LMFDB - Embedded newform 350.2.e.h.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.e (of order $3$, degree $2$, 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:	$2.79476407074$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.51
Dual form			350.2.e.h.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} -5.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} +(-5.00000 - 1.73205i) q^{21} -3.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-2.50000 + 4.33013i) q^{26} -4.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +6.00000 q^{34} +1.00000 q^{36} +(5.50000 - 9.52628i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(5.00000 + 8.66025i) q^{39} +3.00000 q^{41} +(-4.00000 + 3.46410i) q^{42} +10.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(1.50000 - 2.59808i) q^{47} +2.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{51} +(2.50000 + 4.33013i) q^{52} +(1.50000 + 2.59808i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(-2.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(2.00000 - 3.46410i) q^{61} +4.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-5.50000 - 9.52628i) q^{74} -1.00000 q^{76} +(-7.50000 - 2.59808i) q^{77} +10.0000 q^{78} +(5.00000 - 8.66025i) q^{79} +(5.50000 + 9.52628i) q^{81} +(1.50000 - 2.59808i) q^{82} +12.0000 q^{83} +(1.00000 + 5.19615i) q^{84} +(5.00000 - 8.66025i) q^{86} +(6.00000 + 10.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} -3.00000 q^{92} +(4.00000 - 6.92820i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{96} -14.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} - 3 q^{11} - 2 q^{12} - 10 q^{13} - q^{14} - q^{16} + 6 q^{17} + q^{18} + q^{19} - 10 q^{21} - 6 q^{22} + 3 q^{23} + 2 q^{24} - 5 q^{26} - 8 q^{27} - 5 q^{28} - 12 q^{29} + 4 q^{31} + q^{32} - 6 q^{33} + 12 q^{34} + 2 q^{36} + 11 q^{37} - q^{38} + 10 q^{39} + 6 q^{41} - 8 q^{42} + 20 q^{43} - 3 q^{44} - 3 q^{46} + 3 q^{47} + 4 q^{48} + 2 q^{49} + 12 q^{51} + 5 q^{52} + 3 q^{53} - 4 q^{54} - 4 q^{56} - 4 q^{57} - 6 q^{58} + 4 q^{61} + 8 q^{62} + q^{63} + 2 q^{64} + 6 q^{66} - 4 q^{67} + 6 q^{68} - 12 q^{69} + 24 q^{71} + q^{72} - 4 q^{73} - 11 q^{74} - 2 q^{76} - 15 q^{77} + 20 q^{78} + 10 q^{79} + 11 q^{81} + 3 q^{82} + 24 q^{83} + 2 q^{84} + 10 q^{86} + 12 q^{87} + 3 q^{88} - 6 q^{89} - 20 q^{91} - 6 q^{92} + 8 q^{93} - 3 q^{94} + 2 q^{96} - 28 q^{97} - 11 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9 - 3 * q^11 - 2 * q^12 - 10 * q^13 - q^14 - q^16 + 6 * q^17 + q^18 + q^19 - 10 * q^21 - 6 * q^22 + 3 * q^23 + 2 * q^24 - 5 * q^26 - 8 * q^27 - 5 * q^28 - 12 * q^29 + 4 * q^31 + q^32 - 6 * q^33 + 12 * q^34 + 2 * q^36 + 11 * q^37 - q^38 + 10 * q^39 + 6 * q^41 - 8 * q^42 + 20 * q^43 - 3 * q^44 - 3 * q^46 + 3 * q^47 + 4 * q^48 + 2 * q^49 + 12 * q^51 + 5 * q^52 + 3 * q^53 - 4 * q^54 - 4 * q^56 - 4 * q^57 - 6 * q^58 + 4 * q^61 + 8 * q^62 + q^63 + 2 * q^64 + 6 * q^66 - 4 * q^67 + 6 * q^68 - 12 * q^69 + 24 * q^71 + q^72 - 4 * q^73 - 11 * q^74 - 2 * q^76 - 15 * q^77 + 20 * q^78 + 10 * q^79 + 11 * q^81 + 3 * q^82 + 24 * q^83 + 2 * q^84 + 10 * q^86 + 12 * q^87 + 3 * q^88 - 6 * q^89 - 20 * q^91 - 6 * q^92 + 8 * q^93 - 3 * q^94 + 2 * q^96 - 28 * q^97 - 11 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−2.00000			−0.816497
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	−5.00000	−	1.73205i	−1.09109	−	0.377964i
$22$	−3.00000			−0.639602
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$		0			0
$26$	−2.50000	+	4.33013i	−0.490290	+	0.849208i
$27$	−4.00000			−0.769800
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	6.00000			1.02899
$35$		0			0
$36$	1.00000			0.166667
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	5.50000	−	9.52628i	0.904194	−	1.56611i	0.821995	−	0.569495i	$-0.192861\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$	5.00000	+	8.66025i	0.800641	+	1.38675i
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$	−4.00000	+	3.46410i	−0.617213	+	0.534522i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$	2.00000			0.288675
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$	6.00000	−	10.3923i	0.840168	−	1.45521i
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$		0			0
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	−2.00000			−0.264906
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	4.00000			0.508001
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$	−5.50000	−	9.52628i	−0.639362	−	1.10741i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	−7.50000	−	2.59808i	−0.854704	−	0.296078i
$78$	10.0000			1.13228
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$	1.00000	+	5.19615i	0.109109	+	0.566947i
$85$		0			0
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−10.0000	+	8.66025i	−1.04828	+	0.907841i
$92$	−3.00000			−0.312772
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$	1.00000	−	1.73205i	0.102062	−	0.176777i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$	3.00000			0.301511
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$	−6.00000	−	10.3923i	−0.594089	−	1.02899i
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	3.00000			0.291386
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$		0			0
$111$	−22.0000			−2.08815
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	2.50000	−	4.33013i	0.231125	−	0.400320i
$118$		0			0
$119$	15.0000	+	5.19615i	1.37505	+	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.00000	−	3.46410i	−0.181071	−	0.313625i
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	2.50000	+	0.866025i	0.222718	+	0.0771517i
