LMFDB - Embedded newform 324.5.d.f.163.9

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			163.9
Character	$\chi$	$=$	324.163
Dual form			324.5.d.f.163.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16626 - 3.82620i) q^{2} +(-13.2797 + 8.92473i) q^{4} -39.0789 q^{5} -12.2052i q^{7} +(49.6354 + 40.4021i) q^{8} +O(q^{10})$	\(q+(-1.16626 - 3.82620i) q^{2} +(-13.2797 + 8.92473i) q^{4} -39.0789 q^{5} -12.2052i q^{7} +(49.6354 + 40.4021i) q^{8} +(45.5763 + 149.524i) q^{10} +111.018i q^{11} +208.982 q^{13} +(-46.6996 + 14.2345i) q^{14} +(96.6986 - 237.035i) q^{16} +93.3790 q^{17} -26.8894i q^{19} +(518.954 - 348.768i) q^{20} +(424.778 - 129.477i) q^{22} +874.774i q^{23} +902.160 q^{25} +(-243.728 - 799.608i) q^{26} +(108.928 + 162.081i) q^{28} -1301.62 q^{29} -685.305i q^{31} +(-1019.72 - 93.5434i) q^{32} +(-108.905 - 357.287i) q^{34} +476.966i q^{35} -1760.25 q^{37} +(-102.884 + 31.3601i) q^{38} +(-1939.70 - 1578.87i) q^{40} +78.0843 q^{41} -1622.88i q^{43} +(-990.807 - 1474.28i) q^{44} +(3347.06 - 1020.22i) q^{46} -2308.86i q^{47} +2252.03 q^{49} +(-1052.16 - 3451.85i) q^{50} +(-2775.21 + 1865.11i) q^{52} -1313.48 q^{53} -4338.47i q^{55} +(493.116 - 605.810i) q^{56} +(1518.03 + 4980.25i) q^{58} -5563.78i q^{59} +2180.26 q^{61} +(-2622.12 + 799.247i) q^{62} +(831.345 + 4010.75i) q^{64} -8166.79 q^{65} +246.040i q^{67} +(-1240.04 + 833.382i) q^{68} +(1824.97 - 556.268i) q^{70} -4608.15i q^{71} +2564.79 q^{73} +(2052.92 + 6735.08i) q^{74} +(239.980 + 357.082i) q^{76} +1355.00 q^{77} +5180.32i q^{79} +(-3778.87 + 9263.05i) q^{80} +(-91.0669 - 298.766i) q^{82} -1873.35i q^{83} -3649.15 q^{85} +(-6209.48 + 1892.71i) q^{86} +(-4485.37 + 5510.43i) q^{88} -1167.17 q^{89} -2550.67i q^{91} +(-7807.12 - 11616.7i) q^{92} +(-8834.19 + 2692.75i) q^{94} +1050.81i q^{95} -5739.16 q^{97} +(-2626.47 - 8616.73i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.16626	−	3.82620i	−0.291566	−	0.956551i
$2$	−1.16626	−	3.82620i	−0.291566	−	0.956551i
$3$		0			0
$3$		0			0
$4$	−13.2797	+	8.92473i	−0.829979	+	0.557795i
$5$	−39.0789			−1.56316			−0.781578	−	0.623808i	$-0.785585\pi$
$5$	−39.0789			−1.56316			−0.781578	+	0.623808i	$0.785585\pi$
$6$		0			0
$7$		−	12.2052i		−	0.249086i	−0.992214	−	0.124543i	$-0.960254\pi$
$7$		−	12.2052i		−	0.249086i	0.992214	−	0.124543i	$-0.0397464\pi$
$8$	49.6354	+	40.4021i	0.775553	+	0.631282i
$9$		0			0
$10$	45.5763	+	149.524i	0.455763	+	1.49524i
$11$			111.018i			0.917506i	0.888564	+	0.458753i	$0.151704\pi$
$11$			111.018i			0.917506i	−0.888564	+	0.458753i	$0.848296\pi$
$12$		0			0
$13$	208.982			1.23658			0.618290	−	0.785950i	$-0.287826\pi$
$13$	208.982			1.23658			0.618290	+	0.785950i	$0.287826\pi$
$14$	−46.6996	+	14.2345i	−0.238263	+	0.0726250i
$15$		0			0
$16$	96.6986	−	237.035i	0.377729	−	0.925916i
$17$	93.3790			0.323111			0.161555	−	0.986864i	$-0.448349\pi$
$17$	93.3790			0.323111			0.161555	+	0.986864i	$0.448349\pi$
$18$		0			0
$19$		−	26.8894i		−	0.0744859i	−0.999306	−	0.0372429i	$-0.988142\pi$
$19$		−	26.8894i		−	0.0744859i	0.999306	−	0.0372429i	$-0.0118575\pi$
$20$	518.954	−	348.768i	1.29739	−	0.871921i
$21$		0			0
$22$	424.778	−	129.477i	0.877641	−	0.267514i
$23$			874.774i			1.65364i	0.562469	+	0.826819i	$0.309852\pi$
$23$			874.774i			1.65364i	−0.562469	+	0.826819i	$0.690148\pi$
$24$		0			0
$25$	902.160			1.44346
$26$	−243.728	−	799.608i	−0.360545	−	1.18285i
$27$		0			0
$28$	108.928	+	162.081i	0.138939	+	0.206736i
$29$	−1301.62			−1.54770			−0.773851	−	0.633368i	$-0.781672\pi$
$29$	−1301.62			−1.54770			−0.773851	+	0.633368i	$0.781672\pi$
$30$		0			0
$31$		−	685.305i		−	0.713117i	−0.934273	−	0.356558i	$-0.883950\pi$
$31$		−	685.305i		−	0.713117i	0.934273	−	0.356558i	$-0.116050\pi$
$32$	−1019.72	−	93.5434i	−0.995819	−	0.0913509i
$33$		0			0
$34$	−108.905	−	357.287i	−0.0942081	−	0.309072i
$35$			476.966i			0.389360i
$36$		0			0
$37$	−1760.25			−1.28579			−0.642897	−	0.765953i	$-0.722268\pi$
$37$	−1760.25			−1.28579			−0.642897	+	0.765953i	$0.722268\pi$
$38$	−102.884	+	31.3601i	−0.0712495	+	0.0217175i
$39$		0			0
$40$	−1939.70	−	1578.87i	−1.21231	−	0.986793i
$41$	78.0843			0.0464511			0.0232255	−	0.999730i	$-0.492606\pi$
$41$	78.0843			0.0464511			0.0232255	+	0.999730i	$0.492606\pi$
$42$		0			0
$43$		−	1622.88i		−	0.877709i	−0.898558	−	0.438855i	$-0.855384\pi$
$43$		−	1622.88i		−	0.877709i	0.898558	−	0.438855i	$-0.144616\pi$
$44$	−990.807	−	1474.28i	−0.511780	−	0.761510i
$45$		0			0
$46$	3347.06	−	1020.22i	1.58179	−	0.482144i
$47$		−	2308.86i		−	1.04521i	−0.852575	−	0.522604i	$-0.824961\pi$
$47$		−	2308.86i		−	1.04521i	0.852575	−	0.522604i	$-0.175039\pi$
$48$		0			0
$49$	2252.03			0.937956
$50$	−1052.16	−	3451.85i	−0.420863	−	1.38074i
$51$		0			0
$52$	−2775.21	+	1865.11i	−1.02634	+	0.689759i
$53$	−1313.48			−0.467598			−0.233799	−	0.972285i	$-0.575116\pi$
$53$	−1313.48			−0.467598			−0.233799	+	0.972285i	$0.575116\pi$
$54$		0			0
$55$		−	4338.47i		−	1.43420i
$56$	493.116	−	605.810i	0.157243	−	0.193179i
$57$		0			0
$58$	1518.03	+	4980.25i	0.451257	+	1.48046i
$59$		−	5563.78i		−	1.59833i	−0.601113	−	0.799164i	$-0.705276\pi$
$59$		−	5563.78i		−	1.59833i	0.601113	−	0.799164i	$-0.294724\pi$
$60$		0			0
$61$	2180.26			0.585933			0.292967	−	0.956123i	$-0.405358\pi$
$61$	2180.26			0.585933			0.292967	+	0.956123i	$0.405358\pi$
$62$	−2622.12	+	799.247i	−0.682132	+	0.207921i
$63$		0			0
$64$	831.345	+	4010.75i	0.202965	+	0.979186i
$65$	−8166.79			−1.93297
$66$		0			0
$67$			246.040i			0.0548096i	0.999624	+	0.0274048i	$0.00872430\pi$
$67$			246.040i			0.0548096i	−0.999624	+	0.0274048i	$0.991276\pi$
$68$	−1240.04	+	833.382i	−0.268175	+	0.180230i
$69$		0			0
$70$	1824.97	−	556.268i	0.372443	−	0.113524i
$71$		−	4608.15i		−	0.914134i	−0.889432	−	0.457067i	$-0.848900\pi$
$71$		−	4608.15i		−	0.914134i	0.889432	−	0.457067i	$-0.151100\pi$
$72$		0			0
$73$	2564.79			0.481290			0.240645	−	0.970613i	$-0.422641\pi$
$73$	2564.79			0.481290			0.240645	+	0.970613i	$0.422641\pi$
$74$	2052.92	+	6735.08i	0.374894	+	1.22993i
$75$		0			0
$76$	239.980	+	357.082i	0.0415479	+	0.0618217i
$77$	1355.00			0.228538
$78$		0			0
$79$			5180.32i			0.830047i	0.909811	+	0.415023i	$0.136227\pi$
$79$			5180.32i			0.830047i	−0.909811	+	0.415023i	$0.863773\pi$
$80$	−3778.87	+	9263.05i	−0.590449	+	1.44735i
$81$		0			0
$82$	−91.0669	−	298.766i	−0.0135436	−	0.0444328i
$83$		−	1873.35i		−	0.271934i	−0.990713	−	0.135967i	$-0.956586\pi$
