LMFDB - Embedded newform 320.6.l.a.241.2

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			241.2
Character	$\chi$	$=$	320.241
Dual form			320.6.l.a.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.1465 + 21.1465i) q^{3} +(17.6777 + 17.6777i) q^{5} -100.160i q^{7} -651.346i q^{9} +O(q^{10})$	\(q+(-21.1465 + 21.1465i) q^{3} +(17.6777 + 17.6777i) q^{5} -100.160i q^{7} -651.346i q^{9} +(419.591 + 419.591i) q^{11} +(455.822 - 455.822i) q^{13} -747.641 q^{15} -662.910 q^{17} +(-1207.30 + 1207.30i) q^{19} +(2118.04 + 2118.04i) q^{21} +2571.76i q^{23} +625.000i q^{25} +(8635.09 + 8635.09i) q^{27} +(-2023.28 + 2023.28i) q^{29} -3150.05 q^{31} -17745.7 q^{33} +(1770.60 - 1770.60i) q^{35} +(2281.97 + 2281.97i) q^{37} +19278.1i q^{39} +3833.77i q^{41} +(-12989.2 - 12989.2i) q^{43} +(11514.3 - 11514.3i) q^{45} +15693.3 q^{47} +6774.93 q^{49} +(14018.2 - 14018.2i) q^{51} +(14775.3 + 14775.3i) q^{53} +14834.8i q^{55} -51060.5i q^{57} +(-24476.4 - 24476.4i) q^{59} +(-15192.1 + 15192.1i) q^{61} -65239.0 q^{63} +16115.7 q^{65} +(24925.1 - 24925.1i) q^{67} +(-54383.7 - 54383.7i) q^{69} +52032.9i q^{71} -37463.3i q^{73} +(-13216.5 - 13216.5i) q^{75} +(42026.3 - 42026.3i) q^{77} -88799.9 q^{79} -206926. q^{81} +(-61945.4 + 61945.4i) q^{83} +(-11718.7 - 11718.7i) q^{85} -85570.7i q^{87} +1923.83i q^{89} +(-45655.2 - 45655.2i) q^{91} +(66612.5 - 66612.5i) q^{93} -42684.7 q^{95} -57200.4 q^{97} +(273299. - 273299. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

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
$3$	−21.1465	+	21.1465i	−1.35655	+	1.35655i	−0.478410	+	0.878136i	$0.658787\pi$
$3$	−21.1465	+	21.1465i	−1.35655	+	1.35655i	−0.878136	+	0.478410i	$0.841213\pi$
$4$		0			0
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$		0			0
$7$		−	100.160i		−	0.772592i	−0.922375	−	0.386296i	$-0.873754\pi$
$7$		−	100.160i		−	0.772592i	0.922375	−	0.386296i	$-0.126246\pi$
$8$		0			0
$9$		−	651.346i		−	2.68044i
$10$		0			0
$11$	419.591	+	419.591i	1.04555	+	1.04555i	0.998912	+	0.0466369i	$0.0148504\pi$
$11$	419.591	+	419.591i	1.04555	+	1.04555i	0.0466369	+	0.998912i	$0.485150\pi$
$12$		0			0
$13$	455.822	−	455.822i	0.748061	−	0.748061i	−0.226054	−	0.974115i	$-0.572583\pi$
$13$	455.822	−	455.822i	0.748061	−	0.748061i	0.974115	+	0.226054i	$0.0725826\pi$
$14$		0			0
$15$	−747.641			−0.857955
$16$		0			0
$17$	−662.910			−0.556329			−0.278165	−	0.960533i	$-0.589726\pi$
$17$	−662.910			−0.556329			−0.278165	+	0.960533i	$0.589726\pi$
$18$		0			0
$19$	−1207.30	+	1207.30i	−0.767243	+	0.767243i	−0.977620	−	0.210377i	$-0.932531\pi$
$19$	−1207.30	+	1207.30i	−0.767243	+	0.767243i	0.210377	+	0.977620i	$0.432531\pi$
$20$		0			0
$21$	2118.04	+	2118.04i	1.04806	+	1.04806i
$22$		0			0
$23$			2571.76i			1.01370i	0.862033	+	0.506852i	$0.169191\pi$
$23$			2571.76i			1.01370i	−0.862033	+	0.506852i	$0.830809\pi$
$24$		0			0
$25$			625.000i			0.200000i
$26$		0			0
$27$	8635.09	+	8635.09i	2.27959	+	2.27959i
$28$		0			0
$29$	−2023.28	+	2023.28i	−0.446747	+	0.446747i	−0.894272	−	0.447524i	$-0.852306\pi$
$29$	−2023.28	+	2023.28i	−0.446747	+	0.446747i	0.447524	+	0.894272i	$0.352306\pi$
$30$		0			0
$31$	−3150.05			−0.588727			−0.294363	−	0.955694i	$-0.595108\pi$
$31$	−3150.05			−0.588727			−0.294363	+	0.955694i	$0.595108\pi$
$32$		0			0
$33$	−17745.7			−2.83667
$34$		0			0
$35$	1770.60	−	1770.60i	0.244315	−	0.244315i
$36$		0			0
$37$	2281.97	+	2281.97i	0.274034	+	0.274034i	0.830722	−	0.556688i	$-0.187928\pi$
$37$	2281.97	+	2281.97i	0.274034	+	0.274034i	−0.556688	+	0.830722i	$0.687928\pi$
$38$		0			0
$39$			19278.1i			2.02956i
$40$		0			0
$41$			3833.77i			0.356178i	0.984014	+	0.178089i	$0.0569914\pi$
$41$			3833.77i			0.356178i	−0.984014	+	0.178089i	$0.943009\pi$
$42$		0			0
$43$	−12989.2	−	12989.2i	−1.07130	−	1.07130i	−0.997255	−	0.0740429i	$-0.976410\pi$
$43$	−12989.2	−	12989.2i	−1.07130	−	1.07130i	−0.0740429	−	0.997255i	$-0.523590\pi$
$44$		0			0
$45$	11514.3	−	11514.3i	0.847629	−	0.847629i
$46$		0			0
$47$	15693.3			1.03626			0.518132	−	0.855301i	$-0.326628\pi$
$47$	15693.3			1.03626			0.518132	+	0.855301i	$0.326628\pi$
$48$		0			0
$49$	6774.93			0.403102
$50$		0			0
$51$	14018.2	−	14018.2i	0.754687	−	0.754687i
$52$		0			0
$53$	14775.3	+	14775.3i	0.722515	+	0.722515i	0.969117	−	0.246601i	$-0.0793139\pi$
$53$	14775.3	+	14775.3i	0.722515	+	0.722515i	−0.246601	+	0.969117i	$0.579314\pi$
$54$		0			0
$55$			14834.8i			0.661263i
$56$		0			0
$57$		−	51060.5i		−	2.08160i
$58$		0			0
$59$	−24476.4	−	24476.4i	−0.915413	−	0.915413i	0.0812787	−	0.996691i	$-0.474100\pi$
$59$	−24476.4	−	24476.4i	−0.915413	−	0.915413i	−0.996691	+	0.0812787i	$0.974100\pi$
$60$		0			0
$61$	−15192.1	+	15192.1i	−0.522749	+	0.522749i	−0.918401	−	0.395652i	$-0.870519\pi$
$61$	−15192.1	+	15192.1i	−0.522749	+	0.522749i	0.395652	+	0.918401i	$0.370519\pi$
$62$		0			0
$63$	−65239.0			−2.07088
$64$		0			0
$65$	16115.7			0.473115
$66$		0			0
$67$	24925.1	−	24925.1i	0.678343	−	0.678343i	−0.281282	−	0.959625i	$-0.590760\pi$
$67$	24925.1	−	24925.1i	0.678343	−	0.678343i	0.959625	+	0.281282i	$0.0907597\pi$
$68$		0			0
$69$	−54383.7	−	54383.7i	−1.37514	−	1.37514i
$70$		0			0
$71$			52032.9i			1.22499i	0.790475	+	0.612494i	$0.209834\pi$
$71$			52032.9i			1.22499i	−0.790475	+	0.612494i	$0.790166\pi$
$72$		0			0
$73$		−	37463.3i		−	0.822808i	−0.911453	−	0.411404i	$-0.865039\pi$
$73$		−	37463.3i		−	0.822808i	0.911453	−	0.411404i	$-0.134961\pi$
$74$		0			0
$75$	−13216.5	−	13216.5i	−0.271309	−	0.271309i
$76$		0			0
$77$	42026.3	−	42026.3i	0.807783	−	0.807783i
$78$		0			0
$79$	−88799.9			−1.60083			−0.800414	−	0.599448i	$-0.795387\pi$
$79$	−88799.9			−1.60083			−0.800414	+	0.599448i	$0.795387\pi$
$80$		0			0
$81$	−206926.			−3.50431
$82$		0			0
$83$	−61945.4	+	61945.4i	−0.986992	+	0.986992i	−0.999916	−	0.0129242i	$-0.995886\pi$
$83$	−61945.4	+	61945.4i	−0.986992	+	0.986992i	0.0129242	+	0.999916i	$0.495886\pi$
$84$		0			0
$85$	−11718.7	−	11718.7i	−0.175927	−	0.175927i
$86$		0			0
$87$		−	85570.7i		−	1.21207i
$88$		0			0
$89$			1923.83i			0.0257449i	0.999917	+	0.0128725i	$0.00409754\pi$
