LMFDB - Embedded newform 441.4.e.y.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not 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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.5922408960000.19
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 54x^{6} + 176x^{5} + 1307x^{4} - 2912x^{3} - 15314x^{2} + 16800x + 86044 $ x^8 - 4x^7 - 54x^6 + 176x^5 + 1307x^4 - 2912x^3 - 15314x^2 + 16800*x + 86044
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	no (minimal twist has level 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.4
Root			$3.82402 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.y.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26556 + 3.92407i) q^{2} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} -20.5311 q^{8} +O(q^{10})$	\(q+(2.26556 + 3.92407i) q^{2} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} -20.5311 q^{8} +(-30.5377 + 52.8928i) q^{10} +(0.406613 - 0.704275i) q^{11} -34.9564 q^{13} +(3.60992 + 6.25256i) q^{16} +(-58.8660 + 101.959i) q^{17} +(-46.6457 - 80.7927i) q^{19} -168.908 q^{20} +3.68484 q^{22} +(60.1245 + 104.139i) q^{23} +(-28.3424 + 49.0905i) q^{25} +(-79.1960 - 137.171i) q^{26} -8.56420 q^{29} +(-41.0535 + 71.1067i) q^{31} +(-98.4815 + 170.575i) q^{32} -533.458 q^{34} +(-14.4066 - 24.9530i) q^{37} +(211.358 - 366.082i) q^{38} +(-138.370 - 239.664i) q^{40} -70.5291 q^{41} +417.179 q^{43} +(5.09532 + 8.82536i) q^{44} +(-272.432 + 471.866i) q^{46} +(-169.131 - 292.943i) q^{47} -256.846 q^{50} +(219.022 - 379.356i) q^{52} +(74.5603 - 129.142i) q^{53} +10.9615 q^{55} +(-19.4027 - 33.6065i) q^{58} +(47.0914 - 81.5647i) q^{59} +(-60.2623 - 104.377i) q^{61} -372.037 q^{62} -834.706 q^{64} +(-235.590 - 408.053i) q^{65} +(396.183 - 686.209i) q^{67} +(-737.657 - 1277.66i) q^{68} -449.128 q^{71} +(-234.710 + 406.530i) q^{73} +(65.2782 - 113.065i) q^{74} +1169.05 q^{76} +(509.926 + 883.218i) q^{79} +(-48.6583 + 84.2786i) q^{80} +(-159.788 - 276.761i) q^{82} -104.253 q^{83} -1586.91 q^{85} +(945.146 + 1637.04i) q^{86} +(-8.34823 + 14.4596i) q^{88} +(786.460 + 1362.19i) q^{89} -1506.86 q^{92} +(766.352 - 1327.36i) q^{94} +(628.739 - 1089.01i) q^{95} -550.057 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8	$ 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8} + 100 q^{11} + 174 q^{16} - 680 q^{22} + 352 q^{23} + 128 q^{25} - 520 q^{29} - 30 q^{32} - 212 q^{37} + 1080 q^{43} + 460 q^{44} - 696 q^{46} - 2732 q^{50} + 16 q^{53} + 780 q^{58} - 3356 q^{64} - 756 q^{65} + 1944 q^{67} - 4496 q^{71} - 284 q^{74} + 1048 q^{79} - 6568 q^{85} + 4820 q^{86} - 1260 q^{88} - 7024 q^{92} + 2192 q^{95}+O(q^{100}) $ 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8 + 100 * q^11 + 174 * q^16 - 680 * q^22 + 352 * q^23 + 128 * q^25 - 520 * q^29 - 30 * q^32 - 212 * q^37 + 1080 * q^43 + 460 * q^44 - 696 * q^46 - 2732 * q^50 + 16 * q^53 + 780 * q^58 - 3356 * q^64 - 756 * q^65 + 1944 * q^67 - 4496 * q^71 - 284 * q^74 + 1048 * q^79 - 6568 * q^85 + 4820 * q^86 - 1260 * q^88 - 7024 * q^92 + 2192 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	2.26556	+	3.92407i	0.800998	+	1.38737i	0.918960	+	0.394351i	$0.129031\pi$
$2$	2.26556	+	3.92407i	0.800998	+	1.38737i	−0.117962	+	0.993018i	$0.537636\pi$
$3$		0			0
$3$		0			0
$4$	−6.26556	+	10.8523i	−0.783196	+	1.35653i
$5$	6.73953	+	11.6732i	0.602802	+	1.04408i	0.992395	+	0.123096i	$0.0392823\pi$
$5$	6.73953	+	11.6732i	0.602802	+	1.04408i	−0.389593	+	0.920987i	$0.627384\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−20.5311			−0.907356
$9$		0			0
$10$	−30.5377	+	52.8928i	−0.965686	+	1.67262i
$11$	0.406613	−	0.704275i	0.0111453	−	0.0193043i	−0.860399	−	0.509621i	$-0.829786\pi$
$11$	0.406613	−	0.704275i	0.0111453	−	0.0193043i	0.871544	+	0.490317i	$0.163119\pi$
$12$		0			0
$13$	−34.9564			−0.745781			−0.372891	−	0.927875i	$-0.621633\pi$
$13$	−34.9564			−0.745781			−0.372891	+	0.927875i	$0.621633\pi$
$14$		0			0
$15$		0			0
$16$	3.60992	+	6.25256i	0.0564050	+	0.0976963i
$17$	−58.8660	+	101.959i	−0.839829	+	1.45463i	0.0502085	+	0.998739i	$0.484011\pi$
$17$	−58.8660	+	101.959i	−0.839829	+	1.45463i	−0.890037	+	0.455888i	$0.849322\pi$
$18$		0			0
$19$	−46.6457	−	80.7927i	−0.563224	−	0.975532i	−0.997213	−	0.0746138i	$-0.976228\pi$
$19$	−46.6457	−	80.7927i	−0.563224	−	0.975532i	0.433989	−	0.900918i	$-0.357106\pi$
$20$	−168.908			−1.88845
$21$		0			0
$22$	3.68484			0.0357095
$23$	60.1245	+	104.139i	0.545079	+	0.944105i	0.998602	+	0.0528605i	$0.0168339\pi$
$23$	60.1245	+	104.139i	0.545079	+	0.944105i	−0.453522	+	0.891245i	$0.649833\pi$
$24$		0			0
$25$	−28.3424	+	49.0905i	−0.226739	+	0.392724i
$26$	−79.1960	−	137.171i	−0.597369	−	1.03467i
$27$		0			0
$28$		0			0
$29$	−8.56420			−0.0548390			−0.0274195	−	0.999624i	$-0.508729\pi$
$29$	−8.56420			−0.0548390			−0.0274195	+	0.999624i	$0.508729\pi$
$30$		0			0
$31$	−41.0535	+	71.1067i	−0.237852	+	0.411972i	−0.960098	−	0.279665i	$-0.909777\pi$
$31$	−41.0535	+	71.1067i	−0.237852	+	0.411972i	0.722245	+	0.691637i	$0.243110\pi$
$32$	−98.4815	+	170.575i	−0.544039	+	0.942303i
$33$		0			0
$34$	−533.458			−2.69080
$35$		0			0
$36$		0			0
$37$	−14.4066	−	24.9530i	−0.0640117	−	0.110872i	0.832243	−	0.554410i	$-0.187056\pi$
$37$	−14.4066	−	24.9530i	−0.0640117	−	0.110872i	−0.896255	+	0.443539i	$0.853723\pi$
$38$	211.358	−	366.082i	0.902282	−	1.56280i
$39$		0			0
$40$	−138.370	−	239.664i	−0.546956	−	0.947355i
$41$	−70.5291			−0.268654			−0.134327	−	0.990937i	$-0.542887\pi$
$41$	−70.5291			−0.268654			−0.134327	+	0.990937i	$0.542887\pi$
$42$		0			0
$43$	417.179			1.47952			0.739758	−	0.672873i	$-0.234940\pi$
$43$	417.179			1.47952			0.739758	+	0.672873i	$0.234940\pi$
$44$	5.09532	+	8.82536i	0.0174579	+	0.0302380i
$45$		0			0
$46$	−272.432	+	471.866i	−0.873215	+	1.51245i
$47$	−169.131	−	292.943i	−0.524899	−	0.909151i	−0.999580	−	0.0289931i	$-0.990770\pi$
$47$	−169.131	−	292.943i	−0.524899	−	0.909151i	0.474681	−	0.880158i	$-0.342563\pi$
$48$		0			0
$49$		0			0
$50$	−256.846			−0.726471
$51$		0			0
$52$	219.022	−	379.356i	0.584093	−	1.01168i
$53$	74.5603	−	129.142i	0.193239	−	0.334699i	−0.753083	−	0.657925i	$-0.771434\pi$
$53$	74.5603	−	129.142i	0.193239	−	0.334699i	0.946322	+	0.323226i	$0.104768\pi$
$54$		0			0
$55$	10.9615			0.0268737
$56$		0			0
$57$		0			0
$58$	−19.4027	−	33.6065i	−0.0439259	−	0.0760820i
$59$	47.0914	−	81.5647i	0.103911	−	0.179980i	−0.809382	−	0.587283i	$-0.800197\pi$
$59$	47.0914	−	81.5647i	0.103911	−	0.179980i	0.913293	+	0.407303i	$0.133531\pi$
$60$		0			0
$61$	−60.2623	−	104.377i	−0.126488	−	0.219084i	0.795825	−	0.605526i	$-0.207037\pi$
$61$	−60.2623	−	104.377i	−0.126488	−	0.219084i	−0.922314	+	0.386442i	$0.873704\pi$
$62$	−372.037			−0.762077
$63$		0			0
$64$	−834.706			−1.63029
$65$	−235.590	−	408.053i	−0.449558	−	0.778658i
$66$		0			0
