LMFDB - Embedded newform 1232.2.q.o.529.5

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.939795628203.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - 9x^{7} + 10x^{6} - 26x^{5} + 87x^{4} - 48x^{3} - 65x^{2} + 30x + 36 $ x^10 - x^9 + x^8 - 9x^7 + 10x^6 - 26x^5 + 87x^4 - 48x^3 - 65x^2 + 30*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 616)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.5
Root			$-1.60312 + 1.57192i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.o.177.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02046 - 1.76748i) q^{3} +(-2.10312 - 3.64271i) q^{5} +(-1.47127 - 2.19895i) q^{7} +(-0.582662 - 1.00920i) q^{9} +O(q^{10})$	\(q+(1.02046 - 1.76748i) q^{3} +(-2.10312 - 3.64271i) q^{5} +(-1.47127 - 2.19895i) q^{7} +(-0.582662 - 1.00920i) q^{9} +(-0.500000 + 0.866025i) q^{11} +0.725518 q^{13} -8.58456 q^{15} +(-1.45082 + 2.51289i) q^{17} +(-1.83403 - 3.17663i) q^{19} +(-5.38796 + 0.356519i) q^{21} +(-2.70218 - 4.68032i) q^{23} +(-6.34622 + 10.9920i) q^{25} +3.74441 q^{27} +7.97267 q^{29} +(3.35449 - 5.81014i) q^{31} +(1.02046 + 1.76748i) q^{33} +(-4.91586 + 9.98406i) q^{35} +(-0.0458026 - 0.0793324i) q^{37} +(0.740360 - 1.28234i) q^{39} -0.228255 q^{41} -1.35083 q^{43} +(-2.45082 + 4.24494i) q^{45} +(0.549185 + 0.951216i) q^{47} +(-2.67072 + 6.47049i) q^{49} +(2.96099 + 5.12858i) q^{51} +(-5.19595 + 8.99965i) q^{53} +4.20624 q^{55} -7.48619 q^{57} +(-2.22602 + 3.85558i) q^{59} +(4.03621 + 6.99093i) q^{61} +(-1.36192 + 2.76605i) q^{63} +(-1.52585 - 2.64285i) q^{65} +(2.33046 - 4.03647i) q^{67} -11.0298 q^{69} -16.7554 q^{71} +(-1.94137 + 3.36255i) q^{73} +(12.9521 + 22.4336i) q^{75} +(2.63998 - 0.174686i) q^{77} +(2.50475 + 4.33835i) q^{79} +(5.56900 - 9.64578i) q^{81} +3.70758 q^{83} +12.2049 q^{85} +(8.13576 - 14.0915i) q^{87} +(-9.39540 - 16.2733i) q^{89} +(-1.06743 - 1.59537i) q^{91} +(-6.84622 - 11.8580i) q^{93} +(-7.71437 + 13.3617i) q^{95} +13.2198 q^{97} +1.16532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7	$ 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) $ 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.02046	−	1.76748i	0.589161	−	1.02046i	−0.405182	−	0.914236i	$-0.632792\pi$
$3$	1.02046	−	1.76748i	0.589161	−	1.02046i	0.994343	−	0.106220i	$-0.0338749\pi$
$4$		0			0
$5$	−2.10312	−	3.64271i	−0.940543	−	1.62907i	−0.764438	−	0.644697i	$-0.776983\pi$
$5$	−2.10312	−	3.64271i	−0.940543	−	1.62907i	−0.176105	−	0.984371i	$-0.556350\pi$
$6$		0			0
$7$	−1.47127	−	2.19895i	−0.556088	−	0.831123i
$7$	−1.47127	−	2.19895i	−0.556088	−	0.831123i
$8$		0			0
$9$	−0.582662	−	1.00920i	−0.194221	−	0.336400i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	0.725518			0.201223			0.100611	−	0.994926i	$-0.467920\pi$
$13$	0.725518			0.201223			0.100611	+	0.994926i	$0.467920\pi$
$14$		0			0
$15$	−8.58456			−2.21652
$16$		0			0
$17$	−1.45082	+	2.51289i	−0.351874	+	0.609464i	−0.986578	−	0.163291i	$-0.947789\pi$
$17$	−1.45082	+	2.51289i	−0.351874	+	0.609464i	0.634703	+	0.772756i	$0.281122\pi$
$18$		0			0
$19$	−1.83403	−	3.17663i	−0.420756	−	0.728770i	0.575258	−	0.817972i	$-0.304902\pi$
$19$	−1.83403	−	3.17663i	−0.420756	−	0.728770i	−0.996014	+	0.0892021i	$0.971568\pi$
$20$		0			0
$21$	−5.38796	+	0.356519i	−1.17575	+	0.0777989i
$22$		0			0
$23$	−2.70218	−	4.68032i	−0.563444	−	0.975914i	−0.997193	−	0.0748801i	$-0.976143\pi$
$23$	−2.70218	−	4.68032i	−0.563444	−	0.975914i	0.433748	−	0.901034i	$-0.357191\pi$
$24$		0			0
$25$	−6.34622	+	10.9920i	−1.26924	+	2.19839i
$26$		0			0
$27$	3.74441			0.720613
$28$		0			0
$29$	7.97267			1.48049			0.740244	−	0.672339i	$-0.234710\pi$
$29$	7.97267			1.48049			0.740244	+	0.672339i	$0.234710\pi$
$30$		0			0
$31$	3.35449	−	5.81014i	0.602484	−	1.04353i	−0.389960	−	0.920832i	$-0.627511\pi$
$31$	3.35449	−	5.81014i	0.602484	−	1.04353i	0.992444	−	0.122701i	$-0.0391555\pi$
$32$		0			0
$33$	1.02046	+	1.76748i	0.177639	+	0.307679i
$34$		0			0
$35$	−4.91586	+	9.98406i	−0.830931	+	1.68761i
$36$		0			0
$37$	−0.0458026	−	0.0793324i	−0.00752990	−	0.0130422i	0.862236	−	0.506507i	$-0.169064\pi$
$37$	−0.0458026	−	0.0793324i	−0.00752990	−	0.0130422i	−0.869766	+	0.493465i	$0.835730\pi$
$38$		0			0
$39$	0.740360	−	1.28234i	0.118552	−	0.205339i
$40$		0			0
$41$	−0.228255			−0.0356475			−0.0178237	−	0.999841i	$-0.505674\pi$
$41$	−0.228255			−0.0356475			−0.0178237	+	0.999841i	$0.505674\pi$
$42$		0			0
$43$	−1.35083			−0.206000			−0.103000	−	0.994681i	$-0.532844\pi$
$43$	−1.35083			−0.206000			−0.103000	+	0.994681i	$0.532844\pi$
$44$		0			0
$45$	−2.45082	+	4.24494i	−0.365346	+	0.632798i
$46$		0			0
$47$	0.549185	+	0.951216i	0.0801068	+	0.138749i	0.903296	−	0.429019i	$-0.141141\pi$
$47$	0.549185	+	0.951216i	0.0801068	+	0.138749i	−0.823189	+	0.567768i	$0.807807\pi$
$48$		0			0
$49$	−2.67072	+	6.47049i	−0.381531	+	0.924356i
$50$		0			0
$51$	2.96099	+	5.12858i	0.414621	+	0.718145i
$52$		0			0
$53$	−5.19595	+	8.99965i	−0.713719	+	1.23620i	0.249732	+	0.968315i	$0.419657\pi$
$53$	−5.19595	+	8.99965i	−0.713719	+	1.23620i	−0.963452	+	0.267883i	$0.913676\pi$
$54$		0			0
$55$	4.20624			0.567169
$56$		0			0
$57$	−7.48619			−0.991571
$58$		0			0
$59$	−2.22602	+	3.85558i	−0.289803	+	0.501954i	−0.973763	−	0.227566i	$-0.926923\pi$
$59$	−2.22602	+	3.85558i	−0.289803	+	0.501954i	0.683959	+	0.729520i	$0.260257\pi$
$60$		0			0
$61$	4.03621	+	6.99093i	0.516784	+	0.895097i	0.999810	+	0.0194906i	$0.00620444\pi$
$61$	4.03621	+	6.99093i	0.516784	+	0.895097i	−0.483026	+	0.875606i	$0.660462\pi$
$62$		0			0
$63$	−1.36192	+	2.76605i	−0.171586	+	0.348490i
$64$		0			0
$65$	−1.52585	−	2.64285i	−0.189258	−	0.327805i
$66$		0			0
$67$	2.33046	−	4.03647i	0.284711	−	0.493133i	−0.687828	−	0.725873i	$-0.741436\pi$
$67$	2.33046	−	4.03647i	0.284711	−	0.493133i	0.972539	+	0.232740i	$0.0747692\pi$
$68$		0			0
$69$	−11.0298			−1.32784
$70$		0			0
$71$	−16.7554			−1.98850			−0.994248	−	0.107104i	$-0.965842\pi$
$71$	−16.7554			−1.98850			−0.994248	+	0.107104i	$0.965842\pi$
$72$		0			0
$73$	−1.94137	+	3.36255i	−0.227220	+	0.393557i	−0.956983	−	0.290143i	$-0.906297\pi$
$73$	−1.94137	+	3.36255i	−0.227220	+	0.393557i	0.729763	+	0.683700i	$0.239630\pi$
$74$		0			0
$75$	12.9521	+	22.4336i	1.49558	+	2.59041i
$76$		0			0
$77$	2.63998	−	0.174686i	0.300853	−	0.0199073i
$78$		0			0
$79$	2.50475	+	4.33835i	0.281806	+	0.488103i	0.971830	−	0.235684i	$-0.0757331\pi$
$79$	2.50475	+	4.33835i	0.281806	+	0.488103i	−0.690023	+	0.723787i	$0.742400\pi$
$80$		0			0
