LMFDB - Embedded newform 320.6.l.a.81.16

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			81.16
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.24643 - 4.24643i) q^{3} +(17.6777 - 17.6777i) q^{5} -137.329i q^{7} -206.936i q^{9} +O(q^{10})$	\(q+(-4.24643 - 4.24643i) q^{3} +(17.6777 - 17.6777i) q^{5} -137.329i q^{7} -206.936i q^{9} +(315.189 - 315.189i) q^{11} +(792.347 + 792.347i) q^{13} -150.134 q^{15} +1386.22 q^{17} +(213.599 + 213.599i) q^{19} +(-583.156 + 583.156i) q^{21} -1980.52i q^{23} -625.000i q^{25} +(-1910.62 + 1910.62i) q^{27} +(350.393 + 350.393i) q^{29} -6031.52 q^{31} -2676.85 q^{33} +(-2427.65 - 2427.65i) q^{35} +(7587.17 - 7587.17i) q^{37} -6729.29i q^{39} +19441.6i q^{41} +(6074.63 - 6074.63i) q^{43} +(-3658.14 - 3658.14i) q^{45} +23379.1 q^{47} -2052.12 q^{49} +(-5886.49 - 5886.49i) q^{51} +(-15678.0 + 15678.0i) q^{53} -11143.6i q^{55} -1814.07i q^{57} +(24668.2 - 24668.2i) q^{59} +(-6270.63 - 6270.63i) q^{61} -28418.2 q^{63} +28013.7 q^{65} +(-30087.1 - 30087.1i) q^{67} +(-8410.15 + 8410.15i) q^{69} -3064.41i q^{71} -58592.3i q^{73} +(-2654.02 + 2654.02i) q^{75} +(-43284.4 - 43284.4i) q^{77} +1015.01 q^{79} -34058.8 q^{81} +(-42673.4 - 42673.4i) q^{83} +(24505.2 - 24505.2i) q^{85} -2975.84i q^{87} -64493.5i q^{89} +(108812. - 108812. i) q^{91} +(25612.4 + 25612.4i) q^{93} +7551.87 q^{95} -67308.7 q^{97} +(-65223.8 - 65223.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−4.24643	−	4.24643i	−0.272408	−	0.272408i	0.557661	−	0.830069i	$-0.311699\pi$
$3$	−4.24643	−	4.24643i	−0.272408	−	0.272408i	−0.830069	+	0.557661i	$0.811699\pi$
$4$		0			0
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$		0			0
$7$		−	137.329i		−	1.05929i	−0.848219	−	0.529646i	$-0.822325\pi$
$7$		−	137.329i		−	1.05929i	0.848219	−	0.529646i	$-0.177675\pi$
$8$		0			0
$9$		−	206.936i		−	0.851587i
$10$		0			0
$11$	315.189	−	315.189i	0.785397	−	0.785397i	−0.195339	−	0.980736i	$-0.562581\pi$
$11$	315.189	−	315.189i	0.785397	−	0.785397i	0.980736	+	0.195339i	$0.0625807\pi$
$12$		0			0
$13$	792.347	+	792.347i	1.30034	+	1.30034i	0.928161	+	0.372179i	$0.121389\pi$
$13$	792.347	+	792.347i	1.30034	+	1.30034i	0.372179	+	0.928161i	$0.378611\pi$
$14$		0			0
$15$	−150.134			−0.172286
$16$		0			0
$17$	1386.22			1.16335			0.581675	−	0.813421i	$-0.302397\pi$
$17$	1386.22			1.16335			0.581675	+	0.813421i	$0.302397\pi$
$18$		0			0
$19$	213.599	+	213.599i	0.135742	+	0.135742i	0.771713	−	0.635971i	$-0.219400\pi$
$19$	213.599	+	213.599i	0.135742	+	0.135742i	−0.635971	+	0.771713i	$0.719400\pi$
$20$		0			0
$21$	−583.156	+	583.156i	−0.288560	+	0.288560i
$22$		0			0
$23$		−	1980.52i		−	0.780657i	−0.920676	−	0.390329i	$-0.872361\pi$
$23$		−	1980.52i		−	0.780657i	0.920676	−	0.390329i	$-0.127639\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	−1910.62	+	1910.62i	−0.504388	+	0.504388i
$28$		0			0
$29$	350.393	+	350.393i	0.0773679	+	0.0773679i	0.744732	−	0.667364i	$-0.232577\pi$
$29$	350.393	+	350.393i	0.0773679	+	0.0773679i	−0.667364	+	0.744732i	$0.732577\pi$
$30$		0			0
$31$	−6031.52			−1.12726			−0.563628	−	0.826029i	$-0.690595\pi$
$31$	−6031.52			−1.12726			−0.563628	+	0.826029i	$0.690595\pi$
$32$		0			0
$33$	−2676.85			−0.427897
$34$		0			0
$35$	−2427.65	−	2427.65i	−0.334977	−	0.334977i
$36$		0			0
$37$	7587.17	−	7587.17i	0.911120	−	0.911120i	−0.0852401	−	0.996360i	$-0.527166\pi$
$37$	7587.17	−	7587.17i	0.911120	−	0.911120i	0.996360	+	0.0852401i	$0.0271657\pi$
$38$		0			0
$39$		−	6729.29i		−	0.708447i
$40$		0			0
$41$			19441.6i			1.80622i	0.429405	+	0.903112i	$0.358723\pi$
$41$			19441.6i			1.80622i	−0.429405	+	0.903112i	$0.641277\pi$
$42$		0			0
$43$	6074.63	−	6074.63i	0.501013	−	0.501013i	−0.410740	−	0.911753i	$-0.634730\pi$
$43$	6074.63	−	6074.63i	0.501013	−	0.501013i	0.911753	+	0.410740i	$0.134730\pi$
$44$		0			0
$45$	−3658.14	−	3658.14i	−0.269296	−	0.269296i
$46$		0			0
$47$	23379.1			1.54377			0.771885	−	0.635762i	$-0.219314\pi$
$47$	23379.1			1.54377			0.771885	+	0.635762i	$0.219314\pi$
$48$		0			0
$49$	−2052.12			−0.122099
$50$		0			0
$51$	−5886.49	−	5886.49i	−0.316907	−	0.316907i
$52$		0			0
$53$	−15678.0	+	15678.0i	−0.766656	+	0.766656i	−0.977516	−	0.210860i	$-0.932374\pi$
$53$	−15678.0	+	15678.0i	−0.766656	+	0.766656i	0.210860	+	0.977516i	$0.432374\pi$
$54$		0			0
$55$		−	11143.6i		−	0.496728i
$56$		0			0
$57$		−	1814.07i		−	0.0739548i
$58$		0			0
$59$	24668.2	−	24668.2i	0.922588	−	0.922588i	−0.0746242	−	0.997212i	$-0.523776\pi$
$59$	24668.2	−	24668.2i	0.922588	−	0.922588i	0.997212	+	0.0746242i	$0.0237757\pi$
$60$		0			0
$61$	−6270.63	−	6270.63i	−0.215768	−	0.215768i	0.590944	−	0.806712i	$-0.298755\pi$
$61$	−6270.63	−	6270.63i	−0.215768	−	0.215768i	−0.806712	+	0.590944i	$0.798755\pi$
$62$		0			0
$63$	−28418.2			−0.902079
$64$		0			0
$65$	28013.7			0.822407
$66$		0			0
$67$	−30087.1	−	30087.1i	−0.818829	−	0.818829i	0.167110	−	0.985938i	$-0.446557\pi$
$67$	−30087.1	−	30087.1i	−0.818829	−	0.818829i	−0.985938	+	0.167110i	$0.946557\pi$
$68$		0			0
$69$	−8410.15	+	8410.15i	−0.212658	+	0.212658i
$70$		0			0
$71$		−	3064.41i		−	0.0721441i	−0.999349	−	0.0360721i	$-0.988515\pi$
$71$		−	3064.41i		−	0.0721441i	0.999349	−	0.0360721i	$-0.0114846\pi$
$72$		0			0
$73$		−	58592.3i		−	1.28687i	−0.765502	−	0.643433i	$-0.777509\pi$
$73$		−	58592.3i		−	1.28687i	0.765502	−	0.643433i	$-0.222491\pi$
$74$		0			0
$75$	−2654.02	+	2654.02i	−0.0544817	+	0.0544817i
$76$		0			0
$77$	−43284.4	−	43284.4i	−0.831964	−	0.831964i
$78$		0			0
$79$	1015.01			0.0182979			0.00914895	−	0.999958i	$-0.497088\pi$
$79$	1015.01			0.0182979			0.00914895	+	0.999958i	$0.497088\pi$
$80$		0			0
$81$	−34058.8			−0.576788
$82$		0			0
$83$	−42673.4	−	42673.4i	−0.679927	−	0.679927i	0.280057	−	0.959983i	$-0.409647\pi$
$83$	−42673.4	−	42673.4i	−0.679927	−	0.679927i	−0.959983	+	0.280057i	$0.909647\pi$
$84$		0			0
$85$	24505.2	−	24505.2i	0.367884	−	0.367884i
$86$		0			0
$87$		−	2975.84i		−	0.0421514i
$88$		0			0
$89$		−	64493.5i		−	0.863060i	−0.902099	−	0.431530i	$-0.857974\pi$
$89$		−	64493.5i		−	0.863060i	0.902099	−	0.431530i	$-0.142026\pi$
$90$		0			0
$91$	108812.	−	108812.i	1.37744	−	1.37744i
$92$		0			0
