LMFDB - Embedded newform 384.7.l.b.31.7

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			31.7
Character	$\chi$	$=$	384.31
Dual form			384.7.l.b.223.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(9.26689 + 9.26689i) q^{5} -320.373 q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(9.26689 + 9.26689i) q^{5} -320.373 q^{7} +243.000i q^{9} +(-1498.49 + 1498.49i) q^{11} +(-2546.47 + 2546.47i) q^{13} -204.292i q^{15} -7232.04 q^{17} +(4865.79 + 4865.79i) q^{19} +(3531.38 + 3531.38i) q^{21} +12202.6 q^{23} -15453.2i q^{25} +(2678.52 - 2678.52i) q^{27} +(-9527.74 + 9527.74i) q^{29} -13501.8i q^{31} +33034.9 q^{33} +(-2968.86 - 2968.86i) q^{35} +(964.122 + 964.122i) q^{37} +56138.0 q^{39} +94673.7i q^{41} +(-61457.6 + 61457.6i) q^{43} +(-2251.85 + 2251.85i) q^{45} -125325. i q^{47} -15010.0 q^{49} +(79716.7 + 79716.7i) q^{51} +(-92717.8 - 92717.8i) q^{53} -27772.7 q^{55} -107268. i q^{57} +(78971.2 - 78971.2i) q^{59} +(-14025.8 + 14025.8i) q^{61} -77850.7i q^{63} -47195.8 q^{65} +(169382. + 169382. i) q^{67} +(-134506. - 134506. i) q^{69} +239400. q^{71} +668710. i q^{73} +(-170337. + 170337. i) q^{75} +(480077. - 480077. i) q^{77} -572255. i q^{79} -59049.0 q^{81} +(360998. + 360998. i) q^{83} +(-67018.6 - 67018.6i) q^{85} +210043. q^{87} -101646. i q^{89} +(815821. - 815821. i) q^{91} +(-148826. + 148826. i) q^{93} +90181.5i q^{95} -1.29911e6 q^{97} +(-364134. - 364134. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	9.26689	+	9.26689i	0.0741351	+	0.0741351i	0.743202	−	0.669067i	$-0.233306\pi$
$5$	9.26689	+	9.26689i	0.0741351	+	0.0741351i	−0.669067	+	0.743202i	$0.733306\pi$
$6$		0			0
$7$	−320.373			−0.934033			−0.467016	−	0.884249i	$-0.654671\pi$
$7$	−320.373			−0.934033			−0.467016	+	0.884249i	$0.654671\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−1498.49	+	1498.49i	−1.12584	+	1.12584i	−0.134993	+	0.990847i	$0.543101\pi$
$11$	−1498.49	+	1498.49i	−1.12584	+	1.12584i	−0.990847	+	0.134993i	$0.956899\pi$
$12$		0			0
$13$	−2546.47	+	2546.47i	−1.15907	+	1.15907i	−0.174391	+	0.984676i	$0.555796\pi$
$13$	−2546.47	+	2546.47i	−1.15907	+	1.15907i	−0.984676	+	0.174391i	$0.944204\pi$
$14$		0			0
$15$		−	204.292i		−	0.0605311i
$16$		0			0
$17$	−7232.04			−1.47202			−0.736011	−	0.676970i	$-0.763293\pi$
$17$	−7232.04			−1.47202			−0.736011	+	0.676970i	$0.763293\pi$
$18$		0			0
$19$	4865.79	+	4865.79i	0.709402	+	0.709402i	0.966410	−	0.257007i	$-0.0827364\pi$
$19$	4865.79	+	4865.79i	0.709402	+	0.709402i	−0.257007	+	0.966410i	$0.582736\pi$
$20$		0			0
$21$	3531.38	+	3531.38i	0.381317	+	0.381317i
$22$		0			0
$23$	12202.6			1.00292			0.501462	−	0.865179i	$-0.332796\pi$
$23$	12202.6			1.00292			0.501462	+	0.865179i	$0.332796\pi$
$24$		0			0
$25$		−	15453.2i		−	0.989008i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$	−9527.74	+	9527.74i	−0.390657	+	0.390657i	−0.874922	−	0.484264i	$-0.839087\pi$
$29$	−9527.74	+	9527.74i	−0.390657	+	0.390657i	0.484264	+	0.874922i	$0.339087\pi$
$30$		0			0
$31$		−	13501.8i		−	0.453218i	−0.973986	−	0.226609i	$-0.927236\pi$
$31$		−	13501.8i		−	0.453218i	0.973986	−	0.226609i	$-0.0727639\pi$
$32$		0			0
$33$	33034.9			0.919244
$34$		0			0
$35$	−2968.86	−	2968.86i	−0.0692446	−	0.0692446i
$36$		0			0
$37$	964.122	+	964.122i	0.0190339	+	0.0190339i	0.716560	−	0.697526i	$-0.245716\pi$
$37$	964.122	+	964.122i	0.0190339	+	0.0190339i	−0.697526	+	0.716560i	$0.745716\pi$
$38$		0			0
$39$	56138.0			0.946375
$40$		0			0
$41$			94673.7i			1.37366i	0.726820	+	0.686828i	$0.240997\pi$
$41$			94673.7i			1.37366i	−0.726820	+	0.686828i	$0.759003\pi$
$42$		0			0
$43$	−61457.6	+	61457.6i	−0.772984	+	0.772984i	−0.978627	−	0.205643i	$-0.934071\pi$
$43$	−61457.6	+	61457.6i	−0.772984	+	0.772984i	0.205643	+	0.978627i	$0.434071\pi$
$44$		0			0
$45$	−2251.85	+	2251.85i	−0.0247117	+	0.0247117i
$46$		0			0
$47$		−	125325.i		−	1.20710i	−0.797325	−	0.603550i	$-0.793753\pi$
$47$		−	125325.i		−	1.20710i	0.797325	−	0.603550i	$-0.206247\pi$
$48$		0			0
$49$	−15010.0			−0.127583
$50$		0			0
$51$	79716.7	+	79716.7i	0.600950	+	0.600950i
$52$		0			0
$53$	−92717.8	−	92717.8i	−0.622781	−	0.622781i	0.323461	−	0.946242i	$-0.395154\pi$
$53$	−92717.8	−	92717.8i	−0.622781	−	0.622781i	−0.946242	+	0.323461i	$0.895154\pi$
$54$		0			0
$55$	−27772.7			−0.166929
$56$		0			0
$57$		−	107268.i		−	0.579225i
$58$		0			0
$59$	78971.2	−	78971.2i	0.384514	−	0.384514i	−0.488211	−	0.872726i	$-0.662350\pi$
$59$	78971.2	−	78971.2i	0.384514	−	0.384514i	0.872726	+	0.488211i	$0.162350\pi$
$60$		0			0
$61$	−14025.8	+	14025.8i	−0.0617927	+	0.0617927i	−0.737328	−	0.675535i	$-0.763913\pi$
$61$	−14025.8	+	14025.8i	−0.0617927	+	0.0617927i	0.675535	+	0.737328i	$0.263913\pi$
$62$		0			0
$63$		−	77850.7i		−	0.311344i
$64$		0			0
$65$	−47195.8			−0.171855
$66$		0			0
$67$	169382.	+	169382.i	0.563175	+	0.563175i	0.930208	−	0.367033i	$-0.119626\pi$
$67$	169382.	+	169382.i	0.563175	+	0.563175i	−0.367033	+	0.930208i	$0.619626\pi$
$68$		0			0
$69$	−134506.	−	134506.i	−0.409442	−	0.409442i
$70$		0			0
$71$	239400.			0.668882			0.334441	−	0.942417i	$-0.391452\pi$
$71$	239400.			0.668882			0.334441	+	0.942417i	$0.391452\pi$
$72$		0			0
$73$			668710.i			1.71897i	0.511159	+	0.859486i	$0.329216\pi$
$73$			668710.i			1.71897i	−0.511159	+	0.859486i	$0.670784\pi$
$74$		0			0
$75$	−170337.	+	170337.i	−0.403761	+	0.403761i
$76$		0			0
$77$	480077.	−	480077.i	1.05157	−	1.05157i
$78$		0			0
$79$		−	572255.i		−	1.16067i	−0.814378	−	0.580335i	$-0.802922\pi$
$79$		−	572255.i		−	1.16067i	0.814378	−	0.580335i	$-0.197078\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	360998.	+	360998.i	0.631350	+	0.631350i	0.948407	−	0.317057i	$-0.102695\pi$
$83$	360998.	+	360998.i	0.631350	+	0.631350i	−0.317057	+	0.948407i	$0.602695\pi$
$84$		0			0
$85$	−67018.6	−	67018.6i	−0.109129	−	0.109129i
$86$		0			0
$87$	210043.			0.318970
$88$		0			0
$89$		−	101646.i		−	0.144185i	−0.997398	−	0.0720925i	$-0.977032\pi$
$89$		−	101646.i		−	0.144185i	0.997398	−	0.0720925i	$-0.0229677\pi$
$90$		0			0
$91$	815821.	−	815821.i	1.08261	−	1.08261i
$92$		0			0
$93$	−148826.	+	148826.i	−0.185025	+	0.185025i
$94$		0			0
$95$			90181.5i			0.105183i
