LMFDB - Embedded newform 624.2.bv.e.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bv (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:	$4.98266508613$
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:	$\Z[a_1, \ldots, a_{7}]$
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	$\chi$	$=$	624.49
Dual form			624.2.bv.e.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} -3.73205i q^{5} +(-2.36603 - 1.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} -3.73205i q^{5} +(-2.36603 - 1.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.09808 + 0.633975i) q^{11} +(-2.59808 - 2.50000i) q^{13} +(3.23205 - 1.86603i) q^{15} +(-2.86603 + 4.96410i) q^{17} +(-4.09808 - 2.36603i) q^{19} -2.73205i q^{21} +(-2.09808 - 3.63397i) q^{23} -8.92820 q^{25} -1.00000 q^{27} +(2.23205 + 3.86603i) q^{29} +1.46410i q^{31} +(-1.09808 - 0.633975i) q^{33} +(-5.09808 + 8.83013i) q^{35} +(3.06218 - 1.76795i) q^{37} +(0.866025 - 3.50000i) q^{39} +(8.13397 - 4.69615i) q^{41} +(4.83013 - 8.36603i) q^{43} +(3.23205 + 1.86603i) q^{45} -2.19615i q^{47} +(0.232051 + 0.401924i) q^{49} -5.73205 q^{51} -6.46410 q^{53} +(2.36603 + 4.09808i) q^{55} -4.73205i q^{57} +(6.92820 + 4.00000i) q^{59} +(4.59808 - 7.96410i) q^{61} +(2.36603 - 1.36603i) q^{63} +(-9.33013 + 9.69615i) q^{65} +(11.3660 - 6.56218i) q^{67} +(2.09808 - 3.63397i) q^{69} +(-4.09808 - 2.36603i) q^{71} -6.26795i q^{73} +(-4.46410 - 7.73205i) q^{75} +3.46410 q^{77} +2.53590 q^{79} +(-0.500000 - 0.866025i) q^{81} -0.196152i q^{83} +(18.5263 + 10.6962i) q^{85} +(-2.23205 + 3.86603i) q^{87} +(-8.19615 + 4.73205i) q^{89} +(2.73205 + 9.46410i) q^{91} +(-1.26795 + 0.732051i) q^{93} +(-8.83013 + 15.2942i) q^{95} +(-5.19615 - 3.00000i) q^{97} -1.26795i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 6 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 6 q^{15} - 8 q^{17} - 6 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{33} - 10 q^{35} - 12 q^{37} + 36 q^{41} + 2 q^{43} + 6 q^{45} - 6 q^{49} - 16 q^{51} - 12 q^{53} + 6 q^{55} + 8 q^{61} + 6 q^{63} - 20 q^{65} + 42 q^{67} - 2 q^{69} - 6 q^{71} - 4 q^{75} + 24 q^{79} - 2 q^{81} + 36 q^{85} - 2 q^{87} - 12 q^{89} + 4 q^{91} - 12 q^{93} - 18 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^7 - 2 * q^9 + 6 * q^11 + 6 * q^15 - 8 * q^17 - 6 * q^19 + 2 * q^23 - 8 * q^25 - 4 * q^27 + 2 * q^29 + 6 * q^33 - 10 * q^35 - 12 * q^37 + 36 * q^41 + 2 * q^43 + 6 * q^45 - 6 * q^49 - 16 * q^51 - 12 * q^53 + 6 * q^55 + 8 * q^61 + 6 * q^63 - 20 * q^65 + 42 * q^67 - 2 * q^69 - 6 * q^71 - 4 * q^75 + 24 * q^79 - 2 * q^81 + 36 * q^85 - 2 * q^87 - 12 * q^89 + 4 * q^91 - 12 * q^93 - 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$		−	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	$-0.506028\pi$
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.875338	+	0.483512i	$0.839361\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	−0.656322	−	0.754481i	$-0.727889\pi$
$11$	−1.09808	+	0.633975i	−0.331082	+	0.191151i	0.325239	+	0.945632i	$0.394555\pi$
$12$		0			0
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$		0			0
$15$	3.23205	−	1.86603i	0.834512	−	0.481806i
$16$		0			0
$17$	−2.86603	+	4.96410i	−0.695113	+	1.20397i	0.275029	+	0.961436i	$0.411312\pi$
$17$	−2.86603	+	4.96410i	−0.695113	+	1.20397i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	−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
$22$		0			0
$23$	−2.09808	−	3.63397i	−0.437479	−	0.757736i	0.560015	−	0.828482i	$-0.310795\pi$
$23$	−2.09808	−	3.63397i	−0.437479	−	0.757736i	−0.997494	+	0.0707462i	$0.977462\pi$
$24$		0			0
$25$	−8.92820			−1.78564
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.23205	+	3.86603i	0.414481	+	0.717903i	0.995374	−	0.0960774i	$-0.0306296\pi$
$29$	2.23205	+	3.86603i	0.414481	+	0.717903i	−0.580892	+	0.813980i	$0.697296\pi$
$30$		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			0
$33$	−1.09808	−	0.633975i	−0.191151	−	0.110361i
$34$		0			0
$35$	−5.09808	+	8.83013i	−0.861732	+	1.49256i
$36$		0			0
$37$	3.06218	−	1.76795i	0.503419	−	0.290649i	−0.226705	−	0.973963i	$-0.572795\pi$
$37$	3.06218	−	1.76795i	0.503419	−	0.290649i	0.730124	+	0.683314i	$0.239462\pi$
$38$		0			0
$39$	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	$0.0712582\pi$
$42$		0			0
$43$	4.83013	−	8.36603i	0.736587	−	1.27581i	−0.217436	−	0.976075i	$-0.569769\pi$
$43$	4.83013	−	8.36603i	0.736587	−	1.27581i	0.954023	−	0.299732i	$-0.0968974\pi$
$44$		0			0
$45$	3.23205	+	1.86603i	0.481806	+	0.278171i
$46$		0			0
$47$		−	2.19615i		−	0.320342i	−0.987089	−	0.160171i	$-0.948795\pi$
$47$		−	2.19615i		−	0.320342i	0.987089	−	0.160171i	$-0.0512045\pi$
$48$		0			0
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$		0			0
$51$	−5.73205			−0.802648
$52$		0			0
$53$	−6.46410			−0.887913			−0.443956	−	0.896048i	$-0.646425\pi$
$53$	−6.46410			−0.887913			−0.443956	+	0.896048i	$0.646425\pi$
$54$		0			0
$55$	2.36603	+	4.09808i	0.319035	+	0.552584i
$56$		0			0
$57$		−	4.73205i		−	0.626775i
$58$		0			0
$59$	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	$-0.0337026\pi$
$62$		0			0
$63$	2.36603	−	1.36603i	0.298091	−	0.172103i
$64$		0			0
$65$	−9.33013	+	9.69615i	−1.15726	+	1.20266i
$66$		0			0
$67$	11.3660	−	6.56218i	1.38858	−	0.801698i	0.395426	−	0.918498i	$-0.370597\pi$
$67$	11.3660	−	6.56218i	1.38858	−	0.801698i	0.993155	+	0.116800i	$0.0372638\pi$
$68$		0			0
$69$	2.09808	−	3.63397i	0.252579	−	0.437479i
$70$		0			0
$71$	−4.09808	−	2.36603i	−0.486352	−	0.280796i	0.236708	−	0.971581i	$-0.423932\pi$
$71$	−4.09808	−	2.36603i	−0.486352	−	0.280796i	−0.723060	+	0.690785i	$0.757265\pi$
$72$		0			0
$73$		−	6.26795i		−	0.733608i	−0.930298	−	0.366804i	$-0.880452\pi$
$73$		−	6.26795i		−	0.733608i	0.930298	−	0.366804i	$-0.119548\pi$
$74$		0			0
