LMFDB - Embedded newform 324.5.d.e.163.21

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			163.21
Character	$\chi$	$=$	324.163
Dual form			324.5.d.e.163.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.92469 - 0.772521i) q^{2} +(14.8064 - 6.06382i) q^{4} -21.1512 q^{5} -44.6184i q^{7} +(53.4262 - 35.2369i) q^{8} +O(q^{10})$	\(q+(3.92469 - 0.772521i) q^{2} +(14.8064 - 6.06382i) q^{4} -21.1512 q^{5} -44.6184i q^{7} +(53.4262 - 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} -67.7698i q^{11} -29.1038 q^{13} +(-34.4687 - 175.114i) q^{14} +(182.460 - 179.567i) q^{16} -402.841 q^{17} +644.741i q^{19} +(-313.173 + 128.257i) q^{20} +(-52.3536 - 265.976i) q^{22} -387.433i q^{23} -177.628 q^{25} +(-114.223 + 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} -724.420 q^{29} -1259.67i q^{31} +(577.381 - 845.699i) q^{32} +(-1581.03 + 311.203i) q^{34} +943.733i q^{35} -1402.04 q^{37} +(498.076 + 2530.41i) q^{38} +(-1130.03 + 745.302i) q^{40} -1548.33 q^{41} -1871.75i q^{43} +(-410.944 - 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} -4169.19i q^{47} +410.195 q^{49} +(-697.134 + 137.221i) q^{50} +(-430.923 + 176.480i) q^{52} -906.566 q^{53} +1433.41i q^{55} +(-1572.21 - 2383.79i) q^{56} +(-2843.13 + 559.630i) q^{58} +4522.33i q^{59} +2628.44 q^{61} +(-973.119 - 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} +615.579 q^{65} -67.7999i q^{67} +(-5964.64 + 2442.76i) q^{68} +(729.053 + 3703.86i) q^{70} -1315.04i q^{71} +9470.72 q^{73} +(-5502.56 + 1083.10i) q^{74} +(3909.59 + 9546.31i) q^{76} -3023.78 q^{77} +4369.33i q^{79} +(-3859.25 + 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} -762.015i q^{83} +8520.57 q^{85} +(-1445.97 - 7346.04i) q^{86} +(-2388.00 - 3620.69i) q^{88} -8083.40 q^{89} +1298.56i q^{91} +(-2349.32 - 5736.50i) q^{92} +(-3220.79 - 16362.8i) q^{94} -13637.0i q^{95} +6665.42 q^{97} +(1609.89 - 316.884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) $ 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8	$ 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8} + 14 q^{10} + 2 q^{13} + 252 q^{14} + q^{16} + 28 q^{17} - 140 q^{20} + 33 q^{22} + 1752 q^{25} - 548 q^{26} - 258 q^{28} + 526 q^{29} - 121 q^{32} - 385 q^{34} - 4 q^{37} + 1395 q^{38} + 2276 q^{40} - 2762 q^{41} - 3357 q^{44} + 1788 q^{46} - 3428 q^{49} + 6375 q^{50} - 1438 q^{52} + 5044 q^{53} - 7506 q^{56} + 4064 q^{58} + 2 q^{61} + 9162 q^{62} + 4513 q^{64} - 2014 q^{65} - 11405 q^{68} - 3666 q^{70} - 1708 q^{73} + 14620 q^{74} - 1581 q^{76} - 3942 q^{77} - 22760 q^{80} - 4243 q^{82} + 1252 q^{85} + 22113 q^{86} - 1995 q^{88} - 6524 q^{89} - 30294 q^{92} - 7524 q^{94} - 5638 q^{97} + 46469 q^{98}+O(q^{100}) $ 22 * q - q^2 + q^4 - 2 * q^5 - 61 * q^8 + 14 * q^10 + 2 * q^13 + 252 * q^14 + q^16 + 28 * q^17 - 140 * q^20 + 33 * q^22 + 1752 * q^25 - 548 * q^26 - 258 * q^28 + 526 * q^29 - 121 * q^32 - 385 * q^34 - 4 * q^37 + 1395 * q^38 + 2276 * q^40 - 2762 * q^41 - 3357 * q^44 + 1788 * q^46 - 3428 * q^49 + 6375 * q^50 - 1438 * q^52 + 5044 * q^53 - 7506 * q^56 + 4064 * q^58 + 2 * q^61 + 9162 * q^62 + 4513 * q^64 - 2014 * q^65 - 11405 * q^68 - 3666 * q^70 - 1708 * q^73 + 14620 * q^74 - 1581 * q^76 - 3942 * q^77 - 22760 * q^80 - 4243 * q^82 + 1252 * q^85 + 22113 * q^86 - 1995 * q^88 - 6524 * q^89 - 30294 * q^92 - 7524 * q^94 - 5638 * q^97 + 46469 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3.92469	−	0.772521i	0.981173	−	0.193130i
$2$	3.92469	−	0.772521i	0.981173	−	0.193130i
$3$		0			0
$3$		0			0
$4$	14.8064	−	6.06382i	0.925401	−	0.378988i
$5$	−21.1512			−0.846047			−0.423024	−	0.906119i	$-0.639031\pi$
$5$	−21.1512			−0.846047			−0.423024	+	0.906119i	$0.639031\pi$
$6$		0			0
$7$		−	44.6184i		−	0.910580i	−0.890343	−	0.455290i	$-0.849536\pi$
$7$		−	44.6184i		−	0.910580i	0.890343	−	0.455290i	$-0.150464\pi$
$8$	53.4262	−	35.2369i	0.834785	−	0.550576i
$9$		0			0
$10$	−83.0119	+	16.3397i	−0.830119	+	0.163397i
$11$		−	67.7698i		−	0.560081i	−0.959988	−	0.280041i	$-0.909652\pi$
$11$		−	67.7698i		−	0.560081i	0.959988	−	0.280041i	$-0.0903480\pi$
$12$		0			0
$13$	−29.1038			−0.172212			−0.0861058	−	0.996286i	$-0.527442\pi$
$13$	−29.1038			−0.172212			−0.0861058	+	0.996286i	$0.527442\pi$
$14$	−34.4687	−	175.114i	−0.175861	−	0.893437i
$15$		0			0
$16$	182.460	−	179.567i	0.712735	−	0.701433i
$17$	−402.841			−1.39391			−0.696957	−	0.717113i	$-0.745463\pi$
$17$	−402.841			−1.39391			−0.696957	+	0.717113i	$0.745463\pi$
$18$		0			0
$19$			644.741i			1.78599i	0.450070	+	0.892993i	$0.351399\pi$
$19$			644.741i			1.78599i	−0.450070	+	0.892993i	$0.648601\pi$
$20$	−313.173	+	128.257i	−0.782933	+	0.320642i
$21$		0			0
$22$	−52.3536	−	265.976i	−0.108169	−	0.549537i
$23$		−	387.433i		−	0.732388i	−0.930539	−	0.366194i	$-0.880661\pi$
$23$		−	387.433i		−	0.732388i	0.930539	−	0.366194i	$-0.119339\pi$
$24$		0			0
$25$	−177.628			−0.284204
$26$	−114.223	+	22.4833i	−0.168969	+	0.0332593i
$27$		0			0
$28$	−270.558	−	660.639i	−0.345099	−	0.842652i
$29$	−724.420			−0.861380			−0.430690	−	0.902500i	$-0.641730\pi$
$29$	−724.420			−0.861380			−0.430690	+	0.902500i	$0.641730\pi$
$30$		0			0
$31$		−	1259.67i		−	1.31079i	−0.755288	−	0.655393i	$-0.772503\pi$
$31$		−	1259.67i		−	1.31079i	0.755288	−	0.655393i	$-0.227497\pi$
$32$	577.381	−	845.699i	0.563849	−	0.825878i
$33$		0			0
$34$	−1581.03	+	311.203i	−1.36767	+	0.269207i
$35$			943.733i			0.770394i
$36$		0			0
$37$	−1402.04			−1.02413			−0.512066	−	0.858946i	$-0.671120\pi$
$37$	−1402.04			−1.02413			−0.512066	+	0.858946i	$0.671120\pi$
$38$	498.076	+	2530.41i	0.344928	+	1.75236i
$39$		0			0
$40$	−1130.03	+	745.302i	−0.706267	+	0.465814i
$41$	−1548.33			−0.921078			−0.460539	−	0.887640i	$-0.652344\pi$
$41$	−1548.33			−0.921078			−0.460539	+	0.887640i	$0.652344\pi$
$42$		0			0
$43$		−	1871.75i		−	1.01230i	−0.862444	−	0.506152i	$-0.831068\pi$
$43$		−	1871.75i		−	1.01230i	0.862444	−	0.506152i	$-0.168932\pi$
$44$	−410.944	−	1003.43i	−0.212264	−	0.518300i
$45$		0			0
$46$	−299.300	−	1520.56i	−0.141446	−	0.718599i
$47$		−	4169.19i		−	1.88737i	−0.330851	−	0.943683i	$-0.607336\pi$
$47$		−	4169.19i		−	1.88737i	0.330851	−	0.943683i	$-0.392664\pi$
$48$		0			0
$49$	410.195			0.170843
$50$	−697.134	+	137.221i	−0.278854	+	0.0548884i
$51$		0			0
$52$	−430.923	+	176.480i	−0.159365	+	0.0652662i
$53$	−906.566			−0.322736			−0.161368	−	0.986894i	$-0.551591\pi$
$53$	−906.566			−0.322736			−0.161368	+	0.986894i	$0.551591\pi$
$54$		0			0
$55$			1433.41i			0.473855i
$56$	−1572.21	−	2383.79i	−0.501344	−	0.760139i
$57$		0			0
$58$	−2843.13	+	559.630i	−0.845162	+	0.166358i
$59$			4522.33i			1.29915i	0.760299	+	0.649573i	$0.225052\pi$
