LMFDB - Embedded newform 144.6.i.b.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,6,Mod(49,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.49"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	144.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$23.0952700531$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.47347183152.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 $ x^6 - 3x^5 + 118x^4 - 231x^3 + 3700x^2 - 3585*x + 32331
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.1
Root			$0.500000 - 5.23712i$ of defining polynomial
Character	$\chi$	$=$	144.97
Dual form			144.6.i.b.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-15.5145 - 1.51695i) q^{3} +(33.0434 + 57.2329i) q^{5} +(57.0952 - 98.8918i) q^{7} +(238.398 + 47.0695i) q^{9} +(-192.812 + 333.961i) q^{11} +(-516.287 - 894.236i) q^{13} +(-425.832 - 938.063i) q^{15} +959.020 q^{17} +464.576 q^{19} +(-1035.82 + 1447.64i) q^{21} +(1151.70 + 1994.81i) q^{23} +(-621.235 + 1076.01i) q^{25} +(-3627.21 - 1091.90i) q^{27} +(-3549.13 + 6147.28i) q^{29} +(3881.53 + 6723.00i) q^{31} +(3497.98 - 4888.74i) q^{33} +7546.48 q^{35} +9317.57 q^{37} +(6653.41 + 14656.8i) q^{39} +(6661.64 + 11538.3i) q^{41} +(-1056.29 + 1829.55i) q^{43} +(5183.55 + 15199.5i) q^{45} +(1247.40 - 2160.56i) q^{47} +(1883.78 + 3262.80i) q^{49} +(-14878.7 - 1454.79i) q^{51} -10044.2 q^{53} -25484.7 q^{55} +(-7207.66 - 704.741i) q^{57} +(2720.33 + 4711.75i) q^{59} +(-17094.4 + 29608.4i) q^{61} +(18266.1 - 20888.1i) q^{63} +(34119.8 - 59097.2i) q^{65} +(26792.6 + 46406.2i) q^{67} +(-14842.0 - 32695.5i) q^{69} +970.010 q^{71} -72400.3 q^{73} +(11270.4 - 15751.3i) q^{75} +(22017.3 + 38135.1i) q^{77} +(16098.9 - 27884.0i) q^{79} +(54617.9 + 22442.5i) q^{81} +(-18046.6 + 31257.6i) q^{83} +(31689.3 + 54887.5i) q^{85} +(64388.1 - 89987.9i) q^{87} +42622.2 q^{89} -117910. q^{91} +(-50021.4 - 110192. i) q^{93} +(15351.2 + 26589.0i) q^{95} +(21926.9 - 37978.6i) q^{97} +(-61685.4 + 70539.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31}+ \cdots - 282168 q^{99}+O(q^{100}) $ 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9 + 315 * q^11 - 744 * q^13 - 2286 * q^15 + 2898 * q^17 - 2262 * q^19 - 11076 * q^21 + 3168 * q^23 - 2883 * q^25 - 18144 * q^27 - 5148 * q^29 + 8610 * q^31 + 17469 * q^33 - 2700 * q^35 + 39936 * q^37 + 49026 * q^39 + 5049 * q^41 + 31389 * q^43 + 2538 * q^45 - 12924 * q^47 - 52857 * q^49 - 36837 * q^51 - 96048 * q^53 - 126252 * q^55 - 17469 * q^57 - 62955 * q^59 - 75966 * q^61 - 49578 * q^63 + 108702 * q^65 + 32991 * q^67 - 29250 * q^69 + 129672 * q^71 - 8466 * q^73 + 105483 * q^75 + 88740 * q^77 - 89202 * q^79 + 123435 * q^81 - 32634 * q^83 + 71388 * q^85 + 151524 * q^87 + 66132 * q^89 + 301836 * q^91 + 57678 * q^93 + 82944 * q^95 + 46245 * q^97 - 282168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−15.5145	−	1.51695i	−0.995254	−	0.0973126i
$3$	−15.5145	−	1.51695i	−0.995254	−	0.0973126i
$4$		0			0
$5$	33.0434	+	57.2329i	0.591099	+	1.02381i	0.994085	+	0.108607i	$0.0346389\pi$
$5$	33.0434	+	57.2329i	0.591099	+	1.02381i	−0.402986	+	0.915206i	$0.632028\pi$
$6$		0			0
$7$	57.0952	−	98.8918i	0.440407	−	0.762808i	−0.557312	−	0.830303i	$-0.688167\pi$
$7$	57.0952	−	98.8918i	0.440407	−	0.762808i	0.997720	+	0.0674952i	$0.0215007\pi$
$8$		0			0
$9$	238.398	+	47.0695i	0.981061	+	0.193702i
$10$		0			0
$11$	−192.812	+	333.961i	−0.480455	+	0.832173i	−0.999749	−	0.0224231i	$-0.992862\pi$
$11$	−192.812	+	333.961i	−0.480455	+	0.832173i	0.519293	+	0.854596i	$0.326195\pi$
$12$		0			0
$13$	−516.287	−	894.236i	−0.847292	−	1.46755i	−0.883616	−	0.468212i	$-0.844898\pi$
$13$	−516.287	−	894.236i	−0.847292	−	1.46755i	0.0363242	−	0.999340i	$-0.488435\pi$
$14$		0			0
$15$	−425.832	−	938.063i	−0.488663	−	1.07648i
$16$		0			0
$17$	959.020			0.804832			0.402416	−	0.915457i	$-0.368171\pi$
$17$	959.020			0.804832			0.402416	+	0.915457i	$0.368171\pi$
$18$		0			0
$19$	464.576			0.295239			0.147619	−	0.989044i	$-0.452839\pi$
$19$	464.576			0.295239			0.147619	+	0.989044i	$0.452839\pi$
$20$		0			0
$21$	−1035.82	+	1447.64i	−0.512548	+	0.716330i
$22$		0			0
$23$	1151.70	+	1994.81i	0.453963	+	0.786288i	0.998628	−	0.0523662i	$-0.0166763\pi$
$23$	1151.70	+	1994.81i	0.453963	+	0.786288i	−0.544664	+	0.838654i	$0.683343\pi$
$24$		0			0
$25$	−621.235	+	1076.01i	−0.198795	+	0.344323i
$26$		0			0
$27$	−3627.21	−	1091.90i	−0.957555	−	0.288252i
$28$		0			0
$29$	−3549.13	+	6147.28i	−0.783659	+	1.35734i	0.146138	+	0.989264i	$0.453316\pi$
$29$	−3549.13	+	6147.28i	−0.783659	+	1.35734i	−0.929797	+	0.368073i	$0.880018\pi$
$30$		0			0
$31$	3881.53	+	6723.00i	0.725435	+	1.25649i	0.958795	+	0.284100i	$0.0916947\pi$
$31$	3881.53	+	6723.00i	0.725435	+	1.25649i	−0.233360	+	0.972391i	$0.574972\pi$
$32$		0			0
$33$	3497.98	−	4888.74i	0.559156	−	0.781469i
$34$		0			0
$35$	7546.48			1.04130
$36$		0			0
$37$	9317.57			1.11892			0.559459	−	0.828858i	$-0.311009\pi$
$37$	9317.57			1.11892			0.559459	+	0.828858i	$0.311009\pi$
$38$		0			0
$39$	6653.41	+	14656.8i	0.700459	+	1.54304i
$40$		0			0
$41$	6661.64	+	11538.3i	0.618901	+	1.07197i	0.989687	+	0.143250i	$0.0457552\pi$
$41$	6661.64	+	11538.3i	0.618901	+	1.07197i	−0.370785	+	0.928719i	$0.620911\pi$
$42$		0			0
$43$	−1056.29	+	1829.55i	−0.0871190	+	0.150895i	−0.906292	−	0.422652i	$-0.861099\pi$
$43$	−1056.29	+	1829.55i	−0.0871190	+	0.150895i	0.819173	+	0.573546i	$0.194433\pi$
$44$		0			0
$45$	5183.55	+	15199.5i	0.381589	+	1.11892i
$46$		0			0
$47$	1247.40	−	2160.56i	0.0823686	−	0.142667i	−0.821898	−	0.569634i	$-0.807085\pi$
$47$	1247.40	−	2160.56i	0.0823686	−	0.142667i	0.904267	+	0.426968i	$0.140418\pi$
$48$		0			0
$49$	1883.78	+	3262.80i	0.112083	+	0.194133i
$50$		0			0
$51$	−14878.7	−	1454.79i	−0.801012	−	0.0783203i
$52$		0			0
$53$	−10044.2			−0.491163			−0.245582	−	0.969376i	$-0.578979\pi$
$53$	−10044.2			−0.491163			−0.245582	+	0.969376i	$0.578979\pi$
$54$		0			0
$55$	−25484.7			−1.13599
$56$		0			0
$57$	−7207.66	−	704.741i	−0.293837	−	0.0287304i
$58$		0			0
$59$	2720.33	+	4711.75i	0.101740	+	0.176219i	0.912402	−	0.409296i	$-0.134226\pi$
$59$	2720.33	+	4711.75i	0.101740	+	0.176219i	−0.810662	+	0.585515i	$0.800892\pi$
$60$		0			0
$61$	−17094.4	+	29608.4i	−0.588206	+	1.01880i	0.406261	+	0.913757i	$0.366832\pi$
$61$	−17094.4	+	29608.4i	−0.588206	+	1.01880i	−0.994467	+	0.105046i	$0.966501\pi$
$62$		0			0
$63$	18266.1	−	20888.1i	0.579823	−	0.663053i
$64$		0			0
$65$	34119.8	−	59097.2i	1.00167	−	1.73494i
$66$		0			0
$67$	26792.6	+	46406.2i	0.729169	+	1.26296i	0.957235	+	0.289311i	$0.0934263\pi$
$67$	26792.6	+	46406.2i	0.729169	+	1.26296i	−0.228066	+	0.973646i	$0.573240\pi$
$68$		0			0
$69$	−14842.0	−	32695.5i	−0.375293	−	0.826732i
$70$		0			0
$71$	970.010			0.0228365			0.0114183	−	0.999935i	$-0.496365\pi$
