LMFDB - Embedded newform 324.3.d.i.163.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,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, 3, names="a")

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1919698923024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + 12x^{5} - 36x^{4} + 48x^{3} + 32x^{2} - 192x + 256 $ x^8 - 3x^7 + 2x^6 + 12x^5 - 36x^4 + 48x^3 + 32x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.8
Root			$1.81766 - 0.834343i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.i.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81766 + 0.834343i) q^{2} +(2.60775 + 3.03310i) q^{4} -6.14806 q^{5} +0.590679i q^{7} +(2.20934 + 7.68888i) q^{8} +O(q^{10})$	\(q+(1.81766 + 0.834343i) q^{2} +(2.60775 + 3.03310i) q^{4} -6.14806 q^{5} +0.590679i q^{7} +(2.20934 + 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +17.4596i q^{11} +1.78451 q^{13} +(-0.492829 + 1.07365i) q^{14} +(-2.39933 + 15.8191i) q^{16} -16.9171 q^{17} +19.5058i q^{19} +(-16.0326 - 18.6477i) q^{20} +(-14.5673 + 31.7356i) q^{22} +7.93023i q^{23} +12.7987 q^{25} +(3.24362 + 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} -6.35035 q^{29} -31.9342i q^{31} +(-17.5597 + 26.7518i) q^{32} +(-30.7495 - 14.1147i) q^{34} -3.63153i q^{35} +58.2834 q^{37} +(-16.2745 + 35.4548i) q^{38} +(-13.5832 - 47.2717i) q^{40} +5.33896 q^{41} -39.1818i q^{43} +(-52.9567 + 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} -11.1327i q^{47} +48.6511 q^{49} +(23.2636 + 10.6785i) q^{50} +(4.65355 + 5.41259i) q^{52} +35.8770 q^{53} -107.343i q^{55} +(-4.54166 + 1.30501i) q^{56} +(-11.5427 - 5.29836i) q^{58} +24.1303i q^{59} +75.8921 q^{61} +(26.6441 - 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} -10.9713 q^{65} +36.7426i q^{67} +(-44.1155 - 51.3112i) q^{68} +(3.02994 - 6.60088i) q^{70} +87.8370i q^{71} -60.0423 q^{73} +(105.939 + 48.6283i) q^{74} +(-59.1629 + 50.8661i) q^{76} -10.3130 q^{77} +37.1630i q^{79} +(14.7512 - 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} -76.2427i q^{83} +104.007 q^{85} +(32.6910 - 71.2190i) q^{86} +(-134.245 + 38.5743i) q^{88} -27.5873 q^{89} +1.05407i q^{91} +(-24.0531 + 20.6800i) q^{92} +(9.28846 - 20.2354i) q^{94} -119.923i q^{95} -26.1171 q^{97} +(88.4309 + 40.5917i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8	$ 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8} + 10 q^{10} + 46 q^{13} + 12 q^{14} + 17 q^{16} + 6 q^{17} - 36 q^{20} - 33 q^{22} + 30 q^{25} + 36 q^{26} + 6 q^{28} - 42 q^{29} - 87 q^{32} - 11 q^{34} + 28 q^{37} + 99 q^{38} - 68 q^{40} - 84 q^{41} - 111 q^{44} - 132 q^{46} - 58 q^{49} + 219 q^{50} - 110 q^{52} - 36 q^{53} - 270 q^{56} + 16 q^{58} + 34 q^{61} + 258 q^{62} - 127 q^{64} + 30 q^{65} - 375 q^{68} - 150 q^{70} + 58 q^{73} + 372 q^{74} + 15 q^{76} + 330 q^{77} - 360 q^{80} + 127 q^{82} + 140 q^{85} + 273 q^{86} - 75 q^{88} - 192 q^{89} - 258 q^{92} - 36 q^{94} + 148 q^{97} + 585 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8 + 10 * q^10 + 46 * q^13 + 12 * q^14 + 17 * q^16 + 6 * q^17 - 36 * q^20 - 33 * q^22 + 30 * q^25 + 36 * q^26 + 6 * q^28 - 42 * q^29 - 87 * q^32 - 11 * q^34 + 28 * q^37 + 99 * q^38 - 68 * q^40 - 84 * q^41 - 111 * q^44 - 132 * q^46 - 58 * q^49 + 219 * q^50 - 110 * q^52 - 36 * q^53 - 270 * q^56 + 16 * q^58 + 34 * q^61 + 258 * q^62 - 127 * q^64 + 30 * q^65 - 375 * q^68 - 150 * q^70 + 58 * q^73 + 372 * q^74 + 15 * q^76 + 330 * q^77 - 360 * q^80 + 127 * q^82 + 140 * q^85 + 273 * q^86 - 75 * q^88 - 192 * q^89 - 258 * q^92 - 36 * q^94 + 148 * q^97 + 585 * 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 $

$2$	1.81766	+	0.834343i	0.908828	+	0.417171i
$2$	1.81766	+	0.834343i	0.908828	+	0.417171i
$3$		0			0
$3$		0			0
$4$	2.60775	+	3.03310i	0.651936	+	0.758274i
$5$	−6.14806			−1.22961			−0.614806	−	0.788678i	$-0.710766\pi$
$5$	−6.14806			−1.22961			−0.614806	+	0.788678i	$0.710766\pi$
$6$		0			0
$7$			0.590679i			0.0843828i	0.999110	+	0.0421914i	$0.0134339\pi$
$7$			0.590679i			0.0843828i	−0.999110	+	0.0421914i	$0.986566\pi$
$8$	2.20934	+	7.68888i	0.276168	+	0.961109i
$9$		0			0
$10$	−11.1751	−	5.12959i	−1.11751	−	0.512959i
$11$			17.4596i			1.58724i	0.608414	+	0.793620i	$0.291806\pi$
$11$			17.4596i			1.58724i	−0.608414	+	0.793620i	$0.708194\pi$
$12$		0			0
$13$	1.78451			0.137270			0.0686350	−	0.997642i	$-0.478136\pi$
$13$	1.78451			0.137270			0.0686350	+	0.997642i	$0.478136\pi$
$14$	−0.492829	+	1.07365i	−0.0352021	+	0.0766894i
$15$		0			0
$16$	−2.39933	+	15.8191i	−0.149958	+	0.988692i
$17$	−16.9171			−0.995123			−0.497562	−	0.867429i	$-0.665771\pi$
$17$	−16.9171			−0.995123			−0.497562	+	0.867429i	$0.665771\pi$
$18$		0			0
$19$			19.5058i			1.02662i	0.858203	+	0.513310i	$0.171581\pi$
$19$			19.5058i			1.02662i	−0.858203	+	0.513310i	$0.828419\pi$
$20$	−16.0326	−	18.6477i	−0.801629	−	0.932383i
$21$		0			0
$22$	−14.5673	+	31.7356i	−0.662151	+	1.44253i
$23$			7.93023i			0.344793i	0.985028	+	0.172396i	$0.0551510\pi$
$23$			7.93023i			0.344793i	−0.985028	+	0.172396i	$0.944849\pi$
$24$		0			0
$25$	12.7987			0.511947
$26$	3.24362	+	1.48889i	0.124755	+	0.0572651i
$27$		0			0
$28$	−1.79159	+	1.54034i	−0.0639852	+	0.0550122i
$29$	−6.35035			−0.218977			−0.109489	−	0.993988i	$-0.534921\pi$
$29$	−6.35035			−0.218977			−0.109489	+	0.993988i	$0.534921\pi$
$30$		0			0
$31$		−	31.9342i		−	1.03014i	−0.857149	−	0.515068i	$-0.827767\pi$
$31$		−	31.9342i		−	1.03014i	0.857149	−	0.515068i	$-0.172233\pi$
$32$	−17.5597	+	26.7518i	−0.548740	+	0.835993i
$33$		0			0
$34$	−30.7495	−	14.1147i	−0.904396	−	0.415137i
$35$		−	3.63153i		−	0.103758i
$36$		0			0
$37$	58.2834			1.57523			0.787614	−	0.616169i	$-0.211316\pi$
$37$	58.2834			1.57523			0.787614	+	0.616169i	$0.211316\pi$
$38$	−16.2745	+	35.4548i	−0.428276	+	0.933021i
$39$		0			0
$40$	−13.5832	−	47.2717i	−0.339579	−	1.18179i
$41$	5.33896			0.130219			0.0651093	−	0.997878i	$-0.479260\pi$
$41$	5.33896			0.130219			0.0651093	+	0.997878i	$0.479260\pi$
$42$		0			0
$43$		−	39.1818i		−	0.911204i	−0.890184	−	0.455602i	$-0.849424\pi$
$43$		−	39.1818i		−	0.911204i	0.890184	−	0.455602i	$-0.150576\pi$
$44$	−52.9567	+	45.5303i	−1.20356	+	1.03478i
$45$		0			0
$46$	−6.61653	+	14.4144i	−0.143838	+	0.313357i
$47$		−	11.1327i		−	0.236865i	−0.992962	−	0.118433i	$-0.962213\pi$
$47$		−	11.1327i		−	0.236865i	0.992962	−	0.118433i	$-0.0377870\pi$
$48$		0			0
$49$	48.6511			0.992880
$50$	23.2636	+	10.6785i	0.465271	+	0.213569i
$51$		0			0
$52$	4.65355	+	5.41259i	0.0894913	+	0.104088i
$53$	35.8770			0.676925			0.338462	−	0.940980i	$-0.390093\pi$
$53$	35.8770			0.676925			0.338462	+	0.940980i	$0.390093\pi$
$54$		0			0
$55$		−	107.343i		−	1.95169i
$56$	−4.54166	+	1.30501i	−0.0811011	+	0.0233038i
$57$		0			0
$58$	−11.5427	−	5.29836i	−0.199013	−	0.0913511i
$59$			24.1303i			0.408988i	0.978868	+	0.204494i	$0.0655549\pi$
