LMFDB - Embedded newform 320.6.l.a.81.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,6,Mod(81,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("320.81");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	320.l (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$51.3228223402$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.8
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.9697 - 14.9697i) q^{3} +(17.6777 - 17.6777i) q^{5} -66.6523i q^{7} +205.184i q^{9} +O(q^{10})$	\(q+(-14.9697 - 14.9697i) q^{3} +(17.6777 - 17.6777i) q^{5} -66.6523i q^{7} +205.184i q^{9} +(34.0729 - 34.0729i) q^{11} +(292.234 + 292.234i) q^{13} -529.259 q^{15} +610.554 q^{17} +(702.298 + 702.298i) q^{19} +(-997.765 + 997.765i) q^{21} +2859.14i q^{23} -625.000i q^{25} +(-566.093 + 566.093i) q^{27} +(4762.59 + 4762.59i) q^{29} +775.382 q^{31} -1020.12 q^{33} +(-1178.26 - 1178.26i) q^{35} +(-6929.77 + 6929.77i) q^{37} -8749.32i q^{39} +1051.16i q^{41} +(-5645.72 + 5645.72i) q^{43} +(3627.18 + 3627.18i) q^{45} +2247.96 q^{47} +12364.5 q^{49} +(-9139.81 - 9139.81i) q^{51} +(17582.1 - 17582.1i) q^{53} -1204.66i q^{55} -21026.4i q^{57} +(-22506.6 + 22506.6i) q^{59} +(35680.2 + 35680.2i) q^{61} +13676.0 q^{63} +10332.0 q^{65} +(-14570.0 - 14570.0i) q^{67} +(42800.5 - 42800.5i) q^{69} -37150.7i q^{71} -77602.0i q^{73} +(-9356.07 + 9356.07i) q^{75} +(-2271.04 - 2271.04i) q^{77} +103892. q^{79} +66808.2 q^{81} +(30433.5 + 30433.5i) q^{83} +(10793.2 - 10793.2i) q^{85} -142589. i q^{87} -55535.9i q^{89} +(19478.1 - 19478.1i) q^{91} +(-11607.2 - 11607.2i) q^{93} +24830.0 q^{95} +33028.6 q^{97} +(6991.23 + 6991.23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) $ 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−14.9697	−	14.9697i	−0.960307	−	0.960307i	0.0389348	−	0.999242i	$-0.487604\pi$
$3$	−14.9697	−	14.9697i	−0.960307	−	0.960307i	−0.999242	+	0.0389348i	$0.987604\pi$
$4$		0			0
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$		0			0
$7$		−	66.6523i		−	0.514127i	−0.966395	−	0.257063i	$-0.917245\pi$
$7$		−	66.6523i		−	0.514127i	0.966395	−	0.257063i	$-0.0827549\pi$
$8$		0			0
$9$			205.184i			0.844379i
$10$		0			0
$11$	34.0729	−	34.0729i	0.0849040	−	0.0849040i	−0.663379	−	0.748283i	$-0.730878\pi$
$11$	34.0729	−	34.0729i	0.0849040	−	0.0849040i	0.748283	+	0.663379i	$0.230878\pi$
$12$		0			0
$13$	292.234	+	292.234i	0.479593	+	0.479593i	0.905001	−	0.425409i	$-0.139870\pi$
$13$	292.234	+	292.234i	0.479593	+	0.479593i	−0.425409	+	0.905001i	$0.639870\pi$
$14$		0			0
$15$	−529.259			−0.607351
$16$		0			0
$17$	610.554			0.512391			0.256196	−	0.966625i	$-0.417531\pi$
$17$	610.554			0.512391			0.256196	+	0.966625i	$0.417531\pi$
$18$		0			0
$19$	702.298	+	702.298i	0.446311	+	0.446311i	0.894126	−	0.447815i	$-0.147798\pi$
$19$	702.298	+	702.298i	0.446311	+	0.446311i	−0.447815	+	0.894126i	$0.647798\pi$
$20$		0			0
$21$	−997.765	+	997.765i	−0.493719	+	0.493719i
$22$		0			0
$23$			2859.14i			1.12698i	0.826123	+	0.563489i	$0.190541\pi$
$23$			2859.14i			1.12698i	−0.826123	+	0.563489i	$0.809459\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−566.093	+	566.093i	−0.149444	+	0.149444i
$28$		0			0
$29$	4762.59	+	4762.59i	1.05159	+	1.05159i	0.998595	+	0.0529987i	$0.0168779\pi$
$29$	4762.59	+	4762.59i	1.05159	+	1.05159i	0.0529987	+	0.998595i	$0.483122\pi$
$30$		0			0
$31$	775.382			0.144914			0.0724572	−	0.997372i	$-0.476916\pi$
$31$	775.382			0.144914			0.0724572	+	0.997372i	$0.476916\pi$
$32$		0			0
$33$	−1020.12			−0.163068
$34$		0			0
$35$	−1178.26	−	1178.26i	−0.162581	−	0.162581i
$36$		0			0
$37$	−6929.77	+	6929.77i	−0.832174	+	0.832174i	−0.987814	−	0.155640i	$-0.950256\pi$
$37$	−6929.77	+	6929.77i	−0.832174	+	0.832174i	0.155640	+	0.987814i	$0.450256\pi$
$38$		0			0
$39$		−	8749.32i		−	0.921113i
$40$		0			0
$41$			1051.16i			0.0976585i	0.998807	+	0.0488292i	$0.0155490\pi$
$41$			1051.16i			0.0976585i	−0.998807	+	0.0488292i	$0.984451\pi$
$42$		0			0
$43$	−5645.72	+	5645.72i	−0.465638	+	0.465638i	−0.900498	−	0.434860i	$-0.856798\pi$
$43$	−5645.72	+	5645.72i	−0.465638	+	0.465638i	0.434860	+	0.900498i	$0.356798\pi$
$44$		0			0
$45$	3627.18	+	3627.18i	0.267016	+	0.267016i
$46$		0			0
$47$	2247.96			0.148437			0.0742187	−	0.997242i	$-0.476354\pi$
$47$	2247.96			0.148437			0.0742187	+	0.997242i	$0.476354\pi$
$48$		0			0
$49$	12364.5			0.735674
$50$		0			0
$51$	−9139.81	−	9139.81i	−0.492053	−	0.492053i
$52$		0			0
$53$	17582.1	−	17582.1i	0.859769	−	0.859769i	−0.131541	−	0.991311i	$-0.541993\pi$
$53$	17582.1	−	17582.1i	0.859769	−	0.859769i	0.991311	+	0.131541i	$0.0419926\pi$
$54$		0			0
$55$		−	1204.66i		−	0.0536980i
$56$		0			0
$57$		−	21026.4i		−	0.857191i
$58$		0			0
$59$	−22506.6	+	22506.6i	−0.841744	+	0.841744i	−0.989086	−	0.147341i	$-0.952928\pi$
$59$	−22506.6	+	22506.6i	−0.841744	+	0.841744i	0.147341	+	0.989086i	$0.452928\pi$
$60$		0			0
$61$	35680.2	+	35680.2i	1.22773	+	1.22773i	0.964821	+	0.262906i	$0.0846811\pi$
$61$	35680.2	+	35680.2i	1.22773	+	1.22773i	0.262906	+	0.964821i	$0.415319\pi$
$62$		0			0
$63$	13676.0			0.434118
$64$		0			0
$65$	10332.0			0.303321
$66$		0			0
$67$	−14570.0	−	14570.0i	−0.396526	−	0.396526i	0.480480	−	0.877006i	$-0.340462\pi$
$67$	−14570.0	−	14570.0i	−0.396526	−	0.396526i	−0.877006	+	0.480480i	$0.840462\pi$
$68$		0			0
$69$	42800.5	−	42800.5i	1.08225	−	1.08225i
$70$		0			0
$71$		−	37150.7i		−	0.874624i	−0.899310	−	0.437312i	$-0.855930\pi$
$71$		−	37150.7i		−	0.874624i	0.899310	−	0.437312i	$-0.144070\pi$
$72$		0			0
$73$		−	77602.0i		−	1.70438i	−0.523235	−	0.852188i	$-0.675275\pi$
$73$		−	77602.0i		−	1.70438i	0.523235	−	0.852188i	$-0.324725\pi$
$74$		0			0
$75$	−9356.07	+	9356.07i	−0.192061	+	0.192061i
$76$		0			0
$77$	−2271.04	−	2271.04i	−0.0436514	−	0.0436514i
$78$		0			0
$79$	103892.			1.87290			0.936450	−	0.350800i	$-0.114090\pi$
$79$	103892.			1.87290			0.936450	+	0.350800i	$0.114090\pi$
$80$		0			0
$81$	66808.2			1.13140
$82$		0			0
$83$	30433.5	+	30433.5i	0.484905	+	0.484905i	0.906694	−	0.421789i	$-0.138598\pi$
$83$	30433.5	+	30433.5i	0.484905	+	0.484905i	−0.421789	+	0.906694i	$0.638598\pi$
