LMFDB - Embedded newform 384.7.l.b.31.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,7,Mod(31,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("384.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	384.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:	$88.3407681100$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.15
Character	$\chi$	$=$	384.31
Dual form			384.7.l.b.223.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.0227 + 11.0227i) q^{3} +(98.7574 + 98.7574i) q^{5} -218.381 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(11.0227 + 11.0227i) q^{3} +(98.7574 + 98.7574i) q^{5} -218.381 q^{7} +243.000i q^{9} +(24.6313 - 24.6313i) q^{11} +(655.148 - 655.148i) q^{13} +2177.15i q^{15} +6237.49 q^{17} +(-2073.73 - 2073.73i) q^{19} +(-2407.15 - 2407.15i) q^{21} +8165.70 q^{23} +3881.05i q^{25} +(-2678.52 + 2678.52i) q^{27} +(19658.6 - 19658.6i) q^{29} +52923.3i q^{31} +543.008 q^{33} +(-21566.8 - 21566.8i) q^{35} +(64675.2 + 64675.2i) q^{37} +14443.0 q^{39} +57943.8i q^{41} +(48045.7 - 48045.7i) q^{43} +(-23998.0 + 23998.0i) q^{45} +101239. i q^{47} -69958.6 q^{49} +(68754.0 + 68754.0i) q^{51} +(-15769.4 - 15769.4i) q^{53} +4865.06 q^{55} -45716.1i q^{57} +(73856.6 - 73856.6i) q^{59} +(-190072. + 190072. i) q^{61} -53066.7i q^{63} +129401. q^{65} +(-148932. - 148932. i) q^{67} +(90008.1 + 90008.1i) q^{69} +47230.0 q^{71} +81012.8i q^{73} +(-42779.6 + 42779.6i) q^{75} +(-5379.03 + 5379.03i) q^{77} +534649. i q^{79} -59049.0 q^{81} +(-637856. - 637856. i) q^{83} +(615998. + 615998. i) q^{85} +433381. q^{87} -1.13444e6i q^{89} +(-143072. + 143072. i) q^{91} +(-583358. + 583358. i) q^{93} -409592. i q^{95} -518874. q^{97} +(5985.42 + 5985.42i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 2720 q^{11} + 3936 q^{19} + 26240 q^{23} - 66400 q^{29} - 162336 q^{35} + 7200 q^{37} - 340704 q^{43} + 806736 q^{49} - 80352 q^{51} - 443680 q^{53} + 232704 q^{55} + 886144 q^{59} + 326496 q^{61} - 372832 q^{65} + 962112 q^{67} - 541728 q^{69} + 534016 q^{71} + 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} + 2497760 q^{83} + 372000 q^{85} - 775008 q^{91} + 660960 q^{99}+O(q^{100}) $ 48 * q + 2720 * q^11 + 3936 * q^19 + 26240 * q^23 - 66400 * q^29 - 162336 * q^35 + 7200 * q^37 - 340704 * q^43 + 806736 * q^49 - 80352 * q^51 - 443680 * q^53 + 232704 * q^55 + 886144 * q^59 + 326496 * q^61 - 372832 * q^65 + 962112 * q^67 - 541728 * q^69 + 534016 * q^71 + 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 + 2497760 * q^83 + 372000 * q^85 - 775008 * q^91 + 660960 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$3$	11.0227	+	11.0227i	0.408248	+	0.408248i
$4$		0			0
$5$	98.7574	+	98.7574i	0.790059	+	0.790059i	0.981503	−	0.191444i	$-0.0613171\pi$
$5$	98.7574	+	98.7574i	0.790059	+	0.790059i	−0.191444	+	0.981503i	$0.561317\pi$
$6$		0			0
$7$	−218.381			−0.636680			−0.318340	−	0.947977i	$-0.603125\pi$
$7$	−218.381			−0.636680			−0.318340	+	0.947977i	$0.603125\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	24.6313	−	24.6313i	0.0185059	−	0.0185059i	−0.697793	−	0.716299i	$-0.745835\pi$
$11$	24.6313	−	24.6313i	0.0185059	−	0.0185059i	0.716299	+	0.697793i	$0.245835\pi$
$12$		0			0
$13$	655.148	−	655.148i	0.298201	−	0.298201i	−0.542108	−	0.840309i	$-0.682374\pi$
$13$	655.148	−	655.148i	0.298201	−	0.298201i	0.840309	+	0.542108i	$0.182374\pi$
$14$		0			0
$15$			2177.15i			0.645081i
$16$		0			0
$17$	6237.49			1.26959			0.634794	−	0.772681i	$-0.281085\pi$
$17$	6237.49			1.26959			0.634794	+	0.772681i	$0.281085\pi$
$18$		0			0
$19$	−2073.73	−	2073.73i	−0.302336	−	0.302336i	0.539591	−	0.841927i	$-0.318579\pi$
$19$	−2073.73	−	2073.73i	−0.302336	−	0.302336i	−0.841927	+	0.539591i	$0.818579\pi$
$20$		0			0
$21$	−2407.15	−	2407.15i	−0.259924	−	0.259924i
$22$		0			0
$23$	8165.70			0.671135			0.335568	−	0.942016i	$-0.391072\pi$
$23$	8165.70			0.671135			0.335568	+	0.942016i	$0.391072\pi$
$24$		0			0
$25$			3881.05i			0.248387i
$26$		0			0
$27$	−2678.52	+	2678.52i	−0.136083	+	0.136083i
$28$		0			0
$29$	19658.6	−	19658.6i	0.806043	−	0.806043i	−0.177989	−	0.984032i	$-0.556959\pi$
$29$	19658.6	−	19658.6i	0.806043	−	0.806043i	0.984032	+	0.177989i	$0.0569593\pi$
$30$		0			0
$31$			52923.3i			1.77649i	0.459374	+	0.888243i	$0.348074\pi$
$31$			52923.3i			1.77649i	−0.459374	+	0.888243i	$0.651926\pi$
$32$		0			0
$33$	543.008			0.0151100
$34$		0			0
$35$	−21566.8	−	21566.8i	−0.503015	−	0.503015i
$36$		0			0
$37$	64675.2	+	64675.2i	1.27683	+	1.27683i	0.942433	+	0.334396i	$0.108532\pi$
$37$	64675.2	+	64675.2i	1.27683	+	1.27683i	0.334396	+	0.942433i	$0.391468\pi$
$38$		0			0
$39$	14443.0			0.243480
$40$		0			0
$41$			57943.8i			0.840727i	0.907356	+	0.420364i	$0.138098\pi$
$41$			57943.8i			0.840727i	−0.907356	+	0.420364i	$0.861902\pi$
$42$		0			0
$43$	48045.7	−	48045.7i	0.604295	−	0.604295i	−0.337155	−	0.941449i	$-0.609465\pi$
$43$	48045.7	−	48045.7i	0.604295	−	0.604295i	0.941449	+	0.337155i	$0.109465\pi$
$44$		0			0
$45$	−23998.0	+	23998.0i	−0.263353	+	0.263353i
$46$		0			0
$47$			101239.i			0.975108i	0.873093	+	0.487554i	$0.162111\pi$
$47$			101239.i			0.975108i	−0.873093	+	0.487554i	$0.837889\pi$
$48$		0			0
$49$	−69958.6			−0.594638
$50$		0			0
$51$	68754.0	+	68754.0i	0.518307	+	0.518307i
$52$		0			0
$53$	−15769.4	−	15769.4i	−0.105922	−	0.105922i	0.652160	−	0.758082i	$-0.273863\pi$
$53$	−15769.4	−	15769.4i	−0.105922	−	0.105922i	−0.758082	+	0.652160i	$0.773863\pi$
$54$		0			0
$55$	4865.06			0.0292415
$56$		0			0
$57$		−	45716.1i		−	0.246857i
$58$		0			0
$59$	73856.6	−	73856.6i	0.359611	−	0.359611i	−0.504058	−	0.863670i	$-0.668160\pi$
$59$	73856.6	−	73856.6i	0.359611	−	0.359611i	0.863670	+	0.504058i	$0.168160\pi$
$60$		0			0
$61$	−190072.	+	190072.i	−0.837390	+	0.837390i	−0.988515	−	0.151125i	$-0.951710\pi$
$61$	−190072.	+	190072.i	−0.837390	+	0.837390i	0.151125	+	0.988515i	$0.451710\pi$
$62$		0			0
$63$		−	53066.7i		−	0.212227i
$64$		0			0
$65$	129401.			0.471193
$66$		0			0
$67$	−148932.	−	148932.i	−0.495180	−	0.495180i	0.414754	−	0.909934i	$-0.363868\pi$
$67$	−148932.	−	148932.i	−0.495180	−	0.495180i	−0.909934	+	0.414754i	$0.863868\pi$
$68$		0			0
$69$	90008.1	+	90008.1i	0.273990	+	0.273990i
$70$		0			0
$71$	47230.0			0.131960			0.0659801	−	0.997821i	$-0.478983\pi$
$71$	47230.0			0.131960			0.0659801	+	0.997821i	$0.478983\pi$
$72$		0			0
$73$			81012.8i			0.208250i	0.994564	+	0.104125i	$0.0332042\pi$
