LMFDB - Embedded newform 234.2.l.c.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(127,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("234.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.l (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:	$1.86849940730$
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			199.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.199
Dual form			234.2.l.c.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(2.36603 - 1.36603i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(2.36603 - 1.36603i) q^{7} +1.00000i q^{8} +(1.86603 - 3.23205i) q^{10} +(-1.09808 - 0.633975i) q^{11} +(-2.59808 + 2.50000i) q^{13} +2.73205 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} +(4.09808 - 2.36603i) q^{19} +(3.23205 - 1.86603i) q^{20} +(-0.633975 - 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} -8.92820 q^{25} +(-3.50000 + 0.866025i) q^{26} +(2.36603 + 1.36603i) q^{28} +(-2.23205 + 3.86603i) q^{29} +1.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +5.73205i q^{34} +(-5.09808 - 8.83013i) q^{35} +(3.06218 + 1.76795i) q^{37} +4.73205 q^{38} +3.73205 q^{40} +(-8.13397 - 4.69615i) q^{41} +(-4.83013 - 8.36603i) q^{43} -1.26795i q^{44} +(-3.63397 + 2.09808i) q^{46} +2.19615i q^{47} +(0.232051 - 0.401924i) q^{49} +(-7.73205 - 4.46410i) q^{50} +(-3.46410 - 1.00000i) q^{52} +6.46410 q^{53} +(-2.36603 + 4.09808i) q^{55} +(1.36603 + 2.36603i) q^{56} +(-3.86603 + 2.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} -1.00000 q^{64} +(9.33013 + 9.69615i) q^{65} +(-11.3660 - 6.56218i) q^{67} +(-2.86603 + 4.96410i) q^{68} -10.1962i q^{70} +(-4.09808 + 2.36603i) q^{71} +6.26795i q^{73} +(1.76795 + 3.06218i) q^{74} +(4.09808 + 2.36603i) q^{76} -3.46410 q^{77} -2.53590 q^{79} +(3.23205 + 1.86603i) q^{80} +(-4.69615 - 8.13397i) q^{82} +0.196152i q^{83} +(18.5263 - 10.6962i) q^{85} -9.66025i q^{86} +(0.633975 - 1.09808i) q^{88} +(8.19615 + 4.73205i) q^{89} +(-2.73205 + 9.46410i) q^{91} -4.19615 q^{92} +(-1.09808 + 1.90192i) q^{94} +(-8.83013 - 15.2942i) q^{95} +(-5.19615 + 3.00000i) q^{97} +(0.401924 - 0.232051i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 6 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 6 * q^7	$ 4 q + 2 q^{4} + 6 q^{7} + 4 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 2 q^{23} - 8 q^{25} - 14 q^{26} + 6 q^{28} - 2 q^{29} - 10 q^{35} - 12 q^{37} + 12 q^{38} + 8 q^{40} - 36 q^{41} - 2 q^{43} - 18 q^{46} - 6 q^{49} - 24 q^{50} + 12 q^{53} - 6 q^{55} + 2 q^{56} - 12 q^{58} + 8 q^{61} + 4 q^{62} - 4 q^{64} + 20 q^{65} - 42 q^{67} - 8 q^{68} - 6 q^{71} + 14 q^{74} + 6 q^{76} - 24 q^{79} + 6 q^{80} + 2 q^{82} + 36 q^{85} + 6 q^{88} + 12 q^{89} - 4 q^{91} + 4 q^{92} + 6 q^{94} - 18 q^{95} + 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^4 + 6 * q^7 + 4 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 2 * q^23 - 8 * q^25 - 14 * q^26 + 6 * q^28 - 2 * q^29 - 10 * q^35 - 12 * q^37 + 12 * q^38 + 8 * q^40 - 36 * q^41 - 2 * q^43 - 18 * q^46 - 6 * q^49 - 24 * q^50 + 12 * q^53 - 6 * q^55 + 2 * q^56 - 12 * q^58 + 8 * q^61 + 4 * q^62 - 4 * q^64 + 20 * q^65 - 42 * q^67 - 8 * q^68 - 6 * q^71 + 14 * q^74 + 6 * q^76 - 24 * q^79 + 6 * q^80 + 2 * q^82 + 36 * q^85 + 6 * q^88 + 12 * q^89 - 4 * q^91 + 4 * q^92 + 6 * q^94 - 18 * q^95 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	3.73205i		−	1.66902i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$		−	3.73205i		−	1.66902i	0.550990	−	0.834512i	$-0.314250\pi$
$6$		0			0
$7$	2.36603	−	1.36603i	0.894274	−	0.516309i	0.0189356	−	0.999821i	$-0.493972\pi$
$7$	2.36603	−	1.36603i	0.894274	−	0.516309i	0.875338	+	0.483512i	$0.160639\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.86603	−	3.23205i	0.590089	−	1.02206i
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	0.325239	−	0.945632i	$-0.394555\pi$
$11$	−1.09808	−	0.633975i	−0.331082	−	0.191151i	−0.656322	+	0.754481i	$0.727889\pi$
$12$		0			0
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$	2.73205			0.730171
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	2.86603	+	4.96410i	0.695113	+	1.20397i	−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.0501517	−	0.998742i	$-0.484030\pi$
$19$	4.09808	−	2.36603i	0.940163	−	0.542803i	0.890011	+	0.455938i	$0.150696\pi$
$20$	3.23205	−	1.86603i	0.722709	−	0.417256i
$21$		0			0
$22$	−0.633975	−	1.09808i	−0.135164	−	0.234111i
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	−0.997494	−	0.0707462i	$-0.977462\pi$
$23$	−2.09808	+	3.63397i	−0.437479	+	0.757736i	0.560015	+	0.828482i	$0.310795\pi$
$24$		0			0
$25$	−8.92820			−1.78564
$26$	−3.50000	+	0.866025i	−0.686406	+	0.169842i
$27$		0			0
$28$	2.36603	+	1.36603i	0.447137	+	0.258155i
$29$	−2.23205	+	3.86603i	−0.414481	+	0.717903i	−0.995374	−	0.0960774i	$-0.969370\pi$
$29$	−2.23205	+	3.86603i	−0.414481	+	0.717903i	0.580892	+	0.813980i	$0.302704\pi$
$30$		0			0
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			5.73205i			0.983039i
$35$	−5.09808	−	8.83013i	−0.861732	−	1.49256i
$36$		0			0
$37$	3.06218	+	1.76795i	0.503419	+	0.290649i	0.730124	−	0.683314i	$-0.239462\pi$
$37$	3.06218	+	1.76795i	0.503419	+	0.290649i	−0.226705	+	0.973963i	$0.572795\pi$
$38$	4.73205			0.767640
$39$		0			0
$40$	3.73205			0.590089
$41$	−8.13397	−	4.69615i	−1.27031	−	0.733416i	−0.295267	−	0.955415i	$-0.595408\pi$
$41$	−8.13397	−	4.69615i	−1.27031	−	0.733416i	−0.975047	+	0.221999i	$0.928742\pi$
$42$		0			0
$43$	−4.83013	−	8.36603i	−0.736587	−	1.27581i	−0.954023	−	0.299732i	$-0.903103\pi$
$43$	−4.83013	−	8.36603i	−0.736587	−	1.27581i	0.217436	−	0.976075i	$-0.430231\pi$
$44$		−	1.26795i		−	0.191151i
$45$		0			0
$46$	−3.63397	+	2.09808i	−0.535800	+	0.309344i
$47$			2.19615i			0.320342i	0.987089	+	0.160171i	$0.0512045\pi$
$47$			2.19615i			0.320342i	−0.987089	+	0.160171i	$0.948795\pi$
$48$		0			0
$49$	0.232051	−	0.401924i	0.0331501	−	0.0574177i
$50$	−7.73205	−	4.46410i	−1.09348	−	0.631319i
$51$		0			0
$52$	−3.46410	−	1.00000i	−0.480384	−	0.138675i
$53$	6.46410			0.887913			0.443956	−	0.896048i	$-0.353575\pi$
$53$	6.46410			0.887913			0.443956	+	0.896048i	$0.353575\pi$
$54$		0			0
$55$	−2.36603	+	4.09808i	−0.319035	+	0.552584i
$56$	1.36603	+	2.36603i	0.182543	+	0.316173i
$57$		0			0
$58$	−3.86603	+	2.23205i	−0.507634	+	0.293083i
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.0241347	−	0.999709i	$-0.492317\pi$
$59$	6.92820	−	4.00000i	0.901975	−	0.520756i	0.877841	+	0.478953i	$0.158984\pi$
$60$		0			0
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	0.994400	+	0.105682i	$0.0337026\pi$
$61$	4.59808	+	7.96410i	0.588723	+	1.01970i	−0.405677	+	0.914017i	$0.632964\pi$
$62$	−0.732051	+	1.26795i	−0.0929705	+	0.161030i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	9.33013	+	9.69615i	1.15726	+	1.20266i
$66$		0			0
$67$	−11.3660	−	6.56218i	−1.38858	−	0.801698i	−0.395426	−	0.918498i	$-0.629403\pi$
$67$	−11.3660	−	6.56218i	−1.38858	−	0.801698i	−0.993155	+	0.116800i	$0.962736\pi$
$68$	−2.86603	+	4.96410i	−0.347557	+	0.601986i
$69$		0			0
$70$		−	10.1962i		−	1.21867i
$71$	−4.09808	+	2.36603i	−0.486352	+	0.280796i	−0.723060	−	0.690785i	$-0.757265\pi$
$71$	−4.09808	+	2.36603i	−0.486352	+	0.280796i	0.236708	+	0.971581i	$0.423932\pi$
$72$		0			0
$73$			6.26795i			0.733608i	0.930298	+	0.366804i	$0.119548\pi$
$73$			6.26795i			0.733608i	−0.930298	+	0.366804i	$0.880452\pi$
