LMFDB - Embedded newform 1050.2.i.h.151.1

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.151
Dual form			1050.2.i.h.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +1.00000 q^{36} +(-5.00000 - 8.66025i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} -9.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} +10.0000 q^{43} +(1.50000 - 2.59808i) q^{46} +(-1.50000 - 2.59808i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} -2.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-4.00000 - 6.92820i) q^{61} -1.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +3.00000 q^{69} +3.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-5.00000 + 8.66025i) q^{74} +2.00000 q^{76} -4.00000 q^{78} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +(2.50000 - 0.866025i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(7.50000 + 12.9904i) q^{89} +(2.00000 - 10.3923i) q^{91} -3.00000 q^{92} +(-0.500000 - 0.866025i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + q^{12} + 8 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} - q^{18} - 2 q^{19} - 4 q^{21} + 3 q^{23} + q^{24} - 4 q^{26} - 2 q^{27} + 4 q^{28} + q^{31} - q^{32} - 6 q^{34} + 2 q^{36} - 10 q^{37} - 2 q^{38} + 4 q^{39} - 18 q^{41} - q^{42} + 20 q^{43} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 13 q^{49} - 3 q^{51} - 4 q^{52} - 6 q^{53} + q^{54} + q^{56} - 4 q^{57} + 6 q^{59} - 8 q^{61} - 2 q^{62} - 5 q^{63} + 2 q^{64} - 4 q^{67} + 3 q^{68} + 6 q^{69} + 6 q^{71} - q^{72} + 14 q^{73} - 10 q^{74} + 4 q^{76} - 8 q^{78} - 11 q^{79} - q^{81} + 9 q^{82} + 5 q^{84} - 10 q^{86} + 15 q^{89} + 4 q^{91} - 6 q^{92} - q^{93} - 3 q^{94} + q^{96} + 14 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + q^7 + 2 * q^8 - q^9 + q^12 + 8 * q^13 - 5 * q^14 - q^16 + 3 * q^17 - q^18 - 2 * q^19 - 4 * q^21 + 3 * q^23 + q^24 - 4 * q^26 - 2 * q^27 + 4 * q^28 + q^31 - q^32 - 6 * q^34 + 2 * q^36 - 10 * q^37 - 2 * q^38 + 4 * q^39 - 18 * q^41 - q^42 + 20 * q^43 + 3 * q^46 - 3 * q^47 - 2 * q^48 - 13 * q^49 - 3 * q^51 - 4 * q^52 - 6 * q^53 + q^54 + q^56 - 4 * q^57 + 6 * q^59 - 8 * q^61 - 2 * q^62 - 5 * q^63 + 2 * q^64 - 4 * q^67 + 3 * q^68 + 6 * q^69 + 6 * q^71 - q^72 + 14 * q^73 - 10 * q^74 + 4 * q^76 - 8 * q^78 - 11 * q^79 - q^81 + 9 * q^82 + 5 * q^84 - 10 * q^86 + 15 * q^89 + 4 * q^91 - 6 * q^92 - q^93 - 3 * q^94 + q^96 + 14 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−2.50000	+	0.866025i	−0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$	−1.00000			−0.192450
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.00000			−0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	0.735643	−	0.677369i	$-0.236880\pi$
$47$	−1.50000	−	2.59808i	−0.218797	−	0.378968i	−0.954441	+	0.298401i	$0.903547\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$	−2.00000			−0.264906
$58$		0			0
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−1.00000			−0.127000
$63$	−2.50000	+	0.866025i	−0.314970	+	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	3.00000			0.361158
$70$		0			0
$71$	3.00000			0.356034			0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000			0.356034			0.178017	+	0.984027i	$0.443032\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	−5.00000	+	8.66025i	−0.581238	+	1.00673i
$75$		0			0
$76$	2.00000			0.229416
$77$		0			0
$78$	−4.00000			−0.452911
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	2.50000	−	0.866025i	0.272772	−	0.0944911i
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$		0			0
$88$		0			0
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		0			0
$91$	2.00000	−	10.3923i	0.209657	−	1.08941i
$92$	−3.00000			−0.312772
$93$	−0.500000	−	0.866025i	−0.0518476	−	0.0898027i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$		0			0
$100$		0			0
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$	−1.50000	+	2.59808i	−0.148522	+	0.257248i
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	6.00000			0.582772
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−10.0000			−0.949158
$112$	−2.50000	+	0.866025i	−0.236228	+	0.0818317i
$113$	−21.0000			−1.97551			−0.987757	−	0.156001i	$-0.950140\pi$
$113$	−21.0000			−1.97551			−0.987757	+	0.156001i	$0.950140\pi$
$114$	1.00000	+	1.73205i	0.0936586	+	0.162221i
$115$		0			0
$116$		0			0
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	−6.00000			−0.552345
$119$	−6.00000	−	5.19615i	−0.550019	−	0.476331i
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$		0			0
$126$	2.00000	+	1.73205i	0.178174	+	0.154303i
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.00000	−	8.66025i	0.440225	−	0.762493i
$130$		0			0
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$	−5.00000	+	1.73205i	−0.433555	+	0.150188i
$134$	4.00000			0.345547
$135$		0			0
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	−0.991694	−	0.128618i	$-0.958946\pi$
$137$	−4.50000	+	7.79423i	−0.384461	+	0.665906i	0.607233	+	0.794524i	$0.292279\pi$
$138$	−1.50000	−	2.59808i	−0.127688	−	0.221163i