$59$			24.1303i			0.408988i	−0.978868	+	0.204494i	$0.934445\pi$
$60$		0			0
$61$	75.8921			1.24413			0.622066	−	0.782965i	$-0.286294\pi$
$61$	75.8921			1.24413			0.622066	+	0.782965i	$0.286294\pi$
$62$	26.6441	−	58.0454i	0.429743	−	0.936216i
$63$		0			0
$64$	−54.2376	+	33.9747i	−0.847463	+	0.530855i
$65$	−10.9713			−0.168789
$66$		0			0
$67$			36.7426i			0.548396i	0.961673	+	0.274198i	$0.0884124\pi$
$67$			36.7426i			0.548396i	−0.961673	+	0.274198i	$0.911588\pi$
$68$	−44.1155	−	51.3112i	−0.648757	−	0.754576i
$69$		0			0
$70$	3.02994	−	6.60088i	0.0432849	−	0.0942983i
$71$			87.8370i			1.23714i	0.785730	+	0.618570i	$0.212288\pi$
$71$			87.8370i			1.23714i	−0.785730	+	0.618570i	$0.787712\pi$
$72$		0			0
$73$	−60.0423			−0.822498			−0.411249	−	0.911523i	$-0.634907\pi$
$73$	−60.0423			−0.822498			−0.411249	+	0.911523i	$0.634907\pi$
$74$	105.939	+	48.6283i	1.43161	+	0.657140i
$75$		0			0
$76$	−59.1629	+	50.8661i	−0.778459	+	0.669291i
$77$	−10.3130			−0.133936
$78$		0			0
$79$			37.1630i			0.470418i	0.971945	+	0.235209i	$0.0755775\pi$
$79$			37.1630i			0.470418i	−0.971945	+	0.235209i	$0.924423\pi$
$80$	14.7512	−	97.2567i	0.184391	−	1.21571i
$81$		0			0
$82$	9.70439	+	4.45452i	0.118346	+	0.0543234i
$83$		−	76.2427i		−	0.918587i	−0.888285	−	0.459294i	$-0.848103\pi$
$83$		−	76.2427i		−	0.918587i	0.888285	−	0.459294i	$-0.151897\pi$
$84$		0			0
$85$	104.007			1.22362
$86$	32.6910	−	71.2190i	0.380128	−	0.828127i
$87$		0			0
$88$	−134.245	+	38.5743i	−1.52551	+	0.438344i
$89$	−27.5873			−0.309969			−0.154985	−	0.987917i	$-0.549533\pi$
$89$	−27.5873			−0.309969			−0.154985	+	0.987917i	$0.549533\pi$
$90$		0			0
$91$			1.05407i			0.0115832i
$92$	−24.0531	+	20.6800i	−0.261447	+	0.224783i
$93$		0			0
$94$	9.28846	−	20.2354i	0.0988134	−	0.215270i
$95$		−	119.923i		−	1.26234i
$96$		0			0
$97$	−26.1171			−0.269248			−0.134624	−	0.990897i	$-0.542983\pi$
$97$	−26.1171			−0.269248			−0.134624	+	0.990897i	$0.542983\pi$
$98$	88.4309	+	40.5917i	0.902357	+	0.414201i
$99$		0			0
$100$	33.3757	+	38.8196i	0.333757	+	0.388196i
$101$	25.7663			0.255112			0.127556	−	0.991831i	$-0.459287\pi$
$101$	25.7663			0.255112			0.127556	+	0.991831i	$0.459287\pi$
$102$		0			0
$103$			19.6237i			0.190522i	0.995452	+	0.0952609i	$0.0303685\pi$
$103$			19.6237i			0.190522i	−0.995452	+	0.0952609i	$0.969631\pi$
$104$	3.94259	+	13.7209i	0.0379096	+	0.131931i
$105$		0			0
$106$	65.2121	+	29.9337i	0.615208	+	0.282394i
$107$		−	183.200i		−	1.71215i	−0.516850	−	0.856076i	$-0.672895\pi$
$107$		−	183.200i		−	1.71215i	0.516850	−	0.856076i	$-0.327105\pi$
$108$		0			0
$109$	100.841			0.925147			0.462573	−	0.886581i	$-0.346926\pi$
$109$	100.841			0.925147			0.462573	+	0.886581i	$0.346926\pi$
$110$	89.5608	−	195.112i	0.814189	−	1.77375i
$111$		0			0
$112$	−9.34400	−	1.41724i	−0.0834286	−	0.0126539i
$113$	18.2497			0.161502			0.0807508	−	0.996734i	$-0.474268\pi$
$113$	18.2497			0.161502			0.0807508	+	0.996734i	$0.474268\pi$
$114$		0			0
$115$		−	48.7555i		−	0.423961i
$116$	−16.5601	−	19.2612i	−0.142759	−	0.166045i
$117$		0			0
$118$	−20.1329	+	43.8606i	−0.170618	+	0.371700i
$119$		−	9.99258i		−	0.0839713i
$120$		0			0
$121$	−183.839			−1.51933
$122$	137.946	+	63.3200i	1.13070	+	0.519016i
$123$		0			0
$124$	96.8595	−	83.2763i	0.781125	−	0.671583i
$125$	75.0146			0.600117
$126$		0			0
$127$			164.386i			1.29438i	0.762331	+	0.647188i	$0.224055\pi$
$127$			164.386i			1.29438i	−0.762331	+	0.647188i	$0.775945\pi$
$128$	−126.932	+	16.5016i	−0.991655	+	0.128919i
$129$		0			0
$130$	−19.9420	−	9.15380i	−0.153400	−	0.0704139i
$131$			142.514i			1.08789i	0.839120	+	0.543947i	$0.183071\pi$
$131$			142.514i			1.08789i	−0.839120	+	0.543947i	$0.816929\pi$
$132$		0			0
$133$	−11.5217			−0.0866290
$134$	−30.6559	+	66.7853i	−0.228775	+	0.498398i
$135$		0			0
$136$	−37.3757	−	130.073i	−0.274821	−	0.956422i
$137$	6.16352			0.0449892			0.0224946	−	0.999747i	$-0.492839\pi$
$137$	6.16352			0.0449892			0.0224946	+	0.999747i	$0.492839\pi$
$138$		0			0
$139$		−	119.128i		−	0.857039i	−0.903533	−	0.428519i	$-0.859035\pi$
$139$		−	119.128i		−	0.857039i	0.903533	−	0.428519i	$-0.140965\pi$
$140$	11.0148	−	9.47011i	0.0786771	−	0.0676437i
$141$		0			0
$142$	−73.2861	+	159.657i	−0.516099	+	1.12435i
$143$			31.1569i			0.217880i
$144$		0			0
$145$	39.0423			0.269257
$146$	−109.136	−	50.0959i	−0.747509	−	0.343122i
$147$		0			0
$148$	151.988	+	176.779i	1.02695	+	1.19445i
$149$	206.730			1.38745			0.693726	−	0.720239i	$-0.255968\pi$
$149$	206.730			1.38745			0.693726	+	0.720239i	$0.255968\pi$
$150$		0			0
$151$			147.134i			0.974398i	0.873291	+	0.487199i	$0.161981\pi$
$151$			147.134i			0.974398i	−0.873291	+	0.487199i	$0.838019\pi$
$152$	−149.977	+	43.0949i	−0.986694	+	0.283519i
$153$		0			0
$154$	−18.7456	−	8.60461i	−0.121724	−	0.0558741i
$155$			196.334i			1.26667i
$156$		0			0
$157$	−62.8790			−0.400503			−0.200251	−	0.979745i	$-0.564176\pi$
$157$	−62.8790			−0.400503			−0.200251	+	0.979745i	$0.564176\pi$
$158$	−31.0067	+	67.5496i	−0.196245	+	0.427529i
$159$		0			0
$160$	107.958	−	164.472i	0.674738	−	1.02795i
$161$	−4.68422			−0.0290946
$162$		0			0
$163$			143.325i			0.879292i	0.898171	+	0.439646i	$0.144896\pi$
$163$			143.325i			0.879292i	−0.898171	+	0.439646i	$0.855104\pi$
$164$	13.9227	+	16.1936i	0.0848942	+	0.0987413i
$165$		0			0
$166$	63.6126	−	138.583i	0.383208	−	0.834838i
$167$		−	173.818i		−	1.04083i	−0.853915	−	0.520413i	$-0.825778\pi$
$167$		−	173.818i		−	1.04083i	0.853915	−	0.520413i	$-0.174222\pi$
$168$		0			0
$169$	−165.816			−0.981157
$170$	189.050	+	86.7777i	1.11206	+	0.510457i
$171$		0			0
$172$	118.842	−	102.176i	0.690942	−	0.594047i
$173$	251.612			1.45440			0.727201	−	0.686425i	$-0.240821\pi$
$173$	251.612			1.45440			0.727201	+	0.686425i	$0.240821\pi$
$174$		0			0
$175$			7.55991i			0.0431995i
$176$	−276.195	−	41.8915i	−1.56929	−	0.238020i
$177$		0			0
$178$	−50.1442	−	23.0172i	−0.281709	−	0.129310i
$179$		−	96.0059i		−	0.536346i	−0.963371	−	0.268173i	$-0.913580\pi$
$179$		−	96.0059i		−	0.536346i	0.963371	−	0.268173i	$-0.0864199\pi$
$180$		0			0
$181$	−328.757			−1.81634			−0.908170	−	0.418603i	$-0.862520\pi$
$181$	−328.757			−1.81634			−0.908170	+	0.418603i	$0.862520\pi$
$182$	−0.879458	+	1.91594i	−0.00483219	+	0.0105272i
$183$		0			0
$184$	−60.9745	+	17.5206i	−0.331383	+	0.0952206i
$185$	−358.330			−1.93692
$186$		0			0
$187$		−	295.366i		−	1.57950i
$188$	33.7664	−	29.0312i	0.179609	−	0.154421i
$189$		0			0
$190$	100.057	−	217.978i	0.526614	−	1.14725i
$191$		−	0.406356i		−	0.00212752i	−0.999999	−	0.00106376i	$-0.999661\pi$
$191$		−	0.406356i		−	0.00212752i	0.999999	−	0.00106376i	$-0.000338605\pi$
$192$		0			0
$193$	62.4459			0.323554			0.161777	−	0.986827i	$-0.448277\pi$
$193$	62.4459			0.323554			0.161777	+	0.986827i	$0.448277\pi$
$194$	−47.4718	−	21.7906i	−0.244700	−	0.112323i
$195$		0			0
$196$	126.870	+	147.563i	0.647294	+	0.752875i
