LMFDB - Embedded newform 324.5.d.f.163.17

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			163.17
Character	$\chi$	$=$	324.163
Dual form			324.5.d.f.163.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.82463 - 2.83222i) q^{2} +(-0.0429591 - 15.9999i) q^{4} +11.7888 q^{5} +58.3756i q^{7} +(-45.4367 - 45.0722i) q^{8} +O(q^{10})$	\(q+(2.82463 - 2.83222i) q^{2} +(-0.0429591 - 15.9999i) q^{4} +11.7888 q^{5} +58.3756i q^{7} +(-45.4367 - 45.0722i) q^{8} +(33.2988 - 33.3884i) q^{10} +100.429i q^{11} -170.636 q^{13} +(165.333 + 164.889i) q^{14} +(-255.996 + 1.37469i) q^{16} -398.571 q^{17} +404.608i q^{19} +(-0.506434 - 188.619i) q^{20} +(284.438 + 283.675i) q^{22} -336.123i q^{23} -486.025 q^{25} +(-481.982 + 483.278i) q^{26} +(934.007 - 2.50777i) q^{28} -655.342 q^{29} +635.277i q^{31} +(-719.201 + 728.921i) q^{32} +(-1125.81 + 1128.84i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(1145.94 + 1142.87i) q^{38} +(-535.642 - 531.345i) q^{40} +2463.27 q^{41} -2232.48i q^{43} +(1606.86 - 4.31435i) q^{44} +(-951.976 - 949.423i) q^{46} +2903.56i q^{47} -1006.72 q^{49} +(-1372.84 + 1376.53i) q^{50} +(7.33036 + 2730.16i) q^{52} +1291.73 q^{53} +1183.94i q^{55} +(2631.12 - 2652.40i) q^{56} +(-1851.10 + 1856.07i) q^{58} +1157.28i q^{59} +5921.62 q^{61} +(1799.24 + 1794.42i) q^{62} +(32.9923 + 4095.87i) q^{64} -2011.58 q^{65} -3563.26i q^{67} +(17.1222 + 6377.11i) q^{68} +(1949.07 + 1943.84i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(-4519.16 + 4531.31i) q^{74} +(6473.71 - 17.3816i) q^{76} -5862.62 q^{77} -3220.39i q^{79} +(-3017.88 + 16.2058i) q^{80} +(6957.81 - 6976.52i) q^{82} +8156.71i q^{83} -4698.65 q^{85} +(-6322.88 - 6305.92i) q^{86} +(4526.57 - 4563.17i) q^{88} +910.873 q^{89} -9960.97i q^{91} +(-5377.95 + 14.4396i) q^{92} +(8223.52 + 8201.47i) q^{94} +4769.83i q^{95} -17608.9 q^{97} +(-2843.60 + 2851.24i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.82463	−	2.83222i	0.706157	−	0.708055i
$2$	2.82463	−	2.83222i	0.706157	−	0.708055i
$3$		0			0
$3$		0			0
$4$	−0.0429591	−	15.9999i	−0.00268494	−	0.999996i
$5$	11.7888			0.471550			0.235775	−	0.971808i	$-0.424237\pi$
$5$	11.7888			0.471550			0.235775	+	0.971808i	$0.424237\pi$
$6$		0			0
$7$			58.3756i			1.19134i	0.803229	+	0.595670i	$0.203113\pi$
$7$			58.3756i			1.19134i	−0.803229	+	0.595670i	$0.796887\pi$
$8$	−45.4367	−	45.0722i	−0.709949	−	0.704253i
$9$		0			0
$10$	33.2988	−	33.3884i	0.332988	−	0.333884i
$11$			100.429i			0.829993i	0.909823	+	0.414997i	$0.136217\pi$
$11$			100.429i			0.829993i	−0.909823	+	0.414997i	$0.863783\pi$
$12$		0			0
$13$	−170.636			−1.00968			−0.504839	−	0.863213i	$-0.668448\pi$
$13$	−170.636			−1.00968			−0.504839	+	0.863213i	$0.668448\pi$
$14$	165.333	+	164.889i	0.843535	+	0.841273i
$15$		0			0
$16$	−255.996	+	1.37469i	−0.999986	+	0.00536987i
$17$	−398.571			−1.37914			−0.689569	−	0.724220i	$-0.742200\pi$
$17$	−398.571			−1.37914			−0.689569	+	0.724220i	$0.742200\pi$
$18$		0			0
$19$			404.608i			1.12080i	0.828223	+	0.560399i	$0.189352\pi$
$19$			404.608i			1.12080i	−0.828223	+	0.560399i	$0.810648\pi$
$20$	−0.506434	−	188.619i	−0.00126609	−	0.471549i
$21$		0			0
$22$	284.438	+	283.675i	0.587681	+	0.586105i
$23$		−	336.123i		−	0.635394i	−0.948192	−	0.317697i	$-0.897091\pi$
$23$		−	336.123i		−	0.635394i	0.948192	−	0.317697i	$-0.102909\pi$
$24$		0			0
$25$	−486.025			−0.777640
$26$	−481.982	+	483.278i	−0.712991	+	0.714908i
$27$		0			0
$28$	934.007	−	2.50777i	1.19134	−	0.00319868i
$29$	−655.342			−0.779241			−0.389621	−	0.920975i	$-0.627394\pi$
$29$	−655.342			−0.779241			−0.389621	+	0.920975i	$0.627394\pi$
$30$		0			0
$31$			635.277i			0.661058i	0.943796	+	0.330529i	$0.107227\pi$
$31$			635.277i			0.661058i	−0.943796	+	0.330529i	$0.892773\pi$
$32$	−719.201	+	728.921i	−0.702345	+	0.711837i
$33$		0			0
$34$	−1125.81	+	1128.84i	−0.973888	+	0.976506i
$35$			688.176i			0.561776i
$36$		0			0
$37$	−1599.91			−1.16867			−0.584336	−	0.811512i	$-0.698645\pi$
$37$	−1599.91			−1.16867			−0.584336	+	0.811512i	$0.698645\pi$
$38$	1145.94	+	1142.87i	0.793587	+	0.791459i
$39$		0			0
$40$	−535.642	−	531.345i	−0.334777	−	0.332091i
$41$	2463.27			1.46536			0.732679	−	0.680574i	$-0.238270\pi$
$41$	2463.27			1.46536			0.732679	+	0.680574i	$0.238270\pi$
$42$		0			0
$43$		−	2232.48i		−	1.20740i	−0.797212	−	0.603699i	$-0.793693\pi$
$43$		−	2232.48i		−	1.20740i	0.797212	−	0.603699i	$-0.206307\pi$
$44$	1606.86	−	4.31435i	0.829990	−	0.00222849i
$45$		0			0
$46$	−951.976	−	949.423i	−0.449894	−	0.448688i
$47$			2903.56i			1.31442i	0.753707	+	0.657211i	$0.228264\pi$
$47$			2903.56i			1.31442i	−0.753707	+	0.657211i	$0.771736\pi$
$48$		0			0
$49$	−1006.72			−0.419290
$50$	−1372.84	+	1376.53i	−0.549136	+	0.550613i
$51$		0			0
$52$	7.33036	+	2730.16i	0.00271093	+	1.00967i
$53$	1291.73			0.459852			0.229926	−	0.973208i	$-0.426152\pi$
$53$	1291.73			0.459852			0.229926	+	0.973208i	$0.426152\pi$
$54$		0			0
$55$			1183.94i			0.391384i
$56$	2631.12	−	2652.40i	0.839005	−	0.845790i
$57$		0			0
$58$	−1851.10	+	1856.07i	−0.550267	+	0.551746i
$59$			1157.28i			0.332457i	0.986087	+	0.166229i	$0.0531590\pi$
$59$			1157.28i			0.332457i	−0.986087	+	0.166229i	$0.946841\pi$
$60$		0			0
$61$	5921.62			1.59141			0.795703	−	0.605687i	$-0.207101\pi$
$61$	5921.62			1.59141			0.795703	+	0.605687i	$0.207101\pi$
$62$	1799.24	+	1794.42i	0.468066	+	0.466811i
$63$		0			0
$64$	32.9923	+	4095.87i	0.00805476	+	0.999968i
$65$	−2011.58			−0.476114
$66$		0			0
$67$		−	3563.26i		−	0.793775i	−0.917867	−	0.396888i	$-0.870090\pi$
$67$		−	3563.26i		−	0.793775i	0.917867	−	0.396888i	$-0.129910\pi$
$68$	17.1222	+	6377.11i	0.00370291	+	1.37913i
$69$		0			0
$70$	1949.07	+	1943.84i	0.397769	+	0.396702i
$71$			5639.73i			1.11877i	0.828907	+	0.559386i	$0.188963\pi$
$71$			5639.73i			1.11877i	−0.828907	+	0.559386i	$0.811037\pi$
$72$		0			0
$73$	−5496.39			−1.03141			−0.515705	−	0.856766i	$-0.672470\pi$
$73$	−5496.39			−1.03141			−0.515705	+	0.856766i	$0.672470\pi$
$74$	−4519.16	+	4531.31i	−0.825266	+	0.827485i
$75$		0			0
$76$	6473.71	−	17.3816i	1.12079	−	0.00300928i
$77$	−5862.62			−0.988804
$78$		0			0
$79$		−	3220.39i		−	0.516006i	−0.966144	−	0.258003i	$-0.916936\pi$
$79$		−	3220.39i		−	0.516006i	0.966144	−	0.258003i	$-0.0830645\pi$
$80$	−3017.88	+	16.2058i	−0.471543	+	0.00253216i
$81$		0			0
$82$	6957.81	−	6976.52i	1.03477	−	1.03755i
$83$			8156.71i			1.18402i	0.805931	+	0.592010i	$0.201665\pi$
