LMFDB - Embedded newform 1950.2.bc.c.751.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, 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:	$15.5708283941$
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:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.c.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.09808 + 0.633975i) q^{11} -1.00000 q^{12} +(-1.59808 + 3.23205i) q^{13} -1.26795 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(-4.09808 - 2.36603i) q^{19} +1.26795i q^{21} +(-0.633975 + 1.09808i) q^{22} +(4.09808 + 7.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.232051 + 3.59808i) q^{26} +1.00000 q^{27} +(-1.09808 + 0.633975i) q^{28} +(1.50000 + 2.59808i) q^{29} +9.46410i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.09808 + 0.633975i) q^{33} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} -4.73205 q^{38} +(3.59808 - 0.232051i) q^{39} +(5.59808 - 3.23205i) q^{41} +(0.633975 + 1.09808i) q^{42} +(2.09808 - 3.63397i) q^{43} +1.26795i q^{44} +(7.09808 + 4.09808i) q^{46} -4.73205i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.69615 - 4.66987i) q^{49} +5.19615 q^{51} +(2.00000 + 3.00000i) q^{52} -3.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.633975 + 1.09808i) q^{56} +4.73205i q^{57} +(2.59808 + 1.50000i) q^{58} +(-12.0000 - 6.92820i) q^{59} +(-7.59808 + 13.1603i) q^{61} +(4.73205 + 8.19615i) q^{62} +(1.09808 - 0.633975i) q^{63} -1.00000 q^{64} +1.26795 q^{66} +(-6.29423 + 3.63397i) q^{67} +(2.59808 + 4.50000i) q^{68} +(4.09808 - 7.09808i) q^{69} +(1.90192 + 1.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 - 2.59808i) q^{74} +(-4.09808 + 2.36603i) q^{76} +1.60770 q^{77} +(3.00000 - 2.00000i) q^{78} +8.39230 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.23205 - 5.59808i) q^{82} -5.66025i q^{83} +(1.09808 + 0.633975i) q^{84} -4.19615i q^{86} +(1.50000 - 2.59808i) q^{87} +(0.633975 + 1.09808i) q^{88} +(-8.19615 + 4.73205i) q^{89} +(3.80385 - 2.53590i) q^{91} +8.19615 q^{92} +(8.19615 - 4.73205i) q^{93} +(-2.36603 - 4.09808i) q^{94} +1.00000i q^{96} +(5.19615 + 3.00000i) q^{97} +(-4.66987 - 2.69615i) q^{98} -1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 12 q^{14} - 2 q^{16} - 6 q^{19} - 6 q^{22} + 6 q^{23} - 6 q^{26} + 4 q^{27} + 6 q^{28} + 6 q^{29} - 6 q^{33} + 2 q^{36} - 12 q^{38} + 4 q^{39} + 12 q^{41} + 6 q^{42} - 2 q^{43} + 18 q^{46} - 2 q^{48} + 10 q^{49} + 8 q^{52} - 12 q^{53} - 6 q^{56} - 48 q^{59} - 20 q^{61} + 12 q^{62} - 6 q^{63} - 4 q^{64} + 12 q^{66} + 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} - 6 q^{76} + 48 q^{77} + 12 q^{78} - 8 q^{79} - 2 q^{81} + 6 q^{82} - 6 q^{84} + 6 q^{87} + 6 q^{88} - 12 q^{89} + 36 q^{91} + 12 q^{92} + 12 q^{93} - 6 q^{94} - 36 q^{98}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 12 * q^14 - 2 * q^16 - 6 * q^19 - 6 * q^22 + 6 * q^23 - 6 * q^26 + 4 * q^27 + 6 * q^28 + 6 * q^29 - 6 * q^33 + 2 * q^36 - 12 * q^38 + 4 * q^39 + 12 * q^41 + 6 * q^42 - 2 * q^43 + 18 * q^46 - 2 * q^48 + 10 * q^49 + 8 * q^52 - 12 * q^53 - 6 * q^56 - 48 * q^59 - 20 * q^61 + 12 * q^62 - 6 * q^63 - 4 * q^64 + 12 * q^66 + 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 - 6 * q^76 + 48 * q^77 + 12 * q^78 - 8 * q^79 - 2 * q^81 + 6 * q^82 - 6 * q^84 + 6 * q^87 + 6 * q^88 - 12 * q^89 + 36 * q^91 + 12 * q^92 + 12 * q^93 - 6 * q^94 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−0.500000	−	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
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−1.09808	−	0.633975i	−0.415034	−	0.239620i	0.277916	−	0.960605i	$-0.410356\pi$
$7$	−1.09808	−	0.633975i	−0.415034	−	0.239620i	−0.692950	+	0.720985i	$0.743689\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	−0.656322	−	0.754481i	$-0.727889\pi$
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	0.325239	+	0.945632i	$0.394555\pi$
$12$	−1.00000			−0.288675
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$14$	−1.26795			−0.338874
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	0.357400	+	0.933952i	$0.383663\pi$
$17$	−2.59808	+	4.50000i	−0.630126	+	1.09141i	−0.987526	+	0.157459i	$0.949670\pi$
$18$			1.00000i			0.235702i
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.0501517	−	0.998742i	$-0.515970\pi$
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.890011	+	0.455938i	$0.849304\pi$
$20$		0			0
$21$			1.26795i			0.276689i
$22$	−0.633975	+	1.09808i	−0.135164	+	0.234111i
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	0.877101	+	0.480306i	$0.159475\pi$
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	−0.0225928	+	0.999745i	$0.507192\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	0.232051	+	3.59808i	0.0455089	+	0.705641i
$27$	1.00000			0.192450
$28$	−1.09808	+	0.633975i	−0.207517	+	0.119810i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$			9.46410i			1.69980i	0.526942	+	0.849901i	$0.323339\pi$
$31$			9.46410i			1.69980i	−0.526942	+	0.849901i	$0.676661\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.09808	+	0.633975i	0.191151	+	0.110361i
$34$			5.19615i			0.891133i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$	−4.73205			−0.767640
$39$	3.59808	−	0.232051i	0.576153	−	0.0371579i
$40$		0			0
$41$	5.59808	−	3.23205i	0.874273	−	0.504762i	0.00550690	−	0.999985i	$-0.498247\pi$
$41$	5.59808	−	3.23205i	0.874273	−	0.504762i	0.868766	+	0.495223i	$0.164914\pi$
$42$	0.633975	+	1.09808i	0.0978244	+	0.169437i
$43$	2.09808	−	3.63397i	0.319954	−	0.554176i	−0.660524	−	0.750805i	$-0.729666\pi$
$43$	2.09808	−	3.63397i	0.319954	−	0.554176i	0.980478	+	0.196629i	$0.0629993\pi$
$44$			1.26795i			0.191151i
$45$		0			0
$46$	7.09808	+	4.09808i	1.04655	+	0.604228i
$47$		−	4.73205i		−	0.690241i	−0.938558	−	0.345120i	$-0.887838\pi$
$47$		−	4.73205i		−	0.690241i	0.938558	−	0.345120i	$-0.112162\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−2.69615	−	4.66987i	−0.385165	−	0.667125i
$50$		0			0
$51$	5.19615			0.727607
$52$	2.00000	+	3.00000i	0.277350	+	0.416025i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−0.633975	+	1.09808i	−0.0847184	+	0.146737i
$57$			4.73205i			0.626775i
$58$	2.59808	+	1.50000i	0.341144	+	0.196960i
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.997027	−	0.0770484i	$-0.975450\pi$
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.565240	−	0.824927i	$-0.691216\pi$
$60$		0			0
$61$	−7.59808	+	13.1603i	−0.972834	+	1.68500i	−0.285929	+	0.958251i	$0.592302\pi$
$61$	−7.59808	+	13.1603i	−0.972834	+	1.68500i	−0.686905	+	0.726747i	$0.741031\pi$
$62$	4.73205	+	8.19615i	0.600971	+	1.04091i
$63$	1.09808	−	0.633975i	0.138345	−	0.0798733i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	−6.29423	+	3.63397i	−0.768962	+	0.443961i	−0.832504	−	0.554019i	$-0.813094\pi$
$67$	−6.29423	+	3.63397i	−0.768962	+	0.443961i	0.0635419	+	0.997979i	$0.479760\pi$
$68$	2.59808	+	4.50000i	0.315063	+	0.545705i
$69$	4.09808	−	7.09808i	0.493350	−	0.854508i
$70$		0			0
$71$	1.90192	+	1.09808i	0.225717	+	0.130318i	0.608595	−	0.793481i	$-0.291734\pi$
$71$	1.90192	+	1.09808i	0.225717	+	0.130318i	−0.382878	+	0.923799i	$0.625067\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			12.1244i			1.41905i	0.704681	+	0.709524i	$0.251090\pi$
$73$			12.1244i			1.41905i	−0.704681	+	0.709524i	$0.748910\pi$
$74$	1.50000	−	2.59808i	0.174371	−	0.302020i
$75$		0			0
$76$	−4.09808	+	2.36603i	−0.470082	+	0.271402i
$77$	1.60770			0.183214
$78$	3.00000	−	2.00000i	0.339683	−	0.226455i
$79$	8.39230			0.944208			0.472104	−	0.881543i	$-0.343495\pi$
$79$	8.39230			0.944208			0.472104	+	0.881543i	$0.343495\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.23205	−	5.59808i	0.356920	−	0.618204i
$83$		−	5.66025i		−	0.621294i	−0.950525	−	0.310647i	$-0.899454\pi$
