LMFDB - Embedded newform 320.6.l.a.81.12

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			81.12
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.77316 - 9.77316i) q^{3} +(17.6777 - 17.6777i) q^{5} +103.649i q^{7} -51.9707i q^{9} +O(q^{10})$	\(q+(-9.77316 - 9.77316i) q^{3} +(17.6777 - 17.6777i) q^{5} +103.649i q^{7} -51.9707i q^{9} +(-1.18069 + 1.18069i) q^{11} +(-196.412 - 196.412i) q^{13} -345.533 q^{15} +274.760 q^{17} +(464.105 + 464.105i) q^{19} +(1012.98 - 1012.98i) q^{21} +3172.08i q^{23} -625.000i q^{25} +(-2882.80 + 2882.80i) q^{27} +(-3615.12 - 3615.12i) q^{29} -8594.55 q^{31} +23.0781 q^{33} +(1832.27 + 1832.27i) q^{35} +(5380.92 - 5380.92i) q^{37} +3839.13i q^{39} +12794.9i q^{41} +(-2059.02 + 2059.02i) q^{43} +(-918.721 - 918.721i) q^{45} +19.2201 q^{47} +6063.86 q^{49} +(-2685.27 - 2685.27i) q^{51} +(2845.02 - 2845.02i) q^{53} +41.7437i q^{55} -9071.55i q^{57} +(16076.8 - 16076.8i) q^{59} +(28235.3 + 28235.3i) q^{61} +5386.72 q^{63} -6944.22 q^{65} +(41683.6 + 41683.6i) q^{67} +(31001.2 - 31001.2i) q^{69} +25386.5i q^{71} +24731.7i q^{73} +(-6108.22 + 6108.22i) q^{75} +(-122.377 - 122.377i) q^{77} -8180.40 q^{79} +43719.2 q^{81} +(73736.2 + 73736.2i) q^{83} +(4857.11 - 4857.11i) q^{85} +70662.3i q^{87} +31074.5i q^{89} +(20357.9 - 20357.9i) q^{91} +(83995.9 + 83995.9i) q^{93} +16408.6 q^{95} +48319.6 q^{97} +(61.3613 + 61.3613i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−9.77316	−	9.77316i	−0.626948	−	0.626948i	0.320351	−	0.947299i	$-0.396199\pi$
$3$	−9.77316	−	9.77316i	−0.626948	−	0.626948i	−0.947299	+	0.320351i	$0.896199\pi$
$4$		0			0
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$		0			0
$7$			103.649i			0.799504i	0.916623	+	0.399752i	$0.130904\pi$
$7$			103.649i			0.799504i	−0.916623	+	0.399752i	$0.869096\pi$
$8$		0			0
$9$		−	51.9707i		−	0.213871i
$10$		0			0
$11$	−1.18069	+	1.18069i	−0.00294208	+	0.00294208i	−0.708576	−	0.705634i	$-0.750662\pi$
$11$	−1.18069	+	1.18069i	−0.00294208	+	0.00294208i	0.705634	+	0.708576i	$0.250662\pi$
$12$		0			0
$13$	−196.412	−	196.412i	−0.322337	−	0.322337i	0.527326	−	0.849663i	$-0.323195\pi$
$13$	−196.412	−	196.412i	−0.322337	−	0.322337i	−0.849663	+	0.527326i	$0.823195\pi$
$14$		0			0
$15$	−345.533			−0.396517
$16$		0			0
$17$	274.760			0.230585			0.115292	−	0.993332i	$-0.463219\pi$
$17$	274.760			0.230585			0.115292	+	0.993332i	$0.463219\pi$
$18$		0			0
$19$	464.105	+	464.105i	0.294939	+	0.294939i	0.839028	−	0.544089i	$-0.183124\pi$
$19$	464.105	+	464.105i	0.294939	+	0.294939i	−0.544089	+	0.839028i	$0.683124\pi$
$20$		0			0
$21$	1012.98	−	1012.98i	0.501248	−	0.501248i
$22$		0			0
$23$			3172.08i			1.25033i	0.780493	+	0.625164i	$0.214968\pi$
$23$			3172.08i			1.25033i	−0.780493	+	0.625164i	$0.785032\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−2882.80	+	2882.80i	−0.761035	+	0.761035i
$28$		0			0
$29$	−3615.12	−	3615.12i	−0.798229	−	0.798229i	0.184587	−	0.982816i	$-0.440905\pi$
$29$	−3615.12	−	3615.12i	−0.798229	−	0.798229i	−0.982816	+	0.184587i	$0.940905\pi$
$30$		0			0
$31$	−8594.55			−1.60627			−0.803135	−	0.595797i	$-0.796836\pi$
$31$	−8594.55			−1.60627			−0.803135	+	0.595797i	$0.796836\pi$
$32$		0			0
$33$	23.0781			0.00368906
$34$		0			0
$35$	1832.27	+	1832.27i	0.252825	+	0.252825i
$36$		0			0
$37$	5380.92	−	5380.92i	0.646178	−	0.646178i	−0.305889	−	0.952067i	$-0.598954\pi$
$37$	5380.92	−	5380.92i	0.646178	−	0.646178i	0.952067	+	0.305889i	$0.0989538\pi$
$38$		0			0
$39$			3839.13i			0.404177i
$40$		0			0
$41$			12794.9i			1.18871i	0.804203	+	0.594355i	$0.202593\pi$
$41$			12794.9i			1.18871i	−0.804203	+	0.594355i	$0.797407\pi$
$42$		0			0
$43$	−2059.02	+	2059.02i	−0.169820	+	0.169820i	−0.786900	−	0.617080i	$-0.788315\pi$
$43$	−2059.02	+	2059.02i	−0.169820	+	0.169820i	0.617080	+	0.786900i	$0.288315\pi$
$44$		0			0
$45$	−918.721	−	918.721i	−0.0676320	−	0.0676320i
$46$		0			0
$47$	19.2201			0.00126914			0.000634572	−	1.00000i	$-0.499798\pi$
$47$	19.2201			0.00126914			0.000634572		1.00000i	$0.499798\pi$
$48$		0			0
$49$	6063.86			0.360794
$50$		0			0
$51$	−2685.27	−	2685.27i	−0.144565	−	0.144565i
$52$		0			0
$53$	2845.02	−	2845.02i	0.139122	−	0.139122i	−0.634116	−	0.773238i	$-0.718636\pi$
$53$	2845.02	−	2845.02i	0.139122	−	0.139122i	0.773238	+	0.634116i	$0.218636\pi$
$54$		0			0
$55$			41.7437i			0.00186073i
$56$		0			0
$57$		−	9071.55i		−	0.369823i
$58$		0			0
$59$	16076.8	−	16076.8i	0.601268	−	0.601268i	−0.339381	−	0.940649i	$-0.610218\pi$
$59$	16076.8	−	16076.8i	0.601268	−	0.601268i	0.940649	+	0.339381i	$0.110218\pi$
$60$		0			0
$61$	28235.3	+	28235.3i	0.971557	+	0.971557i	0.999607	−	0.0280491i	$-0.00892948\pi$
$61$	28235.3	+	28235.3i	0.971557	+	0.971557i	−0.0280491	+	0.999607i	$0.508929\pi$
$62$		0			0
$63$	5386.72			0.170991
$64$		0			0
$65$	−6944.22			−0.203864
$66$		0			0
$67$	41683.6	+	41683.6i	1.13443	+	1.13443i	0.989432	+	0.145000i	$0.0463182\pi$
$67$	41683.6	+	41683.6i	1.13443	+	1.13443i	0.145000	+	0.989432i	$0.453682\pi$
$68$		0			0
$69$	31001.2	−	31001.2i	0.783891	−	0.783891i
$70$		0			0
$71$			25386.5i			0.597663i	0.954306	+	0.298832i	$0.0965969\pi$
$71$			25386.5i			0.597663i	−0.954306	+	0.298832i	$0.903403\pi$
$72$		0			0
$73$			24731.7i			0.543184i	0.962412	+	0.271592i	$0.0875502\pi$
$73$			24731.7i			0.543184i	−0.962412	+	0.271592i	$0.912450\pi$
$74$		0			0
$75$	−6108.22	+	6108.22i	−0.125390	+	0.125390i
$76$		0			0
$77$	−122.377	−	122.377i	−0.00235220	−	0.00235220i
$78$		0			0
$79$	−8180.40			−0.147471			−0.0737355	−	0.997278i	$-0.523492\pi$
$79$	−8180.40			−0.147471			−0.0737355	+	0.997278i	$0.523492\pi$
$80$		0			0
$81$	43719.2			0.740388
$82$		0			0
$83$	73736.2	+	73736.2i	1.17486	+	1.17486i	0.981037	+	0.193822i	$0.0620885\pi$
$83$	73736.2	+	73736.2i	1.17486	+	1.17486i	0.193822	+	0.981037i	$0.437912\pi$
$84$		0			0
$85$	4857.11	−	4857.11i	0.0729173	−	0.0729173i
$86$		0			0
$87$			70662.3i			1.00090i
$88$		0			0
$89$			31074.5i			0.415842i	0.978146	+	0.207921i	$0.0666698\pi$
$89$			31074.5i			0.415842i	−0.978146	+	0.207921i	$0.933330\pi$
$90$		0			0