$96$		0			0
$97$	−1.29911e6			−1.42341			−0.711705	−	0.702479i	$-0.752076\pi$
$97$	−1.29911e6			−1.42341			−0.711705	+	0.702479i	$0.752076\pi$
$98$		0			0
$99$	−364134.	−	364134.i	−0.375280	−	0.375280i
$100$		0			0
$101$	−1.18300e6	−	1.18300e6i	−1.14821	−	1.14821i	−0.986905	−	0.161305i	$-0.948430\pi$
$101$	−1.18300e6	−	1.18300e6i	−1.14821	−	1.14821i	−0.161305	−	0.986905i	$-0.551570\pi$
$102$		0			0
$103$	−640196.			−0.585870			−0.292935	−	0.956132i	$-0.594632\pi$
$103$	−640196.			−0.585870			−0.292935	+	0.956132i	$0.594632\pi$
$104$		0			0
$105$			65449.8i			0.0565380i
$106$		0			0
$107$	−685436.	+	685436.i	−0.559520	+	0.559520i	−0.929171	−	0.369651i	$-0.879477\pi$
$107$	−685436.	+	685436.i	−0.559520	+	0.559520i	0.369651	+	0.929171i	$0.379477\pi$
$108$		0			0
$109$	1.30645e6	−	1.30645e6i	1.00882	−	1.00882i	0.00885608	−	0.999961i	$-0.497181\pi$
$109$	1.30645e6	−	1.30645e6i	1.00882	−	1.00882i	0.999961	−	0.00885608i	$-0.00281901\pi$
$110$		0			0
$111$		−	21254.5i		−	0.0155411i
$112$		0			0
$113$	−99366.9			−0.0688662			−0.0344331	−	0.999407i	$-0.510963\pi$
$113$	−99366.9			−0.0688662			−0.0344331	+	0.999407i	$0.510963\pi$
$114$		0			0
$115$	113080.	+	113080.i	0.0743520	+	0.0743520i
$116$		0			0
$117$	−618793.	−	618793.i	−0.386356	−	0.386356i
$118$		0			0
$119$	2.31695e6			1.37492
$120$		0			0
$121$		−	2.71940e6i		−	1.53503i
$122$		0			0
$123$	1.04356e6	−	1.04356e6i	0.560792	−	0.560792i
$124$		0			0
$125$	287999.	−	287999.i	0.147455	−	0.147455i
$126$		0			0
$127$		−	205844.i		−	0.100491i	−0.998737	−	0.0502455i	$-0.984000\pi$
$127$		−	205844.i		−	0.100491i	0.998737	−	0.0502455i	$-0.0160004\pi$
$128$		0			0
$129$	1.35486e6			0.631139
$130$		0			0
$131$	−926626.	−	926626.i	−0.412183	−	0.412183i	0.470315	−	0.882499i	$-0.344140\pi$
$131$	−926626.	−	926626.i	−0.412183	−	0.412183i	−0.882499	+	0.470315i	$0.844140\pi$
$132$		0			0
$133$	−1.55887e6	−	1.55887e6i	−0.662605	−	0.662605i
$134$		0			0
$135$	49643.1			0.0201770
$136$		0			0
$137$		−	2.54950e6i		−	0.991501i	−0.868465	−	0.495751i	$-0.834893\pi$
$137$		−	2.54950e6i		−	0.991501i	0.868465	−	0.495751i	$-0.165107\pi$
$138$		0			0
$139$	2.36008e6	−	2.36008e6i	0.878785	−	0.878785i	−0.114624	−	0.993409i	$-0.536566\pi$
$139$	2.36008e6	−	2.36008e6i	0.878785	−	0.878785i	0.993409	+	0.114624i	$0.0365663\pi$
$140$		0			0
$141$	−1.38142e6	+	1.38142e6i	−0.492796	+	0.492796i
$142$		0			0
$143$		−	7.63174e6i		−	2.60985i
$144$		0			0
$145$	−176585.			−0.0579229
$146$		0			0
$147$	165451.	+	165451.i	0.0520855	+	0.0520855i
$148$		0			0
$149$	322325.	+	322325.i	0.0974397	+	0.0974397i	0.754146	−	0.656707i	$-0.228051\pi$
$149$	322325.	+	322325.i	0.0974397	+	0.0974397i	−0.656707	+	0.754146i	$0.728051\pi$
$150$		0			0
$151$	461709.			0.134103			0.0670514	−	0.997750i	$-0.478641\pi$
$151$	461709.			0.134103			0.0670514	+	0.997750i	$0.478641\pi$
$152$		0			0
$153$		−	1.75739e6i		−	0.490674i
$154$		0			0
$155$	125120.	−	125120.i	0.0335993	−	0.0335993i
$156$		0			0
$157$	−689923.	+	689923.i	−0.178280	+	0.178280i	−0.790605	−	0.612326i	$-0.790234\pi$
$157$	−689923.	+	689923.i	−0.178280	+	0.178280i	0.612326	+	0.790605i	$0.290234\pi$
$158$		0			0
$159$			2.04400e6i			0.508499i
$160$		0			0
$161$	−3.90938e6			−0.936765
$162$		0			0
$163$	2.75709e6	+	2.75709e6i	0.636633	+	0.636633i	0.949723	−	0.313091i	$-0.101364\pi$
$163$	2.75709e6	+	2.75709e6i	0.636633	+	0.636633i	−0.313091	+	0.949723i	$0.601364\pi$
$164$		0			0
$165$	306131.	+	306131.i	0.0681483	+	0.0681483i
$166$		0			0
$167$	5.64426e6			1.21188			0.605938	−	0.795512i	$-0.292798\pi$
$167$	5.64426e6			1.21188			0.605938	+	0.795512i	$0.292798\pi$
$168$		0			0
$169$		−	8.14223e6i		−	1.68688i
$170$		0			0
$171$	−1.18239e6	+	1.18239e6i	−0.236467	+	0.236467i
$172$		0			0
$173$	−4.11406e6	+	4.11406e6i	−0.794571	+	0.794571i	−0.982234	−	0.187663i	$-0.939909\pi$
$173$	−4.11406e6	+	4.11406e6i	−0.794571	+	0.794571i	0.187663	+	0.982234i	$0.439909\pi$
$174$		0			0
$175$			4.95081e6i			0.923766i
$176$		0			0
$177$	−1.74095e6			−0.313955
$178$		0			0
$179$	−570577.	−	570577.i	−0.0994844	−	0.0994844i	0.655613	−	0.755097i	$-0.272410\pi$
$179$	−570577.	−	570577.i	−0.0994844	−	0.0994844i	−0.755097	+	0.655613i	$0.772410\pi$
$180$		0			0
$181$	−266807.	−	266807.i	−0.0449947	−	0.0449947i	0.684251	−	0.729246i	$-0.260129\pi$
$181$	−266807.	−	266807.i	−0.0449947	−	0.0449947i	−0.729246	+	0.684251i	$0.760129\pi$
$182$		0			0
$183$	309204.			0.0504535
$184$		0			0
$185$			17868.8i			0.00282216i
$186$		0			0
$187$	1.08372e7	−	1.08372e7i	1.65726	−	1.65726i
$188$		0			0
$189$	−858125.	+	858125.i	−0.127106	+	0.127106i
$190$		0			0
$191$			1.04021e7i			1.49287i	0.665458	+	0.746436i	$0.268236\pi$
$191$			1.04021e7i			1.49287i	−0.665458	+	0.746436i	$0.731764\pi$
$192$		0			0
$193$	2.18186e6			0.303498			0.151749	−	0.988419i	$-0.451509\pi$
$193$	2.18186e6			0.303498			0.151749	+	0.988419i	$0.451509\pi$
$194$		0			0
$195$	520225.	+	520225.i	0.0701596	+	0.0701596i
$196$		0			0
$197$	−5.20197e6	−	5.20197e6i	−0.680407	−	0.680407i	0.279685	−	0.960092i	$-0.409770\pi$
$197$	−5.20197e6	−	5.20197e6i	−0.680407	−	0.680407i	−0.960092	+	0.279685i	$0.909770\pi$
$198$		0			0
$199$	1.41709e7			1.79821			0.899103	−	0.437737i	$-0.144220\pi$
$199$	1.41709e7			1.79821			0.899103	+	0.437737i	$0.144220\pi$
$200$		0			0
$201$		−	3.73410e6i		−	0.459830i
$202$		0			0
$203$	3.05243e6	−	3.05243e6i	0.364887	−	0.364887i
$204$		0			0
$205$	−877331.	+	877331.i	−0.101836	+	0.101836i
$206$		0			0
$207$			2.96523e6i			0.334308i
$208$		0			0
$209$	−1.45827e7			−1.59735
$210$		0			0
$211$	−8.87390e6	−	8.87390e6i	−0.944642	−	0.944642i	0.0539044	−	0.998546i	$-0.482833\pi$
$211$	−8.87390e6	−	8.87390e6i	−0.944642	−	0.944642i	−0.998546	+	0.0539044i	$0.982833\pi$
$212$		0			0
$213$	−2.63884e6	−	2.63884e6i	−0.273070	−	0.273070i
$214$		0			0
$215$	−1.13904e6			−0.114611
$216$		0			0
$217$			4.32562e6i			0.423320i
$218$		0			0
$219$	7.37099e6	−	7.37099e6i	0.701768	−	0.701768i
$220$		0			0
$221$	1.84162e7	−	1.84162e7i	1.70617	−	1.70617i
$222$		0			0
$223$		−	1.84583e7i		−	1.66447i	−0.554422	−	0.832236i	$-0.687061\pi$
$223$		−	1.84583e7i		−	1.66447i	0.554422	−	0.832236i	$-0.312939\pi$