$83$		−	5.66025i		−	0.621294i	0.950525	−	0.310647i	$-0.100546\pi$
$84$	1.09808	+	0.633975i	0.119810	+	0.0691723i
$85$		0			0
$86$		−	4.19615i		−	0.452483i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	0.633975	+	1.09808i	0.0675819	+	0.117055i
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.866946	−	0.498402i	$-0.833920\pi$
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.00184433	+	0.999998i	$0.500587\pi$
$90$		0			0
$91$	3.80385	−	2.53590i	0.398752	−	0.265834i
$92$	8.19615			0.854508
$93$	8.19615	−	4.73205i	0.849901	−	0.490691i
$94$	−2.36603	−	4.09808i	−0.244037	−	0.422684i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	0.740034	−	0.672569i	$-0.234809\pi$
$97$	5.19615	+	3.00000i	0.527589	+	0.304604i	−0.212445	+	0.977173i	$0.568143\pi$
$98$	−4.66987	−	2.69615i	−0.471728	−	0.272353i
$99$		−	1.26795i		−	0.127434i
$100$		0			0
$101$	9.69615	+	16.7942i	0.964803	+	1.67109i	0.710143	+	0.704058i	$0.248630\pi$
$101$	9.69615	+	16.7942i	0.964803	+	1.67109i	0.254660	+	0.967031i	$0.418036\pi$
$102$	4.50000	−	2.59808i	0.445566	−	0.257248i
$103$	6.19615			0.610525			0.305263	−	0.952268i	$-0.401256\pi$
$103$	6.19615			0.610525			0.305263	+	0.952268i	$0.401256\pi$
$104$	3.23205	+	1.59808i	0.316929	+	0.156704i
$105$		0			0
$106$	−2.59808	+	1.50000i	−0.252347	+	0.145693i
$107$	−1.09808	−	1.90192i	−0.106155	−	0.183866i	0.808054	−	0.589108i	$-0.200521\pi$
$107$	−1.09808	−	1.90192i	−0.106155	−	0.183866i	−0.914210	+	0.405242i	$0.867187\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	4.39230i		−	0.420707i	−0.977625	−	0.210353i	$-0.932539\pi$
$109$		−	4.39230i		−	0.420707i	0.977625	−	0.210353i	$-0.0674614\pi$
$110$		0			0
$111$	−2.59808	−	1.50000i	−0.246598	−	0.142374i
$112$			1.26795i			0.119810i
$113$	0.401924	−	0.696152i	0.0378098	−	0.0654885i	−0.846501	−	0.532387i	$-0.821295\pi$
$113$	0.401924	−	0.696152i	0.0378098	−	0.0654885i	0.884311	+	0.466898i	$0.154629\pi$
$114$	2.36603	+	4.09808i	0.221599	+	0.383820i
$115$		0			0
$116$	3.00000			0.278543
$117$	−2.00000	−	3.00000i	−0.184900	−	0.277350i
$118$	−13.8564			−1.27559
$119$	5.70577	−	3.29423i	0.523047	−	0.301981i
$120$		0			0
$121$	−4.69615	+	8.13397i	−0.426923	+	0.739452i
$122$			15.1962i			1.37579i
$123$	−5.59808	−	3.23205i	−0.504762	−	0.291424i
$124$	8.19615	+	4.73205i	0.736036	+	0.424951i
$125$		0			0
$126$	0.633975	−	1.09808i	0.0564789	−	0.0978244i
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	0.941014	−	0.338368i	$-0.109875\pi$
$127$	2.00000	+	3.46410i	0.177471	+	0.307389i	−0.763542	+	0.645758i	$0.776542\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−4.19615			−0.369451
$130$		0			0
$131$	−4.39230			−0.383757			−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230			−0.383757			−0.191879	+	0.981419i	$0.561458\pi$
$132$	1.09808	−	0.633975i	0.0955753	−	0.0551804i
$133$	3.00000	+	5.19615i	0.260133	+	0.450564i
$134$	−3.63397	+	6.29423i	−0.313928	+	0.543739i
$135$		0			0
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	0.794524	−	0.607233i	$-0.207721\pi$
$137$	7.79423	+	4.50000i	0.665906	+	0.384461i	−0.128618	+	0.991694i	$0.541054\pi$
$138$		−	8.19615i		−	0.697703i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	−4.09808	+	2.36603i	−0.345120	+	0.199255i
$142$	2.19615			0.184297
$143$	−0.294229	−	4.56218i	−0.0246046	−	0.381508i
$144$	1.00000			0.0833333
$145$		0			0
$146$	6.06218	+	10.5000i	0.501709	+	0.868986i
$147$	−2.69615	+	4.66987i	−0.222375	+	0.385165i
$148$		−	3.00000i		−	0.246598i
$149$	−5.30385	−	3.06218i	−0.434508	−	0.250863i	0.266757	−	0.963764i	$-0.414048\pi$
$149$	−5.30385	−	3.06218i	−0.434508	−	0.250863i	−0.701265	+	0.712900i	$0.747381\pi$
$150$		0			0
$151$		−	10.7321i		−	0.873362i	−0.899616	−	0.436681i	$-0.856154\pi$
$151$		−	10.7321i		−	0.873362i	0.899616	−	0.436681i	$-0.143846\pi$
$152$	−2.36603	+	4.09808i	−0.191910	+	0.332398i
$153$	−2.59808	−	4.50000i	−0.210042	−	0.363803i
$154$	1.39230	−	0.803848i	0.112195	−	0.0647759i
$155$		0			0
$156$	1.59808	−	3.23205i	0.127948	−	0.258771i
$157$	−7.19615			−0.574315			−0.287158	−	0.957883i	$-0.592710\pi$
$157$	−7.19615			−0.574315			−0.287158	+	0.957883i	$0.592710\pi$
$158$	7.26795	−	4.19615i	0.578207	−	0.333828i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−2.19615	−	1.26795i	−0.172016	−	0.0993134i	0.411520	−	0.911401i	$-0.364998\pi$
$163$	−2.19615	−	1.26795i	−0.172016	−	0.0993134i	−0.583536	+	0.812087i	$0.698331\pi$
$164$		−	6.46410i		−	0.504762i
$165$		0			0
$166$	−2.83013	−	4.90192i	−0.219660	−	0.380463i
$167$	−8.19615	+	4.73205i	−0.634237	+	0.366177i	−0.782391	−	0.622787i	$-0.786000\pi$
$167$	−8.19615	+	4.73205i	−0.634237	+	0.366177i	0.148154	+	0.988964i	$0.452667\pi$
$168$	1.26795			0.0978244
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		0			0
$171$	4.09808	−	2.36603i	0.313388	−	0.180934i
$172$	−2.09808	−	3.63397i	−0.159977	−	0.277088i
$173$	2.19615	−	3.80385i	0.166970	−	0.289201i	−0.770383	−	0.637582i	$-0.779935\pi$
$173$	2.19615	−	3.80385i	0.166970	−	0.289201i	0.937353	+	0.348380i	$0.113268\pi$
$174$		−	3.00000i		−	0.227429i
$175$		0			0
$176$	1.09808	+	0.633975i	0.0827706	+	0.0477876i
$177$			13.8564i			1.04151i
$178$	−4.73205	+	8.19615i	−0.354682	+	0.614328i
$179$	1.09808	+	1.90192i	0.0820741	+	0.142156i	0.904141	−	0.427235i	$-0.140512\pi$
$179$	1.09808	+	1.90192i	0.0820741	+	0.142156i	−0.822067	+	0.569391i	$0.807179\pi$
$180$		0			0
$181$	−19.5885			−1.45600			−0.727999	−	0.685578i	$-0.759550\pi$
$181$	−19.5885			−1.45600			−0.727999	+	0.685578i	$0.759550\pi$
$182$	2.02628	−	4.09808i	0.150198	−	0.303770i
$183$	15.1962			1.12333
$184$	7.09808	−	4.09808i	0.523277	−	0.302114i
$185$		0			0
$186$	4.73205	−	8.19615i	0.346971	−	0.600971i
$187$		−	6.58846i		−	0.481796i
$188$	−4.09808	−	2.36603i	−0.298883	−	0.172560i
$189$	−1.09808	−	0.633975i	−0.0798733	−	0.0461149i
$190$		0			0
$191$	10.3923	−	18.0000i	0.751961	−	1.30243i	−0.194910	−	0.980821i	$-0.562442\pi$
$191$	10.3923	−	18.0000i	0.751961	−	1.30243i	0.946871	−	0.321613i	$-0.104225\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.998240	−	0.0593065i	$-0.981111\pi$
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.447759	+	0.894154i	$0.647778\pi$
$194$	6.00000			0.430775
$195$		0			0
$196$	−5.39230			−0.385165
$197$	6.00000	−	3.46410i	0.427482	−	0.246807i	−0.270791	−	0.962638i	$-0.587285\pi$
$197$	6.00000	−	3.46410i	0.427482	−	0.246807i	0.698273	+	0.715831i	$0.253952\pi$
$198$	−0.633975	−	1.09808i	−0.0450546	−	0.0780369i
$199$	−11.2942	+	19.5622i	−0.800627	+	1.38673i	0.118578	+	0.992945i	$0.462167\pi$
$199$	−11.2942	+	19.5622i	−0.800627	+	1.38673i	−0.919204	+	0.393781i	$0.871167\pi$
$200$		0			0
$201$	6.29423	+	3.63397i	0.443961	+	0.256321i
$202$	16.7942	+	9.69615i	1.18164	+	0.682219i
$203$		−	3.80385i		−	0.266978i
$204$	2.59808	−	4.50000i	0.181902	−	0.315063i
$205$		0			0
$206$	5.36603	−	3.09808i	0.373869	−	0.215853i
$207$	−8.19615			−0.569672
$208$	3.59808	−	0.232051i	0.249482	−	0.0160898i
$209$	6.00000			0.415029
$210$		0			0
$211$	12.1962	+	21.1244i	0.839618	+	1.45426i	0.890215	+	0.455541i	$0.150554\pi$
$211$	12.1962	+	21.1244i	0.839618	+	1.45426i	−0.0505968	+	0.998719i	$0.516112\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		−	2.19615i		−	0.150478i
$214$	−1.90192	−	1.09808i	−0.130013	−	0.0750629i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	6.00000	−	10.3923i	0.407307	−	0.705476i
$218$	−2.19615	−	3.80385i	−0.148742	−	0.257629i
$219$	10.5000	−	6.06218i	0.709524	−	0.409644i
$220$		0			0
$221$	−10.3923	−	15.5885i	−0.699062	−	1.04859i
$222$	−3.00000			−0.201347
$223$	4.39230	−	2.53590i	0.294130	−	0.169816i	−0.345673	−	0.938355i	$-0.612349\pi$
$223$	4.39230	−	2.53590i	0.294130	−	0.169816i	0.639803	+	0.768539i	$0.279016\pi$