$84$		0			0
$85$	10793.2	−	10793.2i	0.162032	−	0.162032i
$86$		0			0
$87$		−	142589.i		−	2.01970i
$88$		0			0
$89$		−	55535.9i		−	0.743188i	−0.928395	−	0.371594i	$-0.878811\pi$
$89$		−	55535.9i		−	0.743188i	0.928395	−	0.371594i	$-0.121189\pi$
$90$		0			0
$91$	19478.1	−	19478.1i	0.246571	−	0.246571i
$92$		0			0
$93$	−11607.2	−	11607.2i	−0.139162	−	0.139162i
$94$		0			0
$95$	24830.0			0.282272
$96$		0			0
$97$	33028.6			0.356419			0.178209	−	0.983993i	$-0.442970\pi$
$97$	33028.6			0.356419			0.178209	+	0.983993i	$0.442970\pi$
$98$		0			0
$99$	6991.23	+	6991.23i	0.0716911	+	0.0716911i
$100$		0			0
$101$	−69109.8	+	69109.8i	−0.674119	+	0.674119i	−0.958663	−	0.284544i	$-0.908158\pi$
$101$	−69109.8	+	69109.8i	−0.674119	+	0.674119i	0.284544	+	0.958663i	$0.408158\pi$
$102$		0			0
$103$		−	59252.8i		−	0.550321i	−0.961398	−	0.275161i	$-0.911269\pi$
$103$		−	59252.8i		−	0.550321i	0.961398	−	0.275161i	$-0.0887310\pi$
$104$		0			0
$105$			35276.3i			0.312256i
$106$		0			0
$107$	132571.	−	132571.i	1.11941	−	1.11941i	0.127585	−	0.991828i	$-0.459277\pi$
$107$	132571.	−	132571.i	1.11941	−	1.11941i	0.991828	−	0.127585i	$-0.0407226\pi$
$108$		0			0
$109$	−151453.	−	151453.i	−1.22099	−	1.22099i	−0.967281	−	0.253708i	$-0.918350\pi$
$109$	−151453.	−	151453.i	−1.22099	−	1.22099i	−0.253708	−	0.967281i	$-0.581650\pi$
$110$		0			0
$111$	207473.			1.59829
$112$		0			0
$113$	−27934.3			−0.205798			−0.102899	−	0.994692i	$-0.532812\pi$
$113$	−27934.3			−0.205798			−0.102899	+	0.994692i	$0.532812\pi$
$114$		0			0
$115$	50542.9	+	50542.9i	0.356382	+	0.356382i
$116$		0			0
$117$	−59961.8	+	59961.8i	−0.404958	+	0.404958i
$118$		0			0
$119$		−	40694.8i		−	0.263434i
$120$		0			0
$121$			158729.i			0.985583i
$122$		0			0
$123$	15735.6	−	15735.6i	0.0937821	−	0.0937821i
$124$		0			0
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	15092.5			0.0830333			0.0415166	−	0.999138i	$-0.486781\pi$
$127$	15092.5			0.0830333			0.0415166	+	0.999138i	$0.486781\pi$
$128$		0			0
$129$	169030.			0.894310
$130$		0			0
$131$	225439.	+	225439.i	1.14776	+	1.14776i	0.986993	+	0.160765i	$0.0513960\pi$
$131$	225439.	+	225439.i	1.14776	+	1.14776i	0.160765	+	0.986993i	$0.448604\pi$
$132$		0			0
$133$	46809.8	−	46809.8i	0.229460	−	0.229460i
$134$		0			0
$135$			20014.4i			0.0945166i
$136$		0			0
$137$			183393.i			0.834798i	0.908723	+	0.417399i	$0.137058\pi$
$137$			183393.i			0.834798i	−0.908723	+	0.417399i	$0.862942\pi$
$138$		0			0
$139$	−227165.	+	227165.i	−0.997252	+	0.997252i	−0.999996	−	0.00274377i	$-0.999127\pi$
$139$	−227165.	+	227165.i	−0.997252	+	0.997252i	0.00274377	+	0.999996i	$0.499127\pi$
$140$		0			0
$141$	−33651.2	−	33651.2i	−0.142545	−	0.142545i
$142$		0			0
$143$	19914.6			0.0814386
$144$		0			0
$145$	168383.			0.665086
$146$		0			0
$147$	−185092.	−	185092.i	−0.706473	−	0.706473i
$148$		0			0
$149$	126186.	−	126186.i	0.465636	−	0.465636i	−0.434862	−	0.900497i	$-0.643203\pi$
$149$	126186.	−	126186.i	0.465636	−	0.465636i	0.900497	+	0.434862i	$0.143203\pi$
$150$		0			0
$151$			406653.i			1.45138i	0.688021	+	0.725691i	$0.258480\pi$
$151$			406653.i			1.45138i	−0.688021	+	0.725691i	$0.741520\pi$
$152$		0			0
$153$			125276.i			0.432652i
$154$		0			0
$155$	13706.9	−	13706.9i	0.0458259	−	0.0458259i
$156$		0			0
$157$	−355078.	−	355078.i	−1.14967	−	1.14967i	−0.986617	−	0.163058i	$-0.947864\pi$
$157$	−355078.	−	355078.i	−1.14967	−	1.14967i	−0.163058	−	0.986617i	$-0.552136\pi$
$158$		0			0
$159$	−526399.			−1.65129
$160$		0			0
$161$	190568.			0.579410
$162$		0			0
$163$	300694.	+	300694.i	0.886454	+	0.886454i	0.994181	−	0.107727i	$-0.0343571\pi$
$163$	300694.	+	300694.i	0.886454	+	0.886454i	−0.107727	+	0.994181i	$0.534357\pi$
$164$		0			0
$165$	−18033.4	+	18033.4i	−0.0515665	+	0.0515665i
$166$		0			0
$167$		−	12377.8i		−	0.0343441i	−0.999853	−	0.0171721i	$-0.994534\pi$
$167$		−	12377.8i		−	0.0343441i	0.999853	−	0.0171721i	$-0.00546630\pi$
$168$		0			0
$169$		−	200491.i		−	0.539982i
$170$		0			0
$171$	−144100.	+	144100.i	−0.376855	+	0.376855i
$172$		0			0
$173$	−207386.	−	207386.i	−0.526823	−	0.526823i	0.392800	−	0.919624i	$-0.371506\pi$
$173$	−207386.	−	207386.i	−0.526823	−	0.526823i	−0.919624	+	0.392800i	$0.871506\pi$
$174$		0			0
$175$	−41657.7			−0.102825
$176$		0			0
$177$	673835.			1.61667
$178$		0			0
$179$	66148.3	+	66148.3i	0.154307	+	0.154307i	0.780039	−	0.625731i	$-0.215199\pi$
$179$	66148.3	+	66148.3i	0.154307	+	0.154307i	−0.625731	+	0.780039i	$0.715199\pi$
$180$		0			0
$181$	−100739.	+	100739.i	−0.228560	+	0.228560i	−0.812091	−	0.583531i	$-0.801671\pi$
$181$	−100739.	+	100739.i	−0.228560	+	0.228560i	0.583531	+	0.812091i	$0.301671\pi$
$182$		0			0
$183$		−	1.06824e6i		−	2.35799i
$184$		0			0
$185$			245004.i			0.526313i
$186$		0			0
$187$	20803.4	−	20803.4i	0.0435040	−	0.0435040i
$188$		0			0
$189$	37731.4	+	37731.4i	0.0768331	+	0.0768331i
$190$		0			0
$191$	−3731.48			−0.00740113			−0.00370056	−	0.999993i	$-0.501178\pi$
$191$	−3731.48			−0.00740113			−0.00370056	+	0.999993i	$0.501178\pi$
$192$		0			0
$193$	−113488.			−0.219309			−0.109654	−	0.993970i	$-0.534974\pi$
$193$	−113488.			−0.219309			−0.109654	+	0.993970i	$0.534974\pi$
$194$		0			0
$195$	−154668.	−	154668.i	−0.291281	−	0.291281i
$196$		0			0
$197$	−299753.	+	299753.i	−0.550298	+	0.550298i	−0.926527	−	0.376228i	$-0.877221\pi$
$197$	−299753.	+	299753.i	−0.550298	+	0.550298i	0.376228	+	0.926527i	$0.377221\pi$
$198$		0			0
$199$		−	754680.i		−	1.35092i	−0.737396	−	0.675460i	$-0.763945\pi$
$199$		−	754680.i		−	1.35092i	0.737396	−	0.675460i	$-0.236055\pi$
$200$		0			0
$201$			436216.i			0.761572i
$202$		0			0
$203$	317437.	−	317437.i	0.540652	−	0.540652i
$204$		0			0
$205$	18582.1	+	18582.1i	0.0308823	+	0.0308823i
$206$		0			0
$207$	−586650.			−0.951597
$208$		0			0
$209$	47858.7			0.0757871
$210$		0			0
$211$	440226.	+	440226.i	0.680722	+	0.680722i	0.960163	−	0.279441i	$-0.0901490\pi$
$211$	440226.	+	440226.i	0.680722	+	0.680722i	−0.279441	+	0.960163i	$0.590149\pi$
$212$		0			0
$213$	−556136.	+	556136.i	−0.839908	+	0.839908i
$214$		0			0
$215$			199606.i			0.294495i
$216$		0			0