$83$		−	1873.35i		−	0.271934i	0.990713	−	0.135967i	$-0.0434141\pi$
$84$		0			0
$85$	−3649.15			−0.505072
$86$	−6209.48	+	1892.71i	−0.839573	+	0.255910i
$87$		0			0
$88$	−4485.37	+	5510.43i	−0.579205	+	0.711574i
$89$	−1167.17			−0.147352			−0.0736759	−	0.997282i	$-0.523473\pi$
$89$	−1167.17			−0.147352			−0.0736759	+	0.997282i	$0.523473\pi$
$90$		0			0
$91$		−	2550.67i		−	0.308015i
$92$	−7807.12	−	11616.7i	−0.922391	−	1.37248i
$93$		0			0
$94$	−8834.19	+	2692.75i	−0.999795	+	0.304747i
$95$			1050.81i			0.116433i
$96$		0			0
$97$	−5739.16			−0.609965			−0.304983	−	0.952358i	$-0.598651\pi$
$97$	−5739.16			−0.609965			−0.304983	+	0.952358i	$0.598651\pi$
$98$	−2626.47	−	8616.73i	−0.273476	−	0.897203i
$99$		0			0
$100$	−11980.4	+	8051.53i	−1.19804	+	0.805153i
$101$	15586.7			1.52796			0.763981	−	0.645238i	$-0.223242\pi$
$101$	15586.7			1.52796			0.763981	+	0.645238i	$0.223242\pi$
$102$		0			0
$103$		−	11127.3i		−	1.04885i	−0.851455	−	0.524427i	$-0.824280\pi$
$103$		−	11127.3i		−	1.04885i	0.851455	−	0.524427i	$-0.175720\pi$
$104$	10372.9	+	8443.31i	0.959034	+	0.780632i
$105$		0			0
$106$	1531.87	+	5025.65i	0.136336	+	0.447281i
$107$		−	4464.91i		−	0.389983i	−0.980805	−	0.194991i	$-0.937532\pi$
$107$		−	4464.91i		−	0.389983i	0.980805	−	0.194991i	$-0.0624679\pi$
$108$		0			0
$109$	−4736.05			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$109$	−4736.05			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$110$	−16599.9	+	5059.80i	−1.37189	+	0.418165i
$111$		0			0
$112$	−2893.06	−	1180.23i	−0.230633	−	0.0940869i
$113$	−18346.1			−1.43677			−0.718385	−	0.695645i	$-0.755119\pi$
$113$	−18346.1			−1.43677			−0.718385	+	0.695645i	$0.755119\pi$
$114$		0			0
$115$		−	34185.2i		−	2.58489i
$116$	17285.0	−	11616.6i	1.28456	−	0.863301i
$117$		0			0
$118$	−21288.2	+	6488.84i	−1.52888	+	0.466018i
$119$		−	1139.71i		−	0.0804823i
$120$		0			0
$121$	2315.96			0.158183
$122$	−2542.76	−	8342.10i	−0.170838	−	0.560475i
$123$		0			0
$124$	6116.16	+	9100.62i	0.397773	+	0.591872i
$125$	−10831.1			−0.693190
$126$		0			0
$127$			8169.42i			0.506505i	0.967400	+	0.253252i	$0.0815003\pi$
$127$			8169.42i			0.506505i	−0.967400	+	0.253252i	$0.918500\pi$
$128$	14376.4	−	7858.48i	0.877463	−	0.479644i
$129$		0			0
$130$	9524.63	+	31247.8i	0.563588	+	1.84898i
$131$			10543.6i			0.614392i	0.951646	+	0.307196i	$0.0993907\pi$
$131$			10543.6i			0.614392i	−0.951646	+	0.307196i	$0.900609\pi$
$132$		0			0
$133$	−328.191			−0.0185534
$134$	941.399	−	286.948i	0.0524281	−	0.0159806i
$135$		0			0
$136$	4634.90	+	3772.70i	0.250589	+	0.203974i
$137$	3225.71			0.171864			0.0859318	−	0.996301i	$-0.472613\pi$
$137$	3225.71			0.171864			0.0859318	+	0.996301i	$0.472613\pi$
$138$		0			0
$139$		−	18794.3i		−	0.972742i	−0.873752	−	0.486371i	$-0.838320\pi$
$139$		−	18794.3i		−	0.972742i	0.873752	−	0.486371i	$-0.161680\pi$
$140$	−4256.79	−	6333.94i	−0.217183	−	0.323160i
$141$		0			0
$142$	−17631.7	+	5374.32i	−0.874415	+	0.266530i
$143$			23200.8i			1.13457i
$144$		0			0
$145$	50865.8			2.41930
$146$	−2991.22	−	9813.41i	−0.140328	−	0.460378i
$147$		0			0
$148$	23375.5	−	15709.8i	1.06718	−	0.717210i
$149$	−7650.25			−0.344590			−0.172295	−	0.985045i	$-0.555118\pi$
$149$	−7650.25			−0.344590			−0.172295	+	0.985045i	$0.555118\pi$
$150$		0			0
$151$		−	1125.80i		−	0.0493751i	−0.999695	−	0.0246876i	$-0.992141\pi$
$151$		−	1125.80i		−	0.0493751i	0.999695	−	0.0246876i	$-0.00785910\pi$
$152$	1086.39	−	1334.67i	0.0470216	−	0.0577677i
$153$		0			0
$154$	−1580.29	−	5184.51i	−0.0666338	−	0.218608i
$155$			26781.0i			1.11471i
$156$		0			0
$157$	−3511.62			−0.142465			−0.0712326	−	0.997460i	$-0.522693\pi$
$157$	−3511.62			−0.142465			−0.0712326	+	0.997460i	$0.522693\pi$
$158$	19821.0	−	6041.62i	0.793982	−	0.242013i
$159$		0			0
$160$	39849.5	+	3655.57i	1.55662	+	0.142796i
$161$	10676.8			0.411898
$162$		0			0
$163$		−	41947.9i		−	1.57883i	−0.613861	−	0.789414i	$-0.710385\pi$
$163$		−	41947.9i		−	1.57883i	0.613861	−	0.789414i	$-0.289615\pi$
$164$	−1036.93	+	696.881i	−0.0385534	+	0.0259102i
$165$		0			0
$166$	−7167.83	+	2184.83i	−0.260119	+	0.0792868i
$167$		−	6813.40i		−	0.244304i	−0.992511	−	0.122152i	$-0.961020\pi$
$167$		−	6813.40i		−	0.244304i	0.992511	−	0.122152i	$-0.0389796\pi$
$168$		0			0
$169$	15112.5			0.529131
$170$	4255.87	+	13962.4i	0.147262	+	0.483127i
$171$		0			0
$172$	14483.8	+	21551.3i	0.489582	+	0.728480i
$173$	15748.3			0.526189			0.263095	−	0.964770i	$-0.415257\pi$
$173$	15748.3			0.526189			0.263095	+	0.964770i	$0.415257\pi$
$174$		0			0
$175$		−	11011.0i		−	0.359544i
$176$	26315.2	+	10735.3i	0.849534	+	0.346568i
$177$		0			0
$178$	1361.23	+	4465.85i	0.0429628	+	0.140950i
$179$		−	22497.6i		−	0.702151i	−0.936347	−	0.351075i	$-0.885816\pi$
$179$		−	22497.6i		−	0.702151i	0.936347	−	0.351075i	$-0.114184\pi$
$180$		0			0
$181$	−21847.2			−0.666867			−0.333434	−	0.942774i	$-0.608207\pi$
$181$	−21847.2			−0.666867			−0.333434	+	0.942774i	$0.608207\pi$
$182$	−9759.38	+	2974.75i	−0.294632	+	0.0898066i
$183$		0			0
$184$	−35342.7	+	43419.8i	−1.04391	+	1.28248i
$185$	68788.7			2.00990
$186$		0			0
$187$			10366.8i			0.296456i
$188$	20606.0	+	30660.9i	0.583012	+	0.867500i
$189$		0			0
$190$	4020.60	−	1225.52i	0.111374	−	0.0339479i
$191$			18685.5i			0.512199i	0.966650	+	0.256099i	$0.0824375\pi$
$191$			18685.5i			0.512199i	−0.966650	+	0.256099i	$0.917563\pi$
$192$		0			0
$193$	46099.4			1.23760			0.618800	−	0.785548i	$-0.287619\pi$
$193$	46099.4			1.23760			0.618800	+	0.785548i	$0.287619\pi$
$194$	6693.38	+	21959.2i	0.177845	+	0.583462i
$195$		0			0
$196$	−29906.2	+	20098.8i	−0.778484	+	0.523188i
$197$	15934.7			0.410592			0.205296	−	0.978700i	$-0.434184\pi$
$197$	15934.7			0.410592			0.205296	+	0.978700i	$0.434184\pi$
$198$		0			0
$199$		−	73733.8i		−	1.86192i	−0.365124	−	0.930959i	$-0.618974\pi$
$199$		−	73733.8i		−	1.86192i	0.365124	−	0.930959i	$-0.381026\pi$
$200$	44779.1	+	36449.1i	1.11948	+	0.911228i
$201$		0			0
$202$	−18178.3	−	59638.1i	−0.445502	−	1.46157i
$203$			15886.5i			0.385511i
$204$		0			0
$205$	−3051.45			−0.0726103
$206$	−42575.3	+	12977.4i	−1.00328	+	0.305810i
$207$		0			0
$208$	20208.3	−	49536.0i	0.467092	−	1.14497i
$209$	2985.21			0.0683412
$210$		0			0
$211$		−	17818.4i		−	0.400224i	−0.979773	−	0.200112i	$-0.935869\pi$
$211$		−	17818.4i		−	0.400224i	0.979773	−	0.200112i	$-0.0641307\pi$
$212$	17442.6	−	11722.5i	0.388096	−	0.260824i
$213$		0			0
$214$	−17083.7	+	5207.26i	−0.373038	+	0.113706i
