LMFDB - Embedded newform 1050.2.i.o.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (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:	$8.38429221223$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			751.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.751
Dual form			1050.2.i.o.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(0.500000 - 2.59808i) q^{21} +5.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(2.50000 - 4.33013i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{39} -9.00000 q^{41} +(-2.00000 - 1.73205i) q^{42} +10.0000 q^{43} +(2.50000 - 4.33013i) q^{44} +(1.50000 + 2.59808i) q^{46} +(6.50000 - 11.2583i) q^{47} +1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +7.00000 q^{57} +(-2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +6.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(1.00000 - 1.73205i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-2.50000 - 4.33013i) q^{74} +7.00000 q^{76} +(-2.50000 + 12.9904i) q^{77} -1.00000 q^{78} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} -10.0000 q^{83} +(-2.50000 + 0.866025i) q^{84} +(5.00000 - 8.66025i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} +3.00000 q^{92} +(3.00000 - 5.19615i) q^{93} +(-6.50000 - 11.2583i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(6.50000 + 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + 5 q^{11} - q^{12} + 2 q^{13} + 5 q^{14} - q^{16} + 2 q^{17} + q^{18} - 7 q^{19} + q^{21} + 10 q^{22} - 3 q^{23} + q^{24} + q^{26} + 2 q^{27} + q^{28} + 6 q^{31} + q^{32} + 5 q^{33} + 4 q^{34} + 2 q^{36} + 5 q^{37} + 7 q^{38} - q^{39} - 18 q^{41} - 4 q^{42} + 20 q^{43} + 5 q^{44} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 2 q^{49} + 2 q^{51} - q^{52} + q^{53} + q^{54} - 4 q^{56} + 14 q^{57} - 4 q^{59} + 2 q^{61} + 12 q^{62} - 5 q^{63} + 2 q^{64} - 5 q^{66} - 6 q^{67} + 2 q^{68} + 6 q^{69} - 4 q^{71} + q^{72} - 4 q^{73} - 5 q^{74} + 14 q^{76} - 5 q^{77} - 2 q^{78} + 14 q^{79} - q^{81} - 9 q^{82} - 20 q^{83} - 5 q^{84} + 10 q^{86} - 5 q^{88} - 10 q^{89} + 4 q^{91} + 6 q^{92} + 6 q^{93} - 13 q^{94} + q^{96} + 16 q^{97} + 13 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9 + 5 * q^11 - q^12 + 2 * q^13 + 5 * q^14 - q^16 + 2 * q^17 + q^18 - 7 * q^19 + q^21 + 10 * q^22 - 3 * q^23 + q^24 + q^26 + 2 * q^27 + q^28 + 6 * q^31 + q^32 + 5 * q^33 + 4 * q^34 + 2 * q^36 + 5 * q^37 + 7 * q^38 - q^39 - 18 * q^41 - 4 * q^42 + 20 * q^43 + 5 * q^44 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 2 * q^49 + 2 * q^51 - q^52 + q^53 + q^54 - 4 * q^56 + 14 * q^57 - 4 * q^59 + 2 * q^61 + 12 * q^62 - 5 * q^63 + 2 * q^64 - 5 * q^66 - 6 * q^67 + 2 * q^68 + 6 * q^69 - 4 * q^71 + q^72 - 4 * q^73 - 5 * q^74 + 14 * q^76 - 5 * q^77 - 2 * q^78 + 14 * q^79 - q^81 - 9 * q^82 - 20 * q^83 - 5 * q^84 + 10 * q^86 - 5 * q^88 - 10 * q^89 + 4 * q^91 + 6 * q^92 + 6 * q^93 - 13 * q^94 + q^96 + 16 * q^97 + 13 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	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
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	0.500000	−	2.59808i	0.109109	−	0.566947i
$22$	5.00000			1.06600
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	1.00000			0.192450
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.50000	−	4.33013i	0.435194	−	0.753778i
$34$	2.00000			0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	−0.584002	−	0.811752i	$-0.698514\pi$
$37$	2.50000	−	4.33013i	0.410997	−	0.711868i	0.994999	+	0.0998840i	$0.0318472\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$	−2.00000	−	1.73205i	−0.308607	−	0.267261i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	2.50000	−	4.33013i	0.376889	−	0.652791i
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	6.50000	−	11.2583i	0.948122	−	1.64220i	0.198747	−	0.980051i	$-0.436313\pi$
$47$	6.50000	−	11.2583i	0.948122	−	1.64220i	0.749375	−	0.662145i	$-0.230354\pi$
$48$	1.00000			0.144338
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	0.898321	−	0.439340i	$-0.144788\pi$
$53$	0.500000	+	0.866025i	0.0686803	+	0.118958i	−0.829640	+	0.558298i	$0.811454\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$	7.00000			0.927173
$58$		0			0
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$		0			0
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	−0.794879	−	0.606768i	$-0.792466\pi$
$61$	1.00000	−	1.73205i	0.128037	−	0.221766i	0.922916	+	0.385002i	$0.125799\pi$
$62$	6.00000			0.762001
$63$	−2.50000	+	0.866025i	−0.314970	+	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	−2.50000	−	4.33013i	−0.307729	−	0.533002i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	3.00000			0.361158
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	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	$0.908542\pi$
$74$	−2.50000	−	4.33013i	−0.290619	−	0.503367i
$75$		0			0
$76$	7.00000			0.802955
$77$	−2.50000	+	12.9904i	−0.284901	+	1.48039i
$78$	−1.00000			−0.113228
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−10.0000			−1.09764			−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000			−1.09764			−0.548821	+	0.835940i	$0.684923\pi$
$84$	−2.50000	+	0.866025i	−0.272772	+	0.0944911i
$85$		0			0
$86$	5.00000	−	8.66025i	0.539164	−	0.933859i
$87$		0			0
$88$	−2.50000	−	4.33013i	−0.266501	−	0.461593i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$		0			0
$91$	2.00000	+	1.73205i	0.209657	+	0.181568i
$92$	3.00000			0.312772
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$	−6.50000	−	11.2583i	−0.670424	−	1.16121i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	6.50000	+	2.59808i	0.656599	+	0.262445i
$99$	−5.00000			−0.502519
$100$		0			0
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	0.595466	−	0.803380i	$-0.296967\pi$
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	−0.993481	+	0.113998i	$0.963634\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	1.00000			0.0971286
$107$	−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	$0.969703\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$		0			0
$111$	−5.00000			−0.474579