$83$			8156.71i			1.18402i	−0.805931	+	0.592010i	$0.798335\pi$
$84$		0			0
$85$	−4698.65			−0.650333
$86$	−6322.88	−	6305.92i	−0.854905	−	0.852612i
$87$		0			0
$88$	4526.57	−	4563.17i	0.584525	−	0.589253i
$89$	910.873			0.114995			0.0574974	−	0.998346i	$-0.481688\pi$
$89$	910.873			0.114995			0.0574974	+	0.998346i	$0.481688\pi$
$90$		0			0
$91$		−	9960.97i		−	1.20287i
$92$	−5377.95	+	14.4396i	−0.635391	+	0.00170600i
$93$		0			0
$94$	8223.52	+	8201.47i	0.930683	+	0.928188i
$95$			4769.83i			0.528513i
$96$		0			0
$97$	−17608.9			−1.87149			−0.935747	−	0.352673i	$-0.885273\pi$
$97$	−17608.9			−1.87149			−0.935747	+	0.352673i	$0.885273\pi$
$98$	−2843.60	+	2851.24i	−0.296085	+	0.296881i
$99$		0			0
$100$	20.8792	+	7776.38i	0.00208792	+	0.777638i
$101$	6660.82			0.652957			0.326479	−	0.945205i	$-0.394138\pi$
$101$	6660.82			0.652957			0.326479	+	0.945205i	$0.394138\pi$
$102$		0			0
$103$		−	6753.50i		−	0.636582i	−0.947993	−	0.318291i	$-0.896891\pi$
$103$		−	6753.50i		−	0.636582i	0.947993	−	0.318291i	$-0.103109\pi$
$104$	7753.12	+	7690.92i	0.716820	+	0.711069i
$105$		0			0
$106$	3648.64	−	3658.45i	0.324728	−	0.325601i
$107$			30.7569i			0.00268643i	0.999999	+	0.00134321i	$0.000427558\pi$
$107$			30.7569i			0.00268643i	−0.999999	+	0.00134321i	$0.999572\pi$
$108$		0			0
$109$	10691.4			0.899872			0.449936	−	0.893061i	$-0.351447\pi$
$109$	10691.4			0.899872			0.449936	+	0.893061i	$0.351447\pi$
$110$	3353.17	+	3344.18i	0.277121	+	0.276378i
$111$		0			0
$112$	−80.2482	−	14943.9i	−0.00639734	−	1.19132i
$113$	10016.2			0.784414			0.392207	−	0.919877i	$-0.371712\pi$
$113$	10016.2			0.784414			0.392207	+	0.919877i	$0.371712\pi$
$114$		0			0
$115$		−	3962.47i		−	0.299620i
$116$	28.1529	+	10485.4i	0.00209222	+	0.779238i
$117$		0			0
$118$	3277.69	+	3268.90i	0.235398	+	0.234767i
$119$		−	23266.8i		−	1.64302i
$120$		0			0
$121$	4554.98			0.311111
$122$	16726.4	−	16771.4i	1.12378	−	1.12680i
$123$		0			0
$124$	10164.4	−	27.2909i	0.661056	−	0.00177490i
$125$	−13097.6			−0.838247
$126$		0			0
$127$		−	16087.8i		−	0.997444i	−0.866762	−	0.498722i	$-0.833803\pi$
$127$		−	16087.8i		−	0.997444i	0.866762	−	0.498722i	$-0.166197\pi$
$128$	11693.6	+	11475.9i	0.713720	+	0.700431i
$129$		0			0
$130$	−5681.97	+	5697.25i	−0.336211	+	0.337115i
$131$			20906.5i			1.21825i	0.793073	+	0.609127i	$0.208480\pi$
$131$			20906.5i			1.21825i	−0.793073	+	0.609127i	$0.791520\pi$
$132$		0			0
$133$	−23619.3			−1.33525
$134$	−10091.9	−	10064.9i	−0.562037	−	0.560530i
$135$		0			0
$136$	18109.8	+	17964.5i	0.979117	+	0.971262i
$137$	4676.05			0.249137			0.124568	−	0.992211i	$-0.460245\pi$
$137$	4676.05			0.249137			0.124568	+	0.992211i	$0.460245\pi$
$138$		0			0
$139$		−	9305.07i		−	0.481604i	−0.970574	−	0.240802i	$-0.922590\pi$
$139$		−	9305.07i		−	0.481604i	0.970574	−	0.240802i	$-0.0774104\pi$
$140$	11010.8	−	29.5634i	0.561774	−	0.00150834i
$141$		0			0
$142$	15973.0	+	15930.1i	0.792152	+	0.790028i
$143$		−	17136.8i		−	0.838026i
$144$		0			0
$145$	−7725.67			−0.367451
$146$	−15525.3	+	15567.0i	−0.728338	+	0.730296i
$147$		0			0
$148$	68.7308	+	25598.5i	0.00313782	+	1.16867i
$149$	−24771.6			−1.11579			−0.557893	−	0.829913i	$-0.688390\pi$
$149$	−24771.6			−1.11579			−0.557893	+	0.829913i	$0.688390\pi$
$150$		0			0
$151$			10209.5i			0.447767i	0.974616	+	0.223884i	$0.0718735\pi$
$151$			10209.5i			0.447767i	−0.974616	+	0.223884i	$0.928126\pi$
$152$	18236.6	−	18384.1i	0.789326	−	0.795709i
$153$		0			0
$154$	−16559.7	+	16604.2i	−0.698251	+	0.700128i
$155$			7489.12i			0.311722i
$156$		0			0
$157$	−28973.0			−1.17542			−0.587712	−	0.809070i	$-0.699971\pi$
$157$	−28973.0			−1.17542			−0.587712	+	0.809070i	$0.699971\pi$
$158$	−9120.87	−	9096.41i	−0.365361	−	0.364381i
$159$		0			0
$160$	−8478.48	+	8593.07i	−0.331191	+	0.335667i
$161$	19621.4			0.756970
$162$		0			0
$163$		−	17736.4i		−	0.667560i	−0.942651	−	0.333780i	$-0.891676\pi$
$163$		−	17736.4i		−	0.667560i	0.942651	−	0.333780i	$-0.108324\pi$
$164$	−105.820	−	39412.1i	−0.00393441	−	1.46535i
$165$		0			0
$166$	23101.6	+	23039.7i	0.838352	+	0.836104i
$167$		−	41063.6i		−	1.47239i	−0.676767	−	0.736197i	$-0.736620\pi$
$167$		−	41063.6i		−	1.47239i	0.676767	−	0.736197i	$-0.263380\pi$
$168$		0			0
$169$	555.522			0.0194504
$170$	−13271.9	+	13307.6i	−0.459237	+	0.460472i
$171$		0			0
$172$	−35719.5	+	95.9053i	−1.20739	+	0.00324180i
$173$	6955.73			0.232408			0.116204	−	0.993225i	$-0.462927\pi$
$173$	6955.73			0.232408			0.116204	+	0.993225i	$0.462927\pi$
$174$		0			0
$175$		−	28372.0i		−	0.926434i
$176$	−138.059	−	25709.5i	−0.00445696	−	0.829981i
$177$		0			0
$178$	2572.88	−	2579.80i	0.0812043	−	0.0814227i
$179$			1754.50i			0.0547580i	0.999625	+	0.0273790i	$0.00871609\pi$
$179$			1754.50i			0.0547580i	−0.999625	+	0.0273790i	$0.991284\pi$
$180$		0			0
$181$	−43787.9			−1.33659			−0.668293	−	0.743898i	$-0.732975\pi$
$181$	−43787.9			−1.33659			−0.668293	+	0.743898i	$0.732975\pi$
$182$	−28211.7	−	28136.0i	−0.851699	−	0.849415i
$183$		0			0
$184$	−15149.8	+	15272.3i	−0.447478	+	0.451097i
$185$	−18861.0			−0.551088
$186$		0			0
$187$		−	40028.1i		−	1.14468i
$188$	46456.8	−	124.734i	1.31442	−	0.00352915i
$189$		0			0
$190$	13509.2	+	13473.0i	0.374216	+	0.373213i
$191$		−	39725.3i		−	1.08893i	−0.838783	−	0.544466i	$-0.816732\pi$
$191$		−	39725.3i		−	1.08893i	0.838783	−	0.544466i	$-0.183268\pi$
$192$		0			0
$193$	−21094.4			−0.566308			−0.283154	−	0.959074i	$-0.591381\pi$
$193$	−21094.4			−0.566308			−0.283154	+	0.959074i	$0.591381\pi$
$194$	−49738.5	+	49872.3i	−1.32157	+	1.32512i
$195$		0			0
$196$	43.2476	+	16107.4i	0.00112577	+	0.419289i
$197$	28256.1			0.728080			0.364040	−	0.931383i	$-0.381397\pi$
$197$	28256.1			0.728080			0.364040	+	0.931383i	$0.381397\pi$
$198$		0			0
$199$			24063.5i			0.607650i	0.952728	+	0.303825i	$0.0982638\pi$
$199$			24063.5i			0.607650i	−0.952728	+	0.303825i	$0.901736\pi$
$200$	22083.4	+	21906.2i	0.552085	+	0.547656i
$201$		0			0
$202$	18814.3	−	18864.9i	0.461090	−	0.462330i
$203$		−	38256.0i		−	0.928341i
$204$		0			0
$205$	29038.9			0.690990
$206$	−19127.4	−	19076.1i	−0.450735	−	0.449527i
$207$		0			0
$208$	43682.1	−	234.571i	1.00966	−	0.00542184i
$209$	−40634.5			−0.930255
$210$		0			0
$211$			58079.8i			1.30455i	0.757983	+	0.652274i	$0.226185\pi$
$211$			58079.8i			1.30455i	−0.757983	+	0.652274i	$0.773815\pi$
$212$	−55.4914	−	20667.5i	−0.00123468	−	0.459851i
$213$		0			0
$214$	87.1104	+	86.8768i	0.00190214	+	0.00189704i
$215$		−	26318.1i		−	0.569349i
