LMFDB - Embedded newform 168.6.q.a.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,6,Mod(25,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("168.25");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	168.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.9444817286$
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} - x^{7} + 118x^{6} + 555x^{5} + 12174x^{4} + 28215x^{3} + 199593x^{2} - 283824x + 1679616 $ x^8 - x^7 + 118x^6 + 555x^5 + 12174x^4 + 28215x^3 + 199593x^2 - 283824x + 1679616
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$5.87364 + 10.1734i$ of defining polynomial
Character	$\chi$	$=$	168.121
Dual form			168.6.q.a.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.50000 - 7.79423i) q^{3} +(21.8866 - 37.9086i) q^{5} +(-65.0901 - 112.117i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-4.50000 - 7.79423i) q^{3} +(21.8866 - 37.9086i) q^{5} +(-65.0901 - 112.117i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-167.022 - 289.291i) q^{11} +51.3608 q^{13} -393.958 q^{15} +(-45.1772 - 78.2492i) q^{17} +(127.305 - 220.500i) q^{19} +(-580.962 + 1011.85i) q^{21} +(208.044 - 360.344i) q^{23} +(604.457 + 1046.95i) q^{25} +729.000 q^{27} -3103.97 q^{29} +(37.3099 + 64.6226i) q^{31} +(-1503.20 + 2603.62i) q^{33} +(-5674.81 + 13.6153i) q^{35} +(-2461.48 + 4263.41i) q^{37} +(-231.124 - 400.318i) q^{39} -3568.39 q^{41} -20365.6 q^{43} +(1772.81 + 3070.60i) q^{45} +(-6721.95 + 11642.8i) q^{47} +(-8333.56 + 14595.4i) q^{49} +(-406.595 + 704.243i) q^{51} +(3131.01 + 5423.06i) q^{53} -14622.2 q^{55} -2291.50 q^{57} +(561.308 + 972.214i) q^{59} +(-15309.5 + 26516.9i) q^{61} +(10501.0 - 25.1944i) q^{63} +(1124.11 - 1947.02i) q^{65} +(-30650.3 - 53087.9i) q^{67} -3744.80 q^{69} +6112.32 q^{71} +(-5203.58 - 9012.87i) q^{73} +(5440.11 - 9422.55i) q^{75} +(-21563.0 + 37556.1i) q^{77} +(21611.5 - 37432.2i) q^{79} +(-3280.50 - 5681.99i) q^{81} +25057.7 q^{83} -3955.09 q^{85} +(13967.9 + 24193.0i) q^{87} +(-43209.1 + 74840.3i) q^{89} +(-3343.08 - 5758.43i) q^{91} +(335.789 - 581.604i) q^{93} +(-5572.56 - 9651.96i) q^{95} -59317.2 q^{97} +27057.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{3} + 64 q^{5} + 42 q^{7} - 324 q^{9}+O(q^{10}) $ 8 * q - 36 * q^3 + 64 * q^5 + 42 * q^7 - 324 * q^9	$ 8 q - 36 q^{3} + 64 q^{5} + 42 q^{7} - 324 q^{9} + 70 q^{11} + 1356 q^{13} - 1152 q^{15} + 944 q^{17} + 606 q^{19} + 1512 q^{21} + 648 q^{23} - 2582 q^{25} + 5832 q^{27} - 8720 q^{29} + 4354 q^{31} + 630 q^{33} + 5824 q^{35} + 19302 q^{37} - 6102 q^{39} + 1832 q^{41} + 16788 q^{43} + 5184 q^{45} + 5104 q^{47} - 15484 q^{49} + 8496 q^{51} - 13244 q^{53} + 35744 q^{55} - 10908 q^{57} + 30742 q^{59} - 2428 q^{61} - 17010 q^{63} + 126004 q^{65} - 8258 q^{67} - 11664 q^{69} + 29664 q^{71} - 12758 q^{73} - 23238 q^{75} - 91672 q^{77} + 21382 q^{79} - 26244 q^{81} - 110500 q^{83} + 275960 q^{85} + 39240 q^{87} - 49072 q^{89} - 35658 q^{91} + 39186 q^{93} - 25292 q^{95} - 135228 q^{97} - 11340 q^{99}+O(q^{100}) $ 8 * q - 36 * q^3 + 64 * q^5 + 42 * q^7 - 324 * q^9 + 70 * q^11 + 1356 * q^13 - 1152 * q^15 + 944 * q^17 + 606 * q^19 + 1512 * q^21 + 648 * q^23 - 2582 * q^25 + 5832 * q^27 - 8720 * q^29 + 4354 * q^31 + 630 * q^33 + 5824 * q^35 + 19302 * q^37 - 6102 * q^39 + 1832 * q^41 + 16788 * q^43 + 5184 * q^45 + 5104 * q^47 - 15484 * q^49 + 8496 * q^51 - 13244 * q^53 + 35744 * q^55 - 10908 * q^57 + 30742 * q^59 - 2428 * q^61 - 17010 * q^63 + 126004 * q^65 - 8258 * q^67 - 11664 * q^69 + 29664 * q^71 - 12758 * q^73 - 23238 * q^75 - 91672 * q^77 + 21382 * q^79 - 26244 * q^81 - 110500 * q^83 + 275960 * q^85 + 39240 * q^87 - 49072 * q^89 - 35658 * q^91 + 39186 * q^93 - 25292 * q^95 - 135228 * q^97 - 11340 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$		0			0
$5$	21.8866	−	37.9086i	0.391519	−	0.678130i	−0.601131	−	0.799150i	$-0.705283\pi$
$5$	21.8866	−	37.9086i	0.391519	−	0.678130i	0.992650	+	0.121020i	$0.0386165\pi$
$6$		0			0
$7$	−65.0901	−	112.117i	−0.502076	−	0.864823i
$7$	−65.0901	−	112.117i	−0.502076	−	0.864823i
$8$		0			0
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$		0			0
$11$	−167.022	−	289.291i	−0.416191	−	0.720864i	0.579361	−	0.815071i	$-0.303302\pi$
$11$	−167.022	−	289.291i	−0.416191	−	0.720864i	−0.995553	+	0.0942064i	$0.969969\pi$
$12$		0			0
$13$	51.3608			0.0842895			0.0421447	−	0.999112i	$-0.486581\pi$
$13$	51.3608			0.0842895			0.0421447	+	0.999112i	$0.486581\pi$
$14$		0			0
$15$	−393.958			−0.452087
$16$		0			0
$17$	−45.1772	−	78.2492i	−0.0379138	−	0.0656685i	0.846446	−	0.532475i	$-0.178738\pi$
$17$	−45.1772	−	78.2492i	−0.0379138	−	0.0656685i	−0.884360	+	0.466806i	$0.845405\pi$
$18$		0			0
$19$	127.305	−	220.500i	0.0809027	−	0.140128i	−0.822735	−	0.568425i	$-0.807553\pi$
$19$	127.305	−	220.500i	0.0809027	−	0.140128i	0.903638	+	0.428297i	$0.140886\pi$
$20$		0			0
$21$	−580.962	+	1011.85i	−0.287475	+	0.500691i
$22$		0			0
$23$	208.044	−	360.344i	0.0820043	−	0.142036i	−0.822106	−	0.569334i	$-0.807201\pi$
$23$	208.044	−	360.344i	0.0820043	−	0.142036i	0.904111	+	0.427298i	$0.140535\pi$
$24$		0			0
$25$	604.457	+	1046.95i	0.193426	+	0.335024i
$26$		0			0
$27$	729.000			0.192450
$28$		0			0
$29$	−3103.97			−0.685366			−0.342683	−	0.939451i	$-0.611336\pi$
$29$	−3103.97			−0.685366			−0.342683	+	0.939451i	$0.611336\pi$
$30$		0			0
$31$	37.3099	+	64.6226i	0.00697300	+	0.0120776i	0.869491	−	0.493949i	$-0.164447\pi$
$31$	37.3099	+	64.6226i	0.00697300	+	0.0120776i	−0.862518	+	0.506027i	$0.831114\pi$
$32$		0			0
$33$	−1503.20	+	2603.62i	−0.240288	+	0.416191i
$34$		0			0
$35$	−5674.81	+	13.6153i	−0.783035	+	0.00187869i
$36$		0			0
$37$	−2461.48	+	4263.41i	−0.295592	+	0.511980i	−0.975122	−	0.221667i	$-0.928850\pi$
$37$	−2461.48	+	4263.41i	−0.295592	+	0.511980i	0.679530	+	0.733647i	$0.262184\pi$
$38$		0			0
$39$	−231.124	−	400.318i	−0.0243323	−	0.0421447i
$40$		0			0
$41$	−3568.39			−0.331522			−0.165761	−	0.986166i	$-0.553008\pi$
$41$	−3568.39			−0.331522			−0.165761	+	0.986166i	$0.553008\pi$
$42$		0			0
$43$	−20365.6			−1.67967			−0.839837	−	0.542838i	$-0.817350\pi$
$43$	−20365.6			−1.67967			−0.839837	+	0.542838i	$0.817350\pi$
$44$		0			0
$45$	1772.81	+	3070.60i	0.130506	+	0.226043i
$46$		0			0
$47$	−6721.95	+	11642.8i	−0.443865	+	0.768797i	−0.997972	−	0.0636486i	$-0.979726\pi$
$47$	−6721.95	+	11642.8i	−0.443865	+	0.768797i	0.554107	+	0.832445i	$0.313060\pi$
$48$		0			0
$49$	−8333.56	+	14595.4i	−0.495839	+	0.868415i
$50$		0			0
$51$	−406.595	+	704.243i	−0.0218895	+	0.0379138i
$52$		0			0
$53$	3131.01	+	5423.06i	0.153107	+	0.265189i	0.932368	−	0.361510i	$-0.117739\pi$
$53$	3131.01	+	5423.06i	0.153107	+	0.265189i	−0.779261	+	0.626699i	$0.784405\pi$
$54$		0			0
$55$	−14622.2			−0.651787
$56$		0			0
$57$	−2291.50			−0.0934184
$58$		0			0
$59$	561.308	+	972.214i	0.0209928	+	0.0363607i	0.876331	−	0.481709i	$-0.159984\pi$