$197$	−207.861			−1.05513			−0.527566	−	0.849514i	$-0.676895\pi$
$197$	−207.861			−1.05513			−0.527566	+	0.849514i	$0.676895\pi$
$198$		0			0
$199$		−	299.128i		−	1.50316i	−0.659643	−	0.751579i	$-0.729293\pi$
$199$		−	299.128i		−	1.50316i	0.659643	−	0.751579i	$-0.270707\pi$
$200$	28.2766	+	98.4073i	0.141383	+	0.492037i
$201$		0			0
$202$	46.8342	+	21.4979i	0.231852	+	0.106425i
$203$		−	3.75102i		−	0.0184779i
$204$		0			0
$205$	−32.8243			−0.160118
$206$	−16.3729	+	35.6692i	−0.0794802	+	0.173152i
$207$		0			0
$208$	−4.28163	+	28.2293i	−0.0205848	+	0.135718i
$209$	−340.564			−1.62949
$210$		0			0
$211$			163.672i			0.775697i	0.921723	+	0.387848i	$0.126782\pi$
$211$			163.672i			0.775697i	−0.921723	+	0.387848i	$0.873218\pi$
$212$	93.5581	+	108.818i	0.441312	+	0.513294i
$213$		0			0
$214$	152.852	−	332.995i	0.714261	−	1.55605i
$215$			240.892i			1.12043i
$216$		0			0
$217$	18.8629			0.0869257
$218$	183.294	+	84.1359i	0.840799	+	0.385945i
$219$		0			0
$220$	325.581	−	279.923i	1.47991	−	1.27238i
$221$	−30.1887			−0.136601
$222$		0			0
$223$			381.837i			1.71228i	0.516748	+	0.856138i	$0.327143\pi$
$223$			381.837i			1.71228i	−0.516748	+	0.856138i	$0.672857\pi$
$224$	−15.8017	−	10.3721i	−0.0705434	−	0.0463042i
$225$		0			0
$226$	33.1717	+	15.2265i	0.146777	+	0.0673739i
$227$		−	59.5216i		−	0.262210i	−0.991369	−	0.131105i	$-0.958148\pi$
$227$		−	59.5216i		−	0.262210i	0.991369	−	0.131105i	$-0.0418525\pi$
$228$		0			0
$229$	−128.873			−0.562765			−0.281383	−	0.959596i	$-0.590793\pi$
$229$	−128.873			−0.562765			−0.281383	+	0.959596i	$0.590793\pi$
$230$	40.6788	−	88.6208i	0.176864	−	0.385308i
$231$		0			0
$232$	−14.0301	−	48.8270i	−0.0604745	−	0.210461i
$233$	14.9939			0.0643513			0.0321757	−	0.999482i	$-0.489756\pi$
$233$	14.9939			0.0643513			0.0321757	+	0.999482i	$0.489756\pi$
$234$		0			0
$235$			68.4443i			0.291252i
$236$	−73.1895	+	62.9256i	−0.310125	+	0.266634i
$237$		0			0
$238$	8.33723	−	18.1631i	0.0350304	−	0.0763154i
$239$			364.012i			1.52306i	0.648128	+	0.761532i	$0.275552\pi$
$239$			364.012i			1.52306i	−0.648128	+	0.761532i	$0.724448\pi$
$240$		0			0
$241$	81.0471			0.336295			0.168147	−	0.985762i	$-0.446222\pi$
$241$	81.0471			0.336295			0.168147	+	0.985762i	$0.446222\pi$
$242$	−334.156	−	153.385i	−1.38081	−	0.633820i
$243$		0			0
$244$	197.907	+	230.188i	0.811095	+	0.943393i
$245$	−299.110			−1.22086
$246$		0			0
$247$			34.8082i			0.140924i
$248$	245.538	−	70.5536i	0.990073	−	0.284490i
$249$		0			0
$250$	136.351	+	62.5878i	0.545403	+	0.250351i
$251$			281.883i			1.12304i	0.827463	+	0.561520i	$0.189783\pi$
$251$			281.883i			1.12304i	−0.827463	+	0.561520i	$0.810217\pi$
$252$		0			0
$253$	−138.459			−0.547268
$254$	−137.154	+	298.797i	−0.539976	+	1.17636i
$255$		0			0
$256$	−244.486	−	75.9104i	−0.955025	−	0.296525i
$257$	75.3127			0.293046			0.146523	−	0.989207i	$-0.453192\pi$
$257$	75.3127			0.293046			0.146523	+	0.989207i	$0.453192\pi$
$258$		0			0
$259$			34.4268i			0.132922i
$260$	−28.6103	−	33.2769i	−0.110040	−	0.127988i
$261$		0			0
$262$	−118.905	+	259.041i	−0.453838	+	0.988708i
$263$		−	122.299i		−	0.465017i	−0.972594	−	0.232508i	$-0.925307\pi$
$263$		−	122.299i		−	0.465017i	0.972594	−	0.232508i	$-0.0746933\pi$
$264$		0			0
$265$	−220.574			−0.832355
$266$	−20.9424	−	9.61301i	−0.0787309	−	0.0361391i
$267$		0			0
$268$	−111.444	+	95.8152i	−0.415835	+	0.357520i
$269$	280.452			1.04257			0.521287	−	0.853382i	$-0.325452\pi$
$269$	280.452			1.04257			0.521287	+	0.853382i	$0.325452\pi$
$270$		0			0
$271$		−	81.4468i		−	0.300542i	−0.988645	−	0.150271i	$-0.951985\pi$
$271$		−	81.4468i		−	0.300542i	0.988645	−	0.150271i	$-0.0480146\pi$
$272$	40.5897	−	267.613i	0.149227	−	0.983871i
$273$		0			0
$274$	11.2032	+	5.14249i	0.0408874	+	0.0187682i
$275$			223.460i			0.812582i
$276$		0			0
$277$	−449.723			−1.62355			−0.811774	−	0.583972i	$-0.801498\pi$
$277$	−449.723			−1.62355			−0.811774	+	0.583972i	$0.801498\pi$
$278$	99.3939	−	216.534i	0.357532	−	0.778901i
$279$		0			0
$280$	27.9224	−	8.02330i	0.0997229	−	0.0286546i
$281$	75.7297			0.269501			0.134750	−	0.990880i	$-0.456977\pi$
$281$	75.7297			0.269501			0.134750	+	0.990880i	$0.456977\pi$
$282$		0			0
$283$			371.884i			1.31408i	0.753856	+	0.657039i	$0.228191\pi$
$283$			371.884i			1.31408i	−0.753856	+	0.657039i	$0.771809\pi$
$284$	−266.418	+	229.056i	−0.938091	+	0.806537i
$285$		0			0
$286$	−25.9955	+	56.6325i	−0.0908934	+	0.198016i
$287$			3.15361i			0.0109882i
$288$		0			0
$289$	−2.81196			−0.00972996
$290$	70.9655	+	32.5747i	0.244709	+	0.112326i
$291$		0			0
$292$	−156.575	−	182.114i	−0.536216	−	0.623678i
$293$	132.789			0.453206			0.226603	−	0.973987i	$-0.427238\pi$
$293$	132.789			0.453206			0.226603	+	0.973987i	$0.427238\pi$
$294$		0			0
$295$		−	148.354i		−	0.502897i
$296$	128.768	+	448.134i	0.435027	+	1.51397i
$297$		0			0
$298$	375.765	+	172.484i	1.26096	+	0.578806i
$299$			14.1516i			0.0473297i
$300$		0			0
$301$	23.1439			0.0768899
$302$	−122.760	+	267.439i	−0.406491	+	0.885560i
$303$		0			0
$304$	−308.563	−	46.8008i	−1.01501	−	0.153950i
$305$	−466.589			−1.52980
$306$		0			0
$307$			336.514i			1.09614i	0.836434	+	0.548068i	$0.184637\pi$
$307$			336.514i			1.09614i	−0.836434	+	0.548068i	$0.815363\pi$
$308$	−26.8938	−	31.2805i	−0.0873175	−	0.101560i
$309$		0			0
$310$	−163.809	+	356.867i	−0.528417	+	1.15118i
$311$		−	351.267i		−	1.12948i	−0.825270	−	0.564738i	$-0.808977\pi$
$311$		−	351.267i		−	1.12948i	0.825270	−	0.564738i	$-0.191023\pi$
$312$		0			0
$313$	190.860			0.609776			0.304888	−	0.952388i	$-0.401381\pi$
$313$	190.860			0.609776			0.304888	+	0.952388i	$0.401381\pi$
$314$	−114.292	−	52.4626i	−0.363988	−	0.167078i
$315$		0			0
$316$	−112.719	+	96.9117i	−0.356706	+	0.306683i
$317$	405.594			1.27948			0.639738	−	0.768593i	$-0.279043\pi$
$317$	405.594			1.27948			0.639738	+	0.768593i	$0.279043\pi$
$318$		0			0
$319$		−	110.875i		−	0.347570i
$320$	333.456	−	208.879i	1.04205	−	0.652746i
$321$		0			0
$322$	−8.51430	−	3.90825i	−0.0264419	−	0.0121374i
$323$		−	329.981i		−	1.02161i
$324$		0			0
$325$	22.8393			0.0702749
$326$	−119.582	+	260.515i	−0.366815	+	0.799125i
$327$		0			0
$328$	11.7956	+	41.0506i	0.0359622	+	0.125154i
$329$	6.57584			0.0199874
$330$		0			0
$331$			443.525i			1.33996i	0.742381	+	0.669978i	$0.233696\pi$
$331$			443.525i			1.33996i	−0.742381	+	0.669978i	$0.766304\pi$
$332$	231.251	−	198.822i	0.696541	−	0.598860i
$333$		0			0
$334$	145.024	−	315.941i	0.434203	−	0.945931i
$335$		−	225.896i		−	0.674315i
$336$		0			0
$337$	508.479			1.50884			0.754420	−	0.656392i	$-0.227918\pi$
$337$	508.479			1.50884			0.754420	+	0.656392i	$0.227918\pi$
$338$	−301.396	−	138.347i	−0.891703	−	0.409310i
$339$		0			0
$340$	271.225	+	315.464i	0.797719	+	0.927836i
$341$	557.560			1.63507
$342$		0			0
$343$			57.6805i			0.168165i
$344$	301.264	−	86.5659i	0.875767	−	0.251645i
$345$		0			0