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	−1.50000	−	2.59808i	−0.125877	−	0.218026i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−14.0000			−1.15865
$147$	−5.50000	+	4.33013i	−0.453632	+	0.357143i
$148$	10.0000			0.821995
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	−3.00000			−0.242536
$154$		0			0
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	−0.661094	−	0.750303i	$-0.729907\pi$
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	0.980329	+	0.197372i	$0.0632408\pi$
$158$	−5.50000	+	9.52628i	−0.437557	+	0.757870i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$		0			0
$161$	7.50000	−	2.59808i	0.591083	−	0.204757i
$162$	1.00000			0.0785674
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	4.00000	+	6.92820i	0.313304	+	0.542659i	−0.665771	+	0.746156i	$0.731897\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$		0			0
$167$	24.0000			1.85718			0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000			1.85718			0.928588	+	0.371113i	$0.121024\pi$
$168$	−2.00000	−	1.73205i	−0.154303	−	0.133631i
$169$	3.00000			0.230769
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	7.50000	−	12.9904i	0.562149	−	0.973670i
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	−10.0000	+	3.46410i	−0.741249	+	0.256776i
$183$	−8.00000			−0.591377
$184$	1.50000	+	2.59808i	0.110581	+	0.191533i
$185$		0			0
$186$	−0.500000	+	0.866025i	−0.0366618	+	0.0635001i
$187$		0			0
$188$	3.00000			0.218797
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		0			0
$191$	10.5000	+	18.1865i	0.759753	+	1.31593i	0.942976	+	0.332860i	$0.108014\pi$
$191$	10.5000	+	18.1865i	0.759753	+	1.31593i	−0.183223	+	0.983071i	$0.558653\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	8.50000	−	14.7224i	0.611843	−	1.05974i	−0.379086	−	0.925361i	$-0.623762\pi$
$193$	8.50000	−	14.7224i	0.611843	−	1.05974i	0.990930	−	0.134382i	$-0.0429051\pi$
$194$	−3.50000	−	6.06218i	−0.251285	−	0.435239i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	0.602549	+	0.798082i	$0.294152\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	18.0000			1.26648
$203$		0			0
$204$	3.00000			0.210042
$205$		0			0
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$		0			0
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	1.50000	−	2.59808i	0.102778	−	0.178017i
$214$	−9.00000	+	15.5885i	−0.615227	+	1.06561i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−2.00000	−	1.73205i	−0.135769	−	0.117579i
$218$	2.00000			0.135457
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$	5.00000	+	8.66025i	0.335578	+	0.581238i
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	10.5000	+	18.1865i	0.698450	+	1.20975i
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$	1.00000	−	1.73205i	0.0662266	−	0.114708i
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.0000	−	25.9808i	−0.982683	−	1.70206i	−0.651813	−	0.758380i	$-0.725991\pi$
$233$	−15.0000	−	25.9808i	−0.982683	−	1.70206i	−0.330870	−	0.943676i	$-0.607342\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−11.0000			−0.714527
$238$	−1.50000	+	7.79423i	−0.0972306	+	0.505225i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	8.00000			0.512148
$245$		0			0
$246$	9.00000			0.573819
$247$	−4.00000	−	6.92820i	−0.254514	−	0.440831i
$248$	0.500000	−	0.866025i	0.0317500	−	0.0549927i
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	0.500000	−	2.59808i	0.0314970	−	0.163663i
$253$		0			0
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$	−10.0000			−0.622573
$259$	−25.0000	+	8.66025i	−1.55342	+	0.538122i
$260$		0			0
$261$		0			0
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	−0.693276	−	0.720672i	$-0.743833\pi$
$263$	4.50000	−	7.79423i	0.277482	−	0.480613i	0.970758	+	0.240059i	$0.0771668\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	+	3.46410i	0.245256	+	0.212398i
$267$	15.0000			0.917985
$268$	−2.00000	−	3.46410i	−0.122169	−	0.211604i
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$	−3.00000			−0.181902
$273$	−8.00000	−	6.92820i	−0.484182	−	0.419314i
$274$	9.00000			0.543710
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	0.0477206	+	0.998861i	$0.484804\pi$
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	−0.888899	+	0.458103i	$0.848529\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	1.50000	+	2.59808i	0.0893237	+	0.154713i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$		0			0
$286$		0			0
$287$	−4.50000	+	23.3827i	−0.265627	+	1.38024i
$288$	1.00000			0.0589256
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	3.50000	−	6.06218i	0.205174	−	0.355371i
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$	6.50000	+	2.59808i	0.379088	+	0.151523i
$295$		0			0
$296$	−5.00000	−	8.66025i	−0.290619	−	0.503367i
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	5.00000	−	25.9808i	0.288195	−	1.49751i
$302$	8.00000			0.460348
$303$	9.00000	+	15.5885i	0.517036	+	0.895533i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$		0			0
$306$	1.50000	+	2.59808i	0.0857493	+	0.148522i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$	5.00000			0.284440