$59$			4522.33i			1.29915i	−0.760299	+	0.649573i	$0.774948\pi$
$60$		0			0
$61$	2628.44			0.706380			0.353190	−	0.935552i	$-0.385097\pi$
$61$	2628.44			0.706380			0.353190	+	0.935552i	$0.385097\pi$
$62$	−973.119	−	4943.80i	−0.253153	−	1.28611i
$63$		0			0
$64$	1612.72	−	3765.15i	0.393731	−	0.919226i
$65$	615.579			0.145699
$66$		0			0
$67$		−	67.7999i		−	0.0151036i	−0.999971	−	0.00755179i	$-0.997596\pi$
$67$		−	67.7999i		−	0.0151036i	0.999971	−	0.00755179i	$-0.00240383\pi$
$68$	−5964.64	+	2442.76i	−1.28993	+	0.528277i
$69$		0			0
$70$	729.053	+	3703.86i	0.148786	+	0.755890i
$71$		−	1315.04i		−	0.260869i	−0.991457	−	0.130434i	$-0.958363\pi$
$71$		−	1315.04i		−	0.260869i	0.991457	−	0.130434i	$-0.0416372\pi$
$72$		0			0
$73$	9470.72			1.77720			0.888602	−	0.458680i	$-0.151678\pi$
$73$	9470.72			1.77720			0.888602	+	0.458680i	$0.151678\pi$
$74$	−5502.56	+	1083.10i	−1.00485	+	0.197791i
$75$		0			0
$76$	3909.59	+	9546.31i	0.676868	+	1.65275i
$77$	−3023.78			−0.509999
$78$		0			0
$79$			4369.33i			0.700101i	0.936731	+	0.350050i	$0.113836\pi$
$79$			4369.33i			0.700101i	−0.936731	+	0.350050i	$0.886164\pi$
$80$	−3859.25	+	3798.05i	−0.603008	+	0.593445i
$81$		0			0
$82$	−6076.73	+	1196.12i	−0.903737	+	0.177888i
$83$		−	762.015i		−	0.110613i	−0.998469	−	0.0553067i	$-0.982386\pi$
$83$		−	762.015i		−	0.110613i	0.998469	−	0.0553067i	$-0.0176136\pi$
$84$		0			0
$85$	8520.57			1.17932
$86$	−1445.97	−	7346.04i	−0.195507	−	0.993245i
$87$		0			0
$88$	−2388.00	−	3620.69i	−0.308368	−	0.467547i
$89$	−8083.40			−1.02050			−0.510251	−	0.860025i	$-0.670448\pi$
$89$	−8083.40			−1.02050			−0.510251	+	0.860025i	$0.670448\pi$
$90$		0			0
$91$			1298.56i			0.156813i
$92$	−2349.32	−	5736.50i	−0.277567	−	0.677753i
$93$		0			0
$94$	−3220.79	−	16362.8i	−0.364508	−	1.85183i
$95$		−	13637.0i		−	1.51103i
$96$		0			0
$97$	6665.42			0.708408			0.354204	−	0.935168i	$-0.384752\pi$
$97$	6665.42			0.708408			0.354204	+	0.935168i	$0.384752\pi$
$98$	1609.89	−	316.884i	0.167627	−	0.0329950i
$99$		0			0
$100$	−2630.03	+	1077.10i	−0.263003	+	0.107710i
$101$	−9286.07			−0.910310			−0.455155	−	0.890412i	$-0.650416\pi$
$101$	−9286.07			−0.910310			−0.455155	+	0.890412i	$0.650416\pi$
$102$		0			0
$103$			11307.4i			1.06583i	0.846169	+	0.532915i	$0.178903\pi$
$103$			11307.4i			1.06583i	−0.846169	+	0.532915i	$0.821097\pi$
$104$	−1554.90	+	1025.53i	−0.143760	+	0.0948156i
$105$		0			0
$106$	−3557.99	+	700.341i	−0.316660	+	0.0623301i
$107$		−	6261.61i		−	0.546913i	−0.961884	−	0.273456i	$-0.911833\pi$
$107$		−	6261.61i		−	0.546913i	0.961884	−	0.273456i	$-0.0881669\pi$
$108$		0			0
$109$	3452.85			0.290620			0.145310	−	0.989386i	$-0.453582\pi$
$109$	3452.85			0.290620			0.145310	+	0.989386i	$0.453582\pi$
$110$	1107.34	+	5625.70i	0.0915158	+	0.464934i
$111$		0			0
$112$	−8011.99	−	8141.09i	−0.638711	−	0.649003i
$113$	2545.11			0.199319			0.0996597	−	0.995022i	$-0.468225\pi$
$113$	2545.11			0.199319			0.0996597	+	0.995022i	$0.468225\pi$
$114$		0			0
$115$			8194.67i			0.619635i
$116$	−10726.1	+	4392.75i	−0.797122	+	0.326453i
$117$		0			0
$118$	3493.59	+	17748.7i	0.250904	+	1.27469i
$119$			17974.1i			1.26927i
$120$		0			0
$121$	10048.2			0.686309
$122$	10315.8	−	2030.52i	0.693081	−	0.136423i
$123$		0			0
$124$	−7638.38	−	18651.1i	−0.496773	−	1.21300i
$125$	16976.5			1.08650
$126$		0			0
$127$		−	530.060i		−	0.0328638i	−0.999865	−	0.0164319i	$-0.994769\pi$
$127$		−	530.060i		−	0.0328638i	0.999865	−	0.0164319i	$-0.00523067\pi$
$128$	3420.79	−	16022.9i	0.208788	−	0.977961i
$129$		0			0
$130$	2415.96	−	475.548i	0.142956	−	0.0281389i
$131$		−	926.298i		−	0.0539769i	−0.999636	−	0.0269885i	$-0.991408\pi$
$131$		−	926.298i		−	0.0539769i	0.999636	−	0.0269885i	$-0.00859174\pi$
$132$		0			0
$133$	28767.3			1.62628
$134$	−52.3769	−	266.094i	−0.00291696	−	0.0148192i
$135$		0			0
$136$	−21522.3	+	14194.9i	−1.16362	+	0.767456i
$137$	−1668.23			−0.0888820			−0.0444410	−	0.999012i	$-0.514151\pi$
$137$	−1668.23			−0.0888820			−0.0444410	+	0.999012i	$0.514151\pi$
$138$		0			0
$139$		−	828.805i		−	0.0428966i	−0.999770	−	0.0214483i	$-0.993172\pi$
$139$		−	828.805i		−	0.0428966i	0.999770	−	0.0214483i	$-0.00682773\pi$
$140$	5722.62	+	13973.3i	0.291970	+	0.712924i
$141$		0			0
$142$	−1015.90	−	5161.13i	−0.0503817	−	0.255958i
$143$			1972.36i			0.0964525i
$144$		0			0
$145$	15322.3			0.728768
$146$	37169.6	−	7316.33i	1.74374	−	0.343232i
$147$		0			0
$148$	−20759.1	+	8501.69i	−0.947732	+	0.388134i
$149$	−3122.76			−0.140658			−0.0703292	−	0.997524i	$-0.522405\pi$
$149$	−3122.76			−0.140658			−0.0703292	+	0.997524i	$0.522405\pi$
$150$		0			0
$151$		−	9159.51i		−	0.401715i	−0.979620	−	0.200858i	$-0.935627\pi$
$151$		−	9159.51i		−	0.401715i	0.979620	−	0.200858i	$-0.0643729\pi$
$152$	22718.7	+	34446.1i	0.983322	+	1.49091i
$153$		0			0
$154$	−11867.4	+	2335.94i	−0.500397	+	0.0984963i
$155$			26643.4i			1.10899i
$156$		0			0
$157$	21103.7			0.856168			0.428084	−	0.903739i	$-0.359189\pi$
$157$	21103.7			0.856168			0.428084	+	0.903739i	$0.359189\pi$
$158$	3375.40	+	17148.3i	0.135211	+	0.686920i
$159$		0			0
$160$	−12212.3	+	17887.5i	−0.477043	+	0.698732i
$161$	−17286.7			−0.666898
$162$		0			0
$163$		−	42771.0i		−	1.60981i	−0.593405	−	0.804904i	$-0.702217\pi$
$163$		−	42771.0i		−	1.60981i	0.593405	−	0.804904i	$-0.297783\pi$
$164$	−22925.3	+	9388.80i	−0.852367	+	0.349078i
$165$		0			0
$166$	−588.673	−	2990.68i	−0.0213628	−	0.108531i
$167$			11048.3i			0.396153i	0.980187	+	0.198077i	$0.0634695\pi$
$167$			11048.3i			0.396153i	−0.980187	+	0.198077i	$0.936531\pi$
$168$		0			0
$169$	−27714.0			−0.970343
$170$	33440.6	−	6582.32i	1.15711	−	0.227762i
$171$		0			0
$172$	−11349.9	−	27713.9i	−0.383651	−	0.936787i
$173$	21935.6			0.732922			0.366461	−	0.930433i	$-0.380569\pi$
$173$	21935.6			0.732922			0.366461	+	0.930433i	$0.380569\pi$
$174$		0			0
$175$			7925.47i			0.258791i
$176$	−12169.2	−	12365.3i	−0.392860	−	0.399190i
$177$		0			0
$178$	−31724.9	+	6244.60i	−1.00129	+	0.197090i
$179$		−	11479.2i		−	0.358265i	−0.983825	−	0.179133i	$-0.942671\pi$
$179$		−	11479.2i		−	0.358265i	0.983825	−	0.179133i	$-0.0573291\pi$
$180$		0			0
$181$	45472.2			1.38800			0.693999	−	0.719976i	$-0.255847\pi$
$181$	45472.2			1.38800			0.693999	+	0.719976i	$0.255847\pi$
$182$	1003.17	+	5096.47i	0.0302852	+	0.153860i
$183$		0			0
$184$	−13651.9	−	20699.1i	−0.403235	−	0.611386i
$185$	29654.7			0.866463
$186$		0			0
$187$			27300.5i			0.780705i
$188$	−25281.2	−	61730.8i	−0.715290	−	1.74657i
$189$		0			0
$190$	−10534.9	−	53521.2i	−0.291825	−	1.48258i
$191$		−	70040.6i		−	1.91992i	−0.280135	−	0.959961i	$-0.590379\pi$
$191$		−	70040.6i		−	1.91992i	0.280135	−	0.959961i	$-0.409621\pi$