$346$	457.343	+	209.930i	1.32180	+	0.606735i
$347$		−	569.006i		−	1.63979i	−0.572517	−	0.819893i	$-0.694033\pi$
$347$		−	569.006i		−	1.63979i	0.572517	−	0.819893i	$-0.305967\pi$
$348$		0			0
$349$	413.802			1.18568			0.592840	−	0.805320i	$-0.298007\pi$
$349$	413.802			1.18568			0.592840	+	0.805320i	$0.298007\pi$
$350$	−6.30755	+	13.7413i	−0.0180216	+	0.0392609i
$351$		0			0
$352$	−467.076	−	306.586i	−1.32692	−	0.870982i
$353$	−124.614			−0.353014			−0.176507	−	0.984299i	$-0.556480\pi$
$353$	−124.614			−0.353014			−0.176507	+	0.984299i	$0.556480\pi$
$354$		0			0
$355$		−	540.027i		−	1.52120i
$356$	−71.9406	−	83.6748i	−0.202080	−	0.235042i
$357$		0			0
$358$	80.1018	−	174.506i	0.223748	−	0.487446i
$359$		−	303.196i		−	0.844557i	−0.906466	−	0.422278i	$-0.861230\pi$
$359$		−	303.196i		−	0.844557i	0.906466	−	0.422278i	$-0.138770\pi$
$360$		0			0
$361$	−19.4752			−0.0539480
$362$	−597.568	−	274.296i	−1.65074	−	0.757724i
$363$		0			0
$364$	−3.19710	+	2.74875i	−0.00878325	+	0.00755152i
$365$	369.144			1.01135
$366$		0			0
$367$		−	710.800i		−	1.93678i	−0.249433	−	0.968392i	$-0.580244\pi$
$367$		−	710.800i		−	1.93678i	0.249433	−	0.968392i	$-0.419756\pi$
$368$	−125.449	−	19.0273i	−0.340894	−	0.0517045i
$369$		0			0
$370$	−651.321	−	298.970i	−1.76033	−	0.808027i
$371$			21.1918i			0.0571208i
$372$		0			0
$373$	−333.481			−0.894051			−0.447025	−	0.894521i	$-0.647517\pi$
$373$	−333.481			−0.894051			−0.447025	+	0.894521i	$0.647517\pi$
$374$	246.437	−	536.874i	0.658921	−	1.43549i
$375$		0			0
$376$	85.5977	−	24.5959i	0.227653	−	0.0654146i
$377$	−11.3323			−0.0300590
$378$		0			0
$379$		−	662.686i		−	1.74851i	−0.485465	−	0.874256i	$-0.661350\pi$
$379$		−	662.686i		−	1.74851i	0.485465	−	0.874256i	$-0.338650\pi$
$380$	363.737	−	312.728i	0.957203	−	0.822968i
$381$		0			0
$382$	0.339040	−	0.738615i	0.000887539	−	0.00193355i
$383$			80.7145i			0.210743i	0.994433	+	0.105371i	$0.0336031\pi$
$383$			80.7145i			0.210743i	−0.994433	+	0.105371i	$0.966397\pi$
$384$		0			0
$385$	63.4052			0.164689
$386$	113.505	+	52.1013i	0.294055	+	0.134977i
$387$		0			0
$388$	−68.1066	−	79.2155i	−0.175533	−	0.204164i
$389$	692.013			1.77895			0.889476	−	0.456981i	$-0.151069\pi$
$389$	692.013			1.77895			0.889476	+	0.456981i	$0.151069\pi$
$390$		0			0
$391$		−	134.156i		−	0.343111i
$392$	107.487	+	374.072i	0.274201	+	0.954266i
$393$		0			0
$394$	−377.819	−	173.427i	−0.958933	−	0.440170i
$395$		−	228.481i		−	0.578432i
$396$		0			0
$397$	657.713			1.65671			0.828354	−	0.560206i	$-0.189278\pi$
$397$	657.713			1.65671			0.828354	+	0.560206i	$0.189278\pi$
$398$	249.576	−	543.713i	0.627074	−	1.36611i
$399$		0			0
$400$	−30.7082	+	202.463i	−0.0767706	+	0.506158i
$401$	−592.866			−1.47847			−0.739235	−	0.673448i	$-0.764813\pi$
$401$	−592.866			−1.47847			−0.739235	+	0.673448i	$0.764813\pi$
$402$		0			0
$403$		−	56.9869i		−	0.141407i
$404$	67.1918	+	78.1515i	0.166316	+	0.193444i
$405$		0			0
$406$	3.12963	−	6.81806i	0.00770846	−	0.0167933i
$407$			1017.61i			2.50026i
$408$		0			0
$409$	323.188			0.790191			0.395095	−	0.918640i	$-0.370712\pi$
$409$	323.188			0.790191			0.395095	+	0.918640i	$0.370712\pi$
$410$	−59.6632	−	27.3867i	−0.145520	−	0.0667968i
$411$		0			0
$412$	−59.5207	+	51.1737i	−0.144468	+	0.124208i
$413$	−14.2533			−0.0345115
$414$		0			0
$415$			468.745i			1.12951i
$416$	−31.3354	+	47.7388i	−0.0753256	+	0.114757i
$417$		0			0
$418$	−619.028	−	284.147i	−1.48093	−	0.679777i
$419$			257.203i			0.613849i	0.951734	+	0.306924i	$0.0992998\pi$
$419$			257.203i			0.613849i	−0.951734	+	0.306924i	$0.900700\pi$
$420$		0			0
$421$	−83.9811			−0.199480			−0.0997400	−	0.995014i	$-0.531801\pi$
$421$	−83.9811			−0.199480			−0.0997400	+	0.995014i	$0.531801\pi$
$422$	−136.559	+	297.499i	−0.323598	+	0.704975i
$423$		0			0
$424$	79.2646	+	275.854i	0.186945	+	0.650599i
$425$	−216.516			−0.509450
$426$		0			0
$427$			44.8279i			0.104983i
$428$	555.664	−	477.740i	1.29828	−	1.11621i
$429$		0			0
$430$	−200.986	+	437.859i	−0.467410	+	1.01828i
$431$		−	144.348i		−	0.334914i	−0.985879	−	0.167457i	$-0.946445\pi$
$431$		−	144.348i		−	0.334914i	0.985879	−	0.167457i	$-0.0535555\pi$
$432$		0			0
$433$	395.353			0.913057			0.456528	−	0.889709i	$-0.349093\pi$
$433$	395.353			0.913057			0.456528	+	0.889709i	$0.349093\pi$
$434$	34.2862	+	15.7381i	0.0790005	+	0.0362629i
$435$		0			0
$436$	262.968	+	305.860i	0.603137	+	0.701514i
$437$	−154.685			−0.353971
$438$		0			0
$439$		−	224.908i		−	0.512320i	−0.966634	−	0.256160i	$-0.917543\pi$
$439$		−	224.908i		−	0.512320i	0.966634	−	0.256160i	$-0.0824574\pi$
$440$	825.346	−	237.157i	1.87579	−	0.538994i
$441$		0			0
$442$	−54.8727	−	25.1877i	−0.124146	−	0.0569858i
$443$		−	426.297i		−	0.962296i	−0.876639	−	0.481148i	$-0.840220\pi$
$443$		−	426.297i		−	0.962296i	0.876639	−	0.481148i	$-0.159780\pi$
$444$		0			0
$445$	169.608			0.381142
$446$	−318.583	+	694.049i	−0.714312	+	1.55616i
$447$		0			0
$448$	−20.0682	−	32.0370i	−0.0447950	−	0.0715113i
$449$	−406.744			−0.905888			−0.452944	−	0.891539i	$-0.649626\pi$
$449$	−406.744			−0.905888			−0.452944	+	0.891539i	$0.649626\pi$
$450$		0			0
$451$			93.2163i			0.206688i
$452$	47.5905	+	55.3530i	0.105289	+	0.122462i
$453$		0			0
$454$	49.6614	−	108.190i	0.109386	−	0.238303i
$455$		−	6.48051i		−	0.0142429i
$456$		0			0
$457$	319.200			0.698468			0.349234	−	0.937035i	$-0.386442\pi$
$457$	319.200			0.698468			0.349234	+	0.937035i	$0.386442\pi$
$458$	−234.247	−	107.524i	−0.511457	−	0.234770i
$459$		0			0
$460$	147.880	−	127.142i	0.321479	−	0.276396i
$461$	−587.776			−1.27500			−0.637501	−	0.770450i	$-0.720032\pi$
$461$	−587.776			−1.27500			−0.637501	+	0.770450i	$0.720032\pi$
$462$		0			0
$463$		−	265.683i		−	0.573829i	−0.957956	−	0.286914i	$-0.907370\pi$
$463$		−	265.683i		−	0.573829i	0.957956	−	0.286914i	$-0.0926296\pi$
$464$	15.2366	−	100.457i	0.0328375	−	0.216501i
$465$		0			0
$466$	27.2537	+	12.5100i	0.0584843	+	0.0268455i
$467$			794.598i			1.70149i	0.525575	+	0.850747i	$0.323850\pi$
$467$			794.598i			1.70149i	−0.525575	+	0.850747i	$0.676150\pi$
$468$		0			0
$469$	−21.7031			−0.0462752
$470$	−57.1060	+	124.408i	−0.121502	+	0.264698i
$471$		0			0
$472$	−185.535	+	53.3121i	−0.393082	+	0.112949i
$473$	684.099			1.44630
$474$		0			0
$475$			249.648i			0.525574i
$476$	30.3084	−	26.0581i	0.0636732	−	0.0547439i
$477$		0			0
$478$	−303.711	+	661.649i	−0.635378	+	1.38420i
$479$		−	661.601i		−	1.38121i	−0.723230	−	0.690607i	$-0.757344\pi$
$479$		−	661.601i		−	1.38121i	0.723230	−	0.690607i	$-0.242656\pi$
$480$		0			0
$481$	104.007			0.216231
$482$	147.316	+	67.6210i	0.305634	+	0.140293i
$483$		0			0
$484$	−479.405	−	557.601i	−0.990506	−	1.15207i
$485$	160.569			0.331071
$486$		0			0
$487$			57.1525i			0.117356i	0.998277	+	0.0586781i	$0.0186886\pi$
$487$			57.1525i			0.117356i	−0.998277	+	0.0586781i	$0.981311\pi$
$488$	167.672	+	583.525i	0.343589	+	1.19575i
