LMFDB - Embedded newform 324.5.d.f.163.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(163,324)]

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, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.d (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:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.6
Character	$\chi$	$=$	324.163
Dual form			324.5.d.f.163.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.19553 + 2.40595i) q^{2} +(4.42285 - 15.3766i) q^{4} -2.03090 q^{5} +23.1347i q^{7} +(22.8618 + 59.7774i) q^{8} +O(q^{10})$	\(q+(-3.19553 + 2.40595i) q^{2} +(4.42285 - 15.3766i) q^{4} -2.03090 q^{5} +23.1347i q^{7} +(22.8618 + 59.7774i) q^{8} +(6.48981 - 4.88624i) q^{10} +4.99936i q^{11} +275.648 q^{13} +(-55.6608 - 73.9276i) q^{14} +(-216.877 - 136.016i) q^{16} -266.009 q^{17} -367.194i q^{19} +(-8.98238 + 31.2283i) q^{20} +(-12.0282 - 15.9756i) q^{22} +628.704i q^{23} -620.875 q^{25} +(-880.842 + 663.194i) q^{26} +(355.732 + 102.321i) q^{28} +638.962 q^{29} -1375.47i q^{31} +(1020.28 - 87.1493i) q^{32} +(850.041 - 640.004i) q^{34} -46.9843i q^{35} +1466.19 q^{37} +(883.449 + 1173.38i) q^{38} +(-46.4301 - 121.402i) q^{40} -1186.04 q^{41} +1651.61i q^{43} +(76.8730 + 22.1114i) q^{44} +(-1512.63 - 2009.04i) q^{46} +355.491i q^{47} +1865.79 q^{49} +(1984.03 - 1493.79i) q^{50} +(1219.15 - 4238.52i) q^{52} +5297.49 q^{53} -10.1532i q^{55} +(-1382.93 + 528.900i) q^{56} +(-2041.82 + 1537.31i) q^{58} +6031.37i q^{59} +1666.73 q^{61} +(3309.31 + 4395.36i) q^{62} +(-3050.68 + 2733.24i) q^{64} -559.815 q^{65} +2203.58i q^{67} +(-1176.52 + 4090.31i) q^{68} +(113.042 + 150.140i) q^{70} +524.299i q^{71} -1492.29 q^{73} +(-4685.25 + 3527.57i) q^{74} +(-5646.18 - 1624.04i) q^{76} -115.659 q^{77} +5136.51i q^{79} +(440.456 + 276.236i) q^{80} +(3790.02 - 2853.54i) q^{82} +7988.66i q^{83} +540.239 q^{85} +(-3973.68 - 5277.77i) q^{86} +(-298.849 + 114.294i) q^{88} -8860.17 q^{89} +6377.03i q^{91} +(9667.30 + 2780.66i) q^{92} +(-855.292 - 1135.98i) q^{94} +745.735i q^{95} +6818.67 q^{97} +(-5962.18 + 4488.98i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) $ 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8	$ 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8} + 14 q^{10} + 2 q^{13} - 252 q^{14} + q^{16} - 28 q^{17} + 140 q^{20} + 33 q^{22} + 1752 q^{25} + 548 q^{26} - 258 q^{28} - 526 q^{29} + 121 q^{32} - 385 q^{34} - 4 q^{37} - 1395 q^{38} + 2276 q^{40} + 2762 q^{41} + 3357 q^{44} + 1788 q^{46} - 3428 q^{49} - 6375 q^{50} - 1438 q^{52} - 5044 q^{53} + 7506 q^{56} + 4064 q^{58} + 2 q^{61} - 9162 q^{62} + 4513 q^{64} + 2014 q^{65} + 11405 q^{68} - 3666 q^{70} - 1708 q^{73} - 14620 q^{74} - 1581 q^{76} + 3942 q^{77} + 22760 q^{80} - 4243 q^{82} + 1252 q^{85} - 22113 q^{86} - 1995 q^{88} + 6524 q^{89} + 30294 q^{92} - 7524 q^{94} - 5638 q^{97} - 46469 q^{98}+O(q^{100}) $ 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8 + 14 * q^10 + 2 * q^13 - 252 * q^14 + q^16 - 28 * q^17 + 140 * q^20 + 33 * q^22 + 1752 * q^25 + 548 * q^26 - 258 * q^28 - 526 * q^29 + 121 * q^32 - 385 * q^34 - 4 * q^37 - 1395 * q^38 + 2276 * q^40 + 2762 * q^41 + 3357 * q^44 + 1788 * q^46 - 3428 * q^49 - 6375 * q^50 - 1438 * q^52 - 5044 * q^53 + 7506 * q^56 + 4064 * q^58 + 2 * q^61 - 9162 * q^62 + 4513 * q^64 + 2014 * q^65 + 11405 * q^68 - 3666 * q^70 - 1708 * q^73 - 14620 * q^74 - 1581 * q^76 + 3942 * q^77 + 22760 * q^80 - 4243 * q^82 + 1252 * q^85 - 22113 * q^86 - 1995 * q^88 + 6524 * q^89 + 30294 * q^92 - 7524 * q^94 - 5638 * q^97 - 46469 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−3.19553	+	2.40595i	−0.798883	+	0.601486i
$2$	−3.19553	+	2.40595i	−0.798883	+	0.601486i
$3$		0			0
$3$		0			0
$4$	4.42285	−	15.3766i	0.276428	−	0.961035i
$5$	−2.03090			−0.0812361			−0.0406181	−	0.999175i	$-0.512933\pi$
$5$	−2.03090			−0.0812361			−0.0406181	+	0.999175i	$0.512933\pi$
$6$		0			0
$7$			23.1347i			0.472136i	0.971737	+	0.236068i	$0.0758589\pi$
$7$			23.1347i			0.472136i	−0.971737	+	0.236068i	$0.924141\pi$
$8$	22.8618	+	59.7774i	0.357216	+	0.934022i
$9$		0			0
$10$	6.48981	−	4.88624i	0.0648981	−	0.0488624i
$11$			4.99936i			0.0413171i	0.999787	+	0.0206585i	$0.00657628\pi$
$11$			4.99936i			0.0413171i	−0.999787	+	0.0206585i	$0.993424\pi$
$12$		0			0
$13$	275.648			1.63105			0.815527	−	0.578719i	$-0.196447\pi$
$13$	275.648			1.63105			0.815527	+	0.578719i	$0.196447\pi$
$14$	−55.6608	−	73.9276i	−0.283984	−	0.377182i
$15$		0			0
$16$	−216.877	−	136.016i	−0.847175	−	0.531314i
$17$	−266.009			−0.920447			−0.460224	−	0.887803i	$-0.652231\pi$
$17$	−266.009			−0.920447			−0.460224	+	0.887803i	$0.652231\pi$
$18$		0			0
$19$		−	367.194i		−	1.01716i	−0.861015	−	0.508579i	$-0.830171\pi$
$19$		−	367.194i		−	1.01716i	0.861015	−	0.508579i	$-0.169829\pi$
$20$	−8.98238	+	31.2283i	−0.0224559	+	0.0780707i
$21$		0			0
$22$	−12.0282	−	15.9756i	−0.0248516	−	0.0330075i
$23$			628.704i			1.18848i	0.804289	+	0.594238i	$0.202546\pi$
$23$			628.704i			1.18848i	−0.804289	+	0.594238i	$0.797454\pi$
$24$		0			0
$25$	−620.875			−0.993401
$26$	−880.842	+	663.194i	−1.30302	+	0.981057i
$27$		0			0
$28$	355.732	+	102.321i	0.453739	+	0.130512i
$29$	638.962			0.759764			0.379882	−	0.925035i	$-0.375965\pi$
$29$	638.962			0.759764			0.379882	+	0.925035i	$0.375965\pi$
$30$		0			0
$31$		−	1375.47i		−	1.43129i	−0.698464	−	0.715645i	$-0.746133\pi$
$31$		−	1375.47i		−	1.43129i	0.698464	−	0.715645i	$-0.253867\pi$
$32$	1020.28	−	87.1493i	0.996372	−	0.0851067i
$33$		0			0
$34$	850.041	−	640.004i	0.735330	−	0.553637i
$35$		−	46.9843i		−	0.0383545i
$36$		0			0
$37$	1466.19			1.07099			0.535496	−	0.844538i	$-0.320125\pi$
$37$	1466.19			1.07099			0.535496	+	0.844538i	$0.320125\pi$
$38$	883.449	+	1173.38i	0.611807	+	0.812590i
$39$		0			0
$40$	−46.4301	−	121.402i	−0.0290188	−	0.0758763i
$41$	−1186.04			−0.705555			−0.352777	−	0.935707i	$-0.614763\pi$
$41$	−1186.04			−0.705555			−0.352777	+	0.935707i	$0.614763\pi$
$42$		0			0
$43$			1651.61i			0.893244i	0.894723	+	0.446622i	$0.147373\pi$
$43$			1651.61i			0.893244i	−0.894723	+	0.446622i	$0.852627\pi$
$44$	76.8730	+	22.1114i	0.0397071	+	0.0114212i
$45$		0			0
$46$	−1512.63	−	2009.04i	−0.714852	−	0.949453i
$47$			355.491i			0.160928i	0.996757	+	0.0804642i	$0.0256403\pi$
$47$			355.491i			0.160928i	−0.996757	+	0.0804642i	$0.974360\pi$
$48$		0			0
$49$	1865.79			0.777087
$50$	1984.03	−	1493.79i	0.793611	−	0.597517i
$51$		0			0
$52$	1219.15	−	4238.52i	0.450869	−	1.56750i
$53$	5297.49			1.88590			0.942950	−	0.332934i	$-0.108039\pi$
$53$	5297.49			1.88590			0.942950	+	0.332934i	$0.108039\pi$
$54$		0			0
$55$		−	10.1532i		−	0.00335644i
$56$	−1382.93	+	528.900i	−0.440986	+	0.168654i
$57$		0			0
$58$	−2041.82	+	1537.31i	−0.606963	+	0.456988i
$59$			6031.37i			1.73265i	0.499478	+	0.866327i	$0.333525\pi$