$71$	970.010			0.0228365			0.0114183	+	0.999935i	$0.496365\pi$
$72$		0			0
$73$	−72400.3			−1.59013			−0.795066	−	0.606523i	$-0.792564\pi$
$73$	−72400.3			−1.59013			−0.795066	+	0.606523i	$0.792564\pi$
$74$		0			0
$75$	11270.4	−	15751.3i	0.231359	−	0.323344i
$76$		0			0
$77$	22017.3	+	38135.1i	0.423192	+	0.732990i
$78$		0			0
$79$	16098.9	−	27884.0i	0.290220	−	0.502676i	−0.683642	−	0.729818i	$-0.739605\pi$
$79$	16098.9	−	27884.0i	0.290220	−	0.502676i	0.973862	+	0.227142i	$0.0729382\pi$
$80$		0			0
$81$	54617.9	+	22442.5i	0.924959	+	0.380066i
$82$		0			0
$83$	−18046.6	+	31257.6i	−0.287541	+	0.498036i	−0.973222	−	0.229866i	$-0.926171\pi$
$83$	−18046.6	+	31257.6i	−0.287541	+	0.498036i	0.685681	+	0.727902i	$0.259504\pi$
$84$		0			0
$85$	31689.3	+	54887.5i	0.475735	+	0.823998i
$86$		0			0
$87$	64388.1	−	89987.9i	0.912026	−	1.27464i
$88$		0			0
$89$	42622.2			0.570375			0.285188	−	0.958472i	$-0.407944\pi$
$89$	42622.2			0.570375			0.285188	+	0.958472i	$0.407944\pi$
$90$		0			0
$91$	−117910.			−1.49261
$92$		0			0
$93$	−50021.4	−	110192.i	−0.599720	−	1.32112i
$94$		0			0
$95$	15351.2	+	26589.0i	0.174515	+	0.302269i
$96$		0			0
$97$	21926.9	−	37978.6i	0.236618	−	0.409835i	−0.723123	−	0.690719i	$-0.757294\pi$
$97$	21926.9	−	37978.6i	0.236618	−	0.409835i	0.959742	+	0.280884i	$0.0906275\pi$
$98$		0			0
$99$	−61685.4	+	70539.9i	−0.632549	+	0.723347i
$100$		0			0
$101$	−12056.7	+	20882.8i	−0.117604	+	0.203697i	−0.918818	−	0.394682i	$-0.870855\pi$
$101$	−12056.7	+	20882.8i	−0.117604	+	0.203697i	0.801213	+	0.598379i	$0.204188\pi$
$102$		0			0
$103$	−68610.4	−	118837.i	−0.637231	−	1.10372i	−0.986038	−	0.166522i	$-0.946746\pi$
$103$	−68610.4	−	118837.i	−0.637231	−	1.10372i	0.348807	−	0.937195i	$-0.386587\pi$
$104$		0			0
$105$	−117080.	−	11447.7i	−1.03635	−	0.101331i
$106$		0			0
$107$	167979.			1.41839			0.709195	−	0.705012i	$-0.249059\pi$
$107$	167979.			1.41839			0.709195	+	0.705012i	$0.249059\pi$
$108$		0			0
$109$	−21224.0			−0.171104			−0.0855521	−	0.996334i	$-0.527265\pi$
$109$	−21224.0			−0.171104			−0.0855521	+	0.996334i	$0.527265\pi$
$110$		0			0
$111$	−144557.	−	14134.3i	−1.11361	−	0.108885i
$112$		0			0
$113$	14420.8	+	24977.5i	0.106241	+	0.184015i	0.914245	−	0.405163i	$-0.132785\pi$
$113$	14420.8	+	24977.5i	0.106241	+	0.184015i	−0.808003	+	0.589178i	$0.799452\pi$
$114$		0			0
$115$	−76112.4	+	131831.i	−0.536674	+	0.929547i
$116$		0			0
$117$	−80990.5	−	237485.i	−0.546977	−	1.60388i
$118$		0			0
$119$	54755.4	−	94839.2i	0.354454	−	0.613932i
$120$		0			0
$121$	6172.35	+	10690.8i	0.0383255	+	0.0663816i
$122$		0			0
$123$	−85848.7	−	189116.i	−0.511648	−	1.12711i
$124$		0			0
$125$	124410.			0.712167
$126$		0			0
$127$	215062.			1.18319			0.591594	−	0.806236i	$-0.298499\pi$
$127$	215062.			1.18319			0.591594	+	0.806236i	$0.298499\pi$
$128$		0			0
$129$	19163.2	−	26782.2i	0.101389	−	0.141701i
$130$		0			0
$131$	−94654.7	−	163947.i	−0.481908	−	0.834688i	0.517877	−	0.855455i	$-0.326723\pi$
$131$	−94654.7	−	163947.i	−0.481908	−	0.834688i	−0.999784	+	0.0207668i	$0.993389\pi$
$132$		0			0
$133$	26525.1	−	45942.8i	0.130025	−	0.225210i
$134$		0			0
$135$	−57363.1	−	243676.i	−0.270893	−	1.15074i
$136$		0			0
$137$	1809.78	−	3134.63i	0.00823805	−	0.0142687i	−0.861877	−	0.507117i	$-0.830711\pi$
$137$	1809.78	−	3134.63i	0.00823805	−	0.0142687i	0.870115	+	0.492849i	$0.164044\pi$
$138$		0			0
$139$	60440.1	+	104685.i	0.265331	+	0.459567i	0.967650	−	0.252295i	$-0.0811854\pi$
$139$	60440.1	+	104685.i	0.265331	+	0.459567i	−0.702319	+	0.711862i	$0.747852\pi$
$140$		0			0
$141$	−22630.2	+	31627.7i	−0.0958609	+	0.133974i
$142$		0			0
$143$	398186.			1.62834
$144$		0			0
$145$	−469102.			−1.85288
$146$		0			0
$147$	−24276.3	−	53478.2i	−0.0926594	−	0.204119i
$148$		0			0
$149$	−37408.2	−	64792.9i	−0.138039	−	0.239090i	0.788715	−	0.614758i	$-0.210746\pi$
$149$	−37408.2	−	64792.9i	−0.138039	−	0.239090i	−0.926754	+	0.375668i	$0.877413\pi$
$150$		0			0
$151$	−179976.	+	311728.i	−0.642352	+	1.11259i	0.342554	+	0.939498i	$0.388708\pi$
$151$	−179976.	+	311728.i	−0.642352	+	1.11259i	−0.984906	+	0.173088i	$0.944625\pi$
$152$		0			0
$153$	228628.	+	45140.6i	0.789589	+	0.155897i
$154$		0			0
$155$	−256518.	+	444302.i	−0.857607	+	1.48542i
$156$		0			0
$157$	−23983.3	−	41540.3i	−0.0776533	−	0.134499i	0.824584	−	0.565740i	$-0.191409\pi$
$157$	−23983.3	−	41540.3i	−0.0776533	−	0.134499i	−0.902237	+	0.431241i	$0.858076\pi$
$158$		0			0
$159$	155831.	+	15236.6i	0.488832	+	0.0477964i
$160$		0			0
$161$	263027.			0.799715
$162$		0			0
$163$	−361063.			−1.06442			−0.532212	−	0.846611i	$-0.678639\pi$
$163$	−361063.			−1.06442			−0.532212	+	0.846611i	$0.678639\pi$
$164$		0			0
$165$	395382.	+	38659.1i	1.13059	+	0.110546i
$166$		0			0
$167$	58233.2	+	100863.i	0.161577	+	0.279860i	0.935434	−	0.353500i	$-0.115009\pi$
$167$	58233.2	+	100863.i	0.161577	+	0.279860i	−0.773857	+	0.633360i	$0.781675\pi$
$168$		0			0
$169$	−347458.	+	601816.i	−0.935807	+	1.62086i
$170$		0			0
$171$	110754.	+	21867.4i	0.289647	+	0.0571882i
$172$		0			0
$173$	−51762.9	+	89656.0i	−0.131493	+	0.227753i	−0.924252	−	0.381782i	$-0.875311\pi$
$173$	−51762.9	+	89656.0i	−0.131493	+	0.227753i	0.792759	+	0.609535i	$0.208644\pi$
$174$		0			0
$175$	70939.0	+	122870.i	0.175102	+	0.303285i
$176$		0			0
$177$	−35057.0	−	77226.9i	−0.0841088	−	0.185283i
$178$		0			0
$179$	78941.2			0.184150			0.0920748	−	0.995752i	$-0.470650\pi$
$179$	78941.2			0.184150			0.0920748	+	0.995752i	$0.470650\pi$
$180$		0			0
$181$	586108.			1.32978			0.664892	−	0.746940i	$-0.268478\pi$
$181$	586108.			1.32978			0.664892	+	0.746940i	$0.268478\pi$
$182$		0			0
$183$	310125.	−	433427.i	0.684557	−	0.956728i
$184$		0			0
$185$	307884.	+	533271.i	0.661391	+	1.14556i
$186$		0			0
$187$	−184911.	+	320275.i	−0.386686	+	0.669760i
$188$		0			0
$189$	−315076.	+	296359.i	−0.641595	+	0.603482i
$190$		0			0
$191$	386026.	−	668617.i	0.765656	−	1.32615i	−0.174243	−	0.984703i	$-0.555748\pi$
$191$	386026.	−	668617.i	0.765656	−	1.32615i	0.939899	−	0.341452i	$-0.110919\pi$
$192$		0			0
$193$	8719.67	+	15102.9i	0.0168503	+	0.0291855i	0.874328	−	0.485336i	$-0.161303\pi$
$193$	8719.67	+	15102.9i	0.0168503	+	0.0291855i	−0.857477	+	0.514522i	$0.827969\pi$
$194$		0			0
$195$	−618998.	+	865104.i	−1.16574	+	1.62923i
$196$		0			0
$197$	340729.			0.625524			0.312762	−	0.949832i	$-0.398746\pi$
$197$	340729.			0.625524			0.312762	+	0.949832i	$0.398746\pi$
$198$		0			0
$199$	−14239.7			−0.0254899			−0.0127450	−	0.999919i	$-0.504057\pi$
$199$	−14239.7			−0.0254899			−0.0127450	+	0.999919i	$0.504057\pi$
$200$		0			0
$201$	−345277.	−	760610.i	−0.602806	−	1.32792i
$202$		0			0
$203$	405277.	+	701960.i	0.690258	+	1.19556i
$204$		0			0
$205$	−440246.	+	762529.i	−0.731663	+	1.26728i
$206$		0			0
$207$	180669.	+	529768.i	0.293061	+	0.859329i
$208$		0			0