$224$	0.633975	+	1.09808i	0.0423592	+	0.0733683i
$225$		0			0
$226$		−	0.803848i		−	0.0534711i
$227$	−17.4904	−	10.0981i	−1.16088	−	0.670233i	−0.209363	−	0.977838i	$-0.567139\pi$
$227$	−17.4904	−	10.0981i	−1.16088	−	0.670233i	−0.951514	+	0.307605i	$0.900472\pi$
$228$	4.09808	+	2.36603i	0.271402	+	0.156694i
$229$			7.85641i			0.519166i	0.965721	+	0.259583i	$0.0835851\pi$
$229$			7.85641i			0.519166i	−0.965721	+	0.259583i	$0.916415\pi$
$230$		0			0
$231$	−0.803848	−	1.39230i	−0.0528893	−	0.0916069i
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	−3.23205	−	1.59808i	−0.211286	−	0.104470i
$235$		0			0
$236$	−12.0000	+	6.92820i	−0.781133	+	0.450988i
$237$	−4.19615	−	7.26795i	−0.272569	−	0.472104i
$238$	3.29423	−	5.70577i	0.213533	−	0.369850i
$239$			6.58846i			0.426172i	0.977033	+	0.213086i	$0.0683514\pi$
$239$			6.58846i			0.426172i	−0.977033	+	0.213086i	$0.931649\pi$
$240$		0			0
$241$	9.69615	+	5.59808i	0.624584	+	0.360604i	0.778652	−	0.627457i	$-0.215904\pi$
$241$	9.69615	+	5.59808i	0.624584	+	0.360604i	−0.154068	+	0.988060i	$0.549237\pi$
$242$			9.39230i			0.603760i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	7.59808	+	13.1603i	0.486417	+	0.842499i
$245$		0			0
$246$	−6.46410			−0.412136
$247$	14.1962	−	9.46410i	0.903280	−	0.602186i
$248$	9.46410			0.600971
$249$	−4.90192	+	2.83013i	−0.310647	+	0.179352i
$250$		0			0
$251$	8.19615	−	14.1962i	0.517337	−	0.896053i	−0.482461	−	0.875918i	$-0.660257\pi$
$251$	8.19615	−	14.1962i	0.517337	−	0.896053i	0.999797	−	0.0201356i	$-0.00640979\pi$
$252$		−	1.26795i		−	0.0798733i
$253$	−9.00000	−	5.19615i	−0.565825	−	0.326679i
$254$	3.46410	+	2.00000i	0.217357	+	0.125491i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.5981	−	20.0885i	−0.723468	−	1.25308i	−0.959601	−	0.281363i	$-0.909214\pi$
$257$	−11.5981	−	20.0885i	−0.723468	−	1.25308i	0.236133	−	0.971721i	$-0.424120\pi$
$258$	−3.63397	+	2.09808i	−0.226241	+	0.130621i
$259$	−3.80385			−0.236360
$260$		0			0
$261$	−3.00000			−0.185695
$262$	−3.80385	+	2.19615i	−0.235002	+	0.135679i
$263$	4.09808	+	7.09808i	0.252698	+	0.437686i	0.964268	−	0.264930i	$-0.0853487\pi$
$263$	4.09808	+	7.09808i	0.252698	+	0.437686i	−0.711570	+	0.702616i	$0.752015\pi$
$264$	0.633975	−	1.09808i	0.0390184	−	0.0675819i
$265$		0			0
$266$	5.19615	+	3.00000i	0.318597	+	0.183942i
$267$	8.19615	+	4.73205i	0.501596	+	0.289597i
$268$			7.26795i			0.443961i
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	−0.726450	−	0.687220i	$-0.758831\pi$
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	0.958374	+	0.285514i	$0.0921644\pi$
$270$		0			0
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	5.19615			0.315063
$273$	−4.09808	−	2.02628i	−0.248027	−	0.122636i
$274$	9.00000			0.543710
$275$		0			0
$276$	−4.09808	−	7.09808i	−0.246675	−	0.427254i
$277$	−2.40192	+	4.16025i	−0.144318	+	0.249965i	−0.929118	−	0.369783i	$-0.879432\pi$
$277$	−2.40192	+	4.16025i	−0.144318	+	0.249965i	0.784801	+	0.619748i	$0.212765\pi$
$278$		−	4.00000i		−	0.239904i
$279$	−8.19615	−	4.73205i	−0.490691	−	0.283300i
$280$		0			0
$281$		−	17.5359i		−	1.04610i	−0.852301	−	0.523052i	$-0.824793\pi$
$281$		−	17.5359i		−	1.04610i	0.852301	−	0.523052i	$-0.175207\pi$
$282$	−2.36603	+	4.09808i	−0.140895	+	0.244037i
$283$	9.90192	+	17.1506i	0.588608	+	1.01950i	0.994415	+	0.105541i	$0.0336573\pi$
$283$	9.90192	+	17.1506i	0.588608	+	1.01950i	−0.405807	+	0.913959i	$0.633009\pi$
$284$	1.90192	−	1.09808i	0.112858	−	0.0651588i
$285$		0			0
$286$	−2.53590	−	3.80385i	−0.149951	−	0.224926i
$287$	−8.19615			−0.483804
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−5.00000	−	8.66025i	−0.294118	−	0.509427i
$290$		0			0
$291$		−	6.00000i		−	0.351726i
$292$	10.5000	+	6.06218i	0.614466	+	0.354762i
$293$	−2.30385	−	1.33013i	−0.134592	−	0.0777069i	0.431192	−	0.902260i	$-0.358093\pi$
$293$	−2.30385	−	1.33013i	−0.134592	−	0.0777069i	−0.565784	+	0.824553i	$0.691426\pi$
$294$			5.39230i			0.314486i
$295$		0			0
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	−1.09808	+	0.633975i	−0.0637168	+	0.0367869i
$298$	−6.12436			−0.354774
$299$	−29.4904	+	1.90192i	−1.70547	+	0.109991i
$300$		0			0
$301$	−4.60770	+	2.66025i	−0.265583	+	0.153334i
$302$	−5.36603	−	9.29423i	−0.308780	−	0.534823i
$303$	9.69615	−	16.7942i	0.557029	−	0.964803i
$304$			4.73205i			0.271402i
$305$		0			0
$306$	−4.50000	−	2.59808i	−0.257248	−	0.148522i
$307$			7.26795i			0.414804i	0.978256	+	0.207402i	$0.0665008\pi$
$307$			7.26795i			0.414804i	−0.978256	+	0.207402i	$0.933499\pi$
$308$	0.803848	−	1.39230i	0.0458035	−	0.0793339i
$309$	−3.09808	−	5.36603i	−0.176243	−	0.305263i
$310$		0			0
$311$	8.19615			0.464761			0.232381	−	0.972625i	$-0.425349\pi$
$311$	8.19615			0.464761			0.232381	+	0.972625i	$0.425349\pi$
$312$	−0.232051	−	3.59808i	−0.0131373	−	0.203701i
$313$	3.60770			0.203919			0.101959	−	0.994789i	$-0.467489\pi$
$313$	3.60770			0.203919			0.101959	+	0.994789i	$0.467489\pi$
$314$	−6.23205	+	3.59808i	−0.351695	+	0.203051i
$315$		0			0
$316$	4.19615	−	7.26795i	0.236052	−	0.408854i
$317$			18.1244i			1.01797i	0.860777	+	0.508983i	$0.169978\pi$
$317$			18.1244i			1.01797i	−0.860777	+	0.508983i	$0.830022\pi$
$318$	2.59808	+	1.50000i	0.145693	+	0.0841158i
$319$	−3.29423	−	1.90192i	−0.184441	−	0.106487i
$320$		0			0
$321$	−1.09808	+	1.90192i	−0.0612886	+	0.106155i
$322$	−5.19615	−	9.00000i	−0.289570	−	0.501550i
$323$	21.2942	−	12.2942i	1.18484	−	0.684069i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−2.53590			−0.140450
$327$	−3.80385	+	2.19615i	−0.210353	+	0.121448i
$328$	−3.23205	−	5.59808i	−0.178460	−	0.309102i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	0.186421	−	0.982470i	$-0.440311\pi$
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	−0.757634	+	0.652680i	$0.773645\pi$
$332$	−4.90192	−	2.83013i	−0.269028	−	0.155323i
$333$			3.00000i			0.164399i
$334$	−4.73205	+	8.19615i	−0.258926	+	0.448474i
$335$		0			0
$336$	1.09808	−	0.633975i	0.0599050	−	0.0345861i
$337$	−31.0000			−1.68868			−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000			−1.68868			−0.844339	+	0.535810i	$0.820006\pi$
$338$	−12.0000	−	5.00000i	−0.652714	−	0.271964i
$339$	−0.803848			−0.0436590
$340$		0			0
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	2.36603	−	4.09808i	0.127940	−	0.221599i
$343$			15.7128i			0.848412i
$344$	−3.63397	−	2.09808i	−0.195931	−	0.113121i
$345$		0			0
$346$		−	4.39230i		−	0.236132i
$347$	9.29423	−	16.0981i	0.498940	−	0.864190i	−0.501059	−	0.865413i	$-0.667056\pi$
$347$	9.29423	−	16.0981i	0.498940	−	0.864190i	0.999999	+	0.00122316i	$0.000389345\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−8.19615	+	4.73205i	−0.438730	+	0.253301i	−0.703059	−	0.711132i	$-0.748183\pi$
$349$	−8.19615	+	4.73205i	−0.438730	+	0.253301i	0.264329	+	0.964433i	$0.414850\pi$
$350$		0			0
$351$	−1.59808	+	3.23205i	−0.0852990	+	0.172514i
$352$	1.26795			0.0675819
$353$	30.9904	−	17.8923i	1.64945	−	0.952311i	0.672162	−	0.740404i	$-0.265366\pi$
$353$	30.9904	−	17.8923i	1.64945	−	0.952311i	0.977290	−	0.211907i	$-0.0679674\pi$
$354$	6.92820	+	12.0000i	0.368230	+	0.637793i
$355$		0			0
$356$			9.46410i			0.501596i
$357$	−5.70577	−	3.29423i	−0.301981	−	0.174349i
$358$	1.90192	+	1.09808i	0.100520	+	0.0580351i
$359$			16.0526i			0.847222i	0.905844	+	0.423611i	$0.139238\pi$
$359$			16.0526i			0.847222i	−0.905844	+	0.423611i	$0.860762\pi$
$360$		0			0
$361$	1.69615	+	2.93782i	0.0892712	+	0.154622i
$362$	−16.9641	+	9.79423i	−0.891613	+	0.514773i
$363$	9.39230			0.492968
$364$	−0.294229	−	4.56218i	−0.0154218	−	0.239123i
$365$		0			0
$366$	13.1603	−	7.59808i	0.687897	−	0.397158i
$367$	−6.90192	−	11.9545i	−0.360277	−	0.624019i	0.627729	−	0.778432i	$-0.283985\pi$
