LMFDB - Embedded newform 1950.2.y.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

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.y (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:	$15.5708283941$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.49
Dual form			1950.2.y.b.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.09808 - 0.633975i) q^{11} -1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.96410 - 2.86603i) q^{17} -1.00000 q^{18} +(-4.09808 - 2.36603i) q^{19} -2.73205i q^{21} +(-1.09808 - 0.633975i) q^{22} +(3.63397 - 2.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} +1.00000i q^{27} +(-1.36603 - 2.36603i) q^{28} +(-2.23205 - 3.86603i) q^{29} -1.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.633975 + 1.09808i) q^{33} +5.73205i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.76795 + 3.06218i) q^{37} +4.73205i q^{38} +(0.866025 - 3.50000i) q^{39} +(8.13397 - 4.69615i) q^{41} +(-2.36603 + 1.36603i) q^{42} +(8.36603 + 4.83013i) q^{43} +1.26795i q^{44} +(-3.63397 - 2.09808i) q^{46} -2.19615 q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.232051 - 0.401924i) q^{49} +5.73205 q^{51} +(-1.00000 - 3.46410i) q^{52} +6.46410i q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(-2.23205 + 3.86603i) q^{58} +(6.92820 + 4.00000i) q^{59} +(4.59808 - 7.96410i) q^{61} +(-1.26795 + 0.732051i) q^{62} +(1.36603 + 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 - 11.3660i) q^{67} +(4.96410 - 2.86603i) q^{68} +(-2.09808 + 3.63397i) q^{69} +(4.09808 + 2.36603i) q^{71} +(0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(1.76795 - 3.06218i) q^{74} +(4.09808 - 2.36603i) q^{76} +3.46410i q^{77} +(-3.46410 + 1.00000i) q^{78} +2.53590 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.13397 - 4.69615i) q^{82} +0.196152 q^{83} +(2.36603 + 1.36603i) q^{84} -9.66025i q^{86} +(3.86603 + 2.23205i) q^{87} +(1.09808 - 0.633975i) q^{88} +(8.19615 - 4.73205i) q^{89} +(-2.73205 - 9.46410i) q^{91} +4.19615i q^{92} +(0.732051 + 1.26795i) q^{93} +(1.09808 + 1.90192i) q^{94} -1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.232051 + 0.401924i) q^{98} -1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33} + 2 q^{36} + 14 q^{37} + 36 q^{41} - 6 q^{42} + 30 q^{43} - 18 q^{46} + 12 q^{47} + 6 q^{49} + 16 q^{51} - 4 q^{52} - 2 q^{56} + 12 q^{57} - 2 q^{58} + 8 q^{61} - 12 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 6 q^{68} + 2 q^{69} + 6 q^{71} + 2 q^{72} - 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} - 36 q^{82} - 20 q^{83} + 6 q^{84} + 12 q^{87} - 6 q^{88} + 12 q^{89} - 4 q^{91} - 4 q^{93} - 6 q^{94} + 12 q^{97} + 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^11 - 10 * q^13 + 4 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 6 * q^22 + 18 * q^23 + 14 * q^26 - 2 * q^28 - 2 * q^29 - 2 * q^32 - 6 * q^33 + 2 * q^36 + 14 * q^37 + 36 * q^41 - 6 * q^42 + 30 * q^43 - 18 * q^46 + 12 * q^47 + 6 * q^49 + 16 * q^51 - 4 * q^52 - 2 * q^56 + 12 * q^57 - 2 * q^58 + 8 * q^61 - 12 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 6 * q^68 + 2 * q^69 + 6 * q^71 + 2 * q^72 - 32 * q^73 + 14 * q^74 + 6 * q^76 + 24 * q^79 - 2 * q^81 - 36 * q^82 - 20 * q^83 + 6 * q^84 + 12 * q^87 - 6 * q^88 + 12 * q^89 - 4 * q^91 - 4 * q^93 - 6 * q^94 + 12 * q^97 + 6 * 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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−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
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	−1.36603	+	2.36603i	−0.516309	+	0.894274i	0.483512	+	0.875338i	$0.339361\pi$
$7$	−1.36603	+	2.36603i	−0.516309	+	0.894274i	−0.999821	+	0.0189356i	$0.993972\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.09808	−	0.633975i	0.331082	−	0.191151i	−0.325239	−	0.945632i	$-0.605445\pi$
$11$	1.09808	−	0.633975i	0.331082	−	0.191151i	0.656322	+	0.754481i	$0.272111\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	2.73205			0.730171
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.96410	−	2.86603i	−1.20397	−	0.695113i	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−4.96410	−	2.86603i	−1.20397	−	0.695113i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−1.00000			−0.235702
$19$	−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
$21$		−	2.73205i		−	0.596182i
$22$	−1.09808	−	0.633975i	−0.234111	−	0.135164i
$23$	3.63397	−	2.09808i	0.757736	−	0.437479i	−0.0707462	−	0.997494i	$-0.522538\pi$
$23$	3.63397	−	2.09808i	0.757736	−	0.437479i	0.828482	+	0.560015i	$0.189205\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$			1.00000i			0.192450i
$28$	−1.36603	−	2.36603i	−0.258155	−	0.447137i
$29$	−2.23205	−	3.86603i	−0.414481	−	0.717903i	0.580892	−	0.813980i	$-0.302704\pi$
$29$	−2.23205	−	3.86603i	−0.414481	−	0.717903i	−0.995374	+	0.0960774i	$0.969370\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.633975	+	1.09808i	−0.110361	+	0.191151i
$34$			5.73205i			0.983039i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	1.76795	+	3.06218i	0.290649	+	0.503419i	0.973963	−	0.226705i	$-0.0727955\pi$
$37$	1.76795	+	3.06218i	0.290649	+	0.503419i	−0.683314	+	0.730124i	$0.739462\pi$
$38$			4.73205i			0.767640i
$39$	0.866025	−	3.50000i	0.138675	−	0.560449i
$40$		0			0
$41$	8.13397	−	4.69615i	1.27031	−	0.733416i	0.295267	−	0.955415i	$-0.404592\pi$
$41$	8.13397	−	4.69615i	1.27031	−	0.733416i	0.975047	+	0.221999i	$0.0712582\pi$
$42$	−2.36603	+	1.36603i	−0.365086	+	0.210782i
$43$	8.36603	+	4.83013i	1.27581	+	0.736587i	0.976075	−	0.217436i	$-0.0697693\pi$
$43$	8.36603	+	4.83013i	1.27581	+	0.736587i	0.299732	+	0.954023i	$0.403103\pi$
$44$			1.26795i			0.191151i
$45$		0			0
$46$	−3.63397	−	2.09808i	−0.535800	−	0.309344i
$47$	−2.19615			−0.320342			−0.160171	−	0.987089i	$-0.551205\pi$
$47$	−2.19615			−0.320342			−0.160171	+	0.987089i	$0.551205\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−0.232051	−	0.401924i	−0.0331501	−	0.0574177i
$50$		0			0
$51$	5.73205			0.802648
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$			6.46410i			0.887913i	0.896048	+	0.443956i	$0.146425\pi$
$53$			6.46410i			0.887913i	−0.896048	+	0.443956i	$0.853575\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−1.36603	+	2.36603i	−0.182543	+	0.316173i
$57$	4.73205			0.626775
$58$	−2.23205	+	3.86603i	−0.293083	+	0.507634i
$59$	6.92820	+	4.00000i	0.901975	+	0.520756i	0.877841	−	0.478953i	$-0.158984\pi$
$59$	6.92820	+	4.00000i	0.901975	+	0.520756i	0.0241347	+	0.999709i	$0.492317\pi$
$60$		0			0
$61$	4.59808	−	7.96410i	0.588723	−	1.01970i	−0.405677	−	0.914017i	$-0.632964\pi$
$61$	4.59808	−	7.96410i	0.588723	−	1.01970i	0.994400	−	0.105682i	$-0.0337026\pi$
$62$	−1.26795	+	0.732051i	−0.161030	+	0.0929705i
$63$	1.36603	+	2.36603i	0.172103	+	0.298091i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.26795			0.156074
$67$	−6.56218	−	11.3660i	−0.801698	−	1.38858i	−0.918498	−	0.395426i	$-0.870597\pi$
$67$	−6.56218	−	11.3660i	−0.801698	−	1.38858i	0.116800	−	0.993155i	$-0.462736\pi$
$68$	4.96410	−	2.86603i	0.601986	−	0.347557i
$69$	−2.09808	+	3.63397i	−0.252579	+	0.437479i
$70$		0			0
$71$	4.09808	+	2.36603i	0.486352	+	0.280796i	0.723060	−	0.690785i	$-0.242735\pi$
$71$	4.09808	+	2.36603i	0.486352	+	0.280796i	−0.236708	+	0.971581i	$0.576068\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−6.26795			−0.733608			−0.366804	−	0.930298i	$-0.619548\pi$
$73$	−6.26795			−0.733608			−0.366804	+	0.930298i	$0.619548\pi$
$74$	1.76795	−	3.06218i	0.205520	−	0.355971i
$75$		0			0
$76$	4.09808	−	2.36603i	0.470082	−	0.271402i
$77$			3.46410i			0.394771i
$78$	−3.46410	+	1.00000i	−0.392232	+	0.113228i
$79$	2.53590			0.285311			0.142655	−	0.989772i	$-0.454436\pi$
$79$	2.53590			0.285311			0.142655	+	0.989772i	$0.454436\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.13397	−	4.69615i	−0.898247	−	0.518603i