$93$	25612.4	+	25612.4i	0.307074	+	0.307074i
$94$		0			0
$95$	7551.87			0.0858510
$96$		0			0
$97$	−67308.7			−0.726343			−0.363172	−	0.931722i	$-0.618306\pi$
$97$	−67308.7			−0.726343			−0.363172	+	0.931722i	$0.618306\pi$
$98$		0			0
$99$	−65223.8	−	65223.8i	−0.668834	−	0.668834i
$100$		0			0
$101$	125484.	−	125484.i	1.22401	−	1.22401i	0.257814	−	0.966194i	$-0.416998\pi$
$101$	125484.	−	125484.i	1.22401	−	1.22401i	0.966194	−	0.257814i	$-0.0830023\pi$
$102$		0			0
$103$			149518.i			1.38868i	0.719649	+	0.694338i	$0.244303\pi$
$103$			149518.i			1.38868i	−0.719649	+	0.694338i	$0.755697\pi$
$104$		0			0
$105$			20617.7i			0.182501i
$106$		0			0
$107$	−114525.	+	114525.i	−0.967032	+	0.967032i	−0.999474	−	0.0324416i	$-0.989672\pi$
$107$	−114525.	+	114525.i	−0.967032	+	0.967032i	0.0324416	+	0.999474i	$0.489672\pi$
$108$		0			0
$109$	−3991.99	−	3991.99i	−0.0321827	−	0.0321827i	0.690832	−	0.723015i	$-0.257244\pi$
$109$	−3991.99	−	3991.99i	−0.0321827	−	0.0321827i	−0.723015	+	0.690832i	$0.757244\pi$
$110$		0			0
$111$	−64436.8			−0.496394
$112$		0			0
$113$	−155317.			−1.14425			−0.572126	−	0.820166i	$-0.693881\pi$
$113$	−155317.			−1.14425			−0.572126	+	0.820166i	$0.693881\pi$
$114$		0			0
$115$	−35011.0	−	35011.0i	−0.246865	−	0.246865i
$116$		0			0
$117$	163965.	−	163965.i	1.10735	−	1.10735i
$118$		0			0
$119$		−	190368.i		−	1.23233i
$120$		0			0
$121$		−	37637.0i		−	0.233696i
$122$		0			0
$123$	82557.2	−	82557.2i	0.492031	−	0.492031i
$124$		0			0
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−168582.			−0.927472			−0.463736	−	0.885973i	$-0.653491\pi$
$127$	−168582.			−0.927472			−0.463736	+	0.885973i	$0.653491\pi$
$128$		0			0
$129$	−51591.0			−0.272960
$130$		0			0
$131$	144916.	+	144916.i	0.737801	+	0.737801i	0.972152	−	0.234351i	$-0.0752966\pi$
$131$	144916.	+	144916.i	0.737801	+	0.737801i	−0.234351	+	0.972152i	$0.575297\pi$
$132$		0			0
$133$	29333.3	−	29333.3i	0.143791	−	0.143791i
$134$		0			0
$135$			67550.6i			0.319003i
$136$		0			0
$137$		−	143106.i		−	0.651411i	−0.945471	−	0.325706i	$-0.894398\pi$
$137$		−	143106.i		−	0.651411i	0.945471	−	0.325706i	$-0.105602\pi$
$138$		0			0
$139$	18067.7	−	18067.7i	0.0793171	−	0.0793171i	−0.666335	−	0.745652i	$-0.732138\pi$
$139$	18067.7	−	18067.7i	0.0793171	−	0.0793171i	0.745652	+	0.666335i	$0.232138\pi$
$140$		0			0
$141$	−99277.5	−	99277.5i	−0.420536	−	0.420536i
$142$		0			0
$143$	499478.			2.04257
$144$		0			0
$145$	12388.3			0.0489318
$146$		0			0
$147$	8714.18	+	8714.18i	0.0332608	+	0.0332608i
$148$		0			0
$149$	30872.6	−	30872.6i	0.113922	−	0.113922i	−0.647848	−	0.761770i	$-0.724331\pi$
$149$	30872.6	−	30872.6i	0.113922	−	0.113922i	0.761770	+	0.647848i	$0.224331\pi$
$150$		0			0
$151$			172996.i			0.617440i	0.951153	+	0.308720i	$0.0999006\pi$
$151$			172996.i			0.617440i	−0.951153	+	0.308720i	$0.900099\pi$
$152$		0			0
$153$		−	286859.i		−	0.990694i
$154$		0			0
$155$	−106623.	+	106623.i	−0.356470	+	0.356470i
$156$		0			0
$157$	290080.	+	290080.i	0.939221	+	0.939221i	0.998256	−	0.0590346i	$-0.0188022\pi$
$157$	290080.	+	290080.i	0.939221	+	0.939221i	−0.0590346	+	0.998256i	$0.518802\pi$
$158$		0			0
$159$	133151.			0.417687
$160$		0			0
$161$	−271982.			−0.826944
$162$		0			0
$163$	−388139.	−	388139.i	−1.14424	−	1.14424i	−0.987666	−	0.156576i	$-0.949954\pi$
$163$	−388139.	−	388139.i	−1.14424	−	1.14424i	−0.156576	−	0.987666i	$-0.550046\pi$
$164$		0			0
$165$	−47320.5	+	47320.5i	−0.135313	+	0.135313i
$166$		0			0
$167$			350253.i			0.971830i	0.874006	+	0.485915i	$0.161513\pi$
$167$			350253.i			0.971830i	−0.874006	+	0.485915i	$0.838487\pi$
$168$		0			0
$169$			884334.i			2.38177i
$170$		0			0
$171$	44201.3	−	44201.3i	0.115597	−	0.115597i
$172$		0			0
$173$	−248040.	−	248040.i	−0.630095	−	0.630095i	0.317997	−	0.948092i	$-0.396990\pi$
$173$	−248040.	−	248040.i	−0.630095	−	0.630095i	−0.948092	+	0.317997i	$0.896990\pi$
$174$		0			0
$175$	−85830.3			−0.211858
$176$		0			0
$177$	−209504.			−0.502641
$178$		0			0
$179$	−401546.	−	401546.i	−0.936704	−	0.936704i	0.0614083	−	0.998113i	$-0.480441\pi$
$179$	−401546.	−	401546.i	−0.936704	−	0.936704i	−0.998113	+	0.0614083i	$0.980441\pi$
$180$		0			0
$181$	155467.	−	155467.i	0.352730	−	0.352730i	−0.508394	−	0.861124i	$-0.669761\pi$
$181$	155467.	−	155467.i	0.352730	−	0.352730i	0.861124	+	0.508394i	$0.169761\pi$
$182$		0			0
$183$			53255.6i			0.117554i
$184$		0			0
$185$		−	268247.i		−	0.576243i
$186$		0			0
$187$	436922.	−	436922.i	0.913692	−	0.913692i
$188$		0			0
$189$	262383.	+	262383.i	0.534294	+	0.534294i
$190$		0			0
$191$	536221.			1.06356			0.531778	−	0.846884i	$-0.321524\pi$
$191$	536221.			1.06356			0.531778	+	0.846884i	$0.321524\pi$
$192$		0			0
$193$	−482705.			−0.932801			−0.466400	−	0.884574i	$-0.654449\pi$
$193$	−482705.			−0.932801			−0.466400	+	0.884574i	$0.654449\pi$
$194$		0			0
$195$	−118958.	−	118958.i	−0.224031	−	0.224031i
$196$		0			0
$197$	69715.5	−	69715.5i	0.127986	−	0.127986i	−0.640212	−	0.768198i	$-0.721153\pi$
$197$	69715.5	−	69715.5i	0.127986	−	0.127986i	0.768198	+	0.640212i	$0.221153\pi$
$198$		0			0
$199$			625225.i			1.11919i	0.828767	+	0.559594i	$0.189043\pi$
$199$			625225.i			1.11919i	−0.828767	+	0.559594i	$0.810957\pi$
$200$		0			0
$201$			255525.i			0.446112i
$202$		0			0
$203$	48119.0	−	48119.0i	0.0819552	−	0.0819552i
$204$		0			0
$205$	343682.	+	343682.i	0.571178	+	0.571178i
$206$		0			0
$207$	−409841.			−0.664798
$208$		0			0
$209$	134648.			0.213223
$210$		0			0
$211$	44496.7	+	44496.7i	0.0688053	+	0.0688053i	0.740672	−	0.671867i	$-0.234507\pi$
$211$	44496.7	+	44496.7i	0.0688053	+	0.0688053i	−0.671867	+	0.740672i	$0.734507\pi$
$212$		0			0
$213$	−13012.8	+	13012.8i	−0.0196527	+	0.0196527i
$214$		0			0
$215$		−	214771.i		−	0.316868i
$216$		0			0
$217$			828300.i			1.19409i
$218$		0			0
$219$	−248808.	+	248808.i	−0.350553	+	0.350553i
$220$		0			0
$221$	1.09837e6	+	1.09837e6i	1.51275	+	1.51275i
$222$		0			0
$223$	−117924.			−0.158796			−0.0793981	−	0.996843i	$-0.525300\pi$
$223$	−117924.			−0.158796			−0.0793981	+	0.996843i	$0.525300\pi$
$224$		0			0
$225$	−129335.			−0.170317
$226$		0			0
$227$	120545.	+	120545.i	0.155269	+	0.155269i	0.780466	−	0.625198i	$-0.214982\pi$