$310$		0			0
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	−0.964942	−	0.262463i	$-0.915465\pi$
$311$	−4.50000	+	7.79423i	−0.255172	+	0.441970i	0.709771	+	0.704433i	$0.248799\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	2.50000	+	4.33013i	0.141308	+	0.244753i	0.927990	−	0.372606i	$-0.121536\pi$
$313$	2.50000	+	4.33013i	0.141308	+	0.244753i	−0.786681	+	0.617359i	$0.788202\pi$
$314$	−8.00000			−0.451466
$315$		0			0
$316$	11.0000			0.618798
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	3.00000	−	5.19615i	0.168232	−	0.291386i
$319$		0			0
$320$		0			0
$321$	−18.0000			−1.00466
$322$	−6.00000	−	5.19615i	−0.334367	−	0.289570i
$323$	−6.00000			−0.333849
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	4.00000	−	6.92820i	0.221540	−	0.383718i
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	−9.00000			−0.496942
$329$	−7.50000	+	2.59808i	−0.413488	+	0.143237i
$330$		0			0
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$		0			0
$333$	−5.00000	+	8.66025i	−0.273998	+	0.474579i
$334$	−12.0000	−	20.7846i	−0.656611	−	1.13728i
$335$		0			0
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	−11.0000			−0.599208			−0.299604	−	0.954064i	$-0.596855\pi$
$337$	−11.0000			−0.599208			−0.299604	+	0.954064i	$0.596855\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−10.5000	+	18.1865i	−0.570282	+	0.987757i
$340$		0			0
$341$		0			0
$342$	2.00000			0.108148
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	10.0000			0.539164
$345$		0			0
$346$	−9.00000	+	15.5885i	−0.483843	+	0.838041i
$347$	−18.0000	+	31.1769i	−0.966291	+	1.67366i	−0.260184	+	0.965559i	$0.583783\pi$
$347$	−18.0000	+	31.1769i	−0.966291	+	1.67366i	−0.706107	+	0.708105i	$0.749550\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	−0.993626	−	0.112731i	$-0.964040\pi$
$353$	−7.50000	+	12.9904i	−0.399185	+	0.691408i	0.594441	+	0.804139i	$0.297373\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$		0			0
$356$	−15.0000			−0.794998
$357$	−7.50000	+	2.59808i	−0.396942	+	0.137505i
$358$	−6.00000			−0.317110
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	0.663123	−	0.748511i	$-0.269231\pi$
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	−0.979791	+	0.200026i	$0.935897\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$	11.0000			0.577350
$364$	8.00000	+	6.92820i	0.419314	+	0.363137i
$365$		0			0
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	4.50000	+	7.79423i	0.234261	+	0.405751i
$370$		0			0
$371$	12.0000	+	10.3923i	0.623009	+	0.539542i
$372$	1.00000			0.0518476
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		0			0
$375$		0			0
$376$	−1.50000	−	2.59808i	−0.0773566	−	0.133986i
$377$		0			0
$378$	2.50000	−	0.866025i	0.128586	−	0.0445435i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$	10.5000	−	18.1865i	0.537227	−	0.930504i
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−17.0000			−0.865277
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	9.00000			0.455150
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	12.0000			0.605320
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$		0			0
$396$		0			0
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	−0.998125	−	0.0612128i	$-0.980503\pi$
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	0.446051	−	0.895008i	$-0.352830\pi$
$398$	11.0000			0.551380
$399$	−1.00000	+	5.19615i	−0.0500626	+	0.260133i
$400$		0			0
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	2.00000	−	3.46410i	0.0997509	−	0.172774i
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.50000	−	2.59808i	−0.0742611	−	0.128624i
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$		0			0
$411$	4.50000	+	7.79423i	0.221969	+	0.384461i
$412$	−5.00000			−0.246332
$413$	−12.0000	−	10.3923i	−0.590481	−	0.511372i
$414$	−3.00000			−0.147442
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	1.00000	−	1.73205i	0.0489702	−	0.0848189i
$418$		0			0
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$		0			0
$421$	−40.0000			−1.94948			−0.974740	−	0.223341i	$-0.928304\pi$
$421$	−40.0000			−1.94948			−0.974740	+	0.223341i	$0.928304\pi$
$422$	−7.00000	−	12.1244i	−0.340755	−	0.590204i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$		0			0
$426$	−3.00000			−0.145350
$427$	−20.0000	+	6.92820i	−0.967868	+	0.335279i
$428$	18.0000			0.870063
$429$		0			0
$430$		0			0
$431$	13.5000	−	23.3827i	0.650272	−	1.12630i	−0.332785	−	0.943003i	$-0.607988\pi$
$431$	13.5000	−	23.3827i	0.650272	−	1.12630i	0.983057	−	0.183301i	$-0.0586785\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−29.0000			−1.39365			−0.696826	−	0.717241i	$-0.745405\pi$
$433$	−29.0000			−1.39365			−0.696826	+	0.717241i	$0.745405\pi$
$434$	−0.500000	+	2.59808i	−0.0240008	+	0.124712i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$	−7.00000	+	12.1244i	−0.334473	+	0.579324i
$439$	−2.50000	−	4.33013i	−0.119318	−	0.206666i	0.800179	−	0.599761i	$-0.204738\pi$
$439$	−2.50000	−	4.33013i	−0.119318	−	0.206666i	−0.919498	+	0.393095i	$0.871404\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	−12.0000			−0.570782