$75$	−4.46410	−	7.73205i	−0.515470	−	0.892820i
$76$		0			0
$77$	3.46410			0.394771
$78$		0			0
$79$	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
$82$		0			0
$83$		−	0.196152i		−	0.0215305i	−0.999942	−	0.0107653i	$-0.996573\pi$
$83$		−	0.196152i		−	0.0215305i	0.999942	−	0.0107653i	$-0.00342676\pi$
$84$		0			0
$85$	18.5263	+	10.6962i	2.00946	+	1.16016i
$86$		0			0
$87$	−2.23205	+	3.86603i	−0.239301	+	0.414481i
$88$		0			0
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.866946	−	0.498402i	$-0.833920\pi$
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.00184433	+	0.999998i	$0.500587\pi$
$90$		0			0
$91$	2.73205	+	9.46410i	0.286397	+	0.992107i
$92$		0			0
$93$	−1.26795	+	0.732051i	−0.131480	+	0.0759101i
$94$		0			0
$95$	−8.83013	+	15.2942i	−0.905952	+	1.56915i
$96$		0			0
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	0.212445	−	0.977173i	$-0.431857\pi$
$97$	−5.19615	−	3.00000i	−0.527589	−	0.304604i	−0.740034	+	0.672569i	$0.765191\pi$
$98$		0			0
$99$		−	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	$0.802750\pi$
$102$		0			0
$103$	−15.2679			−1.50440			−0.752198	−	0.658937i	$-0.771006\pi$
$103$	−15.2679			−1.50440			−0.752198	+	0.658937i	$0.771006\pi$
$104$		0			0
$105$	−10.1962			−0.995043
$106$		0			0
$107$	5.09808	+	8.83013i	0.492850	+	0.853641i	0.999966	−	0.00823695i	$-0.00262193\pi$
$107$	5.09808	+	8.83013i	0.492850	+	0.853641i	−0.507116	+	0.861878i	$0.669289\pi$
$108$		0			0
$109$		−	1.46410i		−	0.140236i	−0.997539	−	0.0701178i	$-0.977662\pi$
$109$		−	1.46410i		−	0.140236i	0.997539	−	0.0701178i	$-0.0223375\pi$
$110$		0			0
$111$	3.06218	+	1.76795i	0.290649	+	0.167806i
$112$		0			0
$113$	0.669873	−	1.16025i	0.0630163	−	0.109148i	−0.832796	−	0.553580i	$-0.813261\pi$
$113$	0.669873	−	1.16025i	0.0630163	−	0.109148i	0.895812	+	0.444432i	$0.146595\pi$
$114$		0			0
$115$	−13.5622	+	7.83013i	−1.26468	+	0.730163i
$116$		0			0
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$		0			0
$119$	13.5622	−	7.83013i	1.24324	−	0.717787i
$120$		0			0
$121$	−4.69615	+	8.13397i	−0.426923	+	0.739452i
$122$		0			0
$123$	8.13397	+	4.69615i	0.733416	+	0.423438i
$124$		0			0
$125$			14.6603i			1.31125i
$126$		0			0
$127$	4.92820	+	8.53590i	0.437307	+	0.757438i	0.997481	−	0.0709368i	$-0.0225989\pi$
$127$	4.92820	+	8.53590i	0.437307	+	0.757438i	−0.560173	+	0.828375i	$0.689266\pi$
$128$		0			0
$129$	9.66025			0.850538
$130$		0			0
$131$	−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
$134$		0			0
$135$			3.73205i			0.321204i
$136$		0			0
$137$	−10.3301	−	5.96410i	−0.882562	−	0.509548i	−0.0110599	−	0.999939i	$-0.503521\pi$
$137$	−10.3301	−	5.96410i	−0.882562	−	0.509548i	−0.871502	+	0.490391i	$0.836854\pi$
$138$		0			0
$139$	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
$142$		0			0
$143$	4.43782	+	1.09808i	0.371109	+	0.0918257i
$144$		0			0
$145$	14.4282	−	8.33013i	1.19820	−	0.691779i
$146$		0			0
$147$	−0.232051	+	0.401924i	−0.0191392	+	0.0331501i
$148$		0			0
$149$	11.4282	+	6.59808i	0.936235	+	0.540535i	0.888778	−	0.458338i	$-0.151555\pi$
$149$	11.4282	+	6.59808i	0.936235	+	0.540535i	0.0474568	+	0.998873i	$0.484888\pi$
$150$		0			0
$151$		−	6.73205i		−	0.547847i	−0.961752	−	0.273923i	$-0.911679\pi$
$151$		−	6.73205i		−	0.547847i	0.961752	−	0.273923i	$-0.0883214\pi$
$152$		0			0
$153$	−2.86603	−	4.96410i	−0.231704	−	0.401324i
$154$		0			0
$155$	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	$0.402074\pi$
$158$		0			0
$159$	−3.23205	−	5.59808i	−0.256318	−	0.443956i
$160$		0			0
$161$			11.4641i			0.903498i
$162$		0			0
$163$	−11.6603	−	6.73205i	−0.913302	−	0.527295i	−0.0318096	−	0.999494i	$-0.510127\pi$
$163$	−11.6603	−	6.73205i	−0.913302	−	0.527295i	−0.881492	+	0.472199i	$0.843460\pi$
$164$		0			0
$165$	−2.36603	+	4.09808i	−0.184195	+	0.319035i
$166$		0			0
$167$	8.19615	−	4.73205i	0.634237	−	0.366177i	−0.148154	−	0.988964i	$-0.547333\pi$
$167$	8.19615	−	4.73205i	0.634237	−	0.366177i	0.782391	+	0.622787i	$0.214000\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	4.09808	−	2.36603i	0.313388	−	0.180934i
$172$		0			0
$173$	2.19615	−	3.80385i	0.166970	−	0.289201i	−0.770383	−	0.637582i	$-0.779935\pi$
$173$	2.19615	−	3.80385i	0.166970	−	0.289201i	0.937353	+	0.348380i	$0.113268\pi$
$174$		0			0
$175$	21.1244	+	12.1962i	1.59685	+	0.921942i
$176$		0			0
$177$			8.00000i			0.601317i
$178$		0			0
$179$	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	$0.752855\pi$
$182$		0			0
$183$	9.19615			0.679799
$184$		0			0
$185$	−6.59808	−	11.4282i	−0.485100	−	0.840218i
$186$		0			0
$187$		−	7.26795i		−	0.531485i
$188$		0			0
$189$	2.36603	+	1.36603i	0.172103	+	0.0993637i
$190$		0			0
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	−0.963706	−	0.266966i	$-0.913979\pi$
$191$	−3.46410	+	6.00000i	−0.250654	+	0.434145i	0.713052	+	0.701111i	$0.247312\pi$
$192$		0			0
$193$	−10.1603	+	5.86603i	−0.731351	+	0.422246i	−0.818916	−	0.573913i	$-0.805425\pi$
$193$	−10.1603	+	5.86603i	−0.731351	+	0.422246i	0.0875652	+	0.996159i	$0.472091\pi$
$194$		0			0
$195$	−13.0622	−	3.23205i	−0.935402	−	0.231452i
$196$		0			0
$197$	15.4641	−	8.92820i	1.10177	−	0.636108i	0.165086	−	0.986279i	$-0.447210\pi$
$197$	15.4641	−	8.92820i	1.10177	−	0.636108i	0.936686	+	0.350171i	$0.113877\pi$
$198$		0			0
$199$	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			0
$203$		−	12.1962i		−	0.856002i
$204$		0			0
$205$	−17.5263	−	30.3564i	−1.22409	−	2.12018i
$206$		0			0
$207$	4.19615			0.291653
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	8.19615	+	14.1962i	0.564246	+	0.977303i	0.997119	+	0.0758485i	$0.0241665\pi$
$211$	8.19615	+	14.1962i	0.564246	+	0.977303i	−0.432873	+	0.901455i	$0.642500\pi$
$212$		0			0
$213$		−	4.73205i		−	0.324235i
$214$		0			0
$215$	−31.2224	−	18.0263i	−2.12935	−	1.22938i
$216$		0			0
