LMFDB - Embedded newform 441.4.e.w.226.1

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.9924270768.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 $ x^6 - x^5 + 25x^4 + 12x^3 + 582x^2 - 144x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-2.27818 + 3.94593i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.w.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(-8.93660 + 15.4786i) q^{5} +21.6905 q^{8} +O(q^{10})$	\(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(-8.93660 + 15.4786i) q^{5} +21.6905 q^{8} +(-40.7184 - 70.5264i) q^{10} +(-5.69708 - 9.86762i) q^{11} +13.0987 q^{13} +(1.62706 - 2.81815i) q^{16} +(-26.6337 - 46.1309i) q^{17} +(-21.2111 + 36.7388i) q^{19} +228.071 q^{20} +51.9159 q^{22} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +(-29.8412 + 51.6864i) q^{26} -186.493 q^{29} +(-78.9369 - 136.723i) q^{31} +(94.1753 + 163.116i) q^{32} +242.706 q^{34} +(-1.87294 + 3.24403i) q^{37} +(-96.6457 - 167.395i) q^{38} +(-193.839 + 335.739i) q^{40} -39.3230 q^{41} +429.439 q^{43} +(-72.6974 + 125.916i) q^{44} +(346.478 + 600.118i) q^{46} +(-10.5934 + 18.3484i) q^{47} +885.992 q^{50} +(-83.5726 - 144.752i) q^{52} +(182.952 + 316.882i) q^{53} +203.650 q^{55} +(424.866 - 735.889i) q^{58} +(113.289 + 196.222i) q^{59} +(325.987 - 564.626i) q^{61} +719.331 q^{62} -832.161 q^{64} +(-117.058 + 202.750i) q^{65} +(-72.7166 - 125.949i) q^{67} +(-339.858 + 588.652i) q^{68} +368.962 q^{71} +(304.453 + 527.328i) q^{73} +(-8.53380 - 14.7810i) q^{74} +541.328 q^{76} +(-455.119 + 788.289i) q^{79} +(29.0808 + 50.3694i) q^{80} +(89.5850 - 155.166i) q^{82} -327.929 q^{83} +952.058 q^{85} +(-978.340 + 1694.53i) q^{86} +(-123.572 - 214.033i) q^{88} +(18.8059 - 32.5728i) q^{89} -1940.68 q^{92} +(-48.2676 - 83.6019i) q^{94} +(-379.111 - 656.640i) q^{95} -722.013 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8}+O(q^{10}) $ 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8	$ 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8} - 55 q^{10} + 35 q^{11} - 124 q^{13} - 241 q^{16} - 48 q^{17} - 202 q^{19} + 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} - 274 q^{26} - 106 q^{29} - 95 q^{31} + 683 q^{32} + 48 q^{34} - 262 q^{37} + 398 q^{38} + 21 q^{40} + 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} + 210 q^{47} + 2756 q^{50} + 324 q^{52} + 393 q^{53} + 2062 q^{55} + 1249 q^{58} - 1143 q^{59} - 70 q^{61} + 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} - 1944 q^{68} - 636 q^{71} + 988 q^{73} + 1002 q^{74} + 4680 q^{76} - 861 q^{79} - 175 q^{80} + 124 q^{82} + 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} - 1766 q^{89} + 1344 q^{92} - 3294 q^{94} - 736 q^{95} - 38 q^{97}+O(q^{100}) $ 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8 - 55 * q^10 + 35 * q^11 - 124 * q^13 - 241 * q^16 - 48 * q^17 - 202 * q^19 + 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 - 274 * q^26 - 106 * q^29 - 95 * q^31 + 683 * q^32 + 48 * q^34 - 262 * q^37 + 398 * q^38 + 21 * q^40 + 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 + 210 * q^47 + 2756 * q^50 + 324 * q^52 + 393 * q^53 + 2062 * q^55 + 1249 * q^58 - 1143 * q^59 - 70 * q^61 + 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 - 1944 * q^68 - 636 * q^71 + 988 * q^73 + 1002 * q^74 + 4680 * q^76 - 861 * q^79 - 175 * q^80 + 124 * q^82 + 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 - 1766 * q^89 + 1344 * q^92 - 3294 * q^94 - 736 * q^95 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.27818	+	3.94593i	−0.805459	+	1.39510i	0.110521	+	0.993874i	$0.464748\pi$
$2$	−2.27818	+	3.94593i	−0.805459	+	1.39510i	−0.915981	+	0.401223i	$0.868585\pi$
$3$		0			0
$3$		0			0
$4$	−6.38024	−	11.0509i	−0.797530	−	1.38136i
$5$	−8.93660	+	15.4786i	−0.799314	+	1.38445i	0.120749	+	0.992683i	$0.461470\pi$
$5$	−8.93660	+	15.4786i	−0.799314	+	1.38445i	−0.920063	+	0.391769i	$0.871863\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	21.6905			0.958592
$9$		0			0
$10$	−40.7184	−	70.5264i	−1.28763	−	2.23024i
$11$	−5.69708	−	9.86762i	−0.156158	−	0.270473i	0.777322	−	0.629102i	$-0.216577\pi$
$11$	−5.69708	−	9.86762i	−0.156158	−	0.270473i	−0.933480	+	0.358630i	$0.883244\pi$
$12$		0			0
$13$	13.0987			0.279455			0.139728	−	0.990190i	$-0.455377\pi$
$13$	13.0987			0.279455			0.139728	+	0.990190i	$0.455377\pi$
$14$		0			0
$15$		0			0
$16$	1.62706	−	2.81815i	0.0254228	−	0.0440336i
$17$	−26.6337	−	46.1309i	−0.379977	−	0.658140i	0.611081	−	0.791568i	$-0.290735\pi$
$17$	−26.6337	−	46.1309i	−0.379977	−	0.658140i	−0.991059	+	0.133428i	$0.957402\pi$
$18$		0			0
$19$	−21.2111	+	36.7388i	−0.256114	+	0.443603i	−0.965198	−	0.261522i	$-0.915776\pi$
$19$	−21.2111	+	36.7388i	−0.256114	+	0.443603i	0.709083	+	0.705125i	$0.249109\pi$
$20$	228.071			2.54991
$21$		0			0
$22$	51.9159			0.503114
$23$	76.0427	−	131.710i	0.689391	−	1.19406i	−0.282644	−	0.959225i	$-0.591211\pi$
$23$	76.0427	−	131.710i	0.689391	−	1.19406i	0.972035	−	0.234836i	$-0.0754553\pi$
$24$		0			0
$25$	−97.2257	−	168.400i	−0.777806	−	1.34720i
$26$	−29.8412	+	51.6864i	−0.225090	+	0.389867i
$27$		0			0
$28$		0			0
$29$	−186.493			−1.19417			−0.597085	−	0.802178i	$-0.703675\pi$
$29$	−186.493			−1.19417			−0.597085	+	0.802178i	$0.703675\pi$
$30$		0			0
$31$	−78.9369	−	136.723i	−0.457338	−	0.792133i	0.541481	−	0.840713i	$-0.317864\pi$
$31$	−78.9369	−	136.723i	−0.457338	−	0.792133i	−0.998819	+	0.0485801i	$0.984530\pi$
$32$	94.1753	+	163.116i	0.520250	+	0.901099i
$33$		0			0
$34$	242.706			1.22423
$35$		0			0
$36$		0			0
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	−0.870156	−	0.492776i	$-0.835982\pi$
$37$	−1.87294	+	3.24403i	−0.00832188	+	0.0144139i	0.861834	+	0.507190i	$0.169316\pi$
$38$	−96.6457	−	167.395i	−0.412579	−	0.714608i
$39$		0			0
$40$	−193.839	+	335.739i	−0.766216	+	1.32712i
$41$	−39.3230			−0.149786			−0.0748930	−	0.997192i	$-0.523862\pi$
$41$	−39.3230			−0.149786			−0.0748930	+	0.997192i	$0.523862\pi$
$42$		0			0
$43$	429.439			1.52300			0.761498	−	0.648168i	$-0.224464\pi$
$43$	429.439			1.52300			0.761498	+	0.648168i	$0.224464\pi$
$44$	−72.6974	+	125.916i	−0.249080	+	0.431420i
$45$		0			0
$46$	346.478	+	600.118i	1.11055	+	1.92354i
$47$	−10.5934	+	18.3484i	−0.0328768	+	0.0569444i	−0.881996	−	0.471258i	$-0.843800\pi$
$47$	−10.5934	+	18.3484i	−0.0328768	+	0.0569444i	0.849119	+	0.528202i	$0.177134\pi$
$48$		0			0
$49$		0			0
$50$	885.992			2.50596
$51$		0			0
$52$	−83.5726	−	144.752i	−0.222874	−	0.386029i
$53$	182.952	+	316.882i	0.474158	+	0.821266i	0.999562	−	0.0295866i	$-0.00941909\pi$
$53$	182.952	+	316.882i	0.474158	+	0.821266i	−0.525404	+	0.850853i	$0.676086\pi$
$54$		0			0
$55$	203.650			0.499276
$56$		0			0
$57$		0			0
$58$	424.866	−	735.889i	0.961856	−	1.66598i
$59$	113.289	+	196.222i	0.249982	+	0.432982i	0.963521	−	0.267634i	$-0.0862419\pi$
$59$	113.289	+	196.222i	0.249982	+	0.432982i	−0.713538	+	0.700616i	$0.752909\pi$
$60$		0			0
$61$	325.987	−	564.626i	0.684235	−	1.18513i	−0.289442	−	0.957196i	$-0.593470\pi$