$91$	20357.9	−	20357.9i	0.257709	−	0.257709i
$92$		0			0
$93$	83995.9	+	83995.9i	1.00705	+	1.00705i
$94$		0			0
$95$	16408.6			0.186536
$96$		0			0
$97$	48319.6			0.521427			0.260714	−	0.965416i	$-0.416042\pi$
$97$	48319.6			0.521427			0.260714	+	0.965416i	$0.416042\pi$
$98$		0			0
$99$	61.3613	+	61.3613i	0.000629225	+	0.000629225i
$100$		0			0
$101$	−83227.2	+	83227.2i	−0.811824	+	0.811824i	−0.984907	−	0.173083i	$-0.944627\pi$
$101$	−83227.2	+	83227.2i	−0.811824	+	0.811824i	0.173083	+	0.984907i	$0.444627\pi$
$102$		0			0
$103$		−	24932.4i		−	0.231564i	−0.993275	−	0.115782i	$-0.963063\pi$
$103$		−	24932.4i		−	0.231564i	0.993275	−	0.115782i	$-0.0369374\pi$
$104$		0			0
$105$		−	35814.2i		−	0.317017i
$106$		0			0
$107$	86761.1	−	86761.1i	0.732598	−	0.732598i	−0.238536	−	0.971134i	$-0.576668\pi$
$107$	86761.1	−	86761.1i	0.732598	−	0.732598i	0.971134	+	0.238536i	$0.0766675\pi$
$108$		0			0
$109$	108586.	+	108586.i	0.875399	+	0.875399i	0.993054	−	0.117656i	$-0.0375379\pi$
$109$	108586.	+	108586.i	0.875399	+	0.875399i	−0.117656	+	0.993054i	$0.537538\pi$
$110$		0			0
$111$	−105177.			−0.810240
$112$		0			0
$113$	−96237.1			−0.709000			−0.354500	−	0.935056i	$-0.615349\pi$
$113$	−96237.1			−0.709000			−0.354500	+	0.935056i	$0.615349\pi$
$114$		0			0
$115$	56074.9	+	56074.9i	0.395388	+	0.395388i
$116$		0			0
$117$	−10207.7	+	10207.7i	−0.0689385	+	0.0689385i
$118$		0			0
$119$			28478.6i			0.184353i
$120$		0			0
$121$			161048.i			0.999983i
$122$		0			0
$123$	125046.	−	125046.i	0.745260	−	0.745260i
$124$		0			0
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	83496.0			0.459363			0.229682	−	0.973266i	$-0.426232\pi$
$127$	83496.0			0.459363			0.229682	+	0.973266i	$0.426232\pi$
$128$		0			0
$129$	40246.3			0.212937
$130$		0			0
$131$	−4990.15	−	4990.15i	−0.0254059	−	0.0254059i	0.694290	−	0.719696i	$-0.255719\pi$
$131$	−4990.15	−	4990.15i	−0.0254059	−	0.0254059i	−0.719696	+	0.694290i	$0.755719\pi$
$132$		0			0
$133$	−48104.1	+	48104.1i	−0.235805	+	0.235805i
$134$		0			0
$135$			101922.i			0.481321i
$136$		0			0
$137$		−	319403.i		−	1.45391i	−0.686686	−	0.726954i	$-0.740935\pi$
$137$		−	319403.i		−	1.45391i	0.686686	−	0.726954i	$-0.259065\pi$
$138$		0			0
$139$	126010.	−	126010.i	0.553182	−	0.553182i	−0.374176	−	0.927358i	$-0.622074\pi$
$139$	126010.	−	126010.i	0.553182	−	0.553182i	0.927358	+	0.374176i	$0.122074\pi$
$140$		0			0
$141$	−187.841	−	187.841i	−0.000795689	−	0.000795689i
$142$		0			0
$143$	463.803			0.00189668
$144$		0			0
$145$	−127814.			−0.504845
$146$		0			0
$147$	−59263.1	−	59263.1i	−0.226199	−	0.226199i
$148$		0			0
$149$	−127764.	+	127764.i	−0.471456	+	0.471456i	−0.902386	−	0.430929i	$-0.858186\pi$
$149$	−127764.	+	127764.i	−0.471456	+	0.471456i	0.430929	+	0.902386i	$0.358186\pi$
$150$		0			0
$151$			313476.i			1.11882i	0.828890	+	0.559412i	$0.188973\pi$
$151$			313476.i			1.11882i	−0.828890	+	0.559412i	$0.811027\pi$
$152$		0			0
$153$		−	14279.5i		−	0.0493154i
$154$		0			0
$155$	−151932.	+	151932.i	−0.507947	+	0.507947i
$156$		0			0
$157$	252249.	+	252249.i	0.816734	+	0.816734i	0.985633	−	0.168899i	$-0.0540212\pi$
$157$	252249.	+	252249.i	0.816734	+	0.816734i	−0.168899	+	0.985633i	$0.554021\pi$
$158$		0			0
$159$	−55609.7			−0.174445
$160$		0			0
$161$	−328783.			−0.999642
$162$		0			0
$163$	−282574.	−	282574.i	−0.833035	−	0.833035i	0.154896	−	0.987931i	$-0.450496\pi$
$163$	−282574.	−	282574.i	−0.833035	−	0.833035i	−0.987931	+	0.154896i	$0.950496\pi$
$164$		0			0
$165$	407.968	−	407.968i	0.00116658	−	0.00116658i
$166$		0			0
$167$		−	52609.2i		−	0.145972i	−0.997333	−	0.0729861i	$-0.976747\pi$
$167$		−	52609.2i		−	0.145972i	0.997333	−	0.0729861i	$-0.0232529\pi$
$168$		0			0
$169$		−	294138.i		−	0.792198i
$170$		0			0
$171$	24119.9	−	24119.9i	0.0630790	−	0.0630790i
$172$		0			0
$173$	538675.	+	538675.i	1.36839	+	1.36839i	0.862731	+	0.505663i	$0.168752\pi$
$173$	538675.	+	538675.i	1.36839	+	1.36839i	0.505663	+	0.862731i	$0.331248\pi$
$174$		0			0
$175$	64780.7			0.159901
$176$		0			0
$177$	−314241.			−0.753928
$178$		0			0
$179$	194994.	+	194994.i	0.454871	+	0.454871i	0.896967	−	0.442097i	$-0.145765\pi$
$179$	194994.	+	194994.i	0.454871	+	0.454871i	−0.442097	+	0.896967i	$0.645765\pi$
$180$		0			0
$181$	−417889.	+	417889.i	−0.948123	+	0.948123i	−0.998719	−	0.0505962i	$-0.983888\pi$
$181$	−417889.	+	417889.i	−0.948123	+	0.948123i	0.0505962	+	0.998719i	$0.483888\pi$
$182$		0			0
$183$		−	551897.i		−	1.21823i
$184$		0			0
$185$		−	190244.i		−	0.408679i
$186$		0			0
$187$	−324.406	+	324.406i	−0.000678398	+	0.000678398i
$188$		0			0
$189$	−298799.	−	298799.i	−0.608450	−	0.608450i
$190$		0			0
$191$	−497076.			−0.985915			−0.492957	−	0.870053i	$-0.664084\pi$
$191$	−497076.			−0.985915			−0.492957	+	0.870053i	$0.664084\pi$
$192$		0			0
$193$	462532.			0.893817			0.446908	−	0.894580i	$-0.352525\pi$
$193$	462532.			0.893817			0.446908	+	0.894580i	$0.352525\pi$
$194$		0			0
$195$	67866.9	+	67866.9i	0.127812	+	0.127812i
$196$		0			0
$197$	286303.	−	286303.i	0.525606	−	0.525606i	−0.393653	−	0.919259i	$-0.628789\pi$
$197$	286303.	−	286303.i	0.525606	−	0.525606i	0.919259	+	0.393653i	$0.128789\pi$
$198$		0			0
$199$			1.00987e6i			1.80772i	0.427828	+	0.903860i	$0.359279\pi$
$199$			1.00987e6i			1.80772i	−0.427828	+	0.903860i	$0.640721\pi$
$200$		0			0
$201$		−	814761.i		−	1.42246i
$202$		0			0
$203$	374704.	−	374704.i	0.638187	−	0.638187i
$204$		0			0
$205$	226183.	+	226183.i	0.375903	+	0.375903i
$206$		0			0
$207$	164855.			0.267409
$208$		0			0
$209$	−1095.93			−0.00173547
$210$		0			0
$211$	−277285.	−	277285.i	−0.428765	−	0.428765i	0.459442	−	0.888208i	$-0.348049\pi$
$211$	−277285.	−	277285.i	−0.428765	−	0.428765i	−0.888208	+	0.459442i	$0.848049\pi$
$212$		0			0
$213$	248106.	−	248106.i	0.374704	−	0.374704i
$214$		0			0
$215$			72797.4i			0.107404i
$216$		0			0
$217$		−	890817.i		−	1.28422i
$218$		0			0
$219$	241707.	−	241707.i	0.340549	−	0.340549i
$220$		0			0
$221$	−53966.1	−	53966.1i	−0.0743259	−	0.0743259i
$222$		0			0
$223$	−912396.			−1.22863			−0.614315	−	0.789061i	$-0.710568\pi$