$73$			81012.8i			0.208250i	−0.994564	+	0.104125i	$0.966796\pi$
$74$		0			0
$75$	−42779.6	+	42779.6i	−0.101404	+	0.101404i
$76$		0			0
$77$	−5379.03	+	5379.03i	−0.0117823	+	0.0117823i
$78$		0			0
$79$			534649.i			1.08439i	0.840251	+	0.542197i	$0.182407\pi$
$79$			534649.i			1.08439i	−0.840251	+	0.542197i	$0.817593\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−637856.	−	637856.i	−1.11555	−	1.11555i	−0.992387	−	0.123162i	$-0.960696\pi$
$83$	−637856.	−	637856.i	−1.11555	−	1.11555i	−0.123162	−	0.992387i	$-0.539304\pi$
$84$		0			0
$85$	615998.	+	615998.i	1.00305	+	1.00305i
$86$		0			0
$87$	433381.			0.658131
$88$		0			0
$89$		−	1.13444e6i		−	1.60921i	−0.593810	−	0.804606i	$-0.702377\pi$
$89$		−	1.13444e6i		−	1.60921i	0.593810	−	0.804606i	$-0.297623\pi$
$90$		0			0
$91$	−143072.	+	143072.i	−0.189859	+	0.189859i
$92$		0			0
$93$	−583358.	+	583358.i	−0.725247	+	0.725247i
$94$		0			0
$95$		−	409592.i		−	0.477727i
$96$		0			0
$97$	−518874.			−0.568521			−0.284260	−	0.958747i	$-0.591748\pi$
$97$	−518874.			−0.568521			−0.284260	+	0.958747i	$0.591748\pi$
$98$		0			0
$99$	5985.42	+	5985.42i	0.00616863	+	0.00616863i
$100$		0			0
$101$	1.29172e6	+	1.29172e6i	1.25373	+	1.25373i	0.954037	+	0.299689i	$0.0968829\pi$
$101$	1.29172e6	+	1.29172e6i	1.25373	+	1.25373i	0.299689	+	0.954037i	$0.403117\pi$
$102$		0			0
$103$	−1.51407e6			−1.38558			−0.692792	−	0.721137i	$-0.743620\pi$
$103$	−1.51407e6			−1.38558			−0.692792	+	0.721137i	$0.743620\pi$
$104$		0			0
$105$		−	475448.i		−	0.410710i
$106$		0			0
$107$	−1.62098e6	+	1.62098e6i	−1.32320	+	1.32320i	−0.412028	+	0.911171i	$0.635179\pi$
$107$	−1.62098e6	+	1.62098e6i	−1.32320	+	1.32320i	−0.911171	+	0.412028i	$0.864821\pi$
$108$		0			0
$109$	617955.	−	617955.i	0.477175	−	0.477175i	−0.427052	−	0.904227i	$-0.640448\pi$
$109$	617955.	−	617955.i	0.477175	−	0.477175i	0.904227	+	0.427052i	$0.140448\pi$
$110$		0			0
$111$			1.42579e6i			1.04253i
$112$		0			0
$113$	1.82929e6			1.26779			0.633895	−	0.773419i	$-0.281455\pi$
$113$	1.82929e6			1.26779			0.633895	+	0.773419i	$0.281455\pi$
$114$		0			0
$115$	806424.	+	806424.i	0.530237	+	0.530237i
$116$		0			0
$117$	159201.	+	159201.i	0.0994004	+	0.0994004i
$118$		0			0
$119$	−1.36215e6			−0.808322
$120$		0			0
$121$			1.77035e6i			0.999315i
$122$		0			0
$123$	−638697.	+	638697.i	−0.343226	+	0.343226i
$124$		0			0
$125$	1.15980e6	−	1.15980e6i	0.593819	−	0.593819i
$126$		0			0
$127$			3.26823e6i			1.59552i	0.602976	+	0.797759i	$0.293981\pi$
$127$			3.26823e6i			1.59552i	−0.602976	+	0.797759i	$0.706019\pi$
$128$		0			0
$129$	1.05919e6			0.493405
$130$		0			0
$131$	344313.	+	344313.i	0.153158	+	0.153158i	0.779527	−	0.626369i	$-0.215460\pi$
$131$	344313.	+	344313.i	0.153158	+	0.153158i	−0.626369	+	0.779527i	$0.715460\pi$
$132$		0			0
$133$	452863.	+	452863.i	0.192492	+	0.192492i
$134$		0			0
$135$	−529047.			−0.215027
$136$		0			0
$137$			3.63281e6i			1.41280i	0.707812	+	0.706401i	$0.249683\pi$
$137$			3.63281e6i			1.41280i	−0.707812	+	0.706401i	$0.750317\pi$
$138$		0			0
$139$	977998.	−	977998.i	0.364161	−	0.364161i	−0.501181	−	0.865342i	$-0.667101\pi$
$139$	977998.	−	977998.i	0.364161	−	0.364161i	0.865342	+	0.501181i	$0.167101\pi$
$140$		0			0
$141$	−1.11592e6	+	1.11592e6i	−0.398086	+	0.398086i
$142$		0			0
$143$		−	32274.4i		−	0.0110370i
$144$		0			0
$145$	3.88286e6			1.27364
$146$		0			0
$147$	−771133.	−	771133.i	−0.242760	−	0.242760i
$148$		0			0
$149$	−1.19230e6	−	1.19230e6i	−0.360435	−	0.360435i	0.503538	−	0.863973i	$-0.332031\pi$
$149$	−1.19230e6	−	1.19230e6i	−0.360435	−	0.360435i	−0.863973	+	0.503538i	$0.832031\pi$
$150$		0			0
$151$	−2.04590e6			−0.594230			−0.297115	−	0.954842i	$-0.596024\pi$
$151$	−2.04590e6			−0.594230			−0.297115	+	0.954842i	$0.596024\pi$
$152$		0			0
$153$			1.51571e6i			0.423196i
$154$		0			0
$155$	−5.22657e6	+	5.22657e6i	−1.40353	+	1.40353i
$156$		0			0
$157$	2.28772e6	−	2.28772e6i	0.591158	−	0.591158i	−0.346786	−	0.937944i	$-0.612727\pi$
$157$	2.28772e6	−	2.28772e6i	0.591158	−	0.591158i	0.937944	+	0.346786i	$0.112727\pi$
$158$		0			0
$159$		−	347642.i		−	0.0864851i
$160$		0			0
$161$	−1.78324e6			−0.427299
$162$		0			0
$163$	−3.24718e6	−	3.24718e6i	−0.749796	−	0.749796i	0.224644	−	0.974441i	$-0.427878\pi$
$163$	−3.24718e6	−	3.24718e6i	−0.749796	−	0.749796i	−0.974441	+	0.224644i	$0.927878\pi$
$164$		0			0
$165$	53626.1	+	53626.1i	0.0119378	+	0.0119378i
$166$		0			0
$167$	−1.81259e6			−0.389180			−0.194590	−	0.980885i	$-0.562338\pi$
$167$	−1.81259e6			−0.389180			−0.194590	+	0.980885i	$0.562338\pi$
$168$		0			0
$169$			3.96837e6i			0.822152i
$170$		0			0
$171$	503915.	−	503915.i	0.100779	−	0.100779i
$172$		0			0
$173$	−772581.	+	772581.i	−0.149213	+	0.149213i	−0.777766	−	0.628554i	$-0.783647\pi$
$173$	−772581.	+	772581.i	−0.149213	+	0.149213i	0.628554	+	0.777766i	$0.283647\pi$
$174$		0			0
$175$		−	847548.i		−	0.158143i
$176$		0			0
$177$	1.62820e6			0.293621
$178$		0			0
$179$	5.61645e6	+	5.61645e6i	0.979270	+	0.979270i	0.999789	−	0.0205195i	$-0.00653202\pi$
$179$	5.61645e6	+	5.61645e6i	0.979270	+	0.979270i	−0.0205195	+	0.999789i	$0.506532\pi$
$180$		0			0
$181$	2.24827e6	+	2.24827e6i	0.379151	+	0.379151i	0.870796	−	0.491645i	$-0.163604\pi$
$181$	2.24827e6	+	2.24827e6i	0.379151	+	0.379151i	−0.491645	+	0.870796i	$0.663604\pi$
$182$		0			0
$183$	−4.19020e6			−0.683726
$184$		0			0
$185$			1.27743e7i			2.01754i
$186$		0			0
$187$	153638.	−	153638.i	0.0234949	−	0.0234949i
$188$		0			0
$189$	584938.	−	584938.i	0.0866412	−	0.0866412i
$190$		0			0
$191$		−	7.10000e6i		−	1.01896i	−0.860482	−	0.509482i	$-0.829837\pi$
$191$		−	7.10000e6i		−	1.01896i	0.860482	−	0.509482i	$-0.170163\pi$
$192$		0			0
$193$	2.50835e6			0.348912			0.174456	−	0.984665i	$-0.444183\pi$
$193$	2.50835e6			0.348912			0.174456	+	0.984665i	$0.444183\pi$
$194$		0			0
$195$	1.42635e6	+	1.42635e6i	0.192364	+	0.192364i
$196$		0			0
$197$	2.05721e6	+	2.05721e6i	0.269079	+	0.269079i	0.828729	−	0.559650i	$-0.189064\pi$
$197$	2.05721e6	+	2.05721e6i	0.269079	+	0.269079i	−0.559650	+	0.828729i	$0.689064\pi$
$198$		0			0
$199$	−4.43201e6			−0.562395			−0.281197	−	0.959650i	$-0.590732\pi$
$199$	−4.43201e6			−0.562395			−0.281197	+	0.959650i	$0.590732\pi$
$200$		0			0
$201$		−	3.28326e6i		−	0.404313i
$202$		0			0
$203$	−4.29307e6	+	4.29307e6i	−0.513192	+	0.513192i
$204$		0			0
$205$	−5.72238e6	+	5.72238e6i	−0.664224	+	0.664224i
$206$		0			0
$207$			1.98427e6i			0.223712i