$81$	5.56900	−	9.64578i	0.618777	−	1.07175i
$82$		0			0
$83$	3.70758			0.406960			0.203480	−	0.979079i	$-0.434775\pi$
$83$	3.70758			0.406960			0.203480	+	0.979079i	$0.434775\pi$
$84$		0			0
$85$	12.2049			1.32381
$86$		0			0
$87$	8.13576	−	14.0915i	0.872245	−	1.51077i
$88$		0			0
$89$	−9.39540	−	16.2733i	−0.995910	−	1.72497i	−0.576198	−	0.817310i	$-0.695464\pi$
$89$	−9.39540	−	16.2733i	−0.995910	−	1.72497i	−0.419713	−	0.907657i	$-0.637869\pi$
$90$		0			0
$91$	−1.06743	−	1.59537i	−0.111898	−	0.167241i
$92$		0			0
$93$	−6.84622	−	11.8580i	−0.709919	−	1.22962i
$94$		0			0
$95$	−7.71437	+	13.3617i	−0.791478	+	1.37088i
$96$		0			0
$97$	13.2198			1.34227			0.671135	−	0.741336i	$-0.265807\pi$
$97$	13.2198			1.34227			0.671135	+	0.741336i	$0.265807\pi$
$98$		0			0
$99$	1.16532			0.117120
$100$		0			0
$101$	5.09960	−	8.83276i	0.507429	−	0.878892i	−0.492534	−	0.870293i	$-0.663929\pi$
$101$	5.09960	−	8.83276i	0.507429	−	0.878892i	0.999963	−	0.00859937i	$-0.00273730\pi$
$102$		0			0
$103$	−3.90842	−	6.76958i	−0.385108	−	0.667027i	0.606676	−	0.794949i	$-0.292503\pi$
$103$	−3.90842	−	6.76958i	−0.385108	−	0.667027i	−0.991784	+	0.127922i	$0.959169\pi$
$104$		0			0
$105$	12.6302	+	18.8770i	1.23258	+	1.84220i
$106$		0			0
$107$	−9.21099	−	15.9539i	−0.890460	−	1.54232i	−0.839325	−	0.543630i	$-0.817050\pi$
$107$	−9.21099	−	15.9539i	−0.890460	−	1.54232i	−0.0511345	−	0.998692i	$-0.516284\pi$
$108$		0			0
$109$	7.55329	−	13.0827i	0.723474	−	1.25309i	−0.236125	−	0.971723i	$-0.575878\pi$
$109$	7.55329	−	13.0827i	0.723474	−	1.25309i	0.959599	−	0.281371i	$-0.0907891\pi$
$110$		0			0
$111$	−0.186958			−0.0177453
$112$		0			0
$113$	−14.7855			−1.39090			−0.695451	−	0.718574i	$-0.744795\pi$
$113$	−14.7855			−1.39090			−0.695451	+	0.718574i	$0.744795\pi$
$114$		0			0
$115$	−11.3660	+	19.6865i	−1.05989	+	1.83578i
$116$		0			0
$117$	−0.422732	−	0.732193i	−0.0390816	−	0.0676913i
$118$		0			0
$119$	7.66024	−	0.506875i	0.702213	−	0.0464651i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−0.232925	+	0.403437i	−0.0210021	+	0.0363767i
$124$		0			0
$125$	32.3562			2.89403
$126$		0			0
$127$	−15.8590			−1.40726			−0.703631	−	0.710565i	$-0.748439\pi$
$127$	−15.8590			−1.40726			−0.703631	+	0.710565i	$0.748439\pi$
$128$		0			0
$129$	−1.37847	+	2.38757i	−0.121367	+	0.210214i
$130$		0			0
$131$	0.0615348	+	0.106581i	0.00537632	+	0.00931206i	0.868701	−	0.495337i	$-0.164955\pi$
$131$	0.0615348	+	0.106581i	0.00537632	+	0.00931206i	−0.863325	+	0.504649i	$0.831622\pi$
$132$		0			0
$133$	−4.28689	+	8.70663i	−0.371720	+	0.754960i
$134$		0			0
$135$	−7.87494	−	13.6398i	−0.677767	−	1.17393i
$136$		0			0
$137$	1.40300	−	2.43007i	0.119866	−	0.207615i	−0.799848	−	0.600202i	$-0.795087\pi$
$137$	1.40300	−	2.43007i	0.119866	−	0.207615i	0.919715	+	0.392588i	$0.128420\pi$
$138$		0			0
$139$	17.1678			1.45615			0.728076	−	0.685496i	$-0.240415\pi$
$139$	17.1678			1.45615			0.728076	+	0.685496i	$0.240415\pi$
$140$		0			0
$141$	2.24168			0.188783
$142$		0			0
$143$	−0.362759	+	0.628317i	−0.0303354	+	0.0525425i
$144$		0			0
$145$	−16.7675	−	29.0421i	−1.39246	−	2.41182i
$146$		0			0
$147$	8.71113	+	11.3233i	0.718482	+	0.933930i
$148$		0			0
$149$	0.488154	+	0.845508i	0.0399911	+	0.0692667i	0.885328	−	0.464967i	$-0.153934\pi$
$149$	0.488154	+	0.845508i	0.0399911	+	0.0692667i	−0.845337	+	0.534233i	$0.820600\pi$
$150$		0			0
$151$	8.05197	−	13.9464i	0.655260	−	1.13494i	−0.326568	−	0.945174i	$-0.605892\pi$
$151$	8.05197	−	13.9464i	0.655260	−	1.13494i	0.981828	−	0.189770i	$-0.0607744\pi$
$152$		0			0
$153$	3.38134			0.273365
$154$		0			0
$155$	−28.2195			−2.26665
$156$		0			0
$157$	2.67550	−	4.63410i	0.213528	−	0.369841i	−0.739288	−	0.673389i	$-0.764838\pi$
$157$	2.67550	−	4.63410i	0.213528	−	0.369841i	0.952816	+	0.303548i	$0.0981712\pi$
$158$		0			0
$159$	10.6045	+	18.3675i	0.840990	+	1.45664i
$160$		0			0
$161$	−6.31612	+	12.8280i	−0.497780	+	1.01099i
$162$		0			0
$163$	5.33928	+	9.24791i	0.418205	+	0.724352i	0.995759	−	0.0920001i	$-0.0293260\pi$
$163$	5.33928	+	9.24791i	0.418205	+	0.724352i	−0.577554	+	0.816353i	$0.695993\pi$
$164$		0			0
$165$	4.29228	−	7.43445i	0.334154	−	0.578771i
$166$		0			0
$167$	8.21171			0.635441			0.317721	−	0.948184i	$-0.397083\pi$
$167$	8.21171			0.635441			0.317721	+	0.948184i	$0.397083\pi$
$168$		0			0
$169$	−12.4736			−0.959510
$170$		0			0
$171$	−2.13724	+	3.70181i	−0.163439	+	0.283084i
$172$		0			0
$173$	−8.07850	−	13.9924i	−0.614197	−	1.06382i	−0.990525	−	0.137334i	$-0.956147\pi$
$173$	−8.07850	−	13.9924i	−0.614197	−	1.06382i	0.376328	−	0.926486i	$-0.377187\pi$
$174$		0			0
$175$	33.5077	−	2.21719i	2.53295	−	0.167604i
$176$		0			0
$177$	4.54312	+	7.86891i	0.341482	+	0.591463i
$178$		0			0
$179$	−5.87207	+	10.1707i	−0.438899	+	0.760195i	−0.997605	−	0.0691707i	$-0.977965\pi$
$179$	−5.87207	+	10.1707i	−0.438899	+	0.760195i	0.558706	+	0.829366i	$0.311298\pi$
$180$		0			0
$181$	−10.0671			−0.748283			−0.374141	−	0.927372i	$-0.622063\pi$
$181$	−10.0671			−0.748283			−0.374141	+	0.927372i	$0.622063\pi$
$182$		0			0
$183$	16.4751			1.21788
$184$		0			0
$185$	−0.192657	+	0.333691i	−0.0141644	+	0.0245335i
$186$		0			0
$187$	−1.45082	−	2.51289i	−0.106094	−	0.183760i
$188$		0			0
$189$	−5.50905	−	8.23376i	−0.400724	−	0.598918i
$190$		0			0
$191$	−10.2914	−	17.8253i	−0.744661	−	1.28979i	−0.950353	−	0.311173i	$-0.899278\pi$
$191$	−10.2914	−	17.8253i	−0.744661	−	1.28979i	0.205692	−	0.978617i	$-0.434055\pi$
$192$		0			0
$193$	2.19724	−	3.80574i	0.158161	−	0.273943i	−0.776045	−	0.630678i	$-0.782777\pi$
$193$	2.19724	−	3.80574i	0.158161	−	0.273943i	0.934206	+	0.356735i	$0.116110\pi$
$194$		0			0
$195$	−6.22826			−0.446015
$196$		0			0
$197$	−23.0051			−1.63905			−0.819524	−	0.573044i	$-0.805762\pi$
$197$	−23.0051			−1.63905			−0.819524	+	0.573044i	$0.805762\pi$
$198$		0			0
$199$	−2.89755	+	5.01871i	−0.205402	+	0.355767i	−0.950261	−	0.311455i	$-0.899184\pi$
$199$	−2.89755	+	5.01871i	−0.205402	+	0.355767i	0.744859	+	0.667222i	$0.232517\pi$
$200$		0			0
$201$	−4.75626	−	8.23808i	−0.335481	−	0.581069i
$202$		0			0
$203$	−11.7300	−	17.5315i	−0.823282	−	1.23047i
$204$		0			0
$205$	0.480048	+	0.831467i	0.0335280	+	0.0580722i
$206$		0			0
$207$	−3.14892	+	5.45409i	−0.218865	+	0.379086i
$208$		0			0
$209$	3.66806			0.253725
$210$		0			0
$211$	17.5116			1.20555			0.602773	−	0.797913i	$-0.294062\pi$
$211$	17.5116			1.20555			0.602773	+	0.797913i	$0.294062\pi$
$212$		0			0
$213$	−17.0981	+	29.6148i	−1.17154	+	2.02917i
$214$		0			0