$224$		0			0
$225$	3.75514e6			0.329669
$226$		0			0
$227$	2.33494e6	+	2.33494e6i	0.199617	+	0.199617i	0.799836	−	0.600219i	$-0.204920\pi$
$227$	2.33494e6	+	2.33494e6i	0.199617	+	0.199617i	−0.600219	+	0.799836i	$0.704920\pi$
$228$		0			0
$229$	1.10078e7	+	1.10078e7i	0.916627	+	0.916627i	0.996782	−	0.0801554i	$-0.0255416\pi$
$229$	1.10078e7	+	1.10078e7i	0.916627	+	0.916627i	−0.0801554	+	0.996782i	$0.525542\pi$
$230$		0			0
$231$	−1.05835e7			−0.858604
$232$		0			0
$233$			8.59203e6i			0.679247i	0.940561	+	0.339624i	$0.110300\pi$
$233$			8.59203e6i			0.679247i	−0.940561	+	0.339624i	$0.889700\pi$
$234$		0			0
$235$	1.16137e6	−	1.16137e6i	0.0894885	−	0.0894885i
$236$		0			0
$237$	−6.30780e6	+	6.30780e6i	−0.473841	+	0.473841i
$238$		0			0
$239$		−	1.57460e6i		−	0.115339i	−0.998336	−	0.0576696i	$-0.981633\pi$
$239$		−	1.57460e6i		−	0.115339i	0.998336	−	0.0576696i	$-0.0183670\pi$
$240$		0			0
$241$	1.53998e7			1.10018			0.550089	−	0.835106i	$-0.314594\pi$
$241$	1.53998e7			1.10018			0.550089	+	0.835106i	$0.314594\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−139096.	−	139096.i	−0.00945838	−	0.00945838i
$246$		0			0
$247$	−2.47812e7			−1.64449
$248$		0			0
$249$		−	7.95834e6i		−	0.515495i
$250$		0			0
$251$	−1.04108e7	+	1.04108e7i	−0.658356	+	0.658356i	−0.954991	−	0.296635i	$-0.904136\pi$
$251$	−1.04108e7	+	1.04108e7i	−0.658356	+	0.658356i	0.296635	+	0.954991i	$0.404136\pi$
$252$		0			0
$253$	−1.82855e7	+	1.82855e7i	−1.12913	+	1.12913i
$254$		0			0
$255$			1.47745e6i			0.0891031i
$256$		0			0
$257$	−6.82403e6			−0.402014			−0.201007	−	0.979590i	$-0.564421\pi$
$257$	−6.82403e6			−0.402014			−0.201007	+	0.979590i	$0.564421\pi$
$258$		0			0
$259$	−308879.	−	308879.i	−0.0177782	−	0.0177782i
$260$		0			0
$261$	−2.31524e6	−	2.31524e6i	−0.130219	−	0.130219i
$262$		0			0
$263$	2.62642e7			1.44377			0.721883	−	0.692015i	$-0.243277\pi$
$263$	2.62642e7			1.44377			0.721883	+	0.692015i	$0.243277\pi$
$264$		0			0
$265$		−	1.71841e6i		−	0.0923399i
$266$		0			0
$267$	−1.12041e6	+	1.12041e6i	−0.0588633	+	0.0588633i
$268$		0			0
$269$	1.87243e7	−	1.87243e7i	0.961941	−	0.961941i	−0.0373605	−	0.999302i	$-0.511895\pi$
$269$	1.87243e7	−	1.87243e7i	0.961941	−	0.961941i	0.999302	+	0.0373605i	$0.0118950\pi$
$270$		0			0
$271$			6.11650e6i			0.307323i	0.988124	+	0.153661i	$0.0491065\pi$
$271$			6.11650e6i			0.307323i	−0.988124	+	0.153661i	$0.950893\pi$
$272$		0			0
$273$	−1.79851e7			−0.883945
$274$		0			0
$275$	2.31566e7	+	2.31566e7i	1.11346	+	1.11346i
$276$		0			0
$277$	−2.42422e7	−	2.42422e7i	−1.14060	−	1.14060i	−0.988341	−	0.152258i	$-0.951345\pi$
$277$	−2.42422e7	−	2.42422e7i	−1.14060	−	1.14060i	−0.152258	−	0.988341i	$-0.548655\pi$
$278$		0			0
$279$	3.28094e6			0.151073
$280$		0			0
$281$			1.13379e7i			0.510993i	0.966810	+	0.255496i	$0.0822389\pi$
$281$			1.13379e7i			0.510993i	−0.966810	+	0.255496i	$0.917761\pi$
$282$		0			0
$283$	−2.38467e7	+	2.38467e7i	−1.05213	+	1.05213i	−0.0535657	+	0.998564i	$0.517059\pi$
$283$	−2.38467e7	+	2.38467e7i	−1.05213	+	1.05213i	−0.998564	+	0.0535657i	$0.982941\pi$
$284$		0			0
$285$	994044.	−	994044.i	0.0429409	−	0.0429409i
$286$		0			0
$287$		−	3.03309e7i		−	1.28304i
$288$		0			0
$289$	2.81649e7			1.16685
$290$		0			0
$291$	1.43197e7	+	1.43197e7i	0.581104	+	0.581104i
$292$		0			0
$293$	−445531.	−	445531.i	−0.0177123	−	0.0177123i	0.698195	−	0.715907i	$-0.253987\pi$
$293$	−445531.	−	445531.i	−0.0177123	−	0.0177123i	−0.715907	+	0.698195i	$0.753987\pi$
$294$		0			0
$295$	1.46363e6			0.0570120
$296$		0			0
$297$			8.02748e6i			0.306415i
$298$		0			0
$299$	−3.10735e7	+	3.10735e7i	−1.16246	+	1.16246i
$300$		0			0
$301$	1.96894e7	−	1.96894e7i	0.721992	−	0.721992i
$302$		0			0
$303$			2.60798e7i			0.937509i
$304$		0			0
$305$	−259950.			−0.00916201
$306$		0			0
$307$	−2.00977e7	−	2.00977e7i	−0.694593	−	0.694593i	0.268646	−	0.963239i	$-0.413424\pi$
$307$	−2.00977e7	−	2.00977e7i	−0.694593	−	0.694593i	−0.963239	+	0.268646i	$0.913424\pi$
$308$		0			0
$309$	7.05669e6	+	7.05669e6i	0.239180	+	0.239180i
$310$		0			0
$311$	−4.83931e7			−1.60880			−0.804401	−	0.594087i	$-0.797514\pi$
$311$	−4.83931e7			−1.60880			−0.804401	+	0.594087i	$0.797514\pi$
$312$		0			0
$313$			2.89787e7i			0.945029i	0.881323	+	0.472515i	$0.156654\pi$
$313$			2.89787e7i			0.945029i	−0.881323	+	0.472515i	$0.843346\pi$
$314$		0			0
$315$	721434.	−	721434.i	0.0230815	−	0.0230815i
$316$		0			0
$317$	−3.32948e7	+	3.32948e7i	−1.04520	+	1.04520i	−0.0462701	+	0.998929i	$0.514733\pi$
$317$	−3.32948e7	+	3.32948e7i	−1.04520	+	1.04520i	−0.998929	+	0.0462701i	$0.985267\pi$
$318$		0			0
$319$		−	2.85545e7i		−	0.879635i
$320$		0			0
$321$	1.51107e7			0.456846
$322$		0			0
$323$	−3.51896e7	−	3.51896e7i	−1.04426	−	1.04426i
$324$		0			0
$325$	3.93513e7	+	3.93513e7i	1.14633	+	1.14633i
$326$		0			0
$327$	−2.88012e7			−0.823696
$328$		0			0
$329$			4.01507e7i			1.12747i
$330$		0			0
$331$	9.41834e6	−	9.41834e6i	0.259711	−	0.259711i	−0.565225	−	0.824937i	$-0.691211\pi$
$331$	9.41834e6	−	9.41834e6i	0.259711	−	0.259711i	0.824937	+	0.565225i	$0.191211\pi$
$332$		0			0
$333$	−234282.	+	234282.i	−0.00634462	+	0.00634462i
$334$		0			0
$335$			3.13929e6i			0.0835020i
$336$		0			0
$337$	6.32702e7			1.65314			0.826570	−	0.562834i	$-0.190289\pi$
$337$	6.32702e7			1.65314			0.826570	+	0.562834i	$0.190289\pi$
$338$		0			0
$339$	1.09529e6	+	1.09529e6i	0.0281145	+	0.0281145i
$340$		0			0
$341$	2.02324e7	+	2.02324e7i	0.510250	+	0.510250i
$342$		0			0
$343$	4.25004e7			1.05320
$344$		0			0
$345$		−	2.49290e6i		−	0.0607081i
$346$		0			0
$347$	−4.92780e7	+	4.92780e7i	−1.17941	+	1.17941i	−0.199516	+	0.979895i	$0.563937\pi$
$347$	−4.92780e7	+	4.92780e7i	−1.17941	+	1.17941i	−0.979895	+	0.199516i	$0.936063\pi$
$348$		0			0
$349$	2.27583e7	−	2.27583e7i	0.535382	−	0.535382i	−0.386787	−	0.922169i	$-0.626415\pi$
$349$	2.27583e7	−	2.27583e7i	0.535382	−	0.535382i	0.922169	+	0.386787i	$0.126415\pi$
$350$		0			0
$351$			1.36415e7i			0.315458i
$352$		0			0
$353$	−3.62510e7			−0.824130			−0.412065	−	0.911154i	$-0.635192\pi$
$353$	−3.62510e7			−0.824130			−0.412065	+	0.911154i	$0.635192\pi$
$354$		0			0
