LMFDB - Embedded newform 49.4.c.e.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,4,Mod(18,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	49.c (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:	$2.89109359028$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			18.1
Root			$3.82402 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	49.18
Dual form			49.4.c.e.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.26556 - 3.92407i) q^{2} +(-1.78978 + 3.09999i) q^{3} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} +16.2194 q^{6} +20.5311 q^{8} +(7.09339 + 12.2861i) q^{9} +O(q^{10})$	\(q+(-2.26556 - 3.92407i) q^{2} +(-1.78978 + 3.09999i) q^{3} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} +16.2194 q^{6} +20.5311 q^{8} +(7.09339 + 12.2861i) q^{9} +(30.5377 - 52.8928i) q^{10} +(-0.406613 + 0.704275i) q^{11} +(-22.4279 - 38.8463i) q^{12} +34.9564 q^{13} -48.2490 q^{15} +(3.60992 + 6.25256i) q^{16} +(-58.8660 + 101.959i) q^{17} +(32.1410 - 55.6699i) q^{18} +(46.6457 + 80.7927i) q^{19} -168.908 q^{20} +3.68484 q^{22} +(-60.1245 - 104.139i) q^{23} +(-36.7462 + 63.6462i) q^{24} +(-28.3424 + 49.0905i) q^{25} +(-79.1960 - 137.171i) q^{26} -147.430 q^{27} +8.56420 q^{29} +(109.311 + 189.333i) q^{30} +(41.0535 - 71.1067i) q^{31} +(98.4815 - 170.575i) q^{32} +(-1.45550 - 2.52099i) q^{33} +533.458 q^{34} -177.776 q^{36} +(-14.4066 - 24.9530i) q^{37} +(211.358 - 366.082i) q^{38} +(-62.5642 + 108.364i) q^{39} +(138.370 + 239.664i) q^{40} -70.5291 q^{41} +417.179 q^{43} +(-5.09532 - 8.82536i) q^{44} +(-95.6121 + 165.605i) q^{45} +(-272.432 + 471.866i) q^{46} +(-169.131 - 292.943i) q^{47} -25.8438 q^{48} +256.846 q^{50} +(-210.714 - 364.967i) q^{51} +(-219.022 + 379.356i) q^{52} +(-74.5603 + 129.142i) q^{53} +(334.013 + 578.528i) q^{54} -10.9615 q^{55} -333.942 q^{57} +(-19.4027 - 33.6065i) q^{58} +(47.0914 - 81.5647i) q^{59} +(302.307 - 523.612i) q^{60} +(60.2623 + 104.377i) q^{61} -372.037 q^{62} -834.706 q^{64} +(235.590 + 408.053i) q^{65} +(-6.59504 + 11.4229i) q^{66} +(396.183 - 686.209i) q^{67} +(-737.657 - 1277.66i) q^{68} +430.438 q^{69} +449.128 q^{71} +(145.635 + 252.248i) q^{72} +(234.710 - 406.530i) q^{73} +(-65.2782 + 113.065i) q^{74} +(-101.453 - 175.722i) q^{75} -1169.05 q^{76} +566.973 q^{78} +(509.926 + 883.218i) q^{79} +(-48.6583 + 84.2786i) q^{80} +(72.3463 - 125.307i) q^{81} +(159.788 + 276.761i) q^{82} -104.253 q^{83} -1586.91 q^{85} +(-945.146 - 1637.04i) q^{86} +(-15.3280 + 26.5489i) q^{87} +(-8.34823 + 14.4596i) q^{88} +(786.460 + 1362.19i) q^{89} +866.462 q^{90} +1506.86 q^{92} +(146.953 + 254.530i) q^{93} +(-766.352 + 1327.36i) q^{94} +(-628.739 + 1089.01i) q^{95} +(352.520 + 610.583i) q^{96} +550.057 q^{97} -11.5371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9	$ 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9} - 100 q^{11} - 128 q^{15} + 174 q^{16} + 370 q^{18} - 680 q^{22} - 352 q^{23} + 128 q^{25} + 520 q^{29} + 552 q^{30} + 30 q^{32} - 100 q^{36} - 212 q^{37} - 952 q^{39} + 1080 q^{43} - 460 q^{44} - 696 q^{46} + 2732 q^{50} - 428 q^{51} - 16 q^{53} - 3768 q^{57} + 780 q^{58} + 1064 q^{60} - 3356 q^{64} + 756 q^{65} + 1944 q^{67} + 4496 q^{71} - 270 q^{72} + 284 q^{74} - 2688 q^{78} + 1048 q^{79} + 1256 q^{81} - 6568 q^{85} - 4820 q^{86} - 1260 q^{88} + 7024 q^{92} + 5368 q^{93} - 2192 q^{95} + 6680 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9 - 100 * q^11 - 128 * q^15 + 174 * q^16 + 370 * q^18 - 680 * q^22 - 352 * q^23 + 128 * q^25 + 520 * q^29 + 552 * q^30 + 30 * q^32 - 100 * q^36 - 212 * q^37 - 952 * q^39 + 1080 * q^43 - 460 * q^44 - 696 * q^46 + 2732 * q^50 - 428 * q^51 - 16 * q^53 - 3768 * q^57 + 780 * q^58 + 1064 * q^60 - 3356 * q^64 + 756 * q^65 + 1944 * q^67 + 4496 * q^71 - 270 * q^72 + 284 * q^74 - 2688 * q^78 + 1048 * q^79 + 1256 * q^81 - 6568 * q^85 - 4820 * q^86 - 1260 * q^88 + 7024 * q^92 + 5368 * q^93 - 2192 * q^95 + 6680 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

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

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	$-0.870969\pi$
$2$	−2.26556	−	3.92407i	−0.800998	−	1.38737i	0.117962	−	0.993018i	$-0.462364\pi$
$3$	−1.78978	+	3.09999i	−0.344443	+	0.596593i	−0.985252	−	0.171107i	$-0.945266\pi$
$3$	−1.78978	+	3.09999i	−0.344443	+	0.596593i	0.640809	+	0.767700i	$0.278599\pi$
$4$	−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	$0.627384\pi$
$6$	16.2194			1.10359
$7$		0			0
$7$		0			0
$8$	20.5311			0.907356
$9$	7.09339	+	12.2861i	0.262718	+	0.455041i
$10$	30.5377	−	52.8928i	0.965686	−	1.67262i
$11$	−0.406613	+	0.704275i	−0.0111453	+	0.0193043i	−0.871544	−	0.490317i	$-0.836881\pi$
$11$	−0.406613	+	0.704275i	−0.0111453	+	0.0193043i	0.860399	+	0.509621i	$0.170214\pi$
$12$	−22.4279	−	38.8463i	−0.539532	−	0.934498i
$13$	34.9564			0.745781			0.372891	−	0.927875i	$-0.378367\pi$
$13$	34.9564			0.745781			0.372891	+	0.927875i	$0.378367\pi$
$14$		0			0
$15$	−48.2490			−0.830523
$16$	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	$0.849322\pi$
$18$	32.1410	−	55.6699i	0.420873	−	0.728974i
$19$	46.6457	+	80.7927i	0.563224	+	0.975532i	0.997213	+	0.0746138i	$0.0237724\pi$
$19$	46.6457	+	80.7927i	0.563224	+	0.975532i	−0.433989	+	0.900918i	$0.642894\pi$
$20$	−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	$-0.983166\pi$
$23$	−60.1245	−	104.139i	−0.545079	−	0.944105i	0.453522	−	0.891245i	$-0.350167\pi$
$24$	−36.7462	+	63.6462i	−0.312533	+	0.541322i
$25$	−28.3424	+	49.0905i	−0.226739	+	0.392724i
$26$	−79.1960	−	137.171i	−0.597369	−	1.03467i
$27$	−147.430			−1.05085
$28$		0			0
$29$	8.56420			0.0548390			0.0274195	−	0.999624i	$-0.491271\pi$
$29$	8.56420			0.0548390			0.0274195	+	0.999624i	$0.491271\pi$
$30$	109.311	+	189.333i	0.665247	+	1.15224i
$31$	41.0535	−	71.1067i	0.237852	−	0.411972i	−0.722245	−	0.691637i	$-0.756890\pi$
$31$	41.0535	−	71.1067i	0.237852	−	0.411972i	0.960098	+	0.279665i	$0.0902232\pi$
$32$	98.4815	−	170.575i	0.544039	−	0.942303i
$33$	−1.45550	−	2.52099i	−0.00767786	−	0.0132984i
$34$	533.458			2.69080
$35$		0			0
$36$	−177.776			−0.823038
$37$	−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
$39$	−62.5642	+	108.364i	−0.256879	+	0.444928i
$40$	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
