LMFDB - Embedded newform 324.4.b.d.323.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,4,Mod(323,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("324.323");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, 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:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.7
Character	$\chi$	$=$	324.323
Dual form			324.4.b.d.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.26792 - 1.69014i) q^{2} +(2.28688 + 7.66617i) q^{4} +16.3324i q^{5} +28.7358i q^{7} +(7.77043 - 21.2514i) q^{8} +(27.6040 - 37.0405i) q^{10} +25.2086 q^{11} +74.9324 q^{13} +(48.5674 - 65.1703i) q^{14} +(-53.5404 + 35.0632i) q^{16} -28.4061i q^{17} +132.976i q^{19} +(-125.207 + 37.3502i) q^{20} +(-57.1709 - 42.6059i) q^{22} -13.9485 q^{23} -141.747 q^{25} +(-169.940 - 126.646i) q^{26} +(-220.293 + 65.7152i) q^{28} -134.473i q^{29} +117.851i q^{31} +(180.687 + 10.9702i) q^{32} +(-48.0102 + 64.4226i) q^{34} -469.324 q^{35} +164.638 q^{37} +(224.747 - 301.577i) q^{38} +(347.086 + 126.910i) q^{40} +83.5882i q^{41} -43.4468i q^{43} +(57.6489 + 193.253i) q^{44} +(31.6341 + 23.5749i) q^{46} -449.188 q^{47} -482.745 q^{49} +(321.471 + 239.572i) q^{50} +(171.361 + 574.445i) q^{52} +5.67062i q^{53} +411.717i q^{55} +(610.674 + 223.289i) q^{56} +(-227.278 + 304.974i) q^{58} +836.816 q^{59} -446.126 q^{61} +(199.185 - 267.277i) q^{62} +(-391.241 - 330.265i) q^{64} +1223.83i q^{65} +130.483i q^{67} +(217.766 - 64.9613i) q^{68} +(1064.39 + 793.222i) q^{70} -209.816 q^{71} +163.546 q^{73} +(-373.384 - 278.260i) q^{74} +(-1019.41 + 304.099i) q^{76} +724.388i q^{77} -1292.83i q^{79} +(-572.666 - 874.443i) q^{80} +(141.275 - 189.571i) q^{82} -444.157 q^{83} +463.940 q^{85} +(-73.4310 + 98.5336i) q^{86} +(195.882 - 535.717i) q^{88} +1173.89i q^{89} +2153.24i q^{91} +(-31.8986 - 106.932i) q^{92} +(1018.72 + 759.189i) q^{94} -2171.81 q^{95} +523.610 q^{97} +(1094.82 + 815.904i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 104 q^{10} + 184 q^{13} - 436 q^{16} + 36 q^{22} - 576 q^{25} - 252 q^{28} - 752 q^{34} - 824 q^{37} + 472 q^{40} - 972 q^{46} - 3136 q^{49} - 1472 q^{52} - 716 q^{58} + 1192 q^{61} + 680 q^{64}+ \cdots + 7264 q^{97}+O(q^{100}) $ 32 * q + 32 * q^4 - 104 * q^10 + 184 * q^13 - 436 * q^16 + 36 * q^22 - 576 * q^25 - 252 * q^28 - 752 * q^34 - 824 * q^37 + 472 * q^40 - 972 * q^46 - 3136 * q^49 - 1472 * q^52 - 716 * q^58 + 1192 * q^61 + 680 * q^64 + 2484 * q^70 - 1184 * q^73 - 396 * q^76 + 748 * q^82 - 6808 * q^85 + 1764 * q^88 + 3312 * q^94 + 7264 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.26792	−	1.69014i	−0.801829	−	0.597553i
$2$	−2.26792	−	1.69014i	−0.801829	−	0.597553i
$3$		0			0
$3$		0			0
$4$	2.28688	+	7.66617i	0.285860	+	0.958271i
$5$			16.3324i			1.46081i	0.683012	+	0.730407i	$0.260670\pi$
$5$			16.3324i			1.46081i	−0.683012	+	0.730407i	$0.739330\pi$
$6$		0			0
$7$			28.7358i			1.55159i	0.630988	+	0.775793i	$0.282650\pi$
$7$			28.7358i			1.55159i	−0.630988	+	0.775793i	$0.717350\pi$
$8$	7.77043	−	21.2514i	0.343408	−	0.939186i
$9$		0			0
$10$	27.6040	−	37.0405i	0.872915	−	1.17132i
$11$	25.2086			0.690970			0.345485	−	0.938424i	$-0.387714\pi$
$11$	25.2086			0.690970			0.345485	+	0.938424i	$0.387714\pi$
$12$		0			0
$13$	74.9324			1.59865			0.799327	−	0.600896i	$-0.205189\pi$
$13$	74.9324			1.59865			0.799327	+	0.600896i	$0.205189\pi$
$14$	48.5674	−	65.1703i	0.927156	−	1.24411i
$15$		0			0
$16$	−53.5404	+	35.0632i	−0.836568	+	0.547862i
$17$		−	28.4061i		−	0.405264i	−0.979255	−	0.202632i	$-0.935050\pi$
$17$		−	28.4061i		−	0.405264i	0.979255	−	0.202632i	$-0.0649496\pi$
$18$		0			0
$19$			132.976i			1.60561i	0.596238	+	0.802807i	$0.296661\pi$
$19$			132.976i			1.60561i	−0.596238	+	0.802807i	$0.703339\pi$
$20$	−125.207	+	37.3502i	−1.39986	+	0.417588i
$21$		0			0
$22$	−57.1709	−	42.6059i	−0.554040	−	0.412892i
$23$	−13.9485			−0.126455			−0.0632276	−	0.997999i	$-0.520139\pi$
$23$	−13.9485			−0.126455			−0.0632276	+	0.997999i	$0.520139\pi$
$24$		0			0
$25$	−141.747			−1.13398
$26$	−169.940	−	126.646i	−1.28185	−	0.955282i
$27$		0			0
$28$	−220.293	+	65.7152i	−1.48684	+	0.443536i
$29$		−	134.473i		−	0.861071i	−0.902574	−	0.430535i	$-0.858325\pi$
$29$		−	134.473i		−	0.861071i	0.902574	−	0.430535i	$-0.141675\pi$
$30$		0			0
$31$			117.851i			0.682798i	0.939919	+	0.341399i	$0.110901\pi$
$31$			117.851i			0.682798i	−0.939919	+	0.341399i	$0.889099\pi$
$32$	180.687	+	10.9702i	0.998162	+	0.0606024i
$33$		0			0
$34$	−48.0102	+	64.4226i	−0.242167	+	0.324953i
$35$	−469.324			−2.26658
$36$		0			0
$37$	164.638			0.731520			0.365760	−	0.930709i	$-0.380809\pi$
$37$	164.638			0.731520			0.365760	+	0.930709i	$0.380809\pi$
$38$	224.747	−	301.577i	0.959441	−	1.28743i
$39$		0			0
$40$	347.086	+	126.910i	1.37198	+	0.501655i
$41$			83.5882i			0.318397i	0.987247	+	0.159199i	$0.0508910\pi$
$41$			83.5882i			0.318397i	−0.987247	+	0.159199i	$0.949109\pi$
$42$		0			0
$43$		−	43.4468i		−	0.154083i	−0.997028	−	0.0770415i	$-0.975453\pi$
$43$		−	43.4468i		−	0.154083i	0.997028	−	0.0770415i	$-0.0245474\pi$
$44$	57.6489	+	193.253i	0.197521	+	0.662137i
$45$		0			0
$46$	31.6341	+	23.5749i	0.101395	+	0.0755638i
$47$	−449.188			−1.39406			−0.697030	−	0.717042i	$-0.745496\pi$
$47$	−449.188			−1.39406			−0.697030	+	0.717042i	$0.745496\pi$
$48$		0			0
$49$	−482.745			−1.40742
$50$	321.471	+	239.572i	0.909258	+	0.677613i
$51$		0			0
$52$	171.361	+	574.445i	0.456991	+	1.53195i
$53$			5.67062i			0.0146966i	0.999973	+	0.00734830i	$0.00233906\pi$
$53$			5.67062i			0.0146966i	−0.999973	+	0.00734830i	$0.997661\pi$
$54$		0			0
$55$			411.717i			1.00938i
$56$	610.674	+	223.289i	1.45723	+	0.532827i
$57$		0			0
$58$	−227.278	+	304.974i	−0.514536	+	0.690432i
$59$	836.816			1.84651			0.923256	−	0.384186i	$-0.125518\pi$
$59$	836.816			1.84651			0.923256	+	0.384186i	$0.125518\pi$
$60$		0			0
$61$	−446.126			−0.936403			−0.468202	−	0.883622i	$-0.655098\pi$
$61$	−446.126			−0.936403			−0.468202	+	0.883622i	$0.655098\pi$
$62$	199.185	−	267.277i	0.408008	−	0.547487i
$63$		0			0
$64$	−391.241	−	330.265i	−0.764142	−	0.645048i
$65$			1223.83i			2.33534i
$66$		0			0
$67$			130.483i			0.237925i	0.992899	+	0.118963i	$0.0379568\pi$
$67$			130.483i			0.237925i	−0.992899	+	0.118963i	$0.962043\pi$
$68$	217.766	−	64.9613i	0.388353	−	0.115849i
$69$		0			0
$70$	1064.39	+	793.222i	1.81741	+	1.35440i
$71$	−209.816			−0.350712			−0.175356	−	0.984505i	$-0.556108\pi$
$71$	−209.816			−0.350712			−0.175356	+	0.984505i	$0.556108\pi$