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	3.50000	−	6.06218i	0.327805	−	0.567775i
$115$		0			0
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.0462250	+	0.0800641i
$118$	−4.00000			−0.368230
$119$	−1.00000	+	5.19615i	−0.0916698	+	0.476331i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$	4.50000	+	7.79423i	0.405751	+	0.702782i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$		0			0
$126$	−0.500000	+	2.59808i	−0.0445435	+	0.231455i
$127$	9.00000			0.798621			0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000			0.798621			0.399310	+	0.916816i	$0.369250\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.00000	−	8.66025i	−0.440225	−	0.762493i
$130$		0			0
$131$	8.50000	−	14.7224i	0.742648	−	1.28630i	−0.208637	−	0.977993i	$-0.566903\pi$
$131$	8.50000	−	14.7224i	0.742648	−	1.28630i	0.951285	−	0.308312i	$-0.0997640\pi$
$132$	−5.00000			−0.435194
$133$	−17.5000	+	6.06218i	−1.51744	+	0.525657i
$134$	−6.00000			−0.518321
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$	1.50000	−	2.59808i	0.127688	−	0.221163i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−13.0000			−1.09480
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$	2.50000	+	4.33013i	0.209061	+	0.362103i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	−4.00000			−0.331042
$147$	5.50000	−	4.33013i	0.453632	−	0.357143i
$148$	−5.00000			−0.410997
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.833597	+	0.552372i	$0.186277\pi$
$151$	11.0000	+	19.0526i	0.895167	+	1.55048i	0.0615699	+	0.998103i	$0.480389\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$	−2.00000			−0.161690
$154$	10.0000	+	8.66025i	0.805823	+	0.697863i
$155$		0			0
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	−0.999762	−	0.0217953i	$-0.993062\pi$
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	0.481006	−	0.876717i	$-0.340272\pi$
$158$	−7.00000	−	12.1244i	−0.556890	−	0.964562i
$159$	0.500000	−	0.866025i	0.0396526	−	0.0686803i
$160$		0			0
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$	−1.00000			−0.0785674
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−5.00000	+	8.66025i	−0.388075	+	0.672166i
$167$	−19.0000			−1.47026			−0.735132	−	0.677924i	$-0.762880\pi$
$167$	−19.0000			−1.47026			−0.735132	+	0.677924i	$0.762880\pi$
$168$	−0.500000	+	2.59808i	−0.0385758	+	0.200446i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−3.50000	−	6.06218i	−0.267652	−	0.463586i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	−0.967851	−	0.251523i	$-0.919068\pi$
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	0.701751	+	0.712422i	$0.252402\pi$
$174$		0			0
$175$		0			0
$176$	−5.00000			−0.376889
$177$	−2.00000	+	3.46410i	−0.150329	+	0.260378i
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	0.995009	−	0.0997838i	$-0.0318151\pi$
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	−0.583920	+	0.811811i	$0.698482\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	2.50000	−	0.866025i	0.185312	−	0.0641941i
$183$	−2.00000			−0.147844
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−5.00000	+	8.66025i	−0.365636	+	0.633300i
$188$	−13.0000			−0.948122
$189$	2.00000	+	1.73205i	0.145479	+	0.125988i
$190$		0			0
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	−0.416751	−	0.909021i	$-0.636831\pi$
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	0.995610	−	0.0935936i	$-0.0298354\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	−27.0000			−1.92367			−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000			−1.92367			−0.961835	+	0.273629i	$0.911776\pi$
$198$	−2.50000	+	4.33013i	−0.177667	+	0.307729i
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	0.999990	−	0.00436292i	$-0.00138876\pi$
$199$	7.00000	+	12.1244i	0.496217	+	0.859473i	−0.503774	+	0.863836i	$0.668055\pi$
$200$		0			0
$201$	−3.00000	+	5.19615i	−0.211604	+	0.366508i
$202$	−8.00000			−0.562878
$203$		0			0
$204$	−2.00000			−0.140028
$205$		0			0
$206$		0			0
$207$	−1.50000	−	2.59808i	−0.104257	−	0.180579i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−35.0000			−2.42100
$210$		0			0
$211$	19.0000			1.30801			0.654007	−	0.756489i	$-0.273087\pi$
$211$	19.0000			1.30801			0.654007	+	0.756489i	$0.273087\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$	1.00000	+	1.73205i	0.0685189	+	0.118678i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−3.00000	+	15.5885i	−0.203653	+	1.05821i
$218$	18.0000			1.21911
$219$	−2.00000	+	3.46410i	−0.135147	+	0.234082i
$220$		0			0
$221$	1.00000	+	1.73205i	0.0672673	+	0.116510i
$222$	−2.50000	+	4.33013i	−0.167789	+	0.290619i
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	3.00000	−	5.19615i	0.199557	−	0.345643i
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$	−3.50000	−	6.06218i	−0.231793	−	0.401478i
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$		0			0
$231$	12.5000	−	4.33013i	0.822440	−	0.284901i
$232$		0			0
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$	0.500000	+	0.866025i	0.0326860	+	0.0566139i
$235$		0			0
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$	−14.0000			−0.909398
$238$	4.00000	+	3.46410i	0.259281	+	0.224544i
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	9.00000			0.573819
$247$	−3.50000	+	6.06218i	−0.222700	+	0.385727i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$	5.00000	+	8.66025i	0.316862	+	0.548821i
$250$		0			0
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$	2.00000	+	1.73205i	0.125988	+	0.109109i
$253$	−15.0000			−0.943042
$254$	4.50000	−	7.79423i	0.282355	−	0.489053i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.00000	−	8.66025i	0.311891	−	0.540212i	−0.666880	−	0.745165i	$-0.732371\pi$
$257$	5.00000	−	8.66025i	0.311891	−	0.540212i	0.978772	+	0.204953i	$0.0657041\pi$
$258$	−10.0000			−0.622573
$259$	12.5000	−	4.33013i	0.776712	−	0.269061i
$260$		0			0
$261$		0			0
$262$	−8.50000	−	14.7224i	−0.525132	−	0.909555i
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	−2.50000	+	4.33013i	−0.153864	+	0.266501i
$265$		0			0
$266$	−3.50000	+	18.1865i	−0.214599	+	1.11509i