$45$	−95.6121	+	165.605i	−0.316734	+	0.548599i
$46$	−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	$-0.342563\pi$
$48$	−25.8438			−0.0777132
$49$		0			0
$50$	256.846			0.726471
$51$	−210.714	−	364.967i	−0.578546	−	1.00207i
$52$	−219.022	+	379.356i	−0.584093	+	1.01168i
$53$	−74.5603	+	129.142i	−0.193239	+	0.334699i	−0.946322	−	0.323226i	$-0.895232\pi$
$53$	−74.5603	+	129.142i	−0.193239	+	0.334699i	0.753083	+	0.657925i	$0.228566\pi$
$54$	334.013	+	578.528i	0.841730	+	1.45792i
$55$	−10.9615			−0.0268737
$56$		0			0
$57$	−333.942			−0.775994
$58$	−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	$0.133531\pi$
$60$	302.307	−	523.612i	0.650462	−	1.12663i
$61$	60.2623	+	104.377i	0.126488	+	0.219084i	0.922314	−	0.386442i	$-0.126296\pi$
$61$	60.2623	+	104.377i	0.126488	+	0.219084i	−0.795825	+	0.605526i	$0.792963\pi$
$62$	−372.037			−0.762077
$63$		0			0
$64$	−834.706			−1.63029
$65$	235.590	+	408.053i	0.449558	+	0.778658i
$66$	−6.59504	+	11.4229i	−0.0122999	+	0.0213040i
$67$	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
$69$	430.438			0.750995
$70$		0			0
$71$	449.128			0.750729			0.375364	−	0.926877i	$-0.377518\pi$
$71$	449.128			0.750729			0.375364	+	0.926877i	$0.377518\pi$
$72$	145.635	+	252.248i	0.238379	+	0.412884i
$73$	234.710	−	406.530i	0.376311	−	0.651790i	−0.614211	−	0.789142i	$-0.710526\pi$
$73$	234.710	−	406.530i	0.376311	−	0.651790i	0.990522	+	0.137352i	$0.0438590\pi$
$74$	−65.2782	+	113.065i	−0.102546	+	0.177616i
$75$	−101.453	−	175.722i	−0.156198	−	0.270542i
$76$	−1169.05			−1.76446
$77$		0			0
$78$	566.973			0.823039
$79$	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
$81$	72.3463	−	125.307i	0.0992405	−	0.171890i
$82$	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
$87$	−15.3280	+	26.5489i	−0.0188889	+	0.0327166i
$88$	−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	$0.447215\pi$
$90$	866.462			1.01481
$91$		0			0
$92$	1506.86			1.70762
$93$	146.953	+	254.530i	0.163853	+	0.283802i
$94$	−766.352	+	1327.36i	−0.840885	+	1.45646i
$95$	−628.739	+	1089.01i	−0.679024	+	1.17610i
$96$	352.520	+	610.583i	0.374781	+	0.649139i
$97$	550.057			0.575772			0.287886	−	0.957665i	$-0.407048\pi$
$97$	550.057			0.575772			0.287886	+	0.957665i	$0.407048\pi$
$98$		0			0
$99$	−11.5371			−0.0117123
$100$	−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	$0.156361\pi$
$102$	−954.772	+	1653.71i	−0.926829	+	1.60531i
$103$	−914.674	−	1584.26i	−0.875005	−	1.51555i	−0.856757	−	0.515720i	$-0.827524\pi$
$103$	−914.674	−	1584.26i	−0.875005	−	1.51555i	−0.0182480	−	0.999833i	$-0.505809\pi$
$104$	717.694			0.676689
$105$		0			0
$106$	675.685			0.619135
$107$	−430.689	−	745.975i	−0.389124	−	0.673982i	0.603208	−	0.797584i	$-0.293889\pi$
$107$	−430.689	−	745.975i	−0.389124	−	0.673982i	−0.992332	+	0.123602i	$0.960556\pi$
$108$	923.735	−	1599.96i	0.823022	−	1.42552i
$109$	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
$111$	103.139			0.0881935
$112$		0			0
$113$	380.409			0.316689			0.158344	−	0.987384i	$-0.449384\pi$
$113$	380.409			0.316689			0.158344	+	0.987384i	$0.449384\pi$
$114$	756.566	+	1310.41i	0.621569	+	1.07659i
$115$	810.421	−	1403.69i	0.657149	−	1.13822i
$116$	−53.6595	+	92.9410i	−0.0429497	+	0.0743910i
$117$	247.959	+	429.478i	0.195930	+	0.339361i
$118$	−426.754			−0.332931
$119$		0			0
$120$	−990.607			−0.753580
$121$	665.169	+	1152.11i	0.499752	+	0.865595i
$122$	273.056	−	472.947i	0.202634	−	0.350972i
$123$	126.231	−	218.639i	0.0925358	−	0.160277i
$124$	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
$129$	−746.658	+	1293.25i	−0.509609	+	0.882669i
$130$	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	$0.958861\pi$
$132$	36.4780			0.0240531
$133$		0			0
$134$	−3590.31			−2.31459
$135$	−993.611	−	1720.98i	−0.633455	−	1.09718i
$136$	−1208.58	+	2093.33i	−0.762024	+	1.31986i
$137$	−178.689	+	309.498i	−0.111434	+	0.193009i	−0.916349	−	0.400382i	$-0.868878\pi$
$137$	−178.689	+	309.498i	−0.111434	+	0.193009i	0.804915	+	0.593390i	$0.202211\pi$
$138$	−975.186	−	1689.07i	−0.601546	−	1.04191i
$139$	−2736.29			−1.66970			−0.834852	−	0.550475i	$-0.814447\pi$
$139$	−2736.29			−1.66970			−0.834852	+	0.550475i	$0.814447\pi$
$140$		0			0
$141$	1210.83			0.723191
$142$	−1017.53	−	1762.41i	−0.601332	−	1.04154i
$143$	−14.2137	+	24.6189i	−0.00831197	+	0.0143968i
$144$	−51.2131	+	88.7037i	−0.0296372	+	0.0513332i
$145$	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	0.604521	−	0.796589i	$-0.293365\pi$
$149$	−704.969	−	1221.04i	−0.387606	−	0.671353i	−0.992127	+	0.125236i	$0.960031\pi$
$150$	−459.698	+	796.220i	−0.250228	+	0.433407i
$151$	−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
$153$	−1670.24			−0.882553
$154$		0			0
$155$	1106.72			0.573511
$156$	−784.000	−	1357.93i	−0.402373	−	0.696931i
$157$	−606.911	+	1051.20i	−0.308514	+	0.534363i	−0.978038	−	0.208429i	$-0.933165\pi$
$157$	−606.911	+	1051.20i	−0.308514	+	0.534363i	0.669523	+	0.742791i	$0.266498\pi$
$158$	2310.54	−	4001.97i	1.16340	−	2.01506i
$159$	−266.893	−	462.272i	−0.133119	−	0.230570i
$160$	2654.88			1.31179
$161$		0			0
$162$	−655.621			−0.317966
$163$	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
$165$	19.6187	−	33.9806i	0.00925645	−	0.0160326i
$166$	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
$171$	−661.751	+	1146.19i	−0.295938	+	0.512580i
$172$	−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	$0.699379\pi$
$174$	138.906			0.0605199
$175$		0			0
$176$	−5.87137			−0.00251461
$177$	168.566	+	291.965i	0.0715831	+	0.123986i
$178$	3563.55	−	6172.25i	1.50056	−	2.59904i
$179$	261.413	−	452.780i	0.109156	−	0.189063i	−0.806273	−	0.591544i	$-0.798519\pi$
$179$	261.413	−	452.780i	0.109156	−	0.189063i	0.915429	+	0.402481i	$0.131852\pi$
$180$	−1198.13	−	2075.22i	−0.496129	−	0.859320i
$181$	2901.38			1.19148			0.595740	−	0.803177i	$-0.296859\pi$
$181$	2901.38			1.19148			0.595740	+	0.803177i	$0.296859\pi$
$182$		0			0
$183$	−431.424			−0.174272
$184$	−1234.42	−	2138.09i	−0.494581	−	0.856640i
$185$	194.187	−	336.343i	0.0771727	−	0.133667i
$186$	665.864	−	1153.31i	0.262492	−	0.454650i
$187$	−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	0.506661	−	0.862145i	$-0.330880\pi$
$191$	−1302.18	−	2255.43i	−0.493309	−	0.854437i	−0.999970	+	0.00770854i	$0.997546\pi$