$72$		0			0
$73$	163.546			0.262214			0.131107	−	0.991368i	$-0.458147\pi$
$73$	163.546			0.262214			0.131107	+	0.991368i	$0.458147\pi$
$74$	−373.384	−	278.260i	−0.586554	−	0.437123i
$75$		0			0
$76$	−1019.41	+	304.099i	−1.53861	+	0.458981i
$77$			724.388i			1.07210i
$78$		0			0
$79$		−	1292.83i		−	1.84120i	−0.390507	−	0.920600i	$-0.627700\pi$
$79$		−	1292.83i		−	1.84120i	0.390507	−	0.920600i	$-0.372300\pi$
$80$	−572.666	−	874.443i	−0.800325	−	1.22207i
$81$		0			0
$82$	141.275	−	189.571i	0.190259	−	0.255300i
$83$	−444.157			−0.587380			−0.293690	−	0.955901i	$-0.594883\pi$
$83$	−444.157			−0.587380			−0.293690	+	0.955901i	$0.594883\pi$
$84$		0			0
$85$	463.940			0.592016
$86$	−73.4310	+	98.5336i	−0.0920728	+	0.123548i
$87$		0			0
$88$	195.882	−	535.717i	0.237285	−	0.648950i
$89$			1173.89i			1.39811i	0.715069	+	0.699054i	$0.246395\pi$
$89$			1173.89i			1.39811i	−0.715069	+	0.699054i	$0.753605\pi$
$90$		0			0
$91$			2153.24i			2.48045i
$92$	−31.8986	−	106.932i	−0.0361485	−	0.121178i
$93$		0			0
$94$	1018.72	+	759.189i	1.11780	+	0.833025i
$95$	−2171.81			−2.34551
$96$		0			0
$97$	523.610			0.548088			0.274044	−	0.961717i	$-0.411639\pi$
$97$	523.610			0.548088			0.274044	+	0.961717i	$0.411639\pi$
$98$	1094.82	+	815.904i	1.12851	+	0.841008i
$99$		0			0
$100$	−324.159	−	1086.66i	−0.324159	−	1.08666i
$101$		−	854.748i		−	0.842085i	−0.907041	−	0.421043i	$-0.861664\pi$
$101$		−	854.748i		−	0.842085i	0.907041	−	0.421043i	$-0.138336\pi$
$102$		0			0
$103$		−	638.740i		−	0.611038i	−0.952186	−	0.305519i	$-0.901170\pi$
$103$		−	638.740i		−	0.611038i	0.952186	−	0.305519i	$-0.0988299\pi$
$104$	582.257	−	1592.42i	0.548991	−	1.50143i
$105$		0			0
$106$	9.58413	−	12.8605i	0.00878201	−	0.0117842i
$107$	−957.902			−0.865457			−0.432728	−	0.901524i	$-0.642449\pi$
$107$	−957.902			−0.865457			−0.432728	+	0.901524i	$0.642449\pi$
$108$		0			0
$109$	1470.56			1.29224			0.646118	−	0.763238i	$-0.276392\pi$
$109$	1470.56			1.29224			0.646118	+	0.763238i	$0.276392\pi$
$110$	695.857	−	933.739i	0.603158	−	0.809350i
$111$		0			0
$112$	−1007.57	−	1538.52i	−0.850056	−	1.29801i
$113$			929.247i			0.773595i	0.922165	+	0.386798i	$0.126419\pi$
$113$			929.247i			0.773595i	−0.922165	+	0.386798i	$0.873581\pi$
$114$		0			0
$115$		−	227.813i		−	0.184728i
$116$	1030.90	−	307.524i	0.825140	−	0.246145i
$117$		0			0
$118$	−1897.83	−	1414.33i	−1.48059	−	1.10339i
$119$	816.272			0.628802
$120$		0			0
$121$	−695.527			−0.522560
$122$	1011.78	+	754.014i	0.750835	+	0.559551i
$123$		0			0
$124$	−903.469	+	269.512i	−0.654305	+	0.195184i
$125$		−	273.525i		−	0.195719i
$126$		0			0
$127$		−	1502.92i		−	1.05010i	−0.851072	−	0.525049i	$-0.824047\pi$
$127$		−	1502.92i		−	1.05010i	0.851072	−	0.525049i	$-0.175953\pi$
$128$	329.109	+	1410.26i	0.227261	+	0.973834i
$129$		0			0
$130$	2068.43	−	2775.53i	1.39549	−	1.87254i
$131$	−1920.19			−1.28067			−0.640334	−	0.768097i	$-0.721204\pi$
$131$	−1920.19			−1.28067			−0.640334	+	0.768097i	$0.721204\pi$
$132$		0			0
$133$	−3821.16			−2.49125
$134$	220.533	−	295.923i	0.142173	−	0.190775i
$135$		0			0
$136$	−603.668	−	220.728i	−0.380619	−	0.139171i
$137$		−	500.027i		−	0.311826i	−0.987771	−	0.155913i	$-0.950168\pi$
$137$		−	500.027i		−	0.311826i	0.987771	−	0.155913i	$-0.0498319\pi$
$138$		0			0
$139$			718.181i			0.438240i	0.975698	+	0.219120i	$0.0703186\pi$
$139$			718.181i			0.438240i	−0.975698	+	0.219120i	$0.929681\pi$
$140$	−1073.29	−	3597.92i	−0.647924	−	2.17200i
$141$		0			0
$142$	475.844	+	354.617i	0.281211	+	0.209569i
$143$	1888.94			1.10462
$144$		0			0
$145$	2196.27			1.25787
$146$	−370.908	−	276.415i	−0.210250	−	0.156687i
$147$		0			0
$148$	376.506	+	1262.14i	0.209112	+	0.700995i
$149$		−	3481.39i		−	1.91414i	−0.289857	−	0.957070i	$-0.593608\pi$
$149$		−	3481.39i		−	1.91414i	0.289857	−	0.957070i	$-0.406392\pi$
$150$		0			0
$151$		−	2004.44i		−	1.08026i	−0.841582	−	0.540129i	$-0.818376\pi$
$151$		−	2004.44i		−	1.08026i	0.841582	−	0.540129i	$-0.181624\pi$
$152$	2825.91	+	1033.28i	1.50797	+	0.551381i
$153$		0			0
$154$	1224.31	−	1642.85i	0.640637	−	0.859641i
$155$	−1924.80			−0.997441
$156$		0			0
$157$	2609.03			1.32626			0.663132	−	0.748502i	$-0.269227\pi$
$157$	2609.03			1.32626			0.663132	+	0.748502i	$0.269227\pi$
$158$	−2185.06	+	2932.03i	−1.10022	+	1.47633i
$159$		0			0
$160$	−179.170	+	2951.05i	−0.0885289	+	1.45813i
$161$		−	400.822i		−	0.196206i
$162$		0			0
$163$		−	470.259i		−	0.225972i	−0.993597	−	0.112986i	$-0.963958\pi$
$163$		−	470.259i		−	0.225972i	0.993597	−	0.112986i	$-0.0360416\pi$
$164$	−640.801	+	191.156i	−0.305111	+	0.0910169i
$165$		0			0
$166$	1007.31	+	750.686i	0.470979	+	0.350991i
$167$	−1387.47			−0.642907			−0.321453	−	0.946925i	$-0.604171\pi$
$167$	−1387.47			−0.642907			−0.321453	+	0.946925i	$0.604171\pi$
$168$		0			0
$169$	3417.87			1.55570
$170$	−1052.18	−	784.122i	−0.474696	−	0.353761i
$171$		0			0
$172$	333.070	−	99.3574i	0.147653	−	0.0440461i
$173$			1786.67i			0.785192i	0.919711	+	0.392596i	$0.128423\pi$
$173$			1786.67i			0.785192i	−0.919711	+	0.392596i	$0.871577\pi$
$174$		0			0
$175$		−	4073.22i		−	1.75947i
$176$	−1349.68	+	883.893i	−0.578044	+	0.378557i
$177$		0			0
$178$	1984.03	−	2662.27i	0.835444	−	1.12104i
$179$	1050.11			0.438485			0.219243	−	0.975670i	$-0.429641\pi$
$179$	1050.11			0.438485			0.219243	+	0.975670i	$0.429641\pi$
$180$		0			0
$181$	−3014.95			−1.23812			−0.619060	−	0.785344i	$-0.712486\pi$
$181$	−3014.95			−1.23812			−0.619060	+	0.785344i	$0.712486\pi$
$182$	3639.27	−	4883.37i	1.48220	−	1.98890i
$183$		0			0
$184$	−108.386	+	296.425i	−0.0434257	+	0.118765i
$185$			2688.93i			1.06862i
$186$		0			0
$187$		−	716.078i		−	0.280026i
$188$	−1027.24	−	3443.55i	−0.398506	−	1.33589i
$189$		0			0
$190$	4925.48	+	3670.66i	1.88069	+	1.40156i
$191$	−1874.50			−0.710127			−0.355063	−	0.934842i	$-0.615541\pi$
$191$	−1874.50			−0.710127			−0.355063	+	0.934842i	$0.615541\pi$
$192$		0			0
$193$	−914.887			−0.341218			−0.170609	−	0.985339i	$-0.554573\pi$
$193$	−914.887			−0.341218			−0.170609	+	0.985339i	$0.554573\pi$
$194$	−1187.50	−	884.973i	−0.439473	−	0.327512i
$195$		0			0
$196$	−1103.98	−	3700.80i	−0.402324	−	1.34869i
$197$			1430.37i			0.517308i	0.965970	+	0.258654i	$0.0832790\pi$
$197$			1430.37i			0.517308i	−0.965970	+	0.258654i	$0.916721\pi$
$198$		0			0
$199$			2018.44i			0.719011i	0.933143	+	0.359505i	$0.117055\pi$
$199$			2018.44i			0.719011i	−0.933143	+	0.359505i	$0.882945\pi$
$200$	−1101.44	+	3012.33i	−0.389417	+	1.06502i
