LMFDB - Embedded newform 1050.2.o.e.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

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, 3, 2]))

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

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

chi := DirichletCharacter("1050.499");

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.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.499
Dual form			1050.2.o.e.949.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 + 1.50000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-2.59808 - 1.50000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} +(0.500000 + 0.866025i) q^{31} +(0.866025 - 0.500000i) q^{32} +3.00000 q^{34} +1.00000 q^{36} +(-8.66025 - 5.00000i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} -9.00000 q^{41} +(2.59808 - 0.500000i) q^{42} -10.0000i q^{43} +(1.50000 + 2.59808i) q^{46} +(-2.59808 - 1.50000i) q^{47} +1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(3.46410 - 2.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} -2.00000i q^{57} +(-3.00000 - 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} -1.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(3.46410 - 2.00000i) q^{67} +(-2.59808 - 1.50000i) q^{68} -3.00000 q^{69} +3.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(5.00000 + 8.66025i) q^{74} +2.00000 q^{76} +4.00000i q^{78} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} +(-2.50000 - 0.866025i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(-7.50000 + 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} -3.00000i q^{92} +(0.866025 + 0.500000i) q^{93} +(1.50000 + 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} +7.00000i q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} + 10 q^{14} - 2 q^{16} + 4 q^{19} - 8 q^{21} - 2 q^{24} - 8 q^{26} + 2 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 36 q^{41} + 6 q^{46} + 26 q^{49} - 6 q^{51} - 2 q^{54} + 2 q^{56} - 12 q^{59} - 16 q^{61} - 4 q^{64} - 12 q^{69} + 12 q^{71} + 20 q^{74} + 8 q^{76} + 22 q^{79} - 2 q^{81} - 10 q^{84} - 20 q^{86} - 30 q^{89} + 8 q^{91} + 6 q^{94} + 2 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 + 10 * q^14 - 2 * q^16 + 4 * q^19 - 8 * q^21 - 2 * q^24 - 8 * q^26 + 2 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 36 * q^41 + 6 * q^46 + 26 * q^49 - 6 * q^51 - 2 * q^54 + 2 * q^56 - 12 * q^59 - 16 * q^61 - 4 * q^64 - 12 * q^69 + 12 * q^71 + 20 * q^74 + 8 * q^76 + 22 * q^79 - 2 * q^81 - 10 * q^84 - 20 * q^86 - 30 * q^89 + 8 * q^91 + 6 * q^94 + 2 * q^96

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	−0.780801	−	0.624780i	$-0.785189\pi$
$17$	−2.59808	+	1.50000i	−0.630126	+	0.363803i	0.150675	+	0.988583i	$0.451855\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$		0			0
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−2.00000	+	3.46410i	−0.392232	+	0.679366i
$27$		−	1.00000i		−	0.192450i
$28$	−1.73205	−	2.00000i	−0.327327	−	0.377964i
$29$		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	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	3.00000			0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	−8.66025	−	5.00000i	−1.42374	−	0.821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	−8.66025	−	5.00000i	−1.42374	−	0.821995i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$	−1.73205	+	1.00000i	−0.280976	+	0.162221i
$39$	−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	$0.748059\pi$
$42$	2.59808	−	0.500000i	0.400892	−	0.0771517i
$43$		−	10.0000i		−	1.52499i	−0.646997	−	0.762493i	$-0.723975\pi$
$43$		−	10.0000i		−	1.52499i	0.646997	−	0.762493i	$-0.276025\pi$
$44$		0			0
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	−2.59808	−	1.50000i	−0.378968	−	0.218797i	0.298401	−	0.954441i	$-0.403547\pi$
$47$	−2.59808	−	1.50000i	−0.378968	−	0.218797i	−0.677369	+	0.735643i	$0.736880\pi$
$48$			1.00000i			0.144338i
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		0			0
$51$	−1.50000	+	2.59808i	−0.210042	+	0.363803i
$52$	3.46410	−	2.00000i	0.480384	−	0.277350i
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	−0.812447	−	0.583036i	$-0.801865\pi$
$53$	−5.19615	+	3.00000i	−0.713746	+	0.412082i	0.0987002	+	0.995117i	$0.468532\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$		−	2.00000i		−	0.264906i
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		−	1.00000i		−	0.127000i
$63$	−0.866025	+	2.50000i	−0.109109	+	0.314970i
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$	−2.59808	−	1.50000i	−0.315063	−	0.181902i
$69$	−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	$0.443032\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.422833	−	0.906208i	$-0.361036\pi$
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.996215	+	0.0869195i	$0.0277023\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$		0			0
$76$	2.00000			0.229416
$77$		0			0
$78$			4.00000i			0.452911i
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.79423	+	4.50000i	0.860729	+	0.496942i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	−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	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$		0			0
$91$	2.00000	+	10.3923i	0.209657	+	1.08941i
$92$		−	3.00000i		−	0.312772i
$93$	0.866025	+	0.500000i	0.0898027	+	0.0518476i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			7.00000i			0.710742i	0.934725	+	0.355371i	$0.115646\pi$
$97$			7.00000i			0.710742i	−0.934725	+	0.355371i	$0.884354\pi$
$98$	−6.92820	−	1.00000i	−0.699854	−	0.101015i
$99$		0			0
$100$		0			0
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$	2.59808	−	1.50000i	0.257248	−	0.148522i
$103$	−4.33013	−	2.50000i	−0.426660	−	0.246332i	0.271263	−	0.962505i	$-0.412559\pi$
$103$	−4.33013	−	2.50000i	−0.426660	−	0.246332i	−0.697923	+	0.716173i	$0.745892\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	6.00000			0.582772
$107$	−15.5885	−	9.00000i	−1.50699	−	0.870063i	−0.999967	−	0.00813215i	$-0.997411\pi$