$192$	1493.94	−	2587.58i	0.561541	−	0.972617i
$193$	−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
$195$	−1686.61			−0.619389
$196$		0			0
$197$	−3685.99			−1.33308			−0.666538	−	0.745471i	$-0.732225\pi$
$197$	−3685.99			−1.33308			−0.666538	+	0.745471i	$0.732225\pi$
$198$	26.1380	+	45.2723i	0.00938154	+	0.0162493i
$199$	399.901	−	692.648i	0.142453	−	0.246736i	−0.785967	−	0.618269i	$-0.787834\pi$
$199$	399.901	−	692.648i	0.142453	−	0.246736i	0.928420	+	0.371533i	$0.121168\pi$
$200$	−581.902	+	1007.88i	−0.205733	+	0.356341i
$201$	1418.16	+	2456.32i	0.497658	+	0.861969i
$202$	−297.772			−0.103719
$203$		0			0
$204$	5280.97			1.81246
$205$	−475.333	−	823.300i	−0.161945	−	0.280497i
$206$	−4144.51	+	7178.50i	−1.40175	+	2.42791i
$207$	852.973	−	1477.39i	0.286404	−	0.496067i
$208$	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
$213$	−803.840	+	1392.29i	−0.258583	+	0.447879i
$214$	−1951.51	+	3380.11i	−0.623375	+	1.07972i
$215$	2811.59	+	4869.81i	0.891855	+	1.54474i
$216$	−3026.91			−0.953497
$217$		0			0
$218$	−7342.77			−2.28126
$219$	840.158	+	1455.20i	0.259236	+	0.449009i
$220$	68.6801	−	118.957i	0.0210473	−	0.0364551i
$221$	−2057.74	+	3564.11i	−0.626329	+	1.08483i
$222$	−233.667	−	404.723i	−0.0706428	−	0.122357i
$223$	2646.82			0.794818			0.397409	−	0.917642i	$-0.369909\pi$
$223$	2646.82			0.794818			0.397409	+	0.917642i	$0.369909\pi$
$224$		0			0
$225$	−804.175			−0.238274
$226$	−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	$0.960844\pi$
$228$	2092.33	−	3624.03i	0.607755	−	1.05266i
$229$	−2033.46	−	3522.06i	−0.586790	−	1.01635i	−0.994650	−	0.103306i	$-0.967058\pi$
$229$	−2033.46	−	3522.06i	−0.586790	−	1.01635i	0.407860	−	0.913045i	$-0.366275\pi$
$230$	−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	$0.0182996\pi$
$233$	1952.33	+	3381.54i	0.548934	+	0.950782i	−0.449414	+	0.893324i	$0.648367\pi$
$234$	1123.54	−	1946.02i	0.313879	−	0.543655i
$235$	2279.72	−	3948.59i	0.632819	−	1.09608i
$236$	590.108	+	1022.10i	0.162766	+	0.281919i
$237$	−3650.62			−1.00056
$238$		0			0
$239$	5425.12			1.46829			0.734146	−	0.678991i	$-0.237583\pi$
$239$	5425.12			1.46829			0.734146	+	0.678991i	$0.237583\pi$
$240$	−174.175	−	301.680i	−0.0468457	−	0.0811391i
$241$	801.446	−	1388.15i	0.214215	−	0.371030i	−0.738815	−	0.673909i	$-0.764614\pi$
$241$	801.446	−	1388.15i	0.214215	−	0.371030i	0.953029	+	0.302878i	$0.0979475\pi$
$242$	3013.97	−	5220.35i	0.800600	−	1.38668i
$243$	−1731.34	−	2998.77i	−0.457060	−	0.791652i
$244$	−1510.31			−0.396261
$245$		0			0
$246$	−1143.94			−0.296484
$247$	1630.56	+	2824.22i	0.420042	+	0.727534i
$248$	842.874	−	1459.90i	0.215817	−	0.373806i
$249$	186.590	−	323.183i	0.0474885	−	0.0822524i
$250$	−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
$255$	2840.23	−	4919.41i	0.697497	−	1.20810i
$256$	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	$-0.354697\pi$
$258$	6766.41			1.63278
$259$		0			0
$260$	−5904.41			−1.40837
$261$	60.7492	+	105.221i	0.0144072	+	0.0249540i
$262$	−2610.29	+	4521.15i	−0.615512	+	1.06610i
$263$	−438.587	+	759.656i	−0.102831	+	0.178108i	−0.912850	−	0.408295i	$-0.866123\pi$
$263$	−438.587	+	759.656i	−0.102831	+	0.178108i	0.810019	+	0.586403i	$0.199457\pi$
$264$	−29.8830	−	51.7588i	−0.00696655	−	0.0120664i
$265$	−2010.00			−0.465938
$266$		0			0
$267$	−5630.35			−1.29053
$268$	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	$-0.0774764\pi$
$270$	−4502.18	+	7798.00i	−1.01479	+	1.75767i
$271$	1744.88	+	3022.22i	0.391122	+	0.677443i	0.992598	−	0.121448i	$-0.0387538\pi$
$271$	1744.88	+	3022.22i	0.391122	+	0.677443i	−0.601476	+	0.798891i	$0.705421\pi$
$272$	−850.006			−0.189482
$273$		0			0
$274$	1619.32			0.357032
$275$	−23.0488	−	39.9217i	−0.00505417	−	0.00875407i
$276$	−2696.94	+	4671.23i	−0.588176	+	1.01875i
$277$	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
$279$	1164.83			0.249952
$280$		0			0
$281$	6914.46			1.46791			0.733954	−	0.679199i	$-0.237673\pi$
$281$	6914.46			1.46791			0.733954	+	0.679199i	$0.237673\pi$
$282$	−2743.20	−	4751.37i	−0.579274	−	1.00333i
$283$	−1779.92	+	3082.92i	−0.373871	+	0.647564i	−0.990157	−	0.139959i	$-0.955303\pi$
$283$	−1779.92	+	3082.92i	−0.373871	+	0.647564i	0.616286	+	0.787522i	$0.288636\pi$
$284$	−2814.04	+	4874.07i	−0.587967	+	1.01839i
$285$	−2250.61	−	3898.17i	−0.467770	−	0.810202i
$286$	128.809			0.0266315
$287$		0			0
$288$	2794.27			0.571715
$289$	−4473.90	−	7749.02i	−0.910625	−	1.57725i
$290$	261.531	−	452.984i	0.0529572	−	0.0917246i
$291$	−984.481	+	1705.17i	−0.198321	+	0.343501i
$292$	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
$297$	59.9472	−	103.832i	0.0117121	−	0.0202859i
$298$	−3194.31	+	5532.70i	−0.620943	+	1.07551i
$299$	−2101.74	−	3640.31i	−0.406510	−	0.704096i
$300$	2542.65			0.489333
$301$		0			0
$302$	10658.8			2.03094
$303$	117.619	+	203.722i	0.0223004	+	0.0386254i
$304$	−336.774	+	583.310i	−0.0635373	+	0.110050i
$305$	−812.278	+	1406.91i	−0.152495	+	0.264129i
$306$	3784.03	+	6554.13i	0.706923	+	1.22443i
$307$	−9094.65			−1.69075			−0.845373	−	0.534176i	$-0.820622\pi$
$307$	−9094.65			−1.69075			−0.845373	+	0.534176i	$0.820622\pi$
$308$		0			0
$309$	6548.26			1.20556
$310$	−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	$-0.100497\pi$
$312$	−1284.51	+	2224.84i	−0.233081	+	0.403708i
$313$	−1489.81	−	2580.42i	−0.269038	−	0.465988i	0.699576	−	0.714559i	$-0.253372\pi$
$313$	−1489.81	−	2580.42i	−0.269038	−	0.465988i	−0.968614	+	0.248571i	$0.920039\pi$
$314$	5499.98			0.988478
$315$		0			0
$316$	−12779.9			−2.27508
$317$	1944.05	+	3367.20i	0.344445	+	0.596596i	0.985253	−	0.171105i	$-0.0547339\pi$
$317$	1944.05	+	3367.20i	0.344445	+	0.596596i	−0.640808	+	0.767701i	$0.721401\pi$
$318$	−1209.33	+	2094.61i	−0.213257	+	0.369371i
$319$	−3.48232	+	6.03155i	−0.000611198	+	0.00105863i
$320$	−5625.52	−	9743.69i	−0.982739	−	1.70215i
$321$	3083.35			0.536124
$322$		0			0
$323$	−10983.4			−1.89205
$324$	906.581	+	1570.24i	0.155449	+	0.269246i
$325$	−990.749	+	1716.03i	−0.169098	+	0.292886i
$326$	1637.49	−	2836.22i	0.278197	−	0.481852i
$327$	2900.37	+	5023.58i	0.490491	+	0.849556i
$328$	−1448.04			−0.243764
$329$		0			0
$330$	−177.790			−0.0296576
$331$	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
$333$	204.383	−	354.002i	0.0336341	−	0.0582559i