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	0.785916	−	0.618333i	$-0.212192\pi$
$443$	−3.00000	−	5.19615i	−0.142534	−	0.246877i	−0.928450	+	0.371457i	$0.878858\pi$
$444$	5.00000	−	8.66025i	0.237289	−	0.410997i
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	6.00000			0.283790
$448$	0.500000	−	2.59808i	0.0236228	−	0.122748i
$449$	−21.0000			−0.991051			−0.495526	−	0.868593i	$-0.665025\pi$
$449$	−21.0000			−0.991051			−0.495526	+	0.868593i	$0.665025\pi$
$450$		0			0
$451$		0			0
$452$	10.5000	−	18.1865i	0.493878	−	0.855423i
$453$	4.00000	+	6.92820i	0.187936	+	0.325515i
$454$	6.00000			0.281594
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	0.888466	−	0.458942i	$-0.151771\pi$
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	−0.841688	+	0.539964i	$0.818438\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$		0			0
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$		0			0
$465$		0			0
$466$	−15.0000	+	25.9808i	−0.694862	+	1.20354i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$	4.00000			0.184900
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$	−4.00000	−	6.92820i	−0.184310	−	0.319235i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$		0			0
$474$	5.50000	+	9.52628i	0.252623	+	0.437557i
$475$		0			0
$476$	7.50000	−	2.59808i	0.343762	−	0.119083i
$477$	6.00000			0.274721
$478$	−7.50000	−	12.9904i	−0.343042	−	0.594166i
$479$	13.5000	−	23.3827i	0.616831	−	1.06838i	−0.373230	−	0.927739i	$-0.621750\pi$
$479$	13.5000	−	23.3827i	0.616831	−	1.06838i	0.990060	−	0.140643i	$-0.0449170\pi$
$480$		0			0
$481$	−20.0000	−	34.6410i	−0.911922	−	1.57949i
$482$	14.0000			0.637683
$483$	1.50000	−	7.79423i	0.0682524	−	0.354650i
$484$	−11.0000			−0.500000
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	8.00000			0.361773
$490$		0			0
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$	−4.50000	−	7.79423i	−0.202876	−	0.351391i
$493$		0			0
$494$	−4.00000	+	6.92820i	−0.179969	+	0.311715i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	1.50000	−	7.79423i	0.0672842	−	0.349619i
$498$		0			0
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	0.246214	−	0.969216i	$-0.420813\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$	−6.00000	−	10.3923i	−0.267793	−	0.463831i
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$	−2.50000	+	0.866025i	−0.111359	+	0.0385758i
$505$		0			0
$506$		0			0
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	0.921023	+	0.389509i	$0.127355\pi$
$509$	18.0000	+	31.1769i	0.797836	+	1.38189i	−0.123187	+	0.992384i	$0.539311\pi$
$510$		0			0
$511$	−28.0000	−	24.2487i	−1.23865	−	1.07270i
$512$	1.00000			0.0441942
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$	15.0000	−	25.9808i	0.661622	−	1.14596i
$515$		0			0
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$		0			0
$518$	20.0000	+	17.3205i	0.878750	+	0.761019i
$519$	−18.0000			−0.790112
$520$		0			0
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	−0.982231	−	0.187678i	$-0.939904\pi$
$521$	−7.50000	+	12.9904i	−0.328581	+	0.569119i	0.653650	+	0.756797i	$0.273237\pi$
$522$		0			0
$523$	16.0000	+	27.7128i	0.699631	+	1.21180i	0.968594	+	0.248646i	$0.0799857\pi$
$523$	16.0000	+	27.7128i	0.699631	+	1.21180i	−0.268963	+	0.963150i	$0.586681\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−9.00000			−0.392419
$527$	−1.50000	−	2.59808i	−0.0653410	−	0.113174i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	1.00000	−	5.19615i	0.0433555	−	0.225282i
$533$	−36.0000			−1.55933
$534$	−7.50000	−	12.9904i	−0.324557	−	0.562149i
$535$		0			0
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$	−6.00000			−0.258678
$539$		0			0
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	3.50000	−	6.06218i	0.150338	−	0.260393i
$543$	4.00000	−	6.92820i	0.171656	−	0.297318i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$		0			0
$546$	−2.00000	+	10.3923i	−0.0855921	+	0.444750i
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$	3.00000			0.127688
$553$	−27.5000	+	9.52628i	−1.16942	+	0.405099i
$554$	28.0000			1.18961
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	−0.795443	−	0.606028i	$-0.792762\pi$
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	0.922557	+	0.385860i	$0.126095\pi$
$558$	0.500000	+	0.866025i	0.0211667	+	0.0366618i
$559$	40.0000			1.69182
$560$		0			0
$561$		0			0
$562$	−4.50000	−	7.79423i	−0.189821	−	0.328780i
$563$	−15.0000	+	25.9808i	−0.632175	+	1.09496i	0.354932	+	0.934892i	$0.384504\pi$
$563$	−15.0000	+	25.9808i	−0.632175	+	1.09496i	−0.987106	+	0.160066i	$0.948829\pi$
$564$	1.50000	−	2.59808i	0.0631614	−	0.109399i
$565$		0			0
$566$	4.00000			0.168133
$567$	2.00000	+	1.73205i	0.0839921	+	0.0727393i
$568$	3.00000			0.125877
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	−0.996961	−	0.0779066i	$-0.975176\pi$
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	0.431011	−	0.902347i	$-0.358157\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$		0			0