$355$	2.21850e6	+	2.21850e6i	0.0495877	+	0.0495877i
$356$		0			0
$357$	−2.55391e7	−	2.55391e7i	−0.561307	−	0.561307i
$358$		0			0
$359$	−2.29503e7			−0.496026			−0.248013	−	0.968757i	$-0.579778\pi$
$359$	−2.29503e7			−0.496026			−0.248013	+	0.968757i	$0.579778\pi$
$360$		0			0
$361$			305966.i			0.00650357i
$362$		0			0
$363$	−2.99751e7	+	2.99751e7i	−0.626673	+	0.626673i
$364$		0			0
$365$	−6.19686e6	+	6.19686e6i	−0.127436	+	0.127436i
$366$		0			0
$367$		−	1.41526e7i		−	0.286311i	−0.989700	−	0.143155i	$-0.954275\pi$
$367$		−	1.41526e7i		−	0.286311i	0.989700	−	0.143155i	$-0.0457249\pi$
$368$		0			0
$369$	−2.30057e7			−0.457885
$370$		0			0
$371$	2.97043e7	+	2.97043e7i	0.581698	+	0.581698i
$372$		0			0
$373$	7.14687e7	+	7.14687e7i	1.37718	+	1.37718i	0.849356	+	0.527820i	$0.176990\pi$
$373$	7.14687e7	+	7.14687e7i	1.37718	+	1.37718i	0.527820	+	0.849356i	$0.323010\pi$
$374$		0			0
$375$	−6.34905e6			−0.120397
$376$		0			0
$377$		−	4.85242e7i		−	0.905596i
$378$		0			0
$379$	6.85276e7	−	6.85276e7i	1.25878	−	1.25878i	0.307097	−	0.951678i	$-0.400642\pi$
$379$	6.85276e7	−	6.85276e7i	1.25878	−	1.25878i	0.951678	−	0.307097i	$-0.0993575\pi$
$380$		0			0
$381$	−2.26896e6	+	2.26896e6i	−0.0410253	+	0.0410253i
$382$		0			0
$383$			8.56510e7i			1.52453i	0.647264	+	0.762266i	$0.275913\pi$
$383$			8.56510e7i			1.52453i	−0.647264	+	0.762266i	$0.724087\pi$
$384$		0			0
$385$	8.89764e6			0.155917
$386$		0			0
$387$	−1.49342e7	−	1.49342e7i	−0.257661	−	0.257661i
$388$		0			0
$389$	−3.62694e7	−	3.62694e7i	−0.616157	−	0.616157i	0.328387	−	0.944543i	$-0.393495\pi$
$389$	−3.62694e7	−	3.62694e7i	−0.616157	−	0.616157i	−0.944543	+	0.328387i	$0.893495\pi$
$390$		0			0
$391$	−8.82496e7			−1.47633
$392$		0			0
$393$			2.04278e7i			0.336546i
$394$		0			0
$395$	5.30303e6	−	5.30303e6i	0.0860464	−	0.0860464i
$396$		0			0
$397$	1.44442e7	−	1.44442e7i	0.230846	−	0.230846i	−0.582200	−	0.813046i	$-0.697808\pi$
$397$	1.44442e7	−	1.44442e7i	0.230846	−	0.230846i	0.813046	+	0.582200i	$0.197808\pi$
$398$		0			0
$399$			3.43659e7i			0.541015i
$400$		0			0
$401$	2.71458e7			0.420988			0.210494	−	0.977595i	$-0.432493\pi$
$401$	2.71458e7			0.420988			0.210494	+	0.977595i	$0.432493\pi$
$402$		0			0
$403$	3.43820e7	+	3.43820e7i	0.525310	+	0.525310i
$404$		0			0
$405$	−547201.	−	547201.i	−0.00823724	−	0.00823724i
$406$		0			0
$407$	−2.88946e6			−0.0428581
$408$		0			0
$409$			9.99364e7i			1.46068i	0.683086	+	0.730338i	$0.260637\pi$
$409$			9.99364e7i			1.46068i	−0.683086	+	0.730338i	$0.739363\pi$
$410$		0			0
$411$	−2.81024e7	+	2.81024e7i	−0.404779	+	0.404779i
$412$		0			0
$413$	−2.53003e7	+	2.53003e7i	−0.359149	+	0.359149i
$414$		0			0
$415$			6.69065e6i			0.0936104i
$416$		0			0
$417$	−5.20290e7			−0.717525
$418$		0			0
$419$	−1.68960e7	−	1.68960e7i	−0.229690	−	0.229690i	0.582873	−	0.812563i	$-0.301928\pi$
$419$	−1.68960e7	−	1.68960e7i	−0.229690	−	0.229690i	−0.812563	+	0.582873i	$0.801928\pi$
$420$		0			0
$421$	6.18271e7	+	6.18271e7i	0.828576	+	0.828576i	0.987320	−	0.158744i	$-0.0507443\pi$
$421$	6.18271e7	+	6.18271e7i	0.828576	+	0.828576i	−0.158744	+	0.987320i	$0.550744\pi$
$422$		0			0
$423$	3.04539e7			0.402366
$424$		0			0
$425$			1.11759e8i			1.45584i
$426$		0			0
$427$	4.49348e6	−	4.49348e6i	0.0577164	−	0.0577164i
$428$		0			0
$429$	−8.41224e7	+	8.41224e7i	−1.06547	+	1.06547i
$430$		0			0
$431$			1.26217e8i			1.57647i	0.615377	+	0.788233i	$0.289004\pi$
$431$			1.26217e8i			1.57647i	−0.615377	+	0.788233i	$0.710996\pi$
$432$		0			0
$433$	1.94684e7			0.239809			0.119905	−	0.992785i	$-0.461741\pi$
$433$	1.94684e7			0.239809			0.119905	+	0.992785i	$0.461741\pi$
$434$		0			0
$435$	1.94644e6	+	1.94644e6i	0.0236469	+	0.0236469i
$436$		0			0
$437$	5.93752e7	+	5.93752e7i	0.711477	+	0.711477i
$438$		0			0
$439$	1.02252e7			0.120858			0.0604292	−	0.998172i	$-0.480753\pi$
$439$	1.02252e7			0.120858			0.0604292	+	0.998172i	$0.480753\pi$
$440$		0			0
$441$		−	3.64743e6i		−	0.0425277i
$442$		0			0
$443$	5.79230e7	−	5.79230e7i	0.666255	−	0.666255i	−0.290592	−	0.956847i	$-0.593852\pi$
$443$	5.79230e7	−	5.79230e7i	0.666255	−	0.666255i	0.956847	+	0.290592i	$0.0938524\pi$
$444$		0			0
$445$	941942.	−	941942.i	0.0106892	−	0.0106892i
$446$		0			0
$447$		−	7.10580e6i		−	0.0795592i
$448$		0			0
$449$	6.91954e7			0.764431			0.382215	−	0.924073i	$-0.375161\pi$
$449$	6.91954e7			0.764431			0.382215	+	0.924073i	$0.375161\pi$
$450$		0			0
$451$	−1.41868e8	−	1.41868e8i	−1.54652	−	1.54652i
$452$		0			0
$453$	−5.08928e6	−	5.08928e6i	−0.0547472	−	0.0547472i
$454$		0			0
$455$	1.51203e7			0.160518
$456$		0			0
$457$		−	1.14975e8i		−	1.20463i	−0.798258	−	0.602316i	$-0.794245\pi$
$457$		−	1.14975e8i		−	1.20463i	0.798258	−	0.602316i	$-0.205755\pi$
$458$		0			0
$459$	−1.93712e7	+	1.93712e7i	−0.200317	+	0.200317i
$460$		0			0
$461$	−1.10716e7	+	1.10716e7i	−0.113008	+	0.113008i	−0.761350	−	0.648342i	$-0.775463\pi$
$461$	−1.10716e7	+	1.10716e7i	−0.113008	+	0.113008i	0.648342	+	0.761350i	$0.275463\pi$
$462$		0			0
$463$		−	4.60447e7i		−	0.463913i	−0.972726	−	0.231956i	$-0.925487\pi$
$463$		−	4.60447e7i		−	0.463913i	0.972726	−	0.231956i	$-0.0745127\pi$
$464$		0			0
$465$	−2.75832e6			−0.0274337
$466$		0			0
$467$	1.78764e7	+	1.78764e7i	0.175521	+	0.175521i	0.789400	−	0.613879i	$-0.210392\pi$
$467$	1.78764e7	+	1.78764e7i	0.175521	+	0.175521i	−0.613879	+	0.789400i	$0.710392\pi$
$468$		0			0
$469$	−5.42655e7	−	5.42655e7i	−0.526023	−	0.526023i
$470$		0			0
$471$	1.52096e7			0.145565
$472$		0			0
$473$		−	1.84188e8i		−	1.74051i
$474$		0			0
$475$	7.51923e7	−	7.51923e7i	0.701605	−	0.701605i
$476$		0			0
$477$	2.25304e7	−	2.25304e7i	0.207594	−	0.207594i
$478$		0			0
$479$			2.69923e7i			0.245603i	0.992431	+	0.122802i	$0.0391879\pi$
$479$			2.69923e7i			0.245603i	−0.992431	+	0.122802i	$0.960812\pi$
$480$		0			0
$481$	−4.91022e6			−0.0441231
$482$		0			0
$483$	4.30920e7	+	4.30920e7i	0.382433	+	0.382433i
$484$		0			0
$485$	−1.20387e7	−	1.20387e7i	−0.105525	−	0.105525i
$486$		0			0
$487$	4.16825e7			0.360883			0.180442	−	0.983586i	$-0.442247\pi$
$487$	4.16825e7			0.360883			0.180442	+	0.983586i	$0.442247\pi$
$488$		0			0
$489$		−	6.07813e7i		−	0.519808i
$490$		0			0