$59$			6031.37i			1.73265i	−0.499478	+	0.866327i	$0.666475\pi$
$60$		0			0
$61$	1666.73			0.447925			0.223962	−	0.974598i	$-0.428101\pi$
$61$	1666.73			0.447925			0.223962	+	0.974598i	$0.428101\pi$
$62$	3309.31	+	4395.36i	0.860902	+	1.14343i
$63$		0			0
$64$	−3050.68	+	2733.24i	−0.744794	+	0.667295i
$65$	−559.815			−0.132500
$66$		0			0
$67$			2203.58i			0.490885i	0.969411	+	0.245443i	$0.0789333\pi$
$67$			2203.58i			0.490885i	−0.969411	+	0.245443i	$0.921067\pi$
$68$	−1176.52	+	4090.31i	−0.254437	+	0.884582i
$69$		0			0
$70$	113.042	+	150.140i	0.0230697	+	0.0306408i
$71$			524.299i			0.104007i	0.998647	+	0.0520035i	$0.0165607\pi$
$71$			524.299i			0.104007i	−0.998647	+	0.0520035i	$0.983439\pi$
$72$		0			0
$73$	−1492.29			−0.280032			−0.140016	−	0.990149i	$-0.544715\pi$
$73$	−1492.29			−0.280032			−0.140016	+	0.990149i	$0.544715\pi$
$74$	−4685.25	+	3527.57i	−0.855597	+	0.644187i
$75$		0			0
$76$	−5646.18	−	1624.04i	−0.977524	−	0.281171i
$77$	−115.659			−0.0195073
$78$		0			0
$79$			5136.51i			0.823027i	0.911404	+	0.411513i	$0.135000\pi$
$79$			5136.51i			0.823027i	−0.911404	+	0.411513i	$0.865000\pi$
$80$	440.456	+	276.236i	0.0688212	+	0.0431619i
$81$		0			0
$82$	3790.02	−	2853.54i	0.563656	−	0.424382i
$83$			7988.66i			1.15963i	0.814750	+	0.579813i	$0.196874\pi$
$83$			7988.66i			1.15963i	−0.814750	+	0.579813i	$0.803126\pi$
$84$		0			0
$85$	540.239			0.0747736
$86$	−3973.68	−	5277.77i	−0.537274	−	0.713597i
$87$		0			0
$88$	−298.849	+	114.294i	−0.0385910	+	0.0147591i
$89$	−8860.17			−1.11857			−0.559283	−	0.828977i	$-0.688924\pi$
$89$	−8860.17			−1.11857			−0.559283	+	0.828977i	$0.688924\pi$
$90$		0			0
$91$			6377.03i			0.770080i
$92$	9667.30	+	2780.66i	1.14217	+	0.328528i
$93$		0			0
$94$	−855.292	−	1135.98i	−0.0967963	−	0.128563i
$95$			745.735i			0.0826300i
$96$		0			0
$97$	6818.67			0.724696			0.362348	−	0.932043i	$-0.381975\pi$
$97$	6818.67			0.724696			0.362348	+	0.932043i	$0.381975\pi$
$98$	−5962.18	+	4488.98i	−0.620802	+	0.467408i
$99$		0			0
$100$	−2746.04	+	9546.92i	−0.274604	+	0.954692i
$101$	3091.05			0.303015			0.151507	−	0.988456i	$-0.451587\pi$
$101$	3091.05			0.303015			0.151507	+	0.988456i	$0.451587\pi$
$102$		0			0
$103$			10865.0i			1.02413i	0.858947	+	0.512065i	$0.171119\pi$
$103$			10865.0i			1.02413i	−0.858947	+	0.512065i	$0.828881\pi$
$104$	6301.81	+	16477.5i	0.582638	+	1.52344i
$105$		0			0
$106$	−16928.3	+	12745.5i	−1.50661	+	1.13434i
$107$			14106.5i			1.23212i	0.787699	+	0.616060i	$0.211272\pi$
$107$			14106.5i			1.23212i	−0.787699	+	0.616060i	$0.788728\pi$
$108$		0			0
$109$	16328.3			1.37432			0.687160	−	0.726506i	$-0.258857\pi$
$109$	16328.3			1.37432			0.687160	+	0.726506i	$0.258857\pi$
$110$	24.4281	+	32.4449i	0.00201885	+	0.00268140i
$111$		0			0
$112$	3146.69	−	5017.38i	0.250853	−	0.399982i
$113$	11822.9			0.925905			0.462952	−	0.886383i	$-0.346790\pi$
$113$	11822.9			0.925905			0.462952	+	0.886383i	$0.346790\pi$
$114$		0			0
$115$		−	1276.84i		−	0.0965472i
$116$	2826.03	−	9825.03i	0.210020	−	0.730160i
$117$		0			0
$118$	−14511.1	−	19273.4i	−1.04217	−	1.38419i
$119$		−	6154.04i		−	0.434577i
$120$		0			0
$121$	14616.0			0.998293
$122$	−5326.08	+	4010.06i	−0.357839	+	0.269421i
$123$		0			0
$124$	−21150.0	−	6083.50i	−1.37552	−	0.395649i
$125$	2530.25			0.161936
$126$		0			0
$127$			20979.9i			1.30076i	0.759609	+	0.650379i	$0.225390\pi$
$127$			20979.9i			1.30076i	−0.759609	+	0.650379i	$0.774610\pi$
$128$	3172.51	−	16073.9i	0.193635	−	0.981074i
$129$		0			0
$130$	1788.91	−	1346.88i	0.105852	−	0.0796972i
$131$		−	28548.7i		−	1.66358i	−0.555092	−	0.831789i	$-0.687317\pi$
$131$		−	28548.7i		−	1.66358i	0.555092	−	0.831789i	$-0.312683\pi$
$132$		0			0
$133$	8494.92			0.480237
$134$	−5301.70	−	7041.62i	−0.295261	−	0.392160i
$135$		0			0
$136$	−6081.45	−	15901.3i	−0.328798	−	0.859718i
$137$	−618.873			−0.0329731			−0.0164866	−	0.999864i	$-0.505248\pi$
$137$	−618.873			−0.0329731			−0.0164866	+	0.999864i	$0.505248\pi$
$138$		0			0
$139$			19422.0i			1.00523i	0.864511	+	0.502613i	$0.167628\pi$
$139$			19422.0i			1.00523i	−0.864511	+	0.502613i	$0.832372\pi$
$140$	−722.456	−	207.804i	−0.0368600	−	0.0106023i
$141$		0			0
$142$	−1261.44	−	1675.41i	−0.0625588	−	0.0830894i
$143$			1378.07i			0.0673903i
$144$		0			0
$145$	−1297.67			−0.0617203
$146$	4768.67	−	3590.38i	0.223713	−	0.168436i
$147$		0			0
$148$	6484.72	−	22544.9i	0.296052	−	1.02926i
$149$	619.281			0.0278943			0.0139471	−	0.999903i	$-0.495560\pi$
$149$	619.281			0.0278943			0.0139471	+	0.999903i	$0.495560\pi$
$150$		0			0
$151$		−	4339.46i		−	0.190319i	−0.995462	−	0.0951593i	$-0.969664\pi$
$151$		−	4339.46i		−	0.190319i	0.995462	−	0.0951593i	$-0.0303361\pi$
$152$	21949.9	−	8394.72i	0.950048	−	0.363345i
$153$		0			0
$154$	369.591	−	278.268i	0.0155840	−	0.0117334i
$155$			2793.45i			0.116272i
$156$		0			0
$157$	−6207.76			−0.251846			−0.125923	−	0.992040i	$-0.540189\pi$
$157$	−6207.76			−0.251846			−0.125923	+	0.992040i	$0.540189\pi$
$158$	−12358.2	−	16413.9i	−0.495039	−	0.657502i
$159$		0			0
$160$	−2072.10	+	176.992i	−0.0809414	+	0.00691374i
$161$	−14544.9			−0.561123
$162$		0			0
$163$		−	15857.0i		−	0.596824i	−0.954437	−	0.298412i	$-0.903543\pi$
$163$		−	15857.0i		−	0.596824i	0.954437	−	0.298412i	$-0.0964569\pi$
$164$	−5245.66	+	18237.2i	−0.195035	+	0.678063i
$165$		0			0
$166$	−19220.3	−	25528.0i	−0.697499	−	0.926406i
$167$			418.996i			0.0150237i	0.999972	+	0.00751186i	$0.00239112\pi$
$167$			418.996i			0.0150237i	−0.999972	+	0.00751186i	$0.997609\pi$
$168$		0			0
$169$	47420.9			1.66034
$170$	−1726.35	+	1299.79i	−0.0597353	+	0.0449753i
$171$		0			0
$172$	25396.0	+	7304.81i	0.858438	+	0.246918i
$173$	−19200.8			−0.641545			−0.320772	−	0.947156i	$-0.603942\pi$
$173$	−19200.8			−0.641545			−0.320772	+	0.947156i	$0.603942\pi$
$174$		0			0
$175$		−	14363.8i		−	0.469021i
$176$	679.995	−	1084.25i	0.0219523	−	0.0350028i
$177$		0			0
$178$	28312.9	−	21317.1i	0.893604	−	0.672803i
$179$		−	49821.7i		−	1.55494i	−0.628922	−	0.777468i	$-0.716504\pi$
$179$		−	49821.7i		−	1.55494i	0.628922	−	0.777468i	$-0.283496\pi$
$180$		0			0
$181$	13970.7			0.426443			0.213222	−	0.977004i	$-0.431604\pi$
$181$	13970.7			0.426443			0.213222	+	0.977004i	$0.431604\pi$
$182$	−15342.8	−	20378.0i	−0.463193	−	0.615204i
$183$		0			0
$184$	−37582.3	+	14373.3i	−1.11006	+	0.424542i
$185$	−2977.68			−0.0870031
$186$		0			0
$187$		−	1329.88i		−	0.0380302i
$188$	5466.22	+	1572.28i	0.154658	+	0.0444851i
$189$		0			0
$190$	−1794.20	−	2383.02i	−0.0497008	−	0.0660117i
$191$		−	31170.9i		−	0.854442i	−0.904147	−	0.427221i	$-0.859493\pi$
$191$		−	31170.9i		−	0.854442i	0.904147	−	0.427221i	$-0.140507\pi$
$192$		0			0
$193$	26996.3			0.724753			0.362377	−	0.932032i	$-0.381965\pi$
$193$	26996.3			0.724753			0.362377	+	0.932032i	$0.381965\pi$
$194$	−21789.3	+	16405.3i	−0.578948	+	0.435895i
$195$		0			0
