999201i	$0.512725\pi$
$109$	−128900.	+	128900.i	−1.03917	+	1.03917i	−0.999201	+	0.0399673i	$0.987275\pi$
$110$		0			0
$111$	73704.4			0.567788
$112$		0			0
$113$	9078.59			0.0668840			0.0334420	−	0.999441i	$-0.489353\pi$
$113$	9078.59			0.0668840			0.0334420	+	0.999441i	$0.489353\pi$
$114$		0			0
$115$	6165.50	−	6165.50i	0.0434734	−	0.0434734i
$116$		0			0
$117$	15953.5	+	15953.5i	0.107744	+	0.107744i
$118$		0			0
$119$		−	121653.i		−	0.787508i
$120$		0			0
$121$		−	43439.9i		−	0.269728i
$122$		0			0
$123$	−59715.1	−	59715.1i	−0.355894	−	0.355894i
$124$		0			0
$125$	134120.	−	134120.i	0.767747	−	0.767747i
$126$		0			0
$127$	−181852.			−1.00048			−0.500240	−	0.865887i	$-0.666755\pi$
$127$	−181852.			−1.00048			−0.500240	+	0.865887i	$0.666755\pi$
$128$		0			0
$129$	−24225.9			−0.128176
$130$		0			0
$131$	63673.5	−	63673.5i	0.324176	−	0.324176i	−0.526191	−	0.850367i	$-0.676380\pi$
$131$	63673.5	−	63673.5i	0.324176	−	0.324176i	0.850367	+	0.526191i	$0.176380\pi$
$132$		0			0
$133$	−117537.	−	117537.i	−0.576161	−	0.576161i
$134$		0			0
$135$			115612.i			0.545971i
$136$		0			0
$137$			44873.3i			0.204262i	0.994771	+	0.102131i	$0.0325660\pi$
$137$			44873.3i			0.204262i	−0.994771	+	0.102131i	$0.967434\pi$
$138$		0			0
$139$	−47157.4	−	47157.4i	−0.207020	−	0.207020i	0.595979	−	0.803000i	$-0.296764\pi$
$139$	−47157.4	−	47157.4i	−0.207020	−	0.207020i	−0.803000	+	0.595979i	$0.796764\pi$
$140$		0			0
$141$	104475.	−	104475.i	0.442553	−	0.442553i
$142$		0			0
$143$	−37073.5			−0.151609
$144$		0			0
$145$	−48567.0			−0.191832
$146$		0			0
$147$	22986.6	−	22986.6i	0.0877366	−	0.0877366i
$148$		0			0
$149$	−152444.	−	152444.i	−0.562530	−	0.562530i	0.367495	−	0.930025i	$-0.380215\pi$
$149$	−152444.	−	152444.i	−0.562530	−	0.562530i	−0.930025	+	0.367495i	$0.880215\pi$
$150$		0			0
$151$		−	256068.i		−	0.913930i	−0.889485	−	0.456965i	$-0.848936\pi$
$151$		−	256068.i		−	0.913930i	0.889485	−	0.456965i	$-0.151064\pi$
$152$		0			0
$153$			239310.i			0.826481i
$154$		0			0
$155$	−76827.5	−	76827.5i	−0.256855	−	0.256855i
$156$		0			0
$157$	−105314.	+	105314.i	−0.340986	+	0.340986i	−0.856738	−	0.515752i	$-0.827513\pi$
$157$	−105314.	+	105314.i	−0.340986	+	0.340986i	0.515752	+	0.856738i	$0.327513\pi$
$158$		0			0
$159$	16708.2			0.0524128
$160$		0			0
$161$	−21166.4			−0.0643549
$162$		0			0
$163$	−408738.	+	408738.i	−1.20497	+	1.20497i	−0.232335	+	0.972636i	$0.574636\pi$
$163$	−408738.	+	408738.i	−1.20497	+	1.20497i	−0.972636	+	0.232335i	$0.925364\pi$
$164$		0			0
$165$	−62066.7	−	62066.7i	−0.177480	−	0.177480i
$166$		0			0
$167$			470864.i			1.30649i	0.757149	+	0.653243i	$0.226592\pi$
$167$			470864.i			1.30649i	−0.757149	+	0.653243i	$0.773408\pi$
$168$		0			0
$169$			359607.i			0.968525i
$170$		0			0
$171$	231213.	+	231213.i	0.604674	+	0.604674i
$172$		0			0
$173$	195267.	−	195267.i	0.496038	−	0.496038i	−0.414165	−	0.910202i	$-0.635926\pi$
$173$	195267.	−	195267.i	0.496038	−	0.496038i	0.910202	+	0.414165i	$0.135926\pi$
$174$		0			0
$175$	−128892.			−0.318150
$176$		0			0
$177$	74797.0			0.179453
$178$		0			0
$179$	−526698.	+	526698.i	−1.22865	+	1.22865i	−0.264178	+	0.964474i	$0.585101\pi$
$179$	−526698.	+	526698.i	−1.22865	+	1.22865i	−0.964474	+	0.264178i	$0.914899\pi$
$180$		0			0
$181$	−48608.7	−	48608.7i	−0.110285	−	0.110285i	0.649811	−	0.760096i	$-0.274848\pi$
$181$	−48608.7	−	48608.7i	−0.110285	−	0.110285i	−0.760096	+	0.649811i	$0.774848\pi$
$182$		0			0
$183$			233616.i			0.515673i
$184$		0			0
$185$			550052.i			1.18161i
$186$		0			0
$187$	−278060.	−	278060.i	−0.581480	−	0.581480i
$188$		0			0
$189$	198450.	−	198450.i	0.404108	−	0.404108i
$190$		0			0
$191$	−556170.			−1.10312			−0.551561	−	0.834134i	$-0.685968\pi$
$191$	−556170.			−1.10312			−0.551561	+	0.834134i	$0.685968\pi$
$192$		0			0
$193$	−314493.			−0.607740			−0.303870	−	0.952713i	$-0.598279\pi$
$193$	−314493.			−0.607740			−0.303870	+	0.952713i	$0.598279\pi$
$194$		0			0
$195$	19564.8	−	19564.8i	0.0368458	−	0.0368458i
$196$		0			0
$197$	−2467.55	−	2467.55i	−0.00453002	−	0.00453002i	0.704838	−	0.709368i	$-0.251020\pi$
$197$	−2467.55	−	2467.55i	−0.00453002	−	0.00453002i	−0.709368	+	0.704838i	$0.751020\pi$
$198$		0			0
$199$			524346.i			0.938611i	0.883036	+	0.469305i	$0.155496\pi$
$199$			524346.i			0.938611i	−0.883036	+	0.469305i	$0.844504\pi$
$200$		0			0
$201$		−	414049.i		−	0.722873i
$202$		0			0
$203$	83365.9	+	83365.9i	0.141987	+	0.141987i
$204$		0			0
$205$	445650.	−	445650.i	0.740644	−	0.740644i
$206$		0			0
$207$	41637.5			0.0675397
$208$		0			0
$209$	−537303.			−0.850852
$210$		0			0
$211$	−518692.	+	518692.i	−0.802054	+	0.802054i	−0.983416	−	0.181362i	$-0.941949\pi$
$211$	−518692.	+	518692.i	−0.802054	+	0.802054i	0.181362	+	0.983416i	$0.441949\pi$
$212$		0			0
$213$	−329406.	−	329406.i	−0.497488	−	0.497488i
$214$		0			0
$215$		−	180796.i		−	0.266743i
$216$		0			0
$217$			263751.i			0.380228i
$218$		0			0
$219$	−288980.	−	288980.i	−0.407153	−	0.407153i
$220$		0			0
$221$	87650.5	−	87650.5i	0.120718	−	0.120718i
$222$		0			0
$223$	−1.23712e6			−1.66591			−0.832955	−	0.553341i	$-0.813353\pi$
$223$	−1.23712e6			−1.66591			−0.832955	+	0.553341i	$0.813353\pi$
$224$		0			0
$225$	253551.			0.333895
$226$		0			0
$227$	624437.	−	624437.i	0.804310	−	0.804310i	−0.179456	−	0.983766i	$-0.557434\pi$