$208$		0			0
$209$	−102157.			−0.0111900
$210$		0			0
$211$	5.05344e6	+	5.05344e6i	0.537947	+	0.537947i	0.922925	−	0.384979i	$-0.125791\pi$
$211$	5.05344e6	+	5.05344e6i	0.537947	+	0.537947i	−0.384979	+	0.922925i	$0.625791\pi$
$212$		0			0
$213$	520603.	+	520603.i	0.0538725	+	0.0538725i
$214$		0			0
$215$	9.48973e6			0.954857
$216$		0			0
$217$		−	1.15575e7i		−	1.13105i
$218$		0			0
$219$	−892980.	+	892980.i	−0.0850177	+	0.0850177i
$220$		0			0
$221$	4.08648e6	−	4.08648e6i	0.378593	−	0.378593i
$222$		0			0
$223$		−	6.05648e6i		−	0.546142i	−0.961994	−	0.273071i	$-0.911961\pi$
$223$		−	6.05648e6i		−	0.546142i	0.961994	−	0.273071i	$-0.0880394\pi$
$224$		0			0
$225$	−943095.			−0.0827957
$226$		0			0
$227$	5.00065e6	+	5.00065e6i	0.427512	+	0.427512i	0.887780	−	0.460268i	$-0.152247\pi$
$227$	5.00065e6	+	5.00065e6i	0.427512	+	0.427512i	−0.460268	+	0.887780i	$0.652247\pi$
$228$		0			0
$229$	1.39107e7	+	1.39107e7i	1.15835	+	1.15835i	0.984830	+	0.173524i	$0.0555155\pi$
$229$	1.39107e7	+	1.39107e7i	1.15835	+	1.15835i	0.173524	+	0.984830i	$0.444485\pi$
$230$		0			0
$231$	−118583.			−0.00962024
$232$		0			0
$233$			1.97371e7i			1.56033i	0.625576	+	0.780163i	$0.284864\pi$
$233$			1.97371e7i			1.56033i	−0.625576	+	0.780163i	$0.715136\pi$
$234$		0			0
$235$	−9.99806e6	+	9.99806e6i	−0.770393	+	0.770393i
$236$		0			0
$237$	−5.89327e6	+	5.89327e6i	−0.442702	+	0.442702i
$238$		0			0
$239$			2.08424e7i			1.52670i	0.645985	+	0.763350i	$0.276447\pi$
$239$			2.08424e7i			1.52670i	−0.645985	+	0.763350i	$0.723553\pi$
$240$		0			0
$241$	2.43397e7			1.73886			0.869428	−	0.494059i	$-0.164487\pi$
$241$	2.43397e7			1.73886			0.869428	+	0.494059i	$0.164487\pi$
$242$		0			0
$243$	−650880.	−	650880.i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−6.90893e6	−	6.90893e6i	−0.469799	−	0.469799i
$246$		0			0
$247$	−2.71720e6			−0.180314
$248$		0			0
$249$		−	1.40618e7i		−	0.910842i
$250$		0			0
$251$	−7.80616e6	+	7.80616e6i	−0.493646	+	0.493646i	−0.909453	−	0.415807i	$-0.863499\pi$
$251$	−7.80616e6	+	7.80616e6i	−0.493646	+	0.493646i	0.415807	+	0.909453i	$0.363499\pi$
$252$		0			0
$253$	201132.	−	201132.i	0.0124200	−	0.0124200i
$254$		0			0
$255$			1.35799e7i			0.818987i
$256$		0			0
$257$	−2.03508e7			−1.19890			−0.599449	−	0.800413i	$-0.704614\pi$
$257$	−2.03508e7			−1.19890			−0.599449	+	0.800413i	$0.704614\pi$
$258$		0			0
$259$	−1.41239e7	−	1.41239e7i	−0.812932	−	0.812932i
$260$		0			0
$261$	4.77704e6	+	4.77704e6i	0.268681	+	0.268681i
$262$		0			0
$263$	7.49515e6			0.412015			0.206008	−	0.978550i	$-0.433953\pi$
$263$	7.49515e6			0.412015			0.206008	+	0.978550i	$0.433953\pi$
$264$		0			0
$265$		−	3.11469e6i		−	0.167370i
$266$		0			0
$267$	1.25046e7	−	1.25046e7i	0.656958	−	0.656958i
$268$		0			0
$269$	9.76248e6	−	9.76248e6i	0.501537	−	0.501537i	−0.410378	−	0.911915i	$-0.634603\pi$
$269$	9.76248e6	−	9.76248e6i	0.501537	−	0.501537i	0.911915	+	0.410378i	$0.134603\pi$
$270$		0			0
$271$		−	1.60227e7i		−	0.805058i	−0.915407	−	0.402529i	$-0.868131\pi$
$271$		−	1.60227e7i		−	0.805058i	0.915407	−	0.402529i	$-0.131869\pi$
$272$		0			0
$273$	−3.15408e6			−0.155019
$274$		0			0
$275$	95595.4	+	95595.4i	0.00459662	+	0.00459662i
$276$		0			0
$277$	−9.05850e6	−	9.05850e6i	−0.426203	−	0.426203i	0.461130	−	0.887333i	$-0.347444\pi$
$277$	−9.05850e6	−	9.05850e6i	−0.426203	−	0.426203i	−0.887333	+	0.461130i	$0.847444\pi$
$278$		0			0
$279$	−1.28604e7			−0.592162
$280$		0			0
$281$		−	2.65526e7i		−	1.19671i	−0.801232	−	0.598354i	$-0.795822\pi$
$281$		−	2.65526e7i		−	1.19671i	0.801232	−	0.598354i	$-0.204178\pi$
$282$		0			0
$283$	2.93930e7	−	2.93930e7i	1.29683	−	1.29683i	0.366361	−	0.930473i	$-0.380604\pi$
$283$	2.93930e7	−	2.93930e7i	1.29683	−	1.29683i	0.930473	−	0.366361i	$-0.119396\pi$
$284$		0			0
$285$	4.51481e6	−	4.51481e6i	0.195031	−	0.195031i
$286$		0			0
$287$		−	1.26538e7i		−	0.535275i
$288$		0			0
$289$	1.47687e7			0.611855
$290$		0			0
$291$	−5.71939e6	−	5.71939e6i	−0.232098	−	0.232098i
$292$		0			0
$293$	−1.15809e7	−	1.15809e7i	−0.460406	−	0.460406i	0.438382	−	0.898789i	$-0.355552\pi$
$293$	−1.15809e7	−	1.15809e7i	−0.460406	−	0.460406i	−0.898789	+	0.438382i	$0.855552\pi$
$294$		0			0
$295$	1.45878e7			0.568229
$296$		0			0
$297$			131951.i			0.00503667i
$298$		0			0
$299$	5.34975e6	−	5.34975e6i	0.200133	−	0.200133i
$300$		0			0
$301$	−1.04923e7	+	1.04923e7i	−0.384742	+	0.384742i
$302$		0			0
$303$			2.84764e7i			1.02366i
$304$		0			0
$305$	−3.75419e7			−1.32317
$306$		0			0
$307$	−3.35383e7	−	3.35383e7i	−1.15911	−	1.15911i	−0.984667	−	0.174446i	$-0.944187\pi$
$307$	−3.35383e7	−	3.35383e7i	−1.15911	−	1.15911i	−0.174446	−	0.984667i	$-0.555813\pi$
$308$		0			0
$309$	−1.66891e7	−	1.66891e7i	−0.565663	−	0.565663i
$310$		0			0
$311$	−1.50237e7			−0.499453			−0.249726	−	0.968316i	$-0.580341\pi$
$311$	−1.50237e7			−0.499453			−0.249726	+	0.968316i	$0.580341\pi$
$312$		0			0
$313$		−	2.85426e7i		−	0.930809i	−0.885098	−	0.465405i	$-0.845909\pi$
$313$		−	2.85426e7i		−	0.930809i	0.885098	−	0.465405i	$-0.154091\pi$
$314$		0			0
$315$	5.24073e6	−	5.24073e6i	0.167672	−	0.167672i
$316$		0			0
$317$	5.80202e6	−	5.80202e6i	0.182138	−	0.182138i	−0.610149	−	0.792287i	$-0.708890\pi$
$317$	5.80202e6	−	5.80202e6i	0.182138	−	0.182138i	0.792287	+	0.610149i	$0.208890\pi$
$318$		0			0
$319$		−	968435.i		−	0.0298331i
$320$		0			0
$321$	−3.57351e7			−1.08039
$322$		0			0
$323$	−1.29348e7	−	1.29348e7i	−0.383843	−	0.383843i
$324$		0			0
$325$	2.54266e6	+	2.54266e6i	0.0740693	+	0.0740693i
$326$		0			0
$327$	1.36231e7			0.389612
$328$		0			0
$329$		−	2.21086e7i		−	0.620832i
$330$		0			0
$331$	2.11049e7	−	2.11049e7i	0.581968	−	0.581968i	−0.353476	−	0.935444i	$-0.615000\pi$
$331$	2.11049e7	−	2.11049e7i	0.581968	−	0.581968i	0.935444	+	0.353476i	$0.115000\pi$
$332$		0			0
$333$	−1.57161e7	+	1.57161e7i	−0.425610	+	0.425610i
$334$		0			0
$335$		−	2.94162e7i		−	0.782443i
$336$		0			0
$337$	−2.04835e7			−0.535198			−0.267599	−	0.963530i	$-0.586230\pi$
$337$	−2.04835e7			−0.535198			−0.267599	+	0.963530i	$0.586230\pi$
$338$		0			0
$339$	2.01637e7	+	2.01637e7i	0.517573	+	0.517573i
$340$		0			0
$341$	1.30357e6	+	1.30357e6i	0.0328755	+	0.0328755i
$342$		0			0
$343$	4.09700e7			1.01527
$344$		0			0
$345$			1.77779e7i			0.432936i
$346$		0			0
$347$	2.53226e7	−	2.53226e7i	0.606066	−	0.606066i	−0.335850	−	0.941916i	$-0.609023\pi$
$347$	2.53226e7	−	2.53226e7i	0.606066	−	0.606066i	0.941916	+	0.335850i	$0.109023\pi$