$74$	1.76795	+	3.06218i	0.205520	+	0.355971i
$75$		0			0
$76$	4.09808	+	2.36603i	0.470082	+	0.271402i
$77$	−3.46410			−0.394771
$78$		0			0
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$	3.23205	+	1.86603i	0.361354	+	0.208628i
$81$		0			0
$82$	−4.69615	−	8.13397i	−0.518603	−	0.898247i
$83$			0.196152i			0.0215305i	0.999942	+	0.0107653i	$0.00342676\pi$
$83$			0.196152i			0.0215305i	−0.999942	+	0.0107653i	$0.996573\pi$
$84$		0			0
$85$	18.5263	−	10.6962i	2.00946	−	1.16016i
$86$		−	9.66025i		−	1.04169i
$87$		0			0
$88$	0.633975	−	1.09808i	0.0675819	−	0.117055i
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.00184433	+	0.999998i	$0.499413\pi$
$90$		0			0
$91$	−2.73205	+	9.46410i	−0.286397	+	0.992107i
$92$	−4.19615			−0.437479
$93$		0			0
$94$	−1.09808	+	1.90192i	−0.113258	+	0.196168i
$95$	−8.83013	−	15.2942i	−0.905952	−	1.56915i
$96$		0			0
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	−0.740034	−	0.672569i	$-0.765191\pi$
$97$	−5.19615	+	3.00000i	−0.527589	+	0.304604i	0.212445	+	0.977173i	$0.431857\pi$
$98$	0.401924	−	0.232051i	0.0406004	−	0.0234407i
$99$		0			0
$100$	−4.46410	−	7.73205i	−0.446410	−	0.773205i
$101$	−0.964102	+	1.66987i	−0.0959317	+	0.166159i	−0.909997	−	0.414615i	$-0.863916\pi$
$101$	−0.964102	+	1.66987i	−0.0959317	+	0.166159i	0.814065	+	0.580773i	$0.197250\pi$
$102$		0			0
$103$	15.2679			1.50440			0.752198	−	0.658937i	$-0.228994\pi$
$103$	15.2679			1.50440			0.752198	+	0.658937i	$0.228994\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	5.59808	+	3.23205i	0.543733	+	0.313925i
$107$	5.09808	−	8.83013i	0.492850	−	0.853641i	−0.507116	−	0.861878i	$-0.669289\pi$
$107$	5.09808	−	8.83013i	0.492850	−	0.853641i	0.999966	+	0.00823695i	$0.00262193\pi$
$108$		0			0
$109$			1.46410i			0.140236i	0.997539	+	0.0701178i	$0.0223375\pi$
$109$			1.46410i			0.140236i	−0.997539	+	0.0701178i	$0.977662\pi$
$110$	−4.09808	+	2.36603i	−0.390736	+	0.225592i
$111$		0			0
$112$			2.73205i			0.258155i
$113$	−0.669873	−	1.16025i	−0.0630163	−	0.109148i	0.832796	−	0.553580i	$-0.186739\pi$
$113$	−0.669873	−	1.16025i	−0.0630163	−	0.109148i	−0.895812	+	0.444432i	$0.853405\pi$
$114$		0			0
$115$	13.5622	+	7.83013i	1.26468	+	0.730163i
$116$	−4.46410			−0.414481
$117$		0			0
$118$	8.00000			0.736460
$119$	13.5622	+	7.83013i	1.24324	+	0.717787i
$120$		0			0
$121$	−4.69615	−	8.13397i	−0.426923	−	0.739452i
$122$			9.19615i			0.832581i
$123$		0			0
$124$	−1.26795	+	0.732051i	−0.113865	+	0.0657401i
$125$			14.6603i			1.31125i
$126$		0			0
$127$	−4.92820	+	8.53590i	−0.437307	+	0.757438i	−0.997481	−	0.0709368i	$-0.977401\pi$
$127$	−4.92820	+	8.53590i	−0.437307	+	0.757438i	0.560173	+	0.828375i	$0.310734\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	3.23205	+	13.0622i	0.283470	+	1.14563i
$131$	−6.53590			−0.571044			−0.285522	−	0.958372i	$-0.592167\pi$
$131$	−6.53590			−0.571044			−0.285522	+	0.958372i	$0.592167\pi$
$132$		0			0
$133$	6.46410	−	11.1962i	0.560509	−	0.970830i
$134$	−6.56218	−	11.3660i	−0.566886	−	0.981875i
$135$		0			0
$136$	−4.96410	+	2.86603i	−0.425668	+	0.245760i
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.0110599	−	0.999939i	$-0.496479\pi$
$137$	10.3301	−	5.96410i	0.882562	−	0.509548i	0.871502	+	0.490391i	$0.163146\pi$
$138$		0			0
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	−0.944233	−	0.329279i	$-0.893194\pi$
$139$	−8.92820	−	15.4641i	−0.757280	−	1.31165i	0.186952	−	0.982369i	$-0.440139\pi$
$140$	5.09808	−	8.83013i	0.430866	−	0.746282i
$141$		0			0
$142$	−4.73205			−0.397105
$143$	4.43782	−	1.09808i	0.371109	−	0.0918257i
$144$		0			0
$145$	14.4282	+	8.33013i	1.19820	+	0.691779i
$146$	−3.13397	+	5.42820i	−0.259370	+	0.449241i
$147$		0			0
$148$			3.53590i			0.290649i
$149$	−11.4282	+	6.59808i	−0.936235	+	0.540535i	−0.888778	−	0.458338i	$-0.848445\pi$
$149$	−11.4282	+	6.59808i	−0.936235	+	0.540535i	−0.0474568	+	0.998873i	$0.515112\pi$
$150$		0			0
$151$		−	6.73205i		−	0.547847i	−0.961752	−	0.273923i	$-0.911679\pi$
$151$		−	6.73205i		−	0.547847i	0.961752	−	0.273923i	$-0.0883214\pi$
$152$	2.36603	+	4.09808i	0.191910	+	0.332398i
$153$		0			0
$154$	−3.00000	−	1.73205i	−0.241747	−	0.139573i
$155$	5.46410			0.438887
$156$		0			0
$157$	7.58846			0.605625			0.302812	−	0.953050i	$-0.402074\pi$
$157$	7.58846			0.605625			0.302812	+	0.953050i	$0.402074\pi$
$158$	−2.19615	−	1.26795i	−0.174717	−	0.100873i
$159$		0			0
$160$	1.86603	+	3.23205i	0.147522	+	0.255516i
$161$			11.4641i			0.903498i
$162$		0			0
$163$	11.6603	−	6.73205i	0.913302	−	0.527295i	0.0318096	−	0.999494i	$-0.489873\pi$
$163$	11.6603	−	6.73205i	0.913302	−	0.527295i	0.881492	+	0.472199i	$0.156540\pi$
$164$		−	9.39230i		−	0.733416i
$165$		0			0
$166$	−0.0980762	+	0.169873i	−0.00761219	+	0.0131847i
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	0.782391	−	0.622787i	$-0.214000\pi$
$167$	8.19615	+	4.73205i	0.634237	+	0.366177i	−0.148154	+	0.988964i	$0.547333\pi$
$168$		0			0
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$	21.3923			1.64071
$171$		0			0
$172$	4.83013	−	8.36603i	0.368294	−	0.637903i
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	0.770383	−	0.637582i	$-0.220065\pi$
$173$	−2.19615	−	3.80385i	−0.166970	−	0.289201i	−0.937353	+	0.348380i	$0.886732\pi$
$174$		0			0
$175$	−21.1244	+	12.1962i	−1.59685	+	0.921942i
$176$	1.09808	−	0.633975i	0.0827706	−	0.0477876i
$177$		0			0
$178$	4.73205	+	8.19615i	0.354682	+	0.614328i
$179$	8.02628	−	13.9019i	0.599912	−	1.03908i	−0.392921	−	0.919572i	$-0.628535\pi$
$179$	8.02628	−	13.9019i	0.599912	−	1.03908i	0.992833	−	0.119506i	$-0.0381312\pi$
$180$		0			0
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$	−7.09808	+	6.83013i	−0.526144	+	0.506283i
$183$		0			0
$184$	−3.63397	−	2.09808i	−0.267900	−	0.154672i
$185$	6.59808	−	11.4282i	0.485100	−	0.840218i
$186$		0			0
$187$		−	7.26795i		−	0.531485i
$188$	−1.90192	+	1.09808i	−0.138712	+	0.0800854i
$189$		0			0
$190$		−	17.6603i		−	1.28121i
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	0.713052	−	0.701111i	$-0.247312\pi$
$191$	−3.46410	−	6.00000i	−0.250654	−	0.434145i	−0.963706	+	0.266966i	$0.913979\pi$
$192$		0			0
$193$	−10.1603	−	5.86603i	−0.731351	−	0.422246i	0.0875652	−	0.996159i	$-0.472091\pi$
$193$	−10.1603	−	5.86603i	−0.731351	−	0.422246i	−0.818916	+	0.573913i	$0.805425\pi$
$194$	−6.00000			−0.430775
$195$		0			0
$196$	0.464102			0.0331501
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.165086	−	0.986279i	$-0.552790\pi$
$197$	−15.4641	−	8.92820i	−1.10177	−	0.636108i	−0.936686	+	0.350171i	$0.886123\pi$
$198$		0			0
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	−0.999993	−	0.00366345i	$-0.998834\pi$
$199$	−7.09808	−	12.2942i	−0.503169	−	0.871515i	0.496824	−	0.867851i	$-0.334499\pi$
$200$		−	8.92820i		−	0.631319i
$201$		0			0
$202$	−1.66987	+	0.964102i	−0.117492	+	0.0678340i
$203$			12.1962i			0.856002i
$204$		0			0
$205$	−17.5263	+	30.3564i	−1.22409	+	2.12018i
$206$	13.2224	+	7.63397i	0.921250	+	0.531884i
$207$		0			0
$208$	−0.866025	−	3.50000i	−0.0600481	−	0.242681i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	0.432873	+	0.901455i	$0.357500\pi$
$211$	−8.19615	+	14.1962i	−0.564246	+	0.977303i	−0.997119	+	0.0758485i	$0.975833\pi$
$212$	3.23205	+	5.59808i	0.221978	+	0.384477i
$213$		0			0
$214$	8.83013	−	5.09808i	0.603615	−	0.348497i
$215$	−31.2224	+	18.0263i	−2.12935	+	1.22938i
$216$		0			0