$127$	19.0000			1.68598			0.842989	−	0.537931i	$-0.180794\pi$
$127$	19.0000			1.68598			0.842989	+	0.537931i	$0.180794\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−10.0000	−	17.3205i	−0.880451	−	1.52499i
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$	6.00000			0.522233
$133$	−0.500000	−	2.59808i	−0.0433555	−	0.225282i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	−3.00000	+	5.19615i	−0.255377	+	0.442326i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	7.50000	+	12.9904i	0.627182	+	1.08631i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	−4.00000			−0.331042
$147$	−13.0000	+	5.19615i	−1.07222	+	0.428571i
$148$	−11.0000			−0.904194
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	−6.00000			−0.485071
$154$	−6.00000	+	5.19615i	−0.483494	+	0.418718i
$155$		0			0
$156$	5.00000	−	8.66025i	0.400320	−	0.693375i
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	0.948373	−	0.317156i	$-0.102728\pi$
$157$	2.50000	+	4.33013i	0.199522	+	0.345582i	−0.748852	+	0.662738i	$0.769394\pi$
$158$	−5.00000	−	8.66025i	−0.397779	−	0.688973i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$	11.0000			0.864242
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$	5.00000	+	1.73205i	0.385758	+	0.133631i
$169$	12.0000			0.923077
$170$		0			0
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$	12.0000			0.909718
$175$		0			0
$176$	3.00000			0.226134
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.50000	+	12.9904i	0.185312	+	0.962911i
$183$	−8.00000			−0.591377
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$		0			0
$186$	−4.00000	−	6.92820i	−0.293294	−	0.508001i
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$	−3.00000			−0.218797
$189$	−8.00000	+	6.92820i	−0.581914	+	0.503953i
$190$		0			0
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	−7.00000	+	12.1244i	−0.502571	+	0.870478i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	0.928166	−	0.372168i	$-0.121385\pi$
$199$	2.00000	+	3.46410i	0.141776	+	0.245564i	−0.786389	+	0.617731i	$0.788052\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$	12.0000			0.844317
$203$	−12.0000	+	10.3923i	−0.842235	+	0.729397i
$204$	−12.0000			−0.840168
$205$		0			0
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$	1.50000	+	2.59808i	0.104257	+	0.180579i
$208$	2.50000	−	4.33013i	0.173344	−	0.300240i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	−1.00000			−0.0688428			−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000			−0.0688428			−0.0344214	+	0.999407i	$0.510959\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	−12.0000	−	20.7846i	−0.822226	−	1.42414i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		0			0
$216$	4.00000			0.272166
$217$	10.0000	+	3.46410i	0.678844	+	0.235159i
$218$	4.00000			0.270914
$219$	−4.00000	+	6.92820i	−0.270295	+	0.468165i
$220$		0			0
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$	−11.0000	+	19.0526i	−0.738272	+	1.27872i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$	2.50000	+	0.866025i	0.167038	+	0.0578638i
$225$		0			0
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$	1.00000	+	1.73205i	0.0662266	+	0.114708i
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.133820	−	0.991006i	$-0.457276\pi$
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.791326	−	0.611394i	$-0.209391\pi$
$230$		0			0
$231$	3.00000	+	15.5885i	0.197386	+	1.02565i
$232$	6.00000			0.393919
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	−2.50000	−	4.33013i	−0.163430	−	0.283069i
$235$		0			0
$236$		0			0
$237$	−20.0000			−1.29914
$238$	12.0000	−	10.3923i	0.777844	−	0.673633i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−4.00000			−0.256074
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	−12.0000	−	20.7846i	−0.760469	−	1.31717i
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	2.00000	−	1.73205i	0.125988	−	0.109109i
$253$	−9.00000			−0.565825
$254$	9.50000	−	16.4545i	0.596083	−	1.03245i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	−0.990217	−	0.139533i	$-0.955440\pi$
$257$	−6.00000	+	10.3923i	−0.374270	+	0.648254i	0.615948	+	0.787787i	$0.288773\pi$
$258$	−20.0000			−1.24515
$259$	−5.50000	−	28.5788i	−0.341753	−	1.77580i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	1.50000	+	2.59808i	0.0926703	+	0.160510i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$	−2.50000	−	0.866025i	−0.153285	−	0.0530994i
$267$	12.0000			0.734388
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	0.988908	−	0.148527i	$-0.0474530\pi$
$269$	6.00000	+	10.3923i	0.365826	+	0.633630i	−0.623082	+	0.782157i	$0.714120\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−6.00000			−0.363803
$273$	25.0000	+	8.66025i	1.51307	+	0.524142i
$274$	12.0000			0.724947
$275$		0			0
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	−4.00000			−0.239474
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	0.936039	+	0.351895i	$0.114463\pi$
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	−0.163270	+	0.986581i	$0.552204\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	15.0000			0.886969
$287$	6.00000	−	5.19615i	0.354169	−	0.306719i
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	14.0000	+	24.2487i	0.820695	+	1.42148i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	27.0000			1.57736			0.788678	−	0.614806i	$-0.210766\pi$
$293$	27.0000			1.57736			0.788678	+	0.614806i	$0.210766\pi$
$294$	−2.00000	+	13.8564i	−0.116642	+	0.808122i
$295$		0			0
$296$	−5.50000	+	9.52628i	−0.319681	+	0.553704i
$297$	6.00000	+	10.3923i	0.348155	+	0.603023i
$298$	9.00000	+	15.5885i	0.521356	+	0.903015i