$67$	396.183	−	686.209i	0.722410	−	1.25125i	−0.237622	−	0.971358i	$-0.576368\pi$
$67$	396.183	−	686.209i	0.722410	−	1.25125i	0.960031	−	0.279892i	$-0.0902988\pi$
$68$	−737.657	−	1277.66i	−1.31550	−	2.27851i
$69$		0			0
$70$		0			0
$71$	−449.128			−0.750729			−0.375364	−	0.926877i	$-0.622482\pi$
$71$	−449.128			−0.750729			−0.375364	+	0.926877i	$0.622482\pi$
$72$		0			0
$73$	−234.710	+	406.530i	−0.376311	+	0.651790i	−0.990522	−	0.137352i	$-0.956141\pi$
$73$	−234.710	+	406.530i	−0.376311	+	0.651790i	0.614211	+	0.789142i	$0.289474\pi$
$74$	65.2782	−	113.065i	0.102546	−	0.177616i
$75$		0			0
$76$	1169.05			1.76446
$77$		0			0
$78$		0			0
$79$	509.926	+	883.218i	0.726217	+	1.25785i	0.958471	+	0.285190i	$0.0920567\pi$
$79$	509.926	+	883.218i	0.726217	+	1.25785i	−0.232254	+	0.972655i	$0.574610\pi$
$80$	−48.6583	+	84.2786i	−0.0680020	+	0.117783i
$81$		0			0
$82$	−159.788	−	276.761i	−0.215191	−	0.372722i
$83$	−104.253			−0.137870			−0.0689352	−	0.997621i	$-0.521960\pi$
$83$	−104.253			−0.137870			−0.0689352	+	0.997621i	$0.521960\pi$
$84$		0			0
$85$	−1586.91			−2.02500
$86$	945.146	+	1637.04i	1.18509	+	2.05264i
$87$		0			0
$88$	−8.34823	+	14.4596i	−0.0101128	+	0.0175158i
$89$	786.460	+	1362.19i	0.936680	+	1.62238i	0.771610	+	0.636096i	$0.219452\pi$
$89$	786.460	+	1362.19i	0.936680	+	1.62238i	0.165071	+	0.986282i	$0.447215\pi$
$90$		0			0
$91$		0			0
$92$	−1506.86			−1.70762
$93$		0			0
$94$	766.352	−	1327.36i	0.840885	−	1.45646i
$95$	628.739	−	1089.01i	0.679024	−	1.17610i
$96$		0			0
$97$	−550.057			−0.575772			−0.287886	−	0.957665i	$-0.592952\pi$
$97$	−550.057			−0.575772			−0.287886	+	0.957665i	$0.592952\pi$
$98$		0			0
$99$		0			0
$100$	−355.162	−	615.159i	−0.355162	−	0.615159i
$101$	32.8585	−	56.9125i	0.0323717	−	0.0560694i	−0.849386	−	0.527773i	$-0.823027\pi$
$101$	32.8585	−	56.9125i	0.0323717	−	0.0560694i	0.881757	+	0.471703i	$0.156361\pi$
$102$		0			0
$103$	914.674	+	1584.26i	0.875005	+	1.51555i	0.856757	+	0.515720i	$0.172476\pi$
$103$	914.674	+	1584.26i	0.875005	+	1.51555i	0.0182480	+	0.999833i	$0.494191\pi$
$104$	717.694			0.676689
$105$		0			0
$106$	675.685			0.619135
$107$	430.689	+	745.975i	0.389124	+	0.673982i	0.992332	−	0.123602i	$-0.0394445\pi$
$107$	430.689	+	745.975i	0.389124	+	0.673982i	−0.603208	+	0.797584i	$0.706111\pi$
$108$		0			0
$109$	810.259	−	1403.41i	0.712007	−	1.23323i	−0.252096	−	0.967702i	$-0.581120\pi$
$109$	810.259	−	1403.41i	0.712007	−	1.23323i	0.964103	−	0.265529i	$-0.0855467\pi$
$110$	24.8340	+	43.0138i	0.0215258	+	0.0372837i
$111$		0			0
$112$		0			0
$113$	−380.409			−0.316689			−0.158344	−	0.987384i	$-0.550616\pi$
$113$	−380.409			−0.316689			−0.158344	+	0.987384i	$0.550616\pi$
$114$		0			0
$115$	−810.421	+	1403.69i	−0.657149	+	1.13822i
$116$	53.6595	−	92.9410i	0.0429497	−	0.0743910i
$117$		0			0
$118$	426.754			0.332931
$119$		0			0
$120$		0			0
$121$	665.169	+	1152.11i	0.499752	+	0.865595i
$122$	273.056	−	472.947i	0.202634	−	0.350972i
$123$		0			0
$124$	−514.446	−	891.047i	−0.372570	−	0.645310i
$125$	920.824			0.658888
$126$		0			0
$127$	958.358			0.669610			0.334805	−	0.942287i	$-0.391329\pi$
$127$	958.358			0.669610			0.334805	+	0.942287i	$0.391329\pi$
$128$	−1103.23	−	1910.85i	−0.761817	−	1.31951i
$129$		0			0
$130$	1067.49	−	1848.94i	0.720190	−	1.24741i
$131$	−576.079	−	997.798i	−0.384216	−	0.665481i	0.607444	−	0.794362i	$-0.292195\pi$
$131$	−576.079	−	997.798i	−0.384216	−	0.665481i	−0.991660	+	0.128881i	$0.958861\pi$
$132$		0			0
$133$		0			0
$134$	3590.31			2.31459
$135$		0			0
$136$	1208.58	−	2093.33i	0.762024	−	1.31986i
$137$	178.689	−	309.498i	0.111434	−	0.193009i	−0.804915	−	0.593390i	$-0.797789\pi$
$137$	178.689	−	309.498i	0.111434	−	0.193009i	0.916349	+	0.400382i	$0.131122\pi$
$138$		0			0
$139$	2736.29			1.66970			0.834852	−	0.550475i	$-0.185553\pi$
$139$	2736.29			1.66970			0.834852	+	0.550475i	$0.185553\pi$
$140$		0			0
$141$		0			0
$142$	−1017.53	−	1762.41i	−0.601332	−	1.04154i
$143$	−14.2137	+	24.6189i	−0.00831197	+	0.0143968i
$144$		0			0
$145$	−57.7186	−	99.9716i	−0.0330570	−	0.0572565i
$146$	−2127.00			−1.20570
$147$		0			0
$148$	361.062			0.200535
$149$	704.969	+	1221.04i	0.387606	+	0.671353i	0.992127	−	0.125236i	$-0.0399687\pi$
$149$	704.969	+	1221.04i	0.387606	+	0.671353i	−0.604521	+	0.796589i	$0.706635\pi$
$150$		0			0
$151$	−1176.18	+	2037.20i	−0.633879	+	1.09791i	0.352872	+	0.935672i	$0.385205\pi$
$151$	−1176.18	+	2037.20i	−0.633879	+	1.09791i	−0.986751	+	0.162240i	$0.948128\pi$
$152$	957.688	+	1658.76i	0.511045	+	0.885155i
$153$		0			0
$154$		0			0
$155$	−1106.72			−0.573511
$156$		0			0
$157$	606.911	−	1051.20i	0.308514	−	0.534363i	−0.669523	−	0.742791i	$-0.733502\pi$
$157$	606.911	−	1051.20i	0.308514	−	0.534363i	0.978038	+	0.208429i	$0.0668349\pi$
$158$	−2310.54	+	4001.97i	−1.16340	+	2.01506i
$159$		0			0
$160$	−2654.88			−1.31179
$161$		0			0
$162$		0			0
$163$	361.387	+	625.941i	0.173657	+	0.300782i	0.939696	−	0.342012i	$-0.111108\pi$
$163$	361.387	+	625.941i	0.173657	+	0.300782i	−0.766039	+	0.642794i	$0.777775\pi$
$164$	441.905	−	765.401i	0.210408	−	0.364438i
$165$		0			0
$166$	−236.192	−	409.096i	−0.110434	−	0.191277i
$167$	753.016			0.348923			0.174462	−	0.984664i	$-0.444182\pi$
$167$	753.016			0.348923			0.174462	+	0.984664i	$0.444182\pi$
$168$		0			0
$169$	−975.051			−0.443810
$170$	−3595.26	−	6227.17i	−1.62202	−	2.80942i
$171$		0			0
$172$	−2613.86	+	4527.34i	−1.15875	+	2.00702i
$173$	929.569	+	1610.06i	0.408519	+	0.707576i	0.994724	−	0.102587i	$-0.0327120\pi$
$173$	929.569	+	1610.06i	0.408519	+	0.707576i	−0.586205	+	0.810163i	$0.699379\pi$
$174$		0			0
$175$		0			0
$176$	5.87137			0.00251461
$177$		0			0
$178$	−3563.55	+	6172.25i	−1.50056	+	2.59904i
$179$	−261.413	+	452.780i	−0.109156	+	0.189063i	−0.915429	−	0.402481i	$-0.868148\pi$
$179$	−261.413	+	452.780i	−0.109156	+	0.189063i	0.806273	+	0.591544i	$0.201481\pi$
$180$		0			0
$181$	−2901.38			−1.19148			−0.595740	−	0.803177i	$-0.703141\pi$
$181$	−2901.38			−1.19148			−0.595740	+	0.803177i	$0.703141\pi$
$182$		0			0
$183$		0			0
$184$	−1234.42	−	2138.09i	−0.494581	−	0.856640i
$185$	194.187	−	336.343i	0.0771727	−	0.133667i
$186$		0			0
$187$	47.8714	+	82.9156i	0.0187203	+	0.0324246i
$188$	4238.79			1.64439
$189$		0			0
$190$	5697.80			2.17559
$191$	1302.18	+	2255.43i	0.493309	+	0.854437i	0.999970	−	0.00770854i	$-0.00245373\pi$
$191$	1302.18	+	2255.43i	0.493309	+	0.854437i	−0.506661	+	0.862145i	$0.669120\pi$
$192$		0			0
$193$	−338.123	+	585.646i	−0.126107	+	0.218423i	−0.922165	−	0.386797i	$-0.873582\pi$
$193$	−338.123	+	585.646i	−0.126107	+	0.218423i	0.796058	+	0.605220i	$0.206915\pi$
$194$	−1246.19	−	2158.47i	−0.461192	−	0.798808i
$195$		0			0
$196$		0			0
$197$	3685.99			1.33308			0.666538	−	0.745471i	$-0.267775\pi$
$197$	3685.99			1.33308			0.666538	+	0.745471i	$0.267775\pi$