$201$		0			0
$202$	−1444.64	+	1938.50i	−0.503191	+	0.675209i
$203$	3864.19			1.33603
$204$		0			0
$205$	−1365.20			−0.465119
$206$	−1079.56	+	1448.61i	−0.365128	+	0.489948i
$207$		0			0
$208$	−4011.91	+	2627.37i	−1.33738	+	0.875843i
$209$			3352.12i			1.10943i
$210$		0			0
$211$		−	559.398i		−	0.182515i	−0.995827	−	0.0912573i	$-0.970911\pi$
$211$		−	559.398i		−	0.182515i	0.995827	−	0.0912573i	$-0.0290886\pi$
$212$	−43.4720	+	12.9680i	−0.0140833	+	0.00420117i
$213$		0			0
$214$	2172.44	+	1618.99i	0.693949	+	0.517157i
$215$	709.590			0.225087
$216$		0			0
$217$	−3386.55			−1.05942
$218$	−3335.09	−	2485.44i	−1.03615	−	0.772180i
$219$		0			0
$220$	−3156.29	+	941.546i	−0.967260	+	0.288541i
$221$		−	2128.54i		−	0.647878i
$222$		0			0
$223$			2917.34i			0.876052i	0.898962	+	0.438026i	$0.144322\pi$
$223$			2917.34i			0.876052i	−0.898962	+	0.438026i	$0.855678\pi$
$224$	−315.238	+	5192.17i	−0.0940299	+	1.54873i
$225$		0			0
$226$	1570.55	−	2107.45i	0.462264	−	0.620291i
$227$	5468.88			1.59904			0.799520	−	0.600639i	$-0.205087\pi$
$227$	5468.88			1.59904			0.799520	+	0.600639i	$0.205087\pi$
$228$		0			0
$229$	−3910.91			−1.12856			−0.564280	−	0.825583i	$-0.690846\pi$
$229$	−3910.91			−1.12856			−0.564280	+	0.825583i	$0.690846\pi$
$230$	−385.035	+	516.661i	−0.110385	+	0.148120i
$231$		0			0
$232$	−2857.74	−	1044.92i	−0.808706	−	0.295699i
$233$		−	102.013i		−	0.0286827i	−0.999897	−	0.0143413i	$-0.995435\pi$
$233$		−	102.013i		−	0.0286827i	0.999897	−	0.0143413i	$-0.00456515\pi$
$234$		0			0
$235$		−	7336.32i		−	2.03646i
$236$	1913.70	+	6415.18i	0.527843	+	1.76946i
$237$		0			0
$238$	−1851.23	−	1379.61i	−0.504192	−	0.375743i
$239$	5650.10			1.52918			0.764592	−	0.644515i	$-0.222941\pi$
$239$	5650.10			1.52918			0.764592	+	0.644515i	$0.222941\pi$
$240$		0			0
$241$	4532.38			1.21144			0.605719	−	0.795679i	$-0.292886\pi$
$241$	4532.38			1.21144			0.605719	+	0.795679i	$0.292886\pi$
$242$	1577.40	+	1175.54i	0.419004	+	0.312258i
$243$		0			0
$244$	−1020.24	−	3420.08i	−0.267680	−	0.897329i
$245$		−	7884.38i		−	2.05598i
$246$		0			0
$247$			9964.18i			2.56682i
$248$	2504.50	+	915.756i	0.641274	+	0.234478i
$249$		0			0
$250$	−462.295	+	620.332i	−0.116952	+	0.156933i
$251$	−1967.05			−0.494659			−0.247329	−	0.968931i	$-0.579553\pi$
$251$	−1967.05			−0.494659			−0.247329	+	0.968931i	$0.579553\pi$
$252$		0			0
$253$	−351.623			−0.0873768
$254$	−2540.14	+	3408.49i	−0.627490	+	0.841999i
$255$		0			0
$256$	1637.15	−	3754.59i	0.399694	−	0.916649i
$257$			1618.17i			0.392758i	0.980528	+	0.196379i	$0.0629183\pi$
$257$			1618.17i			0.392758i	−0.980528	+	0.196379i	$0.937082\pi$
$258$		0			0
$259$			4730.99i			1.13502i
$260$	−9382.06	+	2798.74i	−2.23789	+	0.667579i
$261$		0			0
$262$	4354.82	+	3245.38i	1.02688	+	0.765267i
$263$	4674.88			1.09607			0.548034	−	0.836456i	$-0.315377\pi$
$263$	4674.88			1.09607			0.548034	+	0.836456i	$0.315377\pi$
$264$		0			0
$265$	−92.6149			−0.0214690
$266$	8666.06	+	6458.27i	1.99756	+	1.48865i
$267$		0			0
$268$	−1000.30	+	298.398i	−0.227997	+	0.0680132i
$269$		−	3538.93i		−	0.802127i	−0.916050	−	0.401064i	$-0.868641\pi$
$269$		−	3538.93i		−	0.802127i	0.916050	−	0.401064i	$-0.131359\pi$
$270$		0			0
$271$			319.089i			0.0715250i	0.999360	+	0.0357625i	$0.0113860\pi$
$271$			319.089i			0.0715250i	−0.999360	+	0.0357625i	$0.988614\pi$
$272$	996.009	+	1520.87i	0.222029	+	0.339031i
$273$		0			0
$274$	−845.113	+	1134.02i	−0.186333	+	0.250031i
$275$	−3573.25			−0.783546
$276$		0			0
$277$	5129.90			1.11273			0.556364	−	0.830938i	$-0.312196\pi$
$277$	5129.90			1.11273			0.556364	+	0.830938i	$0.312196\pi$
$278$	1213.82	−	1628.77i	0.261872	−	0.351393i
$279$		0			0
$280$	−3646.85	+	9973.78i	−0.778361	+	2.12874i
$281$		−	2669.38i		−	0.566697i	−0.959017	−	0.283349i	$-0.908555\pi$
$281$		−	2669.38i		−	0.566697i	0.959017	−	0.283349i	$-0.0914454\pi$
$282$		0			0
$283$			1733.18i			0.364053i	0.983294	+	0.182026i	$0.0582656\pi$
$283$			1733.18i			0.364053i	−0.983294	+	0.182026i	$0.941734\pi$
$284$	−479.823	−	1608.48i	−0.100254	−	0.336077i
$285$		0			0
$286$	−4283.96	−	3192.57i	−0.885719	−	0.660071i
$287$	−2401.97			−0.494021
$288$		0			0
$289$	4106.09			0.835761
$290$	−4980.96	−	3712.00i	−1.00859	−	0.751642i
$291$		0			0
$292$	374.009	+	1253.77i	0.0749563	+	0.251272i
$293$			4141.37i			0.825738i	0.910790	+	0.412869i	$0.135473\pi$
$293$			4141.37i			0.825738i	−0.910790	+	0.412869i	$0.864527\pi$
$294$		0			0
$295$			13667.2i			2.69741i
$296$	1279.31	−	3498.77i	0.251210	−	0.687034i
$297$		0			0
$298$	−5884.03	+	7895.50i	−1.14380	+	1.53481i
$299$	−1045.20			−0.202158
$300$		0			0
$301$	1248.48			0.239073
$302$	−3387.77	+	4545.90i	−0.645511	+	0.866182i
$303$		0			0
$304$	−4662.55	−	7119.56i	−0.879656	−	1.34321i
$305$		−	7286.31i		−	1.36791i
$306$		0			0
$307$			3128.44i			0.581595i	0.956785	+	0.290797i	$0.0939206\pi$
$307$			3128.44i			0.581595i	−0.956785	+	0.290797i	$0.906079\pi$
$308$	−5553.28	+	1656.59i	−1.02736	+	0.306470i
$309$		0			0
$310$	4365.27	+	3253.17i	0.799777	+	0.596024i
$311$	8570.21			1.56261			0.781306	−	0.624149i	$-0.214554\pi$
$311$	8570.21			1.56261			0.781306	+	0.624149i	$0.214554\pi$
$312$		0			0
$313$	209.373			0.0378098			0.0189049	−	0.999821i	$-0.493982\pi$
$313$	209.373			0.0378098			0.0189049	+	0.999821i	$0.493982\pi$
$314$	−5917.06	−	4409.62i	−1.06344	−	0.792514i
$315$		0			0
$316$	9911.06	−	2956.54i	1.76437	−	0.526325i
$317$		−	2067.70i		−	0.366353i	−0.983080	−	0.183176i	$-0.941362\pi$
$317$		−	2067.70i		−	0.366353i	0.983080	−	0.183176i	$-0.0586380\pi$
$318$		0			0
$319$		−	3389.88i		−	0.594974i
$320$	5394.01	−	6389.90i	0.942295	−	1.11627i
$321$		0			0
$322$	−677.444	+	909.030i	−0.117244	+	0.157324i
$323$	3777.32			0.650698
$324$		0			0
$325$	−10621.5			−1.81284
$326$	−794.802	+	1066.51i	−0.135031	+	0.181191i
$327$		0			0
$328$	1776.36	+	649.516i	0.299034	+	0.109340i
$329$		−	12907.8i		−	2.16300i
$330$		0			0
$331$		−	3625.24i		−	0.601998i	−0.953624	−	0.300999i	$-0.902680\pi$
$331$		−	3625.24i		−	0.601998i	0.953624	−	0.300999i	$-0.0973201\pi$
$332$	−1015.73	−	3404.98i	−0.167908	−	0.562870i
$333$		0			0
$334$	3146.66	+	2345.01i	0.515501	+	0.384171i
$335$	−2131.09			−0.347564
$336$		0			0
$337$	8703.35			1.40683			0.703415	−	0.710780i	$-0.251658\pi$
$337$	8703.35			1.40683			0.703415	+	0.710780i	$0.251658\pi$
$338$	−7751.43	−	5776.66i	−1.24740	−	0.929612i
$339$		0			0
$340$	1060.97	+	3556.64i	0.169234	+	0.567312i
$341$			2970.86i			0.471793i
$342$		0			0