$267$	10.0000			0.611990
$268$	−3.00000	+	5.19615i	−0.183254	+	0.317406i
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$		0			0
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$	−2.00000			−0.121268
$273$	0.500000	−	2.59808i	0.0302614	−	0.157243i
$274$	4.00000			0.241649
$275$		0			0
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	−4.00000	+	6.92820i	−0.239904	+	0.415526i
$279$	−6.00000			−0.359211
$280$		0			0
$281$	−11.0000			−0.656205			−0.328102	−	0.944642i	$-0.606409\pi$
$281$	−11.0000			−0.656205			−0.328102	+	0.944642i	$0.606409\pi$
$282$	−6.50000	+	11.2583i	−0.387069	+	0.670424i
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	−0.936039	−	0.351895i	$-0.885537\pi$
$283$	−13.0000	−	22.5167i	−0.772770	−	1.33848i	0.163270	−	0.986581i	$-0.447796\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$	5.00000			0.295656
$287$	−18.0000	−	15.5885i	−1.06251	−	0.920158i
$288$	−1.00000			−0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	1.00000			0.0584206			0.0292103	−	0.999573i	$-0.490701\pi$
$293$	1.00000			0.0584206			0.0292103	+	0.999573i	$0.490701\pi$
$294$	−1.00000	−	6.92820i	−0.0583212	−	0.404061i
$295$		0			0
$296$	−2.50000	+	4.33013i	−0.145310	+	0.251684i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$		0			0
$301$	20.0000	+	17.3205i	1.15278	+	0.998337i
$302$	22.0000			1.26596
$303$	−4.00000	+	6.92820i	−0.229794	+	0.398015i
$304$	−3.50000	−	6.06218i	−0.200739	−	0.347690i
$305$		0			0
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	12.5000	−	4.33013i	0.712254	−	0.246732i
$309$		0			0
$310$		0			0
$311$	13.0000	+	22.5167i	0.737162	+	1.27680i	0.953768	+	0.300544i	$0.0971681\pi$
$311$	13.0000	+	22.5167i	0.737162	+	1.27680i	−0.216606	+	0.976259i	$0.569499\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	−14.0000			−0.787562
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	−0.892741	−	0.450570i	$-0.851221\pi$
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	0.836576	+	0.547852i	$0.184554\pi$
$318$	−0.500000	−	0.866025i	−0.0280386	−	0.0485643i
$319$		0			0
$320$		0			0
$321$	12.0000			0.669775
$322$	−1.50000	+	7.79423i	−0.0835917	+	0.434355i
$323$	−14.0000			−0.778981
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−6.00000	−	10.3923i	−0.332309	−	0.575577i
$327$	9.00000	−	15.5885i	0.497701	−	0.862044i
$328$	9.00000			0.496942
$329$	32.5000	−	11.2583i	1.79178	−	0.620692i
$330$		0			0
$331$	7.50000	−	12.9904i	0.412237	−	0.714016i	−0.582897	−	0.812546i	$-0.698081\pi$
$331$	7.50000	−	12.9904i	0.412237	−	0.714016i	0.995134	+	0.0985303i	$0.0314141\pi$
$332$	5.00000	+	8.66025i	0.274411	+	0.475293i
$333$	2.50000	+	4.33013i	0.136999	+	0.237289i
$334$	−9.50000	+	16.4545i	−0.519817	+	0.900349i
$335$		0			0
$336$	2.00000	+	1.73205i	0.109109	+	0.0944911i
$337$	−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
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	−15.0000	+	25.9808i	−0.812296	+	1.40694i
$342$	−7.00000			−0.378517
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	3.50000	+	6.06218i	0.188161	+	0.325905i
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	0.996826	−	0.0796169i	$-0.0253697\pi$
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	−0.567363	+	0.823468i	$0.692036\pi$
$348$		0			0
$349$	−24.0000			−1.28469			−0.642345	−	0.766415i	$-0.722038\pi$
$349$	−24.0000			−1.28469			−0.642345	+	0.766415i	$0.722038\pi$
$350$		0			0
$351$	1.00000			0.0533761
$352$	−2.50000	+	4.33013i	−0.133250	+	0.230797i
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$	10.0000			0.529999
$357$	5.00000	−	1.73205i	0.264628	−	0.0916698i
$358$	11.0000			0.581368
$359$	14.0000	−	24.2487i	0.738892	−	1.27980i	−0.214103	−	0.976811i	$-0.568683\pi$
$359$	14.0000	−	24.2487i	0.738892	−	1.27980i	0.952995	−	0.302987i	$-0.0979839\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$	14.0000			0.734809
$364$	0.500000	−	2.59808i	0.0262071	−	0.136176i
$365$		0			0
$366$	−1.00000	+	1.73205i	−0.0522708	+	0.0905357i
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.707744	+	0.706469i	$0.249713\pi$
$367$	18.5000	+	32.0429i	0.965692	+	1.67263i	0.257948	+	0.966159i	$0.416954\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		0			0
$371$	−0.500000	+	2.59808i	−0.0259587	+	0.134885i
$372$	−6.00000			−0.311086
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	5.00000	+	8.66025i	0.258544	+	0.447811i
$375$		0			0
$376$	−6.50000	+	11.2583i	−0.335212	+	0.580604i
$377$		0			0
$378$	2.50000	−	0.866025i	0.128586	−	0.0445435i
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$	−4.50000	−	7.79423i	−0.230542	−	0.399310i
$382$	−8.00000	−	13.8564i	−0.409316	−	0.708955i
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	−0.727851	−	0.685736i	$-0.759481\pi$
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	0.957790	+	0.287469i	$0.0928139\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	18.0000			0.916176
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$	−4.00000	−	6.92820i	−0.203069	−	0.351726i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	−1.00000	−	6.92820i	−0.0505076	−	0.349927i
$393$	−17.0000			−0.857537
$394$	−13.5000	+	23.3827i	−0.680120	+	1.17800i
$395$		0			0
$396$	2.50000	+	4.33013i	0.125630	+	0.217597i
$397$	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	$0.150684\pi$
$398$	14.0000			0.701757
$399$	14.0000	+	12.1244i	0.700877	+	0.606977i
$400$		0			0
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$	3.00000	+	5.19615i	0.149626	+	0.259161i
$403$	3.00000	+	5.19615i	0.149441	+	0.258839i
$404$	−4.00000	+	6.92820i	−0.199007	+	0.344691i
$405$		0			0
$406$		0			0
$407$	25.0000			1.23920
$408$	−1.00000	+	1.73205i	−0.0495074	+	0.0857493i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	2.00000	−	3.46410i	0.0986527	−	0.170872i
$412$		0			0
$413$	2.00000	−	10.3923i	0.0984136	−	0.511372i
$414$	−3.00000			−0.147442
$415$		0			0
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	4.00000	+	6.92820i	0.195881	+	0.339276i
$418$	−17.5000	+	30.3109i	−0.855953	+	1.48255i
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	9.50000	−	16.4545i	0.462453	−	0.800992i
