LMFDB - Embedded newform 1232.2.q.n.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} - 2x^{5} + 66x^{4} - 9x^{3} + 136x^{2} + 15x + 225 $ x^8 + 9x^6 - 2x^5 + 66x^4 - 9x^3 + 136x^2 + 15x + 225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$-1.35283 - 2.34317i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.n.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66029 - 2.87570i) q^{3} +(-0.852828 + 1.47714i) q^{5} +(1.47905 + 2.19372i) q^{7} +(-4.01312 + 6.95092i) q^{9} +O(q^{10})$	\(q+(-1.66029 - 2.87570i) q^{3} +(-0.852828 + 1.47714i) q^{5} +(1.47905 + 2.19372i) q^{7} +(-4.01312 + 6.95092i) q^{9} +(-0.500000 - 0.866025i) q^{11} -3.32058 q^{13} +5.66376 q^{15} +(-0.433686 - 0.751166i) q^{17} +(1.13934 - 1.97340i) q^{19} +(3.85283 - 7.89553i) q^{21} +(1.30746 - 2.26459i) q^{23} +(1.04537 + 1.81063i) q^{25} +16.6900 q^{27} +9.34681 q^{29} +(-4.29963 - 7.44718i) q^{31} +(-1.66029 + 2.87570i) q^{33} +(-4.50181 + 0.313908i) q^{35} +(3.70566 - 6.41839i) q^{37} +(5.51312 + 9.54900i) q^{39} +4.83828 q^{41} +6.32058 q^{43} +(-6.84500 - 11.8559i) q^{45} +(-1.20384 + 2.08512i) q^{47} +(-2.62480 + 6.48926i) q^{49} +(-1.44009 + 2.49431i) q^{51} +(-3.99217 - 6.91464i) q^{53} +1.70566 q^{55} -7.56655 q^{57} +(-5.53406 - 9.58528i) q^{59} +(3.71696 - 6.43797i) q^{61} +(-21.1840 + 1.47714i) q^{63} +(2.83188 - 4.90496i) q^{65} +(3.24115 + 5.61383i) q^{67} -8.68305 q^{69} -0.867372 q^{71} +(6.82405 + 11.8196i) q^{73} +(3.47122 - 6.01234i) q^{75} +(1.16029 - 2.37776i) q^{77} +(4.73791 - 8.20630i) q^{79} +(-15.6709 - 27.1427i) q^{81} -6.54394 q^{83} +1.47944 q^{85} +(-15.5184 - 26.8787i) q^{87} +(-4.43226 + 7.67690i) q^{89} +(-4.91131 - 7.28441i) q^{91} +(-14.2773 + 24.7289i) q^{93} +(1.94333 + 3.36594i) q^{95} +13.2368 q^{97} +8.02623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9	$ 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 3 q^{17} - 13 q^{19} + 20 q^{21} + 10 q^{23} - 2 q^{25} + 46 q^{27} + 8 q^{29} - q^{31} - 2 q^{33} - 13 q^{35} + 8 q^{37} + 22 q^{39} + 18 q^{41} + 28 q^{43} - 11 q^{45} - 11 q^{47} + 11 q^{49} - 12 q^{51} + q^{53} - 8 q^{55} - 20 q^{57} - 33 q^{59} + 9 q^{61} - 26 q^{63} + q^{65} + 25 q^{67} - 46 q^{69} - 6 q^{71} - 16 q^{75} - 2 q^{77} + 28 q^{79} - 4 q^{81} - 10 q^{83} - 54 q^{85} - 47 q^{87} - 3 q^{89} + 4 q^{91} - 38 q^{93} + 25 q^{95} + 40 q^{97} + 20 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^15 - 3 * q^17 - 13 * q^19 + 20 * q^21 + 10 * q^23 - 2 * q^25 + 46 * q^27 + 8 * q^29 - q^31 - 2 * q^33 - 13 * q^35 + 8 * q^37 + 22 * q^39 + 18 * q^41 + 28 * q^43 - 11 * q^45 - 11 * q^47 + 11 * q^49 - 12 * q^51 + q^53 - 8 * q^55 - 20 * q^57 - 33 * q^59 + 9 * q^61 - 26 * q^63 + q^65 + 25 * q^67 - 46 * q^69 - 6 * q^71 - 16 * q^75 - 2 * q^77 + 28 * q^79 - 4 * q^81 - 10 * q^83 - 54 * q^85 - 47 * q^87 - 3 * q^89 + 4 * q^91 - 38 * q^93 + 25 * q^95 + 40 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	−1.66029	−	2.87570i	−0.958568	−	1.66029i	−0.725983	−	0.687713i	$-0.758615\pi$
$3$	−1.66029	−	2.87570i	−0.958568	−	1.66029i	−0.232585	−	0.972576i	$-0.574718\pi$
$4$		0			0
$5$	−0.852828	+	1.47714i	−0.381396	+	0.660598i	−0.991262	−	0.131907i	$-0.957890\pi$
$5$	−0.852828	+	1.47714i	−0.381396	+	0.660598i	0.609866	+	0.792505i	$0.291223\pi$
$6$		0			0
$7$	1.47905	+	2.19372i	0.559030	+	0.829148i
$7$	1.47905	+	2.19372i	0.559030	+	0.829148i
$8$		0			0
$9$	−4.01312	+	6.95092i	−1.33771	+	2.31697i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−3.32058			−0.920962			−0.460481	−	0.887669i	$-0.652323\pi$
$13$	−3.32058			−0.920962			−0.460481	+	0.887669i	$0.652323\pi$
$14$		0			0
$15$	5.66376			1.46238
$16$		0			0
$17$	−0.433686	−	0.751166i	−0.105184	−	0.182185i	0.808629	−	0.588319i	$-0.200210\pi$
$17$	−0.433686	−	0.751166i	−0.105184	−	0.182185i	−0.913814	+	0.406134i	$0.866877\pi$
$18$		0			0
$19$	1.13934	−	1.97340i	0.261383	−	0.452729i	−0.705227	−	0.708982i	$-0.749155\pi$
$19$	1.13934	−	1.97340i	0.261383	−	0.452729i	0.966610	+	0.256253i	$0.0824881\pi$
$20$		0			0
$21$	3.85283	−	7.89553i	0.840756	−	1.72295i
$22$		0			0
$23$	1.30746	−	2.26459i	0.272624	−	0.472199i	−0.696909	−	0.717160i	$-0.745442\pi$
$23$	1.30746	−	2.26459i	0.272624	−	0.472199i	0.969533	+	0.244961i	$0.0787751\pi$
$24$		0			0
$25$	1.04537	+	1.81063i	0.209074	+	0.362126i
$26$		0			0
$27$	16.6900			3.21199
$28$		0			0
$29$	9.34681			1.73566			0.867830	−	0.496862i	$-0.165514\pi$
$29$	9.34681			1.73566			0.867830	+	0.496862i	$0.165514\pi$
$30$		0			0
$31$	−4.29963	−	7.44718i	−0.772237	−	1.33755i	−0.936335	−	0.351109i	$-0.885805\pi$
$31$	−4.29963	−	7.44718i	−0.772237	−	1.33755i	0.164098	−	0.986444i	$-0.447529\pi$
$32$		0			0
$33$	−1.66029	+	2.87570i	−0.289019	+	0.500596i
$34$		0			0
$35$	−4.50181	+	0.313908i	−0.760945	+	0.0530601i
$36$		0			0
$37$	3.70566	−	6.41839i	0.609206	−	1.05518i	−0.382165	−	0.924094i	$-0.624822\pi$
$37$	3.70566	−	6.41839i	0.609206	−	1.05518i	0.991372	−	0.131082i	$-0.0418451\pi$
$38$		0			0
$39$	5.51312	+	9.54900i	0.882805	+	1.52906i
$40$		0			0
$41$	4.83828			0.755613			0.377807	−	0.925885i	$-0.376678\pi$
$41$	4.83828			0.755613			0.377807	+	0.925885i	$0.376678\pi$
$42$		0			0
$43$	6.32058			0.963879			0.481940	−	0.876204i	$-0.339932\pi$
$43$	6.32058			0.963879			0.481940	+	0.876204i	$0.339932\pi$
$44$		0			0
$45$	−6.84500	−	11.8559i	−1.02039	−	1.76737i
$46$		0			0
$47$	−1.20384	+	2.08512i	−0.175599	+	0.304146i	−0.940368	−	0.340158i	$-0.889519\pi$
$47$	−1.20384	+	2.08512i	−0.175599	+	0.304146i	0.764770	+	0.644304i	$0.222853\pi$
$48$		0			0
$49$	−2.62480	+	6.48926i	−0.374971	+	0.927036i
$50$		0			0
$51$	−1.44009	+	2.49431i	−0.201653	+	0.349273i
$52$		0			0
$53$	−3.99217	−	6.91464i	−0.548367	−	0.949799i	−0.998387	−	0.0567807i	$-0.981916\pi$
$53$	−3.99217	−	6.91464i	−0.548367	−	0.949799i	0.450020	−	0.893019i	$-0.351417\pi$
$54$		0			0
$55$	1.70566			0.229991
$56$		0			0
$57$	−7.56655			−1.00221
$58$		0			0
$59$	−5.53406	−	9.58528i	−0.720474	−	1.24790i	−0.960810	−	0.277207i	$-0.910591\pi$
$59$	−5.53406	−	9.58528i	−0.720474	−	1.24790i	0.240337	−	0.970690i	$-0.422742\pi$
$60$		0			0
$61$	3.71696	−	6.43797i	0.475908	−	0.824297i	−0.523711	−	0.851896i	$-0.675453\pi$
$61$	3.71696	−	6.43797i	0.475908	−	0.824297i	0.999619	+	0.0275990i	$0.00878613\pi$
$62$		0			0
$63$	−21.1840	+	1.47714i	−2.66893	+	0.186102i
$64$		0			0
$65$	2.83188	−	4.90496i	0.351252	−	0.608386i
$66$		0			0
$67$	3.24115	+	5.61383i	0.395969	+	0.685839i	0.993224	−	0.116213i	$-0.0370754\pi$
$67$	3.24115	+	5.61383i	0.395969	+	0.685839i	−0.597255	+	0.802051i	$0.703742\pi$
