LMFDB - Embedded newform 840.2.bg.i.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(121,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("840.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bg (of order $3$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.38363328.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 3x^{4} - 2x^{3} - 21x^{2} - 49x + 343 $ x^6 - x^5 - 3x^4 - 2x^3 - 21x^2 - 49x + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.247423 - 2.63416i$ of defining polynomial
Character	$\chi$	$=$	840.361
Dual form			840.2.bg.i.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.40496 + 1.10280i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.40496 + 1.10280i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.90496 + 3.29948i) q^{11} +4.31507 q^{13} +1.00000 q^{15} +(0.657535 - 1.13888i) q^{17} +(-3.81507 - 6.60790i) q^{19} +(0.247423 - 2.63416i) q^{21} +(-3.41011 - 5.90649i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -4.30476 q^{29} +(-0.747423 + 1.29457i) q^{31} +(-1.90496 - 3.29948i) q^{33} +(2.15754 + 1.53135i) q^{35} +(-4.65238 - 8.05816i) q^{37} +(-2.15754 + 3.73696i) q^{39} -10.4401 q^{41} -4.80992 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.75258 + 3.03555i) q^{47} +(4.56765 - 5.30439i) q^{49} +(0.657535 + 1.13888i) q^{51} +(4.06765 - 7.04537i) q^{53} +3.80992 q^{55} +7.63014 q^{57} +(-4.15238 + 7.19214i) q^{59} +(3.31507 + 5.74187i) q^{61} +(2.15754 + 1.53135i) q^{63} +(-2.15754 - 3.73696i) q^{65} +(7.72003 - 13.3715i) q^{67} +6.82022 q^{69} -4.32538 q^{71} +(-1.91011 + 3.30841i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(0.942661 - 10.0359i) q^{77} +(1.06249 + 1.84029i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.9349 q^{83} -1.31507 q^{85} +(2.15238 - 3.72803i) q^{87} +(-5.65754 - 9.79914i) q^{89} +(-10.3776 + 4.75868i) q^{91} +(-0.747423 - 1.29457i) q^{93} +(-3.81507 + 6.60790i) q^{95} +10.6301 q^{97} +3.80992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9	$ 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} + q^{11} + 2 q^{13} + 6 q^{15} - 8 q^{17} + q^{19} + q^{21} - 9 q^{23} - 3 q^{25} + 6 q^{27} - 4 q^{31} + q^{33} + q^{35} - 15 q^{37} - q^{39} + 10 q^{41} - 4 q^{43} - 3 q^{45} + 11 q^{47} + 4 q^{49} - 8 q^{51} + q^{53} - 2 q^{55} - 2 q^{57} - 12 q^{59} - 4 q^{61} + q^{63} - q^{65} + 10 q^{67} + 18 q^{69} - 4 q^{71} - 3 q^{75} + 31 q^{77} - 18 q^{79} - 3 q^{81} + 8 q^{83} + 16 q^{85} - 22 q^{89} - 14 q^{91} - 4 q^{93} + q^{95} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 + q^11 + 2 * q^13 + 6 * q^15 - 8 * q^17 + q^19 + q^21 - 9 * q^23 - 3 * q^25 + 6 * q^27 - 4 * q^31 + q^33 + q^35 - 15 * q^37 - q^39 + 10 * q^41 - 4 * q^43 - 3 * q^45 + 11 * q^47 + 4 * q^49 - 8 * q^51 + q^53 - 2 * q^55 - 2 * q^57 - 12 * q^59 - 4 * q^61 + q^63 - q^65 + 10 * q^67 + 18 * q^69 - 4 * q^71 - 3 * q^75 + 31 * q^77 - 18 * q^79 - 3 * q^81 + 8 * q^83 + 16 * q^85 - 22 * q^89 - 14 * q^91 - 4 * q^93 + q^95 + 16 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.40496	+	1.10280i	−0.908989	+	0.416821i
$7$	−2.40496	+	1.10280i	−0.908989	+	0.416821i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.90496	+	3.29948i	−0.574366	+	0.994832i	0.421744	+	0.906715i	$0.361418\pi$
$11$	−1.90496	+	3.29948i	−0.574366	+	0.994832i	−0.996110	+	0.0881168i	$0.971915\pi$
$12$		0			0
$13$	4.31507			1.19679			0.598393	−	0.801203i	$-0.295806\pi$
$13$	4.31507			1.19679			0.598393	+	0.801203i	$0.295806\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.657535	−	1.13888i	0.159476	−	0.276220i	−0.775204	−	0.631711i	$-0.782353\pi$
$17$	0.657535	−	1.13888i	0.159476	−	0.276220i	0.934680	+	0.355491i	$0.115686\pi$
$18$		0			0
$19$	−3.81507	−	6.60790i	−0.875237	−	1.51596i	−0.856510	−	0.516131i	$-0.827372\pi$
$19$	−3.81507	−	6.60790i	−0.875237	−	1.51596i	−0.0187273	−	0.999825i	$-0.505961\pi$
$20$		0			0
$21$	0.247423	−	2.63416i	0.0539921	−	0.574820i
$22$		0			0
$23$	−3.41011	−	5.90649i	−0.711058	−	1.23159i	−0.964461	−	0.264227i	$-0.914883\pi$
$23$	−3.41011	−	5.90649i	−0.711058	−	1.23159i	0.253403	−	0.967361i	$-0.418450\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−4.30476			−0.799374			−0.399687	−	0.916652i	$-0.630881\pi$
$29$	−4.30476			−0.799374			−0.399687	+	0.916652i	$0.630881\pi$
$30$		0			0
$31$	−0.747423	+	1.29457i	−0.134241	+	0.232512i	−0.925307	−	0.379218i	$-0.876193\pi$
$31$	−0.747423	+	1.29457i	−0.134241	+	0.232512i	0.791066	+	0.611731i	$0.209526\pi$
$32$		0			0
$33$	−1.90496	−	3.29948i	−0.331611	−	0.574366i
$34$		0			0
$35$	2.15754	+	1.53135i	0.364690	+	0.258846i
$36$		0			0
$37$	−4.65238	−	8.05816i	−0.764847	−	1.32475i	−0.940328	−	0.340271i	$-0.889481\pi$
$37$	−4.65238	−	8.05816i	−0.764847	−	1.32475i	0.175481	−	0.984483i	$-0.443852\pi$
$38$		0			0
$39$	−2.15754	+	3.73696i	−0.345482	+	0.598393i
$40$		0			0
$41$	−10.4401			−1.63046			−0.815231	−	0.579135i	$-0.803390\pi$
$41$	−10.4401			−1.63046			−0.815231	+	0.579135i	$0.803390\pi$
$42$		0			0
$43$	−4.80992			−0.733505			−0.366753	−	0.930318i	$-0.619530\pi$
$43$	−4.80992			−0.733505			−0.366753	+	0.930318i	$0.619530\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	1.75258	+	3.03555i	0.255640	+	0.442781i	0.965069	−	0.261996i	$-0.0843806\pi$
$47$	1.75258	+	3.03555i	0.255640	+	0.442781i	−0.709429	+	0.704776i	$0.751047\pi$
$48$		0			0
$49$	4.56765	−	5.30439i	0.652521	−	0.757771i
$50$		0			0
$51$	0.657535	+	1.13888i	0.0920733	+	0.159476i
$52$		0			0
$53$	4.06765	−	7.04537i	0.558734	−	0.967756i	−0.438868	−	0.898551i	$-0.644620\pi$
$53$	4.06765	−	7.04537i	0.558734	−	0.967756i	0.997602	−	0.0692048i	$-0.0220462\pi$
$54$		0			0
$55$	3.80992			0.513729
$56$		0			0
$57$	7.63014			1.01064
$58$		0			0
$59$	−4.15238	+	7.19214i	−0.540594	+	0.936336i	0.458276	+	0.888810i	$0.348467\pi$
$59$	−4.15238	+	7.19214i	−0.540594	+	0.936336i	−0.998870	+	0.0475263i	$0.984866\pi$
$60$		0			0
$61$	3.31507	+	5.74187i	0.424451	+	0.735171i	0.996369	−	0.0851398i	$-0.0271337\pi$
$61$	3.31507	+	5.74187i	0.424451	+	0.735171i	−0.571918	+	0.820311i	$0.693800\pi$
$62$		0			0
$63$	2.15754	+	1.53135i	0.271824	+	0.192932i
$64$		0			0
$65$	−2.15754	−	3.73696i	−0.267609	−	0.463513i
$66$		0			0
$67$	7.72003	−	13.3715i	0.943152	−	1.63359i	0.183741	−	0.982975i	$-0.441179\pi$
$67$	7.72003	−	13.3715i	0.943152	−	1.63359i	0.759410	−	0.650612i	$-0.225487\pi$
$68$		0			0
$69$	6.82022			0.821059
$70$		0			0
$71$	−4.32538			−0.513328			−0.256664	−	0.966501i	$-0.582623\pi$