$215$	2.84096	+	4.92069i	0.193752	+	0.335588i
$216$		0			0
$217$	−17.7115	+	1.17197i	−1.20234	+	0.0795582i
$218$		0			0
$219$	3.96216	+	6.86267i	0.267738	+	0.463736i
$220$		0			0
$221$	−1.05259	+	1.82314i	−0.0708051	+	0.122638i
$222$		0			0
$223$	−6.53325			−0.437499			−0.218749	−	0.975781i	$-0.570198\pi$
$223$	−6.53325			−0.437499			−0.218749	+	0.975781i	$0.570198\pi$
$224$		0			0
$225$	14.7908			0.986053
$226$		0			0
$227$	1.87444	−	3.24662i	0.124411	−	0.215486i	−0.797092	−	0.603858i	$-0.793629\pi$
$227$	1.87444	−	3.24662i	0.124411	−	0.215486i	0.921503	+	0.388372i	$0.126963\pi$
$228$		0			0
$229$	4.17276	+	7.22743i	0.275744	+	0.477602i	0.970322	−	0.241815i	$-0.0777426\pi$
$229$	4.17276	+	7.22743i	0.275744	+	0.477602i	−0.694579	+	0.719417i	$0.744409\pi$
$230$		0			0
$231$	2.38523	−	4.84437i	0.156936	−	0.318736i
$232$		0			0
$233$	10.0857	+	17.4690i	0.660737	+	1.14443i	0.980422	+	0.196906i	$0.0630895\pi$
$233$	10.0857	+	17.4690i	0.660737	+	1.14443i	−0.319685	+	0.947524i	$0.603577\pi$
$234$		0			0
$235$	2.31000	−	4.00104i	0.150688	−	0.260999i
$236$		0			0
$237$	10.2239			0.664117
$238$		0			0
$239$	25.9981			1.68168			0.840839	−	0.541286i	$-0.182062\pi$
$239$	25.9981			1.68168			0.840839	+	0.541286i	$0.182062\pi$
$240$		0			0
$241$	13.4191	−	23.2426i	0.864402	−	1.49719i	−0.00323820	−	0.999995i	$-0.501031\pi$
$241$	13.4191	−	23.2426i	0.864402	−	1.49719i	0.867640	−	0.497193i	$-0.165636\pi$
$242$		0			0
$243$	−5.74922	−	9.95793i	−0.368812	−	0.638802i
$244$		0			0
$245$	29.1870	−	3.87956i	1.86469	−	0.247856i
$246$		0			0
$247$	−1.33062	−	2.30471i	−0.0846655	−	0.146645i
$248$		0			0
$249$	3.78342	−	6.55308i	0.239765	−	0.415285i
$250$		0			0
$251$	−2.14163			−0.135179			−0.0675893	−	0.997713i	$-0.521531\pi$
$251$	−2.14163			−0.135179			−0.0675893	+	0.997713i	$0.521531\pi$
$252$		0			0
$253$	5.40437			0.339770
$254$		0			0
$255$	12.4546	−	21.5720i	0.779938	−	1.35089i
$256$		0			0
$257$	6.08442	+	10.5385i	0.379536	+	0.657375i	0.990995	−	0.133901i	$-0.0427504\pi$
$257$	6.08442	+	10.5385i	0.379536	+	0.657375i	−0.611459	+	0.791276i	$0.709417\pi$
$258$		0			0
$259$	−0.107060	+	0.217437i	−0.00665236	+	0.0135109i
$260$		0			0
$261$	−4.64537	−	8.04602i	−0.287541	−	0.498036i
$262$		0			0
$263$	−12.1904	+	21.1144i	−0.751692	+	1.30197i	0.195310	+	0.980741i	$0.437429\pi$
$263$	−12.1904	+	21.1144i	−0.751692	+	1.30197i	−0.947002	+	0.321227i	$0.895905\pi$
$264$		0			0
$265$	43.7108			2.68513
$266$		0			0
$267$	−38.3504			−2.34701
$268$		0			0
$269$	−8.64422	+	14.9722i	−0.527048	+	0.912873i	0.472456	+	0.881354i	$0.343368\pi$
$269$	−8.64422	+	14.9722i	−0.527048	+	0.912873i	−0.999503	+	0.0315187i	$0.989966\pi$
$270$		0			0
$271$	−7.93900	−	13.7507i	−0.482260	−	0.835298i	0.517533	−	0.855663i	$-0.326851\pi$
$271$	−7.93900	−	13.7507i	−0.482260	−	0.835298i	−0.999793	+	0.0203649i	$0.993517\pi$
$272$		0			0
$273$	−3.90907	+	0.258661i	−0.236587	+	0.0156549i
$274$		0			0
$275$	−6.34622	−	10.9920i	−0.382691	−	0.662841i
$276$		0			0
$277$	3.85091	−	6.66998i	0.231379	−	0.400760i	−0.726835	−	0.686812i	$-0.759010\pi$
$277$	3.85091	−	6.66998i	0.231379	−	0.400760i	0.958214	+	0.286052i	$0.0923429\pi$
$278$		0			0
$279$	−7.81813			−0.468059
$280$		0			0
$281$	9.19550			0.548558			0.274279	−	0.961650i	$-0.411561\pi$
$281$	9.19550			0.548558			0.274279	+	0.961650i	$0.411561\pi$
$282$		0			0
$283$	5.09130	−	8.81839i	0.302646	−	0.524199i	−0.674088	−	0.738651i	$-0.735463\pi$
$283$	5.09130	−	8.81839i	0.302646	−	0.524199i	0.976734	+	0.214452i	$0.0687966\pi$
$284$		0			0
$285$	15.7444	+	27.2700i	0.932615	+	1.61534i
$286$		0			0
$287$	0.335826	+	0.501921i	0.0198232	+	0.0296274i
$288$		0			0
$289$	4.29027	+	7.43096i	0.252369	+	0.437116i
$290$		0			0
$291$	13.4902	−	23.3658i	0.790812	−	1.36973i
$292$		0			0
$293$	−26.3234			−1.53783			−0.768914	−	0.639352i	$-0.779203\pi$
$293$	−26.3234			−1.53783			−0.768914	+	0.639352i	$0.779203\pi$
$294$		0			0
$295$	18.7264			1.09029
$296$		0			0
$297$	−1.87221	+	3.24276i	−0.108636	+	0.188164i
$298$		0			0
$299$	−1.96048	−	3.39566i	−0.113378	−	0.196376i
$300$		0			0
$301$	1.98744	+	2.97041i	0.114554	+	0.171211i
$302$		0			0
$303$	−10.4078	−	18.0269i	−0.597914	−	1.03562i
$304$		0			0
$305$	16.9773	−	29.4055i	0.972116	−	1.68375i
$306$		0			0
$307$	−12.3043			−0.702242			−0.351121	−	0.936330i	$-0.614199\pi$
$307$	−12.3043			−0.702242			−0.351121	+	0.936330i	$0.614199\pi$
$308$		0			0
$309$	−15.9535			−0.907562
$310$		0			0
$311$	2.25319	−	3.90264i	0.127767	−	0.221298i	−0.795044	−	0.606551i	$-0.792552\pi$
$311$	2.25319	−	3.90264i	0.127767	−	0.221298i	0.922811	+	0.385253i	$0.125886\pi$
$312$		0			0
$313$	0.637100	+	1.10349i	0.0360110	+	0.0623730i	0.883469	−	0.468489i	$-0.155202\pi$
$313$	0.637100	+	1.10349i	0.0360110	+	0.0623730i	−0.847458	+	0.530862i	$0.821868\pi$
$314$		0			0
$315$	12.9402	−	0.856247i	0.729098	−	0.0482441i
$316$		0			0
$317$	−10.1863	−	17.6431i	−0.572117	−	0.990936i	−0.996348	−	0.0853823i	$-0.972789\pi$
$317$	−10.1863	−	17.6431i	−0.572117	−	0.990936i	0.424231	−	0.905554i	$-0.360544\pi$
$318$		0			0
$319$	−3.98633	+	6.90453i	−0.223192	+	0.386580i
$320$		0			0
$321$	−37.5976			−2.09850
$322$		0			0
$323$	10.6434			0.592212
$324$		0			0
$325$	−4.60429	+	7.97487i	−0.255400	+	0.442366i
$326$		0			0
$327$	−15.4156	−	26.7006i	−0.852485	−	1.47655i
$328$		0			0
$329$	1.28367	−	2.60712i	0.0707711	−	0.143735i
$330$		0			0
$331$	9.57828	+	16.5901i	0.526470	+	0.911872i	0.999524	+	0.0308392i	$0.00981799\pi$
$331$	9.57828	+	16.5901i	0.526470	+	0.911872i	−0.473055	+	0.881033i	$0.656849\pi$
$332$		0			0
$333$	−0.0533749	+	0.0924480i	−0.00292493	+	0.00506612i
$334$		0			0
$335$	−19.6049			−1.07113
$336$		0			0
$337$	6.45780			0.351779			0.175889	−	0.984410i	$-0.443720\pi$
$337$	6.45780			0.351779			0.175889	+	0.984410i	$0.443720\pi$
$338$		0			0
$339$	−15.0879	+	26.1331i	−0.819465	+	1.41935i
$340$		0			0
$341$	3.35449	+	5.81014i	0.181656	+	0.314637i
$342$		0			0
$343$	18.1576	−	3.64709i	0.980419	−	0.196924i
$344$		0			0
$345$	23.1971	+	40.1785i	1.24889	+	2.16314i
$346$		0			0
$347$	3.08725	−	5.34727i	0.165732	−	0.287056i	−0.771183	−	0.636614i	$-0.780335\pi$
$347$	3.08725	−	5.34727i	0.165732	−	0.287056i	0.936915	+	0.349557i	$0.113668\pi$
$348$		0			0
$349$	10.1623			0.543976			0.271988	−	0.962301i	$-0.412319\pi$
$349$	10.1623			0.543976			0.271988	+	0.962301i	$0.412319\pi$
$350$		0			0
$351$	2.71664			0.145003
$352$		0			0
$353$	12.1323	−	21.0138i	0.645738	−	1.11845i	−0.338392	−	0.941005i	$-0.609883\pi$
