LMFDB - Embedded newform 30.6.c.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,6,Mod(19,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("30.19");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	30.c (of order $2$, degree $1$, 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:	$4.81151459439$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	30.19
Dual form			30.6.c.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -36.0000 q^{6} +4.00000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -36.0000 q^{6} +4.00000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +(-40.0000 + 220.000i) q^{10} -500.000 q^{11} +144.000i q^{12} -288.000i q^{13} +16.0000 q^{14} +(-90.0000 + 495.000i) q^{15} +256.000 q^{16} -1516.00i q^{17} +324.000i q^{18} +1344.00 q^{19} +(880.000 + 160.000i) q^{20} +36.0000 q^{21} +2000.00i q^{22} -4100.00i q^{23} +576.000 q^{24} +(2925.00 + 1100.00i) q^{25} -1152.00 q^{26} +729.000i q^{27} -64.0000i q^{28} +2646.00 q^{29} +(1980.00 + 360.000i) q^{30} -5612.00 q^{31} -1024.00i q^{32} +4500.00i q^{33} -6064.00 q^{34} +(40.0000 - 220.000i) q^{35} +1296.00 q^{36} +7288.00i q^{37} -5376.00i q^{38} -2592.00 q^{39} +(640.000 - 3520.00i) q^{40} -18986.0 q^{41} -144.000i q^{42} -2404.00i q^{43} +8000.00 q^{44} +(4455.00 + 810.000i) q^{45} -16400.0 q^{46} -8900.00i q^{47} -2304.00i q^{48} +16791.0 q^{49} +(4400.00 - 11700.0i) q^{50} -13644.0 q^{51} +4608.00i q^{52} +39804.0i q^{53} +2916.00 q^{54} +(27500.0 + 5000.00i) q^{55} -256.000 q^{56} -12096.0i q^{57} -10584.0i q^{58} +28300.0 q^{59} +(1440.00 - 7920.00i) q^{60} +18290.0 q^{61} +22448.0i q^{62} -324.000i q^{63} -4096.00 q^{64} +(-2880.00 + 15840.0i) q^{65} +18000.0 q^{66} -65956.0i q^{67} +24256.0i q^{68} -36900.0 q^{69} +(-880.000 - 160.000i) q^{70} -28800.0 q^{71} -5184.00i q^{72} -30808.0i q^{73} +29152.0 q^{74} +(9900.00 - 26325.0i) q^{75} -21504.0 q^{76} -2000.00i q^{77} +10368.0i q^{78} -60228.0 q^{79} +(-14080.0 - 2560.00i) q^{80} +6561.00 q^{81} +75944.0i q^{82} -2468.00i q^{83} -576.000 q^{84} +(-15160.0 + 83380.0i) q^{85} -9616.00 q^{86} -23814.0i q^{87} -32000.0i q^{88} -22678.0 q^{89} +(3240.00 - 17820.0i) q^{90} +1152.00 q^{91} +65600.0i q^{92} +50508.0i q^{93} -35600.0 q^{94} +(-73920.0 - 13440.0i) q^{95} -9216.00 q^{96} +36968.0i q^{97} -67164.0i q^{98} +40500.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{4} - 110 q^{5} - 72 q^{6} - 162 q^{9}+O(q^{10}) $ 2 * q - 32 * q^4 - 110 * q^5 - 72 * q^6 - 162 * q^9	$ 2 q - 32 q^{4} - 110 q^{5} - 72 q^{6} - 162 q^{9} - 80 q^{10} - 1000 q^{11} + 32 q^{14} - 180 q^{15} + 512 q^{16} + 2688 q^{19} + 1760 q^{20} + 72 q^{21} + 1152 q^{24} + 5850 q^{25} - 2304 q^{26} + 5292 q^{29} + 3960 q^{30} - 11224 q^{31} - 12128 q^{34} + 80 q^{35} + 2592 q^{36} - 5184 q^{39} + 1280 q^{40} - 37972 q^{41} + 16000 q^{44} + 8910 q^{45} - 32800 q^{46} + 33582 q^{49} + 8800 q^{50} - 27288 q^{51} + 5832 q^{54} + 55000 q^{55} - 512 q^{56} + 56600 q^{59} + 2880 q^{60} + 36580 q^{61} - 8192 q^{64} - 5760 q^{65} + 36000 q^{66} - 73800 q^{69} - 1760 q^{70} - 57600 q^{71} + 58304 q^{74} + 19800 q^{75} - 43008 q^{76} - 120456 q^{79} - 28160 q^{80} + 13122 q^{81} - 1152 q^{84} - 30320 q^{85} - 19232 q^{86} - 45356 q^{89} + 6480 q^{90} + 2304 q^{91} - 71200 q^{94} - 147840 q^{95} - 18432 q^{96} + 81000 q^{99}+O(q^{100}) $ 2 * q - 32 * q^4 - 110 * q^5 - 72 * q^6 - 162 * q^9 - 80 * q^10 - 1000 * q^11 + 32 * q^14 - 180 * q^15 + 512 * q^16 + 2688 * q^19 + 1760 * q^20 + 72 * q^21 + 1152 * q^24 + 5850 * q^25 - 2304 * q^26 + 5292 * q^29 + 3960 * q^30 - 11224 * q^31 - 12128 * q^34 + 80 * q^35 + 2592 * q^36 - 5184 * q^39 + 1280 * q^40 - 37972 * q^41 + 16000 * q^44 + 8910 * q^45 - 32800 * q^46 + 33582 * q^49 + 8800 * q^50 - 27288 * q^51 + 5832 * q^54 + 55000 * q^55 - 512 * q^56 + 56600 * q^59 + 2880 * q^60 + 36580 * q^61 - 8192 * q^64 - 5760 * q^65 + 36000 * q^66 - 73800 * q^69 - 1760 * q^70 - 57600 * q^71 + 58304 * q^74 + 19800 * q^75 - 43008 * q^76 - 120456 * q^79 - 28160 * q^80 + 13122 * q^81 - 1152 * q^84 - 30320 * q^85 - 19232 * q^86 - 45356 * q^89 + 6480 * q^90 + 2304 * q^91 - 71200 * q^94 - 147840 * q^95 - 18432 * q^96 + 81000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.00000i		−	0.707107i
$2$		−	4.00000i		−	0.707107i
$3$		−	9.00000i		−	0.577350i
$3$		−	9.00000i		−	0.577350i
$4$	−16.0000			−0.500000
$5$	−55.0000	−	10.0000i	−0.983870	−	0.178885i
$5$	−55.0000	−	10.0000i	−0.983870	−	0.178885i
$6$	−36.0000			−0.408248
$7$			4.00000i			0.0308542i	0.999881	+	0.0154271i	$0.00491080\pi$
$7$			4.00000i			0.0308542i	−0.999881	+	0.0154271i	$0.995089\pi$
$8$			64.0000i			0.353553i
$9$	−81.0000			−0.333333
$10$	−40.0000	+	220.000i	−0.126491	+	0.695701i
$11$	−500.000			−1.24591			−0.622957	−	0.782256i	$-0.714069\pi$
$11$	−500.000			−1.24591			−0.622957	+	0.782256i	$0.714069\pi$
$12$			144.000i			0.288675i
$13$		−	288.000i		−	0.472644i	−0.971675	−	0.236322i	$-0.924058\pi$
$13$		−	288.000i		−	0.472644i	0.971675	−	0.236322i	$-0.0759420\pi$
$14$	16.0000			0.0218172
$15$	−90.0000	+	495.000i	−0.103280	+	0.568038i
$16$	256.000			0.250000
$17$		−	1516.00i		−	1.27226i	−0.771581	−	0.636132i	$-0.780534\pi$
$17$		−	1516.00i		−	1.27226i	0.771581	−	0.636132i	$-0.219466\pi$
$18$			324.000i			0.235702i
$19$	1344.00			0.854113			0.427056	−	0.904225i	$-0.359551\pi$
$19$	1344.00			0.854113			0.427056	+	0.904225i	$0.359551\pi$
$20$	880.000	+	160.000i	0.491935	+	0.0894427i
$21$	36.0000			0.0178137
$22$			2000.00i			0.880995i
$23$		−	4100.00i		−	1.61609i	−0.589124	−	0.808043i	$-0.700527\pi$
$23$		−	4100.00i		−	1.61609i	0.589124	−	0.808043i	$-0.299473\pi$
$24$	576.000			0.204124
$25$	2925.00	+	1100.00i	0.936000	+	0.352000i
$26$	−1152.00			−0.334210
$27$			729.000i			0.192450i
$28$		−	64.0000i		−	0.0154271i
$29$	2646.00			0.584245			0.292122	−	0.956381i	$-0.405639\pi$
$29$	2646.00			0.584245			0.292122	+	0.956381i	$0.405639\pi$
$30$	1980.00	+	360.000i	0.401663	+	0.0730297i
$31$	−5612.00			−1.04885			−0.524425	−	0.851457i	$-0.675720\pi$
$31$	−5612.00			−1.04885			−0.524425	+	0.851457i	$0.675720\pi$
$32$		−	1024.00i		−	0.176777i
$33$			4500.00i			0.719329i
$34$	−6064.00			−0.899626
$35$	40.0000	−	220.000i	0.00551937	−	0.0303566i
$36$	1296.00			0.166667
$37$			7288.00i			0.875193i	0.899171	+	0.437597i	$0.144170\pi$
$37$			7288.00i			0.875193i	−0.899171	+	0.437597i	$0.855830\pi$
$38$		−	5376.00i		−	0.603949i
$39$	−2592.00			−0.272881
$40$	640.000	−	3520.00i	0.0632456	−	0.347851i
$41$	−18986.0			−1.76390			−0.881950	−	0.471343i	$-0.843769\pi$
$41$	−18986.0			−1.76390			−0.881950	+	0.471343i	$0.843769\pi$
$42$		−	144.000i		−	0.0125962i
$43$		−	2404.00i		−	0.198273i	−0.995074	−	0.0991364i	$-0.968392\pi$
$43$		−	2404.00i		−	0.198273i	0.995074	−	0.0991364i	$-0.0316080\pi$
$44$	8000.00			0.622957
$45$	4455.00	+	810.000i	0.327957	+	0.0596285i
$46$	−16400.0			−1.14274
$47$		−	8900.00i		−	0.587686i	−0.955854	−	0.293843i	$-0.905066\pi$
$47$		−	8900.00i		−	0.587686i	0.955854	−	0.293843i	$-0.0949343\pi$
$48$		−	2304.00i		−	0.144338i
$49$	16791.0			0.999048
$50$	4400.00	−	11700.0i	0.248902	−	0.661852i
$51$	−13644.0			−0.734541
$52$			4608.00i			0.236322i
$53$			39804.0i			1.94642i	0.229913	+	0.973211i	$0.426156\pi$
$53$			39804.0i			1.94642i	−0.229913	+	0.973211i	$0.573844\pi$
$54$	2916.00			0.136083
$55$	27500.0	+	5000.00i	1.22582	+	0.222876i
$56$	−256.000			−0.0109086
$57$		−	12096.0i		−	0.493122i
$58$		−	10584.0i		−	0.413123i
$59$	28300.0			1.05842			0.529208	−	0.848492i	$-0.322489\pi$