$334$	−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
$339$	−680.847	+	1179.26i	−0.109081	+	0.188934i
$340$	9942.91	−	17221.6i	1.58597	−	2.74698i
$341$	33.3858	+	57.8259i	0.00530188	+	0.00918313i
$342$	5996.96			0.948183
$343$		0			0
$344$	8565.16			1.34245
$345$	2900.95	+	5024.59i	0.452701	+	0.784101i
$346$	4212.00	−	7295.39i	0.654446	−	1.13353i
$347$	119.029	−	206.165i	0.0184145	−	0.0318948i	−0.856671	−	0.515863i	$-0.827471\pi$
$347$	119.029	−	206.165i	0.0184145	−	0.0318948i	0.875086	+	0.483968i	$0.160805\pi$
$348$	−192.077	−	332.688i	−0.0295874	−	0.0512469i
$349$	−10053.1			−1.54192			−0.770959	−	0.636884i	$-0.780223\pi$
$349$	−10053.1			−1.54192			−0.770959	+	0.636884i	$0.780223\pi$
$350$		0			0
$351$	−5153.63			−0.783706
$352$	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	$0.0824126\pi$
$354$	763.795	−	1322.93i	0.114676	−	0.198624i
$355$	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	0.809646	−	0.586919i	$-0.199659\pi$
$359$	−703.770	−	1218.97i	−0.103464	−	0.179205i	−0.913110	+	0.407714i	$0.866326\pi$
$360$	−1963.02	+	3400.06i	−0.287390	+	0.497775i
$361$	−922.136	+	1597.19i	−0.134442	+	0.232860i
$362$	−6573.26	−	11385.2i	−0.954373	−	1.65302i
$363$	−4762.02			−0.688544
$364$		0			0
$365$	6327.34			0.907364
$366$	977.420	+	1692.94i	0.139592	+	0.241780i
$367$	−5566.51	+	9641.48i	−0.791742	+	1.37134i	0.133145	+	0.991097i	$0.457492\pi$
$367$	−5566.51	+	9641.48i	−0.791742	+	1.37134i	−0.924887	+	0.380242i	$0.875841\pi$
$368$	434.089	−	751.865i	0.0614904	−	0.106505i
$369$	−500.290	−	866.528i	−0.0705801	−	0.122248i
$370$	−1759.78			−0.247261
$371$		0			0
$372$	−3682.98			−0.513316
$373$	−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
$375$	−1648.07	+	2854.54i	−0.226949	+	0.393088i
$376$	−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
$381$	−1715.25	+	2970.90i	−0.230643	+	0.399485i
$382$	−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	$0.659445\pi$
$384$	−7898.14			−1.04961
$385$		0			0
$386$	3064.16			0.404045
$387$	2959.21	+	5125.51i	0.388696	+	0.673241i
$388$	−3446.42	+	5969.38i	−0.450942	+	0.781054i
$389$	1907.03	−	3303.07i	0.248560	−	0.430519i	−0.714566	−	0.699568i	$-0.753376\pi$
$389$	1907.03	−	3303.07i	0.248560	−	0.430519i	0.963127	+	0.269048i	$0.0867092\pi$
$390$	3821.13	+	6618.39i	0.496129	+	0.859321i
$391$	14157.1			1.83109
$392$		0			0
$393$	4124.21			0.529362
$394$	8350.85	+	14464.1i	1.06779	+	1.84947i
$395$	−6873.32	+	11904.9i	−0.875530	+	1.51646i
$396$	72.2862	−	125.203i	0.00917303	−	0.0158882i
$397$	5082.64	+	8803.39i	0.642545	+	1.11292i	0.984863	+	0.173336i	$0.0554547\pi$
$397$	5082.64	+	8803.39i	0.642545	+	1.11292i	−0.342318	+	0.939584i	$0.611212\pi$
$398$	−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	$-0.912537\pi$
$401$	−5751.27	−	9961.50i	−0.716222	−	1.24053i	0.246265	−	0.969203i	$-0.420797\pi$
$402$	6425.86	−	11129.9i	0.797246	−	1.38087i
$403$	1435.08	−	2485.63i	0.177386	−	0.307241i
$404$	411.754	+	713.178i	0.0507067	+	0.0878266i
$405$	1950.32			0.239289
$406$		0			0
$407$	23.4317			0.00285372
$408$	−4326.20	−	7493.19i	−0.524948	−	0.909236i
$409$	−1633.14	+	2828.67i	−0.197441	+	0.341978i	−0.947698	−	0.319168i	$-0.896596\pi$
$409$	−1633.14	+	2828.67i	−0.197441	+	0.341978i	0.750257	+	0.661146i	$0.229930\pi$
$410$	−2153.79	+	3730.48i	−0.259435	+	0.449354i
$411$	−639.626	−	1107.87i	−0.0767651	−	0.132961i
$412$	22923.8			2.74120
$413$		0			0
$414$	−7729.86			−0.917637
$415$	−702.615	−	1216.96i	−0.0831084	−	0.143948i
$416$	3442.56	−	5962.69i	0.405734	−	0.702752i
$417$	4897.35	−	8482.45i	0.575118	−	0.996133i
$418$	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
$423$	2399.42	−	4155.91i	0.275801	−	0.477701i
$424$	−1530.81	+	2651.44i	−0.175336	+	0.303691i
$425$	−3336.81	−	5779.52i	−0.380844	−	0.659642i
$426$	7284.61			0.828499
$427$		0			0
$428$	10794.0			1.21904
$429$	−50.8789	−	88.1248i	−0.00572600	−	0.00991773i
$430$	12739.7	−	22065.8i	1.42875	−	2.47466i
$431$	−7571.10	+	13113.5i	−0.846141	+	1.46556i	0.0384849	+	0.999259i	$0.487747\pi$
$431$	−7571.10	+	13113.5i	−0.846141	+	1.46556i	−0.884626	+	0.466301i	$0.845586\pi$
$432$	−532.212	−	921.818i	−0.0592733	−	0.102664i
$433$	−5475.65			−0.607721			−0.303860	−	0.952717i	$-0.598276\pi$
$433$	−5475.65			−0.607721			−0.303860	+	0.952717i	$0.598276\pi$
$434$		0			0
$435$	−413.214			−0.0455451
$436$	10153.5	+	17586.3i	1.11528	+	1.93172i
$437$	5609.10	−	9715.24i	0.614003	−	1.06348i
$438$	3806.86	−	6593.68i	0.415294	−	0.719311i
$439$	−890.272	−	1542.00i	−0.0967890	−	0.167643i	0.813565	−	0.581474i	$-0.197524\pi$
$439$	−890.272	−	1542.00i	−0.0967890	−	0.167643i	−0.910354	+	0.413831i	$0.864191\pi$
$440$	−225.052			−0.0243840
$441$		0			0
$442$	18647.8			2.00675
$443$	1629.82	+	2822.93i	0.174797	+	0.302757i	0.940091	−	0.340924i	$-0.110740\pi$
$443$	1629.82	+	2822.93i	0.174797	+	0.302757i	−0.765294	+	0.643681i	$0.777406\pi$
$444$	−646.221	+	1119.29i	−0.0690728	+	0.119638i
$445$	−10600.7	+	18361.0i	−1.12926	+	1.95594i
$446$	−5996.55	−	10386.3i	−0.636648	−	1.10271i
$447$	5046.95			0.534033
$448$		0			0
$449$	−6826.19			−0.717478			−0.358739	−	0.933438i	$-0.616793\pi$
$449$	−6826.19			−0.717478			−0.358739	+	0.933438i	$0.616793\pi$
$450$	1821.91	+	3155.64i	0.190857	+	0.330574i
$451$	28.6781	−	49.6719i	0.00299423	−	0.00518616i
$452$	−2383.48	+	4128.30i	−0.248029	+	0.429599i
$453$	−4210.19	−	7292.26i	−0.436671	−	0.756336i
$454$	18673.3			1.93036
$455$		0			0
$456$	−6856.20			−0.704103
$457$	−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
$459$	8678.63	−	15031.8i	0.882536	−	1.52860i
$460$	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
$465$	−1980.79	+	3430.83i	−0.197542	+	0.342153i
$466$	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	$0.798480\pi$
$468$	−6214.42			−0.613807
$469$		0			0
$470$	−20659.4			−2.02755
$471$	−2172.47	−	3762.83i	−0.212531	−	0.368115i
$472$	966.839	−	1674.61i	0.0942847	−	0.163306i
$473$	−169.631	+	293.809i	−0.0164897	+	0.0285610i
$474$	8270.71	+	14325.3i	0.801448	+	1.38815i
$475$	−5288.20			−0.510820
$476$		0			0
$477$	−2115.54			−0.203069
$478$	−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	$0.202408\pi$
$480$	−4751.64	+	8230.08i	−0.451837	+	0.782604i
$481$	−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
$486$	−7844.94	+	13587.8i	−0.732209	+	1.26822i
