LMFDB - Embedded newform 294.4.e.e.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(15.0000 + 25.9808i) q^{10} +(4.50000 + 7.79423i) q^{11} +(-6.00000 + 10.3923i) q^{12} +88.0000 q^{13} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(52.0000 - 90.0666i) q^{19} +60.0000 q^{20} +18.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-50.0000 - 86.6025i) q^{25} +(88.0000 - 152.420i) q^{26} +27.0000 q^{27} +51.0000 q^{29} +(45.0000 - 77.9423i) q^{30} +(92.5000 + 160.215i) q^{31} +(16.0000 + 27.7128i) q^{32} +(13.5000 - 23.3827i) q^{33} -168.000 q^{34} +36.0000 q^{36} +(-22.0000 + 38.1051i) q^{37} +(-104.000 - 180.133i) q^{38} +(-132.000 - 228.631i) q^{39} +(60.0000 - 103.923i) q^{40} +168.000 q^{41} +326.000 q^{43} +(18.0000 - 31.1769i) q^{44} +(-67.5000 - 116.913i) q^{45} +(-84.0000 - 145.492i) q^{46} +(-69.0000 + 119.512i) q^{47} +48.0000 q^{48} -200.000 q^{50} +(-126.000 + 218.238i) q^{51} +(-176.000 - 304.841i) q^{52} +(-319.500 - 553.390i) q^{53} +(27.0000 - 46.7654i) q^{54} -135.000 q^{55} -312.000 q^{57} +(51.0000 - 88.3346i) q^{58} +(79.5000 + 137.698i) q^{59} +(-90.0000 - 155.885i) q^{60} +(361.000 - 625.270i) q^{61} +370.000 q^{62} +64.0000 q^{64} +(-660.000 + 1143.15i) q^{65} +(-27.0000 - 46.7654i) q^{66} +(83.0000 + 143.760i) q^{67} +(-168.000 + 290.985i) q^{68} -252.000 q^{69} +1086.00 q^{71} +(36.0000 - 62.3538i) q^{72} +(109.000 + 188.794i) q^{73} +(44.0000 + 76.2102i) q^{74} +(-150.000 + 259.808i) q^{75} -416.000 q^{76} -528.000 q^{78} +(291.500 - 504.893i) q^{79} +(-120.000 - 207.846i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(168.000 - 290.985i) q^{82} +597.000 q^{83} +1260.00 q^{85} +(326.000 - 564.649i) q^{86} +(-76.5000 - 132.502i) q^{87} +(-36.0000 - 62.3538i) q^{88} +(-519.000 + 898.934i) q^{89} -270.000 q^{90} -336.000 q^{92} +(277.500 - 480.644i) q^{93} +(138.000 + 239.023i) q^{94} +(780.000 + 1351.00i) q^{95} +(48.0000 - 83.1384i) q^{96} +169.000 q^{97} -81.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 15 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 15 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 15 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9} + 30 q^{10} + 9 q^{11} - 12 q^{12} + 176 q^{13} + 90 q^{15} - 16 q^{16} - 84 q^{17} + 18 q^{18} + 104 q^{19} + 120 q^{20} + 36 q^{22} + 84 q^{23} + 24 q^{24} - 100 q^{25} + 176 q^{26} + 54 q^{27} + 102 q^{29} + 90 q^{30} + 185 q^{31} + 32 q^{32} + 27 q^{33} - 336 q^{34} + 72 q^{36} - 44 q^{37} - 208 q^{38} - 264 q^{39} + 120 q^{40} + 336 q^{41} + 652 q^{43} + 36 q^{44} - 135 q^{45} - 168 q^{46} - 138 q^{47} + 96 q^{48} - 400 q^{50} - 252 q^{51} - 352 q^{52} - 639 q^{53} + 54 q^{54} - 270 q^{55} - 624 q^{57} + 102 q^{58} + 159 q^{59} - 180 q^{60} + 722 q^{61} + 740 q^{62} + 128 q^{64} - 1320 q^{65} - 54 q^{66} + 166 q^{67} - 336 q^{68} - 504 q^{69} + 2172 q^{71} + 72 q^{72} + 218 q^{73} + 88 q^{74} - 300 q^{75} - 832 q^{76} - 1056 q^{78} + 583 q^{79} - 240 q^{80} - 81 q^{81} + 336 q^{82} + 1194 q^{83} + 2520 q^{85} + 652 q^{86} - 153 q^{87} - 72 q^{88} - 1038 q^{89} - 540 q^{90} - 672 q^{92} + 555 q^{93} + 276 q^{94} + 1560 q^{95} + 96 q^{96} + 338 q^{97} - 162 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 15 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9 + 30 * q^10 + 9 * q^11 - 12 * q^12 + 176 * q^13 + 90 * q^15 - 16 * q^16 - 84 * q^17 + 18 * q^18 + 104 * q^19 + 120 * q^20 + 36 * q^22 + 84 * q^23 + 24 * q^24 - 100 * q^25 + 176 * q^26 + 54 * q^27 + 102 * q^29 + 90 * q^30 + 185 * q^31 + 32 * q^32 + 27 * q^33 - 336 * q^34 + 72 * q^36 - 44 * q^37 - 208 * q^38 - 264 * q^39 + 120 * q^40 + 336 * q^41 + 652 * q^43 + 36 * q^44 - 135 * q^45 - 168 * q^46 - 138 * q^47 + 96 * q^48 - 400 * q^50 - 252 * q^51 - 352 * q^52 - 639 * q^53 + 54 * q^54 - 270 * q^55 - 624 * q^57 + 102 * q^58 + 159 * q^59 - 180 * q^60 + 722 * q^61 + 740 * q^62 + 128 * q^64 - 1320 * q^65 - 54 * q^66 + 166 * q^67 - 336 * q^68 - 504 * q^69 + 2172 * q^71 + 72 * q^72 + 218 * q^73 + 88 * q^74 - 300 * q^75 - 832 * q^76 - 1056 * q^78 + 583 * q^79 - 240 * q^80 - 81 * q^81 + 336 * q^82 + 1194 * q^83 + 2520 * q^85 + 652 * q^86 - 153 * q^87 - 72 * q^88 - 1038 * q^89 - 540 * q^90 - 672 * q^92 + 555 * q^93 + 276 * q^94 + 1560 * q^95 + 96 * q^96 + 338 * q^97 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−7.50000	+	12.9904i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−7.50000	+	12.9904i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	15.0000	+	25.9808i	0.474342	+	0.821584i
$11$	4.50000	+	7.79423i	0.123346	+	0.213641i	0.921085	−	0.389362i	$-0.127304\pi$
$11$	4.50000	+	7.79423i	0.123346	+	0.213641i	−0.797739	+	0.603002i	$0.793971\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	88.0000			1.87745			0.938723	−	0.344671i	$-0.112010\pi$
$13$	88.0000			1.87745			0.938723	+	0.344671i	$0.112010\pi$
$14$		0			0
$15$	45.0000			0.774597
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	−0.992939	−	0.118630i	$-0.962150\pi$
$17$	−42.0000	−	72.7461i	−0.599206	−	1.03785i	0.393733	−	0.919225i	$-0.371183\pi$
$18$	9.00000	+	15.5885i	0.117851	+	0.204124i
$19$	52.0000	−	90.0666i	0.627875	−	1.08751i	−0.360103	−	0.932913i	$-0.617258\pi$
$19$	52.0000	−	90.0666i	0.627875	−	1.08751i	0.987977	−	0.154598i	$-0.0494083\pi$
$20$	60.0000			0.670820
$21$		0			0
$22$	18.0000			0.174437
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	−0.610406	−	0.792088i	$-0.708994\pi$
$23$	42.0000	−	72.7461i	0.380765	−	0.659505i	0.991172	+	0.132583i	$0.0423272\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	−50.0000	−	86.6025i	−0.400000	−	0.692820i
$26$	88.0000	−	152.420i	0.663778	−	1.14970i
$27$	27.0000			0.192450
$28$		0			0
$29$	51.0000			0.326568			0.163284	−	0.986579i	$-0.447791\pi$
$29$	51.0000			0.326568			0.163284	+	0.986579i	$0.447791\pi$
$30$	45.0000	−	77.9423i	0.273861	−	0.474342i
$31$	92.5000	+	160.215i	0.535919	+	0.928239i	0.999118	+	0.0419848i	$0.0133681\pi$
$31$	92.5000	+	160.215i	0.535919	+	0.928239i	−0.463199	+	0.886254i	$0.653299\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	13.5000	−	23.3827i	0.0712136	−	0.123346i
$34$	−168.000			−0.847405
$35$		0			0
$36$	36.0000			0.166667
$37$	−22.0000	+	38.1051i	−0.0977507	+	0.169309i	−0.910753	−	0.412951i	$-0.864498\pi$
$37$	−22.0000	+	38.1051i	−0.0977507	+	0.169309i	0.813003	+	0.582260i	$0.197831\pi$
$38$	−104.000	−	180.133i	−0.443974	−	0.768986i
$39$	−132.000	−	228.631i	−0.541972	−	0.938723i
$40$	60.0000	−	103.923i	0.237171	−	0.410792i
$41$	168.000			0.639932			0.319966	−	0.947429i	$-0.396329\pi$
$41$	168.000			0.639932			0.319966	+	0.947429i	$0.396329\pi$
$42$		0			0
$43$	326.000			1.15615			0.578076	−	0.815983i	$-0.303804\pi$
$43$	326.000			1.15615			0.578076	+	0.815983i	$0.303804\pi$
$44$	18.0000	−	31.1769i	0.0616728	−	0.106820i
$45$	−67.5000	−	116.913i	−0.223607	−	0.387298i
$46$	−84.0000	−	145.492i	−0.269242	−	0.466341i
$47$	−69.0000	+	119.512i	−0.214142	+	0.370905i	−0.953007	−	0.302949i	$-0.902029\pi$
$47$	−69.0000	+	119.512i	−0.214142	+	0.370905i	0.738865	+	0.673854i	$0.235362\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	−200.000			−0.565685
$51$	−126.000	+	218.238i	−0.345952	+	0.599206i
$52$	−176.000	−	304.841i	−0.469362	−	0.812958i
$53$	−319.500	−	553.390i	−0.828051	−	1.43423i	−0.899565	−	0.436787i	$-0.856116\pi$
$53$	−319.500	−	553.390i	−0.828051	−	1.43423i	0.0715141	−	0.997440i	$-0.477217\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−135.000			−0.330971
$56$		0			0
$57$	−312.000			−0.725007
$58$	51.0000	−	88.3346i	0.115459	−	0.199981i
$59$	79.5000	+	137.698i	0.175424	+	0.303843i	0.940308	−	0.340325i	$-0.110537\pi$
$59$	79.5000	+	137.698i	0.175424	+	0.303843i	−0.764884	+	0.644168i	$0.777204\pi$
$60$	−90.0000	−	155.885i	−0.193649	−	0.335410i
$61$	361.000	−	625.270i	0.757726	−	1.31242i	−0.186281	−	0.982497i	$-0.559643\pi$
$61$	361.000	−	625.270i	0.757726	−	1.31242i	0.944007	−	0.329924i	$-0.107023\pi$
$62$	370.000			0.757904
$63$		0			0
$64$	64.0000			0.125000
$65$	−660.000	+	1143.15i	−1.25943	+	2.18140i
$66$	−27.0000	−	46.7654i	−0.0503556	−	0.0872185i
$67$	83.0000	+	143.760i	0.151344	+	0.262136i	0.931722	−	0.363173i	$-0.118306\pi$