$59$	561.308	+	972.214i	0.0209928	+	0.0363607i	−0.855338	+	0.518070i	$0.826651\pi$
$60$		0			0
$61$	−15309.5	+	26516.9i	−0.526790	+	0.912428i	0.472722	+	0.881211i	$0.343271\pi$
$61$	−15309.5	+	26516.9i	−0.526790	+	0.912428i	−0.999513	+	0.0312162i	$0.990062\pi$
$62$		0			0
$63$	10501.0	−	25.1944i	0.333332	−	0.000799746i
$64$		0			0
$65$	1124.11	−	1947.02i	0.0330009	−	0.0571592i
$66$		0			0
$67$	−30650.3	−	53087.9i	−0.834157	−	1.44480i	−0.894715	−	0.446638i	$-0.852621\pi$
$67$	−30650.3	−	53087.9i	−0.834157	−	1.44480i	0.0605570	−	0.998165i	$-0.480712\pi$
$68$		0			0
$69$	−3744.80			−0.0946904
$70$		0			0
$71$	6112.32			0.143900			0.0719499	−	0.997408i	$-0.477078\pi$
$71$	6112.32			0.143900			0.0719499	+	0.997408i	$0.477078\pi$
$72$		0			0
$73$	−5203.58	−	9012.87i	−0.114287	−	0.197950i	0.803208	−	0.595699i	$-0.203125\pi$
$73$	−5203.58	−	9012.87i	−0.114287	−	0.197950i	−0.917494	+	0.397749i	$0.869792\pi$
$74$		0			0
$75$	5440.11	−	9422.55i	0.111675	−	0.193426i
$76$		0			0
$77$	−21563.0	+	37556.1i	−0.414460	+	0.721861i
$78$		0			0
$79$	21611.5	−	37432.2i	0.389598	−	0.674804i	−0.602797	−	0.797895i	$-0.705947\pi$
$79$	21611.5	−	37432.2i	0.389598	−	0.674804i	0.992395	+	0.123090i	$0.0392805\pi$
$80$		0			0
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	25057.7			0.399251			0.199625	−	0.979872i	$-0.436028\pi$
$83$	25057.7			0.399251			0.199625	+	0.979872i	$0.436028\pi$
$84$		0			0
$85$	−3955.09			−0.0593758
$86$		0			0
$87$	13967.9	+	24193.0i	0.197848	+	0.342683i
$88$		0			0
$89$	−43209.1	+	74840.3i	−0.578229	+	1.00152i	0.417453	+	0.908698i	$0.362923\pi$
$89$	−43209.1	+	74840.3i	−0.578229	+	1.00152i	−0.995683	+	0.0928239i	$0.970411\pi$
$90$		0			0
$91$	−3343.08	−	5758.43i	−0.0423197	−	0.0728955i
$92$		0			0
$93$	335.789	−	581.604i	0.00402587	−	0.00697300i
$94$		0			0
$95$	−5572.56	−	9651.96i	−0.0633499	−	0.109725i
$96$		0			0
$97$	−59317.2			−0.640105			−0.320052	−	0.947400i	$-0.603700\pi$
$97$	−59317.2			−0.640105			−0.320052	+	0.947400i	$0.603700\pi$
$98$		0			0
$99$	27057.6			0.277461
$100$		0			0
$101$	18971.6	+	32859.7i	0.185055	+	0.320524i	0.943595	−	0.331102i	$-0.107420\pi$
$101$	18971.6	+	32859.7i	0.185055	+	0.320524i	−0.758540	+	0.651626i	$0.774087\pi$
$102$		0			0
$103$	61903.9	−	107221.i	0.574943	−	0.995830i	−0.421105	−	0.907012i	$-0.638358\pi$
$103$	61903.9	−	107221.i	0.574943	−	0.995830i	0.996048	−	0.0888184i	$-0.0283091\pi$
$104$		0			0
$105$	25642.8	+	44169.5i	0.226982	+	0.390975i
$106$		0			0
$107$	60880.3	−	105448.i	0.514064	−	0.890385i	−0.485803	−	0.874068i	$-0.661473\pi$
$107$	60880.3	−	105448.i	0.514064	−	0.890385i	0.999867	−	0.0163163i	$-0.00519388\pi$
$108$		0			0
$109$	−23898.2	−	41392.8i	−0.192663	−	0.333702i	0.753469	−	0.657484i	$-0.228379\pi$
$109$	−23898.2	−	41392.8i	−0.192663	−	0.333702i	−0.946132	+	0.323781i	$0.895046\pi$
$110$		0			0
$111$	44306.7			0.341320
$112$		0			0
$113$	158165.			1.16523			0.582617	−	0.812747i	$-0.302029\pi$
$113$	158165.			1.16523			0.582617	+	0.812747i	$0.302029\pi$
$114$		0			0
$115$	−9106.76	−	15773.4i	−0.0642124	−	0.111219i
$116$		0			0
$117$	−2080.11	+	3602.86i	−0.0140482	+	0.0243323i
$118$		0			0
$119$	−5832.50	+	10158.4i	−0.0377561	+	0.0657593i
$120$		0			0
$121$	24732.6	−	42838.1i	0.153570	−	0.265991i
$122$		0			0
$123$	16057.7	+	27812.8i	0.0957021	+	0.165761i
$124$		0			0
$125$	189709.			1.08596
$126$		0			0
$127$	−887.264			−0.00488139			−0.00244070	−	0.999997i	$-0.500777\pi$
$127$	−887.264			−0.00488139			−0.00244070	+	0.999997i	$0.500777\pi$
$128$		0			0
$129$	91645.0	+	158734.i	0.484880	+	0.839837i
$130$		0			0
$131$	152395.	−	263956.i	0.775877	−	1.34386i	−0.158424	−	0.987371i	$-0.550641\pi$
$131$	152395.	−	263956.i	0.775877	−	1.34386i	0.934300	−	0.356487i	$-0.116025\pi$
$132$		0			0
$133$	−33008.1	+	79.1946i	−0.161805	+	0.000388210i
$134$		0			0
$135$	15955.3	−	27635.4i	0.0753478	−	0.130506i
$136$		0			0
$137$	191249.	+	331254.i	0.870559	+	1.50785i	0.861419	+	0.507895i	$0.169576\pi$
$137$	191249.	+	331254.i	0.870559	+	1.50785i	0.00914050	+	0.999958i	$0.497090\pi$
$138$		0			0
$139$	−256870.			−1.12765			−0.563827	−	0.825893i	$-0.690672\pi$
$139$	−256870.			−1.12765			−0.563827	+	0.825893i	$0.690672\pi$
$140$		0			0
$141$	120995.			0.512531
$142$		0			0
$143$	−8578.40	−	14858.2i	−0.0350805	−	0.0607613i
$144$		0			0
$145$	−67935.2	+	117667.i	−0.268334	+	0.464767i
$146$		0			0
$147$	151261.	−	725.830i	0.577344	−	0.00277039i
$148$		0			0
$149$	218803.	−	378978.i	0.807398	−	1.39845i	−0.107263	−	0.994231i	$-0.534209\pi$
$149$	218803.	−	378978.i	0.807398	−	1.39845i	0.914661	−	0.404223i	$-0.132458\pi$
$150$		0			0
$151$	−123625.	−	214124.i	−0.441227	−	0.764228i	0.556554	−	0.830812i	$-0.312123\pi$
$151$	−123625.	−	214124.i	−0.441227	−	0.764228i	−0.997781	+	0.0665837i	$0.978790\pi$
$152$		0			0
$153$	7318.70			0.0252758
$154$		0			0
$155$	3266.34			0.0109202
$156$		0			0
$157$	−143559.	−	248652.i	−0.464817	−	0.805086i	0.534377	−	0.845247i	$-0.320546\pi$
$157$	−143559.	−	248652.i	−0.464817	−	0.805086i	−0.999193	+	0.0401604i	$0.987213\pi$
$158$		0			0
$159$	28179.1	−	48807.6i	0.0883962	−	0.153107i
$160$		0			0
$161$	−53942.4	+	129.421i	−0.164008	+	0.000393496i
$162$		0			0
$163$	207591.	−	359558.i	0.611983	−	1.05999i	−0.378923	−	0.925428i	$-0.623705\pi$
$163$	207591.	−	359558.i	0.611983	−	1.05999i	0.990906	−	0.134558i	$-0.0429613\pi$
$164$		0			0
$165$	65799.8	+	113969.i	0.188155	+	0.325893i
$166$		0			0
$167$	−460536.			−1.27783			−0.638914	−	0.769278i	$-0.720616\pi$
$167$	−460536.			−1.27783			−0.638914	+	0.769278i	$0.720616\pi$
$168$		0			0
$169$	−368655.			−0.992895
$170$		0			0
$171$	10311.7	+	17860.5i	0.0269676	+	0.0467092i
$172$		0			0
$173$	86491.7	−	149808.i	0.219715	−	0.380557i	−0.735006	−	0.678061i	$-0.762821\pi$
$173$	86491.7	−	149808.i	0.219715	−	0.380557i	0.954721	+	0.297504i	$0.0961540\pi$
$174$		0			0
$175$	78037.0	−	135916.i	0.192622	−	0.335487i
$176$		0			0
$177$	5051.77	−	8749.92i	0.0121202	−	0.0209928i
$178$		0			0
$179$	335711.	+	581468.i	0.783128	+	1.35642i	0.930111	+	0.367279i	$0.119710\pi$
$179$	335711.	+	581468.i	0.783128	+	1.35642i	−0.146983	+	0.989139i	$0.546956\pi$
$180$		0			0
$181$	−436870.			−0.991187			−0.495594	−	0.868555i	$-0.665049\pi$
$181$	−436870.			−0.991187			−0.495594	+	0.868555i	$0.665049\pi$
$182$		0			0
$183$	275572.			0.608285
$184$		0			0
$185$	107747.	+	186623.i	0.231460	+	0.400900i
$186$		0			0
$187$	−15091.2	+	26138.7i	−0.0315587	+	0.0546613i
$188$		0			0
$189$	−47450.7	−	81733.5i	−0.0966246	−	0.166435i
$190$		0			0
$191$	−343882.	+	595622.i	−0.682066	+	1.18137i	0.292283	+	0.956332i	$0.405585\pi$
$191$	−343882.	+	595622.i	−0.682066	+	1.18137i	−0.974349	+	0.225041i	$0.927748\pi$
$192$		0			0
$193$	−127984.	−	221676.i	−0.247323	−	0.428375i	0.715459	−	0.698654i	$-0.246217\pi$
$193$	−127984.	−	221676.i	−0.247323	−	0.428375i	−0.962782	+	0.270279i	$0.912884\pi$
$194$		0			0