$223$	−912396.			−1.22863			−0.614315	+	0.789061i	$0.710568\pi$
$224$		0			0
$225$	−32481.7			−0.0427742
$226$		0			0
$227$	−173993.	−	173993.i	−0.224113	−	0.224113i	0.586115	−	0.810228i	$-0.300657\pi$
$227$	−173993.	−	173993.i	−0.224113	−	0.224113i	−0.810228	+	0.586115i	$0.800657\pi$
$228$		0			0
$229$	845428.	−	845428.i	1.06534	−	1.06534i	0.0676288	−	0.997711i	$-0.478457\pi$
$229$	845428.	−	845428.i	1.06534	−	1.06534i	0.997711	−	0.0676288i	$-0.0215434\pi$
$230$		0			0
$231$			2392.03i			0.00294942i
$232$		0			0
$233$		−	33744.0i		−	0.0407199i	−0.999793	−	0.0203599i	$-0.993519\pi$
$233$		−	33744.0i		−	0.0407199i	0.999793	−	0.0203599i	$-0.00648122\pi$
$234$		0			0
$235$	339.767	−	339.767i	0.000401339	−	0.000401339i
$236$		0			0
$237$	79948.3	+	79948.3i	0.0924567	+	0.0924567i
$238$		0			0
$239$	−1.42903e6			−1.61825			−0.809125	−	0.587637i	$-0.800058\pi$
$239$	−1.42903e6			−1.61825			−0.809125	+	0.587637i	$0.800058\pi$
$240$		0			0
$241$	−387370.			−0.429619			−0.214809	−	0.976656i	$-0.568913\pi$
$241$	−387370.			−0.429619			−0.214809	+	0.976656i	$0.568913\pi$
$242$		0			0
$243$	273245.	+	273245.i	0.296850	+	0.296850i
$244$		0			0
$245$	107195.	−	107195.i	0.114093	−	0.114093i
$246$		0			0
$247$		−	182312.i		−	0.190140i
$248$		0			0
$249$		−	1.44127e6i		−	1.47315i
$250$		0			0
$251$	151092.	−	151092.i	0.151376	−	0.151376i	−0.627356	−	0.778732i	$-0.715863\pi$
$251$	151092.	−	151092.i	0.151376	−	0.151376i	0.778732	+	0.627356i	$0.215863\pi$
$252$		0			0
$253$	−3745.24	−	3745.24i	−0.00367856	−	0.00367856i
$254$		0			0
$255$	−94938.6			−0.0914308
$256$		0			0
$257$	−1.10772e6			−1.04616			−0.523081	−	0.852283i	$-0.675218\pi$
$257$	−1.10772e6			−1.04616			−0.523081	+	0.852283i	$0.675218\pi$
$258$		0			0
$259$	557727.	+	557727.i	0.516621	+	0.516621i
$260$		0			0
$261$	−187880.	+	187880.i	−0.170718	+	0.170718i
$262$		0			0
$263$			166218.i			0.148179i	0.997252	+	0.0740897i	$0.0236051\pi$
$263$			166218.i			0.148179i	−0.997252	+	0.0740897i	$0.976395\pi$
$264$		0			0
$265$		−	100587.i		−	0.0879884i
$266$		0			0
$267$	303696.	−	303696.i	0.260712	−	0.260712i
$268$		0			0
$269$	−1.20947e6	−	1.20947e6i	−1.01910	−	1.01910i	−0.999814	−	0.0192827i	$-0.993862\pi$
$269$	−1.20947e6	−	1.20947e6i	−1.01910	−	1.01910i	−0.0192827	−	0.999814i	$-0.506138\pi$
$270$		0			0
$271$	−1.78497e6			−1.47641			−0.738207	−	0.674574i	$-0.764327\pi$
$271$	−1.78497e6			−1.47641			−0.738207	+	0.674574i	$0.764327\pi$
$272$		0			0
$273$	−397923.			−0.323141
$274$		0			0
$275$	737.931	+	737.931i	0.000588415	+	0.000588415i
$276$		0			0
$277$	−1.21139e6	+	1.21139e6i	−0.948602	+	0.948602i	−0.998742	−	0.0501403i	$-0.984033\pi$
$277$	−1.21139e6	+	1.21139e6i	−0.948602	+	0.948602i	0.0501403	+	0.998742i	$0.484033\pi$
$278$		0			0
$279$			446665.i			0.343535i
$280$		0			0
$281$			2.33417e6i			1.76347i	0.471748	+	0.881734i	$0.343623\pi$
$281$			2.33417e6i			1.76347i	−0.471748	+	0.881734i	$0.656377\pi$
$282$		0			0
$283$	1.45993e6	−	1.45993e6i	1.08359	−	1.08359i	0.0874233	−	0.996171i	$-0.472137\pi$
$283$	1.45993e6	−	1.45993e6i	1.08359	−	1.08359i	0.996171	−	0.0874233i	$-0.0278633\pi$
$284$		0			0
$285$	−160364.	−	160364.i	−0.116948	−	0.116948i
$286$		0			0
$287$	−1.32618e6			−0.950378
$288$		0			0
$289$	−1.34436e6			−0.946831
$290$		0			0
$291$	−472235.	−	472235.i	−0.326908	−	0.326908i
$292$		0			0
$293$	−268466.	+	268466.i	−0.182692	+	0.182692i	−0.792528	−	0.609836i	$-0.791235\pi$
$293$	−268466.	+	268466.i	−0.182692	+	0.182692i	0.609836	+	0.792528i	$0.291235\pi$
$294$		0			0
$295$		−	568399.i		−	0.380275i
$296$		0			0
$297$		−	6807.37i		−	0.00447804i
$298$		0			0
$299$	623034.	−	623034.i	0.403027	−	0.403027i
$300$		0			0
$301$	−213416.	−	213416.i	−0.135772	−	0.135772i
$302$		0			0
$303$	1.62679e6			1.01794
$304$		0			0
$305$	998270.			0.614467
$306$		0			0
$307$	−1.30877e6	−	1.30877e6i	−0.792534	−	0.792534i	0.189372	−	0.981905i	$-0.439355\pi$
$307$	−1.30877e6	−	1.30877e6i	−0.792534	−	0.792534i	−0.981905	+	0.189372i	$0.939355\pi$
$308$		0			0
$309$	−243668.	+	243668.i	−0.145179	+	0.145179i
$310$		0			0
$311$		−	3.06774e6i		−	1.79853i	−0.437406	−	0.899264i	$-0.644103\pi$
$311$		−	3.06774e6i		−	1.79853i	0.437406	−	0.899264i	$-0.355897\pi$
$312$		0			0
$313$			2.27439e6i			1.31221i	0.754669	+	0.656105i	$0.227797\pi$
$313$			2.27439e6i			1.31221i	−0.754669	+	0.656105i	$0.772203\pi$
$314$		0			0
$315$	95224.6	−	95224.6i	0.0540720	−	0.0540720i
$316$		0			0
$317$	2.44805e6	+	2.44805e6i	1.36827	+	1.36827i	0.862909	+	0.505360i	$0.168640\pi$
$317$	2.44805e6	+	2.44805e6i	1.36827	+	1.36827i	0.505360	+	0.862909i	$0.331360\pi$
$318$		0			0
$319$	8536.67			0.00469690
$320$		0			0
$321$	−1.69586e6			−0.918602
$322$		0			0
$323$	127517.	+	127517.i	0.0680085	+	0.0680085i
$324$		0			0
$325$	−122758.	+	122758.i	−0.0644673	+	0.0644673i
$326$		0			0
$327$		−	2.12245e6i		−	1.09766i
$328$		0			0
$329$			1992.15i			0.00101469i
$330$		0			0
$331$	−786844.	+	786844.i	−0.394747	+	0.394747i	−0.876376	−	0.481628i	$-0.840045\pi$
$331$	−786844.	+	786844.i	−0.394747	+	0.394747i	0.481628	+	0.876376i	$0.340045\pi$
$332$		0			0
$333$	−279650.	−	279650.i	−0.138199	−	0.138199i
$334$		0			0
$335$	1.47374e6			0.717478
$336$		0			0
$337$	−1.52615e6			−0.732021			−0.366010	−	0.930611i	$-0.619276\pi$
$337$	−1.52615e6			−0.732021			−0.366010	+	0.930611i	$0.619276\pi$
$338$		0			0
$339$	940541.	+	940541.i	0.444507	+	0.444507i
$340$		0			0
$341$	10147.5	−	10147.5i	0.00472577	−	0.00472577i
$342$		0			0
$343$			2.37054e6i			1.08796i
$344$		0			0
$345$		−	1.09606e6i		−	0.495776i
$346$		0			0
$347$	−2.37371e6	+	2.37371e6i	−1.05829	+	1.05829i	−0.0600956	+	0.998193i	$0.519141\pi$
$347$	−2.37371e6	+	2.37371e6i	−1.05829	+	1.05829i	−0.998193	+	0.0600956i	$0.980859\pi$
$348$		0			0
$349$	−1.11045e6	−	1.11045e6i	−0.488017	−	0.488017i	0.419663	−	0.907680i	$-0.362148\pi$
$349$	−1.11045e6	−	1.11045e6i	−0.488017	−	0.488017i	−0.907680	+	0.419663i	$0.862148\pi$
$350$		0			0
$351$	1.13243e6			0.490619
$352$		0			0
$353$	4.02943e6			1.72110			0.860551	−	0.509365i	$-0.170120\pi$
$353$	4.02943e6			1.72110			0.860551	+	0.509365i	$0.170120\pi$