$215$			63420.5i			1.37200i
$216$		0			0
$217$	−8364.29			−0.177627
$218$	5523.49	+	18121.1i	0.116225	+	0.381304i
$219$		0			0
$220$	38719.6	+	57613.4i	0.799993	+	1.19036i
$221$	19514.5			0.399552
$222$		0			0
$223$		−	67381.1i		−	1.35497i	−0.735538	−	0.677483i	$-0.763071\pi$
$223$		−	67381.1i		−	1.35497i	0.735538	−	0.677483i	$-0.236929\pi$
$224$	−1141.72	+	12445.9i	−0.0227542	+	0.248044i
$225$		0			0
$226$	21396.4	+	70196.0i	0.418914	+	1.37434i
$227$		−	62794.3i		−	1.21862i	−0.792932	−	0.609310i	$-0.791446\pi$
$227$		−	62794.3i		−	1.21862i	0.792932	−	0.609310i	$-0.208554\pi$
$228$		0			0
$229$	−40926.3			−0.780426			−0.390213	−	0.920725i	$-0.627599\pi$
$229$	−40926.3			−0.780426			−0.390213	+	0.920725i	$0.627599\pi$
$230$	−130800.	+	39869.0i	−2.47258	+	0.753667i
$231$		0			0
$232$	−64606.3	−	52588.0i	−1.20033	−	0.977037i
$233$	79254.5			1.45986			0.729932	−	0.683520i	$-0.239552\pi$
$233$	79254.5			1.45986			0.729932	+	0.683520i	$0.239552\pi$
$234$		0			0
$235$			90227.9i			1.63382i
$236$	49655.2	+	73885.1i	0.891540	+	1.32658i
$237$		0			0
$238$	−4360.76	+	1329.20i	−0.0769854	+	0.0234659i
$239$		−	45131.1i		−	0.790096i	−0.918661	−	0.395048i	$-0.870728\pi$
$239$		−	45131.1i		−	0.790096i	0.918661	−	0.395048i	$-0.129272\pi$
$240$		0			0
$241$	75653.5			1.30255			0.651276	−	0.758841i	$-0.274234\pi$
$241$	75653.5			1.30255			0.651276	+	0.758841i	$0.274234\pi$
$242$	−2701.02	−	8861.32i	−0.0461208	−	0.151310i
$243$		0			0
$244$	−28953.1	+	19458.2i	−0.486312	+	0.326831i
$245$	−88007.0			−1.46617
$246$		0			0
$247$		−	5619.40i		−	0.0921078i
$248$	27687.7	−	34015.4i	0.450178	−	0.553060i
$249$		0			0
$250$	12631.9	+	41442.0i	0.202111	+	0.663072i
$251$		−	78270.9i		−	1.24238i	−0.783662	−	0.621188i	$-0.786650\pi$
$251$		−	78270.9i		−	1.24238i	0.783662	−	0.621188i	$-0.213350\pi$
$252$		0			0
$253$	−97115.9			−1.51722
$254$	31257.8	−	9527.70i	0.484498	−	0.147680i
$255$		0			0
$256$	−46834.8	−	45841.8i	−0.714642	−	0.699490i
$257$	−23012.7			−0.348418			−0.174209	−	0.984709i	$-0.555737\pi$
$257$	−23012.7			−0.348418			−0.174209	+	0.984709i	$0.555737\pi$
$258$		0			0
$259$			21484.2i			0.320273i
$260$	108452.	−	72886.4i	1.60432	−	1.07820i
$261$		0			0
$262$	40341.9	−	12296.6i	0.587697	−	0.179136i
$263$		−	86877.1i		−	1.25601i	−0.778209	−	0.628006i	$-0.783871\pi$
$263$		−	86877.1i		−	1.25601i	0.778209	−	0.628006i	$-0.216129\pi$
$264$		0			0
$265$	51329.5			0.730929
$266$	382.757	+	1255.72i	0.00540953	+	0.0177472i
$267$		0			0
$268$	−2195.84	−	3267.33i	−0.0305725	−	0.0454908i
$269$	−54083.3			−0.747409			−0.373705	−	0.927548i	$-0.621913\pi$
$269$	−54083.3			−0.747409			−0.373705	+	0.927548i	$0.621913\pi$
$270$		0			0
$271$			47957.3i			0.653004i	0.945197	+	0.326502i	$0.105870\pi$
$271$			47957.3i			0.653004i	−0.945197	+	0.326502i	$0.894130\pi$
$272$	9029.61	−	22134.0i	0.122048	−	0.299173i
$273$		0			0
$274$	−3762.03	−	12342.2i	−0.0501096	−	0.164396i
$275$			100156.i			1.32438i
$276$		0			0
$277$	−73723.5			−0.960830			−0.480415	−	0.877041i	$-0.659514\pi$
$277$	−73723.5			−0.960830			−0.480415	+	0.877041i	$0.659514\pi$
$278$	−71911.0	+	21919.2i	−0.930477	+	0.283618i
$279$		0			0
$280$	−19270.4	+	23674.4i	−0.245796	+	0.301969i
$281$	56123.9			0.710780			0.355390	−	0.934718i	$-0.384348\pi$
$281$	56123.9			0.710780			0.355390	+	0.934718i	$0.384348\pi$
$282$		0			0
$283$			152766.i			1.90746i	0.300666	+	0.953730i	$0.402791\pi$
$283$			152766.i			1.90746i	−0.300666	+	0.953730i	$0.597209\pi$
$284$	41126.5	+	61194.6i	0.509900	+	0.758711i
$285$		0			0
$286$	88771.0	−	27058.3i	1.08527	−	0.330802i
$287$		−	953.034i		−	0.0115703i
$288$		0			0
$289$	−74801.4			−0.895600
$290$	−59322.9	−	194623.i	−0.705385	−	2.31418i
$291$		0			0
$292$	−34059.6	+	22890.1i	−0.399460	+	0.268461i
$293$	−38840.3			−0.452426			−0.226213	−	0.974078i	$-0.572634\pi$
$293$	−38840.3			−0.452426			−0.226213	+	0.974078i	$0.572634\pi$
$294$		0			0
$295$			217426.i			2.49844i
$296$	−87370.8	−	71117.8i	−0.997201	−	0.811699i
$297$		0			0
$298$	8922.21	+	29271.4i	0.100471	+	0.329618i
$299$			182812.i			2.04486i
$300$		0			0
$301$	−19807.6			−0.218625
$302$	−4307.55	+	1312.98i	−0.0472298	+	0.0143961i
$303$		0			0
$304$	−6373.72	−	2600.17i	−0.0689677	−	0.0281354i
$305$	−85202.0			−0.915905
$306$		0			0
$307$			457.528i			0.00485446i	0.999997	+	0.00242723i	$0.000772612\pi$
$307$			457.528i			0.00485446i	−0.999997	+	0.00242723i	$0.999227\pi$
$308$	−17993.9	+	12093.0i	−0.189681	+	0.127477i
$309$		0			0
$310$	102469.	−	31233.7i	1.06628	−	0.325012i
$311$			10722.3i			0.110858i	0.998463	+	0.0554292i	$0.0176527\pi$
$311$			10722.3i			0.110858i	−0.998463	+	0.0554292i	$0.982347\pi$
$312$		0			0
$313$	17952.2			0.183244			0.0916218	−	0.995794i	$-0.470795\pi$
$313$	17952.2			0.183244			0.0916218	+	0.995794i	$0.470795\pi$
$314$	4095.48	+	13436.2i	0.0415380	+	0.136275i
$315$		0			0
$316$	−46232.9	−	68792.9i	−0.462996	−	0.688921i
$317$	−61371.8			−0.610732			−0.305366	−	0.952235i	$-0.598779\pi$
$317$	−61371.8			−0.610732			−0.305366	+	0.952235i	$0.598779\pi$
$318$		0			0
$319$		−	144503.i		−	1.42003i
$320$	−32488.0	−	156735.i	−0.317266	−	1.53062i
$321$		0			0
$322$	−12452.0	−	40851.6i	−0.120095	−	0.394001i
$323$		−	2510.90i		−	0.0240672i
$324$		0			0
$325$	188535.			1.78495
$326$	−160501.	+	48922.3i	−1.51023	+	0.460333i
$327$		0			0
$328$	3875.74	+	3154.77i	0.0360253	+	0.0293237i
$329$	−28180.2			−0.260347
$330$		0			0
$331$		−	185899.i		−	1.69676i	−0.529389	−	0.848379i	$-0.677579\pi$
$331$		−	185899.i		−	1.69676i	0.529389	−	0.848379i	$-0.322421\pi$
$332$	16719.2	+	24877.5i	0.151684	+	0.225700i
$333$		0			0
$334$	−26069.4	+	7946.22i	−0.233689	+	0.0712308i
$335$		−	9614.98i		−	0.0856759i
$336$		0			0
$337$	−147998.			−1.30315			−0.651576	−	0.758584i	$-0.725892\pi$
$337$	−147998.			−1.30315			−0.651576	+	0.758584i	$0.725892\pi$
$338$	−17625.2	−	57823.6i	−0.154277	−	0.506141i
$339$		0			0
$340$	48459.4	−	32567.6i	0.419199	−	0.281727i
$341$	76081.3			0.654289
$342$		0			0
$343$		−	56791.2i		−	0.482717i
$344$	65567.9	−	80552.5i	0.554082	−	0.680710i
$345$		0			0
$346$	−18366.7	−	60256.2i	−0.153419	−	0.503326i
$347$		−	144980.i		−	1.20406i	−0.798472	−	0.602031i	$-0.794358\pi$
$347$		−	144980.i		−	1.20406i	0.798472	−	0.602031i	$-0.205642\pi$
$348$		0			0
$349$	−178952.			−1.46921			−0.734606	−	0.678494i	$-0.762633\pi$
$349$	−178952.			−1.46921			−0.734606	+	0.678494i	$0.762633\pi$
$350$	−42130.5	+	12841.8i	−0.343922	+	0.104831i
$351$		0			0