$68$		0			0
$69$	−8.68305			−1.04532
$70$		0			0
$71$	−0.867372			−0.102938			−0.0514691	−	0.998675i	$-0.516390\pi$
$71$	−0.867372			−0.102938			−0.0514691	+	0.998675i	$0.516390\pi$
$72$		0			0
$73$	6.82405	+	11.8196i	0.798695	+	1.38338i	0.920466	+	0.390822i	$0.127809\pi$
$73$	6.82405	+	11.8196i	0.798695	+	1.38338i	−0.121771	+	0.992558i	$0.538857\pi$
$74$		0			0
$75$	3.47122	−	6.01234i	0.400823	−	0.694245i
$76$		0			0
$77$	1.16029	−	2.37776i	0.132227	−	0.270971i
$78$		0			0
$79$	4.73791	−	8.20630i	0.533056	−	0.923280i	−0.466198	−	0.884680i	$-0.654377\pi$
$79$	4.73791	−	8.20630i	0.533056	−	0.923280i	0.999255	−	0.0386003i	$-0.0122899\pi$
$80$		0			0
$81$	−15.6709	−	27.1427i	−1.74121	−	3.01586i
$82$		0			0
$83$	−6.54394			−0.718291			−0.359145	−	0.933282i	$-0.616932\pi$
$83$	−6.54394			−0.718291			−0.359145	+	0.933282i	$0.616932\pi$
$84$		0			0
$85$	1.47944			0.160468
$86$		0			0
$87$	−15.5184	−	26.8787i	−1.66375	−	2.88170i
$88$		0			0
$89$	−4.43226	+	7.67690i	−0.469819	+	0.813750i	−0.999404	−	0.0345067i	$-0.989014\pi$
$89$	−4.43226	+	7.67690i	−0.469819	+	0.813750i	0.529586	+	0.848256i	$0.322347\pi$
$90$		0			0
$91$	−4.91131	−	7.28441i	−0.514846	−	0.763614i
$92$		0			0
$93$	−14.2773	+	24.7289i	−1.48048	+	2.56427i
$94$		0			0
$95$	1.94333	+	3.36594i	0.199381	+	0.345338i
$96$		0			0
$97$	13.2368			1.34399			0.671996	−	0.740554i	$-0.265437\pi$
$97$	13.2368			1.34399			0.671996	+	0.740554i	$0.265437\pi$
$98$		0			0
$99$	8.02623			0.806667
$100$		0			0
$101$	−5.70747	−	9.88563i	−0.567914	−	0.983657i	−0.996772	−	0.0802844i	$-0.974417\pi$
$101$	−5.70747	−	9.88563i	−0.567914	−	0.983657i	0.428858	−	0.903372i	$-0.358916\pi$
$102$		0			0
$103$	5.42443	−	9.39539i	0.534485	−	0.925755i	−0.464703	−	0.885467i	$-0.653839\pi$
$103$	5.42443	−	9.39539i	0.534485	−	0.925755i	0.999188	−	0.0402886i	$-0.0128277\pi$
$104$		0			0
$105$	8.37701	+	12.4247i	0.817513	+	1.21253i
$106$		0			0
$107$	−5.42586	+	9.39786i	−0.524537	+	0.908525i	0.475054	+	0.879956i	$0.342428\pi$
$107$	−5.42586	+	9.39786i	−0.524537	+	0.908525i	−0.999592	+	0.0285690i	$0.990905\pi$
$108$		0			0
$109$	3.67831	+	6.37102i	0.352318	+	0.610233i	0.986655	−	0.162824i	$-0.0520602\pi$
$109$	3.67831	+	6.37102i	0.352318	+	0.610233i	−0.634337	+	0.773057i	$0.718727\pi$
$110$		0			0
$111$	−24.6098			−2.33586
$112$		0			0
$113$	14.9424			1.40567			0.702834	−	0.711354i	$-0.251918\pi$
$113$	14.9424			1.40567			0.702834	+	0.711354i	$0.251918\pi$
$114$		0			0
$115$	2.23008	+	3.86261i	0.207956	+	0.360190i
$116$		0			0
$117$	13.3259	−	23.0811i	1.23198	−	2.13385i
$118$		0			0
$119$	1.00640	−	2.06240i	0.0922567	−	0.189060i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−8.03295	−	13.9135i	−0.724307	−	1.25454i
$124$		0			0
$125$	−12.0944			−1.08175
$126$		0			0
$127$	4.80287			0.426186			0.213093	−	0.977032i	$-0.431646\pi$
$127$	4.80287			0.426186			0.213093	+	0.977032i	$0.431646\pi$
$128$		0			0
$129$	−10.4940	−	18.1761i	−0.923944	−	1.60032i
$130$		0			0
$131$	3.43226	−	5.94485i	0.299878	−	0.519404i	−0.676230	−	0.736691i	$-0.736387\pi$
$131$	3.43226	−	5.94485i	0.299878	−	0.519404i	0.976108	+	0.217287i	$0.0697207\pi$
$132$		0			0
$133$	6.01423	−	0.419367i	0.521500	−	0.0363638i
$134$		0			0
$135$	−14.2337	+	24.6535i	−1.22504	+	2.12184i
$136$		0			0
$137$	−5.46956	−	9.47356i	−0.467296	−	0.809381i	0.532006	−	0.846741i	$-0.321438\pi$
$137$	−5.46956	−	9.47356i	−0.467296	−	0.809381i	−0.999302	+	0.0373601i	$0.988105\pi$
$138$		0			0
$139$	9.84524			0.835062			0.417531	−	0.908663i	$-0.362896\pi$
$139$	9.84524			0.835062			0.417531	+	0.908663i	$0.362896\pi$
$140$		0			0
$141$	7.99492			0.673294
$142$		0			0
$143$	1.66029	+	2.87570i	0.138840	+	0.240478i
$144$		0			0
$145$	−7.97122	+	13.8066i	−0.661974	+	1.14657i
$146$		0			0
$147$	23.0191	−	3.22589i	1.89858	−	0.266067i
$148$		0			0
$149$	5.40491	−	9.36158i	0.442788	−	0.766931i	−0.555108	−	0.831779i	$-0.687323\pi$
$149$	5.40491	−	9.36158i	0.442788	−	0.766931i	0.997895	+	0.0648480i	$0.0206563\pi$
$150$		0			0
$151$	−1.33971	−	2.32045i	−0.109024	−	0.188835i	0.806351	−	0.591437i	$-0.201439\pi$
$151$	−1.33971	−	2.32045i	−0.109024	−	0.188835i	−0.915375	+	0.402602i	$0.868106\pi$
$152$		0			0
$153$	6.96173			0.562823
$154$		0			0
$155$	14.6674			1.17811
$156$		0			0
$157$	10.1525	+	17.5846i	0.810254	+	1.40340i	0.912686	+	0.408662i	$0.134004\pi$
$157$	10.1525	+	17.5846i	0.810254	+	1.40340i	−0.102431	+	0.994740i	$0.532662\pi$
$158$		0			0
$159$	−13.2563	+	22.9606i	−1.05129	+	1.82089i
$160$		0			0
$161$	6.90167	−	0.481248i	0.543928	−	0.0379277i
$162$		0			0
$163$	−11.6170	+	20.1212i	−0.909911	+	1.57601i	−0.0957258	+	0.995408i	$0.530517\pi$
$163$	−11.6170	+	20.1212i	−0.909911	+	1.57601i	−0.814185	+	0.580605i	$0.802816\pi$
$164$		0			0
$165$	−2.83188	−	4.90496i	−0.220462	−	0.381851i
$166$		0			0
$167$	9.69585			0.750287			0.375144	−	0.926967i	$-0.377593\pi$
$167$	9.69585			0.750287			0.375144	+	0.926967i	$0.377593\pi$
$168$		0			0
$169$	−1.97377			−0.151828
$170$		0			0
$171$	9.14463	+	15.8390i	0.699307	+	1.21124i
$172$		0			0
$173$	10.7510	−	18.6213i	0.817385	−	1.41575i	−0.0902172	−	0.995922i	$-0.528756\pi$
$173$	10.7510	−	18.6213i	0.817385	−	1.41575i	0.907602	−	0.419831i	$-0.137911\pi$
$174$		0			0
$175$	−2.42586	+	4.97126i	−0.183378	+	0.375792i
$176$		0			0
$177$	−18.3763	+	31.8287i	−1.38125	+	2.39239i
$178$		0			0
$179$	1.23610	+	2.14098i	0.0923901	+	0.160024i	0.908516	−	0.417849i	$-0.137216\pi$
$179$	1.23610	+	2.14098i	0.0923901	+	0.160024i	−0.816126	+	0.577874i	$0.803883\pi$
$180$		0			0
$181$	9.04552			0.672348			0.336174	−	0.941800i	$-0.390867\pi$
$181$	9.04552			0.672348			0.336174	+	0.941800i	$0.390867\pi$
$182$		0			0
$183$	−24.6849			−1.82476
$184$		0			0
$185$	6.32058	+	10.9476i	0.464698	+	0.804881i
$186$		0			0
$187$	−0.433686	+	0.751166i	−0.0317143	+	0.0549307i
$188$		0			0
$189$	24.6854	+	36.6132i	1.79560	+	2.66321i
$190$		0			0
$191$	−1.99360	+	3.45301i	−0.144252	+	0.249851i	−0.929094	−	0.369845i	$-0.879411\pi$
$191$	−1.99360	+	3.45301i	−0.144252	+	0.249851i	0.784842	+	0.619696i	$0.212744\pi$
$192$		0			0
$193$	6.76595	+	11.7190i	0.487024	+	0.843550i	0.999889	−	0.0149192i	$-0.00474909\pi$
$193$	6.76595	+	11.7190i	0.487024	+	0.843550i	−0.512865	+	0.858469i	$0.671416\pi$
$194$		0			0
$195$	−18.8070			−1.34679
$196$		0			0
$197$	−6.45606			−0.459975			−0.229988	−	0.973194i	$-0.573869\pi$
$197$	−6.45606			−0.459975			−0.229988	+	0.973194i	$0.573869\pi$
$198$		0			0
$199$	2.52299	+	4.36996i	0.178850	+	0.309778i	0.941487	−	0.337049i	$-0.109429\pi$