$354$		0			0
$355$	448774.	+	448774.i	0.188998	+	0.188998i
$356$		0			0
$357$	278326.	−	278326.i	0.115580	−	0.115580i
$358$		0			0
$359$			2.88668e6i			1.18212i	0.806626	+	0.591062i	$0.201291\pi$
$359$			2.88668e6i			1.18212i	−0.806626	+	0.591062i	$0.798709\pi$
$360$		0			0
$361$		−	2.04531e6i		−	0.826022i
$362$		0			0
$363$	1.57395e6	−	1.57395e6i	0.626938	−	0.626938i
$364$		0			0
$365$	437199.	+	437199.i	0.171770	+	0.171770i
$366$		0			0
$367$	1.53810e6			0.596100			0.298050	−	0.954550i	$-0.403664\pi$
$367$	1.53810e6			0.596100			0.298050	+	0.954550i	$0.403664\pi$
$368$		0			0
$369$	664958.			0.254231
$370$		0			0
$371$	294884.	+	294884.i	0.111228	+	0.111228i
$372$		0			0
$373$	665688.	−	665688.i	0.247741	−	0.247741i	−0.572302	−	0.820043i	$-0.693949\pi$
$373$	665688.	−	665688.i	0.247741	−	0.247741i	0.820043	+	0.572302i	$0.193949\pi$
$374$		0			0
$375$			215958.i			0.0793034i
$376$		0			0
$377$			1.42011e6i			0.514597i
$378$		0			0
$379$	−733269.	+	733269.i	−0.262220	+	0.262220i	−0.825955	−	0.563736i	$-0.809364\pi$
$379$	−733269.	+	733269.i	−0.262220	+	0.262220i	0.563736	+	0.825955i	$0.309364\pi$
$380$		0			0
$381$	−816019.	−	816019.i	−0.287997	−	0.287997i
$382$		0			0
$383$	2.45123e6			0.853863			0.426931	−	0.904284i	$-0.359595\pi$
$383$	2.45123e6			0.853863			0.426931	+	0.904284i	$0.359595\pi$
$384$		0			0
$385$	−4326.70			−0.00148766
$386$		0			0
$387$	107009.	+	107009.i	0.0363197	+	0.0363197i
$388$		0			0
$389$	1.54868e6	−	1.54868e6i	0.518906	−	0.518906i	−0.398334	−	0.917240i	$-0.630412\pi$
$389$	1.54868e6	−	1.54868e6i	0.518906	−	0.518906i	0.917240	+	0.398334i	$0.130412\pi$
$390$		0			0
$391$			871558.i			0.288307i
$392$		0			0
$393$			97539.1i			0.0318564i
$394$		0			0
$395$	−144610.	+	144610.i	−0.0466344	+	0.0466344i
$396$		0			0
$397$	552320.	+	552320.i	0.175879	+	0.175879i	0.789557	−	0.613678i	$-0.210311\pi$
$397$	552320.	+	552320.i	0.175879	+	0.175879i	−0.613678	+	0.789557i	$0.710311\pi$
$398$		0			0
$399$	940258.			0.295675
$400$		0			0
$401$	4.92193e6			1.52853			0.764266	−	0.644901i	$-0.223101\pi$
$401$	4.92193e6			1.52853			0.764266	+	0.644901i	$0.223101\pi$
$402$		0			0
$403$	1.68807e6	+	1.68807e6i	0.517760	+	0.517760i
$404$		0			0
$405$	772853.	−	772853.i	0.234131	−	0.234131i
$406$		0			0
$407$			12706.4i			0.00380221i
$408$		0			0
$409$			5.16304e6i			1.52615i	0.646311	+	0.763074i	$0.276311\pi$
$409$			5.16304e6i			1.52615i	−0.646311	+	0.763074i	$0.723689\pi$
$410$		0			0
$411$	−3.12157e6	+	3.12157e6i	−0.911526	+	0.911526i
$412$		0			0
$413$	1.66634e6	+	1.66634e6i	0.480716	+	0.480716i
$414$		0			0
$415$	2.60697e6			0.743046
$416$		0			0
$417$	−2.46303e6			−0.693633
$418$		0			0
$419$	−1.56043e6	−	1.56043e6i	−0.434219	−	0.434219i	0.455842	−	0.890061i	$-0.349338\pi$
$419$	−1.56043e6	−	1.56043e6i	−0.434219	−	0.434219i	−0.890061	+	0.455842i	$0.849338\pi$
$420$		0			0
$421$	−905154.	+	905154.i	−0.248896	+	0.248896i	−0.820517	−	0.571622i	$-0.806315\pi$
$421$	−905154.	+	905154.i	−0.248896	+	0.248896i	0.571622	+	0.820517i	$0.306315\pi$
$422$		0			0
$423$		−	998.883i		−	0.000271434i
$424$		0			0
$425$		−	171725.i		−	0.0461170i
$426$		0			0
$427$	−2.92657e6	+	2.92657e6i	−0.776764	+	0.776764i
$428$		0			0
$429$	−4532.82	−	4532.82i	−0.00118912	−	0.00118912i
$430$		0			0
$431$	1.58952e6			0.412168			0.206084	−	0.978534i	$-0.433928\pi$
$431$	1.58952e6			0.412168			0.206084	+	0.978534i	$0.433928\pi$
$432$		0			0
$433$	6.53092e6			1.67400			0.836998	−	0.547205i	$-0.184308\pi$
$433$	6.53092e6			1.67400			0.836998	+	0.547205i	$0.184308\pi$
$434$		0			0
$435$	1.24914e6	+	1.24914e6i	0.316512	+	0.316512i
$436$		0			0
$437$	−1.47218e6	+	1.47218e6i	−0.368771	+	0.368771i
$438$		0			0
$439$			2.38268e6i			0.590071i	0.955486	+	0.295036i	$0.0953315\pi$
$439$			2.38268e6i			0.590071i	−0.955486	+	0.295036i	$0.904669\pi$
$440$		0			0
$441$		−	315143.i		−	0.0771634i
$442$		0			0
$443$	32077.4	−	32077.4i	0.00776586	−	0.00776586i	−0.703213	−	0.710979i	$-0.748252\pi$
$443$	32077.4	−	32077.4i	0.00776586	−	0.00776586i	0.710979	+	0.703213i	$0.248252\pi$
$444$		0			0
$445$	549324.	+	549324.i	0.131501	+	0.131501i
$446$		0			0
$447$	2.49731e6			0.591158
$448$		0			0
$449$	4.51574e6			1.05709			0.528547	−	0.848904i	$-0.322737\pi$
$449$	4.51574e6			1.05709			0.528547	+	0.848904i	$0.322737\pi$
$450$		0			0
$451$	−15106.8	−	15106.8i	−0.00349728	−	0.00349728i
$452$		0			0
$453$	3.06365e6	−	3.06365e6i	0.701445	−	0.701445i
$454$		0			0
$455$		−	719762.i		−	0.162990i
$456$		0			0
$457$		−	1.27748e6i		−	0.286131i	−0.989713	−	0.143065i	$-0.954304\pi$
$457$		−	1.27748e6i		−	0.286131i	0.989713	−	0.143065i	$-0.0456959\pi$
$458$		0			0
$459$	−792076.	+	792076.i	−0.175483	+	0.175483i
$460$		0			0
$461$	−4.40915e6	−	4.40915e6i	−0.966279	−	0.966279i	0.0331708	−	0.999450i	$-0.489439\pi$
$461$	−4.40915e6	−	4.40915e6i	−0.966279	−	0.966279i	−0.999450	+	0.0331708i	$0.989439\pi$
$462$		0			0
$463$	4.01094e6			0.869548			0.434774	−	0.900540i	$-0.356828\pi$
$463$	4.01094e6			0.869548			0.434774	+	0.900540i	$0.356828\pi$
$464$		0			0
$465$	2.96970e6			0.636914
$466$		0			0
$467$	−2.22576e6	−	2.22576e6i	−0.472266	−	0.472266i	0.430381	−	0.902647i	$-0.358379\pi$
$467$	−2.22576e6	−	2.22576e6i	−0.472266	−	0.472266i	−0.902647	+	0.430381i	$0.858379\pi$
$468$		0			0
$469$	−4.32047e6	+	4.32047e6i	−0.906982	+	0.906982i
$470$		0			0
$471$		−	4.93054e6i		−	1.02410i
$472$		0			0
$473$		−	4862.13i		−	0.000999249i
$474$		0			0
$475$	290066.	−	290066.i	0.0589878	−	0.0589878i
$476$		0			0
$477$	−147858.	−	147858.i	−0.0297542	−	0.0297542i
$478$		0			0
$479$	−2.87342e6			−0.572216			−0.286108	−	0.958197i	$-0.592362\pi$
$479$	−2.87342e6			−0.572216			−0.286108	+	0.958197i	$0.592362\pi$
$480$		0			0
$481$	−2.11375e6			−0.416574
$482$		0			0
$483$	3.21325e6	+	3.21325e6i	0.626724	+	0.626724i
$484$		0			0
$485$	854178.	−	854178.i	0.164890	−	0.164890i
$486$		0			0
$487$			9.71226e6i			1.85566i	0.373007	+	0.927829i	$0.378327\pi$
$487$			9.71226e6i			1.85566i	−0.373007	+	0.927829i	$0.621673\pi$
$488$		0			0
$489$			5.52328e6i			1.04454i