$352$	10385.0	−	113207.i	0.0838150	−	0.913670i
$353$	26395.4			0.211826			0.105913	−	0.994375i	$-0.466224\pi$
$353$	26395.4			0.211826			0.105913	+	0.994375i	$0.466224\pi$
$354$		0			0
$355$			180081.i			1.42893i
$356$	15499.7	−	10416.7i	0.122299	−	0.0821922i
$357$		0			0
$358$	−86080.4	+	26238.2i	−0.671643	+	0.204723i
$359$			181364.i			1.40722i	0.710587	+	0.703609i	$0.248429\pi$
$359$			181364.i			1.40722i	−0.710587	+	0.703609i	$0.751571\pi$
$360$		0			0
$361$	129598.			0.994452
$362$	25479.6	+	83592.0i	0.194436	+	0.637892i
$363$		0			0
$364$	22764.0	+	33872.0i	0.171809	+	0.255646i
$365$	−100229.			−0.752331
$366$		0			0
$367$			209000.i			1.55173i	0.630901	+	0.775863i	$0.282685\pi$
$367$			209000.i			1.55173i	−0.630901	+	0.775863i	$0.717315\pi$
$368$	207352.	+	84589.4i	1.53113	+	0.624626i
$369$		0			0
$370$	−80225.8	−	263199.i	−0.586017	−	1.92257i
$371$			16031.3i			0.116472i
$372$		0			0
$373$	−76595.9			−0.550539			−0.275269	−	0.961367i	$-0.588767\pi$
$373$	−76595.9			−0.550539			−0.275269	+	0.961367i	$0.588767\pi$
$374$	39665.4	−	12090.4i	0.283575	−	0.0864365i
$375$		0			0
$376$	93282.9	−	114601.i	0.659822	−	0.810614i
$377$	−272015.			−1.91386
$378$		0			0
$379$			232118.i			1.61596i	0.589211	+	0.807979i	$0.299439\pi$
$379$			232118.i			1.61596i	−0.589211	+	0.807979i	$0.700561\pi$
$380$	−9378.17	−	13954.4i	−0.0649458	−	0.0966369i
$381$		0			0
$382$	71494.6	−	21792.3i	0.489944	−	0.149340i
$383$		−	85585.3i		−	0.583447i	−0.956503	−	0.291724i	$-0.905771\pi$
$383$		−	85585.3i		−	0.583447i	0.956503	−	0.291724i	$-0.0942288\pi$
$384$		0			0
$385$	−52951.9			−0.357240
$386$	−53764.1	−	176386.i	−0.360842	−	1.18383i
$387$		0			0
$388$	76214.1	−	51220.4i	0.506258	−	0.340236i
$389$	121738.			0.804504			0.402252	−	0.915529i	$-0.368228\pi$
$389$	121738.			0.804504			0.402252	+	0.915529i	$0.368228\pi$
$390$		0			0
$391$			81685.5i			0.534308i
$392$	111781.	+	90986.8i	0.727435	+	0.592115i
$393$		0			0
$394$	−18584.0	−	60969.2i	−0.119715	−	0.392752i
$395$		−	202441.i		−	1.29749i
$396$		0			0
$397$	−71690.8			−0.454865			−0.227432	−	0.973794i	$-0.573033\pi$
$397$	−71690.8			−0.454865			−0.227432	+	0.973794i	$0.573033\pi$
$398$	−282120.	+	85993.1i	−1.78102	+	0.542872i
$399$		0			0
$400$	87237.5	−	213843.i	0.545235	−	1.33652i
$401$	−86280.5			−0.536567			−0.268283	−	0.963340i	$-0.586456\pi$
$401$	−86280.5			−0.536567			−0.268283	+	0.963340i	$0.586456\pi$
$402$		0			0
$403$		−	143217.i		−	0.881826i
$404$	−206987.	+	139107.i	−1.26818	+	0.852291i
$405$		0			0
$406$	60785.0	−	18527.9i	0.368761	−	0.112402i
$407$		−	195420.i		−	1.17972i
$408$		0			0
$409$	230461.			1.37769			0.688844	−	0.724910i	$-0.258118\pi$
$409$	230461.			1.37769			0.688844	+	0.724910i	$0.258118\pi$
$410$	3558.79	+	11675.5i	0.0211707	+	0.0694554i
$411$		0			0
$412$	99308.0	+	147767.i	0.585046	+	0.870526i
$413$	−67907.1			−0.398121
$414$		0			0
$415$			73208.6i			0.425075i
$416$	−213103.	−	19548.9i	−1.23141	−	0.112963i
$417$		0			0
$418$	−3481.55	−	11422.0i	−0.0199260	−	0.0653718i
$419$		−	55624.6i		−	0.316839i	−0.987372	−	0.158420i	$-0.949360\pi$
$419$		−	55624.6i		−	0.316839i	0.987372	−	0.158420i	$-0.0506399\pi$
$420$		0			0
$421$	140971.			0.795366			0.397683	−	0.917523i	$-0.369814\pi$
$421$	140971.			0.795366			0.397683	+	0.917523i	$0.369814\pi$
$422$	−68176.8	+	20781.0i	−0.382835	+	0.116692i
$423$		0			0
$424$	−65195.3	−	53067.4i	−0.362647	−	0.295186i
$425$	84242.8			0.466396
$426$		0			0
$427$		−	26610.5i		−	0.145948i
$428$	39848.1	+	59292.5i	0.217530	+	0.323677i
$429$		0			0
$430$	242660.	−	73965.1i	1.31238	−	0.400027i
$431$		−	191015.i		−	1.02828i	−0.857705	−	0.514142i	$-0.828111\pi$
$431$		−	191015.i		−	1.02828i	0.857705	−	0.514142i	$-0.171889\pi$
$432$		0			0
$433$	48243.4			0.257313			0.128657	−	0.991689i	$-0.458933\pi$
$433$	48243.4			0.257313			0.128657	+	0.991689i	$0.458933\pi$
$434$	9754.97	+	32003.5i	0.0517901	+	0.169909i
$435$		0			0
$436$	62893.1	−	42268.0i	0.330849	−	0.222351i
$437$	23522.1			0.123173
$438$		0			0
$439$			262210.i			1.36057i	0.732948	+	0.680285i	$0.238144\pi$
$439$			262210.i			1.36057i	−0.732948	+	0.680285i	$0.761856\pi$
$440$	175283.	−	215342.i	0.905388	−	1.11230i
$441$		0			0
$442$	−22759.1	−	74666.6i	−0.116496	−	0.382192i
$443$		−	90983.0i		−	0.463610i	−0.972762	−	0.231805i	$-0.925537\pi$
$443$		−	90983.0i		−	0.463610i	0.972762	−	0.231805i	$-0.0744631\pi$
$444$		0			0
$445$	45611.9			0.230334
$446$	−257814.	+	78584.2i	−1.29609	+	0.395062i
$447$		0			0
$448$	48952.0	−	10146.7i	0.243901	−	0.0505557i
$449$	283350.			1.40550			0.702748	−	0.711438i	$-0.251956\pi$
$449$	283350.			1.40550			0.702748	+	0.711438i	$0.251956\pi$
$450$		0			0
$451$			8668.77i			0.0426191i
$452$	243630.	−	163734.i	1.19249	−	0.801424i
$453$		0			0
$454$	−240264.	+	73234.7i	−1.16567	+	0.355308i
$455$			99677.3i			0.481475i
$456$		0			0
$457$	198453.			0.950224			0.475112	−	0.879925i	$-0.342407\pi$
$457$	198453.			0.950224			0.475112	+	0.879925i	$0.342407\pi$
$458$	47730.9	+	156592.i	0.227546	+	0.746517i
$459$		0			0
$460$	305094.	+	453968.i	1.44184	+	2.14541i
$461$	−208695.			−0.981996			−0.490998	−	0.871161i	$-0.663368\pi$
$461$	−208695.			−0.981996			−0.490998	+	0.871161i	$0.663368\pi$
$462$		0			0
$463$			26197.8i			0.122209i	0.998131	+	0.0611044i	$0.0194622\pi$
$463$			26197.8i			0.122209i	−0.998131	+	0.0611044i	$0.980538\pi$
$464$	−125865.	+	308528.i	−0.584612	+	1.43304i
$465$		0			0
$466$	−92431.7	−	303244.i	−0.425647	−	1.39643i
$467$		−	96607.8i		−	0.442974i	−0.975163	−	0.221487i	$-0.928909\pi$
$467$		−	96607.8i		−	0.442974i	0.975163	−	0.221487i	$-0.0710911\pi$
$468$		0			0
$469$	3002.97			0.0136523
$470$	345230.	−	105230.i	1.56283	−	0.476367i
$471$		0			0
$472$	224788.	−	276160.i	1.00900	−	1.23959i
$473$	180170.			0.805303
$474$		0			0
$475$		−	24258.5i		−	0.107517i
$476$	10171.6	+	15135.0i	0.0448926	+	0.0667986i
$477$		0			0
$478$	−172681.	+	52634.7i	−0.755767	+	0.230365i
$479$		−	34253.4i		−	0.149291i	−0.997210	−	0.0746453i	$-0.976218\pi$
$479$		−	34253.4i		−	0.149291i	0.997210	−	0.0746453i	$-0.0237825\pi$
$480$		0			0
$481$	−367861.			−1.58999
$482$	−88232.0	−	289466.i	−0.379780	−	1.24596i
$483$		0			0
$484$	−30755.1	+	20669.3i	−0.131288	+	0.0882337i
$485$	224280.			0.953470
$486$		0			0
$487$			69521.4i			0.293130i	0.989201	+	0.146565i	$0.0468218\pi$
$487$			69521.4i			0.293130i	−0.989201	+	0.146565i	$0.953178\pi$
$488$	108218.	+	88086.9i	0.454422	+	0.369889i