$199$	2.52299	+	4.36996i	0.178850	+	0.309778i	−0.762637	+	0.646827i	$0.776096\pi$
$200$		0			0
$201$	10.7625	−	18.6412i	0.759127	−	1.31485i
$202$		0			0
$203$	13.8244	+	20.5043i	0.970285	+	1.43912i
$204$		0			0
$205$	−4.12623	+	7.14683i	−0.288188	+	0.499156i
$206$		0			0
$207$	10.4940	+	18.1761i	0.729382	+	1.26333i
$208$		0			0
$209$	−2.27869			−0.157620
$210$		0			0
$211$	−2.18147			−0.150179			−0.0750893	−	0.997177i	$-0.523924\pi$
$211$	−2.18147			−0.150179			−0.0750893	+	0.997177i	$0.523924\pi$
$212$		0			0
$213$	1.44009	+	2.49431i	0.0986732	+	0.170907i
$214$		0			0
$215$	−5.39037	+	9.33639i	−0.367620	+	0.636736i
$216$		0			0
$217$	9.97763	−	20.4470i	0.677325	−	1.38803i
$218$		0			0
$219$	22.6598	−	39.2479i	1.53121	−	2.65213i
$220$		0			0
$221$	1.44009	+	2.49431i	0.0968708	+	0.167785i
$222$		0			0
$223$	9.48229			0.634981			0.317491	−	0.948261i	$-0.397160\pi$
$223$	9.48229			0.634981			0.317491	+	0.948261i	$0.397160\pi$
$224$		0			0
$225$	−16.7807			−1.11872
$226$		0			0
$227$	−13.1734	−	22.8170i	−0.874350	−	1.51442i	−0.857454	−	0.514561i	$-0.827955\pi$
$227$	−13.1734	−	22.8170i	−0.874350	−	1.51442i	−0.0168957	−	0.999857i	$-0.505378\pi$
$228$		0			0
$229$	7.12985	−	12.3493i	0.471154	−	0.816062i	−0.528302	−	0.849057i	$-0.677171\pi$
$229$	7.12985	−	12.3493i	0.471154	−	0.816062i	0.999456	+	0.0329944i	$0.0105044\pi$
$230$		0			0
$231$	−8.76414	+	0.611116i	−0.576638	+	0.0402085i
$232$		0			0
$233$	6.87740	−	11.9120i	0.450553	−	0.780381i	−0.547867	−	0.836565i	$-0.684560\pi$
$233$	6.87740	−	11.9120i	0.450553	−	0.780381i	0.998420	+	0.0561841i	$0.0178934\pi$
$234$		0			0
$235$	−2.05335	−	3.55650i	−0.133945	−	0.232000i
$236$		0			0
$237$	−31.4652			−2.04388
$238$		0			0
$239$	6.92569			0.447986			0.223993	−	0.974591i	$-0.428091\pi$
$239$	6.92569			0.447986			0.223993	+	0.974591i	$0.428091\pi$
$240$		0			0
$241$	−10.5454	−	18.2651i	−0.679287	−	1.17656i	−0.975196	−	0.221343i	$-0.928956\pi$
$241$	−10.5454	−	18.2651i	−0.679287	−	1.17656i	0.295909	−	0.955216i	$-0.404377\pi$
$242$		0			0
$243$	−27.0013	+	46.7677i	−1.73214	+	3.00015i
$244$		0			0
$245$	−7.34705	−	9.41142i	−0.469386	−	0.601274i
$246$		0			0
$247$	−3.78328	+	6.55283i	−0.240724	+	0.416946i
$248$		0			0
$249$	10.8648	+	18.8184i	0.688531	+	1.19257i
$250$		0			0
$251$	0.996376			0.0628907			0.0314453	−	0.999505i	$-0.489989\pi$
$251$	0.996376			0.0628907			0.0314453	+	0.999505i	$0.489989\pi$
$252$		0			0
$253$	−2.61492			−0.164399
$254$		0			0
$255$	−2.45630	−	4.25443i	−0.153819	−	0.266423i
$256$		0			0
$257$	12.2690	−	21.2506i	0.765322	−	1.32558i	−0.174754	−	0.984612i	$-0.555913\pi$
$257$	12.2690	−	21.2506i	0.765322	−	1.32558i	0.940076	−	0.340964i	$-0.110754\pi$
$258$		0			0
$259$	19.5610	−	1.36397i	1.21546	−	0.0847531i
$260$		0			0
$261$	−37.5098	+	64.9690i	−2.32180	+	4.02148i
$262$		0			0
$263$	7.41313	+	12.8399i	0.457113	+	0.791743i	0.998807	−	0.0488330i	$-0.0155502\pi$
$263$	7.41313	+	12.8399i	0.457113	+	0.791743i	−0.541694	+	0.840576i	$0.682217\pi$
$264$		0			0
$265$	13.6185			0.836581
$266$		0			0
$267$	29.4353			1.80141
$268$		0			0
$269$	3.97905	+	6.89192i	0.242607	+	0.420208i	0.961456	−	0.274958i	$-0.0886641\pi$
$269$	3.97905	+	6.89192i	0.242607	+	0.420208i	−0.718849	+	0.695166i	$0.755331\pi$
$270$		0			0
$271$	7.80492	−	13.5185i	0.474115	−	0.821191i	−0.525446	−	0.850827i	$-0.676101\pi$
$271$	7.80492	−	13.5185i	0.474115	−	0.821191i	0.999561	+	0.0296357i	$0.00943473\pi$
$272$		0			0
$273$	−12.7936	+	26.2177i	−0.774305	+	1.58677i
$274$		0			0
$275$	1.04537	−	1.81063i	0.0630381	−	0.109185i
$276$		0			0
$277$	13.5220	+	23.4208i	0.812460	+	1.40722i	0.911137	+	0.412102i	$0.135205\pi$
$277$	13.5220	+	23.4208i	0.812460	+	1.40722i	−0.0986775	+	0.995119i	$0.531461\pi$
$278$		0			0
$279$	69.0197			4.13210
$280$		0			0
$281$	−19.6743			−1.17367			−0.586836	−	0.809706i	$-0.699627\pi$
$281$	−19.6743			−1.17367			−0.586836	+	0.809706i	$0.699627\pi$
$282$		0			0
$283$	7.94862	+	13.7674i	0.472496	+	0.818387i	0.999505	−	0.0314727i	$-0.0100197\pi$
$283$	7.94862	+	13.7674i	0.472496	+	0.818387i	−0.527008	+	0.849860i	$0.676686\pi$
$284$		0			0
$285$	6.45297	−	11.1769i	0.382241	−	0.662061i
$286$		0			0
$287$	7.15608	+	10.6138i	0.422410	+	0.626515i
$288$		0			0
$289$	8.12383	−	14.0709i	0.477873	−	0.827699i
$290$		0			0
$291$	−21.9769	−	38.0651i	−1.28831	−	2.23142i
$292$		0			0
$293$	−5.24265			−0.306279			−0.153139	−	0.988205i	$-0.548938\pi$
$293$	−5.24265			−0.306279			−0.153139	+	0.988205i	$0.548938\pi$
$294$		0			0
$295$	18.8784			1.09914
$296$		0			0
$297$	−8.34500	−	14.4540i	−0.484226	−	0.838704i
$298$		0			0
$299$	−4.34152	+	7.51974i	−0.251077	+	0.434878i
$300$		0			0
$301$	9.34847	+	13.8656i	0.538837	+	0.799198i
$302$		0			0
$303$	−18.9521	+	32.8260i	−1.08877	+	1.88580i
$304$		0			0
$305$	6.33986	+	10.9810i	0.363019	+	0.628768i
$306$		0			0
$307$	−14.0363			−0.801096			−0.400548	−	0.916276i	$-0.631180\pi$
$307$	−14.0363			−0.801096			−0.400548	+	0.916276i	$0.631180\pi$
$308$		0			0
$309$	−36.0245			−2.04936
$310$		0			0
$311$	−6.53225	−	11.3142i	−0.370410	−	0.641569i	0.619219	−	0.785219i	$-0.287449\pi$
$311$	−6.53225	−	11.3142i	−0.370410	−	0.641569i	−0.989629	+	0.143650i	$0.954116\pi$
$312$		0			0
$313$	−4.12804	+	7.14997i	−0.233330	+	0.404140i	−0.958786	−	0.284129i	$-0.908296\pi$
$313$	−4.12804	+	7.14997i	−0.233330	+	0.404140i	0.725456	+	0.688269i	$0.241629\pi$
$314$		0			0
$315$	15.8844	−	32.5515i	0.894982	−	1.83407i
$316$		0			0
$317$	5.52276	−	9.56570i	0.310189	−	0.537263i	−0.668214	−	0.743969i	$-0.732941\pi$
$317$	5.52276	−	9.56570i	0.310189	−	0.537263i	0.978403	+	0.206706i	$0.0662743\pi$
$318$		0			0
$319$	−4.67341	−	8.09458i	−0.261660	−	0.453209i
$320$		0			0
$321$	36.0340			2.01122
$322$		0			0
$323$	−1.97647			−0.109974
$324$		0			0
$325$	−3.47122	−	6.01234i	−0.192549	−	0.333504i
$326$		0			0
$327$	12.2141	−	21.1555i	0.675442	−	1.16990i
$328$		0			0
$329$	−6.35472	+	0.443109i	−0.350347	+	0.0244294i
$330$		0			0
$331$	12.9149	−	22.3693i	0.709869	−	1.22953i	−0.255036	−	0.966932i	$-0.582087\pi$
$331$	12.9149	−	22.3693i	0.709869	−	1.22953i	0.964905	−	0.262598i	$-0.0845793\pi$
$332$		0			0
$333$	29.7425	+	51.5155i	1.62988	+	2.82303i
$334$		0			0
$335$	−11.0566			−0.604085
$336$		0			0
$337$	−21.7425			−1.18439			−0.592194	−	0.805796i	$-0.701738\pi$
$337$	−21.7425			−1.18439			−0.592194	+	0.805796i	$0.701738\pi$
$338$		0			0
$339$	−24.8088	−	42.9701i	−1.34743	−	2.33381i
$340$		0			0
$341$	−4.29963	+	7.44718i	−0.232838	+	0.403287i
$342$		0			0
$343$	−18.1178	+	3.83989i	−0.978270	+	0.207335i
$344$		0			0