$573$	21.0000			0.877288
$574$	22.5000	−	7.79423i	0.939132	−	0.325325i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	−0.682730	−	0.730670i	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−8.50000	−	14.7224i	−0.353248	−	0.611843i
$580$		0			0
$581$		0			0
$582$	−7.00000			−0.290159
$583$		0			0
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$		0			0
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$	−1.00000	−	6.92820i	−0.0412393	−	0.285714i
$589$	−2.00000			−0.0824086
$590$		0			0
$591$	6.00000	−	10.3923i	0.246807	−	0.427482i
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$	5.50000	+	9.52628i	0.225100	+	0.389885i
$598$	6.00000	−	10.3923i	0.245358	−	0.424973i
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	−0.833753	−	0.552137i	$-0.813812\pi$
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	0.895042	+	0.445983i	$0.147146\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	−25.0000	+	8.66025i	−1.01892	+	0.352966i
$603$	4.00000			0.162893
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$		0			0
$606$	9.00000	−	15.5885i	0.365600	−	0.633238i
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	0.786212	−	0.617957i	$-0.212039\pi$
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	−0.928272	+	0.371901i	$0.878706\pi$
$608$	2.00000			0.0811107
$609$		0			0
$610$		0			0
$611$	−6.00000	−	10.3923i	−0.242734	−	0.420428i
$612$	1.50000	−	2.59808i	0.0606339	−	0.105021i
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	−0.981129	−	0.193352i	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$	15.0000			0.603877			0.301939	−	0.953327i	$-0.402366\pi$
$617$	15.0000			0.603877			0.301939	+	0.953327i	$0.402366\pi$
$618$	−2.50000	−	4.33013i	−0.100565	−	0.174183i
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	−0.993959	−	0.109749i	$-0.964995\pi$
$619$	−10.0000	+	17.3205i	−0.401934	+	0.696170i	0.592025	+	0.805919i	$0.298329\pi$
$620$		0			0
$621$	−1.50000	−	2.59808i	−0.0601929	−	0.104257i
$622$	9.00000			0.360867
$623$	37.5000	−	12.9904i	1.50241	−	0.520449i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	2.50000	−	4.33013i	0.0999201	−	0.173067i
$627$		0			0
$628$	4.00000	+	6.92820i	0.159617	+	0.276465i
$629$	−30.0000			−1.19618
$630$		0			0
$631$	−37.0000			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$631$	−37.0000			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$632$	−5.50000	−	9.52628i	−0.218778	−	0.378935i
$633$	7.00000	−	12.1244i	0.278225	−	0.481900i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−26.0000	−	10.3923i	−1.03016	−	0.411758i
$638$		0			0
$639$	−1.50000	−	2.59808i	−0.0593391	−	0.102778i
$640$		0			0
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	−0.330997	−	0.943632i	$-0.607385\pi$
$641$	16.5000	−	28.5788i	0.651711	−	1.12880i	0.982708	−	0.185164i	$-0.0592817\pi$
$642$	9.00000	+	15.5885i	0.355202	+	0.615227i
$643$	−38.0000			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$644$	−1.50000	+	7.79423i	−0.0591083	+	0.307136i
$645$		0			0
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$		0			0
$650$		0			0
$651$	−2.50000	+	0.866025i	−0.0979827	+	0.0339422i
$652$	−8.00000			−0.313304
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		0			0
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	−14.0000			−0.546192
$658$	6.00000	+	5.19615i	0.233904	+	0.202567i
$659$	−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
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	5.00000	−	8.66025i	0.194331	−	0.336590i
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$	10.0000			0.387492
$667$		0			0
$668$	−12.0000	+	20.7846i	−0.464294	+	0.804181i
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$		0			0
$672$	2.50000	−	0.866025i	0.0964396	−	0.0334077i
$673$	19.0000			0.732396			0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000			0.732396			0.366198	+	0.930537i	$0.380659\pi$
$674$	5.50000	+	9.52628i	0.211852	+	0.366939i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$	21.0000			0.806500
$679$	3.50000	−	18.1865i	0.134318	−	0.697935i
$680$		0			0
$681$	3.00000	+	5.19615i	0.114960	+	0.199117i
$682$		0			0
$683$	3.00000	−	5.19615i	0.114792	−	0.198825i	−0.802905	−	0.596107i	$-0.796713\pi$
$683$	3.00000	−	5.19615i	0.114792	−	0.198825i	0.917697	+	0.397282i	$0.130047\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	4.00000			0.152610
$688$	−5.00000	−	8.66025i	−0.190623	−	0.330169i
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	36.0000			1.36654
$695$		0			0
$696$		0			0
$697$	−13.5000	+	23.3827i	−0.511349	+	0.885682i
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$	−30.0000			−1.13470
$700$		0			0
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$	2.00000	+	3.46410i	0.0754851	+	0.130744i
$703$	−10.0000	+	17.3205i	−0.377157	+	0.653255i
$704$		0			0
$705$		0			0
$706$	15.0000			0.564532
$707$	36.0000	+	31.1769i	1.35392	+	1.17253i
$708$	6.00000			0.225494
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$		0			0