$299$	−7.50000	+	12.9904i	−0.433736	+	0.751253i
$300$		0			0
$301$	20.0000	−	17.3205i	1.15278	−	0.998337i
$302$	−14.0000			−0.805609
$303$	12.0000	−	20.7846i	0.689382	−	1.19404i
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		0			0
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	1.50000	+	7.79423i	0.0854704	+	0.444117i
$309$	8.00000			0.455104
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	−5.00000	−	8.66025i	−0.283069	−	0.490290i
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	5.00000			0.282166
$315$		0			0
$316$	−10.0000			−0.562544
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	24.0000			1.33955
$322$	−7.50000	−	2.59808i	−0.417959	−	0.144785i
$323$	6.00000			0.333849
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	4.00000	−	6.92820i	0.221201	−	0.383131i
$328$	−3.00000			−0.165647
$329$	−1.50000	−	7.79423i	−0.0826977	−	0.429710i
$330$		0			0
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	5.50000	+	9.52628i	0.301398	+	0.522037i
$334$	−4.50000	+	7.79423i	−0.246229	+	0.426481i
$335$		0			0
$336$	4.00000	−	3.46410i	0.218218	−	0.188982i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	12.0000	+	20.7846i	0.651751	+	1.12887i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	1.00000			0.0540738
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	−1.50000	−	2.59808i	−0.0806405	−	0.139673i
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$	6.00000	−	10.3923i	0.321634	−	0.557086i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	0.980352	−	0.197256i	$-0.0632029\pi$
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	−0.661004	+	0.750382i	$0.729870\pi$
$354$		0			0
$355$		0			0
$356$	6.00000			0.317999
$357$	−6.00000	−	31.1769i	−0.317554	−	1.65006i
$358$	3.00000			0.158555
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	−0.934268	−	0.356572i	$-0.883946\pi$
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	0.775934	+	0.630814i	$0.217279\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	1.00000	−	1.73205i	0.0525588	−	0.0910346i
$363$	−4.00000			−0.209946
$364$	12.5000	+	4.33013i	0.655178	+	0.226960i
$365$		0			0
$366$	−4.00000	+	6.92820i	−0.209083	+	0.362143i
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	0.852680	−	0.522433i	$-0.174975\pi$
$367$	−0.500000	−	0.866025i	−0.0260998	−	0.0452062i	−0.878780	+	0.477227i	$0.841642\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$	−1.50000	+	2.59808i	−0.0780869	+	0.135250i
$370$		0			0
$371$	7.50000	+	2.59808i	0.389381	+	0.134885i
$372$	−8.00000			−0.414781
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.0291379	+	0.999575i	$0.509276\pi$
$373$	−17.0000	+	29.4449i	−0.880227	+	1.52460i	−0.851089	+	0.525022i	$0.824057\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$		0			0
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	30.0000			1.54508
$378$	2.00000	+	10.3923i	0.102869	+	0.534522i
$379$	−25.0000			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$380$		0			0
$381$	−19.0000	−	32.9090i	−0.973399	−	1.68598i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	−4.00000			−0.203595
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$	7.00000	+	12.1244i	0.355371	+	0.615521i
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	−1.00000	+	6.92820i	−0.0505076	+	0.349927i
$393$	6.00000			0.302660
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$		0			0
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$	4.00000			0.200502
$399$	−4.00000	+	3.46410i	−0.200250	+	0.173422i
$400$		0			0
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	0.475253	+	0.879849i	$0.342356\pi$
$401$	−10.5000	+	18.1865i	−0.524345	+	0.908192i	−0.999598	+	0.0283431i	$0.990977\pi$
$402$	4.00000	+	6.92820i	0.199502	+	0.345547i
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$		0			0
$406$	3.00000	+	15.5885i	0.148888	+	0.773642i
$407$	−33.0000			−1.63575
$408$	−6.00000	+	10.3923i	−0.297044	+	0.514496i
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$		0			0
$411$	12.0000	−	20.7846i	0.591916	−	1.02523i
$412$	4.00000			0.197066
$413$		0			0
$414$	3.00000			0.147442
$415$		0			0
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$	4.00000	+	6.92820i	0.195881	+	0.339276i
$418$	−1.50000	+	2.59808i	−0.0733674	+	0.127076i
$419$	15.0000			0.732798			0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000			0.732798			0.366399	+	0.930458i	$0.380591\pi$
$420$		0			0
$421$	−34.0000			−1.65706			−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000			−1.65706			−0.828529	+	0.559946i	$0.810822\pi$
$422$	−0.500000	+	0.866025i	−0.0243396	+	0.0421575i
$423$	1.50000	+	2.59808i	0.0729325	+	0.126323i
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$		0			0
$426$	−24.0000			−1.16280
$427$	−2.00000	−	10.3923i	−0.0967868	−	0.502919i
$428$	12.0000			0.580042
$429$	15.0000	−	25.9808i	0.724207	−	1.25436i
$430$		0			0
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$	8.00000	−	6.92820i	0.384012	−	0.332564i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	−1.50000	−	2.59808i	−0.0717547	−	0.124283i
$438$	4.00000	+	6.92820i	0.191127	+	0.331042i
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	−0.721686	−	0.692220i	$-0.756633\pi$
$439$	5.00000	−	8.66025i	0.238637	−	0.413331i	0.960323	+	0.278889i	$0.0899661\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$	−30.0000			−1.42695
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$	11.0000	+	19.0526i	0.522037	+	0.904194i
$445$		0			0
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$	36.0000			1.70274