$487$	−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
$489$	−2587.21			−0.239259
$490$		0			0
$491$	12586.7			1.15689			0.578444	−	0.815722i	$-0.303660\pi$
$491$	12586.7			1.15689			0.578444	+	0.815722i	$0.303660\pi$
$492$	1581.82	+	2739.80i	0.144947	+	0.251056i
$493$	−504.140	+	873.195i	−0.0460554	+	0.0797703i
$494$	7388.30	−	12796.9i	0.672905	−	1.16551i
$495$	−77.7543	−	134.674i	−0.00706020	−	0.0122286i
$496$	592.799			0.0536642
$497$		0			0
$498$	−1690.92			−0.152153
$499$	−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
$501$	−1347.73	+	2334.34i	−0.120184	+	0.208165i
$502$	−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
$507$	1745.12	−	3022.64i	0.152867	−	0.264774i
$508$	−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	$0.887709\pi$
$510$	−25738.9			−2.23478
$511$		0			0
$512$	2607.89			0.225105
$513$	−6876.99	−	11911.3i	−0.591864	−	1.02514i
$514$	−10397.5	+	18008.9i	−0.892241	+	1.54541i
$515$	12328.9	−	21354.4i	1.05491	−	1.82716i
$516$	−9356.47	−	16205.9i	−0.798247	−	1.38260i
$517$	275.083			0.0234007
$518$		0			0
$519$	−6654.89			−0.562846
$520$	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	$-0.0628162\pi$
$522$	275.262	−	476.768i	0.0230803	−	0.0399762i
$523$	−5076.03	−	8791.95i	−0.424397	−	0.735077i	0.571967	−	0.820277i	$-0.306180\pi$
$523$	−5076.03	−	8791.95i	−0.424397	−	0.735077i	−0.996364	+	0.0851998i	$0.972847\pi$
$524$	14437.8			1.20366
$525$		0			0
$526$	3974.59			0.329469
$527$	4833.30	+	8371.53i	0.399510	+	0.691972i
$528$	10.5084	−	18.2012i	0.000866139	−	0.00150020i
$529$	−1146.41	+	1985.65i	−0.0942233	+	0.163200i
$530$	4553.80	+	7887.41i	0.373216	+	0.646428i
$531$	1336.15			0.109198
$532$		0			0
$533$	−2465.44			−0.200357
$534$	12755.9	+	22093.9i	1.03371	+	1.79044i
$535$	5805.28	−	10055.0i	0.469129	−	0.812555i
$536$	8134.08	−	14088.6i	0.655483	−	1.13533i
$537$	935.741	+	1620.75i	0.0751959	+	0.130243i
$538$	−27746.6			−2.22350
$539$		0			0
$540$	24902.1			1.98448
$541$	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
$543$	−5192.83	+	8994.24i	−0.410397	+	0.710829i
$544$	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
$549$	−854.927	+	1480.78i	−0.0664616	+	0.115115i
$550$	−104.437	+	180.890i	−0.00809675	+	0.0140240i
$551$	399.483	+	691.924i	0.0308866	+	0.0534972i
$552$	8837.38			0.681420
$553$		0			0
$554$	−22164.9			−1.69981
$555$	695.105	+	1203.96i	0.0531632	+	0.0920813i
$556$	17144.4	−	29694.9i	1.30770	−	2.26501i
$557$	8999.13	−	15586.9i	0.684570	−	1.18571i	−0.289002	−	0.957328i	$-0.593323\pi$
$557$	8999.13	−	15586.9i	0.684570	−	1.18571i	0.973572	−	0.228381i	$-0.0733432\pi$
$558$	−2639.00	−	4570.89i	−0.200211	−	0.346776i
$559$	14583.1			1.10340
$560$		0			0
$561$	342.717			0.0257923
$562$	−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	$0.168998\pi$
$564$	−7586.50	+	13140.2i	−0.566400	+	0.981033i
$565$	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	$0.0911517\pi$
$569$	9830.21	+	17026.4i	0.724260	+	1.25445i	−0.235018	+	0.971991i	$0.575515\pi$
$570$	−10197.8	+	17663.1i	−0.749366	+	1.29794i
$571$	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
$573$	9322.42			0.679668
$574$		0			0
$575$	6816.30			0.494364
$576$	−5920.89	−	10255.3i	−0.428305	−	0.741847i
$577$	−11153.2	+	19317.9i	−0.804704	+	1.39379i	0.111786	+	0.993732i	$0.464343\pi$
$577$	−11153.2	+	19317.9i	−0.804704	+	1.39379i	−0.916490	+	0.400057i	$0.868990\pi$
$578$	−20271.8	+	35111.8i	−1.45882	+	2.52675i
$579$	−1210.33	−	2096.35i	−0.0868732	−	0.150469i
$580$	−1446.56			−0.103560
$581$		0			0
$582$	8921.62			0.635418
$583$	−60.6344	−	105.022i	−0.00430741	−	0.00746066i
$584$	4818.86	−	8346.51i	0.341448	−	0.591406i
$585$	−3342.25	+	5788.96i	−0.236214	+	0.409135i
$586$	−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
$591$	6597.11	−	11426.5i	0.459169	−	0.795304i
$592$	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	$0.798484\pi$
$594$	−543.257			−0.0375254
$595$		0			0
$596$	17668.1			1.21429
$597$	1431.47	+	2479.37i	0.0981341	+	0.169973i
$598$	−9523.24	+	16494.7i	−0.651228	+	1.12796i
$599$	−12728.2	+	22045.8i	−0.868212	+	1.50379i	−0.00438889	+	0.999990i	$0.501397\pi$
$599$	−12728.2	+	22045.8i	−0.868212	+	1.50379i	−0.863823	+	0.503796i	$0.831936\pi$
$600$	−2082.95	−	3607.78i	−0.141727	−	0.245478i
$601$	5580.96			0.378789			0.189395	−	0.981901i	$-0.439347\pi$
$601$	5580.96			0.378789			0.189395	+	0.981901i	$0.439347\pi$
$602$		0			0
$603$	11241.1			0.759160
$604$	−14738.8	−	25528.4i	−0.992903	−	1.71976i
$605$	−8965.85	+	15529.3i	−0.602502	+	1.04356i
$606$	532.945	−	923.089i	0.0357251	−	0.0618777i
$607$	−190.566	−	330.071i	−0.0127427	−	0.0220711i	0.859584	−	0.510995i	$-0.170723\pi$
$607$	−190.566	−	330.071i	−0.0127427	−	0.0220711i	−0.872326	+	0.488924i	$0.837390\pi$
$608$	18374.9			1.22566
$609$		0			0
$610$	7361.07			0.488592
$611$	−5912.20	−	10240.2i	−0.391460	−	0.678028i
$612$	10465.0	−	18125.9i	0.691211	−	1.19721i
$613$	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
$615$	3402.96			0.223123
$616$		0			0
$617$	−27419.8			−1.78911			−0.894555	−	0.446958i	$-0.852507\pi$
$617$	−27419.8			−1.78911			−0.894555	+	0.446958i	$0.852507\pi$
$618$	−14835.5	−	25695.8i	−0.965649	−	1.67255i
$619$	8186.69	−	14179.8i	0.531585	−	0.920732i	−0.467736	−	0.883868i	$-0.654930\pi$
$619$	8186.69	−	14179.8i	0.531585	−	0.920732i	0.999320	−	0.0368632i	$-0.0117366\pi$
$620$	−6934.25	+	12010.5i	−0.449171	+	0.777987i
$621$	8864.18	+	15353.2i	0.572798	+	0.992115i
$622$	−36987.9			−2.38437
$623$		0			0
$624$	−903.407			−0.0579571
$625$	9748.72	+	16885.3i	0.623918	+	1.08066i
$626$	−6750.51	+	11692.2i	−0.430998	+	0.746510i
$627$	135.785	−	235.187i	0.00864870	−	0.0149800i
$628$	−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
$633$	1194.47	−	2068.89i	0.0750016	−	0.129906i
$634$	8808.76	−	15257.2i	0.551799	−	0.955744i
$635$	6458.88	+	11187.1i	0.403642	+	0.699129i
$636$	6688.94			0.417034
$637$		0			0
$638$	31.5577			0.00195827
$639$	3185.84	+	5518.04i	0.197230	+	0.341612i
$640$	−14870.5	+	25756.4i	−0.918449	+	1.59080i
$641$	3194.32	−	5532.72i	0.196830	−	0.340919i	−0.750669	−	0.660678i	$-0.770269\pi$
$641$	3194.32	−	5532.72i	0.196830	−	0.340919i	0.947499	+	0.319759i	$0.103602\pi$
$642$	−6985.53	−	12099.3i	−0.429434	−	0.743802i