$423$	6.50000	+	11.2583i	0.316041	+	0.547399i
$424$	−0.500000	−	0.866025i	−0.0242821	−	0.0420579i
$425$		0			0
$426$	2.00000			0.0969003
$427$	5.00000	−	1.73205i	0.241967	−	0.0838198i
$428$	12.0000			0.580042
$429$	2.50000	−	4.33013i	0.120701	−	0.209061i
$430$		0			0
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	4.00000			0.192228			0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000			0.192228			0.0961139	+	0.995370i	$0.469359\pi$
$434$	12.0000	+	10.3923i	0.576018	+	0.498847i
$435$		0			0
$436$	9.00000	−	15.5885i	0.431022	−	0.746552i
$437$	−10.5000	−	18.1865i	−0.502283	−	0.869980i
$438$	2.00000	+	3.46410i	0.0955637	+	0.165521i
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$	2.00000			0.0951303
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	−0.785916	−	0.618333i	$-0.787808\pi$
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	0.928450	+	0.371457i	$0.121142\pi$
$444$	2.50000	+	4.33013i	0.118645	+	0.205499i
$445$		0			0
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$	−6.00000			−0.283790
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	−22.5000	−	38.9711i	−1.05948	−	1.83508i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	11.0000	−	19.0526i	0.516825	−	0.895167i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−7.00000			−0.327805
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.0474665	−	0.998873i	$-0.484885\pi$
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.841316	−	0.540544i	$-0.181781\pi$
$458$	−2.00000	−	3.46410i	−0.0934539	−	0.161867i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$	2.50000	−	12.9904i	0.116311	−	0.604367i
$463$	−15.0000			−0.697109			−0.348555	−	0.937288i	$-0.613327\pi$
$463$	−15.0000			−0.697109			−0.348555	+	0.937288i	$0.613327\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.00000	+	1.73205i	−0.0462745	+	0.0801498i	−0.888235	−	0.459390i	$-0.848068\pi$
$467$	−1.00000	+	1.73205i	−0.0462745	+	0.0801498i	0.841960	+	0.539539i	$0.181402\pi$
$468$	1.00000			0.0462250
$469$	3.00000	−	15.5885i	0.138527	−	0.719808i
$470$		0			0
$471$	−6.50000	+	11.2583i	−0.299504	+	0.518756i
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	25.0000	+	43.3013i	1.14950	+	1.99099i
$474$	−7.00000	+	12.1244i	−0.321521	+	0.556890i
$475$		0			0
$476$	5.00000	−	1.73205i	0.229175	−	0.0793884i
$477$	−1.00000			−0.0457869
$478$	10.0000	−	17.3205i	0.457389	−	0.792222i
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$		0			0
$481$	2.50000	−	4.33013i	0.113990	−	0.197437i
$482$	1.00000			0.0455488
$483$	6.00000	+	5.19615i	0.273009	+	0.236433i
$484$	14.0000			0.636364
$485$		0			0
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−12.0000	−	20.7846i	−0.543772	−	0.941841i	−0.998683	−	0.0513038i	$-0.983662\pi$
$487$	−12.0000	−	20.7846i	−0.543772	−	0.941841i	0.454911	−	0.890537i	$-0.349671\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	−12.0000			−0.542659
$490$		0			0
$491$	24.0000			1.08310			0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000			1.08310			0.541552	+	0.840667i	$0.317837\pi$
$492$	4.50000	−	7.79423i	0.202876	−	0.351391i
$493$		0			0
$494$	3.50000	+	6.06218i	0.157472	+	0.272750i
$495$		0			0
$496$	−6.00000			−0.269408
$497$	−4.00000	−	3.46410i	−0.179425	−	0.155386i
$498$	10.0000			0.448111
$499$	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
$501$	9.50000	+	16.4545i	0.424429	+	0.735132i
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	2.50000	−	0.866025i	0.111359	−	0.0385758i
$505$		0			0
$506$	−7.50000	+	12.9904i	−0.333416	+	0.577493i
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	−4.50000	−	7.79423i	−0.199655	−	0.345813i
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	−0.978421	−	0.206623i	$-0.933753\pi$
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	0.668151	+	0.744026i	$0.267086\pi$
$510$		0			0
$511$	2.00000	−	10.3923i	0.0884748	−	0.459728i
$512$	−1.00000			−0.0441942
$513$	−3.50000	+	6.06218i	−0.154529	+	0.267652i
$514$	−5.00000	−	8.66025i	−0.220541	−	0.381987i
$515$		0			0
$516$	−5.00000	+	8.66025i	−0.220113	+	0.381246i
$517$	65.0000			2.85870
$518$	2.50000	−	12.9904i	0.109844	−	0.570765i
$519$	7.00000			0.307266
$520$		0			0
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	0.982231	−	0.187678i	$-0.0600963\pi$
$521$	7.50000	+	12.9904i	0.328581	+	0.569119i	−0.653650	+	0.756797i	$0.726763\pi$
$522$		0			0
$523$	−6.00000	+	10.3923i	−0.262362	+	0.454424i	−0.966869	−	0.255273i	$-0.917835\pi$
$523$	−6.00000	+	10.3923i	−0.262362	+	0.454424i	0.704507	+	0.709697i	$0.251168\pi$
$524$	−17.0000			−0.742648
$525$		0			0
$526$	−24.0000			−1.04645
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	2.50000	+	4.33013i	0.108799	+	0.188445i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	4.00000			0.173585
$532$	14.0000	+	12.1244i	0.606977	+	0.525657i
$533$	−9.00000			−0.389833
$534$	5.00000	−	8.66025i	0.216371	−	0.374766i
$535$		0			0
$536$	3.00000	+	5.19615i	0.129580	+	0.224440i
$537$	5.50000	−	9.52628i	0.237343	−	0.411089i
$538$	−14.0000			−0.603583
$539$	−27.5000	+	21.6506i	−1.18451	+	0.932559i
$540$		0			0
$541$	−2.00000	+	3.46410i	−0.0859867	+	0.148933i	−0.905811	−	0.423681i	$-0.860738\pi$
$541$	−2.00000	+	3.46410i	−0.0859867	+	0.148933i	0.819825	+	0.572615i	$0.194071\pi$
$542$	4.00000	+	6.92820i	0.171815	+	0.297592i
$543$	1.00000	+	1.73205i	0.0429141	+	0.0743294i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$		0			0
$546$	−2.00000	−	1.73205i	−0.0855921	−	0.0741249i
$547$	−14.0000			−0.598597			−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000			−0.598597			−0.299298	+	0.954160i	$0.596753\pi$
$548$	2.00000	−	3.46410i	0.0854358	−	0.147979i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$		0			0
$552$	−3.00000			−0.127688
$553$	35.0000	−	12.1244i	1.48835	−	0.515580i
$554$	−2.00000			−0.0849719
$555$		0			0
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	0.900967	+	0.433888i	$0.142859\pi$
$557$	19.5000	+	33.7750i	0.826242	+	1.43109i	−0.0747252	+	0.997204i	$0.523808\pi$
$558$	−3.00000	+	5.19615i	−0.127000	+	0.219971i