$217$	2.00000	+	3.46410i	0.135769	+	0.235159i
$218$	−0.732051	+	1.26795i	−0.0495807	+	0.0858764i
$219$		0			0
$220$	−4.73205			−0.319035
$221$	−19.8564	−	5.73205i	−1.33569	−	0.385579i
$222$		0			0
$223$	23.3205	+	13.4641i	1.56166	+	0.901623i	0.997090	+	0.0762356i	$0.0242901\pi$
$223$	23.3205	+	13.4641i	1.56166	+	0.901623i	0.564567	+	0.825387i	$0.309043\pi$
$224$	−1.36603	+	2.36603i	−0.0912714	+	0.158087i
$225$		0			0
$226$		−	1.33975i		−	0.0891186i
$227$	10.5622	−	6.09808i	0.701036	−	0.404744i	−0.106697	−	0.994292i	$-0.534027\pi$
$227$	10.5622	−	6.09808i	0.701036	−	0.404744i	0.807733	+	0.589548i	$0.200694\pi$
$228$		0			0
$229$			11.8564i			0.783493i	0.920073	+	0.391747i	$0.128129\pi$
$229$			11.8564i			0.783493i	−0.920073	+	0.391747i	$0.871871\pi$
$230$	7.83013	+	13.5622i	0.516303	+	0.894264i
$231$		0			0
$232$	−3.86603	−	2.23205i	−0.253817	−	0.146541i
$233$	−7.85641			−0.514690			−0.257345	−	0.966320i	$-0.582848\pi$
$233$	−7.85641			−0.514690			−0.257345	+	0.966320i	$0.582848\pi$
$234$		0			0
$235$	8.19615			0.534658
$236$	6.92820	+	4.00000i	0.450988	+	0.260378i
$237$		0			0
$238$	7.83013	+	13.5622i	0.507552	+	0.879105i
$239$		−	7.66025i		−	0.495501i	−0.968824	−	0.247750i	$-0.920309\pi$
$239$		−	7.66025i		−	0.495501i	0.968824	−	0.247750i	$-0.0796913\pi$
$240$		0			0
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	−0.828592	−	0.559853i	$-0.810857\pi$
$241$	−11.7679	+	6.79423i	−0.758040	+	0.437655i	0.0705514	+	0.997508i	$0.477524\pi$
$242$		−	9.39230i		−	0.603760i
$243$		0			0
$244$	−4.59808	+	7.96410i	−0.294362	+	0.509849i
$245$	−1.50000	−	0.866025i	−0.0958315	−	0.0553283i
$246$		0			0
$247$	−4.73205	+	16.3923i	−0.301093	+	1.04302i
$248$	−1.46410			−0.0929705
$249$		0			0
$250$	−7.33013	+	12.6962i	−0.463598	+	0.802975i
$251$	−6.73205	−	11.6603i	−0.424923	−	0.735989i	0.571490	−	0.820609i	$-0.306366\pi$
$251$	−6.73205	−	11.6603i	−0.424923	−	0.735989i	−0.996413	+	0.0846203i	$0.973032\pi$
$252$		0			0
$253$	4.60770	−	2.66025i	0.289683	−	0.167249i
$254$	−8.53590	+	4.92820i	−0.535590	+	0.309223i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	−0.974117	−	0.226044i	$-0.927421\pi$
$257$	−4.66987	+	8.08846i	−0.291299	+	0.504544i	0.682818	+	0.730588i	$0.260754\pi$
$258$		0			0
$259$	9.66025			0.600259
$260$	−3.73205	+	12.9282i	−0.231452	+	0.801773i
$261$		0			0
$262$	−5.66025	−	3.26795i	−0.349692	−	0.201895i
$263$	−5.02628	+	8.70577i	−0.309934	+	0.536821i	−0.978348	−	0.206969i	$-0.933640\pi$
$263$	−5.02628	+	8.70577i	−0.309934	+	0.536821i	0.668414	+	0.743790i	$0.266974\pi$
$264$		0			0
$265$		−	24.1244i		−	1.48195i
$266$	11.1962	−	6.46410i	0.686480	−	0.396339i
$267$		0			0
$268$		−	13.1244i		−	0.801698i
$269$	2.73205	+	4.73205i	0.166576	+	0.288518i	0.937214	−	0.348755i	$-0.113396\pi$
$269$	2.73205	+	4.73205i	0.166576	+	0.288518i	−0.770638	+	0.637273i	$0.780062\pi$
$270$		0			0
$271$	−18.9282	−	10.9282i	−1.14981	−	0.663841i	−0.200966	−	0.979598i	$-0.564408\pi$
$271$	−18.9282	−	10.9282i	−1.14981	−	0.663841i	−0.948840	+	0.315757i	$0.897742\pi$
$272$	−5.73205			−0.347557
$273$		0			0
$274$	11.9282			0.720609
$275$	9.80385	+	5.66025i	0.591194	+	0.341326i
$276$		0			0
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	0.766987	−	0.641663i	$-0.221755\pi$
$277$	−2.86603	−	4.96410i	−0.172203	−	0.298264i	−0.939190	+	0.343399i	$0.888422\pi$
$278$		−	17.8564i		−	1.07096i
$279$		0			0
$280$	8.83013	−	5.09808i	0.527701	−	0.304668i
$281$			12.3205i			0.734980i	0.930027	+	0.367490i	$0.119783\pi$
$281$			12.3205i			0.734980i	−0.930027	+	0.367490i	$0.880217\pi$
$282$		0			0
$283$	12.8301	−	22.2224i	0.762672	−	1.32099i	−0.178797	−	0.983886i	$-0.557220\pi$
$283$	12.8301	−	22.2224i	0.762672	−	1.32099i	0.941469	−	0.337100i	$-0.109446\pi$
$284$	−4.09808	−	2.36603i	−0.243176	−	0.140398i
$285$		0			0
$286$	4.39230	+	1.26795i	0.259722	+	0.0749754i
$287$	−25.6603			−1.51468
$288$		0			0
$289$	−7.92820	+	13.7321i	−0.466365	+	0.807768i
$290$	8.33013	+	14.4282i	0.489162	+	0.847253i
$291$		0			0
$292$	−5.42820	+	3.13397i	−0.317662	+	0.183402i
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.545368	−	0.838196i	$-0.316390\pi$
$293$	26.4282	−	15.2583i	1.54395	−	0.891401i	0.998584	−	0.0532048i	$-0.0169436\pi$
$294$		0			0
$295$	−14.9282	−	25.8564i	−0.869154	−	1.50542i
$296$	−1.76795	+	3.06218i	−0.102760	+	0.177985i
$297$		0			0
$298$	−13.1962			−0.764433
$299$	−3.63397	−	14.6865i	−0.210158	−	0.849344i
$300$		0			0
$301$	−22.8564	−	13.1962i	−1.31742	−	0.760614i
$302$	3.36603	−	5.83013i	0.193693	−	0.335486i
$303$		0			0
$304$			4.73205i			0.271402i
$305$	29.7224	−	17.1603i	1.70190	−	0.982593i
$306$		0			0
$307$			22.5885i			1.28919i	0.764524	+	0.644596i	$0.222974\pi$
$307$			22.5885i			1.28919i	−0.764524	+	0.644596i	$0.777026\pi$
$308$	−1.73205	−	3.00000i	−0.0986928	−	0.170941i
$309$		0			0
$310$	4.73205	+	2.73205i	0.268762	+	0.155170i
$311$	−1.66025			−0.0941444			−0.0470722	−	0.998891i	$-0.514989\pi$
$311$	−1.66025			−0.0941444			−0.0470722	+	0.998891i	$0.514989\pi$
$312$		0			0
$313$	6.53590			0.369431			0.184715	−	0.982792i	$-0.440864\pi$
$313$	6.53590			0.369431			0.184715	+	0.982792i	$0.440864\pi$
$314$	6.57180	+	3.79423i	0.370868	+	0.214121i
$315$		0			0
$316$	−1.26795	−	2.19615i	−0.0713277	−	0.123543i
$317$		−	20.6603i		−	1.16040i	−0.814476	−	0.580198i	$-0.802975\pi$
$317$		−	20.6603i		−	1.16040i	0.814476	−	0.580198i	$-0.197025\pi$
$318$		0			0
$319$	4.90192	−	2.83013i	0.274455	−	0.158457i
$320$			3.73205i			0.208628i
$321$		0			0
$322$	−5.73205	+	9.92820i	−0.319435	+	0.553277i
$323$	23.4904	+	13.5622i	1.30704	+	0.754620i
$324$		0			0
$325$	23.1962	−	22.3205i	1.28669	−	1.23812i
$326$	13.4641			0.745708
$327$		0			0
$328$	4.69615	−	8.13397i	0.259302	−	0.449124i
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$		0			0
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.0583130	−	0.998298i	$-0.481428\pi$
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.893708	+	0.448649i	$0.148095\pi$
$332$	−0.169873	+	0.0980762i	−0.00932299	+	0.00538263i
$333$		0			0
$334$	4.73205	+	8.19615i	0.258926	+	0.448474i
$335$	−24.4904	+	42.4186i	−1.33805	+	2.31757i
$336$		0			0
$337$	20.8564			1.13612			0.568060	−	0.822987i	$-0.307694\pi$
$337$	20.8564			1.13612			0.568060	+	0.822987i	$0.307694\pi$
$338$	6.92820	−	11.0000i	0.376845	−	0.598321i
$339$		0			0
$340$	18.5263	+	10.6962i	1.00473	+	0.580080i
$341$	0.928203	−	1.60770i	0.0502650	−	0.0870616i
$342$		0			0
$343$			17.8564i			0.964155i
$344$	8.36603	−	4.83013i	0.451066	−	0.260423i
$345$		0			0
$346$		−	4.39230i		−	0.236132i
$347$	16.5622	+	28.6865i	0.889104	+	1.53997i	0.840936	+	0.541135i	$0.182005\pi$
$347$	16.5622	+	28.6865i	0.889104	+	1.53997i	0.0481683	+	0.998839i	$0.484662\pi$
$348$		0			0
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$349$	13.2679	+	7.66025i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$350$	−24.3923			−1.30382
$351$		0			0
$352$	1.26795			0.0675819
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.0946674	−	0.995509i	$-0.530179\pi$
$353$	−18.8660	−	10.8923i	−1.00414	−	0.579739i	−0.909470	+	0.415770i	$0.863512\pi$
$354$		0			0
$355$	8.83013	+	15.2942i	0.468654	+	0.811733i
$356$			9.46410i			0.501596i
$357$		0			0
$358$	13.9019	−	8.02628i	0.734740	−	0.424202i
$359$		−	1.12436i		−	0.0593412i	−0.999560	−	0.0296706i	$-0.990554\pi$
$359$		−	1.12436i		−	0.0593412i	0.999560	−	0.0296706i	$-0.00944584\pi$