$353$	12.1323	−	21.0138i	0.645738	−	1.11845i	0.984131	−	0.177446i	$-0.0567835\pi$
$354$		0			0
$355$	35.2385	+	61.0349i	1.87027	+	3.23940i
$356$		0			0
$357$	6.92105	−	14.0566i	0.366301	−	0.743953i
$358$		0			0
$359$	14.9963	+	25.9744i	0.791476	+	1.37088i	0.925053	+	0.379839i	$0.124021\pi$
$359$	14.9963	+	25.9744i	0.791476	+	1.37088i	−0.133576	+	0.991039i	$0.542646\pi$
$360$		0			0
$361$	2.77266	−	4.80239i	0.145930	−	0.252757i
$362$		0			0
$363$	−2.04091			−0.107120
$364$		0			0
$365$	16.3317			0.854841
$366$		0			0
$367$	4.09439	−	7.09170i	0.213726	−	0.370184i	−0.739152	−	0.673539i	$-0.764773\pi$
$367$	4.09439	−	7.09170i	0.213726	−	0.370184i	0.952878	+	0.303355i	$0.0981068\pi$
$368$		0			0
$369$	0.132996	+	0.230355i	0.00692348	+	0.0119918i
$370$		0			0
$371$	27.4344	−	1.81532i	1.42432	−	0.0942469i
$372$		0			0
$373$	−2.17483	−	3.76691i	−0.112608	−	0.195043i	0.804213	−	0.594341i	$-0.202587\pi$
$373$	−2.17483	−	3.76691i	−0.112608	−	0.195043i	−0.916821	+	0.399298i	$0.869254\pi$
$374$		0			0
$375$	33.0181	−	57.1890i	1.70505	−	2.95323i
$376$		0			0
$377$	5.78431			0.297907
$378$		0			0
$379$	1.20506			0.0618995			0.0309498	−	0.999521i	$-0.490147\pi$
$379$	1.20506			0.0618995			0.0309498	+	0.999521i	$0.490147\pi$
$380$		0			0
$381$	−16.1835	+	28.0306i	−0.829104	+	1.43605i
$382$		0			0
$383$	−13.1057	−	22.6997i	−0.669669	−	1.15990i	−0.977997	−	0.208621i	$-0.933102\pi$
$383$	−13.1057	−	22.6997i	−0.669669	−	1.15990i	0.308327	−	0.951280i	$-0.400231\pi$
$384$		0			0
$385$	−6.18852	−	9.24928i	−0.315396	−	0.471387i
$386$		0			0
$387$	0.787079	+	1.36326i	0.0400095	+	0.0692985i
$388$		0			0
$389$	13.5379	−	23.4483i	0.686399	−	1.18888i	−0.286596	−	0.958051i	$-0.592524\pi$
$389$	13.5379	−	23.4483i	0.686399	−	1.18888i	0.972995	−	0.230826i	$-0.0741428\pi$
$390$		0			0
$391$	15.6815			0.793047
$392$		0			0
$393$	0.251174			0.0126701
$394$		0			0
$395$	10.5356	−	18.2481i	0.530102	−	0.918164i
$396$		0			0
$397$	4.10072	+	7.10265i	0.205809	+	0.356472i	0.950390	−	0.311060i	$-0.100684\pi$
$397$	4.10072	+	7.10265i	0.205809	+	0.356472i	−0.744581	+	0.667532i	$0.767351\pi$
$398$		0			0
$399$	11.0142	+	16.4617i	0.551401	+	0.824117i
$400$		0			0
$401$	−2.78396	−	4.82196i	−0.139024	−	0.240797i	0.788103	−	0.615543i	$-0.211063\pi$
$401$	−2.78396	−	4.82196i	−0.139024	−	0.240797i	−0.927128	+	0.374746i	$0.877730\pi$
$402$		0			0
$403$	2.43374	−	4.21536i	0.121233	−	0.209982i
$404$		0			0
$405$	−46.8490			−2.32795
$406$		0			0
$407$	0.0916052			0.00454070
$408$		0			0
$409$	−15.9342	+	27.5988i	−0.787893	+	1.36467i	0.139362	+	0.990242i	$0.455495\pi$
$409$	−15.9342	+	27.5988i	−0.787893	+	1.36467i	−0.927255	+	0.374430i	$0.877838\pi$
$410$		0			0
$411$	−2.86340	−	4.95956i	−0.141241	−	0.244637i
$412$		0			0
$413$	11.7533	−	0.777711i	0.578342	−	0.0382686i
$414$		0			0
$415$	−7.79748	−	13.5056i	−0.382763	−	0.662966i
$416$		0			0
$417$	17.5190	−	30.3438i	0.857908	−	1.48594i
$418$		0			0
$419$	13.2772			0.648634			0.324317	−	0.945948i	$-0.394865\pi$
$419$	13.2772			0.648634			0.324317	+	0.945948i	$0.394865\pi$
$420$		0			0
$421$	18.7774			0.915156			0.457578	−	0.889169i	$-0.348717\pi$
$421$	18.7774			0.915156			0.457578	+	0.889169i	$0.348717\pi$
$422$		0			0
$423$	0.639978	−	1.10847i	0.0311168	−	0.0538959i
$424$		0			0
$425$	−18.4144	−	31.8946i	−0.893228	−	1.54712i
$426$		0			0
$427$	9.43430	−	19.1610i	0.456558	−	0.927264i
$428$		0			0
$429$	0.740360	+	1.28234i	0.0357449	+	0.0619120i
$430$		0			0
$431$	−12.2050	+	21.1398i	−0.587896	+	1.01827i	0.406611	+	0.913601i	$0.366710\pi$
$431$	−12.2050	+	21.1398i	−0.587896	+	1.01827i	−0.994508	+	0.104665i	$0.966623\pi$
$432$		0			0
$433$	31.9013			1.53308			0.766539	−	0.642197i	$-0.221977\pi$
$433$	31.9013			1.53308			0.766539	+	0.642197i	$0.221977\pi$
$434$		0			0
$435$	−68.4419			−3.28154
$436$		0			0
$437$	−9.91178	+	17.1677i	−0.474145	+	0.821243i
$438$		0			0
$439$	−11.2519	−	19.4888i	−0.537023	−	0.930150i	−0.999062	−	0.0432913i	$-0.986216\pi$
$439$	−11.2519	−	19.4888i	−0.537023	−	0.930150i	0.462040	−	0.886859i	$-0.347118\pi$
$440$		0			0
$441$	8.08615	−	1.07482i	0.385055	−	0.0511819i
$442$		0			0
$443$	−0.686712	−	1.18942i	−0.0326267	−	0.0565111i	0.849251	−	0.527989i	$-0.177054\pi$
$443$	−0.686712	−	1.18942i	−0.0326267	−	0.0565111i	−0.881878	+	0.471478i	$0.843721\pi$
$444$		0			0
$445$	−39.5193	+	68.4494i	−1.87339	+	3.24481i
$446$		0			0
$447$	1.99256			0.0942448
$448$		0			0
$449$	15.8128			0.746251			0.373125	−	0.927781i	$-0.378286\pi$
$449$	15.8128			0.746251			0.373125	+	0.927781i	$0.378286\pi$
$450$		0			0
$451$	0.114128	−	0.197675i	0.00537406	−	0.00930815i
$452$		0			0
$453$	−16.4334	−	28.4634i	−0.772107	−	1.33733i
$454$		0			0
$455$	−3.56654	+	7.24361i	−0.167202	+	0.339586i
$456$		0			0
$457$	7.72502	+	13.3801i	0.361361	+	0.625896i	0.988185	−	0.153265i	$-0.0489789\pi$
$457$	7.72502	+	13.3801i	0.361361	+	0.625896i	−0.626824	+	0.779161i	$0.715646\pi$
$458$		0			0
$459$	−5.43245	+	9.40928i	−0.253565	+	0.439188i
$460$		0			0
$461$	40.2107			1.87280			0.936400	−	0.350935i	$-0.114136\pi$
$461$	40.2107			1.87280			0.936400	+	0.350935i	$0.114136\pi$
$462$		0			0
$463$	−27.9086			−1.29702			−0.648512	−	0.761205i	$-0.724608\pi$
$463$	−27.9086			−1.29702			−0.648512	+	0.761205i	$0.724608\pi$
$464$		0			0
$465$	−28.7968	+	49.8775i	−1.33542	+	2.31302i
$466$		0			0
$467$	−10.4255	−	18.0576i	−0.482437	−	0.835605i	0.517360	−	0.855768i	$-0.326915\pi$
$467$	−10.4255	−	18.0576i	−0.482437	−	0.835605i	−0.999797	+	0.0201629i	$0.993582\pi$
$468$		0			0
$469$	−12.3047	+	0.814197i	−0.568179	+	0.0375961i
$470$		0			0
$471$	−5.46045	−	9.45779i	−0.251604	−	0.435792i
$472$		0			0
$473$	0.675416	−	1.16986i	0.0310557	−	0.0537900i
$474$		0			0
$475$	46.5566			2.13616
$476$		0			0
$477$	12.1099			0.554476
$478$		0			0
$479$	−6.24251	+	10.8123i	−0.285227	+	0.494028i	−0.972664	−	0.232216i	$-0.925402\pi$
$479$	−6.24251	+	10.8123i	−0.285227	+	0.494028i	0.687437	+	0.726244i	$0.258736\pi$
$480$		0			0
$481$	−0.0332306	−	0.0575571i	−0.00151519	−	0.00262438i
$482$		0			0
$483$	16.2279	+	24.2540i	0.738395	+	1.10360i
$484$		0			0
$485$	−27.8028	−	48.1559i	−1.26246	−	2.18665i
$486$		0			0
$487$	−6.77898	+	11.7415i	−0.307185	+	0.532060i	−0.977745	−	0.209795i	$-0.932720\pi$
$487$	−6.77898	+	11.7415i	−0.307185	+	0.532060i	0.670561	+	0.741855i	$0.266054\pi$
$488$		0			0
$489$	21.7940			0.985560
$490$		0			0
$491$	22.3044			1.00658			0.503291	−	0.864117i	$-0.332122\pi$