$489$		0			0
$490$	−543.679	−	249.560i	−1.10955	−	0.509306i
$491$		−	56.1878i		−	0.114435i	−0.998362	−	0.0572177i	$-0.981777\pi$
$491$		−	56.1878i		−	0.114435i	0.998362	−	0.0572177i	$-0.0182229\pi$
$492$		0			0
$493$	107.429			0.217910
$494$	−29.0420	+	63.2694i	−0.0587895	+	0.128076i
$495$		0			0
$496$	505.170	+	76.6208i	1.01849	+	0.154477i
$497$	−51.8835			−0.104393
$498$		0			0
$499$		−	603.013i		−	1.20844i	−0.796816	−	0.604222i	$-0.793484\pi$
$499$		−	603.013i		−	1.20844i	0.796816	−	0.604222i	$-0.206516\pi$
$500$	195.619	+	227.526i	0.391238	+	0.455053i
$501$		0			0
$502$	−235.187	+	512.366i	−0.468500	+	1.02065i
$503$		−	549.354i		−	1.09216i	−0.837734	−	0.546078i	$-0.816120\pi$
$503$		−	549.354i		−	1.09216i	0.837734	−	0.546078i	$-0.183880\pi$
$504$		0			0
$505$	−158.413			−0.313688
$506$	−251.671	−	115.522i	−0.497373	−	0.228305i
$507$		0			0
$508$	−498.597	+	428.676i	−0.981491	+	0.843850i
$509$	238.928			0.469407			0.234704	−	0.972067i	$-0.424588\pi$
$509$	238.928			0.469407			0.234704	+	0.972067i	$0.424588\pi$
$510$		0			0
$511$		−	35.4658i		−	0.0694046i
$512$	−381.057	−	341.964i	−0.744252	−	0.667899i
$513$		0			0
$514$	136.893	+	62.8366i	0.266328	+	0.122250i
$515$		−	120.648i		−	0.234268i
$516$		0			0
$517$	194.372			0.375962
$518$	−28.7238	+	62.5761i	−0.0554513	+	0.120803i
$519$		0			0
$520$	−24.2393	−	84.3568i	−0.0466141	−	0.162225i
$521$	−567.711			−1.08966			−0.544828	−	0.838548i	$-0.683405\pi$
$521$	−567.711			−1.08966			−0.544828	+	0.838548i	$0.683405\pi$
$522$		0			0
$523$		−	941.999i		−	1.80114i	−0.434706	−	0.900572i	$-0.643148\pi$
$523$		−	941.999i		−	1.80114i	0.434706	−	0.900572i	$-0.356852\pi$
$524$	−432.259	+	371.640i	−0.824921	+	0.709237i
$525$		0			0
$526$	102.040	−	222.298i	0.193992	−	0.422620i
$527$			540.234i			1.02511i
$528$		0			0
$529$	466.111			0.881118
$530$	−400.928	−	184.034i	−0.756468	−	0.347235i
$531$		0			0
$532$	−30.0456	−	34.9463i	−0.0564766	−	0.0656885i
$533$	9.52743			0.0178751
$534$		0			0
$535$			1126.33i			2.10528i
$536$	−282.509	+	81.1769i	−0.527069	+	0.151449i
$537$		0			0
$538$	509.766	+	233.993i	0.947520	+	0.434932i
$539$			849.430i			1.57594i
$540$		0			0
$541$	−242.245			−0.447772			−0.223886	−	0.974615i	$-0.571874\pi$
$541$	−242.245			−0.447772			−0.223886	+	0.974615i	$0.571874\pi$
$542$	67.9545	−	148.042i	0.125377	−	0.273141i
$543$		0			0
$544$	297.059	−	452.562i	0.546064	−	0.831916i
$545$	−619.977			−1.13757
$546$		0			0
$547$		−	196.880i		−	0.359927i	−0.983673	−	0.179964i	$-0.942402\pi$
$547$		−	196.880i		−	0.359927i	0.983673	−	0.179964i	$-0.0575980\pi$
$548$	16.0729	+	18.6945i	0.0293301	+	0.0341141i
$549$		0			0
$550$	−186.442	+	406.173i	−0.338986	+	0.738497i
$551$		−	123.868i		−	0.224807i
$552$		0			0
$553$	−21.9514			−0.0396952
$554$	−817.441	−	375.223i	−1.47553	−	0.677297i
$555$		0			0
$556$	361.328	−	310.657i	0.649870	−	0.558735i
$557$	958.121			1.72015			0.860073	−	0.510171i	$-0.170418\pi$
$557$	958.121			1.72015			0.860073	+	0.510171i	$0.170418\pi$
$558$		0			0
$559$		−	69.9202i		−	0.125081i
$560$	57.4475	+	8.71325i	0.102585	+	0.0155594i
$561$		0			0
$562$	137.651	+	63.1845i	0.244930	+	0.112428i
$563$		−	191.419i		−	0.339999i	−0.985444	−	0.169999i	$-0.945623\pi$
$563$		−	191.419i		−	0.339999i	0.985444	−	0.169999i	$-0.0543766\pi$
$564$		0			0
$565$	−112.200			−0.198584
$566$	−310.279	+	675.957i	−0.548196	+	1.19427i
$567$		0			0
$568$	−675.368	+	194.062i	−1.18903	+	0.341658i
$569$	−456.430			−0.802162			−0.401081	−	0.916043i	$-0.631365\pi$
$569$	−456.430			−0.802162			−0.401081	+	0.916043i	$0.631365\pi$
$570$		0			0
$571$			973.140i			1.70427i	0.523320	+	0.852136i	$0.324693\pi$
$571$			973.140i			1.70427i	−0.523320	+	0.852136i	$0.675307\pi$
$572$	−94.5018	+	81.2492i	−0.165213	+	0.142044i
$573$		0			0
$574$	−2.63120	+	5.73219i	−0.00458396	+	0.00998639i
$575$			101.496i			0.176515i
$576$		0			0
$577$	138.527			0.240081			0.120040	−	0.992769i	$-0.461698\pi$
$577$	138.527			0.240081			0.120040	+	0.992769i	$0.461698\pi$
$578$	−5.11118	−	2.34614i	−0.00884286	−	0.00405906i
$579$		0			0
$580$	101.812	+	118.419i	0.175539	+	0.204171i
$581$	45.0350			0.0775129
$582$		0			0
$583$			626.400i			1.07444i
$584$	−132.654	−	461.658i	−0.227147	−	0.790510i
$585$		0			0
$586$	241.365	+	110.792i	0.411886	+	0.189064i
$587$			716.847i			1.22120i	0.791937	+	0.610602i	$0.209073\pi$
$587$			716.847i			1.22120i	−0.791937	+	0.610602i	$0.790927\pi$
$588$		0			0
$589$	622.902			1.05756
$590$	123.778	−	269.657i	0.209794	−	0.457046i
$591$		0			0
$592$	−139.841	+	921.990i	−0.236218	+	1.55742i
$593$	542.129			0.914214			0.457107	−	0.889412i	$-0.348886\pi$
$593$	542.129			0.914214			0.457107	+	0.889412i	$0.348886\pi$
$594$		0			0
$595$			61.4350i			0.103252i
$596$	539.100	+	627.033i	0.904531	+	1.05207i
$597$		0			0
$598$	−11.8073	+	25.7227i	−0.0197446	+	0.0430145i
$599$			283.510i			0.473305i	0.971594	+	0.236653i	$0.0760504\pi$
$599$			283.510i			0.473305i	−0.971594	+	0.236653i	$0.923950\pi$
$600$		0			0
$601$	−754.848			−1.25599			−0.627993	−	0.778219i	$-0.716123\pi$
$601$	−754.848			−1.25599			−0.627993	+	0.778219i	$0.716123\pi$
$602$	42.0676	+	19.3099i	0.0698797	+	0.0320763i
$603$		0			0
$604$	−446.272	+	383.688i	−0.738860	+	0.635245i
$605$	1130.25			1.86819
$606$		0			0
$607$		−	89.1690i		−	0.146901i	−0.997299	−	0.0734506i	$-0.976599\pi$
$607$		−	89.1690i		−	0.146901i	0.997299	−	0.0734506i	$-0.0234011\pi$
$608$	−521.814	−	342.515i	−0.858247	−	0.563348i
$609$		0			0
$610$	−848.098	−	389.295i	−1.39032	−	0.638189i
$611$		−	19.8664i		−	0.0325145i
$612$		0			0
$613$	−316.779			−0.516769			−0.258385	−	0.966042i	$-0.583190\pi$
$613$	−316.779			−0.516769			−0.258385	+	0.966042i	$0.583190\pi$
$614$	−280.768	+	611.667i	−0.457277	+	0.996200i
$615$		0			0
$616$	−22.7851	−	79.2957i	−0.0369887	−	0.128727i
$617$	−1069.87			−1.73398			−0.866992	−	0.498323i	$-0.833949\pi$
$617$	−1069.87			−1.73398			−0.866992	+	0.498323i	$0.833949\pi$
$618$		0			0
$619$			668.043i			1.07923i	0.841912	+	0.539615i	$0.181430\pi$
$619$			668.043i			1.07923i	−0.841912	+	0.539615i	$0.818570\pi$
$620$	−595.498	+	511.988i	−0.960481	+	0.825787i
$621$		0			0
$622$	293.077	−	638.483i	0.471185	−	1.02650i
$623$		−	16.2952i		−	0.0261561i
$624$		0			0
$625$	−781.161			−1.24986
$626$	346.917	+	159.242i	0.554181	+	0.254381i
$627$		0			0
$628$	−163.972	−	190.718i	−0.261102	−	0.303691i
$629$	−985.986			−1.56755
$630$		0			0
$631$			150.631i			0.238718i	0.992851	+	0.119359i	$0.0380839\pi$
$631$			150.631i			0.238718i	−0.992851	+	0.119359i	$0.961916\pi$
$632$	−285.742	+	82.1059i	−0.452123	+	0.129914i
$633$		0			0
$634$	737.230	+	338.404i	1.16282	+	0.533761i
$635$		−	1010.65i		−	1.59158i
$636$		0			0
$637$	86.8184			0.136293
$638$	92.5075	−	201.532i	0.144996	−	0.315881i
$639$		0			0
$640$	780.385	−	101.453i	1.21935	−	0.158520i