$59$	28300.0			1.05842			0.529208	+	0.848492i	$0.322489\pi$
$60$	1440.00	−	7920.00i	0.0516398	−	0.284019i
$61$	18290.0			0.629345			0.314673	−	0.949200i	$-0.398105\pi$
$61$	18290.0			0.629345			0.314673	+	0.949200i	$0.398105\pi$
$62$			22448.0i			0.741649i
$63$		−	324.000i		−	0.0102847i
$64$	−4096.00			−0.125000
$65$	−2880.00	+	15840.0i	−0.0845491	+	0.465020i
$66$	18000.0			0.508643
$67$		−	65956.0i		−	1.79501i	−0.441002	−	0.897506i	$-0.645377\pi$
$67$		−	65956.0i		−	1.79501i	0.441002	−	0.897506i	$-0.354623\pi$
$68$			24256.0i			0.636132i
$69$	−36900.0			−0.933047
$70$	−880.000	−	160.000i	−0.0214653	−	0.00390279i
$71$	−28800.0			−0.678026			−0.339013	−	0.940782i	$-0.610093\pi$
$71$	−28800.0			−0.678026			−0.339013	+	0.940782i	$0.610093\pi$
$72$		−	5184.00i		−	0.117851i
$73$		−	30808.0i		−	0.676638i	−0.941031	−	0.338319i	$-0.890142\pi$
$73$		−	30808.0i		−	0.676638i	0.941031	−	0.338319i	$-0.109858\pi$
$74$	29152.0			0.618855
$75$	9900.00	−	26325.0i	0.203227	−	0.540400i
$76$	−21504.0			−0.427056
$77$		−	2000.00i		−	0.0384418i
$78$			10368.0i			0.192956i
$79$	−60228.0			−1.08575			−0.542876	−	0.839813i	$-0.682665\pi$
$79$	−60228.0			−1.08575			−0.542876	+	0.839813i	$0.682665\pi$
$80$	−14080.0	−	2560.00i	−0.245967	−	0.0447214i
$81$	6561.00			0.111111
$82$			75944.0i			1.24727i
$83$		−	2468.00i		−	0.0393233i	−0.999807	−	0.0196616i	$-0.993741\pi$
$83$		−	2468.00i		−	0.0393233i	0.999807	−	0.0196616i	$-0.00625890\pi$
$84$	−576.000			−0.00890685
$85$	−15160.0	+	83380.0i	−0.227589	+	1.25174i
$86$	−9616.00			−0.140200
$87$		−	23814.0i		−	0.337314i
$88$		−	32000.0i		−	0.440497i
$89$	−22678.0			−0.303480			−0.151740	−	0.988420i	$-0.548488\pi$
$89$	−22678.0			−0.303480			−0.151740	+	0.988420i	$0.548488\pi$
$90$	3240.00	−	17820.0i	0.0421637	−	0.231900i
$91$	1152.00			0.0145831
$92$			65600.0i			0.808043i
$93$			50508.0i			0.605554i
$94$	−35600.0			−0.415557
$95$	−73920.0	−	13440.0i	−0.840336	−	0.152788i
$96$	−9216.00			−0.102062
$97$			36968.0i			0.398930i	0.979905	+	0.199465i	$0.0639204\pi$
$97$			36968.0i			0.398930i	−0.979905	+	0.199465i	$0.936080\pi$
$98$		−	67164.0i		−	0.706434i
$99$	40500.0			0.415305
$100$	−46800.0	−	17600.0i	−0.468000	−	0.176000i
$101$	167918.			1.63792			0.818962	−	0.573848i	$-0.194550\pi$
$101$	167918.			1.63792			0.818962	+	0.573848i	$0.194550\pi$
$102$			54576.0i			0.519399i
$103$		−	154364.i		−	1.43368i	−0.697236	−	0.716841i	$-0.745587\pi$
$103$		−	154364.i		−	1.43368i	0.697236	−	0.716841i	$-0.254413\pi$
$104$	18432.0			0.167105
$105$	−1980.00	−	360.000i	−0.0175264	−	0.00318661i
$106$	159216.			1.37633
$107$		−	136788.i		−	1.15502i	−0.816385	−	0.577509i	$-0.804025\pi$
$107$		−	136788.i		−	1.15502i	0.816385	−	0.577509i	$-0.195975\pi$
$108$		−	11664.0i		−	0.0962250i
$109$	53810.0			0.433807			0.216904	−	0.976193i	$-0.430404\pi$
$109$	53810.0			0.433807			0.216904	+	0.976193i	$0.430404\pi$
$110$	20000.0	−	110000.i	0.157597	−	0.866784i
$111$	65592.0			0.505293
$112$			1024.00i			0.00771356i
$113$			82692.0i			0.609211i	0.952479	+	0.304605i	$0.0985245\pi$
$113$			82692.0i			0.609211i	−0.952479	+	0.304605i	$0.901475\pi$
$114$	−48384.0			−0.348690
$115$	−41000.0	+	225500.i	−0.289094	+	1.59002i
$116$	−42336.0			−0.292122
$117$			23328.0i			0.157548i
$118$		−	113200.i		−	0.748413i
$119$	6064.00			0.0392547
$120$	−31680.0	−	5760.00i	−0.200832	−	0.0365148i
$121$	88949.0			0.552303
$122$		−	73160.0i		−	0.445014i
$123$			170874.i			1.01839i
$124$	89792.0			0.524425
$125$	−149875.	−	89750.0i	−0.857935	−	0.513759i
$126$	−1296.00			−0.00727241
$127$			211780.i			1.16513i	0.812783	+	0.582567i	$0.197952\pi$
$127$			211780.i			1.16513i	−0.812783	+	0.582567i	$0.802048\pi$
$128$			16384.0i			0.0883883i
$129$	−21636.0			−0.114473
$130$	63360.0	+	11520.0i	0.328819	+	0.0597853i
$131$	169500.			0.862962			0.431481	−	0.902122i	$-0.357991\pi$
$131$	169500.			0.862962			0.431481	+	0.902122i	$0.357991\pi$
$132$		−	72000.0i		−	0.359665i
$133$			5376.00i			0.0263530i
$134$	−263824.			−1.26927
$135$	7290.00	−	40095.0i	0.0344265	−	0.189346i
$136$	97024.0			0.449813
$137$		−	252036.i		−	1.14726i	−0.819115	−	0.573629i	$-0.805535\pi$
$137$		−	252036.i		−	1.14726i	0.819115	−	0.573629i	$-0.194465\pi$
$138$			147600.i			0.659764i
$139$	−192016.			−0.842947			−0.421474	−	0.906841i	$-0.638487\pi$
$139$	−192016.			−0.842947			−0.421474	+	0.906841i	$0.638487\pi$
$140$	−640.000	+	3520.00i	−0.00275969	+	0.0151783i
$141$	−80100.0			−0.339301
$142$			115200.i			0.479437i
$143$			144000.i			0.588874i
$144$	−20736.0			−0.0833333
$145$	−145530.	−	26460.0i	−0.574821	−	0.104513i
$146$	−123232.			−0.478455
$147$		−	151119.i		−	0.576801i
$148$		−	116608.i		−	0.437597i
$149$	−235694.			−0.869727			−0.434863	−	0.900496i	$-0.643203\pi$
$149$	−235694.			−0.869727			−0.434863	+	0.900496i	$0.643203\pi$
$150$	−105300.	−	39600.0i	−0.382120	−	0.143703i
$151$	−371492.			−1.32589			−0.662944	−	0.748669i	$-0.730693\pi$
$151$	−371492.			−1.32589			−0.662944	+	0.748669i	$0.730693\pi$
$152$			86016.0i			0.301975i
$153$			122796.i			0.424088i
$154$	−8000.00			−0.0271824
$155$	308660.	+	56120.0i	1.03193	+	0.187624i
$156$	41472.0			0.136441
$157$		−	264952.i		−	0.857863i	−0.903337	−	0.428932i	$-0.858890\pi$
$157$		−	264952.i		−	0.857863i	0.903337	−	0.428932i	$-0.141110\pi$
$158$			240912.i			0.767743i
$159$	358236.			1.12377
$160$	−10240.0	+	56320.0i	−0.0316228	+	0.173925i
$161$	16400.0			0.0498631
$162$		−	26244.0i		−	0.0785674i
$163$		−	403124.i		−	1.18842i	−0.804310	−	0.594210i	$-0.797465\pi$
$163$		−	403124.i		−	1.18842i	0.804310	−	0.594210i	$-0.202535\pi$
$164$	303776.			0.881950
$165$	45000.0	−	247500.i	0.128678	−	0.707726i
$166$	−9872.00			−0.0278058
$167$			261900.i			0.726682i	0.931656	+	0.363341i	$0.118364\pi$
$167$			261900.i			0.726682i	−0.931656	+	0.363341i	$0.881636\pi$
$168$			2304.00i			0.00629810i
$169$	288349.			0.776608
$170$	333520.	+	60640.0i	0.885115	+	0.160930i
$171$	−108864.			−0.284704
$172$			38464.0i			0.0991364i
$173$			326228.i			0.828716i	0.910114	+	0.414358i	$0.135994\pi$
$173$			326228.i			0.828716i	−0.910114	+	0.414358i	$0.864006\pi$
$174$	−95256.0			−0.238517
$175$	−4400.00	+	11700.0i	−0.0108607	+	0.0288796i
$176$	−128000.			−0.311479
$177$		−	254700.i		−	0.611077i
$178$			90712.0i			0.214593i
$179$	109516.			0.255473			0.127736	−	0.991808i	$-0.459229\pi$
$179$	109516.			0.255473			0.127736	+	0.991808i	$0.459229\pi$
$180$	−71280.0	−	12960.0i	−0.163978	−	0.0298142i
$181$	−53146.0			−0.120580			−0.0602898	−	0.998181i	$-0.519202\pi$
$181$	−53146.0			−0.120580			−0.0602898	+	0.998181i	$0.519202\pi$
$182$		−	4608.00i		−	0.0103118i
$183$		−	164610.i		−	0.363353i
$184$	262400.			0.571372
$185$	72880.0	−	400840.i	0.156559	−	0.861076i
$186$	202032.			0.428191
$187$			758000.i			1.58513i
$188$			142400.i			0.293843i
$189$	−2916.00			−0.00593790
$190$	−53760.0	+	295680.i	−0.108038	+	0.594207i
$191$	232056.			0.460267			0.230133	−	0.973159i	$-0.426084\pi$
$191$	232056.			0.460267			0.230133	+	0.973159i	$0.426084\pi$
$192$			36864.0i			0.0721688i
$193$		−	1.03067e6i		−	1.99172i	−0.0909274	−	0.995858i	$-0.528983\pi$
$193$		−	1.03067e6i		−	1.99172i	0.0909274	−	0.995858i	$-0.471017\pi$
$194$	147872.			0.282086
$195$	142560.	+	25920.0i	0.268480	+	0.0488145i
$196$	−268656.			−0.499524
$197$			522796.i			0.959769i	0.877332	+	0.479884i	$0.159321\pi$
$197$			522796.i			0.959769i	−0.877332	+	0.479884i	$0.840679\pi$
$198$		−	162000.i		−	0.293665i
$199$	215292.			0.385385			0.192693	−	0.981259i	$-0.438278\pi$