$491$	22.3044			1.00658			0.503291	+	0.864117i	$0.332122\pi$
$492$		0			0
$493$	−11.5669	+	20.0344i	−0.520946	+	0.902304i
$494$		0			0
$495$	−2.45082	−	4.24494i	−0.110156	−	0.190796i
$496$		0			0
$497$	24.6517	+	36.8441i	1.10578	+	1.65268i
$498$		0			0
$499$	12.7014	+	21.9995i	0.568593	+	0.984831i	0.996705	+	0.0811061i	$0.0258453\pi$
$499$	12.7014	+	21.9995i	0.568593	+	0.984831i	−0.428113	+	0.903725i	$0.640821\pi$
$500$		0			0
$501$	8.37969	−	14.5141i	0.374377	−	0.648440i
$502$		0			0
$503$	−18.2897			−0.815499			−0.407750	−	0.913094i	$-0.633686\pi$
$503$	−18.2897			−0.815499			−0.407750	+	0.913094i	$0.633686\pi$
$504$		0			0
$505$	−42.9002			−1.90903
$506$		0			0
$507$	−12.7288	+	22.0469i	−0.565305	+	0.979138i
$508$		0			0
$509$	−4.76688	−	8.25648i	−0.211288	−	0.365962i	0.740830	−	0.671693i	$-0.234433\pi$
$509$	−4.76688	−	8.25648i	−0.211288	−	0.365962i	−0.952118	+	0.305731i	$0.901099\pi$
$510$		0			0
$511$	10.2503	−	0.678261i	0.453448	−	0.0300045i
$512$		0			0
$513$	−6.86737	−	11.8946i	−0.303202	−	0.525161i
$514$		0			0
$515$	−16.4397	+	28.4745i	−0.724422	+	1.25474i
$516$		0			0
$517$	−1.09837			−0.0483062
$518$		0			0
$519$	−32.9750			−1.44744
$520$		0			0
$521$	−9.62357	+	16.6685i	−0.421616	+	0.730261i	−0.996098	−	0.0882566i	$-0.971870\pi$
$521$	−9.62357	+	16.6685i	−0.421616	+	0.730261i	0.574481	+	0.818518i	$0.305204\pi$
$522$		0			0
$523$	10.0166	+	17.3492i	0.437994	+	0.758628i	0.997535	−	0.0701747i	$-0.0223557\pi$
$523$	10.0166	+	17.3492i	0.437994	+	0.758628i	−0.559540	+	0.828803i	$0.689022\pi$
$524$		0			0
$525$	30.2743	−	61.4869i	1.32128	−	2.68351i
$526$		0			0
$527$	9.73348	+	16.8589i	0.423997	+	0.734385i
$528$		0			0
$529$	−3.10360	+	5.37559i	−0.134939	+	0.233721i
$530$		0			0
$531$	5.18808			0.225143
$532$		0			0
$533$	−0.165603			−0.00717308
$534$		0			0
$535$	−38.7436	+	67.1059i	−1.67503	+	2.90124i
$536$		0			0
$537$	11.9844	+	20.7575i	0.517164	+	0.895754i
$538$		0			0
$539$	−4.26825	−	5.54816i	−0.183847	−	0.238976i
$540$		0			0
$541$	−1.20465	−	2.08651i	−0.0517919	−	0.0897062i	0.838967	−	0.544182i	$-0.183160\pi$
$541$	−1.20465	−	2.08651i	−0.0517919	−	0.0897062i	−0.890759	+	0.454476i	$0.849827\pi$
$542$		0			0
$543$	−10.2731	+	17.7934i	−0.440859	+	0.763590i
$544$		0			0
$545$	−63.5419			−2.72183
$546$		0			0
$547$	10.7758			0.460741			0.230370	−	0.973103i	$-0.426006\pi$
$547$	10.7758			0.460741			0.230370	+	0.973103i	$0.426006\pi$
$548$		0			0
$549$	4.70350	−	8.14670i	0.200740	−	0.347693i
$550$		0			0
$551$	−14.6221	−	25.3263i	−0.622923	−	1.07893i
$552$		0			0
$553$	5.85463	−	11.8907i	0.248964	−	0.505644i
$554$		0			0
$555$	0.393195	+	0.681034i	0.0166902	+	0.0289083i
$556$		0			0
$557$	5.49348	−	9.51499i	0.232766	−	0.403163i	−0.725855	−	0.687848i	$-0.758556\pi$
$557$	5.49348	−	9.51499i	0.232766	−	0.403163i	0.958621	+	0.284685i	$0.0918889\pi$
$558$		0			0
$559$	−0.980054			−0.0414519
$560$		0			0
$561$	−5.92198			−0.250026
$562$		0			0
$563$	3.36681	−	5.83149i	0.141894	−	0.245768i	−0.786316	−	0.617825i	$-0.788014\pi$
$563$	3.36681	−	5.83149i	0.141894	−	0.245768i	0.928210	+	0.372057i	$0.121347\pi$
$564$		0			0
$565$	31.0956	+	53.8592i	1.30820	+	2.26587i
$566$		0			0
$567$	−29.4041	+	1.94565i	−1.23485	+	0.0817098i
$568$		0			0
$569$	−21.8925	−	37.9189i	−0.917780	−	1.58964i	−0.802780	−	0.596276i	$-0.796647\pi$
$569$	−21.8925	−	37.9189i	−0.917780	−	1.58964i	−0.115000	−	0.993365i	$-0.536687\pi$
$570$		0			0
$571$	11.5471	−	20.0001i	0.483231	−	0.836980i	−0.516584	−	0.856236i	$-0.672797\pi$
$571$	11.5471	−	20.0001i	0.483231	−	0.836980i	0.999815	+	0.0192567i	$0.00612996\pi$
$572$		0			0
$573$	−42.0078			−1.75490
$574$		0			0
$575$	68.5946			2.86059
$576$		0			0
$577$	−0.239881	+	0.415485i	−0.00998636	+	0.0172969i	−0.870975	−	0.491327i	$-0.836512\pi$
$577$	−0.239881	+	0.415485i	−0.00998636	+	0.0172969i	0.860989	+	0.508624i	$0.169845\pi$
$578$		0			0
$579$	−4.48438	−	7.76717i	−0.186364	−	0.322793i
$580$		0			0
$581$	−5.45486	−	8.15277i	−0.226306	−	0.338234i
$582$		0			0
$583$	−5.19595	−	8.99965i	−0.215194	−	0.372728i
$584$		0			0
$585$	−1.77811	+	3.07978i	−0.0735158	+	0.127333i
$586$		0			0
$587$	−27.4252			−1.13196			−0.565980	−	0.824419i	$-0.691502\pi$
$587$	−27.4252			−1.13196			−0.565980	+	0.824419i	$0.691502\pi$
$588$		0			0
$589$	−24.6089			−1.01399
$590$		0			0
$591$	−23.4757	+	40.6612i	−0.965663	+	1.67258i
$592$		0			0
$593$	−7.18567	−	12.4459i	−0.295080	−	0.511093i	0.679924	−	0.733283i	$-0.262013\pi$
$593$	−7.18567	−	12.4459i	−0.295080	−	0.511093i	−0.975003	+	0.222190i	$0.928680\pi$
$594$		0			0
$595$	−17.9568	−	26.8380i	−0.736157	−	1.10025i
$596$		0			0
$597$	5.91365	+	10.2427i	0.242030	+	0.419208i
$598$		0			0
$599$	13.3885	−	23.1895i	0.547038	−	0.947498i	−0.451437	−	0.892303i	$-0.649089\pi$
$599$	13.3885	−	23.1895i	0.547038	−	0.947498i	0.998476	−	0.0551951i	$-0.0175781\pi$
$600$		0			0
$601$	46.8878			1.91259			0.956297	−	0.292397i	$-0.0944529\pi$
$601$	46.8878			1.91259			0.956297	+	0.292397i	$0.0944529\pi$
$602$		0			0
$603$	−5.43148			−0.221187
$604$		0			0
$605$	−2.10312	+	3.64271i	−0.0855039	+	0.148097i
$606$		0			0
$607$	−8.44520	−	14.6275i	−0.342780	−	0.593713i	0.642168	−	0.766564i	$-0.278035\pi$
$607$	−8.44520	−	14.6275i	−0.342780	−	0.593713i	−0.984948	+	0.172852i	$0.944702\pi$
$608$		0			0
$609$	−42.9565	+	2.84241i	−1.74068	+	0.115180i
$610$		0			0
$611$	0.398443	+	0.690124i	0.0161193	+	0.0279194i
$612$		0			0
$613$	7.40140	−	12.8196i	0.298940	−	0.517779i	−0.676954	−	0.736026i	$-0.736700\pi$
$613$	7.40140	−	12.8196i	0.298940	−	0.517779i	0.975894	+	0.218246i	$0.0700336\pi$
$614$		0			0
$615$	1.95947			0.0790135
$616$		0			0
$617$	32.5174			1.30910			0.654551	−	0.756018i	$-0.272858\pi$
$617$	32.5174			1.30910			0.654551	+	0.756018i	$0.272858\pi$
$618$		0			0
$619$	−11.8959	+	20.6043i	−0.478136	+	0.828155i	−0.999686	−	0.0250654i	$-0.992021\pi$
$619$	−11.8959	+	20.6043i	−0.478136	+	0.828155i	0.521550	+	0.853221i	$0.325354\pi$
$620$		0			0
$621$	−10.1181	−	17.5250i	−0.406025	−	0.703256i
$622$		0			0
$623$	−21.9609	+	44.6024i	−0.879846	+	1.78696i
$624$		0			0
$625$	−36.3178	−	62.9043i	−1.45271	−	2.51617i
$626$		0			0
$627$	3.74310	−	6.48323i	0.149485	−	0.258915i
$628$		0			0
$629$	0.265805			0.0105983
$630$		0			0
$631$	−2.13626			−0.0850432			−0.0425216	−	0.999096i	$-0.513539\pi$
$631$	−2.13626			−0.0850432			−0.0425216	+	0.999096i	$0.513539\pi$
$632$		0			0
$633$	17.8698	−	30.9514i	0.710261	−	1.23021i
$634$		0			0
$635$	33.3535	+	57.7699i	1.32359	+	2.29253i
$636$		0			0