$198$		0			0
$199$	−399.901	+	692.648i	−0.142453	+	0.246736i	−0.928420	−	0.371533i	$-0.878832\pi$
$199$	−399.901	+	692.648i	−0.142453	+	0.246736i	0.785967	+	0.618269i	$0.212166\pi$
$200$	581.902	−	1007.88i	0.205733	−	0.356341i
$201$		0			0
$202$	297.772			0.103719
$203$		0			0
$204$		0			0
$205$	−475.333	−	823.300i	−0.161945	−	0.280497i
$206$	−4144.51	+	7178.50i	−1.40175	+	2.42791i
$207$		0			0
$208$	−126.190	−	218.567i	−0.0420658	−	0.0728601i
$209$	−75.8670			−0.0251092
$210$		0			0
$211$	−667.385			−0.217747			−0.108874	−	0.994056i	$-0.534724\pi$
$211$	−667.385			−0.217747			−0.108874	+	0.994056i	$0.534724\pi$
$212$	934.325	+	1618.30i	0.302687	+	0.524270i
$213$		0			0
$214$	−1951.51	+	3380.11i	−0.623375	+	1.07972i
$215$	2811.59	+	4869.81i	0.891855	+	1.54474i
$216$		0			0
$217$		0			0
$218$	7342.77			2.28126
$219$		0			0
$220$	−68.6801	+	118.957i	−0.0210473	+	0.0364551i
$221$	2057.74	−	3564.11i	0.626329	−	1.08483i
$222$		0			0
$223$	−2646.82			−0.794818			−0.397409	−	0.917642i	$-0.630091\pi$
$223$	−2646.82			−0.794818			−0.397409	+	0.917642i	$0.630091\pi$
$224$		0			0
$225$		0			0
$226$	−861.840	−	1492.75i	−0.253667	−	0.439364i
$227$	−2060.56	+	3568.99i	−0.602485	+	1.04353i	0.389959	+	0.920832i	$0.372489\pi$
$227$	−2060.56	+	3568.99i	−0.602485	+	1.04353i	−0.992444	+	0.122702i	$0.960844\pi$
$228$		0			0
$229$	2033.46	+	3522.06i	0.586790	+	1.01635i	0.994650	+	0.103306i	$0.0329420\pi$
$229$	2033.46	+	3522.06i	0.586790	+	1.01635i	−0.407860	+	0.913045i	$0.633725\pi$
$230$	−7344.25			−2.10550
$231$		0			0
$232$	175.833			0.0497585
$233$	−1952.33	−	3381.54i	−0.548934	−	0.950782i	−0.998348	−	0.0574584i	$-0.981700\pi$
$233$	−1952.33	−	3381.54i	−0.548934	−	0.950782i	0.449414	−	0.893324i	$-0.351633\pi$
$234$		0			0
$235$	2279.72	−	3948.59i	0.632819	−	1.09608i
$236$	590.108	+	1022.10i	0.162766	+	0.281919i
$237$		0			0
$238$		0			0
$239$	−5425.12			−1.46829			−0.734146	−	0.678991i	$-0.762417\pi$
$239$	−5425.12			−1.46829			−0.734146	+	0.678991i	$0.762417\pi$
$240$		0			0
$241$	−801.446	+	1388.15i	−0.214215	+	0.371030i	−0.953029	−	0.302878i	$-0.902053\pi$
$241$	−801.446	+	1388.15i	−0.214215	+	0.371030i	0.738815	+	0.673909i	$0.235386\pi$
$242$	−3013.97	+	5220.35i	−0.800600	+	1.38668i
$243$		0			0
$244$	1510.31			0.396261
$245$		0			0
$246$		0			0
$247$	1630.56	+	2824.22i	0.420042	+	0.727534i
$248$	842.874	−	1459.90i	0.215817	−	0.373806i
$249$		0			0
$250$	2086.19	+	3613.38i	0.527768	+	0.914121i
$251$	3805.93			0.957085			0.478542	−	0.878064i	$-0.341165\pi$
$251$	3805.93			0.957085			0.478542	+	0.878064i	$0.341165\pi$
$252$		0			0
$253$	97.7897			0.0243003
$254$	2171.22	+	3760.67i	0.536357	+	0.928997i
$255$		0			0
$256$	1660.05	−	2875.28i	0.405285	−	0.701974i
$257$	−2294.67	−	3974.49i	−0.556956	−	0.964676i	−0.997748	−	0.0670671i	$-0.978636\pi$
$257$	−2294.67	−	3974.49i	−0.556956	−	0.964676i	0.440792	−	0.897609i	$-0.354697\pi$
$258$		0			0
$259$		0			0
$260$	5904.41			1.40837
$261$		0			0
$262$	2610.29	−	4521.15i	0.615512	−	1.06610i
$263$	438.587	−	759.656i	0.102831	−	0.178108i	−0.810019	−	0.586403i	$-0.800543\pi$
$263$	438.587	−	759.656i	0.102831	−	0.178108i	0.912850	+	0.408295i	$0.133877\pi$
$264$		0			0
$265$	2010.00			0.465938
$266$		0			0
$267$		0			0
$268$	4964.62	+	8598.97i	1.13158	+	1.95995i
$269$	3061.78	−	5303.15i	0.693977	−	1.20200i	−0.276547	−	0.961000i	$-0.589190\pi$
$269$	3061.78	−	5303.15i	0.693977	−	1.20200i	0.970524	−	0.241003i	$-0.0774764\pi$
$270$		0			0
$271$	−1744.88	−	3022.22i	−0.391122	−	0.677443i	0.601476	−	0.798891i	$-0.294579\pi$
$271$	−1744.88	−	3022.22i	−0.391122	−	0.677443i	−0.992598	+	0.121448i	$0.961246\pi$
$272$	−850.006			−0.189482
$273$		0			0
$274$	1619.32			0.357032
$275$	23.0488	+	39.9217i	0.00505417	+	0.00875407i
$276$		0			0
$277$	2445.85	−	4236.33i	0.530530	−	0.918905i	−0.468836	−	0.883285i	$-0.655326\pi$
$277$	2445.85	−	4236.33i	0.530530	−	0.918905i	0.999365	−	0.0356193i	$-0.0113404\pi$
$278$	6199.23	+	10737.4i	1.33743	+	2.31649i
$279$		0			0
$280$		0			0
$281$	−6914.46			−1.46791			−0.733954	−	0.679199i	$-0.762327\pi$
$281$	−6914.46			−1.46791			−0.733954	+	0.679199i	$0.762327\pi$
$282$		0			0
$283$	1779.92	−	3082.92i	0.373871	−	0.647564i	−0.616286	−	0.787522i	$-0.711364\pi$
$283$	1779.92	−	3082.92i	0.373871	−	0.647564i	0.990157	+	0.139959i	$0.0446969\pi$
$284$	2814.04	−	4874.07i	0.587967	−	1.01839i
$285$		0			0
$286$	−128.809			−0.0266315
$287$		0			0
$288$		0			0
$289$	−4473.90	−	7749.02i	−0.910625	−	1.57725i
$290$	261.531	−	452.984i	0.0529572	−	0.0917246i
$291$		0			0
$292$	−2941.18	−	5094.27i	−0.589451	−	1.02096i
$293$	3285.11			0.655011			0.327505	−	0.944849i	$-0.393792\pi$
$293$	3285.11			0.655011			0.327505	+	0.944849i	$0.393792\pi$
$294$		0			0
$295$	1269.49			0.250552
$296$	295.784	+	512.313i	0.0580814	+	0.100600i
$297$		0			0
$298$	−3194.31	+	5532.70i	−0.620943	+	1.07551i
$299$	−2101.74	−	3640.31i	−0.406510	−	0.704096i
$300$		0			0
$301$		0			0
$302$	−10658.8			−2.03094
$303$		0			0
$304$	336.774	−	583.310i	0.0635373	−	0.110050i
$305$	812.278	−	1406.91i	0.152495	−	0.264129i
$306$		0			0
$307$	9094.65			1.69075			0.845373	−	0.534176i	$-0.179378\pi$
$307$	9094.65			1.69075			0.845373	+	0.534176i	$0.179378\pi$
$308$		0			0
$309$		0			0
$310$	−2507.35	−	4342.86i	−0.459381	−	0.795671i
$311$	4081.53	−	7069.42i	0.744188	−	1.28897i	−0.206386	−	0.978471i	$-0.566170\pi$
$311$	4081.53	−	7069.42i	0.744188	−	1.28897i	0.950573	−	0.310500i	$-0.100497\pi$
$312$		0			0
$313$	1489.81	+	2580.42i	0.269038	+	0.465988i	0.968614	−	0.248571i	$-0.0799609\pi$
$313$	1489.81	+	2580.42i	0.269038	+	0.465988i	−0.699576	+	0.714559i	$0.746628\pi$
$314$	5499.98			0.988478
$315$		0			0
$316$	−12779.9			−2.27508
$317$	−1944.05	−	3367.20i	−0.344445	−	0.596596i	0.640808	−	0.767701i	$-0.278599\pi$
$317$	−1944.05	−	3367.20i	−0.344445	−	0.596596i	−0.985253	+	0.171105i	$0.945266\pi$
$318$		0			0
$319$	−3.48232	+	6.03155i	−0.000611198	+	0.00105863i
$320$	−5625.52	−	9743.69i	−0.982739	−	1.70215i
$321$		0			0
$322$		0			0
$323$	10983.4			1.89205
$324$		0			0
$325$	990.749	−	1716.03i	0.169098	−	0.292886i
$326$	−1637.49	+	2836.22i	−0.278197	+	0.481852i
$327$		0			0
$328$	1448.04			0.243764
$329$		0			0
$330$		0			0
$331$	2446.52	+	4237.49i	0.406262	+	0.703666i	0.994467	−	0.105045i	$-0.0334988\pi$
$331$	2446.52	+	4237.49i	0.406262	+	0.703666i	−0.588206	+	0.808711i	$0.700165\pi$
$332$	653.203	−	1131.38i	0.107979	−	0.187026i
$333$		0			0
$334$	1706.01	+	2954.89i	0.279487	+	0.484085i
$335$	10680.3			1.74188
$336$		0			0
$337$	−1722.10			−0.278364			−0.139182	−	0.990267i	$-0.544447\pi$
$337$	−1722.10			−0.278364			−0.139182	+	0.990267i	$0.544447\pi$
$338$	−2209.04	−	3826.17i	−0.355491	−	0.615728i
$339$		0			0
$340$	9942.91	−	17221.6i	1.58597	−	2.74698i