$199$	215292.			0.385385			0.192693	+	0.981259i	$0.438278\pi$
$200$	−70400.0	+	187200.i	−0.124451	+	0.330926i
$201$	−593604.			−1.03635
$202$		−	671672.i		−	1.15819i
$203$			10584.0i			0.0180264i
$204$	218304.			0.367271
$205$	1.04423e6	+	189860.i	1.73545	+	0.315536i
$206$	−617456.			−1.01377
$207$			332100.i			0.538695i
$208$		−	73728.0i		−	0.118161i
$209$	−672000.			−1.06415
$210$	−1440.00	+	7920.00i	−0.00225328	+	0.0123930i
$211$	−1.03008e6			−1.59281			−0.796407	−	0.604762i	$-0.793268\pi$
$211$	−1.03008e6			−1.59281			−0.796407	+	0.604762i	$0.793268\pi$
$212$		−	636864.i		−	0.973211i
$213$			259200.i			0.391459i
$214$	−547152.			−0.816721
$215$	−24040.0	+	132220.i	−0.0354681	+	0.195075i
$216$	−46656.0			−0.0680414
$217$		−	22448.0i		−	0.0323615i
$218$		−	215240.i		−	0.306748i
$219$	−277272.			−0.390657
$220$	−440000.	−	80000.0i	−0.612909	−	0.111438i
$221$	−436608.			−0.601327
$222$		−	262368.i		−	0.357296i
$223$			456020.i			0.614075i	0.951697	+	0.307038i	$0.0993378\pi$
$223$			456020.i			0.614075i	−0.951697	+	0.307038i	$0.900662\pi$
$224$	4096.00			0.00545431
$225$	−236925.	−	89100.0i	−0.312000	−	0.117333i
$226$	330768.			0.430777
$227$			434252.i			0.559342i	0.960096	+	0.279671i	$0.0902253\pi$
$227$			434252.i			0.559342i	−0.960096	+	0.279671i	$0.909775\pi$
$228$			193536.i			0.246561i
$229$	722710.			0.910700			0.455350	−	0.890313i	$-0.349514\pi$
$229$	722710.			0.910700			0.455350	+	0.890313i	$0.349514\pi$
$230$	902000.	+	164000.i	1.12431	+	0.204420i
$231$	−18000.0			−0.0221944
$232$			169344.i			0.206562i
$233$		−	565348.i		−	0.682223i	−0.940023	−	0.341111i	$-0.889197\pi$
$233$		−	565348.i		−	0.682223i	0.940023	−	0.341111i	$-0.110803\pi$
$234$	93312.0			0.111403
$235$	−89000.0	+	489500.i	−0.105128	+	0.578207i
$236$	−452800.			−0.529208
$237$			542052.i			0.626859i
$238$		−	24256.0i		−	0.0277573i
$239$	−324904.			−0.367926			−0.183963	−	0.982933i	$-0.558893\pi$
$239$	−324904.			−0.367926			−0.183963	+	0.982933i	$0.558893\pi$
$240$	−23040.0	+	126720.i	−0.0258199	+	0.142009i
$241$	915262.			1.01509			0.507543	−	0.861626i	$-0.330554\pi$
$241$	915262.			1.01509			0.507543	+	0.861626i	$0.330554\pi$
$242$		−	355796.i		−	0.390537i
$243$		−	59049.0i		−	0.0641500i
$244$	−292640.			−0.314673
$245$	−923505.	−	167910.i	−0.982933	−	0.178715i
$246$	683496.			0.720109
$247$		−	387072.i		−	0.403691i
$248$		−	359168.i		−	0.370825i
$249$	−22212.0			−0.0227033
$250$	−359000.	+	599500.i	−0.363282	+	0.606651i
$251$	1.36708e6			1.36965			0.684823	−	0.728709i	$-0.259879\pi$
$251$	1.36708e6			1.36965			0.684823	+	0.728709i	$0.259879\pi$
$252$			5184.00i			0.00514237i
$253$			2.05000e6i			2.01350i
$254$	847120.			0.823874
$255$	750420.	+	136440.i	0.722693	+	0.131399i
$256$	65536.0			0.0625000
$257$		−	892932.i		−	0.843307i	−0.906757	−	0.421653i	$-0.861450\pi$
$257$		−	892932.i		−	0.843307i	0.906757	−	0.421653i	$-0.138550\pi$
$258$			86544.0i			0.0809446i
$259$	−29152.0			−0.0270034
$260$	46080.0	−	253440.i	0.0422746	−	0.232510i
$261$	−214326.			−0.194748
$262$		−	678000.i		−	0.610206i
$263$		−	1.86650e6i		−	1.66394i	−0.554818	−	0.831972i	$-0.687212\pi$
$263$		−	1.86650e6i		−	1.66394i	0.554818	−	0.831972i	$-0.312788\pi$
$264$	−288000.			−0.254321
$265$	398040.	−	2.18922e6i	0.348187	−	1.91503i
$266$	21504.0			0.0186344
$267$			204102.i			0.175214i
$268$			1.05530e6i			0.897506i
$269$	1.37227e6			1.15627			0.578133	−	0.815943i	$-0.303782\pi$
$269$	1.37227e6			1.15627			0.578133	+	0.815943i	$0.303782\pi$
$270$	−160380.	−	29160.0i	−0.133888	−	0.0243432i
$271$	458644.			0.379361			0.189680	−	0.981846i	$-0.439255\pi$
$271$	458644.			0.379361			0.189680	+	0.981846i	$0.439255\pi$
$272$		−	388096.i		−	0.318066i
$273$		−	10368.0i		−	0.00841954i
$274$	−1.00814e6			−0.811234
$275$	−1.46250e6	−	550000.i	−1.16618	−	0.438562i
$276$	590400.			0.466524
$277$			985408.i			0.771643i	0.922573	+	0.385822i	$0.126082\pi$
$277$			985408.i			0.771643i	−0.922573	+	0.385822i	$0.873918\pi$
$278$			768064.i			0.596054i
$279$	454572.			0.349617
$280$	14080.0	+	2560.00i	0.0107327	+	0.00195139i
$281$	165798.			0.125260			0.0626302	−	0.998037i	$-0.480051\pi$
$281$	165798.			0.125260			0.0626302	+	0.998037i	$0.480051\pi$
$282$			320400.i			0.239922i
$283$		−	1.66471e6i		−	1.23558i	−0.786342	−	0.617792i	$-0.788028\pi$
$283$		−	1.66471e6i		−	1.23558i	0.786342	−	0.617792i	$-0.211972\pi$
$284$	460800.			0.339013
$285$	−120960.	+	665280.i	−0.0882124	+	0.485168i
$286$	576000.			0.416397
$287$		−	75944.0i		−	0.0544238i
$288$			82944.0i			0.0589256i
$289$	−878399.			−0.618653
$290$	−105840.	+	582120.i	−0.0739018	+	0.406460i
$291$	332712.			0.230322
$292$			492928.i			0.338319i
$293$			2.55104e6i			1.73600i	0.496567	+	0.867998i	$0.334594\pi$
$293$			2.55104e6i			1.73600i	−0.496567	+	0.867998i	$0.665406\pi$
$294$	−604476.			−0.407860
$295$	−1.55650e6	−	283000.i	−1.04134	−	0.189335i
$296$	−466432.			−0.309428
$297$		−	364500.i		−	0.239776i
$298$			942776.i			0.614990i
$299$	−1.18080e6			−0.763833
$300$	−158400.	+	421200.i	−0.101614	+	0.270200i
$301$	9616.00			0.00611756
$302$			1.48597e6i			0.937545i
$303$		−	1.51126e6i		−	0.945656i
$304$	344064.			0.213528
$305$	−1.00595e6	−	182900.i	−0.619194	−	0.112581i
$306$	491184.			0.299875
$307$		−	736020.i		−	0.445701i	−0.974853	−	0.222851i	$-0.928464\pi$
$307$		−	736020.i		−	0.445701i	0.974853	−	0.222851i	$-0.0715362\pi$
$308$			32000.0i			0.0192209i
$309$	−1.38928e6			−0.827737
$310$	224480.	−	1.23464e6i	0.132670	−	0.729686i
$311$	1.71660e6			1.00639			0.503197	−	0.864172i	$-0.332157\pi$
$311$	1.71660e6			1.00639			0.503197	+	0.864172i	$0.332157\pi$
$312$		−	165888.i		−	0.0964780i
$313$			2.83851e6i			1.63768i	0.574020	+	0.818842i	$0.305383\pi$
$313$			2.83851e6i			1.63768i	−0.574020	+	0.818842i	$0.694617\pi$
$314$	−1.05981e6			−0.606601
$315$	−3240.00	+	17820.0i	−0.00183979	+	0.0101189i
$316$	963648.			0.542876
$317$			1.27605e6i			0.713215i	0.934254	+	0.356607i	$0.116067\pi$
$317$			1.27605e6i			0.713215i	−0.934254	+	0.356607i	$0.883933\pi$
$318$		−	1.43294e6i		−	0.794624i
$319$	−1.32300e6			−0.727919
$320$	225280.	+	40960.0i	0.122984	+	0.0223607i
$321$	−1.23109e6			−0.666850
$322$		−	65600.0i		−	0.0352585i
$323$		−	2.03750e6i		−	1.08666i
$324$	−104976.			−0.0555556
$325$	316800.	−	842400.i	0.166371	−	0.442395i
$326$	−1.61250e6			−0.840339
$327$		−	484290.i		−	0.250459i
$328$		−	1.21510e6i		−	0.623633i
$329$	35600.0			0.0181326
$330$	−990000.	−	180000.i	−0.500438	−	0.0909887i
$331$	443992.			0.222744			0.111372	−	0.993779i	$-0.464476\pi$
$331$	443992.			0.222744			0.111372	+	0.993779i	$0.464476\pi$
$332$			39488.0i			0.0196616i
$333$		−	590328.i		−	0.291731i
$334$	1.04760e6			0.513842
$335$	−659560.	+	3.62758e6i	−0.321101	+	1.76606i
$336$	9216.00			0.00445343
$337$		−	2.71326e6i		−	1.30142i	−0.759328	−	0.650708i	$-0.774472\pi$
$337$		−	2.71326e6i		−	1.30142i	0.759328	−	0.650708i	$-0.225528\pi$
$338$		−	1.15340e6i		−	0.549145i
$339$	744228.			0.351728
$340$	242560.	−	1.33408e6i	0.113795	−	0.625871i
$341$	2.80600e6			1.30678
$342$			435456.i			0.201316i
$343$			134392.i			0.0616791i
$344$	153856.			0.0701001
$345$	2.02950e6	+	369000.i	0.917997	+	0.166909i
$346$	1.30491e6			0.585991
$347$			1.31051e6i			0.584273i	0.956377	+	0.292137i	$0.0943662\pi$
$347$			1.31051e6i			0.584273i	−0.956377	+	0.292137i	$0.905634\pi$
$348$			381024.i			0.168657i
$349$	298910.			0.131364			0.0656821	−	0.997841i	$-0.479078\pi$
$349$	298910.			0.131364			0.0656821	+	0.997841i	$0.479078\pi$