$83$	0.196152			0.0215305			0.0107653	−	0.999942i	$-0.496573\pi$
$83$	0.196152			0.0215305			0.0107653	+	0.999942i	$0.496573\pi$
$84$	2.36603	+	1.36603i	0.258155	+	0.149046i
$85$		0			0
$86$		−	9.66025i		−	1.04169i
$87$	3.86603	+	2.23205i	0.414481	+	0.239301i
$88$	1.09808	−	0.633975i	0.117055	−	0.0675819i
$89$	8.19615	−	4.73205i	0.868790	−	0.501596i	0.00184433	−	0.999998i	$-0.499413\pi$
$89$	8.19615	−	4.73205i	0.868790	−	0.501596i	0.866946	+	0.498402i	$0.166080\pi$
$90$		0			0
$91$	−2.73205	−	9.46410i	−0.286397	−	0.992107i
$92$			4.19615i			0.437479i
$93$	0.732051	+	1.26795i	0.0759101	+	0.131480i
$94$	1.09808	+	1.90192i	0.113258	+	0.196168i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	−0.232051	+	0.401924i	−0.0234407	+	0.0406004i
$99$		−	1.26795i		−	0.127434i
$100$		0			0
$101$	0.964102	+	1.66987i	0.0959317	+	0.166159i	0.909997	−	0.414615i	$-0.136084\pi$
$101$	0.964102	+	1.66987i	0.0959317	+	0.166159i	−0.814065	+	0.580773i	$0.802750\pi$
$102$	−2.86603	−	4.96410i	−0.283779	−	0.491519i
$103$		−	15.2679i		−	1.50440i	−0.658937	−	0.752198i	$-0.728994\pi$
$103$		−	15.2679i		−	1.50440i	0.658937	−	0.752198i	$-0.271006\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	5.59808	−	3.23205i	0.543733	−	0.313925i
$107$	8.83013	−	5.09808i	0.853641	−	0.492850i	−0.00823695	−	0.999966i	$-0.502622\pi$
$107$	8.83013	−	5.09808i	0.853641	−	0.492850i	0.861878	+	0.507116i	$0.169289\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$			1.46410i			0.140236i	0.997539	+	0.0701178i	$0.0223375\pi$
$109$			1.46410i			0.140236i	−0.997539	+	0.0701178i	$0.977662\pi$
$110$		0			0
$111$	−3.06218	−	1.76795i	−0.290649	−	0.167806i
$112$	2.73205			0.258155
$113$	−1.16025	−	0.669873i	−0.109148	−	0.0630163i	0.444432	−	0.895812i	$-0.353405\pi$
$113$	−1.16025	−	0.669873i	−0.109148	−	0.0630163i	−0.553580	+	0.832796i	$0.686739\pi$
$114$	−2.36603	−	4.09808i	−0.221599	−	0.383820i
$115$		0			0
$116$	4.46410			0.414481
$117$	1.00000	+	3.46410i	0.0924500	+	0.320256i
$118$		−	8.00000i		−	0.736460i
$119$	13.5622	−	7.83013i	1.24324	−	0.717787i
$120$		0			0
$121$	−4.69615	+	8.13397i	−0.426923	+	0.739452i
$122$	−9.19615			−0.832581
$123$	−4.69615	+	8.13397i	−0.423438	+	0.733416i
$124$	1.26795	+	0.732051i	0.113865	+	0.0657401i
$125$		0			0
$126$	1.36603	−	2.36603i	0.121695	−	0.210782i
$127$	8.53590	−	4.92820i	0.757438	−	0.437307i	−0.0709368	−	0.997481i	$-0.522599\pi$
$127$	8.53590	−	4.92820i	0.757438	−	0.437307i	0.828375	+	0.560173i	$0.189266\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−9.66025			−0.850538
$130$		0			0
$131$	6.53590			0.571044			0.285522	−	0.958372i	$-0.407833\pi$
$131$	6.53590			0.571044			0.285522	+	0.958372i	$0.407833\pi$
$132$	−0.633975	−	1.09808i	−0.0551804	−	0.0955753i
$133$	11.1962	−	6.46410i	0.970830	−	0.560509i
$134$	−6.56218	+	11.3660i	−0.566886	+	0.981875i
$135$		0			0
$136$	−4.96410	−	2.86603i	−0.425668	−	0.245760i
$137$	5.96410	−	10.3301i	0.509548	−	0.882562i	−0.490391	−	0.871502i	$-0.663146\pi$
$137$	5.96410	−	10.3301i	0.509548	−	0.882562i	0.999939	−	0.0110599i	$-0.00352055\pi$
$138$	4.19615			0.357200
$139$	8.92820	−	15.4641i	0.757280	−	1.31165i	−0.186952	−	0.982369i	$-0.559861\pi$
$139$	8.92820	−	15.4641i	0.757280	−	1.31165i	0.944233	−	0.329279i	$-0.106806\pi$
$140$		0			0
$141$	1.90192	−	1.09808i	0.160171	−	0.0924747i
$142$		−	4.73205i		−	0.397105i
$143$	−1.09808	+	4.43782i	−0.0918257	+	0.371109i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	3.13397	+	5.42820i	0.259370	+	0.449241i
$147$	0.401924	+	0.232051i	0.0331501	+	0.0191392i
$148$	−3.53590			−0.290649
$149$	−11.4282	−	6.59808i	−0.936235	−	0.540535i	−0.0474568	−	0.998873i	$-0.515112\pi$
$149$	−11.4282	−	6.59808i	−0.936235	−	0.540535i	−0.888778	+	0.458338i	$0.848445\pi$
$150$		0			0
$151$			6.73205i			0.547847i	0.961752	+	0.273923i	$0.0883214\pi$
$151$			6.73205i			0.547847i	−0.961752	+	0.273923i	$0.911679\pi$
$152$	−4.09808	−	2.36603i	−0.332398	−	0.191910i
$153$	−4.96410	+	2.86603i	−0.401324	+	0.231704i
$154$	3.00000	−	1.73205i	0.241747	−	0.139573i
$155$		0			0
$156$	2.59808	+	2.50000i	0.208013	+	0.200160i
$157$			7.58846i			0.605625i	0.953050	+	0.302812i	$0.0979256\pi$
$157$			7.58846i			0.605625i	−0.953050	+	0.302812i	$0.902074\pi$
$158$	−1.26795	−	2.19615i	−0.100873	−	0.174717i
$159$	−3.23205	−	5.59808i	−0.256318	−	0.443956i
$160$		0			0
$161$			11.4641i			0.903498i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	6.73205	−	11.6603i	0.527295	−	0.913302i	−0.472199	−	0.881492i	$-0.656540\pi$
$163$	6.73205	−	11.6603i	0.527295	−	0.913302i	0.999494	−	0.0318096i	$-0.0101270\pi$
$164$			9.39230i			0.733416i
$165$		0			0
$166$	−0.0980762	−	0.169873i	−0.00761219	−	0.0131847i
$167$	−4.73205	−	8.19615i	−0.366177	−	0.634237i	0.622787	−	0.782391i	$-0.286000\pi$
$167$	−4.73205	−	8.19615i	−0.366177	−	0.634237i	−0.988964	+	0.148154i	$0.952667\pi$
$168$		−	2.73205i		−	0.210782i
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$	−4.09808	+	2.36603i	−0.313388	+	0.180934i
$172$	−8.36603	+	4.83013i	−0.637903	+	0.368294i
$173$	−3.80385	−	2.19615i	−0.289201	−	0.166970i	0.348380	−	0.937353i	$-0.386732\pi$
$173$	−3.80385	−	2.19615i	−0.289201	−	0.166970i	−0.637582	+	0.770383i	$0.720065\pi$
$174$		−	4.46410i		−	0.338423i
$175$		0			0
$176$	−1.09808	−	0.633975i	−0.0827706	−	0.0477876i
$177$	−8.00000			−0.601317
$178$	−8.19615	−	4.73205i	−0.614328	−	0.354682i
$179$	8.02628	+	13.9019i	0.599912	+	1.03908i	0.992833	+	0.119506i	$0.0381312\pi$
$179$	8.02628	+	13.9019i	0.599912	+	1.03908i	−0.392921	+	0.919572i	$0.628535\pi$
$180$		0			0
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$	−6.83013	+	7.09808i	−0.506283	+	0.526144i
$183$			9.19615i			0.679799i
$184$	3.63397	−	2.09808i	0.267900	−	0.154672i
$185$		0			0
$186$	0.732051	−	1.26795i	0.0536766	−	0.0929705i
$187$	−7.26795			−0.531485
$188$	1.09808	−	1.90192i	0.0800854	−	0.138712i
$189$	−2.36603	−	1.36603i	−0.172103	−	0.0993637i
$190$		0			0
$191$	3.46410	−	6.00000i	0.250654	−	0.434145i	−0.713052	−	0.701111i	$-0.752688\pi$
$191$	3.46410	−	6.00000i	0.250654	−	0.434145i	0.963706	+	0.266966i	$0.0860212\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	5.86603	+	10.1603i	0.422246	+	0.731351i	0.996159	−	0.0875652i	$-0.0279086\pi$
$193$	5.86603	+	10.1603i	0.422246	+	0.731351i	−0.573913	+	0.818916i	$0.694575\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	0.464102			0.0331501
$197$	8.92820	+	15.4641i	0.636108	+	1.10177i	0.986279	+	0.165086i	$0.0527901\pi$
$197$	8.92820	+	15.4641i	0.636108	+	1.10177i	−0.350171	+	0.936686i	$0.613877\pi$
$198$	−1.09808	+	0.633975i	−0.0780369	+	0.0450546i
$199$	7.09808	−	12.2942i	0.503169	−	0.871515i	−0.496824	−	0.867851i	$-0.665501\pi$
$199$	7.09808	−	12.2942i	0.503169	−	0.871515i	0.999993	−	0.00366345i	$-0.00116611\pi$
$200$		0			0
$201$	11.3660	+	6.56218i	0.801698	+	0.462860i
$202$	0.964102	−	1.66987i	0.0678340	−	0.117492i
$203$	12.1962			0.856002
$204$	−2.86603	+	4.96410i	−0.200662	+	0.347557i
$205$		0			0
$206$	−13.2224	+	7.63397i	−0.921250	+	0.531884i
$207$		−	4.19615i		−	0.291653i
$208$	3.50000	+	0.866025i	0.242681	+	0.0600481i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−8.19615	−	14.1962i	−0.564246	−	0.977303i	−0.997119	−	0.0758485i	$-0.975833\pi$
$211$	−8.19615	−	14.1962i	−0.564246	−	0.977303i	0.432873	−	0.901455i	$-0.357500\pi$
$212$	−5.59808	−	3.23205i	−0.384477	−	0.221978i
$213$	−4.73205			−0.324235
$214$	−8.83013	−	5.09808i	−0.603615	−	0.348497i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	3.46410	+	2.00000i	0.235159	+	0.135769i
$218$	1.26795	−	0.732051i	0.0858764	−	0.0495807i
$219$	5.42820	−	3.13397i	0.366804	−	0.211774i
$220$		0			0
$221$	19.8564	−	5.73205i	1.33569	−	0.385579i
$222$			3.53590i			0.237314i
$223$	−13.4641	−	23.3205i	−0.901623	−	1.56166i	−0.825387	−	0.564567i	$-0.809043\pi$
$223$	−13.4641	−	23.3205i	−0.901623	−	1.56166i	−0.0762356	−	0.997090i	$-0.524290\pi$