$217$		−	51681.0i		−	0.0745043i
$218$		0			0
$219$	−1.16168e6	+	1.16168e6i	−1.63673	+	1.63673i
$220$		0			0
$221$	178425.	+	178425.i	0.245739	+	0.245739i
$222$		0			0
$223$	597053.			0.803990			0.401995	−	0.915642i	$-0.368317\pi$
$223$	597053.			0.803990			0.401995	+	0.915642i	$0.368317\pi$
$224$		0			0
$225$	128240.			0.168876
$226$		0			0
$227$	−515972.	−	515972.i	−0.664602	−	0.664602i	0.291859	−	0.956461i	$-0.405726\pi$
$227$	−515972.	−	515972.i	−0.664602	−	0.664602i	−0.956461	+	0.291859i	$0.905726\pi$
$228$		0			0
$229$	414064.	−	414064.i	0.521769	−	0.521769i	−0.396336	−	0.918105i	$-0.629719\pi$
$229$	414064.	−	414064.i	0.521769	−	0.521769i	0.918105	+	0.396336i	$0.129719\pi$
$230$		0			0
$231$			67993.6i			0.0838375i
$232$		0			0
$233$			556837.i			0.671952i	0.941870	+	0.335976i	$0.109066\pi$
$233$			556837.i			0.671952i	−0.941870	+	0.335976i	$0.890934\pi$
$234$		0			0
$235$	39738.6	−	39738.6i	0.0469400	−	0.0469400i
$236$		0			0
$237$	−1.55523e6	−	1.55523e6i	−1.79856	−	1.79856i
$238$		0			0
$239$	−16833.0			−0.0190619			−0.00953097	−	0.999955i	$-0.503034\pi$
$239$	−16833.0			−0.0190619			−0.00953097	+	0.999955i	$0.503034\pi$
$240$		0			0
$241$	416006.			0.461378			0.230689	−	0.973027i	$-0.425902\pi$
$241$	416006.			0.461378			0.230689	+	0.973027i	$0.425902\pi$
$242$		0			0
$243$	−862539.	−	862539.i	−0.937050	−	0.937050i
$244$		0			0
$245$	218575.	−	218575.i	0.232641	−	0.232641i
$246$		0			0
$247$			410471.i			0.428095i
$248$		0			0
$249$		−	911162.i		−	0.931316i
$250$		0			0
$251$	−1.23509e6	+	1.23509e6i	−1.23741	+	1.23741i	−0.276359	+	0.961054i	$0.589128\pi$
$251$	−1.23509e6	+	1.23509e6i	−1.23741	+	1.23741i	−0.961054	+	0.276359i	$0.910872\pi$
$252$		0			0
$253$	97419.3	+	97419.3i	0.0956850	+	0.0956850i
$254$		0			0
$255$	−323141.			−0.311202
$256$		0			0
$257$	77341.0			0.0730427			0.0365214	−	0.999333i	$-0.488372\pi$
$257$	77341.0			0.0730427			0.0365214	+	0.999333i	$0.488372\pi$
$258$		0			0
$259$	461885.	+	461885.i	0.427843	+	0.427843i
$260$		0			0
$261$	−977207.	+	977207.i	−0.887943	+	0.887943i
$262$		0			0
$263$		−	1.43109e6i		−	1.27579i	−0.770124	−	0.637894i	$-0.779806\pi$
$263$		−	1.43109e6i		−	1.27579i	0.770124	−	0.637894i	$-0.220194\pi$
$264$		0			0
$265$		−	621622.i		−	0.543766i
$266$		0			0
$267$	−831356.	+	831356.i	−0.713689	+	0.713689i
$268$		0			0
$269$	1.03735e6	+	1.03735e6i	0.874067	+	0.874067i	0.992913	−	0.118846i	$-0.0379194\pi$
$269$	1.03735e6	+	1.03735e6i	0.874067	+	0.874067i	−0.118846	+	0.992913i	$0.537919\pi$
$270$		0			0
$271$	654430.			0.541302			0.270651	−	0.962677i	$-0.412761\pi$
$271$	654430.			0.541302			0.270651	+	0.962677i	$0.412761\pi$
$272$		0			0
$273$	−583162.			−0.473568
$274$		0			0
$275$	−21295.6	−	21295.6i	−0.0169808	−	0.0169808i
$276$		0			0
$277$	−1.12490e6	+	1.12490e6i	−0.880876	+	0.880876i	−0.993624	−	0.112748i	$-0.964035\pi$
$277$	−1.12490e6	+	1.12490e6i	−0.880876	+	0.880876i	0.112748	+	0.993624i	$0.464035\pi$
$278$		0			0
$279$			159096.i			0.122363i
$280$		0			0
$281$			2.15244e6i			1.62617i	0.582148	+	0.813083i	$0.302213\pi$
$281$			2.15244e6i			1.62617i	−0.582148	+	0.813083i	$0.697787\pi$
$282$		0			0
$283$	−1.07730e6	+	1.07730e6i	−0.799597	+	0.799597i	−0.983032	−	0.183435i	$-0.941278\pi$
$283$	−1.07730e6	+	1.07730e6i	−0.799597	+	0.799597i	0.183435	+	0.983032i	$0.441278\pi$
$284$		0			0
$285$	−371697.	−	371697.i	−0.271067	−	0.271067i
$286$		0			0
$287$	70062.3			0.0502088
$288$		0			0
$289$	−1.04708e6			−0.737455
$290$		0			0
$291$	−494428.	−	494428.i	−0.342271	−	0.342271i
$292$		0			0
$293$	201738.	−	201738.i	0.137283	−	0.137283i	−0.635125	−	0.772409i	$-0.719052\pi$
$293$	201738.	−	201738.i	0.137283	−	0.137283i	0.772409	+	0.635125i	$0.219052\pi$
$294$		0			0
$295$			795729.i			0.532366i
$296$		0			0
$297$			38576.9i			0.0253768i
$298$		0			0
$299$	−835538.	+	835538.i	−0.540491	+	0.540491i
$300$		0			0
$301$	376300.	+	376300.i	0.239397	+	0.239397i
$302$		0			0
$303$	2.06911e6			1.29472
$304$		0			0
$305$	1.26148e6			0.776483
$306$		0			0
$307$	2.33520e6	+	2.33520e6i	1.41409	+	1.41409i	0.716310	+	0.697783i	$0.245830\pi$
$307$	2.33520e6	+	2.33520e6i	1.41409	+	1.41409i	0.697783	+	0.716310i	$0.254170\pi$
$308$		0			0
$309$	−886997.	+	886997.i	−0.528477	+	0.528477i
$310$		0			0
$311$		−	1.50514e6i		−	0.882420i	−0.897404	−	0.441210i	$-0.854549\pi$
$311$		−	1.50514e6i		−	0.882420i	0.897404	−	0.441210i	$-0.145451\pi$
$312$		0			0
$313$		−	1.17646e6i		−	0.678763i	−0.940649	−	0.339381i	$-0.889782\pi$
$313$		−	1.17646e6i		−	0.678763i	0.940649	−	0.339381i	$-0.110218\pi$
$314$		0			0
$315$	241760.	−	241760.i	0.137280	−	0.137280i
$316$		0			0
$317$	851779.	+	851779.i	0.476079	+	0.476079i	0.903875	−	0.427796i	$-0.140710\pi$
$317$	851779.	+	851779.i	0.476079	+	0.476079i	−0.427796	+	0.903875i	$0.640710\pi$
$318$		0			0
$319$	324551.			0.178569
$320$		0			0
$321$	−3.96911e6			−2.14996
$322$		0			0
$323$	428791.	+	428791.i	0.228686	+	0.228686i
$324$		0			0
$325$	182646.	−	182646.i	0.0959185	−	0.0959185i
$326$		0			0
$327$			4.53441e6i			2.34505i
$328$		0			0
$329$		−	149831.i		−	0.0763156i
$330$		0			0
$331$	435282.	−	435282.i	0.218374	−	0.218374i	−0.589439	−	0.807813i	$-0.700651\pi$
$331$	435282.	−	435282.i	0.218374	−	0.218374i	0.807813	+	0.589439i	$0.200651\pi$
$332$		0			0
$333$	−1.42188e6	−	1.42188e6i	−0.702671	−	0.702671i
$334$		0			0
$335$	−515126.			−0.250785
$336$		0			0
$337$	2.88013e6			1.38146			0.690728	−	0.723115i	$-0.257290\pi$
$337$	2.88013e6			1.38146			0.690728	+	0.723115i	$0.257290\pi$
$338$		0			0
$339$	418168.	+	418168.i	0.197629	+	0.197629i
$340$		0			0
$341$	26419.5	−	26419.5i	0.0123038	−	0.0123038i
$342$		0			0
$343$		−	1.94435e6i		−	0.892356i
$344$		0			0
$345$		−	1.51323e6i		−	0.684472i
$346$		0			0
$347$	2.63293e6	−	2.63293e6i	1.17386	−	1.17386i	0.192577	−	0.981282i	$-0.438315\pi$
$347$	2.63293e6	−	2.63293e6i	1.17386	−	1.17386i	0.981282	−	0.192577i	$-0.0616846\pi$
$348$		0			0
$349$	2.54010e6	+	2.54010e6i	1.11632	+	1.11632i	0.992277	+	0.124040i	$0.0395852\pi$
$349$	2.54010e6	+	2.54010e6i	1.11632	+	1.11632i	0.124040	+	0.992277i	$0.460415\pi$
$350$		0			0