$341$	33.3858	+	57.8259i	0.00530188	+	0.00918313i
$342$		0			0
$343$		0			0
$344$	−8565.16			−1.34245
$345$		0			0
$346$	−4212.00	+	7295.39i	−0.654446	+	1.13353i
$347$	−119.029	+	206.165i	−0.0184145	+	0.0318948i	−0.875086	−	0.483968i	$-0.839195\pi$
$347$	−119.029	+	206.165i	−0.0184145	+	0.0318948i	0.856671	+	0.515863i	$0.172529\pi$
$348$		0			0
$349$	10053.1			1.54192			0.770959	−	0.636884i	$-0.219777\pi$
$349$	10053.1			1.54192			0.770959	+	0.636884i	$0.219777\pi$
$350$		0			0
$351$		0			0
$352$	80.0878	+	138.716i	0.0121270	+	0.0210045i
$353$	1735.08	−	3005.25i	0.261612	−	0.453125i	−0.705058	−	0.709149i	$-0.749079\pi$
$353$	1735.08	−	3005.25i	0.261612	−	0.453125i	0.966670	+	0.256024i	$0.0824126\pi$
$354$		0			0
$355$	−3026.91	−	5242.77i	−0.452540	−	0.783823i
$356$	−19710.5			−2.93442
$357$		0			0
$358$	−2368.99			−0.349734
$359$	703.770	+	1218.97i	0.103464	+	0.179205i	0.913110	−	0.407714i	$-0.133674\pi$
$359$	703.770	+	1218.97i	0.103464	+	0.179205i	−0.809646	+	0.586919i	$0.800341\pi$
$360$		0			0
$361$	−922.136	+	1597.19i	−0.134442	+	0.232860i
$362$	−6573.26	−	11385.2i	−0.954373	−	1.65302i
$363$		0			0
$364$		0			0
$365$	−6327.34			−0.907364
$366$		0			0
$367$	5566.51	−	9641.48i	0.791742	−	1.37134i	−0.133145	−	0.991097i	$-0.542508\pi$
$367$	5566.51	−	9641.48i	0.791742	−	1.37134i	0.924887	−	0.380242i	$-0.124159\pi$
$368$	−434.089	+	751.865i	−0.0614904	+	0.106505i
$369$		0			0
$370$	1759.78			0.247261
$371$		0			0
$372$		0			0
$373$	−4512.97	−	7816.69i	−0.626468	−	1.08507i	−0.988255	−	0.152814i	$-0.951166\pi$
$373$	−4512.97	−	7816.69i	−0.626468	−	1.08507i	0.361787	−	0.932261i	$-0.382167\pi$
$374$	−216.911	+	375.701i	−0.0299899	+	0.0519440i
$375$		0			0
$376$	3472.44	+	6014.45i	0.476270	+	0.824924i
$377$	299.373			0.0408979
$378$		0			0
$379$	−5855.75			−0.793640			−0.396820	−	0.917896i	$-0.629886\pi$
$379$	−5855.75			−0.793640			−0.396820	+	0.917896i	$0.629886\pi$
$380$	7878.81	+	13646.5i	1.06362	+	1.84224i
$381$		0			0
$382$	−5900.32	+	10219.7i	−0.790280	+	1.36880i
$383$	3894.01	+	6744.63i	0.519517	+	0.899829i	0.999743	+	0.0226844i	$0.00722130\pi$
$383$	3894.01	+	6744.63i	0.519517	+	0.899829i	−0.480226	+	0.877145i	$0.659445\pi$
$384$		0			0
$385$		0			0
$386$	−3064.16			−0.404045
$387$		0			0
$388$	3446.42	−	5969.38i	0.450942	−	0.781054i
$389$	−1907.03	+	3303.07i	−0.248560	+	0.430519i	−0.963127	−	0.269048i	$-0.913291\pi$
$389$	−1907.03	+	3303.07i	−0.248560	+	0.430519i	0.714566	+	0.699568i	$0.246624\pi$
$390$		0			0
$391$	−14157.1			−1.83109
$392$		0			0
$393$		0			0
$394$	8350.85	+	14464.1i	1.06779	+	1.84947i
$395$	−6873.32	+	11904.9i	−0.875530	+	1.51646i
$396$		0			0
$397$	−5082.64	−	8803.39i	−0.642545	−	1.11292i	−0.984863	−	0.173336i	$-0.944545\pi$
$397$	−5082.64	−	8803.39i	−0.642545	−	1.11292i	0.342318	−	0.939584i	$-0.388788\pi$
$398$	−3624.00			−0.456419
$399$		0			0
$400$	−409.255			−0.0511569
$401$	5751.27	+	9961.50i	0.716222	+	1.24053i	0.962486	+	0.271330i	$0.0874634\pi$
$401$	5751.27	+	9961.50i	0.716222	+	1.24053i	−0.246265	+	0.969203i	$0.579203\pi$
$402$		0			0
$403$	1435.08	−	2485.63i	0.177386	−	0.307241i
$404$	411.754	+	713.178i	0.0507067	+	0.0878266i
$405$		0			0
$406$		0			0
$407$	−23.4317			−0.00285372
$408$		0			0
$409$	1633.14	−	2828.67i	0.197441	−	0.341978i	−0.750257	−	0.661146i	$-0.770070\pi$
$409$	1633.14	−	2828.67i	0.197441	−	0.341978i	0.947698	+	0.319168i	$0.103404\pi$
$410$	2153.79	−	3730.48i	0.259435	−	0.449354i
$411$		0			0
$412$	−22923.8			−2.74120
$413$		0			0
$414$		0			0
$415$	−702.615	−	1216.96i	−0.0831084	−	0.143948i
$416$	3442.56	−	5962.69i	0.405734	−	0.702752i
$417$		0			0
$418$	−171.882	−	297.708i	−0.0201124	−	0.0348358i
$419$	−6822.93			−0.795518			−0.397759	−	0.917490i	$-0.630212\pi$
$419$	−6822.93			−0.795518			−0.397759	+	0.917490i	$0.630212\pi$
$420$		0			0
$421$	1431.63			0.165733			0.0828665	−	0.996561i	$-0.473592\pi$
$421$	1431.63			0.165733			0.0828665	+	0.996561i	$0.473592\pi$
$422$	−1512.00	−	2618.87i	−0.174415	−	0.302096i
$423$		0			0
$424$	−1530.81	+	2651.44i	−0.175336	+	0.303691i
$425$	−3336.81	−	5779.52i	−0.380844	−	0.659642i
$426$		0			0
$427$		0			0
$428$	−10794.0			−1.21904
$429$		0			0
$430$	−12739.7	+	22065.8i	−1.42875	+	2.47466i
$431$	7571.10	−	13113.5i	0.846141	−	1.46556i	−0.0384849	−	0.999259i	$-0.512253\pi$
$431$	7571.10	−	13113.5i	0.846141	−	1.46556i	0.884626	−	0.466301i	$-0.154414\pi$
$432$		0			0
$433$	5475.65			0.607721			0.303860	−	0.952717i	$-0.401724\pi$
$433$	5475.65			0.607721			0.303860	+	0.952717i	$0.401724\pi$
$434$		0			0
$435$		0			0
$436$	10153.5	+	17586.3i	1.11528	+	1.93172i
$437$	5609.10	−	9715.24i	0.614003	−	1.06348i
$438$		0			0
$439$	890.272	+	1542.00i	0.0967890	+	0.167643i	0.910354	−	0.413831i	$-0.135809\pi$
$439$	890.272	+	1542.00i	0.0967890	+	0.167643i	−0.813565	+	0.581474i	$0.802476\pi$
$440$	−225.052			−0.0243840
$441$		0			0
$442$	18647.8			2.00675
$443$	−1629.82	−	2822.93i	−0.174797	−	0.302757i	0.765294	−	0.643681i	$-0.222594\pi$
$443$	−1629.82	−	2822.93i	−0.174797	−	0.302757i	−0.940091	+	0.340924i	$0.889260\pi$
$444$		0			0
$445$	−10600.7	+	18361.0i	−1.12926	+	1.95594i
$446$	−5996.55	−	10386.3i	−0.636648	−	1.10271i
$447$		0			0
$448$		0			0
$449$	6826.19			0.717478			0.358739	−	0.933438i	$-0.383207\pi$
$449$	6826.19			0.717478			0.358739	+	0.933438i	$0.383207\pi$
$450$		0			0
$451$	−28.6781	+	49.6719i	−0.00299423	+	0.00518616i
$452$	2383.48	−	4128.30i	0.248029	−	0.429599i
$453$		0			0
$454$	−18673.3			−1.93036
$455$		0			0
$456$		0			0
$457$	−1850.01	−	3204.32i	−0.189365	−	0.327991i	0.755673	−	0.654949i	$-0.227310\pi$
$457$	−1850.01	−	3204.32i	−0.189365	−	0.327991i	−0.945039	+	0.326958i	$0.893976\pi$
$458$	−9213.88	+	15958.9i	−0.940035	+	1.62819i
$459$		0			0
$460$	−10155.5	−	17589.8i	−1.02935	−	1.78289i
$461$	−9400.80			−0.949759			−0.474880	−	0.880051i	$-0.657508\pi$
$461$	−9400.80			−0.949759			−0.474880	+	0.880051i	$0.657508\pi$
$462$		0			0
$463$	15483.9			1.55420			0.777102	−	0.629374i	$-0.216689\pi$
$463$	15483.9			1.55420			0.777102	+	0.629374i	$0.216689\pi$
$464$	−30.9161	−	53.5482i	−0.00309319	−	0.00535757i
$465$		0			0
$466$	8846.28	−	15322.2i	0.879391	−	1.52315i
$467$	1102.81	+	1910.12i	0.109276	+	0.189272i	0.915477	−	0.402370i	$-0.131813\pi$
$467$	1102.81	+	1910.12i	0.109276	+	0.189272i	−0.806201	+	0.591642i	$0.798480\pi$
$468$		0			0
$469$		0			0
$470$	20659.4			2.02755
$471$		0			0
$472$	−966.839	+	1674.61i	−0.0942847	+	0.163306i
$473$	169.631	−	293.809i	0.0164897	−	0.0285610i
$474$		0			0
$475$	5288.20			0.510820
$476$		0			0
$477$		0			0
$478$	−12291.0	−	21288.6i	−1.17610	−	2.03706i
$479$	−1174.66	+	2034.57i	−0.112049	+	0.194075i	−0.916596	−	0.399814i	$-0.869075\pi$
$479$	−1174.66	+	2034.57i	−0.112049	+	0.194075i	0.804547	+	0.593889i	$0.202408\pi$
$480$		0			0
$481$	503.603	+	872.266i	0.0477387	+	0.0826859i