$367$	−6.90192	−	11.9545i	−0.360277	−	0.624019i	−0.988006	+	0.154413i	$0.950651\pi$
$368$	4.09808	−	7.09808i	0.213627	−	0.370013i
$369$			6.46410i			0.336508i
$370$		0			0
$371$	3.29423	+	1.90192i	0.171028	+	0.0987430i
$372$		−	9.46410i		−	0.490691i
$373$	−13.9904	+	24.2321i	−0.724394	+	1.25469i	0.234828	+	0.972037i	$0.424547\pi$
$373$	−13.9904	+	24.2321i	−0.724394	+	1.25469i	−0.959223	+	0.282651i	$0.908786\pi$
$374$	−3.29423	−	5.70577i	−0.170341	−	0.295038i
$375$		0			0
$376$	−4.73205			−0.244037
$377$	−10.7942	+	0.696152i	−0.555931	+	0.0358537i
$378$	−1.26795			−0.0652163
$379$	26.1962	−	15.1244i	1.34561	−	0.776886i	0.357982	−	0.933728i	$-0.383465\pi$
$379$	26.1962	−	15.1244i	1.34561	−	0.776886i	0.987624	+	0.156842i	$0.0501315\pi$
$380$		0			0
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$		−	20.7846i		−	1.06343i
$383$	−20.1962	−	11.6603i	−1.03198	−	0.595811i	−0.114425	−	0.993432i	$-0.536503\pi$
$383$	−20.1962	−	11.6603i	−1.03198	−	0.595811i	−0.917550	+	0.397621i	$0.869836\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−11.5981	+	20.0885i	−0.590327	+	1.02248i
$387$	2.09808	+	3.63397i	0.106651	+	0.184725i
$388$	5.19615	−	3.00000i	0.263795	−	0.152302i
$389$	−7.39230			−0.374805			−0.187402	−	0.982283i	$-0.560007\pi$
$389$	−7.39230			−0.374805			−0.187402	+	0.982283i	$0.560007\pi$
$390$		0			0
$391$	−42.5885			−2.15379
$392$	−4.66987	+	2.69615i	−0.235864	+	0.136176i
$393$	2.19615	+	3.80385i	0.110781	+	0.191879i
$394$	3.46410	−	6.00000i	0.174519	−	0.302276i
$395$		0			0
$396$	−1.09808	−	0.633975i	−0.0551804	−	0.0318584i
$397$	−3.80385	−	2.19615i	−0.190910	−	0.110222i	0.401499	−	0.915860i	$-0.368489\pi$
$397$	−3.80385	−	2.19615i	−0.190910	−	0.110222i	−0.592408	+	0.805638i	$0.701823\pi$
$398$			22.5885i			1.13226i
$399$	3.00000	−	5.19615i	0.150188	−	0.260133i
$400$		0			0
$401$	−18.1865	+	10.5000i	−0.908192	+	0.524345i	−0.879849	−	0.475253i	$-0.842356\pi$
$401$	−18.1865	+	10.5000i	−0.908192	+	0.524345i	−0.0283431	+	0.999598i	$0.509023\pi$
$402$	7.26795			0.362492
$403$	−30.5885	−	15.1244i	−1.52372	−	0.753398i
$404$	19.3923			0.964803
$405$		0			0
$406$	−1.90192	−	3.29423i	−0.0943909	−	0.163490i
$407$	−1.90192	+	3.29423i	−0.0942749	+	0.163289i
$408$		−	5.19615i		−	0.257248i
$409$	17.8923	+	10.3301i	0.884718	+	0.510792i	0.872211	−	0.489130i	$-0.162686\pi$
$409$	17.8923	+	10.3301i	0.884718	+	0.510792i	0.0125066	+	0.999922i	$0.496019\pi$
$410$		0			0
$411$		−	9.00000i		−	0.443937i
$412$	3.09808	−	5.36603i	0.152631	−	0.264365i
$413$	8.78461	+	15.2154i	0.432262	+	0.748700i
$414$	−7.09808	+	4.09808i	−0.348851	+	0.201409i
$415$		0			0
$416$	3.00000	−	2.00000i	0.147087	−	0.0980581i
$417$	−4.00000			−0.195881
$418$	5.19615	−	3.00000i	0.254152	−	0.146735i
$419$	2.19615	+	3.80385i	0.107289	+	0.185830i	0.914671	−	0.404199i	$-0.132450\pi$
$419$	2.19615	+	3.80385i	0.107289	+	0.185830i	−0.807382	+	0.590029i	$0.799116\pi$
$420$		0			0
$421$		−	6.46410i		−	0.315041i	−0.987516	−	0.157521i	$-0.949650\pi$
$421$		−	6.46410i		−	0.315041i	0.987516	−	0.157521i	$-0.0503500\pi$
$422$	21.1244	+	12.1962i	1.02832	+	0.593699i
$423$	4.09808	+	2.36603i	0.199255	+	0.115040i
$424$			3.00000i			0.145693i
$425$		0			0
$426$	−1.09808	−	1.90192i	−0.0532020	−	0.0921485i
$427$	16.6865	−	9.63397i	0.807518	−	0.466221i
$428$	−2.19615			−0.106155
$429$	−3.80385	+	2.53590i	−0.183651	+	0.122434i
$430$		0			0
$431$	33.0788	−	19.0981i	1.59335	−	0.919922i	0.600625	−	0.799531i	$-0.294918\pi$
$431$	33.0788	−	19.0981i	1.59335	−	0.919922i	0.992727	−	0.120391i	$-0.0384149\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−3.89230	+	6.74167i	−0.187052	+	0.323984i	−0.944266	−	0.329183i	$-0.893227\pi$
$433$	−3.89230	+	6.74167i	−0.187052	+	0.323984i	0.757214	+	0.653167i	$0.226560\pi$
$434$		−	12.0000i		−	0.576018i
$435$		0			0
$436$	−3.80385	−	2.19615i	−0.182171	−	0.105177i
$437$		−	38.7846i		−	1.85532i
$438$	6.06218	−	10.5000i	0.289662	−	0.501709i
$439$	−7.29423	−	12.6340i	−0.348135	−	0.602987i	0.637784	−	0.770216i	$-0.279851\pi$
$439$	−7.29423	−	12.6340i	−0.348135	−	0.602987i	−0.985918	+	0.167229i	$0.946518\pi$
$440$		0			0
$441$	5.39230			0.256776
$442$	−16.7942	−	8.30385i	−0.798820	−	0.394974i
$443$	−16.3923			−0.778822			−0.389411	−	0.921064i	$-0.627321\pi$
$443$	−16.3923			−0.778822			−0.389411	+	0.921064i	$0.627321\pi$
$444$	−2.59808	+	1.50000i	−0.123299	+	0.0711868i
$445$		0			0
$446$	2.53590	−	4.39230i	0.120078	−	0.207982i
$447$			6.12436i			0.289672i
$448$	1.09808	+	0.633975i	0.0518792	+	0.0299525i
$449$	22.9808	+	13.2679i	1.08453	+	0.626153i	0.932115	−	0.362163i	$-0.117962\pi$
$449$	22.9808	+	13.2679i	1.08453	+	0.626153i	0.152415	+	0.988317i	$0.451295\pi$
$450$		0			0
$451$	−4.09808	+	7.09808i	−0.192971	+	0.334235i
$452$	−0.401924	−	0.696152i	−0.0189049	−	0.0327443i
$453$	−9.29423	+	5.36603i	−0.436681	+	0.252118i
$454$	−20.1962			−0.947852
$455$		0			0
$456$	4.73205			0.221599
$457$	27.6962	−	15.9904i	1.29557	−	0.747998i	0.315935	−	0.948781i	$-0.397682\pi$
$457$	27.6962	−	15.9904i	1.29557	−	0.747998i	0.979636	+	0.200782i	$0.0643484\pi$
$458$	3.92820	+	6.80385i	0.183553	+	0.317923i
$459$	−2.59808	+	4.50000i	−0.121268	+	0.210042i
$460$		0			0
$461$	−27.6962	−	15.9904i	−1.28994	−	0.744746i	−0.311295	−	0.950313i	$-0.600763\pi$
$461$	−27.6962	−	15.9904i	−1.28994	−	0.744746i	−0.978643	+	0.205567i	$0.934096\pi$
$462$	−1.39230	−	0.803848i	−0.0647759	−	0.0373984i
$463$		−	15.8038i		−	0.734467i	−0.930129	−	0.367234i	$-0.880305\pi$
$463$		−	15.8038i		−	0.734467i	0.930129	−	0.367234i	$-0.119695\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	−15.5885	+	9.00000i	−0.722121	+	0.416917i
$467$	5.41154			0.250416			0.125208	−	0.992130i	$-0.460040\pi$
$467$	5.41154			0.250416			0.125208	+	0.992130i	$0.460040\pi$
$468$	−3.59808	+	0.232051i	−0.166321	+	0.0107266i
$469$	9.21539			0.425527
$470$		0			0
$471$	3.59808	+	6.23205i	0.165791	+	0.287158i
$472$	−6.92820	+	12.0000i	−0.318896	+	0.552345i
$473$			5.32051i			0.244637i
$474$	−7.26795	−	4.19615i	−0.333828	−	0.192736i
$475$		0			0
$476$		−	6.58846i		−	0.301981i
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	3.29423	+	5.70577i	0.150675	+	0.260976i
$479$	0.588457	−	0.339746i	0.0268873	−	0.0155234i	−0.486496	−	0.873683i	$-0.661725\pi$
$479$	0.588457	−	0.339746i	0.0268873	−	0.0155234i	0.513383	+	0.858159i	$0.328392\pi$
$480$		0			0
$481$	0.696152	+	10.7942i	0.0317418	+	0.492174i
$482$	11.1962			0.509971
$483$	−9.00000	+	5.19615i	−0.409514	+	0.236433i
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	−13.0981	−	7.56218i	−0.593530	−	0.342675i	0.172962	−	0.984929i	$-0.444666\pi$
$487$	−13.0981	−	7.56218i	−0.593530	−	0.342675i	−0.766492	+	0.642254i	$0.778000\pi$
$488$	13.1603	+	7.59808i	0.595737	+	0.343949i
$489$			2.53590i			0.114677i
$490$		0			0
$491$	−15.2942	−	26.4904i	−0.690219	−	1.19549i	−0.971766	−	0.235947i	$-0.924181\pi$
$491$	−15.2942	−	26.4904i	−0.690219	−	1.19549i	0.281547	−	0.959547i	$-0.409152\pi$
$492$	−5.59808	+	3.23205i	−0.252381	+	0.145712i
$493$	−15.5885			−0.702069
$494$	7.56218	−	15.2942i	0.340238	−	0.688120i
$495$		0			0
$496$	8.19615	−	4.73205i	0.368018	−	0.212475i
$497$	−1.39230	−	2.41154i	−0.0624534	−	0.108172i
$498$	−2.83013	+	4.90192i	−0.126821	+	0.219660i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	8.19615	+	4.73205i	0.366177	+	0.211412i
$502$		−	16.3923i		−	0.731624i
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	−0.690898	−	0.722952i	$-0.742785\pi$
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	0.971544	+	0.236859i	$0.0761181\pi$
$504$	−0.633975	−	1.09808i	−0.0282395	−	0.0489122i
$505$		0			0
$506$	−10.3923			−0.461994
$507$	−5.00000	+	12.0000i	−0.222058	+	0.532939i
$508$	4.00000			0.177471
