LMFDB - Embedded newform 320.6.l.a.81.6

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			81.6
Character	$\chi$	$=$	320.81
Dual form			320.6.l.a.241.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.2010 - 16.2010i) q^{3} +(17.6777 - 17.6777i) q^{5} -159.660i q^{7} +281.948i q^{9} +O(q^{10})$	\(q+(-16.2010 - 16.2010i) q^{3} +(17.6777 - 17.6777i) q^{5} -159.660i q^{7} +281.948i q^{9} +(-58.7419 + 58.7419i) q^{11} +(-491.490 - 491.490i) q^{13} -572.793 q^{15} +19.3515 q^{17} +(100.520 + 100.520i) q^{19} +(-2586.66 + 2586.66i) q^{21} -3385.86i q^{23} -625.000i q^{25} +(630.993 - 630.993i) q^{27} +(-4743.18 - 4743.18i) q^{29} -5812.35 q^{31} +1903.36 q^{33} +(-2822.42 - 2822.42i) q^{35} +(4047.67 - 4047.67i) q^{37} +15925.3i q^{39} -12957.9i q^{41} +(4599.08 - 4599.08i) q^{43} +(4984.18 + 4984.18i) q^{45} +26155.0 q^{47} -8684.32 q^{49} +(-313.515 - 313.515i) q^{51} +(-26950.5 + 26950.5i) q^{53} +2076.84i q^{55} -3257.07i q^{57} +(-24226.8 + 24226.8i) q^{59} +(-7163.75 - 7163.75i) q^{61} +45015.8 q^{63} -17376.8 q^{65} +(-8141.22 - 8141.22i) q^{67} +(-54854.5 + 54854.5i) q^{69} +56947.6i q^{71} +1144.60i q^{73} +(-10125.7 + 10125.7i) q^{75} +(9378.74 + 9378.74i) q^{77} +100600. q^{79} +48067.8 q^{81} +(17956.9 + 17956.9i) q^{83} +(342.090 - 342.090i) q^{85} +153689. i q^{87} +120441. i q^{89} +(-78471.2 + 78471.2i) q^{91} +(94166.2 + 94166.2i) q^{93} +3553.93 q^{95} +148192. q^{97} +(-16562.1 - 16562.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−16.2010	−	16.2010i	−1.03930	−	1.03930i	−0.999196	−	0.0401019i	$-0.987232\pi$
$3$	−16.2010	−	16.2010i	−1.03930	−	1.03930i	−0.0401019	−	0.999196i	$-0.512768\pi$
$4$		0			0
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$		0			0
$7$		−	159.660i		−	1.23155i	−0.787923	−	0.615774i	$-0.788844\pi$
$7$		−	159.660i		−	1.23155i	0.787923	−	0.615774i	$-0.211156\pi$
$8$		0			0
$9$			281.948i			1.16028i
$10$		0			0
$11$	−58.7419	+	58.7419i	−0.146375	+	0.146375i	−0.776496	−	0.630122i	$-0.783005\pi$
$11$	−58.7419	+	58.7419i	−0.146375	+	0.146375i	0.630122	+	0.776496i	$0.283005\pi$
$12$		0			0
$13$	−491.490	−	491.490i	−0.806596	−	0.806596i	0.177521	−	0.984117i	$-0.443192\pi$
$13$	−491.490	−	491.490i	−0.806596	−	0.806596i	−0.984117	+	0.177521i	$0.943192\pi$
$14$		0			0
$15$	−572.793			−0.657309
$16$		0			0
$17$	19.3515			0.0162403			0.00812013	−	0.999967i	$-0.497415\pi$
$17$	19.3515			0.0162403			0.00812013	+	0.999967i	$0.497415\pi$
$18$		0			0
$19$	100.520	+	100.520i	0.0638808	+	0.0638808i	0.738325	−	0.674445i	$-0.235617\pi$
$19$	100.520	+	100.520i	0.0638808	+	0.0638808i	−0.674445	+	0.738325i	$0.735617\pi$
$20$		0			0
$21$	−2586.66	+	2586.66i	−1.27994	+	1.27994i
$22$		0			0
$23$		−	3385.86i		−	1.33460i	−0.744791	−	0.667298i	$-0.767451\pi$
$23$		−	3385.86i		−	1.33460i	0.744791	−	0.667298i	$-0.232549\pi$
$24$		0			0
$25$		−	625.000i		−	0.200000i
$26$		0			0
$27$	630.993	−	630.993i	0.166577	−	0.166577i
$28$		0			0
$29$	−4743.18	−	4743.18i	−1.04731	−	1.04731i	−0.998824	−	0.0484835i	$-0.984561\pi$
$29$	−4743.18	−	4743.18i	−1.04731	−	1.04731i	−0.0484835	−	0.998824i	$-0.515439\pi$
$30$		0			0
$31$	−5812.35			−1.08629			−0.543147	−	0.839637i	$-0.682767\pi$
$31$	−5812.35			−1.08629			−0.543147	+	0.839637i	$0.682767\pi$
$32$		0			0
$33$	1903.36			0.304254
$34$		0			0
$35$	−2822.42	−	2822.42i	−0.389449	−	0.389449i
$36$		0			0
$37$	4047.67	−	4047.67i	0.486073	−	0.486073i	−0.420992	−	0.907064i	$-0.638318\pi$
$37$	4047.67	−	4047.67i	0.486073	−	0.486073i	0.907064	+	0.420992i	$0.138318\pi$
$38$		0			0
$39$			15925.3i			1.67659i
$40$		0			0
$41$		−	12957.9i		−	1.20386i	−0.798549	−	0.601930i	$-0.794398\pi$
$41$		−	12957.9i		−	1.20386i	0.798549	−	0.601930i	$-0.205602\pi$
$42$		0			0
$43$	4599.08	−	4599.08i	0.379315	−	0.379315i	−0.491540	−	0.870855i	$-0.663566\pi$
$43$	4599.08	−	4599.08i	0.379315	−	0.379315i	0.870855	+	0.491540i	$0.163566\pi$
$44$		0			0
$45$	4984.18	+	4984.18i	0.366912	+	0.366912i
$46$		0			0
$47$	26155.0			1.72707			0.863534	−	0.504290i	$-0.168246\pi$
$47$	26155.0			1.72707			0.863534	+	0.504290i	$0.168246\pi$
$48$		0			0
$49$	−8684.32			−0.516708
$50$		0			0
$51$	−313.515	−	313.515i	−0.0168785	−	0.0168785i
$52$		0			0
$53$	−26950.5	+	26950.5i	−1.31788	+	1.31788i	−0.402436	+	0.915448i	$0.631836\pi$
$53$	−26950.5	+	26950.5i	−1.31788	+	1.31788i	−0.915448	+	0.402436i	$0.868164\pi$
$54$		0			0
$55$			2076.84i			0.0925756i
$56$		0			0
$57$		−	3257.07i		−	0.132782i
$58$		0			0
$59$	−24226.8	+	24226.8i	−0.906081	+	0.906081i	−0.995953	−	0.0898726i	$-0.971354\pi$
$59$	−24226.8	+	24226.8i	−0.906081	+	0.906081i	0.0898726	+	0.995953i	$0.471354\pi$
$60$		0			0
$61$	−7163.75	−	7163.75i	−0.246499	−	0.246499i	0.573033	−	0.819532i	$-0.305767\pi$
$61$	−7163.75	−	7163.75i	−0.246499	−	0.246499i	−0.819532	+	0.573033i	$0.805767\pi$
$62$		0			0
$63$	45015.8			1.42894
$64$		0			0
$65$	−17376.8			−0.510136
$66$		0			0
$67$	−8141.22	−	8141.22i	−0.221566	−	0.221566i	0.587592	−	0.809158i	$-0.300076\pi$
$67$	−8141.22	−	8141.22i	−0.221566	−	0.221566i	−0.809158	+	0.587592i	$0.800076\pi$
$68$		0			0
$69$	−54854.5	+	54854.5i	−1.38704	+	1.38704i
$70$		0			0
$71$			56947.6i			1.34069i	0.742048	+	0.670346i	$0.233854\pi$
$71$			56947.6i			1.34069i	−0.742048	+	0.670346i	$0.766146\pi$
$72$		0			0
$73$			1144.60i			0.0251390i	0.999921	+	0.0125695i	$0.00400110\pi$
$73$			1144.60i			0.0251390i	−0.999921	+	0.0125695i	$0.995999\pi$
$74$		0			0
$75$	−10125.7	+	10125.7i	−0.207859	+	0.207859i
$76$		0			0
$77$	9378.74	+	9378.74i	0.180268	+	0.180268i
$78$		0			0
$79$	100600.			1.81356			0.906781	−	0.421603i	$-0.138532\pi$
$79$	100600.			1.81356			0.906781	+	0.421603i	$0.138532\pi$
$80$		0			0
$81$	48067.8			0.814032
$82$		0			0
$83$	17956.9	+	17956.9i	0.286113	+	0.286113i	0.835541	−	0.549428i	$-0.185154\pi$
$83$	17956.9	+	17956.9i	0.286113	+	0.286113i	−0.549428	+	0.835541i	$0.685154\pi$
$84$		0			0
$85$	342.090	−	342.090i	0.00513562	−	0.00513562i
$86$		0			0
$87$			153689.i			2.17693i
$88$		0			0
$89$			120441.i			1.61175i	0.592083	+	0.805877i	$0.298306\pi$