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$		0			0
$219$	5.42820	−	3.13397i	0.366804	−	0.211774i
$220$		0			0
$221$	19.8564	−	5.73205i	1.33569	−	0.385579i
$222$		0			0
$223$	−23.3205	+	13.4641i	−1.56166	+	0.901623i	−0.564567	+	0.825387i	$0.690957\pi$
$223$	−23.3205	+	13.4641i	−1.56166	+	0.901623i	−0.997090	+	0.0762356i	$0.975710\pi$
$224$		0			0
$225$	4.46410	−	7.73205i	0.297607	−	0.515470i
$226$		0			0
$227$	10.5622	+	6.09808i	0.701036	+	0.404744i	0.807733	−	0.589548i	$-0.200694\pi$
$227$	10.5622	+	6.09808i	0.701036	+	0.404744i	−0.106697	+	0.994292i	$0.534027\pi$
$228$		0			0
$229$		−	11.8564i		−	0.783493i	−0.920073	−	0.391747i	$-0.871871\pi$
$229$		−	11.8564i		−	0.783493i	0.920073	−	0.391747i	$-0.128129\pi$
$230$		0			0
$231$	1.73205	+	3.00000i	0.113961	+	0.197386i
$232$		0			0
$233$	7.85641			0.514690			0.257345	−	0.966320i	$-0.417152\pi$
$233$	7.85641			0.514690			0.257345	+	0.966320i	$0.417152\pi$
$234$		0			0
$235$	−8.19615			−0.534658
$236$		0			0
$237$	1.26795	+	2.19615i	0.0823622	+	0.142655i
$238$		0			0
$239$			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	$0.810857\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	1.50000	−	0.866025i	0.0958315	−	0.0553283i
$246$		0			0
$247$	4.73205	+	16.3923i	0.301093	+	1.04302i
$248$		0			0
$249$	0.169873	−	0.0980762i	0.0107653	−	0.00621533i
$250$		0			0
$251$	−6.73205	+	11.6603i	−0.424923	+	0.735989i	−0.996413	−	0.0846203i	$-0.973032\pi$
$251$	−6.73205	+	11.6603i	−0.424923	+	0.735989i	0.571490	+	0.820609i	$0.306366\pi$
$252$		0			0
$253$	4.60770	+	2.66025i	0.289683	+	0.167249i
$254$		0			0
$255$			21.3923i			1.33964i
$256$		0			0
$257$	4.66987	+	8.08846i	0.291299	+	0.504544i	0.974117	−	0.226044i	$-0.0725793\pi$
$257$	4.66987	+	8.08846i	0.291299	+	0.504544i	−0.682818	+	0.730588i	$0.739246\pi$
$258$		0			0
$259$	−9.66025			−0.600259
$260$		0			0
$261$	−4.46410			−0.276321
$262$		0			0
$263$	−5.02628	−	8.70577i	−0.309934	−	0.536821i	0.668414	−	0.743790i	$-0.266974\pi$
$263$	−5.02628	−	8.70577i	−0.309934	−	0.536821i	−0.978348	+	0.206969i	$0.933640\pi$
$264$		0			0
$265$			24.1244i			1.48195i
$266$		0			0
$267$	−8.19615	−	4.73205i	−0.501596	−	0.289597i
$268$		0			0
$269$	−2.73205	+	4.73205i	−0.166576	+	0.288518i	−0.937214	−	0.348755i	$-0.886604\pi$
$269$	−2.73205	+	4.73205i	−0.166576	+	0.288518i	0.770638	+	0.637273i	$0.219938\pi$
$270$		0			0
$271$	18.9282	−	10.9282i	1.14981	−	0.663841i	0.200966	−	0.979598i	$-0.435592\pi$
$271$	18.9282	−	10.9282i	1.14981	−	0.663841i	0.948840	+	0.315757i	$0.102258\pi$
$272$		0			0
$273$	−6.83013	+	7.09808i	−0.413378	+	0.429595i
$274$		0			0
$275$	9.80385	−	5.66025i	0.591194	−	0.341326i
$276$		0			0
$277$	−2.86603	+	4.96410i	−0.172203	+	0.298264i	−0.939190	−	0.343399i	$-0.888422\pi$
$277$	−2.86603	+	4.96410i	−0.172203	+	0.298264i	0.766987	+	0.641663i	$0.221755\pi$
$278$		0			0
$279$	−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	$0.880217\pi$
$282$		0			0
$283$	−12.8301	−	22.2224i	−0.762672	−	1.32099i	−0.941469	−	0.337100i	$-0.890554\pi$
$283$	−12.8301	−	22.2224i	−0.762672	−	1.32099i	0.178797	−	0.983886i	$-0.442780\pi$
$284$		0			0
$285$	−17.6603			−1.04610
$286$		0			0
$287$	−25.6603			−1.51468
$288$		0			0
$289$	−7.92820	−	13.7321i	−0.466365	−	0.807768i
$290$		0			0
$291$		−	6.00000i		−	0.351726i
$292$		0			0
$293$	−26.4282	−	15.2583i	−1.54395	−	0.891401i	−0.998584	−	0.0532048i	$-0.983056\pi$
$293$	−26.4282	−	15.2583i	−1.54395	−	0.891401i	−0.545368	−	0.838196i	$-0.683610\pi$
$294$		0			0
$295$	14.9282	−	25.8564i	0.869154	−	1.50542i
$296$		0			0
$297$	1.09808	−	0.633975i	0.0637168	−	0.0367869i
$298$		0			0
$299$	−3.63397	+	14.6865i	−0.210158	+	0.849344i
$300$		0			0
$301$	−22.8564	+	13.1962i	−1.31742	+	0.760614i
$302$		0			0
$303$	−0.964102	+	1.66987i	−0.0553862	+	0.0959317i
$304$		0			0
$305$	−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	$0.777026\pi$
$308$		0			0
$309$	−7.63397	−	13.2224i	−0.434282	−	0.752198i
$310$		0			0
$311$	−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	$0.440864\pi$
$314$		0			0
$315$	−5.09808	−	8.83013i	−0.287244	−	0.497521i
$316$		0			0
$317$		−	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
$320$		0			0
$321$	−5.09808	+	8.83013i	−0.284547	+	0.492850i
$322$		0			0
$323$	23.4904	−	13.5622i	1.30704	−	0.754620i
$324$		0			0
$325$	23.1962	+	22.3205i	1.28669	+	1.23812i
$326$		0			0
$327$	1.26795	−	0.732051i	0.0701178	−	0.0404825i
$328$		0			0
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.0583130	−	0.998298i	$-0.518572\pi$
$331$	−17.3205	−	10.0000i	−0.952021	−	0.549650i	−0.893708	+	0.448649i	$0.851905\pi$
$332$		0			0
$333$			3.53590i			0.193766i
$334$		0			0
$335$	−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	$0.307694\pi$
$338$		0			0
$339$	1.33975			0.0727650
$340$		0			0
$341$	−0.928203	−	1.60770i	−0.0502650	−	0.0870616i
$342$		0			0
$343$			17.8564i			0.964155i
$344$		0			0
$345$	−13.5622	−	7.83013i	−0.730163	−	0.421560i
$346$		0			0
$347$	16.5622	−	28.6865i	0.889104	−	1.53997i	0.0481683	−	0.998839i	$-0.484662\pi$
$347$	16.5622	−	28.6865i	0.889104	−	1.53997i	0.840936	−	0.541135i	$-0.182005\pi$
$348$		0			0
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	−0.100924	−	0.994894i	$-0.532180\pi$
$349$	13.2679	−	7.66025i	0.710217	−	0.410044i	0.811141	+	0.584850i	$0.198847\pi$
$350$		0			0
$351$	2.59808	+	2.50000i	0.138675	+	0.133440i
$352$		0			0
$353$	18.8660	−	10.8923i	1.00414	−	0.579739i	0.0946674	−	0.995509i	$-0.469821\pi$
$353$	18.8660	−	10.8923i	1.00414	−	0.579739i	0.909470	+	0.415770i	$0.136488\pi$
$354$		0			0
$355$	−8.83013	+	15.2942i	−0.468654	+	0.811733i
$356$		0			0
$357$	13.5622	+	7.83013i	0.717787	+	0.414414i
$358$		0			0
$359$			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
$362$		0			0
$363$	−9.39230			−0.492968