$490$		0			0
$491$	−941766.	+	941766.i	−0.176295	+	0.176295i	−0.789738	−	0.613444i	$-0.789784\pi$
$491$	−941766.	+	941766.i	−0.176295	+	0.176295i	0.613444	+	0.789738i	$0.289784\pi$
$492$		0			0
$493$	−993289.	−	993289.i	−0.184060	−	0.184060i
$494$		0			0
$495$	2169.45			0.000397957
$496$		0			0
$497$	−2.63129e6			−0.477834
$498$		0			0
$499$	−1.63368e6	−	1.63368e6i	−0.293708	−	0.293708i	0.544835	−	0.838543i	$-0.316592\pi$
$499$	−1.63368e6	−	1.63368e6i	−0.293708	−	0.293708i	−0.838543	+	0.544835i	$0.816592\pi$
$500$		0			0
$501$	−514158.	+	514158.i	−0.0915171	+	0.0915171i
$502$		0			0
$503$		−	3.45939e6i		−	0.609649i	−0.952409	−	0.304825i	$-0.901402\pi$
$503$		−	3.45939e6i		−	0.609649i	0.952409	−	0.304825i	$-0.0985978\pi$
$504$		0			0
$505$			2.94253e6i			0.513443i
$506$		0			0
$507$	−2.87465e6	+	2.87465e6i	−0.496667	+	0.496667i
$508$		0			0
$509$	4.00462e6	+	4.00462e6i	0.685120	+	0.685120i	0.961149	−	0.276029i	$-0.0890186\pi$
$509$	4.00462e6	+	4.00462e6i	0.685120	+	0.685120i	−0.276029	+	0.961149i	$0.589019\pi$
$510$		0			0
$511$	−2.56342e6			−0.434278
$512$		0			0
$513$	−2.67584e6			−0.448918
$514$		0			0
$515$	−440747.	−	440747.i	−0.0732270	−	0.0732270i
$516$		0			0
$517$	−22.6930	+	22.6930i	−3.73392e−6	+	3.73392e-6i
$518$		0			0
$519$		−	1.05291e7i		−	1.71583i
$520$		0			0
$521$			3.26819e6i			0.527489i	0.964593	+	0.263744i	$0.0849575\pi$
$521$			3.26819e6i			0.527489i	−0.964593	+	0.263744i	$0.915042\pi$
$522$		0			0
$523$	−2.30613e6	+	2.30613e6i	−0.368662	+	0.368662i	−0.866989	−	0.498327i	$-0.833948\pi$
$523$	−2.30613e6	+	2.30613e6i	−0.368662	+	0.368662i	0.498327	+	0.866989i	$0.333948\pi$
$524$		0			0
$525$	−633112.	−	633112.i	−0.100250	−	0.100250i
$526$		0			0
$527$	−2.36143e6			−0.370382
$528$		0			0
$529$	−3.62572e6			−0.563320
$530$		0			0
$531$	−835520.	−	835520.i	−0.128594	−	0.128594i
$532$		0			0
$533$	2.51306e6	−	2.51306e6i	0.383165	−	0.383165i
$534$		0			0
$535$		−	3.06747e6i		−	0.463335i
$536$		0			0
$537$		−	3.81141e6i		−	0.570361i
$538$		0			0
$539$	−7159.53	+	7159.53i	−0.00106148	+	0.00106148i
$540$		0			0
$541$	−8.57389e6	−	8.57389e6i	−1.25946	−	1.25946i	−0.951350	−	0.308111i	$-0.900303\pi$
$541$	−8.57389e6	−	8.57389e6i	−1.25946	−	1.25946i	−0.308111	−	0.951350i	$-0.599697\pi$
$542$		0			0
$543$	8.16820e6			1.18885
$544$		0			0
$545$	3.83908e6			0.553651
$546$		0			0
$547$	552021.	+	552021.i	0.0788837	+	0.0788837i	0.745448	−	0.666564i	$-0.232236\pi$
$547$	552021.	+	552021.i	0.0788837	+	0.0788837i	−0.666564	+	0.745448i	$0.732236\pi$
$548$		0			0
$549$	1.46741e6	−	1.46741e6i	0.207788	−	0.207788i
$550$		0			0
$551$		−	3.35559e6i		−	0.470858i
$552$		0			0
$553$		−	847891.i		−	0.117904i
$554$		0			0
$555$	−1.85929e6	+	1.85929e6i	−0.256220	+	0.256220i
$556$		0			0
$557$	−8.78654e6	−	8.78654e6i	−1.20000	−	1.20000i	−0.974167	−	0.225829i	$-0.927491\pi$
$557$	−8.78654e6	−	8.78654e6i	−1.20000	−	1.20000i	−0.225829	−	0.974167i	$-0.572509\pi$
$558$		0			0
$559$	808833.			0.109479
$560$		0			0
$561$	6340.94			0.000850641
$562$		0			0
$563$	−971504.	−	971504.i	−0.129174	−	0.129174i	0.639564	−	0.768738i	$-0.279115\pi$
$563$	−971504.	−	971504.i	−0.129174	−	0.129174i	−0.768738	+	0.639564i	$0.779115\pi$
$564$		0			0
$565$	−1.70125e6	+	1.70125e6i	−0.224206	+	0.224206i
$566$		0			0
$567$			4.53145e6i			0.591943i
$568$		0			0
$569$			2.27634e6i			0.294752i	0.989081	+	0.147376i	$0.0470828\pi$
$569$			2.27634e6i			0.294752i	−0.989081	+	0.147376i	$0.952917\pi$
$570$		0			0
$571$	−8.52439e6	+	8.52439e6i	−1.09414	+	1.09414i	−0.0990592	+	0.995082i	$0.531583\pi$
$571$	−8.52439e6	+	8.52439e6i	−1.09414	+	1.09414i	−0.995082	+	0.0990592i	$0.968417\pi$
$572$		0			0
$573$	4.85800e6	+	4.85800e6i	0.618118	+	0.618118i
$574$		0			0
$575$	1.98255e6			0.250066
$576$		0			0
$577$	−1.05005e7			−1.31301			−0.656506	−	0.754321i	$-0.727966\pi$
$577$	−1.05005e7			−1.31301			−0.656506	+	0.754321i	$0.727966\pi$
$578$		0			0
$579$	−4.52040e6	−	4.52040e6i	−0.560377	−	0.560377i
$580$		0			0
$581$	−7.64270e6	+	7.64270e6i	−0.939304	+	0.939304i
$582$		0			0
$583$			6718.17i			0.000818615i
$584$		0			0
$585$			360896.i			0.0436006i
$586$		0			0
$587$	8.30426e6	−	8.30426e6i	0.994731	−	0.994731i	−0.00525489	−	0.999986i	$-0.501673\pi$
$587$	8.30426e6	−	8.30426e6i	0.994731	−	0.994731i	0.999986	+	0.00525489i	$0.00167269\pi$
$588$		0			0
$589$	−3.98877e6	−	3.98877e6i	−0.473752	−	0.473752i
$590$		0			0
$591$	−5.59617e6			−0.659056
$592$		0			0
$593$	1.25153e7			1.46152			0.730759	−	0.682635i	$-0.239166\pi$
$593$	1.25153e7			1.46152			0.730759	+	0.682635i	$0.239166\pi$
$594$		0			0
$595$	503435.	+	503435.i	0.0582977	+	0.0582977i
$596$		0			0
$597$	9.86958e6	−	9.86958e6i	1.13335	−	1.13335i
$598$		0			0
$599$		−	6.70362e6i		−	0.763383i	−0.924290	−	0.381691i	$-0.875342\pi$
$599$		−	6.70362e6i		−	0.763383i	0.924290	−	0.381691i	$-0.124658\pi$
$600$		0			0
$601$			5.33668e6i			0.602677i	0.953517	+	0.301339i	$0.0974335\pi$
$601$			5.33668e6i			0.602677i	−0.953517	+	0.301339i	$0.902567\pi$
$602$		0			0
$603$	2.16633e6	−	2.16633e6i	0.242622	−	0.242622i
$604$		0			0
$605$	2.84696e6	+	2.84696e6i	0.316222	+	0.316222i
$606$		0			0
$607$	−871941.			−0.0960540			−0.0480270	−	0.998846i	$-0.515293\pi$
$607$	−871941.			−0.0960540			−0.0480270	+	0.998846i	$0.515293\pi$
$608$		0			0
$609$	−7.32408e6			−0.800221
$610$		0			0
$611$	−3775.06	−	3775.06i	−0.000409092	−	0.000409092i
$612$		0			0
$613$	7.72342e6	−	7.72342e6i	0.830154	−	0.830154i	−0.157384	−	0.987537i	$-0.550306\pi$
$613$	7.72342e6	−	7.72342e6i	0.830154	−	0.830154i	0.987537	+	0.157384i	$0.0503060\pi$
$614$		0			0
$615$		−	4.42105e6i		−	0.471344i
$616$		0			0
$617$			644309.i			0.0681367i	0.999420	+	0.0340684i	$0.0108464\pi$
$617$			644309.i			0.0681367i	−0.999420	+	0.0340684i	$0.989154\pi$
$618$		0			0
$619$	1.08770e7	−	1.08770e7i	1.14099	−	1.14099i	0.152725	−	0.988269i	$-0.451195\pi$
$619$	1.08770e7	−	1.08770e7i	1.14099	−	1.14099i	0.988269	−	0.152725i	$-0.0488048\pi$
$620$		0			0
$621$	−9.14445e6	−	9.14445e6i	−0.951543	−	0.951543i
$622$		0			0
$623$	−3.22084e6			−0.332468