$345$	7.40515	−	12.8261i	0.398680	−	0.690534i
$346$		0			0
$347$	−0.639491	−	1.10763i	−0.0343297	−	0.0594607i	0.848350	−	0.529436i	$-0.177596\pi$
$347$	−0.639491	−	1.10763i	−0.0343297	−	0.0594607i	−0.882680	+	0.469975i	$0.844263\pi$
$348$		0			0
$349$	−26.6679			−1.42750			−0.713749	−	0.700402i	$-0.753004\pi$
$349$	−26.6679			−1.42750			−0.713749	+	0.700402i	$0.753004\pi$
$350$		0			0
$351$	−55.4204			−2.95812
$352$		0			0
$353$	3.19292	+	5.53031i	0.169942	+	0.294349i	0.938399	−	0.345553i	$-0.112309\pi$
$353$	3.19292	+	5.53031i	0.169942	+	0.294349i	−0.768457	+	0.639901i	$0.778975\pi$
$354$		0			0
$355$	0.739720	−	1.28123i	0.0392602	−	0.0680007i
$356$		0			0
$357$	−7.60177	+	0.530065i	−0.402328	+	0.0280540i
$358$		0			0
$359$	0.0925478	−	0.160297i	0.00488449	−	0.00846018i	−0.863573	−	0.504224i	$-0.831779\pi$
$359$	0.0925478	−	0.160297i	0.00488449	−	0.00846018i	0.868457	+	0.495764i	$0.165112\pi$
$360$		0			0
$361$	6.90380	+	11.9577i	0.363358	+	0.629354i
$362$		0			0
$363$	3.32058			0.174285
$364$		0			0
$365$	−23.2790			−1.21848
$366$		0			0
$367$	4.76264	+	8.24914i	0.248608	+	0.430601i	0.963140	−	0.269001i	$-0.0866936\pi$
$367$	4.76264	+	8.24914i	0.248608	+	0.430601i	−0.714532	+	0.699603i	$0.753360\pi$
$368$		0			0
$369$	−19.4166	+	33.6305i	−1.01079	+	1.75074i
$370$		0			0
$371$	9.26414	−	18.9848i	0.480970	−	0.985643i
$372$		0			0
$373$	−1.34114	+	2.32292i	−0.0694415	+	0.120276i	−0.898656	−	0.438655i	$-0.855455\pi$
$373$	−1.34114	+	2.32292i	−0.0694415	+	0.120276i	0.829214	+	0.558931i	$0.188788\pi$
$374$		0			0
$375$	20.0801	+	34.7798i	1.03693	+	1.79602i
$376$		0			0
$377$	−31.0368			−1.59848
$378$		0			0
$379$	1.02623			0.0527141			0.0263570	−	0.999653i	$-0.491609\pi$
$379$	1.02623			0.0527141			0.0263570	+	0.999653i	$0.491609\pi$
$380$		0			0
$381$	−7.97415	−	13.8116i	−0.408528	−	0.707591i
$382$		0			0
$383$	4.90144	−	8.48953i	0.250452	−	0.433795i	−0.713199	−	0.700962i	$-0.752754\pi$
$383$	4.90144	−	8.48953i	0.250452	−	0.433795i	0.963650	+	0.267167i	$0.0860876\pi$
$384$		0			0
$385$	2.52276	+	3.74173i	0.128572	+	0.190696i
$386$		0			0
$387$	−25.3652	+	43.9338i	−1.28939	+	2.23328i
$388$		0			0
$389$	−16.4847	−	28.5524i	−0.835809	−	1.44766i	−0.893370	−	0.449321i	$-0.851666\pi$
$389$	−16.4847	−	28.5524i	−0.835809	−	1.44766i	0.0575614	−	0.998342i	$-0.481668\pi$
$390$		0			0
$391$	−2.26811			−0.114703
$392$		0			0
$393$	−22.7942			−1.14981
$394$		0			0
$395$	8.08124	+	13.9971i	0.406611	+	0.704272i
$396$		0			0
$397$	−2.95811	+	5.12359i	−0.148463	+	0.257146i	−0.930660	−	0.365886i	$-0.880766\pi$
$397$	−2.95811	+	5.12359i	−0.148463	+	0.257146i	0.782196	+	0.623032i	$0.214099\pi$
$398$		0			0
$399$	−11.1913	−	16.5989i	−0.560268	−	0.830983i
$400$		0			0
$401$	7.35307	−	12.7359i	0.367195	−	0.636000i	−0.621931	−	0.783072i	$-0.713652\pi$
$401$	7.35307	−	12.7359i	0.367195	−	0.636000i	0.989126	+	0.147072i	$0.0469850\pi$
$402$		0			0
$403$	14.2773	+	24.7289i	0.711201	+	1.23184i
$404$		0			0
$405$	53.4582			2.65636
$406$		0			0
$407$	−7.41131			−0.367365
$408$		0			0
$409$	−5.06284	−	8.76909i	−0.250341	−	0.433604i	0.713279	−	0.700881i	$-0.247209\pi$
$409$	−5.06284	−	8.76909i	−0.250341	−	0.433604i	−0.963620	+	0.267277i	$0.913876\pi$
$410$		0			0
$411$	−18.1621	+	31.4577i	−0.895870	+	1.55169i
$412$		0			0
$413$	12.8422	−	26.3173i	0.631924	−	1.29499i
$414$		0			0
$415$	5.58086	−	9.66633i	0.273954	−	0.474501i
$416$		0			0
$417$	−16.3459	−	28.3120i	−0.800464	−	1.38644i
$418$		0			0
$419$	−33.1348			−1.61874			−0.809370	−	0.587299i	$-0.800191\pi$
$419$	−33.1348			−1.61874			−0.809370	+	0.587299i	$0.800191\pi$
$420$		0			0
$421$	−28.9851			−1.41265			−0.706324	−	0.707889i	$-0.749648\pi$
$421$	−28.9851			−1.41265			−0.706324	+	0.707889i	$0.749648\pi$
$422$		0			0
$423$	−9.66234	−	16.7357i	−0.469799	−	0.813716i
$424$		0			0
$425$	0.906723	−	1.57049i	0.0439825	−	0.0761800i
$426$		0			0
$427$	19.6207	−	1.36813i	0.949511	−	0.0662086i
$428$		0			0
$429$	5.51312	−	9.54900i	0.266176	−	0.461030i
$430$		0			0
$431$	−4.09564	−	7.09385i	−0.197280	−	0.341699i	0.750366	−	0.661023i	$-0.229877\pi$
$431$	−4.09564	−	7.09385i	−0.197280	−	0.341699i	−0.947646	+	0.319324i	$0.896544\pi$
$432$		0			0
$433$	−8.42837			−0.405041			−0.202521	−	0.979278i	$-0.564913\pi$
$433$	−8.42837			−0.405041			−0.202521	+	0.979278i	$0.564913\pi$
$434$		0			0
$435$	52.9381			2.53819
$436$		0			0
$437$	−2.97929	−	5.16028i	−0.142519	−	0.246850i
$438$		0			0
$439$	−11.7982	+	20.4351i	−0.563098	+	0.975314i	0.434126	+	0.900852i	$0.357057\pi$
$439$	−11.7982	+	20.4351i	−0.563098	+	0.975314i	−0.997224	+	0.0744616i	$0.976276\pi$
$440$		0			0
$441$	−34.5727	−	44.2869i	−1.64632	−	2.10890i
$442$		0			0
$443$	−15.7501	+	27.2799i	−0.748308	+	1.29611i	0.200325	+	0.979729i	$0.435800\pi$
$443$	−15.7501	+	27.2799i	−0.748308	+	1.29611i	−0.948633	+	0.316378i	$0.897533\pi$
$444$		0			0
$445$	−7.55991	−	13.0942i	−0.358374	−	0.620722i
$446$		0			0
$447$	−35.8948			−1.69777
$448$		0			0
$449$	19.7615			0.932601			0.466300	−	0.884626i	$-0.345587\pi$
$449$	19.7615			0.932601			0.466300	+	0.884626i	$0.345587\pi$
$450$		0			0
$451$	−2.41914	−	4.19008i	−0.113913	−	0.197303i
$452$		0			0
$453$	−4.44862	+	7.70523i	−0.209014	+	0.362023i
$454$		0			0
$455$	14.9486	−	1.04235i	0.700802	−	0.0488663i
$456$		0			0
$457$	3.95502	−	6.85029i	0.185008	−	0.320443i	−0.758571	−	0.651590i	$-0.774102\pi$
$457$	3.95502	−	6.85029i	0.185008	−	0.320443i	0.943579	+	0.331147i	$0.107436\pi$
$458$		0			0
$459$	−7.23822	−	12.5370i	−0.337851	−	0.585175i
$460$		0			0
$461$	27.4094			1.27658			0.638291	−	0.769795i	$-0.279642\pi$
$461$	27.4094			1.27658			0.638291	+	0.769795i	$0.279642\pi$
$462$		0			0
$463$	7.80224			0.362601			0.181301	−	0.983428i	$-0.441969\pi$
$463$	7.80224			0.362601			0.181301	+	0.983428i	$0.441969\pi$
$464$		0			0
$465$	−24.3521	−	42.1791i	−1.12930	−	1.95601i
$466$		0			0
$467$	−19.7486	+	34.2056i	−0.913858	+	1.58285i	−0.105293	+	0.994441i	$0.533578\pi$
$467$	−19.7486	+	34.2056i	−0.913858	+	1.58285i	−0.808565	+	0.588407i	$0.799755\pi$
$468$		0			0
$469$	−7.52133	+	15.4133i	−0.347303	+	0.711721i
$470$		0			0
$471$	33.7120	−	58.3909i	1.55337	−	2.69051i
$472$		0			0
$473$	−3.16029	−	5.47378i	−0.145310	−	0.251685i
$474$		0			0
$475$	4.76413			0.218593
$476$		0			0
$477$	64.0842			2.93421
$478$		0			0
$479$	1.40167	+	2.42777i	0.0640440	+	0.110928i	0.896270	−	0.443510i	$-0.146267\pi$
$479$	1.40167	+	2.42777i	0.0640440	+	0.110928i	−0.832226	+	0.554437i	$0.812934\pi$
$480$		0			0
$481$	−12.3049	+	21.3127i	−0.561056	+	0.971778i
$482$		0			0