$227$	624437.	−	624437.i	0.804310	−	0.804310i	0.983766	+	0.179456i	$0.0574337\pi$
$228$		0			0
$229$	−337587.	−	337587.i	−0.425400	−	0.425400i	0.461658	−	0.887058i	$-0.347255\pi$
$229$	−337587.	−	337587.i	−0.425400	−	0.425400i	−0.887058	+	0.461658i	$0.847255\pi$
$230$		0			0
$231$			213077.i			0.262728i
$232$		0			0
$233$			1.36771e6i			1.65045i	0.564803	+	0.825226i	$0.308952\pi$
$233$			1.36771e6i			1.65045i	−0.564803	+	0.825226i	$0.691048\pi$
$234$		0			0
$235$	779692.	+	779692.i	0.920986	+	0.920986i
$236$		0			0
$237$	171005.	−	171005.i	0.197759	−	0.197759i
$238$		0			0
$239$	63907.7			0.0723699			0.0361850	−	0.999345i	$-0.488479\pi$
$239$	63907.7			0.0723699			0.0361850	+	0.999345i	$0.488479\pi$
$240$		0			0
$241$	1.48625e6			1.64835			0.824173	−	0.566338i	$-0.191640\pi$
$241$	1.48625e6			1.64835			0.824173	+	0.566338i	$0.191640\pi$
$242$		0			0
$243$	−600394.	+	600394.i	−0.652260	+	0.652260i
$244$		0			0
$245$	171547.	+	171547.i	0.182587	+	0.182587i
$246$		0			0
$247$		−	169369.i		−	0.176642i
$248$		0			0
$249$		−	206873.i		−	0.211449i
$250$		0			0
$251$	−624265.	−	624265.i	−0.625438	−	0.625438i	0.321478	−	0.946917i	$-0.395820\pi$
$251$	−624265.	−	624265.i	−0.625438	−	0.625438i	−0.946917	+	0.321478i	$0.895820\pi$
$252$		0			0
$253$	−48379.7	+	48379.7i	−0.0475184	+	0.0475184i
$254$		0			0
$255$	293481.			0.282637
$256$		0			0
$257$	−448824.			−0.423880			−0.211940	−	0.977283i	$-0.567978\pi$
$257$	−448824.			−0.423880			−0.211940	+	0.977283i	$0.567978\pi$
$258$		0			0
$259$	944172.	−	944172.i	0.874584	−	0.874584i
$260$		0			0
$261$	−163994.	−	163994.i	−0.149014	−	0.149014i
$262$		0			0
$263$			6710.33i			0.00598211i	0.999996	+	0.00299105i	$0.000952084\pi$
$263$			6710.33i			0.00598211i	−0.999996	+	0.00299105i	$0.999048\pi$
$264$		0			0
$265$			124692.i			0.109075i
$266$		0			0
$267$	−334103.	−	334103.i	−0.286816	−	0.286816i
$268$		0			0
$269$	−661872.	+	661872.i	−0.557690	+	0.557690i	−0.928649	−	0.370959i	$-0.879029\pi$
$269$	−661872.	+	661872.i	−0.557690	+	0.557690i	0.370959	+	0.928649i	$0.379029\pi$
$270$		0			0
$271$	2.30343e6			1.90525			0.952627	−	0.304142i	$-0.0983698\pi$
$271$	2.30343e6			1.90525			0.952627	+	0.304142i	$0.0983698\pi$
$272$		0			0
$273$	−67166.4			−0.0545438
$274$		0			0
$275$	−294607.	+	294607.i	−0.234916	+	0.234916i
$276$		0			0
$277$	823249.	+	823249.i	0.644661	+	0.644661i	0.951698	−	0.307036i	$-0.0993374\pi$
$277$	823249.	+	823249.i	0.644661	+	0.644661i	−0.307036	+	0.951698i	$0.599337\pi$
$278$		0			0
$279$		−	518839.i		−	0.399045i
$280$		0			0
$281$		−	1.75615e6i		−	1.32677i	−0.748279	−	0.663384i	$-0.769120\pi$
$281$		−	1.75615e6i		−	1.32677i	0.748279	−	0.663384i	$-0.230880\pi$
$282$		0			0
$283$	155973.	+	155973.i	0.115767	+	0.115767i	0.762617	−	0.646850i	$-0.223914\pi$
$283$	155973.	+	155973.i	0.115767	+	0.115767i	−0.646850	+	0.762617i	$0.723914\pi$
$284$		0			0
$285$	283550.	−	283550.i	0.206785	−	0.206785i
$286$		0			0
$287$	−1.52993e6			−1.09639
$288$		0			0
$289$	−105057.			−0.0739913
$290$		0			0
$291$	357285.	−	357285.i	0.247333	−	0.247333i
$292$		0			0
$293$	683159.	+	683159.i	0.464893	+	0.464893i	0.900255	−	0.435362i	$-0.143380\pi$
$293$	683159.	+	683159.i	0.464893	+	0.464893i	−0.435362	+	0.900255i	$0.643380\pi$
$294$		0			0
$295$			558205.i			0.373456i
$296$		0			0
$297$		−	907190.i		−	0.596770i
$298$		0			0
$299$	−15250.3	−	15250.3i	−0.00986507	−	0.00986507i
$300$		0			0
$301$	−310340.	+	310340.i	−0.197434	+	0.197434i
$302$		0			0
$303$	882997.			0.552526
$304$		0			0
$305$	−1.74346e6			−1.07316
$306$		0			0
$307$	271733.	−	271733.i	0.164549	−	0.164549i	−0.620029	−	0.784579i	$-0.712879\pi$
$307$	271733.	−	271733.i	0.164549	−	0.164549i	0.784579	+	0.620029i	$0.212879\pi$
$308$		0			0
$309$	225049.	+	225049.i	0.134085	+	0.134085i
$310$		0			0
$311$		−	2.61117e6i		−	1.53086i	−0.643521	−	0.765429i	$-0.722527\pi$
$311$		−	2.61117e6i		−	1.53086i	0.643521	−	0.765429i	$-0.277473\pi$
$312$		0			0
$313$		−	1.29214e6i		−	0.745502i	−0.927932	−	0.372751i	$-0.878415\pi$
$313$		−	1.29214e6i		−	0.745502i	0.927932	−	0.372751i	$-0.121585\pi$
$314$		0			0
$315$	684288.	+	684288.i	0.388564	+	0.388564i
$316$		0			0
$317$	−1.61784e6	+	1.61784e6i	−0.904246	+	0.904246i	−0.995800	−	0.0915538i	$-0.970817\pi$
$317$	−1.61784e6	+	1.61784e6i	−0.904246	+	0.904246i	0.0915538	+	0.995800i	$0.470817\pi$
$318$		0			0
$319$	381097.			0.209681
$320$		0			0
$321$	718004.			0.388923
$322$		0			0
$323$	1.27031e6	−	1.27031e6i	0.677492	−	0.677492i
$324$		0			0
$325$	−92866.5	−	92866.5i	−0.0487698	−	0.0487698i
$326$		0			0
$327$			1.06755e6i			0.552100i
$328$		0			0
$329$		−	2.67670e6i		−	1.36336i
$330$		0			0
$331$	2.43745e6	+	2.43745e6i	1.22283	+	1.22283i	0.966623	+	0.256204i	$0.0824720\pi$
$331$	2.43745e6	+	2.43745e6i	1.22283	+	1.22283i	0.256204	+	0.966623i	$0.417528\pi$
$332$		0			0
$333$	−1.85733e6	+	1.85733e6i	−0.917866	+	0.917866i
$334$		0			0
$335$	3.09003e6			1.50435
$336$		0			0
$337$	−559028.			−0.268138			−0.134069	−	0.990972i	$-0.542804\pi$
$337$	−559028.			−0.268138			−0.134069	+	0.990972i	$0.542804\pi$
$338$		0			0
$339$	37594.4	−	37594.4i	0.0177674	−	0.0177674i
$340$		0			0
$341$	602852.	+	602852.i	0.280753	+	0.280753i
$342$		0			0
$343$		−	2.37206e6i		−	1.08865i
$344$		0			0
$345$		−	51062.7i		−	0.0230970i
$346$		0			0
