LMFDB - Embedded newform 30.6.c.a.19.2

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000i q^{2} +9.00000i q^{3} -16.0000 q^{4} +(-55.0000 + 10.0000i) q^{5} -36.0000 q^{6} -4.00000i q^{7} -64.0000i q^{8} -81.0000 q^{9} +O(q^{10})$	\(q+4.00000i q^{2} +9.00000i q^{3} -16.0000 q^{4} +(-55.0000 + 10.0000i) q^{5} -36.0000 q^{6} -4.00000i q^{7} -64.0000i q^{8} -81.0000 q^{9} +(-40.0000 - 220.000i) q^{10} -500.000 q^{11} -144.000i q^{12} +288.000i q^{13} +16.0000 q^{14} +(-90.0000 - 495.000i) q^{15} +256.000 q^{16} +1516.00i q^{17} -324.000i q^{18} +1344.00 q^{19} +(880.000 - 160.000i) q^{20} +36.0000 q^{21} -2000.00i q^{22} +4100.00i q^{23} +576.000 q^{24} +(2925.00 - 1100.00i) q^{25} -1152.00 q^{26} -729.000i q^{27} +64.0000i q^{28} +2646.00 q^{29} +(1980.00 - 360.000i) q^{30} -5612.00 q^{31} +1024.00i q^{32} -4500.00i q^{33} -6064.00 q^{34} +(40.0000 + 220.000i) q^{35} +1296.00 q^{36} -7288.00i q^{37} +5376.00i q^{38} -2592.00 q^{39} +(640.000 + 3520.00i) q^{40} -18986.0 q^{41} +144.000i q^{42} +2404.00i q^{43} +8000.00 q^{44} +(4455.00 - 810.000i) q^{45} -16400.0 q^{46} +8900.00i q^{47} +2304.00i q^{48} +16791.0 q^{49} +(4400.00 + 11700.0i) q^{50} -13644.0 q^{51} -4608.00i q^{52} -39804.0i q^{53} +2916.00 q^{54} +(27500.0 - 5000.00i) q^{55} -256.000 q^{56} +12096.0i q^{57} +10584.0i q^{58} +28300.0 q^{59} +(1440.00 + 7920.00i) q^{60} +18290.0 q^{61} -22448.0i q^{62} +324.000i q^{63} -4096.00 q^{64} +(-2880.00 - 15840.0i) q^{65} +18000.0 q^{66} +65956.0i q^{67} -24256.0i q^{68} -36900.0 q^{69} +(-880.000 + 160.000i) q^{70} -28800.0 q^{71} +5184.00i q^{72} +30808.0i q^{73} +29152.0 q^{74} +(9900.00 + 26325.0i) q^{75} -21504.0 q^{76} +2000.00i q^{77} -10368.0i q^{78} -60228.0 q^{79} +(-14080.0 + 2560.00i) q^{80} +6561.00 q^{81} -75944.0i q^{82} +2468.00i q^{83} -576.000 q^{84} +(-15160.0 - 83380.0i) q^{85} -9616.00 q^{86} +23814.0i q^{87} +32000.0i q^{88} -22678.0 q^{89} +(3240.00 + 17820.0i) q^{90} +1152.00 q^{91} -65600.0i q^{92} -50508.0i q^{93} -35600.0 q^{94} +(-73920.0 + 13440.0i) q^{95} -9216.00 q^{96} -36968.0i q^{97} +67164.0i q^{98} +40500.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.995089\pi$
$7$		−	4.00000i		−	0.0308542i	0.999881	−	0.0154271i	$-0.00491080\pi$
$8$		−	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	$0.0759420\pi$
$13$			288.000i			0.472644i	−0.971675	+	0.236322i	$0.924058\pi$
$14$	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	$0.219466\pi$
$17$			1516.00i			1.27226i	−0.771581	+	0.636132i	$0.780534\pi$
$18$		−	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	$0.299473\pi$
$23$			4100.00i			1.61609i	−0.589124	+	0.808043i	$0.700527\pi$
$24$	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	$-0.855830\pi$
$37$		−	7288.00i		−	0.875193i	0.899171	−	0.437597i	$-0.144170\pi$
$38$			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	$0.0316080\pi$
$43$			2404.00i			0.198273i	−0.995074	+	0.0991364i	$0.968392\pi$
$44$	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	$0.0949343\pi$
$47$			8900.00i			0.587686i	−0.955854	+	0.293843i	$0.905066\pi$
$48$			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	$-0.573844\pi$
$53$		−	39804.0i		−	1.94642i	0.229913	−	0.973211i	$-0.426156\pi$
$54$	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	$0.354623\pi$
$67$			65956.0i			1.79501i	−0.441002	+	0.897506i	$0.645377\pi$
$68$		−	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	$0.109858\pi$
$73$			30808.0i			0.676638i	−0.941031	+	0.338319i	$0.890142\pi$
$74$	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	$0.00625890\pi$
$83$			2468.00i			0.0393233i	−0.999807	+	0.0196616i	$0.993741\pi$
$84$	−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	$-0.936080\pi$
$97$		−	36968.0i		−	0.398930i	0.979905	−	0.199465i	$-0.0639204\pi$