$195$	−20234.0			−0.0381062
$196$		0			0
$197$	−141432.			−0.259647			−0.129824	−	0.991537i	$-0.541441\pi$
$197$	−141432.			−0.259647			−0.129824	+	0.991537i	$0.541441\pi$
$198$		0			0
$199$	109813.	+	190201.i	0.196571	+	0.340472i	0.947415	−	0.320009i	$-0.103686\pi$
$199$	109813.	+	190201.i	0.196571	+	0.340472i	−0.750843	+	0.660481i	$0.770353\pi$
$200$		0			0
$201$	−275853.	+	477791.i	−0.481601	+	0.834157i
$202$		0			0
$203$	202038.	+	348009.i	0.344106	+	0.592720i
$204$		0			0
$205$	−78099.7	+	135273.i	−0.129797	+	0.224815i
$206$		0			0
$207$	16851.6	+	29187.8i	0.0273348	+	0.0473452i
$208$		0			0
$209$	−85051.5			−0.134684
$210$		0			0
$211$	−83847.8			−0.129654			−0.0648270	−	0.997897i	$-0.520650\pi$
$211$	−83847.8			−0.129654			−0.0648270	+	0.997897i	$0.520650\pi$
$212$		0			0
$213$	−27505.4	−	47640.8i	−0.0415403	−	0.0719499i
$214$		0			0
$215$	−445732.	+	772030.i	−0.657624	+	1.13904i
$216$		0			0
$217$	4816.81	−	8389.38i	0.00694401	−	0.0120943i
$218$		0			0
$219$	−46832.3	+	81115.8i	−0.0659834	+	0.114287i
$220$		0			0
$221$	−2320.34	−	4018.94i	−0.00319573	−	0.00553517i
$222$		0			0
$223$	−1.35948e6			−1.83067			−0.915334	−	0.402696i	$-0.868073\pi$
$223$	−1.35948e6			−1.83067			−0.915334	+	0.402696i	$0.868073\pi$
$224$		0			0
$225$	−97922.0			−0.128951
$226$		0			0
$227$	39.6650	+	68.7017i	5.10908e−5	+	8.84918e-5i	0.866051	−	0.499956i	$-0.166650\pi$
$227$	39.6650	+	68.7017i	5.10908e−5	+	8.84918e-5i	−0.866000	+	0.500044i	$0.833317\pi$
$228$		0			0
$229$	−313520.	+	543033.i	−0.395073	+	0.684286i	−0.993110	−	0.117182i	$-0.962614\pi$
$229$	−313520.	+	543033.i	−0.395073	+	0.684286i	0.598038	+	0.801468i	$0.295947\pi$
$230$		0			0
$231$	389754.	−	935.116i	0.480575	−	0.00115302i
$232$		0			0
$233$	437020.	−	756941.i	0.527365	−	0.913423i	−0.472126	−	0.881531i	$-0.656513\pi$
$233$	437020.	−	756941.i	0.527365	−	0.913423i	0.999491	−	0.0318924i	$-0.0101534\pi$
$234$		0			0
$235$	294241.	+	509640.i	0.347563	+	0.601996i
$236$		0			0
$237$	−389007.			−0.449870
$238$		0			0
$239$	−1.24472e6			−1.40954			−0.704768	−	0.709438i	$-0.748949\pi$
$239$	−1.24472e6			−1.40954			−0.704768	+	0.709438i	$0.748949\pi$
$240$		0			0
$241$	−829806.	−	1.43727e6i	−0.920310	−	1.59402i	−0.798935	−	0.601417i	$-0.794603\pi$
$241$	−829806.	−	1.43727e6i	−0.920310	−	1.59402i	−0.121375	−	0.992607i	$-0.538730\pi$
$242$		0			0
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	370900.	+	635358.i	0.394768	+	0.676244i
$246$		0			0
$247$	6538.51	−	11325.0i	0.00681925	−	0.0118113i
$248$		0			0
$249$	−112760.	−	195305.i	−0.115254	−	0.199625i
$250$		0			0
$251$	−683674.			−0.684959			−0.342479	−	0.939525i	$-0.611267\pi$
$251$	−683674.			−0.684959			−0.342479	+	0.939525i	$0.611267\pi$
$252$		0			0
$253$	−138992.			−0.136518
$254$		0			0
$255$	17797.9	+	30826.9i	0.0171403	+	0.0296879i
$256$		0			0
$257$	796279.	−	1.37920e6i	0.752026	−	1.30255i	−0.194814	−	0.980840i	$-0.562410\pi$
$257$	796279.	−	1.37920e6i	0.752026	−	1.30255i	0.946839	−	0.321706i	$-0.104256\pi$
$258$		0			0
$259$	638221.	−	1531.25i	0.591182	−	0.00141839i
$260$		0			0
$261$	125711.	−	217737.i	0.114228	−	0.197848i
$262$		0			0
$263$	368365.	+	638026.i	0.328389	+	0.568786i	0.982192	−	0.187878i	$-0.0601610\pi$
$263$	368365.	+	638026.i	0.328389	+	0.568786i	−0.653803	+	0.756664i	$0.726828\pi$
$264$		0			0
$265$	274108.			0.239777
$266$		0			0
$267$	777763.			0.667682
$268$		0			0
$269$	−782085.	−	1.35461e6i	−0.658981	−	1.14139i	−0.980880	−	0.194615i	$-0.937654\pi$
$269$	−782085.	−	1.35461e6i	−0.658981	−	1.14139i	0.321899	−	0.946774i	$-0.395679\pi$
$270$		0			0
$271$	−817767.	+	1.41641e6i	−0.676404	+	1.17157i	0.299652	+	0.954048i	$0.403129\pi$
$271$	−817767.	+	1.41641e6i	−0.676404	+	1.17157i	−0.976056	+	0.217518i	$0.930204\pi$
$272$		0			0
$273$	−29838.7	+	51969.7i	−0.0242311	+	0.0422030i
$274$		0			0
$275$	201916.	−	349728.i	0.161005	−	0.278868i
$276$		0			0
$277$	113434.	+	196473.i	0.0888264	+	0.153852i	0.907015	−	0.421098i	$-0.138355\pi$
$277$	113434.	+	196473.i	0.0888264	+	0.153852i	−0.818189	+	0.574949i	$0.805022\pi$
$278$		0			0
$279$	−6044.20			−0.00464867
$280$		0			0
$281$	−583971.			−0.441190			−0.220595	−	0.975366i	$-0.570800\pi$
$281$	−583971.			−0.441190			−0.220595	+	0.975366i	$0.570800\pi$
$282$		0			0
$283$	41952.8	+	72664.4i	0.0311383	+	0.0539332i	0.881175	−	0.472791i	$-0.156753\pi$
$283$	41952.8	+	72664.4i	0.0311383	+	0.0539332i	−0.850036	+	0.526724i	$0.823420\pi$
$284$		0			0
$285$	−50153.0	+	86867.6i	−0.0365751	+	0.0633499i
$286$		0			0
$287$	232267.	+	400078.i	0.166449	+	0.286708i
$288$		0			0
$289$	705847.	−	1.22256e6i	0.497125	−	0.861046i
$290$		0			0
$291$	266927.	+	462331.i	0.184782	+	0.320052i
$292$		0			0
$293$	1.25224e6			0.852153			0.426076	−	0.904687i	$-0.359895\pi$
$293$	1.25224e6			0.852153			0.426076	+	0.904687i	$0.359895\pi$
$294$		0			0
$295$	49140.4			0.0328763
$296$		0			0
$297$	−121759.	−	210893.i	−0.0800960	−	0.138730i
$298$		0			0
$299$	10685.3	−	18507.5i	0.00691210	−	0.0119721i
$300$		0			0
$301$	1.32560e6	+	2.28333e6i	0.843325	+	1.45262i
$302$		0			0
$303$	170744.	−	295737.i	0.106841	−	0.185055i
$304$		0			0
$305$	670147.	+	1.16073e6i	0.412497	+	0.714465i
$306$		0			0
$307$	2.47937e6			1.50140			0.750699	−	0.660645i	$-0.229717\pi$
$307$	2.47937e6			1.50140			0.750699	+	0.660645i	$0.229717\pi$
$308$		0			0
$309$	−1.11427e6			−0.663887
$310$		0			0
$311$	−790296.	−	1.36883e6i	−0.463329	−	0.802509i	0.535796	−	0.844348i	$-0.320012\pi$
$311$	−790296.	−	1.36883e6i	−0.463329	−	0.802509i	−0.999124	+	0.0418390i	$0.986678\pi$
$312$		0			0
$313$	−56967.7	+	98670.9i	−0.0328676	+	0.0569283i	−0.881991	−	0.471266i	$-0.843797\pi$
$313$	−56967.7	+	98670.9i	−0.0328676	+	0.0569283i	0.849124	+	0.528194i	$0.177131\pi$
$314$		0			0
$315$	228875.	−	398628.i	0.129964	−	0.226356i
$316$		0			0
$317$	1.34397e6	−	2.32783e6i	0.751176	−	1.30108i	−0.196077	−	0.980589i	$-0.562820\pi$
$317$	1.34397e6	−	2.32783e6i	0.751176	−	1.30108i	0.947253	−	0.320487i	$-0.103847\pi$
$318$		0			0
$319$	518432.	+	897951.i	0.285243	+	0.494056i
$320$		0			0
$321$	−1.09584e6			−0.593590
$322$		0			0
$323$	−23005.2			−0.0122693
$324$		0			0
$325$	31045.4	+	53772.2i	0.0163038	+	0.0282390i
$326$		0			0
$327$	−215083.	+	372536.i	−0.111234	+	0.192663i
$328$		0			0
$329$	1.74289e6	−	4181.61i	0.887727	−	0.00212987i
$330$		0			0
$331$	1.83147e6	−	3.17219e6i	0.918816	−	1.59144i	0.117601	−	0.993061i	$-0.462480\pi$
$331$	1.83147e6	−	3.17219e6i	0.918816	−	1.59144i	0.801216	−	0.598376i	$-0.204187\pi$
$332$		0			0
$333$	−199380.	−	345337.i	−0.0985307	−	0.170660i
$334$		0			0
$335$	−2.68332e6			−1.30635
$336$		0			0
$337$	431607.			0.207021			0.103510	−	0.994628i	$-0.466993\pi$
$337$	431607.			0.207021			0.103510	+	0.994628i	$0.466993\pi$
$338$		0			0
$339$	−711741.	−	1.23277e6i	−0.336374	−	0.582617i
$340$		0			0
$341$	12463.2	−	21586.9i	0.00580421	−	0.0100532i
$342$		0			0