$209$	−89576.0	+	155150.i	−0.141849	+	0.245690i
$210$		0			0
$211$	−24049.2	−	41654.4i	−0.0371873	−	0.0644102i	0.846833	−	0.531859i	$-0.178506\pi$
$211$	−24049.2	−	41654.4i	−0.0371873	−	0.0644102i	−0.884020	+	0.467449i	$0.845173\pi$
$212$		0			0
$213$	−15049.2	−	1471.46i	−0.0227282	−	0.00222228i
$214$		0			0
$215$	−139614.			−0.205984
$216$		0			0
$217$	886466.			1.27795
$218$		0			0
$219$	1.12325e6	+	109828.i	1.58258	+	0.154740i
$220$		0			0
$221$	−495130.	−	857590.i	−0.681928	−	1.18113i
$222$		0			0
$223$	391988.	−	678944.i	0.527851	−	0.914264i	−0.471622	−	0.881801i	$-0.656331\pi$
$223$	391988.	−	678944.i	0.527851	−	0.914264i	0.999473	−	0.0324633i	$-0.0103352\pi$
$224$		0			0
$225$	−198748.	+	227277.i	−0.261726	+	0.299295i
$226$		0			0
$227$	−277898.	+	481334.i	−0.357949	+	0.619986i	−0.987618	−	0.156878i	$-0.949857\pi$
$227$	−277898.	+	481334.i	−0.357949	+	0.619986i	0.629669	+	0.776863i	$0.283190\pi$
$228$		0			0
$229$	−57346.2	−	99326.6i	−0.0722630	−	0.125163i	0.827630	−	0.561274i	$-0.189689\pi$
$229$	−57346.2	−	99326.6i	−0.0722630	−	0.125163i	−0.899893	+	0.436111i	$0.856355\pi$
$230$		0			0
$231$	−283738.	−	625045.i	−0.349854	−	0.770693i
$232$		0			0
$233$	−111177.			−0.134161			−0.0670805	−	0.997748i	$-0.521368\pi$
$233$	−111177.			−0.134161			−0.0670805	+	0.997748i	$0.521368\pi$
$234$		0			0
$235$	164874.			0.194752
$236$		0			0
$237$	−292064.	+	408185.i	−0.337759	+	0.472048i
$238$		0			0
$239$	−369523.	−	640033.i	−0.418453	−	0.724782i	0.577331	−	0.816510i	$-0.304094\pi$
$239$	−369523.	−	640033.i	−0.418453	−	0.724782i	−0.995784	+	0.0917279i	$0.970761\pi$
$240$		0			0
$241$	645180.	−	1.11748e6i	0.715547	−	1.23936i	−0.247201	−	0.968964i	$-0.579511\pi$
$241$	645180.	−	1.11748e6i	0.715547	−	1.23936i	0.962748	−	0.270400i	$-0.0871559\pi$
$242$		0			0
$243$	−813324.	−	431036.i	−0.883584	−	0.468272i
$244$		0			0
$245$	−124493.	+	215628.i	−0.132504	+	0.229504i
$246$		0			0
$247$	−239855.	−	415441.i	−0.250153	−	0.433278i
$248$		0			0
$249$	327400.	−	457569.i	0.334641	−	0.467690i
$250$		0			0
$251$	−1.29383e6			−1.29626			−0.648129	−	0.761530i	$-0.724448\pi$
$251$	−1.29383e6			−1.29626			−0.648129	+	0.761530i	$0.724448\pi$
$252$		0			0
$253$	−888250.			−0.872437
$254$		0			0
$255$	−408381.	−	899621.i	−0.393292	−	0.866382i
$256$		0			0
$257$	−312181.	−	540713.i	−0.294831	−	0.510663i	0.680114	−	0.733106i	$-0.261930\pi$
$257$	−312181.	−	540713.i	−0.294831	−	0.510663i	−0.974946	+	0.222443i	$0.928597\pi$
$258$		0			0
$259$	531988.	−	921431.i	0.492780	−	0.853519i
$260$		0			0
$261$	−1.13545e6	+	1.29844e6i	−1.03174	+	1.17983i
$262$		0			0
$263$	−582495.	+	1.00891e6i	−0.519281	+	0.899421i	0.480468	+	0.877012i	$0.340467\pi$
$263$	−582495.	+	1.00891e6i	−0.519281	+	0.899421i	−0.999749	+	0.0224089i	$0.992866\pi$
$264$		0			0
$265$	−331895.	−	574859.i	−0.290326	−	0.502859i
$266$		0			0
$267$	−661261.	−	64655.9i	−0.567668	−	0.0555047i
$268$		0			0
$269$	1.58951e6			1.33932			0.669659	−	0.742669i	$-0.266440\pi$
$269$	1.58951e6			1.33932			0.669659	+	0.742669i	$0.266440\pi$
$270$		0			0
$271$	977878.			0.808837			0.404419	−	0.914574i	$-0.367474\pi$
$271$	977878.			0.808837			0.404419	+	0.914574i	$0.367474\pi$
$272$		0			0
$273$	1.82931e6	+	178864.i	1.48553	+	0.145250i
$274$		0			0
$275$	−239563.	−	414936.i	−0.191024	−	0.330864i
$276$		0			0
$277$	645243.	−	1.11759e6i	0.505271	−	0.875154i	−0.494711	−	0.869058i	$-0.664726\pi$
$277$	645243.	−	1.11759e6i	0.505271	−	0.875154i	0.999981	−	0.00609677i	$-0.00194067\pi$
$278$		0			0
$279$	608899.	+	1.78545e6i	0.468312	+	1.37321i
$280$		0			0
$281$	−833662.	+	1.44395e6i	−0.629831	+	1.09090i	0.357754	+	0.933816i	$0.383543\pi$
$281$	−833662.	+	1.44395e6i	−0.629831	+	1.09090i	−0.987585	+	0.157084i	$0.949791\pi$
$282$		0			0
$283$	564568.	+	977861.i	0.419035	+	0.725790i	0.995843	−	0.0910901i	$-0.0290351\pi$
$283$	564568.	+	977861.i	0.419035	+	0.725790i	−0.576808	+	0.816880i	$0.695702\pi$
$284$		0			0
$285$	−197831.	−	435802.i	−0.144272	−	0.317817i
$286$		0			0
$287$	1.52139e6			1.09027
$288$		0			0
$289$	−500138.			−0.352245
$290$		0			0
$291$	−397797.	+	555955.i	−0.275378	+	0.384864i
$292$		0			0
$293$	−1.02815e6	−	1.78081e6i	−0.699663	−	1.21185i	−0.968583	−	0.248689i	$-0.920000\pi$
$293$	−1.02815e6	−	1.78081e6i	−0.699663	−	1.21185i	0.268921	−	0.963162i	$-0.413333\pi$
$294$		0			0
$295$	−179778.	+	311385.i	−0.120277	+	0.208325i
$296$		0			0
$297$	1.06402e6	−	1.00082e6i	0.699937	−	0.658359i
$298$		0			0
$299$	1.18922e6	−	2.05979e6i	0.769279	−	1.33243i
$300$		0			0
$301$	120618.	+	208917.i	0.0767357	+	0.132910i
$302$		0			0
$303$	218731.	−	305696.i	0.136869	−	0.191286i
$304$		0			0
$305$	−2.25943e6			−1.39075
$306$		0			0
$307$	−1.52149e6			−0.921346			−0.460673	−	0.887570i	$-0.652392\pi$
$307$	−1.52149e6			−0.921346			−0.460673	+	0.887570i	$0.652392\pi$
$308$		0			0
$309$	884184.	+	1.94777e6i	0.526801	+	1.16049i
$310$		0			0
$311$	−1.35420e6	−	2.34554e6i	−0.793928	−	1.37512i	−0.923517	−	0.383556i	$-0.874699\pi$
$311$	−1.35420e6	−	2.34554e6i	−0.793928	−	1.37512i	0.129589	−	0.991568i	$-0.458634\pi$
$312$		0			0
$313$	325583.	−	563926.i	0.187845	−	0.325358i	−0.756686	−	0.653778i	$-0.773183\pi$
$313$	325583.	−	563926.i	0.187845	−	0.325358i	0.944532	+	0.328420i	$0.106516\pi$
$314$		0			0
$315$	1.79906e6	+	355209.i	1.02157	+	0.201701i
$316$		0			0
$317$	58055.3	−	100555.i	0.0324484	−	0.0562024i	−0.849345	−	0.527838i	$-0.823003\pi$
$317$	58055.3	−	100555.i	0.0324484	−	0.0562024i	0.881794	+	0.471636i	$0.156336\pi$
$318$		0			0
$319$	−1.36863e6	−	2.37054e6i	−0.753026	−	1.30428i
$320$		0			0
$321$	−2.60611e6	−	254816.i	−1.41166	−	0.138027i
$322$		0			0
$323$	445538.			0.237618
$324$		0			0
$325$	1.28294e6			0.673750
$326$		0			0
$327$	329279.	+	32195.8i	0.170292	+	0.0166506i
$328$		0			0
$329$	−142441.	−	246715.i	−0.0725514	−	0.125663i
$330$		0			0
$331$	158828.	−	275099.i	0.0796816	−	0.138013i	−0.823431	−	0.567416i	$-0.807943\pi$
$331$	158828.	−	275099.i	0.0796816	−	0.138013i	0.903113	+	0.429404i	$0.141276\pi$
$332$		0			0
$333$	2.22129e6	+	438573.i	1.09773	+	0.216736i
$334$		0			0
$335$	−1.77064e6	+	3.06684e6i	−0.862021	+	1.49306i
$336$		0			0
$337$	−215275.	−	372867.i	−0.103257	−	0.178846i	0.809768	−	0.586750i	$-0.199593\pi$
$337$	−215275.	−	372867.i	−0.103257	−	0.178846i	−0.913025	+	0.407904i	$0.866260\pi$
$338$		0			0
$339$	−185841.	−	409389.i	−0.0878299	−	0.193480i
$340$		0			0
$341$	−2.99363e6			−1.39416
$342$		0			0
$343$	2.34942e6			1.07826
$344$		0			0
$345$	1.38082e6	−	1.92982e6i	0.624584	−	0.872910i
$346$		0			0
$347$	−2.07020e6	−	3.58569e6i	−0.922971	−	1.59863i	−0.794793	−	0.606881i	$-0.792420\pi$
$347$	−2.07020e6	−	3.58569e6i	−0.922971	−	1.59863i	−0.128178	−	0.991751i	$-0.540913\pi$
$348$		0			0
$349$	1.73048e6	−	2.99727e6i	0.760505	−	1.31723i	−0.182085	−	0.983283i	$-0.558285\pi$