$192$		0			0
$193$	−34852.9			−0.935672			−0.467836	−	0.883815i	$-0.654966\pi$
$193$	−34852.9			−0.935672			−0.467836	+	0.883815i	$0.654966\pi$
$194$	26159.7	−	5149.17i	0.695071	−	0.136815i
$195$		0			0
$196$	6073.52	−	2487.35i	0.158099	−	0.0647477i
$197$	30858.0			0.795124			0.397562	−	0.917575i	$-0.369856\pi$
$197$	30858.0			0.795124			0.397562	+	0.917575i	$0.369856\pi$
$198$		0			0
$199$			34262.5i			0.865192i	0.901588	+	0.432596i	$0.142402\pi$
$199$			34262.5i			0.865192i	−0.901588	+	0.432596i	$0.857598\pi$
$200$	−9489.97	+	6259.04i	−0.237249	+	0.156476i
$201$		0			0
$202$	−36445.0	+	7173.69i	−0.893172	+	0.175808i
$203$			32322.5i			0.784355i
$204$		0			0
$205$	32749.0			0.779275
$206$	8735.19	+	44378.0i	0.205844	+	1.04576i
$207$		0			0
$208$	−5310.28	+	5226.07i	−0.122741	+	0.120795i
$209$	43694.0			1.00030
$210$		0			0
$211$		−	17308.5i		−	0.388772i	−0.980925	−	0.194386i	$-0.937728\pi$
$211$		−	17308.5i		−	0.388772i	0.980925	−	0.194386i	$-0.0622715\pi$
$212$	−13423.0	+	5497.25i	−0.298661	+	0.122313i
$213$		0			0
$214$	−4837.22	−	24574.9i	−0.105625	−	0.536616i
$215$			39589.7i			0.856457i
$216$		0			0
$217$	−56204.3			−1.19358
$218$	13551.4	−	2667.40i	0.285148	−	0.0561274i
$219$		0			0
$220$	8691.95	+	21223.7i	0.179586	+	0.438506i
$221$	11724.2			0.240048
$222$		0			0
$223$		−	64068.3i		−	1.28835i	−0.764879	−	0.644174i	$-0.777201\pi$
$223$		−	64068.3i		−	1.28835i	0.764879	−	0.644174i	$-0.222799\pi$
$224$	−37733.8	−	25761.9i	−0.752028	−	0.513430i
$225$		0			0
$226$	9988.77	−	1966.15i	0.195567	−	0.0384946i
$227$			13692.2i			0.265719i	0.991135	+	0.132859i	$0.0424159\pi$
$227$			13692.2i			0.265719i	−0.991135	+	0.132859i	$0.957584\pi$
$228$		0			0
$229$	65992.3			1.25841			0.629205	−	0.777239i	$-0.283380\pi$
$229$	65992.3			1.25841			0.629205	+	0.777239i	$0.283380\pi$
$230$	6330.55	+	32161.6i	0.119670	+	0.607969i
$231$		0			0
$232$	−38703.0	+	25526.3i	−0.719067	+	0.474255i
$233$	63342.4			1.16676			0.583381	−	0.812198i	$-0.301729\pi$
$233$	63342.4			1.16676			0.583381	+	0.812198i	$0.301729\pi$
$234$		0			0
$235$			88183.3i			1.59680i
$236$	27422.6	+	66959.5i	0.492361	+	1.20223i
$237$		0			0
$238$	13885.4	+	70543.0i	0.245135	+	1.24537i
$239$		−	317.551i		−	0.00555928i	−0.999996	−	0.00277964i	$-0.999115\pi$
$239$		−	317.551i		−	0.00555928i	0.999996	−	0.00277964i	$-0.000884788\pi$
$240$		0			0
$241$	25505.3			0.439133			0.219566	−	0.975598i	$-0.429536\pi$
$241$	25505.3			0.439133			0.219566	+	0.975598i	$0.429536\pi$
$242$	39436.3	−	7762.48i	0.673388	−	0.132547i
$243$		0			0
$244$	38917.8	−	15938.4i	0.653685	−	0.267710i
$245$	−8676.11			−0.144542
$246$		0			0
$247$		−	18764.4i		−	0.307568i
$248$	−44386.7	−	67299.2i	−0.721688	−	1.09423i
$249$		0			0
$250$	66627.6	−	13114.7i	1.06604	−	0.209836i
$251$			40987.7i			0.650588i	0.945613	+	0.325294i	$0.105463\pi$
$251$			40987.7i			0.650588i	−0.945613	+	0.325294i	$0.894537\pi$
$252$		0			0
$253$	−26256.3			−0.410197
$254$	−409.483	−	2080.32i	−0.00634700	−	0.0322451i
$255$		0			0
$256$	1047.51	−	65527.6i	0.0159837	−	0.999872i
$257$	−30958.1			−0.468715			−0.234357	−	0.972151i	$-0.575299\pi$
$257$	−30958.1			−0.468715			−0.234357	+	0.972151i	$0.575299\pi$
$258$		0			0
$259$			62556.6i			0.932554i
$260$	9114.52	−	3732.76i	0.134830	−	0.0552183i
$261$		0			0
$262$	−715.585	−	3635.44i	−0.0104246	−	0.0529607i
$263$		−	15371.1i		−	0.222225i	−0.993808	−	0.111113i	$-0.964559\pi$
$263$		−	15371.1i		−	0.222225i	0.993808	−	0.111113i	$-0.0354414\pi$
$264$		0			0
$265$	19174.9			0.273050
$266$	112903.	−	22223.4i	1.59567	−	0.314085i
$267$		0			0
$268$	−411.126	−	1003.87i	−0.00572408	−	0.0139769i
$269$	−76105.5			−1.05175			−0.525873	−	0.850563i	$-0.676261\pi$
$269$	−76105.5			−1.05175			−0.525873	+	0.850563i	$0.676261\pi$
$270$		0			0
$271$			78076.4i			1.06312i	0.847021	+	0.531559i	$0.178394\pi$
$271$			78076.4i			1.06312i	−0.847021	+	0.531559i	$0.821606\pi$
$272$	−73502.5	+	72336.9i	−0.993492	+	0.977737i
$273$		0			0
$274$	−6547.28	+	1288.74i	−0.0872087	+	0.0171658i
$275$			12037.8i			0.159177i
$276$		0			0
$277$	4739.93			0.0617750			0.0308875	−	0.999523i	$-0.490167\pi$
$277$	4739.93			0.0617750			0.0308875	+	0.999523i	$0.490167\pi$
$278$	−640.269	−	3252.80i	−0.00828463	−	0.0420890i
$279$		0			0
$280$	33254.2	+	50420.1i	0.424161	+	0.643113i
$281$	−43209.3			−0.547223			−0.273612	−	0.961840i	$-0.588218\pi$
$281$	−43209.3			−0.547223			−0.273612	+	0.961840i	$0.588218\pi$
$282$		0			0
$283$		−	36115.6i		−	0.450944i	−0.974250	−	0.225472i	$-0.927608\pi$
$283$		−	36115.6i		−	0.450944i	0.974250	−	0.225472i	$-0.0723924\pi$
$284$	−7974.16	−	19471.0i	−0.0988663	−	0.241408i
$285$		0			0
$286$	1523.69	+	7740.90i	0.0186279	+	0.0946366i
$287$			69084.1i			0.838715i
$288$		0			0
$289$	78760.1			0.942997
$290$	60135.5	−	11836.8i	0.715047	−	0.140747i
$291$		0			0
$292$	140227.	−	57428.7i	1.64463	−	0.673540i
$293$	96093.3			1.11933			0.559665	−	0.828719i	$-0.310930\pi$
$293$	96093.3			1.11933			0.559665	+	0.828719i	$0.310930\pi$
$294$		0			0
$295$		−	95652.6i		−	1.09914i
$296$	−74905.5	+	49403.4i	−0.854929	+	0.563862i
$297$		0			0
$298$	−12255.9	+	2412.40i	−0.138010	+	0.0271654i
$299$			11275.8i			0.126126i
$300$		0			0
$301$	−83514.6			−0.921784
$302$	−7075.92	−	35948.3i	−0.0775834	−	0.394152i
$303$		0			0
$304$	115774.	+	117640.i	1.25275	+	1.27294i
$305$	−55594.6			−0.597631
$306$		0			0
$307$		−	140641.i		−	1.49223i	−0.665817	−	0.746115i	$-0.731917\pi$
$307$		−	140641.i		−	1.49223i	0.665817	−	0.746115i	$-0.268083\pi$
$308$	−44771.4	+	18335.7i	−0.471954	+	0.193284i
$309$		0			0
$310$	20582.6	+	104567.i	0.214179	+	1.08811i
$311$		−	163464.i		−	1.69005i	−0.534724	−	0.845027i	$-0.679584\pi$
$311$		−	163464.i		−	1.69005i	0.534724	−	0.845027i	$-0.320416\pi$
$312$		0			0
$313$	−51290.3			−0.523536			−0.261768	−	0.965131i	$-0.584306\pi$
$313$	−51290.3			−0.523536			−0.261768	+	0.965131i	$0.584306\pi$
$314$	82825.4	−	16303.0i	0.840049	−	0.165352i
$315$		0			0
$316$	26494.8	+	64694.1i	0.265330	+	0.647874i
$317$	28050.0			0.279135			0.139568	−	0.990213i	$-0.455429\pi$
$317$	28050.0			0.279135			0.139568	+	0.990213i	$0.455429\pi$
$318$		0			0
$319$			49093.8i			0.482443i
$320$	−34111.0	+	79637.3i	−0.333115	+	0.777708i
$321$		0			0
$322$	−67844.8	+	13354.3i	−0.654342	+	0.128798i
$323$		−	259728.i		−	2.48951i
$324$		0			0
$325$	5169.63			0.0489433
$326$	−33041.5	−	167863.i	−0.310903	−	1.57950i
$327$		0			0
$328$	−82721.5	+	54558.4i	−0.768902	+	0.507124i
$329$	−186023.			−1.71860
$330$		0			0
$331$			112789.i			1.02946i	0.857352	+	0.514731i	$0.172108\pi$
$331$			112789.i			1.02946i	−0.857352	+	0.514731i	$0.827892\pi$