$343$		−	4015.67i		−	0.632146i
$344$	−923.303	−	337.600i	−0.144713	−	0.0529133i
$345$		0			0
$346$	3019.72	−	4052.02i	0.469194	−	0.629589i
$347$	1836.37			0.284096			0.142048	−	0.989860i	$-0.454631\pi$
$347$	1836.37			0.284096			0.142048	+	0.989860i	$0.454631\pi$
$348$		0			0
$349$	−4573.46			−0.701466			−0.350733	−	0.936476i	$-0.614068\pi$
$349$	−4573.46			−0.701466			−0.350733	+	0.936476i	$0.614068\pi$
$350$	−6884.30	+	9237.72i	−1.05138	+	1.41079i
$351$		0			0
$352$	4554.85	+	276.544i	0.689700	+	0.0418745i
$353$			9649.17i			1.45488i	0.686170	+	0.727441i	$0.259291\pi$
$353$			9649.17i			1.45488i	−0.686170	+	0.727441i	$0.740709\pi$
$354$		0			0
$355$		−	3426.79i		−	0.512325i
$356$	−8999.20	+	2684.53i	−1.33977	+	0.399663i
$357$		0			0
$358$	−2381.56	−	1774.83i	−0.351590	−	0.262018i
$359$	−7152.93			−1.05158			−0.525790	−	0.850614i	$-0.676230\pi$
$359$	−7152.93			−1.05158			−0.525790	+	0.850614i	$0.676230\pi$
$360$		0			0
$361$	−10823.5			−1.57800
$362$	6837.66	+	5095.68i	0.992760	+	0.739843i
$363$		0			0
$364$	−16507.1	+	4924.20i	−2.37694	+	0.709061i
$365$			2671.10i			0.383045i
$366$		0			0
$367$		−	3628.69i		−	0.516120i	−0.966129	−	0.258060i	$-0.916917\pi$
$367$		−	3628.69i		−	0.516120i	0.966129	−	0.258060i	$-0.0830833\pi$
$368$	746.810	−	489.080i	0.105788	−	0.0692801i
$369$		0			0
$370$	4544.65	−	6098.26i	0.638555	−	0.856847i
$371$	−162.950			−0.0228030
$372$		0			0
$373$	−1184.16			−0.164380			−0.0821898	−	0.996617i	$-0.526191\pi$
$373$	−1184.16			−0.164380			−0.0821898	+	0.996617i	$0.526191\pi$
$374$	−1210.27	+	1624.00i	−0.167330	+	0.224533i
$375$		0			0
$376$	−3490.39	+	9545.86i	−0.478731	+	1.30928i
$377$		−	10076.4i		−	1.37656i
$378$		0			0
$379$		−	7627.16i		−	1.03372i	−0.856069	−	0.516861i	$-0.827100\pi$
$379$		−	7627.16i		−	1.03372i	0.856069	−	0.516861i	$-0.172900\pi$
$380$	−4966.66	−	16649.5i	−0.670485	−	2.24763i
$381$		0			0
$382$	4251.21	+	3168.16i	0.569400	+	0.424339i
$383$	11069.3			1.47681			0.738403	−	0.674360i	$-0.235580\pi$
$383$	11069.3			1.47681			0.738403	+	0.674360i	$0.235580\pi$
$384$		0			0
$385$	−11831.0			−1.56614
$386$	2074.89	+	1546.28i	0.273598	+	0.203896i
$387$		0			0
$388$	1197.43	+	4014.09i	0.156676	+	0.525217i
$389$		−	10917.1i		−	1.42293i	−0.702720	−	0.711467i	$-0.748031\pi$
$389$		−	10917.1i		−	1.42293i	0.702720	−	0.711467i	$-0.251969\pi$
$390$		0			0
$391$			396.224i			0.0512478i
$392$	−3751.14	+	10259.0i	−0.483319	+	1.32183i
$393$		0			0
$394$	2417.52	−	3243.96i	0.309119	−	0.414793i
$395$	21115.0			2.68965
$396$		0			0
$397$	6630.04			0.838166			0.419083	−	0.907948i	$-0.362352\pi$
$397$	6630.04			0.838166			0.419083	+	0.907948i	$0.362352\pi$
$398$	3411.43	−	4577.64i	0.429647	−	0.576524i
$399$		0			0
$400$	7589.21	−	4970.12i	0.948651	−	0.621265i
$401$		−	500.859i		−	0.0623733i	−0.999514	−	0.0311866i	$-0.990071\pi$
$401$		−	500.859i		−	0.0623733i	0.999514	−	0.0311866i	$-0.00992863\pi$
$402$		0			0
$403$			8830.88i			1.09156i
$404$	6552.65	−	1954.70i	0.806946	−	0.240718i
$405$		0			0
$406$	−8763.66	−	6531.01i	−1.07126	−	0.798347i
$407$	4150.28			0.505459
$408$		0			0
$409$	−685.198			−0.0828383			−0.0414192	−	0.999142i	$-0.513188\pi$
$409$	−685.198			−0.0828383			−0.0414192	+	0.999142i	$0.513188\pi$
$410$	3096.15	+	2307.37i	0.372946	+	0.277934i
$411$		0			0
$412$	4896.69	−	1460.72i	0.585540	−	0.174671i
$413$			24046.6i			2.86502i
$414$		0			0
$415$		−	7254.15i		−	0.858054i
$416$	13539.3	+	822.025i	1.59572	+	0.0968824i
$417$		0			0
$418$	5665.55	−	7602.33i	0.662945	−	0.889575i
$419$	−8330.78			−0.971325			−0.485662	−	0.874146i	$-0.661422\pi$
$419$	−8330.78			−0.971325			−0.485662	+	0.874146i	$0.661422\pi$
$420$		0			0
$421$	13947.9			1.61467			0.807337	−	0.590091i	$-0.200908\pi$
$421$	13947.9			1.61467			0.807337	+	0.590091i	$0.200908\pi$
$422$	−945.459	+	1268.67i	−0.109062	+	0.146345i
$423$		0			0
$424$	120.508	+	44.0632i	0.0138029	+	0.00504693i
$425$			4026.49i			0.459561i
$426$		0			0
$427$		−	12819.8i		−	1.45291i
$428$	−2190.60	−	7343.44i	−0.247399	−	0.829343i
$429$		0			0
$430$	−1609.29	−	1199.30i	−0.180481	−	0.134501i
$431$	−7150.85			−0.799174			−0.399587	−	0.916695i	$-0.630847\pi$
$431$	−7150.85			−0.799174			−0.399587	+	0.916695i	$0.630847\pi$
$432$		0			0
$433$	15233.5			1.69071			0.845354	−	0.534207i	$-0.179390\pi$
$433$	15233.5			1.69071			0.845354	+	0.534207i	$0.179390\pi$
$434$	7680.41	+	5723.73i	0.849473	+	0.633060i
$435$		0			0
$436$	3362.98	+	11273.5i	0.369398	+	1.23831i
$437$		−	1854.81i		−	0.203038i
$438$		0			0
$439$		−	15988.2i		−	1.73821i	−0.494629	−	0.869104i	$-0.664696\pi$
$439$		−	15988.2i		−	1.73821i	0.494629	−	0.869104i	$-0.335304\pi$
$440$	8749.54	+	3199.22i	0.947995	+	0.346629i
$441$		0			0
$442$	−3597.52	+	4827.34i	−0.387142	+	0.519487i
$443$	−2083.25			−0.223427			−0.111713	−	0.993740i	$-0.535634\pi$
$443$	−2083.25			−0.223427			−0.111713	+	0.993740i	$0.535634\pi$
$444$		0			0
$445$	−19172.4			−2.04238
$446$	4930.70	−	6616.28i	0.523488	−	0.702444i
$447$		0			0
$448$	9490.41	−	11242.6i	1.00085	−	1.18563i
$449$		−	10985.2i		−	1.15462i	−0.816526	−	0.577308i	$-0.804103\pi$
$449$		−	10985.2i		−	1.15462i	0.816526	−	0.577308i	$-0.195897\pi$
$450$		0			0
$451$			2107.14i			0.220003i
$452$	−7123.77	+	2125.07i	−0.741314	+	0.221140i
$453$		0			0
$454$	−12402.9	−	9243.15i	−1.28216	−	0.955512i
$455$	−35167.6			−3.62348
$456$		0			0
$457$	12613.3			1.29108			0.645542	−	0.763724i	$-0.276631\pi$
$457$	12613.3			1.29108			0.645542	+	0.763724i	$0.276631\pi$
$458$	8869.62	+	6609.98i	0.904913	+	0.674375i
$459$		0			0
$460$	1746.45	−	520.981i	0.177019	−	0.0528062i
$461$			9242.85i			0.933802i	0.884310	+	0.466901i	$0.154630\pi$
$461$			9242.85i			0.933802i	−0.884310	+	0.466901i	$0.845370\pi$
$462$		0			0
$463$			8998.82i			0.903263i	0.892205	+	0.451632i	$0.149158\pi$
$463$			8998.82i			0.903263i	−0.892205	+	0.451632i	$0.850842\pi$
$464$	4715.06	+	7199.75i	0.471748	+	0.720345i
$465$		0			0
$466$	−172.415	+	231.356i	−0.0171394	+	0.0229986i
$467$	−7921.96			−0.784978			−0.392489	−	0.919757i	$-0.628386\pi$
$467$	−7921.96			−0.784978			−0.392489	+	0.919757i	$0.628386\pi$
$468$		0			0
$469$	−3749.52			−0.369161
$470$	−12399.4	+	16638.2i	−1.21690	+	1.63290i
$471$		0			0
$472$	6502.42	−	17783.5i	0.634106	−	1.73422i
$473$		−	1095.23i		−	0.106467i
$474$		0			0
$475$		−	18848.9i		−	1.82073i
$476$	1866.71	+	6257.68i	0.179749	+	0.602563i
$477$		0			0
$478$	−12814.0	−	9549.45i	−1.22614	−	0.913769i
$479$	−12970.5			−1.23724			−0.618619	−	0.785691i	$-0.712308\pi$