$224$	−1.36603	−	2.36603i	−0.0912714	−	0.158087i
$225$		0			0
$226$			1.33975i			0.0891186i
$227$	6.09808	−	10.5622i	0.404744	−	0.701036i	−0.589548	−	0.807733i	$-0.700694\pi$
$227$	6.09808	−	10.5622i	0.404744	−	0.701036i	0.994292	+	0.106697i	$0.0340275\pi$
$228$	−2.36603	+	4.09808i	−0.156694	+	0.271402i
$229$			11.8564i			0.783493i	0.920073	+	0.391747i	$0.128129\pi$
$229$			11.8564i			0.783493i	−0.920073	+	0.391747i	$0.871871\pi$
$230$		0			0
$231$	−1.73205	−	3.00000i	−0.113961	−	0.197386i
$232$	−2.23205	−	3.86603i	−0.146541	−	0.253817i
$233$		−	7.85641i		−	0.514690i	−0.966320	−	0.257345i	$-0.917152\pi$
$233$		−	7.85641i		−	0.514690i	0.966320	−	0.257345i	$-0.0828477\pi$
$234$	2.50000	−	2.59808i	0.163430	−	0.169842i
$235$		0			0
$236$	−6.92820	+	4.00000i	−0.450988	+	0.260378i
$237$	−2.19615	+	1.26795i	−0.142655	+	0.0823622i
$238$	−13.5622	−	7.83013i	−0.879105	−	0.507552i
$239$			7.66025i			0.495501i	0.968824	+	0.247750i	$0.0796913\pi$
$239$			7.66025i			0.495501i	−0.968824	+	0.247750i	$0.920309\pi$
$240$		0			0
$241$	−11.7679	−	6.79423i	−0.758040	−	0.437655i	0.0705514	−	0.997508i	$-0.477524\pi$
$241$	−11.7679	−	6.79423i	−0.758040	−	0.437655i	−0.828592	+	0.559853i	$0.810857\pi$
$242$	9.39230			0.603760
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.59808	+	7.96410i	0.294362	+	0.509849i
$245$		0			0
$246$	9.39230			0.598831
$247$	16.3923	−	4.73205i	1.04302	−	0.301093i
$248$		−	1.46410i		−	0.0929705i
$249$	−0.169873	+	0.0980762i	−0.0107653	+	0.00621533i
$250$		0			0
$251$	6.73205	−	11.6603i	0.424923	−	0.735989i	−0.571490	−	0.820609i	$-0.693634\pi$
$251$	6.73205	−	11.6603i	0.424923	−	0.735989i	0.996413	+	0.0846203i	$0.0269677\pi$
$252$	−2.73205			−0.172103
$253$	2.66025	−	4.60770i	0.167249	−	0.289683i
$254$	−8.53590	−	4.92820i	−0.535590	−	0.309223i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.08846	+	4.66987i	−0.504544	+	0.291299i	−0.730588	−	0.682818i	$-0.760754\pi$
$257$	−8.08846	+	4.66987i	−0.504544	+	0.291299i	0.226044	+	0.974117i	$0.427421\pi$
$258$	4.83013	+	8.36603i	0.300711	+	0.520846i
$259$	−9.66025			−0.600259
$260$		0			0
$261$	−4.46410			−0.276321
$262$	−3.26795	−	5.66025i	−0.201895	−	0.349692i
$263$	8.70577	−	5.02628i	0.536821	−	0.309934i	−0.206969	−	0.978348i	$-0.566360\pi$
$263$	8.70577	−	5.02628i	0.536821	−	0.309934i	0.743790	+	0.668414i	$0.233026\pi$
$264$	−0.633975	+	1.09808i	−0.0390184	+	0.0675819i
$265$		0			0
$266$	−11.1962	−	6.46410i	−0.686480	−	0.396339i
$267$	−4.73205	+	8.19615i	−0.289597	+	0.501596i
$268$	13.1244			0.801698
$269$	2.73205	−	4.73205i	0.166576	−	0.288518i	−0.770638	−	0.637273i	$-0.780062\pi$
$269$	2.73205	−	4.73205i	0.166576	−	0.288518i	0.937214	+	0.348755i	$0.113396\pi$
$270$		0			0
$271$	−18.9282	+	10.9282i	−1.14981	+	0.663841i	−0.948840	−	0.315757i	$-0.897742\pi$
$271$	−18.9282	+	10.9282i	−1.14981	+	0.663841i	−0.200966	+	0.979598i	$0.564408\pi$
$272$			5.73205i			0.347557i
$273$	7.09808	+	6.83013i	0.429595	+	0.413378i
$274$	−11.9282			−0.720609
$275$		0			0
$276$	−2.09808	−	3.63397i	−0.126289	−	0.218740i
$277$	−4.96410	−	2.86603i	−0.298264	−	0.172203i	0.343399	−	0.939190i	$-0.388422\pi$
$277$	−4.96410	−	2.86603i	−0.298264	−	0.172203i	−0.641663	+	0.766987i	$0.721755\pi$
$278$	−17.8564			−1.07096
$279$	−1.26795	−	0.732051i	−0.0759101	−	0.0438267i
$280$		0			0
$281$			12.3205i			0.734980i	0.930027	+	0.367490i	$0.119783\pi$
$281$			12.3205i			0.734980i	−0.930027	+	0.367490i	$0.880217\pi$
$282$	−1.90192	−	1.09808i	−0.113258	−	0.0653895i
$283$	22.2224	−	12.8301i	1.32099	−	0.762672i	0.337100	−	0.941469i	$-0.390554\pi$
$283$	22.2224	−	12.8301i	1.32099	−	0.762672i	0.983886	+	0.178797i	$0.0572205\pi$
$284$	−4.09808	+	2.36603i	−0.243176	+	0.140398i
$285$		0			0
$286$	4.39230	−	1.26795i	0.259722	−	0.0749754i
$287$			25.6603i			1.51468i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	7.92820	+	13.7321i	0.466365	+	0.807768i
$290$		0			0
$291$			6.00000i			0.351726i
$292$	3.13397	−	5.42820i	0.183402	−	0.317662i
$293$	−15.2583	+	26.4282i	−0.891401	+	1.54395i	−0.0532048	+	0.998584i	$0.516944\pi$
$293$	−15.2583	+	26.4282i	−0.891401	+	1.54395i	−0.838196	+	0.545368i	$0.816390\pi$
$294$		−	0.464102i		−	0.0270670i
$295$		0			0
$296$	1.76795	+	3.06218i	0.102760	+	0.177985i
$297$	0.633975	+	1.09808i	0.0367869	+	0.0637168i
$298$			13.1962i			0.764433i
$299$	−3.63397	+	14.6865i	−0.210158	+	0.849344i
$300$		0			0
$301$	−22.8564	+	13.1962i	−1.31742	+	0.760614i
$302$	5.83013	−	3.36603i	0.335486	−	0.193693i
$303$	−1.66987	−	0.964102i	−0.0959317	−	0.0553862i
$304$			4.73205i			0.271402i
$305$		0			0
$306$	4.96410	+	2.86603i	0.283779	+	0.163840i
$307$	22.5885			1.28919			0.644596	−	0.764524i	$-0.277026\pi$
$307$	22.5885			1.28919			0.644596	+	0.764524i	$0.277026\pi$
$308$	−3.00000	−	1.73205i	−0.170941	−	0.0986928i
$309$	7.63397	+	13.2224i	0.434282	+	0.752198i
$310$		0			0
$311$	1.66025			0.0941444			0.0470722	−	0.998891i	$-0.485011\pi$
$311$	1.66025			0.0941444			0.0470722	+	0.998891i	$0.485011\pi$
$312$	0.866025	−	3.50000i	0.0490290	−	0.198148i
$313$		−	6.53590i		−	0.369431i	−0.982792	−	0.184715i	$-0.940864\pi$
$313$		−	6.53590i		−	0.369431i	0.982792	−	0.184715i	$-0.0591363\pi$
$314$	6.57180	−	3.79423i	0.370868	−	0.214121i
$315$		0			0
$316$	−1.26795	+	2.19615i	−0.0713277	+	0.123543i
$317$	20.6603			1.16040			0.580198	−	0.814476i	$-0.302975\pi$
$317$	20.6603			1.16040			0.580198	+	0.814476i	$0.302975\pi$
$318$	−3.23205	+	5.59808i	−0.181244	+	0.313925i
$319$	−4.90192	−	2.83013i	−0.274455	−	0.158457i
$320$		0			0
$321$	−5.09808	+	8.83013i	−0.284547	+	0.492850i
$322$	9.92820	−	5.73205i	0.553277	−	0.319435i
$323$	13.5622	+	23.4904i	0.754620	+	1.30704i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−13.4641			−0.745708
$327$	−0.732051	−	1.26795i	−0.0404825	−	0.0701178i
$328$	8.13397	−	4.69615i	0.449124	−	0.259302i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	17.3205	+	10.0000i	0.952021	+	0.549650i	0.893708	−	0.448649i	$-0.148095\pi$
$331$	17.3205	+	10.0000i	0.952021	+	0.549650i	0.0583130	+	0.998298i	$0.481428\pi$
$332$	−0.0980762	+	0.169873i	−0.00538263	+	0.00932299i
$333$	3.53590			0.193766
$334$	−4.73205	+	8.19615i	−0.258926	+	0.448474i
$335$		0			0
$336$	−2.36603	+	1.36603i	−0.129077	+	0.0745228i
$337$			20.8564i			1.13612i	0.822987	+	0.568060i	$0.192306\pi$
$337$			20.8564i			1.13612i	−0.822987	+	0.568060i	$0.807694\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$	1.33975			0.0727650
$340$		0			0
$341$	−0.928203	−	1.60770i	−0.0502650	−	0.0870616i
$342$	4.09808	+	2.36603i	0.221599	+	0.127940i
$343$	−17.8564			−0.964155
$344$	8.36603	+	4.83013i	0.451066	+	0.260423i
$345$		0			0
$346$			4.39230i			0.236132i
$347$	−28.6865	−	16.5622i	−1.53997	−	0.889104i	−0.998839	−	0.0481683i	$-0.984662\pi$
$347$	−28.6865	−	16.5622i	−1.53997	−	0.889104i	−0.541135	−	0.840936i	$-0.682005\pi$
$348$	−3.86603	+	2.23205i	−0.207241	+	0.119650i
$349$	−13.2679	+	7.66025i	−0.710217	+	0.410044i	−0.811141	−	0.584850i	$-0.801153\pi$
$349$	−13.2679	+	7.66025i	−0.710217	+	0.410044i	0.100924	+	0.994894i	$0.467820\pi$
$350$		0			0
$351$	−2.59808	−	2.50000i	−0.138675	−	0.133440i
$352$			1.26795i			0.0675819i
$353$	−10.8923	−	18.8660i	−0.579739	−	1.00414i	−0.995509	−	0.0946674i	$-0.969821\pi$
$353$	−10.8923	−	18.8660i	−0.579739	−	1.00414i	0.415770	−	0.909470i	$-0.363512\pi$
$354$	4.00000	+	6.92820i	0.212598	+	0.368230i
$355$		0			0
$356$			9.46410i			0.501596i
$357$	−7.83013	+	13.5622i	−0.414414	+	0.717787i
$358$	8.02628	−	13.9019i	0.424202	−	0.734740i
$359$			1.12436i			0.0593412i	0.999560	+	0.0296706i	$0.00944584\pi$
$359$			1.12436i			0.0593412i	−0.999560	+	0.0296706i	$0.990554\pi$
$360$		0			0
$361$	1.69615	+	2.93782i	0.0892712	+	0.154622i
$362$	9.59808	+	16.6244i	0.504464	+	0.873757i
$363$		−	9.39230i		−	0.492968i
$364$	9.56218	+	2.36603i	0.501194	+	0.124013i
$365$		0			0
$366$	7.96410	−	4.59808i	0.416290	−	0.240345i