$61$	325.987	−	564.626i	0.684235	−	1.18513i	0.973677	−	0.227934i	$-0.0731970\pi$
$62$	719.331			1.47347
$63$		0			0
$64$	−832.161			−1.62532
$65$	−117.058	+	202.750i	−0.223372	+	0.386892i
$66$		0			0
$67$	−72.7166	−	125.949i	−0.132593	−	0.229658i	0.792082	−	0.610414i	$-0.208997\pi$
$67$	−72.7166	−	125.949i	−0.132593	−	0.229658i	−0.924675	+	0.380756i	$0.875664\pi$
$68$	−339.858	+	588.652i	−0.606086	+	1.04977i
$69$		0			0
$70$		0			0
$71$	368.962			0.616728			0.308364	−	0.951268i	$-0.400218\pi$
$71$	368.962			0.616728			0.308364	+	0.951268i	$0.400218\pi$
$72$		0			0
$73$	304.453	+	527.328i	0.488130	+	0.845466i	0.999907	−	0.0136522i	$-0.00434576\pi$
$73$	304.453	+	527.328i	0.488130	+	0.845466i	−0.511777	+	0.859119i	$0.671012\pi$
$74$	−8.53380	−	14.7810i	−0.0134059	−	0.0232197i
$75$		0			0
$76$	541.328			0.817034
$77$		0			0
$78$		0			0
$79$	−455.119	+	788.289i	−0.648163	+	1.12265i	0.335399	+	0.942076i	$0.391129\pi$
$79$	−455.119	+	788.289i	−0.648163	+	1.12265i	−0.983561	+	0.180574i	$0.942204\pi$
$80$	29.0808	+	50.3694i	0.0406416	+	0.0703933i
$81$		0			0
$82$	89.5850	−	155.166i	0.120646	−	0.208966i
$83$	−327.929			−0.433674			−0.216837	−	0.976208i	$-0.569574\pi$
$83$	−327.929			−0.433674			−0.216837	+	0.976208i	$0.569574\pi$
$84$		0			0
$85$	952.058			1.21489
$86$	−978.340	+	1694.53i	−1.22671	+	2.12473i
$87$		0			0
$88$	−123.572	−	214.033i	−0.149691	−	0.259273i
$89$	18.8059	−	32.5728i	0.0223980	−	0.0387945i	−0.854609	−	0.519272i	$-0.826203\pi$
$89$	18.8059	−	32.5728i	0.0223980	−	0.0387945i	0.877007	+	0.480477i	$0.159537\pi$
$90$		0			0
$91$		0			0
$92$	−1940.68			−2.19924
$93$		0			0
$94$	−48.2676	−	83.6019i	−0.0529619	−	0.0917327i
$95$	−379.111	−	656.640i	−0.409431	−	0.709156i
$96$		0			0
$97$	−722.013			−0.755766			−0.377883	−	0.925853i	$-0.623348\pi$
$97$	−722.013			−0.755766			−0.377883	+	0.925853i	$0.623348\pi$
$98$		0			0
$99$		0			0
$100$	−1240.65	+	2148.86i	−1.24065	+	2.14886i
$101$	−759.336	−	1315.21i	−0.748087	−	1.29572i	−0.948739	−	0.316062i	$-0.897639\pi$
$101$	−759.336	−	1315.21i	−0.748087	−	1.29572i	0.200652	−	0.979663i	$-0.435694\pi$
$102$		0			0
$103$	−525.942	+	910.957i	−0.503132	+	0.871450i	0.496862	+	0.867830i	$0.334486\pi$
$103$	−525.942	+	910.957i	−0.503132	+	0.871450i	−0.999993	+	0.00361990i	$0.998848\pi$
$104$	284.116			0.267883
$105$		0			0
$106$	−1667.19			−1.52766
$107$	383.260	−	663.826i	0.346273	−	0.599762i	−0.639312	−	0.768948i	$-0.720781\pi$
$107$	383.260	−	663.826i	0.346273	−	0.599762i	0.985584	+	0.169186i	$0.0541139\pi$
$108$		0			0
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	0.988150	+	0.153491i	$0.0490516\pi$
$109$	713.524	+	1235.86i	0.627002	+	1.08600i	−0.361148	+	0.932509i	$0.617615\pi$
$110$	−463.952	+	803.588i	−0.402146	+	0.696538i
$111$		0			0
$112$		0			0
$113$	−362.564			−0.301833			−0.150917	−	0.988546i	$-0.548222\pi$
$113$	−362.564			−0.301833			−0.150917	+	0.988546i	$0.548222\pi$
$114$		0			0
$115$	1359.13	+	2354.08i	1.10208	+	1.90886i
$116$	1189.87	+	2060.92i	0.952386	+	1.64958i
$117$		0			0
$118$	−1032.37			−0.805402
$119$		0			0
$120$		0			0
$121$	600.587	−	1040.25i	0.451230	−	0.781553i
$122$	1485.31	+	2572.64i	1.10225	+	1.90915i
$123$		0			0
$124$	−1007.27	+	1744.65i	−0.729481	+	1.26350i
$125$	1241.32			0.888216
$126$		0			0
$127$	974.777			0.681082			0.340541	−	0.940230i	$-0.389390\pi$
$127$	974.777			0.681082			0.340541	+	0.940230i	$0.389390\pi$
$128$	1142.41	−	1978.72i	0.788875	−	1.36637i
$129$		0			0
$130$	−533.357	−	923.802i	−0.359835	−	0.623252i
$131$	896.351	−	1552.53i	0.597821	−	1.03546i	−0.395321	−	0.918543i	$-0.629367\pi$
$131$	896.351	−	1552.53i	0.597821	−	1.03546i	0.993142	−	0.116914i	$-0.0373001\pi$
$132$		0			0
$133$		0			0
$134$	662.647			0.427194
$135$		0			0
$136$	−577.697	−	1000.60i	−0.364243	−	0.630888i
$137$	842.208	+	1458.75i	0.525217	+	0.909702i	0.999569	+	0.0293665i	$0.00934900\pi$
$137$	842.208	+	1458.75i	0.525217	+	0.909702i	−0.474352	+	0.880335i	$0.657318\pi$
$138$		0			0
$139$	−315.089			−0.192270			−0.0961350	−	0.995368i	$-0.530648\pi$
$139$	−315.089			−0.192270			−0.0961350	+	0.995368i	$0.530648\pi$
$140$		0			0
$141$		0			0
$142$	−840.563	+	1455.90i	−0.496750	+	0.860396i
$143$	−74.6241	−	129.253i	−0.0436390	−	0.0755850i
$144$		0			0
$145$	1666.62	−	2886.67i	0.954517	−	1.65327i
$146$	−2774.40			−1.57268
$147$		0			0
$148$	47.7992			0.0265478
$149$	946.887	−	1640.06i	0.520617	−	0.901736i	−0.479095	−	0.877763i	$-0.659035\pi$
$149$	946.887	−	1640.06i	0.520617	−	0.901736i	0.999713	−	0.0239729i	$-0.00763155\pi$
$150$		0			0
$151$	1005.92	+	1742.31i	0.542124	+	0.938986i	0.998782	+	0.0493434i	$0.0157129\pi$
$151$	1005.92	+	1742.31i	0.542124	+	0.938986i	−0.456658	+	0.889642i	$0.650954\pi$
$152$	−460.079	+	796.881i	−0.245509	+	0.425234i
$153$		0			0
$154$		0			0
$155$	2821.71			1.46223
$156$		0			0
$157$	−1914.25	−	3315.58i	−0.973082	−	1.68543i	−0.686125	−	0.727483i	$-0.740690\pi$
$157$	−1914.25	−	3315.58i	−0.973082	−	1.68543i	−0.286956	−	0.957944i	$-0.592643\pi$
$158$	−2073.69	−	3591.73i	−1.04414	−	1.80850i
$159$		0			0
$160$	−3366.43			−1.66337
$161$		0			0
$162$		0			0
$163$	1754.63	−	3039.11i	0.843148	−	1.46038i	−0.0440718	−	0.999028i	$-0.514033\pi$
$163$	1754.63	−	3039.11i	0.843148	−	1.46038i	0.887220	−	0.461347i	$-0.152634\pi$
$164$	250.890	+	434.554i	0.119459	+	0.206909i
$165$		0			0
$166$	747.083	−	1293.99i	0.349307	−	0.605017i
$167$	−343.008			−0.158939			−0.0794694	−	0.996837i	$-0.525323\pi$
$167$	−343.008			−0.158939			−0.0794694	+	0.996837i	$0.525323\pi$
$168$		0			0
$169$	−2025.42			−0.921905
$170$	−2168.96	+	3756.75i	−0.978541	+	1.69488i
$171$		0			0
$172$	−2739.92	−	4745.68i	−1.21463	−	2.10381i
$173$	2093.61	−	3626.23i	0.920081	−	1.59363i	0.120793	−	0.992678i	$-0.461456\pi$
$173$	2093.61	−	3626.23i	0.920081	−	1.59363i	0.799288	−	0.600949i	$-0.205210\pi$
$174$		0			0
$175$		0			0
$176$	−37.0779			−0.0158798
$177$		0			0
$178$	85.6866	+	148.413i	0.0360813	+	0.0624947i
$179$	−985.143	−	1706.32i	−0.411358	−	0.712493i	0.583681	−	0.811983i	$-0.301612\pi$
$179$	−985.143	−	1706.32i	−0.411358	−	0.712493i	−0.995039	+	0.0994906i	$0.968279\pi$
$180$		0			0
$181$	3613.10			1.48376			0.741878	−	0.670535i	$-0.233935\pi$
$181$	3613.10			1.48376			0.741878	+	0.670535i	$0.233935\pi$
$182$		0			0
$183$		0			0
$184$	1649.40	−	2856.85i	0.660845	−	1.14462i
$185$	−33.4755	−	57.9812i	−0.0133036	−	0.0230425i
$186$		0			0
$187$	−303.468	+	525.622i	−0.118673	+	0.205547i
$188$	270.355			0.104881
$189$		0			0
$190$	3454.74			1.31912
$191$	953.884	−	1652.18i	0.361365	−	0.625902i	−0.626821	−	0.779163i	$-0.715644\pi$
$191$	953.884	−	1652.18i	0.361365	−	0.625902i	0.988186	+	0.153261i	$0.0489776\pi$
$192$		0			0
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	0.550685	−	0.834713i	$-0.314366\pi$
$193$	−1199.96	−	2078.40i	−0.447540	−	0.775162i	−0.998225	+	0.0595509i	$0.981033\pi$
$194$	1644.88	−	2849.01i	0.608738	−	1.05437i