$67$	83.0000	+	143.760i	0.151344	+	0.262136i	−0.780378	+	0.625309i	$0.784973\pi$
$68$	−168.000	+	290.985i	−0.299603	+	0.518927i
$69$	−252.000			−0.439670
$70$		0			0
$71$	1086.00			1.81527			0.907637	−	0.419755i	$-0.137884\pi$
$71$	1086.00			1.81527			0.907637	+	0.419755i	$0.137884\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	109.000	+	188.794i	0.174760	+	0.302693i	0.940078	−	0.340959i	$-0.110752\pi$
$73$	109.000	+	188.794i	0.174760	+	0.302693i	−0.765318	+	0.643652i	$0.777418\pi$
$74$	44.0000	+	76.2102i	0.0691202	+	0.119720i
$75$	−150.000	+	259.808i	−0.230940	+	0.400000i
$76$	−416.000			−0.627875
$77$		0			0
$78$	−528.000			−0.766464
$79$	291.500	−	504.893i	0.415143	−	0.719049i	−0.580300	−	0.814403i	$-0.697065\pi$
$79$	291.500	−	504.893i	0.415143	−	0.719049i	0.995443	+	0.0953535i	$0.0303981\pi$
$80$	−120.000	−	207.846i	−0.167705	−	0.290474i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	168.000	−	290.985i	0.226250	−	0.391876i
$83$	597.000			0.789509			0.394755	−	0.918787i	$-0.370830\pi$
$83$	597.000			0.789509			0.394755	+	0.918787i	$0.370830\pi$
$84$		0			0
$85$	1260.00			1.60784
$86$	326.000	−	564.649i	0.408761	−	0.707996i
$87$	−76.5000	−	132.502i	−0.0942720	−	0.163284i
$88$	−36.0000	−	62.3538i	−0.0436092	−	0.0755334i
$89$	−519.000	+	898.934i	−0.618134	+	1.07064i	0.371692	+	0.928356i	$0.378778\pi$
$89$	−519.000	+	898.934i	−0.618134	+	1.07064i	−0.989826	+	0.142283i	$0.954556\pi$
$90$	−270.000			−0.316228
$91$		0			0
$92$	−336.000			−0.380765
$93$	277.500	−	480.644i	0.309413	−	0.535919i
$94$	138.000	+	239.023i	0.151421	+	0.262270i
$95$	780.000	+	1351.00i	0.842382	+	1.45905i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	169.000			0.176901			0.0884503	−	0.996081i	$-0.471809\pi$
$97$	169.000			0.176901			0.0884503	+	0.996081i	$0.471809\pi$
$98$		0			0
$99$	−81.0000			−0.0822304
$100$	−200.000	+	346.410i	−0.200000	+	0.346410i
$101$	321.000	+	555.988i	0.316244	+	0.547752i	0.979701	−	0.200463i	$-0.0642447\pi$
$101$	321.000	+	555.988i	0.316244	+	0.547752i	−0.663457	+	0.748215i	$0.730911\pi$
$102$	252.000	+	436.477i	0.244625	+	0.423702i
$103$	232.000	−	401.836i	0.221938	−	0.384408i	−0.733458	−	0.679735i	$-0.762095\pi$
$103$	232.000	−	401.836i	0.221938	−	0.384408i	0.955396	+	0.295326i	$0.0954283\pi$
$104$	−704.000			−0.663778
$105$		0			0
$106$	−1278.00			−1.17104
$107$	−196.500	+	340.348i	−0.177536	+	0.307502i	−0.941036	−	0.338306i	$-0.890146\pi$
$107$	−196.500	+	340.348i	−0.177536	+	0.307502i	0.763500	+	0.645808i	$0.223479\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	−7.00000	−	12.1244i	−0.00615118	−	0.0106542i	0.862933	−	0.505318i	$-0.168625\pi$
$109$	−7.00000	−	12.1244i	−0.00615118	−	0.0106542i	−0.869085	+	0.494663i	$0.835291\pi$
$110$	−135.000	+	233.827i	−0.117016	+	0.202677i
$111$	132.000			0.112873
$112$		0			0
$113$	−2184.00			−1.81817			−0.909086	−	0.416608i	$-0.863219\pi$
$113$	−2184.00			−1.81817			−0.909086	+	0.416608i	$0.863219\pi$
$114$	−312.000	+	540.400i	−0.256329	+	0.443974i
$115$	630.000	+	1091.19i	0.510850	+	0.884819i
$116$	−102.000	−	176.669i	−0.0816419	−	0.141408i
$117$	−396.000	+	685.892i	−0.312908	+	0.541972i
$118$	318.000			0.248087
$119$		0			0
$120$	−360.000			−0.273861
$121$	625.000	−	1082.53i	0.469572	−	0.813322i
$122$	−722.000	−	1250.54i	−0.535794	−	0.928022i
$123$	−252.000	−	436.477i	−0.184732	−	0.319966i
$124$	370.000	−	640.859i	0.267960	−	0.464120i
$125$	−375.000			−0.268328
$126$		0			0
$127$	−373.000			−0.260617			−0.130309	−	0.991473i	$-0.541597\pi$
$127$	−373.000			−0.260617			−0.130309	+	0.991473i	$0.541597\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−489.000	−	846.973i	−0.333752	−	0.578076i
$130$	1320.00	+	2286.31i	0.890551	+	1.54248i
$131$	−586.500	+	1015.85i	−0.391166	+	0.677519i	−0.992604	−	0.121400i	$-0.961261\pi$
$131$	−586.500	+	1015.85i	−0.391166	+	0.677519i	0.601438	+	0.798920i	$0.294595\pi$
$132$	−108.000			−0.0712136
$133$		0			0
$134$	332.000			0.214033
$135$	−202.500	+	350.740i	−0.129099	+	0.223607i
$136$	336.000	+	581.969i	0.211851	+	0.366937i
$137$	−15.0000	−	25.9808i	−0.00935428	−	0.0162021i	0.861310	−	0.508079i	$-0.169644\pi$
$137$	−15.0000	−	25.9808i	−0.00935428	−	0.0162021i	−0.870665	+	0.491877i	$0.836311\pi$
$138$	−252.000	+	436.477i	−0.155447	+	0.269242i
$139$	82.0000			0.0500370			0.0250185	−	0.999687i	$-0.492036\pi$
$139$	82.0000			0.0500370			0.0250185	+	0.999687i	$0.492036\pi$
$140$		0			0
$141$	414.000			0.247270
$142$	1086.00	−	1881.01i	0.641796	−	1.11162i
$143$	396.000	+	685.892i	0.231575	+	0.401099i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−382.500	+	662.509i	−0.219068	+	0.379437i
$146$	436.000			0.247148
$147$		0			0
$148$	176.000			0.0977507
$149$	717.000	−	1241.88i	0.394221	−	0.682811i	−0.598780	−	0.800913i	$-0.704348\pi$
$149$	717.000	−	1241.88i	0.394221	−	0.682811i	0.993001	+	0.118102i	$0.0376811\pi$
$150$	300.000	+	519.615i	0.163299	+	0.282843i
$151$	1335.50	+	2313.15i	0.719745	+	1.24663i	0.961101	+	0.276198i	$0.0890745\pi$
$151$	1335.50	+	2313.15i	0.719745	+	1.24663i	−0.241356	+	0.970437i	$0.577592\pi$
$152$	−416.000	+	720.533i	−0.221987	+	0.384493i
$153$	756.000			0.399470
$154$		0			0
$155$	−2775.00			−1.43802
$156$	−528.000	+	914.523i	−0.270986	+	0.469362i
$157$	1126.00	+	1950.29i	0.572386	+	0.991401i	0.996320	+	0.0857085i	$0.0273154\pi$
$157$	1126.00	+	1950.29i	0.572386	+	0.991401i	−0.423934	+	0.905693i	$0.639351\pi$
$158$	−583.000	−	1009.79i	−0.293551	−	0.508444i
$159$	−958.500	+	1660.17i	−0.478075	+	0.828051i
$160$	−480.000			−0.237171
$161$		0			0
$162$	−162.000			−0.0785674
$163$	−838.000	+	1451.46i	−0.402682	+	0.697466i	−0.994049	−	0.108937i	$-0.965255\pi$
$163$	−838.000	+	1451.46i	−0.402682	+	0.697466i	0.591366	+	0.806403i	$0.298589\pi$
$164$	−336.000	−	581.969i	−0.159983	−	0.277098i
$165$	202.500	+	350.740i	0.0955431	+	0.165485i
$166$	597.000	−	1034.03i	0.279134	−	0.483474i
$167$	−3030.00			−1.40400			−0.702001	−	0.712176i	$-0.747710\pi$
$167$	−3030.00			−1.40400			−0.702001	+	0.712176i	$0.747710\pi$
$168$		0			0
$169$	5547.00			2.52481
$170$	1260.00	−	2182.38i	0.568456	−	0.984595i
$171$	468.000	+	810.600i	0.209292	+	0.362504i
$172$	−652.000	−	1129.30i	−0.289038	−	0.500628i
$173$	1719.00	−	2977.40i	0.755452	−	1.30848i	−0.189698	−	0.981843i	$-0.560751\pi$
$173$	1719.00	−	2977.40i	0.755452	−	1.30848i	0.945149	−	0.326638i	$-0.105916\pi$
$174$	−306.000			−0.133321
$175$		0			0
$176$	−144.000			−0.0616728
$177$	238.500	−	413.094i	0.101281	−	0.175424i
$178$	1038.00	+	1797.87i	0.437086	+	0.757056i
$179$	606.000	+	1049.62i	0.253042	+	0.438282i	0.964362	−	0.264587i	$-0.0852355\pi$
$179$	606.000	+	1049.62i	0.253042	+	0.438282i	−0.711320	+	0.702869i	$0.751902\pi$
$180$	−270.000	+	467.654i	−0.111803	+	0.193649i
$181$	−3032.00			−1.24512			−0.622560	−	0.782572i	$-0.713907\pi$
$181$	−3032.00			−1.24512			−0.622560	+	0.782572i	$0.713907\pi$
$182$		0			0
$183$	−2166.00			−0.874947
$184$	−336.000	+	581.969i	−0.134621	+	0.233170i
$185$	−330.000	−	571.577i	−0.131146	−	0.227152i
$186$	−555.000	−	961.288i	−0.218788	−	0.378952i
$187$	378.000	−	654.715i	0.147819	−	0.256030i
$188$	552.000			0.214142
$189$		0			0
$190$	3120.00			1.19131
$191$	−1260.00	+	2182.38i	−0.477332	+	0.826763i	−0.999662	−	0.0259799i	$-0.991729\pi$
$191$	−1260.00	+	2182.38i	−0.477332	+	0.826763i	0.522331	+	0.852743i	$0.325063\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	−182.500	−	316.099i	−0.0680655	−	0.117893i	0.829984	−	0.557787i	$-0.188349\pi$
$193$	−182.500	−	316.099i	−0.0680655	−	0.117893i	−0.898050	+	0.439894i	$0.855016\pi$
$194$	169.000	−	292.717i	0.0625438	−	0.108329i
$195$	3960.00			1.45426
$196$		0			0
$197$	−1590.00			−0.575040			−0.287520	−	0.957775i	$-0.592831\pi$
$197$	−1590.00			−0.575040			−0.287520	+	0.957775i	$0.592831\pi$
$198$	−81.0000	+	140.296i	−0.0290728	+	0.0503556i
$199$	−2690.00	−	4659.22i	−0.958236	−	1.65971i	−0.726782	−	0.686868i	$-0.758985\pi$
$199$	−2690.00	−	4659.22i	−0.958236	−	1.65971i	−0.231455	−	0.972846i	$-0.574348\pi$
$200$	400.000	+	692.820i	0.141421	+	0.244949i
$201$	249.000	−	431.281i	0.0873786	−	0.151344i
$202$	1284.00			0.447237