$196$	8252.09	−	28689.4i	0.214809	−	0.746808i
$197$	10416.4			0.268402			0.134201	−	0.990954i	$-0.457153\pi$
$197$	10416.4			0.268402			0.134201	+	0.990954i	$0.457153\pi$
$198$		0			0
$199$			8438.68i			0.213093i	0.994308	+	0.106546i	$0.0339793\pi$
$199$			8438.68i			0.213093i	−0.994308	+	0.106546i	$0.966021\pi$
$200$	−14194.3	−	37114.3i	−0.354858	−	0.927858i
$201$		0			0
$202$	−9877.56	+	7436.91i	−0.242073	+	0.182259i
$203$			14782.2i			0.358712i
$204$		0			0
$205$	2408.73			0.0573165
$206$	−26140.6	−	34719.4i	−0.616000	−	0.818159i
$207$		0			0
$208$	−59781.7	−	37492.7i	−1.38179	−	0.866602i
$209$	1835.74			0.0420260
$210$		0			0
$211$			22945.7i			0.515390i	0.966226	+	0.257695i	$0.0829630\pi$
$211$			22945.7i			0.515390i	−0.966226	+	0.257695i	$0.917037\pi$
$212$	23430.0	−	81457.2i	0.521316	−	1.81242i
$213$		0			0
$214$	−33939.6	−	45077.9i	−0.741104	−	0.984320i
$215$		−	3354.25i		−	0.0725637i
$216$		0			0
$217$	31821.1			0.675764
$218$	−52177.6	+	39285.0i	−1.09792	+	0.826635i
$219$		0			0
$220$	−156.122	−	44.9062i	−0.00322565	−	0.000927813i
$221$	−73325.0			−1.50130
$222$		0			0
$223$			64260.3i			1.29221i	0.763249	+	0.646105i	$0.223603\pi$
$223$			64260.3i			1.29221i	−0.763249	+	0.646105i	$0.776397\pi$
$224$	2016.17	+	23604.0i	0.0401820	+	0.470423i
$225$		0			0
$226$	−37780.4	+	28445.2i	−0.739690	+	0.556919i
$227$			6705.37i			0.130128i	0.997881	+	0.0650641i	$0.0207252\pi$
$227$			6705.37i			0.130128i	−0.997881	+	0.0650641i	$0.979275\pi$
$228$		0			0
$229$	35550.3			0.677910			0.338955	−	0.940803i	$-0.389927\pi$
$229$	35550.3			0.677910			0.338955	+	0.940803i	$0.389927\pi$
$230$	3072.00	+	4080.17i	0.0580718	+	0.0771299i
$231$		0			0
$232$	14607.8	+	38195.5i	0.271400	+	0.709637i
$233$	62439.9			1.15014			0.575070	−	0.818105i	$-0.304975\pi$
$233$	62439.9			1.15014			0.575070	+	0.818105i	$0.304975\pi$
$234$		0			0
$235$		−	721.967i		−	0.0130732i
$236$	92741.6	+	26675.8i	1.66514	+	0.478954i
$237$		0			0
$238$	14806.3	+	19665.4i	0.261392	+	0.347176i
$239$			3753.45i			0.0657106i	0.999460	+	0.0328553i	$0.0104600\pi$
$239$			3753.45i			0.0657106i	−0.999460	+	0.0328553i	$0.989540\pi$
$240$		0			0
$241$	−89665.2			−1.54380			−0.771898	−	0.635747i	$-0.780692\pi$
$241$	−89665.2			−1.54380			−0.771898	+	0.635747i	$0.780692\pi$
$242$	−46705.9	+	35165.3i	−0.797519	+	0.600460i
$243$		0			0
$244$	7371.68	−	25628.5i	0.123819	−	0.430471i
$245$	−3789.23			−0.0631275
$246$		0			0
$247$		−	101216.i		−	1.65904i
$248$	82222.1	−	31445.7i	1.33686	−	0.511279i
$249$		0			0
$250$	−8085.50	+	6087.65i	−0.129368	+	0.0974024i
$251$		−	9246.49i		−	0.146767i	−0.997304	−	0.0733836i	$-0.976620\pi$
$251$		−	9246.49i		−	0.146767i	0.997304	−	0.0733836i	$-0.0233798\pi$
$252$		0			0
$253$	−3143.12			−0.0491043
$254$	−50476.6	−	67042.1i	−0.782389	−	1.03915i
$255$		0			0
$256$	28535.1	+	58997.6i	0.435411	+	0.900232i
$257$	15249.7			0.230885			0.115442	−	0.993314i	$-0.463171\pi$
$257$	15249.7			0.230885			0.115442	+	0.993314i	$0.463171\pi$
$258$		0			0
$259$			33919.8i			0.505654i
$260$	−2475.97	+	8608.02i	−0.0366268	+	0.127338i
$261$		0			0
$262$	68686.5	+	91228.1i	1.00062	+	1.32900i
$263$		−	103320.i		−	1.49374i	−0.664971	−	0.746869i	$-0.731556\pi$
$263$		−	103320.i		−	1.49374i	0.664971	−	0.746869i	$-0.268444\pi$
$264$		0			0
$265$	−10758.7			−0.153203
$266$	−27145.8	+	20438.3i	−0.383653	+	0.288856i
$267$		0			0
$268$	33883.5	+	9746.12i	0.471758	+	0.135694i
$269$	−86017.8			−1.18873			−0.594366	−	0.804195i	$-0.702597\pi$
$269$	−86017.8			−1.18873			−0.594366	+	0.804195i	$0.702597\pi$
$270$		0			0
$271$			15629.0i			0.212810i	0.994323	+	0.106405i	$0.0339340\pi$
$271$			15629.0i			0.212810i	−0.994323	+	0.106405i	$0.966066\pi$
$272$	57691.3	+	36181.6i	0.779780	+	0.489046i
$273$		0			0
$274$	1977.63	−	1488.97i	0.0263417	−	0.0198329i
$275$		−	3103.98i		−	0.0410444i
$276$		0			0
$277$	−56614.6			−0.737851			−0.368926	−	0.929459i	$-0.620274\pi$
$277$	−56614.6			−0.737851			−0.368926	+	0.929459i	$0.620274\pi$
$278$	−46728.2	−	62063.6i	−0.604630	−	0.803059i
$279$		0			0
$280$	2808.60	−	1074.15i	0.0358240	−	0.0137008i
$281$	111067.			1.40661			0.703303	−	0.710890i	$-0.251708\pi$
$281$	111067.			1.40661			0.703303	+	0.710890i	$0.251708\pi$
$282$		0			0
$283$			91197.8i			1.13871i	0.822093	+	0.569353i	$0.192806\pi$
$283$			91197.8i			1.13871i	−0.822093	+	0.569353i	$0.807194\pi$
$284$	8061.91	+	2318.90i	0.0999543	+	0.0287504i
$285$		0			0
$286$	−3315.55	−	4403.65i	−0.0405344	−	0.0538370i
$287$		−	27438.6i		−	0.333118i
$288$		0			0
$289$	−12760.0			−0.152776
$290$	4146.74	−	3122.12i	0.0493073	−	0.0371239i
$291$		0			0
$292$	−6600.19	+	22946.3i	−0.0774088	+	0.269121i
$293$	83015.0			0.966988			0.483494	−	0.875348i	$-0.339367\pi$
$293$	83015.0			0.966988			0.483494	+	0.875348i	$0.339367\pi$
$294$		0			0
$295$		−	12249.1i		−	0.140754i
$296$	33519.7	+	87644.8i	0.382575	+	1.00033i
$297$		0			0
$298$	−1978.93	+	1489.96i	−0.0222843	+	0.0167780i
$299$			173301.i			1.93847i
$300$		0			0
$301$	−38209.4			−0.421733
$302$	10440.5	+	13866.9i	0.114474	+	0.152042i
$303$		0			0
$304$	−49944.4	+	79635.9i	−0.540430	+	0.861711i
$305$	−3384.96			−0.0363876
$306$		0			0
$307$		−	65201.8i		−	0.691803i	−0.938271	−	0.345902i	$-0.887573\pi$
$307$		−	65201.8i		−	0.691803i	0.938271	−	0.345902i	$-0.112427\pi$
$308$	−511.541	+	1778.43i	−0.00539236	+	0.0187472i
$309$		0			0
$310$	−6720.88	−	8926.55i	−0.0699363	−	0.0928881i
$311$			133699.i			1.38231i	0.722705	+	0.691156i	$0.242898\pi$
$311$			133699.i			1.38231i	−0.722705	+	0.691156i	$0.757102\pi$
$312$		0			0
$313$	11240.1			0.114731			0.0573655	−	0.998353i	$-0.481730\pi$
$313$	11240.1			0.114731			0.0573655	+	0.998353i	$0.481730\pi$
$314$	19837.1	−	14935.5i	0.201196	−	0.151482i
$315$		0			0
$316$	78981.8	+	22718.0i	0.790957	+	0.227508i
$317$	−39206.2			−0.390154			−0.195077	−	0.980788i	$-0.562496\pi$
$317$	−39206.2			−0.390154			−0.195077	+	0.980788i	$0.562496\pi$
$318$		0			0
$319$			3194.40i			0.0313912i
$320$	6195.63	−	5550.94i	0.0605042	−	0.0542084i
$321$		0			0
$322$	46478.6	−	34994.1i	0.448271	−	0.337508i
$323$			97677.0i			0.936240i
$324$		0			0
$325$	−171143.			−1.62029
$326$	38151.1	+	50671.6i	0.358981	+	0.476792i
$327$		0			0
$328$	−27115.0	−	70898.2i	−0.252035	−	0.659004i
$329$	−8224.17			−0.0759801
$330$		0			0
$331$		−	74751.4i		−	0.682281i	−0.940012	−	0.341141i	$-0.889187\pi$
$331$		−	74751.4i		−	0.682281i	0.940012	−	0.341141i	$-0.110813\pi$
$332$	122838.	+	35332.7i	1.11444	+	0.320553i
$333$		0			0
$334$	−1008.08	−	1338.92i	−0.00903656	−	0.0120022i
$335$		−	4475.27i		−	0.0398776i
$336$		0			0
$337$	−141818.			−1.24874			−0.624370	−	0.781129i	$-0.714644\pi$
$337$	−141818.			−1.24874			−0.624370	+	0.781129i	$0.714644\pi$
$338$	−151535.	+	114092.i	−1.32642	+	0.998670i
$339$		0			0
$340$	2389.40	−	8307.01i	0.0206695	−	0.0718600i