$482$	−7262.91			−0.686342
$483$		0			0
$484$	−16670.6			−1.56561
$485$	−3707.13	−	6420.93i	−0.347076	−	0.601154i
$486$		0			0
$487$	−5197.14	+	9001.72i	−0.483583	+	0.837591i	−0.999822	−	0.0188537i	$-0.993998\pi$
$487$	−5197.14	+	9001.72i	−0.483583	+	0.837591i	0.516239	+	0.856445i	$0.327332\pi$
$488$	1237.25	+	2142.98i	0.114770	+	0.198788i
$489$		0			0
$490$		0			0
$491$	−12586.7			−1.15689			−0.578444	−	0.815722i	$-0.696340\pi$
$491$	−12586.7			−1.15689			−0.578444	+	0.815722i	$0.696340\pi$
$492$		0			0
$493$	504.140	−	873.195i	0.0460554	−	0.0797703i
$494$	−7388.30	+	12796.9i	−0.672905	+	1.16551i
$495$		0			0
$496$	−592.799			−0.0536642
$497$		0			0
$498$		0			0
$499$	−5313.97	−	9204.06i	−0.476725	−	0.825712i	0.522919	−	0.852382i	$-0.324843\pi$
$499$	−5313.97	−	9204.06i	−0.476725	−	0.825712i	−0.999644	+	0.0266703i	$0.991510\pi$
$500$	−5769.48	+	9993.03i	−0.516038	+	0.893804i
$501$		0			0
$502$	8622.59	+	14934.8i	0.766623	+	1.32783i
$503$	−6719.02			−0.595599			−0.297800	−	0.954628i	$-0.596253\pi$
$503$	−6719.02			−0.595599			−0.297800	+	0.954628i	$0.596253\pi$
$504$		0			0
$505$	885.802			0.0780548
$506$	221.549	+	383.734i	0.0194645	+	0.0337136i
$507$		0			0
$508$	−6004.65	+	10400.4i	−0.524436	+	0.908350i
$509$	−1952.17	−	3381.25i	−0.169997	−	0.294443i	0.768422	−	0.639944i	$-0.221042\pi$
$509$	−1952.17	−	3381.25i	−0.169997	−	0.294443i	−0.938418	+	0.345501i	$0.887709\pi$
$510$		0			0
$511$		0			0
$512$	−2607.89			−0.225105
$513$		0			0
$514$	10397.5	−	18008.9i	0.892241	−	1.54541i
$515$	−12328.9	+	21354.4i	−1.05491	+	1.82716i
$516$		0			0
$517$	−275.083			−0.0234007
$518$		0			0
$519$		0			0
$520$	4836.92	+	8377.79i	0.407909	+	0.706520i
$521$	7849.85	−	13596.3i	0.660092	−	1.14331i	−0.320499	−	0.947249i	$-0.603850\pi$
$521$	7849.85	−	13596.3i	0.660092	−	1.14331i	0.980591	−	0.196064i	$-0.0628162\pi$
$522$		0			0
$523$	5076.03	+	8791.95i	0.424397	+	0.735077i	0.996364	−	0.0851998i	$-0.0271529\pi$
$523$	5076.03	+	8791.95i	0.424397	+	0.735077i	−0.571967	+	0.820277i	$0.693820\pi$
$524$	14437.8			1.20366
$525$		0			0
$526$	3974.59			0.329469
$527$	−4833.30	−	8371.53i	−0.399510	−	0.691972i
$528$		0			0
$529$	−1146.41	+	1985.65i	−0.0942233	+	0.163200i
$530$	4553.80	+	7887.41i	0.373216	+	0.646428i
$531$		0			0
$532$		0			0
$533$	2465.44			0.200357
$534$		0			0
$535$	−5805.28	+	10055.0i	−0.469129	+	0.812555i
$536$	−8134.08	+	14088.6i	−0.655483	+	1.13533i
$537$		0			0
$538$	27746.6			2.22350
$539$		0			0
$540$		0			0
$541$	9923.32	+	17187.7i	0.788608	+	1.36591i	0.926820	+	0.375506i	$0.122531\pi$
$541$	9923.32	+	17187.7i	0.788608	+	1.36591i	−0.138212	+	0.990403i	$0.544136\pi$
$542$	7906.28	−	13694.1i	0.626575	−	1.08526i
$543$		0			0
$544$	−11594.4	−	20082.1i	−0.913799	−	1.58275i
$545$	21843.0			1.71679
$546$		0			0
$547$	−22798.9			−1.78210			−0.891052	−	0.453901i	$-0.850032\pi$
$547$	−22798.9			−1.78210			−0.891052	+	0.453901i	$0.850032\pi$
$548$	2239.17	+	3878.36i	0.174549	+	0.302327i
$549$		0			0
$550$	−104.437	+	180.890i	−0.00809675	+	0.0140240i
$551$	399.483	+	691.924i	0.0308866	+	0.0534972i
$552$		0			0
$553$		0			0
$554$	22164.9			1.69981
$555$		0			0
$556$	−17144.4	+	29694.9i	−1.30770	+	2.26501i
$557$	−8999.13	+	15586.9i	−0.684570	+	1.18571i	0.289002	+	0.957328i	$0.406677\pi$
$557$	−8999.13	+	15586.9i	−0.684570	+	1.18571i	−0.973572	+	0.228381i	$0.926657\pi$
$558$		0			0
$559$	−14583.1			−1.10340
$560$		0			0
$561$		0			0
$562$	−15665.2	−	27132.8i	−1.17579	−	2.03653i
$563$	−97.8182	+	169.426i	−0.00732246	+	0.0126829i	−0.869663	−	0.493645i	$-0.835664\pi$
$563$	−97.8182	+	169.426i	−0.00732246	+	0.0126829i	0.862341	+	0.506328i	$0.168998\pi$
$564$		0			0
$565$	−2563.77	−	4440.59i	−0.190901	−	0.330649i
$566$	16130.1			1.19788
$567$		0			0
$568$	9221.11			0.681178
$569$	−9830.21	−	17026.4i	−0.724260	−	1.25445i	−0.959278	−	0.282464i	$-0.908848\pi$
$569$	−9830.21	−	17026.4i	−0.724260	−	1.25445i	0.235018	−	0.971991i	$-0.424485\pi$
$570$		0			0
$571$	7882.25	−	13652.5i	0.577691	−	1.00059i	−0.418052	−	0.908423i	$-0.637287\pi$
$571$	7882.25	−	13652.5i	0.577691	−	1.00059i	0.995743	−	0.0921678i	$-0.0293796\pi$
$572$	−178.114	−	308.503i	−0.0130198	−	0.0225510i
$573$		0			0
$574$		0			0
$575$	−6816.30			−0.494364
$576$		0			0
$577$	11153.2	−	19317.9i	0.804704	−	1.39379i	−0.111786	−	0.993732i	$-0.535657\pi$
$577$	11153.2	−	19317.9i	0.804704	−	1.39379i	0.916490	−	0.400057i	$-0.131010\pi$
$578$	20271.8	−	35111.8i	1.45882	−	2.52675i
$579$		0			0
$580$	1446.56			0.103560
$581$		0			0
$582$		0			0
$583$	−60.6344	−	105.022i	−0.00430741	−	0.00746066i
$584$	4818.86	−	8346.51i	0.341448	−	0.591406i
$585$		0			0
$586$	7442.63	+	12891.0i	0.524662	+	0.908742i
$587$	−15953.2			−1.12173			−0.560866	−	0.827906i	$-0.689532\pi$
$587$	−15953.2			−1.12173			−0.560866	+	0.827906i	$0.689532\pi$
$588$		0			0
$589$	7659.87			0.535856
$590$	2876.12	+	4981.59i	0.200692	+	0.347608i
$591$		0			0
$592$	104.013	−	180.157i	0.00722116	−	0.0125074i
$593$	1577.84	+	2732.90i	0.109265	+	0.189253i	0.915473	−	0.402380i	$-0.131817\pi$
$593$	1577.84	+	2732.90i	0.109265	+	0.189253i	−0.806208	+	0.591633i	$0.798484\pi$
$594$		0			0
$595$		0			0
$596$	−17668.1			−1.21429
$597$		0			0
$598$	9523.24	−	16494.7i	0.651228	−	1.12796i
$599$	12728.2	−	22045.8i	0.868212	−	1.50379i	0.00438889	−	0.999990i	$-0.498603\pi$
$599$	12728.2	−	22045.8i	0.868212	−	1.50379i	0.863823	−	0.503796i	$-0.168064\pi$
$600$		0			0
$601$	−5580.96			−0.378789			−0.189395	−	0.981901i	$-0.560653\pi$
$601$	−5580.96			−0.378789			−0.189395	+	0.981901i	$0.560653\pi$
$602$		0			0
$603$		0			0
$604$	−14738.8	−	25528.4i	−0.992903	−	1.71976i
$605$	−8965.85	+	15529.3i	−0.602502	+	1.04356i
$606$		0			0
$607$	190.566	+	330.071i	0.0127427	+	0.0220711i	0.872326	−	0.488924i	$-0.162610\pi$
$607$	190.566	+	330.071i	0.0127427	+	0.0220711i	−0.859584	+	0.510995i	$0.829277\pi$
$608$	18374.9			1.22566
$609$		0			0
$610$	7361.07			0.488592
$611$	5912.20	+	10240.2i	0.391460	+	0.678028i
$612$		0			0
$613$	4117.99	−	7132.57i	0.271328	−	0.469954i	−0.697874	−	0.716220i	$-0.745871\pi$
$613$	4117.99	−	7132.57i	0.271328	−	0.469954i	0.969202	+	0.246266i	$0.0792038\pi$
$614$	20604.5	+	35688.1i	1.35428	+	2.34569i
$615$		0			0
$616$		0			0
$617$	27419.8			1.78911			0.894555	−	0.446958i	$-0.147493\pi$
$617$	27419.8			1.78911			0.894555	+	0.446958i	$0.147493\pi$
$618$		0			0
$619$	−8186.69	+	14179.8i	−0.531585	+	0.920732i	0.467736	+	0.883868i	$0.345070\pi$
$619$	−8186.69	+	14179.8i	−0.531585	+	0.920732i	−0.999320	+	0.0368632i	$0.988263\pi$
$620$	6934.25	−	12010.5i	0.449171	−	0.777987i
$621$		0			0
$622$	36987.9			2.38437
$623$		0			0
$624$		0			0
$625$	9748.72	+	16885.3i	0.623918	+	1.08066i
$626$	−6750.51	+	11692.2i	−0.430998	+	0.746510i
$627$		0			0
$628$	7605.28	+	13172.7i	0.483254	+	0.837021i