$509$	23.0885	−	13.3301i	1.02338	−	0.590847i	0.108297	−	0.994119i	$-0.465460\pi$
$509$	23.0885	−	13.3301i	1.02338	−	0.590847i	0.915081	+	0.403271i	$0.132127\pi$
$510$		0			0
$511$	7.68653	−	13.3135i	0.340032	−	0.588953i
$512$			1.00000i			0.0441942i
$513$	−4.09808	−	2.36603i	−0.180934	−	0.104463i
$514$	−20.0885	−	11.5981i	−0.886064	−	0.511569i
$515$		0			0
$516$	−2.09808	+	3.63397i	−0.0923627	+	0.159977i
$517$	3.00000	+	5.19615i	0.131940	+	0.228527i
$518$	−3.29423	+	1.90192i	−0.144740	+	0.0835657i
$519$	−4.39230			−0.192801
$520$		0			0
$521$	−29.1962			−1.27911			−0.639553	−	0.768747i	$-0.720881\pi$
$521$	−29.1962			−1.27911			−0.639553	+	0.768747i	$0.720881\pi$
$522$	−2.59808	+	1.50000i	−0.113715	+	0.0656532i
$523$	16.2942	+	28.2224i	0.712497	+	1.23408i	0.963917	+	0.266203i	$0.0857691\pi$
$523$	16.2942	+	28.2224i	0.712497	+	1.23408i	−0.251420	+	0.967878i	$0.580898\pi$
$524$	−2.19615	+	3.80385i	−0.0959394	+	0.166172i
$525$		0			0
$526$	7.09808	+	4.09808i	0.309491	+	0.178685i
$527$	−42.5885	−	24.5885i	−1.85518	−	1.07109i
$528$		−	1.26795i		−	0.0551804i
$529$	−22.0885	+	38.2583i	−0.960368	+	1.66341i
$530$		0			0
$531$	12.0000	−	6.92820i	0.520756	−	0.300658i
$532$	6.00000			0.260133
$533$	1.50000	+	23.2583i	0.0649722	+	1.00743i
$534$	9.46410			0.409552
$535$		0			0
$536$	3.63397	+	6.29423i	0.156964	+	0.271869i
$537$	1.09808	−	1.90192i	0.0473855	−	0.0820741i
$538$		−	7.60770i		−	0.327991i
$539$	5.92116	+	3.41858i	0.255042	+	0.147249i
$540$		0			0
$541$			10.8564i			0.466753i	0.972386	+	0.233377i	$0.0749775\pi$
$541$			10.8564i			0.466753i	−0.972386	+	0.233377i	$0.925022\pi$
$542$		0			0
$543$	9.79423	+	16.9641i	0.420311	+	0.727999i
$544$	4.50000	−	2.59808i	0.192936	−	0.111392i
$545$		0			0
$546$	−4.56218	+	0.294229i	−0.195243	+	0.0125918i
$547$	−4.19615			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$548$	7.79423	−	4.50000i	0.332953	−	0.192230i
$549$	−7.59808	−	13.1603i	−0.324278	−	0.561666i
$550$		0			0
$551$		−	14.1962i		−	0.604776i
$552$	−7.09808	−	4.09808i	−0.302114	−	0.174426i
$553$	−9.21539	−	5.32051i	−0.391878	−	0.226251i
$554$			4.80385i			0.204096i
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	22.2846	−	12.8660i	0.944229	−	0.545151i	0.0529457	−	0.998597i	$-0.483139\pi$
$557$	22.2846	−	12.8660i	0.944229	−	0.545151i	0.891284	+	0.453446i	$0.149806\pi$
$558$	−9.46410			−0.400647
$559$	8.39230	+	12.5885i	0.354957	+	0.532435i
$560$		0			0
$561$	−5.70577	+	3.29423i	−0.240898	+	0.139082i
$562$	−8.76795	−	15.1865i	−0.369854	−	0.640605i
$563$	16.3923	−	28.3923i	0.690853	−	1.19659i	−0.280705	−	0.959794i	$-0.590568\pi$
$563$	16.3923	−	28.3923i	0.690853	−	1.19659i	0.971559	−	0.236799i	$-0.0760983\pi$
$564$			4.73205i			0.199255i
$565$		0			0
$566$	17.1506	+	9.90192i	0.720895	+	0.416209i
$567$			1.26795i			0.0532489i
$568$	1.09808	−	1.90192i	0.0460743	−	0.0798029i
$569$	4.39230	+	7.60770i	0.184135	+	0.318931i	0.943285	−	0.331985i	$-0.107718\pi$
$569$	4.39230	+	7.60770i	0.184135	+	0.318931i	−0.759150	+	0.650916i	$0.774385\pi$
$570$		0			0
$571$	24.1962			1.01258			0.506289	−	0.862364i	$-0.331017\pi$
$571$	24.1962			1.01258			0.506289	+	0.862364i	$0.331017\pi$
$572$	−4.09808	−	2.02628i	−0.171349	−	0.0847230i
$573$	−20.7846			−0.868290
$574$	−7.09808	+	4.09808i	−0.296268	+	0.171050i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			19.7321i			0.821456i	0.911758	+	0.410728i	$0.134725\pi$
$577$			19.7321i			0.821456i	−0.911758	+	0.410728i	$0.865275\pi$
$578$	−8.66025	−	5.00000i	−0.360219	−	0.207973i
$579$	20.0885	+	11.5981i	0.834848	+	0.482000i
$580$		0			0
$581$	−3.58846	+	6.21539i	−0.148874	+	0.257858i
$582$	−3.00000	−	5.19615i	−0.124354	−	0.215387i
$583$	3.29423	−	1.90192i	0.136433	−	0.0787696i
$584$	12.1244			0.501709
$585$		0			0
$586$	−2.66025			−0.109894
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$	2.69615	+	4.66987i	0.111187	+	0.192582i
$589$	22.3923	−	38.7846i	0.922659	−	1.59809i
$590$		0			0
$591$	−6.00000	−	3.46410i	−0.246807	−	0.142494i
$592$	−2.59808	−	1.50000i	−0.106780	−	0.0616496i
$593$		−	19.1436i		−	0.786133i	−0.919510	−	0.393067i	$-0.871414\pi$
$593$		−	19.1436i		−	0.786133i	0.919510	−	0.393067i	$-0.128586\pi$
$594$	−0.633975	+	1.09808i	−0.0260123	+	0.0450546i
$595$		0			0
$596$	−5.30385	+	3.06218i	−0.217254	+	0.125432i
$597$	22.5885			0.924484
$598$	−24.5885	+	16.3923i	−1.00550	+	0.670331i
$599$	16.3923			0.669771			0.334886	−	0.942259i	$-0.391302\pi$
$599$	16.3923			0.669771			0.334886	+	0.942259i	$0.391302\pi$
$600$		0			0
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	0.994147	−	0.108032i	$-0.0344548\pi$
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	−0.590632	+	0.806941i	$0.701121\pi$
$602$	−2.66025	+	4.60770i	−0.108424	+	0.187796i
$603$		−	7.26795i		−	0.295974i
$604$	−9.29423	−	5.36603i	−0.378177	−	0.218340i
$605$		0			0
$606$		−	19.3923i		−	0.787759i
$607$	−3.60770	+	6.24871i	−0.146432	+	0.253627i	−0.929906	−	0.367797i	$-0.880112\pi$
$607$	−3.60770	+	6.24871i	−0.146432	+	0.253627i	0.783474	+	0.621424i	$0.213446\pi$
$608$	2.36603	+	4.09808i	0.0959550	+	0.166199i
$609$	−3.29423	+	1.90192i	−0.133489	+	0.0770698i
$610$		0			0
$611$	15.2942	+	7.56218i	0.618738	+	0.305933i
$612$	−5.19615			−0.210042
$613$	11.3827	−	6.57180i	0.459742	−	0.265432i	−0.252194	−	0.967677i	$-0.581152\pi$
$613$	11.3827	−	6.57180i	0.459742	−	0.265432i	0.711936	+	0.702244i	$0.247819\pi$
$614$	3.63397	+	6.29423i	0.146655	+	0.254014i
$615$		0			0
$616$		−	1.60770i		−	0.0647759i
$617$	27.1865	+	15.6962i	1.09449	+	0.631903i	0.934768	−	0.355259i	$-0.115607\pi$
$617$	27.1865	+	15.6962i	1.09449	+	0.631903i	0.159721	+	0.987162i	$0.448941\pi$
$618$	−5.36603	−	3.09808i	−0.215853	−	0.124623i
$619$			28.3923i			1.14118i	0.821234	+	0.570592i	$0.193286\pi$
$619$			28.3923i			1.14118i	−0.821234	+	0.570592i	$0.806714\pi$
$620$		0			0
$621$	4.09808	+	7.09808i	0.164450	+	0.284836i
$622$	7.09808	−	4.09808i	0.284607	−	0.164318i
$623$	12.0000			0.480770
$624$	−2.00000	−	3.00000i	−0.0800641	−	0.120096i
$625$		0			0
$626$	3.12436	−	1.80385i	0.124874	−	0.0720962i
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$	−3.59808	+	6.23205i	−0.143579	+	0.248686i
$629$			15.5885i			0.621552i
$630$		0			0
$631$	−1.60770	−	0.928203i	−0.0640013	−	0.0369512i	0.467658	−	0.883910i	$-0.345098\pi$
$631$	−1.60770	−	0.928203i	−0.0640013	−	0.0369512i	−0.531659	+	0.846958i	$0.678431\pi$
$632$		−	8.39230i		−	0.333828i
$633$	12.1962	−	21.1244i	0.484754	−	0.839618i
$634$	9.06218	+	15.6962i	0.359905	+	0.623374i
$635$		0			0
$636$	3.00000			0.118958
$637$	19.4019	−	1.25129i	0.768732	−	0.0495779i
$638$	−3.80385			−0.150596
$639$	−1.90192	+	1.09808i	−0.0752389	+	0.0434392i
$640$		0			0
$641$	−20.5981	+	35.6769i	−0.813575	+	1.40915i	0.0967715	+	0.995307i	$0.469148\pi$
$641$	−20.5981	+	35.6769i	−0.813575	+	1.40915i	−0.910347	+	0.413847i	$0.864185\pi$
$642$			2.19615i			0.0866752i
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.891982	−	0.452071i	$-0.149315\pi$
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.0544858	+	0.998515i	$0.482648\pi$
$644$	−9.00000	−	5.19615i	−0.354650	−	0.204757i
$645$		0			0
$646$	12.2942	−	21.2942i	0.483710	−	0.837810i
$647$	24.5885	+	42.5885i	0.966672	+	1.67433i	0.705054	+	0.709153i	$0.250923\pi$
$647$	24.5885	+	42.5885i	0.966672	+	1.67433i	0.261618	+	0.965172i	$0.415744\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	17.5692			0.689652
$650$		0			0
$651$	−12.0000			−0.470317
$652$	−2.19615	+	1.26795i	−0.0860080	+	0.0496567i
$653$	6.58846	+	11.4115i	0.257826	+	0.446568i	0.965659	−	0.259812i	$-0.0836605\pi$
$653$	6.58846	+	11.4115i	0.257826	+	0.446568i	−0.707833	+	0.706380i	$0.750327\pi$
$654$	−2.19615	+	3.80385i	−0.0858764	+	0.148742i
$655$		0			0