$351$	−330863.			−0.143344
$352$		0			0
$353$	−1.69643e6			−0.724603			−0.362302	−	0.932061i	$-0.618009\pi$
$353$	−1.69643e6			−0.724603			−0.362302	+	0.932061i	$0.618009\pi$
$354$		0			0
$355$	−656738.	−	656738.i	−0.276581	−	0.276581i
$356$		0			0
$357$	−609189.	+	609189.i	−0.252977	+	0.252977i
$358$		0			0
$359$		−	2.86875e6i		−	1.17478i	−0.809304	−	0.587390i	$-0.800156\pi$
$359$		−	2.86875e6i		−	1.17478i	0.809304	−	0.587390i	$-0.199844\pi$
$360$		0			0
$361$		−	1.48965e6i		−	0.601613i
$362$		0			0
$363$	2.37613e6	−	2.37613e6i	0.946462	−	0.946462i
$364$		0			0
$365$	−1.37182e6	−	1.37182e6i	−0.538971	−	0.538971i
$366$		0			0
$367$	−231568.			−0.0897457			−0.0448729	−	0.998993i	$-0.514288\pi$
$367$	−231568.			−0.0897457			−0.0448729	+	0.998993i	$0.514288\pi$
$368$		0			0
$369$	−215682.			−0.0824608
$370$		0			0
$371$	−1.17189e6	−	1.17189e6i	−0.442030	−	0.442030i
$372$		0			0
$373$	1.46826e6	−	1.46826e6i	0.546427	−	0.546427i	−0.378979	−	0.925405i	$-0.623725\pi$
$373$	1.46826e6	−	1.46826e6i	0.546427	−	0.546427i	0.925405	+	0.378979i	$0.123725\pi$
$374$		0			0
$375$			330787.i			0.121470i
$376$		0			0
$377$			2.78358e6i			1.00867i
$378$		0			0
$379$	−460062.	+	460062.i	−0.164520	+	0.164520i	−0.784566	−	0.620046i	$-0.787114\pi$
$379$	−460062.	+	460062.i	−0.164520	+	0.164520i	0.620046	+	0.784566i	$0.287114\pi$
$380$		0			0
$381$	−225930.	−	225930.i	−0.0797375	−	0.0797375i
$382$		0			0
$383$	278081.			0.0968665			0.0484333	−	0.998826i	$-0.484577\pi$
$383$	278081.			0.0968665			0.0484333	+	0.998826i	$0.484577\pi$
$384$		0			0
$385$	−80293.4			−0.0276076
$386$		0			0
$387$	−1.15841e6	−	1.15841e6i	−0.393175	−	0.393175i
$388$		0			0
$389$	3.81927e6	−	3.81927e6i	1.27969	−	1.27969i	0.338855	−	0.940839i	$-0.389960\pi$
$389$	3.81927e6	−	3.81927e6i	1.27969	−	1.27969i	0.940839	−	0.338855i	$-0.110040\pi$
$390$		0			0
$391$			1.74566e6i			0.577454i
$392$		0			0
$393$		−	6.74950e6i		−	2.20440i
$394$		0			0
$395$	1.83657e6	−	1.83657e6i	0.592263	−	0.592263i
$396$		0			0
$397$	−978913.	−	978913.i	−0.311722	−	0.311722i	0.533854	−	0.845576i	$-0.320743\pi$
$397$	−978913.	−	978913.i	−0.311722	−	0.311722i	−0.845576	+	0.533854i	$0.820743\pi$
$398$		0			0
$399$	−1.40146e6			−0.440704
$400$		0			0
$401$	−1.86658e6			−0.579677			−0.289838	−	0.957076i	$-0.593602\pi$
$401$	−1.86658e6			−0.579677			−0.289838	+	0.957076i	$0.593602\pi$
$402$		0			0
$403$	226593.	+	226593.i	0.0694999	+	0.0694999i
$404$		0			0
$405$	1.18101e6	−	1.18101e6i	0.357781	−	0.357781i
$406$		0			0
$407$			472235.i			0.141310i
$408$		0			0
$409$			4.49733e6i			1.32937i	0.747123	+	0.664686i	$0.231435\pi$
$409$			4.49733e6i			1.32937i	−0.747123	+	0.664686i	$0.768565\pi$
$410$		0			0
$411$	2.74534e6	−	2.74534e6i	0.801663	−	0.801663i
$412$		0			0
$413$	1.50012e6	+	1.50012e6i	0.432763	+	0.432763i
$414$		0			0
$415$	1.07599e6			0.306681
$416$		0			0
$417$	6.80120e6			1.91534
$418$		0			0
$419$	289805.	+	289805.i	0.0806438	+	0.0806438i	0.746278	−	0.665634i	$-0.231839\pi$
$419$	289805.	+	289805.i	0.0806438	+	0.0806438i	−0.665634	+	0.746278i	$0.731839\pi$
$420$		0			0
$421$	3.18738e6	−	3.18738e6i	0.876452	−	0.876452i	−0.116714	−	0.993166i	$-0.537236\pi$
$421$	3.18738e6	−	3.18738e6i	0.876452	−	0.876452i	0.993166	+	0.116714i	$0.0372360\pi$
$422$		0			0
$423$			461245.i			0.125337i
$424$		0			0
$425$		−	381596.i		−	0.102478i
$426$		0			0
$427$	2.37816e6	−	2.37816e6i	0.631207	−	0.631207i
$428$		0			0
$429$	−298115.	−	298115.i	−0.0782061	−	0.0782061i
$430$		0			0
$431$	−1.40103e6			−0.363290			−0.181645	−	0.983364i	$-0.558142\pi$
$431$	−1.40103e6			−0.363290			−0.181645	+	0.983364i	$0.558142\pi$
$432$		0			0
$433$	4.92875e6			1.26333			0.631666	−	0.775241i	$-0.282372\pi$
$433$	4.92875e6			1.26333			0.631666	+	0.775241i	$0.282372\pi$
$434$		0			0
$435$	−2.52064e6	−	2.52064e6i	−0.638687	−	0.638687i
$436$		0			0
$437$	−2.00797e6	+	2.00797e6i	−0.502983	+	0.502983i
$438$		0			0
$439$		−	489017.i		−	0.121105i	−0.998165	−	0.0605526i	$-0.980714\pi$
$439$		−	489017.i		−	0.121105i	0.998165	−	0.0605526i	$-0.0192863\pi$
$440$		0			0
$441$			2.53699e6i			0.621188i
$442$		0			0
$443$	5.39962e6	−	5.39962e6i	1.30724	−	1.30724i	0.383833	−	0.923403i	$-0.374604\pi$
$443$	5.39962e6	−	5.39962e6i	1.30724	−	1.30724i	0.923403	−	0.383833i	$-0.125396\pi$
$444$		0			0
$445$	−981746.	−	981746.i	−0.235017	−	0.235017i
$446$		0			0
$447$	−3.77794e6			−0.894307
$448$		0			0
$449$	−1.48009e6			−0.346475			−0.173237	−	0.984880i	$-0.555423\pi$
$449$	−1.48009e6			−0.346475			−0.173237	+	0.984880i	$0.555423\pi$
$450$		0			0
$451$	35816.2	+	35816.2i	0.00829159	+	0.00829159i
$452$		0			0
$453$	6.08748e6	−	6.08748e6i	1.39377	−	1.39377i
$454$		0			0
$455$		−	688654.i		−	0.155945i
$456$		0			0
$457$			5.01425e6i			1.12309i	0.827445	+	0.561546i	$0.189793\pi$
$457$			5.01425e6i			1.12309i	−0.827445	+	0.561546i	$0.810207\pi$
$458$		0			0
$459$	−345630.	+	345630.i	−0.0765738	+	0.0765738i
$460$		0			0
$461$	1.39558e6	+	1.39558e6i	0.305845	+	0.305845i	0.843295	−	0.537450i	$-0.180612\pi$
$461$	1.39558e6	+	1.39558e6i	0.305845	+	0.305845i	−0.537450	+	0.843295i	$0.680612\pi$
$462$		0			0
$463$	−4.41497e6			−0.957139			−0.478570	−	0.878050i	$-0.658845\pi$
$463$	−4.41497e6			−0.957139			−0.478570	+	0.878050i	$0.658845\pi$
$464$		0			0
$465$	−410378.			−0.0880139
$466$		0			0
$467$	833822.	+	833822.i	0.176922	+	0.176922i	0.790013	−	0.613091i	$-0.210074\pi$
$467$	833822.	+	833822.i	0.176922	+	0.176922i	−0.613091	+	0.790013i	$0.710074\pi$
$468$		0			0
$469$	−971121.	+	971121.i	−0.203864	+	0.203864i
$470$		0			0
$471$			1.06308e7i			2.20808i
$472$		0			0
$473$			384733.i			0.0790690i
$474$		0			0
$475$	438936.	−	438936.i	0.0892622	−	0.0892622i
$476$		0			0
$477$	3.60757e6	+	3.60757e6i	0.725971	+	0.725971i
$478$		0			0
$479$	5.84747e6			1.16447			0.582236	−	0.813020i	$-0.302178\pi$
$479$	5.84747e6			1.16447			0.582236	+	0.813020i	$0.302178\pi$
$480$		0			0
$481$	−4.05023e6			−0.798210
$482$		0			0
$483$	−2.85275e6	−	2.85275e6i	−0.556411	−	0.556411i
$484$		0			0
$485$	583868.	−	583868.i	0.112709	−	0.112709i
$486$		0			0