$216$		0			0
$217$	−37084.7			−0.787545
$218$	30199.2	−	30280.4i	0.635451	−	0.637159i
$219$		0			0
$220$	18942.9	−	50.8608i	0.391382	−	0.00105084i
$221$	68010.4			1.39249
$222$		0			0
$223$			16661.8i			0.335053i	0.985868	+	0.167526i	$0.0535779\pi$
$223$			16661.8i			0.335053i	−0.985868	+	0.167526i	$0.946422\pi$
$224$	−42551.3	−	41983.8i	−0.848040	−	0.836731i
$225$		0			0
$226$	28292.0	−	28368.0i	0.553919	−	0.555409i
$227$			56258.7i			1.09179i	0.837855	+	0.545894i	$0.183810\pi$
$227$			56258.7i			1.09179i	−0.837855	+	0.545894i	$0.816190\pi$
$228$		0			0
$229$	2447.82			0.0466775			0.0233388	−	0.999728i	$-0.492570\pi$
$229$	2447.82			0.0466775			0.0233388	+	0.999728i	$0.492570\pi$
$230$	−11222.6	−	11192.5i	−0.212148	−	0.211579i
$231$		0			0
$232$	29776.6	+	29537.7i	0.553221	+	0.548783i
$233$	−76971.2			−1.41781			−0.708903	−	0.705306i	$-0.750809\pi$
$233$	−76971.2			−1.41781			−0.708903	+	0.705306i	$0.750809\pi$
$234$		0			0
$235$			34229.3i			0.619816i
$236$	18516.5	−	49.7159i	0.332456	−	0.000892630i
$237$		0			0
$238$	−65896.8	−	65720.1i	−1.16335	−	1.16023i
$239$			26058.7i			0.456202i	0.973637	+	0.228101i	$0.0732517\pi$
$239$			26058.7i			0.456202i	−0.973637	+	0.228101i	$0.926748\pi$
$240$		0			0
$241$	−27999.6			−0.482079			−0.241039	−	0.970515i	$-0.577488\pi$
$241$	−27999.6			−0.482079			−0.241039	+	0.970515i	$0.577488\pi$
$242$	12866.1	−	12900.7i	0.219693	−	0.220284i
$243$		0			0
$244$	−254.388	−	94745.6i	−0.00427284	−	1.59140i
$245$	−11867.9			−0.197716
$246$		0			0
$247$		−	69040.6i		−	1.13165i
$248$	28633.3	−	28864.9i	0.465552	−	0.469317i
$249$		0			0
$250$	−36995.9	+	37095.3i	−0.591934	+	0.593525i
$251$		−	19782.5i		−	0.314003i	−0.987598	−	0.157001i	$-0.949817\pi$
$251$		−	19782.5i		−	0.314003i	0.987598	−	0.157001i	$-0.0501827\pi$
$252$		0			0
$253$	33756.6			0.527373
$254$	−45564.1	−	45442.0i	−0.706246	−	0.704352i
$255$		0			0
$256$	65532.2	−	703.829i	0.999942	−	0.0107396i
$257$	77273.9			1.16995			0.584974	−	0.811052i	$-0.301105\pi$
$257$	77273.9			1.16995			0.584974	+	0.811052i	$0.301105\pi$
$258$		0			0
$259$		−	93395.9i		−	1.39229i
$260$	86.4158	+	32185.2i	0.00127834	+	0.476112i
$261$		0			0
$262$	59211.7	+	59053.0i	0.862592	+	0.860279i
$263$		−	21212.4i		−	0.306675i	−0.988174	−	0.153337i	$-0.950998\pi$
$263$		−	21212.4i		−	0.306675i	0.988174	−	0.153337i	$-0.0490021\pi$
$264$		0			0
$265$	15227.8			0.216844
$266$	−66715.6	+	66895.0i	−0.942897	+	0.945432i
$267$		0			0
$268$	−57011.9	+	153.074i	−0.793772	+	0.00213124i
$269$	1106.24			0.0152878			0.00764389	−	0.999971i	$-0.497567\pi$
$269$	1106.24			0.0152878			0.00764389	+	0.999971i	$0.497567\pi$
$270$		0			0
$271$		−	33038.3i		−	0.449861i	−0.974375	−	0.224931i	$-0.927784\pi$
$271$		−	33038.3i		−	0.449861i	0.974375	−	0.224931i	$-0.0722155\pi$
$272$	102033.	−	547.910i	1.37912	−	0.00740579i
$273$		0			0
$274$	13208.1	−	13243.6i	0.175930	−	0.176403i
$275$		−	48811.1i		−	0.645436i
$276$		0			0
$277$	28842.5			0.375901			0.187951	−	0.982178i	$-0.439816\pi$
$277$	28842.5			0.375901			0.187951	+	0.982178i	$0.439816\pi$
$278$	−26354.0	−	26283.3i	−0.341002	−	0.340088i
$279$		0			0
$280$	31017.6	−	31268.5i	0.395633	−	0.398833i
$281$	32125.8			0.406856			0.203428	−	0.979090i	$-0.434792\pi$
$281$	32125.8			0.406856			0.203428	+	0.979090i	$0.434792\pi$
$282$		0			0
$283$			71340.3i			0.890763i	0.895341	+	0.445382i	$0.146932\pi$
$283$			71340.3i			0.890763i	−0.895341	+	0.445382i	$0.853068\pi$
$284$	90235.3	−	242.278i	1.11877	−	0.00300384i
$285$		0			0
$286$	−48535.2	−	48405.1i	−0.593369	−	0.591778i
$287$			143795.i			1.74574i
$288$		0			0
$289$	75337.7			0.902021
$290$	−21822.1	+	21880.8i	−0.259478	+	0.260176i
$291$		0			0
$292$	236.120	+	87941.9i	0.00276928	+	1.03141i
$293$	−36641.5			−0.426813			−0.213407	−	0.976963i	$-0.568456\pi$
$293$	−36641.5			−0.426813			−0.213407	+	0.976963i	$0.568456\pi$
$294$		0			0
$295$			13642.9i			0.156770i
$296$	72694.8	+	72111.6i	0.829698	+	0.823041i
$297$		0			0
$298$	−69970.4	+	70158.5i	−0.787920	+	0.790038i
$299$			57354.6i			0.641543i
$300$		0			0
$301$	130322.			1.43842
$302$	28915.7	+	28838.1i	0.317044	+	0.316194i
$303$		0			0
$304$	−556.209	−	103578.i	−0.00601854	−	1.12078i
$305$	69808.6			0.750428
$306$		0			0
$307$		−	11668.1i		−	0.123801i	−0.998082	−	0.0619005i	$-0.980284\pi$
$307$		−	11668.1i		−	0.123801i	0.998082	−	0.0619005i	$-0.0197161\pi$
$308$	251.853	+	93801.6i	0.00265488	+	0.988800i
$309$		0			0
$310$	21210.8	+	21154.0i	0.220716	+	0.220125i
$311$			4336.03i			0.0448303i	0.999749	+	0.0224151i	$0.00713556\pi$
$311$			4336.03i			0.0448303i	−0.999749	+	0.0224151i	$0.992864\pi$
$312$		0			0
$313$	86498.6			0.882918			0.441459	−	0.897282i	$-0.354461\pi$
$313$	86498.6			0.882918			0.441459	+	0.897282i	$0.354461\pi$
$314$	−81838.0	+	82058.1i	−0.830034	+	0.832266i
$315$		0			0
$316$	−51526.1	+	138.345i	−0.516004	+	0.00138545i
$317$	−24632.2			−0.245124			−0.122562	−	0.992461i	$-0.539111\pi$
$317$	−24632.2			−0.245124			−0.122562	+	0.992461i	$0.539111\pi$
$318$		0			0
$319$		−	65815.5i		−	0.646765i
$320$	388.938	+	48285.2i	0.00379822	+	0.471535i
$321$		0			0
$322$	55423.2	−	55572.2i	0.534539	−	0.535977i
$323$		−	161265.i		−	1.54573i
$324$		0			0
$325$	82933.2			0.785167
$326$	−50233.4	−	50098.7i	−0.472669	−	0.471402i
$327$		0			0
$328$	−111923.	−	111025.i	−1.04033	−	1.03198i
$329$	−169497.			−1.56592
$330$		0			0
$331$			187265.i			1.70923i	0.519265	+	0.854614i	$0.326206\pi$
$331$			187265.i			1.70923i	−0.519265	+	0.854614i	$0.673794\pi$
$332$	130507.	−	350.405i	1.18402	−	0.00317903i
$333$		0			0
$334$	−116301.	−	115989.i	−1.04254	−	1.03974i
$335$		−	42006.4i		−	0.374305i
$336$		0			0
$337$	−100959.			−0.888967			−0.444484	−	0.895787i	$-0.646613\pi$
$337$	−100959.			−0.888967			−0.444484	+	0.895787i	$0.646613\pi$
$338$	1569.14	−	1573.36i	0.0137350	−	0.0137719i
$339$		0			0
$340$	201.850	+	75178.2i	0.00174611	+	0.650330i
$341$	−63800.3			−0.548674
$342$		0			0
$343$			81392.2i			0.691823i
$344$	−100623.	+	101437.i	−0.850314	+	0.857191i
$345$		0			0
$346$	19647.4	−	19700.2i	0.164116	−	0.164558i
$347$			174903.i			1.45257i	0.687392	+	0.726287i	$0.258756\pi$
$347$			174903.i			1.45257i	−0.687392	+	0.726287i	$0.741244\pi$
$348$		0			0
$349$	43896.9			0.360399			0.180199	−	0.983630i	$-0.442326\pi$
$349$	43896.9			0.360399			0.180199	+	0.983630i	$0.442326\pi$
$350$	−80355.9	−	80140.4i	−0.655967	−	0.654208i
$351$		0			0
$352$	−73205.0	−	72228.8i	−0.590820	−	0.582941i