$491$	−7.03027e6	+	7.03027e6i	−0.0593920	+	0.0593920i	−0.736179	−	0.676787i	$-0.763372\pi$
$491$	−7.03027e6	+	7.03027e6i	−0.0593920	+	0.0593920i	0.676787	+	0.736179i	$0.263372\pi$
$492$		0			0
$493$	6.89050e7	−	6.89050e7i	0.575056	−	0.575056i
$494$		0			0
$495$		−	6.74877e6i		−	0.0556428i
$496$		0			0
$497$	−7.66975e7			−0.624758
$498$		0			0
$499$	3.49256e7	+	3.49256e7i	0.281088	+	0.281088i	0.833543	−	0.552455i	$-0.186309\pi$
$499$	3.49256e7	+	3.49256e7i	0.281088	+	0.281088i	−0.552455	+	0.833543i	$0.686309\pi$
$500$		0			0
$501$	−6.22151e7	−	6.22151e7i	−0.494746	−	0.494746i
$502$		0			0
$503$	−2.71399e7			−0.213257			−0.106629	−	0.994299i	$-0.534006\pi$
$503$	−2.71399e7			−0.213257			−0.106629	+	0.994299i	$0.534006\pi$
$504$		0			0
$505$		−	2.19255e7i		−	0.170245i
$506$		0			0
$507$	−8.97493e7	+	8.97493e7i	−0.688664	+	0.688664i
$508$		0			0
$509$	−1.51625e8	+	1.51625e8i	−1.14979	+	1.14979i	−0.163196	+	0.986594i	$0.552180\pi$
$509$	−1.51625e8	+	1.51625e8i	−1.14979	+	1.14979i	−0.986594	+	0.163196i	$0.947820\pi$
$510$		0			0
$511$		−	2.14237e8i		−	1.60558i
$512$		0			0
$513$	2.60662e7			0.193075
$514$		0			0
$515$	−5.93262e6	−	5.93262e6i	−0.0434335	−	0.0434335i
$516$		0			0
$517$	1.87798e8	+	1.87798e8i	1.35900	+	1.35900i
$518$		0			0
$519$	9.06962e7			0.648764
$520$		0			0
$521$		−	2.02048e8i		−	1.42870i	−0.699788	−	0.714351i	$-0.746722\pi$
$521$		−	2.02048e8i		−	1.42870i	0.699788	−	0.714351i	$-0.253278\pi$
$522$		0			0
$523$	−7.38808e7	+	7.38808e7i	−0.516448	+	0.516448i	−0.916495	−	0.400047i	$-0.868994\pi$
$523$	−7.38808e7	+	7.38808e7i	−0.516448	+	0.516448i	0.400047	+	0.916495i	$0.368994\pi$
$524$		0			0
$525$	5.45713e7	−	5.45713e7i	0.377126	−	0.377126i
$526$		0			0
$527$			9.76456e7i			0.667146i
$528$		0			0
$529$	867245.			0.00585834
$530$		0			0
$531$	1.91900e7	+	1.91900e7i	0.128171	+	0.128171i
$532$		0			0
$533$	−2.41084e8	−	2.41084e8i	−1.59216	−	1.59216i
$534$		0			0
$535$	−1.27037e7			−0.0829602
$536$		0			0
$537$			1.25786e7i			0.0812287i
$538$		0			0
$539$	2.24924e7	−	2.24924e7i	0.143638	−	0.143638i
$540$		0			0
$541$	1.36253e8	−	1.36253e8i	0.860506	−	0.860506i	−0.130891	−	0.991397i	$-0.541784\pi$
$541$	1.36253e8	−	1.36253e8i	0.860506	−	0.860506i	0.991397	+	0.130891i	$0.0417837\pi$
$542$		0			0
$543$			5.88187e6i			0.0367381i
$544$		0			0
$545$	2.42134e7			0.149578
$546$		0			0
$547$	−5.77218e7	−	5.77218e7i	−0.352678	−	0.352678i	0.508427	−	0.861105i	$-0.330227\pi$
$547$	−5.77218e7	−	5.77218e7i	−0.352678	−	0.352678i	−0.861105	+	0.508427i	$0.830227\pi$
$548$		0			0
$549$	−3.40826e6	−	3.40826e6i	−0.0205976	−	0.0205976i
$550$		0			0
$551$	−9.27200e7			−0.554266
$552$		0			0
$553$			1.83335e8i			1.08410i
$554$		0			0
$555$	196963.	−	196963.i	0.00115214	−	0.00115214i
$556$		0			0
$557$	−7.21755e7	+	7.21755e7i	−0.417661	+	0.417661i	−0.884397	−	0.466736i	$-0.845430\pi$
$557$	−7.21755e7	+	7.21755e7i	−0.417661	+	0.417661i	0.466736	+	0.884397i	$0.345430\pi$
$558$		0			0
$559$		−	3.13000e8i		−	1.79188i
$560$		0			0
$561$	−2.38910e8			−1.35315
$562$		0			0
$563$	−2.63528e6	−	2.63528e6i	−0.0147673	−	0.0147673i	0.699685	−	0.714452i	$-0.253324\pi$
$563$	−2.63528e6	−	2.63528e6i	−0.0147673	−	0.0147673i	−0.714452	+	0.699685i	$0.753324\pi$
$564$		0			0
$565$	−920822.	−	920822.i	−0.00510541	−	0.00510541i
$566$		0			0
$567$	1.89177e7			0.103781
$568$		0			0
$569$		−	1.21428e8i		−	0.659147i	−0.944130	−	0.329574i	$-0.893095\pi$
$569$		−	1.21428e8i		−	0.659147i	0.944130	−	0.329574i	$-0.106905\pi$
$570$		0			0
$571$	1.54218e8	−	1.54218e8i	0.828372	−	0.828372i	−0.158919	−	0.987292i	$-0.550801\pi$
$571$	1.54218e8	−	1.54218e8i	0.828372	−	0.828372i	0.987292	+	0.158919i	$0.0508009\pi$
$572$		0			0
$573$	1.14660e8	−	1.14660e8i	0.609462	−	0.609462i
$574$		0			0
$575$		−	1.88570e8i		−	0.991901i
$576$		0			0
$577$	3.35652e8			1.74728			0.873638	−	0.486576i	$-0.161754\pi$
$577$	3.35652e8			1.74728			0.873638	+	0.486576i	$0.161754\pi$
$578$		0			0
$579$	−2.40500e7	−	2.40500e7i	−0.123903	−	0.123903i
$580$		0			0
$581$	−1.15654e8	−	1.15654e8i	−0.589701	−	0.589701i
$582$		0			0
$583$	2.77874e8			1.40230
$584$		0			0
$585$		−	1.14686e7i		−	0.0572851i
$586$		0			0
$587$	1.46642e8	−	1.46642e8i	0.725012	−	0.725012i	−0.244610	−	0.969622i	$-0.578660\pi$
$587$	1.46642e8	−	1.46642e8i	0.725012	−	0.725012i	0.969622	+	0.244610i	$0.0786599\pi$
$588$		0			0
$589$	6.56970e7	−	6.56970e7i	0.321514	−	0.321514i
$590$		0			0
$591$			1.14679e8i			0.555550i
$592$		0			0
$593$	−2.09211e8			−1.00328			−0.501639	−	0.865077i	$-0.667269\pi$
$593$	−2.09211e8			−1.00328			−0.501639	+	0.865077i	$0.667269\pi$
$594$		0			0
$595$	2.14710e7	+	2.14710e7i	0.101930	+	0.101930i
$596$		0			0
$597$	−1.56202e8	−	1.56202e8i	−0.734114	−	0.734114i
$598$		0			0
$599$	3.54843e7			0.165103			0.0825516	−	0.996587i	$-0.473693\pi$
$599$	3.54843e7			0.165103			0.0825516	+	0.996587i	$0.473693\pi$
$600$		0			0
$601$		−	1.17448e7i		−	0.0541033i	−0.999634	−	0.0270516i	$-0.991388\pi$
$601$		−	1.17448e7i		−	0.0541033i	0.999634	−	0.0270516i	$-0.00861186\pi$
$602$		0			0
$603$	−4.11598e7	+	4.11598e7i	−0.187725	+	0.187725i
$604$		0			0
$605$	2.52004e7	−	2.52004e7i	0.113800	−	0.113800i
$606$		0			0
$607$		−	6.66131e7i		−	0.297847i	−0.988849	−	0.148924i	$-0.952419\pi$
$607$		−	6.66131e7i		−	0.297847i	0.988849	−	0.148924i	$-0.0475809\pi$
$608$		0			0
$609$	−6.72921e7			−0.297929
$610$		0			0
$611$	3.19136e8	+	3.19136e8i	1.39911	+	1.39911i
$612$		0			0
$613$	−2.90977e8	−	2.90977e8i	−1.26321	−	1.26321i	−0.949527	−	0.313687i	$-0.898436\pi$
$613$	−2.90977e8	−	2.90977e8i	−1.26321	−	1.26321i	−0.313687	−	0.949527i	$-0.601564\pi$
$614$		0			0
$615$	1.93411e7			0.0831489
$616$		0			0
$617$			2.26992e8i			0.966398i	0.875511	+	0.483199i	$0.160525\pi$
$617$			2.26992e8i			0.966398i	−0.875511	+	0.483199i	$0.839475\pi$
$618$		0			0
$619$	1.74883e8	−	1.74883e8i	0.737351	−	0.737351i	−0.234713	−	0.972065i	$-0.575415\pi$
$619$	1.74883e8	−	1.74883e8i	0.737351	−	0.737351i	0.972065	+	0.234713i	$0.0754151\pi$
$620$		0			0
$621$	3.26848e7	−	3.26848e7i	0.136481	−	0.136481i
$622$		0			0
$623$			3.25646e7i			0.134673i
$624$		0			0
$625$	−2.36119e8			−0.967145
$626$		0			0