$227$	120545.	+	120545.i	0.155269	+	0.155269i	−0.625198	+	0.780466i	$0.714982\pi$
$228$		0			0
$229$	177413.	−	177413.i	0.223562	−	0.223562i	−0.586435	−	0.809996i	$-0.699469\pi$
$229$	177413.	−	177413.i	0.223562	−	0.223562i	0.809996	+	0.586435i	$0.199469\pi$
$230$		0			0
$231$			367608.i			0.453268i
$232$		0			0
$233$			284456.i			0.343261i	0.985161	+	0.171631i	$0.0549036\pi$
$233$			284456.i			0.343261i	−0.985161	+	0.171631i	$0.945096\pi$
$234$		0			0
$235$	413287.	−	413287.i	0.488183	−	0.488183i
$236$		0			0
$237$	−4310.15	−	4310.15i	−0.00498450	−	0.00498450i
$238$		0			0
$239$	−1.06599e6			−1.20714			−0.603571	−	0.797309i	$-0.706256\pi$
$239$	−1.06599e6			−1.20714			−0.603571	+	0.797309i	$0.706256\pi$
$240$		0			0
$241$	454086.			0.503611			0.251806	−	0.967778i	$-0.418976\pi$
$241$	454086.			0.503611			0.251806	+	0.967778i	$0.418976\pi$
$242$		0			0
$243$	608909.	+	608909.i	0.661510	+	0.661510i
$244$		0			0
$245$	−36276.7	+	36276.7i	−0.0386111	+	0.0386111i
$246$		0			0
$247$			338489.i			0.353023i
$248$		0			0
$249$			362419.i			0.370436i
$250$		0			0
$251$	−266159.	+	266159.i	−0.266659	+	0.266659i	−0.827753	−	0.561093i	$-0.810381\pi$
$251$	−266159.	+	266159.i	−0.266659	+	0.266659i	0.561093	+	0.827753i	$0.310381\pi$
$252$		0			0
$253$	−624239.	−	624239.i	−0.613126	−	0.613126i
$254$		0			0
$255$	−208119.			−0.200429
$256$		0			0
$257$	−1.49252e6			−1.40957			−0.704786	−	0.709420i	$-0.748957\pi$
$257$	−1.49252e6			−1.40957			−0.704786	+	0.709420i	$0.748957\pi$
$258$		0			0
$259$	−1.04194e6	−	1.04194e6i	−0.965142	−	0.965142i
$260$		0			0
$261$	72508.9	−	72508.9i	0.0658855	−	0.0658855i
$262$		0			0
$263$			1.64932e6i			1.47033i	0.677887	+	0.735166i	$0.262896\pi$
$263$			1.64932e6i			1.47033i	−0.677887	+	0.735166i	$0.737104\pi$
$264$		0			0
$265$			554300.i			0.484876i
$266$		0			0
$267$	−273867.	+	273867.i	−0.235105	+	0.235105i
$268$		0			0
$269$	1.22243e6	+	1.22243e6i	1.03002	+	1.03002i	0.999535	+	0.0304819i	$0.00970418\pi$
$269$	1.22243e6	+	1.22243e6i	1.03002	+	1.03002i	0.0304819	+	0.999535i	$0.490296\pi$
$270$		0			0
$271$	1.56240e6			1.29231			0.646157	−	0.763204i	$-0.276375\pi$
$271$	1.56240e6			1.29231			0.646157	+	0.763204i	$0.276375\pi$
$272$		0			0
$273$	−924123.			−0.750452
$274$		0			0
$275$	−196993.	−	196993.i	−0.157079	−	0.157079i
$276$		0			0
$277$	728039.	−	728039.i	0.570105	−	0.570105i	−0.362052	−	0.932158i	$-0.617924\pi$
$277$	728039.	−	728039.i	0.570105	−	0.570105i	0.932158	+	0.362052i	$0.117924\pi$
$278$		0			0
$279$			1.24814e6i			0.959957i
$280$		0			0
$281$			219132.i			0.165554i	0.996568	+	0.0827772i	$0.0263790\pi$
$281$			219132.i			0.165554i	−0.996568	+	0.0827772i	$0.973621\pi$
$282$		0			0
$283$	−612287.	+	612287.i	−0.454453	+	0.454453i	−0.896829	−	0.442377i	$-0.854135\pi$
$283$	−612287.	+	612287.i	−0.454453	+	0.454453i	0.442377	+	0.896829i	$0.354135\pi$
$284$		0			0
$285$	−32068.5	−	32068.5i	−0.0233865	−	0.0233865i
$286$		0			0
$287$	2.66988e6			1.91332
$288$		0			0
$289$	501755.			0.353384
$290$		0			0
$291$	285822.	+	285822.i	0.197862	+	0.197862i
$292$		0			0
$293$	−546245.	+	546245.i	−0.371722	+	0.371722i	−0.868104	−	0.496382i	$-0.834662\pi$
$293$	−546245.	+	546245.i	−0.371722	+	0.371722i	0.496382	+	0.868104i	$0.334662\pi$
$294$		0			0
$295$		−	872153.i		−	0.583496i
$296$		0			0
$297$			1.20441e6i			0.792289i
$298$		0			0
$299$	1.56926e6	−	1.56926e6i	1.01512	−	1.01512i
$300$		0			0
$301$	−834220.	−	834220.i	−0.530719	−	0.530719i
$302$		0			0
$303$	−1.06572e6			−0.666861
$304$		0			0
$305$	−221700.			−0.136464
$306$		0			0
$307$	620775.	+	620775.i	0.375914	+	0.375914i	0.869626	−	0.493712i	$-0.164360\pi$
$307$	620775.	+	620775.i	0.375914	+	0.375914i	−0.493712	+	0.869626i	$0.664360\pi$
$308$		0			0
$309$	634918.	−	634918.i	0.378287	−	0.378287i
$310$		0			0
$311$			2.63407e6i			1.54428i	0.635452	+	0.772141i	$0.280814\pi$
$311$			2.63407e6i			1.54428i	−0.635452	+	0.772141i	$0.719186\pi$
$312$		0			0
$313$		−	1.08782e6i		−	0.627620i	−0.949486	−	0.313810i	$-0.898395\pi$
$313$		−	1.08782e6i		−	0.627620i	0.949486	−	0.313810i	$-0.101605\pi$
$314$		0			0
$315$	−502367.	+	502367.i	−0.285263	+	0.285263i
$316$		0			0
$317$	−450130.	−	450130.i	−0.251588	−	0.251588i	0.570034	−	0.821621i	$-0.306930\pi$
$317$	−450130.	−	450130.i	−0.251588	−	0.251588i	−0.821621	+	0.570034i	$0.806930\pi$
$318$		0			0
$319$	220880.			0.121529
$320$		0			0
$321$	972644.			0.526855
$322$		0			0
$323$	296096.	+	296096.i	0.157916	+	0.157916i
$324$		0			0
$325$	495217.	−	495217.i	0.260068	−	0.260068i
$326$		0			0
$327$			33903.4i			0.0175337i
$328$		0			0
$329$		−	3.21061e6i		−	1.63530i
$330$		0			0
$331$	775026.	−	775026.i	0.388818	−	0.388818i	−0.485448	−	0.874266i	$-0.661343\pi$
$331$	775026.	−	775026.i	0.388818	−	0.388818i	0.874266	+	0.485448i	$0.161343\pi$
$332$		0			0
$333$	−1.57006e6	−	1.57006e6i	−0.775898	−	0.775898i
$334$		0			0
$335$	−1.06374e6			−0.517873
$336$		0			0
$337$	1.83332e6			0.879352			0.439676	−	0.898156i	$-0.355093\pi$
$337$	1.83332e6			0.879352			0.439676	+	0.898156i	$0.355093\pi$
$338$		0			0
$339$	659541.	+	659541.i	0.311704	+	0.311704i
$340$		0			0
$341$	−1.90107e6	+	1.90107e6i	−0.885343	+	0.885343i
$342$		0			0
$343$		−	2.02627e6i		−	0.929953i
$344$		0			0
$345$			297344.i			0.134496i
$346$		0			0
$347$	−619433.	+	619433.i	−0.276166	+	0.276166i	−0.831576	−	0.555410i	$-0.812561\pi$
$347$	−619433.	+	619433.i	−0.276166	+	0.276166i	0.555410	+	0.831576i	$0.312561\pi$
$348$		0			0
$349$	436750.	+	436750.i	0.191942	+	0.191942i	0.796535	−	0.604593i	$-0.206664\pi$
$349$	436750.	+	436750.i	0.191942	+	0.191942i	−0.604593	+	0.796535i	$0.706664\pi$
$350$		0			0
$351$	−3.02775e6			−1.31175
$352$		0			0
$353$	−1.43657e6			−0.613607			−0.306804	−	0.951773i	$-0.599259\pi$
$353$	−1.43657e6			−0.613607			−0.306804	+	0.951773i	$0.599259\pi$
$354$		0			0
$355$	−54171.6	−	54171.6i	−0.0228140	−	0.0228140i
$356$		0			0
$357$	−808383.	+	808383.i	−0.335696	+	0.335696i
$358$		0			0
$359$		−	1.13072e6i		−	0.463042i	−0.972830	−	0.231521i	$-0.925630\pi$
$359$		−	1.13072e6i		−	0.463042i	0.972830	−	0.231521i	$-0.0743701\pi$
$360$		0			0
$361$		−	2.38485e6i		−	0.963148i
$362$		0			0