$89$			1923.83i			0.0257449i	−0.999917	+	0.0128725i	$0.995902\pi$
$90$		0			0
$91$	−45655.2	−	45655.2i	−0.577946	−	0.577946i
$92$		0			0
$93$	66612.5	−	66612.5i	0.798635	−	0.798635i
$94$		0			0
$95$	−42684.7			−0.485247
$96$		0			0
$97$	−57200.4			−0.617263			−0.308631	−	0.951182i	$-0.599871\pi$
$97$	−57200.4			−0.617263			−0.308631	+	0.951182i	$0.599871\pi$
$98$		0			0
$99$	273299.	−	273299.i	2.80253	−	2.80253i
$100$		0			0
$101$	59911.1	+	59911.1i	0.584392	+	0.584392i	0.936107	−	0.351715i	$-0.114402\pi$
$101$	59911.1	+	59911.1i	0.584392	+	0.584392i	−0.351715	+	0.936107i	$0.614402\pi$
$102$		0			0
$103$		−	163644.i		−	1.51987i	−0.650000	−	0.759934i	$-0.725231\pi$
$103$		−	163644.i		−	1.51987i	0.650000	−	0.759934i	$-0.274769\pi$
$104$		0			0
$105$			74883.8i			0.662849i
$106$		0			0
$107$	48203.4	+	48203.4i	0.407022	+	0.407022i	0.880699	−	0.473677i	$-0.157073\pi$
$107$	48203.4	+	48203.4i	0.407022	+	0.407022i	−0.473677	+	0.880699i	$0.657073\pi$
$108$		0			0
$109$	−83668.5	+	83668.5i	−0.674522	+	0.674522i	−0.958755	−	0.284233i	$-0.908261\pi$
$109$	−83668.5	+	83668.5i	−0.674522	+	0.674522i	0.284233	+	0.958755i	$0.408261\pi$
$110$		0			0
$111$	−96511.0			−0.743480
$112$		0			0
$113$	−43813.5			−0.322784			−0.161392	−	0.986890i	$-0.551598\pi$
$113$	−43813.5			−0.322784			−0.161392	+	0.986890i	$0.551598\pi$
$114$		0			0
$115$	−45462.7	+	45462.7i	−0.320561	+	0.320561i
$116$		0			0
$117$	−296898.	−	296898.i	−2.00513	−	2.00513i
$118$		0			0
$119$			66397.2i			0.429816i
$120$		0			0
$121$			191062.i			1.18634i
$122$		0			0
$123$	−81070.7	−	81070.7i	−0.483172	−	0.483172i
$124$		0			0
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−150649.			−0.828816			−0.414408	−	0.910091i	$-0.636011\pi$
$127$	−150649.			−0.828816			−0.414408	+	0.910091i	$0.636011\pi$
$128$		0			0
$129$	549350.			2.90653
$130$		0			0
$131$	−191515.	+	191515.i	−0.975047	+	0.975047i	−0.999696	−	0.0246495i	$-0.992153\pi$
$131$	−191515.	+	191515.i	−0.975047	+	0.975047i	0.0246495	+	0.999696i	$0.492153\pi$
$132$		0			0
$133$	120924.	+	120924.i	0.592766	+	0.592766i
$134$		0			0
$135$			305296.i			1.44174i
$136$		0			0
$137$			127096.i			0.578537i	0.957248	+	0.289268i	$0.0934120\pi$
$137$			127096.i			0.578537i	−0.957248	+	0.289268i	$0.906588\pi$
$138$		0			0
$139$	−8344.58	−	8344.58i	−0.0366326	−	0.0366326i	0.688553	−	0.725186i	$-0.258246\pi$
$139$	−8344.58	−	8344.58i	−0.0366326	−	0.0366326i	−0.725186	+	0.688553i	$0.758246\pi$
$140$		0			0
$141$	−331859.	+	331859.i	−1.40574	+	1.40574i
$142$		0			0
$143$	382518.			1.56427
$144$		0			0
$145$	−71533.9			−0.282548
$146$		0			0
$147$	−143266.	+	143266.i	−0.546826	+	0.546826i
$148$		0			0
$149$	−120025.	−	120025.i	−0.442900	−	0.442900i	0.450085	−	0.892986i	$-0.351394\pi$
$149$	−120025.	−	120025.i	−0.442900	−	0.442900i	−0.892986	+	0.450085i	$0.851394\pi$
$150$		0			0
$151$		−	49519.6i		−	0.176740i	−0.996088	−	0.0883699i	$-0.971834\pi$
$151$		−	49519.6i		−	0.176740i	0.996088	−	0.0883699i	$-0.0281658\pi$
$152$		0			0
$153$			431784.i			1.49121i
$154$		0			0
$155$	−55685.6	−	55685.6i	−0.186172	−	0.186172i
$156$		0			0
$157$	143298.	−	143298.i	0.463971	−	0.463971i	−0.435984	−	0.899955i	$-0.643600\pi$
$157$	143298.	−	143298.i	0.463971	−	0.463971i	0.899955	+	0.435984i	$0.143600\pi$
$158$		0			0
$159$	−624892.			−1.96025
$160$		0			0
$161$	257588.			0.783179
$162$		0			0
$163$	368607.	−	368607.i	1.08666	−	1.08666i	0.0907922	−	0.995870i	$-0.471060\pi$
$163$	368607.	−	368607.i	1.08666	−	1.08666i	0.995870	−	0.0907922i	$-0.0289399\pi$
$164$		0			0
$165$	−313703.	−	313703.i	−0.897034	−	0.897034i
$166$		0			0
$167$		−	373588.i		−	1.03658i	−0.855206	−	0.518288i	$-0.826570\pi$
$167$		−	373588.i		−	1.03658i	0.855206	−	0.518288i	$-0.173430\pi$
$168$		0			0
$169$		−	44254.5i		−	0.119190i
$170$		0			0
$171$	786374.	+	786374.i	2.05655	+	2.05655i
$172$		0			0
$173$	1424.89	−	1424.89i	0.00361964	−	0.00361964i	−0.705295	−	0.708914i	$-0.749185\pi$
$173$	1424.89	−	1424.89i	0.00361964	−	0.00361964i	0.708914	+	0.705295i	$0.249185\pi$
$174$		0			0
$175$	62600.1			0.154518
$176$		0			0
$177$	1.03518e6			2.48360
$178$		0			0
$179$	−171556.	+	171556.i	−0.400196	+	0.400196i	−0.878302	−	0.478106i	$-0.841324\pi$
$179$	−171556.	+	171556.i	−0.400196	+	0.400196i	0.478106	+	0.878302i	$0.341324\pi$
$180$		0			0
$181$	−189955.	−	189955.i	−0.430977	−	0.430977i	0.457984	−	0.888961i	$-0.348572\pi$
$181$	−189955.	−	189955.i	−0.430977	−	0.430977i	−0.888961	+	0.457984i	$0.848572\pi$
$182$		0			0
$183$		−	642518.i		−	1.41827i
$184$		0			0
$185$			80679.7i			0.173314i
$186$		0			0
$187$	−278151.	−	278151.i	−0.581670	−	0.581670i
$188$		0			0
$189$	864892.	−	864892.i	1.76119	−	1.76119i
$190$		0			0
$191$	−701235.			−1.39085			−0.695425	−	0.718599i	$-0.744784\pi$
$191$	−701235.			−1.39085			−0.695425	+	0.718599i	$0.744784\pi$
$192$		0			0
$193$	−780783.			−1.50882			−0.754409	−	0.656405i	$-0.772076\pi$
$193$	−780783.			−1.50882			−0.754409	+	0.656405i	$0.772076\pi$
$194$		0			0
$195$	−340791.	+	340791.i	−0.641803	+	0.641803i
$196$		0			0
$197$	−270606.	−	270606.i	−0.496788	−	0.496788i	0.413649	−	0.910437i	$-0.364254\pi$
$197$	−270606.	−	270606.i	−0.496788	−	0.496788i	−0.910437	+	0.413649i	$0.864254\pi$
$198$		0			0
$199$			124497.i			0.222856i	0.993772	+	0.111428i	$0.0355425\pi$
$199$			124497.i			0.222856i	−0.993772	+	0.111428i	$0.964458\pi$
$200$		0			0
$201$			1.05415e6i			1.84041i
$202$		0			0
$203$	202653.	+	202653.i	0.345153	+	0.345153i
$204$		0			0
$205$	−67772.2	+	67772.2i	−0.112633	+	0.112633i
$206$		0			0
$207$	1.67511e6			2.71717
$208$		0			0
$209$	−1.01315e6			−1.60438
$210$		0			0
$211$	−74262.7	+	74262.7i	−0.114832	+	0.114832i	−0.762188	−	0.647356i	$-0.775875\pi$
$211$	−74262.7	+	74262.7i	−0.114832	+	0.114832i	0.647356	+	0.762188i	$0.275875\pi$
$212$		0			0
$213$	−1.10031e6	−	1.10031e6i	−1.66175	−	1.66175i
$214$		0			0
$215$		−	459237.i		−	0.677548i
$216$		0			0
$217$			315510.i			0.454846i
$218$		0			0
$219$	792216.	+	792216.i	1.11618	+	1.11618i
$220$		0			0
$221$	−302169.	+	302169.i	−0.416168	+	0.416168i
$222$		0			0