$89$			120441.i			1.61175i	−0.592083	+	0.805877i	$0.701694\pi$
$90$		0			0
$91$	−78471.2	+	78471.2i	−0.993361	+	0.993361i
$92$		0			0
$93$	94166.2	+	94166.2i	1.12898	+	1.12898i
$94$		0			0
$95$	3553.93			0.0404018
$96$		0			0
$97$	148192.			1.59918			0.799588	−	0.600549i	$-0.205051\pi$
$97$	148192.			1.59918			0.799588	+	0.600549i	$0.205051\pi$
$98$		0			0
$99$	−16562.1	−	16562.1i	−0.169836	−	0.169836i
$100$		0			0
$101$	−5470.74	+	5470.74i	−0.0533633	+	0.0533633i	−0.733285	−	0.679922i	$-0.762014\pi$
$101$	−5470.74	+	5470.74i	−0.0533633	+	0.0533633i	0.679922	+	0.733285i	$0.262014\pi$
$102$		0			0
$103$		−	127326.i		−	1.18256i	−0.806467	−	0.591279i	$-0.798623\pi$
$103$		−	127326.i		−	1.18256i	0.806467	−	0.591279i	$-0.201377\pi$
$104$		0			0
$105$			91452.2i			0.809508i
$106$		0			0
$107$	−4601.00	+	4601.00i	−0.0388502	+	0.0388502i	−0.726265	−	0.687415i	$-0.758745\pi$
$107$	−4601.00	+	4601.00i	−0.0388502	+	0.0388502i	0.687415	+	0.726265i	$0.258745\pi$
$108$		0			0
$109$	2160.76	+	2160.76i	0.0174197	+	0.0174197i	0.715763	−	0.698343i	$-0.246079\pi$
$109$	2160.76	+	2160.76i	0.0174197	+	0.0174197i	−0.698343	+	0.715763i	$0.746079\pi$
$110$		0			0
$111$	−131153.			−1.01035
$112$		0			0
$113$	26042.2			0.191859			0.0959293	−	0.995388i	$-0.469418\pi$
$113$	26042.2			0.191859			0.0959293	+	0.995388i	$0.469418\pi$
$114$		0			0
$115$	−59854.1	−	59854.1i	−0.422036	−	0.422036i
$116$		0			0
$117$	138574.	−	138574.i	0.935876	−	0.935876i
$118$		0			0
$119$		−	3089.67i		−	0.0200007i
$120$		0			0
$121$			154150.i			0.957149i
$122$		0			0
$123$	−209932.	+	209932.i	−1.25117	+	1.25117i
$124$		0			0
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	−286069.			−1.57384			−0.786921	−	0.617054i	$-0.788326\pi$
$127$	−286069.			−1.57384			−0.786921	+	0.617054i	$0.788326\pi$
$128$		0			0
$129$	−149020.			−0.788443
$130$		0			0
$131$	−135647.	−	135647.i	−0.690608	−	0.690608i	0.271758	−	0.962366i	$-0.412395\pi$
$131$	−135647.	−	135647.i	−0.690608	−	0.690608i	−0.962366	+	0.271758i	$0.912395\pi$
$132$		0			0
$133$	16049.1	−	16049.1i	0.0786722	−	0.0786722i
$134$		0			0
$135$		−	22309.0i		−	0.105353i
$136$		0			0
$137$			402057.i			1.83015i	0.403288	+	0.915073i	$0.367867\pi$
$137$			402057.i			1.83015i	−0.403288	+	0.915073i	$0.632133\pi$
$138$		0			0
$139$	144956.	−	144956.i	0.636357	−	0.636357i	−0.313298	−	0.949655i	$-0.601434\pi$
$139$	144956.	−	144956.i	0.636357	−	0.636357i	0.949655	+	0.313298i	$0.101434\pi$
$140$		0			0
$141$	−423738.	−	423738.i	−1.79494	−	1.79494i
$142$		0			0
$143$	57742.1			0.236131
$144$		0			0
$145$	−167697.			−0.662375
$146$		0			0
$147$	140695.	+	140695.i	0.537014	+	0.537014i
$148$		0			0
$149$	277305.	−	277305.i	1.02327	−	1.02327i	0.0235511	−	0.999723i	$-0.492503\pi$
$149$	277305.	−	277305.i	1.02327	−	1.02327i	0.999723	−	0.0235511i	$-0.00749725\pi$
$150$		0			0
$151$		−	40937.6i		−	0.146110i	−0.997328	−	0.0730550i	$-0.976725\pi$
$151$		−	40937.6i		−	0.146110i	0.997328	−	0.0730550i	$-0.0232749\pi$
$152$		0			0
$153$			5456.12i			0.0188432i
$154$		0			0
$155$	−102749.	+	102749.i	−0.343517	+	0.343517i
$156$		0			0
$157$	−30694.3	−	30694.3i	−0.0993823	−	0.0993823i	0.655667	−	0.755050i	$-0.272387\pi$
$157$	−30694.3	−	30694.3i	−0.0993823	−	0.0993823i	−0.755050	+	0.655667i	$0.772387\pi$
$158$		0			0
$159$	873252.			2.73935
$160$		0			0
$161$	−540587.			−1.64362
$162$		0			0
$163$	160362.	+	160362.i	0.472751	+	0.472751i	0.902804	−	0.430053i	$-0.141505\pi$
$163$	160362.	+	160362.i	0.472751	+	0.472751i	−0.430053	+	0.902804i	$0.641505\pi$
$164$		0			0
$165$	33647.0	−	33647.0i	0.0962136	−	0.0962136i
$166$		0			0
$167$		−	408725.i		−	1.13407i	−0.823693	−	0.567036i	$-0.808090\pi$
$167$		−	408725.i		−	1.13407i	0.823693	−	0.567036i	$-0.191910\pi$
$168$		0			0
$169$			111831.i			0.301194i
$170$		0			0
$171$	−28341.5	+	28341.5i	−0.0741195	+	0.0741195i
$172$		0			0
$173$	94489.5	+	94489.5i	0.240032	+	0.240032i	0.816863	−	0.576832i	$-0.195711\pi$
$173$	94489.5	+	94489.5i	0.240032	+	0.240032i	−0.576832	+	0.816863i	$0.695711\pi$
$174$		0			0
$175$	−99787.5			−0.246309
$176$		0			0
$177$	785000.			1.88337
$178$		0			0
$179$	−24837.2	−	24837.2i	−0.0579389	−	0.0579389i	0.677544	−	0.735483i	$-0.263044\pi$
$179$	−24837.2	−	24837.2i	−0.0579389	−	0.0579389i	−0.735483	+	0.677544i	$0.763044\pi$
$180$		0			0
$181$	−328837.	+	328837.i	−0.746078	+	0.746078i	−0.973740	−	0.227662i	$-0.926892\pi$
$181$	−328837.	+	328837.i	−0.746078	+	0.746078i	0.227662	+	0.973740i	$0.426892\pi$
$182$		0			0
$183$			232120.i			0.512372i
$184$		0			0
$185$		−	143107.i		−	0.307419i
$186$		0			0
$187$	−1136.75	+	1136.75i	−0.00237717	+	0.00237717i
$188$		0			0
$189$	−100744.	−	100744.i	−0.205147	−	0.205147i
$190$		0			0
$191$	−665499.			−1.31997			−0.659985	−	0.751279i	$-0.729437\pi$
$191$	−665499.			−1.31997			−0.659985	+	0.751279i	$0.729437\pi$
$192$		0			0
$193$	−156383.			−0.302200			−0.151100	−	0.988518i	$-0.548282\pi$
$193$	−156383.			−0.302200			−0.151100	+	0.988518i	$0.548282\pi$
$194$		0			0
$195$	281522.	+	281522.i	0.530183	+	0.530183i
$196$		0			0
$197$	617329.	−	617329.i	1.13332	−	1.13332i	0.143695	−	0.989622i	$-0.454102\pi$
$197$	617329.	−	617329.i	1.13332	−	1.13332i	0.989622	−	0.143695i	$-0.0458985\pi$
$198$		0			0
$199$		−	427742.i		−	0.765684i	−0.923814	−	0.382842i	$-0.874945\pi$
$199$		−	427742.i		−	0.765684i	0.923814	−	0.382842i	$-0.125055\pi$
$200$		0			0
$201$			263793.i			0.460545i
$202$		0			0
$203$	−757295.	+	757295.i	−1.28981	+	1.28981i
$204$		0			0
$205$	−229066.	−	229066.i	−0.380694	−	0.380694i
$206$		0			0
$207$	954636.			1.54850
$208$		0			0
$209$	−11809.5			−0.0187011
$210$		0			0
$211$	−600678.	−	600678.i	−0.928828	−	0.928828i	0.0688020	−	0.997630i	$-0.478082\pi$
$211$	−600678.	−	600678.i	−0.928828	−	0.928828i	−0.997630	+	0.0688020i	$0.978082\pi$
$212$		0			0
$213$	922610.	−	922610.i	1.39338	−	1.39338i
$214$		0			0
$215$		−	162602.i		−	0.239900i
$216$		0			0
$217$			928000.i			1.33782i
$218$		0			0
$219$	18543.8	−	18543.8i	0.0261269	−	0.0261269i
$220$		0			0
$221$	−9511.08	−	9511.08i	−0.0130993	−	0.0130993i
$222$		0			0