$203$		0			0
$204$	1008.00			0.345952
$205$	−1260.00	+	2182.38i	−0.429279	+	0.743533i
$206$	−464.000	−	803.672i	−0.156934	−	0.271818i
$207$	378.000	+	654.715i	0.126922	+	0.219835i
$208$	−704.000	+	1219.36i	−0.234681	+	0.406479i
$209$	936.000			0.309782
$210$		0			0
$211$	−5362.00			−1.74946			−0.874728	−	0.484614i	$-0.838960\pi$
$211$	−5362.00			−1.74946			−0.874728	+	0.484614i	$0.838960\pi$
$212$	−1278.00	+	2213.56i	−0.414025	+	0.717113i
$213$	−1629.00	−	2821.51i	−0.524025	−	0.907637i
$214$	393.000	+	680.696i	0.125537	+	0.217437i
$215$	−2445.00	+	4234.86i	−0.775570	+	1.34333i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	−28.0000			−0.00869908
$219$	327.000	−	566.381i	0.100898	−	0.174760i
$220$	270.000	+	467.654i	0.0827427	+	0.143315i
$221$	−3696.00	−	6401.66i	−1.12498	−	1.94852i
$222$	132.000	−	228.631i	0.0399066	−	0.0691202i
$223$	1573.00			0.472358			0.236179	−	0.971710i	$-0.424105\pi$
$223$	1573.00			0.472358			0.236179	+	0.971710i	$0.424105\pi$
$224$		0			0
$225$	900.000			0.266667
$226$	−2184.00	+	3782.80i	−0.642821	+	1.11340i
$227$	460.500	+	797.609i	0.134645	+	0.233212i	0.925462	−	0.378841i	$-0.123677\pi$
$227$	460.500	+	797.609i	0.134645	+	0.233212i	−0.790817	+	0.612053i	$0.790344\pi$
$228$	624.000	+	1080.80i	0.181252	+	0.313937i
$229$	2026.00	−	3509.13i	0.584637	−	1.01262i	−0.410284	−	0.911958i	$-0.634570\pi$
$229$	2026.00	−	3509.13i	0.584637	−	1.01262i	0.994921	−	0.100663i	$-0.0320963\pi$
$230$	2520.00			0.722452
$231$		0			0
$232$	−408.000			−0.115459
$233$	234.000	−	405.300i	0.0657933	−	0.113957i	−0.831252	−	0.555895i	$-0.812376\pi$
$233$	234.000	−	405.300i	0.0657933	−	0.113957i	0.897046	+	0.441938i	$0.145709\pi$
$234$	792.000	+	1371.78i	0.221259	+	0.383232i
$235$	−1035.00	−	1792.67i	−0.287302	−	0.497622i
$236$	318.000	−	550.792i	0.0877120	−	0.151922i
$237$	−1749.00			−0.479366
$238$		0			0
$239$	4932.00			1.33483			0.667415	−	0.744686i	$-0.267401\pi$
$239$	4932.00			1.33483			0.667415	+	0.744686i	$0.267401\pi$
$240$	−360.000	+	623.538i	−0.0968246	+	0.167705i
$241$	−768.500	−	1331.08i	−0.205408	−	0.355778i	0.744854	−	0.667227i	$-0.232519\pi$
$241$	−768.500	−	1331.08i	−0.205408	−	0.355778i	−0.950263	+	0.311449i	$0.899186\pi$
$242$	−1250.00	−	2165.06i	−0.332037	−	0.575106i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	−2888.00			−0.757726
$245$		0			0
$246$	−1008.00			−0.261251
$247$	4576.00	−	7925.86i	1.17880	−	2.04174i
$248$	−740.000	−	1281.72i	−0.189476	−	0.328182i
$249$	−895.500	−	1551.05i	−0.227912	−	0.394755i
$250$	−375.000	+	649.519i	−0.0948683	+	0.164317i
$251$	−5319.00			−1.33758			−0.668789	−	0.743452i	$-0.733187\pi$
$251$	−5319.00			−1.33758			−0.668789	+	0.743452i	$0.733187\pi$
$252$		0			0
$253$	756.000			0.187863
$254$	−373.000	+	646.055i	−0.0921421	+	0.159595i
$255$	−1890.00	−	3273.58i	−0.464143	−	0.803919i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2673.00	−	4629.77i	0.648783	−	1.12372i	−0.334631	−	0.942349i	$-0.608612\pi$
$257$	2673.00	−	4629.77i	0.648783	−	1.12372i	0.983414	−	0.181375i	$-0.0580549\pi$
$258$	−1956.00			−0.471997
$259$		0			0
$260$	5280.00			1.25943
$261$	−229.500	+	397.506i	−0.0544279	+	0.0942720i
$262$	1173.00	+	2031.70i	0.276596	+	0.479079i
$263$	−387.000	−	670.304i	−0.0907355	−	0.157159i	0.817085	−	0.576517i	$-0.195588\pi$
$263$	−387.000	−	670.304i	−0.0907355	−	0.157159i	−0.907821	+	0.419358i	$0.862255\pi$
$264$	−108.000	+	187.061i	−0.0251778	+	0.0436092i
$265$	9585.00			2.22189
$266$		0			0
$267$	3114.00			0.713759
$268$	332.000	−	575.041i	0.0756721	−	0.131068i
$269$	1207.50	+	2091.45i	0.273690	+	0.474045i	0.969804	−	0.243887i	$-0.0784225\pi$
$269$	1207.50	+	2091.45i	0.273690	+	0.474045i	−0.696114	+	0.717931i	$0.745089\pi$
$270$	405.000	+	701.481i	0.0912871	+	0.158114i
$271$	−237.500	+	411.362i	−0.0532365	+	0.0922084i	−0.891416	−	0.453187i	$-0.850287\pi$
$271$	−237.500	+	411.362i	−0.0532365	+	0.0922084i	0.838179	+	0.545395i	$0.183620\pi$
$272$	1344.00			0.299603
$273$		0			0
$274$	−60.0000			−0.0132290
$275$	450.000	−	779.423i	0.0986764	−	0.170913i
$276$	504.000	+	872.954i	0.109918	+	0.190383i
$277$	−1864.00	−	3228.54i	−0.404321	−	0.700304i	0.589921	−	0.807461i	$-0.299159\pi$
$277$	−1864.00	−	3228.54i	−0.404321	−	0.700304i	−0.994242	+	0.107156i	$0.965825\pi$
$278$	82.0000	−	142.028i	0.0176908	−	0.0306413i
$279$	−1665.00			−0.357279
$280$		0			0
$281$	1602.00			0.340097			0.170049	−	0.985436i	$-0.445608\pi$
$281$	1602.00			0.340097			0.170049	+	0.985436i	$0.445608\pi$
$282$	414.000	−	717.069i	0.0874232	−	0.151421i
$283$	343.000	+	594.093i	0.0720468	+	0.124789i	0.899798	−	0.436306i	$-0.143714\pi$
$283$	343.000	+	594.093i	0.0720468	+	0.124789i	−0.827751	+	0.561095i	$0.810380\pi$
$284$	−2172.00	−	3762.01i	−0.453819	−	0.786037i
$285$	2340.00	−	4053.00i	0.486350	−	0.842382i
$286$	1584.00			0.327496
$287$		0			0
$288$	−288.000			−0.0589256
$289$	−1071.50	+	1855.89i	−0.218095	+	0.377751i
$290$	765.000	+	1325.02i	0.154905	+	0.268303i
$291$	−253.500	−	439.075i	−0.0510668	−	0.0884503i
$292$	436.000	−	755.174i	0.0873800	−	0.151347i
$293$	1101.00			0.219526			0.109763	−	0.993958i	$-0.464991\pi$
$293$	1101.00			0.219526			0.109763	+	0.993958i	$0.464991\pi$
$294$		0			0
$295$	−2385.00			−0.470712
$296$	176.000	−	304.841i	0.0345601	−	0.0598599i
$297$	121.500	+	210.444i	0.0237379	+	0.0411152i
$298$	−1434.00	−	2483.76i	−0.278756	−	0.482820i
$299$	3696.00	−	6401.66i	0.714867	−	1.23819i
$300$	1200.00			0.230940
$301$		0			0
$302$	5342.00			1.01787
$303$	963.000	−	1667.96i	0.182584	−	0.316244i
$304$	832.000	+	1441.07i	0.156969	+	0.271878i
$305$	5415.00	+	9379.06i	1.01660	+	1.76080i
$306$	756.000	−	1309.43i	0.141234	−	0.244625i
$307$	−2780.00			−0.516818			−0.258409	−	0.966036i	$-0.583198\pi$
$307$	−2780.00			−0.516818			−0.258409	+	0.966036i	$0.583198\pi$
$308$		0			0
$309$	−1392.00			−0.256272
$310$	−2775.00	+	4806.44i	−0.508417	+	0.880605i
$311$	2148.00	+	3720.45i	0.391646	+	0.678351i	0.992667	−	0.120883i	$-0.0385725\pi$
$311$	2148.00	+	3720.45i	0.391646	+	0.678351i	−0.601021	+	0.799233i	$0.705239\pi$
$312$	1056.00	+	1829.05i	0.191616	+	0.331889i
$313$	2744.50	−	4753.61i	0.495618	−	0.858435i	−0.504370	−	0.863488i	$-0.668275\pi$
$313$	2744.50	−	4753.61i	0.495618	−	0.858435i	0.999987	+	0.00505298i	$0.00160842\pi$
$314$	4504.00			0.809476
$315$		0			0
$316$	−2332.00			−0.415143
$317$	−2245.50	+	3889.32i	−0.397854	+	0.689104i	−0.993461	−	0.114172i	$-0.963578\pi$
$317$	−2245.50	+	3889.32i	−0.397854	+	0.689104i	0.595607	+	0.803276i	$0.296912\pi$
$318$	1917.00	+	3320.34i	0.338050	+	0.585520i
$319$	229.500	+	397.506i	0.0402807	+	0.0697682i
$320$	−480.000	+	831.384i	−0.0838525	+	0.145237i
$321$	1179.00			0.205001
$322$		0			0
$323$	−8736.00			−1.50490
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	−4400.00	−	7621.02i	−0.750979	−	1.30073i
$326$	1676.00	+	2902.92i	0.284739	+	0.493183i
$327$	−21.0000	+	36.3731i	−0.00355138	+	0.00615118i
$328$	−1344.00			−0.226250
$329$		0			0
$330$	810.000			0.135118
$331$	1982.00	−	3432.92i	0.329126	−	0.570062i	−0.653213	−	0.757174i	$-0.726579\pi$
$331$	1982.00	−	3432.92i	0.329126	−	0.570062i	0.982339	+	0.187112i	$0.0599127\pi$
$332$	−1194.00	−	2068.07i	−0.197377	−	0.341868i
$333$	−198.000	−	342.946i	−0.0325836	−	0.0564364i
$334$	−3030.00	+	5248.11i	−0.496390	+	0.859773i
$335$	−2490.00			−0.406099
$336$		0			0
$337$	161.000			0.0260244			0.0130122	−	0.999915i	$-0.495858\pi$
$337$	161.000			0.0260244			0.0130122	+	0.999915i	$0.495858\pi$
$338$	5547.00	−	9607.69i	0.892654	−	1.54612i
$339$	3276.00	+	5674.20i	0.524861	+	0.909086i
$340$	−2520.00	−	4364.77i	−0.401959	−	0.696214i
$341$	−832.500	+	1441.93i	−0.132206	+	0.228988i
$342$	1872.00			0.295983
$343$		0			0
$344$	−2608.00			−0.408761
$345$	1890.00	−	3273.58i	0.294940	−	0.510850i
$346$	−3438.00	−	5954.79i	−0.534185	−	0.925236i
$347$	2958.00	+	5123.41i	0.457619	+	0.792619i	0.998835	−	0.0482646i	$-0.0153691\pi$
$347$	2958.00	+	5123.41i	0.457619	+	0.792619i	−0.541216	+	0.840884i	$0.682036\pi$
$348$	−306.000	+	530.008i	−0.0471360	+	0.0816419i
$349$	142.000			0.0217796			0.0108898	−	0.999941i	$-0.496534\pi$