$223$	−873769.			−1.17662			−0.588308	−	0.808637i	$-0.700206\pi$
$223$	−873769.			−1.17662			−0.588308	+	0.808637i	$0.700206\pi$
$224$		0			0
$225$	407092.			0.536088
$226$		0			0
$227$	804882.	−	804882.i	1.03673	−	1.03673i	0.0374350	−	0.999299i	$-0.488081\pi$
$227$	804882.	−	804882.i	1.03673	−	1.03673i	0.999299	−	0.0374350i	$-0.0119187\pi$
$228$		0			0
$229$	640029.	+	640029.i	0.806512	+	0.806512i	0.984104	−	0.177592i	$-0.0568308\pi$
$229$	640029.	+	640029.i	0.806512	+	0.806512i	−0.177592	+	0.984104i	$0.556831\pi$
$230$		0			0
$231$			1.77742e6i			2.19159i
$232$		0			0
$233$		−	442511.i		−	0.533991i	−0.963698	−	0.266996i	$-0.913969\pi$
$233$		−	442511.i		−	0.533991i	0.963698	−	0.266996i	$-0.0860309\pi$
$234$		0			0
$235$	277422.	+	277422.i	0.327696	+	0.327696i
$236$		0			0
$237$	1.87780e6	−	1.87780e6i	2.17160	−	2.17160i
$238$		0			0
$239$	−779631.			−0.882865			−0.441432	−	0.897294i	$-0.645530\pi$
$239$	−779631.			−0.882865			−0.441432	+	0.897294i	$0.645530\pi$
$240$		0			0
$241$	1.17545e6			1.30365			0.651827	−	0.758368i	$-0.274003\pi$
$241$	1.17545e6			1.30365			0.651827	+	0.758368i	$0.274003\pi$
$242$		0			0
$243$	2.27743e6	−	2.27743e6i	2.47417	−	2.47417i
$244$		0			0
$245$	119765.	+	119765.i	0.127472	+	0.127472i
$246$		0			0
$247$			1.10063e6i			1.14789i
$248$		0			0
$249$		−	2.61985e6i		−	2.67780i
$250$		0			0
$251$	−838767.	−	838767.i	−0.840344	−	0.840344i	0.148559	−	0.988903i	$-0.452536\pi$
$251$	−838767.	−	838767.i	−0.840344	−	0.840344i	−0.988903	+	0.148559i	$0.952536\pi$
$252$		0			0
$253$	−1.07909e6	+	1.07909e6i	−1.05988	+	1.05988i
$254$		0			0
$255$	495618.			0.477306
$256$		0			0
$257$	26562.8			0.0250865			0.0125433	−	0.999921i	$-0.496007\pi$
$257$	26562.8			0.0250865			0.0125433	+	0.999921i	$0.496007\pi$
$258$		0			0
$259$	228562.	−	228562.i	0.211717	−	0.211717i
$260$		0			0
$261$	1.31786e6	+	1.31786e6i	1.19748	+	1.19748i
$262$		0			0
$263$			2.16147e6i			1.92690i	0.267885	+	0.963451i	$0.413675\pi$
$263$			2.16147e6i			1.92690i	−0.267885	+	0.963451i	$0.586325\pi$
$264$		0			0
$265$			522386.i			0.456959i
$266$		0			0
$267$	−40682.2	−	40682.2i	−0.0349242	−	0.0349242i
$268$		0			0
$269$	−553966.	+	553966.i	−0.466770	+	0.466770i	−0.900866	−	0.434097i	$-0.857068\pi$
$269$	−553966.	+	553966.i	−0.466770	+	0.466770i	0.434097	+	0.900866i	$0.357068\pi$
$270$		0			0
$271$	−1.04497e6			−0.864333			−0.432166	−	0.901794i	$-0.642251\pi$
$271$	−1.04497e6			−0.864333			−0.432166	+	0.901794i	$0.642251\pi$
$272$		0			0
$273$	1.93089e6			1.56802
$274$		0			0
$275$	−262244.	+	262244.i	−0.209110	+	0.209110i
$276$		0			0
$277$	−758735.	−	758735.i	−0.594143	−	0.594143i	0.344605	−	0.938748i	$-0.388013\pi$
$277$	−758735.	−	758735.i	−0.594143	−	0.594143i	−0.938748	+	0.344605i	$0.888013\pi$
$278$		0			0
$279$			2.05178e6i			1.57805i
$280$		0			0
$281$			209903.i			0.158582i	0.996852	+	0.0792908i	$0.0252656\pi$
$281$			209903.i			0.158582i	−0.996852	+	0.0792908i	$0.974734\pi$
$282$		0			0
$283$	355669.	+	355669.i	0.263986	+	0.263986i	0.826671	−	0.562685i	$-0.190232\pi$
$283$	355669.	+	355669.i	0.263986	+	0.263986i	−0.562685	+	0.826671i	$0.690232\pi$
$284$		0			0
$285$	902630.	−	902630.i	0.658260	−	0.658260i
$286$		0			0
$287$	383991.			0.275180
$288$		0			0
$289$	−980408.			−0.690498
$290$		0			0
$291$	1.20959e6	−	1.20959e6i	0.837346	−	0.837346i
$292$		0			0
$293$	1.42689e6	+	1.42689e6i	0.971006	+	0.971006i	0.999591	−	0.0285852i	$-0.00910018\pi$
$293$	1.42689e6	+	1.42689e6i	0.971006	+	0.971006i	−0.0285852	+	0.999591i	$0.509100\pi$
$294$		0			0
$295$		−	865370.i		−	0.578958i
$296$		0			0
$297$			7.24641e6i			4.76685i
$298$		0			0
$299$	1.17227e6	+	1.17227e6i	0.758312	+	0.758312i
$300$		0			0
$301$	−1.30100e6	+	1.30100e6i	−0.827676	+	0.827676i
$302$		0			0
$303$	−2.53382e6			−1.58551
$304$		0			0
$305$	−537121.			−0.330615
$306$		0			0
$307$	−1.70499e6	+	1.70499e6i	−1.03247	+	1.03247i	−0.0330100	+	0.999455i	$0.510509\pi$
$307$	−1.70499e6	+	1.70499e6i	−1.03247	+	1.03247i	−0.999455	+	0.0330100i	$0.989491\pi$
$308$		0			0
$309$	3.46048e6	+	3.46048e6i	2.06177	+	2.06177i
$310$		0			0
$311$		−	101227.i		−	0.0593465i	−0.999560	−	0.0296732i	$-0.990553\pi$
$311$		−	101227.i		−	0.0593465i	0.999560	−	0.0296732i	$-0.00944667\pi$
$312$		0			0
$313$		−	98807.4i		−	0.0570071i	−0.999594	−	0.0285035i	$-0.990926\pi$
$313$		−	98807.4i		−	0.0570071i	0.999594	−	0.0285035i	$-0.00907419\pi$
$314$		0			0
$315$	−1.15327e6	−	1.15327e6i	−0.654871	−	0.654871i
$316$		0			0
$317$	−1.62863e6	+	1.62863e6i	−0.910279	+	0.910279i	−0.996294	−	0.0860149i	$-0.972587\pi$
$317$	−1.62863e6	+	1.62863e6i	−0.910279	+	0.910279i	0.0860149	+	0.996294i	$0.472587\pi$
$318$		0			0
$319$	−1.69790e6			−0.934192
$320$		0			0
$321$	−2.03866e6			−1.10429
$322$		0			0
$323$	800334.	−	800334.i	0.426840	−	0.426840i
$324$		0			0
$325$	284889.	+	284889.i	0.149612	+	0.149612i
$326$		0			0
$327$		−	3.53859e6i		−	1.83004i
$328$		0			0
$329$		−	1.57185e6i		−	0.800610i
$330$		0			0
$331$	1.03620e6	+	1.03620e6i	0.519843	+	0.519843i	0.917524	−	0.397681i	$-0.130185\pi$
$331$	1.03620e6	+	1.03620e6i	0.519843	+	0.519843i	−0.397681	+	0.917524i	$0.630185\pi$
$332$		0			0
$333$	1.48635e6	−	1.48635e6i	0.734532	−	0.734532i
$334$		0			0
$335$	881234.			0.429022
$336$		0			0
$337$	−1.54942e6			−0.743179			−0.371590	−	0.928397i	$-0.621187\pi$
$337$	−1.54942e6			−0.743179			−0.371590	+	0.928397i	$0.621187\pi$
$338$		0			0
$339$	926500.	−	926500.i	0.437871	−	0.437871i
$340$		0			0
$341$	−1.32173e6	−	1.32173e6i	−0.615543	−	0.615543i
$342$		0			0
$343$		−	2.36197e6i		−	1.08403i
$344$		0			0
$345$		−	1.92275e6i		−	0.869712i
$346$		0			0
$347$	−620879.	−	620879.i	−0.276811	−	0.276811i	0.555024	−	0.831835i	$-0.312709\pi$
$347$	−620879.	−	620879.i	−0.276811	−	0.276811i	−0.831835	+	0.555024i	$0.812709\pi$
$348$		0			0
$349$	2.10966e6	−	2.10966e6i	0.927146	−	0.927146i	−0.0703743	−	0.997521i	$-0.522419\pi$
$349$	2.10966e6	−	2.10966e6i	0.927146	−	0.927146i	0.997521	+	0.0703743i	$0.0224194\pi$
$350$		0			0
$351$	7.87212e6			3.41055
$352$		0			0
$353$	−2.90680e6			−1.24159			−0.620795	−	0.783973i	$-0.713190\pi$