$483$	−12.8427	−	19.0482i	−0.584363	−	0.866721i
$484$		0			0
$485$	−11.2887	+	19.5526i	−0.512594	+	0.887839i
$486$		0			0
$487$	−2.18290	−	3.78089i	−0.0989166	−	0.171329i	0.812320	−	0.583212i	$-0.198204\pi$
$487$	−2.18290	−	3.78089i	−0.0989166	−	0.171329i	−0.911236	+	0.411884i	$0.864871\pi$
$488$		0			0
$489$	77.1501			3.48885
$490$		0			0
$491$	28.8493			1.30195			0.650976	−	0.759098i	$-0.274360\pi$
$491$	28.8493			1.30195			0.650976	+	0.759098i	$0.274360\pi$
$492$		0			0
$493$	−4.05358	−	7.02101i	−0.182564	−	0.316210i
$494$		0			0
$495$	−6.84500	+	11.8559i	−0.307660	+	0.532882i
$496$		0			0
$497$	−1.28289	−	1.90277i	−0.0575455	−	0.0853509i
$498$		0			0
$499$	1.41945	−	2.45857i	0.0635435	−	0.110061i	−0.832503	−	0.554020i	$-0.813093\pi$
$499$	1.41945	−	2.45857i	0.0635435	−	0.110061i	0.896047	+	0.443959i	$0.146426\pi$
$500$		0			0
$501$	−16.0979	−	27.8824i	−0.719202	−	1.24569i
$502$		0			0
$503$	−22.1701			−0.988514			−0.494257	−	0.869316i	$-0.664560\pi$
$503$	−22.1701			−0.988514			−0.494257	+	0.869316i	$0.664560\pi$
$504$		0			0
$505$	19.4700			0.866402
$506$		0			0
$507$	3.27702	+	5.67597i	0.145538	+	0.252079i
$508$		0			0
$509$	−18.7224	+	32.4281i	−0.829856	+	1.43735i	0.0682954	+	0.997665i	$0.478244\pi$
$509$	−18.7224	+	32.4281i	−0.829856	+	1.43735i	−0.898151	+	0.439687i	$0.855089\pi$
$510$		0			0
$511$	−15.8357	+	32.4519i	−0.700532	+	1.43559i
$512$		0			0
$513$	19.0156	−	32.9360i	0.839560	−	1.45416i
$514$		0			0
$515$	9.25221	+	16.0253i	0.407701	+	0.706159i
$516$		0			0
$517$	2.40769			0.105890
$518$		0			0
$519$	−71.3992			−3.13408
$520$		0			0
$521$	7.13009	+	12.3497i	0.312375	+	0.541049i	0.978876	−	0.204455i	$-0.0655422\pi$
$521$	7.13009	+	12.3497i	0.312375	+	0.541049i	−0.666501	+	0.745504i	$0.732209\pi$
$522$		0			0
$523$	−2.73861	+	4.74340i	−0.119751	+	0.207415i	−0.919669	−	0.392695i	$-0.871543\pi$
$523$	−2.73861	+	4.74340i	−0.119751	+	0.207415i	0.799918	+	0.600109i	$0.204876\pi$
$524$		0			0
$525$	18.3235	−	1.27768i	0.799703	−	0.0557627i
$526$		0			0
$527$	−3.72938	+	6.45948i	−0.162454	+	0.281379i
$528$		0			0
$529$	8.08109	+	13.9969i	0.351352	+	0.608559i
$530$		0			0
$531$	88.8354			3.85513
$532$		0			0
$533$	−16.0659			−0.695891
$534$		0			0
$535$	−9.25465	−	16.0295i	−0.400113	−	0.693017i
$536$		0			0
$537$	4.10455	−	7.10929i	0.177124	−	0.306789i
$538$		0			0
$539$	6.93226	−	0.971485i	0.298594	−	0.0418448i
$540$		0			0
$541$	18.3025	−	31.7009i	0.786887	−	1.36293i	−0.140978	−	0.990013i	$-0.545025\pi$
$541$	18.3025	−	31.7009i	0.786887	−	1.36293i	0.927865	−	0.372916i	$-0.121642\pi$
$542$		0			0
$543$	−15.0182	−	26.0122i	−0.644491	−	1.11629i
$544$		0			0
$545$	−12.5479			−0.537491
$546$		0			0
$547$	−7.42983			−0.317676			−0.158838	−	0.987305i	$-0.550775\pi$
$547$	−7.42983			−0.317676			−0.158838	+	0.987305i	$0.550775\pi$
$548$		0			0
$549$	29.8332	+	51.6726i	1.27325	+	2.20533i
$550$		0			0
$551$	10.6492	−	18.4450i	0.453672	−	0.785783i
$552$		0			0
$553$	25.0099	−	1.74392i	1.06353	−	0.0741591i
$554$		0			0
$555$	20.9880	−	36.3522i	0.890890	−	1.54307i
$556$		0			0
$557$	−0.516593	−	0.894765i	−0.0218887	−	0.0379124i	0.854874	−	0.518836i	$-0.173635\pi$
$557$	−0.516593	−	0.894765i	−0.0218887	−	0.0379124i	−0.876762	+	0.480924i	$0.840301\pi$
$558$		0			0
$559$	−20.9880			−0.887696
$560$		0			0
$561$	2.88018			0.121601
$562$		0			0
$563$	5.01169	+	8.68050i	0.211218	+	0.365840i	0.952096	−	0.305800i	$-0.0989238\pi$
$563$	5.01169	+	8.68050i	0.211218	+	0.365840i	−0.740878	+	0.671639i	$0.765590\pi$
$564$		0			0
$565$	−12.7433	+	22.0721i	−0.536116	+	0.928581i
$566$		0			0
$567$	36.3655	−	74.5230i	1.52721	−	3.12967i
$568$		0			0
$569$	9.90672	−	17.1589i	0.415311	−	0.719341i	−0.580150	−	0.814510i	$-0.697006\pi$
$569$	9.90672	−	17.1589i	0.415311	−	0.719341i	0.995461	+	0.0951694i	$0.0303393\pi$
$570$		0			0
$571$	14.2443	+	24.6718i	0.596104	+	1.03248i	0.993390	+	0.114788i	$0.0366189\pi$
$571$	14.2443	+	24.6718i	0.596104	+	1.03248i	−0.397285	+	0.917695i	$0.630048\pi$
$572$		0			0
$573$	13.2398			0.553100
$574$		0			0
$575$	5.46711			0.227994
$576$		0			0
$577$	5.76919	+	9.99253i	0.240175	+	0.415995i	0.960764	−	0.277368i	$-0.0894620\pi$
$577$	5.76919	+	9.99253i	0.240175	+	0.415995i	−0.720589	+	0.693362i	$0.756129\pi$
$578$		0			0
$579$	22.4669	−	38.9138i	0.933691	−	1.61720i
$580$		0			0
$581$	−9.67884	−	14.3556i	−0.401546	−	0.595569i
$582$		0			0
$583$	−3.99217	+	6.91464i	−0.165339	+	0.286375i
$584$		0			0
$585$	22.7293	+	39.3684i	0.939743	+	1.62768i
$586$		0			0
$587$	−7.07537			−0.292032			−0.146016	−	0.989282i	$-0.546645\pi$
$587$	−7.07537			−0.292032			−0.146016	+	0.989282i	$0.546645\pi$
$588$		0			0
$589$	−19.5950			−0.807398
$590$		0			0
$591$	10.7189	+	18.5657i	0.440918	+	0.763692i
$592$		0			0
$593$	−9.25489	+	16.0299i	−0.380053	+	0.658270i	−0.991069	−	0.133347i	$-0.957427\pi$
$593$	−9.25489	+	16.0299i	−0.380053	+	0.658270i	0.611017	+	0.791618i	$0.290761\pi$
$594$		0			0
$595$	2.18817	+	3.24547i	0.0897062	+	0.133051i
$596$		0			0
$597$	8.37780	−	14.5108i	0.342881	−	0.593886i
$598$		0			0
$599$	7.57808	+	13.1256i	0.309632	+	0.536298i	0.978282	−	0.207279i	$-0.0664608\pi$
$599$	7.57808	+	13.1256i	0.309632	+	0.536298i	−0.668650	+	0.743577i	$0.733127\pi$
$600$		0			0
$601$	12.7540			0.520248			0.260124	−	0.965575i	$-0.416237\pi$
$601$	12.7540			0.520248			0.260124	+	0.965575i	$0.416237\pi$
$602$		0			0
$603$	−52.0284			−2.11876
$604$		0			0
$605$	−0.852828	−	1.47714i	−0.0346724	−	0.0600544i
$606$		0			0
$607$	14.8894	−	25.7892i	0.604342	−	1.04675i	−0.387813	−	0.921738i	$-0.626769\pi$
$607$	14.8894	−	25.7892i	0.604342	−	1.04675i	0.992155	−	0.125013i	$-0.0398973\pi$
$608$		0			0
$609$	36.0117	−	73.7980i	1.45927	−	2.99045i
$610$		0			0
$611$	3.99746	−	6.92380i	0.161720	−	0.280107i
$612$		0			0
$613$	2.63753	+	4.56834i	0.106529	+	0.184513i	0.914362	−	0.404898i	$-0.132693\pi$
$613$	2.63753	+	4.56834i	0.106529	+	0.184513i	−0.807833	+	0.589412i	$0.799360\pi$
$614$		0			0
$615$	27.4029			1.10499
$616$		0			0
$617$	25.8411			1.04033			0.520163	−	0.854067i	$-0.325871\pi$
$617$	25.8411			1.04033			0.520163	+	0.854067i	$0.325871\pi$
$618$		0			0
$619$	−2.11335	−	3.66042i	−0.0849425	−	0.147125i	0.820424	−	0.571755i	$-0.193737\pi$
$619$	−2.11335	−	3.66042i	−0.0849425	−	0.147125i	−0.905367	+	0.424631i	$0.860404\pi$
$620$		0			0
$621$	21.8215	−	37.7960i	0.875667	−	1.51670i
$622$		0			0
$623$	−23.3965	+	1.63142i	−0.937361	+	0.0653614i
$624$		0			0
$625$	5.08757	−	8.81193i	0.203503	−	0.352477i
$626$		0			0
$627$	3.78328	+	6.55283i	0.151089	+	0.261695i
$628$		0			0