$367$	−9.75833	+	5.63397i	−0.509381	+	0.294091i	−0.732579	−	0.680682i	$-0.761684\pi$
$367$	−9.75833	+	5.63397i	−0.509381	+	0.294091i	0.223198	+	0.974773i	$0.428350\pi$
$368$	−3.63397	−	2.09808i	−0.189434	−	0.109370i
$369$		−	9.39230i		−	0.488944i
$370$		0			0
$371$	−15.2942	−	8.83013i	−0.794037	−	0.458437i
$372$	−1.46410			−0.0759101
$373$	−11.8923	−	6.86603i	−0.615760	−	0.355509i	0.159456	−	0.987205i	$-0.449026\pi$
$373$	−11.8923	−	6.86603i	−0.615760	−	0.355509i	−0.775216	+	0.631696i	$0.782359\pi$
$374$	3.63397	+	6.29423i	0.187908	+	0.325467i
$375$		0			0
$376$	−2.19615			−0.113258
$377$	15.6244	+	3.86603i	0.804695	+	0.199110i
$378$			2.73205i			0.140522i
$379$	−4.73205	+	2.73205i	−0.243069	+	0.140336i	−0.616587	−	0.787287i	$-0.711485\pi$
$379$	−4.73205	+	2.73205i	−0.243069	+	0.140336i	0.373517	+	0.927623i	$0.378152\pi$
$380$		0			0
$381$	−4.92820	+	8.53590i	−0.252479	+	0.437307i
$382$	−6.92820			−0.354478
$383$	−0.732051	+	1.26795i	−0.0374060	+	0.0647892i	−0.884122	−	0.467255i	$-0.845243\pi$
$383$	−0.732051	+	1.26795i	−0.0374060	+	0.0647892i	0.846716	+	0.532045i	$0.178576\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	5.86603	−	10.1603i	0.298573	−	0.517143i
$387$	8.36603	−	4.83013i	0.425269	−	0.245529i
$388$	3.00000	+	5.19615i	0.152302	+	0.263795i
$389$	11.7846			0.597503			0.298752	−	0.954331i	$-0.403430\pi$
$389$	11.7846			0.597503			0.298752	+	0.954331i	$0.403430\pi$
$390$		0			0
$391$	−24.0526			−1.21639
$392$	−0.232051	−	0.401924i	−0.0117203	−	0.0203002i
$393$	−5.66025	+	3.26795i	−0.285522	+	0.164846i
$394$	8.92820	−	15.4641i	0.449796	−	0.779070i
$395$		0			0
$396$	1.09808	+	0.633975i	0.0551804	+	0.0318584i
$397$	10.1962	−	17.6603i	0.511730	−	0.886343i	−0.488177	−	0.872744i	$-0.662338\pi$
$397$	10.1962	−	17.6603i	0.511730	−	0.886343i	0.999908	−	0.0135983i	$-0.00432860\pi$
$398$	−14.1962			−0.711589
$399$	−6.46410	+	11.1962i	−0.323610	+	0.560509i
$400$		0			0
$401$	6.99038	−	4.03590i	0.349083	−	0.201543i	−0.315198	−	0.949026i	$-0.602071\pi$
$401$	6.99038	−	4.03590i	0.349083	−	0.201543i	0.664281	+	0.747483i	$0.268738\pi$
$402$		−	13.1244i		−	0.654583i
$403$	3.80385	+	3.66025i	0.189483	+	0.182330i
$404$	−1.92820			−0.0959317
$405$		0			0
$406$	−6.09808	−	10.5622i	−0.302642	−	0.524192i
$407$	3.88269	+	2.24167i	0.192458	+	0.111115i
$408$	5.73205			0.283779
$409$	−15.3564	−	8.86603i	−0.759325	−	0.438397i	0.0697281	−	0.997566i	$-0.477787\pi$
$409$	−15.3564	−	8.86603i	−0.759325	−	0.438397i	−0.829053	+	0.559169i	$0.811120\pi$
$410$		0			0
$411$			11.9282i			0.588375i
$412$	13.2224	+	7.63397i	0.651422	+	0.376099i
$413$	−18.9282	+	10.9282i	−0.931396	+	0.537742i
$414$	−3.63397	+	2.09808i	−0.178600	+	0.103115i
$415$		0			0
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$			17.8564i			0.874432i
$418$	3.00000	+	5.19615i	0.146735	+	0.254152i
$419$	−8.73205	−	15.1244i	−0.426589	−	0.738873i	0.569979	−	0.821659i	$-0.306951\pi$
$419$	−8.73205	−	15.1244i	−0.426589	−	0.738873i	−0.996567	+	0.0827863i	$0.973618\pi$
$420$		0			0
$421$			22.7128i			1.10695i	0.832864	+	0.553477i	$0.186699\pi$
$421$			22.7128i			1.10695i	−0.832864	+	0.553477i	$0.813301\pi$
$422$	−8.19615	+	14.1962i	−0.398982	+	0.691058i
$423$	−1.09808	+	1.90192i	−0.0533903	+	0.0924747i
$424$			6.46410i			0.313925i
$425$		0			0
$426$	2.36603	+	4.09808i	0.114634	+	0.198552i
$427$	12.5622	+	21.7583i	0.607926	+	1.05296i
$428$			10.1962i			0.492850i
$429$	−1.26795	−	4.39230i	−0.0612172	−	0.212062i
$430$		0			0
$431$	−11.3660	+	6.56218i	−0.547482	+	0.316089i	−0.748106	−	0.663579i	$-0.769036\pi$
$431$	−11.3660	+	6.56218i	−0.547482	+	0.316089i	0.200624	+	0.979668i	$0.435703\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−11.1340	−	6.42820i	−0.535065	−	0.308920i	0.208012	−	0.978126i	$-0.433301\pi$
$433$	−11.1340	−	6.42820i	−0.535065	−	0.308920i	−0.743076	+	0.669207i	$0.766634\pi$
$434$		−	4.00000i		−	0.192006i
$435$		0			0
$436$	−1.26795	−	0.732051i	−0.0607238	−	0.0350589i
$437$	−19.8564			−0.949861
$438$	−5.42820	−	3.13397i	−0.259370	−	0.149747i
$439$	0.169873	+	0.294229i	0.00810760	+	0.0140428i	0.870051	−	0.492962i	$-0.164086\pi$
$439$	0.169873	+	0.294229i	0.00810760	+	0.0140428i	−0.861943	+	0.507005i	$0.830753\pi$
$440$		0			0
$441$	−0.464102			−0.0221001
$442$	−14.8923	−	14.3301i	−0.708355	−	0.681615i
$443$		−	15.6077i		−	0.741544i	−0.928724	−	0.370772i	$-0.879093\pi$
$443$		−	15.6077i		−	0.741544i	0.928724	−	0.370772i	$-0.120907\pi$
$444$	3.06218	−	1.76795i	0.145325	−	0.0839032i
$445$		0			0
$446$	−13.4641	+	23.3205i	−0.637544	+	1.10426i
$447$	13.1962			0.624157
$448$	−1.36603	+	2.36603i	−0.0645386	+	0.111784i
$449$	9.80385	+	5.66025i	0.462672	+	0.267124i	0.713167	−	0.700994i	$-0.247260\pi$
$449$	9.80385	+	5.66025i	0.462672	+	0.267124i	−0.250495	+	0.968118i	$0.580593\pi$
$450$		0			0
$451$	5.95448	−	10.3135i	0.280386	−	0.485642i
$452$	1.16025	−	0.669873i	0.0545738	−	0.0315082i
$453$	−3.36603	−	5.83013i	−0.158150	−	0.273923i
$454$	−12.1962			−0.572394
$455$		0			0
$456$	4.73205			0.221599
$457$	−0.669873	−	1.16025i	−0.0313353	−	0.0542744i	0.849932	−	0.526892i	$-0.176643\pi$
$457$	−0.669873	−	1.16025i	−0.0313353	−	0.0542744i	−0.881268	+	0.472617i	$0.843309\pi$
$458$	10.2679	−	5.92820i	0.479790	−	0.277007i
$459$	2.86603	−	4.96410i	0.133775	−	0.231704i
$460$		0			0
$461$	19.2846	+	11.1340i	0.898174	+	0.518561i	0.876607	−	0.481207i	$-0.159801\pi$
$461$	19.2846	+	11.1340i	0.898174	+	0.518561i	0.0215666	+	0.999767i	$0.493135\pi$
$462$	−1.73205	+	3.00000i	−0.0805823	+	0.139573i
$463$	10.0526			0.467182			0.233591	−	0.972335i	$-0.424952\pi$
$463$	10.0526			0.467182			0.233591	+	0.972335i	$0.424952\pi$
$464$	−2.23205	+	3.86603i	−0.103620	+	0.179476i
$465$		0			0
$466$	−6.80385	+	3.92820i	−0.315182	+	0.181971i
$467$		−	18.5885i		−	0.860171i	−0.902788	−	0.430086i	$-0.858483\pi$
$467$		−	18.5885i		−	0.860171i	0.902788	−	0.430086i	$-0.141517\pi$
$468$	−3.50000	−	0.866025i	−0.161788	−	0.0400320i
$469$	35.8564			1.65570
$470$		0			0
$471$	−3.79423	−	6.57180i	−0.174829	−	0.302812i
$472$	6.92820	+	4.00000i	0.318896	+	0.184115i
$473$	12.2487			0.563196
$474$	2.19615	+	1.26795i	0.100873	+	0.0582388i
$475$		0			0
$476$			15.6603i			0.717787i
$477$	5.59808	+	3.23205i	0.256318	+	0.147985i
$478$	6.63397	−	3.83013i	0.303431	−	0.175186i
$479$	−28.9808	+	16.7321i	−1.32416	+	0.764507i	−0.984390	−	0.176000i	$-0.943684\pi$
$479$	−28.9808	+	16.7321i	−1.32416	+	0.764507i	−0.339775	+	0.940507i	$0.610351\pi$
$480$		0			0
$481$	−12.3756	−	3.06218i	−0.564281	−	0.139623i
$482$			13.5885i			0.618937i
$483$	−5.73205	−	9.92820i	−0.260817	−	0.451749i
$484$	−4.69615	−	8.13397i	−0.213461	−	0.369726i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	1.56218	−	2.70577i	0.0707890	−	0.122610i	−0.828458	−	0.560051i	$-0.810782\pi$
$487$	1.56218	−	2.70577i	0.0707890	−	0.122610i	0.899247	+	0.437441i	$0.144115\pi$
$488$	4.59808	−	7.96410i	0.208145	−	0.360518i
$489$			13.4641i			0.608868i
$490$		0			0
$491$	4.36603	+	7.56218i	0.197036	+	0.341276i	0.947566	−	0.319560i	$-0.103535\pi$
$491$	4.36603	+	7.56218i	0.197036	+	0.341276i	−0.750530	+	0.660836i	$0.770202\pi$
$492$	−4.69615	−	8.13397i	−0.211719	−	0.366708i
$493$			25.5885i			1.15245i
$494$	−12.2942	−	11.8301i	−0.553143	−	0.532263i
$495$		0			0
$496$	−1.26795	+	0.732051i	−0.0569326	+	0.0328701i
$497$	−11.1962	+	6.46410i	−0.502216	+	0.289955i
$498$	0.169873	+	0.0980762i	0.00761219	+	0.00439490i
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$		0			0
$501$	8.19615	+	4.73205i	0.366177	+	0.211412i
$502$	−13.4641			−0.600932
$503$	35.4904	+	20.4904i	1.58244	+	0.913621i	0.994502	+	0.104713i	$0.0333924\pi$
$503$	35.4904	+	20.4904i	1.58244	+	0.913621i	0.587935	+	0.808908i	$0.299941\pi$
$504$	1.36603	+	2.36603i	0.0608476	+	0.105391i
$505$		0			0
$506$	−5.32051			−0.236525
$507$	6.92820	+	11.0000i	0.307692	+	0.488527i
$508$			9.85641i			0.437307i