$348$		0			0
$349$	2.32368e7	−	2.32368e7i	0.546638	−	0.546638i	−0.378829	−	0.925467i	$-0.623673\pi$
$349$	2.32368e7	−	2.32368e7i	0.546638	−	0.546638i	0.925467	+	0.378829i	$0.123673\pi$
$350$		0			0
$351$			3.50965e6i			0.0811601i
$352$		0			0
$353$	−2.14856e7			−0.488453			−0.244226	−	0.969718i	$-0.578534\pi$
$353$	−2.14856e7			−0.488453			−0.244226	+	0.969718i	$0.578534\pi$
$354$		0			0
$355$	4.66431e6	+	4.66431e6i	0.104256	+	0.104256i
$356$		0			0
$357$	−1.50146e7	−	1.50146e7i	−0.329996	−	0.329996i
$358$		0			0
$359$	3.42296e7			0.739807			0.369903	−	0.929070i	$-0.379391\pi$
$359$	3.42296e7			0.739807			0.369903	+	0.929070i	$0.379391\pi$
$360$		0			0
$361$		−	3.84452e7i		−	0.817185i
$362$		0			0
$363$	−1.95140e7	+	1.95140e7i	−0.407969	+	0.407969i
$364$		0			0
$365$	−8.00061e6	+	8.00061e6i	−0.164530	+	0.164530i
$366$		0			0
$367$		−	2.19181e7i		−	0.443410i	−0.975114	−	0.221705i	$-0.928838\pi$
$367$		−	2.19181e7i		−	0.443410i	0.975114	−	0.221705i	$-0.0711622\pi$
$368$		0			0
$369$	−1.40803e7			−0.280242
$370$		0			0
$371$	3.44374e6	+	3.44374e6i	0.0674386	+	0.0674386i
$372$		0			0
$373$	1.25229e7	+	1.25229e7i	0.241312	+	0.241312i	0.817393	−	0.576081i	$-0.195419\pi$
$373$	1.25229e7	+	1.25229e7i	0.241312	+	0.241312i	−0.576081	+	0.817393i	$0.695419\pi$
$374$		0			0
$375$	2.55683e7			0.484851
$376$		0			0
$377$		−	2.57586e7i		−	0.480726i
$378$		0			0
$379$	5.79475e7	−	5.79475e7i	1.06443	−	1.06443i	0.0666543	−	0.997776i	$-0.478768\pi$
$379$	5.79475e7	−	5.79475e7i	1.06443	−	1.06443i	0.997776	−	0.0666543i	$-0.0212325\pi$
$380$		0			0
$381$	−3.60248e7	+	3.60248e7i	−0.651368	+	0.651368i
$382$		0			0
$383$		−	2.36206e7i		−	0.420430i	−0.977655	−	0.210215i	$-0.932584\pi$
$383$		−	2.36206e7i		−	0.420430i	0.977655	−	0.210215i	$-0.0674165\pi$
$384$		0			0
$385$	−1.06244e6			−0.0186175
$386$		0			0
$387$	1.16751e7	+	1.16751e7i	0.201432	+	0.201432i
$388$		0			0
$389$	−5.54676e7	−	5.54676e7i	−0.942303	−	0.942303i	0.0561207	−	0.998424i	$-0.482127\pi$
$389$	−5.54676e7	−	5.54676e7i	−0.942303	−	0.942303i	−0.998424	+	0.0561207i	$0.982127\pi$
$390$		0			0
$391$	5.09335e7			0.852066
$392$		0			0
$393$			7.59052e6i			0.125053i
$394$		0			0
$395$	−5.28005e7	+	5.28005e7i	−0.856736	+	0.856736i
$396$		0			0
$397$	1.24085e7	−	1.24085e7i	0.198312	−	0.198312i	−0.600964	−	0.799276i	$-0.705217\pi$
$397$	1.24085e7	−	1.24085e7i	0.198312	−	0.198312i	0.799276	+	0.600964i	$0.205217\pi$
$398$		0			0
$399$			9.98355e6i			0.157169i
$400$		0			0
$401$	9.04484e7			1.40271			0.701355	−	0.712813i	$-0.252579\pi$
$401$	9.04484e7			1.40271			0.701355	+	0.712813i	$0.252579\pi$
$402$		0			0
$403$	3.46726e7	+	3.46726e7i	0.529751	+	0.529751i
$404$		0			0
$405$	−5.83153e6	−	5.83153e6i	−0.0877844	−	0.0877844i
$406$		0			0
$407$	3.18607e6			0.0472577
$408$		0			0
$409$			5.51129e7i			0.805534i	0.915303	+	0.402767i	$0.131951\pi$
$409$			5.51129e7i			0.805534i	−0.915303	+	0.402767i	$0.868049\pi$
$410$		0			0
$411$	−4.00434e7	+	4.00434e7i	−0.576774	+	0.576774i
$412$		0			0
$413$	−1.61289e7	+	1.61289e7i	−0.228957	+	0.228957i
$414$		0			0
$415$		−	1.25986e8i		−	1.76270i
$416$		0			0
$417$	2.15604e7			0.297336
$418$		0			0
$419$	5.58278e7	+	5.58278e7i	0.758942	+	0.758942i	0.976130	−	0.217188i	$-0.0696885\pi$
$419$	5.58278e7	+	5.58278e7i	0.758942	+	0.758942i	−0.217188	+	0.976130i	$0.569689\pi$
$420$		0			0
$421$	393923.	+	393923.i	0.00527916	+	0.00527916i	0.709741	−	0.704462i	$-0.248812\pi$
$421$	393923.	+	393923.i	0.00527916	+	0.00527916i	−0.704462	+	0.709741i	$0.748812\pi$
$422$		0			0
$423$	−2.46010e7			−0.325036
$424$		0			0
$425$			2.42080e7i			0.315349i
$426$		0			0
$427$	4.15081e7	−	4.15081e7i	0.533149	−	0.533149i
$428$		0			0
$429$	355751.	−	355751.i	0.00450582	−	0.00450582i
$430$		0			0
$431$			1.92766e7i			0.240768i	0.992727	+	0.120384i	$0.0384126\pi$
$431$			1.92766e7i			0.240768i	−0.992727	+	0.120384i	$0.961587\pi$
$432$		0			0
$433$	1.00402e8			1.23674			0.618368	−	0.785889i	$-0.287794\pi$
$433$	1.00402e8			1.23674			0.618368	+	0.785889i	$0.287794\pi$
$434$		0			0
$435$	4.27996e7	+	4.27996e7i	0.519963	+	0.519963i
$436$		0			0
$437$	−1.69334e7	−	1.69334e7i	−0.202909	−	0.202909i
$438$		0			0
$439$	−1.51963e8			−1.79616			−0.898080	−	0.439831i	$-0.855038\pi$
$439$	−1.51963e8			−1.79616			−0.898080	+	0.439831i	$0.855038\pi$
$440$		0			0
$441$		−	1.69999e7i		−	0.198213i
$442$		0			0
$443$	2.27338e7	−	2.27338e7i	0.261493	−	0.261493i	−0.564167	−	0.825660i	$-0.690803\pi$
$443$	2.27338e7	−	2.27338e7i	0.261493	−	0.261493i	0.825660	+	0.564167i	$0.190803\pi$
$444$		0			0
$445$	1.12035e8	−	1.12035e8i	1.27137	−	1.27137i
$446$		0			0
$447$		−	2.62848e7i		−	0.294294i
$448$		0			0
$449$	−1.44696e8			−1.59852			−0.799258	−	0.600988i	$-0.794774\pi$
$449$	−1.44696e8			−1.59852			−0.799258	+	0.600988i	$0.794774\pi$
$450$		0			0
$451$	1.42723e6	+	1.42723e6i	0.0155584	+	0.0155584i
$452$		0			0
$453$	−2.25514e7	−	2.25514e7i	−0.242593	−	0.242593i
$454$		0			0
$455$	−2.82589e7			−0.300000
$456$		0			0
$457$			4.41589e7i			0.462668i	0.972874	+	0.231334i	$0.0743091\pi$
$457$			4.41589e7i			0.462668i	−0.972874	+	0.231334i	$0.925691\pi$
$458$		0			0
$459$	−1.67072e7	+	1.67072e7i	−0.172769	+	0.172769i
$460$		0			0
$461$	−6.51505e7	+	6.51505e7i	−0.664990	+	0.664990i	−0.956552	−	0.291562i	$-0.905825\pi$
$461$	−6.51505e7	+	6.51505e7i	−0.664990	+	0.664990i	0.291562	+	0.956552i	$0.405825\pi$
$462$		0			0
$463$		−	1.53999e8i		−	1.55158i	−0.630990	−	0.775791i	$-0.717351\pi$
$463$		−	1.53999e8i		−	1.55158i	0.630990	−	0.775791i	$-0.282649\pi$
$464$		0			0
$465$	−1.15222e8			−1.14598
$466$		0			0
$467$	3.68744e7	+	3.68744e7i	0.362055	+	0.362055i	0.864569	−	0.502514i	$-0.167591\pi$
$467$	3.68744e7	+	3.68744e7i	0.362055	+	0.362055i	−0.502514	+	0.864569i	$0.667591\pi$
$468$		0			0
$469$	3.25239e7	+	3.25239e7i	0.315271	+	0.315271i
$470$		0			0
$471$	5.04337e7			0.482679
$472$		0			0
$473$		−	2.36686e6i		−	0.0223660i
$474$		0			0
$475$	8.04823e6	−	8.04823e6i	0.0750965	−	0.0750965i
$476$		0			0
$477$	3.83196e6	−	3.83196e6i	0.0353074	−	0.0353074i
$478$		0			0
$479$			1.42659e8i			1.29805i	0.760767	+	0.649026i	$0.224823\pi$
$479$			1.42659e8i			1.29805i	−0.760767	+	0.649026i	$0.775177\pi$
$480$		0			0
$481$	8.47437e7			0.761504
$482$		0			0
$483$	−1.96561e7	−	1.96561e7i	−0.174444	−	0.174444i
$484$		0			0
$485$	−5.12426e7	−	5.12426e7i	−0.449165	−	0.449165i
$486$		0			0