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	−3.00000			−0.141579			−0.0707894	−	0.997491i	$-0.522552\pi$
$449$	−3.00000			−0.141579			−0.0707894	+	0.997491i	$0.522552\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−14.0000	+	24.2487i	−0.657777	+	1.13930i
$454$	−24.0000			−1.12638
$455$		0			0
$456$	2.00000			0.0936586
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	−14.0000	−	24.2487i	−0.654177	−	1.13307i
$459$	−12.0000	−	20.7846i	−0.560112	−	0.970143i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$	15.0000	+	5.19615i	0.697863	+	0.241747i
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	−0.995582	−	0.0939008i	$-0.970066\pi$
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	0.579111	+	0.815249i	$0.303400\pi$
$468$	−5.00000			−0.231125
$469$	−10.0000	−	3.46410i	−0.461757	−	0.159957i
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$	−15.0000	−	25.9808i	−0.689701	−	1.19460i
$474$	−10.0000	+	17.3205i	−0.459315	+	0.795557i
$475$		0			0
$476$	−3.00000	−	15.5885i	−0.137505	−	0.714496i
$477$	−3.00000			−0.137361
$478$	3.00000	−	5.19615i	0.137217	−	0.237666i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$		0			0
$481$	−27.5000	+	47.6314i	−1.25389	+	2.17180i
$482$	25.0000			1.13872
$483$	−12.0000	+	10.3923i	−0.546019	+	0.472866i
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	−5.00000	−	8.66025i	−0.226805	−	0.392837i
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	−2.00000	+	3.46410i	−0.0905357	+	0.156813i
$489$	8.00000			0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−3.00000	+	5.19615i	−0.135250	+	0.234261i
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$	2.50000	+	4.33013i	0.112480	+	0.194822i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	24.0000	−	20.7846i	1.07655	−	0.932317i
$498$	−24.0000			−1.07547
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$		0			0
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	−7.50000	+	12.9904i	−0.334741	+	0.579789i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$		0			0
$506$	−4.50000	+	7.79423i	−0.200049	+	0.346496i
$507$	−12.0000	−	20.7846i	−0.532939	−	0.923077i
$508$	−9.50000	−	16.4545i	−0.421494	−	0.730050i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−10.0000	−	3.46410i	−0.442374	−	0.153243i
$512$	−1.00000			−0.0441942
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$		0			0
$516$	−10.0000	+	17.3205i	−0.440225	+	0.762493i
$517$	−9.00000			−0.395820
$518$	−27.5000	−	9.52628i	−1.20828	−	0.418561i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−16.5000	−	28.5788i	−0.722878	−	1.25206i	−0.959841	−	0.280543i	$-0.909485\pi$
$521$	−16.5000	−	28.5788i	−0.722878	−	1.25206i	0.236963	−	0.971519i	$-0.423848\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	−0.560208	−	0.828352i	$-0.689279\pi$
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	0.997478	+	0.0709788i	$0.0226123\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$		0			0
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$	−3.00000	−	5.19615i	−0.130558	−	0.226134i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$	−2.00000	+	1.73205i	−0.0867110	+	0.0750939i
$533$	−15.0000			−0.649722
$534$	6.00000	−	10.3923i	0.259645	−	0.449719i
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$	12.0000			0.517357
$539$	−19.5000	+	7.79423i	−0.839924	+	0.335721i
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	−2.00000	−	3.46410i	−0.0858282	−	0.148659i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$		0			0
$546$	20.0000	−	17.3205i	0.855921	−	0.741249i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$		0			0
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	6.00000			0.255377
$553$	−5.00000	−	25.9808i	−0.212622	−	1.10481i
$554$	2.00000			0.0849719
$555$		0			0
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−13.5000	−	23.3827i	−0.572013	−	0.990756i	−0.996359	−	0.0852559i	$-0.972829\pi$
$557$	−13.5000	−	23.3827i	−0.572013	−	0.990756i	0.424346	−	0.905500i	$-0.360504\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	−50.0000			−2.11477
$560$		0			0
$561$	−36.0000			−1.51992
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	26.0000			1.09286
$567$	27.5000	+	9.52628i	1.15489	+	0.400066i
$568$	−12.0000			−0.503509
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	−0.832870	−	0.553469i	$-0.813304\pi$
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	0.895753	+	0.444552i	$0.146637\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	7.50000	−	12.9904i	0.313591	−	0.543155i
$573$	24.0000			1.00261
$574$	−1.50000	−	7.79423i	−0.0626088	−	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	10.0000	+	17.3205i	0.416305	+	0.721062i	0.995565	−	0.0940813i	$-0.0299914\pi$
$577$	10.0000	+	17.3205i	0.416305	+	0.721062i	−0.579259	+	0.815144i	$0.696658\pi$
$578$	9.50000	+	16.4545i	0.395148	+	0.684416i
$579$	−4.00000	+	6.92820i	−0.166234	+	0.287926i
$580$		0			0
$581$	24.0000	−	20.7846i	0.995688	−	0.862291i
$582$	28.0000			1.16064
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	13.5000	−	23.3827i	0.557680	−	0.965930i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	11.0000	+	8.66025i	0.453632	+	0.357143i
$589$	4.00000			0.164817
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	5.50000	+	9.52628i	0.226049	+	0.391528i
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$	12.0000			0.492366
$595$		0			0
$596$	18.0000			0.737309
$597$	4.00000	−	6.92820i	0.163709	−	0.283552i
$598$	7.50000	+	12.9904i	0.306698	+	0.531216i
$599$	−21.0000	−	36.3731i	−0.858037	−	1.48616i	−0.873799	−	0.486287i	$-0.838351\pi$