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$	7.50000	+	12.9904i	0.281074	+	0.486835i
$713$	3.00000			0.112351
$714$	6.00000	+	5.19615i	0.224544	+	0.194461i
$715$		0			0
$716$	3.00000	+	5.19615i	0.112115	+	0.194189i
$717$	7.50000	−	12.9904i	0.280093	−	0.485135i
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$		0			0
$721$	12.5000	−	4.33013i	0.465524	−	0.161262i
$722$	−15.0000			−0.558242
$723$	7.00000	+	12.1244i	0.260333	+	0.450910i
$724$	−4.00000	+	6.92820i	−0.148659	+	0.257485i
$725$		0			0
$726$	−5.50000	−	9.52628i	−0.204124	−	0.353553i
$727$	37.0000			1.37225			0.686127	−	0.727482i	$-0.259309\pi$
$727$	37.0000			1.37225			0.686127	+	0.727482i	$0.259309\pi$
$728$	2.00000	−	10.3923i	0.0741249	−	0.385164i
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.0000	−	25.9808i	0.554795	−	0.960933i
$732$	4.00000	−	6.92820i	0.147844	−	0.256074i
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	0.965854	−	0.259087i	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	−3.00000			−0.110581
$737$		0			0
$738$	4.50000	−	7.79423i	0.165647	−	0.286910i
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	−0.883832	−	0.467804i	$-0.845045\pi$
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	0.847046	+	0.531519i	$0.178379\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$	3.00000	−	15.5885i	0.110133	−	0.572270i
$743$	51.0000			1.87101			0.935504	−	0.353315i	$-0.114946\pi$
$743$	51.0000			1.87101			0.935504	+	0.353315i	$0.114946\pi$
$744$	−0.500000	−	0.866025i	−0.0183309	−	0.0317500i
$745$		0			0
$746$	−2.00000	+	3.46410i	−0.0732252	+	0.126830i
$747$		0			0
$748$		0			0
$749$	−45.0000	+	15.5885i	−1.64426	+	0.569590i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	6.00000	−	10.3923i	0.218652	−	0.378717i
$754$		0			0
$755$		0			0
$756$	−2.00000	−	1.73205i	−0.0727393	−	0.0629941i
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	8.00000	+	13.8564i	0.290573	+	0.503287i
$759$		0			0
$760$		0			0
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$	−16.0000			−0.579619
$763$	4.00000	+	3.46410i	0.144810	+	0.125409i
$764$	−21.0000			−0.759753
$765$		0			0
$766$	10.5000	−	18.1865i	0.379380	−	0.657106i
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	26.0000			0.937584			0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000			0.937584			0.468792	+	0.883309i	$0.344689\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$	8.50000	+	14.7224i	0.305922	+	0.529872i
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$		0			0
$776$	7.00000			0.251285
$777$	−5.00000	+	25.9808i	−0.179374	+	0.932055i
$778$	6.00000			0.215110
$779$	9.00000	+	15.5885i	0.322458	+	0.558514i
$780$		0			0
$781$		0			0
$782$	−4.50000	−	7.79423i	−0.160920	−	0.278721i
$783$		0			0
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	−0.992727	−	0.120384i	$-0.961587\pi$
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	0.600620	+	0.799535i	$0.294921\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	−4.50000	−	7.79423i	−0.160204	−	0.277482i
$790$		0			0
$791$	−10.5000	+	54.5596i	−0.373337	+	1.93992i
$792$		0			0
$793$	−16.0000	−	27.7128i	−0.568177	−	0.984111i
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$		0			0
$796$	−5.50000	−	9.52628i	−0.194942	−	0.337650i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$	5.00000	−	1.73205i	0.176998	−	0.0613139i
$799$	−9.00000			−0.318397
$800$		0			0
$801$	7.50000	−	12.9904i	0.264999	−	0.458993i
$802$	−9.00000	+	15.5885i	−0.317801	+	0.550448i
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−3.00000	−	5.19615i	−0.105605	−	0.182913i
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	−0.913932	−	0.405868i	$-0.866969\pi$
$809$	−3.00000	+	5.19615i	−0.105474	+	0.182687i	0.808458	+	0.588555i	$0.200303\pi$
$810$		0			0
$811$	56.0000			1.96643			0.983213	−	0.182462i	$-0.0584065\pi$
$811$	56.0000			1.96643			0.983213	+	0.182462i	$0.0584065\pi$
$812$		0			0
$813$	7.00000			0.245501
$814$		0			0
$815$		0			0
$816$	−1.50000	+	2.59808i	−0.0525105	+	0.0909509i
$817$	−10.0000	−	17.3205i	−0.349856	−	0.605968i
$818$	5.00000			0.174821
$819$	−10.0000	+	3.46410i	−0.349428	+	0.121046i
$820$		0			0
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.761056	+	0.648686i	$0.224681\pi$
$821$	27.0000	+	46.7654i	0.942306	+	1.63212i	0.181250	+	0.983437i	$0.441986\pi$
$822$	4.50000	−	7.79423i	0.156956	−	0.271855i
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$	2.50000	+	4.33013i	0.0870916	+	0.150847i
$825$		0			0
$826$	−3.00000	+	15.5885i	−0.104383	+	0.542392i
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$	1.50000	+	2.59808i	0.0521286	+	0.0902894i
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	−0.882869	−	0.469620i	$-0.844391\pi$
$829$	−1.00000	+	1.73205i	−0.0347314	+	0.0601566i	0.848137	+	0.529777i	$0.177724\pi$
$830$		0			0
$831$	14.0000	+	24.2487i	0.485655	+	0.841178i
$832$	4.00000			0.138675
$833$	−16.5000	+	12.9904i	−0.571691	+	0.450090i
$834$	−2.00000			−0.0692543
$835$		0			0
$836$		0			0
$837$	−0.500000	+	0.866025i	−0.0172825	+	0.0299342i