$349$	142.000			0.0217796			0.0108898	+	0.999941i	$0.496534\pi$
$350$		0			0
$351$	2376.00			0.361315
$352$	−144.000	+	249.415i	−0.0218046	+	0.0377667i
$353$	−2220.00	−	3845.15i	−0.334727	−	0.579764i	0.648705	−	0.761040i	$-0.275311\pi$
$353$	−2220.00	−	3845.15i	−0.334727	−	0.579764i	−0.983432	+	0.181275i	$0.941977\pi$
$354$	−477.000	−	826.188i	−0.0716166	−	0.124044i
$355$	−8145.00	+	14107.6i	−1.21772	+	2.10916i
$356$	4152.00			0.618134
$357$		0			0
$358$	2424.00			0.357856
$359$	−1143.00	+	1979.73i	−0.168037	+	0.291048i	−0.937730	−	0.347366i	$-0.887076\pi$
$359$	−1143.00	+	1979.73i	−0.168037	+	0.291048i	0.769693	+	0.638415i	$0.220409\pi$
$360$	540.000	+	935.307i	0.0790569	+	0.136931i
$361$	−1978.50	−	3426.86i	−0.288453	−	0.499615i
$362$	−3032.00	+	5251.58i	−0.440217	+	0.762477i
$363$	−3750.00			−0.542215
$364$		0			0
$365$	−3270.00			−0.468930
$366$	−2166.00	+	3751.62i	−0.309341	+	0.535794i
$367$	−1434.50	−	2484.63i	−0.204033	−	0.353396i	0.745791	−	0.666180i	$-0.232072\pi$
$367$	−1434.50	−	2484.63i	−0.204033	−	0.353396i	−0.949824	+	0.312784i	$0.898738\pi$
$368$	672.000	+	1163.94i	0.0951914	+	0.164876i
$369$	−756.000	+	1309.43i	−0.106655	+	0.184732i
$370$	−1320.00			−0.185469
$371$		0			0
$372$	−2220.00			−0.309413
$373$	1532.00	−	2653.50i	0.212665	−	0.368346i	−0.739883	−	0.672736i	$-0.765119\pi$
$373$	1532.00	−	2653.50i	0.212665	−	0.368346i	0.952548	+	0.304390i	$0.0984524\pi$
$374$	−756.000	−	1309.43i	−0.104524	−	0.181040i
$375$	562.500	+	974.279i	0.0774597	+	0.134164i
$376$	552.000	−	956.092i	0.0757107	−	0.131135i
$377$	4488.00			0.613113
$378$		0			0
$379$	−6040.00			−0.818612			−0.409306	−	0.912397i	$-0.634229\pi$
$379$	−6040.00			−0.818612			−0.409306	+	0.912397i	$0.634229\pi$
$380$	3120.00	−	5404.00i	0.421191	−	0.729524i
$381$	559.500	+	969.082i	0.0752337	+	0.130309i
$382$	2520.00	+	4364.77i	0.337525	+	0.584610i
$383$	921.000	−	1595.22i	0.122874	−	0.212825i	−0.798026	−	0.602623i	$-0.794122\pi$
$383$	921.000	−	1595.22i	0.122874	−	0.212825i	0.920900	+	0.389799i	$0.127455\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	−730.000			−0.0962591
$387$	−1467.00	+	2540.92i	−0.192692	+	0.333752i
$388$	−338.000	−	585.433i	−0.0442251	−	0.0766002i
$389$	−3915.00	−	6780.98i	−0.510279	−	0.883828i	−0.999929	−	0.0119097i	$-0.996209\pi$
$389$	−3915.00	−	6780.98i	−0.510279	−	0.883828i	0.489650	−	0.871919i	$-0.337124\pi$
$390$	3960.00	−	6858.92i	0.514160	−	0.890551i
$391$	−7056.00			−0.912627
$392$		0			0
$393$	3519.00			0.451680
$394$	−1590.00	+	2753.96i	−0.203307	+	0.352138i
$395$	4372.50	+	7573.39i	0.556973	+	0.964706i
$396$	162.000	+	280.592i	0.0205576	+	0.0356068i
$397$	−7382.00	+	12786.0i	−0.933229	+	1.61640i	−0.155467	+	0.987841i	$0.549688\pi$
$397$	−7382.00	+	12786.0i	−0.933229	+	1.61640i	−0.777762	+	0.628559i	$0.783645\pi$
$398$	−10760.0			−1.35515
$399$		0			0
$400$	1600.00			0.200000
$401$	−3132.00	+	5424.78i	−0.390036	+	0.675563i	−0.992454	−	0.122618i	$-0.960871\pi$
$401$	−3132.00	+	5424.78i	−0.390036	+	0.675563i	0.602417	+	0.798181i	$0.294204\pi$
$402$	−498.000	−	862.561i	−0.0617860	−	0.107017i
$403$	8140.00	+	14098.9i	1.00616	+	1.74272i
$404$	1284.00	−	2223.95i	0.158122	−	0.273876i
$405$	1215.00			0.149071
$406$		0			0
$407$	−396.000			−0.0482285
$408$	1008.00	−	1745.91i	0.122312	−	0.211851i
$409$	2375.50	+	4114.49i	0.287191	+	0.497429i	0.973138	−	0.230222i	$-0.0739454\pi$
$409$	2375.50	+	4114.49i	0.287191	+	0.497429i	−0.685948	+	0.727651i	$0.740612\pi$
$410$	2520.00	+	4364.77i	0.303546	+	0.525757i
$411$	−45.0000	+	77.9423i	−0.00540070	+	0.00935428i
$412$	−1856.00			−0.221938
$413$		0			0
$414$	1512.00			0.179495
$415$	−4477.50	+	7755.26i	−0.529619	+	0.917327i
$416$	1408.00	+	2438.73i	0.165944	+	0.287424i
$417$	−123.000	−	213.042i	−0.0144445	−	0.0250185i
$418$	936.000	−	1621.20i	0.109525	−	0.189702i
$419$	4704.00			0.548462			0.274231	−	0.961664i	$-0.411577\pi$
$419$	4704.00			0.548462			0.274231	+	0.961664i	$0.411577\pi$
$420$		0			0
$421$	−4474.00			−0.517932			−0.258966	−	0.965886i	$-0.583382\pi$
$421$	−4474.00			−0.517932			−0.258966	+	0.965886i	$0.583382\pi$
$422$	−5362.00	+	9287.26i	−0.618526	+	1.07132i
$423$	−621.000	−	1075.60i	−0.0713807	−	0.123635i
$424$	2556.00	+	4427.12i	0.292760	+	0.507076i
$425$	−4200.00	+	7274.61i	−0.479365	+	0.830284i
$426$	−6516.00			−0.741083
$427$		0			0
$428$	1572.00			0.177536
$429$	1188.00	−	2057.68i	0.133700	−	0.231575i
$430$	4890.00	+	8469.73i	0.548411	+	0.949876i
$431$	6402.00	+	11088.6i	0.715484	+	1.23925i	0.962773	+	0.270312i	$0.0871270\pi$
$431$	6402.00	+	11088.6i	0.715484	+	1.23925i	−0.247289	+	0.968942i	$0.579540\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	5074.00			0.563143			0.281571	−	0.959540i	$-0.409144\pi$
$433$	5074.00			0.563143			0.281571	+	0.959540i	$0.409144\pi$
$434$		0			0
$435$	2295.00			0.252958
$436$	−28.0000	+	48.4974i	−0.00307559	+	0.00532708i
$437$	−4368.00	−	7565.60i	−0.478146	−	0.828173i
$438$	−654.000	−	1132.76i	−0.0713455	−	0.123574i
$439$	−633.500	+	1097.25i	−0.0688731	+	0.119292i	−0.898406	−	0.439167i	$-0.855274\pi$
$439$	−633.500	+	1097.25i	−0.0688731	+	0.119292i	0.829532	+	0.558459i	$0.188607\pi$
$440$	1080.00			0.117016
$441$		0			0
$442$	−14784.0			−1.59096
$443$	3466.50	−	6004.15i	0.371780	−	0.643941i	−0.618060	−	0.786131i	$-0.712081\pi$
$443$	3466.50	−	6004.15i	0.371780	−	0.643941i	0.989839	+	0.142190i	$0.0454144\pi$
$444$	−264.000	−	457.261i	−0.0282182	−	0.0488754i
$445$	−7785.00	−	13484.0i	−0.829313	−	1.43641i
$446$	1573.00	−	2724.52i	0.167004	−	0.289259i
$447$	−4302.00			−0.455207
$448$		0			0
$449$	11688.0			1.22849			0.614244	−	0.789116i	$-0.289461\pi$
$449$	11688.0			1.22849			0.614244	+	0.789116i	$0.289461\pi$
$450$	900.000	−	1558.85i	0.0942809	−	0.163299i
$451$	756.000	+	1309.43i	0.0789327	+	0.136715i
$452$	4368.00	+	7565.60i	0.454543	+	0.787292i
$453$	4006.50	−	6939.46i	0.415545	−	0.719745i
$454$	1842.00			0.190417
$455$		0			0
$456$	2496.00			0.256329
$457$	−275.500	+	477.180i	−0.0281999	+	0.0488436i	−0.879781	−	0.475379i	$-0.842311\pi$
$457$	−275.500	+	477.180i	−0.0281999	+	0.0488436i	0.851581	+	0.524223i	$0.175644\pi$
$458$	−4052.00	−	7018.27i	−0.413401	−	0.716031i
$459$	−1134.00	−	1964.15i	−0.115317	−	0.199735i
$460$	2520.00	−	4364.77i	0.255425	−	0.442409i
$461$	−13386.0			−1.35238			−0.676191	−	0.736726i	$-0.736371\pi$
$461$	−13386.0			−1.35238			−0.676191	+	0.736726i	$0.736371\pi$
$462$		0			0
$463$	−6376.00			−0.639995			−0.319998	−	0.947418i	$-0.603682\pi$
$463$	−6376.00			−0.639995			−0.319998	+	0.947418i	$0.603682\pi$
$464$	−408.000	+	706.677i	−0.0408210	+	0.0707040i
$465$	4162.50	+	7209.66i	0.415121	+	0.719011i
$466$	−468.000	−	810.600i	−0.0465229	−	0.0805801i
$467$	2850.00	−	4936.34i	0.282403	−	0.489137i	−0.689573	−	0.724216i	$-0.742202\pi$
$467$	2850.00	−	4936.34i	0.282403	−	0.489137i	0.971976	+	0.235080i	$0.0755351\pi$
$468$	3168.00			0.312908
$469$		0			0
$470$	−4140.00			−0.406306
$471$	3378.00	−	5850.87i	0.330467	−	0.572386i
$472$	−636.000	−	1101.58i	−0.0620218	−	0.107425i
$473$	1467.00	+	2540.92i	0.142606	+	0.247001i
$474$	−1749.00	+	3029.36i	−0.169481	+	0.293551i
$475$	−10400.0			−1.00460
$476$		0			0
$477$	5751.00			0.552034
$478$	4932.00	−	8542.47i	0.471934	−	0.817414i
$479$	9897.00	+	17142.1i	0.944062	+	1.63516i	0.757619	+	0.652697i	$0.226362\pi$
$479$	9897.00	+	17142.1i	0.944062	+	1.63516i	0.186442	+	0.982466i	$0.440304\pi$
$480$	720.000	+	1247.08i	0.0684653	+	0.118585i
$481$	−1936.00	+	3353.25i	−0.183522	+	0.317869i
$482$	−3074.00			−0.290491
$483$		0			0
$484$	−5000.00			−0.469572
$485$	−1267.50	+	2195.37i	−0.118668	+	0.205540i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	−7967.50	−	13800.1i	−0.741359	−	1.28407i	−0.951877	−	0.306482i	$-0.900848\pi$
$487$	−7967.50	−	13800.1i	−0.741359	−	1.28407i	0.210517	−	0.977590i	$-0.432485\pi$
$488$	−2888.00	+	5002.16i	−0.267897	+	0.464011i
$489$	5028.00			0.464978
$490$		0			0
$491$	9963.00			0.915731			0.457865	−	0.889021i	$-0.348614\pi$
$491$	9963.00			0.915731			0.457865	+	0.889021i	$0.348614\pi$
$492$	−1008.00	+	1745.91i	−0.0923662	+	0.159983i
$493$	−2142.00	−	3710.05i	−0.195681	−	0.338930i
$494$	−9152.00	−	15851.7i	−0.833538	−	1.44373i