$629$	3392.24			0.215035
$630$		0			0
$631$	4059.60			0.256118			0.128059	−	0.991767i	$-0.459125\pi$
$631$	4059.60			0.256118			0.128059	+	0.991767i	$0.459125\pi$
$632$	−10469.4	−	18133.5i	−0.658938	−	1.14131i
$633$		0			0
$634$	8808.76	−	15257.2i	0.551799	−	0.955744i
$635$	6458.88	+	11187.1i	0.403642	+	0.699129i
$636$		0			0
$637$		0			0
$638$	−31.5577			−0.00195827
$639$		0			0
$640$	14870.5	−	25756.4i	0.918449	−	1.59080i
$641$	−3194.32	+	5532.72i	−0.196830	+	0.340919i	−0.947499	−	0.319759i	$-0.896398\pi$
$641$	−3194.32	+	5532.72i	−0.196830	+	0.340919i	0.750669	+	0.660678i	$0.229731\pi$
$642$		0			0
$643$	18308.0			1.12286			0.561428	−	0.827525i	$-0.310252\pi$
$643$	18308.0			1.12286			0.561428	+	0.827525i	$0.310252\pi$
$644$		0			0
$645$		0			0
$646$	24883.5	+	43099.5i	1.51553	+	2.62497i
$647$	−1651.95	+	2861.26i	−0.100379	+	0.173861i	−0.911841	−	0.410544i	$-0.865339\pi$
$647$	−1651.95	+	2861.26i	−0.100379	+	0.173861i	0.811462	+	0.584405i	$0.198672\pi$
$648$		0			0
$649$	−38.2960	−	66.3306i	−0.00231625	−	0.00401187i
$650$	8978.42			0.541789
$651$		0			0
$652$	−9057.18			−0.544028
$653$	2185.63	+	3785.63i	0.130981	+	0.226865i	0.924055	−	0.382260i	$-0.124854\pi$
$653$	2185.63	+	3785.63i	0.130981	+	0.226865i	−0.793074	+	0.609125i	$0.791521\pi$
$654$		0			0
$655$	7765.00	−	13449.4i	0.463211	−	0.802306i
$656$	−254.604	−	440.988i	−0.0151534	−	0.0262465i
$657$		0			0
$658$		0			0
$659$	−6259.75			−0.370023			−0.185012	−	0.982736i	$-0.559232\pi$
$659$	−6259.75			−0.370023			−0.185012	+	0.982736i	$0.559232\pi$
$660$		0			0
$661$	−7422.87	+	12856.8i	−0.436787	+	0.756537i	−0.997440	−	0.0715138i	$-0.977217\pi$
$661$	−7422.87	+	12856.8i	−0.436787	+	0.756537i	0.560653	+	0.828051i	$0.310550\pi$
$662$	−11085.5	+	19200.6i	−0.650830	+	1.12727i
$663$		0			0
$664$	2140.43			0.125098
$665$		0			0
$666$		0			0
$667$	−514.918	−	891.864i	−0.0298916	−	0.0517738i
$668$	−4718.07	+	8171.94i	−0.273275	+	0.473326i
$669$		0			0
$670$	24197.0	+	41910.4i	1.39524	+	2.41663i
$671$	−98.0138			−0.00563902
$672$		0			0
$673$	9409.13			0.538923			0.269462	−	0.963011i	$-0.413154\pi$
$673$	9409.13			0.538923			0.269462	+	0.963011i	$0.413154\pi$
$674$	−3901.52	−	6757.64i	−0.222969	−	0.386194i
$675$		0			0
$676$	6109.24	−	10581.5i	0.347590	−	0.602044i
$677$	−1475.32	−	2555.32i	−0.0837533	−	0.145065i	0.821106	−	0.570776i	$-0.193357\pi$
$677$	−1475.32	−	2555.32i	−0.0837533	−	0.145065i	−0.904859	+	0.425711i	$0.860024\pi$
$678$		0			0
$679$		0			0
$680$	32581.1			1.83740
$681$		0			0
$682$	−151.275	+	262.016i	−0.00849359	+	0.0147113i
$683$	3140.42	−	5439.38i	0.175937	−	0.304732i	−0.764548	−	0.644567i	$-0.777038\pi$
$683$	3140.42	−	5439.38i	0.175937	−	0.304732i	0.940485	+	0.339835i	$0.110371\pi$
$684$		0			0
$685$	4817.11			0.268689
$686$		0			0
$687$		0			0
$688$	1505.98	+	2608.44i	0.0834521	+	0.144543i
$689$	−2606.36	+	4514.35i	−0.144114	+	0.249612i
$690$		0			0
$691$	16381.6	+	28373.8i	0.901861	+	1.56207i	0.825077	+	0.565021i	$0.191132\pi$
$691$	16381.6	+	28373.8i	0.901861	+	1.56207i	0.0767837	+	0.997048i	$0.475535\pi$
$692$	−23297.1			−1.27980
$693$		0			0
$694$	−1078.67			−0.0589998
$695$	18441.3	+	31941.2i	1.00650	+	1.74331i
$696$		0			0
$697$	4151.76	−	7191.06i	0.225623	−	0.390791i
$698$	22775.9	+	39449.1i	1.23507	+	2.13921i
$699$		0			0
$700$		0			0
$701$	1775.97			0.0956883			0.0478442	−	0.998855i	$-0.484765\pi$
$701$	1775.97			0.0956883			0.0478442	+	0.998855i	$0.484765\pi$
$702$		0			0
$703$	−1344.01	+	2327.90i	−0.0721058	+	0.124891i
$704$	−339.403	+	587.863i	−0.0181701	+	0.0314715i
$705$		0			0
$706$	15723.7			0.838203
$707$		0			0
$708$		0			0
$709$	−4431.22	−	7675.09i	−0.234722	−	0.406550i	0.724470	−	0.689306i	$-0.242085\pi$
$709$	−4431.22	−	7675.09i	−0.234722	−	0.406550i	−0.959192	+	0.282756i	$0.908751\pi$
$710$	13715.3	−	23755.6i	0.724968	−	1.25568i
$711$		0			0
$712$	−16146.9	−	27967.3i	−0.849903	−	1.47207i
$713$	−9873.28			−0.518594
$714$		0			0
$715$	−383.175			−0.0200419
$716$	−3275.79	−	5673.84i	−0.170981	−	0.296147i
$717$		0			0
$718$	−3188.87	+	5523.29i	−0.165749	+	0.287085i
$719$	−13749.6	−	23815.0i	−0.713177	−	1.23526i	−0.963658	−	0.267138i	$-0.913922\pi$
$719$	−13749.6	−	23815.0i	−0.713177	−	1.23526i	0.250481	−	0.968121i	$-0.419411\pi$
$720$		0			0
$721$		0			0
$722$	−8356.64			−0.430750
$723$		0			0
$724$	18178.8	−	31486.6i	0.933162	−	1.61628i
$725$	242.730	−	420.421i	0.0124342	−	0.0215366i
$726$		0			0
$727$	−25434.9			−1.29756			−0.648781	−	0.760975i	$-0.724721\pi$
$727$	−25434.9			−1.29756			−0.648781	+	0.760975i	$0.724721\pi$
$728$		0			0
$729$		0			0
$730$	−14335.0	−	24828.9i	−0.726797	−	1.25885i
$731$	−24557.6	+	42535.1i	−1.24254	+	2.15214i
$732$		0			0
$733$	−12077.8	−	20919.4i	−0.608600	−	1.05413i	−0.991471	−	0.130325i	$-0.958398\pi$
$733$	−12077.8	−	20919.4i	−0.608600	−	1.05413i	0.382871	−	0.923802i	$-0.374935\pi$
$734$	50445.2			2.53674
$735$		0			0
$736$	−23684.6			−1.18618
$737$	−322.187	−	558.043i	−0.0161030	−	0.0278912i
$738$		0			0
$739$	−13756.4	+	23826.9i	−0.684762	+	1.18604i	0.288750	+	0.957405i	$0.406760\pi$
$739$	−13756.4	+	23826.9i	−0.684762	+	1.18604i	−0.973512	+	0.228638i	$0.926573\pi$
$740$	2433.39	+	4214.75i	0.120883	+	0.209375i
$741$		0			0
$742$		0			0
$743$	−5995.09			−0.296014			−0.148007	−	0.988986i	$-0.547286\pi$
$743$	−5995.09			−0.296014			−0.148007	+	0.988986i	$0.547286\pi$
$744$		0			0
$745$	−9502.31	+	16458.5i	−0.467299	+	0.809386i
$746$	20448.8	−	35418.4i	1.00360	−	1.73829i
$747$		0			0
$748$	−1199.76			−0.0586467
$749$		0			0
$750$		0			0
$751$	−772.544	−	1338.09i	−0.0375373	−	0.0650166i	0.846646	−	0.532156i	$-0.178618\pi$
$751$	−772.544	−	1338.09i	−0.0375373	−	0.0650166i	−0.884184	+	0.467139i	$0.845285\pi$
$752$	1221.10	−	2115.00i	0.0592138	−	0.102561i
$753$		0			0
$754$	678.250	+	1174.76i	0.0327591	+	0.0567405i
$755$	−31707.5			−1.52841
$756$		0			0
$757$	−5157.82			−0.247641			−0.123820	−	0.992305i	$-0.539515\pi$
$757$	−5157.82			−0.247641			−0.123820	+	0.992305i	$0.539515\pi$
$758$	−13266.6	−	22978.4i	−0.635704	−	1.10107i
$759$		0			0
$760$	−12908.7	+	22358.6i	−0.616117	+	1.06715i
$761$	1644.98	+	2849.19i	0.0783581	+	0.135720i	0.902542	−	0.430602i	$-0.141699\pi$
$761$	1644.98	+	2849.19i	0.0783581	+	0.135720i	−0.824184	+	0.566323i	$0.808366\pi$
$762$		0			0
$763$		0			0
$764$	−32635.4			−1.54543
$765$		0			0
$766$	−17644.3	+	30560.8i	−0.832264	+	1.44152i
$767$	−1646.14	+	2851.21i	−0.0774952	+	0.134226i
$768$		0			0
$769$	11146.5			0.522697			0.261348	−	0.965245i	$-0.415833\pi$
$769$	11146.5			0.522697			0.261348	+	0.965245i	$0.415833\pi$
$770$		0			0
$771$		0			0
$772$	−4237.06	−	7338.80i	−0.197533	−	0.342136i
$773$	7915.11	−	13709.4i	0.368288	−	0.637894i	−0.621010	−	0.783803i	$-0.713277\pi$
$773$	7915.11	−	13709.4i	0.368288	−	0.637894i	0.989298	+	0.145909i	$0.0466107\pi$