$509$	11.8923	−	6.86603i	0.527117	−	0.304331i	−0.212725	−	0.977112i	$-0.568234\pi$
$509$	11.8923	−	6.86603i	0.527117	−	0.304331i	0.739842	+	0.672781i	$0.234900\pi$
$510$		0			0
$511$	8.56218	−	14.8301i	0.378768	−	0.656046i
$512$	1.00000			0.0441942
$513$	2.36603	−	4.09808i	0.104463	−	0.180934i
$514$	8.08846	+	4.66987i	0.356767	+	0.205979i
$515$		0			0
$516$	4.83013	−	8.36603i	0.212634	−	0.368294i
$517$	−2.41154	+	1.39230i	−0.106060	+	0.0612335i
$518$	4.83013	+	8.36603i	0.212224	+	0.367582i
$519$	4.39230			0.192801
$520$		0			0
$521$	41.4449			1.81573			0.907866	−	0.419260i	$-0.137710\pi$
$521$	41.4449			1.81573			0.907866	+	0.419260i	$0.137710\pi$
$522$	2.23205	+	3.86603i	0.0976942	+	0.169211i
$523$	19.4378	−	11.2224i	0.849957	−	0.490723i	−0.0106796	−	0.999943i	$-0.503399\pi$
$523$	19.4378	−	11.2224i	0.849957	−	0.490723i	0.860636	+	0.509220i	$0.170066\pi$
$524$	−3.26795	+	5.66025i	−0.142761	+	0.247269i
$525$		0			0
$526$	−8.70577	−	5.02628i	−0.379590	−	0.219156i
$527$	−4.19615	+	7.26795i	−0.182787	+	0.316597i
$528$	1.26795			0.0551804
$529$	−2.69615	+	4.66987i	−0.117224	+	0.203038i
$530$		0			0
$531$	6.92820	−	4.00000i	0.300658	−	0.173585i
$532$			12.9282i			0.560509i
$533$	−8.13397	+	32.8731i	−0.352322	+	1.42389i
$534$	9.46410			0.409552
$535$		0			0
$536$	−6.56218	−	11.3660i	−0.283443	−	0.490938i
$537$	−13.9019	−	8.02628i	−0.599912	−	0.346360i
$538$	−5.46410			−0.235574
$539$	−0.509619	−	0.294229i	−0.0219508	−	0.0126733i
$540$		0			0
$541$			5.67949i			0.244180i	0.992519	+	0.122090i	$0.0389597\pi$
$541$			5.67949i			0.244180i	−0.992519	+	0.122090i	$0.961040\pi$
$542$	18.9282	+	10.9282i	0.813036	+	0.469407i
$543$	16.6244	−	9.59808i	0.713419	−	0.411893i
$544$	4.96410	−	2.86603i	0.212834	−	0.122880i
$545$		0			0
$546$	2.36603	−	9.56218i	0.101257	−	0.409223i
$547$		−	4.19615i		−	0.179415i	−0.995968	−	0.0897073i	$-0.971407\pi$
$547$		−	4.19615i		−	0.179415i	0.995968	−	0.0897073i	$-0.0285931\pi$
$548$	5.96410	+	10.3301i	0.254774	+	0.441281i
$549$	−4.59808	−	7.96410i	−0.196241	−	0.339900i
$550$		0			0
$551$			21.1244i			0.899928i
$552$	−2.09808	+	3.63397i	−0.0893001	+	0.154672i
$553$	−3.46410	+	6.00000i	−0.147309	+	0.255146i
$554$			5.73205i			0.243532i
$555$		0			0
$556$	8.92820	+	15.4641i	0.378640	+	0.655824i
$557$	21.1865	+	36.6962i	0.897702	+	1.55487i	0.830424	+	0.557132i	$0.188098\pi$
$557$	21.1865	+	36.6962i	0.897702	+	1.55487i	0.0672780	+	0.997734i	$0.478569\pi$
$558$			1.46410i			0.0619804i
$559$	−33.4641	+	9.66025i	−1.41538	+	0.408585i
$560$		0			0
$561$	6.29423	−	3.63397i	0.265743	−	0.153427i
$562$	10.6699	−	6.16025i	0.450081	−	0.259855i
$563$	−30.2487	−	17.4641i	−1.27483	−	0.736024i	−0.298938	−	0.954273i	$-0.596632\pi$
$563$	−30.2487	−	17.4641i	−1.27483	−	0.736024i	−0.975893	+	0.218248i	$0.929966\pi$
$564$			2.19615i			0.0924747i
$565$		0			0
$566$	−22.2224	−	12.8301i	−0.934078	−	0.539290i
$567$	2.73205			0.114735
$568$	4.09808	+	2.36603i	0.171951	+	0.0992762i
$569$	−15.3205	−	26.5359i	−0.642269	−	1.11244i	−0.984925	−	0.172982i	$-0.944660\pi$
$569$	−15.3205	−	26.5359i	−0.642269	−	1.11244i	0.342656	−	0.939461i	$-0.388674\pi$
$570$		0			0
$571$	−14.0526			−0.588081			−0.294041	−	0.955793i	$-0.595000\pi$
$571$	−14.0526			−0.588081			−0.294041	+	0.955793i	$0.595000\pi$
$572$	−3.29423	−	3.16987i	−0.137739	−	0.132539i
$573$			6.92820i			0.289430i
$574$	22.2224	−	12.8301i	0.927546	−	0.535519i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	3.73205			0.155367			0.0776837	−	0.996978i	$-0.475248\pi$
$577$	3.73205			0.155367			0.0776837	+	0.996978i	$0.475248\pi$
$578$	7.92820	−	13.7321i	0.329770	−	0.571178i
$579$	−10.1603	−	5.86603i	−0.422246	−	0.243784i
$580$		0			0
$581$	−0.267949	+	0.464102i	−0.0111164	+	0.0192542i
$582$	5.19615	−	3.00000i	0.215387	−	0.124354i
$583$	4.09808	+	7.09808i	0.169725	+	0.293972i
$584$	−6.26795			−0.259370
$585$		0			0
$586$	30.5167			1.26063
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	0.652355	−	0.757914i	$-0.273781\pi$
$587$	−8.00000	−	13.8564i	−0.330195	−	0.571915i	−0.982550	+	0.185999i	$0.940448\pi$
$588$	−0.401924	+	0.232051i	−0.0165751	+	0.00956961i
$589$	−3.46410	+	6.00000i	−0.142736	+	0.247226i
$590$		0			0
$591$	−15.4641	−	8.92820i	−0.636108	−	0.367257i
$592$	1.76795	−	3.06218i	0.0726623	−	0.125855i
$593$	−9.14359			−0.375482			−0.187741	−	0.982219i	$-0.560117\pi$
$593$	−9.14359			−0.375482			−0.187741	+	0.982219i	$0.560117\pi$
$594$	0.633975	−	1.09808i	0.0260123	−	0.0450546i
$595$		0			0
$596$	11.4282	−	6.59808i	0.468117	−	0.270268i
$597$			14.1962i			0.581010i
$598$	14.5359	−	4.19615i	0.594417	−	0.171593i
$599$	2.53590			0.103614			0.0518070	−	0.998657i	$-0.483502\pi$
$599$	2.53590			0.103614			0.0518070	+	0.998657i	$0.483502\pi$
$600$		0			0
$601$	−3.96410	−	6.86603i	−0.161699	−	0.280071i	0.773779	−	0.633456i	$-0.218364\pi$
$601$	−3.96410	−	6.86603i	−0.161699	−	0.280071i	−0.935478	+	0.353385i	$0.885031\pi$
$602$	22.8564	+	13.1962i	0.931558	+	0.537835i
$603$	−13.1244			−0.534465
$604$	−5.83013	−	3.36603i	−0.237225	−	0.136962i
$605$		0			0
$606$			1.92820i			0.0783279i
$607$	35.3205	+	20.3923i	1.43362	+	0.827698i	0.997394	−	0.0721415i	$-0.0229833\pi$
$607$	35.3205	+	20.3923i	1.43362	+	0.827698i	0.436221	+	0.899840i	$0.356317\pi$
$608$	4.09808	−	2.36603i	0.166199	−	0.0959550i
$609$	−10.5622	+	6.09808i	−0.428001	+	0.247107i
$610$		0			0
$611$	5.49038	−	5.70577i	0.222117	−	0.230831i
$612$		−	5.73205i		−	0.231704i
$613$	−4.69615	−	8.13397i	−0.189676	−	0.328528i	0.755466	−	0.655187i	$-0.227410\pi$
$613$	−4.69615	−	8.13397i	−0.189676	−	0.328528i	−0.945142	+	0.326659i	$0.894077\pi$
$614$	−11.2942	−	19.5622i	−0.455798	−	0.789465i
$615$		0			0
$616$			3.46410i			0.139573i
$617$	6.62436	−	11.4737i	0.266687	−	0.461915i	−0.701318	−	0.712849i	$-0.747404\pi$
$617$	6.62436	−	11.4737i	0.266687	−	0.461915i	0.968004	+	0.250934i	$0.0807378\pi$
$618$	7.63397	−	13.2224i	0.307083	−	0.531884i
$619$		−	17.4641i		−	0.701942i	−0.936386	−	0.350971i	$-0.885852\pi$
$619$		−	17.4641i		−	0.701942i	0.936386	−	0.350971i	$-0.114148\pi$
$620$		0			0
$621$	2.09808	+	3.63397i	0.0841929	+	0.145826i
$622$	−0.830127	−	1.43782i	−0.0332851	−	0.0576514i
$623$			25.8564i			1.03592i
$624$	−3.46410	+	1.00000i	−0.138675	+	0.0400320i
$625$		0			0
$626$	−5.66025	+	3.26795i	−0.226229	+	0.130614i
$627$	5.19615	−	3.00000i	0.207514	−	0.119808i
$628$	−6.57180	−	3.79423i	−0.262243	−	0.151406i
$629$		−	20.2679i		−	0.808136i
$630$		0			0
$631$	6.67949	+	3.85641i	0.265906	+	0.153521i	0.627026	−	0.778998i	$-0.284272\pi$
$631$	6.67949	+	3.85641i	0.265906	+	0.153521i	−0.361119	+	0.932520i	$0.617605\pi$
$632$	2.53590			0.100873
$633$	14.1962	+	8.19615i	0.564246	+	0.325768i
$634$	−10.3301	−	17.8923i	−0.410262	−	0.710594i
$635$		0			0
$636$	6.46410			0.256318
$637$	1.62436	+	0.401924i	0.0643593	+	0.0159248i
$638$			5.66025i			0.224092i
$639$	4.09808	−	2.36603i	0.162117	−	0.0935985i
$640$		0			0
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	0.486796	+	0.873516i	$0.338166\pi$
$641$	−12.9904	+	22.5000i	−0.513089	+	0.888697i	−0.999885	+	0.0151806i	$0.995168\pi$
$642$	10.1962			0.402410
$643$	−6.92820	+	12.0000i	−0.273222	+	0.473234i	−0.969685	−	0.244359i	$-0.921423\pi$
$643$	−6.92820	+	12.0000i	−0.273222	+	0.473234i	0.696463	+	0.717592i	$0.254756\pi$
$644$	−9.92820	−	5.73205i	−0.391226	−	0.225874i
$645$		0			0
$646$	13.5622	−	23.4904i	0.533597	−	0.924217i
$647$	19.2679	−	11.1244i	0.757501	−	0.437344i	−0.0708966	−	0.997484i	$-0.522586\pi$
$647$	19.2679	−	11.1244i	0.757501	−	0.437344i	0.828398	+	0.560140i	$0.189253\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	10.1436			0.398171
$650$		0			0
$651$	−4.00000			−0.156772
$652$	6.73205	+	11.6603i	0.263647	+	0.456651i
$653$	15.1244	−	8.73205i	0.591862	−	0.341712i	−0.173972	−	0.984751i	$-0.555660\pi$
$653$	15.1244	−	8.73205i	0.591862	−	0.341712i	0.765833	+	0.643039i	$0.222327\pi$