$495$	607.500	−	1052.22i	0.0551618	−	0.0955431i
$496$	−2960.00			−0.267960
$497$		0			0
$498$	−3582.00			−0.322316
$499$	−9571.00	+	16577.5i	−0.858631	+	1.48719i	0.0146043	+	0.999893i	$0.495351\pi$
$499$	−9571.00	+	16577.5i	−0.858631	+	1.48719i	−0.873235	+	0.487299i	$0.837982\pi$
$500$	750.000	+	1299.04i	0.0670820	+	0.116190i
$501$	4545.00	+	7872.17i	0.405301	+	0.702001i
$502$	−5319.00	+	9212.78i	−0.472906	+	0.819096i
$503$	12192.0			1.08074			0.540372	−	0.841426i	$-0.318283\pi$
$503$	12192.0			1.08074			0.540372	+	0.841426i	$0.318283\pi$
$504$		0			0
$505$	−9630.00			−0.848573
$506$	756.000	−	1309.43i	0.0664196	−	0.115042i
$507$	−8320.50	−	14411.5i	−0.728849	−	1.26240i
$508$	746.000	+	1292.11i	0.0651543	+	0.112851i
$509$	−9904.50	+	17155.1i	−0.862494	+	1.49388i	0.00702091	+	0.999975i	$0.497765\pi$
$509$	−9904.50	+	17155.1i	−0.862494	+	1.49388i	−0.869515	+	0.493907i	$0.835568\pi$
$510$	−7560.00			−0.656397
$511$		0			0
$512$	−512.000			−0.0441942
$513$	1404.00	−	2431.80i	0.120835	−	0.209292i
$514$	−5346.00	−	9259.54i	−0.458759	−	0.794593i
$515$	3480.00	+	6027.54i	0.297761	+	0.515738i
$516$	−1956.00	+	3387.89i	−0.166876	+	0.289038i
$517$	−1242.00			−0.105654
$518$		0			0
$519$	−10314.0			−0.872321
$520$	5280.00	−	9145.23i	0.445276	−	0.771240i
$521$	−897.000	−	1553.65i	−0.0754286	−	0.130646i	0.825844	−	0.563899i	$-0.190699\pi$
$521$	−897.000	−	1553.65i	−0.0754286	−	0.130646i	−0.901273	+	0.433253i	$0.857366\pi$
$522$	459.000	+	795.011i	0.0384864	+	0.0666603i
$523$	−3224.00	+	5584.13i	−0.269552	+	0.466878i	−0.968746	−	0.248054i	$-0.920209\pi$
$523$	−3224.00	+	5584.13i	−0.269552	+	0.466878i	0.699194	+	0.714932i	$0.253542\pi$
$524$	4692.00			0.391166
$525$		0			0
$526$	−1548.00			−0.128319
$527$	7770.00	−	13458.0i	0.642251	−	1.11241i
$528$	216.000	+	374.123i	0.0178034	+	0.0308364i
$529$	2555.50	+	4426.26i	0.210035	+	0.363792i
$530$	9585.00	−	16601.7i	0.785558	−	1.36063i
$531$	−1431.00			−0.116949
$532$		0			0
$533$	14784.0			1.20144
$534$	3114.00	−	5393.61i	0.252352	−	0.437086i
$535$	−2947.50	−	5105.22i	−0.238190	−	0.412557i
$536$	−664.000	−	1150.08i	−0.0535083	−	0.0926790i
$537$	1818.00	−	3148.87i	0.146094	−	0.253042i
$538$	4830.00			0.387056
$539$		0			0
$540$	1620.00			0.129099
$541$	−3631.00	+	6289.08i	−0.288556	+	0.499794i	−0.973465	−	0.228835i	$-0.926509\pi$
$541$	−3631.00	+	6289.08i	−0.288556	+	0.499794i	0.684909	+	0.728628i	$0.259842\pi$
$542$	475.000	+	822.724i	0.0376439	+	0.0652012i
$543$	4548.00	+	7877.37i	0.359435	+	0.622560i
$544$	1344.00	−	2327.88i	0.105926	−	0.183469i
$545$	210.000			0.0165053
$546$		0			0
$547$	14204.0			1.11027			0.555136	−	0.831759i	$-0.312666\pi$
$547$	14204.0			1.11027			0.555136	+	0.831759i	$0.312666\pi$
$548$	−60.0000	+	103.923i	−0.00467714	+	0.00810104i
$549$	3249.00	+	5627.43i	0.252575	+	0.437474i
$550$	−900.000	−	1558.85i	−0.0697748	−	0.120853i
$551$	2652.00	−	4593.40i	0.205044	−	0.355146i
$552$	2016.00			0.155447
$553$		0			0
$554$	−7456.00			−0.571796
$555$	−990.000	+	1714.73i	−0.0757174	+	0.131146i
$556$	−164.000	−	284.056i	−0.0125093	−	0.0216667i
$557$	−7912.50	−	13704.9i	−0.601909	−	1.04254i	−0.992532	−	0.121986i	$-0.961074\pi$
$557$	−7912.50	−	13704.9i	−0.601909	−	1.04254i	0.390623	−	0.920551i	$-0.372260\pi$
$558$	−1665.00	+	2883.86i	−0.126317	+	0.218788i
$559$	28688.0			2.17061
$560$		0			0
$561$	−2268.00			−0.170686
$562$	1602.00	−	2774.75i	0.120243	−	0.208266i
$563$	529.500	+	917.121i	0.0396372	+	0.0686537i	0.885163	−	0.465280i	$-0.154046\pi$
$563$	529.500	+	917.121i	0.0396372	+	0.0686537i	−0.845526	+	0.533934i	$0.820713\pi$
$564$	−828.000	−	1434.14i	−0.0618175	−	0.107071i
$565$	16380.0	−	28371.0i	1.21967	−	2.11252i
$566$	1372.00			0.101890
$567$		0			0
$568$	−8688.00			−0.641796
$569$	−1980.00	+	3429.46i	−0.145880	+	0.252672i	−0.929701	−	0.368315i	$-0.879935\pi$
$569$	−1980.00	+	3429.46i	−0.145880	+	0.252672i	0.783821	+	0.620987i	$0.213268\pi$
$570$	−4680.00	−	8106.00i	−0.343901	−	0.595654i
$571$	1265.00	+	2191.04i	0.0927121	+	0.160582i	0.908651	−	0.417555i	$-0.137113\pi$
$571$	1265.00	+	2191.04i	0.0927121	+	0.160582i	−0.815939	+	0.578138i	$0.803780\pi$
$572$	1584.00	−	2743.57i	0.115787	−	0.200550i
$573$	7560.00			0.551175
$574$		0			0
$575$	−8400.00			−0.609225
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	5915.50	+	10245.9i	0.426803	+	0.739245i	0.996587	−	0.0825498i	$-0.0263063\pi$
$577$	5915.50	+	10245.9i	0.426803	+	0.739245i	−0.569784	+	0.821795i	$0.692973\pi$
$578$	2143.00	+	3711.78i	0.154216	+	0.267111i
$579$	−547.500	+	948.298i	−0.0392976	+	0.0680655i
$580$	3060.00			0.219068
$581$		0			0
$582$	−1014.00			−0.0722193
$583$	2875.50	−	4980.51i	0.204273	−	0.353811i
$584$	−872.000	−	1510.35i	−0.0617870	−	0.107018i
$585$	−5940.00	−	10288.4i	−0.419810	−	0.727132i
$586$	1101.00	−	1906.99i	0.0776141	−	0.134432i
$587$	−4809.00			−0.338141			−0.169070	−	0.985604i	$-0.554077\pi$
$587$	−4809.00			−0.338141			−0.169070	+	0.985604i	$0.554077\pi$
$588$		0			0
$589$	19240.0			1.34596
$590$	−2385.00	+	4130.94i	−0.166422	+	0.288251i
$591$	2385.00	+	4130.94i	0.166000	+	0.287520i
$592$	−352.000	−	609.682i	−0.0244377	−	0.0423273i
$593$	10902.0	−	18882.8i	0.754960	−	1.30763i	−0.190434	−	0.981700i	$-0.560989\pi$
$593$	10902.0	−	18882.8i	0.754960	−	1.30763i	0.945394	−	0.325930i	$-0.105677\pi$
$594$	486.000			0.0335704
$595$		0			0
$596$	−5736.00			−0.394221
$597$	−8070.00	+	13977.7i	−0.553238	+	0.958236i
$598$	−7392.00	−	12803.3i	−0.505487	−	0.875530i
$599$	−7083.00	−	12268.1i	−0.483144	−	0.836831i	0.516668	−	0.856186i	$-0.327172\pi$
$599$	−7083.00	−	12268.1i	−0.483144	−	0.836831i	−0.999813	+	0.0193549i	$0.993839\pi$
$600$	1200.00	−	2078.46i	0.0816497	−	0.141421i
$601$	−5891.00			−0.399832			−0.199916	−	0.979813i	$-0.564067\pi$
$601$	−5891.00			−0.399832			−0.199916	+	0.979813i	$0.564067\pi$
$602$		0			0
$603$	−1494.00			−0.100896
$604$	5342.00	−	9252.62i	0.359872	−	0.623317i
$605$	9375.00	+	16238.0i	0.629997	+	1.09119i
$606$	−1926.00	−	3335.93i	−0.129106	−	0.223619i
$607$	−1368.50	+	2370.31i	−0.0915086	+	0.158497i	−0.908146	−	0.418653i	$-0.862502\pi$
$607$	−1368.50	+	2370.31i	−0.0915086	+	0.158497i	0.816638	+	0.577151i	$0.195836\pi$
$608$	3328.00			0.221987
$609$		0			0
$610$	21660.0			1.43768
$611$	−6072.00	+	10517.0i	−0.402041	+	0.696355i
$612$	−1512.00	−	2618.86i	−0.0998676	−	0.172976i
$613$	13094.0	+	22679.5i	0.862743	+	1.49432i	0.869271	+	0.494337i	$0.164589\pi$
$613$	13094.0	+	22679.5i	0.862743	+	1.49432i	−0.00652719	+	0.999979i	$0.502078\pi$
$614$	−2780.00	+	4815.10i	−0.182723	+	0.316485i
$615$	7560.00			0.495689
$616$		0			0
$617$	−2358.00			−0.153857			−0.0769283	−	0.997037i	$-0.524511\pi$
$617$	−2358.00			−0.153857			−0.0769283	+	0.997037i	$0.524511\pi$
$618$	−1392.00	+	2411.01i	−0.0906059	+	0.156934i
$619$	6883.00	+	11921.7i	0.446932	+	0.774110i	0.998185	−	0.0602291i	$-0.0191831\pi$
$619$	6883.00	+	11921.7i	0.446932	+	0.774110i	−0.551252	+	0.834339i	$0.685850\pi$
$620$	5550.00	+	9612.88i	0.359505	+	0.622682i
$621$	1134.00	−	1964.15i	0.0732783	−	0.126922i
$622$	8592.00			0.553871
$623$		0			0
$624$	4224.00			0.270986
$625$	9062.50	−	15696.7i	0.580000	−	1.00459i
$626$	−5489.00	−	9507.23i	−0.350455	−	0.607005i
$627$	−1404.00	−	2431.80i	−0.0894264	−	0.154891i
$628$	4504.00	−	7801.16i	0.286193	−	0.495701i
$629$	3696.00			0.234291
$630$		0			0
$631$	21287.0			1.34298			0.671491	−	0.741012i	$-0.265654\pi$
$631$	21287.0			1.34298			0.671491	+	0.741012i	$0.265654\pi$
$632$	−2332.00	+	4039.14i	−0.146775	+	0.254222i
$633$	8043.00	+	13930.9i	0.505025	+	0.874728i
$634$	4491.00	+	7778.64i	0.281326	+	0.487270i
$635$	2797.50	−	4845.41i	0.174827	−	0.302810i
$636$	7668.00			0.478075
$637$		0			0
$638$	918.000			0.0569655
$639$	−4887.00	+	8464.53i	−0.302546	+	0.524025i
$640$	960.000	+	1662.77i	0.0592927	+	0.102698i
$641$	−10713.0	−	18555.5i	−0.660122	−	1.14336i	−0.980583	−	0.196103i	$-0.937171\pi$
$641$	−10713.0	−	18555.5i	−0.660122	−	1.14336i	0.320462	−	0.947262i	$-0.396162\pi$
$642$	1179.00	−	2042.09i	0.0724788	−	0.125537i
$643$	−9962.00			−0.610984			−0.305492	−	0.952195i	$-0.598821\pi$