$363$	−159823.	+	159823.i	−0.0636607	+	0.0636607i
$364$		0			0
$365$	−1.03578e6	−	1.03578e6i	−0.406943	−	0.406943i
$366$		0			0
$367$	2.60349e6			1.00900			0.504500	−	0.863412i	$-0.331677\pi$
$367$	2.60349e6			1.00900			0.504500	+	0.863412i	$0.331677\pi$
$368$		0			0
$369$	4.02315e6			1.53816
$370$		0			0
$371$	2.15303e6	+	2.15303e6i	0.812112	+	0.812112i
$372$		0			0
$373$	2.30596e6	−	2.30596e6i	0.858183	−	0.858183i	−0.132941	−	0.991124i	$-0.542442\pi$
$373$	2.30596e6	−	2.30596e6i	0.858183	−	0.858183i	0.991124	+	0.132941i	$0.0424422\pi$
$374$		0			0
$375$			93833.7i			0.0344572i
$376$		0			0
$377$			555266.i			0.201209i
$378$		0			0
$379$	−1.35969e6	+	1.35969e6i	−0.486229	+	0.486229i	−0.907114	−	0.420885i	$-0.861720\pi$
$379$	−1.35969e6	+	1.35969e6i	−0.486229	+	0.486229i	0.420885	+	0.907114i	$0.361720\pi$
$380$		0			0
$381$	715869.	+	715869.i	0.252651	+	0.252651i
$382$		0			0
$383$	−3.34749e6			−1.16607			−0.583033	−	0.812449i	$-0.698134\pi$
$383$	−3.34749e6			−1.16607			−0.583033	+	0.812449i	$0.698134\pi$
$384$		0			0
$385$	−1.53033e6			−0.526180
$386$		0			0
$387$	−1.25706e6	−	1.25706e6i	−0.426656	−	0.426656i
$388$		0			0
$389$	−99102.9	+	99102.9i	−0.0332057	+	0.0332057i	−0.723515	−	0.690309i	$-0.757475\pi$
$389$	−99102.9	+	99102.9i	−0.0332057	+	0.0332057i	0.690309	+	0.723515i	$0.257475\pi$
$390$		0			0
$391$		−	2.74545e6i		−	0.908178i
$392$		0			0
$393$		−	1.23075e6i		−	0.401966i
$394$		0			0
$395$	17943.0	−	17943.0i	0.00578630	−	0.00578630i
$396$		0			0
$397$	1.95052e6	+	1.95052e6i	0.621117	+	0.621117i	0.945817	−	0.324700i	$-0.105263\pi$
$397$	1.95052e6	+	1.95052e6i	0.621117	+	0.621117i	−0.324700	+	0.945817i	$0.605263\pi$
$398$		0			0
$399$	−249123.			−0.0783397
$400$		0			0
$401$	965925.			0.299973			0.149987	−	0.988688i	$-0.452077\pi$
$401$	965925.			0.299973			0.149987	+	0.988688i	$0.452077\pi$
$402$		0			0
$403$	−4.77906e6	−	4.77906e6i	−1.46582	−	1.46582i
$404$		0			0
$405$	−602080.	+	602080.i	−0.182396	+	0.182396i
$406$		0			0
$407$		−	4.78278e6i		−	1.43118i
$408$		0			0
$409$			2.85724e6i			0.844576i	0.906462	+	0.422288i	$0.138773\pi$
$409$			2.85724e6i			0.844576i	−0.906462	+	0.422288i	$0.861227\pi$
$410$		0			0
$411$	−607688.	+	607688.i	−0.177450	+	0.177450i
$412$		0			0
$413$	−3.38765e6	−	3.38765e6i	−0.977289	−	0.977289i
$414$		0			0
$415$	−1.50873e6			−0.430023
$416$		0			0
$417$	−153447.			−0.0432133
$418$		0			0
$419$	−2.56222e6	−	2.56222e6i	−0.712988	−	0.712988i	0.254171	−	0.967159i	$-0.418197\pi$
$419$	−2.56222e6	−	2.56222e6i	−0.712988	−	0.712988i	−0.967159	+	0.254171i	$0.918197\pi$
$420$		0			0
$421$	−1.73946e6	+	1.73946e6i	−0.478310	+	0.478310i	−0.904591	−	0.426281i	$-0.859824\pi$
$421$	−1.73946e6	+	1.73946e6i	−0.478310	+	0.478310i	0.426281	+	0.904591i	$0.359824\pi$
$422$		0			0
$423$		−	4.83796e6i		−	1.31465i
$424$		0			0
$425$		−	866389.i		−	0.232670i
$426$		0			0
$427$	−861137.	+	861137.i	−0.228561	+	0.228561i
$428$		0			0
$429$	−2.12100e6	−	2.12100e6i	−0.556412	−	0.556412i
$430$		0			0
$431$	5.18194e6			1.34369			0.671845	−	0.740692i	$-0.265502\pi$
$431$	5.18194e6			1.34369			0.671845	+	0.740692i	$0.265502\pi$
$432$		0			0
$433$	−1.99786e6			−0.512088			−0.256044	−	0.966665i	$-0.582419\pi$
$433$	−1.99786e6			−0.512088			−0.256044	+	0.966665i	$0.582419\pi$
$434$		0			0
$435$	−52605.9	−	52605.9i	−0.0133294	−	0.0133294i
$436$		0			0
$437$	423038.	−	423038.i	0.105968	−	0.105968i
$438$		0			0
$439$		−	3.92238e6i		−	0.971378i	−0.874132	−	0.485689i	$-0.838569\pi$
$439$		−	3.92238e6i		−	0.971378i	0.874132	−	0.485689i	$-0.161431\pi$
$440$		0			0
$441$			424657.i			0.103978i
$442$		0			0
$443$	2.41985e6	−	2.41985e6i	0.585840	−	0.585840i	−0.350662	−	0.936502i	$-0.614043\pi$
$443$	2.41985e6	−	2.41985e6i	0.585840	−	0.585840i	0.936502	+	0.350662i	$0.114043\pi$
$444$		0			0
$445$	−1.14009e6	−	1.14009e6i	−0.272923	−	0.272923i
$446$		0			0
$447$	−262197.			−0.0620667
$448$		0			0
$449$	−3.44112e6			−0.805533			−0.402767	−	0.915303i	$-0.631951\pi$
$449$	−3.44112e6			−0.805533			−0.402767	+	0.915303i	$0.631951\pi$
$450$		0			0
$451$	6.12776e6	+	6.12776e6i	1.41860	+	1.41860i
$452$		0			0
$453$	734617.	−	734617.i	0.168196	−	0.168196i
$454$		0			0
$455$		−	3.84708e6i		−	0.871169i
$456$		0			0
$457$		−	4.04376e6i		−	0.905721i	−0.891581	−	0.452861i	$-0.850403\pi$
$457$		−	4.04376e6i		−	0.905721i	0.891581	−	0.452861i	$-0.149597\pi$
$458$		0			0
$459$	−2.64854e6	+	2.64854e6i	−0.586780	+	0.586780i
$460$		0			0
$461$	1.54404e6	+	1.54404e6i	0.338381	+	0.338381i	0.855758	−	0.517377i	$-0.173091\pi$
$461$	1.54404e6	+	1.54404e6i	0.338381	+	0.338381i	−0.517377	+	0.855758i	$0.673091\pi$
$462$		0			0
$463$	−1.79699e6			−0.389577			−0.194788	−	0.980845i	$-0.562402\pi$
$463$	−1.79699e6			−0.389577			−0.194788	+	0.980845i	$0.562402\pi$
$464$		0			0
$465$	905536.			0.194211
$466$		0			0
$467$	1.57560e6	+	1.57560e6i	0.334314	+	0.334314i	0.854222	−	0.519908i	$-0.174034\pi$
$467$	1.57560e6	+	1.57560e6i	0.334314	+	0.334314i	−0.519908	+	0.854222i	$0.674034\pi$
$468$		0			0
$469$	−4.13181e6	+	4.13181e6i	−0.867379	+	0.867379i
$470$		0			0
$471$		−	2.46360e6i		−	0.511704i
$472$		0			0
$473$		−	3.82931e6i		−	0.786987i
$474$		0			0
$475$	133499.	−	133499.i	0.0271485	−	0.0271485i
$476$		0			0
$477$	3.24433e6	+	3.24433e6i	0.652874	+	0.652874i
$478$		0			0
$479$	5.68108e6			1.13134			0.565669	−	0.824633i	$-0.308618\pi$
$479$	5.68108e6			1.13134			0.565669	+	0.824633i	$0.308618\pi$
$480$		0			0
$481$	1.20233e7			2.36953
$482$		0			0
$483$	1.15495e6	+	1.15495e6i	0.225266	+	0.225266i
$484$		0			0
$485$	−1.18986e6	+	1.18986e6i	−0.229690	+	0.229690i
$486$		0			0
$487$			3.96622e6i			0.757800i	0.925438	+	0.378900i	$0.123698\pi$
$487$			3.96622e6i			0.757800i	−0.925438	+	0.378900i	$0.876302\pi$
$488$		0			0
$489$			3.29640e6i			0.623402i
$490$		0			0
$491$	4.60147e6	−	4.60147e6i	0.861376	−	0.861376i	−0.130122	−	0.991498i	$-0.541537\pi$
$491$	4.60147e6	−	4.60147e6i	0.861376	−	0.861376i	0.991498	+	0.130122i	$0.0415370\pi$
$492$		0			0
$493$	485723.	+	485723.i	0.0900060	+	0.0900060i
$494$		0			0
$495$	−2.30601e6			−0.423008
$496$		0			0
$497$	−420831.			−0.0764217
$498$		0			0