$107$	−15.5885	−	9.00000i	−1.50699	−	0.870063i	−0.507026	−	0.861931i	$-0.669255\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	−10.0000			−0.949158
$112$	0.866025	−	2.50000i	0.0818317	−	0.236228i
$113$			21.0000i			1.97551i	0.156001	+	0.987757i	$0.450140\pi$
$113$			21.0000i			1.97551i	−0.156001	+	0.987757i	$0.549860\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$		0			0
$117$	−3.46410	−	2.00000i	−0.320256	−	0.184900i
$118$			6.00000i			0.552345i
$119$	6.00000	−	5.19615i	0.550019	−	0.476331i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	6.92820	−	4.00000i	0.627250	−	0.362143i
$123$	−7.79423	+	4.50000i	−0.702782	+	0.405751i
$124$	−0.500000	+	0.866025i	−0.0449013	+	0.0777714i
$125$		0			0
$126$	2.00000	−	1.73205i	0.178174	−	0.154303i
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−5.00000	−	8.66025i	−0.440225	−	0.762493i
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−1.73205	+	5.00000i	−0.150188	+	0.433555i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	7.79423	−	4.50000i	0.665906	−	0.384461i	−0.128618	−	0.991694i	$-0.541054\pi$
$137$	7.79423	−	4.50000i	0.665906	−	0.384461i	0.794524	+	0.607233i	$0.207721\pi$
$138$	2.59808	+	1.50000i	0.221163	+	0.127688i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	−2.59808	−	1.50000i	−0.218026	−	0.125877i
$143$		0			0
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	−14.0000			−1.15865
$147$	4.33013	−	5.50000i	0.357143	−	0.453632i
$148$		−	10.0000i		−	0.821995i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−1.73205	−	1.00000i	−0.140488	−	0.0811107i
$153$			3.00000i			0.242536i
$154$		0			0
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−6.92820	+	4.00000i	−0.552931	+	0.319235i	−0.750303	−	0.661094i	$-0.770093\pi$
$157$	−6.92820	+	4.00000i	−0.552931	+	0.319235i	0.197372	+	0.980329i	$0.436759\pi$
$158$	−9.52628	+	5.50000i	−0.757870	+	0.437557i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	7.50000	+	2.59808i	0.591083	+	0.204757i
$162$			1.00000i			0.0785674i
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	0.203497	−	0.979076i	$-0.434769\pi$
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	−0.746156	+	0.665771i	$0.768103\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$		0			0
$167$			24.0000i			1.85718i	0.371113	+	0.928588i	$0.378976\pi$
$167$			24.0000i			1.85718i	−0.371113	+	0.928588i	$0.621024\pi$
$168$	1.73205	+	2.00000i	0.133631	+	0.154303i
$169$	−3.00000			−0.230769
$170$		0			0
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$	8.66025	−	5.00000i	0.660338	−	0.381246i
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.957205	−	0.289412i	$-0.0934598\pi$
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.227964	+	0.973670i	$0.426793\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.19615	−	3.00000i	−0.390567	−	0.225494i
$178$	12.9904	−	7.50000i	0.973670	−	0.562149i
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	3.46410	−	10.0000i	0.256776	−	0.741249i
$183$			8.00000i			0.591377i
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$		0			0
$186$	−0.500000	−	0.866025i	−0.0366618	−	0.0635001i
$187$		0			0
$188$		−	3.00000i		−	0.218797i
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$		0			0
$191$	10.5000	−	18.1865i	0.759753	−	1.31593i	−0.183223	−	0.983071i	$-0.558653\pi$
$191$	10.5000	−	18.1865i	0.759753	−	1.31593i	0.942976	−	0.332860i	$-0.108014\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	14.7224	−	8.50000i	1.05974	−	0.611843i	0.134382	−	0.990930i	$-0.457095\pi$
$193$	14.7224	−	8.50000i	1.05974	−	0.611843i	0.925361	+	0.379086i	$0.123762\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		0			0
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	0.992434	−	0.122782i	$-0.0391815\pi$
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	−0.602549	+	0.798082i	$0.705848\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$			18.0000i			1.26648i
$203$		0			0
$204$	−3.00000			−0.210042
$205$		0			0
$206$	2.50000	+	4.33013i	0.174183	+	0.301694i
$207$	−2.59808	+	1.50000i	−0.180579	+	0.104257i
$208$	3.46410	+	2.00000i	0.240192	+	0.138675i
$209$		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	$0.339947\pi$
$212$	−5.19615	−	3.00000i	−0.356873	−	0.206041i
$213$	2.59808	−	1.50000i	0.178017	−	0.102778i
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−1.73205	−	2.00000i	−0.117579	−	0.135769i
$218$		−	2.00000i		−	0.135457i
$219$	7.00000	−	12.1244i	0.473016	−	0.819288i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	8.66025	+	5.00000i	0.581238	+	0.335578i
$223$		−	19.0000i		−	1.27233i	−0.771551	−	0.636167i	$-0.780519\pi$
$223$		−	19.0000i		−	1.27233i	0.771551	−	0.636167i	$-0.219481\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	10.5000	−	18.1865i	0.698450	−	1.20975i
$227$	5.19615	−	3.00000i	0.344881	−	0.199117i	−0.317547	−	0.948242i	$-0.602859\pi$
$227$	5.19615	−	3.00000i	0.344881	−	0.199117i	0.662428	+	0.749125i	$0.269526\pi$
$228$	1.73205	−	1.00000i	0.114708	−	0.0662266i
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	25.9808	+	15.0000i	1.70206	+	0.982683i	0.943676	+	0.330870i	$0.107342\pi$
$233$	25.9808	+	15.0000i	1.70206	+	0.982683i	0.758380	+	0.651813i	$0.225991\pi$
$234$	2.00000	+	3.46410i	0.130744	+	0.226455i
$235$		0			0
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$		−	11.0000i		−	0.714527i
$238$	−7.79423	+	1.50000i	−0.505225	+	0.0972306i
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−9.52628	+	5.50000i	−0.612372	+	0.353553i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−8.00000			−0.512148
$245$		0			0
$246$	9.00000			0.573819
$247$	−6.92820	−	4.00000i	−0.440831	−	0.254514i
$248$	0.866025	−	0.500000i	0.0549927	−	0.0317500i
$249$		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	$0.376365\pi$
$252$	−2.59808	+	0.500000i	−0.163663	+	0.0314970i
$253$		0			0