$559$	10.0000			0.422955
$560$		0			0
$561$	10.0000			0.422200
$562$	−5.50000	+	9.52628i	−0.232003	+	0.401842i
$563$	−15.0000	−	25.9808i	−0.632175	−	1.09496i	−0.987106	−	0.160066i	$-0.948829\pi$
$563$	−15.0000	−	25.9808i	−0.632175	−	1.09496i	0.354932	−	0.934892i	$-0.384504\pi$
$564$	6.50000	+	11.2583i	0.273699	+	0.474061i
$565$		0			0
$566$	−26.0000			−1.09286
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$	2.00000			0.0839181
$569$	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
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$	2.50000	−	4.33013i	0.104530	−	0.181052i
$573$	−16.0000			−0.668410
$574$	−22.5000	+	7.79423i	−0.939132	+	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−12.0000	−	20.7846i	−0.499567	−	0.865275i	0.500433	−	0.865775i	$-0.333174\pi$
$577$	−12.0000	−	20.7846i	−0.499567	−	0.865275i	−1.00000		0.000500448i	$0.999841\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	9.00000	−	15.5885i	0.374027	−	0.647834i
$580$		0			0
$581$	−20.0000	−	17.3205i	−0.829740	−	0.718576i
$582$	−8.00000			−0.331611
$583$	−2.50000	+	4.33013i	−0.103539	+	0.179336i
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	0.500000	−	0.866025i	0.0206548	−	0.0357752i
$587$	2.00000			0.0825488			0.0412744	−	0.999148i	$-0.486858\pi$
$587$	2.00000			0.0825488			0.0412744	+	0.999148i	$0.486858\pi$
$588$	−6.50000	−	2.59808i	−0.268055	−	0.107143i
$589$	−42.0000			−1.73058
$590$		0			0
$591$	13.5000	+	23.3827i	0.555316	+	0.961835i
$592$	2.50000	+	4.33013i	0.102749	+	0.177967i
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	−0.271016	−	0.962575i	$-0.587360\pi$
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	0.969122	−	0.246581i	$-0.0793071\pi$
$594$	5.00000			0.205152
$595$		0			0
$596$	−6.00000			−0.245770
$597$	7.00000	−	12.1244i	0.286491	−	0.496217i
$598$	1.50000	+	2.59808i	0.0613396	+	0.106243i
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	0.996358	+	0.0852695i	$0.0271751\pi$
$599$	14.0000	+	24.2487i	0.572024	+	0.990775i	−0.424333	+	0.905506i	$0.639492\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$	25.0000	−	8.66025i	1.01892	−	0.352966i
$603$	6.00000			0.244339
$604$	11.0000	−	19.0526i	0.447584	−	0.775238i
$605$		0			0
$606$	4.00000	+	6.92820i	0.162489	+	0.281439i
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	−0.967256	−	0.253804i	$-0.918318\pi$
$607$	−6.50000	+	11.2583i	−0.263827	+	0.456962i	0.703429	+	0.710766i	$0.251651\pi$
$608$	−7.00000			−0.283887
$609$		0			0
$610$		0			0
$611$	6.50000	−	11.2583i	0.262962	−	0.455463i
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	−9.50000	−	16.4545i	−0.383701	−	0.664590i	0.607887	−	0.794024i	$-0.292017\pi$
$613$	−9.50000	−	16.4545i	−0.383701	−	0.664590i	−0.991588	+	0.129433i	$0.958684\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	2.50000	−	12.9904i	0.100728	−	0.523397i
$617$	30.0000			1.20775			0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000			1.20775			0.603877	+	0.797077i	$0.293622\pi$
$618$		0			0
$619$	−7.50000	−	12.9904i	−0.301450	−	0.522127i	0.675014	−	0.737805i	$-0.264137\pi$
$619$	−7.50000	−	12.9904i	−0.301450	−	0.522127i	−0.976465	+	0.215677i	$0.930804\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$	26.0000			1.04251
$623$	−25.0000	+	8.66025i	−1.00160	+	0.346966i
$624$	1.00000			0.0400320
$625$		0			0
$626$	−5.00000	−	8.66025i	−0.199840	−	0.346133i
$627$	17.5000	+	30.3109i	0.698883	+	1.21050i
$628$	−6.50000	+	11.2583i	−0.259378	+	0.449256i
$629$	10.0000			0.398726
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$	−7.00000	+	12.1244i	−0.278445	+	0.482281i
$633$	−9.50000	−	16.4545i	−0.377591	−	0.654007i
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$		0			0
$636$	−1.00000			−0.0396526
$637$	1.00000	+	6.92820i	0.0396214	+	0.274505i
$638$		0			0
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	38.0000			1.49857			0.749287	−	0.662246i	$-0.230396\pi$
$643$	38.0000			1.49857			0.749287	+	0.662246i	$0.230396\pi$
$644$	6.00000	+	5.19615i	0.236433	+	0.204757i
$645$		0			0
$646$	−7.00000	+	12.1244i	−0.275411	+	0.477026i
$647$	0.500000	+	0.866025i	0.0196570	+	0.0340470i	0.875687	−	0.482880i	$-0.160409\pi$
$647$	0.500000	+	0.866025i	0.0196570	+	0.0340470i	−0.856030	+	0.516927i	$0.827076\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$		0			0
$651$	15.0000	−	5.19615i	0.587896	−	0.203653i
$652$	−12.0000			−0.469956
$653$	−2.50000	+	4.33013i	−0.0978326	+	0.169451i	−0.910787	−	0.412876i	$-0.864524\pi$
$653$	−2.50000	+	4.33013i	−0.0978326	+	0.169451i	0.812955	+	0.582327i	$0.197858\pi$
$654$	−9.00000	−	15.5885i	−0.351928	−	0.609557i
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$	4.00000			0.156055
$658$	6.50000	−	33.7750i	0.253396	−	1.31669i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	−20.0000	−	34.6410i	−0.777910	−	1.34738i	−0.933144	−	0.359502i	$-0.882947\pi$
$661$	−20.0000	−	34.6410i	−0.777910	−	1.34738i	0.155235	−	0.987878i	$-0.450387\pi$
$662$	−7.50000	−	12.9904i	−0.291496	−	0.504885i
$663$	1.00000	−	1.73205i	0.0388368	−	0.0672673i
$664$	10.0000			0.388075
$665$		0			0
$666$	5.00000			0.193746
$667$		0			0
$668$	9.50000	+	16.4545i	0.367566	+	0.636643i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$		0			0
$671$	10.0000			0.386046
$672$	2.50000	−	0.866025i	0.0964396	−	0.0334077i
$673$	36.0000			1.38770			0.693849	−	0.720121i	$-0.255914\pi$
$673$	36.0000			1.38770			0.693849	+	0.720121i	$0.255914\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	0.352549	+	0.935793i	$0.385315\pi$
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	−0.986695	+	0.162581i	$0.948018\pi$
$678$	−6.00000			−0.230429
$679$	16.0000	+	13.8564i	0.614024	+	0.531760i
$680$		0			0
$681$	−7.00000	+	12.1244i	−0.268241	+	0.464606i
$682$	15.0000	+	25.9808i	0.574380	+	0.994855i
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	0.901750	−	0.432259i	$-0.142283\pi$
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	−0.825222	+	0.564809i	$0.808950\pi$
$684$	−3.50000	+	6.06218i	−0.133826	+	0.231793i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−4.00000			−0.152610