$627$	1.60741e8	+	1.60741e8i	0.652114	+	0.652114i
$628$		0			0
$629$	−6.97257e6	−	6.97257e6i	−0.0280183	−	0.0280183i
$630$		0			0
$631$	1.45037e8			0.577284			0.288642	−	0.957437i	$-0.406796\pi$
$631$	1.45037e8			0.577284			0.288642	+	0.957437i	$0.406796\pi$
$632$		0			0
$633$			1.95629e8i			0.771297i
$634$		0			0
$635$	1.90753e6	−	1.90753e6i	0.00744991	−	0.00744991i
$636$		0			0
$637$	3.82226e7	−	3.82226e7i	0.147877	−	0.147877i
$638$		0			0
$639$			5.81743e7i			0.222961i
$640$		0			0
$641$	−1.67425e8			−0.635693			−0.317847	−	0.948142i	$-0.602960\pi$
$641$	−1.67425e8			−0.635693			−0.317847	+	0.948142i	$0.602960\pi$
$642$		0			0
$643$	1.26691e8	+	1.26691e8i	0.476553	+	0.476553i	0.904027	−	0.427474i	$-0.140597\pi$
$643$	1.26691e8	+	1.26691e8i	0.476553	+	0.476553i	−0.427474	+	0.904027i	$0.640597\pi$
$644$		0			0
$645$	1.25553e7	+	1.25553e7i	0.0467895	+	0.0467895i
$646$		0			0
$647$	7.73707e7			0.285669			0.142835	−	0.989747i	$-0.454378\pi$
$647$	7.73707e7			0.285669			0.142835	+	0.989747i	$0.454378\pi$
$648$		0			0
$649$			2.36675e8i			0.865803i
$650$		0			0
$651$	4.76800e7	−	4.76800e7i	0.172820	−	0.172820i
$652$		0			0
$653$	2.47347e8	−	2.47347e8i	0.888317	−	0.888317i	−0.106044	−	0.994361i	$-0.533819\pi$
$653$	2.47347e8	−	2.47347e8i	0.888317	−	0.888317i	0.994361	+	0.106044i	$0.0338186\pi$
$654$		0			0
$655$		−	1.71739e7i		−	0.0611145i
$656$		0			0
$657$	−1.62496e8			−0.572991
$658$		0			0
$659$	−2.75597e8	−	2.75597e8i	−0.962982	−	0.962982i	0.0363568	−	0.999339i	$-0.488425\pi$
$659$	−2.75597e8	−	2.75597e8i	−0.962982	−	0.962982i	−0.999339	+	0.0363568i	$0.988425\pi$
$660$		0			0
$661$	−1.54371e8	−	1.54371e8i	−0.534517	−	0.534517i	0.387396	−	0.921913i	$-0.373375\pi$
$661$	−1.54371e8	−	1.54371e8i	−0.534517	−	0.534517i	−0.921913	+	0.387396i	$0.873375\pi$
$662$		0			0
$663$	−4.05992e8			−1.39308
$664$		0			0
$665$		−	2.88917e7i		−	0.0982446i
$666$		0			0
$667$	−1.16263e8	+	1.16263e8i	−0.391800	+	0.391800i
$668$		0			0
$669$	−2.03460e8	+	2.03460e8i	−0.679518	+	0.679518i
$670$		0			0
$671$		−	4.20350e7i		−	0.139137i
$672$		0			0
$673$	−1.40609e7			−0.0461284			−0.0230642	−	0.999734i	$-0.507342\pi$
$673$	−1.40609e7			−0.0461284			−0.0230642	+	0.999734i	$0.507342\pi$
$674$		0			0
$675$	−4.13918e7	−	4.13918e7i	−0.134587	−	0.134587i
$676$		0			0
$677$	1.11330e8	+	1.11330e8i	0.358795	+	0.358795i	0.863369	−	0.504573i	$-0.168350\pi$
$677$	1.11330e8	+	1.11330e8i	0.358795	+	0.358795i	−0.504573	+	0.863369i	$0.668350\pi$
$678$		0			0
$679$	4.16199e8			1.32951
$680$		0			0
$681$		−	5.14747e7i		−	0.162987i
$682$		0			0
$683$	−1.14911e8	+	1.14911e8i	−0.360660	+	0.360660i	−0.864056	−	0.503396i	$-0.832084\pi$
$683$	−1.14911e8	+	1.14911e8i	−0.360660	+	0.360660i	0.503396	+	0.864056i	$0.332084\pi$
$684$		0			0
$685$	2.36259e7	−	2.36259e7i	0.0735051	−	0.0735051i
$686$		0			0
$687$		−	2.42671e8i		−	0.748423i
$688$		0			0
$689$	4.72206e8			1.44369
$690$		0			0
$691$	−3.16526e8	−	3.16526e8i	−0.959345	−	0.959345i	0.0398604	−	0.999205i	$-0.487309\pi$
$691$	−3.16526e8	−	3.16526e8i	−0.959345	−	0.959345i	−0.999205	+	0.0398604i	$0.987309\pi$
$692$		0			0
$693$	1.16659e8	+	1.16659e8i	0.350524	+	0.350524i
$694$		0			0
$695$	4.37412e7			0.130298
$696$		0			0
$697$		−	6.84684e8i		−	2.02205i
$698$		0			0
$699$	9.47074e7	−	9.47074e7i	0.277302	−	0.277302i
$700$		0			0
$701$	−2.13815e8	+	2.13815e8i	−0.620704	+	0.620704i	−0.945711	−	0.325008i	$-0.894633\pi$
$701$	−2.13815e8	+	2.13815e8i	−0.620704	+	0.620704i	0.325008	+	0.945711i	$0.394633\pi$
$702$		0			0
$703$			9.38243e6i			0.0270053i
$704$		0			0
$705$	−2.56029e7			−0.0730670
$706$		0			0
$707$	3.79002e8	+	3.79002e8i	1.07247	+	1.07247i
$708$		0			0
$709$	1.45979e8	+	1.45979e8i	0.409593	+	0.409593i	0.881597	−	0.472003i	$-0.156469\pi$
$709$	1.45979e8	+	1.45979e8i	0.409593	+	0.409593i	−0.472003	+	0.881597i	$0.656469\pi$
$710$		0			0
$711$	1.39058e8			0.386890
$712$		0			0
$713$		−	1.64757e8i		−	0.454543i
$714$		0			0
$715$	7.07225e7	−	7.07225e7i	0.193481	−	0.193481i
$716$		0			0
$717$	−1.73564e7	+	1.73564e7i	−0.0470870	+	0.0470870i
$718$		0			0
$719$			1.30421e8i			0.350882i	0.984490	+	0.175441i	$0.0561351\pi$
$719$			1.30421e8i			0.350882i	−0.984490	+	0.175441i	$0.943865\pi$
$720$		0			0
$721$	2.05102e8			0.547222
$722$		0			0
$723$	−1.69747e8	−	1.69747e8i	−0.449146	−	0.449146i
$724$		0			0
$725$	1.47235e8	+	1.47235e8i	0.386363	+	0.386363i
$726$		0			0
$727$	−1.55032e8			−0.403475			−0.201738	−	0.979440i	$-0.564659\pi$
$727$	−1.55032e8			−0.403475			−0.201738	+	0.979440i	$0.564659\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	4.44464e8	−	4.44464e8i	1.13785	−	1.13785i
$732$		0			0
$733$	−1.89149e8	+	1.89149e8i	−0.480278	+	0.480278i	−0.905220	−	0.424942i	$-0.860294\pi$
$733$	−1.89149e8	+	1.89149e8i	−0.480278	+	0.480278i	0.424942	+	0.905220i	$0.360294\pi$
$734$		0			0
$735$			3.06643e6i			0.00772273i
$736$		0			0
$737$	−5.07635e8			−1.26809
$738$		0			0
$739$	4.72512e7	+	4.72512e7i	0.117079	+	0.117079i	0.763219	−	0.646140i	$-0.223618\pi$
$739$	4.72512e7	+	4.72512e7i	0.117079	+	0.117079i	−0.646140	+	0.763219i	$0.723618\pi$
$740$		0			0
$741$	2.73156e8	+	2.73156e8i	0.671361	+	0.671361i
$742$		0			0
$743$	−1.17829e8			−0.287267			−0.143633	−	0.989631i	$-0.545879\pi$
$743$	−1.17829e8			−0.287267			−0.143633	+	0.989631i	$0.545879\pi$
$744$		0			0
$745$			5.97391e6i			0.0144474i
$746$		0			0
$747$	−8.77224e7	+	8.77224e7i	−0.210450	+	0.210450i
$748$		0			0
$749$	2.19595e8	−	2.19595e8i	0.522610	−	0.522610i
$750$		0			0
$751$		−	3.83595e8i		−	0.905635i	−0.891603	−	0.452818i	$-0.850419\pi$
$751$		−	3.83595e8i		−	0.905635i	0.891603	−	0.452818i	$-0.149581\pi$
$752$		0			0
$753$	2.29509e8			0.537546
$754$		0			0
$755$	4.27861e6	+	4.27861e6i	0.00994172	+	0.00994172i
$756$		0			0
$757$	2.38231e8	+	2.38231e8i	0.549175	+	0.549175i	0.926202	−	0.377027i	$-0.123054\pi$
$757$	2.38231e8	+	2.38231e8i	0.549175	+	0.549175i	−0.377027	+	0.926202i	$0.623054\pi$
$758$		0			0
$759$	4.03111e8			0.921933
$760$		0			0
$761$		−	5.51987e7i		−	0.125249i	−0.998037	−	0.0626246i	$-0.980053\pi$
$761$		−	5.51987e7i		−	0.125249i	0.998037	−	0.0626246i	$-0.0199471\pi$
$762$		0			0