$479$	−12970.5			−1.23724			−0.618619	+	0.785691i	$0.712308\pi$
$480$		0			0
$481$	12336.7			1.16945
$482$	−10279.1	−	7660.35i	−0.971366	−	0.723899i
$483$		0			0
$484$	−1590.59	−	5332.03i	−0.149379	−	0.500754i
$485$			8551.82i			0.800656i
$486$		0			0
$487$			17968.0i			1.67188i	0.548820	+	0.835941i	$0.315077\pi$
$487$			17968.0i			1.67188i	−0.548820	+	0.835941i	$0.684923\pi$
$488$	−3466.59	+	9480.79i	−0.321568	+	0.879457i
$489$		0			0
$490$	−13325.7	+	17881.1i	−1.22856	+	1.64854i
$491$	−3141.82			−0.288774			−0.144387	−	0.989521i	$-0.546121\pi$
$491$	−3141.82			−0.288774			−0.144387	+	0.989521i	$0.546121\pi$
$492$		0			0
$493$	−3819.86			−0.348961
$494$	16840.8	−	22597.9i	1.53381	−	2.05815i
$495$		0			0
$496$	−4132.24	−	6309.81i	−0.374079	−	0.571207i
$497$		−	6029.22i		−	0.544160i
$498$		0			0
$499$			17629.0i			1.58153i	0.612120	+	0.790765i	$0.290317\pi$
$499$			17629.0i			1.58153i	−0.612120	+	0.790765i	$0.709683\pi$
$500$	2096.89	−	625.519i	0.187552	−	0.0559481i
$501$		0			0
$502$	4461.11	+	3324.59i	0.396632	+	0.295585i
$503$	19916.6			1.76548			0.882742	−	0.469857i	$-0.155695\pi$
$503$	19916.6			1.76548			0.882742	+	0.469857i	$0.155695\pi$
$504$		0			0
$505$	13960.1			1.23013
$506$	797.451	+	594.291i	0.0700613	+	0.0522123i
$507$		0			0
$508$	11521.6	−	3436.99i	1.00628	−	0.300181i
$509$			12378.1i			1.07790i	0.842339	+	0.538948i	$0.181178\pi$
$509$			12378.1i			1.07790i	−0.842339	+	0.538948i	$0.818822\pi$
$510$		0			0
$511$			4699.61i			0.406847i
$512$	−10058.7	+	5748.10i	−0.868233	+	0.496157i
$513$		0			0
$514$	2734.93	−	3669.88i	0.234694	−	0.314925i
$515$	10432.2			0.892613
$516$		0			0
$517$	−11323.4			−0.963254
$518$	7996.02	−	10729.5i	0.678233	−	0.910089i
$519$		0			0
$520$	26008.0	+	9509.66i	2.19332	+	0.801973i
$521$		−	7958.58i		−	0.669236i	−0.942354	−	0.334618i	$-0.891393\pi$
$521$		−	7958.58i		−	0.669236i	0.942354	−	0.334618i	$-0.108607\pi$
$522$		0			0
$523$			14041.6i			1.17399i	0.809590	+	0.586995i	$0.199689\pi$
$523$			14041.6i			1.17399i	−0.809590	+	0.586995i	$0.800311\pi$
$524$	−4391.23	−	14720.5i	−0.366091	−	1.22723i
$525$		0			0
$526$	−10602.2	−	7901.19i	−0.878858	−	0.654959i
$527$	3347.70			0.276713
$528$		0			0
$529$	−11972.4			−0.984009
$530$	210.043	+	156.532i	0.0172145	+	0.0128289i
$531$		0			0
$532$	−8738.51	−	29293.6i	−0.712148	−	2.38729i
$533$			6263.47i			0.509007i
$534$		0			0
$535$		−	15644.8i		−	1.26427i
$536$	2772.93	+	1013.91i	0.223456	+	0.0817053i
$537$		0			0
$538$	−5981.27	+	8025.99i	−0.479314	+	0.643169i
$539$	−12169.3			−0.972485
$540$		0			0
$541$	3818.43			0.303451			0.151726	−	0.988423i	$-0.451517\pi$
$541$	3818.43			0.303451			0.151726	+	0.988423i	$0.451517\pi$
$542$	539.304	−	723.667i	0.0427400	−	0.0573508i
$543$		0			0
$544$	311.621	−	5132.60i	0.0245600	−	0.404519i
$545$			24017.7i			1.88772i
$546$		0			0
$547$		−	7896.31i		−	0.617225i	−0.951188	−	0.308612i	$-0.900135\pi$
$547$		−	7896.31i		−	0.617225i	0.951188	−	0.308612i	$-0.0998645\pi$
$548$	3833.29	−	1143.50i	0.298814	−	0.0891385i
$549$		0			0
$550$	8103.83	+	6039.28i	0.628270	+	0.468211i
$551$	17881.7			1.38255
$552$		0			0
$553$	37150.5			2.85678
$554$	−11634.2	−	8670.23i	−0.892218	−	0.664915i
$555$		0			0
$556$	−5505.70	+	1642.39i	−0.419953	+	0.125275i
$557$			18190.9i			1.38379i	0.721996	+	0.691897i	$0.243225\pi$
$557$			18190.9i			1.38379i	−0.721996	+	0.691897i	$0.756775\pi$
$558$		0			0
$559$		−	3255.57i		−	0.246326i
$560$	25127.8	−	16456.0i	1.89615	−	1.24177i
$561$		0			0
$562$	−4511.62	+	6053.93i	−0.338632	+	0.454394i
$563$	−4821.74			−0.360945			−0.180473	−	0.983580i	$-0.557763\pi$
$563$	−4821.74			−0.360945			−0.180473	+	0.983580i	$0.557763\pi$
$564$		0			0
$565$	−15176.8			−1.13008
$566$	2929.31	−	3930.71i	0.217541	−	0.291908i
$567$		0			0
$568$	−1630.36	+	4458.87i	−0.120437	+	0.329384i
$569$			7625.95i			0.561857i	0.959729	+	0.280928i	$0.0906423\pi$
$569$			7625.95i			0.561857i	−0.959729	+	0.280928i	$0.909358\pi$
$570$		0			0
$571$		−	16062.5i		−	1.17722i	−0.808416	−	0.588612i	$-0.799675\pi$
$571$		−	16062.5i		−	1.17722i	0.808416	−	0.588612i	$-0.200325\pi$
$572$	4319.77	+	14480.9i	0.315767	+	1.05853i
$573$		0			0
$574$	5447.47	+	4059.66i	0.396120	+	0.295204i
$575$	1977.17			0.143398
$576$		0			0
$577$	9185.17			0.662710			0.331355	−	0.943506i	$-0.392494\pi$
$577$	9185.17			0.662710			0.331355	+	0.943506i	$0.392494\pi$
$578$	−9312.27	−	6939.86i	−0.670137	−	0.499412i
$579$		0			0
$580$	5022.60	+	16837.0i	0.359573	+	1.20538i
$581$		−	12763.2i		−	0.911371i
$582$		0			0
$583$			142.948i			0.0101549i
$584$	1270.82	−	3475.57i	0.0900462	−	0.246267i
$585$		0			0
$586$	6999.48	−	9392.27i	0.493423	−	0.662101i
$587$	−24311.5			−1.70944			−0.854721	−	0.519087i	$-0.826272\pi$
$587$	−24311.5			−1.70944			−0.854721	+	0.519087i	$0.826272\pi$
$588$		0			0
$589$	−15671.3			−1.09631
$590$	23099.5	−	30996.1i	1.61185	−	2.16286i
$591$		0			0
$592$	−8814.76	+	5772.72i	−0.611967	+	0.400773i
$593$			17807.1i			1.23314i	0.787302	+	0.616568i	$0.211477\pi$
$593$			17807.1i			1.23314i	−0.787302	+	0.616568i	$0.788523\pi$
$594$		0			0
$595$			13331.7i			0.918564i
$596$	26689.0	−	7961.52i	1.83427	−	0.547175i
$597$		0			0
$598$	2370.42	+	1766.53i	0.162096	+	0.120800i
$599$	3443.89			0.234914			0.117457	−	0.993078i	$-0.462526\pi$
$599$	3443.89			0.234914			0.117457	+	0.993078i	$0.462526\pi$
$600$		0			0
$601$	1463.61			0.0993373			0.0496687	−	0.998766i	$-0.484183\pi$
$601$	1463.61			0.0993373			0.0496687	+	0.998766i	$0.484183\pi$
$602$	−2831.44	−	2110.10i	−0.191696	−	0.142859i
$603$		0			0
$604$	15366.4	−	4583.90i	1.03518	−	0.308802i
$605$		−	11359.6i		−	0.763363i
$606$		0			0
$607$		−	8989.33i		−	0.601097i	−0.953767	−	0.300548i	$-0.902830\pi$
$607$		−	8989.33i		−	0.601097i	0.953767	−	0.300548i	$-0.0971697\pi$
$608$	−1458.77	+	24026.9i	−0.0973042	+	1.60266i
$609$		0			0
$610$	−12314.9	+	16524.7i	−0.817400	+	1.09683i
$611$	−33658.7			−2.22862
$612$		0			0
$613$	−27489.4			−1.81124			−0.905619	−	0.424093i	$-0.860593\pi$
$613$	−27489.4			−1.81124			−0.905619	+	0.424093i	$0.860593\pi$
$614$	5287.49	−	7095.04i	0.347534	−	0.466340i
$615$		0			0
$616$	15394.2	+	5628.81i	1.00690	+	0.368168i
$617$		−	16826.3i		−	1.09789i	−0.835857	−	0.548947i	$-0.815029\pi$
$617$		−	16826.3i		−	1.09789i	0.835857	−	0.548947i	$-0.184971\pi$
$618$		0			0
$619$			4809.44i			0.312290i	0.987734	+	0.156145i	$0.0499067\pi$
$619$			4809.44i			0.312290i	−0.987734	+	0.156145i	$0.950093\pi$
$620$	−4401.77	−	14755.8i	−0.285128	−	0.955819i