$499$	5.24693e6	+	5.24693e6i	0.943309	+	0.943309i	0.998477	−	0.0551681i	$-0.0175695\pi$
$499$	5.24693e6	+	5.24693e6i	0.943309	+	0.943309i	−0.0551681	+	0.998477i	$0.517569\pi$
$500$		0			0
$501$	1.48732e6	−	1.48732e6i	0.264735	−	0.264735i
$502$		0			0
$503$		−	8.04275e6i		−	1.41738i	−0.705522	−	0.708688i	$-0.749288\pi$
$503$		−	8.04275e6i		−	1.41738i	0.705522	−	0.708688i	$-0.250712\pi$
$504$		0			0
$505$		−	4.43653e6i		−	0.774131i
$506$		0			0
$507$	3.75526e6	−	3.75526e6i	0.648814	−	0.648814i
$508$		0			0
$509$	−6.36596e6	−	6.36596e6i	−1.08910	−	1.08910i	−0.995621	−	0.0934829i	$-0.970200\pi$
$509$	−6.36596e6	−	6.36596e6i	−1.08910	−	1.08910i	−0.0934829	−	0.995621i	$-0.529800\pi$
$510$		0			0
$511$	−8.04640e6			−1.36317
$512$		0			0
$513$	−816213.			−0.136934
$514$		0			0
$515$	2.64313e6	+	2.64313e6i	0.439138	+	0.439138i
$516$		0			0
$517$	7.36882e6	−	7.36882e6i	1.21247	−	1.21247i
$518$		0			0
$519$			2.10657e6i			0.343286i
$520$		0			0
$521$		−	708657.i		−	0.114378i	−0.998363	−	0.0571889i	$-0.981786\pi$
$521$		−	708657.i		−	0.114378i	0.998363	−	0.0571889i	$-0.0182137\pi$
$522$		0			0
$523$	−2.35262e6	+	2.35262e6i	−0.376095	+	0.376095i	−0.869691	−	0.493596i	$-0.835682\pi$
$523$	−2.35262e6	+	2.35262e6i	−0.376095	+	0.376095i	0.493596	+	0.869691i	$0.335682\pi$
$524$		0			0
$525$	364472.	+	364472.i	0.0577120	+	0.0577120i
$526$		0			0
$527$	−8.36103e6			−1.31139
$528$		0			0
$529$	2.51387e6			0.390574
$530$		0			0
$531$	−5.10473e6	−	5.10473e6i	−0.785664	−	0.785664i
$532$		0			0
$533$	−1.54045e7	+	1.54045e7i	−2.34871	+	2.34871i
$534$		0			0
$535$			4.04907e6i			0.611605i
$536$		0			0
$537$			3.41027e6i			0.510332i
$538$		0			0
$539$	−646805.	+	646805.i	−0.0958962	+	0.0958962i
$540$		0			0
$541$	6.69433e6	+	6.69433e6i	0.983363	+	0.983363i	0.999864	−	0.0165012i	$-0.00525272\pi$
$541$	6.69433e6	+	6.69433e6i	0.983363	+	0.983363i	−0.0165012	+	0.999864i	$0.505253\pi$
$542$		0			0
$543$	−1.32036e6			−0.192173
$544$		0			0
$545$	−141138.			−0.0203542
$546$		0			0
$547$	4.33543e6	+	4.33543e6i	0.619532	+	0.619532i	0.945411	−	0.325879i	$-0.105660\pi$
$547$	4.33543e6	+	4.33543e6i	0.619532	+	0.619532i	−0.325879	+	0.945411i	$0.605660\pi$
$548$		0			0
$549$	−1.29762e6	+	1.29762e6i	−0.183745	+	0.183745i
$550$		0			0
$551$			149687.i			0.0210042i
$552$		0			0
$553$		−	139389.i		−	0.0193828i
$554$		0			0
$555$	−1.13909e6	+	1.13909e6i	−0.156973	+	0.156973i
$556$		0			0
$557$	−6.88535e6	−	6.88535e6i	−0.940347	−	0.940347i	0.0579716	−	0.998318i	$-0.481537\pi$
$557$	−6.88535e6	−	6.88535e6i	−0.940347	−	0.940347i	−0.998318	+	0.0579716i	$0.981537\pi$
$558$		0			0
$559$	9.62643e6			1.30297
$560$		0			0
$561$	−3.71071e6			−0.497795
$562$		0			0
$563$	−8.08998e6	−	8.08998e6i	−1.07566	−	1.07566i	−0.996893	−	0.0787709i	$-0.974900\pi$
$563$	−8.08998e6	−	8.08998e6i	−1.07566	−	1.07566i	−0.0787709	−	0.996893i	$-0.525100\pi$
$564$		0			0
$565$	−2.74564e6	+	2.74564e6i	−0.361844	+	0.361844i
$566$		0			0
$567$			4.67724e6i			0.610987i
$568$		0			0
$569$			4.67050e6i			0.604760i	0.953187	+	0.302380i	$0.0977811\pi$
$569$			4.67050e6i			0.604760i	−0.953187	+	0.302380i	$0.902219\pi$
$570$		0			0
$571$	−7.63682e6	+	7.63682e6i	−0.980217	+	0.980217i	−0.999808	−	0.0195908i	$-0.993764\pi$
$571$	−7.63682e6	+	7.63682e6i	−0.980217	+	0.980217i	0.0195908	+	0.999808i	$0.493764\pi$
$572$		0			0
$573$	−2.27702e6	−	2.27702e6i	−0.289721	−	0.289721i
$574$		0			0
$575$	−1.23783e6			−0.156131
$576$		0			0
$577$	1.52565e7			1.90772			0.953861	−	0.300250i	$-0.0970700\pi$
$577$	1.52565e7			1.90772			0.953861	+	0.300250i	$0.0970700\pi$
$578$		0			0
$579$	2.04977e6	+	2.04977e6i	0.254103	+	0.254103i
$580$		0			0
$581$	−5.86027e6	+	5.86027e6i	−0.720241	+	0.720241i
$582$		0			0
$583$			9.88305e6i			1.20426i
$584$		0			0
$585$		−	5.79703e6i		−	0.700352i
$586$		0			0
$587$	−8.60224e6	+	8.60224e6i	−1.03043	+	1.03043i	−0.0309029	+	0.999522i	$0.509838\pi$
$587$	−8.60224e6	+	8.60224e6i	−1.03043	+	1.03043i	−0.999522	+	0.0309029i	$0.990162\pi$
$588$		0			0
$589$	−1.28833e6	−	1.28833e6i	−0.153016	−	0.153016i
$590$		0			0
$591$	−592083.			−0.0697291
$592$		0			0
$593$	8.02363e6			0.936988			0.468494	−	0.883467i	$-0.344797\pi$
$593$	8.02363e6			0.936988			0.468494	+	0.883467i	$0.344797\pi$
$594$		0			0
$595$	−3.36526e6	−	3.36526e6i	−0.389696	−	0.389696i
$596$		0			0
$597$	2.65497e6	−	2.65497e6i	0.304876	−	0.304876i
$598$		0			0
$599$			4.95056e6i			0.563751i	0.959451	+	0.281875i	$0.0909565\pi$
$599$			4.95056e6i			0.563751i	−0.959451	+	0.281875i	$0.909044\pi$
$600$		0			0
$601$			3.46932e6i			0.391794i	0.980624	+	0.195897i	$0.0627619\pi$
$601$			3.46932e6i			0.391794i	−0.980624	+	0.195897i	$0.937238\pi$
$602$		0			0
$603$	−6.22609e6	+	6.22609e6i	−0.697304	+	0.697304i
$604$		0			0
$605$	−665334.	−	665334.i	−0.0739011	−	0.0739011i
$606$		0			0
$607$	1.60915e7			1.77266			0.886329	−	0.463056i	$-0.153247\pi$
$607$	1.60915e7			1.77266			0.886329	+	0.463056i	$0.153247\pi$
$608$		0			0
$609$	−408668.			−0.0446506
$610$		0			0
$611$	1.85243e7	+	1.85243e7i	2.00743	+	2.00743i
$612$		0			0
$613$	1.10810e7	−	1.10810e7i	1.19105	−	1.19105i	0.214272	−	0.976774i	$-0.431262\pi$
$613$	1.10810e7	−	1.10810e7i	1.19105	−	1.19105i	0.976774	−	0.214272i	$-0.0687380\pi$
$614$		0			0
$615$		−	2.91884e6i		−	0.311188i
$616$		0			0
$617$			1.27858e7i			1.35211i	0.736849	+	0.676057i	$0.236313\pi$
$617$			1.27858e7i			1.35211i	−0.736849	+	0.676057i	$0.763687\pi$
$618$		0			0
$619$	7.49659e6	−	7.49659e6i	0.786388	−	0.786388i	−0.194512	−	0.980900i	$-0.562312\pi$
$619$	7.49659e6	−	7.49659e6i	0.786388	−	0.786388i	0.980900	+	0.194512i	$0.0623124\pi$
$620$		0			0
$621$	3.78403e6	+	3.78403e6i	0.393754	+	0.393754i
$622$		0			0
$623$	−8.85680e6			−0.914232
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	−571774.	−	571774.i	−0.0580838	−	0.0580838i
$628$		0			0
$629$	1.05175e7	−	1.05175e7i	1.05995	−	1.05995i
$630$		0			0
$631$		−	7.02682e6i		−	0.702563i	−0.936270	−	0.351282i	$-0.885746\pi$
$631$		−	7.02682e6i		−	0.702563i	0.936270	−	0.351282i	$-0.114254\pi$
$632$		0			0
$633$		−	377904.i		−	0.0374863i
$634$		0			0
$635$	−2.98013e6	+	2.98013e6i	−0.293292	+	0.293292i
$636$		0			0
$637$	−1.62599e6	−	1.62599e6i	−0.158770	−	0.158770i