$637$	−1.93765	+	4.69446i	−0.0767727	+	0.186001i
$638$		0			0
$639$	9.76272	+	16.9095i	0.386207	+	0.668930i
$640$		0			0
$641$	−15.0364	+	26.0437i	−0.593901	+	1.02867i	0.399800	+	0.916602i	$0.369079\pi$
$641$	−15.0364	+	26.0437i	−0.593901	+	1.02867i	−0.993701	+	0.112064i	$0.964254\pi$
$642$		0			0
$643$	8.95119			0.353001			0.176500	−	0.984301i	$-0.443522\pi$
$643$	8.95119			0.353001			0.176500	+	0.984301i	$0.443522\pi$
$644$		0			0
$645$	11.5963			0.456604
$646$		0			0
$647$	−15.4742	+	26.8020i	−0.608352	+	1.05370i	0.383160	+	0.923682i	$0.374836\pi$
$647$	−15.4742	+	26.8020i	−0.608352	+	1.05370i	−0.991512	+	0.130014i	$0.958498\pi$
$648$		0			0
$649$	−2.22602	−	3.85558i	−0.0873790	−	0.151345i
$650$		0			0
$651$	−16.0024	+	32.5008i	−0.627185	+	1.27381i
$652$		0			0
$653$	9.66728	+	16.7442i	0.378310	+	0.655252i	0.990816	−	0.135214i	$-0.0431721\pi$
$653$	9.66728	+	16.7442i	0.378310	+	0.655252i	−0.612507	+	0.790465i	$0.709839\pi$
$654$		0			0
$655$	0.258830	−	0.448307i	0.0101133	−	0.0175168i
$656$		0			0
$657$	4.52465			0.176523
$658$		0			0
$659$	−8.37559			−0.326267			−0.163133	−	0.986604i	$-0.552160\pi$
$659$	−8.37559			−0.326267			−0.163133	+	0.986604i	$0.552160\pi$
$660$		0			0
$661$	15.8301	−	27.4186i	0.615720	−	1.06646i	−0.374537	−	0.927212i	$-0.622198\pi$
$661$	15.8301	−	27.4186i	0.615720	−	1.06646i	0.990258	−	0.139247i	$-0.0444682\pi$
$662$		0			0
$663$	2.14825	+	3.72088i	0.0834311	+	0.144507i
$664$		0			0
$665$	40.7315	−	2.69519i	1.57950	−	0.104515i
$666$		0			0
$667$	−21.5436	−	37.3146i	−0.834172	−	1.44483i
$668$		0			0
$669$	−6.66689	+	11.5474i	−0.257757	+	0.446448i
$670$		0			0
$671$	−8.07243			−0.311633
$672$		0			0
$673$	−36.5124			−1.40745			−0.703726	−	0.710472i	$-0.748482\pi$
$673$	−36.5124			−1.40745			−0.703726	+	0.710472i	$0.748482\pi$
$674$		0			0
$675$	−23.7628	+	41.1585i	−0.914632	+	1.58419i
$676$		0			0
$677$	−5.29203	−	9.16606i	−0.203389	−	0.352280i	0.746229	−	0.665689i	$-0.231862\pi$
$677$	−5.29203	−	9.16606i	−0.203389	−	0.352280i	−0.949618	+	0.313409i	$0.898529\pi$
$678$		0			0
$679$	−19.4499	−	29.0697i	−0.746420	−	1.11559i
$680$		0			0
$681$	−3.82557	−	6.62608i	−0.146596	−	0.253912i
$682$		0			0
$683$	10.1949	−	17.6581i	0.390097	−	0.675668i	−0.602365	−	0.798221i	$-0.705775\pi$
$683$	10.1949	−	17.6581i	0.390097	−	0.675668i	0.992462	+	0.122553i	$0.0391082\pi$
$684$		0			0
$685$	−11.8027			−0.450958
$686$		0			0
$687$	17.0325			0.649829
$688$		0			0
$689$	−3.76976	+	6.52941i	−0.143616	+	0.248751i
$690$		0			0
$691$	−9.22806	−	15.9835i	−0.351052	−	0.608040i	0.635382	−	0.772198i	$-0.280843\pi$
$691$	−9.22806	−	15.9835i	−0.351052	−	0.608040i	−0.986434	+	0.164158i	$0.947509\pi$
$692$		0			0
$693$	−1.71451	−	2.56248i	−0.0651288	−	0.0973407i
$694$		0			0
$695$	−36.1059	−	62.5372i	−1.36957	−	2.37217i
$696$		0			0
$697$	0.331156	−	0.573580i	0.0125434	−	0.0217259i
$698$		0			0
$699$	41.1681			1.55712
$700$		0			0
$701$	−4.62776			−0.174788			−0.0873941	−	0.996174i	$-0.527854\pi$
$701$	−4.62776			−0.174788			−0.0873941	+	0.996174i	$0.527854\pi$
$702$		0			0
$703$	−0.168007	+	0.290996i	−0.00633650	+	0.0109751i
$704$		0			0
$705$	−4.71451	−	8.16577i	−0.177559	−	0.307541i
$706$		0			0
$707$	−26.9256	+	1.78166i	−1.01264	+	0.0670062i
$708$		0			0
$709$	2.50581	+	4.34019i	0.0941076	+	0.162999i	0.909236	−	0.416281i	$-0.136667\pi$
$709$	2.50581	+	4.34019i	0.0941076	+	0.162999i	−0.815128	+	0.579281i	$0.803334\pi$
$710$		0			0
$711$	2.91885	−	5.05559i	0.109465	−	0.189599i
$712$		0			0
$713$	−36.2578			−1.35786
$714$		0			0
$715$	3.05170			0.114127
$716$		0			0
$717$	26.5299	−	45.9512i	0.990778	−	1.71608i
$718$		0			0
$719$	4.18274	+	7.24471i	0.155990	+	0.270182i	0.933419	−	0.358788i	$-0.116810\pi$
$719$	4.18274	+	7.24471i	0.155990	+	0.270182i	−0.777429	+	0.628970i	$0.783477\pi$
$720$		0			0
$721$	−9.13559	+	18.5543i	−0.340227	+	0.690998i
$722$		0			0
$723$	−27.3873	−	47.4361i	−1.01854	−	1.76417i
$724$		0			0
$725$	−50.5963	+	87.6353i	−1.87910	+	3.25469i
$726$		0			0
$727$	−25.5062			−0.945973			−0.472986	−	0.881070i	$-0.656824\pi$
$727$	−25.5062			−0.945973			−0.472986	+	0.881070i	$0.656824\pi$
$728$		0			0
$729$	9.94668			0.368396
$730$		0			0
$731$	1.95981	−	3.39449i	0.0724862	−	0.125550i
$732$		0			0
$733$	14.7589	+	25.5631i	0.545132	+	0.944196i	0.998599	+	0.0529227i	$0.0168537\pi$
$733$	14.7589	+	25.5631i	0.545132	+	0.944196i	−0.453467	+	0.891273i	$0.649813\pi$
$734$		0			0
$735$	22.9270	−	55.5463i	0.845673	−	2.04886i
$736$		0			0
$737$	2.33046	+	4.03647i	0.0858435	+	0.148685i
$738$		0			0
$739$	−11.7600	+	20.3690i	−0.432600	+	0.749285i	−0.997096	−	0.0761506i	$-0.975737\pi$
$739$	−11.7600	+	20.3690i	−0.432600	+	0.749285i	0.564496	+	0.825435i	$0.309070\pi$
$740$		0			0
$741$	−5.43137			−0.199526
$742$		0			0
$743$	11.1655			0.409622			0.204811	−	0.978802i	$-0.434342\pi$
$743$	11.1655			0.409622			0.204811	+	0.978802i	$0.434342\pi$
$744$		0			0
$745$	2.05329	−	3.55641i	0.0752268	−	0.130297i
$746$		0			0
$747$	−2.16027	−	3.74169i	−0.0790401	−	0.136901i
$748$		0			0
$749$	−21.5299	+	43.7270i	−0.786685	+	1.59775i
$750$		0			0
$751$	3.34040	+	5.78574i	0.121893	+	0.211124i	0.920514	−	0.390709i	$-0.127770\pi$
$751$	3.34040	+	5.78574i	0.121893	+	0.211124i	−0.798621	+	0.601834i	$0.794437\pi$
$752$		0			0
$753$	−2.18544	+	3.78530i	−0.0796419	+	0.137944i
$754$		0			0
$755$	−67.7370			−2.46520
$756$		0			0
$757$	3.27281			0.118952			0.0594761	−	0.998230i	$-0.481057\pi$
$757$	3.27281			0.118952			0.0594761	+	0.998230i	$0.481057\pi$
$758$		0			0
$759$	5.51492	−	9.55212i	0.200179	−	0.346720i
$760$		0			0
$761$	−14.6453	−	25.3663i	−0.530890	−	0.919529i	−0.999350	−	0.0360442i	$-0.988524\pi$
$761$	−14.6453	−	25.3663i	−0.530890	−	0.919529i	0.468460	−	0.883485i	$-0.344809\pi$
$762$		0			0
$763$	−39.8810	+	2.63891i	−1.44379	+	0.0955350i
$764$		0			0
$765$	−7.11136	−	12.3172i	−0.257112	−	0.445331i
$766$		0			0
$767$	−1.61502	+	2.79730i	−0.0583150	+	0.101004i
$768$		0			0
$769$	−14.0914			−0.508150			−0.254075	−	0.967185i	$-0.581771\pi$
$769$	−14.0914			−0.508150			−0.254075	+	0.967185i	$0.581771\pi$
$770$		0			0
$771$	24.8355			0.894430
$772$		0			0
$773$	10.1310	−	17.5474i	0.364387	−	0.631137i	−0.624291	−	0.781192i	$-0.714612\pi$
$773$	10.1310	−	17.5474i	0.364387	−	0.631137i	0.988678	+	0.150055i	$0.0479452\pi$
$774$		0			0
$775$	42.5766	+	73.7448i	1.52940	+	2.64899i
$776$		0			0
$777$	0.275066	+	0.411111i	0.00986795	+	0.0147485i
$778$		0			0
$779$	0.418627	+	0.725084i	0.0149989	+	0.0259788i