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	10710.7	+	10710.7i	0.00108805	+	0.00108805i
$628$		0			0
$629$	1.47846e6	−	1.47846e6i	0.148999	−	0.148999i
$630$		0			0
$631$		−	1.93042e6i		−	0.193010i	−0.995333	−	0.0965048i	$-0.969234\pi$
$631$		−	1.93042e6i		−	0.193010i	0.995333	−	0.0965048i	$-0.0307663\pi$
$632$		0			0
$633$			5.41990e6i			0.537628i
$634$		0			0
$635$	1.47601e6	−	1.47601e6i	0.145263	−	0.145263i
$636$		0			0
$637$	−1.19102e6	−	1.19102e6i	−0.116297	−	0.116297i
$638$		0			0
$639$	1.31935e6			0.127823
$640$		0			0
$641$	4.63206e6			0.445275			0.222638	−	0.974901i	$-0.428533\pi$
$641$	4.63206e6			0.445275			0.222638	+	0.974901i	$0.428533\pi$
$642$		0			0
$643$	8.05489e6	+	8.05489e6i	0.768303	+	0.768303i	0.977808	−	0.209505i	$-0.0671852\pi$
$643$	8.05489e6	+	8.05489e6i	0.768303	+	0.768303i	−0.209505	+	0.977808i	$0.567185\pi$
$644$		0			0
$645$	711460.	−	711460.i	0.0673366	−	0.0673366i
$646$		0			0
$647$		−	5.33268e6i		−	0.500824i	−0.968139	−	0.250412i	$-0.919434\pi$
$647$		−	5.33268e6i		−	0.500824i	0.968139	−	0.250412i	$-0.0805660\pi$
$648$		0			0
$649$			37963.3i			0.00353795i
$650$		0			0
$651$	−8.70610e6	+	8.70610e6i	−0.805139	+	0.805139i
$652$		0			0
$653$	316713.	+	316713.i	0.0290659	+	0.0290659i	0.721490	−	0.692424i	$-0.243457\pi$
$653$	316713.	+	316713.i	0.0290659	+	0.0290659i	−0.692424	+	0.721490i	$0.743457\pi$
$654$		0			0
$655$	−176428.			−0.0160681
$656$		0			0
$657$	1.28532e6			0.116171
$658$		0			0
$659$	−1.13480e7	−	1.13480e7i	−1.01790	−	1.01790i	−0.999837	−	0.0180657i	$-0.994249\pi$
$659$	−1.13480e7	−	1.13480e7i	−1.01790	−	1.01790i	−0.0180657	−	0.999837i	$-0.505751\pi$
$660$		0			0
$661$	−8.40738e6	+	8.40738e6i	−0.748440	+	0.748440i	−0.974186	−	0.225746i	$-0.927518\pi$
$661$	−8.40738e6	+	8.40738e6i	−0.748440	+	0.748440i	0.225746	+	0.974186i	$0.427518\pi$
$662$		0			0
$663$			1.05484e6i			0.0931971i
$664$		0			0
$665$			1.70074e6i			0.149136i
$666$		0			0
$667$	1.14674e7	−	1.14674e7i	0.998048	−	0.998048i
$668$		0			0
$669$	8.91699e6	+	8.91699e6i	0.770288	+	0.770288i
$670$		0			0
$671$	−66674.3			−0.00571679
$672$		0			0
$673$	−1.83364e7			−1.56054			−0.780272	−	0.625440i	$-0.784920\pi$
$673$	−1.83364e7			−1.56054			−0.780272	+	0.625440i	$0.784920\pi$
$674$		0			0
$675$	1.80175e6	+	1.80175e6i	0.152207	+	0.152207i
$676$		0			0
$677$	−1.19331e6	+	1.19331e6i	−0.100065	+	0.100065i	−0.755367	−	0.655302i	$-0.772541\pi$
$677$	−1.19331e6	+	1.19331e6i	−0.100065	+	0.100065i	0.655302	+	0.755367i	$0.272541\pi$
$678$		0			0
$679$			5.00828e6i			0.416883i
$680$		0			0
$681$			3.40092e6i			0.281015i
$682$		0			0
$683$	2.57827e6	−	2.57827e6i	0.211483	−	0.211483i	−0.593414	−	0.804897i	$-0.702220\pi$
$683$	2.57827e6	−	2.57827e6i	0.211483	−	0.211483i	0.804897	+	0.593414i	$0.202220\pi$
$684$		0			0
$685$	−5.64629e6	−	5.64629e6i	−0.459766	−	0.459766i
$686$		0			0
$687$	−1.65250e7			−1.33583
$688$		0			0
$689$	−1.11759e6			−0.0896882
$690$		0			0
$691$	−2.88279e6	−	2.88279e6i	−0.229678	−	0.229678i	0.582880	−	0.812558i	$-0.301926\pi$
$691$	−2.88279e6	−	2.88279e6i	−0.229678	−	0.229678i	−0.812558	+	0.582880i	$0.801926\pi$
$692$		0			0
$693$	−6360.04	+	6360.04i	−0.000503068	+	0.000503068i
$694$		0			0
$695$		−	4.45513e6i		−	0.349863i
$696$		0			0
$697$			3.51551e6i			0.274098i
$698$		0			0
$699$	−329785.	+	329785.i	−0.0255293	+	0.0255293i
$700$		0			0
$701$	−5.60275e6	−	5.60275e6i	−0.430632	−	0.430632i	0.458211	−	0.888843i	$-0.348490\pi$
$701$	−5.60275e6	−	5.60275e6i	−0.430632	−	0.430632i	−0.888843	+	0.458211i	$0.848490\pi$
$702$		0			0
$703$	4.99462e6			0.381166
$704$		0			0
$705$	−6641.19			−0.000503238
$706$		0			0
$707$	−8.62643e6	−	8.62643e6i	−0.649056	−	0.649056i
$708$		0			0
$709$	−1.35415e6	+	1.35415e6i	−0.101170	+	0.101170i	−0.755880	−	0.654710i	$-0.772791\pi$
$709$	−1.35415e6	+	1.35415e6i	−0.101170	+	0.101170i	0.654710	+	0.755880i	$0.272791\pi$
$710$		0			0
$711$			425141.i			0.0315398i
$712$		0			0
$713$		−	2.72625e7i		−	2.00836i
$714$		0			0
$715$	8198.96	−	8198.96i	0.000599782	−	0.000599782i
$716$		0			0
$717$	1.39661e7	+	1.39661e7i	1.01456	+	1.01456i
$718$		0			0
$719$	−2.32962e6			−0.168059			−0.0840297	−	0.996463i	$-0.526779\pi$
$719$	−2.32962e6			−0.168059			−0.0840297	+	0.996463i	$0.526779\pi$
$720$		0			0
$721$	2.58422e6			0.185136
$722$		0			0
$723$	3.78583e6	+	3.78583e6i	0.269349	+	0.269349i
$724$		0			0
$725$	−2.25945e6	+	2.25945e6i	−0.159646	+	0.159646i
$726$		0			0
$727$			7.09851e6i			0.498117i	0.968488	+	0.249058i	$0.0801211\pi$
$727$			7.09851e6i			0.498117i	−0.968488	+	0.249058i	$0.919879\pi$
$728$		0			0
$729$		−	1.59647e7i		−	1.11261i
$730$		0			0
$731$	−565736.	+	565736.i	−0.0391580	+	0.0391580i
$732$		0			0
$733$	−4.97014e6	−	4.97014e6i	−0.341672	−	0.341672i	0.515324	−	0.856995i	$-0.327672\pi$
$733$	−4.97014e6	−	4.97014e6i	−0.341672	−	0.341672i	−0.856995	+	0.515324i	$0.827672\pi$
$734$		0			0
$735$	−2.09527e6			−0.143061
$736$		0			0
$737$	−98430.8			−0.00667517
$738$		0			0
$739$	3.33606e6	+	3.33606e6i	0.224710	+	0.224710i	0.810478	−	0.585768i	$-0.199207\pi$
$739$	3.33606e6	+	3.33606e6i	0.224710	+	0.224710i	−0.585768	+	0.810478i	$0.699207\pi$
$740$		0			0
$741$	−1.78176e6	+	1.78176e6i	−0.119208	+	0.119208i
$742$		0			0
$743$			1.56473e7i			1.03985i	0.854213	+	0.519923i	$0.174039\pi$
$743$			1.56473e7i			1.03985i	−0.854213	+	0.519923i	$0.825961\pi$
$744$		0			0
$745$			4.51713e6i			0.298175i
$746$		0			0
$747$	3.83212e6	−	3.83212e6i	0.251268	−	0.251268i
$748$		0			0
$749$	8.99271e6	+	8.99271e6i	0.585714	+	0.585714i
$750$		0			0
$751$	−2.63215e7			−1.70298			−0.851491	−	0.524369i	$-0.824301\pi$
$751$	−2.63215e7			−1.70298			−0.851491	+	0.524369i	$0.824301\pi$
$752$		0			0
$753$	−2.95330e6			−0.189810
$754$		0			0
$755$	5.54152e6	+	5.54152e6i	0.353803	+	0.353803i
$756$		0			0
$757$	−6.68400e6	+	6.68400e6i	−0.423932	+	0.423932i	−0.886555	−	0.462623i	$-0.846908\pi$
$757$	−6.68400e6	+	6.68400e6i	−0.423932	+	0.423932i	0.462623	+	0.886555i	$0.346908\pi$
$758$		0			0
$759$			73205.6i			0.00461254i
$760$		0			0
$761$		−	2.40574e7i		−	1.50587i	−0.658096	−	0.752934i	$-0.728638\pi$