$71$	−4.32538			−0.513328			−0.256664	+	0.966501i	$0.582623\pi$
$72$		0			0
$73$	−1.91011	+	3.30841i	−0.223562	+	0.387220i	−0.955887	−	0.293735i	$-0.905102\pi$
$73$	−1.91011	+	3.30841i	−0.223562	+	0.387220i	0.732325	+	0.680955i	$0.238435\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	0.942661	−	10.0359i	0.107426	−	1.14370i
$78$		0			0
$79$	1.06249	+	1.84029i	0.119540	+	0.207049i	0.919585	−	0.392890i	$-0.128525\pi$
$79$	1.06249	+	1.84029i	0.119540	+	0.207049i	−0.800046	+	0.599939i	$0.795191\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−10.9349			−1.20026			−0.600131	−	0.799902i	$-0.704885\pi$
$83$	−10.9349			−1.20026			−0.600131	+	0.799902i	$0.704885\pi$
$84$		0			0
$85$	−1.31507			−0.142639
$86$		0			0
$87$	2.15238	−	3.72803i	0.230759	−	0.399687i
$88$		0			0
$89$	−5.65754	−	9.79914i	−0.599698	−	1.03871i	−0.992865	−	0.119240i	$-0.961954\pi$
$89$	−5.65754	−	9.79914i	−0.599698	−	1.03871i	0.393168	−	0.919467i	$-0.371379\pi$
$90$		0			0
$91$	−10.3776	+	4.75868i	−1.08786	+	0.498845i
$92$		0			0
$93$	−0.747423	−	1.29457i	−0.0775041	−	0.134241i
$94$		0			0
$95$	−3.81507	+	6.60790i	−0.391418	+	0.677956i
$96$		0			0
$97$	10.6301			1.07933			0.539664	−	0.841881i	$-0.318551\pi$
$97$	10.6301			1.07933			0.539664	+	0.841881i	$0.318551\pi$
$98$		0			0
$99$	3.80992			0.382911
$100$		0			0
$101$	−5.34246	+	9.25342i	−0.531595	+	0.920750i	0.467725	+	0.883874i	$0.345074\pi$
$101$	−5.34246	+	9.25342i	−0.531595	+	0.920750i	−0.999320	+	0.0368756i	$0.988259\pi$
$102$		0			0
$103$	9.72003	+	16.8356i	0.957743	+	1.65886i	0.727963	+	0.685617i	$0.240467\pi$
$103$	9.72003	+	16.8356i	0.957743	+	1.65886i	0.229780	+	0.973243i	$0.426199\pi$
$104$		0			0
$105$	−2.40496	+	1.10280i	−0.234700	+	0.107623i
$106$		0			0
$107$	−5.15238	−	8.92419i	−0.498099	−	0.862734i	0.501898	−	0.864927i	$-0.332635\pi$
$107$	−5.15238	−	8.92419i	−0.498099	−	0.862734i	−0.999998	+	0.00219314i	$0.999302\pi$
$108$		0			0
$109$	3.55734	−	6.16149i	0.340731	−	0.590164i	−0.643837	−	0.765162i	$-0.722659\pi$
$109$	3.55734	−	6.16149i	0.340731	−	0.590164i	0.984569	+	0.174998i	$0.0559920\pi$
$110$		0			0
$111$	9.30476			0.883169
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−3.41011	+	5.90649i	−0.317995	+	0.550783i
$116$		0			0
$117$	−2.15754	−	3.73696i	−0.199464	−	0.345482i
$118$		0			0
$119$	−0.325379	+	3.46410i	−0.0298274	+	0.317554i
$120$		0			0
$121$	−1.75773	−	3.04448i	−0.159794	−	0.276771i
$122$		0			0
$123$	5.22003	−	9.04135i	0.470674	−	0.815231i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	16.9452			1.50364			0.751822	−	0.659366i	$-0.229175\pi$
$127$	16.9452			1.50364			0.751822	+	0.659366i	$0.229175\pi$
$128$		0			0
$129$	2.40496	−	4.16551i	0.211745	−	0.366753i
$130$		0			0
$131$	6.55219	+	11.3487i	0.572467	+	0.991542i	0.996312	+	0.0858072i	$0.0273469\pi$
$131$	6.55219	+	11.3487i	0.572467	+	0.991542i	−0.423845	+	0.905735i	$0.639320\pi$
$132$		0			0
$133$	16.4623	+	11.6844i	1.42746	+	1.01317i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	−6.46745	+	11.2020i	−0.552552	+	0.957048i	0.445538	+	0.895263i	$0.353012\pi$
$137$	−6.46745	+	11.2020i	−0.552552	+	0.957048i	−0.998090	+	0.0617845i	$0.980321\pi$
$138$		0			0
$139$	−11.7448			−0.996183			−0.498091	−	0.867125i	$-0.665966\pi$
$139$	−11.7448			−0.996183			−0.498091	+	0.867125i	$0.665966\pi$
$140$		0			0
$141$	−3.50515			−0.295187
$142$		0			0
$143$	−8.22003	+	14.2375i	−0.687393	+	1.19060i
$144$		0			0
$145$	2.15238	+	3.72803i	0.178746	+	0.309596i
$146$		0			0
$147$	2.30992	+	6.60790i	0.190519	+	0.545010i
$148$		0			0
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	0.936245	−	0.351348i	$-0.114277\pi$
$149$	2.00000	+	3.46410i	0.163846	+	0.283790i	−0.772399	+	0.635138i	$0.780943\pi$
$150$		0			0
$151$	−0.315070	+	0.545718i	−0.0256401	+	0.0444099i	−0.878561	−	0.477631i	$-0.841496\pi$
$151$	−0.315070	+	0.545718i	−0.0256401	+	0.0444099i	0.852921	+	0.522041i	$0.174829\pi$
$152$		0			0
$153$	−1.31507			−0.106317
$154$		0			0
$155$	1.49485			0.120069
$156$		0			0
$157$	−4.43751	+	7.68599i	−0.354152	+	0.613409i	−0.986972	−	0.160890i	$-0.948564\pi$
$157$	−4.43751	+	7.68599i	−0.354152	+	0.613409i	0.632821	+	0.774298i	$0.281897\pi$
$158$		0			0
$159$	4.06765	+	7.04537i	0.322585	+	0.558734i
$160$		0			0
$161$	14.7149	+	10.4442i	1.15969	+	0.823116i
$162$		0			0
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$		0			0
$165$	−1.90496	+	3.29948i	−0.148301	+	0.256865i
$166$		0			0
$167$	12.0599			0.933222			0.466611	−	0.884463i	$-0.345475\pi$
$167$	12.0599			0.933222			0.466611	+	0.884463i	$0.345475\pi$
$168$		0			0
$169$	5.61983			0.432295
$170$		0			0
$171$	−3.81507	+	6.60790i	−0.291746	+	0.505318i
$172$		0			0
$173$	−8.56249	−	14.8307i	−0.650994	−	1.12756i	−0.982882	−	0.184236i	$-0.941019\pi$
$173$	−8.56249	−	14.8307i	−0.650994	−	1.12756i	0.331888	−	0.943319i	$-0.392315\pi$
$174$		0			0
$175$	0.247423	−	2.63416i	0.0187034	−	0.199124i
$176$		0			0
$177$	−4.15238	−	7.19214i	−0.312112	−	0.540594i
$178$		0			0
$179$	5.75258	−	9.96376i	0.429968	−	0.744726i	−0.566902	−	0.823785i	$-0.691858\pi$
$179$	5.75258	−	9.96376i	0.429968	−	0.744726i	0.996870	+	0.0790591i	$0.0251916\pi$
$180$		0			0
$181$	6.48454			0.481992			0.240996	−	0.970526i	$-0.422526\pi$
$181$	6.48454			0.481992			0.240996	+	0.970526i	$0.422526\pi$
$182$		0			0
$183$	−6.63014			−0.490114
$184$		0			0
$185$	−4.65238	+	8.05816i	−0.342050	+	0.592448i
$186$		0			0
$187$	2.50515	+	4.33905i	0.183195	+	0.317303i
$188$		0			0
$189$	−2.40496	+	1.10280i	−0.174935	+	0.0802172i
$190$		0			0
$191$	6.61983	+	11.4659i	0.478994	+	0.829642i	0.999710	−	0.0240878i	$-0.00766813\pi$
$191$	6.61983	+	11.4659i	0.478994	+	0.829642i	−0.520716	+	0.853730i	$0.674335\pi$
$192$		0			0
$193$	−7.73034	+	13.3893i	−0.556442	+	0.963785i	0.441348	+	0.897336i	$0.354500\pi$
$193$	−7.73034	+	13.3893i	−0.556442	+	0.963785i	−0.997790	+	0.0664495i	$0.978833\pi$
$194$		0			0
$195$	4.31507			0.309009
$196$		0			0
$197$	−14.4401			−1.02881			−0.514406	−	0.857547i	$-0.671987\pi$
$197$	−14.4401			−1.02881			−0.514406	+	0.857547i	$0.671987\pi$
$198$		0			0
$199$	−1.19008	+	2.06129i	−0.0843628	+	0.146121i	−0.905120	−	0.425157i	$-0.860219\pi$
$199$	−1.19008	+	2.06129i	−0.0843628	+	0.146121i	0.820757	+	0.571278i	$0.193552\pi$
$200$		0			0
$201$	7.72003	+	13.3715i	0.544529	+	0.943152i
$202$		0			0
$203$	10.3528	−	4.74731i	0.726622	−	0.333196i
$204$		0			0
$205$	5.22003	+	9.04135i	0.364583	+	0.631476i
$206$		0			0