$643$	−18308.0			−1.12286			−0.561428	−	0.827525i	$-0.689748\pi$
$643$	−18308.0			−1.12286			−0.561428	+	0.827525i	$0.689748\pi$
$644$		0			0
$645$	−20128.5			−1.22877
$646$	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	$0.198672\pi$
$648$	1485.35	−	2572.70i	0.0900465	−	0.155965i
$649$	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	0.793074	−	0.609125i	$-0.208479\pi$
$653$	−2185.63	−	3785.63i	−0.130981	−	0.226865i	−0.924055	+	0.382260i	$0.875146\pi$
$654$	13141.9	−	22762.5i	0.785765	−	1.36099i
$655$	7765.00	−	13449.4i	0.463211	−	0.802306i
$656$	−254.604	−	440.988i	−0.0151534	−	0.0262465i
$657$	6659.55			0.395455
$658$		0			0
$659$	6259.75			0.370023			0.185012	−	0.982736i	$-0.440768\pi$
$659$	6259.75			0.370023			0.185012	+	0.982736i	$0.440768\pi$
$660$	245.844	+	425.815i	0.0144992	+	0.0251134i
$661$	7422.87	−	12856.8i	0.436787	−	0.756537i	−0.560653	−	0.828051i	$-0.689450\pi$
$661$	7422.87	−	12856.8i	0.436787	−	0.756537i	0.997440	+	0.0715138i	$0.0227830\pi$
$662$	11085.5	−	19200.6i	0.650830	−	1.12727i
$663$	−7365.80	−	12757.9i	−0.431469	−	0.747327i
$664$	−2140.43			−0.125098
$665$		0			0
$666$	−1852.17			−0.107763
$667$	−514.918	−	891.864i	−0.0298916	−	0.0517738i
$668$	−4718.07	+	8171.94i	−0.273275	+	0.473326i
$669$	−4737.23	+	8205.12i	−0.273770	+	0.474183i
$670$	−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
$675$	4178.53	−	7237.43i	0.238269	−	0.412695i
$676$	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	$0.860024\pi$
$678$	6170.01			0.349495
$679$		0			0
$680$	−32581.1			−1.83740
$681$	−7375.88	−	12775.4i	−0.415043	−	0.718876i
$682$	151.275	−	262.016i	0.00849359	−	0.0147113i
$683$	−3140.42	+	5439.38i	−0.175937	+	0.304732i	−0.940485	−	0.339835i	$-0.889629\pi$
$683$	−3140.42	+	5439.38i	−0.175937	+	0.304732i	0.764548	+	0.644567i	$0.222962\pi$
$684$	−8292.49	−	14363.0i	−0.463555	−	0.802900i
$685$	−4817.11			−0.268689
$686$		0			0
$687$	14557.8			0.808463
$688$	1505.98	+	2608.44i	0.0834521	+	0.144543i
$689$	−2606.36	+	4514.35i	−0.144114	+	0.249612i
$690$	13144.6	−	22767.1i	0.725225	−	1.25613i
$691$	−16381.6	−	28373.8i	−0.901861	−	1.56207i	−0.825077	−	0.565021i	$-0.808868\pi$
$691$	−16381.6	−	28373.8i	−0.901861	−	1.56207i	−0.0767837	−	0.997048i	$-0.524465\pi$
$692$	−23297.1			−1.27980
$693$		0			0
$694$	−1078.67			−0.0589998
$695$	−18441.3	−	31941.2i	−1.00650	−	1.74331i
$696$	−314.701	+	545.079i	−0.0171390	+	0.0296856i
$697$	4151.76	−	7191.06i	0.225623	−	0.390791i
$698$	22775.9	+	39449.1i	1.23507	+	2.13921i
$699$	−13977.0			−0.756306
$700$		0			0
$701$	−1775.97			−0.0956883			−0.0478442	−	0.998855i	$-0.515235\pi$
$701$	−1775.97			−0.0956883			−0.0478442	+	0.998855i	$0.515235\pi$
$702$	11675.9	+	20223.2i	0.627747	+	1.08729i
$703$	1344.01	−	2327.90i	0.0721058	−	0.124891i
$704$	339.403	−	587.863i	0.0181701	−	0.0314715i
$705$	8160.39	+	14134.2i	0.435940	+	0.755071i
$706$	−15723.7			−0.838203
$707$		0			0
$708$	−4224.65			−0.224254
$709$	−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
$711$	−7234.21	+	12530.0i	−0.381581	+	0.660917i
$712$	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
$717$	−9709.76	+	16817.8i	−0.505743	+	0.875973i
$718$	−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	$-0.419411\pi$
$720$	−1380.61			−0.0714614
$721$		0			0
$722$	8356.64			0.430750
$723$	2868.82	+	4968.95i	0.147569	+	0.255598i
$724$	−18178.8	+	31486.6i	−0.933162	+	1.61628i
$725$	−242.730	+	420.421i	−0.0124342	+	0.0215366i
$726$	10788.7	+	18686.5i	0.551522	+	0.955264i
$727$	25434.9			1.29756			0.648781	−	0.760975i	$-0.275279\pi$
$727$	25434.9			1.29756			0.648781	+	0.760975i	$0.275279\pi$
$728$		0			0
$729$	16301.6			0.828206
$730$	−14335.0	−	24828.9i	−0.726797	−	1.25885i
$731$	−24557.6	+	42535.1i	−1.24254	+	2.15214i
$732$	2703.12	−	4681.94i	0.136489	−	0.236406i
$733$	12077.8	+	20919.4i	0.608600	+	1.05413i	0.991471	+	0.130325i	$0.0416020\pi$
$733$	12077.8	+	20919.4i	0.608600	+	1.05413i	−0.382871	+	0.923802i	$0.625065\pi$
$734$	50445.2			2.53674
$735$		0			0
$736$	−23684.6			−1.18618
$737$	322.187	+	558.043i	0.0161030	+	0.0278912i
$738$	−2266.88	+	3926.35i	−0.113069	+	0.195841i
$739$	−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
$741$	−11673.4			−0.578722
$742$		0			0
$743$	5995.09			0.296014			0.148007	−	0.988986i	$-0.452714\pi$
$743$	5995.09			0.296014			0.148007	+	0.988986i	$0.452714\pi$
$744$	3017.12	+	5225.80i	0.148673	+	0.257509i
$745$	9502.31	−	16458.5i	0.467299	−	0.809386i
$746$	−20448.8	+	35418.4i	−1.00360	+	1.73829i
$747$	−739.506	−	1280.86i	−0.0362210	−	0.0627366i
$748$	1199.76			0.0586467
$749$		0			0
$750$	14935.2			0.727144
$751$	−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
$753$	−6811.78	+	11798.3i	−0.329661	+	0.570990i
$754$	−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
$759$	−175.022	+	303.147i	−0.00837008	+	0.0144974i
$760$	−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	$0.808366\pi$
$762$	15544.0			0.738977
$763$		0			0
$764$	32635.4			1.54543
$765$	−11256.6	−	19497.0i	−0.532004	−	0.921458i
$766$	17644.3	−	30560.8i	0.832264	−	1.44152i
$767$	1646.14	−	2851.21i	0.0774952	−	0.134226i
$768$	5942.23	+	10292.2i	0.279195	+	0.483580i
$769$	−11146.5			−0.522697			−0.261348	−	0.965245i	$-0.584167\pi$
$769$	−11146.5			−0.522697			−0.261348	+	0.965245i	$0.584167\pi$
$770$		0			0
$771$	16427.8			0.767358
$772$	−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	$0.0466107\pi$
$774$	13408.6	−	23224.3i	0.622689	−	1.07853i
$775$	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
$780$	10567.6	−	18303.6i	0.485102	−	0.840222i
$781$	−182.622	+	316.310i	−0.00836711	+	0.0144923i
$782$	−32073.9	−	55553.7i	−1.46670	−	2.54040i
$783$	−1262.62			−0.0576277
$784$		0			0
$785$	−16361.2			−0.743892
$786$	−9343.67	−	16183.7i	−0.424018	−	0.734420i
$787$	7581.72	−	13131.9i	0.343404	−	0.594794i	−0.641658	−	0.766991i	$-0.721753\pi$
$787$	7581.72	−	13131.9i	0.343404	−	0.594794i	0.985063	+	0.172197i	$0.0550865\pi$
$788$	23094.8	−	40001.4i	1.04406	−	1.80836i
$789$	−1569.95	−	2719.23i	−0.0708386	−	0.122696i
$790$	62287.8			2.80519
$791$		0			0
$792$	−236.869			−0.0106272
$793$	2106.55	+	3648.65i	0.0943327	+	0.163389i
$794$	23030.1	−	39889.3i	1.02935	−	1.78289i
$795$	3597.46	−	6230.99i	0.160489	−	0.277975i
$796$	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