$347$	−2.33249e6	−	2.33249e6i	−1.03991	−	1.03991i	−0.999170	−	0.0407409i	$-0.987028\pi$
$347$	−2.33249e6	−	2.33249e6i	−1.03991	−	1.03991i	−0.0407409	−	0.999170i	$-0.512972\pi$
$348$		0			0
$349$	−635152.	+	635152.i	−0.279135	+	0.279135i	−0.832764	−	0.553629i	$-0.813243\pi$
$349$	−635152.	+	635152.i	−0.279135	+	0.279135i	0.553629	+	0.832764i	$0.313243\pi$
$350$		0			0
$351$	285966.			0.123893
$352$		0			0
$353$	1.44800e6			0.618489			0.309245	−	0.950983i	$-0.399924\pi$
$353$	1.44800e6			0.618489			0.309245	+	0.950983i	$0.399924\pi$
$354$		0			0
$355$	2.45834e6	−	2.45834e6i	1.03531	−	1.03531i
$356$		0			0
$357$	−503764.	−	503764.i	−0.209198	−	0.209198i
$358$		0			0
$359$			251926.i			0.103166i	0.998669	+	0.0515831i	$0.0164267\pi$
$359$			251926.i			0.103166i	−0.998669	+	0.0515831i	$0.983573\pi$
$360$		0			0
$361$			21440.8i			0.00865910i
$362$		0			0
$363$	−179885.	−	179885.i	−0.0716518	−	0.0716518i
$364$		0			0
$365$	2.15664e6	−	2.15664e6i	0.847316	−	0.847316i
$366$		0			0
$367$	2.74198e6			1.06267			0.531337	−	0.847161i	$-0.321690\pi$
$367$	2.74198e6			1.06267			0.531337	+	0.847161i	$0.321690\pi$
$368$		0			0
$369$	3.00961e6			1.15065
$370$		0			0
$371$	214036.	−	214036.i	0.0807333	−	0.0807333i
$372$		0			0
$373$	419624.	+	419624.i	0.156167	+	0.156167i	0.780866	−	0.624699i	$-0.214778\pi$
$373$	419624.	+	419624.i	0.156167	+	0.156167i	−0.624699	+	0.780866i	$0.714778\pi$
$374$		0			0
$375$		−	1.11078e6i		−	0.407896i
$376$		0			0
$377$			120130.i			0.0435309i
$378$		0			0
$379$	−2.15651e6	−	2.15651e6i	−0.771176	−	0.771176i	0.207136	−	0.978312i	$-0.433586\pi$
$379$	−2.15651e6	−	2.15651e6i	−0.771176	−	0.771176i	−0.978312	+	0.207136i	$0.933586\pi$
$380$		0			0
$381$	−753048.	+	753048.i	−0.265773	+	0.265773i
$382$		0			0
$383$	−1.57667e6			−0.549218			−0.274609	−	0.961556i	$-0.588548\pi$
$383$	−1.57667e6			−0.549218			−0.274609	+	0.961556i	$0.588548\pi$
$384$		0			0
$385$	−1.59018e6			−0.546758
$386$		0			0
$387$	610487.	−	610487.i	0.207204	−	0.207204i
$388$		0			0
$389$	2.80620e6	+	2.80620e6i	0.940254	+	0.940254i	0.998313	−	0.0580588i	$-0.0184911\pi$
$389$	2.80620e6	+	2.80620e6i	0.940254	+	0.940254i	−0.0580588	+	0.998313i	$0.518491\pi$
$390$		0			0
$391$		−	228762.i		−	0.0756731i
$392$		0			0
$393$		−	527344.i		−	0.172231i
$394$		0			0
$395$	1.27620e6	+	1.27620e6i	0.411553	+	0.411553i
$396$		0			0
$397$	−1.49035e6	+	1.49035e6i	−0.474582	+	0.474582i	−0.903394	−	0.428812i	$-0.858932\pi$
$397$	−1.49035e6	+	1.49035e6i	−0.474582	+	0.474582i	0.428812	+	0.903394i	$0.358932\pi$
$398$		0			0
$399$	−973437.			−0.306109
$400$		0			0
$401$	−304536.			−0.0945753			−0.0472877	−	0.998881i	$-0.515058\pi$
$401$	−304536.			−0.0945753			−0.0472877	+	0.998881i	$0.515058\pi$
$402$		0			0
$403$	−190032.	+	190032.i	−0.0582859	+	0.0582859i
$404$		0			0
$405$	−1.08855e6	−	1.08855e6i	−0.329770	−	0.329770i
$406$		0			0
$407$		−	4.31616e6i		−	1.29155i
$408$		0			0
$409$			1.06484e6i			0.314758i	0.987538	+	0.157379i	$0.0503044\pi$
$409$			1.06484e6i			0.314758i	−0.987538	+	0.157379i	$0.949696\pi$
$410$		0			0
$411$	185820.	+	185820.i	0.0542611	+	0.0542611i
$412$		0			0
$413$	958168.	−	958168.i	0.276418	−	0.276418i
$414$		0			0
$415$	1.54388e6			0.440041
$416$		0			0
$417$	−390557.			−0.109988
$418$		0			0
$419$	674556.	−	674556.i	0.187708	−	0.187708i	−0.606996	−	0.794705i	$-0.707626\pi$
$419$	674556.	−	674556.i	0.187708	−	0.187708i	0.794705	+	0.606996i	$0.207626\pi$
$420$		0			0
$421$	−98026.4	−	98026.4i	−0.0269549	−	0.0269549i	0.693501	−	0.720456i	$-0.256067\pi$
$421$	−98026.4	−	98026.4i	−0.0269549	−	0.0269549i	−0.720456	+	0.693501i	$0.756067\pi$
$422$		0			0
$423$			5.26550e6i			1.43083i
$424$		0			0
$425$		−	1.39304e6i		−	0.374104i
$426$		0			0
$427$	2.99268e6	+	2.99268e6i	0.794311	+	0.794311i
$428$		0			0
$429$	−153521.	+	153521.i	−0.0402741	+	0.0402741i
$430$		0			0
$431$	−6.20674e6			−1.60942			−0.804712	−	0.593665i	$-0.797680\pi$
$431$	−6.20674e6			−1.60942			−0.804712	+	0.593665i	$0.797680\pi$
$432$		0			0
$433$	601366.			0.154141			0.0770707	−	0.997026i	$-0.475443\pi$
$433$	601366.			0.154141			0.0770707	+	0.997026i	$0.475443\pi$
$434$		0			0
$435$	−201116.	+	201116.i	−0.0509592	+	0.0509592i
$436$		0			0
$437$	−221021.	−	221021.i	−0.0553644	−	0.0553644i
$438$		0			0
$439$			6.65283e6i			1.64757i	0.566899	+	0.823787i	$0.308143\pi$
$439$			6.65283e6i			1.64757i	−0.566899	+	0.823787i	$0.691857\pi$
$440$		0			0
$441$			1.15851e6i			0.283664i
$442$		0			0
$443$	−1.01578e6	−	1.01578e6i	−0.245917	−	0.245917i	0.573376	−	0.819293i	$-0.305634\pi$
$443$	−1.01578e6	−	1.01578e6i	−0.245917	−	0.245917i	−0.819293	+	0.573376i	$0.805634\pi$
$444$		0			0
$445$	2.49340e6	−	2.49340e6i	0.596886	−	0.596886i
$446$		0			0
$447$	−1.26254e6			−0.298867
$448$		0			0
$449$	−953508.			−0.223207			−0.111604	−	0.993753i	$-0.535599\pi$
$449$	−953508.			−0.223207			−0.111604	+	0.993753i	$0.535599\pi$
$450$		0			0
$451$	−3.49694e6	+	3.49694e6i	−0.809556	+	0.809556i
$452$		0			0
$453$	−1.06038e6	−	1.06038e6i	−0.242781	−	0.242781i
$454$		0			0
$455$		−	501259.i		−	0.113510i
$456$		0			0
$457$			1.42502e6i			0.319175i	0.987184	+	0.159588i	$0.0510165\pi$
$457$			1.42502e6i			0.319175i	−0.987184	+	0.159588i	$0.948984\pi$
$458$		0			0
$459$	2.14481e6	+	2.14481e6i	0.475179	+	0.475179i
$460$		0			0