$654$	−0.732051	+	1.26795i	−0.0286255	+	0.0495807i
$655$		0			0
$656$	−8.13397	−	4.69615i	−0.317578	−	0.183354i
$657$	−3.13397	+	5.42820i	−0.122268	+	0.211774i
$658$	−6.00000			−0.233904
$659$	−5.12436	+	8.87564i	−0.199617	+	0.345746i	−0.948404	−	0.317064i	$-0.897303\pi$
$659$	−5.12436	+	8.87564i	−0.199617	+	0.345746i	0.748788	+	0.662810i	$0.230636\pi$
$660$		0			0
$661$	9.86603	−	5.69615i	0.383744	−	0.221555i	−0.295702	−	0.955280i	$-0.595554\pi$
$661$	9.86603	−	5.69615i	0.383744	−	0.221555i	0.679446	+	0.733726i	$0.262220\pi$
$662$		−	20.0000i		−	0.777322i
$663$	−14.3301	+	14.8923i	−0.556536	+	0.578369i
$664$	0.196152			0.00761219
$665$		0			0
$666$	−1.76795	−	3.06218i	−0.0685066	−	0.118657i
$667$	−16.2224	−	9.36603i	−0.628135	−	0.362654i
$668$	9.46410			0.366177
$669$	23.3205	+	13.4641i	0.901623	+	0.520552i
$670$		0			0
$671$		−	11.6603i		−	0.450139i
$672$	2.36603	+	1.36603i	0.0912714	+	0.0526956i
$673$	24.1865	−	13.9641i	0.932322	−	0.538277i	0.0447770	−	0.998997i	$-0.485742\pi$
$673$	24.1865	−	13.9641i	0.932322	−	0.538277i	0.887545	+	0.460720i	$0.152409\pi$
$674$	18.0622	−	10.4282i	0.695729	−	0.401679i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$		−	45.4641i		−	1.74733i	−0.486530	−	0.873664i	$-0.661738\pi$
$677$		−	45.4641i		−	1.74733i	0.486530	−	0.873664i	$-0.338262\pi$
$678$	−0.669873	−	1.16025i	−0.0257263	−	0.0445593i
$679$	8.19615	+	14.1962i	0.314539	+	0.544798i
$680$		0			0
$681$			12.1962i			0.467358i
$682$	−0.928203	+	1.60770i	−0.0355427	+	0.0615618i
$683$	5.07180	−	8.78461i	0.194067	−	0.336134i	−0.752527	−	0.658561i	$-0.771165\pi$
$683$	5.07180	−	8.78461i	0.194067	−	0.336134i	0.946594	+	0.322427i	$0.104499\pi$
$684$		−	4.73205i		−	0.180934i
$685$		0			0
$686$	8.92820	+	15.4641i	0.340880	+	0.590422i
$687$	−5.92820	−	10.2679i	−0.226175	−	0.391747i
$688$		−	9.66025i		−	0.368294i
$689$	−16.7942	−	16.1603i	−0.639809	−	0.615657i
$690$		0			0
$691$	−37.8109	+	21.8301i	−1.43839	+	0.830457i	−0.997738	−	0.0672190i	$-0.978587\pi$
$691$	−37.8109	+	21.8301i	−1.43839	+	0.830457i	−0.440656	+	0.897676i	$0.645254\pi$
$692$	3.80385	−	2.19615i	0.144601	−	0.0834852i
$693$	3.00000	+	1.73205i	0.113961	+	0.0657952i
$694$			33.1244i			1.25738i
$695$		0			0
$696$	3.86603	+	2.23205i	0.146541	+	0.0846057i
$697$	−53.8372			−2.03923
$698$	13.2679	+	7.66025i	0.502199	+	0.289945i
$699$	3.92820	+	6.80385i	0.148578	+	0.257345i
$700$		0			0
$701$	3.32051			0.125414			0.0627069	−	0.998032i	$-0.480027\pi$
$701$	3.32051			0.125414			0.0627069	+	0.998032i	$0.480027\pi$
$702$	−0.866025	+	3.50000i	−0.0326860	+	0.132099i
$703$		−	16.7321i		−	0.631061i
$704$	1.09808	−	0.633975i	0.0413853	−	0.0238938i
$705$		0			0
$706$	−10.8923	+	18.8660i	−0.409937	+	0.710032i
$707$	−5.26795			−0.198122
$708$	4.00000	−	6.92820i	0.150329	−	0.260378i
$709$	11.3827	+	6.57180i	0.427486	+	0.246809i	0.698275	−	0.715830i	$-0.253951\pi$
$709$	11.3827	+	6.57180i	0.427486	+	0.246809i	−0.270789	+	0.962639i	$0.587285\pi$
$710$		0			0
$711$	1.26795	−	2.19615i	0.0475518	−	0.0823622i
$712$	8.19615	−	4.73205i	0.307164	−	0.177341i
$713$	−3.07180	−	5.32051i	−0.115040	−	0.199255i
$714$	15.6603			0.586070
$715$		0			0
$716$	−16.0526			−0.599912
$717$	−3.83013	−	6.63397i	−0.143039	−	0.247750i
$718$	0.973721	−	0.562178i	0.0363389	−	0.0209803i
$719$	14.7321	−	25.5167i	0.549413	−	0.951611i	−0.448902	−	0.893581i	$-0.648185\pi$
$719$	14.7321	−	25.5167i	0.549413	−	0.951611i	0.998315	−	0.0580299i	$-0.0184819\pi$
$720$		0			0
$721$	36.1244	+	20.8564i	1.34534	+	0.776733i
$722$	1.69615	−	2.93782i	0.0631243	−	0.109334i
$723$	13.5885			0.505360
$724$	9.59808	−	16.6244i	0.356710	−	0.617839i
$725$		0			0
$726$	−8.13397	+	4.69615i	−0.301880	+	0.174291i
$727$			30.9808i			1.14901i	0.818500	+	0.574506i	$0.194806\pi$
$727$			30.9808i			1.14901i	−0.818500	+	0.574506i	$0.805194\pi$
$728$	−2.73205	−	9.46410i	−0.101257	−	0.350763i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−27.6865	−	47.9545i	−1.02402	−	1.77366i
$732$	−7.96410	−	4.59808i	−0.294362	−	0.169950i
$733$	−19.0000			−0.701781			−0.350891	−	0.936416i	$-0.614121\pi$
$733$	−19.0000			−0.701781			−0.350891	+	0.936416i	$0.614121\pi$
$734$	9.75833	+	5.63397i	0.360187	+	0.207954i
$735$		0			0
$736$			4.19615i			0.154672i
$737$	−14.4115	−	8.32051i	−0.530856	−	0.306490i
$738$	−8.13397	+	4.69615i	−0.299416	+	0.172868i
$739$	−2.53590	+	1.46410i	−0.0932845	+	0.0538578i	−0.545917	−	0.837840i	$-0.683818\pi$
$739$	−2.53590	+	1.46410i	−0.0932845	+	0.0538578i	0.452632	+	0.891697i	$0.350485\pi$
$740$		0			0
$741$	−11.8301	+	12.2942i	−0.434591	+	0.451640i
$742$			17.6603i			0.648328i
$743$	−24.1962	−	41.9090i	−0.887671	−	1.53749i	−0.842622	−	0.538506i	$-0.818989\pi$
$743$	−24.1962	−	41.9090i	−0.887671	−	1.53749i	−0.0450491	−	0.998985i	$-0.514344\pi$
$744$	0.732051	+	1.26795i	0.0268383	+	0.0464853i
$745$		0			0
$746$			13.7321i			0.502766i
$747$	0.0980762	−	0.169873i	0.00358842	−	0.00621533i
$748$	3.63397	−	6.29423i	0.132871	−	0.230140i
$749$			27.8564i			1.01785i
$750$		0			0
$751$	−24.9545	−	43.2224i	−0.910602	−	1.57721i	−0.813216	−	0.581962i	$-0.802285\pi$
$751$	−24.9545	−	43.2224i	−0.910602	−	1.57721i	−0.0973862	−	0.995247i	$-0.531048\pi$
$752$	1.09808	+	1.90192i	0.0400427	+	0.0693560i
$753$			13.4641i			0.490659i
$754$	−4.46410	−	15.4641i	−0.162573	−	0.563169i
$755$		0			0
$756$	2.36603	−	1.36603i	0.0860515	−	0.0496819i
$757$	18.1244	−	10.4641i	0.658741	−	0.380324i	−0.133056	−	0.991109i	$-0.542479\pi$
$757$	18.1244	−	10.4641i	0.658741	−	0.380324i	0.791797	+	0.610784i	$0.209146\pi$
$758$	4.73205	+	2.73205i	0.171876	+	0.0992326i
$759$			5.32051i			0.193122i
$760$		0			0
$761$	−9.80385	−	5.66025i	−0.355389	−	0.205184i	0.311667	−	0.950191i	$-0.399113\pi$
$761$	−9.80385	−	5.66025i	−0.355389	−	0.205184i	−0.667056	+	0.745007i	$0.732446\pi$
$762$	9.85641			0.357060
$763$	−3.46410	−	2.00000i	−0.125409	−	0.0724049i
$764$	3.46410	+	6.00000i	0.125327	+	0.217072i
$765$		0			0
$766$	1.46410			0.0529001
$767$	−27.7128	+	8.00000i	−1.00065	+	0.288863i
$768$		−	1.00000i		−	0.0360844i
$769$	−37.9808	+	21.9282i	−1.36962	+	0.790751i	−0.990879	−	0.134751i	$-0.956977\pi$
$769$	−37.9808	+	21.9282i	−1.36962	+	0.790751i	−0.378742	+	0.925502i	$0.623643\pi$
$770$		0			0
$771$	4.66987	−	8.08846i	0.168181	−	0.291299i
$772$	−11.7321			−0.422246
$773$	−24.4641	+	42.3731i	−0.879913	+	1.52405i	−0.0284768	+	0.999594i	$0.509066\pi$
$773$	−24.4641	+	42.3731i	−0.879913	+	1.52405i	−0.851436	+	0.524459i	$0.824268\pi$
$774$	−8.36603	−	4.83013i	−0.300711	−	0.173615i
$775$		0			0
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	8.36603	−	4.83013i	0.300129	−	0.173280i
$778$	−5.89230	−	10.2058i	−0.211249	−	0.365895i
$779$	−44.4449			−1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$	12.0263	+	20.8301i	0.430059	+	0.744884i
$783$	3.86603	−	2.23205i	0.138160	−	0.0797670i
$784$	−0.232051	+	0.401924i	−0.00828753	+	0.0143544i
$785$		0			0
$786$	5.66025	+	3.26795i	0.201895	+	0.116564i
$787$	2.33975	−	4.05256i	0.0834029	−	0.144458i	−0.821307	−	0.570487i	$-0.806754\pi$
$787$	2.33975	−	4.05256i	0.0834029	−	0.144458i	0.904710	+	0.426029i	$0.140088\pi$
$788$	−17.8564			−0.636108
$789$	−5.02628	+	8.70577i	−0.178940	+	0.309934i
$790$		0			0
$791$	3.16987	−	1.83013i	0.112708	−	0.0650718i
$792$		−	1.26795i		−	0.0450546i
$793$	9.19615	+	31.8564i	0.326565	+	1.13125i
$794$	−20.3923			−0.723696
$795$		0			0
$796$	7.09808	+	12.2942i	0.251585	+	0.435757i
$797$	−29.4449	−	17.0000i	−1.04299	−	0.602171i	−0.122312	−	0.992492i	$-0.539031\pi$
$797$	−29.4449	−	17.0000i	−1.04299	−	0.602171i	−0.920679	+	0.390321i	$0.872364\pi$
$798$	12.9282			0.457653
$799$	10.9019	+	6.29423i	0.385682	+	0.222674i
$800$		0			0
$801$		−	9.46410i		−	0.334398i
$802$	−6.99038	−	4.03590i	−0.246839	−	0.142513i
$803$	−6.88269	+	3.97372i	−0.242885	+	0.140230i
$804$	−11.3660	+	6.56218i	−0.400849	+	0.231430i
$805$		0			0