$643$	−9962.00			−0.610984			−0.305492	+	0.952195i	$0.598821\pi$
$644$		0			0
$645$	14670.0			0.895551
$646$	−8736.00	+	15131.2i	−0.532064	+	0.921562i
$647$	−9087.00	−	15739.1i	−0.552159	−	0.956367i	−0.998119	−	0.0613142i	$-0.980471\pi$
$647$	−9087.00	−	15739.1i	−0.552159	−	0.956367i	0.445960	−	0.895053i	$-0.352863\pi$
$648$	324.000	+	561.184i	0.0196419	+	0.0340207i
$649$	−715.500	+	1239.28i	−0.0432755	+	0.0749555i
$650$	−17600.0			−1.06204
$651$		0			0
$652$	6704.00			0.402682
$653$	9583.50	−	16599.1i	0.574321	−	0.994752i	−0.421795	−	0.906691i	$-0.638600\pi$
$653$	9583.50	−	16599.1i	0.574321	−	0.994752i	0.996115	−	0.0880610i	$-0.0280670\pi$
$654$	42.0000	+	72.7461i	0.00251121	+	0.00434954i
$655$	−8797.50	−	15237.7i	−0.524804	−	0.908988i
$656$	−1344.00	+	2327.88i	−0.0799914	+	0.138549i
$657$	−1962.00			−0.116507
$658$		0			0
$659$	13080.0			0.773178			0.386589	−	0.922252i	$-0.373653\pi$
$659$	13080.0			0.773178			0.386589	+	0.922252i	$0.373653\pi$
$660$	810.000	−	1402.96i	0.0477715	−	0.0827427i
$661$	−7595.00	−	13154.9i	−0.446916	−	0.774081i	0.551268	−	0.834328i	$-0.314144\pi$
$661$	−7595.00	−	13154.9i	−0.446916	−	0.774081i	−0.998183	+	0.0602477i	$0.980811\pi$
$662$	−3964.00	−	6865.85i	−0.232727	−	0.403095i
$663$	−11088.0	+	19205.0i	−0.649506	+	1.12498i
$664$	−4776.00			−0.279134
$665$		0			0
$666$	−792.000			−0.0460801
$667$	2142.00	−	3710.05i	0.124346	−	0.215373i
$668$	6060.00	+	10496.2i	0.351001	+	0.607951i
$669$	−2359.50	−	4086.77i	−0.136358	−	0.236179i
$670$	−2490.00	+	4312.81i	−0.143578	+	0.248684i
$671$	6498.00			0.373849
$672$		0			0
$673$	4397.00			0.251845			0.125923	−	0.992040i	$-0.459811\pi$
$673$	4397.00			0.251845			0.125923	+	0.992040i	$0.459811\pi$
$674$	161.000	−	278.860i	0.00920102	−	0.0159366i
$675$	−1350.00	−	2338.27i	−0.0769800	−	0.133333i
$676$	−11094.0	−	19215.4i	−0.631202	−	1.09327i
$677$	2014.50	−	3489.22i	0.114363	−	0.198082i	−0.803162	−	0.595761i	$-0.796851\pi$
$677$	2014.50	−	3489.22i	0.114363	−	0.198082i	0.917525	+	0.397679i	$0.130184\pi$
$678$	13104.0			0.742266
$679$		0			0
$680$	−10080.0			−0.568456
$681$	1381.50	−	2392.83i	0.0777374	−	0.134645i
$682$	1665.00	+	2883.86i	0.0934841	+	0.161919i
$683$	−7510.50	−	13008.6i	−0.420763	−	0.728783i	0.575251	−	0.817977i	$-0.304904\pi$
$683$	−7510.50	−	13008.6i	−0.420763	−	0.728783i	−0.996014	+	0.0891936i	$0.971571\pi$
$684$	1872.00	−	3242.40i	0.104646	−	0.181252i
$685$	450.000			0.0251002
$686$		0			0
$687$	−12156.0			−0.675081
$688$	−2608.00	+	4517.19i	−0.144519	+	0.250314i
$689$	−28116.0	−	48698.3i	−1.55462	−	2.69268i
$690$	−3780.00	−	6547.15i	−0.208554	−	0.361226i
$691$	−6992.00	+	12110.5i	−0.384932	+	0.666722i	−0.991760	−	0.128111i	$-0.959109\pi$
$691$	−6992.00	+	12110.5i	−0.384932	+	0.666722i	0.606828	+	0.794834i	$0.292442\pi$
$692$	−13752.0			−0.755452
$693$		0			0
$694$	11832.0			0.647171
$695$	−615.000	+	1065.21i	−0.0335659	+	0.0581378i
$696$	612.000	+	1060.02i	0.0333302	+	0.0577296i
$697$	−7056.00	−	12221.4i	−0.383451	−	0.664156i
$698$	142.000	−	245.951i	0.00770026	−	0.0133372i
$699$	−1404.00			−0.0759716
$700$		0			0
$701$	−31053.0			−1.67312			−0.836559	−	0.547877i	$-0.815436\pi$
$701$	−31053.0			−1.67312			−0.836559	+	0.547877i	$0.815436\pi$
$702$	2376.00	−	4115.35i	0.127744	−	0.221259i
$703$	2288.00	+	3962.93i	0.122750	+	0.212610i
$704$	288.000	+	498.831i	0.0154182	+	0.0267051i
$705$	−3105.00	+	5378.02i	−0.165874	+	0.287302i
$706$	−8880.00			−0.473376
$707$		0			0
$708$	−1908.00			−0.101281
$709$	−7543.00	+	13064.9i	−0.399553	+	0.692047i	−0.993671	−	0.112332i	$-0.964168\pi$
$709$	−7543.00	+	13064.9i	−0.399553	+	0.692047i	0.594117	+	0.804378i	$0.297501\pi$
$710$	16290.0	+	28215.1i	0.861060	+	1.49140i
$711$	2623.50	+	4544.04i	0.138381	+	0.239683i
$712$	4152.00	−	7191.47i	0.218543	−	0.378528i
$713$	15540.0			0.816238
$714$		0			0
$715$	−11880.0			−0.621380
$716$	2424.00	−	4198.49i	0.126521	−	0.219141i
$717$	−7398.00	−	12813.7i	−0.385332	−	0.667415i
$718$	2286.00	+	3959.47i	0.118820	+	0.205802i
$719$	−3189.00	+	5523.51i	−0.165410	+	0.286498i	−0.936801	−	0.349863i	$-0.886228\pi$
$719$	−3189.00	+	5523.51i	−0.165410	+	0.286498i	0.771391	+	0.636362i	$0.219561\pi$
$720$	2160.00			0.111803
$721$		0			0
$722$	−7914.00			−0.407934
$723$	−2305.50	+	3993.24i	−0.118593	+	0.205408i
$724$	6064.00	+	10503.2i	0.311280	+	0.539153i
$725$	−2550.00	−	4416.73i	−0.130627	−	0.226253i
$726$	−3750.00	+	6495.19i	−0.191702	+	0.332037i
$727$	7363.00			0.375624			0.187812	−	0.982205i	$-0.439860\pi$
$727$	7363.00			0.375624			0.187812	+	0.982205i	$0.439860\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−3270.00	+	5663.81i	−0.165792	+	0.287160i
$731$	−13692.0	−	23715.2i	−0.692773	−	1.19992i
$732$	4332.00	+	7503.24i	0.218737	+	0.378863i
$733$	16405.0	−	28414.3i	0.826647	−	1.43180i	−0.0740064	−	0.997258i	$-0.523579\pi$
$733$	16405.0	−	28414.3i	0.826647	−	1.43180i	0.900654	−	0.434537i	$-0.143088\pi$
$734$	−5738.00			−0.288547
$735$		0			0
$736$	2688.00			0.134621
$737$	−747.000	+	1293.84i	−0.0373353	+	0.0646666i
$738$	1512.00	+	2618.86i	0.0754167	+	0.130625i
$739$	12017.0	+	20814.1i	0.598177	+	1.03607i	0.993090	+	0.117354i	$0.0374412\pi$
$739$	12017.0	+	20814.1i	0.598177	+	1.03607i	−0.394914	+	0.918718i	$0.629225\pi$
$740$	−1320.00	+	2286.31i	−0.0655732	+	0.113576i
$741$	−27456.0			−1.36116
$742$		0			0
$743$	−8022.00			−0.396095			−0.198048	−	0.980192i	$-0.563460\pi$
$743$	−8022.00			−0.396095			−0.198048	+	0.980192i	$0.563460\pi$
$744$	−2220.00	+	3845.15i	−0.109394	+	0.189476i
$745$	10755.0	+	18628.2i	0.528903	+	0.916087i
$746$	−3064.00	−	5307.00i	−0.150377	−	0.260460i
$747$	−2686.50	+	4653.15i	−0.131585	+	0.227912i
$748$	−3024.00			−0.147819
$749$		0			0
$750$	2250.00			0.109545
$751$	−14759.5	+	25564.2i	−0.717153	+	1.24215i	0.244970	+	0.969531i	$0.421222\pi$
$751$	−14759.5	+	25564.2i	−0.717153	+	1.24215i	−0.962123	+	0.272615i	$0.912112\pi$
$752$	−1104.00	−	1912.18i	−0.0535356	−	0.0927263i
$753$	7978.50	+	13819.2i	0.386126	+	0.668789i
$754$	4488.00	−	7773.44i	0.216768	−	0.375454i
$755$	−40065.0			−1.93128
$756$		0			0
$757$	−3742.00			−0.179664			−0.0898318	−	0.995957i	$-0.528633\pi$
$757$	−3742.00			−0.179664			−0.0898318	+	0.995957i	$0.528633\pi$
$758$	−6040.00	+	10461.6i	−0.289423	+	0.501295i
$759$	−1134.00	−	1964.15i	−0.0542313	−	0.0939314i
$760$	−6240.00	−	10808.0i	−0.297827	−	0.515852i
$761$	−5448.00	+	9436.21i	−0.259514	+	0.449491i	−0.966112	−	0.258124i	$-0.916896\pi$
$761$	−5448.00	+	9436.21i	−0.259514	+	0.449491i	0.706598	+	0.707615i	$0.250229\pi$
$762$	2238.00			0.106397
$763$		0			0
$764$	10080.0			0.477332
$765$	−5670.00	+	9820.73i	−0.267973	+	0.464143i
$766$	−1842.00	−	3190.44i	−0.0868853	−	0.150490i
$767$	6996.00	+	12117.4i	0.329349	+	0.570450i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−17285.0			−0.810550			−0.405275	−	0.914195i	$-0.632824\pi$
$769$	−17285.0			−0.810550			−0.405275	+	0.914195i	$0.632824\pi$
$770$		0			0
$771$	−16038.0			−0.749150
$772$	−730.000	+	1264.40i	−0.0340327	+	0.0589464i
$773$	5913.00	+	10241.6i	0.275130	+	0.476540i	0.970168	−	0.242434i	$-0.0779456\pi$
$773$	5913.00	+	10241.6i	0.275130	+	0.476540i	−0.695038	+	0.718973i	$0.744612\pi$
$774$	2934.00	+	5081.84i	0.136254	+	0.235999i
$775$	9250.00	−	16021.5i	0.428735	−	0.742591i
$776$	−1352.00			−0.0625438
$777$		0			0
$778$	−15660.0			−0.721643
$779$	8736.00	−	15131.2i	0.401797	−	0.695932i
$780$	−7920.00	−	13717.8i	−0.363566	−	0.629715i
$781$	4887.00	+	8464.53i	0.223906	+	0.387817i
$782$	−7056.00	+	12221.4i	−0.322662	+	0.558868i
$783$	1377.00			0.0628480
$784$		0			0
$785$	−33780.0			−1.53587
$786$	3519.00	−	6095.09i	0.159693	−	0.276596i
$787$	8857.00	+	15340.8i	0.401166	+	0.694841i	0.993867	−	0.110582i	$-0.0352716\pi$
$787$	8857.00	+	15340.8i	0.401166	+	0.694841i	−0.592701	+	0.805423i	$0.701938\pi$
$788$	3180.00	+	5507.92i	0.143760	+	0.248999i
$789$	−1161.00	+	2010.91i	−0.0523862	+	0.0907355i
$790$	17490.0			0.787679
$791$		0			0
$792$	648.000			0.0290728
$793$	31768.0	−	55023.8i	1.42259	−	2.46400i
$794$	14764.0	+	25572.0i	0.659893	+	1.14297i
$795$	−14377.5	−	24902.6i	−0.641406	−	1.11095i
$796$	−10760.0	+	18636.9i	−0.479118	+	0.829857i