$461$	2.56159e6	−	2.56159e6i	0.561380	−	0.561380i	−0.368319	−	0.929699i	$-0.620067\pi$
$461$	2.56159e6	−	2.56159e6i	0.561380	−	0.561380i	0.929699	+	0.368319i	$0.120067\pi$
$462$		0			0
$463$	1.33201e6			0.288772			0.144386	−	0.989521i	$-0.453879\pi$
$463$	1.33201e6			0.288772			0.144386	+	0.989521i	$0.453879\pi$
$464$		0			0
$465$	−636284.			−0.136464
$466$		0			0
$467$	−4.95885e6	+	4.95885e6i	−1.05218	+	1.05218i	−0.0536156	+	0.998562i	$0.517075\pi$
$467$	−4.95885e6	+	4.95885e6i	−1.05218	+	1.05218i	−0.998562	+	0.0536156i	$0.982925\pi$
$468$		0			0
$469$	−5.30408e6	−	5.30408e6i	−1.11347	−	1.11347i
$470$		0			0
$471$			872208.i			0.181162i
$472$		0			0
$473$			1.41868e6i			0.291562i
$474$		0			0
$475$	−1.34591e6	−	1.34591e6i	−0.273704	−	0.273704i
$476$		0			0
$477$	−421043.	+	421043.i	−0.0847287	+	0.0847287i
$478$		0			0
$479$	−2.58495e6			−0.514769			−0.257385	−	0.966309i	$-0.582861\pi$
$479$	−2.58495e6			−0.514769			−0.257385	+	0.966309i	$0.582861\pi$
$480$		0			0
$481$	1.36055e6			0.268133
$482$		0			0
$483$	−87649.8	+	87649.8i	−0.0170956	+	0.0170956i
$484$		0			0
$485$	2.66640e6	+	2.66640e6i	0.514719	+	0.514719i
$486$		0			0
$487$			3.24600e6i			0.620193i	0.950705	+	0.310096i	$0.100361\pi$
$487$			3.24600e6i			0.620193i	−0.950705	+	0.310096i	$0.899639\pi$
$488$		0			0
$489$			3.38517e6i			0.640189i
$490$		0			0
$491$	−6.85283e6	−	6.85283e6i	−1.28282	−	1.28282i	−0.939055	−	0.343767i	$-0.888297\pi$
$491$	−6.85283e6	−	6.85283e6i	−1.28282	−	1.28282i	−0.343767	−	0.939055i	$-0.611703\pi$
$492$		0			0
$493$	−901002.	+	901002.i	−0.166959	+	0.166959i
$494$		0			0
$495$	3.12813e6			0.573816
$496$		0			0
$497$	−8.43954e6			−1.53260
$498$		0			0
$499$	−2.73128e6	+	2.73128e6i	−0.491037	+	0.491037i	−0.908633	−	0.417596i	$-0.862873\pi$
$499$	−2.73128e6	+	2.73128e6i	−0.491037	+	0.491037i	0.417596	+	0.908633i	$0.362873\pi$
$500$		0			0
$501$	1.94985e6	+	1.94985e6i	0.347061	+	0.347061i
$502$		0			0
$503$		−	6.10885e6i		−	1.07656i	−0.842765	−	0.538282i	$-0.819074\pi$
$503$		−	6.10885e6i		−	1.07656i	0.842765	−	0.538282i	$-0.180926\pi$
$504$		0			0
$505$			6.58975e6i			1.14985i
$506$		0			0
$507$	1.48913e6	+	1.48913e6i	0.257284	+	0.257284i
$508$		0			0
$509$	6.29864e6	−	6.29864e6i	1.07759	−	1.07759i	0.0808620	−	0.996725i	$-0.474233\pi$
$509$	6.29864e6	−	6.29864e6i	1.07759	−	1.07759i	0.996725	−	0.0808620i	$-0.0257673\pi$
$510$		0			0
$511$	−7.40381e6			−1.25430
$512$		0			0
$513$	4.14448e6			0.695306
$514$		0			0
$515$	−1.67953e6	+	1.67953e6i	−0.279042	+	0.279042i
$516$		0			0
$517$	−6.11811e6	−	6.11811e6i	−1.00668	−	1.00668i
$518$		0			0
$519$		−	1.61720e6i		−	0.263540i
$520$		0			0
$521$			1.07069e7i			1.72810i	0.503407	+	0.864050i	$0.332080\pi$
$521$			1.07069e7i			1.72810i	−0.503407	+	0.864050i	$0.667920\pi$
$522$		0			0
$523$	183125.	+	183125.i	0.0292748	+	0.0292748i	0.721593	−	0.692318i	$-0.243410\pi$
$523$	183125.	+	183125.i	0.0292748	+	0.0292748i	−0.692318	+	0.721593i	$0.743410\pi$
$524$		0			0
$525$	−533743.	+	533743.i	−0.0845150	+	0.0845150i
$526$		0			0
$527$	−2.85057e6			−0.447100
$528$		0			0
$529$	6.39654e6			0.993816
$530$		0			0
$531$	−1.88487e6	+	1.88487e6i	−0.290098	+	0.290098i
$532$		0			0
$533$	−1.10231e6	−	1.10231e6i	−0.168068	−	0.168068i
$534$		0			0
$535$			5.35842e6i			0.809380i
$536$		0			0
$537$			4.36211e6i			0.652770i
$538$		0			0
$539$	−1.34610e6	−	1.34610e6i	−0.199575	−	0.199575i
$540$		0			0
$541$	−1.18352e6	+	1.18352e6i	−0.173853	+	0.173853i	−0.788670	−	0.614817i	$-0.789230\pi$
$541$	−1.18352e6	+	1.18352e6i	−0.173853	+	0.173853i	0.614817	+	0.788670i	$0.289230\pi$
$542$		0			0
$543$	−402577.			−0.0585935
$544$		0			0
$545$	−7.96704e6			−1.14896
$546$		0			0
$547$	−3.51313e6	+	3.51313e6i	−0.502026	+	0.502026i	−0.912067	−	0.410041i	$-0.865514\pi$
$547$	−3.51313e6	+	3.51313e6i	−0.502026	+	0.502026i	0.410041	+	0.912067i	$0.365514\pi$
$548$		0			0
$549$	−5.88707e6	−	5.88707e6i	−0.833620	−	0.833620i
$550$		0			0
$551$			1.74103e6i			0.244302i
$552$		0			0
$553$		−	4.38123e6i		−	0.609232i
$554$		0			0
$555$	2.27776e6	+	2.27776e6i	0.313889	+	0.313889i
$556$		0			0
$557$	7.03090e6	−	7.03090e6i	0.960225	−	0.960225i	−0.0390140	−	0.999239i	$-0.512422\pi$
$557$	7.03090e6	−	7.03090e6i	0.960225	−	0.960225i	0.999239	+	0.0390140i	$0.0124217\pi$
$558$		0			0
$559$	−447198.			−0.0605299
$560$		0			0
$561$	−2.30289e6			−0.308935
$562$		0			0
$563$	1.90977e6	−	1.90977e6i	0.253928	−	0.253928i	−0.568651	−	0.822579i	$-0.692534\pi$
$563$	1.90977e6	−	1.90977e6i	0.253928	−	0.253928i	0.822579	+	0.568651i	$0.192534\pi$
$564$		0			0
$565$	280565.	+	280565.i	0.0369753	+	0.0369753i
$566$		0			0
$567$			3.73703e6i			0.488168i
$568$		0			0
$569$		−	7.90850e6i		−	1.02403i	−0.858976	−	0.512016i	$-0.828899\pi$
$569$		−	7.90850e6i		−	1.02403i	0.858976	−	0.512016i	$-0.171101\pi$
$570$		0			0
$571$	4.47066e6	+	4.47066e6i	0.573827	+	0.573827i	0.933196	−	0.359369i	$-0.117008\pi$
$571$	4.47066e6	+	4.47066e6i	0.573827	+	0.573827i	−0.359369	+	0.933196i	$0.617008\pi$
$572$		0			0
$573$	−2.30310e6	+	2.30310e6i	−0.293039	+	0.293039i
$574$		0			0
$575$	−242375.			−0.0305716
$576$		0			0
$577$	1.01680e7			1.27144			0.635718	−	0.771921i	$-0.280704\pi$
$577$	1.01680e7			1.27144			0.635718	+	0.771921i	$0.280704\pi$
$578$		0			0
$579$	−1.30232e6	+	1.30232e6i	−0.161443	+	0.161443i
$580$		0			0