$223$	999082.			1.34536			0.672681	−	0.739933i	$-0.265143\pi$
$223$	999082.			1.34536			0.672681	+	0.739933i	$0.265143\pi$
$224$		0			0
$225$	176217.			0.232056
$226$		0			0
$227$	302038.	+	302038.i	0.389042	+	0.389042i	0.874346	−	0.485304i	$-0.161291\pi$
$227$	302038.	+	302038.i	0.389042	+	0.389042i	−0.485304	+	0.874346i	$0.661291\pi$
$228$		0			0
$229$	−1.03004e6	+	1.03004e6i	−1.29797	+	1.29797i	−0.368238	+	0.929731i	$0.620039\pi$
$229$	−1.03004e6	+	1.03004e6i	−1.29797	+	1.29797i	−0.929731	+	0.368238i	$0.879961\pi$
$230$		0			0
$231$		−	303891.i		−	0.374703i
$232$		0			0
$233$		−	281166.i		−	0.339292i	−0.985505	−	0.169646i	$-0.945738\pi$
$233$		−	281166.i		−	0.339292i	0.985505	−	0.169646i	$-0.0542624\pi$
$234$		0			0
$235$	462359.	−	462359.i	0.546147	−	0.546147i
$236$		0			0
$237$	−1.62983e6	−	1.62983e6i	−1.88483	−	1.88483i
$238$		0			0
$239$	1.29278e6			1.46397			0.731983	−	0.681323i	$-0.238595\pi$
$239$	1.29278e6			1.46397			0.731983	+	0.681323i	$0.238595\pi$
$240$		0			0
$241$	268892.			0.298219			0.149110	−	0.988821i	$-0.452359\pi$
$241$	268892.			0.298219			0.149110	+	0.988821i	$0.452359\pi$
$242$		0			0
$243$	−932080.	−	932080.i	−1.01260	−	1.01260i
$244$		0			0
$245$	−153518.	+	153518.i	−0.163398	+	0.163398i
$246$		0			0
$247$		−	98809.5i		−	0.103052i
$248$		0			0
$249$		−	581843.i		−	0.594713i
$250$		0			0
$251$	−160551.	+	160551.i	−0.160853	+	0.160853i	−0.782945	−	0.622091i	$-0.786283\pi$
$251$	−160551.	+	160551.i	−0.160853	+	0.160853i	0.622091	+	0.782945i	$0.286283\pi$
$252$		0			0
$253$	198892.	+	198892.i	0.195351	+	0.195351i
$254$		0			0
$255$	−11084.4			−0.0106749
$256$		0			0
$257$	−873555.			−0.825007			−0.412503	−	0.910956i	$-0.635346\pi$
$257$	−873555.			−0.825007			−0.412503	+	0.910956i	$0.635346\pi$
$258$		0			0
$259$	−646251.	−	646251.i	−0.598621	−	0.598621i
$260$		0			0
$261$	1.33733e6	−	1.33733e6i	1.21517	−	1.21517i
$262$		0			0
$263$			1.52024e6i			1.35526i	0.735401	+	0.677632i	$0.236994\pi$
$263$			1.52024e6i			1.35526i	−0.735401	+	0.677632i	$0.763006\pi$
$264$		0			0
$265$			952844.i			0.833503i
$266$		0			0
$267$	1.95127e6	−	1.95127e6i	1.67509	−	1.67509i
$268$		0			0
$269$	304637.	+	304637.i	0.256686	+	0.256686i	0.823705	−	0.567019i	$-0.191903\pi$
$269$	304637.	+	304637.i	0.256686	+	0.256686i	−0.567019	+	0.823705i	$0.691903\pi$
$270$		0			0
$271$	1.32572e6			1.09655			0.548274	−	0.836298i	$-0.315285\pi$
$271$	1.32572e6			1.09655			0.548274	+	0.836298i	$0.315285\pi$
$272$		0			0
$273$	2.54263e6			2.06479
$274$		0			0
$275$	36713.7	+	36713.7i	0.0292750	+	0.0292750i
$276$		0			0
$277$	269409.	−	269409.i	0.210966	−	0.210966i	−0.593712	−	0.804678i	$-0.702338\pi$
$277$	269409.	−	269409.i	0.210966	−	0.210966i	0.804678	+	0.593712i	$0.202338\pi$
$278$		0			0
$279$		−	1.63878e6i		−	1.26040i
$280$		0			0
$281$		−	2.09147e6i		−	1.58010i	−0.613041	−	0.790051i	$-0.710054\pi$
$281$		−	2.09147e6i		−	1.58010i	0.613041	−	0.790051i	$-0.289946\pi$
$282$		0			0
$283$	−707671.	+	707671.i	−0.525249	+	0.525249i	−0.919152	−	0.393903i	$-0.871125\pi$
$283$	−707671.	+	707671.i	−0.525249	+	0.525249i	0.393903	+	0.919152i	$0.371125\pi$
$284$		0			0
$285$	−57577.4	−	57577.4i	−0.0419895	−	0.0419895i
$286$		0			0
$287$	−2.06886e6			−1.48261
$288$		0			0
$289$	−1.41948e6			−0.999736
$290$		0			0
$291$	−2.40087e6	−	2.40087e6i	−1.66202	−	1.66202i
$292$		0			0
$293$	287612.	−	287612.i	0.195721	−	0.195721i	−0.602442	−	0.798163i	$-0.705805\pi$
$293$	287612.	−	287612.i	0.195721	−	0.195721i	0.798163	+	0.602442i	$0.205805\pi$
$294$		0			0
$295$			856548.i			0.573056i
$296$		0			0
$297$			74131.5i			0.0487654i
$298$		0			0
$299$	−1.66412e6	+	1.66412e6i	−1.07648	+	1.07648i
$300$		0			0
$301$	−734290.	−	734290.i	−0.467144	−	0.467144i
$302$		0			0
$303$	177264.			0.110921
$304$		0			0
$305$	−253277.			−0.155900
$306$		0			0
$307$	−706261.	−	706261.i	−0.427681	−	0.427681i	0.460157	−	0.887838i	$-0.347793\pi$
$307$	−706261.	−	706261.i	−0.427681	−	0.427681i	−0.887838	+	0.460157i	$0.847793\pi$
$308$		0			0
$309$	−2.06281e6	+	2.06281e6i	−1.22903	+	1.22903i
$310$		0			0
$311$		−	572959.i		−	0.335909i	−0.985795	−	0.167955i	$-0.946284\pi$
$311$		−	572959.i		−	0.335909i	0.985795	−	0.167955i	$-0.0537162\pi$
$312$		0			0
$313$			341554.i			0.197060i	0.995134	+	0.0985300i	$0.0314140\pi$
$313$			341554.i			0.197060i	−0.995134	+	0.0985300i	$0.968586\pi$
$314$		0			0
$315$	795774.	−	795774.i	0.451870	−	0.451870i
$316$		0			0
$317$	−670516.	−	670516.i	−0.374767	−	0.374767i	0.494443	−	0.869210i	$-0.335372\pi$
$317$	−670516.	−	670516.i	−0.374767	−	0.374767i	−0.869210	+	0.494443i	$0.835372\pi$
$318$		0			0
$319$	557247.			0.306599
$320$		0			0
$321$	149082.			0.0807538
$322$		0			0
$323$	1945.22	+	1945.22i	0.00103744	+	0.00103744i
$324$		0			0
$325$	−307181.	+	307181.i	−0.161319	+	0.161319i
$326$		0			0
$327$		−	70013.1i		−	0.0362084i
$328$		0			0
$329$		−	4.17590e6i		−	2.12697i
$330$		0			0
$331$	−2.44820e6	+	2.44820e6i	−1.22822	+	1.22822i	−0.263589	+	0.964635i	$0.584906\pi$
$331$	−2.44820e6	+	2.44820e6i	−1.22822	+	1.22822i	−0.964635	+	0.263589i	$0.915094\pi$
$332$		0			0
$333$	1.14123e6	+	1.14123e6i	0.563980	+	0.563980i
$334$		0			0
$335$	−287836.			−0.140130
$336$		0			0
$337$	−620990.			−0.297858			−0.148929	−	0.988848i	$-0.547583\pi$
$337$	−620990.			−0.297858			−0.148929	+	0.988848i	$0.547583\pi$
$338$		0			0
$339$	−421910.	−	421910.i	−0.199398	−	0.199398i
$340$		0			0
$341$	341429.	−	341429.i	0.159006	−	0.159006i
$342$		0			0
$343$		−	1.29687e6i		−	0.595196i
$344$		0			0
$345$			1.93940e6i			0.877242i
$346$		0			0
$347$	−1.62058e6	+	1.62058e6i	−0.722514	+	0.722514i	−0.969117	−	0.246603i	$-0.920686\pi$
$347$	−1.62058e6	+	1.62058e6i	−0.722514	+	0.722514i	0.246603	+	0.969117i	$0.420686\pi$
$348$		0			0
$349$	1.28269e6	+	1.28269e6i	0.563712	+	0.563712i	0.930360	−	0.366648i	$-0.119495\pi$
$349$	1.28269e6	+	1.28269e6i	0.563712	+	0.563712i	−0.366648	+	0.930360i	$0.619495\pi$
$350$		0			0
$351$	−620253.			−0.268721
$352$		0			0
$353$	2.65388e6			1.13356			0.566781	−	0.823869i	$-0.308189\pi$