$638$		0			0
$639$	−634136.			−0.0614370
$640$		0			0
$641$	1.07957e7			1.03778			0.518892	−	0.854840i	$-0.326345\pi$
$641$	1.07957e7			1.03778			0.518892	+	0.854840i	$0.326345\pi$
$642$		0			0
$643$	−6.71091e6	−	6.71091e6i	−0.640109	−	0.640109i	0.310473	−	0.950582i	$-0.399512\pi$
$643$	−6.71091e6	−	6.71091e6i	−0.640109	−	0.640109i	−0.950582	+	0.310473i	$0.899512\pi$
$644$		0			0
$645$	−912008.	+	912008.i	−0.0863176	+	0.0863176i
$646$		0			0
$647$			1.14841e7i			1.07854i	0.842134	+	0.539269i	$0.181299\pi$
$647$			1.14841e7i			1.07854i	−0.842134	+	0.539269i	$0.818701\pi$
$648$		0			0
$649$		−	1.55503e7i		−	1.44919i
$650$		0			0
$651$	3.51732e6	−	3.51732e6i	0.325281	−	0.325281i
$652$		0			0
$653$	−535257.	−	535257.i	−0.0491224	−	0.0491224i	0.682119	−	0.731241i	$-0.261059\pi$
$653$	−535257.	−	535257.i	−0.0491224	−	0.0491224i	−0.731241	+	0.682119i	$0.761059\pi$
$654$		0			0
$655$	5.12357e6			0.466626
$656$		0			0
$657$	−1.21248e7			−1.09588
$658$		0			0
$659$	1.11623e7	+	1.11623e7i	1.00125	+	1.00125i	0.999999	+	0.00124901i	$0.000397574\pi$
$659$	1.11623e7	+	1.11623e7i	1.00125	+	1.00125i	0.00124901	+	0.999999i	$0.499602\pi$
$660$		0			0
$661$	−7.45770e6	+	7.45770e6i	−0.663898	+	0.663898i	−0.956296	−	0.292399i	$-0.905546\pi$
$661$	−7.45770e6	+	7.45770e6i	−0.663898	+	0.663898i	0.292399	+	0.956296i	$0.405546\pi$
$662$		0			0
$663$		−	9.32829e6i		−	0.824173i
$664$		0			0
$665$		−	1.03709e6i		−	0.0909413i
$666$		0			0
$667$	693962.	−	693962.i	0.0603978	−	0.0603978i
$668$		0			0
$669$	500756.	+	500756.i	0.0432574	+	0.0432574i
$670$		0			0
$671$	−3.95287e6			−0.338927
$672$		0			0
$673$	−1.29160e7			−1.09924			−0.549619	−	0.835415i	$-0.685227\pi$
$673$	−1.29160e7			−1.09924			−0.549619	+	0.835415i	$0.685227\pi$
$674$		0			0
$675$	1.19414e6	+	1.19414e6i	0.100878	+	0.100878i
$676$		0			0
$677$	−4.19969e6	+	4.19969e6i	−0.352164	+	0.352164i	−0.860914	−	0.508750i	$-0.830108\pi$
$677$	−4.19969e6	+	4.19969e6i	−0.352164	+	0.352164i	0.508750	+	0.860914i	$0.330108\pi$
$678$		0			0
$679$			9.24340e6i			0.769409i
$680$		0			0
$681$		−	1.02377e6i		−	0.0845931i
$682$		0			0
$683$	312963.	−	312963.i	0.0256709	−	0.0256709i	−0.694155	−	0.719826i	$-0.744222\pi$
$683$	312963.	−	312963.i	0.0256709	−	0.0256709i	0.719826	+	0.694155i	$0.244222\pi$
$684$		0			0
$685$	−2.52977e6	−	2.52977e6i	−0.205994	−	0.205994i
$686$		0			0
$687$	−1.50674e6			−0.121800
$688$		0			0
$689$	−2.48448e7			−1.99383
$690$		0			0
$691$	1.29802e7	+	1.29802e7i	1.03416	+	1.03416i	0.999396	+	0.0347642i	$0.0110680\pi$
$691$	1.29802e7	+	1.29802e7i	1.03416	+	1.03416i	0.0347642	+	0.999396i	$0.488932\pi$
$692$		0			0
$693$	−8.95709e6	+	8.95709e6i	−0.708490	+	0.708490i
$694$		0			0
$695$		−	638791.i		−	0.0501645i
$696$		0			0
$697$			2.69503e7i			2.10127i
$698$		0			0
$699$	1.20792e6	−	1.20792e6i	0.0935073	−	0.0935073i
$700$		0			0
$701$	1.09728e7	+	1.09728e7i	0.843376	+	0.843376i	0.989296	−	0.145921i	$-0.0466144\pi$
$701$	1.09728e7	+	1.09728e7i	0.843376	+	0.843376i	−0.145921	+	0.989296i	$0.546614\pi$
$702$		0			0
$703$	3.24123e6			0.247355
$704$		0			0
$705$	−3.50999e6			−0.265970
$706$		0			0
$707$	−1.72325e7	−	1.72325e7i	−1.29658	−	1.29658i
$708$		0			0
$709$	1.95276e6	−	1.95276e6i	0.145892	−	0.145892i	−0.630388	−	0.776280i	$-0.717104\pi$
$709$	1.95276e6	−	1.95276e6i	0.145892	−	0.145892i	0.776280	+	0.630388i	$0.217104\pi$
$710$		0			0
$711$		−	210041.i		−	0.0155823i
$712$		0			0
$713$			1.19456e7i			0.880001i
$714$		0			0
$715$	8.82960e6	−	8.82960e6i	0.645916	−	0.645916i
$716$		0			0
$717$	4.52665e6	+	4.52665e6i	0.328836	+	0.328836i
$718$		0			0
$719$	−2.06195e7			−1.48750			−0.743748	−	0.668460i	$-0.766954\pi$
$719$	−2.06195e7			−1.48750			−0.743748	+	0.668460i	$0.766954\pi$
$720$		0			0
$721$	2.05331e7			1.47101
$722$		0			0
$723$	−1.92824e6	−	1.92824e6i	−0.137188	−	0.137188i
$724$		0			0
$725$	218996.	−	218996.i	0.0154736	−	0.0154736i
$726$		0			0
$727$			3.37651e6i			0.236937i	0.992958	+	0.118468i	$0.0377984\pi$
$727$			3.37651e6i			0.236937i	−0.992958	+	0.118468i	$0.962202\pi$
$728$		0			0
$729$			3.10491e6i			0.216386i
$730$		0			0
$731$	8.42079e6	−	8.42079e6i	0.582853	−	0.582853i
$732$		0			0
$733$	7.30970e6	+	7.30970e6i	0.502504	+	0.502504i	0.912215	−	0.409711i	$-0.134371\pi$
$733$	7.30970e6	+	7.30970e6i	0.502504	+	0.502504i	−0.409711	+	0.912215i	$0.634371\pi$
$734$		0			0
$735$	308093.			0.0210360
$736$		0			0
$737$	−1.89662e7			−1.28621
$738$		0			0
$739$	−1.17792e7	−	1.17792e7i	−0.793425	−	0.793425i	0.188624	−	0.982049i	$-0.439597\pi$
$739$	−1.17792e7	−	1.17792e7i	−0.793425	−	0.793425i	−0.982049	+	0.188624i	$0.939597\pi$
$740$		0			0
$741$	1.43737e6	−	1.43737e6i	0.0961663	−	0.0961663i
$742$		0			0
$743$		−	1.71523e6i		−	0.113986i	−0.998375	−	0.0569928i	$-0.981849\pi$
$743$		−	1.71523e6i		−	0.113986i	0.998375	−	0.0569928i	$-0.0181512\pi$
$744$		0			0
$745$		−	1.09151e6i		−	0.0720506i
$746$		0			0
$747$	−8.83065e6	+	8.83065e6i	−0.579017	+	0.579017i
$748$		0			0
$749$	1.57275e7	+	1.57275e7i	1.02437	+	1.02437i
$750$		0			0
$751$	−7.55264e6			−0.488651			−0.244326	−	0.969693i	$-0.578567\pi$
$751$	−7.55264e6			−0.488651			−0.244326	+	0.969693i	$0.578567\pi$
$752$		0			0
$753$	2.26045e6			0.145280
$754$		0			0
$755$	3.05817e6	+	3.05817e6i	0.195252	+	0.195252i
$756$		0			0
$757$	3.03553e6	−	3.03553e6i	0.192529	−	0.192529i	−0.604259	−	0.796788i	$-0.706531\pi$
$757$	3.03553e6	−	3.03553e6i	0.192529	−	0.192529i	0.796788	+	0.604259i	$0.206531\pi$
$758$		0			0
$759$			5.30157e6i			0.334041i
$760$		0			0
$761$		−	1.66504e7i		−	1.04223i	−0.853486	−	0.521115i	$-0.825516\pi$
$761$		−	1.66504e7i		−	1.04223i	0.853486	−	0.521115i	$-0.174484\pi$
$762$		0			0
$763$	−548214.	+	548214.i	−0.0340909	+	0.0340909i
$764$		0			0
$765$	−5.07100e6	−	5.07100e6i	−0.313285	−	0.313285i
$766$		0			0
$767$	3.90916e7			2.39936
$768$		0			0
$769$	−4.85552e6			−0.296087			−0.148044	−	0.988981i	$-0.547298\pi$
$769$	−4.85552e6			−0.296087			−0.148044	+	0.988981i	$0.547298\pi$
$770$		0			0
$771$	6.33788e6	+	6.33788e6i	0.383979	+	0.383979i
$772$		0			0
$773$	1.32052e7	−	1.32052e7i	0.794871	−	0.794871i	−0.187410	−	0.982282i	$-0.560009\pi$