$341$	6876.48			0.0591367
$342$		0			0
$343$			98710.7i			0.839027i
$344$	−98728.8	+	37758.7i	−0.834309	+	0.319081i
$345$		0			0
$346$	61356.7	−	46196.1i	0.512519	−	0.385880i
$347$		−	183029.i		−	1.52006i	−0.649886	−	0.760032i	$-0.725183\pi$
$347$		−	183029.i		−	1.52006i	0.649886	−	0.760032i	$-0.274817\pi$
$348$		0			0
$349$	134558.			1.10474			0.552368	−	0.833600i	$-0.313724\pi$
$349$	134558.			1.10474			0.552368	+	0.833600i	$0.313724\pi$
$350$	34558.4	+	45899.8i	0.282110	+	0.374693i
$351$		0			0
$352$	435.691	+	5100.77i	0.00351636	+	0.0411671i
$353$	−200278.			−1.60725			−0.803626	−	0.595135i	$-0.797099\pi$
$353$	−200278.			−1.60725			−0.803626	+	0.595135i	$0.797099\pi$
$354$		0			0
$355$		−	1064.80i		−	0.00844912i
$356$	−39187.2	+	136239.i	−0.309203	+	1.07498i
$357$		0			0
$358$	119868.	+	159207.i	0.935273	+	1.24221i
$359$			161179.i			1.25060i	0.780385	+	0.625300i	$0.215023\pi$
$359$			161179.i			1.25060i	−0.780385	+	0.625300i	$0.784977\pi$
$360$		0			0
$361$	−4510.46			−0.0346104
$362$	−44643.8	+	33612.8i	−0.340678	+	0.256500i
$363$		0			0
$364$	98056.8	+	28204.6i	0.740073	+	0.212872i
$365$	3030.70			0.0227487
$366$		0			0
$367$		−	199565.i		−	1.48167i	−0.671686	−	0.740836i	$-0.734429\pi$
$367$		−	199565.i		−	1.48167i	0.671686	−	0.740836i	$-0.265571\pi$
$368$	85514.0	−	136351.i	0.631454	−	1.00685i
$369$		0			0
$370$	9515.28	−	7164.14i	0.0695053	−	0.0523312i
$371$			122556.i			0.890402i
$372$		0			0
$373$	−5788.69			−0.0416066			−0.0208033	−	0.999784i	$-0.506622\pi$
$373$	−5788.69			−0.0416066			−0.0208033	+	0.999784i	$0.506622\pi$
$374$	3199.61	+	4249.67i	0.0228746	+	0.0303817i
$375$		0			0
$376$	−21250.3	+	8127.16i	−0.150311	+	0.0574861i
$377$	176129.			1.23922
$378$		0			0
$379$		−	217930.i		−	1.51719i	−0.651565	−	0.758593i	$-0.725887\pi$
$379$		−	217930.i		−	1.51719i	0.651565	−	0.758593i	$-0.274113\pi$
$380$	11466.8	+	3298.27i	0.0794102	+	0.0228412i
$381$		0			0
$382$	74995.5	+	99607.6i	0.513935	+	0.682599i
$383$			69498.2i			0.473780i	0.971537	+	0.236890i	$0.0761280\pi$
$383$			69498.2i			0.473780i	−0.971537	+	0.236890i	$0.923872\pi$
$384$		0			0
$385$	234.891			0.00158470
$386$	−86267.6	+	64951.7i	−0.578993	+	0.435929i
$387$		0			0
$388$	30157.9	−	104848.i	0.200326	−	0.696458i
$389$	57466.0			0.379762			0.189881	−	0.981807i	$-0.439190\pi$
$389$	57466.0			0.379762			0.189881	+	0.981807i	$0.439190\pi$
$390$		0			0
$391$		−	167241.i		−	1.09393i
$392$	42655.2	+	111532.i	0.277588	+	0.725817i
$393$		0			0
$394$	−33286.0	+	25061.4i	−0.214422	+	0.161440i
$395$		−	10431.7i		−	0.0668595i
$396$		0			0
$397$	13255.8			0.0841056			0.0420528	−	0.999115i	$-0.486610\pi$
$397$	13255.8			0.0841056			0.0420528	+	0.999115i	$0.486610\pi$
$398$	−20303.0	−	26966.1i	−0.128172	−	0.170236i
$399$		0			0
$400$	134653.	+	84449.2i	0.841584	+	0.527808i
$401$	−5375.31			−0.0334283			−0.0167142	−	0.999860i	$-0.505321\pi$
$401$	−5375.31			−0.0334283			−0.0167142	+	0.999860i	$0.505321\pi$
$402$		0			0
$403$		−	379146.i		−	2.33451i
$404$	13671.3	−	47529.7i	0.0837618	−	0.291208i
$405$		0			0
$406$	−35565.1	−	47236.9i	−0.215761	−	0.286569i
$407$			7330.00i			0.0442502i
$408$		0			0
$409$	−240693.			−1.43885			−0.719427	−	0.694568i	$-0.755596\pi$
$409$	−240693.			−1.43885			−0.719427	+	0.694568i	$0.755596\pi$
$410$	−7697.16	+	5795.27i	−0.0457892	+	0.0344751i
$411$		0			0
$412$	167066.	+	48054.2i	0.984224	+	0.283098i
$413$	−139534.			−0.818049
$414$		0			0
$415$		−	16224.2i		−	0.0942035i
$416$	281240.	−	24022.5i	1.62514	−	0.138814i
$417$		0			0
$418$	−5866.15	+	4416.68i	−0.0335738	+	0.0252781i
$419$		−	35414.2i		−	0.201720i	−0.994901	−	0.100860i	$-0.967841\pi$
$419$		−	35414.2i		−	0.201720i	0.994901	−	0.100860i	$-0.0321595\pi$
$420$		0			0
$421$	−165096.			−0.931477			−0.465739	−	0.884922i	$-0.654211\pi$
$421$	−165096.			−0.931477			−0.465739	+	0.884922i	$0.654211\pi$
$422$	−55206.1	−	73323.7i	−0.310000	−	0.411737i
$423$		0			0
$424$	121110.	+	316670.i	0.673673	+	1.76147i
$425$	165159.			0.914373
$426$		0			0
$427$			38559.2i			0.211481i
$428$	216910.	+	62391.1i	1.18411	+	0.340593i
$429$		0			0
$430$	8070.16	+	10718.6i	0.0436461	+	0.0579699i
$431$			161673.i			0.870327i	0.900351	+	0.435163i	$0.143309\pi$
$431$			161673.i			0.870327i	−0.900351	+	0.435163i	$0.856691\pi$
$432$		0			0
$433$	−61835.3			−0.329808			−0.164904	−	0.986310i	$-0.552731\pi$
$433$	−61835.3			−0.329808			−0.164904	+	0.986310i	$0.552731\pi$
$434$	−101685.	+	76559.8i	−0.539857	+	0.406463i
$435$		0			0
$436$	72217.6	−	251073.i	0.379901	−	1.32077i
$437$	230856.			1.20887
$438$		0			0
$439$			309484.i			1.60587i	0.596069	+	0.802933i	$0.296728\pi$
$439$			309484.i			1.60587i	−0.596069	+	0.802933i	$0.703272\pi$
$440$	606.933	−	232.121i	0.00313499	−	0.00119897i
$441$		0			0
$442$	234312.	−	176416.i	1.19936	−	0.903011i
$443$		−	46898.7i		−	0.238976i	−0.992836	−	0.119488i	$-0.961875\pi$
$443$		−	46898.7i		−	0.238976i	0.992836	−	0.119488i	$-0.0381252\pi$
$444$		0			0
$445$	17994.1			0.0908680
$446$	−154607.	−	205346.i	−0.777246	−	1.03232i
$447$		0			0
$448$	−63232.6	−	70576.4i	−0.315054	−	0.351644i
$449$	−124857.			−0.619328			−0.309664	−	0.950846i	$-0.600217\pi$
$449$	−124857.			−0.619328			−0.309664	+	0.950846i	$0.600217\pi$
$450$		0			0
$451$		−	5929.43i		−	0.0291514i
$452$	52290.8	−	181795.i	0.255946	−	0.889827i
$453$		0			0
$454$	−16132.8	−	21427.2i	−0.0782703	−	0.103957i
$455$		−	12951.1i		−	0.0625583i
$456$		0			0
$457$	−125497.			−0.600898			−0.300449	−	0.953798i	$-0.597137\pi$
$457$	−125497.			−0.600898			−0.300449	+	0.953798i	$0.597137\pi$
$458$	−113602.	+	85532.1i	−0.541571	+	0.407754i
$459$		0			0
$460$	−19633.3	−	5647.25i	−0.0927852	−	0.0266883i
$461$	103295.			0.486045			0.243022	−	0.970021i	$-0.421861\pi$
$461$	103295.			0.486045			0.243022	+	0.970021i	$0.421861\pi$
$462$		0			0
$463$		−	320504.i		−	1.49510i	−0.664204	−	0.747552i	$-0.731229\pi$
$463$		−	320504.i		−	1.49510i	0.664204	−	0.747552i	$-0.268771\pi$
$464$	−138576.	−	86909.3i	−0.643654	−	0.403673i
$465$		0			0
$466$	−199529.	+	150227.i	−0.918827	+	0.691793i
$467$		−	427381.i		−	1.95967i	−0.199820	−	0.979833i	$-0.564036\pi$
$467$		−	427381.i		−	1.95967i	0.199820	−	0.979833i	$-0.435964\pi$
$468$		0			0
$469$	−50979.2			−0.231765
$470$	1737.01	+	2307.07i	0.00786335	+	0.0104440i
$471$		0			0
$472$	−360539.	+	137888.i	−1.61834	+	0.618931i
$473$	−8256.99			−0.0369062
$474$		0			0
$475$			227982.i			1.01045i
$476$	−94627.9	−	27218.4i	−0.417643	−	0.120129i
$477$		0			0
$478$	−9030.61	−	11994.3i	−0.0395240	−	0.0524951i
$479$		−	192061.i		−	0.837082i	−0.908198	−	0.418541i	$-0.862542\pi$
$479$		−	192061.i		−	0.837082i	0.908198	−	0.418541i	$-0.137458\pi$
$480$		0			0
$481$	404152.			1.74684
$482$	286528.	−	215730.i	1.23331	−	0.928572i
$483$		0			0
$484$	64644.4	−	224744.i	0.275956	−	0.959394i
$485$	−13848.1			−0.0588715