$487$			5.71510e6i			1.09195i	0.837802	+	0.545974i	$0.183840\pi$
$487$			5.71510e6i			1.09195i	−0.837802	+	0.545974i	$0.816160\pi$
$488$		0			0
$489$		−	9.00261e6i		−	1.70254i
$490$		0			0
$491$	−2.06011e6	+	2.06011e6i	−0.385645	+	0.385645i	−0.873131	−	0.487486i	$-0.837914\pi$
$491$	−2.06011e6	+	2.06011e6i	−0.385645	+	0.385645i	0.487486	+	0.873131i	$0.337914\pi$
$492$		0			0
$493$	2.90781e6	+	2.90781e6i	0.538827	+	0.538827i
$494$		0			0
$495$	247177.			0.0453414
$496$		0			0
$497$	−2.47618e6			−0.449668
$498$		0			0
$499$	4.78177e6	+	4.78177e6i	0.859680	+	0.859680i	0.991300	−	0.131620i	$-0.0420179\pi$
$499$	4.78177e6	+	4.78177e6i	0.859680	+	0.859680i	−0.131620	+	0.991300i	$0.542018\pi$
$500$		0			0
$501$	−185292.	+	185292.i	−0.0329809	+	0.0329809i
$502$		0			0
$503$		−	4.52174e6i		−	0.796867i	−0.917197	−	0.398433i	$-0.869554\pi$
$503$		−	4.52174e6i		−	0.796867i	0.917197	−	0.398433i	$-0.130446\pi$
$504$		0			0
$505$			2.44340e6i			0.426350i
$506$		0			0
$507$	−3.00130e6	+	3.00130e6i	−0.518548	+	0.518548i
$508$		0			0
$509$	296532.	+	296532.i	0.0507314	+	0.0507314i	0.732017	−	0.681286i	$-0.238579\pi$
$509$	296532.	+	296532.i	0.0507314	+	0.0507314i	−0.681286	+	0.732017i	$0.738579\pi$
$510$		0			0
$511$	−5.17235e6			−0.876265
$512$		0			0
$513$	−795132.			−0.133397
$514$		0			0
$515$	−1.04745e6	−	1.04745e6i	−0.174027	−	0.174027i
$516$		0			0
$517$	76594.5	−	76594.5i	0.0126029	−	0.0126029i
$518$		0			0
$519$			6.20903e6i			1.01182i
$520$		0			0
$521$		−	458362.i		−	0.0739800i	−0.999316	−	0.0369900i	$-0.988223\pi$
$521$		−	458362.i		−	0.0739800i	0.999316	−	0.0369900i	$-0.0117770\pi$
$522$		0			0
$523$	−1.31189e6	+	1.31189e6i	−0.209721	+	0.209721i	−0.804149	−	0.594428i	$-0.797379\pi$
$523$	−1.31189e6	+	1.31189e6i	−0.209721	+	0.209721i	0.594428	+	0.804149i	$0.297379\pi$
$524$		0			0
$525$	623603.	+	623603.i	0.0987439	+	0.0987439i
$526$		0			0
$527$	473412.			0.0742528
$528$		0			0
$529$	−1.73834e6			−0.270082
$530$		0			0
$531$	−4.61800e6	−	4.61800e6i	−0.710751	−	0.710751i
$532$		0			0
$533$	−307185.	+	307185.i	−0.0468363	+	0.0468363i
$534$		0			0
$535$		−	4.68710e6i		−	0.707979i
$536$		0			0
$537$		−	1.98044e6i		−	0.296364i
$538$		0			0
$539$	421294.	−	421294.i	0.0624616	−	0.0624616i
$540$		0			0
$541$	7.50591e6	+	7.50591e6i	1.10258	+	1.10258i	0.994098	+	0.108481i	$0.0345988\pi$
$541$	7.50591e6	+	7.50591e6i	1.10258	+	1.10258i	0.108481	+	0.994098i	$0.465401\pi$
$542$		0			0
$543$	3.01606e6			0.438975
$544$		0			0
$545$	−5.35467e6			−0.772221
$546$		0			0
$547$	3.64329e6	+	3.64329e6i	0.520626	+	0.520626i	0.917760	−	0.397135i	$-0.129995\pi$
$547$	3.64329e6	+	3.64329e6i	0.520626	+	0.520626i	−0.397135	+	0.917760i	$0.629995\pi$
$548$		0			0
$549$	−7.32100e6	+	7.32100e6i	−1.03667	+	1.03667i
$550$		0			0
$551$			6.68951e6i			0.938675i
$552$		0			0
$553$		−	6.92465e6i		−	0.962908i
$554$		0			0
$555$	3.66764e6	−	3.66764e6i	0.505422	−	0.505422i
$556$		0			0
$557$	−2.00393e6	−	2.00393e6i	−0.273681	−	0.273681i	0.556899	−	0.830580i	$-0.311991\pi$
$557$	−2.00393e6	−	2.00393e6i	−0.273681	−	0.273681i	−0.830580	+	0.556899i	$0.811991\pi$
$558$		0			0
$559$	−3.29974e6			−0.446633
$560$		0			0
$561$	−622841.			−0.0835545
$562$		0			0
$563$	−4.20161e6	−	4.20161e6i	−0.558656	−	0.558656i	0.370269	−	0.928925i	$-0.379266\pi$
$563$	−4.20161e6	−	4.20161e6i	−0.558656	−	0.558656i	−0.928925	+	0.370269i	$0.879266\pi$
$564$		0			0
$565$	−493813.	+	493813.i	−0.0650791	+	0.0650791i
$566$		0			0
$567$		−	4.45292e6i		−	0.581684i
$568$		0			0
$569$			4.05098e6i			0.524541i	0.964994	+	0.262271i	$0.0844713\pi$
$569$			4.05098e6i			0.524541i	−0.964994	+	0.262271i	$0.915529\pi$
$570$		0			0
$571$	−7.13511e6	+	7.13511e6i	−0.915820	+	0.915820i	−0.996722	−	0.0809020i	$-0.974220\pi$
$571$	−7.13511e6	+	7.13511e6i	−0.915820	+	0.915820i	0.0809020	+	0.996722i	$0.474220\pi$
$572$		0			0
$573$	55859.2	+	55859.2i	0.00710735	+	0.00710735i
$574$		0			0
$575$	1.78696e6			0.225396
$576$		0			0
$577$	−1.29452e7			−1.61871			−0.809355	−	0.587320i	$-0.800183\pi$
$577$	−1.29452e7			−1.61871			−0.809355	+	0.587320i	$0.800183\pi$
$578$		0			0
$579$	1.69888e6	+	1.69888e6i	0.210604	+	0.210604i
$580$		0			0
$581$	2.02846e6	−	2.02846e6i	0.249303	−	0.249303i
$582$		0			0
$583$		−	1.19815e6i		−	0.145996i
$584$		0			0
$585$			2.11997e6i			0.256118i
$586$		0			0
$587$	243385.	−	243385.i	0.0291540	−	0.0291540i	−0.692379	−	0.721534i	$-0.743438\pi$
$587$	243385.	−	243385.i	0.0291540	−	0.0291540i	0.721534	+	0.692379i	$0.243438\pi$
$588$		0			0
$589$	544549.	+	544549.i	0.0646768	+	0.0646768i
$590$		0			0
$591$	8.97443e6			1.05691
$592$		0			0
$593$	−1.13600e7			−1.32661			−0.663305	−	0.748349i	$-0.730847\pi$
$593$	−1.13600e7			−1.32661			−0.663305	+	0.748349i	$0.730847\pi$
$594$		0			0
$595$	−719390.	−	719390.i	−0.0833051	−	0.0833051i
$596$		0			0
$597$	−1.12973e7	+	1.12973e7i	−1.29730	+	1.29730i
$598$		0			0
$599$		−	4.77277e6i		−	0.543505i	−0.962367	−	0.271752i	$-0.912397\pi$
$599$		−	4.77277e6i		−	0.543505i	0.962367	−	0.271752i	$-0.0876032\pi$
$600$		0			0
$601$			6.29410e6i			0.710800i	0.934714	+	0.355400i	$0.115655\pi$
$601$			6.29410e6i			0.710800i	−0.934714	+	0.355400i	$0.884345\pi$
$602$		0			0
$603$	2.98952e6	−	2.98952e6i	0.334818	−	0.334818i
$604$		0			0
$605$	2.80596e6	+	2.80596e6i	0.311669	+	0.311669i
$606$		0			0
$607$	1.46495e6			0.161380			0.0806901	−	0.996739i	$-0.474288\pi$
$607$	1.46495e6			0.161380			0.0806901	+	0.996739i	$0.474288\pi$
$608$		0			0
$609$	−9.50388e6			−1.03838
$610$		0			0
$611$	656929.	+	656929.i	0.0711895	+	0.0711895i
$612$		0			0
$613$	6.75338e6	−	6.75338e6i	0.725888	−	0.725888i	−0.243910	−	0.969798i	$-0.578430\pi$
$613$	6.75338e6	−	6.75338e6i	0.725888	−	0.725888i	0.969798	+	0.243910i	$0.0784300\pi$
$614$		0			0
$615$		−	556337.i		−	0.0593130i
$616$		0			0
$617$		−	1.41502e7i		−	1.49641i	−0.663468	−	0.748205i	$-0.730916\pi$
$617$		−	1.41502e7i		−	1.49641i	0.663468	−	0.748205i	$-0.269084\pi$
$618$		0			0
$619$	5.04550e6	−	5.04550e6i	0.529271	−	0.529271i	−0.391084	−	0.920355i	$-0.627900\pi$
$619$	5.04550e6	−	5.04550e6i	0.529271	−	0.529271i	0.920355	+	0.391084i	$0.127900\pi$