$656$	−5.59808	−	3.23205i	−0.218568	−	0.126190i
$657$	−10.5000	−	6.06218i	−0.409644	−	0.236508i
$658$			6.00000i			0.233904i
$659$	18.5885	−	32.1962i	0.724103	−	1.25418i	−0.235238	−	0.971938i	$-0.575587\pi$
$659$	18.5885	−	32.1962i	0.724103	−	1.25418i	0.959342	−	0.282246i	$-0.0910796\pi$
$660$		0			0
$661$	−7.79423	+	4.50000i	−0.303160	+	0.175030i	−0.643862	−	0.765142i	$-0.722669\pi$
$661$	−7.79423	+	4.50000i	−0.303160	+	0.175030i	0.340701	+	0.940172i	$0.389335\pi$
$662$	−12.0000			−0.466393
$663$	−8.30385	+	16.7942i	−0.322495	+	0.652234i
$664$	−5.66025			−0.219660
$665$		0			0
$666$	1.50000	+	2.59808i	0.0581238	+	0.100673i
$667$	−12.2942	+	21.2942i	−0.476034	+	0.824516i
$668$			9.46410i			0.366177i
$669$	−4.39230	−	2.53590i	−0.169816	−	0.0980435i
$670$		0			0
$671$		−	19.2679i		−	0.743831i
$672$	0.633975	−	1.09808i	0.0244561	−	0.0423592i
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	0.856228	−	0.516599i	$-0.172802\pi$
$673$	−0.500000	−	0.866025i	−0.0192736	−	0.0333828i	−0.875501	+	0.483216i	$0.839469\pi$
$674$	−26.8468	+	15.5000i	−1.03410	+	0.597038i
$675$		0			0
$676$	−12.8923	+	1.66987i	−0.495858	+	0.0642259i
$677$	16.3923			0.630007			0.315004	−	0.949090i	$-0.397994\pi$
$677$	16.3923			0.630007			0.315004	+	0.949090i	$0.397994\pi$
$678$	−0.696152	+	0.401924i	−0.0267356	+	0.0154358i
$679$	−3.80385	−	6.58846i	−0.145978	−	0.252842i
$680$		0			0
$681$			20.1962i			0.773918i
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$	24.0000	+	13.8564i	0.918334	+	0.530201i	0.883103	−	0.469179i	$-0.155450\pi$
$683$	24.0000	+	13.8564i	0.918334	+	0.530201i	0.0352311	+	0.999379i	$0.488783\pi$
$684$		−	4.73205i		−	0.180934i
$685$		0			0
$686$	7.85641	+	13.6077i	0.299959	+	0.519544i
$687$	6.80385	−	3.92820i	0.259583	−	0.149870i
$688$	−4.19615			−0.159977
$689$	4.79423	−	9.69615i	0.182646	−	0.369394i
$690$		0			0
$691$	22.0981	−	12.7583i	0.840650	−	0.485350i	−0.0168348	−	0.999858i	$-0.505359\pi$
$691$	22.0981	−	12.7583i	0.840650	−	0.485350i	0.857485	+	0.514509i	$0.172026\pi$
$692$	−2.19615	−	3.80385i	−0.0834852	−	0.144601i
$693$	−0.803848	+	1.39230i	−0.0305356	+	0.0528893i
$694$		−	18.5885i		−	0.705608i
$695$		0			0
$696$	−2.59808	−	1.50000i	−0.0984798	−	0.0568574i
$697$			33.5885i			1.27225i
$698$	−4.73205	+	8.19615i	−0.179111	+	0.310229i
$699$	9.00000	+	15.5885i	0.340411	+	0.589610i
$700$		0			0
$701$	16.3923			0.619129			0.309564	−	0.950878i	$-0.399817\pi$
$701$	16.3923			0.619129			0.309564	+	0.950878i	$0.399817\pi$
$702$	0.232051	+	3.59808i	0.00875819	+	0.135801i
$703$	−14.1962			−0.535418
$704$	1.09808	−	0.633975i	0.0413853	−	0.0238938i
$705$		0			0
$706$	17.8923	−	30.9904i	0.673386	−	1.16634i
$707$		−	24.5885i		−	0.924744i
$708$	12.0000	+	6.92820i	0.450988	+	0.260378i
$709$	−39.1865	−	22.6244i	−1.47168	−	0.849676i	−0.472188	−	0.881498i	$-0.656536\pi$
$709$	−39.1865	−	22.6244i	−1.47168	−	0.849676i	−0.999494	+	0.0318226i	$0.989869\pi$
$710$		0			0
$711$	−4.19615	+	7.26795i	−0.157368	+	0.272569i
$712$	4.73205	+	8.19615i	0.177341	+	0.307164i
$713$	−67.1769	+	38.7846i	−2.51580	+	1.45250i
$714$	−6.58846			−0.246567
$715$		0			0
$716$	2.19615			0.0820741
$717$	5.70577	−	3.29423i	0.213086	−	0.123025i
$718$	8.02628	+	13.9019i	0.299538	+	0.518815i
$719$	15.8038	−	27.3731i	0.589384	−	1.02084i	−0.404929	−	0.914348i	$-0.632704\pi$
$719$	15.8038	−	27.3731i	0.589384	−	1.02084i	0.994313	−	0.106495i	$-0.0339628\pi$
$720$		0			0
$721$	−6.80385	−	3.92820i	−0.253389	−	0.146294i
$722$	2.93782	+	1.69615i	0.109334	+	0.0631243i
$723$		−	11.1962i		−	0.416389i
$724$	−9.79423	+	16.9641i	−0.364000	+	0.630466i
$725$		0			0
$726$	8.13397	−	4.69615i	0.301880	−	0.174291i
$727$	−13.8038			−0.511956			−0.255978	−	0.966683i	$-0.582398\pi$
$727$	−13.8038			−0.511956			−0.255978	+	0.966683i	$0.582398\pi$
$728$	−2.53590	−	3.80385i	−0.0939866	−	0.140980i
$729$	1.00000			0.0370370
$730$		0			0
$731$	10.9019	+	18.8827i	0.403222	+	0.698401i
$732$	7.59808	−	13.1603i	0.280833	−	0.486417i
$733$		−	20.3205i		−	0.750555i	−0.926912	−	0.375278i	$-0.877547\pi$
$733$		−	20.3205i		−	0.750555i	0.926912	−	0.375278i	$-0.122453\pi$
$734$	−11.9545	−	6.90192i	−0.441248	−	0.254755i
$735$		0			0
$736$		−	8.19615i		−	0.302114i
$737$	4.60770	−	7.98076i	0.169727	−	0.293975i
$738$	3.23205	+	5.59808i	0.118973	+	0.206068i
$739$	4.39230	−	2.53590i	0.161574	−	0.0932845i	−0.417033	−	0.908891i	$-0.636930\pi$
$739$	4.39230	−	2.53590i	0.161574	−	0.0932845i	0.578607	+	0.815607i	$0.303597\pi$
$740$		0			0
$741$	−15.2942	−	7.56218i	−0.561848	−	0.277804i
$742$	3.80385			0.139644
$743$	14.1962	−	8.19615i	0.520806	−	0.300688i	−0.216458	−	0.976292i	$-0.569450\pi$
$743$	14.1962	−	8.19615i	0.520806	−	0.300688i	0.737264	+	0.675604i	$0.236117\pi$
$744$	−4.73205	−	8.19615i	−0.173485	−	0.300486i
$745$		0			0
$746$			27.9808i			1.02445i
$747$	4.90192	+	2.83013i	0.179352	+	0.103549i
$748$	−5.70577	−	3.29423i	−0.208624	−	0.120449i
$749$			2.78461i			0.101747i
$750$		0			0
$751$	13.4904	+	23.3660i	0.492271	+	0.852638i	0.999960	−	0.00890181i	$-0.00283357\pi$
$751$	13.4904	+	23.3660i	0.492271	+	0.852638i	−0.507689	+	0.861540i	$0.669500\pi$
$752$	−4.09808	+	2.36603i	−0.149441	+	0.0862801i
$753$	−16.3923			−0.597369
$754$	−9.00000	+	6.00000i	−0.327761	+	0.218507i
$755$		0			0
$756$	−1.09808	+	0.633975i	−0.0399366	+	0.0230574i
$757$	−11.3923	−	19.7321i	−0.414060	−	0.717174i	0.581269	−	0.813712i	$-0.302556\pi$
$757$	−11.3923	−	19.7321i	−0.414060	−	0.717174i	−0.995329	+	0.0965379i	$0.969223\pi$
$758$	15.1244	−	26.1962i	0.549341	−	0.951487i
$759$			10.3923i			0.377217i
$760$		0			0
$761$	14.1962	+	8.19615i	0.514610	+	0.297110i	0.734727	−	0.678363i	$-0.237310\pi$
$761$	14.1962	+	8.19615i	0.514610	+	0.297110i	−0.220117	+	0.975474i	$0.570644\pi$
$762$		−	4.00000i		−	0.144905i
$763$	−2.78461	+	4.82309i	−0.100810	+	0.174607i
$764$	−10.3923	−	18.0000i	−0.375980	−	0.651217i
$765$		0			0
$766$	−23.3205			−0.842604
$767$	41.5692	−	27.7128i	1.50098	−	1.00065i
$768$	1.00000			0.0360844
$769$	−18.8038	+	10.8564i	−0.678084	+	0.391492i	−0.799133	−	0.601155i	$-0.794708\pi$
$769$	−18.8038	+	10.8564i	−0.678084	+	0.391492i	0.121049	+	0.992647i	$0.461374\pi$
$770$		0			0
$771$	−11.5981	+	20.0885i	−0.417695	+	0.723468i
$772$			23.1962i			0.834848i
$773$	−7.98076	−	4.60770i	−0.287048	−	0.165727i	0.349562	−	0.936913i	$-0.386330\pi$
$773$	−7.98076	−	4.60770i	−0.287048	−	0.165727i	−0.636610	+	0.771186i	$0.719664\pi$
$774$	3.63397	+	2.09808i	0.130621	+	0.0754138i
$775$		0			0
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	1.90192	+	3.29423i	0.0682311	+	0.118180i
$778$	−6.40192	+	3.69615i	−0.229520	+	0.132513i
$779$	−30.5885			−1.09595
$780$		0			0
$781$	−2.78461			−0.0996412
$782$	−36.8827	+	21.2942i	−1.31892	+	0.761480i
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$	−2.69615	+	4.66987i	−0.0962912	+	0.166781i
$785$		0			0
$786$	3.80385	+	2.19615i	0.135679	+	0.0783342i
$787$	18.5885	+	10.7321i	0.662607	+	0.382556i	0.793270	−	0.608871i	$-0.208377\pi$
$787$	18.5885	+	10.7321i	0.662607	+	0.382556i	−0.130663	+	0.991427i	$0.541710\pi$
$788$		−	6.92820i		−	0.246807i
$789$	4.09808	−	7.09808i	0.145895	−	0.252698i
$790$		0			0
$791$	−0.882686	+	0.509619i	−0.0313847	+	0.0181200i
$792$	−1.26795			−0.0450546
$793$	−30.3923	−	45.5885i	−1.07926	−	1.61889i
$794$	−4.39230			−0.155877
$795$		0			0
$796$	11.2942	+	19.5622i	0.400313	+	0.693363i
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	−0.914255	−	0.405140i	$-0.867223\pi$
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	0.807989	+	0.589197i	$0.200556\pi$
$798$		−	6.00000i		−	0.212398i
$799$	21.2942	+	12.2942i	0.753336	+	0.434939i
$800$		0			0
$801$		−	9.46410i		−	0.334398i
$802$	−10.5000	+	18.1865i	−0.370768	+	0.642189i