$332$	−4620.72	−	11282.7i	−0.0419212	−	0.102362i
$333$		0			0
$334$	8535.06	+	43361.2i	0.0765092	+	0.388695i
$335$			1434.05i			0.0127783i
$336$		0			0
$337$	−20819.6			−0.183321			−0.0916606	−	0.995790i	$-0.529217\pi$
$337$	−20819.6			−0.183321			−0.0916606	+	0.995790i	$0.529217\pi$
$338$	−108769.	+	21409.6i	−0.952075	+	0.187403i
$339$		0			0
$340$	126159.	−	51667.2i	1.09134	−	0.446948i
$341$	−85367.4			−0.734147
$342$		0			0
$343$		−	125431.i		−	1.06615i
$344$	−65954.6	−	100001.i	−0.557351	−	0.845056i
$345$		0			0
$346$	86090.5	−	16945.7i	0.719123	−	0.141549i
$347$			161213.i			1.33888i	0.742866	+	0.669440i	$0.233466\pi$
$347$			161213.i			1.33888i	−0.742866	+	0.669440i	$0.766534\pi$
$348$		0			0
$349$	−221484.			−1.81841			−0.909205	−	0.416349i	$-0.863310\pi$
$349$	−221484.			−1.81841			−0.909205	+	0.416349i	$0.863310\pi$
$350$	6122.59	+	31105.0i	0.0499803	+	0.253919i
$351$		0			0
$352$	−57312.9	−	39129.0i	−0.462559	−	0.315801i
$353$	−218790.			−1.75581			−0.877904	−	0.478836i	$-0.841059\pi$
$353$	−218790.			−1.75581			−0.877904	+	0.478836i	$0.841059\pi$
$354$		0			0
$355$			27814.6i			0.220707i
$356$	−119686.	+	49016.2i	−0.944374	+	0.386759i
$357$		0			0
$358$	−8867.91	−	45052.2i	−0.0691919	−	0.351520i
$359$		−	924.606i		−	0.00717411i	−0.999994	−	0.00358705i	$-0.998858\pi$
$359$		−	924.606i		−	0.00717411i	0.999994	−	0.00358705i	$-0.00114180\pi$
$360$		0			0
$361$	−285370.			−2.18975
$362$	178464.	−	35128.2i	1.36187	−	0.268064i
$363$		0			0
$364$	7874.25	+	19227.1i	0.0594301	+	0.145115i
$365$	−200317.			−1.50360
$366$		0			0
$367$		−	40797.9i		−	0.302904i	−0.988465	−	0.151452i	$-0.951605\pi$
$367$		−	40797.9i		−	0.302904i	0.988465	−	0.151452i	$-0.0483950\pi$
$368$	−69570.1	−	70691.2i	−0.513721	−	0.521999i
$369$		0			0
$370$	116386.	−	22908.9i	0.850150	−	0.167340i
$371$			40449.6i			0.293877i
$372$		0			0
$373$	−234530.			−1.68570			−0.842851	−	0.538146i	$-0.819125\pi$
$373$	−234530.			−1.68570			−0.842851	+	0.538146i	$0.819125\pi$
$374$	21090.2	+	107146.i	0.150778	+	0.766007i
$375$		0			0
$376$	−146909.	−	222744.i	−1.03914	−	1.57554i
$377$	21083.4			0.148340
$378$		0			0
$379$		−	185553.i		−	1.29178i	−0.763428	−	0.645892i	$-0.776485\pi$
$379$		−	185553.i		−	1.29178i	0.763428	−	0.645892i	$-0.223515\pi$
$380$	−82692.4	−	201916.i	−0.572662	−	1.39831i
$381$		0			0
$382$	−54107.9	−	274888.i	−0.370795	−	1.88378i
$383$		−	60264.1i		−	0.410829i	−0.978675	−	0.205415i	$-0.934146\pi$
$383$		−	60264.1i		−	0.410829i	0.978675	−	0.205415i	$-0.0658543\pi$
$384$		0			0
$385$	63956.6			0.431483
$386$	−136787.	+	26924.6i	−0.918056	+	0.180707i
$387$		0			0
$388$	98691.0	−	40417.8i	0.655562	−	0.268479i
$389$	12009.3			0.0793633			0.0396816	−	0.999212i	$-0.487366\pi$
$389$	12009.3			0.0793633			0.0396816	+	0.999212i	$0.487366\pi$
$390$		0			0
$391$			156074.i			1.02089i
$392$	21915.2	−	14454.0i	0.142617	−	0.0940623i
$393$		0			0
$394$	121108.	−	23838.4i	0.780154	−	0.153562i
$395$		−	92416.5i		−	0.592318i
$396$		0			0
$397$	32276.3			0.204787			0.102394	−	0.994744i	$-0.467350\pi$
$397$	32276.3			0.204787			0.102394	+	0.994744i	$0.467350\pi$
$398$	26468.5	+	134470.i	0.167095	+	0.848903i
$399$		0			0
$400$	−32410.0	+	31896.0i	−0.202562	+	0.199350i
$401$	187726.			1.16744			0.583722	−	0.811953i	$-0.301596\pi$
$401$	187726.			1.16744			0.583722	+	0.811953i	$0.301596\pi$
$402$		0			0
$403$			36661.0i			0.225733i
$404$	−137494.	+	56309.0i	−0.842402	+	0.344997i
$405$		0			0
$406$	24969.8	+	126856.i	0.151483	+	0.769588i
$407$			95015.7i			0.573597i
$408$		0			0
$409$	−134544.			−0.804299			−0.402149	−	0.915574i	$-0.631737\pi$
$409$	−134544.			−0.804299			−0.402149	+	0.915574i	$0.631737\pi$
$410$	128530.	−	25299.3i	0.764604	−	0.150502i
$411$		0			0
$412$	68565.9	+	167422.i	0.403937	+	0.986320i
$413$	201779.			1.18298
$414$		0			0
$415$			16117.5i			0.0935841i
$416$	−16804.0	+	24613.0i	−0.0971013	+	0.142226i
$417$		0			0
$418$	171486.	−	33754.5i	0.981465	−	0.193188i
$419$		−	84663.5i		−	0.482245i	−0.970495	−	0.241123i	$-0.922484\pi$
$419$		−	84663.5i		−	0.482245i	0.970495	−	0.241123i	$-0.0775156\pi$
$420$		0			0
$421$	−115700.			−0.652782			−0.326391	−	0.945235i	$-0.605833\pi$
$421$	−115700.			−0.652782			−0.326391	+	0.945235i	$0.605833\pi$
$422$	−13371.2	−	67930.7i	−0.0750837	−	0.381453i
$423$		0			0
$424$	−48434.4	+	31944.6i	−0.269415	+	0.177691i
$425$	71555.7			0.396156
$426$		0			0
$427$		−	117277.i		−	0.643216i
$428$	−37969.2	−	92712.0i	−0.207274	−	0.506114i
$429$		0			0
$430$	30583.9	+	155377.i	0.165408	+	0.840332i
$431$			294896.i			1.58750i	0.608241	+	0.793752i	$0.291875\pi$
$431$			294896.i			1.58750i	−0.608241	+	0.793752i	$0.708125\pi$
$432$		0			0
$433$	−151284.			−0.806895			−0.403447	−	0.915003i	$-0.632188\pi$
$433$	−151284.			−0.806895			−0.403447	+	0.915003i	$0.632188\pi$
$434$	−220585.	+	43419.0i	−1.17111	+	0.230516i
$435$		0			0
$436$	51124.4	−	20937.5i	0.268940	−	0.110141i
$437$	249794.			1.30803
$438$		0			0
$439$			20014.1i			0.103850i	0.998651	+	0.0519251i	$0.0165357\pi$
$439$			20014.1i			0.103850i	−0.998651	+	0.0519251i	$0.983464\pi$
$440$	50509.0	+	76581.8i	0.260893	+	0.395567i
$441$		0			0
$442$	46013.9	−	9057.19i	0.235529	−	0.0463606i
$443$			38644.0i			0.196913i	0.995141	+	0.0984567i	$0.0313906\pi$
$443$			38644.0i			0.196913i	−0.995141	+	0.0984567i	$0.968609\pi$
$444$		0			0
$445$	170973.			0.863393
$446$	−49494.1	−	251448.i	−0.248819	−	1.26409i
$447$		0			0
$448$	−167995.	−	71957.2i	−0.837029	−	0.358524i
$449$	−79457.9			−0.394135			−0.197067	−	0.980390i	$-0.563142\pi$
$449$	−79457.9			−0.394135			−0.197067	+	0.980390i	$0.563142\pi$
$450$		0			0
$451$			104930.i			0.515878i
$452$	37684.0	−	15433.1i	0.184450	−	0.0755398i
$453$		0			0
$454$	10577.5	+	53737.8i	0.0513183	+	0.260716i
$455$		−	27466.2i		−	0.132671i
$456$		0			0
$457$	−263552.			−1.26193			−0.630963	−	0.775813i	$-0.717340\pi$
$457$	−263552.			−1.26193			−0.630963	+	0.775813i	$0.717340\pi$
$458$	259000.	−	50980.5i	1.23472	−	0.243037i
$459$		0			0
$460$	49691.0	+	121334.i	0.234834	+	0.573411i
$461$	200610.			0.943952			0.471976	−	0.881611i	$-0.343541\pi$
$461$	200610.			0.943952			0.471976	+	0.881611i	$0.343541\pi$
$462$		0			0
$463$		−	237056.i		−	1.10583i	−0.833237	−	0.552916i	$-0.813515\pi$
$463$		−	237056.i		−	1.10583i	0.833237	−	0.552916i	$-0.186485\pi$
$464$	−132178.	+	130082.i	−0.613936	+	0.604200i
$465$		0			0
$466$	248599.	−	48933.3i	1.14480	−	0.225337i
$467$		−	230464.i		−	1.05674i	−0.849014	−	0.528371i	$-0.822803\pi$
$467$		−	230464.i		−	1.05674i	0.849014	−	0.528371i	$-0.177197\pi$
$468$		0			0
$469$	−3025.13			−0.0137530