$207$	−3.41011	+	5.90649i	−0.237019	+	0.410529i
$208$		0			0
$209$	29.0702			2.01083
$210$		0			0
$211$	−16.1147			−1.10938			−0.554690	−	0.832057i	$-0.687163\pi$
$211$	−16.1147			−1.10938			−0.554690	+	0.832057i	$0.687163\pi$
$212$		0			0
$213$	2.16269	−	3.74589i	0.148185	−	0.256664i
$214$		0			0
$215$	2.40496	+	4.16551i	0.164017	+	0.284085i
$216$		0			0
$217$	0.369859	−	3.93766i	0.0251077	−	0.267306i
$218$		0			0
$219$	−1.91011	−	3.30841i	−0.129073	−	0.223562i
$220$		0			0
$221$	2.83731	−	4.91437i	0.190858	−	0.330576i
$222$		0			0
$223$	12.6095			0.844396			0.422198	−	0.906504i	$-0.361259\pi$
$223$	12.6095			0.844396			0.422198	+	0.906504i	$0.361259\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	1.46745	−	2.54170i	0.0973982	−	0.168699i	−0.813209	−	0.581972i	$-0.802281\pi$
$227$	1.46745	−	2.54170i	0.0973982	−	0.168699i	0.910607	+	0.413273i	$0.135615\pi$
$228$		0			0
$229$	−6.24227	−	10.8119i	−0.412501	−	0.714472i	0.582662	−	0.812715i	$-0.302011\pi$
$229$	−6.24227	−	10.8119i	−0.412501	−	0.714472i	−0.995163	+	0.0982425i	$0.968678\pi$
$230$		0			0
$231$	8.22003	+	5.83433i	0.540838	+	0.383871i
$232$		0			0
$233$	12.3151	+	21.3303i	0.806787	+	1.39740i	0.915078	+	0.403277i	$0.132129\pi$
$233$	12.3151	+	21.3303i	0.806787	+	1.39740i	−0.108291	+	0.994119i	$0.534538\pi$
$234$		0			0
$235$	1.75258	−	3.03555i	0.114326	−	0.198018i
$236$		0			0
$237$	−2.12499			−0.138033
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−7.87756	+	13.6443i	−0.507438	+	0.878909i	0.492524	+	0.870299i	$0.336074\pi$
$241$	−7.87756	+	13.6443i	−0.507438	+	0.878909i	−0.999963	+	0.00861063i	$0.997259\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−6.87756	−	1.30350i	−0.439391	−	0.0832777i
$246$		0			0
$247$	−16.4623	−	28.5135i	−1.04747	−	1.81427i
$248$		0			0
$249$	5.46745	−	9.46990i	0.346486	−	0.600131i
$250$		0			0
$251$	−8.82022			−0.556728			−0.278364	−	0.960476i	$-0.589792\pi$
$251$	−8.82022			−0.556728			−0.278364	+	0.960476i	$0.589792\pi$
$252$		0			0
$253$	25.9845			1.63363
$254$		0			0
$255$	0.657535	−	1.13888i	0.0411765	−	0.0713197i
$256$		0			0
$257$	−7.46745	−	12.9340i	−0.465807	−	0.806801i	0.533431	−	0.845844i	$-0.320903\pi$
$257$	−7.46745	−	12.9340i	−0.465807	−	0.806801i	−0.999238	+	0.0390427i	$0.987569\pi$
$258$		0			0
$259$	20.0754	+	14.2489i	1.24742	+	0.885382i
$260$		0			0
$261$	2.15238	+	3.72803i	0.133229	+	0.230759i
$262$		0			0
$263$	−1.31507	+	2.27777i	−0.0810907	+	0.140453i	−0.903719	−	0.428127i	$-0.859174\pi$
$263$	−1.31507	+	2.27777i	−0.0810907	+	0.140453i	0.822628	+	0.568580i	$0.192507\pi$
$264$		0			0
$265$	−8.13529			−0.499747
$266$		0			0
$267$	11.3151			0.692471
$268$		0			0
$269$	−9.82022	+	17.0091i	−0.598750	+	1.03706i	0.394256	+	0.919001i	$0.371002\pi$
$269$	−9.82022	+	17.0091i	−0.598750	+	1.03706i	−0.993006	+	0.118064i	$0.962331\pi$
$270$		0			0
$271$	−7.44006	−	12.8866i	−0.451951	−	0.782803i	0.546556	−	0.837423i	$-0.315939\pi$
$271$	−7.44006	−	12.8866i	−0.451951	−	0.782803i	−0.998507	+	0.0546200i	$0.982605\pi$
$272$		0			0
$273$	1.06765	−	11.3666i	0.0646170	−	0.687936i
$274$		0			0
$275$	−1.90496	−	3.29948i	−0.114873	−	0.198966i
$276$		0			0
$277$	2.41527	−	4.18336i	0.145119	−	0.251354i	−0.784298	−	0.620384i	$-0.786977\pi$
$277$	2.41527	−	4.18336i	0.145119	−	0.251354i	0.929417	+	0.369030i	$0.120310\pi$
$278$		0			0
$279$	1.49485			0.0894941
$280$		0			0
$281$	−9.50515			−0.567030			−0.283515	−	0.958968i	$-0.591501\pi$
$281$	−9.50515			−0.567030			−0.283515	+	0.958968i	$0.591501\pi$
$282$		0			0
$283$	13.8553	−	23.9981i	0.823613	−	1.42654i	−0.0793609	−	0.996846i	$-0.525288\pi$
$283$	13.8553	−	23.9981i	0.823613	−	1.42654i	0.902974	−	0.429694i	$-0.141379\pi$
$284$		0			0
$285$	−3.81507	−	6.60790i	−0.225985	−	0.391418i
$286$		0			0
$287$	25.1079	−	11.5133i	1.48207	−	0.679611i
$288$		0			0
$289$	7.63529	+	13.2247i	0.449135	+	0.777925i
$290$		0			0
$291$	−5.31507	+	9.20597i	−0.311575	+	0.539664i
$292$		0			0
$293$	−2.49485			−0.145750			−0.0728752	−	0.997341i	$-0.523217\pi$
$293$	−2.49485			−0.145750			−0.0728752	+	0.997341i	$0.523217\pi$
$294$		0			0
$295$	8.30476			0.483522
$296$		0			0
$297$	−1.90496	+	3.29948i	−0.110537	+	0.191455i
$298$		0			0
$299$	−14.7149	−	25.4869i	−0.850983	−	1.47395i
$300$		0			0
$301$	11.5676	−	5.30439i	0.666748	−	0.305740i
$302$		0			0
$303$	−5.34246	−	9.25342i	−0.306917	−	0.531595i
$304$		0			0
$305$	3.31507	−	5.74187i	0.189820	−	0.328779i
$306$		0			0
$307$	1.21070			0.0690983			0.0345492	−	0.999403i	$-0.489000\pi$
$307$	1.21070			0.0690983			0.0345492	+	0.999403i	$0.489000\pi$
$308$		0			0
$309$	−19.4401			−1.10591
$310$		0			0
$311$	−14.6027	+	25.2927i	−0.828046	+	1.43422i	0.0715233	+	0.997439i	$0.477214\pi$
$311$	−14.6027	+	25.2927i	−0.828046	+	1.43422i	−0.899569	+	0.436778i	$0.856119\pi$
$312$		0			0
$313$	0.404958	+	0.701408i	0.0228896	+	0.0396459i	0.877243	−	0.480046i	$-0.159380\pi$
$313$	0.404958	+	0.701408i	0.0228896	+	0.0396459i	−0.854354	+	0.519692i	$0.826047\pi$
$314$		0			0
$315$	0.247423	−	2.63416i	0.0139407	−	0.148418i
$316$		0			0
$317$	4.14207	+	7.17428i	0.232642	+	0.402948i	0.958585	−	0.284807i	$-0.0919296\pi$
$317$	4.14207	+	7.17428i	0.232642	+	0.402948i	−0.725943	+	0.687755i	$0.758596\pi$
$318$		0			0
$319$	8.20039	−	14.2035i	0.459134	−	0.795243i
$320$		0			0
$321$	10.3048			0.575156
$322$		0			0
$323$	−10.0342			−0.558316
$324$		0			0
$325$	−2.15754	+	3.73696i	−0.119679	+	0.207289i
$326$		0			0
$327$	3.55734	+	6.16149i	0.196721	+	0.340731i
$328$		0			0
$329$	−7.56249	−	5.36763i	−0.416934	−	0.295927i
$330$		0			0
$331$	−12.9401	−	22.4128i	−0.711250	−	1.23192i	−0.964388	−	0.264491i	$-0.914796\pi$
$331$	−12.9401	−	22.4128i	−0.711250	−	1.23192i	0.253138	−	0.967430i	$-0.418537\pi$
$332$		0			0
$333$	−4.65238	+	8.05816i	−0.254949	+	0.441584i
$334$		0			0
$335$	−15.4401			−0.843580
$336$		0			0
$337$	−30.6797			−1.67123			−0.835615	−	0.549315i	$-0.814889\pi$
$337$	−30.6797			−1.67123			−0.835615	+	0.549315i	$0.814889\pi$
$338$		0			0
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	−2.84762	−	4.93222i	−0.154207	−	0.267095i
$342$		0			0
$343$	−5.13529	+	17.7941i	−0.277280	+	0.960789i
$344$		0			0
$345$	−3.41011	−	5.90649i	−0.183594	−	0.317995i
$346$		0			0
$347$	15.1250	−	26.1972i	0.811952	−	1.40634i	−0.0995443	−	0.995033i	$-0.531738\pi$
$347$	15.1250	−	26.1972i	0.811952	−	1.40634i	0.911496	−	0.411309i	$-0.134928\pi$
$348$		0			0
$349$	26.9897			1.44473			0.722363	−	0.691515i	$-0.243056\pi$