$195$		0			0
$196$		0			0
$197$	−1514.32			−0.547668			−0.273834	−	0.961777i	$-0.588292\pi$
$197$	−1514.32			−0.547668			−0.273834	+	0.961777i	$0.588292\pi$
$198$		0			0
$199$	683.889	+	1184.53i	0.243616	+	0.421955i	0.961742	−	0.273958i	$-0.0883330\pi$
$199$	683.889	+	1184.53i	0.243616	+	0.421955i	−0.718126	+	0.695914i	$0.755000\pi$
$200$	−2108.87	−	3652.67i	−0.745598	−	1.29141i
$201$		0			0
$202$	6919.63			2.41021
$203$		0			0
$204$		0			0
$205$	351.414	−	608.667i	0.119726	−	0.207371i
$206$	−2396.38	−	4150.66i	−0.810504	−	1.40383i
$207$		0			0
$208$	21.3123	−	36.9140i	0.00710453	−	0.0123054i
$209$	483.366			0.159977
$210$		0			0
$211$	4302.52			1.40378			0.701891	−	0.712285i	$-0.252339\pi$
$211$	4302.52			1.40378			0.701891	+	0.712285i	$0.252339\pi$
$212$	2334.55	−	4043.57i	0.756311	−	1.30997i
$213$		0			0
$214$	1746.27	+	3024.64i	0.557817	+	0.966167i
$215$	−3837.72	+	6647.13i	−1.21735	+	2.10851i
$216$		0			0
$217$		0			0
$218$	−6502.16			−2.02010
$219$		0			0
$220$	−1299.34	−	2250.51i	−0.398187	−	0.689680i
$221$	−348.866	−	604.253i	−0.106187	−	0.183921i
$222$		0			0
$223$	1497.19			0.449592			0.224796	−	0.974406i	$-0.427828\pi$
$223$	1497.19			0.449592			0.224796	+	0.974406i	$0.427828\pi$
$224$		0			0
$225$		0			0
$226$	825.987	−	1430.65i	0.243114	−	0.421086i
$227$	−801.662	−	1388.52i	−0.234397	−	0.405988i	0.724700	−	0.689065i	$-0.241978\pi$
$227$	−801.662	−	1388.52i	−0.234397	−	0.405988i	−0.959097	+	0.283076i	$0.908645\pi$
$228$		0			0
$229$	505.261	−	875.137i	0.145802	−	0.252536i	−0.783870	−	0.620925i	$-0.786757\pi$
$229$	505.261	−	875.137i	0.145802	−	0.252536i	0.929672	+	0.368389i	$0.120091\pi$
$230$	−12385.4			−3.55072
$231$		0			0
$232$	−4045.13			−1.14472
$233$	99.1084	−	171.661i	0.0278661	−	0.0482656i	−0.851756	−	0.523939i	$-0.824462\pi$
$233$	99.1084	−	171.661i	0.0278661	−	0.0482656i	0.879622	+	0.475673i	$0.157795\pi$
$234$		0			0
$235$	−189.339	−	327.944i	−0.0525578	−	0.0910329i
$236$	1445.62	−	2503.88i	0.398736	−	0.690631i
$237$		0			0
$238$		0			0
$239$	1201.19			0.325098			0.162549	−	0.986700i	$-0.448028\pi$
$239$	1201.19			0.325098			0.162549	+	0.986700i	$0.448028\pi$
$240$		0			0
$241$	−1366.35	−	2366.58i	−0.365204	−	0.632551i	0.623605	−	0.781739i	$-0.285667\pi$
$241$	−1366.35	−	2366.58i	−0.365204	−	0.632551i	−0.988809	+	0.149188i	$0.952334\pi$
$242$	2736.49	+	4739.74i	0.726894	+	1.25902i
$243$		0			0
$244$	−8319.49			−2.18279
$245$		0			0
$246$		0			0
$247$	−277.838	+	481.229i	−0.0715724	+	0.123967i
$248$	−1712.18	−	2965.58i	−0.438401	−	0.759332i
$249$		0			0
$250$	−2827.95	+	4898.16i	−0.715422	+	1.23915i
$251$	7565.82			1.90259			0.951295	−	0.308281i	$-0.0997537\pi$
$251$	7565.82			1.90259			0.951295	+	0.308281i	$0.0997537\pi$
$252$		0			0
$253$	−1732.88			−0.430615
$254$	−2220.72	+	3846.40i	−0.548584	+	0.950175i
$255$		0			0
$256$	1876.61	+	3250.38i	0.458156	+	0.793550i
$257$	−2504.34	+	4337.64i	−0.607846	+	1.05282i	0.383749	+	0.923437i	$0.374633\pi$
$257$	−2504.34	+	4337.64i	−0.607846	+	1.05282i	−0.991595	+	0.129382i	$0.958701\pi$
$258$		0			0
$259$		0			0
$260$	2987.42			0.712584
$261$		0			0
$262$	4084.10	+	7073.88i	0.963041	+	1.66804i
$263$	−3124.40	−	5411.63i	−0.732544	−	1.26880i	−0.955793	−	0.294042i	$-0.905000\pi$
$263$	−3124.40	−	5411.63i	−0.732544	−	1.26880i	0.223249	−	0.974761i	$-0.428334\pi$
$264$		0			0
$265$	−6539.88			−1.51601
$266$		0			0
$267$		0			0
$268$	−927.898	+	1607.17i	−0.211494	+	0.366318i
$269$	1794.22	+	3107.69i	0.406676	+	0.704383i	0.994515	−	0.104595i	$-0.0333546\pi$
$269$	1794.22	+	3107.69i	0.406676	+	0.704383i	−0.587839	+	0.808978i	$0.700021\pi$
$270$		0			0
$271$	−991.571	+	1717.45i	−0.222264	+	0.384973i	−0.955495	−	0.295007i	$-0.904678\pi$
$271$	−991.571	+	1717.45i	−0.222264	+	0.384973i	0.733231	+	0.679980i	$0.238012\pi$
$272$	−173.338			−0.0386404
$273$		0			0
$274$	−7674.81			−1.69216
$275$	−1107.80	+	1918.77i	−0.242920	+	0.420751i
$276$		0			0
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	−0.920493	−	0.390760i	$-0.872212\pi$
$277$	−3681.96	−	6377.33i	−0.798654	−	1.38331i	0.121838	−	0.992550i	$-0.461121\pi$
$278$	717.831	−	1243.32i	0.154866	−	0.268235i
$279$		0			0
$280$		0			0
$281$	5312.05			1.12772			0.563861	−	0.825869i	$-0.309315\pi$
$281$	5312.05			1.12772			0.563861	+	0.825869i	$0.309315\pi$
$282$		0			0
$283$	−545.882	−	945.495i	−0.114662	−	0.198600i	0.802983	−	0.596002i	$-0.203245\pi$
$283$	−545.882	−	945.495i	−0.114662	−	0.198600i	−0.917645	+	0.397402i	$0.869912\pi$
$284$	−2354.06	−	4077.36i	−0.491859	−	0.851925i
$285$		0			0
$286$	680.030			0.140598
$287$		0			0
$288$		0			0
$289$	1037.79	−	1797.51i	0.211234	−	0.365869i
$290$	7593.72	+	13152.7i	1.53765	+	2.66329i
$291$		0			0
$292$	3884.96	−	6728.95i	0.778597	−	1.34857i
$293$	−7191.86			−1.43397			−0.716985	−	0.697089i	$-0.754478\pi$
$293$	−7191.86			−1.43397			−0.716985	+	0.697089i	$0.754478\pi$
$294$		0			0
$295$	−4049.67			−0.799257
$296$	−40.6249	+	70.3645i	−0.00797729	+	0.0138171i
$297$		0			0
$298$	4314.36	+	7472.70i	0.838672	+	1.45262i
$299$	996.058	−	1725.22i	0.192654	−	0.333687i
$300$		0			0
$301$		0			0
$302$	−9166.69			−1.74663
$303$		0			0
$304$	69.0236	+	119.552i	0.0130223	+	0.0225552i
$305$	5826.43	+	10091.7i	1.09384	+	1.89458i
$306$		0			0
$307$	−541.355			−0.100641			−0.0503204	−	0.998733i	$-0.516024\pi$
$307$	−541.355			−0.100641			−0.0503204	+	0.998733i	$0.516024\pi$
$308$		0			0
$309$		0			0
$310$	−6428.37	+	11134.3i	−1.17776	+	2.03995i
$311$	−27.0084	−	46.7799i	−0.00492446	−	0.00852941i	0.863553	−	0.504259i	$-0.168234\pi$
$311$	−27.0084	−	46.7799i	−0.00492446	−	0.00852941i	−0.868477	+	0.495729i	$0.834901\pi$
$312$		0			0
$313$	1886.47	−	3267.46i	0.340670	−	0.590058i	−0.643887	−	0.765120i	$-0.722679\pi$
$313$	1886.47	−	3267.46i	0.340670	−	0.590058i	0.984557	+	0.175063i	$0.0560128\pi$
$314$	17444.1			3.13511
$315$		0			0
$316$	11615.1			2.06772
$317$	859.618	−	1488.90i	0.152306	−	0.263802i	−0.779769	−	0.626068i	$-0.784663\pi$
$317$	859.618	−	1488.90i	0.152306	−	0.263802i	0.932075	+	0.362266i	$0.117997\pi$
$318$		0			0
$319$	1062.47	+	1840.25i	0.186479	+	0.322991i
$320$	7436.70	−	12880.7i	1.29914	−	2.25017i
$321$		0			0
$322$		0			0
$323$	2259.72			0.389270
$324$		0			0
$325$	−1273.53	−	2205.81i	−0.217362	−	0.376482i
$326$	7994.73	+	13847.3i	1.35824	+	2.35255i
$327$		0			0
$328$	−852.934			−0.143584
$329$		0			0
$330$		0			0
$331$	−4204.11	+	7281.73i	−0.698123	+	1.20918i	0.270994	+	0.962581i	$0.412648\pi$
$331$	−4204.11	+	7281.73i	−0.698123	+	1.20918i	−0.969117	+	0.246603i	$0.920686\pi$
$332$	2092.27	+	3623.91i	0.345868	+	0.599060i
$333$		0			0
$334$	781.436	−	1353.49i	0.128019	−	0.221735i
$335$	2599.36			0.423935
$336$		0			0
$337$	2789.46			0.450894			0.225447	−	0.974255i	$-0.427616\pi$
$337$	2789.46			0.450894			0.225447	+	0.974255i	$0.427616\pi$
$338$	4614.29	−	7992.18i	0.742557	−	1.28615i
$339$		0			0
$340$	−6074.36	−	10521.1i	−0.968907	−	1.67820i
$341$	−899.419	+	1557.84i	−0.142834	+	0.247395i