$98$			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	$0.254413\pi$
$103$			154364.i			1.43368i	−0.697236	+	0.716841i	$0.745587\pi$
$104$	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	$0.195975\pi$
$107$			136788.i			1.15502i	−0.816385	+	0.577509i	$0.804025\pi$
$108$			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	$-0.901475\pi$
$113$		−	82692.0i		−	0.609211i	0.952479	−	0.304605i	$-0.0985245\pi$
$114$	−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	$-0.802048\pi$
$127$		−	211780.i		−	1.16513i	0.812783	−	0.582567i	$-0.197952\pi$
$128$		−	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	$0.194465\pi$
$137$			252036.i			1.14726i	−0.819115	+	0.573629i	$0.805535\pi$
$138$		−	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	$0.141110\pi$
$157$			264952.i			0.857863i	−0.903337	+	0.428932i	$0.858890\pi$
$158$		−	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	$0.202535\pi$
$163$			403124.i			1.18842i	−0.804310	+	0.594210i	$0.797465\pi$
$164$	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	$-0.881636\pi$
$167$		−	261900.i		−	0.726682i	0.931656	−	0.363341i	$-0.118364\pi$
$168$		−	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	$-0.864006\pi$
$173$		−	326228.i		−	0.828716i	0.910114	−	0.414358i	$-0.135994\pi$
$174$	−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	$0.471017\pi$
$193$			1.03067e6i			1.99172i	−0.0909274	+	0.995858i	$0.528983\pi$
$194$	147872.			0.282086
$195$	142560.	−	25920.0i	0.268480	−	0.0488145i
$196$	−268656.			−0.499524
$197$		−	522796.i		−	0.959769i	−0.877332	−	0.479884i	$-0.840679\pi$
$197$		−	522796.i		−	0.959769i	0.877332	−	0.479884i	$-0.159321\pi$
$198$			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	$-0.900662\pi$
$223$		−	456020.i		−	0.614075i	0.951697	−	0.307038i	$-0.0993378\pi$
$224$	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	$-0.909775\pi$
$227$		−	434252.i		−	0.559342i	0.960096	−	0.279671i	$-0.0902253\pi$
$228$		−	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	$0.110803\pi$
$233$			565348.i			0.682223i	−0.940023	+	0.341111i	$0.889197\pi$
$234$	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	$0.138550\pi$
$257$			892932.i			0.843307i	−0.906757	+	0.421653i	$0.861450\pi$
$258$		−	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	$0.312788\pi$
$263$			1.86650e6i			1.66394i	−0.554818	+	0.831972i	$0.687212\pi$
$264$	−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	$-0.873918\pi$
$277$		−	985408.i		−	0.771643i	0.922573	−	0.385822i	$-0.126082\pi$
$278$		−	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	$0.211972\pi$
$283$			1.66471e6i			1.23558i	−0.786342	+	0.617792i	$0.788028\pi$
$284$	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	$-0.665406\pi$
$293$		−	2.55104e6i		−	1.73600i	0.496567	−	0.867998i	$-0.334594\pi$
$294$	−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	$0.0715362\pi$
$307$			736020.i			0.445701i	−0.974853	+	0.222851i	$0.928464\pi$
$308$		−	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	$-0.694617\pi$
$313$		−	2.83851e6i		−	1.63768i	0.574020	−	0.818842i	$-0.305383\pi$
$314$	−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	$-0.883933\pi$
$317$		−	1.27605e6i		−	0.713215i	0.934254	−	0.356607i	$-0.116067\pi$
$318$			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	$0.225528\pi$
$337$			2.71326e6i			1.30142i	−0.759328	+	0.650708i	$0.774472\pi$
$338$			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	$-0.905634\pi$
$347$		−	1.31051e6i		−	0.584273i	0.956377	−	0.292137i	$-0.0943662\pi$
$348$		−	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	$-0.949621\pi$
$353$		−	737996.i		−	0.315223i	0.987501	−	0.157611i	$-0.0503793\pi$
$354$	−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	$0.00785236\pi$
$367$			127292.i			0.0493328i	−0.999696	+	0.0246664i	$0.992148\pi$