$349$	26.9897			1.44473			0.722363	+	0.691515i	$0.243056\pi$
$350$		0			0
$351$	4.31507			0.230321
$352$		0			0
$353$	7.46745	−	12.9340i	0.397452	−	0.688408i	−0.595959	−	0.803015i	$-0.703228\pi$
$353$	7.46745	−	12.9340i	0.397452	−	0.688408i	0.993411	+	0.114608i	$0.0365611\pi$
$354$		0			0
$355$	2.16269	+	3.74589i	0.114784	+	0.198811i
$356$		0			0
$357$	−2.83731	−	2.01384i	−0.150166	−	0.106584i
$358$		0			0
$359$	7.84762	+	13.5925i	0.414181	+	0.717383i	0.995342	−	0.0964055i	$-0.0307345\pi$
$359$	7.84762	+	13.5925i	0.414181	+	0.717383i	−0.581161	+	0.813789i	$0.697401\pi$
$360$		0			0
$361$	−19.6095	+	33.9647i	−1.03208	+	1.78762i
$362$		0			0
$363$	3.51546			0.184514
$364$		0			0
$365$	3.82022			0.199960
$366$		0			0
$367$	−10.1575	+	17.5934i	−0.530219	+	0.918366i	0.469159	+	0.883113i	$0.344557\pi$
$367$	−10.1575	+	17.5934i	−0.530219	+	0.918366i	−0.999378	+	0.0352528i	$0.988776\pi$
$368$		0			0
$369$	5.22003	+	9.04135i	0.271744	+	0.470674i
$370$		0			0
$371$	−2.01286	+	21.4296i	−0.104502	+	1.11257i
$372$		0			0
$373$	3.40496	+	5.89756i	0.176302	+	0.305364i	0.940611	−	0.339486i	$-0.110253\pi$
$373$	3.40496	+	5.89756i	0.176302	+	0.305364i	−0.764309	+	0.644850i	$0.776920\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−18.5754			−0.956679
$378$		0			0
$379$	−30.2397			−1.55331			−0.776654	−	0.629928i	$-0.783084\pi$
$379$	−30.2397			−1.55331			−0.776654	+	0.629928i	$0.783084\pi$
$380$		0			0
$381$	−8.47261	+	14.6750i	−0.434065	+	0.751822i
$382$		0			0
$383$	−4.06765	−	7.04537i	−0.207847	−	0.360002i	0.743189	−	0.669082i	$-0.233312\pi$
$383$	−4.06765	−	7.04537i	−0.207847	−	0.360002i	−0.951036	+	0.309080i	$0.899979\pi$
$384$		0			0
$385$	−9.16269	+	4.20159i	−0.466974	+	0.214133i
$386$		0			0
$387$	2.40496	+	4.16551i	0.122251	+	0.211745i
$388$		0			0
$389$	14.4675	−	25.0584i	0.733529	−	1.27051i	−0.221837	−	0.975084i	$-0.571205\pi$
$389$	14.4675	−	25.0584i	0.733529	−	1.27051i	0.955366	−	0.295426i	$-0.0954614\pi$
$390$		0			0
$391$	−8.96908			−0.453586
$392$		0			0
$393$	−13.1044			−0.661028
$394$		0			0
$395$	1.06249	−	1.84029i	0.0534598	−	0.0925952i
$396$		0			0
$397$	0.214874	+	0.372173i	0.0107842	+	0.0186789i	0.871367	−	0.490631i	$-0.163234\pi$
$397$	0.214874	+	0.372173i	0.0107842	+	0.0186789i	−0.860583	+	0.509310i	$0.829901\pi$
$398$		0			0
$399$	−18.3502	+	8.41455i	−0.918658	+	0.421254i
$400$		0			0
$401$	−1.55219	−	2.68846i	−0.0775124	−	0.134255i	0.824664	−	0.565623i	$-0.191364\pi$
$401$	−1.55219	−	2.68846i	−0.0775124	−	0.134255i	−0.902176	+	0.431368i	$0.858031\pi$
$402$		0			0
$403$	−3.22518	+	5.58618i	−0.160658	+	0.278267i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	35.4504			1.75721
$408$		0			0
$409$	5.75773	−	9.97268i	0.284701	−	0.493117i	−0.687835	−	0.725867i	$-0.741439\pi$
$409$	5.75773	−	9.97268i	0.284701	−	0.493117i	0.972537	+	0.232749i	$0.0747722\pi$
$410$		0			0
$411$	−6.46745	−	11.2020i	−0.319016	−	0.552552i
$412$		0			0
$413$	2.05479	−	21.8760i	0.101110	−	1.07645i
$414$		0			0
$415$	5.46745	+	9.46990i	0.268387	+	0.464859i
$416$		0			0
$417$	5.87241	−	10.1713i	0.287573	−	0.498091i
$418$		0			0
$419$	−9.86471			−0.481922			−0.240961	−	0.970535i	$-0.577463\pi$
$419$	−9.86471			−0.481922			−0.240961	+	0.970535i	$0.577463\pi$
$420$		0			0
$421$	−21.1353			−1.03007			−0.515036	−	0.857169i	$-0.672221\pi$
$421$	−21.1353			−1.03007			−0.515036	+	0.857169i	$0.672221\pi$
$422$		0			0
$423$	1.75258	−	3.03555i	0.0852132	−	0.147594i
$424$		0			0
$425$	0.657535	+	1.13888i	0.0318951	+	0.0552440i
$426$		0			0
$427$	−14.3048	−	10.1531i	−0.692256	−	0.491342i
$428$		0			0
$429$	−8.22003	−	14.2375i	−0.396867	−	0.687393i
$430$		0			0
$431$	19.0599	−	33.0127i	0.918083	−	1.59017i	0.115758	−	0.993277i	$-0.463070\pi$
$431$	19.0599	−	33.0127i	0.918083	−	1.59017i	0.802324	−	0.596888i	$-0.203596\pi$
$432$		0			0
$433$	16.8099			0.807833			0.403917	−	0.914796i	$-0.367649\pi$
$433$	16.8099			0.807833			0.403917	+	0.914796i	$0.367649\pi$
$434$		0			0
$435$	−4.30476			−0.206398
$436$		0			0
$437$	−26.0196	+	45.0673i	−1.24469	+	2.15586i
$438$		0			0
$439$	−4.50515	−	7.80316i	−0.215019	−	0.372424i	0.738259	−	0.674517i	$-0.235648\pi$
$439$	−4.50515	−	7.80316i	−0.215019	−	0.372424i	−0.953279	+	0.302093i	$0.902315\pi$
$440$		0			0
$441$	−6.87756	−	1.30350i	−0.327503	−	0.0620715i
$442$		0			0
$443$	−6.30476	−	10.9202i	−0.299548	−	0.518833i	0.676484	−	0.736457i	$-0.263503\pi$
$443$	−6.30476	−	10.9202i	−0.299548	−	0.518833i	−0.976033	+	0.217624i	$0.930169\pi$
$444$		0			0
$445$	−5.65754	+	9.79914i	−0.268193	+	0.464524i
$446$		0			0
$447$	−4.00000			−0.189194
$448$		0			0
$449$	6.74482			0.318308			0.159154	−	0.987254i	$-0.449123\pi$
$449$	6.74482			0.318308			0.159154	+	0.987254i	$0.449123\pi$
$450$		0			0
$451$	19.8879	−	34.4468i	0.936483	−	1.62204i
$452$		0			0
$453$	−0.315070	−	0.545718i	−0.0148033	−	0.0256401i
$454$		0			0
$455$	9.30992	+	6.60790i	0.436456	+	0.309783i
$456$		0			0
$457$	−17.0454	−	29.5235i	−0.797351	−	1.38105i	−0.921336	−	0.388768i	$-0.872901\pi$
$457$	−17.0454	−	29.5235i	−0.797351	−	1.38105i	0.123985	−	0.992284i	$-0.460432\pi$
$458$		0			0
$459$	0.657535	−	1.13888i	0.0306911	−	0.0531586i
$460$		0			0
$461$	31.5857			1.47109			0.735545	−	0.677475i	$-0.236926\pi$
$461$	31.5857			1.47109			0.735545	+	0.677475i	$0.236926\pi$
$462$		0			0
$463$	−30.5857			−1.42144			−0.710718	−	0.703477i	$-0.751630\pi$
$463$	−30.5857			−1.42144			−0.710718	+	0.703477i	$0.751630\pi$
$464$		0			0
$465$	−0.747423	+	1.29457i	−0.0346609	+	0.0600345i
$466$		0			0
$467$	3.51546	+	6.08896i	0.162676	+	0.281763i	0.935828	−	0.352458i	$-0.114654\pi$
$467$	3.51546	+	6.08896i	0.162676	+	0.281763i	−0.773151	+	0.634221i	$0.781321\pi$
$468$		0			0
$469$	−3.82022	+	40.6715i	−0.176402	+	1.87804i
$470$		0			0
$471$	−4.43751	−	7.68599i	−0.204470	−	0.354152i
$472$		0			0
$473$	9.16269	−	15.8702i	0.421301	−	0.729715i
$474$		0			0
$475$	7.63014			0.350095
$476$		0			0
$477$	−8.13529			−0.372490
$478$		0			0
$479$	15.7551	−	27.2887i	0.719870	−	1.24685i	−0.241181	−	0.970480i	$-0.577535\pi$
$479$	15.7551	−	27.2887i	0.719870	−	1.24685i	0.961051	−	0.276371i	$-0.0891320\pi$
$480$		0			0
$481$	−20.0754	−	34.7715i	−0.915357	−	1.58545i
$482$		0			0
$483$	−16.4024	+	7.52137i	−0.746333	+	0.342234i
$484$		0			0
$485$	−5.31507	−	9.20597i	−0.241345	−	0.418022i
$486$		0			0
$487$	10.0248	−	17.3634i	0.454267	−	0.786813i	−0.544379	−	0.838839i	$-0.683235\pi$