$620$		0			0
$621$	−1.61854e6	−	1.61854e6i	−0.168420	−	0.168420i
$622$		0			0
$623$	−3.70160e6			−0.382093
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−716431.	−	716431.i	−0.0727789	−	0.0727789i
$628$		0			0
$629$	−4.23100e6	+	4.23100e6i	−0.426399	+	0.426399i
$630$		0			0
$631$			1.77040e7i			1.77010i	0.465495	+	0.885051i	$0.345876\pi$
$631$			1.77040e7i			1.77010i	−0.465495	+	0.885051i	$0.654124\pi$
$632$		0			0
$633$		−	1.31801e7i		−	1.30740i
$634$		0			0
$635$	266800.	−	266800.i	0.0262574	−	0.0262574i
$636$		0			0
$637$	3.61332e6	+	3.61332e6i	0.352824	+	0.352824i
$638$		0			0
$639$	7.62274e6			0.738514
$640$		0			0
$641$	−1.04525e7			−1.00479			−0.502395	−	0.864638i	$-0.667548\pi$
$641$	−1.04525e7			−1.00479			−0.502395	+	0.864638i	$0.667548\pi$
$642$		0			0
$643$	5.43319e6	+	5.43319e6i	0.518236	+	0.518236i	0.917037	−	0.398801i	$-0.130574\pi$
$643$	5.43319e6	+	5.43319e6i	0.518236	+	0.518236i	−0.398801	+	0.917037i	$0.630574\pi$
$644$		0			0
$645$	2.98805e6	−	2.98805e6i	0.282806	−	0.282806i
$646$		0			0
$647$		−	1.39010e7i		−	1.30552i	−0.757563	−	0.652762i	$-0.773610\pi$
$647$		−	1.39010e7i		−	1.30552i	0.757563	−	0.652762i	$-0.226390\pi$
$648$		0			0
$649$			1.53373e6i			0.142935i
$650$		0			0
$651$	−773649.	+	773649.i	−0.0715470	+	0.0715470i
$652$		0			0
$653$	−1.15514e7	−	1.15514e7i	−1.06011	−	1.06011i	−0.998074	−	0.0620336i	$-0.980241\pi$
$653$	−1.15514e7	−	1.15514e7i	−1.06011	−	1.06011i	−0.0620336	−	0.998074i	$-0.519759\pi$
$654$		0			0
$655$	7.97046e6			0.725906
$656$		0			0
$657$	1.59227e7			1.43914
$658$		0			0
$659$	−1.20268e7	−	1.20268e7i	−1.07879	−	1.07879i	−0.996618	−	0.0821756i	$-0.973813\pi$
$659$	−1.20268e7	−	1.20268e7i	−1.07879	−	1.07879i	−0.0821756	−	0.996618i	$-0.526187\pi$
$660$		0			0
$661$	−3.95930e6	+	3.95930e6i	−0.352464	+	0.352464i	−0.861026	−	0.508562i	$-0.830177\pi$
$661$	−3.95930e6	+	3.95930e6i	−0.352464	+	0.352464i	0.508562	+	0.861026i	$0.330177\pi$
$662$		0			0
$663$		−	5.34193e6i		−	0.471970i
$664$		0			0
$665$		−	1.65498e6i		−	0.145123i
$666$		0			0
$667$	−1.36169e7	+	1.36169e7i	−1.18512	+	1.18512i
$668$		0			0
$669$	−8.93770e6	−	8.93770e6i	−0.772077	−	0.772077i
$670$		0			0
$671$	2.43146e6			0.208478
$672$		0			0
$673$	1.00027e7			0.851297			0.425649	−	0.904889i	$-0.360046\pi$
$673$	1.00027e7			0.851297			0.425649	+	0.904889i	$0.360046\pi$
$674$		0			0
$675$	353808.	+	353808.i	0.0298888	+	0.0298888i
$676$		0			0
$677$	−943407.	+	943407.i	−0.0791093	+	0.0791093i	−0.745554	−	0.666445i	$-0.767815\pi$
$677$	−943407.	+	943407.i	−0.0791093	+	0.0791093i	0.666445	+	0.745554i	$0.267815\pi$
$678$		0			0
$679$		−	2.20143e6i		−	0.183244i
$680$		0			0
$681$			1.54479e7i			1.27644i
$682$		0			0
$683$	−1.13632e7	+	1.13632e7i	−0.932069	+	0.932069i	−0.997835	−	0.0657662i	$-0.979051\pi$
$683$	−1.13632e7	+	1.13632e7i	−0.932069	+	0.932069i	0.0657662	+	0.997835i	$0.479051\pi$
$684$		0			0
$685$	3.24196e6	+	3.24196e6i	0.263986	+	0.263986i
$686$		0			0
$687$	−1.23968e7			−1.00212
$688$		0			0
$689$	1.02762e7			0.824678
$690$		0			0
$691$	−2.49054e6	−	2.49054e6i	−0.198426	−	0.198426i	0.600899	−	0.799325i	$-0.294809\pi$
$691$	−2.49054e6	−	2.49054e6i	−0.198426	−	0.198426i	−0.799325	+	0.600899i	$0.794809\pi$
$692$		0			0
$693$	465981.	−	465981.i	0.0368583	−	0.0368583i
$694$		0			0
$695$			8.03151e6i			0.630718i
$696$		0			0
$697$			641791.i			0.0500393i
$698$		0			0
$699$	8.33569e6	−	8.33569e6i	0.645281	−	0.645281i
$700$		0			0
$701$	1.13666e7	+	1.13666e7i	0.873643	+	0.873643i	0.992867	−	0.119224i	$-0.0380408\pi$
$701$	1.13666e7	+	1.13666e7i	0.873643	+	0.873643i	−0.119224	+	0.992867i	$0.538041\pi$
$702$		0			0
$703$	−9.73352e6			−0.742817
$704$		0			0
$705$	−1.18975e6			−0.0901536
$706$		0			0
$707$	4.60633e6	+	4.60633e6i	0.346582	+	0.346582i
$708$		0			0
$709$	−6.22852e6	+	6.22852e6i	−0.465339	+	0.465339i	−0.900401	−	0.435062i	$-0.856727\pi$
$709$	−6.22852e6	+	6.22852e6i	−0.465339	+	0.465339i	0.435062	+	0.900401i	$0.356727\pi$
$710$		0			0
$711$			2.13170e7i			1.58144i
$712$		0			0
$713$			2.21693e6i			0.163315i
$714$		0			0
$715$	352043.	−	352043.i	0.0257532	−	0.0257532i
$716$		0			0
$717$	251985.	+	251985.i	0.0183053	+	0.0183053i
$718$		0			0
$719$	−2.31572e7			−1.67057			−0.835283	−	0.549820i	$-0.814696\pi$
$719$	−2.31572e7			−1.67057			−0.835283	+	0.549820i	$0.814696\pi$
$720$		0			0
$721$	−3.94934e6			−0.282935
$722$		0			0
$723$	−6.22749e6	−	6.22749e6i	−0.443065	−	0.443065i
$724$		0			0
$725$	2.97662e6	−	2.97662e6i	0.210319	−	0.210319i
$726$		0			0
$727$		−	2.19864e7i		−	1.54283i	−0.636331	−	0.771416i	$-0.719549\pi$
$727$		−	2.19864e7i		−	1.54283i	0.636331	−	0.771416i	$-0.280451\pi$
$728$		0			0
$729$			9.58950e6i			0.668309i
$730$		0			0
$731$	−3.44702e6	+	3.44702e6i	−0.238589	+	0.238589i
$732$		0			0
$733$	−7.72418e6	−	7.72418e6i	−0.530998	−	0.530998i	0.389872	−	0.920869i	$-0.372519\pi$
$733$	−7.72418e6	−	7.72418e6i	−0.530998	−	0.530998i	−0.920869	+	0.389872i	$0.872519\pi$
$734$		0			0
$735$	−6.54401e6			−0.446813
$736$		0			0
$737$	−992882.			−0.0673332
$738$		0			0
$739$	7.11778e6	+	7.11778e6i	0.479439	+	0.479439i	0.904952	−	0.425513i	$-0.139906\pi$
$739$	7.11778e6	+	7.11778e6i	0.479439	+	0.479439i	−0.425513	+	0.904952i	$0.639906\pi$
$740$		0			0
$741$	6.14463e6	−	6.14463e6i	0.411102	−	0.411102i
$742$		0			0
$743$		−	1.83694e6i		−	0.122074i	−0.998136	−	0.0610368i	$-0.980559\pi$
$743$		−	1.83694e6i		−	0.122074i	0.998136	−	0.0610368i	$-0.0194407\pi$
$744$		0			0
$745$		−	4.46136e6i		−	0.294494i
$746$		0			0
$747$	−6.24448e6	+	6.24448e6i	−0.409444	+	0.409444i
$748$		0			0
$749$	−8.83618e6	−	8.83618e6i	−0.575520	−	0.575520i
$750$		0			0
$751$	2.46486e6			0.159475			0.0797375	−	0.996816i	$-0.474592\pi$
$751$	2.46486e6			0.159475			0.0797375	+	0.996816i	$0.474592\pi$
$752$		0			0
$753$	3.69779e7			2.37659
$754$		0			0
$755$	7.18868e6	+	7.18868e6i	0.458967	+	0.458967i
$756$		0			0
$757$	737006.	−	737006.i	0.0467446	−	0.0467446i	−0.683348	−	0.730093i	$-0.739477\pi$
$757$	737006.	−	737006.i	0.0467446	−	0.0467446i	0.730093	+	0.683348i	$0.239477\pi$
$758$		0			0
$759$		−	2.91668e6i		−	0.183774i