$486$		0			0
$487$		−	52885.1i		−	0.222985i	−0.993765	−	0.111492i	$-0.964437\pi$
$487$		−	52885.1i		−	0.222985i	0.993765	−	0.111492i	$-0.0355631\pi$
$488$	38104.4	+	99632.6i	0.160006	+	0.418371i
$489$		0			0
$490$	12108.6	−	9116.68i	0.0504315	−	0.0379704i
$491$		−	7354.16i		−	0.0305049i	−0.999884	−	0.0152525i	$-0.995145\pi$
$491$		−	7354.16i		−	0.0305049i	0.999884	−	0.0152525i	$-0.00485520\pi$
$492$		0			0
$493$	−169970.			−0.699323
$494$	243521.	+	323440.i	0.997890	+	1.32538i
$495$		0			0
$496$	−187086.	+	298308.i	−0.760465	+	1.21255i
$497$	−12129.5			−0.0491055
$498$		0			0
$499$			415048.i			1.66685i	0.552632	+	0.833426i	$0.313624\pi$
$499$			415048.i			1.66685i	−0.552632	+	0.833426i	$0.686376\pi$
$500$	11190.9	−	38906.6i	0.0447637	−	0.155626i
$501$		0			0
$502$	22246.5	+	29547.4i	0.0882785	+	0.117250i
$503$		−	53242.3i		−	0.210436i	−0.994449	−	0.105218i	$-0.966446\pi$
$503$		−	53242.3i		−	0.210436i	0.994449	−	0.105218i	$-0.0335541\pi$
$504$		0			0
$505$	−6277.63			−0.0246157
$506$	10043.9	−	7562.17i	0.0392286	−	0.0295356i
$507$		0			0
$508$	322599.	+	92791.1i	1.25007	+	0.359566i
$509$	−497261.			−1.91932			−0.959662	−	0.281155i	$-0.909283\pi$
$509$	−497261.			−1.91932			−0.959662	+	0.281155i	$0.909283\pi$
$510$		0			0
$511$		−	34523.7i		−	0.132214i
$512$	−233130.	−	119875.i	−0.889320	−	0.457286i
$513$		0			0
$514$	−48730.9	+	36689.9i	−0.184450	+	0.138874i
$515$		−	22065.7i		−	0.0831963i
$516$		0			0
$517$	−1777.23			−0.00664909
$518$	−81609.1	−	108392.i	−0.304144	−	0.403958i
$519$		0			0
$520$	−12798.4	−	33464.3i	−0.0473312	−	0.123758i
$521$	−58965.8			−0.217233			−0.108616	−	0.994084i	$-0.534642\pi$
$521$	−58965.8			−0.217233			−0.108616	+	0.994084i	$0.534642\pi$
$522$		0			0
$523$		−	117488.i		−	0.429527i	−0.976666	−	0.214763i	$-0.931102\pi$
$523$		−	117488.i		−	0.429527i	0.976666	−	0.214763i	$-0.0688980\pi$
$524$	−438980.	−	126266.i	−1.59876	−	0.459859i
$525$		0			0
$526$	248583.	+	330163.i	0.898463	+	1.19332i
$527$			365888.i			1.31743i
$528$		0			0
$529$	−115428.			−0.412475
$530$	34379.8	−	25884.8i	0.122391	−	0.0921497i
$531$		0			0
$532$	37571.7	−	130623.i	0.132751	−	0.461525i
$533$	−326929.			−1.15080
$534$		0			0
$535$		−	28649.0i		−	0.100093i
$536$	−131725.	+	50377.9i	−0.458498	+	0.175352i
$537$		0			0
$538$	274873.	−	206954.i	0.949658	−	0.715006i
$539$			9327.75i			0.0321070i
$540$		0			0
$541$	−16461.8			−0.0562448			−0.0281224	−	0.999604i	$-0.508953\pi$
$541$	−16461.8			−0.0562448			−0.0281224	+	0.999604i	$0.508953\pi$
$542$	−37602.5	−	49943.0i	−0.128002	−	0.170011i
$543$		0			0
$544$	−271405.	+	23182.5i	−0.917108	+	0.0783363i
$545$	−33161.2			−0.111644
$546$		0			0
$547$			389586.i			1.30205i	0.759056	+	0.651026i	$0.225661\pi$
$547$			389586.i			1.30205i	−0.759056	+	0.651026i	$0.774339\pi$
$548$	−2737.18	+	9516.13i	−0.00911470	+	0.0316883i
$549$		0			0
$550$	7468.01	+	9918.87i	0.0246876	+	0.0327897i
$551$		−	234623.i		−	0.772801i
$552$		0			0
$553$	−118831.			−0.388581
$554$	180914.	−	136212.i	0.589457	−	0.443807i
$555$		0			0
$556$	298643.	+	85900.5i	0.966058	+	0.277873i
$557$	434133.			1.39931			0.699653	−	0.714483i	$-0.253338\pi$
$557$	434133.			1.39931			0.699653	+	0.714483i	$0.253338\pi$
$558$		0			0
$559$			455263.i			1.45693i
$560$	−6390.63	+	10189.8i	−0.0203783	+	0.0324930i
$561$		0			0
$562$	−354918.	+	267221.i	−1.12371	+	0.846054i
$563$		−	222254.i		−	0.701185i	−0.936528	−	0.350592i	$-0.885980\pi$
$563$		−	222254.i		−	0.701185i	0.936528	−	0.350592i	$-0.114020\pi$
$564$		0			0
$565$	−24011.1			−0.0752169
$566$	−219417.	−	291425.i	−0.684916	−	0.909692i
$567$		0			0
$568$	−31341.2	+	11986.4i	−0.0971448	+	0.0371529i
$569$	3925.12			0.0121235			0.00606175	−	0.999982i	$-0.498070\pi$
$569$	3925.12			0.0121235			0.00606175	+	0.999982i	$0.498070\pi$
$570$		0			0
$571$		−	382845.i		−	1.17422i	−0.809505	−	0.587112i	$-0.800265\pi$
$571$		−	382845.i		−	1.17422i	0.809505	−	0.587112i	$-0.199735\pi$
$572$	21189.9	+	6094.97i	0.0647645	+	0.0186286i
$573$		0			0
$574$	66015.8	+	87680.9i	0.200366	+	0.266122i
$575$		−	390347.i		−	1.18063i
$576$		0			0
$577$	18219.2			0.0547239			0.0273620	−	0.999626i	$-0.491289\pi$
$577$	18219.2			0.0547239			0.0273620	+	0.999626i	$0.491289\pi$
$578$	40775.1	−	30700.0i	0.122051	−	0.0918930i
$579$		0			0
$580$	−5739.40	+	19953.7i	−0.0170612	+	0.0593154i
$581$	−184815.			−0.547502
$582$		0			0
$583$			26484.1i			0.0779198i
$584$	−34116.5	−	89205.4i	−0.100032	−	0.261556i
$585$		0			0
$586$	−265277.	+	199730.i	−0.772510	+	0.581630i
$587$			52925.7i			0.153600i	0.997047	+	0.0767998i	$0.0244702\pi$
$587$			52925.7i			0.153600i	−0.997047	+	0.0767998i	$0.975530\pi$
$588$		0			0
$589$	−505065.			−1.45585
$590$	29470.7	+	39142.4i	0.0846616	+	0.112446i
$591$		0			0
$592$	−317982.	−	199425.i	−0.907317	−	0.569032i
$593$	216280.			0.615046			0.307523	−	0.951541i	$-0.400500\pi$
$593$	216280.			0.615046			0.307523	+	0.951541i	$0.400500\pi$
$594$		0			0
$595$			12498.3i			0.0353033i
$596$	2738.99	−	9522.41i	0.00771077	−	0.0268074i
$597$		0			0
$598$	−416953.	−	553789.i	−1.16596	−	1.54861i
$599$		−	300397.i		−	0.837223i	−0.908165	−	0.418612i	$-0.862517\pi$
$599$		−	300397.i		−	0.837223i	0.908165	−	0.418612i	$-0.137483\pi$
$600$		0			0
$601$	510971.			1.41464			0.707322	−	0.706892i	$-0.249903\pi$
$601$	510971.			1.41464			0.707322	+	0.706892i	$0.249903\pi$
$602$	122099.	−	91929.8i	0.336915	−	0.253667i
$603$		0			0
$604$	−66725.9	−	19192.8i	−0.182903	−	0.0526094i
$605$	−29683.7			−0.0810974
$606$		0			0
$607$			178075.i			0.483310i	0.970362	+	0.241655i	$0.0776902\pi$
$607$			178075.i			0.483310i	−0.970362	+	0.241655i	$0.922310\pi$
$608$	−32000.7	−	374642.i	−0.0865670	−	1.01347i
$609$		0			0
$610$	10816.8	−	8144.03i	0.0290695	−	0.0218867i
$611$			97990.4i			0.262483i
$612$		0			0
$613$	570495.			1.51821			0.759103	−	0.650970i	$-0.225638\pi$
$613$	570495.			1.51821			0.759103	+	0.650970i	$0.225638\pi$
$614$	156872.	+	208354.i	0.416110	+	0.552670i
$615$		0			0
$616$	−2644.17	−	6913.77i	−0.00696831	−	0.0182202i
$617$	215902.			0.567134			0.283567	−	0.958952i	$-0.408482\pi$
$617$	215902.			0.567134			0.283567	+	0.958952i	$0.408482\pi$
$618$		0			0
$619$		−	182810.i		−	0.477110i	−0.971129	−	0.238555i	$-0.923326\pi$
$619$		−	182810.i		−	0.477110i	0.971129	−	0.238555i	$-0.0766737\pi$
$620$	42953.6	+	12355.0i	0.111742	+	0.0321410i
$621$		0			0
$622$	−321672.	−	427238.i	−0.831442	−	1.10431i
$623$		−	204977.i		−	0.528116i
$624$		0			0
$625$	382908.			0.980246
$626$	−35918.0	+	27043.0i	−0.0916566	+	0.0690091i
$627$		0			0
$628$	−27456.0	+	95454.0i	−0.0696174	+	0.242033i
$629$	−390019.			−0.985791
$630$		0			0
$631$		−	153307.i		−	0.385037i	−0.981293	−	0.192518i	$-0.938335\pi$
$631$		−	153307.i		−	0.385037i	0.981293	−	0.192518i	$-0.0616655\pi$
$632$	−307047.	+	117430.i	−0.768725	+	0.293998i