$629$	−6.42837			−0.256316
$630$		0			0
$631$	20.8779			0.831138			0.415569	−	0.909562i	$-0.363582\pi$
$631$	20.8779			0.831138			0.415569	+	0.909562i	$0.363582\pi$
$632$		0			0
$633$	3.62187	+	6.27327i	0.143957	+	0.249340i
$634$		0			0
$635$	−4.09602	+	7.09452i	−0.162546	+	0.281537i
$636$		0			0
$637$	8.71585	−	21.5481i	0.345334	−	0.853766i
$638$		0			0
$639$	3.48087	−	6.02904i	0.137701	−	0.238505i
$640$		0			0
$641$	21.2238	+	36.7607i	0.838291	+	1.45196i	0.891323	+	0.453369i	$0.149778\pi$
$641$	21.2238	+	36.7607i	0.838291	+	1.45196i	−0.0530321	+	0.998593i	$0.516889\pi$
$642$		0			0
$643$	35.7064			1.40812			0.704062	−	0.710139i	$-0.251368\pi$
$643$	35.7064			1.40812			0.704062	+	0.710139i	$0.251368\pi$
$644$		0			0
$645$	35.7983			1.40956
$646$		0			0
$647$	1.15524	+	2.00093i	0.0454171	+	0.0786647i	0.887840	−	0.460152i	$-0.152205\pi$
$647$	1.15524	+	2.00093i	0.0454171	+	0.0786647i	−0.842423	+	0.538816i	$0.818872\pi$
$648$		0			0
$649$	−5.53406	+	9.58528i	−0.217231	+	0.376255i
$650$		0			0
$651$	−75.3652	+	5.25515i	−2.95379	+	0.205966i
$652$		0			0
$653$	−1.59699	+	2.76607i	−0.0624950	+	0.108245i	−0.895580	−	0.444900i	$-0.853239\pi$
$653$	−1.59699	+	2.76607i	−0.0624950	+	0.108245i	0.833085	+	0.553145i	$0.186572\pi$
$654$		0			0
$655$	5.85426	+	10.1399i	0.228745	+	0.396197i
$656$		0			0
$657$	−109.543			−4.27368
$658$		0			0
$659$	−7.94970			−0.309676			−0.154838	−	0.987940i	$-0.549486\pi$
$659$	−7.94970			−0.309676			−0.154838	+	0.987940i	$0.549486\pi$
$660$		0			0
$661$	8.53950	+	14.7908i	0.332148	+	0.575297i	0.982933	−	0.183965i	$-0.0588933\pi$
$661$	8.53950	+	14.7908i	0.332148	+	0.575297i	−0.650785	+	0.759262i	$0.725560\pi$
$662$		0			0
$663$	4.78192	−	8.28254i	0.185715	−	0.321667i
$664$		0			0
$665$	−4.50964	+	9.24152i	−0.174876	+	0.358371i
$666$		0			0
$667$	12.2206	−	21.1667i	0.473183	−	0.819577i
$668$		0			0
$669$	−15.7433	−	27.2683i	−0.608673	−	1.05425i
$670$		0			0
$671$	−7.43392			−0.286983
$672$		0			0
$673$	−43.7770			−1.68748			−0.843741	−	0.536751i	$-0.819651\pi$
$673$	−43.7770			−1.68748			−0.843741	+	0.536751i	$0.819651\pi$
$674$		0			0
$675$	17.4472	+	30.2194i	0.671543	+	1.16315i
$676$		0			0
$677$	−2.37281	+	4.10982i	−0.0911944	+	0.157953i	−0.908014	−	0.418940i	$-0.862402\pi$
$677$	−2.37281	+	4.10982i	−0.0911944	+	0.157953i	0.816820	+	0.576893i	$0.195735\pi$
$678$		0			0
$679$	19.5779	+	29.0378i	0.751332	+	1.11437i
$680$		0			0
$681$	−43.7433	+	75.7656i	−1.67625	+	2.90335i
$682$		0			0
$683$	−23.7907	−	41.2067i	−0.910325	−	1.57673i	−0.813605	−	0.581418i	$-0.802498\pi$
$683$	−23.7907	−	41.2067i	−0.910325	−	1.57673i	−0.0967205	−	0.995312i	$-0.530835\pi$
$684$		0			0
$685$	18.6584			0.712900
$686$		0			0
$687$	−47.3504			−1.80653
$688$		0			0
$689$	13.2563	+	22.9606i	0.505025	+	0.874729i
$690$		0			0
$691$	−16.7829	+	29.0688i	−0.638450	+	1.10583i	0.347323	+	0.937746i	$0.387091\pi$
$691$	−16.7829	+	29.0688i	−0.638450	+	1.10583i	−0.985773	+	0.168082i	$0.946243\pi$
$692$		0			0
$693$	11.8712	+	17.6073i	0.450951	+	0.668846i
$694$		0			0
$695$	−8.39630	+	14.5428i	−0.318490	+	0.551640i
$696$		0			0
$697$	−2.09830	−	3.63436i	−0.0794787	−	0.137661i
$698$		0			0
$699$	−45.6739			−1.72754
$700$		0			0
$701$	−1.34967			−0.0509761			−0.0254881	−	0.999675i	$-0.508114\pi$
$701$	−1.34967			−0.0509761			−0.0254881	+	0.999675i	$0.508114\pi$
$702$		0			0
$703$	−8.44403	−	14.6255i	−0.318472	−	0.551610i
$704$		0			0
$705$	−6.81829	+	11.8096i	−0.256792	+	0.444776i
$706$		0			0
$707$	13.2446	−	27.1420i	0.498115	−	1.02078i
$708$		0			0
$709$	22.5336	−	39.0293i	0.846266	−	1.46578i	−0.0382512	−	0.999268i	$-0.512179\pi$
$709$	22.5336	−	39.0293i	0.846266	−	1.46578i	0.884517	−	0.466508i	$-0.154488\pi$
$710$		0			0
$711$	38.0276	+	65.8657i	1.42614	+	2.47016i
$712$		0			0
$713$	−22.4864			−0.842122
$714$		0			0
$715$	−5.66376			−0.211813
$716$		0			0
$717$	−11.4986	−	19.9162i	−0.429425	−	0.743786i
$718$		0			0
$719$	−4.62661	+	8.01352i	−0.172543	+	0.298854i	−0.939308	−	0.343074i	$-0.888532\pi$
$719$	−4.62661	+	8.01352i	−0.172543	+	0.298854i	0.766765	+	0.641928i	$0.221865\pi$
$720$		0			0
$721$	28.6339	−	1.99662i	1.06638	−	0.0743579i
$722$		0			0
$723$	−35.0167	+	60.6507i	−1.30229	+	2.25562i
$724$		0			0
$725$	9.77086	+	16.9236i	0.362880	+	0.628527i
$726$		0			0
$727$	25.1437			0.932527			0.466264	−	0.884646i	$-0.345600\pi$
$727$	25.1437			0.932527			0.466264	+	0.884646i	$0.345600\pi$
$728$		0			0
$729$	85.2948			3.15906
$730$		0			0
$731$	−2.74115	−	4.74780i	−0.101385	−	0.175604i
$732$		0			0
$733$	−16.3874	+	28.3839i	−0.605284	+	1.04838i	0.386723	+	0.922196i	$0.373607\pi$
$733$	−16.3874	+	28.3839i	−0.605284	+	1.04838i	−0.992007	+	0.126186i	$0.959726\pi$
$734$		0			0
$735$	−14.8662	+	36.7536i	−0.548350	+	1.35568i
$736$		0			0
$737$	3.24115	−	5.61383i	0.119389	−	0.206788i
$738$		0			0
$739$	−26.1680	−	45.3243i	−0.962606	−	1.66728i	−0.715914	−	0.698188i	$-0.753990\pi$
$739$	−26.1680	−	45.3243i	−0.962606	−	1.66728i	−0.246691	−	0.969094i	$-0.579343\pi$
$740$		0			0
$741$	25.1253			0.923002
$742$		0			0
$743$	−37.0985			−1.36101			−0.680505	−	0.732743i	$-0.738240\pi$
$743$	−37.0985			−1.36101			−0.680505	+	0.732743i	$0.738240\pi$
$744$		0			0
$745$	9.21892	+	15.9676i	0.337755	+	0.585009i
$746$		0			0
$747$	26.2616	−	45.4864i	0.960862	−	1.66426i
$748$		0			0
$749$	−28.6414	+	1.99714i	−1.04653	+	0.0729739i
$750$		0			0
$751$	25.6110	−	44.3595i	0.934557	−	1.61870i	0.159135	−	0.987257i	$-0.449130\pi$
$751$	25.6110	−	44.3595i	0.934557	−	1.61870i	0.775422	−	0.631443i	$-0.217537\pi$
$752$		0			0
$753$	−1.65427	−	2.86528i	−0.0602850	−	0.104417i
$754$		0			0
$755$	4.57017			0.166326
$756$		0			0
$757$	−27.1299			−0.986054			−0.493027	−	0.870014i	$-0.664110\pi$
$757$	−27.1299			−0.986054			−0.493027	+	0.870014i	$0.664110\pi$
$758$		0			0
$759$	4.34152	+	7.51974i	0.157587	+	0.272949i
$760$		0			0
$761$	13.0011	−	22.5185i	0.471289	−	0.816296i	−0.528172	−	0.849138i	$-0.677122\pi$
$761$	13.0011	−	22.5185i	0.471289	−	0.816296i	0.999461	+	0.0328413i	$0.0104556\pi$
$762$		0			0
$763$	−8.53580	+	17.4922i	−0.309017	+	0.633262i
$764$		0			0
$765$	−5.93716	+	10.2835i	−0.214659	+	0.371800i
$766$		0			0
$767$	18.3763	+	31.8287i	0.663529	+	1.14927i
$768$		0			0
$769$	31.0365			1.11921			0.559603	−	0.828761i	$-0.310954\pi$
$769$	31.0365			1.11921			0.559603	+	0.828761i	$0.310954\pi$
$770$		0			0
$771$	−81.4806			−2.93445
$772$		0			0
$773$	−10.5769	−	18.3197i	−0.380424	−	0.658914i	0.610699	−	0.791863i	$-0.290889\pi$
$773$	−10.5769	−	18.3197i	−0.380424	−	0.658914i	−0.991123	+	0.132949i	$0.957555\pi$