$487$	10.0248	−	17.3634i	0.454267	−	0.786813i	0.998646	+	0.0520264i	$0.0165680\pi$
$488$		0			0
$489$	16.0000			0.723545
$490$		0			0
$491$	4.60952			0.208025			0.104012	−	0.994576i	$-0.466832\pi$
$491$	4.60952			0.208025			0.104012	+	0.994576i	$0.466832\pi$
$492$		0			0
$493$	−2.83053	+	4.90263i	−0.127481	+	0.220803i
$494$		0			0
$495$	−1.90496	−	3.29948i	−0.0856215	−	0.148301i
$496$		0			0
$497$	10.4024	−	4.77004i	0.466609	−	0.213966i
$498$		0			0
$499$	−21.1327	−	36.6029i	−0.946029	−	1.63857i	−0.753677	−	0.657245i	$-0.771722\pi$
$499$	−21.1327	−	36.6029i	−0.946029	−	1.63857i	−0.192352	−	0.981326i	$-0.561611\pi$
$500$		0			0
$501$	−6.02994	+	10.4442i	−0.269398	+	0.466611i
$502$		0			0
$503$	5.61983			0.250576			0.125288	−	0.992120i	$-0.460015\pi$
$503$	5.61983			0.250576			0.125288	+	0.992120i	$0.460015\pi$
$504$		0			0
$505$	10.6849			0.475473
$506$		0			0
$507$	−2.80992	+	4.86692i	−0.124793	+	0.216147i
$508$		0			0
$509$	14.5650	+	25.2274i	0.645584	+	1.11818i	0.984166	+	0.177248i	$0.0567194\pi$
$509$	14.5650	+	25.2274i	0.645584	+	1.11818i	−0.338582	+	0.940937i	$0.609947\pi$
$510$		0			0
$511$	0.945211	−	10.0631i	0.0418137	−	0.445164i
$512$		0			0
$513$	−3.81507	−	6.60790i	−0.168439	−	0.291746i
$514$		0			0
$515$	9.72003	−	16.8356i	0.428316	−	0.741864i
$516$		0			0
$517$	−13.3543			−0.587323
$518$		0			0
$519$	17.1250			0.751703
$520$		0			0
$521$	7.68748	−	13.3151i	0.336795	−	0.583345i	−0.647033	−	0.762462i	$-0.723991\pi$
$521$	7.68748	−	13.3151i	0.336795	−	0.583345i	0.983828	+	0.179116i	$0.0573239\pi$
$522$		0			0
$523$	2.59504	+	4.49474i	0.113473	+	0.196541i	0.917168	−	0.398500i	$-0.130469\pi$
$523$	2.59504	+	4.49474i	0.113473	+	0.196541i	−0.803695	+	0.595041i	$0.797136\pi$
$524$		0			0
$525$	2.15754	+	1.53135i	0.0941626	+	0.0668337i
$526$		0			0
$527$	0.982914	+	1.70246i	0.0428164	+	0.0741602i
$528$		0			0
$529$	−11.7577	+	20.3650i	−0.511206	+	0.885434i
$530$		0			0
$531$	8.30476			0.360396
$532$		0			0
$533$	−45.0496			−1.95131
$534$		0			0
$535$	−5.15238	+	8.92419i	−0.222757	+	0.385826i
$536$		0			0
$537$	5.75258	+	9.96376i	0.248242	+	0.429968i
$538$		0			0
$539$	8.80059	+	25.1755i	0.379068	+	1.08439i
$540$		0			0
$541$	−2.24227	−	3.88372i	−0.0964027	−	0.166974i	0.813790	−	0.581158i	$-0.197400\pi$
$541$	−2.24227	−	3.88372i	−0.0964027	−	0.166974i	−0.910193	+	0.414184i	$0.864067\pi$
$542$		0			0
$543$	−3.24227	+	5.61577i	−0.139139	+	0.240996i
$544$		0			0
$545$	−7.11468			−0.304759
$546$		0			0
$547$	−0.650757			−0.0278244			−0.0139122	−	0.999903i	$-0.504429\pi$
$547$	−0.650757			−0.0278244			−0.0139122	+	0.999903i	$0.504429\pi$
$548$		0			0
$549$	3.31507	−	5.74187i	0.141484	−	0.245057i
$550$		0			0
$551$	16.4230	+	28.4454i	0.699642	+	1.21182i
$552$		0			0
$553$	−4.58473	−	3.25410i	−0.194963	−	0.138379i
$554$		0			0
$555$	−4.65238	−	8.05816i	−0.197483	−	0.342050i
$556$		0			0
$557$	−17.5077	+	30.3242i	−0.741825	+	1.28488i	0.209838	+	0.977736i	$0.432706\pi$
$557$	−17.5077	+	30.3242i	−0.741825	+	1.28488i	−0.951663	+	0.307143i	$0.900627\pi$
$558$		0			0
$559$	−20.7551			−0.877848
$560$		0			0
$561$	−5.01031			−0.211535
$562$		0			0
$563$	15.6301	−	27.0722i	0.658732	−	1.14096i	−0.322212	−	0.946667i	$-0.604426\pi$
$563$	15.6301	−	27.0722i	0.658732	−	1.14096i	0.980944	−	0.194290i	$-0.0622402\pi$
$564$		0			0
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$		0			0
$567$	0.247423	−	2.63416i	0.0103908	−	0.110624i
$568$		0			0
$569$	0.779971	+	1.35095i	0.0326981	+	0.0566348i	0.881911	−	0.471415i	$-0.156257\pi$
$569$	0.779971	+	1.35095i	0.0326981	+	0.0566348i	−0.849213	+	0.528050i	$0.822923\pi$
$570$		0			0
$571$	4.57796	−	7.92925i	0.191581	−	0.331829i	−0.754193	−	0.656653i	$-0.771972\pi$
$571$	4.57796	−	7.92925i	0.191581	−	0.331829i	0.945775	+	0.324824i	$0.105305\pi$
$572$		0			0
$573$	−13.2397			−0.553095
$574$		0			0
$575$	6.82022			0.284423
$576$		0			0
$577$	0.415266	−	0.719262i	0.0172878	−	0.0299433i	−0.857252	−	0.514897i	$-0.827830\pi$
$577$	0.415266	−	0.719262i	0.0172878	−	0.0299433i	0.874540	+	0.484954i	$0.161164\pi$
$578$		0			0
$579$	−7.73034	−	13.3893i	−0.321262	−	0.556442i
$580$		0			0
$581$	26.2980	−	12.0591i	1.09102	−	0.500294i
$582$		0			0
$583$	15.4974	+	26.8423i	0.641837	+	1.11169i
$584$		0			0
$585$	−2.15754	+	3.73696i	−0.0892031	+	0.154504i
$586$		0			0
$587$	−23.0651			−0.951998			−0.475999	−	0.879446i	$-0.657913\pi$
$587$	−23.0651			−0.951998			−0.475999	+	0.879446i	$0.657913\pi$
$588$		0			0
$589$	11.4059			0.469971
$590$		0			0
$591$	7.22003	−	12.5055i	0.296992	−	0.514406i
$592$		0			0
$593$	11.7928	+	20.4258i	0.484273	+	0.838786i	0.999837	−	0.0180652i	$-0.00575064\pi$
$593$	11.7928	+	20.4258i	0.484273	+	0.838786i	−0.515563	+	0.856851i	$0.672417\pi$
$594$		0			0
$595$	3.16269	−	1.45026i	0.129658	−	0.0594551i
$596$		0			0
$597$	−1.19008	−	2.06129i	−0.0487069	−	0.0843628i
$598$		0			0
$599$	0.190084	−	0.329235i	0.00776661	−	0.0134522i	−0.862116	−	0.506711i	$-0.830861\pi$
$599$	0.190084	−	0.329235i	0.00776661	−	0.0134522i	0.869883	+	0.493259i	$0.164194\pi$
$600$		0			0
$601$	−6.10437			−0.249002			−0.124501	−	0.992219i	$-0.539733\pi$
$601$	−6.10437			−0.249002			−0.124501	+	0.992219i	$0.539733\pi$
$602$		0			0
$603$	−15.4401			−0.628768
$604$		0			0
$605$	−1.75773	+	3.04448i	−0.0714619	+	0.123776i
$606$		0			0
$607$	4.71748	+	8.17091i	0.191477	+	0.331647i	0.945740	−	0.324925i	$-0.105339\pi$
$607$	4.71748	+	8.17091i	0.191477	+	0.331647i	−0.754263	+	0.656572i	$0.772006\pi$
$608$		0			0
$609$	−1.06510	+	11.3394i	−0.0431599	+	0.459496i
$610$		0			0
$611$	7.56249	+	13.0986i	0.305946	+	0.529914i
$612$		0			0
$613$	−12.0676	+	20.9018i	−0.487408	+	0.844215i	−0.999895	−	0.0144798i	$-0.995391\pi$
$613$	−12.0676	+	20.9018i	−0.487408	+	0.844215i	0.512487	+	0.858695i	$0.328724\pi$
$614$		0			0
$615$	−10.4401			−0.420984
$616$		0			0
$617$	36.8595			1.48391			0.741954	−	0.670451i	$-0.233899\pi$
$617$	36.8595			1.48391			0.741954	+	0.670451i	$0.233899\pi$
$618$		0			0
$619$	−16.0650	+	27.8255i	−0.645709	+	1.11840i	0.338429	+	0.940992i	$0.390105\pi$
$619$	−16.0650	+	27.8255i	−0.645709	+	1.11840i	−0.984137	+	0.177408i	$0.943229\pi$
$620$		0			0
$621$	−3.41011	−	5.90649i	−0.136843	−	0.237019i
$622$		0			0
$623$	24.4127	+	17.3274i	0.978073	+	0.694206i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−14.5351	+	25.1755i	−0.580476	+	1.00541i
$628$		0			0
$629$	−12.2364			−0.487898
$630$		0			0
$631$	22.2912			0.887399			0.443699	−	0.896176i	$-0.353666\pi$