$633$		0			0
$634$	125285.	−	94328.0i	0.311687	−	0.234672i
$635$		−	42608.2i		−	0.105669i
$636$		0			0
$637$	514301.			1.26747
$638$	−7685.56	−	10207.8i	−0.0188814	−	0.0250779i
$639$		0			0
$640$	−6443.06	+	32644.5i	−0.0157301	+	0.0796986i
$641$	393252.			0.957095			0.478547	−	0.878062i	$-0.341163\pi$
$641$	393252.			0.957095			0.478547	+	0.878062i	$0.341163\pi$
$642$		0			0
$643$			444526.i			1.07517i	0.843211	+	0.537583i	$0.180662\pi$
$643$			444526.i			1.07517i	−0.843211	+	0.537583i	$0.819338\pi$
$644$	−64329.7	+	223650.i	−0.155110	+	0.539258i
$645$		0			0
$646$	−235006.	−	312130.i	−0.563136	−	0.747947i
$647$		−	152505.i		−	0.364314i	−0.983269	−	0.182157i	$-0.941692\pi$
$647$		−	152505.i		−	0.364314i	0.983269	−	0.182157i	$-0.0583079\pi$
$648$		0			0
$649$	−30153.0			−0.0715881
$650$	546893.	−	411761.i	1.29442	−	0.974583i
$651$		0			0
$652$	−243826.	−	70133.1i	−0.573568	−	0.164979i
$653$	−299234.			−0.701753			−0.350876	−	0.936422i	$-0.614116\pi$
$653$	−299234.			−0.701753			−0.350876	+	0.936422i	$0.614116\pi$
$654$		0			0
$655$			57979.5i			0.135143i
$656$	257224.	+	161321.i	0.597728	+	0.374871i
$657$		0			0
$658$	26280.6	−	19786.9i	0.0606992	−	0.0457010i
$659$			417069.i			0.960367i	0.877168	+	0.480183i	$0.159430\pi$
$659$			417069.i			0.960367i	−0.877168	+	0.480183i	$0.840570\pi$
$660$		0			0
$661$	759550.			1.73842			0.869208	−	0.494447i	$-0.164629\pi$
$661$	759550.			1.73842			0.869208	+	0.494447i	$0.164629\pi$
$662$	179848.	+	238870.i	0.410383	+	0.545063i
$663$		0			0
$664$	−477542.	+	182635.i	−1.08312	+	0.414237i
$665$	−17252.3			−0.0390126
$666$		0			0
$667$			401718.i			0.902962i
$668$	6442.72	+	1853.16i	0.0144383	+	0.00415298i
$669$		0			0
$670$	10767.2	+	14300.9i	0.0239858	+	0.0318575i
$671$			8332.58i			0.0185069i
$672$		0			0
$673$	−37672.0			−0.0831742			−0.0415871	−	0.999135i	$-0.513241\pi$
$673$	−37672.0			−0.0831742			−0.0415871	+	0.999135i	$0.513241\pi$
$674$	453184.	−	341207.i	0.997597	−	0.751100i
$675$		0			0
$676$	209735.	−	729170.i	0.458964	−	1.59564i
$677$	−694020.			−1.51424			−0.757120	−	0.653276i	$-0.773394\pi$
$677$	−694020.			−1.51424			−0.757120	+	0.653276i	$0.773394\pi$
$678$		0			0
$679$			157748.i			0.342156i
$680$	12350.8	+	32294.1i	0.0267103	+	0.0698402i
$681$		0			0
$682$	−21974.0	+	16544.4i	−0.0472433	+	0.0355699i
$683$			357197.i			0.765714i	0.923808	+	0.382857i	$0.125060\pi$
$683$			357197.i			0.765714i	−0.923808	+	0.382857i	$0.874940\pi$
$684$		0			0
$685$	1256.87			0.00267861
$686$	−237493.	−	315433.i	−0.504664	−	0.670285i
$687$		0			0
$688$	224646.	−	358195.i	0.474593	−	0.756734i
$689$	1.46024e6			3.07601
$690$		0			0
$691$		−	443952.i		−	0.929778i	−0.885369	−	0.464889i	$-0.846094\pi$
$691$		−	443952.i		−	0.929778i	0.885369	−	0.464889i	$-0.153906\pi$
$692$	−84922.2	+	295242.i	−0.177341	+	0.616547i
$693$		0			0
$694$	440359.	+	584876.i	0.914297	+	1.21435i
$695$		−	39444.2i		−	0.0816607i
$696$		0			0
$697$	315497.			0.649426
$698$	−429984.	+	323739.i	−0.882555	+	0.664484i
$699$		0			0
$700$	−220865.	−	63528.7i	−0.450745	−	0.129650i
$701$	−483771.			−0.984474			−0.492237	−	0.870461i	$-0.663821\pi$
$701$	−483771.			−0.984474			−0.492237	+	0.870461i	$0.663821\pi$
$702$		0			0
$703$		−	538375.i		−	1.08937i
$704$	−13664.5	−	15251.4i	−0.0275706	−	0.0307727i
$705$		0			0
$706$	639995.	−	481858.i	1.28401	−	0.966740i
$707$			71510.5i			0.143064i
$708$		0			0
$709$	158339.			0.314989			0.157494	−	0.987520i	$-0.449658\pi$
$709$	158339.			0.314989			0.157494	+	0.987520i	$0.449658\pi$
$710$	2561.85	+	3402.60i	0.00508203	+	0.00674986i
$711$		0			0
$712$	−202559.	−	529638.i	−0.399569	−	1.04477i
$713$	864764.			1.70105
$714$		0			0
$715$		−	2798.72i		−	0.00547453i
$716$	−766087.	−	220354.i	−1.49435	−	0.429828i
$717$		0			0
$718$	−387787.	−	515051.i	−0.752219	−	0.999083i
$719$			781622.i			1.51196i	0.654597	+	0.755978i	$0.272838\pi$
$719$			781622.i			1.51196i	−0.654597	+	0.755978i	$0.727162\pi$
$720$		0			0
$721$	−251358.			−0.483529
$722$	14413.3	−	10851.9i	0.0276496	−	0.0208177i
$723$		0			0
$724$	61790.3	−	214821.i	0.117881	−	0.409827i
$725$	−396716.			−0.754751
$726$		0			0
$727$		−	59571.1i		−	0.112711i	−0.998411	−	0.0563556i	$-0.982052\pi$
$727$		−	59571.1i		−	0.112711i	0.998411	−	0.0563556i	$-0.0179480\pi$
$728$	−381202.	+	145790.i	−0.719271	+	0.275085i
$729$		0			0
$730$	−9684.71	+	7291.71i	−0.0181736	+	0.0136831i
$731$		−	439343.i		−	0.822184i
$732$		0			0
$733$	−213845.			−0.398008			−0.199004	−	0.979999i	$-0.563771\pi$
$733$	−213845.			−0.398008			−0.199004	+	0.979999i	$0.563771\pi$
$734$	480143.	+	637716.i	0.891206	+	1.18368i
$735$		0			0
$736$	54791.1	+	641457.i	0.101147	+	1.18416i
$737$	−11016.5			−0.0202819
$738$		0			0
$739$			218903.i			0.400832i	0.979711	+	0.200416i	$0.0642294\pi$
$739$			218903.i			0.400832i	−0.979711	+	0.200416i	$0.935771\pi$
$740$	−13169.8	+	45786.5i	−0.0240501	+	0.0836130i
$741$		0			0
$742$	−294863.	−	391631.i	−0.535565	−	0.711327i
$743$		−	498238.i		−	0.902525i	−0.892391	−	0.451263i	$-0.850974\pi$
$743$		−	498238.i		−	0.902525i	0.892391	−	0.451263i	$-0.149026\pi$
$744$		0			0
$745$	−1257.70			−0.00226602
$746$	18497.9	−	13927.3i	0.0332388	−	0.0250258i
$747$		0			0
$748$	−20448.9	−	5881.85i	−0.0365483	−	0.0105126i
$749$	−326350.			−0.581729
$750$		0			0
$751$			617010.i			1.09399i	0.837137	+	0.546994i	$0.184228\pi$
$751$			617010.i			1.09399i	−0.837137	+	0.546994i	$0.815772\pi$
$752$	48352.6	−	77097.7i	0.0855035	−	0.136335i
$753$		0			0
$754$	−562825.	+	423756.i	−0.989989	+	0.745372i
$755$			8813.01i			0.0154607i
$756$		0			0
$757$	483106.			0.843045			0.421523	−	0.906818i	$-0.361496\pi$
$757$	483106.			0.843045			0.421523	+	0.906818i	$0.361496\pi$
$758$	524328.	+	696403.i	0.912567	+	1.21205i
$759$		0			0
$760$	−44578.1	+	17048.9i	−0.0771782	+	0.0295167i
$761$	−137695.			−0.237765			−0.118882	−	0.992908i	$-0.537931\pi$
$761$	−137695.			−0.237765			−0.118882	+	0.992908i	$0.537931\pi$
$762$		0			0
$763$			377750.i			0.648866i
$764$	−479301.	−	137864.i	−0.821148	−	0.236192i
$765$		0			0
$766$	−167209.	−	222084.i	−0.284972	−	0.378494i
$767$			1.66254e6i			2.82605i
$768$		0			0
$769$	−346769.			−0.586392			−0.293196	−	0.956052i	$-0.594719\pi$
$769$	−346769.			−0.586392			−0.293196	+	0.956052i	$0.594719\pi$
$770$	−750.603	+	565.136i	−0.00126599	+	0.000953173i
$771$		0			0
$772$	119401.	−	415110.i	0.200342	−	0.696513i
$773$	−456941.			−0.764717			−0.382358	−	0.924014i	$-0.624888\pi$
$773$	−456941.			−0.764717			−0.382358	+	0.924014i	$0.624888\pi$
$774$		0			0
$775$			853996.i			1.42185i
$776$	155887.	+	407602.i	0.258873	+	0.676882i
$777$		0			0
$778$	−183634.	+	138260.i	−0.303386	+	0.228422i
$779$			435506.i			0.717661i
$780$		0			0
$781$	−2621.16			−0.00429726
$782$	402373.	+	534424.i	0.657984	+	0.873922i
$783$		0			0