$489$		0			0
$490$	102639.	+	336732.i	0.427486	+	1.40247i
$491$			201271.i			0.834867i	0.908707	+	0.417433i	$0.137070\pi$
$491$			201271.i			0.834867i	−0.908707	+	0.417433i	$0.862930\pi$
$492$		0			0
$493$	−121544.			−0.500079
$494$	−21501.0	+	6553.71i	−0.0881057	+	0.0268555i
$495$		0			0
$496$	−162441.	−	66268.0i	−0.660286	−	0.269365i
$497$	−56243.4			−0.227698
$498$		0			0
$499$		−	54098.6i		−	0.217263i	−0.994082	−	0.108631i	$-0.965353\pi$
$499$		−	54098.6i		−	0.217263i	0.994082	−	0.108631i	$-0.0346468\pi$
$500$	143833.	−	96664.6i	0.575333	−	0.386658i
$501$		0			0
$502$	−299480.	+	91284.6i	−1.18840	+	0.362235i
$503$			239548.i			0.946795i	0.880849	+	0.473397i	$0.156973\pi$
$503$			239548.i			0.946795i	−0.880849	+	0.473397i	$0.843027\pi$
$504$		0			0
$505$	−609113.			−2.38844
$506$	113263.	+	371585.i	0.442370	+	1.45130i
$507$		0			0
$508$	−72909.8	−	108487.i	−0.282526	−	0.420388i
$509$	115476.			0.445714			0.222857	−	0.974851i	$-0.428462\pi$
$509$	115476.			0.445714			0.222857	+	0.974851i	$0.428462\pi$
$510$		0			0
$511$		−	31303.8i		−	0.119882i
$512$	−120778.	+	232663.i	−0.460733	+	0.887539i
$513$		0			0
$514$	26838.8	+	88051.1i	0.101587	+	0.333279i
$515$			434842.i			1.63952i
$516$		0			0
$517$	256326.			0.958985
$518$	82203.0	−	25056.3i	0.306357	−	0.0933807i
$519$		0			0
$520$	−405362.	−	329955.i	−1.49912	−	1.22025i
$521$	217267.			0.800420			0.400210	−	0.916424i	$-0.368937\pi$
$521$	217267.			0.800420			0.400210	+	0.916424i	$0.368937\pi$
$522$		0			0
$523$		−	39683.4i		−	0.145079i	−0.997366	−	0.0725397i	$-0.976890\pi$
$523$		−	39683.4i		−	0.145079i	0.997366	−	0.0725397i	$-0.0231104\pi$
$524$	−94098.5	−	140015.i	−0.342705	−	0.509932i
$525$		0			0
$526$	−332409.	+	101322.i	−1.20144	+	0.366210i
$527$		−	63993.1i		−	0.230416i
$528$		0			0
$529$	−485389.			−1.73452
$530$	−59863.7	−	196397.i	−0.213114	−	0.699170i
$531$		0			0
$532$	4358.26	−	2929.01i	0.0153989	−	0.0103490i
$533$	16318.2			0.0574405
$534$		0			0
$535$			174484.i			0.609603i
$536$	−9940.53	+	12212.3i	−0.0346003	+	0.0425077i
$537$		0			0
$538$	63075.4	+	206934.i	0.217919	+	0.714935i
$539$			250017.i			0.860580i
$540$		0			0
$541$	−194992.			−0.666228			−0.333114	−	0.942887i	$-0.608099\pi$
$541$	−194992.			−0.666228			−0.333114	+	0.942887i	$0.608099\pi$
$542$	183494.	−	55930.8i	0.624631	−	0.190394i
$543$		0			0
$544$	−95220.3	−	8734.98i	−0.321760	−	0.0295165i
$545$	185080.			0.623111
$546$		0			0
$547$			94267.3i			0.315055i	0.987515	+	0.157527i	$0.0503523\pi$
$547$			94267.3i			0.315055i	−0.987515	+	0.157527i	$0.949648\pi$
$548$	−42836.3	+	28788.5i	−0.142643	+	0.0958647i
$549$		0			0
$550$	383218.	−	116809.i	1.26684	−	0.386144i
$551$			34999.7i			0.115282i
$552$		0			0
$553$	63226.9			0.206753
$554$	85981.1	+	282081.i	0.280145	+	0.919083i
$555$		0			0
$556$	167734.	+	249582.i	0.542591	+	0.807355i
$557$	−563587.			−1.81656			−0.908282	−	0.418358i	$-0.862606\pi$
$557$	−563587.			−1.81656			−0.908282	+	0.418358i	$0.862606\pi$
$558$		0			0
$559$		−	339154.i		−	1.08536i
$560$	113057.	+	46121.9i	0.360515	+	0.147072i
$561$		0			0
$562$	−65455.3	−	214741.i	−0.207239	−	0.679897i
$563$			627590.i			1.97997i	0.141165	+	0.989986i	$0.454915\pi$
$563$			627590.i			1.97997i	−0.141165	+	0.989986i	$0.545085\pi$
$564$		0			0
$565$	716946.			2.24590
$566$	584516.	−	178166.i	1.82458	−	0.556150i
$567$		0			0
$568$	186179.	−	228727.i	0.577077	−	0.708959i
$569$	−77719.7			−0.240053			−0.120026	−	0.992771i	$-0.538298\pi$
$569$	−77719.7			−0.240053			−0.120026	+	0.992771i	$0.538298\pi$
$570$		0			0
$571$			318806.i			0.977811i	0.872337	+	0.488905i	$0.162604\pi$
$571$			318806.i			0.977811i	−0.872337	+	0.488905i	$0.837396\pi$
$572$	−207061.	−	308099.i	−0.632858	−	0.941669i
$573$		0			0
$574$	−3646.50	+	1111.49i	−0.0110676	+	0.00337351i
$575$			789186.i			2.38695i
$576$		0			0
$577$	40053.7			0.120307			0.0601534	−	0.998189i	$-0.480841\pi$
$577$	40053.7			0.120307			0.0601534	+	0.998189i	$0.480841\pi$
$578$	87238.1	+	286205.i	0.261126	+	0.856686i
$579$		0			0
$580$	−675480.	+	453963.i	−2.00797	+	1.34947i
$581$	−22864.7			−0.0677349
$582$		0			0
$583$		−	145821.i		−	0.429024i
$584$	127304.	+	103623.i	0.373266	+	0.303830i
$585$		0			0
$586$	45298.0	+	148611.i	0.131912	+	0.432768i
$587$		−	13734.6i		−	0.0398601i	−0.999801	−	0.0199301i	$-0.993656\pi$
$587$		−	13734.6i		−	0.0398601i	0.999801	−	0.0199301i	$-0.00634436\pi$
$588$		0			0
$589$	−18427.4			−0.0531171
$590$	831917.	−	253577.i	2.38988	−	0.728459i
$591$		0			0
$592$	−170214.	+	417240.i	−0.485681	+	1.19054i
$593$	537582.			1.52875			0.764373	−	0.644775i	$-0.223049\pi$
$593$	537582.			1.52875			0.764373	+	0.644775i	$0.223049\pi$
$594$		0			0
$595$			44538.6i			0.125806i
$596$	101593.	−	68276.4i	0.286003	−	0.192211i
$597$		0			0
$598$	699476.	−	213207.i	1.95601	−	0.596210i
$599$		−	455415.i		−	1.26927i	−0.772812	−	0.634635i	$-0.781151\pi$
$599$		−	455415.i		−	1.26927i	0.772812	−	0.634635i	$-0.218849\pi$
$600$		0			0
$601$	−237993.			−0.658892			−0.329446	−	0.944174i	$-0.606862\pi$
$601$	−237993.			−0.658892			−0.329446	+	0.944174i	$0.606862\pi$
$602$	23100.9	+	75788.0i	0.0637436	+	0.209126i
$603$		0			0
$604$	10047.5	+	14950.3i	0.0275412	+	0.0409803i
$605$	−90505.0			−0.247265
$606$		0			0
$607$		−	595989.i		−	1.61756i	−0.588109	−	0.808781i	$-0.700127\pi$
$607$		−	595989.i		−	1.61756i	0.588109	−	0.808781i	$-0.299873\pi$
$608$	−2515.32	+	27419.6i	−0.00680435	+	0.0741744i
$609$		0			0
$610$	99368.1	+	326000.i	0.267047	+	0.876109i
$611$		−	482511.i		−	1.29248i
$612$		0			0
$613$	547275.			1.45641			0.728206	−	0.685358i	$-0.240354\pi$
$613$	547275.			1.45641			0.728206	+	0.685358i	$0.240354\pi$
$614$	1750.60	−	533.599i	0.00464354	−	0.00141540i
$615$		0			0
$616$	67256.0	+	54744.8i	0.177243	+	0.144272i
$617$	518155.			1.36110			0.680549	−	0.732703i	$-0.261741\pi$
$617$	518155.			1.36110			0.680549	+	0.732703i	$0.261741\pi$
$618$		0			0
$619$			204231.i			0.533016i	0.963833	+	0.266508i	$0.0858698\pi$
$619$			204231.i			0.533016i	−0.963833	+	0.266508i	$0.914130\pi$
$620$	−239013.	−	355642.i	−0.621781	−	0.925187i
$621$		0			0
$622$	41025.8	−	12505.1i	0.106042	−	0.0323226i
$623$			14245.6i			0.0367033i
$624$		0			0
$625$	−140583.			−0.359891
$626$	−20937.0	−	68688.8i	−0.0534276	−	0.175282i
$627$		0			0
$628$	46633.1	−	31340.3i	0.118243	−	0.0794664i
$629$	−164370.			−0.415454
$630$		0			0
$631$			177036.i			0.444633i	0.974975	+	0.222317i	$0.0713618\pi$