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	25.9808	+	15.0000i	1.62064	+	0.935674i	0.986750	+	0.162247i	$0.0518742\pi$
$257$	25.9808	+	15.0000i	1.62064	+	0.935674i	0.633885	+	0.773427i	$0.281459\pi$
$258$			10.0000i			0.622573i
$259$	25.0000	+	8.66025i	1.55342	+	0.538122i
$260$		0			0
$261$		0			0
$262$	−10.3923	+	6.00000i	−0.642039	+	0.370681i
$263$	7.79423	−	4.50000i	0.480613	−	0.277482i	−0.240059	−	0.970758i	$-0.577167\pi$
$263$	7.79423	−	4.50000i	0.480613	−	0.277482i	0.720672	+	0.693276i	$0.243833\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$			15.0000i			0.917985i
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$		−	3.00000i		−	0.181902i
$273$	6.92820	+	8.00000i	0.419314	+	0.484182i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.458103	−	0.888899i	$-0.348529\pi$
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.998861	+	0.0477206i	$0.0151957\pi$
$278$	1.73205	+	1.00000i	0.103882	+	0.0599760i
$279$	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	$0.413489\pi$
$282$	2.59808	+	1.50000i	0.154713	+	0.0893237i
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	−0.599414	−	0.800439i	$-0.704600\pi$
$283$	−3.46410	+	2.00000i	−0.205919	+	0.118888i	0.393494	+	0.919327i	$0.371266\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$		0			0
$286$		0			0
$287$	23.3827	−	4.50000i	1.38024	−	0.265627i
$288$		−	1.00000i		−	0.0589256i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	3.50000	+	6.06218i	0.205174	+	0.355371i
$292$	12.1244	+	7.00000i	0.709524	+	0.409644i
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$	−6.50000	+	2.59808i	−0.379088	+	0.151523i
$295$		0			0
$296$	−5.00000	+	8.66025i	−0.290619	+	0.503367i
$297$		0			0
$298$	5.19615	−	3.00000i	0.301005	−	0.173785i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$	5.00000	+	25.9808i	0.288195	+	1.49751i
$302$			8.00000i			0.460348i
$303$	−15.5885	−	9.00000i	−0.895533	−	0.517036i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$		0			0
$306$	1.50000	−	2.59808i	0.0857493	−	0.148522i
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$		0			0
$309$	−5.00000			−0.284440
$310$		0			0
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	0.709771	−	0.704433i	$-0.248799\pi$
$311$	−4.50000	−	7.79423i	−0.255172	−	0.441970i	−0.964942	+	0.262463i	$0.915465\pi$
$312$	−3.46410	+	2.00000i	−0.196116	+	0.113228i
$313$	−4.33013	−	2.50000i	−0.244753	−	0.141308i	0.372606	−	0.927990i	$-0.378464\pi$
$313$	−4.33013	−	2.50000i	−0.244753	−	0.141308i	−0.617359	+	0.786681i	$0.711798\pi$
$314$	8.00000			0.451466
$315$		0			0
$316$	11.0000			0.618798
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.00635137	−	0.999980i	$-0.502022\pi$
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.869184	+	0.494489i	$0.835355\pi$
$318$	5.19615	−	3.00000i	0.291386	−	0.168232i
$319$		0			0
$320$		0			0
$321$	−18.0000			−1.00466
$322$	−5.19615	−	6.00000i	−0.289570	−	0.334367i
$323$			6.00000i			0.333849i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	1.73205	+	1.00000i	0.0957826	+	0.0553001i
$328$			9.00000i			0.496942i
$329$	7.50000	+	2.59808i	0.413488	+	0.143237i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$		0			0
$333$	−8.66025	+	5.00000i	−0.474579	+	0.273998i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$		0			0
$336$	−0.500000	−	2.59808i	−0.0272772	−	0.141737i
$337$		−	11.0000i		−	0.599208i	−0.954064	−	0.299604i	$-0.903145\pi$
$337$		−	11.0000i		−	0.599208i	0.954064	−	0.299604i	$-0.0968546\pi$
$338$	2.59808	+	1.50000i	0.141317	+	0.0815892i
$339$	10.5000	+	18.1865i	0.570282	+	0.987757i
$340$		0			0
$341$		0			0
$342$			2.00000i			0.108148i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	31.1769	−	18.0000i	1.67366	−	0.966291i	0.708105	−	0.706107i	$-0.249550\pi$
$347$	31.1769	−	18.0000i	1.67366	−	0.966291i	0.965559	−	0.260184i	$-0.0837832\pi$
$348$		0			0
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−12.9904	+	7.50000i	−0.691408	+	0.399185i	−0.804139	−	0.594441i	$-0.797373\pi$
$353$	−12.9904	+	7.50000i	−0.691408	+	0.399185i	0.112731	+	0.993626i	$0.464040\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$		0			0
$356$	−15.0000			−0.794998
$357$	2.59808	−	7.50000i	0.137505	−	0.396942i
$358$			6.00000i			0.317110i
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−6.92820	−	4.00000i	−0.364138	−	0.210235i
$363$		−	11.0000i		−	0.577350i
$364$	−8.00000	+	6.92820i	−0.419314	+	0.363137i
$365$		0			0
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	−0.669804	−	0.742538i	$-0.733622\pi$
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	0.308155	+	0.951336i	$0.400289\pi$
$368$	2.59808	−	1.50000i	0.135434	−	0.0781929i
$369$	−4.50000	+	7.79423i	−0.234261	+	0.405751i
$370$		0			0
$371$	12.0000	−	10.3923i	0.623009	−	0.539542i
$372$			1.00000i			0.0518476i
$373$	3.46410	+	2.00000i	0.179364	+	0.103556i	0.586994	−	0.809591i	$-0.300311\pi$
$373$	3.46410	+	2.00000i	0.179364	+	0.103556i	−0.407630	+	0.913147i	$0.633645\pi$
$374$		0			0
$375$		0			0
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$		0			0
$378$	0.866025	−	2.50000i	0.0445435	−	0.128586i
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	−18.1865	+	10.5000i	−0.930504	+	0.537227i
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.0427020	−	0.999088i	$-0.513597\pi$
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.886586	+	0.462563i	$0.846930\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	−17.0000			−0.865277
$387$	−8.66025	−	5.00000i	−0.440225	−	0.254164i
$388$	−6.06218	+	3.50000i	−0.307760	+	0.177686i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	9.00000			0.455150
$392$	−2.59808	−	6.50000i	−0.131223	−	0.328300i
$393$		−	12.0000i		−	0.605320i
$394$	6.00000	−	10.3923i	0.302276	−	0.523557i
$395$		0			0
$396$		0			0
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.0612128	−	0.998125i	$-0.519497\pi$
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.895008	+	0.446051i	$0.852830\pi$
$398$		−	11.0000i		−	0.551380i