$353$	155579.			1.24854			0.624270	−	0.781209i	$-0.285397\pi$
$353$	155579.			1.24854			0.624270	+	0.781209i	$0.285397\pi$
$354$		0			0
$355$			66485.4i			0.527557i
$356$	−39.1303	−	14573.9i	−0.000308755	−	0.114994i
$357$		0			0
$358$	4969.13	+	4955.81i	0.0387717	+	0.0386677i
$359$			184004.i			1.42771i	0.700295	+	0.713853i	$0.253052\pi$
$359$			184004.i			1.42771i	−0.700295	+	0.713853i	$0.746948\pi$
$360$		0			0
$361$	−33386.7			−0.256188
$362$	−123685.	+	124017.i	−0.943840	+	0.946377i
$363$		0			0
$364$	−159375.	+	427.914i	−1.20287	+	0.00322964i
$365$	−64795.6			−0.486362
$366$		0			0
$367$			165901.i			1.23173i	0.787851	+	0.615866i	$0.211194\pi$
$367$			165901.i			1.23173i	−0.787851	+	0.615866i	$0.788806\pi$
$368$	462.064	+	86046.3i	0.00341198	+	0.635385i
$369$		0			0
$370$	−53275.2	+	53418.5i	−0.389154	+	0.390201i
$371$			75405.3i			0.547841i
$372$		0			0
$373$	130320.			0.936685			0.468343	−	0.883547i	$-0.344851\pi$
$373$	130320.			0.936685			0.468343	+	0.883547i	$0.344851\pi$
$374$	−113369.	−	113065.i	−0.810493	−	0.808320i
$375$		0			0
$376$	130870.	−	131928.i	0.925686	−	0.933172i
$377$	111825.			0.786783
$378$		0			0
$379$		−	43645.6i		−	0.303852i	−0.988392	−	0.151926i	$-0.951453\pi$
$379$		−	43645.6i		−	0.303852i	0.988392	−	0.151926i	$-0.0485475\pi$
$380$	76316.9	−	204.907i	0.528511	−	0.00141903i
$381$		0			0
$382$	−112511.	−	112209.i	−0.771024	−	0.768957i
$383$			273879.i			1.86707i	0.358485	+	0.933535i	$0.383293\pi$
$383$			273879.i			1.86707i	−0.358485	+	0.933535i	$0.616707\pi$
$384$		0			0
$385$	−69113.0			−0.466271
$386$	−59583.9	+	59744.1i	−0.399902	+	0.400978i
$387$		0			0
$388$	756.462	+	281741.i	0.00502486	+	1.87149i
$389$	−245188.			−1.62032			−0.810159	−	0.586211i	$-0.800619\pi$
$389$	−245188.			−1.62032			−0.810159	+	0.586211i	$0.800619\pi$
$390$		0			0
$391$			133969.i			0.876295i
$392$	45741.9	+	45374.9i	0.297675	+	0.295287i
$393$		0			0
$394$	79812.9	−	80027.4i	0.514139	−	0.515521i
$395$		−	37964.4i		−	0.243323i
$396$		0			0
$397$	−4252.39			−0.0269806			−0.0134903	−	0.999909i	$-0.504294\pi$
$397$	−4252.39			−0.0269806			−0.0134903	+	0.999909i	$0.504294\pi$
$398$	68153.3	+	67970.6i	0.430250	+	0.429096i
$399$		0			0
$400$	124421.	−	668.132i	0.777629	−	0.00417583i
$401$	7331.22			0.0455919			0.0227959	−	0.999740i	$-0.492743\pi$
$401$	7331.22			0.0455919			0.0227959	+	0.999740i	$0.492743\pi$
$402$		0			0
$403$		−	108401.i		−	0.667456i
$404$	−286.143	−	106573.i	−0.00175315	−	0.652955i
$405$		0			0
$406$	−108349.	−	108059.i	−0.657317	−	0.655554i
$407$		−	160678.i		−	0.969990i
$408$		0			0
$409$	−28414.0			−0.169858			−0.0849289	−	0.996387i	$-0.527066\pi$
$409$	−28414.0			−0.169858			−0.0849289	+	0.996387i	$0.527066\pi$
$410$	82023.9	−	82244.5i	0.487947	−	0.489259i
$411$		0			0
$412$	−108056.	+	290.124i	−0.636580	+	0.00170919i
$413$	−67557.2			−0.396070
$414$		0			0
$415$			96157.5i			0.558325i
$416$	122721.	−	124380.i	0.709142	−	0.718727i
$417$		0			0
$418$	−114777.	+	115086.i	−0.656906	+	0.658672i
$419$		−	158490.i		−	0.902763i	−0.892331	−	0.451382i	$-0.850931\pi$
$419$		−	158490.i		−	0.902763i	0.892331	−	0.451382i	$-0.149069\pi$
$420$		0			0
$421$	−285592.			−1.61132			−0.805659	−	0.592379i	$-0.798189\pi$
$421$	−285592.			−1.61132			−0.805659	+	0.592379i	$0.798189\pi$
$422$	164495.	+	164054.i	0.923693	+	0.921216i
$423$		0			0
$424$	−58691.8	−	58220.9i	−0.326472	−	0.323853i
$425$	193715.			1.07247
$426$		0			0
$427$			345679.i			1.89591i
$428$	492.109	−	1.32129i	0.00268642	−	7.21291e-6i
$429$		0			0
$430$	−74538.8	−	74339.0i	−0.403130	−	0.402050i
$431$			115124.i			0.619741i	0.950779	+	0.309870i	$0.100286\pi$
$431$			115124.i			0.619741i	−0.950779	+	0.309870i	$0.899714\pi$
$432$		0			0
$433$	95600.5			0.509899			0.254950	−	0.966954i	$-0.417941\pi$
$433$	95600.5			0.509899			0.254950	+	0.966954i	$0.417941\pi$
$434$	−104750.	+	105032.i	−0.556130	+	0.557625i
$435$		0			0
$436$	−459.292	−	171061.i	−0.00241611	−	0.899869i
$437$	135998.			0.712148
$438$		0			0
$439$			371524.i			1.92778i	0.266300	+	0.963890i	$0.414199\pi$
$439$			371524.i			1.92778i	−0.266300	+	0.963890i	$0.585801\pi$
$440$	53362.6	−	53794.1i	0.275633	−	0.277862i
$441$		0			0
$442$	192104.	−	192620.i	0.983313	−	0.985957i
$443$			138264.i			0.704536i	0.935899	+	0.352268i	$0.114589\pi$
$443$			138264.i			0.704536i	−0.935899	+	0.352268i	$0.885411\pi$
$444$		0			0
$445$	10738.1			0.0542258
$446$	47190.0	+	47063.5i	0.237236	+	0.236600i
$447$		0			0
$448$	−239099.	+	1925.95i	−1.19130	+	0.00959595i
$449$	128427.			0.637035			0.318518	−	0.947917i	$-0.396815\pi$
$449$	128427.			0.637035			0.318518	+	0.947917i	$0.396815\pi$
$450$		0			0
$451$			247384.i			1.21624i
$452$	−430.286	−	160258.i	−0.00210611	−	0.784411i
$453$		0			0
$454$	159337.	+	158910.i	0.773046	+	0.770973i
$455$		−	117427.i		−	0.567214i
$456$		0			0
$457$	293085.			1.40334			0.701668	−	0.712504i	$-0.252439\pi$
$457$	293085.			1.40334			0.701668	+	0.712504i	$0.252439\pi$
$458$	6914.17	−	6932.76i	0.0329617	−	0.0330503i
$459$		0			0
$460$	−63399.4	+	170.224i	−0.299619	+	0.000804463i
$461$	296134.			1.39343			0.696717	−	0.717346i	$-0.254643\pi$
$461$	296134.			1.39343			0.696717	+	0.717346i	$0.254643\pi$
$462$		0			0
$463$		−	354683.i		−	1.65455i	−0.561801	−	0.827273i	$-0.689891\pi$
$463$		−	354683.i		−	1.65455i	0.561801	−	0.827273i	$-0.310109\pi$
$464$	167765.	−	900.890i	0.779230	−	0.00418442i
$465$		0			0
$466$	−217415.	+	218000.i	−1.00119	+	1.00388i
$467$		−	116644.i		−	0.534848i	−0.963579	−	0.267424i	$-0.913828\pi$
$467$		−	116644.i		−	0.534848i	0.963579	−	0.267424i	$-0.0861724\pi$
$468$		0			0
$469$	208007.			0.945656
$470$	96945.0	+	96685.1i	0.438864	+	0.437687i
$471$		0			0
$472$	52161.4	−	52583.2i	0.234134	−	0.236028i
$473$	224206.			1.00213
$474$		0			0
$475$		−	196650.i		−	0.871578i
$476$	−372268.	+	999.522i	−1.64302	+	0.00441142i
$477$		0			0
$478$	73804.1	+	73606.2i	0.323017	+	0.322151i
$479$			104079.i			0.453618i	0.973939	+	0.226809i	$0.0728293\pi$
$479$			104079.i			0.453618i	−0.973939	+	0.226809i	$0.927171\pi$
$480$		0			0
$481$	273002.			1.17998
$482$	−79088.5	+	79301.1i	−0.340423	+	0.341338i
$483$		0			0
$484$	−195.678	−	72879.4i	−0.000835316	−	0.311110i
$485$	−207587.			−0.882503
$486$		0			0
$487$		−	101284.i		−	0.427055i	−0.976937	−	0.213527i	$-0.931505\pi$
$487$		−	101284.i		−	0.427055i	0.976937	−	0.213527i	$-0.0684953\pi$
$488$	−269059.	−	266901.i	−1.12982	−	1.12075i
$489$		0			0