$470$	68123.5	+	346092.i	0.308391	+	1.56674i
$471$		0			0
$472$	159353.	+	241611.i	0.715279	+	1.08451i
$473$	−126848.			−0.566973
$474$		0			0
$475$		−	114524.i		−	0.507585i
$476$	108992.	+	266133.i	0.481039	+	1.17459i
$477$		0			0
$478$	−245.315	−	1246.29i	−0.00107366	−	0.00545461i
$479$			2401.48i			0.0104666i	0.999986	+	0.00523332i	$0.00166583\pi$
$479$			2401.48i			0.0104666i	−0.999986	+	0.00523332i	$0.998334\pi$
$480$		0			0
$481$	40804.5			0.176367
$482$	100100.	−	19703.4i	0.430865	−	0.0848098i
$483$		0			0
$484$	148779.	−	60930.7i	0.635111	−	0.260103i
$485$	−140981.			−0.599347
$486$		0			0
$487$			405227.i			1.70860i	0.519781	+	0.854300i	$0.326014\pi$
$487$			405227.i			1.70860i	−0.519781	+	0.854300i	$0.673986\pi$
$488$	140428.	−	92618.0i	0.589675	−	0.388916i
$489$		0			0
$490$	−34051.1	+	6702.48i	−0.141820	+	0.0279154i
$491$		−	128547.i		−	0.533210i	−0.963806	−	0.266605i	$-0.914098\pi$
$491$		−	128547.i		−	0.533210i	0.963806	−	0.266605i	$-0.0859019\pi$
$492$		0			0
$493$	291826.			1.20069
$494$	−14495.9	−	73644.5i	−0.0594006	−	0.301777i
$495$		0			0
$496$	−226194.	−	229839.i	−0.919429	−	0.934244i
$497$	−58675.0			−0.237542
$498$		0			0
$499$		−	128607.i		−	0.516493i	−0.966079	−	0.258246i	$-0.916855\pi$
$499$		−	128607.i		−	0.516493i	0.966079	−	0.258246i	$-0.0831446\pi$
$500$	251362.	−	102942.i	1.00545	−	0.411770i
$501$		0			0
$502$	31663.8	+	160864.i	0.125648	+	0.638339i
$503$			368128.i			1.45500i	0.686109	+	0.727499i	$0.259317\pi$
$503$			368128.i			1.45500i	−0.686109	+	0.727499i	$0.740683\pi$
$504$		0			0
$505$	196411.			0.770165
$506$	−103048.	+	20283.5i	−0.402474	+	0.0792214i
$507$		0			0
$508$	−3214.19	−	7848.30i	−0.0124550	−	0.0304122i
$509$	81396.7			0.314175			0.157087	−	0.987585i	$-0.449790\pi$
$509$	81396.7			0.314175			0.157087	+	0.987585i	$0.449790\pi$
$510$		0			0
$511$		−	422569.i		−	1.61829i
$512$	−46510.3	−	257985.i	−0.177423	−	0.984135i
$513$		0			0
$514$	−121501.	+	23915.8i	−0.459890	+	0.0905230i
$515$		−	239164.i		−	0.901742i
$516$		0			0
$517$	−282545.			−1.05708
$518$	48326.3	+	245516.i	0.180104	+	0.914997i
$519$		0			0
$520$	32888.1	−	21691.1i	0.121627	−	0.0802185i
$521$	17832.5			0.0656956			0.0328478	−	0.999460i	$-0.489542\pi$
$521$	17832.5			0.0656956			0.0328478	+	0.999460i	$0.489542\pi$
$522$		0			0
$523$			51996.2i			0.190094i	0.995473	+	0.0950470i	$0.0303001\pi$
$523$			51996.2i			0.190094i	−0.995473	+	0.0950470i	$0.969700\pi$
$524$	−5616.90	−	13715.2i	−0.0204566	−	0.0499503i
$525$		0			0
$526$	−11874.5	−	60326.8i	−0.0429184	−	0.218041i
$527$			507446.i			1.82712i
$528$		0			0
$529$	129737.			0.463608
$530$	75255.7	−	14813.0i	0.267909	−	0.0527342i
$531$		0			0
$532$	425941.	−	174440.i	1.50497	−	0.616343i
$533$	45062.3			0.158620
$534$		0			0
$535$			132440.i			0.462714i
$536$	−2389.06	−	3622.30i	−0.00831567	−	0.0126082i
$537$		0			0
$538$	−298691.	+	58793.1i	−1.03195	+	0.203124i
$539$		−	27798.8i		−	0.0956862i
$540$		0			0
$541$	−329819.			−1.12689			−0.563444	−	0.826154i	$-0.690524\pi$
$541$	−329819.			−1.12689			−0.563444	+	0.826154i	$0.690524\pi$
$542$	60315.7	+	306426.i	0.205320	+	1.04310i
$543$		0			0
$544$	−232593.	+	340682.i	−0.785957	+	1.15120i
$545$	−73031.9			−0.245878
$546$		0			0
$547$			353376.i			1.18103i	0.807025	+	0.590517i	$0.201076\pi$
$547$			353376.i			1.18103i	−0.807025	+	0.590517i	$0.798924\pi$
$548$	−24700.5	+	10115.8i	−0.0822516	+	0.0336853i
$549$		0			0
$550$	9299.45	+	47244.6i	0.0307420	+	0.156181i
$551$		−	467063.i		−	1.53841i
$552$		0			0
$553$	194953.			0.637498
$554$	18602.8	−	3661.70i	0.0606120	−	0.0119306i
$555$		0			0
$556$	−5025.72	−	12271.6i	−0.0162573	−	0.0396966i
$557$	381405.			1.22935			0.614676	−	0.788780i	$-0.289287\pi$
$557$	381405.			1.22935			0.614676	+	0.788780i	$0.289287\pi$
$558$		0			0
$559$			54475.0i			0.174330i
$560$	169463.	+	172194.i	0.540380	+	0.549087i
$561$		0			0
$562$	−169583.	+	33380.1i	−0.536921	+	0.105685i
$563$			235336.i			0.742459i	0.928541	+	0.371229i	$0.121064\pi$
$563$			235336.i			0.742459i	−0.928541	+	0.371229i	$0.878936\pi$
$564$		0			0
$565$	−53832.1			−0.168634
$566$	−27900.1	−	141743.i	−0.0870909	−	0.442454i
$567$		0			0
$568$	−46337.9	−	70257.6i	−0.143628	−	0.217769i
$569$	221943.			0.685515			0.342757	−	0.939424i	$-0.388639\pi$
$569$	221943.			0.685515			0.342757	+	0.939424i	$0.388639\pi$
$570$		0			0
$571$		−	39939.1i		−	0.122497i	−0.998123	−	0.0612486i	$-0.980492\pi$
$571$		−	39939.1i		−	0.122497i	0.998123	−	0.0612486i	$-0.0195082\pi$
$572$	11960.0	+	29203.6i	0.0365544	+	0.0892573i
$573$		0			0
$574$	53369.0	+	271134.i	0.161981	+	0.822925i
$575$			68818.8i			0.208148i
$576$		0			0
$577$	511135.			1.53527			0.767634	−	0.640889i	$-0.221434\pi$
$577$	511135.			1.53527			0.767634	+	0.640889i	$0.221434\pi$
$578$	309109.	−	60843.8i	0.925244	−	0.182121i
$579$		0			0
$580$	226869.	−	92911.9i	0.674403	−	0.276195i
$581$	−33999.9			−0.100722
$582$		0			0
$583$			61437.8i			0.180759i
$584$	505985.	−	333719.i	1.48358	−	0.978486i
$585$		0			0
$586$	377137.	−	74234.1i	1.09826	−	0.216176i
$587$			69870.4i			0.202776i	0.994847	+	0.101388i	$0.0323284\pi$
$587$			69870.4i			0.202776i	−0.994847	+	0.101388i	$0.967672\pi$
$588$		0			0
$589$	812158.			2.34105
$590$	−73893.6	−	375407.i	−0.212277	−	1.07845i
$591$		0			0
$592$	−255816.	+	251759.i	−0.729935	+	0.718359i
$593$	−206980.			−0.588599			−0.294299	−	0.955713i	$-0.595086\pi$
$593$	−206980.			−0.588599			−0.294299	+	0.955713i	$0.595086\pi$
$594$		0			0
$595$		−	380174.i		−	1.07386i
$596$	−46236.9	+	18935.8i	−0.130165	+	0.0533079i
$597$		0			0
$598$	8710.76	+	44253.9i	0.0243587	+	0.123751i
$599$		−	278466.i		−	0.776101i	−0.921638	−	0.388051i	$-0.873149\pi$
$599$		−	278466.i		−	0.776101i	0.921638	−	0.388051i	$-0.126851\pi$
$600$		0			0
$601$	427472.			1.18347			0.591737	−	0.806131i	$-0.298443\pi$
$601$	427472.			1.18347			0.591737	+	0.806131i	$0.298443\pi$
$602$	−327769.	+	64516.8i	−0.904430	+	0.178024i
$603$		0			0
$604$	−55541.6	−	135620.i	−0.152246	−	0.371748i
$605$	−212532.			−0.580650
$606$		0			0
$607$			417400.i			1.13286i	0.824111	+	0.566428i	$0.191675\pi$
$607$			417400.i			1.13286i	−0.824111	+	0.566428i	$0.808325\pi$
$608$	545257.	+	372261.i	1.47501	+	1.00703i
$609$		0			0
$610$	−218192.	+	42948.0i	−0.586379	+	0.115421i
$611$			121339.i			0.325026i
$612$		0			0
$613$	−23327.6			−0.0620796			−0.0310398	−	0.999518i	$-0.509882\pi$
$613$	−23327.6			−0.0620796			−0.0310398	+	0.999518i	$0.509882\pi$
$614$	−108648.	−	551973.i	−0.288195	−	1.46414i
$615$		0			0
$616$	−161549.	+	106549.i	−0.425740	+	0.280793i
$617$	−78771.3			−0.206918			−0.103459	−	0.994634i	$-0.532991\pi$