$838$	−9.00000	−	15.5885i	−0.310900	−	0.538494i
$839$	27.0000			0.932144			0.466072	−	0.884747i	$-0.345669\pi$
$839$	27.0000			0.932144			0.466072	+	0.884747i	$0.345669\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	20.0000	+	34.6410i	0.689246	+	1.19381i
$843$	4.50000	−	7.79423i	0.154988	−	0.268447i
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$		0			0
$846$	3.00000			0.103142
$847$	27.5000	−	9.52628i	0.944911	−	0.327327i
$848$	6.00000			0.206041
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		0			0
$851$	15.0000	−	25.9808i	0.514193	−	0.890609i
$852$	1.50000	+	2.59808i	0.0513892	+	0.0890086i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	16.0000	+	13.8564i	0.547509	+	0.474156i
$855$		0			0
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.126459	−	0.991972i	$-0.459639\pi$
$857$	27.0000	−	46.7654i	0.922302	−	1.59747i	0.795843	−	0.605503i	$-0.207028\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$		0			0
$861$	18.0000	+	15.5885i	0.613438	+	0.531253i
$862$	−27.0000			−0.919624
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	0.709675	−	0.704529i	$-0.248842\pi$
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	−0.964978	+	0.262332i	$0.915509\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	14.5000	+	25.1147i	0.492730	+	0.853433i
$867$	8.00000			0.271694
$868$	2.50000	−	0.866025i	0.0848555	−	0.0293948i
$869$		0			0
$870$		0			0
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$	−3.50000	−	6.06218i	−0.118457	−	0.205174i
$874$	−6.00000			−0.202953
$875$		0			0
$876$	14.0000			0.473016
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$	−2.50000	+	4.33013i	−0.0843709	+	0.146135i
$879$	12.0000	−	20.7846i	0.404750	−	0.701047i
$880$		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
$883$	−38.0000			−1.27880			−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000			−1.27880			−0.639401	+	0.768874i	$0.720818\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	−3.00000	+	5.19615i	−0.100787	+	0.174568i
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$	−10.0000			−0.335578
$889$	8.00000	−	41.5692i	0.268311	−	1.39419i
$890$		0			0
$891$		0			0
$892$	−9.50000	+	16.4545i	−0.318084	+	0.550937i
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$		0			0
$896$	−2.50000	+	0.866025i	−0.0835191	+	0.0289319i
$897$	12.0000			0.400668
$898$	10.5000	+	18.1865i	0.350390	+	0.606892i
$899$		0			0
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$	−20.0000	−	17.3205i	−0.665558	−	0.576390i
$904$	−21.0000			−0.698450
$905$		0			0
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	−0.967730	−	0.251990i	$-0.918915\pi$
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	0.702094	+	0.712084i	$0.252248\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$	18.0000			0.597022
$910$		0			0
$911$	39.0000			1.29213			0.646064	−	0.763283i	$-0.276414\pi$
$911$	39.0000			1.29213			0.646064	+	0.763283i	$0.276414\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$		0			0
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	30.0000	−	10.3923i	0.990687	−	0.343184i
$918$	3.00000			0.0990148
$919$	9.50000	+	16.4545i	0.313376	+	0.542783i	0.979091	−	0.203423i	$-0.0652066\pi$
$919$	9.50000	+	16.4545i	0.313376	+	0.542783i	−0.665715	+	0.746206i	$0.731873\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	6.00000	+	10.3923i	0.197599	+	0.342252i
$923$	12.0000			0.394985
$924$		0			0
$925$		0			0
$926$	2.50000	+	4.33013i	0.0821551	+	0.142297i
$927$	2.50000	−	4.33013i	0.0821108	−	0.142220i
$928$		0			0
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	2.00000	+	13.8564i	0.0655474	+	0.454125i
$932$	30.0000			0.982683
$933$	4.50000	+	7.79423i	0.147323	+	0.255172i
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−26.0000			−0.849383			−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000			−0.849383			−0.424691	+	0.905338i	$0.639617\pi$
$938$	2.00000	−	10.3923i	0.0653023	−	0.339321i
$939$	5.00000			0.163169
$940$		0			0
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	−0.999920	−	0.0126715i	$-0.995966\pi$
$941$	−15.0000	+	25.9808i	−0.488986	+	0.846949i	0.510934	+	0.859620i	$0.329300\pi$
$942$	−4.00000	+	6.92820i	−0.130327	+	0.225733i
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$	−6.00000			−0.195283
$945$		0			0
$946$		0			0
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	−0.932002	−	0.362454i	$-0.881939\pi$
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	0.152106	−	0.988364i	$-0.451394\pi$
$948$	5.50000	−	9.52628i	0.178632	−	0.309399i
$949$	28.0000	−	48.4974i	0.908918	−	1.57429i
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−6.00000	−	5.19615i	−0.194461	−	0.168408i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−3.00000	−	5.19615i	−0.0971286	−	0.168232i
$955$		0			0
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$		0			0
$958$	−27.0000			−0.872330
$959$	18.0000	+	15.5885i	0.581250	+	0.503378i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	−20.0000	+	34.6410i	−0.644826	+	1.11687i