$490$	−33522.5	+	33612.6i	−0.139619	+	0.139994i
$491$		−	175225.i		−	0.726831i	−0.931627	−	0.363416i	$-0.881611\pi$
$491$		−	175225.i		−	0.726831i	0.931627	−	0.363416i	$-0.118389\pi$
$492$		0			0
$493$	261200.			1.07468
$494$	−195538.	−	195014.i	−0.801268	−	0.799119i
$495$		0			0
$496$	−873.306	−	162628.i	−0.00354979	−	0.661048i
$497$	−329223.			−1.33284
$498$		0			0
$499$		−	96102.5i		−	0.385952i	−0.981203	−	0.192976i	$-0.938186\pi$
$499$		−	96102.5i		−	0.385952i	0.981203	−	0.192976i	$-0.0618140\pi$
$500$	562.661	+	209561.i	0.00225065	+	0.838244i
$501$		0			0
$502$	−56028.4	−	55878.2i	−0.222331	−	0.221735i
$503$		−	164729.i		−	0.651080i	−0.945528	−	0.325540i	$-0.894454\pi$
$503$		−	164729.i		−	0.651080i	0.945528	−	0.325540i	$-0.105546\pi$
$504$		0			0
$505$	78522.7			0.307902
$506$	95349.8	−	95606.1i	0.372408	−	0.373409i
$507$		0			0
$508$	−257403.	+	691.117i	−0.997440	+	0.00267808i
$509$	−85940.1			−0.331711			−0.165856	−	0.986150i	$-0.553039\pi$
$509$	−85940.1			−0.331711			−0.165856	+	0.986150i	$0.553039\pi$
$510$		0			0
$511$		−	320855.i		−	1.22876i
$512$	183111.	−	187590.i	0.698512	−	0.715598i
$513$		0			0
$514$	218270.	−	218857.i	0.826166	−	0.828388i
$515$		−	79615.3i		−	0.300180i
$516$		0			0
$517$	−291602.			−1.09096
$518$	−264518.	−	263809.i	−0.985815	−	0.983172i
$519$		0			0
$520$	91399.7	+	90666.4i	0.338017	+	0.335305i
$521$	−173047.			−0.637514			−0.318757	−	0.947836i	$-0.603265\pi$
$521$	−173047.			−0.637514			−0.318757	+	0.947836i	$0.603265\pi$
$522$		0			0
$523$		−	252188.i		−	0.921978i	−0.887406	−	0.460989i	$-0.847495\pi$
$523$		−	252188.i		−	0.921978i	0.887406	−	0.460989i	$-0.152505\pi$
$524$	334502.	−	898.123i	1.21825	−	0.00327095i
$525$		0			0
$526$	−60078.2	−	59917.1i	−0.217143	−	0.216560i
$527$		−	253203.i		−	0.911690i
$528$		0			0
$529$	166862.			0.596275
$530$	43013.0	−	43128.6i	0.153126	−	0.153537i
$531$		0			0
$532$	1014.66	+	377907.i	0.00358508	+	1.33525i
$533$	−420321.			−1.47954
$534$		0			0
$535$			362.586i			0.00126679i
$536$	−160604.	+	161903.i	−0.559019	+	0.563540i
$537$		0			0
$538$	3124.71	−	3133.11i	0.0107956	−	0.0108246i
$539$		−	101104.i		−	0.348008i
$540$		0			0
$541$	−472358.			−1.61390			−0.806950	−	0.590620i	$-0.798883\pi$
$541$	−472358.			−1.61390			−0.806950	+	0.590620i	$0.798883\pi$
$542$	−93571.7	−	93320.8i	−0.318527	−	0.317673i
$543$		0			0
$544$	286652.	−	290527.i	0.968630	−	0.981721i
$545$	126038.			0.424335
$546$		0			0
$547$		−	384377.i		−	1.28465i	−0.766434	−	0.642323i	$-0.777971\pi$
$547$		−	384377.i		−	1.28465i	0.766434	−	0.642323i	$-0.222029\pi$
$548$	−200.879	−	74816.5i	−0.000668918	−	0.249136i
$549$		0			0
$550$	−138244.	−	137873.i	−0.457005	−	0.455779i
$551$		−	265157.i		−	0.873372i
$552$		0			0
$553$	187993.			0.614739
$554$	81469.4	−	81688.4i	0.265445	−	0.266159i
$555$		0			0
$556$	−148881.	+	399.737i	−0.481602	+	0.00129308i
$557$	−19803.1			−0.0638297			−0.0319148	−	0.999491i	$-0.510161\pi$
$557$	−19803.1			−0.0638297			−0.0319148	+	0.999491i	$0.510161\pi$
$558$		0			0
$559$			380940.i			1.21908i
$560$	−946.027	−	176171.i	−0.00301667	−	0.561768i
$561$		0			0
$562$	90743.4	−	90987.4i	0.287304	−	0.288077i
$563$		−	153074.i		−	0.482929i	−0.970410	−	0.241465i	$-0.922372\pi$
$563$		−	153074.i		−	0.482929i	0.970410	−	0.241465i	$-0.0776278\pi$
$564$		0			0
$565$	118078.			0.369891
$566$	202052.	+	201510.i	0.630710	+	0.629019i
$567$		0			0
$568$	254195.	−	256251.i	0.787898	−	0.794271i
$569$	−51911.0			−0.160337			−0.0801687	−	0.996781i	$-0.525546\pi$
$569$	−51911.0			−0.160337			−0.0801687	+	0.996781i	$0.525546\pi$
$570$		0			0
$571$		−	107343.i		−	0.329232i	−0.986358	−	0.164616i	$-0.947361\pi$
$571$		−	107343.i		−	0.329232i	0.986358	−	0.164616i	$-0.0526385\pi$
$572$	−274188.	+	736.182i	−0.838023	+	0.00225005i
$573$		0			0
$574$	407259.	+	406167.i	1.23608	+	1.23277i
$575$			163364.i			0.494108i
$576$		0			0
$577$	−114098.			−0.342710			−0.171355	−	0.985209i	$-0.554814\pi$
$577$	−114098.			−0.342710			−0.171355	+	0.985209i	$0.554814\pi$
$578$	212801.	−	213373.i	0.636968	−	0.638681i
$579$		0			0
$580$	331.888	+	123610.i	0.000986587	+	0.367450i
$581$	−476153.			−1.41057
$582$		0			0
$583$			129727.i			0.381674i
$584$	249738.	+	247734.i	0.732249	+	0.726374i
$585$		0			0
$586$	−103499.	+	103777.i	−0.301397	+	0.302208i
$587$			52235.3i			0.151596i	0.997123	+	0.0757980i	$0.0241504\pi$
$587$			52235.3i			0.151596i	−0.997123	+	0.0757980i	$0.975850\pi$
$588$		0			0
$589$	−257038.			−0.740912
$590$	38639.8	+	38536.2i	0.111002	+	0.110704i
$591$		0			0
$592$	409572.	−	2199.38i	1.16866	−	0.00627562i
$593$	277354.			0.788724			0.394362	−	0.918955i	$-0.370966\pi$
$593$	277354.			0.788724			0.394362	+	0.918955i	$0.370966\pi$
$594$		0			0
$595$		−	274287.i		−	0.774767i
$596$	1064.16	+	396343.i	0.00299582	+	1.11578i
$597$		0			0
$598$	162441.	+	162005.i	0.454248	+	0.453030i
$599$			19107.2i			0.0532528i	0.999645	+	0.0266264i	$0.00847645\pi$
$599$			19107.2i			0.0532528i	−0.999645	+	0.0266264i	$0.991524\pi$
$600$		0			0
$601$	−418892.			−1.15972			−0.579861	−	0.814716i	$-0.696893\pi$
$601$	−418892.			−1.15972			−0.579861	+	0.814716i	$0.696893\pi$
$602$	368112.	−	369102.i	1.01575	−	1.01848i
$603$		0			0
$604$	163352.	−	438.593i	0.447765	−	0.00120223i
$605$	53697.5			0.146704
$606$		0			0
$607$			382383.i			1.03782i	0.854830	+	0.518909i	$0.173662\pi$
$607$			382383.i			1.03782i	−0.854830	+	0.518909i	$0.826338\pi$
$608$	−294927.	−	290994.i	−0.797826	−	0.787186i
$609$		0			0
$610$	197183.	−	197713.i	0.529920	−	0.531345i
$611$		−	495450.i		−	1.32714i
$612$		0			0
$613$	−210852.			−0.561121			−0.280560	−	0.959836i	$-0.590520\pi$
$613$	−210852.			−0.561121			−0.280560	+	0.959836i	$0.590520\pi$
$614$	−33046.7	−	32958.1i	−0.0876579	−	0.0874229i
$615$		0			0
$616$	266378.	+	264241.i	0.702000	+	0.696368i
$617$	626580.			1.64591			0.822955	−	0.568106i	$-0.192324\pi$
$617$	626580.			1.64591			0.822955	+	0.568106i	$0.192324\pi$
$618$		0			0
$619$		−	41204.9i		−	0.107539i	−0.998553	−	0.0537697i	$-0.982876\pi$
$619$		−	41204.9i		−	0.107539i	0.998553	−	0.0537697i	$-0.0171237\pi$
$620$	119825.	−	321.726i	0.311721	−	0.000836956i
$621$		0			0
$622$	12280.6	+	12247.7i	0.0317423	+	0.0316572i
$623$			53172.8i			0.136998i
$624$		0			0
$625$	149361.			0.382365
$626$	244326.	−	244983.i	0.623478	−	0.625155i
$627$		0			0
$628$	1244.66	+	463567.i	0.00315595	+	1.17542i
$629$	637678.			1.61176
$630$		0			0
$631$		−	150814.i		−	0.378777i	−0.981902	−	0.189389i	$-0.939349\pi$