$774$		0			0
$775$	8.98939	−	15.5701i	0.322909	−	0.559294i
$776$		0			0
$777$	−36.3993	−	53.9870i	−1.30582	−	1.93677i
$778$		0			0
$779$	5.51246	−	9.54787i	0.197505	−	0.342088i
$780$		0			0
$781$	0.433686	+	0.751166i	0.0155185	+	0.0268788i
$782$		0			0
$783$	155.998			5.57492
$784$		0			0
$785$	−34.6332			−1.23611
$786$		0			0
$787$	19.3809	+	33.5687i	0.690854	+	1.19659i	0.971559	+	0.236799i	$0.0760984\pi$
$787$	19.3809	+	33.5687i	0.690854	+	1.19659i	−0.280705	+	0.959794i	$0.590568\pi$
$788$		0			0
$789$	24.6159	−	42.6359i	0.876348	−	1.51788i
$790$		0			0
$791$	22.1007	+	32.7795i	0.785810	+	1.16551i
$792$		0			0
$793$	−12.3425	+	21.3778i	−0.438294	+	0.759147i
$794$		0			0
$795$	−22.6107	−	39.1629i	−0.801919	−	1.38897i
$796$		0			0
$797$	−22.9384			−0.812518			−0.406259	−	0.913758i	$-0.633167\pi$
$797$	−22.9384			−0.812518			−0.406259	+	0.913758i	$0.633167\pi$
$798$		0			0
$799$	2.08836			0.0738810
$800$		0			0
$801$	−35.5743	−	61.6166i	−1.25696	−	2.17711i
$802$		0			0
$803$	6.82405	−	11.8196i	0.240816	−	0.417105i
$804$		0			0
$805$	−5.17507	+	10.6052i	−0.182397	+	0.373783i
$806$		0			0
$807$	13.2128	−	22.8852i	0.465111	−	0.805596i
$808$		0			0
$809$	−26.1496	−	45.2924i	−0.919371	−	1.59240i	−0.800372	−	0.599503i	$-0.795365\pi$
$809$	−26.1496	−	45.2924i	−0.919371	−	1.59240i	−0.118999	−	0.992894i	$-0.537968\pi$
$810$		0			0
$811$	−10.5808			−0.371540			−0.185770	−	0.982593i	$-0.559478\pi$
$811$	−10.5808			−0.371540			−0.185770	+	0.982593i	$0.559478\pi$
$812$		0			0
$813$	−51.8337			−1.81789
$814$		0			0
$815$	−19.8146	−	34.3198i	−0.694074	−	1.20217i
$816$		0			0
$817$	7.20130	−	12.4730i	0.251942	−	0.436376i
$818$		0			0
$819$	70.3430	−	4.90496i	2.45799	−	0.171393i
$820$		0			0
$821$	−6.27907	+	10.8757i	−0.219141	+	0.379563i	−0.954546	−	0.298065i	$-0.903659\pi$
$821$	−6.27907	+	10.8757i	−0.219141	+	0.379563i	0.735405	+	0.677628i	$0.236992\pi$
$822$		0			0
$823$	5.11531	+	8.85997i	0.178308	+	0.308839i	0.941301	−	0.337568i	$-0.109604\pi$
$823$	5.11531	+	8.85997i	0.178308	+	0.308839i	−0.762993	+	0.646407i	$0.776271\pi$
$824$		0			0
$825$	−6.94245			−0.241705
$826$		0			0
$827$	−38.3160			−1.33238			−0.666188	−	0.745784i	$-0.732075\pi$
$827$	−38.3160			−1.33238			−0.666188	+	0.745784i	$0.732075\pi$
$828$		0			0
$829$	0.762405	+	1.32052i	0.0264794	+	0.0458637i	0.878961	−	0.476893i	$-0.158237\pi$
$829$	0.762405	+	1.32052i	0.0264794	+	0.0458637i	−0.852482	+	0.522757i	$0.824904\pi$
$830$		0			0
$831$	44.9009	−	77.7707i	1.55760	−	2.69784i
$832$		0			0
$833$	6.01285	−	0.842639i	0.208333	−	0.0291957i
$834$		0			0
$835$	−8.26890	+	14.3221i	−0.286157	+	0.495638i
$836$		0			0
$837$	−71.7608	−	124.293i	−2.48042	−	4.29621i
$838$		0			0
$839$	2.04204			0.0704992			0.0352496	−	0.999379i	$-0.488777\pi$
$839$	2.04204			0.0704992			0.0352496	+	0.999379i	$0.488777\pi$
$840$		0			0
$841$	58.3629			2.01251
$842$		0			0
$843$	32.6651	+	56.5776i	1.12505	+	1.94864i
$844$		0			0
$845$	1.68328	−	2.91553i	0.0579067	−	0.100297i
$846$		0			0
$847$	−2.63934	+	0.184039i	−0.0906889	+	0.00632366i
$848$		0			0
$849$	26.3940	−	45.7157i	0.905839	−	1.56896i
$850$		0			0
$851$	−9.69000	−	16.7836i	−0.332169	−	0.575333i
$852$		0			0
$853$	15.1192			0.517671			0.258836	−	0.965921i	$-0.416661\pi$
$853$	15.1192			0.517671			0.258836	+	0.965921i	$0.416661\pi$
$854$		0			0
$855$	−31.1952			−1.06685
$856$		0			0
$857$	14.2820	+	24.7371i	0.487864	+	0.845005i	0.999903	−	0.0139575i	$-0.00444297\pi$
$857$	14.2820	+	24.7371i	0.487864	+	0.845005i	−0.512039	+	0.858962i	$0.671110\pi$
$858$		0			0
$859$	−16.8519	+	29.1883i	−0.574978	+	0.995891i	0.421066	+	0.907030i	$0.361656\pi$
$859$	−16.8519	+	29.1883i	−0.574978	+	0.995891i	−0.996044	+	0.0888613i	$0.971677\pi$
$860$		0			0
$861$	18.6411	−	38.2008i	0.635286	−	1.30188i
$862$		0			0
$863$	10.7464	−	18.6134i	0.365813	−	0.633606i	−0.623093	−	0.782147i	$-0.714124\pi$
$863$	10.7464	−	18.6134i	0.365813	−	0.633606i	0.988906	+	0.148541i	$0.0474577\pi$
$864$		0			0
$865$	18.3376	+	31.7616i	0.623496	+	1.07993i
$866$		0			0
$867$	−53.9516			−1.83229
$868$		0			0
$869$	−9.47581			−0.321445
$870$		0			0
$871$	−10.7625	−	18.6412i	−0.364673	−	0.631632i
$872$		0			0
$873$	−53.1208	+	92.0079i	−1.79787	+	3.11400i
$874$		0			0
$875$	−17.8882	−	26.5316i	−0.604732	−	0.896932i
$876$		0			0
$877$	−2.06520	+	3.57703i	−0.0697368	+	0.120788i	−0.898785	−	0.438389i	$-0.855549\pi$
$877$	−2.06520	+	3.57703i	−0.0697368	+	0.120788i	0.829049	+	0.559177i	$0.188883\pi$
$878$		0			0
$879$	8.70431	+	15.0763i	0.293589	+	0.508511i
$880$		0			0
$881$	−25.0692			−0.844604			−0.422302	−	0.906455i	$-0.638778\pi$
$881$	−25.0692			−0.844604			−0.422302	+	0.906455i	$0.638778\pi$
$882$		0			0
$883$	−25.6579			−0.863457			−0.431729	−	0.902003i	$-0.642096\pi$
$883$	−25.6579			−0.863457			−0.431729	+	0.902003i	$0.642096\pi$
$884$		0			0
$885$	−31.3436	−	54.2888i	−1.05360	−	1.82490i
$886$		0			0
$887$	−1.18892	+	2.05926i	−0.0399199	+	0.0691433i	−0.885295	−	0.465030i	$-0.846044\pi$
$887$	−1.18892	+	2.05926i	−0.0399199	+	0.0691433i	0.845375	+	0.534173i	$0.179377\pi$
$888$		0			0
$889$	7.10370	+	10.5361i	0.238251	+	0.353371i
$890$		0			0
$891$	−15.6709	+	27.1427i	−0.524994	+	0.909316i
$892$		0			0
$893$	2.74318	+	4.75133i	0.0917971	+	0.158997i
$894$		0			0
$895$	−4.21671			−0.140949
$896$		0			0
$897$	28.8327			0.962697
$898$		0			0
$899$	−40.1878	−	69.6074i	−1.34034	−	2.32154i
$900$		0			0
$901$	−3.46270	+	5.99757i	−0.115359	+	0.199808i
$902$		0			0
$903$	24.3521	−	49.9043i	0.810387	−	1.66071i
$904$		0			0
$905$	−7.71427	+	13.3615i	−0.256431	+	0.444152i
$906$		0			0
$907$	7.91058	+	13.7015i	0.262667	+	0.454952i	0.966950	−	0.254967i	$-0.0820647\pi$
$907$	7.91058	+	13.7015i	0.262667	+	0.454952i	−0.704283	+	0.709919i	$0.748731\pi$
$908$		0			0
$909$	91.6190			3.03881
$910$		0			0
$911$	32.4388			1.07475			0.537373	−	0.843345i	$-0.319417\pi$
$911$	32.4388			1.07475			0.537373	+	0.843345i	$0.319417\pi$
$912$		0			0
$913$	3.27197	+	5.66722i	0.108286	+	0.187558i
$914$		0			0
$915$	21.0520	−	36.4631i	0.695957	−	1.20543i
$916$		0			0
$917$	18.1178	−	1.26334i	0.598303	−	0.0417192i
$918$		0			0
$919$	−29.2957	+	50.7416i	−0.966375	+	1.67381i	−0.260500	+	0.965474i	$0.583887\pi$
$919$	−29.2957	+	50.7416i	−0.966375	+	1.67381i	−0.705875	+	0.708336i	$0.749446\pi$
$920$		0			0
$921$	23.3044	+	40.3644i	0.767905	+	1.33005i
$922$		0			0
$923$	2.88018			0.0948022
$924$		0			0
$925$	15.4951			0.509476
$926$		0			0
$927$	43.5377	+	75.4096i	1.42997	+	2.47678i
$928$		0			0