$780$		0			0
$781$	8.37768	−	14.5106i	0.299777	−	0.519229i
$782$		0			0
$783$	29.8530			1.06686
$784$		0			0
$785$	−22.5075			−0.803329
$786$		0			0
$787$	13.7563	−	23.8265i	0.490357	−	0.849324i	−0.509581	−	0.860423i	$-0.670200\pi$
$787$	13.7563	−	23.8265i	0.490357	−	0.849324i	0.999938	+	0.0110988i	$0.00353293\pi$
$788$		0			0
$789$	24.8795	+	43.0926i	0.885735	+	1.53414i
$790$		0			0
$791$	21.7535	+	32.5125i	0.773464	+	1.15601i
$792$		0			0
$793$	2.92835	+	5.07205i	0.103989	+	0.180114i
$794$		0			0
$795$	44.6050	−	77.2581i	1.58198	−	2.74006i
$796$		0			0
$797$	51.8802			1.83769			0.918845	−	0.394619i	$-0.129123\pi$
$797$	51.8802			1.83769			0.918845	+	0.394619i	$0.129123\pi$
$798$		0			0
$799$	−3.18706			−0.112750
$800$		0			0
$801$	−10.9487	+	18.9637i	−0.386853	+	0.670049i
$802$		0			0
$803$	−1.94137	−	3.36255i	−0.0685094	−	0.118662i
$804$		0			0
$805$	60.0121	−	3.97098i	2.11515	−	0.139959i
$806$		0			0
$807$	17.6421	+	30.5570i	0.621032	+	1.07566i
$808$		0			0
$809$	10.6440	−	18.4359i	0.374222	−	0.648172i	−0.615988	−	0.787756i	$-0.711243\pi$
$809$	10.6440	−	18.4359i	0.374222	−	0.648172i	0.990210	+	0.139583i	$0.0445763\pi$
$810$		0			0
$811$	−13.0249			−0.457365			−0.228682	−	0.973501i	$-0.573442\pi$
$811$	−13.0249			−0.457365			−0.228682	+	0.973501i	$0.573442\pi$
$812$		0			0
$813$	−32.4056			−1.13651
$814$		0			0
$815$	22.4583	−	38.8989i	0.786680	−	1.36257i
$816$		0			0
$817$	2.47747	+	4.29110i	0.0866757	+	0.150127i
$818$		0			0
$819$	−0.988099	+	2.00682i	−0.0345270	+	0.0701240i
$820$		0			0
$821$	−12.1479	−	21.0407i	−0.423963	−	0.734326i	0.572360	−	0.820003i	$-0.306028\pi$
$821$	−12.1479	−	21.0407i	−0.423963	−	0.734326i	−0.996323	+	0.0856766i	$0.972695\pi$
$822$		0			0
$823$	−19.0317	+	32.9638i	−0.663402	+	1.14905i	0.316314	+	0.948655i	$0.397555\pi$
$823$	−19.0317	+	32.9638i	−0.663402	+	1.14905i	−0.979716	+	0.200392i	$0.935779\pi$
$824$		0			0
$825$	−25.9041			−0.901866
$826$		0			0
$827$	23.6155			0.821191			0.410595	−	0.911818i	$-0.365321\pi$
$827$	23.6155			0.821191			0.410595	+	0.911818i	$0.365321\pi$
$828$		0			0
$829$	3.78991	−	6.56431i	0.131629	−	0.227988i	−0.792676	−	0.609643i	$-0.791313\pi$
$829$	3.78991	−	6.56431i	0.131629	−	0.227988i	0.924305	+	0.381656i	$0.124646\pi$
$830$		0			0
$831$	−7.85938	−	13.6128i	−0.272639	−	0.472224i
$832$		0			0
$833$	−12.3849	−	16.0987i	−0.429111	−	0.557787i
$834$		0			0
$835$	−17.2702	−	29.9129i	−0.597660	−	1.03518i
$836$		0			0
$837$	12.5606	−	21.7556i	0.434157	−	0.751982i
$838$		0			0
$839$	26.1717			0.903549			0.451774	−	0.892132i	$-0.350791\pi$
$839$	26.1717			0.903549			0.451774	+	0.892132i	$0.350791\pi$
$840$		0			0
$841$	34.5634			1.19184
$842$		0			0
$843$	9.38361	−	16.2529i	0.323189	−	0.559779i
$844$		0			0
$845$	26.2335	+	45.4378i	0.902460	+	1.56311i
$846$		0			0
$847$	−1.16871	+	2.37363i	−0.0401572	+	0.0815589i
$848$		0			0
$849$	−10.3909	−	17.9976i	−0.356615	−	0.617675i
$850$		0			0
$851$	−0.247534	+	0.428742i	−0.00848536	+	0.0146971i
$852$		0			0
$853$	8.21316			0.281213			0.140607	−	0.990066i	$-0.455095\pi$
$853$	8.21316			0.281213			0.140607	+	0.990066i	$0.455095\pi$
$854$		0			0
$855$	17.9795			0.614885
$856$		0			0
$857$	−25.3066	+	43.8323i	−0.864457	+	1.49728i	0.00312768	+	0.999995i	$0.499004\pi$
$857$	−25.3066	+	43.8323i	−0.864457	+	1.49728i	−0.867585	+	0.497289i	$0.834329\pi$
$858$		0			0
$859$	13.4615	+	23.3160i	0.459300	+	0.795531i	0.998924	−	0.0463752i	$-0.0147670\pi$
$859$	13.4615	+	23.3160i	0.459300	+	0.795531i	−0.539624	+	0.841906i	$0.681434\pi$
$860$		0			0
$861$	1.22983	−	0.0813774i	0.0419125	−	0.00277333i
$862$		0			0
$863$	−4.22715	−	7.32163i	−0.143894	−	0.249231i	0.785066	−	0.619412i	$-0.212629\pi$
$863$	−4.22715	−	7.32163i	−0.143894	−	0.249231i	−0.928960	+	0.370181i	$0.879296\pi$
$864$		0			0
$865$	−33.9801	+	58.8552i	−1.15536	+	2.00114i
$866$		0			0
$867$	17.5121			0.594743
$868$		0			0
$869$	−5.00950			−0.169936
$870$		0			0
$871$	1.69079	−	2.92853i	0.0572902	−	0.0992295i
$872$		0			0
$873$	−7.70269	−	13.3414i	−0.260697	−	0.451540i
$874$		0			0
$875$	−47.6047	−	71.1495i	−1.60933	−	2.40529i
$876$		0			0
$877$	16.1471	+	27.9677i	0.545250	+	0.944401i	0.998591	+	0.0530635i	$0.0168986\pi$
$877$	16.1471	+	27.9677i	0.545250	+	0.944401i	−0.453341	+	0.891337i	$0.649768\pi$
$878$		0			0
$879$	−26.8619	+	46.5261i	−0.906028	+	1.56929i
$880$		0			0
$881$	41.3145			1.39192			0.695961	−	0.718080i	$-0.254979\pi$
$881$	41.3145			1.39192			0.695961	+	0.718080i	$0.254979\pi$
$882$		0			0
$883$	22.5182			0.757799			0.378899	−	0.925438i	$-0.376303\pi$
$883$	22.5182			0.757799			0.378899	+	0.925438i	$0.376303\pi$
$884$		0			0
$885$	19.1094	−	33.0985i	0.642356	−	1.11259i
$886$		0			0
$887$	16.0326	+	27.7693i	0.538322	+	0.932401i	0.998995	+	0.0448312i	$0.0142750\pi$
$887$	16.0326	+	27.7693i	0.538322	+	0.932401i	−0.460672	+	0.887570i	$0.652392\pi$
$888$		0			0
$889$	23.3330	+	34.8732i	0.782563	+	1.16961i
$890$		0			0
$891$	5.56900	+	9.64578i	0.186568	+	0.323146i
$892$		0			0
$893$	2.01444	−	3.48912i	0.0674108	−	0.116759i
$894$		0			0
$895$	49.3986			1.65121
$896$		0			0
$897$	−8.00235			−0.267191
$898$		0			0
$899$	26.7442	−	46.3223i	0.891969	−	1.54494i
$900$		0			0
$901$	−15.0767	−	26.1137i	−0.502279	−	0.869973i
$902$		0			0
$903$	7.27824	−	0.481598i	0.242205	−	0.0160266i
$904$		0			0
$905$	21.1723	+	36.6716i	0.703792	+	1.21900i
$906$		0			0
$907$	17.0670	−	29.5608i	0.566699	−	0.981552i	−0.430190	−	0.902738i	$-0.641554\pi$
$907$	17.0670	−	29.5608i	0.566699	−	0.981552i	0.996889	−	0.0788135i	$-0.0251131\pi$
$908$		0			0
$909$	−11.8854			−0.394213
$910$		0			0
$911$	38.8409			1.28686			0.643428	−	0.765507i	$-0.277512\pi$
$911$	38.8409			1.28686			0.643428	+	0.765507i	$0.277512\pi$
$912$		0			0
$913$	−1.85379	+	3.21086i	−0.0613515	+	0.106264i
$914$		0			0
$915$	−34.6491	−	60.0141i	−1.14547	−	1.98400i
$916$		0			0
$917$	0.143832	−	0.292122i	0.00474976	−	0.00964671i
$918$		0			0
$919$	19.6209	+	33.9844i	0.647233	+	1.12104i	0.983781	+	0.179374i	$0.0574073\pi$
$919$	19.6209	+	33.9844i	0.647233	+	1.12104i	−0.336548	+	0.941666i	$0.609259\pi$
$920$		0			0
$921$	−12.5560	+	21.7476i	−0.413733	+	0.716607i
$922$		0			0
$923$	−12.1563			−0.400130
$924$		0			0
$925$	1.16269			0.0382291
$926$		0			0
$927$	−4.55458	+	7.88876i	−0.149592	+	0.259101i
$928$		0			0
$929$	4.95022	+	8.57404i	0.162412	+	0.281305i	0.935733	−	0.352709i	$-0.114739\pi$
$929$	4.95022	+	8.57404i	0.162412	+	0.281305i	−0.773321	+	0.634014i	$0.781406\pi$