$631$		−	150814.i		−	0.378777i	0.981902	−	0.189389i	$-0.0606506\pi$
$632$	−145150.	+	146324.i	−0.363399	+	0.366338i
$633$		0			0
$634$	−69576.9	+	69764.0i	−0.173096	+	0.173561i
$635$		−	189655.i		−	0.470345i
$636$		0			0
$637$	171782.			0.423348
$638$	−186404.	−	185904.i	−0.457946	−	0.456718i
$639$		0			0
$640$	137853.	+	135286.i	0.336555	+	0.330288i
$641$	428379.			1.04259			0.521293	−	0.853378i	$-0.325450\pi$
$641$	428379.			1.04259			0.521293	+	0.853378i	$0.325450\pi$
$642$		0			0
$643$			85771.0i			0.207452i	0.994606	+	0.103726i	$0.0330766\pi$
$643$			85771.0i			0.207452i	−0.994606	+	0.103726i	$0.966923\pi$
$644$	−842.919	−	313941.i	−0.00203242	−	0.756967i
$645$		0			0
$646$	−456738.	−	455513.i	−1.09447	−	1.09153i
$647$			128368.i			0.306653i	0.988176	+	0.153327i	$0.0489986\pi$
$647$			128368.i			0.306653i	−0.988176	+	0.153327i	$0.951001\pi$
$648$		0			0
$649$	−116225.			−0.275937
$650$	234255.	−	234885.i	0.554451	−	0.555942i
$651$		0			0
$652$	−283781.	+	761.940i	−0.667557	+	0.00179236i
$653$	−465879.			−1.09256			−0.546282	−	0.837601i	$-0.683957\pi$
$653$	−465879.			−1.09256			−0.546282	+	0.837601i	$0.683957\pi$
$654$		0			0
$655$			246461.i			0.574468i
$656$	−630587.	+	3386.22i	−1.46534	+	0.00786878i
$657$		0			0
$658$	−478766.	+	480053.i	−1.10579	+	1.10876i
$659$		−	351017.i		−	0.808271i	−0.914699	−	0.404135i	$-0.867573\pi$
$659$		−	351017.i		−	0.808271i	0.914699	−	0.404135i	$-0.132427\pi$
$660$		0			0
$661$	−282262.			−0.646026			−0.323013	−	0.946395i	$-0.604696\pi$
$661$	−282262.			−0.646026			−0.323013	+	0.946395i	$0.604696\pi$
$662$	530375.	+	528953.i	1.21023	+	1.20698i
$663$		0			0
$664$	367641.	−	370614.i	0.833850	−	0.840594i
$665$	−278442.			−0.629638
$666$		0			0
$667$			220276.i			0.495125i
$668$	−657015.	+	1764.06i	−1.47239	+	0.00395330i
$669$		0			0
$670$	−118971.	−	118652.i	−0.265029	−	0.264318i
$671$			594704.i			1.32086i
$672$		0			0
$673$	−797180.			−1.76006			−0.880028	−	0.474922i	$-0.842476\pi$
$673$	−797180.			−1.76006			−0.880028	+	0.474922i	$0.842476\pi$
$674$	−285172.	+	285939.i	−0.627751	+	0.629438i
$675$		0			0
$676$	−23.8647	−	8888.32i	−5.22231e−5	−	0.0194503i
$677$	281346.			0.613852			0.306926	−	0.951733i	$-0.400700\pi$
$677$	281346.			0.613852			0.306926	+	0.951733i	$0.400700\pi$
$678$		0			0
$679$		−	1.02793e6i		−	2.22958i
$680$	213491.	+	211779.i	0.461703	+	0.457999i
$681$		0			0
$682$	−180212.	+	180697.i	−0.387450	+	0.388491i
$683$			687094.i			1.47291i	0.676489	+	0.736453i	$0.263501\pi$
$683$			687094.i			1.47291i	−0.676489	+	0.736453i	$0.736499\pi$
$684$		0			0
$685$	55124.8			0.117480
$686$	230521.	+	229903.i	0.489849	+	0.488535i
$687$		0			0
$688$	3068.96	+	571506.i	0.00648357	+	1.20738i
$689$	−220414.			−0.464303
$690$		0			0
$691$			329040.i			0.689116i	0.938765	+	0.344558i	$0.111971\pi$
$691$			329040.i			0.689116i	−0.938765	+	0.344558i	$0.888029\pi$
$692$	−298.812	−	111291.i	−0.000624002	−	0.232407i
$693$		0			0
$694$	495364.	+	494036.i	1.02850	+	1.02574i
$695$		−	109695.i		−	0.227100i
$696$		0			0
$697$	−981786.			−2.02093
$698$	123992.	−	124326.i	0.254498	−	0.255182i
$699$		0			0
$700$	−453951.	+	1218.84i	−0.926431	+	0.00248742i
$701$	−961471.			−1.95659			−0.978296	−	0.207214i	$-0.933560\pi$
$701$	−961471.			−1.95659			−0.978296	+	0.207214i	$0.933560\pi$
$702$		0			0
$703$		−	647338.i		−	1.30985i
$704$	−411345.	+	3313.39i	−0.829966	+	0.00668539i
$705$		0			0
$706$	439453.	−	440635.i	0.881665	−	0.884035i
$707$			388830.i			0.777894i
$708$		0			0
$709$	−598276.			−1.19017			−0.595085	−	0.803663i	$-0.702882\pi$
$709$	−598276.			−1.19017			−0.595085	+	0.803663i	$0.702882\pi$
$710$	188301.	+	187796.i	0.373540	+	0.372538i
$711$		0			0
$712$	−41387.1	−	41055.1i	−0.0816404	−	0.0809854i
$713$	213531.			0.420032
$714$		0			0
$715$		−	202022.i		−	0.395171i
$716$	28071.9	−	75.3717i	0.0547578	−	0.000147022i
$717$		0			0
$718$	521141.	+	519744.i	1.01090	+	1.00819i
$719$		−	608601.i		−	1.17727i	−0.808400	−	0.588633i	$-0.799666\pi$
$719$		−	608601.i		−	1.17727i	0.808400	−	0.588633i	$-0.200334\pi$
$720$		0			0
$721$	394240.			0.758385
$722$	−94305.1	+	94558.6i	−0.180909	+	0.181396i
$723$		0			0
$724$	1881.09	+	700604.i	0.00358866	+	1.33658i
$725$	318513.			0.605970
$726$		0			0
$727$		−	458391.i		−	0.867296i	−0.901082	−	0.433648i	$-0.857226\pi$
$727$		−	458391.i		−	0.867296i	0.901082	−	0.433648i	$-0.142774\pi$
$728$	−448963.	+	452594.i	−0.847125	+	0.853976i
$729$		0			0
$730$	−183023.	+	183515.i	−0.343448	+	0.344371i
$731$			889801.i			1.66517i
$732$		0			0
$733$	70695.6			0.131578			0.0657892	−	0.997834i	$-0.479044\pi$
$733$	70695.6			0.131578			0.0657892	+	0.997834i	$0.479044\pi$
$734$	469868.	+	468608.i	0.872135	+	0.869796i
$735$		0			0
$736$	245007.	+	241740.i	0.452297	+	0.446265i
$737$	357855.			0.658828
$738$		0			0
$739$		−	476430.i		−	0.872390i	−0.899852	−	0.436195i	$-0.856326\pi$
$739$		−	476430.i		−	0.872390i	0.899852	−	0.436195i	$-0.143674\pi$
$740$	810.251	+	301775.i	0.00147964	+	0.551086i
$741$		0			0
$742$	213565.	+	212992.i	0.387901	+	0.386861i
$743$		−	126020.i		−	0.228277i	−0.993465	−	0.114139i	$-0.963589\pi$
$743$		−	126020.i		−	0.228277i	0.993465	−	0.114139i	$-0.0364108\pi$
$744$		0			0
$745$	−292026.			−0.526149
$746$	368106.	−	369095.i	0.661447	−	0.663225i
$747$		0			0
$748$	−640448.	+	1719.57i	−1.14467	+	0.00307339i
$749$	−1795.45			−0.00320045
$750$		0			0
$751$			204276.i			0.362191i	0.983465	+	0.181096i	$0.0579644\pi$
$751$			204276.i			0.362191i	−0.983465	+	0.181096i	$0.942036\pi$
$752$	−3991.48	−	743300.i	−0.00705827	−	1.31440i
$753$		0			0
$754$	315863.	−	316712.i	0.555592	−	0.557086i
$755$			120358.i			0.211145i
$756$		0			0
$757$	588244.			1.02652			0.513258	−	0.858235i	$-0.328438\pi$
$757$	588244.			1.02652			0.513258	+	0.858235i	$0.328438\pi$
$758$	−123614.	−	123282.i	−0.215144	−	0.214567i
$759$		0			0
$760$	214987.	−	216725.i	0.372207	−	0.375217i
$761$	−50737.5			−0.0876113			−0.0438056	−	0.999040i	$-0.513948\pi$
$761$	−50737.5			−0.0876113			−0.0438056	+	0.999040i	$0.513948\pi$
$762$		0			0
$763$			624116.i			1.07205i
$764$	−635603.	+	1706.56i	−1.08893	+	0.00292372i
$765$		0			0
$766$	775685.	+	773605.i	1.32199	+	1.31844i
$767$		−	197474.i		−	0.335675i
$768$		0			0
$769$	882679.			1.49262			0.746312	−	0.665597i	$-0.231823\pi$
$769$	882679.			1.49262			0.746312	+	0.665597i	$0.231823\pi$
$770$	−195218.	+	195743.i	−0.329260	+	0.330146i
$771$		0			0