$487$	1.47962e8			1.28104			0.640521	−	0.767940i	$-0.278718\pi$
$487$	1.47962e8			1.28104			0.640521	+	0.767940i	$0.278718\pi$
$488$		0			0
$489$		−	7.15854e7i		−	0.612206i
$490$		0			0
$491$	2.15897e7	−	2.15897e7i	0.182390	−	0.182390i	−0.610006	−	0.792397i	$-0.708833\pi$
$491$	2.15897e7	−	2.15897e7i	0.182390	−	0.182390i	0.792397	+	0.610006i	$0.208833\pi$
$492$		0			0
$493$	1.22620e8	−	1.22620e8i	1.02334	−	1.02334i
$494$		0			0
$495$			1.18221e6i			0.00974717i
$496$		0			0
$497$	−1.03142e7			−0.0840165
$498$		0			0
$499$	−1.29594e8	−	1.29594e8i	−1.04299	−	1.04299i	−0.999033	−	0.0439610i	$-0.986002\pi$
$499$	−1.29594e8	−	1.29594e8i	−1.04299	−	1.04299i	−0.0439610	−	0.999033i	$-0.513998\pi$
$500$		0			0
$501$	−1.99797e7	−	1.99797e7i	−0.158882	−	0.158882i
$502$		0			0
$503$	3.70265e7			0.290944			0.145472	−	0.989362i	$-0.453530\pi$
$503$	3.70265e7			0.290944			0.145472	+	0.989362i	$0.453530\pi$
$504$		0			0
$505$			2.55133e8i			1.98104i
$506$		0			0
$507$	−4.37422e7	+	4.37422e7i	−0.335642	+	0.335642i
$508$		0			0
$509$	−1.20130e8	+	1.20130e8i	−0.910956	+	0.910956i	−0.996347	−	0.0853912i	$-0.972786\pi$
$509$	−1.20130e8	+	1.20130e8i	−0.910956	+	0.910956i	0.0853912	+	0.996347i	$0.472786\pi$
$510$		0			0
$511$		−	1.76917e7i		−	0.132589i
$512$		0			0
$513$	1.11090e7			0.0822856
$514$		0			0
$515$	−1.49525e8	−	1.49525e8i	−1.09469	−	1.09469i
$516$		0			0
$517$	2.49364e6	+	2.49364e6i	0.0180452	+	0.0180452i
$518$		0			0
$519$	−1.70319e7			−0.121832
$520$		0			0
$521$		−	7.98476e7i		−	0.564610i	−0.959325	−	0.282305i	$-0.908901\pi$
$521$		−	7.98476e7i		−	0.564610i	0.959325	−	0.282305i	$-0.0910990\pi$
$522$		0			0
$523$	−4.31134e7	+	4.31134e7i	−0.301375	+	0.301375i	−0.841552	−	0.540177i	$-0.818357\pi$
$523$	−4.31134e7	+	4.31134e7i	−0.301375	+	0.301375i	0.540177	+	0.841552i	$0.318357\pi$
$524$		0			0
$525$	9.34227e6	−	9.34227e6i	0.0645617	−	0.0645617i
$526$		0			0
$527$			3.30108e8i			2.25541i
$528$		0			0
$529$	−8.13572e7			−0.549577
$530$		0			0
$531$	1.79472e7	+	1.79472e7i	0.119870	+	0.119870i
$532$		0			0
$533$	3.79618e7	+	3.79618e7i	0.250706	+	0.250706i
$534$		0			0
$535$	−3.20167e8			−2.09081
$536$		0			0
$537$			1.23817e8i			0.799571i
$538$		0			0
$539$	−1.72317e6	+	1.72317e6i	−0.0110043	+	0.0110043i
$540$		0			0
$541$	−2.31672e7	+	2.31672e7i	−0.146313	+	0.146313i	−0.776469	−	0.630156i	$-0.782991\pi$
$541$	−2.31672e7	+	2.31672e7i	−0.146313	+	0.146313i	0.630156	+	0.776469i	$0.282991\pi$
$542$		0			0
$543$			4.95639e7i			0.309575i
$544$		0			0
$545$	1.22055e8			0.753993
$546$		0			0
$547$	−7.12487e7	−	7.12487e7i	−0.435327	−	0.435327i	0.455109	−	0.890436i	$-0.349600\pi$
$547$	−7.12487e7	−	7.12487e7i	−0.435327	−	0.435327i	−0.890436	+	0.455109i	$0.849600\pi$
$548$		0			0
$549$	−4.61874e7	−	4.61874e7i	−0.279130	−	0.279130i
$550$		0			0
$551$	−8.15330e7			−0.487392
$552$		0			0
$553$		−	1.16757e8i		−	0.690412i
$554$		0			0
$555$	−1.40807e8	+	1.40807e8i	−0.823657	+	0.823657i
$556$		0			0
$557$	−3.39546e7	+	3.39546e7i	−0.196487	+	0.196487i	−0.798492	−	0.602005i	$-0.794369\pi$
$557$	−3.39546e7	+	3.39546e7i	−0.196487	+	0.196487i	0.602005	+	0.798492i	$0.294369\pi$
$558$		0			0
$559$		−	6.29541e7i		−	0.360403i
$560$		0			0
$561$	3.38701e6			0.0191835
$562$		0			0
$563$	1.86115e8	+	1.86115e8i	1.04293	+	1.04293i	0.999036	+	0.0438973i	$0.0139774\pi$
$563$	1.86115e8	+	1.86115e8i	1.04293	+	1.04293i	0.0438973	+	0.999036i	$0.486023\pi$
$564$		0			0
$565$	1.80656e8	+	1.80656e8i	1.00163	+	1.00163i
$566$		0			0
$567$	1.28952e7			0.0707422
$568$		0			0
$569$			7.08693e7i			0.384699i	0.981326	+	0.192350i	$0.0616108\pi$
$569$			7.08693e7i			0.384699i	−0.981326	+	0.192350i	$0.938389\pi$
$570$		0			0
$571$	1.22930e7	−	1.22930e7i	0.0660315	−	0.0660315i	−0.673320	−	0.739351i	$-0.735132\pi$
$571$	1.22930e7	−	1.22930e7i	0.0660315	−	0.0660315i	0.739351	+	0.673320i	$0.235132\pi$
$572$		0			0
$573$	7.82613e7	−	7.82613e7i	0.415990	−	0.415990i
$574$		0			0
$575$			3.16915e7i			0.166701i
$576$		0			0
$577$	3.64071e8			1.89522			0.947608	−	0.319436i	$-0.103494\pi$
$577$	3.64071e8			1.89522			0.947608	+	0.319436i	$0.103494\pi$
$578$		0			0
$579$	2.76488e7	+	2.76488e7i	0.142443	+	0.142443i
$580$		0			0
$581$	1.39296e8	+	1.39296e8i	0.710248	+	0.710248i
$582$		0			0
$583$	−776842.			−0.00392037
$584$		0			0
$585$			3.14446e7i			0.157064i
$586$		0			0
$587$	3.81585e6	−	3.81585e6i	0.0188659	−	0.0188659i	−0.697611	−	0.716477i	$-0.745754\pi$
$587$	3.81585e6	−	3.81585e6i	0.0188659	−	0.0188659i	0.716477	+	0.697611i	$0.245754\pi$
$588$		0			0
$589$	1.09748e8	−	1.09748e8i	0.537097	−	0.537097i
$590$		0			0
$591$			4.53520e7i			0.219702i
$592$		0			0
$593$	−3.34746e7			−0.160528			−0.0802642	−	0.996774i	$-0.525576\pi$
$593$	−3.34746e7			−0.160528			−0.0802642	+	0.996774i	$0.525576\pi$
$594$		0			0
$595$	−1.34522e8	−	1.34522e8i	−0.638622	−	0.638622i
$596$		0			0
$597$	−4.88527e7	−	4.88527e7i	−0.229597	−	0.229597i
$598$		0			0
$599$	−1.51470e8			−0.704769			−0.352385	−	0.935855i	$-0.614629\pi$
$599$	−1.51470e8			−0.704769			−0.352385	+	0.935855i	$0.614629\pi$
$600$		0			0
$601$		−	1.95455e8i		−	0.900377i	−0.892934	−	0.450189i	$-0.851357\pi$
$601$		−	1.95455e8i		−	0.900377i	0.892934	−	0.450189i	$-0.148643\pi$
$602$		0			0
$603$	3.61904e7	−	3.61904e7i	0.165060	−	0.165060i
$604$		0			0
$605$	−1.74835e8	+	1.74835e8i	−0.789518	+	0.789518i
$606$		0			0
$607$			8.33525e7i			0.372694i	0.982484	+	0.186347i	$0.0596649\pi$
$607$			8.33525e7i			0.372694i	−0.982484	+	0.186347i	$0.940335\pi$
$608$		0			0
$609$	−9.46424e7			−0.419019
$610$		0			0
$611$	6.63263e7	+	6.63263e7i	0.290778	+	0.290778i
$612$		0			0
$613$	2.79225e8	+	2.79225e8i	1.21220	+	1.21220i	0.970303	+	0.241894i	$0.0777687\pi$
$613$	2.79225e8	+	2.79225e8i	1.21220	+	1.21220i	0.241894	+	0.970303i	$0.422231\pi$
$614$		0			0
$615$	−1.26152e8			−0.542337
$616$		0			0
$617$		−	3.09401e8i		−	1.31724i	−0.752474	−	0.658622i	$-0.771140\pi$
$617$		−	3.09401e8i		−	1.31724i	0.752474	−	0.658622i	$-0.228860\pi$
$618$		0			0
$619$	−2.38698e8	+	2.38698e8i	−1.00641	+	1.00641i	−0.00643555	+	0.999979i	$0.502049\pi$
$619$	−2.38698e8	+	2.38698e8i	−1.00641	+	1.00641i	−0.999979	+	0.00643555i	$0.997951\pi$
$620$		0			0
$621$	−2.18720e7	+	2.18720e7i	−0.0913299	+	0.0913299i
$622$		0			0
$623$			2.47741e8i			1.02455i
$624$		0			0
$625$	2.89719e8			1.18669
$626$		0			0
$627$	−1.12605e6	−	1.12605e6i	−0.00456830	−	0.00456830i
$628$		0			0