$353$	2.65388e6			1.13356			0.566781	+	0.823869i	$0.308189\pi$
$354$		0			0
$355$	1.00670e6	+	1.00670e6i	0.423964	+	0.423964i
$356$		0			0
$357$	−50055.8	+	50055.8i	−0.0207866	+	0.0207866i
$358$		0			0
$359$			598613.i			0.245138i	0.992460	+	0.122569i	$0.0391132\pi$
$359$			598613.i			0.245138i	−0.992460	+	0.122569i	$0.960887\pi$
$360$		0			0
$361$		−	2.45589e6i		−	0.991838i
$362$		0			0
$363$	2.49739e6	−	2.49739e6i	0.994762	−	0.994762i
$364$		0			0
$365$	20233.9	+	20233.9i	0.00794965	+	0.00794965i
$366$		0			0
$367$	−3.24825e6			−1.25888			−0.629439	−	0.777050i	$-0.716715\pi$
$367$	−3.24825e6			−1.25888			−0.629439	+	0.777050i	$0.716715\pi$
$368$		0			0
$369$	3.65346e6			1.39681
$370$		0			0
$371$	4.30292e6	+	4.30292e6i	1.62304	+	1.62304i
$372$		0			0
$373$	−3.04556e6	+	3.04556e6i	−1.13343	+	1.13343i	−0.143829	+	0.989603i	$0.545942\pi$
$373$	−3.04556e6	+	3.04556e6i	−1.13343	+	1.13343i	−0.989603	+	0.143829i	$0.954058\pi$
$374$		0			0
$375$			357996.i			0.131462i
$376$		0			0
$377$			4.66244e6i			1.68951i
$378$		0			0
$379$	−1.26344e6	+	1.26344e6i	−0.451809	+	0.451809i	−0.895955	−	0.444145i	$-0.853507\pi$
$379$	−1.26344e6	+	1.26344e6i	−0.451809	+	0.451809i	0.444145	+	0.895955i	$0.353507\pi$
$380$		0			0
$381$	4.63461e6	+	4.63461e6i	1.63569	+	1.63569i
$382$		0			0
$383$	1.82851e6			0.636943			0.318471	−	0.947932i	$-0.396831\pi$
$383$	1.82851e6			0.636943			0.318471	+	0.947932i	$0.396831\pi$
$384$		0			0
$385$	331588.			0.114011
$386$		0			0
$387$	1.29670e6	+	1.29670e6i	0.440111	+	0.440111i
$388$		0			0
$389$	1.27278e6	−	1.27278e6i	0.426462	−	0.426462i	−0.460959	−	0.887421i	$-0.652495\pi$
$389$	1.27278e6	−	1.27278e6i	0.426462	−	0.426462i	0.887421	+	0.460959i	$0.152495\pi$
$390$		0			0
$391$		−	65521.6i		−	0.0216742i
$392$		0			0
$393$			4.39524e6i			1.43549i
$394$		0			0
$395$	1.77838e6	−	1.77838e6i	0.573498	−	0.573498i
$396$		0			0
$397$	−2.10438e6	−	2.10438e6i	−0.670111	−	0.670111i	0.287630	−	0.957742i	$-0.407133\pi$
$397$	−2.10438e6	−	2.10438e6i	−0.670111	−	0.670111i	−0.957742	+	0.287630i	$0.907133\pi$
$398$		0			0
$399$	−520024.			−0.163528
$400$		0			0
$401$	−3.53859e6			−1.09893			−0.549464	−	0.835517i	$-0.685168\pi$
$401$	−3.53859e6			−1.09893			−0.549464	+	0.835517i	$0.685168\pi$
$402$		0			0
$403$	2.85671e6	+	2.85671e6i	0.876201	+	0.876201i
$404$		0			0
$405$	849727.	−	849727.i	0.257420	−	0.257420i
$406$		0			0
$407$			475536.i			0.142298i
$408$		0			0
$409$			3.94310e6i			1.16555i	0.812635	+	0.582773i	$0.198033\pi$
$409$			3.94310e6i			1.16555i	−0.812635	+	0.582773i	$0.801967\pi$
$410$		0			0
$411$	6.51374e6	−	6.51374e6i	1.90207	−	1.90207i
$412$		0			0
$413$	3.86806e6	+	3.86806e6i	1.11588	+	1.11588i
$414$		0			0
$415$	634874.			0.180954
$416$		0			0
$417$	−4.69689e6			−1.32273
$418$		0			0
$419$	115793.	+	115793.i	0.0322216	+	0.0322216i	0.723034	−	0.690812i	$-0.242747\pi$
$419$	115793.	+	115793.i	0.0322216	+	0.0322216i	−0.690812	+	0.723034i	$0.742747\pi$
$420$		0			0
$421$	1.16233e6	−	1.16233e6i	0.319612	−	0.319612i	−0.529006	−	0.848618i	$-0.677435\pi$
$421$	1.16233e6	−	1.16233e6i	0.319612	−	0.319612i	0.848618	+	0.529006i	$0.177435\pi$
$422$		0			0
$423$			7.37433e6i			2.00388i
$424$		0			0
$425$		−	12094.7i		−	0.00324805i
$426$		0			0
$427$	−1.14376e6	+	1.14376e6i	−0.303575	+	0.303575i
$428$		0			0
$429$	−935482.	−	935482.i	−0.245410	−	0.245410i
$430$		0			0
$431$	−3.60001e6			−0.933491			−0.466745	−	0.884392i	$-0.654574\pi$
$431$	−3.60001e6			−0.933491			−0.466745	+	0.884392i	$0.654574\pi$
$432$		0			0
$433$	−2.84506e6			−0.729243			−0.364622	−	0.931156i	$-0.618802\pi$
$433$	−2.84506e6			−0.729243			−0.364622	+	0.931156i	$0.618802\pi$
$434$		0			0
$435$	2.71686e6	+	2.71686e6i	0.688405	+	0.688405i
$436$		0			0
$437$	340348.	−	340348.i	0.0852550	−	0.0852550i
$438$		0			0
$439$			713139.i			0.176609i	0.996094	+	0.0883045i	$0.0281448\pi$
$439$			713139.i			0.176609i	−0.996094	+	0.0883045i	$0.971855\pi$
$440$		0			0
$441$		−	2.44852e6i		−	0.599526i
$442$		0			0
$443$	−2.89448e6	+	2.89448e6i	−0.700747	+	0.700747i	−0.964571	−	0.263824i	$-0.915016\pi$
$443$	−2.89448e6	+	2.89448e6i	−0.700747	+	0.700747i	0.263824	+	0.964571i	$0.415016\pi$
$444$		0			0
$445$	2.12911e6	+	2.12911e6i	0.509681	+	0.509681i
$446$		0			0
$447$	−8.98526e6			−2.12697
$448$		0			0
$449$	−8.34000e6			−1.95232			−0.976159	−	0.217058i	$-0.930354\pi$
$449$	−8.34000e6			−1.95232			−0.976159	+	0.217058i	$0.930354\pi$
$450$		0			0
$451$	761174.	+	761174.i	0.176215	+	0.176215i
$452$		0			0
$453$	−663232.	+	663232.i	−0.151852	+	0.151852i
$454$		0			0
$455$			2.77438e6i			0.628257i
$456$		0			0
$457$		−	2.29162e6i		−	0.513277i	−0.966507	−	0.256639i	$-0.917385\pi$
$457$		−	2.29162e6i		−	0.513277i	0.966507	−	0.256639i	$-0.0826150\pi$
$458$		0			0
$459$	12210.7	−	12210.7i	0.00270525	−	0.00270525i
$460$		0			0
$461$	−621052.	−	621052.i	−0.136106	−	0.136106i	0.635772	−	0.771877i	$-0.280682\pi$
$461$	−621052.	−	621052.i	−0.136106	−	0.136106i	−0.771877	+	0.635772i	$0.780682\pi$
$462$		0			0
$463$	−5.61610e6			−1.21754			−0.608768	−	0.793348i	$-0.708336\pi$
$463$	−5.61610e6			−1.21754			−0.608768	+	0.793348i	$0.708336\pi$
$464$		0			0
$465$	3.32928e6			0.714032
$466$		0			0
$467$	2.90097e6	+	2.90097e6i	0.615532	+	0.615532i	0.944382	−	0.328850i	$-0.106661\pi$
$467$	2.90097e6	+	2.90097e6i	0.615532	+	0.615532i	−0.328850	+	0.944382i	$0.606661\pi$
$468$		0			0
$469$	−1.29983e6	+	1.29983e6i	−0.272869	+	0.272869i
$470$		0			0
$471$			994561.i			0.206576i
$472$		0			0
$473$			540318.i			0.111044i
$474$		0			0
$475$	62825.3	−	62825.3i	0.0127762	−	0.0127762i
$476$		0			0
$477$	−7.59863e6	−	7.59863e6i	−1.52911	−	1.52911i
$478$		0			0
$479$	4.90782e6			0.977349			0.488674	−	0.872466i	$-0.337481\pi$
$479$	4.90782e6			0.977349			0.488674	+	0.872466i	$0.337481\pi$
$480$		0			0
$481$	−3.97878e6			−0.784128
$482$		0			0
$483$	8.75807e6	+	8.75807e6i	1.70821	+	1.70821i
$484$		0			0
$485$	2.61969e6	−	2.61969e6i	0.505704	−	0.505704i
$486$		0			0
$487$		−	6.38029e6i		−	1.21904i	−0.792771	−	0.609520i	$-0.791362\pi$
$487$		−	6.38029e6i		−	1.21904i	0.792771	−	0.609520i	$-0.208638\pi$