$399$	1.00000	+	5.19615i	0.0500626	+	0.260133i
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	−3.46410	+	2.00000i	−0.172774	+	0.0997509i
$403$	3.46410	−	2.00000i	0.172559	−	0.0996271i
$404$	9.00000	−	15.5885i	0.447767	−	0.775555i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.59808	+	1.50000i	0.128624	+	0.0742611i
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$		0			0
$411$	4.50000	−	7.79423i	0.221969	−	0.384461i
$412$		−	5.00000i		−	0.246332i
$413$	10.3923	+	12.0000i	0.511372	+	0.590481i
$414$	3.00000			0.147442
$415$		0			0
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	−1.73205	+	1.00000i	−0.0848189	+	0.0489702i
$418$		0			0
$419$	−18.0000			−0.879358			−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000			−0.879358			−0.439679	+	0.898155i	$0.644908\pi$
$420$		0			0
$421$	−40.0000			−1.94948			−0.974740	−	0.223341i	$-0.928304\pi$
$421$	−40.0000			−1.94948			−0.974740	+	0.223341i	$0.928304\pi$
$422$	−12.1244	−	7.00000i	−0.590204	−	0.340755i
$423$	−2.59808	+	1.50000i	−0.126323	+	0.0729325i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$		0			0
$426$	−3.00000			−0.145350
$427$	6.92820	−	20.0000i	0.335279	−	0.967868i
$428$		−	18.0000i		−	0.870063i
$429$		0			0
$430$		0			0
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	0.983057	+	0.183301i	$0.0586785\pi$
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	−0.332785	+	0.943003i	$0.607988\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			29.0000i			1.39365i	0.717241	+	0.696826i	$0.245405\pi$
$433$			29.0000i			1.39365i	−0.717241	+	0.696826i	$0.754595\pi$
$434$	0.500000	+	2.59808i	0.0240008	+	0.124712i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−5.19615	+	3.00000i	−0.248566	+	0.143509i
$438$	−12.1244	+	7.00000i	−0.579324	+	0.334473i
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	−0.800179	−	0.599761i	$-0.795262\pi$
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	0.919498	+	0.393095i	$0.128596\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		−	12.0000i		−	0.570782i
$443$	5.19615	+	3.00000i	0.246877	+	0.142534i	0.618333	−	0.785916i	$-0.287808\pi$
$443$	5.19615	+	3.00000i	0.246877	+	0.142534i	−0.371457	+	0.928450i	$0.621142\pi$
$444$	−5.00000	−	8.66025i	−0.237289	−	0.410997i
$445$		0			0
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$			6.00000i			0.283790i
$448$	2.59808	−	0.500000i	0.122748	−	0.0236228i
$449$	21.0000			0.991051			0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000			0.991051			0.495526	+	0.868593i	$0.334975\pi$
$450$		0			0
$451$		0			0
$452$	−18.1865	+	10.5000i	−0.855423	+	0.493878i
$453$	−6.92820	−	4.00000i	−0.325515	−	0.187936i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	1.73205	+	1.00000i	0.0810219	+	0.0467780i	0.539964	−	0.841688i	$-0.318438\pi$
$457$	1.73205	+	1.00000i	0.0810219	+	0.0467780i	−0.458942	+	0.888466i	$0.651771\pi$
$458$	3.46410	−	2.00000i	0.161867	−	0.0934539i
$459$	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
$463$			5.00000i			0.232370i	0.993228	+	0.116185i	$0.0370665\pi$
$463$			5.00000i			0.232370i	−0.993228	+	0.116185i	$0.962933\pi$
$464$		0			0
$465$		0			0
$466$	−15.0000	−	25.9808i	−0.694862	−	1.20354i
$467$	10.3923	+	6.00000i	0.480899	+	0.277647i	0.720791	−	0.693153i	$-0.243779\pi$
$467$	10.3923	+	6.00000i	0.480899	+	0.277647i	−0.239892	+	0.970799i	$0.577112\pi$
$468$		−	4.00000i		−	0.184900i
$469$	−8.00000	+	6.92820i	−0.369406	+	0.319915i
$470$		0			0
$471$	−4.00000	+	6.92820i	−0.184310	+	0.319235i
$472$	−5.19615	+	3.00000i	−0.239172	+	0.138086i
$473$		0			0
$474$	−5.50000	+	9.52628i	−0.252623	+	0.437557i
$475$		0			0
$476$	7.50000	+	2.59808i	0.343762	+	0.119083i
$477$			6.00000i			0.274721i
$478$	12.9904	+	7.50000i	0.594166	+	0.343042i
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	−0.990060	−	0.140643i	$-0.955083\pi$
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	0.373230	−	0.927739i	$-0.378250\pi$
$480$		0			0
$481$	−20.0000	+	34.6410i	−0.911922	+	1.57949i
$482$			14.0000i			0.637683i
$483$	7.79423	−	1.50000i	0.354650	−	0.0682524i
$484$	11.0000			0.500000
$485$		0			0
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	26.8468	−	15.5000i	1.21654	−	0.702372i	0.252367	−	0.967632i	$-0.418791\pi$
$487$	26.8468	−	15.5000i	1.21654	−	0.702372i	0.964177	+	0.265260i	$0.0854576\pi$
$488$	6.92820	+	4.00000i	0.313625	+	0.181071i
$489$	−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	$0.543228\pi$
$492$	−7.79423	−	4.50000i	−0.351391	−	0.202876i
$493$		0			0
$494$	4.00000	+	6.92820i	0.179969	+	0.311715i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	−7.79423	+	1.50000i	−0.349619	+	0.0672842i
$498$		0			0
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$		0			0
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	−10.3923	−	6.00000i	−0.463831	−	0.267793i
$503$		−	36.0000i		−	1.60516i	−0.596544	−	0.802580i	$-0.703460\pi$
$503$		−	36.0000i		−	1.60516i	0.596544	−	0.802580i	$-0.296540\pi$
$504$	2.50000	+	0.866025i	0.111359	+	0.0385758i
$505$		0			0
$506$		0			0
$507$	−2.59808	+	1.50000i	−0.115385	+	0.0666173i
$508$	−13.8564	+	8.00000i	−0.614779	+	0.354943i
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$		0			0
$511$	−28.0000	+	24.2487i	−1.23865	+	1.07270i
$512$			1.00000i			0.0441942i
$513$	−1.73205	−	1.00000i	−0.0764719	−	0.0441511i
$514$	−15.0000	−	25.9808i	−0.661622	−	1.14596i
$515$		0			0
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$		0			0
$518$	−17.3205	−	20.0000i	−0.761019	−	0.878750i
$519$	18.0000			0.790112
$520$		0			0
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	0.653650	−	0.756797i	$-0.273237\pi$
$521$	−7.50000	−	12.9904i	−0.328581	−	0.569119i	−0.982231	+	0.187678i	$0.939904\pi$
$522$		0			0
$523$	−27.7128	−	16.0000i	−1.21180	−	0.699631i	−0.248646	−	0.968594i	$-0.579986\pi$
$523$	−27.7128	−	16.0000i	−1.21180	−	0.699631i	−0.963150	+	0.268963i	$0.913319\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	−9.00000			−0.392419