$360$		0			0
$361$	1.69615	−	2.93782i	0.0892712	−	0.154622i
$362$	−16.6244	−	9.59808i	−0.873757	−	0.504464i
$363$		0			0
$364$	−9.56218	+	2.36603i	−0.501194	+	0.124013i
$365$	23.3923			1.22441
$366$		0			0
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	−0.680682	−	0.732579i	$-0.738316\pi$
$367$	5.63397	−	9.75833i	0.294091	−	0.509381i	0.974773	+	0.223198i	$0.0716498\pi$
$368$	−2.09808	−	3.63397i	−0.109370	−	0.189434i
$369$		0			0
$370$	11.4282	−	6.59808i	0.594124	−	0.343018i
$371$	15.2942	−	8.83013i	0.794037	−	0.458437i
$372$		0			0
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	0.987205	−	0.159456i	$-0.0509741\pi$
$373$	6.86603	+	11.8923i	0.355509	+	0.615760i	−0.631696	+	0.775216i	$0.717641\pi$
$374$	3.63397	−	6.29423i	0.187908	−	0.325467i
$375$		0			0
$376$	−2.19615			−0.113258
$377$	−3.86603	−	15.6244i	−0.199110	−	0.804695i
$378$		0			0
$379$	4.73205	+	2.73205i	0.243069	+	0.140336i	0.616587	−	0.787287i	$-0.288515\pi$
$379$	4.73205	+	2.73205i	0.243069	+	0.140336i	−0.373517	+	0.927623i	$0.621848\pi$
$380$	8.83013	−	15.2942i	0.452976	−	0.784577i
$381$		0			0
$382$		−	6.92820i		−	0.354478i
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	−0.467255	−	0.884122i	$-0.654757\pi$
$383$	1.26795	−	0.732051i	0.0647892	−	0.0374060i	0.532045	+	0.846716i	$0.321424\pi$
$384$		0			0
$385$			12.9282i			0.658882i
$386$	−5.86603	−	10.1603i	−0.298573	−	0.517143i
$387$		0			0
$388$	−5.19615	−	3.00000i	−0.263795	−	0.152302i
$389$	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
$392$	0.401924	+	0.232051i	0.0203002	+	0.0117203i
$393$		0			0
$394$	−8.92820	−	15.4641i	−0.449796	−	0.779070i
$395$			9.46410i			0.476191i
$396$		0			0
$397$	−17.6603	+	10.1962i	−0.886343	+	0.511730i	−0.872744	−	0.488177i	$-0.837662\pi$
$397$	−17.6603	+	10.1962i	−0.886343	+	0.511730i	−0.0135983	+	0.999908i	$0.504329\pi$
$398$		−	14.1962i		−	0.711589i
$399$		0			0
$400$	4.46410	−	7.73205i	0.223205	−	0.386603i
$401$	−6.99038	−	4.03590i	−0.349083	−	0.201543i	0.315198	−	0.949026i	$-0.397929\pi$
$401$	−6.99038	−	4.03590i	−0.349083	−	0.201543i	−0.664281	+	0.747483i	$0.731262\pi$
$402$		0			0
$403$	−3.66025	−	3.80385i	−0.182330	−	0.189483i
$404$	−1.92820			−0.0959317
$405$		0			0
$406$	−6.09808	+	10.5622i	−0.302642	+	0.524192i
$407$	−2.24167	−	3.88269i	−0.111115	−	0.192458i
$408$		0			0
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	−0.0697281	−	0.997566i	$-0.522213\pi$
$409$	15.3564	−	8.86603i	0.759325	−	0.438397i	0.829053	+	0.559169i	$0.188880\pi$
$410$	−30.3564	+	17.5263i	−1.49920	+	0.865561i
$411$		0			0
$412$	7.63397	+	13.2224i	0.376099	+	0.651422i
$413$	10.9282	−	18.9282i	0.537742	−	0.931396i
$414$		0			0
$415$	0.732051			0.0359350
$416$	1.00000	−	3.46410i	0.0490290	−	0.169842i
$417$		0			0
$418$	−5.19615	−	3.00000i	−0.254152	−	0.146735i
$419$	−8.73205	+	15.1244i	−0.426589	+	0.738873i	−0.996567	−	0.0827863i	$-0.973618\pi$
$419$	−8.73205	+	15.1244i	−0.426589	+	0.738873i	0.569979	+	0.821659i	$0.306951\pi$
$420$		0			0
$421$		−	22.7128i		−	1.10695i	−0.832864	−	0.553477i	$-0.813301\pi$
$421$		−	22.7128i		−	1.10695i	0.832864	−	0.553477i	$-0.186699\pi$
$422$	−14.1962	+	8.19615i	−0.691058	+	0.398982i
$423$		0			0
$424$			6.46410i			0.313925i
$425$	−25.5885	−	44.3205i	−1.24122	−	2.14986i
$426$		0			0
$427$	21.7583	+	12.5622i	1.05296	+	0.607926i
$428$	10.1962			0.492850
$429$		0			0
$430$	−36.0526			−1.73861
$431$	11.3660	+	6.56218i	0.547482	+	0.316089i	0.748106	−	0.663579i	$-0.230964\pi$
$431$	11.3660	+	6.56218i	0.547482	+	0.316089i	−0.200624	+	0.979668i	$0.564297\pi$
$432$		0			0
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	0.978126	−	0.208012i	$-0.0666992\pi$
$433$	6.42820	+	11.1340i	0.308920	+	0.535065i	−0.669207	+	0.743076i	$0.733366\pi$
$434$			4.00000i			0.192006i
$435$		0			0
$436$	−1.26795	+	0.732051i	−0.0607238	+	0.0350589i
$437$			19.8564i			0.949861i
$438$		0			0
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	−0.870051	−	0.492962i	$-0.835914\pi$
$439$	−0.169873	+	0.294229i	−0.00810760	+	0.0140428i	0.861943	+	0.507005i	$0.169247\pi$
$440$	−4.09808	−	2.36603i	−0.195368	−	0.112796i
$441$		0			0
$442$	−14.3301	−	14.8923i	−0.681615	−	0.708355i
$443$	−15.6077			−0.741544			−0.370772	−	0.928724i	$-0.620907\pi$
$443$	−15.6077			−0.741544			−0.370772	+	0.928724i	$0.620907\pi$
$444$		0			0
$445$	17.6603	−	30.5885i	0.837176	−	1.45003i
$446$	13.4641	+	23.3205i	0.637544	+	1.10426i
$447$		0			0
$448$	−2.36603	+	1.36603i	−0.111784	+	0.0645386i
$449$	9.80385	−	5.66025i	0.462672	−	0.267124i	−0.250495	−	0.968118i	$-0.580593\pi$
$449$	9.80385	−	5.66025i	0.462672	−	0.267124i	0.713167	+	0.700994i	$0.247260\pi$
$450$		0			0
$451$	5.95448	+	10.3135i	0.280386	+	0.485642i
$452$	0.669873	−	1.16025i	0.0315082	−	0.0545738i
$453$		0			0
$454$	12.1962			0.572394
$455$	35.3205	+	10.1962i	1.65585	+	0.478003i
$456$		0			0
$457$	−1.16025	−	0.669873i	−0.0542744	−	0.0313353i	0.472617	−	0.881268i	$-0.343309\pi$
$457$	−1.16025	−	0.669873i	−0.0542744	−	0.0313353i	−0.526892	+	0.849932i	$0.676643\pi$
$458$	−5.92820	+	10.2679i	−0.277007	+	0.479790i
$459$		0			0
$460$			15.6603i			0.730163i
$461$	−19.2846	+	11.1340i	−0.898174	+	0.518561i	−0.876607	−	0.481207i	$-0.840199\pi$
$461$	−19.2846	+	11.1340i	−0.898174	+	0.518561i	−0.0215666	+	0.999767i	$0.506865\pi$
$462$		0			0
$463$		−	10.0526i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$463$		−	10.0526i		−	0.467182i	0.972335	−	0.233591i	$-0.0750477\pi$
$464$	−2.23205	−	3.86603i	−0.103620	−	0.179476i
$465$		0			0
$466$	−6.80385	−	3.92820i	−0.315182	−	0.181971i
$467$	18.5885			0.860171			0.430086	−	0.902788i	$-0.358483\pi$
$467$	18.5885			0.860171			0.430086	+	0.902788i	$0.358483\pi$
$468$		0			0
$469$	−35.8564			−1.65570
$470$	7.09808	+	4.09808i	0.327410	+	0.189030i
$471$		0			0
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$			12.2487i			0.563196i
$474$		0			0
$475$	−36.5885	+	21.1244i	−1.67879	+	0.969252i
$476$			15.6603i			0.717787i
$477$		0			0
$478$	3.83013	−	6.63397i	0.175186	−	0.303431i
$479$	−28.9808	−	16.7321i	−1.32416	−	0.764507i	−0.339775	−	0.940507i	$-0.610351\pi$
$479$	−28.9808	−	16.7321i	−1.32416	−	0.764507i	−0.984390	+	0.176000i	$0.943684\pi$
$480$		0			0
$481$	−12.3756	+	3.06218i	−0.564281	+	0.139623i
$482$	−13.5885			−0.618937
$483$		0			0
$484$	4.69615	−	8.13397i	0.213461	−	0.369726i
$485$	11.1962	+	19.3923i	0.508391	+	0.880559i
$486$		0			0
$487$	−2.70577	+	1.56218i	−0.122610	+	0.0707890i	−0.560051	−	0.828458i	$-0.689218\pi$
$487$	−2.70577	+	1.56218i	−0.122610	+	0.0707890i	0.437441	+	0.899247i	$0.355885\pi$
$488$	−7.96410	+	4.59808i	−0.360518	+	0.208145i
$489$		0			0
$490$	−0.866025	−	1.50000i	−0.0391230	−	0.0677631i
$491$	−4.36603	+	7.56218i	−0.197036	+	0.341276i	−0.947566	−	0.319560i	$-0.896465\pi$
$491$	−4.36603	+	7.56218i	−0.197036	+	0.341276i	0.750530	+	0.660836i	$0.229798\pi$
$492$		0			0
$493$	−25.5885			−1.15245
$494$	−12.2942	+	11.8301i	−0.553143	+	0.532263i
$495$		0			0
$496$	−1.26795	−	0.732051i	−0.0569326	−	0.0328701i
$497$	−6.46410	+	11.1962i	−0.289955	+	0.502216i
$498$		0			0
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$	−12.6962	+	7.33013i	−0.567789	+	0.327813i
$501$		0			0
$502$		−	13.4641i		−	0.600932i
$503$	20.4904	+	35.4904i	0.913621	+	1.58244i	0.808908	+	0.587935i	$0.200059\pi$
$503$	20.4904	+	35.4904i	0.913621	+	1.58244i	0.104713	+	0.994502i	$0.466608\pi$