$631$	22.2912			0.887399			0.443699	+	0.896176i	$0.353666\pi$
$632$		0			0
$633$	8.05734	−	13.9557i	0.320250	−	0.554690i
$634$		0			0
$635$	−8.47261	−	14.6750i	−0.336225	−	0.582359i
$636$		0			0
$637$	19.7097	−	22.8888i	0.780928	−	0.906889i
$638$		0			0
$639$	2.16269	+	3.74589i	0.0855547	+	0.148185i
$640$		0			0
$641$	17.0196	−	29.4789i	0.672235	−	1.16435i	−0.305034	−	0.952342i	$-0.598668\pi$
$641$	17.0196	−	29.4789i	0.672235	−	1.16435i	0.977269	−	0.212004i	$-0.0679990\pi$
$642$		0			0
$643$	36.4297			1.43665			0.718325	−	0.695708i	$-0.244909\pi$
$643$	36.4297			1.43665			0.718325	+	0.695708i	$0.244909\pi$
$644$		0			0
$645$	−4.80992			−0.189390
$646$		0			0
$647$	11.0196	−	19.0866i	0.433227	−	0.750371i	−0.563922	−	0.825828i	$-0.690708\pi$
$647$	11.0196	−	19.0866i	0.433227	−	0.750371i	0.997149	+	0.0754573i	$0.0240416\pi$
$648$		0			0
$649$	−15.8202	−	27.4014i	−0.620998	−	1.07560i
$650$		0			0
$651$	3.22518	+	2.28914i	0.126405	+	0.0897183i
$652$		0			0
$653$	4.79028	+	8.29701i	0.187458	+	0.324687i	0.944402	−	0.328793i	$-0.106642\pi$
$653$	4.79028	+	8.29701i	0.187458	+	0.324687i	−0.756944	+	0.653480i	$0.773308\pi$
$654$		0			0
$655$	6.55219	−	11.3487i	0.256015	−	0.443431i
$656$		0			0
$657$	3.82022			0.149041
$658$		0			0
$659$	−25.2603			−0.984001			−0.492000	−	0.870595i	$-0.663734\pi$
$659$	−25.2603			−0.984001			−0.492000	+	0.870595i	$0.663734\pi$
$660$		0			0
$661$	12.8827	−	22.3135i	0.501080	−	0.867895i	−0.498920	−	0.866648i	$-0.666270\pi$
$661$	12.8827	−	22.3135i	0.501080	−	0.867895i	0.999999	−	0.00124712i	$-0.000396971\pi$
$662$		0			0
$663$	2.83731	+	4.91437i	0.110192	+	0.190858i
$664$		0			0
$665$	1.88787	−	20.0990i	0.0732085	−	0.779405i
$666$		0			0
$667$	14.6797	+	25.4260i	0.568401	+	0.984500i
$668$		0			0
$669$	−6.30476	+	10.9202i	−0.243756	+	0.422198i
$670$		0			0
$671$	−25.2603			−0.975162
$672$		0			0
$673$	−5.82022			−0.224353			−0.112177	−	0.993688i	$-0.535782\pi$
$673$	−5.82022			−0.224353			−0.112177	+	0.993688i	$0.535782\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	−9.05056	−	15.6760i	−0.347841	−	0.602479i	0.638024	−	0.770016i	$-0.279752\pi$
$677$	−9.05056	−	15.6760i	−0.347841	−	0.602479i	−0.985866	+	0.167537i	$0.946419\pi$
$678$		0			0
$679$	−25.5650	+	11.7230i	−0.981096	+	0.449886i
$680$		0			0
$681$	1.46745	+	2.54170i	0.0562329	+	0.0973982i
$682$		0			0
$683$	4.65754	−	8.06709i	0.178216	−	0.308679i	−0.763054	−	0.646335i	$-0.776301\pi$
$683$	4.65754	−	8.06709i	0.178216	−	0.308679i	0.941269	+	0.337656i	$0.109634\pi$
$684$		0			0
$685$	12.9349			0.494217
$686$		0			0
$687$	12.4845			0.476315
$688$		0			0
$689$	17.5522	−	30.4013i	0.668685	−	1.15820i
$690$		0			0
$691$	19.1875	+	33.2337i	0.729926	+	1.26427i	0.956914	+	0.290372i	$0.0937789\pi$
$691$	19.1875	+	33.2337i	0.729926	+	1.26427i	−0.226988	+	0.973898i	$0.572888\pi$
$692$		0			0
$693$	−9.16269	+	4.20159i	−0.348062	+	0.159605i
$694$		0			0
$695$	5.87241	+	10.1713i	0.222753	+	0.385820i
$696$		0			0
$697$	−6.86471	+	11.8900i	−0.260019	+	0.450367i
$698$		0			0
$699$	−24.6301			−0.931597
$700$		0			0
$701$	0.575352			0.0217307			0.0108654	−	0.999941i	$-0.496541\pi$
$701$	0.575352			0.0217307			0.0108654	+	0.999941i	$0.496541\pi$
$702$		0			0
$703$	−35.4983	+	61.4849i	−1.33884	+	2.31895i
$704$		0			0
$705$	1.75258	+	3.03555i	0.0660059	+	0.114326i
$706$		0			0
$707$	2.64370	−	28.1458i	0.0994265	−	1.05853i
$708$		0			0
$709$	−11.3151	−	19.5983i	−0.424946	−	0.736029i	0.571469	−	0.820624i	$-0.306374\pi$
$709$	−11.3151	−	19.5983i	−0.424946	−	0.736029i	−0.996415	+	0.0845949i	$0.973040\pi$
$710$		0			0
$711$	1.06249	−	1.84029i	0.0398466	−	0.0690164i
$712$		0			0
$713$	10.1952			0.381813
$714$		0			0
$715$	16.4401			0.614823
$716$		0			0
$717$	3.00000	−	5.19615i	0.112037	−	0.194054i
$718$		0			0
$719$	−10.3151	−	17.8662i	−0.384687	−	0.666298i	0.607039	−	0.794672i	$-0.292357\pi$
$719$	−10.3151	−	17.8662i	−0.384687	−	0.666298i	−0.991726	+	0.128375i	$0.959024\pi$
$720$		0			0
$721$	−41.9426	−	29.7696i	−1.56202	−	1.10868i
$722$		0			0
$723$	−7.87756	−	13.6443i	−0.292970	−	0.507438i
$724$		0			0
$725$	2.15238	−	3.72803i	0.0799374	−	0.138456i
$726$		0			0
$727$	6.27384			0.232684			0.116342	−	0.993209i	$-0.462883\pi$
$727$	6.27384			0.232684			0.116342	+	0.993209i	$0.462883\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.16269	+	5.47794i	−0.116976	+	0.202609i
$732$		0			0
$733$	−3.33731	−	5.78039i	−0.123266	−	0.213504i	0.797788	−	0.602939i	$-0.206004\pi$
$733$	−3.33731	−	5.78039i	−0.123266	−	0.213504i	−0.921054	+	0.389435i	$0.872670\pi$
$734$		0			0
$735$	4.56765	−	5.30439i	0.168480	−	0.195656i
$736$		0			0
$737$	29.4127	+	50.9442i	1.08343	+	1.87655i
$738$		0			0
$739$	−5.13014	+	8.88566i	−0.188715	+	0.326864i	−0.944822	−	0.327584i	$-0.893766\pi$
$739$	−5.13014	+	8.88566i	−0.188715	+	0.326864i	0.756107	+	0.654448i	$0.227099\pi$
$740$		0			0
$741$	32.9246			1.20952
$742$		0			0
$743$	−1.85115			−0.0679121			−0.0339560	−	0.999423i	$-0.510811\pi$
$743$	−1.85115			−0.0679121			−0.0339560	+	0.999423i	$0.510811\pi$
$744$		0			0
$745$	2.00000	−	3.46410i	0.0732743	−	0.126915i
$746$		0			0
$747$	5.46745	+	9.46990i	0.200044	+	0.346486i
$748$		0			0
$749$	22.2329	+	15.7802i	0.812372	+	0.576597i
$750$		0			0
$751$	−7.68233	−	13.3062i	−0.280332	−	0.485549i	0.691134	−	0.722726i	$-0.257111\pi$
$751$	−7.68233	−	13.3062i	−0.280332	−	0.485549i	−0.971466	+	0.237177i	$0.923778\pi$
$752$		0			0
$753$	4.41011	−	7.63854i	0.160713	−	0.278364i
$754$		0			0
$755$	0.630141			0.0229332
$756$		0			0
$757$	32.0206			1.16381			0.581905	−	0.813257i	$-0.302308\pi$
$757$	32.0206			1.16381			0.581905	+	0.813257i	$0.302308\pi$
$758$		0			0
$759$	−12.9922	+	22.5032i	−0.471589	+	0.816815i
$760$		0			0
$761$	−7.70457	−	13.3447i	−0.279290	−	0.483745i	0.691918	−	0.721976i	$-0.256766\pi$
$761$	−7.70457	−	13.3447i	−0.279290	−	0.483745i	−0.971209	+	0.238231i	$0.923433\pi$
$762$		0			0
$763$	−1.76033	+	18.7412i	−0.0637284	+	0.678476i
$764$		0			0
$765$	0.657535	+	1.13888i	0.0237732	+	0.0411765i
$766$		0			0
$767$	−17.9178	+	31.0346i	−0.646975	+	1.12059i
$768$		0			0
$769$	39.2500			1.41539			0.707695	−	0.706518i	$-0.249735\pi$
$769$	39.2500			1.41539			0.707695	+	0.706518i	$0.249735\pi$
$770$		0			0
$771$	14.9349			0.537867
$772$		0			0
$773$	−11.0196	+	19.0866i	−0.396349	+	0.686496i	−0.993272	−	0.115802i	$-0.963056\pi$
$773$	−11.0196	+	19.0866i	−0.396349	+	0.686496i	0.596924	+	0.802298i	$0.296390\pi$