$527$	−2.59808	−	1.50000i	−0.113174	−	0.0653410i
$528$		0			0
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	−5.19615	+	1.00000i	−0.225282	+	0.0433555i
$533$			36.0000i			1.55933i
$534$	7.50000	−	12.9904i	0.324557	−	0.562149i
$535$		0			0
$536$	−2.00000	−	3.46410i	−0.0863868	−	0.149626i
$537$	−5.19615	−	3.00000i	−0.224231	−	0.129460i
$538$			6.00000i			0.258678i
$539$		0			0
$540$		0			0
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$	−6.06218	+	3.50000i	−0.260393	+	0.150338i
$543$	6.92820	−	4.00000i	0.297318	−	0.171656i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		0			0
$546$	−2.00000	−	10.3923i	−0.0855921	−	0.444750i
$547$		−	26.0000i		−	1.11168i	−0.831289	−	0.555840i	$-0.812397\pi$
$547$		−	26.0000i		−	1.11168i	0.831289	−	0.555840i	$-0.187603\pi$
$548$	7.79423	+	4.50000i	0.332953	+	0.192230i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$			3.00000i			0.127688i
$553$	−9.52628	+	27.5000i	−0.405099	+	1.16942i
$554$	−28.0000			−1.18961
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−5.19615	+	3.00000i	−0.220168	+	0.127114i	−0.606028	−	0.795443i	$-0.707238\pi$
$557$	−5.19615	+	3.00000i	−0.220168	+	0.127114i	0.385860	+	0.922557i	$0.373905\pi$
$558$	−0.866025	−	0.500000i	−0.0366618	−	0.0211667i
$559$	−40.0000			−1.69182
$560$		0			0
$561$		0			0
$562$	−7.79423	−	4.50000i	−0.328780	−	0.189821i
$563$	−25.9808	+	15.0000i	−1.09496	+	0.632175i	−0.934892	−	0.354932i	$-0.884504\pi$
$563$	−25.9808	+	15.0000i	−1.09496	+	0.632175i	−0.160066	+	0.987106i	$0.551171\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$		0			0
$566$	4.00000			0.168133
$567$	1.73205	+	2.00000i	0.0727393	+	0.0839921i
$568$		−	3.00000i		−	0.125877i
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	−0.431011	−	0.902347i	$-0.641843\pi$
$569$	13.5000	−	23.3827i	0.565949	−	0.980253i	0.996961	−	0.0779066i	$-0.0248236\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$		0			0
$573$		−	21.0000i		−	0.877288i
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−12.1244	+	7.00000i	−0.504744	+	0.291414i	−0.730670	−	0.682730i	$-0.760792\pi$
$577$	−12.1244	+	7.00000i	−0.504744	+	0.291414i	0.225927	+	0.974144i	$0.427459\pi$
$578$	6.92820	−	4.00000i	0.288175	−	0.166378i
$579$	8.50000	−	14.7224i	0.353248	−	0.611843i
$580$		0			0
$581$		0			0
$582$		−	7.00000i		−	0.290159i
$583$		0			0
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$		−	42.0000i		−	1.73353i	−0.498721	−	0.866763i	$-0.666197\pi$
$587$		−	42.0000i		−	1.73353i	0.498721	−	0.866763i	$-0.333803\pi$
$588$	6.92820	+	1.00000i	0.285714	+	0.0412393i
$589$	2.00000			0.0824086
$590$		0			0
$591$	6.00000	+	10.3923i	0.246807	+	0.427482i
$592$	8.66025	−	5.00000i	0.355934	−	0.205499i
$593$	−18.1865	−	10.5000i	−0.746831	−	0.431183i	0.0777165	−	0.996976i	$-0.475237\pi$
$593$	−18.1865	−	10.5000i	−0.746831	−	0.431183i	−0.824548	+	0.565792i	$0.808570\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000			−0.245770
$597$	9.52628	+	5.50000i	0.389885	+	0.225100i
$598$	10.3923	−	6.00000i	0.424973	−	0.245358i
$599$	−1.50000	−	2.59808i	−0.0612883	−	0.106155i	0.833753	−	0.552137i	$-0.186188\pi$
$599$	−1.50000	−	2.59808i	−0.0612883	−	0.106155i	−0.895042	+	0.445983i	$0.852854\pi$
$600$		0			0
$601$	−10.0000			−0.407909			−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000			−0.407909			−0.203954	+	0.978980i	$0.565379\pi$
$602$	8.66025	−	25.0000i	0.352966	−	1.01892i
$603$		−	4.00000i		−	0.162893i
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$		0			0
$606$	9.00000	+	15.5885i	0.365600	+	0.633238i
$607$	−6.06218	−	3.50000i	−0.246056	−	0.142061i	0.371901	−	0.928272i	$-0.378706\pi$
$607$	−6.06218	−	3.50000i	−0.246056	−	0.142061i	−0.617957	+	0.786212i	$0.712039\pi$
$608$		−	2.00000i		−	0.0811107i
$609$		0			0
$610$		0			0
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	−2.59808	+	1.50000i	−0.105021	+	0.0606339i
$613$	−13.8564	+	8.00000i	−0.559655	+	0.323117i	−0.753007	−	0.658012i	$-0.771397\pi$
$613$	−13.8564	+	8.00000i	−0.559655	+	0.323117i	0.193352	+	0.981129i	$0.438064\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$		0			0
$617$			15.0000i			0.603877i	0.953327	+	0.301939i	$0.0976338\pi$
$617$			15.0000i			0.603877i	−0.953327	+	0.301939i	$0.902366\pi$
$618$	4.33013	+	2.50000i	0.174183	+	0.100565i
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$			9.00000i			0.360867i
$623$	12.9904	−	37.5000i	0.520449	−	1.50241i
$624$	4.00000			0.160128
$625$		0			0
$626$	2.50000	+	4.33013i	0.0999201	+	0.173067i
$627$		0			0
$628$	−6.92820	−	4.00000i	−0.276465	−	0.159617i
$629$	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	$0.763510\pi$
$632$	−9.52628	−	5.50000i	−0.378935	−	0.218778i
$633$	12.1244	−	7.00000i	0.481900	−	0.278225i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−10.3923	−	26.0000i	−0.411758	−	1.03016i
$638$		0			0
$639$	1.50000	−	2.59808i	0.0593391	−	0.102778i
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$	15.5885	+	9.00000i	0.615227	+	0.355202i
$643$			38.0000i			1.49857i	0.662246	+	0.749287i	$0.269604\pi$
$643$			38.0000i			1.49857i	−0.662246	+	0.749287i	$0.730396\pi$
$644$	1.50000	+	7.79423i	0.0591083	+	0.307136i
$645$		0			0
$646$	3.00000	−	5.19615i	0.118033	−	0.204440i
$647$	−20.7846	+	12.0000i	−0.817127	+	0.471769i	−0.849425	−	0.527710i	$-0.823051\pi$
$647$	−20.7846	+	12.0000i	−0.817127	+	0.471769i	0.0322975	+	0.999478i	$0.489718\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$	−2.50000	−	0.866025i	−0.0979827	−	0.0339422i
$652$		−	8.00000i		−	0.313304i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$		0			0
$656$	4.50000	−	7.79423i	0.175695	−	0.304314i
$657$		−	14.0000i		−	0.546192i
$658$	−5.19615	−	6.00000i	−0.202567	−	0.233904i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−8.66025	+	5.00000i	−0.336590	+	0.194331i
$663$	10.3923	+	6.00000i	0.403604	+	0.233021i
$664$		0			0
$665$		0			0
$666$	10.0000			0.387492