$504$		0			0
$505$	6.23205	+	3.59808i	0.277323	+	0.160112i
$506$	5.32051			0.236525
$507$		0			0
$508$	−9.85641			−0.437307
$509$	11.8923	+	6.86603i	0.527117	+	0.304331i	0.739842	−	0.672781i	$-0.234900\pi$
$509$	11.8923	+	6.86603i	0.527117	+	0.304331i	−0.212725	+	0.977112i	$0.568234\pi$
$510$		0			0
$511$	8.56218	+	14.8301i	0.378768	+	0.656046i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−8.08846	+	4.66987i	−0.356767	+	0.205979i
$515$		−	56.9808i		−	2.51087i
$516$		0			0
$517$	1.39230	−	2.41154i	0.0612335	−	0.106060i
$518$	8.36603	+	4.83013i	0.367582	+	0.212224i
$519$		0			0
$520$	−9.69615	+	9.33013i	−0.425204	+	0.409153i
$521$	−41.4449			−1.81573			−0.907866	−	0.419260i	$-0.862290\pi$
$521$	−41.4449			−1.81573			−0.907866	+	0.419260i	$0.862290\pi$
$522$		0			0
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	−0.509220	−	0.860636i	$-0.670066\pi$
$523$	11.2224	−	19.4378i	0.490723	−	0.849957i	0.999943	+	0.0106796i	$0.00339949\pi$
$524$	−3.26795	−	5.66025i	−0.142761	−	0.247269i
$525$		0			0
$526$	−8.70577	+	5.02628i	−0.379590	+	0.219156i
$527$	−7.26795	+	4.19615i	−0.316597	+	0.182787i
$528$		0			0
$529$	2.69615	+	4.66987i	0.117224	+	0.203038i
$530$	12.0622	−	20.8923i	0.523948	−	0.907504i
$531$		0			0
$532$	12.9282			0.560509
$533$	32.8731	−	8.13397i	1.42389	−	0.352322i
$534$		0			0
$535$	−32.9545	−	19.0263i	−1.42475	−	0.822578i
$536$	6.56218	−	11.3660i	0.283443	−	0.490938i
$537$		0			0
$538$			5.46410i			0.235574i
$539$	−0.509619	+	0.294229i	−0.0219508	+	0.0126733i
$540$		0			0
$541$		−	5.67949i		−	0.244180i	−0.992519	−	0.122090i	$-0.961040\pi$
$541$		−	5.67949i		−	0.244180i	0.992519	−	0.122090i	$-0.0389597\pi$
$542$	−10.9282	−	18.9282i	−0.469407	−	0.813036i
$543$		0			0
$544$	−4.96410	−	2.86603i	−0.212834	−	0.122880i
$545$	5.46410			0.234056
$546$		0			0
$547$	−4.19615			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$548$	10.3301	+	5.96410i	0.441281	+	0.254774i
$549$		0			0
$550$	5.66025	+	9.80385i	0.241354	+	0.418037i
$551$			21.1244i			0.899928i
$552$		0			0
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$		−	5.73205i		−	0.243532i
$555$		0			0
$556$	8.92820	−	15.4641i	0.378640	−	0.655824i
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.997734	−	0.0672780i	$-0.978569\pi$
$557$	−36.6962	−	21.1865i	−1.55487	−	0.897702i	−0.557132	−	0.830424i	$-0.688098\pi$
$558$		0			0
$559$	33.4641	+	9.66025i	1.41538	+	0.408585i
$560$	10.1962			0.430866
$561$		0			0
$562$	−6.16025	+	10.6699i	−0.259855	+	0.450081i
$563$	−17.4641	−	30.2487i	−0.736024	−	1.27483i	−0.954273	−	0.298938i	$-0.903368\pi$
$563$	−17.4641	−	30.2487i	−0.736024	−	1.27483i	0.218248	−	0.975893i	$-0.429966\pi$
$564$		0			0
$565$	−4.33013	+	2.50000i	−0.182170	+	0.105176i
$566$	22.2224	−	12.8301i	0.934078	−	0.539290i
$567$		0			0
$568$	−2.36603	−	4.09808i	−0.0992762	−	0.171951i
$569$	−15.3205	+	26.5359i	−0.642269	+	1.11244i	0.342656	+	0.939461i	$0.388674\pi$
$569$	−15.3205	+	26.5359i	−0.642269	+	1.11244i	−0.984925	+	0.172982i	$0.944660\pi$
$570$		0			0
$571$	−14.0526			−0.588081			−0.294041	−	0.955793i	$-0.595000\pi$
$571$	−14.0526			−0.588081			−0.294041	+	0.955793i	$0.595000\pi$
$572$	3.16987	+	3.29423i	0.132539	+	0.137739i
$573$		0			0
$574$	−22.2224	−	12.8301i	−0.927546	−	0.535519i
$575$	18.7321	−	32.4449i	0.781181	−	1.35304i
$576$		0			0
$577$			3.73205i			0.155367i	0.996978	+	0.0776837i	$0.0247524\pi$
$577$			3.73205i			0.155367i	−0.996978	+	0.0776837i	$0.975248\pi$
$578$	−13.7321	+	7.92820i	−0.571178	+	0.329770i
$579$		0			0
$580$			16.6603i			0.691779i
$581$	0.267949	+	0.464102i	0.0111164	+	0.0192542i
$582$		0			0
$583$	−7.09808	−	4.09808i	−0.293972	−	0.169725i
$584$	−6.26795			−0.259370
$585$		0			0
$586$	30.5167			1.26063
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	0.757914	−	0.652355i	$-0.226219\pi$
$587$	13.8564	+	8.00000i	0.571915	+	0.330195i	−0.185999	+	0.982550i	$0.559552\pi$
$588$		0			0
$589$	3.46410	+	6.00000i	0.142736	+	0.247226i
$590$		−	29.8564i		−	1.22917i
$591$		0			0
$592$	−3.06218	+	1.76795i	−0.125855	+	0.0726623i
$593$		−	9.14359i		−	0.375482i	−0.982219	−	0.187741i	$-0.939883\pi$
$593$		−	9.14359i		−	0.375482i	0.982219	−	0.187741i	$-0.0601166\pi$
$594$		0			0
$595$	29.2224	−	50.6147i	1.19800	−	2.07500i
$596$	−11.4282	−	6.59808i	−0.468117	−	0.270268i
$597$		0			0
$598$	4.19615	−	14.5359i	0.171593	−	0.594417i
$599$	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	−0.935478	−	0.353385i	$-0.885031\pi$
$601$	−3.96410	+	6.86603i	−0.161699	+	0.280071i	0.773779	+	0.633456i	$0.218364\pi$
$602$	−13.1962	−	22.8564i	−0.537835	−	0.931558i
$603$		0			0
$604$	5.83013	−	3.36603i	0.237225	−	0.136962i
$605$	−30.3564	+	17.5263i	−1.23416	+	0.712545i
$606$		0			0
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	0.899840	+	0.436221i	$0.143683\pi$
$607$	20.3923	+	35.3205i	0.827698	+	1.43362i	−0.0721415	+	0.997394i	$0.522983\pi$
$608$	−2.36603	+	4.09808i	−0.0959550	+	0.166199i
$609$		0			0
$610$	34.3205			1.38960
$611$	−5.49038	−	5.70577i	−0.222117	−	0.230831i
$612$		0			0
$613$	8.13397	+	4.69615i	0.328528	+	0.189676i	0.655187	−	0.755466i	$-0.272590\pi$
$613$	8.13397	+	4.69615i	0.328528	+	0.189676i	−0.326659	+	0.945142i	$0.605923\pi$
$614$	−11.2942	+	19.5622i	−0.455798	+	0.789465i
$615$		0			0
$616$		−	3.46410i		−	0.139573i
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	−0.250934	−	0.968004i	$-0.580738\pi$
$617$	11.4737	−	6.62436i	0.461915	−	0.266687i	0.712849	+	0.701318i	$0.247404\pi$
$618$		0			0
$619$		−	17.4641i		−	0.701942i	−0.936386	−	0.350971i	$-0.885852\pi$
$619$		−	17.4641i		−	0.701942i	0.936386	−	0.350971i	$-0.114148\pi$
$620$	2.73205	+	4.73205i	0.109722	+	0.190044i
$621$		0			0
$622$	−1.43782	−	0.830127i	−0.0576514	−	0.0332851i
$623$	25.8564			1.03592
$624$		0			0
$625$	10.0718			0.402872
$626$	5.66025	+	3.26795i	0.226229	+	0.130614i
$627$		0			0
$628$	3.79423	+	6.57180i	0.151406	+	0.262243i
$629$			20.2679i			0.808136i
$630$		0			0
$631$	6.67949	−	3.85641i	0.265906	−	0.153521i	−0.361119	−	0.932520i	$-0.617605\pi$
$631$	6.67949	−	3.85641i	0.265906	−	0.153521i	0.627026	+	0.778998i	$0.284272\pi$
$632$		−	2.53590i		−	0.100873i
$633$		0			0
$634$	10.3301	−	17.8923i	0.410262	−	0.710594i
$635$	31.8564	+	18.3923i	1.26418	+	0.729876i
$636$		0			0
$637$	0.401924	+	1.62436i	0.0159248	+	0.0643593i
$638$	5.66025			0.224092
$639$		0			0
$640$	−1.86603	+	3.23205i	−0.0737611	+	0.127758i
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	0.999885	+	0.0151806i	$0.00483233\pi$
$641$	12.9904	+	22.5000i	0.513089	+	0.888697i	−0.486796	+	0.873516i	$0.661834\pi$
$642$		0			0
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	−0.717592	−	0.696463i	$-0.754756\pi$
$643$	−12.0000	+	6.92820i	−0.473234	+	0.273222i	0.244359	+	0.969685i	$0.421423\pi$
$644$	−9.92820	+	5.73205i	−0.391226	+	0.225874i
$645$		0			0
$646$	13.5622	+	23.4904i	0.533597	+	0.924217i
$647$	11.1244	−	19.2679i	0.437344	−	0.757501i	−0.560140	−	0.828398i	$-0.689253\pi$
$647$	11.1244	−	19.2679i	0.437344	−	0.757501i	0.997484	+	0.0708966i	$0.0225860\pi$
$648$		0			0
$649$	−10.1436			−0.398171
$650$	31.2487	−	7.73205i	1.22568	−	0.303276i
$651$		0			0
$652$	11.6603	+	6.73205i	0.456651	+	0.263647i
$653$	−8.73205	+	15.1244i	−0.341712	+	0.591862i	−0.984751	−	0.173972i	$-0.944340\pi$
$653$	−8.73205	+	15.1244i	−0.341712	+	0.591862i	0.643039	+	0.765833i	$0.277673\pi$