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	0.500000	+	0.866025i	0.0190485	+	0.0329929i
$690$		0			0
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	7.00000			0.266100
$693$	−10.0000	−	8.66025i	−0.379869	−	0.328976i
$694$	16.0000			0.607352
$695$		0			0
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$	−12.0000	+	20.7846i	−0.454207	+	0.786709i
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	0.500000	−	0.866025i	0.0188713	−	0.0326860i
$703$	17.5000	+	30.3109i	0.660025	+	1.14320i
$704$	2.50000	+	4.33013i	0.0942223	+	0.163198i
$705$		0			0
$706$		0			0
$707$	4.00000	−	20.7846i	0.150435	−	0.781686i
$708$	4.00000			0.150329
$709$	−8.00000	+	13.8564i	−0.300446	+	0.520388i	−0.976237	−	0.216705i	$-0.930469\pi$
$709$	−8.00000	+	13.8564i	−0.300446	+	0.520388i	0.675791	+	0.737093i	$0.263802\pi$
$710$		0			0
$711$	7.00000	+	12.1244i	0.262521	+	0.454699i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$	−18.0000			−0.674105
$714$	1.00000	−	5.19615i	0.0374241	−	0.194461i
$715$		0			0
$716$	5.50000	−	9.52628i	0.205545	−	0.356014i
$717$	−10.0000	−	17.3205i	−0.373457	−	0.646846i
$718$	−14.0000	−	24.2487i	−0.522475	−	0.904954i
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	−0.846776	−	0.531949i	$-0.821460\pi$
$719$	1.00000	−	1.73205i	0.0372937	−	0.0645946i	0.884070	+	0.467355i	$0.154793\pi$
$720$		0			0
$721$		0			0
$722$	−30.0000			−1.11648
$723$	0.500000	−	0.866025i	0.0185952	−	0.0322078i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$	7.00000	−	12.1244i	0.259794	−	0.449977i
$727$	53.0000			1.96566			0.982831	−	0.184510i	$-0.0590699\pi$
$727$	53.0000			1.96566			0.982831	+	0.184510i	$0.0590699\pi$
$728$	−2.00000	−	1.73205i	−0.0741249	−	0.0641941i
$729$	1.00000			0.0370370
$730$		0			0
$731$	10.0000	+	17.3205i	0.369863	+	0.640622i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$	10.5000	−	18.1865i	0.387826	−	0.671735i	−0.604331	−	0.796734i	$-0.706559\pi$
$733$	10.5000	−	18.1865i	0.387826	−	0.671735i	0.992157	+	0.124999i	$0.0398927\pi$
$734$	37.0000			1.36569
$735$		0			0
$736$	−3.00000			−0.110581
$737$	15.0000	−	25.9808i	0.552532	−	0.957014i
$738$	−4.50000	−	7.79423i	−0.165647	−	0.286910i
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	−0.867581	−	0.497296i	$-0.834326\pi$
$739$	−23.5000	−	40.7032i	−0.864461	−	1.49729i	0.00311943	−	0.999995i	$-0.499007\pi$
$740$		0			0
$741$	7.00000			0.257151
$742$	2.00000	+	1.73205i	0.0734223	+	0.0635856i
$743$	−31.0000			−1.13728			−0.568640	−	0.822587i	$-0.692530\pi$
$743$	−31.0000			−1.13728			−0.568640	+	0.822587i	$0.692530\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$		0			0
$746$	3.00000	+	5.19615i	0.109838	+	0.190245i
$747$	5.00000	−	8.66025i	0.182940	−	0.316862i
$748$	10.0000			0.365636
$749$	−30.0000	+	10.3923i	−1.09618	+	0.379727i
$750$		0			0
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	−0.900207	−	0.435463i	$-0.856585\pi$
$751$	−2.00000	+	3.46410i	−0.0729810	+	0.126407i	0.827225	+	0.561870i	$0.189918\pi$
$752$	6.50000	+	11.2583i	0.237031	+	0.410549i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$		0			0
$755$		0			0
$756$	0.500000	−	2.59808i	0.0181848	−	0.0944911i
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$	7.50000	+	12.9904i	0.272233	+	0.471521i
$760$		0			0
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$	−9.00000			−0.326036
$763$	−9.00000	+	46.7654i	−0.325822	+	1.69302i
$764$	−16.0000			−0.578860
$765$		0			0
$766$	−4.50000	−	7.79423i	−0.162592	−	0.281617i
$767$	−2.00000	−	3.46410i	−0.0722158	−	0.125081i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	51.0000			1.83911			0.919554	−	0.392965i	$-0.128551\pi$
$769$	51.0000			1.83911			0.919554	+	0.392965i	$0.128551\pi$
$770$		0			0
$771$	−10.0000			−0.360141
$772$	9.00000	−	15.5885i	0.323917	−	0.561041i
$773$	18.5000	+	32.0429i	0.665399	+	1.15250i	0.979177	+	0.203008i	$0.0650718\pi$
$773$	18.5000	+	32.0429i	0.665399	+	1.15250i	−0.313778	+	0.949496i	$0.601595\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$		0			0
$776$	−8.00000			−0.287183
$777$	−10.0000	−	8.66025i	−0.358748	−	0.310685i
$778$	−6.00000			−0.215110
$779$	31.5000	−	54.5596i	1.12860	−	1.95480i
$780$		0			0
$781$	−5.00000	−	8.66025i	−0.178914	−	0.309888i
$782$	−3.00000	+	5.19615i	−0.107280	+	0.185814i
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$	−8.50000	+	14.7224i	−0.303185	+	0.525132i
$787$	−19.0000	−	32.9090i	−0.677277	−	1.17308i	−0.975798	−	0.218675i	$-0.929827\pi$
$787$	−19.0000	−	32.9090i	−0.677277	−	1.17308i	0.298521	−	0.954403i	$-0.403507\pi$
$788$	13.5000	+	23.3827i	0.480918	+	0.832974i
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$		0			0
$791$	12.0000	+	10.3923i	0.426671	+	0.369508i
$792$	5.00000			0.177667
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$	17.5000	−	6.06218i	0.619493	−	0.214599i
$799$	26.0000			0.919814
$800$		0			0
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$	−13.5000	−	23.3827i	−0.476702	−	0.825671i
$803$	10.0000	−	17.3205i	0.352892	−	0.611227i
$804$	6.00000			0.211604
$805$		0			0
$806$	6.00000			0.211341
$807$	−7.00000	+	12.1244i	−0.246412	+	0.426798i
$808$	4.00000	+	6.92820i	0.140720	+	0.243733i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$		0			0
$811$	11.0000			0.386262			0.193131	−	0.981173i	$-0.438136\pi$
$811$	11.0000			0.386262			0.193131	+	0.981173i	$0.438136\pi$
$812$		0			0
$813$	8.00000			0.280572
$814$	12.5000	−	21.6506i	0.438125	−	0.758854i
$815$		0			0
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	−35.0000	+	60.6218i	−1.22449	+	2.12089i
$818$	−10.0000			−0.349642
$819$	−2.50000	+	0.866025i	−0.0873571	+	0.0302614i
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$	−2.00000	−	3.46410i	−0.0697580	−	0.120824i
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		0			0
$825$		0			0
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$	−1.50000	+	2.59808i	−0.0521286	+	0.0902894i
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$		0			0
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	1.00000			0.0346688