$772$	906.197	+	337509.i	0.00152051	+	0.566306i
$773$	−100820.			−0.168728			−0.0843642	−	0.996435i	$-0.526886\pi$
$773$	−100820.			−0.168728			−0.0843642	+	0.996435i	$0.526886\pi$
$774$		0			0
$775$		−	308760.i		−	0.514065i
$776$	800090.	+	793671.i	1.32866	+	1.31801i
$777$		0			0
$778$	−692565.	+	694427.i	−1.14420	+	1.14727i
$779$			996658.i			1.64237i
$780$		0			0
$781$	−566393.			−0.928573
$782$	379430.	+	378412.i	0.620466	+	0.618802i
$783$		0			0
$784$	257716.	−	1383.92i	0.419284	−	0.00225153i
$785$	−341556.			−0.554272
$786$		0			0
$787$		−	113818.i		−	0.183765i	−0.995770	−	0.0918826i	$-0.970712\pi$
$787$		−	113818.i		−	0.183765i	0.995770	−	0.0918826i	$-0.0292884\pi$
$788$	−1213.86	−	452095.i	−0.00195485	−	0.728078i
$789$		0			0
$790$	−107524.	−	107235.i	−0.172286	−	0.171824i
$791$			584701.i			0.934504i
$792$		0			0
$793$	−1.01044e6			−1.60681
$794$	−12011.4	+	12043.7i	−0.0190526	+	0.0191038i
$795$		0			0
$796$	385015.	−	1033.75i	0.607648	−	0.00163151i
$797$	−701182.			−1.10386			−0.551930	−	0.833890i	$-0.686108\pi$
$797$	−701182.			−1.10386			−0.551930	+	0.833890i	$0.686108\pi$
$798$		0			0
$799$		−	1.15727e6i		−	1.81277i
$800$	349550.	−	354274.i	0.546171	−	0.553553i
$801$		0			0
$802$	20708.0	−	20763.6i	0.0321950	−	0.0322816i
$803$		−	551998.i		−	0.856064i
$804$		0			0
$805$	231312.			0.356949
$806$	−307015.	−	306192.i	−0.472596	−	0.471329i
$807$		0			0
$808$	−302646.	−	300218.i	−0.463566	−	0.459847i
$809$	514560.			0.786211			0.393105	−	0.919493i	$-0.371401\pi$
$809$	514560.			0.786211			0.393105	+	0.919493i	$0.371401\pi$
$810$		0			0
$811$			36669.2i			0.0557519i	0.999611	+	0.0278759i	$0.00887434\pi$
$811$			36669.2i			0.0557519i	−0.999611	+	0.0278759i	$0.991126\pi$
$812$	−612094.	+	1643.44i	−0.928338	+	0.00249254i
$813$		0			0
$814$	−455075.	−	453855.i	−0.686807	−	0.684965i
$815$		−	209090.i		−	0.314788i
$816$		0			0
$817$	903279.			1.35325
$818$	−80258.9	+	80474.7i	−0.119946	+	0.120269i
$819$		0			0
$820$	−1247.48	−	464620.i	−0.00185527	−	0.690987i
$821$	−478983.			−0.710614			−0.355307	−	0.934750i	$-0.615624\pi$
$821$	−478983.			−0.710614			−0.355307	+	0.934750i	$0.615624\pi$
$822$		0			0
$823$			784187.i			1.15776i	0.815411	+	0.578882i	$0.196511\pi$
$823$			784187.i			1.15776i	−0.815411	+	0.578882i	$0.803489\pi$
$824$	−304395.	+	306857.i	−0.448315	+	0.451941i
$825$		0			0
$826$	−190824.	+	191337.i	−0.279687	+	0.280439i
$827$			1.21724e6i			1.77978i	0.456175	+	0.889890i	$0.349219\pi$
$827$			1.21724e6i			1.77978i	−0.456175	+	0.889890i	$0.650781\pi$
$828$		0			0
$829$	−335235.			−0.487799			−0.243900	−	0.969801i	$-0.578427\pi$
$829$	−335235.			−0.487799			−0.243900	+	0.969801i	$0.578427\pi$
$830$	272339.	+	271609.i	0.395325	+	0.394265i
$831$		0			0
$832$	−5629.66	−	698901.i	−0.00813271	−	1.00965i
$833$	401248.			0.578259
$834$		0			0
$835$		−	484089.i		−	0.694308i
$836$	1745.62	+	650149.i	0.00249768	+	0.930252i
$837$		0			0
$838$	−448879.	−	447675.i	−0.639206	−	0.637492i
$839$			933549.i			1.32621i	0.748525	+	0.663107i	$0.230762\pi$
$839$			933549.i			1.32621i	−0.748525	+	0.663107i	$0.769238\pi$
$840$		0			0
$841$	−277808.			−0.392783
$842$	−806690.	+	808859.i	−1.13784	+	1.14090i
$843$		0			0
$844$	929274.	−	2495.06i	1.30454	−	0.00350264i
$845$	6548.91			0.00917182
$846$		0			0
$847$			265900.i			0.370639i
$848$	−330677.	+	1775.72i	−0.459846	+	0.00246935i
$849$		0			0
$850$	547174.	−	548645.i	0.757334	−	0.759370i
$851$			537768.i			0.742567i
$852$		0			0
$853$	249820.			0.343343			0.171672	−	0.985154i	$-0.445083\pi$
$853$	249820.			0.343343			0.171672	+	0.985154i	$0.445083\pi$
$854$	979039.	+	976413.i	1.34241	+	1.33881i
$855$		0			0
$856$	1386.28	−	1397.49i	0.00189193	−	0.00190723i
$857$	660987.			0.899976			0.449988	−	0.893035i	$-0.351428\pi$
$857$	660987.			0.899976			0.449988	+	0.893035i	$0.351428\pi$
$858$		0			0
$859$		−	827557.i		−	1.12153i	−0.827974	−	0.560766i	$-0.810507\pi$
$859$		−	827557.i		−	1.12153i	0.827974	−	0.560766i	$-0.189493\pi$
$860$	−421089.	+	1130.60i	−0.569347	+	0.00152867i
$861$		0			0
$862$	326056.	+	325181.i	0.438811	+	0.437634i
$863$		−	1.22724e6i		−	1.64781i	−0.566728	−	0.823905i	$-0.691791\pi$
$863$		−	1.22724e6i		−	1.64781i	0.566728	−	0.823905i	$-0.308209\pi$
$864$		0			0
$865$	81999.4			0.109592
$866$	270036.	−	270762.i	0.360069	−	0.361037i
$867$		0			0
$868$	1593.13	+	593353.i	0.00211451	+	0.787542i
$869$	323422.			0.428282
$870$		0			0
$871$			608019.i			0.801458i
$872$	−485781.	−	481884.i	−0.638863	−	0.633738i
$873$		0			0
$874$	384144.	−	385177.i	0.502888	−	0.504240i
$875$		−	764581.i		−	0.998637i
$876$		0			0
$877$	−626211.			−0.814182			−0.407091	−	0.913388i	$-0.633457\pi$
$877$	−626211.			−0.814182			−0.407091	+	0.913388i	$0.633457\pi$
$878$	1.05224e6	+	1.04942e6i	1.36498	+	1.36132i
$879$		0			0
$880$	−1627.54	−	303083.i	−0.00210168	−	0.391378i
$881$	447853.			0.577011			0.288505	−	0.957478i	$-0.406842\pi$
$881$	447853.			0.577011			0.288505	+	0.957478i	$0.406842\pi$
$882$		0			0
$883$			1.38655e6i			1.77833i	0.457582	+	0.889167i	$0.348715\pi$
$883$			1.38655e6i			1.77833i	−0.457582	+	0.889167i	$0.651285\pi$
$884$	−2921.67	−	1.08816e6i	−0.00373875	−	1.39248i
$885$		0			0
$886$	391595.	+	390545.i	0.498850	+	0.497513i
$887$		−	1.53191e6i		−	1.94709i	−0.228490	−	0.973546i	$-0.573379\pi$
$887$		−	1.53191e6i		−	1.94709i	0.228490	−	0.973546i	$-0.426621\pi$
$888$		0			0
$889$	939134.			1.18829
$890$	30331.0	−	30412.6i	0.0382919	−	0.0383949i
$891$		0			0
$892$	266588.	−	715.777i	0.335051	−	0.000899598i
$893$	−1.17480e6			−1.47320
$894$		0			0
$895$			20683.4i			0.0258211i
$896$	−669911.	+	682621.i	−0.834451	+	0.850283i
$897$		0			0
$898$	362758.	−	363734.i	0.449847	−	0.451056i
$899$		−	416323.i		−	0.515124i
$900$		0			0
$901$	−514844.			−0.634200
$902$	700646.	+	698767.i	0.861164	+	0.858854i
$903$		0			0
$904$	−455103.	−	451451.i	−0.556894	−	0.552426i
$905$	−516205.			−0.630268
$906$		0			0
$907$			326429.i			0.396802i	0.980121	+	0.198401i	$0.0635749\pi$
$907$			326429.i			0.396802i	−0.980121	+	0.198401i	$0.936425\pi$
$908$	900136.	−	2416.82i	1.09178	−	0.00293139i
$909$		0			0
$910$	−332580.	−	331689.i	−0.401619	−	0.400542i
$911$			1.29034e6i			1.55477i	0.629026	+	0.777384i	$0.283454\pi$
$911$			1.29034e6i			1.55477i	−0.629026	+	0.777384i	$0.716546\pi$
$912$		0			0
$913$	−819172.			−0.982729
$914$	827856.	−	830082.i	0.990975	−	0.993639i
$915$		0			0
$916$	−105.156	−	39164.9i	−0.000125327	−	0.0466774i