$761$		−	2.40574e7i		−	1.50587i	0.658096	−	0.752934i	$-0.271362\pi$
$762$		0			0
$763$	−1.12548e7	+	1.12548e7i	−0.699885	+	0.699885i
$764$		0			0
$765$	−252427.	−	252427.i	−0.0155949	−	0.0155949i
$766$		0			0
$767$	−6.31534e6			−0.387622
$768$		0			0
$769$	−4.66056e6			−0.284199			−0.142099	−	0.989852i	$-0.545385\pi$
$769$	−4.66056e6			−0.284199			−0.142099	+	0.989852i	$0.545385\pi$
$770$		0			0
$771$	1.08260e7	+	1.08260e7i	0.655890	+	0.655890i
$772$		0			0
$773$	5.41580e6	−	5.41580e6i	0.325997	−	0.325997i	−0.525065	−	0.851062i	$-0.675959\pi$
$773$	5.41580e6	−	5.41580e6i	0.325997	−	0.325997i	0.851062	+	0.525065i	$0.175959\pi$
$774$		0			0
$775$			5.37159e6i			0.321254i
$776$		0			0
$777$		−	1.09015e7i		−	0.647790i
$778$		0			0
$779$	−5.93816e6	+	5.93816e6i	−0.350597	+	0.350597i
$780$		0			0
$781$	−29973.5	−	29973.5i	−0.00175837	−	0.00175837i
$782$		0			0
$783$	2.08433e7			1.21496
$784$		0			0
$785$	8.91836e6			0.516548
$786$		0			0
$787$	−1.95136e7	−	1.95136e7i	−1.12306	−	1.12306i	−0.991279	−	0.131777i	$-0.957932\pi$
$787$	−1.95136e7	−	1.95136e7i	−1.12306	−	1.12306i	−0.131777	−	0.991279i	$-0.542068\pi$
$788$		0			0
$789$	1.62447e6	−	1.62447e6i	0.0929009	−	0.0929009i
$790$		0			0
$791$		−	9.97489e6i		−	0.566849i
$792$		0			0
$793$		−	1.10915e7i		−	0.626337i
$794$		0			0
$795$	−983049.	+	983049.i	−0.0551642	+	0.0551642i
$796$		0			0
$797$	4.44673e6	+	4.44673e6i	0.247968	+	0.247968i	0.820136	−	0.572168i	$-0.193898\pi$
$797$	4.44673e6	+	4.44673e6i	0.247968	+	0.247968i	−0.572168	+	0.820136i	$0.693898\pi$
$798$		0			0
$799$	5280.91			0.000292646
$800$		0			0
$801$	1.61496e6			0.0889367
$802$		0			0
$803$	−29200.5	−	29200.5i	−0.00159809	−	0.00159809i
$804$		0			0
$805$	−5.81211e6	+	5.81211e6i	−0.316115	+	0.316115i
$806$		0			0
$807$			2.36407e7i			1.27784i
$808$		0			0
$809$		−	2.99189e7i		−	1.60722i	−0.595158	−	0.803609i	$-0.702910\pi$
$809$		−	2.99189e7i		−	1.60722i	0.595158	−	0.803609i	$-0.297090\pi$
$810$		0			0
$811$	−2.42789e7	+	2.42789e7i	−1.29622	+	1.29622i	−0.365343	+	0.930873i	$0.619048\pi$
$811$	−2.42789e7	+	2.42789e7i	−1.29622	+	1.29622i	−0.930873	+	0.365343i	$0.880952\pi$
$812$		0			0
$813$	1.74448e7	+	1.74448e7i	0.925636	+	0.925636i
$814$		0			0
$815$	−9.99050e6			−0.526858
$816$		0			0
$817$	−1.91121e6			−0.100173
$818$		0			0
$819$	−1.05802e6	−	1.05802e6i	−0.0551166	−	0.0551166i
$820$		0			0
$821$	−1.14896e7	+	1.14896e7i	−0.594906	+	0.594906i	−0.938953	−	0.344047i	$-0.888202\pi$
$821$	−1.14896e7	+	1.14896e7i	−0.594906	+	0.594906i	0.344047	+	0.938953i	$0.388202\pi$
$822$		0			0
$823$			7.71299e6i			0.396938i	0.980107	+	0.198469i	$0.0635970\pi$
$823$			7.71299e6i			0.396938i	−0.980107	+	0.198469i	$0.936403\pi$
$824$		0			0
$825$		−	14423.8i		−	0.000737812i
$826$		0			0
$827$	2.71359e7	−	2.71359e7i	1.37969	−	1.37969i	0.534549	−	0.845138i	$-0.320482\pi$
$827$	2.71359e7	−	2.71359e7i	1.37969	−	1.37969i	0.845138	−	0.534549i	$-0.179518\pi$
$828$		0			0
$829$	2.12728e7	+	2.12728e7i	1.07507	+	1.07507i	0.996943	+	0.0781283i	$0.0248944\pi$
$829$	2.12728e7	+	2.12728e7i	1.07507	+	1.07507i	0.0781283	+	0.996943i	$0.475106\pi$
$830$		0			0
$831$	2.36782e7			1.18945
$832$		0			0
$833$	1.66610e6			0.0831935
$834$		0			0
$835$	−930008.	−	930008.i	−0.0461605	−	0.0461605i
$836$		0			0
$837$	2.47763e7	−	2.47763e7i	1.22243	−	1.22243i
$838$		0			0
$839$			1.96910e7i			0.965745i	0.875691	+	0.482873i	$0.160407\pi$
$839$			1.96910e7i			0.965745i	−0.875691	+	0.482873i	$0.839593\pi$
$840$		0			0
$841$			5.62703e6i			0.274340i
$842$		0			0
$843$	2.28123e7	−	2.28123e7i	1.10560	−	1.10560i
$844$		0			0
$845$	−5.19967e6	−	5.19967e6i	−0.250515	−	0.250515i
$846$		0			0
$847$	−1.66925e7			−0.799490
$848$		0			0
$849$	−2.85363e7			−1.35872
$850$		0			0
$851$	1.70687e7	+	1.70687e7i	0.807934	+	0.807934i
$852$		0			0
$853$	−9.12953e6	+	9.12953e6i	−0.429612	+	0.429612i	−0.888496	−	0.458884i	$-0.848249\pi$
$853$	−9.12953e6	+	9.12953e6i	−0.429612	+	0.429612i	0.458884	+	0.888496i	$0.348249\pi$
$854$		0			0
$855$		−	852766.i		−	0.0398947i
$856$		0			0
$857$			2.16457e7i			1.00674i	0.864070	+	0.503372i	$0.167907\pi$
$857$			2.16457e7i			1.00674i	−0.864070	+	0.503372i	$0.832093\pi$
$858$		0			0
$859$	−7.40375e6	+	7.40375e6i	−0.342349	+	0.342349i	−0.857250	−	0.514901i	$-0.827829\pi$
$859$	−7.40375e6	+	7.40375e6i	−0.342349	+	0.342349i	0.514901	+	0.857250i	$0.327829\pi$
$860$		0			0
$861$	1.29609e7	+	1.29609e7i	0.595838	+	0.595838i
$862$		0			0
$863$	−1.53905e7			−0.703438			−0.351719	−	0.936106i	$-0.614403\pi$
$863$	−1.53905e7			−0.703438			−0.351719	+	0.936106i	$0.614403\pi$
$864$		0			0
$865$	1.90450e7			0.865448
$866$		0			0
$867$	1.31387e7	+	1.31387e7i	0.593614	+	0.593614i
$868$		0			0
$869$	9658.51	−	9658.51i	0.000433871	−	0.000433871i
$870$		0			0
$871$		−	1.63743e7i		−	0.731338i
$872$		0			0
$873$		−	2.51120e6i		−	0.111518i
$874$		0			0
$875$	1.14517e6	−	1.14517e6i	0.0505651	−	0.0505651i
$876$		0			0
$877$	2.65611e7	+	2.65611e7i	1.16613	+	1.16613i	0.983109	+	0.183023i	$0.0585882\pi$
$877$	2.65611e7	+	2.65611e7i	1.16613	+	1.16613i	0.183023	+	0.983109i	$0.441412\pi$
$878$		0			0
$879$	5.24752e6			0.229077
$880$		0			0
$881$	1.79339e7			0.778457			0.389229	−	0.921141i	$-0.372742\pi$
$881$	1.79339e7			0.778457			0.389229	+	0.921141i	$0.372742\pi$
$882$		0			0
$883$	−1.62943e7	−	1.62943e7i	−0.703287	−	0.703287i	0.261827	−	0.965115i	$-0.415675\pi$
$883$	−1.62943e7	−	1.62943e7i	−0.703287	−	0.703287i	−0.965115	+	0.261827i	$0.915675\pi$
$884$		0			0
$885$	−5.55505e6	+	5.55505e6i	−0.238413	+	0.238413i
$886$		0			0
$887$			2.41655e7i			1.03131i	0.856798	+	0.515653i	$0.172451\pi$
$887$			2.41655e7i			1.03131i	−0.856798	+	0.515653i	$0.827549\pi$
$888$		0			0
$889$			8.65428e6i			0.367263i
$890$		0			0
$891$	−51618.8	+	51618.8i	−0.00217828	+	0.00217828i
$892$		0			0
$893$	8920.16	+	8920.16i	0.000374321	+	0.000374321i
$894$		0			0
$895$	6.89407e6			0.287685
$896$		0			0
$897$	−1.21780e7			−0.505354
$898$		0			0
$899$	3.10703e7	+	3.10703e7i	1.28217	+	1.28217i
$900$		0			0
$901$	781696.	−	781696.i	0.0320794	−	0.0320794i