$364$		0			0
$365$	−23.3923			−1.22441
$366$		0			0
$367$	−5.63397	−	9.75833i	−0.294091	−	0.509381i	0.680682	−	0.732579i	$-0.261684\pi$
$367$	−5.63397	−	9.75833i	−0.294091	−	0.509381i	−0.974773	+	0.223198i	$0.928350\pi$
$368$		0			0
$369$			9.39230i			0.488944i
$370$		0			0
$371$	15.2942	+	8.83013i	0.794037	+	0.458437i
$372$		0			0
$373$	6.86603	−	11.8923i	0.355509	−	0.615760i	−0.631696	−	0.775216i	$-0.717641\pi$
$373$	6.86603	−	11.8923i	0.355509	−	0.615760i	0.987205	+	0.159456i	$0.0509741\pi$
$374$		0			0
$375$	−12.6962	+	7.33013i	−0.655626	+	0.378526i
$376$		0			0
$377$	3.86603	−	15.6244i	0.199110	−	0.804695i
$378$		0			0
$379$	−4.73205	+	2.73205i	−0.243069	+	0.140336i	−0.616587	−	0.787287i	$-0.711485\pi$
$379$	−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
$382$		0			0
$383$	1.26795	+	0.732051i	0.0647892	+	0.0374060i	0.532045	−	0.846716i	$-0.321424\pi$
$383$	1.26795	+	0.732051i	0.0647892	+	0.0374060i	−0.467255	+	0.884122i	$0.654757\pi$
$384$		0			0
$385$		−	12.9282i		−	0.658882i
$386$		0			0
$387$	4.83013	+	8.36603i	0.245529	+	0.425269i
$388$		0			0
$389$	−11.7846			−0.597503			−0.298752	−	0.954331i	$-0.596570\pi$
$389$	−11.7846			−0.597503			−0.298752	+	0.954331i	$0.596570\pi$
$390$		0			0
$391$	24.0526			1.21639
$392$		0			0
$393$	−3.26795	−	5.66025i	−0.164846	−	0.285522i
$394$		0			0
$395$		−	9.46410i		−	0.476191i
$396$		0			0
$397$	−17.6603	−	10.1962i	−0.886343	−	0.511730i	−0.0135983	−	0.999908i	$-0.504329\pi$
$397$	−17.6603	−	10.1962i	−0.886343	−	0.511730i	−0.872744	+	0.488177i	$0.837662\pi$
$398$		0			0
$399$	−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	$0.268738\pi$
$402$		0			0
$403$	3.66025	−	3.80385i	0.182330	−	0.189483i
$404$		0			0
$405$	−3.23205	+	1.86603i	−0.160602	+	0.0927235i
$406$		0			0
$407$	−2.24167	+	3.88269i	−0.111115	+	0.192458i
$408$		0			0
$409$	15.3564	+	8.86603i	0.759325	+	0.438397i	0.829053	−	0.559169i	$-0.188880\pi$
$409$	15.3564	+	8.86603i	0.759325	+	0.438397i	−0.0697281	+	0.997566i	$0.522213\pi$
$410$		0			0
$411$		−	11.9282i		−	0.588375i
$412$		0			0
$413$	−10.9282	−	18.9282i	−0.537742	−	0.931396i
$414$		0			0
$415$	−0.732051			−0.0359350
$416$		0			0
$417$	17.8564			0.874432
$418$		0			0
$419$	−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	$0.813301\pi$
$422$		0			0
$423$	1.90192	+	1.09808i	0.0924747	+	0.0533903i
$424$		0			0
$425$	25.5885	−	44.3205i	1.24122	−	2.14986i
$426$		0			0
$427$	−21.7583	+	12.5622i	−1.05296	+	0.607926i
$428$		0			0
$429$	1.26795	+	4.39230i	0.0612172	+	0.212062i
$430$		0			0
$431$	11.3660	−	6.56218i	0.547482	−	0.316089i	−0.200624	−	0.979668i	$-0.564297\pi$
$431$	11.3660	−	6.56218i	0.547482	−	0.316089i	0.748106	+	0.663579i	$0.230964\pi$
$432$		0			0
$433$	6.42820	−	11.1340i	0.308920	−	0.535065i	−0.669207	−	0.743076i	$-0.733366\pi$
$433$	6.42820	−	11.1340i	0.308920	−	0.535065i	0.978126	+	0.208012i	$0.0666992\pi$
$434$		0			0
$435$	14.4282	+	8.33013i	0.691779	+	0.399399i
$436$		0			0
$437$			19.8564i			0.949861i
$438$		0			0
$439$	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
$442$		0			0
$443$	−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
$446$		0			0
$447$			13.1962i			0.624157i
$448$		0			0
$449$	−9.80385	−	5.66025i	−0.462672	−	0.267124i	0.250495	−	0.968118i	$-0.419407\pi$
$449$	−9.80385	−	5.66025i	−0.462672	−	0.267124i	−0.713167	+	0.700994i	$0.752740\pi$
$450$		0			0
$451$	−5.95448	+	10.3135i	−0.280386	+	0.485642i
$452$		0			0
$453$	5.83013	−	3.36603i	0.273923	−	0.158150i
$454$		0			0
$455$	35.3205	−	10.1962i	1.65585	−	0.478003i
$456$		0			0
$457$	−1.16025	+	0.669873i	−0.0542744	+	0.0313353i	−0.526892	−	0.849932i	$-0.676643\pi$
$457$	−1.16025	+	0.669873i	−0.0542744	+	0.0313353i	0.472617	+	0.881268i	$0.343309\pi$
$458$		0			0
$459$	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	$0.493135\pi$
$462$		0			0
$463$		−	10.0526i		−	0.467182i	−0.972335	−	0.233591i	$-0.924952\pi$
$463$		−	10.0526i		−	0.467182i	0.972335	−	0.233591i	$-0.0750477\pi$
$464$		0			0
$465$	2.73205	+	4.73205i	0.126696	+	0.219444i
$466$		0			0
$467$	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
$470$		0			0
$471$	3.79423	+	6.57180i	0.174829	+	0.302812i
$472$		0			0
$473$			12.2487i			0.563196i
$474$		0			0
$475$	36.5885	+	21.1244i	1.67879	+	0.969252i
$476$		0			0
$477$	3.23205	−	5.59808i	0.147985	−	0.256318i
$478$		0			0
$479$	−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
$482$		0			0
$483$	−9.92820	+	5.73205i	−0.451749	+	0.260817i
$484$		0			0
$485$	−11.1962	+	19.3923i	−0.508391	+	0.880559i
$486$		0			0
$487$	2.70577	+	1.56218i	0.122610	+	0.0707890i	0.560051	−	0.828458i	$-0.310782\pi$
$487$	2.70577	+	1.56218i	0.122610	+	0.0707890i	−0.437441	+	0.899247i	$0.644115\pi$
$488$		0			0
$489$		−	13.4641i		−	0.608868i
$490$		0			0
$491$	−4.36603	−	7.56218i	−0.197036	−	0.341276i	0.750530	−	0.660836i	$-0.229798\pi$
$491$	−4.36603	−	7.56218i	−0.197036	−	0.341276i	−0.947566	+	0.319560i	$0.896465\pi$
$492$		0			0
$493$	−25.5885			−1.15245
$494$		0			0
$495$	−4.73205			−0.212690
$496$		0			0
$497$	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	$0.745853\pi$
$500$		0			0
$501$	8.19615	+	4.73205i	0.366177	+	0.211412i
$502$		0			0
$503$	20.4904	−	35.4904i	0.913621	−	1.58244i	0.104713	−	0.994502i	$-0.466608\pi$
$503$	20.4904	−	35.4904i	0.913621	−	1.58244i	0.808908	−	0.587935i	$-0.200059\pi$
$504$		0			0
$505$	6.23205	−	3.59808i	0.277323	−	0.160112i
$506$		0			0
$507$	−11.0000	+	6.92820i	−0.488527	+	0.307692i
$508$		0			0
$509$	−11.8923	+	6.86603i	−0.527117	+	0.304331i	−0.739842	−	0.672781i	$-0.765100\pi$
$509$	−11.8923	+	6.86603i	−0.527117	+	0.304331i	0.212725	+	0.977112i	$0.431766\pi$
$510$		0			0
$511$	−8.56218	+	14.8301i	−0.378768	+	0.656046i
$512$		0			0
$513$	4.09808	+	2.36603i	0.180934	+	0.104463i
$514$		0			0