$629$	4.03411e8	+	4.03411e8i	1.62105	+	1.62105i
$630$		0			0
$631$	3.78149e8			1.50513			0.752566	−	0.658517i	$-0.228816\pi$
$631$	3.78149e8			1.50513			0.752566	+	0.658517i	$0.228816\pi$
$632$		0			0
$633$			1.11405e8i			0.439232i
$634$		0			0
$635$	−3.22762e8	+	3.22762e8i	−1.26055	+	1.26055i
$636$		0			0
$637$	−4.58333e7	+	4.58333e7i	−0.177322	+	0.177322i
$638$		0			0
$639$			1.14769e7i			0.0439867i
$640$		0			0
$641$	−6.24282e7			−0.237032			−0.118516	−	0.992952i	$-0.537814\pi$
$641$	−6.24282e7			−0.237032			−0.118516	+	0.992952i	$0.537814\pi$
$642$		0			0
$643$	9.95566e7	+	9.95566e7i	0.374487	+	0.374487i	0.869109	−	0.494621i	$-0.164693\pi$
$643$	9.95566e7	+	9.95566e7i	0.374487	+	0.374487i	−0.494621	+	0.869109i	$0.664693\pi$
$644$		0			0
$645$	1.04602e8	+	1.04602e8i	0.389819	+	0.389819i
$646$		0			0
$647$	−2.59219e8			−0.957092			−0.478546	−	0.878063i	$-0.658836\pi$
$647$	−2.59219e8			−0.957092			−0.478546	+	0.878063i	$0.658836\pi$
$648$		0			0
$649$		−	3.63838e6i		−	0.0133099i
$650$		0			0
$651$	1.27394e8	−	1.27394e8i	0.461751	−	0.461751i
$652$		0			0
$653$	−2.52195e7	+	2.52195e7i	−0.0905725	+	0.0905725i	−0.750941	−	0.660369i	$-0.770400\pi$
$653$	−2.52195e7	+	2.52195e7i	−0.0905725	+	0.0905725i	0.660369	+	0.750941i	$0.270400\pi$
$654$		0			0
$655$			6.80069e7i			0.242008i
$656$		0			0
$657$	−1.96861e7			−0.0694167
$658$		0			0
$659$	−3.42808e7	−	3.42808e7i	−0.119783	−	0.119783i	0.644674	−	0.764457i	$-0.276993\pi$
$659$	−3.42808e7	−	3.42808e7i	−0.119783	−	0.119783i	−0.764457	+	0.644674i	$0.776993\pi$
$660$		0			0
$661$	1.76286e8	+	1.76286e8i	0.610397	+	0.610397i	0.943050	−	0.332652i	$-0.107944\pi$
$661$	1.76286e8	+	1.76286e8i	0.610397	+	0.610397i	−0.332652	+	0.943050i	$0.607944\pi$
$662$		0			0
$663$	9.00881e7			0.309120
$664$		0			0
$665$			8.94471e7i			0.304160i
$666$		0			0
$667$	1.60526e8	−	1.60526e8i	0.540964	−	0.540964i
$668$		0			0
$669$	6.67588e7	−	6.67588e7i	0.222962	−	0.222962i
$670$		0			0
$671$			9.36343e6i			0.0309933i
$672$		0			0
$673$	−1.64739e8			−0.540446			−0.270223	−	0.962798i	$-0.587097\pi$
$673$	−1.64739e8			−0.540446			−0.270223	+	0.962798i	$0.587097\pi$
$674$		0			0
$675$	−1.03955e7	−	1.03955e7i	−0.0338012	−	0.0338012i
$676$		0			0
$677$	−3.62126e8	−	3.62126e8i	−1.16706	−	1.16706i	−0.982895	−	0.184165i	$-0.941042\pi$
$677$	−3.62126e8	−	3.62126e8i	−1.16706	−	1.16706i	−0.184165	−	0.982895i	$-0.558958\pi$
$678$		0			0
$679$	1.13312e8			0.361966
$680$		0			0
$681$			1.10241e8i			0.349062i
$682$		0			0
$683$	1.86266e8	−	1.86266e8i	0.584616	−	0.584616i	−0.351552	−	0.936168i	$-0.614346\pi$
$683$	1.86266e8	−	1.86266e8i	0.584616	−	0.584616i	0.936168	+	0.351552i	$0.114346\pi$
$684$		0			0
$685$	−3.58767e8	+	3.58767e8i	−1.11620	+	1.11620i
$686$		0			0
$687$			3.06666e8i			0.945792i
$688$		0			0
$689$	−2.06626e7			−0.0631723
$690$		0			0
$691$	−1.99965e8	−	1.99965e8i	−0.606065	−	0.606065i	0.335851	−	0.941915i	$-0.390976\pi$
$691$	−1.99965e8	−	1.99965e8i	−0.606065	−	0.606065i	−0.941915	+	0.335851i	$0.890976\pi$
$692$		0			0
$693$	−1.30710e6	−	1.30710e6i	−0.00392745	−	0.00392745i
$694$		0			0
$695$	1.93169e8			0.575418
$696$		0			0
$697$			3.61424e8i			1.06738i
$698$		0			0
$699$	−2.17556e8	+	2.17556e8i	−0.637000	+	0.637000i
$700$		0			0
$701$	1.60772e8	−	1.60772e8i	0.466720	−	0.466720i	−0.434130	−	0.900850i	$-0.642944\pi$
$701$	1.60772e8	−	1.60772e8i	0.466720	−	0.466720i	0.900850	+	0.434130i	$0.142944\pi$
$702$		0			0
$703$		−	2.68237e8i		−	0.772064i
$704$		0			0
$705$	−2.20411e8			−0.629023
$706$		0			0
$707$	−2.82086e8	−	2.82086e8i	−0.798223	−	0.798223i
$708$		0			0
$709$	−4.85445e8	−	4.85445e8i	−1.36208	−	1.36208i	−0.871267	−	0.490809i	$-0.836701\pi$
$709$	−4.85445e8	−	4.85445e8i	−1.36208	−	1.36208i	−0.490809	−	0.871267i	$-0.663299\pi$
$710$		0			0
$711$	−1.29920e8			−0.361465
$712$		0			0
$713$			4.32156e8i			1.19226i
$714$		0			0
$715$	3.18733e6	−	3.18733e6i	0.00871986	−	0.00871986i
$716$		0			0
$717$	−2.29740e8	+	2.29740e8i	−0.623273	+	0.623273i
$718$		0			0
$719$		−	1.61892e8i		−	0.435550i	−0.975999	−	0.217775i	$-0.930120\pi$
$719$		−	1.61892e8i		−	0.435550i	0.975999	−	0.217775i	$-0.0698798\pi$
$720$		0			0
$721$	3.30644e8			0.882174
$722$		0			0
$723$	2.68289e8	+	2.68289e8i	0.709885	+	0.709885i
$724$		0			0
$725$	7.62959e7	+	7.62959e7i	0.200211	+	0.200211i
$726$		0			0
$727$	1.21527e8			0.316278			0.158139	−	0.987417i	$-0.449451\pi$
$727$	1.21527e8			0.316278			0.158139	+	0.987417i	$0.449451\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	2.99684e8	−	2.99684e8i	0.767206	−	0.767206i
$732$		0			0
$733$	1.19651e8	−	1.19651e8i	0.303812	−	0.303812i	−0.538691	−	0.842503i	$-0.681081\pi$
$733$	1.19651e8	−	1.19651e8i	0.303812	−	0.303812i	0.842503	+	0.538691i	$0.181081\pi$
$734$		0			0
$735$		−	1.52310e8i		−	0.383590i
$736$		0			0
$737$	−7.33678e6			−0.0183275
$738$		0			0
$739$	3.61143e8	+	3.61143e8i	0.894841	+	0.894841i	0.994974	−	0.100133i	$-0.0319267\pi$
$739$	3.61143e8	+	3.61143e8i	0.894841	+	0.894841i	−0.100133	+	0.994974i	$0.531927\pi$
$740$		0			0
$741$	−2.99508e7	−	2.99508e7i	−0.0736130	−	0.0736130i
$742$		0			0
$743$	6.27184e6			0.0152907			0.00764537	−	0.999971i	$-0.497566\pi$
$743$	6.27184e6			0.0152907			0.00764537	+	0.999971i	$0.497566\pi$
$744$		0			0
$745$		−	2.35497e8i		−	0.569530i
$746$		0			0
$747$	1.54999e8	−	1.54999e8i	0.371850	−	0.371850i
$748$		0			0
$749$	3.53991e8	−	3.53991e8i	0.842455	−	0.842455i
$750$		0			0
$751$		−	4.58642e8i		−	1.08281i	−0.840761	−	0.541407i	$-0.817892\pi$
$751$		−	4.58642e8i		−	1.08281i	0.840761	−	0.541407i	$-0.182108\pi$
$752$		0			0
$753$	−1.72090e8			−0.403061
$754$		0			0
$755$	−2.02048e8	−	2.02048e8i	−0.469477	−	0.469477i
$756$		0			0
$757$	−4.71531e7	−	4.71531e7i	−0.108698	−	0.108698i	0.650666	−	0.759364i	$-0.274490\pi$
$757$	−4.71531e7	−	4.71531e7i	−0.108698	−	0.108698i	−0.759364	+	0.650666i	$0.774490\pi$
$758$		0			0
$759$	4.43404e6			0.0101409
$760$		0			0
$761$			2.48288e8i			0.563381i	0.959505	+	0.281690i	$0.0908951\pi$
$761$			2.48288e8i			0.563381i	−0.959505	+	0.281690i	$0.909105\pi$
$762$		0			0
$763$	−1.34950e8	+	1.34950e8i	−0.303808	+	0.303808i
$764$		0			0
$765$	−1.49688e8	+	1.49688e8i	−0.334350	+	0.334350i
$766$		0			0
$767$		−	9.67741e7i		−	0.214473i
$768$		0			0
$769$	−6.07402e8			−1.33566			−0.667831	−	0.744313i	$-0.732777\pi$
$769$	−6.07402e8			−1.33566			−0.667831	+	0.744313i	$0.732777\pi$
$770$		0			0