$806$	1.26795	−	5.12436i	0.0446616	−	0.180498i
$807$			5.46410i			0.192345i
$808$	0.964102	+	1.66987i	0.0339170	+	0.0587459i
$809$	−26.7942	−	46.4090i	−0.942035	−	1.63165i	−0.761582	−	0.648069i	$-0.775577\pi$
$809$	−26.7942	−	46.4090i	−0.942035	−	1.63165i	−0.180453	−	0.983584i	$-0.557756\pi$
$810$		0			0
$811$		−	17.1769i		−	0.603163i	−0.953440	−	0.301582i	$-0.902485\pi$
$811$		−	17.1769i		−	0.603163i	0.953440	−	0.301582i	$-0.0975145\pi$
$812$	−6.09808	+	10.5622i	−0.214001	+	0.370660i
$813$	10.9282	−	18.9282i	0.383269	−	0.663841i
$814$		−	4.48334i		−	0.157141i
$815$		0			0
$816$	−2.86603	−	4.96410i	−0.100331	−	0.173778i
$817$	−22.8564	−	39.5885i	−0.799644	−	1.38502i
$818$			17.7321i			0.619987i
$819$	−9.56218	−	2.36603i	−0.334130	−	0.0826756i
$820$		0			0
$821$	0.803848	−	0.464102i	0.0280545	−	0.0161973i	−0.485907	−	0.874010i	$-0.661511\pi$
$821$	0.803848	−	0.464102i	0.0280545	−	0.0161973i	0.513962	+	0.857813i	$0.328177\pi$
$822$	10.3301	−	5.96410i	0.360305	−	0.208022i
$823$	−36.0000	−	20.7846i	−1.25488	−	0.724506i	−0.282806	−	0.959177i	$-0.591265\pi$
$823$	−36.0000	−	20.7846i	−1.25488	−	0.724506i	−0.972075	+	0.234671i	$0.924599\pi$
$824$		−	15.2679i		−	0.531884i
$825$		0			0
$826$	18.9282	+	10.9282i	0.658596	+	0.380241i
$827$	−26.5359			−0.922744			−0.461372	−	0.887207i	$-0.652643\pi$
$827$	−26.5359			−0.922744			−0.461372	+	0.887207i	$0.652643\pi$
$828$	3.63397	+	2.09808i	0.126289	+	0.0729132i
$829$	6.06218	+	10.5000i	0.210548	+	0.364680i	0.951886	−	0.306452i	$-0.0991418\pi$
$829$	6.06218	+	10.5000i	0.210548	+	0.364680i	−0.741338	+	0.671132i	$0.765808\pi$
$830$		0			0
$831$	5.73205			0.198843
$832$	−2.50000	+	2.59808i	−0.0866719	+	0.0900721i
$833$			2.66025i			0.0921723i
$834$	15.4641	−	8.92820i	0.535478	−	0.309158i
$835$		0			0
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$	1.46410			0.0506068
$838$	−8.73205	+	15.1244i	−0.301644	+	0.522462i
$839$	36.2487	+	20.9282i	1.25144	+	0.722522i	0.971396	−	0.237464i	$-0.0763162\pi$
$839$	36.2487	+	20.9282i	1.25144	+	0.722522i	0.280048	+	0.959986i	$0.409650\pi$
$840$		0			0
$841$	4.53590	−	7.85641i	0.156410	−	0.270911i
$842$	19.6699	−	11.3564i	0.677869	−	0.391368i
$843$	−6.16025	−	10.6699i	−0.212170	−	0.367490i
$844$	16.3923			0.564246
$845$		0			0
$846$	2.19615			0.0755053
$847$	−12.8301	−	22.2224i	−0.440848	−	0.763572i
$848$	5.59808	−	3.23205i	0.192239	−	0.110989i
$849$	−12.8301	+	22.2224i	−0.440329	+	0.762672i
$850$		0			0
$851$	12.8494	+	7.41858i	0.440471	+	0.254306i
$852$	2.36603	−	4.09808i	0.0810587	−	0.140398i
$853$	−54.1769			−1.85498			−0.927491	−	0.373845i	$-0.878039\pi$
$853$	−54.1769			−1.85498			−0.927491	+	0.373845i	$0.878039\pi$
$854$	12.5622	−	21.7583i	0.429869	−	0.744555i
$855$		0			0
$856$	8.83013	−	5.09808i	0.301808	−	0.174249i
$857$		−	39.4449i		−	1.34741i	−0.739000	−	0.673705i	$-0.764702\pi$
$857$		−	39.4449i		−	1.34741i	0.739000	−	0.673705i	$-0.235298\pi$
$858$	−3.16987	+	3.29423i	−0.108218	+	0.112463i
$859$	47.1244			1.60786			0.803931	−	0.594722i	$-0.202738\pi$
$859$	47.1244			1.60786			0.803931	+	0.594722i	$0.202738\pi$
$860$		0			0
$861$	−12.8301	−	22.2224i	−0.437250	−	0.757338i
$862$	11.3660	+	6.56218i	0.387128	+	0.223509i
$863$	17.1244			0.582920			0.291460	−	0.956583i	$-0.405859\pi$
$863$	17.1244			0.582920			0.291460	+	0.956583i	$0.405859\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			12.8564i			0.436878i
$867$	−13.7321	−	7.92820i	−0.466365	−	0.269256i
$868$	−3.46410	+	2.00000i	−0.117579	+	0.0678844i
$869$	2.78461	−	1.60770i	0.0944614	−	0.0545373i
$870$		0			0
$871$	45.9352	+	11.3660i	1.55646	+	0.385123i
$872$			1.46410i			0.0495807i
$873$	−3.00000	−	5.19615i	−0.101535	−	0.175863i
$874$	9.92820	+	17.1962i	0.335826	+	0.581669i
$875$		0			0
$876$			6.26795i			0.211774i
$877$	−11.9641	+	20.7224i	−0.403999	+	0.699747i	−0.994204	−	0.107506i	$-0.965713\pi$
$877$	−11.9641	+	20.7224i	−0.403999	+	0.699747i	0.590205	+	0.807253i	$0.299047\pi$
$878$	0.169873	−	0.294229i	0.00573294	−	0.00992974i
$879$		−	30.5167i		−	1.02930i
$880$		0			0
$881$	−13.9186	−	24.1077i	−0.468929	−	0.812209i	0.530440	−	0.847722i	$-0.322027\pi$
$881$	−13.9186	−	24.1077i	−0.468929	−	0.812209i	−0.999369	+	0.0355135i	$0.988693\pi$
$882$	0.232051	+	0.401924i	0.00781356	+	0.0135335i
$883$			42.9282i			1.44465i	0.691554	+	0.722325i	$0.256926\pi$
$883$			42.9282i			1.44465i	−0.691554	+	0.722325i	$0.743074\pi$
$884$	−4.96410	+	20.0622i	−0.166961	+	0.674764i
$885$		0			0
$886$	−13.5167	+	7.80385i	−0.454101	+	0.262175i
$887$	32.7846	−	18.9282i	1.10080	−	0.635547i	0.164369	−	0.986399i	$-0.447441\pi$
$887$	32.7846	−	18.9282i	1.10080	−	0.635547i	0.936431	+	0.350852i	$0.114108\pi$
$888$	−3.06218	−	1.76795i	−0.102760	−	0.0593285i
$889$			26.9282i			0.903143i
$890$		0			0
$891$	−1.09808	−	0.633975i	−0.0367869	−	0.0212389i
$892$	26.9282			0.901623
$893$	9.00000	+	5.19615i	0.301174	+	0.173883i
$894$	−6.59808	−	11.4282i	−0.220673	−	0.382216i
$895$		0			0
$896$	2.73205			0.0912714
$897$	−4.19615	−	14.5359i	−0.140105	−	0.485340i
$898$		−	11.3205i		−	0.377770i
$899$	−5.66025	+	3.26795i	−0.188780	+	0.108992i
$900$		0			0
$901$	18.5263	−	32.0885i	0.617200	−	1.06902i
$902$	−11.9090			−0.396525
$903$	13.1962	−	22.8564i	0.439140	−	0.760614i
$904$	−1.16025	−	0.669873i	−0.0385895	−	0.0222796i
$905$		0			0
$906$	−3.36603	+	5.83013i	−0.111829	+	0.193693i
$907$	−31.5167	+	18.1962i	−1.04649	+	0.604193i	−0.921666	−	0.387985i	$-0.873171\pi$
$907$	−31.5167	+	18.1962i	−1.04649	+	0.604193i	−0.124828	+	0.992178i	$0.539838\pi$
$908$	6.09808	+	10.5622i	0.202372	+	0.350518i
$909$	1.92820			0.0639545
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$	−2.36603	−	4.09808i	−0.0783469	−	0.135701i
$913$	0.215390	−	0.124356i	0.00712838	−	0.00411557i
$914$	−0.669873	+	1.16025i	−0.0221574	+	0.0383778i
$915$		0			0
$916$	−10.2679	−	5.92820i	−0.339263	−	0.195873i
$917$	−8.92820	+	15.4641i	−0.294835	+	0.510670i
$918$	−5.73205			−0.189186
$919$	22.9808	−	39.8038i	0.758065	−	1.31301i	−0.185770	−	0.982593i	$-0.559478\pi$
$919$	22.9808	−	39.8038i	0.758065	−	1.31301i	0.943836	−	0.330415i	$-0.107189\pi$
$920$		0			0
$921$	−19.5622	+	11.2942i	−0.644596	+	0.372157i
$922$		−	22.2679i		−	0.733356i
$923$	−16.3923	+	4.73205i	−0.539559	+	0.155757i
$924$	3.46410			0.113961
$925$		0			0
$926$	−5.02628	−	8.70577i	−0.165174	−	0.286089i
$927$	−13.2224	−	7.63397i	−0.434282	−	0.250733i
$928$	4.46410			0.146541
$929$	33.9904	+	19.6244i	1.11519	+	0.643854i	0.940168	−	0.340711i	$-0.110668\pi$
$929$	33.9904	+	19.6244i	1.11519	+	0.643854i	0.175020	+	0.984565i	$0.444001\pi$
$930$		0			0
$931$			2.19615i			0.0719760i
$932$	6.80385	+	3.92820i	0.222867	+	0.128673i
$933$	−1.43782	+	0.830127i	−0.0470722	+	0.0271771i
$934$	−16.0981	+	9.29423i	−0.526745	+	0.304116i
$935$		0			0
$936$	1.00000	+	3.46410i	0.0326860	+	0.113228i
$937$		−	5.24871i		−	0.171468i	−0.996318	−	0.0857340i	$-0.972676\pi$
$937$		−	5.24871i		−	0.171468i	0.996318	−	0.0857340i	$-0.0273235\pi$
$938$	−17.9282	−	31.0526i	−0.585377	−	1.01390i
$939$	3.26795	+	5.66025i	0.106645	+	0.184715i
$940$		0			0
$941$		−	12.6410i		−	0.412085i	−0.978543	−	0.206043i	$-0.933941\pi$
$941$		−	12.6410i		−	0.412085i	0.978543	−	0.206043i	$-0.0660586\pi$
$942$	−3.79423	+	6.57180i	−0.123623	+	0.214121i
$943$	19.7058	−	34.1314i	0.641708	−	1.11147i
$944$		−	8.00000i		−	0.260378i
$945$		0			0
$946$	−6.12436	−	10.6077i	−0.199120	−	0.344886i
$947$	10.5359	+	18.2487i	0.342371	+	0.593003i	0.984872	−	0.173281i	$-0.0554368\pi$
$947$	10.5359	+	18.2487i	0.342371	+	0.593003i	−0.642502	+	0.766284i	$0.722103\pi$
$948$		−	2.53590i		−	0.0823622i
$949$	15.6699	−	16.2846i	0.508666	−	0.528621i
$950$		0			0
$951$	−17.8923	+	10.3301i	−0.580198	+	0.334977i
$952$	13.5622	−	7.83013i	0.439553	−	0.253776i
$953$	−36.0000	−	20.7846i	−1.16615	−	0.673280i	−0.213383	−	0.976969i	$-0.568448\pi$
$953$	−36.0000	−	20.7846i	−1.16615	−	0.673280i	−0.952771	+	0.303689i	$0.901782\pi$