$803$	−7.68653	−	13.3135i	−0.271252	−	0.469822i
$804$	6.29423	−	3.63397i	0.221980	−	0.128160i
$805$		0			0
$806$	−34.0526	+	2.19615i	−1.19945	+	0.0773562i
$807$	−7.60770			−0.267804
$808$	16.7942	−	9.69615i	0.590819	−	0.341109i
$809$	18.4019	+	31.8731i	0.646977	+	1.12060i	0.983841	+	0.179044i	$0.0573004\pi$
$809$	18.4019	+	31.8731i	0.646977	+	1.12060i	−0.336864	+	0.941553i	$0.609366\pi$
$810$		0			0
$811$		−	16.3923i		−	0.575612i	−0.957689	−	0.287806i	$-0.907074\pi$
$811$		−	16.3923i		−	0.575612i	0.957689	−	0.287806i	$-0.0929258\pi$
$812$	−3.29423	−	1.90192i	−0.115605	−	0.0667444i
$813$		0			0
$814$			3.80385i			0.133325i
$815$		0			0
$816$	−2.59808	−	4.50000i	−0.0909509	−	0.157532i
$817$	−17.1962	+	9.92820i	−0.601617	+	0.347344i
$818$	20.6603			0.722369
$819$	0.294229	+	4.56218i	0.0102812	+	0.159415i
$820$		0			0
$821$	24.8038	−	14.3205i	0.865660	−	0.499789i	−0.000243419	−	1.00000i	$-0.500077\pi$
$821$	24.8038	−	14.3205i	0.865660	−	0.499789i	0.865904	+	0.500211i	$0.166744\pi$
$822$	−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	$-0.0216589\pi$
$824$		−	6.19615i		−	0.215853i
$825$		0			0
$826$	15.2154	+	8.78461i	0.529411	+	0.305656i
$827$			44.1051i			1.53369i	0.641835	+	0.766843i	$0.278173\pi$
$827$			44.1051i			1.53369i	−0.641835	+	0.766843i	$0.721827\pi$
$828$	−4.09808	+	7.09808i	−0.142418	+	0.246675i
$829$	19.9904	+	34.6244i	0.694295	+	1.20255i	0.970418	+	0.241431i	$0.0776169\pi$
$829$	19.9904	+	34.6244i	0.694295	+	1.20255i	−0.276123	+	0.961122i	$0.589050\pi$
$830$		0			0
$831$	4.80385			0.166644
$832$	1.59808	−	3.23205i	0.0554033	−	0.112051i
$833$	28.0192			0.970809
$834$	−3.46410	+	2.00000i	−0.119952	+	0.0692543i
$835$		0			0
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$			9.46410i			0.327127i
$838$	3.80385	+	2.19615i	0.131402	+	0.0758648i
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	0.309764	−	0.950813i	$-0.399750\pi$
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	−0.668546	+	0.743670i	$0.733083\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−3.23205	−	5.59808i	−0.111384	−	0.192922i
$843$	−15.1865	+	8.76795i	−0.523052	+	0.301984i
$844$	24.3923			0.839618
$845$		0			0
$846$	4.73205			0.162691
$847$	10.3135	−	5.95448i	0.354375	−	0.204598i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	9.90192	−	17.1506i	0.339833	−	0.588608i
$850$		0			0
$851$	21.2942	+	12.2942i	0.729957	+	0.421441i
$852$	−1.90192	−	1.09808i	−0.0651588	−	0.0376195i
$853$			9.00000i			0.308154i	0.988059	+	0.154077i	$0.0492404\pi$
$853$			9.00000i			0.308154i	−0.988059	+	0.154077i	$0.950760\pi$
$854$	9.63397	−	16.6865i	0.329668	−	0.571001i
$855$		0			0
$856$	−1.90192	+	1.09808i	−0.0650064	+	0.0375315i
$857$	18.3731			0.627612			0.313806	−	0.949487i	$-0.398396\pi$
$857$	18.3731			0.627612			0.313806	+	0.949487i	$0.398396\pi$
$858$	−2.02628	+	4.09808i	−0.0691760	+	0.139906i
$859$	−20.5885			−0.702469			−0.351235	−	0.936288i	$-0.614238\pi$
$859$	−20.5885			−0.702469			−0.351235	+	0.936288i	$0.614238\pi$
$860$		0			0
$861$	4.09808	+	7.09808i	0.139662	+	0.241902i
$862$	19.0981	−	33.0788i	0.650483	−	1.12667i
$863$		−	49.5167i		−	1.68557i	−0.538253	−	0.842783i	$-0.680915\pi$
$863$		−	49.5167i		−	1.68557i	0.538253	−	0.842783i	$-0.319085\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			7.78461i			0.264532i
$867$	−5.00000	+	8.66025i	−0.169809	+	0.294118i
$868$	−6.00000	−	10.3923i	−0.203653	−	0.352738i
$869$	−9.21539	+	5.32051i	−0.312611	+	0.180486i
$870$		0			0
$871$	−1.68653	−	26.1506i	−0.0571460	−	0.886080i
$872$	−4.39230			−0.148742
$873$	−5.19615	+	3.00000i	−0.175863	+	0.101535i
$874$	−19.3923	−	33.5885i	−0.655954	−	1.13615i
$875$		0			0
$876$		−	12.1244i		−	0.409644i
$877$	19.5788	+	11.3038i	0.661130	+	0.381704i	0.792708	−	0.609602i	$-0.208671\pi$
$877$	19.5788	+	11.3038i	0.661130	+	0.381704i	−0.131577	+	0.991306i	$0.542004\pi$
$878$	−12.6340	−	7.29423i	−0.426376	−	0.246168i
$879$			2.66025i			0.0897281i
$880$		0			0
$881$	−6.99038	−	12.1077i	−0.235512	−	0.407919i	0.723909	−	0.689895i	$-0.242343\pi$
$881$	−6.99038	−	12.1077i	−0.235512	−	0.407919i	−0.959421	+	0.281976i	$0.909010\pi$
$882$	4.66987	−	2.69615i	0.157243	−	0.0907842i
$883$	16.7846			0.564847			0.282424	−	0.959290i	$-0.408862\pi$
$883$	16.7846			0.564847			0.282424	+	0.959290i	$0.408862\pi$
$884$	−18.6962	+	1.20577i	−0.628820	+	0.0405545i
$885$		0			0
$886$	−14.1962	+	8.19615i	−0.476929	+	0.275355i
$887$	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	$0.535047\pi$
$888$	−1.50000	+	2.59808i	−0.0503367	+	0.0871857i
$889$		−	5.07180i		−	0.170103i
$890$		0			0
$891$	1.09808	+	0.633975i	0.0367869	+	0.0212389i
$892$		−	5.07180i		−	0.169816i
$893$	−11.1962	+	19.3923i	−0.374665	+	0.648939i
$894$	3.06218	+	5.30385i	0.102415	+	0.177387i
$895$		0			0
$896$	1.26795			0.0423592
$897$	16.3923	+	24.5885i	0.547323	+	0.820985i
$898$	26.5359			0.885514
$899$	−24.5885	+	14.1962i	−0.820071	+	0.473468i
$900$		0			0
$901$	7.79423	−	13.5000i	0.259663	−	0.449750i
$902$			8.19615i			0.272902i
$903$	4.60770	+	2.66025i	0.153334	+	0.0885277i
$904$	−0.696152	−	0.401924i	−0.0231537	−	0.0133678i
$905$		0			0
$906$	−5.36603	+	9.29423i	−0.178274	+	0.308780i
$907$	−10.5885	−	18.3397i	−0.351584	−	0.608961i	0.634943	−	0.772559i	$-0.281023\pi$
$907$	−10.5885	−	18.3397i	−0.351584	−	0.608961i	−0.986527	+	0.163598i	$0.947690\pi$
$908$	−17.4904	+	10.0981i	−0.580439	+	0.335116i
$909$	−19.3923			−0.643202
$910$		0			0
$911$	−25.1769			−0.834148			−0.417074	−	0.908872i	$-0.636944\pi$
$911$	−25.1769			−0.834148			−0.417074	+	0.908872i	$0.636944\pi$
$912$	4.09808	−	2.36603i	0.135701	−	0.0783469i
$913$	3.58846	+	6.21539i	0.118761	+	0.205699i
$914$	15.9904	−	27.6962i	0.528915	−	0.916107i
$915$		0			0
$916$	6.80385	+	3.92820i	0.224805	+	0.129791i
$917$	4.82309	+	2.78461i	0.159272	+	0.0919559i
$918$			5.19615i			0.171499i
$919$	−5.80385	+	10.0526i	−0.191451	+	0.331603i	−0.945731	−	0.324949i	$-0.894653\pi$
$919$	−5.80385	+	10.0526i	−0.191451	+	0.331603i	0.754280	+	0.656553i	$0.227986\pi$
$920$		0			0
$921$	6.29423	−	3.63397i	0.207402	−	0.119744i
$922$	−31.9808			−1.05323
$923$	−6.58846	+	4.39230i	−0.216862	+	0.144574i
$924$	−1.60770			−0.0528893
$925$		0			0
$926$	−7.90192	−	13.6865i	−0.259673	−	0.449767i
$927$	−3.09808	+	5.36603i	−0.101754	+	0.176243i
$928$		−	3.00000i		−	0.0984798i
$929$	47.9711	+	27.6962i	1.57388	+	0.908681i	0.995686	+	0.0927833i	$0.0295764\pi$
$929$	47.9711	+	27.6962i	1.57388	+	0.908681i	0.578196	+	0.815898i	$0.303757\pi$
$930$		0			0
$931$			25.5167i			0.836275i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$	−4.09808	−	7.09808i	−0.134165	−	0.232381i
$934$	4.68653	−	2.70577i	0.153348	−	0.0885355i
$935$		0			0
$936$	−3.00000	+	2.00000i	−0.0980581	+	0.0653720i
$937$	15.3923			0.502845			0.251422	−	0.967877i	$-0.419102\pi$
$937$	15.3923			0.502845			0.251422	+	0.967877i	$0.419102\pi$
$938$	7.98076	−	4.60770i	0.260581	−	0.150447i
$939$	−1.80385	−	3.12436i	−0.0588663	−	0.101959i
$940$		0			0
$941$		−	38.7846i		−	1.26434i	−0.774829	−	0.632171i	$-0.782164\pi$
$941$		−	38.7846i		−	1.26434i	0.774829	−	0.632171i	$-0.217836\pi$
$942$	6.23205	+	3.59808i	0.203051	+	0.117232i
$943$	45.8827	+	26.4904i	1.49415	+	0.862645i
$944$			13.8564i			0.450988i
$945$		0			0
$946$	2.66025	+	4.60770i	0.0864923	+	0.149809i
$947$	−25.1769	+	14.5359i	−0.818140	+	0.472353i	−0.849775	−	0.527146i	$-0.823262\pi$
$947$	−25.1769	+	14.5359i	−0.818140	+	0.472353i	0.0316348	+	0.999499i	$0.489929\pi$
$948$	−8.39230			−0.272569
$949$	−39.1865	−	19.3756i	−1.27205	−	0.628960i
$950$		0			0
$951$	15.6962	−	9.06218i	0.508983	−	0.293861i
$952$	−3.29423	−	5.70577i	−0.106767	−	0.184925i
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	−0.603559	−	0.797318i	$-0.706251\pi$