$599$	−21.0000	−	36.3731i	−0.858037	−	1.48616i	0.0157622	−	0.999876i	$-0.494983\pi$
$600$		0			0
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	−5.00000	−	25.9808i	−0.203785	−	1.05890i
$603$	4.00000			0.162893
$604$	−7.00000	+	12.1244i	−0.284826	+	0.493333i
$605$		0			0
$606$	−12.0000	−	20.7846i	−0.487467	−	0.844317i
$607$	−9.50000	+	16.4545i	−0.385593	+	0.667867i	−0.991851	−	0.127401i	$-0.959336\pi$
$607$	−9.50000	+	16.4545i	−0.385593	+	0.667867i	0.606258	+	0.795268i	$0.292670\pi$
$608$	1.00000			0.0405554
$609$	30.0000	+	10.3923i	1.21566	+	0.421117i
$610$		0			0
$611$	−7.50000	+	12.9904i	−0.303418	+	0.525535i
$612$	3.00000	+	5.19615i	0.121268	+	0.210042i
$613$	23.5000	+	40.7032i	0.949156	+	1.64399i	0.747208	+	0.664590i	$0.231394\pi$
$613$	23.5000	+	40.7032i	0.949156	+	1.64399i	0.201948	+	0.979396i	$0.435273\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$		0			0
$616$	7.50000	+	2.59808i	0.302184	+	0.104679i
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	0.500000	+	0.866025i	0.0200967	+	0.0348085i	0.875899	−	0.482495i	$-0.160269\pi$
$619$	0.500000	+	0.866025i	0.0200967	+	0.0348085i	−0.855802	+	0.517303i	$0.826936\pi$
$620$		0			0
$621$	−6.00000	+	10.3923i	−0.240772	+	0.417029i
$622$	−12.0000			−0.481156
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$	−10.0000			−0.400320
$625$		0			0
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	2.50000	−	4.33013i	0.0997609	−	0.172791i
$629$	66.0000			2.63159
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$	−5.00000	+	8.66025i	−0.198889	+	0.344486i
$633$	1.00000	+	1.73205i	0.0397464	+	0.0688428i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−5.00000	+	34.6410i	−0.198107	+	1.37253i
$638$	18.0000			0.712627
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$		0			0
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.841417	+	0.540386i	$0.181722\pi$
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.0472793	+	0.998882i	$0.484945\pi$
$642$	12.0000	−	20.7846i	0.473602	−	0.820303i
$643$	−38.0000			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$644$	−6.00000	+	5.19615i	−0.236433	+	0.204757i
$645$		0			0
$646$	3.00000	−	5.19615i	0.118033	−	0.204440i
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	0.582397	−	0.812905i	$-0.302115\pi$
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	−0.995194	+	0.0979182i	$0.968782\pi$
$648$	−5.50000	−	9.52628i	−0.216060	−	0.374228i
$649$		0			0
$650$		0			0
$651$	−4.00000	−	20.7846i	−0.156772	−	0.814613i
$652$	4.00000			0.156652
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	−0.584091	−	0.811688i	$-0.698549\pi$
$653$	10.5000	−	18.1865i	0.410897	−	0.711694i	0.994988	+	0.0999939i	$0.0318823\pi$
$654$	−4.00000	−	6.92820i	−0.156412	−	0.270914i
$655$		0			0
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$	4.00000			0.156055
$658$	−7.50000	−	2.59808i	−0.292380	−	0.101284i
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	−0.875993	−	0.482323i	$-0.839793\pi$
$661$	−22.0000	−	38.1051i	−0.855701	−	1.48212i	0.0202925	−	0.999794i	$-0.493540\pi$
$662$	−3.50000	−	6.06218i	−0.136031	−	0.235613i
$663$	−30.0000	+	51.9615i	−1.16510	+	2.01802i
$664$	−12.0000			−0.465690
$665$		0			0
$666$	11.0000			0.426241
$667$	−9.00000	+	15.5885i	−0.348481	+	0.603587i
$668$	4.50000	+	7.79423i	0.174110	+	0.301568i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$		0			0
$671$	−12.0000			−0.463255
$672$	−1.00000	−	5.19615i	−0.0385758	−	0.200446i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$		0			0
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	−1.50000	+	2.59808i	−0.0576497	+	0.0998522i	−0.893410	−	0.449242i	$-0.851694\pi$
$677$	−1.50000	+	2.59808i	−0.0576497	+	0.0998522i	0.835760	+	0.549095i	$0.185027\pi$
$678$	24.0000			0.921714
$679$	−28.0000	+	24.2487i	−1.07454	+	0.930580i
$680$		0			0
$681$	−24.0000	+	41.5692i	−0.919682	+	1.59294i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	0.500000	−	0.866025i	0.0191180	−	0.0331133i
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$	−56.0000			−2.13653
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	−7.50000	−	12.9904i	−0.285727	−	0.494894i
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	−3.00000			−0.114043
$693$	6.00000	−	5.19615i	0.227921	−	0.197386i
$694$	24.0000			0.911028
$695$		0			0
$696$	−6.00000	−	10.3923i	−0.227429	−	0.393919i
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	12.0000			0.453882
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	10.0000	−	17.3205i	0.377426	−	0.653720i
$703$	−5.50000	−	9.52628i	−0.207436	−	0.359290i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	12.0000			0.451626
$707$	30.0000	+	10.3923i	1.12827	+	0.390843i
$708$		0			0
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$	5.00000	+	8.66025i	0.187515	+	0.324785i
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	12.0000			0.449404
$714$	−30.0000	−	10.3923i	−1.12272	−	0.388922i
$715$		0			0
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	−0.306253	−	0.951950i	$-0.599075\pi$
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	0.977539	−	0.210752i	$-0.0675914\pi$
$720$		0			0
$721$	2.00000	+	10.3923i	0.0744839	+	0.387030i
$722$	18.0000			0.669891
$723$	25.0000	−	43.3013i	0.929760	−	1.61039i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$		0			0
$726$	−2.00000	+	3.46410i	−0.0742270	+	0.128565i
$727$	−29.0000			−1.07555			−0.537775	−	0.843088i	$-0.680735\pi$
$727$	−29.0000			−1.07555			−0.537775	+	0.843088i	$0.680735\pi$
$728$	10.0000	−	8.66025i	0.370625	−	0.320970i
$729$	13.0000			0.481481
$730$		0			0