$641$	−703.042			−1.09679			−0.548395	−	0.836220i	$-0.684761\pi$
$641$	−703.042			−1.09679			−0.548395	+	0.836220i	$0.684761\pi$
$642$		0			0
$643$		−	856.853i		−	1.33259i	−0.745690	−	0.666293i	$-0.767880\pi$
$643$		−	856.853i		−	1.33259i	0.745690	−	0.666293i	$-0.232120\pi$
$644$	−12.2153	−	14.2077i	−0.0189678	−	0.0220616i
$645$		0			0
$646$	275.317	−	599.792i	0.426188	−	0.928470i
$647$			156.257i			0.241510i	0.992682	+	0.120755i	$0.0385316\pi$
$647$			156.257i			0.241510i	−0.992682	+	0.120755i	$0.961468\pi$
$648$		0			0
$649$	−421.306			−0.649162
$650$	41.5141	+	19.0558i	0.0638678	+	0.0293167i
$651$		0			0
$652$	−434.717	+	373.754i	−0.666744	+	0.573242i
$653$	883.545			1.35306			0.676528	−	0.736417i	$-0.263484\pi$
$653$	883.545			1.35306			0.676528	+	0.736417i	$0.263484\pi$
$654$		0			0
$655$		−	876.185i		−	1.33769i
$656$	−12.8099	+	84.4574i	−0.0195273	+	0.128746i
$657$		0			0
$658$	11.9526	+	5.48650i	0.0181651	+	0.00833815i
$659$		−	438.246i		−	0.665017i	−0.943100	−	0.332509i	$-0.892105\pi$
$659$		−	438.246i		−	0.665017i	0.943100	−	0.332509i	$-0.107895\pi$
$660$		0			0
$661$	−467.848			−0.707788			−0.353894	−	0.935285i	$-0.615143\pi$
$661$	−467.848			−0.707788			−0.353894	+	0.935285i	$0.615143\pi$
$662$	−370.052	+	806.176i	−0.558991	+	1.21779i
$663$		0			0
$664$	586.221	−	168.446i	0.882863	−	0.253684i
$665$	70.8359			0.106520
$666$		0			0
$667$		−	50.3597i		−	0.0755018i
$668$	527.206	−	453.273i	0.789231	−	0.678552i
$669$		0			0
$670$	188.474	−	410.600i	0.281305	−	0.612836i
$671$			1325.05i			1.97474i
$672$		0			0
$673$	−546.603			−0.812189			−0.406094	−	0.913831i	$-0.633110\pi$
$673$	−546.603			−0.812189			−0.406094	+	0.913831i	$0.633110\pi$
$674$	924.240	+	424.246i	1.37128	+	0.629444i
$675$		0			0
$676$	−432.405	−	502.934i	−0.639652	−	0.743986i
$677$	−455.212			−0.672396			−0.336198	−	0.941791i	$-0.609141\pi$
$677$	−455.212			−0.672396			−0.336198	+	0.941791i	$0.609141\pi$
$678$		0			0
$679$		−	15.4268i		−	0.0227199i
$680$	229.788	+	799.699i	0.337923	+	1.17603i
$681$		0			0
$682$	1013.45	+	465.196i	1.48600	+	0.682105i
$683$			123.214i			0.180400i	0.995924	+	0.0902002i	$0.0287507\pi$
$683$			123.214i			0.180400i	−0.995924	+	0.0902002i	$0.971249\pi$
$684$		0			0
$685$	−37.8937			−0.0553193
$686$	−48.1253	+	104.843i	−0.0701535	+	0.152833i
$687$		0			0
$688$	619.819	+	94.0101i	0.900900	+	0.136643i
$689$	64.0229			0.0929215
$690$		0			0
$691$		−	188.593i		−	0.272928i	−0.990645	−	0.136464i	$-0.956426\pi$
$691$		−	188.593i		−	0.272928i	0.990645	−	0.136464i	$-0.0435737\pi$
$692$	656.139	+	763.162i	0.948177	+	1.10283i
$693$		0			0
$694$	474.746	−	1034.26i	0.684071	−	1.49028i
$695$			732.409i			1.05383i
$696$		0			0
$697$	−90.3197			−0.129584
$698$	752.150	+	345.253i	1.07758	+	0.494631i
$699$		0			0
$700$	−22.9299	+	19.7143i	−0.0327570	+	0.0281633i
$701$	−810.064			−1.15558			−0.577792	−	0.816184i	$-0.696085\pi$
$701$	−810.064			−1.15558			−0.577792	+	0.816184i	$0.696085\pi$
$702$		0			0
$703$			1136.86i			1.61716i
$704$	−593.186	−	946.969i	−0.842594	−	1.34513i
$705$		0			0
$706$	−226.505	−	103.971i	−0.320829	−	0.147267i
$707$			15.2196i			0.0215270i
$708$		0			0
$709$	1303.64			1.83870			0.919349	−	0.393442i	$-0.128716\pi$
$709$	1303.64			1.83870			0.919349	+	0.393442i	$0.128716\pi$
$710$	450.568	−	981.583i	0.634602	−	1.38251i
$711$		0			0
$712$	−60.9497	−	212.115i	−0.0856035	−	0.297914i
$713$	253.246			0.355183
$714$		0			0
$715$		−	191.554i		−	0.267908i
$716$	291.195	−	250.359i	0.406697	−	0.349663i
$717$		0			0
$718$	252.969	−	551.106i	0.352325	−	0.767557i
$719$		−	788.981i		−	1.09733i	−0.836042	−	0.548666i	$-0.815136\pi$
$719$		−	788.981i		−	1.09733i	0.836042	−	0.548666i	$-0.184864\pi$
$720$		0			0
$721$	−11.5913			−0.0160768
$722$	−35.3993	−	16.2490i	−0.0490294	−	0.0225056i
$723$		0			0
$724$	−857.315	−	997.152i	−1.18414	−	1.37728i
$725$	−81.2759			−0.112105
$726$		0			0
$727$		−	268.671i		−	0.369561i	−0.982780	−	0.184780i	$-0.940843\pi$
$727$		−	268.671i		−	0.369561i	0.982780	−	0.184780i	$-0.0591574\pi$
$728$	−8.10464	+	2.32881i	−0.0111327	+	0.00319891i
$729$		0			0
$730$	670.977	+	307.992i	0.919146	+	0.421907i
$731$			662.842i			0.906760i
$732$		0			0
$733$	73.6686			0.100503			0.0502514	−	0.998737i	$-0.483998\pi$
$733$	73.6686			0.100503			0.0502514	+	0.998737i	$0.483998\pi$
$734$	593.050	−	1291.99i	0.807971	−	1.76020i
$735$		0			0
$736$	−212.148	−	139.252i	−0.288244	−	0.189202i
$737$	−641.512			−0.870437
$738$		0			0
$739$			448.249i			0.606562i	0.952901	+	0.303281i	$0.0980820\pi$
$739$			448.249i			0.606562i	−0.952901	+	0.303281i	$0.901918\pi$
$740$	−934.433	−	1086.85i	−1.26275	−	1.46871i
$741$		0			0
$742$	−17.6812	+	38.5194i	−0.0238292	+	0.0519130i
$743$		−	758.179i		−	1.02043i	−0.860047	−	0.510215i	$-0.829566\pi$
$743$		−	758.179i		−	1.02043i	0.860047	−	0.510215i	$-0.170434\pi$
$744$		0			0
$745$	−1270.99			−1.70603
$746$	−606.153	−	278.237i	−0.812538	−	0.372972i
$747$		0			0
$748$	895.874	−	770.240i	1.19769	−	1.02973i
$749$	108.213			0.144476
$750$		0			0
$751$		−	1318.18i		−	1.75524i	−0.479361	−	0.877618i	$-0.659132\pi$
$751$		−	1318.18i		−	1.75524i	0.479361	−	0.877618i	$-0.340868\pi$
$752$	176.109	+	26.7110i	0.234187	+	0.0355199i
$753$		0			0
$754$	−20.5981	−	9.45498i	−0.0273185	−	0.0125398i
$755$		−	904.589i		−	1.19813i
$756$		0			0
$757$	587.874			0.776583			0.388292	−	0.921537i	$-0.373065\pi$
$757$	587.874			0.776583			0.388292	+	0.921537i	$0.373065\pi$
$758$	552.907	−	1204.54i	0.729429	−	1.58910i
$759$		0			0
$760$	922.071	−	264.950i	1.21325	−	0.348619i
$761$	376.992			0.495391			0.247695	−	0.968838i	$-0.420327\pi$
$761$	376.992			0.495391			0.247695	+	0.968838i	$0.420327\pi$
$762$		0			0
$763$			59.5647i			0.0780664i
$764$	1.23252	−	1.05967i	0.00161324	−	0.00138701i
$765$		0			0
$766$	−67.3435	+	146.711i	−0.0879158	+	0.191529i
$767$			43.0607i			0.0561418i
$768$		0			0
$769$	−1287.88			−1.67474			−0.837372	−	0.546633i	$-0.815909\pi$
$769$	−1287.88			−1.67474			−0.837372	+	0.546633i	$0.815909\pi$
$770$	115.249	+	52.9017i	0.149674	+	0.0687035i
$771$		0			0
$772$	162.843	+	189.404i	0.210937	+	0.245343i
$773$	778.578			1.00722			0.503608	−	0.863932i	$-0.332006\pi$
$773$	778.578			1.00722			0.503608	+	0.863932i	$0.332006\pi$
$774$		0			0
$775$		−	408.715i		−	0.527375i
$776$	−57.7015	−	200.811i	−0.0743577	−	0.258777i
$777$		0			0
$778$	1257.84	+	577.376i	1.61676	+	0.742128i
$779$			104.141i			0.133685i
$780$		0			0
$781$	−1533.60			−1.96364
$782$	111.932	−	243.850i	0.143136	−	0.311829i
$783$		0			0
$784$	−116.730	+	769.615i	−0.148890	+	0.981652i
$785$	386.584			0.492463
$786$		0			0
$787$			450.660i			0.572631i	0.958135	+	0.286315i	$0.0924305\pi$
$787$			450.660i			0.572631i	−0.958135	+	0.286315i	$0.907570\pi$
$788$	−542.048	−	630.462i	−0.687878	−	0.800078i
$789$		0			0
$790$	190.631	−	415.299i	0.241305	−	0.525695i
$791$			10.7797i			0.0136280i