$488$		0			0
$489$		−	5.19606e6i		−	0.982657i
$490$		0			0
$491$	2.60358e6	−	2.60358e6i	0.487380	−	0.487380i	−0.420099	−	0.907478i	$-0.638005\pi$
$491$	2.60358e6	−	2.60358e6i	0.487380	−	0.487380i	0.907478	+	0.420099i	$0.138005\pi$
$492$		0			0
$493$	−91787.7	−	91787.7i	−0.0170086	−	0.0170086i
$494$		0			0
$495$	−585560.			−0.107413
$496$		0			0
$497$	9.09225e6			1.65113
$498$		0			0
$499$	−4.43405e6	−	4.43405e6i	−0.797167	−	0.797167i	0.185481	−	0.982648i	$-0.440616\pi$
$499$	−4.43405e6	−	4.43405e6i	−0.797167	−	0.797167i	−0.982648	+	0.185481i	$0.940616\pi$
$500$		0			0
$501$	−6.62178e6	+	6.62178e6i	−1.17864	+	1.17864i
$502$		0			0
$503$			165.625i			2.91880e-5i	1.00000		1.45940e-5i	$4.64542e-6\pi$
$503$			165.625i			2.91880e-5i	−1.00000		1.45940e-5i	$0.999995\pi$
$504$		0			0
$505$			193420.i			0.0337499i
$506$		0			0
$507$	1.81178e6	−	1.81178e6i	0.313030	−	0.313030i
$508$		0			0
$509$	3.01710e6	+	3.01710e6i	0.516173	+	0.516173i	0.916411	−	0.400238i	$-0.131073\pi$
$509$	3.01710e6	+	3.01710e6i	0.516173	+	0.516173i	−0.400238	+	0.916411i	$0.631073\pi$
$510$		0			0
$511$	182748.			0.0309599
$512$		0			0
$513$	126855.			0.0212821
$514$		0			0
$515$	−2.25082e6	−	2.25082e6i	−0.373958	−	0.373958i
$516$		0			0
$517$	−1.53639e6	+	1.53639e6i	−0.252799	+	0.252799i
$518$		0			0
$519$		−	3.06166e6i		−	0.498928i
$520$		0			0
$521$		−	6.89876e6i		−	1.11347i	−0.830692	−	0.556733i	$-0.812055\pi$
$521$		−	6.89876e6i		−	1.11347i	0.830692	−	0.556733i	$-0.187945\pi$
$522$		0			0
$523$	−611830.	+	611830.i	−0.0978084	+	0.0978084i	−0.754318	−	0.656509i	$-0.772032\pi$
$523$	−611830.	+	611830.i	−0.0978084	+	0.0978084i	0.656509	+	0.754318i	$0.272032\pi$
$524$		0			0
$525$	1.61666e6	+	1.61666e6i	0.255989	+	0.255989i
$526$		0			0
$527$	−112478.			−0.0176417
$528$		0			0
$529$	−5.02771e6			−0.781144
$530$		0			0
$531$	−6.83070e6	−	6.83070e6i	−1.05131	−	1.05131i
$532$		0			0
$533$	−6.36869e6	+	6.36869e6i	−0.971029	+	0.971029i
$534$		0			0
$535$			162670.i			0.0245710i
$536$		0			0
$537$			804777.i			0.120431i
$538$		0			0
$539$	510134.	−	510134.i	0.0756331	−	0.0756331i
$540$		0			0
$541$	−1.08458e6	−	1.08458e6i	−0.159320	−	0.159320i	0.622945	−	0.782265i	$-0.285936\pi$
$541$	−1.08458e6	−	1.08458e6i	−0.159320	−	0.159320i	−0.782265	+	0.622945i	$0.785936\pi$
$542$		0			0
$543$	1.06550e7			1.55079
$544$		0			0
$545$	76394.4			0.0110172
$546$		0			0
$547$	−6.82821e6	−	6.82821e6i	−0.975750	−	0.975750i	0.0239628	−	0.999713i	$-0.492372\pi$
$547$	−6.82821e6	−	6.82821e6i	−0.975750	−	0.975750i	−0.999713	+	0.0239628i	$0.992372\pi$
$548$		0			0
$549$	2.01980e6	−	2.01980e6i	0.286008	−	0.286008i
$550$		0			0
$551$		−	953572.i		−	0.133806i
$552$		0			0
$553$		−	1.60619e7i		−	2.23349i
$554$		0			0
$555$	−2.31848e6	+	2.31848e6i	−0.319500	+	0.319500i
$556$		0			0
$557$	5.26644e6	+	5.26644e6i	0.719249	+	0.719249i	0.968451	−	0.249202i	$-0.0801684\pi$
$557$	5.26644e6	+	5.26644e6i	0.719249	+	0.719249i	−0.249202	+	0.968451i	$0.580168\pi$
$558$		0			0
$559$	−4.52080e6			−0.611908
$560$		0			0
$561$	36833.0			0.00494117
$562$		0			0
$563$	−1.11973e6	−	1.11973e6i	−0.148883	−	0.148883i	0.628736	−	0.777619i	$-0.283573\pi$
$563$	−1.11973e6	−	1.11973e6i	−0.148883	−	0.148883i	−0.777619	+	0.628736i	$0.783573\pi$
$564$		0			0
$565$	460365.	−	460365.i	0.0606710	−	0.0606710i
$566$		0			0
$567$		−	7.67450e6i		−	1.00252i
$568$		0			0
$569$		−	2.32892e6i		−	0.301561i	−0.988567	−	0.150780i	$-0.951821\pi$
$569$		−	2.32892e6i		−	0.301561i	0.988567	−	0.150780i	$-0.0481786\pi$
$570$		0			0
$571$	4.32124e6	−	4.32124e6i	0.554649	−	0.554649i	−0.373130	−	0.927779i	$-0.621715\pi$
$571$	4.32124e6	−	4.32124e6i	0.554649	−	0.554649i	0.927779	+	0.373130i	$0.121715\pi$
$572$		0			0
$573$	1.07818e7	+	1.07818e7i	1.37184	+	1.37184i
$574$		0			0
$575$	−2.11616e6			−0.266919
$576$		0			0
$577$	7.18841e6			0.898862			0.449431	−	0.893315i	$-0.351627\pi$
$577$	7.18841e6			0.898862			0.449431	+	0.893315i	$0.351627\pi$
$578$		0			0
$579$	2.53356e6	+	2.53356e6i	0.314076	+	0.314076i
$580$		0			0
$581$	2.86701e6	−	2.86701e6i	0.352361	−	0.352361i
$582$		0			0
$583$		−	3.16625e6i		−	0.385810i
$584$		0			0
$585$		−	4.89934e6i		−	0.591900i
$586$		0			0
$587$	3.11220e6	−	3.11220e6i	0.372796	−	0.372796i	−0.495698	−	0.868495i	$-0.665088\pi$
$587$	3.11220e6	−	3.11220e6i	0.372796	−	0.372796i	0.868495	+	0.495698i	$0.165088\pi$
$588$		0			0
$589$	−584260.	−	584260.i	−0.0693934	−	0.0693934i
$590$		0			0
$591$	−2.00028e7			−2.35571
$592$		0			0
$593$	2.94318e6			0.343700			0.171850	−	0.985123i	$-0.445026\pi$
$593$	2.94318e6			0.343700			0.171850	+	0.985123i	$0.445026\pi$
$594$		0			0
$595$	−54618.1	−	54618.1i	−0.00632476	−	0.00632476i
$596$		0			0
$597$	−6.92987e6	+	6.92987e6i	−0.795774	+	0.795774i
$598$		0			0
$599$			1.29219e7i			1.47150i	0.677252	+	0.735751i	$0.263171\pi$
$599$			1.29219e7i			1.47150i	−0.677252	+	0.735751i	$0.736829\pi$
$600$		0			0
$601$			347524.i			0.0392463i	0.999807	+	0.0196232i	$0.00624665\pi$
$601$			347524.i			0.0392463i	−0.999807	+	0.0196232i	$0.993753\pi$
$602$		0			0
$603$	2.29540e6	−	2.29540e6i	0.257078	−	0.257078i
$604$		0			0
$605$	2.72501e6	+	2.72501e6i	0.302677	+	0.302677i
$606$		0			0
$607$	5.96692e6			0.657322			0.328661	−	0.944448i	$-0.393403\pi$
$607$	5.96692e6			0.657322			0.328661	+	0.944448i	$0.393403\pi$
$608$		0			0
$609$	2.45380e7			2.68099
$610$		0			0
$611$	−1.28549e7	−	1.28549e7i	−1.39305	−	1.39305i
$612$		0			0
$613$	6.88238e6	−	6.88238e6i	0.739754	−	0.739754i	−0.232776	−	0.972530i	$-0.574781\pi$
$613$	6.88238e6	−	6.88238e6i	0.739754	−	0.739754i	0.972530	+	0.232776i	$0.0747810\pi$
$614$		0			0
$615$			7.42222e6i			0.791309i
$616$		0			0
$617$		−	1.20232e7i		−	1.27147i	−0.771907	−	0.635736i	$-0.780697\pi$
$617$		−	1.20232e7i		−	1.27147i	0.771907	−	0.635736i	$-0.219303\pi$
$618$		0			0
$619$	−2.21459e6	+	2.21459e6i	−0.232309	+	0.232309i	−0.813656	−	0.581347i	$-0.802526\pi$
$619$	−2.21459e6	+	2.21459e6i	−0.232309	+	0.232309i	0.581347	+	0.813656i	$0.302526\pi$
$620$		0			0
$621$	−2.13645e6	−	2.13645e6i	−0.222313	−	0.222313i