$621$		0			0
$622$	−19436.5	−	14484.8i	−1.25295	−	0.933744i
$623$	−33732.5			−2.16928
$624$		0			0
$625$	−13251.1			−0.848070
$626$	−474.840	−	353.869i	−0.0303170	−	0.0225933i
$627$		0			0
$628$	5966.54	+	20001.3i	0.379125	+	1.27092i
$629$		−	4676.71i		−	0.296459i
$630$		0			0
$631$			1519.28i			0.0958501i	0.998851	+	0.0479250i	$0.0152609\pi$
$631$			1519.28i			0.0958501i	−0.998851	+	0.0479250i	$0.984739\pi$
$632$	−27474.4	−	10045.9i	−1.72923	−	0.632282i
$633$		0			0
$634$	−3494.70	+	4689.38i	−0.218915	+	0.293752i
$635$	24546.3			1.53400
$636$		0			0
$637$	−36173.2			−2.24998
$638$	−5729.36	+	7687.96i	−0.355529	+	0.477068i
$639$		0			0
$640$	−23033.0	+	5375.13i	−1.42259	+	0.331986i
$641$			25895.1i			1.59563i	0.602905	+	0.797813i	$0.294010\pi$
$641$			25895.1i			1.59563i	−0.602905	+	0.797813i	$0.705990\pi$
$642$		0			0
$643$			13730.8i			0.842128i	0.907031	+	0.421064i	$0.138343\pi$
$643$			13730.8i			0.842128i	−0.907031	+	0.421064i	$0.861657\pi$
$644$	3072.77	−	916.631i	0.188019	−	0.0560874i
$645$		0			0
$646$	−8566.64	−	6384.18i	−0.521749	−	0.388827i
$647$	−2661.25			−0.161707			−0.0808537	−	0.996726i	$-0.525765\pi$
$647$	−2661.25			−0.161707			−0.0808537	+	0.996726i	$0.525765\pi$
$648$		0			0
$649$	21094.9			1.27588
$650$	24088.6	+	17951.7i	1.45359	+	1.08327i
$651$		0			0
$652$	3605.08	−	1075.42i	0.216543	−	0.0645964i
$653$		−	3829.74i		−	0.229509i	−0.993394	−	0.114754i	$-0.963392\pi$
$653$		−	3829.74i		−	0.229509i	0.993394	−	0.114754i	$-0.0366081\pi$
$654$		0			0
$655$		−	31361.3i		−	1.87082i
$656$	−2930.87	−	4475.34i	−0.174438	−	0.266361i
$657$		0			0
$658$	−21815.9	+	29273.7i	−1.29251	+	1.73436i
$659$	3096.41			0.183033			0.0915166	−	0.995804i	$-0.470829\pi$
$659$	3096.41			0.183033			0.0915166	+	0.995804i	$0.470829\pi$
$660$		0			0
$661$	−2973.62			−0.174978			−0.0874890	−	0.996165i	$-0.527884\pi$
$661$	−2973.62			−0.174978			−0.0874890	+	0.996165i	$0.527884\pi$
$662$	−6127.15	+	8221.74i	−0.359726	+	0.482699i
$663$		0			0
$664$	−3451.29	+	9438.94i	−0.201711	+	0.551660i
$665$		−	62408.6i		−	3.63925i
$666$		0			0
$667$			1875.71i			0.108887i
$668$	−3172.97	−	10636.6i	−0.183781	−	0.616079i
$669$		0			0
$670$	4833.14	+	3601.84i	0.278687	+	0.207688i
$671$	−11246.2			−0.647027
$672$		0			0
$673$	−11999.8			−0.687307			−0.343653	−	0.939097i	$-0.611665\pi$
$673$	−11999.8			−0.687307			−0.343653	+	0.939097i	$0.611665\pi$
$674$	−19738.4	−	14709.8i	−1.12804	−	0.840656i
$675$		0			0
$676$	7816.24	+	26201.9i	0.444711	+	1.49078i
$677$		−	12465.0i		−	0.707633i	−0.935315	−	0.353817i	$-0.884884\pi$
$677$		−	12465.0i		−	0.707633i	0.935315	−	0.353817i	$-0.115116\pi$
$678$		0			0
$679$			15046.3i			0.850406i
$680$	3605.01	−	9859.36i	0.203303	−	0.556013i
$681$		0			0
$682$	5021.17	−	6737.67i	0.281921	−	0.378297i
$683$	−27869.9			−1.56136			−0.780682	−	0.624928i	$-0.785128\pi$
$683$	−27869.9			−1.56136			−0.780682	+	0.624928i	$0.785128\pi$
$684$		0			0
$685$	8166.64			0.455520
$686$	−6787.04	+	9107.21i	−0.377741	+	0.506873i
$687$		0			0
$688$	1523.38	+	2326.16i	0.0844163	+	0.128901i
$689$			424.914i			0.0234948i
$690$		0			0
$691$			10519.7i			0.579143i	0.957156	+	0.289571i	$0.0935127\pi$
$691$			10519.7i			0.579143i	−0.957156	+	0.289571i	$0.906487\pi$
$692$	−13696.9	+	4085.90i	−0.752427	+	0.224455i
$693$		0			0
$694$	−4164.73	−	3103.71i	−0.227797	−	0.169763i
$695$	−11729.6			−0.640187
$696$		0			0
$697$	2374.42			0.129035
$698$	10372.2	+	7729.77i	0.562456	+	0.419163i
$699$		0			0
$700$	31226.0	−	9314.96i	1.68605	−	0.502960i
$701$			30219.3i			1.62820i	0.580726	+	0.814099i	$0.302769\pi$
$701$			30219.3i			1.62820i	−0.580726	+	0.814099i	$0.697231\pi$
$702$		0			0
$703$			21892.8i			1.17454i
$704$	−9862.62	−	8325.50i	−0.527999	−	0.445709i
$705$		0			0
$706$	16308.4	−	21883.5i	0.869370	−	1.16657i
$707$	24561.9			1.30657
$708$		0			0
$709$	11964.2			0.633744			0.316872	−	0.948468i	$-0.397367\pi$
$709$	11964.2			0.633744			0.316872	+	0.948468i	$0.397367\pi$
$710$	−5791.75	+	7771.68i	−0.306142	+	0.410797i
$711$		0			0
$712$	24946.7	+	9121.59i	1.31308	+	0.480121i
$713$		−	1643.85i		−	0.0863433i
$714$		0			0
$715$			30850.9i			1.61365i
$716$	2401.47	+	8050.32i	0.125345	+	0.420188i
$717$		0			0
$718$	16222.2	+	12089.4i	0.843188	+	0.628376i
$719$	4225.51			0.219172			0.109586	−	0.993977i	$-0.465047\pi$
$719$	4225.51			0.219172			0.109586	+	0.993977i	$0.465047\pi$
$720$		0			0
$721$	18354.7			0.948078
$722$	24546.8	+	18293.2i	1.26529	+	0.942939i
$723$		0			0
$724$	−6894.83	−	23113.1i	−0.353928	−	1.18645i
$725$			19061.2i			0.976437i
$726$		0			0
$727$			11508.9i			0.587128i	0.955939	+	0.293564i	$0.0948413\pi$
$727$			11508.9i			0.587128i	−0.955939	+	0.293564i	$0.905159\pi$
$728$	45759.3	+	16731.6i	2.32961	+	0.851806i
$729$		0			0
$730$	4514.52	−	6057.82i	0.228890	−	0.307137i
$731$	−1234.15			−0.0624443
$732$		0			0
$733$	4536.67			0.228602			0.114301	−	0.993446i	$-0.463537\pi$
$733$	4536.67			0.228602			0.114301	+	0.993446i	$0.463537\pi$
$734$	−6132.98	+	8229.56i	−0.308409	+	0.413840i
$735$		0			0
$736$	−2520.31	−	153.018i	−0.126223	−	0.00766350i
$737$			3289.28i			0.164399i
$738$		0			0
$739$			7388.95i			0.367804i	0.982945	+	0.183902i	$0.0588728\pi$
$739$			7388.95i			0.367804i	−0.982945	+	0.183902i	$0.941127\pi$
$740$	−20613.8	+	6149.25i	−1.02402	+	0.305474i
$741$		0			0
$742$	369.556	+	275.407i	0.0182841	+	0.0136260i
$743$	−1185.60			−0.0585402			−0.0292701	−	0.999572i	$-0.509318\pi$
$743$	−1185.60			−0.0585402			−0.0292701	+	0.999572i	$0.509318\pi$
$744$		0			0
$745$	56859.5			2.79620
$746$	2685.58	+	2001.40i	0.131804	+	0.0982256i
$747$		0			0
$748$	5489.57	−	1637.58i	0.268341	−	0.0800480i
$749$		−	27526.1i		−	1.34283i
$750$		0			0
$751$		−	16788.0i		−	0.815718i	−0.913045	−	0.407859i	$-0.866276\pi$
$751$		−	16788.0i		−	0.815718i	0.913045	−	0.407859i	$-0.133724\pi$
$752$	24049.7	−	15750.0i	1.16623	−	0.763753i
$753$		0			0
$754$	−17030.5	+	22852.4i	−0.822565	+	1.10376i
$755$	32737.3			1.57806
$756$		0			0
$757$	−18854.0			−0.905230			−0.452615	−	0.891706i	$-0.649509\pi$
$757$	−18854.0			−0.905230			−0.452615	+	0.891706i	$0.649509\pi$
$758$	−12890.9	+	17297.7i	−0.617704	+	0.828869i
$759$		0			0
$760$	−16875.9	+	46153.9i	−0.805465	+	2.20287i
$761$			28006.1i			1.33406i	0.745030	+	0.667031i	$0.232435\pi$
$761$			28006.1i			1.33406i	−0.745030	+	0.667031i	$0.767565\pi$
$762$		0			0
$763$			42257.5i			2.00501i
$764$	−4286.76	−	14370.3i	−0.202997	−	0.680494i
$765$		0			0