$833$	−11.0000	+	8.66025i	−0.381127	+	0.300060i
$834$	8.00000			0.277017
$835$		0			0
$836$	17.5000	+	30.3109i	0.605250	+	1.04832i
$837$	3.00000	+	5.19615i	0.103695	+	0.179605i
$838$	1.50000	−	2.59808i	0.0518166	−	0.0897491i
$839$	2.00000			0.0690477			0.0345238	−	0.999404i	$-0.489009\pi$
$839$	2.00000			0.0690477			0.0345238	+	0.999404i	$0.489009\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−10.0000	+	17.3205i	−0.344623	+	0.596904i
$843$	5.50000	+	9.52628i	0.189430	+	0.328102i
$844$	−9.50000	−	16.4545i	−0.327003	−	0.566387i
$845$		0			0
$846$	13.0000			0.446949
$847$	−35.0000	+	12.1244i	−1.20261	+	0.416598i
$848$	−1.00000			−0.0343401
$849$	−13.0000	+	22.5167i	−0.446159	+	0.772770i
$850$		0			0
$851$	7.50000	+	12.9904i	0.257097	+	0.445305i
$852$	1.00000	−	1.73205i	0.0342594	−	0.0593391i
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	1.00000	−	5.19615i	0.0342193	−	0.177809i
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	28.0000	+	48.4974i	0.956462	+	1.65664i	0.730987	+	0.682391i	$0.239060\pi$
$857$	28.0000	+	48.4974i	0.956462	+	1.65664i	0.225475	+	0.974249i	$0.427607\pi$
$858$	−2.50000	−	4.33013i	−0.0853486	−	0.147828i
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	0.376381	+	0.926465i	$0.377169\pi$
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	−0.990533	+	0.137277i	$0.956165\pi$
$860$		0			0
$861$	−4.50000	+	23.3827i	−0.153360	+	0.796880i
$862$	−18.0000			−0.613082
$863$	−7.50000	+	12.9904i	−0.255303	+	0.442198i	−0.964978	−	0.262332i	$-0.915509\pi$
$863$	−7.50000	+	12.9904i	−0.255303	+	0.442198i	0.709675	+	0.704529i	$0.248842\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	2.00000	−	3.46410i	0.0679628	−	0.117715i
$867$	−13.0000			−0.441503
$868$	15.0000	−	5.19615i	0.509133	−	0.176369i
$869$	70.0000			2.37459
$870$		0			0
$871$	−3.00000	−	5.19615i	−0.101651	−	0.176065i
$872$	−9.00000	−	15.5885i	−0.304778	−	0.527892i
$873$	−4.00000	+	6.92820i	−0.135379	+	0.234484i
$874$	−21.0000			−0.710336
$875$		0			0
$876$	4.00000			0.135147
$877$	13.5000	−	23.3827i	0.455863	−	0.789577i	−0.542875	−	0.839814i	$-0.682664\pi$
$877$	13.5000	−	23.3827i	0.455863	−	0.789577i	0.998737	+	0.0502365i	$0.0159975\pi$
$878$		0			0
$879$	−0.500000	−	0.866025i	−0.0168646	−	0.0292103i
$880$		0			0
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$	−5.50000	+	4.33013i	−0.185195	+	0.145803i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	1.00000	−	1.73205i	0.0336336	−	0.0582552i
$885$		0			0
$886$	−3.00000	−	5.19615i	−0.100787	−	0.174568i
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$	5.00000			0.167789
$889$	18.0000	+	15.5885i	0.603701	+	0.522820i
$890$		0			0
$891$	2.50000	−	4.33013i	0.0837532	−	0.145065i
$892$	−8.00000	−	13.8564i	−0.267860	−	0.463947i
$893$	45.5000	+	78.8083i	1.52260	+	2.63722i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$	3.00000			0.100167
$898$	4.50000	−	7.79423i	0.150167	−	0.260097i
$899$		0			0
$900$		0			0
$901$	−1.00000	+	1.73205i	−0.0333148	+	0.0577030i
$902$	−45.0000			−1.49834
$903$	5.00000	−	25.9808i	0.166390	−	0.864586i
$904$	−6.00000			−0.199557
$905$		0			0
$906$	−11.0000	−	19.0526i	−0.365451	−	0.632979i
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	0.967730	−	0.251990i	$-0.0810849\pi$
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	−0.702094	+	0.712084i	$0.747752\pi$
$908$	−7.00000	+	12.1244i	−0.232303	+	0.402361i
$909$	8.00000			0.265343
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	−3.50000	+	6.06218i	−0.115897	+	0.200739i
$913$	−25.0000	−	43.3013i	−0.827379	−	1.43306i
$914$	−19.0000	−	32.9090i	−0.628464	−	1.08853i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	42.5000	−	14.7224i	1.40347	−	0.486178i
$918$	2.00000			0.0660098
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.129893	+	0.991528i	$0.541463\pi$
$919$	−28.0000	+	48.4974i	−0.923635	+	1.59978i	−0.793742	+	0.608254i	$0.791870\pi$
$920$		0			0
$921$	−1.00000	−	1.73205i	−0.0329511	−	0.0570730i
$922$	−6.00000	+	10.3923i	−0.197599	+	0.342252i
$923$	−2.00000			−0.0658308
$924$	−10.0000	−	8.66025i	−0.328976	−	0.284901i
$925$		0			0
$926$	−7.50000	+	12.9904i	−0.246465	+	0.426890i
$927$		0			0
$928$		0			0
$929$	−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
$931$	−45.5000	−	18.1865i	−1.49120	−	0.596040i
$932$		0			0
$933$	13.0000	−	22.5167i	0.425601	−	0.737162i
$934$	1.00000	+	1.73205i	0.0327210	+	0.0566744i
$935$		0			0
$936$	0.500000	−	0.866025i	0.0163430	−	0.0283069i
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	−12.0000	−	10.3923i	−0.391814	−	0.339321i
$939$	−10.0000			−0.326338
$940$		0			0
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	6.50000	+	11.2583i	0.211781	+	0.366816i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$	4.00000			0.130189
$945$		0			0
$946$	50.0000			1.62564
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	7.00000	+	12.1244i	0.227349	+	0.393781i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	2.00000			0.0648544
$952$	1.00000	−	5.19615i	0.0324102	−	0.168408i
$953$	−24.0000			−0.777436			−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000			−0.777436			−0.388718	+	0.921357i	$0.627082\pi$
$954$	−0.500000	+	0.866025i	−0.0161881	+	0.0280386i
$955$		0			0
$956$	−10.0000	−	17.3205i	−0.323423	−	0.560185i
$957$		0			0
$958$	−8.00000			−0.258468
$959$	−2.00000	+	10.3923i	−0.0645834	+	0.335585i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−2.50000	−	4.33013i	−0.0806032	−	0.139609i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	0.500000	−	0.866025i	0.0161039	−	0.0278928i
$965$		0			0
$966$	7.50000	−	2.59808i	0.241309	−	0.0835917i
$967$	−24.0000			−0.771788			−0.385894	−	0.922543i	$-0.626107\pi$
$967$	−24.0000			−0.771788			−0.385894	+	0.922543i	$0.626107\pi$
$968$	7.00000	−	12.1244i	0.224989	−	0.389692i
$969$	7.00000	+	12.1244i	0.224872	+	0.389490i
$970$		0			0
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	0.362604	+	0.931943i	$0.381888\pi$
$971$	−19.5000	+	33.7750i	−0.625785	+	1.08389i	−0.988389	+	0.151948i	$0.951445\pi$
$972$	1.00000			0.0320750