$801$	−11157.3	+	19325.1i	−0.492166	+	0.852456i
$802$	−26059.8	+	45136.8i	−1.14738	+	1.98733i
$803$	190.872	+	330.601i	0.00838822	+	0.0145288i
$804$	−35542.3			−1.55905
$805$		0			0
$806$	−13005.1			−0.568343
$807$	10959.8	+	18982.9i	0.478071	+	0.828043i
$808$	674.621	−	1168.48i	0.0293726	−	0.0508749i
$809$	10356.4	−	17937.9i	0.450078	−	0.779557i	−0.548313	−	0.836273i	$-0.684730\pi$
$809$	10356.4	−	17937.9i	0.450078	−	0.779557i	0.998390	+	0.0567160i	$0.0180630\pi$
$810$	−4418.57	−	7653.19i	−0.191670	−	0.331982i
$811$	27369.9			1.18506			0.592532	−	0.805547i	$-0.298128\pi$
$811$	27369.9			1.18506			0.592532	+	0.805547i	$0.298128\pi$
$812$		0			0
$813$	−12491.8			−0.538876
$814$	−53.0860	−	91.9476i	−0.00228583	−	0.00395917i
$815$	−4871.16	+	8437.09i	−0.209361	+	0.362624i
$816$	1521.32	−	2635.01i	0.0652658	−	0.113044i
$817$	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	$0.104062\pi$
$821$	17681.3	+	30625.0i	0.751623	+	1.30185i	−0.195412	+	0.980721i	$0.562604\pi$
$822$	−2898.23	+	5019.88i	−0.122977	+	0.213003i
$823$	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
$825$	165.009			0.00696349
$826$		0			0
$827$	−7302.08			−0.307035			−0.153518	−	0.988146i	$-0.549060\pi$
$827$	−7302.08			−0.307035			−0.153518	+	0.988146i	$0.549060\pi$
$828$	10688.7	+	18513.4i	0.448621	+	0.777035i
$829$	−2125.38	+	3681.27i	−0.0890442	+	0.154229i	−0.907107	−	0.420899i	$-0.861715\pi$
$829$	−2125.38	+	3681.27i	−0.0890442	+	0.154229i	0.818063	+	0.575128i	$0.195048\pi$
$830$	−3183.64	+	5514.22i	−0.133139	+	0.230604i
$831$	8755.05	+	15164.2i	0.365475	+	0.633021i
$832$	−29178.3			−1.21584
$833$		0			0
$834$	−44381.0			−1.84267
$835$	5074.97	+	8790.11i	0.210331	+	0.364305i
$836$	475.350	−	823.330i	0.0196654	−	0.0340615i
$837$	−6052.53	+	10483.3i	−0.249947	+	0.432922i
$838$	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
$843$	−12375.3	+	21434.7i	−0.505611	+	0.875743i
$844$	4181.54	−	7242.65i	0.170539	−	0.295382i
$845$	−6571.38	−	11382.0i	−0.267529	−	0.463374i
$846$	−21744.1			−0.883663
$847$		0			0
$848$	−1076.63			−0.0435985
$849$	−6371.34	−	11035.5i	−0.257555	−	0.446098i
$850$	−15119.5	+	26187.7i	−0.610111	+	1.05674i
$851$	−1732.38	+	3000.57i	−0.0697829	+	0.120868i
$852$	−10073.0	−	17447.0i	−0.405042	−	0.701554i
$853$	31656.1			1.27067			0.635337	−	0.772235i	$-0.280861\pi$
$853$	31656.1			1.27067			0.635337	+	0.772235i	$0.280861\pi$
$854$		0			0
$855$	−17839.6			−0.713568
$856$	−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	$0.174237\pi$
$858$	−230.539	+	399.305i	−0.00917303	+	0.0158882i
$859$	−14530.0	−	25166.7i	−0.577134	−	0.999625i	−0.995806	−	0.0914874i	$-0.970838\pi$
$859$	−14530.0	−	25166.7i	−0.577134	−	0.999625i	0.418673	−	0.908137i	$-0.362495\pi$
$860$	−70464.8			−2.79399
$861$		0			0
$862$	68611.2			2.71103
$863$	−11531.5	−	19973.1i	−0.454851	−	0.787825i	0.543828	−	0.839196i	$-0.316974\pi$
$863$	−11531.5	−	19973.1i	−0.454851	−	0.787825i	−0.998680	+	0.0513711i	$0.983641\pi$
$864$	−14519.2	+	25147.9i	−0.571704	+	0.990220i
$865$	−12529.7	+	21702.1i	−0.492512	+	0.853056i
$866$	12405.4	+	21486.9i	0.486783	+	0.843133i
$867$	32029.2			1.25463
$868$		0			0
$869$	−829.371			−0.0323757
$870$	936.163	+	1621.48i	0.0364815	+	0.0631878i
$871$	13849.1	−	23987.4i	0.538760	−	0.933159i
$872$	16635.5	−	28813.6i	0.646044	−	1.11898i
$873$	3901.77	+	6758.06i	0.151266	+	0.262000i
$874$	−50831.1			−1.96726
$875$		0			0
$876$	−21056.2			−0.812129
$877$	−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
$879$	−5879.62	+	10183.8i	−0.225614	+	0.390775i
$880$	−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
$885$	−2272.11	+	3935.42i	−0.0863008	+	0.149477i
$886$	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	$0.508135\pi$
$888$	2117.55			0.0800229
$889$		0			0
$890$	96066.5			3.61816
$891$	58.8339	+	101.903i	0.00221213	+	0.00383153i
$892$	−16583.9	+	28724.1i	−0.622498	+	1.07820i
$893$	15778.4	−	27329.0i	0.591271	−	1.02411i
$894$	−11434.2	−	19804.6i	−0.427759	−	0.740901i
$895$	7047.19			0.263197
$896$		0			0
$897$	15046.6			0.560078
$898$	15465.2	+	26786.5i	0.574699	+	0.995407i
$899$	351.590	−	608.972i	0.0130436	−	0.0225922i
$900$	5038.61	−	8727.13i	0.186615	−	0.323227i
$901$	−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
$906$	−19076.9	+	33042.1i	−0.699545	+	1.21165i
$907$	−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
$909$	932.311			0.0340185
$910$		0			0
$911$	−41646.1			−1.51460			−0.757298	−	0.653070i	$-0.773481\pi$
$911$	−41646.1			−1.51460			−0.757298	+	0.653070i	$0.773481\pi$
$912$	−1205.50	−	2087.99i	−0.0437699	−	0.0758117i
$913$	42.3906	−	73.4227i	0.00153661	−	0.00266149i
$914$	−8382.65	+	14519.2i	−0.303363	+	0.525440i
$915$	−2907.60	−	5036.10i	−0.105052	−	0.181955i
$916$	50963.1			1.83829
$917$		0			0
$918$	−78648.0			−2.82764
$919$	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
$921$	16277.4	−	28193.3i	0.582366	−	1.00869i
$922$	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
$927$	12976.3	−	22475.6i	0.459759	−	0.796326i
$928$	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	$-0.360253\pi$
$930$	17950.4			0.632922
$931$		0			0
$932$	−48929.9			−1.71969
$933$	14610.1	+	25305.4i	0.512660	+	0.887954i
$934$	4996.97	−	8655.01i	0.175060	−	0.303213i
$935$	645.261	−	1117.62i	0.0225693	−	0.0390911i
$936$	5090.88	+	8817.67i	0.177779	+	0.307921i
$937$	32947.0			1.14870			0.574350	−	0.818610i	$-0.305255\pi$
$937$	32947.0			1.14870			0.574350	+	0.818610i	$0.305255\pi$
$938$		0			0
$939$	10665.7			0.370673
$940$	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	$0.163901\pi$
$942$	−9843.75	+	17049.9i	−0.340474	+	0.589719i
$943$	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	0.915947	−	0.401299i	$-0.131441\pi$
$947$	3218.45	+	5574.52i	0.110439	+	0.191286i	−0.805508	+	0.592584i	$0.798108\pi$
$948$	22873.2	−	39617.5i	0.783636	−	1.35730i
$949$	8204.61	−	14210.8i	0.280646	−	0.486093i
$950$	11980.8	+	20751.3i	0.409166	+	0.708696i
$951$	−13917.7			−0.474566
$952$		0			0
$953$	47511.2			1.61494			0.807470	−	0.589908i	$-0.200836\pi$
$953$	47511.2			1.61494			0.807470	+	0.589908i	$0.200836\pi$
$954$	4792.89	+	8301.54i	0.162658	+	0.281732i
$955$	17552.1	−	30401.1i	0.594735	−	1.03011i
$956$	−33991.4	+	58874.9i	−1.14996	+	1.99179i