$622$		0			0
$623$	1.92296e7			1.98495
$624$		0			0
$625$	−390625.			−0.0400000
$626$		0			0
$627$	191327.	+	191327.i	0.0194360	+	0.0194360i
$628$		0			0
$629$	78328.7	−	78328.7i	0.00789395	−	0.00789395i
$630$		0			0
$631$		−	4.57210e6i		−	0.457133i	−0.973528	−	0.228566i	$-0.926596\pi$
$631$		−	4.57210e6i		−	0.457133i	0.973528	−	0.228566i	$-0.0734038\pi$
$632$		0			0
$633$			1.94632e7i			1.93066i
$634$		0			0
$635$	−5.05703e6	+	5.05703e6i	−0.497692	+	0.497692i
$636$		0			0
$637$	4.26825e6	+	4.26825e6i	0.416775	+	0.416775i
$638$		0			0
$639$	−1.60562e7			−1.55558
$640$		0			0
$641$	−1.36808e7			−1.31512			−0.657561	−	0.753402i	$-0.728412\pi$
$641$	−1.36808e7			−1.31512			−0.657561	+	0.753402i	$0.728412\pi$
$642$		0			0
$643$	5.26928e6	+	5.26928e6i	0.502602	+	0.502602i	0.912246	−	0.409644i	$-0.134347\pi$
$643$	5.26928e6	+	5.26928e6i	0.502602	+	0.502602i	−0.409644	+	0.912246i	$0.634347\pi$
$644$		0			0
$645$	−2.63432e6	+	2.63432e6i	−0.249327	+	0.249327i
$646$		0			0
$647$			9.42384e6i			0.885048i	0.896757	+	0.442524i	$0.145917\pi$
$647$			9.42384e6i			0.885048i	−0.896757	+	0.442524i	$0.854083\pi$
$648$		0			0
$649$		−	2.84626e6i		−	0.265255i
$650$		0			0
$651$	1.50346e7	−	1.50346e7i	1.39040	−	1.39040i
$652$		0			0
$653$	−3.39100e6	−	3.39100e6i	−0.311204	−	0.311204i	0.534172	−	0.845376i	$-0.320624\pi$
$653$	−3.39100e6	−	3.39100e6i	−0.311204	−	0.311204i	−0.845376	+	0.534172i	$0.820624\pi$
$654$		0			0
$655$	−4.79584e6			−0.436779
$656$		0			0
$657$	−322719.			−0.0291683
$658$		0			0
$659$	2.25541e6	+	2.25541e6i	0.202307	+	0.202307i	0.800988	−	0.598681i	$-0.204308\pi$
$659$	2.25541e6	+	2.25541e6i	0.202307	+	0.202307i	−0.598681	+	0.800988i	$0.704308\pi$
$660$		0			0
$661$	−1.11241e6	+	1.11241e6i	−0.0990283	+	0.0990283i	−0.754885	−	0.655857i	$-0.772307\pi$
$661$	−1.11241e6	+	1.11241e6i	−0.0990283	+	0.0990283i	0.655857	+	0.754885i	$0.272307\pi$
$662$		0			0
$663$			308179.i			0.0272282i
$664$		0			0
$665$		−	567421.i		−	0.0497567i
$666$		0			0
$667$	−1.60597e7	+	1.60597e7i	−1.39773	+	1.39773i
$668$		0			0
$669$	−1.61862e7	−	1.61862e7i	−1.39823	−	1.39823i
$670$		0			0
$671$	841624.			0.0721626
$672$		0			0
$673$	−3.56919e6			−0.303761			−0.151881	−	0.988399i	$-0.548533\pi$
$673$	−3.56919e6			−0.303761			−0.151881	+	0.988399i	$0.548533\pi$
$674$		0			0
$675$	−394370.	−	394370.i	−0.0333154	−	0.0333154i
$676$		0			0
$677$	1.44560e7	−	1.44560e7i	1.21221	−	1.21221i	0.241911	−	0.970298i	$-0.422226\pi$
$677$	1.44560e7	−	1.44560e7i	1.21221	−	1.21221i	0.970298	−	0.241911i	$-0.0777742\pi$
$678$		0			0
$679$		−	2.36604e7i		−	1.96946i
$680$		0			0
$681$		−	9.78666e6i		−	0.808661i
$682$		0			0
$683$	1.13328e7	−	1.13328e7i	0.929573	−	0.929573i	−0.0681048	−	0.997678i	$-0.521695\pi$
$683$	1.13328e7	−	1.13328e7i	0.929573	−	0.929573i	0.997678	+	0.0681048i	$0.0216952\pi$
$684$		0			0
$685$	7.10742e6	+	7.10742e6i	0.578743	+	0.578743i
$686$		0			0
$687$	3.33754e7			2.69795
$688$		0			0
$689$	2.64918e7			2.12600
$690$		0			0
$691$	−3.10221e6	−	3.10221e6i	−0.247159	−	0.247159i	0.572645	−	0.819804i	$-0.305917\pi$
$691$	−3.10221e6	−	3.10221e6i	−0.247159	−	0.247159i	−0.819804	+	0.572645i	$0.805917\pi$
$692$		0			0
$693$	−2.64431e6	+	2.64431e6i	−0.209161	+	0.209161i
$694$		0			0
$695$		−	5.12499e6i		−	0.402467i
$696$		0			0
$697$		−	250756.i		−	0.0195510i
$698$		0			0
$699$	−4.55519e6	+	4.55519e6i	−0.352625	+	0.352625i
$700$		0			0
$701$	−7.70510e6	−	7.70510e6i	−0.592220	−	0.592220i	0.346011	−	0.938231i	$-0.387536\pi$
$701$	−7.70510e6	−	7.70510e6i	−0.592220	−	0.592220i	−0.938231	+	0.346011i	$0.887536\pi$
$702$		0			0
$703$	813748.			0.0621014
$704$		0			0
$705$	−1.49814e7			−1.13522
$706$		0			0
$707$	873459.	+	873459.i	0.0657195	+	0.0657195i
$708$		0			0
$709$	4.52566e6	−	4.52566e6i	0.338116	−	0.338116i	−0.517542	−	0.855658i	$-0.673153\pi$
$709$	4.52566e6	−	4.52566e6i	0.338116	−	0.338116i	0.855658	+	0.517542i	$0.173153\pi$
$710$		0			0
$711$			2.83641e7i			2.10424i
$712$		0			0
$713$			1.96798e7i			1.44976i
$714$		0			0
$715$	1.02075e6	−	1.02075e6i	0.0746711	−	0.0746711i
$716$		0			0
$717$	−2.09444e7	−	2.09444e7i	−1.52150	−	1.52150i
$718$		0			0
$719$	−3.59039e6			−0.259012			−0.129506	−	0.991579i	$-0.541339\pi$
$719$	−3.59039e6			−0.259012			−0.129506	+	0.991579i	$0.541339\pi$
$720$		0			0
$721$	−2.03288e7			−1.45638
$722$		0			0
$723$	−4.35634e6	−	4.35634e6i	−0.309939	−	0.309939i
$724$		0			0
$725$	−2.96448e6	+	2.96448e6i	−0.209462	+	0.209462i
$726$		0			0
$727$		−	2.03036e7i		−	1.42474i	−0.701802	−	0.712372i	$-0.747621\pi$
$727$		−	2.03036e7i		−	1.42474i	0.701802	−	0.712372i	$-0.252379\pi$
$728$		0			0
$729$			1.85209e7i			1.29075i
$730$		0			0
$731$	88999.3	−	88999.3i	0.00616018	−	0.00616018i
$732$		0			0
$733$	−2.31094e6	−	2.31094e6i	−0.158865	−	0.158865i	0.623199	−	0.782064i	$-0.285833\pi$
$733$	−2.31094e6	−	2.31094e6i	−0.158865	−	0.158865i	−0.782064	+	0.623199i	$0.785833\pi$
$734$		0			0
$735$	4.97432e6			0.339637
$736$		0			0
$737$	956462.			0.0648633
$738$		0			0
$739$	1.93049e7	+	1.93049e7i	1.30034	+	1.30034i	0.928161	+	0.372179i	$0.121389\pi$
$739$	1.93049e7	+	1.93049e7i	1.30034	+	1.30034i	0.372179	+	0.928161i	$0.378611\pi$
$740$		0			0
$741$	−1.60082e6	+	1.60082e6i	−0.107102	+	0.107102i
$742$		0			0
$743$		−	2.55799e7i		−	1.69992i	−0.526850	−	0.849958i	$-0.676627\pi$
$743$		−	2.55799e7i		−	1.69992i	0.526850	−	0.849958i	$-0.323373\pi$
$744$		0			0
$745$		−	9.80421e6i		−	0.647175i
$746$		0			0
$747$	−5.06292e6	+	5.06292e6i	−0.331971	+	0.331971i
$748$		0			0
$749$	734596.	+	734596.i	0.0478458	+	0.0478458i
$750$		0			0
$751$	−1.42628e7			−0.922794			−0.461397	−	0.887194i	$-0.652652\pi$
$751$	−1.42628e7			−0.922794			−0.461397	+	0.887194i	$0.652652\pi$
$752$		0			0
$753$	5.20220e6			0.334349
$754$		0			0
$755$	−723681.	−	723681.i	−0.0462040	−	0.0462040i
$756$		0			0
$757$	−7.92801e6	+	7.92801e6i	−0.502834	+	0.502834i	−0.912317	−	0.409484i	$-0.865709\pi$
$757$	−7.92801e6	+	7.92801e6i	−0.502834	+	0.502834i	0.409484	+	0.912317i	$0.365709\pi$
$758$		0			0
$759$		−	6.44452e6i		−	0.406056i
$760$		0			0