$963$	−9.00000	+	15.5885i	−0.290021	+	0.502331i
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$		0			0
$966$	−7.50000	+	2.59808i	−0.241309	+	0.0835917i
$967$	49.0000			1.57573			0.787867	−	0.615846i	$-0.211185\pi$
$967$	49.0000			1.57573			0.787867	+	0.615846i	$0.211185\pi$
$968$	5.50000	+	9.52628i	0.176777	+	0.306186i
$969$	−3.00000	+	5.19615i	−0.0963739	+	0.166924i
$970$		0			0
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$	−1.00000			−0.0320750
$973$	1.00000	−	5.19615i	0.0320585	−	0.166581i
$974$	31.0000			0.993304
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	13.5000	−	23.3827i	0.431903	−	0.748078i	−0.565134	−	0.824999i	$-0.691176\pi$
$977$	13.5000	−	23.3827i	0.431903	−	0.748078i	0.997037	+	0.0769208i	$0.0245089\pi$
$978$	−4.00000	−	6.92820i	−0.127906	−	0.221540i
$979$		0			0
$980$		0			0
$981$	2.00000			0.0638551
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	−0.945705	−	0.325027i	$-0.894626\pi$
$983$	−6.00000	+	10.3923i	−0.191370	+	0.331463i	0.754334	+	0.656490i	$0.227960\pi$
$984$	−4.50000	+	7.79423i	−0.143455	+	0.248471i
$985$		0			0
$986$		0			0
$987$	−1.50000	+	7.79423i	−0.0477455	+	0.248093i
$988$	8.00000			0.254514
$989$	15.0000	+	25.9808i	0.476972	+	0.826140i
$990$		0			0
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.166250	+	0.986084i	$0.553166\pi$
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.770849	+	0.637018i	$0.780168\pi$
$992$	0.500000	+	0.866025i	0.0158750	+	0.0274963i
$993$	10.0000			0.317340
$994$	−7.50000	+	2.59808i	−0.237886	+	0.0824060i
$995$		0			0
$996$		0			0
$997$	−20.0000	+	34.6410i	−0.633406	+	1.09709i	0.353444	+	0.935456i	$0.385010\pi$
$997$	−20.0000	+	34.6410i	−0.633406	+	1.09709i	−0.986850	+	0.161636i	$0.948323\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.h.151.1	✓	2
5.2	odd	4		1050.2.o.e.949.2		4
5.3	odd	4		1050.2.o.e.949.1		4
5.4	even	2		1050.2.i.m.151.1	yes	2
7.2	even	3	inner	1050.2.i.h.751.1	yes	2
7.3	odd	6		7350.2.a.cq.1.1		1
7.4	even	3		7350.2.a.by.1.1		1
35.2	odd	12		1050.2.o.e.499.1		4
35.4	even	6		7350.2.a.bb.1.1		1
35.9	even	6		1050.2.i.m.751.1	yes	2
35.23	odd	12		1050.2.o.e.499.2		4
35.24	odd	6		7350.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.h.151.1	✓	2	1.1	even	1	trivial
1050.2.i.h.751.1	yes	2	7.2	even	3	inner
1050.2.i.m.151.1	yes	2	5.4	even	2
1050.2.i.m.751.1	yes	2	35.9	even	6
1050.2.o.e.499.1		4	35.2	odd	12
1050.2.o.e.499.2		4	35.23	odd	12
1050.2.o.e.949.1		4	5.3	odd	4
1050.2.o.e.949.2		4	5.2	odd	4
7350.2.a.n.1.1		1	35.24	odd	6
7350.2.a.bb.1.1		1	35.4	even	6
7350.2.a.by.1.1		1	7.4	even	3
7350.2.a.cq.1.1		1	7.3	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} -3.00000 q^{34} +1.00000 q^{36} +(-5.00000 - 8.66025i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} -9.00000 q^{41} +(-0.500000 + 2.59808i) q^{42} +10.0000 q^{43} +(1.50000 - 2.59808i) q^{46} +(-1.50000 - 2.59808i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(-2.00000 + 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} -2.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-4.00000 - 6.92820i) q^{61} -1.00000 q^{62} +(-2.50000 + 0.866025i) q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +3.00000 q^{69} +3.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-5.00000 + 8.66025i) q^{74} +2.00000 q^{76} -4.00000 q^{78} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +(2.50000 - 0.866025i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(7.50000 + 12.9904i) q^{89} +(2.00000 - 10.3923i) q^{91} -3.00000 q^{92} +(-0.500000 - 0.866025i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + q^{7} + 2 q^{8} - q^{9} + q^{12} + 8 q^{13} - 5 q^{14} - q^{16} + 3 q^{17} - q^{18} - 2 q^{19} - 4 q^{21} + 3 q^{23} + q^{24} - 4 q^{26} - 2 q^{27} + 4 q^{28} + q^{31} - q^{32} - 6 q^{34} + 2 q^{36} - 10 q^{37} - 2 q^{38} + 4 q^{39} - 18 q^{41} - q^{42} + 20 q^{43} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 13 q^{49} - 3 q^{51} - 4 q^{52} - 6 q^{53} + q^{54} + q^{56} - 4 q^{57} + 6 q^{59} - 8 q^{61} - 2 q^{62} - 5 q^{63} + 2 q^{64} - 4 q^{67} + 3 q^{68} + 6 q^{69} + 6 q^{71} - q^{72} + 14 q^{73} - 10 q^{74} + 4 q^{76} - 8 q^{78} - 11 q^{79} - q^{81} + 9 q^{82} + 5 q^{84} - 10 q^{86} + 15 q^{89} + 4 q^{91} - 6 q^{92} - q^{93} - 3 q^{94} + q^{96} + 14 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + q^7 + 2 * q^8 - q^9 + q^12 + 8 * q^13 - 5 * q^14 - q^16 + 3 * q^17 - q^18 - 2 * q^19 - 4 * q^21 + 3 * q^23 + q^24 - 4 * q^26 - 2 * q^27 + 4 * q^28 + q^31 - q^32 - 6 * q^34 + 2 * q^36 - 10 * q^37 - 2 * q^38 + 4 * q^39 - 18 * q^41 - q^42 + 20 * q^43 + 3 * q^46 - 3 * q^47 - 2 * q^48 - 13 * q^49 - 3 * q^51 - 4 * q^52 - 6 * q^53 + q^54 + q^56 - 4 * q^57 + 6 * q^59 - 8 * q^61 - 2 * q^62 - 5 * q^63 + 2 * q^64 - 4 * q^67 + 3 * q^68 + 6 * q^69 + 6 * q^71 - q^72 + 14 * q^73 - 10 * q^74 + 4 * q^76 - 8 * q^78 - 11 * q^79 - q^81 + 9 * q^82 + 5 * q^84 - 10 * q^86 + 15 * q^89 + 4 * q^91 - 6 * q^92 - q^93 - 3 * q^94 + q^96 + 14 * q^97 + 2 * q^98

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