$792$		0			0
$793$	135.430			0.170782
$794$	1195.50	+	548.758i	1.50566	+	0.691131i
$795$		0			0
$796$	907.285	−	780.051i	1.13981	−	0.979963i
$797$	365.782			0.458948			0.229474	−	0.973315i	$-0.426299\pi$
$797$	365.782			0.458948			0.229474	+	0.973315i	$0.426299\pi$
$798$		0			0
$799$			188.332i			0.235710i
$800$	−224.741	+	342.387i	−0.280926	+	0.427984i
$801$		0			0
$802$	−1077.63	−	494.653i	−1.34367	−	0.616775i
$803$		−	1048.32i		−	1.30550i
$804$		0			0
$805$	28.7989			0.0357750
$806$	47.5466	−	103.583i	0.0589908	−	0.128514i
$807$		0			0
$808$	56.9265	+	198.114i	0.0704536	+	0.245190i
$809$	1167.70			1.44339			0.721695	−	0.692212i	$-0.243364\pi$
$809$	1167.70			1.44339			0.721695	+	0.692212i	$0.243364\pi$
$810$		0			0
$811$			810.121i			0.998916i	0.866338	+	0.499458i	$0.166467\pi$
$811$			810.121i			0.998916i	−0.866338	+	0.499458i	$0.833533\pi$
$812$	11.3772	−	9.78170i	0.0140113	−	0.0120464i
$813$		0			0
$814$	−849.033	+	1849.66i	−1.04304	+	2.27231i
$815$		−	881.168i		−	1.08119i
$816$		0			0
$817$	764.271			0.935460
$818$	587.445	+	269.650i	0.718148	+	0.329645i
$819$		0			0
$820$	−85.5973	−	99.5591i	−0.104387	−	0.121414i
$821$	561.026			0.683344			0.341672	−	0.939819i	$-0.389007\pi$
$821$	561.026			0.683344			0.341672	+	0.939819i	$0.389007\pi$
$822$		0			0
$823$			1173.22i			1.42555i	0.701394	+	0.712773i	$0.252561\pi$
$823$			1173.22i			1.42555i	−0.701394	+	0.712773i	$0.747439\pi$
$824$	−150.885	+	43.3556i	−0.183112	+	0.0526160i
$825$		0			0
$826$	−25.9075	−	11.8921i	−0.0313650	−	0.0143972i
$827$			267.739i			0.323747i	0.986811	+	0.161874i	$0.0517537\pi$
$827$			267.739i			0.323747i	−0.986811	+	0.161874i	$0.948246\pi$
$828$		0			0
$829$	−432.474			−0.521682			−0.260841	−	0.965382i	$-0.584000\pi$
$829$	−432.474			−0.521682			−0.260841	+	0.965382i	$0.584000\pi$
$830$	−391.094	+	852.017i	−0.471197	+	1.02653i
$831$		0			0
$832$	−96.7876	+	60.6282i	−0.116331	+	0.0728705i
$833$	−823.035			−0.988037
$834$		0			0
$835$			1068.64i			1.27981i
$836$	−888.103	−	1032.96i	−1.06232	−	1.23560i
$837$		0			0
$838$	−214.595	+	467.506i	−0.256080	+	0.557883i
$839$		−	530.126i		−	0.631855i	−0.948783	−	0.315927i	$-0.897684\pi$
$839$		−	530.126i		−	0.631855i	0.948783	−	0.315927i	$-0.102316\pi$
$840$		0			0
$841$	−800.673			−0.952049
$842$	−152.649	−	70.0690i	−0.181293	−	0.0832173i
$843$		0			0
$844$	−496.433	+	426.815i	−0.588191	+	0.505705i
$845$	1019.44			1.20644
$846$		0			0
$847$		−	108.590i		−	0.128205i
$848$	−86.0809	+	567.541i	−0.101510	+	0.669271i
$849$		0			0
$850$	−393.552	−	180.649i	−0.463002	−	0.212528i
$851$			462.201i			0.543127i
$852$		0			0
$853$	−176.774			−0.207238			−0.103619	−	0.994617i	$-0.533042\pi$
$853$	−176.774			−0.207238			−0.103619	+	0.994617i	$0.533042\pi$
$854$	−37.4018	+	81.4816i	−0.0437960	+	0.0954118i
$855$		0			0
$856$	1408.60	−	404.752i	1.64557	−	0.472841i
$857$	389.717			0.454746			0.227373	−	0.973808i	$-0.426986\pi$
$857$	389.717			0.454746			0.227373	+	0.973808i	$0.426986\pi$
$858$		0			0
$859$			581.137i			0.676527i	0.941051	+	0.338263i	$0.109839\pi$
$859$			581.137i			0.676527i	−0.941051	+	0.338263i	$0.890161\pi$
$860$	−730.648	+	628.185i	−0.849591	+	0.730447i
$861$		0			0
$862$	120.436	−	262.375i	0.139716	−	0.304379i
$863$		−	827.326i		−	0.958663i	−0.877634	−	0.479331i	$-0.840879\pi$
$863$		−	827.326i		−	0.958663i	0.877634	−	0.479331i	$-0.159121\pi$
$864$		0			0
$865$	−1546.92			−1.78835
$866$	718.617	+	329.860i	0.829811	+	0.380901i
$867$		0			0
$868$	49.1896	+	57.2129i	0.0566700	+	0.0659135i
$869$	−648.853			−0.746666
$870$		0			0
$871$			65.5675i			0.0752784i
$872$	222.792	+	775.354i	0.255496	+	0.889167i
$873$		0			0
$874$	−281.165	−	129.060i	−0.321699	−	0.147666i
$875$			44.3096i			0.0506395i
$876$		0			0
$877$	559.629			0.638118			0.319059	−	0.947735i	$-0.396633\pi$
$877$	559.629			0.638118			0.319059	+	0.947735i	$0.396633\pi$
$878$	187.651	−	408.806i	0.213725	−	0.465611i
$879$		0			0
$880$	1698.07	+	257.551i	1.92962	+	0.292672i
$881$	−957.127			−1.08641			−0.543205	−	0.839600i	$-0.682789\pi$
$881$	−957.127			−1.08641			−0.543205	+	0.839600i	$0.682789\pi$
$882$		0			0
$883$		−	625.252i		−	0.708100i	−0.935227	−	0.354050i	$-0.884804\pi$
$883$		−	625.252i		−	0.708100i	0.935227	−	0.354050i	$-0.115196\pi$
$884$	−78.7245	−	91.5653i	−0.0890549	−	0.103581i
$885$		0			0
$886$	355.678	−	774.861i	0.401442	−	0.874561i
$887$		−	1063.69i		−	1.19920i	−0.800298	−	0.599602i	$-0.795325\pi$
$887$		−	1063.69i		−	1.19920i	0.800298	−	0.599602i	$-0.204675\pi$
$888$		0			0
$889$	−97.0992			−0.109223
$890$	308.289	+	141.511i	0.346393	+	0.159002i
$891$		0			0
$892$	−1158.15	+	995.735i	−1.29837	+	1.11629i
$893$	217.151			0.243171
$894$		0			0
$895$			590.251i			0.659498i
$896$	−9.74715	−	74.9760i	−0.0108785	−	0.0836786i
$897$		0			0
$898$	−739.320	−	339.363i	−0.823296	−	0.377910i
$899$			202.793i			0.225577i
$900$		0			0
$901$	−606.935			−0.673624
$902$	−77.7743	+	169.435i	−0.0862243	+	0.187844i
$903$		0			0
$904$	40.3198	+	140.320i	0.0446016	+	0.155221i
$905$	2021.22			2.23339
$906$		0			0
$907$			239.262i			0.263795i	0.991263	+	0.131898i	$0.0421070\pi$
$907$			239.262i			0.263795i	−0.991263	+	0.131898i	$0.957893\pi$
$908$	180.535	−	155.217i	0.198827	−	0.170944i
$909$		0			0
$910$	5.40696	−	11.7793i	0.00594172	−	0.0129443i
$911$			203.001i			0.222834i	0.993774	+	0.111417i	$0.0355389\pi$
$911$			203.001i			0.222834i	−0.993774	+	0.111417i	$0.964461\pi$
$912$		0			0
$913$	1331.17			1.45802
$914$	580.196	+	266.322i	0.634788	+	0.291381i
$915$		0			0
$916$	−336.069	−	390.885i	−0.366887	−	0.426730i
$917$	−84.1801			−0.0917994
$918$		0			0
$919$		−	878.708i		−	0.956156i	−0.878317	−	0.478078i	$-0.841334\pi$
$919$		−	878.708i		−	0.956156i	0.878317	−	0.478078i	$-0.158666\pi$
$920$	374.875	−	107.718i	0.407473	−	0.117084i
$921$		0			0
$922$	−1068.37	−	490.406i	−1.15876	−	0.531894i
$923$			156.746i			0.169822i
$924$		0			0
$925$	745.950			0.806432
$926$	221.670	−	482.920i	0.239385	−	0.521512i
$927$		0			0
$928$	111.510	−	169.883i	0.120162	−	0.183064i
$929$	−600.518			−0.646413			−0.323207	−	0.946328i	$-0.604761\pi$
$929$	−600.518			−0.646413			−0.323207	+	0.946328i	$0.604761\pi$
$930$		0			0
$931$			948.977i			1.01931i
$932$	39.1001	+	45.4778i	0.0419529	+	0.0487959i
$933$		0			0
$934$	−662.967	+	1444.31i	−0.709815	+	1.54637i
$935$			1815.93i			1.94217i
$936$		0			0
$937$	−184.325			−0.196718			−0.0983589	−	0.995151i	$-0.531359\pi$
$937$	−184.325			−0.196718			−0.0983589	+	0.995151i	$0.531359\pi$
$938$	−39.4487	−	18.1078i	−0.0420562	−	0.0193047i
$939$		0			0
$940$	−207.598	+	178.485i	−0.220849	+	0.189878i
$941$	755.173			0.802522			0.401261	−	0.915964i	$-0.368572\pi$
$941$	755.173			0.802522			0.401261	+	0.915964i	$0.368572\pi$
$942$		0			0
$943$			42.3392i			0.0448984i
$944$	−381.719	−	57.8966i	−0.404363	−	0.0613311i
$945$		0			0
$946$	1243.46	+	570.773i	1.31444	+	0.603354i