$631$			177036.i			0.444633i	−0.974975	+	0.222317i	$0.928638\pi$
$632$	−209296.	+	257127.i	−0.523994	+	0.643745i
$633$		0			0
$634$	71575.8	+	234821.i	0.178069	+	0.584196i
$635$		−	319252.i		−	0.791746i
$636$		0			0
$637$	470635.			1.15986
$638$	−552899.	+	168529.i	−1.35833	+	0.414031i
$639$		0			0
$640$	−561812.	+	307101.i	−1.37161	+	0.749758i
$641$	218888.			0.532728			0.266364	−	0.963873i	$-0.414178\pi$
$641$	218888.			0.532728			0.266364	+	0.963873i	$0.414178\pi$
$642$		0			0
$643$		−	345184.i		−	0.834889i	−0.908702	−	0.417445i	$-0.862926\pi$
$643$		−	345184.i		−	0.834889i	0.908702	−	0.417445i	$-0.137074\pi$
$644$	−141784.	+	95287.5i	−0.341866	+	0.229755i
$645$		0			0
$646$	−9607.23	+	2928.38i	−0.0230215	+	0.00701717i
$647$		−	398251.i		−	0.951366i	−0.879617	−	0.475683i	$-0.842201\pi$
$647$		−	398251.i		−	0.951366i	0.879617	−	0.475683i	$-0.157799\pi$
$648$		0			0
$649$	617681.			1.46648
$650$	−219882.	−	721374.i	−0.520431	−	1.70739i
$651$		0			0
$652$	374373.	+	557053.i	0.880663	+	1.31039i
$653$	−342288.			−0.802722			−0.401361	−	0.915920i	$-0.631463\pi$
$653$	−342288.			−0.802722			−0.401361	+	0.915920i	$0.631463\pi$
$654$		0			0
$655$		−	412031.i		−	0.960390i
$656$	7550.63	−	18508.7i	0.0175459	−	0.0430098i
$657$		0			0
$658$	32865.5	+	107823.i	0.0759082	+	0.249035i
$659$		−	522927.i		−	1.20412i	−0.798450	−	0.602061i	$-0.794346\pi$
$659$		−	522927.i		−	1.20412i	0.798450	−	0.602061i	$-0.205654\pi$
$660$		0			0
$661$	308588.			0.706279			0.353140	−	0.935571i	$-0.385114\pi$
$661$	308588.			0.706279			0.353140	+	0.935571i	$0.385114\pi$
$662$	−711286.	+	216807.i	−1.62304	+	0.494717i
$663$		0			0
$664$	75687.4	−	92984.7i	0.171667	−	0.210899i
$665$	12825.3			0.0290018
$666$		0			0
$667$		−	1.13862e6i		−	2.55934i
$668$	60807.7	+	90479.6i	0.136272	+	0.202767i
$669$		0			0
$670$	−36788.8	+	11213.6i	−0.0819533	+	0.0249802i
$671$			242048.i			0.537597i
$672$		0			0
$673$	−248520.			−0.548695			−0.274348	−	0.961631i	$-0.588462\pi$
$673$	−248520.			−0.548695			−0.274348	+	0.961631i	$0.588462\pi$
$674$	172604.	+	566269.i	0.379955	+	1.24653i
$675$		0			0
$676$	−200689.	+	134875.i	−0.439168	+	0.295147i
$677$	269522.			0.588054			0.294027	−	0.955797i	$-0.405004\pi$
$677$	269522.			0.588054			0.294027	+	0.955797i	$0.405004\pi$
$678$		0			0
$679$			70047.6i			0.151934i
$680$	−181127.	−	147433.i	−0.391710	−	0.318843i
$681$		0			0
$682$	−88730.9	−	291103.i	−0.190768	−	0.625860i
$683$		−	124482.i		−	0.266848i	−0.991059	−	0.133424i	$-0.957403\pi$
$683$		−	124482.i		−	0.266848i	0.991059	−	0.133424i	$-0.0425972\pi$
$684$		0			0
$685$	−126057.			−0.268649
$686$	−217295.	+	66233.6i	−0.461744	+	0.140744i
$687$		0			0
$688$	−384680.	−	156931.i	−0.812685	−	0.331536i
$689$	−274495.			−0.578223
$690$		0			0
$691$		−	890738.i		−	1.86549i	−0.360531	−	0.932747i	$-0.617404\pi$
$691$		−	890738.i		−	1.86549i	0.360531	−	0.932747i	$-0.382596\pi$
$692$	−209132.	+	140549.i	−0.436726	+	0.293506i
$693$		0			0
$694$	−554723.	+	169085.i	−1.15175	+	0.351064i
$695$			734462.i			1.52055i
$696$		0			0
$697$	7291.43			0.0150088
$698$	208705.	+	684705.i	0.428372	+	1.40538i
$699$		0			0
$700$	98270.6	+	146223.i	0.200552	+	0.298414i
$701$	−170934.			−0.347851			−0.173925	−	0.984759i	$-0.555645\pi$
$701$	−170934.			−0.347851			−0.173925	+	0.984759i	$0.555645\pi$
$702$		0			0
$703$			47332.1i			0.0957734i
$704$	−445266.	+	92294.4i	−0.898409	+	0.186222i
$705$		0			0
$706$	−30784.0	−	100994.i	−0.0617611	−	0.202622i
$707$		−	190239.i		−	0.380594i
$708$		0			0
$709$	−701926.			−1.39637			−0.698183	−	0.715920i	$-0.746008\pi$
$709$	−701926.			−1.39637			−0.698183	+	0.715920i	$0.746008\pi$
$710$	689028.	−	210022.i	1.36685	−	0.416628i
$711$		0			0
$712$	−57933.2	−	47156.3i	−0.114279	−	0.0930206i
$713$	599487.			1.17924
$714$		0			0
$715$		−	906662.i		−	1.77351i
$716$	200785.	+	298761.i	0.391657	+	0.582770i
$717$		0			0
$718$	693934.	−	211518.i	1.34608	−	0.410297i
$719$		−	768366.i		−	1.48631i	−0.669117	−	0.743157i	$-0.733328\pi$
$719$		−	768366.i		−	1.48631i	0.669117	−	0.743157i	$-0.266672\pi$
$720$		0			0
$721$	−135811.			−0.261255
$722$	−151145.	−	495868.i	−0.289948	−	0.951244i
$723$		0			0
$724$	290124.	−	194981.i	0.553486	−	0.371975i
$725$	−1.17427e6			−2.23404
$726$		0			0
$727$		−	255758.i		−	0.483905i	−0.970288	−	0.241952i	$-0.922212\pi$
$727$		−	255758.i		−	0.483905i	0.970288	−	0.241952i	$-0.0777878\pi$
$728$	103052.	−	126604.i	0.194444	−	0.238882i
$729$		0			0
$730$	116894.	+	383497.i	0.219354	+	0.719642i
$731$		−	151543.i		−	0.283597i
$732$		0			0
$733$	369658.			0.688006			0.344003	−	0.938968i	$-0.388217\pi$
$733$	369658.			0.688006			0.344003	+	0.938968i	$0.388217\pi$
$734$	799678.	−	243750.i	1.48430	−	0.452431i
$735$		0			0
$736$	81829.3	−	892023.i	0.151061	−	1.64672i
$737$	−27314.9			−0.0502881
$738$		0			0
$739$			1.03557e6i			1.89623i	0.317932	+	0.948114i	$0.397012\pi$
$739$			1.03557e6i			1.89623i	−0.317932	+	0.948114i	$0.602988\pi$
$740$	−913490.	+	613920.i	−1.66817	+	1.12111i
$741$		0			0
$742$	61339.1	−	18696.8i	0.111411	−	0.0339593i
$743$		−	561187.i		−	1.01655i	−0.861194	−	0.508276i	$-0.830283\pi$
$743$		−	561187.i		−	1.01655i	0.861194	−	0.508276i	$-0.169717\pi$
$744$		0			0
$745$	298963.			0.538648
$746$	89331.1	+	293072.i	0.160518	+	0.526618i
$747$		0			0
$748$	−92520.5	−	137667.i	−0.165362	−	0.246052i
$749$	−54495.1			−0.0971391
$750$		0			0
$751$			190408.i			0.337603i	0.985650	+	0.168801i	$0.0539896\pi$
$751$			190408.i			0.337603i	−0.985650	+	0.168801i	$0.946010\pi$
$752$	−547281.	−	223264.i	−0.967775	−	0.394805i
$753$		0			0
$754$	317241.	+	1.04078e6i	0.558016	+	1.83070i
$755$			43995.1i			0.0771810i
$756$		0			0
$757$	523077.			0.912797			0.456398	−	0.889776i	$-0.349139\pi$
$757$	523077.			0.912797			0.456398	+	0.889776i	$0.349139\pi$
$758$	888130.	−	270711.i	1.54575	−	0.471159i
$759$		0			0
$760$	−42454.8	+	52157.3i	−0.0735021	+	0.0903000i
$761$	−160897.			−0.277830			−0.138915	−	0.990304i	$-0.544362\pi$
$761$	−160897.			−0.277830			−0.138915	+	0.990304i	$0.544362\pi$
$762$		0			0
$763$			57804.5i			0.0992916i
$764$	−166763.	−	248137.i	−0.285702	−	0.425114i
$765$		0			0
$766$	−327467.	+	99815.1i	−0.558097	+	0.170113i
$767$		−	1.16273e6i		−	1.97646i
$768$		0			0
$769$	−595609.			−1.00718			−0.503591	−	0.863942i	$-0.667988\pi$
$769$	−595609.			−1.00718			−0.503591	+	0.863942i	$0.667988\pi$
$770$	61755.9	+	202605.i	0.104159	+	0.341718i
$771$		0			0
$772$	−612184.	+	411424.i	−1.02718	+	0.690328i