$342$		0			0
$343$		0			0
$344$	9314.72			1.45993
$345$		0			0
$346$	9539.24	+	16522.4i	1.48217	+	2.56720i
$347$	−1735.98	−	3006.81i	−0.268566	−	0.465170i	0.699926	−	0.714216i	$-0.253216\pi$
$347$	−1735.98	−	3006.81i	−0.268566	−	0.465170i	−0.968492	+	0.249046i	$0.919883\pi$
$348$		0			0
$349$	6626.12			1.01630			0.508149	−	0.861269i	$-0.330330\pi$
$349$	6626.12			1.01630			0.508149	+	0.861269i	$0.330330\pi$
$350$		0			0
$351$		0			0
$352$	1073.05	−	1858.57i	0.162482	−	0.281427i
$353$	−4734.20	−	8199.87i	−0.713813	−	1.23636i	−0.963416	−	0.268012i	$-0.913633\pi$
$353$	−4734.20	−	8199.87i	−0.713813	−	1.23636i	0.249603	−	0.968348i	$-0.419700\pi$
$354$		0			0
$355$	−3297.27	+	5711.03i	−0.492960	+	0.853831i
$356$	−479.944			−0.0714522
$357$		0			0
$358$	8977.35			1.32533
$359$	−3139.78	+	5438.25i	−0.461591	+	0.799499i	−0.999040	−	0.0437971i	$-0.986054\pi$
$359$	−3139.78	+	5438.25i	−0.461591	+	0.799499i	0.537450	+	0.843296i	$0.319388\pi$
$360$		0			0
$361$	2529.68	+	4381.53i	0.368811	+	0.638800i
$362$	−8231.31	+	14257.0i	−1.19510	+	2.06998i
$363$		0			0
$364$		0			0
$365$	−10883.1			−1.56068
$366$		0			0
$367$	−5413.91	−	9377.17i	−0.770038	−	1.33374i	−0.937542	−	0.347873i	$-0.886904\pi$
$367$	−5413.91	−	9377.17i	−0.770038	−	1.33374i	0.167504	−	0.985871i	$-0.446429\pi$
$368$	−247.452	−	428.599i	−0.0350525	−	0.0607127i
$369$		0			0
$370$	305.053			0.0428620
$371$		0			0
$372$		0			0
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	−0.988557	−	0.150846i	$-0.951800\pi$
$373$	−2619.61	+	4537.30i	−0.363642	+	0.629846i	0.624915	+	0.780693i	$0.285134\pi$
$374$	−1382.71	−	2394.93i	−0.191172	−	0.331120i
$375$		0			0
$376$	−229.777	+	397.985i	−0.0315155	+	0.0545864i
$377$	−2442.81			−0.333717
$378$		0			0
$379$	−11050.4			−1.49768			−0.748839	−	0.662751i	$-0.769389\pi$
$379$	−11050.4			−1.49768			−0.748839	+	0.662751i	$0.769389\pi$
$380$	−4837.64	+	8379.03i	−0.653067	+	1.13115i
$381$		0			0
$382$	4346.25	+	7527.92i	0.582129	+	1.00828i
$383$	5234.02	−	9065.59i	0.698292	−	1.20948i	−0.270766	−	0.962645i	$-0.587277\pi$
$383$	5234.02	−	9065.59i	0.698292	−	1.20948i	0.969058	−	0.246832i	$-0.0793897\pi$
$384$		0			0
$385$		0			0
$386$	10934.9			1.44190
$387$		0			0
$388$	4606.61	+	7978.88i	0.602745	+	1.04399i
$389$	−5807.02	−	10058.1i	−0.756884	−	1.31096i	−0.944432	−	0.328705i	$-0.893388\pi$
$389$	−5807.02	−	10058.1i	−0.756884	−	1.31096i	0.187549	−	0.982255i	$-0.439946\pi$
$390$		0			0
$391$	−8101.19			−1.04781
$392$		0			0
$393$		0			0
$394$	3449.89	−	5975.38i	0.441124	−	0.764049i
$395$	−8134.43	−	14089.2i	−1.03617	−	1.79470i
$396$		0			0
$397$	−3353.65	+	5808.69i	−0.423967	+	0.734332i	−0.996323	−	0.0856726i	$-0.972696\pi$
$397$	−3353.65	+	5808.69i	−0.423967	+	0.734332i	0.572356	+	0.820005i	$0.306029\pi$
$398$	−6232.10			−0.784892
$399$		0			0
$400$	−632.768			−0.0790960
$401$	2763.19	−	4785.98i	0.344107	−	0.596011i	−0.641084	−	0.767471i	$-0.721515\pi$
$401$	2763.19	−	4785.98i	0.344107	−	0.596011i	0.985191	+	0.171459i	$0.0548482\pi$
$402$		0			0
$403$	−1033.97	−	1790.89i	−0.127805	−	0.221366i
$404$	−9689.49	+	16782.7i	−1.19324	+	2.06676i
$405$		0			0
$406$		0			0
$407$	42.6811			0.00519810
$408$		0			0
$409$	−659.453	−	1142.21i	−0.0797258	−	0.138089i	0.823406	−	0.567453i	$-0.192071\pi$
$409$	−659.453	−	1142.21i	−0.0797258	−	0.138089i	−0.903132	+	0.429364i	$0.858738\pi$
$410$	1601.17	+	2773.31i	0.192869	+	0.334059i
$411$		0			0
$412$	13422.5			1.60505
$413$		0			0
$414$		0			0
$415$	2930.57	−	5075.90i	0.346641	−	0.600401i
$416$	1233.57	+	2136.61i	0.145387	+	0.251817i
$417$		0			0
$418$	−1101.20	+	1907.33i	−0.128855	+	0.223183i
$419$	3656.13			0.426286			0.213143	−	0.977021i	$-0.431630\pi$
$419$	3656.13			0.426286			0.213143	+	0.977021i	$0.431630\pi$
$420$		0			0
$421$	−135.389			−0.0156733			−0.00783663	−	0.999969i	$-0.502495\pi$
$421$	−135.389			−0.0156733			−0.00783663	+	0.999969i	$0.502495\pi$
$422$	−9801.93	+	16977.4i	−1.13069	+	1.95841i
$423$		0			0
$424$	3968.31	+	6873.32i	0.454524	+	0.787259i
$425$	−5178.96	+	8970.22i	−0.591097	+	1.02381i
$426$		0			0
$427$		0			0
$428$	−9781.16			−1.10465
$429$		0			0
$430$	−17486.1	−	30286.8i	−1.96105	−	3.39665i
$431$	4194.58	+	7265.23i	0.468784	+	0.811958i	0.999363	−	0.0356776i	$-0.0113589\pi$
$431$	4194.58	+	7265.23i	0.468784	+	0.811958i	−0.530579	+	0.847635i	$0.678026\pi$
$432$		0			0
$433$	8243.02			0.914859			0.457430	−	0.889246i	$-0.348770\pi$
$433$	8243.02			0.914859			0.457430	+	0.889246i	$0.348770\pi$
$434$		0			0
$435$		0			0
$436$	9104.91	−	15770.2i	1.00011	−	1.73223i
$437$	3225.91	+	5587.43i	0.353126	+	0.611632i
$438$		0			0
$439$	−9141.59	+	15833.7i	−0.993859	+	1.72142i	−0.401104	+	0.916032i	$0.631374\pi$
$439$	−9141.59	+	15833.7i	−0.993859	+	1.72142i	−0.592755	+	0.805383i	$0.701960\pi$
$440$	4417.26			0.478602
$441$		0			0
$442$	3179.12			0.342116
$443$	605.218	−	1048.27i	0.0649092	−	0.112426i	−0.831745	−	0.555159i	$-0.812658\pi$
$443$	605.218	−	1048.27i	0.0649092	−	0.112426i	0.896654	+	0.442733i	$0.145991\pi$
$444$		0			0
$445$	336.122	+	582.180i	0.0358061	+	0.0620179i
$446$	−3410.86	+	5907.79i	−0.362128	+	0.627224i
$447$		0			0
$448$		0			0
$449$	8301.16			0.872508			0.436254	−	0.899824i	$-0.356305\pi$
$449$	8301.16			0.872508			0.436254	+	0.899824i	$0.356305\pi$
$450$		0			0
$451$	224.026	+	388.025i	0.0233902	+	0.0405130i
$452$	2313.24	+	4006.66i	0.240721	+	0.416941i
$453$		0			0
$454$	7305.34			0.755190
$455$		0			0
$456$		0			0
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	−0.358527	−	0.933519i	$-0.616721\pi$
$457$	6146.88	−	10646.7i	0.629188	−	1.08979i	0.987715	−	0.156266i	$-0.0499458\pi$
$458$	2302.15	+	3987.45i	0.234875	+	0.406815i
$459$		0			0
$460$	17343.1	−	30039.1i	1.75788	−	3.04474i
$461$	19434.2			1.96343			0.981717	−	0.190346i	$-0.0609609\pi$
$461$	19434.2			1.96343			0.981717	+	0.190346i	$0.0609609\pi$
$462$		0			0
$463$	−12491.1			−1.25380			−0.626902	−	0.779098i	$-0.715678\pi$
$463$	−12491.1			−1.25380			−0.626902	+	0.779098i	$0.715678\pi$
$464$	−303.436	+	525.566i	−0.0303592	+	0.0525836i
$465$		0			0
$466$	451.574	+	782.150i	0.0448901	+	0.0777519i
$467$	−1692.59	+	2931.65i	−0.167716	+	0.290493i	−0.937617	−	0.347671i	$-0.886973\pi$
$467$	−1692.59	+	2931.65i	−0.167716	+	0.290493i	0.769900	+	0.638164i	$0.220306\pi$
$468$		0			0
$469$		0			0
$470$	1725.39			0.169333
$471$		0			0
$472$	2457.29	+	4256.14i	0.239631	+	0.415053i
$473$	−2446.54	−	4237.54i	−0.237827	−	0.411929i
$474$		0			0
$475$	8249.07			0.796828
$476$		0			0
$477$		0			0
$478$	−2736.53	+	4739.80i	−0.261853	+	0.453543i
$479$	−2989.71	−	5178.32i	−0.285184	−	0.493953i	0.687470	−	0.726213i	$-0.258721\pi$
$479$	−2989.71	−	5178.32i	−0.285184	−	0.493953i	−0.972654	+	0.232260i	$0.925388\pi$
$480$		0			0
$481$	−24.5330	+	42.4925i	−0.00232559	+	0.00402804i
$482$	12451.1			1.17663
$483$		0			0
$484$	−15327.5			−1.43948
$485$	6452.34	−	11175.8i	0.604094	−	1.04632i
$486$		0			0