$947$		−	889.079i		−	0.938837i	−0.882976	−	0.469419i	$-0.844464\pi$
$947$		−	889.079i		−	0.938837i	0.882976	−	0.469419i	$-0.155536\pi$
$948$		0			0
$949$	−107.146			−0.112904
$950$	−208.292	+	453.774i	−0.219255	+	0.477657i
$951$		0			0
$952$	76.8317	−	22.0770i	0.0807056	−	0.0231902i
$953$	15.5920			0.0163610			0.00818050	−	0.999967i	$-0.497396\pi$
$953$	15.5920			0.0163610			0.00818050	+	0.999967i	$0.497396\pi$
$954$		0			0
$955$			2.49830i			0.00261602i
$956$	−1104.08	+	949.251i	−1.15490	+	0.992940i
$957$		0			0
$958$	552.002	−	1202.56i	0.576203	−	1.25529i
$959$			3.64066i			0.00379631i
$960$		0			0
$961$	−58.7941			−0.0611801
$962$	189.050	+	86.7777i	0.196517	+	0.0902056i
$963$		0			0
$964$	211.350	+	245.824i	0.219243	+	0.255004i
$965$	−383.921			−0.397846
$966$		0			0
$967$		−	979.095i		−	1.01251i	−0.862384	−	0.506254i	$-0.831030\pi$
$967$		−	979.095i		−	1.01251i	0.862384	−	0.506254i	$-0.168970\pi$
$968$	−406.163	−	1413.51i	−0.419590	−	1.46024i
$969$		0			0
$970$	291.860	+	133.970i	0.300886	+	0.138113i
$971$		−	67.3838i		−	0.0693963i	−0.999398	−	0.0346982i	$-0.988953\pi$
$971$		−	67.3838i		−	0.0693963i	0.999398	−	0.0346982i	$-0.0110470\pi$
$972$		0			0
$973$	70.3667			0.0723193
$974$	−47.6847	+	103.883i	−0.0489576	+	0.106657i
$975$		0			0
$976$	−182.090	+	1200.54i	−0.186568	+	1.23006i
$977$	−707.420			−0.724074			−0.362037	−	0.932164i	$-0.617919\pi$
$977$	−707.420			−0.724074			−0.362037	+	0.932164i	$0.617919\pi$
$978$		0			0
$979$		−	481.664i		−	0.491995i
$980$	−780.002	−	907.229i	−0.795921	−	0.925744i
$981$		0			0
$982$	46.8799	−	102.130i	0.0477392	−	0.104002i
$983$		−	391.246i		−	0.398012i	−0.979998	−	0.199006i	$-0.936229\pi$
$983$		−	391.246i		−	0.398012i	0.979998	−	0.199006i	$-0.0637713\pi$
$984$		0			0
$985$	1277.94			1.29740
$986$	195.270	+	89.6329i	0.198042	+	0.0909056i
$987$		0			0
$988$	−105.577	+	90.7710i	−0.106859	+	0.0918735i
$989$	310.720			0.314176
$990$		0			0
$991$		−	104.988i		−	0.105941i	−0.998596	−	0.0529706i	$-0.983131\pi$
$991$		−	104.988i		−	0.105941i	0.998596	−	0.0529706i	$-0.0168690\pi$
$992$	854.297	+	560.755i	0.861186	+	0.565277i
$993$		0			0
$994$	−94.3063	−	43.2886i	−0.0948756	−	0.0435499i
$995$			1839.06i			1.84830i
$996$		0			0
$997$	78.0055			0.0782402			0.0391201	−	0.999235i	$-0.487545\pi$
$997$	78.0055			0.0782402			0.0391201	+	0.999235i	$0.487545\pi$
$998$	503.120	−	1096.07i	0.504128	−	1.09827i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.i.163.8		8
3.2	odd	2		324.3.d.g.163.1		8
4.3	odd	2	inner	324.3.d.i.163.7		8
9.2	odd	6		108.3.f.c.91.5		16
9.4	even	3		36.3.f.c.7.3	✓	16
9.5	odd	6		108.3.f.c.19.6		16
9.7	even	3		36.3.f.c.31.4	yes	16
12.11	even	2		324.3.d.g.163.2		8
36.7	odd	6		36.3.f.c.31.3	yes	16
36.11	even	6		108.3.f.c.91.6		16
36.23	even	6		108.3.f.c.19.5		16
36.31	odd	6		36.3.f.c.7.4	yes	16
72.5	odd	6		1728.3.o.g.127.7		16
72.11	even	6		1728.3.o.g.1279.7		16
72.13	even	6		576.3.o.g.511.2		16
72.29	odd	6		1728.3.o.g.1279.8		16
72.43	odd	6		576.3.o.g.319.2		16
72.59	even	6		1728.3.o.g.127.8		16
72.61	even	6		576.3.o.g.319.7		16
72.67	odd	6		576.3.o.g.511.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.3	✓	16	9.4	even	3
36.3.f.c.7.4	yes	16	36.31	odd	6
36.3.f.c.31.3	yes	16	36.7	odd	6
36.3.f.c.31.4	yes	16	9.7	even	3
108.3.f.c.19.5		16	36.23	even	6
108.3.f.c.19.6		16	9.5	odd	6
108.3.f.c.91.5		16	9.2	odd	6
108.3.f.c.91.6		16	36.11	even	6
324.3.d.g.163.1		8	3.2	odd	2
324.3.d.g.163.2		8	12.11	even	2
324.3.d.i.163.7		8	4.3	odd	2	inner
324.3.d.i.163.8		8	1.1	even	1	trivial
576.3.o.g.319.2		16	72.43	odd	6
576.3.o.g.319.7		16	72.61	even	6
576.3.o.g.511.2		16	72.13	even	6
576.3.o.g.511.7		16	72.67	odd	6
1728.3.o.g.127.7		16	72.5	odd	6
1728.3.o.g.127.8		16	72.59	even	6
1728.3.o.g.1279.7		16	72.11	even	6
1728.3.o.g.1279.8		16	72.29	odd	6

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81766 + 0.834343i) q^{2} +(2.60775 + 3.03310i) q^{4} -6.14806 q^{5} +0.590679i q^{7} +(2.20934 + 7.68888i) q^{8} +O(q^{10})\)	\(q+(1.81766 + 0.834343i) q^{2} +(2.60775 + 3.03310i) q^{4} -6.14806 q^{5} +0.590679i q^{7} +(2.20934 + 7.68888i) q^{8} +(-11.1751 - 5.12959i) q^{10} +17.4596i q^{11} +1.78451 q^{13} +(-0.492829 + 1.07365i) q^{14} +(-2.39933 + 15.8191i) q^{16} -16.9171 q^{17} +19.5058i q^{19} +(-16.0326 - 18.6477i) q^{20} +(-14.5673 + 31.7356i) q^{22} +7.93023i q^{23} +12.7987 q^{25} +(3.24362 + 1.48889i) q^{26} +(-1.79159 + 1.54034i) q^{28} -6.35035 q^{29} -31.9342i q^{31} +(-17.5597 + 26.7518i) q^{32} +(-30.7495 - 14.1147i) q^{34} -3.63153i q^{35} +58.2834 q^{37} +(-16.2745 + 35.4548i) q^{38} +(-13.5832 - 47.2717i) q^{40} +5.33896 q^{41} -39.1818i q^{43} +(-52.9567 + 45.5303i) q^{44} +(-6.61653 + 14.4144i) q^{46} -11.1327i q^{47} +48.6511 q^{49} +(23.2636 + 10.6785i) q^{50} +(4.65355 + 5.41259i) q^{52} +35.8770 q^{53} -107.343i q^{55} +(-4.54166 + 1.30501i) q^{56} +(-11.5427 - 5.29836i) q^{58} +24.1303i q^{59} +75.8921 q^{61} +(26.6441 - 58.0454i) q^{62} +(-54.2376 + 33.9747i) q^{64} -10.9713 q^{65} +36.7426i q^{67} +(-44.1155 - 51.3112i) q^{68} +(3.02994 - 6.60088i) q^{70} +87.8370i q^{71} -60.0423 q^{73} +(105.939 + 48.6283i) q^{74} +(-59.1629 + 50.8661i) q^{76} -10.3130 q^{77} +37.1630i q^{79} +(14.7512 - 97.2567i) q^{80} +(9.70439 + 4.45452i) q^{82} -76.2427i q^{83} +104.007 q^{85} +(32.6910 - 71.2190i) q^{86} +(-134.245 + 38.5743i) q^{88} -27.5873 q^{89} +1.05407i q^{91} +(-24.0531 + 20.6800i) q^{92} +(9.28846 - 20.2354i) q^{94} -119.923i q^{95} -26.1171 q^{97} +(88.4309 + 40.5917i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8	\( 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8} + 10 q^{10} + 46 q^{13} + 12 q^{14} + 17 q^{16} + 6 q^{17} - 36 q^{20} - 33 q^{22} + 30 q^{25} + 36 q^{26} + 6 q^{28} - 42 q^{29} - 87 q^{32} - 11 q^{34} + 28 q^{37} + 99 q^{38} - 68 q^{40} - 84 q^{41} - 111 q^{44} - 132 q^{46} - 58 q^{49} + 219 q^{50} - 110 q^{52} - 36 q^{53} - 270 q^{56} + 16 q^{58} + 34 q^{61} + 258 q^{62} - 127 q^{64} + 30 q^{65} - 375 q^{68} - 150 q^{70} + 58 q^{73} + 372 q^{74} + 15 q^{76} + 330 q^{77} - 360 q^{80} + 127 q^{82} + 140 q^{85} + 273 q^{86} - 75 q^{88} - 192 q^{89} - 258 q^{92} - 36 q^{94} + 148 q^{97} + 585 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8 + 10 * q^10 + 46 * q^13 + 12 * q^14 + 17 * q^16 + 6 * q^17 - 36 * q^20 - 33 * q^22 + 30 * q^25 + 36 * q^26 + 6 * q^28 - 42 * q^29 - 87 * q^32 - 11 * q^34 + 28 * q^37 + 99 * q^38 - 68 * q^40 - 84 * q^41 - 111 * q^44 - 132 * q^46 - 58 * q^49 + 219 * q^50 - 110 * q^52 - 36 * q^53 - 270 * q^56 + 16 * q^58 + 34 * q^61 + 258 * q^62 - 127 * q^64 + 30 * q^65 - 375 * q^68 - 150 * q^70 + 58 * q^73 + 372 * q^74 + 15 * q^76 + 330 * q^77 - 360 * q^80 + 127 * q^82 + 140 * q^85 + 273 * q^86 - 75 * q^88 - 192 * q^89 - 258 * q^92 - 36 * q^94 + 148 * q^97 + 585 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more