$773$	−583394.			−0.976345			−0.488172	−	0.872747i	$-0.662336\pi$
$773$	−583394.			−0.976345			−0.488172	+	0.872747i	$0.662336\pi$
$774$		0			0
$775$		−	618255.i		−	1.02935i
$776$	−284866.	−	231874.i	−0.473060	−	0.385060i
$777$		0			0
$778$	−141979.	−	465796.i	−0.234566	−	0.769549i
$779$		−	2099.64i		−	0.00345995i
$780$		0			0
$781$	511588.			0.838723
$782$	312545.	−	95266.9i	0.511092	−	0.155786i
$783$		0			0
$784$	217768.	−	533810.i	0.354293	−	0.868469i
$785$	137230.			0.222695
$786$		0			0
$787$		−	174412.i		−	0.281597i	−0.990038	−	0.140798i	$-0.955033\pi$
$787$		−	174412.i		−	0.281597i	0.990038	−	0.140798i	$-0.0449669\pi$
$788$	−211607.	+	142212.i	−0.340782	+	0.229026i
$789$		0			0
$790$	−774581.	+	236100.i	−1.24112	+	0.378305i
$791$			223918.i			0.357879i
$792$		0			0
$793$	455635.			0.724553
$794$	83610.4	+	274303.i	0.132623	+	0.435101i
$795$		0			0
$796$	658054.	+	979159.i	1.03857	+	1.54535i
$797$	847152.			1.33366			0.666829	−	0.745211i	$-0.267651\pi$
$797$	847152.			1.33366			0.666829	+	0.745211i	$0.267651\pi$
$798$		0			0
$799$		−	215599.i		−	0.337718i
$800$	−919949.	−	84391.1i	−1.43742	−	0.131861i
$801$		0			0
$802$	100626.	+	330127.i	0.156445	+	0.513254i
$803$			284739.i			0.441586i
$804$		0			0
$805$	−417237.			−0.643860
$806$	−547975.	+	167028.i	−0.843512	+	0.257111i
$807$		0			0
$808$	773654.	+	629737.i	1.18502	+	0.964576i
$809$	43118.8			0.0658824			0.0329412	−	0.999457i	$-0.489513\pi$
$809$	43118.8			0.0658824			0.0329412	+	0.999457i	$0.489513\pi$
$810$		0			0
$811$		−	372984.i		−	0.567085i	−0.958960	−	0.283543i	$-0.908490\pi$
$811$		−	372984.i		−	0.567085i	0.958960	−	0.283543i	$-0.0915097\pi$
$812$	−141783.	−	210967.i	−0.215036	−	0.319966i
$813$		0			0
$814$	−747716.	+	227911.i	−1.12847	+	0.343967i
$815$			1.63928e6i			2.46795i
$816$		0			0
$817$	−43638.4			−0.0653769
$818$	−268778.	−	881791.i	−0.401687	−	1.31783i
$819$		0			0
$820$	40522.2	−	27233.3i	0.0602650	−	0.0405017i
$821$	−1.33004e6			−1.97324			−0.986620	−	0.163037i	$-0.947871\pi$
$821$	−1.33004e6			−1.97324			−0.986620	+	0.163037i	$0.947871\pi$
$822$		0			0
$823$		−	734655.i		−	1.08464i	−0.840173	−	0.542318i	$-0.817547\pi$
$823$		−	734655.i		−	1.08464i	0.840173	−	0.542318i	$-0.182453\pi$
$824$	449566.	−	552308.i	0.662123	−	0.813442i
$825$		0			0
$826$	79197.6	+	259826.i	0.116079	+	0.380823i
$827$			1.27112e6i			1.85856i	0.369375	+	0.929281i	$0.379572\pi$
$827$			1.27112e6i			1.85856i	−0.369375	+	0.929281i	$0.620428\pi$
$828$		0			0
$829$	−427267.			−0.621714			−0.310857	−	0.950457i	$-0.600616\pi$
$829$	−427267.			−0.621714			−0.310857	+	0.950457i	$0.600616\pi$
$830$	280111.	−	85380.6i	0.406606	−	0.123938i
$831$		0			0
$832$	173736.	+	838174.i	0.250983	+	1.21084i
$833$	210293.			0.303064
$834$		0			0
$835$			266260.i			0.381885i
$836$	−39642.6	+	26642.2i	−0.0567217	+	0.0381204i
$837$		0			0
$838$	−212831.	+	64873.0i	−0.303073	+	0.0923796i
$839$			694916.i			0.987207i	0.869687	+	0.493604i	$0.164321\pi$
$839$			694916.i			0.987207i	−0.869687	+	0.493604i	$0.835679\pi$
$840$		0			0
$841$	986927.			1.39538
$842$	−164410.	−	539385.i	−0.231902	−	0.760808i
$843$		0			0
$844$	159024.	+	236622.i	0.223243	+	0.332178i
$845$	−590581.			−0.827115
$846$		0			0
$847$		−	28266.7i		−	0.0394011i
$848$	−127012.	+	311341.i	−0.176625	+	0.432957i
$849$		0			0
$850$	−98249.3	−	322330.i	−0.135985	−	0.446131i
$851$		−	1.53982e6i		−	2.12624i
$852$		0			0
$853$	144629.			0.198773			0.0993867	−	0.995049i	$-0.468312\pi$
$853$	144629.			0.198773			0.0993867	+	0.995049i	$0.468312\pi$
$854$	−101817.	+	31034.8i	−0.139606	+	0.0425534i
$855$		0			0
$856$	180392.	−	221618.i	0.246189	−	0.302452i
$857$	−636010.			−0.865968			−0.432984	−	0.901402i	$-0.642539\pi$
$857$	−636010.			−0.865968			−0.432984	+	0.901402i	$0.642539\pi$
$858$		0			0
$859$			1.34994e6i			1.82948i	0.404041	+	0.914741i	$0.367605\pi$
$859$			1.34994e6i			1.82948i	−0.404041	+	0.914741i	$0.632395\pi$
$860$	−566011.	−	842203.i	−0.765293	−	1.13873i
$861$		0			0
$862$	−730862.	+	222774.i	−0.983605	+	0.299812i
$863$		−	916363.i		−	1.23040i	−0.788372	−	0.615199i	$-0.789076\pi$
$863$		−	916363.i		−	1.23040i	0.788372	−	0.615199i	$-0.210924\pi$
$864$		0			0
$865$	−615427.			−0.822515
$866$	−56264.6	−	184589.i	−0.0750238	−	0.246133i
$867$		0			0
$868$	111075.	−	74649.0i	0.147427	−	0.0990797i
$869$	−575110.			−0.761573
$870$		0			0
$871$			51418.0i			0.0677764i
$872$	−235076.	−	191346.i	−0.309154	−	0.251644i
$873$		0			0
$874$	−27433.0	−	90000.5i	−0.0359129	−	0.117821i
$875$			132196.i			0.172664i
$876$		0			0
$877$	−546256.			−0.710226			−0.355113	−	0.934823i	$-0.615558\pi$
$877$	−546256.			−0.710226			−0.355113	+	0.934823i	$0.615558\pi$
$878$	1.00327e6	−	305807.i	1.30145	−	0.396696i
$879$		0			0
$880$	−1.02837e6	−	419524.i	−1.32795	−	0.541740i
$881$	446863.			0.575735			0.287867	−	0.957670i	$-0.407054\pi$
$881$	446863.			0.575735			0.287867	+	0.957670i	$0.407054\pi$
$882$		0			0
$883$			140436.i			0.180119i	0.995936	+	0.0900593i	$0.0287056\pi$
$883$			140436.i			0.180119i	−0.995936	+	0.0900593i	$0.971294\pi$
$884$	−259146.	+	174162.i	−0.331620	+	0.222868i
$885$		0			0
$886$	−348119.	+	106110.i	−0.443466	+	0.135173i
$887$			354688.i			0.450816i	0.974264	+	0.225408i	$0.0723715\pi$
$887$			354688.i			0.450816i	−0.974264	+	0.225408i	$0.927628\pi$
$888$		0			0
$889$	99709.4			0.126163
$890$	−53195.5	−	174520.i	−0.0671575	−	0.220326i
$891$		0			0
$892$	601358.	+	894798.i	0.755794	+	1.12459i
$893$	−62084.0			−0.0778532
$894$		0			0
$895$			879182.i			1.09757i
$896$	−95914.4	−	175466.i	−0.119472	−	0.218564i
$897$		0			0
$898$	−330460.	−	1.08415e6i	−0.409795	−	1.34443i
$899$			892005.i			1.10369i
$900$		0			0
$901$	−122652.			−0.151086
$902$	33168.5	−	10110.1i	0.0407674	−	0.0124263i
$903$		0			0
$904$	−910617.	−	741222.i	−1.11429	−	0.907008i
$905$	853766.			1.04242
$906$		0			0
$907$			1.47749e6i			1.79602i	0.439978	+	0.898008i	$0.354986\pi$
$907$			1.47749e6i			1.79602i	−0.439978	+	0.898008i	$0.645014\pi$
$908$	560422.	+	833887.i	0.679741	+	1.01143i
$909$		0			0
$910$	381386.	−	116250.i	0.460555	−	0.140382i
$911$			48152.2i			0.0580202i	0.999579	+	0.0290101i	$0.00923549\pi$
$911$			48152.2i			0.0580202i	−0.999579	+	0.0290101i	$0.990765\pi$
$912$		0			0
$913$	207976.			0.249501
$914$	−231449.	−	759323.i	−0.277053	−	0.908938i
$915$		0			0
$916$	543487.	−	365256.i	0.647737	−	0.435318i
$917$	128687.			0.153036
$918$		0			0