$654$		0			0
$655$			24.3923i			0.953086i
$656$	8.13397	−	4.69615i	0.317578	−	0.183354i
$657$		0			0
$658$			6.00000i			0.233904i
$659$	−5.12436	−	8.87564i	−0.199617	−	0.345746i	0.748788	−	0.662810i	$-0.230636\pi$
$659$	−5.12436	−	8.87564i	−0.199617	−	0.345746i	−0.948404	+	0.317064i	$0.897303\pi$
$660$		0			0
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	0.679446	−	0.733726i	$-0.262220\pi$
$661$	9.86603	+	5.69615i	0.383744	+	0.221555i	−0.295702	+	0.955280i	$0.595554\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	−0.196152			−0.00761219
$665$	−41.7846	−	24.1244i	−1.62034	−	0.935502i
$666$		0			0
$667$	−9.36603	−	16.2224i	−0.362654	−	0.628135i
$668$			9.46410i			0.366177i
$669$		0			0
$670$	−42.4186	+	24.4904i	−1.63877	+	0.946146i
$671$		−	11.6603i		−	0.450139i
$672$		0			0
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	−0.460720	−	0.887545i	$-0.652409\pi$
$673$	13.9641	−	24.1865i	0.538277	−	0.932322i	0.998997	−	0.0447770i	$-0.0142577\pi$
$674$	18.0622	+	10.4282i	0.695729	+	0.401679i
$675$		0			0
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	45.4641			1.74733			0.873664	−	0.486530i	$-0.161738\pi$
$677$	45.4641			1.74733			0.873664	+	0.486530i	$0.161738\pi$
$678$		0			0
$679$	−8.19615	+	14.1962i	−0.314539	+	0.544798i
$680$	10.6962	+	18.5263i	0.410179	+	0.710450i
$681$		0			0
$682$	1.60770	−	0.928203i	0.0615618	−	0.0355427i
$683$	−8.78461	+	5.07180i	−0.336134	+	0.194067i	−0.658561	−	0.752527i	$-0.728835\pi$
$683$	−8.78461	+	5.07180i	−0.336134	+	0.194067i	0.322427	+	0.946594i	$0.395501\pi$
$684$		0			0
$685$	−22.2583	−	38.5526i	−0.850447	−	1.47302i
$686$	−8.92820	+	15.4641i	−0.340880	+	0.590422i
$687$		0			0
$688$	9.66025			0.368294
$689$	−16.7942	+	16.1603i	−0.639809	+	0.615657i
$690$		0			0
$691$	−37.8109	−	21.8301i	−1.43839	−	0.830457i	−0.440656	−	0.897676i	$-0.645254\pi$
$691$	−37.8109	−	21.8301i	−1.43839	−	0.830457i	−0.997738	+	0.0672190i	$0.978587\pi$
$692$	2.19615	−	3.80385i	0.0834852	−	0.144601i
$693$		0			0
$694$			33.1244i			1.25738i
$695$	−57.7128	+	33.3205i	−2.18917	+	1.26392i
$696$		0			0
$697$		−	53.8372i		−	2.03923i
$698$	7.66025	+	13.2679i	0.289945	+	0.502199i
$699$		0			0
$700$	−21.1244	−	12.1962i	−0.798426	−	0.460971i
$701$	−3.32051			−0.125414			−0.0627069	−	0.998032i	$-0.519973\pi$
$701$	−3.32051			−0.125414			−0.0627069	+	0.998032i	$0.519973\pi$
$702$		0			0
$703$	16.7321			0.631061
$704$	1.09808	+	0.633975i	0.0413853	+	0.0238938i
$705$		0			0
$706$	−10.8923	−	18.8660i	−0.409937	−	0.710032i
$707$			5.26795i			0.198122i
$708$		0			0
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	−0.698275	−	0.715830i	$-0.746049\pi$
$709$	−11.3827	+	6.57180i	−0.427486	+	0.246809i	0.270789	+	0.962639i	$0.412715\pi$
$710$			17.6603i			0.662778i
$711$		0			0
$712$	−4.73205	+	8.19615i	−0.177341	+	0.307164i
$713$	−5.32051	−	3.07180i	−0.199255	−	0.115040i
$714$		0			0
$715$	−4.09808	−	16.5622i	−0.153259	−	0.619390i
$716$	16.0526			0.599912
$717$		0			0
$718$	0.562178	−	0.973721i	0.0209803	−	0.0363389i
$719$	14.7321	+	25.5167i	0.549413	+	0.951611i	0.998315	+	0.0580299i	$0.0184819\pi$
$719$	14.7321	+	25.5167i	0.549413	+	0.951611i	−0.448902	+	0.893581i	$0.648185\pi$
$720$		0			0
$721$	36.1244	−	20.8564i	1.34534	−	0.776733i
$722$	2.93782	−	1.69615i	0.109334	−	0.0631243i
$723$		0			0
$724$	−9.59808	−	16.6244i	−0.356710	−	0.617839i
$725$	19.9282	−	34.5167i	0.740115	−	1.28192i
$726$		0			0
$727$	30.9808			1.14901			0.574506	−	0.818500i	$-0.305194\pi$
$727$	30.9808			1.14901			0.574506	+	0.818500i	$0.305194\pi$
$728$	−9.46410	−	2.73205i	−0.350763	−	0.101257i
$729$		0			0
$730$	20.2583	+	11.6962i	0.749794	+	0.432894i
$731$	27.6865	−	47.9545i	1.02402	−	1.77366i
$732$		0			0
$733$			19.0000i			0.701781i	0.936416	+	0.350891i	$0.114121\pi$
$733$			19.0000i			0.701781i	−0.936416	+	0.350891i	$0.885879\pi$
$734$	9.75833	−	5.63397i	0.360187	−	0.207954i
$735$		0			0
$736$		−	4.19615i		−	0.154672i
$737$	8.32051	+	14.4115i	0.306490	+	0.530856i
$738$		0			0
$739$	2.53590	+	1.46410i	0.0932845	+	0.0538578i	0.545917	−	0.837840i	$-0.316182\pi$
$739$	2.53590	+	1.46410i	0.0932845	+	0.0538578i	−0.452632	+	0.891697i	$0.649515\pi$
$740$	13.1962			0.485100
$741$		0			0
$742$	17.6603			0.648328
$743$	−41.9090	−	24.1962i	−1.53749	−	0.887671i	−0.998985	−	0.0450491i	$-0.985656\pi$
$743$	−41.9090	−	24.1962i	−1.53749	−	0.887671i	−0.538506	−	0.842622i	$-0.681011\pi$
$744$		0			0
$745$	24.6244	+	42.6506i	0.902167	+	1.56260i
$746$			13.7321i			0.502766i
$747$		0			0
$748$	6.29423	−	3.63397i	0.230140	−	0.132871i
$749$		−	27.8564i		−	1.01785i
$750$		0			0
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.0973862	+	0.995247i	$0.531048\pi$
$751$	−24.9545	+	43.2224i	−0.910602	+	1.57721i	−0.813216	+	0.581962i	$0.802285\pi$
$752$	−1.90192	−	1.09808i	−0.0693560	−	0.0400427i
$753$		0			0
$754$	4.46410	−	15.4641i	0.162573	−	0.563169i
$755$	−25.1244			−0.914369
$756$		0			0
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	−0.991109	−	0.133056i	$-0.957521\pi$
$757$	−10.4641	+	18.1244i	−0.380324	+	0.658741i	0.610784	+	0.791797i	$0.290854\pi$
$758$	2.73205	+	4.73205i	0.0992326	+	0.171876i
$759$		0			0
$760$	15.2942	−	8.83013i	0.554780	−	0.320302i
$761$	9.80385	−	5.66025i	0.355389	−	0.205184i	−0.311667	−	0.950191i	$-0.600887\pi$
$761$	9.80385	−	5.66025i	0.355389	−	0.205184i	0.667056	+	0.745007i	$0.267554\pi$
$762$		0			0
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	3.46410	−	6.00000i	0.125327	−	0.217072i
$765$		0			0
$766$	1.46410			0.0529001
$767$	−8.00000	+	27.7128i	−0.288863	+	1.00065i
$768$		0			0
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.990879	−	0.134751i	$-0.0430235\pi$
$769$	37.9808	+	21.9282i	1.36962	+	0.790751i	0.378742	+	0.925502i	$0.376357\pi$
$770$	−6.46410	+	11.1962i	−0.232950	+	0.403481i
$771$		0			0
$772$		−	11.7321i		−	0.422246i
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.524459	−	0.851436i	$-0.324268\pi$
$773$	42.3731	−	24.4641i	1.52405	−	0.879913i	0.999594	−	0.0284768i	$-0.00906566\pi$
$774$		0			0
$775$		−	13.0718i		−	0.469553i
$776$	−3.00000	−	5.19615i	−0.107694	−	0.186531i
$777$		0			0
$778$	10.2058	+	5.89230i	0.365895	+	0.211249i
$779$	−44.4449			−1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$	−20.8301	−	12.0263i	−0.744884	−	0.430059i
$783$		0			0
$784$	0.232051	+	0.401924i	0.00828753	+	0.0143544i
$785$		−	28.3205i		−	1.01080i
$786$		0			0
$787$	−4.05256	+	2.33975i	−0.144458	+	0.0834029i	−0.570487	−	0.821307i	$-0.693246\pi$
$787$	−4.05256	+	2.33975i	−0.144458	+	0.0834029i	0.426029	+	0.904710i	$0.359912\pi$
$788$		−	17.8564i		−	0.636108i
$789$		0			0
$790$	−4.73205	+	8.19615i	−0.168359	+	0.291606i
$791$	−3.16987	−	1.83013i	−0.112708	−	0.0650718i
$792$		0			0
$793$	−31.8564	−	9.19615i	−1.13125	−	0.326565i
$794$	−20.3923			−0.723696
$795$		0			0
$796$	7.09808	−	12.2942i	0.251585	−	0.435757i
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	0.992492	+	0.122312i	$0.0390308\pi$
$797$	17.0000	+	29.4449i	0.602171	+	1.04299i	−0.390321	+	0.920679i	$0.627636\pi$
$798$		0			0
$799$	−10.9019	+	6.29423i	−0.385682	+	0.222674i
$800$	7.73205	−	4.46410i	0.273369	−	0.157830i
$801$		0			0
$802$	−4.03590	−	6.99038i	−0.142513	−	0.246839i
$803$	3.97372	−	6.88269i	0.140230	−	0.242885i
$804$		0			0
$805$	42.7846			1.50796
$806$	−1.26795	−	5.12436i	−0.0446616	−	0.180498i
$807$		0			0