$487$	557.481	+	965.586i	0.0518725	+	0.0898457i	0.890796	−	0.454404i	$-0.150148\pi$
$487$	557.481	+	965.586i	0.0518725	+	0.0898457i	−0.838923	+	0.544250i	$0.816814\pi$
$488$	7070.80	−	12247.0i	0.655902	−	1.13606i
$489$		0			0
$490$		0			0
$491$	−1086.23			−0.0998387			−0.0499194	−	0.998753i	$-0.515896\pi$
$491$	−1086.23			−0.0998387			−0.0499194	+	0.998753i	$0.515896\pi$
$492$		0			0
$493$	4967.00	+	8603.10i	0.453758	+	0.785932i
$494$	−1265.93	−	2192.66i	−0.115297	−	0.199701i
$495$		0			0
$496$	−513.740			−0.0465073
$497$		0			0
$498$		0			0
$499$	1106.75	−	1916.95i	0.0992884	−	0.171973i	−0.812102	−	0.583516i	$-0.801677\pi$
$499$	1106.75	−	1916.95i	0.0992884	−	0.171973i	0.911390	+	0.411543i	$0.135010\pi$
$500$	−7919.92	−	13717.7i	−0.708379	−	1.22695i
$501$		0			0
$502$	−17236.3	+	29854.2i	−1.53246	+	2.65430i
$503$	−2643.32			−0.234314			−0.117157	−	0.993113i	$-0.537378\pi$
$503$	−2643.32			−0.234314			−0.117157	+	0.993113i	$0.537378\pi$
$504$		0			0
$505$	27143.5			2.39183
$506$	3947.83	−	6837.84i	0.346843	−	0.600749i
$507$		0			0
$508$	−6219.31	−	10772.2i	−0.543183	−	0.940821i
$509$	332.584	−	576.053i	0.0289618	−	0.0501633i	−0.851181	−	0.524872i	$-0.824113\pi$
$509$	332.584	−	576.053i	0.0289618	−	0.0501633i	0.880143	+	0.474709i	$0.157447\pi$
$510$		0			0
$511$		0			0
$512$	1177.58			0.101645
$513$		0			0
$514$	−11410.7	−	19763.9i	−0.979190	−	1.69601i
$515$	−9400.26	−	16281.7i	−0.804320	−	1.39312i
$516$		0			0
$517$	241.406			0.0205359
$518$		0			0
$519$		0			0
$520$	−2539.03	+	4397.73i	−0.214123	+	0.370872i
$521$	5880.99	+	10186.2i	0.494531	+	0.856554i	0.999980	−	0.00630307i	$-0.00200634\pi$
$521$	5880.99	+	10186.2i	0.494531	+	0.856554i	−0.505449	+	0.862857i	$0.668673\pi$
$522$		0			0
$523$	5061.30	−	8766.43i	0.423165	−	0.732943i	−0.573082	−	0.819498i	$-0.694252\pi$
$523$	5061.30	−	8766.43i	0.423165	−	0.732943i	0.996247	+	0.0865547i	$0.0275857\pi$
$524$	−22875.7			−1.90712
$525$		0			0
$526$	28471.9			2.36014
$527$	−4204.76	+	7282.85i	−0.347556	+	0.601985i
$528$		0			0
$529$	−5481.49	−	9494.22i	−0.450521	−	0.780325i
$530$	14899.0	−	25805.9i	1.22108	−	2.11497i
$531$		0			0
$532$		0			0
$533$	−515.079			−0.0418585
$534$		0			0
$535$	6850.09	+	11864.7i	0.553561	+	0.958796i
$536$	−1577.26	−	2731.89i	−0.127103	−	0.220148i
$537$		0			0
$538$	−16350.3			−1.31024
$539$		0			0
$540$		0			0
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	0.344884	+	0.938645i	$0.387918\pi$
$541$	−8058.98	+	13958.6i	−0.640449	+	1.10929i	−0.985333	+	0.170644i	$0.945415\pi$
$542$	−4517.96	−	7825.34i	−0.358050	−	0.620161i
$543$		0			0
$544$	5016.47	−	8688.78i	0.395366	−	0.684795i
$545$	−25505.9			−2.00469
$546$		0			0
$547$	−626.100			−0.0489399			−0.0244699	−	0.999701i	$-0.507790\pi$
$547$	−626.100			−0.0489399			−0.0244699	+	0.999701i	$0.507790\pi$
$548$	10747.0	−	18614.3i	0.837751	−	1.45103i
$549$		0			0
$550$	−5047.56	−	8742.64i	−0.391325	−	0.677795i
$551$	3955.74	−	6851.54i	0.305844	−	0.529737i
$552$		0			0
$553$		0			0
$554$	33552.7			2.57313
$555$		0			0
$556$	2010.34	+	3482.02i	0.153341	+	0.265594i
$557$	10385.6	+	17988.4i	0.790039	+	1.36839i	0.925942	+	0.377665i	$0.123273\pi$
$557$	10385.6	+	17988.4i	0.790039	+	1.36839i	−0.135903	+	0.990722i	$0.543394\pi$
$558$		0			0
$559$	5625.08			0.425609
$560$		0			0
$561$		0			0
$562$	−12101.8	+	20961.0i	−0.908335	+	1.57328i
$563$	2760.86	+	4781.95i	0.206672	+	0.357966i	0.950664	−	0.310222i	$-0.100403\pi$
$563$	2760.86	+	4781.95i	0.206672	+	0.357966i	−0.743992	+	0.668188i	$0.767070\pi$
$564$		0			0
$565$	3240.09	−	5612.00i	0.241260	−	0.417874i
$566$	4974.48			0.369422
$567$		0			0
$568$	8002.95			0.591191
$569$	3787.40	−	6559.97i	0.279044	−	0.483319i	−0.692103	−	0.721799i	$-0.743316\pi$
$569$	3787.40	−	6559.97i	0.279044	−	0.483319i	0.971147	+	0.238480i	$0.0766491\pi$
$570$		0			0
$571$	165.624	+	286.869i	0.0121386	+	0.0210247i	0.872031	−	0.489451i	$-0.162803\pi$
$571$	165.624	+	286.869i	0.0121386	+	0.0210247i	−0.859892	+	0.510476i	$0.829469\pi$
$572$	−952.239	+	1649.33i	−0.0696068	+	0.120563i
$573$		0			0
$574$		0			0
$575$	−29573.2			−2.14485
$576$		0			0
$577$	1019.06	+	1765.06i	0.0735248	+	0.127349i	0.900444	−	0.434972i	$-0.143242\pi$
$577$	1019.06	+	1765.06i	0.0735248	+	0.127349i	−0.826919	+	0.562321i	$0.809909\pi$
$578$	4728.57	+	8190.13i	0.340281	+	0.589385i
$579$		0			0
$580$	−42533.6			−3.04502
$581$		0			0
$582$		0			0
$583$	2084.58	−	3610.60i	0.148087	−	0.256494i
$584$	6603.72	+	11438.0i	0.467918	+	0.810457i
$585$		0			0
$586$	16384.4	−	28378.6i	1.15500	−	2.00053i
$587$	5232.90			0.367947			0.183973	−	0.982931i	$-0.441104\pi$
$587$	5232.90			0.367947			0.183973	+	0.982931i	$0.441104\pi$
$588$		0			0
$589$	6697.36			0.468523
$590$	9225.88	−	15979.7i	0.643769	−	1.11504i
$591$		0			0
$592$	6.09477	+	10.5565i	0.000423131	+	0.000732884i
$593$	2860.12	−	4953.87i	0.198062	−	0.343054i	−0.749838	−	0.661622i	$-0.769868\pi$
$593$	2860.12	−	4953.87i	0.198062	−	0.343054i	0.947900	+	0.318568i	$0.103202\pi$
$594$		0			0
$595$		0			0
$596$	−24165.5			−1.66083
$597$		0			0
$598$	4538.41	+	7860.75i	0.310350	+	0.537542i
$599$	9044.21	+	15665.0i	0.616922	+	1.06854i	0.990044	+	0.140758i	$0.0449540\pi$
$599$	9044.21	+	15665.0i	0.616922	+	1.06854i	−0.373122	+	0.927782i	$0.621713\pi$
$600$		0			0
$601$	1821.43			0.123623			0.0618117	−	0.998088i	$-0.480312\pi$
$601$	1821.43			0.123623			0.0618117	+	0.998088i	$0.480312\pi$
$602$		0			0
$603$		0			0
$604$	12836.0	−	22232.6i	0.864719	−	1.49774i
$605$	10734.4	+	18592.5i	0.721348	+	1.24941i
$606$		0			0
$607$	1186.10	−	2054.39i	0.0793120	−	0.137372i	−0.823641	−	0.567111i	$-0.808061\pi$
$607$	1186.10	−	2054.39i	0.0793120	−	0.137372i	0.902953	+	0.429739i	$0.141394\pi$
$608$	−7990.26			−0.532974
$609$		0			0
$610$	−53094.7			−3.52416
$611$	−138.760	+	240.339i	−0.00918760	+	0.0159134i
$612$		0			0
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	0.660182	−	0.751105i	$-0.270479\pi$
$613$	−4862.54	−	8422.16i	−0.320385	−	0.554923i	−0.980567	+	0.196182i	$0.937146\pi$
$614$	1233.30	−	2136.15i	0.0810621	−	0.140404i
$615$		0			0
$616$		0			0
$617$	5329.51			0.347744			0.173872	−	0.984768i	$-0.444372\pi$
$617$	5329.51			0.347744			0.173872	+	0.984768i	$0.444372\pi$
$618$		0			0
$619$	−7988.29	−	13836.1i	−0.518702	−	0.898418i	−0.999764	−	0.0217314i	$-0.993082\pi$
$619$	−7988.29	−	13836.1i	−0.518702	−	0.898418i	0.481062	−	0.876687i	$-0.340251\pi$
$620$	−18003.2	−	31182.4i	−1.16617	−	2.01986i
$621$		0			0
$622$	246.120			0.0158658
$623$		0			0
$624$		0			0
$625$	1060.03	−	1836.03i	0.0678420	−	0.117506i
$626$	8595.45	+	14887.8i	0.548791	+	0.950535i
$627$		0			0
$628$	−24426.7	+	42308.4i	−1.55212	+	2.68836i
$629$	199.533			0.0126485
$630$		0			0
$631$	−4199.98			−0.264974			−0.132487	−	0.991185i	$-0.542296\pi$
$631$	−4199.98			−0.264974			−0.132487	+	0.991185i	$0.542296\pi$
$632$	−9871.73	+	17098.3i	−0.621324	+	1.07616i
$633$		0			0
$634$	3916.74	+	6783.99i	0.245352	+	0.424963i
$635$	−8711.19	+	15088.2i	−0.544399	+	0.942926i