$349$	1.73048e6	−	2.99727e6i	0.760505	−	1.31723i	0.942590	−	0.333951i	$-0.108382\pi$
$350$		0			0
$351$	896271.	+	3.80731e6i	0.388304	+	1.64949i
$352$		0			0
$353$	−1.32229e6	+	2.29027e6i	−0.564792	+	0.978249i	0.432277	+	0.901741i	$0.357710\pi$
$353$	−1.32229e6	+	2.29027e6i	−0.564792	+	0.978249i	−0.997069	+	0.0765076i	$0.975623\pi$
$354$		0			0
$355$	32052.5	+	55516.5i	0.0134987	+	0.0233804i
$356$		0			0
$357$	−993368.	+	1.38832e6i	−0.412515	+	0.576526i
$358$		0			0
$359$	−2.13123e6			−0.872761			−0.436380	−	0.899762i	$-0.643740\pi$
$359$	−2.13123e6			−0.872761			−0.436380	+	0.899762i	$0.643740\pi$
$360$		0			0
$361$	−2.26027e6			−0.912834
$362$		0			0
$363$	−79543.3	−	175226.i	−0.0316838	−	0.0697961i
$364$		0			0
$365$	−2.39235e6	−	4.14368e6i	−0.939925	−	1.62800i
$366$		0			0
$367$	−640035.	+	1.10857e6i	−0.248049	+	0.429634i	−0.962985	−	0.269557i	$-0.913123\pi$
$367$	−640035.	+	1.10857e6i	−0.248049	+	0.429634i	0.714935	+	0.699191i	$0.246456\pi$
$368$		0			0
$369$	1.04502e6	+	3.06426e6i	0.399538	+	1.17155i
$370$		0			0
$371$	−573476.	+	993289.i	−0.216312	+	0.374663i
$372$		0			0
$373$	1.94733e6	+	3.37288e6i	0.724716	+	1.25524i	0.959091	+	0.283099i	$0.0913623\pi$
$373$	1.94733e6	+	3.37288e6i	0.724716	+	1.25524i	−0.234375	+	0.972146i	$0.575304\pi$
$374$		0			0
$375$	−1.93016e6	−	188725.i	−0.708787	−	0.0693028i
$376$		0			0
$377$	7.32949e6			2.65595
$378$		0			0
$379$	2.83335e6			1.01322			0.506609	−	0.862176i	$-0.330899\pi$
$379$	2.83335e6			1.01322			0.506609	+	0.862176i	$0.330899\pi$
$380$		0			0
$381$	−3.33657e6	−	326239.i	−1.17757	−	0.115139i
$382$		0			0
$383$	1.18249e6	+	2.04814e6i	0.411909	+	0.713448i	0.995099	−	0.0988883i	$-0.0315287\pi$
$383$	1.18249e6	+	2.04814e6i	0.411909	+	0.713448i	−0.583189	+	0.812336i	$0.698195\pi$
$384$		0			0
$385$	−1.45505e6	+	2.52023e6i	−0.500296	+	0.866539i
$386$		0			0
$387$	−337934.	+	386442.i	−0.114698	+	0.131162i
$388$		0			0
$389$	871692.	−	1.50981e6i	0.292071	−	0.505882i	−0.682228	−	0.731139i	$-0.738989\pi$
$389$	871692.	−	1.50981e6i	0.292071	−	0.505882i	0.974299	+	0.225257i	$0.0723222\pi$
$390$		0			0
$391$	1.10451e6	+	1.91306e6i	0.365364	+	0.632830i
$392$		0			0
$393$	1.21982e6	+	2.68713e6i	0.398395	+	0.877623i
$394$		0			0
$395$	2.12785e6			0.686195
$396$		0			0
$397$	4.81109e6			1.53203			0.766015	−	0.642823i	$-0.222237\pi$
$397$	4.81109e6			1.53203			0.766015	+	0.642823i	$0.222237\pi$
$398$		0			0
$399$	−481216.	+	672541.i	−0.151324	+	0.211488i
$400$		0			0
$401$	2.27703e6	+	3.94394e6i	0.707145	+	1.22481i	0.965912	+	0.258871i	$0.0833506\pi$
$401$	2.27703e6	+	3.94394e6i	0.707145	+	1.22481i	−0.258767	+	0.965940i	$0.583316\pi$
$402$		0			0
$403$	4.00797e6	−	6.94200e6i	1.22931	−	2.12923i
$404$		0			0
$405$	520314.	+	3.86752e6i	0.157626	+	1.17164i
$406$		0			0
$407$	−1.79654e6	+	3.11170e6i	−0.537590	+	0.931133i
$408$		0			0
$409$	−956414.	−	1.65656e6i	−0.282708	−	0.489664i	0.689343	−	0.724435i	$-0.257899\pi$
$409$	−956414.	−	1.65656e6i	−0.282708	−	0.489664i	−0.972051	+	0.234771i	$0.924566\pi$
$410$		0			0
$411$	−32832.9	+	45886.8i	−0.00958748	+	0.0133993i
$412$		0			0
$413$	621271.			0.179228
$414$		0			0
$415$	−2.38528e6			−0.679860
$416$		0			0
$417$	−778894.	−	1.71582e6i	−0.219350	−	0.483206i
$418$		0			0
$419$	2.20697e6	+	3.82259e6i	0.614132	+	1.06371i	0.990536	+	0.137252i	$0.0438272\pi$
$419$	2.20697e6	+	3.82259e6i	0.614132	+	1.06371i	−0.376404	+	0.926456i	$0.622839\pi$
$420$		0			0
$421$	872253.	−	1.51079e6i	0.239848	−	0.415430i	−0.720822	−	0.693120i	$-0.756236\pi$
$421$	872253.	−	1.51079e6i	0.239848	−	0.415430i	0.960671	+	0.277690i	$0.0895689\pi$
$422$		0			0
$423$	399074.	−	456359.i	0.108443	−	0.124010i
$424$		0			0
$425$	−595777.	+	1.03192e6i	−0.159997	+	0.277122i
$426$		0			0
$427$	1.95202e6	+	3.38099e6i	0.518100	+	0.897376i
$428$		0			0
$429$	−6.17765e6	−	604030.i	−1.62061	−	0.158458i
$430$		0			0
$431$	2.21740e6			0.574976			0.287488	−	0.957784i	$-0.407180\pi$
$431$	2.21740e6			0.574976			0.287488	+	0.957784i	$0.407180\pi$
$432$		0			0
$433$	−3.63511e6			−0.931746			−0.465873	−	0.884851i	$-0.654260\pi$
$433$	−3.63511e6			−0.931746			−0.465873	+	0.884851i	$0.654260\pi$
$434$		0			0
$435$	7.27787e6	+	711606.i	1.84409	+	0.180309i
$436$		0			0
$437$	535054.	+	926741.i	0.134028	+	0.232143i
$438$		0			0
$439$	−1.54413e6	+	2.67452e6i	−0.382405	+	0.662345i	−0.991405	−	0.130825i	$-0.958237\pi$
$439$	−1.54413e6	+	2.67452e6i	−0.382405	+	0.662345i	0.609001	+	0.793170i	$0.291571\pi$
$440$		0			0
$441$	295510.	+	866512.i	0.0723562	+	0.212167i
$442$		0			0
$443$	−3.50048e6	+	6.06302e6i	−0.847459	+	1.46784i	0.0360092	+	0.999351i	$0.488535\pi$
$443$	−3.50048e6	+	6.06302e6i	−0.847459	+	1.46784i	−0.883468	+	0.468491i	$0.844798\pi$
$444$		0			0
$445$	1.40838e6	+	2.43939e6i	0.337148	+	0.583958i
$446$		0			0
$447$	482080.	+	1.06197e6i	0.114117	+	0.251388i
$448$		0			0
$449$	−5.00196e6			−1.17091			−0.585456	−	0.810704i	$-0.699084\pi$
$449$	−5.00196e6			−1.17091			−0.585456	+	0.810704i	$0.699084\pi$
$450$		0			0
$451$	−5.13778e6			−1.18942
$452$		0			0
$453$	3.26511e6	−	4.56328e6i	0.747572	−	1.04480i
$454$		0			0
$455$	−3.89615e6	−	6.74833e6i	−0.882282	−	1.52816i
$456$		0			0
$457$	−1.78581e6	+	3.09311e6i	−0.399985	+	0.692795i	−0.993724	−	0.111863i	$-0.964318\pi$
$457$	−1.78581e6	+	3.09311e6i	−0.399985	+	0.692795i	0.593738	+	0.804658i	$0.297651\pi$
$458$		0			0
$459$	−3.47857e6	−	1.04715e6i	−0.770671	−	0.231994i
$460$		0			0
$461$	−2.75061e6	+	4.76420e6i	−0.602805	+	1.04409i	0.389589	+	0.920989i	$0.372617\pi$
$461$	−2.75061e6	+	4.76420e6i	−0.602805	+	1.04409i	−0.992394	+	0.123100i	$0.960716\pi$
$462$		0			0
$463$	−1.42708e6	−	2.47177e6i	−0.309382	−	0.535866i	0.668845	−	0.743402i	$-0.266789\pi$
$463$	−1.42708e6	−	2.47177e6i	−0.309382	−	0.535866i	−0.978227	+	0.207536i	$0.933456\pi$
$464$		0			0
$465$	4.65373e6	−	6.50399e6i	0.998087	−	1.39491i
$466$		0			0
$467$	7.16552e6			1.52039			0.760196	−	0.649694i	$-0.225103\pi$
$467$	7.16552e6			1.52039			0.760196	+	0.649694i	$0.225103\pi$
$468$		0			0
$469$	6.11892e6			1.28452
$470$		0			0
$471$	309074.	+	680857.i	0.0641962	+	0.141418i
$472$		0			0
$473$	−407332.	−	705520.i	−0.0837136	−	0.144996i
$474$		0			0
$475$	−288611.	+	499889.i	−0.0586920	+	0.101658i
$476$		0			0
$477$	−2.39452e6	−	472775.i	−0.481861	−	0.0951391i
$478$		0			0
$479$	1.64185e6	−	2.84377e6i	0.326961	−	0.566312i	−0.654947	−	0.755675i	$-0.727309\pi$
$479$	1.64185e6	−	2.84377e6i	0.326961	−	0.566312i	0.981907	+	0.189363i	$0.0606423\pi$
$480$		0			0
$481$	−4.81054e6	−	8.33210e6i	−0.948050	−	1.64207i
$482$		0			0
$483$	−4.08072e6	−	398999.i	−0.795920	−	0.0778224i
$484$		0			0
$485$	2.89816e6			0.559459
$486$		0			0
$487$	−2.18097e6			−0.416704			−0.208352	−	0.978054i	$-0.566810\pi$
$487$	−2.18097e6			−0.416704			−0.208352	+	0.978054i	$0.566810\pi$
$488$		0			0