$771$	−2.24321e8	−	2.24321e8i	−0.489448	−	0.489448i
$772$		0			0
$773$	−3.08047e8	−	3.08047e8i	−0.666927	−	0.666927i	0.290076	−	0.957004i	$-0.406319\pi$
$773$	−3.08047e8	−	3.08047e8i	−0.666927	−	0.666927i	−0.957004	+	0.290076i	$0.906319\pi$
$774$		0			0
$775$	−2.05398e8			−0.441256
$776$		0			0
$777$		−	3.11366e8i		−	0.663756i
$778$		0			0
$779$	1.20160e8	−	1.20160e8i	0.254183	−	0.254183i
$780$		0			0
$781$	1.16334e6	−	1.16334e6i	0.00244204	−	0.00244204i
$782$		0			0
$783$			1.05312e8i			0.219377i
$784$		0			0
$785$	4.51858e8			0.934100
$786$		0			0
$787$	4.84286e8	+	4.84286e8i	0.993523	+	0.993523i	0.999979	−	0.00645601i	$-0.00205502\pi$
$787$	4.84286e8	+	4.84286e8i	0.993523	+	0.993523i	−0.00645601	+	0.999979i	$0.502055\pi$
$788$		0			0
$789$	8.26168e7	+	8.26168e7i	0.168204	+	0.168204i
$790$		0			0
$791$	−3.99483e8			−0.807177
$792$		0			0
$793$			2.49050e8i			0.499421i
$794$		0			0
$795$	3.43323e7	−	3.43323e7i	0.0683283	−	0.0683283i
$796$		0			0
$797$	5.56676e8	−	5.56676e8i	1.09958	−	1.09958i	0.105122	−	0.994459i	$-0.466477\pi$
$797$	5.56676e8	−	5.56676e8i	1.09958	−	1.09958i	0.994459	−	0.105122i	$-0.0335234\pi$
$798$		0			0
$799$			6.31475e8i			1.23799i
$800$		0			0
$801$	2.75670e8			0.536404
$802$		0			0
$803$	1.99545e6	+	1.99545e6i	0.00385385	+	0.00385385i
$804$		0			0
$805$	−1.76108e8	−	1.76108e8i	−0.337591	−	0.337591i
$806$		0			0
$807$	2.15218e8			0.409503
$808$		0			0
$809$		−	4.96612e8i		−	0.937933i	−0.883216	−	0.468967i	$-0.844626\pi$
$809$		−	4.96612e8i		−	0.937933i	0.883216	−	0.468967i	$-0.155374\pi$
$810$		0			0
$811$	8.24885e7	−	8.24885e7i	0.154643	−	0.154643i	−0.625545	−	0.780188i	$-0.715123\pi$
$811$	8.24885e7	−	8.24885e7i	0.154643	−	0.154643i	0.780188	+	0.625545i	$0.215123\pi$
$812$		0			0
$813$	1.76613e8	−	1.76613e8i	0.328663	−	0.328663i
$814$		0			0
$815$		−	6.41366e8i		−	1.18477i
$816$		0			0
$817$	−1.99267e8			−0.365401
$818$		0			0
$819$	−3.47665e7	−	3.47665e7i	−0.0632863	−	0.0632863i
$820$		0			0
$821$	−5.21896e8	−	5.21896e8i	−0.943094	−	0.943094i	0.0553722	−	0.998466i	$-0.482365\pi$
$821$	−5.21896e8	−	5.21896e8i	−0.943094	−	0.943094i	−0.998466	+	0.0553722i	$0.982365\pi$
$822$		0			0
$823$	−4.99091e8			−0.895323			−0.447662	−	0.894203i	$-0.647743\pi$
$823$	−4.99091e8			−0.895323			−0.447662	+	0.894203i	$0.647743\pi$
$824$		0			0
$825$			2.10744e6i			0.00375313i
$826$		0			0
$827$	−6.24524e8	+	6.24524e8i	−1.10416	+	1.10416i	−0.110259	+	0.993903i	$0.535168\pi$
$827$	−6.24524e8	+	6.24524e8i	−1.10416	+	1.10416i	−0.993903	+	0.110259i	$0.964832\pi$
$828$		0			0
$829$	5.70596e8	−	5.70596e8i	1.00153	−	1.00153i	0.00153454	−	0.999999i	$-0.499512\pi$
$829$	5.70596e8	−	5.70596e8i	1.00153	−	1.00153i	0.999999	−	0.00153454i	$-0.000488459\pi$
$830$		0			0
$831$		−	1.99698e8i		−	0.347994i
$832$		0			0
$833$	−4.36366e8			−0.754946
$834$		0			0
$835$	−1.79007e8	−	1.79007e8i	−0.307475	−	0.307475i
$836$		0			0
$837$	−1.41756e8	−	1.41756e8i	−0.241749	−	0.241749i
$838$		0			0
$839$	6.48411e8			1.09790			0.548952	−	0.835854i	$-0.315027\pi$
$839$	6.48411e8			1.09790			0.548952	+	0.835854i	$0.315027\pi$
$840$		0			0
$841$		−	1.78097e8i		−	0.299411i
$842$		0			0
$843$	2.92682e8	−	2.92682e8i	0.488554	−	0.488554i
$844$		0			0
$845$	−3.91906e8	+	3.91906e8i	−0.649549	+	0.649549i
$846$		0			0
$847$		−	3.86611e8i		−	0.636244i
$848$		0			0
$849$	6.47980e8			1.05886
$850$		0			0
$851$	5.28119e8	+	5.28119e8i	0.856925	+	0.856925i
$852$		0			0
$853$	−3.46877e8	−	3.46877e8i	−0.558893	−	0.558893i	0.370099	−	0.928992i	$-0.379324\pi$
$853$	−3.46877e8	−	3.46877e8i	−0.558893	−	0.558893i	−0.928992	+	0.370099i	$0.879324\pi$
$854$		0			0
$855$	9.95308e7			0.159242
$856$		0			0
$857$			7.77142e7i			0.123469i	0.998093	+	0.0617345i	$0.0196632\pi$
$857$			7.77142e7i			0.123469i	−0.998093	+	0.0617345i	$0.980337\pi$
$858$		0			0
$859$	6.66335e8	−	6.66335e8i	1.05127	−	1.05127i	0.0526542	−	0.998613i	$-0.483232\pi$
$859$	6.66335e8	−	6.66335e8i	1.05127	−	1.05127i	0.998613	−	0.0526542i	$-0.0167681\pi$
$860$		0			0
$861$	1.39480e8	−	1.39480e8i	0.218525	−	0.218525i
$862$		0			0
$863$		−	9.49612e8i		−	1.47745i	−0.674005	−	0.738727i	$-0.735427\pi$
$863$		−	9.49612e8i		−	1.47745i	0.674005	−	0.738727i	$-0.264573\pi$
$864$		0			0
$865$	−1.52596e8			−0.235774
$866$		0			0
$867$	1.62791e8	+	1.62791e8i	0.249789	+	0.249789i
$868$		0			0
$869$	1.31691e7	+	1.31691e7i	0.0200677	+	0.0200677i
$870$		0			0
$871$	−1.95145e8			−0.295327
$872$		0			0
$873$		−	1.26086e8i		−	0.189507i
$874$		0			0
$875$	−2.53279e8	+	2.53279e8i	−0.378073	+	0.378073i
$876$		0			0
$877$	−8.30040e8	+	8.30040e8i	−1.23055	+	1.23055i	−0.266802	+	0.963751i	$0.585967\pi$
$877$	−8.30040e8	+	8.30040e8i	−1.23055	+	1.23055i	−0.963751	+	0.266802i	$0.914033\pi$
$878$		0			0
$879$		−	2.55307e8i		−	0.375920i
$880$		0			0
$881$	1.71915e8			0.251412			0.125706	−	0.992068i	$-0.459880\pi$
$881$	1.71915e8			0.251412			0.125706	+	0.992068i	$0.459880\pi$
$882$		0			0
$883$	−5.31814e8	−	5.31814e8i	−0.772462	−	0.772462i	0.206074	−	0.978536i	$-0.433931\pi$
$883$	−5.31814e8	−	5.31814e8i	−0.772462	−	0.772462i	−0.978536	+	0.206074i	$0.933931\pi$
$884$		0			0
$885$	1.60797e8	+	1.60797e8i	0.231978	+	0.231978i
$886$		0			0
$887$	1.05662e9			1.51408			0.757042	−	0.653367i	$-0.226644\pi$
$887$	1.05662e9			1.51408			0.757042	+	0.653367i	$0.226644\pi$
$888$		0			0
$889$		−	7.13721e8i		−	1.01584i
$890$		0			0
$891$	−1.45446e6	+	1.45446e6i	−0.00205621	+	0.00205621i
$892$		0			0
$893$	2.09941e8	−	2.09941e8i	0.294811	−	0.294811i
$894$		0			0
$895$			1.10933e9i			1.54736i
$896$		0			0
$897$	1.17937e8			0.163408
$898$		0			0
$899$	1.04040e9	+	1.04040e9i	1.43192	+	1.43192i
$900$		0			0
$901$	−9.83613e7	−	9.83613e7i	−0.134478	−	0.134478i
$902$		0			0
$903$	−2.31306e8			−0.314141
$904$		0			0
$905$			4.44066e8i			0.599103i
$906$		0			0
$907$	−4.49823e8	+	4.49823e8i	−0.602864	+	0.602864i	−0.941072	−	0.338207i	$-0.890179\pi$
$907$	−4.49823e8	+	4.49823e8i	−0.602864	+	0.602864i	0.338207	+	0.941072i	$0.390179\pi$
$908$		0			0
$909$	−3.13887e8	+	3.13887e8i	−0.417909	+	0.417909i
$910$		0			0
$911$		−	5.54744e8i		−	0.733731i	−0.930274	−	0.366866i	$-0.880431\pi$
$911$		−	5.54744e8i		−	0.733731i	0.930274	−	0.366866i	$-0.119569\pi$
$912$		0			0
$913$	−3.14225e7			−0.0412885
$914$		0			0
$915$	−4.13814e8	−	4.13814e8i	−0.540184	−	0.540184i
$916$		0			0
$917$	−7.51915e7	−	7.51915e7i	−0.0975126	−	0.0975126i
$918$		0			0
$919$	2.54062e8			0.327335			0.163668	−	0.986516i	$-0.447668\pi$