$350$	46800.0	+	17600.0i	0.0204209	+	0.00767967i
$351$	209952.			0.0909604
$352$			512000.i			0.220249i
$353$			737996.i			0.315223i	0.987501	+	0.157611i	$0.0503793\pi$
$353$			737996.i			0.315223i	−0.987501	+	0.157611i	$0.949621\pi$
$354$	−1.01880e6			−0.432097
$355$	1.58400e6	+	288000.i	0.667090	+	0.121289i
$356$	362848.			0.151740
$357$		−	54576.0i		−	0.0226637i
$358$		−	438064.i		−	0.180647i
$359$	2.34074e6			0.958557			0.479278	−	0.877663i	$-0.340898\pi$
$359$	2.34074e6			0.958557			0.479278	+	0.877663i	$0.340898\pi$
$360$	−51840.0	+	285120.i	−0.0210819	+	0.115950i
$361$	−669763.			−0.270491
$362$			212584.i			0.0852627i
$363$		−	800541.i		−	0.318872i
$364$	−18432.0			−0.00729154
$365$	−308080.	+	1.69444e6i	−0.121041	+	0.665724i
$366$	−658440.			−0.256929
$367$		−	127292.i		−	0.0493328i	−0.999696	−	0.0246664i	$-0.992148\pi$
$367$		−	127292.i		−	0.0493328i	0.999696	−	0.0246664i	$-0.00785236\pi$
$368$		−	1.04960e6i		−	0.404021i
$369$	1.53787e6			0.587966
$370$	−1.60336e6	−	291520.i	−0.608873	−	0.110704i
$371$	−159216.			−0.0600554
$372$		−	808128.i		−	0.302777i
$373$			4.03870e6i			1.50303i	0.659713	+	0.751517i	$0.270678\pi$
$373$			4.03870e6i			1.50303i	−0.659713	+	0.751517i	$0.729322\pi$
$374$	3.03200e6			1.12086
$375$	−807750.	+	1.34888e6i	−0.296619	+	0.495329i
$376$	569600.			0.207778
$377$		−	762048.i		−	0.276140i
$378$			11664.0i			0.00419873i
$379$	−1.01214e6			−0.361944			−0.180972	−	0.983488i	$-0.557924\pi$
$379$	−1.01214e6			−0.361944			−0.180972	+	0.983488i	$0.557924\pi$
$380$	1.18272e6	+	215040.i	0.420168	+	0.0763942i
$381$	1.90602e6			0.672690
$382$		−	928224.i		−	0.325458i
$383$		−	2.37610e6i		−	0.827690i	−0.910347	−	0.413845i	$-0.864186\pi$
$383$		−	2.37610e6i		−	0.827690i	0.910347	−	0.413845i	$-0.135814\pi$
$384$	147456.			0.0510310
$385$	−20000.0	+	110000.i	−0.00687667	+	0.0378217i
$386$	−4.12269e6			−1.40836
$387$			194724.i			0.0660910i
$388$		−	591488.i		−	0.199465i
$389$	−1.42497e6			−0.477456			−0.238728	−	0.971087i	$-0.576730\pi$
$389$	−1.42497e6			−0.477456			−0.238728	+	0.971087i	$0.576730\pi$
$390$	103680.	−	570240.i	0.0345170	−	0.189844i
$391$	−6.21560e6			−2.05609
$392$			1.07462e6i			0.353217i
$393$		−	1.52550e6i		−	0.498231i
$394$	2.09118e6			0.678659
$395$	3.31254e6	+	602280.i	1.06824	+	0.194225i
$396$	−648000.			−0.207652
$397$		−	1.69345e6i		−	0.539257i	−0.962964	−	0.269628i	$-0.913099\pi$
$397$		−	1.69345e6i		−	0.539257i	0.962964	−	0.269628i	$-0.0869009\pi$
$398$		−	861168.i		−	0.272509i
$399$	48384.0			0.0152149
$400$	748800.	+	281600.i	0.234000	+	0.0880000i
$401$	−2.84501e6			−0.883532			−0.441766	−	0.897130i	$-0.645648\pi$
$401$	−2.84501e6			−0.883532			−0.441766	+	0.897130i	$0.645648\pi$
$402$			2.37442e6i			0.732810i
$403$			1.61626e6i			0.495733i
$404$	−2.68669e6			−0.818962
$405$	−360855.	−	65610.0i	−0.109319	−	0.0198762i
$406$	42336.0			0.0127466
$407$		−	3.64400e6i		−	1.09042i
$408$		−	873216.i		−	0.259700i
$409$	1.89069e6			0.558873			0.279436	−	0.960164i	$-0.409852\pi$
$409$	1.89069e6			0.558873			0.279436	+	0.960164i	$0.409852\pi$
$410$	759440.	−	4.17692e6i	0.223118	−	1.22715i
$411$	−2.26832e6			−0.662370
$412$			2.46982e6i			0.716841i
$413$			113200.i			0.0326566i
$414$	1.32840e6			0.380915
$415$	−24680.0	+	135740.i	−0.00703437	+	0.0386890i
$416$	−294912.			−0.0835524
$417$			1.72814e6i			0.486676i
$418$			2.68800e6i			0.752469i
$419$	−4.60930e6			−1.28263			−0.641313	−	0.767280i	$-0.721610\pi$
$419$	−4.60930e6			−1.28263			−0.641313	+	0.767280i	$0.721610\pi$
$420$	31680.0	+	5760.00i	0.00876318	+	0.00159331i
$421$	−6.04151e6			−1.66127			−0.830635	−	0.556817i	$-0.812022\pi$
$421$	−6.04151e6			−1.66127			−0.830635	+	0.556817i	$0.812022\pi$
$422$			4.12032e6i			1.12629i
$423$			720900.i			0.195895i
$424$	−2.54746e6			−0.688164
$425$	1.66760e6	−	4.43430e6i	0.447837	−	1.19084i
$426$	1.03680e6			0.276803
$427$			73160.0i			0.0194180i
$428$			2.18861e6i			0.577509i
$429$	1.29600e6			0.339987
$430$	528880.	+	96160.0i	0.137939	+	0.0250798i
$431$	−3800.00			−0.000985350			−0.000492675	−	1.00000i	$-0.500157\pi$
$431$	−3800.00			−0.000985350			−0.000492675		1.00000i	$0.500157\pi$
$432$			186624.i			0.0481125i
$433$			250736.i			0.0642683i	0.999484	+	0.0321342i	$0.0102304\pi$
$433$			250736.i			0.0642683i	−0.999484	+	0.0321342i	$0.989770\pi$
$434$	−89792.0			−0.0228830
$435$	−238140.	+	1.30977e6i	−0.0603405	+	0.331873i
$436$	−860960.			−0.216904
$437$		−	5.51040e6i		−	1.38032i
$438$			1.10909e6i			0.276236i
$439$	3.58873e6			0.888750			0.444375	−	0.895841i	$-0.353426\pi$
$439$	3.58873e6			0.888750			0.444375	+	0.895841i	$0.353426\pi$
$440$	−320000.	+	1.76000e6i	−0.0787986	+	0.433392i
$441$	−1.36007e6			−0.333016
$442$			1.74643e6i			0.425203i
$443$		−	1.41479e6i		−	0.342517i	−0.985226	−	0.171258i	$-0.945217\pi$
$443$		−	1.41479e6i		−	0.342517i	0.985226	−	0.171258i	$-0.0547833\pi$
$444$	−1.04947e6			−0.252647
$445$	1.24729e6	+	226780.i	0.298585	+	0.0542881i
$446$	1.82408e6			0.434217
$447$			2.12125e6i			0.502137i
$448$		−	16384.0i		−	0.00385678i
$449$	829806.			0.194250			0.0971249	−	0.995272i	$-0.469035\pi$
$449$	829806.			0.194250			0.0971249	+	0.995272i	$0.469035\pi$
$450$	−356400.	+	947700.i	−0.0829672	+	0.220617i
$451$	9.49300e6			2.19767
$452$		−	1.32307e6i		−	0.304605i
$453$			3.34343e6i			0.765502i
$454$	1.73701e6			0.395514
$455$	−63360.0	−	11520.0i	−0.0143478	−	0.00260870i
$456$	774144.			0.174345
$457$		−	4.68198e6i		−	1.04867i	−0.851512	−	0.524335i	$-0.824314\pi$
$457$		−	4.68198e6i		−	1.04867i	0.851512	−	0.524335i	$-0.175686\pi$
$458$		−	2.89084e6i		−	0.643962i
$459$	1.10516e6			0.244847
$460$	656000.	−	3.60800e6i	0.144547	−	0.795009i
$461$	−141930.			−0.0311044			−0.0155522	−	0.999879i	$-0.504951\pi$
$461$	−141930.			−0.0311044			−0.0155522	+	0.999879i	$0.504951\pi$
$462$			72000.0i			0.0156938i
$463$			727476.i			0.157713i	0.996886	+	0.0788563i	$0.0251268\pi$
$463$			727476.i			0.157713i	−0.996886	+	0.0788563i	$0.974873\pi$
$464$	677376.			0.146061
$465$	505080.	−	2.77794e6i	0.108325	−	0.595786i
$466$	−2.26139e6			−0.482404
$467$			4.47640e6i			0.949809i	0.880037	+	0.474905i	$0.157517\pi$
$467$			4.47640e6i			0.949809i	−0.880037	+	0.474905i	$0.842483\pi$
$468$		−	373248.i		−	0.0787740i
$469$	263824.			0.0553837
$470$	1.95800e6	+	356000.i	0.408854	+	0.0743371i
$471$	−2.38457e6			−0.495288
$472$			1.81120e6i			0.374207i
$473$			1.20200e6i			0.247031i
$474$	2.16821e6			0.443256
$475$	3.93120e6	+	1.47840e6i	0.799450	+	0.300648i
$476$	−97024.0			−0.0196274
$477$		−	3.22412e6i		−	0.648807i
$478$			1.29962e6i			0.260163i
$479$	1.32718e6			0.264297			0.132149	−	0.991230i	$-0.457812\pi$
$479$	1.32718e6			0.264297			0.132149	+	0.991230i	$0.457812\pi$
$480$	506880.	+	92160.0i	0.100416	+	0.0182574i
$481$	2.09894e6			0.413655
$482$		−	3.66105e6i		−	0.717774i
$483$		−	147600.i		−	0.0287885i
$484$	−1.42318e6			−0.276152
$485$	369680.	−	2.03324e6i	0.0713628	−	0.392495i
$486$	−236196.			−0.0453609
$487$			4.11647e6i			0.786507i	0.919430	+	0.393253i	$0.128650\pi$
$487$			4.11647e6i			0.786507i	−0.919430	+	0.393253i	$0.871350\pi$
$488$			1.17056e6i			0.222507i
$489$	−3.62812e6			−0.686134
$490$	−671640.	+	3.69402e6i	−0.126371	+	0.695039i
$491$	−6.12316e6			−1.14623			−0.573115	−	0.819475i	$-0.694265\pi$
$491$	−6.12316e6			−1.14623			−0.573115	+	0.819475i	$0.694265\pi$
$492$		−	2.73398e6i		−	0.509194i
$493$		−	4.01134e6i		−	0.743313i
$494$	−1.54829e6			−0.285453
$495$	−2.22750e6	−	405000.i	−0.408606	−	0.0742920i