$617$	−78771.3			−0.206918			−0.103459	+	0.994634i	$0.532991\pi$
$618$		0			0
$619$			441852.i			1.15317i	0.817036	+	0.576587i	$0.195616\pi$
$619$			441852.i			1.15317i	−0.817036	+	0.576587i	$0.804384\pi$
$620$	161561.	+	394494.i	0.420293	+	1.02626i
$621$		0			0
$622$	−126279.	−	641545.i	−0.326401	−	1.65824i
$623$			360669.i			0.929249i
$624$		0			0
$625$	−248056.			−0.635024
$626$	−201299.	+	39622.8i	−0.513679	+	0.101111i
$627$		0			0
$628$	312470.	−	127969.i	0.792299	−	0.324478i
$629$	564798.			1.42755
$630$		0			0
$631$			211599.i			0.531440i	0.964050	+	0.265720i	$0.0856097\pi$
$631$			211599.i			0.531440i	−0.964050	+	0.265720i	$0.914390\pi$
$632$	153962.	+	233437.i	0.385459	+	0.584434i
$633$		0			0
$634$	110088.	−	21669.2i	0.273880	−	0.0539094i
$635$			11211.4i			0.0278043i
$636$		0			0
$637$	−11938.2			−0.0294212
$638$	37926.0	+	192678.i	0.0931743	+	0.473360i
$639$		0			0
$640$	−72353.7	+	338903.i	−0.176645	+	0.827401i
$641$	5105.48			0.0124257			0.00621284	−	0.999981i	$-0.498022\pi$
$641$	5105.48			0.0124257			0.00621284	+	0.999981i	$0.498022\pi$
$642$		0			0
$643$			79821.9i			0.193064i	0.995330	+	0.0965318i	$0.0307749\pi$
$643$			79821.9i			0.193064i	−0.995330	+	0.0965318i	$0.969225\pi$
$644$	−255954.	+	104823.i	−0.617148	+	0.252747i
$645$		0			0
$646$	−200646.	−	1.01935e6i	−0.480800	−	2.44264i
$647$		−	531516.i		−	1.26972i	−0.772628	−	0.634859i	$-0.781058\pi$
$647$		−	531516.i		−	1.26972i	0.772628	−	0.634859i	$-0.218942\pi$
$648$		0			0
$649$	306477.			0.727627
$650$	20289.2	−	3993.65i	0.0480218	−	0.00945243i
$651$		0			0
$652$	−259355.	−	633285.i	−0.610099	−	1.48972i
$653$	471230.			1.10511			0.552556	−	0.833476i	$-0.313653\pi$
$653$	471230.			1.10511			0.552556	+	0.833476i	$0.313653\pi$
$654$		0			0
$655$			19592.3i			0.0456670i
$656$	−282509.	+	278029.i	−0.656485	+	0.646074i
$657$		0			0
$658$	−730082.	+	143707.i	−1.68624	+	0.331913i
$659$			357344.i			0.822841i	0.911446	+	0.411420i	$0.134967\pi$
$659$			357344.i			0.822841i	−0.911446	+	0.411420i	$0.865033\pi$
$660$		0			0
$661$	−565583.			−1.29447			−0.647237	−	0.762289i	$-0.724076\pi$
$661$	−565583.			−1.29447			−0.647237	+	0.762289i	$0.724076\pi$
$662$	87131.7	+	442661.i	0.198820	+	1.01008i
$663$		0			0
$664$	−26851.0	−	40711.6i	−0.0609011	−	0.0923383i
$665$	−608463.			−1.37591
$666$		0			0
$667$			280664.i			0.630864i
$668$	66995.0	+	163586.i	0.150138	+	0.366601i
$669$		0			0
$670$	1107.83	+	5628.20i	0.00246788	+	0.0125378i
$671$		−	178129.i		−	0.395630i
$672$		0			0
$673$	−316237.			−0.698205			−0.349103	−	0.937085i	$-0.613514\pi$
$673$	−316237.			−0.698205			−0.349103	+	0.937085i	$0.613514\pi$
$674$	−81710.5	+	16083.6i	−0.179870	+	0.0354049i
$675$		0			0
$676$	−410345.	+	168052.i	−0.897957	+	0.367749i
$677$	601827.			1.31309			0.656545	−	0.754287i	$-0.272017\pi$
$677$	601827.			1.31309			0.656545	+	0.754287i	$0.272017\pi$
$678$		0			0
$679$		−	297400.i		−	0.645063i
$680$	455222.	−	300238.i	0.984476	−	0.649304i
$681$		0			0
$682$	−335041.	+	65948.1i	−0.720326	+	0.141786i
$683$			385277.i			0.825909i	0.910752	+	0.412955i	$0.135503\pi$
$683$			385277.i			0.825909i	−0.910752	+	0.412955i	$0.864497\pi$
$684$		0			0
$685$	35285.0			0.0751984
$686$	−96898.2	−	492279.i	−0.205905	−	1.04607i
$687$		0			0
$688$	−336104.	−	341520.i	−0.710063	−	0.721505i
$689$	26384.5			0.0555789
$690$		0			0
$691$		−	459302.i		−	0.961927i	−0.876741	−	0.480963i	$-0.840287\pi$
$691$		−	459302.i		−	0.961927i	0.876741	−	0.480963i	$-0.159713\pi$
$692$	324788.	−	133014.i	0.678247	−	0.277769i
$693$		0			0
$694$	124541.	+	632712.i	0.258578	+	1.31367i
$695$			17530.2i			0.0362925i
$696$		0			0
$697$	623732.			1.28390
$698$	−869257.	+	171101.i	−1.78418	+	0.351190i
$699$		0			0
$700$	48058.6	+	117348.i	0.0980787	+	0.239485i
$701$	127011.			0.258467			0.129234	−	0.991614i	$-0.458748\pi$
$701$	127011.			0.258467			0.129234	+	0.991614i	$0.458748\pi$
$702$		0			0
$703$		−	903950.i		−	1.82908i
$704$	−255163.	−	109294.i	−0.514841	−	0.220522i
$705$		0			0
$706$	−858682.	+	169020.i	−1.72275	+	0.339100i
$707$			414330.i			0.828910i
$708$		0			0
$709$	494816.			0.984353			0.492177	−	0.870495i	$-0.336201\pi$
$709$	494816.			0.984353			0.492177	+	0.870495i	$0.336201\pi$
$710$	21487.4	+	109164.i	0.0426253	+	0.216552i
$711$		0			0
$712$	−431865.	+	284834.i	−0.851900	+	0.561864i
$713$	−488036.			−0.960004
$714$		0			0
$715$		−	41717.7i		−	0.0816034i
$716$	−69607.6	−	169966.i	−0.135778	−	0.331539i
$717$		0			0
$718$	−714.278	−	3628.80i	−0.00138554	−	0.00703904i
$719$		−	614613.i		−	1.18890i	−0.804134	−	0.594448i	$-0.797371\pi$
$719$		−	614613.i		−	1.18890i	0.804134	−	0.594448i	$-0.202629\pi$
$720$		0			0
$721$	504518.			0.970523
$722$	−1.11999e6	+	220454.i	−2.14852	+	0.422906i
$723$		0			0
$724$	673280.	−	275735.i	1.28445	−	0.526035i
$725$	128677.			0.244808
$726$		0			0
$727$		−	331397.i		−	0.627018i	−0.949585	−	0.313509i	$-0.898495\pi$
$727$		−	331397.i		−	0.627018i	0.949585	−	0.313509i	$-0.101505\pi$
$728$	45757.4	+	69377.4i	0.0863373	+	0.130905i
$729$		0			0
$730$	−786182.	+	154749.i	−1.47529	+	0.290390i
$731$			754018.i			1.41106i
$732$		0			0
$733$	−51616.8			−0.0960690			−0.0480345	−	0.998846i	$-0.515296\pi$
$733$	−51616.8			−0.0960690			−0.0480345	+	0.998846i	$0.515296\pi$
$734$	−31517.2	−	160119.i	−0.0585000	−	0.297202i
$735$		0			0
$736$	−327652.	−	223697.i	−0.604863	−	0.412956i
$737$	−4594.79			−0.00845923
$738$		0			0
$739$		−	228968.i		−	0.419263i	−0.977780	−	0.209631i	$-0.932774\pi$
$739$		−	228968.i		−	0.419263i	0.977780	−	0.209631i	$-0.0672264\pi$
$740$	439080.	−	179821.i	0.801826	−	0.328380i
$741$		0			0
$742$	31248.1	+	158752.i	0.0567566	+	0.288344i
$743$		−	1.05079e6i		−	1.90343i	−0.306980	−	0.951716i	$-0.599319\pi$
$743$		−	1.05079e6i		−	1.90343i	0.306980	−	0.951716i	$-0.400681\pi$
$744$		0			0
$745$	66050.0			0.119004
$746$	−920459.	+	181179.i	−1.65397	+	0.325560i
$747$		0			0
$748$	165545.	+	404223.i	0.295878	+	0.722466i
$749$	−279383.			−0.498008
$750$		0			0
$751$			269386.i			0.477634i	0.971065	+	0.238817i	$0.0767596\pi$
$751$			269386.i			0.477634i	−0.971065	+	0.238817i	$0.923240\pi$
$752$	−748649.	−	760712.i	−1.32386	−	1.34519i
$753$		0			0
$754$	82745.7	−	16287.3i	0.145547	−	0.0286489i
$755$			193735.i			0.339870i
$756$		0			0
$757$	−476176.			−0.830952			−0.415476	−	0.909604i	$-0.636385\pi$
$757$	−476176.			−0.830952			−0.415476	+	0.909604i	$0.636385\pi$
$758$	−143344.	−	728239.i	−0.249483	−	1.26746i
$759$		0			0
$760$	−480527.	−	728575.i	−0.831937	−	1.26138i
$761$	−484394.			−0.836430			−0.418215	−	0.908348i	$-0.637344\pi$
$761$	−484394.			−0.836430			−0.418215	+	0.908348i	$0.637344\pi$
$762$		0			0