$919$	2.54062e8			0.327335			0.163668	+	0.986516i	$0.447668\pi$
$920$		0			0
$921$		−	7.39365e8i		−	0.946411i
$922$		0			0
$923$	3.09427e7	−	3.09427e7i	0.0393507	−	0.0393507i
$924$		0			0
$925$	−2.51008e8	+	2.51008e8i	−0.317148	+	0.317148i
$926$		0			0
$927$		−	3.67918e8i		−	0.461862i
$928$		0			0
$929$	−1.22849e9			−1.53223			−0.766117	−	0.642701i	$-0.777814\pi$
$929$	−1.22849e9			−1.53223			−0.766117	+	0.642701i	$0.777814\pi$
$930$		0			0
$931$	1.45075e8	+	1.45075e8i	0.179781	+	0.179781i
$932$		0			0
$933$	−1.65601e8	−	1.65601e8i	−0.203901	−	0.203901i
$934$		0			0
$935$	3.03457e7			0.0371247
$936$		0			0
$937$		−	6.50976e8i		−	0.791309i	−0.918399	−	0.395655i	$-0.870518\pi$
$937$		−	6.50976e8i		−	0.791309i	0.918399	−	0.395655i	$-0.129482\pi$
$938$		0			0
$939$	3.14617e8	−	3.14617e8i	0.380001	−	0.380001i
$940$		0			0
$941$	−1.79397e8	+	1.79397e8i	−0.215301	+	0.215301i	−0.806515	−	0.591214i	$-0.798649\pi$
$941$	−1.79397e8	+	1.79397e8i	−0.215301	+	0.215301i	0.591214	+	0.806515i	$0.298649\pi$
$942$		0			0
$943$			4.73152e8i			0.564242i
$944$		0			0
$945$	1.15534e8			0.136903
$946$		0			0
$947$	−8.89683e8	−	8.89683e8i	−1.04758	−	1.04758i	−0.998810	−	0.0487651i	$-0.984471\pi$
$947$	−8.89683e8	−	8.89683e8i	−1.04758	−	1.04758i	−0.0487651	−	0.998810i	$-0.515529\pi$
$948$		0			0
$949$	5.30754e7	+	5.30754e7i	0.0621004	+	0.0621004i
$950$		0			0
$951$	1.27908e8			0.148715
$952$		0			0
$953$		−	6.66120e8i		−	0.769615i	−0.922997	−	0.384808i	$-0.874268\pi$
$953$		−	6.66120e8i		−	0.769615i	0.922997	−	0.384808i	$-0.125732\pi$
$954$		0			0
$955$	7.01178e8	−	7.01178e8i	0.805041	−	0.805041i
$956$		0			0
$957$	1.06748e7	−	1.06748e7i	0.0121793	−	0.0121793i
$958$		0			0
$959$		−	7.93339e8i		−	0.899503i
$960$		0			0
$961$	−1.91337e9			−2.15590
$962$		0			0
$963$	−3.93897e8	−	3.93897e8i	−0.441066	−	0.441066i
$964$		0			0
$965$	2.47718e8	+	2.47718e8i	0.275662	+	0.275662i
$966$		0			0
$967$	1.00795e9			1.11470			0.557352	−	0.830276i	$-0.311817\pi$
$967$	1.00795e9			1.11470			0.557352	+	0.830276i	$0.311817\pi$
$968$		0			0
$969$		−	2.85154e8i		−	0.313406i
$970$		0			0
$971$	1.00817e9	−	1.00817e9i	1.10123	−	1.10123i	0.106963	−	0.994263i	$-0.465887\pi$
$971$	1.00817e9	−	1.00817e9i	1.10123	−	1.10123i	0.994263	−	0.106963i	$-0.0341125\pi$
$972$		0			0
$973$	−2.13577e8	+	2.13577e8i	−0.231854	+	0.231854i
$974$		0			0
$975$			5.60540e7i			0.0604774i
$976$		0			0
$977$	1.84329e7			0.0197656			0.00988281	−	0.999951i	$-0.496854\pi$
$977$	1.84329e7			0.0197656			0.00988281	+	0.999951i	$0.496854\pi$
$978$		0			0
$979$	−2.79429e7	−	2.79429e7i	−0.0297799	−	0.0297799i
$980$		0			0
$981$	1.50163e8	+	1.50163e8i	0.159058	+	0.159058i
$982$		0			0
$983$	1.22451e9			1.28914			0.644572	−	0.764544i	$-0.277036\pi$
$983$	1.22451e9			1.28914			0.644572	+	0.764544i	$0.277036\pi$
$984$		0			0
$985$			4.06329e8i			0.425177i
$986$		0			0
$987$	2.43697e8	−	2.43697e8i	0.253454	−	0.253454i
$988$		0			0
$989$	3.92327e8	−	3.92327e8i	0.405563	−	0.405563i
$990$		0			0
$991$			1.09994e9i			1.13018i	0.825031	+	0.565088i	$0.191158\pi$
$991$			1.09994e9i			1.13018i	−0.825031	+	0.565088i	$0.808842\pi$
$992$		0			0
$993$	4.65266e8			0.475175
$994$		0			0
$995$	−4.37693e8	−	4.37693e8i	−0.444325	−	0.444325i
$996$		0			0
$997$	−2.65092e8	−	2.65092e8i	−0.267492	−	0.267492i	0.560597	−	0.828089i	$-0.310572\pi$
$997$	−2.65092e8	−	2.65092e8i	−0.267492	−	0.267492i	−0.828089	+	0.560597i	$0.810572\pi$
$998$		0			0
$999$	−3.46467e8			−0.347509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.b.31.15		48
4.3	odd	2		384.7.l.a.31.10		48
8.3	odd	2		192.7.l.a.79.15		48
8.5	even	2		48.7.l.a.43.9	yes	48
16.3	odd	4	inner	384.7.l.b.223.15		48
16.5	even	4		192.7.l.a.175.15		48
16.11	odd	4		48.7.l.a.19.9	✓	48
16.13	even	4		384.7.l.a.223.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.9	✓	48	16.11	odd	4
48.7.l.a.43.9	yes	48	8.5	even	2
192.7.l.a.79.15		48	8.3	odd	2
192.7.l.a.175.15		48	16.5	even	4
384.7.l.a.31.10		48	4.3	odd	2
384.7.l.a.223.10		48	16.13	even	4
384.7.l.b.31.15		48	1.1	even	1	trivial
384.7.l.b.223.15		48	16.3	odd	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	384.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(11.0227 + 11.0227i) q^{3} +(98.7574 + 98.7574i) q^{5} -218.381 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(11.0227 + 11.0227i) q^{3} +(98.7574 + 98.7574i) q^{5} -218.381 q^{7} +243.000i q^{9} +(24.6313 - 24.6313i) q^{11} +(655.148 - 655.148i) q^{13} +2177.15i q^{15} +6237.49 q^{17} +(-2073.73 - 2073.73i) q^{19} +(-2407.15 - 2407.15i) q^{21} +8165.70 q^{23} +3881.05i q^{25} +(-2678.52 + 2678.52i) q^{27} +(19658.6 - 19658.6i) q^{29} +52923.3i q^{31} +543.008 q^{33} +(-21566.8 - 21566.8i) q^{35} +(64675.2 + 64675.2i) q^{37} +14443.0 q^{39} +57943.8i q^{41} +(48045.7 - 48045.7i) q^{43} +(-23998.0 + 23998.0i) q^{45} +101239. i q^{47} -69958.6 q^{49} +(68754.0 + 68754.0i) q^{51} +(-15769.4 - 15769.4i) q^{53} +4865.06 q^{55} -45716.1i q^{57} +(73856.6 - 73856.6i) q^{59} +(-190072. + 190072. i) q^{61} -53066.7i q^{63} +129401. q^{65} +(-148932. - 148932. i) q^{67} +(90008.1 + 90008.1i) q^{69} +47230.0 q^{71} +81012.8i q^{73} +(-42779.6 + 42779.6i) q^{75} +(-5379.03 + 5379.03i) q^{77} +534649. i q^{79} -59049.0 q^{81} +(-637856. - 637856. i) q^{83} +(615998. + 615998. i) q^{85} +433381. q^{87} -1.13444e6i q^{89} +(-143072. + 143072. i) q^{91} +(-583358. + 583358. i) q^{93} -409592. i q^{95} -518874. q^{97} +(5985.42 + 5985.42i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 2720 q^{11} + 3936 q^{19} + 26240 q^{23} - 66400 q^{29} - 162336 q^{35} + 7200 q^{37} - 340704 q^{43} + 806736 q^{49} - 80352 q^{51} - 443680 q^{53} + 232704 q^{55} + 886144 q^{59} + 326496 q^{61} - 372832 q^{65} + 962112 q^{67} - 541728 q^{69} + 534016 q^{71} + 1073088 q^{75} + 932960 q^{77} - 2834352 q^{81} + 2497760 q^{83} + 372000 q^{85} - 775008 q^{91} + 660960 q^{99}+O(q^{100}) \) 48 * q + 2720 * q^11 + 3936 * q^19 + 26240 * q^23 - 66400 * q^29 - 162336 * q^35 + 7200 * q^37 - 340704 * q^43 + 806736 * q^49 - 80352 * q^51 - 443680 * q^53 + 232704 * q^55 + 886144 * q^59 + 326496 * q^61 - 372832 * q^65 + 962112 * q^67 - 541728 * q^69 + 534016 * q^71 + 1073088 * q^75 + 932960 * q^77 - 2834352 * q^81 + 2497760 * q^83 + 372000 * q^85 - 775008 * q^91 + 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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