$343$	2.17883e6	−	15682.9i	0.999974	−	0.00719766i
$344$		0			0
$345$	−81960.8	+	141960.i	−0.0370731	+	0.0642124i
$346$		0			0
$347$	171029.	+	296231.i	0.0762511	+	0.132071i	0.901630	−	0.432509i	$-0.142372\pi$
$347$	171029.	+	296231.i	0.0762511	+	0.132071i	−0.825379	+	0.564580i	$0.809038\pi$
$348$		0			0
$349$	827018.			0.363456			0.181728	−	0.983349i	$-0.441831\pi$
$349$	827018.			0.363456			0.181728	+	0.983349i	$0.441831\pi$
$350$		0			0
$351$	37442.0			0.0162215
$352$		0			0
$353$	−133454.	−	231149.i	−0.0570026	−	0.0987314i	0.836116	−	0.548553i	$-0.184821\pi$
$353$	−133454.	−	231149.i	−0.0570026	−	0.0987314i	−0.893119	+	0.449821i	$0.851488\pi$
$354$		0			0
$355$	133778.	−	231710.i	0.0563394	−	0.0975828i
$356$		0			0
$357$	105423.	−	252.936i	0.0437789	−	0.000105036i
$358$		0			0
$359$	−124401.	+	215469.i	−0.0509434	+	0.0882366i	−0.890373	−	0.455232i	$-0.849556\pi$
$359$	−124401.	+	215469.i	−0.0509434	+	0.0882366i	0.839429	+	0.543469i	$0.182889\pi$
$360$		0			0
$361$	1.20564e6	+	2.08822e6i	0.486909	+	0.843352i
$362$		0			0
$363$	−445186.			−0.177327
$364$		0			0
$365$	−455554.			−0.178981
$366$		0			0
$367$	329673.	+	571010.i	0.127767	+	0.221299i	0.922811	−	0.385253i	$-0.125886\pi$
$367$	329673.	+	571010.i	0.127767	+	0.221299i	−0.795044	+	0.606551i	$0.792552\pi$
$368$		0			0
$369$	144520.	−	250315.i	0.0552536	−	0.0957021i
$370$		0			0
$371$	404221.	−	704028.i	0.152470	−	0.265555i
$372$		0			0
$373$	199710.	−	345907.i	0.0743236	−	0.128732i	−0.826468	−	0.562983i	$-0.809654\pi$
$373$	199710.	−	345907.i	0.0743236	−	0.128732i	0.900792	+	0.434251i	$0.142987\pi$
$374$		0			0
$375$	−853690.	−	1.47863e6i	−0.313489	−	0.542979i
$376$		0			0
$377$	−159422.			−0.0577691
$378$		0			0
$379$	3.42582e6			1.22509			0.612543	−	0.790437i	$-0.290147\pi$
$379$	3.42582e6			1.22509			0.612543	+	0.790437i	$0.290147\pi$
$380$		0			0
$381$	3992.69	+	6915.54i	0.00140914	+	0.00244070i
$382$		0			0
$383$	−2.34375e6	+	4.05949e6i	−0.816421	+	1.41408i	0.0918822	+	0.995770i	$0.470712\pi$
$383$	−2.34375e6	+	4.05949e6i	−0.816421	+	1.41408i	−0.908303	+	0.418313i	$0.862622\pi$
$384$		0			0
$385$	951759.	+	1.63940e6i	0.327247	+	0.563680i
$386$		0			0
$387$	824805.	−	1.42860e6i	0.279946	−	0.484880i
$388$		0			0
$389$	660449.	+	1.14393e6i	0.221292	+	0.383289i	0.955201	−	0.295959i	$-0.0956393\pi$
$389$	660449.	+	1.14393e6i	0.221292	+	0.383289i	−0.733909	+	0.679248i	$0.762306\pi$
$390$		0			0
$391$	−37595.4			−0.0124364
$392$		0			0
$393$	−2.74311e6			−0.895905
$394$		0			0
$395$	−946003.	−	1.63853e6i	−0.305070	−	0.528397i
$396$		0			0
$397$	146821.	−	254301.i	0.0467531	−	0.0809788i	−0.841702	−	0.539943i	$-0.818446\pi$
$397$	146821.	−	254301.i	0.0467531	−	0.0809788i	0.888455	+	0.458964i	$0.151779\pi$
$398$		0			0
$399$	149154.	+	256917.i	0.0469032	+	0.0807904i
$400$		0			0
$401$	1.41600e6	−	2.45258e6i	0.439745	−	0.761661i	−0.557925	−	0.829892i	$-0.688402\pi$
$401$	1.41600e6	−	2.45258e6i	0.439745	−	0.761661i	0.997670	+	0.0682310i	$0.0217355\pi$
$402$		0			0
$403$	1916.27	+	3319.07i	0.000587751	+	0.00101801i
$404$		0			0
$405$	−287195.			−0.0870042
$406$		0			0
$407$	1.64449e6			0.492091
$408$		0			0
$409$	379369.	+	657086.i	0.112138	+	0.194229i	0.916632	−	0.399732i	$-0.130897\pi$
$409$	379369.	+	657086.i	0.112138	+	0.194229i	−0.804494	+	0.593961i	$0.797563\pi$
$410$		0			0
$411$	1.72124e6	−	2.98128e6i	0.502618	−	0.870559i
$412$		0			0
$413$	72466.4	−	126214.i	0.0209055	−	0.0364109i
$414$		0			0
$415$	548426.	−	949902.i	0.156314	−	0.270744i
$416$		0			0
$417$	1.15591e6	+	2.00210e6i	0.325526	+	0.563827i
$418$		0			0
$419$	−5.52140e6			−1.53643			−0.768217	−	0.640190i	$-0.778856\pi$
$419$	−5.52140e6			−1.53643			−0.768217	+	0.640190i	$0.778856\pi$
$420$		0			0
$421$	−2.49511e6			−0.686095			−0.343047	−	0.939318i	$-0.611459\pi$
$421$	−2.49511e6			−0.686095			−0.343047	+	0.939318i	$0.611459\pi$
$422$		0			0
$423$	−544478.	−	943064.i	−0.147955	−	0.256266i
$424$		0			0
$425$	54615.3	−	94596.5i	0.0146670	−	0.0254040i
$426$		0			0
$427$	3.96950e6	−	9523.81i	1.05358	−	0.00252779i
$428$		0			0
$429$	−77205.6	+	133724.i	−0.0202538	+	0.0350805i
$430$		0			0
$431$	−1.27016e6	−	2.19999e6i	−0.329357	−	0.570463i	0.653028	−	0.757334i	$-0.273499\pi$
$431$	−1.27016e6	−	2.19999e6i	−0.329357	−	0.570463i	−0.982384	+	0.186871i	$0.940165\pi$
$432$		0			0
$433$	−5.61890e6			−1.44023			−0.720114	−	0.693855i	$-0.755911\pi$
$433$	−5.61890e6			−1.44023			−0.720114	+	0.693855i	$0.755911\pi$
$434$		0			0
$435$	1.22283e6			0.309845
$436$		0			0
$437$	−52970.4	−	91747.4i	−0.0132687	−	0.0229821i
$438$		0			0
$439$	−1.88879e6	+	3.27147e6i	−0.467758	+	0.810181i	−0.999321	−	0.0368379i	$-0.988271\pi$
$439$	−1.88879e6	+	3.27147e6i	−0.467758	+	0.810181i	0.531563	+	0.847019i	$0.321605\pi$
$440$		0			0
$441$	−686333.	−	1.17570e6i	−0.168050	−	0.287872i
$442$		0			0
$443$	1.79882e6	−	3.11565e6i	0.435491	−	0.754292i	−0.561845	−	0.827243i	$-0.689908\pi$
$443$	1.79882e6	−	3.11565e6i	0.435491	−	0.754292i	0.997336	+	0.0729505i	$0.0232415\pi$
$444$		0			0
$445$	1.89140e6	+	3.27599e6i	0.452775	+	0.784229i
$446$		0			0
$447$	−3.93845e6			−0.932302
$448$		0			0
$449$	−2.97694e6			−0.696873			−0.348437	−	0.937332i	$-0.613287\pi$
$449$	−2.97694e6			−0.696873			−0.348437	+	0.937332i	$0.613287\pi$
$450$		0			0
$451$	596000.	+	1.03230e6i	0.137976	+	0.238982i
$452$		0			0
$453$	−1.11262e6	+	1.92712e6i	−0.254743	+	0.441227i
$454$		0			0
$455$	−291463.	+	699.291i	−0.0660016	+	0.000158354i
$456$		0			0
$457$	−539924.	+	935176.i	−0.120932	+	0.209461i	−0.920136	−	0.391600i	$-0.871922\pi$
$457$	−539924.	+	935176.i	−0.120932	+	0.209461i	0.799203	+	0.601061i	$0.205255\pi$
$458$		0			0
$459$	−32934.2	−	57043.6i	−0.00729651	−	0.0126379i
$460$		0			0
$461$	−5.35905e6			−1.17445			−0.587226	−	0.809423i	$-0.699780\pi$
$461$	−5.35905e6			−1.17445			−0.587226	+	0.809423i	$0.699780\pi$
$462$		0			0
$463$	−5.63745e6			−1.22217			−0.611083	−	0.791567i	$-0.709266\pi$
$463$	−5.63745e6			−1.22217			−0.611083	+	0.791567i	$0.709266\pi$
$464$		0			0
$465$	−14698.5	−	25458.6i	−0.00315240	−	0.00546012i
$466$		0			0
$467$	−789613.	+	1.36765e6i	−0.167541	+	0.290190i	−0.937555	−	0.347837i	$-0.886916\pi$
$467$	−789613.	+	1.36765e6i	−0.167541	+	0.290190i	0.770013	+	0.638028i	$0.220249\pi$
$468$		0			0
$469$	−3.95704e6	+	6.89193e6i	−0.830689	+	1.44680i
$470$		0			0
$471$	−1.29203e6	+	2.23787e6i	−0.268362	+	0.464817i
$472$		0			0
$473$	3.40150e6	+	5.89158e6i	0.699066	+	1.21082i
$474$		0			0
$475$	307803.			0.0625948
$476$		0			0
$477$	−507223.			−0.102071
$478$		0			0
$479$	−1.41132e6	−	2.44448e6i	−0.281053	−	0.486797i	0.690592	−	0.723245i	$-0.257350\pi$
$479$	−1.41132e6	−	2.44448e6i	−0.281053	−	0.486797i	−0.971644	+	0.236447i	$0.924017\pi$
$480$		0			0
$481$	−126424.	+	218972.i	−0.0249153	+	0.0431545i
$482$		0			0
$483$	243749.	+	419857.i	0.0475418	+	0.0818905i
$484$		0			0