$667$		0			0
$668$	−20.7846	+	12.0000i	−0.804181	+	0.464294i
$669$	−9.50000	−	16.4545i	−0.367291	−	0.636167i
$670$		0			0
$671$		0			0
$672$	−0.866025	+	2.50000i	−0.0334077	+	0.0964396i
$673$		−	19.0000i		−	0.732396i	−0.930537	−	0.366198i	$-0.880659\pi$
$673$		−	19.0000i		−	0.732396i	0.930537	−	0.366198i	$-0.119341\pi$
$674$	−5.50000	+	9.52628i	−0.211852	+	0.366939i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−10.3923	−	6.00000i	−0.399409	−	0.230599i	0.286820	−	0.957984i	$-0.407402\pi$
$677$	−10.3923	−	6.00000i	−0.399409	−	0.230599i	−0.686229	+	0.727386i	$0.740735\pi$
$678$		−	21.0000i		−	0.806500i
$679$	−3.50000	−	18.1865i	−0.134318	−	0.697935i
$680$		0			0
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$		0			0
$683$	5.19615	−	3.00000i	0.198825	−	0.114792i	−0.397282	−	0.917697i	$-0.630047\pi$
$683$	5.19615	−	3.00000i	0.198825	−	0.114792i	0.596107	+	0.802905i	$0.296713\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$		0			0
$686$	18.5000	−	0.866025i	0.706333	−	0.0330650i
$687$			4.00000i			0.152610i
$688$	8.66025	+	5.00000i	0.330169	+	0.190623i
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$			18.0000i			0.684257i
$693$		0			0
$694$	−36.0000			−1.36654
$695$		0			0
$696$		0			0
$697$	23.3827	−	13.5000i	0.885682	−	0.511349i
$698$	22.5167	+	13.0000i	0.852268	+	0.492057i
$699$	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	$0.572767\pi$
$702$	3.46410	+	2.00000i	0.130744	+	0.0754851i
$703$	−17.3205	+	10.0000i	−0.653255	+	0.377157i
$704$		0			0
$705$		0			0
$706$	15.0000			0.564532
$707$	31.1769	+	36.0000i	1.17253	+	1.35392i
$708$		−	6.00000i		−	0.225494i
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	0.347325	+	0.937745i	$0.387090\pi$
$709$	−17.0000	+	29.4449i	−0.638448	+	1.10583i	−0.985773	+	0.168080i	$0.946243\pi$
$710$		0			0
$711$	−5.50000	−	9.52628i	−0.206266	−	0.357263i
$712$	12.9904	+	7.50000i	0.486835	+	0.281074i
$713$		−	3.00000i		−	0.112351i
$714$	−6.00000	+	5.19615i	−0.224544	+	0.194461i
$715$		0			0
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$	−12.9904	+	7.50000i	−0.485135	+	0.280093i
$718$	−10.3923	+	6.00000i	−0.387837	+	0.223918i
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	0.496527	+	0.868021i	$0.334608\pi$
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	−0.999992	+	0.00400572i	$0.998725\pi$
$720$		0			0
$721$	12.5000	+	4.33013i	0.465524	+	0.161262i
$722$		−	15.0000i		−	0.558242i
$723$	−12.1244	−	7.00000i	−0.450910	−	0.260333i
$724$	4.00000	+	6.92820i	0.148659	+	0.257485i
$725$		0			0
$726$	−5.50000	+	9.52628i	−0.204124	+	0.353553i
$727$			37.0000i			1.37225i	0.727482	+	0.686127i	$0.240691\pi$
$727$			37.0000i			1.37225i	−0.727482	+	0.686127i	$0.759309\pi$
$728$	10.3923	−	2.00000i	0.385164	−	0.0741249i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	15.0000	+	25.9808i	0.554795	+	0.960933i
$732$	−6.92820	+	4.00000i	−0.256074	+	0.147844i
$733$	−12.1244	−	7.00000i	−0.447823	−	0.258551i	0.259087	−	0.965854i	$-0.416578\pi$
$733$	−12.1244	−	7.00000i	−0.447823	−	0.258551i	−0.706910	+	0.707303i	$0.749912\pi$
$734$	8.00000			0.295285
$735$		0			0
$736$	−3.00000			−0.110581
$737$		0			0
$738$	7.79423	−	4.50000i	0.286910	−	0.165647i
$739$	1.00000	+	1.73205i	0.0367856	+	0.0637145i	0.883832	−	0.467804i	$-0.154955\pi$
$739$	1.00000	+	1.73205i	0.0367856	+	0.0637145i	−0.847046	+	0.531519i	$0.821621\pi$
$740$		0			0
$741$	−8.00000			−0.293887
$742$	−15.5885	+	3.00000i	−0.572270	+	0.110133i
$743$		−	51.0000i		−	1.87101i	−0.353315	−	0.935504i	$-0.614946\pi$
$743$		−	51.0000i		−	1.87101i	0.353315	−	0.935504i	$-0.385054\pi$
$744$	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	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	2.59808	−	1.50000i	0.0947421	−	0.0546994i
$753$	10.3923	−	6.00000i	0.378717	−	0.218652i
$754$		0			0
$755$		0			0
$756$	−2.00000	+	1.73205i	−0.0727393	+	0.0629941i
$757$			16.0000i			0.581530i	0.956795	+	0.290765i	$0.0939098\pi$
$757$			16.0000i			0.581530i	−0.956795	+	0.290765i	$0.906090\pi$
$758$	−13.8564	−	8.00000i	−0.503287	−	0.290573i
$759$		0			0
$760$		0			0
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	−0.999925	−	0.0122260i	$-0.996108\pi$
$761$	−13.5000	+	23.3827i	−0.489375	+	0.847622i	0.510551	+	0.859848i	$0.329442\pi$
$762$		−	16.0000i		−	0.579619i
$763$	−3.46410	−	4.00000i	−0.125409	−	0.144810i
$764$	21.0000			0.759753
$765$		0			0
$766$	10.5000	+	18.1865i	0.379380	+	0.657106i
$767$	−20.7846	+	12.0000i	−0.750489	+	0.433295i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$	14.7224	+	8.50000i	0.529872	+	0.305922i
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$		0			0
$776$	7.00000			0.251285
$777$	25.9808	−	5.00000i	0.932055	−	0.179374i
$778$		−	6.00000i		−	0.215110i
$779$	−9.00000	+	15.5885i	−0.322458	+	0.558514i
$780$		0			0
$781$		0			0
$782$	−7.79423	−	4.50000i	−0.278721	−	0.160920i
$783$		0			0
$784$	−1.00000	+	6.92820i	−0.0357143	+	0.247436i
$785$		0			0
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	19.0526	−	11.0000i	0.679150	−	0.392108i	−0.120384	−	0.992727i	$-0.538413\pi$
$787$	19.0526	−	11.0000i	0.679150	−	0.392108i	0.799535	+	0.600620i	$0.205079\pi$
$788$	−10.3923	+	6.00000i	−0.370211	+	0.213741i
$789$	4.50000	−	7.79423i	0.160204	−	0.277482i
$790$		0			0
$791$	−10.5000	−	54.5596i	−0.373337	−	1.93992i
$792$		0			0
$793$	27.7128	+	16.0000i	0.984111	+	0.568177i
$794$	11.0000	+	19.0526i	0.390375	+	0.676150i
$795$		0			0
$796$	−5.50000	+	9.52628i	−0.194942	+	0.337650i
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$	1.73205	−	5.00000i	0.0613139	−	0.176998i
$799$	9.00000			0.318397
$800$		0			0
$801$	7.50000	+	12.9904i	0.264999	+	0.458993i
$802$	15.5885	−	9.00000i	0.550448	−	0.317801i
$803$		0			0
$804$	4.00000			0.141069
$805$		0			0
$806$	−4.00000			−0.140894
$807$	−5.19615	−	3.00000i	−0.182913	−	0.105605i
$808$	−15.5885	+	9.00000i	−0.548400	+	0.316619i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$		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