$973$	−16.0000	−	13.8564i	−0.512936	−	0.444216i
$974$	−24.0000			−0.769010
$975$		0			0
$976$	1.00000	+	1.73205i	0.0320092	+	0.0554416i
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	−6.00000	+	10.3923i	−0.191859	+	0.332309i
$979$	−50.0000			−1.59801
$980$		0			0
$981$	−18.0000			−0.574696
$982$	12.0000	−	20.7846i	0.382935	−	0.663264i
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	−0.999532	−	0.0306024i	$-0.990257\pi$
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	0.473263	−	0.880921i	$-0.343076\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$		0			0
$986$		0			0
$987$	−26.0000	−	22.5167i	−0.827589	−	0.716713i
$988$	7.00000			0.222700
$989$	−15.0000	+	25.9808i	−0.476972	+	0.826140i
$990$		0			0
$991$	18.0000	+	31.1769i	0.571789	+	0.990367i	0.996382	+	0.0849833i	$0.0270837\pi$
$991$	18.0000	+	31.1769i	0.571789	+	0.990367i	−0.424594	+	0.905384i	$0.639583\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$	−15.0000			−0.476011
$994$	−5.00000	+	1.73205i	−0.158590	+	0.0549373i
$995$		0			0
$996$	5.00000	−	8.66025i	0.158431	−	0.274411i
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$	2.50000	−	4.33013i	0.0790965	−	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.o.751.1		2
5.2	odd	4		210.2.n.a.79.2	yes	4
5.3	odd	4		210.2.n.a.79.1	✓	4
5.4	even	2		1050.2.i.f.751.1		2
7.2	even	3		7350.2.a.t.1.1		1
7.4	even	3	inner	1050.2.i.o.151.1		2
7.5	odd	6		7350.2.a.b.1.1		1
15.2	even	4		630.2.u.c.289.1		4
15.8	even	4		630.2.u.c.289.2		4
20.3	even	4		1680.2.di.a.289.1		4
20.7	even	4		1680.2.di.a.289.2		4
35.2	odd	12		1470.2.g.f.589.1		2
35.3	even	12		1470.2.n.i.949.2		4
35.4	even	6		1050.2.i.f.151.1		2
35.9	even	6		7350.2.a.bn.1.1		1
35.12	even	12		1470.2.g.a.589.1		2
35.13	even	4		1470.2.n.i.79.1		4
35.17	even	12		1470.2.n.i.949.1		4
35.18	odd	12		210.2.n.a.109.2	yes	4
35.19	odd	6		7350.2.a.ch.1.1		1
35.23	odd	12		1470.2.g.f.589.2		2
35.27	even	4		1470.2.n.i.79.2		4
35.32	odd	12		210.2.n.a.109.1	yes	4
35.33	even	12		1470.2.g.a.589.2		2
105.32	even	12		630.2.u.c.109.2		4
105.53	even	12		630.2.u.c.109.1		4
140.67	even	12		1680.2.di.a.529.1		4
140.123	even	12		1680.2.di.a.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.n.a.79.1	✓	4	5.3	odd	4
210.2.n.a.79.2	yes	4	5.2	odd	4
210.2.n.a.109.1	yes	4	35.32	odd	12
210.2.n.a.109.2	yes	4	35.18	odd	12
630.2.u.c.109.1		4	105.53	even	12
630.2.u.c.109.2		4	105.32	even	12
630.2.u.c.289.1		4	15.2	even	4
630.2.u.c.289.2		4	15.8	even	4
1050.2.i.f.151.1		2	35.4	even	6
1050.2.i.f.751.1		2	5.4	even	2
1050.2.i.o.151.1		2	7.4	even	3	inner
1050.2.i.o.751.1		2	1.1	even	1	trivial
1470.2.g.a.589.1		2	35.12	even	12
1470.2.g.a.589.2		2	35.33	even	12
1470.2.g.f.589.1		2	35.2	odd	12
1470.2.g.f.589.2		2	35.23	odd	12
1470.2.n.i.79.1		4	35.13	even	4
1470.2.n.i.79.2		4	35.27	even	4
1470.2.n.i.949.1		4	35.17	even	12
1470.2.n.i.949.2		4	35.3	even	12
1680.2.di.a.289.1		4	20.3	even	4
1680.2.di.a.289.2		4	20.7	even	4
1680.2.di.a.529.1		4	140.67	even	12
1680.2.di.a.529.2		4	140.123	even	12
7350.2.a.b.1.1		1	7.5	odd	6
7350.2.a.t.1.1		1	7.2	even	3
7350.2.a.bn.1.1		1	35.9	even	6
7350.2.a.ch.1.1		1	35.19	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(0.500000 - 2.59808i) q^{21} +5.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{26} +1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +1.00000 q^{36} +(2.50000 - 4.33013i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{39} -9.00000 q^{41} +(-2.00000 - 1.73205i) q^{42} +10.0000 q^{43} +(2.50000 - 4.33013i) q^{44} +(1.50000 + 2.59808i) q^{46} +(6.50000 - 11.2583i) q^{47} +1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(0.500000 + 0.866025i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} +7.00000 q^{57} +(-2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +6.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(1.00000 - 1.73205i) q^{68} +3.00000 q^{69} -2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-2.50000 - 4.33013i) q^{74} +7.00000 q^{76} +(-2.50000 + 12.9904i) q^{77} -1.00000 q^{78} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} -10.0000 q^{83} +(-2.50000 + 0.866025i) q^{84} +(5.00000 - 8.66025i) q^{86} +(-2.50000 - 4.33013i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} +3.00000 q^{92} +(3.00000 - 5.19615i) q^{93} +(-6.50000 - 11.2583i) q^{94} +(0.500000 - 0.866025i) q^{96} +8.00000 q^{97} +(6.50000 + 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} + 5 q^{11} - q^{12} + 2 q^{13} + 5 q^{14} - q^{16} + 2 q^{17} + q^{18} - 7 q^{19} + q^{21} + 10 q^{22} - 3 q^{23} + q^{24} + q^{26} + 2 q^{27} + q^{28} + 6 q^{31} + q^{32} + 5 q^{33} + 4 q^{34} + 2 q^{36} + 5 q^{37} + 7 q^{38} - q^{39} - 18 q^{41} - 4 q^{42} + 20 q^{43} + 5 q^{44} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 2 q^{49} + 2 q^{51} - q^{52} + q^{53} + q^{54} - 4 q^{56} + 14 q^{57} - 4 q^{59} + 2 q^{61} + 12 q^{62} - 5 q^{63} + 2 q^{64} - 5 q^{66} - 6 q^{67} + 2 q^{68} + 6 q^{69} - 4 q^{71} + q^{72} - 4 q^{73} - 5 q^{74} + 14 q^{76} - 5 q^{77} - 2 q^{78} + 14 q^{79} - q^{81} - 9 q^{82} - 20 q^{83} - 5 q^{84} + 10 q^{86} - 5 q^{88} - 10 q^{89} + 4 q^{91} + 6 q^{92} + 6 q^{93} - 13 q^{94} + q^{96} + 16 q^{97} + 13 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 2 * q^6 + 4 * q^7 - 2 * q^8 - q^9 + 5 * q^11 - q^12 + 2 * q^13 + 5 * q^14 - q^16 + 2 * q^17 + q^18 - 7 * q^19 + q^21 + 10 * q^22 - 3 * q^23 + q^24 + q^26 + 2 * q^27 + q^28 + 6 * q^31 + q^32 + 5 * q^33 + 4 * q^34 + 2 * q^36 + 5 * q^37 + 7 * q^38 - q^39 - 18 * q^41 - 4 * q^42 + 20 * q^43 + 5 * q^44 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 2 * q^49 + 2 * q^51 - q^52 + q^53 + q^54 - 4 * q^56 + 14 * q^57 - 4 * q^59 + 2 * q^61 + 12 * q^62 - 5 * q^63 + 2 * q^64 - 5 * q^66 - 6 * q^67 + 2 * q^68 + 6 * q^69 - 4 * q^71 + q^72 - 4 * q^73 - 5 * q^74 + 14 * q^76 - 5 * q^77 - 2 * q^78 + 14 * q^79 - q^81 - 9 * q^82 - 20 * q^83 - 5 * q^84 + 10 * q^86 - 5 * q^88 - 10 * q^89 + 4 * q^91 + 6 * q^92 + 6 * q^93 - 13 * q^94 + q^96 + 16 * q^97 + 13 * q^98 - 10 * q^99

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