$957$	−12.4651	−	21.5903i	−0.000421046	−	0.000729273i
$958$	10645.1			0.359004
$959$		0			0
$960$	40273.8			1.35399
$961$	11524.7	+	19961.4i	0.386853	+	0.670048i
$962$	−2281.89	+	3952.35i	−0.0764773	+	0.132462i
$963$	6110.08	−	10583.0i	0.204460	−	0.354135i
$964$	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
$969$	19657.8	−	34048.3i	0.651702	−	1.12878i
$970$	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	$0.841243\pi$
$972$	43391.4			1.43187
$973$		0			0
$974$	47097.9			1.54940
$975$	−3546.44	−	6142.62i	−0.116489	−	0.201765i
$976$	−435.084	+	753.587i	−0.0142692	+	0.0247149i
$977$	−16694.6	+	28915.8i	−0.546680	+	0.946877i	0.451819	+	0.892109i	$0.350775\pi$
$977$	−16694.6	+	28915.8i	−0.546680	+	0.946877i	−0.998499	+	0.0547675i	$0.982558\pi$
$978$	5861.50	+	10152.4i	0.191646	+	0.331941i
$979$	−1279.14			−0.0417584
$980$		0			0
$981$	22989.9			0.748228
$982$	−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	$0.138481\pi$
$984$	2591.67	−	4488.91i	0.0839630	−	0.145428i
$985$	−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
$990$	−352.315	+	610.227i	−0.0113104	+	0.0195902i
$991$	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
$993$	−17514.9			−0.559736
$994$		0			0
$995$	10780.6			0.343484
$996$	2338.18	+	4049.84i	0.0743855	+	0.128840i
$997$	−5704.98	+	9881.31i	−0.181222	+	0.313886i	−0.942297	−	0.334778i	$-0.891339\pi$
$997$	−5704.98	+	9881.31i	−0.181222	+	0.313886i	0.761075	+	0.648664i	$0.224672\pi$
$998$	−24078.3	+	41704.8i	−0.763711	+	1.32279i
$999$	2123.97	+	3678.83i	0.0672668	+	0.116509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.4.c.e.18.1		8
3.2	odd	2		441.4.e.y.361.3		8
7.2	even	3	inner	49.4.c.e.30.1		8
7.3	odd	6		49.4.a.e.1.3	✓	4
7.4	even	3		49.4.a.e.1.4	yes	4
7.5	odd	6	inner	49.4.c.e.30.2		8
7.6	odd	2	inner	49.4.c.e.18.2		8
21.2	odd	6		441.4.e.y.226.3		8
21.5	even	6		441.4.e.y.226.4		8
21.11	odd	6		441.4.a.u.1.2		4
21.17	even	6		441.4.a.u.1.1		4
21.20	even	2		441.4.e.y.361.4		8
28.3	even	6		784.4.a.bf.1.3		4
28.11	odd	6		784.4.a.bf.1.2		4
35.4	even	6		1225.4.a.bb.1.1		4
35.24	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	7.3	odd	6
49.4.a.e.1.4	yes	4	7.4	even	3
49.4.c.e.18.1		8	1.1	even	1	trivial
49.4.c.e.18.2		8	7.6	odd	2	inner
49.4.c.e.30.1		8	7.2	even	3	inner
49.4.c.e.30.2		8	7.5	odd	6	inner
441.4.a.u.1.1		4	21.17	even	6
441.4.a.u.1.2		4	21.11	odd	6
441.4.e.y.226.3		8	21.2	odd	6
441.4.e.y.226.4		8	21.5	even	6
441.4.e.y.361.3		8	3.2	odd	2
441.4.e.y.361.4		8	21.20	even	2
784.4.a.bf.1.2		4	28.11	odd	6
784.4.a.bf.1.3		4	28.3	even	6
1225.4.a.bb.1.1		4	35.4	even	6
1225.4.a.bb.1.2		4	35.24	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.26556 - 3.92407i) q^{2} +(-1.78978 + 3.09999i) q^{3} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} +16.2194 q^{6} +20.5311 q^{8} +(7.09339 + 12.2861i) q^{9} +O(q^{10})\)	\(q+(-2.26556 - 3.92407i) q^{2} +(-1.78978 + 3.09999i) q^{3} +(-6.26556 + 10.8523i) q^{4} +(6.73953 + 11.6732i) q^{5} +16.2194 q^{6} +20.5311 q^{8} +(7.09339 + 12.2861i) q^{9} +(30.5377 - 52.8928i) q^{10} +(-0.406613 + 0.704275i) q^{11} +(-22.4279 - 38.8463i) q^{12} +34.9564 q^{13} -48.2490 q^{15} +(3.60992 + 6.25256i) q^{16} +(-58.8660 + 101.959i) q^{17} +(32.1410 - 55.6699i) q^{18} +(46.6457 + 80.7927i) q^{19} -168.908 q^{20} +3.68484 q^{22} +(-60.1245 - 104.139i) q^{23} +(-36.7462 + 63.6462i) q^{24} +(-28.3424 + 49.0905i) q^{25} +(-79.1960 - 137.171i) q^{26} -147.430 q^{27} +8.56420 q^{29} +(109.311 + 189.333i) q^{30} +(41.0535 - 71.1067i) q^{31} +(98.4815 - 170.575i) q^{32} +(-1.45550 - 2.52099i) q^{33} +533.458 q^{34} -177.776 q^{36} +(-14.4066 - 24.9530i) q^{37} +(211.358 - 366.082i) q^{38} +(-62.5642 + 108.364i) q^{39} +(138.370 + 239.664i) q^{40} -70.5291 q^{41} +417.179 q^{43} +(-5.09532 - 8.82536i) q^{44} +(-95.6121 + 165.605i) q^{45} +(-272.432 + 471.866i) q^{46} +(-169.131 - 292.943i) q^{47} -25.8438 q^{48} +256.846 q^{50} +(-210.714 - 364.967i) q^{51} +(-219.022 + 379.356i) q^{52} +(-74.5603 + 129.142i) q^{53} +(334.013 + 578.528i) q^{54} -10.9615 q^{55} -333.942 q^{57} +(-19.4027 - 33.6065i) q^{58} +(47.0914 - 81.5647i) q^{59} +(302.307 - 523.612i) q^{60} +(60.2623 + 104.377i) q^{61} -372.037 q^{62} -834.706 q^{64} +(235.590 + 408.053i) q^{65} +(-6.59504 + 11.4229i) q^{66} +(396.183 - 686.209i) q^{67} +(-737.657 - 1277.66i) q^{68} +430.438 q^{69} +449.128 q^{71} +(145.635 + 252.248i) q^{72} +(234.710 - 406.530i) q^{73} +(-65.2782 + 113.065i) q^{74} +(-101.453 - 175.722i) q^{75} -1169.05 q^{76} +566.973 q^{78} +(509.926 + 883.218i) q^{79} +(-48.6583 + 84.2786i) q^{80} +(72.3463 - 125.307i) q^{81} +(159.788 + 276.761i) q^{82} -104.253 q^{83} -1586.91 q^{85} +(-945.146 - 1637.04i) q^{86} +(-15.3280 + 26.5489i) q^{87} +(-8.34823 + 14.4596i) q^{88} +(786.460 + 1362.19i) q^{89} +866.462 q^{90} +1506.86 q^{92} +(146.953 + 254.530i) q^{93} +(-766.352 + 1327.36i) q^{94} +(-628.739 + 1089.01i) q^{95} +(352.520 + 610.583i) q^{96} +550.057 q^{97} -11.5371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9	\( 8 q - 2 q^{2} - 34 q^{4} + 132 q^{8} - 40 q^{9} - 100 q^{11} - 128 q^{15} + 174 q^{16} + 370 q^{18} - 680 q^{22} - 352 q^{23} + 128 q^{25} + 520 q^{29} + 552 q^{30} + 30 q^{32} - 100 q^{36} - 212 q^{37} - 952 q^{39} + 1080 q^{43} - 460 q^{44} - 696 q^{46} + 2732 q^{50} - 428 q^{51} - 16 q^{53} - 3768 q^{57} + 780 q^{58} + 1064 q^{60} - 3356 q^{64} + 756 q^{65} + 1944 q^{67} + 4496 q^{71} - 270 q^{72} + 284 q^{74} - 2688 q^{78} + 1048 q^{79} + 1256 q^{81} - 6568 q^{85} - 4820 q^{86} - 1260 q^{88} + 7024 q^{92} + 5368 q^{93} - 2192 q^{95} + 6680 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 34 * q^4 + 132 * q^8 - 40 * q^9 - 100 * q^11 - 128 * q^15 + 174 * q^16 + 370 * q^18 - 680 * q^22 - 352 * q^23 + 128 * q^25 + 520 * q^29 + 552 * q^30 + 30 * q^32 - 100 * q^36 - 212 * q^37 - 952 * q^39 + 1080 * q^43 - 460 * q^44 - 696 * q^46 + 2732 * q^50 - 428 * q^51 - 16 * q^53 - 3768 * q^57 + 780 * q^58 + 1064 * q^60 - 3356 * q^64 + 756 * q^65 + 1944 * q^67 + 4496 * q^71 - 270 * q^72 + 284 * q^74 - 2688 * q^78 + 1048 * q^79 + 1256 * q^81 - 6568 * q^85 - 4820 * q^86 - 1260 * q^88 + 7024 * q^92 + 5368 * q^93 - 2192 * q^95 + 6680 * q^99

Introduction

L-functions

Modular forms

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