$784$	−404646.	−	253777.i	−0.658329	−	0.412877i
$785$	12607.4			0.0204590
$786$		0			0
$787$		−	696264.i		−	1.12415i	−0.827086	−	0.562075i	$-0.810003\pi$
$787$		−	696264.i		−	1.12415i	0.827086	−	0.562075i	$-0.189997\pi$
$788$	46070.3	−	160169.i	0.0741940	−	0.257944i
$789$		0			0
$790$	25098.2	+	33335.0i	0.0402151	+	0.0534129i
$791$			273518.i			0.437153i
$792$		0			0
$793$	459430.			0.730589
$794$	−42359.3	+	31892.7i	−0.0671905	+	0.0505884i
$795$		0			0
$796$	129758.	+	37323.0i	0.204789	+	0.0589048i
$797$	131361.			0.206799			0.103399	−	0.994640i	$-0.467028\pi$
$797$	131361.			0.206799			0.103399	+	0.994640i	$0.467028\pi$
$798$		0			0
$799$		−	94563.9i		−	0.148126i
$800$	−633470.	+	54108.9i	−0.989796	+	0.0845451i
$801$		0			0
$802$	17177.0	−	12932.7i	0.0267053	−	0.0201067i
$803$		−	7460.52i		−	0.0115701i
$804$		0			0
$805$	29539.2			0.0455834
$806$	912204.	+	1.21157e6i	1.40418	+	1.86500i
$807$		0			0
$808$	70667.0	+	184775.i	0.108242	+	0.283022i
$809$	796199.			1.21653			0.608267	−	0.793732i	$-0.291865\pi$
$809$	796199.			1.21653			0.608267	+	0.793732i	$0.291865\pi$
$810$		0			0
$811$		−	116976.i		−	0.177851i	−0.996038	−	0.0889253i	$-0.971657\pi$
$811$		−	116976.i		−	0.177851i	0.996038	−	0.0889253i	$-0.0283432\pi$
$812$	227299.	+	65379.3i	0.344735	+	0.0991582i
$813$		0			0
$814$	−17635.6	−	23423.3i	−0.0266159	−	0.0353507i
$815$			32204.0i			0.0484836i
$816$		0			0
$817$	606461.			0.908570
$818$	769142.	−	579094.i	1.14948	−	0.865451i
$819$		0			0
$820$	10653.4	−	37037.9i	0.0158439	−	0.0550832i
$821$	293547.			0.435503			0.217751	−	0.976004i	$-0.430128\pi$
$821$	293547.			0.435503			0.217751	+	0.976004i	$0.430128\pi$
$822$		0			0
$823$			229452.i			0.338760i	0.985551	+	0.169380i	$0.0541765\pi$
$823$			229452.i			0.338760i	−0.985551	+	0.169380i	$0.945824\pi$
$824$	−649481.	+	248393.i	−0.956559	+	0.365835i
$825$		0			0
$826$	445885.	−	335711.i	0.653525	−	0.492045i
$827$			673431.i			0.984651i	0.870411	+	0.492326i	$0.163853\pi$
$827$			673431.i			0.984651i	−0.870411	+	0.492326i	$0.836147\pi$
$828$		0			0
$829$	268282.			0.390375			0.195188	−	0.980766i	$-0.437468\pi$
$829$	268282.			0.390375			0.195188	+	0.980766i	$0.437468\pi$
$830$	39034.5	+	51844.9i	0.0566621	+	0.0752576i
$831$		0			0
$832$	−840913.	+	753412.i	−1.21480	+	1.08839i
$833$	−496317.			−0.715268
$834$		0			0
$835$		−	850.941i		−	0.00122047i
$836$	8119.18	−	28227.3i	0.0116172	−	0.0403884i
$837$		0			0
$838$	85204.7	+	113167.i	0.121332	+	0.161151i
$839$		−	1.00219e6i		−	1.42373i	−0.702317	−	0.711865i	$-0.747851\pi$
$839$		−	1.00219e6i		−	1.42373i	0.702317	−	0.711865i	$-0.252149\pi$
$840$		0			0
$841$	−299009.			−0.422758
$842$	527569.	−	397212.i	0.744141	−	0.560271i
$843$		0			0
$844$	352826.	+	101485.i	0.495308	+	0.142468i
$845$	−96307.2			−0.134879
$846$		0			0
$847$			338137.i			0.471330i
$848$	−1.14890e6	−	720546.i	−1.59769	−	1.00201i
$849$		0			0
$850$	−527770.	+	397363.i	−0.730477	+	0.549983i
$851$			921797.i			1.27285i
$852$		0			0
$853$	411590.			0.565675			0.282837	−	0.959168i	$-0.408724\pi$
$853$	411590.			0.565675			0.282837	+	0.959168i	$0.408724\pi$
$854$	−92771.3	−	123217.i	−0.127203	−	0.168949i
$855$		0			0
$856$	−843253.	+	322501.i	−1.15083	+	0.440133i
$857$	−920807.			−1.25374			−0.626869	−	0.779125i	$-0.715664\pi$
$857$	−920807.			−1.25374			−0.626869	+	0.779125i	$0.715664\pi$
$858$		0			0
$859$			601367.i			0.814992i	0.913207	+	0.407496i	$0.133598\pi$
$859$			601367.i			0.814992i	−0.913207	+	0.407496i	$0.866402\pi$
$860$	−51576.9	−	14835.4i	−0.0697362	−	0.0200586i
$861$		0			0
$862$	−388976.	−	516631.i	−0.523490	−	0.695289i
$863$		−	1.01872e6i		−	1.36783i	−0.729560	−	0.683917i	$-0.760275\pi$
$863$		−	1.01872e6i		−	1.36783i	0.729560	−	0.683917i	$-0.239725\pi$
$864$		0			0
$865$	38994.9			0.0521166
$866$	197597.	−	148772.i	0.263478	−	0.198375i
$867$		0			0
$868$	140740.	−	489298.i	0.186800	−	0.649433i
$869$	−25679.3			−0.0340050
$870$		0			0
$871$			607414.i			0.800661i
$872$	373294.	+	976063.i	0.490929	+	1.28365i
$873$		0			0
$874$	−737709.	+	555428.i	−0.965744	+	0.727118i
$875$			58536.6i			0.0764559i
$876$		0			0
$877$	865345.			1.12510			0.562549	−	0.826764i	$-0.309821\pi$
$877$	865345.			1.12510			0.562549	+	0.826764i	$0.309821\pi$
$878$	−744602.	−	988967.i	−0.965907	−	1.28290i
$879$		0			0
$880$	−1381.00	+	2202.00i	−0.00178332	+	0.00284349i
$881$	1.46275e6			1.88459			0.942296	−	0.334780i	$-0.108662\pi$
$881$	1.46275e6			1.88459			0.942296	+	0.334780i	$0.108662\pi$
$882$		0			0
$883$			162909.i			0.208941i	0.994528	+	0.104470i	$0.0333148\pi$
$883$			162909.i			0.208941i	−0.994528	+	0.104470i	$0.966685\pi$
$884$	−324305.	+	1.12749e6i	−0.415001	+	1.44280i
$885$		0			0
$886$	112836.	+	149866.i	0.143741	+	0.190914i
$887$			222309.i			0.282559i	0.989970	+	0.141280i	$0.0451217\pi$
$887$			222309.i			0.282559i	−0.989970	+	0.141280i	$0.954878\pi$
$888$		0			0
$889$	−485364.			−0.614136
$890$	−57500.8	+	43292.9i	−0.0725929	+	0.0546559i
$891$		0			0
$892$	988102.	+	284213.i	1.24186	+	0.357203i
$893$	130534.			0.163690
$894$		0			0
$895$			101183.i			0.126317i
$896$	371865.	+	73395.0i	0.463201	+	0.0914219i
$897$		0			0
$898$	398985.	−	300400.i	0.494771	−	0.372518i
$899$		−	878873.i		−	1.08744i
$900$		0			0
$901$	−1.40918e6			−1.73587
$902$	14265.9	+	18947.7i	0.0175342	+	0.0232886i
$903$		0			0
$904$	270292.	+	706741.i	0.330748	+	0.864815i
$905$	−28373.1			−0.0346426
$906$		0			0
$907$			1.19701e6i			1.45507i	0.686071	+	0.727534i	$0.259334\pi$
$907$			1.19701e6i			1.45507i	−0.686071	+	0.727534i	$0.740666\pi$
$908$	103106.	+	29656.8i	0.125058	+	0.0359711i
$909$		0			0
$910$	31159.7	+	41385.7i	0.0376280	+	0.0499767i
$911$			930730.i			1.12147i	0.827996	+	0.560734i	$0.189481\pi$
$911$			930730.i			1.12147i	−0.827996	+	0.560734i	$0.810519\pi$
$912$		0			0
$913$	−39938.2			−0.0479123
$914$	401029.	−	301939.i	0.480047	−	0.361432i
$915$		0			0
$916$	157234.	−	546641.i	0.187393	−	0.651495i
$917$	660464.			0.785435
$918$		0			0
$919$		−	1.46503e6i		−	1.73467i	−0.497725	−	0.867335i	$-0.665831\pi$
$919$		−	1.46503e6i		−	1.73467i	0.497725	−	0.867335i	$-0.334169\pi$
$920$	76326.0	−	29190.8i	0.0901772	−	0.0344882i
$921$		0			0
$922$	−330082.	+	248522.i	−0.388293	+	0.292349i
$923$			144522.i			0.169641i
$924$		0			0
$925$	−910319.			−1.06392
$926$	771115.	+	1.02418e6i	0.899284	+	1.19441i
$927$		0			0
$928$	651923.	−	55685.1i	0.757008	−	0.0646611i
$929$	987182.			1.14384			0.571921	−	0.820309i	$-0.306198\pi$
$929$	987182.			1.14384			0.571921	+	0.820309i	$0.306198\pi$
$930$		0			0
$931$		−	685106.i		−	0.790421i
$932$	276162.	−	960111.i	0.317931	−	1.10532i
$933$		0			0
$934$	1.02826e6	+	1.36571e6i	1.17871	+	1.56554i
$935$			2700.85i			0.00308942i
$936$		0			0
$937$	−287243.			−0.327167			−0.163584	−	0.986529i	$-0.552305\pi$
$937$	−287243.			−0.327167			−0.163584	+	0.986529i	$0.552305\pi$