$760$		0			0
$761$			2.99911e7i			1.87729i	0.344887	+	0.938644i	$0.387917\pi$
$761$			2.99911e7i			1.87729i	−0.344887	+	0.938644i	$0.612083\pi$
$762$		0			0
$763$	−1.00947e7	+	1.00947e7i	−0.627743	+	0.627743i
$764$		0			0
$765$	2.21459e6	+	2.21459e6i	0.136817	+	0.136817i
$766$		0			0
$767$	−1.31544e7			−0.807389
$768$		0			0
$769$	1.88084e7			1.14693			0.573464	−	0.819231i	$-0.305599\pi$
$769$	1.88084e7			1.14693			0.573464	+	0.819231i	$0.305599\pi$
$770$		0			0
$771$	−1.15777e6	−	1.15777e6i	−0.0701435	−	0.0701435i
$772$		0			0
$773$	4.46987e6	−	4.46987e6i	0.269058	−	0.269058i	−0.559662	−	0.828721i	$-0.689069\pi$
$773$	4.46987e6	−	4.46987e6i	0.269058	−	0.269058i	0.828721	+	0.559662i	$0.189069\pi$
$774$		0			0
$775$		−	484614.i		−	0.0289829i
$776$		0			0
$777$		−	1.38286e7i		−	0.821721i
$778$		0			0
$779$	−738229.	+	738229.i	−0.0435860	+	0.0435860i
$780$		0			0
$781$	−1.26584e6	−	1.26584e6i	−0.0742591	−	0.0742591i
$782$		0			0
$783$	−5.39213e6			−0.314308
$784$		0			0
$785$	−1.25539e7			−0.727118
$786$		0			0
$787$	1.97424e7	+	1.97424e7i	1.13622	+	1.13622i	0.989121	+	0.147103i	$0.0469948\pi$
$787$	1.97424e7	+	1.97424e7i	1.13622	+	1.13622i	0.147103	+	0.989121i	$0.453005\pi$
$788$		0			0
$789$	−2.14230e7	+	2.14230e7i	−1.22515	+	1.22515i
$790$		0			0
$791$			1.86188e6i			0.105806i
$792$		0			0
$793$			2.08539e7i			1.17762i
$794$		0			0
$795$	−9.30550e6	+	9.30550e6i	−0.522182	+	0.522182i
$796$		0			0
$797$	−1.72739e7	−	1.72739e7i	−0.963264	−	0.963264i	0.0360843	−	0.999349i	$-0.488512\pi$
$797$	−1.72739e7	−	1.72739e7i	−0.963264	−	0.963264i	−0.999349	+	0.0360843i	$0.988512\pi$
$798$		0			0
$799$	1.37250e6			0.0760580
$800$		0			0
$801$	1.13951e7			0.627533
$802$		0			0
$803$	−2.64413e6	−	2.64413e6i	−0.144708	−	0.144708i
$804$		0			0
$805$	3.36880e6	−	3.36880e6i	0.183225	−	0.183225i
$806$		0			0
$807$		−	3.10577e7i		−	1.67875i
$808$		0			0
$809$			164511.i			0.00883740i	0.999990	+	0.00441870i	$0.00140652\pi$
$809$			164511.i			0.00883740i	−0.999990	+	0.00441870i	$0.998593\pi$
$810$		0			0
$811$	1.53151e7	−	1.53151e7i	0.817650	−	0.817650i	−0.168117	−	0.985767i	$-0.553769\pi$
$811$	1.53151e7	−	1.53151e7i	0.817650	−	0.817650i	0.985767	+	0.168117i	$0.0537686\pi$
$812$		0			0
$813$	−9.79662e6	−	9.79662e6i	−0.519817	−	0.519817i
$814$		0			0
$815$	1.06311e7			0.560643
$816$		0			0
$817$	−7.92995e6			−0.415638
$818$		0			0
$819$	3.99659e6	+	3.99659e6i	0.208200	+	0.208200i
$820$		0			0
$821$	1.42105e7	−	1.42105e7i	0.735786	−	0.735786i	−0.235973	−	0.971760i	$-0.575828\pi$
$821$	1.42105e7	−	1.42105e7i	0.735786	−	0.735786i	0.971760	+	0.235973i	$0.0758277\pi$
$822$		0			0
$823$			1.30021e7i			0.669136i	0.942372	+	0.334568i	$0.108590\pi$
$823$			1.30021e7i			0.669136i	−0.942372	+	0.334568i	$0.891410\pi$
$824$		0			0
$825$			637577.i			0.0326135i
$826$		0			0
$827$	−2.26007e7	+	2.26007e7i	−1.14910	+	1.14910i	−0.162374	+	0.986729i	$0.551915\pi$
$827$	−2.26007e7	+	2.26007e7i	−1.14910	+	1.14910i	−0.986729	+	0.162374i	$0.948085\pi$
$828$		0			0
$829$	−4.23018e6	−	4.23018e6i	−0.213783	−	0.213783i	0.592090	−	0.805872i	$-0.298303\pi$
$829$	−4.23018e6	−	4.23018e6i	−0.213783	−	0.213783i	−0.805872	+	0.592090i	$0.798303\pi$
$830$		0			0
$831$	3.36789e7			1.69182
$832$		0			0
$833$	7.54917e6			0.376953
$834$		0			0
$835$	−218811.	−	218811.i	−0.0108606	−	0.0108606i
$836$		0			0
$837$	−438938.	+	438938.i	−0.0216566	+	0.0216566i
$838$		0			0
$839$		−	1.41204e7i		−	0.692534i	−0.938136	−	0.346267i	$-0.887449\pi$
$839$		−	1.41204e7i		−	0.692534i	0.938136	−	0.346267i	$-0.112551\pi$
$840$		0			0
$841$			2.48533e7i			1.21170i
$842$		0			0
$843$	3.22214e7	−	3.22214e7i	1.56162	−	1.56162i
$844$		0			0
$845$	−3.54422e6	−	3.54422e6i	−0.170757	−	0.170757i
$846$		0			0
$847$	1.05797e7			0.506714
$848$		0			0
$849$	3.22538e7			1.53572
$850$		0			0
$851$	−1.98132e7	−	1.98132e7i	−0.937843	−	0.937843i
$852$		0			0
$853$	−1.45744e7	+	1.45744e7i	−0.685830	+	0.685830i	−0.961308	−	0.275477i	$-0.911164\pi$
$853$	−1.45744e7	+	1.45744e7i	−0.685830	+	0.685830i	0.275477	+	0.961308i	$0.411164\pi$
$854$		0			0
$855$			5.09472e6i			0.238344i
$856$		0			0
$857$			5.14411e6i			0.239253i	0.992819	+	0.119627i	$0.0381698\pi$
$857$			5.14411e6i			0.239253i	−0.992819	+	0.119627i	$0.961830\pi$
$858$		0			0
$859$	1.85655e7	−	1.85655e7i	0.858466	−	0.858466i	−0.132691	−	0.991157i	$-0.542362\pi$
$859$	1.85655e7	−	1.85655e7i	0.858466	−	0.858466i	0.991157	+	0.132691i	$0.0423618\pi$
$860$		0			0
$861$	−1.04881e6	−	1.04881e6i	−0.0482159	−	0.0482159i
$862$		0			0
$863$	3.27994e7			1.49913			0.749564	−	0.661931i	$-0.230263\pi$
$863$	3.27994e7			1.49913			0.749564	+	0.661931i	$0.230263\pi$
$864$		0			0
$865$	−7.33222e6			−0.333192
$866$		0			0
$867$	1.56745e7	+	1.56745e7i	0.708183	+	0.708183i
$868$		0			0
$869$	3.53991e6	−	3.53991e6i	0.159017	−	0.159017i
$870$		0			0
$871$		−	8.51568e6i		−	0.380342i
$872$		0			0
$873$			6.77694e6i			0.300952i
$874$		0			0
$875$	−736411.	+	736411.i	−0.0325162	+	0.0325162i
$876$		0			0
$877$	1.17858e7	+	1.17858e7i	0.517442	+	0.517442i	0.916797	−	0.399355i	$-0.130766\pi$
$877$	1.17858e7	+	1.17858e7i	0.517442	+	0.517442i	−0.399355	+	0.916797i	$0.630766\pi$
$878$		0			0
$879$	−6.03991e6			−0.263669
$880$		0			0
$881$	−1.75082e6			−0.0759981			−0.0379991	−	0.999278i	$-0.512098\pi$
$881$	−1.75082e6			−0.0759981			−0.0379991	+	0.999278i	$0.512098\pi$
$882$		0			0
$883$	3.93751e6	+	3.93751e6i	0.169950	+	0.169950i	0.786957	−	0.617008i	$-0.211655\pi$
$883$	3.93751e6	+	3.93751e6i	0.169950	+	0.169950i	−0.617008	+	0.786957i	$0.711655\pi$
$884$		0			0
$885$	1.19118e7	−	1.19118e7i	0.511235	−	0.511235i
$886$		0			0
$887$		−	3.95570e7i		−	1.68816i	−0.536214	−	0.844082i	$-0.680146\pi$
$887$		−	3.95570e7i		−	1.68816i	0.536214	−	0.844082i	$-0.319854\pi$
$888$		0			0
$889$		−	1.00595e6i		−	0.0426896i
$890$		0			0
$891$	2.27635e6	−	2.27635e6i	0.0960606	−	0.0960606i
$892$		0			0
$893$	1.57873e6	+	1.57873e6i	0.0662492	+	0.0662492i
$894$		0			0
$895$	2.33869e6			0.0975924
$896$		0			0
$897$	2.50155e7			1.03807
$898$		0			0
$899$	3.69282e6	+	3.69282e6i	0.152391	+	0.152391i