$515$			56.9808i			2.51087i
$516$		0			0
$517$	1.39230	+	2.41154i	0.0612335	+	0.106060i
$518$		0			0
$519$	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	$0.137710\pi$
$522$		0			0
$523$	−11.2224	−	19.4378i	−0.490723	−	0.849957i	0.509220	−	0.860636i	$-0.329934\pi$
$523$	−11.2224	−	19.4378i	−0.490723	−	0.849957i	−0.999943	+	0.0106796i	$0.996601\pi$
$524$		0			0
$525$			24.3923i			1.06457i
$526$		0			0
$527$	−7.26795	−	4.19615i	−0.316597	−	0.182787i
$528$		0			0
$529$	2.69615	−	4.66987i	0.117224	−	0.203038i
$530$		0			0
$531$	−6.92820	+	4.00000i	−0.300658	+	0.173585i
$532$		0			0
$533$	−32.8731	−	8.13397i	−1.42389	−	0.352322i
$534$		0			0
$535$	32.9545	−	19.0263i	1.42475	−	0.822578i
$536$		0			0
$537$	−8.02628	+	13.9019i	−0.346360	+	0.599912i
$538$		0			0
$539$	−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	$0.961040\pi$
$542$		0			0
$543$	−9.59808	−	16.6244i	−0.411893	−	0.713419i
$544$		0			0
$545$	−5.46410			−0.234056
$546$		0			0
$547$	4.19615			0.179415			0.0897073	−	0.995968i	$-0.471407\pi$
$547$	4.19615			0.179415			0.0897073	+	0.995968i	$0.471407\pi$
$548$		0			0
$549$	4.59808	+	7.96410i	0.196241	+	0.339900i
$550$		0			0
$551$		−	21.1244i		−	0.899928i
$552$		0			0
$553$	−6.00000	−	3.46410i	−0.255146	−	0.147309i
$554$		0			0
$555$	6.59808	−	11.4282i	0.280073	−	0.485100i
$556$		0			0
$557$	36.6962	−	21.1865i	1.55487	−	0.897702i	0.557132	−	0.830424i	$-0.311902\pi$
$557$	36.6962	−	21.1865i	1.55487	−	0.897702i	0.997734	−	0.0672780i	$-0.0214314\pi$
$558$		0			0
$559$	−33.4641	+	9.66025i	−1.41538	+	0.408585i
$560$		0			0
$561$	6.29423	−	3.63397i	0.265743	−	0.153427i
$562$		0			0
$563$	−17.4641	+	30.2487i	−0.736024	+	1.27483i	0.218248	+	0.975893i	$0.429966\pi$
$563$	−17.4641	+	30.2487i	−0.736024	+	1.27483i	−0.954273	+	0.298938i	$0.903368\pi$
$564$		0			0
$565$	−4.33013	−	2.50000i	−0.182170	−	0.105176i
$566$		0			0
$567$			2.73205i			0.114735i
$568$		0			0
$569$	15.3205	+	26.5359i	0.642269	+	1.11244i	0.984925	+	0.172982i	$0.0553402\pi$
$569$	15.3205	+	26.5359i	0.642269	+	1.11244i	−0.342656	+	0.939461i	$0.611326\pi$
$570$		0			0
$571$	14.0526			0.588081			0.294041	−	0.955793i	$-0.405000\pi$
$571$	14.0526			0.588081			0.294041	+	0.955793i	$0.405000\pi$
$572$		0			0
$573$	−6.92820			−0.289430
$574$		0			0
$575$	18.7321	+	32.4449i	0.781181	+	1.35304i
$576$		0			0
$577$		−	3.73205i		−	0.155367i	−0.996978	−	0.0776837i	$-0.975248\pi$
$577$		−	3.73205i		−	0.155367i	0.996978	−	0.0776837i	$-0.0247524\pi$
$578$		0			0
$579$	−10.1603	−	5.86603i	−0.422246	−	0.243784i
$580$		0			0
$581$	−0.267949	+	0.464102i	−0.0111164	+	0.0192542i
$582$		0			0
$583$	7.09808	−	4.09808i	0.293972	−	0.169725i
$584$		0			0
$585$	−3.73205	−	12.9282i	−0.154301	−	0.534515i
$586$		0			0
$587$	13.8564	−	8.00000i	0.571915	−	0.330195i	−0.185999	−	0.982550i	$-0.559552\pi$
$587$	13.8564	−	8.00000i	0.571915	−	0.330195i	0.757914	+	0.652355i	$0.226219\pi$
$588$		0			0
$589$	3.46410	−	6.00000i	0.142736	−	0.247226i
$590$		0			0
$591$	15.4641	+	8.92820i	0.636108	+	0.367257i
$592$		0			0
$593$		−	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
$596$		0			0
$597$	14.1962			0.581010
$598$		0			0
$599$	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	$0.885031\pi$
$602$		0			0
$603$			13.1244i			0.534465i
$604$		0			0
$605$	30.3564	+	17.5263i	1.23416	+	0.712545i
$606$		0			0
$607$	−20.3923	+	35.3205i	−0.827698	+	1.43362i	0.0721415	+	0.997394i	$0.477017\pi$
$607$	−20.3923	+	35.3205i	−0.827698	+	1.43362i	−0.899840	+	0.436221i	$0.856317\pi$
$608$		0			0
$609$	10.5622	−	6.09808i	0.428001	−	0.247107i
$610$		0			0
$611$	−5.49038	+	5.70577i	−0.222117	+	0.230831i
$612$		0			0
$613$	8.13397	−	4.69615i	0.328528	−	0.189676i	−0.326659	−	0.945142i	$-0.605923\pi$
$613$	8.13397	−	4.69615i	0.328528	−	0.189676i	0.655187	+	0.755466i	$0.272590\pi$
$614$		0			0
$615$	17.5263	−	30.3564i	0.706728	−	1.22409i
$616$		0			0
$617$	−11.4737	−	6.62436i	−0.461915	−	0.266687i	0.250934	−	0.968004i	$-0.419262\pi$
$617$	−11.4737	−	6.62436i	−0.461915	−	0.266687i	−0.712849	+	0.701318i	$0.752596\pi$
$618$		0			0
$619$		−	17.4641i		−	0.701942i	−0.936386	−	0.350971i	$-0.885852\pi$
$619$		−	17.4641i		−	0.701942i	0.936386	−	0.350971i	$-0.114148\pi$
$620$		0			0
$621$	2.09808	+	3.63397i	0.0841929	+	0.145826i
$622$		0			0
$623$	25.8564			1.03592
$624$		0			0
$625$	10.0718			0.402872
$626$		0			0
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$		0			0
$629$			20.2679i			0.808136i
$630$		0			0
$631$	−6.67949	−	3.85641i	−0.265906	−	0.153521i	0.361119	−	0.932520i	$-0.382395\pi$
$631$	−6.67949	−	3.85641i	−0.265906	−	0.153521i	−0.627026	+	0.778998i	$0.715728\pi$
$632$		0			0
$633$	−8.19615	+	14.1962i	−0.325768	+	0.564246i
$634$		0			0
$635$	31.8564	−	18.3923i	1.26418	−	0.729876i
$636$		0			0
$637$	0.401924	−	1.62436i	0.0159248	−	0.0643593i
$638$		0			0
$639$	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	$0.995168\pi$
$642$		0			0
$643$	12.0000	+	6.92820i	0.473234	+	0.273222i	0.717592	−	0.696463i	$-0.245244\pi$
$643$	12.0000	+	6.92820i	0.473234	+	0.273222i	−0.244359	+	0.969685i	$0.578577\pi$
$644$		0			0
$645$		−	36.0526i		−	1.41957i
$646$		0			0
$647$	11.1244	+	19.2679i	0.437344	+	0.757501i	0.997484	−	0.0708966i	$-0.0225860\pi$
$647$	11.1244	+	19.2679i	0.437344	+	0.757501i	−0.560140	+	0.828398i	$0.689253\pi$
$648$		0			0
$649$	−10.1436			−0.398171
$650$		0			0
$651$	4.00000			0.156772
$652$		0			0
$653$	8.73205	+	15.1244i	0.341712	+	0.591862i	0.984751	−	0.173972i	$-0.0556601\pi$
$653$	8.73205	+	15.1244i	0.341712	+	0.591862i	−0.643039	+	0.765833i	$0.722327\pi$
$654$		0			0
$655$			24.3923i			0.953086i
$656$		0			0
$657$	5.42820	+	3.13397i	0.211774	+	0.122268i
$658$		0			0
$659$	−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	$0.262220\pi$
$662$		0			0