$763$	−4.18551e8	+	4.18551e8i	−0.942268	+	0.942268i
$764$		0			0
$765$	1.62855e7	−	1.62855e7i	0.0363762	−	0.0363762i
$766$		0			0
$767$			4.02196e8i			0.891356i
$768$		0			0
$769$	6.75649e8			1.48574			0.742869	−	0.669437i	$-0.233465\pi$
$769$	6.75649e8			1.48574			0.742869	+	0.669437i	$0.233465\pi$
$770$		0			0
$771$	7.52192e7	+	7.52192e7i	0.164122	+	0.164122i
$772$		0			0
$773$	−4.62396e7	−	4.62396e7i	−0.100110	−	0.100110i	0.655278	−	0.755388i	$-0.272551\pi$
$773$	−4.62396e7	−	4.62396e7i	−0.100110	−	0.100110i	−0.755388	+	0.655278i	$0.772551\pi$
$774$		0			0
$775$	−2.08647e8			−0.448236
$776$		0			0
$777$			6.80936e6i			0.0145159i
$778$		0			0
$779$	−4.60662e8	+	4.60662e8i	−0.974474	+	0.974474i
$780$		0			0
$781$	−3.58740e8	+	3.58740e8i	−0.753054	+	0.753054i
$782$		0			0
$783$			5.10404e7i			0.106323i
$784$		0			0
$785$	−1.27869e7			−0.0264336
$786$		0			0
$787$	1.72365e8	+	1.72365e8i	0.353610	+	0.353610i	0.861451	−	0.507841i	$-0.169556\pi$
$787$	1.72365e8	+	1.72365e8i	0.353610	+	0.353610i	−0.507841	+	0.861451i	$0.669556\pi$
$788$		0			0
$789$	−2.89503e8	−	2.89503e8i	−0.589415	−	0.589415i
$790$		0			0
$791$	3.18345e7			0.0643233
$792$		0			0
$793$		−	7.14324e7i		−	0.143244i
$794$		0			0
$795$	−1.89415e7	+	1.89415e7i	−0.0376976	+	0.0376976i
$796$		0			0
$797$	−2.67781e8	+	2.67781e8i	−0.528939	+	0.528939i	−0.920256	−	0.391317i	$-0.872020\pi$
$797$	−2.67781e8	+	2.67781e8i	−0.528939	+	0.528939i	0.391317	+	0.920256i	$0.372020\pi$
$798$		0			0
$799$			9.06354e8i			1.77688i
$800$		0			0
$801$	2.47000e7			0.0480617
$802$		0			0
$803$	−1.00206e9	−	1.00206e9i	−1.93529	−	1.93529i
$804$		0			0
$805$	−3.62278e7	−	3.62278e7i	−0.0694472	−	0.0694472i
$806$		0			0
$807$	−4.12785e8			−0.785422
$808$		0			0
$809$			5.16479e8i			0.975454i	0.872996	+	0.487727i	$0.162174\pi$
$809$			5.16479e8i			0.975454i	−0.872996	+	0.487727i	$0.837826\pi$
$810$		0			0
$811$	2.03401e8	−	2.03401e8i	0.381321	−	0.381321i	−0.490257	−	0.871578i	$-0.663097\pi$
$811$	2.03401e8	−	2.03401e8i	0.381321	−	0.381321i	0.871578	+	0.490257i	$0.163097\pi$
$812$		0			0
$813$	6.74203e7	−	6.74203e7i	0.125464	−	0.125464i
$814$		0			0
$815$			5.10994e7i			0.0943937i
$816$		0			0
$817$	−5.98080e8			−1.09671
$818$		0			0
$819$	1.98245e8	+	1.98245e8i	0.360869	+	0.360869i
$820$		0			0
$821$	−2.23660e8	−	2.23660e8i	−0.404165	−	0.404165i	0.475533	−	0.879698i	$-0.342255\pi$
$821$	−2.23660e8	−	2.23660e8i	−0.404165	−	0.404165i	−0.879698	+	0.475533i	$0.842255\pi$
$822$		0			0
$823$	−5.55024e8			−0.995663			−0.497831	−	0.867274i	$-0.665870\pi$
$823$	−5.55024e8			−0.995663			−0.497831	+	0.867274i	$0.665870\pi$
$824$		0			0
$825$		−	5.10496e8i		−	0.909140i
$826$		0			0
$827$	−3.43167e8	+	3.43167e8i	−0.606722	+	0.606722i	−0.942088	−	0.335366i	$-0.891140\pi$
$827$	−3.43167e8	+	3.43167e8i	−0.606722	+	0.606722i	0.335366	+	0.942088i	$0.391140\pi$
$828$		0			0
$829$	−3.19773e8	+	3.19773e8i	−0.561278	+	0.561278i	−0.929670	−	0.368393i	$-0.879908\pi$
$829$	−3.19773e8	+	3.19773e8i	−0.561278	+	0.561278i	0.368393	+	0.929670i	$0.379908\pi$
$830$		0			0
$831$			5.34430e8i			0.931295i
$832$		0			0
$833$	1.08553e8			0.187805
$834$		0			0
$835$	5.23048e7	+	5.23048e7i	0.0898425	+	0.0898425i
$836$		0			0
$837$	−3.61648e7	−	3.61648e7i	−0.0616751	−	0.0616751i
$838$		0			0
$839$	−3.67753e8			−0.622687			−0.311344	−	0.950297i	$-0.600779\pi$
$839$	−3.67753e8			−0.622687			−0.311344	+	0.950297i	$0.600779\pi$
$840$		0			0
$841$			4.13268e8i			0.694774i
$842$		0			0
$843$	1.24975e8	−	1.24975e8i	0.208612	−	0.208612i
$844$		0			0
$845$	7.54531e7	−	7.54531e7i	0.125057	−	0.125057i
$846$		0			0
$847$			8.71223e8i			1.43377i
$848$		0			0
$849$	5.25711e8			0.859061
$850$		0			0
$851$	1.17648e7	+	1.17648e7i	0.0190895	+	0.0190895i
$852$		0			0
$853$	4.71292e8	+	4.71292e8i	0.759351	+	0.759351i	0.976204	−	0.216853i	$-0.0695792\pi$
$853$	4.71292e8	+	4.71292e8i	0.759351	+	0.759351i	−0.216853	+	0.976204i	$0.569579\pi$
$854$		0			0
$855$	−2.19141e7			−0.0350611
$856$		0			0
$857$			4.41918e8i			0.702101i	0.936357	+	0.351050i	$0.114175\pi$
$857$			4.41918e8i			0.702101i	−0.936357	+	0.351050i	$0.885825\pi$
$858$		0			0
$859$	2.13804e8	−	2.13804e8i	0.337316	−	0.337316i	−0.518040	−	0.855356i	$-0.673338\pi$
$859$	2.13804e8	−	2.13804e8i	0.337316	−	0.337316i	0.855356	+	0.518040i	$0.173338\pi$
$860$		0			0
$861$	−3.34329e8	+	3.34329e8i	−0.523799	+	0.523799i
$862$		0			0
$863$		−	8.85672e8i		−	1.37797i	−0.724774	−	0.688987i	$-0.758056\pi$
$863$		−	8.85672e8i		−	1.37797i	0.724774	−	0.688987i	$-0.241944\pi$
$864$		0			0
$865$	−7.62491e7			−0.117811
$866$		0			0
$867$	−3.10453e8	−	3.10453e8i	−0.476364	−	0.476364i
$868$		0			0
$869$	8.57520e8	+	8.57520e8i	1.30673	+	1.30673i
$870$		0			0
$871$	−8.62653e8			−1.30551
$872$		0			0
$873$		−	3.15683e8i		−	0.474470i
$874$		0			0
$875$	−9.22671e7	+	9.22671e7i	−0.137728	+	0.137728i
$876$		0			0
$877$	5.18981e8	−	5.18981e8i	0.769401	−	0.769401i	−0.208600	−	0.978001i	$-0.566891\pi$
$877$	5.18981e8	−	5.18981e8i	0.769401	−	0.769401i	0.978001	+	0.208600i	$0.0668908\pi$
$878$		0			0
$879$			9.82192e6i			0.0144620i
$880$		0			0
$881$	1.55711e7			0.0227715			0.0113858	−	0.999935i	$-0.496376\pi$
$881$	1.55711e7			0.0227715			0.0113858	+	0.999935i	$0.496376\pi$
$882$		0			0
$883$	−1.82187e8	−	1.82187e8i	−0.264628	−	0.264628i	0.562303	−	0.826931i	$-0.309915\pi$
$883$	−1.82187e8	−	1.82187e8i	−0.264628	−	0.264628i	−0.826931	+	0.562303i	$0.809915\pi$
$884$		0			0
$885$	−1.61332e7	−	1.61332e7i	−0.0232751	−	0.0232751i
$886$		0			0
$887$	3.07661e8			0.440860			0.220430	−	0.975403i	$-0.429254\pi$
$887$	3.07661e8			0.440860			0.220430	+	0.975403i	$0.429254\pi$
$888$		0			0
$889$			6.59469e7i			0.0938618i
$890$		0			0
$891$	8.84845e7	−	8.84845e7i	0.125093	−	0.125093i
$892$		0			0
$893$	6.09804e8	−	6.09804e8i	0.856319	−	0.856319i
$894$		0			0
$895$		−	1.05749e7i		−	0.0147506i
$896$		0			0
$897$	6.85029e8			0.949143
$898$		0			0
$899$	1.28642e8	+	1.28642e8i	0.177053	+	0.177053i
$900$		0			0
$901$	6.70539e8	+	6.70539e8i	0.916747	+	0.916747i
$902$		0			0
$903$	−4.34060e8			−0.589504
$904$		0			0
$905$		−	4.94495e6i		−	0.00667138i
$906$		0			0
$907$	−3.83442e8	+	3.83442e8i	−0.513900	+	0.513900i	−0.915719	−	0.401819i	$-0.868378\pi$