$808$	−1.66987	−	0.964102i	−0.0587459	−	0.0339170i
$809$	−26.7942	+	46.4090i	−0.942035	+	1.63165i	−0.180453	+	0.983584i	$0.557756\pi$
$809$	−26.7942	+	46.4090i	−0.942035	+	1.63165i	−0.761582	+	0.648069i	$0.775577\pi$
$810$		0			0
$811$			17.1769i			0.603163i	0.953440	+	0.301582i	$0.0975145\pi$
$811$			17.1769i			0.603163i	−0.953440	+	0.301582i	$0.902485\pi$
$812$	−10.5622	+	6.09808i	−0.370660	+	0.214001i
$813$		0			0
$814$		−	4.48334i		−	0.157141i
$815$	−25.1244	−	43.5167i	−0.880068	−	1.52432i
$816$		0			0
$817$	−39.5885	−	22.8564i	−1.38502	−	0.799644i
$818$	17.7321			0.619987
$819$		0			0
$820$	−35.0526			−1.22409
$821$	−0.803848	−	0.464102i	−0.0280545	−	0.0161973i	0.485907	−	0.874010i	$-0.338489\pi$
$821$	−0.803848	−	0.464102i	−0.0280545	−	0.0161973i	−0.513962	+	0.857813i	$0.671823\pi$
$822$		0			0
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	0.959177	+	0.282806i	$0.0912654\pi$
$823$	20.7846	+	36.0000i	0.724506	+	1.25488i	−0.234671	+	0.972075i	$0.575401\pi$
$824$			15.2679i			0.531884i
$825$		0			0
$826$	18.9282	−	10.9282i	0.658596	−	0.380241i
$827$			26.5359i			0.922744i	0.887207	+	0.461372i	$0.152643\pi$
$827$			26.5359i			0.922744i	−0.887207	+	0.461372i	$0.847357\pi$
$828$		0			0
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	−0.951886	−	0.306452i	$-0.900858\pi$
$829$	−6.06218	+	10.5000i	−0.210548	+	0.364680i	0.741338	+	0.671132i	$0.234192\pi$
$830$	0.633975	+	0.366025i	0.0220056	+	0.0127049i
$831$		0			0
$832$	2.59808	−	2.50000i	0.0900721	−	0.0866719i
$833$	2.66025			0.0921723
$834$		0			0
$835$	17.6603	−	30.5885i	0.611158	−	1.05856i
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$		0			0
$838$	−15.1244	+	8.73205i	−0.522462	+	0.301644i
$839$	36.2487	−	20.9282i	1.25144	−	0.722522i	0.280048	−	0.959986i	$-0.409650\pi$
$839$	36.2487	−	20.9282i	1.25144	−	0.722522i	0.971396	+	0.237464i	$0.0763162\pi$
$840$		0			0
$841$	4.53590	+	7.85641i	0.156410	+	0.270911i
$842$	11.3564	−	19.6699i	0.391368	−	0.677869i
$843$		0			0
$844$	−16.3923			−0.564246
$845$	−48.4808	−	1.86603i	−1.66779	−	0.0641932i
$846$		0			0
$847$	−22.2224	−	12.8301i	−0.763572	−	0.440848i
$848$	−3.23205	+	5.59808i	−0.110989	+	0.192239i
$849$		0			0
$850$		−	51.1769i		−	1.75535i
$851$	−12.8494	+	7.41858i	−0.440471	+	0.254306i
$852$		0			0
$853$			54.1769i			1.85498i	0.373845	+	0.927491i	$0.378039\pi$
$853$			54.1769i			1.85498i	−0.373845	+	0.927491i	$0.621961\pi$
$854$	12.5622	+	21.7583i	0.429869	+	0.744555i
$855$		0			0
$856$	8.83013	+	5.09808i	0.301808	+	0.174249i
$857$	39.4449			1.34741			0.673705	−	0.739000i	$-0.264702\pi$
$857$	39.4449			1.34741			0.673705	+	0.739000i	$0.264702\pi$
$858$		0			0
$859$	−47.1244			−1.60786			−0.803931	−	0.594722i	$-0.797262\pi$
$859$	−47.1244			−1.60786			−0.803931	+	0.594722i	$0.797262\pi$
$860$	−31.2224	−	18.0263i	−1.06468	−	0.614691i
$861$		0			0
$862$	6.56218	+	11.3660i	0.223509	+	0.387128i
$863$			17.1244i			0.582920i	0.956583	+	0.291460i	$0.0941410\pi$
$863$			17.1244i			0.582920i	−0.956583	+	0.291460i	$0.905859\pi$
$864$		0			0
$865$	−14.1962	+	8.19615i	−0.482684	+	0.278678i
$866$			12.8564i			0.436878i
$867$		0			0
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	2.78461	+	1.60770i	0.0944614	+	0.0545373i
$870$		0			0
$871$	45.9352	−	11.3660i	1.55646	−	0.385123i
$872$	−1.46410			−0.0495807
$873$		0			0
$874$	−9.92820	+	17.1962i	−0.335826	+	0.581669i
$875$	20.0263	+	34.6865i	0.677012	+	1.17262i
$876$		0			0
$877$	20.7224	−	11.9641i	0.699747	−	0.403999i	−0.107506	−	0.994204i	$-0.534287\pi$
$877$	20.7224	−	11.9641i	0.699747	−	0.403999i	0.807253	+	0.590205i	$0.200953\pi$
$878$	−0.294229	+	0.169873i	−0.00992974	+	0.00573294i
$879$		0			0
$880$	−2.36603	−	4.09808i	−0.0797587	−	0.138146i
$881$	13.9186	−	24.1077i	0.468929	−	0.812209i	−0.530440	−	0.847722i	$-0.677973\pi$
$881$	13.9186	−	24.1077i	0.468929	−	0.812209i	0.999369	+	0.0355135i	$0.0113067\pi$
$882$		0			0
$883$	−42.9282			−1.44465			−0.722325	−	0.691554i	$-0.756926\pi$
$883$	−42.9282			−1.44465			−0.722325	+	0.691554i	$0.756926\pi$
$884$	−4.96410	−	20.0622i	−0.166961	−	0.674764i
$885$		0			0
$886$	−13.5167	−	7.80385i	−0.454101	−	0.262175i
$887$	18.9282	−	32.7846i	0.635547	−	1.10080i	−0.350852	−	0.936431i	$-0.614108\pi$
$887$	18.9282	−	32.7846i	0.635547	−	1.10080i	0.986399	−	0.164369i	$-0.0525586\pi$
$888$		0			0
$889$			26.9282i			0.903143i
$890$	30.5885	−	17.6603i	1.02533	−	0.591973i
$891$		0			0
$892$			26.9282i			0.901623i
$893$	5.19615	+	9.00000i	0.173883	+	0.301174i
$894$		0			0
$895$	−51.8827	−	29.9545i	−1.73425	−	1.00127i
$896$	−2.73205			−0.0912714
$897$		0			0
$898$	11.3205			0.377770
$899$	−5.66025	−	3.26795i	−0.188780	−	0.108992i
$900$		0			0
$901$	18.5263	+	32.0885i	0.617200	+	1.06902i
$902$			11.9090i			0.396525i
$903$		0			0
$904$	1.16025	−	0.669873i	0.0385895	−	0.0222796i
$905$			71.6410i			2.38143i
$906$		0			0
$907$	18.1962	−	31.5167i	0.604193	−	1.04649i	−0.387985	−	0.921666i	$-0.626829\pi$
$907$	18.1962	−	31.5167i	0.604193	−	1.04649i	0.992178	−	0.124828i	$-0.0398379\pi$
$908$	10.5622	+	6.09808i	0.350518	+	0.202372i
$909$		0			0
$910$	25.4904	+	26.4904i	0.844998	+	0.878148i
$911$	2.53590			0.0840181			0.0420090	−	0.999117i	$-0.486624\pi$
$911$	2.53590			0.0840181			0.0420090	+	0.999117i	$0.486624\pi$
$912$		0			0
$913$	0.124356	−	0.215390i	0.00411557	−	0.00712838i
$914$	−0.669873	−	1.16025i	−0.0221574	−	0.0383778i
$915$		0			0
$916$	−10.2679	+	5.92820i	−0.339263	+	0.195873i
$917$	−15.4641	+	8.92820i	−0.510670	+	0.294835i
$918$		0			0
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	−0.943836	−	0.330415i	$-0.892811\pi$
$919$	−22.9808	−	39.8038i	−0.758065	−	1.31301i	0.185770	−	0.982593i	$-0.440522\pi$
$920$	−7.83013	+	13.5622i	−0.258152	+	0.447132i
$921$		0			0
$922$	−22.2679			−0.733356
$923$	4.73205	−	16.3923i	0.155757	−	0.539559i
$924$		0			0
$925$	−27.3397	−	15.7846i	−0.898925	−	0.518995i
$926$	5.02628	−	8.70577i	0.165174	−	0.286089i
$927$		0			0
$928$		−	4.46410i		−	0.146541i
$929$	33.9904	−	19.6244i	1.11519	−	0.643854i	0.175020	−	0.984565i	$-0.444001\pi$
$929$	33.9904	−	19.6244i	1.11519	−	0.643854i	0.940168	+	0.340711i	$0.110668\pi$
$930$		0			0
$931$		−	2.19615i		−	0.0719760i
$932$	−3.92820	−	6.80385i	−0.128673	−	0.222867i
$933$		0			0
$934$	16.0981	+	9.29423i	0.526745	+	0.304116i
$935$	−27.1244			−0.887061
$936$		0			0
$937$	−5.24871			−0.171468			−0.0857340	−	0.996318i	$-0.527324\pi$
$937$	−5.24871			−0.171468			−0.0857340	+	0.996318i	$0.527324\pi$
$938$	−31.0526	−	17.9282i	−1.01390	−	0.585377i
$939$		0			0
$940$	4.09808	+	7.09808i	0.133665	+	0.231514i
$941$		−	12.6410i		−	0.412085i	−0.978543	−	0.206043i	$-0.933941\pi$
$941$		−	12.6410i		−	0.412085i	0.978543	−	0.206043i	$-0.0660586\pi$
$942$		0			0
$943$	34.1314	−	19.7058i	1.11147	−	0.641708i
$944$			8.00000i			0.260378i
$945$		0			0
$946$	−6.12436	+	10.6077i	−0.199120	+	0.344886i
$947$	−18.2487	−	10.5359i	−0.593003	−	0.342371i	0.173281	−	0.984872i	$-0.444563\pi$
$947$	−18.2487	−	10.5359i	−0.593003	−	0.342371i	−0.766284	+	0.642502i	$0.777897\pi$
$948$		0			0
$949$	−15.6699	−	16.2846i	−0.508666	−	0.528621i
$950$	−42.2487			−1.37073
$951$		0			0
$952$	−7.83013	+	13.5622i	−0.253776	+	0.439553i
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	−0.976969	−	0.213383i	$-0.931552\pi$
$953$	−20.7846	−	36.0000i	−0.673280	−	1.16615i	0.303689	−	0.952771i	$-0.401782\pi$
$954$		0			0