$797$	24939.0			1.10839			0.554194	−	0.832388i	$-0.313027\pi$
$797$	24939.0			1.10839			0.554194	+	0.832388i	$0.313027\pi$
$798$		0			0
$799$	11592.0			0.513261
$800$	1600.00	−	2771.28i	0.0707107	−	0.122474i
$801$	−4671.00	−	8090.41i	−0.206045	−	0.356880i
$802$	6264.00	+	10849.6i	0.275797	+	0.477695i
$803$	−981.000	+	1699.14i	−0.0431118	+	0.0746717i
$804$	−1992.00			−0.0873786
$805$		0			0
$806$	32560.0			1.42292
$807$	3622.50	−	6274.35i	0.158015	−	0.273690i
$808$	−2568.00	−	4447.91i	−0.111809	−	0.193659i
$809$	14532.0	+	25170.2i	0.631543	+	1.09386i	0.987236	+	0.159261i	$0.0509112\pi$
$809$	14532.0	+	25170.2i	0.631543	+	1.09386i	−0.355694	+	0.934602i	$0.615755\pi$
$810$	1215.00	−	2104.44i	0.0527046	−	0.0912871i
$811$	15370.0			0.665492			0.332746	−	0.943017i	$-0.392025\pi$
$811$	15370.0			0.665492			0.332746	+	0.943017i	$0.392025\pi$
$812$		0			0
$813$	1425.00			0.0614722
$814$	−396.000	+	685.892i	−0.0170513	+	0.0295338i
$815$	−12570.0	−	21771.9i	−0.540255	−	0.935749i
$816$	−2016.00	−	3491.81i	−0.0864879	−	0.149801i
$817$	16952.0	−	29361.7i	0.725918	−	1.25733i
$818$	9502.00			0.406149
$819$		0			0
$820$	10080.0			0.429279
$821$	−22015.5	+	38132.0i	−0.935866	+	1.62097i	−0.162785	+	0.986662i	$0.552048\pi$
$821$	−22015.5	+	38132.0i	−0.935866	+	1.62097i	−0.773082	+	0.634306i	$0.781286\pi$
$822$	90.0000	+	155.885i	0.00381887	+	0.00661448i
$823$	2096.00	+	3630.38i	0.0887752	+	0.153763i	0.906994	−	0.421144i	$-0.138371\pi$
$823$	2096.00	+	3630.38i	0.0887752	+	0.153763i	−0.818218	+	0.574907i	$0.805038\pi$
$824$	−1856.00	+	3214.69i	−0.0784670	+	0.135909i
$825$	−2700.00			−0.113942
$826$		0			0
$827$	33195.0			1.39577			0.697886	−	0.716209i	$-0.254124\pi$
$827$	33195.0			1.39577			0.697886	+	0.716209i	$0.254124\pi$
$828$	1512.00	−	2618.86i	0.0634609	−	0.109918i
$829$	8224.00	+	14244.4i	0.344549	+	0.596777i	0.985272	−	0.170996i	$-0.0546984\pi$
$829$	8224.00	+	14244.4i	0.344549	+	0.596777i	−0.640723	+	0.767773i	$0.721365\pi$
$830$	8955.00	+	15510.5i	0.374497	+	0.648648i
$831$	−5592.00	+	9685.63i	−0.233435	+	0.404321i
$832$	5632.00			0.234681
$833$		0			0
$834$	−492.000			−0.0204275
$835$	22725.0	−	39360.9i	0.941834	−	1.63130i
$836$	−1872.00	−	3242.40i	−0.0774455	−	0.134140i
$837$	2497.50	+	4325.80i	0.103138	+	0.178640i
$838$	4704.00	−	8147.57i	0.193910	−	0.335863i
$839$	−16860.0			−0.693769			−0.346884	−	0.937908i	$-0.612760\pi$
$839$	−16860.0			−0.693769			−0.346884	+	0.937908i	$0.612760\pi$
$840$		0			0
$841$	−21788.0			−0.893354
$842$	−4474.00	+	7749.20i	−0.183117	+	0.317167i
$843$	−2403.00	−	4162.12i	−0.0981776	−	0.170049i
$844$	10724.0	+	18574.5i	0.437364	+	0.757537i
$845$	−41602.5	+	72057.6i	−1.69369	+	2.93356i
$846$	−2484.00			−0.100948
$847$		0			0
$848$	10224.0			0.414025
$849$	1029.00	−	1782.28i	0.0415962	−	0.0720468i
$850$	8400.00	+	14549.2i	0.338962	+	0.587099i
$851$	1848.00	+	3200.83i	0.0744402	+	0.128934i
$852$	−6516.00	+	11286.0i	−0.262012	+	0.453819i
$853$	−29054.0			−1.16623			−0.583113	−	0.812391i	$-0.698165\pi$
$853$	−29054.0			−1.16623			−0.583113	+	0.812391i	$0.698165\pi$
$854$		0			0
$855$	−14040.0			−0.561588
$856$	1572.00	−	2722.78i	0.0627685	−	0.108718i
$857$	20979.0	+	36336.7i	0.836207	+	1.44835i	0.893044	+	0.449969i	$0.148565\pi$
$857$	20979.0	+	36336.7i	0.836207	+	1.44835i	−0.0568378	+	0.998383i	$0.518102\pi$
$858$	−2376.00	−	4115.35i	−0.0945400	−	0.163748i
$859$	2773.00	−	4802.98i	0.110144	−	0.190775i	−0.805684	−	0.592345i	$-0.798202\pi$
$859$	2773.00	−	4802.98i	0.110144	−	0.190775i	0.915828	+	0.401570i	$0.131536\pi$
$860$	19560.0			0.775570
$861$		0			0
$862$	25608.0			1.01185
$863$	16269.0	−	28178.7i	0.641719	−	1.11149i	−0.343330	−	0.939215i	$-0.611555\pi$
$863$	16269.0	−	28178.7i	0.641719	−	1.11149i	0.985049	−	0.172275i	$-0.0551116\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	25785.0	+	44660.9i	1.01354	+	1.75551i
$866$	5074.00	−	8788.43i	0.199101	−	0.344853i
$867$	6429.00			0.251834
$868$		0			0
$869$	5247.00			0.204824
$870$	2295.00	−	3975.06i	0.0894342	−	0.154905i
$871$	7304.00	+	12650.9i	0.284141	+	0.492146i
$872$	56.0000	+	96.9948i	0.00217477	+	0.00376681i
$873$	−760.500	+	1317.22i	−0.0294834	+	0.0510668i
$874$	−17472.0			−0.676200
$875$		0			0
$876$	−2616.00			−0.100898
$877$	−16048.0	+	27796.0i	−0.617905	+	1.07024i	0.371963	+	0.928248i	$0.378685\pi$
$877$	−16048.0	+	27796.0i	−0.617905	+	1.07024i	−0.989867	+	0.141995i	$0.954648\pi$
$878$	1267.00	+	2194.51i	0.0487007	+	0.0843520i
$879$	−1651.50	−	2860.48i	−0.0633717	−	0.109763i
$880$	1080.00	−	1870.61i	0.0413714	−	0.0716573i
$881$	8490.00			0.324671			0.162336	−	0.986736i	$-0.448097\pi$
$881$	8490.00			0.324671			0.162336	+	0.986736i	$0.448097\pi$
$882$		0			0
$883$	−48352.0			−1.84278			−0.921390	−	0.388640i	$-0.872945\pi$
$883$	−48352.0			−1.84278			−0.921390	+	0.388640i	$0.872945\pi$
$884$	−14784.0	+	25606.6i	−0.562488	+	0.974258i
$885$	3577.50	+	6196.41i	0.135883	+	0.235356i
$886$	−6933.00	−	12008.3i	−0.262888	−	0.455335i
$887$	7746.00	−	13416.5i	0.293219	−	0.507870i	−0.681350	−	0.731958i	$-0.738607\pi$
$887$	7746.00	−	13416.5i	0.293219	−	0.507870i	0.974569	+	0.224088i	$0.0719402\pi$
$888$	−1056.00			−0.0399066
$889$		0			0
$890$	−31140.0			−1.17283
$891$	364.500	−	631.333i	0.0137051	−	0.0237379i
$892$	−3146.00	−	5449.03i	−0.118090	−	0.204537i
$893$	7176.00	+	12429.2i	0.268909	+	0.465764i
$894$	−4302.00	+	7451.28i	−0.160940	+	0.278756i
$895$	−18180.0			−0.678984
$896$		0			0
$897$	−22176.0			−0.825457
$898$	11688.0	−	20244.2i	0.434336	−	0.752292i
$899$	4717.50	+	8170.95i	0.175014	+	0.303133i
$900$	−1800.00	−	3117.69i	−0.0666667	−	0.115470i
$901$	−26838.0	+	46484.8i	−0.992346	+	1.71879i
$902$	3024.00			0.111628
$903$		0			0
$904$	17472.0			0.642821
$905$	22740.0	−	39386.8i	0.835252	−	1.44670i
$906$	−8013.00	−	13878.9i	−0.293835	−	0.508936i
$907$	4058.00	+	7028.66i	0.148560	+	0.257313i	0.930695	−	0.365795i	$-0.119203\pi$
$907$	4058.00	+	7028.66i	0.148560	+	0.257313i	−0.782136	+	0.623108i	$0.785870\pi$
$908$	1842.00	−	3190.44i	0.0673226	−	0.116606i
$909$	−5778.00			−0.210830
$910$		0			0
$911$	−4446.00			−0.161693			−0.0808466	−	0.996727i	$-0.525762\pi$
$911$	−4446.00			−0.161693			−0.0808466	+	0.996727i	$0.525762\pi$
$912$	2496.00	−	4323.20i	0.0906259	−	0.156969i
$913$	2686.50	+	4653.15i	0.0973824	+	0.168671i
$914$	551.000	+	954.360i	0.0199403	+	0.0345377i
$915$	16245.0	−	28137.2i	0.586932	−	1.01660i
$916$	−16208.0			−0.584637
$917$		0			0
$918$	−4536.00			−0.163083
$919$	−13252.0	+	22953.1i	−0.475673	+	0.823889i	−0.999612	−	0.0278666i	$-0.991129\pi$
$919$	−13252.0	+	22953.1i	−0.475673	+	0.823889i	0.523939	+	0.851756i	$0.324462\pi$
$920$	−5040.00	−	8729.54i	−0.180613	−	0.312831i
$921$	4170.00	+	7222.65i	0.149192	+	0.258409i
$922$	−13386.0	+	23185.2i	−0.478139	+	0.828162i
$923$	95568.0			3.40808
$924$		0			0
$925$	4400.00			0.156401
$926$	−6376.00	+	11043.6i	−0.226273	+	0.391916i
$927$	2088.00	+	3616.52i	0.0739794	+	0.128136i
$928$	816.000	+	1413.35i	0.0288648	+	0.0499953i
$929$	−2715.00	+	4702.52i	−0.0958840	+	0.166076i	−0.909977	−	0.414658i	$-0.863901\pi$
$929$	−2715.00	+	4702.52i	−0.0958840	+	0.166076i	0.814093	+	0.580734i	$0.197234\pi$
$930$	16650.0			0.587070
$931$		0			0
$932$	−1872.00			−0.0657933
$933$	6444.00	−	11161.3i	0.226117	−	0.391646i
$934$	−5700.00	−	9872.69i	−0.199689	−	0.345872i
$935$	5670.00	+	9820.73i	0.198320	+	0.343500i
$936$	3168.00	−	5487.14i	0.110630	−	0.191616i
$937$	−33803.0			−1.17854			−0.589272	−	0.807935i	$-0.700585\pi$
$937$	−33803.0			−1.17854			−0.589272	+	0.807935i	$0.700585\pi$
$938$		0			0
$939$	−16467.0			−0.572290
$940$	−4140.00	+	7170.69i	−0.143651	+	0.248811i
$941$	−24241.5	−	41987.5i	−0.839798	−	1.45457i	−0.890063	−	0.455838i	$-0.849340\pi$
$941$	−24241.5	−	41987.5i	−0.839798	−	1.45457i	0.0502645	−	0.998736i	$-0.483994\pi$
$942$	−6756.00	−	11701.7i	−0.233676	−	0.404738i
$943$	7056.00	−	12221.4i	0.243664	−	0.422038i
$944$	−2544.00			−0.0877120
$945$		0			0
$946$	5868.00			0.201676
$947$	−18648.0	+	32299.3i	−0.639893	+	1.10833i	0.345563	+	0.938396i	$0.387688\pi$
$947$	−18648.0	+	32299.3i	−0.639893	+	1.10833i	−0.985456	+	0.169931i	$0.945645\pi$