$636$		0			0
$637$		0			0
$638$	−9681.97			−0.600804
$639$		0			0
$640$	20418.6	+	35366.0i	1.26112	+	2.18432i
$641$	1324.25	+	2293.67i	0.0815988	+	0.141333i	0.903937	−	0.427666i	$-0.140664\pi$
$641$	1324.25	+	2293.67i	0.0815988	+	0.141333i	−0.822338	+	0.568999i	$0.807331\pi$
$642$		0			0
$643$	−13.4305			−0.000823715			−0.000411857	−	1.00000i	$-0.500131\pi$
$643$	−13.4305			−0.000823715			−0.000411857		1.00000i	$0.500131\pi$
$644$		0			0
$645$		0			0
$646$	−5148.06	+	8916.70i	−0.313541	+	0.543070i
$647$	−5812.07	−	10066.8i	−0.353162	−	0.611695i	0.633639	−	0.773628i	$-0.281560\pi$
$647$	−5812.07	−	10066.8i	−0.353162	−	0.611695i	−0.986802	+	0.161934i	$0.948227\pi$
$648$		0			0
$649$	1290.83	−	2235.78i	0.0780732	−	0.135227i
$650$	11605.3			0.700305
$651$		0			0
$652$	−44779.8			−2.68974
$653$	−14258.3	+	24696.1i	−0.854471	+	1.47999i	0.0226638	+	0.999743i	$0.492785\pi$
$653$	−14258.3	+	24696.1i	−0.854471	+	1.47999i	−0.877135	+	0.480244i	$0.840548\pi$
$654$		0			0
$655$	16020.7	+	27748.6i	0.955694	+	1.65531i
$656$	−63.9809	+	110.818i	−0.00380798	+	0.00659561i
$657$		0			0
$658$		0			0
$659$	−18048.6			−1.06688			−0.533440	−	0.845838i	$-0.679101\pi$
$659$	−18048.6			−1.06688			−0.533440	+	0.845838i	$0.679101\pi$
$660$		0			0
$661$	8920.72	+	15451.1i	0.524926	+	0.909198i	0.999579	+	0.0290250i	$0.00924023\pi$
$661$	8920.72	+	15451.1i	0.524926	+	0.909198i	−0.474653	+	0.880173i	$0.657426\pi$
$662$	−19155.5	−	33178.2i	−1.12462	−	1.94790i
$663$		0			0
$664$	−7112.94			−0.415716
$665$		0			0
$666$		0			0
$667$	−14181.5	+	24563.0i	−0.823251	+	1.42591i
$668$	2188.47	+	3790.55i	0.126758	+	0.219552i
$669$		0			0
$670$	−5921.81	+	10256.9i	−0.341462	+	0.591430i
$671$	−7428.68			−0.427394
$672$		0			0
$673$	−6826.13			−0.390978			−0.195489	−	0.980706i	$-0.562629\pi$
$673$	−6826.13			−0.390978			−0.195489	+	0.980706i	$0.562629\pi$
$674$	−6354.89	+	11007.0i	−0.363177	+	0.629041i
$675$		0			0
$676$	12922.7	+	22382.8i	0.735246	+	1.27348i
$677$	10643.4	−	18435.0i	0.604225	−	1.04655i	−0.387949	−	0.921681i	$-0.626816\pi$
$677$	10643.4	−	18435.0i	0.604225	−	1.04655i	0.992173	−	0.124867i	$-0.0398505\pi$
$678$		0			0
$679$		0			0
$680$	20650.6			1.16458
$681$		0			0
$682$	−4098.08	−	7098.08i	−0.230093	−	0.398533i
$683$	−10348.4	−	17924.0i	−0.579753	−	1.00416i	−0.995507	−	0.0946842i	$-0.969816\pi$
$683$	−10348.4	−	17924.0i	−0.579753	−	1.00416i	0.415755	−	0.909477i	$-0.363517\pi$
$684$		0			0
$685$	−30105.9			−1.67925
$686$		0			0
$687$		0			0
$688$	698.722	−	1210.22i	0.0387188	−	0.0670629i
$689$	2396.43	+	4150.74i	0.132506	+	0.229507i
$690$		0			0
$691$	15671.0	−	27142.9i	0.862738	−	1.49431i	−0.00653825	−	0.999979i	$-0.502081\pi$
$691$	15671.0	−	27142.9i	0.862738	−	1.49431i	0.869276	−	0.494327i	$-0.164585\pi$
$692$	−53430.8			−2.93517
$693$		0			0
$694$	15819.5			0.865276
$695$	2815.83	−	4877.16i	0.153684	−	0.266189i
$696$		0			0
$697$	1047.32	+	1814.01i	0.0569153	+	0.0985801i
$698$	−15095.5	+	26146.2i	−0.818587	+	1.41783i
$699$		0			0
$700$		0			0
$701$	9213.32			0.496408			0.248204	−	0.968708i	$-0.420160\pi$
$701$	9213.32			0.496408			0.248204	+	0.968708i	$0.420160\pi$
$702$		0			0
$703$	−79.4544	−	137.619i	−0.00426270	−	0.00738322i
$704$	4740.89	+	8211.46i	0.253805	+	0.439604i
$705$		0			0
$706$	43141.5			2.29979
$707$		0			0
$708$		0			0
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	−0.991696	−	0.128607i	$-0.958949\pi$
$709$	−7258.27	+	12571.7i	−0.384471	+	0.665923i	0.607225	+	0.794530i	$0.292283\pi$
$710$	−15023.5	−	26021.6i	−0.794118	−	1.37545i
$711$		0			0
$712$	407.908	−	706.518i	0.0214705	−	0.0371880i
$713$	−24010.3			−1.26114
$714$		0			0
$715$	2667.54			0.139525
$716$	−12570.9	+	21773.4i	−0.656140	+	1.13647i
$717$		0			0
$718$	−14306.0	−	24778.7i	−0.743585	−	1.28793i
$719$	−12941.2	+	22414.8i	−0.671246	+	1.16263i	0.306306	+	0.951933i	$0.400907\pi$
$719$	−12941.2	+	22414.8i	−0.671246	+	1.16263i	−0.977551	+	0.210698i	$0.932426\pi$
$720$		0			0
$721$		0			0
$722$	−23052.3			−1.18825
$723$		0			0
$724$	−23052.4	−	39928.0i	−1.18334	−	2.04960i
$725$	18132.0	+	31405.5i	0.928833	+	1.60879i
$726$		0			0
$727$	−32181.2			−1.64172			−0.820862	−	0.571127i	$-0.806506\pi$
$727$	−32181.2			−1.64172			−0.820862	+	0.571127i	$0.806506\pi$
$728$		0			0
$729$		0			0
$730$	24793.7	−	42943.9i	1.25706	−	2.17730i
$731$	−11437.5	−	19810.4i	−0.578704	−	1.00234i
$732$		0			0
$733$	10418.1	−	18044.6i	0.524966	−	0.909268i	−0.474611	−	0.880195i	$-0.657411\pi$
$733$	10418.1	−	18044.6i	0.524966	−	0.909268i	0.999577	−	0.0290722i	$-0.00925528\pi$
$734$	49335.5			2.48094
$735$		0			0
$736$	28645.4			1.43462
$737$	−828.544	+	1435.08i	−0.0414109	+	0.0717257i
$738$		0			0
$739$	−13217.4	−	22893.3i	−0.657931	−	1.13957i	−0.981150	−	0.193246i	$-0.938098\pi$
$739$	−13217.4	−	22893.3i	−0.657931	−	1.13957i	0.323219	−	0.946324i	$-0.395235\pi$
$740$	−427.163	+	739.867i	−0.0212200	+	0.0367541i
$741$		0			0
$742$		0			0
$743$	−9954.69			−0.491524			−0.245762	−	0.969330i	$-0.579038\pi$
$743$	−9954.69			−0.491524			−0.245762	+	0.969330i	$0.579038\pi$
$744$		0			0
$745$	16923.9	+	29313.1i	0.832274	+	1.44154i
$746$	−11935.9	−	20673.6i	−0.585798	−	1.01463i
$747$		0			0
$748$	7744.79			0.378580
$749$		0			0
$750$		0			0
$751$	16602.3	−	28756.0i	0.806692	−	1.39723i	−0.108451	−	0.994102i	$-0.534589\pi$
$751$	16602.3	−	28756.0i	0.806692	−	1.39723i	0.915143	−	0.403129i	$-0.132077\pi$
$752$	34.4723	+	59.7078i	0.00167164	+	0.00289537i
$753$		0			0
$754$	5565.18	−	9639.17i	0.268796	−	0.465568i
$755$	−35958.1			−1.73331
$756$		0			0
$757$	1964.06			0.0942998			0.0471499	−	0.998888i	$-0.484986\pi$
$757$	1964.06			0.0942998			0.0471499	+	0.998888i	$0.484986\pi$
$758$	25174.8	−	43604.0i	1.20632	−	2.08941i
$759$		0			0
$760$	−8223.09	−	14242.8i	−0.392477	−	0.679791i
$761$	19276.9	−	33388.6i	0.918248	−	1.59045i	0.116174	−	0.993229i	$-0.462937\pi$
$761$	19276.9	−	33388.6i	0.918248	−	1.59045i	0.802075	−	0.597224i	$-0.203730\pi$
$762$		0			0
$763$		0			0
$764$	−24344.0			−1.15280
$765$		0			0
$766$	23848.1	+	41306.1i	1.12489	+	1.94837i
$767$	1483.93	+	2570.25i	0.0698588	+	0.120999i
$768$		0			0
$769$	19715.0			0.924501			0.462251	−	0.886749i	$-0.347042\pi$
$769$	19715.0			0.924501			0.462251	+	0.886749i	$0.347042\pi$
$770$		0			0
$771$		0			0
$772$	−15312.1	+	26521.3i	−0.713853	+	1.23643i
$773$	7350.34	+	12731.2i	0.342010	+	0.592378i	0.984806	−	0.173659i	$-0.0555591\pi$
$773$	7350.34	+	12731.2i	0.342010	+	0.592378i	−0.642796	+	0.766037i	$0.722226\pi$
$774$		0			0
$775$	−15349.4	+	26585.9i	−0.711440	+	1.23225i
$776$	−15660.8			−0.724471
$777$		0			0
$778$	52917.8			2.43856
$779$	834.086	−	1444.68i	0.0383623	−	0.0664454i
$780$		0			0
$781$	−2102.00	−	3640.78i	−0.0963068	−	0.166808i
$782$	18456.0	−	31966.7i	0.843970	−	1.46180i
$783$		0			0
$784$		0			0
$785$	68427.6			3.11119
$786$		0			0
$787$	−11959.3	−	20714.1i	−0.541681	−	0.938218i	−0.998808	−	0.0488169i	$-0.984455\pi$