$353$	−2.90680e6			−1.24159			−0.620795	+	0.783973i	$0.713190\pi$
$354$		0			0
$355$	−919820.	+	919820.i	−0.387376	+	0.387376i
$356$		0			0
$357$	−1.40407e6	−	1.40407e6i	−0.583065	−	0.583065i
$358$		0			0
$359$			322431.i			0.132038i	0.997818	+	0.0660192i	$0.0210299\pi$
$359$			322431.i			0.132038i	−0.997818	+	0.0660192i	$0.978970\pi$
$360$		0			0
$361$		−	439070.i		−	0.177323i
$362$		0			0
$363$	−4.04029e6	−	4.04029e6i	−1.60933	−	1.60933i
$364$		0			0
$365$	662263.	−	662263.i	0.260195	−	0.260195i
$366$		0			0
$367$	540469.			0.209462			0.104731	−	0.994501i	$-0.466602\pi$
$367$	540469.			0.209462			0.104731	+	0.994501i	$0.466602\pi$
$368$		0			0
$369$	2.49711e6			0.954712
$370$		0			0
$371$	1.47990e6	−	1.47990e6i	0.558210	−	0.558210i
$372$		0			0
$373$	−1.77590e6	−	1.77590e6i	−0.660914	−	0.660914i	0.294681	−	0.955596i	$-0.404787\pi$
$373$	−1.77590e6	−	1.77590e6i	−0.660914	−	0.660914i	−0.955596	+	0.294681i	$0.904787\pi$
$374$		0			0
$375$		−	467275.i		−	0.171591i
$376$		0			0
$377$			1.84452e6i			0.668388i
$378$		0			0
$379$	2.43945e6	+	2.43945e6i	0.872357	+	0.872357i	0.992729	−	0.120371i	$-0.0384086\pi$
$379$	2.43945e6	+	2.43945e6i	0.872357	+	0.872357i	−0.120371	+	0.992729i	$0.538409\pi$
$380$		0			0
$381$	3.18570e6	−	3.18570e6i	1.12433	−	1.12433i
$382$		0			0
$383$	−1.05785e6			−0.368490			−0.184245	−	0.982880i	$-0.558984\pi$
$383$	−1.05785e6			−0.368490			−0.184245	+	0.982880i	$0.558984\pi$
$384$		0			0
$385$	1.48585e6			0.510887
$386$		0			0
$387$	−8.46045e6	+	8.46045e6i	−2.87155	+	2.87155i
$388$		0			0
$389$	−2.38220e6	−	2.38220e6i	−0.798186	−	0.798186i	0.184624	−	0.982809i	$-0.440893\pi$
$389$	−2.38220e6	−	2.38220e6i	−0.798186	−	0.798186i	−0.982809	+	0.184624i	$0.940893\pi$
$390$		0			0
$391$		−	1.70484e6i		−	0.563953i
$392$		0			0
$393$		−	8.09975e6i		−	2.64539i
$394$		0			0
$395$	−1.56977e6	−	1.56977e6i	−0.506226	−	0.506226i
$396$		0			0
$397$	−4.13447e6	+	4.13447e6i	−1.31657	+	1.31657i	−0.400096	+	0.916473i	$0.631023\pi$
$397$	−4.13447e6	+	4.13447e6i	−1.31657	+	1.31657i	−0.916473	+	0.400096i	$0.868977\pi$
$398$		0			0
$399$	−5.11423e6			−1.60823
$400$		0			0
$401$	456569.			0.141790			0.0708951	−	0.997484i	$-0.477414\pi$
$401$	456569.			0.141790			0.0708951	+	0.997484i	$0.477414\pi$
$402$		0			0
$403$	−1.43586e6	+	1.43586e6i	−0.440403	+	0.440403i
$404$		0			0
$405$	−3.65797e6	−	3.65797e6i	−1.10816	−	1.10816i
$406$		0			0
$407$			1.91498e6i			0.573032i
$408$		0			0
$409$		−	4.96200e6i		−	1.46673i	−0.679838	−	0.733363i	$-0.737950\pi$
$409$		−	4.96200e6i		−	1.46673i	0.679838	−	0.733363i	$-0.262050\pi$
$410$		0			0
$411$	−2.68763e6	−	2.68763e6i	−0.784812	−	0.784812i
$412$		0			0
$413$	−2.45156e6	+	2.45156e6i	−0.707240	+	0.707240i
$414$		0			0
$415$	−2.19010e6			−0.624229
$416$		0			0
$417$	352917.			0.0993876
$418$		0			0
$419$	−119480.	+	119480.i	−0.0332476	+	0.0332476i	−0.723535	−	0.690288i	$-0.757484\pi$
$419$	−119480.	+	119480.i	−0.0332476	+	0.0332476i	0.690288	+	0.723535i	$0.257484\pi$
$420$		0			0
$421$	2.01225e6	+	2.01225e6i	0.553321	+	0.553321i	0.927398	−	0.374077i	$-0.122040\pi$
$421$	2.01225e6	+	2.01225e6i	0.553321	+	0.553321i	−0.374077	+	0.927398i	$0.622040\pi$
$422$		0			0
$423$		−	1.02218e7i		−	2.77764i
$424$		0			0
$425$		−	414319.i		−	0.111266i
$426$		0			0
$427$	1.52164e6	+	1.52164e6i	0.403871	+	0.403871i
$428$		0			0
$429$	−8.08890e6	+	8.08890e6i	−2.12200	+	2.12200i
$430$		0			0
$431$	2.42671e6			0.629253			0.314626	−	0.949216i	$-0.398121\pi$
$431$	2.42671e6			0.629253			0.314626	+	0.949216i	$0.398121\pi$
$432$		0			0
$433$	2.83723e6			0.727234			0.363617	−	0.931548i	$-0.381542\pi$
$433$	2.83723e6			0.727234			0.363617	+	0.931548i	$0.381542\pi$
$434$		0			0
$435$	1.51269e6	−	1.51269e6i	0.383289	−	0.383289i
$436$		0			0
$437$	−3.10490e6	−	3.10490e6i	−0.777757	−	0.777757i
$438$		0			0
$439$			2.45058e6i			0.606886i	0.952850	+	0.303443i	$0.0981361\pi$
$439$			2.45058e6i			0.606886i	−0.952850	+	0.303443i	$0.901864\pi$
$440$		0			0
$441$		−	4.41283e6i		−	1.08049i
$442$		0			0
$443$	3.37357e6	+	3.37357e6i	0.816734	+	0.816734i	0.985633	−	0.168899i	$-0.0540212\pi$
$443$	3.37357e6	+	3.37357e6i	0.816734	+	0.816734i	−0.168899	+	0.985633i	$0.554021\pi$
$444$		0			0
$445$	−34008.8	+	34008.8i	−0.00814125	+	0.00814125i
$446$		0			0
$447$	5.07621e6			1.20163
$448$		0			0
$449$	−4.06254e6			−0.951002			−0.475501	−	0.879715i	$-0.657733\pi$
$449$	−4.06254e6			−0.951002			−0.475501	+	0.879715i	$0.657733\pi$
$450$		0			0
$451$	−1.60862e6	+	1.60862e6i	−0.372401	+	0.372401i
$452$		0			0
$453$	1.04716e6	+	1.04716e6i	0.239756	+	0.239756i
$454$		0			0
$455$		−	1.61416e6i		−	0.365525i
$456$		0			0
$457$			5.58191e6i			1.25024i	0.780530	+	0.625119i	$0.214949\pi$
$457$			5.58191e6i			1.25024i	−0.780530	+	0.625119i	$0.785051\pi$
$458$		0			0
$459$	−5.72428e6	−	5.72428e6i	−1.26820	−	1.26820i
$460$		0			0
$461$	−1.91750e6	+	1.91750e6i	−0.420227	+	0.420227i	−0.885282	−	0.465055i	$-0.846034\pi$
$461$	−1.91750e6	+	1.91750e6i	−0.420227	+	0.420227i	0.465055	+	0.885282i	$0.346034\pi$
$462$		0			0
$463$	−847727.			−0.183782			−0.0918911	−	0.995769i	$-0.529291\pi$
$463$	−847727.			−0.183782			−0.0918911	+	0.995769i	$0.529291\pi$
$464$		0			0
$465$	2.35511e6			0.505101
$466$		0			0
$467$	971517.	−	971517.i	0.206138	−	0.206138i	−0.596486	−	0.802624i	$-0.703437\pi$
$467$	971517.	−	971517.i	0.206138	−	0.206138i	0.802624	+	0.596486i	$0.203437\pi$
$468$		0			0
$469$	−2.49650e6	−	2.49650e6i	−0.524082	−	0.524082i
$470$		0			0
$471$			6.06049e6i			1.25880i
$472$		0			0
$473$		−	1.09003e7i		−	2.24019i
$474$		0			0
$475$	−754565.	−	754565.i	−0.153449	−	0.153449i
$476$		0			0
$477$	9.62385e6	−	9.62385e6i	1.93666	−	1.93666i
$478$		0			0
$479$	2.09178e6			0.416559			0.208280	−	0.978069i	$-0.433214\pi$
$479$	2.09178e6			0.416559			0.208280	+	0.978069i	$0.433214\pi$
$480$		0			0
$481$	2.08034e6			0.409989
$482$		0			0
$483$	−5.44708e6	+	5.44708e6i	−1.06242	+	1.06242i
$484$		0			0
$485$	−1.01117e6	−	1.01117e6i	−0.195196	−	0.195196i
$486$		0			0
$487$		−	1.79078e6i		−	0.342153i	−0.985258	−	0.171076i	$-0.945276\pi$