$948$	3498.00	+	6058.71i	0.119842	+	0.207572i
$949$	9592.00	+	16613.8i	0.328103	+	0.568291i
$950$	−10400.0	+	18013.3i	−0.355180	+	0.615189i
$951$	13473.0			0.459403
$952$		0			0
$953$	−38478.0			−1.30790			−0.653948	−	0.756540i	$-0.726888\pi$
$953$	−38478.0			−1.30790			−0.653948	+	0.756540i	$0.726888\pi$
$954$	5751.00	−	9961.02i	0.195173	−	0.338050i
$955$	−18900.0	−	32735.8i	−0.640408	−	1.10922i
$956$	−9864.00	−	17084.9i	−0.333708	−	0.577999i
$957$	688.500	−	1192.52i	0.0232561	−	0.0402807i
$958$	39588.0			1.33510
$959$		0			0
$960$	2880.00			0.0968246
$961$	−2217.00	+	3839.96i	−0.0744184	+	0.128897i
$962$	3872.00	+	6706.50i	0.129770	+	0.224767i
$963$	−1768.50	−	3063.13i	−0.0591787	−	0.102501i
$964$	−3074.00	+	5324.32i	−0.102704	+	0.177889i
$965$	5475.00			0.182639
$966$		0			0
$967$	27257.0			0.906438			0.453219	−	0.891399i	$-0.350275\pi$
$967$	27257.0			0.906438			0.453219	+	0.891399i	$0.350275\pi$
$968$	−5000.00	+	8660.25i	−0.166019	+	0.287553i
$969$	13104.0	+	22696.8i	0.434428	+	0.752452i
$970$	2535.00	+	4390.75i	0.0839113	+	0.145339i
$971$	17170.5	−	29740.2i	0.567485	−	0.982912i	−0.429329	−	0.903148i	$-0.641250\pi$
$971$	17170.5	−	29740.2i	0.567485	−	0.982912i	0.996814	−	0.0797641i	$-0.0254167\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	−31870.0			−1.04844
$975$	−13200.0	+	22863.1i	−0.433578	+	0.750979i
$976$	5776.00	+	10004.3i	0.189432	+	0.328105i
$977$	−13713.0	−	23751.6i	−0.449046	−	0.777770i	0.549278	−	0.835639i	$-0.314903\pi$
$977$	−13713.0	−	23751.6i	−0.449046	−	0.777770i	−0.998324	+	0.0578693i	$0.981569\pi$
$978$	5028.00	−	8708.75i	0.164394	−	0.284739i
$979$	−9342.00			−0.304976
$980$		0			0
$981$	126.000			0.00410079
$982$	9963.00	−	17256.4i	0.323760	−	0.560768i
$983$	6162.00	+	10672.9i	0.199936	+	0.346300i	0.948508	−	0.316755i	$-0.102593\pi$
$983$	6162.00	+	10672.9i	0.199936	+	0.346300i	−0.748571	+	0.663054i	$0.769260\pi$
$984$	2016.00	+	3491.81i	0.0653127	+	0.113125i
$985$	11925.0	−	20654.7i	0.385748	−	0.668136i
$986$	−8568.00			−0.276735
$987$		0			0
$988$	−36608.0			−1.17880
$989$	13692.0	−	23715.2i	0.440223	−	0.762488i
$990$	−1215.00	−	2104.44i	−0.0390053	−	0.0675591i
$991$	−23798.5	−	41220.2i	−0.762850	−	1.32129i	−0.941376	−	0.337360i	$-0.890466\pi$
$991$	−23798.5	−	41220.2i	−0.762850	−	1.32129i	0.178526	−	0.983935i	$-0.442867\pi$
$992$	−2960.00	+	5126.87i	−0.0947380	+	0.164091i
$993$	−11892.0			−0.380042
$994$		0			0
$995$	80700.0			2.57122
$996$	−3582.00	+	6204.21i	−0.113956	+	0.197377i
$997$	−5621.00	−	9735.86i	−0.178555	−	0.309266i	0.762831	−	0.646598i	$-0.223809\pi$
$997$	−5621.00	−	9735.86i	−0.178555	−	0.309266i	−0.941386	+	0.337332i	$0.890475\pi$
$998$	19142.0	+	33154.9i	0.607144	+	1.05160i
$999$	−594.000	+	1028.84i	−0.0188121	+	0.0325836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.e.79.1		2
3.2	odd	2		882.4.g.l.667.1		2
7.2	even	3		294.4.a.g.1.1		1
7.3	odd	6		42.4.e.b.25.1	✓	2
7.4	even	3	inner	294.4.e.e.67.1		2
7.5	odd	6		294.4.a.a.1.1		1
7.6	odd	2		42.4.e.b.37.1	yes	2
21.2	odd	6		882.4.a.h.1.1		1
21.5	even	6		882.4.a.r.1.1		1
21.11	odd	6		882.4.g.l.361.1		2
21.17	even	6		126.4.g.a.109.1		2
21.20	even	2		126.4.g.a.37.1		2
28.3	even	6		336.4.q.d.193.1		2
28.19	even	6		2352.4.a.u.1.1		1
28.23	odd	6		2352.4.a.q.1.1		1
28.27	even	2		336.4.q.d.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.b.25.1	✓	2	7.3	odd	6
42.4.e.b.37.1	yes	2	7.6	odd	2
126.4.g.a.37.1		2	21.20	even	2
126.4.g.a.109.1		2	21.17	even	6
294.4.a.a.1.1		1	7.5	odd	6
294.4.a.g.1.1		1	7.2	even	3
294.4.e.e.67.1		2	7.4	even	3	inner
294.4.e.e.79.1		2	1.1	even	1	trivial
336.4.q.d.193.1		2	28.3	even	6
336.4.q.d.289.1		2	28.27	even	2
882.4.a.h.1.1		1	21.2	odd	6
882.4.a.r.1.1		1	21.5	even	6
882.4.g.l.361.1		2	21.11	odd	6
882.4.g.l.667.1		2	3.2	odd	2
2352.4.a.q.1.1		1	28.23	odd	6
2352.4.a.u.1.1		1	28.19	even	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(15.0000 + 25.9808i) q^{10} +(4.50000 + 7.79423i) q^{11} +(-6.00000 + 10.3923i) q^{12} +88.0000 q^{13} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(52.0000 - 90.0666i) q^{19} +60.0000 q^{20} +18.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-50.0000 - 86.6025i) q^{25} +(88.0000 - 152.420i) q^{26} +27.0000 q^{27} +51.0000 q^{29} +(45.0000 - 77.9423i) q^{30} +(92.5000 + 160.215i) q^{31} +(16.0000 + 27.7128i) q^{32} +(13.5000 - 23.3827i) q^{33} -168.000 q^{34} +36.0000 q^{36} +(-22.0000 + 38.1051i) q^{37} +(-104.000 - 180.133i) q^{38} +(-132.000 - 228.631i) q^{39} +(60.0000 - 103.923i) q^{40} +168.000 q^{41} +326.000 q^{43} +(18.0000 - 31.1769i) q^{44} +(-67.5000 - 116.913i) q^{45} +(-84.0000 - 145.492i) q^{46} +(-69.0000 + 119.512i) q^{47} +48.0000 q^{48} -200.000 q^{50} +(-126.000 + 218.238i) q^{51} +(-176.000 - 304.841i) q^{52} +(-319.500 - 553.390i) q^{53} +(27.0000 - 46.7654i) q^{54} -135.000 q^{55} -312.000 q^{57} +(51.0000 - 88.3346i) q^{58} +(79.5000 + 137.698i) q^{59} +(-90.0000 - 155.885i) q^{60} +(361.000 - 625.270i) q^{61} +370.000 q^{62} +64.0000 q^{64} +(-660.000 + 1143.15i) q^{65} +(-27.0000 - 46.7654i) q^{66} +(83.0000 + 143.760i) q^{67} +(-168.000 + 290.985i) q^{68} -252.000 q^{69} +1086.00 q^{71} +(36.0000 - 62.3538i) q^{72} +(109.000 + 188.794i) q^{73} +(44.0000 + 76.2102i) q^{74} +(-150.000 + 259.808i) q^{75} -416.000 q^{76} -528.000 q^{78} +(291.500 - 504.893i) q^{79} +(-120.000 - 207.846i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(168.000 - 290.985i) q^{82} +597.000 q^{83} +1260.00 q^{85} +(326.000 - 564.649i) q^{86} +(-76.5000 - 132.502i) q^{87} +(-36.0000 - 62.3538i) q^{88} +(-519.000 + 898.934i) q^{89} -270.000 q^{90} -336.000 q^{92} +(277.500 - 480.644i) q^{93} +(138.000 + 239.023i) q^{94} +(780.000 + 1351.00i) q^{95} +(48.0000 - 83.1384i) q^{96} +169.000 q^{97} -81.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 15 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 15 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} - 15 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9} + 30 q^{10} + 9 q^{11} - 12 q^{12} + 176 q^{13} + 90 q^{15} - 16 q^{16} - 84 q^{17} + 18 q^{18} + 104 q^{19} + 120 q^{20} + 36 q^{22} + 84 q^{23} + 24 q^{24} - 100 q^{25} + 176 q^{26} + 54 q^{27} + 102 q^{29} + 90 q^{30} + 185 q^{31} + 32 q^{32} + 27 q^{33} - 336 q^{34} + 72 q^{36} - 44 q^{37} - 208 q^{38} - 264 q^{39} + 120 q^{40} + 336 q^{41} + 652 q^{43} + 36 q^{44} - 135 q^{45} - 168 q^{46} - 138 q^{47} + 96 q^{48} - 400 q^{50} - 252 q^{51} - 352 q^{52} - 639 q^{53} + 54 q^{54} - 270 q^{55} - 624 q^{57} + 102 q^{58} + 159 q^{59} - 180 q^{60} + 722 q^{61} + 740 q^{62} + 128 q^{64} - 1320 q^{65} - 54 q^{66} + 166 q^{67} - 336 q^{68} - 504 q^{69} + 2172 q^{71} + 72 q^{72} + 218 q^{73} + 88 q^{74} - 300 q^{75} - 832 q^{76} - 1056 q^{78} + 583 q^{79} - 240 q^{80} - 81 q^{81} + 336 q^{82} + 1194 q^{83} + 2520 q^{85} + 652 q^{86} - 153 q^{87} - 72 q^{88} - 1038 q^{89} - 540 q^{90} - 672 q^{92} + 555 q^{93} + 276 q^{94} + 1560 q^{95} + 96 q^{96} + 338 q^{97} - 162 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 - 15 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9 + 30 * q^10 + 9 * q^11 - 12 * q^12 + 176 * q^13 + 90 * q^15 - 16 * q^16 - 84 * q^17 + 18 * q^18 + 104 * q^19 + 120 * q^20 + 36 * q^22 + 84 * q^23 + 24 * q^24 - 100 * q^25 + 176 * q^26 + 54 * q^27 + 102 * q^29 + 90 * q^30 + 185 * q^31 + 32 * q^32 + 27 * q^33 - 336 * q^34 + 72 * q^36 - 44 * q^37 - 208 * q^38 - 264 * q^39 + 120 * q^40 + 336 * q^41 + 652 * q^43 + 36 * q^44 - 135 * q^45 - 168 * q^46 - 138 * q^47 + 96 * q^48 - 400 * q^50 - 252 * q^51 - 352 * q^52 - 639 * q^53 + 54 * q^54 - 270 * q^55 - 624 * q^57 + 102 * q^58 + 159 * q^59 - 180 * q^60 + 722 * q^61 + 740 * q^62 + 128 * q^64 - 1320 * q^65 - 54 * q^66 + 166 * q^67 - 336 * q^68 - 504 * q^69 + 2172 * q^71 + 72 * q^72 + 218 * q^73 + 88 * q^74 - 300 * q^75 - 832 * q^76 - 1056 * q^78 + 583 * q^79 - 240 * q^80 - 81 * q^81 + 336 * q^82 + 1194 * q^83 + 2520 * q^85 + 652 * q^86 - 153 * q^87 - 72 * q^88 - 1038 * q^89 - 540 * q^90 - 672 * q^92 + 555 * q^93 + 276 * q^94 + 1560 * q^95 + 96 * q^96 + 338 * q^97 - 162 * q^99

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