$774$		0			0
$775$	−2327.11	−	4030.67i	−0.107861	−	0.186821i
$776$	11293.3			0.522430
$777$		0			0
$778$	−17282.0			−0.796386
$779$	3289.88	+	5698.23i	0.151312	+	0.262080i
$780$		0			0
$781$	−182.622	+	316.310i	−0.00836711	+	0.0144923i
$782$	−32073.9	−	55553.7i	−1.46670	−	2.54040i
$783$		0			0
$784$		0			0
$785$	16361.2			0.743892
$786$		0			0
$787$	−7581.72	+	13131.9i	−0.343404	+	0.594794i	−0.985063	−	0.172197i	$-0.944913\pi$
$787$	−7581.72	+	13131.9i	−0.343404	+	0.594794i	0.641658	+	0.766991i	$0.278247\pi$
$788$	−23094.8	+	40001.4i	−1.04406	+	1.80836i
$789$		0			0
$790$	−62287.8			−2.80519
$791$		0			0
$792$		0			0
$793$	2106.55	+	3648.65i	0.0943327	+	0.163389i
$794$	23030.1	−	39889.3i	1.02935	−	1.78289i
$795$		0			0
$796$	−5011.21	−	8679.66i	−0.223138	−	0.386486i
$797$	29398.3			1.30658			0.653289	−	0.757109i	$-0.273389\pi$
$797$	29398.3			1.30658			0.653289	+	0.757109i	$0.273389\pi$
$798$		0			0
$799$	39824.1			1.76330
$800$	−5582.41	−	9669.02i	−0.246710	−	0.427314i
$801$		0			0
$802$	−26059.8	+	45136.8i	−1.14738	+	1.98733i
$803$	190.872	+	330.601i	0.00838822	+	0.0145288i
$804$		0			0
$805$		0			0
$806$	13005.1			0.568343
$807$		0			0
$808$	−674.621	+	1168.48i	−0.0293726	+	0.0508749i
$809$	−10356.4	+	17937.9i	−0.450078	+	0.779557i	−0.998390	−	0.0567160i	$-0.981937\pi$
$809$	−10356.4	+	17937.9i	−0.450078	+	0.779557i	0.548313	+	0.836273i	$0.315270\pi$
$810$		0			0
$811$	−27369.9			−1.18506			−0.592532	−	0.805547i	$-0.701872\pi$
$811$	−27369.9			−1.18506			−0.592532	+	0.805547i	$0.701872\pi$
$812$		0			0
$813$		0			0
$814$	−53.0860	−	91.9476i	−0.00228583	−	0.00395917i
$815$	−4871.16	+	8437.09i	−0.209361	+	0.362624i
$816$		0			0
$817$	−19459.6	−	33705.0i	−0.833299	−	1.44332i
$818$	14799.9			0.632600
$819$		0			0
$820$	11912.9			0.507338
$821$	−17681.3	−	30625.0i	−0.751623	−	1.30185i	−0.947036	−	0.321129i	$-0.895938\pi$
$821$	−17681.3	−	30625.0i	−0.751623	−	1.30185i	0.195412	−	0.980721i	$-0.437396\pi$
$822$		0			0
$823$	14595.2	−	25279.6i	0.618174	−	1.07071i	−0.371645	−	0.928375i	$-0.621206\pi$
$823$	14595.2	−	25279.6i	0.618174	−	1.07071i	0.989819	−	0.142333i	$-0.0454605\pi$
$824$	−18779.3	−	32526.7i	−0.793941	−	1.37515i
$825$		0			0
$826$		0			0
$827$	7302.08			0.307035			0.153518	−	0.988146i	$-0.450940\pi$
$827$	7302.08			0.307035			0.153518	+	0.988146i	$0.450940\pi$
$828$		0			0
$829$	2125.38	−	3681.27i	0.0890442	−	0.154229i	−0.818063	−	0.575128i	$-0.804952\pi$
$829$	2125.38	−	3681.27i	0.0890442	−	0.154229i	0.907107	+	0.420899i	$0.138285\pi$
$830$	3183.64	−	5514.22i	0.133139	−	0.230604i
$831$		0			0
$832$	29178.3			1.21584
$833$		0			0
$834$		0			0
$835$	5074.97	+	8790.11i	0.210331	+	0.364305i
$836$	475.350	−	823.330i	0.0196654	−	0.0340615i
$837$		0			0
$838$	−15457.8	−	26773.7i	−0.637208	−	1.10368i
$839$	−39527.7			−1.62652			−0.813258	−	0.581903i	$-0.802308\pi$
$839$	−39527.7			−1.62652			−0.813258	+	0.581903i	$0.802308\pi$
$840$		0			0
$841$	−24315.7			−0.996993
$842$	3243.46	+	5617.84i	0.132752	+	0.229933i
$843$		0			0
$844$	4181.54	−	7242.65i	0.170539	−	0.295382i
$845$	−6571.38	−	11382.0i	−0.267529	−	0.463374i
$846$		0			0
$847$		0			0
$848$	1076.63			0.0435985
$849$		0			0
$850$	15119.5	−	26187.7i	0.610111	−	1.05674i
$851$	1732.38	−	3000.57i	0.0697829	−	0.120868i
$852$		0			0
$853$	−31656.1			−1.27067			−0.635337	−	0.772235i	$-0.719139\pi$
$853$	−31656.1			−1.27067			−0.635337	+	0.772235i	$0.719139\pi$
$854$		0			0
$855$		0			0
$856$	−8842.53	−	15315.7i	−0.353074	−	0.611542i
$857$	−596.579	+	1033.31i	−0.0237792	+	0.0411867i	−0.877670	−	0.479265i	$-0.840903\pi$
$857$	−596.579	+	1033.31i	−0.0237792	+	0.0411867i	0.853891	+	0.520452i	$0.174237\pi$
$858$		0			0
$859$	14530.0	+	25166.7i	0.577134	+	0.999625i	0.995806	+	0.0914874i	$0.0291621\pi$
$859$	14530.0	+	25166.7i	0.577134	+	0.999625i	−0.418673	+	0.908137i	$0.637505\pi$
$860$	−70464.8			−2.79399
$861$		0			0
$862$	68611.2			2.71103
$863$	11531.5	+	19973.1i	0.454851	+	0.787825i	0.998680	−	0.0513711i	$-0.0163591\pi$
$863$	11531.5	+	19973.1i	0.454851	+	0.787825i	−0.543828	+	0.839196i	$0.683026\pi$
$864$		0			0
$865$	−12529.7	+	21702.1i	−0.492512	+	0.853056i
$866$	12405.4	+	21486.9i	0.486783	+	0.843133i
$867$		0			0
$868$		0			0
$869$	829.371			0.0323757
$870$		0			0
$871$	−13849.1	+	23987.4i	−0.538760	+	0.933159i
$872$	−16635.5	+	28813.6i	−0.646044	+	1.11898i
$873$		0			0
$874$	50831.1			1.96726
$875$		0			0
$876$		0			0
$877$	−16935.5	−	29333.2i	−0.652077	−	1.12943i	−0.982618	−	0.185639i	$-0.940565\pi$
$877$	−16935.5	−	29333.2i	−0.652077	−	1.12943i	0.330541	−	0.943792i	$-0.392769\pi$
$878$	−4033.94	+	6986.98i	−0.155056	+	0.268564i
$879$		0			0
$880$	39.5702	+	68.5377i	0.00151581	+	0.00262546i
$881$	−43331.1			−1.65705			−0.828525	−	0.559953i	$-0.810819\pi$
$881$	−43331.1			−1.65705			−0.828525	+	0.559953i	$0.810819\pi$
$882$		0			0
$883$	−40897.3			−1.55867			−0.779334	−	0.626609i	$-0.784442\pi$
$883$	−40897.3			−1.55867			−0.779334	+	0.626609i	$0.784442\pi$
$884$	25785.8	+	44662.4i	0.981076	+	1.69927i
$885$		0			0
$886$	7384.91	−	12791.0i	0.280024	−	0.485015i
$887$	22532.9	+	39028.1i	0.852965	+	1.47738i	0.878520	+	0.477705i	$0.158531\pi$
$887$	22532.9	+	39028.1i	0.852965	+	1.47738i	−0.0255550	+	0.999673i	$0.508135\pi$
$888$		0			0
$889$		0			0
$890$	−96066.5			−3.61816
$891$		0			0
$892$	16583.9	−	28724.1i	0.622498	−	1.07820i
$893$	−15778.4	+	27329.0i	−0.591271	+	1.02411i
$894$		0			0
$895$	−7047.19			−0.263197
$896$		0			0
$897$		0			0
$898$	15465.2	+	26786.5i	0.574699	+	0.995407i
$899$	351.590	−	608.972i	0.0130436	−	0.0225922i
$900$		0			0
$901$	8778.13	+	15204.2i	0.324575	+	0.562180i
$902$	−259.888			−0.00959349
$903$		0			0
$904$	7810.22			0.287350
$905$	−19553.9	−	33868.4i	−0.718226	−	1.24400i
$906$		0			0
$907$	−12641.2	+	21895.3i	−0.462785	+	0.801567i	−0.999099	−	0.0424520i	$-0.986483\pi$
$907$	−12641.2	+	21895.3i	−0.462785	+	0.801567i	0.536314	+	0.844019i	$0.319816\pi$
$908$	−25821.1	−	44723.5i	−0.943726	−	1.63458i
$909$		0			0
$910$		0			0
$911$	41646.1			1.51460			0.757298	−	0.653070i	$-0.226519\pi$
$911$	41646.1			1.51460			0.757298	+	0.653070i	$0.226519\pi$
$912$		0			0
$913$	−42.3906	+	73.4227i	−0.00153661	+	0.00266149i
$914$	8382.65	−	14519.2i	0.303363	−	0.525440i
$915$		0			0
$916$	−50963.1			−1.83829
$917$		0			0
$918$		0			0
$919$	13056.2	+	22614.1i	0.468646	+	0.811719i	0.999358	−	0.0358337i	$-0.0114087\pi$
$919$	13056.2	+	22614.1i	0.468646	+	0.811719i	−0.530712	+	0.847552i	$0.678075\pi$
$920$	16638.9	−	28819.4i	0.596269	−	1.03277i
$921$		0			0
$922$	−21298.1	−	36889.4i	−0.760755	−	1.31767i
$923$	15699.9			0.559879
$924$		0			0
$925$	1633.27			0.0580559
$926$	35079.7	+	60759.9i	1.24491	+	2.15626i
$927$		0			0
$928$	843.415	−	1460.84i	0.0298345	−	0.0516749i