$489$	5.60171e6	+	547716.i	1.05937	+	0.103582i
$490$		0			0
$491$	−4.96974e6	−	8.60785e6i	−0.930315	−	1.61135i	−0.782782	−	0.622297i	$-0.786200\pi$
$491$	−4.96974e6	−	8.60785e6i	−0.930315	−	1.61135i	−0.147534	−	0.989057i	$-0.547134\pi$
$492$		0			0
$493$	−3.40369e6	+	5.89536e6i	−0.630714	+	1.09243i
$494$		0			0
$495$	−6.07550e6	−	1.19955e6i	−1.11447	−	0.220042i
$496$		0			0
$497$	55382.9	−	95926.0i	0.0100574	−	0.0174199i
$498$		0			0
$499$	−2.26386e6	−	3.92112e6i	−0.407004	−	0.704951i	0.587549	−	0.809189i	$-0.300093\pi$
$499$	−2.26386e6	−	3.92112e6i	−0.407004	−	0.704951i	−0.994552	+	0.104238i	$0.966760\pi$
$500$		0			0
$501$	−750453.	−	1.65317e6i	−0.133576	−	0.294255i
$502$		0			0
$503$	4.40282e6			0.775909			0.387955	−	0.921679i	$-0.373182\pi$
$503$	4.40282e6			0.775909			0.387955	+	0.921679i	$0.373182\pi$
$504$		0			0
$505$	−1.59357e6			−0.278063
$506$		0			0
$507$	6.30356e6	−	8.80977e6i	1.08910	−	1.52211i
$508$		0			0
$509$	−2.91063e6	−	5.04135e6i	−0.497957	−	0.862487i	0.502040	−	0.864844i	$-0.332583\pi$
$509$	−2.91063e6	−	5.04135e6i	−0.497957	−	0.862487i	−0.999997	+	0.00235703i	$0.999250\pi$
$510$		0			0
$511$	−4.13371e6	+	7.15979e6i	−0.700306	+	1.21296i
$512$		0			0
$513$	−1.68512e6	−	507269.i	−0.282707	−	0.0851030i
$514$		0			0
$515$	4.53424e6	−	7.85354e6i	0.753333	−	1.30481i
$516$		0			0
$517$	481028.	+	833166.i	0.0791488	+	0.137090i
$518$		0			0
$519$	939078.	−	1.31244e6i	0.153032	−	0.213876i
$520$		0			0
$521$	1.09649e7			1.76975			0.884875	−	0.465829i	$-0.154244\pi$
$521$	1.09649e7			1.76975			0.884875	+	0.465829i	$0.154244\pi$
$522$		0			0
$523$	3.83705e6			0.613399			0.306700	−	0.951806i	$-0.400775\pi$
$523$	3.83705e6			0.613399			0.306700	+	0.951806i	$0.400775\pi$
$524$		0			0
$525$	−914194.	−	2.01387e6i	−0.144757	−	0.318885i
$526$		0			0
$527$	3.72246e6	+	6.44750e6i	0.583854	+	1.01126i
$528$		0			0
$529$	565332.	−	979183.i	0.0878343	−	0.152133i
$530$		0			0
$531$	426741.	+	1.25131e6i	0.0656792	+	0.192588i
$532$		0			0
$533$	6.87864e6	−	1.19141e7i	1.04878	−	1.81654i
$534$		0			0
$535$	5.55060e6	+	9.61392e6i	0.838408	+	1.45217i
$536$		0			0
$537$	−1.22473e6	−	119750.i	−0.183276	−	0.0179201i
$538$		0			0
$539$	−1.45286e6			−0.215403
$540$		0			0
$541$	−4.88767e6			−0.717974			−0.358987	−	0.933343i	$-0.616878\pi$
$541$	−4.88767e6			−0.717974			−0.358987	+	0.933343i	$0.616878\pi$
$542$		0			0
$543$	−9.09315e6	−	889098.i	−1.32347	−	0.129405i
$544$		0			0
$545$	−701313.	−	1.21471e6i	−0.101139	−	0.175179i
$546$		0			0
$547$	−3.46672e6	+	6.00454e6i	−0.495394	+	0.858047i	−0.999986	−	0.00531061i	$-0.998310\pi$
$547$	−3.46672e6	+	6.00454e6i	−0.495394	+	0.858047i	0.504592	+	0.863358i	$0.331643\pi$
$548$		0			0
$549$	−5.46892e6	+	6.25395e6i	−0.774410	+	0.885571i
$550$		0			0
$551$	−1.64884e6	+	2.85588e6i	−0.231366	+	0.400739i
$552$		0			0
$553$	−1.83834e6	−	3.18409e6i	−0.255630	−	0.442764i
$554$		0			0
$555$	−3.96772e6	−	8.74047e6i	−0.546774	−	1.20449i
$556$		0			0
$557$	−9.83771e6			−1.34356			−0.671778	−	0.740752i	$-0.734469\pi$
$557$	−9.83771e6			−1.34356			−0.671778	+	0.740752i	$0.734469\pi$
$558$		0			0
$559$	2.18140e6			0.295261
$560$		0			0
$561$	3.35464e6	−	4.68840e6i	0.450027	−	0.628951i
$562$		0			0
$563$	1.36609e6	+	2.36613e6i	0.181638	+	0.314607i	0.942439	−	0.334379i	$-0.108527\pi$
$563$	1.36609e6	+	2.36613e6i	0.181638	+	0.314607i	−0.760800	+	0.648986i	$0.775193\pi$
$564$		0			0
$565$	−953024.	+	1.65069e6i	−0.125598	+	0.217542i
$566$		0			0
$567$	5.33780e6	−	4.11990e6i	0.697276	−	0.538182i
$568$		0			0
$569$	−4.71998e6	+	8.17525e6i	−0.611167	+	1.05857i	0.379877	+	0.925037i	$0.375966\pi$
$569$	−4.71998e6	+	8.17525e6i	−0.611167	+	1.05857i	−0.991044	+	0.133535i	$0.957367\pi$
$570$		0			0
$571$	−6.33948e6	−	1.09803e7i	−0.813698	−	1.40937i	−0.910259	−	0.414039i	$-0.864118\pi$
$571$	−6.33948e6	−	1.09803e7i	−0.813698	−	1.40937i	0.0965611	−	0.995327i	$-0.469216\pi$
$572$		0			0
$573$	−7.00326e6	+	9.78766e6i	−0.891073	+	1.24535i
$574$		0			0
$575$	−2.86191e6			−0.360983
$576$		0			0
$577$	−1.51657e7			−1.89637			−0.948187	−	0.317712i	$-0.897086\pi$
$577$	−1.51657e7			−1.89637			−0.948187	+	0.317712i	$0.897086\pi$
$578$		0			0
$579$	−112371.	−	247541.i	−0.0139302	−	0.0306867i
$580$		0			0
$581$	2.06075e6	+	3.56932e6i	0.253270	+	0.438677i
$582$		0			0
$583$	1.93665e6	−	3.35437e6i	0.235982	−	0.408733i
$584$		0			0
$585$	1.09158e7	−	1.24826e7i	1.31875	−	1.50805i
$586$		0			0
$587$	911702.	−	1.57911e6i	0.109209	−	0.189155i	−0.806241	−	0.591587i	$-0.798502\pi$
$587$	911702.	−	1.57911e6i	0.109209	−	0.189155i	0.915450	+	0.402432i	$0.131835\pi$
$588$		0			0
$589$	1.80327e6	+	3.12335e6i	0.214176	+	0.370965i
$590$		0			0
$591$	−5.28623e6	−	516870.i	−0.622555	−	0.0608713i
$592$		0			0
$593$	1.27957e7			1.49427			0.747133	−	0.664674i	$-0.231430\pi$
$593$	1.27957e7			1.49427			0.747133	+	0.664674i	$0.231430\pi$
$594$		0			0
$595$	7.23723e6			0.838069
$596$		0			0
$597$	220922.	+	21601.0i	0.0253689	+	0.00248049i
$598$		0			0
$599$	4.38212e6	+	7.59006e6i	0.499020	+	0.864327i	0.999999	−	0.00113166i	$-0.000360218\pi$
$599$	4.38212e6	+	7.59006e6i	0.499020	+	0.864327i	−0.500980	+	0.865459i	$0.667027\pi$
$600$		0			0
$601$	−834793.	+	1.44590e6i	−0.0942741	+	0.163288i	−0.909305	−	0.416129i	$-0.863386\pi$
$601$	−834793.	+	1.44590e6i	−0.0942741	+	0.163288i	0.815031	+	0.579417i	$0.196720\pi$
$602$		0			0
$603$	4.20298e6	+	1.23242e7i	0.470722	+	1.38028i
$604$		0			0
$605$	−407911.	+	706523.i	−0.0453082	+	0.0784762i
$606$		0			0
$607$	−5.08535e6	−	8.80809e6i	−0.560208	−	0.970308i	−0.997478	−	0.0709782i	$-0.977388\pi$
$607$	−5.08535e6	−	8.80809e6i	−0.560208	−	0.970308i	0.437270	−	0.899330i	$-0.355945\pi$
$608$		0			0
$609$	−5.22282e6	−	1.15053e7i	−0.570639	−	1.25706i
$610$		0			0
$611$	−2.57607e6			−0.279161
$612$		0			0
$613$	1.37829e7			1.48146			0.740730	−	0.671803i	$-0.234480\pi$
$613$	1.37829e7			1.48146			0.740730	+	0.671803i	$0.234480\pi$
$614$		0			0
$615$	7.98691e6	−	1.11624e7i	0.851513	−	1.19006i
$616$		0			0
$617$	6.05409e6	+	1.04860e7i	0.640230	+	1.10891i	0.985381	+	0.170363i	$0.0544942\pi$
$617$	6.05409e6	+	1.04860e7i	0.640230	+	1.10891i	−0.345152	+	0.938547i	$0.612173\pi$
$618$		0			0
$619$	−8.48665e6	+	1.46993e7i	−0.890245	+	1.54195i	−0.0506641	+	0.998716i	$0.516134\pi$
$619$	−8.48665e6	+	1.46993e7i	−0.890245	+	1.54195i	−0.839581	+	0.543234i	$0.817200\pi$
$620$		0			0
$621$	−1.99935e6	−	8.49313e6i	−0.208046	−	0.883769i
$622$		0			0
$623$	2.43352e6	−	4.21498e6i	0.251197	−	0.435087i
$624$		0			0
$625$	6.05231e6	+	1.04829e7i	0.619756	+	1.07345i
$626$		0			0
$627$	1.62508e6	−	2.27119e6i	0.165084	−	0.230720i
$628$		0			0
$629$	8.93574e6			0.900541
$630$		0			0
$631$	−7.90092e6			−0.789958			−0.394979	−	0.918690i	$-0.629248\pi$
$631$	−7.90092e6			−0.789958			−0.394979	+	0.918690i	$0.629248\pi$