$485$	−1.29825e6	+	2.24863e6i	−0.250613	+	0.434074i
$486$		0			0
$487$	−232457.	−	402627.i	−0.0444140	−	0.0769273i	0.842964	−	0.537970i	$-0.180809\pi$
$487$	−232457.	−	402627.i	−0.0444140	−	0.0769273i	−0.887378	+	0.461043i	$0.847475\pi$
$488$		0			0
$489$	−3.73664e6			−0.706657
$490$		0			0
$491$	5.75237e6			1.07682			0.538410	−	0.842683i	$-0.319025\pi$
$491$	5.75237e6			1.07682			0.538410	+	0.842683i	$0.319025\pi$
$492$		0			0
$493$	140229.	+	242883.i	0.0259848	+	0.0450070i
$494$		0			0
$495$	592198.	−	1.02572e6i	0.108631	−	0.188155i
$496$		0			0
$497$	−397851.	−	685296.i	−0.0722486	−	0.124448i
$498$		0			0
$499$	2.25961e6	−	3.91376e6i	0.406240	−	0.703628i	−0.588225	−	0.808697i	$-0.700173\pi$
$499$	2.25961e6	−	3.91376e6i	0.406240	−	0.703628i	0.994465	+	0.105069i	$0.0335064\pi$
$500$		0			0
$501$	2.07241e6	+	3.58952e6i	0.368877	+	0.638914i
$502$		0			0
$503$	−9.11694e6			−1.60668			−0.803340	−	0.595521i	$-0.796946\pi$
$503$	−9.11694e6			−1.60668			−0.803340	+	0.595521i	$0.796946\pi$
$504$		0			0
$505$	1.66089e6			0.289809
$506$		0			0
$507$	1.65895e6	+	2.87338e6i	0.286624	+	0.496448i
$508$		0			0
$509$	1564.91	−	2710.50i	0.000267729	−	0.000463719i	−0.865892	−	0.500232i	$-0.833248\pi$
$509$	1564.91	−	2710.50i	0.000267729	−	0.000463719i	0.866159	+	0.499768i	$0.166581\pi$
$510$		0			0
$511$	−671797.	+	1.17006e6i	−0.113811	+	0.198224i
$512$		0			0
$513$	92805.7	−	160744.i	0.0155697	−	0.0269676i
$514$		0			0
$515$	−2.70973e6	−	4.69338e6i	−0.450202	−	0.779772i
$516$		0			0
$517$	4.49087e6			0.738931
$518$		0			0
$519$	−1.55685e6			−0.253705
$520$		0			0
$521$	1.82812e6	+	3.16640e6i	0.295060	+	0.511059i	0.974999	−	0.222210i	$-0.0713271\pi$
$521$	1.82812e6	+	3.16640e6i	0.295060	+	0.511059i	−0.679939	+	0.733269i	$0.737994\pi$
$522$		0			0
$523$	−1.16664e6	+	2.02069e6i	−0.186502	+	0.323031i	−0.944082	−	0.329712i	$-0.893048\pi$
$523$	−1.16664e6	+	2.02069e6i	−0.186502	+	0.323031i	0.757580	+	0.652743i	$0.226382\pi$
$524$		0			0
$525$	−1.41053e6	+	3384.20i	−0.223349	+	0.000535868i
$526$		0			0
$527$	3371.11	−	5838.94i	0.000528745	−	0.000915814i
$528$		0			0
$529$	3.13161e6	+	5.42410e6i	0.486551	+	0.842730i
$530$		0			0
$531$	−90931.9			−0.0139952
$532$		0			0
$533$	−183275.			−0.0279438
$534$		0			0
$535$	−2.66492e6	−	4.61578e6i	−0.402531	−	0.697205i
$536$		0			0
$537$	3.02140e6	−	5.23321e6i	0.452139	−	0.783128i
$538$		0			0
$539$	5.61422e6	−	26940.0i	0.832373	−	0.00399416i
$540$		0			0
$541$	4.23089e6	−	7.32811e6i	0.621496	−	1.07646i	−0.367712	−	0.929940i	$-0.619859\pi$
$541$	4.23089e6	−	7.32811e6i	0.621496	−	1.07646i	0.989207	−	0.146522i	$-0.0468081\pi$
$542$		0			0
$543$	1.96591e6	+	3.40506e6i	0.286131	+	0.495594i
$544$		0			0
$545$	−2.09219e6			−0.301725
$546$		0			0
$547$	−584951.			−0.0835893			−0.0417947	−	0.999126i	$-0.513308\pi$
$547$	−584951.			−0.0835893			−0.0417947	+	0.999126i	$0.513308\pi$
$548$		0			0
$549$	−1.24007e6	−	2.14787e6i	−0.175597	−	0.304143i
$550$		0			0
$551$	−395152.	+	684424.i	−0.0554480	+	0.0960387i
$552$		0			0
$553$	−5.60349e6	+	13444.2i	−0.779195	+	0.00186948i
$554$		0			0
$555$	969722.	−	1.67961e6i	0.133633	−	0.231460i
$556$		0			0
$557$	617407.	+	1.06938e6i	0.0843206	+	0.146048i	0.905101	−	0.425196i	$-0.139795\pi$
$557$	617407.	+	1.06938e6i	0.0843206	+	0.146048i	−0.820781	+	0.571243i	$0.806461\pi$
$558$		0			0
$559$	−1.04599e6			−0.141579
$560$		0			0
$561$	271642.			0.0364409
$562$		0			0
$563$	4.70627e6	+	8.15150e6i	0.625757	+	1.08384i	0.988394	+	0.151913i	$0.0485433\pi$
$563$	4.70627e6	+	8.15150e6i	0.625757	+	1.08384i	−0.362636	+	0.931931i	$0.618123\pi$
$564$		0			0
$565$	3.46168e6	−	5.99580e6i	0.456211	−	0.790180i
$566$		0			0
$567$	−423521.	+	737642.i	−0.0553245	+	0.0963581i
$568$		0			0
$569$	−360053.	+	623630.i	−0.0466215	+	0.0807508i	−0.888394	−	0.459081i	$-0.848179\pi$
$569$	−360053.	+	623630.i	−0.0466215	+	0.0807508i	0.841773	+	0.539832i	$0.181512\pi$
$570$		0			0
$571$	−6.18233e6	−	1.07081e7i	−0.793528	−	1.37443i	−0.923770	−	0.382948i	$-0.874909\pi$
$571$	−6.18233e6	−	1.07081e7i	−0.793528	−	1.37443i	0.130242	−	0.991482i	$-0.458425\pi$
$572$		0			0
$573$	6.18988e6			0.787582
$574$		0			0
$575$	503015.			0.0634471
$576$		0			0
$577$	−2.95903e6	−	5.12519e6i	−0.370007	−	0.640871i	0.619559	−	0.784950i	$-0.287311\pi$
$577$	−2.95903e6	−	5.12519e6i	−0.370007	−	0.640871i	−0.989566	+	0.144079i	$0.953978\pi$
$578$		0			0
$579$	−1.15186e6	+	1.99508e6i	−0.142792	+	0.247323i
$580$		0			0
$581$	−1.63101e6	−	2.80940e6i	−0.200454	−	0.345281i
$582$		0			0
$583$	1.04590e6	−	1.81155e6i	0.127443	−	0.220738i
$584$		0			0
$585$	91053.0	+	157708.i	0.0110003	+	0.0190531i
$586$		0			0
$587$	9.99600e6			1.19738			0.598688	−	0.800982i	$-0.295689\pi$
$587$	9.99600e6			1.19738			0.598688	+	0.800982i	$0.295689\pi$
$588$		0			0
$589$	18999.0			0.00225654
$590$		0			0
$591$	636446.	+	1.10236e6i	0.0749537	+	0.129824i
$592$		0			0
$593$	2.58800e6	−	4.48255e6i	0.302223	−	0.523466i	−0.674416	−	0.738352i	$-0.735605\pi$
$593$	2.58800e6	−	4.48255e6i	0.302223	−	0.523466i	0.976639	+	0.214886i	$0.0689378\pi$
$594$		0			0
$595$	257437.	+	443434.i	0.0298112	+	0.0513496i
$596$		0			0
$597$	988316.	−	1.71181e6i	0.113491	−	0.196571i
$598$		0			0
$599$	−904038.	−	1.56584e6i	−0.102948	−	0.178312i	0.809950	−	0.586499i	$-0.199494\pi$
$599$	−904038.	−	1.56584e6i	−0.102948	−	0.178312i	−0.912898	+	0.408187i	$0.866161\pi$
$600$		0			0
$601$	3.55217e6			0.401151			0.200575	−	0.979678i	$-0.435719\pi$
$601$	3.55217e6			0.401151			0.200575	+	0.979678i	$0.435719\pi$
$602$		0			0
$603$	4.96535e6			0.556105
$604$		0			0
$605$	−1.08262e6	−	1.87516e6i	−0.120251	−	0.208281i
$606$		0			0
$607$	−4.25611e6	+	7.37181e6i	−0.468858	+	0.812086i	−0.999366	−	0.0355935i	$-0.988668\pi$
$607$	−4.25611e6	+	7.37181e6i	−0.468858	+	0.812086i	0.530508	+	0.847680i	$0.322001\pi$
$608$		0			0
$609$	1.80329e6	−	3.14077e6i	0.197025	−	0.343157i
$610$		0			0
$611$	−345245.	+	597981.i	−0.0374131	+	0.0648014i
$612$		0			0
$613$	−6.30029e6	−	1.09124e7i	−0.677188	−	1.17292i	−0.975824	−	0.218557i	$-0.929865\pi$
$613$	−6.30029e6	−	1.09124e7i	−0.677188	−	1.17292i	0.298636	−	0.954367i	$-0.403468\pi$
$614$		0			0
$615$	1.40579e6			0.149877
$616$		0			0
$617$	8.92514e6			0.943848			0.471924	−	0.881639i	$-0.343560\pi$
$617$	8.92514e6			0.943848			0.471924	+	0.881639i	$0.343560\pi$
$618$		0			0
$619$	4.20749e6	+	7.28758e6i	0.441363	+	0.764464i	0.997791	−	0.0664325i	$-0.0211617\pi$
$619$	4.20749e6	+	7.28758e6i	0.441363	+	0.764464i	−0.556428	+	0.830896i	$0.687828\pi$
$620$		0			0
$621$	151664.	−	262690.i	0.0157817	−	0.0273348i
$622$		0			0
$623$	1.12034e7	−	26879.6i	1.15645	−	0.00277462i
$624$		0			0
$625$	2.26315e6	−	3.91989e6i	0.231746	−	0.401397i
$626$		0			0
$627$	382732.	+	662911.i	0.0388799	+	0.0673420i
$628$		0			0
$629$	444812.			0.0448280
$630$		0			0
$631$	−1.12046e7			−1.12027			−0.560135	−	0.828401i	$-0.689251\pi$