$761$		−	2.09915e7i		−	1.31396i	−0.753909	−	0.656979i	$-0.771834\pi$
$761$		−	2.09915e7i		−	1.31396i	0.753909	−	0.656979i	$-0.228166\pi$
$762$		0			0
$763$	344987.	−	344987.i	0.0214532	−	0.0214532i
$764$		0			0
$765$	96451.5	+	96451.5i	0.00595875	+	0.00595875i
$766$		0			0
$767$	2.38145e7			1.46168
$768$		0			0
$769$	−2.23328e7			−1.36185			−0.680923	−	0.732355i	$-0.738421\pi$
$769$	−2.23328e7			−1.36185			−0.680923	+	0.732355i	$0.738421\pi$
$770$		0			0
$771$	1.41525e7	+	1.41525e7i	0.857428	+	0.857428i
$772$		0			0
$773$	1.38445e7	−	1.38445e7i	0.833352	−	0.833352i	−0.154622	−	0.987974i	$-0.549416\pi$
$773$	1.38445e7	−	1.38445e7i	0.833352	−	0.833352i	0.987974	+	0.154622i	$0.0494159\pi$
$774$		0			0
$775$			3.63272e6i			0.217259i
$776$		0			0
$777$			2.09399e7i			1.24429i
$778$		0			0
$779$	1.30254e6	−	1.30254e6i	0.0769036	−	0.0769036i
$780$		0			0
$781$	−3.34521e6	−	3.34521e6i	−0.196244	−	0.196244i
$782$		0			0
$783$	−5.98582e6			−0.348915
$784$		0			0
$785$	−1.08521e6			−0.0628549
$786$		0			0
$787$	−1.73911e7	−	1.73911e7i	−1.00090	−	1.00090i	−1.00000		0.000898008i	$-0.999714\pi$
$787$	−1.73911e7	−	1.73911e7i	−1.00090	−	1.00090i	−0.000898008	−	1.00000i	$-0.500286\pi$
$788$		0			0
$789$	2.46296e7	−	2.46296e7i	1.40852	−	1.40852i
$790$		0			0
$791$		−	4.15789e6i		−	0.236283i
$792$		0			0
$793$			7.04181e6i			0.397651i
$794$		0			0
$795$	1.54371e7	−	1.54371e7i	0.866258	−	0.866258i
$796$		0			0
$797$	1.24042e7	+	1.24042e7i	0.691709	+	0.691709i	0.962608	−	0.270898i	$-0.0873208\pi$
$797$	1.24042e7	+	1.24042e7i	0.691709	+	0.691709i	−0.270898	+	0.962608i	$0.587321\pi$
$798$		0			0
$799$	506139.			0.0280481
$800$		0			0
$801$	−3.39580e7			−1.87008
$802$		0			0
$803$	−67236.3	−	67236.3i	−0.00367972	−	0.00367972i
$804$		0			0
$805$	−9.55631e6	+	9.55631e6i	−0.519757	+	0.519757i
$806$		0			0
$807$		−	9.87086e6i		−	0.533545i
$808$		0			0
$809$			1.68964e7i			0.907662i	0.891088	+	0.453831i	$0.149943\pi$
$809$			1.68964e7i			0.907662i	−0.891088	+	0.453831i	$0.850057\pi$
$810$		0			0
$811$	−1.30209e7	+	1.30209e7i	−0.695167	+	0.695167i	−0.963364	−	0.268197i	$-0.913572\pi$
$811$	−1.30209e7	+	1.30209e7i	−0.695167	+	0.695167i	0.268197	+	0.963364i	$0.413572\pi$
$812$		0			0
$813$	−2.14780e7	−	2.14780e7i	−1.13964	−	1.13964i
$814$		0			0
$815$	5.66965e6			0.298994
$816$		0			0
$817$	924604.			0.0484619
$818$		0			0
$819$	−2.21248e7	−	2.21248e7i	−1.15258	−	1.15258i
$820$		0			0
$821$	2.01017e7	−	2.01017e7i	1.04082	−	1.04082i	0.0416853	−	0.999131i	$-0.486727\pi$
$821$	2.01017e7	−	2.01017e7i	1.04082	−	1.04082i	0.999131	−	0.0416853i	$-0.0132727\pi$
$822$		0			0
$823$			3.32855e7i			1.71299i	0.516151	+	0.856497i	$0.327364\pi$
$823$			3.32855e7i			1.71299i	−0.516151	+	0.856497i	$0.672636\pi$
$824$		0			0
$825$		−	1.18960e6i		−	0.0608508i
$826$		0			0
$827$	−2.39916e7	+	2.39916e7i	−1.21982	+	1.21982i	−0.252123	+	0.967695i	$0.581129\pi$
$827$	−2.39916e7	+	2.39916e7i	−1.21982	+	1.21982i	−0.967695	+	0.252123i	$0.918871\pi$
$828$		0			0
$829$	−1.45426e7	−	1.45426e7i	−0.734945	−	0.734945i	0.236650	−	0.971595i	$-0.423951\pi$
$829$	−1.45426e7	−	1.45426e7i	−0.734945	−	0.734945i	−0.971595	+	0.236650i	$0.923951\pi$
$830$		0			0
$831$	−8.72942e6			−0.438513
$832$		0			0
$833$	−168055.			−0.00839148
$834$		0			0
$835$	−7.22531e6	−	7.22531e6i	−0.358625	−	0.358625i
$836$		0			0
$837$	−3.66755e6	+	3.66755e6i	−0.180952	+	0.180952i
$838$		0			0
$839$			1.66297e7i			0.815605i	0.913070	+	0.407803i	$0.133705\pi$
$839$			1.66297e7i			0.815605i	−0.913070	+	0.407803i	$0.866295\pi$
$840$		0			0
$841$			2.44843e7i			1.19371i
$842$		0			0
$843$	−3.38839e7	+	3.38839e7i	−1.64220	+	1.64220i
$844$		0			0
$845$	1.97691e6	+	1.97691e6i	0.0952458	+	0.0952458i
$846$		0			0
$847$	2.46116e7			1.17877
$848$		0			0
$849$	2.29300e7			1.09178
$850$		0			0
$851$	−1.37049e7	−	1.37049e7i	−0.648710	−	0.648710i
$852$		0			0
$853$	−5.15629e6	+	5.15629e6i	−0.242642	+	0.242642i	−0.817942	−	0.575301i	$-0.804885\pi$
$853$	−5.15629e6	+	5.15629e6i	−0.242642	+	0.242642i	0.575301	+	0.817942i	$0.304885\pi$
$854$		0			0
$855$			1.00202e6i			0.0468773i
$856$		0			0
$857$		−	9.10286e6i		−	0.423376i	−0.977337	−	0.211688i	$-0.932104\pi$
$857$		−	9.10286e6i		−	0.423376i	0.977337	−	0.211688i	$-0.0678960\pi$
$858$		0			0
$859$	−2.89214e6	+	2.89214e6i	−0.133733	+	0.133733i	−0.770804	−	0.637072i	$-0.780145\pi$
$859$	−2.89214e6	+	2.89214e6i	−0.133733	+	0.133733i	0.637072	+	0.770804i	$0.280145\pi$
$860$		0			0
$861$	3.35178e7	+	3.35178e7i	1.54087	+	1.54087i
$862$		0			0
$863$	−1.32527e7			−0.605729			−0.302864	−	0.953034i	$-0.597943\pi$
$863$	−1.32527e7			−0.605729			−0.302864	+	0.953034i	$0.597943\pi$
$864$		0			0
$865$	3.34071e6			0.151809
$866$		0			0
$867$	2.29971e7	+	2.29971e7i	1.03902	+	1.03902i
$868$		0			0
$869$	−5.90946e6	+	5.90946e6i	−0.265460	+	0.265460i
$870$		0			0
$871$			8.00265e6i			0.357428i
$872$		0			0
$873$			4.17825e7i			1.85549i
$874$		0			0
$875$	−1.76401e6	+	1.76401e6i	−0.0778899	+	0.0778899i
$876$		0			0
$877$	−4.35852e6	−	4.35852e6i	−0.191355	−	0.191355i	0.604926	−	0.796281i	$-0.293203\pi$
$877$	−4.35852e6	−	4.35852e6i	−0.191355	−	0.191355i	−0.796281	+	0.604926i	$0.793203\pi$
$878$		0			0
$879$	−9.31922e6			−0.406825
$880$		0			0
$881$	4.99443e6			0.216793			0.108397	−	0.994108i	$-0.465428\pi$
$881$	4.99443e6			0.216793			0.108397	+	0.994108i	$0.465428\pi$
$882$		0			0
$883$	5.59795e6	+	5.59795e6i	0.241617	+	0.241617i	0.817519	−	0.575902i	$-0.195349\pi$
$883$	5.59795e6	+	5.59795e6i	0.241617	+	0.241617i	−0.575902	+	0.817519i	$0.695349\pi$
$884$		0			0
$885$	1.38770e7	−	1.38770e7i	0.595575	−	0.595575i
$886$		0			0
$887$		−	2.65874e7i		−	1.13466i	−0.823490	−	0.567331i	$-0.807976\pi$
$887$		−	2.65874e7i		−	1.13466i	0.823490	−	0.567331i	$-0.192024\pi$
$888$		0			0
$889$			4.56737e7i			1.93826i
$890$		0			0
$891$	−2.82360e6	+	2.82360e6i	−0.119154	+	0.119154i
$892$		0			0
$893$	2.62911e6	+	2.62911e6i	0.110327	+	0.110327i
$894$		0			0
$895$	−878128.			−0.0366438
$896$		0			0
$897$	5.39208e7			2.23756
$898$		0			0
$899$	2.75690e7	+	2.75690e7i	1.13768	+	1.13768i