$763$		−	154061.i		−	0.264632i
$764$	−424714.	−	1.03705e6i	−0.727628	−	1.77670i
$765$		0			0
$766$	−46555.3	−	236518.i	−0.0793436	−	0.403095i
$767$		−	131617.i		−	0.223728i
$768$		0			0
$769$	502123.			0.849097			0.424549	−	0.905405i	$-0.360433\pi$
$769$	502123.			0.849097			0.424549	+	0.905405i	$0.360433\pi$
$770$	251010.	−	49407.8i	0.423360	−	0.0833325i
$771$		0			0
$772$	−516046.	+	211341.i	−0.865872	+	0.354609i
$773$	−435529.			−0.728884			−0.364442	−	0.931226i	$-0.618740\pi$
$773$	−435529.			−0.728884			−0.364442	+	0.931226i	$0.618740\pi$
$774$		0			0
$775$			223752.i			0.372531i
$776$	356108.	−	234868.i	0.591369	−	0.390033i
$777$		0			0
$778$	47132.9	−	9277.46i	0.0778691	−	0.0153275i
$779$		−	998273.i		−	1.64503i
$780$		0			0
$781$	−89120.1			−0.146108
$782$	120571.	+	612543.i	0.197164	+	1.00167i
$783$		0			0
$784$	74844.3	−	73657.4i	0.121766	−	0.119835i
$785$	−446368.			−0.724358
$786$		0			0
$787$			429485.i			0.693423i	0.937972	+	0.346711i	$0.112702\pi$
$787$			429485.i			0.693423i	−0.937972	+	0.346711i	$0.887298\pi$
$788$	456896.	−	187117.i	0.735809	−	0.301343i
$789$		0			0
$790$	−71393.7	−	362706.i	−0.114395	−	0.581167i
$791$		−	113559.i		−	0.181496i
$792$		0			0
$793$	−76497.5			−0.121647
$794$	126675.	−	24934.1i	0.200932	−	0.0395506i
$795$		0			0
$796$	207761.	+	507304.i	0.327898	+	0.800650i
$797$	−725429.			−1.14203			−0.571016	−	0.820939i	$-0.693450\pi$
$797$	−725429.			−1.14203			−0.571016	+	0.820939i	$0.693450\pi$
$798$		0			0
$799$			1.67952e6i			2.63083i
$800$	−102559.	+	150220.i	−0.160248	+	0.234718i
$801$		0			0
$802$	736768.	−	145023.i	1.14547	−	0.225469i
$803$		−	641829.i		−	0.995378i
$804$		0			0
$805$	365633.			0.564227
$806$	28321.4	+	143883.i	0.0435958	+	0.221483i
$807$		0			0
$808$	−496120.	+	327212.i	−0.759913	+	0.501195i
$809$	−144295.			−0.220473			−0.110237	−	0.993905i	$-0.535161\pi$
$809$	−144295.			−0.220473			−0.110237	+	0.993905i	$0.535161\pi$
$810$		0			0
$811$			321928.i			0.489460i	0.969591	+	0.244730i	$0.0786993\pi$
$811$			321928.i			0.489460i	−0.969591	+	0.244730i	$0.921301\pi$
$812$	195998.	+	478581.i	0.297262	+	0.725843i
$813$		0			0
$814$	73401.7	+	372908.i	0.110779	+	0.562798i
$815$			904657.i			1.36197i
$816$		0			0
$817$	1.20679e6			1.80796
$818$	−528044.	+	103938.i	−0.789156	+	0.155334i
$819$		0			0
$820$	484896.	−	198584.i	0.721142	−	0.295336i
$821$	−907782.			−1.34678			−0.673388	−	0.739289i	$-0.735162\pi$
$821$	−907782.			−1.34678			−0.673388	+	0.739289i	$0.735162\pi$
$822$		0			0
$823$		−	843973.i		−	1.24603i	−0.782209	−	0.623016i	$-0.785907\pi$
$823$		−	843973.i		−	1.24603i	0.782209	−	0.623016i	$-0.214093\pi$
$824$	398437.	+	604111.i	0.586820	+	0.889738i
$825$		0			0
$826$	791921.	−	155879.i	1.16071	−	0.228469i
$827$		−	658309.i		−	0.962540i	−0.876572	−	0.481270i	$-0.840176\pi$
$827$		−	658309.i		−	0.962540i	0.876572	−	0.481270i	$-0.159824\pi$
$828$		0			0
$829$	1.22965e6			1.78925			0.894625	−	0.446818i	$-0.147443\pi$
$829$	1.22965e6			1.78925			0.894625	+	0.446818i	$0.147443\pi$
$830$	12451.1	+	63256.3i	0.0180739	+	0.0918222i
$831$		0			0
$832$	−46936.3	+	109580.i	−0.0678051	+	0.158301i
$833$	−165243.			−0.238141
$834$		0			0
$835$		−	233685.i		−	0.335164i
$836$	646952.	−	264952.i	0.925677	−	0.379101i
$837$		0			0
$838$	−65404.3	−	332278.i	−0.0931362	−	0.473166i
$839$		−	52593.0i		−	0.0747144i	−0.999302	−	0.0373572i	$-0.988106\pi$
$839$		−	52593.0i		−	0.0747144i	0.999302	−	0.0373572i	$-0.0118939\pi$
$840$		0			0
$841$	−182496.			−0.258025
$842$	−454086.	+	89380.4i	−0.640492	+	0.126072i
$843$		0			0
$844$	−104956.	−	256278.i	−0.147340	−	0.359771i
$845$	586183.			0.820956
$846$		0			0
$847$		−	448337.i		−	0.624939i
$848$	−165412.	+	162789.i	−0.230026	+	0.226378i
$849$		0			0
$850$	280834.	−	55278.3i	0.388698	−	0.0765098i
$851$			543195.i			0.750061i
$852$		0			0
$853$	−644516.			−0.885800			−0.442900	−	0.896571i	$-0.646050\pi$
$853$	−644516.			−0.885800			−0.442900	+	0.896571i	$0.646050\pi$
$854$	−90598.9	−	460276.i	−0.124224	−	0.631106i
$855$		0			0
$856$	−220639.	−	334534.i	−0.301117	−	0.456555i
$857$	−351639.			−0.478779			−0.239390	−	0.970924i	$-0.576947\pi$
$857$	−351639.			−0.478779			−0.239390	+	0.970924i	$0.576947\pi$
$858$		0			0
$859$			760737.i			1.03097i	0.856897	+	0.515487i	$0.172389\pi$
$859$			760737.i			1.03097i	−0.856897	+	0.515487i	$0.827611\pi$
$860$	240065.	+	586182.i	0.324587	+	0.792566i
$861$		0			0
$862$	227814.	+	1.15738e6i	0.306595	+	1.55762i
$863$			363360.i			0.487883i	0.969790	+	0.243942i	$0.0784406\pi$
$863$			363360.i			0.487883i	−0.969790	+	0.243942i	$0.921559\pi$
$864$		0			0
$865$	−463964.			−0.620086
$866$	−593743.	+	116870.i	−0.791703	+	0.155836i
$867$		0			0
$868$	−832185.	+	340813.i	−1.10454	+	0.452352i
$869$	296109.			0.392114
$870$		0			0
$871$			1973.23i			0.00260101i
$872$	184473.	−	121668.i	0.242605	−	0.160008i
$873$		0			0
$874$	980365.	−	192971.i	1.28341	−	0.252621i
$875$		−	757466.i		−	0.989343i
$876$		0			0
$877$	72069.9			0.0937033			0.0468516	−	0.998902i	$-0.485081\pi$
$877$	72069.9			0.0937033			0.0468516	+	0.998902i	$0.485081\pi$
$878$	15461.3	+	78549.3i	0.0200566	+	0.101895i
$879$		0			0
$880$	257393.	+	261541.i	0.332378	+	0.337733i
$881$	−1.34754e6			−1.73616			−0.868082	−	0.496422i	$-0.834647\pi$
$881$	−1.34754e6			−1.73616			−0.868082	+	0.496422i	$0.834647\pi$
$882$		0			0
$883$			675925.i			0.866916i	0.901174	+	0.433458i	$0.142707\pi$
$883$			675925.i			0.866916i	−0.901174	+	0.433458i	$0.857293\pi$
$884$	173593.	−	71093.4i	0.222141	−	0.0909755i
$885$		0			0
$886$	29853.3	+	151666.i	0.0380299	+	0.193206i
$887$			1.02538e6i			1.30328i	0.758527	+	0.651642i	$0.225920\pi$
$887$			1.02538e6i			1.30328i	−0.758527	+	0.651642i	$0.774080\pi$
$888$		0			0
$889$	−23650.5			−0.0299251
$890$	671018.	−	132081.i	0.847138	−	0.166747i
$891$		0			0
$892$	−388498.	−	948622.i	−0.488269	−	1.19224i
$893$	2.68805e6			3.37081
$894$		0			0
$895$			242798.i			0.303109i
$896$	−714917.	−	152630.i	−0.890512	−	0.190119i
$897$		0			0
$898$	−311848.	+	61382.9i	−0.386714	+	0.0761193i
$899$			912528.i			1.12908i
$900$		0			0
$901$	365202.			0.449867
$902$	81060.8	+	411819.i	0.0996317	+	0.506166i
$903$		0			0
$904$	135976.	−	89681.7i	0.166389	−	0.109741i
$905$	−961790.			−1.17431
$906$		0			0
$907$		−	1.61577e6i		−	1.96411i	−0.188604	−	0.982053i	$-0.560396\pi$
$907$		−	1.61577e6i		−	1.96411i	0.188604	−	0.982053i	$-0.439604\pi$
$908$	83027.1	+	202733.i	0.100704	+	0.245896i
$909$		0			0
$910$	−21218.2	−	107796.i	−0.0256227	−	0.130173i
$911$		−	285027.i		−	0.343439i	−0.985146	−	0.171719i	$-0.945068\pi$
$911$		−	285027.i		−	0.343439i	0.985146	−	0.171719i	$-0.0549323\pi$