$930$		0			0
$931$	25.4526	−	3.38318i	0.834174	−	0.110879i
$932$		0			0
$933$	−4.59856	−	7.96494i	−0.150550	−	0.260760i
$934$		0			0
$935$	−6.10247	+	10.5698i	−0.199572	+	0.345669i
$936$		0			0
$937$	8.37468			0.273589			0.136794	−	0.990599i	$-0.456320\pi$
$937$	8.37468			0.273589			0.136794	+	0.990599i	$0.456320\pi$
$938$		0			0
$939$	2.60053			0.0848652
$940$		0			0
$941$	18.5337	−	32.1014i	0.604183	−	1.04647i	−0.387998	−	0.921660i	$-0.626833\pi$
$941$	18.5337	−	32.1014i	0.604183	−	1.04647i	0.992180	−	0.124814i	$-0.0398336\pi$
$942$		0			0
$943$	0.616788	+	1.06831i	0.0200854	+	0.0347889i
$944$		0			0
$945$	−18.4070	+	37.3844i	−0.598780	+	1.21612i
$946$		0			0
$947$	7.65429	+	13.2576i	0.248731	+	0.430815i	0.963174	−	0.268879i	$-0.0866532\pi$
$947$	7.65429	+	13.2576i	0.248731	+	0.430815i	−0.714443	+	0.699694i	$0.753320\pi$
$948$		0			0
$949$	−1.40850	+	2.43959i	−0.0457218	+	0.0791924i
$950$		0			0
$951$	−41.5785			−1.34828
$952$		0			0
$953$	−10.9482			−0.354646			−0.177323	−	0.984153i	$-0.556744\pi$
$953$	−10.9482			−0.354646			−0.177323	+	0.984153i	$0.556744\pi$
$954$		0			0
$955$	−43.2881	+	74.9772i	−1.40077	+	2.42621i
$956$		0			0
$957$	8.13576	+	14.0915i	0.262992	+	0.455515i
$958$		0			0
$959$	−7.40778	+	0.490170i	−0.239210	+	0.0158284i
$960$		0			0
$961$	−7.00517	−	12.1333i	−0.225973	−	0.391397i
$962$		0			0
$963$	−10.7338	+	18.5915i	−0.345891	+	0.599102i
$964$		0			0
$965$	−18.4842			−0.595029
$966$		0			0
$967$	−30.3952			−0.977443			−0.488722	−	0.872440i	$-0.662537\pi$
$967$	−30.3952			−0.977443			−0.488722	+	0.872440i	$0.662537\pi$
$968$		0			0
$969$	10.8611	−	18.8120i	0.348908	−	0.604327i
$970$		0			0
$971$	−17.2206	−	29.8269i	−0.552634	−	0.957191i	−0.998083	−	0.0618834i	$-0.980289\pi$
$971$	−17.2206	−	29.8269i	−0.552634	−	0.957191i	0.445449	−	0.895307i	$-0.353044\pi$
$972$		0			0
$973$	−25.2585	−	37.7510i	−0.809750	−	1.21024i
$974$		0			0
$975$	9.39696	+	16.2760i	0.300944	+	0.521250i
$976$		0			0
$977$	−18.4375	+	31.9346i	−0.589866	+	1.02168i	0.404383	+	0.914590i	$0.367486\pi$
$977$	−18.4375	+	31.9346i	−0.589866	+	1.02168i	−0.994249	+	0.107089i	$0.965847\pi$
$978$		0			0
$979$	18.7908			0.600557
$980$		0			0
$981$	−17.6041			−0.562055
$982$		0			0
$983$	−5.46531	+	9.46620i	−0.174316	+	0.301925i	−0.939924	−	0.341382i	$-0.889105\pi$
$983$	−5.46531	+	9.46620i	−0.174316	+	0.301925i	0.765608	+	0.643307i	$0.222438\pi$
$984$		0			0
$985$	48.3825	+	83.8010i	1.54160	+	2.67012i
$986$		0			0
$987$	−3.29811	−	4.92932i	−0.104980	−	0.156902i
$988$		0			0
$989$	3.65020	+	6.32233i	0.116070	+	0.201038i
$990$		0			0
$991$	−7.34890	+	12.7287i	−0.233445	+	0.404339i	−0.958820	−	0.284015i	$-0.908333\pi$
$991$	−7.34890	+	12.7287i	−0.233445	+	0.404339i	0.725374	+	0.688355i	$0.241667\pi$
$992$		0			0
$993$	39.0969			1.24070
$994$		0			0
$995$	24.3756			0.772758
$996$		0			0
$997$	23.4494	−	40.6156i	0.742651	−	1.28631i	−0.208633	−	0.977994i	$-0.566901\pi$
$997$	23.4494	−	40.6156i	0.742651	−	1.28631i	0.951284	−	0.308316i	$-0.0997653\pi$
$998$		0			0
$999$	−0.171504	−	0.297053i	−0.00542614	−	0.00939835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.o.529.5		10
4.3	odd	2		616.2.q.f.529.1	yes	10
7.2	even	3	inner	1232.2.q.o.177.5		10
7.3	odd	6		8624.2.a.db.1.5		5
7.4	even	3		8624.2.a.dc.1.1		5
28.3	even	6		4312.2.a.bg.1.1		5
28.11	odd	6		4312.2.a.bf.1.5		5
28.23	odd	6		616.2.q.f.177.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.q.f.177.1	✓	10	28.23	odd	6
616.2.q.f.529.1	yes	10	4.3	odd	2
1232.2.q.o.177.5		10	7.2	even	3	inner
1232.2.q.o.529.5		10	1.1	even	1	trivial
4312.2.a.bf.1.5		5	28.11	odd	6
4312.2.a.bg.1.1		5	28.3	even	6
8624.2.a.db.1.5		5	7.3	odd	6
8624.2.a.dc.1.1		5	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02046 - 1.76748i) q^{3} +(-2.10312 - 3.64271i) q^{5} +(-1.47127 - 2.19895i) q^{7} +(-0.582662 - 1.00920i) q^{9} +O(q^{10})\)	\(q+(1.02046 - 1.76748i) q^{3} +(-2.10312 - 3.64271i) q^{5} +(-1.47127 - 2.19895i) q^{7} +(-0.582662 - 1.00920i) q^{9} +(-0.500000 + 0.866025i) q^{11} +0.725518 q^{13} -8.58456 q^{15} +(-1.45082 + 2.51289i) q^{17} +(-1.83403 - 3.17663i) q^{19} +(-5.38796 + 0.356519i) q^{21} +(-2.70218 - 4.68032i) q^{23} +(-6.34622 + 10.9920i) q^{25} +3.74441 q^{27} +7.97267 q^{29} +(3.35449 - 5.81014i) q^{31} +(1.02046 + 1.76748i) q^{33} +(-4.91586 + 9.98406i) q^{35} +(-0.0458026 - 0.0793324i) q^{37} +(0.740360 - 1.28234i) q^{39} -0.228255 q^{41} -1.35083 q^{43} +(-2.45082 + 4.24494i) q^{45} +(0.549185 + 0.951216i) q^{47} +(-2.67072 + 6.47049i) q^{49} +(2.96099 + 5.12858i) q^{51} +(-5.19595 + 8.99965i) q^{53} +4.20624 q^{55} -7.48619 q^{57} +(-2.22602 + 3.85558i) q^{59} +(4.03621 + 6.99093i) q^{61} +(-1.36192 + 2.76605i) q^{63} +(-1.52585 - 2.64285i) q^{65} +(2.33046 - 4.03647i) q^{67} -11.0298 q^{69} -16.7554 q^{71} +(-1.94137 + 3.36255i) q^{73} +(12.9521 + 22.4336i) q^{75} +(2.63998 - 0.174686i) q^{77} +(2.50475 + 4.33835i) q^{79} +(5.56900 - 9.64578i) q^{81} +3.70758 q^{83} +12.2049 q^{85} +(8.13576 - 14.0915i) q^{87} +(-9.39540 - 16.2733i) q^{89} +(-1.06743 - 1.59537i) q^{91} +(-6.84622 - 11.8580i) q^{93} +(-7.71437 + 13.3617i) q^{95} +13.2198 q^{97} +1.16532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7}+O(q^{10}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7	\( 10 q - q^{3} - 4 q^{5} + 2 q^{7} - 5 q^{11} + 2 q^{13} - 14 q^{15} - 9 q^{17} + q^{19} - 12 q^{21} - 8 q^{23} - 5 q^{25} + 8 q^{27} + 18 q^{29} + 3 q^{31} - q^{33} + 15 q^{35} - 2 q^{37} - 7 q^{39} + 30 q^{41} - 28 q^{43} - 19 q^{45} + 11 q^{47} - 18 q^{49} - 14 q^{51} + 9 q^{53} + 8 q^{55} + 8 q^{57} + 4 q^{59} + 2 q^{61} + 28 q^{63} - 7 q^{65} - 8 q^{67} + 22 q^{69} - 30 q^{71} - 26 q^{73} + 27 q^{75} + 2 q^{77} - 3 q^{79} + 19 q^{81} + 2 q^{83} + 26 q^{85} + 14 q^{87} - 41 q^{89} + 39 q^{91} - 10 q^{93} - 19 q^{95} + 14 q^{97}+O(q^{100}) \) 10 * q - q^3 - 4 * q^5 + 2 * q^7 - 5 * q^11 + 2 * q^13 - 14 * q^15 - 9 * q^17 + q^19 - 12 * q^21 - 8 * q^23 - 5 * q^25 + 8 * q^27 + 18 * q^29 + 3 * q^31 - q^33 + 15 * q^35 - 2 * q^37 - 7 * q^39 + 30 * q^41 - 28 * q^43 - 19 * q^45 + 11 * q^47 - 18 * q^49 - 14 * q^51 + 9 * q^53 + 8 * q^55 + 8 * q^57 + 4 * q^59 + 2 * q^61 + 28 * q^63 - 7 * q^65 - 8 * q^67 + 22 * q^69 - 30 * q^71 - 26 * q^73 + 27 * q^75 + 2 * q^77 - 3 * q^79 + 19 * q^81 + 2 * q^83 + 26 * q^85 + 14 * q^87 - 41 * q^89 + 39 * q^91 - 10 * q^93 - 19 * q^95 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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