$731$	30.0000	+	51.9615i	1.10959	+	1.92187i
$732$	4.00000	+	6.92820i	0.147844	+	0.256074i
$733$	23.5000	−	40.7032i	0.867992	−	1.50341i	0.00394730	−	0.999992i	$-0.498744\pi$
$733$	23.5000	−	40.7032i	0.867992	−	1.50341i	0.864045	−	0.503415i	$-0.167923\pi$
$734$	−1.00000			−0.0369107
$735$		0			0
$736$	3.00000			0.110581
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	18.5000	+	32.0429i	0.680534	+	1.17872i	0.974818	+	0.223001i	$0.0715853\pi$
$739$	18.5000	+	32.0429i	0.680534	+	1.17872i	−0.294285	+	0.955718i	$0.595081\pi$
$740$		0			0
$741$	10.0000			0.367359
$742$	6.00000	−	5.19615i	0.220267	−	0.190757i
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$	−4.00000	+	6.92820i	−0.146647	+	0.254000i
$745$		0			0
$746$	17.0000	+	29.4449i	0.622414	+	1.07805i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	−18.0000			−0.658145
$749$	6.00000	+	31.1769i	0.219235	+	1.13918i
$750$		0			0
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	−0.999570	−	0.0293387i	$-0.990660\pi$
$751$	−13.0000	+	22.5167i	−0.474377	+	0.821645i	0.525193	+	0.850983i	$0.323993\pi$
$752$	1.50000	+	2.59808i	0.0546994	+	0.0947421i
$753$	15.0000	+	25.9808i	0.546630	+	0.946792i
$754$	15.0000	−	25.9808i	0.546268	−	0.946164i
$755$		0			0
$756$	10.0000	+	3.46410i	0.363696	+	0.125988i
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−12.5000	+	21.6506i	−0.454020	+	0.786386i
$759$	9.00000	+	15.5885i	0.326679	+	0.565825i
$760$		0			0
$761$	25.5000	−	44.1673i	0.924374	−	1.60106i	0.131810	−	0.991275i	$-0.457921\pi$
$761$	25.5000	−	44.1673i	0.924374	−	1.60106i	0.792564	−	0.609788i	$-0.208745\pi$
$762$	−38.0000			−1.37659
$763$	10.0000	+	3.46410i	0.362024	+	0.125409i
$764$	12.0000			0.434145
$765$		0			0
$766$	−7.50000	−	12.9904i	−0.270986	−	0.469362i
$767$		0			0
$768$	−1.00000	+	1.73205i	−0.0360844	+	0.0625000i
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	−2.00000	+	3.46410i	−0.0719816	+	0.124676i
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	0.967987	+	0.251000i	$0.0807596\pi$
$773$	19.5000	+	33.7750i	0.701366	+	1.21480i	−0.266621	+	0.963802i	$0.585907\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$		0			0
$776$	14.0000			0.502571
$777$	−44.0000	+	38.1051i	−1.57849	+	1.36701i
$778$	24.0000			0.860442
$779$	1.50000	−	2.59808i	0.0537431	−	0.0930857i
$780$		0			0
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$	24.0000			0.857690
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$		0			0
$786$	3.00000	−	5.19615i	0.107006	−	0.185341i
$787$	−17.0000	−	29.4449i	−0.605985	−	1.04960i	−0.991895	−	0.127060i	$-0.959446\pi$
$787$	−17.0000	−	29.4449i	−0.605985	−	1.04960i	0.385911	−	0.922536i	$-0.373887\pi$
$788$	−1.50000	−	2.59808i	−0.0534353	−	0.0925526i
$789$		0			0
$790$		0			0
$791$	−24.0000	+	20.7846i	−0.853342	+	0.739016i
$792$	−3.00000			−0.106600
$793$	−10.0000	+	17.3205i	−0.355110	+	0.615069i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	30.0000			1.06265			0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000			1.06265			0.531327	+	0.847167i	$0.321693\pi$
$798$	1.00000	+	5.19615i	0.0353996	+	0.183942i
$799$	18.0000			0.636794
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	10.5000	+	18.1865i	0.370768	+	0.642189i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$	8.00000			0.282138
$805$		0			0
$806$	−20.0000			−0.704470
$807$	12.0000	−	20.7846i	0.422420	−	0.731653i
$808$	−6.00000	−	10.3923i	−0.211079	−	0.365600i
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	−0.973253	−	0.229736i	$-0.926214\pi$
$809$	−19.5000	−	33.7750i	−0.685583	−	1.18747i	0.287670	−	0.957730i	$-0.407120\pi$
$810$		0			0
$811$	47.0000			1.65039			0.825197	−	0.564846i	$-0.191064\pi$
$811$	47.0000			1.65039			0.825197	+	0.564846i	$0.191064\pi$
$812$	15.0000	+	5.19615i	0.526397	+	0.182349i
$813$	−32.0000			−1.12229
$814$	−16.5000	+	28.5788i	−0.578325	+	1.00169i
$815$		0			0
$816$	6.00000	+	10.3923i	0.210042	+	0.363803i
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	22.0000			0.769212
$819$	−2.50000	−	12.9904i	−0.0873571	−	0.453921i
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	−12.0000	−	20.7846i	−0.418548	−	0.724947i
$823$	22.0000	+	38.1051i	0.766872	+	1.32826i	0.939251	+	0.343230i	$0.111521\pi$
$823$	22.0000	+	38.1051i	0.766872	+	1.32826i	−0.172379	+	0.985031i	$0.555146\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$		0			0
$826$		0			0
$827$	54.0000			1.87776			0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000			1.87776			0.938882	+	0.344239i	$0.111863\pi$
$828$	1.50000	−	2.59808i	0.0521286	−	0.0902894i
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$	2.00000	−	3.46410i	0.0693792	−	0.120168i
$832$	−5.00000			−0.173344
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$	8.00000			0.277017
$835$		0			0
$836$	1.50000	+	2.59808i	0.0518786	+	0.0898563i
$837$	−8.00000	−	13.8564i	−0.276520	−	0.478947i
$838$	7.50000	−	12.9904i	0.259083	−	0.448745i
$839$	−6.00000			−0.207143			−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000			−0.207143			−0.103572	+	0.994622i	$0.533027\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−17.0000	+	29.4449i	−0.585859	+	1.01474i
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$	0.500000	+	0.866025i	0.0172107	+	0.0298098i
$845$		0			0
$846$	3.00000			0.103142
$847$	−1.00000	−	5.19615i	−0.0343604	−	0.178542i
$848$	−3.00000			−0.103020
$849$	26.0000	−	45.0333i	0.892318	−	1.54554i
$850$		0			0
$851$	−16.5000	−	28.5788i	−0.565613	−	0.979670i
$852$	−12.0000	+	20.7846i	−0.411113	+	0.712069i
$853$	1.00000			0.0342393			0.0171197	−	0.999853i	$-0.494550\pi$