$912$		0			0
$913$	−51641.7			−0.0619525
$914$	−1.03436e6	+	203600.i	−1.23817	+	0.243716i
$915$		0			0
$916$	977110.	−	400165.i	1.16453	−	0.476923i
$917$	−41330.0			−0.0491503
$918$		0			0
$919$			662333.i			0.784233i	0.919916	+	0.392117i	$0.128257\pi$
$919$			662333.i			0.784233i	−0.919916	+	0.392117i	$0.871743\pi$
$920$	288755.	+	437810.i	0.341156	+	0.517262i
$921$		0			0
$922$	787331.	−	154975.i	0.926181	−	0.182306i
$923$			38272.6i			0.0449246i
$924$		0			0
$925$	249040.			0.291062
$926$	−183131.	−	930373.i	−0.213570	−	1.08501i
$927$		0			0
$928$	−418267.	+	612641.i	−0.485688	+	0.711394i
$929$	−1.24055e6			−1.43742			−0.718708	−	0.695312i	$-0.755266\pi$
$929$	−1.24055e6			−1.43742			−0.718708	+	0.695312i	$0.755266\pi$
$930$		0			0
$931$			264469.i			0.305124i
$932$	937874.	−	384096.i	1.07972	−	0.442190i
$933$		0			0
$934$	−178038.	−	904499.i	−0.204089	−	1.03685i
$935$		−	577438.i		−	0.660514i
$936$		0			0
$937$	−593717.			−0.676239			−0.338119	−	0.941103i	$-0.609791\pi$
$937$	−593717.			−0.676239			−0.338119	+	0.941103i	$0.609791\pi$
$938$	−11872.7	+	2336.97i	−0.0134941	+	0.00265612i
$939$		0			0
$940$	534727.	+	1.30568e6i	0.605169	+	1.47768i
$941$	1.22702e6			1.38571			0.692854	−	0.721078i	$-0.256353\pi$
$941$	1.22702e6			1.38571			0.692854	+	0.721078i	$0.256353\pi$
$942$		0			0
$943$			599875.i			0.674586i
$944$	812060.	+	825145.i	0.911264	+	0.925947i
$945$		0			0
$946$	−497840.	+	97992.9i	−0.556298	+	0.109500i
$947$		−	1.71443e6i		−	1.91170i	−0.293863	−	0.955848i	$-0.594941\pi$
$947$		−	1.71443e6i		−	1.91170i	0.293863	−	0.955848i	$-0.405059\pi$
$948$		0			0
$949$	−275633.			−0.306055
$950$	−88472.1	−	449471.i	−0.0980300	−	0.498029i
$951$		0			0
$952$	633353.	+	960291.i	0.698831	+	1.05957i
$953$	1.23751e6			1.36258			0.681290	−	0.732014i	$-0.261419\pi$
$953$	1.23751e6			1.36258			0.681290	+	0.732014i	$0.261419\pi$
$954$		0			0
$955$			1.48144e6i			1.62434i
$956$	−1925.57	−	4701.80i	−0.00210690	−	0.00514456i
$957$		0			0
$958$	1855.19	+	9425.06i	0.00202143	+	0.0102696i
$959$			74433.7i			0.0809342i
$960$		0			0
$961$	−663238.			−0.718162
$962$	160145.	−	31522.3i	0.173047	−	0.0340619i
$963$		0			0
$964$	377642.	−	154659.i	0.406374	−	0.166426i
$965$	737179.			0.791623
$966$		0			0
$967$		−	991317.i		−	1.06013i	−0.847957	−	0.530066i	$-0.822167\pi$
$967$		−	991317.i		−	1.06013i	0.847957	−	0.530066i	$-0.177833\pi$
$968$	536840.	−	354069.i	0.572920	−	0.377865i
$969$		0			0
$970$	−553309.	+	108911.i	−0.588063	+	0.115752i
$971$			1.45182e6i			1.53984i	0.638141	+	0.769920i	$0.279704\pi$
$971$			1.45182e6i			1.53984i	−0.638141	+	0.769920i	$0.720296\pi$
$972$		0			0
$973$	−36980.0			−0.0390608
$974$	313046.	+	1.59039e6i	0.329982	+	1.67643i
$975$		0			0
$976$	479586.	−	471981.i	0.503462	−	0.495478i
$977$	−612179.			−0.641342			−0.320671	−	0.947191i	$-0.603908\pi$
$977$	−612179.			−0.641342			−0.320671	+	0.947191i	$0.603908\pi$
$978$		0			0
$979$			547811.i			0.571564i
$980$	−128462.	+	52610.3i	−0.133759	+	0.0547796i
$981$		0			0
$982$	−99305.1	−	504507.i	−0.102979	−	0.523171i
$983$			1.20680e6i			1.24890i	0.781064	+	0.624452i	$0.214677\pi$
$983$			1.20680e6i			1.24890i	−0.781064	+	0.624452i	$0.785323\pi$
$984$		0			0
$985$	−652682.			−0.672712
$986$	1.14533e6	−	225442.i	1.17808	−	0.231889i
$987$		0			0
$988$	−113784.	−	277833.i	−0.116565	−	0.284623i
$989$	−725178.			−0.741399
$990$		0			0
$991$		−	860509.i		−	0.876210i	−0.898924	−	0.438105i	$-0.855650\pi$
$991$		−	860509.i		−	0.876210i	0.898924	−	0.438105i	$-0.144350\pi$
$992$	−1.06530e6	−	727308.i	−1.08255	−	0.739086i
$993$		0			0
$994$	−230281.	+	45327.7i	−0.233070	+	0.0458766i
$995$		−	724691.i		−	0.731993i
$996$		0			0
$997$	−486966.			−0.489901			−0.244951	−	0.969536i	$-0.578772\pi$
$997$	−486966.			−0.489901			−0.244951	+	0.969536i	$0.578772\pi$
$998$	−99351.8	−	504744.i	−0.0997504	−	0.506769i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.d.e.163.21		22
3.2	odd	2		324.5.d.f.163.2		22
4.3	odd	2	inner	324.5.d.e.163.22		22
9.2	odd	6		36.5.f.a.31.17	yes	44
9.4	even	3		108.5.f.a.19.9		44
9.5	odd	6		36.5.f.a.7.14	✓	44
9.7	even	3		108.5.f.a.91.6		44
12.11	even	2		324.5.d.f.163.1		22
36.7	odd	6		108.5.f.a.91.9		44
36.11	even	6		36.5.f.a.31.14	yes	44
36.23	even	6		36.5.f.a.7.17	yes	44
36.31	odd	6		108.5.f.a.19.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.14	✓	44	9.5	odd	6
36.5.f.a.7.17	yes	44	36.23	even	6
36.5.f.a.31.14	yes	44	36.11	even	6
36.5.f.a.31.17	yes	44	9.2	odd	6
108.5.f.a.19.6		44	36.31	odd	6
108.5.f.a.19.9		44	9.4	even	3
108.5.f.a.91.6		44	9.7	even	3
108.5.f.a.91.9		44	36.7	odd	6
324.5.d.e.163.21		22	1.1	even	1	trivial
324.5.d.e.163.22		22	4.3	odd	2	inner
324.5.d.f.163.1		22	12.11	even	2
324.5.d.f.163.2		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.92469 - 0.772521i) q^{2} +(14.8064 - 6.06382i) q^{4} -21.1512 q^{5} -44.6184i q^{7} +(53.4262 - 35.2369i) q^{8} +O(q^{10})\)	\(q+(3.92469 - 0.772521i) q^{2} +(14.8064 - 6.06382i) q^{4} -21.1512 q^{5} -44.6184i q^{7} +(53.4262 - 35.2369i) q^{8} +(-83.0119 + 16.3397i) q^{10} -67.7698i q^{11} -29.1038 q^{13} +(-34.4687 - 175.114i) q^{14} +(182.460 - 179.567i) q^{16} -402.841 q^{17} +644.741i q^{19} +(-313.173 + 128.257i) q^{20} +(-52.3536 - 265.976i) q^{22} -387.433i q^{23} -177.628 q^{25} +(-114.223 + 22.4833i) q^{26} +(-270.558 - 660.639i) q^{28} -724.420 q^{29} -1259.67i q^{31} +(577.381 - 845.699i) q^{32} +(-1581.03 + 311.203i) q^{34} +943.733i q^{35} -1402.04 q^{37} +(498.076 + 2530.41i) q^{38} +(-1130.03 + 745.302i) q^{40} -1548.33 q^{41} -1871.75i q^{43} +(-410.944 - 1003.43i) q^{44} +(-299.300 - 1520.56i) q^{46} -4169.19i q^{47} +410.195 q^{49} +(-697.134 + 137.221i) q^{50} +(-430.923 + 176.480i) q^{52} -906.566 q^{53} +1433.41i q^{55} +(-1572.21 - 2383.79i) q^{56} +(-2843.13 + 559.630i) q^{58} +4522.33i q^{59} +2628.44 q^{61} +(-973.119 - 4943.80i) q^{62} +(1612.72 - 3765.15i) q^{64} +615.579 q^{65} -67.7999i q^{67} +(-5964.64 + 2442.76i) q^{68} +(729.053 + 3703.86i) q^{70} -1315.04i q^{71} +9470.72 q^{73} +(-5502.56 + 1083.10i) q^{74} +(3909.59 + 9546.31i) q^{76} -3023.78 q^{77} +4369.33i q^{79} +(-3859.25 + 3798.05i) q^{80} +(-6076.73 + 1196.12i) q^{82} -762.015i q^{83} +8520.57 q^{85} +(-1445.97 - 7346.04i) q^{86} +(-2388.00 - 3620.69i) q^{88} -8083.40 q^{89} +1298.56i q^{91} +(-2349.32 - 5736.50i) q^{92} +(-3220.79 - 16362.8i) q^{94} -13637.0i q^{95} +6665.42 q^{97} +(1609.89 - 316.884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{2} + q^{4} - 2 q^{5} - 61 q^{8}+O(q^{10}) \) 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

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