$581$	−2.65009e6	−	2.65009e6i	−0.325702	−	0.325702i
$582$		0			0
$583$		−	978440.i		−	0.119224i
$584$		0			0
$585$			986055.i			0.119127i
$586$		0			0
$587$	−8.14994e6	−	8.14994e6i	−0.976245	−	0.976245i	0.0234789	−	0.999724i	$-0.492526\pi$
$587$	−8.14994e6	−	8.14994e6i	−0.976245	−	0.976245i	−0.999724	+	0.0234789i	$0.992526\pi$
$588$		0			0
$589$	−2.75411e6	+	2.75411e6i	−0.327110	+	0.327110i
$590$		0			0
$591$	−20436.2			−0.00240676
$592$		0			0
$593$	−6.47036e6			−0.755599			−0.377800	−	0.925887i	$-0.623319\pi$
$593$	−6.47036e6			−0.755599			−0.377800	+	0.925887i	$0.623319\pi$
$594$		0			0
$595$	3.75956e6	−	3.75956e6i	0.435356	−	0.435356i
$596$		0			0
$597$	2.17132e6	+	2.17132e6i	0.249337	+	0.249337i
$598$		0			0
$599$			6.94195e6i			0.790522i	0.918569	+	0.395261i	$0.129346\pi$
$599$			6.94195e6i			0.790522i	−0.918569	+	0.395261i	$0.870654\pi$
$600$		0			0
$601$		−	1.37265e6i		−	0.155015i	−0.996992	−	0.0775077i	$-0.975304\pi$
$601$		−	1.37265e6i		−	0.155015i	0.996992	−	0.0775077i	$-0.0246962\pi$
$602$		0			0
$603$	1.04339e7	+	1.04339e7i	1.16857	+	1.16857i
$604$		0			0
$605$	1.34247e6	−	1.34247e6i	0.149113	−	0.149113i
$606$		0			0
$607$	−4.97819e6			−0.548403			−0.274202	−	0.961672i	$-0.588414\pi$
$607$	−4.97819e6			−0.548403			−0.274202	+	0.961672i	$0.588414\pi$
$608$		0			0
$609$	690436.			0.0754363
$610$		0			0
$611$	1.92856e6	−	1.92856e6i	0.208992	−	0.208992i
$612$		0			0
$613$	1.08631e7	+	1.08631e7i	1.16762	+	1.16762i	0.982766	+	0.184853i	$0.0591811\pi$
$613$	1.08631e7	+	1.08631e7i	1.16762	+	1.16762i	0.184853	+	0.982766i	$0.440819\pi$
$614$		0			0
$615$		−	3.69087e6i		−	0.393497i
$616$		0			0
$617$		−	2.49531e6i		−	0.263883i	−0.991257	−	0.131942i	$-0.957879\pi$
$617$		−	2.49531e6i		−	0.263883i	0.991257	−	0.131942i	$-0.0421212\pi$
$618$		0			0
$619$	−1.42870e6	−	1.42870e6i	−0.149869	−	0.149869i	0.628190	−	0.778060i	$-0.283796\pi$
$619$	−1.42870e6	−	1.42870e6i	−0.149869	−	0.149869i	−0.778060	+	0.628190i	$0.783796\pi$
$620$		0			0
$621$	373175.	−	373175.i	0.0388315	−	0.0388315i
$622$		0			0
$623$	−8.55990e6			−0.883585
$624$		0			0
$625$	4.49317e6			0.460101
$626$		0			0
$627$	−2.22497e6	+	2.22497e6i	−0.226025	+	0.226025i
$628$		0			0
$629$	1.02044e7	+	1.02044e7i	1.02840	+	1.02840i
$630$		0			0
$631$			6.58495e6i			0.658383i	0.944263	+	0.329192i	$0.106776\pi$
$631$			6.58495e6i			0.658383i	−0.944263	+	0.329192i	$0.893224\pi$
$632$		0			0
$633$			4.29581e6i			0.426123i
$634$		0			0
$635$	−5.61995e6	−	5.61995e6i	−0.553093	−	0.553093i
$636$		0			0
$637$	424320.	−	424320.i	0.0414329	−	0.0414329i
$638$		0			0
$639$	1.66019e7			1.60844
$640$		0			0
$641$	−1.49887e7			−1.44085			−0.720424	−	0.693534i	$-0.756053\pi$
$641$	−1.49887e7			−1.44085			−0.720424	+	0.693534i	$0.756053\pi$
$642$		0			0
$643$	−866306.	+	866306.i	−0.0826312	+	0.0826312i	−0.747214	−	0.664583i	$-0.768609\pi$
$643$	−866306.	+	866306.i	−0.0826312	+	0.0826312i	0.664583	+	0.747214i	$0.268609\pi$
$644$		0			0
$645$	−748677.	−	748677.i	−0.0708591	−	0.0708591i
$646$		0			0
$647$		−	1.73107e7i		−	1.62575i	−0.582435	−	0.812877i	$-0.697900\pi$
$647$		−	1.73107e7i		−	1.62575i	0.582435	−	0.812877i	$-0.302100\pi$
$648$		0			0
$649$		−	4.38014e6i		−	0.408203i
$650$		0			0
$651$	1.09219e6	+	1.09219e6i	0.101006	+	0.101006i
$652$		0			0
$653$	−6.59868e6	+	6.59868e6i	−0.605583	+	0.605583i	−0.941789	−	0.336205i	$-0.890856\pi$
$653$	−6.59868e6	+	6.59868e6i	−0.605583	+	0.605583i	0.336205	+	0.941789i	$0.390856\pi$
$654$		0			0
$655$	3.93554e6			0.358427
$656$		0			0
$657$	1.45645e7			1.31638
$658$		0			0
$659$	9.31741e6	−	9.31741e6i	0.835760	−	0.835760i	−0.152537	−	0.988298i	$-0.548744\pi$
$659$	9.31741e6	−	9.31741e6i	0.835760	−	0.835760i	0.988298	+	0.152537i	$0.0487445\pi$
$660$		0			0
$661$	−7.53377e6	−	7.53377e6i	−0.670670	−	0.670670i	0.287200	−	0.957871i	$-0.407275\pi$
$661$	−7.53377e6	−	7.53377e6i	−0.670670	−	0.670670i	−0.957871	+	0.287200i	$0.907275\pi$
$662$		0			0
$663$		−	725921.i		−	0.0641365i
$664$		0			0
$665$		−	7.26471e6i		−	0.637036i
$666$		0			0
$667$	156765.	+	156765.i	0.0136438	+	0.0136438i
$668$		0			0
$669$	−5.12293e6	+	5.12293e6i	−0.442541	+	0.442541i
$670$		0			0
$671$	1.36807e7			1.17301
$672$		0			0
$673$	5.96425e6			0.507596			0.253798	−	0.967257i	$-0.418320\pi$
$673$	5.96425e6			0.507596			0.253798	+	0.967257i	$0.418320\pi$
$674$		0			0
$675$	2.27245e6	−	2.27245e6i	0.191970	−	0.191970i
$676$		0			0
$677$	1.43516e7	+	1.43516e7i	1.20345	+	1.20345i	0.973110	+	0.230340i	$0.0739840\pi$
$677$	1.43516e7	+	1.43516e7i	1.20345	+	1.20345i	0.230340	+	0.973110i	$0.426016\pi$
$678$		0			0
$679$		−	9.15381e6i		−	0.761952i
$680$		0			0
$681$		−	5.17158e6i		−	0.427322i
$682$		0			0
$683$	−2.28096e6	−	2.28096e6i	−0.187096	−	0.187096i	0.607343	−	0.794440i	$-0.292235\pi$
$683$	−2.28096e6	−	2.28096e6i	−0.187096	−	0.187096i	−0.794440	+	0.607343i	$0.792235\pi$
$684$		0			0
$685$	−1.38677e6	+	1.38677e6i	−0.112922	+	0.112922i
$686$		0			0
$687$	−2.79589e6			−0.226011
$688$		0			0
$689$	308425.			0.0247515
$690$		0			0
$691$	1.07640e7	−	1.07640e7i	0.857592	−	0.857592i	−0.133462	−	0.991054i	$-0.542610\pi$
$691$	1.07640e7	−	1.07640e7i	0.857592	−	0.857592i	0.991054	+	0.133462i	$0.0426095\pi$
$692$		0			0
$693$	−5.36949e6	−	5.36949e6i	−0.424717	−	0.424717i
$694$		0			0
$695$		−	2.91471e6i		−	0.228893i