$929$	−11.9683	+	20.7297i	−0.392667	+	0.680119i	−0.992800	−	0.119781i	$-0.961781\pi$
$929$	−11.9683	+	20.7297i	−0.392667	+	0.680119i	0.600133	+	0.799900i	$0.295114\pi$
$930$		0			0
$931$	9.81535	+	12.5733i	0.321685	+	0.412072i
$932$		0			0
$933$	−21.6908	+	37.5696i	−0.710126	+	1.22997i
$934$		0			0
$935$	−0.739720	−	1.28123i	−0.0241914	−	0.0419008i
$936$		0			0
$937$	−22.3735			−0.730911			−0.365455	−	0.930829i	$-0.619087\pi$
$937$	−22.3735			−0.730911			−0.365455	+	0.930829i	$0.619087\pi$
$938$		0			0
$939$	27.4149			0.894653
$940$		0			0
$941$	−0.368723	−	0.638647i	−0.0120200	−	0.0208193i	0.859953	−	0.510374i	$-0.170493\pi$
$941$	−0.368723	−	0.638647i	−0.0120200	−	0.0208193i	−0.871973	+	0.489554i	$0.837160\pi$
$942$		0			0
$943$	6.32587	−	10.9567i	0.205999	−	0.356800i
$944$		0			0
$945$	−75.1352	+	5.23912i	−2.44415	+	0.170429i
$946$		0			0
$947$	−1.99526	+	3.45589i	−0.0648373	+	0.112301i	−0.896622	−	0.442797i	$-0.853986\pi$
$947$	−1.99526	+	3.45589i	−0.0648373	+	0.112301i	0.831785	+	0.555099i	$0.187320\pi$
$948$		0			0
$949$	−22.6598	−	39.2479i	−0.735568	−	1.27404i
$950$		0			0
$951$	−36.6775			−1.18935
$952$		0			0
$953$	3.16504			0.102526			0.0512629	−	0.998685i	$-0.483675\pi$
$953$	3.16504			0.102526			0.0512629	+	0.998685i	$0.483675\pi$
$954$		0			0
$955$	−3.40039	−	5.88965i	−0.110034	−	0.190585i
$956$		0			0
$957$	−15.5184	+	26.8787i	−0.501639	+	0.868864i
$958$		0			0
$959$	12.6925	−	26.0106i	0.409863	−	0.839925i
$960$		0			0
$961$	−21.4737	+	37.1935i	−0.692699	+	1.19979i
$962$		0			0
$963$	−43.5492	−	75.4294i	−1.40335	−	2.43068i
$964$		0			0
$965$	−23.0808			−0.742997
$966$		0			0
$967$	−42.3673			−1.36244			−0.681221	−	0.732078i	$-0.738551\pi$
$967$	−42.3673			−1.36244			−0.681221	+	0.732078i	$0.738551\pi$
$968$		0			0
$969$	3.28151	+	5.68374i	0.105417	+	0.182588i
$970$		0			0
$971$	−2.01385	+	3.48808i	−0.0646274	+	0.111938i	−0.896529	−	0.442986i	$-0.853919\pi$
$971$	−2.01385	+	3.48808i	−0.0646274	+	0.111938i	0.831901	+	0.554924i	$0.187253\pi$
$972$		0			0
$973$	14.5616	+	21.5977i	0.466825	+	0.692390i
$974$		0			0
$975$	−11.5265	+	19.9644i	−0.369142	+	0.639374i
$976$		0			0
$977$	20.3990	+	35.3320i	0.652621	+	1.13037i	0.982485	+	0.186344i	$0.0596638\pi$
$977$	20.3990	+	35.3320i	0.652621	+	1.13037i	−0.329864	+	0.944029i	$0.607003\pi$
$978$		0			0
$979$	8.86452			0.283311
$980$		0			0
$981$	−59.0459			−1.88519
$982$		0			0
$983$	−14.5104	−	25.1328i	−0.462811	−	0.801612i	0.536289	−	0.844034i	$-0.319826\pi$
$983$	−14.5104	−	25.1328i	−0.462811	−	0.801612i	−0.999100	+	0.0424227i	$0.986492\pi$
$984$		0			0
$985$	5.50591	−	9.53652i	0.175433	−	0.303859i
$986$		0			0
$987$	11.8249	+	17.5386i	0.376391	+	0.558260i
$988$		0			0
$989$	8.26390	−	14.3135i	0.262777	−	0.455143i
$990$		0			0
$991$	−15.3015	−	26.5030i	−0.486069	−	0.841897i	0.513803	−	0.857908i	$-0.328236\pi$
$991$	−15.3015	−	26.5030i	−0.486069	−	0.841897i	−0.999872	+	0.0160119i	$0.994903\pi$
$992$		0			0
$993$	−85.7701			−2.72183
$994$		0			0
$995$	−8.60673			−0.272852
$996$		0			0
$997$	−22.0056	−	38.1148i	−0.696924	−	1.20711i	−0.969528	−	0.244982i	$-0.921218\pi$
$997$	−22.0056	−	38.1148i	−0.696924	−	1.20711i	0.272603	−	0.962127i	$-0.412115\pi$
$998$		0			0
$999$	61.8474	−	107.123i	1.95677	−	3.38922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.n.177.1		8
4.3	odd	2		616.2.q.d.177.4	✓	8
7.2	even	3		8624.2.a.cz.1.4		4
7.4	even	3	inner	1232.2.q.n.529.1		8
7.5	odd	6		8624.2.a.cr.1.1		4
28.11	odd	6		616.2.q.d.529.4	yes	8
28.19	even	6		4312.2.a.bd.1.4		4
28.23	odd	6		4312.2.a.y.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.d.177.4	✓	8	4.3	odd	2
616.2.q.d.529.4	yes	8	28.11	odd	6
1232.2.q.n.177.1		8	1.1	even	1	trivial
1232.2.q.n.529.1		8	7.4	even	3	inner
4312.2.a.y.1.1		4	28.23	odd	6
4312.2.a.bd.1.4		4	28.19	even	6
8624.2.a.cr.1.1		4	7.5	odd	6
8624.2.a.cz.1.4		4	7.2	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.66029 - 2.87570i) q^{3} +(-0.852828 + 1.47714i) q^{5} +(1.47905 + 2.19372i) q^{7} +(-4.01312 + 6.95092i) q^{9} +O(q^{10})\)	\(q+(-1.66029 - 2.87570i) q^{3} +(-0.852828 + 1.47714i) q^{5} +(1.47905 + 2.19372i) q^{7} +(-4.01312 + 6.95092i) q^{9} +(-0.500000 - 0.866025i) q^{11} -3.32058 q^{13} +5.66376 q^{15} +(-0.433686 - 0.751166i) q^{17} +(1.13934 - 1.97340i) q^{19} +(3.85283 - 7.89553i) q^{21} +(1.30746 - 2.26459i) q^{23} +(1.04537 + 1.81063i) q^{25} +16.6900 q^{27} +9.34681 q^{29} +(-4.29963 - 7.44718i) q^{31} +(-1.66029 + 2.87570i) q^{33} +(-4.50181 + 0.313908i) q^{35} +(3.70566 - 6.41839i) q^{37} +(5.51312 + 9.54900i) q^{39} +4.83828 q^{41} +6.32058 q^{43} +(-6.84500 - 11.8559i) q^{45} +(-1.20384 + 2.08512i) q^{47} +(-2.62480 + 6.48926i) q^{49} +(-1.44009 + 2.49431i) q^{51} +(-3.99217 - 6.91464i) q^{53} +1.70566 q^{55} -7.56655 q^{57} +(-5.53406 - 9.58528i) q^{59} +(3.71696 - 6.43797i) q^{61} +(-21.1840 + 1.47714i) q^{63} +(2.83188 - 4.90496i) q^{65} +(3.24115 + 5.61383i) q^{67} -8.68305 q^{69} -0.867372 q^{71} +(6.82405 + 11.8196i) q^{73} +(3.47122 - 6.01234i) q^{75} +(1.16029 - 2.37776i) q^{77} +(4.73791 - 8.20630i) q^{79} +(-15.6709 - 27.1427i) q^{81} -6.54394 q^{83} +1.47944 q^{85} +(-15.5184 - 26.8787i) q^{87} +(-4.43226 + 7.67690i) q^{89} +(-4.91131 - 7.28441i) q^{91} +(-14.2773 + 24.7289i) q^{93} +(1.94333 + 3.36594i) q^{95} +13.2368 q^{97} +8.02623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9	\( 8 q - 2 q^{3} + 4 q^{5} + q^{7} - 10 q^{9} - 4 q^{11} - 4 q^{13} + 2 q^{15} - 3 q^{17} - 13 q^{19} + 20 q^{21} + 10 q^{23} - 2 q^{25} + 46 q^{27} + 8 q^{29} - q^{31} - 2 q^{33} - 13 q^{35} + 8 q^{37} + 22 q^{39} + 18 q^{41} + 28 q^{43} - 11 q^{45} - 11 q^{47} + 11 q^{49} - 12 q^{51} + q^{53} - 8 q^{55} - 20 q^{57} - 33 q^{59} + 9 q^{61} - 26 q^{63} + q^{65} + 25 q^{67} - 46 q^{69} - 6 q^{71} - 16 q^{75} - 2 q^{77} + 28 q^{79} - 4 q^{81} - 10 q^{83} - 54 q^{85} - 47 q^{87} - 3 q^{89} + 4 q^{91} - 38 q^{93} + 25 q^{95} + 40 q^{97} + 20 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^5 + q^7 - 10 * q^9 - 4 * q^11 - 4 * q^13 + 2 * q^15 - 3 * q^17 - 13 * q^19 + 20 * q^21 + 10 * q^23 - 2 * q^25 + 46 * q^27 + 8 * q^29 - q^31 - 2 * q^33 - 13 * q^35 + 8 * q^37 + 22 * q^39 + 18 * q^41 + 28 * q^43 - 11 * q^45 - 11 * q^47 + 11 * q^49 - 12 * q^51 + q^53 - 8 * q^55 - 20 * q^57 - 33 * q^59 + 9 * q^61 - 26 * q^63 + q^65 + 25 * q^67 - 46 * q^69 - 6 * q^71 - 16 * q^75 - 2 * q^77 + 28 * q^79 - 4 * q^81 - 10 * q^83 - 54 * q^85 - 47 * q^87 - 3 * q^89 + 4 * q^91 - 38 * q^93 + 25 * q^95 + 40 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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