$853$	1.00000			0.0342393			0.0171197	+	0.999853i	$0.494550\pi$
$854$	−10.0000	−	3.46410i	−0.342193	−	0.118539i
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$	−15.0000	−	25.9808i	−0.512092	−	0.886969i
$859$	−16.0000	+	27.7128i	−0.545913	+	0.945549i	0.452636	+	0.891695i	$0.350484\pi$
$859$	−16.0000	+	27.7128i	−0.545913	+	0.945549i	−0.998549	+	0.0538535i	$0.982850\pi$
$860$		0			0
$861$	−15.0000	−	5.19615i	−0.511199	−	0.177084i
$862$		0			0
$863$	19.5000	−	33.7750i	0.663788	−	1.14971i	−0.315825	−	0.948818i	$-0.602281\pi$
$863$	19.5000	−	33.7750i	0.663788	−	1.14971i	0.979612	−	0.200897i	$-0.0643855\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$		0			0
$866$	8.00000	−	13.8564i	0.271851	−	0.470860i
$867$	38.0000			1.29055
$868$	−2.00000	−	10.3923i	−0.0678844	−	0.352738i
$869$	−30.0000			−1.01768
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	−2.00000	−	3.46410i	−0.0677285	−	0.117309i
$873$	7.00000	−	12.1244i	0.236914	−	0.410347i
$874$	−3.00000			−0.101477
$875$		0			0
$876$	8.00000			0.270295
$877$	−3.50000	+	6.06218i	−0.118187	+	0.204705i	−0.919049	−	0.394143i	$-0.871041\pi$
$877$	−3.50000	+	6.06218i	−0.118187	+	0.204705i	0.800862	+	0.598848i	$0.204375\pi$
$878$	−5.00000	−	8.66025i	−0.168742	−	0.292269i
$879$	−27.0000	−	46.7654i	−0.910687	−	1.57736i
$880$		0			0
$881$	33.0000			1.11180			0.555899	−	0.831250i	$-0.312374\pi$
$881$	33.0000			1.11180			0.555899	+	0.831250i	$0.312374\pi$
$882$	6.50000	−	2.59808i	0.218866	−	0.0874818i
$883$	−8.00000			−0.269221			−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000			−0.269221			−0.134611	+	0.990899i	$0.542978\pi$
$884$	−15.0000	+	25.9808i	−0.504505	+	0.873828i
$885$		0			0
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	22.0000			0.738272
$889$	38.0000	−	32.9090i	1.27448	−	1.10373i
$890$		0			0
$891$	16.5000	−	28.5788i	0.552771	−	0.957427i
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$	−1.50000	−	2.59808i	−0.0501956	−	0.0869413i
$894$	18.0000	−	31.1769i	0.602010	−	1.04271i
$895$		0			0
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	30.0000			1.00167
$898$	−1.50000	+	2.59808i	−0.0500556	+	0.0866989i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$		0			0
$901$	−9.00000	+	15.5885i	−0.299833	+	0.519327i
$902$	−9.00000			−0.299667
$903$	−50.0000	−	17.3205i	−1.66390	−	0.576390i
$904$	12.0000			0.399114
$905$		0			0
$906$	14.0000	+	24.2487i	0.465119	+	0.805609i
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	1.00000	−	1.73205i	0.0331133	−	0.0573539i
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$	11.0000	+	19.0526i	0.363848	+	0.630203i
$915$		0			0
$916$	−28.0000			−0.925146
$917$	1.50000	+	7.79423i	0.0495344	+	0.257388i
$918$	−24.0000			−0.792118
$919$	−19.0000	+	32.9090i	−0.626752	+	1.08557i	0.361447	+	0.932393i	$0.382283\pi$
$919$	−19.0000	+	32.9090i	−0.626752	+	1.08557i	−0.988199	+	0.153174i	$0.951051\pi$
$920$		0			0
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	3.00000	−	5.19615i	0.0987997	−	0.171126i
$923$	−60.0000			−1.97492
$924$	12.0000	−	10.3923i	0.394771	−	0.341882i
$925$		0			0
$926$	9.50000	−	16.4545i	0.312189	−	0.540728i
$927$	−2.00000	−	3.46410i	−0.0656886	−	0.113776i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	0.457480	+	0.889220i	$0.348752\pi$
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	−0.998827	+	0.0484211i	$0.984581\pi$
$930$		0			0
$931$	−5.50000	−	4.33013i	−0.180255	−	0.141914i
$932$	6.00000			0.196537
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$	9.00000	+	15.5885i	0.294489	+	0.510070i
$935$		0			0
$936$	−2.50000	+	4.33013i	−0.0817151	+	0.141535i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−8.00000	+	6.92820i	−0.261209	+	0.226214i
$939$	−16.0000			−0.522140
$940$		0			0
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	0.601418	−	0.798935i	$-0.294603\pi$
$941$	−12.0000	−	20.7846i	−0.391189	−	0.677559i	−0.992607	+	0.121376i	$0.961269\pi$
$942$	−5.00000	−	8.66025i	−0.162909	−	0.282166i
$943$	4.50000	−	7.79423i	0.146540	−	0.253815i
$944$		0			0
$945$		0			0
$946$	−30.0000			−0.975384
$947$	15.0000	−	25.9808i	0.487435	−	0.844261i	−0.512461	−	0.858710i	$-0.671266\pi$
$947$	15.0000	−	25.9808i	0.487435	−	0.844261i	0.999896	+	0.0144491i	$0.00459946\pi$
$948$	10.0000	+	17.3205i	0.324785	+	0.562544i
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$		0			0
$951$	−36.0000			−1.16738
$952$	−15.0000	−	5.19615i	−0.486153	−	0.168408i
$953$	12.0000			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$954$	−1.50000	+	2.59808i	−0.0485643	+	0.0841158i
$955$		0			0
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$	−24.0000			−0.775405
$959$	30.0000	+	10.3923i	0.968751	+	0.335585i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	27.5000	+	47.6314i	0.886636	+	1.53570i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	12.5000	−	21.6506i	0.402598	−	0.697320i
$965$		0			0
$966$	3.00000	+	15.5885i	0.0965234	+	0.501550i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	−0.997150	−	0.0754473i	$-0.975962\pi$
$971$	−13.5000	+	23.3827i	−0.433236	+	0.750386i	0.563914	+	0.825833i	$0.309295\pi$
$972$	−10.0000			−0.320750
$973$	−8.00000	+	6.92820i	−0.256468	+	0.222108i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	18.0000			0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	28.5000	+	49.3634i	0.909009	+	1.57445i	0.815444	+	0.578836i	$0.196493\pi$
$983$	28.5000	+	49.3634i	0.909009	+	1.57445i	0.0935651	+	0.995613i	$0.470174\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$		0			0
$986$	−36.0000			−1.14647
$987$	−12.0000	+	10.3923i	−0.381964	+	0.330791i