$696$		0			0
$697$		−	1.65352e7i		−	1.28922i
$698$		0			0
$699$	5.66366e6	+	5.66366e6i	0.438434	+	0.438434i
$700$		0			0
$701$	−6.90269e6	+	6.90269e6i	−0.530546	+	0.530546i	−0.920735	−	0.390189i	$-0.872410\pi$
$701$	−6.90269e6	+	6.90269e6i	−0.530546	+	0.530546i	0.390189	+	0.920735i	$0.372410\pi$
$702$		0			0
$703$	1.97183e7			1.50481
$704$		0			0
$705$	6.45740e6			0.489311
$706$		0			0
$707$	1.13114e7	−	1.13114e7i	0.851076	−	0.851076i
$708$		0			0
$709$	−1.40814e7	−	1.40814e7i	−1.05203	−	1.05203i	−0.998570	−	0.0534618i	$-0.982974\pi$
$709$	−1.40814e7	−	1.40814e7i	−1.05203	−	1.05203i	−0.0534618	−	0.998570i	$-0.517026\pi$
$710$		0			0
$711$			8.61856e6i			0.639382i
$712$		0			0
$713$			495970.i			0.0365369i
$714$		0			0
$715$	−1.14572e6	−	1.14572e6i	−0.0838134	−	0.0838134i
$716$		0			0
$717$	264641.	−	264641.i	0.0192247	−	0.0192247i
$718$		0			0
$719$	−7.42194e6			−0.535421			−0.267710	−	0.963499i	$-0.586267\pi$
$719$	−7.42194e6			−0.535421			−0.267710	+	0.963499i	$0.586267\pi$
$720$		0			0
$721$	5.76588e6			0.413073
$722$		0			0
$723$	6.15454e6	−	6.15454e6i	0.437875	−	0.437875i
$724$		0			0
$725$	954620.	+	954620.i	0.0674506	+	0.0674506i
$726$		0			0
$727$		−	9.63189e6i		−	0.675889i	−0.941166	−	0.337945i	$-0.890268\pi$
$727$		−	9.63189e6i		−	0.675889i	0.941166	−	0.337945i	$-0.109732\pi$
$728$		0			0
$729$		−	3.58688e6i		−	0.249976i
$730$		0			0
$731$	−3.35409e6	−	3.35409e6i	−0.232157	−	0.232157i
$732$		0			0
$733$	−1.28845e7	+	1.28845e7i	−0.885743	+	0.885743i	−0.994111	−	0.108368i	$-0.965438\pi$
$733$	−1.28845e7	+	1.28845e7i	−0.885743	+	0.885743i	0.108368	+	0.994111i	$0.465438\pi$
$734$		0			0
$735$	1.42076e6			0.0970065
$736$		0			0
$737$	−2.42469e7			−1.64433
$738$		0			0
$739$	−1.36646e7	+	1.36646e7i	−0.920419	+	0.920419i	−0.997059	−	0.0766398i	$-0.975581\pi$
$739$	−1.36646e7	+	1.36646e7i	−0.920419	+	0.920419i	0.0766398	+	0.997059i	$0.475581\pi$
$740$		0			0
$741$	−701358.	−	701358.i	−0.0469239	−	0.0469239i
$742$		0			0
$743$		−	2.75851e7i		−	1.83317i	−0.399839	−	0.916585i	$-0.630934\pi$
$743$		−	2.75851e7i		−	1.83317i	0.399839	−	0.916585i	$-0.369066\pi$
$744$		0			0
$745$		−	9.42229e6i		−	0.621965i
$746$		0			0
$747$	5.21314e6	+	5.21314e6i	0.341820	+	0.341820i
$748$		0			0
$749$	9.19781e6	−	9.19781e6i	0.599073	−	0.599073i
$750$		0			0
$751$	7.42138e6			0.480159			0.240079	−	0.970753i	$-0.422827\pi$
$751$	7.42138e6			0.480159			0.240079	+	0.970753i	$0.422827\pi$
$752$		0			0
$753$	−5.17016e6			−0.332289
$754$		0			0
$755$	7.91353e6	−	7.91353e6i	0.505246	−	0.505246i
$756$		0			0
$757$	1.45162e7	+	1.45162e7i	0.920688	+	0.920688i	0.997078	−	0.0763903i	$-0.0243395\pi$
$757$	1.45162e7	+	1.45162e7i	0.920688	+	0.920688i	−0.0763903	+	0.997078i	$0.524340\pi$
$758$		0			0
$759$			400680.i			0.0252460i
$760$		0			0
$761$		−	3.30896e6i		−	0.207124i	−0.994623	−	0.103562i	$-0.966976\pi$
$761$		−	3.30896e6i		−	0.207124i	0.994623	−	0.103562i	$-0.0330240\pi$
$762$		0			0
$763$	1.36755e7	+	1.36755e7i	0.850420	+	0.850420i
$764$		0			0
$765$	−7.39565e6	+	7.39565e6i	−0.456902	+	0.456902i
$766$		0			0
$767$	1.38071e6			0.0847452
$768$		0			0
$769$	2.42921e6			0.148132			0.0740660	−	0.997253i	$-0.476402\pi$
$769$	2.42921e6			0.148132			0.0740660	+	0.997253i	$0.476402\pi$
$770$		0			0
$771$	−1.85858e6	+	1.85858e6i	−0.112602	+	0.112602i
$772$		0			0
$773$	1.11912e7	+	1.11912e7i	0.673638	+	0.673638i	0.958553	−	0.284915i	$-0.0919652\pi$
$773$	1.11912e7	+	1.11912e7i	0.673638	+	0.673638i	−0.284915	+	0.958553i	$0.591965\pi$
$774$		0			0
$775$			3.02020e6i			0.180627i
$776$		0			0
$777$		−	7.81962e6i		−	0.464658i
$778$		0			0
$779$	−1.59757e7	−	1.59757e7i	−0.943227	−	0.943227i
$780$		0			0
$781$	−1.92901e7	+	1.92901e7i	−1.13164	+	1.13164i
$782$		0			0
$783$	−2.93958e6			−0.171349
$784$		0			0
$785$	−6.50924e6			−0.377013
$786$		0			0
$787$	1.46098e7	−	1.46098e7i	0.840827	−	0.840827i	−0.148140	−	0.988966i	$-0.547329\pi$
$787$	1.46098e7	−	1.46098e7i	0.840827	−	0.840827i	0.988966	+	0.148140i	$0.0473285\pi$
$788$		0			0
$789$	27787.4	+	27787.4i	0.00158912	+	0.00158912i
$790$		0			0
$791$		−	963187.i		−	0.0547356i
$792$		0			0
$793$			4.31243e6i			0.243523i
$794$		0			0
$795$	516351.	+	516351.i	0.0289752	+	0.0289752i
$796$		0			0
$797$	1.39108e7	−	1.39108e7i	0.775722	−	0.775722i	−0.203378	−	0.979100i	$-0.565192\pi$
$797$	1.39108e7	−	1.39108e7i	0.775722	−	0.775722i	0.979100	+	0.203378i	$0.0651921\pi$
$798$		0			0
$799$	2.89293e7			1.60314
$800$		0			0
$801$	1.68387e7			0.927313
$802$		0			0
$803$	−1.69228e7	+	1.69228e7i	−0.926154	+	0.926154i
$804$		0			0
$805$	−654126.	−	654126.i	−0.0355772	−	0.0355772i
$806$		0			0
$807$			5.48162e6i			0.296295i
$808$		0			0
$809$		−	1.33829e7i		−	0.718915i	−0.933161	−	0.359458i	$-0.882962\pi$
$809$		−	1.33829e7i		−	0.718915i	0.933161	−	0.359458i	$-0.117038\pi$
$810$		0			0
$811$	2.91352e6	+	2.91352e6i	0.155548	+	0.155548i	0.780591	−	0.625042i	$-0.214918\pi$
$811$	2.91352e6	+	2.91352e6i	0.155548	+	0.155548i	−0.625042	+	0.780591i	$0.714918\pi$
$812$		0			0
$813$	9.53852e6	−	9.53852e6i	0.506121	−	0.506121i
$814$		0			0
$815$	−2.52633e7			−1.33228
$816$		0			0
$817$	−6.48120e6			−0.339704
$818$		0			0
$819$	1.69258e6	−	1.69258e6i	0.0881736	−	0.0881736i
$820$		0			0
$821$	1.82737e7	+	1.82737e7i	0.946170	+	0.946170i	0.998623	−	0.0524535i	$-0.0167041\pi$