$766$	−25104.3	−	18708.7i	−1.18415	−	0.882470i
$767$	62704.6			2.95193
$768$		0			0
$769$	−16324.7			−0.765517			−0.382759	−	0.923848i	$-0.625026\pi$
$769$	−16324.7			−0.765517			−0.382759	+	0.923848i	$0.625026\pi$
$770$	26831.7	+	19996.0i	1.25578	+	0.935852i
$771$		0			0
$772$	−2092.23	−	7013.68i	−0.0975404	−	0.326979i
$773$		−	10017.2i		−	0.466100i	−0.972465	−	0.233050i	$-0.925129\pi$
$773$		−	10017.2i		−	0.466100i	0.972465	−	0.233050i	$-0.0748706\pi$
$774$		0			0
$775$		−	16705.1i		−	0.774278i
$776$	4068.68	−	11127.4i	0.188218	−	0.514757i
$777$		0			0
$778$	−18451.5	+	24759.2i	−0.850279	+	1.14095i
$779$	−11115.2			−0.511223
$780$		0			0
$781$	−5289.16			−0.242331
$782$	669.672	−	898.602i	0.0306233	−	0.0410920i
$783$		0			0
$784$	25846.3	−	16926.6i	1.17740	−	0.771072i
$785$			42611.8i			1.93743i
$786$		0			0
$787$			5638.43i			0.255386i	0.991814	+	0.127693i	$0.0407572\pi$
$787$			5638.43i			0.255386i	−0.991814	+	0.127693i	$0.959243\pi$
$788$	−10965.5	+	3271.08i	−0.495722	+	0.147878i
$789$		0			0
$790$	−47887.1	−	35687.3i	−2.15664	−	1.60721i
$791$	−26702.6			−1.20030
$792$		0			0
$793$	−33429.3			−1.49699
$794$	−15036.4	−	11205.7i	−0.672066	−	0.500849i
$795$		0			0
$796$	−15473.7	+	4615.91i	−0.689007	+	0.205536i
$797$		−	8971.06i		−	0.398709i	−0.979927	−	0.199355i	$-0.936115\pi$
$797$		−	8971.06i		−	0.398709i	0.979927	−	0.199355i	$-0.0638845\pi$
$798$		0			0
$799$			12759.7i			0.564963i
$800$	−25611.9	−	1555.00i	−1.13189	−	0.0687219i
$801$		0			0
$802$	−846.519	+	1135.90i	−0.0372714	+	0.0500127i
$803$	4122.76			0.181182
$804$		0			0
$805$	6546.39			0.286621
$806$	14925.4	−	20027.7i	0.652264	−	0.875242i
$807$		0			0
$808$	−18164.6	−	6641.76i	−0.790875	−	0.289179i
$809$			17977.5i			0.781282i	0.920543	+	0.390641i	$0.127747\pi$
$809$			17977.5i			0.781282i	−0.920543	+	0.390641i	$0.872253\pi$
$810$		0			0
$811$		−	22820.8i		−	0.988095i	−0.869435	−	0.494048i	$-0.835517\pi$
$811$		−	22820.8i		−	0.988095i	0.869435	−	0.494048i	$-0.164483\pi$
$812$	8836.94	+	29623.6i	0.381916	+	1.28028i
$813$		0			0
$814$	−9412.48	−	7014.54i	−0.405292	−	0.302039i
$815$	7680.46			0.330104
$816$		0			0
$817$	5777.36			0.247398
$818$	1553.97	+	1158.08i	0.0664222	+	0.0495003i
$819$		0			0
$820$	−3122.04	−	10465.8i	−0.132959	−	0.445710i
$821$		−	33659.1i		−	1.43083i	−0.698701	−	0.715414i	$-0.746238\pi$
$821$		−	33659.1i		−	1.43083i	0.698701	−	0.715414i	$-0.253762\pi$
$822$		0			0
$823$		−	16220.2i		−	0.687001i	−0.939152	−	0.343501i	$-0.888387\pi$
$823$		−	16220.2i		−	0.687001i	0.939152	−	0.343501i	$-0.111613\pi$
$824$	−13574.1	−	4963.28i	−0.573878	−	0.209835i
$825$		0			0
$826$	40642.0	−	54535.5i	1.71200	−	2.29726i
$827$	25875.9			1.08802			0.544010	−	0.839078i	$-0.316905\pi$
$827$	25875.9			1.08802			0.544010	+	0.839078i	$0.316905\pi$
$828$		0			0
$829$	4852.05			0.203279			0.101640	−	0.994821i	$-0.467591\pi$
$829$	4852.05			0.203279			0.101640	+	0.994821i	$0.467591\pi$
$830$	−12260.5	+	16451.8i	−0.512733	+	0.688012i
$831$		0			0
$832$	−29316.6	−	24747.5i	−1.22160	−	1.03121i
$833$			13712.9i			0.570377i
$834$		0			0
$835$		−	22660.7i		−	0.939168i
$836$	−25698.0	+	7665.90i	−1.06314	+	0.317142i
$837$		0			0
$838$	18893.5	+	14080.1i	0.778836	+	0.580418i
$839$	10799.9			0.444402			0.222201	−	0.975001i	$-0.428676\pi$
$839$	10799.9			0.444402			0.222201	+	0.975001i	$0.428676\pi$
$840$		0			0
$841$	6305.94			0.258557
$842$	−31632.6	−	23573.8i	−1.29469	−	0.964854i
$843$		0			0
$844$	4288.44	−	1279.28i	0.174898	−	0.0521735i
$845$			55822.0i			2.27258i
$846$		0			0
$847$		−	19986.5i		−	0.810797i
$848$	−198.830	−	303.607i	−0.00805172	−	0.0122947i
$849$		0			0
$850$	6805.32	−	9131.74i	0.274612	−	0.368490i
$851$	−2296.45			−0.0925046
$852$		0			0
$853$	−2346.64			−0.0941939			−0.0470970	−	0.998890i	$-0.514997\pi$
$853$	−2346.64			−0.0941939			−0.0470970	+	0.998890i	$0.514997\pi$
$854$	−21667.2	+	29074.2i	−0.868192	+	1.16499i
$855$		0			0
$856$	−7443.31	+	20356.7i	−0.297205	+	0.812825i
$857$			36754.7i			1.46501i	0.680761	+	0.732506i	$0.261649\pi$
$857$			36754.7i			1.46501i	−0.680761	+	0.732506i	$0.738351\pi$
$858$		0			0
$859$		−	1569.67i		−	0.0623475i	−0.999514	−	0.0311737i	$-0.990075\pi$
$859$		−	1569.67i		−	0.0623475i	0.999514	−	0.0311737i	$-0.00992452\pi$
$860$	1622.75	+	5439.84i	0.0643432	+	0.215694i
$861$		0			0
$862$	16217.5	+	12085.9i	0.640801	+	0.477549i
$863$	38951.9			1.53643			0.768215	−	0.640192i	$-0.221145\pi$
$863$	38951.9			1.53643			0.768215	+	0.640192i	$0.221145\pi$
$864$		0			0
$865$	−29180.6			−1.14702
$866$	−34548.3	−	25746.7i	−1.35566	−	1.01029i
$867$		0			0
$868$	−7744.62	−	25961.9i	−0.302845	−	1.01521i
$869$		−	32590.4i		−	1.27221i
$870$		0			0
$871$			9777.37i			0.380360i
$872$	11426.9	−	31251.3i	0.443764	−	1.21365i
$873$		0			0
$874$	−3134.89	+	4206.56i	−0.121326	+	0.162802i
$875$	7859.96			0.303675
$876$		0			0
$877$	15187.5			0.584772			0.292386	−	0.956300i	$-0.405551\pi$
$877$	15187.5			0.584772			0.292386	+	0.956300i	$0.405551\pi$
$878$	−27022.2	+	36259.8i	−1.03867	+	1.39375i
$879$		0			0
$880$	−14436.1	−	22043.5i	−0.553001	−	0.844415i
$881$		−	40482.4i		−	1.54811i	−0.633118	−	0.774055i	$-0.718225\pi$
$881$		−	40482.4i		−	1.54811i	0.633118	−	0.774055i	$-0.281775\pi$
$882$		0			0
$883$			6705.26i			0.255549i	0.991803	+	0.127775i	$0.0407834\pi$
$883$			6705.26i			0.255549i	−0.991803	+	0.127775i	$0.959217\pi$
$884$	16317.7	−	4867.71i	0.620843	−	0.185202i
$885$		0			0
$886$	4724.63	+	3520.97i	0.179150	+	0.133510i
$887$	3567.45			0.135043			0.0675215	−	0.997718i	$-0.478491\pi$
$887$	3567.45			0.135043			0.0675215	+	0.997718i	$0.478491\pi$
$888$		0			0
$889$	43187.5			1.62932
$890$	43481.3	+	32403.9i	1.63764	+	1.22043i
$891$		0			0
$892$	−22364.8	+	6671.60i	−0.839496	+	0.250428i
$893$		−	59731.0i		−	2.23832i
$894$		0			0
$895$			17150.8i			0.640545i
$896$	−40525.0	+	9457.19i	−1.51099	+	0.352614i
$897$		0			0
$898$	−18566.5	+	24913.5i	−0.689945	+	0.925805i
$899$	15847.9			0.587937
$900$		0			0
$901$	161.080			0.00595601
$902$	3561.35	−	4778.81i	0.131464	−	0.176405i
$903$		0			0
$904$	19747.8	+	7220.65i	0.726550	+	0.265659i
$905$		−	49241.4i		−	1.80866i
$906$		0			0
$907$		−	24925.1i		−	0.912487i	−0.889855	−	0.456243i	$-0.849195\pi$
$907$		−	24925.1i		−	0.912487i	0.889855	−	0.456243i	$-0.150805\pi$
$908$	12506.7	+	41925.4i	0.457101	+	1.53231i
$909$		0			0
$910$	79757.1	+	59438.0i	2.90541	+	2.16522i
$911$	−5019.02			−0.182533			−0.0912664	−	0.995827i	$-0.529091\pi$
$911$	−5019.02			−0.182533			−0.0912664	+	0.995827i	$0.529091\pi$