$663$	14.8923	+	14.3301i	0.578369	+	0.556536i
$664$		0			0
$665$	41.7846	−	24.1244i	1.62034	−	0.935502i
$666$		0			0
$667$	9.36603	−	16.2224i	0.362654	−	0.628135i
$668$		0			0
$669$	−23.3205	−	13.4641i	−0.901623	−	0.520552i
$670$		0			0
$671$			11.6603i			0.450139i
$672$		0			0
$673$	13.9641	+	24.1865i	0.538277	+	0.932322i	0.998997	+	0.0447770i	$0.0142577\pi$
$673$	13.9641	+	24.1865i	0.538277	+	0.932322i	−0.460720	+	0.887545i	$0.652409\pi$
$674$		0			0
$675$	8.92820			0.343647
$676$		0			0
$677$	−45.4641			−1.74733			−0.873664	−	0.486530i	$-0.838262\pi$
$677$	−45.4641			−1.74733			−0.873664	+	0.486530i	$0.838262\pi$
$678$		0			0
$679$	8.19615	+	14.1962i	0.314539	+	0.544798i
$680$		0			0
$681$			12.1962i			0.467358i
$682$		0			0
$683$	−8.78461	−	5.07180i	−0.336134	−	0.194067i	0.322427	−	0.946594i	$-0.395501\pi$
$683$	−8.78461	−	5.07180i	−0.336134	−	0.194067i	−0.658561	+	0.752527i	$0.728835\pi$
$684$		0			0
$685$	−22.2583	+	38.5526i	−0.850447	+	1.47302i
$686$		0			0
$687$	10.2679	−	5.92820i	0.391747	−	0.226175i
$688$		0			0
$689$	16.7942	+	16.1603i	0.639809	+	0.615657i
$690$		0			0
$691$	37.8109	−	21.8301i	1.43839	−	0.830457i	0.440656	−	0.897676i	$-0.354746\pi$
$691$	37.8109	−	21.8301i	1.43839	−	0.830457i	0.997738	+	0.0672190i	$0.0214126\pi$
$692$		0			0
$693$	−1.73205	+	3.00000i	−0.0657952	+	0.113961i
$694$		0			0
$695$	−57.7128	−	33.3205i	−2.18917	−	1.26392i
$696$		0			0
$697$			53.8372i			2.03923i
$698$		0			0
$699$	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			0
$703$	−16.7321			−0.631061
$704$		0			0
$705$	−4.09808	−	7.09808i	−0.154342	−	0.267329i
$706$		0			0
$707$		−	5.26795i		−	0.198122i
$708$		0			0
$709$	−11.3827	−	6.57180i	−0.427486	−	0.246809i	0.270789	−	0.962639i	$-0.412715\pi$
$709$	−11.3827	−	6.57180i	−0.427486	−	0.246809i	−0.698275	+	0.715830i	$0.746049\pi$
$710$		0			0
$711$	−1.26795	+	2.19615i	−0.0475518	+	0.0823622i
$712$		0			0
$713$	5.32051	−	3.07180i	0.199255	−	0.115040i
$714$		0			0
$715$	4.09808	−	16.5622i	0.153259	−	0.619390i
$716$		0			0
$717$	−6.63397	+	3.83013i	−0.247750	+	0.143039i
$718$		0			0
$719$	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
$722$		0			0
$723$		−	13.5885i		−	0.505360i
$724$		0			0
$725$	−19.9282	−	34.5167i	−0.740115	−	1.28192i
$726$		0			0
$727$	−30.9808			−1.14901			−0.574506	−	0.818500i	$-0.694806\pi$
$727$	−30.9808			−1.14901			−0.574506	+	0.818500i	$0.694806\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	27.6865	+	47.9545i	1.02402	+	1.77366i
$732$		0			0
$733$		−	19.0000i		−	0.701781i	−0.936416	−	0.350891i	$-0.885879\pi$
$733$		−	19.0000i		−	0.701781i	0.936416	−	0.350891i	$-0.114121\pi$
$734$		0			0
$735$	1.50000	+	0.866025i	0.0553283	+	0.0319438i
$736$		0			0
$737$	−8.32051	+	14.4115i	−0.306490	+	0.530856i
$738$		0			0
$739$	−2.53590	+	1.46410i	−0.0932845	+	0.0538578i	−0.545917	−	0.837840i	$-0.683818\pi$
$739$	−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
$742$		0			0
$743$	−41.9090	+	24.1962i	−1.53749	+	0.887671i	−0.538506	+	0.842622i	$0.681011\pi$
$743$	−41.9090	+	24.1962i	−1.53749	+	0.887671i	−0.998985	+	0.0450491i	$0.985656\pi$
$744$		0			0
$745$	24.6244	−	42.6506i	0.902167	−	1.56260i
$746$		0			0
$747$	0.169873	+	0.0980762i	0.00621533	+	0.00358842i
$748$		0			0
$749$		−	27.8564i		−	1.01785i
$750$		0			0
$751$	24.9545	+	43.2224i	0.910602	+	1.57721i	0.813216	+	0.581962i	$0.197715\pi$
$751$	24.9545	+	43.2224i	0.910602	+	1.57721i	0.0973862	+	0.995247i	$0.468952\pi$
$752$		0			0
$753$	−13.4641			−0.490659
$754$		0			0
$755$	−25.1244			−0.914369
$756$		0			0
$757$	−10.4641	−	18.1244i	−0.380324	−	0.658741i	0.610784	−	0.791797i	$-0.290854\pi$
$757$	−10.4641	−	18.1244i	−0.380324	−	0.658741i	−0.991109	+	0.133056i	$0.957521\pi$
$758$		0			0
$759$			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	$0.732446\pi$
$762$		0			0
$763$	−2.00000	+	3.46410i	−0.0724049	+	0.125409i
$764$		0			0
$765$	−18.5263	+	10.6962i	−0.669819	+	0.386720i
$766$		0			0
$767$	−8.00000	−	27.7128i	−0.288863	−	1.00065i
$768$		0			0
$769$	37.9808	−	21.9282i	1.36962	−	0.790751i	0.378742	−	0.925502i	$-0.376357\pi$
$769$	37.9808	−	21.9282i	1.36962	−	0.790751i	0.990879	+	0.134751i	$0.0430235\pi$
$770$		0			0
$771$	−4.66987	+	8.08846i	−0.168181	+	0.291299i
$772$		0			0
$773$	−42.3731	−	24.4641i	−1.52405	−	0.879913i	−0.999594	−	0.0284768i	$-0.990934\pi$
$773$	−42.3731	−	24.4641i	−1.52405	−	0.879913i	−0.524459	−	0.851436i	$-0.675732\pi$
$774$		0			0
$775$		−	13.0718i		−	0.469553i
$776$		0			0
$777$	−4.83013	−	8.36603i	−0.173280	−	0.300129i
$778$		0			0
$779$	−44.4449			−1.59240
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$	−2.23205	−	3.86603i	−0.0797670	−	0.138160i
$784$		0			0
$785$		−	28.3205i		−	1.01080i
$786$		0			0
$787$	4.05256	+	2.33975i	0.144458	+	0.0834029i	0.570487	−	0.821307i	$-0.306754\pi$
$787$	4.05256	+	2.33975i	0.144458	+	0.0834029i	−0.426029	+	0.904710i	$0.640088\pi$
$788$		0			0
$789$	5.02628	−	8.70577i	0.178940	−	0.309934i
$790$		0			0
$791$	−3.16987	+	1.83013i	−0.112708	+	0.0650718i
$792$		0			0
$793$	−31.8564	+	9.19615i	−1.13125	+	0.326565i
$794$		0			0
$795$	−20.8923	+	12.0622i	−0.740974	+	0.427801i
$796$		0			0
$797$	−17.0000	+	29.4449i	−0.602171	+	1.04299i	0.390321	+	0.920679i	$0.372364\pi$
$797$	−17.0000	+	29.4449i	−0.602171	+	1.04299i	−0.992492	+	0.122312i	$0.960969\pi$
$798$		0			0
$799$	10.9019	+	6.29423i	0.385682	+	0.222674i
$800$		0			0
$801$		−	9.46410i		−	0.334398i
$802$		0			0
$803$	3.97372	+	6.88269i	0.140230	+	0.242885i
$804$		0			0
$805$	42.7846			1.50796
$806$		0			0
$807$	−5.46410			−0.192345
$808$		0			0
$809$	26.7942	+	46.4090i	0.942035	+	1.63165i	0.761582	+	0.648069i	$0.224423\pi$
$809$	26.7942	+	46.4090i	0.942035	+	1.63165i	0.180453	+	0.983584i	$0.442244\pi$
$810$		0			0
$811$			17.1769i			0.603163i	0.953440	+	0.301582i	$0.0975145\pi$