$632$		0			0
$633$	309923.	+	682728.i	0.0307428	+	0.0677233i
$634$		0			0
$635$	7.10637e6	+	1.23086e7i	0.699381	+	1.21136i
$636$		0			0
$637$	1.94514e6	−	3.36908e6i	0.189934	−	0.328975i
$638$		0			0
$639$	231248.	+	45657.9i	0.0224040	+	0.00442347i
$640$		0			0
$641$	−5.33807e6	+	9.24581e6i	−0.513144	+	0.888792i	0.486740	+	0.873547i	$0.338186\pi$
$641$	−5.33807e6	+	9.24581e6i	−0.513144	+	0.888792i	−0.999884	+	0.0152446i	$0.995147\pi$
$642$		0			0
$643$	4.68885e6	+	8.12132e6i	0.447238	+	0.774639i	0.998205	−	0.0598882i	$-0.0190744\pi$
$643$	4.68885e6	+	8.12132e6i	0.447238	+	0.774639i	−0.550967	+	0.834527i	$0.685741\pi$
$644$		0			0
$645$	2.16604e6	+	211788.i	0.205006	+	0.0200448i
$646$		0			0
$647$	9.44013e6			0.886579			0.443289	−	0.896379i	$-0.353811\pi$
$647$	9.44013e6			0.886579			0.443289	+	0.896379i	$0.353811\pi$
$648$		0			0
$649$	−2.09805e6			−0.195526
$650$		0			0
$651$	−1.37531e7	−	1.34473e6i	−1.27188	−	0.124360i
$652$		0			0
$653$	−7.44455e6	−	1.28943e7i	−0.683212	−	1.18336i	−0.973995	−	0.226569i	$-0.927249\pi$
$653$	−7.44455e6	−	1.28943e7i	−0.683212	−	1.18336i	0.290783	−	0.956789i	$-0.406084\pi$
$654$		0			0
$655$	6.25543e6	−	1.08347e7i	0.569710	−	0.986766i
$656$		0			0
$657$	−1.72601e7	−	3.40784e6i	−1.56002	−	0.308011i
$658$		0			0
$659$	−3.82391e6	+	6.62320e6i	−0.343000	+	0.594093i	−0.984988	−	0.172621i	$-0.944776\pi$
$659$	−3.82391e6	+	6.62320e6i	−0.343000	+	0.594093i	0.641989	+	0.766714i	$0.278110\pi$
$660$		0			0
$661$	2.50269e6	+	4.33479e6i	0.222794	+	0.385891i	0.955655	−	0.294487i	$-0.0951489\pi$
$661$	2.50269e6	+	4.33479e6i	0.222794	+	0.385891i	−0.732861	+	0.680378i	$0.761816\pi$
$662$		0			0
$663$	6.38075e6	+	1.40561e7i	0.563752	+	1.24189i
$664$		0			0
$665$	3.50592e6			0.307431
$666$		0			0
$667$	−1.63502e7			−1.42301
$668$		0			0
$669$	−7.11142e6	+	9.93882e6i	−0.614315	+	0.858558i
$670$		0			0
$671$	−6.59202e6	−	1.14177e7i	−0.565214	−	0.978979i
$672$		0			0
$673$	−1.07220e6	+	1.85710e6i	−0.0912511	+	0.158051i	−0.908038	−	0.418888i	$-0.862420\pi$
$673$	−1.07220e6	+	1.85710e6i	−0.0912511	+	0.158051i	0.816787	+	0.576940i	$0.195753\pi$
$674$		0			0
$675$	3.42824e6	−	3.22459e6i	0.289609	−	0.272405i
$676$		0			0
$677$	4.75463e6	−	8.23526e6i	0.398699	−	0.690567i	−0.594867	−	0.803824i	$-0.702795\pi$
$677$	4.75463e6	−	8.23526e6i	0.398699	−	0.690567i	0.993566	+	0.113257i	$0.0361285\pi$
$678$		0			0
$679$	−2.50385e6	−	4.33679e6i	−0.208417	−	0.360989i
$680$		0			0
$681$	5.04161e6	−	7.04608e6i	0.416583	−	0.582210i
$682$		0			0
$683$	5.47266e6			0.448897			0.224449	−	0.974486i	$-0.427942\pi$
$683$	5.47266e6			0.448897			0.224449	+	0.974486i	$0.427942\pi$
$684$		0			0
$685$	239205.			0.0194780
$686$		0			0
$687$	739023.	+	1.62799e6i	0.0597401	+	0.131601i
$688$		0			0
$689$	5.18570e6	+	8.98189e6i	0.416159	+	0.720808i
$690$		0			0
$691$	3.44084e6	−	5.95970e6i	0.274138	−	0.474821i	−0.695779	−	0.718255i	$-0.744941\pi$
$691$	3.44084e6	−	5.95970e6i	0.274138	−	0.474821i	0.969917	+	0.243435i	$0.0782742\pi$
$692$		0			0
$693$	3.45388e6	+	1.01277e7i	0.273196	+	0.801080i
$694$		0			0
$695$	−3.99430e6	+	6.91832e6i	−0.313674	+	0.543299i
$696$		0			0
$697$	6.38864e6	+	1.10655e7i	0.498112	+	0.862755i
$698$		0			0
$699$	1.72486e6	+	168651.i	0.133524	+	0.0130556i
$700$		0			0
$701$	5.19615e6			0.399380			0.199690	−	0.979859i	$-0.436006\pi$
$701$	5.19615e6			0.399380			0.199690	+	0.979859i	$0.436006\pi$
$702$		0			0
$703$	4.32872e6			0.330348
$704$		0			0
$705$	−2.55793e6	−	250106.i	−0.193827	−	0.0189518i
$706$		0			0
$707$	1.37676e6	+	2.38461e6i	0.103588	+	0.179419i
$708$		0			0
$709$	−287410.	+	497809.i	−0.0214727	+	0.0371918i	−0.876562	−	0.481289i	$-0.840169\pi$
$709$	−287410.	+	497809.i	−0.0214727	+	0.0371918i	0.855089	+	0.518481i	$0.173502\pi$
$710$		0			0
$711$	5.15042e6	−	5.88973e6i	0.382093	−	0.436939i
$712$		0			0
$713$	−8.94074e6	+	1.54858e7i	−0.658642	+	1.14080i
$714$		0			0
$715$	1.31574e7	+	2.27893e7i	0.962511	+	1.66712i
$716$		0			0
$717$	4.76206e6	+	1.04903e7i	0.345937	+	0.762063i
$718$		0			0
$719$	400906.			0.0289215			0.0144607	−	0.999895i	$-0.495397\pi$
$719$	400906.			0.0289215			0.0144607	+	0.999895i	$0.495397\pi$
$720$		0			0
$721$	−1.56693e7			−1.12256
$722$		0			0
$723$	−1.17048e7	+	1.63585e7i	−0.832757	+	1.16385i
$724$		0			0
$725$	−4.40969e6	−	7.63781e6i	−0.311575	−	0.539664i
$726$		0			0
$727$	5.27154e6	−	9.13058e6i	0.369915	−	0.640711i	−0.619637	−	0.784889i	$-0.712720\pi$
$727$	5.27154e6	−	9.13058e6i	0.369915	−	0.640711i	0.989552	+	0.144177i	$0.0460535\pi$
$728$		0			0
$729$	1.19644e7	+	7.92108e6i	0.833822	+	0.552034i
$730$		0			0
$731$	−1.01301e6	+	1.75458e6i	−0.0701162	+	0.121445i
$732$		0			0
$733$	−6.96868e6	−	1.20701e7i	−0.479061	−	0.829758i	0.520651	−	0.853770i	$-0.325689\pi$
$733$	−6.96868e6	−	1.20701e7i	−0.479061	−	0.829758i	−0.999712	+	0.0240119i	$0.992356\pi$
$734$		0			0
$735$	2.25854e6	−	3.15651e6i	0.154209	−	0.215520i
$736$		0			0
$737$	−2.06638e7			−1.40133
$738$		0			0
$739$	9.88034e6			0.665519			0.332760	−	0.943012i	$-0.392020\pi$
$739$	9.88034e6			0.665519			0.332760	+	0.943012i	$0.392020\pi$
$740$		0			0
$741$	3.09102e6	+	6.80919e6i	0.206803	+	0.455565i
$742$		0			0
$743$	−4.66695e6	−	8.08339e6i	−0.310142	−	0.537182i	0.668251	−	0.743936i	$-0.267043\pi$
$743$	−4.66695e6	−	8.08339e6i	−0.310142	−	0.537182i	−0.978393	+	0.206754i	$0.933710\pi$
$744$		0			0
$745$	2.47219e6	−	4.28195e6i	0.163189	−	0.282652i
$746$		0			0
$747$	−5.77354e6	+	6.60230e6i	−0.378565	+	0.432906i
$748$		0			0
$749$	9.59080e6	−	1.66117e7i	0.624669	−	1.08196i
$750$		0			0
$751$	1.43761e7	+	2.49001e7i	0.930124	+	1.61102i	0.783106	+	0.621888i	$0.213634\pi$
$751$	1.43761e7	+	2.49001e7i	0.930124	+	1.61102i	0.147018	+	0.989134i	$0.453032\pi$
$752$		0			0
$753$	2.00730e7	+	1.96267e6i	1.29011	+	0.126142i
$754$		0			0
$755$	−2.37881e7			−1.51877
$756$		0			0
$757$	−4.94587e6			−0.313691			−0.156846	−	0.987623i	$-0.550133\pi$
$757$	−4.94587e6			−0.313691			−0.156846	+	0.987623i	$0.550133\pi$
$758$		0			0
$759$	1.37807e7	+	1.34743e6i	0.868296	+	0.0848991i
$760$		0			0
$761$	−4.56829e6	−	7.91251e6i	−0.285951	−	0.495282i	0.686888	−	0.726763i	$-0.258976\pi$
$761$	−4.56829e6	−	7.91251e6i	−0.285951	−	0.495282i	−0.972839	+	0.231481i	$0.925643\pi$
$762$		0			0
$763$	−1.21179e6	+	2.09888e6i	−0.0753555	+	0.130520i
$764$		0			0
$765$	4.97113e6	+	1.45766e7i	0.307115	+	0.900542i
$766$		0			0
$767$	2.80894e6	−	4.86523e6i	0.172407	−	0.298617i
$768$		0			0
$769$	−8.26221e6	−	1.43106e7i	−0.503826	−	0.872652i	−0.999990	−	0.00442349i	$-0.998592\pi$
$769$	−8.26221e6	−	1.43106e7i	−0.503826	−	0.872652i	0.496164	−	0.868229i	$-0.334741\pi$
$770$		0			0
$771$	4.02309e6	+	8.86244e6i	0.243738	+	0.536930i
$772$		0			0
$773$	1.01763e7			0.612550			0.306275	−	0.951943i	$-0.400917\pi$
$773$	1.01763e7			0.612550			0.306275	+	0.951943i	$0.400917\pi$