$631$	−1.12046e7			−1.12027			−0.560135	+	0.828401i	$0.689251\pi$
$632$		0			0
$633$	377315.	+	653529.i	0.0374279	+	0.0648270i
$634$		0			0
$635$	−19419.2	+	33635.0i	−0.00191116	+	0.00331022i
$636$		0			0
$637$	−428018.	+	749634.i	−0.0417940	+	0.0731982i
$638$		0			0
$639$	−247549.	+	428767.i	−0.0239833	+	0.0415403i
$640$		0			0
$641$	2.97074e6	+	5.14547e6i	0.285574	+	0.494629i	0.972748	−	0.231864i	$-0.0744823\pi$
$641$	2.97074e6	+	5.14547e6i	0.285574	+	0.494629i	−0.687174	+	0.726493i	$0.741149\pi$
$642$		0			0
$643$	3.03768e6			0.289744			0.144872	−	0.989450i	$-0.453723\pi$
$643$	3.03768e6			0.289744			0.144872	+	0.989450i	$0.453723\pi$
$644$		0			0
$645$	8.02318e6			0.759359
$646$		0			0
$647$	6.36312e6	+	1.10212e7i	0.597598	+	1.03507i	0.993175	+	0.116637i	$0.0372115\pi$
$647$	6.36312e6	+	1.10212e7i	0.597598	+	1.03507i	−0.395576	+	0.918433i	$0.629455\pi$
$648$		0			0
$649$	187502.	−	324763.i	0.0174741	−	0.0302660i
$650$		0			0
$651$	−87064.4	+	208.889i	−0.00805171	+	1.93180e-5i
$652$		0			0
$653$	3.13179e6	−	5.42442e6i	0.287415	−	0.497818i	−0.685777	−	0.727812i	$-0.740537\pi$
$653$	3.13179e6	−	5.42442e6i	0.287415	−	0.497818i	0.973192	+	0.229994i	$0.0738707\pi$
$654$		0			0
$655$	−6.67081e6	−	1.15542e7i	−0.607540	−	1.05229i
$656$		0			0
$657$	842981.			0.0761911
$658$		0			0
$659$	1.17924e7			1.05777			0.528884	−	0.848694i	$-0.322611\pi$
$659$	1.17924e7			1.05777			0.528884	+	0.848694i	$0.322611\pi$
$660$		0			0
$661$	−9.26979e6	−	1.60557e7i	−0.825213	−	1.42931i	−0.901756	−	0.432245i	$-0.857722\pi$
$661$	−9.26979e6	−	1.60557e7i	−0.825213	−	1.42931i	0.0765432	−	0.997066i	$-0.475612\pi$
$662$		0			0
$663$	−20883.0	+	36170.5i	−0.00184506	+	0.00319573i
$664$		0			0
$665$	−719432.	+	1.25303e6i	−0.0630864	+	0.109877i
$666$		0			0
$667$	−645764.	+	1.11850e6i	−0.0562029	+	0.0973463i
$668$		0			0
$669$	6.11764e6	+	1.05961e7i	0.528468	+	0.915334i
$670$		0			0
$671$	1.02281e7			0.876982
$672$		0			0
$673$	−3.90083e6			−0.331985			−0.165993	−	0.986127i	$-0.553083\pi$
$673$	−3.90083e6			−0.331985			−0.165993	+	0.986127i	$0.553083\pi$
$674$		0			0
$675$	440649.	+	763226.i	0.0372249	+	0.0644754i
$676$		0			0
$677$	3.41266e6	−	5.91091e6i	0.286168	−	0.495658i	−0.686723	−	0.726919i	$-0.740952\pi$
$677$	3.41266e6	−	5.91091e6i	0.286168	−	0.495658i	0.972892	+	0.231260i	$0.0742850\pi$
$678$		0			0
$679$	3.86096e6	+	6.65048e6i	0.321381	+	0.553577i
$680$		0			0
$681$	356.985	−	618.316i	2.94973e−5	−	5.10908e-5i
$682$		0			0
$683$	−2.36231e6	−	4.09164e6i	−0.193769	−	0.335619i	0.752727	−	0.658333i	$-0.228738\pi$
$683$	−2.36231e6	−	4.09164e6i	−0.193769	−	0.335619i	−0.946496	+	0.322714i	$0.895405\pi$
$684$		0			0
$685$	1.67432e7			1.36336
$686$		0			0
$687$	5.64337e6			0.456191
$688$		0			0
$689$	160811.	+	278533.i	0.0129053	+	0.0223526i
$690$		0			0
$691$	−7.96331e6	+	1.37929e7i	−0.634452	+	1.09890i	0.352179	+	0.935933i	$0.385441\pi$
$691$	−7.96331e6	+	1.37929e7i	−0.634452	+	1.09890i	−0.986631	+	0.162970i	$0.947893\pi$
$692$		0			0
$693$	−1.76118e6	−	3.03363e6i	−0.139307	−	0.239955i
$694$		0			0
$695$	−5.62200e6	+	9.73758e6i	−0.441498	+	0.764697i
$696$		0			0
$697$	161210.	+	279223.i	0.0125692	+	0.0217706i
$698$		0			0
$699$	−7.86636e6			−0.608949
$700$		0			0
$701$	−2.22412e7			−1.70948			−0.854738	−	0.519060i	$-0.826282\pi$
$701$	−2.22412e7			−1.70948			−0.854738	+	0.519060i	$0.826282\pi$
$702$		0			0
$703$	626721.	+	1.08551e6i	0.0478284	+	0.0828412i
$704$		0			0
$705$	2.64817e6	−	4.58676e6i	0.200665	−	0.347563i
$706$		0			0
$707$	2.44928e6	−	4.26588e6i	0.184285	−	0.320967i
$708$		0			0
$709$	1.68408e6	−	2.91691e6i	0.125819	−	0.217925i	−0.796234	−	0.604989i	$-0.793177\pi$
$709$	1.68408e6	−	2.91691e6i	0.125819	−	0.217925i	0.922053	+	0.387064i	$0.126511\pi$
$710$		0			0
$711$	1.75053e6	+	3.03201e6i	0.129866	+	0.224935i
$712$		0			0
$713$	31048.5			0.00228726
$714$		0			0
$715$	−751007.			−0.0549387
$716$		0			0
$717$	5.60123e6	+	9.70162e6i	0.406898	+	0.704768i
$718$		0			0
$719$	−2.36961e6	+	4.10428e6i	−0.170944	+	0.296084i	−0.938750	−	0.344598i	$-0.888015\pi$
$719$	−2.36961e6	+	4.10428e6i	−0.170944	+	0.296084i	0.767806	+	0.640682i	$0.221348\pi$
$720$		0			0
$721$	−1.60506e7	+	38509.3i	−1.14988	+	0.00275885i
$722$		0			0
$723$	−7.46826e6	+	1.29354e7i	−0.531341	+	0.920310i
$724$		0			0
$725$	−1.87622e6	−	3.24970e6i	−0.132568	−	0.229614i
$726$		0			0
$727$	2.03003e7			1.42451			0.712256	−	0.701919i	$-0.247673\pi$
$727$	2.03003e7			1.42451			0.712256	+	0.701919i	$0.247673\pi$
$728$		0			0
$729$	531441.			0.0370370
$730$		0			0
$731$	920058.	+	1.59359e6i	0.0636828	+	0.110302i
$732$		0			0
$733$	1.26709e6	−	2.19466e6i	0.0871057	−	0.150871i	−0.819181	−	0.573535i	$-0.805572\pi$
$733$	1.26709e6	−	2.19466e6i	0.0871057	−	0.150871i	0.906287	+	0.422664i	$0.138905\pi$
$734$		0			0
$735$	3.28307e6	−	5.74999e6i	0.224162	−	0.392599i
$736$		0			0
$737$	−1.02386e7	+	1.77337e7i	−0.694338	+	1.20263i
$738$		0			0
$739$	−1.35597e7	−	2.34860e7i	−0.913352	−	1.58197i	−0.809296	−	0.587401i	$-0.800151\pi$
$739$	−1.35597e7	−	2.34860e7i	−0.913352	−	1.58197i	−0.104056	−	0.994571i	$-0.533182\pi$
$740$		0			0
$741$	−117693.			−0.00787419
$742$		0			0
$743$	1.58583e7			1.05386			0.526932	−	0.849908i	$-0.323342\pi$
$743$	1.58583e7			1.05386			0.526932	+	0.849908i	$0.323342\pi$
$744$		0			0
$745$	−9.57769e6	−	1.65890e7i	−0.632223	−	1.09504i
$746$		0			0
$747$	−1.01484e6	+	1.75775e6i	−0.0665418	+	0.115254i
$748$		0			0
$749$	−1.57852e7	+	37872.6i	−1.02812	+	0.00246672i
$750$		0			0
$751$	−1.09937e7	+	1.90416e7i	−0.711284	+	1.23198i	0.253091	+	0.967442i	$0.418553\pi$
$751$	−1.09937e7	+	1.90416e7i	−0.711284	+	1.23198i	−0.964375	+	0.264538i	$0.914781\pi$
$752$		0			0
$753$	3.07653e6	+	5.32871e6i	0.197731	+	0.342479i
$754$		0			0
$755$	−1.08229e7			−0.690995
$756$		0			0
$757$	−1.45560e7			−0.923213			−0.461607	−	0.887085i	$-0.652727\pi$
$757$	−1.45560e7			−0.923213			−0.461607	+	0.887085i	$0.652727\pi$
$758$		0			0
$759$	625465.	+	1.08334e6i	0.0394093	+	0.0682589i
$760$		0			0
$761$	1.23612e7	−	2.14103e7i	0.773749	−	1.34017i	−0.161745	−	0.986833i	$-0.551712\pi$
$761$	1.23612e7	−	2.14103e7i	0.773749	−	1.34017i	0.935495	−	0.353341i	$-0.114954\pi$
$762$		0			0
$763$	−3.08532e6	+	5.37366e6i	−0.191862	+	0.334163i
$764$		0			0
$765$	160181.	−	277442.i	0.00989596	−	0.0171403i
$766$		0			0
$767$	28829.2	+	49933.7i	0.00176947	+	0.00306482i
$768$		0			0
$769$	1.14189e7			0.696322			0.348161	−	0.937435i	$-0.386806\pi$
$769$	1.14189e7			0.696322			0.348161	+	0.937435i	$0.386806\pi$
$770$		0			0
$771$	−1.43330e7			−0.868364
$772$		0			0
$773$	−4.52146e6	−	7.83141e6i	−0.272164	−	0.471402i	0.697252	−	0.716826i	$-0.254406\pi$
$773$	−4.52146e6	−	7.83141e6i	−0.272164	−	0.471402i	−0.969416	+	0.245425i	$0.921073\pi$
$774$		0			0
$775$	−45104.4	+	78123.2i	−0.00269752	+	0.00467225i
$776$		0			0
$777$	−2.88393e6	−	4.96755e6i	−0.171369	−	0.295182i
$778$		0			0