$954$		−	6.46410i		−	0.209283i
$955$		0			0
$956$	−6.63397	−	3.83013i	−0.214558	−	0.123875i
$957$	5.66025			0.182970
$958$	28.9808	+	16.7321i	0.936326	+	0.540588i
$959$	16.2942	+	28.2224i	0.526168	+	0.911350i
$960$		0			0
$961$	28.8564			0.930852
$962$	3.53590	+	12.2487i	0.114002	+	0.394914i
$963$		−	10.1962i		−	0.328566i
$964$	11.7679	−	6.79423i	0.379020	−	0.218827i
$965$		0			0
$966$	−5.73205	+	9.92820i	−0.184426	+	0.319435i
$967$	−43.1244			−1.38679			−0.693393	−	0.720560i	$-0.743885\pi$
$967$	−43.1244			−1.38679			−0.693393	+	0.720560i	$0.743885\pi$
$968$	−4.69615	+	8.13397i	−0.150940	+	0.261436i
$969$	−23.4904	−	13.5622i	−0.754620	−	0.435680i
$970$		0			0
$971$	−15.1244	+	26.1962i	−0.485364	+	0.840675i	−0.999859	−	0.0168189i	$-0.994646\pi$
$971$	−15.1244	+	26.1962i	−0.485364	+	0.840675i	0.514495	+	0.857493i	$0.327979\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	24.3923	+	42.2487i	0.781981	+	1.35443i
$974$	−3.12436			−0.100111
$975$		0			0
$976$	−9.19615			−0.294362
$977$	−22.9641	−	39.7750i	−0.734687	−	1.27251i	−0.954861	−	0.297054i	$-0.903996\pi$
$977$	−22.9641	−	39.7750i	−0.734687	−	1.27251i	0.220174	−	0.975461i	$-0.429337\pi$
$978$	11.6603	−	6.73205i	0.372854	−	0.215267i
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	1.26795	+	0.732051i	0.0404825	+	0.0233726i
$982$	4.36603	−	7.56218i	0.139325	−	0.241319i
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$	−4.69615	+	8.13397i	−0.149708	+	0.259302i
$985$		0			0
$986$	22.1603	−	12.7942i	0.705726	−	0.407451i
$987$			6.00000i			0.190982i
$988$	−4.09808	+	16.5622i	−0.130377	+	0.526913i
$989$	40.5359			1.28897
$990$		0			0
$991$	−11.2942	−	19.5622i	−0.358773	−	0.621413i	0.628983	−	0.777419i	$-0.283471\pi$
$991$	−11.2942	−	19.5622i	−0.358773	−	0.621413i	−0.987756	+	0.156006i	$0.950138\pi$
$992$	1.26795	+	0.732051i	0.0402574	+	0.0232426i
$993$	−20.0000			−0.634681
$994$	11.1962	+	6.46410i	0.355120	+	0.205029i
$995$		0			0
$996$		−	0.196152i		−	0.00621533i
$997$	−18.4808	−	10.6699i	−0.585292	−	0.337918i	0.177942	−	0.984041i	$-0.443056\pi$
$997$	−18.4808	−	10.6699i	−0.585292	−	0.337918i	−0.763234	+	0.646123i	$0.776389\pi$
$998$	27.7128	−	16.0000i	0.877234	−	0.506471i
$999$	−3.06218	+	1.76795i	−0.0968830	+	0.0559354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.y.b.49.1		4
5.2	odd	4		1950.2.bc.d.751.2		4
5.3	odd	4		78.2.i.a.49.1	yes	4
5.4	even	2		1950.2.y.g.49.2		4
13.4	even	6		1950.2.y.g.199.2		4
15.8	even	4		234.2.l.c.127.2		4
20.3	even	4		624.2.bv.e.49.1		4
60.23	odd	4		1872.2.by.h.1297.2		4
65.3	odd	12		1014.2.b.e.337.1		4
65.4	even	6	inner	1950.2.y.b.199.1		4
65.8	even	4		1014.2.e.g.991.2		4
65.17	odd	12		1950.2.bc.d.901.2		4
65.18	even	4		1014.2.e.i.991.1		4
65.23	odd	12		1014.2.b.e.337.4		4
65.28	even	12		1014.2.a.i.1.1		2
65.33	even	12		1014.2.e.g.529.2		4
65.38	odd	4		1014.2.i.a.361.2		4
65.43	odd	12		78.2.i.a.43.1	✓	4
65.48	odd	12		1014.2.i.a.823.2		4
65.58	even	12		1014.2.e.i.529.1		4
65.63	even	12		1014.2.a.k.1.2		2
195.23	even	12		3042.2.b.i.1351.1		4
195.68	even	12		3042.2.b.i.1351.4		4
195.128	odd	12		3042.2.a.p.1.1		2
195.158	odd	12		3042.2.a.y.1.2		2
195.173	even	12		234.2.l.c.199.2		4
260.43	even	12		624.2.bv.e.433.2		4
260.63	odd	12		8112.2.a.bp.1.2		2
260.223	odd	12		8112.2.a.bj.1.1		2
780.563	odd	12		1872.2.by.h.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	65.43	odd	12
78.2.i.a.49.1	yes	4	5.3	odd	4
234.2.l.c.127.2		4	15.8	even	4
234.2.l.c.199.2		4	195.173	even	12
624.2.bv.e.49.1		4	20.3	even	4
624.2.bv.e.433.2		4	260.43	even	12
1014.2.a.i.1.1		2	65.28	even	12
1014.2.a.k.1.2		2	65.63	even	12
1014.2.b.e.337.1		4	65.3	odd	12
1014.2.b.e.337.4		4	65.23	odd	12
1014.2.e.g.529.2		4	65.33	even	12
1014.2.e.g.991.2		4	65.8	even	4
1014.2.e.i.529.1		4	65.58	even	12
1014.2.e.i.991.1		4	65.18	even	4
1014.2.i.a.361.2		4	65.38	odd	4
1014.2.i.a.823.2		4	65.48	odd	12
1872.2.by.h.433.1		4	780.563	odd	12
1872.2.by.h.1297.2		4	60.23	odd	4
1950.2.y.b.49.1		4	1.1	even	1	trivial
1950.2.y.b.199.1		4	65.4	even	6	inner
1950.2.y.g.49.2		4	5.4	even	2
1950.2.y.g.199.2		4	13.4	even	6
1950.2.bc.d.751.2		4	5.2	odd	4
1950.2.bc.d.901.2		4	65.17	odd	12
3042.2.a.p.1.1		2	195.128	odd	12
3042.2.a.y.1.2		2	195.158	odd	12
3042.2.b.i.1351.1		4	195.23	even	12
3042.2.b.i.1351.4		4	195.68	even	12
8112.2.a.bj.1.1		2	260.223	odd	12
8112.2.a.bp.1.2		2	260.63	odd	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.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.36603 + 2.36603i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.09808 - 0.633975i) q^{11} -1.00000i q^{12} +(-2.50000 + 2.59808i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.96410 - 2.86603i) q^{17} -1.00000 q^{18} +(-4.09808 - 2.36603i) q^{19} -2.73205i q^{21} +(-1.09808 - 0.633975i) q^{22} +(3.63397 - 2.09808i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.50000 + 0.866025i) q^{26} +1.00000i q^{27} +(-1.36603 - 2.36603i) q^{28} +(-2.23205 - 3.86603i) q^{29} -1.46410i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.633975 + 1.09808i) q^{33} +5.73205i q^{34} +(0.500000 + 0.866025i) q^{36} +(1.76795 + 3.06218i) q^{37} +4.73205i q^{38} +(0.866025 - 3.50000i) q^{39} +(8.13397 - 4.69615i) q^{41} +(-2.36603 + 1.36603i) q^{42} +(8.36603 + 4.83013i) q^{43} +1.26795i q^{44} +(-3.63397 - 2.09808i) q^{46} -2.19615 q^{47} +(0.866025 + 0.500000i) q^{48} +(-0.232051 - 0.401924i) q^{49} +5.73205 q^{51} +(-1.00000 - 3.46410i) q^{52} +6.46410i q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.36603 + 2.36603i) q^{56} +4.73205 q^{57} +(-2.23205 + 3.86603i) q^{58} +(6.92820 + 4.00000i) q^{59} +(4.59808 - 7.96410i) q^{61} +(-1.26795 + 0.732051i) q^{62} +(1.36603 + 2.36603i) q^{63} +1.00000 q^{64} +1.26795 q^{66} +(-6.56218 - 11.3660i) q^{67} +(4.96410 - 2.86603i) q^{68} +(-2.09808 + 3.63397i) q^{69} +(4.09808 + 2.36603i) q^{71} +(0.500000 - 0.866025i) q^{72} -6.26795 q^{73} +(1.76795 - 3.06218i) q^{74} +(4.09808 - 2.36603i) q^{76} +3.46410i q^{77} +(-3.46410 + 1.00000i) q^{78} +2.53590 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-8.13397 - 4.69615i) q^{82} +0.196152 q^{83} +(2.36603 + 1.36603i) q^{84} -9.66025i q^{86} +(3.86603 + 2.23205i) q^{87} +(1.09808 - 0.633975i) q^{88} +(8.19615 - 4.73205i) q^{89} +(-2.73205 - 9.46410i) q^{91} +4.19615i q^{92} +(0.732051 + 1.26795i) q^{93} +(1.09808 + 1.90192i) q^{94} -1.00000i q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.232051 + 0.401924i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{11} - 10 q^{13} + 4 q^{14} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} + 6 q^{22} + 18 q^{23} + 14 q^{26} - 2 q^{28} - 2 q^{29} - 2 q^{32} - 6 q^{33} + 2 q^{36} + 14 q^{37} + 36 q^{41} - 6 q^{42} + 30 q^{43} - 18 q^{46} + 12 q^{47} + 6 q^{49} + 16 q^{51} - 4 q^{52} - 2 q^{56} + 12 q^{57} - 2 q^{58} + 8 q^{61} - 12 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 6 q^{68} + 2 q^{69} + 6 q^{71} + 2 q^{72} - 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} - 36 q^{82} - 20 q^{83} + 6 q^{84} + 12 q^{87} - 6 q^{88} + 12 q^{89} - 4 q^{91} - 4 q^{93} - 6 q^{94} + 12 q^{97} + 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^11 - 10 * q^13 + 4 * q^14 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 + 6 * q^22 + 18 * q^23 + 14 * q^26 - 2 * q^28 - 2 * q^29 - 2 * q^32 - 6 * q^33 + 2 * q^36 + 14 * q^37 + 36 * q^41 - 6 * q^42 + 30 * q^43 - 18 * q^46 + 12 * q^47 + 6 * q^49 + 16 * q^51 - 4 * q^52 - 2 * q^56 + 12 * q^57 - 2 * q^58 + 8 * q^61 - 12 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^66 - 2 * q^67 + 6 * q^68 + 2 * q^69 + 6 * q^71 + 2 * q^72 - 32 * q^73 + 14 * q^74 + 6 * q^76 + 24 * q^79 - 2 * q^81 - 36 * q^82 - 20 * q^83 + 6 * q^84 + 12 * q^87 - 6 * q^88 + 12 * q^89 - 4 * q^91 - 4 * q^93 - 6 * q^94 + 12 * q^97 + 6 * q^98

Introduction

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