$900$		0			0
$901$	1.07348e7	−	1.07348e7i	0.440538	−	0.440538i
$902$		0			0
$903$		−	1.12662e7i		−	0.459789i
$904$		0			0
$905$			3.56165e6i			0.144554i
$906$		0			0
$907$	−2.23900e6	+	2.23900e6i	−0.0903725	+	0.0903725i	−0.750848	−	0.660475i	$-0.770355\pi$
$907$	−2.23900e6	+	2.23900e6i	−0.0903725	+	0.0903725i	0.660475	+	0.750848i	$0.270355\pi$
$908$		0			0
$909$	−1.41802e7	−	1.41802e7i	−0.569212	−	0.569212i
$910$		0			0
$911$	−2.13412e7			−0.851968			−0.425984	−	0.904731i	$-0.640072\pi$
$911$	−2.13412e7			−0.851968			−0.425984	+	0.904731i	$0.640072\pi$
$912$		0			0
$913$	2.07392e6			0.0823408
$914$		0			0
$915$	−1.88840e7	−	1.88840e7i	−0.745662	−	0.745662i
$916$		0			0
$917$	1.50260e7	−	1.50260e7i	0.590093	−	0.590093i
$918$		0			0
$919$			9.55716e6i			0.373285i	0.982428	+	0.186642i	$0.0597605\pi$
$919$			9.55716e6i			0.373285i	−0.982428	+	0.186642i	$0.940239\pi$
$920$		0			0
$921$		−	6.99144e7i		−	2.71593i
$922$		0			0
$923$	1.08567e7	−	1.08567e7i	0.419464	−	0.419464i
$924$		0			0
$925$	4.33110e6	+	4.33110e6i	0.166435	+	0.166435i
$926$		0			0
$927$	1.21577e7			0.464680
$928$		0			0
$929$	3.19905e7			1.21613			0.608067	−	0.793886i	$-0.291945\pi$
$929$	3.19905e7			1.21613			0.608067	+	0.793886i	$0.291945\pi$
$930$		0			0
$931$	8.68354e6	+	8.68354e6i	0.328339	+	0.328339i
$932$		0			0
$933$	−2.25315e7	+	2.25315e7i	−0.847394	+	0.847394i
$934$		0			0
$935$		−	735510.i		−	0.0275144i
$936$		0			0
$937$		−	4.44804e7i		−	1.65508i	−0.561404	−	0.827542i	$-0.689739\pi$
$937$		−	4.44804e7i		−	1.65508i	0.561404	−	0.827542i	$-0.310261\pi$
$938$		0			0
$939$	−1.76113e7	+	1.76113e7i	−0.651821	+	0.651821i
$940$		0			0
$941$	−2.66460e7	−	2.66460e7i	−0.980974	−	0.980974i	0.0188485	−	0.999822i	$-0.494000\pi$
$941$	−2.66460e7	−	2.66460e7i	−0.980974	−	0.980974i	−0.999822	+	0.0188485i	$0.994000\pi$
$942$		0			0
$943$	−3.00542e6			−0.110059
$944$		0			0
$945$	1.33401e6			0.0485935
$946$		0			0
$947$	2.00230e7	+	2.00230e7i	0.725527	+	0.725527i	0.969725	−	0.244198i	$-0.0785248\pi$
$947$	2.00230e7	+	2.00230e7i	0.725527	+	0.725527i	−0.244198	+	0.969725i	$0.578525\pi$
$948$		0			0
$949$	2.26779e7	−	2.26779e7i	0.817407	−	0.817407i
$950$		0			0
$951$		−	2.55018e7i		−	0.914363i
$952$		0			0
$953$		−	3.12385e7i		−	1.11419i	−0.830449	−	0.557094i	$-0.811916\pi$
$953$		−	3.12385e7i		−	1.11419i	0.830449	−	0.557094i	$-0.188084\pi$
$954$		0			0
$955$	−65963.9	+	65963.9i	−0.00234044	+	0.00234044i
$956$		0			0
$957$	−4.85843e6	−	4.85843e6i	−0.171481	−	0.171481i
$958$		0			0
$959$	1.22236e7			0.429192
$960$		0			0
$961$	−2.80279e7			−0.979000
$962$		0			0
$963$	2.72015e7	+	2.72015e7i	0.945209	+	0.945209i
$964$		0			0
$965$	−2.00620e6	+	2.00620e6i	−0.0693515	+	0.0693515i
$966$		0			0
$967$			2.90918e7i			1.00047i	0.865890	+	0.500235i	$0.166753\pi$
$967$			2.90918e7i			1.00047i	−0.865890	+	0.500235i	$0.833247\pi$
$968$		0			0
$969$		−	1.28377e7i		−	0.439217i
$970$		0			0
$971$	9.56962e6	−	9.56962e6i	0.325722	−	0.325722i	−0.525235	−	0.850957i	$-0.676023\pi$
$971$	9.56962e6	−	9.56962e6i	0.325722	−	0.325722i	0.850957	+	0.525235i	$0.176023\pi$
$972$		0			0
$973$	1.51411e7	+	1.51411e7i	0.512714	+	0.512714i
$974$		0			0
$975$	−5.46832e6			−0.184223
$976$		0			0
$977$	3.40916e6			0.114264			0.0571321	−	0.998367i	$-0.481804\pi$
$977$	3.40916e6			0.114264			0.0571321	+	0.998367i	$0.481804\pi$
$978$		0			0
$979$	−1.89227e6	−	1.89227e6i	−0.0630996	−	0.0630996i
$980$		0			0
$981$	3.10757e7	−	3.10757e7i	1.03098	−	1.03098i
$982$		0			0
$983$		−	7.27622e6i		−	0.240172i	−0.992764	−	0.120086i	$-0.961683\pi$
$983$		−	7.27622e6i		−	0.240172i	0.992764	−	0.120086i	$-0.0383170\pi$
$984$		0			0
$985$			1.05979e7i			0.348039i
$986$		0			0
$987$	−2.24293e6	+	2.24293e6i	−0.0732864	+	0.0732864i
$988$		0			0
$989$	−1.61419e7	−	1.61419e7i	−0.524764	−	0.524764i
$990$		0			0
$991$	2.90156e7			0.938529			0.469265	−	0.883058i	$-0.344519\pi$
$991$	2.90156e7			0.938529			0.469265	+	0.883058i	$0.344519\pi$
$992$		0			0
$993$	−1.30321e7			−0.419412
$994$		0			0
$995$	−1.33410e7	−	1.33410e7i	−0.427199	−	0.427199i
$996$		0			0
$997$	−3.34377e7	+	3.34377e7i	−1.06537	+	1.06537i	−0.0676564	+	0.997709i	$0.521552\pi$
$997$	−3.34377e7	+	3.34377e7i	−1.06537	+	1.06537i	−0.997709	+	0.0676564i	$0.978448\pi$
$998$		0			0
$999$		−	7.84578e6i		−	0.248727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.8		80
4.3	odd	2		80.6.l.a.61.30	yes	80
16.5	even	4	inner	320.6.l.a.241.8		80
16.11	odd	4		80.6.l.a.21.30	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.30	✓	80	16.11	odd	4
80.6.l.a.61.30	yes	80	4.3	odd	2
320.6.l.a.81.8		80	1.1	even	1	trivial
320.6.l.a.241.8		80	16.5	even	4	inner

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	320.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-14.9697 - 14.9697i) q^{3} +(17.6777 - 17.6777i) q^{5} -66.6523i q^{7} +205.184i q^{9} +O(q^{10})\)	\(q+(-14.9697 - 14.9697i) q^{3} +(17.6777 - 17.6777i) q^{5} -66.6523i q^{7} +205.184i q^{9} +(34.0729 - 34.0729i) q^{11} +(292.234 + 292.234i) q^{13} -529.259 q^{15} +610.554 q^{17} +(702.298 + 702.298i) q^{19} +(-997.765 + 997.765i) q^{21} +2859.14i q^{23} -625.000i q^{25} +(-566.093 + 566.093i) q^{27} +(4762.59 + 4762.59i) q^{29} +775.382 q^{31} -1020.12 q^{33} +(-1178.26 - 1178.26i) q^{35} +(-6929.77 + 6929.77i) q^{37} -8749.32i q^{39} +1051.16i q^{41} +(-5645.72 + 5645.72i) q^{43} +(3627.18 + 3627.18i) q^{45} +2247.96 q^{47} +12364.5 q^{49} +(-9139.81 - 9139.81i) q^{51} +(17582.1 - 17582.1i) q^{53} -1204.66i q^{55} -21026.4i q^{57} +(-22506.6 + 22506.6i) q^{59} +(35680.2 + 35680.2i) q^{61} +13676.0 q^{63} +10332.0 q^{65} +(-14570.0 - 14570.0i) q^{67} +(42800.5 - 42800.5i) q^{69} -37150.7i q^{71} -77602.0i q^{73} +(-9356.07 + 9356.07i) q^{75} +(-2271.04 - 2271.04i) q^{77} +103892. q^{79} +66808.2 q^{81} +(30433.5 + 30433.5i) q^{83} +(10793.2 - 10793.2i) q^{85} -142589. i q^{87} -55535.9i q^{89} +(19478.1 - 19478.1i) q^{91} +(-11607.2 - 11607.2i) q^{93} +24830.0 q^{95} +33028.6 q^{97} +(6991.23 + 6991.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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