$821$	1.82737e7	+	1.82737e7i	0.946170	+	0.946170i	−0.0524535	+	0.998623i	$0.516704\pi$
$822$		0			0
$823$			3.21353e7i			1.65380i	0.562350	+	0.826899i	$0.309897\pi$
$823$			3.21353e7i			1.65380i	−0.562350	+	0.826899i	$0.690103\pi$
$824$		0			0
$825$			2.43994e6i			0.124808i
$826$		0			0
$827$	−6.74973e6	−	6.74973e6i	−0.343181	−	0.343181i	0.514381	−	0.857562i	$-0.328022\pi$
$827$	−6.74973e6	−	6.74973e6i	−0.343181	−	0.343181i	−0.857562	+	0.514381i	$0.828022\pi$
$828$		0			0
$829$	6.28329e6	−	6.28329e6i	0.317542	−	0.317542i	−0.530280	−	0.847822i	$-0.677913\pi$
$829$	6.28329e6	−	6.28329e6i	0.317542	−	0.317542i	0.847822	+	0.530280i	$0.177913\pi$
$830$		0			0
$831$	6.81814e6			0.342502
$832$		0			0
$833$	6.36501e6			0.317824
$834$		0			0
$835$	−1.45516e7	+	1.45516e7i	−0.722261	+	0.722261i
$836$		0			0
$837$	−4.65008e6	−	4.65008e6i	−0.229428	−	0.229428i
$838$		0			0
$839$			444643.i			0.0218076i	0.999941	+	0.0109038i	$0.00347085\pi$
$839$			444643.i			0.0218076i	−0.999941	+	0.0109038i	$0.996529\pi$
$840$		0			0
$841$			1.92763e7i			0.939795i
$842$		0			0
$843$	−7.27220e6	−	7.27220e6i	−0.352449	−	0.352449i
$844$		0			0
$845$	−1.11133e7	+	1.11133e7i	−0.535428	+	0.535428i
$846$		0			0
$847$	−4.60873e6			−0.220736
$848$		0			0
$849$	1.29177e6			0.0615056
$850$		0			0
$851$	1.77547e6	−	1.77547e6i	0.0840404	−	0.0840404i
$852$		0			0
$853$	−2.78792e7	−	2.78792e7i	−1.31192	−	1.31192i	−0.919997	−	0.391926i	$-0.871809\pi$
$853$	−2.78792e7	−	2.78792e7i	−1.31192	−	1.31192i	−0.391926	−	0.919997i	$-0.628191\pi$
$854$		0			0
$855$			1.42908e7i			0.668562i
$856$		0			0
$857$			3.64539e6i			0.169548i	0.996400	+	0.0847739i	$0.0270168\pi$
$857$			3.64539e6i			0.169548i	−0.996400	+	0.0847739i	$0.972983\pi$
$858$		0			0
$859$	2.62514e7	+	2.62514e7i	1.21386	+	1.21386i	0.969745	+	0.244119i	$0.0784989\pi$
$859$	2.62514e7	+	2.62514e7i	1.21386	+	1.21386i	0.244119	+	0.969745i	$0.421501\pi$
$860$		0			0
$861$	−6.33544e6	+	6.33544e6i	−0.291252	+	0.291252i
$862$		0			0
$863$	−1.28317e7			−0.586484			−0.293242	−	0.956038i	$-0.594734\pi$
$863$	−1.28317e7			−0.586484			−0.293242	+	0.956038i	$0.594734\pi$
$864$		0			0
$865$	1.20691e7			0.548447
$866$		0			0
$867$	−435041.	+	435041.i	−0.0196554	+	0.0196554i
$868$		0			0
$869$	−1.00141e7	−	1.00141e7i	−0.449845	−	0.449845i
$870$		0			0
$871$		−	7.64314e6i		−	0.341371i
$872$		0			0
$873$			1.80070e7i			0.799660i
$874$		0			0
$875$	−1.42294e7	−	1.42294e7i	−0.628298	−	0.628298i
$876$		0			0
$877$	2.24287e7	−	2.24287e7i	0.984702	−	0.984702i	−0.0151830	−	0.999885i	$-0.504833\pi$
$877$	2.24287e7	−	2.24287e7i	0.984702	−	0.984702i	0.999885	+	0.0151830i	$0.00483307\pi$
$878$		0			0
$879$	5.65792e6			0.246993
$880$		0			0
$881$	−1.01470e6			−0.0440451			−0.0220226	−	0.999757i	$-0.507011\pi$
$881$	−1.01470e6			−0.0440451			−0.0220226	+	0.999757i	$0.507011\pi$
$882$		0			0
$883$	5.83316e6	−	5.83316e6i	0.251769	−	0.251769i	−0.569927	−	0.821696i	$-0.693028\pi$
$883$	5.83316e6	−	5.83316e6i	0.251769	−	0.251769i	0.821696	+	0.569927i	$0.193028\pi$
$884$		0			0
$885$	2.31153e6	+	2.31153e6i	0.0992066	+	0.0992066i
$886$		0			0
$887$		−	2.57739e7i		−	1.09994i	−0.835183	−	0.549972i	$-0.814638\pi$
$887$		−	2.57739e7i		−	1.09994i	0.835183	−	0.549972i	$-0.185362\pi$
$888$		0			0
$889$			1.92935e7i			0.818758i
$890$		0			0
$891$	8.54168e6	+	8.54168e6i	0.360453	+	0.360453i
$892$		0			0
$893$	2.79504e7	−	2.79504e7i	1.17290	−	1.17290i
$894$		0			0
$895$	−3.25541e7			−1.35847
$896$		0			0
$897$	−126303.			−0.00524122
$898$		0			0
$899$	1.95343e6	−	1.95343e6i	0.0806117	−	0.0806117i
$900$		0			0
$901$	2.31326e6	+	2.31326e6i	0.0949321	+	0.0949321i
$902$		0			0
$903$			2.57023e6i			0.104895i
$904$		0			0
$905$		−	3.00441e6i		−	0.121938i
$906$		0			0
$907$	−2.87884e6	−	2.87884e6i	−0.116198	−	0.116198i	0.646617	−	0.762815i	$-0.276183\pi$
$907$	−2.87884e6	−	2.87884e6i	−0.116198	−	0.116198i	−0.762815	+	0.646617i	$0.776183\pi$
$908$		0			0
$909$	−2.22513e7	+	2.22513e7i	−0.893194	+	0.893194i
$910$		0			0
$911$	−3.57373e7			−1.42668			−0.713338	−	0.700820i	$-0.752818\pi$
$911$	−3.57373e7			−1.42668			−0.713338	+	0.700820i	$0.752818\pi$
$912$		0			0
$913$	−1.21145e7			−0.480984
$914$		0			0
$915$	−7.21967e6	+	7.21967e6i	−0.285079	+	0.285079i
$916$		0			0
$917$	−6.75541e6	−	6.75541e6i	−0.265294	−	0.265294i
$918$		0			0
$919$			2.91848e7i			1.13990i	0.821678	+	0.569952i	$0.193038\pi$
$919$			2.91848e7i			1.13990i	−0.821678	+	0.569952i	$0.806962\pi$
$920$		0			0
$921$		−	2.25049e6i		−	0.0874234i
$922$		0			0
$923$	−6.08066e6	−	6.08066e6i	−0.234934	−	0.234934i
$924$		0			0
$925$	1.08117e7	−	1.08117e7i	0.415469	−	0.415469i
$926$		0			0
$927$	−1.13424e7			−0.433516
$928$		0			0
$929$	−3.60526e6			−0.137056			−0.0685279	−	0.997649i	$-0.521830\pi$
$929$	−3.60526e6			−0.137056			−0.0685279	+	0.997649i	$0.521830\pi$
$930$		0			0
$931$	6.14964e6	−	6.14964e6i	0.232528	−	0.232528i
$932$		0			0
$933$	−1.08129e7	−	1.08129e7i	−0.406665	−	0.406665i
$934$		0			0
$935$		−	1.71864e7i		−	0.642917i
$936$		0			0
$937$			4.92155e7i			1.83127i	0.402010	+	0.915635i	$0.368312\pi$
$937$			4.92155e7i			1.83127i	−0.402010	+	0.915635i	$0.631688\pi$
$938$		0			0
$939$	−5.35075e6	−	5.35075e6i	−0.198039	−	0.198039i
$940$		0			0
$941$	3.04022e7	−	3.04022e7i	1.11926	−	1.11926i	0.127410	−	0.991850i	$-0.459334\pi$