$487$		−	1.79078e6i		−	0.342153i	0.985258	−	0.171076i	$-0.0547245\pi$
$488$		0			0
$489$			1.55895e7i			2.94822i
$490$		0			0
$491$	584391.	+	584391.i	0.109396	+	0.109396i	0.759686	−	0.650290i	$-0.225353\pi$
$491$	584391.	+	584391.i	0.109396	+	0.109396i	−0.650290	+	0.759686i	$0.725353\pi$
$492$		0			0
$493$	1.34126e6	−	1.34126e6i	0.248539	−	0.248539i
$494$		0			0
$495$	9.66258e6			1.77247
$496$		0			0
$497$	5.21163e6			0.946417
$498$		0			0
$499$	−541829.	+	541829.i	−0.0974116	+	0.0974116i	−0.754133	−	0.656722i	$-0.771943\pi$
$499$	−541829.	+	541829.i	−0.0974116	+	0.0974116i	0.656722	+	0.754133i	$0.271943\pi$
$500$		0			0
$501$	7.90006e6	+	7.90006e6i	1.40616	+	1.40616i
$502$		0			0
$503$		−	3.68224e6i		−	0.648922i	−0.945899	−	0.324461i	$-0.894817\pi$
$503$		−	3.68224e6i		−	0.648922i	0.945899	−	0.324461i	$-0.105183\pi$
$504$		0			0
$505$			2.11818e6i			0.369602i
$506$		0			0
$507$	935826.	+	935826.i	0.161687	+	0.161687i
$508$		0			0
$509$	−3.31091e6	+	3.31091e6i	−0.566438	+	0.566438i	−0.931129	−	0.364690i	$-0.881175\pi$
$509$	−3.31091e6	+	3.31091e6i	−0.566438	+	0.566438i	0.364690	+	0.931129i	$0.381175\pi$
$510$		0			0
$511$	−3.75233e6			−0.635695
$512$		0			0
$513$	−2.08504e7			−3.49800
$514$		0			0
$515$	2.89284e6	−	2.89284e6i	0.480624	−	0.480624i
$516$		0			0
$517$	6.58478e6	+	6.58478e6i	1.08347	+	1.08347i
$518$		0			0
$519$			60262.8i			0.00982043i
$520$		0			0
$521$		−	6.70813e6i		−	1.08270i	−0.840798	−	0.541348i	$-0.817914\pi$
$521$		−	6.70813e6i		−	1.08270i	0.840798	−	0.541348i	$-0.182086\pi$
$522$		0			0
$523$	46922.8	+	46922.8i	0.00750118	+	0.00750118i	0.710847	−	0.703346i	$-0.248312\pi$
$523$	46922.8	+	46922.8i	0.00750118	+	0.00750118i	−0.703346	+	0.710847i	$0.748312\pi$
$524$		0			0
$525$	−1.32377e6	+	1.32377e6i	−0.209611	+	0.209611i
$526$		0			0
$527$	2.08820e6			0.327526
$528$		0			0
$529$	−177608.			−0.0275945
$530$		0			0
$531$	−1.59426e7	+	1.59426e7i	−2.45371	+	2.45371i
$532$		0			0
$533$	1.74752e6	+	1.74752e6i	0.266443	+	0.266443i
$534$		0			0
$535$			1.70425e6i			0.257424i
$536$		0			0
$537$		−	7.25561e6i		−	1.08577i
$538$		0			0
$539$	2.84270e6	+	2.84270e6i	0.421463	+	0.421463i
$540$		0			0
$541$	−4.04930e6	+	4.04930e6i	−0.594822	+	0.594822i	−0.938930	−	0.344108i	$-0.888181\pi$
$541$	−4.04930e6	+	4.04930e6i	−0.594822	+	0.594822i	0.344108	+	0.938930i	$0.388181\pi$
$542$		0			0
$543$	8.03375e6			1.16928
$544$		0			0
$545$	−2.95813e6			−0.426605
$546$		0			0
$547$	−5.29104e6	+	5.29104e6i	−0.756089	+	0.756089i	−0.975608	−	0.219519i	$-0.929551\pi$
$547$	−5.29104e6	+	5.29104e6i	−0.756089	+	0.756089i	0.219519	+	0.975608i	$0.429551\pi$
$548$		0			0
$549$	9.89531e6	+	9.89531e6i	1.40120	+	1.40120i
$550$		0			0
$551$		−	4.88544e6i		−	0.685528i
$552$		0			0
$553$			8.89422e6i			1.23679i
$554$		0			0
$555$	−1.70609e6	−	1.70609e6i	−0.235109	−	0.235109i
$556$		0			0
$557$	−2.03827e6	+	2.03827e6i	−0.278371	+	0.278371i	−0.832458	−	0.554087i	$-0.813067\pi$
$557$	−2.03827e6	+	2.03827e6i	−0.278371	+	0.278371i	0.554087	+	0.832458i	$0.313067\pi$
$558$		0			0
$559$	−1.18415e7			−1.60279
$560$		0			0
$561$	1.17638e7			1.57812
$562$		0			0
$563$	6.46130e6	−	6.46130e6i	0.859111	−	0.859111i	−0.132123	−	0.991233i	$-0.542179\pi$
$563$	6.46130e6	−	6.46130e6i	0.859111	−	0.859111i	0.991233	+	0.132123i	$0.0421793\pi$
$564$		0			0
$565$	−774520.	−	774520.i	−0.102073	−	0.102073i
$566$		0			0
$567$			2.07258e7i			2.70740i
$568$		0			0
$569$			3.86309e6i			0.500212i	0.968218	+	0.250106i	$0.0804655\pi$
$569$			3.86309e6i			0.500212i	−0.968218	+	0.250106i	$0.919535\pi$
$570$		0			0
$571$	3.01051e6	+	3.01051e6i	0.386411	+	0.386411i	0.873405	−	0.486994i	$-0.161907\pi$
$571$	3.01051e6	+	3.01051e6i	0.386411	+	0.386411i	−0.486994	+	0.873405i	$0.661907\pi$
$572$		0			0
$573$	1.48286e7	−	1.48286e7i	1.88675	−	1.88675i
$574$		0			0
$575$	−1.60735e6			−0.202741
$576$		0			0
$577$	−6.06843e6			−0.758816			−0.379408	−	0.925229i	$-0.623872\pi$
$577$	−6.06843e6			−0.758816			−0.379408	+	0.925229i	$0.623872\pi$
$578$		0			0
$579$	1.65108e7	−	1.65108e7i	2.04678	−	2.04678i
$580$		0			0
$581$	6.20446e6	+	6.20446e6i	0.762542	+	0.762542i
$582$		0			0
$583$			1.23992e7i			1.51085i
$584$		0			0
$585$		−	1.04969e7i		−	1.26816i
$586$		0			0
$587$	8.94817e6	+	8.94817e6i	1.07186	+	1.07186i	0.997210	+	0.0746522i	$0.0237847\pi$
$587$	8.94817e6	+	8.94817e6i	1.07186	+	1.07186i	0.0746522	+	0.997210i	$0.476215\pi$
$588$		0			0
$589$	3.80307e6	−	3.80307e6i	0.451696	−	0.451696i
$590$		0			0
$591$	1.14447e7			1.34783
$592$		0			0
$593$	6.63893e6			0.775285			0.387643	−	0.921810i	$-0.373289\pi$
$593$	6.63893e6			0.775285			0.387643	+	0.921810i	$0.373289\pi$
$594$		0			0
$595$	−1.17375e6	+	1.17375e6i	−0.135920	+	0.135920i
$596$		0			0
$597$	−2.63266e6	−	2.63266e6i	−0.302315	−	0.302315i
$598$		0			0
$599$		−	1.55670e7i		−	1.77271i	−0.463003	−	0.886357i	$-0.653228\pi$
$599$		−	1.55670e7i		−	1.77271i	0.463003	−	0.886357i	$-0.346772\pi$
$600$		0			0
$601$		−	7.58219e6i		−	0.856265i	−0.903716	−	0.428133i	$-0.859172\pi$
$601$		−	7.58219e6i		−	0.856265i	0.903716	−	0.428133i	$-0.140828\pi$
$602$		0			0
$603$	−1.62349e7	−	1.62349e7i	−1.81826	−	1.81826i
$604$		0			0
$605$	−3.37753e6	+	3.37753e6i	−0.375155	+	0.375155i
$606$		0			0
$607$	−1.10026e7			−1.21206			−0.606030	−	0.795442i	$-0.707239\pi$
$607$	−1.10026e7			−1.21206			−0.606030	+	0.795442i	$0.707239\pi$
$608$		0			0
$609$	−8.57078e6			−0.936433
$610$		0			0
$611$	7.15337e6	−	7.15337e6i	0.775189	−	0.775189i
$612$		0			0
$613$	−1.92065e6	−	1.92065e6i	−0.206441	−	0.206441i	0.596312	−	0.802753i	$-0.296632\pi$
$613$	−1.92065e6	−	1.92065e6i	−0.206441	−	0.206441i	−0.802753	+	0.596312i	$0.796632\pi$
$614$		0			0
$615$		−	2.86628e6i		−	0.305585i
$616$		0			0
$617$		−	666574.i		−	0.0704913i	−0.999379	−	0.0352456i	$-0.988779\pi$
$617$		−	666574.i		−	0.0704913i	0.999379	−	0.0352456i	$-0.0112214\pi$
$618$		0			0
$619$	−776525.	−	776525.i	−0.0814571	−	0.0814571i	0.665204	−	0.746661i	$-0.268344\pi$
$619$	−776525.	−	776525.i	−0.0814571	−	0.0814571i	−0.746661	+	0.665204i	$0.768344\pi$
$620$		0			0