$773$	1.32052e7	−	1.32052e7i	0.794871	−	0.794871i	0.982282	+	0.187410i	$0.0600094\pi$
$774$		0			0
$775$			3.76970e6i			0.225451i
$776$		0			0
$777$			8.84901e6i			0.525826i
$778$		0			0
$779$	−4.15270e6	+	4.15270e6i	−0.245181	+	0.245181i
$780$		0			0
$781$	−965868.	−	965868.i	−0.0566618	−	0.0566618i
$782$		0			0
$783$	−1.33894e6			−0.0780469
$784$		0			0
$785$	1.02559e7			0.594016
$786$		0			0
$787$	−2.34228e7	−	2.34228e7i	−1.34804	−	1.34804i	−0.887793	−	0.460243i	$-0.847762\pi$
$787$	−2.34228e7	−	2.34228e7i	−1.34804	−	1.34804i	−0.460243	−	0.887793i	$-0.652238\pi$
$788$		0			0
$789$	7.00372e6	−	7.00372e6i	0.400531	−	0.400531i
$790$		0			0
$791$			2.13294e7i			1.21210i
$792$		0			0
$793$		−	9.93704e6i		−	0.561143i
$794$		0			0
$795$	2.35380e6	−	2.35380e6i	0.132084	−	0.132084i
$796$		0			0
$797$	3.50205e6	+	3.50205e6i	0.195289	+	0.195289i	0.797977	−	0.602688i	$-0.205904\pi$
$797$	3.50205e6	+	3.50205e6i	0.195289	+	0.195289i	−0.602688	+	0.797977i	$0.705904\pi$
$798$		0			0
$799$	3.24086e7			1.79595
$800$		0			0
$801$	−1.33460e7			−0.734971
$802$		0			0
$803$	−1.84676e7	−	1.84676e7i	−1.01070	−	1.01070i
$804$		0			0
$805$	−4.80801e6	+	4.80801e6i	−0.261503	+	0.261503i
$806$		0			0
$807$		−	1.03819e7i		−	0.561171i
$808$		0			0
$809$			1.24073e7i			0.666508i	0.942837	+	0.333254i	$0.108147\pi$
$809$			1.24073e7i			0.666508i	−0.942837	+	0.333254i	$0.891853\pi$
$810$		0			0
$811$	1.83249e7	−	1.83249e7i	0.978338	−	0.978338i	−0.0214326	−	0.999770i	$-0.506823\pi$
$811$	1.83249e7	−	1.83249e7i	0.978338	−	0.978338i	0.999770	+	0.0214326i	$0.00682274\pi$
$812$		0			0
$813$	−6.63461e6	−	6.63461e6i	−0.352037	−	0.352037i
$814$		0			0
$815$	−1.37228e7			−0.723682
$816$		0			0
$817$	2.59507e6			0.136017
$818$		0			0
$819$	−2.25171e7	−	2.25171e7i	−1.17301	−	1.17301i
$820$		0			0
$821$	846306.	−	846306.i	0.0438197	−	0.0438197i	−0.684857	−	0.728677i	$-0.740136\pi$
$821$	846306.	−	846306.i	0.0438197	−	0.0438197i	0.728677	+	0.684857i	$0.240136\pi$
$822$		0			0
$823$			3.47983e6i			0.179085i	0.995983	+	0.0895423i	$0.0285404\pi$
$823$			3.47983e6i			0.179085i	−0.995983	+	0.0895423i	$0.971460\pi$
$824$		0			0
$825$			1.67303e6i			0.0855795i
$826$		0			0
$827$	1.93597e7	−	1.93597e7i	0.984318	−	0.984318i	−0.0155613	−	0.999879i	$-0.504954\pi$
$827$	1.93597e7	−	1.93597e7i	0.984318	−	0.984318i	0.999879	+	0.0155613i	$0.00495350\pi$
$828$		0			0
$829$	4.87899e6	+	4.87899e6i	0.246572	+	0.246572i	0.819562	−	0.572990i	$-0.194217\pi$
$829$	4.87899e6	+	4.87899e6i	0.246572	+	0.246572i	−0.572990	+	0.819562i	$0.694217\pi$
$830$		0			0
$831$	−6.18313e6			−0.310603
$832$		0			0
$833$	−2.84469e6			−0.142044
$834$		0			0
$835$	6.19165e6	+	6.19165e6i	0.307319	+	0.307319i
$836$		0			0
$837$	1.15239e7	−	1.15239e7i	0.568575	−	0.568575i
$838$		0			0
$839$			2.24603e7i			1.10157i	0.834648	+	0.550784i	$0.185671\pi$
$839$			2.24603e7i			1.10157i	−0.834648	+	0.550784i	$0.814329\pi$
$840$		0			0
$841$		−	2.02656e7i		−	0.988028i
$842$		0			0
$843$	930530.	−	930530.i	0.0450984	−	0.0450984i
$844$		0			0
$845$	1.56330e7	+	1.56330e7i	0.753182	+	0.753182i
$846$		0			0
$847$	−5.16863e6			−0.247552
$848$		0			0
$849$	5.20006e6			0.247594
$850$		0			0
$851$	−1.50266e7	−	1.50266e7i	−0.711273	−	0.711273i
$852$		0			0
$853$	2.34846e7	−	2.34846e7i	1.10512	−	1.10512i	0.111340	−	0.993782i	$-0.464486\pi$
$853$	2.34846e7	−	2.34846e7i	1.10512	−	1.10512i	0.993782	−	0.111340i	$-0.0355142\pi$
$854$		0			0
$855$		−	1.56275e6i		−	0.0731096i
$856$		0			0
$857$		−	3.07910e7i		−	1.43210i	−0.698051	−	0.716048i	$-0.745949\pi$
$857$		−	3.07910e7i		−	1.43210i	0.698051	−	0.716048i	$-0.254051\pi$
$858$		0			0
$859$	−1.87131e7	+	1.87131e7i	−0.865291	+	0.865291i	−0.991947	−	0.126656i	$-0.959576\pi$
$859$	−1.87131e7	+	1.87131e7i	−0.865291	+	0.865291i	0.126656	+	0.991947i	$0.459576\pi$
$860$		0			0
$861$	−1.13375e7	−	1.13375e7i	−0.521204	−	0.521204i
$862$		0			0
$863$	−1.11745e7			−0.510739			−0.255370	−	0.966843i	$-0.582197\pi$
$863$	−1.11745e7			−0.510739			−0.255370	+	0.966843i	$0.582197\pi$
$864$		0			0
$865$	−8.76953e6			−0.398507
$866$		0			0
$867$	−2.13067e6	−	2.13067e6i	−0.0962649	−	0.0962649i
$868$		0			0
$869$	319919.	−	319919.i	0.0143711	−	0.0143711i
$870$		0			0
$871$		−	4.76788e7i		−	2.12951i
$872$		0			0
$873$			1.39286e7i			0.618545i
$874$		0			0
$875$	−1.51728e6	+	1.51728e6i	−0.0669955	+	0.0669955i
$876$		0			0
$877$	−1.10977e7	−	1.10977e7i	−0.487231	−	0.487231i	0.420200	−	0.907431i	$-0.361960\pi$
$877$	−1.10977e7	−	1.10977e7i	−0.487231	−	0.487231i	−0.907431	+	0.420200i	$0.861960\pi$
$878$		0			0
$879$	4.63918e6			0.202521
$880$		0			0
$881$	−1.38137e7			−0.599610			−0.299805	−	0.954001i	$-0.596922\pi$
$881$	−1.38137e7			−0.599610			−0.299805	+	0.954001i	$0.596922\pi$
$882$		0			0
$883$	2.93312e7	+	2.93312e7i	1.26598	+	1.26598i	0.948144	+	0.317841i	$0.102958\pi$
$883$	2.93312e7	+	2.93312e7i	1.26598	+	1.26598i	0.317841	+	0.948144i	$0.397042\pi$
$884$		0			0
$885$	−3.70353e6	+	3.70353e6i	−0.158949	+	0.158949i
$886$		0			0
$887$			1.83380e7i			0.782606i	0.920262	+	0.391303i	$0.127976\pi$
$887$			1.83380e7i			0.782606i	−0.920262	+	0.391303i	$0.872024\pi$
$888$		0			0
$889$			2.31511e7i			0.982463i
$890$		0			0
$891$	−1.07349e7	+	1.07349e7i	−0.453007	+	0.453007i
$892$		0			0
$893$	4.99375e6	+	4.99375e6i	0.209555	+	0.209555i
$894$		0			0
$895$	−1.41968e7			−0.592424
$896$		0			0
$897$	−1.33275e7			−0.553054
$898$		0			0
$899$	−2.11341e6	−	2.11341e6i	−0.0872135	−	0.0872135i
$900$		0			0
$901$	−2.17332e7	+	2.17332e7i	−0.891890	+	0.891890i
$902$		0			0
$903$			7.08491e6i			0.289144i
$904$		0			0
$905$		−	5.49660e6i		−	0.223086i
$906$		0			0
$907$	1.71936e7	−	1.71936e7i	0.693983	−	0.693983i	−0.269123	−	0.963106i	$-0.586734\pi$
$907$	1.71936e7	−	1.71936e7i	0.693983	−	0.693983i	0.963106	+	0.269123i	$0.0867338\pi$
$908$		0			0
$909$	−2.59671e7	−	2.59671e7i	−1.04235	−	1.04235i
$910$		0			0
$911$	−3.45419e7			−1.37896			−0.689478	−	0.724306i	$-0.742160\pi$
$911$	−3.45419e7			−1.37896			−0.689478	+	0.724306i	$0.742160\pi$
$912$		0			0
$913$	−2.69004e7			−1.06802
$914$		0			0
$915$	941435.	+	941435.i	0.0371738	+	0.0371738i
$916$		0			0
$917$	1.99011e7	−	1.99011e7i	0.781546	−	0.781546i