$907$	−3.83442e8	+	3.83442e8i	−0.513900	+	0.513900i	0.401819	+	0.915719i	$0.368378\pi$
$908$		0			0
$909$	2.87469e8	−	2.87469e8i	0.382737	−	0.382737i
$910$		0			0
$911$		−	8.08876e8i		−	1.06986i	−0.844896	−	0.534930i	$-0.820338\pi$
$911$		−	8.08876e8i		−	1.06986i	0.844896	−	0.534930i	$-0.179662\pi$
$912$		0			0
$913$	−1.08190e9			−1.42160
$914$		0			0
$915$	2.86536e6	+	2.86536e6i	0.00374038	+	0.00374038i
$916$		0			0
$917$	2.96866e8	+	2.96866e8i	0.384993	+	0.384993i
$918$		0			0
$919$	−3.67372e8			−0.473326			−0.236663	−	0.971592i	$-0.576054\pi$
$919$	−3.67372e8			−0.473326			−0.236663	+	0.971592i	$0.576054\pi$
$920$		0			0
$921$			4.43061e8i			0.567133i
$922$		0			0
$923$	−6.09626e8	+	6.09626e8i	−0.775280	+	0.775280i
$924$		0			0
$925$	1.48988e7	−	1.48988e7i	0.0188246	−	0.0188246i
$926$		0			0
$927$		−	1.55568e8i		−	0.195290i
$928$		0			0
$929$	1.50587e9			1.87819			0.939097	−	0.343653i	$-0.111664\pi$
$929$	1.50587e9			1.87819			0.939097	+	0.343653i	$0.111664\pi$
$930$		0			0
$931$	−7.30356e7	−	7.30356e7i	−0.0905077	−	0.0905077i
$932$		0			0
$933$	5.33423e8	+	5.33423e8i	0.656791	+	0.656791i
$934$		0			0
$935$	2.00854e8			0.245722
$936$		0			0
$937$			5.87413e8i			0.714044i	0.934096	+	0.357022i	$0.116208\pi$
$937$			5.87413e8i			0.714044i	−0.934096	+	0.357022i	$0.883792\pi$
$938$		0			0
$939$	3.19423e8	−	3.19423e8i	0.385807	−	0.385807i
$940$		0			0
$941$	8.18451e8	−	8.18451e8i	0.982253	−	0.982253i	−0.0175918	−	0.999845i	$-0.505600\pi$
$941$	8.18451e8	−	8.18451e8i	0.982253	−	0.982253i	0.999845	+	0.0175918i	$0.00559994\pi$
$942$		0			0
$943$			1.15526e9i			1.37767i
$944$		0			0
$945$	−1.59043e7			−0.0188460
$946$		0			0
$947$	5.49457e8	+	5.49457e8i	0.646970	+	0.646970i	0.952259	−	0.305290i	$-0.0987534\pi$
$947$	5.49457e8	+	5.49457e8i	0.646970	+	0.646970i	−0.305290	+	0.952259i	$0.598753\pi$
$948$		0			0
$949$	−1.70285e9	−	1.70285e9i	−1.99241	−	1.99241i
$950$		0			0
$951$	7.33998e8			0.853401
$952$		0			0
$953$		−	2.49315e8i		−	0.288051i	−0.989574	−	0.144026i	$-0.953995\pi$
$953$		−	2.49315e8i		−	0.288051i	0.989574	−	0.144026i	$-0.0460048\pi$
$954$		0			0
$955$	−9.63955e7	+	9.63955e7i	−0.110674	+	0.110674i
$956$		0			0
$957$	−3.14748e8	+	3.14748e8i	−0.359109	+	0.359109i
$958$		0			0
$959$			8.16792e8i			0.926095i
$960$		0			0
$961$	7.05205e8			0.794594
$962$		0			0
$963$	−1.66561e8	−	1.66561e8i	−0.186507	−	0.186507i
$964$		0			0
$965$	2.02191e7	+	2.02191e7i	0.0224999	+	0.0224999i
$966$		0			0
$967$	−1.57264e9			−1.73920			−0.869600	−	0.493756i	$-0.835623\pi$
$967$	−1.57264e9			−1.73920			−0.869600	+	0.493756i	$0.835623\pi$
$968$		0			0
$969$			7.75769e8i			0.852631i
$970$		0			0
$971$	−2.68210e8	+	2.68210e8i	−0.292966	+	0.292966i	−0.838251	−	0.545285i	$-0.816421\pi$
$971$	−2.68210e8	+	2.68210e8i	−0.292966	+	0.292966i	0.545285	+	0.838251i	$0.316421\pi$
$972$		0			0
$973$	−7.56107e8	+	7.56107e8i	−0.820814	+	0.820814i
$974$		0			0
$975$		−	8.67515e8i		−	0.935972i
$976$		0			0
$977$	−1.62967e9			−1.74750			−0.873749	−	0.486376i	$-0.838318\pi$
$977$	−1.62967e9			−1.74750			−0.873749	+	0.486376i	$0.838318\pi$
$978$		0			0
$979$	1.52316e8	+	1.52316e8i	0.162329	+	0.162329i
$980$		0			0
$981$	3.17467e8	+	3.17467e8i	0.336272	+	0.336272i
$982$		0			0
$983$	1.52921e9			1.60993			0.804967	−	0.593320i	$-0.202183\pi$
$983$	1.52921e9			1.60993			0.804967	+	0.593320i	$0.202183\pi$
$984$		0			0
$985$		−	9.64121e7i		−	0.100884i
$986$		0			0
$987$	4.42569e8	−	4.42569e8i	0.460288	−	0.460288i
$988$		0			0
$989$	−7.49942e8	+	7.49942e8i	−0.775245	+	0.775245i
$990$		0			0
$991$			5.68031e8i			0.583648i	0.956472	+	0.291824i	$0.0942622\pi$
$991$			5.68031e8i			0.583648i	−0.956472	+	0.291824i	$0.905738\pi$
$992$		0			0
$993$	−2.07631e8			−0.212053
$994$		0			0
$995$	1.31321e8	+	1.31321e8i	0.133310	+	0.133310i
$996$		0			0
$997$	2.71452e7	+	2.71452e7i	0.0273910	+	0.0273910i	0.720670	−	0.693279i	$-0.243834\pi$
$997$	2.71452e7	+	2.71452e7i	0.0273910	+	0.0273910i	−0.693279	+	0.720670i	$0.743834\pi$
$998$		0			0
$999$	5.16484e6			0.00518036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.7.l.b.31.7		48
4.3	odd	2		384.7.l.a.31.18		48
8.3	odd	2		192.7.l.a.79.7		48
8.5	even	2		48.7.l.a.43.7	yes	48
16.3	odd	4	inner	384.7.l.b.223.7		48
16.5	even	4		192.7.l.a.175.7		48
16.11	odd	4		48.7.l.a.19.7	✓	48
16.13	even	4		384.7.l.a.223.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.7.l.a.19.7	✓	48	16.11	odd	4
48.7.l.a.43.7	yes	48	8.5	even	2
192.7.l.a.79.7		48	8.3	odd	2
192.7.l.a.175.7		48	16.5	even	4
384.7.l.a.31.18		48	4.3	odd	2
384.7.l.a.223.18		48	16.13	even	4
384.7.l.b.31.7		48	1.1	even	1	trivial
384.7.l.b.223.7		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)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(9.26689 + 9.26689i) q^{5} -320.373 q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(9.26689 + 9.26689i) q^{5} -320.373 q^{7} +243.000i q^{9} +(-1498.49 + 1498.49i) q^{11} +(-2546.47 + 2546.47i) q^{13} -204.292i q^{15} -7232.04 q^{17} +(4865.79 + 4865.79i) q^{19} +(3531.38 + 3531.38i) q^{21} +12202.6 q^{23} -15453.2i q^{25} +(2678.52 - 2678.52i) q^{27} +(-9527.74 + 9527.74i) q^{29} -13501.8i q^{31} +33034.9 q^{33} +(-2968.86 - 2968.86i) q^{35} +(964.122 + 964.122i) q^{37} +56138.0 q^{39} +94673.7i q^{41} +(-61457.6 + 61457.6i) q^{43} +(-2251.85 + 2251.85i) q^{45} -125325. i q^{47} -15010.0 q^{49} +(79716.7 + 79716.7i) q^{51} +(-92717.8 - 92717.8i) q^{53} -27772.7 q^{55} -107268. i q^{57} +(78971.2 - 78971.2i) q^{59} +(-14025.8 + 14025.8i) q^{61} -77850.7i q^{63} -47195.8 q^{65} +(169382. + 169382. i) q^{67} +(-134506. - 134506. i) q^{69} +239400. q^{71} +668710. i q^{73} +(-170337. + 170337. i) q^{75} +(480077. - 480077. i) q^{77} -572255. i q^{79} -59049.0 q^{81} +(360998. + 360998. i) q^{83} +(-67018.6 - 67018.6i) q^{85} +210043. q^{87} -101646. i q^{89} +(815821. - 815821. i) q^{91} +(-148826. + 148826. i) q^{93} +90181.5i q^{95} -1.29911e6 q^{97} +(-364134. - 364134. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 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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