$953$	12.0000	−	20.7846i	0.388718	−	0.673280i	0.992277	+	0.124039i	$0.0395847\pi$
$954$		−	3.00000i		−	0.0971286i
$955$		0			0
$956$	5.70577	+	3.29423i	0.184538	+	0.106543i
$957$			3.80385i			0.122961i
$958$	0.339746	−	0.588457i	0.0109767	−	0.0190122i
$959$	−5.70577	−	9.88269i	−0.184249	−	0.319129i
$960$		0			0
$961$	−58.5692			−1.88933
$962$	6.00000	+	9.00000i	0.193448	+	0.290172i
$963$	2.19615			0.0707700
$964$	9.69615	−	5.59808i	0.312292	−	0.180302i
$965$		0			0
$966$	−5.19615	+	9.00000i	−0.167183	+	0.289570i
$967$			39.1244i			1.25815i	0.777343	+	0.629077i	$0.216567\pi$
$967$			39.1244i			1.25815i	−0.777343	+	0.629077i	$0.783433\pi$
$968$	8.13397	+	4.69615i	0.261436	+	0.150940i
$969$	−21.2942	−	12.2942i	−0.684069	−	0.394948i
$970$		0			0
$971$	−24.5885	+	42.5885i	−0.789081	+	1.36673i	0.137449	+	0.990509i	$0.456110\pi$
$971$	−24.5885	+	42.5885i	−0.789081	+	1.36673i	−0.926530	+	0.376220i	$0.877224\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−4.39230	+	2.53590i	−0.140811	+	0.0812972i
$974$	−15.1244			−0.484616
$975$		0			0
$976$	15.1962			0.486417
$977$	−9.40192	+	5.42820i	−0.300794	+	0.173664i	−0.642800	−	0.766034i	$-0.722227\pi$
$977$	−9.40192	+	5.42820i	−0.300794	+	0.173664i	0.342005	+	0.939698i	$0.388894\pi$
$978$	1.26795	+	2.19615i	0.0405445	+	0.0702252i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	3.80385	+	2.19615i	0.121448	+	0.0701178i
$982$	−26.4904	−	15.2942i	−0.845342	−	0.488058i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$	−3.23205	+	5.59808i	−0.103034	+	0.178460i
$985$		0			0
$986$	−13.5000	+	7.79423i	−0.429928	+	0.248219i
$987$	6.00000			0.190982
$988$	−1.09808	−	17.0263i	−0.0349345	−	0.541678i
$989$	34.3923			1.09361
$990$		0			0
$991$	21.6865	+	37.5622i	0.688895	+	1.19320i	0.972196	+	0.234171i	$0.0752374\pi$
$991$	21.6865	+	37.5622i	0.688895	+	1.19320i	−0.283300	+	0.959031i	$0.591429\pi$
$992$	4.73205	−	8.19615i	0.150243	−	0.260228i
$993$			12.0000i			0.380808i
$994$	−2.41154	−	1.39230i	−0.0764895	−	0.0441612i
$995$		0			0
$996$			5.66025i			0.179352i
$997$	1.40192	−	2.42820i	0.0443994	−	0.0769020i	−0.842972	−	0.537958i	$-0.819196\pi$
$997$	1.40192	−	2.42820i	0.0443994	−	0.0769020i	0.887371	+	0.461056i	$0.152529\pi$
$998$		0			0
$999$	2.59808	−	1.50000i	0.0821995	−	0.0474579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.c.751.2		4
5.2	odd	4		1950.2.y.h.49.1		4
5.3	odd	4		1950.2.y.a.49.2		4
5.4	even	2		78.2.i.b.49.1	yes	4
13.4	even	6	inner	1950.2.bc.c.901.2		4
15.14	odd	2		234.2.l.a.127.2		4
20.19	odd	2		624.2.bv.d.49.1		4
60.59	even	2		1872.2.by.k.1297.1		4
65.4	even	6		78.2.i.b.43.1	✓	4
65.9	even	6		1014.2.i.f.823.2		4
65.17	odd	12		1950.2.y.a.199.2		4
65.19	odd	12		1014.2.e.j.529.2		4
65.24	odd	12		1014.2.a.j.1.1		2
65.29	even	6		1014.2.b.d.337.2		4
65.34	odd	4		1014.2.e.h.991.1		4
65.43	odd	12		1950.2.y.h.199.1		4
65.44	odd	4		1014.2.e.j.991.2		4
65.49	even	6		1014.2.b.d.337.3		4
65.54	odd	12		1014.2.a.h.1.2		2
65.59	odd	12		1014.2.e.h.529.1		4
65.64	even	2		1014.2.i.f.361.2		4
195.29	odd	6		3042.2.b.l.1351.3		4
195.89	even	12		3042.2.a.s.1.2		2
195.119	even	12		3042.2.a.v.1.1		2
195.134	odd	6		234.2.l.a.199.2		4
195.179	odd	6		3042.2.b.l.1351.2		4
260.119	even	12		8112.2.a.bq.1.2		2
260.199	odd	6		624.2.bv.d.433.1		4
260.219	even	12		8112.2.a.bx.1.1		2
780.719	even	6		1872.2.by.k.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.b.43.1	✓	4	65.4	even	6
78.2.i.b.49.1	yes	4	5.4	even	2
234.2.l.a.127.2		4	15.14	odd	2
234.2.l.a.199.2		4	195.134	odd	6
624.2.bv.d.49.1		4	20.19	odd	2
624.2.bv.d.433.1		4	260.199	odd	6
1014.2.a.h.1.2		2	65.54	odd	12
1014.2.a.j.1.1		2	65.24	odd	12
1014.2.b.d.337.2		4	65.29	even	6
1014.2.b.d.337.3		4	65.49	even	6
1014.2.e.h.529.1		4	65.59	odd	12
1014.2.e.h.991.1		4	65.34	odd	4
1014.2.e.j.529.2		4	65.19	odd	12
1014.2.e.j.991.2		4	65.44	odd	4
1014.2.i.f.361.2		4	65.64	even	2
1014.2.i.f.823.2		4	65.9	even	6
1872.2.by.k.433.1		4	780.719	even	6
1872.2.by.k.1297.1		4	60.59	even	2
1950.2.y.a.49.2		4	5.3	odd	4
1950.2.y.a.199.2		4	65.17	odd	12
1950.2.y.h.49.1		4	5.2	odd	4
1950.2.y.h.199.1		4	65.43	odd	12
1950.2.bc.c.751.2		4	1.1	even	1	trivial
1950.2.bc.c.901.2		4	13.4	even	6	inner
3042.2.a.s.1.2		2	195.89	even	12
3042.2.a.v.1.1		2	195.119	even	12
3042.2.b.l.1351.2		4	195.179	odd	6
3042.2.b.l.1351.3		4	195.29	odd	6
8112.2.a.bq.1.2		2	260.119	even	12
8112.2.a.bx.1.1		2	260.219	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-1.09808 - 0.633975i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.09808 + 0.633975i) q^{11} -1.00000 q^{12} +(-1.59808 + 3.23205i) q^{13} -1.26795 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 + 4.50000i) q^{17} +1.00000i q^{18} +(-4.09808 - 2.36603i) q^{19} +1.26795i q^{21} +(-0.633975 + 1.09808i) q^{22} +(4.09808 + 7.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.232051 + 3.59808i) q^{26} +1.00000 q^{27} +(-1.09808 + 0.633975i) q^{28} +(1.50000 + 2.59808i) q^{29} +9.46410i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.09808 + 0.633975i) q^{33} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(2.59808 - 1.50000i) q^{37} -4.73205 q^{38} +(3.59808 - 0.232051i) q^{39} +(5.59808 - 3.23205i) q^{41} +(0.633975 + 1.09808i) q^{42} +(2.09808 - 3.63397i) q^{43} +1.26795i q^{44} +(7.09808 + 4.09808i) q^{46} -4.73205i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.69615 - 4.66987i) q^{49} +5.19615 q^{51} +(2.00000 + 3.00000i) q^{52} -3.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.633975 + 1.09808i) q^{56} +4.73205i q^{57} +(2.59808 + 1.50000i) q^{58} +(-12.0000 - 6.92820i) q^{59} +(-7.59808 + 13.1603i) q^{61} +(4.73205 + 8.19615i) q^{62} +(1.09808 - 0.633975i) q^{63} -1.00000 q^{64} +1.26795 q^{66} +(-6.29423 + 3.63397i) q^{67} +(2.59808 + 4.50000i) q^{68} +(4.09808 - 7.09808i) q^{69} +(1.90192 + 1.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} +12.1244i q^{73} +(1.50000 - 2.59808i) q^{74} +(-4.09808 + 2.36603i) q^{76} +1.60770 q^{77} +(3.00000 - 2.00000i) q^{78} +8.39230 q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.23205 - 5.59808i) q^{82} -5.66025i q^{83} +(1.09808 + 0.633975i) q^{84} -4.19615i q^{86} +(1.50000 - 2.59808i) q^{87} +(0.633975 + 1.09808i) q^{88} +(-8.19615 + 4.73205i) q^{89} +(3.80385 - 2.53590i) q^{91} +8.19615 q^{92} +(8.19615 - 4.73205i) q^{93} +(-2.36603 - 4.09808i) q^{94} +1.00000i q^{96} +(5.19615 + 3.00000i) q^{97} +(-4.66987 - 2.69615i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 12 q^{14} - 2 q^{16} - 6 q^{19} - 6 q^{22} + 6 q^{23} - 6 q^{26} + 4 q^{27} + 6 q^{28} + 6 q^{29} - 6 q^{33} + 2 q^{36} - 12 q^{38} + 4 q^{39} + 12 q^{41} + 6 q^{42} - 2 q^{43} + 18 q^{46} - 2 q^{48} + 10 q^{49} + 8 q^{52} - 12 q^{53} - 6 q^{56} - 48 q^{59} - 20 q^{61} + 12 q^{62} - 6 q^{63} - 4 q^{64} + 12 q^{66} + 6 q^{67} + 6 q^{69} + 18 q^{71} + 6 q^{74} - 6 q^{76} + 48 q^{77} + 12 q^{78} - 8 q^{79} - 2 q^{81} + 6 q^{82} - 6 q^{84} + 6 q^{87} + 6 q^{88} - 12 q^{89} + 36 q^{91} + 12 q^{92} + 12 q^{93} - 6 q^{94} - 36 q^{98}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 + 6 * q^7 - 2 * q^9 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 12 * q^14 - 2 * q^16 - 6 * q^19 - 6 * q^22 + 6 * q^23 - 6 * q^26 + 4 * q^27 + 6 * q^28 + 6 * q^29 - 6 * q^33 + 2 * q^36 - 12 * q^38 + 4 * q^39 + 12 * q^41 + 6 * q^42 - 2 * q^43 + 18 * q^46 - 2 * q^48 + 10 * q^49 + 8 * q^52 - 12 * q^53 - 6 * q^56 - 48 * q^59 - 20 * q^61 + 12 * q^62 - 6 * q^63 - 4 * q^64 + 12 * q^66 + 6 * q^67 + 6 * q^69 + 18 * q^71 + 6 * q^74 - 6 * q^76 + 48 * q^77 + 12 * q^78 - 8 * q^79 - 2 * q^81 + 6 * q^82 - 6 * q^84 + 6 * q^87 + 6 * q^88 - 12 * q^89 + 36 * q^91 + 12 * q^92 + 12 * q^93 - 6 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more