$774$		0			0
$775$	−9.64536e6			−0.576852
$776$		0			0
$777$	−9.65129e6	+	1.34885e7i	−0.573499	+	0.801515i
$778$		0			0
$779$	3.09484e6	+	5.36042e6i	0.182724	+	0.316486i
$780$		0			0
$781$	−187030.	+	323945.i	−0.0109719	+	0.0190040i
$782$		0			0
$783$	1.95856e7	−	1.84222e7i	1.14165	−	1.07383i
$784$		0			0
$785$	1.58498e6	−	2.74527e6i	0.0918015	−	0.159005i
$786$		0			0
$787$	−9.38173e6	−	1.62496e7i	−0.539941	−	0.935205i	−0.998907	−	0.0467507i	$-0.985113\pi$
$787$	−9.38173e6	−	1.62496e7i	−0.539941	−	0.935205i	0.458966	−	0.888454i	$-0.348220\pi$
$788$		0			0
$789$	1.05676e7	−	1.47691e7i	0.604342	−	0.844620i
$790$		0			0
$791$	3.29343e6			0.187158
$792$		0			0
$793$	3.53025e7			1.99353
$794$		0			0
$795$	4.27714e6	+	9.42210e6i	0.240014	+	0.528725i
$796$		0			0
$797$	1.23982e6	+	2.14744e6i	0.0691376	+	0.119750i	0.898522	−	0.438929i	$-0.144642\pi$
$797$	1.23982e6	+	2.14744e6i	0.0691376	+	0.119750i	−0.829384	+	0.558678i	$0.811309\pi$
$798$		0			0
$799$	1.19628e6	−	2.07202e6i	0.0662929	−	0.114823i
$800$		0			0
$801$	1.01610e7	+	2.00620e6i	0.559573	+	0.110483i
$802$		0			0
$803$	1.39597e7	−	2.41788e7i	0.763987	−	1.32326i
$804$		0			0
$805$	8.69130e6	+	1.50538e7i	0.472711	+	0.818759i
$806$		0			0
$807$	−2.46605e7	−	2.41122e6i	−1.33296	−	0.130332i
$808$		0			0
$809$	−2.50880e7			−1.34770			−0.673852	−	0.738867i	$-0.735361\pi$
$809$	−2.50880e7			−1.34770			−0.673852	+	0.738867i	$0.735361\pi$
$810$		0			0
$811$	4.28465e6			0.228751			0.114376	−	0.993438i	$-0.463513\pi$
$811$	4.28465e6			0.228751			0.114376	+	0.993438i	$0.463513\pi$
$812$		0			0
$813$	−1.51713e7	−	1.48339e6i	−0.804999	−	0.0787101i
$814$		0			0
$815$	−1.19308e7	−	2.06647e7i	−0.629179	−	1.08977i
$816$		0			0
$817$	−490728.	+	849967.i	−0.0257209	+	0.0445499i
$818$		0			0
$819$	−2.81095e7	−	5.54996e6i	−1.46434	−	0.289121i
$820$		0			0
$821$	−1.01563e7	+	1.75913e7i	−0.525871	+	0.910836i	0.473675	+	0.880700i	$0.342927\pi$
$821$	−1.01563e7	+	1.75913e7i	−0.525871	+	0.910836i	−0.999546	+	0.0301356i	$0.990406\pi$
$822$		0			0
$823$	−6.58313e6	−	1.14023e7i	−0.338792	−	0.586804i	0.645414	−	0.763833i	$-0.276685\pi$
$823$	−6.58313e6	−	1.14023e7i	−0.338792	−	0.586804i	−0.984206	+	0.177029i	$0.943351\pi$
$824$		0			0
$825$	3.08726e6	+	6.80092e6i	0.157920	+	0.347883i
$826$		0			0
$827$	−2.82859e7			−1.43816			−0.719079	−	0.694928i	$-0.755436\pi$
$827$	−2.82859e7			−1.43816			−0.719079	+	0.694928i	$0.755436\pi$
$828$		0			0
$829$	1.36608e7			0.690381			0.345190	−	0.938533i	$-0.387814\pi$
$829$	1.36608e7			0.690381			0.345190	+	0.938533i	$0.387814\pi$
$830$		0			0
$831$	−1.17059e7	+	1.63601e7i	−0.588036	+	0.821832i
$832$		0			0
$833$	1.80658e6	+	3.12909e6i	0.0902080	+	0.156245i
$834$		0			0
$835$	−3.84845e6	+	6.66571e6i	−0.191016	+	0.330849i
$836$		0			0
$837$	−6.73831e6	−	2.86240e7i	−0.332458	−	1.41227i
$838$		0			0
$839$	−75641.6	+	131015.i	−0.00370984	+	0.00642564i	−0.867874	−	0.496784i	$-0.834514\pi$
$839$	−75641.6	+	131015.i	−0.00370984	+	0.00642564i	0.864165	+	0.503209i	$0.167848\pi$
$840$		0			0
$841$	−1.49371e7	−	2.58718e7i	−0.728244	−	1.26135i
$842$		0			0
$843$	1.51242e7	−	2.11374e7i	0.733000	−	1.02443i
$844$		0			0
$845$	−4.59249e7			−2.21262
$846$		0			0
$847$	1.40965e6			0.0675152
$848$		0			0
$849$	−7.27561e6	−	1.60274e7i	−0.346418	−	0.763123i
$850$		0			0
$851$	1.07311e7	+	1.85868e7i	0.507948	+	0.879792i
$852$		0			0
$853$	1.38831e7	−	2.40462e7i	0.653301	−	1.13155i	−0.329015	−	0.944325i	$-0.606717\pi$
$853$	1.38831e7	−	2.40462e7i	0.653301	−	1.13155i	0.982317	−	0.187226i	$-0.0599498\pi$
$854$		0			0
$855$	2.40816e6	+	7.06134e6i	0.112660	+	0.330348i
$856$		0			0
$857$	1.76136e7	−	3.05077e7i	0.819212	−	1.41892i	−0.0870512	−	0.996204i	$-0.527744\pi$
$857$	1.76136e7	−	3.05077e7i	0.819212	−	1.41892i	0.906263	−	0.422713i	$-0.138922\pi$
$858$		0			0
$859$	−2.02341e7	−	3.50464e7i	−0.935622	−	1.62054i	−0.773522	−	0.633770i	$-0.781507\pi$
$859$	−2.02341e7	−	3.50464e7i	−0.935622	−	1.62054i	−0.162100	−	0.986774i	$-0.551827\pi$
$860$		0			0
$861$	−2.36036e7	−	2.30788e6i	−1.08510	−	0.106097i
$862$		0			0
$863$	1.96865e7			0.899789			0.449895	−	0.893082i	$-0.351462\pi$
$863$	1.96865e7			0.899789			0.449895	+	0.893082i	$0.351462\pi$
$864$		0			0
$865$	−6.84170e6			−0.310902
$866$		0			0
$867$	7.75937e6	+	758686.i	0.350573	+	0.0342779i
$868$		0			0
$869$	6.20812e6	+	1.07528e7i	0.278876	+	0.483027i
$870$		0			0
$871$	2.76654e7	−	4.79178e7i	1.23564	−	2.14019i
$872$		0			0
$873$	7.01496e6	−	8.02191e6i	0.311523	−	0.356240i
$874$		0			0
$875$	7.10324e6	−	1.23032e7i	0.313644	−	0.543247i
$876$		0			0
$877$	−1.31221e7	−	2.27282e7i	−0.576109	−	0.997850i	−0.995920	−	0.0902384i	$-0.971237\pi$
$877$	−1.31221e7	−	2.27282e7i	−0.576109	−	0.997850i	0.419811	−	0.907611i	$-0.362096\pi$
$878$		0			0
$879$	1.32498e7	+	2.91880e7i	0.578414	+	1.27419i
$880$		0			0
$881$	−1.29423e7			−0.561786			−0.280893	−	0.959739i	$-0.590631\pi$
$881$	−1.29423e7			−0.561786			−0.280893	+	0.959739i	$0.590631\pi$
$882$		0			0
$883$	−3.39097e6			−0.146360			−0.0731800	−	0.997319i	$-0.523315\pi$
$883$	−3.39097e6			−0.146360			−0.0731800	+	0.997319i	$0.523315\pi$
$884$		0			0
$885$	3.26152e6	−	4.55825e6i	0.139979	−	0.195632i
$886$		0			0
$887$	3.83796e6	+	6.64753e6i	0.163791	+	0.283695i	0.936225	−	0.351400i	$-0.114294\pi$
$887$	3.83796e6	+	6.64753e6i	0.163791	+	0.283695i	−0.772434	+	0.635095i	$0.780961\pi$
$888$		0			0
$889$	1.22790e7	−	2.12678e7i	0.521085	−	0.902545i
$890$		0			0
$891$	−1.80259e7	+	1.39130e7i	−0.760682	+	0.587122i
$892$		0			0
$893$	579513.	−	1.00375e6i	0.0243184	−	0.0421207i
$894$		0			0
$895$	2.60849e6	+	4.51803e6i	0.108851	+	0.188535i
$896$		0			0
$897$	−2.15747e7	+	3.01525e7i	−0.895290	+	1.25125i
$898$		0			0
$899$	−5.51042e7			−2.27398
$900$		0			0
$901$	−9.63260e6			−0.395304
$902$		0			0
$903$	−1.55441e6	−	3.42421e6i	−0.0634377	−	0.139747i
$904$		0			0
$905$	1.93670e7	+	3.35446e7i	0.786033	+	1.36145i
$906$		0			0
$907$	5.44435e6	−	9.42990e6i	0.219750	−	0.380618i	−0.734982	−	0.678087i	$-0.762809\pi$
$907$	5.44435e6	−	9.42990e6i	0.219750	−	0.380618i	0.954731	+	0.297469i	$0.0961426\pi$
$908$		0			0
$909$	−3.85722e6	+	4.41090e6i	−0.154834	+	0.177059i
$910$		0			0
$911$	−90239.2	+	156299.i	−0.00360246	+	0.00623964i	−0.867821	−	0.496877i	$-0.834480\pi$
$911$	−90239.2	+	156299.i	−0.00360246	+	0.00623964i	0.864219	+	0.503117i	$0.167813\pi$
$912$		0			0
$913$	−6.95920e6	−	1.20537e7i	−0.276301	−	0.478568i
$914$		0			0
$915$	3.50539e7	+	3.42745e6i	1.38415	+	0.135338i
$916$		0			0
$917$	−2.16173e7			−0.848942
$918$		0			0
$919$	2.24831e7			0.878148			0.439074	−	0.898451i	$-0.355307\pi$
$919$	2.24831e7			0.878148			0.439074	+	0.898451i	$0.355307\pi$
$920$		0			0
$921$	2.36051e7	+	2.30803e6i	0.916973	+	0.0896586i
$922$		0			0
$923$	−500804.	−	867418.i	−0.0193492	−	0.0335138i