$938$	162906.	−	122653.i	0.185153	−	0.139403i
$939$		0			0
$940$	−11101.4	−	3193.15i	−0.0125638	−	0.00361380i
$941$	−298195.			−0.336760			−0.168380	−	0.985722i	$-0.553854\pi$
$941$	−298195.			−0.336760			−0.168380	+	0.985722i	$0.553854\pi$
$942$		0			0
$943$		−	745666.i		−	0.838535i
$944$	820364.	−	1.30806e6i	0.920583	−	1.46786i
$945$		0			0
$946$	26385.5	−	19865.9i	0.0294837	−	0.0221986i
$947$		−	1.04409e6i		−	1.16423i	−0.813106	−	0.582115i	$-0.802225\pi$
$947$		−	1.04409e6i		−	1.16423i	0.813106	−	0.582115i	$-0.197775\pi$
$948$		0			0
$949$	−411348.			−0.456748
$950$	−548512.	−	728523.i	−0.607769	−	0.807228i
$951$		0			0
$952$	367873.	−	140692.i	0.405904	−	0.155238i
$953$	−1.38691e6			−1.52708			−0.763539	−	0.645762i	$-0.776540\pi$
$953$	−1.38691e6			−1.52708			−0.763539	+	0.645762i	$0.776540\pi$
$954$		0			0
$955$			63305.1i			0.0694115i
$956$	57715.2	+	16601.0i	0.0631501	+	0.0181642i
$957$		0			0
$958$	462088.	+	613737.i	0.503494	+	0.668731i
$959$		−	14317.4i		−	0.0155678i
$960$		0			0
$961$	−968398.			−1.04859
$962$	−1.29148e6	+	972367.i	−1.39552	+	1.05070i
$963$		0			0
$964$	−396576.	+	1.37874e6i	−0.426748	+	1.48364i
$965$	−54826.9			−0.0588761
$966$		0			0
$967$		−	805010.i		−	0.860892i	−0.902616	−	0.430446i	$-0.858356\pi$
$967$		−	805010.i		−	0.860892i	0.902616	−	0.430446i	$-0.141644\pi$
$968$	334148.	+	873707.i	0.356606	+	0.932427i
$969$		0			0
$970$	44251.9	−	33317.7i	0.0470315	−	0.0354104i
$971$			643421.i			0.682428i	0.939986	+	0.341214i	$0.110838\pi$
$971$			643421.i			0.682428i	−0.939986	+	0.341214i	$0.889162\pi$
$972$		0			0
$973$	−449321.			−0.474604
$974$	127239.	+	168996.i	0.134122	+	0.178139i
$975$		0			0
$976$	−361475.	−	226702.i	−0.379471	−	0.237989i
$977$	−127012.			−0.133062			−0.0665311	−	0.997784i	$-0.521193\pi$
$977$	−127012.			−0.133062			−0.0665311	+	0.997784i	$0.521193\pi$
$978$		0			0
$979$		−	44295.2i		−	0.0462159i
$980$	−16759.2	+	58265.3i	−0.0174502	+	0.0606678i
$981$		0			0
$982$	17693.7	+	23500.5i	0.0183483	+	0.0243699i
$983$			183207.i			0.189599i	0.995496	+	0.0947994i	$0.0302210\pi$
$983$			183207.i			0.189599i	−0.995496	+	0.0947994i	$0.969779\pi$
$984$		0			0
$985$	−21154.8			−0.0218040
$986$	543144.	−	408938.i	0.558677	−	0.420633i
$987$		0			0
$988$	−1.55636e6	−	447665.i	−1.59439	−	0.458605i
$989$	−1.03837e6			−1.06160
$990$		0			0
$991$		−	684255.i		−	0.696740i	−0.937357	−	0.348370i	$-0.886735\pi$
$991$		−	684255.i		−	0.696740i	0.937357	−	0.348370i	$-0.113265\pi$
$992$	−119871.	−	1.40337e6i	−0.121813	−	1.42610i
$993$		0			0
$994$	38760.2	−	29182.9i	0.0392295	−	0.0295363i
$995$		−	17138.1i		−	0.0173108i
$996$		0			0
$997$	−543633.			−0.546909			−0.273455	−	0.961885i	$-0.588166\pi$
$997$	−543633.			−0.546909			−0.273455	+	0.961885i	$0.588166\pi$
$998$	−998582.	−	1.32630e6i	−1.00259	−	1.33162i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.f.163.6		22
3.2	odd	2		324.5.d.e.163.17		22
4.3	odd	2	inner	324.5.d.f.163.5		22
9.2	odd	6		108.5.f.a.91.3		44
9.4	even	3		36.5.f.a.7.11	✓	44
9.5	odd	6		108.5.f.a.19.12		44
9.7	even	3		36.5.f.a.31.20	yes	44
12.11	even	2		324.5.d.e.163.18		22
36.7	odd	6		36.5.f.a.31.11	yes	44
36.11	even	6		108.5.f.a.91.12		44
36.23	even	6		108.5.f.a.19.3		44
36.31	odd	6		36.5.f.a.7.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.11	✓	44	9.4	even	3
36.5.f.a.7.20	yes	44	36.31	odd	6
36.5.f.a.31.11	yes	44	36.7	odd	6
36.5.f.a.31.20	yes	44	9.7	even	3
108.5.f.a.19.3		44	36.23	even	6
108.5.f.a.19.12		44	9.5	odd	6
108.5.f.a.91.3		44	9.2	odd	6
108.5.f.a.91.12		44	36.11	even	6
324.5.d.e.163.17		22	3.2	odd	2
324.5.d.e.163.18		22	12.11	even	2
324.5.d.f.163.5		22	4.3	odd	2	inner
324.5.d.f.163.6		22	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.19553 + 2.40595i) q^{2} +(4.42285 - 15.3766i) q^{4} -2.03090 q^{5} +23.1347i q^{7} +(22.8618 + 59.7774i) q^{8} +O(q^{10})\)	\(q+(-3.19553 + 2.40595i) q^{2} +(4.42285 - 15.3766i) q^{4} -2.03090 q^{5} +23.1347i q^{7} +(22.8618 + 59.7774i) q^{8} +(6.48981 - 4.88624i) q^{10} +4.99936i q^{11} +275.648 q^{13} +(-55.6608 - 73.9276i) q^{14} +(-216.877 - 136.016i) q^{16} -266.009 q^{17} -367.194i q^{19} +(-8.98238 + 31.2283i) q^{20} +(-12.0282 - 15.9756i) q^{22} +628.704i q^{23} -620.875 q^{25} +(-880.842 + 663.194i) q^{26} +(355.732 + 102.321i) q^{28} +638.962 q^{29} -1375.47i q^{31} +(1020.28 - 87.1493i) q^{32} +(850.041 - 640.004i) q^{34} -46.9843i q^{35} +1466.19 q^{37} +(883.449 + 1173.38i) q^{38} +(-46.4301 - 121.402i) q^{40} -1186.04 q^{41} +1651.61i q^{43} +(76.8730 + 22.1114i) q^{44} +(-1512.63 - 2009.04i) q^{46} +355.491i q^{47} +1865.79 q^{49} +(1984.03 - 1493.79i) q^{50} +(1219.15 - 4238.52i) q^{52} +5297.49 q^{53} -10.1532i q^{55} +(-1382.93 + 528.900i) q^{56} +(-2041.82 + 1537.31i) q^{58} +6031.37i q^{59} +1666.73 q^{61} +(3309.31 + 4395.36i) q^{62} +(-3050.68 + 2733.24i) q^{64} -559.815 q^{65} +2203.58i q^{67} +(-1176.52 + 4090.31i) q^{68} +(113.042 + 150.140i) q^{70} +524.299i q^{71} -1492.29 q^{73} +(-4685.25 + 3527.57i) q^{74} +(-5646.18 - 1624.04i) q^{76} -115.659 q^{77} +5136.51i q^{79} +(440.456 + 276.236i) q^{80} +(3790.02 - 2853.54i) q^{82} +7988.66i q^{83} +540.239 q^{85} +(-3973.68 - 5277.77i) q^{86} +(-298.849 + 114.294i) q^{88} -8860.17 q^{89} +6377.03i q^{91} +(9667.30 + 2780.66i) q^{92} +(-855.292 - 1135.98i) q^{94} +745.735i q^{95} +6818.67 q^{97} +(-5962.18 + 4488.98i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) \) 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8} + 14 q^{10} + 2 q^{13} - 252 q^{14} + q^{16} - 28 q^{17} + 140 q^{20} + 33 q^{22} + 1752 q^{25} + 548 q^{26} - 258 q^{28} - 526 q^{29} + 121 q^{32} - 385 q^{34} - 4 q^{37} - 1395 q^{38} + 2276 q^{40} + 2762 q^{41} + 3357 q^{44} + 1788 q^{46} - 3428 q^{49} - 6375 q^{50} - 1438 q^{52} - 5044 q^{53} + 7506 q^{56} + 4064 q^{58} + 2 q^{61} - 9162 q^{62} + 4513 q^{64} + 2014 q^{65} + 11405 q^{68} - 3666 q^{70} - 1708 q^{73} - 14620 q^{74} - 1581 q^{76} + 3942 q^{77} + 22760 q^{80} - 4243 q^{82} + 1252 q^{85} - 22113 q^{86} - 1995 q^{88} + 6524 q^{89} + 30294 q^{92} - 7524 q^{94} - 5638 q^{97} - 46469 q^{98}+O(q^{100}) \) 22 * q + q^2 + q^4 + 2 * q^5 + 61 * q^8 + 14 * q^10 + 2 * q^13 - 252 * q^14 + q^16 - 28 * q^17 + 140 * q^20 + 33 * q^22 + 1752 * q^25 + 548 * q^26 - 258 * q^28 - 526 * q^29 + 121 * q^32 - 385 * q^34 - 4 * q^37 - 1395 * q^38 + 2276 * q^40 + 2762 * q^41 + 3357 * q^44 + 1788 * q^46 - 3428 * q^49 - 6375 * q^50 - 1438 * q^52 - 5044 * q^53 + 7506 * q^56 + 4064 * q^58 + 2 * q^61 - 9162 * q^62 + 4513 * q^64 + 2014 * q^65 + 11405 * q^68 - 3666 * q^70 - 1708 * q^73 - 14620 * q^74 - 1581 * q^76 + 3942 * q^77 + 22760 * q^80 - 4243 * q^82 + 1252 * q^85 - 22113 * q^86 - 1995 * q^88 + 6524 * q^89 + 30294 * q^92 - 7524 * q^94 - 5638 * q^97 - 46469 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more