$813$		−	7.00000i		−	0.245501i
$814$		0			0
$815$		0			0
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−17.3205	−	10.0000i	−0.605968	−	0.349856i
$818$		−	5.00000i		−	0.174821i
$819$	10.0000	+	3.46410i	0.349428	+	0.121046i
$820$		0			0
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.181250	−	0.983437i	$-0.441986\pi$
$821$	27.0000	−	46.7654i	0.942306	−	1.63212i	0.761056	−	0.648686i	$-0.224681\pi$
$822$	−7.79423	+	4.50000i	−0.271855	+	0.156956i
$823$	27.7128	−	16.0000i	0.966008	−	0.557725i	0.0679910	−	0.997686i	$-0.478341\pi$
$823$	27.7128	−	16.0000i	0.966008	−	0.557725i	0.898017	+	0.439961i	$0.145008\pi$
$824$	−2.50000	+	4.33013i	−0.0870916	+	0.150847i
$825$		0			0
$826$	−3.00000	−	15.5885i	−0.104383	−	0.542392i
$827$		−	48.0000i		−	1.66912i	−0.550914	−	0.834562i	$-0.685721\pi$
$827$		−	48.0000i		−	1.66912i	0.550914	−	0.834562i	$-0.314279\pi$
$828$	−2.59808	−	1.50000i	−0.0902894	−	0.0521286i
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	14.0000	−	24.2487i	0.485655	−	0.841178i
$832$			4.00000i			0.138675i
$833$	−12.9904	+	16.5000i	−0.450090	+	0.571691i
$834$	2.00000			0.0692543
$835$		0			0
$836$		0			0
$837$	0.866025	−	0.500000i	0.0299342	−	0.0172825i
$838$	15.5885	+	9.00000i	0.538494	+	0.310900i
$839$	−27.0000			−0.932144			−0.466072	−	0.884747i	$-0.654331\pi$
$839$	−27.0000			−0.932144			−0.466072	+	0.884747i	$0.654331\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	34.6410	+	20.0000i	1.19381	+	0.689246i
$843$	7.79423	−	4.50000i	0.268447	−	0.154988i
$844$	7.00000	+	12.1244i	0.240950	+	0.417338i
$845$		0			0
$846$	3.00000			0.103142
$847$	−9.52628	+	27.5000i	−0.327327	+	0.944911i
$848$		−	6.00000i		−	0.206041i
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$		0			0
$851$	15.0000	+	25.9808i	0.514193	+	0.890609i
$852$	2.59808	+	1.50000i	0.0890086	+	0.0513892i
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$	−16.0000	+	13.8564i	−0.547509	+	0.474156i
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	−46.7654	+	27.0000i	−1.59747	+	0.922302i	−0.605503	+	0.795843i	$0.707028\pi$
$857$	−46.7654	+	27.0000i	−1.59747	+	0.922302i	−0.991972	+	0.126459i	$0.959639\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$		0			0
$861$	18.0000	−	15.5885i	0.613438	−	0.531253i
$862$		−	27.0000i		−	0.919624i
$863$	12.9904	+	7.50000i	0.442198	+	0.255303i	0.704529	−	0.709675i	$-0.251158\pi$
$863$	12.9904	+	7.50000i	0.442198	+	0.255303i	−0.262332	+	0.964978i	$0.584491\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	14.5000	−	25.1147i	0.492730	−	0.853433i
$867$			8.00000i			0.271694i
$868$	0.866025	−	2.50000i	0.0293948	−	0.0848555i
$869$		0			0
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	1.73205	−	1.00000i	0.0586546	−	0.0338643i
$873$	6.06218	+	3.50000i	0.205174	+	0.118457i
$874$	6.00000			0.202953
$875$		0			0
$876$	14.0000			0.473016
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.939155	−	0.343495i	$-0.111611\pi$
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.172102	+	0.985079i	$0.444944\pi$
$878$	−4.33013	+	2.50000i	−0.146135	+	0.0843709i
$879$	−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	$0.516093\pi$
$882$	−4.33013	+	5.50000i	−0.145803	+	0.185195i
$883$			38.0000i			1.27880i	0.768874	+	0.639401i	$0.220818\pi$
$883$			38.0000i			1.27880i	−0.768874	+	0.639401i	$0.779182\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	−3.00000	−	5.19615i	−0.100787	−	0.174568i
$887$	41.5692	+	24.0000i	1.39576	+	0.805841i	0.993945	−	0.109881i	$-0.0350469\pi$
$887$	41.5692	+	24.0000i	1.39576	+	0.805841i	0.401813	+	0.915722i	$0.368380\pi$
$888$			10.0000i			0.335578i
$889$	−8.00000	−	41.5692i	−0.268311	−	1.39419i
$890$		0			0
$891$		0			0
$892$	16.4545	−	9.50000i	0.550937	−	0.318084i
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$		0			0
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$			12.0000i			0.400668i
$898$	−18.1865	−	10.5000i	−0.606892	−	0.350390i
$899$		0			0
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		0			0
$903$	17.3205	+	20.0000i	0.576390	+	0.665558i
$904$	21.0000			0.698450
$905$		0			0
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	13.8564	−	8.00000i	0.460094	−	0.265636i	−0.251990	−	0.967730i	$-0.581085\pi$
$907$	13.8564	−	8.00000i	0.460094	−	0.265636i	0.712084	+	0.702094i	$0.247752\pi$
$908$	5.19615	+	3.00000i	0.172440	+	0.0995585i
$909$	−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	$0.276414\pi$
$912$	1.73205	+	1.00000i	0.0573539	+	0.0331133i
$913$		0			0
$914$	−1.00000	−	1.73205i	−0.0330771	−	0.0572911i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	−10.3923	+	30.0000i	−0.343184	+	0.990687i
$918$		−	3.00000i		−	0.0990148i
$919$	−9.50000	+	16.4545i	−0.313376	+	0.542783i	−0.979091	−	0.203423i	$-0.934793\pi$
$919$	−9.50000	+	16.4545i	−0.313376	+	0.542783i	0.665715	+	0.746206i	$0.268127\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	10.3923	+	6.00000i	0.342252	+	0.197599i
$923$		−	12.0000i		−	0.394985i
$924$		0			0
$925$		0			0
$926$	2.50000	−	4.33013i	0.0821551	−	0.142297i
$927$	−4.33013	+	2.50000i	−0.142220	+	0.0821108i
$928$		0			0
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$	2.00000	−	13.8564i	0.0655474	−	0.454125i
$932$			30.0000i			0.982683i
$933$	−7.79423	−	4.50000i	−0.255172	−	0.147323i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$		0			0
$936$	−2.00000	+	3.46410i	−0.0653720	+	0.113228i
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$	10.3923	−	2.00000i	0.339321	−	0.0653023i
$939$	−5.00000			−0.163169
$940$		0			0
$941$	−15.0000	−	25.9808i	−0.488986	−	0.846949i	0.510934	−	0.859620i	$-0.329300\pi$
$941$	−15.0000	−	25.9808i	−0.488986	−	0.846949i	−0.999920	+	0.0126715i	$0.995966\pi$
$942$	6.92820	−	4.00000i	0.225733	−	0.130327i
$943$	23.3827	+	13.5000i	0.761445	+	0.439620i
$944$	6.00000			0.195283
$945$		0			0
$946$		0			0
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.362454	−	0.932002i	$-0.618061\pi$