$774$		0			0
$775$	−0.747423	−	1.29457i	−0.0268482	−	0.0465025i
$776$		0			0
$777$	−22.3776	+	10.2613i	−0.802791	+	0.368123i
$778$		0			0
$779$	39.8296	+	68.9868i	1.42704	+	2.47171i
$780$		0			0
$781$	8.23967	−	14.2715i	0.294838	−	0.510675i
$782$		0			0
$783$	−4.30476			−0.153840
$784$		0			0
$785$	8.87501			0.316763
$786$		0			0
$787$	−24.4401	+	42.3314i	−0.871194	+	1.50895i	−0.0104313	+	0.999946i	$0.503320\pi$
$787$	−24.4401	+	42.3314i	−0.871194	+	1.50895i	−0.860763	+	0.509007i	$0.830013\pi$
$788$		0			0
$789$	−1.31507	−	2.27777i	−0.0468177	−	0.0810907i
$790$		0			0
$791$	14.4297	−	6.61682i	0.513063	−	0.235267i
$792$		0			0
$793$	14.3048	+	24.7766i	0.507977	+	0.879842i
$794$		0			0
$795$	4.06765	−	7.04537i	0.144265	−	0.249874i
$796$		0			0
$797$	28.1746			0.997994			0.498997	−	0.866604i	$-0.333702\pi$
$797$	28.1746			0.997994			0.498997	+	0.866604i	$0.333702\pi$
$798$		0			0
$799$	4.60952			0.163073
$800$		0			0
$801$	−5.65754	+	9.79914i	−0.199899	+	0.346236i
$802$		0			0
$803$	−7.27737	−	12.6048i	−0.256813	−	0.444813i
$804$		0			0
$805$	1.68748	−	17.9655i	0.0594759	−	0.633202i
$806$		0			0
$807$	−9.82022	−	17.0091i	−0.345688	−	0.598750i
$808$		0			0
$809$	−27.1275	+	46.9863i	−0.953753	+	1.65195i	−0.216558	+	0.976270i	$0.569483\pi$
$809$	−27.1275	+	46.9863i	−0.953753	+	1.65195i	−0.737195	+	0.675680i	$0.763850\pi$
$810$		0			0
$811$	−13.5258			−0.474954			−0.237477	−	0.971393i	$-0.576320\pi$
$811$	−13.5258			−0.474954			−0.237477	+	0.971393i	$0.576320\pi$
$812$		0			0
$813$	14.8801			0.521868
$814$		0			0
$815$	−8.00000	+	13.8564i	−0.280228	+	0.485369i
$816$		0			0
$817$	18.3502	+	31.7834i	0.641991	+	1.11196i
$818$		0			0
$819$	9.30992	+	6.60790i	0.325315	+	0.230899i
$820$		0			0
$821$	5.85793	+	10.1462i	0.204443	+	0.354106i	0.949955	−	0.312386i	$-0.101128\pi$
$821$	5.85793	+	10.1462i	0.204443	+	0.354106i	−0.745512	+	0.666492i	$0.767795\pi$
$822$		0			0
$823$	8.50515	−	14.7314i	0.296471	−	0.513503i	−0.678855	−	0.734272i	$-0.737524\pi$
$823$	8.50515	−	14.7314i	0.296471	−	0.513503i	0.975326	+	0.220769i	$0.0708568\pi$
$824$		0			0
$825$	3.80992			0.132644
$826$		0			0
$827$	25.3905			0.882913			0.441457	−	0.897283i	$-0.354462\pi$
$827$	25.3905			0.882913			0.441457	+	0.897283i	$0.354462\pi$
$828$		0			0
$829$	26.6275	−	46.1202i	0.924813	−	1.60182i	0.132950	−	0.991123i	$-0.457555\pi$
$829$	26.6275	−	46.1202i	0.924813	−	1.60182i	0.791862	−	0.610700i	$-0.209112\pi$
$830$		0			0
$831$	2.41527	+	4.18336i	0.0837847	+	0.145119i
$832$		0			0
$833$	−3.03770	−	8.68985i	−0.105250	−	0.301085i
$834$		0			0
$835$	−6.02994	−	10.4442i	−0.208675	−	0.361435i
$836$		0			0
$837$	−0.747423	+	1.29457i	−0.0258347	+	0.0447470i
$838$		0			0
$839$	−23.6952			−0.818050			−0.409025	−	0.912523i	$-0.634131\pi$
$839$	−23.6952			−0.818050			−0.409025	+	0.912523i	$0.634131\pi$
$840$		0			0
$841$	−10.4690			−0.361001
$842$		0			0
$843$	4.75258	−	8.23170i	0.163687	−	0.283515i
$844$		0			0
$845$	−2.80992	−	4.86692i	−0.0966641	−	0.167427i
$846$		0			0
$847$	7.58473	+	5.38341i	0.260615	+	0.184976i
$848$		0			0
$849$	13.8553	+	23.9981i	0.475513	+	0.823613i
$850$		0			0
$851$	−31.7303	+	54.9585i	−1.08770	+	1.88395i
$852$		0			0
$853$	22.5238			0.771201			0.385600	−	0.922666i	$-0.373994\pi$
$853$	22.5238			0.771201			0.385600	+	0.922666i	$0.373994\pi$
$854$		0			0
$855$	7.63014			0.260945
$856$		0			0
$857$	−22.7380	+	39.3834i	−0.776717	+	1.34531i	0.157108	+	0.987581i	$0.449783\pi$
$857$	−22.7380	+	39.3834i	−0.776717	+	1.34531i	−0.933825	+	0.357731i	$0.883550\pi$
$858$		0			0
$859$	20.7345	+	35.9132i	0.707452	+	1.22534i	0.965799	+	0.259291i	$0.0834890\pi$
$859$	20.7345	+	35.9132i	0.707452	+	1.22534i	−0.258347	+	0.966052i	$0.583178\pi$
$860$		0			0
$861$	−2.58311	+	27.5007i	−0.0880321	+	0.937223i
$862$		0			0
$863$	−21.8331	−	37.8160i	−0.743207	−	1.28727i	−0.951028	−	0.309105i	$-0.899971\pi$
$863$	−21.8331	−	37.8160i	−0.743207	−	1.28727i	0.207821	−	0.978167i	$-0.433363\pi$
$864$		0			0
$865$	−8.56249	+	14.8307i	−0.291134	+	0.504258i
$866$		0			0
$867$	−15.2706			−0.518616
$868$		0			0
$869$	−8.09602			−0.274639
$870$		0			0
$871$	33.3125	−	57.6989i	1.12875	−	1.95505i
$872$		0			0
$873$	−5.31507	−	9.20597i	−0.179888	−	0.311575i
$874$		0			0
$875$	−2.40496	+	1.10280i	−0.0813024	+	0.0372816i
$876$		0			0
$877$	−20.7423	−	35.9267i	−0.700417	−	1.21316i	−0.968320	−	0.249712i	$-0.919664\pi$
$877$	−20.7423	−	35.9267i	−0.700417	−	1.21316i	0.267904	−	0.963446i	$-0.413669\pi$
$878$		0			0
$879$	1.24742	−	2.16060i	0.0420745	−	0.0728752i
$880$		0			0
$881$	13.0154			0.438500			0.219250	−	0.975669i	$-0.429639\pi$
$881$	13.0154			0.438500			0.219250	+	0.975669i	$0.429639\pi$
$882$		0			0
$883$	22.2996			0.750440			0.375220	−	0.926936i	$-0.377567\pi$
$883$	22.2996			0.750440			0.375220	+	0.926936i	$0.377567\pi$
$884$		0			0
$885$	−4.15238	+	7.19214i	−0.139581	+	0.241761i
$886$		0			0
$887$	13.7722	+	23.8542i	0.462426	+	0.800945i	0.999081	−	0.0428566i	$-0.0136459\pi$
$887$	13.7722	+	23.8542i	0.462426	+	0.800945i	−0.536656	+	0.843801i	$0.680313\pi$
$888$		0			0
$889$	−40.7525	+	18.6872i	−1.36680	+	0.626750i
$890$		0			0
$891$	−1.90496	−	3.29948i	−0.0638185	−	0.110537i
$892$		0			0
$893$	13.3724	−	23.1617i	0.447491	−	0.775077i
$894$		0			0
$895$	−11.5052			−0.384575
$896$		0			0
$897$	29.4297			0.982631
$898$		0			0
$899$	3.21748	−	5.57284i	0.107309	−	0.185864i
$900$		0			0
$901$	−5.34924	−	9.26516i	−0.178209	−	0.308667i
$902$		0			0
$903$	−1.19008	+	12.6701i	−0.0396035	+	0.421634i
$904$		0			0
$905$	−3.24227	−	5.61577i	−0.107777	−	0.186675i
$906$		0			0
$907$	−16.1601	+	27.9901i	−0.536587	+	0.929396i	0.462498	+	0.886620i	$0.346953\pi$
$907$	−16.1601	+	27.9901i	−0.536587	+	0.929396i	−0.999085	+	0.0427753i	$0.986380\pi$
$908$		0			0
$909$	10.6849			0.354397
$910$		0			0
$911$	−2.55474			−0.0846422			−0.0423211	−	0.999104i	$-0.513475\pi$
$911$	−2.55474			−0.0846422			−0.0423211	+	0.999104i	$0.513475\pi$
$912$		0			0
$913$	20.8305	−	36.0795i	0.689390	−	1.19406i
$914$		0			0
$915$	3.31507	+	5.74187i	0.109593	+	0.189820i
$916$		0			0
$917$	−28.2731	−	20.0674i	−0.933661	−	0.662684i
$918$		0			0
$919$	20.5573	+	35.6064i	0.678124	+	1.17455i	0.975545	+	0.219799i	$0.0705401\pi$
$919$	20.5573	+	35.6064i	0.678124	+	1.17455i	−0.297421	+	0.954746i	$0.596127\pi$
$920$		0			0
$921$	−0.605350	+	1.04850i	−0.0199470	+	0.0345492i
$922$		0			0
$923$	−18.6643			−0.614343
$924$		0			0
$925$	9.30476			0.305939
$926$		0			0