$621$	−2.22074e7	+	2.22074e7i	−2.31083	+	2.31083i
$622$		0			0
$623$	192691.			0.0198903
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	2.14245e7	−	2.14245e7i	2.17642	−	2.17642i
$628$		0			0
$629$	−1.51274e6	−	1.51274e6i	−0.152453	−	0.152453i
$630$		0			0
$631$			8.87851e6i			0.887700i	0.896101	+	0.443850i	$0.146388\pi$
$631$			8.87851e6i			0.887700i	−0.896101	+	0.443850i	$0.853612\pi$
$632$		0			0
$633$		−	3.14079e6i		−	0.311551i
$634$		0			0
$635$	−2.66313e6	−	2.66313e6i	−0.262095	−	0.262095i
$636$		0			0
$637$	3.08816e6	−	3.08816e6i	0.301545	−	0.301545i
$638$		0			0
$639$	3.38914e7			3.28351
$640$		0			0
$641$	9.05119e6			0.870083			0.435041	−	0.900411i	$-0.356734\pi$
$641$	9.05119e6			0.870083			0.435041	+	0.900411i	$0.356734\pi$
$642$		0			0
$643$	1.05074e7	−	1.05074e7i	1.00224	−	1.00224i	0.00223776	−	0.999997i	$-0.499288\pi$
$643$	1.05074e7	−	1.05074e7i	1.00224	−	1.00224i	0.999997	−	0.00223776i	$-0.000712300\pi$
$644$		0			0
$645$	9.71123e6	+	9.71123e6i	0.919126	+	0.919126i
$646$		0			0
$647$		−	1.63451e7i		−	1.53507i	−0.641007	−	0.767535i	$-0.721483\pi$
$647$		−	1.63451e7i		−	1.53507i	0.641007	−	0.767535i	$-0.278517\pi$
$648$		0			0
$649$		−	2.05401e7i		−	1.91422i
$650$		0			0
$651$	−6.67192e6	−	6.67192e6i	−0.617019	−	0.617019i
$652$		0			0
$653$	−5.46500e6	+	5.46500e6i	−0.501542	+	0.501542i	−0.911917	−	0.410375i	$-0.865398\pi$
$653$	−5.46500e6	+	5.46500e6i	−0.501542	+	0.501542i	0.410375	+	0.911917i	$0.365398\pi$
$654$		0			0
$655$	−6.77109e6			−0.616674
$656$		0			0
$657$	−2.44016e7			−2.20549
$658$		0			0
$659$	−1.11299e7	+	1.11299e7i	−0.998334	+	0.998334i	−0.999999	−	0.00166454i	$-0.999470\pi$
$659$	−1.11299e7	+	1.11299e7i	−0.998334	+	0.998334i	0.00166454	+	0.999999i	$0.499470\pi$
$660$		0			0
$661$	8.50684e6	+	8.50684e6i	0.757295	+	0.757295i	0.975829	−	0.218535i	$-0.0701277\pi$
$661$	8.50684e6	+	8.50684e6i	0.757295	+	0.757295i	−0.218535	+	0.975829i	$0.570128\pi$
$662$		0			0
$663$		−	1.27796e7i		−	1.12910i
$664$		0			0
$665$			4.27531e6i			0.374898i
$666$		0			0
$667$	−5.20340e6	−	5.20340e6i	−0.452869	−	0.452869i
$668$		0			0
$669$	1.84771e7	−	1.84771e7i	1.59613	−	1.59613i
$670$		0			0
$671$	−1.27489e7			−1.09312
$672$		0			0
$673$	1.91012e7			1.62563			0.812816	−	0.582521i	$-0.197933\pi$
$673$	1.91012e7			1.62563			0.812816	+	0.582521i	$0.197933\pi$
$674$		0			0
$675$	−5.39693e6	+	5.39693e6i	−0.455919	+	0.455919i
$676$		0			0
$677$	1.35318e7	+	1.35318e7i	1.13470	+	1.13470i	0.989385	+	0.145319i	$0.0464209\pi$
$677$	1.35318e7	+	1.35318e7i	1.13470	+	1.13470i	0.145319	+	0.989385i	$0.453579\pi$
$678$		0			0
$679$			5.72921e6i			0.476892i
$680$		0			0
$681$			3.40408e7i			2.81276i
$682$		0			0
$683$	−4506.05	−	4506.05i	−0.000369610	−	0.000369610i	0.706922	−	0.707292i	$-0.250083\pi$
$683$	−4506.05	−	4506.05i	−0.000369610	−	0.000369610i	−0.707292	+	0.706922i	$0.750083\pi$
$684$		0			0
$685$	−2.24676e6	+	2.24676e6i	−0.182949	+	0.182949i
$686$		0			0
$687$	−2.70687e7			−2.18814
$688$		0			0
$689$	1.34698e7			1.08097
$690$		0			0
$691$	−8.92380e6	+	8.92380e6i	−0.710976	+	0.710976i	−0.966739	−	0.255764i	$-0.917673\pi$
$691$	−8.92380e6	+	8.92380e6i	−0.710976	+	0.710976i	0.255764	+	0.966739i	$0.417673\pi$
$692$		0			0
$693$	−2.73737e7	−	2.73737e7i	−2.16521	−	2.16521i
$694$		0			0
$695$		−	295025.i		−	0.0231685i
$696$		0			0
$697$		−	2.54144e6i		−	0.198152i
$698$		0			0
$699$	9.35755e6	+	9.35755e6i	0.724384	+	0.724384i
$700$		0			0
$701$	5.86907e6	−	5.86907e6i	0.451101	−	0.451101i	−0.444619	−	0.895720i	$-0.646661\pi$
$701$	5.86907e6	−	5.86907e6i	0.451101	−	0.451101i	0.895720	+	0.444619i	$0.146661\pi$
$702$		0			0
$703$	−5.51006e6			−0.420502
$704$		0			0
$705$	−1.17330e7			−0.889069
$706$		0			0
$707$	6.00071e6	−	6.00071e6i	0.451496	−	0.451496i
$708$		0			0
$709$	1.26108e7	+	1.26108e7i	0.942166	+	0.942166i	0.998417	−	0.0562506i	$-0.0179146\pi$
$709$	1.26108e7	+	1.26108e7i	0.942166	+	0.942166i	−0.0562506	+	0.998417i	$0.517915\pi$
$710$		0			0
$711$			5.78395e7i			4.29092i
$712$		0			0
$713$		−	8.10118e6i		−	0.596794i
$714$		0			0
$715$	6.76202e6	+	6.76202e6i	0.494665	+	0.494665i
$716$		0			0
$717$	1.64864e7	−	1.64864e7i	1.19765	−	1.19765i
$718$		0			0
$719$	2.40190e7			1.73274			0.866368	−	0.499407i	$-0.166449\pi$
$719$	2.40190e7			1.73274			0.866368	+	0.499407i	$0.166449\pi$
$720$		0			0
$721$	−1.63906e7			−1.17424
$722$		0			0
$723$	−2.48567e7	+	2.48567e7i	−1.76847	+	1.76847i
$724$		0			0
$725$	−1.26455e6	−	1.26455e6i	−0.0893495	−	0.0893495i
$726$		0			0
$727$		−	1.69795e7i		−	1.19149i	−0.803175	−	0.595743i	$-0.796858\pi$
$727$		−	1.69795e7i		−	1.19149i	0.803175	−	0.595743i	$-0.203142\pi$
$728$		0			0
$729$			4.60361e7i			3.20834i
$730$		0			0
$731$	8.61065e6	+	8.61065e6i	0.595995	+	0.595995i
$732$		0			0
$733$	6.03684e6	−	6.03684e6i	0.415001	−	0.415001i	−0.468475	−	0.883477i	$-0.655196\pi$
$733$	6.03684e6	−	6.03684e6i	0.415001	−	0.415001i	0.883477	+	0.468475i	$0.155196\pi$
$734$		0			0
$735$	−5.06521e6			−0.345843
$736$		0			0
$737$	2.09167e7			1.41848
$738$		0			0
$739$	−6.99975e6	+	6.99975e6i	−0.471489	+	0.471489i	−0.902396	−	0.430908i	$-0.858194\pi$
$739$	−6.99975e6	+	6.99975e6i	−0.471489	+	0.471489i	0.430908	+	0.902396i	$0.358194\pi$
$740$		0			0
$741$	−2.32745e7	−	2.32745e7i	−1.55716	−	1.55716i
$742$		0			0
$743$			1.72605e7i			1.14705i	0.819188	+	0.573525i	$0.194425\pi$
$743$			1.72605e7i			1.14705i	−0.819188	+	0.573525i	$0.805575\pi$
$744$		0			0
$745$		−	4.24352e6i		−	0.280115i
$746$		0			0
$747$	4.03479e7	+	4.03479e7i	2.64557	+	2.64557i
$748$		0			0
$749$	4.82806e6	−	4.82806e6i	0.314462	−	0.314462i
$750$		0			0
$751$	2.57275e7			1.66455			0.832277	−	0.554360i	$-0.187037\pi$
$751$	2.57275e7			1.66455			0.832277	+	0.554360i	$0.187037\pi$
$752$		0			0
$753$	3.54739e7			2.27993
$754$		0			0
$755$	875391.	−	875391.i	0.0558901	−	0.0558901i
$756$		0			0
$757$	6.50319e6	+	6.50319e6i	0.412464	+	0.412464i	0.882596	−	0.470132i	$-0.155794\pi$
$757$	6.50319e6	+	6.50319e6i	0.412464	+	0.412464i	−0.470132	+	0.882596i	$0.655794\pi$
$758$		0			0
$759$		−	4.56378e7i		−	2.87554i
$760$		0			0