$496$	−1.43667e6			−0.262213
$497$		−	115200.i		−	0.0209200i
$498$			88848.0i			0.0160537i
$499$	7.90490e6			1.42117			0.710584	−	0.703613i	$-0.248431\pi$
$499$	7.90490e6			1.42117			0.710584	+	0.703613i	$0.248431\pi$
$500$	2.39800e6	+	1.43600e6i	0.428967	+	0.256879i
$501$	2.35710e6			0.419550
$502$		−	5.46830e6i		−	0.968486i
$503$			3.97628e6i			0.700741i	0.936611	+	0.350370i	$0.113944\pi$
$503$			3.97628e6i			0.700741i	−0.936611	+	0.350370i	$0.886056\pi$
$504$	20736.0			0.00363621
$505$	−9.23549e6	−	1.67918e6i	−1.61150	−	0.293001i
$506$	8.20000e6			1.42376
$507$		−	2.59514e6i		−	0.448375i
$508$		−	3.38848e6i		−	0.582567i
$509$	−781914.			−0.133772			−0.0668859	−	0.997761i	$-0.521306\pi$
$509$	−781914.			−0.133772			−0.0668859	+	0.997761i	$0.521306\pi$
$510$	545760.	−	3.00168e6i	0.0929130	−	0.511021i
$511$	123232.			0.0208772
$512$		−	262144.i		−	0.0441942i
$513$			979776.i			0.164374i
$514$	−3.57173e6			−0.596308
$515$	−1.54364e6	+	8.49002e6i	−0.256465	+	1.41056i
$516$	346176.			0.0572365
$517$			4.45000e6i			0.732207i
$518$			116608.i			0.0190943i
$519$	2.93605e6			0.478460
$520$	−1.01376e6	−	184320.i	−0.164409	−	0.0298926i
$521$	5.82694e6			0.940472			0.470236	−	0.882541i	$-0.344169\pi$
$521$	5.82694e6			0.940472			0.470236	+	0.882541i	$0.344169\pi$
$522$			857304.i			0.137708i
$523$		−	9.78938e6i		−	1.56495i	−0.622681	−	0.782476i	$-0.713957\pi$
$523$		−	9.78938e6i		−	1.56495i	0.622681	−	0.782476i	$-0.286043\pi$
$524$	−2.71200e6			−0.431481
$525$	105300.	+	39600.0i	0.0166736	+	0.00627042i
$526$	−7.46600e6			−1.17659
$527$			8.50779e6i			1.33441i
$528$			1.15200e6i			0.179832i
$529$	−1.03737e7			−1.61173
$530$	−8.75688e6	−	1.59216e6i	−1.35413	−	0.246205i
$531$	−2.29230e6			−0.352805
$532$		−	86016.0i		−	0.0131765i
$533$			5.46797e6i			0.833696i
$534$	816408.			0.123895
$535$	−1.36788e6	+	7.52334e6i	−0.206616	+	1.13639i
$536$	4.22118e6			0.634633
$537$		−	985644.i		−	0.147497i
$538$		−	5.48906e6i		−	0.817603i
$539$	−8.39550e6			−1.24473
$540$	−116640.	+	641520.i	−0.0172133	+	0.0946729i
$541$	4.76059e6			0.699307			0.349653	−	0.936879i	$-0.386299\pi$
$541$	4.76059e6			0.699307			0.349653	+	0.936879i	$0.386299\pi$
$542$		−	1.83458e6i		−	0.268249i
$543$			478314.i			0.0696167i
$544$	−1.55238e6			−0.224906
$545$	−2.95955e6	−	538100.i	−0.426810	−	0.0776018i
$546$	−41472.0			−0.00595351
$547$			1.16595e6i			0.166614i	0.996524	+	0.0833069i	$0.0265482\pi$
$547$			1.16595e6i			0.166614i	−0.996524	+	0.0833069i	$0.973452\pi$
$548$			4.03258e6i			0.573629i
$549$	−1.48149e6			−0.209782
$550$	−2.20000e6	+	5.85000e6i	−0.310110	+	0.824611i
$551$	3.55622e6			0.499011
$552$		−	2.36160e6i		−	0.329882i
$553$		−	240912.i		−	0.0335001i
$554$	3.94163e6			0.545634
$555$	−3.60756e6	−	655920.i	−0.497143	−	0.0903896i
$556$	3.07226e6			0.421474
$557$			1.61293e6i			0.220282i	0.993916	+	0.110141i	$0.0351302\pi$
$557$			1.61293e6i			0.220282i	−0.993916	+	0.110141i	$0.964870\pi$
$558$		−	1.81829e6i		−	0.247216i
$559$	−692352.			−0.0937125
$560$	10240.0	−	56320.0i	0.00137984	−	0.00758914i
$561$	6.82200e6			0.915176
$562$		−	663192.i		−	0.0885724i
$563$			3.40603e6i			0.452874i	0.974026	+	0.226437i	$0.0727077\pi$
$563$			3.40603e6i			0.452874i	−0.974026	+	0.226437i	$0.927292\pi$
$564$	1.28160e6			0.169650
$565$	826920.	−	4.54806e6i	0.108979	−	0.599384i
$566$	−6.65883e6			−0.873689
$567$			26244.0i			0.00342825i
$568$		−	1.84320e6i		−	0.239719i
$569$	1.44009e7			1.86470			0.932350	−	0.361557i	$-0.117755\pi$
$569$	1.44009e7			1.86470			0.932350	+	0.361557i	$0.117755\pi$
$570$	2.66112e6	+	483840.i	0.343066	+	0.0623756i
$571$	4.74772e6			0.609389			0.304695	−	0.952450i	$-0.401446\pi$
$571$	4.74772e6			0.609389			0.304695	+	0.952450i	$0.401446\pi$
$572$		−	2.30400e6i		−	0.294437i
$573$		−	2.08850e6i		−	0.265735i
$574$	−303776.			−0.0384834
$575$	4.51000e6	−	1.19925e7i	0.568862	−	1.51266i
$576$	331776.			0.0416667
$577$			1.09094e7i			1.36415i	0.731283	+	0.682074i	$0.238922\pi$
$577$			1.09094e7i			1.36415i	−0.731283	+	0.682074i	$0.761078\pi$
$578$			3.51360e6i			0.437454i
$579$	−9.27605e6			−1.14992
$580$	2.32848e6	+	423360.i	0.287410	+	0.0522564i
$581$	9872.00			0.00121329
$582$		−	1.33085e6i		−	0.162862i
$583$		−	1.99020e7i		−	2.42508i
$584$	1.97171e6			0.239228
$585$	233280.	−	1.28304e6i	0.0281830	−	0.155007i
$586$	1.02042e7			1.22754
$587$		−	8.53223e6i		−	1.02204i	−0.859569	−	0.511019i	$-0.829268\pi$
$587$		−	8.53223e6i		−	1.02204i	0.859569	−	0.511019i	$-0.170732\pi$
$588$			2.41790e6i			0.288400i
$589$	−7.54253e6			−0.895836
$590$	−1.13200e6	+	6.22600e6i	−0.133880	+	0.736341i
$591$	4.70516e6			0.554123
$592$			1.86573e6i			0.218798i
$593$		−	4.63182e6i		−	0.540897i	−0.962734	−	0.270449i	$-0.912828\pi$
$593$		−	4.63182e6i		−	0.540897i	0.962734	−	0.270449i	$-0.0871721\pi$
$594$	−1.45800e6			−0.169548
$595$	−333520.	−	60640.0i	−0.0386215	−	0.00702210i
$596$	3.77110e6			0.434863
$597$		−	1.93763e6i		−	0.222502i
$598$			4.72320e6i			0.540111i
$599$	−6.27598e6			−0.714684			−0.357342	−	0.933974i	$-0.616317\pi$
$599$	−6.27598e6			−0.714684			−0.357342	+	0.933974i	$0.616317\pi$
$600$	1.68480e6	+	633600.i	0.191060	+	0.0718517i
$601$	7.71988e6			0.871815			0.435907	−	0.899992i	$-0.356428\pi$
$601$	7.71988e6			0.871815			0.435907	+	0.899992i	$0.356428\pi$
$602$		−	38464.0i		−	0.00432577i
$603$			5.34244e6i			0.598337i
$604$	5.94387e6			0.662944
$605$	−4.89220e6	−	889490.i	−0.543395	−	0.0987990i
$606$	−6.04505e6			−0.668680
$607$			6.06160e6i			0.667753i	0.942617	+	0.333876i	$0.108357\pi$
$607$			6.06160e6i			0.667753i	−0.942617	+	0.333876i	$0.891643\pi$
$608$		−	1.37626e6i		−	0.150987i
$609$	95256.0			0.0104076
$610$	−731600.	+	4.02380e6i	−0.0796066	+	0.437836i
$611$	−2.56320e6			−0.277766
$612$		−	1.96474e6i		−	0.212044i
$613$		−	3.66489e6i		−	0.393921i	−0.980411	−	0.196961i	$-0.936893\pi$
$613$		−	3.66489e6i		−	0.393921i	0.980411	−	0.196961i	$-0.0631071\pi$
$614$	−2.94408e6			−0.315158
$615$	1.70874e6	−	9.39807e6i	0.182175	−	1.00196i
$616$	128000.			0.0135912
$617$			9.32522e6i			0.986157i	0.869985	+	0.493079i	$0.164129\pi$
$617$			9.32522e6i			0.986157i	−0.869985	+	0.493079i	$0.835871\pi$
$618$			5.55710e6i			0.585298i
$619$	7.40162e6			0.776426			0.388213	−	0.921570i	$-0.373093\pi$
$619$	7.40162e6			0.776426			0.388213	+	0.921570i	$0.373093\pi$
$620$	−4.93856e6	−	897920.i	−0.515966	−	0.0938120i
$621$	2.98890e6			0.311016
$622$		−	6.86640e6i		−	0.711628i
$623$		−	90712.0i		−	0.00936364i
$624$	−663552.			−0.0682203
$625$	7.34562e6	+	6.43500e6i	0.752192	+	0.658944i
$626$	1.13540e7			1.15802
$627$			6.04800e6i			0.614388i
$628$			4.23923e6i			0.428932i
$629$	1.10486e7			1.11348
$630$	71280.0	+	12960.0i	0.00715511	+	0.00130093i
$631$	160052.			0.0160025			0.00800125	−	0.999968i	$-0.497453\pi$
$631$	160052.			0.0160025			0.00800125	+	0.999968i	$0.497453\pi$
$632$		−	3.85459e6i		−	0.383871i
$633$			9.27072e6i			0.919611i
$634$	5.10421e6			0.504319
$635$	2.11780e6	−	1.16479e7i	0.208425	−	1.14634i
$636$	−5.73178e6			−0.561884
$637$		−	4.83581e6i		−	0.472194i
$638$			5.29200e6i			0.514717i
$639$	2.33280e6			0.226009
$640$	163840.	−	901120.i	0.0158114	−	0.0869626i
$641$	−1.69565e7			−1.63002			−0.815008	−	0.579450i	$-0.803268\pi$
$641$	−1.69565e7			−1.63002			−0.815008	+	0.579450i	$0.803268\pi$
$642$			4.92437e6i			0.471534i
$643$			1.10128e7i			1.05044i	0.850967	+	0.525219i	$0.176016\pi$
$643$			1.10128e7i			1.05044i	−0.850967	+	0.525219i	$0.823984\pi$
$644$	−262400.			−0.0249315