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.988364	+	0.152106i	$0.951394\pi$
$948$	9.52628	−	5.50000i	0.309399	−	0.178632i
$949$	−28.0000	−	48.4974i	−0.908918	−	1.57429i
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−5.19615	−	6.00000i	−0.168408	−	0.194461i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	3.00000	−	5.19615i	0.0971286	−	0.168232i
$955$		0			0
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$		0			0
$958$			27.0000i			0.872330i
$959$	−18.0000	+	15.5885i	−0.581250	+	0.503378i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	34.6410	−	20.0000i	1.11687	−	0.644826i
$963$	−15.5885	+	9.00000i	−0.502331	+	0.290021i
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$		0			0
$966$	−7.50000	−	2.59808i	−0.241309	−	0.0835917i
$967$			49.0000i			1.57573i	0.615846	+	0.787867i	$0.288815\pi$
$967$			49.0000i			1.57573i	−0.615846	+	0.787867i	$0.711185\pi$
$968$	−9.52628	−	5.50000i	−0.306186	−	0.176777i
$969$	3.00000	+	5.19615i	0.0963739	+	0.166924i
$970$		0			0
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	−0.418101	−	0.908401i	$-0.637304\pi$
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	0.995748	−	0.0921142i	$-0.0293625\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	5.19615	−	1.00000i	0.166581	−	0.0320585i
$974$	−31.0000			−0.993304
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−23.3827	+	13.5000i	−0.748078	+	0.431903i	−0.824999	−	0.565134i	$-0.808824\pi$
$977$	−23.3827	+	13.5000i	−0.748078	+	0.431903i	0.0769208	+	0.997037i	$0.475491\pi$
$978$	6.92820	+	4.00000i	0.221540	+	0.127906i
$979$		0			0
$980$		0			0
$981$	2.00000			0.0638551
$982$	5.19615	+	3.00000i	0.165816	+	0.0957338i
$983$	−10.3923	+	6.00000i	−0.331463	+	0.191370i	−0.656490	−	0.754334i	$-0.727960\pi$
$983$	−10.3923	+	6.00000i	−0.331463	+	0.191370i	0.325027	+	0.945705i	$0.394626\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$		0			0
$986$		0			0
$987$	7.79423	−	1.50000i	0.248093	−	0.0477455i
$988$		−	8.00000i		−	0.254514i
$989$	−15.0000	+	25.9808i	−0.476972	+	0.826140i
$990$		0			0
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.770849	−	0.637018i	$-0.780168\pi$
$991$	−29.5000	−	51.0955i	−0.937098	−	1.62310i	−0.166250	−	0.986084i	$-0.553166\pi$
$992$	0.866025	+	0.500000i	0.0274963	+	0.0158750i
$993$		−	10.0000i		−	0.317340i
$994$	7.50000	+	2.59808i	0.237886	+	0.0824060i
$995$		0			0
$996$		0			0
$997$	34.6410	−	20.0000i	1.09709	−	0.633406i	0.161636	−	0.986850i	$-0.448323\pi$
$997$	34.6410	−	20.0000i	1.09709	−	0.633406i	0.935456	+	0.353444i	$0.114990\pi$
$998$	−27.7128	+	16.0000i	−0.877234	+	0.506471i
$999$	−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.o.e.499.1		4
5.2	odd	4		1050.2.i.m.751.1	yes	2
5.3	odd	4		1050.2.i.h.751.1	yes	2
5.4	even	2	inner	1050.2.o.e.499.2		4
7.4	even	3	inner	1050.2.o.e.949.2		4
35.2	odd	12		7350.2.a.bb.1.1		1
35.4	even	6	inner	1050.2.o.e.949.1		4
35.12	even	12		7350.2.a.n.1.1		1
35.18	odd	12		1050.2.i.h.151.1	✓	2
35.23	odd	12		7350.2.a.by.1.1		1
35.32	odd	12		1050.2.i.m.151.1	yes	2
35.33	even	12		7350.2.a.cq.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.h.151.1	✓	2	35.18	odd	12
1050.2.i.h.751.1	yes	2	5.3	odd	4
1050.2.i.m.151.1	yes	2	35.32	odd	12
1050.2.i.m.751.1	yes	2	5.2	odd	4
1050.2.o.e.499.1		4	1.1	even	1	trivial
1050.2.o.e.499.2		4	5.4	even	2	inner
1050.2.o.e.949.1		4	35.4	even	6	inner
1050.2.o.e.949.2		4	7.4	even	3	inner
7350.2.a.n.1.1		1	35.12	even	12
7350.2.a.bb.1.1		1	35.2	odd	12
7350.2.a.by.1.1		1	35.23	odd	12
7350.2.a.cq.1.1		1	35.33	even	12

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.59808 + 1.50000i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(-2.59808 - 1.50000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-1.73205 - 2.00000i) q^{28} +(0.500000 + 0.866025i) q^{31} +(0.866025 - 0.500000i) q^{32} +3.00000 q^{34} +1.00000 q^{36} +(-8.66025 - 5.00000i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} -9.00000 q^{41} +(2.59808 - 0.500000i) q^{42} -10.0000i q^{43} +(1.50000 + 2.59808i) q^{46} +(-2.59808 - 1.50000i) q^{47} +1.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(3.46410 - 2.00000i) q^{52} +(-5.19615 + 3.00000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 + 2.59808i) q^{56} -2.00000i q^{57} +(-3.00000 - 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} -1.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} -1.00000 q^{64} +(3.46410 - 2.00000i) q^{67} +(-2.59808 - 1.50000i) q^{68} -3.00000 q^{69} +3.00000 q^{71} +(-0.866025 - 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(5.00000 + 8.66025i) q^{74} +2.00000 q^{76} +4.00000i q^{78} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(7.79423 + 4.50000i) q^{82} +(-2.50000 - 0.866025i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(-7.50000 + 12.9904i) q^{89} +(2.00000 + 10.3923i) q^{91} -3.00000i q^{92} +(0.866025 + 0.500000i) q^{93} +(1.50000 + 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} +7.00000i q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} - 4 q^{6} + 2 q^{9} + 10 q^{14} - 2 q^{16} + 4 q^{19} - 8 q^{21} - 2 q^{24} - 8 q^{26} + 2 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 36 q^{41} + 6 q^{46} + 26 q^{49} - 6 q^{51} - 2 q^{54} + 2 q^{56} - 12 q^{59} - 16 q^{61} - 4 q^{64} - 12 q^{69} + 12 q^{71} + 20 q^{74} + 8 q^{76} + 22 q^{79} - 2 q^{81} - 10 q^{84} - 20 q^{86} - 30 q^{89} + 8 q^{91} + 6 q^{94} + 2 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^6 + 2 * q^9 + 10 * q^14 - 2 * q^16 + 4 * q^19 - 8 * q^21 - 2 * q^24 - 8 * q^26 + 2 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 36 * q^41 + 6 * q^46 + 26 * q^49 - 6 * q^51 - 2 * q^54 + 2 * q^56 - 12 * q^59 - 16 * q^61 - 4 * q^64 - 12 * q^69 + 12 * q^71 + 20 * q^74 + 8 * q^76 + 22 * q^79 - 2 * q^81 - 10 * q^84 - 20 * q^86 - 30 * q^89 + 8 * q^91 + 6 * q^94 + 2 * q^96

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