$902$		0			0
$903$			4.17149e6i			0.170244i
$904$		0			0
$905$			1.47746e7i			0.599646i
$906$		0			0
$907$	2.80535e7	−	2.80535e7i	1.13232	−	1.13232i	0.142530	−	0.989791i	$-0.454476\pi$
$907$	2.80535e7	−	2.80535e7i	1.13232	−	1.13232i	0.989791	−	0.142530i	$-0.0455237\pi$
$908$		0			0
$909$	4.32538e6	+	4.32538e6i	0.173626	+	0.173626i
$910$		0			0
$911$	3.79892e7			1.51658			0.758288	−	0.651920i	$-0.226036\pi$
$911$	3.79892e7			1.51658			0.758288	+	0.651920i	$0.226036\pi$
$912$		0			0
$913$	−174119.			−0.00691305
$914$		0			0
$915$	−9.75625e6	−	9.75625e6i	−0.385239	−	0.385239i
$916$		0			0
$917$	517225.	−	517225.i	0.0203122	−	0.0203122i
$918$		0			0
$919$			2.68420e7i			1.04840i	0.851595	+	0.524200i	$0.175635\pi$
$919$			2.68420e7i			1.04840i	−0.851595	+	0.524200i	$0.824365\pi$
$920$		0			0
$921$			2.55817e7i			0.993755i
$922$		0			0
$923$	4.98621e6	−	4.98621e6i	0.192649	−	0.192649i
$924$		0			0
$925$	−3.36307e6	−	3.36307e6i	−0.129236	−	0.129236i
$926$		0			0
$927$	−1.29575e6			−0.0495249
$928$		0			0
$929$	3.48868e6			0.132624			0.0663120	−	0.997799i	$-0.478877\pi$
$929$	3.48868e6			0.132624			0.0663120	+	0.997799i	$0.478877\pi$
$930$		0			0
$931$	2.81427e6	+	2.81427e6i	0.106412	+	0.106412i
$932$		0			0
$933$	−2.99815e7	+	2.99815e7i	−1.12758	+	1.12758i
$934$		0			0
$935$			11469.5i			0.000429057i
$936$		0			0
$937$			3.53133e6i			0.131398i	0.997839	+	0.0656990i	$0.0209277\pi$
$937$			3.53133e6i			0.131398i	−0.997839	+	0.0656990i	$0.979072\pi$
$938$		0			0
$939$	2.22279e7	−	2.22279e7i	0.822688	−	0.822688i
$940$		0			0
$941$	−8.19988e6	−	8.19988e6i	−0.301879	−	0.301879i	0.539870	−	0.841749i	$-0.318474\pi$
$941$	−8.19988e6	−	8.19988e6i	−0.301879	−	0.301879i	−0.841749	+	0.539870i	$0.818474\pi$
$942$		0			0
$943$	−4.05863e7			−1.48628
$944$		0			0
$945$	−1.05641e7			−0.384818
$946$		0			0
$947$	1.46571e7	+	1.46571e7i	0.531096	+	0.531096i	0.920898	−	0.389803i	$-0.127457\pi$
$947$	1.46571e7	+	1.46571e7i	0.531096	+	0.531096i	−0.389803	+	0.920898i	$0.627457\pi$
$948$		0			0
$949$	4.85761e6	−	4.85761e6i	0.175088	−	0.175088i
$950$		0			0
$951$		−	4.78503e7i		−	1.71567i
$952$		0			0
$953$			2.06766e7i			0.737474i	0.929534	+	0.368737i	$0.120210\pi$
$953$			2.06766e7i			0.737474i	−0.929534	+	0.368737i	$0.879790\pi$
$954$		0			0
$955$	−8.78714e6	+	8.78714e6i	−0.311774	+	0.311774i
$956$		0			0
$957$	−83430.2	−	83430.2i	−0.00294472	−	0.00294472i
$958$		0			0
$959$	3.31058e7			1.16241
$960$		0			0
$961$	4.52371e7			1.58010
$962$		0			0
$963$	−4.50903e6	−	4.50903e6i	−0.156681	−	0.156681i
$964$		0			0
$965$	8.17649e6	−	8.17649e6i	0.282650	−	0.282650i
$966$		0			0
$967$			2.80312e7i			0.963998i	0.876172	+	0.481999i	$0.160089\pi$
$967$			2.80312e7i			0.963998i	−0.876172	+	0.481999i	$0.839911\pi$
$968$		0			0
$969$		−	2.49250e6i		−	0.0852757i
$970$		0			0
$971$	2.48615e7	−	2.48615e7i	0.846214	−	0.846214i	−0.143445	−	0.989658i	$-0.545818\pi$
$971$	2.48615e7	−	2.48615e7i	0.846214	−	0.846214i	0.989658	+	0.143445i	$0.0458179\pi$
$972$		0			0
$973$	1.30608e7	+	1.30608e7i	0.442271	+	0.442271i
$974$		0			0
$975$	2.39946e6			0.0808354
$976$		0			0
$977$	−4.94994e7			−1.65906			−0.829532	−	0.558459i	$-0.811393\pi$
$977$	−4.94994e7			−1.65906			−0.829532	+	0.558459i	$0.811393\pi$
$978$		0			0
$979$	−36689.3	−	36689.3i	−0.00122344	−	0.00122344i
$980$		0			0
$981$	5.64327e6	−	5.64327e6i	0.187223	−	0.187223i
$982$		0			0
$983$		−	3.48169e7i		−	1.14923i	−0.818424	−	0.574615i	$-0.805152\pi$
$983$		−	3.48169e7i		−	1.14923i	0.818424	−	0.574615i	$-0.194848\pi$
$984$		0			0
$985$		−	1.01223e7i		−	0.332422i
$986$		0			0
$987$	19469.6	−	19469.6i	0.000636156	−	0.000636156i
$988$		0			0
$989$	−6.53137e6	−	6.53137e6i	−0.212331	−	0.212331i
$990$		0			0
$991$	−1.18705e7			−0.383959			−0.191979	−	0.981399i	$-0.561491\pi$
$991$	−1.18705e7			−0.383959			−0.191979	+	0.981399i	$0.561491\pi$
$992$		0			0
$993$	1.53799e7			0.494972
$994$		0			0
$995$	1.78521e7	+	1.78521e7i	0.571651	+	0.571651i
$996$		0			0
$997$	−8.43454e6	+	8.43454e6i	−0.268735	+	0.268735i	−0.828590	−	0.559856i	$-0.810857\pi$
$997$	−8.43454e6	+	8.43454e6i	−0.268735	+	0.268735i	0.559856	+	0.828590i	$0.310857\pi$
$998$		0			0
$999$			3.10242e7i			0.983527i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.12		80
4.3	odd	2		80.6.l.a.61.4	yes	80
16.5	even	4	inner	320.6.l.a.241.12		80
16.11	odd	4		80.6.l.a.21.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.4	✓	80	16.11	odd	4
80.6.l.a.61.4	yes	80	4.3	odd	2
320.6.l.a.81.12		80	1.1	even	1	trivial
320.6.l.a.241.12		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)

\(f(q)\)	\(=\)	\(q+(-9.77316 - 9.77316i) q^{3} +(17.6777 - 17.6777i) q^{5} +103.649i q^{7} -51.9707i q^{9} +O(q^{10})\)	\(q+(-9.77316 - 9.77316i) q^{3} +(17.6777 - 17.6777i) q^{5} +103.649i q^{7} -51.9707i q^{9} +(-1.18069 + 1.18069i) q^{11} +(-196.412 - 196.412i) q^{13} -345.533 q^{15} +274.760 q^{17} +(464.105 + 464.105i) q^{19} +(1012.98 - 1012.98i) q^{21} +3172.08i q^{23} -625.000i q^{25} +(-2882.80 + 2882.80i) q^{27} +(-3615.12 - 3615.12i) q^{29} -8594.55 q^{31} +23.0781 q^{33} +(1832.27 + 1832.27i) q^{35} +(5380.92 - 5380.92i) q^{37} +3839.13i q^{39} +12794.9i q^{41} +(-2059.02 + 2059.02i) q^{43} +(-918.721 - 918.721i) q^{45} +19.2201 q^{47} +6063.86 q^{49} +(-2685.27 - 2685.27i) q^{51} +(2845.02 - 2845.02i) q^{53} +41.7437i q^{55} -9071.55i q^{57} +(16076.8 - 16076.8i) q^{59} +(28235.3 + 28235.3i) q^{61} +5386.72 q^{63} -6944.22 q^{65} +(41683.6 + 41683.6i) q^{67} +(31001.2 - 31001.2i) q^{69} +25386.5i q^{71} +24731.7i q^{73} +(-6108.22 + 6108.22i) q^{75} +(-122.377 - 122.377i) q^{77} -8180.40 q^{79} +43719.2 q^{81} +(73736.2 + 73736.2i) q^{83} +(4857.11 - 4857.11i) q^{85} +70662.3i q^{87} +31074.5i q^{89} +(20357.9 - 20357.9i) q^{91} +(83995.9 + 83995.9i) q^{93} +16408.6 q^{95} +48319.6 q^{97} +(61.3613 + 61.3613i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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

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Database

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