$645$	1.18998e6	+	216360.i	0.112626	+	0.0204775i
$646$	−8.15002e6			−0.768382
$647$		−	3.33848e6i		−	0.313537i	−0.987635	−	0.156768i	$-0.949892\pi$
$647$		−	3.33848e6i		−	0.313537i	0.987635	−	0.156768i	$-0.0501076\pi$
$648$			419904.i			0.0392837i
$649$	−1.41500e7			−1.31870
$650$	−3.36960e6	−	1.26720e6i	−0.312820	−	0.117642i
$651$	−202032.			−0.0186839
$652$			6.44998e6i			0.594210i
$653$		−	4.76181e6i		−	0.437008i	−0.975836	−	0.218504i	$-0.929882\pi$
$653$		−	4.76181e6i		−	0.437008i	0.975836	−	0.218504i	$-0.0701177\pi$
$654$	−1.93716e6			−0.177101
$655$	−9.32250e6	−	1.69500e6i	−0.849042	−	0.154371i
$656$	−4.86042e6			−0.440975
$657$			2.49545e6i			0.225546i
$658$		−	142400.i		−	0.0128217i
$659$	−798188.			−0.0715965			−0.0357982	−	0.999359i	$-0.511397\pi$
$659$	−798188.			−0.0715965			−0.0357982	+	0.999359i	$0.511397\pi$
$660$	−720000.	+	3.96000e6i	−0.0643388	+	0.353863i
$661$	−1.54048e7			−1.37136			−0.685682	−	0.727901i	$-0.740496\pi$
$661$	−1.54048e7			−1.37136			−0.685682	+	0.727901i	$0.740496\pi$
$662$		−	1.77597e6i		−	0.157503i
$663$			3.92947e6i			0.347177i
$664$	157952.			0.0139029
$665$	53760.0	−	295680.i	0.00471417	−	0.0259279i
$666$	−2.36131e6			−0.206285
$667$		−	1.08486e7i		−	0.944189i
$668$		−	4.19040e6i		−	0.363341i
$669$	4.10418e6			0.354537
$670$	1.45103e7	+	2.63824e6i	1.24879	+	0.227053i
$671$	−9.14500e6			−0.784111
$672$		−	36864.0i		−	0.00314905i
$673$		−	976704.i		−	0.0831238i	−0.999136	−	0.0415619i	$-0.986767\pi$
$673$		−	976704.i		−	0.0831238i	0.999136	−	0.0415619i	$-0.0132334\pi$
$674$	−1.08530e7			−0.920240
$675$	−801900.	+	2.13232e6i	−0.0677424	+	0.180133i
$676$	−4.61358e6			−0.388304
$677$		−	1.93885e7i		−	1.62582i	−0.582388	−	0.812911i	$-0.697881\pi$
$677$		−	1.93885e7i		−	1.62582i	0.582388	−	0.812911i	$-0.302119\pi$
$678$		−	2.97691e6i		−	0.248709i
$679$	−147872.			−0.0123087
$680$	−5.33632e6	−	970240.i	−0.442557	−	0.0804650i
$681$	3.90827e6			0.322936
$682$		−	1.12240e7i		−	0.924031i
$683$		−	5.25573e6i		−	0.431103i	−0.976492	−	0.215552i	$-0.930845\pi$
$683$		−	5.25573e6i		−	0.431103i	0.976492	−	0.215552i	$-0.0691550\pi$
$684$	1.74182e6			0.142352
$685$	−2.52036e6	+	1.38620e7i	−0.205228	+	1.12875i
$686$	537568.			0.0436137
$687$		−	6.50439e6i		−	0.525793i
$688$		−	615424.i		−	0.0495682i
$689$	1.14636e7			0.919965
$690$	1.47600e6	−	8.11800e6i	0.118022	−	0.649122i
$691$	−5.45034e6			−0.434238			−0.217119	−	0.976145i	$-0.569666\pi$
$691$	−5.45034e6			−0.434238			−0.217119	+	0.976145i	$0.569666\pi$
$692$		−	5.21965e6i		−	0.414358i
$693$			162000.i			0.0128139i
$694$	5.24203e6			0.413144
$695$	1.05609e7	+	1.92016e6i	0.829350	+	0.150791i
$696$	1.52410e6			0.119258
$697$			2.87828e7i			2.24414i
$698$		−	1.19564e6i		−	0.0928885i
$699$	−5.08813e6			−0.393881
$700$	70400.0	−	187200.i	0.00543035	−	0.0144398i
$701$	−4.43961e6			−0.341232			−0.170616	−	0.985338i	$-0.554576\pi$
$701$	−4.43961e6			−0.341232			−0.170616	+	0.985338i	$0.554576\pi$
$702$		−	839808.i		−	0.0643187i
$703$			9.79507e6i			0.747514i
$704$	2.04800e6			0.155739
$705$	4.40550e6	+	801000.i	0.333828	+	0.0606960i
$706$	2.95198e6			0.222896
$707$			671672.i			0.0505369i
$708$			4.07520e6i			0.305538i
$709$	−4.55918e6			−0.340621			−0.170310	−	0.985390i	$-0.554477\pi$
$709$	−4.55918e6			−0.340621			−0.170310	+	0.985390i	$0.554477\pi$
$710$	1.15200e6	−	6.33600e6i	0.0857643	−	0.471704i
$711$	4.87847e6			0.361917
$712$		−	1.45139e6i		−	0.107296i
$713$			2.30092e7i			1.69503i
$714$	−218304.			−0.0160257
$715$	1.44000e6	−	7.92000e6i	0.105341	−	0.579375i
$716$	−1.75226e6			−0.127736
$717$			2.92414e6i			0.212422i
$718$		−	9.36298e6i		−	0.677802i
$719$	2.06630e7			1.49063			0.745317	−	0.666710i	$-0.232298\pi$
$719$	2.06630e7			1.49063			0.745317	+	0.666710i	$0.232298\pi$
$720$	1.14048e6	+	207360.i	0.0819892	+	0.0149071i
$721$	617456.			0.0442352
$722$			2.67905e6i			0.191266i
$723$		−	8.23736e6i		−	0.586060i
$724$	850336.			0.0602898
$725$	7.73955e6	+	2.91060e6i	0.546853	+	0.205654i
$726$	−3.20216e6			−0.225477
$727$		−	5.48161e6i		−	0.384656i	−0.981331	−	0.192328i	$-0.938396\pi$
$727$		−	5.48161e6i		−	0.384656i	0.981331	−	0.192328i	$-0.0616037\pi$
$728$			73728.0i			0.00515589i
$729$	−531441.			−0.0370370
$730$	6.77776e6	+	1.23232e6i	0.470738	+	0.0855887i
$731$	−3.64446e6			−0.252255
$732$			2.63376e6i			0.181676i
$733$		−	8.55579e6i		−	0.588166i	−0.955780	−	0.294083i	$-0.904986\pi$
$733$		−	8.55579e6i		−	0.588166i	0.955780	−	0.294083i	$-0.0950143\pi$
$734$	−509168.			−0.0348836
$735$	−1.51119e6	+	8.31154e6i	−0.103181	+	0.567497i
$736$	−4.19840e6			−0.285686
$737$			3.29780e7i			2.23643i
$738$		−	6.15146e6i		−	0.415755i
$739$	5.29119e6			0.356404			0.178202	−	0.983994i	$-0.442972\pi$
$739$	5.29119e6			0.356404			0.178202	+	0.983994i	$0.442972\pi$
$740$	−1.16608e6	+	6.41344e6i	−0.0782797	+	0.430538i
$741$	−3.48365e6			−0.233071
$742$			636864.i			0.0424656i
$743$		−	2.36432e6i		−	0.157121i	−0.996909	−	0.0785606i	$-0.974968\pi$
$743$		−	2.36432e6i		−	0.157121i	0.996909	−	0.0785606i	$-0.0250324\pi$
$744$	−3.23251e6			−0.214096
$745$	1.29632e7	+	2.35694e6i	0.855698	+	0.155581i
$746$	1.61548e7			1.06281
$747$			199908.i			0.0131078i
$748$		−	1.21280e7i		−	0.792566i
$749$	547152.			0.0356372
$750$	5.39550e6	+	3.23100e6i	0.350250	+	0.209741i
$751$	−8.79694e6			−0.569157			−0.284578	−	0.958653i	$-0.591854\pi$
$751$	−8.79694e6			−0.569157			−0.284578	+	0.958653i	$0.591854\pi$
$752$		−	2.27840e6i		−	0.146922i
$753$		−	1.23037e7i		−	0.790766i
$754$	−3.04819e6			−0.195260
$755$	2.04321e7	+	3.71492e6i	1.30450	+	0.237182i
$756$	46656.0			0.00296895
$757$		−	2.95808e7i		−	1.87616i	−0.346421	−	0.938079i	$-0.612603\pi$
$757$		−	2.95808e7i		−	1.87616i	0.346421	−	0.938079i	$-0.387397\pi$
$758$			4.04854e6i			0.255933i
$759$	1.84500e7			1.16250
$760$	860160.	−	4.73088e6i	0.0540188	−	0.297104i
$761$	−1.26296e7			−0.790549			−0.395274	−	0.918563i	$-0.629351\pi$
$761$	−1.26296e7			−0.790549			−0.395274	+	0.918563i	$0.629351\pi$
$762$		−	7.62408e6i		−	0.475664i
$763$			215240.i			0.0133848i
$764$	−3.71290e6			−0.230133
$765$	1.22796e6	−	6.75378e6i	0.0758631	−	0.417247i
$766$	−9.50440e6			−0.585265
$767$		−	8.15040e6i		−	0.500254i
$768$		−	589824.i		−	0.0360844i
$769$	2.32186e7			1.41586			0.707929	−	0.706283i	$-0.249630\pi$
$769$	2.32186e7			1.41586			0.707929	+	0.706283i	$0.249630\pi$
$770$	440000.	+	80000.0i	0.0267440	+	0.00486254i
$771$	−8.03639e6			−0.486883
$772$			1.64908e7i			0.995858i
$773$		−	1.73201e7i		−	1.04256i	−0.853386	−	0.521280i	$-0.825455\pi$
$773$		−	1.73201e7i		−	1.04256i	0.853386	−	0.521280i	$-0.174545\pi$
$774$	778896.			0.0467334
$775$	−1.64151e7	−	6.17320e6i	−0.981724	−	0.369195i
$776$	−2.36595e6			−0.141043
$777$			262368.i			0.0155904i
$778$			5.69990e6i			0.337612i
$779$	−2.55172e7			−1.50657
$780$	−2.28096e6	−	414720.i	−0.134240	−	0.0244072i
$781$	1.44000e7			0.844763
$782$			2.48624e7i			1.45387i
$783$			1.92893e6i			0.112438i
$784$	4.29850e6			0.249762
$785$	−2.64952e6	+	1.45724e7i	−0.153459	+	0.844026i
$786$	−6.10200e6			−0.352303
$787$		−	556676.i		−	0.0320380i	−0.999872	−	0.0160190i	$-0.994901\pi$
$787$		−	556676.i		−	0.0320380i	0.999872	−	0.0160190i	$-0.00509923\pi$
$788$		−	8.36474e6i		−	0.479884i
$789$	−1.67985e7			−0.960678
$790$	2.40912e6	−	1.32502e7i	0.137338	−	0.755359i
$791$	−330768.			−0.0187967
$792$			2.59200e6i			0.146832i
$793$		−	5.26752e6i		−	0.297456i
$794$	−6.77379e6			−0.381312
$795$	−1.97030e7	−	3.58236e6i	−1.10564	−	0.201026i