$787$	−11959.3	−	20714.1i	−0.541681	−	0.938218i	0.457127	−	0.889401i	$-0.348878\pi$
$788$	9661.69	+	16734.5i	0.436781	+	0.756527i
$789$		0			0
$790$	74126.9			3.33837
$791$		0			0
$792$		0			0
$793$	4269.99	−	7395.84i	0.191213	−	0.331191i
$794$	−15280.5	−	26466.5i	−0.682976	−	1.18295i
$795$		0			0
$796$	8726.75	−	15115.2i	0.388582	−	0.673044i
$797$	38252.7			1.70010			0.850051	−	0.526700i	$-0.176571\pi$
$797$	38252.7			1.70010			0.850051	+	0.526700i	$0.176571\pi$
$798$		0			0
$799$	1128.57			0.0499698
$800$	18312.5	−	31718.2i	0.809307	−	1.40176i
$801$		0			0
$802$	12590.1	+	21806.7i	0.554329	+	0.960126i
$803$	3468.98	−	6008.45i	0.152450	−	0.264052i
$804$		0			0
$805$		0			0
$806$	9422.27			0.411769
$807$		0			0
$808$	−16470.3	−	28527.5i	−0.717110	−	1.24207i
$809$	−15717.8	−	27224.0i	−0.683075	−	1.18312i	−0.974038	−	0.226386i	$-0.927309\pi$
$809$	−15717.8	−	27224.0i	−0.683075	−	1.18312i	0.290962	−	0.956734i	$-0.406025\pi$
$810$		0			0
$811$	−11467.0			−0.496501			−0.248250	−	0.968696i	$-0.579856\pi$
$811$	−11467.0			−0.496501			−0.248250	+	0.968696i	$0.579856\pi$
$812$		0			0
$813$		0			0
$814$	−97.2354	+	168.417i	−0.00418686	+	0.00725185i
$815$	31360.8	+	54318.6i	1.34788	+	2.33460i
$816$		0			0
$817$	−9108.88	+	15777.1i	−0.390061	+	0.675605i
$818$	6009.42			0.256864
$819$		0			0
$820$	−8968.42			−0.381940
$821$	−2515.29	+	4356.60i	−0.106923	+	0.185197i	−0.914522	−	0.404535i	$-0.867433\pi$
$821$	−2515.29	+	4356.60i	−0.106923	+	0.185197i	0.807599	+	0.589732i	$0.200767\pi$
$822$		0			0
$823$	6992.59	+	12111.5i	0.296168	+	0.512978i	0.975256	−	0.221079i	$-0.0709578\pi$
$823$	6992.59	+	12111.5i	0.296168	+	0.512978i	−0.679088	+	0.734057i	$0.737625\pi$
$824$	−11407.9	+	19759.1i	−0.482298	+	0.835364i
$825$		0			0
$826$		0			0
$827$	13939.5			0.586125			0.293063	−	0.956093i	$-0.405326\pi$
$827$	13939.5			0.586125			0.293063	+	0.956093i	$0.405326\pi$
$828$		0			0
$829$	−10052.2	−	17410.9i	−0.421143	−	0.729441i	0.574909	−	0.818218i	$-0.305038\pi$
$829$	−10052.2	−	17410.9i	−0.421143	−	0.729441i	−0.996052	+	0.0887769i	$0.971704\pi$
$830$	13352.8	+	23127.7i	0.558411	+	0.967197i
$831$		0			0
$832$	−10900.2			−0.454203
$833$		0			0
$834$		0			0
$835$	3065.33	−	5309.31i	0.127042	−	0.220043i
$836$	−3083.99	−	5341.62i	−0.127586	−	0.220986i
$837$		0			0
$838$	−8329.33	+	14426.8i	−0.343356	+	0.594710i
$839$	15949.5			0.656302			0.328151	−	0.944625i	$-0.393575\pi$
$839$	15949.5			0.656302			0.328151	+	0.944625i	$0.393575\pi$
$840$		0			0
$841$	10390.8			0.426043
$842$	308.440	−	534.235i	0.0126242	−	0.0218657i
$843$		0			0
$844$	−27451.1	−	47546.7i	−1.11956	−	1.93913i
$845$	18100.4	−	31350.8i	0.736891	−	1.27633i
$846$		0			0
$847$		0			0
$848$	1190.70			0.0482177
$849$		0			0
$850$	−23597.2	−	40871.6i	−0.952210	−	1.64928i
$851$	284.847	+	493.369i	0.0114741	+	0.0198737i
$852$		0			0
$853$	−11802.0			−0.473730			−0.236865	−	0.971543i	$-0.576120\pi$
$853$	−11802.0			−0.473730			−0.236865	+	0.971543i	$0.576120\pi$
$854$		0			0
$855$		0			0
$856$	8313.09	−	14398.7i	0.331934	−	0.574927i
$857$	−4797.64	−	8309.76i	−0.191230	−	0.331220i	0.754428	−	0.656383i	$-0.227914\pi$
$857$	−4797.64	−	8309.76i	−0.191230	−	0.331220i	−0.945658	+	0.325162i	$0.894581\pi$
$858$		0			0
$859$	10920.4	−	18914.7i	0.433760	−	0.751295i	−0.563433	−	0.826162i	$-0.690520\pi$
$859$	10920.4	−	18914.7i	0.433760	−	0.751295i	0.997194	+	0.0748666i	$0.0238531\pi$
$860$	97942.3			3.88350
$861$		0			0
$862$	−38224.1			−1.51035
$863$	−13265.8	+	22977.1i	−0.523260	+	0.906313i	0.476374	+	0.879243i	$0.341951\pi$
$863$	−13265.8	+	22977.1i	−0.523260	+	0.906313i	−0.999634	+	0.0270699i	$0.991382\pi$
$864$		0			0
$865$	37419.5	+	64812.4i	1.47087	+	2.54762i
$866$	−18779.1	+	32526.4i	−0.736882	+	1.27632i
$867$		0			0
$868$		0			0
$869$	10371.4			0.404862
$870$		0			0
$871$	−952.491	−	1649.76i	−0.0370539	−	0.0641792i
$872$	15476.7	+	26806.4i	0.601039	+	1.04103i
$873$		0			0
$874$	−29396.8			−1.13771
$875$		0			0
$876$		0			0
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	−0.792732	−	0.609570i	$-0.791342\pi$
$877$	3416.23	−	5917.09i	0.131537	−	0.227829i	0.924269	+	0.381741i	$0.124675\pi$
$878$	−41652.4	−	72144.1i	−1.60103	−	2.77306i
$879$		0			0
$880$	331.351	−	573.916i	0.0126930	−	0.0219849i
$881$	−3994.77			−0.152766			−0.0763832	−	0.997079i	$-0.524337\pi$
$881$	−3994.77			−0.152766			−0.0763832	+	0.997079i	$0.524337\pi$
$882$		0			0
$883$	13727.0			0.523161			0.261580	−	0.965182i	$-0.415756\pi$
$883$	13727.0			0.523161			0.261580	+	0.965182i	$0.415756\pi$
$884$	−4451.69	+	7710.56i	−0.169374	+	0.293364i
$885$		0			0
$886$	2757.59	+	4776.29i	0.104563	+	0.181109i
$887$	−22059.7	+	38208.5i	−0.835054	+	1.44636i	0.0589333	+	0.998262i	$0.481230\pi$
$887$	−22059.7	+	38208.5i	−0.835054	+	1.44636i	−0.893987	+	0.448093i	$0.852103\pi$
$888$		0			0
$889$		0			0
$890$	−3062.99			−0.115361
$891$		0			0
$892$	−9552.40	−	16545.2i	−0.358563	−	0.621049i
$893$	−449.398	−	778.380i	−0.0168405	−	0.0291685i
$894$		0			0
$895$	35215.3			1.31522
$896$		0			0
$897$		0			0
$898$	−18911.6	+	32755.8i	−0.702769	+	1.21723i
$899$	14721.2	+	25497.9i	0.546140	+	0.945942i
$900$		0			0
$901$	9745.37	−	16879.5i	0.360339	−	0.624125i
$902$	−2041.49			−0.0753594
$903$		0			0
$904$	−7864.18			−0.289335
$905$	−32288.9	+	55925.9i	−1.18599	+	2.05419i
$906$		0			0
$907$	−18452.9	−	31961.4i	−0.675545	−	1.17008i	−0.976309	−	0.216380i	$-0.930575\pi$
$907$	−18452.9	−	31961.4i	−0.675545	−	1.17008i	0.300764	−	0.953698i	$-0.402758\pi$
$908$	−10229.6	+	17718.2i	−0.373878	+	0.647575i
$909$		0			0
$910$		0			0
$911$	3169.56			0.115271			0.0576356	−	0.998338i	$-0.481644\pi$
$911$	3169.56			0.115271			0.0576356	+	0.998338i	$0.481644\pi$
$912$		0			0
$913$	1868.24	+	3235.88i	0.0677214	+	0.117297i
$914$	28007.4	+	48510.3i	1.01357	+	1.75556i
$915$		0			0
$916$	−12894.7			−0.465124
$917$		0			0
$918$		0			0
$919$	−4363.50	+	7557.80i	−0.156625	+	0.271283i	−0.933650	−	0.358188i	$-0.883395\pi$
$919$	−4363.50	+	7557.80i	−0.156625	+	0.271283i	0.777024	+	0.629470i	$0.216728\pi$
$920$	29480.1	+	51061.0i	1.05645	+	1.82982i
$921$		0			0
$922$	−44274.8	+	76686.2i	−1.58147	+	2.73918i
$923$	4832.91			0.172348
$924$		0			0
$925$	728.392			0.0258912
$926$	28457.1	−	49289.1i	1.00989	−	1.74918i
$927$		0			0
$928$	−17563.1	−	30420.1i	−0.621267	−	1.07607i
$929$	−9702.54	+	16805.3i	−0.342659	+	0.593502i	−0.984926	−	0.172979i	$-0.944661\pi$
$929$	−9702.54	+	16805.3i	−0.342659	+	0.593502i	0.642267	+	0.766481i	$0.277994\pi$
$930$		0			0
$931$		0			0
$932$	−2529.34			−0.0888963
$933$		0			0
$934$	−7712.04	−	13357.6i	−0.270177	−	0.467961i
$935$	−5423.95	−	9394.55i	−0.189713	−	0.328593i
$936$		0			0
$937$	615.692			0.0214662			0.0107331	−	0.999942i	$-0.496583\pi$
$937$	615.692			0.0214662			0.0107331	+	0.999942i	$0.496583\pi$
$938$		0			0
$939$		0			0
$940$	−2416.05	+	4184.72i	−0.0838329	+	0.145203i
$941$	14801.0	+	25636.1i	0.512751	+	0.888111i	0.999891	+	0.0147865i	$0.00470687\pi$