$924$		0			0
$925$	−5.78840e6	+	1.00258e7i	−0.222436	+	0.385270i
$926$		0			0
$927$	−1.07630e7	−	3.15598e7i	−0.411371	−	1.20625i
$928$		0			0
$929$	2.06620e7	−	3.57877e7i	0.785477	−	1.36049i	−0.143237	−	0.989688i	$-0.545751\pi$
$929$	2.06620e7	−	3.57877e7i	0.785477	−	1.36049i	0.928714	−	0.370797i	$-0.120916\pi$
$930$		0			0
$931$	875159.	+	1.51582e6i	0.0330912	+	0.0573157i
$932$		0			0
$933$	1.74516e7	+	3.84441e7i	0.656343	+	1.44586i
$934$		0			0
$935$	−2.44403e7			−0.914278
$936$		0			0
$937$	2.56470e7			0.954305			0.477153	−	0.878820i	$-0.341669\pi$
$937$	2.56470e7			0.954305			0.477153	+	0.878820i	$0.341669\pi$
$938$		0			0
$939$	−5.90670e6	+	8.25512e6i	−0.218615	+	0.305534i
$940$		0			0
$941$	−8.99880e6	−	1.55864e7i	−0.331292	−	0.573814i	0.651474	−	0.758671i	$-0.274151\pi$
$941$	−8.99880e6	−	1.55864e7i	−0.331292	−	0.573814i	−0.982765	+	0.184857i	$0.940818\pi$
$942$		0			0
$943$	−1.53445e7	+	2.65774e7i	−0.561917	+	0.973269i
$944$		0			0
$945$	−2.73727e7	−	8.23997e6i	−0.997098	−	0.300155i
$946$		0			0
$947$	−2.25398e7	+	3.90400e7i	−0.816723	+	1.41461i	0.0913614	+	0.995818i	$0.470878\pi$
$947$	−2.25398e7	+	3.90400e7i	−0.816723	+	1.41461i	−0.908084	+	0.418788i	$0.862455\pi$
$948$		0			0
$949$	3.73793e7	+	6.47429e7i	1.34731	+	2.33360i
$950$		0			0
$951$	−1.05323e6	+	1.47199e6i	−0.0377636	+	0.0527780i
$952$		0			0
$953$	2.21374e7			0.789577			0.394788	−	0.918772i	$-0.370818\pi$
$953$	2.21374e7			0.789577			0.394788	+	0.918772i	$0.370818\pi$
$954$		0			0
$955$	5.10225e7			1.81031
$956$		0			0
$957$	1.76376e7	+	3.88539e7i	0.622530	+	1.37137i
$958$		0			0
$959$	−206660.	−	357945.i	−0.00725619	−	0.0125681i
$960$		0			0
$961$	−1.58180e7	+	2.73975e7i	−0.552512	+	0.956979i
$962$		0			0
$963$	4.00458e7	+	7.90668e6i	1.39153	+	0.274744i
$964$		0			0
$965$	−576255.	+	998103.i	−0.0199203	+	0.0345030i
$966$		0			0
$967$	−9.81614e6	−	1.70020e7i	−0.337578	−	0.584703i	0.646398	−	0.763000i	$-0.276274\pi$
$967$	−9.81614e6	−	1.70020e7i	−0.337578	−	0.584703i	−0.983977	+	0.178297i	$0.942941\pi$
$968$		0			0
$969$	−6.91229e6	−	675861.i	−0.236490	−	0.0231232i
$970$		0			0
$971$	3.46539e7			1.17952			0.589758	−	0.807580i	$-0.299223\pi$
$971$	3.46539e7			1.17952			0.589758	+	0.807580i	$0.299223\pi$
$972$		0			0
$973$	1.38034e7			0.467415
$974$		0			0
$975$	−1.99042e7	−	1.94616e6i	−0.670552	−	0.0655644i
$976$		0			0
$977$	−1.34006e7	−	2.32106e7i	−0.449148	−	0.777947i	0.549183	−	0.835702i	$-0.314939\pi$
$977$	−1.34006e7	−	2.32106e7i	−0.449148	−	0.777947i	−0.998331	+	0.0577553i	$0.981606\pi$
$978$		0			0
$979$	−8.21808e6	+	1.42341e7i	−0.274040	+	0.474651i
$980$		0			0
$981$	−5.05975e6	−	999002.i	−0.167864	−	0.0331431i
$982$		0			0
$983$	−1.19040e7	+	2.06183e7i	−0.392924	+	0.680565i	−0.992834	−	0.119503i	$-0.961870\pi$
$983$	−1.19040e7	+	2.06183e7i	−0.392924	+	0.680565i	0.599910	+	0.800068i	$0.295203\pi$
$984$		0			0
$985$	1.12589e7	+	1.95009e7i	0.369746	+	0.640419i
$986$		0			0
$987$	1.83564e6	+	4.04374e6i	0.0599785	+	0.132126i
$988$		0			0
$989$	−4.86614e6			−0.158195
$990$		0			0
$991$	2.37156e7			0.767096			0.383548	−	0.923521i	$-0.374702\pi$
$991$	2.37156e7			0.767096			0.383548	+	0.923521i	$0.374702\pi$
$992$		0			0
$993$	−2.88145e6	+	4.02708e6i	−0.0927338	+	0.129603i
$994$		0			0
$995$	−470529.	−	814980.i	−0.0150671	−	0.0260969i
$996$		0			0
$997$	2.04170e7	−	3.53633e7i	0.650511	−	1.12672i	−0.332488	−	0.943107i	$-0.607888\pi$
$997$	2.04170e7	−	3.53633e7i	0.650511	−	1.12672i	0.982999	−	0.183610i	$-0.0587785\pi$
$998$		0			0
$999$	−3.37968e7	−	1.01738e7i	−1.07143	−	0.322530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.6.i.b.97.1		6
3.2	odd	2		432.6.i.b.289.1		6
4.3	odd	2		18.6.c.b.7.3	✓	6
9.4	even	3	inner	144.6.i.b.49.1		6
9.5	odd	6		432.6.i.b.145.1		6
12.11	even	2		54.6.c.b.19.1		6
36.7	odd	6		162.6.a.j.1.1		3
36.11	even	6		162.6.a.i.1.3		3
36.23	even	6		54.6.c.b.37.1		6
36.31	odd	6		18.6.c.b.13.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.6.c.b.7.3	✓	6	4.3	odd	2
18.6.c.b.13.3	yes	6	36.31	odd	6
54.6.c.b.19.1		6	12.11	even	2
54.6.c.b.37.1		6	36.23	even	6
144.6.i.b.49.1		6	9.4	even	3	inner
144.6.i.b.97.1		6	1.1	even	1	trivial
162.6.a.i.1.3		3	36.11	even	6
162.6.a.j.1.1		3	36.7	odd	6
432.6.i.b.145.1		6	9.5	odd	6
432.6.i.b.289.1		6	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	144.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-15.5145 - 1.51695i) q^{3} +(33.0434 + 57.2329i) q^{5} +(57.0952 - 98.8918i) q^{7} +(238.398 + 47.0695i) q^{9} +(-192.812 + 333.961i) q^{11} +(-516.287 - 894.236i) q^{13} +(-425.832 - 938.063i) q^{15} +959.020 q^{17} +464.576 q^{19} +(-1035.82 + 1447.64i) q^{21} +(1151.70 + 1994.81i) q^{23} +(-621.235 + 1076.01i) q^{25} +(-3627.21 - 1091.90i) q^{27} +(-3549.13 + 6147.28i) q^{29} +(3881.53 + 6723.00i) q^{31} +(3497.98 - 4888.74i) q^{33} +7546.48 q^{35} +9317.57 q^{37} +(6653.41 + 14656.8i) q^{39} +(6661.64 + 11538.3i) q^{41} +(-1056.29 + 1829.55i) q^{43} +(5183.55 + 15199.5i) q^{45} +(1247.40 - 2160.56i) q^{47} +(1883.78 + 3262.80i) q^{49} +(-14878.7 - 1454.79i) q^{51} -10044.2 q^{53} -25484.7 q^{55} +(-7207.66 - 704.741i) q^{57} +(2720.33 + 4711.75i) q^{59} +(-17094.4 + 29608.4i) q^{61} +(18266.1 - 20888.1i) q^{63} +(34119.8 - 59097.2i) q^{65} +(26792.6 + 46406.2i) q^{67} +(-14842.0 - 32695.5i) q^{69} +970.010 q^{71} -72400.3 q^{73} +(11270.4 - 15751.3i) q^{75} +(22017.3 + 38135.1i) q^{77} +(16098.9 - 27884.0i) q^{79} +(54617.9 + 22442.5i) q^{81} +(-18046.6 + 31257.6i) q^{83} +(31689.3 + 54887.5i) q^{85} +(64388.1 - 89987.9i) q^{87} +42622.2 q^{89} -117910. q^{91} +(-50021.4 - 110192. i) q^{93} +(15351.2 + 26589.0i) q^{95} +(21926.9 - 37978.6i) q^{97} +(-61685.4 + 70539.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{3} - 54 q^{5} + 132 q^{7} - 177 q^{9} + 315 q^{11} - 744 q^{13} - 2286 q^{15} + 2898 q^{17} - 2262 q^{19} - 11076 q^{21} + 3168 q^{23} - 2883 q^{25} - 18144 q^{27} - 5148 q^{29} + 8610 q^{31}+ \cdots - 282168 q^{99}+O(q^{100}) \) 6 * q - 9 * q^3 - 54 * q^5 + 132 * q^7 - 177 * q^9 + 315 * q^11 - 744 * q^13 - 2286 * q^15 + 2898 * q^17 - 2262 * q^19 - 11076 * q^21 + 3168 * q^23 - 2883 * q^25 - 18144 * q^27 - 5148 * q^29 + 8610 * q^31 + 17469 * q^33 - 2700 * q^35 + 39936 * q^37 + 49026 * q^39 + 5049 * q^41 + 31389 * q^43 + 2538 * q^45 - 12924 * q^47 - 52857 * q^49 - 36837 * q^51 - 96048 * q^53 - 126252 * q^55 - 17469 * q^57 - 62955 * q^59 - 75966 * q^61 - 49578 * q^63 + 108702 * q^65 + 32991 * q^67 - 29250 * q^69 + 129672 * q^71 - 8466 * q^73 + 105483 * q^75 + 88740 * q^77 - 89202 * q^79 + 123435 * q^81 - 32634 * q^83 + 71388 * q^85 + 151524 * q^87 + 66132 * q^89 + 301836 * q^91 + 57678 * q^93 + 82944 * q^95 + 46245 * q^97 - 282168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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