$796$	−3.44467e6			−0.192693
$797$		−	3.00562e6i		−	0.167606i	−0.996482	−	0.0838028i	$-0.973293\pi$
$797$		−	3.00562e6i		−	0.167606i	0.996482	−	0.0838028i	$-0.0267066\pi$
$798$		−	193536.i		−	0.0107586i
$799$	−1.34924e7			−0.747691
$800$	1.12640e6	−	2.99520e6i	0.0622254	−	0.165463i
$801$	1.83692e6			0.101160
$802$			1.13800e7i			0.624751i
$803$			1.54040e7i			0.843033i
$804$	9.49766e6			0.518175
$805$	−902000.	−	164000.i	−0.0490588	−	0.00891978i
$806$	6.46502e6			0.350536
$807$		−	1.23504e7i		−	0.667570i
$808$			1.07468e7i			0.579094i
$809$	−2.23153e6			−0.119876			−0.0599378	−	0.998202i	$-0.519090\pi$
$809$	−2.23153e6			−0.119876			−0.0599378	+	0.998202i	$0.519090\pi$
$810$	−262440.	+	1.44342e6i	−0.0140546	+	0.0773001i
$811$	2.24862e7			1.20051			0.600253	−	0.799810i	$-0.295067\pi$
$811$	2.24862e7			1.20051			0.600253	+	0.799810i	$0.295067\pi$
$812$		−	169344.i		−	0.00901322i
$813$		−	4.12780e6i		−	0.219024i
$814$	−1.45760e7			−0.771041
$815$	−4.03124e6	+	2.21718e7i	−0.212591	+	1.16925i
$816$	−3.49286e6			−0.183635
$817$		−	3.23098e6i		−	0.169347i
$818$		−	7.56278e6i		−	0.395183i
$819$	−93312.0			−0.00486102
$820$	−1.67077e7	−	3.03776e6i	−0.867724	−	0.157768i
$821$	−1.65921e7			−0.859098			−0.429549	−	0.903044i	$-0.641327\pi$
$821$	−1.65921e7			−0.859098			−0.429549	+	0.903044i	$0.641327\pi$
$822$			9.07330e6i			0.468366i
$823$			1.47544e7i			0.759316i	0.925127	+	0.379658i	$0.123958\pi$
$823$			1.47544e7i			0.759316i	−0.925127	+	0.379658i	$0.876042\pi$
$824$	9.87930e6			0.506883
$825$	−4.95000e6	+	1.31625e7i	−0.253204	+	0.673292i
$826$	452800.			0.0230917
$827$			3.39475e6i			0.172601i	0.996269	+	0.0863006i	$0.0275045\pi$
$827$			3.39475e6i			0.172601i	−0.996269	+	0.0863006i	$0.972495\pi$
$828$		−	5.31360e6i		−	0.269348i
$829$	509442.			0.0257459			0.0128730	−	0.999917i	$-0.495902\pi$
$829$	509442.			0.0257459			0.0128730	+	0.999917i	$0.495902\pi$
$830$	542960.	+	98720.0i	0.0273573	+	0.00497405i
$831$	8.86867e6			0.445509
$832$			1.17965e6i			0.0590805i
$833$		−	2.54552e7i		−	1.27105i
$834$	6.91258e6			0.344132
$835$	2.61900e6	−	1.44045e7i	0.129993	−	0.714960i
$836$	1.07520e7			0.532076
$837$		−	4.09115e6i		−	0.201851i
$838$			1.84372e7i			0.906953i
$839$	−4.00609e7			−1.96479			−0.982394	−	0.186819i	$-0.940182\pi$
$839$	−4.00609e7			−1.96479			−0.982394	+	0.186819i	$0.940182\pi$
$840$	23040.0	−	126720.i	0.00112664	−	0.00619651i
$841$	−1.35098e7			−0.658658
$842$			2.41660e7i			1.17470i
$843$		−	1.49218e6i		−	0.0723191i
$844$	1.64813e7			0.796407
$845$	−1.58592e7	−	2.88349e6i	−0.764081	−	0.138924i
$846$	2.88360e6			0.138519
$847$			355796.i			0.0170409i
$848$			1.01898e7i			0.486606i
$849$	−1.49824e7			−0.713364
$850$	−1.77372e7	−	6.67040e6i	−0.842050	−	0.316668i
$851$	2.98808e7			1.41439
$852$		−	4.14720e6i		−	0.195729i
$853$			9.67506e6i			0.455283i	0.973745	+	0.227641i	$0.0731014\pi$
$853$			9.67506e6i			0.455283i	−0.973745	+	0.227641i	$0.926899\pi$
$854$	292640.			0.0137306
$855$	5.98752e6	+	1.08864e6i	0.280112	+	0.0509295i
$856$	8.75443e6			0.408360
$857$		−	3.27535e7i		−	1.52337i	−0.647946	−	0.761686i	$-0.724372\pi$
$857$		−	3.27535e7i		−	1.52337i	0.647946	−	0.761686i	$-0.275628\pi$
$858$		−	5.18400e6i		−	0.240407i
$859$	2.17420e7			1.00535			0.502675	−	0.864476i	$-0.332349\pi$
$859$	2.17420e7			1.00535			0.502675	+	0.864476i	$0.332349\pi$
$860$	384640.	−	2.11552e6i	0.0177341	−	0.0975374i
$861$	−683496.			−0.0314216
$862$			15200.0i			0.000696748i
$863$			2.08744e7i			0.954087i	0.878880	+	0.477043i	$0.158292\pi$
$863$			2.08744e7i			0.954087i	−0.878880	+	0.477043i	$0.841708\pi$
$864$	746496.			0.0340207
$865$	3.26228e6	−	1.79425e7i	0.148245	−	0.815349i
$866$	1.00294e6			0.0454446
$867$			7.90559e6i			0.357180i
$868$			359168.i			0.0161807i
$869$	3.01140e7			1.35275
$870$	5.23908e6	+	952560.i	0.234670	+	0.0426672i
$871$	−1.89953e7			−0.848401
$872$			3.44384e6i			0.153374i
$873$		−	2.99441e6i		−	0.132977i
$874$	−2.20416e7			−0.976033
$875$	359000.	−	599500.i	0.0158516	−	0.0264709i
$876$	4.43635e6			0.195329
$877$		−	3.96804e7i		−	1.74212i	−0.491181	−	0.871058i	$-0.663434\pi$
$877$		−	3.96804e7i		−	1.74212i	0.491181	−	0.871058i	$-0.336566\pi$
$878$		−	1.43549e7i		−	0.628441i
$879$	2.29594e7			1.00228
$880$	7.04000e6	+	1.28000e6i	0.306454	+	0.0557190i
$881$	2.60742e7			1.13180			0.565902	−	0.824472i	$-0.308528\pi$
$881$	2.60742e7			1.13180			0.565902	+	0.824472i	$0.308528\pi$
$882$			5.44028e6i			0.235478i
$883$			4.10486e7i			1.77172i	0.463949	+	0.885862i	$0.346432\pi$
$883$			4.10486e7i			1.77172i	−0.463949	+	0.885862i	$0.653568\pi$
$884$	6.98573e6			0.300664
$885$	−2.54700e6	+	1.40085e7i	−0.109313	+	0.601220i
$886$	−5.65915e6			−0.242196
$887$		−	1.37553e7i		−	0.587031i	−0.955954	−	0.293515i	$-0.905175\pi$
$887$		−	1.37553e7i		−	0.587031i	0.955954	−	0.293515i	$-0.0948252\pi$
$888$			4.19789e6i			0.178648i
$889$	−847120.			−0.0359493
$890$	907120.	−	4.98916e6i	0.0383875	−	0.211131i
$891$	−3.28050e6			−0.138435
$892$		−	7.29632e6i		−	0.307038i
$893$		−	1.19616e7i		−	0.501950i
$894$	8.48498e6			0.355064
$895$	−6.02338e6	−	1.09516e6i	−0.251352	−	0.0457004i
$896$	−65536.0			−0.00272716
$897$			1.06272e7i			0.440999i
$898$		−	3.31922e6i		−	0.137355i
$899$	−1.48494e7			−0.612785
$900$	3.79080e6	+	1.42560e6i	0.156000	+	0.0586667i
$901$	6.03429e7			2.47636
$902$		−	3.79720e7i		−	1.55399i
$903$		−	86544.0i		−	0.00353197i
$904$	−5.29229e6			−0.215388
$905$	2.92303e6	+	531460.i	0.118635	+	0.0215699i
$906$	1.33737e7			0.541292
$907$			5.86936e6i			0.236904i	0.992960	+	0.118452i	$0.0377932\pi$
$907$			5.86936e6i			0.236904i	−0.992960	+	0.118452i	$0.962207\pi$
$908$		−	6.94803e6i		−	0.279671i
$909$	−1.36014e7			−0.545975
$910$	−46080.0	+	253440.i	−0.00184463	+	0.0101455i
$911$	4.63982e7			1.85227			0.926137	−	0.377188i	$-0.123109\pi$
$911$	4.63982e7			1.85227			0.926137	+	0.377188i	$0.123109\pi$
$912$		−	3.09658e6i		−	0.123281i
$913$			1.23400e6i			0.0489935i
$914$	−1.87279e7			−0.741521
$915$	−1.64610e6	+	9.05355e6i	−0.0649985	+	0.357492i
$916$	−1.15634e7			−0.455350
$917$			678000.i			0.0266260i
$918$		−	4.42066e6i		−	0.173133i
$919$	−2.27859e7			−0.889975			−0.444988	−	0.895537i	$-0.646792\pi$
$919$	−2.27859e7			−0.889975			−0.444988	+	0.895537i	$0.646792\pi$
$920$	−1.44320e7	−	2.62400e6i	−0.562156	−	0.102210i
$921$	−6.62418e6			−0.257326
$922$			567720.i			0.0219941i
$923$			8.29440e6i			0.320465i
$924$	288000.			0.0110972
$925$	−8.01680e6	+	2.13174e7i	−0.308068	+	0.819181i
$926$	2.90990e6			0.111520
$927$			1.25035e7i			0.477894i
$928$		−	2.70950e6i		−	0.103281i
$929$	−2.70352e7			−1.02775			−0.513877	−	0.857864i	$-0.671791\pi$
$929$	−2.70352e7			−1.02775			−0.513877	+	0.857864i	$0.671791\pi$
$930$	−1.11118e7	−	2.02032e6i	−0.421285	−	0.0765972i
$931$	2.25671e7			0.853300
$932$			9.04557e6i			0.341111i
$933$		−	1.54494e7i		−	0.581042i
$934$	1.79056e7			0.671616
$935$	7.58000e6	−	4.16900e7i	0.283557	−	1.55956i
$936$	−1.49299e6			−0.0557016
$937$			2.86149e7i			1.06474i	0.846512	+	0.532370i	$0.178699\pi$
$937$			2.86149e7i			1.06474i	−0.846512	+	0.532370i	$0.821301\pi$
$938$		−	1.05530e6i		−	0.0391622i
$939$	2.55466e7			0.945517
$940$	1.42400e6	−	7.83200e6i	0.0525642	−	0.289103i
$941$	−3.67892e7			−1.35440			−0.677200	−	0.735799i	$-0.736807\pi$
$941$	−3.67892e7			−1.35440			−0.677200	+	0.735799i	$0.736807\pi$
$942$			9.53827e6i			0.350221i
$943$			7.78426e7i			2.85061i
$944$	7.24480e6			0.264604
$945$	160380.	+	29160.0i	0.00584212	+	0.00106220i
$946$	4.80800e6			0.174677