$900$		0			0
$901$	−521534.	+	521534.i	−0.0214028	+	0.0214028i
$902$		0			0
$903$			2.37925e7i			0.971004i
$904$		0			0
$905$			1.16261e7i			0.471861i
$906$		0			0
$907$	−4.22670e6	+	4.22670e6i	−0.170602	+	0.170602i	−0.787244	−	0.616642i	$-0.788493\pi$
$907$	−4.22670e6	+	4.22670e6i	−0.170602	+	0.170602i	0.616642	+	0.787244i	$0.288493\pi$
$908$		0			0
$909$	−1.54246e6	−	1.54246e6i	−0.0619163	−	0.0619163i
$910$		0			0
$911$	−3.66894e6			−0.146469			−0.0732344	−	0.997315i	$-0.523332\pi$
$911$	−3.66894e6			−0.146469			−0.0732344	+	0.997315i	$0.523332\pi$
$912$		0			0
$913$	−2.10965e6			−0.0837594
$914$		0			0
$915$	4.10335e6	+	4.10335e6i	0.162026	+	0.162026i
$916$		0			0
$917$	−2.16574e7	+	2.16574e7i	−0.850516	+	0.850516i
$918$		0			0
$919$		−	1.33795e6i		−	0.0522579i	−0.999659	−	0.0261289i	$-0.991682\pi$
$919$		−	1.33795e6i		−	0.0522579i	0.999659	−	0.0261289i	$-0.00831805\pi$
$920$		0			0
$921$			2.28843e7i			0.888975i
$922$		0			0
$923$	2.79891e7	−	2.79891e7i	1.08140	−	1.08140i
$924$		0			0
$925$	−2.52980e6	−	2.52980e6i	−0.0972145	−	0.0972145i
$926$		0			0
$927$	3.58992e7			1.37210
$928$		0			0
$929$	−1.40767e7			−0.535133			−0.267567	−	0.963539i	$-0.586220\pi$
$929$	−1.40767e7			−0.535133			−0.267567	+	0.963539i	$0.586220\pi$
$930$		0			0
$931$	−872951.	−	872951.i	−0.0330077	−	0.0330077i
$932$		0			0
$933$	−9.28253e6	+	9.28253e6i	−0.349110	+	0.349110i
$934$		0			0
$935$			40190.1i			0.00150345i
$936$		0			0
$937$		−	8.06411e6i		−	0.300059i	−0.988681	−	0.150030i	$-0.952063\pi$
$937$		−	8.06411e6i		−	0.300059i	0.988681	−	0.150030i	$-0.0479369\pi$
$938$		0			0
$939$	5.53353e6	−	5.53353e6i	0.204804	−	0.204804i
$940$		0			0
$941$	3.32092e7	+	3.32092e7i	1.22260	+	1.22260i	0.966705	+	0.255894i	$0.0823697\pi$
$941$	3.32092e7	+	3.32092e7i	1.22260	+	1.22260i	0.255894	+	0.966705i	$0.417630\pi$
$942$		0			0
$943$	−4.38738e7			−1.60667
$944$		0			0
$945$	−3.56185e6			−0.129747
$946$		0			0
$947$	1.21073e7	+	1.21073e7i	0.438703	+	0.438703i	0.891575	−	0.452872i	$-0.149601\pi$
$947$	1.21073e7	+	1.21073e7i	0.438703	+	0.438703i	−0.452872	+	0.891575i	$0.649601\pi$
$948$		0			0
$949$	562561.	−	562561.i	0.0202770	−	0.0202770i
$950$		0			0
$951$			2.17261e7i			0.778988i
$952$		0			0
$953$		−	1.82821e7i		−	0.652068i	−0.945358	−	0.326034i	$-0.894288\pi$
$953$		−	1.82821e7i		−	0.652068i	0.945358	−	0.326034i	$-0.105712\pi$
$954$		0			0
$955$	−1.17645e7	+	1.17645e7i	−0.417411	+	0.417411i
$956$		0			0
$957$	−9.02798e6	−	9.02798e6i	−0.318648	−	0.318648i
$958$		0			0
$959$	6.41924e7			2.25391
$960$		0			0
$961$	5.15427e6			0.180036
$962$		0			0
$963$	−1.29724e6	−	1.29724e6i	−0.0450770	−	0.0450770i
$964$		0			0
$965$	−2.76448e6	+	2.76448e6i	−0.0955642	+	0.0955642i
$966$		0			0
$967$			5.06832e6i			0.174300i	0.996195	+	0.0871501i	$0.0277760\pi$
$967$			5.06832e6i			0.174300i	−0.996195	+	0.0871501i	$0.972224\pi$
$968$		0			0
$969$		−	63029.3i		−	0.00215642i
$970$		0			0
$971$	2.57335e7	−	2.57335e7i	0.875893	−	0.875893i	−0.117214	−	0.993107i	$-0.537396\pi$
$971$	2.57335e7	−	2.57335e7i	0.875893	−	0.875893i	0.993107	+	0.117214i	$0.0373962\pi$
$972$		0			0
$973$	−2.31438e7	−	2.31438e7i	−0.783703	−	0.783703i
$974$		0			0
$975$	9.95331e6			0.335317
$976$		0			0
$977$	−3.47061e7			−1.16324			−0.581620	−	0.813461i	$-0.697581\pi$
$977$	−3.47061e7			−1.16324			−0.581620	+	0.813461i	$0.697581\pi$
$978$		0			0
$979$	−7.07493e6	−	7.07493e6i	−0.235920	−	0.235920i
$980$		0			0
$981$	−609221.	+	609221.i	−0.0202117	+	0.0202117i
$982$		0			0
$983$			733190.i			0.0242010i	0.999927	+	0.0121005i	$0.00385180\pi$
$983$			733190.i			0.0242010i	−0.999927	+	0.0121005i	$0.996148\pi$
$984$		0			0
$985$		−	2.18259e7i		−	0.716773i
$986$		0			0
$987$	−6.76540e7	+	6.76540e7i	−2.21055	+	2.21055i
$988$		0			0
$989$	−1.55719e7	−	1.55719e7i	−0.506232	−	0.506232i
$990$		0			0
$991$	3.66903e7			1.18677			0.593386	−	0.804918i	$-0.297791\pi$
$991$	3.66903e7			1.18677			0.593386	+	0.804918i	$0.297791\pi$
$992$		0			0
$993$	7.93269e7			2.55298
$994$		0			0
$995$	−7.56149e6	−	7.56149e6i	−0.242131	−	0.242131i
$996$		0			0
$997$	−3.52017e7	+	3.52017e7i	−1.12157	+	1.12157i	−0.130062	+	0.991506i	$0.541518\pi$
$997$	−3.52017e7	+	3.52017e7i	−1.12157	+	1.12157i	−0.991506	+	0.130062i	$0.958482\pi$
$998$		0			0
$999$		−	5.10810e6i		−	0.161937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.6.l.a.81.6		80
4.3	odd	2		80.6.l.a.61.37	yes	80
16.5	even	4	inner	320.6.l.a.241.6		80
16.11	odd	4		80.6.l.a.21.37	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.37	✓	80	16.11	odd	4
80.6.l.a.61.37	yes	80	4.3	odd	2
320.6.l.a.81.6		80	1.1	even	1	trivial
320.6.l.a.241.6		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)

\(f(q)\)	\(=\)	\(q+(-16.2010 - 16.2010i) q^{3} +(17.6777 - 17.6777i) q^{5} -159.660i q^{7} +281.948i q^{9} +O(q^{10})\)	\(q+(-16.2010 - 16.2010i) q^{3} +(17.6777 - 17.6777i) q^{5} -159.660i q^{7} +281.948i q^{9} +(-58.7419 + 58.7419i) q^{11} +(-491.490 - 491.490i) q^{13} -572.793 q^{15} +19.3515 q^{17} +(100.520 + 100.520i) q^{19} +(-2586.66 + 2586.66i) q^{21} -3385.86i q^{23} -625.000i q^{25} +(630.993 - 630.993i) q^{27} +(-4743.18 - 4743.18i) q^{29} -5812.35 q^{31} +1903.36 q^{33} +(-2822.42 - 2822.42i) q^{35} +(4047.67 - 4047.67i) q^{37} +15925.3i q^{39} -12957.9i q^{41} +(4599.08 - 4599.08i) q^{43} +(4984.18 + 4984.18i) q^{45} +26155.0 q^{47} -8684.32 q^{49} +(-313.515 - 313.515i) q^{51} +(-26950.5 + 26950.5i) q^{53} +2076.84i q^{55} -3257.07i q^{57} +(-24226.8 + 24226.8i) q^{59} +(-7163.75 - 7163.75i) q^{61} +45015.8 q^{63} -17376.8 q^{65} +(-8141.22 - 8141.22i) q^{67} +(-54854.5 + 54854.5i) q^{69} +56947.6i q^{71} +1144.60i q^{73} +(-10125.7 + 10125.7i) q^{75} +(9378.74 + 9378.74i) q^{77} +100600. q^{79} +48067.8 q^{81} +(17956.9 + 17956.9i) q^{83} +(342.090 - 342.090i) q^{85} +153689. i q^{87} +120441. i q^{89} +(-78471.2 + 78471.2i) q^{91} +(94166.2 + 94166.2i) q^{93} +3553.93 q^{95} +148192. q^{97} +(-16562.1 - 16562.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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