$912$		0			0
$913$	−11196.6			−0.405862
$914$	−28605.9	−	21318.2i	−1.03523	−	0.771492i
$915$		0			0
$916$	−8943.78	−	29981.7i	−0.322610	−	1.08147i
$917$		−	55178.0i		−	1.98707i
$918$		0			0
$919$		−	40328.5i		−	1.44757i	−0.690027	−	0.723784i	$-0.742401\pi$
$919$		−	40328.5i		−	1.44757i	0.690027	−	0.723784i	$-0.257599\pi$
$920$	−4841.34	−	1770.21i	−0.173494	−	0.0634369i
$921$		0			0
$922$	15621.7	−	20962.0i	0.557997	−	0.748749i
$923$	−15722.0			−0.560667
$924$		0			0
$925$	−23337.0			−0.829529
$926$	15209.2	−	20408.6i	0.539748	−	0.724263i
$927$		0			0
$928$	1475.20	−	24297.5i	0.0521830	−	0.859488i
$929$		−	7714.26i		−	0.272440i	−0.990679	−	0.136220i	$-0.956505\pi$
$929$		−	7714.26i		−	0.272440i	0.990679	−	0.136220i	$-0.0434954\pi$
$930$		0			0
$931$		−	64193.2i		−	2.25977i
$932$	782.046	−	233.290i	0.0274858	−	0.00819923i
$933$		0			0
$934$	17966.3	+	13389.2i	0.629418	+	0.469066i
$935$	11695.3			0.409065
$936$		0			0
$937$	3225.39			0.112453			0.0562267	−	0.998418i	$-0.482093\pi$
$937$	3225.39			0.112453			0.0562267	+	0.998418i	$0.482093\pi$
$938$	8503.58	+	6337.19i	0.296004	+	0.220594i
$939$		0			0
$940$	56241.5	−	16777.3i	1.95148	−	0.582143i
$941$			1577.19i			0.0546385i	0.999627	+	0.0273193i	$0.00869707\pi$
$941$			1577.19i			0.0546385i	−0.999627	+	0.0273193i	$0.991303\pi$
$942$		0			0
$943$		−	1165.93i		−	0.0402630i
$944$	−44803.4	+	29341.4i	−1.54473	+	1.01163i
$945$		0			0
$946$	−1851.09	+	2483.89i	−0.0636196	+	0.0853682i
$947$	−15469.4			−0.530822			−0.265411	−	0.964135i	$-0.585508\pi$
$947$	−15469.4			−0.530822			−0.265411	+	0.964135i	$0.585508\pi$
$948$		0			0
$949$	12254.9			0.419189
$950$	−31857.3	+	42747.8i	−1.08799	+	1.45992i
$951$		0			0
$952$	6342.78	−	17346.9i	0.215936	−	0.590563i
$953$		−	18386.7i		−	0.624979i	−0.949921	−	0.312489i	$-0.898837\pi$
$953$		−	18386.7i		−	0.624979i	0.949921	−	0.312489i	$-0.101163\pi$
$954$		0			0
$955$		−	30615.1i		−	1.03736i
$956$	12921.1	+	43314.7i	0.437132	+	1.46537i
$957$		0			0
$958$	29416.0	+	21921.9i	0.992054	+	0.739316i
$959$	14368.7			0.483825
$960$		0			0
$961$	15902.1			0.533788
$962$	−27978.6	−	20850.7i	−0.937698	−	0.698808i
$963$		0			0
$964$	10365.0	+	34746.0i	0.346301	+	1.16089i
$965$		−	14942.3i		−	0.498456i
$966$		0			0
$967$			39747.2i			1.32180i	0.750472	+	0.660902i	$0.229826\pi$
$967$			39747.2i			1.32180i	−0.750472	+	0.660902i	$0.770174\pi$
$968$	−5404.55	+	14780.9i	−0.179451	+	0.490781i
$969$		0			0
$970$	14453.7	−	19394.8i	0.478434	−	0.641989i
$971$	−3005.74			−0.0993396			−0.0496698	−	0.998766i	$-0.515817\pi$
$971$	−3005.74			−0.0993396			−0.0496698	+	0.998766i	$0.515817\pi$
$972$		0			0
$973$	−20637.5			−0.679967
$974$	30368.3	−	40749.8i	0.999038	−	1.34056i
$975$		0			0
$976$	23885.8	−	15642.6i	0.783366	−	0.513020i
$977$		−	27553.3i		−	0.902261i	−0.892458	−	0.451130i	$-0.851021\pi$
$977$		−	27553.3i		−	0.902261i	0.892458	−	0.451130i	$-0.148979\pi$
$978$		0			0
$979$			29592.0i			0.966051i
$980$	60443.0	−	18030.6i	1.97019	−	0.587721i
$981$		0			0
$982$	7125.38	+	5310.10i	0.231548	+	0.172558i
$983$	−59679.1			−1.93639			−0.968193	−	0.250203i	$-0.919503\pi$
$983$	−59679.1			−1.93639			−0.968193	+	0.250203i	$0.919503\pi$
$984$		0			0
$985$	−23361.4			−0.755692
$986$	8663.12	+	6456.09i	0.279807	+	0.208523i
$987$		0			0
$988$	−76387.1	+	22786.9i	−2.45971	+	0.733751i
$989$			606.019i			0.0194846i
$990$		0			0
$991$		−	46352.5i		−	1.48581i	−0.669398	−	0.742904i	$-0.733448\pi$
$991$		−	46352.5i		−	1.48581i	0.669398	−	0.742904i	$-0.266552\pi$
$992$	−1292.85	+	21294.2i	−0.0413792	+	0.681543i
$993$		0			0
$994$	−10190.2	+	13673.8i	−0.325164	+	0.436323i
$995$	−32965.9			−1.05034
$996$		0			0
$997$	−38260.4			−1.21537			−0.607683	−	0.794180i	$-0.707901\pi$
$997$	−38260.4			−1.21537			−0.607683	+	0.794180i	$0.707901\pi$
$998$	29795.5	−	39981.1i	0.945049	−	1.26812i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.d.323.7	✓	32
3.2	odd	2	inner	324.4.b.d.323.26	yes	32
4.3	odd	2	inner	324.4.b.d.323.25	yes	32
12.11	even	2	inner	324.4.b.d.323.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.4.b.d.323.7	✓	32	1.1	even	1	trivial
324.4.b.d.323.8	yes	32	12.11	even	2	inner
324.4.b.d.323.25	yes	32	4.3	odd	2	inner
324.4.b.d.323.26	yes	32	3.2	odd	2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26792 - 1.69014i) q^{2} +(2.28688 + 7.66617i) q^{4} +16.3324i q^{5} +28.7358i q^{7} +(7.77043 - 21.2514i) q^{8} +(27.6040 - 37.0405i) q^{10} +25.2086 q^{11} +74.9324 q^{13} +(48.5674 - 65.1703i) q^{14} +(-53.5404 + 35.0632i) q^{16} -28.4061i q^{17} +132.976i q^{19} +(-125.207 + 37.3502i) q^{20} +(-57.1709 - 42.6059i) q^{22} -13.9485 q^{23} -141.747 q^{25} +(-169.940 - 126.646i) q^{26} +(-220.293 + 65.7152i) q^{28} -134.473i q^{29} +117.851i q^{31} +(180.687 + 10.9702i) q^{32} +(-48.0102 + 64.4226i) q^{34} -469.324 q^{35} +164.638 q^{37} +(224.747 - 301.577i) q^{38} +(347.086 + 126.910i) q^{40} +83.5882i q^{41} -43.4468i q^{43} +(57.6489 + 193.253i) q^{44} +(31.6341 + 23.5749i) q^{46} -449.188 q^{47} -482.745 q^{49} +(321.471 + 239.572i) q^{50} +(171.361 + 574.445i) q^{52} +5.67062i q^{53} +411.717i q^{55} +(610.674 + 223.289i) q^{56} +(-227.278 + 304.974i) q^{58} +836.816 q^{59} -446.126 q^{61} +(199.185 - 267.277i) q^{62} +(-391.241 - 330.265i) q^{64} +1223.83i q^{65} +130.483i q^{67} +(217.766 - 64.9613i) q^{68} +(1064.39 + 793.222i) q^{70} -209.816 q^{71} +163.546 q^{73} +(-373.384 - 278.260i) q^{74} +(-1019.41 + 304.099i) q^{76} +724.388i q^{77} -1292.83i q^{79} +(-572.666 - 874.443i) q^{80} +(141.275 - 189.571i) q^{82} -444.157 q^{83} +463.940 q^{85} +(-73.4310 + 98.5336i) q^{86} +(195.882 - 535.717i) q^{88} +1173.89i q^{89} +2153.24i q^{91} +(-31.8986 - 106.932i) q^{92} +(1018.72 + 759.189i) q^{94} -2171.81 q^{95} +523.610 q^{97} +(1094.82 + 815.904i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 104 q^{10} + 184 q^{13} - 436 q^{16} + 36 q^{22} - 576 q^{25} - 252 q^{28} - 752 q^{34} - 824 q^{37} + 472 q^{40} - 972 q^{46} - 3136 q^{49} - 1472 q^{52} - 716 q^{58} + 1192 q^{61} + 680 q^{64}+ \cdots + 7264 q^{97}+O(q^{100}) \) 32 * q + 32 * q^4 - 104 * q^10 + 184 * q^13 - 436 * q^16 + 36 * q^22 - 576 * q^25 - 252 * q^28 - 752 * q^34 - 824 * q^37 + 472 * q^40 - 972 * q^46 - 3136 * q^49 - 1472 * q^52 - 716 * q^58 + 1192 * q^61 + 680 * q^64 + 2484 * q^70 - 1184 * q^73 - 396 * q^76 + 748 * q^82 - 6808 * q^85 + 1764 * q^88 + 3312 * q^94 + 7264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more