$929$	−16178.5	−	28022.0i	−0.571366	−	0.989636i	−0.996426	−	0.0844704i	$-0.973080\pi$
$929$	−16178.5	−	28022.0i	−0.571366	−	0.989636i	0.425060	−	0.905165i	$-0.360253\pi$
$930$		0			0
$931$		0			0
$932$	48929.9			1.71969
$933$		0			0
$934$	−4996.97	+	8655.01i	−0.175060	+	0.303213i
$935$	−645.261	+	1117.62i	−0.0225693	+	0.0390911i
$936$		0			0
$937$	−32947.0			−1.14870			−0.574350	−	0.818610i	$-0.694745\pi$
$937$	−32947.0			−1.14870			−0.574350	+	0.818610i	$0.694745\pi$
$938$		0			0
$939$		0			0
$940$	28567.5	+	49480.3i	0.991243	+	1.71688i
$941$	250.801	−	434.400i	0.00868849	−	0.0150489i	−0.861648	−	0.507506i	$-0.830568\pi$
$941$	250.801	−	434.400i	0.00868849	−	0.0150489i	0.870337	+	0.492457i	$0.163901\pi$
$942$		0			0
$943$	−4240.53	−	7344.81i	−0.146438	−	0.253637i
$944$	679.984			0.0234445
$945$		0			0
$946$	1537.24			0.0528328
$947$	−3218.45	−	5574.52i	−0.110439	−	0.191286i	0.805508	−	0.592584i	$-0.201892\pi$
$947$	−3218.45	−	5574.52i	−0.110439	−	0.191286i	−0.915947	+	0.401299i	$0.868559\pi$
$948$		0			0
$949$	8204.61	−	14210.8i	0.280646	−	0.486093i
$950$	11980.8	+	20751.3i	0.409166	+	0.708696i
$951$		0			0
$952$		0			0
$953$	−47511.2			−1.61494			−0.807470	−	0.589908i	$-0.799164\pi$
$953$	−47511.2			−1.61494			−0.807470	+	0.589908i	$0.799164\pi$
$954$		0			0
$955$	−17552.1	+	30401.1i	−0.594735	+	1.03011i
$956$	33991.4	−	58874.9i	1.14996	−	1.99179i
$957$		0			0
$958$	−10645.1			−0.359004
$959$		0			0
$960$		0			0
$961$	11524.7	+	19961.4i	0.386853	+	0.670048i
$962$	−2281.89	+	3952.35i	−0.0764773	+	0.132462i
$963$		0			0
$964$	−10043.0	−	17395.0i	−0.335544	−	0.581179i
$965$	−9115.15			−0.304069
$966$		0			0
$967$	7817.32			0.259967			0.129984	−	0.991516i	$-0.458508\pi$
$967$	7817.32			0.259967			0.129984	+	0.991516i	$0.458508\pi$
$968$	−13656.7	−	23654.1i	−0.453453	−	0.785403i
$969$		0			0
$970$	16797.5	−	29094.1i	0.556015	−	0.963046i
$971$	−751.748	−	1302.07i	−0.0248453	−	0.0430332i	0.853335	−	0.521362i	$-0.174576\pi$
$971$	−751.748	−	1302.07i	−0.0248453	−	0.0430332i	−0.878181	+	0.478329i	$0.841243\pi$
$972$		0			0
$973$		0			0
$974$	−47097.9			−1.54940
$975$		0			0
$976$	435.084	−	753.587i	0.0142692	−	0.0247149i
$977$	16694.6	−	28915.8i	0.546680	−	0.946877i	−0.451819	−	0.892109i	$-0.649225\pi$
$977$	16694.6	−	28915.8i	0.546680	−	0.946877i	0.998499	−	0.0547675i	$-0.0174418\pi$
$978$		0			0
$979$	1279.14			0.0417584
$980$		0			0
$981$		0			0
$982$	−28516.1	−	49391.3i	−0.926665	−	1.60503i
$983$	2725.51	−	4720.73i	0.0884337	−	0.153172i	−0.818416	−	0.574627i	$-0.805147\pi$
$983$	2725.51	−	4720.73i	0.0884337	−	0.153172i	0.906849	+	0.421455i	$0.138481\pi$
$984$		0			0
$985$	24841.8	+	43027.3i	0.803581	+	1.39184i
$986$	4568.64			0.147561
$987$		0			0
$988$	−40865.6			−1.31590
$989$	25082.7	+	43444.5i	0.806454	+	1.39682i
$990$		0			0
$991$	23265.0	−	40296.2i	0.745750	−	1.29168i	−0.204094	−	0.978951i	$-0.565425\pi$
$991$	23265.0	−	40296.2i	0.745750	−	1.29168i	0.949844	−	0.312725i	$-0.101242\pi$
$992$	−8086.02	−	14005.4i	−0.258802	−	0.448258i
$993$		0			0
$994$		0			0
$995$	−10780.6			−0.343484
$996$		0			0
$997$	5704.98	−	9881.31i	0.181222	−	0.313886i	−0.761075	−	0.648664i	$-0.775328\pi$
$997$	5704.98	−	9881.31i	0.181222	−	0.313886i	0.942297	+	0.334778i	$0.108661\pi$
$998$	24078.3	−	41704.8i	0.763711	−	1.32279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.y.361.4		8
3.2	odd	2		49.4.c.e.18.2		8
7.2	even	3	inner	441.4.e.y.226.4		8
7.3	odd	6		441.4.a.u.1.2		4
7.4	even	3		441.4.a.u.1.1		4
7.5	odd	6	inner	441.4.e.y.226.3		8
7.6	odd	2	inner	441.4.e.y.361.3		8
21.2	odd	6		49.4.c.e.30.2		8
21.5	even	6		49.4.c.e.30.1		8
21.11	odd	6		49.4.a.e.1.3	✓	4
21.17	even	6		49.4.a.e.1.4	yes	4
21.20	even	2		49.4.c.e.18.1		8
84.11	even	6		784.4.a.bf.1.3		4
84.59	odd	6		784.4.a.bf.1.2		4
105.59	even	6		1225.4.a.bb.1.1		4
105.74	odd	6		1225.4.a.bb.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.4.a.e.1.3	✓	4	21.11	odd	6
49.4.a.e.1.4	yes	4	21.17	even	6
49.4.c.e.18.1		8	21.20	even	2
49.4.c.e.18.2		8	3.2	odd	2
49.4.c.e.30.1		8	21.5	even	6
49.4.c.e.30.2		8	21.2	odd	6
441.4.a.u.1.1		4	7.4	even	3
441.4.a.u.1.2		4	7.3	odd	6
441.4.e.y.226.3		8	7.5	odd	6	inner
441.4.e.y.226.4		8	7.2	even	3	inner
441.4.e.y.361.3		8	7.6	odd	2	inner
441.4.e.y.361.4		8	1.1	even	1	trivial
784.4.a.bf.1.2		4	84.59	odd	6
784.4.a.bf.1.3		4	84.11	even	6
1225.4.a.bb.1.1		4	105.59	even	6
1225.4.a.bb.1.2		4	105.74	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.26556 + 3.92407i) q^{2} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} -20.5311 q^{8} +O(q^{10})\)	\(q+(2.26556 + 3.92407i) q^{2} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} -20.5311 q^{8} +(-30.5377 + 52.8928i) q^{10} +(0.406613 - 0.704275i) q^{11} -34.9564 q^{13} +(3.60992 + 6.25256i) q^{16} +(-58.8660 + 101.959i) q^{17} +(-46.6457 - 80.7927i) q^{19} -168.908 q^{20} +3.68484 q^{22} +(60.1245 + 104.139i) q^{23} +(-28.3424 + 49.0905i) q^{25} +(-79.1960 - 137.171i) q^{26} -8.56420 q^{29} +(-41.0535 + 71.1067i) q^{31} +(-98.4815 + 170.575i) q^{32} -533.458 q^{34} +(-14.4066 - 24.9530i) q^{37} +(211.358 - 366.082i) q^{38} +(-138.370 - 239.664i) q^{40} -70.5291 q^{41} +417.179 q^{43} +(5.09532 + 8.82536i) q^{44} +(-272.432 + 471.866i) q^{46} +(-169.131 - 292.943i) q^{47} -256.846 q^{50} +(219.022 - 379.356i) q^{52} +(74.5603 - 129.142i) q^{53} +10.9615 q^{55} +(-19.4027 - 33.6065i) q^{58} +(47.0914 - 81.5647i) q^{59} +(-60.2623 - 104.377i) q^{61} -372.037 q^{62} -834.706 q^{64} +(-235.590 - 408.053i) q^{65} +(396.183 - 686.209i) q^{67} +(-737.657 - 1277.66i) q^{68} -449.128 q^{71} +(-234.710 + 406.530i) q^{73} +(65.2782 - 113.065i) q^{74} +1169.05 q^{76} +(509.926 + 883.218i) q^{79} +(-48.6583 + 84.2786i) q^{80} +(-159.788 - 276.761i) q^{82} -104.253 q^{83} -1586.91 q^{85} +(945.146 + 1637.04i) q^{86} +(-8.34823 + 14.4596i) q^{88} +(786.460 + 1362.19i) q^{89} -1506.86 q^{92} +(766.352 - 1327.36i) q^{94} +(628.739 - 1089.01i) q^{95} -550.057 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8	\( 8 q + 2 q^{2} - 34 q^{4} - 132 q^{8} + 100 q^{11} + 174 q^{16} - 680 q^{22} + 352 q^{23} + 128 q^{25} - 520 q^{29} - 30 q^{32} - 212 q^{37} + 1080 q^{43} + 460 q^{44} - 696 q^{46} - 2732 q^{50} + 16 q^{53} + 780 q^{58} - 3356 q^{64} - 756 q^{65} + 1944 q^{67} - 4496 q^{71} - 284 q^{74} + 1048 q^{79} - 6568 q^{85} + 4820 q^{86} - 1260 q^{88} - 7024 q^{92} + 2192 q^{95}+O(q^{100}) \) 8 * q + 2 * q^2 - 34 * q^4 - 132 * q^8 + 100 * q^11 + 174 * q^16 - 680 * q^22 + 352 * q^23 + 128 * q^25 - 520 * q^29 - 30 * q^32 - 212 * q^37 + 1080 * q^43 + 460 * q^44 - 696 * q^46 - 2732 * q^50 + 16 * q^53 + 780 * q^58 - 3356 * q^64 - 756 * q^65 + 1944 * q^67 - 4496 * q^71 - 284 * q^74 + 1048 * q^79 - 6568 * q^85 + 4820 * q^86 - 1260 * q^88 - 7024 * q^92 + 2192 * q^95

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