$941$	3.04022e7	−	3.04022e7i	1.11926	−	1.11926i	0.991850	−	0.127410i	$-0.0406664\pi$
$942$		0			0
$943$	−2.87695e6			−0.105355
$944$		0			0
$945$	1.22658e7			0.446804
$946$		0			0
$947$	−3.27173e7	+	3.27173e7i	−1.18550	+	1.18550i	−0.207203	+	0.978298i	$0.566436\pi$
$947$	−3.27173e7	+	3.27173e7i	−1.18550	+	1.18550i	−0.978298	+	0.207203i	$0.933564\pi$
$948$		0			0
$949$	−5.33442e6	−	5.33442e6i	−0.192275	−	0.192275i
$950$		0			0
$951$			1.33989e7i			0.480417i
$952$		0			0
$953$			2.41105e7i			0.859953i	0.902840	+	0.429976i	$0.141478\pi$
$953$			2.41105e7i			0.859953i	−0.902840	+	0.429976i	$0.858522\pi$
$954$		0			0
$955$	−1.71879e7	−	1.71879e7i	−0.609837	−	0.609837i
$956$		0			0
$957$	1.57812e6	−	1.57812e6i	0.0557006	−	0.0557006i
$958$		0			0
$959$	4.76081e6			0.167161
$960$		0			0
$961$	−2.24489e7			−0.784129
$962$		0			0
$963$	−1.80935e7	+	1.80935e7i	−0.628720	+	0.628720i
$964$		0			0
$965$	−9.71911e6	−	9.71911e6i	−0.335976	−	0.335976i
$966$		0			0
$967$			5.12206e6i			0.176148i	0.996114	+	0.0880742i	$0.0280713\pi$
$967$			5.12206e6i			0.176148i	−0.996114	+	0.0880742i	$0.971929\pi$
$968$		0			0
$969$		−	1.05207e7i		−	0.359945i
$970$		0			0
$971$	2.08093e6	+	2.08093e6i	0.0708288	+	0.0708288i	0.741634	−	0.670805i	$-0.234051\pi$
$971$	2.08093e6	+	2.08093e6i	0.0708288	+	0.0708288i	−0.670805	+	0.741634i	$0.734051\pi$
$972$		0			0
$973$	−5.00314e6	+	5.00314e6i	−0.169418	+	0.169418i
$974$		0			0
$975$	−769120.			−0.0259109
$976$		0			0
$977$	−2.50049e7			−0.838085			−0.419043	−	0.907967i	$-0.637634\pi$
$977$	−2.50049e7			−0.838085			−0.419043	+	0.907967i	$0.637634\pi$
$978$		0			0
$979$	−1.95652e7	+	1.95652e7i	−0.652422	+	0.652422i
$980$		0			0
$981$	−2.69019e7	−	2.69019e7i	−0.892506	−	0.892506i
$982$		0			0
$983$			3.32909e7i			1.09886i	0.835541	+	0.549429i	$0.185155\pi$
$983$			3.32909e7i			1.09886i	−0.835541	+	0.549429i	$0.814845\pi$
$984$		0			0
$985$		−	152514.i		−	0.00500864i
$986$		0			0
$987$	−1.10842e7	−	1.10842e7i	−0.362170	−	0.362170i
$988$		0			0
$989$	−583577.	+	583577.i	−0.0189718	+	0.0189718i
$990$		0			0
$991$	1.62983e7			0.527179			0.263589	−	0.964635i	$-0.415094\pi$
$991$	1.62983e7			0.527179			0.263589	+	0.964635i	$0.415094\pi$
$992$		0			0
$993$	2.01869e7			0.649676
$994$		0			0
$995$	−1.62044e7	+	1.62044e7i	−0.518890	+	0.518890i
$996$		0			0
$997$	2.79951e7	+	2.79951e7i	0.891957	+	0.891957i	0.994707	−	0.102750i	$-0.0327643\pi$
$997$	2.79951e7	+	2.79951e7i	0.891957	+	0.891957i	−0.102750	+	0.994707i	$0.532764\pi$
$998$		0			0
$999$			3.32926e7i			1.05544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.6.e.c.193.7	yes	24
4.3	odd	2	inner	256.6.e.c.193.6	yes	24
8.3	odd	2		256.6.e.d.193.7	yes	24
8.5	even	2		256.6.e.d.193.6	yes	24
16.3	odd	4	inner	256.6.e.c.65.6	✓	24
16.5	even	4		256.6.e.d.65.6	yes	24
16.11	odd	4		256.6.e.d.65.7	yes	24
16.13	even	4	inner	256.6.e.c.65.7	yes	24
32.3	odd	8		1024.6.a.h.1.7		12
32.13	even	8		1024.6.a.h.1.8		12
32.19	odd	8		1024.6.a.j.1.6		12
32.29	even	8		1024.6.a.j.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.6.e.c.65.6	✓	24	16.3	odd	4	inner
256.6.e.c.65.7	yes	24	16.13	even	4	inner
256.6.e.c.193.6	yes	24	4.3	odd	2	inner
256.6.e.c.193.7	yes	24	1.1	even	1	trivial
256.6.e.d.65.6	yes	24	16.5	even	4
256.6.e.d.65.7	yes	24	16.11	odd	4
256.6.e.d.193.6	yes	24	8.5	even	2
256.6.e.d.193.7	yes	24	8.3	odd	2
1024.6.a.h.1.7		12	32.3	odd	8
1024.6.a.h.1.8		12	32.13	even	8
1024.6.a.j.1.5		12	32.29	even	8
1024.6.a.j.1.6		12	32.19	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(4.14100 - 4.14100i) q^{3} +(30.9040 + 30.9040i) q^{5} -106.094i q^{7} +208.704i q^{9} +(-242.499 - 242.499i) q^{11} +(76.4407 - 76.4407i) q^{13} +255.947 q^{15} +1146.65 q^{17} +(1107.85 - 1107.85i) q^{19} +(-439.337 - 439.337i) q^{21} -199.505i q^{23} -1214.88i q^{25} +(1870.51 + 1870.51i) q^{27} +(-785.771 + 785.771i) q^{29} -2486.00 q^{31} -2008.37 q^{33} +(3278.74 - 3278.74i) q^{35} +(8899.35 + 8899.35i) q^{37} -633.081i q^{39} -14420.5i q^{41} +(-2925.13 - 2925.13i) q^{43} +(-6449.80 + 6449.80i) q^{45} +25229.5 q^{47} +5550.98 q^{49} +(4748.26 - 4748.26i) q^{51} +(2017.41 + 2017.41i) q^{53} -14988.4i q^{55} -9175.20i q^{57} +(9031.27 + 9031.27i) q^{59} +(-28207.7 + 28207.7i) q^{61} +22142.4 q^{63} +4724.65 q^{65} +(49993.9 - 49993.9i) q^{67} +(-826.149 - 826.149i) q^{69} -79547.5i q^{71} -69785.1i q^{73} +(-5030.83 - 5030.83i) q^{75} +(-25727.7 + 25727.7i) q^{77} +41295.6 q^{79} -35223.6 q^{81} +(24978.6 - 24978.6i) q^{83} +(35436.0 + 35436.0i) q^{85} +6507.75i q^{87} -80681.9i q^{89} +(-8109.93 - 8109.93i) q^{91} +(-10294.5 + 10294.5i) q^{93} +68474.0 q^{95} +86279.9 q^{97} +(50610.5 - 50610.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 160 q^{5} - 1040 q^{13} + 384 q^{17} + 7376 q^{21} - 14624 q^{29} + 78208 q^{33} - 35248 q^{37} - 118288 q^{45} + 100072 q^{49} - 104144 q^{53} - 174640 q^{61} + 464496 q^{65} - 29968 q^{69} - 667920 q^{77}+ \cdots + 833152 q^{97}+O(q^{100}) \) 24 * q - 160 * q^5 - 1040 * q^13 + 384 * q^17 + 7376 * q^21 - 14624 * q^29 + 78208 * q^33 - 35248 * q^37 - 118288 * q^45 + 100072 * q^49 - 104144 * q^53 - 174640 * q^61 + 464496 * q^65 - 29968 * q^69 - 667920 * q^77 + 750440 * q^81 - 419856 * q^85 - 391136 * q^93 + 833152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more