$368$			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	$-0.729322\pi$
$373$		−	4.03870e6i		−	1.50303i	0.659713	−	0.751517i	$-0.270678\pi$
$374$	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	$0.135814\pi$
$383$			2.37610e6i			0.827690i	−0.910347	+	0.413845i	$0.864186\pi$
$384$	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	$0.0869009\pi$
$397$			1.69345e6i			0.539257i	−0.962964	+	0.269628i	$0.913099\pi$
$398$			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	$-0.989770\pi$
$433$		−	250736.i		−	0.0642683i	0.999484	−	0.0321342i	$-0.0102304\pi$
$434$	−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	$0.0547833\pi$
$443$			1.41479e6i			0.342517i	−0.985226	+	0.171258i	$0.945217\pi$
$444$	−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	$0.175686\pi$
$457$			4.68198e6i			1.04867i	−0.851512	+	0.524335i	$0.824314\pi$
$458$			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	$-0.974873\pi$
$463$		−	727476.i		−	0.157713i	0.996886	−	0.0788563i	$-0.0251268\pi$
$464$	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	$-0.842483\pi$
$467$		−	4.47640e6i		−	0.949809i	0.880037	−	0.474905i	$-0.157517\pi$
$468$			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	$-0.871350\pi$
$487$		−	4.11647e6i		−	0.786507i	0.919430	−	0.393253i	$-0.128650\pi$
$488$		−	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	$-0.886056\pi$
$503$		−	3.97628e6i		−	0.700741i	0.936611	−	0.350370i	$-0.113944\pi$
$504$	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	$0.286043\pi$
$523$			9.78938e6i			1.56495i	−0.622681	+	0.782476i	$0.713957\pi$
$524$	−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	$-0.973452\pi$
$547$		−	1.16595e6i		−	0.166614i	0.996524	−	0.0833069i	$-0.0265482\pi$
$548$		−	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	$-0.964870\pi$
$557$		−	1.61293e6i		−	0.220282i	0.993916	−	0.110141i	$-0.0351302\pi$
$558$			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	$-0.927292\pi$
$563$		−	3.40603e6i		−	0.452874i	0.974026	−	0.226437i	$-0.0727077\pi$
$564$	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	$-0.761078\pi$
$577$		−	1.09094e7i		−	1.36415i	0.731283	−	0.682074i	$-0.238922\pi$
$578$		−	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	$0.170732\pi$
$587$			8.53223e6i			1.02204i	−0.859569	+	0.511019i	$0.829268\pi$
$588$		−	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	$0.0871721\pi$
$593$			4.63182e6i			0.540897i	−0.962734	+	0.270449i	$0.912828\pi$
$594$	−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	$-0.891643\pi$
$607$		−	6.06160e6i		−	0.667753i	0.942617	−	0.333876i	$-0.108357\pi$
$608$			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	$0.0631071\pi$
$613$			3.66489e6i			0.393921i	−0.980411	+	0.196961i	$0.936893\pi$
$614$	−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	$-0.835871\pi$
$617$		−	9.32522e6i		−	0.986157i	0.869985	−	0.493079i	$-0.164129\pi$
$618$		−	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	$-0.823984\pi$
$643$		−	1.10128e7i		−	1.05044i	0.850967	−	0.525219i	$-0.176016\pi$
$644$	−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	$0.0501076\pi$
$647$			3.33848e6i			0.313537i	−0.987635	+	0.156768i	$0.949892\pi$
$648$		−	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	$0.0701177\pi$
$653$			4.76181e6i			0.437008i	−0.975836	+	0.218504i	$0.929882\pi$
$654$	−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	$0.0132334\pi$
$673$			976704.i			0.0831238i	−0.999136	+	0.0415619i	$0.986767\pi$
$674$	−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	$0.302119\pi$
$677$			1.93885e7i			1.62582i	−0.582388	+	0.812911i	$0.697881\pi$
$678$			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	$0.0691550\pi$
$683$			5.25573e6i			0.431103i	−0.976492	+	0.215552i	$0.930845\pi$