$955$	−22.3923	+	12.9282i	−0.724598	+	0.418347i
$956$	6.63397	−	3.83013i	0.214558	−	0.123875i
$957$		0			0
$958$	−16.7321	−	28.9808i	−0.540588	−	0.936326i
$959$	16.2942	−	28.2224i	0.526168	−	0.911350i
$960$		0			0
$961$	28.8564			0.930852
$962$	−12.2487	−	3.53590i	−0.394914	−	0.114002i
$963$		0			0
$964$	−11.7679	−	6.79423i	−0.379020	−	0.218827i
$965$	−21.8923	+	37.9186i	−0.704738	+	1.22064i
$966$		0			0
$967$		−	43.1244i		−	1.38679i	−0.720560	−	0.693393i	$-0.756115\pi$
$967$		−	43.1244i		−	1.38679i	0.720560	−	0.693393i	$-0.243885\pi$
$968$	8.13397	−	4.69615i	0.261436	−	0.150940i
$969$		0			0
$970$			22.3923i			0.718974i
$971$	15.1244	+	26.1962i	0.485364	+	0.840675i	0.999859	−	0.0168189i	$-0.00535388\pi$
$971$	15.1244	+	26.1962i	0.485364	+	0.840675i	−0.514495	+	0.857493i	$0.672021\pi$
$972$		0			0
$973$	−42.2487	−	24.3923i	−1.35443	−	0.781981i
$974$	−3.12436			−0.100111
$975$		0			0
$976$	−9.19615			−0.294362
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.975461	−	0.220174i	$-0.0706625\pi$
$977$	39.7750	+	22.9641i	1.27251	+	0.734687i	0.297054	+	0.954861i	$0.403996\pi$
$978$		0			0
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		−	1.73205i		−	0.0553283i
$981$		0			0
$982$	−7.56218	+	4.36603i	−0.241319	+	0.139325i
$983$			20.7846i			0.662926i	0.943468	+	0.331463i	$0.107542\pi$
$983$			20.7846i			0.662926i	−0.943468	+	0.331463i	$0.892458\pi$
$984$		0			0
$985$	−33.3205	+	57.7128i	−1.06168	+	1.83888i
$986$	−22.1603	−	12.7942i	−0.705726	−	0.407451i
$987$		0			0
$988$	−16.5622	+	4.09808i	−0.526913	+	0.130377i
$989$	40.5359			1.28897
$990$		0			0
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	−0.987756	−	0.156006i	$-0.950138\pi$
$991$	−11.2942	+	19.5622i	−0.358773	+	0.621413i	0.628983	+	0.777419i	$0.283471\pi$
$992$	−0.732051	−	1.26795i	−0.0232426	−	0.0402574i
$993$		0			0
$994$	−11.1962	+	6.46410i	−0.355120	+	0.205029i
$995$	−45.8827	+	26.4904i	−1.45458	+	0.839802i
$996$		0			0
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	0.646123	−	0.763234i	$-0.276389\pi$
$997$	−10.6699	−	18.4808i	−0.337918	−	0.585292i	−0.984041	+	0.177942i	$0.943056\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.l.c.199.2		4
3.2	odd	2		78.2.i.a.43.1	✓	4
4.3	odd	2		1872.2.by.h.433.1		4
12.11	even	2		624.2.bv.e.433.2		4
13.4	even	6		3042.2.b.i.1351.4		4
13.6	odd	12		3042.2.a.p.1.1		2
13.7	odd	12		3042.2.a.y.1.2		2
13.9	even	3		3042.2.b.i.1351.1		4
13.10	even	6	inner	234.2.l.c.127.2		4
15.2	even	4		1950.2.y.g.199.2		4
15.8	even	4		1950.2.y.b.199.1		4
15.14	odd	2		1950.2.bc.d.901.2		4
39.2	even	12		1014.2.e.g.991.2		4
39.5	even	4		1014.2.e.g.529.2		4
39.8	even	4		1014.2.e.i.529.1		4
39.11	even	12		1014.2.e.i.991.1		4
39.17	odd	6		1014.2.b.e.337.1		4
39.20	even	12		1014.2.a.i.1.1		2
39.23	odd	6		78.2.i.a.49.1	yes	4
39.29	odd	6		1014.2.i.a.361.2		4
39.32	even	12		1014.2.a.k.1.2		2
39.35	odd	6		1014.2.b.e.337.4		4
39.38	odd	2		1014.2.i.a.823.2		4
52.23	odd	6		1872.2.by.h.1297.2		4
156.23	even	6		624.2.bv.e.49.1		4
156.59	odd	12		8112.2.a.bj.1.1		2
156.71	odd	12		8112.2.a.bp.1.2		2
195.23	even	12		1950.2.y.g.49.2		4
195.62	even	12		1950.2.y.b.49.1		4
195.179	odd	6		1950.2.bc.d.751.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	3.2	odd	2
78.2.i.a.49.1	yes	4	39.23	odd	6
234.2.l.c.127.2		4	13.10	even	6	inner
234.2.l.c.199.2		4	1.1	even	1	trivial
624.2.bv.e.49.1		4	156.23	even	6
624.2.bv.e.433.2		4	12.11	even	2
1014.2.a.i.1.1		2	39.20	even	12
1014.2.a.k.1.2		2	39.32	even	12
1014.2.b.e.337.1		4	39.17	odd	6
1014.2.b.e.337.4		4	39.35	odd	6
1014.2.e.g.529.2		4	39.5	even	4
1014.2.e.g.991.2		4	39.2	even	12
1014.2.e.i.529.1		4	39.8	even	4
1014.2.e.i.991.1		4	39.11	even	12
1014.2.i.a.361.2		4	39.29	odd	6
1014.2.i.a.823.2		4	39.38	odd	2
1872.2.by.h.433.1		4	4.3	odd	2
1872.2.by.h.1297.2		4	52.23	odd	6
1950.2.y.b.49.1		4	195.62	even	12
1950.2.y.b.199.1		4	15.8	even	4
1950.2.y.g.49.2		4	195.23	even	12
1950.2.y.g.199.2		4	15.2	even	4
1950.2.bc.d.751.2		4	195.179	odd	6
1950.2.bc.d.901.2		4	15.14	odd	2
3042.2.a.p.1.1		2	13.6	odd	12
3042.2.a.y.1.2		2	13.7	odd	12
3042.2.b.i.1351.1		4	13.9	even	3
3042.2.b.i.1351.4		4	13.4	even	6
8112.2.a.bj.1.1		2	156.59	odd	12
8112.2.a.bp.1.2		2	156.71	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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(2.36603 - 1.36603i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -3.73205i q^{5} +(2.36603 - 1.36603i) q^{7} +1.00000i q^{8} +(1.86603 - 3.23205i) q^{10} +(-1.09808 - 0.633975i) q^{11} +(-2.59808 + 2.50000i) q^{13} +2.73205 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 + 4.96410i) q^{17} +(4.09808 - 2.36603i) q^{19} +(3.23205 - 1.86603i) q^{20} +(-0.633975 - 1.09808i) q^{22} +(-2.09808 + 3.63397i) q^{23} -8.92820 q^{25} +(-3.50000 + 0.866025i) q^{26} +(2.36603 + 1.36603i) q^{28} +(-2.23205 + 3.86603i) q^{29} +1.46410i q^{31} +(-0.866025 + 0.500000i) q^{32} +5.73205i q^{34} +(-5.09808 - 8.83013i) q^{35} +(3.06218 + 1.76795i) q^{37} +4.73205 q^{38} +3.73205 q^{40} +(-8.13397 - 4.69615i) q^{41} +(-4.83013 - 8.36603i) q^{43} -1.26795i q^{44} +(-3.63397 + 2.09808i) q^{46} +2.19615i q^{47} +(0.232051 - 0.401924i) q^{49} +(-7.73205 - 4.46410i) q^{50} +(-3.46410 - 1.00000i) q^{52} +6.46410 q^{53} +(-2.36603 + 4.09808i) q^{55} +(1.36603 + 2.36603i) q^{56} +(-3.86603 + 2.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(-0.732051 + 1.26795i) q^{62} -1.00000 q^{64} +(9.33013 + 9.69615i) q^{65} +(-11.3660 - 6.56218i) q^{67} +(-2.86603 + 4.96410i) q^{68} -10.1962i q^{70} +(-4.09808 + 2.36603i) q^{71} +6.26795i q^{73} +(1.76795 + 3.06218i) q^{74} +(4.09808 + 2.36603i) q^{76} -3.46410 q^{77} -2.53590 q^{79} +(3.23205 + 1.86603i) q^{80} +(-4.69615 - 8.13397i) q^{82} +0.196152i q^{83} +(18.5263 - 10.6962i) q^{85} -9.66025i q^{86} +(0.633975 - 1.09808i) q^{88} +(8.19615 + 4.73205i) q^{89} +(-2.73205 + 9.46410i) q^{91} -4.19615 q^{92} +(-1.09808 + 1.90192i) q^{94} +(-8.83013 - 15.2942i) q^{95} +(-5.19615 + 3.00000i) q^{97} +(0.401924 - 0.232051i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 6 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 6 * q^7	\( 4 q + 2 q^{4} + 6 q^{7} + 4 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} + 8 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 2 q^{23} - 8 q^{25} - 14 q^{26} + 6 q^{28} - 2 q^{29} - 10 q^{35} - 12 q^{37} + 12 q^{38} + 8 q^{40} - 36 q^{41} - 2 q^{43} - 18 q^{46} - 6 q^{49} - 24 q^{50} + 12 q^{53} - 6 q^{55} + 2 q^{56} - 12 q^{58} + 8 q^{61} + 4 q^{62} - 4 q^{64} + 20 q^{65} - 42 q^{67} - 8 q^{68} - 6 q^{71} + 14 q^{74} + 6 q^{76} - 24 q^{79} + 6 q^{80} + 2 q^{82} + 36 q^{85} + 6 q^{88} + 12 q^{89} - 4 q^{91} + 4 q^{92} + 6 q^{94} - 18 q^{95} + 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^4 + 6 * q^7 + 4 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 + 8 * q^17 + 6 * q^19 + 6 * q^20 - 6 * q^22 + 2 * q^23 - 8 * q^25 - 14 * q^26 + 6 * q^28 - 2 * q^29 - 10 * q^35 - 12 * q^37 + 12 * q^38 + 8 * q^40 - 36 * q^41 - 2 * q^43 - 18 * q^46 - 6 * q^49 - 24 * q^50 + 12 * q^53 - 6 * q^55 + 2 * q^56 - 12 * q^58 + 8 * q^61 + 4 * q^62 - 4 * q^64 + 20 * q^65 - 42 * q^67 - 8 * q^68 - 6 * q^71 + 14 * q^74 + 6 * q^76 - 24 * q^79 + 6 * q^80 + 2 * q^82 + 36 * q^85 + 6 * q^88 + 12 * q^89 - 4 * q^91 + 4 * q^92 + 6 * q^94 - 18 * q^95 + 12 * q^98

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