$941$	14801.0	+	25636.1i	0.512751	+	0.888111i	−0.487140	+	0.873324i	$0.661960\pi$
$942$		0			0
$943$	−2990.23	+	5179.23i	−0.103261	+	0.178854i
$944$	737.310			0.0254210
$945$		0			0
$946$	22294.7			0.766240
$947$	6768.71	−	11723.8i	0.232264	−	0.402292i	−0.726210	−	0.687473i	$-0.758720\pi$
$947$	6768.71	−	11723.8i	0.232264	−	0.402292i	0.958474	+	0.285180i	$0.0920535\pi$
$948$		0			0
$949$	3987.93	+	6907.29i	0.136411	+	0.236270i
$950$	−18792.9	+	32550.3i	−0.641813	+	1.11165i
$951$		0			0
$952$		0			0
$953$	−33468.5			−1.13762			−0.568810	−	0.822469i	$-0.692596\pi$
$953$	−33468.5			−1.13762			−0.568810	+	0.822469i	$0.692596\pi$
$954$		0			0
$955$	17049.0	+	29529.7i	0.577688	+	1.00058i
$956$	−7663.86	−	13274.2i	−0.259275	−	0.449078i
$957$		0			0
$958$	27244.4			0.918817
$959$		0			0
$960$		0			0
$961$	2433.44	−	4214.85i	0.0816838	−	0.141480i
$962$	−111.781	−	193.611i	−0.00374634	−	0.00648885i
$963$		0			0
$964$	−17435.2	+	30198.7i	−0.582521	+	1.00896i
$965$	42894.4			1.43090
$966$		0			0
$967$	−55733.5			−1.85343			−0.926715	−	0.375764i	$-0.877380\pi$
$967$	−55733.5			−1.85343			−0.926715	+	0.375764i	$0.877380\pi$
$968$	13027.0	−	22563.4i	0.432545	−	0.749190i
$969$		0			0
$970$	29399.2	+	50920.9i	0.973146	+	1.68554i
$971$	9745.65	−	16880.0i	0.322094	−	0.557882i	−0.658826	−	0.752295i	$-0.728947\pi$
$971$	9745.65	−	16880.0i	0.322094	−	0.557882i	0.980920	+	0.194413i	$0.0622801\pi$
$972$		0			0
$973$		0			0
$974$	−5080.18			−0.167125
$975$		0			0
$976$	−1060.80	−	1837.36i	−0.0347903	−	0.0602586i
$977$	−3120.78	−	5405.35i	−0.102193	−	0.177004i	0.810395	−	0.585884i	$-0.199253\pi$
$977$	−3120.78	−	5405.35i	−0.102193	−	0.177004i	−0.912588	+	0.408881i	$0.865919\pi$
$978$		0			0
$979$	−428.554			−0.0139905
$980$		0			0
$981$		0			0
$982$	2474.63	−	4286.18i	0.0804160	−	0.139285i
$983$	−29847.3	−	51697.0i	−0.968444	−	1.67739i	−0.700062	−	0.714082i	$-0.746845\pi$
$983$	−29847.3	−	51697.0i	−0.968444	−	1.67739i	−0.268382	−	0.963313i	$-0.586489\pi$
$984$		0			0
$985$	13532.8	−	23439.6i	0.437758	−	0.758220i
$986$	−45263.0			−1.46193
$987$		0			0
$988$	7090.68			0.228324
$989$	32655.7	−	56561.3i	1.04994	−	1.81855i
$990$		0			0
$991$	−7780.82	−	13476.8i	−0.249411	−	0.431992i	0.713952	−	0.700195i	$-0.246904\pi$
$991$	−7780.82	−	13476.8i	−0.249411	−	0.431992i	−0.963362	+	0.268203i	$0.913570\pi$
$992$	14867.8	−	25751.8i	0.475860	−	0.824214i
$993$		0			0
$994$		0			0
$995$	−24446.6			−0.778903
$996$		0			0
$997$	9942.47	+	17220.9i	0.315829	+	0.547031i	0.979613	−	0.200892i	$-0.0643842\pi$
$997$	9942.47	+	17220.9i	0.315829	+	0.547031i	−0.663785	+	0.747924i	$0.731051\pi$
$998$	5042.76	+	8734.31i	0.159946	+	0.277034i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.w.226.1		6
3.2	odd	2		147.4.e.n.79.3		6
7.2	even	3		441.4.a.t.1.3		3
7.3	odd	6		63.4.e.c.46.1		6
7.4	even	3	inner	441.4.e.w.361.1		6
7.5	odd	6		441.4.a.s.1.3		3
7.6	odd	2		63.4.e.c.37.1		6
21.2	odd	6		147.4.a.m.1.1		3
21.5	even	6		147.4.a.l.1.1		3
21.11	odd	6		147.4.e.n.67.3		6
21.17	even	6		21.4.e.b.4.3	✓	6
21.20	even	2		21.4.e.b.16.3	yes	6
84.23	even	6		2352.4.a.cg.1.1		3
84.47	odd	6		2352.4.a.ci.1.3		3
84.59	odd	6		336.4.q.k.193.1		6
84.83	odd	2		336.4.q.k.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.3	✓	6	21.17	even	6
21.4.e.b.16.3	yes	6	21.20	even	2
63.4.e.c.37.1		6	7.6	odd	2
63.4.e.c.46.1		6	7.3	odd	6
147.4.a.l.1.1		3	21.5	even	6
147.4.a.m.1.1		3	21.2	odd	6
147.4.e.n.67.3		6	21.11	odd	6
147.4.e.n.79.3		6	3.2	odd	2
336.4.q.k.193.1		6	84.59	odd	6
336.4.q.k.289.1		6	84.83	odd	2
441.4.a.s.1.3		3	7.5	odd	6
441.4.a.t.1.3		3	7.2	even	3
441.4.e.w.226.1		6	1.1	even	1	trivial
441.4.e.w.361.1		6	7.4	even	3	inner
2352.4.a.cg.1.1		3	84.23	even	6
2352.4.a.ci.1.3		3	84.47	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)

\(f(q)\)	\(=\)	\(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(-8.93660 + 15.4786i) q^{5} +21.6905 q^{8} +O(q^{10})\)	\(q+(-2.27818 + 3.94593i) q^{2} +(-6.38024 - 11.0509i) q^{4} +(-8.93660 + 15.4786i) q^{5} +21.6905 q^{8} +(-40.7184 - 70.5264i) q^{10} +(-5.69708 - 9.86762i) q^{11} +13.0987 q^{13} +(1.62706 - 2.81815i) q^{16} +(-26.6337 - 46.1309i) q^{17} +(-21.2111 + 36.7388i) q^{19} +228.071 q^{20} +51.9159 q^{22} +(76.0427 - 131.710i) q^{23} +(-97.2257 - 168.400i) q^{25} +(-29.8412 + 51.6864i) q^{26} -186.493 q^{29} +(-78.9369 - 136.723i) q^{31} +(94.1753 + 163.116i) q^{32} +242.706 q^{34} +(-1.87294 + 3.24403i) q^{37} +(-96.6457 - 167.395i) q^{38} +(-193.839 + 335.739i) q^{40} -39.3230 q^{41} +429.439 q^{43} +(-72.6974 + 125.916i) q^{44} +(346.478 + 600.118i) q^{46} +(-10.5934 + 18.3484i) q^{47} +885.992 q^{50} +(-83.5726 - 144.752i) q^{52} +(182.952 + 316.882i) q^{53} +203.650 q^{55} +(424.866 - 735.889i) q^{58} +(113.289 + 196.222i) q^{59} +(325.987 - 564.626i) q^{61} +719.331 q^{62} -832.161 q^{64} +(-117.058 + 202.750i) q^{65} +(-72.7166 - 125.949i) q^{67} +(-339.858 + 588.652i) q^{68} +368.962 q^{71} +(304.453 + 527.328i) q^{73} +(-8.53380 - 14.7810i) q^{74} +541.328 q^{76} +(-455.119 + 788.289i) q^{79} +(29.0808 + 50.3694i) q^{80} +(89.5850 - 155.166i) q^{82} -327.929 q^{83} +952.058 q^{85} +(-978.340 + 1694.53i) q^{86} +(-123.572 - 214.033i) q^{88} +(18.8059 - 32.5728i) q^{89} -1940.68 q^{92} +(-48.2676 - 83.6019i) q^{94} +(-379.111 - 656.640i) q^{95} -722.013 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8}+O(q^{10}) \) 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8	\( 6 q + q^{2} - 25 q^{4} - 11 q^{5} - 78 q^{8} - 55 q^{10} + 35 q^{11} - 124 q^{13} - 241 q^{16} - 48 q^{17} - 202 q^{19} + 878 q^{20} - 14 q^{22} + 216 q^{23} - 130 q^{25} - 274 q^{26} - 106 q^{29} - 95 q^{31} + 683 q^{32} + 48 q^{34} - 262 q^{37} + 398 q^{38} + 21 q^{40} + 488 q^{41} + 720 q^{43} - 905 q^{44} + 1056 q^{46} + 210 q^{47} + 2756 q^{50} + 324 q^{52} + 393 q^{53} + 2062 q^{55} + 1249 q^{58} - 1143 q^{59} - 70 q^{61} + 2118 q^{62} - 798 q^{64} - 472 q^{65} + 628 q^{67} - 1944 q^{68} - 636 q^{71} + 988 q^{73} + 1002 q^{74} + 4680 q^{76} - 861 q^{79} - 175 q^{80} + 124 q^{82} + 1038 q^{83} + 3600 q^{85} - 3208 q^{86} + 891 q^{88} - 1766 q^{89} + 1344 q^{92} - 3294 q^{94} - 736 q^{95} - 38 q^{97}+O(q^{100}) \) 6 * q + q^2 - 25 * q^4 - 11 * q^5 - 78 * q^8 - 55 * q^10 + 35 * q^11 - 124 * q^13 - 241 * q^16 - 48 * q^17 - 202 * q^19 + 878 * q^20 - 14 * q^22 + 216 * q^23 - 130 * q^25 - 274 * q^26 - 106 * q^29 - 95 * q^31 + 683 * q^32 + 48 * q^34 - 262 * q^37 + 398 * q^38 + 21 * q^40 + 488 * q^41 + 720 * q^43 - 905 * q^44 + 1056 * q^46 + 210 * q^47 + 2756 * q^50 + 324 * q^52 + 393 * q^53 + 2062 * q^55 + 1249 * q^58 - 1143 * q^59 - 70 * q^61 + 2118 * q^62 - 798 * q^64 - 472 * q^65 + 628 * q^67 - 1944 * q^68 - 636 * q^71 + 988 * q^73 + 1002 * q^74 + 4680 * q^76 - 861 * q^79 - 175 * q^80 + 124 * q^82 + 1038 * q^83 + 3600 * q^85 - 3208 * q^86 + 891 * q^88 - 1766 * q^89 + 1344 * q^92 - 3294 * q^94 - 736 * q^95 - 38 * q^97

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