$761$		−	1.22816e7i		−	0.768766i	−0.923174	−	0.384383i	$-0.874414\pi$
$761$		−	1.22816e7i		−	0.768766i	0.923174	−	0.384383i	$-0.125586\pi$
$762$		0			0
$763$	8.38026e6	+	8.38026e6i	0.521130	+	0.521130i
$764$		0			0
$765$	−7.63293e6	+	7.63293e6i	−0.471561	+	0.471561i
$766$		0			0
$767$	−2.23137e7			−1.36957
$768$		0			0
$769$	−6.88429e6			−0.419801			−0.209900	−	0.977723i	$-0.567314\pi$
$769$	−6.88429e6			−0.419801			−0.209900	+	0.977723i	$0.567314\pi$
$770$		0			0
$771$	−561709.	+	561709.i	−0.0340311	+	0.0340311i
$772$		0			0
$773$	−7.34275e6	−	7.34275e6i	−0.441987	−	0.441987i	0.450692	−	0.892679i	$-0.351177\pi$
$773$	−7.34275e6	−	7.34275e6i	−0.441987	−	0.441987i	−0.892679	+	0.450692i	$0.851177\pi$
$774$		0			0
$775$		−	1.96878e6i		−	0.117745i
$776$		0			0
$777$			9.66657e6i			0.574407i
$778$		0			0
$779$	−4.62853e6	−	4.62853e6i	−0.273275	−	0.273275i
$780$		0			0
$781$	−2.18325e7	+	2.18325e7i	−1.28079	+	1.28079i
$782$		0			0
$783$	−3.49425e7			−2.03680
$784$		0			0
$785$	5.06634e6			0.293441
$786$		0			0
$787$	2.13048e7	−	2.13048e7i	1.22614	−	1.22614i	0.260731	−	0.965411i	$-0.416036\pi$
$787$	2.13048e7	−	2.13048e7i	1.22614	−	1.22614i	0.965411	−	0.260731i	$-0.0839636\pi$
$788$		0			0
$789$	−4.57074e7	−	4.57074e7i	−2.61393	−	2.61393i
$790$		0			0
$791$			4.38837e6i			0.249380i
$792$		0			0
$793$			1.38498e7i			0.782095i
$794$		0			0
$795$	−1.10466e7	−	1.10466e7i	−0.619886	−	0.619886i
$796$		0			0
$797$	−8.42729e6	+	8.42729e6i	−0.469940	+	0.469940i	−0.901895	−	0.431955i	$-0.857824\pi$
$797$	−8.42729e6	+	8.42729e6i	−0.469940	+	0.469940i	0.431955	+	0.901895i	$0.357824\pi$
$798$		0			0
$799$	−1.04033e7			−0.576504
$800$		0			0
$801$	1.25308e6			0.0690076
$802$		0			0
$803$	1.57192e7	−	1.57192e7i	0.860286	−	0.860286i
$804$		0			0
$805$	4.55356e6	+	4.55356e6i	0.247663	+	0.247663i
$806$		0			0
$807$		−	2.34289e7i		−	1.26639i
$808$		0			0
$809$			8.57539e6i			0.460662i	0.973112	+	0.230331i	$0.0739809\pi$
$809$			8.57539e6i			0.460662i	−0.973112	+	0.230331i	$0.926019\pi$
$810$		0			0
$811$	1.09687e7	+	1.09687e7i	0.585605	+	0.585605i	0.936438	−	0.350833i	$-0.114102\pi$
$811$	1.09687e7	+	1.09687e7i	0.585605	+	0.585605i	−0.350833	+	0.936438i	$0.614102\pi$
$812$		0			0
$813$	2.20974e7	−	2.20974e7i	1.17251	−	1.17251i
$814$		0			0
$815$	1.30322e7			0.687265
$816$		0			0
$817$	3.13638e7			1.64389
$818$		0			0
$819$	−2.97374e7	+	2.97374e7i	−1.54915	+	1.54915i
$820$		0			0
$821$	−2.97780e6	−	2.97780e6i	−0.154183	−	0.154183i	0.625800	−	0.779983i	$-0.284773\pi$
$821$	−2.97780e6	−	2.97780e6i	−0.154183	−	0.154183i	−0.779983	+	0.625800i	$0.784773\pi$
$822$		0			0
$823$			1.70748e7i			0.878730i	0.898309	+	0.439365i	$0.144796\pi$
$823$			1.70748e7i			0.878730i	−0.898309	+	0.439365i	$0.855204\pi$
$824$		0			0
$825$		−	1.10911e7i		−	0.567334i
$826$		0			0
$827$	−1.20004e7	−	1.20004e7i	−0.610142	−	0.610142i	0.332841	−	0.942983i	$-0.391993\pi$
$827$	−1.20004e7	−	1.20004e7i	−0.610142	−	0.610142i	−0.942983	+	0.332841i	$0.891993\pi$
$828$		0			0
$829$	−1.93431e7	+	1.93431e7i	−0.977549	+	0.977549i	−0.999753	−	0.0222041i	$-0.992932\pi$
$829$	−1.93431e7	+	1.93431e7i	−0.977549	+	0.977549i	0.0222041	+	0.999753i	$0.492932\pi$
$830$		0			0
$831$	3.20891e7			1.61196
$832$		0			0
$833$	−4.49117e6			−0.224257
$834$		0			0
$835$	6.60416e6	−	6.60416e6i	0.327794	−	0.327794i
$836$		0			0
$837$	−2.72010e7	−	2.72010e7i	−1.34206	−	1.34206i
$838$		0			0
$839$			3.25986e6i			0.159880i	0.996800	+	0.0799400i	$0.0254729\pi$
$839$			3.25986e6i			0.159880i	−0.996800	+	0.0799400i	$0.974527\pi$
$840$		0			0
$841$			1.23238e7i			0.600834i
$842$		0			0
$843$	−4.43871e6	−	4.43871e6i	−0.215123	−	0.215123i
$844$		0			0
$845$	782316.	−	782316.i	0.0376913	−	0.0376913i
$846$		0			0
$847$	1.91368e7			0.916560
$848$		0			0
$849$	−1.50423e7			−0.716218
$850$		0			0
$851$	−5.86867e6	+	5.86867e6i	−0.277789	+	0.277789i
$852$		0			0
$853$	4.96734e6	+	4.96734e6i	0.233750	+	0.233750i	0.814256	−	0.580506i	$-0.197145\pi$
$853$	4.96734e6	+	4.96734e6i	0.233750	+	0.233750i	−0.580506	+	0.814256i	$0.697145\pi$
$854$		0			0
$855$			2.78025e7i			1.30067i
$856$		0			0
$857$		−	1.82436e7i		−	0.848512i	−0.905542	−	0.424256i	$-0.860536\pi$
$857$		−	1.82436e7i		−	0.848512i	0.905542	−	0.424256i	$-0.139464\pi$
$858$		0			0
$859$	8.27729e6	+	8.27729e6i	0.382741	+	0.382741i	0.872089	−	0.489348i	$-0.162765\pi$
$859$	8.27729e6	+	8.27729e6i	0.382741	+	0.382741i	−0.489348	+	0.872089i	$0.662765\pi$
$860$		0			0
$861$	−8.12006e6	+	8.12006e6i	−0.373294	+	0.373294i
$862$		0			0
$863$	2.86914e7			1.31137			0.655685	−	0.755035i	$-0.272380\pi$
$863$	2.86914e7			1.31137			0.655685	+	0.755035i	$0.272380\pi$
$864$		0			0
$865$	50377.5			0.00228926
$866$		0			0
$867$	2.07322e7	−	2.07322e7i	0.936692	−	0.936692i
$868$		0			0
$869$	−3.72596e7	−	3.72596e7i	−1.67374	−	1.67374i
$870$		0			0
$871$		−	2.27228e7i		−	1.01488i
$872$		0			0
$873$			3.72573e7i			1.65453i
$874$		0			0
$875$	1.10662e6	+	1.10662e6i	0.0488630	+	0.0488630i
$876$		0			0
$877$	−1.54237e7	+	1.54237e7i	−0.677156	+	0.677156i	−0.959356	−	0.282200i	$-0.908936\pi$
$877$	−1.54237e7	+	1.54237e7i	−0.677156	+	0.677156i	0.282200	+	0.959356i	$0.408936\pi$
$878$		0			0
$879$	−6.03475e7			−2.63443
$880$		0			0
$881$	2.44458e7			1.06112			0.530559	−	0.847648i	$-0.321982\pi$
$881$	2.44458e7			1.06112			0.530559	+	0.847648i	$0.321982\pi$
$882$		0			0
$883$	−1.62559e7	+	1.62559e7i	−0.701632	+	0.701632i	−0.964761	−	0.263128i	$-0.915246\pi$
$883$	−1.62559e7	+	1.62559e7i	−0.701632	+	0.701632i	0.263128	+	0.964761i	$0.415246\pi$
$884$		0			0
$885$	1.82995e7	+	1.82995e7i	0.785383	+	0.785383i
$886$		0			0
$887$			4.06785e7i			1.73602i	0.496544	+	0.868011i	$0.334602\pi$
$887$			4.06785e7i			1.73602i	−0.496544	+	0.868011i	$0.665398\pi$
$888$		0			0
$889$			1.50891e7i			0.640336i
$890$		0			0
$891$	−8.68243e7	−	8.68243e7i	−3.66393	−	3.66393i
$892$		0			0
$893$	−1.89466e7	+	1.89466e7i	−0.795067	+	0.795067i
$894$		0			0
$895$	−6.06542e6			−0.253106
$896$		0			0
$897$	−4.95785e7			−2.05737
$898$		0			0
$899$	6.37346e6	−	6.37346e6i	0.263012	−	0.263012i
$900$		0			0