$779$	−454275.	+	786828.i	−0.0268210	+	0.0464554i
$780$		0			0
$781$	−1.02089e6	−	1.76824e6i	−0.0598898	−	0.103732i
$782$		0			0
$783$	−2.26279e6			−0.131899
$784$		0			0
$785$	−1.25681e7			−0.727938
$786$		0			0
$787$	−700700.	−	1.21365e6i	−0.0403270	−	0.0698483i	0.845157	−	0.534517i	$-0.179507\pi$
$787$	−700700.	−	1.21365e6i	−0.0403270	−	0.0698483i	−0.885484	+	0.464669i	$0.846173\pi$
$788$		0			0
$789$	3.31528e6	−	5.74223e6i	0.189595	−	0.328389i
$790$		0			0
$791$	−1.02949e7	−	1.77330e7i	−0.585036	−	1.00772i
$792$		0			0
$793$	−786310.	+	1.36193e6i	−0.0444029	+	0.0769080i
$794$		0			0
$795$	−1.23349e6	−	2.13646e6i	−0.0692176	−	0.119888i
$796$		0			0
$797$	9.96609e6			0.555750			0.277875	−	0.960617i	$-0.410370\pi$
$797$	9.96609e6			0.555750			0.277875	+	0.960617i	$0.410370\pi$
$798$		0			0
$799$	1.21472e6			0.0673143
$800$		0			0
$801$	−3.49994e6	−	6.06207e6i	−0.192743	−	0.333841i
$802$		0			0
$803$	−1.73823e6	+	3.01070e6i	−0.0951302	+	0.164770i
$804$		0			0
$805$	−1.17571e6	+	2.04771e6i	−0.0639454	+	0.111373i
$806$		0			0
$807$	−7.03876e6	+	1.21915e7i	−0.380463	+	0.658981i
$808$		0			0
$809$	1.51409e7	+	2.62248e7i	0.813355	+	1.40877i	0.910503	+	0.413502i	$0.135694\pi$
$809$	1.51409e7	+	2.62248e7i	0.813355	+	1.40877i	−0.0971485	+	0.995270i	$0.530972\pi$
$810$		0			0
$811$	−2.52190e7			−1.34641			−0.673203	−	0.739458i	$-0.735082\pi$
$811$	−2.52190e7			−1.34641			−0.673203	+	0.739458i	$0.735082\pi$
$812$		0			0
$813$	1.47198e7			0.781044
$814$		0			0
$815$	−9.08691e6	−	1.57390e7i	−0.479206	−	0.830009i
$816$		0			0
$817$	−2.59265e6	+	4.49060e6i	−0.135890	+	0.235369i
$818$		0			0
$819$	539337.	−	1294.00i	0.0280964	−	6.74102e-5i
$820$		0			0
$821$	−1.38467e7	+	2.39832e7i	−0.716950	+	1.24179i	0.245252	+	0.969459i	$0.421129\pi$
$821$	−1.38467e7	+	2.39832e7i	−0.716950	+	1.24179i	−0.962203	+	0.272335i	$0.912204\pi$
$822$		0			0
$823$	−7.42671e6	−	1.28634e7i	−0.382206	−	0.661999i	0.609172	−	0.793038i	$-0.291502\pi$
$823$	−7.42671e6	−	1.28634e7i	−0.382206	−	0.661999i	−0.991377	+	0.131039i	$0.958169\pi$
$824$		0			0
$825$	−3.63448e6			−0.185912
$826$		0			0
$827$	9.88266e6			0.502470			0.251235	−	0.967926i	$-0.419163\pi$
$827$	9.88266e6			0.502470			0.251235	+	0.967926i	$0.419163\pi$
$828$		0			0
$829$	1.71460e7	+	2.96978e7i	0.866516	+	1.50085i	0.865534	+	0.500851i	$0.166979\pi$
$829$	1.71460e7	+	2.96978e7i	0.866516	+	1.50085i	0.000982496		1.00000i	$0.499687\pi$
$830$		0			0
$831$	1.02090e6	−	1.76825e6i	0.0512840	−	0.0888264i
$832$		0			0
$833$	1.51857e6	−	7286.88i	0.0758266	−	0.000363855i
$834$		0			0
$835$	−1.00796e7	+	1.74583e7i	−0.500294	+	0.866534i
$836$		0			0
$837$	27198.9	+	47109.9i	0.00134196	+	0.00232433i
$838$		0			0
$839$	1.40547e7			0.689312			0.344656	−	0.938729i	$-0.387996\pi$
$839$	1.40547e7			0.689312			0.344656	+	0.938729i	$0.387996\pi$
$840$		0			0
$841$	−1.08765e7			−0.530274
$842$		0			0
$843$	2.62787e6	+	4.55160e6i	0.127361	+	0.220595i
$844$		0			0
$845$	−8.06859e6	+	1.39752e7i	−0.388737	+	0.673312i
$846$		0			0
$847$	−6.41273e6	+	15385.7i	−0.307139	+	0.000736901i
$848$		0			0
$849$	377575.	−	653980.i	0.0179777	−	0.0311383i
$850$		0			0
$851$	1.02420e6	+	1.77396e6i	0.0484796	+	0.0839692i
$852$		0			0
$853$	3.38937e7			1.59495			0.797474	−	0.603354i	$-0.206169\pi$
$853$	3.38937e7			1.59495			0.797474	+	0.603354i	$0.206169\pi$
$854$		0			0
$855$	902755.			0.0422332
$856$		0			0
$857$	1.56740e7	+	2.71482e7i	0.729002	+	1.26267i	0.957305	+	0.289079i	$0.0933491\pi$
$857$	1.56740e7	+	2.71482e7i	0.729002	+	1.26267i	−0.228303	+	0.973590i	$0.573318\pi$
$858$		0			0
$859$	−8.78882e6	+	1.52227e7i	−0.406394	+	0.703896i	−0.994483	−	0.104901i	$-0.966547\pi$
$859$	−8.78882e6	+	1.52227e7i	−0.406394	+	0.703896i	0.588088	+	0.808797i	$0.299881\pi$
$860$		0			0
$861$	2.07310e6	−	3.61069e6i	0.0953042	−	0.165990i
$862$		0			0
$863$	−1.02906e7	+	1.78239e7i	−0.470343	+	0.814657i	−0.999425	−	0.0339134i	$-0.989203\pi$
$863$	−1.02906e7	+	1.78239e7i	−0.470343	+	0.814657i	0.529082	+	0.848571i	$0.322536\pi$
$864$		0			0
$865$	−3.78601e6	−	6.55756e6i	−0.172045	−	0.297990i
$866$		0			0
$867$	−1.27052e7			−0.574031
$868$		0			0
$869$	−1.44384e7			−0.648590
$870$		0			0
$871$	−1.57422e6	−	2.72664e6i	−0.0703107	−	0.121782i
$872$		0			0
$873$	2.40234e6	−	4.16098e6i	0.106684	−	0.184782i
$874$		0			0
$875$	−1.23482e7	−	2.12696e7i	−0.545234	−	0.939161i
$876$		0			0
$877$	−1.63733e7	+	2.83593e7i	−0.718847	+	1.24508i	0.242610	+	0.970124i	$0.421996\pi$
$877$	−1.63733e7	+	2.83593e7i	−0.718847	+	1.24508i	−0.961457	+	0.274955i	$0.911337\pi$
$878$		0			0
$879$	−5.63507e6	−	9.76022e6i	−0.245995	−	0.426076i
$880$		0			0
$881$	−2.45099e7			−1.06390			−0.531950	−	0.846776i	$-0.678541\pi$
$881$	−2.45099e7			−1.06390			−0.531950	+	0.846776i	$0.678541\pi$
$882$		0			0
$883$	1.49986e7			0.647365			0.323682	−	0.946166i	$-0.395079\pi$
$883$	1.49986e7			0.647365			0.323682	+	0.946166i	$0.395079\pi$
$884$		0			0
$885$	−221132.	−	383011.i	−0.00949058	−	0.0164382i
$886$		0			0
$887$	1.27679e7	−	2.21147e7i	0.544894	−	0.943784i	−0.453720	−	0.891144i	$-0.649903\pi$
$887$	1.27679e7	−	2.21147e7i	0.544894	−	0.943784i	0.998614	−	0.0526394i	$-0.0167634\pi$
$888$		0			0
$889$	57752.1	+	99477.7i	0.00245083	+	0.00422154i
$890$		0			0
$891$	−1.09583e6	+	1.89804e6i	−0.0462435	+	0.0800960i
$892$		0			0
$893$	1.71148e6	+	2.96438e6i	0.0718198	+	0.124395i
$894$		0			0
$895$	2.93902e7			1.22644
$896$		0			0
$897$	−192336.			−0.00798140
$898$		0			0
$899$	−115809.	−	200587.i	−0.00477906	−	0.00827757i
$900$		0			0
$901$	282900.	−	489997.i	0.0116097	−	0.0201086i
$902$		0			0
$903$	1.18316e7	−	2.06070e7i	0.482864	−	0.840998i
$904$		0			0
$905$	−9.56158e6	+	1.65611e7i	−0.388068	+	0.672154i
$906$		0			0
$907$	−1.14946e7	−	1.99093e7i	−0.463956	−	0.803596i	0.535198	−	0.844727i	$-0.320237\pi$
$907$	−1.14946e7	−	1.99093e7i	−0.463956	−	0.803596i	−0.999154	+	0.0411313i	$0.986904\pi$
$908$		0			0
$909$	−3.07339e6			−0.123370
$910$		0			0
$911$	1.81822e7			0.725857			0.362928	−	0.931817i	$-0.381777\pi$
$911$	1.81822e7			0.725857			0.362928	+	0.931817i	$0.381777\pi$
$912$		0			0
$913$	−4.18519e6	−	7.24896e6i	−0.166165	−	0.287805i
$914$		0			0
$915$	6.03132e6	−	1.04466e7i	0.238155	−	0.412497i
$916$		0			0
$917$	−3.95134e7	+	94802.4i	−1.55175	+	0.00372303i
$918$		0			0
$919$	1.41468e7	−	2.45029e7i	0.552546	−	0.957037i	−0.445544	−	0.895260i	$-0.646990\pi$
$919$	1.41468e7	−	2.45029e7i	0.552546	−	0.957037i	0.998090	−	0.0617775i	$-0.0196769\pi$
$920$		0			0
$921$	−1.11572e7	−	1.93248e7i	−0.433416	−	0.750699i
$922$		0			0
$923$	313933.			0.0121292
$924$		0			0
$925$	−5.95144e6			−0.228701
$926$		0			0
$927$	5.01421e6	+	8.68487e6i	0.191648	+	0.331943i
$928$		0			0
$929$	1.43383e7	−	2.48347e7i	0.545079	−	0.944105i	−0.453523	−	0.891245i	$-0.649833\pi$
$929$	1.43383e7	−	2.48347e7i	0.545079	−	0.944105i	0.998602	−	0.0528603i	$-0.0168338\pi$
$930$		0			0