$684$	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	$0.0616037\pi$
$727$			5.48161e6i			0.384656i	−0.981331	+	0.192328i	$0.938396\pi$
$728$		−	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	$0.0950143\pi$
$733$			8.55579e6i			0.588166i	−0.955780	+	0.294083i	$0.904986\pi$
$734$	−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	$0.0250324\pi$
$743$			2.36432e6i			0.157121i	−0.996909	+	0.0785606i	$0.974968\pi$
$744$	−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	$0.387397\pi$
$757$			2.95808e7i			1.87616i	−0.346421	+	0.938079i	$0.612603\pi$
$758$		−	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	$0.174545\pi$
$773$			1.73201e7i			1.04256i	−0.853386	+	0.521280i	$0.825455\pi$
$774$	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	$0.00509923\pi$
$787$			556676.i			0.0320380i	−0.999872	+	0.0160190i	$0.994901\pi$
$788$			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	$0.0267066\pi$
$797$			3.00562e6i			0.167606i	−0.996482	+	0.0838028i	$0.973293\pi$
$798$			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	$-0.876042\pi$
$823$		−	1.47544e7i		−	0.759316i	0.925127	−	0.379658i	$-0.123958\pi$
$824$	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	$-0.972495\pi$
$827$		−	3.39475e6i		−	0.172601i	0.996269	−	0.0863006i	$-0.0275045\pi$
$828$			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	$-0.926899\pi$
$853$		−	9.67506e6i		−	0.455283i	0.973745	−	0.227641i	$-0.0731014\pi$
$854$	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	$0.275628\pi$
$857$			3.27535e7i			1.52337i	−0.647946	+	0.761686i	$0.724372\pi$
$858$			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	$-0.841708\pi$
$863$		−	2.08744e7i		−	0.954087i	0.878880	−	0.477043i	$-0.158292\pi$
$864$	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	$0.336566\pi$
$877$			3.96804e7i			1.74212i	−0.491181	+	0.871058i	$0.663434\pi$
$878$			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	$-0.653568\pi$
$883$		−	4.10486e7i		−	1.77172i	0.463949	−	0.885862i	$-0.346432\pi$
$884$	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	$0.0948252\pi$
$887$			1.37553e7i			0.587031i	−0.955954	+	0.293515i	$0.905175\pi$
$888$		−	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	$-0.962207\pi$
$907$		−	5.86936e6i		−	0.236904i	0.992960	−	0.118452i	$-0.0377932\pi$
$908$			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	$-0.821301\pi$
$937$		−	2.86149e7i		−	1.06474i	0.846512	−	0.532370i	$-0.178699\pi$
$938$			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	$0.0461137\pi$
$947$			7.96828e6i			0.288728i	−0.989525	+	0.144364i	$0.953886\pi$
$948$			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	$0.329497\pi$
$953$			4.82202e7i			1.71987i	−0.510400	+	0.859937i	$0.670503\pi$
$954$	−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	$0.312459\pi$
$967$			4.83510e7i			1.66280i	−0.555678	+	0.831398i	$0.687541\pi$
$968$		−	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	$-0.740044\pi$
$977$		−	4.34929e7i		−	1.45775i	0.684648	−	0.728874i	$-0.259956\pi$
$978$		−	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	$0.0176022\pi$
$983$			3.34896e6i			0.110542i	−0.998471	+	0.0552709i	$0.982398\pi$
$984$	−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	$-0.934975\pi$
$997$		−	1.27342e7i		−	0.405726i	0.979207	−	0.202863i	$-0.0650247\pi$
$998$			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.19.2	yes	2
3.2	odd	2		90.6.c.b.19.1		2
4.3	odd	2		240.6.f.a.49.1		2
5.2	odd	4		150.6.a.f.1.1		1
5.3	odd	4		150.6.a.j.1.1		1
5.4	even	2	inner	30.6.c.a.19.1	✓	2
12.11	even	2		720.6.f.g.289.1		2
15.2	even	4		450.6.a.s.1.1		1
15.8	even	4		450.6.a.f.1.1		1
15.14	odd	2		90.6.c.b.19.2		2
20.19	odd	2		240.6.f.a.49.2		2
60.59	even	2		720.6.f.g.289.2		2

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