$901$	−9.79470e6	−	9.79470e6i	−0.401957	−	0.401957i
$902$		0			0
$903$		−	5.50230e7i		−	2.24556i
$904$		0			0
$905$		−	6.71592e6i		−	0.272574i
$906$		0			0
$907$	7.74072e6	+	7.74072e6i	0.312438	+	0.312438i	0.845853	−	0.533416i	$-0.179092\pi$
$907$	7.74072e6	+	7.74072e6i	0.312438	+	0.312438i	−0.533416	+	0.845853i	$0.679092\pi$
$908$		0			0
$909$	3.90229e7	−	3.90229e7i	1.56643	−	1.56643i
$910$		0			0
$911$	−4.08521e7			−1.63087			−0.815433	−	0.578852i	$-0.803501\pi$
$911$	−4.08521e7			−1.63087			−0.815433	+	0.578852i	$0.803501\pi$
$912$		0			0
$913$	−5.19834e7			−2.06390
$914$		0			0
$915$	1.13582e7	−	1.13582e7i	0.448495	−	0.448495i
$916$		0			0
$917$	1.91822e7	+	1.91822e7i	0.753313	+	0.753313i
$918$		0			0
$919$			3.49397e7i			1.36468i	0.731035	+	0.682340i	$0.239037\pi$
$919$			3.49397e7i			1.36468i	−0.731035	+	0.682340i	$0.760963\pi$
$920$		0			0
$921$		−	7.21090e7i		−	2.80117i
$922$		0			0
$923$	2.37177e7	+	2.37177e7i	0.916366	+	0.916366i
$924$		0			0
$925$	−1.42623e6	+	1.42623e6i	−0.0548068	+	0.0548068i
$926$		0			0
$927$	−1.06589e8			−4.07391
$928$		0			0
$929$	4.20533e7			1.59868			0.799339	−	0.600880i	$-0.205183\pi$
$929$	4.20533e7			1.59868			0.799339	+	0.600880i	$0.205183\pi$
$930$		0			0
$931$	−8.17941e6	+	8.17941e6i	−0.309277	+	0.309277i
$932$		0			0
$933$	2.14059e6	+	2.14059e6i	0.0805063	+	0.0805063i
$934$		0			0
$935$		−	9.83412e6i		−	0.367880i
$936$		0			0
$937$			1.91624e7i			0.713018i	0.934292	+	0.356509i	$0.116033\pi$
$937$			1.91624e7i			0.713018i	−0.934292	+	0.356509i	$0.883967\pi$
$938$		0			0
$939$	2.08943e6	+	2.08943e6i	0.0773328	+	0.0773328i
$940$		0			0
$941$	2.40682e7	−	2.40682e7i	0.886072	−	0.886072i	−0.108071	−	0.994143i	$-0.534467\pi$
$941$	2.40682e7	−	2.40682e7i	0.886072	−	0.886072i	0.994143	+	0.108071i	$0.0344675\pi$
$942$		0			0
$943$	−9.85954e6			−0.361058
$944$		0			0
$945$	3.05786e7			1.11388
$946$		0			0
$947$	2.86713e7	−	2.86713e7i	1.03890	−	1.03890i	0.0396835	−	0.999212i	$-0.487365\pi$
$947$	2.86713e7	−	2.86713e7i	1.03890	−	1.03890i	0.999212	−	0.0396835i	$-0.0126350\pi$
$948$		0			0
$949$	−1.70766e7	−	1.70766e7i	−0.615511	−	0.615511i
$950$		0			0
$951$		−	6.88796e7i		−	2.46967i
$952$		0			0
$953$		−	3.16783e6i		−	0.112987i	−0.998403	−	0.0564936i	$-0.982008\pi$
$953$		−	3.16783e6i		−	0.112987i	0.998403	−	0.0564936i	$-0.0179921\pi$
$954$		0			0
$955$	−1.23962e7	−	1.23962e7i	−0.439825	−	0.439825i
$956$		0			0
$957$	3.59047e7	−	3.59047e7i	1.26728	−	1.26728i
$958$		0			0
$959$	1.27300e7			0.446973
$960$		0			0
$961$	−1.87063e7			−0.653401
$962$		0			0
$963$	3.13971e7	−	3.13971e7i	1.09100	−	1.09100i
$964$		0			0
$965$	−1.38024e7	−	1.38024e7i	−0.477130	−	0.477130i
$966$		0			0
$967$		−	4.57637e7i		−	1.57382i	−0.617068	−	0.786910i	$-0.711680\pi$
$967$		−	4.57637e7i		−	1.57382i	0.617068	−	0.786910i	$-0.288320\pi$
$968$		0			0
$969$			3.38485e7i			1.15806i
$970$		0			0
$971$	−3.29393e7	−	3.29393e7i	−1.12116	−	1.12116i	−0.991568	−	0.129588i	$-0.958635\pi$
$971$	−3.29393e7	−	3.29393e7i	−1.12116	−	1.12116i	−0.129588	−	0.991568i	$-0.541365\pi$
$972$		0			0
$973$	−835795.	+	835795.i	−0.0283020	+	0.0283020i
$974$		0			0
$975$	−1.20488e7			−0.405912
$976$		0			0
$977$	−4.56792e7			−1.53103			−0.765513	−	0.643421i	$-0.777515\pi$
$977$	−4.56792e7			−1.53103			−0.765513	+	0.643421i	$0.777515\pi$
$978$		0			0
$979$	−807221.	+	807221.i	−0.0269176	+	0.0269176i
$980$		0			0
$981$	5.44972e7	+	5.44972e7i	1.80801	+	1.80801i
$982$		0			0
$983$		−	2.92212e7i		−	0.964527i	−0.876026	−	0.482264i	$-0.839815\pi$
$983$		−	2.92212e7i		−	0.964527i	0.876026	−	0.482264i	$-0.160185\pi$
$984$		0			0
$985$		−	9.56735e6i		−	0.314196i
$986$		0			0
$987$	3.32390e7	+	3.32390e7i	1.08606	+	1.08606i
$988$		0			0
$989$	3.34050e7	−	3.34050e7i	1.08598	−	1.08598i
$990$		0			0
$991$	5.86900e7			1.89836			0.949182	−	0.314727i	$-0.101913\pi$
$991$	5.86900e7			1.89836			0.949182	+	0.314727i	$0.101913\pi$
$992$		0			0
$993$	−4.38238e7			−1.41038
$994$		0			0
$995$	−2.20081e6	+	2.20081e6i	−0.0704733	+	0.0704733i
$996$		0			0
$997$	8.76827e6	+	8.76827e6i	0.279368	+	0.279368i	0.832857	−	0.553489i	$-0.186704\pi$
$997$	8.76827e6	+	8.76827e6i	0.279368	+	0.279368i	−0.553489	+	0.832857i	$0.686704\pi$
$998$		0			0
$999$			3.94099e7i			1.24937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.241.2		80
4.3	odd	2		80.6.l.a.21.10	✓	80
16.3	odd	4		80.6.l.a.61.10	yes	80
16.13	even	4	inner	320.6.l.a.81.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.10	✓	80	4.3	odd	2
80.6.l.a.61.10	yes	80	16.3	odd	4
320.6.l.a.81.2		80	16.13	even	4	inner
320.6.l.a.241.2		80	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-21.1465 + 21.1465i) q^{3} +(17.6777 + 17.6777i) q^{5} -100.160i q^{7} -651.346i q^{9} +O(q^{10})\)	\(q+(-21.1465 + 21.1465i) q^{3} +(17.6777 + 17.6777i) q^{5} -100.160i q^{7} -651.346i q^{9} +(419.591 + 419.591i) q^{11} +(455.822 - 455.822i) q^{13} -747.641 q^{15} -662.910 q^{17} +(-1207.30 + 1207.30i) q^{19} +(2118.04 + 2118.04i) q^{21} +2571.76i q^{23} +625.000i q^{25} +(8635.09 + 8635.09i) q^{27} +(-2023.28 + 2023.28i) q^{29} -3150.05 q^{31} -17745.7 q^{33} +(1770.60 - 1770.60i) q^{35} +(2281.97 + 2281.97i) q^{37} +19278.1i q^{39} +3833.77i q^{41} +(-12989.2 - 12989.2i) q^{43} +(11514.3 - 11514.3i) q^{45} +15693.3 q^{47} +6774.93 q^{49} +(14018.2 - 14018.2i) q^{51} +(14775.3 + 14775.3i) q^{53} +14834.8i q^{55} -51060.5i q^{57} +(-24476.4 - 24476.4i) q^{59} +(-15192.1 + 15192.1i) q^{61} -65239.0 q^{63} +16115.7 q^{65} +(24925.1 - 24925.1i) q^{67} +(-54383.7 - 54383.7i) q^{69} +52032.9i q^{71} -37463.3i q^{73} +(-13216.5 - 13216.5i) q^{75} +(42026.3 - 42026.3i) q^{77} -88799.9 q^{79} -206926. q^{81} +(-61945.4 + 61945.4i) q^{83} +(-11718.7 - 11718.7i) q^{85} -85570.7i q^{87} +1923.83i q^{89} +(-45655.2 - 45655.2i) q^{91} +(66612.5 - 66612.5i) q^{93} -42684.7 q^{95} -57200.4 q^{97} +(273299. - 273299. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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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Database

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