$988$	5.00000			0.159071
$989$	15.0000	−	25.9808i	0.476972	−	0.826140i
$990$		0			0
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	−14.0000			−0.444277
$994$	−6.00000	−	31.1769i	−0.190308	−	0.988872i
$995$		0			0
$996$	−12.0000	+	20.7846i	−0.380235	+	0.658586i
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	0.955322	−	0.295567i	$-0.0955086\pi$
$997$	7.00000	+	12.1244i	0.221692	+	0.383982i	−0.733630	+	0.679549i	$0.762175\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$	−22.0000	+	38.1051i	−0.696049	+	1.20559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.e.h.51.1		2
5.2	odd	4		350.2.j.a.149.2		4
5.3	odd	4		350.2.j.a.149.1		4
5.4	even	2		70.2.e.b.51.1	yes	2
7.2	even	3		2450.2.a.p.1.1		1
7.4	even	3	inner	350.2.e.h.151.1		2
7.5	odd	6		2450.2.a.f.1.1		1
15.14	odd	2		630.2.k.e.541.1		2
20.19	odd	2		560.2.q.d.401.1		2
35.2	odd	12		2450.2.c.f.99.1		2
35.4	even	6		70.2.e.b.11.1	✓	2
35.9	even	6		490.2.a.g.1.1		1
35.12	even	12		2450.2.c.p.99.1		2
35.18	odd	12		350.2.j.a.249.2		4
35.19	odd	6		490.2.a.j.1.1		1
35.23	odd	12		2450.2.c.f.99.2		2
35.24	odd	6		490.2.e.a.361.1		2
35.32	odd	12		350.2.j.a.249.1		4
35.33	even	12		2450.2.c.p.99.2		2
35.34	odd	2		490.2.e.a.471.1		2
105.44	odd	6		4410.2.a.m.1.1		1
105.74	odd	6		630.2.k.e.361.1		2
105.89	even	6		4410.2.a.c.1.1		1
140.19	even	6		3920.2.a.g.1.1		1
140.39	odd	6		560.2.q.d.81.1		2
140.79	odd	6		3920.2.a.be.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.b.11.1	✓	2	35.4	even	6
70.2.e.b.51.1	yes	2	5.4	even	2
350.2.e.h.51.1		2	1.1	even	1	trivial
350.2.e.h.151.1		2	7.4	even	3	inner
350.2.j.a.149.1		4	5.3	odd	4
350.2.j.a.149.2		4	5.2	odd	4
350.2.j.a.249.1		4	35.32	odd	12
350.2.j.a.249.2		4	35.18	odd	12
490.2.a.g.1.1		1	35.9	even	6
490.2.a.j.1.1		1	35.19	odd	6
490.2.e.a.361.1		2	35.24	odd	6
490.2.e.a.471.1		2	35.34	odd	2
560.2.q.d.81.1		2	140.39	odd	6
560.2.q.d.401.1		2	20.19	odd	2
630.2.k.e.361.1		2	105.74	odd	6
630.2.k.e.541.1		2	15.14	odd	2
2450.2.a.f.1.1		1	7.5	odd	6
2450.2.a.p.1.1		1	7.2	even	3
2450.2.c.f.99.1		2	35.2	odd	12
2450.2.c.f.99.2		2	35.23	odd	12
2450.2.c.p.99.1		2	35.12	even	12
2450.2.c.p.99.2		2	35.33	even	12
3920.2.a.g.1.1		1	140.19	even	6
3920.2.a.be.1.1		1	140.79	odd	6
4410.2.a.c.1.1		1	105.89	even	6
4410.2.a.m.1.1		1	105.44	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{6} +(2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-1.00000 + 1.73205i) q^{12} -5.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} +(-5.00000 - 1.73205i) q^{21} -3.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-2.50000 + 4.33013i) q^{26} -4.00000 q^{27} +(-2.50000 - 0.866025i) q^{28} -6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +6.00000 q^{34} +1.00000 q^{36} +(5.50000 - 9.52628i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(5.00000 + 8.66025i) q^{39} +3.00000 q^{41} +(-4.00000 + 3.46410i) q^{42} +10.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(1.50000 - 2.59808i) q^{47} +2.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(6.00000 - 10.3923i) q^{51} +(2.50000 + 4.33013i) q^{52} +(1.50000 + 2.59808i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(-2.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(2.00000 - 3.46410i) q^{61} +4.00000 q^{62} +(0.500000 + 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +12.0000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-5.50000 - 9.52628i) q^{74} -1.00000 q^{76} +(-7.50000 - 2.59808i) q^{77} +10.0000 q^{78} +(5.00000 - 8.66025i) q^{79} +(5.50000 + 9.52628i) q^{81} +(1.50000 - 2.59808i) q^{82} +12.0000 q^{83} +(1.00000 + 5.19615i) q^{84} +(5.00000 - 8.66025i) q^{86} +(6.00000 + 10.3923i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} -3.00000 q^{92} +(4.00000 - 6.92820i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{96} -14.0000 q^{97} +(-5.50000 - 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} - 3 q^{11} - 2 q^{12} - 10 q^{13} - q^{14} - q^{16} + 6 q^{17} + q^{18} + q^{19} - 10 q^{21} - 6 q^{22} + 3 q^{23} + 2 q^{24} - 5 q^{26} - 8 q^{27} - 5 q^{28} - 12 q^{29} + 4 q^{31} + q^{32} - 6 q^{33} + 12 q^{34} + 2 q^{36} + 11 q^{37} - q^{38} + 10 q^{39} + 6 q^{41} - 8 q^{42} + 20 q^{43} - 3 q^{44} - 3 q^{46} + 3 q^{47} + 4 q^{48} + 2 q^{49} + 12 q^{51} + 5 q^{52} + 3 q^{53} - 4 q^{54} - 4 q^{56} - 4 q^{57} - 6 q^{58} + 4 q^{61} + 8 q^{62} + q^{63} + 2 q^{64} + 6 q^{66} - 4 q^{67} + 6 q^{68} - 12 q^{69} + 24 q^{71} + q^{72} - 4 q^{73} - 11 q^{74} - 2 q^{76} - 15 q^{77} + 20 q^{78} + 10 q^{79} + 11 q^{81} + 3 q^{82} + 24 q^{83} + 2 q^{84} + 10 q^{86} + 12 q^{87} + 3 q^{88} - 6 q^{89} - 20 q^{91} - 6 q^{92} + 8 q^{93} - 3 q^{94} + 2 q^{96} - 28 q^{97} - 11 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9 - 3 * q^11 - 2 * q^12 - 10 * q^13 - q^14 - q^16 + 6 * q^17 + q^18 + q^19 - 10 * q^21 - 6 * q^22 + 3 * q^23 + 2 * q^24 - 5 * q^26 - 8 * q^27 - 5 * q^28 - 12 * q^29 + 4 * q^31 + q^32 - 6 * q^33 + 12 * q^34 + 2 * q^36 + 11 * q^37 - q^38 + 10 * q^39 + 6 * q^41 - 8 * q^42 + 20 * q^43 - 3 * q^44 - 3 * q^46 + 3 * q^47 + 4 * q^48 + 2 * q^49 + 12 * q^51 + 5 * q^52 + 3 * q^53 - 4 * q^54 - 4 * q^56 - 4 * q^57 - 6 * q^58 + 4 * q^61 + 8 * q^62 + q^63 + 2 * q^64 + 6 * q^66 - 4 * q^67 + 6 * q^68 - 12 * q^69 + 24 * q^71 + q^72 - 4 * q^73 - 11 * q^74 - 2 * q^76 - 15 * q^77 + 20 * q^78 + 10 * q^79 + 11 * q^81 + 3 * q^82 + 24 * q^83 + 2 * q^84 + 10 * q^86 + 12 * q^87 + 3 * q^88 - 6 * q^89 - 20 * q^91 - 6 * q^92 + 8 * q^93 - 3 * q^94 + 2 * q^96 - 28 * q^97 - 11 * q^98 + 6 * q^99

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