$931$	2.15738e6	+	3.69563e6i	0.0815742	+	0.139738i
$932$		0			0
$933$	−7.11267e6	+	1.23195e7i	−0.267503	+	0.463329i
$934$		0			0
$935$	660589.	+	1.14417e6i	0.0247117	+	0.0428019i
$936$		0			0
$937$	4.99596e7			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$937$	4.99596e7			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$938$		0			0
$939$	1.02542e6			0.0379522
$940$		0			0
$941$	−5.77422e6	−	1.00012e7i	−0.212578	−	0.368196i	0.739942	−	0.672670i	$-0.234853\pi$
$941$	−5.77422e6	−	1.00012e7i	−0.212578	−	0.368196i	−0.952521	+	0.304474i	$0.901519\pi$
$942$		0			0
$943$	−742383.	+	1.28585e6i	−0.0271862	+	0.0470879i
$944$		0			0
$945$	−4.13694e6	+	9925.52i	−0.150695	+	0.000361555i
$946$		0			0
$947$	6.04254e6	−	1.04660e7i	0.218950	−	0.379232i	−0.735537	−	0.677484i	$-0.763070\pi$
$947$	6.04254e6	−	1.04660e7i	0.218950	−	0.379232i	0.954487	+	0.298252i	$0.0964035\pi$
$948$		0			0
$949$	−267260.	−	462908.i	−0.00963316	−	0.0166851i
$950$		0			0
$951$	−2.41915e7			−0.867384
$952$		0			0
$953$	5.34953e6			0.190802			0.0954011	−	0.995439i	$-0.469587\pi$
$953$	5.34953e6			0.190802			0.0954011	+	0.995439i	$0.469587\pi$
$954$		0			0
$955$	1.50528e7	+	2.60722e7i	0.534083	+	0.925059i
$956$		0			0
$957$	4.66589e6	−	8.08156e6i	0.164685	−	0.285243i
$958$		0			0
$959$	2.46908e7	−	4.30037e7i	0.866939	−	1.50994i
$960$		0			0
$961$	1.43118e7	−	2.47887e7i	0.499903	−	0.865857i
$962$		0			0
$963$	4.93130e6	+	8.54126e6i	0.171355	+	0.296795i
$964$		0			0
$965$	−1.12046e7			−0.387326
$966$		0			0
$967$	4.79471e7			1.64891			0.824454	−	0.565929i	$-0.191482\pi$
$967$	4.79471e7			1.64891			0.824454	+	0.565929i	$0.191482\pi$
$968$		0			0
$969$	103523.	+	179308.i	0.00354184	+	0.00613465i
$970$		0			0
$971$	−3.28388e6	+	5.68785e6i	−0.111774	+	0.193598i	−0.916485	−	0.400068i	$-0.868986\pi$
$971$	−3.28388e6	+	5.68785e6i	−0.111774	+	0.193598i	0.804712	+	0.593666i	$0.202320\pi$
$972$		0			0
$973$	1.67197e7	+	2.87995e7i	0.566169	+	0.975222i
$974$		0			0
$975$	279408.	−	483950.i	0.00941300	−	0.0163038i
$976$		0			0
$977$	5.10448e6	+	8.84122e6i	0.171086	+	0.296330i	0.938800	−	0.344463i	$-0.111939\pi$
$977$	5.10448e6	+	8.84122e6i	0.171086	+	0.296330i	−0.767714	+	0.640793i	$0.778606\pi$
$978$		0			0
$979$	2.88675e7			0.962616
$980$		0			0
$981$	3.87150e6			0.128442
$982$		0			0
$983$	−337772.	−	585038.i	−0.0111491	−	0.0193108i	0.860397	−	0.509624i	$-0.170216\pi$
$983$	−337772.	−	585038.i	−0.0111491	−	0.0193108i	−0.871546	+	0.490314i	$0.836882\pi$
$984$		0			0
$985$	−3.09547e6	+	5.36151e6i	−0.101657	+	0.176075i
$986$		0			0
$987$	−7.87558e6	−	1.35656e7i	−0.257330	−	0.443249i
$988$		0			0
$989$	−4.23694e6	+	7.33860e6i	−0.137740	+	0.238574i
$990$		0			0
$991$	−1.48979e7	−	2.58040e7i	−0.481883	−	0.834646i	0.517901	−	0.855441i	$-0.326714\pi$
$991$	−1.48979e7	−	2.58040e7i	−0.481883	−	0.834646i	−0.999784	+	0.0207947i	$0.993380\pi$
$992$		0			0
$993$	−3.29664e7			−1.06096
$994$		0			0
$995$	9.61370e6			0.307846
$996$		0			0
$997$	2.52562e7	+	4.37449e7i	0.804691	+	1.39377i	0.916499	+	0.400036i	$0.131002\pi$
$997$	2.52562e7	+	4.37449e7i	0.804691	+	1.39377i	−0.111808	+	0.993730i	$0.535664\pi$
$998$		0			0
$999$	−1.79442e6	+	3.10803e6i	−0.0568867	+	0.0985307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.6.q.a.121.3	yes	8
3.2	odd	2		504.6.s.a.289.2		8
4.3	odd	2		336.6.q.k.289.3		8
7.4	even	3	inner	168.6.q.a.25.3	✓	8
21.11	odd	6		504.6.s.a.361.2		8
28.11	odd	6		336.6.q.k.193.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.6.q.a.25.3	✓	8	7.4	even	3	inner
168.6.q.a.121.3	yes	8	1.1	even	1	trivial
336.6.q.k.193.3		8	28.11	odd	6
336.6.q.k.289.3		8	4.3	odd	2
504.6.s.a.289.2		8	3.2	odd	2
504.6.s.a.361.2		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	168.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.50000 - 7.79423i) q^{3} +(21.8866 - 37.9086i) q^{5} +(-65.0901 - 112.117i) q^{7} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-4.50000 - 7.79423i) q^{3} +(21.8866 - 37.9086i) q^{5} +(-65.0901 - 112.117i) q^{7} +(-40.5000 + 70.1481i) q^{9} +(-167.022 - 289.291i) q^{11} +51.3608 q^{13} -393.958 q^{15} +(-45.1772 - 78.2492i) q^{17} +(127.305 - 220.500i) q^{19} +(-580.962 + 1011.85i) q^{21} +(208.044 - 360.344i) q^{23} +(604.457 + 1046.95i) q^{25} +729.000 q^{27} -3103.97 q^{29} +(37.3099 + 64.6226i) q^{31} +(-1503.20 + 2603.62i) q^{33} +(-5674.81 + 13.6153i) q^{35} +(-2461.48 + 4263.41i) q^{37} +(-231.124 - 400.318i) q^{39} -3568.39 q^{41} -20365.6 q^{43} +(1772.81 + 3070.60i) q^{45} +(-6721.95 + 11642.8i) q^{47} +(-8333.56 + 14595.4i) q^{49} +(-406.595 + 704.243i) q^{51} +(3131.01 + 5423.06i) q^{53} -14622.2 q^{55} -2291.50 q^{57} +(561.308 + 972.214i) q^{59} +(-15309.5 + 26516.9i) q^{61} +(10501.0 - 25.1944i) q^{63} +(1124.11 - 1947.02i) q^{65} +(-30650.3 - 53087.9i) q^{67} -3744.80 q^{69} +6112.32 q^{71} +(-5203.58 - 9012.87i) q^{73} +(5440.11 - 9422.55i) q^{75} +(-21563.0 + 37556.1i) q^{77} +(21611.5 - 37432.2i) q^{79} +(-3280.50 - 5681.99i) q^{81} +25057.7 q^{83} -3955.09 q^{85} +(13967.9 + 24193.0i) q^{87} +(-43209.1 + 74840.3i) q^{89} +(-3343.08 - 5758.43i) q^{91} +(335.789 - 581.604i) q^{93} +(-5572.56 - 9651.96i) q^{95} -59317.2 q^{97} +27057.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{3} + 64 q^{5} + 42 q^{7} - 324 q^{9}+O(q^{10}) \) 8 * q - 36 * q^3 + 64 * q^5 + 42 * q^7 - 324 * q^9	\( 8 q - 36 q^{3} + 64 q^{5} + 42 q^{7} - 324 q^{9} + 70 q^{11} + 1356 q^{13} - 1152 q^{15} + 944 q^{17} + 606 q^{19} + 1512 q^{21} + 648 q^{23} - 2582 q^{25} + 5832 q^{27} - 8720 q^{29} + 4354 q^{31} + 630 q^{33} + 5824 q^{35} + 19302 q^{37} - 6102 q^{39} + 1832 q^{41} + 16788 q^{43} + 5184 q^{45} + 5104 q^{47} - 15484 q^{49} + 8496 q^{51} - 13244 q^{53} + 35744 q^{55} - 10908 q^{57} + 30742 q^{59} - 2428 q^{61} - 17010 q^{63} + 126004 q^{65} - 8258 q^{67} - 11664 q^{69} + 29664 q^{71} - 12758 q^{73} - 23238 q^{75} - 91672 q^{77} + 21382 q^{79} - 26244 q^{81} - 110500 q^{83} + 275960 q^{85} + 39240 q^{87} - 49072 q^{89} - 35658 q^{91} + 39186 q^{93} - 25292 q^{95} - 135228 q^{97} - 11340 q^{99}+O(q^{100}) \) 8 * q - 36 * q^3 + 64 * q^5 + 42 * q^7 - 324 * q^9 + 70 * q^11 + 1356 * q^13 - 1152 * q^15 + 944 * q^17 + 606 * q^19 + 1512 * q^21 + 648 * q^23 - 2582 * q^25 + 5832 * q^27 - 8720 * q^29 + 4354 * q^31 + 630 * q^33 + 5824 * q^35 + 19302 * q^37 - 6102 * q^39 + 1832 * q^41 + 16788 * q^43 + 5184 * q^45 + 5104 * q^47 - 15484 * q^49 + 8496 * q^51 - 13244 * q^53 + 35744 * q^55 - 10908 * q^57 + 30742 * q^59 - 2428 * q^61 - 17010 * q^63 + 126004 * q^65 - 8258 * q^67 - 11664 * q^69 + 29664 * q^71 - 12758 * q^73 - 23238 * q^75 - 91672 * q^77 + 21382 * q^79 - 26244 * q^81 - 110500 * q^83 + 275960 * q^85 + 39240 * q^87 - 49072 * q^89 - 35658 * q^91 + 39186 * q^93 - 25292 * q^95 - 135228 * q^97 - 11340 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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