$917$	−1.22043e6			−1.45135
$918$		0			0
$919$		−	844321.i		−	0.999715i	−0.866108	−	0.499858i	$-0.833386\pi$
$919$		−	844321.i		−	0.999715i	0.866108	−	0.499858i	$-0.166614\pi$
$920$	−178597.	+	180042.i	−0.211008	+	0.212715i
$921$		0			0
$922$	836468.	−	838717.i	0.983983	−	0.986628i
$923$		−	962338.i		−	1.12960i
$924$		0			0
$925$	777598.			0.908807
$926$	−1.00454e6	−	1.00185e6i	−1.17151	−	1.16837i
$927$		0			0
$928$	471322.	−	477693.i	0.547296	−	0.554693i
$929$	603267.			0.699002			0.349501	−	0.936936i	$-0.386351\pi$
$929$	603267.			0.699002			0.349501	+	0.936936i	$0.386351\pi$
$930$		0			0
$931$		−	407325.i		−	0.469940i
$932$	3306.62	+	1.23154e6i	0.00380673	+	1.41780i
$933$		0			0
$934$	−330363.	−	329477.i	−0.378702	−	0.377687i
$935$		−	471882.i		−	0.539772i
$936$		0			0
$937$	−109044.			−0.124200			−0.0621002	−	0.998070i	$-0.519780\pi$
$937$	−109044.			−0.124200			−0.0621002	+	0.998070i	$0.519780\pi$
$938$	587544.	−	589123.i	0.667782	−	0.669577i
$939$		0			0
$940$	547667.	−	1470.46i	0.619814	−	0.00166417i
$941$	690952.			0.780312			0.390156	−	0.920749i	$-0.372421\pi$
$941$	690952.			0.780312			0.390156	+	0.920749i	$0.372421\pi$
$942$		0			0
$943$		−	827961.i		−	0.931079i
$944$	−1590.90	−	296261.i	−0.00178525	−	0.332453i
$945$		0			0
$946$	633299.	−	635001.i	0.707663	−	0.709565i
$947$			1.20349e6i			1.34197i	0.741472	+	0.670984i	$0.234128\pi$
$947$			1.20349e6i			1.34197i	−0.741472	+	0.670984i	$0.765872\pi$
$948$		0			0
$949$	937880.			1.04139
$950$	−556956.	−	555462.i	−0.617125	−	0.615471i
$951$		0			0
$952$	−1.04869e6	+	1.05717e6i	−1.15710	+	1.16646i
$953$	1.58732e6			1.74775			0.873873	−	0.486154i	$-0.161600\pi$
$953$	1.58732e6			1.74775			0.873873	+	0.486154i	$0.161600\pi$
$954$		0			0
$955$		−	468312.i		−	0.513486i
$956$	416938.	−	1119.46i	0.456201	−	0.00122488i
$957$		0			0
$958$	294773.	+	293983.i	0.321187	+	0.320325i
$959$			272967.i			0.296806i
$960$		0			0
$961$	519945.			0.563002
$962$	771129.	−	773202.i	0.833253	−	0.835493i
$963$		0			0
$964$	1202.84	+	447992.i	0.00129435	+	0.482077i
$965$	−248677.			−0.267043
$966$		0			0
$967$			986601.i			1.05509i	0.849528	+	0.527544i	$0.176887\pi$
$967$			986601.i			1.05509i	−0.849528	+	0.527544i	$0.823113\pi$
$968$	−206963.	−	205303.i	−0.220873	−	0.219101i
$969$		0			0
$970$	−586355.	+	587932.i	−0.623186	+	0.624861i
$971$			1.42706e6i			1.51358i	0.653658	+	0.756790i	$0.273233\pi$
$971$			1.42706e6i			1.51358i	−0.653658	+	0.756790i	$0.726767\pi$
$972$		0			0
$973$	543189.			0.573754
$974$	−286859.	−	286090.i	−0.302378	−	0.301568i
$975$		0			0
$976$	−1.51591e6	+	8140.38i	−1.59138	+	0.00854565i
$977$	1.60332e6			1.67969			0.839847	−	0.542823i	$-0.182645\pi$
$977$	1.60332e6			1.67969			0.839847	+	0.542823i	$0.182645\pi$
$978$		0			0
$979$			91478.3i			0.0954449i
$980$	509.836	+	189886.i	0.000530858	+	0.197716i
$981$		0			0
$982$	−496277.	−	494946.i	−0.514637	−	0.513257i
$983$		−	1.46864e6i		−	1.51987i	−0.649997	−	0.759936i	$-0.725230\pi$
$983$		−	1.46864e6i		−	1.51987i	0.649997	−	0.759936i	$-0.274770\pi$
$984$		0			0
$985$	333104.			0.343326
$986$	737793.	−	739777.i	0.758893	−	0.760934i
$987$		0			0
$988$	−1.10465e6	+	2965.92i	−1.13164	+	0.00303841i
$989$	−750388.			−0.767173
$990$		0			0
$991$			1.48147e6i			1.50850i	0.656585	+	0.754252i	$0.272000\pi$
$991$			1.48147e6i			1.50850i	−0.656585	+	0.754252i	$0.728000\pi$
$992$	−463067.	−	456891.i	−0.470566	−	0.464290i
$993$		0			0
$994$	−929931.	+	932432.i	−0.941192	+	0.943722i
$995$			283679.i			0.286537i
$996$		0			0
$997$	−46935.8			−0.0472187			−0.0236093	−	0.999721i	$-0.507516\pi$
$997$	−46935.8			−0.0472187			−0.0236093	+	0.999721i	$0.507516\pi$
$998$	−272184.	−	271454.i	−0.273276	−	0.272543i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.f.163.17		22
3.2	odd	2		324.5.d.e.163.6		22
4.3	odd	2	inner	324.5.d.f.163.18		22
9.2	odd	6		108.5.f.a.91.20		44
9.4	even	3		36.5.f.a.7.13	yes	44
9.5	odd	6		108.5.f.a.19.10		44
9.7	even	3		36.5.f.a.31.3	yes	44
12.11	even	2		324.5.d.e.163.5		22
36.7	odd	6		36.5.f.a.31.13	yes	44
36.11	even	6		108.5.f.a.91.10		44
36.23	even	6		108.5.f.a.19.20		44
36.31	odd	6		36.5.f.a.7.3	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.3	✓	44	36.31	odd	6
36.5.f.a.7.13	yes	44	9.4	even	3
36.5.f.a.31.3	yes	44	9.7	even	3
36.5.f.a.31.13	yes	44	36.7	odd	6
108.5.f.a.19.10		44	9.5	odd	6
108.5.f.a.19.20		44	36.23	even	6
108.5.f.a.91.10		44	36.11	even	6
108.5.f.a.91.20		44	9.2	odd	6
324.5.d.e.163.5		22	12.11	even	2
324.5.d.e.163.6		22	3.2	odd	2
324.5.d.f.163.17		22	1.1	even	1	trivial
324.5.d.f.163.18		22	4.3	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.82463 - 2.83222i) q^{2} +(-0.0429591 - 15.9999i) q^{4} +11.7888 q^{5} +58.3756i q^{7} +(-45.4367 - 45.0722i) q^{8} +O(q^{10})\)	\(q+(2.82463 - 2.83222i) q^{2} +(-0.0429591 - 15.9999i) q^{4} +11.7888 q^{5} +58.3756i q^{7} +(-45.4367 - 45.0722i) q^{8} +(33.2988 - 33.3884i) q^{10} +100.429i q^{11} -170.636 q^{13} +(165.333 + 164.889i) q^{14} +(-255.996 + 1.37469i) q^{16} -398.571 q^{17} +404.608i q^{19} +(-0.506434 - 188.619i) q^{20} +(284.438 + 283.675i) q^{22} -336.123i q^{23} -486.025 q^{25} +(-481.982 + 483.278i) q^{26} +(934.007 - 2.50777i) q^{28} -655.342 q^{29} +635.277i q^{31} +(-719.201 + 728.921i) q^{32} +(-1125.81 + 1128.84i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(1145.94 + 1142.87i) q^{38} +(-535.642 - 531.345i) q^{40} +2463.27 q^{41} -2232.48i q^{43} +(1606.86 - 4.31435i) q^{44} +(-951.976 - 949.423i) q^{46} +2903.56i q^{47} -1006.72 q^{49} +(-1372.84 + 1376.53i) q^{50} +(7.33036 + 2730.16i) q^{52} +1291.73 q^{53} +1183.94i q^{55} +(2631.12 - 2652.40i) q^{56} +(-1851.10 + 1856.07i) q^{58} +1157.28i q^{59} +5921.62 q^{61} +(1799.24 + 1794.42i) q^{62} +(32.9923 + 4095.87i) q^{64} -2011.58 q^{65} -3563.26i q^{67} +(17.1222 + 6377.11i) q^{68} +(1949.07 + 1943.84i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(-4519.16 + 4531.31i) q^{74} +(6473.71 - 17.3816i) q^{76} -5862.62 q^{77} -3220.39i q^{79} +(-3017.88 + 16.2058i) q^{80} +(6957.81 - 6976.52i) q^{82} +8156.71i q^{83} -4698.65 q^{85} +(-6322.88 - 6305.92i) q^{86} +(4526.57 - 4563.17i) q^{88} +910.873 q^{89} -9960.97i q^{91} +(-5377.95 + 14.4396i) q^{92} +(8223.52 + 8201.47i) q^{94} +4769.83i q^{95} -17608.9 q^{97} +(-2843.60 + 2851.24i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) \) 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

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