$919$		−	346372.i		−	0.410120i	−0.978749	−	0.205060i	$-0.934261\pi$
$919$		−	346372.i		−	0.410120i	0.978749	−	0.205060i	$-0.0657390\pi$
$920$	1.38115e6	−	1.69680e6i	1.63180	−	2.00472i
$921$		0			0
$922$	243393.	+	798508.i	0.286317	+	0.939329i
$923$		−	963021.i		−	1.13040i
$924$		0			0
$925$	−1.58803e6			−1.85599
$926$	100238.	−	30553.5i	0.116899	−	0.0356319i
$927$		0			0
$928$	1.32728e6	+	121758.i	1.54123	+	0.141384i
$929$	870783.			1.00897			0.504485	−	0.863420i	$-0.331682\pi$
$929$	870783.			1.00897			0.504485	+	0.863420i	$0.331682\pi$
$930$		0			0
$931$		−	60555.8i		−	0.0698645i
$932$	−1.05247e6	+	707325.i	−1.21166	+	0.814305i
$933$		0			0
$934$	−369641.	+	112670.i	−0.423727	+	0.129156i
$935$		−	405122.i		−	0.463407i
$936$		0			0
$937$	−1.00280e6			−1.14219			−0.571094	−	0.820885i	$-0.693481\pi$
$937$	−1.00280e6			−1.14219			−0.571094	+	0.820885i	$0.693481\pi$
$938$	−3502.26	−	11490.0i	−0.00398054	−	0.0130591i
$939$		0			0
$940$	−805259.	−	1.19820e6i	−0.911339	−	1.35604i
$941$	−1.26190e6			−1.42510			−0.712550	−	0.701622i	$-0.752460\pi$
$941$	−1.26190e6			−1.42510			−0.712550	+	0.701622i	$0.752460\pi$
$942$		0			0
$943$			68306.1i			0.0768132i
$944$	−1.31881e6	−	538010.i	−1.47992	−	0.603735i
$945$		0			0
$946$	−210125.	−	689366.i	−0.234799	−	0.770314i
$947$		−	187145.i		−	0.208678i	−0.994542	−	0.104339i	$-0.966727\pi$
$947$		−	187145.i		−	0.208678i	0.994542	−	0.104339i	$-0.0332728\pi$
$948$		0			0
$949$	535996.			0.595153
$950$	−92818.1	+	28291.8i	−0.102845	+	0.0313483i
$951$		0			0
$952$	46046.6	−	56569.9i	0.0508070	−	0.0624183i
$953$	194925.			0.214626			0.107313	−	0.994225i	$-0.465775\pi$
$953$	194925.			0.214626			0.107313	+	0.994225i	$0.465775\pi$
$954$		0			0
$955$		−	730210.i		−	0.800647i
$956$	402782.	+	599325.i	0.440712	+	0.655763i
$957$		0			0
$958$	−131060.	+	39948.5i	−0.142804	+	0.0435281i
$959$		−	39370.4i		−	0.0428088i
$960$		0			0
$961$	453878.			0.491465
$962$	429023.	+	1.40751e6i	0.463586	+	1.52090i
$963$		0			0
$964$	−1.00465e6	+	675187.i	−1.08109	+	0.726557i
$965$	−1.80151e6			−1.93456
$966$		0			0
$967$		−	432253.i		−	0.462259i	−0.972923	−	0.231129i	$-0.925758\pi$
$967$		−	432253.i		−	0.462259i	0.972923	−	0.231129i	$-0.0742421\pi$
$968$	114953.	+	93569.5i	0.122679	+	0.0998581i
$969$		0			0
$970$	−261570.	−	858141.i	−0.278000	−	0.912043i
$971$		−	756598.i		−	0.802467i	−0.915976	−	0.401233i	$-0.868582\pi$
$971$		−	756598.i		−	0.802467i	0.915976	−	0.401233i	$-0.131418\pi$
$972$		0			0
$973$	−229389.			−0.242296
$974$	266003.	−	81080.4i	0.280394	−	0.0854669i
$975$		0			0
$976$	210828.	−	516796.i	0.221324	−	0.542525i
$977$	1.80719e6			1.89328			0.946638	−	0.322299i	$-0.104456\pi$
$977$	1.80719e6			1.89328			0.946638	+	0.322299i	$0.104456\pi$
$978$		0			0
$979$		−	129578.i		−	0.135196i
$980$	1.16870e6	−	785438.i	1.21689	−	0.817824i
$981$		0			0
$982$	770102.	−	234735.i	0.798593	−	0.243419i
$983$			209985.i			0.217311i	0.994079	+	0.108655i	$0.0346545\pi$
$983$			209985.i			0.217311i	−0.994079	+	0.108655i	$0.965346\pi$
$984$		0			0
$985$	−622709.			−0.641819
$986$	141752.	+	465051.i	0.145806	+	0.478351i
$987$		0			0
$988$	50151.6	+	74623.7i	0.0513773	+	0.0764475i
$989$	1.41966e6			1.45141
$990$		0			0
$991$			1.66713e6i			1.69755i	0.528754	+	0.848775i	$0.322659\pi$
$991$			1.66713e6i			1.69755i	−0.528754	+	0.848775i	$0.677341\pi$
$992$	−64105.7	+	698818.i	−0.0651439	+	0.710135i
$993$		0			0
$994$	65594.7	+	215199.i	0.0663889	+	0.217804i
$995$			2.88144e6i			2.91047i
$996$		0			0
$997$	1.34283e6			1.35093			0.675464	−	0.737393i	$-0.263943\pi$
$997$	1.34283e6			1.35093			0.675464	+	0.737393i	$0.263943\pi$
$998$	−206992.	+	63093.3i	−0.207823	+	0.0633464i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.f.163.9		22
3.2	odd	2		324.5.d.e.163.14		22
4.3	odd	2	inner	324.5.d.f.163.10		22
9.2	odd	6		108.5.f.a.91.17		44
9.4	even	3		36.5.f.a.7.21	yes	44
9.5	odd	6		108.5.f.a.19.2		44
9.7	even	3		36.5.f.a.31.6	yes	44
12.11	even	2		324.5.d.e.163.13		22
36.7	odd	6		36.5.f.a.31.21	yes	44
36.11	even	6		108.5.f.a.91.2		44
36.23	even	6		108.5.f.a.19.17		44
36.31	odd	6		36.5.f.a.7.6	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.6	✓	44	36.31	odd	6
36.5.f.a.7.21	yes	44	9.4	even	3
36.5.f.a.31.6	yes	44	9.7	even	3
36.5.f.a.31.21	yes	44	36.7	odd	6
108.5.f.a.19.2		44	9.5	odd	6
108.5.f.a.19.17		44	36.23	even	6
108.5.f.a.91.2		44	36.11	even	6
108.5.f.a.91.17		44	9.2	odd	6
324.5.d.e.163.13		22	12.11	even	2
324.5.d.e.163.14		22	3.2	odd	2
324.5.d.f.163.9		22	1.1	even	1	trivial
324.5.d.f.163.10		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)

\(f(q)\)	\(=\)	\(q+(-1.16626 - 3.82620i) q^{2} +(-13.2797 + 8.92473i) q^{4} -39.0789 q^{5} -12.2052i q^{7} +(49.6354 + 40.4021i) q^{8} +O(q^{10})\)	\(q+(-1.16626 - 3.82620i) q^{2} +(-13.2797 + 8.92473i) q^{4} -39.0789 q^{5} -12.2052i q^{7} +(49.6354 + 40.4021i) q^{8} +(45.5763 + 149.524i) q^{10} +111.018i q^{11} +208.982 q^{13} +(-46.6996 + 14.2345i) q^{14} +(96.6986 - 237.035i) q^{16} +93.3790 q^{17} -26.8894i q^{19} +(518.954 - 348.768i) q^{20} +(424.778 - 129.477i) q^{22} +874.774i q^{23} +902.160 q^{25} +(-243.728 - 799.608i) q^{26} +(108.928 + 162.081i) q^{28} -1301.62 q^{29} -685.305i q^{31} +(-1019.72 - 93.5434i) q^{32} +(-108.905 - 357.287i) q^{34} +476.966i q^{35} -1760.25 q^{37} +(-102.884 + 31.3601i) q^{38} +(-1939.70 - 1578.87i) q^{40} +78.0843 q^{41} -1622.88i q^{43} +(-990.807 - 1474.28i) q^{44} +(3347.06 - 1020.22i) q^{46} -2308.86i q^{47} +2252.03 q^{49} +(-1052.16 - 3451.85i) q^{50} +(-2775.21 + 1865.11i) q^{52} -1313.48 q^{53} -4338.47i q^{55} +(493.116 - 605.810i) q^{56} +(1518.03 + 4980.25i) q^{58} -5563.78i q^{59} +2180.26 q^{61} +(-2622.12 + 799.247i) q^{62} +(831.345 + 4010.75i) q^{64} -8166.79 q^{65} +246.040i q^{67} +(-1240.04 + 833.382i) q^{68} +(1824.97 - 556.268i) q^{70} -4608.15i q^{71} +2564.79 q^{73} +(2052.92 + 6735.08i) q^{74} +(239.980 + 357.082i) q^{76} +1355.00 q^{77} +5180.32i q^{79} +(-3778.87 + 9263.05i) q^{80} +(-91.0669 - 298.766i) q^{82} -1873.35i q^{83} -3649.15 q^{85} +(-6209.48 + 1892.71i) q^{86} +(-4485.37 + 5510.43i) q^{88} -1167.17 q^{89} -2550.67i q^{91} +(-7807.12 - 11616.7i) q^{92} +(-8834.19 + 2692.75i) q^{94} +1050.81i q^{95} -5739.16 q^{97} +(-2626.47 - 8616.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} + q^{4} + 2 q^{5} + 61 q^{8}+O(q^{10}) \) 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

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