$811$			17.1769i			0.603163i	−0.953440	+	0.301582i	$0.902485\pi$
$812$		0			0
$813$	18.9282	+	10.9282i	0.663841	+	0.383269i
$814$		0			0
$815$	−25.1244	+	43.5167i	−0.880068	+	1.52432i
$816$		0			0
$817$	−39.5885	+	22.8564i	−1.38502	+	0.799644i
$818$		0			0
$819$	−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	$0.328177\pi$
$822$		0			0
$823$	−20.7846	+	36.0000i	−0.724506	+	1.25488i	0.234671	+	0.972075i	$0.424599\pi$
$823$	−20.7846	+	36.0000i	−0.724506	+	1.25488i	−0.959177	+	0.282806i	$0.908735\pi$
$824$		0			0
$825$	9.80385	+	5.66025i	0.341326	+	0.197065i
$826$		0			0
$827$		−	26.5359i		−	0.922744i	−0.887207	−	0.461372i	$-0.847357\pi$
$827$		−	26.5359i		−	0.922744i	0.887207	−	0.461372i	$-0.152643\pi$
$828$		0			0
$829$	−6.06218	−	10.5000i	−0.210548	−	0.364680i	0.741338	−	0.671132i	$-0.234192\pi$
$829$	−6.06218	−	10.5000i	−0.210548	−	0.364680i	−0.951886	+	0.306452i	$0.900858\pi$
$830$		0			0
$831$	−5.73205			−0.198843
$832$		0			0
$833$	−2.66025			−0.0921723
$834$		0			0
$835$	−17.6603	−	30.5885i	−0.611158	−	1.05856i
$836$		0			0
$837$		−	1.46410i		−	0.0506068i
$838$		0			0
$839$	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
$842$		0			0
$843$	−10.6699	+	6.16025i	−0.367490	+	0.212170i
$844$		0			0
$845$	48.4808	−	1.86603i	1.66779	−	0.0641932i
$846$		0			0
$847$	22.2224	−	12.8301i	0.763572	−	0.440848i
$848$		0			0
$849$	12.8301	−	22.2224i	0.440329	−	0.762672i
$850$		0			0
$851$	−12.8494	−	7.41858i	−0.440471	−	0.254306i
$852$		0			0
$853$		−	54.1769i		−	1.85498i	−0.373845	−	0.927491i	$-0.621961\pi$
$853$		−	54.1769i		−	1.85498i	0.373845	−	0.927491i	$-0.378039\pi$
$854$		0			0
$855$	−8.83013	−	15.2942i	−0.301984	−	0.523052i
$856$		0			0
$857$	−39.4449			−1.34741			−0.673705	−	0.739000i	$-0.735298\pi$
$857$	−39.4449			−1.34741			−0.673705	+	0.739000i	$0.735298\pi$
$858$		0			0
$859$	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
$862$		0			0
$863$		−	17.1244i		−	0.582920i	−0.956583	−	0.291460i	$-0.905859\pi$
$863$		−	17.1244i		−	0.582920i	0.956583	−	0.291460i	$-0.0941410\pi$
$864$		0			0
$865$	−14.1962	−	8.19615i	−0.482684	−	0.278678i
$866$		0			0
$867$	7.92820	−	13.7321i	0.269256	−	0.466365i
$868$		0			0
$869$	−2.78461	+	1.60770i	−0.0944614	+	0.0545373i
$870$		0			0
$871$	−45.9352	−	11.3660i	−1.55646	−	0.385123i
$872$		0			0
$873$	5.19615	−	3.00000i	0.175863	−	0.101535i
$874$		0			0
$875$	20.0263	−	34.6865i	0.677012	−	1.17262i
$876$		0			0
$877$	20.7224	+	11.9641i	0.699747	+	0.403999i	0.807253	−	0.590205i	$-0.200953\pi$
$877$	20.7224	+	11.9641i	0.699747	+	0.403999i	−0.107506	+	0.994204i	$0.534287\pi$
$878$		0			0
$879$		−	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			0
$883$	42.9282			1.44465			0.722325	−	0.691554i	$-0.243074\pi$
$883$	42.9282			1.44465			0.722325	+	0.691554i	$0.243074\pi$
$884$		0			0
$885$	29.8564			1.00361
$886$		0			0
$887$	18.9282	+	32.7846i	0.635547	+	1.10080i	0.986399	+	0.164369i	$0.0525586\pi$
$887$	18.9282	+	32.7846i	0.635547	+	1.10080i	−0.350852	+	0.936431i	$0.614108\pi$
$888$		0			0
$889$		−	26.9282i		−	0.903143i
$890$		0			0
$891$	1.09808	+	0.633975i	0.0367869	+	0.0212389i
$892$		0			0
$893$	−5.19615	+	9.00000i	−0.173883	+	0.301174i
$894$		0			0
$895$	51.8827	−	29.9545i	1.73425	−	1.00127i
$896$		0			0
$897$	−14.5359	+	4.19615i	−0.485340	+	0.140105i
$898$		0			0
$899$	−5.66025	+	3.26795i	−0.188780	+	0.108992i
$900$		0			0
$901$	18.5263	−	32.0885i	0.617200	−	1.06902i
$902$		0			0
$903$	−22.8564	−	13.1962i	−0.760614	−	0.439140i
$904$		0			0
$905$			71.6410i			2.38143i
$906$		0			0
$907$	−18.1962	−	31.5167i	−0.604193	−	1.04649i	−0.992178	−	0.124828i	$-0.960162\pi$
$907$	−18.1962	−	31.5167i	−0.604193	−	1.04649i	0.387985	−	0.921666i	$-0.373171\pi$
$908$		0			0
$909$	−1.92820			−0.0639545
$910$		0			0
$911$	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			0
$915$		−	34.3205i		−	1.13460i
$916$		0			0
$917$	15.4641	+	8.92820i	0.510670	+	0.294835i
$918$		0			0
$919$	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
$922$		0			0
$923$	4.73205	+	16.3923i	0.155757	+	0.539559i
$924$		0			0
$925$	−27.3397	+	15.7846i	−0.898925	+	0.518995i
$926$		0			0
$927$	7.63397	−	13.2224i	0.250733	−	0.434282i
$928$		0			0
$929$	−33.9904	−	19.6244i	−1.11519	−	0.643854i	−0.175020	−	0.984565i	$-0.555999\pi$
$929$	−33.9904	−	19.6244i	−1.11519	−	0.643854i	−0.940168	+	0.340711i	$0.889332\pi$
$930$		0			0
$931$		−	2.19615i		−	0.0719760i
$932$		0			0
$933$	−0.830127	−	1.43782i	−0.0271771	−	0.0470722i
$934$		0			0
$935$	−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	$0.527324\pi$
$938$		0			0
$939$	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	$-0.0660586\pi$
$942$		0			0
$943$	−34.1314	−	19.7058i	−1.11147	−	0.641708i
$944$		0			0
$945$	5.09808	−	8.83013i	0.165840	−	0.287244i
$946$		0			0
$947$	−18.2487	+	10.5359i	−0.593003	+	0.342371i	−0.766284	−	0.642502i	$-0.777897\pi$
$947$	−18.2487	+	10.5359i	−0.593003	+	0.342371i	0.173281	+	0.984872i	$0.444563\pi$
$948$		0			0
$949$	−15.6699	+	16.2846i	−0.508666	+	0.528621i
$950$		0			0
$951$	17.8923	−	10.3301i	0.580198	−	0.334977i
$952$		0			0
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	−0.303689	−	0.952771i	$-0.598218\pi$
$953$	20.7846	−	36.0000i	0.673280	−	1.16615i	0.976969	−	0.213383i	$-0.0684483\pi$
$954$		0			0
$955$	22.3923	+	12.9282i	0.724598	+	0.418347i
$956$		0			0
$957$		−	5.66025i		−	0.182970i
$958$		0			0
$959$	16.2942	+	28.2224i	0.526168	+	0.911350i
$960$		0			0
$961$	28.8564			0.930852
$962$		0			0
$963$	−10.1962			−0.328566
$964$		0			0
$965$	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	$-0.243885\pi$
$968$		0			0
$969$	23.4904	+	13.5622i	0.754620	+	0.435680i
$970$		0			0
$971$	15.1244	−	26.1962i	0.485364	−	0.840675i	−0.514495	−	0.857493i	$-0.672021\pi$