$947$		−	7.96828e6i		−	0.288728i	−0.989525	−	0.144364i	$-0.953886\pi$
$947$		−	7.96828e6i		−	0.288728i	0.989525	−	0.144364i	$-0.0461137\pi$
$948$		−	8.67283e6i		−	0.313430i
$949$	−8.87270e6			−0.319809
$950$	5.91360e6	−	1.57248e7i	0.212590	−	0.565296i
$951$	1.14845e7			0.411775
$952$			388096.i			0.0138786i
$953$		−	4.82202e7i		−	1.71987i	−0.510400	−	0.859937i	$-0.670503\pi$
$953$		−	4.82202e7i		−	1.71987i	0.510400	−	0.859937i	$-0.329497\pi$
$954$	−1.28965e7			−0.458776
$955$	−1.27631e7	−	2.32056e6i	−0.452842	−	0.0823350i
$956$	5.19846e6			0.183963
$957$			1.19070e7i			0.420264i
$958$		−	5.30874e6i		−	0.186886i
$959$	1.00814e6			0.0353978
$960$	368640.	−	2.02752e6i	0.0129099	−	0.0710047i
$961$	2.86539e6			0.100087
$962$		−	8.39578e6i		−	0.292498i
$963$			1.10798e7i			0.385006i
$964$	−1.46442e7			−0.507543
$965$	−1.03067e7	+	5.66870e7i	−0.356289	+	1.95959i
$966$	−590400.			−0.0203565
$967$		−	4.83510e7i		−	1.66280i	−0.555678	−	0.831398i	$-0.687541\pi$
$967$		−	4.83510e7i		−	1.66280i	0.555678	−	0.831398i	$-0.312459\pi$
$968$			5.69274e6i			0.195269i
$969$	−1.83375e7			−0.627381
$970$	−8.13296e6	−	1.47872e6i	−0.277536	−	0.0504611i
$971$	−4.05515e7			−1.38025			−0.690127	−	0.723688i	$-0.742445\pi$
$971$	−4.05515e7			−1.38025			−0.690127	+	0.723688i	$0.742445\pi$
$972$			944784.i			0.0320750i
$973$		−	768064.i		−	0.0260085i
$974$	1.64659e7			0.556144
$975$	−7.58160e6	−	2.85120e6i	−0.255417	−	0.0960542i
$976$	4.68224e6			0.157336
$977$			4.34929e7i			1.45775i	0.684648	+	0.728874i	$0.259956\pi$
$977$			4.34929e7i			1.45775i	−0.684648	+	0.728874i	$0.740044\pi$
$978$			1.45125e7i			0.485170i
$979$	1.13390e7			0.378110
$980$	1.47761e7	+	2.68656e6i	0.491467	+	0.0893576i
$981$	−4.35861e6			−0.144602
$982$			2.44926e7i			0.810507i
$983$		−	3.34896e6i		−	0.110542i	−0.998471	−	0.0552709i	$-0.982398\pi$
$983$		−	3.34896e6i		−	0.110542i	0.998471	−	0.0552709i	$-0.0176022\pi$
$984$	−1.09359e7			−0.360054
$985$	5.22796e6	−	2.87538e7i	0.171689	−	0.944288i
$986$	−1.60453e7			−0.525602
$987$		−	320400.i		−	0.0104689i
$988$			6.19315e6i			0.201846i
$989$	−9.85640e6			−0.320426
$990$	−1.62000e6	+	8.91000e6i	−0.0525324	+	0.288928i
$991$	−5.55726e7			−1.79753			−0.898766	−	0.438429i	$-0.855535\pi$
$991$	−5.55726e7			−1.79753			−0.898766	+	0.438429i	$0.855535\pi$
$992$			5.74669e6i			0.185412i
$993$		−	3.99593e6i		−	0.128601i
$994$	−460800.			−0.0147927
$995$	−1.18411e7	−	2.15292e6i	−0.379169	−	0.0689398i
$996$	355392.			0.0113517
$997$			1.27342e7i			0.405726i	0.979207	+	0.202863i	$0.0650247\pi$
$997$			1.27342e7i			0.405726i	−0.979207	+	0.202863i	$0.934975\pi$
$998$		−	3.16196e7i		−	1.00492i
$999$	−5.31295e6			−0.168431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.6.c.a.19.1	✓	2
3.2	odd	2		90.6.c.b.19.2		2
4.3	odd	2		240.6.f.a.49.2		2
5.2	odd	4		150.6.a.j.1.1		1
5.3	odd	4		150.6.a.f.1.1		1
5.4	even	2	inner	30.6.c.a.19.2	yes	2
12.11	even	2		720.6.f.g.289.2		2
15.2	even	4		450.6.a.f.1.1		1
15.8	even	4		450.6.a.s.1.1		1
15.14	odd	2		90.6.c.b.19.1		2
20.19	odd	2		240.6.f.a.49.1		2
60.59	even	2		720.6.f.g.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.6.c.a.19.1	✓	2	1.1	even	1	trivial
30.6.c.a.19.2	yes	2	5.4	even	2	inner
90.6.c.b.19.1		2	15.14	odd	2
90.6.c.b.19.2		2	3.2	odd	2
150.6.a.f.1.1		1	5.3	odd	4
150.6.a.j.1.1		1	5.2	odd	4
240.6.f.a.49.1		2	20.19	odd	2
240.6.f.a.49.2		2	4.3	odd	2
450.6.a.f.1.1		1	15.2	even	4
450.6.a.s.1.1		1	15.8	even	4
720.6.f.g.289.1		2	60.59	even	2
720.6.f.g.289.2		2	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	30.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -36.0000 q^{6} +4.00000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +O(q^{10})\)	\(q-4.00000i q^{2} -9.00000i q^{3} -16.0000 q^{4} +(-55.0000 - 10.0000i) q^{5} -36.0000 q^{6} +4.00000i q^{7} +64.0000i q^{8} -81.0000 q^{9} +(-40.0000 + 220.000i) q^{10} -500.000 q^{11} +144.000i q^{12} -288.000i q^{13} +16.0000 q^{14} +(-90.0000 + 495.000i) q^{15} +256.000 q^{16} -1516.00i q^{17} +324.000i q^{18} +1344.00 q^{19} +(880.000 + 160.000i) q^{20} +36.0000 q^{21} +2000.00i q^{22} -4100.00i q^{23} +576.000 q^{24} +(2925.00 + 1100.00i) q^{25} -1152.00 q^{26} +729.000i q^{27} -64.0000i q^{28} +2646.00 q^{29} +(1980.00 + 360.000i) q^{30} -5612.00 q^{31} -1024.00i q^{32} +4500.00i q^{33} -6064.00 q^{34} +(40.0000 - 220.000i) q^{35} +1296.00 q^{36} +7288.00i q^{37} -5376.00i q^{38} -2592.00 q^{39} +(640.000 - 3520.00i) q^{40} -18986.0 q^{41} -144.000i q^{42} -2404.00i q^{43} +8000.00 q^{44} +(4455.00 + 810.000i) q^{45} -16400.0 q^{46} -8900.00i q^{47} -2304.00i q^{48} +16791.0 q^{49} +(4400.00 - 11700.0i) q^{50} -13644.0 q^{51} +4608.00i q^{52} +39804.0i q^{53} +2916.00 q^{54} +(27500.0 + 5000.00i) q^{55} -256.000 q^{56} -12096.0i q^{57} -10584.0i q^{58} +28300.0 q^{59} +(1440.00 - 7920.00i) q^{60} +18290.0 q^{61} +22448.0i q^{62} -324.000i q^{63} -4096.00 q^{64} +(-2880.00 + 15840.0i) q^{65} +18000.0 q^{66} -65956.0i q^{67} +24256.0i q^{68} -36900.0 q^{69} +(-880.000 - 160.000i) q^{70} -28800.0 q^{71} -5184.00i q^{72} -30808.0i q^{73} +29152.0 q^{74} +(9900.00 - 26325.0i) q^{75} -21504.0 q^{76} -2000.00i q^{77} +10368.0i q^{78} -60228.0 q^{79} +(-14080.0 - 2560.00i) q^{80} +6561.00 q^{81} +75944.0i q^{82} -2468.00i q^{83} -576.000 q^{84} +(-15160.0 + 83380.0i) q^{85} -9616.00 q^{86} -23814.0i q^{87} -32000.0i q^{88} -22678.0 q^{89} +(3240.00 - 17820.0i) q^{90} +1152.00 q^{91} +65600.0i q^{92} +50508.0i q^{93} -35600.0 q^{94} +(-73920.0 - 13440.0i) q^{95} -9216.00 q^{96} +36968.0i q^{97} -67164.0i q^{98} +40500.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{4} - 110 q^{5} - 72 q^{6} - 162 q^{9}+O(q^{10}) \) 2 * q - 32 * q^4 - 110 * q^5 - 72 * q^6 - 162 * q^9	\( 2 q - 32 q^{4} - 110 q^{5} - 72 q^{6} - 162 q^{9} - 80 q^{10} - 1000 q^{11} + 32 q^{14} - 180 q^{15} + 512 q^{16} + 2688 q^{19} + 1760 q^{20} + 72 q^{21} + 1152 q^{24} + 5850 q^{25} - 2304 q^{26} + 5292 q^{29} + 3960 q^{30} - 11224 q^{31} - 12128 q^{34} + 80 q^{35} + 2592 q^{36} - 5184 q^{39} + 1280 q^{40} - 37972 q^{41} + 16000 q^{44} + 8910 q^{45} - 32800 q^{46} + 33582 q^{49} + 8800 q^{50} - 27288 q^{51} + 5832 q^{54} + 55000 q^{55} - 512 q^{56} + 56600 q^{59} + 2880 q^{60} + 36580 q^{61} - 8192 q^{64} - 5760 q^{65} + 36000 q^{66} - 73800 q^{69} - 1760 q^{70} - 57600 q^{71} + 58304 q^{74} + 19800 q^{75} - 43008 q^{76} - 120456 q^{79} - 28160 q^{80} + 13122 q^{81} - 1152 q^{84} - 30320 q^{85} - 19232 q^{86} - 45356 q^{89} + 6480 q^{90} + 2304 q^{91} - 71200 q^{94} - 147840 q^{95} - 18432 q^{96} + 81000 q^{99}+O(q^{100}) \) 2 * q - 32 * q^4 - 110 * q^5 - 72 * q^6 - 162 * q^9 - 80 * q^10 - 1000 * q^11 + 32 * q^14 - 180 * q^15 + 512 * q^16 + 2688 * q^19 + 1760 * q^20 + 72 * q^21 + 1152 * q^24 + 5850 * q^25 - 2304 * q^26 + 5292 * q^29 + 3960 * q^30 - 11224 * q^31 - 12128 * q^34 + 80 * q^35 + 2592 * q^36 - 5184 * q^39 + 1280 * q^40 - 37972 * q^41 + 16000 * q^44 + 8910 * q^45 - 32800 * q^46 + 33582 * q^49 + 8800 * q^50 - 27288 * q^51 + 5832 * q^54 + 55000 * q^55 - 512 * q^56 + 56600 * q^59 + 2880 * q^60 + 36580 * q^61 - 8192 * q^64 - 5760 * q^65 + 36000 * q^66 - 73800 * q^69 - 1760 * q^70 - 57600 * q^71 + 58304 * q^74 + 19800 * q^75 - 43008 * q^76 - 120456 * q^79 - 28160 * q^80 + 13122 * q^81 - 1152 * q^84 - 30320 * q^85 - 19232 * q^86 - 45356 * q^89 + 6480 * q^90 + 2304 * q^91 - 71200 * q^94 - 147840 * q^95 - 18432 * q^96 + 81000 * q^99

Introduction

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