$918$		0			0
$919$		−	4.56912e7i		−	1.78461i	−0.451430	−	0.892307i	$-0.649086\pi$
$919$		−	4.56912e7i		−	1.78461i	0.451430	−	0.892307i	$-0.350914\pi$
$920$		0			0
$921$		−	5.27215e6i		−	0.204804i
$922$		0			0
$923$	2.42808e6	−	2.42808e6i	0.0938119	−	0.0938119i
$924$		0			0
$925$	−4.74198e6	−	4.74198e6i	−0.182224	−	0.182224i
$926$		0			0
$927$	3.09406e7			1.18258
$928$		0			0
$929$	−2.46768e7			−0.938100			−0.469050	−	0.883172i	$-0.655404\pi$
$929$	−2.46768e7			−0.938100			−0.469050	+	0.883172i	$0.655404\pi$
$930$		0			0
$931$	−438331.	−	438331.i	−0.0165740	−	0.0165740i
$932$		0			0
$933$	1.11854e7	−	1.11854e7i	0.420675	−	0.420675i
$934$		0			0
$935$		−	1.54475e7i		−	0.577869i
$936$		0			0
$937$		−	9.52819e6i		−	0.354537i	−0.984163	−	0.177268i	$-0.943274\pi$
$937$		−	9.52819e6i		−	0.354537i	0.984163	−	0.177268i	$-0.0567261\pi$
$938$		0			0
$939$	−4.61935e6	+	4.61935e6i	−0.170969	+	0.170969i
$940$		0			0
$941$	−1.15872e7	−	1.15872e7i	−0.426582	−	0.426582i	0.460880	−	0.887462i	$-0.347534\pi$
$941$	−1.15872e7	−	1.15872e7i	−0.426582	−	0.426582i	−0.887462	+	0.460880i	$0.847534\pi$
$942$		0			0
$943$	3.85045e7			1.41004
$944$		0			0
$945$	9.27662e6			0.337917
$946$		0			0
$947$	−2.51480e7	−	2.51480e7i	−0.911232	−	0.911232i	0.0851370	−	0.996369i	$-0.472867\pi$
$947$	−2.51480e7	−	2.51480e7i	−0.911232	−	0.911232i	−0.996369	+	0.0851370i	$0.972867\pi$
$948$		0			0
$949$	4.64255e7	−	4.64255e7i	1.67336	−	1.67336i
$950$		0			0
$951$			3.82288e6i			0.137069i
$952$		0			0
$953$		−	2.43672e7i		−	0.869106i	−0.900646	−	0.434553i	$-0.856906\pi$
$953$		−	2.43672e7i		−	0.869106i	0.900646	−	0.434553i	$-0.143094\pi$
$954$		0			0
$955$	9.47913e6	−	9.47913e6i	0.336326	−	0.336326i
$956$		0			0
$957$	−937952.	−	937952.i	−0.0331055	−	0.0331055i
$958$		0			0
$959$	−1.96525e7			−0.690035
$960$		0			0
$961$	7.75011e6			0.270707
$962$		0			0
$963$	2.36993e7	+	2.36993e7i	0.823512	+	0.823512i
$964$		0			0
$965$	−8.53311e6	+	8.53311e6i	−0.294978	+	0.294978i
$966$		0			0
$967$			5.03403e7i			1.73121i	0.500727	+	0.865605i	$0.333066\pi$
$967$			5.03403e7i			1.73121i	−0.500727	+	0.865605i	$0.666934\pi$
$968$		0			0
$969$		−	2.51470e6i		−	0.0860353i
$970$		0			0
$971$	106900.	−	106900.i	0.00363857	−	0.00363857i	−0.705285	−	0.708924i	$-0.749181\pi$
$971$	106900.	−	106900.i	0.00363857	−	0.00363857i	0.708924	+	0.705285i	$0.249181\pi$
$972$		0			0
$973$	−2.48122e6	−	2.48122e6i	−0.0840200	−	0.0840200i
$974$		0			0
$975$	−4.20580e6			−0.141689
$976$		0			0
$977$	−3.49317e7			−1.17080			−0.585401	−	0.810744i	$-0.699063\pi$
$977$	−3.49317e7			−1.17080			−0.585401	+	0.810744i	$0.699063\pi$
$978$		0			0
$979$	−2.03276e7	−	2.03276e7i	−0.677844	−	0.677844i
$980$		0			0
$981$	−826085.	+	826085.i	−0.0274064	+	0.0274064i
$982$		0			0
$983$			1.27038e7i			0.419323i	0.977774	+	0.209661i	$0.0672362\pi$
$983$			1.27038e7i			0.419323i	−0.977774	+	0.209661i	$0.932764\pi$
$984$		0			0
$985$		−	2.46481e6i		−	0.0809457i
$986$		0			0
$987$	−1.36336e7	+	1.36336e7i	−0.445470	+	0.445470i
$988$		0			0
$989$	−1.20309e7	−	1.20309e7i	−0.391119	−	0.391119i
$990$		0			0
$991$	2.31792e6			0.0749745			0.0374873	−	0.999297i	$-0.488065\pi$
$991$	2.31792e6			0.0749745			0.0374873	+	0.999297i	$0.488065\pi$
$992$		0			0
$993$	−6.58218e6			−0.211835
$994$		0			0
$995$	1.10525e7	+	1.10525e7i	0.353919	+	0.353919i
$996$		0			0
$997$	4.99205e6	−	4.99205e6i	0.159053	−	0.159053i	−0.623094	−	0.782147i	$-0.714125\pi$
$997$	4.99205e6	−	4.99205e6i	0.159053	−	0.159053i	0.782147	+	0.623094i	$0.214125\pi$
$998$		0			0
$999$			2.89924e7i			0.919116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.16		80
4.3	odd	2		80.6.l.a.61.18	yes	80
16.5	even	4	inner	320.6.l.a.241.16		80
16.11	odd	4		80.6.l.a.21.18	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.18	✓	80	16.11	odd	4
80.6.l.a.61.18	yes	80	4.3	odd	2
320.6.l.a.81.16		80	1.1	even	1	trivial
320.6.l.a.241.16		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)

\(f(q)\)	\(=\)	\(q+(-4.24643 - 4.24643i) q^{3} +(17.6777 - 17.6777i) q^{5} -137.329i q^{7} -206.936i q^{9} +O(q^{10})\)	\(q+(-4.24643 - 4.24643i) q^{3} +(17.6777 - 17.6777i) q^{5} -137.329i q^{7} -206.936i q^{9} +(315.189 - 315.189i) q^{11} +(792.347 + 792.347i) q^{13} -150.134 q^{15} +1386.22 q^{17} +(213.599 + 213.599i) q^{19} +(-583.156 + 583.156i) q^{21} -1980.52i q^{23} -625.000i q^{25} +(-1910.62 + 1910.62i) q^{27} +(350.393 + 350.393i) q^{29} -6031.52 q^{31} -2676.85 q^{33} +(-2427.65 - 2427.65i) q^{35} +(7587.17 - 7587.17i) q^{37} -6729.29i q^{39} +19441.6i q^{41} +(6074.63 - 6074.63i) q^{43} +(-3658.14 - 3658.14i) q^{45} +23379.1 q^{47} -2052.12 q^{49} +(-5886.49 - 5886.49i) q^{51} +(-15678.0 + 15678.0i) q^{53} -11143.6i q^{55} -1814.07i q^{57} +(24668.2 - 24668.2i) q^{59} +(-6270.63 - 6270.63i) q^{61} -28418.2 q^{63} +28013.7 q^{65} +(-30087.1 - 30087.1i) q^{67} +(-8410.15 + 8410.15i) q^{69} -3064.41i q^{71} -58592.3i q^{73} +(-2654.02 + 2654.02i) q^{75} +(-43284.4 - 43284.4i) q^{77} +1015.01 q^{79} -34058.8 q^{81} +(-42673.4 - 42673.4i) q^{83} +(24505.2 - 24505.2i) q^{85} -2975.84i q^{87} -64493.5i q^{89} +(108812. - 108812. i) q^{91} +(25612.4 + 25612.4i) q^{93} +7551.87 q^{95} -67308.7 q^{97} +(-65223.8 - 65223.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q - 1208 q^{11} + 1800 q^{15} - 2360 q^{19} + 7464 q^{27} - 8144 q^{29} + 21296 q^{37} - 32072 q^{43} + 88360 q^{47} - 192080 q^{49} + 5920 q^{51} - 49456 q^{53} - 44984 q^{59} + 48080 q^{61} - 158760 q^{63} - 61160 q^{67} - 22320 q^{69} - 14896 q^{77} - 177680 q^{79} - 524880 q^{81} + 329240 q^{83} + 132400 q^{85} - 364832 q^{91} - 362352 q^{93} - 288800 q^{95} - 659000 q^{99}+O(q^{100}) \) 80 * q - 1208 * q^11 + 1800 * q^15 - 2360 * q^19 + 7464 * q^27 - 8144 * q^29 + 21296 * q^37 - 32072 * q^43 + 88360 * q^47 - 192080 * q^49 + 5920 * q^51 - 49456 * q^53 - 44984 * q^59 + 48080 * q^61 - 158760 * q^63 - 61160 * q^67 - 22320 * q^69 - 14896 * q^77 - 177680 * q^79 - 524880 * q^81 + 329240 * q^83 + 132400 * q^85 - 364832 * q^91 - 362352 * q^93 - 288800 * q^95 - 659000 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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