$971$	15.1244	−	26.1962i	0.485364	−	0.840675i	0.999859	+	0.0168189i	$0.00535388\pi$
$972$		0			0
$973$	−42.2487	+	24.3923i	−1.35443	+	0.781981i
$974$		0			0
$975$	−7.73205	+	31.2487i	−0.247624	+	1.00076i
$976$		0			0
$977$	−39.7750	+	22.9641i	−1.27251	+	0.734687i	−0.975461	−	0.220174i	$-0.929337\pi$
$977$	−39.7750	+	22.9641i	−1.27251	+	0.734687i	−0.297054	+	0.954861i	$0.596004\pi$
$978$		0			0
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$		0			0
$981$	1.26795	+	0.732051i	0.0404825	+	0.0233726i
$982$		0			0
$983$		−	20.7846i		−	0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$		−	20.7846i		−	0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$		0			0
$985$	−33.3205	−	57.7128i	−1.06168	−	1.83888i
$986$		0			0
$987$	−6.00000			−0.190982
$988$		0			0
$989$	−40.5359			−1.28897
$990$		0			0
$991$	11.2942	+	19.5622i	0.358773	+	0.621413i	0.987756	−	0.156006i	$-0.0498619\pi$
$991$	11.2942	+	19.5622i	0.358773	+	0.621413i	−0.628983	+	0.777419i	$0.716529\pi$
$992$		0			0
$993$		−	20.0000i		−	0.634681i
$994$		0			0
$995$	−45.8827	−	26.4904i	−1.45458	−	0.839802i
$996$		0			0
$997$	−10.6699	+	18.4808i	−0.337918	+	0.585292i	−0.984041	−	0.177942i	$-0.943056\pi$
$997$	−10.6699	+	18.4808i	−0.337918	+	0.585292i	0.646123	+	0.763234i	$0.276389\pi$
$998$		0			0
$999$	−3.06218	+	1.76795i	−0.0968830	+	0.0559354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bv.e.49.1		4
3.2	odd	2		1872.2.by.h.1297.2		4
4.3	odd	2		78.2.i.a.49.1	yes	4
12.11	even	2		234.2.l.c.127.2		4
13.2	odd	12		8112.2.a.bj.1.1		2
13.4	even	6	inner	624.2.bv.e.433.2		4
13.11	odd	12		8112.2.a.bp.1.2		2
20.3	even	4		1950.2.y.g.49.2		4
20.7	even	4		1950.2.y.b.49.1		4
20.19	odd	2		1950.2.bc.d.751.2		4
39.17	odd	6		1872.2.by.h.433.1		4
52.3	odd	6		1014.2.b.e.337.1		4
52.7	even	12		1014.2.e.g.529.2		4
52.11	even	12		1014.2.a.k.1.2		2
52.15	even	12		1014.2.a.i.1.1		2
52.19	even	12		1014.2.e.i.529.1		4
52.23	odd	6		1014.2.b.e.337.4		4
52.31	even	4		1014.2.e.i.991.1		4
52.35	odd	6		1014.2.i.a.823.2		4
52.43	odd	6		78.2.i.a.43.1	✓	4
52.47	even	4		1014.2.e.g.991.2		4
52.51	odd	2		1014.2.i.a.361.2		4
156.11	odd	12		3042.2.a.p.1.1		2
156.23	even	6		3042.2.b.i.1351.1		4
156.95	even	6		234.2.l.c.199.2		4
156.107	even	6		3042.2.b.i.1351.4		4
156.119	odd	12		3042.2.a.y.1.2		2
260.43	even	12		1950.2.y.b.199.1		4
260.147	even	12		1950.2.y.g.199.2		4
260.199	odd	6		1950.2.bc.d.901.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.1	✓	4	52.43	odd	6
78.2.i.a.49.1	yes	4	4.3	odd	2
234.2.l.c.127.2		4	12.11	even	2
234.2.l.c.199.2		4	156.95	even	6
624.2.bv.e.49.1		4	1.1	even	1	trivial
624.2.bv.e.433.2		4	13.4	even	6	inner
1014.2.a.i.1.1		2	52.15	even	12
1014.2.a.k.1.2		2	52.11	even	12
1014.2.b.e.337.1		4	52.3	odd	6
1014.2.b.e.337.4		4	52.23	odd	6
1014.2.e.g.529.2		4	52.7	even	12
1014.2.e.g.991.2		4	52.47	even	4
1014.2.e.i.529.1		4	52.19	even	12
1014.2.e.i.991.1		4	52.31	even	4
1014.2.i.a.361.2		4	52.51	odd	2
1014.2.i.a.823.2		4	52.35	odd	6
1872.2.by.h.433.1		4	39.17	odd	6
1872.2.by.h.1297.2		4	3.2	odd	2
1950.2.y.b.49.1		4	20.7	even	4
1950.2.y.b.199.1		4	260.43	even	12
1950.2.y.g.49.2		4	20.3	even	4
1950.2.y.g.199.2		4	260.147	even	12
1950.2.bc.d.751.2		4	20.19	odd	2
1950.2.bc.d.901.2		4	260.199	odd	6
3042.2.a.p.1.1		2	156.11	odd	12
3042.2.a.y.1.2		2	156.119	odd	12
3042.2.b.i.1351.1		4	156.23	even	6
3042.2.b.i.1351.4		4	156.107	even	6
8112.2.a.bj.1.1		2	13.2	odd	12
8112.2.a.bp.1.2		2	13.11	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} -3.73205i q^{5} +(-2.36603 - 1.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} -3.73205i q^{5} +(-2.36603 - 1.36603i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.09808 + 0.633975i) q^{11} +(-2.59808 - 2.50000i) q^{13} +(3.23205 - 1.86603i) q^{15} +(-2.86603 + 4.96410i) q^{17} +(-4.09808 - 2.36603i) q^{19} -2.73205i q^{21} +(-2.09808 - 3.63397i) q^{23} -8.92820 q^{25} -1.00000 q^{27} +(2.23205 + 3.86603i) q^{29} +1.46410i q^{31} +(-1.09808 - 0.633975i) q^{33} +(-5.09808 + 8.83013i) q^{35} +(3.06218 - 1.76795i) q^{37} +(0.866025 - 3.50000i) q^{39} +(8.13397 - 4.69615i) q^{41} +(4.83013 - 8.36603i) q^{43} +(3.23205 + 1.86603i) q^{45} -2.19615i q^{47} +(0.232051 + 0.401924i) q^{49} -5.73205 q^{51} -6.46410 q^{53} +(2.36603 + 4.09808i) q^{55} -4.73205i q^{57} +(6.92820 + 4.00000i) q^{59} +(4.59808 - 7.96410i) q^{61} +(2.36603 - 1.36603i) q^{63} +(-9.33013 + 9.69615i) q^{65} +(11.3660 - 6.56218i) q^{67} +(2.09808 - 3.63397i) q^{69} +(-4.09808 - 2.36603i) q^{71} -6.26795i q^{73} +(-4.46410 - 7.73205i) q^{75} +3.46410 q^{77} +2.53590 q^{79} +(-0.500000 - 0.866025i) q^{81} -0.196152i q^{83} +(18.5263 + 10.6962i) q^{85} +(-2.23205 + 3.86603i) q^{87} +(-8.19615 + 4.73205i) q^{89} +(2.73205 + 9.46410i) q^{91} +(-1.26795 + 0.732051i) q^{93} +(-8.83013 + 15.2942i) q^{95} +(-5.19615 - 3.00000i) q^{97} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 6 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 6 q^{15} - 8 q^{17} - 6 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{33} - 10 q^{35} - 12 q^{37} + 36 q^{41} + 2 q^{43} + 6 q^{45} - 6 q^{49} - 16 q^{51} - 12 q^{53} + 6 q^{55} + 8 q^{61} + 6 q^{63} - 20 q^{65} + 42 q^{67} - 2 q^{69} - 6 q^{71} - 4 q^{75} + 24 q^{79} - 2 q^{81} + 36 q^{85} - 2 q^{87} - 12 q^{89} + 4 q^{91} - 12 q^{93} - 18 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^7 - 2 * q^9 + 6 * q^11 + 6 * q^15 - 8 * q^17 - 6 * q^19 + 2 * q^23 - 8 * q^25 - 4 * q^27 + 2 * q^29 + 6 * q^33 - 10 * q^35 - 12 * q^37 + 36 * q^41 + 2 * q^43 + 6 * q^45 - 6 * q^49 - 16 * q^51 - 12 * q^53 + 6 * q^55 + 8 * q^61 + 6 * q^63 - 20 * q^65 + 42 * q^67 - 2 * q^69 - 6 * q^71 - 4 * q^75 + 24 * q^79 - 2 * q^81 + 36 * q^85 - 2 * q^87 - 12 * q^89 + 4 * q^91 - 12 * q^93 - 18 * q^95

Introduction

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