$927$	9.72003	−	16.8356i	0.319248	−	0.552953i
$928$		0			0
$929$	1.10535	+	1.91452i	0.0362654	+	0.0628134i	0.883588	−	0.468264i	$-0.155121\pi$
$929$	1.10535	+	1.91452i	0.0362654	+	0.0628134i	−0.847323	+	0.531078i	$0.821787\pi$
$930$		0			0
$931$	−52.4768	−	9.94590i	−1.71986	−	0.325964i
$932$		0			0
$933$	−14.6027	−	25.2927i	−0.478072	−	0.828046i
$934$		0			0
$935$	2.50515	−	4.33905i	0.0819273	−	0.141902i
$936$		0			0
$937$	−48.7003			−1.59097			−0.795485	−	0.605973i	$-0.792784\pi$
$937$	−48.7003			−1.59097			−0.795485	+	0.605973i	$0.792784\pi$
$938$		0			0
$939$	−0.809916			−0.0264306
$940$		0			0
$941$	13.9075	−	24.0885i	0.453372	−	0.785263i	−0.545221	−	0.838292i	$-0.683554\pi$
$941$	13.9075	−	24.0885i	0.453372	−	0.785263i	0.998593	+	0.0530292i	$0.0168876\pi$
$942$		0			0
$943$	35.6018	+	61.6641i	1.15935	+	2.00806i
$944$		0			0
$945$	2.15754	+	1.53135i	0.0701846	+	0.0498149i
$946$		0			0
$947$	18.9520	+	32.8258i	0.615857	+	1.06670i	0.990234	+	0.139419i	$0.0445234\pi$
$947$	18.9520	+	32.8258i	0.615857	+	1.06670i	−0.374377	+	0.927277i	$0.622143\pi$
$948$		0			0
$949$	−8.24227	+	14.2760i	−0.267555	+	0.463419i
$950$		0			0
$951$	−8.28415			−0.268632
$952$		0			0
$953$	−13.9110			−0.450623			−0.225311	−	0.974287i	$-0.572340\pi$
$953$	−13.9110			−0.450623			−0.225311	+	0.974287i	$0.572340\pi$
$954$		0			0
$955$	6.61983	−	11.4659i	0.214213	−	0.371027i
$956$		0			0
$957$	8.20039	+	14.2035i	0.265081	+	0.459134i
$958$		0			0
$959$	3.20039	−	34.0726i	0.103346	−	1.10026i
$960$		0			0
$961$	14.3827	+	24.9116i	0.463959	+	0.803600i
$962$		0			0
$963$	−5.15238	+	8.92419i	−0.166033	+	0.287578i
$964$		0			0
$965$	15.4607			0.497697
$966$		0			0
$967$	4.80992			0.154676			0.0773382	−	0.997005i	$-0.475358\pi$
$967$	4.80992			0.154676			0.0773382	+	0.997005i	$0.475358\pi$
$968$		0			0
$969$	5.01709	−	8.68985i	0.161172	−	0.279158i
$970$		0			0
$971$	−2.25773	−	3.91051i	−0.0724540	−	0.125494i	0.827522	−	0.561433i	$-0.189750\pi$
$971$	−2.25773	−	3.91051i	−0.0724540	−	0.125494i	−0.899976	+	0.435939i	$0.856416\pi$
$972$		0			0
$973$	28.2458	−	12.9522i	0.905519	−	0.415229i
$974$		0			0
$975$	−2.15754	−	3.73696i	−0.0690964	−	0.119679i
$976$		0			0
$977$	21.5480	−	37.3222i	0.689380	−	1.19404i	−0.282658	−	0.959221i	$-0.591216\pi$
$977$	21.5480	−	37.3222i	0.689380	−	1.19404i	0.972039	−	0.234821i	$-0.0754504\pi$
$978$		0			0
$979$	43.1095			1.37778
$980$		0			0
$981$	−7.11468			−0.227154
$982$		0			0
$983$	−7.57958	+	13.1282i	−0.241751	+	0.418725i	−0.961213	−	0.275807i	$-0.911055\pi$
$983$	−7.57958	+	13.1282i	−0.241751	+	0.418725i	0.719462	+	0.694532i	$0.244388\pi$
$984$		0			0
$985$	7.22003	+	12.5055i	0.230049	+	0.398457i
$986$		0			0
$987$	8.42975	−	3.86550i	0.268322	−	0.123040i
$988$		0			0
$989$	16.4024	+	28.4097i	0.521565	+	0.903376i
$990$		0			0
$991$	7.68233	−	13.3062i	0.244037	−	0.422685i	−0.717823	−	0.696225i	$-0.754861\pi$
$991$	7.68233	−	13.3062i	0.244037	−	0.422685i	0.961860	+	0.273541i	$0.0881948\pi$
$992$		0			0
$993$	25.8801			0.821281
$994$		0			0
$995$	2.38017			0.0754564
$996$		0			0
$997$	−22.4153	+	38.8244i	−0.709899	+	1.22958i	0.254996	+	0.966942i	$0.417926\pi$
$997$	−22.4153	+	38.8244i	−0.709899	+	1.22958i	−0.964894	+	0.262638i	$0.915407\pi$
$998$		0			0
$999$	−4.65238	−	8.05816i	−0.147195	−	0.254949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bg.i.361.1	yes	6
3.2	odd	2		2520.2.bi.o.361.1		6
4.3	odd	2		1680.2.bg.u.1201.3		6
7.2	even	3	inner	840.2.bg.i.121.1	✓	6
7.3	odd	6		5880.2.a.bt.1.3		3
7.4	even	3		5880.2.a.bw.1.3		3
21.2	odd	6		2520.2.bi.o.1801.1		6
28.23	odd	6		1680.2.bg.u.961.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.i.121.1	✓	6	7.2	even	3	inner
840.2.bg.i.361.1	yes	6	1.1	even	1	trivial
1680.2.bg.u.961.3		6	28.23	odd	6
1680.2.bg.u.1201.3		6	4.3	odd	2
2520.2.bi.o.361.1		6	3.2	odd	2
2520.2.bi.o.1801.1		6	21.2	odd	6
5880.2.a.bt.1.3		3	7.3	odd	6
5880.2.a.bw.1.3		3	7.4	even	3

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.40496 + 1.10280i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.40496 + 1.10280i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.90496 + 3.29948i) q^{11} +4.31507 q^{13} +1.00000 q^{15} +(0.657535 - 1.13888i) q^{17} +(-3.81507 - 6.60790i) q^{19} +(0.247423 - 2.63416i) q^{21} +(-3.41011 - 5.90649i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -4.30476 q^{29} +(-0.747423 + 1.29457i) q^{31} +(-1.90496 - 3.29948i) q^{33} +(2.15754 + 1.53135i) q^{35} +(-4.65238 - 8.05816i) q^{37} +(-2.15754 + 3.73696i) q^{39} -10.4401 q^{41} -4.80992 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.75258 + 3.03555i) q^{47} +(4.56765 - 5.30439i) q^{49} +(0.657535 + 1.13888i) q^{51} +(4.06765 - 7.04537i) q^{53} +3.80992 q^{55} +7.63014 q^{57} +(-4.15238 + 7.19214i) q^{59} +(3.31507 + 5.74187i) q^{61} +(2.15754 + 1.53135i) q^{63} +(-2.15754 - 3.73696i) q^{65} +(7.72003 - 13.3715i) q^{67} +6.82022 q^{69} -4.32538 q^{71} +(-1.91011 + 3.30841i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(0.942661 - 10.0359i) q^{77} +(1.06249 + 1.84029i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.9349 q^{83} -1.31507 q^{85} +(2.15238 - 3.72803i) q^{87} +(-5.65754 - 9.79914i) q^{89} +(-10.3776 + 4.75868i) q^{91} +(-0.747423 - 1.29457i) q^{93} +(-3.81507 + 6.60790i) q^{95} +10.6301 q^{97} +3.80992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9	\( 6 q - 3 q^{3} - 3 q^{5} - 2 q^{7} - 3 q^{9} + q^{11} + 2 q^{13} + 6 q^{15} - 8 q^{17} + q^{19} + q^{21} - 9 q^{23} - 3 q^{25} + 6 q^{27} - 4 q^{31} + q^{33} + q^{35} - 15 q^{37} - q^{39} + 10 q^{41} - 4 q^{43} - 3 q^{45} + 11 q^{47} + 4 q^{49} - 8 q^{51} + q^{53} - 2 q^{55} - 2 q^{57} - 12 q^{59} - 4 q^{61} + q^{63} - q^{65} + 10 q^{67} + 18 q^{69} - 4 q^{71} - 3 q^{75} + 31 q^{77} - 18 q^{79} - 3 q^{81} + 8 q^{83} + 16 q^{85} - 22 q^{89} - 14 q^{91} - 4 q^{93} + q^{95} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 3 * q^5 - 2 * q^7 - 3 * q^9 + q^11 + 2 * q^13 + 6 * q^15 - 8 * q^17 + q^19 + q^21 - 9 * q^23 - 3 * q^25 + 6 * q^27 - 4 * q^31 + q^33 + q^35 - 15 * q^37 - q^39 + 10 * q^41 - 4 * q^43 - 3 * q^45 + 11 * q^47 + 4 * q^49 - 8 * q^51 + q^53 - 2 * q^55 - 2 * q^57 - 12 * q^59 - 4 * q^61 + q^63 - q^65 + 10 * q^67 + 18 * q^69 - 4 * q^71 - 3 * q^75 + 31 * q^77 - 18 * q^79 - 3 * q^81 + 8 * q^83 + 16 * q^85 - 22 * q^89 - 14 * q^91 - 4 * q^93 + q^95 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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